id	sid	tid	token	lemma	pos
ejpam-5637	1	1	european	european	PROPN
ejpam-5637	1	2	journal	journal	PROPN
ejpam-5637	1	3	of	of	ADP
ejpam-5637	1	4	pure	pure	ADJ
ejpam-5637	1	5	and	and	CCONJ
ejpam-5637	1	6	applied	applied	ADJ
ejpam-5637	1	7	mathematics	mathematic	NOUN
ejpam-5637	1	8	2025	2025	NUM
ejpam-5637	1	9	,	,	PUNCT
ejpam-5637	1	10	vol	vol	NOUN
ejpam-5637	1	11	.	.	PROPN
ejpam-5637	1	12	18	18	NUM
ejpam-5637	1	13	,	,	PUNCT
ejpam-5637	1	14	issue	issue	NOUN
ejpam-5637	1	15	1	1	NUM
ejpam-5637	1	16	,	,	PUNCT
ejpam-5637	1	17	article	article	NOUN
ejpam-5637	1	18	number	number	NOUN
ejpam-5637	1	19	5637	5637	NUM
ejpam-5637	1	20	issn	issn	PROPN
ejpam-5637	1	21	1307	1307	NUM
ejpam-5637	1	22	-	-	SYM
ejpam-5637	1	23	5543	5543	NUM
ejpam-5637	1	24	–	–	PUNCT
ejpam-5637	1	25	ejpam.com	ejpam.com	X
ejpam-5637	1	26	published	publish	VERB
ejpam-5637	1	27	by	by	ADP
ejpam-5637	1	28	new	new	PROPN
ejpam-5637	1	29	york	york	PROPN
ejpam-5637	1	30	business	business	PROPN
ejpam-5637	1	31	global	global	ADJ
ejpam-5637	1	32	spectral	spectral	ADJ
ejpam-5637	1	33	properties	property	NOUN
ejpam-5637	1	34	of	of	ADP
ejpam-5637	1	35	structured	structured	ADJ
ejpam-5637	1	36	matrices	matrix	NOUN
ejpam-5637	1	37	in	in	ADP
ejpam-5637	1	38	transportation	transportation	NOUN
ejpam-5637	1	39	problems	problem	NOUN
ejpam-5637	1	40	mutti	mutti	PROPN
ejpam-5637	1	41	-	-	PUNCT
ejpam-5637	1	42	ur	ur	NOUN
ejpam-5637	1	43	rehman1	rehman1	NOUN
ejpam-5637	1	44	,	,	PUNCT
ejpam-5637	1	45	behkzod	behkzod	PROPN
ejpam-5637	1	46	aminov2	aminov2	PROPN
ejpam-5637	1	47	,	,	PUNCT
ejpam-5637	1	48	mohammed	mohammed	PROPN
ejpam-5637	1	49	n.	n.	PROPN
ejpam-5637	1	50	alshehri3	alshehri3	PROPN
ejpam-5637	1	51	,	,	PUNCT
ejpam-5637	1	52	mustafa	mustafa	PROPN
ejpam-5637	1	53	m.	m.	PROPN
ejpam-5637	1	54	mohammed4	mohammed4	PROPN
ejpam-5637	1	55	,	,	PUNCT
ejpam-5637	1	56	arafa	arafa	ADJ
ejpam-5637	1	57	o.	o.	NOUN
ejpam-5637	1	58	mustafa5,∗	mustafa5,∗	PROPN
ejpam-5637	1	59	,	,	PUNCT
ejpam-5637	1	60	nhla	nhla	NOUN
ejpam-5637	1	61	a.	a.	PROPN
ejpam-5637	1	62	abdalrahman5	abdalrahman5	PROPN
ejpam-5637	1	63	,	,	PUNCT
ejpam-5637	1	64	mona	mona	PROPN
ejpam-5637	1	65	magzoub6	magzoub6	PROPN
ejpam-5637	1	66	,	,	PUNCT
ejpam-5637	1	67	sakeena	sakeena	PROPN
ejpam-5637	1	68	e.	e.	PROPN
ejpam-5637	1	69	m.	m.	PROPN
ejpam-5637	1	70	hamed5	hamed5	PROPN
ejpam-5637	1	71	,	,	PUNCT
ejpam-5637	1	72	runda	runda	PROPN
ejpam-5637	1	73	a.	a.	PROPN
ejpam-5637	1	74	a.	a.	NOUN
ejpam-5637	1	75	bashir4	bashir4	PROPN
ejpam-5637	1	76	,	,	PUNCT
ejpam-5637	1	77	awad	awad	PROPN
ejpam-5637	1	78	a.	a.	NOUN
ejpam-5637	1	79	bakery4,7,∗	bakery4,7,∗	ADV
ejpam-5637	1	80	1	1	NUM
ejpam-5637	1	81	center	center	NOUN
ejpam-5637	1	82	of	of	ADP
ejpam-5637	1	83	research	research	NOUN
ejpam-5637	1	84	and	and	CCONJ
ejpam-5637	1	85	innovation	innovation	NOUN
ejpam-5637	1	86	,	,	PUNCT
ejpam-5637	1	87	asia	asia	PROPN
ejpam-5637	1	88	international	international	PROPN
ejpam-5637	1	89	university	university	PROPN
ejpam-5637	1	90	,	,	PUNCT
ejpam-5637	1	91	yangiobod	yangiobod	ADJ
ejpam-5637	1	92	mfy	mfy	NOUN
ejpam-5637	1	93	,	,	PUNCT
ejpam-5637	1	94	g‘ijduvon	g‘ijduvon	PROPN
ejpam-5637	1	95	street	street	PROPN
ejpam-5637	1	96	,	,	PUNCT
ejpam-5637	1	97	house	house	NOUN
ejpam-5637	1	98	74	74	NUM
ejpam-5637	1	99	,	,	PUNCT
ejpam-5637	1	100	bukhara	bukhara	PROPN
ejpam-5637	1	101	,	,	PUNCT
ejpam-5637	1	102	uzbekistan	uzbekistan	PROPN
ejpam-5637	1	103	2	2	NUM
ejpam-5637	1	104	school	school	NOUN
ejpam-5637	1	105	of	of	ADP
ejpam-5637	1	106	engineering	engineering	NOUN
ejpam-5637	1	107	,	,	PUNCT
ejpam-5637	1	108	central	central	ADJ
ejpam-5637	1	109	asian	asian	ADJ
ejpam-5637	1	110	university	university	NOUN
ejpam-5637	1	111	,	,	PUNCT
ejpam-5637	1	112	tashkent	tashkent	NOUN
ejpam-5637	1	113	,	,	PUNCT
ejpam-5637	1	114	100027	100027	NUM
ejpam-5637	1	115	,	,	PUNCT
ejpam-5637	1	116	uzbekistan	uzbekistan	PROPN
ejpam-5637	1	117	3	3	NUM
ejpam-5637	1	118	department	department	NOUN
ejpam-5637	1	119	of	of	ADP
ejpam-5637	1	120	mathematics	mathematics	PROPN
ejpam-5637	1	121	,	,	PUNCT
ejpam-5637	1	122	college	college	NOUN
ejpam-5637	1	123	of	of	ADP
ejpam-5637	1	124	science	science	NOUN
ejpam-5637	1	125	and	and	CCONJ
ejpam-5637	1	126	arts	art	NOUN
ejpam-5637	1	127	,	,	PUNCT
ejpam-5637	1	128	najran	najran	ADJ
ejpam-5637	1	129	university	university	NOUN
ejpam-5637	1	130	,	,	PUNCT
ejpam-5637	1	131	najran	najran	NOUN
ejpam-5637	1	132	,	,	PUNCT
ejpam-5637	1	133	saudi	saudi	PROPN
ejpam-5637	1	134	arabia	arabia	PROPN
ejpam-5637	1	135	4	4	NUM
ejpam-5637	1	136	university	university	NOUN
ejpam-5637	1	137	of	of	ADP
ejpam-5637	1	138	jeddah	jeddah	PROPN
ejpam-5637	1	139	,	,	PUNCT
ejpam-5637	1	140	applied	apply	VERB
ejpam-5637	1	141	college	college	NOUN
ejpam-5637	1	142	at	at	ADP
ejpam-5637	1	143	khulis	khulis	PROPN
ejpam-5637	1	144	,	,	PUNCT
ejpam-5637	1	145	department	department	NOUN
ejpam-5637	1	146	of	of	ADP
ejpam-5637	1	147	mathematics	mathematics	PROPN
ejpam-5637	1	148	,	,	PUNCT
ejpam-5637	1	149	jeddah	jeddah	PROPN
ejpam-5637	1	150	,	,	PUNCT
ejpam-5637	1	151	saudi	saudi	PROPN
ejpam-5637	1	152	arabia	arabia	PROPN
ejpam-5637	1	153	5	5	NUM
ejpam-5637	1	154	university	university	NOUN
ejpam-5637	1	155	of	of	ADP
ejpam-5637	1	156	jeddah	jeddah	PROPN
ejpam-5637	1	157	,	,	PUNCT
ejpam-5637	1	158	college	college	NOUN
ejpam-5637	1	159	of	of	ADP
ejpam-5637	1	160	business	business	NOUN
ejpam-5637	1	161	at	at	ADP
ejpam-5637	1	162	khulis	khulis	PROPN
ejpam-5637	1	163	,	,	PUNCT
ejpam-5637	1	164	jeddah	jeddah	PROPN
ejpam-5637	1	165	,	,	PUNCT
ejpam-5637	1	166	saudi	saudi	PROPN
ejpam-5637	1	167	arabia	arabia	PROPN
ejpam-5637	1	168	6	6	NUM
ejpam-5637	1	169	mathematics	mathematics	PROPN
ejpam-5637	1	170	department	department	NOUN
ejpam-5637	1	171	,	,	PUNCT
ejpam-5637	1	172	applied	apply	VERB
ejpam-5637	1	173	college	college	NOUN
ejpam-5637	1	174	at	at	ADP
ejpam-5637	1	175	alkamil	alkamil	NOUN
ejpam-5637	1	176	,	,	PUNCT
ejpam-5637	1	177	university	university	NOUN
ejpam-5637	1	178	of	of	ADP
ejpam-5637	1	179	jeddah	jeddah	PROPN
ejpam-5637	1	180	,	,	PUNCT
ejpam-5637	1	181	saudi	saudi	PROPN
ejpam-5637	1	182	arabia	arabia	PROPN
ejpam-5637	1	183	7	7	NUM
ejpam-5637	1	184	ain	ain	PROPN
ejpam-5637	1	185	shams	sham	NOUN
ejpam-5637	1	186	university	university	NOUN
ejpam-5637	1	187	,	,	PUNCT
ejpam-5637	1	188	faculty	faculty	NOUN
ejpam-5637	1	189	of	of	ADP
ejpam-5637	1	190	science	science	NOUN
ejpam-5637	1	191	,	,	PUNCT
ejpam-5637	1	192	department	department	NOUN
ejpam-5637	1	193	of	of	ADP
ejpam-5637	1	194	mathematics	mathematics	PROPN
ejpam-5637	1	195	,	,	PUNCT
ejpam-5637	1	196	cairo	cairo	PROPN
ejpam-5637	1	197	,	,	PUNCT
ejpam-5637	1	198	abbassia	abbassia	PROPN
ejpam-5637	1	199	,	,	PUNCT
ejpam-5637	1	200	egypt	egypt	PROPN
ejpam-5637	1	201	abstract	abstract	PROPN
ejpam-5637	1	202	.	.	PUNCT
ejpam-5637	2	1	the	the	DET
ejpam-5637	2	2	hitchcock	hitchcock	PROPN
ejpam-5637	2	3	-	-	PUNCT
ejpam-5637	2	4	koopmans	koopmans	PROPN
ejpam-5637	2	5	transportation	transportation	NOUN
ejpam-5637	2	6	problem	problem	NOUN
ejpam-5637	2	7	is	be	AUX
ejpam-5637	2	8	a	a	DET
ejpam-5637	2	9	well	well	ADV
ejpam-5637	2	10	-	-	PUNCT
ejpam-5637	2	11	known	know	VERB
ejpam-5637	2	12	and	and	CCONJ
ejpam-5637	2	13	fundamental	fundamental	ADJ
ejpam-5637	2	14	optimization	optimization	NOUN
ejpam-5637	2	15	problem	problem	NOUN
ejpam-5637	2	16	which	which	PRON
ejpam-5637	2	17	focuses	focus	VERB
ejpam-5637	2	18	on	on	ADP
ejpam-5637	2	19	minimization	minimization	NOUN
ejpam-5637	2	20	of	of	ADP
ejpam-5637	2	21	the	the	DET
ejpam-5637	2	22	objective	objective	ADJ
ejpam-5637	2	23	function	function	NOUN
ejpam-5637	2	24	which	which	PRON
ejpam-5637	2	25	is	be	AUX
ejpam-5637	2	26	basically	basically	ADV
ejpam-5637	2	27	the	the	DET
ejpam-5637	2	28	transportation	transportation	NOUN
ejpam-5637	2	29	cost	cost	NOUN
ejpam-5637	2	30	from	from	ADP
ejpam-5637	2	31	multiple	multiple	ADJ
ejpam-5637	2	32	sources	source	NOUN
ejpam-5637	2	33	to	to	ADP
ejpam-5637	2	34	multiple	multiple	ADJ
ejpam-5637	2	35	destinations	destination	NOUN
ejpam-5637	2	36	.	.	PUNCT
ejpam-5637	3	1	in	in	ADP
ejpam-5637	3	2	this	this	DET
ejpam-5637	3	3	article	article	NOUN
ejpam-5637	3	4	,	,	PUNCT
ejpam-5637	3	5	we	we	PRON
ejpam-5637	3	6	present	present	VERB
ejpam-5637	3	7	some	some	DET
ejpam-5637	3	8	novel	novel	ADJ
ejpam-5637	3	9	results	result	NOUN
ejpam-5637	3	10	on	on	ADP
ejpam-5637	3	11	the	the	DET
ejpam-5637	3	12	spectral	spectral	ADJ
ejpam-5637	3	13	properties	property	NOUN
ejpam-5637	3	14	of	of	ADP
ejpam-5637	3	15	structured	structured	ADJ
ejpam-5637	3	16	matrices	matrix	NOUN
ejpam-5637	3	17	appearing	appear	VERB
ejpam-5637	3	18	in	in	ADP
ejpam-5637	3	19	hitchcock	hitchcock	NOUN
ejpam-5637	3	20	-	-	PUNCT
ejpam-5637	3	21	koopmans	koopmans	PROPN
ejpam-5637	3	22	transportation	transportation	NOUN
ejpam-5637	3	23	problems	problem	NOUN
ejpam-5637	3	24	.	.	PUNCT
ejpam-5637	4	1	the	the	DET
ejpam-5637	4	2	results	result	NOUN
ejpam-5637	4	3	on	on	ADP
ejpam-5637	4	4	the	the	DET
ejpam-5637	4	5	computation	computation	NOUN
ejpam-5637	4	6	of	of	ADP
ejpam-5637	4	7	singular	singular	ADJ
ejpam-5637	4	8	values	value	NOUN
ejpam-5637	4	9	are	be	AUX
ejpam-5637	4	10	presented	present	VERB
ejpam-5637	4	11	with	with	ADP
ejpam-5637	4	12	usage	usage	NOUN
ejpam-5637	4	13	of	of	ADP
ejpam-5637	4	14	tools	tool	NOUN
ejpam-5637	4	15	from	from	ADP
ejpam-5637	4	16	linear	linear	ADJ
ejpam-5637	4	17	algebra	algebra	NOUN
ejpam-5637	4	18	and	and	CCONJ
ejpam-5637	4	19	matrix	matrix	NOUN
ejpam-5637	4	20	analysis	analysis	NOUN
ejpam-5637	4	21	.	.	PUNCT
ejpam-5637	5	1	the	the	DET
ejpam-5637	5	2	new	new	ADJ
ejpam-5637	5	3	results	result	NOUN
ejpam-5637	5	4	are	be	AUX
ejpam-5637	5	5	derived	derive	VERB
ejpam-5637	5	6	on	on	ADP
ejpam-5637	5	7	interconnection	interconnection	NOUN
ejpam-5637	5	8	between	between	ADP
ejpam-5637	5	9	structured	structured	ADJ
ejpam-5637	5	10	singular	singular	ADJ
ejpam-5637	5	11	values	value	NOUN
ejpam-5637	5	12	of	of	ADP
ejpam-5637	5	13	pseudo	pseudo	NOUN
ejpam-5637	5	14	-	-	NOUN
ejpam-5637	5	15	inverse	inverse	ADJ
ejpam-5637	5	16	and	and	CCONJ
ejpam-5637	5	17	d	d	ADJ
ejpam-5637	5	18	-	-	ADJ
ejpam-5637	5	19	stable	stable	ADJ
ejpam-5637	5	20	matrices	matrix	NOUN
ejpam-5637	5	21	of	of	ADP
ejpam-5637	5	22	hitchcockkoopmans	hitchcockkoopmans	PROPN
ejpam-5637	5	23	transportation	transportation	NOUN
ejpam-5637	5	24	models	model	NOUN
ejpam-5637	5	25	.	.	PUNCT
ejpam-5637	6	1	the	the	DET
ejpam-5637	6	2	numerical	numerical	PROPN
ejpam-5637	6	3	experimentation	experimentation	NOUN
ejpam-5637	6	4	shows	show	VERB
ejpam-5637	6	5	the	the	DET
ejpam-5637	6	6	behavior	behavior	NOUN
ejpam-5637	6	7	of	of	ADP
ejpam-5637	6	8	singular	singular	ADJ
ejpam-5637	6	9	values	value	NOUN
ejpam-5637	6	10	.	.	PUNCT
ejpam-5637	7	1	the	the	DET
ejpam-5637	7	2	matlab	matlab	PROPN
ejpam-5637	7	3	eigtool	eigtool	NOUN
ejpam-5637	7	4	is	be	AUX
ejpam-5637	7	5	used	use	VERB
ejpam-5637	7	6	for	for	ADP
ejpam-5637	7	7	the	the	DET
ejpam-5637	7	8	computation	computation	NOUN
ejpam-5637	7	9	of	of	ADP
ejpam-5637	7	10	pseudo	pseudo	NOUN
ejpam-5637	7	11	-	-	NOUN
ejpam-5637	7	12	spectrum	spectrum	NOUN
ejpam-5637	7	13	of	of	ADP
ejpam-5637	7	14	pseudo	pseudo	NOUN
ejpam-5637	7	15	-	-	ADJ
ejpam-5637	7	16	inverse	inverse	ADJ
ejpam-5637	7	17	matrix	matrix	NOUN
ejpam-5637	7	18	corresponding	correspond	VERB
ejpam-5637	7	19	to	to	ADP
ejpam-5637	7	20	the	the	DET
ejpam-5637	7	21	transportation	transportation	NOUN
ejpam-5637	7	22	model	model	NOUN
ejpam-5637	7	23	.	.	PUNCT
ejpam-5637	8	1	2020	2020	NUM
ejpam-5637	8	2	mathematics	mathematics	PROPN
ejpam-5637	8	3	subject	subject	NOUN
ejpam-5637	8	4	classifications	classification	NOUN
ejpam-5637	8	5	:	:	PUNCT
ejpam-5637	8	6	15a18	15a18	NUM
ejpam-5637	8	7	,	,	PUNCT
ejpam-5637	8	8	15a16	15a16	NUM
ejpam-5637	8	9	15a23	15a23	NUM
ejpam-5637	8	10	key	key	ADJ
ejpam-5637	8	11	words	word	NOUN
ejpam-5637	8	12	and	and	CCONJ
ejpam-5637	8	13	phrases	phrase	NOUN
ejpam-5637	8	14	:	:	PUNCT
ejpam-5637	8	15	hitchcock	hitchcock	NOUN
ejpam-5637	8	16	-	-	PUNCT
ejpam-5637	8	17	koompan	koompan	PROPN
ejpam-5637	8	18	model	model	NOUN
ejpam-5637	8	19	,	,	PUNCT
ejpam-5637	8	20	singular	singular	ADJ
ejpam-5637	8	21	values	value	NOUN
ejpam-5637	8	22	,	,	PUNCT
ejpam-5637	8	23	structured	structure	VERB
ejpam-5637	8	24	singular	singular	ADJ
ejpam-5637	8	25	values	value	NOUN
ejpam-5637	8	26	,	,	PUNCT
ejpam-5637	8	27	d	d	ADJ
ejpam-5637	8	28	-	-	ADJ
ejpam-5637	8	29	stable	stable	ADJ
ejpam-5637	8	30	matrices	matrix	NOUN
ejpam-5637	8	31	,	,	PUNCT
ejpam-5637	8	32	pseudo	pseudo	NOUN
ejpam-5637	8	33	-	-	NOUN
ejpam-5637	8	34	spectrum	spectrum	ADJ
ejpam-5637	8	35	∗corresponding	∗corresponde	VERB
ejpam-5637	8	36	author	author	NOUN
ejpam-5637	8	37	.	.	PUNCT
ejpam-5637	9	1	∗corresponding	∗corresponde	VERB
ejpam-5637	9	2	author	author	NOUN
ejpam-5637	9	3	.	.	PUNCT
ejpam-5637	10	1	doi	doi	NOUN
ejpam-5637	10	2	:	:	PUNCT
ejpam-5637	10	3	https://doi.org/10.29020/nybg.ejpam.v18i1.5637	https://doi.org/10.29020/nybg.ejpam.v18i1.5637	NUM
ejpam-5637	10	4	email	email	NOUN
ejpam-5637	10	5	addresses	address	NOUN
ejpam-5637	10	6	:	:	PUNCT
ejpam-5637	10	7	muttiur.abbasi@oxu.uz	muttiur.abbasi@oxu.uz	NOUN
ejpam-5637	10	8	(	(	PUNCT
ejpam-5637	10	9	mutti	mutti	PROPN
ejpam-5637	10	10	-	-	PUNCT
ejpam-5637	10	11	ur	ur	PROPN
ejpam-5637	10	12	rehman	rehman	PROPN
ejpam-5637	10	13	)	)	PUNCT
ejpam-5637	10	14	,	,	PUNCT
ejpam-5637	10	15	b.aminov@centralasian.uz	b.aminov@centralasian.uz	PUNCT
ejpam-5637	10	16	(	(	PUNCT
ejpam-5637	10	17	behkzod	behkzod	NOUN
ejpam-5637	10	18	aminov	aminov	PROPN
ejpam-5637	10	19	)	)	PUNCT
ejpam-5637	10	20	,	,	PUNCT
ejpam-5637	10	21	mnalshhri@nu.edu.sa	mnalshhri@nu.edu.sa	PROPN
ejpam-5637	10	22	(	(	PUNCT
ejpam-5637	10	23	mohammed	mohammed	PROPN
ejpam-5637	10	24	n.	n.	PROPN
ejpam-5637	10	25	alshehri	alshehri	PROPN
ejpam-5637	10	26	)	)	PUNCT
ejpam-5637	10	27	,	,	PUNCT
ejpam-5637	10	28	mustasta@yahoo.com	mustasta@yahoo.com	X
ejpam-5637	10	29	and	and	CCONJ
ejpam-5637	10	30	mmibrahim@uj.edu.sa	mmibrahim@uj.edu.sa	PROPN
ejpam-5637	10	31	(	(	PUNCT
ejpam-5637	10	32	mustafa	mustafa	PROPN
ejpam-5637	10	33	m.	m.	PROPN
ejpam-5637	10	34	mohammed	mohammed	PROPN
ejpam-5637	10	35	)	)	PUNCT
ejpam-5637	10	36	,	,	PUNCT
ejpam-5637	10	37	arafaomustafa2020@yahoo.com	arafaomustafa2020@yahoo.com	PUNCT
ejpam-5637	10	38	and	and	CCONJ
ejpam-5637	10	39	04220355@uj.edu.sa	04220355@uj.edu.sa	PROPN
ejpam-5637	10	40	(	(	PUNCT
ejpam-5637	10	41	arafa	arafa	PROPN
ejpam-5637	10	42	o.	o.	PROPN
ejpam-5637	10	43	mustafa	mustafa	PROPN
ejpam-5637	10	44	)	)	PUNCT
ejpam-5637	10	45	,	,	PUNCT
ejpam-5637	10	46	04220332@uj.edu.sa	04220332@uj.edu.sa	PROPN
ejpam-5637	10	47	(	(	PUNCT
ejpam-5637	10	48	nhla	nhla	NOUN
ejpam-5637	10	49	a.	a.	NOUN
ejpam-5637	10	50	abdalrahman	abdalrahman	PROPN
ejpam-5637	10	51	)	)	PUNCT
ejpam-5637	10	52	,	,	PUNCT
ejpam-5637	11	1	mmahmed@uj.edu.sa	mmahmed@uj.edu.sa	PROPN
ejpam-5637	11	2	(	(	PUNCT
ejpam-5637	11	3	mona	mona	PROPN
ejpam-5637	11	4	magzoub	magzoub	PROPN
ejpam-5637	11	5	)	)	PUNCT
ejpam-5637	11	6	,	,	PUNCT
ejpam-5637	11	7	04220347@uj.edu.sa	04220347@uj.edu.sa	PROPN
ejpam-5637	11	8	(	(	PUNCT
ejpam-5637	11	9	sakeena	sakeena	PROPN
ejpam-5637	11	10	e.	e.	PROPN
ejpam-5637	11	11	m.	m.	PROPN
ejpam-5637	11	12	hamed	hamed	PROPN
ejpam-5637	11	13	)	)	PUNCT
ejpam-5637	11	14	,	,	PUNCT
ejpam-5637	11	15	rabasher@uj.edu.sa	rabasher@uj.edu.sa	PROPN
ejpam-5637	11	16	(	(	PUNCT
ejpam-5637	11	17	runda	runda	PROPN
ejpam-5637	11	18	a.	a.	PROPN
ejpam-5637	11	19	a.	a.	PROPN
ejpam-5637	11	20	bashir	bashir	PROPN
ejpam-5637	11	21	)	)	PUNCT
ejpam-5637	11	22	,	,	PUNCT
ejpam-5637	11	23	aabhassan@uj.edu.sa	aabhassan@uj.edu.sa	PROPN
ejpam-5637	11	24	(	(	PUNCT
ejpam-5637	11	25	awad	awad	PROPN
ejpam-5637	11	26	a.	a.	PROPN
ejpam-5637	11	27	bakery	bakery	PROPN
ejpam-5637	11	28	)	)	PUNCT
ejpam-5637	11	29	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-5637	12	1	1	1	NUM
ejpam-5637	12	2	copyright	copyright	NOUN
ejpam-5637	12	3	:	:	PUNCT
ejpam-5637	12	4	©	©	PROPN
ejpam-5637	12	5	2025	2025	NUM
ejpam-5637	12	6	the	the	DET
ejpam-5637	12	7	author(s	author(s	NOUN
ejpam-5637	12	8	)	)	PUNCT
ejpam-5637	12	9	.	.	PUNCT
ejpam-5637	13	1	(	(	PUNCT
ejpam-5637	13	2	cc	cc	NOUN
ejpam-5637	13	3	by	by	ADP
ejpam-5637	13	4	-	-	PUNCT
ejpam-5637	13	5	nc	nc	PROPN
ejpam-5637	13	6	4.0	4.0	NUM
ejpam-5637	13	7	)	)	PUNCT
ejpam-5637	13	8	m.u	m.u	PROPN
ejpam-5637	13	9	.	.	PUNCT
ejpam-5637	13	10	rahman	rahman	PROPN
ejpam-5637	13	11	et	et	PROPN
ejpam-5637	13	12	al	al	PROPN
ejpam-5637	13	13	.	.	PUNCT
ejpam-5637	13	14	/	/	SYM
ejpam-5637	13	15	eur	eur	PROPN
ejpam-5637	13	16	.	.	PUNCT
ejpam-5637	14	1	j.	j.	PROPN
ejpam-5637	14	2	pure	pure	PROPN
ejpam-5637	14	3	appl	appl	PROPN
ejpam-5637	14	4	.	.	PROPN
ejpam-5637	14	5	math	math	PROPN
ejpam-5637	14	6	,	,	PUNCT
ejpam-5637	14	7	18	18	NUM
ejpam-5637	14	8	(	(	PUNCT
ejpam-5637	14	9	1	1	NUM
ejpam-5637	14	10	)	)	PUNCT
ejpam-5637	14	11	(	(	PUNCT
ejpam-5637	14	12	2025	2025	NUM
ejpam-5637	14	13	)	)	PUNCT
ejpam-5637	14	14	,	,	PUNCT
ejpam-5637	14	15	5637	5637	NUM
ejpam-5637	14	16	2	2	NUM
ejpam-5637	14	17	of	of	ADP
ejpam-5637	14	18	20	20	NUM
ejpam-5637	14	19	1	1	NUM
ejpam-5637	14	20	.	.	PUNCT
ejpam-5637	15	1	introduction	introduction	NOUN
ejpam-5637	15	2	the	the	DET
ejpam-5637	15	3	transportation	transportation	NOUN
ejpam-5637	15	4	theory	theory	NOUN
ejpam-5637	15	5	is	be	AUX
ejpam-5637	15	6	a	a	DET
ejpam-5637	15	7	name	name	NOUN
ejpam-5637	15	8	given	give	VERB
ejpam-5637	15	9	to	to	PART
ejpam-5637	15	10	study	study	VERB
ejpam-5637	15	11	of	of	ADP
ejpam-5637	15	12	optimal	optimal	ADJ
ejpam-5637	15	13	transportation	transportation	NOUN
ejpam-5637	15	14	and	and	CCONJ
ejpam-5637	15	15	the	the	DET
ejpam-5637	15	16	allocation	allocation	NOUN
ejpam-5637	15	17	of	of	ADP
ejpam-5637	15	18	resources	resource	NOUN
ejpam-5637	15	19	.	.	PUNCT
ejpam-5637	16	1	in	in	ADP
ejpam-5637	16	2	optimization	optimization	NOUN
ejpam-5637	16	3	,	,	PUNCT
ejpam-5637	16	4	the	the	DET
ejpam-5637	16	5	transportation	transportation	NOUN
ejpam-5637	16	6	problem	problem	NOUN
ejpam-5637	16	7	was	be	AUX
ejpam-5637	16	8	earlier	early	ADV
ejpam-5637	16	9	formalized	formalize	VERB
ejpam-5637	16	10	by	by	ADP
ejpam-5637	16	11	a	a	DET
ejpam-5637	16	12	french	french	ADJ
ejpam-5637	16	13	mathematician	mathematician	NOUN
ejpam-5637	16	14	gaspard	gaspard	PROPN
ejpam-5637	16	15	monge	monge	PROPN
ejpam-5637	16	16	,	,	PUNCT
ejpam-5637	16	17	and	and	CCONJ
ejpam-5637	16	18	then	then	ADV
ejpam-5637	16	19	a.n	a.n	PROPN
ejpam-5637	16	20	.	.	PROPN
ejpam-5637	16	21	talstoi	talstoi	PROPN
ejpam-5637	16	22	first	first	ADJ
ejpam-5637	16	23	studied	study	VERB
ejpam-5637	16	24	transport	transport	NOUN
ejpam-5637	16	25	problem	problem	NOUN
ejpam-5637	16	26	mathematically	mathematically	ADV
ejpam-5637	16	27	in	in	ADP
ejpam-5637	16	28	1920	1920	NUM
ejpam-5637	16	29	and	and	CCONJ
ejpam-5637	16	30	published	publish	VERB
ejpam-5637	16	31	an	an	DET
ejpam-5637	16	32	article	article	NOUN
ejpam-5637	16	33	with	with	ADP
ejpam-5637	16	34	titled	title	VERB
ejpam-5637	16	35	:	:	PUNCT
ejpam-5637	16	36	methods	method	NOUN
ejpam-5637	16	37	of	of	ADP
ejpam-5637	16	38	finding	find	VERB
ejpam-5637	16	39	minimal	minimal	ADJ
ejpam-5637	16	40	kilometrage	kilometrage	NOUN
ejpam-5637	16	41	in	in	ADP
ejpam-5637	16	42	the	the	DET
ejpam-5637	16	43	cargo	cargo	NOUN
ejpam-5637	16	44	-	-	PUNCT
ejpam-5637	16	45	transportation	transportation	NOUN
ejpam-5637	16	46	in	in	ADP
ejpam-5637	16	47	space	space	NOUN
ejpam-5637	16	48	.	.	PUNCT
ejpam-5637	17	1	the	the	DET
ejpam-5637	17	2	transportation	transportation	NOUN
ejpam-5637	17	3	problem	problem	NOUN
ejpam-5637	17	4	for	for	ADP
ejpam-5637	17	5	m	m	NOUN
ejpam-5637	17	6	numbers	number	NOUN
ejpam-5637	17	7	of	of	ADP
ejpam-5637	17	8	sources	source	NOUN
ejpam-5637	17	9	x1	x1	NUM
ejpam-5637	17	10	,	,	PUNCT
ejpam-5637	17	11	x2	x2	PROPN
ejpam-5637	17	12	,	,	PUNCT
ejpam-5637	17	13	·	·	PUNCT
ejpam-5637	17	14	·	·	PUNCT
ejpam-5637	17	15	·	·	PUNCT
ejpam-5637	17	16	,	,	PUNCT
ejpam-5637	17	17	xm	xm	PROPN
ejpam-5637	17	18	for	for	ADP
ejpam-5637	17	19	a	a	DET
ejpam-5637	17	20	given	give	VERB
ejpam-5637	17	21	commodity	commodity	NOUN
ejpam-5637	17	22	having	have	VERB
ejpam-5637	17	23	a(xi	a(xi	PROPN
ejpam-5637	17	24	)	)	PUNCT
ejpam-5637	17	25	number	number	NOUN
ejpam-5637	17	26	of	of	ADP
ejpam-5637	17	27	units	unit	NOUN
ejpam-5637	17	28	of	of	ADP
ejpam-5637	17	29	supply	supply	NOUN
ejpam-5637	17	30	at	at	ADP
ejpam-5637	17	31	xi	xi	NOUN
ejpam-5637	17	32	points	point	NOUN
ejpam-5637	17	33	and	and	CCONJ
ejpam-5637	17	34	n	n	DET
ejpam-5637	17	35	number	number	NOUN
ejpam-5637	17	36	of	of	ADP
ejpam-5637	17	37	sinks	sink	NOUN
ejpam-5637	17	38	y1	y1	PROPN
ejpam-5637	17	39	,	,	PUNCT
ejpam-5637	17	40	y2	y2	PROPN
ejpam-5637	17	41	,	,	PUNCT
ejpam-5637	17	42	·	·	PUNCT
ejpam-5637	17	43	·	·	PUNCT
ejpam-5637	17	44	·	·	PUNCT
ejpam-5637	17	45	,	,	PUNCT
ejpam-5637	17	46	yn	yn	PROPN
ejpam-5637	17	47	for	for	ADP
ejpam-5637	17	48	commodity	commodity	NOUN
ejpam-5637	17	49	.	.	PUNCT
ejpam-5637	18	1	the	the	DET
ejpam-5637	18	2	demand	demand	NOUN
ejpam-5637	18	3	at	at	ADP
ejpam-5637	18	4	yj	yj	PROPN
ejpam-5637	18	5	is	be	AUX
ejpam-5637	18	6	considered	consider	VERB
ejpam-5637	18	7	as	as	ADP
ejpam-5637	18	8	b(yj	b(yj	NOUN
ejpam-5637	18	9	)	)	PUNCT
ejpam-5637	18	10	.	.	PUNCT
ejpam-5637	19	1	let	let	VERB
ejpam-5637	19	2	xi	xi	NOUN
ejpam-5637	19	3	and	and	CCONJ
ejpam-5637	19	4	yi	yi	PROPN
ejpam-5637	19	5	,	,	PUNCT
ejpam-5637	19	6	a(xi	a(xi	PROPN
ejpam-5637	19	7	,	,	PUNCT
ejpam-5637	19	8	yi	yi	NOUN
ejpam-5637	19	9	)	)	PUNCT
ejpam-5637	19	10	represents	represent	VERB
ejpam-5637	19	11	the	the	DET
ejpam-5637	19	12	unit	unit	NOUN
ejpam-5637	19	13	cost	cost	NOUN
ejpam-5637	19	14	of	of	ADP
ejpam-5637	19	15	shipment	shipment	NOUN
ejpam-5637	19	16	.	.	PUNCT
ejpam-5637	20	1	then	then	ADV
ejpam-5637	20	2	,	,	PUNCT
ejpam-5637	20	3	the	the	DET
ejpam-5637	20	4	question	question	NOUN
ejpam-5637	20	5	of	of	ADP
ejpam-5637	20	6	finding	find	VERB
ejpam-5637	20	7	flow	flow	NOUN
ejpam-5637	20	8	satisfying	satisfy	VERB
ejpam-5637	20	9	the	the	DET
ejpam-5637	20	10	demand	demand	NOUN
ejpam-5637	20	11	from	from	ADP
ejpam-5637	20	12	supplies	supply	NOUN
ejpam-5637	20	13	,	,	PUNCT
ejpam-5637	20	14	and	and	CCONJ
ejpam-5637	20	15	to	to	PART
ejpam-5637	20	16	minimize	minimize	VERB
ejpam-5637	20	17	the	the	DET
ejpam-5637	20	18	cost	cost	NOUN
ejpam-5637	20	19	was	be	AUX
ejpam-5637	20	20	studied	study	VERB
ejpam-5637	20	21	in	in	ADP
ejpam-5637	20	22	[	[	X
ejpam-5637	20	23	15	15	NUM
ejpam-5637	20	24	,	,	PUNCT
ejpam-5637	20	25	16	16	NUM
ejpam-5637	20	26	,	,	PUNCT
ejpam-5637	20	27	18	18	NUM
ejpam-5637	20	28	]	]	PUNCT
ejpam-5637	20	29	.	.	PUNCT
ejpam-5637	21	1	transportation	transportation	NOUN
ejpam-5637	21	2	problems	problem	NOUN
ejpam-5637	21	3	can	can	AUX
ejpam-5637	21	4	be	be	AUX
ejpam-5637	21	5	considered	consider	VERB
ejpam-5637	21	6	as	as	ADP
ejpam-5637	21	7	an	an	DET
ejpam-5637	21	8	optimization	optimization	NOUN
ejpam-5637	21	9	problems	problem	NOUN
ejpam-5637	21	10	,	,	PUNCT
ejpam-5637	21	11	particularly	particularly	ADV
ejpam-5637	21	12	the	the	DET
ejpam-5637	21	13	linear	linear	PROPN
ejpam-5637	21	14	optimization	optimization	NOUN
ejpam-5637	21	15	.	.	PUNCT
ejpam-5637	22	1	in	in	ADP
ejpam-5637	22	2	linear	linear	PROPN
ejpam-5637	22	3	optimization	optimization	NOUN
ejpam-5637	22	4	the	the	DET
ejpam-5637	22	5	aim	aim	NOUN
ejpam-5637	22	6	could	could	AUX
ejpam-5637	22	7	be	be	AUX
ejpam-5637	22	8	in	in	ADP
ejpam-5637	22	9	finding	find	VERB
ejpam-5637	22	10	effective	effective	ADJ
ejpam-5637	22	11	techniques	technique	NOUN
ejpam-5637	22	12	in	in	ADP
ejpam-5637	22	13	order	order	NOUN
ejpam-5637	22	14	to	to	PART
ejpam-5637	22	15	distribute	distribute	VERB
ejpam-5637	22	16	goods	good	NOUN
ejpam-5637	22	17	from	from	ADP
ejpam-5637	22	18	many	many	ADJ
ejpam-5637	22	19	suppliers	supplier	NOUN
ejpam-5637	22	20	to	to	ADP
ejpam-5637	22	21	many	many	ADJ
ejpam-5637	22	22	final	final	ADJ
ejpam-5637	22	23	destinations	destination	NOUN
ejpam-5637	22	24	.	.	PUNCT
ejpam-5637	23	1	the	the	DET
ejpam-5637	23	2	mathematical	mathematical	ADJ
ejpam-5637	23	3	concepts	concept	NOUN
ejpam-5637	23	4	dealing	deal	VERB
ejpam-5637	23	5	with	with	ADP
ejpam-5637	23	6	transportation	transportation	NOUN
ejpam-5637	23	7	problems	problem	NOUN
ejpam-5637	23	8	involves	involve	VERB
ejpam-5637	23	9	the	the	DET
ejpam-5637	23	10	analysis	analysis	NOUN
ejpam-5637	23	11	of	of	ADP
ejpam-5637	23	12	structured	structured	ADJ
ejpam-5637	23	13	and	and	CCONJ
ejpam-5637	23	14	,	,	PUNCT
ejpam-5637	23	15	unstructured	unstructured	ADJ
ejpam-5637	23	16	matrices	matrix	NOUN
ejpam-5637	23	17	representing	represent	VERB
ejpam-5637	23	18	supply	supply	NOUN
ejpam-5637	23	19	,	,	PUNCT
ejpam-5637	23	20	demand	demand	NOUN
ejpam-5637	23	21	,	,	PUNCT
ejpam-5637	23	22	and	and	CCONJ
ejpam-5637	23	23	transportation	transportation	NOUN
ejpam-5637	23	24	costs	cost	NOUN
ejpam-5637	23	25	.	.	PUNCT
ejpam-5637	24	1	the	the	DET
ejpam-5637	24	2	notable	notable	ADJ
ejpam-5637	24	3	methods	method	NOUN
ejpam-5637	24	4	likewise	likewise	ADV
ejpam-5637	24	5	northwest	northwest	NOUN
ejpam-5637	24	6	corner	corner	NOUN
ejpam-5637	24	7	rule	rule	NOUN
ejpam-5637	24	8	,	,	PUNCT
ejpam-5637	24	9	least	least	ADJ
ejpam-5637	24	10	cost	cost	NOUN
ejpam-5637	24	11	technique	technique	NOUN
ejpam-5637	24	12	,	,	PUNCT
ejpam-5637	24	13	and	and	CCONJ
ejpam-5637	24	14	vogel	vogel	NOUN
ejpam-5637	24	15	’s	’s	PART
ejpam-5637	24	16	approximation	approximation	NOUN
ejpam-5637	24	17	method	method	NOUN
ejpam-5637	24	18	are	be	AUX
ejpam-5637	24	19	developed	develop	VERB
ejpam-5637	24	20	to	to	PART
ejpam-5637	24	21	find	find	VERB
ejpam-5637	24	22	initial	initial	ADJ
ejpam-5637	24	23	feasible	feasible	ADJ
ejpam-5637	24	24	solutions	solution	NOUN
ejpam-5637	24	25	corresponding	correspond	VERB
ejpam-5637	24	26	to	to	ADP
ejpam-5637	24	27	the	the	DET
ejpam-5637	24	28	optimization	optimization	NOUN
ejpam-5637	24	29	problems	problem	NOUN
ejpam-5637	24	30	.	.	PUNCT
ejpam-5637	25	1	on	on	ADP
ejpam-5637	25	2	the	the	DET
ejpam-5637	25	3	other	other	ADJ
ejpam-5637	25	4	hand	hand	NOUN
ejpam-5637	25	5	,	,	PUNCT
ejpam-5637	25	6	the	the	DET
ejpam-5637	25	7	optimization	optimization	NOUN
ejpam-5637	25	8	methods	method	NOUN
ejpam-5637	25	9	for	for	ADP
ejpam-5637	25	10	instance	instance	NOUN
ejpam-5637	25	11	modified	modify	VERB
ejpam-5637	25	12	distribution	distribution	NOUN
ejpam-5637	25	13	(	(	PUNCT
ejpam-5637	25	14	modi	modi	PROPN
ejpam-5637	25	15	)	)	PUNCT
ejpam-5637	25	16	method	method	NOUN
ejpam-5637	25	17	or	or	CCONJ
ejpam-5637	25	18	stepping	stepping	ADJ
ejpam-5637	25	19	-	-	PUNCT
ejpam-5637	25	20	stone	stone	NOUN
ejpam-5637	25	21	method	method	NOUN
ejpam-5637	25	22	are	be	AUX
ejpam-5637	25	23	used	use	VERB
ejpam-5637	25	24	to	to	PART
ejpam-5637	25	25	analyze	analyze	VERB
ejpam-5637	25	26	and	and	CCONJ
ejpam-5637	25	27	refine	refine	VERB
ejpam-5637	25	28	obtained	obtain	VERB
ejpam-5637	25	29	solutions	solution	NOUN
ejpam-5637	25	30	for	for	ADP
ejpam-5637	25	31	the	the	DET
ejpam-5637	25	32	purpose	purpose	NOUN
ejpam-5637	25	33	of	of	ADP
ejpam-5637	25	34	achieving	achieve	VERB
ejpam-5637	25	35	optimality	optimality	NOUN
ejpam-5637	25	36	conditions	condition	NOUN
ejpam-5637	25	37	.	.	PUNCT
ejpam-5637	26	1	the	the	DET
ejpam-5637	26	2	transportation	transportation	NOUN
ejpam-5637	26	3	problems	problem	NOUN
ejpam-5637	26	4	have	have	VERB
ejpam-5637	26	5	an	an	DET
ejpam-5637	26	6	extensive	extensive	ADJ
ejpam-5637	26	7	amount	amount	NOUN
ejpam-5637	26	8	of	of	ADP
ejpam-5637	26	9	applications	application	NOUN
ejpam-5637	26	10	in	in	ADP
ejpam-5637	26	11	many	many	ADJ
ejpam-5637	26	12	diverse	diverse	ADJ
ejpam-5637	26	13	range	range	NOUN
ejpam-5637	26	14	of	of	ADP
ejpam-5637	26	15	research	research	NOUN
ejpam-5637	26	16	directions	direction	NOUN
ejpam-5637	26	17	[	[	X
ejpam-5637	26	18	2	2	NUM
ejpam-5637	26	19	,	,	PUNCT
ejpam-5637	26	20	10	10	NUM
ejpam-5637	26	21	]	]	PUNCT
ejpam-5637	26	22	.	.	PUNCT
ejpam-5637	27	1	in	in	ADP
ejpam-5637	27	2	[	[	X
ejpam-5637	27	3	4	4	NUM
ejpam-5637	27	4	]	]	PUNCT
ejpam-5637	27	5	,	,	PUNCT
ejpam-5637	27	6	the	the	DET
ejpam-5637	27	7	service	service	NOUN
ejpam-5637	27	8	network	network	NOUN
ejpam-5637	27	9	design	design	NOUN
ejpam-5637	27	10	problems	problem	NOUN
ejpam-5637	27	11	were	be	AUX
ejpam-5637	27	12	studied	study	VERB
ejpam-5637	27	13	in	in	ADP
ejpam-5637	27	14	order	order	NOUN
ejpam-5637	27	15	to	to	PART
ejpam-5637	27	16	measure	measure	VERB
ejpam-5637	27	17	the	the	DET
ejpam-5637	27	18	minimum	minimum	ADJ
ejpam-5637	27	19	cost	cost	NOUN
ejpam-5637	27	20	with	with	ADP
ejpam-5637	27	21	given	give	VERB
ejpam-5637	27	22	constraints	constraint	NOUN
ejpam-5637	27	23	.	.	PUNCT
ejpam-5637	28	1	to	to	PART
ejpam-5637	28	2	study	study	VERB
ejpam-5637	28	3	the	the	DET
ejpam-5637	28	4	evolution	evolution	NOUN
ejpam-5637	28	5	of	of	ADP
ejpam-5637	28	6	coalition	coalition	NOUN
ejpam-5637	28	7	over	over	ADP
ejpam-5637	28	8	a	a	DET
ejpam-5637	28	9	given	give	VERB
ejpam-5637	28	10	time	time	NOUN
ejpam-5637	28	11	with	with	ADP
ejpam-5637	28	12	trust	trust	NOUN
ejpam-5637	28	13	-	-	PUNCT
ejpam-5637	28	14	related	relate	VERB
ejpam-5637	28	15	issues	issue	NOUN
ejpam-5637	28	16	,	,	PUNCT
ejpam-5637	28	17	an	an	DET
ejpam-5637	28	18	agent	agent	NOUN
ejpam-5637	28	19	-	-	PUNCT
ejpam-5637	28	20	based	base	VERB
ejpam-5637	28	21	model	model	NOUN
ejpam-5637	28	22	was	be	AUX
ejpam-5637	28	23	developed	develop	VERB
ejpam-5637	28	24	in	in	ADP
ejpam-5637	28	25	[	[	X
ejpam-5637	28	26	45	45	NUM
ejpam-5637	28	27	]	]	PUNCT
ejpam-5637	28	28	.	.	PUNCT
ejpam-5637	29	1	the	the	DET
ejpam-5637	29	2	traditional	traditional	ADJ
ejpam-5637	29	3	transportation	transportation	NOUN
ejpam-5637	29	4	models	model	NOUN
ejpam-5637	29	5	deals	deal	VERB
ejpam-5637	29	6	with	with	ADP
ejpam-5637	29	7	the	the	DET
ejpam-5637	29	8	problems	problem	NOUN
ejpam-5637	29	9	like	like	ADP
ejpam-5637	29	10	transportation	transportation	NOUN
ejpam-5637	29	11	costs	cost	NOUN
ejpam-5637	29	12	,	,	PUNCT
ejpam-5637	29	13	delivery	delivery	NOUN
ejpam-5637	29	14	routes	route	NOUN
ejpam-5637	29	15	,	,	PUNCT
ejpam-5637	29	16	production	production	NOUN
ejpam-5637	29	17	places	place	NOUN
ejpam-5637	29	18	,	,	PUNCT
ejpam-5637	29	19	and	and	CCONJ
ejpam-5637	29	20	the	the	DET
ejpam-5637	29	21	reduction	reduction	NOUN
ejpam-5637	29	22	of	of	ADP
ejpam-5637	29	23	carbon	carbon	NOUN
ejpam-5637	29	24	emissions	emission	NOUN
ejpam-5637	29	25	[	[	X
ejpam-5637	29	26	42	42	NUM
ejpam-5637	29	27	,	,	PUNCT
ejpam-5637	29	28	43	43	NUM
ejpam-5637	29	29	,	,	PUNCT
ejpam-5637	29	30	48	48	NUM
ejpam-5637	29	31	,	,	PUNCT
ejpam-5637	29	32	54	54	NUM
ejpam-5637	29	33	]	]	PUNCT
ejpam-5637	29	34	.	.	PUNCT
ejpam-5637	30	1	the	the	DET
ejpam-5637	30	2	transportation	transportation	NOUN
ejpam-5637	30	3	algorithms	algorithm	NOUN
ejpam-5637	30	4	[	[	X
ejpam-5637	30	5	17	17	NUM
ejpam-5637	30	6	,	,	PUNCT
ejpam-5637	30	7	34	34	NUM
ejpam-5637	30	8	,	,	PUNCT
ejpam-5637	30	9	51	51	NUM
ejpam-5637	30	10	]	]	PUNCT
ejpam-5637	30	11	were	be	AUX
ejpam-5637	30	12	developed	develop	VERB
ejpam-5637	30	13	to	to	PART
ejpam-5637	30	14	solve	solve	VERB
ejpam-5637	30	15	practical	practical	ADJ
ejpam-5637	30	16	nature	nature	NOUN
ejpam-5637	30	17	of	of	ADP
ejpam-5637	30	18	the	the	DET
ejpam-5637	30	19	problems	problem	NOUN
ejpam-5637	30	20	.	.	PUNCT
ejpam-5637	31	1	a	a	DET
ejpam-5637	31	2	new	new	ADJ
ejpam-5637	31	3	method	method	NOUN
ejpam-5637	31	4	was	be	AUX
ejpam-5637	31	5	developed	develop	VERB
ejpam-5637	31	6	in	in	ADP
ejpam-5637	31	7	[	[	X
ejpam-5637	31	8	31	31	NUM
ejpam-5637	31	9	]	]	PUNCT
ejpam-5637	31	10	to	to	PART
ejpam-5637	31	11	solve	solve	VERB
ejpam-5637	31	12	the	the	DET
ejpam-5637	31	13	transport	transport	NOUN
ejpam-5637	31	14	problems	problem	NOUN
ejpam-5637	31	15	on	on	ADP
ejpam-5637	31	16	northwest	northwest	PROPN
ejpam-5637	31	17	corner	corner	NOUN
ejpam-5637	31	18	method	method	NOUN
ejpam-5637	31	19	in	in	ADP
ejpam-5637	31	20	order	order	NOUN
ejpam-5637	31	21	to	to	PART
ejpam-5637	31	22	reduce	reduce	VERB
ejpam-5637	31	23	the	the	DET
ejpam-5637	31	24	number	number	NOUN
ejpam-5637	31	25	of	of	ADP
ejpam-5637	31	26	steps	step	NOUN
ejpam-5637	31	27	to	to	PART
ejpam-5637	31	28	determine	determine	VERB
ejpam-5637	31	29	the	the	DET
ejpam-5637	31	30	number	number	NOUN
ejpam-5637	31	31	of	of	ADP
ejpam-5637	31	32	iteration	iteration	NOUN
ejpam-5637	31	33	given	give	VERB
ejpam-5637	31	34	in	in	ADP
ejpam-5637	31	35	[	[	X
ejpam-5637	31	36	29	29	NUM
ejpam-5637	31	37	]	]	PUNCT
ejpam-5637	31	38	.	.	PUNCT
ejpam-5637	32	1	a	a	DET
ejpam-5637	32	2	new	new	ADJ
ejpam-5637	32	3	technique	technique	NOUN
ejpam-5637	32	4	for	for	ADP
ejpam-5637	32	5	solving	solve	VERB
ejpam-5637	32	6	balanced	balanced	ADJ
ejpam-5637	32	7	transport	transport	NOUN
ejpam-5637	32	8	problem	problem	NOUN
ejpam-5637	32	9	based	base	VERB
ejpam-5637	32	10	on	on	ADP
ejpam-5637	32	11	geometric	geometric	ADJ
ejpam-5637	32	12	average	average	NOUN
ejpam-5637	32	13	for	for	ADP
ejpam-5637	32	14	transport	transport	NOUN
ejpam-5637	32	15	costs	cost	NOUN
ejpam-5637	32	16	was	be	AUX
ejpam-5637	32	17	developed	develop	VERB
ejpam-5637	32	18	in	in	ADP
ejpam-5637	32	19	[	[	X
ejpam-5637	32	20	8	8	NUM
ejpam-5637	32	21	]	]	PUNCT
ejpam-5637	32	22	.	.	PUNCT
ejpam-5637	33	1	a	a	DET
ejpam-5637	33	2	number	number	NOUN
ejpam-5637	33	3	of	of	ADP
ejpam-5637	33	4	transportation	transportation	NOUN
ejpam-5637	33	5	problems	problem	NOUN
ejpam-5637	33	6	can	can	AUX
ejpam-5637	33	7	be	be	AUX
ejpam-5637	33	8	solved	solve	VERB
ejpam-5637	33	9	by	by	ADP
ejpam-5637	33	10	using	use	VERB
ejpam-5637	33	11	numeric	numeric	ADJ
ejpam-5637	33	12	techniques	technique	NOUN
ejpam-5637	33	13	implemented	implement	VERB
ejpam-5637	33	14	in	in	ADP
ejpam-5637	33	15	matlab	matlab	PROPN
ejpam-5637	33	16	software	software	NOUN
ejpam-5637	33	17	.	.	PUNCT
ejpam-5637	34	1	the	the	DET
ejpam-5637	34	2	northwest	northwest	PROPN
ejpam-5637	34	3	corner	corner	NOUN
ejpam-5637	34	4	method	method	NOUN
ejpam-5637	34	5	was	be	AUX
ejpam-5637	34	6	used	use	VERB
ejpam-5637	34	7	to	to	PART
ejpam-5637	34	8	analyze	analyze	VERB
ejpam-5637	34	9	the	the	DET
ejpam-5637	34	10	transport	transport	NOUN
ejpam-5637	34	11	of	of	ADP
ejpam-5637	34	12	chemical	chemical	ADJ
ejpam-5637	34	13	substance	substance	NOUN
ejpam-5637	34	14	of	of	ADP
ejpam-5637	34	15	a	a	DET
ejpam-5637	34	16	pharmaceutical	pharmaceutical	ADJ
ejpam-5637	34	17	company	company	NOUN
ejpam-5637	34	18	[	[	X
ejpam-5637	34	19	37	37	NUM
ejpam-5637	34	20	]	]	PUNCT
ejpam-5637	34	21	.	.	PUNCT
ejpam-5637	35	1	the	the	DET
ejpam-5637	35	2	vogel	vogel	NOUN
ejpam-5637	35	3	’s	’s	PART
ejpam-5637	35	4	approximation	approximation	NOUN
ejpam-5637	35	5	and	and	CCONJ
ejpam-5637	35	6	modified	modify	VERB
ejpam-5637	35	7	distribution	distribution	NOUN
ejpam-5637	35	8	method	method	NOUN
ejpam-5637	35	9	were	be	AUX
ejpam-5637	35	10	used	use	VERB
ejpam-5637	35	11	to	to	PART
ejpam-5637	35	12	deal	deal	VERB
ejpam-5637	35	13	with	with	ADP
ejpam-5637	35	14	large	large	ADJ
ejpam-5637	35	15	scale	scale	NOUN
ejpam-5637	35	16	cost	cost	NOUN
ejpam-5637	35	17	matrices	matrix	NOUN
ejpam-5637	35	18	[	[	X
ejpam-5637	35	19	27	27	NUM
ejpam-5637	35	20	]	]	PUNCT
ejpam-5637	35	21	.	.	PUNCT
ejpam-5637	36	1	the	the	DET
ejpam-5637	36	2	vogel	vogel	NOUN
ejpam-5637	36	3	’s	’s	PART
ejpam-5637	36	4	approximation	approximation	NOUN
ejpam-5637	36	5	method	method	NOUN
ejpam-5637	36	6	primarily	primarily	ADV
ejpam-5637	36	7	determine	determine	VERB
ejpam-5637	36	8	the	the	DET
ejpam-5637	36	9	number	number	NOUN
ejpam-5637	36	10	of	of	ADP
ejpam-5637	36	11	penalties	penalty	NOUN
ejpam-5637	36	12	appearing	appear	VERB
ejpam-5637	36	13	in	in	ADP
ejpam-5637	36	14	each	each	DET
ejpam-5637	36	15	row	row	NOUN
ejpam-5637	36	16	and	and	CCONJ
ejpam-5637	36	17	column	column	NOUN
ejpam-5637	36	18	of	of	ADP
ejpam-5637	36	19	the	the	DET
ejpam-5637	36	20	matrix	matrix	NOUN
ejpam-5637	36	21	by	by	ADP
ejpam-5637	36	22	computing	compute	VERB
ejpam-5637	36	23	the	the	DET
ejpam-5637	36	24	difference	difference	NOUN
ejpam-5637	36	25	among	among	ADP
ejpam-5637	36	26	minimum	minimum	NOUN
ejpam-5637	36	27	and	and	CCONJ
ejpam-5637	36	28	second	second	ADJ
ejpam-5637	36	29	minimum	minimum	ADJ
ejpam-5637	36	30	cost	cost	NOUN
ejpam-5637	36	31	.	.	PUNCT
ejpam-5637	37	1	further	far	ADV
ejpam-5637	37	2	,	,	PUNCT
ejpam-5637	37	3	this	this	DET
ejpam-5637	37	4	method	method	NOUN
ejpam-5637	37	5	also	also	ADV
ejpam-5637	37	6	allocate	allocate	VERB
ejpam-5637	37	7	to	to	ADP
ejpam-5637	37	8	the	the	DET
ejpam-5637	37	9	cell	cell	NOUN
ejpam-5637	37	10	having	have	VERB
ejpam-5637	37	11	minimum	minimum	ADJ
ejpam-5637	37	12	cost	cost	NOUN
ejpam-5637	37	13	across	across	ADP
ejpam-5637	37	14	each	each	PRON
ejpam-5637	37	15	of	of	ADP
ejpam-5637	37	16	the	the	DET
ejpam-5637	37	17	row	row	NOUN
ejpam-5637	37	18	or	or	CCONJ
ejpam-5637	37	19	column	column	NOUN
ejpam-5637	37	20	with	with	ADP
ejpam-5637	37	21	maximum	maximum	ADJ
ejpam-5637	37	22	penalty	penalty	NOUN
ejpam-5637	37	23	.	.	PUNCT
ejpam-5637	38	1	once	once	SCONJ
ejpam-5637	38	2	compared	compare	VERB
ejpam-5637	38	3	with	with	ADP
ejpam-5637	38	4	m.u	m.u	PROPN
ejpam-5637	38	5	.	.	PROPN
ejpam-5637	38	6	rahman	rahman	PROPN
ejpam-5637	38	7	et	et	PROPN
ejpam-5637	38	8	al	al	PROPN
ejpam-5637	38	9	.	.	PUNCT
ejpam-5637	38	10	/	/	SYM
ejpam-5637	38	11	eur	eur	PROPN
ejpam-5637	38	12	.	.	PUNCT
ejpam-5637	39	1	j.	j.	PROPN
ejpam-5637	39	2	pure	pure	PROPN
ejpam-5637	39	3	appl	appl	PROPN
ejpam-5637	39	4	.	.	PROPN
ejpam-5637	39	5	math	math	PROPN
ejpam-5637	39	6	,	,	PUNCT
ejpam-5637	39	7	18	18	NUM
ejpam-5637	39	8	(	(	PUNCT
ejpam-5637	39	9	1	1	NUM
ejpam-5637	39	10	)	)	PUNCT
ejpam-5637	39	11	(	(	PUNCT
ejpam-5637	39	12	2025	2025	NUM
ejpam-5637	39	13	)	)	PUNCT
ejpam-5637	39	14	,	,	PUNCT
ejpam-5637	39	15	5637	5637	NUM
ejpam-5637	39	16	3	3	NUM
ejpam-5637	39	17	of	of	ADP
ejpam-5637	39	18	20	20	NUM
ejpam-5637	39	19	northwest	northwest	ADJ
ejpam-5637	39	20	corner	corner	NOUN
ejpam-5637	39	21	rule	rule	NOUN
ejpam-5637	40	1	,	,	PUNCT
ejpam-5637	40	2	this	this	DET
ejpam-5637	40	3	technique	technique	NOUN
ejpam-5637	40	4	generates	generate	VERB
ejpam-5637	40	5	an	an	DET
ejpam-5637	40	6	initial	initial	ADJ
ejpam-5637	40	7	solution	solution	NOUN
ejpam-5637	40	8	which	which	PRON
ejpam-5637	40	9	is	be	AUX
ejpam-5637	40	10	very	very	ADV
ejpam-5637	40	11	much	much	ADV
ejpam-5637	40	12	near	near	ADJ
ejpam-5637	40	13	to	to	ADP
ejpam-5637	40	14	optimality	optimality	NOUN
ejpam-5637	40	15	condition	condition	NOUN
ejpam-5637	40	16	.	.	PUNCT
ejpam-5637	41	1	on	on	ADP
ejpam-5637	41	2	the	the	DET
ejpam-5637	41	3	other	other	ADJ
ejpam-5637	41	4	hand	hand	NOUN
ejpam-5637	41	5	,	,	PUNCT
ejpam-5637	41	6	the	the	DET
ejpam-5637	41	7	modified	modify	VERB
ejpam-5637	41	8	distribution	distribution	NOUN
ejpam-5637	41	9	method	method	NOUN
ejpam-5637	41	10	is	be	AUX
ejpam-5637	41	11	being	be	AUX
ejpam-5637	41	12	mainly	mainly	ADV
ejpam-5637	41	13	used	use	VERB
ejpam-5637	41	14	for	for	ADP
ejpam-5637	41	15	the	the	DET
ejpam-5637	41	16	analysis	analysis	NOUN
ejpam-5637	41	17	of	of	ADP
ejpam-5637	41	18	the	the	DET
ejpam-5637	41	19	optimization	optimization	NOUN
ejpam-5637	41	20	to	to	ADP
ejpam-5637	41	21	an	an	DET
ejpam-5637	41	22	initial	initial	ADJ
ejpam-5637	41	23	feasible	feasible	ADJ
ejpam-5637	41	24	solution	solution	NOUN
ejpam-5637	41	25	which	which	PRON
ejpam-5637	41	26	is	be	AUX
ejpam-5637	41	27	first	first	ADV
ejpam-5637	41	28	obtained	obtain	VERB
ejpam-5637	41	29	by	by	ADP
ejpam-5637	41	30	vogel	vogel	NOUN
ejpam-5637	41	31	’s	’s	PART
ejpam-5637	41	32	approximation	approximation	NOUN
ejpam-5637	41	33	,	,	PUNCT
ejpam-5637	41	34	and	and	CCONJ
ejpam-5637	41	35	northwest	northwest	ADJ
ejpam-5637	41	36	corner	corner	NOUN
ejpam-5637	41	37	techniques	technique	NOUN
ejpam-5637	41	38	.	.	PUNCT
ejpam-5637	42	1	the	the	DET
ejpam-5637	42	2	main	main	ADJ
ejpam-5637	42	3	advantage	advantage	NOUN
ejpam-5637	42	4	of	of	ADP
ejpam-5637	42	5	modified	modify	VERB
ejpam-5637	42	6	distribution	distribution	NOUN
ejpam-5637	42	7	method	method	NOUN
ejpam-5637	42	8	compared	compare	VERB
ejpam-5637	42	9	to	to	ADP
ejpam-5637	42	10	northwest	northwest	PROPN
ejpam-5637	42	11	corner	corner	PROPN
ejpam-5637	42	12	method	method	NOUN
ejpam-5637	42	13	is	be	AUX
ejpam-5637	42	14	the	the	DET
ejpam-5637	42	15	insurance	insurance	NOUN
ejpam-5637	42	16	that	that	SCONJ
ejpam-5637	42	17	an	an	DET
ejpam-5637	42	18	optimal	optimal	ADJ
ejpam-5637	42	19	solution	solution	NOUN
ejpam-5637	42	20	has	have	AUX
ejpam-5637	42	21	reached	reach	VERB
ejpam-5637	42	22	up	up	ADP
ejpam-5637	42	23	to	to	ADP
ejpam-5637	42	24	a	a	DET
ejpam-5637	42	25	desired	desire	VERB
ejpam-5637	42	26	level	level	NOUN
ejpam-5637	42	27	.	.	PUNCT
ejpam-5637	43	1	the	the	DET
ejpam-5637	43	2	vogel	vogel	NOUN
ejpam-5637	43	3	’s	’s	PART
ejpam-5637	43	4	approximation	approximation	NOUN
ejpam-5637	43	5	method	method	NOUN
ejpam-5637	43	6	(	(	PUNCT
ejpam-5637	43	7	vam	vam	NOUN
ejpam-5637	43	8	)	)	PUNCT
ejpam-5637	43	9	,	,	PUNCT
ejpam-5637	43	10	modified	modify	VERB
ejpam-5637	43	11	distribution	distribution	NOUN
ejpam-5637	43	12	method	method	NOUN
ejpam-5637	43	13	(	(	PUNCT
ejpam-5637	43	14	modi	modi	PROPN
ejpam-5637	43	15	)	)	PUNCT
ejpam-5637	43	16	,	,	PUNCT
ejpam-5637	43	17	and	and	CCONJ
ejpam-5637	43	18	northwest	northwest	ADJ
ejpam-5637	43	19	corner	corner	NOUN
ejpam-5637	43	20	method	method	NOUN
ejpam-5637	43	21	(	(	PUNCT
ejpam-5637	43	22	nwc	nwc	PROPN
ejpam-5637	43	23	)	)	PUNCT
ejpam-5637	43	24	are	be	AUX
ejpam-5637	43	25	mainly	mainly	ADV
ejpam-5637	43	26	used	use	VERB
ejpam-5637	43	27	to	to	PART
ejpam-5637	43	28	deal	deal	VERB
ejpam-5637	43	29	with	with	ADP
ejpam-5637	43	30	analysis	analysis	NOUN
ejpam-5637	43	31	and	and	CCONJ
ejpam-5637	43	32	the	the	DET
ejpam-5637	43	33	solution	solution	NOUN
ejpam-5637	43	34	of	of	ADP
ejpam-5637	43	35	transportation	transportation	NOUN
ejpam-5637	43	36	problems	problem	NOUN
ejpam-5637	43	37	appearing	appear	VERB
ejpam-5637	43	38	in	in	ADP
ejpam-5637	43	39	the	the	DET
ejpam-5637	43	40	operations	operation	NOUN
ejpam-5637	43	41	research	research	NOUN
ejpam-5637	43	42	,	,	PUNCT
ejpam-5637	43	43	specifically	specifically	ADV
ejpam-5637	43	44	for	for	ADP
ejpam-5637	43	45	the	the	DET
ejpam-5637	43	46	optimization	optimization	NOUN
ejpam-5637	43	47	of	of	ADP
ejpam-5637	43	48	the	the	DET
ejpam-5637	43	49	logistics	logistic	NOUN
ejpam-5637	43	50	.	.	PUNCT
ejpam-5637	44	1	the	the	DET
ejpam-5637	44	2	nwc	nwc	PROPN
ejpam-5637	44	3	method	method	NOUN
ejpam-5637	44	4	is	be	AUX
ejpam-5637	44	5	being	be	AUX
ejpam-5637	44	6	used	use	VERB
ejpam-5637	44	7	as	as	ADP
ejpam-5637	44	8	an	an	DET
ejpam-5637	44	9	initial	initial	ADJ
ejpam-5637	44	10	approach	approach	NOUN
ejpam-5637	44	11	for	for	ADP
ejpam-5637	44	12	the	the	DET
ejpam-5637	44	13	location	location	NOUN
ejpam-5637	44	14	of	of	ADP
ejpam-5637	44	15	resources	resource	NOUN
ejpam-5637	44	16	when	when	SCONJ
ejpam-5637	44	17	the	the	DET
ejpam-5637	44	18	consideration	consideration	NOUN
ejpam-5637	44	19	of	of	ADP
ejpam-5637	44	20	cost	cost	NOUN
ejpam-5637	44	21	function	function	NOUN
ejpam-5637	44	22	are	be	AUX
ejpam-5637	44	23	much	much	ADV
ejpam-5637	44	24	smaller	small	ADJ
ejpam-5637	44	25	than	than	ADP
ejpam-5637	44	26	critical	critical	ADJ
ejpam-5637	44	27	values	value	NOUN
ejpam-5637	44	28	.	.	PUNCT
ejpam-5637	45	1	vam	vam	PROPN
ejpam-5637	45	2	mainly	mainly	ADV
ejpam-5637	45	3	does	do	AUX
ejpam-5637	45	4	focus	focus	VERB
ejpam-5637	45	5	on	on	ADP
ejpam-5637	45	6	penalties	penalty	NOUN
ejpam-5637	45	7	.	.	PUNCT
ejpam-5637	46	1	it	it	PRON
ejpam-5637	46	2	helps	help	VERB
ejpam-5637	46	3	to	to	PART
ejpam-5637	46	4	finds	find	VERB
ejpam-5637	46	5	applications	application	NOUN
ejpam-5637	46	6	once	once	SCONJ
ejpam-5637	46	7	the	the	DET
ejpam-5637	46	8	minimization	minimization	NOUN
ejpam-5637	46	9	of	of	ADP
ejpam-5637	46	10	transportation	transportation	NOUN
ejpam-5637	46	11	cost	cost	NOUN
ejpam-5637	46	12	function	function	NOUN
ejpam-5637	46	13	is	be	AUX
ejpam-5637	46	14	in	in	ADP
ejpam-5637	46	15	a	a	DET
ejpam-5637	46	16	crucial	crucial	ADJ
ejpam-5637	46	17	stage	stage	NOUN
ejpam-5637	46	18	.	.	PUNCT
ejpam-5637	47	1	modi	modi	PROPN
ejpam-5637	47	2	is	be	AUX
ejpam-5637	47	3	being	be	AUX
ejpam-5637	47	4	used	use	VERB
ejpam-5637	47	5	to	to	PART
ejpam-5637	47	6	ensure	ensure	VERB
ejpam-5637	47	7	the	the	DET
ejpam-5637	47	8	efficiency	efficiency	NOUN
ejpam-5637	47	9	of	of	ADP
ejpam-5637	47	10	cost	cost	NOUN
ejpam-5637	47	11	solution	solution	NOUN
ejpam-5637	47	12	.	.	PUNCT
ejpam-5637	48	1	it	it	PRON
ejpam-5637	48	2	does	do	AUX
ejpam-5637	48	3	makes	make	VERB
ejpam-5637	48	4	its	its	PRON
ejpam-5637	48	5	vital	vital	ADJ
ejpam-5637	48	6	role	role	NOUN
ejpam-5637	48	7	to	to	PART
ejpam-5637	48	8	optimize	optimize	VERB
ejpam-5637	48	9	the	the	DET
ejpam-5637	48	10	transportation	transportation	NOUN
ejpam-5637	48	11	networks	network	NOUN
ejpam-5637	48	12	at	at	ADP
ejpam-5637	48	13	very	very	ADV
ejpam-5637	48	14	large	large	ADJ
ejpam-5637	48	15	scale	scale	NOUN
ejpam-5637	48	16	,	,	PUNCT
ejpam-5637	48	17	to	to	PART
ejpam-5637	48	18	balance	balance	VERB
ejpam-5637	48	19	both	both	DET
ejpam-5637	48	20	supply	supply	NOUN
ejpam-5637	48	21	and	and	CCONJ
ejpam-5637	48	22	demands	demand	NOUN
ejpam-5637	48	23	.	.	PUNCT
ejpam-5637	49	1	furthermore	furthermore	ADV
ejpam-5637	49	2	,	,	PUNCT
ejpam-5637	49	3	it	it	PRON
ejpam-5637	49	4	ensure	ensure	VERB
ejpam-5637	49	5	the	the	DET
ejpam-5637	49	6	cost	cost	NOUN
ejpam-5637	49	7	efficiencies	efficiency	NOUN
ejpam-5637	49	8	across	across	ADP
ejpam-5637	49	9	the	the	DET
ejpam-5637	49	10	industries	industry	NOUN
ejpam-5637	49	11	,	,	PUNCT
ejpam-5637	49	12	for	for	ADP
ejpam-5637	49	13	instance	instance	NOUN
ejpam-5637	49	14	,	,	PUNCT
ejpam-5637	49	15	the	the	DET
ejpam-5637	49	16	manufacturing	manufacturing	NOUN
ejpam-5637	49	17	,	,	PUNCT
ejpam-5637	49	18	retail	retail	ADJ
ejpam-5637	49	19	industry	industry	NOUN
ejpam-5637	49	20	.	.	PUNCT
ejpam-5637	50	1	a	a	DET
ejpam-5637	50	2	new	new	ADJ
ejpam-5637	50	3	mathematical	mathematical	ADJ
ejpam-5637	50	4	technique	technique	NOUN
ejpam-5637	50	5	[	[	X
ejpam-5637	50	6	11	11	NUM
ejpam-5637	50	7	]	]	PUNCT
ejpam-5637	50	8	based	base	VERB
ejpam-5637	50	9	on	on	ADP
ejpam-5637	50	10	simplex	simplex	NOUN
ejpam-5637	50	11	algorithm	algorithm	NOUN
ejpam-5637	50	12	was	be	AUX
ejpam-5637	50	13	developed	develop	VERB
ejpam-5637	50	14	to	to	PART
ejpam-5637	50	15	solve	solve	VERB
ejpam-5637	50	16	transport	transport	NOUN
ejpam-5637	50	17	problem	problem	NOUN
ejpam-5637	50	18	.	.	PUNCT
ejpam-5637	51	1	a	a	DET
ejpam-5637	51	2	bi	bi	ADJ
ejpam-5637	51	3	-	-	NOUN
ejpam-5637	51	4	criterion	criterion	NOUN
ejpam-5637	51	5	transportation	transportation	NOUN
ejpam-5637	51	6	problem	problem	NOUN
ejpam-5637	51	7	was	be	AUX
ejpam-5637	51	8	solved	solve	VERB
ejpam-5637	51	9	by	by	ADP
ejpam-5637	51	10	aneya	aneya	NOUN
ejpam-5637	51	11	and	and	CCONJ
ejpam-5637	51	12	nair	nair	NOUN
ejpam-5637	52	1	[	[	X
ejpam-5637	52	2	1	1	NUM
ejpam-5637	52	3	]	]	PUNCT
ejpam-5637	52	4	.	.	PUNCT
ejpam-5637	53	1	in	in	ADP
ejpam-5637	53	2	[	[	X
ejpam-5637	53	3	28	28	NUM
ejpam-5637	53	4	,	,	PUNCT
ejpam-5637	53	5	52	52	NUM
ejpam-5637	53	6	]	]	PUNCT
ejpam-5637	53	7	,	,	PUNCT
ejpam-5637	53	8	the	the	DET
ejpam-5637	53	9	optimization	optimization	NOUN
ejpam-5637	53	10	of	of	ADP
ejpam-5637	53	11	passenger	passenger	NOUN
ejpam-5637	53	12	transport	transport	NOUN
ejpam-5637	53	13	problems	problem	NOUN
ejpam-5637	53	14	and	and	CCONJ
ejpam-5637	53	15	passenger	passenger	NOUN
ejpam-5637	53	16	control	control	NOUN
ejpam-5637	53	17	flow	flow	NOUN
ejpam-5637	53	18	problems	problem	NOUN
ejpam-5637	53	19	were	be	AUX
ejpam-5637	53	20	studied	study	VERB
ejpam-5637	53	21	and	and	CCONJ
ejpam-5637	53	22	analyzed	analyze	VERB
ejpam-5637	53	23	.	.	PUNCT
ejpam-5637	54	1	an	an	DET
ejpam-5637	54	2	extensive	extensive	ADJ
ejpam-5637	54	3	amount	amount	NOUN
ejpam-5637	54	4	of	of	ADP
ejpam-5637	54	5	literature	literature	NOUN
ejpam-5637	54	6	has	have	AUX
ejpam-5637	54	7	been	be	AUX
ejpam-5637	54	8	written	write	VERB
ejpam-5637	54	9	to	to	PART
ejpam-5637	54	10	deal	deal	VERB
ejpam-5637	54	11	with	with	ADP
ejpam-5637	54	12	time	time	NOUN
ejpam-5637	54	13	-	-	PUNCT
ejpam-5637	54	14	minimization	minimization	NOUN
ejpam-5637	54	15	transport	transport	NOUN
ejpam-5637	54	16	problems	problem	NOUN
ejpam-5637	54	17	,	,	PUNCT
ejpam-5637	54	18	we	we	PRON
ejpam-5637	54	19	refer	refer	VERB
ejpam-5637	54	20	interested	interested	ADJ
ejpam-5637	54	21	readers	reader	NOUN
ejpam-5637	54	22	to	to	PART
ejpam-5637	54	23	see	see	VERB
ejpam-5637	54	24	[	[	X
ejpam-5637	54	25	5	5	NUM
ejpam-5637	54	26	,	,	PUNCT
ejpam-5637	54	27	24	24	NUM
ejpam-5637	54	28	,	,	PUNCT
ejpam-5637	54	29	40	40	NUM
ejpam-5637	54	30	,	,	PUNCT
ejpam-5637	54	31	46	46	NUM
ejpam-5637	54	32	,	,	PUNCT
ejpam-5637	54	33	47	47	NUM
ejpam-5637	54	34	]	]	PUNCT
ejpam-5637	54	35	and	and	CCONJ
ejpam-5637	54	36	the	the	DET
ejpam-5637	54	37	references	reference	NOUN
ejpam-5637	54	38	therein	therein	ADV
ejpam-5637	54	39	.	.	PUNCT
ejpam-5637	55	1	the	the	DET
ejpam-5637	55	2	structured	structured	ADJ
ejpam-5637	55	3	singular	singular	ADJ
ejpam-5637	55	4	values	value	NOUN
ejpam-5637	55	5	are	be	AUX
ejpam-5637	55	6	non	non	ADJ
ejpam-5637	55	7	-	-	ADJ
ejpam-5637	55	8	negative	negative	ADJ
ejpam-5637	55	9	numbers	number	NOUN
ejpam-5637	55	10	obtained	obtain	VERB
ejpam-5637	55	11	by	by	ADP
ejpam-5637	55	12	computing	compute	VERB
ejpam-5637	55	13	the	the	DET
ejpam-5637	55	14	singular	singular	ADJ
ejpam-5637	55	15	values	value	NOUN
ejpam-5637	55	16	of	of	ADP
ejpam-5637	55	17	perturbation	perturbation	NOUN
ejpam-5637	55	18	matrix	matrix	NOUN
ejpam-5637	55	19	∆̂	∆̂	NOUN
ejpam-5637	55	20	from	from	ADP
ejpam-5637	55	21	the	the	DET
ejpam-5637	55	22	set	set	NOUN
ejpam-5637	55	23	of	of	ADP
ejpam-5637	55	24	block	block	NOUN
ejpam-5637	55	25	-	-	PUNCT
ejpam-5637	55	26	diagonal	diagonal	ADJ
ejpam-5637	55	27	matrices	matrix	NOUN
ejpam-5637	55	28	∆.	∆.	PRON
ejpam-5637	55	29	the	the	DET
ejpam-5637	55	30	structured	structured	ADJ
ejpam-5637	55	31	singular	singular	ADJ
ejpam-5637	55	32	values	value	NOUN
ejpam-5637	55	33	were	be	AUX
ejpam-5637	55	34	first	first	ADV
ejpam-5637	55	35	introduced	introduce	VERB
ejpam-5637	55	36	by	by	ADP
ejpam-5637	55	37	doyle	doyle	NOUN
ejpam-5637	56	1	[	[	X
ejpam-5637	56	2	12	12	NUM
ejpam-5637	56	3	]	]	PUNCT
ejpam-5637	56	4	to	to	PART
ejpam-5637	56	5	study	study	VERB
ejpam-5637	56	6	and	and	CCONJ
ejpam-5637	56	7	investigate	investigate	VERB
ejpam-5637	56	8	both	both	DET
ejpam-5637	56	9	stability	stability	NOUN
ejpam-5637	56	10	and	and	CCONJ
ejpam-5637	56	11	instability	instability	NOUN
ejpam-5637	56	12	of	of	ADP
ejpam-5637	56	13	feedback	feedback	NOUN
ejpam-5637	56	14	systems	system	NOUN
ejpam-5637	56	15	.	.	PUNCT
ejpam-5637	57	1	the	the	DET
ejpam-5637	57	2	computation	computation	NOUN
ejpam-5637	57	3	of	of	ADP
ejpam-5637	57	4	structured	structured	ADJ
ejpam-5637	57	5	singular	singular	NOUN
ejpam-5637	57	6	is	be	AUX
ejpam-5637	57	7	a	a	DET
ejpam-5637	57	8	np	np	ADV
ejpam-5637	57	9	-	-	PUNCT
ejpam-5637	57	10	hard	hard	ADJ
ejpam-5637	57	11	problem	problem	NOUN
ejpam-5637	57	12	[	[	X
ejpam-5637	57	13	7	7	NUM
ejpam-5637	57	14	]	]	PUNCT
ejpam-5637	57	15	.	.	PUNCT
ejpam-5637	58	1	the	the	DET
ejpam-5637	58	2	global	global	ADJ
ejpam-5637	58	3	search	search	PROPN
ejpam-5637	58	4	numerical	numerical	ADJ
ejpam-5637	58	5	and	and	CCONJ
ejpam-5637	58	6	analytical	analytical	ADJ
ejpam-5637	58	7	techniques	technique	NOUN
ejpam-5637	58	8	were	be	AUX
ejpam-5637	58	9	developed	develop	VERB
ejpam-5637	58	10	[	[	X
ejpam-5637	58	11	19	19	NUM
ejpam-5637	58	12	,	,	PUNCT
ejpam-5637	58	13	32	32	NUM
ejpam-5637	58	14	]	]	PUNCT
ejpam-5637	58	15	to	to	PART
ejpam-5637	58	16	deal	deal	VERB
ejpam-5637	58	17	with	with	ADP
ejpam-5637	58	18	lower	low	ADJ
ejpam-5637	58	19	dimensional	dimensional	ADJ
ejpam-5637	58	20	mathematical	mathematical	ADJ
ejpam-5637	58	21	problems	problem	NOUN
ejpam-5637	58	22	.	.	PUNCT
ejpam-5637	59	1	the	the	DET
ejpam-5637	59	2	concept	concept	NOUN
ejpam-5637	59	3	of	of	ADP
ejpam-5637	59	4	d	d	NOUN
ejpam-5637	59	5	-	-	NOUN
ejpam-5637	59	6	stability	stability	NOUN
ejpam-5637	59	7	for	for	ADP
ejpam-5637	59	8	the	the	DET
ejpam-5637	59	9	very	very	ADV
ejpam-5637	59	10	first	first	ADJ
ejpam-5637	59	11	time	time	NOUN
ejpam-5637	59	12	was	be	AUX
ejpam-5637	59	13	introduced	introduce	VERB
ejpam-5637	59	14	by	by	ADP
ejpam-5637	59	15	arrow	arrow	NOUN
ejpam-5637	59	16	and	and	CCONJ
ejpam-5637	59	17	mcmanus	mcmanus	PROPN
ejpam-5637	60	1	[	[	X
ejpam-5637	60	2	3	3	NUM
ejpam-5637	60	3	]	]	PUNCT
ejpam-5637	60	4	,	,	PUNCT
ejpam-5637	60	5	and	and	CCONJ
ejpam-5637	60	6	then	then	ADV
ejpam-5637	60	7	enthoven	enthoven	ADV
ejpam-5637	60	8	and	and	CCONJ
ejpam-5637	60	9	arrow	arrow	NOUN
ejpam-5637	61	1	[	[	X
ejpam-5637	61	2	14	14	NUM
ejpam-5637	61	3	]	]	PUNCT
ejpam-5637	61	4	in	in	ADP
ejpam-5637	61	5	their	their	PRON
ejpam-5637	61	6	classical	classical	ADJ
ejpam-5637	61	7	papers	paper	NOUN
ejpam-5637	61	8	.	.	PUNCT
ejpam-5637	62	1	the	the	DET
ejpam-5637	62	2	main	main	ADJ
ejpam-5637	62	3	aim	aim	NOUN
ejpam-5637	62	4	in	in	ADP
ejpam-5637	62	5	these	these	DET
ejpam-5637	62	6	classical	classical	ADJ
ejpam-5637	62	7	papers	paper	NOUN
ejpam-5637	62	8	was	be	AUX
ejpam-5637	62	9	to	to	PART
ejpam-5637	62	10	study	study	VERB
ejpam-5637	62	11	and	and	CCONJ
ejpam-5637	62	12	investigate	investigate	VERB
ejpam-5637	62	13	the	the	DET
ejpam-5637	62	14	dynamic	dynamic	ADJ
ejpam-5637	62	15	models	model	NOUN
ejpam-5637	62	16	from	from	ADP
ejpam-5637	62	17	the	the	DET
ejpam-5637	62	18	economics	economic	NOUN
ejpam-5637	62	19	.	.	PUNCT
ejpam-5637	63	1	the	the	DET
ejpam-5637	63	2	theory	theory	NOUN
ejpam-5637	63	3	of	of	ADP
ejpam-5637	63	4	d	d	NOUN
ejpam-5637	63	5	-	-	NOUN
ejpam-5637	63	6	stability	stability	NOUN
ejpam-5637	63	7	plays	play	VERB
ejpam-5637	63	8	an	an	DET
ejpam-5637	63	9	important	important	ADJ
ejpam-5637	63	10	role	role	NOUN
ejpam-5637	63	11	in	in	ADP
ejpam-5637	63	12	a	a	DET
ejpam-5637	63	13	vast	vast	ADJ
ejpam-5637	63	14	amount	amount	NOUN
ejpam-5637	63	15	of	of	ADP
ejpam-5637	63	16	application	application	NOUN
ejpam-5637	63	17	areas	area	NOUN
ejpam-5637	63	18	in	in	ADP
ejpam-5637	63	19	economic	economic	ADJ
ejpam-5637	63	20	analysis	analysis	NOUN
ejpam-5637	63	21	[	[	X
ejpam-5637	63	22	20	20	NUM
ejpam-5637	63	23	,	,	PUNCT
ejpam-5637	63	24	22	22	NUM
ejpam-5637	63	25	,	,	PUNCT
ejpam-5637	63	26	25	25	NUM
ejpam-5637	63	27	,	,	PUNCT
ejpam-5637	63	28	26	26	NUM
ejpam-5637	63	29	,	,	PUNCT
ejpam-5637	63	30	33	33	NUM
ejpam-5637	63	31	,	,	PUNCT
ejpam-5637	63	32	38	38	NUM
ejpam-5637	63	33	,	,	PUNCT
ejpam-5637	63	34	53	53	NUM
ejpam-5637	63	35	]	]	PUNCT
ejpam-5637	63	36	.	.	PUNCT
ejpam-5637	64	1	the	the	DET
ejpam-5637	64	2	main	main	ADJ
ejpam-5637	64	3	objective	objective	NOUN
ejpam-5637	64	4	of	of	ADP
ejpam-5637	64	5	this	this	DET
ejpam-5637	64	6	paper	paper	NOUN
ejpam-5637	64	7	is	be	AUX
ejpam-5637	64	8	two	two	NUM
ejpam-5637	64	9	-	-	PUNCT
ejpam-5637	64	10	fold	fold	VERB
ejpam-5637	64	11	:	:	PUNCT
ejpam-5637	64	12	first	first	ADV
ejpam-5637	64	13	to	to	PART
ejpam-5637	64	14	study	study	VERB
ejpam-5637	64	15	and	and	CCONJ
ejpam-5637	64	16	analyze	analyze	VERB
ejpam-5637	64	17	the	the	DET
ejpam-5637	64	18	spectral	spectral	ADJ
ejpam-5637	64	19	properties	property	NOUN
ejpam-5637	64	20	of	of	ADP
ejpam-5637	64	21	structured	structured	ADJ
ejpam-5637	64	22	matrices	matrix	NOUN
ejpam-5637	64	23	appearing	appear	VERB
ejpam-5637	64	24	across	across	ADP
ejpam-5637	64	25	the	the	DET
ejpam-5637	64	26	hitchcock	hitchcock	NOUN
ejpam-5637	64	27	-	-	PUNCT
ejpam-5637	64	28	koopmans	koopmans	PROPN
ejpam-5637	64	29	transportation	transportation	NOUN
ejpam-5637	64	30	models	model	NOUN
ejpam-5637	64	31	.	.	PUNCT
ejpam-5637	65	1	the	the	DET
ejpam-5637	65	2	computation	computation	NOUN
ejpam-5637	65	3	of	of	ADP
ejpam-5637	65	4	various	various	ADJ
ejpam-5637	65	5	tools	tool	NOUN
ejpam-5637	65	6	like	like	ADP
ejpam-5637	65	7	eigenvalues	eigenvalue	NOUN
ejpam-5637	65	8	,	,	PUNCT
ejpam-5637	65	9	singular	singular	ADJ
ejpam-5637	65	10	values	value	NOUN
ejpam-5637	65	11	,	,	PUNCT
ejpam-5637	65	12	right	right	ADJ
ejpam-5637	65	13	and	and	CCONJ
ejpam-5637	65	14	left	leave	VERB
ejpam-5637	65	15	singular	singular	ADJ
ejpam-5637	65	16	vectors	vector	NOUN
ejpam-5637	65	17	,	,	PUNCT
ejpam-5637	65	18	structured	structure	VERB
ejpam-5637	65	19	singular	singular	ADJ
ejpam-5637	65	20	values	value	NOUN
ejpam-5637	65	21	,	,	PUNCT
ejpam-5637	65	22	and	and	CCONJ
ejpam-5637	65	23	pseudo	pseudo	NOUN
ejpam-5637	65	24	-	-	ADJ
ejpam-5637	65	25	inverse	inverse	NOUN
ejpam-5637	65	26	describes	describe	VERB
ejpam-5637	65	27	various	various	ADJ
ejpam-5637	65	28	spectral	spectral	ADJ
ejpam-5637	65	29	properties	property	NOUN
ejpam-5637	65	30	of	of	ADP
ejpam-5637	65	31	structured	structured	ADJ
ejpam-5637	65	32	matrices	matrix	NOUN
ejpam-5637	65	33	under	under	ADP
ejpam-5637	65	34	consideration	consideration	NOUN
ejpam-5637	65	35	.	.	PUNCT
ejpam-5637	66	1	on	on	ADP
ejpam-5637	66	2	the	the	DET
ejpam-5637	66	3	other	other	ADJ
ejpam-5637	66	4	hand	hand	NOUN
ejpam-5637	66	5	,	,	PUNCT
ejpam-5637	66	6	we	we	PRON
ejpam-5637	66	7	present	present	VERB
ejpam-5637	66	8	new	new	ADJ
ejpam-5637	66	9	results	result	NOUN
ejpam-5637	66	10	on	on	ADP
ejpam-5637	66	11	the	the	DET
ejpam-5637	66	12	interconnection	interconnection	NOUN
ejpam-5637	66	13	between	between	ADP
ejpam-5637	66	14	structured	structured	ADJ
ejpam-5637	66	15	singular	singular	ADJ
ejpam-5637	66	16	values	value	NOUN
ejpam-5637	66	17	,	,	PUNCT
ejpam-5637	66	18	and	and	CCONJ
ejpam-5637	66	19	d	d	X
ejpam-5637	66	20	-	-	NOUN
ejpam-5637	66	21	stability	stability	NOUN
ejpam-5637	66	22	of	of	ADP
ejpam-5637	66	23	structured	structured	ADJ
ejpam-5637	66	24	matrices	matrix	NOUN
ejpam-5637	66	25	across	across	ADP
ejpam-5637	66	26	hitchcock	hitchcock	PROPN
ejpam-5637	66	27	-	-	PUNCT
ejpam-5637	66	28	koopmans	koopmans	PROPN
ejpam-5637	66	29	transportation	transportation	NOUN
ejpam-5637	66	30	problem	problem	NOUN
ejpam-5637	66	31	.	.	PUNCT
ejpam-5637	67	1	m.u	m.u	PROPN
ejpam-5637	67	2	.	.	PROPN
ejpam-5637	68	1	rahman	rahman	PROPN
ejpam-5637	68	2	et	et	PROPN
ejpam-5637	68	3	al	al	PROPN
ejpam-5637	68	4	.	.	PUNCT
ejpam-5637	68	5	/	/	SYM
ejpam-5637	68	6	eur	eur	PROPN
ejpam-5637	68	7	.	.	PUNCT
ejpam-5637	69	1	j.	j.	PROPN
ejpam-5637	69	2	pure	pure	PROPN
ejpam-5637	69	3	appl	appl	PROPN
ejpam-5637	69	4	.	.	PROPN
ejpam-5637	69	5	math	math	PROPN
ejpam-5637	69	6	,	,	PUNCT
ejpam-5637	69	7	18	18	NUM
ejpam-5637	69	8	(	(	PUNCT
ejpam-5637	69	9	1	1	NUM
ejpam-5637	69	10	)	)	PUNCT
ejpam-5637	69	11	(	(	PUNCT
ejpam-5637	69	12	2025	2025	NUM
ejpam-5637	69	13	)	)	PUNCT
ejpam-5637	69	14	,	,	PUNCT
ejpam-5637	69	15	5637	5637	NUM
ejpam-5637	69	16	4	4	NUM
ejpam-5637	69	17	of	of	ADP
ejpam-5637	69	18	20	20	NUM
ejpam-5637	69	19	1.1	1.1	NUM
ejpam-5637	69	20	.	.	PUNCT
ejpam-5637	70	1	overview	overview	NOUN
ejpam-5637	70	2	of	of	ADP
ejpam-5637	70	3	the	the	DET
ejpam-5637	70	4	article	article	NOUN
ejpam-5637	70	5	.	.	PUNCT
ejpam-5637	71	1	in	in	ADP
ejpam-5637	71	2	section	section	NOUN
ejpam-5637	71	3	2	2	NUM
ejpam-5637	71	4	,	,	PUNCT
ejpam-5637	71	5	we	we	PRON
ejpam-5637	71	6	provide	provide	VERB
ejpam-5637	71	7	new	new	ADJ
ejpam-5637	71	8	results	result	NOUN
ejpam-5637	71	9	on	on	ADP
ejpam-5637	71	10	singular	singular	ADJ
ejpam-5637	71	11	values	value	NOUN
ejpam-5637	71	12	of	of	ADP
ejpam-5637	71	13	a	a	DET
ejpam-5637	71	14	matrix	matrix	NOUN
ejpam-5637	71	15	corresponding	correspond	VERB
ejpam-5637	71	16	to	to	ADP
ejpam-5637	71	17	hitchcock	hitchcock	NOUN
ejpam-5637	71	18	-	-	PUNCT
ejpam-5637	71	19	koopmans	koopmans	PROPN
ejpam-5637	71	20	transportation	transportation	NOUN
ejpam-5637	71	21	problem	problem	NOUN
ejpam-5637	71	22	.	.	PUNCT
ejpam-5637	72	1	we	we	PRON
ejpam-5637	72	2	have	have	AUX
ejpam-5637	72	3	employed	employ	VERB
ejpam-5637	72	4	some	some	DET
ejpam-5637	72	5	tools	tool	NOUN
ejpam-5637	72	6	from	from	ADP
ejpam-5637	72	7	linear	linear	ADJ
ejpam-5637	72	8	algebra	algebra	NOUN
ejpam-5637	72	9	and	and	CCONJ
ejpam-5637	72	10	matrix	matrix	NOUN
ejpam-5637	72	11	analysis	analysis	NOUN
ejpam-5637	72	12	to	to	PART
ejpam-5637	72	13	develop	develop	VERB
ejpam-5637	72	14	these	these	DET
ejpam-5637	72	15	results	result	NOUN
ejpam-5637	72	16	.	.	PUNCT
ejpam-5637	73	1	furthermore	furthermore	ADV
ejpam-5637	73	2	,	,	PUNCT
ejpam-5637	73	3	we	we	PRON
ejpam-5637	73	4	also	also	ADV
ejpam-5637	73	5	provide	provide	VERB
ejpam-5637	73	6	numerical	numerical	ADJ
ejpam-5637	73	7	experimentation	experimentation	NOUN
ejpam-5637	73	8	on	on	ADP
ejpam-5637	73	9	the	the	DET
ejpam-5637	73	10	computation	computation	NOUN
ejpam-5637	73	11	of	of	ADP
ejpam-5637	73	12	singular	singular	ADJ
ejpam-5637	73	13	values	value	NOUN
ejpam-5637	73	14	and	and	CCONJ
ejpam-5637	73	15	pseudo	pseudo	NOUN
ejpam-5637	73	16	-	-	NOUN
ejpam-5637	73	17	inverse	inverse	NOUN
ejpam-5637	73	18	of	of	ADP
ejpam-5637	73	19	transportation	transportation	NOUN
ejpam-5637	73	20	matrices	matrix	NOUN
ejpam-5637	73	21	.	.	PUNCT
ejpam-5637	74	1	in	in	ADP
ejpam-5637	74	2	section	section	NOUN
ejpam-5637	74	3	3	3	NUM
ejpam-5637	74	4	of	of	ADP
ejpam-5637	74	5	this	this	DET
ejpam-5637	74	6	article	article	NOUN
ejpam-5637	74	7	,	,	PUNCT
ejpam-5637	74	8	we	we	PRON
ejpam-5637	74	9	provide	provide	VERB
ejpam-5637	74	10	some	some	DET
ejpam-5637	74	11	new	new	ADJ
ejpam-5637	74	12	results	result	NOUN
ejpam-5637	74	13	on	on	ADP
ejpam-5637	74	14	the	the	DET
ejpam-5637	74	15	interconnection	interconnection	NOUN
ejpam-5637	74	16	between	between	ADP
ejpam-5637	74	17	structured	structured	ADJ
ejpam-5637	74	18	singular	singular	ADJ
ejpam-5637	74	19	values	value	NOUN
ejpam-5637	74	20	of	of	ADP
ejpam-5637	74	21	(	(	PUNCT
ejpam-5637	74	22	m∗m)−1m∗	m∗m)−1m∗	PROPN
ejpam-5637	74	23	and	and	CCONJ
ejpam-5637	74	24	m∗(mm∗)−1	m∗(mm∗)−1	NOUN
ejpam-5637	74	25	.	.	PUNCT
ejpam-5637	75	1	the	the	DET
ejpam-5637	75	2	numerical	numerical	ADJ
ejpam-5637	75	3	experimentation	experimentation	NOUN
ejpam-5637	75	4	on	on	ADP
ejpam-5637	75	5	comparison	comparison	NOUN
ejpam-5637	75	6	of	of	ADP
ejpam-5637	75	7	bounds	bound	NOUN
ejpam-5637	75	8	of	of	ADP
ejpam-5637	75	9	structured	structured	ADJ
ejpam-5637	75	10	singular	singular	ADJ
ejpam-5637	75	11	values	value	NOUN
ejpam-5637	75	12	are	be	AUX
ejpam-5637	75	13	presented	present	VERB
ejpam-5637	75	14	in	in	ADP
ejpam-5637	75	15	section	section	NOUN
ejpam-5637	75	16	4	4	NUM
ejpam-5637	75	17	,	,	PUNCT
ejpam-5637	75	18	and	and	CCONJ
ejpam-5637	75	19	finally	finally	ADV
ejpam-5637	75	20	we	we	PRON
ejpam-5637	75	21	have	have	AUX
ejpam-5637	75	22	presented	present	VERB
ejpam-5637	75	23	conclusion	conclusion	NOUN
ejpam-5637	75	24	in	in	ADP
ejpam-5637	75	25	section	section	NOUN
ejpam-5637	75	26	5	5	NUM
ejpam-5637	75	27	.	.	SYM
ejpam-5637	75	28	2	2	NUM
ejpam-5637	75	29	.	.	NOUN
ejpam-5637	75	30	singular	singular	ADJ
ejpam-5637	75	31	values	value	NOUN
ejpam-5637	75	32	for	for	ADP
ejpam-5637	75	33	hitchcock	hitchcock	NOUN
ejpam-5637	75	34	-	-	PUNCT
ejpam-5637	75	35	koopmans	koopmans	PROPN
ejpam-5637	75	36	transportation	transportation	NOUN
ejpam-5637	75	37	problem	problem	NOUN
ejpam-5637	75	38	the	the	DET
ejpam-5637	75	39	hitchcock	hitchcock	PROPN
ejpam-5637	75	40	-	-	PUNCT
ejpam-5637	75	41	koopmans	koopmans	PROPN
ejpam-5637	75	42	transportation	transportation	NOUN
ejpam-5637	75	43	problem	problem	NOUN
ejpam-5637	75	44	was	be	AUX
ejpam-5637	75	45	first	first	ADV
ejpam-5637	75	46	developed	develop	VERB
ejpam-5637	75	47	by	by	ADP
ejpam-5637	75	48	hitchcock	hitchcock	PROPN
ejpam-5637	75	49	in	in	ADP
ejpam-5637	75	50	1941	1941	NUM
ejpam-5637	75	51	,	,	PUNCT
ejpam-5637	75	52	and	and	CCONJ
ejpam-5637	75	53	then	then	ADV
ejpam-5637	75	54	investigated	investigate	VERB
ejpam-5637	75	55	and	and	CCONJ
ejpam-5637	75	56	analyzed	analyze	VERB
ejpam-5637	75	57	by	by	ADP
ejpam-5637	75	58	koopmans	koopman	NOUN
ejpam-5637	75	59	in	in	ADP
ejpam-5637	75	60	1947	1947	NUM
ejpam-5637	75	61	.	.	PUNCT
ejpam-5637	76	1	this	this	DET
ejpam-5637	76	2	problem	problem	NOUN
ejpam-5637	76	3	was	be	AUX
ejpam-5637	76	4	applied	apply	VERB
ejpam-5637	76	5	to	to	ADP
ejpam-5637	76	6	simplex	simplex	NOUN
ejpam-5637	76	7	algorithm	algorithm	NOUN
ejpam-5637	76	8	by	by	ADP
ejpam-5637	76	9	dantzig	dantzig	NOUN
ejpam-5637	76	10	in	in	ADP
ejpam-5637	76	11	1951	1951	NUM
ejpam-5637	76	12	.	.	PUNCT
ejpam-5637	77	1	for	for	ADP
ejpam-5637	77	2	m	m	PROPN
ejpam-5637	77	3	numbers	number	NOUN
ejpam-5637	77	4	of	of	ADP
ejpam-5637	77	5	origins	origin	NOUN
ejpam-5637	77	6	and	and	CCONJ
ejpam-5637	77	7	n	n	DET
ejpam-5637	77	8	numebrs	numebrs	NOUN
ejpam-5637	77	9	of	of	ADP
ejpam-5637	77	10	destinations	destination	NOUN
ejpam-5637	77	11	,	,	PUNCT
ejpam-5637	77	12	the	the	DET
ejpam-5637	77	13	hitchcock	hitchcock	NOUN
ejpam-5637	77	14	-	-	PUNCT
ejpam-5637	77	15	koopmans	koopmans	PROPN
ejpam-5637	77	16	transportation	transportation	NOUN
ejpam-5637	77	17	is	be	AUX
ejpam-5637	77	18	to	to	PART
ejpam-5637	77	19	study	study	VERB
ejpam-5637	77	20	and	and	CCONJ
ejpam-5637	77	21	solve	solve	VERB
ejpam-5637	77	22	following	follow	VERB
ejpam-5637	77	23	optimization	optimization	NOUN
ejpam-5637	77	24	problem	problem	NOUN
ejpam-5637	77	25	:	:	PUNCT
ejpam-5637	77	26	min{ctx	min{ctx	NOUN
ejpam-5637	77	27	:	:	PUNCT
ejpam-5637	77	28	mx	mx	PROPN
ejpam-5637	77	29	=	=	SYM
ejpam-5637	77	30	g	g	PROPN
ejpam-5637	77	31	,	,	PUNCT
ejpam-5637	77	32	1ma	1ma	NOUN
ejpam-5637	77	33	=	=	SYM
ejpam-5637	77	34	1nb	1nb	NOUN
ejpam-5637	77	35	,	,	PUNCT
ejpam-5637	77	36	x	x	X
ejpam-5637	77	37	≥	≥	NOUN
ejpam-5637	77	38	0	0	NUM
ejpam-5637	77	39	}	}	PUNCT
ejpam-5637	77	40	,	,	PUNCT
ejpam-5637	77	41	where	where	SCONJ
ejpam-5637	77	42	min	min	NOUN
ejpam-5637	77	43	is	be	AUX
ejpam-5637	77	44	taken	take	VERB
ejpam-5637	77	45	over	over	ADP
ejpam-5637	77	46	x	x	NOUN
ejpam-5637	77	47	,	,	PUNCT
ejpam-5637	77	48	also	also	ADV
ejpam-5637	77	49	at	at	ADP
ejpam-5637	77	50	=	=	NOUN
ejpam-5637	78	1	[	[	X
ejpam-5637	78	2	a1	a1	NOUN
ejpam-5637	78	3	,	,	PUNCT
ejpam-5637	78	4	a2	a2	PROPN
ejpam-5637	78	5	,	,	PUNCT
ejpam-5637	78	6	·	·	PUNCT
ejpam-5637	78	7	·	·	PUNCT
ejpam-5637	79	1	·	·	PUNCT
ejpam-5637	79	2	,	,	PUNCT
ejpam-5637	79	3	am	be	AUX
ejpam-5637	79	4	]	]	X
ejpam-5637	79	5	,	,	PUNCT
ejpam-5637	79	6	bt	bt	X
ejpam-5637	79	7	=	=	PUNCT
ejpam-5637	80	1	[	[	X
ejpam-5637	80	2	b1	b1	NOUN
ejpam-5637	80	3	,	,	PUNCT
ejpam-5637	80	4	b2	b2	NOUN
ejpam-5637	80	5	,	,	PUNCT
ejpam-5637	80	6	·	·	PUNCT
ejpam-5637	80	7	·	·	PUNCT
ejpam-5637	80	8	·	·	PUNCT
ejpam-5637	80	9	,	,	PUNCT
ejpam-5637	80	10	bm	bm	PROPN
ejpam-5637	80	11	]	]	X
ejpam-5637	80	12	,	,	PUNCT
ejpam-5637	80	13	xt	xt	X
ejpam-5637	80	14	=	=	SYM
ejpam-5637	81	1	[	[	X
ejpam-5637	81	2	x11	x11	NOUN
ejpam-5637	81	3	,	,	PUNCT
ejpam-5637	81	4	x12	x12	NUM
ejpam-5637	81	5	,	,	PUNCT
ejpam-5637	81	6	·	·	PUNCT
ejpam-5637	81	7	·	·	PUNCT
ejpam-5637	81	8	·	·	PUNCT
ejpam-5637	81	9	,	,	PUNCT
ejpam-5637	81	10	xmn	xmn	PROPN
ejpam-5637	81	11	]	]	X
ejpam-5637	81	12	,	,	PUNCT
ejpam-5637	81	13	ct	ct	NOUN
ejpam-5637	81	14	=	=	PUNCT
ejpam-5637	82	1	[	[	X
ejpam-5637	82	2	c11	c11	NOUN
ejpam-5637	82	3	,	,	PUNCT
ejpam-5637	82	4	c12	c12	PROPN
ejpam-5637	82	5	,	,	PUNCT
ejpam-5637	82	6	·	·	PUNCT
ejpam-5637	82	7	·	·	PUNCT
ejpam-5637	82	8	·	·	PUNCT
ejpam-5637	82	9	,	,	PUNCT
ejpam-5637	82	10	cmn	cmn	VERB
ejpam-5637	82	11	]	]	PUNCT
ejpam-5637	82	12	,	,	PUNCT
ejpam-5637	82	13	and	and	CCONJ
ejpam-5637	82	14	gt	gt	INTJ
ejpam-5637	82	15	=	=	PUNCT
ejpam-5637	83	1	[	[	X
ejpam-5637	83	2	at	at	ADP
ejpam-5637	83	3	:	:	PUNCT
ejpam-5637	83	4	bt	bt	X
ejpam-5637	83	5	]	]	X
ejpam-5637	83	6	.	.	PUNCT
ejpam-5637	84	1	the	the	DET
ejpam-5637	84	2	coefficient	coefficient	NOUN
ejpam-5637	84	3	matrix	matrix	NOUN
ejpam-5637	84	4	m	m	AUX
ejpam-5637	84	5	is	be	AUX
ejpam-5637	84	6	given	give	VERB
ejpam-5637	84	7	as	as	ADP
ejpam-5637	84	8	m	m	NOUN
ejpam-5637	84	9	=	=	PUNCT
ejpam-5637	84	10	(	(	PUNCT
ejpam-5637	84	11	1n	1n	NUM
ejpam-5637	84	12	⊗	⊗	PROPN
ejpam-5637	84	13	i	i	PRON
ejpam-5637	84	14	m	m	VERB
ejpam-5637	84	15	in	in	ADP
ejpam-5637	84	16	⊗	⊗	PROPN
ejpam-5637	84	17	1n	1n	NUM
ejpam-5637	84	18	)	)	PUNCT
ejpam-5637	84	19	,	,	PUNCT
ejpam-5637	84	20	where	where	SCONJ
ejpam-5637	84	21	i	i	PRON
ejpam-5637	84	22	m	m	VERB
ejpam-5637	84	23	is	be	AUX
ejpam-5637	84	24	m	m	ADJ
ejpam-5637	84	25	-	-	ADJ
ejpam-5637	84	26	dimensional	dimensional	ADJ
ejpam-5637	84	27	identity	identity	NOUN
ejpam-5637	84	28	matrix	matrix	NOUN
ejpam-5637	84	29	,	,	PUNCT
ejpam-5637	84	30	1	1	NUM
ejpam-5637	84	31	m	m	NOUN
ejpam-5637	84	32	is	be	AUX
ejpam-5637	84	33	1	1	NUM
ejpam-5637	84	34	×m	×m	NOUN
ejpam-5637	84	35	vector	vector	NOUN
ejpam-5637	84	36	of	of	ADP
ejpam-5637	84	37	all	all	DET
ejpam-5637	84	38	1′s	1′s	NUM
ejpam-5637	84	39	,	,	PUNCT
ejpam-5637	84	40	and	and	CCONJ
ejpam-5637	84	41	⊗	⊗	PROPN
ejpam-5637	84	42	denotes	denote	NOUN
ejpam-5637	84	43	kronecker	kronecker	NOUN
ejpam-5637	84	44	product	product	NOUN
ejpam-5637	84	45	.	.	PUNCT
ejpam-5637	85	1	in	in	ADP
ejpam-5637	85	2	[	[	X
ejpam-5637	85	3	6	6	NUM
ejpam-5637	85	4	]	]	PUNCT
ejpam-5637	85	5	,	,	PUNCT
ejpam-5637	85	6	a	a	DET
ejpam-5637	85	7	relation	relation	NOUN
ejpam-5637	85	8	between	between	ADP
ejpam-5637	85	9	eigenvectors	eigenvector	NOUN
ejpam-5637	85	10	of	of	ADP
ejpam-5637	85	11	m+m	m+m	PROPN
ejpam-5637	85	12	and	and	CCONJ
ejpam-5637	85	13	mmt	mmt	PROPN
ejpam-5637	85	14	was	be	AUX
ejpam-5637	85	15	developed	develop	VERB
ejpam-5637	85	16	.	.	PUNCT
ejpam-5637	86	1	the	the	DET
ejpam-5637	86	2	moorepenrose	moorepenrose	ADJ
ejpam-5637	86	3	inverse	inverse	NOUN
ejpam-5637	86	4	m+	m+	NUM
ejpam-5637	86	5	for	for	ADP
ejpam-5637	86	6	m	m	PROPN
ejpam-5637	86	7	was	be	AUX
ejpam-5637	86	8	obtained	obtain	VERB
ejpam-5637	86	9	in	in	ADP
ejpam-5637	86	10	[	[	X
ejpam-5637	86	11	9	9	NUM
ejpam-5637	86	12	]	]	PUNCT
ejpam-5637	86	13	as	as	ADP
ejpam-5637	86	14	m+	m+	NUM
ejpam-5637	86	15	=	=	SYM
ejpam-5637	86	16	1	1	NUM
ejpam-5637	86	17	mn	mn	PROPN
ejpam-5637	86	18	(	(	PUNCT
ejpam-5637	86	19	m1tn	m1tn	PROPN
ejpam-5637	86	20	⊗	⊗	PROPN
ejpam-5637	86	21	(	(	PUNCT
ejpam-5637	86	22	(	(	PUNCT
ejpam-5637	86	23	m	m	VERB
ejpam-5637	86	24	+	+	ADJ
ejpam-5637	87	1	n)im	n)im	PROPN
ejpam-5637	87	2	−	−	PROPN
ejpam-5637	88	1	jm)n((m	jm)n((m	NOUN
ejpam-5637	88	2	+	+	CCONJ
ejpam-5637	89	1	n)in	n)in	PROPN
ejpam-5637	89	2	)	)	PUNCT
ejpam-5637	89	3	−	−	PROPN
ejpam-5637	90	1	jn	jn	PROPN
ejpam-5637	90	2	⊗	⊗	PROPN
ejpam-5637	90	3	1tm	1tm	PROPN
ejpam-5637	90	4	)	)	PUNCT
ejpam-5637	90	5	,	,	PUNCT
ejpam-5637	90	6	with	with	ADP
ejpam-5637	90	7	jm	jm	PROPN
ejpam-5637	90	8	as	as	ADP
ejpam-5637	90	9	an	an	DET
ejpam-5637	90	10	m×m	m×m	ADJ
ejpam-5637	90	11	matrix	matrix	NOUN
ejpam-5637	90	12	of	of	ADP
ejpam-5637	90	13	all	all	DET
ejpam-5637	90	14	1′s	1′s	NOUN
ejpam-5637	90	15	,	,	PUNCT
ejpam-5637	90	16	means	mean	VERB
ejpam-5637	90	17	that	that	SCONJ
ejpam-5637	90	18	,	,	PUNCT
ejpam-5637	90	19	jm	jm	PROPN
ejpam-5637	90	20	=	=	SYM
ejpam-5637	90	21	1tm1	1tm1	NUM
ejpam-5637	90	22	m.	m.	NOUN
ejpam-5637	90	23	furthermore	furthermore	ADV
ejpam-5637	90	24	,	,	PUNCT
ejpam-5637	90	25	m+m	m+m	PROPN
ejpam-5637	91	1	=	=	PUNCT
ejpam-5637	91	2	i	i	PRON
ejpam-5637	91	3	−	−	PROPN
ejpam-5637	91	4	1	1	NUM
ejpam-5637	91	5	mn	mn	PROPN
ejpam-5637	91	6	(	(	PUNCT
ejpam-5637	91	7	nin	nin	PROPN
ejpam-5637	91	8	−	−	PROPN
ejpam-5637	91	9	jn	jn	PROPN
ejpam-5637	91	10	)	)	PUNCT
ejpam-5637	91	11	⊗	⊗	PROPN
ejpam-5637	91	12	(	(	PUNCT
ejpam-5637	91	13	mim	mim	PROPN
ejpam-5637	91	14	−	−	PROPN
ejpam-5637	91	15	jm	jm	PROPN
ejpam-5637	91	16	)	)	PUNCT
ejpam-5637	91	17	,	,	PUNCT
ejpam-5637	91	18	with	with	ADP
ejpam-5637	91	19	i	i	PROPN
ejpam-5637	91	20	−m+m	−m+m	PROPN
ejpam-5637	91	21	,	,	PUNCT
ejpam-5637	91	22	a	a	DET
ejpam-5637	91	23	symmetric	symmetric	ADJ
ejpam-5637	91	24	and	and	CCONJ
ejpam-5637	91	25	idempotent	idempotent	ADJ
ejpam-5637	91	26	matrix	matrix	NOUN
ejpam-5637	91	27	.	.	PUNCT
ejpam-5637	92	1	the	the	DET
ejpam-5637	92	2	relation	relation	NOUN
ejpam-5637	92	3	between	between	ADP
ejpam-5637	92	4	eigenvectors	eigenvector	NOUN
ejpam-5637	92	5	of	of	ADP
ejpam-5637	92	6	jn	jn	PROPN
ejpam-5637	92	7	,	,	PUNCT
ejpam-5637	92	8	jm	jm	PROPN
ejpam-5637	92	9	,	,	PUNCT
ejpam-5637	92	10	and	and	CCONJ
ejpam-5637	92	11	i	i	PRON
ejpam-5637	92	12	−m+m	−m+m	PROPN
ejpam-5637	92	13	was	be	AUX
ejpam-5637	92	14	developed	develop	VERB
ejpam-5637	92	15	in	in	ADP
ejpam-5637	92	16	the	the	DET
ejpam-5637	92	17	theorem	theorem	ADJ
ejpam-5637	92	18	2	2	NUM
ejpam-5637	92	19	[	[	X
ejpam-5637	92	20	6	6	NUM
ejpam-5637	92	21	]	]	PUNCT
ejpam-5637	92	22	.	.	PUNCT
ejpam-5637	93	1	the	the	DET
ejpam-5637	93	2	following	follow	VERB
ejpam-5637	93	3	theorem	theorem	NOUN
ejpam-5637	93	4	gives	give	VERB
ejpam-5637	93	5	moore	moore	PROPN
ejpam-5637	93	6	-	-	PUNCT
ejpam-5637	93	7	penrose	penrose	NOUN
ejpam-5637	93	8	inverse	inverse	NOUN
ejpam-5637	93	9	of	of	ADP
ejpam-5637	93	10	a	a	DET
ejpam-5637	93	11	matrix	matrix	NOUN
ejpam-5637	93	12	m	m	NOUN
ejpam-5637	93	13	.	.	PUNCT
ejpam-5637	94	1	m.u	m.u	PROPN
ejpam-5637	94	2	.	.	PROPN
ejpam-5637	95	1	rahman	rahman	PROPN
ejpam-5637	95	2	et	et	PROPN
ejpam-5637	95	3	al	al	PROPN
ejpam-5637	95	4	.	.	PUNCT
ejpam-5637	95	5	/	/	SYM
ejpam-5637	95	6	eur	eur	PROPN
ejpam-5637	95	7	.	.	PUNCT
ejpam-5637	96	1	j.	j.	PROPN
ejpam-5637	96	2	pure	pure	PROPN
ejpam-5637	96	3	appl	appl	PROPN
ejpam-5637	96	4	.	.	PROPN
ejpam-5637	96	5	math	math	PROPN
ejpam-5637	96	6	,	,	PUNCT
ejpam-5637	96	7	18	18	NUM
ejpam-5637	96	8	(	(	PUNCT
ejpam-5637	96	9	1	1	NUM
ejpam-5637	96	10	)	)	PUNCT
ejpam-5637	96	11	(	(	PUNCT
ejpam-5637	96	12	2025	2025	NUM
ejpam-5637	96	13	)	)	PUNCT
ejpam-5637	96	14	,	,	PUNCT
ejpam-5637	96	15	5637	5637	NUM
ejpam-5637	96	16	5	5	NUM
ejpam-5637	96	17	of	of	ADP
ejpam-5637	96	18	20	20	NUM
ejpam-5637	96	19	theorem	theorem	NOUN
ejpam-5637	96	20	1	1	NUM
ejpam-5637	96	21	.	.	PUNCT
ejpam-5637	97	1	let	let	VERB
ejpam-5637	97	2	m	m	PROPN
ejpam-5637	97	3	∈	∈	PROPN
ejpam-5637	97	4	rn	rn	PROPN
ejpam-5637	97	5	,	,	PUNCT
ejpam-5637	97	6	n.	n.	PROPN
ejpam-5637	97	7	then	then	ADV
ejpam-5637	97	8	,	,	PUNCT
ejpam-5637	97	9	then	then	ADV
ejpam-5637	97	10	m+	m+	PRON
ejpam-5637	97	11	is	be	AUX
ejpam-5637	97	12	the	the	DET
ejpam-5637	97	13	moore	moore	PROPN
ejpam-5637	97	14	-	-	PUNCT
ejpam-5637	97	15	penrose	penrose	PROPN
ejpam-5637	97	16	inverse	inverse	NOUN
ejpam-5637	97	17	satisfying	satisfy	VERB
ejpam-5637	97	18	the	the	DET
ejpam-5637	97	19	matrix	matrix	NOUN
ejpam-5637	97	20	equation	equation	NOUN
ejpam-5637	97	21	m	m	NOUN
ejpam-5637	97	22	=	=	SYM
ejpam-5637	97	23	mm+m	mm+m	PROPN
ejpam-5637	97	24	.	.	PUNCT
ejpam-5637	98	1	theorem	theorem	NOUN
ejpam-5637	98	2	2	2	NUM
ejpam-5637	98	3	.	.	PUNCT
ejpam-5637	99	1	let	let	VERB
ejpam-5637	99	2	vj	vj	INTJ
ejpam-5637	99	3	be	be	AUX
ejpam-5637	99	4	all	all	DET
ejpam-5637	99	5	eigenvectors	eigenvector	NOUN
ejpam-5637	99	6	of	of	ADP
ejpam-5637	99	7	jm	jm	PROPN
ejpam-5637	99	8	,	,	PUNCT
ejpam-5637	99	9	and	and	CCONJ
ejpam-5637	99	10	uk	uk	PROPN
ejpam-5637	99	11	,	,	PUNCT
ejpam-5637	99	12	the	the	DET
ejpam-5637	99	13	eigenvectors	eigenvector	NOUN
ejpam-5637	99	14	corresponding	correspond	VERB
ejpam-5637	99	15	to	to	ADP
ejpam-5637	99	16	jn	jn	PROPN
ejpam-5637	99	17	.	.	PUNCT
ejpam-5637	100	1	then	then	ADV
ejpam-5637	100	2	eigenvectors	eigenvector	VERB
ejpam-5637	100	3	corresponding	correspond	VERB
ejpam-5637	100	4	to	to	ADP
ejpam-5637	100	5	simple	simple	ADJ
ejpam-5637	100	6	eigenvalues	eigenvalue	NOUN
ejpam-5637	100	7	1	1	NUM
ejpam-5637	100	8	of	of	ADP
ejpam-5637	100	9	i	i	PRON
ejpam-5637	100	10	−m+m	−m+m	PROPN
ejpam-5637	100	11	are	be	AUX
ejpam-5637	100	12	v̂i	v̂i	ADP
ejpam-5637	100	13	=	=	SYM
ejpam-5637	100	14	uj	uj	PROPN
ejpam-5637	100	15	⊗	⊗	PROPN
ejpam-5637	100	16	xk	xk	PROPN
ejpam-5637	100	17	,	,	PUNCT
ejpam-5637	100	18	where	where	SCONJ
ejpam-5637	100	19	j	j	PROPN
ejpam-5637	100	20	=	=	NOUN
ejpam-5637	100	21	1	1	NUM
ejpam-5637	100	22	:	:	PUNCT
ejpam-5637	100	23	n−	n−	NOUN
ejpam-5637	100	24	1	1	NUM
ejpam-5637	100	25	;	;	PUNCT
ejpam-5637	100	26	k	k	X
ejpam-5637	100	27	=	=	SYM
ejpam-5637	100	28	1	1	NUM
ejpam-5637	100	29	:	:	PUNCT
ejpam-5637	100	30	m−	m−	PROPN
ejpam-5637	100	31	1	1	NUM
ejpam-5637	100	32	;	;	PUNCT
ejpam-5637	101	1	i	i	PRON
ejpam-5637	101	2	=	=	VERB
ejpam-5637	101	3	m	m	VERB
ejpam-5637	101	4	+	+	NOUN
ejpam-5637	101	5	n	n	CCONJ
ejpam-5637	101	6	,	,	PUNCT
ejpam-5637	101	7	·	·	PUNCT
ejpam-5637	101	8	·	·	PUNCT
ejpam-5637	101	9	·	·	PUNCT
ejpam-5637	101	10	,	,	PUNCT
ejpam-5637	101	11	(	(	PUNCT
ejpam-5637	101	12	m−	m−	PROPN
ejpam-5637	101	13	1)(n−	1)(n−	NUM
ejpam-5637	101	14	1	1	NUM
ejpam-5637	101	15	)	)	PUNCT
ejpam-5637	101	16	.	.	PUNCT
ejpam-5637	102	1	definition	definition	NOUN
ejpam-5637	102	2	1	1	NUM
ejpam-5637	102	3	.	.	PUNCT
ejpam-5637	103	1	the	the	DET
ejpam-5637	103	2	singular	singular	ADJ
ejpam-5637	103	3	value	value	NOUN
ejpam-5637	103	4	of	of	ADP
ejpam-5637	103	5	a	a	DET
ejpam-5637	103	6	square	square	ADJ
ejpam-5637	103	7	or	or	CCONJ
ejpam-5637	103	8	rectangular	rectangular	ADJ
ejpam-5637	103	9	matrix	matrix	NOUN
ejpam-5637	103	10	m	m	NOUN
ejpam-5637	103	11	are	be	AUX
ejpam-5637	103	12	the	the	DET
ejpam-5637	103	13	positive	positive	ADJ
ejpam-5637	103	14	square	square	ADJ
ejpam-5637	103	15	root	root	NOUN
ejpam-5637	103	16	of	of	ADP
ejpam-5637	103	17	eigenvalue	eigenvalue	PROPN
ejpam-5637	103	18	of	of	ADP
ejpam-5637	103	19	mtm	mtm	PROPN
ejpam-5637	103	20	,	,	PUNCT
ejpam-5637	103	21	where	where	SCONJ
ejpam-5637	103	22	t	t	PROPN
ejpam-5637	103	23	denotes	denote	VERB
ejpam-5637	103	24	the	the	DET
ejpam-5637	103	25	transpose	transpose	NOUN
ejpam-5637	103	26	of	of	ADP
ejpam-5637	103	27	m	m	PROPN
ejpam-5637	103	28	.	.	PUNCT
ejpam-5637	104	1	theorem	theorem	ADJ
ejpam-5637	104	2	3	3	X
ejpam-5637	104	3	.	.	PUNCT
ejpam-5637	105	1	let	let	VERB
ejpam-5637	105	2	m	m	PROPN
ejpam-5637	105	3	∈	∈	PROPN
ejpam-5637	105	4	rn	rn	PROPN
ejpam-5637	105	5	,	,	PUNCT
ejpam-5637	105	6	n.	n.	PROPN
ejpam-5637	105	7	then	then	ADV
ejpam-5637	105	8	there	there	PRON
ejpam-5637	105	9	exists	exist	VERB
ejpam-5637	105	10	unitary	unitary	ADJ
ejpam-5637	105	11	matrices	matrix	NOUN
ejpam-5637	105	12	u	u	NOUN
ejpam-5637	105	13	,	,	PUNCT
ejpam-5637	105	14	v	v	NOUN
ejpam-5637	105	15	,	,	PUNCT
ejpam-5637	105	16	and	and	CCONJ
ejpam-5637	105	17	a	a	DET
ejpam-5637	105	18	diagonal	diagonal	ADJ
ejpam-5637	105	19	matrix	matrix	NOUN
ejpam-5637	105	20	σ	σ	NOUN
ejpam-5637	105	21	such	such	ADJ
ejpam-5637	105	22	that	that	SCONJ
ejpam-5637	105	23	m	m	PROPN
ejpam-5637	105	24	can	can	AUX
ejpam-5637	105	25	be	be	AUX
ejpam-5637	105	26	decomposed	decompose	VERB
ejpam-5637	105	27	as	as	ADP
ejpam-5637	105	28	m	m	NOUN
ejpam-5637	105	29	=	=	NOUN
ejpam-5637	105	30	uσv	uσv	PROPN
ejpam-5637	105	31	t	t	NOUN
ejpam-5637	105	32	.	.	PUNCT
ejpam-5637	106	1	further	far	ADV
ejpam-5637	106	2	,	,	PUNCT
ejpam-5637	106	3	the	the	DET
ejpam-5637	106	4	non	non	ADJ
ejpam-5637	106	5	-	-	ADJ
ejpam-5637	106	6	zero	zero	ADJ
ejpam-5637	106	7	singular	singular	ADJ
ejpam-5637	106	8	values	value	NOUN
ejpam-5637	106	9	of	of	ADP
ejpam-5637	106	10	m	m	NOUN
ejpam-5637	106	11	are	be	AUX
ejpam-5637	106	12	contained	contain	VERB
ejpam-5637	106	13	along	along	ADP
ejpam-5637	106	14	the	the	DET
ejpam-5637	106	15	main	main	ADJ
ejpam-5637	106	16	diagonal	diagonal	NOUN
ejpam-5637	106	17	of	of	ADP
ejpam-5637	106	18	σ	σ	PROPN
ejpam-5637	106	19	.	.	PUNCT
ejpam-5637	106	20	corollary	corollary	NOUN
ejpam-5637	106	21	1	1	NUM
ejpam-5637	107	1	[	[	X
ejpam-5637	107	2	6	6	NUM
ejpam-5637	107	3	]	]	PUNCT
ejpam-5637	107	4	.	.	PUNCT
ejpam-5637	108	1	let	let	VERB
ejpam-5637	108	2	{	{	PUNCT
ejpam-5637	108	3	a1	a1	PROPN
ejpam-5637	108	4	,	,	PUNCT
ejpam-5637	108	5	a2	a2	PROPN
ejpam-5637	108	6	,	,	PUNCT
ejpam-5637	108	7	·	·	PUNCT
ejpam-5637	108	8	·	·	PUNCT
ejpam-5637	108	9	·	·	PUNCT
ejpam-5637	108	10	,	,	PUNCT
ejpam-5637	108	11	am+n−1	am+n−1	ADJ
ejpam-5637	108	12	}	}	PUNCT
ejpam-5637	108	13	and	and	CCONJ
ejpam-5637	108	14	{	{	PUNCT
ejpam-5637	108	15	b1	b1	NOUN
ejpam-5637	108	16	,	,	PUNCT
ejpam-5637	108	17	b2	b2	NOUN
ejpam-5637	108	18	,	,	PUNCT
ejpam-5637	108	19	·	·	PUNCT
ejpam-5637	108	20	·	·	PUNCT
ejpam-5637	108	21	·	·	PUNCT
ejpam-5637	108	22	,	,	PUNCT
ejpam-5637	108	23	bm+n−1	bm+n−1	PROPN
ejpam-5637	108	24	}	}	PUNCT
ejpam-5637	108	25	are	be	AUX
ejpam-5637	108	26	the	the	DET
ejpam-5637	108	27	sets	set	NOUN
ejpam-5637	108	28	of	of	ADP
ejpam-5637	108	29	eigenvectors	eigenvector	NOUN
ejpam-5637	108	30	corresponding	correspond	VERB
ejpam-5637	108	31	to	to	ADP
ejpam-5637	108	32	eigenvalues	eigenvalue	NOUN
ejpam-5637	108	33	of	of	ADP
ejpam-5637	108	34	mmt	mmt	PROPN
ejpam-5637	108	35	and	and	CCONJ
ejpam-5637	108	36	mtm	mtm	PROPN
ejpam-5637	108	37	,	,	PUNCT
ejpam-5637	108	38	and	and	CCONJ
ejpam-5637	108	39	consider	consider	VERB
ejpam-5637	108	40	that	that	SCONJ
ejpam-5637	108	41	σ1	σ1	NOUN
ejpam-5637	108	42	,	,	PUNCT
ejpam-5637	108	43	σ2	σ2	PROPN
ejpam-5637	108	44	,	,	PUNCT
ejpam-5637	108	45	·	·	PUNCT
ejpam-5637	108	46	·	·	PUNCT
ejpam-5637	108	47	·	·	PUNCT
ejpam-5637	108	48	,	,	PUNCT
ejpam-5637	108	49	σm+n−1	σm+n−1	PROPN
ejpam-5637	108	50	are	be	AUX
ejpam-5637	108	51	singular	singular	ADJ
ejpam-5637	108	52	values	value	NOUN
ejpam-5637	108	53	of	of	ADP
ejpam-5637	108	54	m	m	PROPN
ejpam-5637	108	55	.	.	PUNCT
ejpam-5637	109	1	then	then	ADV
ejpam-5637	109	2	,	,	PUNCT
ejpam-5637	109	3	mmtai	mmtai	PROPN
ejpam-5637	109	4	=	=	PROPN
ejpam-5637	109	5	σ2	σ2	PROPN
ejpam-5637	109	6	i	i	PRON
ejpam-5637	109	7	ai	ai	VERB
ejpam-5637	109	8	,	,	PUNCT
ejpam-5637	109	9	i	i	PRON
ejpam-5637	109	10	=	=	NOUN
ejpam-5637	109	11	1	1	NUM
ejpam-5637	109	12	:	:	PUNCT
ejpam-5637	109	13	m	m	VERB
ejpam-5637	109	14	+	+	ADJ
ejpam-5637	109	15	n−	n−	NOUN
ejpam-5637	109	16	1	1	NUM
ejpam-5637	109	17	,	,	PUNCT
ejpam-5637	109	18	mtmbi	mtmbi	NOUN
ejpam-5637	109	19	=	=	PROPN
ejpam-5637	109	20	σ2	σ2	PROPN
ejpam-5637	109	21	i	i	PROPN
ejpam-5637	109	22	bi	bi	PROPN
ejpam-5637	109	23	,	,	PUNCT
ejpam-5637	109	24	i	i	PRON
ejpam-5637	109	25	=	=	NOUN
ejpam-5637	109	26	1	1	NUM
ejpam-5637	109	27	:	:	PUNCT
ejpam-5637	109	28	m	m	VERB
ejpam-5637	109	29	+	+	ADJ
ejpam-5637	109	30	n−	n−	NOUN
ejpam-5637	109	31	1	1	NUM
ejpam-5637	109	32	.	.	PUNCT
ejpam-5637	109	33	corollary	corollary	ADJ
ejpam-5637	109	34	2	2	NUM
ejpam-5637	110	1	[	[	X
ejpam-5637	110	2	6	6	NUM
ejpam-5637	110	3	]	]	PUNCT
ejpam-5637	110	4	.	.	PUNCT
ejpam-5637	111	1	the	the	DET
ejpam-5637	111	2	eigenvectors	eigenvector	NOUN
ejpam-5637	111	3	ai	ai	AUX
ejpam-5637	111	4	corresponding	correspond	VERB
ejpam-5637	111	5	to	to	ADP
ejpam-5637	111	6	the	the	DET
ejpam-5637	111	7	eigenvalue	eigenvalue	PROPN
ejpam-5637	111	8	0	0	PUNCT
ejpam-5637	111	9	and	and	CCONJ
ejpam-5637	111	10	m	m	PROPN
ejpam-5637	111	11	+	+	NOUN
ejpam-5637	111	12	n	n	CCONJ
ejpam-5637	111	13	are	be	AUX
ejpam-5637	111	14	jmxi	jmxi	NOUN
ejpam-5637	111	15	=	=	SYM
ejpam-5637	111	16	mxi	mxi	PROPN
ejpam-5637	111	17	,	,	PUNCT
ejpam-5637	111	18	jnyi	jnyi	PROPN
ejpam-5637	111	19	=	=	PROPN
ejpam-5637	111	20	nyi	nyi	PROPN
ejpam-5637	111	21	.	.	PUNCT
ejpam-5637	112	1	the	the	DET
ejpam-5637	112	2	eigenvectors	eigenvector	NOUN
ejpam-5637	112	3	corresponding	correspond	VERB
ejpam-5637	112	4	to	to	AUX
ejpam-5637	112	5	eigenvalues	eigenvalues	VERB
ejpam-5637	112	6	m	m	PRON
ejpam-5637	112	7	and	and	CCONJ
ejpam-5637	112	8	n	n	PROPN
ejpam-5637	112	9	are	be	AUX
ejpam-5637	112	10	given	give	VERB
ejpam-5637	112	11	by	by	ADP
ejpam-5637	112	12	jmxi	jmxi	PROPN
ejpam-5637	112	13	=	=	SYM
ejpam-5637	112	14	0⃗	0⃗	PROPN
ejpam-5637	112	15	,	,	PUNCT
ejpam-5637	112	16	jnyi	jnyi	PROPN
ejpam-5637	112	17	=	=	NOUN
ejpam-5637	112	18	0⃗	0⃗	NOUN
ejpam-5637	112	19	with	with	ADP
ejpam-5637	112	20	xi	xi	PROPN
ejpam-5637	112	21	are	be	AUX
ejpam-5637	112	22	m×	m×	PROPN
ejpam-5637	112	23	1	1	NUM
ejpam-5637	112	24	vectors	vector	NOUN
ejpam-5637	112	25	and	and	CCONJ
ejpam-5637	112	26	yi	yi	PROPN
ejpam-5637	112	27	are	be	AUX
ejpam-5637	112	28	n×	n×	PROPN
ejpam-5637	112	29	1	1	NUM
ejpam-5637	112	30	vectors	vector	NOUN
ejpam-5637	112	31	.	.	PUNCT
ejpam-5637	113	1	let	let	VERB
ejpam-5637	113	2	m+	m+	NOUN
ejpam-5637	113	3	=	=	SYM
ejpam-5637	113	4	(	(	PUNCT
ejpam-5637	113	5	m∗m)−1m∗	m∗m)−1m∗	PROPN
ejpam-5637	113	6	be	be	VERB
ejpam-5637	113	7	the	the	DET
ejpam-5637	113	8	moore	moore	PROPN
ejpam-5637	113	9	-	-	PUNCT
ejpam-5637	113	10	penrose	penrose	NOUN
ejpam-5637	113	11	inverse	inverse	NOUN
ejpam-5637	113	12	matrix	matrix	NOUN
ejpam-5637	113	13	of	of	ADP
ejpam-5637	113	14	the	the	DET
ejpam-5637	113	15	matrix	matrix	NOUN
ejpam-5637	113	16	m	m	VERB
ejpam-5637	113	17	,	,	PUNCT
ejpam-5637	113	18	∗	∗	PROPN
ejpam-5637	113	19	denotes	denote	VERB
ejpam-5637	113	20	the	the	DET
ejpam-5637	113	21	complex	complex	ADJ
ejpam-5637	113	22	conjugate	conjugate	ADJ
ejpam-5637	113	23	transpose	transpose	NOUN
ejpam-5637	113	24	.	.	PUNCT
ejpam-5637	114	1	let	let	VERB
ejpam-5637	114	2	m∗(mm∗)−1	m∗(mm∗)−1	NOUN
ejpam-5637	114	3	be	be	AUX
ejpam-5637	114	4	the	the	DET
ejpam-5637	114	5	right	right	ADJ
ejpam-5637	114	6	inverse	inverse	NOUN
ejpam-5637	114	7	of	of	ADP
ejpam-5637	114	8	m	m	PROPN
ejpam-5637	114	9	.	.	PUNCT
ejpam-5637	115	1	the	the	DET
ejpam-5637	115	2	following	follow	VERB
ejpam-5637	115	3	theorem	theorem	NOUN
ejpam-5637	115	4	4	4	NUM
ejpam-5637	115	5	gives	give	VERB
ejpam-5637	115	6	the	the	DET
ejpam-5637	115	7	orthogonal	orthogonal	ADJ
ejpam-5637	115	8	nature	nature	NOUN
ejpam-5637	115	9	of	of	ADP
ejpam-5637	115	10	the	the	DET
ejpam-5637	115	11	leading	lead	VERB
ejpam-5637	115	12	singular	singular	ADJ
ejpam-5637	115	13	values	value	NOUN
ejpam-5637	115	14	.	.	PUNCT
ejpam-5637	116	1	m.u	m.u	PROPN
ejpam-5637	116	2	.	.	PROPN
ejpam-5637	117	1	rahman	rahman	PROPN
ejpam-5637	117	2	et	et	PROPN
ejpam-5637	117	3	al	al	PROPN
ejpam-5637	117	4	.	.	PUNCT
ejpam-5637	117	5	/	/	SYM
ejpam-5637	117	6	eur	eur	PROPN
ejpam-5637	117	7	.	.	PUNCT
ejpam-5637	118	1	j.	j.	PROPN
ejpam-5637	118	2	pure	pure	PROPN
ejpam-5637	118	3	appl	appl	PROPN
ejpam-5637	118	4	.	.	PROPN
ejpam-5637	118	5	math	math	PROPN
ejpam-5637	118	6	,	,	PUNCT
ejpam-5637	118	7	18	18	NUM
ejpam-5637	118	8	(	(	PUNCT
ejpam-5637	118	9	1	1	NUM
ejpam-5637	118	10	)	)	PUNCT
ejpam-5637	118	11	(	(	PUNCT
ejpam-5637	118	12	2025	2025	NUM
ejpam-5637	118	13	)	)	PUNCT
ejpam-5637	118	14	,	,	PUNCT
ejpam-5637	118	15	5637	5637	NUM
ejpam-5637	118	16	6	6	NUM
ejpam-5637	118	17	of	of	ADP
ejpam-5637	118	18	20	20	NUM
ejpam-5637	118	19	theorem	theorem	NOUN
ejpam-5637	118	20	4	4	NUM
ejpam-5637	118	21	.	.	PUNCT
ejpam-5637	119	1	let	let	VERB
ejpam-5637	119	2	(	(	PUNCT
ejpam-5637	119	3	m∗m)−1m∗	m∗m)−1m∗	PROPN
ejpam-5637	119	4	and	and	CCONJ
ejpam-5637	119	5	m∗(mm∗)−1	m∗(mm∗)−1	NOUN
ejpam-5637	119	6	be	be	AUX
ejpam-5637	119	7	n	n	ADV
ejpam-5637	119	8	-	-	PUNCT
ejpam-5637	119	9	dimensional	dimensional	ADJ
ejpam-5637	119	10	matrices	matrix	NOUN
ejpam-5637	119	11	.	.	PUNCT
ejpam-5637	120	1	let	let	VERB
ejpam-5637	120	2	{	{	PUNCT
ejpam-5637	120	3	σi	σi	NOUN
ejpam-5637	120	4	}	}	PUNCT
ejpam-5637	120	5	,	,	PUNCT
ejpam-5637	120	6	∀i	∀i	NOUN
ejpam-5637	120	7	=	=	SYM
ejpam-5637	120	8	1	1	NUM
ejpam-5637	120	9	:	:	PUNCT
ejpam-5637	120	10	n	n	CCONJ
ejpam-5637	120	11	be	be	AUX
ejpam-5637	120	12	sequence	sequence	NOUN
ejpam-5637	120	13	of	of	ADP
ejpam-5637	120	14	singular	singular	ADJ
ejpam-5637	120	15	values	value	NOUN
ejpam-5637	120	16	with	with	ADP
ejpam-5637	120	17	{	{	PUNCT
ejpam-5637	120	18	vi	vi	NOUN
ejpam-5637	120	19	}	}	PUNCT
ejpam-5637	120	20	,	,	PUNCT
ejpam-5637	120	21	and	and	CCONJ
ejpam-5637	120	22	{	{	PUNCT
ejpam-5637	120	23	v̂i	v̂i	NOUN
ejpam-5637	120	24	}	}	PUNCT
ejpam-5637	120	25	,	,	PUNCT
ejpam-5637	120	26	∀i	∀i	NOUN
ejpam-5637	120	27	=	=	SYM
ejpam-5637	120	28	1	1	NUM
ejpam-5637	120	29	:	:	SYM
ejpam-5637	120	30	n	n	CCONJ
ejpam-5637	120	31	as	as	ADP
ejpam-5637	120	32	the	the	DET
ejpam-5637	120	33	left	left	ADJ
ejpam-5637	120	34	hand	hand	NOUN
ejpam-5637	120	35	side	side	NOUN
ejpam-5637	120	36	and	and	CCONJ
ejpam-5637	120	37	right	right	ADJ
ejpam-5637	120	38	hand	hand	NOUN
ejpam-5637	120	39	side	side	NOUN
ejpam-5637	120	40	singular	singular	ADJ
ejpam-5637	120	41	vectors	vector	NOUN
ejpam-5637	120	42	such	such	ADJ
ejpam-5637	120	43	that	that	DET
ejpam-5637	120	44	||vi||2	||vi||2	NOUN
ejpam-5637	120	45	=	=	SYM
ejpam-5637	120	46	1	1	NUM
ejpam-5637	120	47	=	=	SYM
ejpam-5637	120	48	||v̂i||2	||v̂i||2	NOUN
ejpam-5637	120	49	,	,	PUNCT
ejpam-5637	120	50	and	and	CCONJ
ejpam-5637	120	51	{	{	PUNCT
ejpam-5637	120	52	ui	ui	NOUN
ejpam-5637	120	53	}	}	PUNCT
ejpam-5637	120	54	,	,	PUNCT
ejpam-5637	120	55	and	and	CCONJ
ejpam-5637	120	56	{	{	PUNCT
ejpam-5637	120	57	ûi	ûi	ADJ
ejpam-5637	120	58	}	}	PUNCT
ejpam-5637	120	59	,	,	PUNCT
ejpam-5637	120	60	∀i	∀i	NOUN
ejpam-5637	120	61	=	=	SYM
ejpam-5637	120	62	1	1	NUM
ejpam-5637	120	63	:	:	SYM
ejpam-5637	120	64	n	n	CCONJ
ejpam-5637	120	65	as	as	ADP
ejpam-5637	120	66	the	the	DET
ejpam-5637	120	67	left	left	ADJ
ejpam-5637	120	68	hand	hand	NOUN
ejpam-5637	120	69	side	side	NOUN
ejpam-5637	120	70	and	and	CCONJ
ejpam-5637	120	71	right	right	ADJ
ejpam-5637	120	72	hand	hand	NOUN
ejpam-5637	120	73	side	side	NOUN
ejpam-5637	120	74	singular	singular	ADJ
ejpam-5637	120	75	vectors	vector	NOUN
ejpam-5637	120	76	for	for	ADP
ejpam-5637	120	77	{	{	PUNCT
ejpam-5637	120	78	σ̂i	σ̂i	X
ejpam-5637	120	79	}	}	PUNCT
ejpam-5637	120	80	such	such	ADJ
ejpam-5637	120	81	that	that	DET
ejpam-5637	120	82	||ui||2	||ui||2	NOUN
ejpam-5637	120	83	=	=	SYM
ejpam-5637	120	84	1	1	NUM
ejpam-5637	120	85	=	=	SYM
ejpam-5637	120	86	||ûi||2	||ûi||2	NOUN
ejpam-5637	120	87	.	.	PUNCT
ejpam-5637	121	1	the	the	DET
ejpam-5637	121	2	leading	lead	VERB
ejpam-5637	121	3	singular	singular	ADJ
ejpam-5637	121	4	vectors	vector	NOUN
ejpam-5637	121	5	v1	v1	VERB
ejpam-5637	121	6	and	and	CCONJ
ejpam-5637	121	7	u1	u1	NOUN
ejpam-5637	121	8	are	be	AUX
ejpam-5637	121	9	orthogonal	orthogonal	ADJ
ejpam-5637	121	10	to	to	ADP
ejpam-5637	121	11	σ1	σ1	PROPN
ejpam-5637	121	12	and	and	CCONJ
ejpam-5637	121	13	σ̂1	σ̂1	NOUN
ejpam-5637	121	14	.	.	PUNCT
ejpam-5637	122	1	then	then	ADV
ejpam-5637	122	2	any	any	DET
ejpam-5637	122	3	non	non	ADJ
ejpam-5637	122	4	-	-	ADJ
ejpam-5637	122	5	zero	zero	NUM
ejpam-5637	122	6	vector	vector	NOUN
ejpam-5637	122	7	ṽ	ṽ	PROPN
ejpam-5637	122	8	=	=	SYM
ejpam-5637	122	9	{	{	PUNCT
ejpam-5637	122	10	ṽ1	ṽ1	NOUN
ejpam-5637	122	11	,	,	PUNCT
ejpam-5637	122	12	ṽ2	ṽ2	PROPN
ejpam-5637	122	13	,	,	PUNCT
ejpam-5637	122	14	·	·	PUNCT
ejpam-5637	122	15	·	·	PUNCT
ejpam-5637	122	16	·	·	PUNCT
ejpam-5637	122	17	,	,	PUNCT
ejpam-5637	122	18	ṽn	ṽn	X
ejpam-5637	122	19	}	}	PUNCT
ejpam-5637	122	20	is	be	AUX
ejpam-5637	122	21	an	an	DET
ejpam-5637	122	22	orthogonal	orthogonal	NOUN
ejpam-5637	122	23	to	to	AUX
ejpam-5637	122	24	vector	vector	VERB
ejpam-5637	122	25	en	en	X
ejpam-5637	122	26	=	=	PROPN
ejpam-5637	122	27	1√	1√	PROPN
ejpam-5637	122	28	n	n	CCONJ
ejpam-5637	122	29	(	(	PUNCT
ejpam-5637	122	30	1	1	NUM
ejpam-5637	122	31	,	,	PUNCT
ejpam-5637	122	32	1	1	NUM
ejpam-5637	122	33	,	,	PUNCT
ejpam-5637	122	34	·	·	PUNCT
ejpam-5637	122	35	·	·	PUNCT
ejpam-5637	122	36	·	·	PUNCT
ejpam-5637	122	37	,	,	PUNCT
ejpam-5637	122	38	1)t	1)t	PROPN
ejpam-5637	122	39	and	and	CCONJ
ejpam-5637	122	40	is	be	AUX
ejpam-5637	122	41	not	not	PART
ejpam-5637	122	42	a	a	DET
ejpam-5637	122	43	singular	singular	ADJ
ejpam-5637	122	44	vector	vector	NOUN
ejpam-5637	122	45	σ1	σ1	PROPN
ejpam-5637	122	46	and	and	CCONJ
ejpam-5637	122	47	σ̂1	σ̂1	NOUN
ejpam-5637	122	48	.	.	PUNCT
ejpam-5637	123	1	proof	proof	NOUN
ejpam-5637	123	2	.	.	PUNCT
ejpam-5637	124	1	for	for	ADP
ejpam-5637	124	2	the	the	DET
ejpam-5637	124	3	prove	prove	NOUN
ejpam-5637	124	4	,	,	PUNCT
ejpam-5637	124	5	we	we	PRON
ejpam-5637	124	6	consider	consider	VERB
ejpam-5637	124	7	singular	singular	ADJ
ejpam-5637	124	8	value	value	NOUN
ejpam-5637	124	9	problem	problem	NOUN
ejpam-5637	124	10	of	of	ADP
ejpam-5637	124	11	form	form	NOUN
ejpam-5637	124	12	mṽ	mṽ	PUNCT
ejpam-5637	124	13	=	=	SYM
ejpam-5637	124	14	σṽ	σṽ	PROPN
ejpam-5637	124	15	,	,	PUNCT
ejpam-5637	124	16	where	where	SCONJ
ejpam-5637	124	17	σ	σ	PROPN
ejpam-5637	124	18	is	be	AUX
ejpam-5637	124	19	singular	singular	ADJ
ejpam-5637	124	20	value	value	NOUN
ejpam-5637	124	21	of	of	ADP
ejpam-5637	124	22	m	m	PROPN
ejpam-5637	124	23	corresponding	correspond	VERB
ejpam-5637	124	24	to	to	ADP
ejpam-5637	124	25	singular	singular	ADJ
ejpam-5637	124	26	vector	vector	NOUN
ejpam-5637	124	27	ṽ.	ṽ.	NOUN
ejpam-5637	124	28	the	the	DET
ejpam-5637	124	29	vector	vector	NOUN
ejpam-5637	124	30	ṽ	ṽ	PROPN
ejpam-5637	124	31	does	do	AUX
ejpam-5637	124	32	n’t	not	PART
ejpam-5637	124	33	act	act	VERB
ejpam-5637	124	34	as	as	ADP
ejpam-5637	124	35	singular	singular	PROPN
ejpam-5637	124	36	vector	vector	NOUN
ejpam-5637	124	37	corresponding	correspond	VERB
ejpam-5637	124	38	to	to	ADP
ejpam-5637	124	39	singular	singular	ADJ
ejpam-5637	124	40	values	value	NOUN
ejpam-5637	124	41	σ1	σ1	PROPN
ejpam-5637	124	42	and	and	CCONJ
ejpam-5637	124	43	σ̂1	σ̂1	NOUN
ejpam-5637	124	44	.	.	PUNCT
ejpam-5637	125	1	the	the	DET
ejpam-5637	125	2	matrix	matrix	NOUN
ejpam-5637	125	3	-	-	PUNCT
ejpam-5637	125	4	vector	vector	NOUN
ejpam-5637	125	5	product	product	NOUN
ejpam-5637	125	6	mṽ	mṽ	NOUN
ejpam-5637	125	7	,	,	PUNCT
ejpam-5637	125	8	can	can	AUX
ejpam-5637	125	9	be	be	AUX
ejpam-5637	125	10	rewritten	rewrite	VERB
ejpam-5637	125	11	as	as	ADP
ejpam-5637	125	12	mṽ	mṽ	NOUN
ejpam-5637	125	13	=	=	SYM
ejpam-5637	125	14			NOUN
ejpam-5637	125	15	m11ṽ1	m11ṽ1	PROPN
ejpam-5637	125	16	+	+	CCONJ
ejpam-5637	125	17	m12ṽ2	m12ṽ2	NUM
ejpam-5637	125	18	+	+	CCONJ
ejpam-5637	125	19	·	·	PUNCT
ejpam-5637	125	20	·	·	PUNCT
ejpam-5637	125	21	·	·	PUNCT
ejpam-5637	125	22	m1nṽn	m1nṽn	X
ejpam-5637	125	23	·	·	PUNCT
ejpam-5637	125	24	·	·	PUNCT
ejpam-5637	125	25	·	·	PUNCT
ejpam-5637	125	26	·	·	PUNCT
ejpam-5637	125	27	·	·	PUNCT
ejpam-5637	125	28	·	·	PUNCT
ejpam-5637	125	29	·	·	PUNCT
ejpam-5637	125	30	·	·	PUNCT
ejpam-5637	125	31	·	·	PUNCT
ejpam-5637	125	32	mn1ṽ1	mn1ṽ1	NOUN
ejpam-5637	125	33	+	+	CCONJ
ejpam-5637	125	34	mn2ṽ2	mn2ṽ2	NOUN
ejpam-5637	125	35	+	+	CCONJ
ejpam-5637	125	36	·	·	PUNCT
ejpam-5637	125	37	·	·	PUNCT
ejpam-5637	125	38	·	·	PUNCT
ejpam-5637	125	39	mnnṽn	mnnṽn	NUM
ejpam-5637	125	40			NOUN
ejpam-5637	125	41	.	.	PUNCT
ejpam-5637	126	1	take	take	VERB
ejpam-5637	126	2	∑	∑	PROPN
ejpam-5637	126	3	on	on	ADP
ejpam-5637	126	4	the	the	DET
ejpam-5637	126	5	components	component	NOUN
ejpam-5637	126	6	of	of	ADP
ejpam-5637	126	7	mṽ	mṽ	PROPN
ejpam-5637	126	8	,	,	PUNCT
ejpam-5637	126	9	we	we	PRON
ejpam-5637	126	10	have	have	VERB
ejpam-5637	126	11	∑	∑	ADV
ejpam-5637	126	12	(	(	PUNCT
ejpam-5637	126	13	mṽ	mṽ	NOUN
ejpam-5637	126	14	)	)	PUNCT
ejpam-5637	126	15	=	=	SYM
ejpam-5637	126	16	∑	∑	PUNCT
ejpam-5637	126	17			NOUN
ejpam-5637	126	18	m11ṽ1	m11ṽ1	PROPN
ejpam-5637	127	1	+	+	CCONJ
ejpam-5637	127	2	m12ṽ2	m12ṽ2	NUM
ejpam-5637	127	3	+	+	CCONJ
ejpam-5637	127	4	·	·	PUNCT
ejpam-5637	127	5	·	·	PUNCT
ejpam-5637	127	6	·	·	PUNCT
ejpam-5637	127	7	m1nṽn	m1nṽn	X
ejpam-5637	127	8	·	·	PUNCT
ejpam-5637	127	9	·	·	PUNCT
ejpam-5637	127	10	·	·	PUNCT
ejpam-5637	127	11	·	·	PUNCT
ejpam-5637	127	12	·	·	PUNCT
ejpam-5637	127	13	·	·	PUNCT
ejpam-5637	127	14	·	·	PUNCT
ejpam-5637	127	15	·	·	PUNCT
ejpam-5637	127	16	·	·	PUNCT
ejpam-5637	127	17	mn1ṽ1	mn1ṽ1	NOUN
ejpam-5637	127	18	+	+	CCONJ
ejpam-5637	127	19	mn2ṽ2	mn2ṽ2	NOUN
ejpam-5637	127	20	+	+	CCONJ
ejpam-5637	127	21	·	·	PUNCT
ejpam-5637	127	22	·	·	PUNCT
ejpam-5637	127	23	·	·	PUNCT
ejpam-5637	127	24	mnnṽn	mnnṽn	NUM
ejpam-5637	127	25			NOUN
ejpam-5637	127	26	=	=	SYM
ejpam-5637	127	27	v1	v1	PROPN
ejpam-5637	127	28	∑	∑	PUNCT
ejpam-5637	127	29	(	(	PUNCT
ejpam-5637	127	30	mi1)+···+vn	mi1)+···+vn	VERB
ejpam-5637	127	31	∑	∑	PUNCT
ejpam-5637	127	32	(	(	PUNCT
ejpam-5637	127	33	min	min	NOUN
ejpam-5637	127	34	)	)	PUNCT
ejpam-5637	127	35	=	=	SYM
ejpam-5637	127	36	v1(σ1)+···+vn(σ1	v1(σ1)+···+vn(σ1	NOUN
ejpam-5637	127	37	)	)	PUNCT
ejpam-5637	127	38	.	.	PUNCT
ejpam-5637	128	1	thus	thus	ADV
ejpam-5637	128	2	,	,	PUNCT
ejpam-5637	128	3	∑	∑	PROPN
ejpam-5637	128	4	(	(	PUNCT
ejpam-5637	128	5	mv	mv	NOUN
ejpam-5637	128	6	)	)	PUNCT
ejpam-5637	128	7	=	=	SYM
ejpam-5637	128	8	σ1	σ1	PROPN
ejpam-5637	128	9	∑	∑	PUNCT
ejpam-5637	128	10	(	(	PUNCT
ejpam-5637	128	11	v	v	NOUN
ejpam-5637	128	12	)	)	PUNCT
ejpam-5637	128	13	.	.	PUNCT
ejpam-5637	129	1	taking	take	VERB
ejpam-5637	129	2	∑	∑	PUNCT
ejpam-5637	129	3	of	of	ADP
ejpam-5637	129	4	right	right	ADJ
ejpam-5637	129	5	hand	hand	NOUN
ejpam-5637	129	6	side	side	NOUN
ejpam-5637	129	7	of	of	ADP
ejpam-5637	129	8	mv	mv	PROPN
ejpam-5637	129	9	=	=	SYM
ejpam-5637	129	10	σv	σv	PROPN
ejpam-5637	129	11	,	,	PUNCT
ejpam-5637	129	12	we	we	PRON
ejpam-5637	129	13	get∑	get∑	X
ejpam-5637	129	14	(	(	PUNCT
ejpam-5637	129	15	σv	σv	NOUN
ejpam-5637	129	16	)	)	PUNCT
ejpam-5637	129	17	=	=	SYM
ejpam-5637	130	1	σ	σ	PROPN
ejpam-5637	130	2	∑	∑	PROPN
ejpam-5637	130	3	(	(	PUNCT
ejpam-5637	130	4	v	v	NOUN
ejpam-5637	130	5	)	)	PUNCT
ejpam-5637	130	6	.	.	PUNCT
ejpam-5637	131	1	we	we	PRON
ejpam-5637	131	2	conclude	conclude	VERB
ejpam-5637	131	3	from	from	ADP
ejpam-5637	131	4	last	last	ADJ
ejpam-5637	131	5	two	two	NUM
ejpam-5637	131	6	equations	equation	NOUN
ejpam-5637	131	7	that	that	SCONJ
ejpam-5637	131	8	(	(	PUNCT
ejpam-5637	131	9	σ	σ	PROPN
ejpam-5637	131	10	−	−	PROPN
ejpam-5637	131	11	σ1	σ1	PROPN
ejpam-5637	131	12	)	)	PUNCT
ejpam-5637	131	13	=	=	PUNCT
ejpam-5637	131	14	∑	∑	PUNCT
ejpam-5637	131	15	(	(	PUNCT
ejpam-5637	131	16	v	v	NOUN
ejpam-5637	131	17	)	)	PUNCT
ejpam-5637	131	18	=	=	SYM
ejpam-5637	132	1	0	0	X
ejpam-5637	132	2	.	.	PUNCT
ejpam-5637	133	1	this	this	PRON
ejpam-5637	133	2	implies	imply	VERB
ejpam-5637	133	3	that	that	SCONJ
ejpam-5637	133	4	σ	σ	PROPN
ejpam-5637	133	5	̸=	̸=	PROPN
ejpam-5637	133	6	σ1	σ1	PROPN
ejpam-5637	133	7	,	,	PUNCT
ejpam-5637	133	8	and	and	CCONJ
ejpam-5637	133	9	∑	∑	PROPN
ejpam-5637	133	10	(	(	PUNCT
ejpam-5637	133	11	v	v	NOUN
ejpam-5637	133	12	)	)	PUNCT
ejpam-5637	133	13	=	=	SYM
ejpam-5637	133	14	0	0	X
ejpam-5637	133	15	.	.	PUNCT
ejpam-5637	134	1	this	this	PRON
ejpam-5637	134	2	proves	prove	VERB
ejpam-5637	134	3	that	that	SCONJ
ejpam-5637	134	4	v	v	NOUN
ejpam-5637	134	5	=	=	SYM
ejpam-5637	134	6	(	(	PUNCT
ejpam-5637	134	7	v1	v1	PROPN
ejpam-5637	134	8	,	,	PUNCT
ejpam-5637	134	9	v2	v2	PROPN
ejpam-5637	134	10	,	,	PUNCT
ejpam-5637	134	11	·	·	PUNCT
ejpam-5637	134	12	·	·	PUNCT
ejpam-5637	134	13	·	·	PUNCT
ejpam-5637	134	14	,	,	PUNCT
ejpam-5637	134	15	vn	vn	PROPN
ejpam-5637	134	16	)	)	PUNCT
ejpam-5637	134	17	is	be	AUX
ejpam-5637	134	18	orthogonal	orthogonal	ADJ
ejpam-5637	134	19	to	to	ADP
ejpam-5637	134	20	vector	vector	VERB
ejpam-5637	134	21	en	en	X
ejpam-5637	134	22	=	=	PROPN
ejpam-5637	134	23	1√	1√	PROPN
ejpam-5637	134	24	n	n	CCONJ
ejpam-5637	134	25	(	(	PUNCT
ejpam-5637	134	26	1	1	NUM
ejpam-5637	134	27	,	,	PUNCT
ejpam-5637	134	28	1	1	NUM
ejpam-5637	134	29	,	,	PUNCT
ejpam-5637	134	30	·	·	PUNCT
ejpam-5637	134	31	·	·	PUNCT
ejpam-5637	134	32	·	·	PUNCT
ejpam-5637	134	33	,	,	PUNCT
ejpam-5637	134	34	1)t	1)t	PROPN
ejpam-5637	134	35	.	.	PUNCT
ejpam-5637	135	1	the	the	DET
ejpam-5637	135	2	vector	vector	NOUN
ejpam-5637	135	3	en	en	X
ejpam-5637	135	4	is	be	AUX
ejpam-5637	135	5	not	not	PART
ejpam-5637	135	6	a	a	DET
ejpam-5637	135	7	singular	singular	ADJ
ejpam-5637	135	8	vector	vector	NOUN
ejpam-5637	135	9	corresponding	correspond	VERB
ejpam-5637	135	10	to	to	ADP
ejpam-5637	135	11	singular	singular	ADJ
ejpam-5637	135	12	values	value	NOUN
ejpam-5637	135	13	σ1	σ1	PROPN
ejpam-5637	135	14	and	and	CCONJ
ejpam-5637	135	15	σ̂1	σ̂1	NOUN
ejpam-5637	135	16	.	.	PUNCT
ejpam-5637	136	1	m.u	m.u	PROPN
ejpam-5637	136	2	.	.	PROPN
ejpam-5637	137	1	rahman	rahman	PROPN
ejpam-5637	137	2	et	et	PROPN
ejpam-5637	137	3	al	al	PROPN
ejpam-5637	137	4	.	.	PUNCT
ejpam-5637	137	5	/	/	SYM
ejpam-5637	137	6	eur	eur	PROPN
ejpam-5637	137	7	.	.	PUNCT
ejpam-5637	138	1	j.	j.	PROPN
ejpam-5637	138	2	pure	pure	PROPN
ejpam-5637	138	3	appl	appl	PROPN
ejpam-5637	138	4	.	.	PROPN
ejpam-5637	138	5	math	math	PROPN
ejpam-5637	138	6	,	,	PUNCT
ejpam-5637	138	7	18	18	NUM
ejpam-5637	138	8	(	(	PUNCT
ejpam-5637	138	9	1	1	NUM
ejpam-5637	138	10	)	)	PUNCT
ejpam-5637	138	11	(	(	PUNCT
ejpam-5637	138	12	2025	2025	NUM
ejpam-5637	138	13	)	)	PUNCT
ejpam-5637	138	14	,	,	PUNCT
ejpam-5637	138	15	5637	5637	NUM
ejpam-5637	138	16	7	7	NUM
ejpam-5637	138	17	of	of	ADP
ejpam-5637	138	18	20	20	NUM
ejpam-5637	138	19	theorem	theorem	NOUN
ejpam-5637	138	20	5	5	NUM
ejpam-5637	138	21	.	.	PUNCT
ejpam-5637	139	1	let	let	VERB
ejpam-5637	139	2	(	(	PUNCT
ejpam-5637	139	3	m∗m)−1m∗	m∗m)−1m∗	PROPN
ejpam-5637	139	4	and	and	CCONJ
ejpam-5637	139	5	m∗(mm∗)−1	m∗(mm∗)−1	NOUN
ejpam-5637	139	6	be	be	AUX
ejpam-5637	139	7	n	n	ADV
ejpam-5637	139	8	-	-	PUNCT
ejpam-5637	139	9	dimensional	dimensional	ADJ
ejpam-5637	139	10	matrices	matrix	NOUN
ejpam-5637	139	11	.	.	PUNCT
ejpam-5637	140	1	let	let	VERB
ejpam-5637	140	2	σi	σi	PRON
ejpam-5637	140	3	and	and	CCONJ
ejpam-5637	140	4	σ̂i	σ̂i	PROPN
ejpam-5637	140	5	are	be	AUX
ejpam-5637	140	6	leading	lead	VERB
ejpam-5637	140	7	singular	singular	ADJ
ejpam-5637	140	8	values	value	NOUN
ejpam-5637	140	9	corresponding	correspond	VERB
ejpam-5637	140	10	to	to	ADP
ejpam-5637	140	11	singular	singular	ADJ
ejpam-5637	140	12	vectors	vector	NOUN
ejpam-5637	140	13	vi	vi	PROPN
ejpam-5637	140	14	and	and	CCONJ
ejpam-5637	140	15	v̂i	v̂i	ADV
ejpam-5637	140	16	,	,	PUNCT
ejpam-5637	140	17	respectively	respectively	ADV
ejpam-5637	140	18	.	.	PUNCT
ejpam-5637	141	1	let	let	VERB
ejpam-5637	141	2	m̂	m̂	NOUN
ejpam-5637	141	3	=	=	PUNCT
ejpam-5637	141	4	(	(	PUNCT
ejpam-5637	141	5	(	(	PUNCT
ejpam-5637	141	6	m∗m)−1m∗	m∗m)−1m∗	X
ejpam-5637	141	7	+	+	NOUN
ejpam-5637	141	8	αin	αin	NOUN
ejpam-5637	141	9	2αv̂2v	2αv̂2v	NUM
ejpam-5637	141	10	t	t	NOUN
ejpam-5637	141	11	1	1	NUM
ejpam-5637	141	12	2αv1v̂	2αv1v̂	NUM
ejpam-5637	141	13	t	t	NOUN
ejpam-5637	141	14	2	2	NUM
ejpam-5637	141	15	m∗(mm∗)−1	m∗(mm∗)−1	NOUN
ejpam-5637	141	16	+	+	NOUN
ejpam-5637	141	17	αin	αin	NOUN
ejpam-5637	141	18	)	)	PUNCT
ejpam-5637	141	19	,	,	PUNCT
ejpam-5637	141	20	with	with	ADP
ejpam-5637	141	21	in	in	ADP
ejpam-5637	141	22	is	be	AUX
ejpam-5637	141	23	an	an	DET
ejpam-5637	141	24	identity	identity	NOUN
ejpam-5637	141	25	matrix	matrix	NOUN
ejpam-5637	141	26	,	,	PUNCT
ejpam-5637	141	27	α	α	PROPN
ejpam-5637	141	28	is	be	AUX
ejpam-5637	141	29	any	any	DET
ejpam-5637	141	30	scalar	scalar	NOUN
ejpam-5637	141	31	.	.	PUNCT
ejpam-5637	142	1	the	the	DET
ejpam-5637	142	2	singular	singular	ADJ
ejpam-5637	142	3	values	value	NOUN
ejpam-5637	142	4	of	of	ADP
ejpam-5637	142	5	m̂	m̂	PROPN
ejpam-5637	142	6	does	do	AUX
ejpam-5637	142	7	not	not	PART
ejpam-5637	142	8	have	have	VERB
ejpam-5637	142	9	leading	lead	VERB
ejpam-5637	142	10	singular	singular	ADJ
ejpam-5637	142	11	values	value	NOUN
ejpam-5637	142	12	of	of	ADP
ejpam-5637	142	13	matrices	matrix	NOUN
ejpam-5637	142	14	(	(	PUNCT
ejpam-5637	142	15	m∗m)−1m∗	m∗m)−1m∗	PROPN
ejpam-5637	142	16	and	and	CCONJ
ejpam-5637	142	17	m∗(mm∗)−1	m∗(mm∗)−1	NOUN
ejpam-5637	142	18	.	.	PUNCT
ejpam-5637	143	1	the	the	DET
ejpam-5637	143	2	leading	lead	VERB
ejpam-5637	143	3	singular	singular	ADJ
ejpam-5637	143	4	values	value	NOUN
ejpam-5637	143	5	σ1	σ1	PROPN
ejpam-5637	143	6	and	and	CCONJ
ejpam-5637	143	7	σ̂1	σ̂1	NOUN
ejpam-5637	143	8	are	be	AUX
ejpam-5637	143	9	along	along	ADP
ejpam-5637	143	10	the	the	DET
ejpam-5637	143	11	main	main	ADJ
ejpam-5637	143	12	diagonal	diagonal	NOUN
ejpam-5637	143	13	of	of	ADP
ejpam-5637	143	14	m̂1	m̂1	PROPN
ejpam-5637	143	15	with	with	ADP
ejpam-5637	143	16	m̂1	m̂1	PROPN
ejpam-5637	143	17	=	=	SYM
ejpam-5637	143	18	(	(	PUNCT
ejpam-5637	143	19	3α	3α	NOUN
ejpam-5637	143	20	+	+	X
ejpam-5637	143	21	σ1	σ1	NOUN
ejpam-5637	143	22	0	0	NUM
ejpam-5637	143	23	0	0	NUM
ejpam-5637	143	24	α−	α−	ADP
ejpam-5637	143	25	σ̂1	σ̂1	NOUN
ejpam-5637	143	26	)	)	PUNCT
ejpam-5637	143	27	.	.	PUNCT
ejpam-5637	144	1	proof	proof	NOUN
ejpam-5637	144	2	.	.	PUNCT
ejpam-5637	145	1	consider	consider	VERB
ejpam-5637	145	2	the	the	DET
ejpam-5637	145	3	singular	singular	ADJ
ejpam-5637	145	4	value	value	NOUN
ejpam-5637	145	5	problem	problem	NOUN
ejpam-5637	145	6	of	of	ADP
ejpam-5637	145	7	the	the	DET
ejpam-5637	145	8	form	form	NOUN
ejpam-5637	145	9	m̂vi	m̂vi	NOUN
ejpam-5637	145	10	=	=	SYM
ejpam-5637	145	11	(	(	PUNCT
ejpam-5637	145	12	σ1	σ1	PROPN
ejpam-5637	145	13	+	+	CCONJ
ejpam-5637	145	14	α)vi	α)vi	PROPN
ejpam-5637	145	15	,	,	PUNCT
ejpam-5637	145	16	∀i	∀i	NOUN
ejpam-5637	145	17	=	=	SYM
ejpam-5637	145	18	1	1	NUM
ejpam-5637	145	19	:	:	PUNCT
ejpam-5637	145	20	n.	n.	NOUN
ejpam-5637	145	21	let	let	VERB
ejpam-5637	145	22	β1	β1	PROPN
ejpam-5637	145	23	,	,	PUNCT
ejpam-5637	145	24	σ2+α	σ2+α	PROPN
ejpam-5637	145	25	,	,	PUNCT
ejpam-5637	145	26	σ3+α	σ3+α	PROPN
ejpam-5637	145	27	,	,	PUNCT
ejpam-5637	145	28	·	·	PUNCT
ejpam-5637	145	29	·	·	PUNCT
ejpam-5637	145	30	·	·	SYM
ejpam-5637	145	31	,	,	PUNCT
ejpam-5637	145	32	σn+α	σn+α	PROPN
ejpam-5637	145	33	,	,	PUNCT
ejpam-5637	145	34	and	and	CCONJ
ejpam-5637	145	35	β̂2	β̂2	PROPN
ejpam-5637	145	36	,	,	PUNCT
ejpam-5637	145	37	σ̂2+α	σ̂2+α	ADV
ejpam-5637	145	38	,	,	PUNCT
ejpam-5637	145	39	σ̂3+α	σ̂3+α	X
ejpam-5637	145	40	,	,	PUNCT
ejpam-5637	145	41	·	·	PUNCT
ejpam-5637	145	42	·	·	PUNCT
ejpam-5637	145	43	·	·	PUNCT
ejpam-5637	145	44	,	,	PUNCT
ejpam-5637	145	45	σ̂n+α	σ̂n+α	PROPN
ejpam-5637	145	46	with	with	ADP
ejpam-5637	145	47	β	β	PROPN
ejpam-5637	145	48	,	,	PUNCT
ejpam-5637	145	49	β̂	β̂	ADP
ejpam-5637	145	50	∈	∈	PROPN
ejpam-5637	145	51	{	{	PUNCT
ejpam-5637	145	52	3α+σ1	3α+σ1	NUM
ejpam-5637	145	53	,	,	PUNCT
ejpam-5637	145	54	α−σ̂1	α−σ̂1	NOUN
ejpam-5637	145	55	}	}	PUNCT
ejpam-5637	145	56	are	be	AUX
ejpam-5637	145	57	the	the	DET
ejpam-5637	145	58	singular	singular	ADJ
ejpam-5637	145	59	values	value	NOUN
ejpam-5637	145	60	of	of	ADP
ejpam-5637	145	61	matrix	matrix	NOUN
ejpam-5637	145	62	(	(	PUNCT
ejpam-5637	145	63	3α	3α	NOUN
ejpam-5637	146	1	+	+	X
ejpam-5637	146	2	σ1	σ1	NOUN
ejpam-5637	146	3	0	0	NUM
ejpam-5637	146	4	0	0	NUM
ejpam-5637	146	5	α−	α−	ADP
ejpam-5637	146	6	σ̂1	σ̂1	NOUN
ejpam-5637	146	7	)	)	PUNCT
ejpam-5637	146	8	.	.	PUNCT
ejpam-5637	147	1	for	for	ADP
ejpam-5637	147	2	the	the	DET
ejpam-5637	147	3	singular	singular	PROPN
ejpam-5637	147	4	values	value	VERB
ejpam-5637	147	5	σi	σi	NOUN
ejpam-5637	147	6	,	,	PUNCT
ejpam-5637	147	7	∀i	∀i	X
ejpam-5637	147	8	=	=	SYM
ejpam-5637	147	9	2	2	NUM
ejpam-5637	147	10	:	:	SYM
ejpam-5637	147	11	n	n	CCONJ
ejpam-5637	147	12	,	,	PUNCT
ejpam-5637	147	13	the	the	DET
ejpam-5637	147	14	singular	singular	ADJ
ejpam-5637	147	15	vectors	vector	NOUN
ejpam-5637	147	16	can	can	AUX
ejpam-5637	147	17	be	be	AUX
ejpam-5637	147	18	written	write	VERB
ejpam-5637	147	19	as	as	ADP
ejpam-5637	147	20	[	[	X
ejpam-5637	147	21	vi	vi	X
ejpam-5637	147	22	0]t	0]t	NOUN
ejpam-5637	147	23	,	,	PUNCT
ejpam-5637	147	24	∀i	∀i	NOUN
ejpam-5637	147	25	=	=	SYM
ejpam-5637	147	26	2	2	NUM
ejpam-5637	147	27	:	:	PUNCT
ejpam-5637	147	28	m.	m.	NOUN
ejpam-5637	147	29	for	for	ADP
ejpam-5637	147	30	the	the	DET
ejpam-5637	147	31	singular	singular	PROPN
ejpam-5637	147	32	values	value	NOUN
ejpam-5637	147	33	σ̂i	σ̂i	PRON
ejpam-5637	147	34	,	,	PUNCT
ejpam-5637	147	35	∀i	∀i	NOUN
ejpam-5637	147	36	=	=	SYM
ejpam-5637	147	37	2	2	NUM
ejpam-5637	147	38	:	:	SYM
ejpam-5637	147	39	n	n	CCONJ
ejpam-5637	147	40	,	,	PUNCT
ejpam-5637	147	41	the	the	DET
ejpam-5637	147	42	singular	singular	ADJ
ejpam-5637	147	43	vectors	vector	NOUN
ejpam-5637	147	44	can	can	AUX
ejpam-5637	147	45	be	be	AUX
ejpam-5637	147	46	written	write	VERB
ejpam-5637	147	47	as	as	ADP
ejpam-5637	147	48	[	[	X
ejpam-5637	147	49	0	0	NUM
ejpam-5637	147	50	v̂i	v̂i	NOUN
ejpam-5637	147	51	]	]	X
ejpam-5637	147	52	t	t	NOUN
ejpam-5637	147	53	,	,	PUNCT
ejpam-5637	147	54	∀i	∀i	X
ejpam-5637	147	55	=	=	SYM
ejpam-5637	147	56	2	2	NUM
ejpam-5637	147	57	:	:	PUNCT
ejpam-5637	147	58	n.	n.	NOUN
ejpam-5637	147	59	this	this	PRON
ejpam-5637	147	60	ensures	ensure	VERB
ejpam-5637	147	61	that	that	SCONJ
ejpam-5637	147	62	singular	singular	ADJ
ejpam-5637	147	63	vectors	vector	NOUN
ejpam-5637	147	64	corresponding	correspond	VERB
ejpam-5637	147	65	to	to	ADP
ejpam-5637	147	66	m̂	m̂	PROPN
ejpam-5637	147	67	can	can	AUX
ejpam-5637	147	68	be	be	AUX
ejpam-5637	147	69	expressed	express	VERB
ejpam-5637	147	70	as	as	ADP
ejpam-5637	147	71	[	[	X
ejpam-5637	147	72	βivi	βivi	NOUN
ejpam-5637	147	73	β̂iv̂i	β̂iv̂i	NOUN
ejpam-5637	147	74	]	]	PUNCT
ejpam-5637	147	75	t	t	PROPN
ejpam-5637	147	76	.	.	PUNCT
ejpam-5637	148	1	thus	thus	ADV
ejpam-5637	148	2	,	,	PUNCT
ejpam-5637	148	3	[	[	X
ejpam-5637	148	4	βi	βi	ADP
ejpam-5637	148	5	β̂i	β̂i	NOUN
ejpam-5637	148	6	]	]	NOUN
ejpam-5637	148	7	,	,	PUNCT
ejpam-5637	148	8	∀i	∀i	NOUN
ejpam-5637	148	9	=	=	SYM
ejpam-5637	148	10	2	2	NUM
ejpam-5637	148	11	:	:	PUNCT
ejpam-5637	148	12	n	n	X
ejpam-5637	148	13	are	be	AUX
ejpam-5637	148	14	the	the	DET
ejpam-5637	148	15	singular	singular	ADJ
ejpam-5637	148	16	vectors	vector	NOUN
ejpam-5637	148	17	corresponding	correspond	VERB
ejpam-5637	148	18	to	to	ADP
ejpam-5637	148	19	singular	singular	ADJ
ejpam-5637	148	20	values	value	NOUN
ejpam-5637	148	21	σ1	σ1	PROPN
ejpam-5637	148	22	+	+	CCONJ
ejpam-5637	148	23	3α	3α	NOUN
ejpam-5637	148	24	and	and	CCONJ
ejpam-5637	148	25	α−	α−	ADP
ejpam-5637	148	26	σ̂.	σ̂.	PRON
ejpam-5637	148	27	the	the	DET
ejpam-5637	148	28	following	follow	VERB
ejpam-5637	148	29	theorem	theorem	NOUN
ejpam-5637	148	30	shows	show	VERB
ejpam-5637	148	31	that	that	SCONJ
ejpam-5637	148	32	singular	singular	ADJ
ejpam-5637	148	33	values	value	NOUN
ejpam-5637	148	34	of	of	ADP
ejpam-5637	148	35	a	a	DET
ejpam-5637	148	36	matrix	matrix	NOUN
ejpam-5637	148	37	does	do	AUX
ejpam-5637	148	38	not	not	PART
ejpam-5637	148	39	depend	depend	VERB
ejpam-5637	148	40	continuously	continuously	ADV
ejpam-5637	148	41	on	on	ADP
ejpam-5637	148	42	the	the	DET
ejpam-5637	148	43	entries	entry	NOUN
ejpam-5637	148	44	of	of	ADP
ejpam-5637	148	45	that	that	DET
ejpam-5637	148	46	matrix	matrix	NOUN
ejpam-5637	148	47	.	.	PUNCT
ejpam-5637	149	1	theorem	theorem	VERB
ejpam-5637	149	2	6	6	NUM
ejpam-5637	149	3	.	.	PUNCT
ejpam-5637	150	1	let	let	VERB
ejpam-5637	150	2	m1	m1	PROPN
ejpam-5637	150	3	=	=	SYM
ejpam-5637	150	4	(	(	PUNCT
ejpam-5637	150	5	m∗m)−1m∗	m∗m)−1m∗	PROPN
ejpam-5637	150	6	and	and	CCONJ
ejpam-5637	150	7	m2	m2	PROPN
ejpam-5637	150	8	=	=	NOUN
ejpam-5637	150	9	m∗(mm∗)−1	m∗(mm∗)−1	NOUN
ejpam-5637	150	10	be	be	VERB
ejpam-5637	150	11	n	n	ADV
ejpam-5637	150	12	-	-	PUNCT
ejpam-5637	150	13	dimensional	dimensional	ADJ
ejpam-5637	150	14	matrices	matrix	NOUN
ejpam-5637	150	15	.	.	PUNCT
ejpam-5637	151	1	let	let	VERB
ejpam-5637	151	2	limk→∞(mk	limk→∞(mk	NOUN
ejpam-5637	151	3	)	)	PUNCT
ejpam-5637	152	1	=	=	PUNCT
ejpam-5637	152	2	m	m	PROPN
ejpam-5637	152	3	,	,	PUNCT
ejpam-5637	152	4	and	and	CCONJ
ejpam-5637	152	5	let	let	VERB
ejpam-5637	152	6	q	q	NOUN
ejpam-5637	152	7	=	=	SYM
ejpam-5637	152	8	minm	minm	ADJ
ejpam-5637	152	9	,	,	PUNCT
ejpam-5637	152	10	n.	n.	PROPN
ejpam-5637	152	11	consider	consider	VERB
ejpam-5637	152	12	that	that	SCONJ
ejpam-5637	152	13	σ1(m	σ1(m	NOUN
ejpam-5637	152	14	)	)	PUNCT
ejpam-5637	152	15	≥	≥	NOUN
ejpam-5637	152	16	σ2(m	σ2(m	NOUN
ejpam-5637	152	17	)	)	PUNCT
ejpam-5637	152	18	≥	≥	NOUN
ejpam-5637	152	19	·	·	PUNCT
ejpam-5637	152	20	·	·	PUNCT
ejpam-5637	152	21	·	·	PUNCT
ejpam-5637	152	22	≥	≥	X
ejpam-5637	152	23	σq(m	σq(m	NOUN
ejpam-5637	152	24	)	)	PUNCT
ejpam-5637	152	25	,	,	PUNCT
ejpam-5637	152	26	and	and	CCONJ
ejpam-5637	152	27	σ1(mk	σ1(mk	PROPN
ejpam-5637	152	28	)	)	PUNCT
ejpam-5637	152	29	≥	≥	NOUN
ejpam-5637	152	30	·	·	PUNCT
ejpam-5637	152	31	·	·	PUNCT
ejpam-5637	152	32	·	·	PUNCT
ejpam-5637	152	33	≥	≥	NUM
ejpam-5637	152	34	σq(mk	σq(mk	PROPN
ejpam-5637	152	35	)	)	PUNCT
ejpam-5637	152	36	be	be	VERB
ejpam-5637	152	37	non	non	ADJ
ejpam-5637	152	38	-	-	ADJ
ejpam-5637	152	39	increasing	increasing	ADJ
ejpam-5637	152	40	ordered	order	VERB
ejpam-5637	152	41	singular	singular	ADJ
ejpam-5637	152	42	values	value	NOUN
ejpam-5637	152	43	of	of	ADP
ejpam-5637	152	44	m	m	PROPN
ejpam-5637	152	45	and	and	CCONJ
ejpam-5637	152	46	mk	mk	PROPN
ejpam-5637	152	47	,	,	PUNCT
ejpam-5637	152	48	respectively	respectively	ADV
ejpam-5637	152	49	for	for	ADP
ejpam-5637	152	50	k	k	PROPN
ejpam-5637	152	51	=	=	SYM
ejpam-5637	152	52	1	1	NUM
ejpam-5637	152	53	,	,	PUNCT
ejpam-5637	152	54	2	2	NUM
ejpam-5637	152	55	,	,	PUNCT
ejpam-5637	152	56	·	·	PUNCT
ejpam-5637	152	57	·	·	PUNCT
ejpam-5637	152	58	·	·	PUNCT
ejpam-5637	152	59	.	.	PUNCT
ejpam-5637	153	1	then	then	ADV
ejpam-5637	153	2	the	the	DET
ejpam-5637	153	3	limk→∞	limk→∞	NOUN
ejpam-5637	153	4	σi(mk	σi(mk	NOUN
ejpam-5637	153	5	)	)	PUNCT
ejpam-5637	153	6	=	=	SYM
ejpam-5637	153	7	σi(m	σi(m	NOUN
ejpam-5637	153	8	)	)	PUNCT
ejpam-5637	153	9	for	for	ADP
ejpam-5637	153	10	all	all	DET
ejpam-5637	153	11	i	i	PRON
ejpam-5637	153	12	=	=	NOUN
ejpam-5637	153	13	1	1	X
ejpam-5637	153	14	:	:	PUNCT
ejpam-5637	153	15	q.	q.	NOUN
ejpam-5637	153	16	proof	proof	NOUN
ejpam-5637	153	17	.	.	PUNCT
ejpam-5637	154	1	let	let	VERB
ejpam-5637	154	2	k1	k1	PROPN
ejpam-5637	154	3	<	<	X
ejpam-5637	154	4	k2	k2	X
ejpam-5637	154	5	<	<	X
ejpam-5637	154	6	·	·	PUNCT
ejpam-5637	154	7	·	·	PUNCT
ejpam-5637	154	8	·	·	PUNCT
ejpam-5637	154	9	,	,	PUNCT
ejpam-5637	154	10	be	be	AUX
ejpam-5637	154	11	the	the	DET
ejpam-5637	154	12	sequence	sequence	NOUN
ejpam-5637	154	13	of	of	ADP
ejpam-5637	154	14	positive	positive	ADJ
ejpam-5637	154	15	integers	integer	NOUN
ejpam-5637	154	16	,	,	PUNCT
ejpam-5637	154	17	and	and	CCONJ
ejpam-5637	154	18	let	let	VERB
ejpam-5637	154	19	ϵ	ϵ	PRON
ejpam-5637	154	20	>	>	X
ejpam-5637	154	21	0	0	NUM
ejpam-5637	154	22	,	,	PUNCT
ejpam-5637	154	23	we	we	PRON
ejpam-5637	154	24	have	have	VERB
ejpam-5637	154	25	that	that	DET
ejpam-5637	154	26	max|σi(mkj	max|σi(mkj	NOUN
ejpam-5637	154	27	)	)	PUNCT
ejpam-5637	154	28	−	−	PROPN
ejpam-5637	155	1	σi(m)|	σi(m)|	X
ejpam-5637	155	2	>	>	X
ejpam-5637	155	3	ϵ	ϵ	X
ejpam-5637	155	4	,	,	PUNCT
ejpam-5637	155	5	where	where	SCONJ
ejpam-5637	155	6	max	max	PROPN
ejpam-5637	155	7	is	be	AUX
ejpam-5637	155	8	taken	take	VERB
ejpam-5637	155	9	over	over	ADP
ejpam-5637	155	10	all	all	PRON
ejpam-5637	155	11	i	i	PRON
ejpam-5637	155	12	=	=	NOUN
ejpam-5637	155	13	1	1	NUM
ejpam-5637	155	14	:	:	PUNCT
ejpam-5637	155	15	q.	q.	PROPN
ejpam-5637	155	16	consider	consider	VERB
ejpam-5637	155	17	the	the	DET
ejpam-5637	155	18	singular	singular	ADJ
ejpam-5637	155	19	value	value	NOUN
ejpam-5637	155	20	decomposition	decomposition	NOUN
ejpam-5637	155	21	of	of	ADP
ejpam-5637	155	22	mkj	mkj	NOUN
ejpam-5637	155	23	as	as	ADP
ejpam-5637	155	24	mkj	mkj	NOUN
ejpam-5637	155	25	=	=	SYM
ejpam-5637	155	26	ukjσkjv	ukjσkjv	ADJ
ejpam-5637	155	27	∗	∗	X
ejpam-5637	155	28	kj	kj	PROPN
ejpam-5637	155	29	,	,	PUNCT
ejpam-5637	155	30	where	where	SCONJ
ejpam-5637	155	31	ukj	ukj	NOUN
ejpam-5637	155	32	and	and	CCONJ
ejpam-5637	155	33	vkj	vkj	NOUN
ejpam-5637	155	34	are	be	AUX
ejpam-5637	155	35	the	the	DET
ejpam-5637	155	36	unitary	unitary	ADJ
ejpam-5637	155	37	matrices	matrix	NOUN
ejpam-5637	155	38	and	and	CCONJ
ejpam-5637	155	39	σkj	σkj	PROPN
ejpam-5637	155	40	is	be	AUX
ejpam-5637	155	41	a	a	DET
ejpam-5637	155	42	diagonal	diagonal	ADJ
ejpam-5637	155	43	matrix	matrix	NOUN
ejpam-5637	155	44	with	with	ADP
ejpam-5637	155	45	structure	structure	NOUN
ejpam-5637	155	46	σkj	σkj	NOUN
ejpam-5637	155	47	=	=	PUNCT
ejpam-5637	156	1	[	[	X
ejpam-5637	156	2	σ1(mkj	σ1(mkj	NOUN
ejpam-5637	156	3	)	)	PUNCT
ejpam-5637	156	4	·	·	PUNCT
ejpam-5637	156	5	·	·	PUNCT
ejpam-5637	156	6	·	·	PUNCT
ejpam-5637	157	1	σq(mkj	σq(mkj	NOUN
ejpam-5637	157	2	)	)	PUNCT
ejpam-5637	157	3	]	]	PUNCT
ejpam-5637	158	1	t	t	PROPN
ejpam-5637	158	2	.	.	PUNCT
ejpam-5637	159	1	m.u	m.u	PROPN
ejpam-5637	159	2	.	.	PROPN
ejpam-5637	160	1	rahman	rahman	PROPN
ejpam-5637	160	2	et	et	PROPN
ejpam-5637	160	3	al	al	PROPN
ejpam-5637	160	4	.	.	PUNCT
ejpam-5637	160	5	/	/	SYM
ejpam-5637	160	6	eur	eur	PROPN
ejpam-5637	160	7	.	.	PUNCT
ejpam-5637	161	1	j.	j.	PROPN
ejpam-5637	161	2	pure	pure	PROPN
ejpam-5637	161	3	appl	appl	PROPN
ejpam-5637	161	4	.	.	PROPN
ejpam-5637	161	5	math	math	PROPN
ejpam-5637	161	6	,	,	PUNCT
ejpam-5637	161	7	18	18	NUM
ejpam-5637	161	8	(	(	PUNCT
ejpam-5637	161	9	1	1	NUM
ejpam-5637	161	10	)	)	PUNCT
ejpam-5637	161	11	(	(	PUNCT
ejpam-5637	161	12	2025	2025	NUM
ejpam-5637	161	13	)	)	PUNCT
ejpam-5637	161	14	,	,	PUNCT
ejpam-5637	161	15	5637	5637	NUM
ejpam-5637	161	16	8	8	NUM
ejpam-5637	161	17	of	of	ADP
ejpam-5637	161	18	20	20	NUM
ejpam-5637	161	19	(	(	PUNCT
ejpam-5637	161	20	a	a	PRON
ejpam-5637	161	21	)	)	PUNCT
ejpam-5637	161	22	singular	singular	ADJ
ejpam-5637	161	23	values	value	NOUN
ejpam-5637	161	24	and	and	CCONJ
ejpam-5637	161	25	pseudo	pseudo	NOUN
ejpam-5637	161	26	singular	singular	ADJ
ejpam-5637	161	27	values	value	NOUN
ejpam-5637	161	28	(	(	PUNCT
ejpam-5637	161	29	b	b	NOUN
ejpam-5637	161	30	)	)	PUNCT
ejpam-5637	161	31	surface	surface	NOUN
ejpam-5637	161	32	plot	plot	NOUN
ejpam-5637	161	33	of	of	ADP
ejpam-5637	161	34	pseudo	pseudo	NOUN
ejpam-5637	161	35	-	-	ADJ
ejpam-5637	161	36	spectrum	spectrum	ADJ
ejpam-5637	161	37	figure	figure	NOUN
ejpam-5637	161	38	1	1	NUM
ejpam-5637	161	39	:	:	PUNCT
ejpam-5637	161	40	the	the	DET
ejpam-5637	161	41	graphs	graph	NOUN
ejpam-5637	161	42	of	of	ADP
ejpam-5637	161	43	singular	singular	ADJ
ejpam-5637	161	44	values	value	NOUN
ejpam-5637	161	45	and	and	CCONJ
ejpam-5637	161	46	pseudo	pseudo	NOUN
ejpam-5637	161	47	-	-	NOUN
ejpam-5637	161	48	inverse	inverse	NOUN
ejpam-5637	161	49	of	of	ADP
ejpam-5637	161	50	m	m	PRON
ejpam-5637	161	51	in	in	ADP
ejpam-5637	161	52	example-1	example-1	NOUN
ejpam-5637	161	53	then	then	ADV
ejpam-5637	161	54	,	,	PUNCT
ejpam-5637	161	55	lim	lim	PROPN
ejpam-5637	161	56	r→∞	r→∞	ADJ
ejpam-5637	161	57	σkjr	σkjr	NOUN
ejpam-5637	161	58	=	=	SYM
ejpam-5637	161	59	lim	lim	PROPN
ejpam-5637	161	60	r→∞	r→∞	PRON
ejpam-5637	161	61	u∗	u∗	ADJ
ejpam-5637	161	62	kjrmkjrvkjr	kjrmkjrvkjr	NOUN
ejpam-5637	161	63	=	=	PUNCT
ejpam-5637	161	64	(	(	PUNCT
ejpam-5637	161	65	lim	lim	PROPN
ejpam-5637	161	66	r→∞	r→∞	PROPN
ejpam-5637	161	67	u∗	u∗	PROPN
ejpam-5637	161	68	kjr	kjr	PROPN
ejpam-5637	161	69	)	)	PUNCT
ejpam-5637	161	70	(	(	PUNCT
ejpam-5637	161	71	lim	lim	PROPN
ejpam-5637	161	72	r→∞	r→∞	NUM
ejpam-5637	161	73	mkjr	mkjr	NOUN
ejpam-5637	161	74	)	)	PUNCT
ejpam-5637	161	75	(	(	PUNCT
ejpam-5637	161	76	lim	lim	PROPN
ejpam-5637	161	77	r→∞	r→∞	ADJ
ejpam-5637	161	78	vkjr	vkjr	NOUN
ejpam-5637	161	79	)	)	PUNCT
ejpam-5637	161	80	=	=	SYM
ejpam-5637	161	81	u∗mv	u∗mv	NOUN
ejpam-5637	161	82	.	.	PUNCT
ejpam-5637	162	1	the	the	DET
ejpam-5637	162	2	matrix	matrix	NOUN
ejpam-5637	162	3	u∗mv	u∗mv	NOUN
ejpam-5637	162	4	is	be	AUX
ejpam-5637	162	5	a	a	DET
ejpam-5637	162	6	non	non	ADJ
ejpam-5637	162	7	-	-	ADJ
ejpam-5637	162	8	negative	negative	ADJ
ejpam-5637	162	9	diagonal	diagonal	ADJ
ejpam-5637	162	10	matrix	matrix	NOUN
ejpam-5637	162	11	.	.	PUNCT
ejpam-5637	163	1	the	the	DET
ejpam-5637	163	2	uniqueness	uniqueness	NOUN
ejpam-5637	163	3	of	of	ADP
ejpam-5637	163	4	the	the	DET
ejpam-5637	163	5	singular	singular	ADJ
ejpam-5637	163	6	values	value	NOUN
ejpam-5637	163	7	of	of	ADP
ejpam-5637	163	8	m	m	PROPN
ejpam-5637	163	9	implies	imply	VERB
ejpam-5637	163	10	that	that	SCONJ
ejpam-5637	163	11	diag	diag	PROPN
ejpam-5637	163	12	σ	σ	NOUN
ejpam-5637	164	1	=	=	PUNCT
ejpam-5637	165	1	[	[	X
ejpam-5637	165	2	σ1(m	σ1(m	NOUN
ejpam-5637	165	3	)	)	PUNCT
ejpam-5637	165	4	,	,	PUNCT
ejpam-5637	165	5	σ2(m	σ2(m	NOUN
ejpam-5637	165	6	)	)	PUNCT
ejpam-5637	165	7	,	,	PUNCT
ejpam-5637	165	8	·	·	PUNCT
ejpam-5637	165	9	·	·	PUNCT
ejpam-5637	165	10	·	·	PUNCT
ejpam-5637	165	11	,	,	PUNCT
ejpam-5637	165	12	σq(m)]t	σq(m)]t	VERB
ejpam-5637	165	13	,	,	PUNCT
ejpam-5637	165	14	a	a	DET
ejpam-5637	165	15	contradiction	contradiction	NOUN
ejpam-5637	165	16	with	with	ADP
ejpam-5637	165	17	inequality	inequality	NOUN
ejpam-5637	165	18	max|σi(mkj	max|σi(mkj	NOUN
ejpam-5637	165	19	)	)	PUNCT
ejpam-5637	165	20	−	−	PROPN
ejpam-5637	166	1	σi(m)|	σi(m)|	X
ejpam-5637	166	2	>	>	X
ejpam-5637	166	3	ϵ.	ϵ.	NOUN
ejpam-5637	166	4	this	this	PRON
ejpam-5637	166	5	proves	prove	VERB
ejpam-5637	166	6	required	required	ADJ
ejpam-5637	166	7	result	result	NOUN
ejpam-5637	166	8	.	.	PUNCT
ejpam-5637	167	1	next	next	ADV
ejpam-5637	167	2	,	,	PUNCT
ejpam-5637	167	3	we	we	PRON
ejpam-5637	167	4	give	give	VERB
ejpam-5637	167	5	numerical	numerical	ADJ
ejpam-5637	167	6	examples	example	NOUN
ejpam-5637	167	7	on	on	ADP
ejpam-5637	167	8	the	the	DET
ejpam-5637	167	9	computation	computation	NOUN
ejpam-5637	167	10	of	of	ADP
ejpam-5637	167	11	singular	singular	ADJ
ejpam-5637	167	12	values	value	NOUN
ejpam-5637	167	13	and	and	CCONJ
ejpam-5637	167	14	pseudo	pseudo	NOUN
ejpam-5637	167	15	inverse	inverse	NOUN
ejpam-5637	167	16	of	of	ADP
ejpam-5637	167	17	transportation	transportation	NOUN
ejpam-5637	167	18	matrices	matrix	NOUN
ejpam-5637	167	19	.	.	PUNCT
ejpam-5637	167	20	example	example	NOUN
ejpam-5637	168	1	1	1	NUM
ejpam-5637	168	2	.	.	X
ejpam-5637	168	3	consider	consider	VERB
ejpam-5637	168	4	7×	7×	NUM
ejpam-5637	168	5	5	5	NUM
ejpam-5637	168	6	transportation	transportation	NOUN
ejpam-5637	168	7	matrix	matrix	NOUN
ejpam-5637	168	8	(	(	PUNCT
ejpam-5637	168	9	staircase	staircase	NOUN
ejpam-5637	168	10	matrix	matrix	NOUN
ejpam-5637	168	11	)	)	PUNCT
ejpam-5637	168	12	taken	take	VERB
ejpam-5637	168	13	from	from	ADP
ejpam-5637	168	14	[	[	X
ejpam-5637	168	15	16	16	NUM
ejpam-5637	168	16	]	]	PUNCT
ejpam-5637	168	17	.	.	PUNCT
ejpam-5637	169	1	m	m	VERB
ejpam-5637	169	2	=	=	NOUN
ejpam-5637	169	3			NOUN
ejpam-5637	169	4	1	1	NUM
ejpam-5637	169	5	1	1	NUM
ejpam-5637	169	6	1	1	NUM
ejpam-5637	169	7	0	0	NUM
ejpam-5637	169	8	0	0	NUM
ejpam-5637	169	9	0	0	NUM
ejpam-5637	169	10	0	0	NUM
ejpam-5637	169	11	1	1	NUM
ejpam-5637	169	12	1	1	NUM
ejpam-5637	169	13	1	1	NUM
ejpam-5637	169	14	0	0	NUM
ejpam-5637	169	15	0	0	NUM
ejpam-5637	169	16	0	0	NUM
ejpam-5637	169	17	0	0	NUM
ejpam-5637	169	18	0	0	NUM
ejpam-5637	169	19	0	0	NUM
ejpam-5637	169	20	1	1	NUM
ejpam-5637	169	21	1	1	NUM
ejpam-5637	169	22	1	1	NUM
ejpam-5637	169	23	0	0	NUM
ejpam-5637	169	24	0	0	NUM
ejpam-5637	169	25	0	0	NUM
ejpam-5637	169	26	0	0	NUM
ejpam-5637	169	27	1	1	NUM
ejpam-5637	169	28	1	1	NUM
ejpam-5637	169	29	1	1	NUM
ejpam-5637	169	30	1	1	NUM
ejpam-5637	169	31	0	0	NUM
ejpam-5637	169	32	0	0	NUM
ejpam-5637	169	33	0	0	NUM
ejpam-5637	169	34	0	0	NUM
ejpam-5637	169	35	0	0	NUM
ejpam-5637	169	36	1	1	NUM
ejpam-5637	169	37	1	1	NUM
ejpam-5637	169	38	1	1	NUM
ejpam-5637	169	39			NOUN
ejpam-5637	169	40	.	.	PUNCT
ejpam-5637	170	1	the	the	DET
ejpam-5637	170	2	computation	computation	NOUN
ejpam-5637	170	3	of	of	ADP
ejpam-5637	170	4	singular	singular	ADJ
ejpam-5637	170	5	values	value	NOUN
ejpam-5637	170	6	and	and	CCONJ
ejpam-5637	170	7	the	the	DET
ejpam-5637	170	8	graphs	graph	NOUN
ejpam-5637	170	9	of	of	ADP
ejpam-5637	170	10	the	the	DET
ejpam-5637	170	11	pseudo	pseudo	NOUN
ejpam-5637	170	12	-	-	NOUN
ejpam-5637	170	13	inverse	inverse	NOUN
ejpam-5637	170	14	are	be	AUX
ejpam-5637	170	15	shown	show	VERB
ejpam-5637	170	16	in	in	ADP
ejpam-5637	170	17	figure	figure	NOUN
ejpam-5637	170	18	1	1	NUM
ejpam-5637	170	19	.	.	PUNCT
ejpam-5637	170	20	example	example	NOUN
ejpam-5637	170	21	2	2	NUM
ejpam-5637	170	22	.	.	X
ejpam-5637	170	23	consider	consider	VERB
ejpam-5637	170	24	7	7	NUM
ejpam-5637	170	25	×	×	NOUN
ejpam-5637	170	26	5	5	NUM
ejpam-5637	170	27	transportation	transportation	NOUN
ejpam-5637	170	28	matrix	matrix	NOUN
ejpam-5637	170	29	(	(	PUNCT
ejpam-5637	170	30	distribution	distribution	NOUN
ejpam-5637	170	31	matrix	matrix	NOUN
ejpam-5637	170	32	)	)	PUNCT
ejpam-5637	170	33	taken	take	VERB
ejpam-5637	170	34	from	from	ADP
ejpam-5637	170	35	[	[	X
ejpam-5637	170	36	16	16	NUM
ejpam-5637	170	37	]	]	PUNCT
ejpam-5637	170	38	.	.	PUNCT
ejpam-5637	171	1	m	m	VERB
ejpam-5637	171	2	=	=	X
ejpam-5637	171	3			NOUN
ejpam-5637	171	4	4	4	NUM
ejpam-5637	171	5	0	0	NUM
ejpam-5637	171	6	0	0	NUM
ejpam-5637	171	7	0	0	NUM
ejpam-5637	171	8	0	0	NUM
ejpam-5637	171	9	0	0	NUM
ejpam-5637	171	10	0	0	NUM
ejpam-5637	171	11	0	0	NUM
ejpam-5637	171	12	2	2	NUM
ejpam-5637	171	13	4	4	NUM
ejpam-5637	171	14	0	0	NUM
ejpam-5637	171	15	0	0	NUM
ejpam-5637	171	16	0	0	NUM
ejpam-5637	171	17	0	0	NUM
ejpam-5637	171	18	0	0	NUM
ejpam-5637	171	19	0	0	NUM
ejpam-5637	171	20	1	1	NUM
ejpam-5637	171	21	2	2	NUM
ejpam-5637	171	22	0	0	NUM
ejpam-5637	171	23	0	0	NUM
ejpam-5637	171	24	0	0	NUM
ejpam-5637	171	25	0	0	NUM
ejpam-5637	171	26	0	0	NUM
ejpam-5637	171	27	0	0	NUM
ejpam-5637	171	28	1	1	NUM
ejpam-5637	171	29	1	1	NUM
ejpam-5637	171	30	0	0	NUM
ejpam-5637	171	31	0	0	NUM
ejpam-5637	171	32	0	0	NUM
ejpam-5637	171	33	0	0	NUM
ejpam-5637	171	34	0	0	NUM
ejpam-5637	171	35	0	0	NUM
ejpam-5637	171	36	1	1	NUM
ejpam-5637	171	37	1.4	1.4	NUM
ejpam-5637	171	38	0.6	0.6	NUM
ejpam-5637	171	39			NOUN
ejpam-5637	171	40	.	.	PUNCT
ejpam-5637	172	1	m.u	m.u	PROPN
ejpam-5637	172	2	.	.	PROPN
ejpam-5637	173	1	rahman	rahman	PROPN
ejpam-5637	173	2	et	et	PROPN
ejpam-5637	173	3	al	al	PROPN
ejpam-5637	173	4	.	.	PUNCT
ejpam-5637	173	5	/	/	SYM
ejpam-5637	173	6	eur	eur	PROPN
ejpam-5637	173	7	.	.	PUNCT
ejpam-5637	174	1	j.	j.	PROPN
ejpam-5637	174	2	pure	pure	PROPN
ejpam-5637	174	3	appl	appl	PROPN
ejpam-5637	174	4	.	.	PROPN
ejpam-5637	174	5	math	math	PROPN
ejpam-5637	174	6	,	,	PUNCT
ejpam-5637	174	7	18	18	NUM
ejpam-5637	174	8	(	(	PUNCT
ejpam-5637	174	9	1	1	NUM
ejpam-5637	174	10	)	)	PUNCT
ejpam-5637	174	11	(	(	PUNCT
ejpam-5637	174	12	2025	2025	NUM
ejpam-5637	174	13	)	)	PUNCT
ejpam-5637	174	14	,	,	PUNCT
ejpam-5637	174	15	5637	5637	NUM
ejpam-5637	174	16	9	9	NUM
ejpam-5637	174	17	of	of	ADP
ejpam-5637	174	18	20	20	NUM
ejpam-5637	174	19	(	(	PUNCT
ejpam-5637	174	20	a	a	PRON
ejpam-5637	174	21	)	)	PUNCT
ejpam-5637	174	22	singular	singular	ADJ
ejpam-5637	174	23	values	value	NOUN
ejpam-5637	174	24	and	and	CCONJ
ejpam-5637	174	25	pseudo	pseudo	NOUN
ejpam-5637	174	26	singular	singular	ADJ
ejpam-5637	174	27	values	value	NOUN
ejpam-5637	174	28	(	(	PUNCT
ejpam-5637	174	29	b	b	NOUN
ejpam-5637	174	30	)	)	PUNCT
ejpam-5637	174	31	surface	surface	NOUN
ejpam-5637	174	32	plot	plot	NOUN
ejpam-5637	174	33	of	of	ADP
ejpam-5637	174	34	pseudo	pseudo	NOUN
ejpam-5637	174	35	-	-	ADJ
ejpam-5637	174	36	spectrum	spectrum	ADJ
ejpam-5637	174	37	figure	figure	NOUN
ejpam-5637	174	38	2	2	NUM
ejpam-5637	174	39	:	:	PUNCT
ejpam-5637	174	40	the	the	DET
ejpam-5637	174	41	graphs	graph	NOUN
ejpam-5637	174	42	of	of	ADP
ejpam-5637	174	43	singular	singular	ADJ
ejpam-5637	174	44	values	value	NOUN
ejpam-5637	174	45	and	and	CCONJ
ejpam-5637	174	46	pseudo	pseudo	NOUN
ejpam-5637	174	47	-	-	NOUN
ejpam-5637	174	48	inverse	inverse	NOUN
ejpam-5637	174	49	of	of	ADP
ejpam-5637	174	50	m	m	PRON
ejpam-5637	174	51	in	in	ADP
ejpam-5637	174	52	example-2	example-2	NUM
ejpam-5637	174	53	(	(	PUNCT
ejpam-5637	174	54	a	a	X
ejpam-5637	174	55	)	)	PUNCT
ejpam-5637	174	56	singular	singular	ADJ
ejpam-5637	174	57	values	value	NOUN
ejpam-5637	174	58	and	and	CCONJ
ejpam-5637	174	59	pseudo	pseudo	NOUN
ejpam-5637	174	60	singular	singular	ADJ
ejpam-5637	174	61	values	value	NOUN
ejpam-5637	174	62	(	(	PUNCT
ejpam-5637	174	63	b	b	NOUN
ejpam-5637	174	64	)	)	PUNCT
ejpam-5637	174	65	surface	surface	NOUN
ejpam-5637	174	66	plot	plot	NOUN
ejpam-5637	174	67	of	of	ADP
ejpam-5637	174	68	pseudo	pseudo	NOUN
ejpam-5637	174	69	-	-	ADJ
ejpam-5637	174	70	spectrum	spectrum	ADJ
ejpam-5637	174	71	figure	figure	NOUN
ejpam-5637	174	72	3	3	NUM
ejpam-5637	174	73	:	:	PUNCT
ejpam-5637	174	74	the	the	DET
ejpam-5637	174	75	graphs	graph	NOUN
ejpam-5637	174	76	of	of	ADP
ejpam-5637	174	77	singular	singular	ADJ
ejpam-5637	174	78	values	value	NOUN
ejpam-5637	174	79	and	and	CCONJ
ejpam-5637	174	80	pseudo	pseudo	NOUN
ejpam-5637	174	81	-	-	NOUN
ejpam-5637	174	82	inverse	inverse	NOUN
ejpam-5637	174	83	of	of	ADP
ejpam-5637	174	84	m	m	PRON
ejpam-5637	174	85	in	in	ADP
ejpam-5637	174	86	example-3	example-3	NUM
ejpam-5637	174	87	the	the	DET
ejpam-5637	174	88	computation	computation	NOUN
ejpam-5637	174	89	of	of	ADP
ejpam-5637	174	90	singular	singular	ADJ
ejpam-5637	174	91	values	value	NOUN
ejpam-5637	174	92	and	and	CCONJ
ejpam-5637	174	93	the	the	DET
ejpam-5637	174	94	graphs	graph	NOUN
ejpam-5637	174	95	of	of	ADP
ejpam-5637	174	96	the	the	DET
ejpam-5637	174	97	pseudo	pseudo	NOUN
ejpam-5637	174	98	-	-	NOUN
ejpam-5637	174	99	inverse	inverse	NOUN
ejpam-5637	174	100	are	be	AUX
ejpam-5637	174	101	shown	show	VERB
ejpam-5637	174	102	in	in	ADP
ejpam-5637	174	103	figure	figure	NOUN
ejpam-5637	174	104	2	2	NUM
ejpam-5637	174	105	.	.	NOUN
ejpam-5637	174	106	example	example	NOUN
ejpam-5637	175	1	3	3	X
ejpam-5637	175	2	.	.	X
ejpam-5637	175	3	consider	consider	VERB
ejpam-5637	175	4	7	7	NUM
ejpam-5637	175	5	×	×	NOUN
ejpam-5637	175	6	5	5	NUM
ejpam-5637	175	7	transportation	transportation	NOUN
ejpam-5637	175	8	matrix	matrix	NOUN
ejpam-5637	175	9	(	(	PUNCT
ejpam-5637	175	10	distribution	distribution	NOUN
ejpam-5637	175	11	matrix	matrix	NOUN
ejpam-5637	175	12	)	)	PUNCT
ejpam-5637	175	13	taken	take	VERB
ejpam-5637	175	14	from	from	ADP
ejpam-5637	175	15	[	[	X
ejpam-5637	175	16	16	16	NUM
ejpam-5637	175	17	]	]	PUNCT
ejpam-5637	175	18	.	.	PUNCT
ejpam-5637	176	1	m	m	VERB
ejpam-5637	176	2	=	=	NOUN
ejpam-5637	176	3			NOUN
ejpam-5637	176	4	1.6	1.6	NUM
ejpam-5637	177	1	0.8	0.8	NUM
ejpam-5637	177	2	1.6	1.6	NUM
ejpam-5637	177	3	0	0	NUM
ejpam-5637	177	4	0	0	NUM
ejpam-5637	177	5	0	0	NUM
ejpam-5637	177	6	0	0	NUM
ejpam-5637	177	7	2.4	2.4	NUM
ejpam-5637	177	8	1.2	1.2	NUM
ejpam-5637	177	9	2.4	2.4	NUM
ejpam-5637	177	10	0	0	NUM
ejpam-5637	177	11	0	0	NUM
ejpam-5637	177	12	0	0	NUM
ejpam-5637	177	13	0	0	NUM
ejpam-5637	177	14	0	0	NUM
ejpam-5637	177	15	0	0	NUM
ejpam-5637	177	16	0.6	0.6	NUM
ejpam-5637	177	17	1.8	1.8	NUM
ejpam-5637	177	18	0.6	0.6	NUM
ejpam-5637	177	19	0	0	NUM
ejpam-5637	177	20	0	0	NUM
ejpam-5637	177	21	0	0	NUM
ejpam-5637	177	22	0	0	NUM
ejpam-5637	177	23	0.4	0.4	NUM
ejpam-5637	177	24	1.2	1.2	NUM
ejpam-5637	177	25	0.2	0.2	NUM
ejpam-5637	177	26	0.2	0.2	NUM
ejpam-5637	177	27	0	0	NUM
ejpam-5637	177	28	0	0	NUM
ejpam-5637	177	29	0	0	NUM
ejpam-5637	177	30	0	0	NUM
ejpam-5637	177	31	0	0	NUM
ejpam-5637	177	32	1.2	1.2	NUM
ejpam-5637	177	33	1.2	1.2	NUM
ejpam-5637	177	34	0.6	0.6	NUM
ejpam-5637	177	35			NOUN
ejpam-5637	177	36	.	.	PUNCT
ejpam-5637	178	1	the	the	DET
ejpam-5637	178	2	computation	computation	NOUN
ejpam-5637	178	3	of	of	ADP
ejpam-5637	178	4	singular	singular	ADJ
ejpam-5637	178	5	values	value	NOUN
ejpam-5637	178	6	and	and	CCONJ
ejpam-5637	178	7	the	the	DET
ejpam-5637	178	8	graphs	graph	NOUN
ejpam-5637	178	9	of	of	ADP
ejpam-5637	178	10	the	the	DET
ejpam-5637	178	11	pseudo	pseudo	NOUN
ejpam-5637	178	12	-	-	NOUN
ejpam-5637	178	13	inverse	inverse	NOUN
ejpam-5637	178	14	are	be	AUX
ejpam-5637	178	15	shown	show	VERB
ejpam-5637	178	16	in	in	ADP
ejpam-5637	178	17	figure	figure	NOUN
ejpam-5637	178	18	3	3	NUM
ejpam-5637	179	1	.	.	PUNCT
ejpam-5637	179	2	m.u	m.u	PROPN
ejpam-5637	179	3	.	.	PROPN
ejpam-5637	180	1	rahman	rahman	PROPN
ejpam-5637	180	2	et	et	PROPN
ejpam-5637	180	3	al	al	PROPN
ejpam-5637	180	4	.	.	PUNCT
ejpam-5637	180	5	/	/	SYM
ejpam-5637	180	6	eur	eur	PROPN
ejpam-5637	180	7	.	.	PUNCT
ejpam-5637	181	1	j.	j.	PROPN
ejpam-5637	181	2	pure	pure	PROPN
ejpam-5637	181	3	appl	appl	PROPN
ejpam-5637	181	4	.	.	PROPN
ejpam-5637	181	5	math	math	PROPN
ejpam-5637	181	6	,	,	PUNCT
ejpam-5637	181	7	18	18	NUM
ejpam-5637	181	8	(	(	PUNCT
ejpam-5637	181	9	1	1	NUM
ejpam-5637	181	10	)	)	PUNCT
ejpam-5637	181	11	(	(	PUNCT
ejpam-5637	181	12	2025	2025	NUM
ejpam-5637	181	13	)	)	PUNCT
ejpam-5637	181	14	,	,	PUNCT
ejpam-5637	181	15	5637	5637	NUM
ejpam-5637	181	16	10	10	NUM
ejpam-5637	181	17	of	of	ADP
ejpam-5637	181	18	20	20	NUM
ejpam-5637	181	19	3	3	NUM
ejpam-5637	181	20	.	.	PUNCT
ejpam-5637	182	1	structured	structure	VERB
ejpam-5637	182	2	singular	singular	ADJ
ejpam-5637	182	3	values	value	NOUN
ejpam-5637	182	4	for	for	ADP
ejpam-5637	182	5	hitchcock	hitchcock	NOUN
ejpam-5637	182	6	-	-	PUNCT
ejpam-5637	182	7	koopmans	koopmans	PROPN
ejpam-5637	182	8	transportation	transportation	NOUN
ejpam-5637	182	9	problem	problem	NOUN
ejpam-5637	182	10	in	in	ADP
ejpam-5637	182	11	this	this	DET
ejpam-5637	182	12	section	section	NOUN
ejpam-5637	183	1	,	,	PUNCT
ejpam-5637	183	2	we	we	PRON
ejpam-5637	183	3	present	present	VERB
ejpam-5637	183	4	new	new	ADJ
ejpam-5637	183	5	results	result	NOUN
ejpam-5637	183	6	on	on	ADP
ejpam-5637	183	7	the	the	DET
ejpam-5637	183	8	computation	computation	NOUN
ejpam-5637	183	9	of	of	ADP
ejpam-5637	183	10	structured	structured	ADJ
ejpam-5637	183	11	singular	singular	ADJ
ejpam-5637	183	12	values	value	NOUN
ejpam-5637	183	13	for	for	ADP
ejpam-5637	183	14	matrices	matrix	NOUN
ejpam-5637	183	15	appearing	appear	VERB
ejpam-5637	183	16	in	in	ADP
ejpam-5637	183	17	hitchcock	hitchcock	NOUN
ejpam-5637	183	18	-	-	PUNCT
ejpam-5637	183	19	koopmans	koopmans	PROPN
ejpam-5637	183	20	transportation	transportation	NOUN
ejpam-5637	183	21	problems	problem	NOUN
ejpam-5637	183	22	.	.	PUNCT
ejpam-5637	184	1	we	we	PRON
ejpam-5637	184	2	make	make	VERB
ejpam-5637	184	3	use	use	NOUN
ejpam-5637	184	4	of	of	ADP
ejpam-5637	184	5	mathematical	mathematical	ADJ
ejpam-5637	184	6	tools	tool	NOUN
ejpam-5637	184	7	from	from	ADP
ejpam-5637	184	8	linear	linear	PROPN
ejpam-5637	184	9	algebra	algebra	NOUN
ejpam-5637	184	10	,	,	PUNCT
ejpam-5637	184	11	system	system	NOUN
ejpam-5637	184	12	theory	theory	NOUN
ejpam-5637	184	13	and	and	CCONJ
ejpam-5637	184	14	matrix	matrix	NOUN
ejpam-5637	184	15	theory	theory	NOUN
ejpam-5637	184	16	to	to	PART
ejpam-5637	184	17	provide	provide	VERB
ejpam-5637	184	18	and	and	CCONJ
ejpam-5637	184	19	analyzed	analyze	VERB
ejpam-5637	184	20	the	the	DET
ejpam-5637	184	21	results	result	NOUN
ejpam-5637	184	22	on	on	ADP
ejpam-5637	184	23	structured	structured	ADJ
ejpam-5637	184	24	singular	singular	ADJ
ejpam-5637	184	25	values	value	NOUN
ejpam-5637	184	26	.	.	PUNCT
ejpam-5637	185	1	definition	definition	NOUN
ejpam-5637	185	2	2	2	NUM
ejpam-5637	185	3	.	.	PUNCT
ejpam-5637	186	1	the	the	DET
ejpam-5637	186	2	n	n	ADV
ejpam-5637	186	3	-	-	PUNCT
ejpam-5637	186	4	dimensional	dimensional	ADJ
ejpam-5637	186	5	matrix	matrix	NOUN
ejpam-5637	186	6	m	m	NOUN
ejpam-5637	186	7	is	be	AUX
ejpam-5637	186	8	stable	stable	ADJ
ejpam-5637	186	9	if	if	SCONJ
ejpam-5637	186	10	all	all	DET
ejpam-5637	186	11	the	the	DET
ejpam-5637	186	12	real	real	ADJ
ejpam-5637	186	13	parts	part	NOUN
ejpam-5637	186	14	of	of	ADP
ejpam-5637	186	15	the	the	DET
ejpam-5637	186	16	eigenvalues	eigenvalue	NOUN
ejpam-5637	186	17	are	be	AUX
ejpam-5637	186	18	strictly	strictly	ADV
ejpam-5637	186	19	positive	positive	ADJ
ejpam-5637	186	20	,	,	PUNCT
ejpam-5637	186	21	that	that	ADV
ejpam-5637	186	22	is	is	ADV
ejpam-5637	186	23	,	,	PUNCT
ejpam-5637	186	24	re(λi(m	re(λi(m	PROPN
ejpam-5637	186	25	)	)	PUNCT
ejpam-5637	186	26	)	)	PUNCT
ejpam-5637	187	1	>	>	X
ejpam-5637	187	2	0	0	X
ejpam-5637	187	3	.	.	PUNCT
ejpam-5637	188	1	definition	definition	NOUN
ejpam-5637	188	2	3	3	NUM
ejpam-5637	188	3	.	.	PUNCT
ejpam-5637	189	1	the	the	DET
ejpam-5637	189	2	n	n	ADV
ejpam-5637	189	3	-	-	PUNCT
ejpam-5637	189	4	dimensional	dimensional	ADJ
ejpam-5637	189	5	matrix	matrix	NOUN
ejpam-5637	189	6	m	m	NOUN
ejpam-5637	189	7	is	be	AUX
ejpam-5637	189	8	d	d	NOUN
ejpam-5637	189	9	-	-	ADJ
ejpam-5637	189	10	stable	stable	ADJ
ejpam-5637	189	11	if	if	SCONJ
ejpam-5637	189	12	all	all	DET
ejpam-5637	189	13	the	the	DET
ejpam-5637	189	14	real	real	ADJ
ejpam-5637	189	15	parts	part	NOUN
ejpam-5637	189	16	of	of	ADP
ejpam-5637	189	17	the	the	DET
ejpam-5637	189	18	eigenvalues	eigenvalue	NOUN
ejpam-5637	189	19	of	of	ADP
ejpam-5637	189	20	md	md	PROPN
ejpam-5637	189	21	are	be	AUX
ejpam-5637	189	22	strictly	strictly	ADV
ejpam-5637	189	23	positive	positive	ADJ
ejpam-5637	189	24	,	,	PUNCT
ejpam-5637	189	25	that	that	ADV
ejpam-5637	189	26	is	is	ADV
ejpam-5637	189	27	,	,	PUNCT
ejpam-5637	189	28	re(λi(md	re(λi(md	PUNCT
ejpam-5637	189	29	)	)	PUNCT
ejpam-5637	189	30	)	)	PUNCT
ejpam-5637	190	1	>	>	X
ejpam-5637	190	2	0	0	NUM
ejpam-5637	190	3	,	,	PUNCT
ejpam-5637	190	4	where	where	SCONJ
ejpam-5637	190	5	d	d	PROPN
ejpam-5637	190	6	=	=	SYM
ejpam-5637	190	7	diag(dii	diag(dii	PROPN
ejpam-5637	190	8	)	)	PUNCT
ejpam-5637	190	9	>	>	X
ejpam-5637	190	10	0	0	NUM
ejpam-5637	190	11	,	,	PUNCT
ejpam-5637	190	12	for	for	ADP
ejpam-5637	190	13	all	all	PRON
ejpam-5637	191	1	i	i	PRON
ejpam-5637	191	2	=	=	NOUN
ejpam-5637	191	3	1	1	X
ejpam-5637	191	4	:	:	PUNCT
ejpam-5637	191	5	n.	n.	VERB
ejpam-5637	191	6	the	the	DET
ejpam-5637	191	7	structured	structured	ADJ
ejpam-5637	191	8	singular	singular	ADJ
ejpam-5637	191	9	value	value	NOUN
ejpam-5637	191	10	of	of	ADP
ejpam-5637	191	11	a	a	DET
ejpam-5637	191	12	given	give	VERB
ejpam-5637	191	13	matrix	matrix	NOUN
ejpam-5637	191	14	m	m	NOUN
ejpam-5637	191	15	with	with	ADP
ejpam-5637	191	16	respect	respect	NOUN
ejpam-5637	191	17	to	to	ADP
ejpam-5637	191	18	set	set	NOUN
ejpam-5637	191	19	of	of	ADP
ejpam-5637	191	20	block	block	NOUN
ejpam-5637	191	21	-	-	PUNCT
ejpam-5637	191	22	diagonal	diagonal	ADJ
ejpam-5637	191	23	matrices	matrix	NOUN
ejpam-5637	191	24	∆	∆	PROPN
ejpam-5637	191	25	,	,	PUNCT
ejpam-5637	191	26	where	where	SCONJ
ejpam-5637	191	27	∆	∆	PROPN
ejpam-5637	191	28	:	:	PUNCT
ejpam-5637	192	1	=	=	SYM
ejpam-5637	192	2	{	{	PUNCT
ejpam-5637	192	3	diag	diag	X
ejpam-5637	192	4	(	(	PUNCT
ejpam-5637	192	5	δ1ir1	δ1ir1	ADJ
ejpam-5637	192	6	,	,	PUNCT
ejpam-5637	192	7	δ2ir2	δ2ir2	NOUN
ejpam-5637	192	8	,	,	PUNCT
ejpam-5637	192	9	·	·	PUNCT
ejpam-5637	192	10	·	·	PUNCT
ejpam-5637	192	11	·	·	PUNCT
ejpam-5637	192	12	,	,	PUNCT
ejpam-5637	192	13	δsirs	δsir	NOUN
ejpam-5637	192	14	;	;	PUNCT
ejpam-5637	192	15	∆1,∆2	∆1,∆2	NOUN
ejpam-5637	192	16	,	,	PUNCT
ejpam-5637	192	17	·	·	PUNCT
ejpam-5637	192	18	·	·	PUNCT
ejpam-5637	192	19	·	·	PUNCT
ejpam-5637	192	20	,	,	PUNCT
ejpam-5637	192	21	∆f	∆f	PROPN
ejpam-5637	192	22	)	)	PUNCT
ejpam-5637	192	23	:	:	PUNCT
ejpam-5637	192	24	δi	δi	VERB
ejpam-5637	192	25	∈	∈	PROPN
ejpam-5637	192	26	r(c	r(c	NUM
ejpam-5637	192	27	)	)	PUNCT
ejpam-5637	192	28	,	,	PUNCT
ejpam-5637	192	29	∆j	∆j	PROPN
ejpam-5637	192	30	∈	∈	PROPN
ejpam-5637	192	31	kmj	kmj	NOUN
ejpam-5637	192	32	,	,	PUNCT
ejpam-5637	192	33	mj	mj	INTJ
ejpam-5637	192	34	,	,	PUNCT
ejpam-5637	192	35	i	i	PRON
ejpam-5637	192	36	=	=	NOUN
ejpam-5637	192	37	1	1	NUM
ejpam-5637	192	38	:	:	SYM
ejpam-5637	192	39	s	s	X
ejpam-5637	192	40	;	;	PUNCT
ejpam-5637	192	41	j	j	PROPN
ejpam-5637	192	42	=	=	SYM
ejpam-5637	192	43	1	1	NUM
ejpam-5637	192	44	:	:	SYM
ejpam-5637	192	45	f	f	X
ejpam-5637	192	46	}	}	PUNCT
ejpam-5637	192	47	,	,	PUNCT
ejpam-5637	192	48	with	with	ADP
ejpam-5637	192	49	k	k	PROPN
ejpam-5637	192	50	=	=	PUNCT
ejpam-5637	192	51	r(c	r(c	PROPN
ejpam-5637	192	52	)	)	PUNCT
ejpam-5637	192	53	,	,	PUNCT
ejpam-5637	192	54	is	be	AUX
ejpam-5637	192	55	the	the	DET
ejpam-5637	192	56	computation	computation	NOUN
ejpam-5637	192	57	of	of	ADP
ejpam-5637	192	58	largest	large	ADJ
ejpam-5637	192	59	singular	singular	ADJ
ejpam-5637	192	60	value	value	NOUN
ejpam-5637	192	61	of	of	ADP
ejpam-5637	192	62	∆̂	∆̂	PUNCT
ejpam-5637	192	63	∈	∈	PROPN
ejpam-5637	192	64	∆.	∆.	X
ejpam-5637	192	65	the	the	DET
ejpam-5637	192	66	structured	structured	ADJ
ejpam-5637	192	67	singular	singular	ADJ
ejpam-5637	192	68	value	value	NOUN
ejpam-5637	192	69	is	be	AUX
ejpam-5637	192	70	denoted	denote	VERB
ejpam-5637	192	71	by	by	ADP
ejpam-5637	192	72	µ	µ	NOUN
ejpam-5637	192	73	,	,	PUNCT
ejpam-5637	192	74	and	and	CCONJ
ejpam-5637	192	75	for	for	ADP
ejpam-5637	192	76	a	a	DET
ejpam-5637	192	77	given	give	VERB
ejpam-5637	192	78	matrix	matrix	NOUN
ejpam-5637	192	79	m	m	NOUN
ejpam-5637	192	80	and	and	CCONJ
ejpam-5637	192	81	∆	∆	NUM
ejpam-5637	192	82	,	,	PUNCT
ejpam-5637	192	83	it	it	PRON
ejpam-5637	192	84	is	be	AUX
ejpam-5637	192	85	defined	define	VERB
ejpam-5637	192	86	as	as	ADP
ejpam-5637	192	87	(	(	PUNCT
ejpam-5637	192	88	see	see	VERB
ejpam-5637	192	89	[	[	X
ejpam-5637	192	90	12	12	NUM
ejpam-5637	192	91	]	]	SYM
ejpam-5637	192	92	):	):	PUNCT
ejpam-5637	192	93	µ∆(m	µ∆(m	X
ejpam-5637	192	94	)	)	PUNCT
ejpam-5637	192	95	:	:	PUNCT
ejpam-5637	193	1	=	=	SYM
ejpam-5637	193	2	(	(	PUNCT
ejpam-5637	193	3	min{||∆̂||2	min{||∆̂||2	ADV
ejpam-5637	193	4	:	:	PUNCT
ejpam-5637	193	5	det(in	det(in	ADJ
ejpam-5637	193	6	−m∆̂	−m∆̂	NOUN
ejpam-5637	193	7	)	)	PUNCT
ejpam-5637	193	8	=	=	SYM
ejpam-5637	193	9	0	0	NUM
ejpam-5637	193	10	,	,	PUNCT
ejpam-5637	193	11	∀	∀	X
ejpam-5637	193	12	∆̂	∆̂	NOUN
ejpam-5637	193	13	∈	∈	NOUN
ejpam-5637	193	14	∆	∆	PROPN
ejpam-5637	193	15	}	}	PUNCT
ejpam-5637	193	16	)	)	PUNCT
ejpam-5637	193	17	−1	−1	NOUN
ejpam-5637	193	18	,	,	PUNCT
ejpam-5637	193	19	where	where	SCONJ
ejpam-5637	193	20	min	min	NOUN
ejpam-5637	193	21	is	be	AUX
ejpam-5637	193	22	taken	take	VERB
ejpam-5637	193	23	over	over	ADP
ejpam-5637	193	24	∆̂	∆̂	NOUN
ejpam-5637	193	25	∈	∈	NOUN
ejpam-5637	193	26	∆	∆	PROPN
ejpam-5637	193	27	,	,	PUNCT
ejpam-5637	193	28	and	and	CCONJ
ejpam-5637	193	29	µ∆(m	µ∆(m	PRON
ejpam-5637	193	30	)	)	PUNCT
ejpam-5637	193	31	=	=	SYM
ejpam-5637	193	32	0	0	PUNCT
ejpam-5637	193	33	if	if	SCONJ
ejpam-5637	193	34	det(in	det(in	NOUN
ejpam-5637	193	35	−m∆̂	−m∆̂	NOUN
ejpam-5637	193	36	)	)	PUNCT
ejpam-5637	193	37	̸=	̸=	PROPN
ejpam-5637	193	38	0	0	NUM
ejpam-5637	193	39	,	,	PUNCT
ejpam-5637	193	40	∀	∀	X
ejpam-5637	193	41	∆̂	∆̂	NOUN
ejpam-5637	193	42	∈	∈	PROPN
ejpam-5637	193	43	∆.	∆.	NOUN
ejpam-5637	193	44	remark	remark	NOUN
ejpam-5637	193	45	1	1	NUM
ejpam-5637	193	46	.	.	PUNCT
ejpam-5637	194	1	the	the	DET
ejpam-5637	194	2	block	block	NOUN
ejpam-5637	194	3	-	-	PUNCT
ejpam-5637	194	4	diagonal	diagonal	ADJ
ejpam-5637	194	5	structure	structure	NOUN
ejpam-5637	194	6	∆	∆	PROPN
ejpam-5637	194	7	can	can	AUX
ejpam-5637	194	8	be	be	AUX
ejpam-5637	194	9	associated	associate	VERB
ejpam-5637	194	10	with	with	ADP
ejpam-5637	194	11	multi	multi	ADJ
ejpam-5637	194	12	-	-	NOUN
ejpam-5637	194	13	index	index	NOUN
ejpam-5637	194	14	of	of	ADP
ejpam-5637	194	15	the	the	DET
ejpam-5637	194	16	positive	positive	ADJ
ejpam-5637	194	17	integers	integer	NOUN
ejpam-5637	194	18	.	.	PUNCT
ejpam-5637	195	1	remark	remark	PROPN
ejpam-5637	195	2	2	2	NUM
ejpam-5637	195	3	.	.	PUNCT
ejpam-5637	196	1	the	the	DET
ejpam-5637	196	2	full	full	ADJ
ejpam-5637	196	3	blocks	block	NOUN
ejpam-5637	196	4	in	in	ADP
ejpam-5637	196	5	∆	∆	PROPN
ejpam-5637	196	6	can	can	AUX
ejpam-5637	196	7	be	be	AUX
ejpam-5637	196	8	taken	take	VERB
ejpam-5637	196	9	as	as	ADP
ejpam-5637	196	10	either	either	CCONJ
ejpam-5637	196	11	pure	pure	ADJ
ejpam-5637	196	12	real	real	ADJ
ejpam-5637	196	13	blocks	block	NOUN
ejpam-5637	196	14	,	,	PUNCT
ejpam-5637	196	15	pure	pure	ADJ
ejpam-5637	196	16	complex	complex	ADJ
ejpam-5637	196	17	blocks	block	NOUN
ejpam-5637	196	18	or	or	CCONJ
ejpam-5637	196	19	a	a	DET
ejpam-5637	196	20	mixture	mixture	NOUN
ejpam-5637	196	21	of	of	ADP
ejpam-5637	196	22	both	both	PRON
ejpam-5637	196	23	.	.	PUNCT
ejpam-5637	197	1	these	these	DET
ejpam-5637	197	2	blocks	block	NOUN
ejpam-5637	197	3	can	can	AUX
ejpam-5637	197	4	be	be	AUX
ejpam-5637	197	5	chosen	choose	VERB
ejpam-5637	197	6	as	as	ADP
ejpam-5637	197	7	rank-1	rank-1	NUM
ejpam-5637	197	8	matrices	matrix	NOUN
ejpam-5637	197	9	.	.	PUNCT
ejpam-5637	198	1	remark	remark	PROPN
ejpam-5637	198	2	3	3	NUM
ejpam-5637	198	3	.	.	PUNCT
ejpam-5637	199	1	for	for	ADP
ejpam-5637	199	2	any	any	DET
ejpam-5637	199	3	α	α	NOUN
ejpam-5637	199	4	∈	∈	PROPN
ejpam-5637	199	5	c	c	X
ejpam-5637	199	6	,	,	PUNCT
ejpam-5637	199	7	µ∆(αm	µ∆(αm	VERB
ejpam-5637	199	8	)	)	PUNCT
ejpam-5637	199	9	=	=	SYM
ejpam-5637	199	10	|α|µ∆(m	|α|µ∆(m	PROPN
ejpam-5637	199	11	)	)	PUNCT
ejpam-5637	199	12	.	.	PUNCT
ejpam-5637	200	1	corollary	corollary	ADJ
ejpam-5637	200	2	1	1	NUM
ejpam-5637	200	3	.	.	PUNCT
ejpam-5637	201	1	[	[	X
ejpam-5637	201	2	12	12	NUM
ejpam-5637	201	3	]	]	PUNCT
ejpam-5637	201	4	the	the	DET
ejpam-5637	201	5	structured	structured	ADJ
ejpam-5637	201	6	singular	singular	ADJ
ejpam-5637	201	7	value	value	NOUN
ejpam-5637	201	8	µ∆(m	µ∆(m	PUNCT
ejpam-5637	201	9	)	)	PUNCT
ejpam-5637	201	10	is	be	AUX
ejpam-5637	201	11	equal	equal	ADJ
ejpam-5637	201	12	to	to	ADP
ejpam-5637	201	13	the	the	DET
ejpam-5637	201	14	computation	computation	NOUN
ejpam-5637	201	15	of	of	ADP
ejpam-5637	201	16	spectral	spectral	ADJ
ejpam-5637	201	17	radius	radius	NOUN
ejpam-5637	201	18	ρ	ρ	PROPN
ejpam-5637	201	19	of	of	ADP
ejpam-5637	201	20	v	v	NUM
ejpam-5637	201	21	tmw	tmw	NOUN
ejpam-5637	201	22	,	,	PUNCT
ejpam-5637	201	23	that	that	ADV
ejpam-5637	201	24	is	is	ADV
ejpam-5637	201	25	,	,	PUNCT
ejpam-5637	201	26	µ∆(m	µ∆(m	X
ejpam-5637	201	27	)	)	PUNCT
ejpam-5637	201	28	=	=	PUNCT
ejpam-5637	201	29	ρ(v	ρ(v	PROPN
ejpam-5637	201	30	tmv	tmv	NOUN
ejpam-5637	201	31	)	)	PUNCT
ejpam-5637	201	32	,	,	PUNCT
ejpam-5637	201	33	with	with	ADP
ejpam-5637	201	34	v	v	NOUN
ejpam-5637	201	35	,	,	PUNCT
ejpam-5637	201	36	w	w	ADP
ejpam-5637	201	37	having	have	VERB
ejpam-5637	201	38	the	the	DET
ejpam-5637	201	39	block	block	NOUN
ejpam-5637	201	40	-	-	PUNCT
ejpam-5637	201	41	diagonal	diagonal	ADJ
ejpam-5637	201	42	structure	structure	NOUN
ejpam-5637	201	43	.	.	PUNCT
ejpam-5637	202	1	the	the	DET
ejpam-5637	202	2	µ∆(m	µ∆(m	NOUN
ejpam-5637	202	3	)	)	PUNCT
ejpam-5637	202	4	can	can	AUX
ejpam-5637	202	5	be	be	AUX
ejpam-5637	202	6	considered	consider	VERB
ejpam-5637	202	7	as	as	ADP
ejpam-5637	202	8	the	the	DET
ejpam-5637	202	9	computation	computation	NOUN
ejpam-5637	202	10	of	of	ADP
ejpam-5637	202	11	spectral	spectral	ADJ
ejpam-5637	202	12	radius	radius	NOUN
ejpam-5637	202	13	ρ	ρ	PROPN
ejpam-5637	202	14	of	of	ADP
ejpam-5637	202	15	m∆̂	m∆̂	PROPN
ejpam-5637	202	16	,	,	PUNCT
ejpam-5637	202	17	∆̂	∆̂	PUNCT
ejpam-5637	202	18	∈	∈	PROPN
ejpam-5637	202	19	∆.	∆.	X
ejpam-5637	202	20	lemma	lemma	PROPN
ejpam-5637	202	21	1	1	X
ejpam-5637	202	22	.	.	PUNCT
ejpam-5637	203	1	[	[	X
ejpam-5637	203	2	35	35	NUM
ejpam-5637	203	3	]	]	PUNCT
ejpam-5637	203	4	for	for	ADP
ejpam-5637	203	5	m	m	PROPN
ejpam-5637	203	6	,	,	PUNCT
ejpam-5637	203	7	and	and	CCONJ
ejpam-5637	203	8	a	a	DET
ejpam-5637	203	9	block	block	NOUN
ejpam-5637	203	10	-	-	PUNCT
ejpam-5637	203	11	diagonal	diagonal	ADJ
ejpam-5637	203	12	structure	structure	NOUN
ejpam-5637	203	13	∆	∆	PROPN
ejpam-5637	203	14	,	,	PUNCT
ejpam-5637	203	15	µ∆(m	µ∆(m	X
ejpam-5637	203	16	)	)	PUNCT
ejpam-5637	203	17	=	=	SYM
ejpam-5637	203	18	maxρ(m∆̂	maxρ(m∆̂	NOUN
ejpam-5637	203	19	)	)	PUNCT
ejpam-5637	203	20	,	,	PUNCT
ejpam-5637	203	21	where	where	SCONJ
ejpam-5637	203	22	max	max	PROPN
ejpam-5637	203	23	is	be	AUX
ejpam-5637	203	24	taken	take	VERB
ejpam-5637	203	25	over	over	ADP
ejpam-5637	203	26	∆̂	∆̂	NOUN
ejpam-5637	203	27	∈	∈	PROPN
ejpam-5637	203	28	∆.	∆.	PROPN
ejpam-5637	203	29	m.u	m.u	PROPN
ejpam-5637	203	30	.	.	PROPN
ejpam-5637	204	1	rahman	rahman	PROPN
ejpam-5637	204	2	et	et	PROPN
ejpam-5637	204	3	al	al	PROPN
ejpam-5637	204	4	.	.	PUNCT
ejpam-5637	204	5	/	/	SYM
ejpam-5637	204	6	eur	eur	PROPN
ejpam-5637	204	7	.	.	PUNCT
ejpam-5637	205	1	j.	j.	PROPN
ejpam-5637	205	2	pure	pure	PROPN
ejpam-5637	205	3	appl	appl	PROPN
ejpam-5637	205	4	.	.	PROPN
ejpam-5637	205	5	math	math	PROPN
ejpam-5637	205	6	,	,	PUNCT
ejpam-5637	205	7	18	18	NUM
ejpam-5637	205	8	(	(	PUNCT
ejpam-5637	205	9	1	1	NUM
ejpam-5637	205	10	)	)	PUNCT
ejpam-5637	205	11	(	(	PUNCT
ejpam-5637	205	12	2025	2025	NUM
ejpam-5637	205	13	)	)	PUNCT
ejpam-5637	205	14	,	,	PUNCT
ejpam-5637	205	15	5637	5637	NUM
ejpam-5637	205	16	11	11	NUM
ejpam-5637	205	17	of	of	ADP
ejpam-5637	205	18	20	20	NUM
ejpam-5637	205	19	theorem	theorem	VERB
ejpam-5637	205	20	7	7	NUM
ejpam-5637	205	21	is	be	AUX
ejpam-5637	205	22	a	a	DET
ejpam-5637	205	23	well	well	ADV
ejpam-5637	205	24	-	-	PUNCT
ejpam-5637	205	25	known	know	VERB
ejpam-5637	205	26	result	result	NOUN
ejpam-5637	205	27	on	on	ADP
ejpam-5637	205	28	d	d	NOUN
ejpam-5637	205	29	-	-	NOUN
ejpam-5637	205	30	stability	stability	NOUN
ejpam-5637	205	31	of	of	ADP
ejpam-5637	205	32	a	a	DET
ejpam-5637	205	33	given	give	VERB
ejpam-5637	205	34	matrix	matrix	NOUN
ejpam-5637	205	35	while	while	SCONJ
ejpam-5637	205	36	computing	compute	VERB
ejpam-5637	205	37	the	the	DET
ejpam-5637	205	38	strictly	strictly	ADV
ejpam-5637	205	39	positive	positive	ADJ
ejpam-5637	205	40	real	real	ADJ
ejpam-5637	205	41	part	part	NOUN
ejpam-5637	205	42	of	of	ADP
ejpam-5637	205	43	the	the	DET
ejpam-5637	205	44	spectrum	spectrum	NOUN
ejpam-5637	205	45	of	of	ADP
ejpam-5637	205	46	the	the	DET
ejpam-5637	205	47	product	product	NOUN
ejpam-5637	205	48	of	of	ADP
ejpam-5637	205	49	given	give	VERB
ejpam-5637	205	50	matrix	matrix	NOUN
ejpam-5637	205	51	with	with	ADP
ejpam-5637	205	52	a	a	DET
ejpam-5637	205	53	positive	positive	ADJ
ejpam-5637	205	54	diagonal	diagonal	ADJ
ejpam-5637	205	55	matrix	matrix	NOUN
ejpam-5637	205	56	.	.	PUNCT
ejpam-5637	206	1	theorem	theorem	VERB
ejpam-5637	206	2	7	7	NUM
ejpam-5637	206	3	.	.	PUNCT
ejpam-5637	207	1	[	[	X
ejpam-5637	207	2	14	14	NUM
ejpam-5637	207	3	]	]	X
ejpam-5637	207	4	if	if	SCONJ
ejpam-5637	207	5	m	m	PROPN
ejpam-5637	207	6	has	have	VERB
ejpam-5637	207	7	all	all	DET
ejpam-5637	207	8	negative	negative	ADJ
ejpam-5637	207	9	diagonal	diagonal	ADJ
ejpam-5637	207	10	elements	element	NOUN
ejpam-5637	207	11	,	,	PUNCT
ejpam-5637	207	12	and	and	CCONJ
ejpam-5637	207	13	no	no	DET
ejpam-5637	207	14	negative	negative	ADJ
ejpam-5637	207	15	off	off	ADP
ejpam-5637	207	16	diagonal	diagonal	ADJ
ejpam-5637	207	17	elements	element	NOUN
ejpam-5637	207	18	,	,	PUNCT
ejpam-5637	207	19	for	for	ADP
ejpam-5637	207	20	d	d	PROPN
ejpam-5637	207	21	=	=	SYM
ejpam-5637	207	22	diag(dii	diag(dii	PROPN
ejpam-5637	207	23	)	)	PUNCT
ejpam-5637	207	24	,	,	PUNCT
ejpam-5637	207	25	the	the	DET
ejpam-5637	207	26	matrices	matrix	NOUN
ejpam-5637	207	27	m	m	VERB
ejpam-5637	207	28	,	,	PUNCT
ejpam-5637	207	29	and	and	CCONJ
ejpam-5637	207	30	dm	dm	PRON
ejpam-5637	207	31	are	be	AUX
ejpam-5637	207	32	stable	stable	ADJ
ejpam-5637	207	33	,	,	PUNCT
ejpam-5637	207	34	then	then	ADV
ejpam-5637	207	35	d	d	PROPN
ejpam-5637	207	36	=	=	SYM
ejpam-5637	207	37	diag(dii	diag(dii	PROPN
ejpam-5637	207	38	)	)	PUNCT
ejpam-5637	207	39	>	>	X
ejpam-5637	207	40	0	0	NUM
ejpam-5637	207	41	,	,	PUNCT
ejpam-5637	207	42	∀i	∀i	NOUN
ejpam-5637	207	43	.	.	PUNCT
ejpam-5637	208	1	the	the	DET
ejpam-5637	208	2	following	follow	VERB
ejpam-5637	208	3	theorem	theorem	NOUN
ejpam-5637	208	4	8	8	NUM
ejpam-5637	208	5	is	be	AUX
ejpam-5637	208	6	the	the	DET
ejpam-5637	208	7	characterization	characterization	NOUN
ejpam-5637	208	8	of	of	ADP
ejpam-5637	208	9	d	d	NOUN
ejpam-5637	208	10	-	-	NOUN
ejpam-5637	208	11	stability	stability	NOUN
ejpam-5637	208	12	and	and	CCONJ
ejpam-5637	208	13	bridge	bridge	NOUN
ejpam-5637	208	14	a	a	DET
ejpam-5637	208	15	link	link	NOUN
ejpam-5637	208	16	between	between	ADP
ejpam-5637	208	17	µ-values	µ-value	NOUN
ejpam-5637	208	18	and	and	CCONJ
ejpam-5637	208	19	d	d	ADJ
ejpam-5637	208	20	-	-	ADJ
ejpam-5637	208	21	stable	stable	ADJ
ejpam-5637	208	22	matrices	matrix	NOUN
ejpam-5637	208	23	.	.	PUNCT
ejpam-5637	209	1	theorem	theorem	VERB
ejpam-5637	209	2	8	8	NUM
ejpam-5637	209	3	.	.	PUNCT
ejpam-5637	210	1	consider	consider	VERB
ejpam-5637	210	2	m	m	PRON
ejpam-5637	210	3	be	be	AUX
ejpam-5637	210	4	a	a	DET
ejpam-5637	210	5	n	n	CCONJ
ejpam-5637	210	6	-	-	PUNCT
ejpam-5637	210	7	dimensional	dimensional	ADJ
ejpam-5637	210	8	matrix	matrix	NOUN
ejpam-5637	210	9	.	.	PUNCT
ejpam-5637	211	1	then	then	ADV
ejpam-5637	211	2	m	m	PROPN
ejpam-5637	211	3	is	be	AUX
ejpam-5637	211	4	d	d	ADJ
ejpam-5637	211	5	-	-	ADJ
ejpam-5637	211	6	stable	stable	ADJ
ejpam-5637	211	7	matrix	matrix	NOUN
ejpam-5637	211	8	if	if	SCONJ
ejpam-5637	211	9	and	and	CCONJ
ejpam-5637	211	10	only	only	ADV
ejpam-5637	211	11	if	if	SCONJ
ejpam-5637	211	12	m	m	NOUN
ejpam-5637	211	13	is	be	AUX
ejpam-5637	211	14	stable	stable	ADJ
ejpam-5637	211	15	and	and	CCONJ
ejpam-5637	211	16	0	0	NUM
ejpam-5637	211	17	≤	≤	NUM
ejpam-5637	211	18	µ∆(iin	µ∆(iin	NOUN
ejpam-5637	212	1	+	+	NUM
ejpam-5637	212	2	m)−1(iin	m)−1(iin	NOUN
ejpam-5637	212	3	−m	−m	NOUN
ejpam-5637	212	4	)	)	PUNCT
ejpam-5637	212	5	<	<	X
ejpam-5637	212	6	1	1	X
ejpam-5637	212	7	.	.	PUNCT
ejpam-5637	212	8	theorem	theorem	NOUN
ejpam-5637	212	9	9	9	NUM
ejpam-5637	212	10	.	.	PUNCT
ejpam-5637	213	1	let	let	VERB
ejpam-5637	213	2	(	(	PUNCT
ejpam-5637	213	3	mm∗)−1m∗	mm∗)−1m∗	NOUN
ejpam-5637	213	4	be	be	AUX
ejpam-5637	213	5	n−dimensional	n−dimensional	ADV
ejpam-5637	213	6	complex	complex	ADJ
ejpam-5637	213	7	valued	value	VERB
ejpam-5637	213	8	matrix	matrix	NOUN
ejpam-5637	213	9	.	.	PUNCT
ejpam-5637	214	1	then	then	ADV
ejpam-5637	214	2	0	0	NUM
ejpam-5637	214	3	≤	≤	NUM
ejpam-5637	214	4	µ∆((in	µ∆((in	NOUN
ejpam-5637	214	5	+	+	CCONJ
ejpam-5637	214	6	(	(	PUNCT
ejpam-5637	214	7	mm∗)−1m∗)−1(in	mm∗)−1m∗)−1(in	ADJ
ejpam-5637	214	8	−	−	PROPN
ejpam-5637	214	9	(	(	PUNCT
ejpam-5637	214	10	mm∗)−1m∗	mm∗)−1m∗	PROPN
ejpam-5637	214	11	)	)	PUNCT
ejpam-5637	214	12	)	)	PUNCT
ejpam-5637	215	1	<	<	X
ejpam-5637	215	2	1	1	X
ejpam-5637	215	3	.	.	PUNCT
ejpam-5637	215	4	proof	proof	NOUN
ejpam-5637	215	5	.	.	PUNCT
ejpam-5637	216	1	to	to	PART
ejpam-5637	216	2	prove	prove	VERB
ejpam-5637	216	3	this	this	DET
ejpam-5637	216	4	result	result	NOUN
ejpam-5637	216	5	,	,	PUNCT
ejpam-5637	216	6	we	we	PRON
ejpam-5637	216	7	use	use	VERB
ejpam-5637	216	8	the	the	DET
ejpam-5637	216	9	concept	concept	NOUN
ejpam-5637	216	10	of	of	ADP
ejpam-5637	216	11	d−stability	d−stability	PROPN
ejpam-5637	216	12	of	of	ADP
ejpam-5637	216	13	a	a	DET
ejpam-5637	216	14	matrix	matrix	NOUN
ejpam-5637	216	15	.	.	PUNCT
ejpam-5637	217	1	that	that	ADV
ejpam-5637	217	2	is	be	AUX
ejpam-5637	217	3	,	,	PUNCT
ejpam-5637	217	4	the	the	DET
ejpam-5637	217	5	given	give	VERB
ejpam-5637	217	6	(	(	PUNCT
ejpam-5637	217	7	mm∗)−1	mm∗)−1	NOUN
ejpam-5637	217	8	m	m	NOUN
ejpam-5637	217	9	is	be	AUX
ejpam-5637	217	10	d−stable	d−stable	ADJ
ejpam-5637	217	11	,	,	PUNCT
ejpam-5637	217	12	means	mean	VERB
ejpam-5637	217	13	that	that	SCONJ
ejpam-5637	217	14	,	,	PUNCT
ejpam-5637	218	1	λk(in	λk(in	NOUN
ejpam-5637	218	2	+	+	CCONJ
ejpam-5637	218	3	(	(	PUNCT
ejpam-5637	218	4	mm∗)−1mp	mm∗)−1mp	X
ejpam-5637	218	5	)	)	PUNCT
ejpam-5637	218	6	̸=	̸=	NOUN
ejpam-5637	218	7	0,∀k	0,∀k	NUM
ejpam-5637	219	1	=	=	SYM
ejpam-5637	219	2	1	1	NUM
ejpam-5637	219	3	:	:	SYM
ejpam-5637	219	4	n	n	CCONJ
ejpam-5637	219	5	,	,	PUNCT
ejpam-5637	219	6	with	with	ADP
ejpam-5637	219	7	p	p	NOUN
ejpam-5637	219	8	=	=	SYM
ejpam-5637	219	9	diag(p11	diag(p11	PROPN
ejpam-5637	219	10	,	,	PUNCT
ejpam-5637	219	11	p22	p22	VERB
ejpam-5637	219	12	,	,	PUNCT
ejpam-5637	219	13	.	.	PUNCT
ejpam-5637	219	14	.	.	PUNCT
ejpam-5637	219	15	.	.	PUNCT
ejpam-5637	220	1	,	,	PUNCT
ejpam-5637	220	2	pnn	pnn	PROPN
ejpam-5637	220	3	)	)	PUNCT
ejpam-5637	220	4	>	>	X
ejpam-5637	221	1	0	0	X
ejpam-5637	221	2	.	.	PUNCT
ejpam-5637	222	1	let	let	VERB
ejpam-5637	222	2	p	p	NOUN
ejpam-5637	222	3	=	=	X
ejpam-5637	222	4	(	(	PUNCT
ejpam-5637	222	5	in	in	ADP
ejpam-5637	222	6	+	+	NUM
ejpam-5637	222	7	r)−1(in	r)−1(in	X
ejpam-5637	222	8	−r),∀r	−r),∀r	PROPN
ejpam-5637	222	9	∈	∈	PROPN
ejpam-5637	222	10	∆	∆	PROPN
ejpam-5637	222	11	,	,	PUNCT
ejpam-5637	222	12	then	then	ADV
ejpam-5637	222	13	λk(in	λk(in	PROPN
ejpam-5637	222	14	+	+	CCONJ
ejpam-5637	222	15	(	(	PUNCT
ejpam-5637	222	16	m∗m)−1m∗(in	m∗m)−1m∗(in	X
ejpam-5637	222	17	+	+	SYM
ejpam-5637	222	18	r)−1(in	r)−1(in	NOUN
ejpam-5637	222	19	−r	−r	ADJ
ejpam-5637	222	20	)	)	PUNCT
ejpam-5637	222	21	)	)	PUNCT
ejpam-5637	223	1	̸=	̸=	PROPN
ejpam-5637	223	2	0	0	NUM
ejpam-5637	223	3	,	,	PUNCT
ejpam-5637	223	4	∀k	∀k	NOUN
ejpam-5637	223	5	=	=	SYM
ejpam-5637	223	6	1	1	NUM
ejpam-5637	223	7	:	:	SYM
ejpam-5637	223	8	n,∀r	n,∀r	X
ejpam-5637	223	9	∈	∈	PROPN
ejpam-5637	224	1	∆.	∆.	NOUN
ejpam-5637	224	2	this	this	DET
ejpam-5637	224	3	further	far	ADV
ejpam-5637	224	4	implies	imply	VERB
ejpam-5637	224	5	that	that	SCONJ
ejpam-5637	224	6	λk((in	λk((in	PRON
ejpam-5637	224	7	+	+	CCONJ
ejpam-5637	224	8	(	(	PUNCT
ejpam-5637	224	9	m∗m)−1m∗	m∗m)−1m∗	PROPN
ejpam-5637	224	10	)	)	PUNCT
ejpam-5637	224	11	+	+	CCONJ
ejpam-5637	224	12	(	(	PUNCT
ejpam-5637	224	13	in	in	ADP
ejpam-5637	224	14	−	−	PROPN
ejpam-5637	224	15	(	(	PUNCT
ejpam-5637	224	16	m∗m)−1m∗r	m∗m)−1m∗r	NOUN
ejpam-5637	224	17	)	)	PUNCT
ejpam-5637	224	18	)	)	PUNCT
ejpam-5637	224	19	̸=	̸=	PROPN
ejpam-5637	224	20	0	0	NUM
ejpam-5637	224	21	,	,	PUNCT
ejpam-5637	224	22	∀k	∀k	NOUN
ejpam-5637	224	23	=	=	SYM
ejpam-5637	224	24	1	1	NUM
ejpam-5637	224	25	:	:	SYM
ejpam-5637	224	26	n,∀r	n,∀r	X
ejpam-5637	224	27	∈	∈	PROPN
ejpam-5637	224	28	∆.	∆.	X
ejpam-5637	224	29	since	since	SCONJ
ejpam-5637	224	30	,	,	PUNCT
ejpam-5637	224	31	λk(in+(m∗m)−1m∗	λk(in+(m∗m)−1m∗	NOUN
ejpam-5637	224	32	)	)	PUNCT
ejpam-5637	224	33	̸=	̸=	NOUN
ejpam-5637	224	34	0	0	NUM
ejpam-5637	224	35	∼	∼	NOUN
ejpam-5637	224	36	λk((in+(m∗m)−1m∗)+(in−(m∗m)−1m∗r	λk((in+(m∗m)−1m∗)+(in−(m∗m)−1m∗r	NOUN
ejpam-5637	224	37	)	)	PUNCT
ejpam-5637	224	38	)	)	PUNCT
ejpam-5637	225	1	̸=	̸=	NOUN
ejpam-5637	225	2	0,∀k	0,∀k	NUM
ejpam-5637	226	1	=	=	SYM
ejpam-5637	226	2	1	1	NUM
ejpam-5637	226	3	:	:	SYM
ejpam-5637	226	4	n	n	CCONJ
ejpam-5637	226	5	,	,	PUNCT
ejpam-5637	226	6	∀r	∀r	PROPN
ejpam-5637	226	7	∈	∈	NOUN
ejpam-5637	226	8	∆	∆	X
ejpam-5637	226	9	finally	finally	ADV
ejpam-5637	226	10	,	,	PUNCT
ejpam-5637	226	11	this	this	DET
ejpam-5637	226	12	yields	yield	VERB
ejpam-5637	226	13	that	that	SCONJ
ejpam-5637	226	14	0	0	NUM
ejpam-5637	226	15	≤	≤	NUM
ejpam-5637	226	16	µ∆((in	µ∆((in	NOUN
ejpam-5637	226	17	+	+	CCONJ
ejpam-5637	226	18	(	(	PUNCT
ejpam-5637	226	19	mm∗)−1m∗)−1(in	mm∗)−1m∗)−1(in	ADJ
ejpam-5637	226	20	−	−	PROPN
ejpam-5637	226	21	(	(	PUNCT
ejpam-5637	226	22	mm∗)−1m∗	mm∗)−1m∗	PROPN
ejpam-5637	226	23	)	)	PUNCT
ejpam-5637	226	24	)	)	PUNCT
ejpam-5637	227	1	<	<	X
ejpam-5637	227	2	1	1	NUM
ejpam-5637	227	3	,	,	PUNCT
ejpam-5637	227	4	which	which	PRON
ejpam-5637	227	5	is	be	AUX
ejpam-5637	227	6	the	the	DET
ejpam-5637	227	7	required	require	VERB
ejpam-5637	227	8	prove	prove	NOUN
ejpam-5637	227	9	.	.	PUNCT
ejpam-5637	228	1	theorem	theorem	ADJ
ejpam-5637	228	2	10	10	NUM
ejpam-5637	228	3	.	.	PUNCT
ejpam-5637	229	1	let	let	VERB
ejpam-5637	229	2	(	(	PUNCT
ejpam-5637	229	3	m∗m)−1m∗	m∗m)−1m∗	PROPN
ejpam-5637	229	4	be	be	VERB
ejpam-5637	229	5	n−dimensional	n−dimensional	ADV
ejpam-5637	229	6	complex	complex	ADJ
ejpam-5637	229	7	valued	value	VERB
ejpam-5637	229	8	matrix	matrix	NOUN
ejpam-5637	229	9	.	.	PUNCT
ejpam-5637	230	1	then	then	ADV
ejpam-5637	230	2	0	0	NUM
ejpam-5637	230	3	≤	≤	NUM
ejpam-5637	230	4	µ∆(a	µ∆(a	NOUN
ejpam-5637	230	5	)	)	PUNCT
ejpam-5637	230	6	<	<	X
ejpam-5637	230	7	1	1	NUM
ejpam-5637	230	8	if	if	SCONJ
ejpam-5637	230	9	(	(	PUNCT
ejpam-5637	230	10	m∗m)−1m∗	m∗m)−1m∗	PROPN
ejpam-5637	230	11	is	be	AUX
ejpam-5637	230	12	d−stable	d−stable	ADJ
ejpam-5637	230	13	,	,	PUNCT
ejpam-5637	230	14	with	with	ADP
ejpam-5637	230	15	a	a	DET
ejpam-5637	230	16	=	=	X
ejpam-5637	230	17	(	(	PUNCT
ejpam-5637	230	18	iin	iin	NOUN
ejpam-5637	230	19	+	+	CCONJ
ejpam-5637	230	20	p	p	X
ejpam-5637	230	21	(	(	PUNCT
ejpam-5637	230	22	m∗m)−1m∗	m∗m)−1m∗	PROPN
ejpam-5637	230	23	+	+	CCONJ
ejpam-5637	230	24	m((m∗m)−1)∗)(iin	m((m∗m)−1)∗)(iin	NOUN
ejpam-5637	230	25	−	−	PROPN
ejpam-5637	230	26	p	p	X
ejpam-5637	230	27	(	(	PUNCT
ejpam-5637	230	28	m∗m)−1m∗	m∗m)−1m∗	PROPN
ejpam-5637	230	29	−m((m∗m)−1)∗p	−m((m∗m)−1)∗p	NOUN
ejpam-5637	230	30	)	)	PUNCT
ejpam-5637	230	31	with	with	ADP
ejpam-5637	230	32	p	p	NOUN
ejpam-5637	230	33	=	=	SYM
ejpam-5637	230	34	diag(p11	diag(p11	PROPN
ejpam-5637	230	35	,	,	PUNCT
ejpam-5637	230	36	p22	p22	VERB
ejpam-5637	230	37	,	,	PUNCT
ejpam-5637	230	38	.	.	PUNCT
ejpam-5637	230	39	.	.	PUNCT
ejpam-5637	230	40	.	.	PUNCT
ejpam-5637	231	1	,	,	PUNCT
ejpam-5637	231	2	pnn	pnn	PROPN
ejpam-5637	231	3	)	)	PUNCT
ejpam-5637	231	4	,	,	PUNCT
ejpam-5637	231	5	pii	pii	PROPN
ejpam-5637	231	6	>	>	X
ejpam-5637	231	7	0	0	NUM
ejpam-5637	231	8	,	,	PUNCT
ejpam-5637	231	9	∀i	∀i	NOUN
ejpam-5637	231	10	=	=	SYM
ejpam-5637	231	11	1	1	NUM
ejpam-5637	231	12	:	:	SYM
ejpam-5637	231	13	n	n	CCONJ
ejpam-5637	231	14	,	,	PUNCT
ejpam-5637	231	15	i	i	PRON
ejpam-5637	231	16	=	=	PUNCT
ejpam-5637	231	17	√	√	NUM
ejpam-5637	231	18	−1	−1	NOUN
ejpam-5637	231	19	.	.	PUNCT
ejpam-5637	232	1	m.u	m.u	PROPN
ejpam-5637	232	2	.	.	PROPN
ejpam-5637	233	1	rahman	rahman	PROPN
ejpam-5637	233	2	et	et	PROPN
ejpam-5637	233	3	al	al	PROPN
ejpam-5637	233	4	.	.	PUNCT
ejpam-5637	233	5	/	/	SYM
ejpam-5637	233	6	eur	eur	PROPN
ejpam-5637	233	7	.	.	PUNCT
ejpam-5637	234	1	j.	j.	PROPN
ejpam-5637	234	2	pure	pure	PROPN
ejpam-5637	234	3	appl	appl	PROPN
ejpam-5637	234	4	.	.	PROPN
ejpam-5637	234	5	math	math	PROPN
ejpam-5637	234	6	,	,	PUNCT
ejpam-5637	234	7	18	18	NUM
ejpam-5637	234	8	(	(	PUNCT
ejpam-5637	234	9	1	1	NUM
ejpam-5637	234	10	)	)	PUNCT
ejpam-5637	234	11	(	(	PUNCT
ejpam-5637	234	12	2025	2025	NUM
ejpam-5637	234	13	)	)	PUNCT
ejpam-5637	234	14	,	,	PUNCT
ejpam-5637	234	15	5637	5637	NUM
ejpam-5637	234	16	12	12	NUM
ejpam-5637	234	17	of	of	ADP
ejpam-5637	234	18	20	20	NUM
ejpam-5637	234	19	proof	proof	NOUN
ejpam-5637	234	20	.	.	PUNCT
ejpam-5637	235	1	the	the	DET
ejpam-5637	235	2	given	give	VERB
ejpam-5637	235	3	matrix	matrix	NOUN
ejpam-5637	235	4	(	(	PUNCT
ejpam-5637	235	5	m∗m)−1m∗	m∗m)−1m∗	PROPN
ejpam-5637	235	6	is	be	AUX
ejpam-5637	235	7	d−stable	d−stable	ADJ
ejpam-5637	235	8	if	if	SCONJ
ejpam-5637	235	9	re(λk(p	re(λk(p	X
ejpam-5637	235	10	(	(	PUNCT
ejpam-5637	235	11	m∗m)−1m∗+m(m∗m−1)∗	m∗m)−1m∗+m(m∗m−1)∗	NOUN
ejpam-5637	235	12	)	)	PUNCT
ejpam-5637	235	13	)	)	PUNCT
ejpam-5637	235	14	>	>	X
ejpam-5637	235	15	0,∀k	0,∀k	PUNCT
ejpam-5637	236	1	=	=	SYM
ejpam-5637	236	2	1	1	NUM
ejpam-5637	236	3	:	:	SYM
ejpam-5637	236	4	n	n	CCONJ
ejpam-5637	236	5	,	,	PUNCT
ejpam-5637	236	6	see	see	VERB
ejpam-5637	236	7	[	[	X
ejpam-5637	236	8	13	13	NUM
ejpam-5637	236	9	]	]	PUNCT
ejpam-5637	236	10	.	.	PUNCT
ejpam-5637	237	1	to	to	PART
ejpam-5637	237	2	prove	prove	VERB
ejpam-5637	237	3	that	that	SCONJ
ejpam-5637	237	4	0	0	NUM
ejpam-5637	237	5	≤	≤	NUM
ejpam-5637	237	6	µ∆(a	µ∆(a	NOUN
ejpam-5637	237	7	)	)	PUNCT
ejpam-5637	237	8	<	<	X
ejpam-5637	237	9	1	1	NUM
ejpam-5637	237	10	,	,	PUNCT
ejpam-5637	237	11	we	we	PRON
ejpam-5637	237	12	consider	consider	VERB
ejpam-5637	237	13	a	a	DET
ejpam-5637	237	14	block	block	NOUN
ejpam-5637	237	15	-	-	PUNCT
ejpam-5637	237	16	diagonal	diagonal	ADJ
ejpam-5637	237	17	structure	structure	NOUN
ejpam-5637	237	18	∆̂	∆̂	NOUN
ejpam-5637	238	1	=	=	CCONJ
ejpam-5637	238	2	(	(	PUNCT
ejpam-5637	238	3	iin	iin	NOUN
ejpam-5637	238	4	−	−	PROPN
ejpam-5637	238	5	p	p	NOUN
ejpam-5637	238	6	)	)	PUNCT
ejpam-5637	238	7	(	(	PUNCT
ejpam-5637	238	8	iin	iin	NOUN
ejpam-5637	238	9	+	+	CCONJ
ejpam-5637	238	10	p	p	NOUN
ejpam-5637	238	11	)	)	PUNCT
ejpam-5637	238	12	−1	−1	NOUN
ejpam-5637	238	13	with	with	ADP
ejpam-5637	238	14	∆̂	∆̂	PUNCT
ejpam-5637	238	15	∈	∈	PROPN
ejpam-5637	238	16	∆.	∆.	PROPN
ejpam-5637	238	17	for	for	ADP
ejpam-5637	238	18	all	all	DET
ejpam-5637	238	19	p	p	NOUN
ejpam-5637	238	20	,	,	PUNCT
ejpam-5637	238	21	the	the	DET
ejpam-5637	238	22	diagonal	diagonal	ADJ
ejpam-5637	238	23	positive	positive	ADJ
ejpam-5637	238	24	definite	definite	ADJ
ejpam-5637	238	25	matrices	matrix	NOUN
ejpam-5637	238	26	,	,	PUNCT
ejpam-5637	238	27	we	we	PRON
ejpam-5637	238	28	have	have	AUX
ejpam-5637	238	29	λk(p	λk(p	X
ejpam-5637	238	30	(	(	PUNCT
ejpam-5637	238	31	m∗m)−1m∗	m∗m)−1m∗	PROPN
ejpam-5637	238	32	+	+	X
ejpam-5637	238	33	m((m∗m)−1)∗p	m((m∗m)−1)∗p	ADJ
ejpam-5637	238	34	+	+	PUNCT
ejpam-5637	238	35	i(iin	i(iin	NOUN
ejpam-5637	238	36	+	+	NUM
ejpam-5637	238	37	∆̂)−1(iin	∆̂)−1(iin	NOUN
ejpam-5637	238	38	−	−	NUM
ejpam-5637	238	39	∆̂	∆̂	NOUN
ejpam-5637	238	40	)	)	PUNCT
ejpam-5637	238	41	)	)	PUNCT
ejpam-5637	239	1	̸=	̸=	NOUN
ejpam-5637	239	2	0∀k	0∀k	X
ejpam-5637	240	1	=	=	SYM
ejpam-5637	240	2	1	1	X
ejpam-5637	240	3	:	:	PUNCT
ejpam-5637	240	4	n.	n.	NOUN
ejpam-5637	240	5	in	in	ADP
ejpam-5637	240	6	turn	turn	NOUN
ejpam-5637	240	7	,	,	PUNCT
ejpam-5637	240	8	the	the	DET
ejpam-5637	240	9	expression	expression	NOUN
ejpam-5637	240	10	for	for	ADP
ejpam-5637	240	11	λk,∀k	λk,∀k	PROPN
ejpam-5637	240	12	=	=	NOUN
ejpam-5637	240	13	1	1	NUM
ejpam-5637	240	14	:	:	PUNCT
ejpam-5637	240	15	n	n	X
ejpam-5637	240	16	takes	take	VERB
ejpam-5637	240	17	the	the	DET
ejpam-5637	240	18	form	form	NOUN
ejpam-5637	240	19	λk((iin+p	λk((iin+p	NOUN
ejpam-5637	240	20	(	(	PUNCT
ejpam-5637	240	21	m∗m)−1m∗+m((m∗m)−1)∗p	m∗m)−1m∗+m((m∗m)−1)∗p	NOUN
ejpam-5637	240	22	)	)	PUNCT
ejpam-5637	240	23	−(iin−p	−(iin−p	NOUN
ejpam-5637	240	24	(	(	PUNCT
ejpam-5637	240	25	m∗m)−1m∗−m((m∗m)−1)∗p	m∗m)−1m∗−m((m∗m)−1)∗p	PROPN
ejpam-5637	240	26	)	)	PUNCT
ejpam-5637	240	27	∆̂	∆̂	NOUN
ejpam-5637	240	28	)	)	PUNCT
ejpam-5637	240	29	̸=	̸=	NOUN
ejpam-5637	240	30	0,∀∆̂	0,∀∆̂	NUM
ejpam-5637	240	31	∈	∈	PROPN
ejpam-5637	241	1	∆.	∆.	X
ejpam-5637	241	2	thus	thus	ADV
ejpam-5637	241	3	,	,	PUNCT
ejpam-5637	241	4	λk(in−(iin+p	λk(in−(iin+p	PROPN
ejpam-5637	241	5	(	(	PUNCT
ejpam-5637	241	6	m∗m)−1m∗+m((m∗m)−1)∗p	m∗m)−1m∗+m((m∗m)−1)∗p	PROPN
ejpam-5637	241	7	)	)	PUNCT
ejpam-5637	241	8	)	)	PUNCT
ejpam-5637	241	9	(	(	PUNCT
ejpam-5637	241	10	iin−p	iin−p	X
ejpam-5637	241	11	(	(	PUNCT
ejpam-5637	241	12	m∗m)−1m∗−m((m∗m)−1)∗p	m∗m)−1m∗−m((m∗m)−1)∗p	PROPN
ejpam-5637	241	13	)	)	PUNCT
ejpam-5637	241	14	∆̂	∆̂	NOUN
ejpam-5637	241	15	)	)	PUNCT
ejpam-5637	241	16	̸=	̸=	PROPN
ejpam-5637	241	17	0	0	NUM
ejpam-5637	241	18	,	,	PUNCT
ejpam-5637	241	19	∀∆̂	∀∆̂	PROPN
ejpam-5637	241	20	∈	∈	PROPN
ejpam-5637	242	1	∆.	∆.	ADP
ejpam-5637	242	2	the	the	DET
ejpam-5637	242	3	last	last	ADJ
ejpam-5637	242	4	expression	expression	NOUN
ejpam-5637	242	5	for	for	ADP
ejpam-5637	242	6	λk	λk	PRON
ejpam-5637	242	7	,	,	PUNCT
ejpam-5637	242	8	∀k	∀k	NOUN
ejpam-5637	242	9	=	=	SYM
ejpam-5637	242	10	1	1	NUM
ejpam-5637	242	11	:	:	PUNCT
ejpam-5637	242	12	n	n	PRON
ejpam-5637	242	13	implies	imply	VERB
ejpam-5637	242	14	that	that	SCONJ
ejpam-5637	242	15	0	0	NUM
ejpam-5637	242	16	≤	≤	NUM
ejpam-5637	242	17	µ∆(a	µ∆(a	NOUN
ejpam-5637	242	18	)	)	PUNCT
ejpam-5637	242	19	<	<	X
ejpam-5637	242	20	1	1	NUM
ejpam-5637	242	21	theorem	theorem	NOUN
ejpam-5637	242	22	11	11	NUM
ejpam-5637	242	23	.	.	PUNCT
ejpam-5637	243	1	let	let	VERB
ejpam-5637	243	2	(	(	PUNCT
ejpam-5637	243	3	m∗m)−1m∗	m∗m)−1m∗	PROPN
ejpam-5637	243	4	be	be	VERB
ejpam-5637	243	5	n−dimensional	n−dimensional	ADV
ejpam-5637	243	6	complex	complex	ADJ
ejpam-5637	243	7	valued	value	VERB
ejpam-5637	243	8	matrix	matrix	NOUN
ejpam-5637	243	9	.	.	PUNCT
ejpam-5637	244	1	then	then	ADV
ejpam-5637	244	2	,	,	PUNCT
ejpam-5637	244	3	0	0	NUM
ejpam-5637	244	4	≤	≤	NUM
ejpam-5637	244	5	µ∆(a	µ∆(a	NOUN
ejpam-5637	244	6	)	)	PUNCT
ejpam-5637	244	7	<	<	X
ejpam-5637	244	8	1	1	NUM
ejpam-5637	244	9	if	if	SCONJ
ejpam-5637	244	10	x∗(m((m∗m)−1)∗p	x∗(m((m∗m)−1)∗p	PROPN
ejpam-5637	244	11	2	2	NUM
ejpam-5637	244	12	+	+	CCONJ
ejpam-5637	244	13	p	p	X
ejpam-5637	244	14	2(m∗m)−1m∗)x	2(m∗m)−1m∗)x	NOUN
ejpam-5637	244	15	>	>	X
ejpam-5637	244	16	0	0	PUNCT
ejpam-5637	245	1	for	for	ADP
ejpam-5637	245	2	x	x	PROPN
ejpam-5637	245	3	∈	∈	PROPN
ejpam-5637	245	4	cn,1	cn,1	PROPN
ejpam-5637	245	5	,	,	PUNCT
ejpam-5637	245	6	and	and	CCONJ
ejpam-5637	245	7	for	for	ADP
ejpam-5637	245	8	all	all	DET
ejpam-5637	245	9	p	p	NOUN
ejpam-5637	245	10	=	=	ADJ
ejpam-5637	245	11	diag(p11	diag(p11	PROPN
ejpam-5637	245	12	,	,	PUNCT
ejpam-5637	245	13	p22	p22	VERB
ejpam-5637	245	14	,	,	PUNCT
ejpam-5637	245	15	.	.	PUNCT
ejpam-5637	245	16	.	.	PUNCT
ejpam-5637	245	17	.	.	PUNCT
ejpam-5637	246	1	,	,	PUNCT
ejpam-5637	246	2	pnn	pnn	PROPN
ejpam-5637	246	3	)	)	PUNCT
ejpam-5637	246	4	>	>	X
ejpam-5637	247	1	0	0	NUM
ejpam-5637	247	2	,	,	PUNCT
ejpam-5637	247	3	with	with	ADP
ejpam-5637	247	4	a	a	DET
ejpam-5637	247	5	=	=	X
ejpam-5637	247	6	(	(	PUNCT
ejpam-5637	247	7	iin	iin	NOUN
ejpam-5637	247	8	+	+	CCONJ
ejpam-5637	247	9	(	(	PUNCT
ejpam-5637	247	10	m∗m)−1m∗)−1(iin	m∗m)−1m∗)−1(iin	NOUN
ejpam-5637	247	11	−	−	PROPN
ejpam-5637	247	12	(	(	PUNCT
ejpam-5637	247	13	m∗m)−1m∗	m∗m)−1m∗	PROPN
ejpam-5637	247	14	)	)	PUNCT
ejpam-5637	247	15	.	.	PUNCT
ejpam-5637	248	1	proof	proof	NOUN
ejpam-5637	248	2	.	.	PUNCT
ejpam-5637	249	1	the	the	DET
ejpam-5637	249	2	structured	structured	ADJ
ejpam-5637	249	3	singular	singular	ADJ
ejpam-5637	249	4	value	value	NOUN
ejpam-5637	249	5	is	be	AUX
ejpam-5637	249	6	the	the	DET
ejpam-5637	249	7	computation	computation	NOUN
ejpam-5637	249	8	of	of	ADP
ejpam-5637	249	9	αmax	αmax	NOUN
ejpam-5637	249	10	≥	≥	NOUN
ejpam-5637	249	11	0	0	NUM
ejpam-5637	249	12	such	such	ADJ
ejpam-5637	249	13	that	that	PRON
ejpam-5637	249	14	for	for	ADP
ejpam-5637	249	15	each	each	DET
ejpam-5637	249	16	p	p	NOUN
ejpam-5637	249	17	,	,	PUNCT
ejpam-5637	249	18	the	the	DET
ejpam-5637	249	19	matrix	matrix	NOUN
ejpam-5637	249	20	inequality	inequality	NOUN
ejpam-5637	249	21	∥p	∥p	PROPN
ejpam-5637	249	22	(	(	PUNCT
ejpam-5637	249	23	m∗m)−1m∗x∥	m∗m)−1m∗x∥	NOUN
ejpam-5637	249	24	)	)	PUNCT
ejpam-5637	249	25	∥px∥	∥px∥	PART
ejpam-5637	249	26	≥	≥	NOUN
ejpam-5637	249	27	αmax	αmax	NOUN
ejpam-5637	249	28	.	.	PUNCT
ejpam-5637	250	1	for	for	ADP
ejpam-5637	250	2	given	give	VERB
ejpam-5637	250	3	a	a	DET
ejpam-5637	250	4	,	,	PUNCT
ejpam-5637	250	5	0	0	NUM
ejpam-5637	250	6	≤	≤	NUM
ejpam-5637	250	7	µ∆(a	µ∆(a	NOUN
ejpam-5637	250	8	)	)	PUNCT
ejpam-5637	250	9	<	<	X
ejpam-5637	250	10	1	1	NUM
ejpam-5637	250	11	if	if	SCONJ
ejpam-5637	250	12	∥pax∥	∥pax∥	X
ejpam-5637	250	13	<	<	X
ejpam-5637	250	14	∥px∥	∥px∥	NOUN
ejpam-5637	250	15	for	for	ADP
ejpam-5637	250	16	every	every	DET
ejpam-5637	250	17	x	x	PROPN
ejpam-5637	250	18	∈	∈	PROPN
ejpam-5637	250	19	cn,1	cn,1	PROPN
ejpam-5637	250	20	and	and	CCONJ
ejpam-5637	250	21	positive	positive	ADJ
ejpam-5637	250	22	diagonal	diagonal	ADJ
ejpam-5637	250	23	matrix	matrix	NOUN
ejpam-5637	250	24	p	p	NOUN
ejpam-5637	250	25	.	.	PUNCT
ejpam-5637	251	1	the	the	DET
ejpam-5637	251	2	above	above	ADJ
ejpam-5637	251	3	inequality	inequality	NOUN
ejpam-5637	251	4	holds	hold	VERB
ejpam-5637	251	5	true	true	ADJ
ejpam-5637	251	6	for	for	ADP
ejpam-5637	251	7	iin	iin	NOUN
ejpam-5637	251	8	+	+	CCONJ
ejpam-5637	251	9	(	(	PUNCT
ejpam-5637	251	10	m∗m)−1m∗	m∗m)−1m∗	PROPN
ejpam-5637	251	11	,	,	PUNCT
ejpam-5637	251	12	means	mean	VERB
ejpam-5637	251	13	that	that	SCONJ
ejpam-5637	251	14	,	,	PUNCT
ejpam-5637	251	15	∥pa(iin	∥pa(iin	PROPN
ejpam-5637	251	16	+	+	CCONJ
ejpam-5637	251	17	(	(	PUNCT
ejpam-5637	251	18	m∗m)−1m∗)x∥	m∗m)−1m∗)x∥	NOUN
ejpam-5637	251	19	<	<	X
ejpam-5637	251	20	∥p	∥p	X
ejpam-5637	251	21	(	(	PUNCT
ejpam-5637	251	22	iin	iin	NOUN
ejpam-5637	251	23	+	+	CCONJ
ejpam-5637	251	24	(	(	PUNCT
ejpam-5637	251	25	m∗m)−1m∗)x∥.	m∗m)−1m∗)x∥.	NOUN
ejpam-5637	251	26	also	also	ADV
ejpam-5637	251	27	,	,	PUNCT
ejpam-5637	251	28	∥pa(iin	∥pa(iin	PROPN
ejpam-5637	251	29	+	+	CCONJ
ejpam-5637	251	30	(	(	PUNCT
ejpam-5637	251	31	m∗m)−1m∗)x∥2	m∗m)−1m∗)x∥2	NOUN
ejpam-5637	251	32	<	<	X
ejpam-5637	251	33	∥p	∥p	PROPN
ejpam-5637	251	34	(	(	PUNCT
ejpam-5637	251	35	iin	iin	NOUN
ejpam-5637	251	36	+	+	CCONJ
ejpam-5637	251	37	(	(	PUNCT
ejpam-5637	251	38	m∗m)−1m∗)x∥2	m∗m)−1m∗)x∥2	NOUN
ejpam-5637	251	39	.	.	PUNCT
ejpam-5637	252	1	this	this	DET
ejpam-5637	252	2	further	far	ADV
ejpam-5637	252	3	implies	imply	VERB
ejpam-5637	252	4	that	that	SCONJ
ejpam-5637	252	5	x∗((iin	x∗((iin	PROPN
ejpam-5637	253	1	+	+	CCONJ
ejpam-5637	253	2	(	(	PUNCT
ejpam-5637	253	3	m∗m)−1m∗)∗a∗p	m∗m)−1m∗)∗a∗p	X
ejpam-5637	253	4	∗pa(iin	∗pa(iin	PROPN
ejpam-5637	253	5	+	+	PUNCT
ejpam-5637	253	6	(	(	PUNCT
ejpam-5637	253	7	m∗m)−1m∗))x	m∗m)−1m∗))x	X
ejpam-5637	253	8	<	<	X
ejpam-5637	253	9	x∗((iin	x∗((iin	X
ejpam-5637	254	1	+	+	PUNCT
ejpam-5637	254	2	(	(	PUNCT
ejpam-5637	254	3	m∗m)−1m∗)∗p	m∗m)−1m∗)∗p	INTJ
ejpam-5637	254	4	∗p	∗p	PROPN
ejpam-5637	254	5	(	(	PUNCT
ejpam-5637	254	6	iin	iin	NOUN
ejpam-5637	254	7	+	+	CCONJ
ejpam-5637	254	8	(	(	PUNCT
ejpam-5637	254	9	m∗m)−1m∗))x	m∗m)−1m∗))x	NOUN
ejpam-5637	254	10	.	.	PUNCT
ejpam-5637	255	1	this	this	DET
ejpam-5637	255	2	inequality	inequality	NOUN
ejpam-5637	255	3	further	far	ADV
ejpam-5637	255	4	reduces	reduce	VERB
ejpam-5637	255	5	to	to	ADP
ejpam-5637	255	6	x∗((iin+(m∗m)−1m∗)∗a∗p	x∗((iin+(m∗m)−1m∗)∗a∗p	PROPN
ejpam-5637	255	7	2a(iin+(m∗m)−1m∗))x	2a(iin+(m∗m)−1m∗))x	NOUN
ejpam-5637	255	8	<	<	X
ejpam-5637	255	9	x∗(iin+(m∗m)−1m∗p	x∗(iin+(m∗m)−1m∗p	PROPN
ejpam-5637	255	10	2(iin+(m∗m)−1m∗))x	2(iin+(m∗m)−1m∗))x	NUM
ejpam-5637	255	11	.	.	PUNCT
ejpam-5637	256	1	m.u	m.u	PROPN
ejpam-5637	256	2	.	.	PROPN
ejpam-5637	257	1	rahman	rahman	PROPN
ejpam-5637	257	2	et	et	PROPN
ejpam-5637	257	3	al	al	PROPN
ejpam-5637	257	4	.	.	PUNCT
ejpam-5637	257	5	/	/	SYM
ejpam-5637	257	6	eur	eur	PROPN
ejpam-5637	257	7	.	.	PUNCT
ejpam-5637	258	1	j.	j.	PROPN
ejpam-5637	258	2	pure	pure	PROPN
ejpam-5637	258	3	appl	appl	PROPN
ejpam-5637	258	4	.	.	PROPN
ejpam-5637	258	5	math	math	PROPN
ejpam-5637	258	6	,	,	PUNCT
ejpam-5637	258	7	18	18	NUM
ejpam-5637	258	8	(	(	PUNCT
ejpam-5637	258	9	1	1	NUM
ejpam-5637	258	10	)	)	PUNCT
ejpam-5637	258	11	(	(	PUNCT
ejpam-5637	258	12	2025	2025	NUM
ejpam-5637	258	13	)	)	PUNCT
ejpam-5637	258	14	,	,	PUNCT
ejpam-5637	258	15	5637	5637	NUM
ejpam-5637	258	16	13	13	NUM
ejpam-5637	258	17	of	of	ADP
ejpam-5637	258	18	20	20	NUM
ejpam-5637	258	19	since	since	SCONJ
ejpam-5637	258	20	,	,	PUNCT
ejpam-5637	258	21	a	a	PRON
ejpam-5637	258	22	=	=	X
ejpam-5637	258	23	(	(	PUNCT
ejpam-5637	258	24	iin	iin	NOUN
ejpam-5637	258	25	+	+	CCONJ
ejpam-5637	258	26	(	(	PUNCT
ejpam-5637	258	27	m∗m)−1m∗)−1(iin	m∗m)−1m∗)−1(iin	NOUN
ejpam-5637	258	28	−	−	PROPN
ejpam-5637	258	29	(	(	PUNCT
ejpam-5637	258	30	m∗m)−1m∗	m∗m)−1m∗	PROPN
ejpam-5637	258	31	)	)	PUNCT
ejpam-5637	258	32	.	.	PUNCT
ejpam-5637	259	1	thus	thus	ADV
ejpam-5637	259	2	,	,	PUNCT
ejpam-5637	259	3	above	above	ADP
ejpam-5637	259	4	inequality	inequality	NOUN
ejpam-5637	259	5	rewritten	rewrite	VERB
ejpam-5637	259	6	as	as	ADP
ejpam-5637	259	7	x∗((iin+(m∗m)−1m∗)∗(iin−(m∗m)−1m∗)∗(iin+(m∗m)−1m∗)−1p	x∗((iin+(m∗m)−1m∗)∗(iin−(m∗m)−1m∗)∗(iin+(m∗m)−1m∗)−1p	PROPN
ejpam-5637	259	8	2(iin+(m∗m)−1m∗)−1	2(iin+(m∗m)−1m∗)−1	PROPN
ejpam-5637	259	9	(	(	PUNCT
ejpam-5637	259	10	iin−(m∗m)−1m∗)(iin+(m∗m)−1m∗)x−x∗((iin+(m∗m)−1m∗)∗p	iin−(m∗m)−1m∗)(iin+(m∗m)−1m∗)x−x∗((iin+(m∗m)−1m∗)∗p	PROPN
ejpam-5637	259	11	2(iin+(m∗m)−1m∗))x	2(iin+(m∗m)−1m∗))x	PROPN
ejpam-5637	259	12	<	<	X
ejpam-5637	259	13	0	0	NUM
ejpam-5637	259	14	.	.	PROPN
ejpam-5637	259	15	or	or	CCONJ
ejpam-5637	259	16	x∗(iin−(m∗m)−1m∗)∗p	x∗(iin−(m∗m)−1m∗)∗p	PROPN
ejpam-5637	259	17	2(iin−(m∗m)−1m∗)x−x∗(iin+(m∗m)−1m∗)∗p	2(iin−(m∗m)−1m∗)x−x∗(iin+(m∗m)−1m∗)∗p	NUM
ejpam-5637	259	18	2(iin+(m∗m)−1m∗)x	2(iin+(m∗m)−1m∗)x	NUM
ejpam-5637	259	19	<	<	X
ejpam-5637	259	20	0	0	NUM
ejpam-5637	259	21	.	.	PUNCT
ejpam-5637	260	1	in	in	ADP
ejpam-5637	260	2	turn	turn	NOUN
ejpam-5637	260	3	,	,	PUNCT
ejpam-5637	260	4	we	we	PRON
ejpam-5637	260	5	have	have	VERB
ejpam-5637	260	6	that	that	PRON
ejpam-5637	260	7	x∗((iin−(m∗m)−1m∗)∗p	x∗((iin−(m∗m)−1m∗)∗p	PROPN
ejpam-5637	260	8	2(iin−(m∗m)−1m∗)−(iin+(m∗m)−1m∗)∗p	2(iin−(m∗m)−1m∗)−(iin+(m∗m)−1m∗)∗p	PROPN
ejpam-5637	260	9	2(iin+(m∗m)−1m∗))κ	2(iin+(m∗m)−1m∗))κ	PROPN
ejpam-5637	260	10	<	<	X
ejpam-5637	260	11	0	0	NUM
ejpam-5637	260	12	.	.	PUNCT
ejpam-5637	261	1	thus	thus	ADV
ejpam-5637	261	2	,	,	PUNCT
ejpam-5637	261	3	x∗((iin−(m∗m)−1m∗)∗(ip	x∗((iin−(m∗m)−1m∗)∗(ip	PROPN
ejpam-5637	261	4	2−p	2−p	NUM
ejpam-5637	262	1	2(m∗m)−1m∗)−(iin+(m∗m)−1m∗)∗(ip	2(m∗m)−1m∗)−(iin+(m∗m)−1m∗)∗(ip	NUM
ejpam-5637	262	2	2+p	2+p	NUM
ejpam-5637	262	3	2(m∗m)−1m∗))x	2(m∗m)−1m∗))x	NOUN
ejpam-5637	262	4	<	<	X
ejpam-5637	262	5	0	0	NUM
ejpam-5637	262	6	.	.	PUNCT
ejpam-5637	263	1	also	also	ADV
ejpam-5637	263	2	,	,	PUNCT
ejpam-5637	263	3	x∗(−2ip	x∗(−2ip	PROPN
ejpam-5637	263	4	2(m∗m)−1m∗	2(m∗m)−1m∗	NUM
ejpam-5637	263	5	−	−	NOUN
ejpam-5637	263	6	2im(m∗m)−1p	2im(m∗m)−1p	NUM
ejpam-5637	263	7	2)x	2)x	NUM
ejpam-5637	263	8	<	<	X
ejpam-5637	263	9	0	0	NUM
ejpam-5637	263	10	or	or	CCONJ
ejpam-5637	263	11	x∗(−2i(m(m∗m)−1)∗p	x∗(−2i(m(m∗m)−1)∗p	NUM
ejpam-5637	263	12	2	2	NUM
ejpam-5637	263	13	+	+	CCONJ
ejpam-5637	263	14	p	p	X
ejpam-5637	263	15	2(m∗m)−1m∗)x	2(m∗m)−1m∗)x	NOUN
ejpam-5637	263	16	<	<	X
ejpam-5637	263	17	0	0	X
ejpam-5637	263	18	.	.	PUNCT
ejpam-5637	264	1	finally	finally	ADV
ejpam-5637	264	2	,	,	PUNCT
ejpam-5637	264	3	x∗(m(m∗m)−1)∗p	x∗(m(m∗m)−1)∗p	PROPN
ejpam-5637	264	4	2	2	NUM
ejpam-5637	265	1	+	+	CCONJ
ejpam-5637	265	2	p	p	X
ejpam-5637	265	3	2(m∗m)−1m∗)x	2(m∗m)−1m∗)x	NUM
ejpam-5637	265	4	>	>	X
ejpam-5637	265	5	0	0	PROPN
ejpam-5637	265	6	,	,	PUNCT
ejpam-5637	265	7	which	which	PRON
ejpam-5637	265	8	completes	complete	VERB
ejpam-5637	265	9	required	required	ADJ
ejpam-5637	265	10	proof	proof	NOUN
ejpam-5637	265	11	.	.	PUNCT
ejpam-5637	266	1	pseudo	pseudo	NOUN
ejpam-5637	266	2	-	-	NOUN
ejpam-5637	266	3	spectrum	spectrum	NOUN
ejpam-5637	266	4	:	:	PUNCT
ejpam-5637	266	5	the	the	DET
ejpam-5637	266	6	pseudo	pseudo	NOUN
ejpam-5637	266	7	-	-	NOUN
ejpam-5637	266	8	spectrum	spectrum	NOUN
ejpam-5637	266	9	of	of	ADP
ejpam-5637	266	10	a	a	DET
ejpam-5637	266	11	matrix	matrix	NOUN
ejpam-5637	266	12	m	m	VERB
ejpam-5637	266	13	is	be	AUX
ejpam-5637	266	14	the	the	DET
ejpam-5637	266	15	set	set	NOUN
ejpam-5637	266	16	of	of	ADP
ejpam-5637	266	17	which	which	PRON
ejpam-5637	266	18	contains	contain	VERB
ejpam-5637	266	19	the	the	DET
ejpam-5637	266	20	spectrum	spectrum	NOUN
ejpam-5637	266	21	,	,	PUNCT
ejpam-5637	266	22	that	that	ADV
ejpam-5637	266	23	is	is	ADV
ejpam-5637	266	24	,	,	PUNCT
ejpam-5637	266	25	all	all	DET
ejpam-5637	266	26	the	the	DET
ejpam-5637	266	27	eigenvalues	eigenvalue	NOUN
ejpam-5637	266	28	of	of	ADP
ejpam-5637	266	29	m	m	PROPN
ejpam-5637	266	30	.	.	PUNCT
ejpam-5637	267	1	the	the	DET
ejpam-5637	267	2	important	important	ADJ
ejpam-5637	267	3	question	question	NOUN
ejpam-5637	267	4	one	one	PRON
ejpam-5637	267	5	can	can	AUX
ejpam-5637	267	6	raise	raise	VERB
ejpam-5637	267	7	is	be	AUX
ejpam-5637	267	8	about	about	ADP
ejpam-5637	267	9	the	the	DET
ejpam-5637	267	10	singularity	singularity	NOUN
ejpam-5637	267	11	of	of	ADP
ejpam-5637	267	12	m	m	PRON
ejpam-5637	267	13	which	which	PRON
ejpam-5637	267	14	does	do	AUX
ejpam-5637	267	15	not	not	PART
ejpam-5637	267	16	appear	appear	VERB
ejpam-5637	267	17	as	as	ADP
ejpam-5637	267	18	a	a	DET
ejpam-5637	267	19	robust	robust	ADJ
ejpam-5637	267	20	in	in	ADP
ejpam-5637	267	21	the	the	DET
ejpam-5637	267	22	sense	sense	NOUN
ejpam-5637	267	23	that	that	SCONJ
ejpam-5637	267	24	a	a	DET
ejpam-5637	267	25	small	small	ADJ
ejpam-5637	267	26	perturbation	perturbation	NOUN
ejpam-5637	267	27	ϵ	ϵ	X
ejpam-5637	267	28	may	may	AUX
ejpam-5637	267	29	vary	vary	VERB
ejpam-5637	267	30	the	the	DET
ejpam-5637	267	31	answer	answer	NOUN
ejpam-5637	267	32	from	from	ADP
ejpam-5637	267	33	yes	yes	INTJ
ejpam-5637	267	34	to	to	ADP
ejpam-5637	267	35	no	no	PRON
ejpam-5637	267	36	in	in	ADP
ejpam-5637	267	37	a	a	DET
ejpam-5637	267	38	dramatic	dramatic	ADJ
ejpam-5637	267	39	way	way	NOUN
ejpam-5637	267	40	.	.	PUNCT
ejpam-5637	268	1	this	this	PRON
ejpam-5637	268	2	helps	help	VERB
ejpam-5637	268	3	to	to	PART
ejpam-5637	268	4	think	think	VERB
ejpam-5637	268	5	that	that	SCONJ
ejpam-5637	268	6	either	either	CCONJ
ejpam-5637	268	7	||m−1||	||m−1||	PROPN
ejpam-5637	268	8	is	be	AUX
ejpam-5637	268	9	large	large	ADJ
ejpam-5637	268	10	enough	enough	ADV
ejpam-5637	268	11	or	or	CCONJ
ejpam-5637	268	12	not	not	PART
ejpam-5637	268	13	?	?	PUNCT
ejpam-5637	269	1	for	for	ADP
ejpam-5637	269	2	λ	λ	PROPN
ejpam-5637	269	3	,	,	PUNCT
ejpam-5637	269	4	an	an	DET
ejpam-5637	269	5	eigenvalue	eigenvalue	NOUN
ejpam-5637	269	6	of	of	ADP
ejpam-5637	269	7	m	m	PROPN
ejpam-5637	269	8	,	,	PUNCT
ejpam-5637	269	9	a	a	DET
ejpam-5637	269	10	much	much	ADV
ejpam-5637	269	11	better	well	ADJ
ejpam-5637	269	12	question	question	NOUN
ejpam-5637	269	13	is	be	AUX
ejpam-5637	269	14	to	to	PART
ejpam-5637	269	15	ask	ask	VERB
ejpam-5637	269	16	:	:	PUNCT
ejpam-5637	269	17	does	do	AUX
ejpam-5637	269	18	||(λin	||(λin	PROPN
ejpam-5637	269	19	−	−	PROPN
ejpam-5637	269	20	m)−1||	m)−1||	NOUN
ejpam-5637	269	21	is	be	AUX
ejpam-5637	269	22	large	large	ADJ
ejpam-5637	269	23	or	or	CCONJ
ejpam-5637	269	24	not	not	PART
ejpam-5637	269	25	?	?	PUNCT
ejpam-5637	270	1	such	such	DET
ejpam-5637	270	2	a	a	DET
ejpam-5637	270	3	pattern	pattern	NOUN
ejpam-5637	270	4	allows	allow	VERB
ejpam-5637	270	5	following	follow	VERB
ejpam-5637	270	6	definitions	definition	NOUN
ejpam-5637	270	7	and	and	CCONJ
ejpam-5637	270	8	results	result	NOUN
ejpam-5637	270	9	[	[	X
ejpam-5637	270	10	49	49	NUM
ejpam-5637	270	11	]	]	PUNCT
ejpam-5637	270	12	of	of	ADP
ejpam-5637	270	13	pseudospectrum	pseudospectrum	NOUN
ejpam-5637	270	14	.	.	PUNCT
ejpam-5637	271	1	definition	definition	NOUN
ejpam-5637	271	2	4	4	NUM
ejpam-5637	271	3	.	.	PUNCT
ejpam-5637	272	1	let	let	VERB
ejpam-5637	272	2	m	m	PRON
ejpam-5637	272	3	be	be	AUX
ejpam-5637	272	4	a	a	DET
ejpam-5637	272	5	given	give	VERB
ejpam-5637	272	6	n	n	CCONJ
ejpam-5637	272	7	-	-	PUNCT
ejpam-5637	272	8	dimensional	dimensional	ADJ
ejpam-5637	272	9	matrix	matrix	NOUN
ejpam-5637	272	10	,	,	PUNCT
ejpam-5637	272	11	ϵ	ϵ	X
ejpam-5637	272	12	>	>	X
ejpam-5637	272	13	0	0	PROPN
ejpam-5637	272	14	,	,	PUNCT
ejpam-5637	272	15	a	a	DET
ejpam-5637	272	16	small	small	ADJ
ejpam-5637	272	17	perturbation	perturbation	NOUN
ejpam-5637	272	18	.	.	PUNCT
ejpam-5637	273	1	the	the	DET
ejpam-5637	273	2	ϵ-pseudospectrum	ϵ-pseudospectrum	PROPN
ejpam-5637	273	3	σϵ(m	σϵ(m	ADV
ejpam-5637	273	4	)	)	PUNCT
ejpam-5637	273	5	is	be	AUX
ejpam-5637	273	6	the	the	DET
ejpam-5637	273	7	set	set	NOUN
ejpam-5637	273	8	of	of	ADP
ejpam-5637	273	9	eigenvalues	eigenvalue	NOUN
ejpam-5637	273	10	λ	λ	X
ejpam-5637	273	11	∈	∈	PROPN
ejpam-5637	273	12	c	c	NOUN
ejpam-5637	273	13	such	such	ADJ
ejpam-5637	273	14	that	that	SCONJ
ejpam-5637	273	15	||(λin	||(λin	PROPN
ejpam-5637	273	16	−m)−1||	−m)−1||	PROPN
ejpam-5637	273	17	>	>	ADP
ejpam-5637	273	18	1	1	NUM
ejpam-5637	273	19	ϵ	ϵ	NOUN
ejpam-5637	273	20	.	.	PUNCT
ejpam-5637	274	1	remark	remark	PROPN
ejpam-5637	274	2	4	4	NUM
ejpam-5637	274	3	.	.	PUNCT
ejpam-5637	275	1	for	for	ADP
ejpam-5637	275	2	λ	λ	PROPN
ejpam-5637	275	3	∈	∈	PROPN
ejpam-5637	275	4	σ(m	σ(m	NOUN
ejpam-5637	275	5	)	)	PUNCT
ejpam-5637	275	6	,	,	PUNCT
ejpam-5637	275	7	σ(m	σ(m	NOUN
ejpam-5637	275	8	)	)	PUNCT
ejpam-5637	275	9	being	be	AUX
ejpam-5637	275	10	as	as	ADP
ejpam-5637	275	11	the	the	DET
ejpam-5637	275	12	set	set	NOUN
ejpam-5637	275	13	of	of	ADP
ejpam-5637	275	14	eigenvalues	eigenvalue	NOUN
ejpam-5637	275	15	of	of	ADP
ejpam-5637	275	16	m	m	PROPN
ejpam-5637	275	17	,	,	PUNCT
ejpam-5637	275	18	||(λin	||(λin	PROPN
ejpam-5637	275	19	−	−	PROPN
ejpam-5637	275	20	m)−1||	m)−1||	NOUN
ejpam-5637	275	21	=	=	PROPN
ejpam-5637	275	22	∞.	∞.	PROPN
ejpam-5637	275	23	the	the	DET
ejpam-5637	275	24	second	second	ADJ
ejpam-5637	275	25	definition	definition	NOUN
ejpam-5637	275	26	of	of	ADP
ejpam-5637	275	27	pseudo	pseudo	NOUN
ejpam-5637	275	28	-	-	NOUN
ejpam-5637	275	29	spectrum	spectrum	NOUN
ejpam-5637	275	30	is	be	AUX
ejpam-5637	275	31	given	give	VERB
ejpam-5637	275	32	as	as	SCONJ
ejpam-5637	275	33	follows	follow	VERB
ejpam-5637	275	34	.	.	PUNCT
ejpam-5637	276	1	m.u	m.u	PROPN
ejpam-5637	276	2	.	.	PROPN
ejpam-5637	277	1	rahman	rahman	PROPN
ejpam-5637	277	2	et	et	PROPN
ejpam-5637	277	3	al	al	PROPN
ejpam-5637	277	4	.	.	PUNCT
ejpam-5637	277	5	/	/	SYM
ejpam-5637	277	6	eur	eur	PROPN
ejpam-5637	277	7	.	.	PUNCT
ejpam-5637	278	1	j.	j.	PROPN
ejpam-5637	278	2	pure	pure	PROPN
ejpam-5637	278	3	appl	appl	PROPN
ejpam-5637	278	4	.	.	PROPN
ejpam-5637	278	5	math	math	PROPN
ejpam-5637	278	6	,	,	PUNCT
ejpam-5637	278	7	18	18	NUM
ejpam-5637	278	8	(	(	PUNCT
ejpam-5637	278	9	1	1	NUM
ejpam-5637	278	10	)	)	PUNCT
ejpam-5637	278	11	(	(	PUNCT
ejpam-5637	278	12	2025	2025	NUM
ejpam-5637	278	13	)	)	PUNCT
ejpam-5637	278	14	,	,	PUNCT
ejpam-5637	278	15	5637	5637	NUM
ejpam-5637	278	16	14	14	NUM
ejpam-5637	278	17	of	of	ADP
ejpam-5637	278	18	20	20	NUM
ejpam-5637	278	19	definition	definition	NOUN
ejpam-5637	278	20	5	5	NUM
ejpam-5637	278	21	.	.	PUNCT
ejpam-5637	279	1	let	let	VERB
ejpam-5637	279	2	m	m	PRON
ejpam-5637	279	3	be	be	AUX
ejpam-5637	279	4	a	a	DET
ejpam-5637	279	5	given	give	VERB
ejpam-5637	279	6	n	n	CCONJ
ejpam-5637	279	7	-	-	PUNCT
ejpam-5637	279	8	dimensional	dimensional	ADJ
ejpam-5637	279	9	matrix	matrix	NOUN
ejpam-5637	279	10	,	,	PUNCT
ejpam-5637	279	11	ϵ	ϵ	X
ejpam-5637	279	12	>	>	X
ejpam-5637	279	13	0	0	PROPN
ejpam-5637	279	14	,	,	PUNCT
ejpam-5637	279	15	a	a	DET
ejpam-5637	279	16	small	small	ADJ
ejpam-5637	279	17	perturbation	perturbation	NOUN
ejpam-5637	279	18	.	.	PUNCT
ejpam-5637	280	1	the	the	DET
ejpam-5637	280	2	ϵ-pseudospectrum	ϵ-pseudospectrum	PROPN
ejpam-5637	280	3	σϵ(m	σϵ(m	ADV
ejpam-5637	280	4	)	)	PUNCT
ejpam-5637	280	5	is	be	AUX
ejpam-5637	280	6	the	the	DET
ejpam-5637	280	7	set	set	NOUN
ejpam-5637	280	8	of	of	ADP
ejpam-5637	280	9	eigenvalues	eigenvalue	NOUN
ejpam-5637	280	10	λ	λ	X
ejpam-5637	280	11	∈	∈	PROPN
ejpam-5637	280	12	c	c	NOUN
ejpam-5637	280	13	such	such	ADJ
ejpam-5637	280	14	that	that	SCONJ
ejpam-5637	280	15	λ	λ	PROPN
ejpam-5637	280	16	∈	∈	PRON
ejpam-5637	280	17	σ(m	σ(m	NOUN
ejpam-5637	280	18	+	+	CCONJ
ejpam-5637	280	19	e	e	NOUN
ejpam-5637	280	20	)	)	PUNCT
ejpam-5637	280	21	,	,	PUNCT
ejpam-5637	280	22	for	for	ADP
ejpam-5637	280	23	some	some	DET
ejpam-5637	280	24	e	e	NOUN
ejpam-5637	280	25	with	with	ADP
ejpam-5637	280	26	||e||	||e||	PROPN
ejpam-5637	280	27	<	<	X
ejpam-5637	280	28	ϵ.	ϵ.	NOUN
ejpam-5637	281	1	the	the	DET
ejpam-5637	281	2	third	third	ADJ
ejpam-5637	281	3	characterization	characterization	NOUN
ejpam-5637	281	4	of	of	ADP
ejpam-5637	281	5	pseudo	pseudo	NOUN
ejpam-5637	281	6	-	-	NOUN
ejpam-5637	281	7	spectrum	spectrum	NOUN
ejpam-5637	281	8	is	be	AUX
ejpam-5637	281	9	given	give	VERB
ejpam-5637	281	10	as	as	ADP
ejpam-5637	281	11	bellow	bellow	ADJ
ejpam-5637	281	12	.	.	PUNCT
ejpam-5637	282	1	definition	definition	NOUN
ejpam-5637	282	2	6	6	NUM
ejpam-5637	282	3	.	.	PUNCT
ejpam-5637	283	1	let	let	VERB
ejpam-5637	283	2	m	m	PRON
ejpam-5637	283	3	be	be	AUX
ejpam-5637	283	4	a	a	DET
ejpam-5637	283	5	given	give	VERB
ejpam-5637	283	6	n	n	CCONJ
ejpam-5637	283	7	-	-	PUNCT
ejpam-5637	283	8	dimensional	dimensional	ADJ
ejpam-5637	283	9	matrix	matrix	NOUN
ejpam-5637	283	10	,	,	PUNCT
ejpam-5637	283	11	ϵ	ϵ	X
ejpam-5637	283	12	>	>	X
ejpam-5637	283	13	0	0	PROPN
ejpam-5637	283	14	,	,	PUNCT
ejpam-5637	283	15	a	a	DET
ejpam-5637	283	16	small	small	ADJ
ejpam-5637	283	17	perturbation	perturbation	NOUN
ejpam-5637	283	18	.	.	PUNCT
ejpam-5637	284	1	the	the	DET
ejpam-5637	284	2	ϵ-pseudo	ϵ-pseudo	PROPN
ejpam-5637	284	3	spectrum	spectrum	NOUN
ejpam-5637	284	4	σϵ(m	σϵ(m	ADV
ejpam-5637	284	5	)	)	PUNCT
ejpam-5637	284	6	is	be	AUX
ejpam-5637	284	7	the	the	DET
ejpam-5637	284	8	set	set	NOUN
ejpam-5637	284	9	of	of	ADP
ejpam-5637	284	10	eigenvalues	eigenvalue	NOUN
ejpam-5637	284	11	λ	λ	X
ejpam-5637	284	12	∈	∈	PROPN
ejpam-5637	284	13	c	c	NOUN
ejpam-5637	284	14	such	such	ADJ
ejpam-5637	284	15	that	that	DET
ejpam-5637	284	16	||(λin	||(λin	PROPN
ejpam-5637	284	17	−m)v||	−m)v||	PROPN
ejpam-5637	284	18	<	<	X
ejpam-5637	284	19	ϵ	ϵ	NOUN
ejpam-5637	284	20	for	for	ADP
ejpam-5637	284	21	some	some	DET
ejpam-5637	284	22	v	v	ADP
ejpam-5637	284	23	∈	∈	PROPN
ejpam-5637	284	24	cn,1	cn,1	PROPN
ejpam-5637	284	25	,	,	PUNCT
ejpam-5637	284	26	||v||	||v||	PROPN
ejpam-5637	284	27	=	=	SYM
ejpam-5637	284	28	1	1	X
ejpam-5637	284	29	.	.	PUNCT
ejpam-5637	285	1	the	the	DET
ejpam-5637	285	2	following	follow	VERB
ejpam-5637	285	3	theorem	theorem	NOUN
ejpam-5637	285	4	gives	give	VERB
ejpam-5637	285	5	an	an	DET
ejpam-5637	285	6	equivalence	equivalence	NOUN
ejpam-5637	285	7	of	of	ADP
ejpam-5637	285	8	all	all	DET
ejpam-5637	285	9	above	above	ADJ
ejpam-5637	285	10	definitions	definition	NOUN
ejpam-5637	285	11	of	of	ADP
ejpam-5637	285	12	pseudo	pseudo	NOUN
ejpam-5637	285	13	-	-	NOUN
ejpam-5637	285	14	spectrum	spectrum	NOUN
ejpam-5637	285	15	.	.	PUNCT
ejpam-5637	286	1	theorem	theorem	NOUN
ejpam-5637	286	2	12	12	NUM
ejpam-5637	286	3	.	.	PUNCT
ejpam-5637	287	1	[	[	X
ejpam-5637	287	2	13	13	NUM
ejpam-5637	287	3	]	]	PUNCT
ejpam-5637	287	4	let	let	VERB
ejpam-5637	287	5	||	||	NOUN
ejpam-5637	287	6	·	·	PUNCT
ejpam-5637	288	1	||	||	NUM
ejpam-5637	288	2	denotes	denote	VERB
ejpam-5637	288	3	a	a	DET
ejpam-5637	288	4	matrix	matrix	NOUN
ejpam-5637	288	5	norm	norm	NOUN
ejpam-5637	288	6	for	for	ADP
ejpam-5637	288	7	a	a	DET
ejpam-5637	288	8	matrix	matrix	NOUN
ejpam-5637	288	9	m	m	VERB
ejpam-5637	288	10	which	which	PRON
ejpam-5637	288	11	is	be	AUX
ejpam-5637	288	12	induced	induce	VERB
ejpam-5637	288	13	by	by	ADP
ejpam-5637	288	14	a	a	DET
ejpam-5637	288	15	vector	vector	NOUN
ejpam-5637	288	16	norm	norm	NOUN
ejpam-5637	288	17	.	.	PUNCT
ejpam-5637	289	1	then	then	ADV
ejpam-5637	289	2	following	follow	VERB
ejpam-5637	289	3	are	be	AUX
ejpam-5637	289	4	equivalent	equivalent	ADJ
ejpam-5637	289	5	:	:	PUNCT
ejpam-5637	289	6	(	(	PUNCT
ejpam-5637	289	7	i	i	NOUN
ejpam-5637	289	8	)	)	PUNCT
ejpam-5637	289	9	λϵ(m	λϵ(m	PUNCT
ejpam-5637	289	10	)	)	PUNCT
ejpam-5637	290	1	=	=	PRON
ejpam-5637	290	2	{	{	PUNCT
ejpam-5637	290	3	z	z	NOUN
ejpam-5637	290	4	∈	∈	PROPN
ejpam-5637	290	5	c	c	NOUN
ejpam-5637	290	6	:	:	PUNCT
ejpam-5637	290	7	||(zin	||(zin	ADP
ejpam-5637	290	8	−m)−1||	−m)−1||	PROPN
ejpam-5637	290	9	≥	≥	NUM
ejpam-5637	290	10	1	1	NUM
ejpam-5637	290	11	ϵ	ϵ	NOUN
ejpam-5637	290	12	}	}	PUNCT
ejpam-5637	290	13	.	.	PUNCT
ejpam-5637	291	1	(	(	PUNCT
ejpam-5637	291	2	ii	ii	NOUN
ejpam-5637	291	3	)	)	PUNCT
ejpam-5637	291	4	λϵ(m	λϵ(m	PUNCT
ejpam-5637	291	5	)	)	PUNCT
ejpam-5637	292	1	=	=	PRON
ejpam-5637	292	2	{	{	PUNCT
ejpam-5637	292	3	z	z	NOUN
ejpam-5637	292	4	∈	∈	PROPN
ejpam-5637	292	5	c	c	NOUN
ejpam-5637	292	6	:	:	PUNCT
ejpam-5637	292	7	z	z	PROPN
ejpam-5637	292	8	∈	∈	PROPN
ejpam-5637	293	1	λ(m	λ(m	PROPN
ejpam-5637	293	2	+	+	CCONJ
ejpam-5637	293	3	e	e	NOUN
ejpam-5637	293	4	)	)	PUNCT
ejpam-5637	293	5	,	,	PUNCT
ejpam-5637	293	6	||e||	||e||	VERB
ejpam-5637	293	7	≤	≤	NOUN
ejpam-5637	293	8	ϵ	ϵ	X
ejpam-5637	293	9	}	}	PUNCT
ejpam-5637	293	10	.	.	PUNCT
ejpam-5637	294	1	(	(	PUNCT
ejpam-5637	294	2	iii	iii	NOUN
ejpam-5637	294	3	)	)	PUNCT
ejpam-5637	294	4	λϵ(m	λϵ(m	PUNCT
ejpam-5637	294	5	)	)	PUNCT
ejpam-5637	295	1	=	=	PRON
ejpam-5637	295	2	{	{	PUNCT
ejpam-5637	295	3	z	z	NOUN
ejpam-5637	295	4	∈	∈	PROPN
ejpam-5637	295	5	c	c	NOUN
ejpam-5637	295	6	:	:	PUNCT
ejpam-5637	295	7	∃	∃	PROPN
ejpam-5637	295	8	v	v	NOUN
ejpam-5637	295	9	∈	∈	PROPN
ejpam-5637	295	10	cn,1	cn,1	PROPN
ejpam-5637	295	11	s.t	s.t	PROPN
ejpam-5637	295	12	||(m	||(m	NOUN
ejpam-5637	295	13	−	−	PROPN
ejpam-5637	296	1	zin)v||	zin)v||	PROPN
ejpam-5637	296	2	≤	≤	NOUN
ejpam-5637	296	3	ϵ	ϵ	X
ejpam-5637	296	4	}	}	PUNCT
ejpam-5637	296	5	.	.	PUNCT
ejpam-5637	297	1	remark	remark	PROPN
ejpam-5637	297	2	1	1	NUM
ejpam-5637	297	3	.	.	PUNCT
ejpam-5637	298	1	in	in	ADP
ejpam-5637	298	2	above	above	ADP
ejpam-5637	298	3	theorem	theorem	NOUN
ejpam-5637	298	4	12	12	NUM
ejpam-5637	298	5	,	,	PUNCT
ejpam-5637	298	6	the	the	DET
ejpam-5637	298	7	second	second	ADJ
ejpam-5637	298	8	statement	statement	NOUN
ejpam-5637	298	9	is	be	AUX
ejpam-5637	298	10	true	true	ADJ
ejpam-5637	298	11	for	for	ADP
ejpam-5637	298	12	some	some	DET
ejpam-5637	298	13	matrix	matrix	NOUN
ejpam-5637	298	14	e.	e.	PROPN
ejpam-5637	298	15	also	also	ADV
ejpam-5637	298	16	,	,	PUNCT
ejpam-5637	298	17	in	in	ADP
ejpam-5637	298	18	the	the	DET
ejpam-5637	298	19	last	last	ADJ
ejpam-5637	298	20	statement	statement	NOUN
ejpam-5637	298	21	the	the	DET
ejpam-5637	298	22	column	column	NOUN
ejpam-5637	298	23	vector	vector	NOUN
ejpam-5637	298	24	v	v	PROPN
ejpam-5637	298	25	is	be	AUX
ejpam-5637	298	26	such	such	ADJ
ejpam-5637	298	27	that	that	PRON
ejpam-5637	298	28	||v||2	||v||2	ADJ
ejpam-5637	298	29	=	=	SYM
ejpam-5637	298	30	1	1	NUM
ejpam-5637	298	31	.	.	NOUN
ejpam-5637	298	32	4	4	NUM
ejpam-5637	298	33	.	.	NOUN
ejpam-5637	298	34	numerical	numerical	ADJ
ejpam-5637	298	35	experimentation	experimentation	NOUN
ejpam-5637	298	36	we	we	PRON
ejpam-5637	298	37	present	present	VERB
ejpam-5637	298	38	a	a	DET
ejpam-5637	298	39	comparison	comparison	NOUN
ejpam-5637	298	40	on	on	ADP
ejpam-5637	298	41	the	the	DET
ejpam-5637	298	42	numerical	numerical	ADJ
ejpam-5637	298	43	approximation	approximation	NOUN
ejpam-5637	298	44	of	of	ADP
ejpam-5637	298	45	structured	structured	ADJ
ejpam-5637	298	46	singular	singular	ADJ
ejpam-5637	298	47	values	value	NOUN
ejpam-5637	298	48	.	.	PUNCT
ejpam-5637	299	1	the	the	DET
ejpam-5637	299	2	numerical	numerical	ADJ
ejpam-5637	299	3	algorithms	algorithm	NOUN
ejpam-5637	299	4	are	be	AUX
ejpam-5637	299	5	:	:	PUNCT
ejpam-5637	299	6	the	the	DET
ejpam-5637	299	7	matlab	matlab	PROPN
ejpam-5637	299	8	function	function	PROPN
ejpam-5637	299	9	mussv	mussv	PROPN
ejpam-5637	299	10	,	,	PUNCT
ejpam-5637	299	11	the	the	DET
ejpam-5637	299	12	power	power	NOUN
ejpam-5637	299	13	algorithm	algorithm	NOUN
ejpam-5637	299	14	(	(	PUNCT
ejpam-5637	299	15	pa	pa	PROPN
ejpam-5637	299	16	)	)	PUNCT
ejpam-5637	300	1	[	[	X
ejpam-5637	300	2	36	36	NUM
ejpam-5637	300	3	]	]	PUNCT
ejpam-5637	300	4	,	,	PUNCT
ejpam-5637	300	5	gain	gain	VERB
ejpam-5637	300	6	based	base	VERB
ejpam-5637	300	7	algorithm	algorithm	NOUN
ejpam-5637	300	8	(	(	PUNCT
ejpam-5637	300	9	gba	gba	NOUN
ejpam-5637	300	10	)	)	PUNCT
ejpam-5637	301	1	[	[	X
ejpam-5637	301	2	44	44	NUM
ejpam-5637	301	3	]	]	PUNCT
ejpam-5637	301	4	,	,	PUNCT
ejpam-5637	301	5	poles	pole	NOUN
ejpam-5637	301	6	migration	migration	NOUN
ejpam-5637	301	7	algorithm	algorithm	NOUN
ejpam-5637	301	8	(	(	PUNCT
ejpam-5637	301	9	pma	pma	NOUN
ejpam-5637	301	10	)	)	PUNCT
ejpam-5637	302	1	[	[	X
ejpam-5637	302	2	30	30	NUM
ejpam-5637	302	3	]	]	PUNCT
ejpam-5637	302	4	,	,	PUNCT
ejpam-5637	302	5	non	non	ADJ
ejpam-5637	302	6	-	-	ADJ
ejpam-5637	302	7	linear	linear	ADJ
ejpam-5637	302	8	optimization	optimization	NOUN
ejpam-5637	302	9	algorithm	algorithm	NOUN
ejpam-5637	302	10	(	(	PUNCT
ejpam-5637	302	11	nla	nla	NOUN
ejpam-5637	302	12	)	)	PUNCT
ejpam-5637	303	1	[	[	X
ejpam-5637	303	2	23	23	NUM
ejpam-5637	303	3	]	]	PUNCT
ejpam-5637	303	4	,	,	PUNCT
ejpam-5637	303	5	and	and	CCONJ
ejpam-5637	303	6	the	the	DET
ejpam-5637	303	7	low	low	ADJ
ejpam-5637	303	8	-	-	PUNCT
ejpam-5637	303	9	rank	rank	NOUN
ejpam-5637	303	10	ode	ode	PROPN
ejpam-5637	303	11	’s	’s	PART
ejpam-5637	303	12	based	base	VERB
ejpam-5637	303	13	algorithm	algorithm	NOUN
ejpam-5637	303	14	(	(	PUNCT
ejpam-5637	303	15	lra	lra	NOUN
ejpam-5637	303	16	)	)	PUNCT
ejpam-5637	303	17	given	give	VERB
ejpam-5637	303	18	by	by	ADP
ejpam-5637	303	19	first	first	ADJ
ejpam-5637	303	20	author	author	NOUN
ejpam-5637	303	21	[	[	X
ejpam-5637	303	22	21	21	NUM
ejpam-5637	303	23	]	]	PUNCT
ejpam-5637	303	24	.	.	PUNCT
ejpam-5637	304	1	we	we	PRON
ejpam-5637	304	2	consider	consider	VERB
ejpam-5637	304	3	structured	structured	ADJ
ejpam-5637	304	4	matrices	matrix	NOUN
ejpam-5637	304	5	appearing	appear	VERB
ejpam-5637	304	6	across	across	ADP
ejpam-5637	304	7	transportation	transportation	NOUN
ejpam-5637	304	8	models	model	NOUN
ejpam-5637	304	9	.	.	PUNCT
ejpam-5637	305	1	the	the	DET
ejpam-5637	305	2	matlab	matlab	PROPN
ejpam-5637	305	3	eigtool	eigtool	NOUN
ejpam-5637	305	4	[	[	X
ejpam-5637	305	5	13	13	NUM
ejpam-5637	305	6	]	]	PUNCT
ejpam-5637	305	7	is	be	AUX
ejpam-5637	305	8	being	be	AUX
ejpam-5637	305	9	used	use	VERB
ejpam-5637	305	10	for	for	ADP
ejpam-5637	305	11	graphical	graphical	ADJ
ejpam-5637	305	12	interpretation	interpretation	NOUN
ejpam-5637	305	13	of	of	ADP
ejpam-5637	305	14	the	the	DET
ejpam-5637	305	15	pseudospectrum	pseudospectrum	NOUN
ejpam-5637	305	16	.	.	PUNCT
ejpam-5637	306	1	in	in	ADP
ejpam-5637	306	2	each	each	DET
ejpam-5637	306	3	example	example	NOUN
ejpam-5637	306	4	,	,	PUNCT
ejpam-5637	306	5	we	we	PRON
ejpam-5637	306	6	have	have	AUX
ejpam-5637	306	7	shown	show	VERB
ejpam-5637	306	8	different	different	ADJ
ejpam-5637	306	9	graphics	graphic	NOUN
ejpam-5637	306	10	.	.	PUNCT
ejpam-5637	307	1	the	the	DET
ejpam-5637	307	2	graphical	graphical	ADJ
ejpam-5637	307	3	representations	representation	NOUN
ejpam-5637	307	4	in	in	ADP
ejpam-5637	307	5	a	a	DET
ejpam-5637	307	6	2	2	NUM
ejpam-5637	307	7	-	-	PUNCT
ejpam-5637	307	8	dimensional	dimensional	ADJ
ejpam-5637	307	9	space	space	NOUN
ejpam-5637	307	10	presents	present	VERB
ejpam-5637	307	11	the	the	DET
ejpam-5637	307	12	spectrum	spectrum	NOUN
ejpam-5637	307	13	and	and	CCONJ
ejpam-5637	307	14	pseudo	pseudo	NOUN
ejpam-5637	307	15	-	-	NOUN
ejpam-5637	307	16	spectrum	spectrum	NOUN
ejpam-5637	307	17	of	of	ADP
ejpam-5637	307	18	structured	structured	ADJ
ejpam-5637	307	19	matrices	matrix	NOUN
ejpam-5637	307	20	.	.	PUNCT
ejpam-5637	308	1	the	the	DET
ejpam-5637	308	2	black	black	ADJ
ejpam-5637	308	3	dots	dot	NOUN
ejpam-5637	308	4	around	around	ADP
ejpam-5637	308	5	the	the	DET
ejpam-5637	308	6	spectrum	spectrum	NOUN
ejpam-5637	308	7	and	and	CCONJ
ejpam-5637	308	8	pseudo	pseudo	NOUN
ejpam-5637	308	9	-	-	ADJ
ejpam-5637	308	10	spectrum	spectrum	NOUN
ejpam-5637	308	11	denotes	denote	NOUN
ejpam-5637	308	12	the	the	DET
ejpam-5637	308	13	field	field	NOUN
ejpam-5637	308	14	of	of	ADP
ejpam-5637	308	15	values	value	NOUN
ejpam-5637	308	16	enclosing	enclose	VERB
ejpam-5637	308	17	spectrum	spectrum	NOUN
ejpam-5637	308	18	and	and	CCONJ
ejpam-5637	308	19	pseudo	pseudo	NOUN
ejpam-5637	308	20	-	-	NOUN
ejpam-5637	308	21	spectrum	spectrum	NOUN
ejpam-5637	308	22	.	.	PUNCT
ejpam-5637	309	1	the	the	DET
ejpam-5637	309	2	visualization	visualization	NOUN
ejpam-5637	309	3	of	of	ADP
ejpam-5637	309	4	the	the	DET
ejpam-5637	309	5	pseudo	pseudo	NOUN
ejpam-5637	309	6	-	-	NOUN
ejpam-5637	309	7	spectrum	spectrum	NOUN
ejpam-5637	309	8	in	in	ADP
ejpam-5637	309	9	the	the	DET
ejpam-5637	309	10	complex	complex	ADJ
ejpam-5637	309	11	plane	plane	NOUN
ejpam-5637	309	12	are	be	AUX
ejpam-5637	309	13	level	level	NOUN
ejpam-5637	309	14	sets	set	NOUN
ejpam-5637	309	15	of	of	ADP
ejpam-5637	309	16	the	the	DET
ejpam-5637	309	17	resolvent	resolvent	ADJ
ejpam-5637	309	18	norm	norm	NOUN
ejpam-5637	309	19	||(m	||(m	NOUN
ejpam-5637	310	1	−	−	PROPN
ejpam-5637	310	2	zin)−1||	zin)−1||	PROPN
ejpam-5637	310	3	which	which	PRON
ejpam-5637	310	4	indicates	indicate	VERB
ejpam-5637	310	5	various	various	ADJ
ejpam-5637	310	6	ϵ-values	ϵ-value	NOUN
ejpam-5637	310	7	.	.	PUNCT
ejpam-5637	311	1	these	these	DET
ejpam-5637	311	2	visualizations	visualization	NOUN
ejpam-5637	311	3	of	of	ADP
ejpam-5637	311	4	the	the	DET
ejpam-5637	311	5	level	level	NOUN
ejpam-5637	311	6	sets	set	NOUN
ejpam-5637	311	7	helps	help	VERB
ejpam-5637	311	8	to	to	PART
ejpam-5637	311	9	analyze	analyze	VERB
ejpam-5637	311	10	the	the	DET
ejpam-5637	311	11	stability	stability	NOUN
ejpam-5637	311	12	analysis	analysis	NOUN
ejpam-5637	311	13	and	and	CCONJ
ejpam-5637	311	14	robustness	robustness	NOUN
ejpam-5637	311	15	in	in	ADP
ejpam-5637	311	16	various	various	ADJ
ejpam-5637	311	17	applications	application	NOUN
ejpam-5637	311	18	like	like	ADP
ejpam-5637	311	19	control	control	NOUN
ejpam-5637	311	20	systems	system	NOUN
ejpam-5637	311	21	and	and	CCONJ
ejpam-5637	311	22	fluid	fluid	ADJ
ejpam-5637	311	23	dynamics	dynamic	NOUN
ejpam-5637	311	24	.	.	PUNCT
ejpam-5637	312	1	m.u	m.u	PROPN
ejpam-5637	312	2	.	.	PROPN
ejpam-5637	313	1	rahman	rahman	PROPN
ejpam-5637	313	2	et	et	PROPN
ejpam-5637	313	3	al	al	PROPN
ejpam-5637	313	4	.	.	PUNCT
ejpam-5637	313	5	/	/	SYM
ejpam-5637	313	6	eur	eur	PROPN
ejpam-5637	313	7	.	.	PUNCT
ejpam-5637	314	1	j.	j.	PROPN
ejpam-5637	314	2	pure	pure	PROPN
ejpam-5637	314	3	appl	appl	PROPN
ejpam-5637	314	4	.	.	PROPN
ejpam-5637	314	5	math	math	PROPN
ejpam-5637	314	6	,	,	PUNCT
ejpam-5637	314	7	18	18	NUM
ejpam-5637	314	8	(	(	PUNCT
ejpam-5637	314	9	1	1	NUM
ejpam-5637	314	10	)	)	PUNCT
ejpam-5637	314	11	(	(	PUNCT
ejpam-5637	314	12	2025	2025	NUM
ejpam-5637	314	13	)	)	PUNCT
ejpam-5637	314	14	,	,	PUNCT
ejpam-5637	314	15	5637	5637	NUM
ejpam-5637	314	16	15	15	NUM
ejpam-5637	314	17	of	of	ADP
ejpam-5637	314	18	20	20	NUM
ejpam-5637	314	19	(	(	PUNCT
ejpam-5637	314	20	a	a	NOUN
ejpam-5637	314	21	)	)	PUNCT
ejpam-5637	314	22	field	field	NOUN
ejpam-5637	314	23	of	of	ADP
ejpam-5637	314	24	values	value	NOUN
ejpam-5637	314	25	enclosing	enclose	VERB
ejpam-5637	314	26	spectrum	spectrum	NOUN
ejpam-5637	314	27	and	and	CCONJ
ejpam-5637	314	28	pseudo	pseudo	NOUN
ejpam-5637	314	29	-	-	NOUN
ejpam-5637	314	30	spectrum	spectrum	ADJ
ejpam-5637	314	31	(	(	PUNCT
ejpam-5637	314	32	b	b	NOUN
ejpam-5637	314	33	)	)	PUNCT
ejpam-5637	314	34	resolvent	resolvent	ADJ
ejpam-5637	314	35	norm	norm	NOUN
ejpam-5637	314	36	figure	figure	NOUN
ejpam-5637	314	37	4	4	NUM
ejpam-5637	314	38	:	:	PUNCT
ejpam-5637	314	39	pseudo	pseudo	NOUN
ejpam-5637	314	40	-	-	NOUN
ejpam-5637	314	41	spectrum	spectrum	NOUN
ejpam-5637	314	42	of	of	ADP
ejpam-5637	314	43	a	a	PRON
ejpam-5637	314	44	in	in	ADP
ejpam-5637	314	45	example-1	example-1	NOUN
ejpam-5637	314	46	example	example	NOUN
ejpam-5637	314	47	1	1	NUM
ejpam-5637	314	48	.	.	X
ejpam-5637	314	49	consider	consider	VERB
ejpam-5637	314	50	4	4	NUM
ejpam-5637	314	51	-	-	PUNCT
ejpam-5637	314	52	dimensional	dimensional	ADJ
ejpam-5637	314	53	matrix	matrix	NOUN
ejpam-5637	314	54	for	for	ADP
ejpam-5637	314	55	traveling	travel	VERB
ejpam-5637	314	56	salesman	salesman	ADJ
ejpam-5637	314	57	problem	problem	NOUN
ejpam-5637	314	58	[	[	X
ejpam-5637	314	59	39	39	NUM
ejpam-5637	314	60	]	]	PUNCT
ejpam-5637	314	61	.	.	PUNCT
ejpam-5637	315	1	a	a	DET
ejpam-5637	315	2	=	=	PUNCT
ejpam-5637	315	3			ADJ
ejpam-5637	315	4	−1	−1	NOUN
ejpam-5637	315	5	1	1	NUM
ejpam-5637	315	6	0	0	NUM
ejpam-5637	315	7	0	0	NUM
ejpam-5637	315	8	1	1	NUM
ejpam-5637	315	9	1	1	NUM
ejpam-5637	315	10	0	0	NUM
ejpam-5637	315	11	0	0	NUM
ejpam-5637	315	12	0	0	NUM
ejpam-5637	315	13	1	1	NUM
ejpam-5637	315	14	1	1	NUM
ejpam-5637	315	15	1	1	NUM
ejpam-5637	315	16	3	3	NUM
ejpam-5637	315	17	0	0	NUM
ejpam-5637	315	18	2	2	NUM
ejpam-5637	315	19	1	1	NUM
ejpam-5637	315	20			NOUN
ejpam-5637	315	21	.	.	PUNCT
ejpam-5637	316	1	we	we	PRON
ejpam-5637	316	2	present	present	VERB
ejpam-5637	316	3	the	the	DET
ejpam-5637	316	4	comparison	comparison	NOUN
ejpam-5637	316	5	on	on	ADP
ejpam-5637	316	6	numerical	numerical	ADJ
ejpam-5637	316	7	approximation	approximation	NOUN
ejpam-5637	316	8	of	of	ADP
ejpam-5637	316	9	the	the	DET
ejpam-5637	316	10	lower	low	ADJ
ejpam-5637	316	11	bounds	bound	NOUN
ejpam-5637	316	12	of	of	ADP
ejpam-5637	316	13	structured	structured	ADJ
ejpam-5637	316	14	singular	singular	ADJ
ejpam-5637	316	15	values	value	NOUN
ejpam-5637	316	16	in	in	ADP
ejpam-5637	316	17	following	follow	VERB
ejpam-5637	316	18	table-1	table-1	NUM
ejpam-5637	316	19	.	.	PUNCT
ejpam-5637	317	1	the	the	DET
ejpam-5637	317	2	numerical	numerical	ADJ
ejpam-5637	317	3	approximation	approximation	NOUN
ejpam-5637	317	4	of	of	ADP
ejpam-5637	317	5	lower	low	ADJ
ejpam-5637	317	6	bounds	bound	NOUN
ejpam-5637	317	7	of	of	ADP
ejpam-5637	317	8	structured	structured	ADJ
ejpam-5637	317	9	singular	singular	ADJ
ejpam-5637	317	10	values	value	NOUN
ejpam-5637	317	11	mussv	mussv	VERB
ejpam-5637	317	12	pa	pa	PROPN
ejpam-5637	317	13	gba	gba	PROPN
ejpam-5637	317	14	pma	pma	PROPN
ejpam-5637	317	15	nla	nla	PROPN
ejpam-5637	317	16	lra	lra	PROPN
ejpam-5637	317	17	3.9984	3.9984	NUM
ejpam-5637	317	18	3.9992	3.9992	NUM
ejpam-5637	317	19	3.9987	3.9987	NUM
ejpam-5637	317	20	3.9990	3.9990	NUM
ejpam-5637	317	21	3.9988	3.9988	NUM
ejpam-5637	317	22	3.9985	3.9985	NUM
ejpam-5637	317	23	example	example	NOUN
ejpam-5637	317	24	2	2	NUM
ejpam-5637	317	25	.	.	X
ejpam-5637	317	26	consider	consider	VERB
ejpam-5637	317	27	6	6	NUM
ejpam-5637	317	28	-	-	PUNCT
ejpam-5637	317	29	dimensional	dimensional	ADJ
ejpam-5637	317	30	symmetric	symmetric	ADJ
ejpam-5637	317	31	circulant	circulant	NOUN
ejpam-5637	317	32	matrix	matrix	NOUN
ejpam-5637	317	33	for	for	ADP
ejpam-5637	317	34	travelling	travel	VERB
ejpam-5637	317	35	salesman	salesman	ADJ
ejpam-5637	317	36	problem	problem	NOUN
ejpam-5637	317	37	[	[	X
ejpam-5637	317	38	50	50	NUM
ejpam-5637	317	39	]	]	PUNCT
ejpam-5637	317	40	.	.	PUNCT
ejpam-5637	318	1	a	a	DET
ejpam-5637	318	2	=	=	ADJ
ejpam-5637	318	3			NOUN
ejpam-5637	318	4	0	0	NUM
ejpam-5637	318	5	4	4	NUM
ejpam-5637	318	6	1	1	NUM
ejpam-5637	318	7	6	6	NUM
ejpam-5637	318	8	1	1	NUM
ejpam-5637	318	9	4	4	NUM
ejpam-5637	318	10	4	4	NUM
ejpam-5637	318	11	0	0	NUM
ejpam-5637	318	12	4	4	NUM
ejpam-5637	318	13	1	1	NUM
ejpam-5637	318	14	6	6	NUM
ejpam-5637	318	15	1	1	NUM
ejpam-5637	318	16	1	1	NUM
ejpam-5637	318	17	4	4	NUM
ejpam-5637	318	18	0	0	NUM
ejpam-5637	318	19	4	4	NUM
ejpam-5637	318	20	1	1	NUM
ejpam-5637	318	21	6	6	NUM
ejpam-5637	318	22	6	6	NUM
ejpam-5637	318	23	1	1	NUM
ejpam-5637	318	24	4	4	NUM
ejpam-5637	318	25	0	0	NUM
ejpam-5637	318	26	4	4	NUM
ejpam-5637	318	27	1	1	NUM
ejpam-5637	318	28	1	1	NUM
ejpam-5637	318	29	6	6	NUM
ejpam-5637	318	30	1	1	NUM
ejpam-5637	318	31	4	4	NUM
ejpam-5637	318	32	0	0	NUM
ejpam-5637	318	33	4	4	NUM
ejpam-5637	318	34	4	4	NUM
ejpam-5637	318	35	1	1	NUM
ejpam-5637	318	36	6	6	NUM
ejpam-5637	318	37	1	1	NUM
ejpam-5637	318	38	4	4	NUM
ejpam-5637	318	39	0	0	NUM
ejpam-5637	318	40			NOUN
ejpam-5637	318	41	.	.	PUNCT
ejpam-5637	319	1	we	we	PRON
ejpam-5637	319	2	present	present	VERB
ejpam-5637	319	3	the	the	DET
ejpam-5637	319	4	comparison	comparison	NOUN
ejpam-5637	319	5	on	on	ADP
ejpam-5637	319	6	numerical	numerical	ADJ
ejpam-5637	319	7	approximation	approximation	NOUN
ejpam-5637	319	8	of	of	ADP
ejpam-5637	319	9	the	the	DET
ejpam-5637	319	10	lower	low	ADJ
ejpam-5637	319	11	bounds	bound	NOUN
ejpam-5637	319	12	of	of	ADP
ejpam-5637	319	13	structured	structured	ADJ
ejpam-5637	319	14	singular	singular	ADJ
ejpam-5637	319	15	values	value	NOUN
ejpam-5637	319	16	in	in	ADP
ejpam-5637	319	17	following	follow	VERB
ejpam-5637	319	18	table-2	table-2	PROPN
ejpam-5637	319	19	.	.	PUNCT
ejpam-5637	320	1	the	the	DET
ejpam-5637	320	2	numerical	numerical	ADJ
ejpam-5637	320	3	approximation	approximation	NOUN
ejpam-5637	320	4	of	of	ADP
ejpam-5637	320	5	lower	low	ADJ
ejpam-5637	320	6	bounds	bound	NOUN
ejpam-5637	320	7	of	of	ADP
ejpam-5637	320	8	structured	structured	ADJ
ejpam-5637	320	9	singular	singular	ADJ
ejpam-5637	320	10	values	value	NOUN
ejpam-5637	320	11	mussv	mussv	VERB
ejpam-5637	320	12	pa	pa	PROPN
ejpam-5637	320	13	gba	gba	PROPN
ejpam-5637	320	14	pma	pma	PROPN
ejpam-5637	320	15	nla	nla	PROPN
ejpam-5637	320	16	lra	lra	PROPN
ejpam-5637	320	17	3.9984	3.9984	NUM
ejpam-5637	320	18	3.9992	3.9992	NUM
ejpam-5637	320	19	3.9987	3.9987	NUM
ejpam-5637	320	20	3.9990	3.9990	NUM
ejpam-5637	320	21	3.9988	3.9988	NUM
ejpam-5637	320	22	3.9985	3.9985	NUM
ejpam-5637	320	23	m.u	m.u	PROPN
ejpam-5637	320	24	.	.	PUNCT
ejpam-5637	321	1	rahman	rahman	PROPN
ejpam-5637	321	2	et	et	PROPN
ejpam-5637	321	3	al	al	PROPN
ejpam-5637	321	4	.	.	PUNCT
ejpam-5637	321	5	/	/	SYM
ejpam-5637	321	6	eur	eur	PROPN
ejpam-5637	321	7	.	.	PUNCT
ejpam-5637	322	1	j.	j.	PROPN
ejpam-5637	322	2	pure	pure	PROPN
ejpam-5637	322	3	appl	appl	PROPN
ejpam-5637	322	4	.	.	PROPN
ejpam-5637	322	5	math	math	PROPN
ejpam-5637	322	6	,	,	PUNCT
ejpam-5637	322	7	18	18	NUM
ejpam-5637	322	8	(	(	PUNCT
ejpam-5637	322	9	1	1	NUM
ejpam-5637	322	10	)	)	PUNCT
ejpam-5637	322	11	(	(	PUNCT
ejpam-5637	322	12	2025	2025	NUM
ejpam-5637	322	13	)	)	PUNCT
ejpam-5637	322	14	,	,	PUNCT
ejpam-5637	322	15	5637	5637	NUM
ejpam-5637	322	16	16	16	NUM
ejpam-5637	322	17	of	of	ADP
ejpam-5637	322	18	20	20	NUM
ejpam-5637	322	19	(	(	PUNCT
ejpam-5637	322	20	a	a	NOUN
ejpam-5637	322	21	)	)	PUNCT
ejpam-5637	322	22	field	field	NOUN
ejpam-5637	322	23	of	of	ADP
ejpam-5637	322	24	values	value	NOUN
ejpam-5637	322	25	enclosing	enclose	VERB
ejpam-5637	322	26	spectrum	spectrum	NOUN
ejpam-5637	322	27	and	and	CCONJ
ejpam-5637	322	28	pseudo	pseudo	NOUN
ejpam-5637	322	29	-	-	NOUN
ejpam-5637	322	30	spectrum	spectrum	ADJ
ejpam-5637	322	31	(	(	PUNCT
ejpam-5637	322	32	b	b	NOUN
ejpam-5637	322	33	)	)	PUNCT
ejpam-5637	322	34	resolvent	resolvent	ADJ
ejpam-5637	322	35	norm	norm	NOUN
ejpam-5637	322	36	figure	figure	NOUN
ejpam-5637	322	37	5	5	NUM
ejpam-5637	322	38	:	:	PUNCT
ejpam-5637	322	39	pseudo	pseudo	NOUN
ejpam-5637	322	40	-	-	NOUN
ejpam-5637	322	41	spectrum	spectrum	NOUN
ejpam-5637	322	42	of	of	ADP
ejpam-5637	322	43	a	a	PRON
ejpam-5637	322	44	in	in	ADP
ejpam-5637	322	45	example-2	example-2	NUM
ejpam-5637	322	46	example	example	NOUN
ejpam-5637	322	47	3	3	NUM
ejpam-5637	322	48	.	.	X
ejpam-5637	322	49	consider	consider	VERB
ejpam-5637	322	50	4	4	NUM
ejpam-5637	322	51	-	-	PUNCT
ejpam-5637	322	52	dimensional	dimensional	ADJ
ejpam-5637	322	53	matrix	matrix	NOUN
ejpam-5637	322	54	taken	take	VERB
ejpam-5637	322	55	from	from	ADP
ejpam-5637	322	56	[	[	X
ejpam-5637	322	57	41	41	NUM
ejpam-5637	322	58	]	]	PUNCT
ejpam-5637	322	59	.	.	PUNCT
ejpam-5637	323	1	a	a	DET
ejpam-5637	323	2	=	=	PUNCT
ejpam-5637	323	3			ADJ
ejpam-5637	323	4	3	3	NUM
ejpam-5637	323	5	5	5	NUM
ejpam-5637	323	6	1	1	NUM
ejpam-5637	323	7	−2	−2	NOUN
ejpam-5637	323	8	0	0	NUM
ejpam-5637	323	9	−1	−1	NOUN
ejpam-5637	323	10	5	5	NUM
ejpam-5637	323	11	10	10	NUM
ejpam-5637	323	12	3	3	NUM
ejpam-5637	323	13	5	5	NUM
ejpam-5637	323	14	1	1	NUM
ejpam-5637	323	15	9	9	NUM
ejpam-5637	323	16	−2	−2	NOUN
ejpam-5637	323	17	1	1	NUM
ejpam-5637	323	18	6	6	NUM
ejpam-5637	323	19	6	6	NUM
ejpam-5637	323	20			NOUN
ejpam-5637	323	21	.	.	PUNCT
ejpam-5637	324	1	we	we	PRON
ejpam-5637	324	2	present	present	VERB
ejpam-5637	324	3	the	the	DET
ejpam-5637	324	4	comparison	comparison	NOUN
ejpam-5637	324	5	on	on	ADP
ejpam-5637	324	6	numerical	numerical	ADJ
ejpam-5637	324	7	approximation	approximation	NOUN
ejpam-5637	324	8	of	of	ADP
ejpam-5637	324	9	the	the	DET
ejpam-5637	324	10	lower	low	ADJ
ejpam-5637	324	11	bounds	bound	NOUN
ejpam-5637	324	12	of	of	ADP
ejpam-5637	324	13	structured	structured	ADJ
ejpam-5637	324	14	singular	singular	ADJ
ejpam-5637	324	15	values	value	NOUN
ejpam-5637	324	16	in	in	ADP
ejpam-5637	324	17	following	follow	VERB
ejpam-5637	324	18	table-3	table-3	PROPN
ejpam-5637	324	19	.	.	PUNCT
ejpam-5637	325	1	the	the	DET
ejpam-5637	325	2	numerical	numerical	ADJ
ejpam-5637	325	3	approximation	approximation	NOUN
ejpam-5637	325	4	of	of	ADP
ejpam-5637	325	5	lower	low	ADJ
ejpam-5637	325	6	bounds	bound	NOUN
ejpam-5637	325	7	of	of	ADP
ejpam-5637	325	8	structured	structured	ADJ
ejpam-5637	325	9	singular	singular	ADJ
ejpam-5637	325	10	values	value	NOUN
ejpam-5637	325	11	mussv	mussv	VERB
ejpam-5637	325	12	pa	pa	PROPN
ejpam-5637	325	13	gba	gba	PROPN
ejpam-5637	325	14	pma	pma	PROPN
ejpam-5637	325	15	nla	nla	PROPN
ejpam-5637	325	16	lra	lra	PROPN
ejpam-5637	325	17	16.4123	16.4123	NUM
ejpam-5637	325	18	16.4176	16.4176	NUM
ejpam-5637	325	19	16.4198	16.4198	NUM
ejpam-5637	325	20	16.4183	16.4183	NUM
ejpam-5637	325	21	16.4142	16.4142	NUM
ejpam-5637	325	22	16.4130	16.4130	NUM
ejpam-5637	325	23	5	5	NUM
ejpam-5637	325	24	.	.	PUNCT
ejpam-5637	325	25	conclusion	conclusion	NOUN
ejpam-5637	325	26	in	in	ADP
ejpam-5637	325	27	this	this	DET
ejpam-5637	325	28	article	article	NOUN
ejpam-5637	325	29	we	we	PRON
ejpam-5637	325	30	have	have	AUX
ejpam-5637	325	31	presented	present	VERB
ejpam-5637	325	32	new	new	ADJ
ejpam-5637	325	33	results	result	NOUN
ejpam-5637	325	34	on	on	ADP
ejpam-5637	325	35	the	the	DET
ejpam-5637	325	36	spectral	spectral	ADJ
ejpam-5637	325	37	properties	property	NOUN
ejpam-5637	325	38	(	(	PUNCT
ejpam-5637	325	39	singular	singular	ADJ
ejpam-5637	325	40	values	value	NOUN
ejpam-5637	325	41	)	)	PUNCT
ejpam-5637	325	42	of	of	ADP
ejpam-5637	325	43	structured	structured	ADJ
ejpam-5637	325	44	matrices	matrix	NOUN
ejpam-5637	325	45	appearing	appear	VERB
ejpam-5637	325	46	across	across	ADP
ejpam-5637	325	47	hitchcock	hitchcock	NOUN
ejpam-5637	325	48	-	-	PUNCT
ejpam-5637	325	49	koopmans	koopmans	PROPN
ejpam-5637	325	50	transportation	transportation	NOUN
ejpam-5637	325	51	models	model	NOUN
ejpam-5637	325	52	.	.	PUNCT
ejpam-5637	326	1	the	the	DET
ejpam-5637	326	2	interconnection	interconnection	NOUN
ejpam-5637	326	3	between	between	ADP
ejpam-5637	326	4	d	d	ADJ
ejpam-5637	326	5	-	-	ADJ
ejpam-5637	326	6	stable	stable	ADJ
ejpam-5637	326	7	matrices	matrix	NOUN
ejpam-5637	326	8	and	and	CCONJ
ejpam-5637	326	9	structured	structure	VERB
ejpam-5637	326	10	singular	singular	ADJ
ejpam-5637	326	11	values	value	NOUN
ejpam-5637	326	12	of	of	ADP
ejpam-5637	326	13	pseudo	pseudo	NOUN
ejpam-5637	326	14	-	-	ADJ
ejpam-5637	326	15	inverse	inverse	NOUN
ejpam-5637	326	16	are	be	AUX
ejpam-5637	326	17	analyzed	analyze	VERB
ejpam-5637	326	18	.	.	PUNCT
ejpam-5637	327	1	the	the	DET
ejpam-5637	327	2	numerical	numerical	ADJ
ejpam-5637	327	3	experimentation	experimentation	NOUN
ejpam-5637	327	4	carried	carry	VERB
ejpam-5637	327	5	with	with	ADP
ejpam-5637	327	6	matlab	matlab	PROPN
ejpam-5637	327	7	shows	show	VERB
ejpam-5637	327	8	the	the	DET
ejpam-5637	327	9	dynamics	dynamic	NOUN
ejpam-5637	327	10	of	of	ADP
ejpam-5637	327	11	singular	singular	ADJ
ejpam-5637	327	12	values	value	NOUN
ejpam-5637	327	13	,	,	PUNCT
ejpam-5637	327	14	structured	structure	VERB
ejpam-5637	327	15	singular	singular	ADJ
ejpam-5637	327	16	values	value	NOUN
ejpam-5637	327	17	,	,	PUNCT
ejpam-5637	327	18	and	and	CCONJ
ejpam-5637	327	19	pseudo	pseudo	NOUN
ejpam-5637	327	20	-	-	NOUN
ejpam-5637	327	21	spectrum	spectrum	NOUN
ejpam-5637	327	22	.	.	PUNCT
ejpam-5637	328	1	the	the	DET
ejpam-5637	328	2	advantages	advantage	NOUN
ejpam-5637	328	3	of	of	ADP
ejpam-5637	328	4	the	the	DET
ejpam-5637	328	5	proposed	propose	VERB
ejpam-5637	328	6	methodology	methodology	NOUN
ejpam-5637	328	7	are	be	AUX
ejpam-5637	328	8	listed	list	VERB
ejpam-5637	328	9	as	as	ADP
ejpam-5637	328	10	:	:	PUNCT
ejpam-5637	328	11	1	1	X
ejpam-5637	328	12	.	.	PUNCT
ejpam-5637	329	1	the	the	DET
ejpam-5637	329	2	proposed	propose	VERB
ejpam-5637	329	3	methodology	methodology	NOUN
ejpam-5637	329	4	helps	help	VERB
ejpam-5637	329	5	to	to	PART
ejpam-5637	329	6	study	study	VERB
ejpam-5637	329	7	the	the	DET
ejpam-5637	329	8	spectral	spectral	ADJ
ejpam-5637	329	9	properties	property	NOUN
ejpam-5637	329	10	via	via	ADP
ejpam-5637	329	11	the	the	DET
ejpam-5637	329	12	computation	computation	NOUN
ejpam-5637	329	13	of	of	ADP
ejpam-5637	329	14	eigenvalues	eigenvalue	NOUN
ejpam-5637	329	15	,	,	PUNCT
ejpam-5637	329	16	eigenvectors	eigenvector	NOUN
ejpam-5637	329	17	,	,	PUNCT
ejpam-5637	329	18	singular	singular	ADJ
ejpam-5637	329	19	values	value	NOUN
ejpam-5637	329	20	,	,	PUNCT
ejpam-5637	329	21	right	right	ADJ
ejpam-5637	329	22	and	and	CCONJ
ejpam-5637	329	23	left	leave	VERB
ejpam-5637	329	24	handed	hand	VERB
ejpam-5637	329	25	singular	singular	ADJ
ejpam-5637	329	26	vectors	vector	NOUN
ejpam-5637	329	27	,	,	PUNCT
ejpam-5637	329	28	and	and	CCONJ
ejpam-5637	329	29	structured	structure	VERB
ejpam-5637	329	30	singular	singular	ADJ
ejpam-5637	329	31	values	value	NOUN
ejpam-5637	329	32	.	.	PUNCT
ejpam-5637	330	1	2	2	X
ejpam-5637	330	2	.	.	X
ejpam-5637	330	3	the	the	DET
ejpam-5637	330	4	proposed	propose	VERB
ejpam-5637	330	5	methodology	methodology	NOUN
ejpam-5637	330	6	has	have	VERB
ejpam-5637	330	7	an	an	DET
ejpam-5637	330	8	advantage	advantage	NOUN
ejpam-5637	330	9	in	in	ADP
ejpam-5637	330	10	the	the	DET
ejpam-5637	330	11	sense	sense	NOUN
ejpam-5637	330	12	that	that	SCONJ
ejpam-5637	330	13	it	it	PRON
ejpam-5637	330	14	allow	allow	VERB
ejpam-5637	330	15	us	we	PRON
ejpam-5637	330	16	to	to	PART
ejpam-5637	330	17	establish	establish	VERB
ejpam-5637	330	18	new	new	ADJ
ejpam-5637	330	19	interconnections	interconnection	NOUN
ejpam-5637	330	20	between	between	ADP
ejpam-5637	330	21	structured	structured	ADJ
ejpam-5637	330	22	singular	singular	ADJ
ejpam-5637	330	23	values	value	NOUN
ejpam-5637	330	24	and	and	CCONJ
ejpam-5637	330	25	d	d	NOUN
ejpam-5637	330	26	-	-	NOUN
ejpam-5637	330	27	stability	stability	NOUN
ejpam-5637	330	28	analysis	analysis	NOUN
ejpam-5637	330	29	of	of	ADP
ejpam-5637	330	30	structured	structured	ADJ
ejpam-5637	330	31	matrices	matrix	NOUN
ejpam-5637	330	32	appearing	appear	VERB
ejpam-5637	330	33	across	across	ADP
ejpam-5637	330	34	the	the	DET
ejpam-5637	330	35	hitchcock	hitchcock	NOUN
ejpam-5637	330	36	-	-	PUNCT
ejpam-5637	330	37	koopmans	koopmans	PROPN
ejpam-5637	330	38	transportation	transportation	NOUN
ejpam-5637	330	39	model	model	NOUN
ejpam-5637	330	40	.	.	PUNCT
ejpam-5637	331	1	m.u	m.u	PROPN
ejpam-5637	331	2	.	.	PROPN
ejpam-5637	332	1	rahman	rahman	PROPN
ejpam-5637	332	2	et	et	PROPN
ejpam-5637	332	3	al	al	PROPN
ejpam-5637	332	4	.	.	PUNCT
ejpam-5637	332	5	/	/	SYM
ejpam-5637	332	6	eur	eur	PROPN
ejpam-5637	332	7	.	.	PUNCT
ejpam-5637	333	1	j.	j.	PROPN
ejpam-5637	333	2	pure	pure	PROPN
ejpam-5637	333	3	appl	appl	PROPN
ejpam-5637	333	4	.	.	PROPN
ejpam-5637	333	5	math	math	PROPN
ejpam-5637	333	6	,	,	PUNCT
ejpam-5637	333	7	18	18	NUM
ejpam-5637	333	8	(	(	PUNCT
ejpam-5637	333	9	1	1	NUM
ejpam-5637	333	10	)	)	PUNCT
ejpam-5637	333	11	(	(	PUNCT
ejpam-5637	333	12	2025	2025	NUM
ejpam-5637	333	13	)	)	PUNCT
ejpam-5637	333	14	,	,	PUNCT
ejpam-5637	333	15	5637	5637	NUM
ejpam-5637	333	16	17	17	NUM
ejpam-5637	333	17	of	of	ADP
ejpam-5637	333	18	20	20	NUM
ejpam-5637	333	19	(	(	PUNCT
ejpam-5637	333	20	a	a	NOUN
ejpam-5637	333	21	)	)	PUNCT
ejpam-5637	333	22	field	field	NOUN
ejpam-5637	333	23	of	of	ADP
ejpam-5637	333	24	values	value	NOUN
ejpam-5637	333	25	enclosing	enclose	VERB
ejpam-5637	333	26	spectrum	spectrum	NOUN
ejpam-5637	333	27	and	and	CCONJ
ejpam-5637	333	28	pseudo	pseudo	NOUN
ejpam-5637	333	29	-	-	NOUN
ejpam-5637	333	30	spectrum	spectrum	ADJ
ejpam-5637	333	31	(	(	PUNCT
ejpam-5637	333	32	b	b	NOUN
ejpam-5637	333	33	)	)	PUNCT
ejpam-5637	333	34	resolvent	resolvent	ADJ
ejpam-5637	333	35	norm	norm	NOUN
ejpam-5637	333	36	figure	figure	NOUN
ejpam-5637	333	37	6	6	NUM
ejpam-5637	333	38	:	:	PUNCT
ejpam-5637	333	39	pseudo	pseudo	NOUN
ejpam-5637	333	40	-	-	NOUN
ejpam-5637	333	41	spectrum	spectrum	NOUN
ejpam-5637	333	42	of	of	ADP
ejpam-5637	333	43	a	a	DET
ejpam-5637	333	44	in	in	ADP
ejpam-5637	333	45	example-3	example-3	NUM
ejpam-5637	333	46	3	3	NUM
ejpam-5637	333	47	.	.	PUNCT
ejpam-5637	334	1	the	the	DET
ejpam-5637	334	2	computation	computation	NOUN
ejpam-5637	334	3	and	and	CCONJ
ejpam-5637	334	4	graphical	graphical	ADJ
ejpam-5637	334	5	representation	representation	NOUN
ejpam-5637	334	6	of	of	ADP
ejpam-5637	334	7	spectrum	spectrum	NOUN
ejpam-5637	334	8	and	and	CCONJ
ejpam-5637	334	9	pseudo	pseudo	NOUN
ejpam-5637	334	10	-	-	NOUN
ejpam-5637	334	11	spectrum	spectrum	NOUN
ejpam-5637	334	12	gives	give	VERB
ejpam-5637	334	13	an	an	DET
ejpam-5637	334	14	advantage	advantage	NOUN
ejpam-5637	334	15	to	to	PART
ejpam-5637	334	16	exploit	exploit	VERB
ejpam-5637	334	17	the	the	DET
ejpam-5637	334	18	hidden	hide	VERB
ejpam-5637	334	19	structures	structure	NOUN
ejpam-5637	334	20	and	and	CCONJ
ejpam-5637	334	21	properties	property	NOUN
ejpam-5637	334	22	of	of	ADP
ejpam-5637	334	23	structured	structured	ADJ
ejpam-5637	334	24	matrices	matrix	NOUN
ejpam-5637	334	25	.	.	PUNCT
ejpam-5637	335	1	4	4	X
ejpam-5637	335	2	.	.	X
ejpam-5637	335	3	the	the	DET
ejpam-5637	335	4	proposed	propose	VERB
ejpam-5637	335	5	methodology	methodology	NOUN
ejpam-5637	335	6	is	be	AUX
ejpam-5637	335	7	well	well	ADV
ejpam-5637	335	8	-	-	PUNCT
ejpam-5637	335	9	established	establish	VERB
ejpam-5637	335	10	in	in	ADP
ejpam-5637	335	11	the	the	DET
ejpam-5637	335	12	sense	sense	NOUN
ejpam-5637	335	13	that	that	SCONJ
ejpam-5637	335	14	it	it	PRON
ejpam-5637	335	15	has	have	AUX
ejpam-5637	335	16	strong	strong	ADJ
ejpam-5637	335	17	theoretical	theoretical	ADJ
ejpam-5637	335	18	foundations	foundation	NOUN
ejpam-5637	335	19	and	and	CCONJ
ejpam-5637	335	20	also	also	ADV
ejpam-5637	335	21	numerical	numerical	ADJ
ejpam-5637	335	22	experimentation	experimentation	NOUN
ejpam-5637	335	23	to	to	PART
ejpam-5637	335	24	support	support	VERB
ejpam-5637	335	25	the	the	DET
ejpam-5637	335	26	theoretical	theoretical	ADJ
ejpam-5637	335	27	construction	construction	NOUN
ejpam-5637	335	28	.	.	PUNCT
ejpam-5637	336	1	acknowledgements	acknowledgement	NOUN
ejpam-5637	336	2	this	this	DET
ejpam-5637	336	3	work	work	NOUN
ejpam-5637	336	4	was	be	AUX
ejpam-5637	336	5	funded	fund	VERB
ejpam-5637	336	6	by	by	ADP
ejpam-5637	336	7	the	the	DET
ejpam-5637	336	8	university	university	PROPN
ejpam-5637	336	9	of	of	ADP
ejpam-5637	336	10	jeddah	jeddah	PROPN
ejpam-5637	336	11	,	,	PUNCT
ejpam-5637	336	12	jeddah	jeddah	PROPN
ejpam-5637	336	13	,	,	PUNCT
ejpam-5637	336	14	saudi	saudi	PROPN
ejpam-5637	336	15	arabia	arabia	PROPN
ejpam-5637	336	16	,	,	PUNCT
ejpam-5637	336	17	under	under	ADP
ejpam-5637	336	18	grant	grant	NOUN
ejpam-5637	336	19	no	no	NOUN
ejpam-5637	336	20	.	.	PUNCT
ejpam-5637	337	1	(	(	PUNCT
ejpam-5637	337	2	uj-23	uj-23	NOUN
ejpam-5637	337	3	-	-	PUNCT
ejpam-5637	337	4	dr-128	dr-128	NOUN
ejpam-5637	337	5	)	)	PUNCT
ejpam-5637	337	6	.	.	PUNCT
ejpam-5637	338	1	therefore	therefore	ADV
ejpam-5637	338	2	,	,	PUNCT
ejpam-5637	338	3	the	the	DET
ejpam-5637	338	4	authors	author	NOUN
ejpam-5637	338	5	thank	thank	VERB
ejpam-5637	338	6	the	the	DET
ejpam-5637	338	7	university	university	NOUN
ejpam-5637	338	8	of	of	ADP
ejpam-5637	338	9	jeddah	jeddah	PROPN
ejpam-5637	338	10	for	for	ADP
ejpam-5637	338	11	its	its	PRON
ejpam-5637	338	12	technical	technical	ADJ
ejpam-5637	338	13	and	and	CCONJ
ejpam-5637	338	14	financial	financial	ADJ
ejpam-5637	338	15	support	support	NOUN
ejpam-5637	338	16	.	.	PUNCT
ejpam-5637	339	1	references	reference	NOUN
ejpam-5637	339	2	[	[	X
ejpam-5637	339	3	1	1	NUM
ejpam-5637	339	4	]	]	PUNCT
ejpam-5637	339	5	aneya	aneya	NOUN
ejpam-5637	339	6	,	,	PUNCT
ejpam-5637	339	7	y.p	y.p	PROPN
ejpam-5637	339	8	.	.	PROPN
ejpam-5637	339	9	;	;	PUNCT
ejpam-5637	339	10	nair	nair	PROPN
ejpam-5637	339	11	,	,	PUNCT
ejpam-5637	339	12	k.p.k	k.p.k	PROPN
ejpam-5637	339	13	.	.	PUNCT
ejpam-5637	339	14	bi	bi	ADJ
ejpam-5637	339	15	-	-	PUNCT
ejpam-5637	339	16	criteria	criterion	NOUN
ejpam-5637	339	17	transportation	transportation	NOUN
ejpam-5637	339	18	problem	problem	NOUN
ejpam-5637	339	19	.	.	PUNCT
ejpam-5637	340	1	manag	manag	PROPN
ejpam-5637	340	2	.	.	PUNCT
ejpam-5637	341	1	sci	sci	PROPN
ejpam-5637	341	2	.	.	PROPN
ejpam-5637	341	3	1979	1979	NUM
ejpam-5637	341	4	,	,	PUNCT
ejpam-5637	341	5	25	25	NUM
ejpam-5637	341	6	,	,	PUNCT
ejpam-5637	341	7	73–78	73–78	NUM
ejpam-5637	341	8	.	.	PUNCT
ejpam-5637	342	1	[	[	X
ejpam-5637	342	2	2	2	NUM
ejpam-5637	342	3	]	]	X
ejpam-5637	342	4	angelelli	angelelli	PROPN
ejpam-5637	342	5	,	,	PUNCT
ejpam-5637	342	6	e.	e.	PROPN
ejpam-5637	342	7	;	;	PUNCT
ejpam-5637	342	8	morandi	morandi	PROPN
ejpam-5637	342	9	,	,	PUNCT
ejpam-5637	342	10	v.	v.	PROPN
ejpam-5637	342	11	;	;	PUNCT
ejpam-5637	342	12	savelsbergh	savelsbergh	NOUN
ejpam-5637	342	13	,	,	PUNCT
ejpam-5637	342	14	m.	m.	NOUN
ejpam-5637	342	15	;	;	PUNCT
ejpam-5637	342	16	speranza	speranza	PROPN
ejpam-5637	342	17	,	,	PUNCT
ejpam-5637	342	18	m.g	m.g	PROPN
ejpam-5637	342	19	.	.	PROPN
ejpam-5637	342	20	system	system	NOUN
ejpam-5637	342	21	optimal	optimal	ADJ
ejpam-5637	342	22	routing	routing	NOUN
ejpam-5637	342	23	of	of	ADP
ejpam-5637	342	24	traffic	traffic	NOUN
ejpam-5637	342	25	flows	flow	NOUN
ejpam-5637	342	26	with	with	ADP
ejpam-5637	342	27	user	user	NOUN
ejpam-5637	342	28	constraints	constraint	NOUN
ejpam-5637	342	29	using	use	VERB
ejpam-5637	342	30	linear	linear	ADJ
ejpam-5637	342	31	programming	programming	NOUN
ejpam-5637	342	32	.	.	PUNCT
ejpam-5637	343	1	eur	eur	PROPN
ejpam-5637	343	2	.	.	PUNCT
ejpam-5637	344	1	j.	j.	PROPN
ejpam-5637	344	2	oper	oper	PROPN
ejpam-5637	344	3	.	.	PUNCT
ejpam-5637	345	1	res	res	PROPN
ejpam-5637	345	2	.	.	PROPN
ejpam-5637	345	3	2021	2021	NUM
ejpam-5637	345	4	,	,	PUNCT
ejpam-5637	345	5	293	293	NUM
ejpam-5637	345	6	,	,	PUNCT
ejpam-5637	345	7	863–879	863–879	NUM
ejpam-5637	345	8	.	.	PUNCT
ejpam-5637	346	1	[	[	X
ejpam-5637	346	2	3	3	X
ejpam-5637	346	3	]	]	PUNCT
ejpam-5637	346	4	k.	k.	PROPN
ejpam-5637	346	5	j.	j.	PROPN
ejpam-5637	346	6	arrow	arrow	PROPN
ejpam-5637	346	7	and	and	CCONJ
ejpam-5637	346	8	m.	m.	NOUN
ejpam-5637	346	9	mcmanus	mcmanus	PROPN
ejpam-5637	346	10	,	,	PUNCT
ejpam-5637	346	11	“	"	PUNCT
ejpam-5637	346	12	a	a	DET
ejpam-5637	346	13	note	note	NOUN
ejpam-5637	346	14	on	on	ADP
ejpam-5637	346	15	dynamic	dynamic	ADJ
ejpam-5637	346	16	stability	stability	NOUN
ejpam-5637	346	17	,	,	PUNCT
ejpam-5637	346	18	”	"	PUNCT
ejpam-5637	346	19	econometrica	econometrica	PROPN
ejpam-5637	346	20	26	26	NUM
ejpam-5637	346	21	,	,	PUNCT
ejpam-5637	346	22	448–454	448–454	NUM
ejpam-5637	346	23	(	(	PUNCT
ejpam-5637	346	24	1958	1958	NUM
ejpam-5637	346	25	)	)	PUNCT
ejpam-5637	346	26	.	.	PUNCT
ejpam-5637	347	1	[	[	X
ejpam-5637	347	2	4	4	NUM
ejpam-5637	347	3	]	]	X
ejpam-5637	347	4	barnhart	barnhart	PROPN
ejpam-5637	347	5	,	,	PUNCT
ejpam-5637	347	6	c.	c.	PROPN
ejpam-5637	347	7	;	;	PUNCT
ejpam-5637	347	8	krishnan	krishnan	PROPN
ejpam-5637	347	9	,	,	PUNCT
ejpam-5637	347	10	n.	n.	PROPN
ejpam-5637	347	11	;	;	PUNCT
ejpam-5637	347	12	kim	kim	PROPN
ejpam-5637	347	13	,	,	PUNCT
ejpam-5637	347	14	d.	d.	PROPN
ejpam-5637	347	15	;	;	PUNCT
ejpam-5637	347	16	ware	ware	PROPN
ejpam-5637	347	17	,	,	PUNCT
ejpam-5637	347	18	k.	k.	PROPN
ejpam-5637	347	19	network	network	PROPN
ejpam-5637	347	20	design	design	NOUN
ejpam-5637	347	21	for	for	ADP
ejpam-5637	347	22	express	express	ADJ
ejpam-5637	347	23	shipment	shipment	NOUN
ejpam-5637	347	24	delivery	delivery	NOUN
ejpam-5637	347	25	.	.	PUNCT
ejpam-5637	348	1	comput	comput	NOUN
ejpam-5637	348	2	.	.	PUNCT
ejpam-5637	349	1	optim	optim	PROPN
ejpam-5637	349	2	.	.	PUNCT
ejpam-5637	350	1	appl	appl	PROPN
ejpam-5637	350	2	.	.	PROPN
ejpam-5637	351	1	2002	2002	NUM
ejpam-5637	351	2	,	,	PUNCT
ejpam-5637	351	3	21	21	NUM
ejpam-5637	351	4	,	,	PUNCT
ejpam-5637	351	5	239–262	239–262	NUM
ejpam-5637	351	6	.	.	PUNCT
ejpam-5637	352	1	[	[	X
ejpam-5637	352	2	5	5	NUM
ejpam-5637	352	3	]	]	X
ejpam-5637	352	4	bhatia	bhatia	PROPN
ejpam-5637	352	5	,	,	PUNCT
ejpam-5637	352	6	h.l	h.l	PROPN
ejpam-5637	352	7	.	.	PROPN
ejpam-5637	352	8	;	;	PUNCT
ejpam-5637	352	9	swarup	swarup	PROPN
ejpam-5637	352	10	,	,	PUNCT
ejpam-5637	352	11	k.	k.	PROPN
ejpam-5637	352	12	;	;	PUNCT
ejpam-5637	352	13	puri	puri	PROPN
ejpam-5637	352	14	,	,	PUNCT
ejpam-5637	352	15	m.c	m.c	PROPN
ejpam-5637	352	16	.	.	PROPN
ejpam-5637	352	17	a	a	DET
ejpam-5637	352	18	procedure	procedure	NOUN
ejpam-5637	352	19	for	for	ADP
ejpam-5637	352	20	time	time	NOUN
ejpam-5637	352	21	minimization	minimization	NOUN
ejpam-5637	352	22	transportation	transportation	NOUN
ejpam-5637	352	23	problem	problem	NOUN
ejpam-5637	352	24	.	.	PUNCT
ejpam-5637	353	1	indian	indian	PROPN
ejpam-5637	353	2	j.	j.	PROPN
ejpam-5637	353	3	pure	pure	PROPN
ejpam-5637	353	4	appl	appl	PROPN
ejpam-5637	353	5	.	.	PUNCT
ejpam-5637	353	6	math	math	PROPN
ejpam-5637	353	7	.	.	PUNCT
ejpam-5637	354	1	1977	1977	NUM
ejpam-5637	354	2	,	,	PUNCT
ejpam-5637	354	3	8	8	NUM
ejpam-5637	354	4	,	,	PUNCT
ejpam-5637	354	5	920–929	920–929	NUM
ejpam-5637	354	6	.	.	PUNCT
ejpam-5637	355	1	[	[	X
ejpam-5637	355	2	6	6	NUM
ejpam-5637	355	3	]	]	SYM
ejpam-5637	355	4	bulut	bulut	NOUN
ejpam-5637	355	5	,	,	PUNCT
ejpam-5637	355	6	h.	h.	PROPN
ejpam-5637	355	7	”	"	PUNCT
ejpam-5637	355	8	algebraic	algebraic	PROPN
ejpam-5637	355	9	characterizations	characterization	NOUN
ejpam-5637	355	10	of	of	ADP
ejpam-5637	355	11	the	the	DET
ejpam-5637	355	12	singular	singular	ADJ
ejpam-5637	355	13	value	value	NOUN
ejpam-5637	355	14	decompositions	decomposition	NOUN
ejpam-5637	355	15	in	in	ADP
ejpam-5637	355	16	the	the	DET
ejpam-5637	355	17	transportation	transportation	NOUN
ejpam-5637	355	18	problem	problem	NOUN
ejpam-5637	355	19	.	.	PUNCT
ejpam-5637	355	20	”	"	PUNCT
ejpam-5637	356	1	journal	journal	NOUN
ejpam-5637	356	2	of	of	ADP
ejpam-5637	356	3	mathematical	mathematical	ADJ
ejpam-5637	356	4	analysis	analysis	NOUN
ejpam-5637	356	5	and	and	CCONJ
ejpam-5637	356	6	applications	application	NOUN
ejpam-5637	356	7	154	154	NUM
ejpam-5637	356	8	,	,	PUNCT
ejpam-5637	356	9	no	no	INTJ
ejpam-5637	356	10	.	.	NOUN
ejpam-5637	356	11	1	1	NUM
ejpam-5637	356	12	(	(	PUNCT
ejpam-5637	356	13	1991	1991	NUM
ejpam-5637	356	14	):	):	PUNCT
ejpam-5637	356	15	13	13	NUM
ejpam-5637	356	16	-	-	SYM
ejpam-5637	356	17	21	21	NUM
ejpam-5637	356	18	.	.	PUNCT
ejpam-5637	357	1	m.u	m.u	PROPN
ejpam-5637	357	2	.	.	PROPN
ejpam-5637	358	1	rahman	rahman	PROPN
ejpam-5637	358	2	et	et	PROPN
ejpam-5637	358	3	al	al	PROPN
ejpam-5637	358	4	.	.	PUNCT
ejpam-5637	358	5	/	/	SYM
ejpam-5637	358	6	eur	eur	PROPN
ejpam-5637	358	7	.	.	PUNCT
ejpam-5637	359	1	j.	j.	PROPN
ejpam-5637	359	2	pure	pure	PROPN
ejpam-5637	359	3	appl	appl	PROPN
ejpam-5637	359	4	.	.	PROPN
ejpam-5637	359	5	math	math	PROPN
ejpam-5637	359	6	,	,	PUNCT
ejpam-5637	359	7	18	18	NUM
ejpam-5637	359	8	(	(	PUNCT
ejpam-5637	359	9	1	1	NUM
ejpam-5637	359	10	)	)	PUNCT
ejpam-5637	359	11	(	(	PUNCT
ejpam-5637	359	12	2025	2025	NUM
ejpam-5637	359	13	)	)	PUNCT
ejpam-5637	359	14	,	,	PUNCT
ejpam-5637	359	15	5637	5637	NUM
ejpam-5637	359	16	18	18	NUM
ejpam-5637	359	17	of	of	ADP
ejpam-5637	359	18	20	20	NUM
ejpam-5637	360	1	[	[	SYM
ejpam-5637	360	2	7	7	NUM
ejpam-5637	360	3	]	]	X
ejpam-5637	360	4	r.	r.	PROPN
ejpam-5637	360	5	p.	p.	PROPN
ejpam-5637	360	6	braatz	braatz	PROPN
ejpam-5637	360	7	,	,	PUNCT
ejpam-5637	361	1	p.	p.	PROPN
ejpam-5637	361	2	m.	m.	PROPN
ejpam-5637	361	3	young	young	PROPN
ejpam-5637	361	4	,	,	PUNCT
ejpam-5637	361	5	j.	j.	PROPN
ejpam-5637	361	6	c.	c.	PROPN
ejpam-5637	361	7	doyle	doyle	PROPN
ejpam-5637	361	8	,	,	PUNCT
ejpam-5637	361	9	and	and	CCONJ
ejpam-5637	361	10	m.	m.	NOUN
ejpam-5637	361	11	morari	morari	PROPN
ejpam-5637	361	12	,	,	PUNCT
ejpam-5637	361	13	“	"	PUNCT
ejpam-5637	361	14	computational	computational	ADJ
ejpam-5637	361	15	complexity	complexity	NOUN
ejpam-5637	361	16	of	of	ADP
ejpam-5637	361	17	µ	µ	DET
ejpam-5637	361	18	calculation	calculation	NOUN
ejpam-5637	361	19	,	,	PUNCT
ejpam-5637	361	20	”	"	PUNCT
ejpam-5637	361	21	ieee	ieee	NOUN
ejpam-5637	361	22	trans	trans	PROPN
ejpam-5637	361	23	.	.	PUNCT
ejpam-5637	362	1	autom	autom	PROPN
ejpam-5637	362	2	.	.	PUNCT
ejpam-5637	363	1	control	control	NOUN
ejpam-5637	363	2	39	39	NUM
ejpam-5637	363	3	,	,	PUNCT
ejpam-5637	363	4	1000–1002	1000–1002	NUM
ejpam-5637	363	5	(	(	PUNCT
ejpam-5637	363	6	1994	1994	NUM
ejpam-5637	363	7	)	)	PUNCT
ejpam-5637	363	8	.	.	PUNCT
ejpam-5637	364	1	[	[	X
ejpam-5637	364	2	8	8	NUM
ejpam-5637	364	3	]	]	PUNCT
ejpam-5637	364	4	can	can	AUX
ejpam-5637	364	5	,	,	PUNCT
ejpam-5637	364	6	t.	t.	PROPN
ejpam-5637	364	7	;	;	PUNCT
ejpam-5637	364	8	koçak	koçak	PROPN
ejpam-5637	364	9	,	,	PUNCT
ejpam-5637	364	10	h.	h.	PROPN
ejpam-5637	364	11	tuncay	tuncay	PROPN
ejpam-5637	364	12	can	can	AUX
ejpam-5637	364	13	’s	’s	PART
ejpam-5637	364	14	approximation	approximation	NOUN
ejpam-5637	364	15	method	method	NOUN
ejpam-5637	364	16	to	to	PART
ejpam-5637	364	17	obtain	obtain	VERB
ejpam-5637	364	18	initial	initial	ADJ
ejpam-5637	364	19	basic	basic	ADJ
ejpam-5637	364	20	feasible	feasible	ADJ
ejpam-5637	364	21	solution	solution	NOUN
ejpam-5637	364	22	to	to	ADP
ejpam-5637	364	23	transport	transport	NOUN
ejpam-5637	364	24	problem	problem	NOUN
ejpam-5637	364	25	.	.	PUNCT
ejpam-5637	365	1	appl	appl	PROPN
ejpam-5637	365	2	.	.	PUNCT
ejpam-5637	366	1	comput	comput	PROPN
ejpam-5637	366	2	.	.	PUNCT
ejpam-5637	367	1	math	math	NOUN
ejpam-5637	367	2	.	.	PUNCT
ejpam-5637	368	1	2016	2016	NUM
ejpam-5637	368	2	,	,	PUNCT
ejpam-5637	368	3	5	5	NUM
ejpam-5637	368	4	,	,	PUNCT
ejpam-5637	368	5	78–82	78–82	NUM
ejpam-5637	368	6	.	.	PUNCT
ejpam-5637	369	1	[	[	X
ejpam-5637	369	2	9	9	NUM
ejpam-5637	369	3	]	]	PUNCT
ejpam-5637	369	4	r.	r.	PROPN
ejpam-5637	369	5	e.	e.	PROPN
ejpam-5637	369	6	cline	cline	PROPN
ejpam-5637	369	7	and	and	CCONJ
ejpam-5637	369	8	l.	l.	PROPN
ejpam-5637	369	9	d.	d.	PROPN
ejpam-5637	369	10	pyle	pyle	PROPN
ejpam-5637	369	11	,	,	PUNCT
ejpam-5637	369	12	the	the	DET
ejpam-5637	369	13	generalized	generalized	ADJ
ejpam-5637	369	14	inverse	inverse	NOUN
ejpam-5637	369	15	in	in	ADP
ejpam-5637	369	16	linear	linear	ADJ
ejpam-5637	369	17	programmingan	programmingan	NOUN
ejpam-5637	369	18	intersection	intersection	NOUN
ejpam-5637	369	19	projection	projection	NOUN
ejpam-5637	369	20	methods	method	NOUN
ejpam-5637	369	21	and	and	CCONJ
ejpam-5637	369	22	the	the	DET
ejpam-5637	369	23	solution	solution	NOUN
ejpam-5637	369	24	of	of	ADP
ejpam-5637	369	25	a	a	DET
ejpam-5637	369	26	class	class	NOUN
ejpam-5637	369	27	of	of	ADP
ejpam-5637	369	28	structured	structured	ADJ
ejpam-5637	369	29	linear	linear	ADJ
ejpam-5637	369	30	programming	programming	NOUN
ejpam-5637	369	31	problems	problem	NOUN
ejpam-5637	369	32	,	,	PUNCT
ejpam-5637	369	33	siam	siam	PROPN
ejpam-5637	369	34	j.	j.	PROPN
ejpam-5637	369	35	appl	appl	PROPN
ejpam-5637	369	36	.	.	PROPN
ejpam-5637	369	37	math	math	PROPN
ejpam-5637	369	38	.	.	PUNCT
ejpam-5637	370	1	24	24	NUM
ejpam-5637	370	2	(	(	PUNCT
ejpam-5637	370	3	1973	1973	NUM
ejpam-5637	370	4	)	)	PUNCT
ejpam-5637	370	5	,	,	PUNCT
ejpam-5637	370	6	338	338	NUM
ejpam-5637	370	7	-	-	SYM
ejpam-5637	370	8	351	351	NUM
ejpam-5637	370	9	.	.	PUNCT
ejpam-5637	371	1	[	[	X
ejpam-5637	371	2	10	10	NUM
ejpam-5637	371	3	]	]	SYM
ejpam-5637	371	4	dahl	dahl	PROPN
ejpam-5637	371	5	,	,	PUNCT
ejpam-5637	371	6	geir	geir	PROPN
ejpam-5637	371	7	.	.	PUNCT
ejpam-5637	372	1	transportation	transportation	NOUN
ejpam-5637	372	2	matrices	matrix	NOUN
ejpam-5637	372	3	with	with	ADP
ejpam-5637	372	4	staircase	staircase	NOUN
ejpam-5637	372	5	patterns	pattern	NOUN
ejpam-5637	372	6	and	and	CCONJ
ejpam-5637	372	7	majorization	majorization	NOUN
ejpam-5637	372	8	.	.	PUNCT
ejpam-5637	373	1	linear	linear	ADJ
ejpam-5637	373	2	algebra	algebra	NOUN
ejpam-5637	373	3	and	and	CCONJ
ejpam-5637	373	4	its	its	PRON
ejpam-5637	373	5	applications	application	NOUN
ejpam-5637	373	6	429	429	NUM
ejpam-5637	373	7	,	,	PUNCT
ejpam-5637	373	8	no	no	INTJ
ejpam-5637	373	9	.	.	NOUN
ejpam-5637	373	10	7	7	NUM
ejpam-5637	373	11	(	(	PUNCT
ejpam-5637	373	12	2008	2008	NUM
ejpam-5637	373	13	):	):	PUNCT
ejpam-5637	373	14	1840	1840	NUM
ejpam-5637	373	15	-	-	SYM
ejpam-5637	373	16	1850	1850	NUM
ejpam-5637	373	17	.	.	PUNCT
ejpam-5637	374	1	[	[	X
ejpam-5637	374	2	11	11	NUM
ejpam-5637	374	3	]	]	PUNCT
ejpam-5637	374	4	dantzig	dantzig	NOUN
ejpam-5637	374	5	,	,	PUNCT
ejpam-5637	374	6	g.b	g.b	PROPN
ejpam-5637	374	7	.	.	PROPN
ejpam-5637	374	8	linear	linear	PROPN
ejpam-5637	374	9	programming	programming	NOUN
ejpam-5637	374	10	and	and	CCONJ
ejpam-5637	374	11	extensions	extension	NOUN
ejpam-5637	374	12	;	;	PUNCT
ejpam-5637	374	13	princeton	princeton	PROPN
ejpam-5637	374	14	university	university	PROPN
ejpam-5637	374	15	press	press	NOUN
ejpam-5637	374	16	:	:	PUNCT
ejpam-5637	374	17	princeton	princeton	PROPN
ejpam-5637	374	18	,	,	PUNCT
ejpam-5637	374	19	nj	nj	PROPN
ejpam-5637	374	20	,	,	PUNCT
ejpam-5637	374	21	usa	usa	PROPN
ejpam-5637	374	22	,	,	PUNCT
ejpam-5637	374	23	1963	1963	NUM
ejpam-5637	374	24	.	.	PUNCT
ejpam-5637	375	1	[	[	X
ejpam-5637	375	2	12	12	NUM
ejpam-5637	375	3	]	]	PUNCT
ejpam-5637	375	4	j.	j.	PROPN
ejpam-5637	375	5	doyle	doyle	PROPN
ejpam-5637	375	6	,	,	PUNCT
ejpam-5637	375	7	“	"	PUNCT
ejpam-5637	375	8	analysis	analysis	NOUN
ejpam-5637	375	9	of	of	ADP
ejpam-5637	375	10	feedback	feedback	NOUN
ejpam-5637	375	11	systems	system	NOUN
ejpam-5637	375	12	with	with	ADP
ejpam-5637	375	13	structured	structured	ADJ
ejpam-5637	375	14	uncertainties	uncertainty	NOUN
ejpam-5637	375	15	,	,	PUNCT
ejpam-5637	375	16	”	"	PUNCT
ejpam-5637	375	17	ieee	ieee	NOUN
ejpam-5637	375	18	proc	proc	NOUN
ejpam-5637	375	19	.	.	PUNCT
ejpam-5637	376	1	d	d	X
ejpam-5637	376	2	:	:	PUNCT
ejpam-5637	376	3	control	control	NOUN
ejpam-5637	376	4	theory	theory	NOUN
ejpam-5637	376	5	appl	appl	PROPN
ejpam-5637	376	6	.	.	PROPN
ejpam-5637	377	1	129	129	NUM
ejpam-5637	377	2	,	,	PUNCT
ejpam-5637	377	3	242–250	242–250	NUM
ejpam-5637	377	4	(	(	PUNCT
ejpam-5637	377	5	1982	1982	NUM
ejpam-5637	377	6	)	)	PUNCT
ejpam-5637	377	7	.	.	PUNCT
ejpam-5637	378	1	[	[	X
ejpam-5637	378	2	13	13	NUM
ejpam-5637	378	3	]	]	PUNCT
ejpam-5637	378	4	mark	mark	PROPN
ejpam-5637	378	5	embree	embree	PROPN
ejpam-5637	378	6	and	and	CCONJ
ejpam-5637	378	7	lloyd	lloyd	PROPN
ejpam-5637	378	8	n.	n.	PROPN
ejpam-5637	378	9	trefethen	trefethen	PROPN
ejpam-5637	378	10	.	.	PUNCT
ejpam-5637	379	1	pseudospectra	pseudospectra	PROPN
ejpam-5637	379	2	gateway	gateway	PROPN
ejpam-5637	379	3	.	.	PUNCT
ejpam-5637	380	1	[	[	X
ejpam-5637	380	2	14	14	NUM
ejpam-5637	380	3	]	]	PUNCT
ejpam-5637	380	4	a.	a.	NOUN
ejpam-5637	380	5	c.	c.	PROPN
ejpam-5637	380	6	enthoven	enthoven	PROPN
ejpam-5637	380	7	and	and	CCONJ
ejpam-5637	380	8	k.	k.	PROPN
ejpam-5637	380	9	j.	j.	PROPN
ejpam-5637	380	10	arrow	arrow	PROPN
ejpam-5637	380	11	,	,	PUNCT
ejpam-5637	380	12	“	"	PUNCT
ejpam-5637	380	13	a	a	DET
ejpam-5637	380	14	theorem	theorem	NOUN
ejpam-5637	380	15	on	on	ADP
ejpam-5637	380	16	expectations	expectation	NOUN
ejpam-5637	380	17	and	and	CCONJ
ejpam-5637	380	18	the	the	DET
ejpam-5637	380	19	stability	stability	NOUN
ejpam-5637	380	20	of	of	ADP
ejpam-5637	380	21	equilibrium	equilibrium	NOUN
ejpam-5637	380	22	,	,	PUNCT
ejpam-5637	380	23	”	"	PUNCT
ejpam-5637	380	24	econometrica	econometrica	PROPN
ejpam-5637	380	25	24	24	NUM
ejpam-5637	380	26	,	,	PUNCT
ejpam-5637	380	27	448–293	448–293	NUM
ejpam-5637	380	28	(	(	PUNCT
ejpam-5637	380	29	1956	1956	NUM
ejpam-5637	380	30	)	)	PUNCT
ejpam-5637	380	31	.	.	PUNCT
ejpam-5637	381	1	[	[	X
ejpam-5637	381	2	15	15	NUM
ejpam-5637	381	3	]	]	X
ejpam-5637	381	4	ford	ford	NOUN
ejpam-5637	381	5	,	,	PUNCT
ejpam-5637	381	6	lester	lester	PROPN
ejpam-5637	381	7	r.	r.	PROPN
ejpam-5637	381	8	”	"	PUNCT
ejpam-5637	381	9	dr	dr	PROPN
ejpam-5637	381	10	fulkerson	fulkerson	PROPN
ejpam-5637	381	11	flows	flow	VERB
ejpam-5637	381	12	in	in	ADP
ejpam-5637	381	13	networks	network	NOUN
ejpam-5637	381	14	.	.	PUNCT
ejpam-5637	381	15	”	"	PUNCT
ejpam-5637	382	1	proc	proc	NOUN
ejpam-5637	382	2	.	.	PUNCT
ejpam-5637	383	1	of	of	ADP
ejpam-5637	383	2	princeton	princeton	PROPN
ejpam-5637	383	3	university	university	PROPN
ejpam-5637	383	4	press	press	NOUN
ejpam-5637	383	5	(	(	PUNCT
ejpam-5637	383	6	1962	1962	NUM
ejpam-5637	383	7	)	)	PUNCT
ejpam-5637	383	8	.	.	PUNCT
ejpam-5637	384	1	[	[	X
ejpam-5637	384	2	16	16	NUM
ejpam-5637	384	3	]	]	X
ejpam-5637	384	4	hitchcock	hitchcock	PROPN
ejpam-5637	384	5	,	,	PUNCT
ejpam-5637	384	6	frank	frank	PROPN
ejpam-5637	384	7	l.	l.	PROPN
ejpam-5637	384	8	”	"	PUNCT
ejpam-5637	384	9	the	the	DET
ejpam-5637	384	10	distribution	distribution	NOUN
ejpam-5637	384	11	of	of	ADP
ejpam-5637	384	12	a	a	DET
ejpam-5637	384	13	product	product	NOUN
ejpam-5637	384	14	from	from	ADP
ejpam-5637	384	15	several	several	ADJ
ejpam-5637	384	16	sources	source	NOUN
ejpam-5637	384	17	to	to	ADP
ejpam-5637	384	18	numerous	numerous	ADJ
ejpam-5637	384	19	localities	locality	NOUN
ejpam-5637	384	20	.	.	PUNCT
ejpam-5637	384	21	”	"	PUNCT
ejpam-5637	384	22	journal	journal	NOUN
ejpam-5637	384	23	of	of	ADP
ejpam-5637	384	24	mathematics	mathematics	PROPN
ejpam-5637	384	25	and	and	CCONJ
ejpam-5637	384	26	physics	physics	NOUN
ejpam-5637	384	27	20	20	NUM
ejpam-5637	384	28	,	,	PUNCT
ejpam-5637	384	29	no	no	INTJ
ejpam-5637	384	30	.	.	NOUN
ejpam-5637	384	31	1	1	NUM
ejpam-5637	384	32	-	-	SYM
ejpam-5637	384	33	4	4	NUM
ejpam-5637	384	34	(	(	PUNCT
ejpam-5637	384	35	1941	1941	NUM
ejpam-5637	384	36	):	):	PUNCT
ejpam-5637	384	37	224	224	NUM
ejpam-5637	384	38	-	-	SYM
ejpam-5637	384	39	230	230	NUM
ejpam-5637	384	40	.	.	PUNCT
ejpam-5637	385	1	[	[	X
ejpam-5637	385	2	17	17	NUM
ejpam-5637	385	3	]	]	X
ejpam-5637	385	4	fricker	fricker	NOUN
ejpam-5637	385	5	,	,	PUNCT
ejpam-5637	385	6	j.	j.	PROPN
ejpam-5637	385	7	;	;	PUNCT
ejpam-5637	385	8	whitford	whitford	PROPN
ejpam-5637	385	9	,	,	PUNCT
ejpam-5637	385	10	r.	r.	PROPN
ejpam-5637	385	11	fundamentals	fundamental	NOUN
ejpam-5637	385	12	of	of	ADP
ejpam-5637	385	13	transportation	transportation	NOUN
ejpam-5637	385	14	engineering	engineering	NOUN
ejpam-5637	385	15	.	.	PUNCT
ejpam-5637	386	1	in	in	ADP
ejpam-5637	386	2	a	a	DET
ejpam-5637	386	3	multimodal	multimodal	NOUN
ejpam-5637	386	4	systems	system	NOUN
ejpam-5637	386	5	approach	approach	NOUN
ejpam-5637	386	6	;	;	PUNCT
ejpam-5637	386	7	pearson	pearson	PROPN
ejpam-5637	386	8	education	education	PROPN
ejpam-5637	386	9	,	,	PUNCT
ejpam-5637	386	10	inc	inc	PROPN
ejpam-5637	386	11	.	.	PROPN
ejpam-5637	386	12	:	:	PUNCT
ejpam-5637	386	13	upper	upper	ADJ
ejpam-5637	386	14	saddle	saddle	PROPN
ejpam-5637	386	15	river	river	PROPN
ejpam-5637	386	16	,	,	PUNCT
ejpam-5637	386	17	ny	ny	PROPN
ejpam-5637	386	18	,	,	PUNCT
ejpam-5637	386	19	usa	usa	PROPN
ejpam-5637	386	20	,	,	PUNCT
ejpam-5637	386	21	2004	2004	NUM
ejpam-5637	386	22	.	.	PUNCT
ejpam-5637	387	1	[	[	X
ejpam-5637	387	2	18	18	NUM
ejpam-5637	387	3	]	]	X
ejpam-5637	387	4	fulkerson	fulkerson	NOUN
ejpam-5637	387	5	,	,	PUNCT
ejpam-5637	387	6	d.	d.	PROPN
ejpam-5637	387	7	r.	r.	PROPN
ejpam-5637	387	8	hitchcock	hitchcock	PROPN
ejpam-5637	387	9	transportation	transportation	PROPN
ejpam-5637	387	10	problem	problem	NOUN
ejpam-5637	387	11	.	.	PUNCT
ejpam-5637	388	1	rand	rand	NOUN
ejpam-5637	388	2	corporation	corporation	NOUN
ejpam-5637	388	3	,	,	PUNCT
ejpam-5637	388	4	1956	1956	NUM
ejpam-5637	388	5	.	.	PUNCT
ejpam-5637	389	1	[	[	X
ejpam-5637	389	2	19	19	NUM
ejpam-5637	389	3	]	]	X
ejpam-5637	389	4	r.	r.	PROPN
ejpam-5637	389	5	r.	r.	PROPN
ejpam-5637	389	6	de	de	PROPN
ejpam-5637	389	7	gaston	gaston	PROPN
ejpam-5637	389	8	and	and	CCONJ
ejpam-5637	389	9	m.	m.	PROPN
ejpam-5637	389	10	g.	g.	PROPN
ejpam-5637	389	11	safonov	safonov	PROPN
ejpam-5637	389	12	,	,	PUNCT
ejpam-5637	389	13	“	"	PUNCT
ejpam-5637	389	14	exact	exact	ADJ
ejpam-5637	389	15	calculation	calculation	NOUN
ejpam-5637	389	16	of	of	ADP
ejpam-5637	389	17	the	the	DET
ejpam-5637	389	18	multiloop	multiloop	NOUN
ejpam-5637	389	19	stability	stability	NOUN
ejpam-5637	389	20	margin	margin	NOUN
ejpam-5637	389	21	,	,	PUNCT
ejpam-5637	389	22	”	"	PUNCT
ejpam-5637	389	23	ieee	ieee	NOUN
ejpam-5637	389	24	trans	trans	PROPN
ejpam-5637	389	25	.	.	PUNCT
ejpam-5637	390	1	autom	autom	PROPN
ejpam-5637	390	2	.	.	PUNCT
ejpam-5637	391	1	control	control	PROPN
ejpam-5637	391	2	33	33	NUM
ejpam-5637	391	3	,	,	PUNCT
ejpam-5637	391	4	156–171	156–171	NUM
ejpam-5637	391	5	(	(	PUNCT
ejpam-5637	391	6	1988	1988	NUM
ejpam-5637	391	7	)	)	PUNCT
ejpam-5637	391	8	.	.	PUNCT
ejpam-5637	392	1	[	[	X
ejpam-5637	392	2	20	20	NUM
ejpam-5637	392	3	]	]	PUNCT
ejpam-5637	392	4	g.	g.	PROPN
ejpam-5637	392	5	giorgio	giorgio	PROPN
ejpam-5637	392	6	,	,	PUNCT
ejpam-5637	392	7	“	"	PUNCT
ejpam-5637	392	8	stable	stable	ADJ
ejpam-5637	392	9	and	and	CCONJ
ejpam-5637	392	10	related	related	ADJ
ejpam-5637	392	11	matrices	matrix	NOUN
ejpam-5637	392	12	in	in	ADP
ejpam-5637	392	13	economic	economic	ADJ
ejpam-5637	392	14	theory	theory	NOUN
ejpam-5637	392	15	,	,	PUNCT
ejpam-5637	392	16	”	"	PUNCT
ejpam-5637	392	17	control	control	NOUN
ejpam-5637	392	18	cybern	cybern	NOUN
ejpam-5637	392	19	.	.	PUNCT
ejpam-5637	393	1	2	2	NUM
ejpam-5637	393	2	(	(	PUNCT
ejpam-5637	393	3	32	32	NUM
ejpam-5637	393	4	)	)	PUNCT
ejpam-5637	393	5	,	,	PUNCT
ejpam-5637	393	6	397–410	397–410	NUM
ejpam-5637	393	7	(	(	PUNCT
ejpam-5637	393	8	2003	2003	NUM
ejpam-5637	393	9	)	)	PUNCT
ejpam-5637	393	10	.	.	PUNCT
ejpam-5637	394	1	[	[	X
ejpam-5637	394	2	21	21	NUM
ejpam-5637	394	3	]	]	X
ejpam-5637	394	4	guglielmi	guglielmi	PROPN
ejpam-5637	394	5	nicola	nicola	PROPN
ejpam-5637	394	6	,	,	PUNCT
ejpam-5637	394	7	mutti	mutti	PROPN
ejpam-5637	394	8	-	-	PUNCT
ejpam-5637	394	9	ur	ur	PROPN
ejpam-5637	394	10	rehman	rehman	PROPN
ejpam-5637	394	11	,	,	PUNCT
ejpam-5637	394	12	and	and	CCONJ
ejpam-5637	394	13	daniel	daniel	PROPN
ejpam-5637	394	14	kressner	kressner	PROPN
ejpam-5637	394	15	.	.	PUNCT
ejpam-5637	395	1	a	a	DET
ejpam-5637	395	2	novel	novel	ADJ
ejpam-5637	395	3	iterative	iterative	NOUN
ejpam-5637	395	4	method	method	NOUN
ejpam-5637	395	5	to	to	PART
ejpam-5637	395	6	approximate	approximate	VERB
ejpam-5637	395	7	structured	structured	ADJ
ejpam-5637	395	8	singular	singular	ADJ
ejpam-5637	395	9	values	value	NOUN
ejpam-5637	395	10	.	.	PUNCT
ejpam-5637	396	1	siam	siam	PROPN
ejpam-5637	396	2	journal	journal	PROPN
ejpam-5637	396	3	on	on	ADP
ejpam-5637	396	4	matrix	matrix	NOUN
ejpam-5637	396	5	analysis	analysis	NOUN
ejpam-5637	396	6	and	and	CCONJ
ejpam-5637	396	7	applications	application	NOUN
ejpam-5637	396	8	38.2	38.2	NUM
ejpam-5637	396	9	(	(	PUNCT
ejpam-5637	396	10	2017	2017	NUM
ejpam-5637	396	11	)	)	PUNCT
ejpam-5637	396	12	,	,	PUNCT
ejpam-5637	396	13	361	361	NUM
ejpam-5637	396	14	-	-	SYM
ejpam-5637	396	15	386	386	NUM
ejpam-5637	396	16	.	.	PUNCT
ejpam-5637	397	1	[	[	X
ejpam-5637	397	2	22	22	NUM
ejpam-5637	397	3	]	]	X
ejpam-5637	397	4	f.	f.	PROPN
ejpam-5637	397	5	hahn	hahn	PROPN
ejpam-5637	397	6	,	,	PUNCT
ejpam-5637	397	7	stability	stability	NOUN
ejpam-5637	397	8	,	,	PUNCT
ejpam-5637	397	9	in	in	ADP
ejpam-5637	397	10	handbook	handbook	NOUN
ejpam-5637	397	11	of	of	ADP
ejpam-5637	397	12	mathematical	mathematical	ADJ
ejpam-5637	397	13	economics	economic	NOUN
ejpam-5637	397	14	,	,	PUNCT
ejpam-5637	397	15	ed	ed	NOUN
ejpam-5637	397	16	.	.	PUNCT
ejpam-5637	397	17	by	by	ADP
ejpam-5637	397	18	k.	k.	PROPN
ejpam-5637	397	19	j.	j.	PROPN
ejpam-5637	397	20	arrow	arrow	PROPN
ejpam-5637	397	21	and	and	CCONJ
ejpam-5637	397	22	m.	m.	PROPN
ejpam-5637	397	23	d.	d.	PROPN
ejpam-5637	397	24	intriligator	intriligator	PROPN
ejpam-5637	397	25	(	(	PUNCT
ejpam-5637	397	26	north	north	NOUN
ejpam-5637	397	27	-	-	PUNCT
ejpam-5637	397	28	holland	holland	PROPN
ejpam-5637	397	29	,	,	PUNCT
ejpam-5637	397	30	amsterdam	amsterdam	PROPN
ejpam-5637	397	31	,	,	PUNCT
ejpam-5637	397	32	1982	1982	NUM
ejpam-5637	397	33	)	)	PUNCT
ejpam-5637	397	34	,	,	PUNCT
ejpam-5637	397	35	vol	vol	NOUN
ejpam-5637	397	36	.	.	PROPN
ejpam-5637	397	37	2	2	NUM
ejpam-5637	397	38	,	,	PUNCT
ejpam-5637	397	39	pp	pp	ADJ
ejpam-5637	397	40	.	.	PUNCT
ejpam-5637	398	1	745–793	745–793	NUM
ejpam-5637	398	2	.	.	PUNCT
ejpam-5637	399	1	[	[	X
ejpam-5637	399	2	23	23	NUM
ejpam-5637	399	3	]	]	X
ejpam-5637	399	4	halton	halton	PROPN
ejpam-5637	399	5	,	,	PUNCT
ejpam-5637	399	6	m.	m.	NOUN
ejpam-5637	399	7	,	,	PUNCT
ejpam-5637	399	8	hayes	hayes	PROPN
ejpam-5637	399	9	,	,	PUNCT
ejpam-5637	399	10	m.	m.	NOUN
ejpam-5637	399	11	,	,	PUNCT
ejpam-5637	399	12	iordanov	iordanov	NOUN
ejpam-5637	399	13	,	,	PUNCT
ejpam-5637	399	14	p.	p.	NOUN
ejpam-5637	399	15	state	state	NOUN
ejpam-5637	399	16	-	-	PUNCT
ejpam-5637	399	17	space	space	NOUN
ejpam-5637	399	18	analysis	analysis	NOUN
ejpam-5637	399	19	for	for	ADP
ejpam-5637	399	20	an	an	DET
ejpam-5637	399	21	experimental	experimental	ADJ
ejpam-5637	399	22	drivebywire	drivebywire	NOUN
ejpam-5637	399	23	vehicle	vehicle	NOUN
ejpam-5637	399	24	.	.	PUNCT
ejpam-5637	400	1	international	international	ADJ
ejpam-5637	400	2	journal	journal	PROPN
ejpam-5637	400	3	of	of	ADP
ejpam-5637	400	4	robust	robust	ADJ
ejpam-5637	400	5	and	and	CCONJ
ejpam-5637	400	6	non	non	ADJ
ejpam-5637	400	7	-	-	ADJ
ejpam-5637	400	8	linear	linear	ADJ
ejpam-5637	400	9	control	control	NOUN
ejpam-5637	400	10	,	,	PUNCT
ejpam-5637	400	11	18(9	18(9	NOUN
ejpam-5637	400	12	)	)	PUNCT
ejpam-5637	400	13	(	(	PUNCT
ejpam-5637	400	14	2008	2008	NUM
ejpam-5637	400	15	)	)	PUNCT
ejpam-5637	400	16	975–992	975–992	NUM
ejpam-5637	400	17	.	.	PUNCT
ejpam-5637	401	1	[	[	X
ejpam-5637	401	2	24	24	NUM
ejpam-5637	401	3	]	]	X
ejpam-5637	401	4	hammer	hammer	NOUN
ejpam-5637	401	5	,	,	PUNCT
ejpam-5637	401	6	p.l.time	p.l.time	NOUN
ejpam-5637	401	7	-	-	PUNCT
ejpam-5637	401	8	minimizing	minimize	VERB
ejpam-5637	401	9	transportation	transportation	NOUN
ejpam-5637	401	10	problem	problem	NOUN
ejpam-5637	401	11	.	.	PUNCT
ejpam-5637	402	1	nav	nav	NOUN
ejpam-5637	402	2	.	.	PUNCT
ejpam-5637	403	1	res	re	NOUN
ejpam-5637	403	2	.	.	PUNCT
ejpam-5637	403	3	logist	logist	PROPN
ejpam-5637	403	4	.	.	PUNCT
ejpam-5637	404	1	1969	1969	NUM
ejpam-5637	404	2	,	,	PUNCT
ejpam-5637	404	3	16	16	NUM
ejpam-5637	404	4	,	,	PUNCT
ejpam-5637	404	5	345–357	345–357	NUM
ejpam-5637	404	6	.	.	PUNCT
ejpam-5637	405	1	[	[	X
ejpam-5637	405	2	25	25	NUM
ejpam-5637	405	3	]	]	X
ejpam-5637	405	4	e.	e.	PROPN
ejpam-5637	405	5	kaszkurewicz	kaszkurewicz	PROPN
ejpam-5637	405	6	and	and	CCONJ
ejpam-5637	405	7	a.	a.	PROPN
ejpam-5637	405	8	bhaya	bhaya	PROPN
ejpam-5637	405	9	,	,	PUNCT
ejpam-5637	405	10	“	"	PUNCT
ejpam-5637	405	11	matrix	matrix	NOUN
ejpam-5637	405	12	diagonal	diagonal	ADJ
ejpam-5637	405	13	and	and	CCONJ
ejpam-5637	405	14	d	d	NOUN
ejpam-5637	405	15	-	-	NOUN
ejpam-5637	405	16	stability	stability	NOUN
ejpam-5637	405	17	,	,	PUNCT
ejpam-5637	405	18	”	"	PUNCT
ejpam-5637	405	19	in	in	ADP
ejpam-5637	405	20	matrix	matrix	NOUN
ejpam-5637	405	21	diagonal	diagonal	ADJ
ejpam-5637	405	22	stability	stability	NOUN
ejpam-5637	405	23	in	in	ADP
ejpam-5637	405	24	systems	system	NOUN
ejpam-5637	405	25	and	and	CCONJ
ejpam-5637	405	26	computation	computation	NOUN
ejpam-5637	405	27	(	(	PUNCT
ejpam-5637	405	28	birkhauser	birkhauser	PROPN
ejpam-5637	405	29	,	,	PUNCT
ejpam-5637	405	30	boston	boston	PROPN
ejpam-5637	405	31	,	,	PUNCT
ejpam-5637	405	32	ma	ma	PROPN
ejpam-5637	405	33	,	,	PUNCT
ejpam-5637	405	34	2000	2000	NUM
ejpam-5637	405	35	)	)	PUNCT
ejpam-5637	405	36	.	.	PUNCT
ejpam-5637	406	1	[	[	X
ejpam-5637	406	2	26	26	NUM
ejpam-5637	406	3	]	]	PUNCT
ejpam-5637	406	4	m.	m.	NOUN
ejpam-5637	406	5	c.	c.	PROPN
ejpam-5637	406	6	kemp	kemp	PROPN
ejpam-5637	406	7	and	and	CCONJ
ejpam-5637	406	8	y.	y.	PROPN
ejpam-5637	406	9	kimura	kimura	PROPN
ejpam-5637	406	10	,	,	PUNCT
ejpam-5637	406	11	“	"	PUNCT
ejpam-5637	406	12	linear	linear	ADJ
ejpam-5637	406	13	inequalities	inequality	NOUN
ejpam-5637	406	14	,	,	PUNCT
ejpam-5637	406	15	”	"	PUNCT
ejpam-5637	406	16	in	in	ADP
ejpam-5637	406	17	introduction	introduction	NOUN
ejpam-5637	406	18	to	to	ADP
ejpam-5637	406	19	mathematical	mathematical	ADJ
ejpam-5637	406	20	economics	economic	NOUN
ejpam-5637	406	21	(	(	PUNCT
ejpam-5637	406	22	springer	springer	NOUN
ejpam-5637	406	23	,	,	PUNCT
ejpam-5637	406	24	new	new	PROPN
ejpam-5637	406	25	york	york	PROPN
ejpam-5637	406	26	,	,	PUNCT
ejpam-5637	406	27	1978	1978	NUM
ejpam-5637	406	28	)	)	PUNCT
ejpam-5637	406	29	.	.	PUNCT
ejpam-5637	407	1	[	[	X
ejpam-5637	407	2	27	27	NUM
ejpam-5637	407	3	]	]	X
ejpam-5637	407	4	ghadle	ghadle	NOUN
ejpam-5637	407	5	kirtiwant	kirtiwant	VERB
ejpam-5637	407	6	,	,	PUNCT
ejpam-5637	407	7	p.	p.	PROPN
ejpam-5637	407	8	;	;	PUNCT
ejpam-5637	407	9	muley	muley	PROPN
ejpam-5637	407	10	yogesh	yogesh	PROPN
ejpam-5637	407	11	,	,	PUNCT
ejpam-5637	407	12	m.	m.	NOUN
ejpam-5637	407	13	new	new	ADJ
ejpam-5637	407	14	approach	approach	NOUN
ejpam-5637	407	15	to	to	PART
ejpam-5637	407	16	solve	solve	VERB
ejpam-5637	407	17	assignment	assignment	NOUN
ejpam-5637	407	18	problem	problem	NOUN
ejpam-5637	407	19	m.u	m.u	PROPN
ejpam-5637	407	20	.	.	PROPN
ejpam-5637	408	1	rahman	rahman	PROPN
ejpam-5637	408	2	et	et	PROPN
ejpam-5637	408	3	al	al	PROPN
ejpam-5637	408	4	.	.	PUNCT
ejpam-5637	408	5	/	/	SYM
ejpam-5637	408	6	eur	eur	PROPN
ejpam-5637	408	7	.	.	PUNCT
ejpam-5637	409	1	j.	j.	PROPN
ejpam-5637	409	2	pure	pure	PROPN
ejpam-5637	409	3	appl	appl	PROPN
ejpam-5637	409	4	.	.	PROPN
ejpam-5637	409	5	math	math	PROPN
ejpam-5637	409	6	,	,	PUNCT
ejpam-5637	409	7	18	18	NUM
ejpam-5637	409	8	(	(	PUNCT
ejpam-5637	409	9	1	1	NUM
ejpam-5637	409	10	)	)	PUNCT
ejpam-5637	409	11	(	(	PUNCT
ejpam-5637	409	12	2025	2025	NUM
ejpam-5637	409	13	)	)	PUNCT
ejpam-5637	409	14	,	,	PUNCT
ejpam-5637	409	15	5637	5637	NUM
ejpam-5637	409	16	19	19	NUM
ejpam-5637	409	17	of	of	ADP
ejpam-5637	409	18	20	20	NUM
ejpam-5637	409	19	using	use	VERB
ejpam-5637	409	20	matlab	matlab	PROPN
ejpam-5637	409	21	.	.	PUNCT
ejpam-5637	410	1	int	int	PROPN
ejpam-5637	410	2	.	.	PUNCT
ejpam-5637	411	1	j.	j.	PROPN
ejpam-5637	411	2	latest	late	ADJ
ejpam-5637	411	3	technol	technol	PROPN
ejpam-5637	411	4	.	.	PUNCT
ejpam-5637	412	1	eng	eng	PROPN
ejpam-5637	412	2	.	.	PROPN
ejpam-5637	413	1	manag	manag	PROPN
ejpam-5637	413	2	.	.	PUNCT
ejpam-5637	414	1	appl	appl	PROPN
ejpam-5637	414	2	.	.	PUNCT
ejpam-5637	415	1	sci	sci	PROPN
ejpam-5637	415	2	.	.	PROPN
ejpam-5637	415	3	2015	2015	NUM
ejpam-5637	415	4	,	,	PUNCT
ejpam-5637	415	5	4	4	NUM
ejpam-5637	415	6	,	,	PUNCT
ejpam-5637	415	7	36–39	36–39	NUM
ejpam-5637	415	8	.	.	PUNCT
ejpam-5637	416	1	[	[	X
ejpam-5637	416	2	28	28	NUM
ejpam-5637	416	3	]	]	X
ejpam-5637	416	4	liu	liu	PROPN
ejpam-5637	416	5	,	,	PUNCT
ejpam-5637	416	6	l.	l.	PROPN
ejpam-5637	416	7	;	;	PUNCT
ejpam-5637	416	8	chen	chen	PROPN
ejpam-5637	416	9	,	,	PUNCT
ejpam-5637	416	10	r.c	r.c	PROPN
ejpam-5637	416	11	.	.	PROPN
ejpam-5637	416	12	a	a	DET
ejpam-5637	416	13	novel	novel	ADJ
ejpam-5637	416	14	passenger	passenger	NOUN
ejpam-5637	416	15	flow	flow	NOUN
ejpam-5637	416	16	prediction	prediction	NOUN
ejpam-5637	416	17	model	model	NOUN
ejpam-5637	416	18	using	use	VERB
ejpam-5637	416	19	deep	deep	ADJ
ejpam-5637	416	20	learning	learning	NOUN
ejpam-5637	416	21	methods	method	NOUN
ejpam-5637	416	22	.	.	PUNCT
ejpam-5637	417	1	transp	transp	PROPN
ejpam-5637	417	2	.	.	PUNCT
ejpam-5637	418	1	res	re	NOUN
ejpam-5637	418	2	.	.	PUNCT
ejpam-5637	419	1	part	part	NOUN
ejpam-5637	420	1	c	c	NOUN
ejpam-5637	420	2	:	:	PUNCT
ejpam-5637	420	3	emerg	emerg	PROPN
ejpam-5637	420	4	.	.	PUNCT
ejpam-5637	421	1	technol	technol	PROPN
ejpam-5637	421	2	.	.	PROPN
ejpam-5637	421	3	2017	2017	NUM
ejpam-5637	421	4	,	,	PUNCT
ejpam-5637	421	5	84	84	NUM
ejpam-5637	421	6	,	,	PUNCT
ejpam-5637	421	7	74–91	74–91	NUM
ejpam-5637	421	8	.	.	PUNCT
ejpam-5637	422	1	[	[	X
ejpam-5637	422	2	29	29	NUM
ejpam-5637	422	3	]	]	X
ejpam-5637	422	4	loch	loch	NOUN
ejpam-5637	422	5	,	,	PUNCT
ejpam-5637	422	6	g.v	g.v	PROPN
ejpam-5637	422	7	.	.	PROPN
ejpam-5637	422	8	;	;	PUNCT
ejpam-5637	422	9	da	da	PROPN
ejpam-5637	422	10	silva	silva	PROPN
ejpam-5637	422	11	,	,	PUNCT
ejpam-5637	422	12	a.c.l	a.c.l	NOUN
ejpam-5637	422	13	.	.	PUNCT
ejpam-5637	423	1	a	a	DET
ejpam-5637	423	2	computational	computational	ADJ
ejpam-5637	423	3	study	study	NOUN
ejpam-5637	423	4	on	on	ADP
ejpam-5637	423	5	the	the	DET
ejpam-5637	423	6	number	number	NOUN
ejpam-5637	423	7	of	of	ADP
ejpam-5637	423	8	iterations	iteration	NOUN
ejpam-5637	423	9	to	to	PART
ejpam-5637	423	10	solve	solve	VERB
ejpam-5637	423	11	the	the	DET
ejpam-5637	423	12	transportation	transportation	NOUN
ejpam-5637	423	13	problem	problem	NOUN
ejpam-5637	423	14	.	.	PUNCT
ejpam-5637	424	1	appl	appl	PROPN
ejpam-5637	424	2	.	.	PROPN
ejpam-5637	424	3	math	math	PROPN
ejpam-5637	424	4	.	.	PUNCT
ejpam-5637	425	1	sci	sci	PROPN
ejpam-5637	425	2	.	.	PROPN
ejpam-5637	425	3	2014	2014	NUM
ejpam-5637	425	4	,	,	PUNCT
ejpam-5637	425	5	8	8	NUM
ejpam-5637	425	6	,	,	PUNCT
ejpam-5637	425	7	4579–4583	4579–4583	NUM
ejpam-5637	425	8	.	.	PUNCT
ejpam-5637	426	1	[	[	X
ejpam-5637	426	2	30	30	NUM
ejpam-5637	426	3	]	]	X
ejpam-5637	426	4	magni	magni	X
ejpam-5637	426	5	,	,	PUNCT
ejpam-5637	426	6	j.	j.	PROPN
ejpam-5637	426	7	,	,	PUNCT
ejpam-5637	426	8	doll	doll	PROPN
ejpam-5637	426	9	,	,	PUNCT
ejpam-5637	426	10	c.	c.	PROPN
ejpam-5637	426	11	,	,	PUNCT
ejpam-5637	426	12	chiappa	chiappa	PROPN
ejpam-5637	426	13	,	,	PUNCT
ejpam-5637	426	14	c.	c.	PROPN
ejpam-5637	426	15	,	,	PUNCT
ejpam-5637	426	16	frappard	frappard	NOUN
ejpam-5637	426	17	,	,	PUNCT
ejpam-5637	426	18	b.	b.	PROPN
ejpam-5637	426	19	,	,	PUNCT
ejpam-5637	426	20	girouart	girouart	PROPN
ejpam-5637	426	21	,	,	PUNCT
ejpam-5637	426	22	b.	b.	PROPN
ejpam-5637	426	23	mixed	mix	VERB
ejpam-5637	426	24	-analysis	-analysis	NOUN
ejpam-5637	426	25	for	for	ADP
ejpam-5637	426	26	flexible	flexible	ADJ
ejpam-5637	426	27	systems	system	NOUN
ejpam-5637	426	28	.	.	PUNCT
ejpam-5637	427	1	part	part	NOUN
ejpam-5637	427	2	1	1	NUM
ejpam-5637	427	3	:	:	PUNCT
ejpam-5637	427	4	theory	theory	NOUN
ejpam-5637	427	5	.	.	PUNCT
ejpam-5637	428	1	in	in	ADP
ejpam-5637	428	2	proceedings	proceeding	NOUN
ejpam-5637	428	3	of	of	ADP
ejpam-5637	428	4	the	the	DET
ejpam-5637	428	5	14th	14th	ADJ
ejpam-5637	428	6	ifac	ifac	NOUN
ejpam-5637	428	7	world	world	PROPN
ejpam-5637	428	8	congress	congress	PROPN
ejpam-5637	428	9	,	,	PUNCT
ejpam-5637	428	10	beijing	beijing	PROPN
ejpam-5637	428	11	,	,	PUNCT
ejpam-5637	428	12	china	china	PROPN
ejpam-5637	428	13	,	,	PUNCT
ejpam-5637	428	14	(	(	PUNCT
ejpam-5637	428	15	1999	1999	NUM
ejpam-5637	428	16	)	)	PUNCT
ejpam-5637	428	17	,	,	PUNCT
ejpam-5637	428	18	325–360	325–360	NUM
ejpam-5637	428	19	.	.	PUNCT
ejpam-5637	429	1	[	[	X
ejpam-5637	429	2	31	31	NUM
ejpam-5637	429	3	]	]	X
ejpam-5637	429	4	mhlanga	mhlanga	PROPN
ejpam-5637	429	5	,	,	PUNCT
ejpam-5637	429	6	a.	a.	NOUN
ejpam-5637	429	7	;	;	PUNCT
ejpam-5637	429	8	nduna	nduna	PROPN
ejpam-5637	429	9	,	,	PUNCT
ejpam-5637	429	10	i.s	i.s	PROPN
ejpam-5637	429	11	.	.	PROPN
ejpam-5637	429	12	;	;	PUNCT
ejpam-5637	429	13	matarise	matarise	PROPN
ejpam-5637	429	14	,	,	PUNCT
ejpam-5637	429	15	d.f	d.f	PROPN
ejpam-5637	429	16	.	.	PROPN
ejpam-5637	429	17	;	;	PUNCT
ejpam-5637	429	18	machisvo	machisvo	NOUN
ejpam-5637	429	19	,	,	PUNCT
ejpam-5637	429	20	a.	a.	NOUN
ejpam-5637	429	21	innovative	innovative	ADJ
ejpam-5637	429	22	application	application	NOUN
ejpam-5637	429	23	of	of	ADP
ejpam-5637	429	24	dantzig	dantzig	PROPN
ejpam-5637	429	25	’s	’s	PART
ejpam-5637	429	26	north	north	PROPN
ejpam-5637	429	27	–	–	PUNCT
ejpam-5637	429	28	west	west	NOUN
ejpam-5637	429	29	corner	corner	NOUN
ejpam-5637	429	30	rule	rule	NOUN
ejpam-5637	429	31	to	to	PART
ejpam-5637	429	32	solve	solve	VERB
ejpam-5637	429	33	a	a	DET
ejpam-5637	429	34	transportation	transportation	NOUN
ejpam-5637	429	35	problem	problem	NOUN
ejpam-5637	429	36	.	.	PUNCT
ejpam-5637	430	1	int	int	NOUN
ejpam-5637	430	2	.	.	PUNCT
ejpam-5637	431	1	j.	j.	PROPN
ejpam-5637	431	2	educ	educ	PROPN
ejpam-5637	431	3	.	.	PUNCT
ejpam-5637	432	1	res	re	NOUN
ejpam-5637	432	2	.	.	PROPN
ejpam-5637	432	3	2014	2014	NUM
ejpam-5637	432	4	,	,	PUNCT
ejpam-5637	432	5	2	2	NUM
ejpam-5637	432	6	,	,	PUNCT
ejpam-5637	432	7	1–12	1–12	NOUN
ejpam-5637	432	8	.	.	PUNCT
ejpam-5637	433	1	[	[	X
ejpam-5637	433	2	32	32	NUM
ejpam-5637	433	3	]	]	PUNCT
ejpam-5637	433	4	m.	m.	NOUN
ejpam-5637	433	5	p.	p.	PROPN
ejpam-5637	433	6	newlin	newlin	PROPN
ejpam-5637	433	7	and	and	CCONJ
ejpam-5637	433	8	p.	p.	PROPN
ejpam-5637	433	9	m.	m.	PROPN
ejpam-5637	433	10	young	young	PROPN
ejpam-5637	433	11	,	,	PUNCT
ejpam-5637	433	12	“	"	PUNCT
ejpam-5637	433	13	mixed	mixed	ADJ
ejpam-5637	433	14	problems	problem	NOUN
ejpam-5637	433	15	and	and	CCONJ
ejpam-5637	433	16	branch	branch	NOUN
ejpam-5637	433	17	and	and	CCONJ
ejpam-5637	433	18	bound	bound	ADJ
ejpam-5637	433	19	techniques	technique	NOUN
ejpam-5637	433	20	,	,	PUNCT
ejpam-5637	433	21	”	"	PUNCT
ejpam-5637	433	22	int	int	NOUN
ejpam-5637	433	23	.	.	PUNCT
ejpam-5637	434	1	j.	j.	PROPN
ejpam-5637	434	2	robust	robust	PROPN
ejpam-5637	434	3	nonlin	nonlin	PROPN
ejpam-5637	434	4	.	.	PUNCT
ejpam-5637	435	1	control	control	PROPN
ejpam-5637	435	2	7	7	NUM
ejpam-5637	435	3	,	,	PUNCT
ejpam-5637	435	4	145–164	145–164	NUM
ejpam-5637	435	5	(	(	PUNCT
ejpam-5637	435	6	1997	1997	NUM
ejpam-5637	435	7	)	)	PUNCT
ejpam-5637	435	8	.	.	PUNCT
ejpam-5637	436	1	[	[	X
ejpam-5637	436	2	33	33	NUM
ejpam-5637	436	3	]	]	PUNCT
ejpam-5637	436	4	p.	p.	PROPN
ejpam-5637	436	5	k.	k.	PROPN
ejpam-5637	436	6	newman	newman	PROPN
ejpam-5637	436	7	,	,	PUNCT
ejpam-5637	436	8	“	"	PUNCT
ejpam-5637	436	9	some	some	DET
ejpam-5637	436	10	notes	note	NOUN
ejpam-5637	436	11	on	on	ADP
ejpam-5637	436	12	stability	stability	NOUN
ejpam-5637	436	13	conditions	condition	NOUN
ejpam-5637	436	14	,	,	PUNCT
ejpam-5637	436	15	”	"	PUNCT
ejpam-5637	436	16	rev	rev	PROPN
ejpam-5637	436	17	.	.	PROPN
ejpam-5637	436	18	econ	econ	PROPN
ejpam-5637	436	19	.	.	PUNCT
ejpam-5637	437	1	studies	study	NOUN
ejpam-5637	437	2	1	1	NUM
ejpam-5637	437	3	(	(	PUNCT
ejpam-5637	437	4	27	27	NUM
ejpam-5637	437	5	)	)	PUNCT
ejpam-5637	437	6	,	,	PUNCT
ejpam-5637	437	7	1–9	1–9	NUM
ejpam-5637	437	8	(	(	PUNCT
ejpam-5637	437	9	1959	1959	NUM
ejpam-5637	437	10	)	)	PUNCT
ejpam-5637	437	11	.	.	PUNCT
ejpam-5637	438	1	[	[	X
ejpam-5637	438	2	34	34	NUM
ejpam-5637	438	3	]	]	X
ejpam-5637	438	4	ozkok	ozkok	PROPN
ejpam-5637	438	5	,	,	PUNCT
ejpam-5637	438	6	b.a	b.a	PROPN
ejpam-5637	438	7	.	.	PROPN
ejpam-5637	438	8	an	an	DET
ejpam-5637	438	9	iterative	iterative	NOUN
ejpam-5637	438	10	algorithm	algorithm	NOUN
ejpam-5637	438	11	to	to	PART
ejpam-5637	438	12	solve	solve	VERB
ejpam-5637	438	13	a	a	DET
ejpam-5637	438	14	linear	linear	ADJ
ejpam-5637	438	15	fractional	fractional	ADJ
ejpam-5637	438	16	programming	programming	NOUN
ejpam-5637	438	17	problem	problem	NOUN
ejpam-5637	438	18	.	.	PUNCT
ejpam-5637	439	1	comput	comput	NOUN
ejpam-5637	439	2	.	.	PUNCT
ejpam-5637	440	1	ind	ind	PROPN
ejpam-5637	440	2	.	.	PUNCT
ejpam-5637	441	1	eng	eng	PROPN
ejpam-5637	441	2	.	.	PROPN
ejpam-5637	441	3	2020	2020	NUM
ejpam-5637	441	4	,	,	PUNCT
ejpam-5637	441	5	140	140	NUM
ejpam-5637	441	6	,	,	PUNCT
ejpam-5637	441	7	106234	106234	NUM
ejpam-5637	441	8	.	.	PUNCT
ejpam-5637	442	1	[	[	X
ejpam-5637	442	2	35	35	NUM
ejpam-5637	442	3	]	]	X
ejpam-5637	442	4	packard	packard	PROPN
ejpam-5637	442	5	,	,	PUNCT
ejpam-5637	442	6	andrew	andrew	PROPN
ejpam-5637	442	7	,	,	PUNCT
ejpam-5637	442	8	and	and	CCONJ
ejpam-5637	442	9	john	john	PROPN
ejpam-5637	442	10	doyle	doyle	PROPN
ejpam-5637	442	11	.	.	PUNCT
ejpam-5637	443	1	”	"	PUNCT
ejpam-5637	443	2	the	the	DET
ejpam-5637	443	3	complex	complex	ADJ
ejpam-5637	443	4	structured	structured	ADJ
ejpam-5637	443	5	singular	singular	ADJ
ejpam-5637	443	6	value	value	NOUN
ejpam-5637	443	7	.	.	PUNCT
ejpam-5637	443	8	”	"	PUNCT
ejpam-5637	443	9	automatica	automatica	PROPN
ejpam-5637	443	10	29	29	NUM
ejpam-5637	443	11	,	,	PUNCT
ejpam-5637	443	12	no	no	INTJ
ejpam-5637	443	13	.	.	NOUN
ejpam-5637	443	14	1	1	NUM
ejpam-5637	443	15	(	(	PUNCT
ejpam-5637	443	16	1993	1993	NUM
ejpam-5637	443	17	):	):	PUNCT
ejpam-5637	443	18	71	71	NUM
ejpam-5637	443	19	-	-	SYM
ejpam-5637	443	20	109	109	NUM
ejpam-5637	443	21	.	.	PUNCT
ejpam-5637	444	1	[	[	X
ejpam-5637	444	2	36	36	NUM
ejpam-5637	444	3	]	]	X
ejpam-5637	444	4	packard	packard	NOUN
ejpam-5637	444	5	,	,	PUNCT
ejpam-5637	444	6	andy	andy	PROPN
ejpam-5637	444	7	,	,	PUNCT
ejpam-5637	444	8	michael	michael	PROPN
ejpam-5637	444	9	kh	kh	PROPN
ejpam-5637	444	10	fan	fan	PROPN
ejpam-5637	444	11	,	,	PUNCT
ejpam-5637	444	12	and	and	CCONJ
ejpam-5637	444	13	john	john	PROPN
ejpam-5637	444	14	doyle	doyle	PROPN
ejpam-5637	444	15	.	.	PUNCT
ejpam-5637	445	1	a	a	DET
ejpam-5637	445	2	power	power	NOUN
ejpam-5637	445	3	method	method	NOUN
ejpam-5637	445	4	for	for	ADP
ejpam-5637	445	5	the	the	DET
ejpam-5637	445	6	structured	structured	ADJ
ejpam-5637	445	7	singular	singular	NOUN
ejpam-5637	445	8	value	value	NOUN
ejpam-5637	445	9	.	.	PUNCT
ejpam-5637	446	1	ieee	ieee	NOUN
ejpam-5637	446	2	conf	conf	NOUN
ejpam-5637	446	3	.	.	PUNCT
ejpam-5637	447	1	on	on	ADP
ejpam-5637	447	2	decision	decision	NOUN
ejpam-5637	447	3	and	and	CCONJ
ejpam-5637	447	4	control	control	NOUN
ejpam-5637	447	5	,	,	PUNCT
ejpam-5637	447	6	(	(	PUNCT
ejpam-5637	447	7	1988	1988	NUM
ejpam-5637	447	8	)	)	PUNCT
ejpam-5637	447	9	.	.	PUNCT
ejpam-5637	448	1	[	[	X
ejpam-5637	448	2	37	37	NUM
ejpam-5637	448	3	]	]	PUNCT
ejpam-5637	448	4	pallavi	pallavi	PROPN
ejpam-5637	448	5	,	,	PUNCT
ejpam-5637	448	6	p.l	p.l	PROPN
ejpam-5637	448	7	.	.	PROPN
ejpam-5637	448	8	;	;	PUNCT
ejpam-5637	448	9	lakshmi	lakshmi	PROPN
ejpam-5637	448	10	,	,	PUNCT
ejpam-5637	448	11	r.a	r.a	PROPN
ejpam-5637	448	12	.	.	PROPN
ejpam-5637	448	13	a	a	DET
ejpam-5637	448	14	mat	mat	NOUN
ejpam-5637	448	15	lab	lab	NOUN
ejpam-5637	448	16	oriented	orient	VERB
ejpam-5637	448	17	approach	approach	NOUN
ejpam-5637	448	18	to	to	PART
ejpam-5637	448	19	solve	solve	VERB
ejpam-5637	448	20	the	the	DET
ejpam-5637	448	21	transportation	transportation	NOUN
ejpam-5637	448	22	problem	problem	NOUN
ejpam-5637	448	23	.	.	PUNCT
ejpam-5637	449	1	int	int	NOUN
ejpam-5637	449	2	.	.	PUNCT
ejpam-5637	450	1	j.	j.	PROPN
ejpam-5637	450	2	adv	adv	PROPN
ejpam-5637	450	3	.	.	PUNCT
ejpam-5637	451	1	res	re	NOUN
ejpam-5637	451	2	.	.	PROPN
ejpam-5637	451	3	found	find	VERB
ejpam-5637	451	4	.	.	PUNCT
ejpam-5637	452	1	2015	2015	NUM
ejpam-5637	452	2	,	,	PUNCT
ejpam-5637	452	3	50	50	NUM
ejpam-5637	452	4	,	,	PUNCT
ejpam-5637	452	5	6000	6000	NUM
ejpam-5637	452	6	.	.	PUNCT
ejpam-5637	453	1	[	[	X
ejpam-5637	453	2	38	38	NUM
ejpam-5637	453	3	]	]	PUNCT
ejpam-5637	453	4	j.	j.	PROPN
ejpam-5637	453	5	quirk	quirk	PROPN
ejpam-5637	453	6	and	and	CCONJ
ejpam-5637	453	7	r.	r.	PROPN
ejpam-5637	453	8	saposnik	saposnik	PROPN
ejpam-5637	453	9	,	,	PUNCT
ejpam-5637	453	10	introduction	introduction	NOUN
ejpam-5637	453	11	to	to	ADP
ejpam-5637	453	12	general	general	ADJ
ejpam-5637	453	13	equilibrium	equilibrium	NOUN
ejpam-5637	453	14	theory	theory	NOUN
ejpam-5637	453	15	and	and	CCONJ
ejpam-5637	453	16	welfare	welfare	NOUN
ejpam-5637	453	17	economics	economic	NOUN
ejpam-5637	453	18	(	(	PUNCT
ejpam-5637	453	19	mcgraw	mcgraw	NOUN
ejpam-5637	453	20	-	-	PUNCT
ejpam-5637	453	21	hill	hill	PROPN
ejpam-5637	453	22	,	,	PUNCT
ejpam-5637	453	23	new	new	PROPN
ejpam-5637	453	24	york	york	PROPN
ejpam-5637	453	25	,	,	PUNCT
ejpam-5637	453	26	1968	1968	NUM
ejpam-5637	453	27	)	)	PUNCT
ejpam-5637	453	28	.	.	PUNCT
ejpam-5637	454	1	[	[	X
ejpam-5637	454	2	39	39	NUM
ejpam-5637	454	3	]	]	PUNCT
ejpam-5637	454	4	warren	warren	PROPN
ejpam-5637	454	5	,	,	PUNCT
ejpam-5637	454	6	richard	richard	PROPN
ejpam-5637	454	7	h.	h.	PROPN
ejpam-5637	454	8	”	"	PUNCT
ejpam-5637	454	9	classes	class	NOUN
ejpam-5637	454	10	of	of	ADP
ejpam-5637	454	11	matrices	matrix	NOUN
ejpam-5637	454	12	for	for	ADP
ejpam-5637	454	13	the	the	DET
ejpam-5637	454	14	traveling	travel	VERB
ejpam-5637	454	15	salesman	salesman	ADJ
ejpam-5637	454	16	problem	problem	NOUN
ejpam-5637	454	17	.	.	PUNCT
ejpam-5637	454	18	”	"	PUNCT
ejpam-5637	455	1	linear	linear	ADJ
ejpam-5637	455	2	algebra	algebra	NOUN
ejpam-5637	455	3	and	and	CCONJ
ejpam-5637	455	4	its	its	PRON
ejpam-5637	455	5	applications	application	NOUN
ejpam-5637	455	6	139	139	NUM
ejpam-5637	455	7	(	(	PUNCT
ejpam-5637	455	8	1990	1990	NUM
ejpam-5637	455	9	):	):	PUNCT
ejpam-5637	455	10	53	53	NUM
ejpam-5637	455	11	-	-	SYM
ejpam-5637	455	12	62	62	NUM
ejpam-5637	455	13	.	.	PUNCT
ejpam-5637	456	1	[	[	X
ejpam-5637	456	2	40	40	NUM
ejpam-5637	456	3	]	]	X
ejpam-5637	456	4	roy	roy	PROPN
ejpam-5637	456	5	,	,	PUNCT
ejpam-5637	456	6	s.	s.	PROPN
ejpam-5637	456	7	k.	k.	PROPN
ejpam-5637	456	8	;	;	PUNCT
ejpam-5637	456	9	maity	maity	NOUN
ejpam-5637	456	10	,	,	PUNCT
ejpam-5637	456	11	g.	g.	NOUN
ejpam-5637	456	12	minimizing	minimize	VERB
ejpam-5637	456	13	cost	cost	NOUN
ejpam-5637	456	14	and	and	CCONJ
ejpam-5637	456	15	time	time	NOUN
ejpam-5637	456	16	through	through	ADP
ejpam-5637	456	17	single	single	ADJ
ejpam-5637	456	18	objective	objective	ADJ
ejpam-5637	456	19	function	function	NOUN
ejpam-5637	456	20	in	in	ADP
ejpam-5637	456	21	multi	multi	ADJ
ejpam-5637	456	22	-	-	ADJ
ejpam-5637	456	23	choice	choice	ADJ
ejpam-5637	456	24	interval	interval	NOUN
ejpam-5637	456	25	valued	value	VERB
ejpam-5637	456	26	transportation	transportation	NOUN
ejpam-5637	456	27	problem	problem	NOUN
ejpam-5637	456	28	.	.	PUNCT
ejpam-5637	457	1	j.	j.	PROPN
ejpam-5637	457	2	intell	intell	PROPN
ejpam-5637	457	3	.	.	PUNCT
ejpam-5637	458	1	fuzzy	fuzzy	ADJ
ejpam-5637	458	2	syst	syst	PROPN
ejpam-5637	458	3	.	.	PUNCT
ejpam-5637	458	4	2017	2017	NUM
ejpam-5637	458	5	,	,	PUNCT
ejpam-5637	458	6	32	32	NUM
ejpam-5637	458	7	,	,	PUNCT
ejpam-5637	458	8	1697–1709	1697–1709	NUM
ejpam-5637	458	9	.	.	PUNCT
ejpam-5637	459	1	[	[	X
ejpam-5637	459	2	41	41	NUM
ejpam-5637	459	3	]	]	X
ejpam-5637	459	4	rückert	rückert	NOUN
ejpam-5637	459	5	,	,	PUNCT
ejpam-5637	459	6	darius	darius	PROPN
ejpam-5637	459	7	,	,	PUNCT
ejpam-5637	459	8	and	and	CCONJ
ejpam-5637	459	9	marc	marc	PROPN
ejpam-5637	459	10	stamminger	stamminger	PROPN
ejpam-5637	459	11	.	.	PUNCT
ejpam-5637	460	1	”	"	PUNCT
ejpam-5637	460	2	an	an	DET
ejpam-5637	460	3	efficient	efficient	ADJ
ejpam-5637	460	4	solution	solution	NOUN
ejpam-5637	460	5	to	to	ADP
ejpam-5637	460	6	structured	structured	ADJ
ejpam-5637	460	7	optimization	optimization	NOUN
ejpam-5637	460	8	problems	problem	NOUN
ejpam-5637	460	9	using	use	VERB
ejpam-5637	460	10	recursive	recursive	ADJ
ejpam-5637	460	11	matrices	matrix	NOUN
ejpam-5637	460	12	.	.	PUNCT
ejpam-5637	460	13	”	"	PUNCT
ejpam-5637	461	1	in	in	ADP
ejpam-5637	461	2	computer	computer	NOUN
ejpam-5637	461	3	graphics	graphic	NOUN
ejpam-5637	461	4	forum	forum	PROPN
ejpam-5637	461	5	,	,	PUNCT
ejpam-5637	461	6	vol	vol	NOUN
ejpam-5637	461	7	.	.	PROPN
ejpam-5637	461	8	38	38	NUM
ejpam-5637	461	9	,	,	PUNCT
ejpam-5637	461	10	no	no	INTJ
ejpam-5637	461	11	.	.	NOUN
ejpam-5637	461	12	8	8	NUM
ejpam-5637	461	13	,	,	PUNCT
ejpam-5637	461	14	pp	pp	ADJ
ejpam-5637	461	15	.	.	PUNCT
ejpam-5637	461	16	33	33	NUM
ejpam-5637	461	17	-	-	SYM
ejpam-5637	461	18	39	39	NUM
ejpam-5637	461	19	.	.	PUNCT
ejpam-5637	461	20	2019	2019	NUM
ejpam-5637	461	21	.	.	PUNCT
ejpam-5637	462	1	[	[	X
ejpam-5637	462	2	42	42	NUM
ejpam-5637	462	3	]	]	PUNCT
ejpam-5637	462	4	sagratella	sagratella	NOUN
ejpam-5637	462	5	,	,	PUNCT
ejpam-5637	462	6	s.	s.	PROPN
ejpam-5637	462	7	;	;	PUNCT
ejpam-5637	462	8	schmidt	schmidt	PROPN
ejpam-5637	462	9	,	,	PUNCT
ejpam-5637	462	10	m.	m.	NOUN
ejpam-5637	462	11	;	;	PUNCT
ejpam-5637	462	12	sudermann	sudermann	NOUN
ejpam-5637	462	13	-	-	PUNCT
ejpam-5637	462	14	merx	merx	ADJ
ejpam-5637	462	15	,	,	PUNCT
ejpam-5637	462	16	n.	n.	NOUN
ejpam-5637	462	17	the	the	DET
ejpam-5637	462	18	noncooperative	noncooperative	ADJ
ejpam-5637	462	19	fixed	fix	VERB
ejpam-5637	462	20	charge	charge	NOUN
ejpam-5637	462	21	transportation	transportation	NOUN
ejpam-5637	462	22	problem	problem	NOUN
ejpam-5637	462	23	.	.	PUNCT
ejpam-5637	463	1	eur	eur	PROPN
ejpam-5637	463	2	.	.	PUNCT
ejpam-5637	464	1	j.	j.	PROPN
ejpam-5637	464	2	oper	oper	PROPN
ejpam-5637	464	3	.	.	PUNCT
ejpam-5637	465	1	res	res	PROPN
ejpam-5637	465	2	.	.	PUNCT
ejpam-5637	466	1	2020	2020	NUM
ejpam-5637	466	2	,	,	PUNCT
ejpam-5637	466	3	284	284	NUM
ejpam-5637	466	4	,	,	PUNCT
ejpam-5637	466	5	373–382	373–382	NUM
ejpam-5637	466	6	.	.	PUNCT
ejpam-5637	467	1	[	[	X
ejpam-5637	467	2	43	43	NUM
ejpam-5637	467	3	]	]	X
ejpam-5637	467	4	salehi	salehi	NOUN
ejpam-5637	467	5	,	,	PUNCT
ejpam-5637	467	6	m.	m.	NOUN
ejpam-5637	467	7	;	;	PUNCT
ejpam-5637	467	8	jalalian	jalalian	NOUN
ejpam-5637	467	9	,	,	PUNCT
ejpam-5637	467	10	m.	m.	NOUN
ejpam-5637	467	11	;	;	PUNCT
ejpam-5637	467	12	vali	vali	PROPN
ejpam-5637	467	13	siar	siar	PROPN
ejpam-5637	467	14	,	,	PUNCT
ejpam-5637	467	15	m.	m.	NOUN
ejpam-5637	467	16	green	green	PROPN
ejpam-5637	467	17	transportation	transportation	NOUN
ejpam-5637	467	18	scheduling	scheduling	NOUN
ejpam-5637	467	19	with	with	ADP
ejpam-5637	467	20	speed	speed	NOUN
ejpam-5637	467	21	control	control	NOUN
ejpam-5637	467	22	:	:	PUNCT
ejpam-5637	467	23	trade	trade	NOUN
ejpam-5637	467	24	-	-	PUNCT
ejpam-5637	467	25	off	off	NOUN
ejpam-5637	467	26	between	between	ADP
ejpam-5637	467	27	total	total	ADJ
ejpam-5637	467	28	transportation	transportation	NOUN
ejpam-5637	467	29	cost	cost	NOUN
ejpam-5637	467	30	and	and	CCONJ
ejpam-5637	467	31	carbon	carbon	NOUN
ejpam-5637	467	32	emission	emission	NOUN
ejpam-5637	467	33	.	.	PUNCT
ejpam-5637	468	1	comput	comput	NOUN
ejpam-5637	468	2	.	.	PUNCT
ejpam-5637	469	1	ind	ind	PROPN
ejpam-5637	469	2	.	.	PUNCT
ejpam-5637	470	1	eng	eng	PROPN
ejpam-5637	470	2	.	.	PROPN
ejpam-5637	470	3	2017	2017	NUM
ejpam-5637	470	4	,	,	PUNCT
ejpam-5637	470	5	113	113	NUM
ejpam-5637	470	6	,	,	PUNCT
ejpam-5637	470	7	392–404	392–404	NUM
ejpam-5637	470	8	.	.	PUNCT
ejpam-5637	471	1	[	[	X
ejpam-5637	471	2	44	44	NUM
ejpam-5637	471	3	]	]	SYM
ejpam-5637	471	4	seiler	seiler	NOUN
ejpam-5637	471	5	,	,	PUNCT
ejpam-5637	471	6	p.	p.	PROPN
ejpam-5637	471	7	,	,	PUNCT
ejpam-5637	471	8	balas	balas	PROPN
ejpam-5637	471	9	,	,	PUNCT
ejpam-5637	471	10	g.	g.	PROPN
ejpam-5637	471	11	,	,	PUNCT
ejpam-5637	471	12	packard	packard	PROPN
ejpam-5637	471	13	,	,	PUNCT
ejpam-5637	471	14	a.	a.	NOUN
ejpam-5637	471	15	a	a	DET
ejpam-5637	471	16	gain	gain	NOUN
ejpam-5637	471	17	-	-	PUNCT
ejpam-5637	471	18	based	base	VERB
ejpam-5637	471	19	lower	low	ADJ
ejpam-5637	471	20	bound	bind	VERB
ejpam-5637	471	21	algorithm	algorithm	NOUN
ejpam-5637	471	22	for	for	ADP
ejpam-5637	471	23	real	real	ADJ
ejpam-5637	471	24	and	and	CCONJ
ejpam-5637	471	25	mixed	mixed	ADJ
ejpam-5637	471	26	µ	µ	PRON
ejpam-5637	471	27	problems	problem	NOUN
ejpam-5637	471	28	.	.	PUNCT
ejpam-5637	472	1	in	in	ADP
ejpam-5637	472	2	proceedings	proceeding	NOUN
ejpam-5637	472	3	of	of	ADP
ejpam-5637	472	4	the	the	DET
ejpam-5637	472	5	45th	45th	ADJ
ejpam-5637	472	6	ieee	ieee	NOUN
ejpam-5637	472	7	conference	conference	NOUN
ejpam-5637	472	8	on	on	ADP
ejpam-5637	472	9	decision	decision	NOUN
ejpam-5637	472	10	and	and	CCONJ
ejpam-5637	472	11	control	control	NOUN
ejpam-5637	472	12	,	,	PUNCT
ejpam-5637	472	13	san	san	PROPN
ejpam-5637	472	14	diego	diego	PROPN
ejpam-5637	472	15	,	,	PUNCT
ejpam-5637	472	16	california	california	PROPN
ejpam-5637	472	17	,	,	PUNCT
ejpam-5637	472	18	(	(	PUNCT
ejpam-5637	472	19	2006	2006	NUM
ejpam-5637	472	20	)	)	PUNCT
ejpam-5637	472	21	,	,	PUNCT
ejpam-5637	472	22	3548–3553	3548–3553	NUM
ejpam-5637	472	23	.	.	PUNCT
ejpam-5637	473	1	[	[	X
ejpam-5637	473	2	45	45	NUM
ejpam-5637	473	3	]	]	PUNCT
ejpam-5637	473	4	serrano	serrano	PROPN
ejpam-5637	473	5	-	-	PUNCT
ejpam-5637	473	6	hernandez	hernandez	PROPN
ejpam-5637	473	7	,	,	PUNCT
ejpam-5637	473	8	a.	a.	PROPN
ejpam-5637	473	9	;	;	PUNCT
ejpam-5637	473	10	faulin	faulin	PROPN
ejpam-5637	473	11	,	,	PUNCT
ejpam-5637	473	12	j.	j.	PROPN
ejpam-5637	473	13	;	;	PUNCT
ejpam-5637	473	14	hirsch	hirsch	PROPN
ejpam-5637	473	15	,	,	PUNCT
ejpam-5637	473	16	p.	p.	NOUN
ejpam-5637	473	17	;	;	PUNCT
ejpam-5637	473	18	fikar	fikar	NOUN
ejpam-5637	473	19	,	,	PUNCT
ejpam-5637	473	20	c.	c.	PROPN
ejpam-5637	473	21	agent	agent	NOUN
ejpam-5637	473	22	-	-	PUNCT
ejpam-5637	473	23	based	base	VERB
ejpam-5637	473	24	simulation	simulation	NOUN
ejpam-5637	473	25	for	for	ADP
ejpam-5637	473	26	horizontal	horizontal	ADJ
ejpam-5637	473	27	cooperation	cooperation	NOUN
ejpam-5637	473	28	in	in	ADP
ejpam-5637	473	29	logistics	logistic	NOUN
ejpam-5637	473	30	and	and	CCONJ
ejpam-5637	473	31	transportation	transportation	NOUN
ejpam-5637	473	32	:	:	PUNCT
ejpam-5637	473	33	from	from	ADP
ejpam-5637	473	34	the	the	DET
ejpam-5637	473	35	individual	individual	NOUN
ejpam-5637	473	36	to	to	ADP
ejpam-5637	473	37	the	the	DET
ejpam-5637	473	38	m.u	m.u	PROPN
ejpam-5637	473	39	.	.	PUNCT
ejpam-5637	473	40	rahman	rahman	PROPN
ejpam-5637	473	41	et	et	PROPN
ejpam-5637	473	42	al	al	PROPN
ejpam-5637	473	43	.	.	PUNCT
ejpam-5637	473	44	/	/	SYM
ejpam-5637	473	45	eur	eur	PROPN
ejpam-5637	473	46	.	.	PUNCT
ejpam-5637	474	1	j.	j.	PROPN
ejpam-5637	474	2	pure	pure	PROPN
ejpam-5637	474	3	appl	appl	PROPN
ejpam-5637	474	4	.	.	PROPN
ejpam-5637	474	5	math	math	PROPN
ejpam-5637	474	6	,	,	PUNCT
ejpam-5637	474	7	18	18	NUM
ejpam-5637	474	8	(	(	PUNCT
ejpam-5637	474	9	1	1	NUM
ejpam-5637	474	10	)	)	PUNCT
ejpam-5637	474	11	(	(	PUNCT
ejpam-5637	474	12	2025	2025	NUM
ejpam-5637	474	13	)	)	PUNCT
ejpam-5637	474	14	,	,	PUNCT
ejpam-5637	474	15	5637	5637	NUM
ejpam-5637	474	16	20	20	NUM
ejpam-5637	474	17	of	of	ADP
ejpam-5637	474	18	20	20	NUM
ejpam-5637	474	19	grand	grand	ADJ
ejpam-5637	474	20	coalition	coalition	NOUN
ejpam-5637	474	21	.	.	PUNCT
ejpam-5637	475	1	simul	simul	PROPN
ejpam-5637	475	2	.	.	PUNCT
ejpam-5637	475	3	model	model	PROPN
ejpam-5637	475	4	.	.	PUNCT
ejpam-5637	476	1	pract	pract	PROPN
ejpam-5637	476	2	.	.	PUNCT
ejpam-5637	477	1	theory	theory	NOUN
ejpam-5637	477	2	2018	2018	NUM
ejpam-5637	477	3	,	,	PUNCT
ejpam-5637	477	4	85	85	NUM
ejpam-5637	477	5	,	,	PUNCT
ejpam-5637	477	6	47–59	47–59	NOUN
ejpam-5637	477	7	.	.	PUNCT
ejpam-5637	478	1	[	[	X
ejpam-5637	478	2	46	46	NUM
ejpam-5637	478	3	]	]	X
ejpam-5637	478	4	sharma	sharma	PROPN
ejpam-5637	478	5	,	,	PUNCT
ejpam-5637	478	6	j.k	j.k	PROPN
ejpam-5637	478	7	.	.	PROPN
ejpam-5637	478	8	;	;	PUNCT
ejpam-5637	478	9	swarup	swarup	PROPN
ejpam-5637	478	10	,	,	PUNCT
ejpam-5637	478	11	k.	k.	PROPN
ejpam-5637	478	12	time	time	NOUN
ejpam-5637	478	13	minimizing	minimize	VERB
ejpam-5637	478	14	transportation	transportation	NOUN
ejpam-5637	478	15	problem	problem	NOUN
ejpam-5637	478	16	.	.	PUNCT
ejpam-5637	479	1	proc	proc	NOUN
ejpam-5637	479	2	.	.	PUNCT
ejpam-5637	480	1	indian	indian	PROPN
ejpam-5637	480	2	acad	acad	PROPN
ejpam-5637	480	3	.	.	PUNCT
ejpam-5637	481	1	sci	sci	PROPN
ejpam-5637	481	2	.	.	PROPN
ejpam-5637	481	3	1977	1977	NUM
ejpam-5637	481	4	,	,	PUNCT
ejpam-5637	481	5	86	86	NUM
ejpam-5637	481	6	,	,	PUNCT
ejpam-5637	481	7	513–518	513–518	NUM
ejpam-5637	481	8	.	.	PUNCT
ejpam-5637	482	1	[	[	X
ejpam-5637	482	2	47	47	NUM
ejpam-5637	482	3	]	]	X
ejpam-5637	482	4	szware	szware	NOUN
ejpam-5637	482	5	,	,	PUNCT
ejpam-5637	482	6	w.	w.	PROPN
ejpam-5637	482	7	some	some	DET
ejpam-5637	482	8	remarks	remark	VERB
ejpam-5637	482	9	on	on	ADP
ejpam-5637	482	10	the	the	DET
ejpam-5637	482	11	time	time	NOUN
ejpam-5637	482	12	transportation	transportation	NOUN
ejpam-5637	482	13	problem	problem	NOUN
ejpam-5637	482	14	.	.	PUNCT
ejpam-5637	483	1	nav	nav	NOUN
ejpam-5637	483	2	.	.	PUNCT
ejpam-5637	484	1	res	re	NOUN
ejpam-5637	484	2	.	.	PUNCT
ejpam-5637	485	1	logist	logist	PROPN
ejpam-5637	485	2	.	.	PUNCT
ejpam-5637	486	1	q.	q.	PROPN
ejpam-5637	486	2	1971	1971	NUM
ejpam-5637	486	3	,	,	PUNCT
ejpam-5637	486	4	18	18	NUM
ejpam-5637	486	5	,	,	PUNCT
ejpam-5637	486	6	473–485	473–485	NUM
ejpam-5637	486	7	.	.	PUNCT
ejpam-5637	487	1	[	[	X
ejpam-5637	487	2	48	48	NUM
ejpam-5637	487	3	]	]	SYM
ejpam-5637	487	4	tamannaei	tamannaei	ADJ
ejpam-5637	487	5	,	,	PUNCT
ejpam-5637	487	6	m.	m.	NOUN
ejpam-5637	487	7	;	;	PUNCT
ejpam-5637	487	8	rasti	rasti	NOUN
ejpam-5637	487	9	-	-	PUNCT
ejpam-5637	487	10	barzoki	barzoki	NOUN
ejpam-5637	487	11	,	,	PUNCT
ejpam-5637	487	12	m.	m.	NOUN
ejpam-5637	487	13	mathematical	mathematical	ADJ
ejpam-5637	487	14	programming	programming	NOUN
ejpam-5637	487	15	and	and	CCONJ
ejpam-5637	487	16	solution	solution	NOUN
ejpam-5637	487	17	approaches	approach	NOUN
ejpam-5637	487	18	for	for	ADP
ejpam-5637	487	19	minimizing	minimize	VERB
ejpam-5637	487	20	tardiness	tardiness	NOUN
ejpam-5637	487	21	and	and	CCONJ
ejpam-5637	487	22	transportation	transportation	NOUN
ejpam-5637	487	23	costs	cost	NOUN
ejpam-5637	487	24	in	in	ADP
ejpam-5637	487	25	the	the	DET
ejpam-5637	487	26	supply	supply	NOUN
ejpam-5637	487	27	chain	chain	NOUN
ejpam-5637	487	28	scheduling	scheduling	NOUN
ejpam-5637	487	29	problem	problem	NOUN
ejpam-5637	487	30	.	.	PUNCT
ejpam-5637	488	1	comput	comput	NOUN
ejpam-5637	488	2	.	.	PUNCT
ejpam-5637	489	1	ind	ind	PROPN
ejpam-5637	489	2	.	.	PUNCT
ejpam-5637	490	1	eng	eng	PROPN
ejpam-5637	490	2	.	.	PROPN
ejpam-5637	490	3	2019	2019	NUM
ejpam-5637	490	4	,	,	PUNCT
ejpam-5637	490	5	127	127	NUM
ejpam-5637	490	6	,	,	PUNCT
ejpam-5637	490	7	643–656	643–656	NUM
ejpam-5637	490	8	.	.	PUNCT
ejpam-5637	491	1	[	[	X
ejpam-5637	491	2	49	49	NUM
ejpam-5637	491	3	]	]	X
ejpam-5637	491	4	trefethen	trefethen	NOUN
ejpam-5637	491	5	,	,	PUNCT
ejpam-5637	491	6	lloyd	lloyd	PROPN
ejpam-5637	491	7	n.	n.	PROPN
ejpam-5637	491	8	spectra	spectra	PROPN
ejpam-5637	491	9	and	and	CCONJ
ejpam-5637	491	10	pseudospectra	pseudospectra	PROPN
ejpam-5637	491	11	:	:	PUNCT
ejpam-5637	491	12	the	the	DET
ejpam-5637	491	13	behavior	behavior	NOUN
ejpam-5637	491	14	of	of	ADP
ejpam-5637	491	15	nonnormal	nonnormal	ADJ
ejpam-5637	491	16	matrices	matrix	NOUN
ejpam-5637	491	17	and	and	CCONJ
ejpam-5637	491	18	operators	operator	NOUN
ejpam-5637	491	19	.	.	PUNCT
ejpam-5637	492	1	(	(	PUNCT
ejpam-5637	492	2	2020	2020	NUM
ejpam-5637	492	3	):	):	PUNCT
ejpam-5637	492	4	1	1	NUM
ejpam-5637	492	5	-	-	SYM
ejpam-5637	492	6	624	624	NUM
ejpam-5637	492	7	.	.	PUNCT
ejpam-5637	493	1	[	[	X
ejpam-5637	493	2	50	50	NUM
ejpam-5637	493	3	]	]	PUNCT
ejpam-5637	493	4	van	van	PROPN
ejpam-5637	493	5	der	der	PROPN
ejpam-5637	493	6	veen	veen	PROPN
ejpam-5637	493	7	,	,	PUNCT
ejpam-5637	493	8	jack	jack	PROPN
ejpam-5637	493	9	,	,	PUNCT
ejpam-5637	493	10	rené	rené	ADJ
ejpam-5637	493	11	van	van	PROPN
ejpam-5637	493	12	dal	dal	PROPN
ejpam-5637	493	13	,	,	PUNCT
ejpam-5637	493	14	and	and	CCONJ
ejpam-5637	493	15	gerard	gerard	PROPN
ejpam-5637	493	16	sierksma	sierksma	PROPN
ejpam-5637	493	17	.	.	PUNCT
ejpam-5637	494	1	the	the	DET
ejpam-5637	494	2	symmetric	symmetric	ADJ
ejpam-5637	494	3	circulant	circulant	ADJ
ejpam-5637	494	4	traveling	travel	VERB
ejpam-5637	494	5	salesman	salesman	ADJ
ejpam-5637	494	6	problem	problem	NOUN
ejpam-5637	494	7	.	.	PUNCT
ejpam-5637	495	1	institute	institute	PROPN
ejpam-5637	495	2	of	of	ADP
ejpam-5637	495	3	faculty	faculty	NOUN
ejpam-5637	495	4	research	research	NOUN
ejpam-5637	495	5	,	,	PUNCT
ejpam-5637	495	6	faculty	faculty	NOUN
ejpam-5637	495	7	of	of	ADP
ejpam-5637	495	8	economics	economic	NOUN
ejpam-5637	495	9	,	,	PUNCT
ejpam-5637	495	10	university	university	NOUN
ejpam-5637	495	11	of	of	ADP
ejpam-5637	495	12	groningen	groningen	PROPN
ejpam-5637	495	13	,	,	PUNCT
ejpam-5637	495	14	1991	1991	NUM
ejpam-5637	495	15	.	.	PUNCT
ejpam-5637	496	1	[	[	X
ejpam-5637	496	2	51	51	NUM
ejpam-5637	496	3	]	]	SYM
ejpam-5637	496	4	venkatachalapathy	venkatachalapathy	ADJ
ejpam-5637	496	5	,	,	PUNCT
ejpam-5637	496	6	m.	m.	NOUN
ejpam-5637	496	7	;	;	PUNCT
ejpam-5637	496	8	pandiarajan	pandiarajan	PROPN
ejpam-5637	496	9	,	,	PUNCT
ejpam-5637	496	10	r.	r.	PROPN
ejpam-5637	496	11	;	;	PUNCT
ejpam-5637	496	12	ganeshkumar	ganeshkumar	PROPN
ejpam-5637	496	13	,	,	PUNCT
ejpam-5637	496	14	s.	s.	PROPN
ejpam-5637	496	15	a	a	DET
ejpam-5637	496	16	special	special	ADJ
ejpam-5637	496	17	type	type	NOUN
ejpam-5637	496	18	of	of	ADP
ejpam-5637	496	19	solving	solve	VERB
ejpam-5637	496	20	transportation	transportation	NOUN
ejpam-5637	496	21	problems	problem	NOUN
ejpam-5637	496	22	using	use	VERB
ejpam-5637	496	23	generalized	generalized	ADJ
ejpam-5637	496	24	quadratic	quadratic	ADJ
ejpam-5637	496	25	fuzzy	fuzzy	ADJ
ejpam-5637	496	26	number	number	NOUN
ejpam-5637	496	27	.	.	PUNCT
ejpam-5637	497	1	int	int	NOUN
ejpam-5637	497	2	.	.	PUNCT
ejpam-5637	498	1	j.	j.	PROPN
ejpam-5637	498	2	sci	sci	PROPN
ejpam-5637	498	3	.	.	PROPN
ejpam-5637	499	1	technol	technol	PROPN
ejpam-5637	499	2	.	.	PUNCT
ejpam-5637	500	1	res	re	NOUN
ejpam-5637	500	2	.	.	PUNCT
ejpam-5637	501	1	2020	2020	NUM
ejpam-5637	501	2	,	,	PUNCT
ejpam-5637	501	3	9	9	NUM
ejpam-5637	501	4	,	,	PUNCT
ejpam-5637	501	5	6344–6348	6344–6348	NOUN
ejpam-5637	501	6	.	.	PUNCT
ejpam-5637	502	1	[	[	X
ejpam-5637	502	2	52	52	NUM
ejpam-5637	502	3	]	]	PUNCT
ejpam-5637	502	4	wagenaar	wagenaar	NOUN
ejpam-5637	502	5	,	,	PUNCT
ejpam-5637	502	6	j.	j.	PROPN
ejpam-5637	502	7	;	;	PUNCT
ejpam-5637	502	8	kroon	kroon	PROPN
ejpam-5637	502	9	,	,	PUNCT
ejpam-5637	502	10	l.	l.	PROPN
ejpam-5637	502	11	;	;	PUNCT
ejpam-5637	502	12	fragkos	fragkos	PROPN
ejpam-5637	502	13	,	,	PUNCT
ejpam-5637	502	14	i.	i.	NOUN
ejpam-5637	502	15	rolling	roll	VERB
ejpam-5637	502	16	stock	stock	NOUN
ejpam-5637	502	17	rescheduling	reschedule	VERB
ejpam-5637	502	18	in	in	ADP
ejpam-5637	502	19	passenger	passenger	NOUN
ejpam-5637	502	20	railway	railway	NOUN
ejpam-5637	502	21	transportation	transportation	NOUN
ejpam-5637	502	22	using	use	VERB
ejpam-5637	502	23	dead	dead	ADV
ejpam-5637	502	24	-	-	PUNCT
ejpam-5637	502	25	heading	head	VERB
ejpam-5637	502	26	trips	trip	NOUN
ejpam-5637	502	27	and	and	CCONJ
ejpam-5637	502	28	adjusted	adjusted	ADJ
ejpam-5637	502	29	passenger	passenger	NOUN
ejpam-5637	502	30	demand	demand	NOUN
ejpam-5637	502	31	.	.	PUNCT
ejpam-5637	503	1	transp	transp	PROPN
ejpam-5637	503	2	.	.	PUNCT
ejpam-5637	504	1	res	re	NOUN
ejpam-5637	504	2	.	.	PUNCT
ejpam-5637	505	1	part	part	NOUN
ejpam-5637	505	2	b	b	PROPN
ejpam-5637	505	3	methodol	methodol	NOUN
ejpam-5637	505	4	.	.	PUNCT
ejpam-5637	506	1	2017	2017	NUM
ejpam-5637	506	2	,	,	PUNCT
ejpam-5637	506	3	101	101	NUM
ejpam-5637	506	4	,	,	PUNCT
ejpam-5637	506	5	140–161	140–161	NUM
ejpam-5637	506	6	.	.	PUNCT
ejpam-5637	507	1	[	[	X
ejpam-5637	507	2	53	53	NUM
ejpam-5637	507	3	]	]	PUNCT
ejpam-5637	507	4	j.	j.	PROPN
ejpam-5637	507	5	e.	e.	PROPN
ejpam-5637	507	6	woods	woods	PROPN
ejpam-5637	507	7	,	,	PUNCT
ejpam-5637	507	8	mathematical	mathematical	ADJ
ejpam-5637	507	9	economics	economic	NOUN
ejpam-5637	507	10	.	.	PUNCT
ejpam-5637	508	1	topics	topic	NOUN
ejpam-5637	508	2	in	in	ADP
ejpam-5637	508	3	multi	multi	ADJ
ejpam-5637	508	4	-	-	ADJ
ejpam-5637	508	5	sectoral	sectoral	ADJ
ejpam-5637	508	6	economics	economic	NOUN
ejpam-5637	508	7	(	(	PUNCT
ejpam-5637	508	8	longman	longman	NOUN
ejpam-5637	508	9	group	group	NOUN
ejpam-5637	508	10	,	,	PUNCT
ejpam-5637	508	11	london	london	PROPN
ejpam-5637	508	12	,	,	PUNCT
ejpam-5637	508	13	1978	1978	NUM
ejpam-5637	508	14	)	)	PUNCT
ejpam-5637	508	15	.	.	PUNCT
ejpam-5637	509	1	[	[	X
ejpam-5637	509	2	54	54	NUM
ejpam-5637	509	3	]	]	SYM
ejpam-5637	509	4	żurek	żurek	PROPN
ejpam-5637	509	5	,	,	PUNCT
ejpam-5637	509	6	j.	j.	PROPN
ejpam-5637	509	7	;	;	PUNCT
ejpam-5637	509	8	ma	ma	PROPN
ejpam-5637	509	9	lachowski	lachowski	PROPN
ejpam-5637	509	10	,	,	PUNCT
ejpam-5637	509	11	j.	j.	PROPN
ejpam-5637	509	12	;	;	PUNCT
ejpam-5637	509	13	zió	zió	X
ejpam-5637	509	14	lkowski	lkowski	PROPN
ejpam-5637	509	15	,	,	PUNCT
ejpam-5637	509	16	j.	j.	PROPN
ejpam-5637	509	17	;	;	PUNCT
ejpam-5637	509	18	szkutnik	szkutnik	X
ejpam-5637	509	19	-	-	PUNCT
ejpam-5637	509	20	rogoż	rogoż	NOUN
ejpam-5637	509	21	,	,	PUNCT
ejpam-5637	509	22	j.	j.	PROPN
ejpam-5637	509	23	reliability	reliability	NOUN
ejpam-5637	509	24	analysis	analysis	NOUN
ejpam-5637	509	25	of	of	ADP
ejpam-5637	509	26	technical	technical	ADJ
ejpam-5637	509	27	means	mean	NOUN
ejpam-5637	509	28	of	of	ADP
ejpam-5637	509	29	transport	transport	NOUN
ejpam-5637	509	30	.	.	PUNCT
ejpam-5637	510	1	app	app	PROPN
ejpam-5637	510	2	.	.	PUNCT
ejpam-5637	511	1	sci	sci	PROPN
ejpam-5637	511	2	.	.	PROPN
ejpam-5637	511	3	2020	2020	NUM
ejpam-5637	511	4	,	,	PUNCT
ejpam-5637	511	5	10	10	NUM
ejpam-5637	511	6	,	,	PUNCT
ejpam-5637	511	7	3016	3016	NUM
ejpam-5637	511	8	.	.	PUNCT