id	sid	tid	token	lemma	pos
ejpam-5317	1	1	european	european	PROPN
ejpam-5317	1	2	journal	journal	PROPN
ejpam-5317	1	3	of	of	ADP
ejpam-5317	1	4	pure	pure	ADJ
ejpam-5317	1	5	and	and	CCONJ
ejpam-5317	1	6	applied	apply	VERB
ejpam-5317	1	7	mathematics	mathematic	NOUN
ejpam-5317	1	8	vol	vol	NOUN
ejpam-5317	1	9	.	.	PROPN
ejpam-5317	2	1	17	17	NUM
ejpam-5317	2	2	,	,	PUNCT
ejpam-5317	2	3	no	no	INTJ
ejpam-5317	2	4	.	.	NOUN
ejpam-5317	2	5	4	4	NUM
ejpam-5317	2	6	,	,	PUNCT
ejpam-5317	2	7	2024	2024	NUM
ejpam-5317	2	8	,	,	PUNCT
ejpam-5317	2	9	2550	2550	NUM
ejpam-5317	2	10	-	-	SYM
ejpam-5317	2	11	2561	2561	NUM
ejpam-5317	2	12	issn	issn	VERB
ejpam-5317	2	13	1307	1307	NUM
ejpam-5317	2	14	-	-	SYM
ejpam-5317	2	15	5543	5543	NUM
ejpam-5317	2	16	–	–	PUNCT
ejpam-5317	2	17	ejpam.com	ejpam.com	X
ejpam-5317	2	18	published	publish	VERB
ejpam-5317	2	19	by	by	ADP
ejpam-5317	2	20	new	new	PROPN
ejpam-5317	2	21	york	york	PROPN
ejpam-5317	2	22	business	business	PROPN
ejpam-5317	2	23	global	global	PROPN
ejpam-5317	2	24	the	the	DET
ejpam-5317	2	25	spectrum	spectrum	NOUN
ejpam-5317	2	26	of	of	ADP
ejpam-5317	2	27	a	a	DET
ejpam-5317	2	28	certain	certain	ADJ
ejpam-5317	2	29	large	large	ADJ
ejpam-5317	2	30	block	block	NOUN
ejpam-5317	2	31	matrix	matrix	NOUN
ejpam-5317	2	32	edris	edris	PROPN
ejpam-5317	2	33	rawashdeh1	rawashdeh1	PROPN
ejpam-5317	2	34	,	,	PUNCT
ejpam-5317	2	35	heba	heba	PROPN
ejpam-5317	2	36	adel	adel	PROPN
ejpam-5317	2	37	abdelkarim2	abdelkarim2	PROPN
ejpam-5317	2	38	,	,	PUNCT
ejpam-5317	2	39	eman	eman	PROPN
ejpam-5317	2	40	rawshdeh3,∗	rawshdeh3,∗	VERB
ejpam-5317	2	41	1	1	NUM
ejpam-5317	2	42	department	department	NOUN
ejpam-5317	2	43	of	of	ADP
ejpam-5317	2	44	mathematics	mathematic	NOUN
ejpam-5317	2	45	,	,	PUNCT
ejpam-5317	2	46	yarmouk	yarmouk	CCONJ
ejpam-5317	2	47	university	university	NOUN
ejpam-5317	2	48	,	,	PUNCT
ejpam-5317	2	49	irbid	irbid	PROPN
ejpam-5317	2	50	,	,	PUNCT
ejpam-5317	2	51	jordan	jordan	PROPN
ejpam-5317	2	52	2	2	NUM
ejpam-5317	2	53	department	department	NOUN
ejpam-5317	2	54	of	of	ADP
ejpam-5317	2	55	mathematics	mathematic	NOUN
ejpam-5317	2	56	,	,	PUNCT
ejpam-5317	2	57	irbid	irbid	ADJ
ejpam-5317	2	58	national	national	ADJ
ejpam-5317	2	59	university	university	NOUN
ejpam-5317	2	60	,	,	PUNCT
ejpam-5317	2	61	irbid	irbid	PROPN
ejpam-5317	2	62	,	,	PUNCT
ejpam-5317	2	63	jordan	jordan	PROPN
ejpam-5317	2	64	3	3	NUM
ejpam-5317	2	65	department	department	PROPN
ejpam-5317	2	66	of	of	ADP
ejpam-5317	2	67	basic	basic	ADJ
ejpam-5317	2	68	scientific	scientific	ADJ
ejpam-5317	2	69	sciences	science	NOUN
ejpam-5317	2	70	,	,	PUNCT
ejpam-5317	2	71	al	al	PROPN
ejpam-5317	2	72	-	-	PUNCT
ejpam-5317	2	73	huson	huson	PROPN
ejpam-5317	2	74	university	university	PROPN
ejpam-5317	2	75	college	college	NOUN
ejpam-5317	2	76	,	,	PUNCT
ejpam-5317	2	77	al	al	PROPN
ejpam-5317	2	78	-	-	PUNCT
ejpam-5317	2	79	balqa	balqa	NOUN
ejpam-5317	2	80	applied	apply	VERB
ejpam-5317	2	81	university	university	NOUN
ejpam-5317	2	82	,	,	PUNCT
ejpam-5317	2	83	irbid	irbid	PROPN
ejpam-5317	2	84	,	,	PUNCT
ejpam-5317	2	85	jordan	jordan	PROPN
ejpam-5317	2	86	abstract	abstract	PROPN
ejpam-5317	2	87	.	.	PUNCT
ejpam-5317	3	1	large	large	ADJ
ejpam-5317	3	2	matrices	matrix	NOUN
ejpam-5317	3	3	appear	appear	VERB
ejpam-5317	3	4	in	in	ADP
ejpam-5317	3	5	many	many	ADJ
ejpam-5317	3	6	applications	application	NOUN
ejpam-5317	3	7	in	in	ADP
ejpam-5317	3	8	computer	computer	NOUN
ejpam-5317	3	9	science	science	NOUN
ejpam-5317	3	10	,	,	PUNCT
ejpam-5317	3	11	physics	physics	NOUN
ejpam-5317	3	12	,	,	PUNCT
ejpam-5317	3	13	chemistry	chemistry	NOUN
ejpam-5317	3	14	and	and	CCONJ
ejpam-5317	3	15	many	many	ADJ
ejpam-5317	3	16	other	other	ADJ
ejpam-5317	3	17	disciplines	discipline	NOUN
ejpam-5317	3	18	.	.	PUNCT
ejpam-5317	4	1	this	this	PRON
ejpam-5317	4	2	is	be	AUX
ejpam-5317	4	3	because	because	SCONJ
ejpam-5317	4	4	such	such	ADJ
ejpam-5317	4	5	matrices	matrix	NOUN
ejpam-5317	4	6	have	have	VERB
ejpam-5317	4	7	the	the	DET
ejpam-5317	4	8	ability	ability	NOUN
ejpam-5317	4	9	to	to	PART
ejpam-5317	4	10	hold	hold	VERB
ejpam-5317	4	11	huge	huge	ADJ
ejpam-5317	4	12	amounts	amount	NOUN
ejpam-5317	4	13	of	of	ADP
ejpam-5317	4	14	memory	memory	NOUN
ejpam-5317	4	15	.	.	PUNCT
ejpam-5317	5	1	on	on	ADP
ejpam-5317	5	2	of	of	ADP
ejpam-5317	5	3	the	the	DET
ejpam-5317	5	4	main	main	ADJ
ejpam-5317	5	5	properties	property	NOUN
ejpam-5317	5	6	that	that	PRON
ejpam-5317	5	7	researchers	researcher	NOUN
ejpam-5317	5	8	are	be	AUX
ejpam-5317	5	9	interested	interested	ADJ
ejpam-5317	5	10	is	be	AUX
ejpam-5317	5	11	studying	study	VERB
ejpam-5317	5	12	the	the	DET
ejpam-5317	5	13	spectral	spectral	ADJ
ejpam-5317	5	14	theory	theory	NOUN
ejpam-5317	5	15	of	of	ADP
ejpam-5317	5	16	these	these	DET
ejpam-5317	5	17	matrices	matrix	NOUN
ejpam-5317	5	18	.	.	PUNCT
ejpam-5317	6	1	in	in	ADP
ejpam-5317	6	2	this	this	DET
ejpam-5317	6	3	paper	paper	NOUN
ejpam-5317	6	4	,	,	PUNCT
ejpam-5317	6	5	we	we	PRON
ejpam-5317	6	6	compute	compute	VERB
ejpam-5317	6	7	the	the	DET
ejpam-5317	6	8	spectrum	spectrum	NOUN
ejpam-5317	6	9	of	of	ADP
ejpam-5317	6	10	a	a	DET
ejpam-5317	6	11	certain	certain	ADJ
ejpam-5317	6	12	large	large	ADJ
ejpam-5317	6	13	matrix	matrix	NOUN
ejpam-5317	6	14	that	that	PRON
ejpam-5317	6	15	can	can	AUX
ejpam-5317	6	16	serve	serve	VERB
ejpam-5317	6	17	as	as	ADP
ejpam-5317	6	18	an	an	DET
ejpam-5317	6	19	adjacency	adjacency	NOUN
ejpam-5317	6	20	matrix	matrix	NOUN
ejpam-5317	6	21	of	of	ADP
ejpam-5317	6	22	a	a	DET
ejpam-5317	6	23	certain	certain	ADJ
ejpam-5317	6	24	clean	clean	ADJ
ejpam-5317	6	25	graph	graph	NOUN
ejpam-5317	6	26	.	.	PUNCT
ejpam-5317	7	1	in	in	ADP
ejpam-5317	7	2	particular	particular	ADJ
ejpam-5317	7	3	,	,	PUNCT
ejpam-5317	7	4	we	we	PRON
ejpam-5317	7	5	give	give	VERB
ejpam-5317	7	6	a	a	DET
ejpam-5317	7	7	full	full	ADJ
ejpam-5317	7	8	characterization	characterization	NOUN
ejpam-5317	7	9	of	of	ADP
ejpam-5317	7	10	the	the	DET
ejpam-5317	7	11	eigenvalues	eigenvalue	NOUN
ejpam-5317	7	12	and	and	CCONJ
ejpam-5317	7	13	eigenvectors	eigenvector	NOUN
ejpam-5317	7	14	of	of	ADP
ejpam-5317	7	15	the	the	DET
ejpam-5317	7	16	intended	intend	VERB
ejpam-5317	7	17	matrix	matrix	NOUN
ejpam-5317	7	18	.	.	PUNCT
ejpam-5317	8	1	2020	2020	NUM
ejpam-5317	8	2	mathematics	mathematic	NOUN
ejpam-5317	8	3	subject	subject	NOUN
ejpam-5317	8	4	classifications	classification	NOUN
ejpam-5317	8	5	:	:	PUNCT
ejpam-5317	8	6	15a18	15a18	NUM
ejpam-5317	8	7	,	,	PUNCT
ejpam-5317	8	8	90c35	90c35	NUM
ejpam-5317	8	9	,	,	PUNCT
ejpam-5317	8	10	05c50	05c50	ADP
ejpam-5317	8	11	key	key	ADJ
ejpam-5317	8	12	words	word	NOUN
ejpam-5317	8	13	and	and	CCONJ
ejpam-5317	8	14	phrases	phrase	NOUN
ejpam-5317	8	15	:	:	PUNCT
ejpam-5317	8	16	block	block	NOUN
ejpam-5317	8	17	matrices	matrix	NOUN
ejpam-5317	8	18	,	,	PUNCT
ejpam-5317	8	19	adjacency	adjacency	NOUN
ejpam-5317	8	20	matrices	matrix	NOUN
ejpam-5317	8	21	,	,	PUNCT
ejpam-5317	8	22	eigenvalues	eigenvalue	NOUN
ejpam-5317	8	23	,	,	PUNCT
ejpam-5317	8	24	eigenvectors	eigenvector	NOUN
ejpam-5317	8	25	1	1	NUM
ejpam-5317	8	26	.	.	PUNCT
ejpam-5317	9	1	introduction	introduction	NOUN
ejpam-5317	9	2	large	large	ADJ
ejpam-5317	9	3	matrices	matrix	NOUN
ejpam-5317	9	4	are	be	AUX
ejpam-5317	9	5	being	be	AUX
ejpam-5317	9	6	used	use	VERB
ejpam-5317	9	7	more	more	ADV
ejpam-5317	9	8	and	and	CCONJ
ejpam-5317	9	9	more	more	ADJ
ejpam-5317	9	10	in	in	ADP
ejpam-5317	9	11	the	the	DET
ejpam-5317	9	12	big	big	ADJ
ejpam-5317	9	13	data	datum	NOUN
ejpam-5317	9	14	era	era	NOUN
ejpam-5317	9	15	because	because	SCONJ
ejpam-5317	9	16	of	of	ADP
ejpam-5317	9	17	their	their	PRON
ejpam-5317	9	18	potential	potential	NOUN
ejpam-5317	9	19	to	to	PART
ejpam-5317	9	20	integrate	integrate	VERB
ejpam-5317	9	21	and	and	CCONJ
ejpam-5317	9	22	connect	connect	VERB
ejpam-5317	9	23	massive	massive	ADJ
ejpam-5317	9	24	data	datum	NOUN
ejpam-5317	9	25	sources	source	NOUN
ejpam-5317	9	26	across	across	ADP
ejpam-5317	9	27	a	a	DET
ejpam-5317	9	28	wide	wide	ADJ
ejpam-5317	9	29	range	range	NOUN
ejpam-5317	9	30	of	of	ADP
ejpam-5317	9	31	industries	industry	NOUN
ejpam-5317	9	32	,	,	PUNCT
ejpam-5317	9	33	including	include	VERB
ejpam-5317	9	34	social	social	ADJ
ejpam-5317	9	35	media	medium	NOUN
ejpam-5317	9	36	,	,	PUNCT
ejpam-5317	9	37	biology	biology	NOUN
ejpam-5317	9	38	,	,	PUNCT
ejpam-5317	9	39	communication	communication	NOUN
ejpam-5317	9	40	networks	network	NOUN
ejpam-5317	9	41	,	,	PUNCT
ejpam-5317	9	42	etc	etc	X
ejpam-5317	9	43	(	(	PUNCT
ejpam-5317	9	44	see	see	VERB
ejpam-5317	9	45	for	for	ADP
ejpam-5317	9	46	example	example	NOUN
ejpam-5317	9	47	[	[	X
ejpam-5317	9	48	2	2	NUM
ejpam-5317	9	49	]	]	PUNCT
ejpam-5317	9	50	,	,	PUNCT
ejpam-5317	9	51	[	[	X
ejpam-5317	9	52	3	3	NUM
ejpam-5317	9	53	]	]	PUNCT
ejpam-5317	9	54	,	,	PUNCT
ejpam-5317	9	55	[	[	X
ejpam-5317	9	56	4	4	NUM
ejpam-5317	9	57	]	]	PUNCT
ejpam-5317	9	58	,	,	PUNCT
ejpam-5317	9	59	[	[	X
ejpam-5317	9	60	6	6	NUM
ejpam-5317	9	61	]	]	PUNCT
ejpam-5317	9	62	,	,	PUNCT
ejpam-5317	9	63	[	[	X
ejpam-5317	9	64	12	12	NUM
ejpam-5317	9	65	]	]	PUNCT
ejpam-5317	9	66	,	,	PUNCT
ejpam-5317	9	67	[	[	X
ejpam-5317	9	68	13	13	NUM
ejpam-5317	9	69	]	]	PUNCT
ejpam-5317	9	70	,	,	PUNCT
ejpam-5317	9	71	and	and	CCONJ
ejpam-5317	9	72	[	[	X
ejpam-5317	9	73	14	14	NUM
ejpam-5317	9	74	]	]	PUNCT
ejpam-5317	9	75	)	)	PUNCT
ejpam-5317	9	76	.	.	PUNCT
ejpam-5317	10	1	for	for	ADP
ejpam-5317	10	2	instance	instance	NOUN
ejpam-5317	10	3	,	,	PUNCT
ejpam-5317	10	4	large	large	ADJ
ejpam-5317	10	5	networks	network	NOUN
ejpam-5317	10	6	,	,	PUNCT
ejpam-5317	10	7	such	such	ADJ
ejpam-5317	10	8	as	as	ADP
ejpam-5317	10	9	the	the	DET
ejpam-5317	10	10	internet	internet	NOUN
ejpam-5317	10	11	,	,	PUNCT
ejpam-5317	10	12	can	can	AUX
ejpam-5317	10	13	be	be	AUX
ejpam-5317	10	14	utilized	utilize	VERB
ejpam-5317	10	15	to	to	PART
ejpam-5317	10	16	describe	describe	VERB
ejpam-5317	10	17	intriguing	intriguing	ADJ
ejpam-5317	10	18	global	global	ADJ
ejpam-5317	10	19	patterns	pattern	NOUN
ejpam-5317	10	20	and	and	CCONJ
ejpam-5317	10	21	occurrences	occurrence	NOUN
ejpam-5317	10	22	.	.	PUNCT
ejpam-5317	11	1	these	these	DET
ejpam-5317	11	2	networks	network	NOUN
ejpam-5317	11	3	attracted	attract	VERB
ejpam-5317	11	4	the	the	DET
ejpam-5317	11	5	mathematician	mathematician	NOUN
ejpam-5317	11	6	who	who	PRON
ejpam-5317	11	7	are	be	AUX
ejpam-5317	11	8	interested	interested	ADJ
ejpam-5317	11	9	in	in	ADP
ejpam-5317	11	10	graph	graph	NOUN
ejpam-5317	11	11	theory	theory	NOUN
ejpam-5317	11	12	.	.	PUNCT
ejpam-5317	12	1	this	this	PRON
ejpam-5317	12	2	is	be	AUX
ejpam-5317	12	3	because	because	SCONJ
ejpam-5317	12	4	graphs	graph	NOUN
ejpam-5317	12	5	are	be	AUX
ejpam-5317	12	6	very	very	ADV
ejpam-5317	12	7	useful	useful	ADJ
ejpam-5317	12	8	ways	way	NOUN
ejpam-5317	12	9	of	of	ADP
ejpam-5317	12	10	presenting	present	VERB
ejpam-5317	12	11	information	information	NOUN
ejpam-5317	12	12	about	about	ADP
ejpam-5317	12	13	these	these	DET
ejpam-5317	12	14	networks	network	NOUN
ejpam-5317	12	15	.	.	PUNCT
ejpam-5317	13	1	in	in	ADP
ejpam-5317	13	2	fact	fact	NOUN
ejpam-5317	13	3	,	,	PUNCT
ejpam-5317	13	4	the	the	DET
ejpam-5317	13	5	term	term	NOUN
ejpam-5317	13	6	graph	graph	NOUN
ejpam-5317	13	7	,	,	PUNCT
ejpam-5317	13	8	which	which	PRON
ejpam-5317	13	9	represents	represent	VERB
ejpam-5317	13	10	an	an	DET
ejpam-5317	13	11	abstract	abstract	ADJ
ejpam-5317	13	12	mathematical	mathematical	ADJ
ejpam-5317	13	13	concept	concept	NOUN
ejpam-5317	13	14	,	,	PUNCT
ejpam-5317	13	15	generally	generally	ADV
ejpam-5317	13	16	refers	refer	VERB
ejpam-5317	13	17	to	to	ADP
ejpam-5317	13	18	an	an	DET
ejpam-5317	13	19	artificial	artificial	ADJ
ejpam-5317	13	20	formation	formation	NOUN
ejpam-5317	13	21	of	of	ADP
ejpam-5317	13	22	nodes	node	NOUN
ejpam-5317	13	23	and	and	CCONJ
ejpam-5317	13	24	edges	edge	NOUN
ejpam-5317	13	25	whereas	whereas	SCONJ
ejpam-5317	13	26	the	the	DET
ejpam-5317	13	27	term	term	NOUN
ejpam-5317	13	28	network	network	NOUN
ejpam-5317	13	29	is	be	AUX
ejpam-5317	13	30	then	then	ADV
ejpam-5317	13	31	reserved	reserve	VERB
ejpam-5317	13	32	for	for	ADP
ejpam-5317	13	33	the	the	DET
ejpam-5317	13	34	graphs	graph	NOUN
ejpam-5317	13	35	representing	represent	VERB
ejpam-5317	13	36	real	real	ADJ
ejpam-5317	13	37	-	-	PUNCT
ejpam-5317	13	38	world	world	NOUN
ejpam-5317	13	39	objects	object	NOUN
ejpam-5317	13	40	in	in	ADP
ejpam-5317	13	41	which	which	PRON
ejpam-5317	13	42	the	the	DET
ejpam-5317	13	43	nodes	node	NOUN
ejpam-5317	13	44	represent	represent	VERB
ejpam-5317	13	45	units	unit	NOUN
ejpam-5317	13	46	of	of	ADP
ejpam-5317	13	47	the	the	DET
ejpam-5317	13	48	system	system	NOUN
ejpam-5317	13	49	and	and	CCONJ
ejpam-5317	14	1	the	the	DET
ejpam-5317	14	2	edges	edge	NOUN
ejpam-5317	14	3	represent	represent	VERB
ejpam-5317	14	4	the	the	DET
ejpam-5317	14	5	relationships	relationship	NOUN
ejpam-5317	14	6	between	between	ADP
ejpam-5317	14	7	them	they	PRON
ejpam-5317	14	8	,	,	PUNCT
ejpam-5317	14	9	see	see	VERB
ejpam-5317	14	10	[	[	X
ejpam-5317	14	11	7	7	NUM
ejpam-5317	14	12	]	]	PUNCT
ejpam-5317	14	13	.	.	PUNCT
ejpam-5317	15	1	the	the	DET
ejpam-5317	15	2	best	good	ADJ
ejpam-5317	15	3	way	way	NOUN
ejpam-5317	15	4	to	to	ADP
ejpam-5317	15	5	dealing	deal	VERB
ejpam-5317	15	6	with	with	ADP
ejpam-5317	15	7	graphs	graph	NOUN
ejpam-5317	15	8	is	be	AUX
ejpam-5317	15	9	the	the	DET
ejpam-5317	15	10	linear	linear	ADJ
ejpam-5317	15	11	algebraic	algebraic	ADJ
ejpam-5317	15	12	approach	approach	NOUN
ejpam-5317	15	13	,	,	PUNCT
ejpam-5317	15	14	which	which	PRON
ejpam-5317	15	15	is	be	AUX
ejpam-5317	15	16	to	to	PART
ejpam-5317	15	17	view	view	VERB
ejpam-5317	15	18	graphs	graph	NOUN
ejpam-5317	15	19	as	as	ADP
ejpam-5317	15	20	matrices	matrix	NOUN
ejpam-5317	15	21	and	and	CCONJ
ejpam-5317	15	22	use	use	VERB
ejpam-5317	15	23	concepts	concept	NOUN
ejpam-5317	15	24	in	in	ADP
ejpam-5317	15	25	linear	linear	PROPN
ejpam-5317	15	26	algebra	algebra	NOUN
ejpam-5317	15	27	to	to	PART
ejpam-5317	15	28	design	design	VERB
ejpam-5317	15	29	and	and	CCONJ
ejpam-5317	15	30	analyze	analyze	VERB
ejpam-5317	15	31	algorithms	algorithm	NOUN
ejpam-5317	15	32	for	for	ADP
ejpam-5317	15	33	∗corresponding	∗corresponde	VERB
ejpam-5317	15	34	author	author	NOUN
ejpam-5317	15	35	.	.	PUNCT
ejpam-5317	16	1	doi	doi	NOUN
ejpam-5317	16	2	:	:	PUNCT
ejpam-5317	16	3	https://doi.org/10.29020/nybg.ejpam.v17i4.5317	https://doi.org/10.29020/nybg.ejpam.v17i4.5317	ADJ
ejpam-5317	16	4	email	email	NOUN
ejpam-5317	16	5	addresses	address	NOUN
ejpam-5317	16	6	:	:	PUNCT
ejpam-5317	17	1	edris@yu.edu.jo	edris@yu.edu.jo	ADJ
ejpam-5317	17	2	(	(	PUNCT
ejpam-5317	17	3	e.	e.	PROPN
ejpam-5317	17	4	rawashdeh	rawashdeh	PROPN
ejpam-5317	17	5	)	)	PUNCT
ejpam-5317	17	6	,	,	PUNCT
ejpam-5317	17	7	dr.heba@inu.edu.jo	dr.heba@inu.edu.jo	PROPN
ejpam-5317	17	8	(	(	PUNCT
ejpam-5317	17	9	h.	h.	PROPN
ejpam-5317	17	10	adel	adel	PROPN
ejpam-5317	17	11	abdelkarim	abdelkarim	PROPN
ejpam-5317	17	12	)	)	PUNCT
ejpam-5317	17	13	,	,	PUNCT
ejpam-5317	17	14	eman.rw@bau.edu.jo	eman.rw@bau.edu.jo	PROPN
ejpam-5317	17	15	(	(	PUNCT
ejpam-5317	17	16	e.	e.	PROPN
ejpam-5317	17	17	rawshdeh	rawshdeh	PROPN
ejpam-5317	17	18	)	)	PUNCT
ejpam-5317	17	19	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-5317	17	20	2550	2550	NUM
ejpam-5317	17	21	copyright	copyright	NOUN
ejpam-5317	17	22	:	:	PUNCT
ejpam-5317	17	23	©	©	PROPN
ejpam-5317	17	24	2024	2024	NUM
ejpam-5317	17	25	the	the	DET
ejpam-5317	17	26	author(s	author(s	NOUN
ejpam-5317	17	27	)	)	PUNCT
ejpam-5317	17	28	.	.	PUNCT
ejpam-5317	18	1	(	(	PUNCT
ejpam-5317	18	2	cc	cc	NOUN
ejpam-5317	18	3	by	by	ADP
ejpam-5317	18	4	-	-	PUNCT
ejpam-5317	18	5	nc	nc	PROPN
ejpam-5317	18	6	4.0	4.0	NUM
ejpam-5317	18	7	)	)	PUNCT
ejpam-5317	18	8	e.	e.	PROPN
ejpam-5317	18	9	rawaswhdeh	rawaswhdeh	PROPN
ejpam-5317	18	10	,	,	PUNCT
ejpam-5317	18	11	h.	h.	PROPN
ejpam-5317	18	12	adel	adel	PROPN
ejpam-5317	18	13	abdelkarim	abdelkarim	PROPN
ejpam-5317	18	14	,	,	PUNCT
ejpam-5317	18	15	e.	e.	PROPN
ejpam-5317	18	16	rawshdeh	rawshdeh	PROPN
ejpam-5317	18	17	/	/	SYM
ejpam-5317	18	18	eur	eur	PROPN
ejpam-5317	18	19	.	.	PUNCT
ejpam-5317	19	1	j.	j.	PROPN
ejpam-5317	19	2	pure	pure	PROPN
ejpam-5317	19	3	appl	appl	PROPN
ejpam-5317	19	4	.	.	PROPN
ejpam-5317	19	5	math	math	PROPN
ejpam-5317	19	6	,	,	PUNCT
ejpam-5317	19	7	17	17	NUM
ejpam-5317	19	8	(	(	PUNCT
ejpam-5317	19	9	4	4	NUM
ejpam-5317	19	10	)	)	PUNCT
ejpam-5317	19	11	(	(	PUNCT
ejpam-5317	19	12	2024	2024	NUM
ejpam-5317	19	13	)	)	PUNCT
ejpam-5317	19	14	,	,	PUNCT
ejpam-5317	19	15	2550	2550	NUM
ejpam-5317	19	16	-	-	SYM
ejpam-5317	19	17	2561	2561	NUM
ejpam-5317	19	18	2551	2551	NUM
ejpam-5317	19	19	graph	graph	NOUN
ejpam-5317	19	20	problems	problem	NOUN
ejpam-5317	19	21	.	.	PUNCT
ejpam-5317	20	1	moreover	moreover	ADV
ejpam-5317	20	2	,	,	PUNCT
ejpam-5317	20	3	using	use	VERB
ejpam-5317	20	4	matrices	matrix	NOUN
ejpam-5317	20	5	allows	allow	VERB
ejpam-5317	20	6	us	we	PRON
ejpam-5317	20	7	to	to	PART
ejpam-5317	20	8	apply	apply	VERB
ejpam-5317	20	9	mathematical	mathematical	ADJ
ejpam-5317	20	10	and	and	CCONJ
ejpam-5317	20	11	computational	computational	ADJ
ejpam-5317	20	12	tools	tool	NOUN
ejpam-5317	20	13	to	to	PART
ejpam-5317	20	14	summarize	summarize	VERB
ejpam-5317	20	15	and	and	CCONJ
ejpam-5317	20	16	find	find	VERB
ejpam-5317	20	17	patterns	pattern	NOUN
ejpam-5317	20	18	,	,	PUNCT
ejpam-5317	20	19	especially	especially	ADV
ejpam-5317	20	20	when	when	SCONJ
ejpam-5317	20	21	complex	complex	ADJ
ejpam-5317	20	22	relationships	relationship	NOUN
ejpam-5317	20	23	exist	exist	VERB
ejpam-5317	20	24	between	between	ADP
ejpam-5317	20	25	vertices	vertex	NOUN
ejpam-5317	20	26	and	and	CCONJ
ejpam-5317	20	27	edges	edge	NOUN
ejpam-5317	20	28	in	in	ADP
ejpam-5317	20	29	a	a	DET
ejpam-5317	20	30	graph	graph	NOUN
ejpam-5317	20	31	.	.	PUNCT
ejpam-5317	21	1	in	in	ADP
ejpam-5317	21	2	fact	fact	NOUN
ejpam-5317	21	3	,	,	PUNCT
ejpam-5317	21	4	many	many	ADJ
ejpam-5317	21	5	mathematical	mathematical	ADJ
ejpam-5317	21	6	problems	problem	NOUN
ejpam-5317	21	7	necessarily	necessarily	ADV
ejpam-5317	21	8	involve	involve	VERB
ejpam-5317	21	9	inputting	inputte	VERB
ejpam-5317	21	10	certain	certain	ADJ
ejpam-5317	21	11	coefficients	coefficient	NOUN
ejpam-5317	21	12	into	into	ADP
ejpam-5317	21	13	a	a	DET
ejpam-5317	21	14	matrix	matrix	NOUN
ejpam-5317	21	15	and	and	CCONJ
ejpam-5317	21	16	studying	study	VERB
ejpam-5317	21	17	its	its	PRON
ejpam-5317	21	18	spectral	spectral	ADJ
ejpam-5317	21	19	properties	property	NOUN
ejpam-5317	21	20	.	.	PUNCT
ejpam-5317	22	1	this	this	PRON
ejpam-5317	22	2	includes	include	VERB
ejpam-5317	22	3	studying	study	VERB
ejpam-5317	22	4	the	the	DET
ejpam-5317	22	5	properties	property	NOUN
ejpam-5317	22	6	of	of	ADP
ejpam-5317	22	7	a	a	DET
ejpam-5317	22	8	graph	graph	NOUN
ejpam-5317	22	9	in	in	ADP
ejpam-5317	22	10	terms	term	NOUN
ejpam-5317	22	11	of	of	ADP
ejpam-5317	22	12	the	the	DET
ejpam-5317	22	13	characteristic	characteristic	ADJ
ejpam-5317	22	14	polynomials	polynomial	NOUN
ejpam-5317	22	15	,	,	PUNCT
ejpam-5317	22	16	eigenvalues	eigenvalue	NOUN
ejpam-5317	22	17	,	,	PUNCT
ejpam-5317	22	18	and	and	CCONJ
ejpam-5317	22	19	eigenvectors	eigenvector	NOUN
ejpam-5317	22	20	of	of	ADP
ejpam-5317	22	21	a	a	DET
ejpam-5317	22	22	particular	particular	ADJ
ejpam-5317	22	23	matrix	matrix	NOUN
ejpam-5317	22	24	associated	associate	VERB
ejpam-5317	22	25	with	with	ADP
ejpam-5317	22	26	a	a	DET
ejpam-5317	22	27	graph	graph	NOUN
ejpam-5317	22	28	in	in	ADP
ejpam-5317	22	29	order	order	NOUN
ejpam-5317	22	30	to	to	PART
ejpam-5317	22	31	characterize	characterize	VERB
ejpam-5317	22	32	the	the	DET
ejpam-5317	22	33	properties	property	NOUN
ejpam-5317	22	34	of	of	ADP
ejpam-5317	22	35	a	a	DET
ejpam-5317	22	36	graph	graph	NOUN
ejpam-5317	22	37	and	and	CCONJ
ejpam-5317	22	38	extract	extract	VERB
ejpam-5317	22	39	information	information	NOUN
ejpam-5317	22	40	from	from	ADP
ejpam-5317	22	41	its	its	PRON
ejpam-5317	22	42	structure	structure	NOUN
ejpam-5317	22	43	.	.	PUNCT
ejpam-5317	23	1	a	a	DET
ejpam-5317	23	2	variety	variety	NOUN
ejpam-5317	23	3	of	of	ADP
ejpam-5317	23	4	matrices	matrix	NOUN
ejpam-5317	23	5	associated	associate	VERB
ejpam-5317	23	6	with	with	ADP
ejpam-5317	23	7	a	a	DET
ejpam-5317	23	8	graph	graph	NOUN
ejpam-5317	23	9	are	be	AUX
ejpam-5317	23	10	used	use	VERB
ejpam-5317	23	11	,	,	PUNCT
ejpam-5317	23	12	including	include	VERB
ejpam-5317	23	13	adjacency	adjacency	NOUN
ejpam-5317	23	14	matrices	matrix	NOUN
ejpam-5317	23	15	,	,	PUNCT
ejpam-5317	23	16	laplace	laplace	NOUN
ejpam-5317	23	17	matrices	matrix	NOUN
ejpam-5317	23	18	,	,	PUNCT
ejpam-5317	23	19	and	and	CCONJ
ejpam-5317	23	20	normalized	normalize	VERB
ejpam-5317	23	21	laplace	laplace	NOUN
ejpam-5317	23	22	matrices	matrix	NOUN
ejpam-5317	23	23	.	.	PUNCT
ejpam-5317	24	1	the	the	DET
ejpam-5317	24	2	adjacency	adjacency	NOUN
ejpam-5317	24	3	matrix	matrix	NOUN
ejpam-5317	24	4	of	of	ADP
ejpam-5317	24	5	a	a	DET
ejpam-5317	24	6	simple	simple	ADJ
ejpam-5317	24	7	undirected	undirected	ADJ
ejpam-5317	24	8	graph	graph	NOUN
ejpam-5317	24	9	is	be	AUX
ejpam-5317	24	10	a	a	DET
ejpam-5317	24	11	real	real	ADJ
ejpam-5317	24	12	symmetric	symmetric	ADJ
ejpam-5317	24	13	matrix	matrix	NOUN
ejpam-5317	24	14	and	and	CCONJ
ejpam-5317	24	15	is	be	AUX
ejpam-5317	24	16	therefore	therefore	ADV
ejpam-5317	24	17	orthogonally	orthogonally	ADV
ejpam-5317	24	18	diagonalizable	diagonalizable	ADJ
ejpam-5317	24	19	;	;	PUNCT
ejpam-5317	24	20	its	its	PRON
ejpam-5317	24	21	eigenvalues	eigenvalue	NOUN
ejpam-5317	24	22	are	be	AUX
ejpam-5317	24	23	real	real	ADJ
ejpam-5317	24	24	algebraic	algebraic	ADJ
ejpam-5317	24	25	integers	integer	NOUN
ejpam-5317	24	26	.	.	PUNCT
ejpam-5317	25	1	although	although	SCONJ
ejpam-5317	25	2	the	the	DET
ejpam-5317	25	3	adjacency	adjacency	NOUN
ejpam-5317	25	4	matrix	matrix	NOUN
ejpam-5317	25	5	depends	depend	VERB
ejpam-5317	25	6	on	on	ADP
ejpam-5317	25	7	the	the	DET
ejpam-5317	25	8	vertex	vertex	NOUN
ejpam-5317	25	9	labels	label	NOUN
ejpam-5317	25	10	,	,	PUNCT
ejpam-5317	25	11	its	its	PRON
ejpam-5317	25	12	spectrum	spectrum	NOUN
ejpam-5317	25	13	is	be	AUX
ejpam-5317	25	14	a	a	DET
ejpam-5317	25	15	graph	graph	NOUN
ejpam-5317	25	16	invariant	invariant	ADJ
ejpam-5317	25	17	,	,	PUNCT
ejpam-5317	25	18	for	for	ADP
ejpam-5317	25	19	more	more	ADJ
ejpam-5317	25	20	details	detail	NOUN
ejpam-5317	25	21	,	,	PUNCT
ejpam-5317	25	22	one	one	PRON
ejpam-5317	25	23	can	can	AUX
ejpam-5317	25	24	see	see	VERB
ejpam-5317	25	25	[	[	X
ejpam-5317	25	26	1	1	X
ejpam-5317	25	27	]	]	PUNCT
ejpam-5317	25	28	and	and	CCONJ
ejpam-5317	25	29	[	[	X
ejpam-5317	25	30	5	5	NUM
ejpam-5317	25	31	]	]	PUNCT
ejpam-5317	25	32	.	.	PUNCT
ejpam-5317	26	1	the	the	DET
ejpam-5317	26	2	clean	clean	ADJ
ejpam-5317	26	3	graph	graph	NOUN
ejpam-5317	26	4	cl(r	cl(r	NOUN
ejpam-5317	26	5	)	)	PUNCT
ejpam-5317	26	6	is	be	AUX
ejpam-5317	26	7	defined	define	VERB
ejpam-5317	26	8	to	to	PART
ejpam-5317	26	9	be	be	AUX
ejpam-5317	26	10	the	the	DET
ejpam-5317	26	11	graph	graph	NOUN
ejpam-5317	26	12	in	in	ADP
ejpam-5317	26	13	which	which	PRON
ejpam-5317	26	14	every	every	DET
ejpam-5317	26	15	vertex	vertex	NOUN
ejpam-5317	26	16	has	have	VERB
ejpam-5317	26	17	the	the	DET
ejpam-5317	26	18	form	form	NOUN
ejpam-5317	26	19	(	(	PUNCT
ejpam-5317	26	20	a	a	DET
ejpam-5317	26	21	,	,	PUNCT
ejpam-5317	26	22	v	v	NOUN
ejpam-5317	26	23	)	)	PUNCT
ejpam-5317	26	24	where	where	SCONJ
ejpam-5317	26	25	,	,	PUNCT
ejpam-5317	26	26	a	a	PRON
ejpam-5317	26	27	is	be	AUX
ejpam-5317	26	28	an	an	DET
ejpam-5317	26	29	idempotent	idempotent	NOUN
ejpam-5317	26	30	in	in	ADP
ejpam-5317	26	31	the	the	DET
ejpam-5317	26	32	ring	ring	NOUN
ejpam-5317	26	33	r	r	NOUN
ejpam-5317	26	34	and	and	CCONJ
ejpam-5317	26	35	v	v	NOUN
ejpam-5317	26	36	is	be	AUX
ejpam-5317	26	37	a	a	DET
ejpam-5317	26	38	unit	unit	NOUN
ejpam-5317	26	39	.	.	PUNCT
ejpam-5317	27	1	nicholson	nicholson	PROPN
ejpam-5317	28	1	[	[	X
ejpam-5317	28	2	10	10	NUM
ejpam-5317	28	3	]	]	PUNCT
ejpam-5317	28	4	was	be	AUX
ejpam-5317	28	5	the	the	DET
ejpam-5317	28	6	first	first	ADJ
ejpam-5317	28	7	to	to	PART
ejpam-5317	28	8	introduce	introduce	VERB
ejpam-5317	28	9	the	the	DET
ejpam-5317	28	10	clean	clean	ADJ
ejpam-5317	28	11	rings	ring	NOUN
ejpam-5317	28	12	.	.	PUNCT
ejpam-5317	29	1	the	the	DET
ejpam-5317	29	2	clean	clean	ADJ
ejpam-5317	29	3	graph	graph	NOUN
ejpam-5317	29	4	of	of	ADP
ejpam-5317	29	5	a	a	DET
ejpam-5317	29	6	commutative	commutative	ADJ
ejpam-5317	29	7	ring	ring	NOUN
ejpam-5317	29	8	was	be	AUX
ejpam-5317	29	9	introduced	introduce	VERB
ejpam-5317	29	10	by	by	ADP
ejpam-5317	29	11	petrovi´c	petrovi´c	NOUN
ejpam-5317	29	12	and	and	CCONJ
ejpam-5317	29	13	pucanovic	pucanovic	ADJ
ejpam-5317	29	14	´	´	NOUN
ejpam-5317	30	1	[	[	X
ejpam-5317	30	2	11	11	NUM
ejpam-5317	30	3	]	]	PUNCT
ejpam-5317	30	4	in	in	ADP
ejpam-5317	30	5	2017	2017	NUM
ejpam-5317	30	6	.	.	PUNCT
ejpam-5317	31	1	also	also	ADV
ejpam-5317	31	2	,	,	PUNCT
ejpam-5317	31	3	in	in	ADP
ejpam-5317	31	4	2021	2021	NUM
ejpam-5317	31	5	,	,	PUNCT
ejpam-5317	31	6	habibi	habibi	PROPN
ejpam-5317	31	7	et.al	et.al	PROPN
ejpam-5317	31	8	.	.	PUNCT
ejpam-5317	32	1	[	[	X
ejpam-5317	32	2	8	8	NUM
ejpam-5317	32	3	]	]	PUNCT
ejpam-5317	32	4	,	,	PUNCT
ejpam-5317	32	5	has	have	AUX
ejpam-5317	32	6	determined	determine	VERB
ejpam-5317	32	7	the	the	DET
ejpam-5317	32	8	clique	clique	NOUN
ejpam-5317	32	9	number	number	NOUN
ejpam-5317	32	10	,	,	PUNCT
ejpam-5317	32	11	the	the	DET
ejpam-5317	32	12	chromatic	chromatic	ADJ
ejpam-5317	32	13	number	number	NOUN
ejpam-5317	32	14	and	and	CCONJ
ejpam-5317	32	15	the	the	DET
ejpam-5317	32	16	domination	domination	NOUN
ejpam-5317	32	17	number	number	NOUN
ejpam-5317	32	18	of	of	ADP
ejpam-5317	32	19	the	the	DET
ejpam-5317	32	20	clean	clean	ADJ
ejpam-5317	32	21	graph	graph	NOUN
ejpam-5317	32	22	cl(r	cl(r	NOUN
ejpam-5317	32	23	)	)	PUNCT
ejpam-5317	32	24	for	for	ADP
ejpam-5317	32	25	some	some	DET
ejpam-5317	32	26	classes	class	NOUN
ejpam-5317	32	27	of	of	ADP
ejpam-5317	32	28	rings	ring	NOUN
ejpam-5317	32	29	.	.	PUNCT
ejpam-5317	33	1	in	in	ADP
ejpam-5317	33	2	this	this	DET
ejpam-5317	33	3	paper	paper	NOUN
ejpam-5317	33	4	,	,	PUNCT
ejpam-5317	33	5	we	we	PRON
ejpam-5317	33	6	evaluate	evaluate	VERB
ejpam-5317	33	7	the	the	DET
ejpam-5317	33	8	spectrum	spectrum	NOUN
ejpam-5317	33	9	of	of	ADP
ejpam-5317	33	10	a	a	DET
ejpam-5317	33	11	certain	certain	ADJ
ejpam-5317	33	12	large	large	ADJ
ejpam-5317	33	13	block	block	NOUN
ejpam-5317	33	14	matrix	matrix	NOUN
ejpam-5317	33	15	that	that	PRON
ejpam-5317	33	16	forms	form	VERB
ejpam-5317	33	17	an	an	DET
ejpam-5317	33	18	adjacency	adjacency	NOUN
ejpam-5317	33	19	matrix	matrix	NOUN
ejpam-5317	33	20	of	of	ADP
ejpam-5317	33	21	a	a	DET
ejpam-5317	33	22	clean	clean	ADJ
ejpam-5317	33	23	graph	graph	NOUN
ejpam-5317	33	24	.	.	PUNCT
ejpam-5317	34	1	2	2	X
ejpam-5317	34	2	.	.	X
ejpam-5317	34	3	the	the	DET
ejpam-5317	34	4	main	main	ADJ
ejpam-5317	34	5	result	result	NOUN
ejpam-5317	34	6	2.1	2.1	NUM
ejpam-5317	34	7	.	.	PUNCT
ejpam-5317	35	1	general	general	PROPN
ejpam-5317	35	2	let	let	VERB
ejpam-5317	35	3	g	g	PROPN
ejpam-5317	35	4	=	=	SYM
ejpam-5317	35	5	(	(	PUNCT
ejpam-5317	35	6	v	v	NOUN
ejpam-5317	35	7	,	,	PUNCT
ejpam-5317	35	8	e	e	NOUN
ejpam-5317	35	9	)	)	PUNCT
ejpam-5317	35	10	be	be	AUX
ejpam-5317	35	11	a	a	DET
ejpam-5317	35	12	graph	graph	NOUN
ejpam-5317	35	13	with	with	ADP
ejpam-5317	35	14	vertex	vertex	NOUN
ejpam-5317	35	15	set	set	VERB
ejpam-5317	35	16	v	v	NOUN
ejpam-5317	35	17	(	(	PUNCT
ejpam-5317	35	18	g	g	NOUN
ejpam-5317	35	19	)	)	PUNCT
ejpam-5317	35	20	and	and	CCONJ
ejpam-5317	35	21	edge	edge	VERB
ejpam-5317	35	22	set	set	VERB
ejpam-5317	35	23	e(g	e(g	PROPN
ejpam-5317	35	24	)	)	PUNCT
ejpam-5317	35	25	.	.	PUNCT
ejpam-5317	36	1	the	the	DET
ejpam-5317	36	2	adjacency	adjacency	NOUN
ejpam-5317	36	3	matrix	matrix	NOUN
ejpam-5317	36	4	of	of	ADP
ejpam-5317	36	5	g	g	NOUN
ejpam-5317	36	6	,	,	PUNCT
ejpam-5317	36	7	denoted	denote	VERB
ejpam-5317	36	8	by	by	ADP
ejpam-5317	36	9	a(g	a(g	PROPN
ejpam-5317	36	10	)	)	PUNCT
ejpam-5317	36	11	,	,	PUNCT
ejpam-5317	36	12	is	be	AUX
ejpam-5317	36	13	a	a	DET
ejpam-5317	36	14	square	square	ADJ
ejpam-5317	36	15	matrix	matrix	NOUN
ejpam-5317	36	16	of	of	ADP
ejpam-5317	36	17	order	order	NOUN
ejpam-5317	36	18	|v	|v	X
ejpam-5317	36	19	(	(	PUNCT
ejpam-5317	36	20	g)|	g)|	VERB
ejpam-5317	36	21	with	with	ADP
ejpam-5317	36	22	ij	ij	NOUN
ejpam-5317	36	23	-	-	PUNCT
ejpam-5317	36	24	th	th	VERB
ejpam-5317	36	25	entry	entry	NOUN
ejpam-5317	36	26	equals	equal	VERB
ejpam-5317	36	27	1	1	NUM
ejpam-5317	36	28	if	if	SCONJ
ejpam-5317	36	29	vivj	vivj	NOUN
ejpam-5317	36	30	in	in	ADP
ejpam-5317	36	31	e(g	e(g	PROPN
ejpam-5317	36	32	)	)	PUNCT
ejpam-5317	36	33	and	and	CCONJ
ejpam-5317	36	34	0	0	NUM
ejpam-5317	36	35	otherwise	otherwise	ADV
ejpam-5317	36	36	,	,	PUNCT
ejpam-5317	36	37	where	where	SCONJ
ejpam-5317	36	38	vi	vi	NOUN
ejpam-5317	36	39	and	and	CCONJ
ejpam-5317	36	40	vj	vj	PROPN
ejpam-5317	36	41	are	be	AUX
ejpam-5317	36	42	vertices	vertex	NOUN
ejpam-5317	36	43	in	in	ADP
ejpam-5317	36	44	v	v	ADP
ejpam-5317	36	45	(	(	PUNCT
ejpam-5317	36	46	g	g	NOUN
ejpam-5317	36	47	)	)	PUNCT
ejpam-5317	36	48	.	.	PUNCT
ejpam-5317	37	1	let	let	VERB
ejpam-5317	37	2	p	p	PRON
ejpam-5317	37	3	be	be	AUX
ejpam-5317	37	4	any	any	DET
ejpam-5317	37	5	prime	prime	ADJ
ejpam-5317	37	6	number	number	NOUN
ejpam-5317	37	7	that	that	PRON
ejpam-5317	37	8	is	be	AUX
ejpam-5317	37	9	greater	great	ADJ
ejpam-5317	37	10	than	than	ADP
ejpam-5317	37	11	or	or	CCONJ
ejpam-5317	37	12	equal	equal	ADJ
ejpam-5317	37	13	5	5	NUM
ejpam-5317	37	14	,	,	PUNCT
ejpam-5317	37	15	s	s	PART
ejpam-5317	37	16	=	=	PUNCT
ejpam-5317	37	17	(	(	PUNCT
ejpam-5317	37	18	p	p	X
ejpam-5317	37	19	−	−	PROPN
ejpam-5317	37	20	1)2	1)2	NUM
ejpam-5317	37	21	,	,	PUNCT
ejpam-5317	37	22	is	be	AUX
ejpam-5317	37	23	is	be	AUX
ejpam-5317	37	24	the	the	DET
ejpam-5317	37	25	identity	identity	NOUN
ejpam-5317	37	26	matrix	matrix	NOUN
ejpam-5317	37	27	of	of	ADP
ejpam-5317	37	28	order	order	NOUN
ejpam-5317	37	29	s	s	NOUN
ejpam-5317	37	30	,	,	PUNCT
ejpam-5317	37	31	and	and	CCONJ
ejpam-5317	37	32	js	js	PROPN
ejpam-5317	37	33	denote	denote	VERB
ejpam-5317	37	34	the	the	DET
ejpam-5317	37	35	all-1	all-1	ADJ
ejpam-5317	37	36	square	square	ADJ
ejpam-5317	37	37	matrix	matrix	NOUN
ejpam-5317	37	38	of	of	ADP
ejpam-5317	37	39	order	order	NOUN
ejpam-5317	37	40	s.	s.	PROPN
ejpam-5317	37	41	define	define	VERB
ejpam-5317	37	42	a	a	PRON
ejpam-5317	37	43	as	as	ADP
ejpam-5317	37	44	a	a	DET
ejpam-5317	37	45	block	block	NOUN
ejpam-5317	37	46	matrix	matrix	NOUN
ejpam-5317	37	47	a	a	DET
ejpam-5317	37	48	=	=	SYM
ejpam-5317	37	49			ADJ
ejpam-5317	37	50	ks	k	NOUN
ejpam-5317	38	1	js	js	INTJ
ejpam-5317	38	2	js	js	INTJ
ejpam-5317	38	3	js	js	INTJ
ejpam-5317	38	4	js	js	INTJ
ejpam-5317	38	5	qs	qs	ADP
ejpam-5317	38	6	js	js	NOUN
ejpam-5317	38	7	qs	qs	ADP
ejpam-5317	38	8	js	js	ADV
ejpam-5317	38	9	js	js	INTJ
ejpam-5317	38	10	qs	qs	ADP
ejpam-5317	38	11	qs	qs	NOUN
ejpam-5317	38	12	js	js	NOUN
ejpam-5317	38	13	qs	qs	ADP
ejpam-5317	38	14	qs	qs	X
ejpam-5317	38	15	qs	qs	X
ejpam-5317	38	16			NOUN
ejpam-5317	38	17	(	(	PUNCT
ejpam-5317	38	18	1	1	NUM
ejpam-5317	38	19	)	)	PUNCT
ejpam-5317	38	20	of	of	ADP
ejpam-5317	38	21	order	order	NOUN
ejpam-5317	38	22	4s	4s	NUM
ejpam-5317	38	23	,	,	PUNCT
ejpam-5317	38	24	where	where	SCONJ
ejpam-5317	38	25	ks	ks	NOUN
ejpam-5317	38	26	=	=	PUNCT
ejpam-5317	38	27	js	js	PROPN
ejpam-5317	38	28	−	−	PROPN
ejpam-5317	38	29	is	be	AUX
ejpam-5317	38	30	and	and	CCONJ
ejpam-5317	38	31	qs	qs	PROPN
ejpam-5317	38	32	is	be	AUX
ejpam-5317	38	33	a	a	DET
ejpam-5317	38	34	triadiognal	triadiognal	ADJ
ejpam-5317	38	35	matrix	matrix	NOUN
ejpam-5317	38	36	of	of	ADP
ejpam-5317	38	37	oredr	oredr	PROPN
ejpam-5317	38	38	s	s	PART
ejpam-5317	38	39	defined	define	VERB
ejpam-5317	38	40	by	by	ADP
ejpam-5317	38	41	(	(	PUNCT
ejpam-5317	38	42	qs)i	qs)i	PROPN
ejpam-5317	38	43	,	,	PUNCT
ejpam-5317	38	44	j	j	PROPN
ejpam-5317	39	1	=	=	SYM
ejpam-5317	39	2			NOUN
ejpam-5317	39	3	0	0	NUM
ejpam-5317	39	4	,	,	PUNCT
ejpam-5317	39	5	if	if	SCONJ
ejpam-5317	39	6	i	i	PRON
ejpam-5317	39	7	or	or	CCONJ
ejpam-5317	39	8	j	j	PROPN
ejpam-5317	39	9	∈	∈	PROPN
ejpam-5317	39	10	{	{	PUNCT
ejpam-5317	39	11	1	1	NUM
ejpam-5317	39	12	,	,	PUNCT
ejpam-5317	39	13	2	2	NUM
ejpam-5317	39	14	,	,	PUNCT
ejpam-5317	39	15	3	3	NUM
ejpam-5317	39	16	,	,	PUNCT
ejpam-5317	39	17	4	4	NUM
ejpam-5317	39	18	}	}	PUNCT
ejpam-5317	39	19	,	,	PUNCT
ejpam-5317	39	20	0	0	NUM
ejpam-5317	39	21	,	,	PUNCT
ejpam-5317	39	22	if	if	SCONJ
ejpam-5317	39	23	i	i	PRON
ejpam-5317	39	24	=	=	SYM
ejpam-5317	39	25	j	j	PROPN
ejpam-5317	39	26	,	,	PUNCT
ejpam-5317	39	27	1	1	NUM
ejpam-5317	39	28	,	,	PUNCT
ejpam-5317	39	29	if	if	SCONJ
ejpam-5317	39	30	j	j	PROPN
ejpam-5317	40	1	=	=	VERB
ejpam-5317	40	2	i	i	PRON
ejpam-5317	40	3	+	+	CCONJ
ejpam-5317	40	4	1	1	NUM
ejpam-5317	40	5	and	and	CCONJ
ejpam-5317	40	6	j	j	PROPN
ejpam-5317	40	7	≥	≥	NUM
ejpam-5317	40	8	6	6	NUM
ejpam-5317	40	9	is	be	AUX
ejpam-5317	40	10	even	even	ADV
ejpam-5317	40	11	,	,	PUNCT
ejpam-5317	40	12	1	1	NUM
ejpam-5317	40	13	,	,	PUNCT
ejpam-5317	40	14	if	if	SCONJ
ejpam-5317	40	15	j	j	PROPN
ejpam-5317	40	16	=	=	SYM
ejpam-5317	40	17	i−	i−	PROPN
ejpam-5317	40	18	1	1	NUM
ejpam-5317	40	19	and	and	CCONJ
ejpam-5317	40	20	j	j	PROPN
ejpam-5317	40	21	≥	≥	NUM
ejpam-5317	40	22	7	7	NUM
ejpam-5317	40	23	is	be	AUX
ejpam-5317	40	24	odd	odd	ADJ
ejpam-5317	40	25	,	,	PUNCT
ejpam-5317	40	26	0	0	NUM
ejpam-5317	40	27	,	,	PUNCT
ejpam-5317	40	28	otherwise	otherwise	ADV
ejpam-5317	40	29	.	.	PUNCT
ejpam-5317	41	1	e.	e.	PROPN
ejpam-5317	41	2	rawaswhdeh	rawaswhdeh	PROPN
ejpam-5317	41	3	,	,	PUNCT
ejpam-5317	41	4	h.	h.	PROPN
ejpam-5317	41	5	adel	adel	PROPN
ejpam-5317	41	6	abdelkarim	abdelkarim	PROPN
ejpam-5317	41	7	,	,	PUNCT
ejpam-5317	41	8	e.	e.	PROPN
ejpam-5317	41	9	rawshdeh	rawshdeh	PROPN
ejpam-5317	41	10	/	/	SYM
ejpam-5317	41	11	eur	eur	PROPN
ejpam-5317	41	12	.	.	PUNCT
ejpam-5317	42	1	j.	j.	PROPN
ejpam-5317	42	2	pure	pure	PROPN
ejpam-5317	42	3	appl	appl	PROPN
ejpam-5317	42	4	.	.	PROPN
ejpam-5317	42	5	math	math	PROPN
ejpam-5317	42	6	,	,	PUNCT
ejpam-5317	42	7	17	17	NUM
ejpam-5317	42	8	(	(	PUNCT
ejpam-5317	42	9	4	4	NUM
ejpam-5317	42	10	)	)	PUNCT
ejpam-5317	42	11	(	(	PUNCT
ejpam-5317	42	12	2024	2024	NUM
ejpam-5317	42	13	)	)	PUNCT
ejpam-5317	42	14	,	,	PUNCT
ejpam-5317	42	15	2550	2550	NUM
ejpam-5317	42	16	-	-	SYM
ejpam-5317	42	17	2561	2561	NUM
ejpam-5317	42	18	2552	2552	NUM
ejpam-5317	42	19	in	in	ADP
ejpam-5317	42	20	this	this	DET
ejpam-5317	42	21	section	section	NOUN
ejpam-5317	43	1	,	,	PUNCT
ejpam-5317	43	2	we	we	PRON
ejpam-5317	43	3	study	study	VERB
ejpam-5317	43	4	the	the	DET
ejpam-5317	43	5	spectrum	spectrum	NOUN
ejpam-5317	43	6	of	of	ADP
ejpam-5317	43	7	the	the	DET
ejpam-5317	43	8	matrix	matrix	NOUN
ejpam-5317	43	9	a	a	PRON
ejpam-5317	43	10	that	that	PRON
ejpam-5317	43	11	is	be	AUX
ejpam-5317	43	12	given	give	VERB
ejpam-5317	43	13	by	by	ADP
ejpam-5317	43	14	(	(	PUNCT
ejpam-5317	43	15	1	1	NUM
ejpam-5317	43	16	)	)	PUNCT
ejpam-5317	43	17	.	.	PUNCT
ejpam-5317	44	1	this	this	DET
ejpam-5317	44	2	matrix	matrix	NOUN
ejpam-5317	44	3	appears	appear	VERB
ejpam-5317	44	4	in	in	ADP
ejpam-5317	44	5	graph	graph	NOUN
ejpam-5317	44	6	theory	theory	NOUN
ejpam-5317	44	7	and	and	CCONJ
ejpam-5317	44	8	it	it	PRON
ejpam-5317	44	9	is	be	AUX
ejpam-5317	44	10	an	an	DET
ejpam-5317	44	11	adjacency	adjacency	NOUN
ejpam-5317	44	12	matrix	matrix	NOUN
ejpam-5317	44	13	of	of	ADP
ejpam-5317	44	14	a	a	DET
ejpam-5317	44	15	clean	clean	ADJ
ejpam-5317	44	16	graph	graph	NOUN
ejpam-5317	44	17	[	[	X
ejpam-5317	44	18	9	9	NUM
ejpam-5317	44	19	]	]	PUNCT
ejpam-5317	44	20	.	.	PUNCT
ejpam-5317	45	1	let	let	VERB
ejpam-5317	45	2	x	x	PRON
ejpam-5317	45	3	be	be	AUX
ejpam-5317	45	4	an	an	DET
ejpam-5317	45	5	eigenvector	eigenvector	NOUN
ejpam-5317	45	6	of	of	ADP
ejpam-5317	45	7	the	the	DET
ejpam-5317	45	8	matrix	matrix	NOUN
ejpam-5317	45	9	a	a	DET
ejpam-5317	45	10	corresponding	corresponding	NOUN
ejpam-5317	45	11	to	to	ADP
ejpam-5317	45	12	the	the	DET
ejpam-5317	45	13	eigenvalue	eigenvalue	PROPN
ejpam-5317	45	14	λ	λ	PROPN
ejpam-5317	45	15	,	,	PUNCT
ejpam-5317	45	16	by	by	ADP
ejpam-5317	45	17	looking	look	VERB
ejpam-5317	45	18	deeply	deeply	ADV
ejpam-5317	45	19	to	to	ADP
ejpam-5317	45	20	the	the	DET
ejpam-5317	45	21	construction	construction	NOUN
ejpam-5317	45	22	of	of	ADP
ejpam-5317	45	23	the	the	DET
ejpam-5317	45	24	matrix	matrix	NOUN
ejpam-5317	45	25	a	a	PRON
ejpam-5317	45	26	,	,	PUNCT
ejpam-5317	45	27	we	we	PRON
ejpam-5317	45	28	may	may	AUX
ejpam-5317	45	29	consider	consider	VERB
ejpam-5317	45	30	the	the	DET
ejpam-5317	45	31	entries	entry	NOUN
ejpam-5317	45	32	of	of	ADP
ejpam-5317	45	33	the	the	DET
ejpam-5317	45	34	vector	vector	NOUN
ejpam-5317	45	35	x	x	PART
ejpam-5317	45	36	to	to	PART
ejpam-5317	45	37	be	be	AUX
ejpam-5317	45	38	(	(	PUNCT
ejpam-5317	45	39	x)i	x)i	PUNCT
ejpam-5317	45	40	=	=	SYM
ejpam-5317	45	41			PROPN
ejpam-5317	45	42	ai	ai	VERB
ejpam-5317	45	43	,	,	PUNCT
ejpam-5317	45	44	if	if	SCONJ
ejpam-5317	45	45	i	i	PRON
ejpam-5317	45	46	=	=	NOUN
ejpam-5317	45	47	1	1	NUM
ejpam-5317	45	48	,	,	PUNCT
ejpam-5317	45	49	2	2	NUM
ejpam-5317	45	50	,	,	PUNCT
ejpam-5317	45	51	.	.	PUNCT
ejpam-5317	45	52	.	.	PUNCT
ejpam-5317	46	1	.	.	PUNCT
ejpam-5317	47	1	,	,	PUNCT
ejpam-5317	47	2	s	s	X
ejpam-5317	47	3	,	,	PUNCT
ejpam-5317	47	4	bi−s	bi−s	NOUN
ejpam-5317	47	5	,	,	PUNCT
ejpam-5317	47	6	if	if	SCONJ
ejpam-5317	47	7	i	i	PRON
ejpam-5317	47	8	=	=	SYM
ejpam-5317	47	9	s	s	X
ejpam-5317	48	1	+	+	ADJ
ejpam-5317	48	2	1	1	NUM
ejpam-5317	48	3	,	,	PUNCT
ejpam-5317	48	4	s	s	PART
ejpam-5317	48	5	+	+	ADJ
ejpam-5317	48	6	2	2	NUM
ejpam-5317	48	7	,	,	PUNCT
ejpam-5317	48	8	.	.	PUNCT
ejpam-5317	48	9	.	.	PUNCT
ejpam-5317	49	1	.	.	PUNCT
ejpam-5317	50	1	,	,	PUNCT
ejpam-5317	50	2	s	s	PART
ejpam-5317	50	3	+	+	ADJ
ejpam-5317	50	4	4	4	NUM
ejpam-5317	50	5	,	,	PUNCT
ejpam-5317	50	6	b∗i−s−4	b∗i−s−4	ADJ
ejpam-5317	50	7	,	,	PUNCT
ejpam-5317	50	8	if	if	SCONJ
ejpam-5317	50	9	i	i	PRON
ejpam-5317	50	10	=	=	SYM
ejpam-5317	50	11	s	s	PART
ejpam-5317	51	1	+	+	NOUN
ejpam-5317	51	2	5	5	NUM
ejpam-5317	51	3	,	,	PUNCT
ejpam-5317	51	4	s	s	PART
ejpam-5317	51	5	+	+	NOUN
ejpam-5317	51	6	6	6	NUM
ejpam-5317	51	7	,	,	PUNCT
ejpam-5317	51	8	.	.	PUNCT
ejpam-5317	51	9	.	.	PUNCT
ejpam-5317	52	1	.	.	PUNCT
ejpam-5317	53	1	,	,	PUNCT
ejpam-5317	53	2	2s	2s	X
ejpam-5317	53	3	,	,	PUNCT
ejpam-5317	53	4	ci−2s	ci−2s	PROPN
ejpam-5317	53	5	,	,	PUNCT
ejpam-5317	53	6	if	if	SCONJ
ejpam-5317	53	7	i	i	PRON
ejpam-5317	53	8	=	=	PUNCT
ejpam-5317	54	1	2s	2s	NUM
ejpam-5317	55	1	+	+	NOUN
ejpam-5317	55	2	1	1	NUM
ejpam-5317	55	3	,	,	PUNCT
ejpam-5317	55	4	2s	2s	PROPN
ejpam-5317	55	5	+	+	NOUN
ejpam-5317	55	6	2	2	NUM
ejpam-5317	55	7	,	,	PUNCT
ejpam-5317	55	8	.	.	PUNCT
ejpam-5317	55	9	.	.	PUNCT
ejpam-5317	56	1	.	.	PUNCT
ejpam-5317	57	1	,	,	PUNCT
ejpam-5317	58	1	2s	2s	NUM
ejpam-5317	58	2	+	+	ADJ
ejpam-5317	58	3	4	4	NUM
ejpam-5317	58	4	,	,	PUNCT
ejpam-5317	58	5	c∗i−2s−4	c∗i−2s−4	PROPN
ejpam-5317	58	6	,	,	PUNCT
ejpam-5317	58	7	if	if	SCONJ
ejpam-5317	58	8	i	i	PRON
ejpam-5317	58	9	=	=	PUNCT
ejpam-5317	59	1	2s	2s	NUM
ejpam-5317	60	1	+	+	NOUN
ejpam-5317	60	2	5	5	NUM
ejpam-5317	60	3	,	,	PUNCT
ejpam-5317	60	4	2s	2s	PROPN
ejpam-5317	60	5	+	+	NOUN
ejpam-5317	60	6	6	6	NUM
ejpam-5317	60	7	,	,	PUNCT
ejpam-5317	60	8	.	.	PUNCT
ejpam-5317	60	9	.	.	PUNCT
ejpam-5317	60	10	.	.	PUNCT
ejpam-5317	61	1	,	,	PUNCT
ejpam-5317	61	2	3s	3s	NOUN
ejpam-5317	61	3	,	,	PUNCT
ejpam-5317	61	4	di−3s	di−3s	NOUN
ejpam-5317	61	5	,	,	PUNCT
ejpam-5317	61	6	if	if	SCONJ
ejpam-5317	61	7	i	i	PRON
ejpam-5317	61	8	=	=	SYM
ejpam-5317	61	9	3s	3s	NUM
ejpam-5317	61	10	+	+	CCONJ
ejpam-5317	61	11	1	1	NUM
ejpam-5317	61	12	,	,	PUNCT
ejpam-5317	61	13	3s	3s	NUM
ejpam-5317	61	14	+	+	CCONJ
ejpam-5317	61	15	2	2	NUM
ejpam-5317	61	16	,	,	PUNCT
ejpam-5317	61	17	.	.	PUNCT
ejpam-5317	61	18	.	.	PUNCT
ejpam-5317	61	19	.	.	PUNCT
ejpam-5317	62	1	,	,	PUNCT
ejpam-5317	62	2	3s	3s	NUM
ejpam-5317	62	3	+	+	CCONJ
ejpam-5317	62	4	4	4	NUM
ejpam-5317	62	5	,	,	PUNCT
ejpam-5317	62	6	d∗i−3s−4	d∗i−3s−4	PROPN
ejpam-5317	62	7	,	,	PUNCT
ejpam-5317	62	8	if	if	SCONJ
ejpam-5317	62	9	i	i	PRON
ejpam-5317	62	10	=	=	SYM
ejpam-5317	62	11	3s	3s	NUM
ejpam-5317	62	12	+	+	CCONJ
ejpam-5317	62	13	5	5	NUM
ejpam-5317	62	14	,	,	PUNCT
ejpam-5317	62	15	3s	3s	NUM
ejpam-5317	62	16	+	+	CCONJ
ejpam-5317	62	17	6	6	NUM
ejpam-5317	62	18	,	,	PUNCT
ejpam-5317	62	19	.	.	PUNCT
ejpam-5317	62	20	.	.	PUNCT
ejpam-5317	62	21	.	.	PUNCT
ejpam-5317	63	1	,	,	PUNCT
ejpam-5317	63	2	4s	4s	NUM
ejpam-5317	63	3	.	.	PUNCT
ejpam-5317	64	1	(	(	PUNCT
ejpam-5317	64	2	2	2	NUM
ejpam-5317	64	3	)	)	PUNCT
ejpam-5317	64	4	since	since	ADV
ejpam-5317	64	5	,	,	PUNCT
ejpam-5317	64	6	we	we	PRON
ejpam-5317	64	7	have	have	VERB
ejpam-5317	64	8	to	to	PART
ejpam-5317	64	9	find	find	VERB
ejpam-5317	64	10	λ	λ	NOUN
ejpam-5317	64	11	so	so	SCONJ
ejpam-5317	64	12	that	that	SCONJ
ejpam-5317	64	13	ax	ax	NOUN
ejpam-5317	64	14	=	=	PROPN
ejpam-5317	64	15	λx	λx	PROPN
ejpam-5317	64	16	,	,	PUNCT
ejpam-5317	64	17	then	then	ADV
ejpam-5317	64	18	x	x	PUNCT
ejpam-5317	64	19	is	be	AUX
ejpam-5317	64	20	an	an	DET
ejpam-5317	64	21	eigenvector	eigenvector	NOUN
ejpam-5317	64	22	of	of	ADP
ejpam-5317	64	23	the	the	DET
ejpam-5317	64	24	matrix	matrix	NOUN
ejpam-5317	64	25	a	a	DET
ejpam-5317	64	26	corresponding	corresponding	NOUN
ejpam-5317	64	27	to	to	ADP
ejpam-5317	64	28	the	the	DET
ejpam-5317	64	29	eigenvalue	eigenvalue	PROPN
ejpam-5317	64	30	λ	λ	PROPN
ejpam-5317	64	31	if	if	SCONJ
ejpam-5317	65	1	and	and	CCONJ
ejpam-5317	65	2	only	only	ADV
ejpam-5317	65	3	if	if	SCONJ
ejpam-5317	65	4	all	all	DET
ejpam-5317	65	5	the	the	DET
ejpam-5317	65	6	following	follow	VERB
ejpam-5317	65	7	equations	equation	NOUN
ejpam-5317	65	8	are	be	AUX
ejpam-5317	65	9	satisfied	satisfied	ADJ
ejpam-5317	65	10	:	:	PUNCT
ejpam-5317	65	11	s∑	s∑	PROPN
ejpam-5317	65	12	i=1	i=1	PROPN
ejpam-5317	65	13	ai	ai	VERB
ejpam-5317	65	14	+	+	NOUN
ejpam-5317	65	15	4∑	4∑	NOUN
ejpam-5317	65	16	j=1	j=1	NOUN
ejpam-5317	65	17	bj	bj	VERB
ejpam-5317	65	18	+	+	CCONJ
ejpam-5317	65	19	s−4∑	s−4∑	NOUN
ejpam-5317	65	20	i=1	i=1	PROPN
ejpam-5317	65	21	b∗i	b∗i	X
ejpam-5317	66	1	+	+	CCONJ
ejpam-5317	66	2	4∑	4∑	NUM
ejpam-5317	66	3	j=1	j=1	NOUN
ejpam-5317	66	4	cj	cj	NOUN
ejpam-5317	67	1	+	+	CCONJ
ejpam-5317	67	2	s−4∑	s−4∑	VERB
ejpam-5317	67	3	i=1	i=1	PROPN
ejpam-5317	67	4	c∗i	c∗i	X
ejpam-5317	68	1	+	+	PUNCT
ejpam-5317	68	2	4∑	4∑	NUM
ejpam-5317	68	3	j=1	j=1	NOUN
ejpam-5317	68	4	dj	dj	NOUN
ejpam-5317	68	5	+	+	CCONJ
ejpam-5317	68	6	s−4∑	s−4∑	X
ejpam-5317	68	7	i=1	i=1	PRON
ejpam-5317	68	8	d∗i	d∗i	X
ejpam-5317	68	9	=	=	SYM
ejpam-5317	68	10	(	(	PUNCT
ejpam-5317	68	11	λ	λ	X
ejpam-5317	68	12	+	+	PROPN
ejpam-5317	68	13	1)ar	1)ar	NOUN
ejpam-5317	68	14	,	,	PUNCT
ejpam-5317	68	15	(	(	PUNCT
ejpam-5317	68	16	3	3	X
ejpam-5317	68	17	)	)	PUNCT
ejpam-5317	68	18	s∑	s∑	PROPN
ejpam-5317	69	1	i=1	i=1	PROPN
ejpam-5317	69	2	ai	ai	VERB
ejpam-5317	70	1	+	+	NOUN
ejpam-5317	70	2	4∑	4∑	NUM
ejpam-5317	70	3	j=1	j=1	NOUN
ejpam-5317	70	4	cj	cj	NOUN
ejpam-5317	71	1	+	+	CCONJ
ejpam-5317	71	2	s−4∑	s−4∑	X
ejpam-5317	71	3	i=1	i=1	PROPN
ejpam-5317	71	4	c∗i	c∗i	PROPN
ejpam-5317	71	5	=	=	SYM
ejpam-5317	71	6	λbm	λbm	PROPN
ejpam-5317	71	7	,	,	PUNCT
ejpam-5317	71	8	(	(	PUNCT
ejpam-5317	71	9	4	4	NUM
ejpam-5317	71	10	)	)	PUNCT
ejpam-5317	71	11	s∑	s∑	PROPN
ejpam-5317	71	12	i=1	i=1	PROPN
ejpam-5317	72	1	ai	ai	VERB
ejpam-5317	72	2	+	+	X
ejpam-5317	72	3	b∗k+1	b∗k+1	X
ejpam-5317	72	4	+	+	X
ejpam-5317	72	5	4∑	4∑	NUM
ejpam-5317	72	6	j=1	j=1	NOUN
ejpam-5317	72	7	cj	cj	NOUN
ejpam-5317	73	1	+	+	CCONJ
ejpam-5317	73	2	s−4∑	s−4∑	X
ejpam-5317	73	3	i=1	i=1	PROPN
ejpam-5317	73	4	c∗i	c∗i	PUNCT
ejpam-5317	73	5	+	+	CCONJ
ejpam-5317	73	6	d∗k+1	d∗k+1	NOUN
ejpam-5317	73	7	=	=	SYM
ejpam-5317	73	8	λb∗k	λb∗k	PROPN
ejpam-5317	73	9	,	,	PUNCT
ejpam-5317	73	10	(	(	PUNCT
ejpam-5317	73	11	5	5	NUM
ejpam-5317	73	12	)	)	PUNCT
ejpam-5317	73	13	s∑	s∑	PROPN
ejpam-5317	74	1	i=1	i=1	PROPN
ejpam-5317	74	2	ai	ai	VERB
ejpam-5317	74	3	+	+	PUNCT
ejpam-5317	74	4	b∗k	b∗k	SYM
ejpam-5317	74	5	+	+	SYM
ejpam-5317	74	6	4∑	4∑	NUM
ejpam-5317	74	7	j=1	j=1	NOUN
ejpam-5317	74	8	cj	cj	NOUN
ejpam-5317	75	1	+	+	CCONJ
ejpam-5317	75	2	s−4∑	s−4∑	VERB
ejpam-5317	75	3	i=1	i=1	PROPN
ejpam-5317	75	4	c∗i	c∗i	X
ejpam-5317	75	5	+	+	PUNCT
ejpam-5317	75	6	d∗k	d∗k	PUNCT
ejpam-5317	75	7	=	=	SYM
ejpam-5317	75	8	λb∗k+1	λb∗k+1	PROPN
ejpam-5317	75	9	,	,	PUNCT
ejpam-5317	75	10	(	(	PUNCT
ejpam-5317	75	11	6	6	NUM
ejpam-5317	75	12	)	)	PUNCT
ejpam-5317	75	13	s∑	s∑	PROPN
ejpam-5317	76	1	i=1	i=1	PROPN
ejpam-5317	76	2	ai	ai	VERB
ejpam-5317	76	3	+	+	NOUN
ejpam-5317	76	4	4∑	4∑	NOUN
ejpam-5317	76	5	j=1	j=1	NOUN
ejpam-5317	76	6	bj	bj	VERB
ejpam-5317	76	7	+	+	CCONJ
ejpam-5317	76	8	s−4∑	s−4∑	NOUN
ejpam-5317	76	9	i=1	i=1	PRON
ejpam-5317	76	10	b∗i	b∗i	PROPN
ejpam-5317	76	11	=	=	PUNCT
ejpam-5317	76	12	λcm	λcm	ADJ
ejpam-5317	76	13	,	,	PUNCT
ejpam-5317	76	14	(	(	PUNCT
ejpam-5317	76	15	7	7	X
ejpam-5317	76	16	)	)	PUNCT
ejpam-5317	76	17	s∑	s∑	PROPN
ejpam-5317	76	18	i=1	i=1	PROPN
ejpam-5317	77	1	ai	ai	VERB
ejpam-5317	78	1	+	+	NUM
ejpam-5317	78	2	c∗k+1	c∗k+1	X
ejpam-5317	79	1	+	+	CCONJ
ejpam-5317	79	2	4∑	4∑	NOUN
ejpam-5317	79	3	j=1	j=1	NOUN
ejpam-5317	79	4	bj	bj	VERB
ejpam-5317	79	5	+	+	CCONJ
ejpam-5317	79	6	s−4∑	s−4∑	NOUN
ejpam-5317	79	7	i=1	i=1	PRON
ejpam-5317	79	8	b∗i	b∗i	PUNCT
ejpam-5317	79	9	+	+	CCONJ
ejpam-5317	79	10	d∗k+1	d∗k+1	NOUN
ejpam-5317	79	11	=	=	SYM
ejpam-5317	79	12	λc∗k	λc∗k	NOUN
ejpam-5317	79	13	,	,	PUNCT
ejpam-5317	79	14	(	(	PUNCT
ejpam-5317	79	15	8)	8)	NUM
ejpam-5317	79	16	s∑	s∑	PROPN
ejpam-5317	79	17	i=1	i=1	PRON
ejpam-5317	79	18	ai	ai	VERB
ejpam-5317	79	19	+	+	NOUN
ejpam-5317	79	20	c∗k	c∗k	NOUN
ejpam-5317	79	21	+	+	SYM
ejpam-5317	79	22	4∑	4∑	NOUN
ejpam-5317	79	23	j=1	j=1	NOUN
ejpam-5317	79	24	bj	bj	VERB
ejpam-5317	79	25	+	+	CCONJ
ejpam-5317	79	26	s−4∑	s−4∑	NOUN
ejpam-5317	79	27	i=1	i=1	X
ejpam-5317	79	28	b∗i	b∗i	PUNCT
ejpam-5317	79	29	+	+	CCONJ
ejpam-5317	79	30	d∗k	d∗k	PUNCT
ejpam-5317	79	31	=	=	SYM
ejpam-5317	79	32	λc∗k+1	λc∗k+1	PROPN
ejpam-5317	79	33	,	,	PUNCT
ejpam-5317	79	34	(	(	PUNCT
ejpam-5317	79	35	9	9	NUM
ejpam-5317	79	36	)	)	PUNCT
ejpam-5317	79	37	s∑	s∑	PROPN
ejpam-5317	80	1	i=1	i=1	PROPN
ejpam-5317	81	1	ai	ai	VERB
ejpam-5317	82	1	=	=	SYM
ejpam-5317	83	1	λdm	λdm	PROPN
ejpam-5317	83	2	,	,	PUNCT
ejpam-5317	83	3	(	(	PUNCT
ejpam-5317	83	4	10	10	NUM
ejpam-5317	83	5	)	)	PUNCT
ejpam-5317	83	6	s∑	s∑	PROPN
ejpam-5317	84	1	i=1	i=1	PROPN
ejpam-5317	84	2	ai	ai	VERB
ejpam-5317	84	3	+	+	X
ejpam-5317	84	4	b∗k+1	b∗k+1	X
ejpam-5317	84	5	+	+	CCONJ
ejpam-5317	84	6	c∗k+1	c∗k+1	NOUN
ejpam-5317	85	1	+	+	CCONJ
ejpam-5317	85	2	d∗k+1	d∗k+1	NOUN
ejpam-5317	85	3	=	=	SYM
ejpam-5317	85	4	λd∗k	λd∗k	PROPN
ejpam-5317	85	5	,	,	PUNCT
ejpam-5317	85	6	(	(	PUNCT
ejpam-5317	85	7	11	11	NUM
ejpam-5317	85	8	)	)	PUNCT
ejpam-5317	85	9	e.	e.	PROPN
ejpam-5317	85	10	rawaswhdeh	rawaswhdeh	PROPN
ejpam-5317	85	11	,	,	PUNCT
ejpam-5317	85	12	h.	h.	PROPN
ejpam-5317	85	13	adel	adel	PROPN
ejpam-5317	85	14	abdelkarim	abdelkarim	PROPN
ejpam-5317	85	15	,	,	PUNCT
ejpam-5317	85	16	e.	e.	PROPN
ejpam-5317	85	17	rawshdeh	rawshdeh	PROPN
ejpam-5317	85	18	/	/	SYM
ejpam-5317	85	19	eur	eur	PROPN
ejpam-5317	85	20	.	.	PUNCT
ejpam-5317	86	1	j.	j.	PROPN
ejpam-5317	86	2	pure	pure	PROPN
ejpam-5317	86	3	appl	appl	PROPN
ejpam-5317	86	4	.	.	PROPN
ejpam-5317	86	5	math	math	PROPN
ejpam-5317	86	6	,	,	PUNCT
ejpam-5317	86	7	17	17	NUM
ejpam-5317	86	8	(	(	PUNCT
ejpam-5317	86	9	4	4	NUM
ejpam-5317	86	10	)	)	PUNCT
ejpam-5317	86	11	(	(	PUNCT
ejpam-5317	86	12	2024	2024	NUM
ejpam-5317	86	13	)	)	PUNCT
ejpam-5317	86	14	,	,	PUNCT
ejpam-5317	86	15	2550	2550	NUM
ejpam-5317	86	16	-	-	SYM
ejpam-5317	86	17	2561	2561	NUM
ejpam-5317	86	18	2553	2553	NUM
ejpam-5317	86	19	and	and	CCONJ
ejpam-5317	86	20	s∑	s∑	PROPN
ejpam-5317	86	21	i=1	i=1	PROPN
ejpam-5317	86	22	ai	ai	VERB
ejpam-5317	86	23	+	+	PUNCT
ejpam-5317	86	24	b∗k	b∗k	PRON
ejpam-5317	86	25	+	+	CCONJ
ejpam-5317	86	26	c∗k	c∗k	NOUN
ejpam-5317	86	27	+	+	CCONJ
ejpam-5317	86	28	d∗k	d∗k	PUNCT
ejpam-5317	86	29	=	=	SYM
ejpam-5317	86	30	λd∗k+1	λd∗k+1	PROPN
ejpam-5317	86	31	,	,	PUNCT
ejpam-5317	86	32	(	(	PUNCT
ejpam-5317	86	33	12	12	NUM
ejpam-5317	86	34	)	)	PUNCT
ejpam-5317	86	35	where	where	SCONJ
ejpam-5317	86	36	r	r	NOUN
ejpam-5317	86	37	=	=	SYM
ejpam-5317	86	38	1	1	NUM
ejpam-5317	86	39	,	,	PUNCT
ejpam-5317	86	40	2	2	NUM
ejpam-5317	86	41	,	,	PUNCT
ejpam-5317	86	42	.	.	PUNCT
ejpam-5317	86	43	.	.	PUNCT
ejpam-5317	86	44	.	.	PUNCT
ejpam-5317	87	1	,	,	PUNCT
ejpam-5317	87	2	s	s	X
ejpam-5317	87	3	,	,	PUNCT
ejpam-5317	87	4	m	m	VERB
ejpam-5317	87	5	=	=	NOUN
ejpam-5317	87	6	1	1	NUM
ejpam-5317	87	7	,	,	PUNCT
ejpam-5317	87	8	2	2	NUM
ejpam-5317	87	9	,	,	PUNCT
ejpam-5317	87	10	3	3	NUM
ejpam-5317	87	11	,	,	PUNCT
ejpam-5317	87	12	4	4	NUM
ejpam-5317	87	13	,	,	PUNCT
ejpam-5317	87	14	and	and	CCONJ
ejpam-5317	87	15	k	k	X
ejpam-5317	87	16	=	=	SYM
ejpam-5317	87	17	1	1	NUM
ejpam-5317	87	18	,	,	PUNCT
ejpam-5317	87	19	3	3	NUM
ejpam-5317	87	20	,	,	PUNCT
ejpam-5317	87	21	.	.	PUNCT
ejpam-5317	87	22	.	.	PUNCT
ejpam-5317	88	1	.	.	PUNCT
ejpam-5317	89	1	,	,	PUNCT
ejpam-5317	89	2	s−	s−	PROPN
ejpam-5317	89	3	5	5	NUM
ejpam-5317	89	4	.	.	PUNCT
ejpam-5317	90	1	since	since	SCONJ
ejpam-5317	90	2	equation	equation	NOUN
ejpam-5317	90	3	(	(	PUNCT
ejpam-5317	90	4	10	10	NUM
ejpam-5317	90	5	)	)	PUNCT
ejpam-5317	90	6	is	be	AUX
ejpam-5317	90	7	true	true	ADJ
ejpam-5317	90	8	for	for	ADP
ejpam-5317	90	9	all	all	DET
ejpam-5317	90	10	m	m	NOUN
ejpam-5317	90	11	=	=	NOUN
ejpam-5317	90	12	1	1	NUM
ejpam-5317	90	13	,	,	PUNCT
ejpam-5317	90	14	2	2	NUM
ejpam-5317	90	15	,	,	PUNCT
ejpam-5317	90	16	3	3	NUM
ejpam-5317	90	17	,	,	PUNCT
ejpam-5317	90	18	4	4	NUM
ejpam-5317	90	19	,	,	PUNCT
ejpam-5317	90	20	we	we	PRON
ejpam-5317	90	21	get	get	VERB
ejpam-5317	90	22	4	4	NUM
ejpam-5317	90	23	s∑	s∑	PROPN
ejpam-5317	90	24	i=1	i=1	PROPN
ejpam-5317	91	1	ai	ai	VERB
ejpam-5317	91	2	=	=	PUNCT
ejpam-5317	92	1	λ	λ	X
ejpam-5317	92	2	4∑	4∑	NOUN
ejpam-5317	92	3	j=1	j=1	NOUN
ejpam-5317	92	4	dj	dj	X
ejpam-5317	92	5	.	.	PUNCT
ejpam-5317	93	1	(	(	PUNCT
ejpam-5317	93	2	13	13	NUM
ejpam-5317	93	3	)	)	PUNCT
ejpam-5317	93	4	in	in	ADP
ejpam-5317	93	5	order	order	NOUN
ejpam-5317	93	6	to	to	PART
ejpam-5317	93	7	find	find	VERB
ejpam-5317	93	8	the	the	DET
ejpam-5317	93	9	eigenvalues	eigenvalue	NOUN
ejpam-5317	93	10	of	of	ADP
ejpam-5317	93	11	the	the	DET
ejpam-5317	93	12	matrix	matrix	NOUN
ejpam-5317	93	13	a	a	PRON
ejpam-5317	93	14	,	,	PUNCT
ejpam-5317	93	15	we	we	PRON
ejpam-5317	93	16	need	need	VERB
ejpam-5317	93	17	first	first	ADV
ejpam-5317	93	18	to	to	PART
ejpam-5317	93	19	prove	prove	VERB
ejpam-5317	93	20	the	the	DET
ejpam-5317	93	21	following	follow	VERB
ejpam-5317	93	22	lemma	lemma	PROPN
ejpam-5317	93	23	.	.	PUNCT
ejpam-5317	94	1	lemma	lemma	PROPN
ejpam-5317	94	2	1	1	NUM
ejpam-5317	94	3	.	.	PUNCT
ejpam-5317	94	4	suppose	suppose	VERB
ejpam-5317	94	5	that	that	SCONJ
ejpam-5317	94	6	x	x	PRON
ejpam-5317	94	7	is	be	AUX
ejpam-5317	94	8	given	give	VERB
ejpam-5317	94	9	by	by	ADP
ejpam-5317	94	10	equation	equation	NOUN
ejpam-5317	94	11	(	(	PUNCT
ejpam-5317	94	12	2	2	NUM
ejpam-5317	94	13	)	)	PUNCT
ejpam-5317	94	14	.	.	PUNCT
ejpam-5317	95	1	if	if	SCONJ
ejpam-5317	95	2	x	x	PRON
ejpam-5317	95	3	is	be	AUX
ejpam-5317	95	4	an	an	DET
ejpam-5317	95	5	eigenvector	eigenvector	NOUN
ejpam-5317	95	6	of	of	ADP
ejpam-5317	95	7	the	the	DET
ejpam-5317	95	8	matrix	matrix	NOUN
ejpam-5317	95	9	a	a	DET
ejpam-5317	95	10	corresponding	corresponding	NOUN
ejpam-5317	95	11	to	to	ADP
ejpam-5317	95	12	the	the	DET
ejpam-5317	95	13	eigenvalue	eigenvalue	PROPN
ejpam-5317	95	14	λ	λ	NOUN
ejpam-5317	95	15	such	such	ADJ
ejpam-5317	95	16	that	that	SCONJ
ejpam-5317	95	17	λ	λ	PROPN
ejpam-5317	95	18	̸=	̸=	PROPN
ejpam-5317	95	19	1	1	NUM
ejpam-5317	95	20	and	and	CCONJ
ejpam-5317	95	21	λ	λ	NOUN
ejpam-5317	95	22	is	be	AUX
ejpam-5317	95	23	not	not	PART
ejpam-5317	95	24	a	a	DET
ejpam-5317	95	25	root	root	NOUN
ejpam-5317	95	26	of	of	ADP
ejpam-5317	95	27	the	the	DET
ejpam-5317	95	28	polynomial	polynomial	ADJ
ejpam-5317	95	29	q(x	q(x	PROPN
ejpam-5317	95	30	)	)	PUNCT
ejpam-5317	95	31	=	=	PUNCT
ejpam-5317	96	1	x5−(2s+1)x4−(2s2−2s−1)x3+(s3−2s2	x5−(2s+1)x4−(2s2−2s−1)x3+(s3−2s2	PROPN
ejpam-5317	96	2	+	+	PROPN
ejpam-5317	96	3	26s+7)x2−(8s2−8s−4)x−16s	26s+7)x2−(8s2−8s−4)x−16s	NUM
ejpam-5317	96	4	,	,	PUNCT
ejpam-5317	96	5	(	(	PUNCT
ejpam-5317	96	6	14	14	NUM
ejpam-5317	96	7	)	)	PUNCT
ejpam-5317	96	8	then	then	ADV
ejpam-5317	96	9	∑4	∑4	PROPN
ejpam-5317	96	10	j=1(bj	j=1(bj	NOUN
ejpam-5317	97	1	+	+	CCONJ
ejpam-5317	97	2	cj	cj	NOUN
ejpam-5317	97	3	)	)	PUNCT
ejpam-5317	97	4	=	=	SYM
ejpam-5317	97	5	0	0	NUM
ejpam-5317	97	6	,	,	PUNCT
ejpam-5317	97	7	∑4	∑4	PROPN
ejpam-5317	98	1	j	j	PROPN
ejpam-5317	98	2	dj	dj	X
ejpam-5317	98	3	=	=	SYM
ejpam-5317	98	4	0	0	NUM
ejpam-5317	98	5	,	,	PUNCT
ejpam-5317	98	6	and	and	CCONJ
ejpam-5317	98	7	∑s−4	∑s−4	VERB
ejpam-5317	98	8	i=1	i=1	PROPN
ejpam-5317	99	1	d	d	NOUN
ejpam-5317	99	2	∗	∗	VERB
ejpam-5317	99	3	i	i	NOUN
ejpam-5317	99	4	=	=	NOUN
ejpam-5317	99	5	0	0	X
ejpam-5317	99	6	.	.	PUNCT
ejpam-5317	100	1	proof	proof	NOUN
ejpam-5317	100	2	.	.	PUNCT
ejpam-5317	101	1	let	let	VERB
ejpam-5317	101	2	x	x	PRON
ejpam-5317	101	3	be	be	AUX
ejpam-5317	101	4	given	give	VERB
ejpam-5317	101	5	by	by	ADP
ejpam-5317	101	6	(	(	PUNCT
ejpam-5317	101	7	2	2	NUM
ejpam-5317	101	8	)	)	PUNCT
ejpam-5317	101	9	.	.	PUNCT
ejpam-5317	102	1	if	if	SCONJ
ejpam-5317	102	2	x	x	PRON
ejpam-5317	102	3	is	be	AUX
ejpam-5317	102	4	an	an	DET
ejpam-5317	102	5	eigenvector	eigenvector	NOUN
ejpam-5317	102	6	of	of	ADP
ejpam-5317	102	7	the	the	DET
ejpam-5317	102	8	matrix	matrix	NOUN
ejpam-5317	102	9	a	a	DET
ejpam-5317	102	10	corresponding	corresponding	NOUN
ejpam-5317	102	11	to	to	ADP
ejpam-5317	102	12	the	the	DET
ejpam-5317	102	13	eigenvalue	eigenvalue	PROPN
ejpam-5317	102	14	λ	λ	PROPN
ejpam-5317	102	15	,	,	PUNCT
ejpam-5317	102	16	then	then	ADV
ejpam-5317	102	17	all	all	DET
ejpam-5317	102	18	equations	equation	NOUN
ejpam-5317	102	19	from	from	ADP
ejpam-5317	102	20	(	(	PUNCT
ejpam-5317	102	21	3	3	NUM
ejpam-5317	102	22	)	)	PUNCT
ejpam-5317	102	23	up	up	ADP
ejpam-5317	102	24	to	to	PART
ejpam-5317	102	25	(	(	PUNCT
ejpam-5317	102	26	12	12	NUM
ejpam-5317	102	27	)	)	PUNCT
ejpam-5317	102	28	have	have	VERB
ejpam-5317	102	29	to	to	PART
ejpam-5317	102	30	be	be	AUX
ejpam-5317	102	31	satisfied	satisfied	ADJ
ejpam-5317	102	32	for	for	ADP
ejpam-5317	102	33	all	all	DET
ejpam-5317	102	34	r	r	NOUN
ejpam-5317	102	35	=	=	SYM
ejpam-5317	102	36	1	1	NUM
ejpam-5317	102	37	,	,	PUNCT
ejpam-5317	102	38	2	2	NUM
ejpam-5317	102	39	,	,	PUNCT
ejpam-5317	102	40	.	.	PUNCT
ejpam-5317	102	41	.	.	PUNCT
ejpam-5317	103	1	.	.	PUNCT
ejpam-5317	104	1	,	,	PUNCT
ejpam-5317	105	1	5,m	5,m	NUM
ejpam-5317	105	2	=	=	SYM
ejpam-5317	105	3	1	1	NUM
ejpam-5317	105	4	,	,	PUNCT
ejpam-5317	105	5	2	2	NUM
ejpam-5317	105	6	,	,	PUNCT
ejpam-5317	105	7	3	3	NUM
ejpam-5317	105	8	,	,	PUNCT
ejpam-5317	105	9	4	4	NUM
ejpam-5317	105	10	,	,	PUNCT
ejpam-5317	105	11	and	and	CCONJ
ejpam-5317	105	12	k	k	X
ejpam-5317	105	13	=	=	SYM
ejpam-5317	105	14	1	1	NUM
ejpam-5317	105	15	,	,	PUNCT
ejpam-5317	105	16	3	3	NUM
ejpam-5317	105	17	,	,	PUNCT
ejpam-5317	105	18	.	.	PUNCT
ejpam-5317	105	19	.	.	PUNCT
ejpam-5317	105	20	.	.	PUNCT
ejpam-5317	106	1	,	,	PUNCT
ejpam-5317	106	2	s−	s−	PROPN
ejpam-5317	106	3	5	5	NUM
ejpam-5317	106	4	.	.	PUNCT
ejpam-5317	106	5	substitute	substitute	NOUN
ejpam-5317	106	6	equations	equation	NOUN
ejpam-5317	106	7	(	(	PUNCT
ejpam-5317	106	8	4	4	NUM
ejpam-5317	106	9	)	)	PUNCT
ejpam-5317	106	10	and	and	CCONJ
ejpam-5317	106	11	(	(	PUNCT
ejpam-5317	106	12	7	7	X
ejpam-5317	106	13	)	)	PUNCT
ejpam-5317	106	14	in	in	ADP
ejpam-5317	106	15	equation	equation	NOUN
ejpam-5317	106	16	(	(	PUNCT
ejpam-5317	106	17	3	3	NUM
ejpam-5317	106	18	)	)	PUNCT
ejpam-5317	106	19	to	to	PART
ejpam-5317	106	20	get	get	VERB
ejpam-5317	106	21	λ(bm	λ(bm	PRON
ejpam-5317	106	22	+	+	CCONJ
ejpam-5317	106	23	cm	cm	NOUN
ejpam-5317	106	24	)	)	PUNCT
ejpam-5317	106	25	−	−	PROPN
ejpam-5317	107	1	s∑	s∑	PROPN
ejpam-5317	107	2	i=1	i=1	PROPN
ejpam-5317	107	3	ai	ai	VERB
ejpam-5317	107	4	+	+	NOUN
ejpam-5317	107	5	4∑	4∑	NOUN
ejpam-5317	107	6	j=1	j=1	NOUN
ejpam-5317	107	7	dj	dj	NOUN
ejpam-5317	107	8	+	+	CCONJ
ejpam-5317	107	9	s−4∑	s−4∑	X
ejpam-5317	107	10	i=1	i=1	PRON
ejpam-5317	107	11	d∗i	d∗i	X
ejpam-5317	107	12	=	=	SYM
ejpam-5317	107	13	(	(	PUNCT
ejpam-5317	107	14	λ	λ	X
ejpam-5317	107	15	+	+	NOUN
ejpam-5317	107	16	1)ar	1)ar	NOUN
ejpam-5317	107	17	.	.	PUNCT
ejpam-5317	108	1	(	(	PUNCT
ejpam-5317	108	2	15	15	NUM
ejpam-5317	108	3	)	)	PUNCT
ejpam-5317	108	4	since	since	SCONJ
ejpam-5317	108	5	this	this	DET
ejpam-5317	108	6	equation	equation	NOUN
ejpam-5317	108	7	is	be	AUX
ejpam-5317	108	8	true	true	ADJ
ejpam-5317	108	9	for	for	ADP
ejpam-5317	108	10	all	all	DET
ejpam-5317	108	11	r	r	NOUN
ejpam-5317	108	12	=	=	SYM
ejpam-5317	108	13	1	1	NUM
ejpam-5317	108	14	,	,	PUNCT
ejpam-5317	108	15	2	2	NUM
ejpam-5317	108	16	,	,	PUNCT
ejpam-5317	108	17	.	.	PUNCT
ejpam-5317	108	18	.	.	PUNCT
ejpam-5317	109	1	.	.	PUNCT
ejpam-5317	110	1	,	,	PUNCT
ejpam-5317	110	2	s	s	VERB
ejpam-5317	110	3	and	and	CCONJ
ejpam-5317	110	4	m	m	PROPN
ejpam-5317	110	5	=	=	ADJ
ejpam-5317	110	6	1	1	NUM
ejpam-5317	110	7	,	,	PUNCT
ejpam-5317	110	8	2	2	NUM
ejpam-5317	110	9	,	,	PUNCT
ejpam-5317	110	10	3	3	NUM
ejpam-5317	110	11	,	,	PUNCT
ejpam-5317	110	12	4	4	NUM
ejpam-5317	110	13	,	,	PUNCT
ejpam-5317	110	14	we	we	PRON
ejpam-5317	110	15	get	get	VERB
ejpam-5317	110	16	by	by	ADP
ejpam-5317	110	17	the	the	DET
ejpam-5317	110	18	help	help	NOUN
ejpam-5317	110	19	of	of	ADP
ejpam-5317	110	20	equation	equation	NOUN
ejpam-5317	110	21	(	(	PUNCT
ejpam-5317	110	22	13	13	NUM
ejpam-5317	110	23	)	)	PUNCT
ejpam-5317	110	24	that	that	PRON
ejpam-5317	110	25	sλ	sλ	AUX
ejpam-5317	110	26	4∑	4∑	NOUN
ejpam-5317	110	27	j=1	j=1	NOUN
ejpam-5317	110	28	(	(	PUNCT
ejpam-5317	110	29	bj	bj	X
ejpam-5317	110	30	+	+	CCONJ
ejpam-5317	110	31	cj	cj	NOUN
ejpam-5317	110	32	)	)	PUNCT
ejpam-5317	110	33	−	−	PROPN
ejpam-5317	111	1	(	(	PUNCT
ejpam-5317	111	2	λ(λ	λ(λ	X
ejpam-5317	111	3	+	+	NUM
ejpam-5317	111	4	1	1	NUM
ejpam-5317	111	5	+	+	NUM
ejpam-5317	111	6	s	s	X
ejpam-5317	111	7	)	)	PUNCT
ejpam-5317	111	8	−	−	NOUN
ejpam-5317	111	9	4s	4s	NUM
ejpam-5317	111	10	)	)	PUNCT
ejpam-5317	111	11	4∑	4∑	NOUN
ejpam-5317	111	12	j=1	j=1	NOUN
ejpam-5317	111	13	dj	dj	NOUN
ejpam-5317	111	14	+	+	CCONJ
ejpam-5317	111	15	4s	4s	NUM
ejpam-5317	111	16	s−4∑	s−4∑	NUM
ejpam-5317	111	17	i=1	i=1	PRON
ejpam-5317	112	1	d∗i	d∗i	PROPN
ejpam-5317	112	2	=	=	SYM
ejpam-5317	112	3	0	0	PROPN
ejpam-5317	112	4	.	.	PUNCT
ejpam-5317	113	1	(	(	PUNCT
ejpam-5317	113	2	16	16	NUM
ejpam-5317	113	3	)	)	PUNCT
ejpam-5317	113	4	subtract	subtract	NOUN
ejpam-5317	113	5	equation	equation	NOUN
ejpam-5317	113	6	(	(	PUNCT
ejpam-5317	113	7	4	4	NUM
ejpam-5317	113	8	)	)	PUNCT
ejpam-5317	113	9	from	from	ADP
ejpam-5317	113	10	equation	equation	NOUN
ejpam-5317	113	11	(	(	PUNCT
ejpam-5317	113	12	5	5	NUM
ejpam-5317	113	13	)	)	PUNCT
ejpam-5317	113	14	and	and	CCONJ
ejpam-5317	113	15	equation	equation	NOUN
ejpam-5317	113	16	(	(	PUNCT
ejpam-5317	113	17	4	4	NUM
ejpam-5317	113	18	)	)	PUNCT
ejpam-5317	113	19	from	from	ADP
ejpam-5317	113	20	equation	equation	NOUN
ejpam-5317	113	21	(	(	PUNCT
ejpam-5317	113	22	6	6	NUM
ejpam-5317	113	23	)	)	PUNCT
ejpam-5317	113	24	and	and	CCONJ
ejpam-5317	113	25	in	in	ADP
ejpam-5317	113	26	the	the	DET
ejpam-5317	113	27	same	same	ADJ
ejpam-5317	113	28	way	way	NOUN
ejpam-5317	113	29	subtract	subtract	NOUN
ejpam-5317	113	30	equation	equation	NOUN
ejpam-5317	113	31	(	(	PUNCT
ejpam-5317	113	32	7	7	NUM
ejpam-5317	113	33	)	)	PUNCT
ejpam-5317	113	34	from	from	ADP
ejpam-5317	113	35	equation	equation	NOUN
ejpam-5317	113	36	(	(	PUNCT
ejpam-5317	113	37	8)	8)	NUM
ejpam-5317	113	38	and	and	CCONJ
ejpam-5317	113	39	equation	equation	NOUN
ejpam-5317	113	40	(	(	PUNCT
ejpam-5317	113	41	7	7	NUM
ejpam-5317	113	42	)	)	PUNCT
ejpam-5317	113	43	from	from	ADP
ejpam-5317	113	44	equation	equation	NOUN
ejpam-5317	113	45	(	(	PUNCT
ejpam-5317	113	46	9	9	NUM
ejpam-5317	113	47	)	)	PUNCT
ejpam-5317	113	48	to	to	PART
ejpam-5317	113	49	get	get	VERB
ejpam-5317	113	50	(	(	PUNCT
ejpam-5317	113	51	λ−	λ−	PROPN
ejpam-5317	113	52	1)(b∗k	1)(b∗k	NUM
ejpam-5317	113	53	+	+	CCONJ
ejpam-5317	113	54	b∗k+1	b∗k+1	X
ejpam-5317	113	55	+	+	CCONJ
ejpam-5317	113	56	c∗k	c∗k	NOUN
ejpam-5317	113	57	+	+	X
ejpam-5317	113	58	c∗k+1	c∗k+1	NOUN
ejpam-5317	113	59	)	)	PUNCT
ejpam-5317	113	60	=	=	SYM
ejpam-5317	114	1	2(d∗k	2(d∗k	NUM
ejpam-5317	114	2	+	+	CCONJ
ejpam-5317	114	3	d∗k+1	d∗k+1	NOUN
ejpam-5317	114	4	)	)	PUNCT
ejpam-5317	114	5	+	+	CCONJ
ejpam-5317	114	6	2λ(bm	2λ(bm	NUM
ejpam-5317	114	7	+	+	CCONJ
ejpam-5317	114	8	cm	cm	NOUN
ejpam-5317	114	9	)	)	PUNCT
ejpam-5317	114	10	,	,	PUNCT
ejpam-5317	114	11	(	(	PUNCT
ejpam-5317	114	12	17	17	NUM
ejpam-5317	114	13	)	)	PUNCT
ejpam-5317	114	14	using	use	VERB
ejpam-5317	114	15	equations	equation	NOUN
ejpam-5317	114	16	(	(	PUNCT
ejpam-5317	114	17	11	11	NUM
ejpam-5317	114	18	)	)	PUNCT
ejpam-5317	114	19	and	and	CCONJ
ejpam-5317	114	20	(	(	PUNCT
ejpam-5317	114	21	12	12	NUM
ejpam-5317	114	22	)	)	PUNCT
ejpam-5317	114	23	,	,	PUNCT
ejpam-5317	114	24	equation	equation	NOUN
ejpam-5317	114	25	(	(	PUNCT
ejpam-5317	114	26	17	17	NUM
ejpam-5317	114	27	)	)	PUNCT
ejpam-5317	114	28	becomes	become	VERB
ejpam-5317	114	29	(	(	PUNCT
ejpam-5317	114	30	λ−	λ−	PROPN
ejpam-5317	114	31	1)2(d∗k	1)2(d∗k	NUM
ejpam-5317	114	32	+	+	CCONJ
ejpam-5317	114	33	d∗k+1	d∗k+1	NOUN
ejpam-5317	114	34	)	)	PUNCT
ejpam-5317	114	35	−	−	PROPN
ejpam-5317	115	1	2(λ−	2(λ−	NUM
ejpam-5317	115	2	1	1	NUM
ejpam-5317	115	3	)	)	PUNCT
ejpam-5317	115	4	s∑	s∑	PROPN
ejpam-5317	115	5	i=1	i=1	PROPN
ejpam-5317	115	6	ai	ai	VERB
ejpam-5317	115	7	=	=	PROPN
ejpam-5317	115	8	2(d∗k	2(d∗k	NUM
ejpam-5317	115	9	+	+	CCONJ
ejpam-5317	115	10	d∗k+1	d∗k+1	NOUN
ejpam-5317	115	11	)	)	PUNCT
ejpam-5317	116	1	+	+	CCONJ
ejpam-5317	116	2	2λ(bm	2λ(bm	NUM
ejpam-5317	116	3	+	+	CCONJ
ejpam-5317	116	4	cm	cm	NOUN
ejpam-5317	116	5	)	)	PUNCT
ejpam-5317	116	6	.	.	PUNCT
ejpam-5317	117	1	(	(	PUNCT
ejpam-5317	117	2	18	18	NUM
ejpam-5317	117	3	)	)	PUNCT
ejpam-5317	117	4	since	since	SCONJ
ejpam-5317	117	5	this	this	DET
ejpam-5317	117	6	equation	equation	NOUN
ejpam-5317	117	7	is	be	AUX
ejpam-5317	117	8	true	true	ADJ
ejpam-5317	117	9	for	for	ADP
ejpam-5317	117	10	all	all	PRON
ejpam-5317	117	11	k	k	NOUN
ejpam-5317	117	12	=	=	SYM
ejpam-5317	117	13	1	1	NUM
ejpam-5317	117	14	,	,	PUNCT
ejpam-5317	117	15	3	3	NUM
ejpam-5317	117	16	,	,	PUNCT
ejpam-5317	117	17	5	5	NUM
ejpam-5317	117	18	,	,	PUNCT
ejpam-5317	117	19	.	.	PUNCT
ejpam-5317	117	20	.	.	PUNCT
ejpam-5317	118	1	.	.	PUNCT
ejpam-5317	119	1	,	,	PUNCT
ejpam-5317	119	2	s	s	VERB
ejpam-5317	119	3	−	−	NOUN
ejpam-5317	119	4	4	4	NUM
ejpam-5317	119	5	and	and	CCONJ
ejpam-5317	119	6	m	m	NOUN
ejpam-5317	119	7	=	=	ADJ
ejpam-5317	119	8	1	1	NUM
ejpam-5317	119	9	,	,	PUNCT
ejpam-5317	119	10	2	2	NUM
ejpam-5317	119	11	,	,	PUNCT
ejpam-5317	119	12	3	3	NUM
ejpam-5317	119	13	,	,	PUNCT
ejpam-5317	119	14	4	4	NUM
ejpam-5317	119	15	,	,	PUNCT
ejpam-5317	119	16	we	we	PRON
ejpam-5317	119	17	get	get	VERB
ejpam-5317	119	18	by	by	ADP
ejpam-5317	119	19	the	the	DET
ejpam-5317	119	20	help	help	NOUN
ejpam-5317	119	21	of	of	ADP
ejpam-5317	119	22	equation	equation	NOUN
ejpam-5317	119	23	(	(	PUNCT
ejpam-5317	119	24	13	13	NUM
ejpam-5317	119	25	)	)	PUNCT
ejpam-5317	119	26	that	that	SCONJ
ejpam-5317	120	1	4((λ−	4((λ−	NUM
ejpam-5317	120	2	1)2	1)2	NUM
ejpam-5317	120	3	−	−	NOUN
ejpam-5317	120	4	2	2	NUM
ejpam-5317	120	5	)	)	PUNCT
ejpam-5317	120	6	s−4∑	s−4∑	VERB
ejpam-5317	120	7	i=1	i=1	PRON
ejpam-5317	121	1	d∗i	d∗i	X
ejpam-5317	121	2	=	=	SYM
ejpam-5317	121	3	λ(λ−	λ(λ−	PROPN
ejpam-5317	121	4	1)(s−	1)(s−	NUM
ejpam-5317	121	5	4	4	NUM
ejpam-5317	121	6	)	)	PUNCT
ejpam-5317	121	7	4∑	4∑	NOUN
ejpam-5317	121	8	j=1	j=1	NOUN
ejpam-5317	121	9	dj	dj	NOUN
ejpam-5317	121	10	+	+	CCONJ
ejpam-5317	121	11	λ(s−	λ(s−	PROPN
ejpam-5317	121	12	4	4	NUM
ejpam-5317	121	13	)	)	PUNCT
ejpam-5317	121	14	4∑	4∑	NOUN
ejpam-5317	121	15	j=1	j=1	NOUN
ejpam-5317	121	16	(	(	PUNCT
ejpam-5317	121	17	bj	bj	X
ejpam-5317	121	18	+	+	CCONJ
ejpam-5317	121	19	cj	cj	NOUN
ejpam-5317	121	20	)	)	PUNCT
ejpam-5317	121	21	.	.	PUNCT
ejpam-5317	122	1	(	(	PUNCT
ejpam-5317	122	2	19	19	NUM
ejpam-5317	122	3	)	)	PUNCT
ejpam-5317	122	4	e.	e.	PROPN
ejpam-5317	122	5	rawaswhdeh	rawaswhdeh	PROPN
ejpam-5317	122	6	,	,	PUNCT
ejpam-5317	122	7	h.	h.	PROPN
ejpam-5317	122	8	adel	adel	PROPN
ejpam-5317	122	9	abdelkarim	abdelkarim	PROPN
ejpam-5317	122	10	,	,	PUNCT
ejpam-5317	122	11	e.	e.	PROPN
ejpam-5317	122	12	rawshdeh	rawshdeh	PROPN
ejpam-5317	122	13	/	/	SYM
ejpam-5317	122	14	eur	eur	PROPN
ejpam-5317	122	15	.	.	PUNCT
ejpam-5317	123	1	j.	j.	PROPN
ejpam-5317	123	2	pure	pure	PROPN
ejpam-5317	123	3	appl	appl	PROPN
ejpam-5317	123	4	.	.	PROPN
ejpam-5317	123	5	math	math	PROPN
ejpam-5317	123	6	,	,	PUNCT
ejpam-5317	123	7	17	17	NUM
ejpam-5317	123	8	(	(	PUNCT
ejpam-5317	123	9	4	4	NUM
ejpam-5317	123	10	)	)	PUNCT
ejpam-5317	123	11	(	(	PUNCT
ejpam-5317	123	12	2024	2024	NUM
ejpam-5317	123	13	)	)	PUNCT
ejpam-5317	123	14	,	,	PUNCT
ejpam-5317	123	15	2550	2550	NUM
ejpam-5317	123	16	-	-	SYM
ejpam-5317	123	17	2561	2561	NUM
ejpam-5317	123	18	2554	2554	NUM
ejpam-5317	123	19	from	from	ADP
ejpam-5317	123	20	equation	equation	NOUN
ejpam-5317	123	21	(	(	PUNCT
ejpam-5317	123	22	17	17	NUM
ejpam-5317	123	23	)	)	PUNCT
ejpam-5317	123	24	,	,	PUNCT
ejpam-5317	123	25	we	we	PRON
ejpam-5317	123	26	get	get	VERB
ejpam-5317	123	27	(	(	PUNCT
ejpam-5317	123	28	λ−	λ−	PROPN
ejpam-5317	123	29	1	1	NUM
ejpam-5317	123	30	)	)	PUNCT
ejpam-5317	123	31	s−4∑	s−4∑	X
ejpam-5317	123	32	i=1	i=1	PROPN
ejpam-5317	124	1	(	(	PUNCT
ejpam-5317	124	2	b∗i	b∗i	PROPN
ejpam-5317	124	3	+	+	CCONJ
ejpam-5317	124	4	c∗i	c∗i	X
ejpam-5317	124	5	)	)	PUNCT
ejpam-5317	124	6	=	=	SYM
ejpam-5317	124	7	2	2	NUM
ejpam-5317	124	8	s−4∑	s−4∑	VERB
ejpam-5317	124	9	i=1	i=1	PROPN
ejpam-5317	124	10	d∗i	d∗i	X
ejpam-5317	125	1	+	+	PUNCT
ejpam-5317	125	2	λ(s−	λ(s−	PROPN
ejpam-5317	125	3	4)(bm	4)(bm	NOUN
ejpam-5317	125	4	+	+	NOUN
ejpam-5317	125	5	cm	cm	NOUN
ejpam-5317	125	6	)	)	PUNCT
ejpam-5317	125	7	.	.	PUNCT
ejpam-5317	126	1	(	(	PUNCT
ejpam-5317	126	2	20	20	X
ejpam-5317	126	3	)	)	PUNCT
ejpam-5317	126	4	adding	add	VERB
ejpam-5317	126	5	equation	equation	NOUN
ejpam-5317	126	6	(	(	PUNCT
ejpam-5317	126	7	4	4	NUM
ejpam-5317	126	8	)	)	PUNCT
ejpam-5317	126	9	to	to	ADP
ejpam-5317	126	10	equation	equation	NOUN
ejpam-5317	126	11	(	(	PUNCT
ejpam-5317	126	12	7	7	NUM
ejpam-5317	126	13	)	)	PUNCT
ejpam-5317	126	14	and	and	CCONJ
ejpam-5317	126	15	use	use	NOUN
ejpam-5317	126	16	(	(	PUNCT
ejpam-5317	126	17	13	13	NUM
ejpam-5317	126	18	)	)	PUNCT
ejpam-5317	126	19	,	,	PUNCT
ejpam-5317	126	20	equation	equation	NOUN
ejpam-5317	126	21	(	(	PUNCT
ejpam-5317	126	22	28	28	NUM
ejpam-5317	126	23	)	)	PUNCT
ejpam-5317	126	24	becomes	become	VERB
ejpam-5317	126	25	8	8	NUM
ejpam-5317	126	26	s−4∑	s−4∑	NUM
ejpam-5317	126	27	i=1	i=1	PRON
ejpam-5317	127	1	d∗i	d∗i	PROPN
ejpam-5317	127	2	=	=	SYM
ejpam-5317	127	3	2λ(1	2λ(1	NUM
ejpam-5317	128	1	−	−	NUM
ejpam-5317	129	1	λ	λ	NOUN
ejpam-5317	129	2	)	)	PUNCT
ejpam-5317	129	3	4∑	4∑	NOUN
ejpam-5317	129	4	j=1	j=1	NOUN
ejpam-5317	129	5	dj	dj	NOUN
ejpam-5317	129	6	+	+	CCONJ
ejpam-5317	129	7	(	(	PUNCT
ejpam-5317	129	8	λ2	λ2	NOUN
ejpam-5317	129	9	−	−	PROPN
ejpam-5317	129	10	(	(	PUNCT
ejpam-5317	129	11	s	s	NOUN
ejpam-5317	129	12	+	+	NUM
ejpam-5317	129	13	1)λ	1)λ	NUM
ejpam-5317	129	14	+	+	CCONJ
ejpam-5317	129	15	4	4	NUM
ejpam-5317	129	16	)	)	PUNCT
ejpam-5317	129	17	4∑	4∑	NOUN
ejpam-5317	129	18	j=1	j=1	NOUN
ejpam-5317	129	19	(	(	PUNCT
ejpam-5317	129	20	bj	bj	X
ejpam-5317	129	21	+	+	CCONJ
ejpam-5317	129	22	cj	cj	NOUN
ejpam-5317	129	23	)	)	PUNCT
ejpam-5317	129	24	.	.	PUNCT
ejpam-5317	130	1	(	(	PUNCT
ejpam-5317	130	2	21	21	NUM
ejpam-5317	130	3	)	)	PUNCT
ejpam-5317	130	4	equations	equation	NOUN
ejpam-5317	130	5	(	(	PUNCT
ejpam-5317	130	6	16	16	NUM
ejpam-5317	130	7	)	)	PUNCT
ejpam-5317	130	8	,	,	PUNCT
ejpam-5317	130	9	(	(	PUNCT
ejpam-5317	130	10	19	19	NUM
ejpam-5317	130	11	)	)	PUNCT
ejpam-5317	130	12	,	,	PUNCT
ejpam-5317	130	13	and	and	CCONJ
ejpam-5317	130	14	(	(	PUNCT
ejpam-5317	130	15	21	21	NUM
ejpam-5317	130	16	)	)	PUNCT
ejpam-5317	130	17	form	form	VERB
ejpam-5317	130	18	a	a	DET
ejpam-5317	130	19	homogeneous	homogeneous	ADJ
ejpam-5317	130	20	linear	linear	NOUN
ejpam-5317	130	21	system	system	NOUN
ejpam-5317	130	22	with	with	ADP
ejpam-5317	130	23	the	the	DET
ejpam-5317	130	24	variables∑4	variables∑4	NOUN
ejpam-5317	130	25	j	j	PROPN
ejpam-5317	130	26	dj	dj	NOUN
ejpam-5317	130	27	,	,	PUNCT
ejpam-5317	130	28	∑s−4	∑s−4	PROPN
ejpam-5317	130	29	i=1	i=1	PROPN
ejpam-5317	131	1	d	d	NOUN
ejpam-5317	131	2	∗	∗	VERB
ejpam-5317	131	3	i	i	PRON
ejpam-5317	131	4	,	,	PUNCT
ejpam-5317	131	5	and	and	CCONJ
ejpam-5317	131	6	∑4	∑4	PROPN
ejpam-5317	131	7	j=1(bj	j=1(bj	NOUN
ejpam-5317	131	8	+	+	CCONJ
ejpam-5317	131	9	cj	cj	NOUN
ejpam-5317	131	10	)	)	PUNCT
ejpam-5317	131	11	that	that	PRON
ejpam-5317	131	12	has	have	VERB
ejpam-5317	131	13	the	the	DET
ejpam-5317	131	14	coefficient	coefficient	NOUN
ejpam-5317	131	15	matrix	matrix	NOUN
ejpam-5317	131	16	b	b	NOUN
ejpam-5317	131	17	=	=	SYM
ejpam-5317	131	18			PROPN
ejpam-5317	131	19	sλ	sλ	NOUN
ejpam-5317	131	20	−(λ(λ	−(λ(λ	NOUN
ejpam-5317	132	1	+	+	CCONJ
ejpam-5317	133	1	1	1	NUM
ejpam-5317	133	2	+	+	NUM
ejpam-5317	133	3	s	s	X
ejpam-5317	133	4	)	)	PUNCT
ejpam-5317	134	1	−	−	NOUN
ejpam-5317	134	2	4s	4s	NUM
ejpam-5317	134	3	)	)	PUNCT
ejpam-5317	134	4	4s	4s	NUM
ejpam-5317	134	5	λ(s−	λ(s−	PROPN
ejpam-5317	134	6	4	4	X
ejpam-5317	134	7	)	)	PUNCT
ejpam-5317	134	8	λ(λ−	λ(λ−	PROPN
ejpam-5317	134	9	1)(s−	1)(s−	NUM
ejpam-5317	134	10	4	4	NUM
ejpam-5317	134	11	)	)	PUNCT
ejpam-5317	134	12	4(2	4(2	NUM
ejpam-5317	134	13	−	−	PROPN
ejpam-5317	134	14	(	(	PUNCT
ejpam-5317	134	15	λ−	λ−	PROPN
ejpam-5317	134	16	1)2	1)2	NUM
ejpam-5317	134	17	)	)	PUNCT
ejpam-5317	134	18	(	(	PUNCT
ejpam-5317	134	19	λ2	λ2	NOUN
ejpam-5317	134	20	−	−	PROPN
ejpam-5317	135	1	(	(	PUNCT
ejpam-5317	135	2	s	s	NOUN
ejpam-5317	135	3	+	+	NUM
ejpam-5317	135	4	1)λ	1)λ	NUM
ejpam-5317	135	5	+	+	CCONJ
ejpam-5317	135	6	4	4	NUM
ejpam-5317	135	7	)	)	PUNCT
ejpam-5317	135	8	2λ(1	2λ(1	NUM
ejpam-5317	136	1	−	−	ADP
ejpam-5317	136	2	λ	λ	SYM
ejpam-5317	136	3	)	)	PUNCT
ejpam-5317	136	4	−8	−8	X
ejpam-5317	136	5			PROPN
ejpam-5317	136	6	.	.	PUNCT
ejpam-5317	137	1	(	(	PUNCT
ejpam-5317	137	2	22	22	NUM
ejpam-5317	137	3	)	)	PUNCT
ejpam-5317	137	4	using	use	VERB
ejpam-5317	137	5	maple	maple	NOUN
ejpam-5317	137	6	,	,	PUNCT
ejpam-5317	137	7	we	we	PRON
ejpam-5317	137	8	can	can	AUX
ejpam-5317	137	9	compute	compute	VERB
ejpam-5317	137	10	the	the	DET
ejpam-5317	137	11	determinant	determinant	NOUN
ejpam-5317	137	12	of	of	ADP
ejpam-5317	137	13	the	the	DET
ejpam-5317	137	14	matrix	matrix	NOUN
ejpam-5317	137	15	b	b	NOUN
ejpam-5317	137	16	to	to	PART
ejpam-5317	137	17	get	get	VERB
ejpam-5317	137	18	det(b	det(b	NOUN
ejpam-5317	137	19	)	)	PUNCT
ejpam-5317	137	20	=	=	SYM
ejpam-5317	138	1	4(λ−	4(λ−	NUM
ejpam-5317	138	2	1)q(λ	1)q(λ	NUM
ejpam-5317	138	3	)	)	PUNCT
ejpam-5317	138	4	,	,	PUNCT
ejpam-5317	138	5	where	where	SCONJ
ejpam-5317	138	6	q(λ	q(λ	VERB
ejpam-5317	138	7	)	)	PUNCT
ejpam-5317	138	8	=	=	SYM
ejpam-5317	138	9	(	(	PUNCT
ejpam-5317	138	10	λ5−	λ5−	NOUN
ejpam-5317	138	11	(	(	PUNCT
ejpam-5317	138	12	2s+	2s+	NUM
ejpam-5317	138	13	1)λ4−	1)λ4−	PROPN
ejpam-5317	138	14	(	(	PUNCT
ejpam-5317	138	15	2s2−	2s2−	NUM
ejpam-5317	139	1	2s−	2s−	NUM
ejpam-5317	139	2	1)λ3	1)λ3	NUM
ejpam-5317	139	3	+	+	CCONJ
ejpam-5317	139	4	(	(	PUNCT
ejpam-5317	139	5	s3−	s3−	PROPN
ejpam-5317	139	6	2s2	2s2	NUM
ejpam-5317	139	7	+	+	CCONJ
ejpam-5317	139	8	26s+	26s+	NUM
ejpam-5317	139	9	7)λ2−	7)λ2−	NOUN
ejpam-5317	139	10	(	(	PUNCT
ejpam-5317	139	11	8s2−	8s2−	NUM
ejpam-5317	139	12	8s−	8s−	PROPN
ejpam-5317	139	13	4)λ−	4)λ−	NUM
ejpam-5317	139	14	16s	16	NOUN
ejpam-5317	139	15	)	)	PUNCT
ejpam-5317	139	16	.	.	PUNCT
ejpam-5317	140	1	thus	thus	ADV
ejpam-5317	140	2	if	if	SCONJ
ejpam-5317	140	3	λ	λ	PROPN
ejpam-5317	140	4	̸=	̸=	PROPN
ejpam-5317	140	5	1	1	NUM
ejpam-5317	140	6	and	and	CCONJ
ejpam-5317	140	7	λ	λ	NOUN
ejpam-5317	140	8	is	be	AUX
ejpam-5317	140	9	not	not	PART
ejpam-5317	140	10	a	a	DET
ejpam-5317	140	11	root	root	NOUN
ejpam-5317	140	12	of	of	ADP
ejpam-5317	140	13	the	the	DET
ejpam-5317	140	14	polynomial	polynomial	ADJ
ejpam-5317	140	15	q(x	q(x	PROPN
ejpam-5317	140	16	)	)	PUNCT
ejpam-5317	140	17	,	,	PUNCT
ejpam-5317	140	18	then	then	ADV
ejpam-5317	140	19	∑4	∑4	PROPN
ejpam-5317	140	20	j=1(bj	j=1(bj	PROPN
ejpam-5317	140	21	+	+	CCONJ
ejpam-5317	140	22	cj	cj	NOUN
ejpam-5317	140	23	)	)	PUNCT
ejpam-5317	140	24	=	=	PUNCT
ejpam-5317	141	1	0,∑4	0,∑4	NUM
ejpam-5317	141	2	j	j	PROPN
ejpam-5317	141	3	dj	dj	X
ejpam-5317	141	4	=	=	SYM
ejpam-5317	141	5	0	0	NUM
ejpam-5317	141	6	,	,	PUNCT
ejpam-5317	141	7	and	and	CCONJ
ejpam-5317	141	8	∑s−4	∑s−4	VERB
ejpam-5317	141	9	i=1	i=1	PROPN
ejpam-5317	142	1	d	d	NOUN
ejpam-5317	142	2	∗	∗	VERB
ejpam-5317	142	3	i	i	NOUN
ejpam-5317	143	1	=	=	NOUN
ejpam-5317	143	2	0	0	X
ejpam-5317	143	3	.	.	PUNCT
ejpam-5317	143	4	remark	remark	PROPN
ejpam-5317	143	5	1	1	NUM
ejpam-5317	143	6	.	.	PUNCT
ejpam-5317	144	1	let	let	VERB
ejpam-5317	144	2	λ	λ	NOUN
ejpam-5317	144	3	be	be	AUX
ejpam-5317	144	4	an	an	DET
ejpam-5317	144	5	eigenvalue	eigenvalue	NOUN
ejpam-5317	144	6	of	of	ADP
ejpam-5317	144	7	the	the	DET
ejpam-5317	144	8	matrix	matrix	NOUN
ejpam-5317	144	9	a	a	NOUN
ejpam-5317	144	10	with	with	ADP
ejpam-5317	144	11	corresponding	correspond	VERB
ejpam-5317	144	12	eigenvector	eigenvector	NOUN
ejpam-5317	144	13	x	x	PUNCT
ejpam-5317	144	14	given	give	VERB
ejpam-5317	144	15	by	by	ADP
ejpam-5317	144	16	(	(	PUNCT
ejpam-5317	144	17	2	2	NUM
ejpam-5317	144	18	)	)	PUNCT
ejpam-5317	144	19	.	.	PUNCT
ejpam-5317	145	1	(	(	PUNCT
ejpam-5317	145	2	i	i	NOUN
ejpam-5317	145	3	)	)	PUNCT
ejpam-5317	145	4	it	it	PRON
ejpam-5317	145	5	is	be	AUX
ejpam-5317	145	6	clear	clear	ADJ
ejpam-5317	145	7	from	from	ADP
ejpam-5317	145	8	equation	equation	NOUN
ejpam-5317	145	9	(	(	PUNCT
ejpam-5317	145	10	3	3	NUM
ejpam-5317	145	11	)	)	PUNCT
ejpam-5317	145	12	that	that	SCONJ
ejpam-5317	145	13	if	if	SCONJ
ejpam-5317	145	14	λ	λ	PROPN
ejpam-5317	145	15	̸=	̸=	PROPN
ejpam-5317	145	16	−1	−1	NOUN
ejpam-5317	145	17	,	,	PUNCT
ejpam-5317	145	18	then	then	ADV
ejpam-5317	145	19	a1	a1	NOUN
ejpam-5317	145	20	=	=	PROPN
ejpam-5317	145	21	a2	a2	PROPN
ejpam-5317	145	22	=	=	SYM
ejpam-5317	145	23	·	·	PUNCT
ejpam-5317	145	24	·	·	PUNCT
ejpam-5317	145	25	·	·	PUNCT
ejpam-5317	146	1	=	=	PUNCT
ejpam-5317	146	2	as	as	ADP
ejpam-5317	146	3	=	=	NOUN
ejpam-5317	146	4	a.	a.	NOUN
ejpam-5317	146	5	(	(	PUNCT
ejpam-5317	146	6	ii	ii	NOUN
ejpam-5317	146	7	)	)	PUNCT
ejpam-5317	146	8	subtracting	subtract	VERB
ejpam-5317	146	9	equation	equation	NOUN
ejpam-5317	146	10	(	(	PUNCT
ejpam-5317	146	11	5	5	NUM
ejpam-5317	146	12	)	)	PUNCT
ejpam-5317	146	13	from	from	ADP
ejpam-5317	146	14	(	(	PUNCT
ejpam-5317	146	15	6	6	NUM
ejpam-5317	146	16	)	)	PUNCT
ejpam-5317	146	17	and	and	CCONJ
ejpam-5317	146	18	equation	equation	NOUN
ejpam-5317	146	19	(	(	PUNCT
ejpam-5317	146	20	8)	8)	NUM
ejpam-5317	146	21	from	from	ADP
ejpam-5317	146	22	equation	equation	NOUN
ejpam-5317	146	23	(	(	PUNCT
ejpam-5317	146	24	9	9	NUM
ejpam-5317	146	25	)	)	PUNCT
ejpam-5317	146	26	,	,	PUNCT
ejpam-5317	146	27	we	we	PRON
ejpam-5317	146	28	find	find	VERB
ejpam-5317	146	29	that	that	SCONJ
ejpam-5317	146	30	(	(	PUNCT
ejpam-5317	146	31	λ	λ	X
ejpam-5317	146	32	+	+	NOUN
ejpam-5317	146	33	1)(b∗k+1	1)(b∗k+1	NUM
ejpam-5317	146	34	−	−	NUM
ejpam-5317	146	35	b∗k	b∗k	NUM
ejpam-5317	146	36	)	)	PUNCT
ejpam-5317	146	37	=	=	SYM
ejpam-5317	146	38	(	(	PUNCT
ejpam-5317	146	39	λ	λ	X
ejpam-5317	146	40	+	+	NOUN
ejpam-5317	146	41	1)(c∗k+1	1)(c∗k+1	NUM
ejpam-5317	146	42	−	−	NOUN
ejpam-5317	146	43	c∗k	c∗k	NOUN
ejpam-5317	146	44	)	)	PUNCT
ejpam-5317	146	45	=	=	SYM
ejpam-5317	146	46	d∗k	d∗k	NUM
ejpam-5317	146	47	−	−	NUM
ejpam-5317	146	48	d∗k+1	d∗k+1	NOUN
ejpam-5317	146	49	.	.	PUNCT
ejpam-5317	147	1	(	(	PUNCT
ejpam-5317	147	2	23	23	NUM
ejpam-5317	147	3	)	)	PUNCT
ejpam-5317	147	4	also	also	ADV
ejpam-5317	147	5	subtract	subtract	VERB
ejpam-5317	147	6	equation	equation	NOUN
ejpam-5317	147	7	(	(	PUNCT
ejpam-5317	147	8	11	11	NUM
ejpam-5317	147	9	)	)	PUNCT
ejpam-5317	147	10	from	from	ADP
ejpam-5317	147	11	equation	equation	NOUN
ejpam-5317	147	12	(	(	PUNCT
ejpam-5317	147	13	12	12	NUM
ejpam-5317	147	14	)	)	PUNCT
ejpam-5317	147	15	to	to	PART
ejpam-5317	147	16	get	get	VERB
ejpam-5317	147	17	(	(	PUNCT
ejpam-5317	147	18	λ	λ	X
ejpam-5317	147	19	+	+	NOUN
ejpam-5317	147	20	1)(d∗k	1)(d∗k	NUM
ejpam-5317	147	21	−	−	NUM
ejpam-5317	147	22	d∗k+1	d∗k+1	NOUN
ejpam-5317	147	23	)	)	PUNCT
ejpam-5317	148	1	=	=	SYM
ejpam-5317	148	2	b∗k+1	b∗k+1	ADP
ejpam-5317	148	3	−	−	PROPN
ejpam-5317	148	4	b∗k	b∗k	NOUN
ejpam-5317	148	5	+	+	CCONJ
ejpam-5317	148	6	c∗k+1	c∗k+1	VERB
ejpam-5317	149	1	−	−	NOUN
ejpam-5317	149	2	c∗k	c∗k	NOUN
ejpam-5317	149	3	.	.	PUNCT
ejpam-5317	150	1	(	(	PUNCT
ejpam-5317	150	2	24	24	NUM
ejpam-5317	150	3	)	)	PUNCT
ejpam-5317	150	4	thus	thus	ADV
ejpam-5317	150	5	from	from	ADP
ejpam-5317	150	6	equations	equation	NOUN
ejpam-5317	150	7	(	(	PUNCT
ejpam-5317	150	8	23	23	NUM
ejpam-5317	150	9	)	)	PUNCT
ejpam-5317	150	10	and	and	CCONJ
ejpam-5317	150	11	(	(	PUNCT
ejpam-5317	150	12	24	24	NUM
ejpam-5317	150	13	)	)	PUNCT
ejpam-5317	150	14	,	,	PUNCT
ejpam-5317	150	15	we	we	PRON
ejpam-5317	150	16	obtain	obtain	VERB
ejpam-5317	150	17	(	(	PUNCT
ejpam-5317	150	18	λ2	λ2	NOUN
ejpam-5317	150	19	+	+	CCONJ
ejpam-5317	150	20	2λ−	2λ−	NUM
ejpam-5317	150	21	1)(d∗k	1)(d∗k	NUM
ejpam-5317	150	22	−	−	NUM
ejpam-5317	150	23	d∗k+1	d∗k+1	NOUN
ejpam-5317	150	24	)	)	PUNCT
ejpam-5317	150	25	=	=	SYM
ejpam-5317	151	1	0	0	X
ejpam-5317	151	2	.	.	PUNCT
ejpam-5317	152	1	(	(	PUNCT
ejpam-5317	152	2	25	25	NUM
ejpam-5317	152	3	)	)	PUNCT
ejpam-5317	152	4	this	this	PRON
ejpam-5317	152	5	gives	give	VERB
ejpam-5317	152	6	us	we	PRON
ejpam-5317	152	7	that	that	SCONJ
ejpam-5317	152	8	if	if	SCONJ
ejpam-5317	152	9	λ2	λ2	PROPN
ejpam-5317	152	10	+	+	CCONJ
ejpam-5317	152	11	2λ	2λ	NOUN
ejpam-5317	152	12	−	−	NOUN
ejpam-5317	152	13	1	1	NUM
ejpam-5317	152	14	̸=	̸=	PROPN
ejpam-5317	152	15	0	0	NUM
ejpam-5317	152	16	and	and	CCONJ
ejpam-5317	152	17	λ	λ	PROPN
ejpam-5317	152	18	̸=	̸=	PROPN
ejpam-5317	152	19	−1	−1	NOUN
ejpam-5317	152	20	,	,	PUNCT
ejpam-5317	152	21	then	then	ADV
ejpam-5317	152	22	from	from	ADP
ejpam-5317	152	23	equations	equation	NOUN
ejpam-5317	152	24	(	(	PUNCT
ejpam-5317	152	25	23	23	NUM
ejpam-5317	152	26	)	)	PUNCT
ejpam-5317	152	27	and	and	CCONJ
ejpam-5317	152	28	(	(	PUNCT
ejpam-5317	152	29	25	25	NUM
ejpam-5317	152	30	)	)	PUNCT
ejpam-5317	152	31	we	we	PRON
ejpam-5317	152	32	have	have	VERB
ejpam-5317	152	33	b∗k	b∗k	NOUN
ejpam-5317	152	34	=	=	SYM
ejpam-5317	152	35	b∗k+1	b∗k+1	X
ejpam-5317	152	36	,	,	PUNCT
ejpam-5317	152	37	c	c	PROPN
ejpam-5317	152	38	∗	∗	NOUN
ejpam-5317	152	39	k	k	NOUN
ejpam-5317	152	40	=	=	PUNCT
ejpam-5317	152	41	c∗k+1	c∗k+1	NOUN
ejpam-5317	152	42	and	and	CCONJ
ejpam-5317	152	43	d∗k	d∗k	PUNCT
ejpam-5317	152	44	=	=	SYM
ejpam-5317	152	45	d∗k+1	d∗k+1	NOUN
ejpam-5317	152	46	for	for	ADP
ejpam-5317	152	47	all	all	PRON
ejpam-5317	152	48	k	k	NOUN
ejpam-5317	152	49	=	=	SYM
ejpam-5317	152	50	1	1	NUM
ejpam-5317	152	51	,	,	PUNCT
ejpam-5317	152	52	3	3	NUM
ejpam-5317	152	53	,	,	PUNCT
ejpam-5317	152	54	.	.	PUNCT
ejpam-5317	152	55	.	.	PUNCT
ejpam-5317	153	1	.	.	PUNCT
ejpam-5317	154	1	,	,	PUNCT
ejpam-5317	154	2	s−	s−	PROPN
ejpam-5317	154	3	5	5	NUM
ejpam-5317	154	4	.	.	PUNCT
ejpam-5317	154	5	e.	e.	PROPN
ejpam-5317	154	6	rawaswhdeh	rawaswhdeh	PROPN
ejpam-5317	154	7	,	,	PUNCT
ejpam-5317	154	8	h.	h.	PROPN
ejpam-5317	154	9	adel	adel	PROPN
ejpam-5317	154	10	abdelkarim	abdelkarim	PROPN
ejpam-5317	154	11	,	,	PUNCT
ejpam-5317	154	12	e.	e.	PROPN
ejpam-5317	154	13	rawshdeh	rawshdeh	PROPN
ejpam-5317	154	14	/	/	SYM
ejpam-5317	154	15	eur	eur	PROPN
ejpam-5317	154	16	.	.	PUNCT
ejpam-5317	155	1	j.	j.	PROPN
ejpam-5317	155	2	pure	pure	PROPN
ejpam-5317	155	3	appl	appl	PROPN
ejpam-5317	155	4	.	.	PROPN
ejpam-5317	155	5	math	math	PROPN
ejpam-5317	155	6	,	,	PUNCT
ejpam-5317	155	7	17	17	NUM
ejpam-5317	155	8	(	(	PUNCT
ejpam-5317	155	9	4	4	NUM
ejpam-5317	155	10	)	)	PUNCT
ejpam-5317	155	11	(	(	PUNCT
ejpam-5317	155	12	2024	2024	NUM
ejpam-5317	155	13	)	)	PUNCT
ejpam-5317	155	14	,	,	PUNCT
ejpam-5317	155	15	2550	2550	NUM
ejpam-5317	155	16	-	-	SYM
ejpam-5317	155	17	2561	2561	NUM
ejpam-5317	155	18	2555	2555	NUM
ejpam-5317	155	19	(	(	PUNCT
ejpam-5317	155	20	iii	iii	NOUN
ejpam-5317	155	21	)	)	PUNCT
ejpam-5317	155	22	if	if	SCONJ
ejpam-5317	155	23	λ2	λ2	PROPN
ejpam-5317	155	24	−	−	PROPN
ejpam-5317	156	1	2λ−	2λ−	NUM
ejpam-5317	156	2	1	1	NUM
ejpam-5317	156	3	̸=	̸=	PROPN
ejpam-5317	156	4	0	0	NUM
ejpam-5317	156	5	,	,	PUNCT
ejpam-5317	156	6	∑s	∑s	PROPN
ejpam-5317	156	7	i=1	i=1	PROPN
ejpam-5317	156	8	ai	ai	VERB
ejpam-5317	156	9	=	=	SYM
ejpam-5317	156	10	0	0	PROPN
ejpam-5317	156	11	and	and	CCONJ
ejpam-5317	156	12	bm	bm	PROPN
ejpam-5317	157	1	+	+	CCONJ
ejpam-5317	157	2	cm	cm	NOUN
ejpam-5317	157	3	=	=	SYM
ejpam-5317	157	4	0	0	NUM
ejpam-5317	158	1	for	for	ADP
ejpam-5317	158	2	all	all	DET
ejpam-5317	158	3	m	m	NOUN
ejpam-5317	158	4	=	=	NOUN
ejpam-5317	158	5	1	1	NUM
ejpam-5317	158	6	,	,	PUNCT
ejpam-5317	158	7	2	2	NUM
ejpam-5317	158	8	,	,	PUNCT
ejpam-5317	158	9	3	3	NUM
ejpam-5317	158	10	,	,	PUNCT
ejpam-5317	158	11	4	4	NUM
ejpam-5317	158	12	,	,	PUNCT
ejpam-5317	158	13	then	then	ADV
ejpam-5317	158	14	from	from	ADP
ejpam-5317	158	15	equation	equation	NOUN
ejpam-5317	158	16	(	(	PUNCT
ejpam-5317	158	17	18	18	NUM
ejpam-5317	158	18	)	)	PUNCT
ejpam-5317	158	19	,	,	PUNCT
ejpam-5317	158	20	d∗k	d∗k	PUNCT
ejpam-5317	158	21	=	=	SYM
ejpam-5317	158	22	−d∗k+1	−d∗k+1	NOUN
ejpam-5317	158	23	for	for	ADP
ejpam-5317	158	24	all	all	PRON
ejpam-5317	158	25	k	k	NOUN
ejpam-5317	158	26	=	=	SYM
ejpam-5317	158	27	1	1	NUM
ejpam-5317	158	28	,	,	PUNCT
ejpam-5317	158	29	3	3	NUM
ejpam-5317	158	30	,	,	PUNCT
ejpam-5317	158	31	.	.	PUNCT
ejpam-5317	158	32	.	.	PUNCT
ejpam-5317	158	33	.	.	PUNCT
ejpam-5317	159	1	,	,	PUNCT
ejpam-5317	159	2	s−	s−	PROPN
ejpam-5317	159	3	5	5	NUM
ejpam-5317	159	4	.	.	PUNCT
ejpam-5317	159	5	(	(	PUNCT
ejpam-5317	159	6	iv	iv	X
ejpam-5317	159	7	)	)	PUNCT
ejpam-5317	159	8	if	if	SCONJ
ejpam-5317	159	9	λ	λ	PROPN
ejpam-5317	159	10	̸=	̸=	PROPN
ejpam-5317	159	11	0	0	NUM
ejpam-5317	159	12	,	,	PUNCT
ejpam-5317	159	13	we	we	PRON
ejpam-5317	159	14	get	get	VERB
ejpam-5317	159	15	from	from	ADP
ejpam-5317	159	16	equations	equation	NOUN
ejpam-5317	159	17	(	(	PUNCT
ejpam-5317	159	18	4	4	NUM
ejpam-5317	159	19	)	)	PUNCT
ejpam-5317	159	20	,	,	PUNCT
ejpam-5317	159	21	(	(	PUNCT
ejpam-5317	159	22	6	6	NUM
ejpam-5317	159	23	)	)	PUNCT
ejpam-5317	159	24	,	,	PUNCT
ejpam-5317	159	25	and	and	CCONJ
ejpam-5317	159	26	(	(	PUNCT
ejpam-5317	159	27	12	12	NUM
ejpam-5317	159	28	)	)	PUNCT
ejpam-5317	159	29	that	that	PRON
ejpam-5317	159	30	b1	b1	NOUN
ejpam-5317	159	31	=	=	SYM
ejpam-5317	159	32	b2	b2	NOUN
ejpam-5317	159	33	=	=	SYM
ejpam-5317	159	34	·	·	PUNCT
ejpam-5317	159	35	·	·	PUNCT
ejpam-5317	159	36	·	·	PUNCT
ejpam-5317	160	1	=	=	SYM
ejpam-5317	160	2	b4	b4	NOUN
ejpam-5317	160	3	=	=	SYM
ejpam-5317	160	4	b	b	PROPN
ejpam-5317	160	5	,	,	PUNCT
ejpam-5317	160	6	c1	c1	PROPN
ejpam-5317	160	7	=	=	PROPN
ejpam-5317	160	8	c2	c2	PROPN
ejpam-5317	160	9	=	=	PUNCT
ejpam-5317	160	10	·	·	PUNCT
ejpam-5317	160	11	·	·	PUNCT
ejpam-5317	160	12	·	·	PUNCT
ejpam-5317	161	1	=	=	SYM
ejpam-5317	161	2	c4	c4	NOUN
ejpam-5317	161	3	=	=	SYM
ejpam-5317	161	4	c	c	NOUN
ejpam-5317	161	5	,	,	PUNCT
ejpam-5317	161	6	and	and	CCONJ
ejpam-5317	161	7	d1	d1	PROPN
ejpam-5317	161	8	=	=	SYM
ejpam-5317	161	9	d2	d2	PROPN
ejpam-5317	161	10	=	=	SYM
ejpam-5317	161	11	·	·	PUNCT
ejpam-5317	161	12	·	·	PUNCT
ejpam-5317	161	13	·	·	PUNCT
ejpam-5317	162	1	=	=	PUNCT
ejpam-5317	162	2	d4	d4	PROPN
ejpam-5317	162	3	=	=	SYM
ejpam-5317	162	4	d.	d.	PROPN
ejpam-5317	162	5	(	(	PUNCT
ejpam-5317	162	6	v	v	NOUN
ejpam-5317	162	7	)	)	PUNCT
ejpam-5317	162	8	if	if	SCONJ
ejpam-5317	162	9	λ	λ	PROPN
ejpam-5317	162	10	̸=	̸=	PROPN
ejpam-5317	162	11	0	0	NUM
ejpam-5317	162	12	and	and	CCONJ
ejpam-5317	162	13	λ2	λ2	PROPN
ejpam-5317	162	14	+	+	CCONJ
ejpam-5317	162	15	2λ	2λ	NOUN
ejpam-5317	162	16	−	−	NOUN
ejpam-5317	162	17	1	1	NUM
ejpam-5317	162	18	̸=	̸=	PROPN
ejpam-5317	162	19	0	0	NUM
ejpam-5317	162	20	then	then	ADV
ejpam-5317	162	21	by	by	ADP
ejpam-5317	162	22	subtracting	subtract	VERB
ejpam-5317	162	23	equation	equation	NOUN
ejpam-5317	162	24	(	(	PUNCT
ejpam-5317	162	25	4	4	NUM
ejpam-5317	162	26	)	)	PUNCT
ejpam-5317	162	27	from	from	ADP
ejpam-5317	162	28	(	(	PUNCT
ejpam-5317	162	29	5	5	NUM
ejpam-5317	162	30	)	)	PUNCT
ejpam-5317	162	31	,	,	PUNCT
ejpam-5317	162	32	we	we	PRON
ejpam-5317	162	33	get	get	VERB
ejpam-5317	162	34	b∗k	b∗k	PRON
ejpam-5317	162	35	+	+	CCONJ
ejpam-5317	162	36	d∗k	d∗k	PUNCT
ejpam-5317	162	37	=	=	SYM
ejpam-5317	162	38	λb∗k	λb∗k	PROPN
ejpam-5317	162	39	−	−	NOUN
ejpam-5317	162	40	λb	λb	NOUN
ejpam-5317	162	41	.	.	PUNCT
ejpam-5317	163	1	thus	thus	ADV
ejpam-5317	163	2	if	if	SCONJ
ejpam-5317	163	3	∑s−4	∑s−4	PROPN
ejpam-5317	163	4	i=1	i=1	PROPN
ejpam-5317	164	1	d	d	NOUN
ejpam-5317	164	2	∗	∗	NOUN
ejpam-5317	164	3	i	i	NOUN
ejpam-5317	164	4	=	=	NOUN
ejpam-5317	164	5	0	0	NUM
ejpam-5317	164	6	,	,	PUNCT
ejpam-5317	164	7	then	then	ADV
ejpam-5317	164	8	(	(	PUNCT
ejpam-5317	164	9	λ−	λ−	PROPN
ejpam-5317	164	10	1	1	NUM
ejpam-5317	164	11	)	)	PUNCT
ejpam-5317	164	12	s−4∑	s−4∑	NUM
ejpam-5317	164	13	i=1	i=1	PRON
ejpam-5317	164	14	b∗i	b∗i	PROPN
ejpam-5317	164	15	=	=	SYM
ejpam-5317	164	16	λ(s−	λ(s−	PROPN
ejpam-5317	164	17	4)b	4)b	NUM
ejpam-5317	164	18	.	.	PUNCT
ejpam-5317	165	1	(	(	PUNCT
ejpam-5317	165	2	26	26	NUM
ejpam-5317	165	3	)	)	PUNCT
ejpam-5317	165	4	(	(	PUNCT
ejpam-5317	165	5	vi	vi	NOUN
ejpam-5317	165	6	)	)	PUNCT
ejpam-5317	165	7	if	if	SCONJ
ejpam-5317	165	8	λ	λ	PROPN
ejpam-5317	165	9	̸=	̸=	PROPN
ejpam-5317	165	10	0	0	NUM
ejpam-5317	165	11	,	,	PUNCT
ejpam-5317	165	12	λ	λ	PROPN
ejpam-5317	165	13	̸=	̸=	PROPN
ejpam-5317	165	14	1	1	NUM
ejpam-5317	165	15	,	,	PUNCT
ejpam-5317	165	16	λ2	λ2	PROPN
ejpam-5317	165	17	+	+	CCONJ
ejpam-5317	165	18	2λ	2λ	NOUN
ejpam-5317	165	19	−	−	NOUN
ejpam-5317	165	20	1	1	NUM
ejpam-5317	165	21	̸=	̸=	PROPN
ejpam-5317	165	22	0	0	NUM
ejpam-5317	165	23	,	,	PUNCT
ejpam-5317	165	24	and	and	CCONJ
ejpam-5317	165	25	q(λ	q(λ	NOUN
ejpam-5317	165	26	)	)	PUNCT
ejpam-5317	165	27	̸=	̸=	PROPN
ejpam-5317	165	28	0	0	NUM
ejpam-5317	165	29	,	,	PUNCT
ejpam-5317	165	30	then	then	ADV
ejpam-5317	165	31	from	from	ADP
ejpam-5317	165	32	lemma	lemma	PROPN
ejpam-5317	165	33	1	1	NUM
ejpam-5317	165	34	and	and	CCONJ
ejpam-5317	165	35	part	part	NOUN
ejpam-5317	165	36	(	(	PUNCT
ejpam-5317	165	37	iv	iv	X
ejpam-5317	165	38	)	)	PUNCT
ejpam-5317	165	39	of	of	ADP
ejpam-5317	165	40	this	this	DET
ejpam-5317	165	41	remark	remark	NOUN
ejpam-5317	165	42	,	,	PUNCT
ejpam-5317	165	43	we	we	PRON
ejpam-5317	165	44	have	have	VERB
ejpam-5317	165	45	4∑	4∑	NUM
ejpam-5317	165	46	j	j	NOUN
ejpam-5317	165	47	dj	dj	NOUN
ejpam-5317	165	48	=	=	PUNCT
ejpam-5317	165	49	s−4∑	s−4∑	X
ejpam-5317	165	50	i=1	i=1	PRON
ejpam-5317	166	1	d∗i	d∗i	X
ejpam-5317	166	2	=	=	SYM
ejpam-5317	166	3	4(b	4(b	NUM
ejpam-5317	166	4	+	+	CCONJ
ejpam-5317	166	5	c	c	X
ejpam-5317	166	6	)	)	PUNCT
ejpam-5317	166	7	=	=	SYM
ejpam-5317	167	1	0	0	NUM
ejpam-5317	167	2	,	,	PUNCT
ejpam-5317	167	3	so	so	ADV
ejpam-5317	167	4	from	from	ADP
ejpam-5317	167	5	equation	equation	NOUN
ejpam-5317	167	6	(	(	PUNCT
ejpam-5317	167	7	13	13	NUM
ejpam-5317	167	8	)	)	PUNCT
ejpam-5317	167	9	,	,	PUNCT
ejpam-5317	167	10	we	we	PRON
ejpam-5317	167	11	obtain	obtain	VERB
ejpam-5317	167	12	∑s	∑s	PROPN
ejpam-5317	168	1	i=1	i=1	PROPN
ejpam-5317	168	2	ai	ai	PROPN
ejpam-5317	168	3	=	=	ADJ
ejpam-5317	168	4	0	0	NUM
ejpam-5317	168	5	.	.	PUNCT
ejpam-5317	169	1	thus	thus	ADV
ejpam-5317	169	2	,	,	PUNCT
ejpam-5317	169	3	equation	equation	NOUN
ejpam-5317	169	4	(	(	PUNCT
ejpam-5317	169	5	7	7	NUM
ejpam-5317	169	6	)	)	PUNCT
ejpam-5317	169	7	implies	imply	VERB
ejpam-5317	169	8	that	that	SCONJ
ejpam-5317	169	9	4b	4b	PROPN
ejpam-5317	169	10	+	+	CCONJ
ejpam-5317	169	11	s−4∑	s−4∑	X
ejpam-5317	169	12	i=1	i=1	X
ejpam-5317	169	13	b∗i	b∗i	PUNCT
ejpam-5317	169	14	=	=	SYM
ejpam-5317	169	15	−λb	−λb	X
ejpam-5317	169	16	.	.	X
ejpam-5317	169	17	(	(	PUNCT
ejpam-5317	169	18	27	27	NUM
ejpam-5317	169	19	)	)	PUNCT
ejpam-5317	169	20	from	from	ADP
ejpam-5317	169	21	equations	equation	NOUN
ejpam-5317	169	22	(	(	PUNCT
ejpam-5317	169	23	26	26	NUM
ejpam-5317	169	24	)	)	PUNCT
ejpam-5317	169	25	and	and	CCONJ
ejpam-5317	169	26	(	(	PUNCT
ejpam-5317	169	27	27	27	NUM
ejpam-5317	169	28	)	)	PUNCT
ejpam-5317	169	29	,	,	PUNCT
ejpam-5317	169	30	we	we	PRON
ejpam-5317	169	31	get	get	VERB
ejpam-5317	169	32	(	(	PUNCT
ejpam-5317	169	33	λ2	λ2	NOUN
ejpam-5317	169	34	+	+	CCONJ
ejpam-5317	169	35	(	(	PUNCT
ejpam-5317	169	36	s−	s−	PROPN
ejpam-5317	169	37	1)λ−	1)λ−	NUM
ejpam-5317	169	38	4)b	4)b	NUM
ejpam-5317	170	1	=	=	SYM
ejpam-5317	170	2	0	0	X
ejpam-5317	170	3	.	.	PUNCT
ejpam-5317	171	1	(	(	PUNCT
ejpam-5317	171	2	28	28	NUM
ejpam-5317	171	3	)	)	PUNCT
ejpam-5317	171	4	based	base	VERB
ejpam-5317	171	5	on	on	ADP
ejpam-5317	171	6	this	this	DET
ejpam-5317	171	7	remark	remark	NOUN
ejpam-5317	171	8	and	and	CCONJ
ejpam-5317	171	9	lemma	lemma	PROPN
ejpam-5317	171	10	1	1	NUM
ejpam-5317	171	11	,	,	PUNCT
ejpam-5317	171	12	we	we	PRON
ejpam-5317	171	13	have	have	VERB
ejpam-5317	171	14	the	the	DET
ejpam-5317	171	15	following	follow	VERB
ejpam-5317	171	16	results	result	NOUN
ejpam-5317	171	17	.	.	PUNCT
ejpam-5317	172	1	lemma	lemma	PROPN
ejpam-5317	172	2	2	2	NUM
ejpam-5317	172	3	.	.	PUNCT
ejpam-5317	173	1	λ	λ	NOUN
ejpam-5317	173	2	=	=	PRON
ejpam-5317	173	3	−1	−1	NOUN
ejpam-5317	173	4	is	be	AUX
ejpam-5317	173	5	an	an	DET
ejpam-5317	173	6	eigenvalue	eigenvalue	NOUN
ejpam-5317	173	7	of	of	ADP
ejpam-5317	173	8	the	the	DET
ejpam-5317	173	9	matrix	matrix	NOUN
ejpam-5317	173	10	a	a	PRON
ejpam-5317	173	11	with	with	ADP
ejpam-5317	173	12	multiplicity	multiplicity	NOUN
ejpam-5317	173	13	is	be	AUX
ejpam-5317	173	14	greater	great	ADJ
ejpam-5317	173	15	than	than	ADP
ejpam-5317	173	16	or	or	CCONJ
ejpam-5317	173	17	equal	equal	ADJ
ejpam-5317	173	18	to	to	ADP
ejpam-5317	173	19	s−	s−	PROPN
ejpam-5317	173	20	1	1	NUM
ejpam-5317	174	1	+	+	CCONJ
ejpam-5317	174	2	s−4	s−4	PROPN
ejpam-5317	174	3	2	2	NUM
ejpam-5317	174	4	.	.	PUNCT
ejpam-5317	175	1	proof	proof	NOUN
ejpam-5317	175	2	.	.	PUNCT
ejpam-5317	176	1	we	we	PRON
ejpam-5317	176	2	have	have	VERB
ejpam-5317	176	3	to	to	PART
ejpam-5317	176	4	show	show	VERB
ejpam-5317	176	5	that	that	SCONJ
ejpam-5317	176	6	all	all	DET
ejpam-5317	176	7	equations	equation	NOUN
ejpam-5317	176	8	from	from	ADP
ejpam-5317	176	9	(	(	PUNCT
ejpam-5317	176	10	3	3	NUM
ejpam-5317	176	11	)	)	PUNCT
ejpam-5317	176	12	to	to	ADP
ejpam-5317	176	13	(	(	PUNCT
ejpam-5317	176	14	12	12	NUM
ejpam-5317	176	15	)	)	PUNCT
ejpam-5317	176	16	are	be	AUX
ejpam-5317	176	17	satisfied	satisfied	ADJ
ejpam-5317	176	18	with	with	ADP
ejpam-5317	176	19	λ	λ	X
ejpam-5317	176	20	=	=	NOUN
ejpam-5317	176	21	−1	−1	NOUN
ejpam-5317	176	22	.	.	PUNCT
ejpam-5317	177	1	if	if	SCONJ
ejpam-5317	177	2	λ	λ	X
ejpam-5317	177	3	=	=	SYM
ejpam-5317	177	4	−1	−1	NOUN
ejpam-5317	177	5	,	,	PUNCT
ejpam-5317	177	6	then	then	ADV
ejpam-5317	177	7	from	from	ADP
ejpam-5317	177	8	equation	equation	NOUN
ejpam-5317	177	9	(	(	PUNCT
ejpam-5317	177	10	13	13	NUM
ejpam-5317	177	11	)	)	PUNCT
ejpam-5317	177	12	,	,	PUNCT
ejpam-5317	177	13	lemma	lemma	PROPN
ejpam-5317	177	14	1	1	NUM
ejpam-5317	177	15	,	,	PUNCT
ejpam-5317	177	16	and	and	CCONJ
ejpam-5317	177	17	remark	remark	NOUN
ejpam-5317	177	18	1	1	NUM
ejpam-5317	177	19	,	,	PUNCT
ejpam-5317	177	20	we	we	PRON
ejpam-5317	177	21	get	get	VERB
ejpam-5317	177	22	∑s	∑s	PROPN
ejpam-5317	177	23	i=1	i=1	PROPN
ejpam-5317	177	24	ai	ai	PROPN
ejpam-5317	177	25	=	=	SYM
ejpam-5317	177	26	0	0	NUM
ejpam-5317	177	27	,	,	PUNCT
ejpam-5317	177	28	b1	b1	NOUN
ejpam-5317	177	29	=	=	SYM
ejpam-5317	177	30	b2	b2	NOUN
ejpam-5317	177	31	=	=	SYM
ejpam-5317	177	32	·	·	PUNCT
ejpam-5317	177	33	·	·	PUNCT
ejpam-5317	177	34	·	·	PUNCT
ejpam-5317	178	1	=	=	SYM
ejpam-5317	178	2	b4	b4	NOUN
ejpam-5317	178	3	=	=	SYM
ejpam-5317	178	4	b	b	PROPN
ejpam-5317	178	5	=	=	SYM
ejpam-5317	178	6	0	0	PROPN
ejpam-5317	178	7	,	,	PUNCT
ejpam-5317	178	8	c1	c1	NOUN
ejpam-5317	178	9	=	=	PROPN
ejpam-5317	178	10	c2	c2	PROPN
ejpam-5317	178	11	=	=	PUNCT
ejpam-5317	178	12	·	·	PUNCT
ejpam-5317	178	13	·	·	PUNCT
ejpam-5317	178	14	·	·	PUNCT
ejpam-5317	179	1	=	=	SYM
ejpam-5317	179	2	c4	c4	NOUN
ejpam-5317	179	3	=	=	SYM
ejpam-5317	179	4	c	c	NOUN
ejpam-5317	179	5	=	=	SYM
ejpam-5317	179	6	0	0	NUM
ejpam-5317	179	7	,	,	PUNCT
ejpam-5317	179	8	and	and	CCONJ
ejpam-5317	179	9	d1	d1	PROPN
ejpam-5317	179	10	=	=	SYM
ejpam-5317	179	11	d2	d2	PROPN
ejpam-5317	179	12	=	=	PUNCT
ejpam-5317	179	13	d3	d3	PROPN
ejpam-5317	179	14	=	=	SYM
ejpam-5317	179	15	d4	d4	PROPN
ejpam-5317	179	16	=	=	SYM
ejpam-5317	180	1	d	d	PROPN
ejpam-5317	180	2	=	=	SYM
ejpam-5317	180	3	0	0	X
ejpam-5317	180	4	.	.	PUNCT
ejpam-5317	181	1	now	now	ADV
ejpam-5317	181	2	,	,	PUNCT
ejpam-5317	181	3	from	from	ADP
ejpam-5317	181	4	equations	equation	NOUN
ejpam-5317	181	5	(	(	PUNCT
ejpam-5317	181	6	18	18	NUM
ejpam-5317	181	7	)	)	PUNCT
ejpam-5317	181	8	and	and	CCONJ
ejpam-5317	181	9	(	(	PUNCT
ejpam-5317	181	10	23	23	NUM
ejpam-5317	181	11	)	)	PUNCT
ejpam-5317	181	12	,	,	PUNCT
ejpam-5317	181	13	we	we	PRON
ejpam-5317	181	14	get	get	VERB
ejpam-5317	181	15	d∗k	d∗k	PUNCT
ejpam-5317	181	16	=	=	SYM
ejpam-5317	181	17	0(d∗k	0(d∗k	NUM
ejpam-5317	182	1	=	=	SYM
ejpam-5317	182	2	d∗k+1	d∗k+1	NOUN
ejpam-5317	182	3	=	=	SYM
ejpam-5317	182	4	−d∗k+1	−d∗k+1	NOUN
ejpam-5317	182	5	)	)	PUNCT
ejpam-5317	182	6	for	for	ADP
ejpam-5317	182	7	all	all	PRON
ejpam-5317	182	8	k	k	NOUN
ejpam-5317	182	9	=	=	SYM
ejpam-5317	182	10	1	1	NUM
ejpam-5317	182	11	,	,	PUNCT
ejpam-5317	182	12	2	2	NUM
ejpam-5317	182	13	,	,	PUNCT
ejpam-5317	182	14	.	.	PUNCT
ejpam-5317	182	15	.	.	PUNCT
ejpam-5317	182	16	.	.	PUNCT
ejpam-5317	183	1	,	,	PUNCT
ejpam-5317	183	2	s	s	VERB
ejpam-5317	183	3	−	−	NOUN
ejpam-5317	183	4	4	4	NUM
ejpam-5317	183	5	.	.	PUNCT
ejpam-5317	184	1	by	by	ADP
ejpam-5317	184	2	subtracting	subtract	VERB
ejpam-5317	184	3	equation	equation	NOUN
ejpam-5317	184	4	(	(	PUNCT
ejpam-5317	184	5	4	4	NUM
ejpam-5317	184	6	)	)	PUNCT
ejpam-5317	184	7	from	from	ADP
ejpam-5317	184	8	equations	equation	NOUN
ejpam-5317	184	9	(	(	PUNCT
ejpam-5317	184	10	5	5	NUM
ejpam-5317	184	11	)	)	PUNCT
ejpam-5317	184	12	and	and	CCONJ
ejpam-5317	184	13	equation	equation	NOUN
ejpam-5317	184	14	(	(	PUNCT
ejpam-5317	184	15	7	7	NUM
ejpam-5317	184	16	)	)	PUNCT
ejpam-5317	184	17	from	from	ADP
ejpam-5317	184	18	equation	equation	NOUN
ejpam-5317	184	19	(	(	PUNCT
ejpam-5317	184	20	8)	8)	NUM
ejpam-5317	184	21	,	,	PUNCT
ejpam-5317	184	22	we	we	PRON
ejpam-5317	184	23	get	get	VERB
ejpam-5317	184	24	b∗k	b∗k	NOUN
ejpam-5317	184	25	=	=	SYM
ejpam-5317	184	26	−b∗k+1	−b∗k+1	NOUN
ejpam-5317	184	27	and	and	CCONJ
ejpam-5317	184	28	c∗k	c∗k	NOUN
ejpam-5317	184	29	=	=	SYM
ejpam-5317	184	30	−c∗k+1	−c∗k+1	X
ejpam-5317	184	31	for	for	ADP
ejpam-5317	184	32	all	all	PRON
ejpam-5317	184	33	k	k	NOUN
ejpam-5317	184	34	=	=	SYM
ejpam-5317	184	35	1	1	NUM
ejpam-5317	184	36	,	,	PUNCT
ejpam-5317	184	37	3	3	NUM
ejpam-5317	184	38	,	,	PUNCT
ejpam-5317	184	39	.	.	PUNCT
ejpam-5317	184	40	.	.	PUNCT
ejpam-5317	185	1	.	.	PUNCT
ejpam-5317	186	1	,	,	PUNCT
ejpam-5317	186	2	s	s	VERB
ejpam-5317	186	3	−	−	NOUN
ejpam-5317	186	4	5	5	NUM
ejpam-5317	186	5	.	.	PUNCT
ejpam-5317	186	6	from	from	ADP
ejpam-5317	186	7	equation	equation	NOUN
ejpam-5317	186	8	(	(	PUNCT
ejpam-5317	186	9	12	12	NUM
ejpam-5317	186	10	)	)	PUNCT
ejpam-5317	186	11	,	,	PUNCT
ejpam-5317	186	12	we	we	PRON
ejpam-5317	186	13	get	get	VERB
ejpam-5317	186	14	b∗k	b∗k	NOUN
ejpam-5317	186	15	=	=	SYM
ejpam-5317	186	16	−c∗k	−c∗k	NOUN
ejpam-5317	186	17	for	for	ADP
ejpam-5317	186	18	all	all	PRON
ejpam-5317	186	19	k	k	NOUN
ejpam-5317	186	20	=	=	SYM
ejpam-5317	186	21	1	1	NUM
ejpam-5317	186	22	,	,	PUNCT
ejpam-5317	186	23	2	2	NUM
ejpam-5317	186	24	,	,	PUNCT
ejpam-5317	186	25	.	.	PUNCT
ejpam-5317	186	26	.	.	PUNCT
ejpam-5317	187	1	.	.	PUNCT
ejpam-5317	188	1	,	,	PUNCT
ejpam-5317	188	2	s−	s−	PROPN
ejpam-5317	188	3	4	4	NUM
ejpam-5317	188	4	.	.	PUNCT
ejpam-5317	188	5	based	base	VERB
ejpam-5317	188	6	on	on	ADP
ejpam-5317	188	7	these	these	DET
ejpam-5317	188	8	facts	fact	NOUN
ejpam-5317	188	9	,	,	PUNCT
ejpam-5317	188	10	the	the	DET
ejpam-5317	188	11	vector	vector	NOUN
ejpam-5317	188	12	x	x	PUNCT
ejpam-5317	188	13	with	with	ADP
ejpam-5317	188	14	entries	entry	NOUN
ejpam-5317	188	15	(	(	PUNCT
ejpam-5317	188	16	x)i	x)i	PUNCT
ejpam-5317	188	17	=	=	SYM
ejpam-5317	188	18			PROPN
ejpam-5317	188	19	ai	ai	VERB
ejpam-5317	188	20	,	,	PUNCT
ejpam-5317	188	21	if	if	SCONJ
ejpam-5317	188	22	i	i	PRON
ejpam-5317	188	23	=	=	NOUN
ejpam-5317	188	24	1	1	NUM
ejpam-5317	188	25	,	,	PUNCT
ejpam-5317	188	26	2	2	NUM
ejpam-5317	188	27	,	,	PUNCT
ejpam-5317	188	28	.	.	PUNCT
ejpam-5317	188	29	.	.	PUNCT
ejpam-5317	189	1	.	.	PUNCT
ejpam-5317	190	1	,	,	PUNCT
ejpam-5317	190	2	s	s	X
ejpam-5317	190	3	,	,	PUNCT
ejpam-5317	190	4	0	0	NUM
ejpam-5317	190	5	,	,	PUNCT
ejpam-5317	190	6	if	if	SCONJ
ejpam-5317	190	7	i	i	PRON
ejpam-5317	190	8	=	=	SYM
ejpam-5317	190	9	s	s	X
ejpam-5317	191	1	+	+	ADJ
ejpam-5317	191	2	1	1	NUM
ejpam-5317	191	3	,	,	PUNCT
ejpam-5317	191	4	s	s	PART
ejpam-5317	191	5	+	+	ADJ
ejpam-5317	191	6	2	2	NUM
ejpam-5317	191	7	,	,	PUNCT
ejpam-5317	191	8	.	.	PUNCT
ejpam-5317	191	9	.	.	PUNCT
ejpam-5317	192	1	.	.	PUNCT
ejpam-5317	193	1	,	,	PUNCT
ejpam-5317	193	2	s	s	PART
ejpam-5317	193	3	+	+	ADJ
ejpam-5317	193	4	4	4	NUM
ejpam-5317	193	5	,	,	PUNCT
ejpam-5317	193	6	b∗i−s−4	b∗i−s−4	ADJ
ejpam-5317	193	7	,	,	PUNCT
ejpam-5317	193	8	if	if	SCONJ
ejpam-5317	193	9	i	i	PRON
ejpam-5317	193	10	=	=	SYM
ejpam-5317	193	11	s	s	PART
ejpam-5317	194	1	+	+	NOUN
ejpam-5317	194	2	5	5	NUM
ejpam-5317	194	3	,	,	PUNCT
ejpam-5317	194	4	s	s	PART
ejpam-5317	194	5	+	+	NOUN
ejpam-5317	194	6	6	6	NUM
ejpam-5317	194	7	,	,	PUNCT
ejpam-5317	194	8	.	.	PUNCT
ejpam-5317	194	9	.	.	PUNCT
ejpam-5317	195	1	.	.	PUNCT
ejpam-5317	196	1	,	,	PUNCT
ejpam-5317	196	2	2s	2s	X
ejpam-5317	196	3	,	,	PUNCT
ejpam-5317	196	4	0	0	NUM
ejpam-5317	196	5	,	,	PUNCT
ejpam-5317	196	6	if	if	SCONJ
ejpam-5317	196	7	i	i	PRON
ejpam-5317	196	8	=	=	PUNCT
ejpam-5317	197	1	2s	2s	NUM
ejpam-5317	198	1	+	+	NOUN
ejpam-5317	198	2	1	1	NUM
ejpam-5317	198	3	,	,	PUNCT
ejpam-5317	198	4	2s	2s	PROPN
ejpam-5317	198	5	+	+	NOUN
ejpam-5317	198	6	2	2	NUM
ejpam-5317	198	7	,	,	PUNCT
ejpam-5317	198	8	.	.	PUNCT
ejpam-5317	198	9	.	.	PUNCT
ejpam-5317	199	1	.	.	PUNCT
ejpam-5317	200	1	,	,	PUNCT
ejpam-5317	201	1	2s	2s	PROPN
ejpam-5317	201	2	+	+	CCONJ
ejpam-5317	201	3	4	4	NUM
ejpam-5317	201	4	,	,	PUNCT
ejpam-5317	201	5	−b∗i−2s−4	−b∗i−2s−4	INTJ
ejpam-5317	201	6	,	,	PUNCT
ejpam-5317	201	7	if	if	SCONJ
ejpam-5317	201	8	i	i	PRON
ejpam-5317	201	9	=	=	PUNCT
ejpam-5317	202	1	2s	2s	NUM
ejpam-5317	203	1	+	+	NOUN
ejpam-5317	203	2	5	5	NUM
ejpam-5317	203	3	,	,	PUNCT
ejpam-5317	203	4	2s	2s	PROPN
ejpam-5317	203	5	+	+	NOUN
ejpam-5317	203	6	6	6	NUM
ejpam-5317	203	7	,	,	PUNCT
ejpam-5317	203	8	.	.	PUNCT
ejpam-5317	203	9	.	.	PUNCT
ejpam-5317	204	1	.	.	PUNCT
ejpam-5317	205	1	,	,	PUNCT
ejpam-5317	205	2	3s	3s	NUM
ejpam-5317	205	3	,	,	PUNCT
ejpam-5317	205	4	0	0	NUM
ejpam-5317	205	5	,	,	PUNCT
ejpam-5317	205	6	if	if	SCONJ
ejpam-5317	205	7	i	i	PRON
ejpam-5317	205	8	=	=	SYM
ejpam-5317	205	9	3s	3s	NUM
ejpam-5317	205	10	+	+	CCONJ
ejpam-5317	205	11	1	1	NUM
ejpam-5317	205	12	,	,	PUNCT
ejpam-5317	205	13	3s	3s	NUM
ejpam-5317	205	14	+	+	CCONJ
ejpam-5317	205	15	2	2	NUM
ejpam-5317	205	16	,	,	PUNCT
ejpam-5317	205	17	.	.	PUNCT
ejpam-5317	205	18	.	.	PUNCT
ejpam-5317	205	19	.	.	PUNCT
ejpam-5317	206	1	,	,	PUNCT
ejpam-5317	206	2	3s	3s	NUM
ejpam-5317	206	3	+	+	CCONJ
ejpam-5317	206	4	4	4	NUM
ejpam-5317	206	5	,	,	PUNCT
ejpam-5317	206	6	0	0	NUM
ejpam-5317	206	7	,	,	PUNCT
ejpam-5317	206	8	if	if	SCONJ
ejpam-5317	206	9	i	i	PRON
ejpam-5317	206	10	=	=	SYM
ejpam-5317	206	11	3s	3s	NUM
ejpam-5317	206	12	+	+	CCONJ
ejpam-5317	206	13	5	5	NUM
ejpam-5317	206	14	,	,	PUNCT
ejpam-5317	206	15	3s	3s	NUM
ejpam-5317	206	16	+	+	CCONJ
ejpam-5317	206	17	6	6	NUM
ejpam-5317	206	18	,	,	PUNCT
ejpam-5317	206	19	.	.	PUNCT
ejpam-5317	206	20	.	.	PUNCT
ejpam-5317	206	21	.	.	PUNCT
ejpam-5317	207	1	,	,	PUNCT
ejpam-5317	207	2	4s	4s	NUM
ejpam-5317	207	3	.	.	PUNCT
ejpam-5317	208	1	(	(	PUNCT
ejpam-5317	208	2	29	29	NUM
ejpam-5317	208	3	)	)	PUNCT
ejpam-5317	208	4	e.	e.	PROPN
ejpam-5317	208	5	rawaswhdeh	rawaswhdeh	PROPN
ejpam-5317	208	6	,	,	PUNCT
ejpam-5317	208	7	h.	h.	PROPN
ejpam-5317	208	8	adel	adel	PROPN
ejpam-5317	208	9	abdelkarim	abdelkarim	PROPN
ejpam-5317	208	10	,	,	PUNCT
ejpam-5317	208	11	e.	e.	PROPN
ejpam-5317	208	12	rawshdeh	rawshdeh	PROPN
ejpam-5317	208	13	/	/	SYM
ejpam-5317	208	14	eur	eur	PROPN
ejpam-5317	208	15	.	.	PUNCT
ejpam-5317	209	1	j.	j.	PROPN
ejpam-5317	209	2	pure	pure	PROPN
ejpam-5317	209	3	appl	appl	PROPN
ejpam-5317	209	4	.	.	PROPN
ejpam-5317	209	5	math	math	PROPN
ejpam-5317	209	6	,	,	PUNCT
ejpam-5317	209	7	17	17	NUM
ejpam-5317	209	8	(	(	PUNCT
ejpam-5317	209	9	4	4	NUM
ejpam-5317	209	10	)	)	PUNCT
ejpam-5317	209	11	(	(	PUNCT
ejpam-5317	209	12	2024	2024	NUM
ejpam-5317	209	13	)	)	PUNCT
ejpam-5317	209	14	,	,	PUNCT
ejpam-5317	209	15	2550	2550	NUM
ejpam-5317	209	16	-	-	SYM
ejpam-5317	209	17	2561	2561	NUM
ejpam-5317	209	18	2556	2556	NUM
ejpam-5317	209	19	satisfy	satisfy	NOUN
ejpam-5317	209	20	all	all	DET
ejpam-5317	209	21	equations	equation	NOUN
ejpam-5317	209	22	from	from	ADP
ejpam-5317	209	23	(	(	PUNCT
ejpam-5317	209	24	3	3	NUM
ejpam-5317	209	25	)	)	PUNCT
ejpam-5317	209	26	to	to	ADP
ejpam-5317	209	27	(	(	PUNCT
ejpam-5317	209	28	12	12	NUM
ejpam-5317	209	29	)	)	PUNCT
ejpam-5317	209	30	with	with	ADP
ejpam-5317	209	31	λ	λ	NOUN
ejpam-5317	209	32	=	=	PRON
ejpam-5317	209	33	−1	−1	NOUN
ejpam-5317	209	34	provided	provide	VERB
ejpam-5317	209	35	that	that	SCONJ
ejpam-5317	209	36	∑s	∑s	PROPN
ejpam-5317	209	37	i=1	i=1	PROPN
ejpam-5317	209	38	ai	ai	VERB
ejpam-5317	209	39	=	=	SYM
ejpam-5317	209	40	0	0	NUM
ejpam-5317	209	41	and	and	CCONJ
ejpam-5317	209	42	b∗k	b∗k	NUM
ejpam-5317	209	43	=	=	PUNCT
ejpam-5317	209	44	−b∗k+1	−b∗k+1	X
ejpam-5317	209	45	for	for	ADP
ejpam-5317	209	46	all	all	PRON
ejpam-5317	209	47	k	k	NOUN
ejpam-5317	209	48	=	=	SYM
ejpam-5317	209	49	1	1	NUM
ejpam-5317	209	50	,	,	PUNCT
ejpam-5317	209	51	3	3	NUM
ejpam-5317	209	52	,	,	PUNCT
ejpam-5317	209	53	.	.	PUNCT
ejpam-5317	209	54	.	.	PUNCT
ejpam-5317	209	55	.	.	PUNCT
ejpam-5317	210	1	s−5	s−5	X
ejpam-5317	210	2	.	.	PUNCT
ejpam-5317	211	1	thus	thus	ADV
ejpam-5317	211	2	,	,	PUNCT
ejpam-5317	211	3	x	x	PRON
ejpam-5317	211	4	is	be	AUX
ejpam-5317	211	5	the	the	DET
ejpam-5317	211	6	corresponding	corresponding	ADJ
ejpam-5317	211	7	eigenvector	eigenvector	NOUN
ejpam-5317	211	8	for	for	ADP
ejpam-5317	211	9	the	the	DET
ejpam-5317	211	10	eigenvalue	eigenvalue	PROPN
ejpam-5317	211	11	λ	λ	PROPN
ejpam-5317	211	12	=	=	SYM
ejpam-5317	211	13	−1	−1	NOUN
ejpam-5317	211	14	of	of	ADP
ejpam-5317	211	15	a.	a.	NOUN
ejpam-5317	211	16	therefore	therefore	ADV
ejpam-5317	211	17	,	,	PUNCT
ejpam-5317	211	18	λ	λ	PROPN
ejpam-5317	211	19	=	=	PRON
ejpam-5317	211	20	−1	−1	NOUN
ejpam-5317	211	21	is	be	AUX
ejpam-5317	211	22	an	an	DET
ejpam-5317	211	23	eigenvalue	eigenvalue	NOUN
ejpam-5317	211	24	of	of	ADP
ejpam-5317	211	25	the	the	DET
ejpam-5317	211	26	matrix	matrix	NOUN
ejpam-5317	211	27	a	a	PRON
ejpam-5317	211	28	with	with	ADP
ejpam-5317	211	29	multiplicity	multiplicity	NOUN
ejpam-5317	211	30	is	be	AUX
ejpam-5317	211	31	greater	great	ADJ
ejpam-5317	211	32	than	than	ADP
ejpam-5317	211	33	or	or	CCONJ
ejpam-5317	211	34	equal	equal	ADJ
ejpam-5317	211	35	to	to	ADP
ejpam-5317	211	36	s−	s−	PROPN
ejpam-5317	211	37	1	1	NUM
ejpam-5317	212	1	+	+	CCONJ
ejpam-5317	212	2	s−4	s−4	PROPN
ejpam-5317	212	3	2	2	NUM
ejpam-5317	212	4	.	.	PUNCT
ejpam-5317	213	1	corollary	corollary	ADJ
ejpam-5317	213	2	1	1	NUM
ejpam-5317	213	3	.	.	PUNCT
ejpam-5317	214	1	λ	λ	NOUN
ejpam-5317	214	2	=	=	SYM
ejpam-5317	214	3	0	0	NUM
ejpam-5317	214	4	is	be	AUX
ejpam-5317	214	5	an	an	DET
ejpam-5317	214	6	eigenvalue	eigenvalue	NOUN
ejpam-5317	214	7	of	of	ADP
ejpam-5317	214	8	the	the	DET
ejpam-5317	214	9	matrix	matrix	NOUN
ejpam-5317	214	10	a	a	PRON
ejpam-5317	214	11	with	with	ADP
ejpam-5317	214	12	multiplicity	multiplicity	NOUN
ejpam-5317	214	13	is	be	AUX
ejpam-5317	214	14	greater	great	ADJ
ejpam-5317	214	15	than	than	ADP
ejpam-5317	214	16	or	or	CCONJ
ejpam-5317	214	17	equal	equal	ADJ
ejpam-5317	214	18	to	to	ADP
ejpam-5317	214	19	9	9	NUM
ejpam-5317	214	20	.	.	PUNCT
ejpam-5317	215	1	proof	proof	NOUN
ejpam-5317	215	2	.	.	PUNCT
ejpam-5317	216	1	if	if	SCONJ
ejpam-5317	216	2	λ	λ	X
ejpam-5317	216	3	=	=	SYM
ejpam-5317	216	4	0	0	NUM
ejpam-5317	216	5	,	,	PUNCT
ejpam-5317	216	6	then	then	ADV
ejpam-5317	216	7	subtraction	subtraction	NOUN
ejpam-5317	216	8	equation	equation	NOUN
ejpam-5317	216	9	(	(	PUNCT
ejpam-5317	216	10	4	4	NUM
ejpam-5317	216	11	)	)	PUNCT
ejpam-5317	216	12	from	from	ADP
ejpam-5317	216	13	(	(	PUNCT
ejpam-5317	216	14	5	5	NUM
ejpam-5317	216	15	)	)	PUNCT
ejpam-5317	216	16	and	and	CCONJ
ejpam-5317	216	17	(	(	PUNCT
ejpam-5317	216	18	7	7	X
ejpam-5317	216	19	)	)	PUNCT
ejpam-5317	216	20	from	from	ADP
ejpam-5317	216	21	(	(	PUNCT
ejpam-5317	216	22	8)	8)	NUM
ejpam-5317	216	23	,	,	PUNCT
ejpam-5317	216	24	we	we	PRON
ejpam-5317	216	25	get	get	VERB
ejpam-5317	216	26	b∗k	b∗k	PRON
ejpam-5317	216	27	+	+	CCONJ
ejpam-5317	216	28	d∗k	d∗k	PUNCT
ejpam-5317	216	29	=	=	SYM
ejpam-5317	216	30	c∗k	c∗k	NOUN
ejpam-5317	216	31	+	+	PUNCT
ejpam-5317	216	32	d∗k	d∗k	PUNCT
ejpam-5317	216	33	=	=	SYM
ejpam-5317	216	34	0	0	NUM
ejpam-5317	216	35	.	.	PUNCT
ejpam-5317	217	1	(	(	PUNCT
ejpam-5317	217	2	30	30	NUM
ejpam-5317	217	3	)	)	PUNCT
ejpam-5317	217	4	from	from	ADP
ejpam-5317	217	5	lemma	lemma	PROPN
ejpam-5317	217	6	1	1	NUM
ejpam-5317	217	7	,	,	PUNCT
ejpam-5317	217	8	equation	equation	NOUN
ejpam-5317	217	9	(	(	PUNCT
ejpam-5317	217	10	13	13	NUM
ejpam-5317	217	11	)	)	PUNCT
ejpam-5317	217	12	,	,	PUNCT
ejpam-5317	217	13	equation	equation	NOUN
ejpam-5317	217	14	(	(	PUNCT
ejpam-5317	217	15	12	12	NUM
ejpam-5317	217	16	)	)	PUNCT
ejpam-5317	217	17	,	,	PUNCT
ejpam-5317	217	18	and	and	CCONJ
ejpam-5317	217	19	equation	equation	NOUN
ejpam-5317	217	20	(	(	PUNCT
ejpam-5317	217	21	30	30	NUM
ejpam-5317	217	22	)	)	PUNCT
ejpam-5317	217	23	,	,	PUNCT
ejpam-5317	217	24	we	we	PRON
ejpam-5317	217	25	get	get	VERB
ejpam-5317	217	26	a1	a1	NOUN
ejpam-5317	217	27	=	=	NOUN
ejpam-5317	217	28	a2	a2	PROPN
ejpam-5317	217	29	=	=	SYM
ejpam-5317	217	30	·	·	PUNCT
ejpam-5317	217	31	·	·	PUNCT
ejpam-5317	217	32	·	·	PUNCT
ejpam-5317	218	1	=	=	PUNCT
ejpam-5317	218	2	as	as	ADP
ejpam-5317	218	3	=	=	PROPN
ejpam-5317	218	4	0	0	PROPN
ejpam-5317	218	5	,	,	PUNCT
ejpam-5317	218	6	b∗1	b∗1	NOUN
ejpam-5317	218	7	=	=	SYM
ejpam-5317	218	8	b∗2	b∗2	NOUN
ejpam-5317	218	9	=	=	SYM
ejpam-5317	218	10	·	·	PUNCT
ejpam-5317	218	11	·	·	PUNCT
ejpam-5317	218	12	·	·	PUNCT
ejpam-5317	218	13	=	=	PUNCT
ejpam-5317	218	14	b∗s−4	b∗s−4	X
ejpam-5317	218	15	=	=	SYM
ejpam-5317	218	16	0	0	NUM
ejpam-5317	218	17	,	,	PUNCT
ejpam-5317	218	18	c∗1	c∗1	ADJ
ejpam-5317	218	19	=	=	SYM
ejpam-5317	218	20	c∗2	c∗2	NOUN
ejpam-5317	218	21	=	=	PUNCT
ejpam-5317	218	22	·	·	PUNCT
ejpam-5317	218	23	·	·	PUNCT
ejpam-5317	218	24	·	·	PUNCT
ejpam-5317	219	1	=	=	SYM
ejpam-5317	219	2	c∗s−4	c∗s−4	PROPN
ejpam-5317	219	3	=	=	SYM
ejpam-5317	219	4	0	0	NUM
ejpam-5317	219	5	,	,	PUNCT
ejpam-5317	219	6	and	and	CCONJ
ejpam-5317	219	7	d∗1	d∗1	NOUN
ejpam-5317	219	8	=	=	SYM
ejpam-5317	219	9	d∗2	d∗2	NOUN
ejpam-5317	219	10	=	=	SYM
ejpam-5317	219	11	·	·	PUNCT
ejpam-5317	219	12	·	·	PUNCT
ejpam-5317	219	13	·	·	PUNCT
ejpam-5317	219	14	=	=	SYM
ejpam-5317	219	15	d∗s−4	d∗s−4	NOUN
ejpam-5317	219	16	=	=	SYM
ejpam-5317	219	17	0	0	NUM
ejpam-5317	219	18	.	.	PUNCT
ejpam-5317	220	1	thus	thus	ADV
ejpam-5317	220	2	,	,	PUNCT
ejpam-5317	220	3	from	from	ADP
ejpam-5317	220	4	equations	equation	NOUN
ejpam-5317	220	5	(	(	PUNCT
ejpam-5317	220	6	4	4	NUM
ejpam-5317	220	7	)	)	PUNCT
ejpam-5317	220	8	and	and	CCONJ
ejpam-5317	220	9	(	(	PUNCT
ejpam-5317	220	10	7	7	NUM
ejpam-5317	220	11	)	)	PUNCT
ejpam-5317	220	12	,	,	PUNCT
ejpam-5317	220	13	we	we	PRON
ejpam-5317	220	14	get	get	VERB
ejpam-5317	220	15	4∑	4∑	NOUN
ejpam-5317	220	16	j=1	j=1	NOUN
ejpam-5317	220	17	bj	bj	NOUN
ejpam-5317	220	18	=	=	SYM
ejpam-5317	220	19	4∑	4∑	NUM
ejpam-5317	220	20	j=1	j=1	NOUN
ejpam-5317	220	21	cj	cj	NOUN
ejpam-5317	221	1	=	=	SYM
ejpam-5317	221	2	4∑	4∑	NUM
ejpam-5317	221	3	j=1	j=1	NOUN
ejpam-5317	221	4	dj	dj	X
ejpam-5317	221	5	=	=	SYM
ejpam-5317	221	6	0	0	PROPN
ejpam-5317	221	7	.	.	PUNCT
ejpam-5317	222	1	under	under	ADP
ejpam-5317	222	2	these	these	DET
ejpam-5317	222	3	conditions	condition	NOUN
ejpam-5317	222	4	,	,	PUNCT
ejpam-5317	222	5	the	the	DET
ejpam-5317	222	6	vector	vector	NOUN
ejpam-5317	222	7	x	x	PUNCT
ejpam-5317	222	8	that	that	PRON
ejpam-5317	222	9	has	have	VERB
ejpam-5317	222	10	the	the	DET
ejpam-5317	222	11	entries	entry	NOUN
ejpam-5317	222	12	(	(	PUNCT
ejpam-5317	222	13	x)i	x)i	PUNCT
ejpam-5317	222	14	=	=	PUNCT
ejpam-5317	222	15			PROPN
ejpam-5317	222	16	0	0	NUM
ejpam-5317	222	17	,	,	PUNCT
ejpam-5317	222	18	if	if	SCONJ
ejpam-5317	222	19	i	i	PRON
ejpam-5317	222	20	=	=	NOUN
ejpam-5317	222	21	1	1	NUM
ejpam-5317	222	22	,	,	PUNCT
ejpam-5317	222	23	2	2	NUM
ejpam-5317	222	24	,	,	PUNCT
ejpam-5317	222	25	.	.	PUNCT
ejpam-5317	222	26	.	.	PUNCT
ejpam-5317	223	1	.	.	PUNCT
ejpam-5317	224	1	,	,	PUNCT
ejpam-5317	224	2	s	s	X
ejpam-5317	224	3	,	,	PUNCT
ejpam-5317	224	4	bi	bi	NOUN
ejpam-5317	224	5	,	,	PUNCT
ejpam-5317	224	6	if	if	SCONJ
ejpam-5317	224	7	i	i	PRON
ejpam-5317	224	8	=	=	SYM
ejpam-5317	224	9	s	s	X
ejpam-5317	225	1	+	+	ADJ
ejpam-5317	225	2	1	1	NUM
ejpam-5317	225	3	,	,	PUNCT
ejpam-5317	225	4	s	s	PART
ejpam-5317	225	5	+	+	ADJ
ejpam-5317	225	6	2	2	NUM
ejpam-5317	225	7	,	,	PUNCT
ejpam-5317	225	8	.	.	PUNCT
ejpam-5317	225	9	.	.	PUNCT
ejpam-5317	226	1	.	.	PUNCT
ejpam-5317	227	1	,	,	PUNCT
ejpam-5317	227	2	s	s	PART
ejpam-5317	227	3	+	+	ADJ
ejpam-5317	227	4	4	4	NUM
ejpam-5317	227	5	,	,	PUNCT
ejpam-5317	227	6	0	0	NUM
ejpam-5317	227	7	,	,	PUNCT
ejpam-5317	227	8	if	if	SCONJ
ejpam-5317	227	9	i	i	PRON
ejpam-5317	227	10	=	=	SYM
ejpam-5317	227	11	s	s	PART
ejpam-5317	228	1	+	+	NOUN
ejpam-5317	228	2	5	5	NUM
ejpam-5317	228	3	,	,	PUNCT
ejpam-5317	228	4	s	s	PART
ejpam-5317	228	5	+	+	NOUN
ejpam-5317	228	6	6	6	NUM
ejpam-5317	228	7	,	,	PUNCT
ejpam-5317	228	8	.	.	PUNCT
ejpam-5317	228	9	.	.	PUNCT
ejpam-5317	229	1	.	.	PUNCT
ejpam-5317	230	1	,	,	PUNCT
ejpam-5317	230	2	2s	2s	X
ejpam-5317	230	3	,	,	PUNCT
ejpam-5317	230	4	ci	ci	NOUN
ejpam-5317	230	5	,	,	PUNCT
ejpam-5317	230	6	if	if	SCONJ
ejpam-5317	230	7	i	i	PRON
ejpam-5317	230	8	=	=	PUNCT
ejpam-5317	231	1	2s	2s	NUM
ejpam-5317	232	1	+	+	NOUN
ejpam-5317	232	2	1	1	NUM
ejpam-5317	232	3	,	,	PUNCT
ejpam-5317	232	4	2s	2s	PROPN
ejpam-5317	232	5	+	+	NOUN
ejpam-5317	232	6	2	2	NUM
ejpam-5317	232	7	,	,	PUNCT
ejpam-5317	232	8	.	.	PUNCT
ejpam-5317	232	9	.	.	PUNCT
ejpam-5317	233	1	.	.	PUNCT
ejpam-5317	234	1	,	,	PUNCT
ejpam-5317	235	1	2s	2s	PROPN
ejpam-5317	235	2	+	+	ADJ
ejpam-5317	235	3	4	4	NUM
ejpam-5317	235	4	,	,	PUNCT
ejpam-5317	235	5	0	0	NUM
ejpam-5317	235	6	,	,	PUNCT
ejpam-5317	235	7	if	if	SCONJ
ejpam-5317	235	8	i	i	PRON
ejpam-5317	235	9	=	=	PUNCT
ejpam-5317	236	1	2s	2s	NUM
ejpam-5317	237	1	+	+	NOUN
ejpam-5317	237	2	5	5	NUM
ejpam-5317	237	3	,	,	PUNCT
ejpam-5317	237	4	2s	2s	PROPN
ejpam-5317	237	5	+	+	NOUN
ejpam-5317	237	6	6	6	NUM
ejpam-5317	237	7	,	,	PUNCT
ejpam-5317	237	8	.	.	PUNCT
ejpam-5317	237	9	.	.	PUNCT
ejpam-5317	238	1	.	.	PUNCT
ejpam-5317	239	1	,	,	PUNCT
ejpam-5317	239	2	3s	3s	NUM
ejpam-5317	239	3	,	,	PUNCT
ejpam-5317	239	4	di	di	NOUN
ejpam-5317	239	5	,	,	PUNCT
ejpam-5317	239	6	if	if	SCONJ
ejpam-5317	239	7	i	i	PRON
ejpam-5317	239	8	=	=	SYM
ejpam-5317	239	9	3s	3s	NUM
ejpam-5317	239	10	+	+	CCONJ
ejpam-5317	239	11	1	1	NUM
ejpam-5317	239	12	,	,	PUNCT
ejpam-5317	239	13	3s	3s	NUM
ejpam-5317	239	14	+	+	CCONJ
ejpam-5317	239	15	2	2	NUM
ejpam-5317	239	16	,	,	PUNCT
ejpam-5317	239	17	.	.	PUNCT
ejpam-5317	239	18	.	.	PUNCT
ejpam-5317	239	19	.	.	PUNCT
ejpam-5317	240	1	,	,	PUNCT
ejpam-5317	240	2	3s	3s	NUM
ejpam-5317	240	3	+	+	CCONJ
ejpam-5317	240	4	4	4	NUM
ejpam-5317	240	5	,	,	PUNCT
ejpam-5317	240	6	0	0	NUM
ejpam-5317	240	7	,	,	PUNCT
ejpam-5317	240	8	if	if	SCONJ
ejpam-5317	240	9	i	i	PRON
ejpam-5317	240	10	=	=	SYM
ejpam-5317	240	11	3s	3s	NUM
ejpam-5317	240	12	+	+	CCONJ
ejpam-5317	240	13	5	5	NUM
ejpam-5317	240	14	,	,	PUNCT
ejpam-5317	240	15	3s	3s	NUM
ejpam-5317	240	16	+	+	CCONJ
ejpam-5317	240	17	6	6	NUM
ejpam-5317	240	18	,	,	PUNCT
ejpam-5317	240	19	.	.	PUNCT
ejpam-5317	240	20	.	.	PUNCT
ejpam-5317	240	21	.	.	PUNCT
ejpam-5317	241	1	,	,	PUNCT
ejpam-5317	241	2	4s	4s	NUM
ejpam-5317	241	3	.	.	PUNCT
ejpam-5317	242	1	(	(	PUNCT
ejpam-5317	242	2	31	31	NUM
ejpam-5317	242	3	)	)	PUNCT
ejpam-5317	242	4	such	such	ADJ
ejpam-5317	242	5	that	that	SCONJ
ejpam-5317	242	6	∑4	∑4	PROPN
ejpam-5317	242	7	j=1	j=1	NOUN
ejpam-5317	242	8	bj	bj	VERB
ejpam-5317	242	9	=	=	SYM
ejpam-5317	242	10	∑4	∑4	PROPN
ejpam-5317	243	1	j=1	j=1	NOUN
ejpam-5317	243	2	cj	cj	VERB
ejpam-5317	244	1	=	=	SYM
ejpam-5317	244	2	∑4	∑4	PROPN
ejpam-5317	244	3	j=1	j=1	NOUN
ejpam-5317	244	4	dj	dj	PROPN
ejpam-5317	245	1	=	=	SYM
ejpam-5317	245	2	0	0	NUM
ejpam-5317	245	3	is	be	AUX
ejpam-5317	245	4	the	the	DET
ejpam-5317	245	5	corresponding	corresponding	ADJ
ejpam-5317	245	6	eigenvector	eigenvector	NOUN
ejpam-5317	245	7	for	for	ADP
ejpam-5317	245	8	the	the	DET
ejpam-5317	245	9	eigenvalue	eigenvalue	PROPN
ejpam-5317	245	10	λ	λ	PROPN
ejpam-5317	245	11	=	=	SYM
ejpam-5317	245	12	0	0	NUM
ejpam-5317	245	13	of	of	ADP
ejpam-5317	245	14	a.	a.	NOUN
ejpam-5317	245	15	thus	thus	ADV
ejpam-5317	245	16	,	,	PUNCT
ejpam-5317	245	17	λ	λ	PROPN
ejpam-5317	245	18	=	=	SYM
ejpam-5317	245	19	0	0	NUM
ejpam-5317	245	20	is	be	AUX
ejpam-5317	245	21	an	an	DET
ejpam-5317	245	22	eigenvalue	eigenvalue	NOUN
ejpam-5317	245	23	of	of	ADP
ejpam-5317	245	24	the	the	DET
ejpam-5317	245	25	matrix	matrix	NOUN
ejpam-5317	245	26	a	a	PRON
ejpam-5317	245	27	with	with	ADP
ejpam-5317	245	28	multiplicity	multiplicity	NOUN
ejpam-5317	245	29	is	be	AUX
ejpam-5317	245	30	greater	great	ADJ
ejpam-5317	245	31	than	than	ADP
ejpam-5317	245	32	or	or	CCONJ
ejpam-5317	245	33	equal	equal	ADJ
ejpam-5317	245	34	to	to	ADP
ejpam-5317	245	35	9	9	NUM
ejpam-5317	245	36	.	.	PUNCT
ejpam-5317	245	37	corollary	corollary	ADJ
ejpam-5317	245	38	2	2	NUM
ejpam-5317	245	39	.	.	PUNCT
ejpam-5317	246	1	the	the	DET
ejpam-5317	246	2	roots	root	NOUN
ejpam-5317	246	3	of	of	ADP
ejpam-5317	246	4	the	the	DET
ejpam-5317	246	5	quadratic	quadratic	ADJ
ejpam-5317	246	6	polynomial	polynomial	ADJ
ejpam-5317	246	7	x2	x2	PROPN
ejpam-5317	247	1	+	+	CCONJ
ejpam-5317	247	2	2x	2x	NUM
ejpam-5317	247	3	−	−	NOUN
ejpam-5317	247	4	1	1	NUM
ejpam-5317	247	5	=	=	SYM
ejpam-5317	247	6	0	0	NUM
ejpam-5317	247	7	are	be	AUX
ejpam-5317	247	8	eigenvalues	eigenvalue	NOUN
ejpam-5317	247	9	of	of	ADP
ejpam-5317	247	10	the	the	DET
ejpam-5317	247	11	matrix	matrix	NOUN
ejpam-5317	247	12	a	a	PRON
ejpam-5317	247	13	with	with	ADP
ejpam-5317	247	14	multiplicity	multiplicity	NOUN
ejpam-5317	247	15	is	be	AUX
ejpam-5317	247	16	greater	great	ADJ
ejpam-5317	247	17	than	than	ADP
ejpam-5317	247	18	or	or	CCONJ
ejpam-5317	247	19	equal	equal	ADJ
ejpam-5317	247	20	to	to	ADP
ejpam-5317	247	21	s−4	s−4	PROPN
ejpam-5317	247	22	2	2	NUM
ejpam-5317	247	23	.	.	PUNCT
ejpam-5317	248	1	proof	proof	NOUN
ejpam-5317	248	2	.	.	PUNCT
ejpam-5317	249	1	if	if	SCONJ
ejpam-5317	249	2	λ	λ	X
ejpam-5317	249	3	=	=	PUNCT
ejpam-5317	249	4	−1±	−1±	NOUN
ejpam-5317	249	5	√	√	NUM
ejpam-5317	249	6	2	2	NUM
ejpam-5317	249	7	are	be	AUX
ejpam-5317	249	8	the	the	DET
ejpam-5317	249	9	roots	root	NOUN
ejpam-5317	249	10	of	of	ADP
ejpam-5317	249	11	the	the	DET
ejpam-5317	249	12	quadratic	quadratic	ADJ
ejpam-5317	249	13	equation	equation	NOUN
ejpam-5317	249	14	x2	x2	PROPN
ejpam-5317	249	15	+	+	NOUN
ejpam-5317	249	16	2x−1	2x−1	NUM
ejpam-5317	249	17	=	=	SYM
ejpam-5317	249	18	0	0	NUM
ejpam-5317	249	19	,	,	PUNCT
ejpam-5317	249	20	then	then	ADV
ejpam-5317	249	21	from	from	ADP
ejpam-5317	249	22	equation	equation	NOUN
ejpam-5317	249	23	(	(	PUNCT
ejpam-5317	249	24	18	18	NUM
ejpam-5317	249	25	)	)	PUNCT
ejpam-5317	249	26	,	,	PUNCT
ejpam-5317	249	27	remark	remark	VERB
ejpam-5317	249	28	1	1	NUM
ejpam-5317	249	29	and	and	CCONJ
ejpam-5317	249	30	lemma	lemma	PROPN
ejpam-5317	249	31	1	1	NUM
ejpam-5317	249	32	,	,	PUNCT
ejpam-5317	249	33	we	we	PRON
ejpam-5317	249	34	get	get	VERB
ejpam-5317	249	35	d∗k	d∗k	PUNCT
ejpam-5317	249	36	=	=	SYM
ejpam-5317	249	37	−d∗k+1	−d∗k+1	NOUN
ejpam-5317	249	38	for	for	ADP
ejpam-5317	249	39	all	all	PRON
ejpam-5317	249	40	k	k	NOUN
ejpam-5317	249	41	=	=	SYM
ejpam-5317	249	42	1	1	NUM
ejpam-5317	249	43	,	,	PUNCT
ejpam-5317	249	44	3	3	NUM
ejpam-5317	249	45	,	,	PUNCT
ejpam-5317	249	46	.	.	PUNCT
ejpam-5317	249	47	.	.	PUNCT
ejpam-5317	249	48	.	.	PUNCT
ejpam-5317	250	1	s−5	s−5	X
ejpam-5317	250	2	.	.	PUNCT
ejpam-5317	251	1	then	then	ADV
ejpam-5317	251	2	,	,	PUNCT
ejpam-5317	251	3	if	if	SCONJ
ejpam-5317	251	4	we	we	PRON
ejpam-5317	251	5	add	add	VERB
ejpam-5317	251	6	equation	equation	NOUN
ejpam-5317	251	7	(	(	PUNCT
ejpam-5317	251	8	5	5	NUM
ejpam-5317	251	9	)	)	PUNCT
ejpam-5317	251	10	to	to	ADP
ejpam-5317	251	11	(	(	PUNCT
ejpam-5317	251	12	6	6	NUM
ejpam-5317	251	13	)	)	PUNCT
ejpam-5317	251	14	and	and	CCONJ
ejpam-5317	251	15	equation	equation	NOUN
ejpam-5317	251	16	(	(	PUNCT
ejpam-5317	251	17	7	7	NUM
ejpam-5317	251	18	)	)	PUNCT
ejpam-5317	251	19	to	to	ADP
ejpam-5317	251	20	(	(	PUNCT
ejpam-5317	251	21	8)	8)	NUM
ejpam-5317	251	22	,	,	PUNCT
ejpam-5317	251	23	we	we	PRON
ejpam-5317	251	24	get	get	VERB
ejpam-5317	251	25	b∗k	b∗k	NOUN
ejpam-5317	251	26	=	=	SYM
ejpam-5317	251	27	−b∗k+1	−b∗k+1	NOUN
ejpam-5317	251	28	and	and	CCONJ
ejpam-5317	251	29	c∗k	c∗k	NOUN
ejpam-5317	251	30	=	=	SYM
ejpam-5317	251	31	−c∗k+1	−c∗k+1	X
ejpam-5317	251	32	,	,	PUNCT
ejpam-5317	251	33	respectively	respectively	ADV
ejpam-5317	251	34	,	,	PUNCT
ejpam-5317	251	35	for	for	ADP
ejpam-5317	251	36	all	all	PRON
ejpam-5317	251	37	k	k	NOUN
ejpam-5317	251	38	=	=	SYM
ejpam-5317	251	39	1	1	NUM
ejpam-5317	251	40	,	,	PUNCT
ejpam-5317	251	41	3	3	NUM
ejpam-5317	251	42	,	,	PUNCT
ejpam-5317	251	43	.	.	PUNCT
ejpam-5317	251	44	.	.	PUNCT
ejpam-5317	252	1	.	.	PUNCT
ejpam-5317	253	1	s−5	s−5	INTJ
ejpam-5317	253	2	and	and	CCONJ
ejpam-5317	253	3	so	so	ADV
ejpam-5317	253	4	∑s−4	∑s−4	VERB
ejpam-5317	253	5	i=1	i=1	PROPN
ejpam-5317	254	1	b	b	NOUN
ejpam-5317	254	2	∗	∗	NOUN
ejpam-5317	255	1	i	i	PRON
ejpam-5317	255	2	=	=	PUNCT
ejpam-5317	256	1	∑s−4	∑s−4	VERB
ejpam-5317	257	1	i=1	i=1	PROPN
ejpam-5317	257	2	c	c	NOUN
ejpam-5317	257	3	∗	∗	NOUN
ejpam-5317	257	4	i	i	PRON
ejpam-5317	257	5	=	=	NOUN
ejpam-5317	257	6	0	0	NUM
ejpam-5317	257	7	.	.	PUNCT
ejpam-5317	258	1	thus	thus	ADV
ejpam-5317	258	2	,	,	PUNCT
ejpam-5317	258	3	from	from	ADP
ejpam-5317	258	4	equations	equation	NOUN
ejpam-5317	258	5	(	(	PUNCT
ejpam-5317	258	6	4	4	NUM
ejpam-5317	258	7	)	)	PUNCT
ejpam-5317	258	8	and	and	CCONJ
ejpam-5317	258	9	(	(	PUNCT
ejpam-5317	258	10	7	7	NUM
ejpam-5317	258	11	)	)	PUNCT
ejpam-5317	258	12	,	,	PUNCT
ejpam-5317	258	13	we	we	PRON
ejpam-5317	258	14	obtain	obtain	VERB
ejpam-5317	258	15	b	b	X
ejpam-5317	258	16	=	=	SYM
ejpam-5317	258	17	c	c	NOUN
ejpam-5317	258	18	=	=	SYM
ejpam-5317	258	19	0	0	PROPN
ejpam-5317	258	20	.	.	PUNCT
ejpam-5317	258	21	from	from	ADP
ejpam-5317	258	22	equation	equation	NOUN
ejpam-5317	258	23	(	(	PUNCT
ejpam-5317	258	24	23	23	NUM
ejpam-5317	258	25	)	)	PUNCT
ejpam-5317	258	26	,	,	PUNCT
ejpam-5317	258	27	we	we	PRON
ejpam-5317	258	28	get	get	VERB
ejpam-5317	258	29	b∗k	b∗k	NOUN
ejpam-5317	258	30	=	=	SYM
ejpam-5317	258	31	c∗k	c∗k	NOUN
ejpam-5317	258	32	and	and	CCONJ
ejpam-5317	258	33	d∗i	d∗i	NOUN
ejpam-5317	258	34	=	=	SYM
ejpam-5317	258	35	(	(	PUNCT
ejpam-5317	258	36	λ	λ	PROPN
ejpam-5317	258	37	+	+	CCONJ
ejpam-5317	258	38	1)b∗i	1)b∗i	NUM
ejpam-5317	258	39	e.	e.	PROPN
ejpam-5317	258	40	rawaswhdeh	rawaswhdeh	PROPN
ejpam-5317	258	41	,	,	PUNCT
ejpam-5317	258	42	h.	h.	PROPN
ejpam-5317	258	43	adel	adel	PROPN
ejpam-5317	258	44	abdelkarim	abdelkarim	PROPN
ejpam-5317	258	45	,	,	PUNCT
ejpam-5317	258	46	e.	e.	PROPN
ejpam-5317	258	47	rawshdeh	rawshdeh	PROPN
ejpam-5317	258	48	/	/	SYM
ejpam-5317	258	49	eur	eur	PROPN
ejpam-5317	258	50	.	.	PUNCT
ejpam-5317	259	1	j.	j.	PROPN
ejpam-5317	259	2	pure	pure	PROPN
ejpam-5317	259	3	appl	appl	PROPN
ejpam-5317	259	4	.	.	PROPN
ejpam-5317	259	5	math	math	PROPN
ejpam-5317	259	6	,	,	PUNCT
ejpam-5317	259	7	17	17	NUM
ejpam-5317	259	8	(	(	PUNCT
ejpam-5317	259	9	4	4	NUM
ejpam-5317	259	10	)	)	PUNCT
ejpam-5317	259	11	(	(	PUNCT
ejpam-5317	259	12	2024	2024	NUM
ejpam-5317	259	13	)	)	PUNCT
ejpam-5317	259	14	,	,	PUNCT
ejpam-5317	259	15	2550	2550	NUM
ejpam-5317	259	16	-	-	SYM
ejpam-5317	259	17	2561	2561	NUM
ejpam-5317	259	18	2557	2557	NUM
ejpam-5317	259	19	for	for	ADP
ejpam-5317	259	20	all	all	PRON
ejpam-5317	259	21	k	k	NOUN
ejpam-5317	259	22	=	=	SYM
ejpam-5317	259	23	1	1	NUM
ejpam-5317	259	24	,	,	PUNCT
ejpam-5317	259	25	2	2	NUM
ejpam-5317	259	26	,	,	PUNCT
ejpam-5317	259	27	.	.	PUNCT
ejpam-5317	259	28	.	.	PUNCT
ejpam-5317	260	1	.	.	PUNCT
ejpam-5317	261	1	,	,	PUNCT
ejpam-5317	261	2	s−	s−	PROPN
ejpam-5317	261	3	5	5	NUM
ejpam-5317	261	4	.	.	PUNCT
ejpam-5317	262	1	hence	hence	ADV
ejpam-5317	262	2	,	,	PUNCT
ejpam-5317	262	3	one	one	PRON
ejpam-5317	262	4	can	can	AUX
ejpam-5317	262	5	show	show	VERB
ejpam-5317	262	6	that	that	SCONJ
ejpam-5317	262	7	the	the	DET
ejpam-5317	262	8	vector	vector	NOUN
ejpam-5317	262	9	x	x	PUNCT
ejpam-5317	262	10	with	with	ADP
ejpam-5317	262	11	entries	entry	NOUN
ejpam-5317	262	12	(	(	PUNCT
ejpam-5317	262	13	x)i	x)i	PUNCT
ejpam-5317	262	14	=	=	PUNCT
ejpam-5317	262	15			PROPN
ejpam-5317	262	16	0	0	NUM
ejpam-5317	262	17	,	,	PUNCT
ejpam-5317	262	18	if	if	SCONJ
ejpam-5317	262	19	i	i	PRON
ejpam-5317	262	20	=	=	NOUN
ejpam-5317	262	21	1	1	NUM
ejpam-5317	262	22	,	,	PUNCT
ejpam-5317	262	23	2	2	NUM
ejpam-5317	262	24	,	,	PUNCT
ejpam-5317	262	25	.	.	PUNCT
ejpam-5317	262	26	.	.	PUNCT
ejpam-5317	262	27	.	.	PUNCT
ejpam-5317	263	1	,	,	PUNCT
ejpam-5317	263	2	s	s	X
ejpam-5317	263	3	,	,	PUNCT
ejpam-5317	263	4	0	0	NUM
ejpam-5317	263	5	,	,	PUNCT
ejpam-5317	263	6	if	if	SCONJ
ejpam-5317	263	7	i	i	PRON
ejpam-5317	263	8	=	=	SYM
ejpam-5317	263	9	s	s	X
ejpam-5317	264	1	+	+	ADJ
ejpam-5317	264	2	1	1	NUM
ejpam-5317	264	3	,	,	PUNCT
ejpam-5317	264	4	s	s	PART
ejpam-5317	264	5	+	+	ADJ
ejpam-5317	264	6	2	2	NUM
ejpam-5317	264	7	,	,	PUNCT
ejpam-5317	264	8	.	.	PUNCT
ejpam-5317	264	9	.	.	PUNCT
ejpam-5317	265	1	.	.	PUNCT
ejpam-5317	266	1	,	,	PUNCT
ejpam-5317	266	2	s	s	PART
ejpam-5317	266	3	+	+	ADJ
ejpam-5317	266	4	4	4	NUM
ejpam-5317	266	5	,	,	PUNCT
ejpam-5317	266	6	b∗i−s−4	b∗i−s−4	ADJ
ejpam-5317	266	7	,	,	PUNCT
ejpam-5317	266	8	if	if	SCONJ
ejpam-5317	266	9	i	i	PRON
ejpam-5317	266	10	=	=	SYM
ejpam-5317	266	11	s	s	PART
ejpam-5317	267	1	+	+	NOUN
ejpam-5317	267	2	5	5	NUM
ejpam-5317	267	3	,	,	PUNCT
ejpam-5317	267	4	s	s	PART
ejpam-5317	267	5	+	+	NOUN
ejpam-5317	267	6	6	6	NUM
ejpam-5317	267	7	,	,	PUNCT
ejpam-5317	267	8	.	.	PUNCT
ejpam-5317	267	9	.	.	PUNCT
ejpam-5317	268	1	.	.	PUNCT
ejpam-5317	269	1	,	,	PUNCT
ejpam-5317	269	2	2s	2s	X
ejpam-5317	269	3	,	,	PUNCT
ejpam-5317	269	4	0	0	NUM
ejpam-5317	269	5	,	,	PUNCT
ejpam-5317	269	6	if	if	SCONJ
ejpam-5317	269	7	i	i	PRON
ejpam-5317	269	8	=	=	PUNCT
ejpam-5317	270	1	2s	2s	NUM
ejpam-5317	271	1	+	+	NOUN
ejpam-5317	271	2	1	1	NUM
ejpam-5317	271	3	,	,	PUNCT
ejpam-5317	271	4	2s	2s	PROPN
ejpam-5317	271	5	+	+	NOUN
ejpam-5317	271	6	2	2	NUM
ejpam-5317	271	7	,	,	PUNCT
ejpam-5317	271	8	.	.	PUNCT
ejpam-5317	271	9	.	.	PUNCT
ejpam-5317	272	1	.	.	PUNCT
ejpam-5317	273	1	,	,	PUNCT
ejpam-5317	274	1	2s	2s	PROPN
ejpam-5317	274	2	+	+	CCONJ
ejpam-5317	274	3	4	4	NUM
ejpam-5317	274	4	,	,	PUNCT
ejpam-5317	274	5	b∗i−2s−4	b∗i−2s−4	NOUN
ejpam-5317	274	6	,	,	PUNCT
ejpam-5317	274	7	if	if	SCONJ
ejpam-5317	274	8	i	i	PRON
ejpam-5317	274	9	=	=	PUNCT
ejpam-5317	275	1	2s	2s	NUM
ejpam-5317	276	1	+	+	NOUN
ejpam-5317	276	2	5	5	NUM
ejpam-5317	276	3	,	,	PUNCT
ejpam-5317	276	4	2s	2s	PROPN
ejpam-5317	276	5	+	+	NOUN
ejpam-5317	276	6	6	6	NUM
ejpam-5317	276	7	,	,	PUNCT
ejpam-5317	276	8	.	.	PUNCT
ejpam-5317	276	9	.	.	PUNCT
ejpam-5317	277	1	.	.	PUNCT
ejpam-5317	278	1	,	,	PUNCT
ejpam-5317	278	2	3s	3s	NUM
ejpam-5317	278	3	,	,	PUNCT
ejpam-5317	278	4	0	0	NUM
ejpam-5317	278	5	,	,	PUNCT
ejpam-5317	278	6	if	if	SCONJ
ejpam-5317	278	7	i	i	PRON
ejpam-5317	278	8	=	=	SYM
ejpam-5317	278	9	3s	3s	NUM
ejpam-5317	278	10	+	+	CCONJ
ejpam-5317	278	11	1	1	NUM
ejpam-5317	278	12	,	,	PUNCT
ejpam-5317	278	13	3s	3s	NUM
ejpam-5317	278	14	+	+	CCONJ
ejpam-5317	278	15	2	2	NUM
ejpam-5317	278	16	,	,	PUNCT
ejpam-5317	278	17	.	.	PUNCT
ejpam-5317	278	18	.	.	PUNCT
ejpam-5317	278	19	.	.	PUNCT
ejpam-5317	279	1	,	,	PUNCT
ejpam-5317	279	2	3s	3s	NUM
ejpam-5317	279	3	+	+	CCONJ
ejpam-5317	279	4	4	4	NUM
ejpam-5317	279	5	,	,	PUNCT
ejpam-5317	279	6	d∗i−2s−4	d∗i−2s−4	ADJ
ejpam-5317	279	7	,	,	PUNCT
ejpam-5317	279	8	if	if	SCONJ
ejpam-5317	279	9	i	i	PRON
ejpam-5317	279	10	=	=	SYM
ejpam-5317	279	11	3s	3s	NUM
ejpam-5317	279	12	+	+	CCONJ
ejpam-5317	279	13	5	5	NUM
ejpam-5317	279	14	,	,	PUNCT
ejpam-5317	279	15	3s	3s	NUM
ejpam-5317	279	16	+	+	CCONJ
ejpam-5317	279	17	6	6	NUM
ejpam-5317	279	18	,	,	PUNCT
ejpam-5317	279	19	.	.	PUNCT
ejpam-5317	279	20	.	.	PUNCT
ejpam-5317	279	21	.	.	PUNCT
ejpam-5317	280	1	,	,	PUNCT
ejpam-5317	280	2	4s	4s	NUM
ejpam-5317	280	3	.	.	PUNCT
ejpam-5317	281	1	(	(	PUNCT
ejpam-5317	281	2	32	32	NUM
ejpam-5317	281	3	)	)	PUNCT
ejpam-5317	281	4	such	such	ADJ
ejpam-5317	281	5	that	that	SCONJ
ejpam-5317	281	6	b∗k	b∗k	NOUN
ejpam-5317	281	7	=	=	SYM
ejpam-5317	281	8	−b∗k+1	−b∗k+1	NOUN
ejpam-5317	281	9	for	for	ADP
ejpam-5317	281	10	all	all	PRON
ejpam-5317	281	11	k	k	NOUN
ejpam-5317	281	12	=	=	SYM
ejpam-5317	281	13	1	1	NUM
ejpam-5317	281	14	,	,	PUNCT
ejpam-5317	281	15	3	3	NUM
ejpam-5317	281	16	,	,	PUNCT
ejpam-5317	281	17	.	.	PUNCT
ejpam-5317	281	18	.	.	PUNCT
ejpam-5317	281	19	.	.	PUNCT
ejpam-5317	282	1	s−	s−	PROPN
ejpam-5317	282	2	5	5	NUM
ejpam-5317	282	3	and	and	CCONJ
ejpam-5317	282	4	d∗i	d∗i	NOUN
ejpam-5317	282	5	=	=	SYM
ejpam-5317	282	6	(	(	PUNCT
ejpam-5317	282	7	λ	λ	X
ejpam-5317	282	8	+	+	X
ejpam-5317	282	9	1)b∗i	1)b∗i	NUM
ejpam-5317	282	10	for	for	ADP
ejpam-5317	282	11	all	all	DET
ejpam-5317	282	12	i	i	PRON
ejpam-5317	282	13	=	=	NOUN
ejpam-5317	282	14	1	1	NUM
ejpam-5317	282	15	,	,	PUNCT
ejpam-5317	282	16	2	2	NUM
ejpam-5317	282	17	,	,	PUNCT
ejpam-5317	282	18	.	.	PUNCT
ejpam-5317	282	19	.	.	PUNCT
ejpam-5317	283	1	.	.	PUNCT
ejpam-5317	284	1	,	,	PUNCT
ejpam-5317	284	2	s−	s−	PROPN
ejpam-5317	284	3	4	4	NUM
ejpam-5317	284	4	is	be	AUX
ejpam-5317	284	5	the	the	DET
ejpam-5317	284	6	corresponding	corresponding	ADJ
ejpam-5317	284	7	eigenvector	eigenvector	NOUN
ejpam-5317	284	8	for	for	ADP
ejpam-5317	284	9	the	the	DET
ejpam-5317	284	10	eigenvalues	eigenvalues	PROPN
ejpam-5317	284	11	λ	λ	NOUN
ejpam-5317	284	12	=	=	SYM
ejpam-5317	284	13	−1	−1	NOUN
ejpam-5317	284	14	±	±	NOUN
ejpam-5317	284	15	√	√	ADV
ejpam-5317	284	16	2	2	NUM
ejpam-5317	284	17	.	.	PUNCT
ejpam-5317	285	1	thus	thus	ADV
ejpam-5317	285	2	,	,	PUNCT
ejpam-5317	285	3	if	if	SCONJ
ejpam-5317	285	4	λ	λ	PROPN
ejpam-5317	285	5	=	=	VERB
ejpam-5317	285	6	−1	−1	NOUN
ejpam-5317	285	7	±	±	NOUN
ejpam-5317	285	8	√	√	ADV
ejpam-5317	285	9	2	2	NUM
ejpam-5317	285	10	,	,	PUNCT
ejpam-5317	285	11	then	then	ADV
ejpam-5317	285	12	they	they	PRON
ejpam-5317	285	13	are	be	AUX
ejpam-5317	285	14	eigenvalues	eigenvalue	NOUN
ejpam-5317	285	15	of	of	ADP
ejpam-5317	285	16	the	the	DET
ejpam-5317	285	17	matrix	matrix	NOUN
ejpam-5317	285	18	a	a	PRON
ejpam-5317	285	19	with	with	ADP
ejpam-5317	285	20	multiplicity	multiplicity	NOUN
ejpam-5317	285	21	is	be	AUX
ejpam-5317	285	22	greater	great	ADJ
ejpam-5317	285	23	than	than	ADP
ejpam-5317	285	24	or	or	CCONJ
ejpam-5317	285	25	equal	equal	ADJ
ejpam-5317	285	26	to	to	ADP
ejpam-5317	285	27	s−4	s−4	PROPN
ejpam-5317	285	28	2	2	NUM
ejpam-5317	285	29	.	.	PUNCT
ejpam-5317	285	30	similar	similar	ADJ
ejpam-5317	285	31	to	to	ADP
ejpam-5317	285	32	corollary	corollary	VERB
ejpam-5317	285	33	2.5	2.5	NUM
ejpam-5317	285	34	,	,	PUNCT
ejpam-5317	285	35	one	one	PRON
ejpam-5317	285	36	can	can	AUX
ejpam-5317	285	37	prove	prove	VERB
ejpam-5317	285	38	that	that	SCONJ
ejpam-5317	285	39	the	the	DET
ejpam-5317	285	40	vector	vector	NOUN
ejpam-5317	285	41	x	x	PUNCT
ejpam-5317	285	42	with	with	ADP
ejpam-5317	285	43	entries	entry	NOUN
ejpam-5317	285	44	(	(	PUNCT
ejpam-5317	285	45	x)i	x)i	PUNCT
ejpam-5317	285	46	=	=	PUNCT
ejpam-5317	285	47			PROPN
ejpam-5317	285	48	0	0	NUM
ejpam-5317	285	49	,	,	PUNCT
ejpam-5317	285	50	if	if	SCONJ
ejpam-5317	285	51	i	i	PRON
ejpam-5317	285	52	=	=	NOUN
ejpam-5317	285	53	1	1	NUM
ejpam-5317	285	54	,	,	PUNCT
ejpam-5317	285	55	2	2	NUM
ejpam-5317	285	56	,	,	PUNCT
ejpam-5317	285	57	.	.	PUNCT
ejpam-5317	285	58	.	.	PUNCT
ejpam-5317	286	1	.	.	PUNCT
ejpam-5317	287	1	,	,	PUNCT
ejpam-5317	287	2	s	s	X
ejpam-5317	287	3	,	,	PUNCT
ejpam-5317	287	4	0	0	NUM
ejpam-5317	287	5	,	,	PUNCT
ejpam-5317	287	6	if	if	SCONJ
ejpam-5317	287	7	i	i	PRON
ejpam-5317	287	8	=	=	SYM
ejpam-5317	287	9	s	s	X
ejpam-5317	288	1	+	+	ADJ
ejpam-5317	288	2	1	1	NUM
ejpam-5317	288	3	,	,	PUNCT
ejpam-5317	288	4	s	s	PART
ejpam-5317	288	5	+	+	ADJ
ejpam-5317	288	6	2	2	NUM
ejpam-5317	288	7	,	,	PUNCT
ejpam-5317	288	8	.	.	PUNCT
ejpam-5317	288	9	.	.	PUNCT
ejpam-5317	289	1	.	.	PUNCT
ejpam-5317	290	1	,	,	PUNCT
ejpam-5317	290	2	s	s	PART
ejpam-5317	290	3	+	+	ADJ
ejpam-5317	290	4	4	4	NUM
ejpam-5317	290	5	,	,	PUNCT
ejpam-5317	290	6	b∗i−s−4	b∗i−s−4	ADJ
ejpam-5317	290	7	,	,	PUNCT
ejpam-5317	290	8	if	if	SCONJ
ejpam-5317	290	9	i	i	PRON
ejpam-5317	290	10	=	=	SYM
ejpam-5317	290	11	s	s	PART
ejpam-5317	291	1	+	+	NOUN
ejpam-5317	291	2	5	5	NUM
ejpam-5317	291	3	,	,	PUNCT
ejpam-5317	291	4	s	s	PART
ejpam-5317	291	5	+	+	NOUN
ejpam-5317	291	6	6	6	NUM
ejpam-5317	291	7	,	,	PUNCT
ejpam-5317	291	8	.	.	PUNCT
ejpam-5317	291	9	.	.	PUNCT
ejpam-5317	292	1	.	.	PUNCT
ejpam-5317	293	1	,	,	PUNCT
ejpam-5317	293	2	2s	2s	X
ejpam-5317	293	3	,	,	PUNCT
ejpam-5317	293	4	0	0	NUM
ejpam-5317	293	5	,	,	PUNCT
ejpam-5317	293	6	if	if	SCONJ
ejpam-5317	293	7	i	i	PRON
ejpam-5317	293	8	=	=	PUNCT
ejpam-5317	294	1	2s	2s	NUM
ejpam-5317	295	1	+	+	NOUN
ejpam-5317	295	2	1	1	NUM
ejpam-5317	295	3	,	,	PUNCT
ejpam-5317	295	4	2s	2s	PROPN
ejpam-5317	295	5	+	+	NOUN
ejpam-5317	295	6	2	2	NUM
ejpam-5317	295	7	,	,	PUNCT
ejpam-5317	295	8	.	.	PUNCT
ejpam-5317	295	9	.	.	PUNCT
ejpam-5317	296	1	.	.	PUNCT
ejpam-5317	297	1	,	,	PUNCT
ejpam-5317	298	1	2s	2s	PROPN
ejpam-5317	298	2	+	+	CCONJ
ejpam-5317	298	3	4	4	NUM
ejpam-5317	298	4	,	,	PUNCT
ejpam-5317	298	5	b∗i−2s−4	b∗i−2s−4	NOUN
ejpam-5317	298	6	,	,	PUNCT
ejpam-5317	298	7	if	if	SCONJ
ejpam-5317	298	8	i	i	PRON
ejpam-5317	298	9	=	=	PUNCT
ejpam-5317	299	1	2s	2s	NUM
ejpam-5317	300	1	+	+	NOUN
ejpam-5317	300	2	5	5	NUM
ejpam-5317	300	3	,	,	PUNCT
ejpam-5317	300	4	2s	2s	PROPN
ejpam-5317	300	5	+	+	NOUN
ejpam-5317	300	6	6	6	NUM
ejpam-5317	300	7	,	,	PUNCT
ejpam-5317	300	8	.	.	PUNCT
ejpam-5317	300	9	.	.	PUNCT
ejpam-5317	301	1	.	.	PUNCT
ejpam-5317	302	1	,	,	PUNCT
ejpam-5317	302	2	3s	3s	NUM
ejpam-5317	302	3	,	,	PUNCT
ejpam-5317	302	4	0	0	NUM
ejpam-5317	302	5	,	,	PUNCT
ejpam-5317	302	6	if	if	SCONJ
ejpam-5317	302	7	i	i	PRON
ejpam-5317	302	8	=	=	SYM
ejpam-5317	302	9	3s	3s	NUM
ejpam-5317	302	10	+	+	CCONJ
ejpam-5317	302	11	1	1	NUM
ejpam-5317	302	12	,	,	PUNCT
ejpam-5317	302	13	3s	3s	NUM
ejpam-5317	302	14	+	+	CCONJ
ejpam-5317	302	15	2	2	NUM
ejpam-5317	302	16	,	,	PUNCT
ejpam-5317	302	17	.	.	PUNCT
ejpam-5317	302	18	.	.	PUNCT
ejpam-5317	302	19	.	.	PUNCT
ejpam-5317	303	1	,	,	PUNCT
ejpam-5317	303	2	3s	3s	NUM
ejpam-5317	303	3	+	+	CCONJ
ejpam-5317	303	4	4	4	NUM
ejpam-5317	303	5	,	,	PUNCT
ejpam-5317	303	6	d∗i−2s−4	d∗i−2s−4	ADJ
ejpam-5317	303	7	,	,	PUNCT
ejpam-5317	303	8	if	if	SCONJ
ejpam-5317	303	9	i	i	PRON
ejpam-5317	303	10	=	=	SYM
ejpam-5317	303	11	3s	3s	NUM
ejpam-5317	303	12	+	+	CCONJ
ejpam-5317	303	13	5	5	NUM
ejpam-5317	303	14	,	,	PUNCT
ejpam-5317	303	15	3s	3s	NUM
ejpam-5317	303	16	+	+	CCONJ
ejpam-5317	303	17	6	6	NUM
ejpam-5317	303	18	,	,	PUNCT
ejpam-5317	303	19	.	.	PUNCT
ejpam-5317	303	20	.	.	PUNCT
ejpam-5317	303	21	.	.	PUNCT
ejpam-5317	304	1	,	,	PUNCT
ejpam-5317	304	2	4s	4s	NUM
ejpam-5317	304	3	.	.	PUNCT
ejpam-5317	305	1	(	(	PUNCT
ejpam-5317	305	2	33	33	NUM
ejpam-5317	305	3	)	)	PUNCT
ejpam-5317	305	4	with	with	ADP
ejpam-5317	305	5	∑s−4	∑s−4	PROPN
ejpam-5317	305	6	i=1	i=1	PROPN
ejpam-5317	305	7	b	b	PROPN
ejpam-5317	305	8	∗	∗	NOUN
ejpam-5317	305	9	i	i	PRON
ejpam-5317	306	1	=	=	NOUN
ejpam-5317	306	2	0	0	NUM
ejpam-5317	306	3	and	and	CCONJ
ejpam-5317	306	4	b∗k	b∗k	PROPN
ejpam-5317	306	5	=	=	SYM
ejpam-5317	306	6	b∗k+1	b∗k+1	NOUN
ejpam-5317	306	7	for	for	ADP
ejpam-5317	306	8	all	all	PRON
ejpam-5317	306	9	k	k	NOUN
ejpam-5317	306	10	=	=	SYM
ejpam-5317	306	11	1	1	NUM
ejpam-5317	306	12	,	,	PUNCT
ejpam-5317	306	13	3	3	NUM
ejpam-5317	306	14	,	,	PUNCT
ejpam-5317	306	15	.	.	PUNCT
ejpam-5317	306	16	.	.	PUNCT
ejpam-5317	307	1	.	.	PUNCT
ejpam-5317	308	1	s	s	VERB
ejpam-5317	308	2	−	−	PROPN
ejpam-5317	308	3	5	5	NUM
ejpam-5317	308	4	and	and	CCONJ
ejpam-5317	308	5	d∗i	d∗i	NOUN
ejpam-5317	308	6	=	=	SYM
ejpam-5317	308	7	(	(	PUNCT
ejpam-5317	308	8	λ	λ	X
ejpam-5317	308	9	−	−	PROPN
ejpam-5317	308	10	1)b∗i	1)b∗i	NUM
ejpam-5317	308	11	for	for	ADP
ejpam-5317	308	12	all	all	DET
ejpam-5317	308	13	i	i	PRON
ejpam-5317	308	14	=	=	NOUN
ejpam-5317	308	15	1	1	NUM
ejpam-5317	308	16	,	,	PUNCT
ejpam-5317	308	17	2	2	NUM
ejpam-5317	308	18	,	,	PUNCT
ejpam-5317	308	19	.	.	PUNCT
ejpam-5317	308	20	.	.	PUNCT
ejpam-5317	309	1	.	.	PUNCT
ejpam-5317	310	1	,	,	PUNCT
ejpam-5317	310	2	s−	s−	PROPN
ejpam-5317	310	3	4	4	NUM
ejpam-5317	310	4	is	be	AUX
ejpam-5317	310	5	an	an	DET
ejpam-5317	310	6	eigenvector	eigenvector	NOUN
ejpam-5317	310	7	of	of	ADP
ejpam-5317	310	8	a	a	DET
ejpam-5317	310	9	associated	associate	VERB
ejpam-5317	310	10	with	with	ADP
ejpam-5317	310	11	the	the	DET
ejpam-5317	310	12	eigenvalues	eigenvalues	PROPN
ejpam-5317	310	13	λ	λ	NOUN
ejpam-5317	310	14	=	=	SYM
ejpam-5317	310	15	1±	1±	NUM
ejpam-5317	310	16	√	√	NUM
ejpam-5317	310	17	2	2	NUM
ejpam-5317	310	18	which	which	PRON
ejpam-5317	310	19	are	be	AUX
ejpam-5317	310	20	the	the	DET
ejpam-5317	310	21	roots	root	NOUN
ejpam-5317	310	22	of	of	ADP
ejpam-5317	310	23	the	the	DET
ejpam-5317	310	24	equation	equation	NOUN
ejpam-5317	310	25	x2	x2	NOUN
ejpam-5317	311	1	−	−	PROPN
ejpam-5317	312	1	2x−	2x−	NUM
ejpam-5317	312	2	1	1	NUM
ejpam-5317	312	3	=	=	SYM
ejpam-5317	312	4	0	0	NUM
ejpam-5317	312	5	.	.	PUNCT
ejpam-5317	313	1	therefor	therefor	PROPN
ejpam-5317	313	2	,	,	PUNCT
ejpam-5317	313	3	we	we	PRON
ejpam-5317	313	4	have	have	VERB
ejpam-5317	313	5	the	the	DET
ejpam-5317	313	6	following	follow	VERB
ejpam-5317	313	7	result	result	NOUN
ejpam-5317	313	8	.	.	PUNCT
ejpam-5317	314	1	corollary	corollary	ADJ
ejpam-5317	314	2	3	3	NUM
ejpam-5317	314	3	.	.	PUNCT
ejpam-5317	315	1	λ	λ	NOUN
ejpam-5317	315	2	=	=	NOUN
ejpam-5317	316	1	1±	1±	NUM
ejpam-5317	316	2	√	√	NUM
ejpam-5317	316	3	2	2	NUM
ejpam-5317	316	4	are	be	AUX
ejpam-5317	316	5	eigenvalues	eigenvalue	NOUN
ejpam-5317	316	6	of	of	ADP
ejpam-5317	316	7	the	the	DET
ejpam-5317	316	8	matrix	matrix	NOUN
ejpam-5317	316	9	a	a	PRON
ejpam-5317	316	10	with	with	ADP
ejpam-5317	316	11	multiplicity	multiplicity	NOUN
ejpam-5317	316	12	is	be	AUX
ejpam-5317	316	13	greater	great	ADJ
ejpam-5317	316	14	than	than	ADP
ejpam-5317	316	15	or	or	CCONJ
ejpam-5317	316	16	equal	equal	ADJ
ejpam-5317	316	17	to	to	ADP
ejpam-5317	316	18	s−4	s−4	PROPN
ejpam-5317	316	19	2	2	NUM
ejpam-5317	316	20	−	−	PROPN
ejpam-5317	316	21	1	1	NUM
ejpam-5317	316	22	.	.	PUNCT
ejpam-5317	316	23	corollary	corollary	ADJ
ejpam-5317	316	24	4	4	NUM
ejpam-5317	316	25	.	.	PUNCT
ejpam-5317	317	1	the	the	DET
ejpam-5317	317	2	roots	root	NOUN
ejpam-5317	317	3	of	of	ADP
ejpam-5317	317	4	the	the	DET
ejpam-5317	317	5	equation	equation	NOUN
ejpam-5317	317	6	x2	x2	PROPN
ejpam-5317	318	1	+	+	PROPN
ejpam-5317	318	2	(	(	PUNCT
ejpam-5317	318	3	s−1)x−4	s−1)x−4	PROPN
ejpam-5317	318	4	=	=	SYM
ejpam-5317	318	5	0	0	NUM
ejpam-5317	318	6	are	be	AUX
ejpam-5317	318	7	eigenvalues	eigenvalue	NOUN
ejpam-5317	318	8	of	of	ADP
ejpam-5317	318	9	the	the	DET
ejpam-5317	318	10	matrix	matrix	NOUN
ejpam-5317	318	11	a	a	PRON
ejpam-5317	318	12	with	with	ADP
ejpam-5317	318	13	multiplicity	multiplicity	NOUN
ejpam-5317	318	14	is	be	AUX
ejpam-5317	318	15	greater	great	ADJ
ejpam-5317	318	16	than	than	ADP
ejpam-5317	318	17	or	or	CCONJ
ejpam-5317	318	18	equal	equal	ADJ
ejpam-5317	318	19	to	to	ADP
ejpam-5317	318	20	one	one	NUM
ejpam-5317	318	21	.	.	PUNCT
ejpam-5317	319	1	proof	proof	NOUN
ejpam-5317	319	2	.	.	PUNCT
ejpam-5317	320	1	if	if	SCONJ
ejpam-5317	320	2	λ	λ	PROPN
ejpam-5317	320	3	is	be	AUX
ejpam-5317	320	4	a	a	DET
ejpam-5317	320	5	root	root	NOUN
ejpam-5317	320	6	of	of	ADP
ejpam-5317	320	7	x2	x2	PROPN
ejpam-5317	320	8	+	+	CCONJ
ejpam-5317	320	9	(	(	PUNCT
ejpam-5317	320	10	s	s	AUX
ejpam-5317	320	11	−	−	NOUN
ejpam-5317	320	12	1)x	1)x	NUM
ejpam-5317	320	13	−	−	PROPN
ejpam-5317	320	14	4	4	NUM
ejpam-5317	320	15	=	=	SYM
ejpam-5317	320	16	0	0	NUM
ejpam-5317	320	17	,	,	PUNCT
ejpam-5317	320	18	then	then	ADV
ejpam-5317	320	19	from	from	ADP
ejpam-5317	320	20	lemma	lemma	PROPN
ejpam-5317	320	21	1	1	NUM
ejpam-5317	320	22	and	and	CCONJ
ejpam-5317	320	23	equation	equation	NOUN
ejpam-5317	320	24	(	(	PUNCT
ejpam-5317	320	25	10	10	NUM
ejpam-5317	320	26	)	)	PUNCT
ejpam-5317	320	27	,	,	PUNCT
ejpam-5317	320	28	we	we	PRON
ejpam-5317	320	29	get	get	VERB
ejpam-5317	320	30	∑4	∑4	PROPN
ejpam-5317	320	31	j=1(bj	j=1(bj	PROPN
ejpam-5317	320	32	+	+	CCONJ
ejpam-5317	320	33	cj	cj	NOUN
ejpam-5317	320	34	)	)	PUNCT
ejpam-5317	321	1	=	=	PUNCT
ejpam-5317	322	1	∑4	∑4	PROPN
ejpam-5317	322	2	j	j	PROPN
ejpam-5317	322	3	dj	dj	NOUN
ejpam-5317	323	1	=	=	NOUN
ejpam-5317	323	2	∑s−4	∑s−4	NUM
ejpam-5317	323	3	i=1	i=1	PROPN
ejpam-5317	324	1	d	d	NOUN
ejpam-5317	324	2	∗	∗	VERB
ejpam-5317	324	3	i	i	NOUN
ejpam-5317	324	4	=	=	NOUN
ejpam-5317	324	5	0	0	NUM
ejpam-5317	324	6	and	and	CCONJ
ejpam-5317	324	7	d1	d1	PROPN
ejpam-5317	324	8	=	=	SYM
ejpam-5317	324	9	d2	d2	PROPN
ejpam-5317	324	10	=	=	PUNCT
ejpam-5317	324	11	d3	d3	PROPN
ejpam-5317	324	12	=	=	SYM
ejpam-5317	324	13	d4	d4	PROPN
ejpam-5317	324	14	=	=	SYM
ejpam-5317	324	15	0	0	NUM
ejpam-5317	324	16	,	,	PUNCT
ejpam-5317	324	17	respectively	respectively	ADV
ejpam-5317	324	18	.	.	PUNCT
ejpam-5317	325	1	from	from	ADP
ejpam-5317	325	2	equations	equation	NOUN
ejpam-5317	325	3	(	(	PUNCT
ejpam-5317	325	4	18	18	NUM
ejpam-5317	325	5	)	)	PUNCT
ejpam-5317	325	6	and	and	CCONJ
ejpam-5317	325	7	(	(	PUNCT
ejpam-5317	325	8	23	23	NUM
ejpam-5317	325	9	)	)	PUNCT
ejpam-5317	325	10	,	,	PUNCT
ejpam-5317	325	11	we	we	PRON
ejpam-5317	325	12	get	get	VERB
ejpam-5317	325	13	d∗k	d∗k	PUNCT
ejpam-5317	325	14	=	=	SYM
ejpam-5317	325	15	0(d∗k	0(d∗k	NUM
ejpam-5317	326	1	=	=	SYM
ejpam-5317	326	2	d∗k+1	d∗k+1	NOUN
ejpam-5317	326	3	=	=	SYM
ejpam-5317	326	4	−d∗k+1	−d∗k+1	NOUN
ejpam-5317	326	5	)	)	PUNCT
ejpam-5317	326	6	for	for	ADP
ejpam-5317	326	7	all	all	PRON
ejpam-5317	326	8	k	k	NOUN
ejpam-5317	326	9	=	=	SYM
ejpam-5317	326	10	1	1	NUM
ejpam-5317	326	11	,	,	PUNCT
ejpam-5317	326	12	2	2	NUM
ejpam-5317	326	13	,	,	PUNCT
ejpam-5317	326	14	.	.	PUNCT
ejpam-5317	326	15	.	.	PUNCT
ejpam-5317	326	16	.	.	PUNCT
ejpam-5317	327	1	,	,	PUNCT
ejpam-5317	327	2	s	s	VERB
ejpam-5317	327	3	−	−	NOUN
ejpam-5317	327	4	4	4	NUM
ejpam-5317	327	5	.	.	PUNCT
ejpam-5317	328	1	then	then	ADV
ejpam-5317	328	2	,	,	PUNCT
ejpam-5317	328	3	from	from	ADP
ejpam-5317	328	4	equations	equation	NOUN
ejpam-5317	328	5	(	(	PUNCT
ejpam-5317	328	6	5	5	NUM
ejpam-5317	328	7	)	)	PUNCT
ejpam-5317	328	8	and	and	CCONJ
ejpam-5317	328	9	(	(	PUNCT
ejpam-5317	328	10	8)	8)	NUM
ejpam-5317	328	11	,	,	PUNCT
ejpam-5317	328	12	we	we	PRON
ejpam-5317	328	13	get	get	VERB
ejpam-5317	328	14	b∗1	b∗1	NOUN
ejpam-5317	328	15	=	=	NOUN
ejpam-5317	328	16	b∗2	b∗2	NOUN
ejpam-5317	328	17	=	=	SYM
ejpam-5317	328	18	·	·	PUNCT
ejpam-5317	328	19	·	·	PUNCT
ejpam-5317	328	20	·	·	PUNCT
ejpam-5317	329	1	=	=	PUNCT
ejpam-5317	329	2	b∗s−4	b∗s−4	NUM
ejpam-5317	329	3	=	=	SYM
ejpam-5317	329	4	b∗	b∗	ADJ
ejpam-5317	329	5	and	and	CCONJ
ejpam-5317	329	6	c∗1	c∗1	ADJ
ejpam-5317	329	7	=	=	SYM
ejpam-5317	329	8	c∗2	c∗2	NOUN
ejpam-5317	329	9	=	=	PUNCT
ejpam-5317	329	10	·	·	PUNCT
ejpam-5317	329	11	·	·	PUNCT
ejpam-5317	329	12	·	·	PUNCT
ejpam-5317	330	1	=	=	SYM
ejpam-5317	330	2	c∗s−4	c∗s−4	PROPN
ejpam-5317	330	3	=	=	PUNCT
ejpam-5317	330	4	c∗.	c∗.	X
ejpam-5317	330	5	thus	thus	ADV
ejpam-5317	330	6	from	from	ADP
ejpam-5317	330	7	equation	equation	NOUN
ejpam-5317	330	8	(	(	PUNCT
ejpam-5317	330	9	17	17	NUM
ejpam-5317	330	10	)	)	PUNCT
ejpam-5317	330	11	,	,	PUNCT
ejpam-5317	330	12	we	we	PRON
ejpam-5317	330	13	have	have	VERB
ejpam-5317	330	14	c∗	c∗	NOUN
ejpam-5317	331	1	=	=	SYM
ejpam-5317	331	2	−b∗.	−b∗.	PRON
ejpam-5317	331	3	finally	finally	ADV
ejpam-5317	331	4	,	,	PUNCT
ejpam-5317	331	5	from	from	ADP
ejpam-5317	331	6	e.	e.	PROPN
ejpam-5317	331	7	rawaswhdeh	rawaswhdeh	PROPN
ejpam-5317	331	8	,	,	PUNCT
ejpam-5317	331	9	h.	h.	PROPN
ejpam-5317	331	10	adel	adel	PROPN
ejpam-5317	331	11	abdelkarim	abdelkarim	PROPN
ejpam-5317	331	12	,	,	PUNCT
ejpam-5317	331	13	e.	e.	PROPN
ejpam-5317	331	14	rawshdeh	rawshdeh	PROPN
ejpam-5317	331	15	/	/	SYM
ejpam-5317	331	16	eur	eur	PROPN
ejpam-5317	331	17	.	.	PUNCT
ejpam-5317	332	1	j.	j.	PROPN
ejpam-5317	332	2	pure	pure	PROPN
ejpam-5317	332	3	appl	appl	PROPN
ejpam-5317	332	4	.	.	PROPN
ejpam-5317	332	5	math	math	PROPN
ejpam-5317	332	6	,	,	PUNCT
ejpam-5317	332	7	17	17	NUM
ejpam-5317	332	8	(	(	PUNCT
ejpam-5317	332	9	4	4	NUM
ejpam-5317	332	10	)	)	PUNCT
ejpam-5317	332	11	(	(	PUNCT
ejpam-5317	332	12	2024	2024	NUM
ejpam-5317	332	13	)	)	PUNCT
ejpam-5317	332	14	,	,	PUNCT
ejpam-5317	332	15	2550	2550	NUM
ejpam-5317	332	16	-	-	SYM
ejpam-5317	332	17	2561	2561	NUM
ejpam-5317	332	18	2558	2558	NUM
ejpam-5317	332	19	equations	equation	NOUN
ejpam-5317	332	20	(	(	PUNCT
ejpam-5317	332	21	26	26	NUM
ejpam-5317	332	22	)	)	PUNCT
ejpam-5317	332	23	,	,	PUNCT
ejpam-5317	332	24	we	we	PRON
ejpam-5317	332	25	get	get	VERB
ejpam-5317	332	26	b∗	b∗	ADJ
ejpam-5317	333	1	=	=	SYM
ejpam-5317	333	2	λ	λ	X
ejpam-5317	333	3	λ−1b	λ−1b	NOUN
ejpam-5317	333	4	.	.	PUNCT
ejpam-5317	334	1	hence	hence	ADV
ejpam-5317	334	2	,	,	PUNCT
ejpam-5317	334	3	the	the	DET
ejpam-5317	334	4	vector	vector	NOUN
ejpam-5317	334	5	x	x	PUNCT
ejpam-5317	334	6	with	with	ADP
ejpam-5317	334	7	entries	entry	NOUN
ejpam-5317	334	8	(	(	PUNCT
ejpam-5317	334	9	x)i	x)i	PUNCT
ejpam-5317	334	10	=	=	PUNCT
ejpam-5317	334	11			PROPN
ejpam-5317	334	12	0	0	NUM
ejpam-5317	334	13	,	,	PUNCT
ejpam-5317	334	14	if	if	SCONJ
ejpam-5317	334	15	i	i	PRON
ejpam-5317	334	16	=	=	NOUN
ejpam-5317	334	17	1	1	NUM
ejpam-5317	334	18	,	,	PUNCT
ejpam-5317	334	19	2	2	NUM
ejpam-5317	334	20	,	,	PUNCT
ejpam-5317	334	21	.	.	PUNCT
ejpam-5317	334	22	.	.	PUNCT
ejpam-5317	334	23	.	.	PUNCT
ejpam-5317	335	1	,	,	PUNCT
ejpam-5317	335	2	s	s	X
ejpam-5317	335	3	,	,	PUNCT
ejpam-5317	335	4	b	b	NOUN
ejpam-5317	335	5	,	,	PUNCT
ejpam-5317	335	6	if	if	SCONJ
ejpam-5317	335	7	i	i	PRON
ejpam-5317	335	8	=	=	SYM
ejpam-5317	335	9	s	s	X
ejpam-5317	336	1	+	+	ADJ
ejpam-5317	336	2	1	1	NUM
ejpam-5317	336	3	,	,	PUNCT
ejpam-5317	336	4	s	s	PART
ejpam-5317	336	5	+	+	ADJ
ejpam-5317	336	6	2	2	NUM
ejpam-5317	336	7	,	,	PUNCT
ejpam-5317	336	8	.	.	PUNCT
ejpam-5317	336	9	.	.	PUNCT
ejpam-5317	337	1	.	.	PUNCT
ejpam-5317	338	1	,	,	PUNCT
ejpam-5317	338	2	s	s	PART
ejpam-5317	338	3	+	+	ADJ
ejpam-5317	338	4	4	4	NUM
ejpam-5317	338	5	,	,	PUNCT
ejpam-5317	338	6	b∗	b∗	ADJ
ejpam-5317	338	7	,	,	PUNCT
ejpam-5317	338	8	if	if	SCONJ
ejpam-5317	338	9	i	i	PRON
ejpam-5317	338	10	=	=	SYM
ejpam-5317	338	11	s	s	PART
ejpam-5317	339	1	+	+	NOUN
ejpam-5317	339	2	5	5	NUM
ejpam-5317	339	3	,	,	PUNCT
ejpam-5317	339	4	s	s	PART
ejpam-5317	339	5	+	+	NOUN
ejpam-5317	339	6	6	6	NUM
ejpam-5317	339	7	,	,	PUNCT
ejpam-5317	339	8	.	.	PUNCT
ejpam-5317	339	9	.	.	PUNCT
ejpam-5317	340	1	.	.	PUNCT
ejpam-5317	341	1	,	,	PUNCT
ejpam-5317	341	2	2s	2s	X
ejpam-5317	341	3	,	,	PUNCT
ejpam-5317	341	4	−b	−b	VERB
ejpam-5317	341	5	,	,	PUNCT
ejpam-5317	341	6	if	if	SCONJ
ejpam-5317	341	7	i	i	PRON
ejpam-5317	341	8	=	=	PUNCT
ejpam-5317	342	1	2s	2s	NUM
ejpam-5317	343	1	+	+	NOUN
ejpam-5317	343	2	1	1	NUM
ejpam-5317	343	3	,	,	PUNCT
ejpam-5317	343	4	2s	2s	PROPN
ejpam-5317	343	5	+	+	NOUN
ejpam-5317	343	6	2	2	NUM
ejpam-5317	343	7	,	,	PUNCT
ejpam-5317	343	8	.	.	PUNCT
ejpam-5317	343	9	.	.	PUNCT
ejpam-5317	344	1	.	.	PUNCT
ejpam-5317	345	1	,	,	PUNCT
ejpam-5317	346	1	2s	2s	PROPN
ejpam-5317	346	2	+	+	ADJ
ejpam-5317	346	3	4	4	NUM
ejpam-5317	346	4	,	,	PUNCT
ejpam-5317	346	5	−b∗	−b∗	PROPN
ejpam-5317	346	6	,	,	PUNCT
ejpam-5317	346	7	if	if	SCONJ
ejpam-5317	346	8	i	i	PRON
ejpam-5317	346	9	=	=	PUNCT
ejpam-5317	347	1	2s	2s	NUM
ejpam-5317	348	1	+	+	NOUN
ejpam-5317	348	2	5	5	NUM
ejpam-5317	348	3	,	,	PUNCT
ejpam-5317	348	4	2s	2s	PROPN
ejpam-5317	348	5	+	+	NOUN
ejpam-5317	348	6	6	6	NUM
ejpam-5317	348	7	,	,	PUNCT
ejpam-5317	348	8	.	.	PUNCT
ejpam-5317	348	9	.	.	PUNCT
ejpam-5317	349	1	.	.	PUNCT
ejpam-5317	350	1	,	,	PUNCT
ejpam-5317	350	2	3s	3s	NUM
ejpam-5317	350	3	,	,	PUNCT
ejpam-5317	350	4	0	0	NUM
ejpam-5317	350	5	,	,	PUNCT
ejpam-5317	350	6	if	if	SCONJ
ejpam-5317	350	7	i	i	PRON
ejpam-5317	350	8	=	=	SYM
ejpam-5317	350	9	3s	3s	NUM
ejpam-5317	350	10	+	+	CCONJ
ejpam-5317	350	11	1	1	NUM
ejpam-5317	350	12	,	,	PUNCT
ejpam-5317	350	13	3s	3s	NUM
ejpam-5317	350	14	+	+	CCONJ
ejpam-5317	350	15	2	2	NUM
ejpam-5317	350	16	,	,	PUNCT
ejpam-5317	350	17	.	.	PUNCT
ejpam-5317	350	18	.	.	PUNCT
ejpam-5317	350	19	.	.	PUNCT
ejpam-5317	351	1	,	,	PUNCT
ejpam-5317	351	2	3s	3s	NUM
ejpam-5317	351	3	+	+	CCONJ
ejpam-5317	351	4	4	4	NUM
ejpam-5317	351	5	0	0	NUM
ejpam-5317	351	6	,	,	PUNCT
ejpam-5317	351	7	if	if	SCONJ
ejpam-5317	351	8	i	i	PRON
ejpam-5317	351	9	=	=	SYM
ejpam-5317	351	10	3s	3s	NUM
ejpam-5317	351	11	+	+	CCONJ
ejpam-5317	351	12	5	5	NUM
ejpam-5317	351	13	,	,	PUNCT
ejpam-5317	351	14	3s	3s	NUM
ejpam-5317	351	15	+	+	CCONJ
ejpam-5317	351	16	6	6	NUM
ejpam-5317	351	17	,	,	PUNCT
ejpam-5317	351	18	.	.	PUNCT
ejpam-5317	351	19	.	.	PUNCT
ejpam-5317	351	20	.	.	PUNCT
ejpam-5317	352	1	,	,	PUNCT
ejpam-5317	352	2	4s	4s	NUM
ejpam-5317	352	3	.	.	PUNCT
ejpam-5317	353	1	(	(	PUNCT
ejpam-5317	353	2	34	34	NUM
ejpam-5317	353	3	)	)	PUNCT
ejpam-5317	354	1	such	such	ADJ
ejpam-5317	354	2	that	that	PRON
ejpam-5317	354	3	b∗	b∗	ADJ
ejpam-5317	354	4	=	=	PUNCT
ejpam-5317	354	5	λ	λ	NOUN
ejpam-5317	354	6	λ−1b	λ−1b	X
ejpam-5317	354	7	is	be	AUX
ejpam-5317	354	8	an	an	DET
ejpam-5317	354	9	eigenvectora	eigenvectora	NOUN
ejpam-5317	354	10	associated	associate	VERB
ejpam-5317	354	11	with	with	ADP
ejpam-5317	354	12	the	the	DET
ejpam-5317	354	13	eigenvalue	eigenvalue	PROPN
ejpam-5317	354	14	λ	λ	PROPN
ejpam-5317	354	15	,	,	PUNCT
ejpam-5317	354	16	where	where	SCONJ
ejpam-5317	354	17	λ2	λ2	NOUN
ejpam-5317	354	18	+	+	CCONJ
ejpam-5317	354	19	(	(	PUNCT
ejpam-5317	354	20	s−	s−	PROPN
ejpam-5317	354	21	1)λ	1)λ	NUM
ejpam-5317	354	22	−	−	PROPN
ejpam-5317	354	23	4	4	NUM
ejpam-5317	354	24	=	=	SYM
ejpam-5317	354	25	0	0	NUM
ejpam-5317	354	26	.	.	PUNCT
ejpam-5317	355	1	hence	hence	ADV
ejpam-5317	355	2	,	,	PUNCT
ejpam-5317	355	3	if	if	SCONJ
ejpam-5317	355	4	λ	λ	PROPN
ejpam-5317	355	5	is	be	AUX
ejpam-5317	355	6	a	a	DET
ejpam-5317	355	7	root	root	NOUN
ejpam-5317	355	8	of	of	ADP
ejpam-5317	355	9	the	the	DET
ejpam-5317	355	10	equation	equation	NOUN
ejpam-5317	355	11	x2	x2	PROPN
ejpam-5317	356	1	+	+	CCONJ
ejpam-5317	356	2	(	(	PUNCT
ejpam-5317	356	3	s	s	NOUN
ejpam-5317	356	4	−	−	NOUN
ejpam-5317	356	5	1)x	1)x	NUM
ejpam-5317	356	6	−	−	PROPN
ejpam-5317	356	7	4	4	NUM
ejpam-5317	356	8	=	=	SYM
ejpam-5317	356	9	0	0	NUM
ejpam-5317	356	10	,	,	PUNCT
ejpam-5317	356	11	then	then	ADV
ejpam-5317	356	12	it	it	PRON
ejpam-5317	356	13	is	be	AUX
ejpam-5317	356	14	an	an	DET
ejpam-5317	356	15	eigenvalue	eigenvalue	NOUN
ejpam-5317	356	16	of	of	ADP
ejpam-5317	356	17	the	the	DET
ejpam-5317	356	18	matrix	matrix	NOUN
ejpam-5317	356	19	a	a	PRON
ejpam-5317	356	20	with	with	ADP
ejpam-5317	356	21	multiplicity	multiplicity	NOUN
ejpam-5317	356	22	is	be	AUX
ejpam-5317	356	23	greater	great	ADJ
ejpam-5317	356	24	than	than	ADP
ejpam-5317	356	25	or	or	CCONJ
ejpam-5317	356	26	equal	equal	ADJ
ejpam-5317	356	27	to	to	ADP
ejpam-5317	356	28	one	one	NUM
ejpam-5317	356	29	.	.	PUNCT
ejpam-5317	357	1	remark	remark	PROPN
ejpam-5317	357	2	2	2	NUM
ejpam-5317	357	3	.	.	PUNCT
ejpam-5317	358	1	(	(	PUNCT
ejpam-5317	358	2	1	1	X
ejpam-5317	358	3	)	)	PUNCT
ejpam-5317	358	4	it	it	PRON
ejpam-5317	358	5	is	be	AUX
ejpam-5317	358	6	not	not	PART
ejpam-5317	358	7	difficult	difficult	ADJ
ejpam-5317	358	8	to	to	PART
ejpam-5317	358	9	show	show	VERB
ejpam-5317	358	10	that	that	SCONJ
ejpam-5317	358	11	the	the	DET
ejpam-5317	358	12	eigenvalues	eigenvalue	NOUN
ejpam-5317	358	13	that	that	PRON
ejpam-5317	358	14	we	we	PRON
ejpam-5317	358	15	so	so	ADV
ejpam-5317	358	16	far	far	ADV
ejpam-5317	358	17	discovered	discover	VERB
ejpam-5317	358	18	none	none	NOUN
ejpam-5317	358	19	of	of	ADP
ejpam-5317	358	20	them	they	PRON
ejpam-5317	358	21	is	be	AUX
ejpam-5317	358	22	a	a	DET
ejpam-5317	358	23	root	root	NOUN
ejpam-5317	358	24	of	of	ADP
ejpam-5317	358	25	the	the	DET
ejpam-5317	358	26	polynomial	polynomial	ADJ
ejpam-5317	358	27	q(x	q(x	PROPN
ejpam-5317	358	28	)	)	PUNCT
ejpam-5317	358	29	that	that	PRON
ejpam-5317	358	30	is	be	AUX
ejpam-5317	358	31	given	give	VERB
ejpam-5317	358	32	by	by	ADP
ejpam-5317	358	33	(	(	PUNCT
ejpam-5317	358	34	14	14	NUM
ejpam-5317	358	35	)	)	PUNCT
ejpam-5317	358	36	.	.	PUNCT
ejpam-5317	359	1	(	(	PUNCT
ejpam-5317	359	2	2	2	X
ejpam-5317	359	3	)	)	PUNCT
ejpam-5317	359	4	suppose	suppose	VERB
ejpam-5317	359	5	λ	λ	X
ejpam-5317	359	6	=	=	SYM
ejpam-5317	359	7	1	1	NUM
ejpam-5317	359	8	or	or	CCONJ
ejpam-5317	359	9	λ	λ	PROPN
ejpam-5317	359	10	is	be	AUX
ejpam-5317	359	11	a	a	DET
ejpam-5317	359	12	root	root	NOUN
ejpam-5317	359	13	of	of	ADP
ejpam-5317	359	14	the	the	DET
ejpam-5317	359	15	polynomial	polynomial	ADJ
ejpam-5317	359	16	q(x	q(x	PROPN
ejpam-5317	359	17	)	)	PUNCT
ejpam-5317	359	18	.	.	PUNCT
ejpam-5317	360	1	then	then	ADV
ejpam-5317	360	2	,	,	PUNCT
ejpam-5317	360	3	from	from	ADP
ejpam-5317	360	4	equation	equation	NOUN
ejpam-5317	360	5	(	(	PUNCT
ejpam-5317	360	6	3	3	NUM
ejpam-5317	360	7	)	)	PUNCT
ejpam-5317	360	8	,	,	PUNCT
ejpam-5317	360	9	we	we	PRON
ejpam-5317	360	10	have	have	VERB
ejpam-5317	360	11	a1	a1	NOUN
ejpam-5317	360	12	=	=	SYM
ejpam-5317	360	13	a2	a2	PROPN
ejpam-5317	360	14	=	=	SYM
ejpam-5317	360	15	·	·	PUNCT
ejpam-5317	360	16	·	·	PUNCT
ejpam-5317	360	17	·	·	PUNCT
ejpam-5317	361	1	=	=	PUNCT
ejpam-5317	361	2	as	as	ADP
ejpam-5317	361	3	=	=	NOUN
ejpam-5317	361	4	a.	a.	NOUN
ejpam-5317	361	5	since	since	SCONJ
ejpam-5317	361	6	λ2	λ2	PROPN
ejpam-5317	361	7	+	+	CCONJ
ejpam-5317	361	8	2λ	2λ	NOUN
ejpam-5317	361	9	−	−	NOUN
ejpam-5317	361	10	1	1	NUM
ejpam-5317	361	11	̸=	̸=	PROPN
ejpam-5317	361	12	0	0	NUM
ejpam-5317	361	13	,	,	PUNCT
ejpam-5317	361	14	then	then	ADV
ejpam-5317	361	15	we	we	PRON
ejpam-5317	361	16	get	get	VERB
ejpam-5317	361	17	from	from	ADP
ejpam-5317	361	18	remark	remark	NOUN
ejpam-5317	361	19	(	(	PUNCT
ejpam-5317	361	20	1	1	NUM
ejpam-5317	361	21	)	)	PUNCT
ejpam-5317	361	22	that	that	SCONJ
ejpam-5317	361	23	d∗k	d∗k	NUM
ejpam-5317	361	24	=	=	SYM
ejpam-5317	361	25	d∗k+1	d∗k+1	NOUN
ejpam-5317	361	26	,	,	PUNCT
ejpam-5317	361	27	b	b	NOUN
ejpam-5317	361	28	∗	∗	X
ejpam-5317	361	29	k	k	NOUN
ejpam-5317	361	30	=	=	PUNCT
ejpam-5317	361	31	b∗k+1	b∗k+1	X
ejpam-5317	361	32	and	and	CCONJ
ejpam-5317	361	33	c∗k	c∗k	NOUN
ejpam-5317	361	34	=	=	SYM
ejpam-5317	361	35	c∗k+1	c∗k+1	NOUN
ejpam-5317	361	36	for	for	ADP
ejpam-5317	361	37	all	all	PRON
ejpam-5317	361	38	k	k	NOUN
ejpam-5317	361	39	=	=	SYM
ejpam-5317	361	40	1	1	NUM
ejpam-5317	361	41	,	,	PUNCT
ejpam-5317	361	42	3	3	NUM
ejpam-5317	361	43	,	,	PUNCT
ejpam-5317	361	44	.	.	PUNCT
ejpam-5317	361	45	.	.	PUNCT
ejpam-5317	361	46	.	.	PUNCT
ejpam-5317	362	1	s	s	VERB
ejpam-5317	362	2	−	−	PROPN
ejpam-5317	362	3	5	5	NUM
ejpam-5317	362	4	.	.	PUNCT
ejpam-5317	363	1	since	since	SCONJ
ejpam-5317	363	2	λ	λ	PROPN
ejpam-5317	363	3	̸=	̸=	PROPN
ejpam-5317	363	4	0	0	NUM
ejpam-5317	363	5	,	,	PUNCT
ejpam-5317	363	6	then	then	ADV
ejpam-5317	363	7	from	from	ADP
ejpam-5317	363	8	equations	equation	NOUN
ejpam-5317	363	9	(	(	PUNCT
ejpam-5317	363	10	4	4	NUM
ejpam-5317	363	11	)	)	PUNCT
ejpam-5317	363	12	,	,	PUNCT
ejpam-5317	363	13	(	(	PUNCT
ejpam-5317	363	14	7	7	NUM
ejpam-5317	363	15	)	)	PUNCT
ejpam-5317	363	16	,	,	PUNCT
ejpam-5317	363	17	and	and	CCONJ
ejpam-5317	363	18	(	(	PUNCT
ejpam-5317	363	19	10	10	NUM
ejpam-5317	363	20	)	)	PUNCT
ejpam-5317	363	21	,	,	PUNCT
ejpam-5317	363	22	we	we	PRON
ejpam-5317	363	23	obtain	obtain	VERB
ejpam-5317	363	24	b1	b1	NOUN
ejpam-5317	363	25	=	=	SYM
ejpam-5317	363	26	b2	b2	NOUN
ejpam-5317	363	27	=	=	SYM
ejpam-5317	363	28	·	·	PUNCT
ejpam-5317	363	29	·	·	PUNCT
ejpam-5317	363	30	·	·	PUNCT
ejpam-5317	364	1	=	=	SYM
ejpam-5317	364	2	b	b	X
ejpam-5317	364	3	,	,	PUNCT
ejpam-5317	364	4	c1	c1	PROPN
ejpam-5317	364	5	=	=	PROPN
ejpam-5317	364	6	c2	c2	PROPN
ejpam-5317	364	7	=	=	PUNCT
ejpam-5317	364	8	·	·	PUNCT
ejpam-5317	364	9	·	·	PUNCT
ejpam-5317	364	10	·	·	PUNCT
ejpam-5317	365	1	=	=	PUNCT
ejpam-5317	365	2	c	c	X
ejpam-5317	365	3	,	,	PUNCT
ejpam-5317	365	4	and	and	CCONJ
ejpam-5317	365	5	d1	d1	PROPN
ejpam-5317	365	6	=	=	SYM
ejpam-5317	365	7	d2	d2	PROPN
ejpam-5317	365	8	=	=	PUNCT
ejpam-5317	365	9	d3	d3	PROPN
ejpam-5317	365	10	=	=	SYM
ejpam-5317	365	11	d4	d4	PROPN
ejpam-5317	365	12	=	=	SYM
ejpam-5317	365	13	0	0	X
ejpam-5317	365	14	.	.	PUNCT
ejpam-5317	366	1	moreover	moreover	ADV
ejpam-5317	366	2	,	,	PUNCT
ejpam-5317	366	3	from	from	ADP
ejpam-5317	366	4	equation	equation	NOUN
ejpam-5317	366	5	(	(	PUNCT
ejpam-5317	366	6	18	18	NUM
ejpam-5317	366	7	)	)	PUNCT
ejpam-5317	366	8	,	,	PUNCT
ejpam-5317	366	9	we	we	PRON
ejpam-5317	366	10	get	get	VERB
ejpam-5317	366	11	d∗1	d∗1	NOUN
ejpam-5317	366	12	=	=	SYM
ejpam-5317	366	13	d∗2	d∗2	NOUN
ejpam-5317	366	14	=	=	SYM
ejpam-5317	366	15	·	·	PUNCT
ejpam-5317	366	16	·	·	PUNCT
ejpam-5317	366	17	·	·	PUNCT
ejpam-5317	367	1	=	=	PUNCT
ejpam-5317	367	2	d∗s−4	d∗s−4	PROPN
ejpam-5317	367	3	=	=	SYM
ejpam-5317	367	4	d∗	d∗	NOUN
ejpam-5317	367	5	and	and	CCONJ
ejpam-5317	367	6	if	if	SCONJ
ejpam-5317	367	7	λ	λ	PROPN
ejpam-5317	367	8	̸=	̸=	PROPN
ejpam-5317	367	9	1	1	NUM
ejpam-5317	367	10	,	,	PUNCT
ejpam-5317	367	11	we	we	PRON
ejpam-5317	367	12	get	get	VERB
ejpam-5317	367	13	from	from	ADP
ejpam-5317	367	14	equation	equation	NOUN
ejpam-5317	367	15	(	(	PUNCT
ejpam-5317	367	16	5	5	NUM
ejpam-5317	367	17	)	)	PUNCT
ejpam-5317	367	18	and	and	CCONJ
ejpam-5317	367	19	(	(	PUNCT
ejpam-5317	367	20	8)	8)	NUM
ejpam-5317	367	21	that	that	DET
ejpam-5317	367	22	b∗1	b∗1	NOUN
ejpam-5317	367	23	=	=	NOUN
ejpam-5317	367	24	b∗2	b∗2	NOUN
ejpam-5317	367	25	=	=	SYM
ejpam-5317	367	26	·	·	PUNCT
ejpam-5317	367	27	·	·	PUNCT
ejpam-5317	367	28	·	·	PUNCT
ejpam-5317	368	1	=	=	PUNCT
ejpam-5317	368	2	b∗s−4	b∗s−4	NUM
ejpam-5317	368	3	=	=	SYM
ejpam-5317	368	4	b∗	b∗	ADJ
ejpam-5317	368	5	and	and	CCONJ
ejpam-5317	368	6	c∗1	c∗1	ADJ
ejpam-5317	368	7	=	=	SYM
ejpam-5317	368	8	c∗2	c∗2	NOUN
ejpam-5317	368	9	=	=	PUNCT
ejpam-5317	368	10	·	·	PUNCT
ejpam-5317	368	11	·	·	PUNCT
ejpam-5317	368	12	·	·	PUNCT
ejpam-5317	369	1	=	=	SYM
ejpam-5317	369	2	c∗s−4	c∗s−4	PROPN
ejpam-5317	369	3	=	=	PUNCT
ejpam-5317	369	4	c∗.	c∗.	NOUN
ejpam-5317	369	5	therefore	therefore	ADV
ejpam-5317	369	6	,	,	PUNCT
ejpam-5317	369	7	we	we	PRON
ejpam-5317	369	8	have	have	VERB
ejpam-5317	369	9	the	the	DET
ejpam-5317	369	10	following	follow	VERB
ejpam-5317	369	11	lemmas	lemmas	PROPN
ejpam-5317	369	12	.	.	PUNCT
ejpam-5317	370	1	lemma	lemma	PROPN
ejpam-5317	370	2	3	3	X
ejpam-5317	370	3	.	.	PUNCT
ejpam-5317	371	1	λ	λ	NOUN
ejpam-5317	371	2	=	=	NOUN
ejpam-5317	371	3	1	1	NUM
ejpam-5317	371	4	is	be	AUX
ejpam-5317	371	5	an	an	DET
ejpam-5317	371	6	eigenvalue	eigenvalue	NOUN
ejpam-5317	371	7	of	of	ADP
ejpam-5317	371	8	the	the	DET
ejpam-5317	371	9	matrix	matrix	NOUN
ejpam-5317	371	10	a	a	PRON
ejpam-5317	371	11	with	with	ADP
ejpam-5317	371	12	multiplicity	multiplicity	NOUN
ejpam-5317	371	13	is	be	AUX
ejpam-5317	371	14	greater	great	ADJ
ejpam-5317	371	15	than	than	ADP
ejpam-5317	371	16	or	or	CCONJ
ejpam-5317	371	17	equal	equal	ADJ
ejpam-5317	371	18	to	to	ADP
ejpam-5317	371	19	s−4	s−4	PROPN
ejpam-5317	371	20	2	2	NUM
ejpam-5317	371	21	−	−	NOUN
ejpam-5317	371	22	1	1	NUM
ejpam-5317	371	23	.	.	PUNCT
ejpam-5317	372	1	proof	proof	NOUN
ejpam-5317	372	2	.	.	PUNCT
ejpam-5317	373	1	if	if	SCONJ
ejpam-5317	373	2	λ	λ	X
ejpam-5317	373	3	=	=	SYM
ejpam-5317	373	4	1	1	NUM
ejpam-5317	373	5	,	,	PUNCT
ejpam-5317	373	6	then	then	ADV
ejpam-5317	373	7	using	use	VERB
ejpam-5317	373	8	remark	remark	NOUN
ejpam-5317	373	9	(	(	PUNCT
ejpam-5317	373	10	2	2	NUM
ejpam-5317	373	11	)	)	PUNCT
ejpam-5317	373	12	and	and	CCONJ
ejpam-5317	373	13	by	by	ADP
ejpam-5317	373	14	subtracting	subtract	VERB
ejpam-5317	373	15	equation	equation	NOUN
ejpam-5317	373	16	(	(	PUNCT
ejpam-5317	373	17	4	4	NUM
ejpam-5317	373	18	)	)	PUNCT
ejpam-5317	373	19	from	from	ADP
ejpam-5317	373	20	equation	equation	NOUN
ejpam-5317	373	21	(	(	PUNCT
ejpam-5317	373	22	5	5	NUM
ejpam-5317	373	23	)	)	PUNCT
ejpam-5317	373	24	and	and	CCONJ
ejpam-5317	373	25	equation	equation	NOUN
ejpam-5317	373	26	(	(	PUNCT
ejpam-5317	373	27	7	7	NUM
ejpam-5317	373	28	)	)	PUNCT
ejpam-5317	373	29	from	from	ADP
ejpam-5317	373	30	equation	equation	NOUN
ejpam-5317	373	31	(	(	PUNCT
ejpam-5317	373	32	8)	8)	NUM
ejpam-5317	373	33	,	,	PUNCT
ejpam-5317	373	34	we	we	PRON
ejpam-5317	373	35	get	get	VERB
ejpam-5317	373	36	d∗	d∗	NOUN
ejpam-5317	373	37	=	=	NOUN
ejpam-5317	373	38	−c	−c	NOUN
ejpam-5317	373	39	=	=	PUNCT
ejpam-5317	373	40	−b	−b	NOUN
ejpam-5317	373	41	.	.	PUNCT
ejpam-5317	374	1	equation	equation	NOUN
ejpam-5317	374	2	(	(	PUNCT
ejpam-5317	374	3	12	12	NUM
ejpam-5317	374	4	)	)	PUNCT
ejpam-5317	374	5	gives	give	VERB
ejpam-5317	374	6	sa	sa	X
ejpam-5317	374	7	=	=	PUNCT
ejpam-5317	374	8	−(b∗k	−(b∗k	NOUN
ejpam-5317	374	9	+	+	CCONJ
ejpam-5317	374	10	c∗k	c∗k	X
ejpam-5317	374	11	)	)	PUNCT
ejpam-5317	374	12	for	for	ADP
ejpam-5317	374	13	all	all	PRON
ejpam-5317	374	14	k	k	NOUN
ejpam-5317	374	15	=	=	SYM
ejpam-5317	374	16	1	1	NUM
ejpam-5317	374	17	,	,	PUNCT
ejpam-5317	374	18	2	2	NUM
ejpam-5317	374	19	,	,	PUNCT
ejpam-5317	374	20	.	.	PUNCT
ejpam-5317	374	21	.	.	PUNCT
ejpam-5317	374	22	.	.	PUNCT
ejpam-5317	375	1	s−	s−	PROPN
ejpam-5317	375	2	4	4	NUM
ejpam-5317	375	3	.	.	PUNCT
ejpam-5317	375	4	add	add	VERB
ejpam-5317	375	5	equation	equation	NOUN
ejpam-5317	375	6	(	(	PUNCT
ejpam-5317	375	7	4	4	NUM
ejpam-5317	375	8	)	)	PUNCT
ejpam-5317	375	9	to	to	ADP
ejpam-5317	375	10	equation	equation	NOUN
ejpam-5317	375	11	(	(	PUNCT
ejpam-5317	375	12	7	7	NUM
ejpam-5317	375	13	)	)	PUNCT
ejpam-5317	375	14	to	to	PART
ejpam-5317	375	15	get	get	VERB
ejpam-5317	375	16	6b	6b	NOUN
ejpam-5317	375	17	+	+	CCONJ
ejpam-5317	375	18	(	(	PUNCT
ejpam-5317	375	19	6s−	6s−	NUM
ejpam-5317	375	20	s2)a	s2)a	ADJ
ejpam-5317	375	21	=	=	PUNCT
ejpam-5317	375	22	0	0	NUM
ejpam-5317	375	23	and	and	CCONJ
ejpam-5317	375	24	from	from	ADP
ejpam-5317	375	25	equation	equation	NOUN
ejpam-5317	375	26	(	(	PUNCT
ejpam-5317	375	27	10	10	NUM
ejpam-5317	375	28	)	)	PUNCT
ejpam-5317	375	29	and	and	CCONJ
ejpam-5317	375	30	(	(	PUNCT
ejpam-5317	375	31	15	15	NUM
ejpam-5317	375	32	)	)	PUNCT
ejpam-5317	375	33	,	,	PUNCT
ejpam-5317	375	34	we	we	PRON
ejpam-5317	375	35	get	get	VERB
ejpam-5317	375	36	(	(	PUNCT
ejpam-5317	375	37	6	6	NUM
ejpam-5317	375	38	−	−	NOUN
ejpam-5317	375	39	s)b	s)b	VERB
ejpam-5317	376	1	+	+	CCONJ
ejpam-5317	377	1	(	(	PUNCT
ejpam-5317	377	2	3s−	3s−	NUM
ejpam-5317	377	3	2)a	2)a	NUM
ejpam-5317	377	4	=	=	SYM
ejpam-5317	377	5	0	0	X
ejpam-5317	377	6	.	.	PUNCT
ejpam-5317	378	1	since	since	SCONJ
ejpam-5317	378	2	s	s	PROPN
ejpam-5317	378	3	>	>	X
ejpam-5317	378	4	16	16	NUM
ejpam-5317	378	5	,	,	PUNCT
ejpam-5317	378	6	then	then	ADV
ejpam-5317	378	7	we	we	PRON
ejpam-5317	378	8	can	can	AUX
ejpam-5317	378	9	show	show	VERB
ejpam-5317	378	10	that	that	PRON
ejpam-5317	378	11	b	b	NOUN
ejpam-5317	378	12	=	=	PUNCT
ejpam-5317	378	13	a	a	PRON
ejpam-5317	378	14	=	=	SYM
ejpam-5317	378	15	0	0	NUM
ejpam-5317	378	16	and	and	CCONJ
ejpam-5317	378	17	d∗	d∗	NOUN
ejpam-5317	378	18	=	=	SYM
ejpam-5317	378	19	−c	−c	NOUN
ejpam-5317	378	20	=	=	PUNCT
ejpam-5317	379	1	d	d	NOUN
ejpam-5317	379	2	=	=	SYM
ejpam-5317	379	3	0	0	NUM
ejpam-5317	379	4	and	and	CCONJ
ejpam-5317	379	5	so	so	ADV
ejpam-5317	379	6	c∗k	c∗k	NOUN
ejpam-5317	379	7	=	=	SYM
ejpam-5317	379	8	−b∗k	−b∗k	NOUN
ejpam-5317	379	9	for	for	ADP
ejpam-5317	379	10	all	all	PRON
ejpam-5317	379	11	k	k	NOUN
ejpam-5317	379	12	=	=	SYM
ejpam-5317	379	13	1	1	NUM
ejpam-5317	379	14	,	,	PUNCT
ejpam-5317	379	15	2	2	NUM
ejpam-5317	379	16	,	,	PUNCT
ejpam-5317	379	17	.	.	PUNCT
ejpam-5317	379	18	.	.	PUNCT
ejpam-5317	379	19	.	.	PUNCT
ejpam-5317	380	1	s	s	VERB
ejpam-5317	380	2	−	−	NOUN
ejpam-5317	380	3	4	4	NUM
ejpam-5317	380	4	.	.	PUNCT
ejpam-5317	381	1	moreover	moreover	ADV
ejpam-5317	381	2	,	,	PUNCT
ejpam-5317	381	3	from	from	ADP
ejpam-5317	381	4	equation	equation	NOUN
ejpam-5317	381	5	(	(	PUNCT
ejpam-5317	381	6	7	7	NUM
ejpam-5317	381	7	)	)	PUNCT
ejpam-5317	381	8	,	,	PUNCT
ejpam-5317	381	9	we	we	PRON
ejpam-5317	381	10	get	get	VERB
ejpam-5317	381	11	∑4	∑4	PROPN
ejpam-5317	381	12	j=1	j=1	PROPN
ejpam-5317	381	13	b	b	PROPN
ejpam-5317	381	14	∗	∗	X
ejpam-5317	381	15	j	j	NOUN
ejpam-5317	382	1	=	=	SYM
ejpam-5317	382	2	0	0	PROPN
ejpam-5317	382	3	.	.	PUNCT
ejpam-5317	383	1	therefore	therefore	ADV
ejpam-5317	383	2	,	,	PUNCT
ejpam-5317	383	3	the	the	DET
ejpam-5317	383	4	e.	e.	PROPN
ejpam-5317	383	5	rawaswhdeh	rawaswhdeh	PROPN
ejpam-5317	383	6	,	,	PUNCT
ejpam-5317	383	7	h.	h.	PROPN
ejpam-5317	383	8	adel	adel	PROPN
ejpam-5317	383	9	abdelkarim	abdelkarim	PROPN
ejpam-5317	383	10	,	,	PUNCT
ejpam-5317	383	11	e.	e.	PROPN
ejpam-5317	383	12	rawshdeh	rawshdeh	PROPN
ejpam-5317	383	13	/	/	SYM
ejpam-5317	383	14	eur	eur	PROPN
ejpam-5317	383	15	.	.	PUNCT
ejpam-5317	384	1	j.	j.	PROPN
ejpam-5317	384	2	pure	pure	PROPN
ejpam-5317	384	3	appl	appl	PROPN
ejpam-5317	384	4	.	.	PROPN
ejpam-5317	384	5	math	math	PROPN
ejpam-5317	384	6	,	,	PUNCT
ejpam-5317	384	7	17	17	NUM
ejpam-5317	384	8	(	(	PUNCT
ejpam-5317	384	9	4	4	NUM
ejpam-5317	384	10	)	)	PUNCT
ejpam-5317	384	11	(	(	PUNCT
ejpam-5317	384	12	2024	2024	NUM
ejpam-5317	384	13	)	)	PUNCT
ejpam-5317	384	14	,	,	PUNCT
ejpam-5317	384	15	2550	2550	NUM
ejpam-5317	384	16	-	-	SYM
ejpam-5317	384	17	2561	2561	NUM
ejpam-5317	384	18	2559	2559	NUM
ejpam-5317	384	19	vector	vector	NOUN
ejpam-5317	384	20	x	x	PUNCT
ejpam-5317	384	21	with	with	ADP
ejpam-5317	384	22	entries	entry	NOUN
ejpam-5317	384	23	(	(	PUNCT
ejpam-5317	384	24	x)i	x)i	PUNCT
ejpam-5317	384	25	=	=	PUNCT
ejpam-5317	384	26			PROPN
ejpam-5317	384	27	0	0	NUM
ejpam-5317	384	28	,	,	PUNCT
ejpam-5317	384	29	if	if	SCONJ
ejpam-5317	384	30	i	i	PRON
ejpam-5317	384	31	=	=	NOUN
ejpam-5317	384	32	1	1	NUM
ejpam-5317	384	33	,	,	PUNCT
ejpam-5317	384	34	2	2	NUM
ejpam-5317	384	35	,	,	PUNCT
ejpam-5317	384	36	.	.	PUNCT
ejpam-5317	384	37	.	.	PUNCT
ejpam-5317	385	1	.	.	PUNCT
ejpam-5317	386	1	,	,	PUNCT
ejpam-5317	386	2	s	s	X
ejpam-5317	386	3	,	,	PUNCT
ejpam-5317	386	4	0	0	NUM
ejpam-5317	386	5	,	,	PUNCT
ejpam-5317	386	6	if	if	SCONJ
ejpam-5317	386	7	i	i	PRON
ejpam-5317	386	8	=	=	SYM
ejpam-5317	386	9	s	s	X
ejpam-5317	387	1	+	+	ADJ
ejpam-5317	387	2	1	1	NUM
ejpam-5317	387	3	,	,	PUNCT
ejpam-5317	387	4	s	s	PART
ejpam-5317	387	5	+	+	ADJ
ejpam-5317	387	6	2	2	NUM
ejpam-5317	387	7	,	,	PUNCT
ejpam-5317	387	8	.	.	PUNCT
ejpam-5317	387	9	.	.	PUNCT
ejpam-5317	388	1	.	.	PUNCT
ejpam-5317	389	1	,	,	PUNCT
ejpam-5317	389	2	s	s	PART
ejpam-5317	389	3	+	+	ADJ
ejpam-5317	389	4	4	4	NUM
ejpam-5317	389	5	,	,	PUNCT
ejpam-5317	389	6	b∗i−s−4	b∗i−s−4	ADJ
ejpam-5317	389	7	,	,	PUNCT
ejpam-5317	389	8	if	if	SCONJ
ejpam-5317	389	9	i	i	PRON
ejpam-5317	389	10	=	=	SYM
ejpam-5317	389	11	s	s	PART
ejpam-5317	390	1	+	+	NOUN
ejpam-5317	390	2	5	5	NUM
ejpam-5317	390	3	,	,	PUNCT
ejpam-5317	390	4	s	s	PART
ejpam-5317	390	5	+	+	NOUN
ejpam-5317	390	6	6	6	NUM
ejpam-5317	390	7	,	,	PUNCT
ejpam-5317	390	8	.	.	PUNCT
ejpam-5317	390	9	.	.	PUNCT
ejpam-5317	391	1	.	.	PUNCT
ejpam-5317	392	1	,	,	PUNCT
ejpam-5317	392	2	2s	2s	X
ejpam-5317	392	3	,	,	PUNCT
ejpam-5317	392	4	0	0	NUM
ejpam-5317	392	5	,	,	PUNCT
ejpam-5317	392	6	if	if	SCONJ
ejpam-5317	392	7	i	i	PRON
ejpam-5317	392	8	=	=	PUNCT
ejpam-5317	393	1	2s	2s	NUM
ejpam-5317	394	1	+	+	NOUN
ejpam-5317	394	2	1	1	NUM
ejpam-5317	394	3	,	,	PUNCT
ejpam-5317	394	4	2s	2s	PROPN
ejpam-5317	394	5	+	+	NOUN
ejpam-5317	394	6	2	2	NUM
ejpam-5317	394	7	,	,	PUNCT
ejpam-5317	394	8	.	.	PUNCT
ejpam-5317	394	9	.	.	PUNCT
ejpam-5317	395	1	.	.	PUNCT
ejpam-5317	396	1	,	,	PUNCT
ejpam-5317	397	1	2s	2s	PROPN
ejpam-5317	397	2	+	+	CCONJ
ejpam-5317	397	3	4	4	NUM
ejpam-5317	397	4	,	,	PUNCT
ejpam-5317	397	5	−b∗i−2s−4	−b∗i−2s−4	INTJ
ejpam-5317	397	6	,	,	PUNCT
ejpam-5317	397	7	if	if	SCONJ
ejpam-5317	397	8	i	i	PRON
ejpam-5317	397	9	=	=	PUNCT
ejpam-5317	398	1	2s	2s	NUM
ejpam-5317	399	1	+	+	NOUN
ejpam-5317	399	2	5	5	NUM
ejpam-5317	399	3	,	,	PUNCT
ejpam-5317	399	4	2s	2s	PROPN
ejpam-5317	399	5	+	+	NOUN
ejpam-5317	399	6	6	6	NUM
ejpam-5317	399	7	,	,	PUNCT
ejpam-5317	399	8	.	.	PUNCT
ejpam-5317	399	9	.	.	PUNCT
ejpam-5317	400	1	.	.	PUNCT
ejpam-5317	401	1	,	,	PUNCT
ejpam-5317	401	2	3s	3s	NUM
ejpam-5317	401	3	,	,	PUNCT
ejpam-5317	401	4	0	0	NUM
ejpam-5317	401	5	,	,	PUNCT
ejpam-5317	401	6	if	if	SCONJ
ejpam-5317	401	7	i	i	PRON
ejpam-5317	401	8	=	=	SYM
ejpam-5317	401	9	3s	3s	NUM
ejpam-5317	401	10	+	+	CCONJ
ejpam-5317	401	11	1	1	NUM
ejpam-5317	401	12	,	,	PUNCT
ejpam-5317	401	13	3s	3s	NUM
ejpam-5317	401	14	+	+	CCONJ
ejpam-5317	401	15	2	2	NUM
ejpam-5317	401	16	,	,	PUNCT
ejpam-5317	401	17	.	.	PUNCT
ejpam-5317	401	18	.	.	PUNCT
ejpam-5317	401	19	.	.	PUNCT
ejpam-5317	402	1	,	,	PUNCT
ejpam-5317	402	2	3s	3s	NUM
ejpam-5317	402	3	+	+	CCONJ
ejpam-5317	402	4	4	4	NUM
ejpam-5317	402	5	,	,	PUNCT
ejpam-5317	402	6	0	0	NUM
ejpam-5317	402	7	,	,	PUNCT
ejpam-5317	402	8	if	if	SCONJ
ejpam-5317	402	9	i	i	PRON
ejpam-5317	402	10	=	=	SYM
ejpam-5317	402	11	3s	3s	NUM
ejpam-5317	402	12	+	+	CCONJ
ejpam-5317	402	13	5	5	NUM
ejpam-5317	402	14	,	,	PUNCT
ejpam-5317	402	15	3s	3s	NUM
ejpam-5317	402	16	+	+	CCONJ
ejpam-5317	402	17	6	6	NUM
ejpam-5317	402	18	,	,	PUNCT
ejpam-5317	402	19	.	.	PUNCT
ejpam-5317	402	20	.	.	PUNCT
ejpam-5317	402	21	.	.	PUNCT
ejpam-5317	403	1	,	,	PUNCT
ejpam-5317	403	2	4s	4s	NUM
ejpam-5317	403	3	.	.	PUNCT
ejpam-5317	404	1	(	(	PUNCT
ejpam-5317	404	2	35	35	NUM
ejpam-5317	404	3	)	)	PUNCT
ejpam-5317	404	4	such	such	ADJ
ejpam-5317	404	5	that	that	SCONJ
ejpam-5317	404	6	∑s−4	∑s−4	VERB
ejpam-5317	404	7	i=1	i=1	PROPN
ejpam-5317	405	1	b	b	NOUN
ejpam-5317	405	2	∗	∗	NOUN
ejpam-5317	405	3	i	i	PRON
ejpam-5317	406	1	=	=	NOUN
ejpam-5317	406	2	0	0	NUM
ejpam-5317	406	3	and	and	CCONJ
ejpam-5317	406	4	b∗k	b∗k	PROPN
ejpam-5317	406	5	=	=	SYM
ejpam-5317	406	6	b∗k+1	b∗k+1	NOUN
ejpam-5317	406	7	for	for	ADP
ejpam-5317	406	8	all	all	PRON
ejpam-5317	406	9	k	k	NOUN
ejpam-5317	406	10	=	=	SYM
ejpam-5317	406	11	1	1	NUM
ejpam-5317	406	12	,	,	PUNCT
ejpam-5317	406	13	3	3	NUM
ejpam-5317	406	14	,	,	PUNCT
ejpam-5317	406	15	.	.	PUNCT
ejpam-5317	406	16	.	.	PUNCT
ejpam-5317	407	1	.	.	PUNCT
ejpam-5317	408	1	,	,	PUNCT
ejpam-5317	408	2	s−	s−	PROPN
ejpam-5317	408	3	5	5	NUM
ejpam-5317	408	4	is	be	AUX
ejpam-5317	408	5	an	an	DET
ejpam-5317	408	6	eigenvector	eigenvector	NOUN
ejpam-5317	408	7	for	for	ADP
ejpam-5317	408	8	λ	λ	PROPN
ejpam-5317	408	9	=	=	SYM
ejpam-5317	408	10	1	1	NUM
ejpam-5317	408	11	of	of	ADP
ejpam-5317	408	12	the	the	DET
ejpam-5317	408	13	matrix	matrix	NOUN
ejpam-5317	408	14	a	a	PRON
ejpam-5317	408	15	,	,	PUNCT
ejpam-5317	408	16	which	which	PRON
ejpam-5317	408	17	means	mean	VERB
ejpam-5317	408	18	that	that	SCONJ
ejpam-5317	408	19	λ	λ	NOUN
ejpam-5317	408	20	=	=	PRON
ejpam-5317	408	21	1	1	NUM
ejpam-5317	408	22	is	be	AUX
ejpam-5317	408	23	an	an	DET
ejpam-5317	408	24	eigenvalue	eigenvalue	NOUN
ejpam-5317	408	25	of	of	ADP
ejpam-5317	408	26	the	the	DET
ejpam-5317	408	27	matrix	matrix	NOUN
ejpam-5317	408	28	a	a	PRON
ejpam-5317	408	29	with	with	ADP
ejpam-5317	408	30	multiplicity	multiplicity	NOUN
ejpam-5317	408	31	is	be	AUX
ejpam-5317	408	32	greater	great	ADJ
ejpam-5317	408	33	than	than	ADP
ejpam-5317	408	34	or	or	CCONJ
ejpam-5317	408	35	equal	equal	ADJ
ejpam-5317	408	36	to	to	ADP
ejpam-5317	408	37	s−4	s−4	PROPN
ejpam-5317	408	38	2	2	NUM
ejpam-5317	408	39	−	−	PROPN
ejpam-5317	408	40	1	1	NUM
ejpam-5317	408	41	.	.	PUNCT
ejpam-5317	409	1	lemma	lemma	PROPN
ejpam-5317	409	2	4	4	X
ejpam-5317	409	3	.	.	PUNCT
ejpam-5317	410	1	let	let	VERB
ejpam-5317	410	2	λ	λ	PRON
ejpam-5317	410	3	be	be	AUX
ejpam-5317	410	4	a	a	DET
ejpam-5317	410	5	root	root	NOUN
ejpam-5317	410	6	of	of	ADP
ejpam-5317	410	7	the	the	DET
ejpam-5317	410	8	polynomial	polynomial	ADJ
ejpam-5317	410	9	q(x	q(x	PROPN
ejpam-5317	410	10	)	)	PUNCT
ejpam-5317	410	11	that	that	PRON
ejpam-5317	410	12	is	be	AUX
ejpam-5317	410	13	given	give	VERB
ejpam-5317	410	14	by	by	ADP
ejpam-5317	410	15	(	(	PUNCT
ejpam-5317	410	16	14	14	NUM
ejpam-5317	410	17	)	)	PUNCT
ejpam-5317	410	18	,	,	PUNCT
ejpam-5317	410	19	then	then	ADV
ejpam-5317	410	20	λ	λ	PROPN
ejpam-5317	410	21	is	be	AUX
ejpam-5317	410	22	an	an	DET
ejpam-5317	410	23	eigenvalue	eigenvalue	NOUN
ejpam-5317	410	24	of	of	ADP
ejpam-5317	410	25	the	the	DET
ejpam-5317	410	26	matrix	matrix	NOUN
ejpam-5317	410	27	a	a	PRON
ejpam-5317	410	28	with	with	ADP
ejpam-5317	410	29	multiplicity	multiplicity	NOUN
ejpam-5317	410	30	is	be	AUX
ejpam-5317	410	31	greater	great	ADJ
ejpam-5317	410	32	than	than	ADP
ejpam-5317	410	33	or	or	CCONJ
ejpam-5317	410	34	equal	equal	ADJ
ejpam-5317	410	35	to	to	ADP
ejpam-5317	410	36	one	one	NUM
ejpam-5317	410	37	.	.	PUNCT
ejpam-5317	411	1	proof	proof	NOUN
ejpam-5317	411	2	.	.	PUNCT
ejpam-5317	412	1	if	if	SCONJ
ejpam-5317	412	2	q(λ	q(λ	NOUN
ejpam-5317	412	3	)	)	PUNCT
ejpam-5317	412	4	=	=	SYM
ejpam-5317	412	5	0	0	NUM
ejpam-5317	412	6	,	,	PUNCT
ejpam-5317	412	7	then	then	ADV
ejpam-5317	412	8	from	from	ADP
ejpam-5317	412	9	remark	remark	NOUN
ejpam-5317	412	10	2	2	NUM
ejpam-5317	412	11	and	and	CCONJ
ejpam-5317	412	12	since	since	SCONJ
ejpam-5317	412	13	λ	λ	PROPN
ejpam-5317	412	14	̸=	̸=	PROPN
ejpam-5317	412	15	1	1	NUM
ejpam-5317	412	16	,	,	PUNCT
ejpam-5317	412	17	we	we	PRON
ejpam-5317	412	18	have	have	VERB
ejpam-5317	412	19	a1	a1	NOUN
ejpam-5317	412	20	=	=	SYM
ejpam-5317	412	21	a2	a2	PROPN
ejpam-5317	412	22	=	=	SYM
ejpam-5317	412	23	·	·	PUNCT
ejpam-5317	412	24	·	·	PUNCT
ejpam-5317	412	25	·	·	PUNCT
ejpam-5317	413	1	=	=	PUNCT
ejpam-5317	413	2	as	as	ADP
ejpam-5317	413	3	=	=	PROPN
ejpam-5317	413	4	a	a	PRON
ejpam-5317	413	5	,	,	PUNCT
ejpam-5317	413	6	b1	b1	NOUN
ejpam-5317	413	7	=	=	SYM
ejpam-5317	413	8	b2	b2	NOUN
ejpam-5317	413	9	=	=	SYM
ejpam-5317	413	10	·	·	PUNCT
ejpam-5317	413	11	·	·	PUNCT
ejpam-5317	413	12	·	·	PUNCT
ejpam-5317	413	13	=	=	SYM
ejpam-5317	413	14	b	b	X
ejpam-5317	413	15	,	,	PUNCT
ejpam-5317	413	16	c1	c1	PROPN
ejpam-5317	413	17	=	=	PROPN
ejpam-5317	413	18	c2	c2	PROPN
ejpam-5317	413	19	=	=	PUNCT
ejpam-5317	413	20	·	·	PUNCT
ejpam-5317	413	21	·	·	PUNCT
ejpam-5317	413	22	·	·	PUNCT
ejpam-5317	413	23	=	=	PUNCT
ejpam-5317	413	24	c	c	X
ejpam-5317	413	25	,	,	PUNCT
ejpam-5317	413	26	b∗1	b∗1	NOUN
ejpam-5317	413	27	=	=	NOUN
ejpam-5317	413	28	b∗2	b∗2	NOUN
ejpam-5317	413	29	=	=	SYM
ejpam-5317	413	30	·	·	PUNCT
ejpam-5317	413	31	·	·	PUNCT
ejpam-5317	413	32	·	·	PUNCT
ejpam-5317	414	1	=	=	PUNCT
ejpam-5317	414	2	b∗s−4	b∗s−4	NUM
ejpam-5317	414	3	=	=	SYM
ejpam-5317	414	4	b∗	b∗	ADJ
ejpam-5317	414	5	and	and	CCONJ
ejpam-5317	414	6	c∗1	c∗1	ADJ
ejpam-5317	414	7	=	=	SYM
ejpam-5317	414	8	c∗2	c∗2	NOUN
ejpam-5317	414	9	=	=	PUNCT
ejpam-5317	414	10	·	·	PUNCT
ejpam-5317	414	11	·	·	PUNCT
ejpam-5317	414	12	·	·	PUNCT
ejpam-5317	415	1	=	=	SYM
ejpam-5317	415	2	c∗s−4	c∗s−4	PROPN
ejpam-5317	415	3	=	=	PUNCT
ejpam-5317	415	4	c∗.	c∗.	NOUN
ejpam-5317	415	5	now	now	ADV
ejpam-5317	415	6	subtraction	subtraction	NOUN
ejpam-5317	415	7	equation	equation	NOUN
ejpam-5317	415	8	(	(	PUNCT
ejpam-5317	415	9	7	7	NUM
ejpam-5317	415	10	)	)	PUNCT
ejpam-5317	415	11	from	from	ADP
ejpam-5317	415	12	equation	equation	NOUN
ejpam-5317	415	13	(	(	PUNCT
ejpam-5317	415	14	4	4	X
ejpam-5317	415	15	)	)	PUNCT
ejpam-5317	415	16	gives	give	VERB
ejpam-5317	415	17	4(c−	4(c−	NUM
ejpam-5317	415	18	b	b	NOUN
ejpam-5317	415	19	)	)	PUNCT
ejpam-5317	416	1	+	+	CCONJ
ejpam-5317	416	2	(	(	PUNCT
ejpam-5317	416	3	s−	s−	PROPN
ejpam-5317	416	4	4)(c∗	4)(c∗	NOUN
ejpam-5317	416	5	−	−	PROPN
ejpam-5317	416	6	b∗	b∗	ADJ
ejpam-5317	416	7	)	)	PUNCT
ejpam-5317	416	8	=	=	SYM
ejpam-5317	416	9	λ(b−	λ(b−	NOUN
ejpam-5317	416	10	c	c	NOUN
ejpam-5317	416	11	)	)	PUNCT
ejpam-5317	416	12	.	.	PUNCT
ejpam-5317	417	1	also	also	ADV
ejpam-5317	417	2	,	,	PUNCT
ejpam-5317	417	3	subtraction	subtraction	NOUN
ejpam-5317	417	4	equation	equation	NOUN
ejpam-5317	417	5	(	(	PUNCT
ejpam-5317	417	6	8)	8)	NUM
ejpam-5317	417	7	from	from	ADP
ejpam-5317	417	8	equation	equation	NOUN
ejpam-5317	417	9	(	(	PUNCT
ejpam-5317	417	10	6	6	NUM
ejpam-5317	417	11	)	)	PUNCT
ejpam-5317	417	12	gives	give	VERB
ejpam-5317	417	13	(	(	PUNCT
ejpam-5317	417	14	b∗	b∗	ADJ
ejpam-5317	417	15	−	−	PROPN
ejpam-5317	417	16	c∗	c∗	NOUN
ejpam-5317	417	17	)	)	PUNCT
ejpam-5317	418	1	+	+	CCONJ
ejpam-5317	418	2	4(c−	4(c−	NUM
ejpam-5317	418	3	b	b	NOUN
ejpam-5317	418	4	)	)	PUNCT
ejpam-5317	419	1	+	+	CCONJ
ejpam-5317	419	2	(	(	PUNCT
ejpam-5317	419	3	s−	s−	PROPN
ejpam-5317	419	4	4)(c∗	4)(c∗	NOUN
ejpam-5317	419	5	−	−	PROPN
ejpam-5317	419	6	b∗	b∗	ADJ
ejpam-5317	419	7	)	)	PUNCT
ejpam-5317	420	1	=	=	SYM
ejpam-5317	420	2	λ(b∗	λ(b∗	X
ejpam-5317	420	3	−	−	PROPN
ejpam-5317	420	4	c∗	c∗	PROPN
ejpam-5317	420	5	)	)	PUNCT
ejpam-5317	420	6	.	.	PUNCT
ejpam-5317	421	1	solve	solve	VERB
ejpam-5317	421	2	these	these	DET
ejpam-5317	421	3	equations	equation	NOUN
ejpam-5317	421	4	to	to	PART
ejpam-5317	421	5	get	get	VERB
ejpam-5317	421	6	b	b	NOUN
ejpam-5317	421	7	=	=	SYM
ejpam-5317	421	8	c	c	NOUN
ejpam-5317	421	9	and	and	CCONJ
ejpam-5317	421	10	b∗	b∗	ADJ
ejpam-5317	421	11	=	=	PUNCT
ejpam-5317	421	12	c∗.	c∗.	NOUN
ejpam-5317	421	13	equations	equation	NOUN
ejpam-5317	421	14	(	(	PUNCT
ejpam-5317	421	15	3	3	NUM
ejpam-5317	421	16	)	)	PUNCT
ejpam-5317	421	17	to	to	ADP
ejpam-5317	421	18	(	(	PUNCT
ejpam-5317	421	19	12	12	NUM
ejpam-5317	421	20	)	)	PUNCT
ejpam-5317	421	21	will	will	AUX
ejpam-5317	421	22	be	be	AUX
ejpam-5317	421	23	reduced	reduce	VERB
ejpam-5317	421	24	to	to	ADP
ejpam-5317	421	25	the	the	DET
ejpam-5317	421	26	following	follow	VERB
ejpam-5317	421	27	linear	linear	ADJ
ejpam-5317	421	28	system	system	NOUN
ejpam-5317	421	29	:	:	PUNCT
ejpam-5317	421	30	(	(	PUNCT
ejpam-5317	421	31	s−	s−	PROPN
ejpam-5317	421	32	(	(	PUNCT
ejpam-5317	421	33	λ	λ	X
ejpam-5317	421	34	+	+	NOUN
ejpam-5317	421	35	1))a	1))a	NUM
ejpam-5317	421	36	+	+	CCONJ
ejpam-5317	421	37	8b	8b	NUM
ejpam-5317	421	38	+	+	CCONJ
ejpam-5317	421	39	2(s−	2(s−	NUM
ejpam-5317	421	40	4)b∗	4)b∗	NUM
ejpam-5317	422	1	+	+	NUM
ejpam-5317	422	2	4d	4d	NUM
ejpam-5317	422	3	+	+	CCONJ
ejpam-5317	422	4	(	(	PUNCT
ejpam-5317	422	5	s−	s−	PROPN
ejpam-5317	422	6	4)d∗	4)d∗	NUM
ejpam-5317	422	7	=	=	SYM
ejpam-5317	422	8	0	0	NUM
ejpam-5317	422	9	sa	sa	NOUN
ejpam-5317	423	1	+	+	CCONJ
ejpam-5317	423	2	(	(	PUNCT
ejpam-5317	423	3	4	4	NUM
ejpam-5317	423	4	−	−	NOUN
ejpam-5317	423	5	λ)b	λ)b	NOUN
ejpam-5317	424	1	+	+	CCONJ
ejpam-5317	424	2	(	(	PUNCT
ejpam-5317	424	3	s−	s−	PROPN
ejpam-5317	424	4	4)b∗	4)b∗	NUM
ejpam-5317	424	5	=	=	SYM
ejpam-5317	424	6	0	0	PUNCT
ejpam-5317	424	7	sa	sa	PROPN
ejpam-5317	424	8	+	+	NUM
ejpam-5317	424	9	4b	4b	X
ejpam-5317	424	10	+	+	CCONJ
ejpam-5317	424	11	(	(	PUNCT
ejpam-5317	424	12	s−	s−	PROPN
ejpam-5317	424	13	3	3	NUM
ejpam-5317	424	14	−	−	NOUN
ejpam-5317	424	15	λ)b∗	λ)b∗	PROPN
ejpam-5317	424	16	+	+	NUM
ejpam-5317	424	17	d∗	d∗	NOUN
ejpam-5317	424	18	=	=	SYM
ejpam-5317	424	19	0	0	PROPN
ejpam-5317	424	20	sa	sa	NOUN
ejpam-5317	424	21	−	−	NOUN
ejpam-5317	424	22	λd	λd	NOUN
ejpam-5317	424	23	=	=	SYM
ejpam-5317	424	24	0	0	PUNCT
ejpam-5317	424	25	sa	sa	NOUN
ejpam-5317	425	1	+	+	NOUN
ejpam-5317	426	1	2b∗	2b∗	NUM
ejpam-5317	426	2	+	+	CCONJ
ejpam-5317	426	3	(	(	PUNCT
ejpam-5317	426	4	1	1	NUM
ejpam-5317	426	5	−	−	NOUN
ejpam-5317	426	6	λ)d∗	λ)d∗	NUM
ejpam-5317	426	7	=	=	NOUN
ejpam-5317	426	8	0	0	PROPN
ejpam-5317	426	9	.	.	PUNCT
ejpam-5317	427	1	(	(	PUNCT
ejpam-5317	427	2	36	36	NUM
ejpam-5317	427	3	)	)	PUNCT
ejpam-5317	427	4	thus	thus	ADV
ejpam-5317	427	5	,	,	PUNCT
ejpam-5317	427	6	λ	λ	PROPN
ejpam-5317	427	7	is	be	AUX
ejpam-5317	427	8	an	an	DET
ejpam-5317	427	9	eigenvalue	eigenvalue	NOUN
ejpam-5317	427	10	of	of	ADP
ejpam-5317	427	11	a	a	PRON
ejpam-5317	427	12	if	if	SCONJ
ejpam-5317	427	13	the	the	DET
ejpam-5317	427	14	system	system	NOUN
ejpam-5317	427	15	given	give	VERB
ejpam-5317	427	16	by	by	ADP
ejpam-5317	427	17	(	(	PUNCT
ejpam-5317	427	18	36	36	NUM
ejpam-5317	427	19	)	)	PUNCT
ejpam-5317	427	20	has	have	VERB
ejpam-5317	427	21	a	a	DET
ejpam-5317	427	22	nontrivial	nontrivial	ADJ
ejpam-5317	427	23	solution	solution	NOUN
ejpam-5317	427	24	.	.	PUNCT
ejpam-5317	428	1	using	use	VERB
ejpam-5317	428	2	maple	maple	NOUN
ejpam-5317	428	3	,	,	PUNCT
ejpam-5317	428	4	we	we	PRON
ejpam-5317	428	5	can	can	AUX
ejpam-5317	428	6	see	see	VERB
ejpam-5317	428	7	that	that	SCONJ
ejpam-5317	428	8	this	this	DET
ejpam-5317	428	9	system	system	NOUN
ejpam-5317	428	10	has	have	VERB
ejpam-5317	428	11	only	only	ADV
ejpam-5317	428	12	one	one	NUM
ejpam-5317	428	13	free	free	ADJ
ejpam-5317	428	14	variable	variable	NOUN
ejpam-5317	428	15	if	if	SCONJ
ejpam-5317	428	16	q(λ	q(λ	VERB
ejpam-5317	428	17	)	)	PUNCT
ejpam-5317	428	18	=	=	SYM
ejpam-5317	428	19	0	0	PUNCT
ejpam-5317	428	20	and	and	CCONJ
ejpam-5317	428	21	has	have	VERB
ejpam-5317	428	22	only	only	ADV
ejpam-5317	428	23	the	the	DET
ejpam-5317	428	24	trivial	trivial	ADJ
ejpam-5317	428	25	solution	solution	NOUN
ejpam-5317	428	26	if	if	SCONJ
ejpam-5317	428	27	q(λ	q(λ	NOUN
ejpam-5317	428	28	)	)	PUNCT
ejpam-5317	428	29	̸=	̸=	PROPN
ejpam-5317	428	30	0	0	NUM
ejpam-5317	428	31	.	.	PUNCT
ejpam-5317	429	1	thus	thus	ADV
ejpam-5317	429	2	the	the	DET
ejpam-5317	429	3	roots	root	NOUN
ejpam-5317	429	4	of	of	ADP
ejpam-5317	429	5	the	the	DET
ejpam-5317	429	6	polynomial	polynomial	ADJ
ejpam-5317	429	7	q(x	q(x	PROPN
ejpam-5317	429	8	)	)	PUNCT
ejpam-5317	429	9	form	form	NOUN
ejpam-5317	429	10	eigenvalues	eigenvalue	NOUN
ejpam-5317	429	11	of	of	ADP
ejpam-5317	429	12	the	the	DET
ejpam-5317	429	13	matrix	matrix	NOUN
ejpam-5317	429	14	a	a	PRON
ejpam-5317	429	15	with	with	ADP
ejpam-5317	429	16	multiplicity	multiplicity	NOUN
ejpam-5317	429	17	is	be	AUX
ejpam-5317	429	18	at	at	ADP
ejpam-5317	429	19	least	least	ADJ
ejpam-5317	429	20	one	one	NUM
ejpam-5317	429	21	.	.	PUNCT
ejpam-5317	430	1	considering	consider	VERB
ejpam-5317	430	2	the	the	DET
ejpam-5317	430	3	above	above	ADJ
ejpam-5317	430	4	lemmas	lemma	NOUN
ejpam-5317	430	5	and	and	CCONJ
ejpam-5317	430	6	corollaries	corollary	NOUN
ejpam-5317	430	7	,	,	PUNCT
ejpam-5317	430	8	we	we	PRON
ejpam-5317	430	9	reach	reach	VERB
ejpam-5317	430	10	to	to	ADP
ejpam-5317	430	11	the	the	DET
ejpam-5317	430	12	main	main	ADJ
ejpam-5317	430	13	theorem	theorem	NOUN
ejpam-5317	430	14	of	of	ADP
ejpam-5317	430	15	the	the	DET
ejpam-5317	430	16	paper	paper	NOUN
ejpam-5317	430	17	.	.	PUNCT
ejpam-5317	431	1	references	reference	NOUN
ejpam-5317	431	2	2560	2560	NUM
ejpam-5317	431	3	theorem	theorem	VERB
ejpam-5317	431	4	1	1	NUM
ejpam-5317	431	5	.	.	PUNCT
ejpam-5317	432	1	the	the	DET
ejpam-5317	432	2	spectral	spectral	ADJ
ejpam-5317	432	3	radius	radius	NOUN
ejpam-5317	432	4	of	of	ADP
ejpam-5317	432	5	the	the	DET
ejpam-5317	432	6	matrix	matrix	NOUN
ejpam-5317	432	7	a	a	PRON
ejpam-5317	432	8	is	be	AUX
ejpam-5317	432	9	given	give	VERB
ejpam-5317	432	10	by	by	ADP
ejpam-5317	432	11	σ(a	σ(a	PROPN
ejpam-5317	432	12	)	)	PUNCT
ejpam-5317	433	1	=	=	PRON
ejpam-5317	433	2	(	(	PUNCT
ejpam-5317	433	3	−1	−1	NOUN
ejpam-5317	433	4	0	0	NUM
ejpam-5317	433	5	−1	−1	NOUN
ejpam-5317	433	6	±	±	NOUN
ejpam-5317	433	7	√	√	NOUN
ejpam-5317	433	8	2	2	NUM
ejpam-5317	433	9	1	1	NUM
ejpam-5317	433	10	±	±	NUM
ejpam-5317	433	11	√	√	ADV
ejpam-5317	433	12	2	2	NUM
ejpam-5317	433	13	1	1	NUM
ejpam-5317	433	14	λ1	λ1	ADJ
ejpam-5317	433	15	λ2	λ2	NOUN
ejpam-5317	433	16	.	.	PUNCT
ejpam-5317	433	17	.	.	PUNCT
ejpam-5317	433	18	.	.	PUNCT
ejpam-5317	434	1	λ7	λ7	ADV
ejpam-5317	434	2	3s−6	3s−6	NUM
ejpam-5317	434	3	2	2	NUM
ejpam-5317	434	4	9	9	NUM
ejpam-5317	434	5	s−4	s−4	PROPN
ejpam-5317	434	6	2	2	NUM
ejpam-5317	434	7	s−6	s−6	PROPN
ejpam-5317	434	8	2	2	NUM
ejpam-5317	435	1	s−6	s−6	NOUN
ejpam-5317	435	2	2	2	NUM
ejpam-5317	435	3	1	1	NUM
ejpam-5317	435	4	1	1	NUM
ejpam-5317	435	5	.	.	PUNCT
ejpam-5317	435	6	.	.	PUNCT
ejpam-5317	435	7	.	.	PUNCT
ejpam-5317	436	1	1	1	X
ejpam-5317	436	2	)	)	PUNCT
ejpam-5317	436	3	,	,	PUNCT
ejpam-5317	436	4	where	where	SCONJ
ejpam-5317	436	5	λ1	λ1	ADJ
ejpam-5317	436	6	,	,	PUNCT
ejpam-5317	436	7	λ2	λ2	NOUN
ejpam-5317	436	8	,	,	PUNCT
ejpam-5317	436	9	.	.	PUNCT
ejpam-5317	436	10	.	.	PUNCT
ejpam-5317	436	11	.	.	PUNCT
ejpam-5317	437	1	,	,	PUNCT
ejpam-5317	437	2	λ7	λ7	PROPN
ejpam-5317	437	3	are	be	AUX
ejpam-5317	437	4	the	the	DET
ejpam-5317	437	5	distinct	distinct	ADJ
ejpam-5317	437	6	real	real	ADJ
ejpam-5317	437	7	roots	root	NOUN
ejpam-5317	437	8	of	of	ADP
ejpam-5317	437	9	the	the	DET
ejpam-5317	437	10	polynomial	polynomial	ADJ
ejpam-5317	437	11	(	(	PUNCT
ejpam-5317	437	12	x2	x2	PROPN
ejpam-5317	437	13	+	+	CCONJ
ejpam-5317	437	14	(	(	PUNCT
ejpam-5317	437	15	s−	s−	PROPN
ejpam-5317	437	16	1)x−	1)x−	PROPN
ejpam-5317	437	17	4)q(x	4)q(x	NUM
ejpam-5317	437	18	)	)	PUNCT
ejpam-5317	437	19	,	,	PUNCT
ejpam-5317	437	20	where	where	SCONJ
ejpam-5317	437	21	q(x	q(x	NOUN
ejpam-5317	437	22	)	)	PUNCT
ejpam-5317	437	23	is	be	AUX
ejpam-5317	437	24	given	give	VERB
ejpam-5317	437	25	by	by	ADP
ejpam-5317	437	26	(	(	PUNCT
ejpam-5317	437	27	14	14	NUM
ejpam-5317	437	28	)	)	PUNCT
ejpam-5317	437	29	.	.	PUNCT
ejpam-5317	438	1	proof	proof	NOUN
ejpam-5317	438	2	.	.	PUNCT
ejpam-5317	439	1	it	it	PRON
ejpam-5317	439	2	is	be	AUX
ejpam-5317	439	3	not	not	PART
ejpam-5317	439	4	difficult	difficult	ADJ
ejpam-5317	439	5	to	to	PART
ejpam-5317	439	6	show	show	VERB
ejpam-5317	439	7	that	that	SCONJ
ejpam-5317	439	8	the	the	DET
ejpam-5317	439	9	sign	sign	NOUN
ejpam-5317	439	10	of	of	ADP
ejpam-5317	439	11	q(0	q(0	PROPN
ejpam-5317	439	12	)	)	PUNCT
ejpam-5317	439	13	,	,	PUNCT
ejpam-5317	439	14	q(s	q(s	NOUN
ejpam-5317	439	15	)	)	PUNCT
ejpam-5317	439	16	,	,	PUNCT
ejpam-5317	439	17	and	and	CCONJ
ejpam-5317	439	18	q(−s	q(−	NOUN
ejpam-5317	439	19	)	)	PUNCT
ejpam-5317	439	20	is	be	AUX
ejpam-5317	439	21	negative	negative	ADJ
ejpam-5317	439	22	and	and	CCONJ
ejpam-5317	439	23	the	the	DET
ejpam-5317	439	24	sign	sign	NOUN
ejpam-5317	439	25	of	of	ADP
ejpam-5317	439	26	q(1	q(1	PROPN
ejpam-5317	439	27	)	)	PUNCT
ejpam-5317	439	28	,	,	PUNCT
ejpam-5317	439	29	q(−1	q(−1	PROPN
ejpam-5317	439	30	)	)	PUNCT
ejpam-5317	439	31	,	,	PUNCT
ejpam-5317	439	32	and	and	CCONJ
ejpam-5317	439	33	q(3s	q(3	NOUN
ejpam-5317	439	34	)	)	PUNCT
ejpam-5317	439	35	is	be	AUX
ejpam-5317	439	36	positive	positive	ADJ
ejpam-5317	439	37	,	,	PUNCT
ejpam-5317	439	38	thus	thus	ADV
ejpam-5317	439	39	by	by	ADP
ejpam-5317	439	40	applying	apply	VERB
ejpam-5317	439	41	the	the	DET
ejpam-5317	439	42	intermediate	intermediate	ADJ
ejpam-5317	439	43	value	value	NOUN
ejpam-5317	439	44	theorem	theorem	VERB
ejpam-5317	439	45	,	,	PUNCT
ejpam-5317	439	46	the	the	DET
ejpam-5317	439	47	polynomial	polynomial	ADJ
ejpam-5317	439	48	q(x	q(x	PROPN
ejpam-5317	439	49	)	)	PUNCT
ejpam-5317	439	50	has	have	VERB
ejpam-5317	439	51	five	five	NUM
ejpam-5317	439	52	different	different	ADJ
ejpam-5317	439	53	real	real	ADJ
ejpam-5317	439	54	roots	root	NOUN
ejpam-5317	439	55	,	,	PUNCT
ejpam-5317	439	56	and	and	CCONJ
ejpam-5317	439	57	since	since	SCONJ
ejpam-5317	439	58	the	the	DET
ejpam-5317	439	59	roots	root	NOUN
ejpam-5317	439	60	of	of	ADP
ejpam-5317	439	61	the	the	DET
ejpam-5317	439	62	quadratic	quadratic	ADJ
ejpam-5317	439	63	polynomial	polynomial	NOUN
ejpam-5317	439	64	(	(	PUNCT
ejpam-5317	439	65	x2−	x2−	PROPN
ejpam-5317	439	66	(	(	PUNCT
ejpam-5317	439	67	s−	s−	PROPN
ejpam-5317	439	68	1)x+	1)x+	NUM
ejpam-5317	439	69	4	4	NUM
ejpam-5317	439	70	)	)	PUNCT
ejpam-5317	439	71	are	be	AUX
ejpam-5317	439	72	not	not	PART
ejpam-5317	439	73	roots	root	NOUN
ejpam-5317	439	74	of	of	ADP
ejpam-5317	439	75	q(x	q(x	NOUN
ejpam-5317	439	76	)	)	PUNCT
ejpam-5317	439	77	,	,	PUNCT
ejpam-5317	439	78	we	we	PRON
ejpam-5317	439	79	get	get	VERB
ejpam-5317	439	80	that	that	SCONJ
ejpam-5317	439	81	the	the	DET
ejpam-5317	439	82	polynomial	polynomial	ADJ
ejpam-5317	439	83	(	(	PUNCT
ejpam-5317	439	84	x2	x2	INTJ
ejpam-5317	439	85	−	−	PROPN
ejpam-5317	439	86	(	(	PUNCT
ejpam-5317	439	87	s	s	NOUN
ejpam-5317	439	88	−	−	NOUN
ejpam-5317	439	89	1)x	1)x	NUM
ejpam-5317	439	90	+	+	CCONJ
ejpam-5317	439	91	4)q(x	4)q(x	NUM
ejpam-5317	439	92	)	)	PUNCT
ejpam-5317	439	93	has	have	VERB
ejpam-5317	439	94	seven	seven	NUM
ejpam-5317	439	95	distinct	distinct	ADJ
ejpam-5317	439	96	real	real	ADJ
ejpam-5317	439	97	roots	root	NOUN
ejpam-5317	439	98	.	.	PUNCT
ejpam-5317	440	1	moreover	moreover	ADV
ejpam-5317	440	2	,	,	PUNCT
ejpam-5317	440	3	the	the	DET
ejpam-5317	440	4	summation	summation	NOUN
ejpam-5317	440	5	of	of	ADP
ejpam-5317	440	6	the	the	DET
ejpam-5317	440	7	lower	low	ADJ
ejpam-5317	440	8	bound	bind	VERB
ejpam-5317	440	9	of	of	ADP
ejpam-5317	440	10	the	the	DET
ejpam-5317	440	11	multiplicity	multiplicity	NOUN
ejpam-5317	440	12	of	of	ADP
ejpam-5317	440	13	each	each	DET
ejpam-5317	440	14	eigenvalues	eigenvalue	NOUN
ejpam-5317	440	15	of	of	ADP
ejpam-5317	440	16	the	the	DET
ejpam-5317	440	17	matrix	matrix	NOUN
ejpam-5317	440	18	a	a	PRON
ejpam-5317	440	19	that	that	SCONJ
ejpam-5317	440	20	we	we	PRON
ejpam-5317	440	21	found	find	VERB
ejpam-5317	440	22	through	through	ADP
ejpam-5317	440	23	this	this	DET
ejpam-5317	440	24	section	section	NOUN
ejpam-5317	440	25	is	be	AUX
ejpam-5317	440	26	4s	4s	NUM
ejpam-5317	440	27	which	which	PRON
ejpam-5317	440	28	is	be	AUX
ejpam-5317	440	29	the	the	DET
ejpam-5317	440	30	size	size	NOUN
ejpam-5317	440	31	of	of	ADP
ejpam-5317	440	32	the	the	DET
ejpam-5317	440	33	matrix	matrix	NOUN
ejpam-5317	440	34	a.	a.	NOUN
ejpam-5317	440	35	therefore	therefore	ADV
ejpam-5317	440	36	,	,	PUNCT
ejpam-5317	440	37	the	the	DET
ejpam-5317	440	38	multiplicity	multiplicity	NOUN
ejpam-5317	440	39	of	of	ADP
ejpam-5317	440	40	each	each	DET
ejpam-5317	440	41	eigenvalue	eigenvalue	NOUN
ejpam-5317	440	42	is	be	AUX
ejpam-5317	440	43	exactly	exactly	ADV
ejpam-5317	440	44	the	the	DET
ejpam-5317	440	45	lower	lower	ADV
ejpam-5317	440	46	bound	bind	VERB
ejpam-5317	440	47	.	.	PUNCT
ejpam-5317	441	1	this	this	PRON
ejpam-5317	441	2	completes	complete	VERB
ejpam-5317	441	3	the	the	DET
ejpam-5317	441	4	proof	proof	NOUN
ejpam-5317	441	5	.	.	PUNCT
ejpam-5317	442	1	3	3	X
ejpam-5317	442	2	.	.	X
ejpam-5317	442	3	conclusions	conclusion	NOUN
ejpam-5317	442	4	the	the	DET
ejpam-5317	442	5	spectrum	spectrum	NOUN
ejpam-5317	442	6	of	of	ADP
ejpam-5317	442	7	a	a	DET
ejpam-5317	442	8	certain	certain	ADJ
ejpam-5317	442	9	large	large	ADJ
ejpam-5317	442	10	block	block	NOUN
ejpam-5317	442	11	matrix	matrix	NOUN
ejpam-5317	442	12	has	have	AUX
ejpam-5317	442	13	been	be	AUX
ejpam-5317	442	14	determined	determine	VERB
ejpam-5317	442	15	.	.	PUNCT
ejpam-5317	443	1	this	this	DET
ejpam-5317	443	2	matrix	matrix	NOUN
ejpam-5317	443	3	can	can	AUX
ejpam-5317	443	4	be	be	AUX
ejpam-5317	443	5	considered	consider	VERB
ejpam-5317	443	6	as	as	ADP
ejpam-5317	443	7	an	an	DET
ejpam-5317	443	8	adjacency	adjacency	NOUN
ejpam-5317	443	9	matrix	matrix	NOUN
ejpam-5317	443	10	of	of	ADP
ejpam-5317	443	11	a	a	DET
ejpam-5317	443	12	certain	certain	ADJ
ejpam-5317	443	13	graph	graph	NOUN
ejpam-5317	443	14	.	.	PUNCT
ejpam-5317	444	1	more	more	ADV
ejpam-5317	444	2	precisely	precisely	ADV
ejpam-5317	444	3	,	,	PUNCT
ejpam-5317	444	4	it	it	PRON
ejpam-5317	444	5	has	have	AUX
ejpam-5317	444	6	been	be	AUX
ejpam-5317	444	7	proved	prove	VERB
ejpam-5317	444	8	that	that	SCONJ
ejpam-5317	444	9	the	the	DET
ejpam-5317	444	10	proposed	propose	VERB
ejpam-5317	444	11	matrix	matrix	NOUN
ejpam-5317	444	12	has	have	VERB
ejpam-5317	444	13	fourteen	fourteen	NUM
ejpam-5317	444	14	distinct	distinct	ADJ
ejpam-5317	444	15	eigenvectors	eigenvector	NOUN
ejpam-5317	444	16	.	.	PUNCT
ejpam-5317	445	1	in	in	ADP
ejpam-5317	445	2	addition	addition	NOUN
ejpam-5317	445	3	the	the	DET
ejpam-5317	445	4	eigenspace	eigenspace	NOUN
ejpam-5317	445	5	of	of	ADP
ejpam-5317	445	6	each	each	DET
ejpam-5317	445	7	eigenvalue	eigenvalue	NOUN
ejpam-5317	445	8	has	have	AUX
ejpam-5317	445	9	been	be	AUX
ejpam-5317	445	10	determined	determine	VERB
ejpam-5317	445	11	.	.	PUNCT
ejpam-5317	446	1	references	reference	NOUN
ejpam-5317	446	2	[	[	X
ejpam-5317	446	3	1	1	X
ejpam-5317	446	4	]	]	X
ejpam-5317	446	5	n.l	n.l	PROPN
ejpam-5317	446	6	.	.	PROPN
ejpam-5317	446	7	biggs	biggs	PROPN
ejpam-5317	446	8	.	.	PUNCT
ejpam-5317	447	1	algebraic	algebraic	PROPN
ejpam-5317	447	2	graph	graph	NOUN
ejpam-5317	447	3	theory	theory	NOUN
ejpam-5317	447	4	.	.	PUNCT
ejpam-5317	448	1	cambridge	cambridge	PROPN
ejpam-5317	448	2	university	university	PROPN
ejpam-5317	448	3	press	press	PROPN
ejpam-5317	448	4	,	,	PUNCT
ejpam-5317	448	5	cambridge	cambridge	PROPN
ejpam-5317	448	6	,	,	PUNCT
ejpam-5317	448	7	1993	1993	NUM
ejpam-5317	448	8	.	.	PUNCT
ejpam-5317	449	1	[	[	X
ejpam-5317	449	2	2	2	NUM
ejpam-5317	449	3	]	]	PUNCT
ejpam-5317	449	4	a.	a.	NOUN
ejpam-5317	449	5	bonato	bonato	PROPN
ejpam-5317	449	6	,	,	PUNCT
ejpam-5317	449	7	d.	d.	PROPN
ejpam-5317	449	8	gleich	gleich	PROPN
ejpam-5317	449	9	,	,	PUNCT
ejpam-5317	449	10	m.	m.	PROPN
ejpam-5317	449	11	kim	kim	PROPN
ejpam-5317	449	12	,	,	PUNCT
ejpam-5317	449	13	d.	d.	PROPN
ejpam-5317	449	14	mitsche	mitsche	PROPN
ejpam-5317	449	15	d	d	PROPN
ejpam-5317	449	16	,	,	PUNCT
ejpam-5317	449	17	p.	p.	PROPN
ejpam-5317	449	18	pra	pra	PROPN
ejpam-5317	449	19	lat	lat	PROPN
ejpam-5317	449	20	,	,	PUNCT
ejpam-5317	449	21	and	and	CCONJ
ejpam-5317	449	22	and	and	CCONJ
ejpam-5317	449	23	s.	s.	PROPN
ejpam-5317	449	24	young	young	PROPN
ejpam-5317	449	25	y.	y.	PROPN
ejpam-5317	449	26	tian	tian	PROPN
ejpam-5317	449	27	.	.	PUNCT
ejpam-5317	450	1	dimensionality	dimensionality	NOUN
ejpam-5317	450	2	of	of	ADP
ejpam-5317	450	3	social	social	ADJ
ejpam-5317	450	4	networks	network	NOUN
ejpam-5317	450	5	using	use	VERB
ejpam-5317	450	6	motifs	motif	NOUN
ejpam-5317	450	7	and	and	CCONJ
ejpam-5317	450	8	eigenvalues	eigenvalue	NOUN
ejpam-5317	450	9	.	.	PUNCT
ejpam-5317	451	1	plos	plos	PROPN
ejpam-5317	451	2	one	one	NUM
ejpam-5317	451	3	,	,	PUNCT
ejpam-5317	451	4	9:1–7	9:1–7	NUM
ejpam-5317	451	5	,	,	PUNCT
ejpam-5317	451	6	2014	2014	NUM
ejpam-5317	451	7	.	.	PUNCT
ejpam-5317	452	1	[	[	X
ejpam-5317	452	2	3	3	X
ejpam-5317	452	3	]	]	X
ejpam-5317	452	4	f.	f.	PROPN
ejpam-5317	452	5	w.	w.	PROPN
ejpam-5317	452	6	byron	byron	PROPN
ejpam-5317	452	7	and	and	CCONJ
ejpam-5317	452	8	r.	r.	PROPN
ejpam-5317	452	9	w.	w.	PROPN
ejpam-5317	452	10	fuller	fuller	PROPN
ejpam-5317	452	11	.	.	PUNCT
ejpam-5317	453	1	mathematics	mathematic	NOUN
ejpam-5317	453	2	of	of	ADP
ejpam-5317	453	3	classical	classical	ADJ
ejpam-5317	453	4	and	and	CCONJ
ejpam-5317	453	5	quantum	quantum	ADJ
ejpam-5317	453	6	physics	physics	NOUN
ejpam-5317	453	7	.	.	PUNCT
ejpam-5317	454	1	dover	dover	PROPN
ejpam-5317	454	2	,	,	PUNCT
ejpam-5317	454	3	new	new	PROPN
ejpam-5317	454	4	york	york	PROPN
ejpam-5317	454	5	,	,	PUNCT
ejpam-5317	454	6	1992	1992	NUM
ejpam-5317	454	7	.	.	PUNCT
ejpam-5317	455	1	[	[	X
ejpam-5317	455	2	4	4	NUM
ejpam-5317	455	3	]	]	PUNCT
ejpam-5317	455	4	r.	r.	PROPN
ejpam-5317	455	5	k.	k.	PROPN
ejpam-5317	455	6	chouhan	chouhan	PROPN
ejpam-5317	455	7	,	,	PUNCT
ejpam-5317	455	8	a.	a.	PROPN
ejpam-5317	455	9	alam	alam	PROPN
ejpam-5317	455	10	,	,	PUNCT
ejpam-5317	455	11	s.	s.	PROPN
ejpam-5317	455	12	ghosh	ghosh	PROPN
ejpam-5317	455	13	,	,	PUNCT
ejpam-5317	455	14	and	and	CCONJ
ejpam-5317	455	15	a.	a.	NOUN
ejpam-5317	455	16	mookerjee	mookerjee	PROPN
ejpam-5317	455	17	.	.	PUNCT
ejpam-5317	456	1	ab	ab	PROPN
ejpam-5317	456	2	initio	initio	PROPN
ejpam-5317	456	3	study	study	NOUN
ejpam-5317	456	4	of	of	ADP
ejpam-5317	456	5	phonon	phonon	NOUN
ejpam-5317	456	6	spectrum	spectrum	NOUN
ejpam-5317	456	7	,	,	PUNCT
ejpam-5317	456	8	entropy	entropy	NOUN
ejpam-5317	456	9	and	and	CCONJ
ejpam-5317	456	10	lattice	lattice	PROPN
ejpam-5317	456	11	heat	heat	NOUN
ejpam-5317	456	12	capacity	capacity	NOUN
ejpam-5317	456	13	of	of	ADP
ejpam-5317	456	14	disordered	disordered	ADJ
ejpam-5317	456	15	re	re	NOUN
ejpam-5317	456	16	-	-	NOUN
ejpam-5317	456	17	w	w	ADJ
ejpam-5317	456	18	alloys	alloy	NOUN
ejpam-5317	456	19	.	.	PUNCT
ejpam-5317	457	1	j	j	PROPN
ejpam-5317	457	2	phys	phy	NOUN
ejpam-5317	457	3	condens	conden	NOUN
ejpam-5317	457	4	matter	matter	ADV
ejpam-5317	457	5	,	,	PUNCT
ejpam-5317	457	6	24(37):375401	24(37):375401	NUM
ejpam-5317	457	7	,	,	PUNCT
ejpam-5317	457	8	2012	2012	NUM
ejpam-5317	457	9	.	.	PUNCT
ejpam-5317	458	1	[	[	X
ejpam-5317	458	2	5	5	NUM
ejpam-5317	458	3	]	]	X
ejpam-5317	458	4	f.r.k	f.r.k	PROPN
ejpam-5317	458	5	.	.	PUNCT
ejpam-5317	458	6	chung	chung	PROPN
ejpam-5317	458	7	.	.	PUNCT
ejpam-5317	459	1	spectral	spectral	ADJ
ejpam-5317	459	2	graph	graph	NOUN
ejpam-5317	459	3	theory	theory	NOUN
ejpam-5317	459	4	.	.	PUNCT
ejpam-5317	460	1	american	american	PROPN
ejpam-5317	460	2	mathematical	mathematical	PROPN
ejpam-5317	460	3	society	society	NOUN
ejpam-5317	460	4	,	,	PUNCT
ejpam-5317	460	5	rhode	rhode	NOUN
ejpam-5317	460	6	island	island	NOUN
ejpam-5317	460	7	,	,	PUNCT
ejpam-5317	460	8	1997	1997	NUM
ejpam-5317	460	9	.	.	PUNCT
ejpam-5317	461	1	references	reference	NOUN
ejpam-5317	461	2	2561	2561	NUM
ejpam-5317	462	1	[	[	X
ejpam-5317	462	2	6	6	NUM
ejpam-5317	462	3	]	]	PUNCT
ejpam-5317	462	4	l.	l.	PROPN
ejpam-5317	462	5	covaci	covaci	PROPN
ejpam-5317	462	6	,	,	PUNCT
ejpam-5317	462	7	f.	f.	PROPN
ejpam-5317	462	8	m.	m.	PROPN
ejpam-5317	462	9	peeters	peeter	NOUN
ejpam-5317	462	10	,	,	PUNCT
ejpam-5317	462	11	and	and	CCONJ
ejpam-5317	462	12	m.	m.	NOUN
ejpam-5317	462	13	berciu	berciu	VERB
ejpam-5317	462	14	.	.	PUNCT
ejpam-5317	463	1	efficient	efficient	PROPN
ejpam-5317	463	2	numerical	numerical	PROPN
ejpam-5317	463	3	approach	approach	NOUN
ejpam-5317	463	4	to	to	ADP
ejpam-5317	463	5	inhomogeneous	inhomogeneous	ADJ
ejpam-5317	463	6	superconductivity	superconductivity	NOUN
ejpam-5317	463	7	:	:	PUNCT
ejpam-5317	463	8	the	the	DET
ejpam-5317	463	9	chebyshev	chebyshev	PROPN
ejpam-5317	463	10	-	-	PUNCT
ejpam-5317	463	11	bogoliubov	bogoliubov	NOUN
ejpam-5317	463	12	-	-	PUNCT
ejpam-5317	463	13	de	de	ADJ
ejpam-5317	463	14	gennes	genne	NOUN
ejpam-5317	463	15	method	method	NOUN
ejpam-5317	463	16	.	.	PUNCT
ejpam-5317	464	1	phys	phy	NOUN
ejpam-5317	464	2	.	.	PUNCT
ejpam-5317	465	1	rev	rev	PROPN
ejpam-5317	465	2	.	.	PROPN
ejpam-5317	465	3	lett	lett	PROPN
ejpam-5317	465	4	.	.	PROPN
ejpam-5317	465	5	,	,	PUNCT
ejpam-5317	465	6	105:167006	105:167006	NUM
ejpam-5317	465	7	,	,	PUNCT
ejpam-5317	465	8	2010	2010	NUM
ejpam-5317	465	9	.	.	PUNCT
ejpam-5317	466	1	[	[	X
ejpam-5317	466	2	7	7	X
ejpam-5317	466	3	]	]	PUNCT
ejpam-5317	466	4	j.	j.	PROPN
ejpam-5317	466	5	garcia	garcia	PROPN
ejpam-5317	466	6	.	.	PUNCT
ejpam-5317	467	1	communication	communication	NOUN
ejpam-5317	467	2	using	use	VERB
ejpam-5317	467	3	eigenvalues	eigenvalue	NOUN
ejpam-5317	467	4	of	of	ADP
ejpam-5317	467	5	higher	high	ADJ
ejpam-5317	467	6	multiplicity	multiplicity	NOUN
ejpam-5317	467	7	of	of	ADP
ejpam-5317	467	8	the	the	DET
ejpam-5317	467	9	nonlinear	nonlinear	ADJ
ejpam-5317	467	10	fourier	fourier	NOUN
ejpam-5317	467	11	transform	transform	NOUN
ejpam-5317	467	12	.	.	PUNCT
ejpam-5317	468	1	journal	journal	PROPN
ejpam-5317	468	2	of	of	ADP
ejpam-5317	468	3	lightwave	lightwave	PROPN
ejpam-5317	468	4	technology	technology	PROPN
ejpam-5317	468	5	,	,	PUNCT
ejpam-5317	468	6	36(23):5442–5450	36(23):5442–5450	NUM
ejpam-5317	468	7	,	,	PUNCT
ejpam-5317	468	8	2018	2018	NUM
ejpam-5317	468	9	.	.	PUNCT
ejpam-5317	469	1	[	[	X
ejpam-5317	469	2	8	8	NUM
ejpam-5317	469	3	]	]	PUNCT
ejpam-5317	469	4	m.	m.	NOUN
ejpam-5317	469	5	habib	habib	PROPN
ejpam-5317	469	6	,	,	PUNCT
ejpam-5317	469	7	e.	e.	PROPN
ejpam-5317	469	8	y.	y.	PROPN
ejpam-5317	469	9	celikel	celikel	PROPN
ejpam-5317	469	10	,	,	PUNCT
ejpam-5317	469	11	and	and	CCONJ
ejpam-5317	469	12	c.	c.	PROPN
ejpam-5317	469	13	abdioglu	abdioglu	PROPN
ejpam-5317	469	14	.	.	PUNCT
ejpam-5317	470	1	clean	clean	ADJ
ejpam-5317	470	2	graph	graph	NOUN
ejpam-5317	470	3	of	of	ADP
ejpam-5317	470	4	a	a	DET
ejpam-5317	470	5	ring	ring	NOUN
ejpam-5317	470	6	.	.	PUNCT
ejpam-5317	471	1	j.	j.	PROPN
ejpam-5317	471	2	algebra	algebra	PROPN
ejpam-5317	471	3	appl	appl	PROPN
ejpam-5317	471	4	.	.	PROPN
ejpam-5317	471	5	,	,	PUNCT
ejpam-5317	471	6	20(9):2150156	20(9):2150156	NUM
ejpam-5317	471	7	,	,	PUNCT
ejpam-5317	471	8	2021	2021	NUM
ejpam-5317	471	9	.	.	PUNCT
ejpam-5317	472	1	[	[	X
ejpam-5317	472	2	9	9	NUM
ejpam-5317	472	3	]	]	PUNCT
ejpam-5317	472	4	f.	f.	PROPN
ejpam-5317	472	5	harary	harary	PROPN
ejpam-5317	472	6	.	.	PUNCT
ejpam-5317	473	1	graph	graph	NOUN
ejpam-5317	473	2	theory	theory	NOUN
ejpam-5317	473	3	.	.	PUNCT
ejpam-5317	474	1	addison	addison	PROPN
ejpam-5317	474	2	-	-	PUNCT
ejpam-5317	474	3	wesley	wesley	PROPN
ejpam-5317	474	4	,	,	PUNCT
ejpam-5317	474	5	ann	ann	PROPN
ejpam-5317	474	6	arbor	arbor	PROPN
ejpam-5317	474	7	,	,	PUNCT
ejpam-5317	474	8	michigan	michigan	PROPN
ejpam-5317	474	9	,	,	PUNCT
ejpam-5317	474	10	1970	1970	NUM
ejpam-5317	474	11	.	.	PUNCT
ejpam-5317	475	1	[	[	X
ejpam-5317	475	2	10	10	NUM
ejpam-5317	475	3	]	]	X
ejpam-5317	475	4	w.	w.	PROPN
ejpam-5317	475	5	k.	k.	PROPN
ejpam-5317	475	6	nicholson	nicholson	PROPN
ejpam-5317	475	7	.	.	PUNCT
ejpam-5317	476	1	lifting	lift	VERB
ejpam-5317	476	2	idempotents	idempotent	NOUN
ejpam-5317	476	3	and	and	CCONJ
ejpam-5317	476	4	exchange	exchange	NOUN
ejpam-5317	476	5	rings	ring	NOUN
ejpam-5317	476	6	.	.	PUNCT
ejpam-5317	477	1	trans	trans	PROPN
ejpam-5317	477	2	.	.	PUNCT
ejpam-5317	478	1	amer	amer	PROPN
ejpam-5317	478	2	.	.	PUNCT
ejpam-5317	478	3	math	math	PROPN
ejpam-5317	478	4	.	.	PUNCT
ejpam-5317	479	1	soc	soc	PROPN
ejpam-5317	479	2	.	.	PROPN
ejpam-5317	479	3	,	,	PUNCT
ejpam-5317	479	4	229:269–278	229:269–278	NUM
ejpam-5317	479	5	,	,	PUNCT
ejpam-5317	479	6	1977	1977	NUM
ejpam-5317	479	7	.	.	PUNCT
ejpam-5317	480	1	[	[	X
ejpam-5317	480	2	11	11	NUM
ejpam-5317	480	3	]	]	PUNCT
ejpam-5317	480	4	z.	z.	PROPN
ejpam-5317	480	5	petrovic	petrovic	PROPN
ejpam-5317	480	6	and	and	CCONJ
ejpam-5317	480	7	zoran	zoran	PROPN
ejpam-5317	480	8	s.	s.	PROPN
ejpam-5317	480	9	pucanovic	pucanovic	PROPN
ejpam-5317	480	10	.	.	PUNCT
ejpam-5317	481	1	the	the	DET
ejpam-5317	481	2	clean	clean	ADJ
ejpam-5317	481	3	graph	graph	NOUN
ejpam-5317	481	4	of	of	ADP
ejpam-5317	481	5	a	a	DET
ejpam-5317	481	6	commutative	commutative	ADJ
ejpam-5317	481	7	ring	ring	NOUN
ejpam-5317	481	8	.	.	PUNCT
ejpam-5317	482	1	ars	ars	PROPN
ejpam-5317	482	2	comb	comb	PROPN
ejpam-5317	482	3	.	.	PUNCT
ejpam-5317	482	4	,	,	PUNCT
ejpam-5317	482	5	134:363–378	134:363–378	NUM
ejpam-5317	482	6	,	,	PUNCT
ejpam-5317	482	7	2017	2017	NUM
ejpam-5317	482	8	.	.	PUNCT
ejpam-5317	483	1	[	[	X
ejpam-5317	483	2	12	12	NUM
ejpam-5317	483	3	]	]	X
ejpam-5317	483	4	l.	l.	PROPN
ejpam-5317	483	5	tsoulfidis	tsoulfidis	PROPN
ejpam-5317	483	6	and	and	CCONJ
ejpam-5317	483	7	i.	i.	PROPN
ejpam-5317	483	8	athanasiadis	athanasiadis	PROPN
ejpam-5317	483	9	.	.	PUNCT
ejpam-5317	484	1	a	a	DET
ejpam-5317	484	2	new	new	ADJ
ejpam-5317	484	3	method	method	NOUN
ejpam-5317	484	4	of	of	ADP
ejpam-5317	484	5	identifying	identify	VERB
ejpam-5317	484	6	key	key	ADJ
ejpam-5317	484	7	industries	industry	NOUN
ejpam-5317	484	8	:	:	PUNCT
ejpam-5317	484	9	a	a	DET
ejpam-5317	484	10	principal	principal	ADJ
ejpam-5317	484	11	component	component	NOUN
ejpam-5317	484	12	analysis	analysis	NOUN
ejpam-5317	484	13	.	.	PUNCT
ejpam-5317	485	1	journal	journal	NOUN
ejpam-5317	485	2	of	of	ADP
ejpam-5317	485	3	economic	economic	ADJ
ejpam-5317	485	4	structures	structure	NOUN
ejpam-5317	485	5	,	,	PUNCT
ejpam-5317	485	6	2(23):1–23	2(23):1–23	NOUN
ejpam-5317	485	7	,	,	PUNCT
ejpam-5317	485	8	2022	2022	NUM
ejpam-5317	485	9	.	.	PUNCT
ejpam-5317	486	1	[	[	X
ejpam-5317	486	2	13	13	NUM
ejpam-5317	486	3	]	]	PUNCT
ejpam-5317	486	4	v.	v.	CCONJ
ejpam-5317	486	5	wedeen	wedeen	PROPN
ejpam-5317	486	6	,	,	PUNCT
ejpam-5317	486	7	r.	r.	PROPN
ejpam-5317	486	8	wang	wang	PROPN
ejpam-5317	486	9	,	,	PUNCT
ejpam-5317	486	10	j.	j.	PROPN
ejpam-5317	486	11	schmahmann	schmahmann	PROPN
ejpam-5317	486	12	,	,	PUNCT
ejpam-5317	486	13	t.	t.	PROPN
ejpam-5317	486	14	benner	benner	PROPN
ejpam-5317	486	15	,	,	PUNCT
ejpam-5317	486	16	w.	w.	PROPN
ejpam-5317	486	17	tseng	tseng	PROPN
ejpam-5317	486	18	,	,	PUNCT
ejpam-5317	486	19	g.	g.	PROPN
ejpam-5317	486	20	dai	dai	PROPN
ejpam-5317	486	21	,	,	PUNCT
ejpam-5317	486	22	d.	d.	PROPN
ejpam-5317	486	23	pandya	pandya	PROPN
ejpam-5317	486	24	,	,	PUNCT
ejpam-5317	486	25	p.	p.	PROPN
ejpam-5317	486	26	hagmann	hagmann	PROPN
ejpam-5317	486	27	,	,	PUNCT
ejpam-5317	486	28	h.	h.	PROPN
ejpam-5317	486	29	d’arceuil	d’arceuil	PROPN
ejpam-5317	486	30	,	,	PUNCT
ejpam-5317	486	31	and	and	CCONJ
ejpam-5317	486	32	a.	a.	PROPN
ejpam-5317	486	33	de	de	PROPN
ejpam-5317	486	34	crespigny	crespigny	PROPN
ejpam-5317	486	35	.	.	PUNCT
ejpam-5317	487	1	diffusion	diffusion	NOUN
ejpam-5317	487	2	spectrum	spectrum	PROPN
ejpam-5317	487	3	magnetic	magnetic	ADJ
ejpam-5317	487	4	resonance	resonance	NOUN
ejpam-5317	487	5	imaging	imaging	NOUN
ejpam-5317	487	6	(	(	PUNCT
ejpam-5317	487	7	dsi	dsi	PROPN
ejpam-5317	487	8	)	)	PUNCT
ejpam-5317	487	9	tractography	tractography	NOUN
ejpam-5317	487	10	of	of	ADP
ejpam-5317	487	11	crossing	crossing	NOUN
ejpam-5317	487	12	fibers	fiber	NOUN
ejpam-5317	487	13	.	.	PUNCT
ejpam-5317	488	1	neuroimage	neuroimage	NOUN
ejpam-5317	488	2	,	,	PUNCT
ejpam-5317	488	3	41(4):1267–1277	41(4):1267–1277	NUM
ejpam-5317	488	4	,	,	PUNCT
ejpam-5317	488	5	2008	2008	NUM
ejpam-5317	488	6	.	.	PUNCT
ejpam-5317	489	1	[	[	X
ejpam-5317	489	2	14	14	NUM
ejpam-5317	489	3	]	]	X
ejpam-5317	489	4	yi	yi	PROPN
ejpam-5317	489	5	-	-	PUNCT
ejpam-5317	489	6	hui	hui	PROPN
ejpam-5317	489	7	zhou	zhou	PROPN
ejpam-5317	489	8	,	,	PUNCT
ejpam-5317	489	9	j.	j.	PROPN
ejpam-5317	489	10	s.	s.	PROPN
ejpam-5317	489	11	marron	marron	PROPN
ejpam-5317	489	12	,	,	PUNCT
ejpam-5317	489	13	and	and	CCONJ
ejpam-5317	489	14	a.	a.	NOUN
ejpam-5317	489	15	fred	fred	PROPN
ejpam-5317	489	16	.	.	PUNCT
ejpam-5317	490	1	eigenvalue	eigenvalue	NOUN
ejpam-5317	490	2	significance	significance	NOUN
ejpam-5317	490	3	testing	testing	NOUN
ejpam-5317	490	4	for	for	ADP
ejpam-5317	490	5	genetic	genetic	ADJ
ejpam-5317	490	6	association	association	NOUN
ejpam-5317	490	7	.	.	PUNCT
ejpam-5317	491	1	biometrics	biometric	NOUN
ejpam-5317	491	2	,	,	PUNCT
ejpam-5317	491	3	74(2):439–447	74(2):439–447	NUM
ejpam-5317	491	4	,	,	PUNCT
ejpam-5317	491	5	2018	2018	NUM
ejpam-5317	491	6	.	.	PUNCT