id	sid	tid	token	lemma	pos
ejpam-5776	1	1	european	european	PROPN
ejpam-5776	1	2	journal	journal	PROPN
ejpam-5776	1	3	of	of	ADP
ejpam-5776	1	4	pure	pure	ADJ
ejpam-5776	1	5	and	and	CCONJ
ejpam-5776	1	6	applied	applied	ADJ
ejpam-5776	1	7	mathematics	mathematic	NOUN
ejpam-5776	1	8	2025	2025	NUM
ejpam-5776	1	9	,	,	PUNCT
ejpam-5776	1	10	vol	vol	NOUN
ejpam-5776	1	11	.	.	PROPN
ejpam-5776	1	12	18	18	NUM
ejpam-5776	1	13	,	,	PUNCT
ejpam-5776	1	14	issue	issue	NOUN
ejpam-5776	1	15	2	2	NUM
ejpam-5776	1	16	,	,	PUNCT
ejpam-5776	1	17	article	article	NOUN
ejpam-5776	1	18	number	number	NOUN
ejpam-5776	1	19	5776	5776	NUM
ejpam-5776	1	20	issn	issn	VERB
ejpam-5776	1	21	1307	1307	NUM
ejpam-5776	1	22	-	-	SYM
ejpam-5776	1	23	5543	5543	NUM
ejpam-5776	1	24	–	–	PUNCT
ejpam-5776	1	25	ejpam.com	ejpam.com	X
ejpam-5776	1	26	published	publish	VERB
ejpam-5776	1	27	by	by	ADP
ejpam-5776	1	28	new	new	PROPN
ejpam-5776	1	29	york	york	PROPN
ejpam-5776	1	30	business	business	PROPN
ejpam-5776	1	31	global	global	ADJ
ejpam-5776	1	32	eccentricity	eccentricity	NOUN
ejpam-5776	1	33	-	-	PUNCT
ejpam-5776	1	34	based	base	VERB
ejpam-5776	1	35	energies	energy	NOUN
ejpam-5776	1	36	of	of	ADP
ejpam-5776	1	37	non	non	ADJ
ejpam-5776	1	38	-	-	ADJ
ejpam-5776	1	39	commuting	commuting	ADJ
ejpam-5776	1	40	graph	graph	NOUN
ejpam-5776	1	41	for	for	ADP
ejpam-5776	1	42	dihedral	dihedral	ADJ
ejpam-5776	1	43	groups	group	NOUN
ejpam-5776	1	44	mamika	mamika	PROPN
ejpam-5776	1	45	ujianita	ujianita	PROPN
ejpam-5776	1	46	romdhini1,∗	romdhini1,∗	PROPN
ejpam-5776	1	47	,	,	PUNCT
ejpam-5776	1	48	athirah	athirah	PROPN
ejpam-5776	1	49	nawawi2	nawawi2	PROPN
ejpam-5776	1	50	,	,	PUNCT
ejpam-5776	1	51	faisal	faisal	PROPN
ejpam-5776	1	52	al	al	PROPN
ejpam-5776	1	53	-	-	PUNCT
ejpam-5776	1	54	sharqi3,4	sharqi3,4	PROPN
ejpam-5776	1	55	,	,	PUNCT
ejpam-5776	1	56	abdurahim1	abdurahim1	NOUN
ejpam-5776	1	57	,	,	PUNCT
ejpam-5776	1	58	andika	andika	PROPN
ejpam-5776	1	59	ellena	ellena	PROPN
ejpam-5776	1	60	saufika	saufika	PROPN
ejpam-5776	1	61	hakim	hakim	PROPN
ejpam-5776	1	62	maharani1	maharani1	PROPN
ejpam-5776	1	63	,	,	PUNCT
ejpam-5776	1	64	ifan	ifan	PROPN
ejpam-5776	1	65	hasnan	hasnan	PROPN
ejpam-5776	1	66	dani1	dani1	PROPN
ejpam-5776	1	67	1	1	NUM
ejpam-5776	1	68	department	department	NOUN
ejpam-5776	1	69	of	of	ADP
ejpam-5776	1	70	mathematics	mathematic	NOUN
ejpam-5776	1	71	,	,	PUNCT
ejpam-5776	1	72	faculty	faculty	NOUN
ejpam-5776	1	73	of	of	ADP
ejpam-5776	1	74	mathematics	mathematic	NOUN
ejpam-5776	1	75	and	and	CCONJ
ejpam-5776	1	76	natural	natural	ADJ
ejpam-5776	1	77	sciences	science	NOUN
ejpam-5776	1	78	,	,	PUNCT
ejpam-5776	1	79	university	university	NOUN
ejpam-5776	1	80	of	of	ADP
ejpam-5776	1	81	mataram	mataram	PROPN
ejpam-5776	1	82	,	,	PUNCT
ejpam-5776	1	83	mataram	mataram	PROPN
ejpam-5776	1	84	83125	83125	NUM
ejpam-5776	1	85	,	,	PUNCT
ejpam-5776	1	86	indonesia	indonesia	PROPN
ejpam-5776	1	87	2	2	NUM
ejpam-5776	1	88	department	department	NOUN
ejpam-5776	1	89	of	of	ADP
ejpam-5776	1	90	mathematics	mathematic	NOUN
ejpam-5776	1	91	and	and	CCONJ
ejpam-5776	1	92	statistics	statistic	NOUN
ejpam-5776	1	93	,	,	PUNCT
ejpam-5776	1	94	faculty	faculty	NOUN
ejpam-5776	1	95	of	of	ADP
ejpam-5776	1	96	science	science	NOUN
ejpam-5776	1	97	,	,	PUNCT
ejpam-5776	1	98	universiti	universiti	PROPN
ejpam-5776	1	99	putra	putra	PROPN
ejpam-5776	1	100	malaysia	malaysia	PROPN
ejpam-5776	1	101	,	,	PUNCT
ejpam-5776	1	102	43400	43400	NUM
ejpam-5776	1	103	serdang	serdang	PROPN
ejpam-5776	1	104	,	,	PUNCT
ejpam-5776	1	105	selangor	selangor	PROPN
ejpam-5776	1	106	,	,	PUNCT
ejpam-5776	1	107	malaysia	malaysia	PROPN
ejpam-5776	1	108	3	3	NUM
ejpam-5776	1	109	department	department	NOUN
ejpam-5776	1	110	of	of	ADP
ejpam-5776	1	111	mathematics	mathematic	NOUN
ejpam-5776	1	112	,	,	PUNCT
ejpam-5776	1	113	faculty	faculty	NOUN
ejpam-5776	1	114	of	of	ADP
ejpam-5776	1	115	education	education	NOUN
ejpam-5776	1	116	for	for	ADP
ejpam-5776	1	117	pure	pure	ADJ
ejpam-5776	1	118	sciences	science	NOUN
ejpam-5776	1	119	,	,	PUNCT
ejpam-5776	1	120	university	university	NOUN
ejpam-5776	1	121	of	of	ADP
ejpam-5776	1	122	anbar	anbar	PROPN
ejpam-5776	1	123	,	,	PUNCT
ejpam-5776	1	124	ramadi	ramadi	PROPN
ejpam-5776	1	125	,	,	PUNCT
ejpam-5776	1	126	anbar	anbar	NOUN
ejpam-5776	1	127	,	,	PUNCT
ejpam-5776	1	128	iraq	iraq	PROPN
ejpam-5776	1	129	4	4	NUM
ejpam-5776	1	130	college	college	NOUN
ejpam-5776	1	131	of	of	ADP
ejpam-5776	1	132	engineering	engineering	NOUN
ejpam-5776	1	133	,	,	PUNCT
ejpam-5776	1	134	national	national	ADJ
ejpam-5776	1	135	university	university	PROPN
ejpam-5776	1	136	of	of	ADP
ejpam-5776	1	137	science	science	NOUN
ejpam-5776	1	138	and	and	CCONJ
ejpam-5776	1	139	technology	technology	NOUN
ejpam-5776	1	140	,	,	PUNCT
ejpam-5776	1	141	dhi	dhi	PROPN
ejpam-5776	1	142	qar	qar	PROPN
ejpam-5776	1	143	,	,	PUNCT
ejpam-5776	1	144	iraq	iraq	PROPN
ejpam-5776	1	145	abstract	abstract	NOUN
ejpam-5776	1	146	.	.	PUNCT
ejpam-5776	2	1	spectral	spectral	ADJ
ejpam-5776	2	2	graph	graph	NOUN
ejpam-5776	2	3	theory	theory	NOUN
ejpam-5776	2	4	is	be	AUX
ejpam-5776	2	5	a	a	DET
ejpam-5776	2	6	research	research	NOUN
ejpam-5776	2	7	topic	topic	NOUN
ejpam-5776	2	8	that	that	PRON
ejpam-5776	2	9	combines	combine	VERB
ejpam-5776	2	10	algebra	algebra	NOUN
ejpam-5776	2	11	and	and	CCONJ
ejpam-5776	2	12	graph	graph	NOUN
ejpam-5776	2	13	theory	theory	NOUN
ejpam-5776	2	14	,	,	PUNCT
ejpam-5776	2	15	with	with	ADP
ejpam-5776	2	16	the	the	DET
ejpam-5776	2	17	intersection	intersection	NOUN
ejpam-5776	2	18	representing	represent	VERB
ejpam-5776	2	19	a	a	DET
ejpam-5776	2	20	graph	graph	NOUN
ejpam-5776	2	21	as	as	ADP
ejpam-5776	2	22	a	a	DET
ejpam-5776	2	23	matrix	matrix	NOUN
ejpam-5776	2	24	.	.	PUNCT
ejpam-5776	3	1	the	the	DET
ejpam-5776	3	2	eigenvalues	eigenvalue	NOUN
ejpam-5776	3	3	of	of	ADP
ejpam-5776	3	4	the	the	DET
ejpam-5776	3	5	matrix	matrix	NOUN
ejpam-5776	3	6	give	give	VERB
ejpam-5776	3	7	the	the	DET
ejpam-5776	3	8	value	value	NOUN
ejpam-5776	3	9	of	of	ADP
ejpam-5776	3	10	graph	graph	NOUN
ejpam-5776	3	11	energy	energy	NOUN
ejpam-5776	3	12	.	.	PUNCT
ejpam-5776	4	1	this	this	DET
ejpam-5776	4	2	research	research	NOUN
ejpam-5776	4	3	focuses	focus	VERB
ejpam-5776	4	4	on	on	ADP
ejpam-5776	4	5	the	the	DET
ejpam-5776	4	6	non	non	ADJ
ejpam-5776	4	7	-	-	ADJ
ejpam-5776	4	8	commuting	commuting	ADJ
ejpam-5776	4	9	graph	graph	NOUN
ejpam-5776	4	10	for	for	ADP
ejpam-5776	4	11	dihedral	dihedral	ADJ
ejpam-5776	4	12	groups	group	NOUN
ejpam-5776	4	13	corresponding	correspond	VERB
ejpam-5776	4	14	to	to	ADP
ejpam-5776	4	15	eccentricity	eccentricity	NOUN
ejpam-5776	4	16	-	-	PUNCT
ejpam-5776	4	17	based	base	VERB
ejpam-5776	4	18	matrices	matrix	NOUN
ejpam-5776	4	19	including	include	VERB
ejpam-5776	4	20	eccentricity	eccentricity	NOUN
ejpam-5776	4	21	,	,	PUNCT
ejpam-5776	4	22	sum	sum	NOUN
ejpam-5776	4	23	eccentricity	eccentricity	NOUN
ejpam-5776	4	24	,	,	PUNCT
ejpam-5776	4	25	and	and	CCONJ
ejpam-5776	4	26	average	average	ADJ
ejpam-5776	4	27	degree	degree	NOUN
ejpam-5776	4	28	eccentricity	eccentricity	NOUN
ejpam-5776	4	29	matrices	matrix	NOUN
ejpam-5776	4	30	.	.	PUNCT
ejpam-5776	5	1	2020	2020	NUM
ejpam-5776	5	2	mathematics	mathematic	NOUN
ejpam-5776	5	3	subject	subject	NOUN
ejpam-5776	5	4	classifications	classification	NOUN
ejpam-5776	5	5	:	:	PUNCT
ejpam-5776	5	6	05c25	05c25	NUM
ejpam-5776	5	7	,	,	PUNCT
ejpam-5776	5	8	15a18	15a18	NUM
ejpam-5776	5	9	key	key	ADJ
ejpam-5776	5	10	words	word	NOUN
ejpam-5776	5	11	and	and	CCONJ
ejpam-5776	5	12	phrases	phrase	NOUN
ejpam-5776	5	13	:	:	PUNCT
ejpam-5776	5	14	eccentricity	eccentricity	NOUN
ejpam-5776	5	15	-	-	PUNCT
ejpam-5776	5	16	based	base	VERB
ejpam-5776	5	17	matrices	matrix	NOUN
ejpam-5776	5	18	,	,	PUNCT
ejpam-5776	5	19	energy	energy	NOUN
ejpam-5776	5	20	of	of	ADP
ejpam-5776	5	21	a	a	DET
ejpam-5776	5	22	graph	graph	NOUN
ejpam-5776	5	23	,	,	PUNCT
ejpam-5776	5	24	non	non	ADJ
ejpam-5776	5	25	-	-	ADJ
ejpam-5776	5	26	commuting	commuting	ADJ
ejpam-5776	5	27	graph	graph	NOUN
ejpam-5776	5	28	,	,	PUNCT
ejpam-5776	5	29	dihedral	dihedral	ADJ
ejpam-5776	5	30	groups	group	NOUN
ejpam-5776	5	31	1	1	NUM
ejpam-5776	5	32	.	.	X
ejpam-5776	6	1	introduction	introduction	NOUN
ejpam-5776	6	2	spectral	spectral	ADJ
ejpam-5776	6	3	graph	graph	NOUN
ejpam-5776	6	4	theory	theory	NOUN
ejpam-5776	6	5	is	be	AUX
ejpam-5776	6	6	a	a	DET
ejpam-5776	6	7	combined	combined	ADJ
ejpam-5776	6	8	research	research	NOUN
ejpam-5776	6	9	topic	topic	NOUN
ejpam-5776	6	10	between	between	ADP
ejpam-5776	6	11	algebra	algebra	NOUN
ejpam-5776	6	12	and	and	CCONJ
ejpam-5776	6	13	graph	graph	NOUN
ejpam-5776	6	14	theory	theory	NOUN
ejpam-5776	6	15	with	with	ADP
ejpam-5776	6	16	the	the	DET
ejpam-5776	6	17	intersection	intersection	NOUN
ejpam-5776	6	18	being	be	AUX
ejpam-5776	6	19	a	a	DET
ejpam-5776	6	20	matrix	matrix	NOUN
ejpam-5776	6	21	representation	representation	NOUN
ejpam-5776	6	22	of	of	ADP
ejpam-5776	6	23	a	a	DET
ejpam-5776	6	24	graph	graph	NOUN
ejpam-5776	6	25	.	.	PUNCT
ejpam-5776	7	1	originally	originally	ADV
ejpam-5776	7	2	,	,	PUNCT
ejpam-5776	7	3	the	the	DET
ejpam-5776	7	4	adjacency	adjacency	NOUN
ejpam-5776	7	5	matrix	matrix	NOUN
ejpam-5776	7	6	was	be	AUX
ejpam-5776	7	7	the	the	DET
ejpam-5776	7	8	first	first	ADJ
ejpam-5776	7	9	representation	representation	NOUN
ejpam-5776	7	10	of	of	ADP
ejpam-5776	7	11	a	a	DET
ejpam-5776	7	12	graph	graph	NOUN
ejpam-5776	7	13	.	.	PUNCT
ejpam-5776	8	1	the	the	DET
ejpam-5776	8	2	research	research	NOUN
ejpam-5776	8	3	has	have	AUX
ejpam-5776	8	4	extended	extend	VERB
ejpam-5776	8	5	to	to	ADP
ejpam-5776	8	6	the	the	DET
ejpam-5776	8	7	degreebased	degreebase	VERB
ejpam-5776	8	8	and	and	CCONJ
ejpam-5776	8	9	distance	distance	NOUN
ejpam-5776	8	10	-	-	PUNCT
ejpam-5776	8	11	based	base	VERB
ejpam-5776	8	12	matrices	matrix	NOUN
ejpam-5776	8	13	,	,	PUNCT
ejpam-5776	8	14	and	and	CCONJ
ejpam-5776	8	15	recently	recently	ADV
ejpam-5776	8	16	,	,	PUNCT
ejpam-5776	8	17	eccentricity	eccentricity	NOUN
ejpam-5776	8	18	-	-	PUNCT
ejpam-5776	8	19	based	base	VERB
ejpam-5776	8	20	matrices	matrix	NOUN
ejpam-5776	8	21	have	have	AUX
ejpam-5776	8	22	been	be	AUX
ejpam-5776	8	23	developed	develop	VERB
ejpam-5776	8	24	.	.	PUNCT
ejpam-5776	9	1	wang	wang	PROPN
ejpam-5776	9	2	,	,	PUNCT
ejpam-5776	9	3	et	et	PROPN
ejpam-5776	9	4	al	al	PROPN
ejpam-5776	9	5	.	.	PUNCT
ejpam-5776	10	1	[	[	X
ejpam-5776	10	2	1	1	X
ejpam-5776	10	3	]	]	PUNCT
ejpam-5776	10	4	defined	define	VERB
ejpam-5776	10	5	the	the	DET
ejpam-5776	10	6	eccentricity	eccentricity	NOUN
ejpam-5776	10	7	matrix	matrix	NOUN
ejpam-5776	10	8	and	and	CCONJ
ejpam-5776	10	9	is	be	AUX
ejpam-5776	10	10	inspired	inspire	VERB
ejpam-5776	10	11	by	by	ADP
ejpam-5776	10	12	the	the	DET
ejpam-5776	10	13	idea	idea	NOUN
ejpam-5776	10	14	of	of	ADP
ejpam-5776	10	15	randic	randic	ADJ
ejpam-5776	10	16	[	[	X
ejpam-5776	10	17	2	2	NUM
ejpam-5776	10	18	]	]	PUNCT
ejpam-5776	10	19	.	.	PUNCT
ejpam-5776	11	1	later	later	ADV
ejpam-5776	11	2	,	,	PUNCT
ejpam-5776	11	3	mahato	mahato	PROPN
ejpam-5776	12	1	[	[	X
ejpam-5776	12	2	3	3	NUM
ejpam-5776	12	3	]	]	PUNCT
ejpam-5776	12	4	continued	continue	VERB
ejpam-5776	12	5	to	to	PART
ejpam-5776	12	6	discuss	discuss	VERB
ejpam-5776	12	7	this	this	DET
ejpam-5776	12	8	type	type	NOUN
ejpam-5776	12	9	of	of	ADP
ejpam-5776	12	10	matrix	matrix	NOUN
ejpam-5776	12	11	and	and	CCONJ
ejpam-5776	12	12	presented	present	VERB
ejpam-5776	12	13	the	the	DET
ejpam-5776	12	14	spectra	spectra	ADJ
ejpam-5776	12	15	perspectives	perspective	NOUN
ejpam-5776	12	16	in	in	ADP
ejpam-5776	12	17	2020	2020	NUM
ejpam-5776	12	18	.	.	PUNCT
ejpam-5776	13	1	meanwhile	meanwhile	ADV
ejpam-5776	13	2	,	,	PUNCT
ejpam-5776	13	3	the	the	DET
ejpam-5776	13	4	sum	sum	NOUN
ejpam-5776	13	5	eccentricity	eccentricity	NOUN
ejpam-5776	13	6	was	be	AUX
ejpam-5776	13	7	introduced	introduce	VERB
ejpam-5776	13	8	by	by	ADP
ejpam-5776	13	9	sowaity	sowaity	NOUN
ejpam-5776	13	10	∗corresponding	∗corresponde	VERB
ejpam-5776	13	11	author	author	NOUN
ejpam-5776	13	12	.	.	PUNCT
ejpam-5776	14	1	doi	doi	NOUN
ejpam-5776	14	2	:	:	PUNCT
ejpam-5776	14	3	https://doi.org/10.29020/nybg.ejpam.v18i2.5776	https://doi.org/10.29020/nybg.ejpam.v18i2.5776	PROPN
ejpam-5776	14	4	email	email	NOUN
ejpam-5776	14	5	addresses	address	NOUN
ejpam-5776	14	6	:	:	PUNCT
ejpam-5776	14	7	mamika@unram.ac.id	mamika@unram.ac.id	NOUN
ejpam-5776	14	8	(	(	PUNCT
ejpam-5776	14	9	m.	m.	PROPN
ejpam-5776	14	10	u.	u.	PROPN
ejpam-5776	14	11	romdhini	romdhini	PROPN
ejpam-5776	14	12	)	)	PUNCT
ejpam-5776	14	13	,	,	PUNCT
ejpam-5776	14	14	athirah@upm.edu.my	athirah@upm.edu.my	PROPN
ejpam-5776	14	15	(	(	PUNCT
ejpam-5776	14	16	a.	a.	NOUN
ejpam-5776	14	17	nawawi	nawawi	PROPN
ejpam-5776	14	18	)	)	PUNCT
ejpam-5776	14	19	,	,	PUNCT
ejpam-5776	14	20	faisal.ghazi@uoanbar.edu.iq	faisal.ghazi@uoanbar.edu.iq	NOUN
ejpam-5776	14	21	(	(	PUNCT
ejpam-5776	14	22	f.	f.	PROPN
ejpam-5776	14	23	al	al	PROPN
ejpam-5776	14	24	-	-	PUNCT
ejpam-5776	14	25	sharqi	sharqi	NOUN
ejpam-5776	14	26	)	)	PUNCT
ejpam-5776	14	27	,	,	PUNCT
ejpam-5776	14	28	abdurahim@staff.unram.ac.id	abdurahim@staff.unram.ac.id	NOUN
ejpam-5776	14	29	(	(	PUNCT
ejpam-5776	14	30	abdurahim	abdurahim	PROPN
ejpam-5776	14	31	)	)	PUNCT
ejpam-5776	14	32	,	,	PUNCT
ejpam-5776	14	33	a.ellena.saufika@staff.unram.ac.id	a.ellena.saufika@staff.unram.ac.id	NOUN
ejpam-5776	14	34	(	(	PUNCT
ejpam-5776	14	35	a.	a.	PROPN
ejpam-5776	14	36	e.	e.	PROPN
ejpam-5776	14	37	s.	s.	PROPN
ejpam-5776	14	38	h.	h.	PROPN
ejpam-5776	14	39	maharani	maharani	PROPN
ejpam-5776	14	40	)	)	PUNCT
ejpam-5776	14	41	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5776	15	1	1	1	NUM
ejpam-5776	15	2	copyright	copyright	NOUN
ejpam-5776	15	3	:	:	PUNCT
ejpam-5776	15	4	©	©	PROPN
ejpam-5776	15	5	2025	2025	NUM
ejpam-5776	15	6	the	the	DET
ejpam-5776	15	7	author(s	author(s	NOUN
ejpam-5776	15	8	)	)	PUNCT
ejpam-5776	15	9	.	.	PUNCT
ejpam-5776	16	1	(	(	PUNCT
ejpam-5776	16	2	cc	cc	NOUN
ejpam-5776	16	3	by	by	ADP
ejpam-5776	16	4	-	-	PUNCT
ejpam-5776	16	5	nc	nc	PROPN
ejpam-5776	16	6	4.0	4.0	NUM
ejpam-5776	16	7	)	)	PUNCT
ejpam-5776	16	8	m.	m.	NOUN
ejpam-5776	16	9	u.	u.	PROPN
ejpam-5776	16	10	romdhini	romdhini	PROPN
ejpam-5776	16	11	et	et	PROPN
ejpam-5776	16	12	al	al	PROPN
ejpam-5776	16	13	.	.	PUNCT
ejpam-5776	16	14	/	/	SYM
ejpam-5776	16	15	eur	eur	PROPN
ejpam-5776	16	16	.	.	PUNCT
ejpam-5776	17	1	j.	j.	PROPN
ejpam-5776	17	2	pure	pure	PROPN
ejpam-5776	17	3	appl	appl	PROPN
ejpam-5776	17	4	.	.	PROPN
ejpam-5776	17	5	math	math	PROPN
ejpam-5776	17	6	,	,	PUNCT
ejpam-5776	17	7	18	18	NUM
ejpam-5776	17	8	(	(	PUNCT
ejpam-5776	17	9	2	2	NUM
ejpam-5776	17	10	)	)	PUNCT
ejpam-5776	17	11	(	(	PUNCT
ejpam-5776	17	12	2025	2025	NUM
ejpam-5776	17	13	)	)	PUNCT
ejpam-5776	17	14	,	,	PUNCT
ejpam-5776	17	15	5776	5776	NUM
ejpam-5776	17	16	2	2	NUM
ejpam-5776	17	17	of	of	ADP
ejpam-5776	17	18	13	13	NUM
ejpam-5776	17	19	and	and	CCONJ
ejpam-5776	17	20	sharada	sharada	PRON
ejpam-5776	18	1	[	[	X
ejpam-5776	18	2	4	4	X
ejpam-5776	18	3	]	]	PUNCT
ejpam-5776	18	4	and	and	CCONJ
ejpam-5776	18	5	the	the	DET
ejpam-5776	18	6	average	average	ADJ
ejpam-5776	18	7	degree	degree	NOUN
ejpam-5776	18	8	eccentricity	eccentricity	NOUN
ejpam-5776	18	9	matrix	matrix	NOUN
ejpam-5776	18	10	was	be	AUX
ejpam-5776	18	11	pioneered	pioneer	VERB
ejpam-5776	18	12	by	by	ADP
ejpam-5776	18	13	mathad	mathad	VERB
ejpam-5776	18	14	et	et	PROPN
ejpam-5776	18	15	al	al	PROPN
ejpam-5776	18	16	.	.	PUNCT
ejpam-5776	19	1	[	[	X
ejpam-5776	19	2	5	5	NUM
ejpam-5776	19	3	]	]	PUNCT
ejpam-5776	19	4	.	.	PUNCT
ejpam-5776	20	1	the	the	DET
ejpam-5776	20	2	matrix	matrix	NOUN
ejpam-5776	20	3	of	of	ADP
ejpam-5776	20	4	a	a	DET
ejpam-5776	20	5	graph	graph	NOUN
ejpam-5776	20	6	is	be	AUX
ejpam-5776	20	7	a	a	DET
ejpam-5776	20	8	square	square	ADJ
ejpam-5776	20	9	matrix	matrix	NOUN
ejpam-5776	20	10	whose	whose	DET
ejpam-5776	20	11	size	size	NOUN
ejpam-5776	20	12	depends	depend	VERB
ejpam-5776	20	13	on	on	ADP
ejpam-5776	20	14	the	the	DET
ejpam-5776	20	15	order	order	NOUN
ejpam-5776	20	16	of	of	ADP
ejpam-5776	20	17	the	the	DET
ejpam-5776	20	18	graph	graph	NOUN
ejpam-5776	20	19	.	.	PUNCT
ejpam-5776	21	1	therefore	therefore	ADV
ejpam-5776	21	2	,	,	PUNCT
ejpam-5776	21	3	we	we	PRON
ejpam-5776	21	4	can	can	AUX
ejpam-5776	21	5	calculate	calculate	VERB
ejpam-5776	21	6	the	the	DET
ejpam-5776	21	7	eigenvalues	eigenvalue	NOUN
ejpam-5776	21	8	of	of	ADP
ejpam-5776	21	9	a	a	DET
ejpam-5776	21	10	matrix	matrix	NOUN
ejpam-5776	21	11	,	,	PUNCT
ejpam-5776	21	12	which	which	PRON
ejpam-5776	21	13	are	be	AUX
ejpam-5776	21	14	hereinafter	hereinafter	NOUN
ejpam-5776	21	15	referred	refer	VERB
ejpam-5776	21	16	to	to	ADP
ejpam-5776	21	17	as	as	ADP
ejpam-5776	21	18	the	the	DET
ejpam-5776	21	19	eigenvalues	eigenvalue	NOUN
ejpam-5776	21	20	of	of	ADP
ejpam-5776	21	21	the	the	DET
ejpam-5776	21	22	corresponding	corresponding	ADJ
ejpam-5776	21	23	graph	graph	NOUN
ejpam-5776	21	24	.	.	PUNCT
ejpam-5776	22	1	the	the	DET
ejpam-5776	22	2	sum	sum	NOUN
ejpam-5776	22	3	of	of	ADP
ejpam-5776	22	4	absolute	absolute	ADJ
ejpam-5776	22	5	eigenvalues	eigenvalue	NOUN
ejpam-5776	22	6	is	be	AUX
ejpam-5776	22	7	the	the	DET
ejpam-5776	22	8	energy	energy	NOUN
ejpam-5776	22	9	of	of	ADP
ejpam-5776	22	10	a	a	DET
ejpam-5776	22	11	graph	graph	NOUN
ejpam-5776	22	12	defined	define	VERB
ejpam-5776	22	13	by	by	ADP
ejpam-5776	22	14	gutman	gutman	NOUN
ejpam-5776	22	15	[	[	X
ejpam-5776	22	16	6	6	NUM
ejpam-5776	22	17	]	]	PUNCT
ejpam-5776	22	18	in	in	ADP
ejpam-5776	22	19	1978	1978	NUM
ejpam-5776	22	20	.	.	PUNCT
ejpam-5776	23	1	moreover	moreover	ADV
ejpam-5776	23	2	,	,	PUNCT
ejpam-5776	23	3	the	the	DET
ejpam-5776	23	4	graph	graph	NOUN
ejpam-5776	23	5	energy	energy	NOUN
ejpam-5776	23	6	value	value	NOUN
ejpam-5776	23	7	has	have	AUX
ejpam-5776	23	8	been	be	AUX
ejpam-5776	23	9	discussed	discuss	VERB
ejpam-5776	23	10	in	in	ADP
ejpam-5776	23	11	[	[	X
ejpam-5776	23	12	7	7	NUM
ejpam-5776	23	13	]	]	PUNCT
ejpam-5776	23	14	and	and	CCONJ
ejpam-5776	23	15	[	[	X
ejpam-5776	23	16	8	8	NUM
ejpam-5776	23	17	]	]	PUNCT
ejpam-5776	23	18	.	.	PUNCT
ejpam-5776	24	1	the	the	DET
ejpam-5776	24	2	graph	graph	NOUN
ejpam-5776	24	3	energy	energy	NOUN
ejpam-5776	24	4	can	can	AUX
ejpam-5776	24	5	further	far	ADV
ejpam-5776	24	6	be	be	AUX
ejpam-5776	24	7	associated	associate	VERB
ejpam-5776	24	8	with	with	ADP
ejpam-5776	24	9	the	the	DET
ejpam-5776	24	10	graph	graph	NOUN
ejpam-5776	24	11	defined	define	VERB
ejpam-5776	24	12	on	on	ADP
ejpam-5776	24	13	the	the	DET
ejpam-5776	24	14	group	group	NOUN
ejpam-5776	24	15	including	include	VERB
ejpam-5776	24	16	the	the	DET
ejpam-5776	24	17	non	non	ADJ
ejpam-5776	24	18	-	-	ADJ
ejpam-5776	24	19	commuting	commuting	ADJ
ejpam-5776	24	20	graph	graph	NOUN
ejpam-5776	24	21	.	.	PUNCT
ejpam-5776	25	1	it	it	PRON
ejpam-5776	25	2	is	be	AUX
ejpam-5776	25	3	shown	show	VERB
ejpam-5776	25	4	in	in	ADP
ejpam-5776	25	5	[	[	X
ejpam-5776	25	6	9	9	NUM
ejpam-5776	25	7	]	]	PUNCT
ejpam-5776	25	8	who	who	PRON
ejpam-5776	25	9	discussed	discuss	VERB
ejpam-5776	25	10	the	the	DET
ejpam-5776	25	11	wiener	wiener	NOUN
ejpam-5776	25	12	-	-	PUNCT
ejpam-5776	25	13	hosoya	hosoya	NOUN
ejpam-5776	25	14	energy	energy	NOUN
ejpam-5776	25	15	,	,	PUNCT
ejpam-5776	25	16	and	and	CCONJ
ejpam-5776	25	17	for	for	ADP
ejpam-5776	25	18	sombor	sombor	NOUN
ejpam-5776	25	19	energy	energy	NOUN
ejpam-5776	25	20	can	can	AUX
ejpam-5776	25	21	be	be	AUX
ejpam-5776	25	22	found	find	VERB
ejpam-5776	25	23	in	in	ADP
ejpam-5776	25	24	[	[	X
ejpam-5776	25	25	10	10	NUM
ejpam-5776	25	26	]	]	PUNCT
ejpam-5776	25	27	.	.	PUNCT
ejpam-5776	26	1	the	the	DET
ejpam-5776	26	2	algebraic	algebraic	ADJ
ejpam-5776	26	3	discussion	discussion	NOUN
ejpam-5776	26	4	also	also	ADV
ejpam-5776	26	5	can	can	AUX
ejpam-5776	26	6	be	be	AUX
ejpam-5776	26	7	found	find	VERB
ejpam-5776	26	8	in	in	ADP
ejpam-5776	26	9	[	[	X
ejpam-5776	26	10	11	11	NUM
ejpam-5776	26	11	,	,	PUNCT
ejpam-5776	26	12	12	12	NUM
ejpam-5776	26	13	]	]	PUNCT
ejpam-5776	26	14	.	.	PUNCT
ejpam-5776	27	1	therefore	therefore	ADV
ejpam-5776	27	2	,	,	PUNCT
ejpam-5776	27	3	this	this	DET
ejpam-5776	27	4	research	research	NOUN
ejpam-5776	27	5	aims	aim	VERB
ejpam-5776	27	6	to	to	PART
ejpam-5776	27	7	analyze	analyze	VERB
ejpam-5776	27	8	the	the	DET
ejpam-5776	27	9	non	non	ADJ
ejpam-5776	27	10	-	-	ADJ
ejpam-5776	27	11	commuting	commuting	ADJ
ejpam-5776	27	12	graph	graph	NOUN
ejpam-5776	27	13	energy	energy	NOUN
ejpam-5776	27	14	associated	associate	VERB
ejpam-5776	27	15	with	with	ADP
ejpam-5776	27	16	the	the	DET
ejpam-5776	27	17	eccentricity	eccentricity	NOUN
ejpam-5776	27	18	-	-	PUNCT
ejpam-5776	27	19	based	base	VERB
ejpam-5776	27	20	matrices	matrix	NOUN
ejpam-5776	27	21	and	and	CCONJ
ejpam-5776	27	22	dihedral	dihedral	ADJ
ejpam-5776	27	23	groups	group	NOUN
ejpam-5776	27	24	as	as	ADP
ejpam-5776	27	25	its	its	PRON
ejpam-5776	27	26	vertex	vertex	NOUN
ejpam-5776	27	27	set	set	NOUN
ejpam-5776	27	28	.	.	PUNCT
ejpam-5776	28	1	2	2	X
ejpam-5776	28	2	.	.	X
ejpam-5776	28	3	preliminaries	preliminary	NOUN
ejpam-5776	28	4	in	in	ADP
ejpam-5776	28	5	this	this	DET
ejpam-5776	28	6	section	section	NOUN
ejpam-5776	28	7	,	,	PUNCT
ejpam-5776	28	8	we	we	PRON
ejpam-5776	28	9	recall	recall	VERB
ejpam-5776	28	10	the	the	DET
ejpam-5776	28	11	fundamental	fundamental	ADJ
ejpam-5776	28	12	definitions	definition	NOUN
ejpam-5776	28	13	and	and	CCONJ
ejpam-5776	28	14	theorems	theorem	NOUN
ejpam-5776	28	15	useful	useful	ADJ
ejpam-5776	28	16	for	for	ADP
ejpam-5776	28	17	our	our	PRON
ejpam-5776	28	18	main	main	ADJ
ejpam-5776	28	19	results	result	NOUN
ejpam-5776	28	20	.	.	PUNCT
ejpam-5776	29	1	we	we	PRON
ejpam-5776	29	2	start	start	VERB
ejpam-5776	29	3	with	with	ADP
ejpam-5776	29	4	the	the	DET
ejpam-5776	29	5	definition	definition	NOUN
ejpam-5776	29	6	of	of	ADP
ejpam-5776	29	7	the	the	DET
ejpam-5776	29	8	non	non	ADJ
ejpam-5776	29	9	-	-	ADJ
ejpam-5776	29	10	commuting	commuting	ADJ
ejpam-5776	29	11	graph	graph	NOUN
ejpam-5776	29	12	.	.	PUNCT
ejpam-5776	30	1	definition	definition	NOUN
ejpam-5776	30	2	1	1	NUM
ejpam-5776	30	3	.	.	PUNCT
ejpam-5776	31	1	[	[	X
ejpam-5776	31	2	13	13	NUM
ejpam-5776	31	3	]	]	PUNCT
ejpam-5776	31	4	let	let	VERB
ejpam-5776	31	5	g	g	PRON
ejpam-5776	31	6	be	be	AUX
ejpam-5776	31	7	a	a	DET
ejpam-5776	31	8	finite	finite	ADJ
ejpam-5776	31	9	group	group	NOUN
ejpam-5776	31	10	.	.	PUNCT
ejpam-5776	32	1	the	the	DET
ejpam-5776	32	2	non	non	ADJ
ejpam-5776	32	3	-	-	ADJ
ejpam-5776	32	4	commuting	commuting	ADJ
ejpam-5776	32	5	graph	graph	NOUN
ejpam-5776	32	6	of	of	ADP
ejpam-5776	32	7	g	g	PROPN
ejpam-5776	32	8	is	be	AUX
ejpam-5776	32	9	denoted	denote	VERB
ejpam-5776	32	10	by	by	ADP
ejpam-5776	32	11	ωg	ωg	PROPN
ejpam-5776	32	12	,	,	PUNCT
ejpam-5776	32	13	in	in	ADP
ejpam-5776	32	14	which	which	PRON
ejpam-5776	32	15	the	the	DET
ejpam-5776	32	16	vertex	vertex	NOUN
ejpam-5776	32	17	set	set	NOUN
ejpam-5776	32	18	is	be	AUX
ejpam-5776	32	19	g\z(g	g\z(g	NOUN
ejpam-5776	32	20	)	)	PUNCT
ejpam-5776	32	21	,	,	PUNCT
ejpam-5776	32	22	where	where	SCONJ
ejpam-5776	32	23	z(g	z(g	NOUN
ejpam-5776	32	24	)	)	PUNCT
ejpam-5776	32	25	is	be	AUX
ejpam-5776	32	26	the	the	DET
ejpam-5776	32	27	center	center	NOUN
ejpam-5776	32	28	of	of	ADP
ejpam-5776	32	29	g	g	PROPN
ejpam-5776	32	30	,	,	PUNCT
ejpam-5776	32	31	and	and	CCONJ
ejpam-5776	32	32	two	two	NUM
ejpam-5776	32	33	distinct	distinct	ADJ
ejpam-5776	32	34	vertices	vertex	NOUN
ejpam-5776	32	35	u	u	NOUN
ejpam-5776	32	36	and	and	CCONJ
ejpam-5776	32	37	v	v	NOUN
ejpam-5776	32	38	are	be	AUX
ejpam-5776	32	39	joined	join	VERB
ejpam-5776	32	40	by	by	ADP
ejpam-5776	32	41	an	an	DET
ejpam-5776	32	42	edge	edge	NOUN
ejpam-5776	32	43	whenever	whenever	SCONJ
ejpam-5776	32	44	uv	uv	NOUN
ejpam-5776	32	45	̸=	̸=	PROPN
ejpam-5776	32	46	vu	vu	X
ejpam-5776	32	47	.	.	PUNCT
ejpam-5776	33	1	throughout	throughout	ADP
ejpam-5776	33	2	this	this	DET
ejpam-5776	33	3	paper	paper	NOUN
ejpam-5776	33	4	,	,	PUNCT
ejpam-5776	33	5	we	we	PRON
ejpam-5776	33	6	denote	denote	VERB
ejpam-5776	33	7	the	the	DET
ejpam-5776	33	8	non	non	ADJ
ejpam-5776	33	9	-	-	ADJ
ejpam-5776	33	10	commuting	commuting	ADJ
ejpam-5776	33	11	graph	graph	NOUN
ejpam-5776	33	12	for	for	ADP
ejpam-5776	33	13	dihedral	dihedral	ADJ
ejpam-5776	33	14	groups	group	NOUN
ejpam-5776	33	15	of	of	ADP
ejpam-5776	33	16	order	order	NOUN
ejpam-5776	33	17	2n	2n	NUM
ejpam-5776	33	18	,	,	PUNCT
ejpam-5776	33	19	d2n	d2n	PROPN
ejpam-5776	33	20	,	,	PUNCT
ejpam-5776	33	21	as	as	ADP
ejpam-5776	33	22	ωd2n	ωd2n	PROPN
ejpam-5776	33	23	,	,	PUNCT
ejpam-5776	33	24	where	where	SCONJ
ejpam-5776	33	25	n	n	PRON
ejpam-5776	33	26	≥	≥	NOUN
ejpam-5776	33	27	3	3	NUM
ejpam-5776	33	28	.	.	PUNCT
ejpam-5776	34	1	the	the	DET
ejpam-5776	34	2	vertex	vertex	NOUN
ejpam-5776	34	3	set	set	NOUN
ejpam-5776	34	4	and	and	CCONJ
ejpam-5776	34	5	edge	edge	NOUN
ejpam-5776	34	6	set	set	NOUN
ejpam-5776	34	7	of	of	ADP
ejpam-5776	34	8	ωd2n	ωd2n	PROPN
ejpam-5776	34	9	are	be	AUX
ejpam-5776	34	10	denoted	denote	VERB
ejpam-5776	34	11	by	by	ADP
ejpam-5776	34	12	v	v	NOUN
ejpam-5776	34	13	(	(	PUNCT
ejpam-5776	34	14	ωd2n	ωd2n	PROPN
ejpam-5776	34	15	)	)	PUNCT
ejpam-5776	34	16	and	and	CCONJ
ejpam-5776	34	17	l(ωd2n	l(ωd2n	NOUN
ejpam-5776	34	18	)	)	PUNCT
ejpam-5776	34	19	,	,	PUNCT
ejpam-5776	34	20	respectively	respectively	ADV
ejpam-5776	34	21	.	.	PUNCT
ejpam-5776	35	1	vertex	vertex	NOUN
ejpam-5776	35	2	x	x	SYM
ejpam-5776	35	3	∈	∈	NOUN
ejpam-5776	35	4	v	v	NOUN
ejpam-5776	35	5	(	(	PUNCT
ejpam-5776	35	6	ωd2n	ωd2n	NOUN
ejpam-5776	35	7	)	)	PUNCT
ejpam-5776	35	8	is	be	AUX
ejpam-5776	35	9	adjacent	adjacent	ADJ
ejpam-5776	35	10	to	to	ADP
ejpam-5776	35	11	y	y	PROPN
ejpam-5776	35	12	∈	∈	PROPN
ejpam-5776	35	13	v	v	NOUN
ejpam-5776	35	14	(	(	PUNCT
ejpam-5776	35	15	ωd2n	ωd2n	PROPN
ejpam-5776	35	16	)	)	PUNCT
ejpam-5776	35	17	if	if	SCONJ
ejpam-5776	35	18	and	and	CCONJ
ejpam-5776	35	19	only	only	ADV
ejpam-5776	35	20	if	if	SCONJ
ejpam-5776	35	21	edge	edge	NOUN
ejpam-5776	35	22	xy	xy	PROPN
ejpam-5776	35	23	∈	∈	PROPN
ejpam-5776	35	24	l(ωd2n	l(ωd2n	NOUN
ejpam-5776	35	25	)	)	PUNCT
ejpam-5776	35	26	.	.	PUNCT
ejpam-5776	36	1	the	the	DET
ejpam-5776	36	2	distance	distance	NOUN
ejpam-5776	36	3	between	between	ADP
ejpam-5776	36	4	both	both	DET
ejpam-5776	36	5	vertices	vertex	NOUN
ejpam-5776	36	6	in	in	ADP
ejpam-5776	36	7	ωd2n	ωd2n	PROPN
ejpam-5776	36	8	is	be	AUX
ejpam-5776	36	9	denoted	denote	VERB
ejpam-5776	36	10	by	by	ADP
ejpam-5776	36	11	dxy	dxy	PROPN
ejpam-5776	36	12	and	and	CCONJ
ejpam-5776	36	13	the	the	DET
ejpam-5776	36	14	degree	degree	NOUN
ejpam-5776	36	15	of	of	ADP
ejpam-5776	36	16	x	x	PROPN
ejpam-5776	36	17	is	be	AUX
ejpam-5776	36	18	denoted	denote	VERB
ejpam-5776	36	19	by	by	ADP
ejpam-5776	36	20	d(x	d(x	PROPN
ejpam-5776	36	21	)	)	PUNCT
ejpam-5776	36	22	.	.	PUNCT
ejpam-5776	37	1	the	the	DET
ejpam-5776	37	2	eccentricity	eccentricity	NOUN
ejpam-5776	37	3	of	of	ADP
ejpam-5776	37	4	x	x	PROPN
ejpam-5776	37	5	is	be	AUX
ejpam-5776	37	6	given	give	VERB
ejpam-5776	37	7	by	by	ADP
ejpam-5776	37	8	e(x	e(x	NUM
ejpam-5776	37	9	)	)	PUNCT
ejpam-5776	38	1	=	=	PUNCT
ejpam-5776	38	2	max{dxy|y	max{dxy|y	PROPN
ejpam-5776	38	3	∈	∈	PROPN
ejpam-5776	38	4	v	v	NOUN
ejpam-5776	38	5	(	(	PUNCT
ejpam-5776	38	6	ωd2n	ωd2n	PROPN
ejpam-5776	38	7	)	)	PUNCT
ejpam-5776	38	8	}	}	PUNCT
ejpam-5776	38	9	.	.	PUNCT
ejpam-5776	39	1	the	the	DET
ejpam-5776	39	2	construction	construction	NOUN
ejpam-5776	39	3	of	of	ADP
ejpam-5776	39	4	the	the	DET
ejpam-5776	39	5	graph	graph	NOUN
ejpam-5776	39	6	matrices	matrix	NOUN
ejpam-5776	39	7	of	of	ADP
ejpam-5776	39	8	ωd2n	ωd2n	PROPN
ejpam-5776	39	9	is	be	AUX
ejpam-5776	39	10	based	base	VERB
ejpam-5776	39	11	on	on	ADP
ejpam-5776	39	12	the	the	DET
ejpam-5776	39	13	definition	definition	NOUN
ejpam-5776	39	14	of	of	ADP
ejpam-5776	39	15	eccentricity	eccentricity	NOUN
ejpam-5776	39	16	,	,	PUNCT
ejpam-5776	39	17	sum	sum	NOUN
ejpam-5776	39	18	-	-	PUNCT
ejpam-5776	39	19	eccentricity	eccentricity	NOUN
ejpam-5776	39	20	,	,	PUNCT
ejpam-5776	39	21	and	and	CCONJ
ejpam-5776	39	22	average	average	ADJ
ejpam-5776	39	23	degree	degree	NOUN
ejpam-5776	39	24	-	-	PUNCT
ejpam-5776	39	25	eccentricity	eccentricity	NOUN
ejpam-5776	39	26	matrices	matrix	NOUN
ejpam-5776	39	27	as	as	SCONJ
ejpam-5776	39	28	presented	present	VERB
ejpam-5776	39	29	below	below	ADV
ejpam-5776	39	30	:	:	PUNCT
ejpam-5776	39	31	definition	definition	NOUN
ejpam-5776	39	32	2	2	NUM
ejpam-5776	39	33	.	.	PUNCT
ejpam-5776	40	1	[	[	X
ejpam-5776	40	2	1	1	X
ejpam-5776	40	3	]	]	PUNCT
ejpam-5776	40	4	the	the	DET
ejpam-5776	40	5	eccentricity	eccentricity	NOUN
ejpam-5776	40	6	matrix	matrix	NOUN
ejpam-5776	40	7	of	of	ADP
ejpam-5776	40	8	ωd2n	ωd2n	PROPN
ejpam-5776	40	9	is	be	AUX
ejpam-5776	40	10	e(ωd2n	e(ωd2n	NOUN
ejpam-5776	40	11	)	)	PUNCT
ejpam-5776	40	12	=	=	PUNCT
ejpam-5776	41	1	[	[	X
ejpam-5776	41	2	ϵij	ϵij	X
ejpam-5776	41	3	]	]	PUNCT
ejpam-5776	41	4	in	in	ADP
ejpam-5776	41	5	which	which	PRON
ejpam-5776	41	6	(	(	PUNCT
ejpam-5776	41	7	i	i	PRON
ejpam-5776	41	8	,	,	PUNCT
ejpam-5776	41	9	j)-th	j)-th	PROPN
ejpam-5776	41	10	entry	entry	NOUN
ejpam-5776	41	11	is	be	AUX
ejpam-5776	41	12	ϵij	ϵij	NOUN
ejpam-5776	41	13	=	=	PRON
ejpam-5776	41	14	{	{	PUNCT
ejpam-5776	41	15	dxixj	dxixj	PROPN
ejpam-5776	41	16	,	,	PUNCT
ejpam-5776	41	17	if	if	SCONJ
ejpam-5776	41	18	dxixj	dxixj	PROPN
ejpam-5776	41	19	=	=	SYM
ejpam-5776	41	20	min{e(xi	min{e(xi	PROPN
ejpam-5776	41	21	)	)	PUNCT
ejpam-5776	41	22	,	,	PUNCT
ejpam-5776	41	23	e(xj	e(xj	PROPN
ejpam-5776	41	24	)	)	PUNCT
ejpam-5776	41	25	}	}	PUNCT
ejpam-5776	41	26	0	0	NUM
ejpam-5776	41	27	,	,	PUNCT
ejpam-5776	41	28	if	if	SCONJ
ejpam-5776	41	29	dxixj	dxixj	PROPN
ejpam-5776	41	30	<	<	X
ejpam-5776	41	31	min{e(xi	min{e(xi	PROPN
ejpam-5776	41	32	)	)	PUNCT
ejpam-5776	41	33	,	,	PUNCT
ejpam-5776	41	34	e(xj	e(xj	PROPN
ejpam-5776	41	35	)	)	PUNCT
ejpam-5776	41	36	}	}	PUNCT
ejpam-5776	41	37	.	.	PUNCT
ejpam-5776	42	1	definition	definition	NOUN
ejpam-5776	42	2	3	3	NUM
ejpam-5776	42	3	.	.	PUNCT
ejpam-5776	43	1	[	[	X
ejpam-5776	43	2	4	4	X
ejpam-5776	43	3	]	]	PUNCT
ejpam-5776	43	4	the	the	DET
ejpam-5776	43	5	sum	sum	NOUN
ejpam-5776	43	6	eccentricity	eccentricity	NOUN
ejpam-5776	43	7	matrix	matrix	NOUN
ejpam-5776	43	8	of	of	ADP
ejpam-5776	43	9	ωd2n	ωd2n	PROPN
ejpam-5776	43	10	is	be	AUX
ejpam-5776	43	11	se(ωd2n	se(ωd2n	ADJ
ejpam-5776	43	12	)	)	PUNCT
ejpam-5776	43	13	=	=	PUNCT
ejpam-5776	44	1	[	[	X
ejpam-5776	44	2	sij	sij	X
ejpam-5776	44	3	]	]	PUNCT
ejpam-5776	44	4	in	in	ADP
ejpam-5776	44	5	which	which	PRON
ejpam-5776	44	6	(	(	PUNCT
ejpam-5776	44	7	i	i	PRON
ejpam-5776	44	8	,	,	PUNCT
ejpam-5776	44	9	j)-th	j)-th	PROPN
ejpam-5776	44	10	entry	entry	NOUN
ejpam-5776	44	11	is	be	AUX
ejpam-5776	44	12	sij	sij	PROPN
ejpam-5776	44	13	=	=	PUNCT
ejpam-5776	44	14	{	{	PUNCT
ejpam-5776	44	15	e(xi	e(xi	PROPN
ejpam-5776	44	16	)	)	PUNCT
ejpam-5776	44	17	+	+	NUM
ejpam-5776	44	18	e(xj	e(xj	NOUN
ejpam-5776	44	19	)	)	PUNCT
ejpam-5776	44	20	,	,	PUNCT
ejpam-5776	44	21	if	if	SCONJ
ejpam-5776	44	22	xixj	xixj	PROPN
ejpam-5776	44	23	∈	∈	PROPN
ejpam-5776	44	24	l(ωd2n	l(ωd2n	X
ejpam-5776	44	25	)	)	PUNCT
ejpam-5776	44	26	0	0	NUM
ejpam-5776	44	27	,	,	PUNCT
ejpam-5776	44	28	otherwise	otherwise	ADV
ejpam-5776	44	29	.	.	PUNCT
ejpam-5776	45	1	definition	definition	NOUN
ejpam-5776	45	2	4	4	NUM
ejpam-5776	45	3	.	.	PUNCT
ejpam-5776	46	1	[	[	X
ejpam-5776	46	2	5	5	X
ejpam-5776	46	3	]	]	PUNCT
ejpam-5776	46	4	the	the	DET
ejpam-5776	46	5	average	average	ADJ
ejpam-5776	46	6	degree	degree	NOUN
ejpam-5776	46	7	eccentricity	eccentricity	NOUN
ejpam-5776	46	8	matrix	matrix	NOUN
ejpam-5776	46	9	of	of	ADP
ejpam-5776	46	10	ωd2n	ωd2n	PROPN
ejpam-5776	46	11	is	be	AUX
ejpam-5776	46	12	ade(ωd2n	ade(ωd2n	NOUN
ejpam-5776	46	13	)	)	PUNCT
ejpam-5776	46	14	=	=	PUNCT
ejpam-5776	47	1	[	[	X
ejpam-5776	47	2	aij	aij	X
ejpam-5776	47	3	]	]	X
ejpam-5776	47	4	whose	whose	DET
ejpam-5776	47	5	(	(	PUNCT
ejpam-5776	47	6	i	i	NOUN
ejpam-5776	47	7	,	,	PUNCT
ejpam-5776	47	8	j)-th	j)-th	PROPN
ejpam-5776	47	9	entry	entry	NOUN
ejpam-5776	47	10	is	be	AUX
ejpam-5776	47	11	aij	aij	PROPN
ejpam-5776	47	12	=	=	SYM
ejpam-5776	47	13	{	{	PUNCT
ejpam-5776	47	14	1	1	NUM
ejpam-5776	47	15	4(d(xi	4(d(xi	NUM
ejpam-5776	47	16	)	)	PUNCT
ejpam-5776	47	17	+	+	CCONJ
ejpam-5776	47	18	d(xj	d(xj	NUM
ejpam-5776	47	19	)	)	PUNCT
ejpam-5776	48	1	+	+	CCONJ
ejpam-5776	48	2	e(xi	e(xi	NUM
ejpam-5776	48	3	)	)	PUNCT
ejpam-5776	49	1	+	+	NUM
ejpam-5776	49	2	e(xj	e(xj	NOUN
ejpam-5776	49	3	)	)	PUNCT
ejpam-5776	49	4	)	)	PUNCT
ejpam-5776	50	1	,	,	PUNCT
ejpam-5776	50	2	if	if	SCONJ
ejpam-5776	50	3	xixj	xixj	PROPN
ejpam-5776	50	4	∈	∈	PROPN
ejpam-5776	50	5	l(ωd2n	l(ωd2n	X
ejpam-5776	50	6	)	)	PUNCT
ejpam-5776	50	7	0	0	NUM
ejpam-5776	50	8	,	,	PUNCT
ejpam-5776	50	9	otherwise	otherwise	ADV
ejpam-5776	50	10	.	.	PUNCT
ejpam-5776	51	1	m.	m.	NOUN
ejpam-5776	51	2	u.	u.	PROPN
ejpam-5776	51	3	romdhini	romdhini	PROPN
ejpam-5776	51	4	et	et	PROPN
ejpam-5776	51	5	al	al	PROPN
ejpam-5776	51	6	.	.	PUNCT
ejpam-5776	51	7	/	/	SYM
ejpam-5776	51	8	eur	eur	PROPN
ejpam-5776	51	9	.	.	PUNCT
ejpam-5776	52	1	j.	j.	PROPN
ejpam-5776	52	2	pure	pure	PROPN
ejpam-5776	52	3	appl	appl	PROPN
ejpam-5776	52	4	.	.	PROPN
ejpam-5776	52	5	math	math	PROPN
ejpam-5776	52	6	,	,	PUNCT
ejpam-5776	52	7	18	18	NUM
ejpam-5776	52	8	(	(	PUNCT
ejpam-5776	52	9	2	2	NUM
ejpam-5776	52	10	)	)	PUNCT
ejpam-5776	52	11	(	(	PUNCT
ejpam-5776	52	12	2025	2025	NUM
ejpam-5776	52	13	)	)	PUNCT
ejpam-5776	52	14	,	,	PUNCT
ejpam-5776	52	15	5776	5776	NUM
ejpam-5776	52	16	3	3	NUM
ejpam-5776	52	17	of	of	ADP
ejpam-5776	52	18	13	13	NUM
ejpam-5776	52	19	the	the	DET
ejpam-5776	52	20	characteristic	characteristic	ADJ
ejpam-5776	52	21	polynomial	polynomial	NOUN
ejpam-5776	52	22	of	of	ADP
ejpam-5776	52	23	e(ωd2n	e(ωd2n	NOUN
ejpam-5776	52	24	)	)	PUNCT
ejpam-5776	52	25	is	be	AUX
ejpam-5776	52	26	defined	define	VERB
ejpam-5776	52	27	by	by	ADP
ejpam-5776	52	28	pe(ωd2n	pe(ωd2n	NOUN
ejpam-5776	52	29	)	)	PUNCT
ejpam-5776	52	30	(	(	PUNCT
ejpam-5776	52	31	µ	µ	NOUN
ejpam-5776	52	32	)	)	PUNCT
ejpam-5776	52	33	=	=	SYM
ejpam-5776	53	1	|µin	|µin	ADP
ejpam-5776	53	2	−	−	ADP
ejpam-5776	53	3	e(ωd2n)|	e(ωd2n)|	PROPN
ejpam-5776	53	4	,	,	PUNCT
ejpam-5776	53	5	(	(	PUNCT
ejpam-5776	53	6	1	1	X
ejpam-5776	53	7	)	)	PUNCT
ejpam-5776	53	8	where	where	SCONJ
ejpam-5776	53	9	in	in	ADP
ejpam-5776	53	10	is	be	AUX
ejpam-5776	53	11	an	an	DET
ejpam-5776	53	12	n×	n×	PROPN
ejpam-5776	53	13	n	n	PRON
ejpam-5776	53	14	identity	identity	NOUN
ejpam-5776	53	15	matrix	matrix	NOUN
ejpam-5776	53	16	.	.	PUNCT
ejpam-5776	54	1	furthermore	furthermore	ADV
ejpam-5776	54	2	,	,	PUNCT
ejpam-5776	54	3	the	the	DET
ejpam-5776	54	4	eigenvalues	eigenvalue	NOUN
ejpam-5776	54	5	of	of	ADP
ejpam-5776	54	6	ωd2n	ωd2n	PROPN
ejpam-5776	54	7	are	be	AUX
ejpam-5776	54	8	the	the	DET
ejpam-5776	54	9	roots	root	NOUN
ejpam-5776	54	10	of	of	ADP
ejpam-5776	54	11	pe(ωd2n	pe(ωd2n	NOUN
ejpam-5776	54	12	)	)	PUNCT
ejpam-5776	54	13	(	(	PUNCT
ejpam-5776	54	14	µ	µ	NOUN
ejpam-5776	54	15	)	)	PUNCT
ejpam-5776	54	16	=	=	SYM
ejpam-5776	54	17	0	0	X
ejpam-5776	54	18	.	.	PUNCT
ejpam-5776	55	1	the	the	DET
ejpam-5776	55	2	eccentricity	eccentricity	NOUN
ejpam-5776	55	3	energy	energy	NOUN
ejpam-5776	55	4	definition	definition	NOUN
ejpam-5776	55	5	is	be	AUX
ejpam-5776	55	6	based	base	VERB
ejpam-5776	55	7	on	on	ADP
ejpam-5776	55	8	the	the	DET
ejpam-5776	55	9	eigenvalues	eigenvalue	NOUN
ejpam-5776	55	10	of	of	ADP
ejpam-5776	55	11	ωd2n	ωd2n	PROPN
ejpam-5776	55	12	[	[	X
ejpam-5776	55	13	6	6	NUM
ejpam-5776	55	14	]	]	PUNCT
ejpam-5776	55	15	as	as	ADP
ejpam-5776	55	16	εe(ωd2n	εe(ωd2n	NOUN
ejpam-5776	55	17	)	)	PUNCT
ejpam-5776	56	1	=	=	SYM
ejpam-5776	57	1	n∑	n∑	NOUN
ejpam-5776	57	2	i=1	i=1	PROPN
ejpam-5776	58	1	|µi|	|µi|	PROPN
ejpam-5776	58	2	.	.	PUNCT
ejpam-5776	59	1	the	the	DET
ejpam-5776	59	2	eccentricity	eccentricity	NOUN
ejpam-5776	59	3	spectral	spectral	ADJ
ejpam-5776	59	4	radius	radius	NOUN
ejpam-5776	59	5	of	of	ADP
ejpam-5776	59	6	ωd2n	ωd2n	PROPN
ejpam-5776	60	1	[	[	X
ejpam-5776	60	2	14	14	NUM
ejpam-5776	60	3	]	]	PUNCT
ejpam-5776	60	4	is	be	AUX
ejpam-5776	60	5	ρe(ωd2n	ρe(ωd2n	NOUN
ejpam-5776	60	6	)	)	PUNCT
ejpam-5776	61	1	=	=	SYM
ejpam-5776	61	2	max{|µi|	max{|µi|	PROPN
ejpam-5776	61	3	:	:	PUNCT
ejpam-5776	62	1	i	i	NOUN
ejpam-5776	62	2	=	=	NOUN
ejpam-5776	62	3	1	1	NUM
ejpam-5776	62	4	,	,	PUNCT
ejpam-5776	62	5	2	2	NUM
ejpam-5776	62	6	,	,	PUNCT
ejpam-5776	62	7	.	.	PUNCT
ejpam-5776	62	8	.	.	PUNCT
ejpam-5776	62	9	.	.	PUNCT
ejpam-5776	62	10	,	,	PUNCT
ejpam-5776	62	11	n	n	CCONJ
ejpam-5776	62	12	}	}	PUNCT
ejpam-5776	62	13	,	,	PUNCT
ejpam-5776	62	14	where	where	SCONJ
ejpam-5776	62	15	µ1	µ1	NOUN
ejpam-5776	62	16	,	,	PUNCT
ejpam-5776	62	17	µ2	µ2	PROPN
ejpam-5776	62	18	,	,	PUNCT
ejpam-5776	62	19	.	.	PUNCT
ejpam-5776	62	20	.	.	PUNCT
ejpam-5776	62	21	.	.	PUNCT
ejpam-5776	63	1	,	,	PUNCT
ejpam-5776	63	2	µn	µn	PROPN
ejpam-5776	63	3	are	be	AUX
ejpam-5776	63	4	eigenvalues	eigenvalue	NOUN
ejpam-5776	63	5	of	of	ADP
ejpam-5776	63	6	e(ωd2n	e(ωd2n	NOUN
ejpam-5776	63	7	)	)	PUNCT
ejpam-5776	63	8	.	.	PUNCT
ejpam-5776	64	1	similarly	similarly	ADV
ejpam-5776	64	2	,	,	PUNCT
ejpam-5776	64	3	one	one	PRON
ejpam-5776	64	4	can	can	AUX
ejpam-5776	64	5	apply	apply	VERB
ejpam-5776	64	6	the	the	DET
ejpam-5776	64	7	notation	notation	NOUN
ejpam-5776	64	8	for	for	ADP
ejpam-5776	64	9	se	se	PROPN
ejpam-5776	64	10	and	and	CCONJ
ejpam-5776	64	11	ade	ade	NOUN
ejpam-5776	64	12	-	-	PUNCT
ejpam-5776	64	13	matrices	matrix	NOUN
ejpam-5776	64	14	in	in	ADP
ejpam-5776	64	15	the	the	DET
ejpam-5776	64	16	same	same	ADJ
ejpam-5776	64	17	manner	manner	NOUN
ejpam-5776	64	18	.	.	PUNCT
ejpam-5776	65	1	the	the	DET
ejpam-5776	65	2	energy	energy	NOUN
ejpam-5776	65	3	value	value	NOUN
ejpam-5776	65	4	of	of	ADP
ejpam-5776	65	5	ωd2n	ωd2n	PROPN
ejpam-5776	65	6	is	be	AUX
ejpam-5776	65	7	classified	classify	VERB
ejpam-5776	65	8	as	as	ADP
ejpam-5776	65	9	hyperenergetic	hyperenergetic	ADJ
ejpam-5776	65	10	if	if	SCONJ
ejpam-5776	65	11	the	the	DET
ejpam-5776	65	12	energy	energy	NOUN
ejpam-5776	65	13	of	of	ADP
ejpam-5776	65	14	ωd2n	ωd2n	PROPN
ejpam-5776	65	15	is	be	AUX
ejpam-5776	65	16	greater	great	ADJ
ejpam-5776	65	17	than	than	ADP
ejpam-5776	65	18	4(n−	4(n−	NUM
ejpam-5776	65	19	1	1	NUM
ejpam-5776	65	20	)	)	PUNCT
ejpam-5776	65	21	for	for	ADP
ejpam-5776	65	22	odd	odd	ADJ
ejpam-5776	65	23	n	n	CCONJ
ejpam-5776	65	24	(	(	PUNCT
ejpam-5776	65	25	or	or	CCONJ
ejpam-5776	65	26	2(2n−	2(2n−	NUM
ejpam-5776	65	27	3	3	NUM
ejpam-5776	65	28	)	)	PUNCT
ejpam-5776	65	29	for	for	ADP
ejpam-5776	65	30	even	even	ADV
ejpam-5776	65	31	n)[15	n)[15	NOUN
ejpam-5776	65	32	]	]	PUNCT
ejpam-5776	65	33	.	.	PUNCT
ejpam-5776	66	1	let	let	VERB
ejpam-5776	66	2	d2n	d2n	NOUN
ejpam-5776	66	3	=	=	PUNCT
ejpam-5776	67	1	〈	〈	PROPN
ejpam-5776	67	2	a	a	NOUN
ejpam-5776	67	3	,	,	PUNCT
ejpam-5776	67	4	b	b	NOUN
ejpam-5776	67	5	:	:	PUNCT
ejpam-5776	67	6	an	an	DET
ejpam-5776	67	7	=	=	NOUN
ejpam-5776	67	8	b2	b2	NOUN
ejpam-5776	67	9	=	=	SYM
ejpam-5776	67	10	e	e	PROPN
ejpam-5776	67	11	,	,	PUNCT
ejpam-5776	67	12	bab	bab	PROPN
ejpam-5776	67	13	=	=	SYM
ejpam-5776	67	14	a−1	a−1	PROPN
ejpam-5776	67	15	〉	〉	NOUN
ejpam-5776	67	16	.	.	PUNCT
ejpam-5776	68	1	we	we	PRON
ejpam-5776	68	2	denote	denote	VERB
ejpam-5776	68	3	ω1	ω1	PROPN
ejpam-5776	68	4	=	=	PUNCT
ejpam-5776	68	5	{	{	PUNCT
ejpam-5776	68	6	ap	ap	NOUN
ejpam-5776	68	7	:	:	PUNCT
ejpam-5776	68	8	1	1	NUM
ejpam-5776	68	9	≤	≤	NOUN
ejpam-5776	68	10	p	p	NOUN
ejpam-5776	68	11	≤	≤	NOUN
ejpam-5776	68	12	n}\z	n}\z	NOUN
ejpam-5776	68	13	(	(	PUNCT
ejpam-5776	68	14	d2n	d2n	NUM
ejpam-5776	68	15	)	)	PUNCT
ejpam-5776	68	16	and	and	CCONJ
ejpam-5776	68	17	ω2	ω2	NOUN
ejpam-5776	68	18	=	=	SYM
ejpam-5776	68	19	{	{	PUNCT
ejpam-5776	68	20	apb	apb	NOUN
ejpam-5776	68	21	:	:	PUNCT
ejpam-5776	68	22	1	1	NUM
ejpam-5776	68	23	≤	≤	NOUN
ejpam-5776	68	24	p	p	NOUN
ejpam-5776	68	25	≤	≤	NOUN
ejpam-5776	68	26	n	n	CCONJ
ejpam-5776	68	27	}	}	PUNCT
ejpam-5776	68	28	,	,	PUNCT
ejpam-5776	68	29	where	where	SCONJ
ejpam-5776	68	30	z	z	NOUN
ejpam-5776	68	31	(	(	PUNCT
ejpam-5776	68	32	d2n	d2n	PROPN
ejpam-5776	68	33	)	)	PUNCT
ejpam-5776	68	34	is	be	AUX
ejpam-5776	68	35	the	the	DET
ejpam-5776	68	36	center	center	NOUN
ejpam-5776	68	37	of	of	ADP
ejpam-5776	68	38	d2n	d2n	PROPN
ejpam-5776	68	39	.	.	PUNCT
ejpam-5776	69	1	we	we	PRON
ejpam-5776	69	2	need	need	VERB
ejpam-5776	69	3	the	the	DET
ejpam-5776	69	4	following	follow	VERB
ejpam-5776	69	5	results	result	NOUN
ejpam-5776	69	6	to	to	PART
ejpam-5776	69	7	determine	determine	VERB
ejpam-5776	69	8	the	the	DET
ejpam-5776	69	9	entries	entry	NOUN
ejpam-5776	69	10	of	of	ADP
ejpam-5776	69	11	the	the	DET
ejpam-5776	69	12	matrix	matrix	NOUN
ejpam-5776	69	13	of	of	ADP
ejpam-5776	69	14	ωd2n	ωd2n	PROPN
ejpam-5776	69	15	.	.	PUNCT
ejpam-5776	70	1	theorem	theorem	NOUN
ejpam-5776	70	2	1	1	NUM
ejpam-5776	70	3	.	.	PUNCT
ejpam-5776	71	1	[	[	X
ejpam-5776	71	2	16	16	NUM
ejpam-5776	71	3	]	]	PUNCT
ejpam-5776	71	4	in	in	ADP
ejpam-5776	71	5	ωd2n	ωd2n	PROPN
ejpam-5776	71	6	,	,	PUNCT
ejpam-5776	71	7	the	the	DET
ejpam-5776	71	8	distance	distance	NOUN
ejpam-5776	71	9	between	between	ADP
ejpam-5776	71	10	xi	xi	PROPN
ejpam-5776	71	11	and	and	CCONJ
ejpam-5776	71	12	xj	xj	PROPN
ejpam-5776	71	13	in	in	ADP
ejpam-5776	71	14	v	v	NUM
ejpam-5776	71	15	(	(	PUNCT
ejpam-5776	71	16	ωd2n	ωd2n	PROPN
ejpam-5776	71	17	)	)	PUNCT
ejpam-5776	71	18	is	be	AUX
ejpam-5776	71	19	(	(	PUNCT
ejpam-5776	71	20	i	i	NOUN
ejpam-5776	71	21	)	)	PUNCT
ejpam-5776	71	22	for	for	ADP
ejpam-5776	71	23	odd	odd	ADJ
ejpam-5776	71	24	n	n	CCONJ
ejpam-5776	71	25	,	,	PUNCT
ejpam-5776	71	26	dxixj	dxixj	PROPN
ejpam-5776	71	27	=	=	SYM
ejpam-5776	71	28	{	{	PUNCT
ejpam-5776	71	29	2	2	NUM
ejpam-5776	71	30	,	,	PUNCT
ejpam-5776	71	31	if	if	SCONJ
ejpam-5776	71	32	xi	xi	PROPN
ejpam-5776	71	33	,	,	PUNCT
ejpam-5776	71	34	xj	xj	PROPN
ejpam-5776	71	35	∈	∈	PROPN
ejpam-5776	71	36	ω1	ω1	PROPN
ejpam-5776	71	37	1	1	NUM
ejpam-5776	71	38	,	,	PUNCT
ejpam-5776	71	39	otherwise	otherwise	ADV
ejpam-5776	71	40	,	,	PUNCT
ejpam-5776	71	41	,	,	PUNCT
ejpam-5776	71	42	and	and	CCONJ
ejpam-5776	71	43	(	(	PUNCT
ejpam-5776	71	44	ii	ii	NOUN
ejpam-5776	71	45	)	)	PUNCT
ejpam-5776	71	46	for	for	ADP
ejpam-5776	71	47	the	the	DET
ejpam-5776	71	48	even	even	ADJ
ejpam-5776	71	49	n	n	CCONJ
ejpam-5776	71	50	,	,	PUNCT
ejpam-5776	71	51	dxixj	dxixj	PROPN
ejpam-5776	71	52	=	=	SYM
ejpam-5776	72	1			PROPN
ejpam-5776	72	2	2	2	NUM
ejpam-5776	72	3	,	,	PUNCT
ejpam-5776	72	4	if	if	SCONJ
ejpam-5776	72	5	xi	xi	PROPN
ejpam-5776	72	6	,	,	PUNCT
ejpam-5776	72	7	xj	xj	PROPN
ejpam-5776	72	8	∈	∈	PROPN
ejpam-5776	72	9	ω1	ω1	PROPN
ejpam-5776	72	10	2	2	NUM
ejpam-5776	72	11	,	,	PUNCT
ejpam-5776	72	12	xi	xi	PROPN
ejpam-5776	72	13	∈	∈	PROPN
ejpam-5776	72	14	ω2	ω2	PROPN
ejpam-5776	72	15	,	,	PUNCT
ejpam-5776	72	16	xj	xj	PROPN
ejpam-5776	72	17	∈	∈	PROPN
ejpam-5776	72	18	{	{	PUNCT
ejpam-5776	72	19	a	a	DET
ejpam-5776	72	20	n	n	PRON
ejpam-5776	72	21	2	2	NUM
ejpam-5776	72	22	+	+	NOUN
ejpam-5776	72	23	ib	ib	X
ejpam-5776	72	24	}	}	PUNCT
ejpam-5776	72	25	,	,	PUNCT
ejpam-5776	72	26	for	for	ADP
ejpam-5776	72	27	i	i	PROPN
ejpam-5776	72	28	=	=	SYM
ejpam-5776	72	29	1	1	NUM
ejpam-5776	72	30	,	,	PUNCT
ejpam-5776	72	31	2	2	NUM
ejpam-5776	72	32	,	,	PUNCT
ejpam-5776	72	33	.	.	PUNCT
ejpam-5776	72	34	.	.	PUNCT
ejpam-5776	73	1	.	.	PUNCT
ejpam-5776	74	1	,	,	PUNCT
ejpam-5776	74	2	n	n	PROPN
ejpam-5776	74	3	1	1	NUM
ejpam-5776	74	4	,	,	PUNCT
ejpam-5776	74	5	otherwise	otherwise	ADV
ejpam-5776	74	6	.	.	PUNCT
ejpam-5776	75	1	theorem	theorem	NOUN
ejpam-5776	75	2	2	2	NUM
ejpam-5776	75	3	.	.	PUNCT
ejpam-5776	76	1	[	[	X
ejpam-5776	76	2	17	17	NUM
ejpam-5776	76	3	]	]	PUNCT
ejpam-5776	76	4	in	in	ADP
ejpam-5776	76	5	ωd2n	ωd2n	PROPN
ejpam-5776	76	6	,	,	PUNCT
ejpam-5776	76	7	(	(	PUNCT
ejpam-5776	76	8	i	i	NOUN
ejpam-5776	76	9	)	)	PUNCT
ejpam-5776	76	10	the	the	DET
ejpam-5776	76	11	degree	degree	NOUN
ejpam-5776	76	12	of	of	ADP
ejpam-5776	76	13	ai	ai	NOUN
ejpam-5776	76	14	on	on	ADP
ejpam-5776	76	15	ωd2n	ωd2n	PROPN
ejpam-5776	76	16	is	be	AUX
ejpam-5776	76	17	dai	dai	PROPN
ejpam-5776	76	18	=	=	PUNCT
ejpam-5776	76	19	n	n	CCONJ
ejpam-5776	76	20	,	,	PUNCT
ejpam-5776	76	21	and	and	CCONJ
ejpam-5776	76	22	(	(	PUNCT
ejpam-5776	76	23	ii	ii	NOUN
ejpam-5776	76	24	)	)	PUNCT
ejpam-5776	76	25	the	the	DET
ejpam-5776	76	26	degree	degree	NOUN
ejpam-5776	76	27	of	of	ADP
ejpam-5776	76	28	aib	aib	PROPN
ejpam-5776	76	29	on	on	ADP
ejpam-5776	76	30	ωd2n	ωd2n	PROPN
ejpam-5776	76	31	is	be	AUX
ejpam-5776	76	32	daib	daib	NOUN
ejpam-5776	76	33	=	=	PUNCT
ejpam-5776	76	34	{	{	PUNCT
ejpam-5776	76	35	2(n−	2(n−	NUM
ejpam-5776	76	36	1	1	NUM
ejpam-5776	76	37	)	)	PUNCT
ejpam-5776	76	38	,	,	PUNCT
ejpam-5776	76	39	if	if	SCONJ
ejpam-5776	76	40	n	n	PRON
ejpam-5776	76	41	is	be	AUX
ejpam-5776	76	42	odd	odd	ADJ
ejpam-5776	76	43	2(n−	2(n−	NUM
ejpam-5776	76	44	2	2	NUM
ejpam-5776	76	45	)	)	PUNCT
ejpam-5776	76	46	,	,	PUNCT
ejpam-5776	76	47	if	if	SCONJ
ejpam-5776	76	48	n	n	PRON
ejpam-5776	76	49	is	be	AUX
ejpam-5776	76	50	even	even	ADV
ejpam-5776	76	51	.	.	PUNCT
ejpam-5776	77	1	the	the	DET
ejpam-5776	77	2	eccentricity	eccentricity	NOUN
ejpam-5776	77	3	of	of	ADP
ejpam-5776	77	4	every	every	DET
ejpam-5776	77	5	vertex	vertex	NOUN
ejpam-5776	77	6	in	in	ADP
ejpam-5776	77	7	ωd2n	ωd2n	PROPN
ejpam-5776	77	8	can	can	AUX
ejpam-5776	77	9	be	be	AUX
ejpam-5776	77	10	found	find	VERB
ejpam-5776	77	11	in	in	ADP
ejpam-5776	77	12	[	[	X
ejpam-5776	77	13	17	17	NUM
ejpam-5776	77	14	]	]	PUNCT
ejpam-5776	77	15	as	as	SCONJ
ejpam-5776	77	16	follows	follow	VERB
ejpam-5776	77	17	.	.	PUNCT
ejpam-5776	78	1	theorem	theorem	NOUN
ejpam-5776	78	2	3	3	NUM
ejpam-5776	78	3	.	.	PUNCT
ejpam-5776	79	1	[	[	X
ejpam-5776	79	2	17	17	NUM
ejpam-5776	79	3	]	]	PUNCT
ejpam-5776	79	4	in	in	ADP
ejpam-5776	79	5	ωd2n	ωd2n	PROPN
ejpam-5776	79	6	,	,	PUNCT
ejpam-5776	79	7	the	the	DET
ejpam-5776	79	8	eccentricity	eccentricity	NOUN
ejpam-5776	79	9	of	of	ADP
ejpam-5776	79	10	x	x	PROPN
ejpam-5776	79	11	∈	∈	PROPN
ejpam-5776	79	12	v	v	NOUN
ejpam-5776	79	13	(	(	PUNCT
ejpam-5776	79	14	ωd2n	ωd2n	PROPN
ejpam-5776	79	15	)	)	PUNCT
ejpam-5776	79	16	is	be	AUX
ejpam-5776	79	17	(	(	PUNCT
ejpam-5776	79	18	i	i	NOUN
ejpam-5776	79	19	)	)	PUNCT
ejpam-5776	79	20	for	for	ADP
ejpam-5776	79	21	odd	odd	ADJ
ejpam-5776	79	22	n	n	CCONJ
ejpam-5776	79	23	,	,	PUNCT
ejpam-5776	79	24	e(x	e(x	NUM
ejpam-5776	79	25	)	)	PUNCT
ejpam-5776	79	26	=	=	PRON
ejpam-5776	79	27	{	{	PUNCT
ejpam-5776	79	28	2	2	NUM
ejpam-5776	79	29	,	,	PUNCT
ejpam-5776	79	30	if	if	SCONJ
ejpam-5776	79	31	x	x	PROPN
ejpam-5776	79	32	∈	∈	PROPN
ejpam-5776	79	33	ω1	ω1	PROPN
ejpam-5776	79	34	1	1	NUM
ejpam-5776	79	35	,	,	PUNCT
ejpam-5776	79	36	if	if	SCONJ
ejpam-5776	79	37	x	x	SYM
ejpam-5776	79	38	∈	∈	PROPN
ejpam-5776	79	39	ω2	ω2	ADJ
ejpam-5776	79	40	and	and	CCONJ
ejpam-5776	79	41	(	(	PUNCT
ejpam-5776	79	42	ii	ii	NOUN
ejpam-5776	79	43	)	)	PUNCT
ejpam-5776	79	44	for	for	ADP
ejpam-5776	79	45	even	even	ADV
ejpam-5776	79	46	n	n	CCONJ
ejpam-5776	79	47	,	,	PUNCT
ejpam-5776	79	48	e(x	e(x	NUM
ejpam-5776	79	49	)	)	PUNCT
ejpam-5776	79	50	=	=	SYM
ejpam-5776	80	1	2	2	X
ejpam-5776	80	2	.	.	X
ejpam-5776	80	3	m.	m.	NOUN
ejpam-5776	80	4	u.	u.	PROPN
ejpam-5776	80	5	romdhini	romdhini	PROPN
ejpam-5776	80	6	et	et	PROPN
ejpam-5776	80	7	al	al	PROPN
ejpam-5776	80	8	.	.	PUNCT
ejpam-5776	80	9	/	/	SYM
ejpam-5776	80	10	eur	eur	PROPN
ejpam-5776	80	11	.	.	PUNCT
ejpam-5776	81	1	j.	j.	PROPN
ejpam-5776	81	2	pure	pure	PROPN
ejpam-5776	81	3	appl	appl	PROPN
ejpam-5776	81	4	.	.	PROPN
ejpam-5776	81	5	math	math	PROPN
ejpam-5776	81	6	,	,	PUNCT
ejpam-5776	81	7	18	18	NUM
ejpam-5776	81	8	(	(	PUNCT
ejpam-5776	81	9	2	2	NUM
ejpam-5776	81	10	)	)	PUNCT
ejpam-5776	81	11	(	(	PUNCT
ejpam-5776	81	12	2025	2025	NUM
ejpam-5776	81	13	)	)	PUNCT
ejpam-5776	81	14	,	,	PUNCT
ejpam-5776	81	15	5776	5776	NUM
ejpam-5776	81	16	4	4	NUM
ejpam-5776	81	17	of	of	ADP
ejpam-5776	81	18	13	13	NUM
ejpam-5776	81	19	the	the	DET
ejpam-5776	81	20	following	follow	VERB
ejpam-5776	81	21	theorems	theorem	NOUN
ejpam-5776	81	22	simplify	simplify	VERB
ejpam-5776	81	23	the	the	DET
ejpam-5776	81	24	process	process	NOUN
ejpam-5776	81	25	of	of	ADP
ejpam-5776	81	26	formulating	formulate	VERB
ejpam-5776	81	27	the	the	DET
ejpam-5776	81	28	characteristic	characteristic	ADJ
ejpam-5776	81	29	formula	formula	NOUN
ejpam-5776	81	30	.	.	PUNCT
ejpam-5776	82	1	theorem	theorem	ADJ
ejpam-5776	82	2	4	4	NUM
ejpam-5776	82	3	.	.	PUNCT
ejpam-5776	83	1	[	[	X
ejpam-5776	83	2	18	18	NUM
ejpam-5776	83	3	]	]	X
ejpam-5776	83	4	if	if	SCONJ
ejpam-5776	83	5	t	t	NOUN
ejpam-5776	83	6	=	=	SYM
ejpam-5776	83	7			NUM
ejpam-5776	83	8	a(j	a(j	PROPN
ejpam-5776	83	9	−	−	PROPN
ejpam-5776	83	10	i)n−2	i)n−2	PROPN
ejpam-5776	83	11	cj(n−2)×n	cj(n−2)×n	NUM
ejpam-5776	83	12	2	2	NUM
ejpam-5776	83	13	cj(n−2)×n	cj(n−2)×n	NUM
ejpam-5776	83	14	2	2	NUM
ejpam-5776	83	15	cjn	cjn	NOUN
ejpam-5776	83	16	2	2	NUM
ejpam-5776	83	17	×(n−2	×(n−2	NOUN
ejpam-5776	83	18	)	)	PUNCT
ejpam-5776	83	19	d(j	d(j	PROPN
ejpam-5776	83	20	−	−	NUM
ejpam-5776	83	21	i)n	i)n	NOUN
ejpam-5776	83	22	2	2	NUM
ejpam-5776	83	23	d(j	d(j	PROPN
ejpam-5776	83	24	−	−	NUM
ejpam-5776	83	25	i)n	i)n	NOUN
ejpam-5776	83	26	2	2	NUM
ejpam-5776	83	27	+	+	CCONJ
ejpam-5776	83	28	bin	bin	NOUN
ejpam-5776	83	29	2	2	NUM
ejpam-5776	83	30	cjn	cjn	NOUN
ejpam-5776	83	31	2	2	NUM
ejpam-5776	83	32	×(n−2	×(n−2	NOUN
ejpam-5776	83	33	)	)	PUNCT
ejpam-5776	83	34	d(j	d(j	PROPN
ejpam-5776	83	35	−	−	NUM
ejpam-5776	83	36	i)n	i)n	NOUN
ejpam-5776	83	37	2	2	NUM
ejpam-5776	84	1	+	+	CCONJ
ejpam-5776	84	2	bin	bin	NOUN
ejpam-5776	84	3	2	2	NUM
ejpam-5776	84	4	d(j	d(j	PROPN
ejpam-5776	84	5	−	−	NUM
ejpam-5776	84	6	i)n	i)n	NOUN
ejpam-5776	84	7	2	2	NUM
ejpam-5776	84	8			NUM
ejpam-5776	84	9	,	,	PUNCT
ejpam-5776	84	10	then	then	ADV
ejpam-5776	84	11	for	for	ADP
ejpam-5776	84	12	real	real	ADJ
ejpam-5776	84	13	numbers	number	NOUN
ejpam-5776	84	14	a	a	DET
ejpam-5776	84	15	,	,	PUNCT
ejpam-5776	84	16	b	b	NOUN
ejpam-5776	84	17	,	,	PUNCT
ejpam-5776	84	18	c	c	NOUN
ejpam-5776	84	19	,	,	PUNCT
ejpam-5776	84	20	d	d	NOUN
ejpam-5776	84	21	,	,	PUNCT
ejpam-5776	84	22	the	the	DET
ejpam-5776	84	23	characteristic	characteristic	ADJ
ejpam-5776	84	24	polynomial	polynomial	NOUN
ejpam-5776	84	25	of	of	ADP
ejpam-5776	84	26	t	t	PROPN
ejpam-5776	84	27	is	be	AUX
ejpam-5776	84	28	pt	pt	X
ejpam-5776	84	29	(	(	PUNCT
ejpam-5776	84	30	µ	µ	NUM
ejpam-5776	84	31	)	)	PUNCT
ejpam-5776	84	32	=	=	PUNCT
ejpam-5776	84	33	(	(	PUNCT
ejpam-5776	85	1	µ+	µ+	X
ejpam-5776	85	2	a)n−3	a)n−3	PROPN
ejpam-5776	85	3	(	(	PUNCT
ejpam-5776	85	4	µ−	µ−	PROPN
ejpam-5776	85	5	b+	b+	ADP
ejpam-5776	85	6	2d	2d	NOUN
ejpam-5776	85	7	)	)	PUNCT
ejpam-5776	85	8	n	n	PRON
ejpam-5776	85	9	2	2	NUM
ejpam-5776	85	10	−1	−1	NOUN
ejpam-5776	85	11	(	(	PUNCT
ejpam-5776	85	12	µ+	µ+	PROPN
ejpam-5776	85	13	b	b	NOUN
ejpam-5776	85	14	)	)	PUNCT
ejpam-5776	85	15	n	n	PRON
ejpam-5776	85	16	2	2	NUM
ejpam-5776	85	17	(	(	PUNCT
ejpam-5776	85	18	µ2	µ2	PROPN
ejpam-5776	85	19	−	−	PROPN
ejpam-5776	85	20	(	(	PUNCT
ejpam-5776	85	21	b+	b+	X
ejpam-5776	85	22	(	(	PUNCT
ejpam-5776	85	23	n−	n−	NOUN
ejpam-5776	85	24	2)d+	2)d+	NUM
ejpam-5776	85	25	a(n−	a(n−	PROPN
ejpam-5776	85	26	3))µ+	3))µ+	NUM
ejpam-5776	85	27	a(n−	a(n−	PROPN
ejpam-5776	85	28	3	3	NUM
ejpam-5776	85	29	)	)	PUNCT
ejpam-5776	85	30	(	(	PUNCT
ejpam-5776	85	31	b+	b+	X
ejpam-5776	85	32	(	(	PUNCT
ejpam-5776	85	33	n−	n−	NOUN
ejpam-5776	85	34	2)d)−	2)d)−	NUM
ejpam-5776	85	35	n(n−	n(n−	VERB
ejpam-5776	85	36	2)c2	2)c2	PROPN
ejpam-5776	85	37	)	)	PUNCT
ejpam-5776	85	38	.	.	PUNCT
ejpam-5776	86	1	lemma	lemma	PROPN
ejpam-5776	86	2	1	1	NUM
ejpam-5776	86	3	.	.	PUNCT
ejpam-5776	87	1	[	[	X
ejpam-5776	87	2	19	19	NUM
ejpam-5776	87	3	]	]	PUNCT
ejpam-5776	87	4	let	let	VERB
ejpam-5776	87	5	a	a	DET
ejpam-5776	87	6	,	,	PUNCT
ejpam-5776	87	7	b	b	NOUN
ejpam-5776	87	8	,	,	PUNCT
ejpam-5776	87	9	c	c	NOUN
ejpam-5776	87	10	,	,	PUNCT
ejpam-5776	87	11	and	and	CCONJ
ejpam-5776	87	12	d	d	NOUN
ejpam-5776	87	13	be	be	AUX
ejpam-5776	87	14	real	real	ADJ
ejpam-5776	87	15	numbers	number	NOUN
ejpam-5776	87	16	.	.	PUNCT
ejpam-5776	88	1	then	then	ADV
ejpam-5776	88	2	the	the	DET
ejpam-5776	88	3	determinant	determinant	ADJ
ejpam-5776	88	4	of∣∣∣∣(µ+	of∣∣∣∣(µ+	NOUN
ejpam-5776	88	5	a)in1	a)in1	ADP
ejpam-5776	88	6	−	−	PROPN
ejpam-5776	88	7	ajn1	ajn1	PROPN
ejpam-5776	88	8	−cjn1×n2	−cjn1×n2	VERB
ejpam-5776	88	9	−djn2×n1	−djn2×n1	NOUN
ejpam-5776	88	10	(	(	PUNCT
ejpam-5776	88	11	µ+	µ+	PROPN
ejpam-5776	88	12	b)in2	b)in2	NOUN
ejpam-5776	88	13	−	−	NOUN
ejpam-5776	88	14	bjn2	bjn2	PROPN
ejpam-5776	88	15	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5776	88	16	can	can	AUX
ejpam-5776	88	17	be	be	AUX
ejpam-5776	88	18	simplified	simplify	VERB
ejpam-5776	88	19	as	as	ADP
ejpam-5776	88	20	(	(	PUNCT
ejpam-5776	88	21	µ+	µ+	X
ejpam-5776	88	22	a)n1−1(µ+	a)n1−1(µ+	ADJ
ejpam-5776	88	23	b)n2−1	b)n2−1	NOUN
ejpam-5776	88	24	(	(	PUNCT
ejpam-5776	88	25	(	(	PUNCT
ejpam-5776	88	26	µ−	µ−	PROPN
ejpam-5776	88	27	(	(	PUNCT
ejpam-5776	88	28	n1	n1	PROPN
ejpam-5776	88	29	−	−	PROPN
ejpam-5776	88	30	1)a)(µ−	1)a)(µ−	NUM
ejpam-5776	88	31	(	(	PUNCT
ejpam-5776	88	32	n2	n2	NOUN
ejpam-5776	88	33	−	−	PROPN
ejpam-5776	88	34	1)b)−	1)b)−	NUM
ejpam-5776	88	35	n1n2cd	n1n2cd	NOUN
ejpam-5776	88	36	)	)	PUNCT
ejpam-5776	88	37	,	,	PUNCT
ejpam-5776	88	38	where	where	SCONJ
ejpam-5776	88	39	1	1	NUM
ejpam-5776	88	40	≤	≤	NUM
ejpam-5776	88	41	n1	n1	NOUN
ejpam-5776	88	42	,	,	PUNCT
ejpam-5776	88	43	n2	n2	ADJ
ejpam-5776	88	44	≤	≤	NOUN
ejpam-5776	88	45	n	n	CCONJ
ejpam-5776	88	46	and	and	CCONJ
ejpam-5776	88	47	n1	n1	PROPN
ejpam-5776	88	48	+	+	CCONJ
ejpam-5776	88	49	n2	n2	NOUN
ejpam-5776	88	50	=	=	SYM
ejpam-5776	88	51	n.	n.	NOUN
ejpam-5776	88	52	3	3	NUM
ejpam-5776	88	53	.	.	PUNCT
ejpam-5776	88	54	main	main	ADJ
ejpam-5776	88	55	results	result	NOUN
ejpam-5776	88	56	in	in	ADP
ejpam-5776	88	57	this	this	DET
ejpam-5776	88	58	section	section	NOUN
ejpam-5776	88	59	,	,	PUNCT
ejpam-5776	88	60	we	we	PRON
ejpam-5776	88	61	find	find	VERB
ejpam-5776	88	62	the	the	DET
ejpam-5776	88	63	eccentricity	eccentricity	NOUN
ejpam-5776	88	64	-	-	PUNCT
ejpam-5776	88	65	based	base	VERB
ejpam-5776	88	66	energies	energy	NOUN
ejpam-5776	88	67	of	of	ADP
ejpam-5776	88	68	ωd2n	ωd2n	PROPN
ejpam-5776	88	69	.	.	PUNCT
ejpam-5776	89	1	3.1	3.1	NUM
ejpam-5776	89	2	.	.	NOUN
ejpam-5776	89	3	eccentricity	eccentricity	NOUN
ejpam-5776	89	4	energy	energy	NOUN
ejpam-5776	89	5	this	this	DET
ejpam-5776	89	6	part	part	NOUN
ejpam-5776	89	7	aims	aim	VERB
ejpam-5776	89	8	to	to	PART
ejpam-5776	89	9	determine	determine	VERB
ejpam-5776	89	10	the	the	DET
ejpam-5776	89	11	energy	energy	NOUN
ejpam-5776	89	12	formula	formula	NOUN
ejpam-5776	89	13	of	of	ADP
ejpam-5776	89	14	ωd2n	ωd2n	PROPN
ejpam-5776	89	15	associated	associate	VERB
ejpam-5776	89	16	with	with	ADP
ejpam-5776	89	17	the	the	DET
ejpam-5776	89	18	eccentricity	eccentricity	NOUN
ejpam-5776	89	19	matrix	matrix	NOUN
ejpam-5776	89	20	.	.	PUNCT
ejpam-5776	90	1	theorem	theorem	NOUN
ejpam-5776	90	2	5	5	NUM
ejpam-5776	90	3	.	.	PUNCT
ejpam-5776	91	1	in	in	ADP
ejpam-5776	91	2	ωd2n	ωd2n	PROPN
ejpam-5776	91	3	,	,	PUNCT
ejpam-5776	91	4	the	the	DET
ejpam-5776	91	5	eccentricity	eccentricity	NOUN
ejpam-5776	91	6	energy	energy	NOUN
ejpam-5776	91	7	of	of	ADP
ejpam-5776	91	8	ωd2n	ωd2n	PROPN
ejpam-5776	91	9	is	be	AUX
ejpam-5776	91	10	εe(ωd2n	εe(ωd2n	ADJ
ejpam-5776	91	11	)	)	PUNCT
ejpam-5776	91	12	=	=	PRON
ejpam-5776	91	13	{	{	PUNCT
ejpam-5776	91	14	2(3n−	2(3n−	NUM
ejpam-5776	91	15	5	5	NUM
ejpam-5776	91	16	)	)	PUNCT
ejpam-5776	91	17	,	,	PUNCT
ejpam-5776	91	18	if	if	SCONJ
ejpam-5776	91	19	n	n	PRON
ejpam-5776	91	20	is	be	AUX
ejpam-5776	91	21	odd	odd	ADJ
ejpam-5776	91	22	6(n−	6(n−	NUM
ejpam-5776	91	23	2	2	NUM
ejpam-5776	91	24	)	)	PUNCT
ejpam-5776	91	25	,	,	PUNCT
ejpam-5776	91	26	if	if	SCONJ
ejpam-5776	91	27	n	n	PRON
ejpam-5776	91	28	is	be	AUX
ejpam-5776	91	29	even	even	ADV
ejpam-5776	91	30	.	.	PUNCT
ejpam-5776	92	1	proof	proof	NOUN
ejpam-5776	92	2	.	.	PUNCT
ejpam-5776	93	1	(	(	PUNCT
ejpam-5776	93	2	i	i	NOUN
ejpam-5776	93	3	)	)	PUNCT
ejpam-5776	93	4	let	let	VERB
ejpam-5776	93	5	n	n	PRON
ejpam-5776	93	6	be	be	AUX
ejpam-5776	93	7	odd	odd	ADJ
ejpam-5776	93	8	.	.	PUNCT
ejpam-5776	94	1	according	accord	VERB
ejpam-5776	94	2	to	to	ADP
ejpam-5776	94	3	theorem	theorem	ADJ
ejpam-5776	94	4	1	1	NUM
ejpam-5776	94	5	(	(	PUNCT
ejpam-5776	94	6	i	i	NOUN
ejpam-5776	94	7	)	)	PUNCT
ejpam-5776	94	8	and	and	CCONJ
ejpam-5776	94	9	definition	definition	NOUN
ejpam-5776	94	10	2	2	NUM
ejpam-5776	94	11	,	,	PUNCT
ejpam-5776	94	12	we	we	PRON
ejpam-5776	94	13	can	can	AUX
ejpam-5776	94	14	construct	construct	VERB
ejpam-5776	94	15	the	the	DET
ejpam-5776	94	16	eccentricity	eccentricity	NOUN
ejpam-5776	94	17	matrix	matrix	NOUN
ejpam-5776	94	18	of	of	ADP
ejpam-5776	94	19	ωd2n	ωd2n	PROPN
ejpam-5776	94	20	.	.	PUNCT
ejpam-5776	95	1	the	the	DET
ejpam-5776	95	2	matrix	matrix	NOUN
ejpam-5776	95	3	size	size	NOUN
ejpam-5776	95	4	is	be	AUX
ejpam-5776	95	5	(	(	PUNCT
ejpam-5776	95	6	2n	2n	NUM
ejpam-5776	95	7	−	−	NOUN
ejpam-5776	95	8	1	1	X
ejpam-5776	95	9	)	)	PUNCT
ejpam-5776	95	10	×	×	NOUN
ejpam-5776	95	11	(	(	PUNCT
ejpam-5776	95	12	2n	2n	NUM
ejpam-5776	95	13	−	−	NOUN
ejpam-5776	95	14	1	1	NUM
ejpam-5776	95	15	)	)	PUNCT
ejpam-5776	95	16	excluding	exclude	VERB
ejpam-5776	95	17	one	one	NUM
ejpam-5776	95	18	center	center	NOUN
ejpam-5776	95	19	’s	’s	PART
ejpam-5776	95	20	element	element	NOUN
ejpam-5776	95	21	of	of	ADP
ejpam-5776	95	22	d2n	d2n	PROPN
ejpam-5776	95	23	.	.	PUNCT
ejpam-5776	96	1	the	the	DET
ejpam-5776	96	2	entries	entry	NOUN
ejpam-5776	96	3	of	of	ADP
ejpam-5776	96	4	e(ωd2n	e(ωd2n	NOUN
ejpam-5776	96	5	)	)	PUNCT
ejpam-5776	96	6	=	=	PUNCT
ejpam-5776	97	1	[	[	X
ejpam-5776	97	2	ϵij	ϵij	X
ejpam-5776	97	3	]	]	X
ejpam-5776	97	4	are	be	AUX
ejpam-5776	97	5	(	(	PUNCT
ejpam-5776	97	6	a	a	NOUN
ejpam-5776	97	7	)	)	PUNCT
ejpam-5776	97	8	for	for	ADP
ejpam-5776	97	9	1	1	NUM
ejpam-5776	97	10	≤	≤	NOUN
ejpam-5776	97	11	i	i	PRON
ejpam-5776	97	12	,	,	PUNCT
ejpam-5776	97	13	j	j	PROPN
ejpam-5776	97	14	≤	≤	PROPN
ejpam-5776	97	15	n−	n−	PROPN
ejpam-5776	97	16	1	1	NUM
ejpam-5776	97	17	and	and	CCONJ
ejpam-5776	97	18	i	i	PRON
ejpam-5776	97	19	̸=	̸=	PROPN
ejpam-5776	97	20	j	j	PROPN
ejpam-5776	97	21	,	,	PUNCT
ejpam-5776	97	22	ϵij	ϵij	NOUN
ejpam-5776	97	23	=	=	PUNCT
ejpam-5776	97	24	2	2	NUM
ejpam-5776	97	25	since	since	SCONJ
ejpam-5776	97	26	dxixj	dxixj	PROPN
ejpam-5776	97	27	=	=	SYM
ejpam-5776	97	28	min{e(xi	min{e(xi	PROPN
ejpam-5776	97	29	)	)	PUNCT
ejpam-5776	97	30	,	,	PUNCT
ejpam-5776	97	31	e(xj	e(xj	PROPN
ejpam-5776	97	32	)	)	PUNCT
ejpam-5776	97	33	}	}	PUNCT
ejpam-5776	97	34	=	=	SYM
ejpam-5776	97	35	2	2	NUM
ejpam-5776	97	36	;	;	PUNCT
ejpam-5776	97	37	(	(	PUNCT
ejpam-5776	97	38	b	b	X
ejpam-5776	97	39	)	)	PUNCT
ejpam-5776	97	40	for	for	ADP
ejpam-5776	97	41	1	1	NUM
ejpam-5776	97	42	≤	≤	NUM
ejpam-5776	97	43	i	i	PRON
ejpam-5776	97	44	≤	≤	NOUN
ejpam-5776	97	45	n	n	CCONJ
ejpam-5776	97	46	−	−	PROPN
ejpam-5776	97	47	1	1	NUM
ejpam-5776	97	48	and	and	CCONJ
ejpam-5776	97	49	j	j	PROPN
ejpam-5776	97	50	=	=	SYM
ejpam-5776	97	51	n	n	CCONJ
ejpam-5776	97	52	,	,	PUNCT
ejpam-5776	97	53	n	n	PROPN
ejpam-5776	97	54	+	+	NOUN
ejpam-5776	97	55	1	1	NUM
ejpam-5776	97	56	,	,	PUNCT
ejpam-5776	97	57	.	.	PUNCT
ejpam-5776	97	58	.	.	PUNCT
ejpam-5776	97	59	.	.	PUNCT
ejpam-5776	98	1	,	,	PUNCT
ejpam-5776	98	2	2n	2n	NUM
ejpam-5776	98	3	−	−	NOUN
ejpam-5776	98	4	1	1	NUM
ejpam-5776	98	5	or	or	CCONJ
ejpam-5776	98	6	vice	vice	NOUN
ejpam-5776	98	7	versa	versa	ADV
ejpam-5776	98	8	,	,	PUNCT
ejpam-5776	98	9	ϵij	ϵij	NOUN
ejpam-5776	98	10	=	=	PUNCT
ejpam-5776	98	11	1	1	NUM
ejpam-5776	98	12	since	since	SCONJ
ejpam-5776	98	13	dxixj	dxixj	PROPN
ejpam-5776	98	14	=	=	SYM
ejpam-5776	98	15	min{e(xi	min{e(xi	PROPN
ejpam-5776	98	16	)	)	PUNCT
ejpam-5776	98	17	,	,	PUNCT
ejpam-5776	98	18	e(xj	e(xj	PROPN
ejpam-5776	98	19	)	)	PUNCT
ejpam-5776	98	20	}	}	PUNCT
ejpam-5776	98	21	=	=	SYM
ejpam-5776	98	22	1	1	NUM
ejpam-5776	98	23	;	;	PUNCT
ejpam-5776	98	24	m.	m.	PROPN
ejpam-5776	98	25	u.	u.	PROPN
ejpam-5776	98	26	romdhini	romdhini	PROPN
ejpam-5776	98	27	et	et	PROPN
ejpam-5776	98	28	al	al	PROPN
ejpam-5776	98	29	.	.	PUNCT
ejpam-5776	98	30	/	/	SYM
ejpam-5776	98	31	eur	eur	PROPN
ejpam-5776	98	32	.	.	PUNCT
ejpam-5776	99	1	j.	j.	PROPN
ejpam-5776	99	2	pure	pure	PROPN
ejpam-5776	99	3	appl	appl	PROPN
ejpam-5776	99	4	.	.	PROPN
ejpam-5776	99	5	math	math	PROPN
ejpam-5776	99	6	,	,	PUNCT
ejpam-5776	99	7	18	18	NUM
ejpam-5776	99	8	(	(	PUNCT
ejpam-5776	99	9	2	2	NUM
ejpam-5776	99	10	)	)	PUNCT
ejpam-5776	99	11	(	(	PUNCT
ejpam-5776	99	12	2025	2025	NUM
ejpam-5776	99	13	)	)	PUNCT
ejpam-5776	99	14	,	,	PUNCT
ejpam-5776	99	15	5776	5776	NUM
ejpam-5776	99	16	5	5	NUM
ejpam-5776	99	17	of	of	ADP
ejpam-5776	99	18	13	13	NUM
ejpam-5776	99	19	(	(	PUNCT
ejpam-5776	99	20	c	c	NOUN
ejpam-5776	99	21	)	)	PUNCT
ejpam-5776	99	22	for	for	ADP
ejpam-5776	99	23	n	n	NOUN
ejpam-5776	99	24	≤	≤	NOUN
ejpam-5776	100	1	i	i	PROPN
ejpam-5776	100	2	,	,	PUNCT
ejpam-5776	100	3	j	j	PROPN
ejpam-5776	100	4	≤	≤	PROPN
ejpam-5776	101	1	2n−	2n−	NUM
ejpam-5776	101	2	1	1	NUM
ejpam-5776	101	3	,	,	PUNCT
ejpam-5776	101	4	ϵij	ϵij	NOUN
ejpam-5776	101	5	=	=	PUNCT
ejpam-5776	101	6	1	1	NUM
ejpam-5776	101	7	since	since	SCONJ
ejpam-5776	101	8	dxixj	dxixj	PROPN
ejpam-5776	101	9	=	=	SYM
ejpam-5776	101	10	min{e(xi	min{e(xi	PROPN
ejpam-5776	101	11	)	)	PUNCT
ejpam-5776	101	12	,	,	PUNCT
ejpam-5776	101	13	e(xj	e(xj	PROPN
ejpam-5776	101	14	)	)	PUNCT
ejpam-5776	101	15	}	}	PUNCT
ejpam-5776	101	16	=	=	SYM
ejpam-5776	101	17	1	1	NUM
ejpam-5776	101	18	;	;	PUNCT
ejpam-5776	101	19	(	(	PUNCT
ejpam-5776	101	20	d	d	X
ejpam-5776	101	21	)	)	PUNCT
ejpam-5776	101	22	for	for	ADP
ejpam-5776	101	23	i	i	PROPN
ejpam-5776	101	24	=	=	SYM
ejpam-5776	101	25	j	j	PROPN
ejpam-5776	101	26	,	,	PUNCT
ejpam-5776	101	27	ϵij	ϵij	NOUN
ejpam-5776	101	28	=	=	PUNCT
ejpam-5776	102	1	0	0	X
ejpam-5776	102	2	.	.	PUNCT
ejpam-5776	102	3	then	then	ADV
ejpam-5776	102	4	e(ωd2n	e(ωd2n	NOUN
ejpam-5776	102	5	)	)	PUNCT
ejpam-5776	102	6	is	be	AUX
ejpam-5776	102	7	as	as	SCONJ
ejpam-5776	102	8	follows	follow	VERB
ejpam-5776	102	9	:	:	PUNCT
ejpam-5776	102	10	e(ωd2n	e(ωd2n	X
ejpam-5776	102	11	)	)	PUNCT
ejpam-5776	102	12	=	=	PUNCT
ejpam-5776	102	13	a	a	DET
ejpam-5776	102	14	a2	a2	PROPN
ejpam-5776	102	15	.	.	PUNCT
ejpam-5776	102	16	.	.	PUNCT
ejpam-5776	102	17	.	.	PUNCT
ejpam-5776	103	1	an−1	an−1	PROPN
ejpam-5776	103	2	b	b	PROPN
ejpam-5776	103	3	ab	ab	PROPN
ejpam-5776	103	4	.	.	PUNCT
ejpam-5776	103	5	.	.	PUNCT
ejpam-5776	103	6	.	.	PUNCT
ejpam-5776	104	1	an−1b	an−1b	PROPN
ejpam-5776	104	2			PROPN
ejpam-5776	104	3	a	a	DET
ejpam-5776	104	4	0	0	NUM
ejpam-5776	104	5	2	2	NUM
ejpam-5776	104	6	.	.	PUNCT
ejpam-5776	104	7	.	.	PUNCT
ejpam-5776	105	1	.	.	PUNCT
ejpam-5776	106	1	2	2	NUM
ejpam-5776	106	2	1	1	NUM
ejpam-5776	106	3	1	1	NUM
ejpam-5776	106	4	.	.	PUNCT
ejpam-5776	106	5	.	.	PUNCT
ejpam-5776	106	6	.	.	PUNCT
ejpam-5776	107	1	1	1	NUM
ejpam-5776	107	2	a2	a2	PROPN
ejpam-5776	107	3	2	2	NUM
ejpam-5776	107	4	0	0	NUM
ejpam-5776	107	5	.	.	PUNCT
ejpam-5776	107	6	.	.	PUNCT
ejpam-5776	107	7	.	.	PUNCT
ejpam-5776	108	1	2	2	NUM
ejpam-5776	108	2	1	1	NUM
ejpam-5776	108	3	1	1	NUM
ejpam-5776	108	4	.	.	PUNCT
ejpam-5776	108	5	.	.	PUNCT
ejpam-5776	108	6	.	.	PUNCT
ejpam-5776	109	1	1	1	NUM
ejpam-5776	109	2	...	...	PUNCT
ejpam-5776	109	3	...	...	PUNCT
ejpam-5776	109	4	...	...	PUNCT
ejpam-5776	109	5	.	.	PUNCT
ejpam-5776	109	6	.	.	PUNCT
ejpam-5776	109	7	.	.	PUNCT
ejpam-5776	110	1	...	...	PUNCT
ejpam-5776	110	2	...	...	PUNCT
ejpam-5776	110	3	...	...	PUNCT
ejpam-5776	110	4	.	.	PUNCT
ejpam-5776	110	5	.	.	PUNCT
ejpam-5776	111	1	.	.	PUNCT
ejpam-5776	112	1	...	...	PUNCT
ejpam-5776	113	1	an−1	an−1	ADJ
ejpam-5776	113	2	2	2	NUM
ejpam-5776	113	3	2	2	NUM
ejpam-5776	113	4	.	.	PUNCT
ejpam-5776	113	5	.	.	PUNCT
ejpam-5776	113	6	.	.	PUNCT
ejpam-5776	114	1	0	0	NUM
ejpam-5776	114	2	1	1	NUM
ejpam-5776	114	3	1	1	NUM
ejpam-5776	114	4	.	.	PUNCT
ejpam-5776	114	5	.	.	PUNCT
ejpam-5776	114	6	.	.	PUNCT
ejpam-5776	115	1	1	1	NUM
ejpam-5776	115	2	b	b	X
ejpam-5776	115	3	1	1	NUM
ejpam-5776	115	4	1	1	NUM
ejpam-5776	115	5	.	.	PUNCT
ejpam-5776	115	6	.	.	PUNCT
ejpam-5776	115	7	.	.	PUNCT
ejpam-5776	116	1	1	1	NUM
ejpam-5776	116	2	0	0	NUM
ejpam-5776	116	3	1	1	NUM
ejpam-5776	116	4	.	.	PUNCT
ejpam-5776	116	5	.	.	PUNCT
ejpam-5776	116	6	.	.	PUNCT
ejpam-5776	117	1	1	1	NUM
ejpam-5776	117	2	ab	ab	PROPN
ejpam-5776	117	3	1	1	NUM
ejpam-5776	117	4	1	1	NUM
ejpam-5776	117	5	.	.	PUNCT
ejpam-5776	117	6	.	.	PUNCT
ejpam-5776	117	7	.	.	PUNCT
ejpam-5776	118	1	1	1	NUM
ejpam-5776	118	2	1	1	NUM
ejpam-5776	118	3	0	0	NUM
ejpam-5776	118	4	.	.	PUNCT
ejpam-5776	118	5	.	.	PUNCT
ejpam-5776	118	6	.	.	PUNCT
ejpam-5776	119	1	1	1	NUM
ejpam-5776	119	2	...	...	PUNCT
ejpam-5776	119	3	...	...	PUNCT
ejpam-5776	119	4	...	...	PUNCT
ejpam-5776	119	5	.	.	PUNCT
ejpam-5776	119	6	.	.	PUNCT
ejpam-5776	119	7	.	.	PUNCT
ejpam-5776	120	1	...	...	PUNCT
ejpam-5776	120	2	...	...	PUNCT
ejpam-5776	120	3	...	...	PUNCT
ejpam-5776	120	4	.	.	PUNCT
ejpam-5776	120	5	.	.	PUNCT
ejpam-5776	121	1	.	.	PUNCT
ejpam-5776	122	1	...	...	PUNCT
ejpam-5776	123	1	an−1b	an−1b	PUNCT
ejpam-5776	123	2	1	1	NUM
ejpam-5776	123	3	1	1	NUM
ejpam-5776	123	4	.	.	PUNCT
ejpam-5776	123	5	.	.	PUNCT
ejpam-5776	123	6	.	.	PUNCT
ejpam-5776	124	1	1	1	NUM
ejpam-5776	124	2	1	1	NUM
ejpam-5776	124	3	1	1	NUM
ejpam-5776	124	4	.	.	PUNCT
ejpam-5776	124	5	.	.	PUNCT
ejpam-5776	125	1	.	.	PUNCT
ejpam-5776	126	1	0	0	PUNCT
ejpam-5776	127	1	,	,	PUNCT
ejpam-5776	127	2	and	and	CCONJ
ejpam-5776	127	3	the	the	DET
ejpam-5776	127	4	characteristic	characteristic	ADJ
ejpam-5776	127	5	formula	formula	NOUN
ejpam-5776	127	6	of	of	ADP
ejpam-5776	127	7	e(ωd2n	e(ωd2n	NOUN
ejpam-5776	127	8	)	)	PUNCT
ejpam-5776	127	9	,	,	PUNCT
ejpam-5776	127	10	pe(ωd2n	pe(ωd2n	NOUN
ejpam-5776	127	11	)	)	PUNCT
ejpam-5776	127	12	(	(	PUNCT
ejpam-5776	127	13	µ	µ	NOUN
ejpam-5776	127	14	)	)	PUNCT
ejpam-5776	127	15	=	=	SYM
ejpam-5776	127	16	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5776	127	17	(	(	PUNCT
ejpam-5776	127	18	µ+	µ+	PROPN
ejpam-5776	127	19	2)in−1	2)in−1	NUM
ejpam-5776	127	20	−	−	NUM
ejpam-5776	127	21	2jn−1	2jn−1	NUM
ejpam-5776	127	22	−j(n−1)×n	−j(n−1)×n	VERB
ejpam-5776	127	23	−jn×(n−1	−jn×(n−1	PROPN
ejpam-5776	127	24	)	)	PUNCT
ejpam-5776	127	25	(	(	PUNCT
ejpam-5776	127	26	µ+	µ+	PROPN
ejpam-5776	127	27	1)in	1)in	NUM
ejpam-5776	127	28	−	−	PROPN
ejpam-5776	127	29	jn	jn	PROPN
ejpam-5776	127	30	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5776	127	31	.	.	PUNCT
ejpam-5776	128	1	by	by	ADP
ejpam-5776	128	2	lemma	lemma	PROPN
ejpam-5776	128	3	1	1	NUM
ejpam-5776	128	4	,	,	PUNCT
ejpam-5776	128	5	with	with	ADP
ejpam-5776	128	6	a	a	DET
ejpam-5776	128	7	=	=	SYM
ejpam-5776	128	8	2	2	NUM
ejpam-5776	128	9	,	,	PUNCT
ejpam-5776	128	10	b	b	NOUN
ejpam-5776	128	11	=	=	SYM
ejpam-5776	128	12	c	c	NOUN
ejpam-5776	128	13	=	=	SYM
ejpam-5776	128	14	d	d	NOUN
ejpam-5776	128	15	=	=	SYM
ejpam-5776	128	16	1	1	NUM
ejpam-5776	128	17	,	,	PUNCT
ejpam-5776	128	18	n1	n1	NOUN
ejpam-5776	128	19	=	=	SYM
ejpam-5776	128	20	n−	n−	NOUN
ejpam-5776	128	21	1	1	NUM
ejpam-5776	128	22	and	and	CCONJ
ejpam-5776	128	23	n2	n2	ADJ
ejpam-5776	128	24	=	=	SYM
ejpam-5776	128	25	n	n	CCONJ
ejpam-5776	128	26	,	,	PUNCT
ejpam-5776	128	27	we	we	PRON
ejpam-5776	128	28	obtain	obtain	VERB
ejpam-5776	128	29	pe(ωd2n	pe(ωd2n	NOUN
ejpam-5776	128	30	)	)	PUNCT
ejpam-5776	128	31	(	(	PUNCT
ejpam-5776	128	32	µ	µ	NOUN
ejpam-5776	128	33	)	)	PUNCT
ejpam-5776	128	34	=	=	PUNCT
ejpam-5776	128	35	(	(	PUNCT
ejpam-5776	128	36	µ+	µ+	X
ejpam-5776	128	37	2)n−2(µ+	2)n−2(µ+	NUM
ejpam-5776	128	38	1)n−1	1)n−1	NUM
ejpam-5776	128	39	(	(	PUNCT
ejpam-5776	128	40	µ2	µ2	PROPN
ejpam-5776	128	41	−	−	PROPN
ejpam-5776	128	42	(	(	PUNCT
ejpam-5776	128	43	3n−	3n−	PROPN
ejpam-5776	128	44	5)µ+	5)µ+	NUM
ejpam-5776	128	45	(	(	PUNCT
ejpam-5776	128	46	n−	n−	NOUN
ejpam-5776	128	47	1)(n−	1)(n−	NUM
ejpam-5776	128	48	4	4	NUM
ejpam-5776	128	49	)	)	PUNCT
ejpam-5776	128	50	)	)	PUNCT
ejpam-5776	128	51	.	.	PUNCT
ejpam-5776	129	1	the	the	DET
ejpam-5776	129	2	eigenvalues	eigenvalue	NOUN
ejpam-5776	129	3	of	of	ADP
ejpam-5776	129	4	ωd2n	ωd2n	PROPN
ejpam-5776	129	5	are	be	AUX
ejpam-5776	129	6	µ1	µ1	NOUN
ejpam-5776	129	7	=	=	NOUN
ejpam-5776	129	8	−2	−2	NOUN
ejpam-5776	129	9	of	of	ADP
ejpam-5776	129	10	multiplicity	multiplicity	NOUN
ejpam-5776	129	11	n	n	CCONJ
ejpam-5776	129	12	−	−	PROPN
ejpam-5776	129	13	2	2	NUM
ejpam-5776	129	14	,	,	PUNCT
ejpam-5776	129	15	µ2	µ2	PROPN
ejpam-5776	129	16	=	=	PUNCT
ejpam-5776	129	17	−1	−1	NOUN
ejpam-5776	129	18	of	of	ADP
ejpam-5776	129	19	multiplicity	multiplicity	NOUN
ejpam-5776	129	20	n−	n−	NOUN
ejpam-5776	129	21	1	1	NUM
ejpam-5776	129	22	,	,	PUNCT
ejpam-5776	129	23	and	and	CCONJ
ejpam-5776	129	24	µ3,4	µ3,4	ADJ
ejpam-5776	129	25	=	=	SYM
ejpam-5776	129	26	1	1	NUM
ejpam-5776	129	27	2	2	NUM
ejpam-5776	129	28	(	(	PUNCT
ejpam-5776	129	29	3n−	3n−	NUM
ejpam-5776	129	30	5±	5±	NUM
ejpam-5776	129	31	√	√	ADP
ejpam-5776	129	32	5n2	5n2	NUM
ejpam-5776	129	33	−	−	PROPN
ejpam-5776	129	34	10n+	10n+	NUM
ejpam-5776	129	35	9	9	NUM
ejpam-5776	129	36	)	)	PUNCT
ejpam-5776	129	37	.	.	PUNCT
ejpam-5776	130	1	the	the	DET
ejpam-5776	130	2	eccentricity	eccentricity	NOUN
ejpam-5776	130	3	spectral	spectral	ADJ
ejpam-5776	130	4	radius	radius	NOUN
ejpam-5776	130	5	of	of	ADP
ejpam-5776	130	6	ωd2n	ωd2n	PROPN
ejpam-5776	130	7	is	be	AUX
ejpam-5776	130	8	ρe(ωd2n	ρe(ωd2n	NOUN
ejpam-5776	130	9	)	)	PUNCT
ejpam-5776	130	10	=	=	SYM
ejpam-5776	130	11	1	1	NUM
ejpam-5776	130	12	2	2	NUM
ejpam-5776	130	13	(	(	PUNCT
ejpam-5776	130	14	3n−	3n−	NUM
ejpam-5776	130	15	5	5	NUM
ejpam-5776	130	16	+	+	CCONJ
ejpam-5776	130	17	√	√	NUM
ejpam-5776	130	18	5n2	5n2	NUM
ejpam-5776	130	19	−	−	NOUN
ejpam-5776	130	20	10n+	10n+	NUM
ejpam-5776	130	21	9	9	NUM
ejpam-5776	130	22	)	)	PUNCT
ejpam-5776	130	23	.	.	PUNCT
ejpam-5776	131	1	the	the	DET
ejpam-5776	131	2	eccentricity	eccentricity	NOUN
ejpam-5776	131	3	energy	energy	NOUN
ejpam-5776	131	4	of	of	ADP
ejpam-5776	131	5	ωd2n	ωd2n	PROPN
ejpam-5776	131	6	is	be	AUX
ejpam-5776	131	7	εe(ωd2n	εe(ωd2n	NOUN
ejpam-5776	131	8	)	)	PUNCT
ejpam-5776	131	9	=(	=(	NOUN
ejpam-5776	132	1	n−	n−	NOUN
ejpam-5776	132	2	2)|	2)|	NUM
ejpam-5776	133	1	−	−	NUM
ejpam-5776	133	2	2|+	2|+	NUM
ejpam-5776	133	3	(	(	PUNCT
ejpam-5776	133	4	n−	n−	NOUN
ejpam-5776	133	5	1)|	1)|	NUM
ejpam-5776	133	6	−	−	NOUN
ejpam-5776	133	7	1|+	1|+	NUM
ejpam-5776	133	8	∣∣∣∣12	∣∣∣∣12	NOUN
ejpam-5776	133	9	(	(	PUNCT
ejpam-5776	133	10	3n−	3n−	NUM
ejpam-5776	133	11	5±	5±	NUM
ejpam-5776	133	12	√	√	ADP
ejpam-5776	133	13	5n2	5n2	NUM
ejpam-5776	133	14	−	−	PROPN
ejpam-5776	133	15	10n+	10n+	NUM
ejpam-5776	133	16	9	9	NUM
ejpam-5776	133	17	)	)	PUNCT
ejpam-5776	133	18	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5776	133	19	=	=	NOUN
ejpam-5776	133	20	2(3n−	2(3n−	NUM
ejpam-5776	133	21	5	5	NUM
ejpam-5776	133	22	)	)	PUNCT
ejpam-5776	133	23	(	(	PUNCT
ejpam-5776	133	24	ii	ii	NOUN
ejpam-5776	133	25	)	)	PUNCT
ejpam-5776	133	26	let	let	VERB
ejpam-5776	133	27	n	n	PRON
ejpam-5776	133	28	be	be	AUX
ejpam-5776	133	29	even	even	ADV
ejpam-5776	133	30	.	.	PUNCT
ejpam-5776	134	1	based	base	VERB
ejpam-5776	134	2	on	on	ADP
ejpam-5776	134	3	theorem	theorem	ADJ
ejpam-5776	134	4	1	1	NUM
ejpam-5776	134	5	(	(	PUNCT
ejpam-5776	134	6	ii	ii	NOUN
ejpam-5776	134	7	)	)	PUNCT
ejpam-5776	134	8	and	and	CCONJ
ejpam-5776	134	9	definition	definition	NOUN
ejpam-5776	134	10	2	2	NUM
ejpam-5776	134	11	,	,	PUNCT
ejpam-5776	134	12	e(ωd2n	e(ωd2n	X
ejpam-5776	134	13	)	)	PUNCT
ejpam-5776	134	14	=	=	PUNCT
ejpam-5776	135	1	[	[	X
ejpam-5776	135	2	ϵij	ϵij	X
ejpam-5776	135	3	]	]	PUNCT
ejpam-5776	135	4	is	be	AUX
ejpam-5776	135	5	(	(	PUNCT
ejpam-5776	135	6	2n	2n	NUM
ejpam-5776	135	7	−	−	PROPN
ejpam-5776	135	8	2)×	2)×	NUM
ejpam-5776	135	9	(	(	PUNCT
ejpam-5776	135	10	2n−	2n−	PROPN
ejpam-5776	135	11	2	2	NUM
ejpam-5776	135	12	)	)	PUNCT
ejpam-5776	135	13	excluding	exclude	VERB
ejpam-5776	135	14	two	two	NUM
ejpam-5776	135	15	center	center	NOUN
ejpam-5776	135	16	’s	’s	PART
ejpam-5776	135	17	elements	element	NOUN
ejpam-5776	135	18	of	of	ADP
ejpam-5776	135	19	d2n	d2n	PROPN
ejpam-5776	135	20	.	.	PUNCT
ejpam-5776	136	1	the	the	DET
ejpam-5776	136	2	entries	entry	NOUN
ejpam-5776	136	3	of	of	ADP
ejpam-5776	136	4	e(ωd2n	e(ωd2n	NOUN
ejpam-5776	136	5	)	)	PUNCT
ejpam-5776	136	6	are	be	AUX
ejpam-5776	136	7	(	(	PUNCT
ejpam-5776	136	8	a	a	NOUN
ejpam-5776	136	9	)	)	PUNCT
ejpam-5776	136	10	for	for	ADP
ejpam-5776	136	11	i	i	PRON
ejpam-5776	136	12	,	,	PUNCT
ejpam-5776	136	13	j	j	PROPN
ejpam-5776	136	14	=	=	SYM
ejpam-5776	136	15	1	1	NUM
ejpam-5776	136	16	,	,	PUNCT
ejpam-5776	136	17	2	2	NUM
ejpam-5776	136	18	,	,	PUNCT
ejpam-5776	136	19	.	.	PUNCT
ejpam-5776	136	20	.	.	PUNCT
ejpam-5776	137	1	.	.	PUNCT
ejpam-5776	138	1	,	,	PUNCT
ejpam-5776	138	2	n−	n−	NOUN
ejpam-5776	138	3	2	2	NUM
ejpam-5776	138	4	and	and	CCONJ
ejpam-5776	138	5	i	i	PRON
ejpam-5776	138	6	̸=	̸=	PROPN
ejpam-5776	138	7	j	j	PROPN
ejpam-5776	138	8	,	,	PUNCT
ejpam-5776	138	9	ϵij	ϵij	NOUN
ejpam-5776	138	10	=	=	PUNCT
ejpam-5776	138	11	2	2	NUM
ejpam-5776	138	12	since	since	SCONJ
ejpam-5776	138	13	dxixj	dxixj	PROPN
ejpam-5776	138	14	=	=	SYM
ejpam-5776	138	15	min{e(xi	min{e(xi	PROPN
ejpam-5776	138	16	)	)	PUNCT
ejpam-5776	138	17	,	,	PUNCT
ejpam-5776	138	18	e(xj	e(xj	PROPN
ejpam-5776	138	19	)	)	PUNCT
ejpam-5776	138	20	}	}	PUNCT
ejpam-5776	138	21	=	=	SYM
ejpam-5776	138	22	2	2	NUM
ejpam-5776	138	23	;	;	PUNCT
ejpam-5776	138	24	(	(	PUNCT
ejpam-5776	138	25	b	b	X
ejpam-5776	138	26	)	)	PUNCT
ejpam-5776	138	27	for	for	ADP
ejpam-5776	138	28	i	i	PROPN
ejpam-5776	138	29	=	=	NOUN
ejpam-5776	138	30	1	1	NUM
ejpam-5776	138	31	,	,	PUNCT
ejpam-5776	138	32	2	2	NUM
ejpam-5776	138	33	,	,	PUNCT
ejpam-5776	138	34	.	.	PUNCT
ejpam-5776	138	35	.	.	PUNCT
ejpam-5776	139	1	.	.	PUNCT
ejpam-5776	140	1	,	,	PUNCT
ejpam-5776	141	1	n	n	CCONJ
ejpam-5776	141	2	−	−	PROPN
ejpam-5776	141	3	2	2	NUM
ejpam-5776	141	4	and	and	CCONJ
ejpam-5776	141	5	j	j	NOUN
ejpam-5776	141	6	=	=	SYM
ejpam-5776	141	7	n	n	CCONJ
ejpam-5776	141	8	−	−	PROPN
ejpam-5776	141	9	1	1	NUM
ejpam-5776	141	10	,	,	PUNCT
ejpam-5776	141	11	n	n	CCONJ
ejpam-5776	141	12	,	,	PUNCT
ejpam-5776	141	13	n	n	PROPN
ejpam-5776	141	14	+	+	NOUN
ejpam-5776	141	15	1	1	NUM
ejpam-5776	141	16	,	,	PUNCT
ejpam-5776	141	17	.	.	PUNCT
ejpam-5776	141	18	.	.	PUNCT
ejpam-5776	142	1	.	.	PUNCT
ejpam-5776	143	1	,	,	PUNCT
ejpam-5776	143	2	2n	2n	NUM
ejpam-5776	143	3	−	−	ADP
ejpam-5776	143	4	2	2	NUM
ejpam-5776	143	5	or	or	CCONJ
ejpam-5776	143	6	vice	vice	NOUN
ejpam-5776	143	7	versa	versa	ADV
ejpam-5776	143	8	,	,	PUNCT
ejpam-5776	143	9	ϵij	ϵij	PROPN
ejpam-5776	144	1	=	=	NOUN
ejpam-5776	144	2	0	0	PUNCT
ejpam-5776	144	3	since	since	SCONJ
ejpam-5776	144	4	dxixj	dxixj	PROPN
ejpam-5776	144	5	=	=	SYM
ejpam-5776	144	6	1	1	NUM
ejpam-5776	144	7	<	<	X
ejpam-5776	144	8	min{e(xi	min{e(xi	PROPN
ejpam-5776	144	9	)	)	PUNCT
ejpam-5776	144	10	,	,	PUNCT
ejpam-5776	144	11	e(xj	e(xj	PROPN
ejpam-5776	144	12	)	)	PUNCT
ejpam-5776	144	13	}	}	PUNCT
ejpam-5776	144	14	=	=	SYM
ejpam-5776	144	15	2	2	NUM
ejpam-5776	144	16	;	;	PUNCT
ejpam-5776	144	17	m.	m.	NOUN
ejpam-5776	144	18	u.	u.	PROPN
ejpam-5776	144	19	romdhini	romdhini	PROPN
ejpam-5776	144	20	et	et	PROPN
ejpam-5776	144	21	al	al	PROPN
ejpam-5776	144	22	.	.	PUNCT
ejpam-5776	144	23	/	/	SYM
ejpam-5776	144	24	eur	eur	PROPN
ejpam-5776	144	25	.	.	PUNCT
ejpam-5776	145	1	j.	j.	PROPN
ejpam-5776	145	2	pure	pure	PROPN
ejpam-5776	145	3	appl	appl	PROPN
ejpam-5776	145	4	.	.	PROPN
ejpam-5776	145	5	math	math	PROPN
ejpam-5776	145	6	,	,	PUNCT
ejpam-5776	145	7	18	18	NUM
ejpam-5776	145	8	(	(	PUNCT
ejpam-5776	145	9	2	2	NUM
ejpam-5776	145	10	)	)	PUNCT
ejpam-5776	145	11	(	(	PUNCT
ejpam-5776	145	12	2025	2025	NUM
ejpam-5776	145	13	)	)	PUNCT
ejpam-5776	145	14	,	,	PUNCT
ejpam-5776	145	15	5776	5776	NUM
ejpam-5776	145	16	6	6	NUM
ejpam-5776	145	17	of	of	ADP
ejpam-5776	145	18	13	13	NUM
ejpam-5776	145	19	(	(	PUNCT
ejpam-5776	145	20	c	c	NOUN
ejpam-5776	145	21	)	)	PUNCT
ejpam-5776	145	22	for	for	ADP
ejpam-5776	145	23	i	i	PRON
ejpam-5776	145	24	=	=	SYM
ejpam-5776	145	25	n	n	CCONJ
ejpam-5776	145	26	−	−	NUM
ejpam-5776	145	27	2	2	NUM
ejpam-5776	145	28	+	+	CCONJ
ejpam-5776	145	29	p	p	NOUN
ejpam-5776	145	30	and	and	CCONJ
ejpam-5776	145	31	j	j	PROPN
ejpam-5776	145	32	=	=	SYM
ejpam-5776	145	33	n	n	CCONJ
ejpam-5776	145	34	−	−	NUM
ejpam-5776	145	35	2	2	NUM
ejpam-5776	145	36	+	+	CCONJ
ejpam-5776	145	37	n	n	DET
ejpam-5776	145	38	2	2	NUM
ejpam-5776	145	39	+	+	CCONJ
ejpam-5776	145	40	p	p	NOUN
ejpam-5776	145	41	or	or	CCONJ
ejpam-5776	145	42	vice	vice	NOUN
ejpam-5776	145	43	versa	versa	ADV
ejpam-5776	145	44	where	where	SCONJ
ejpam-5776	145	45	p	p	NOUN
ejpam-5776	145	46	=	=	NOUN
ejpam-5776	145	47	1	1	NUM
ejpam-5776	145	48	,	,	PUNCT
ejpam-5776	145	49	2	2	NUM
ejpam-5776	145	50	,	,	PUNCT
ejpam-5776	145	51	.	.	PUNCT
ejpam-5776	145	52	.	.	PUNCT
ejpam-5776	146	1	.	.	PUNCT
ejpam-5776	147	1	,	,	PUNCT
ejpam-5776	147	2	n2	n2	NOUN
ejpam-5776	147	3	,	,	PUNCT
ejpam-5776	147	4	ϵij	ϵij	NOUN
ejpam-5776	147	5	=	=	SYM
ejpam-5776	147	6	2	2	NUM
ejpam-5776	147	7	since	since	SCONJ
ejpam-5776	147	8	dxixj	dxixj	PROPN
ejpam-5776	147	9	=	=	SYM
ejpam-5776	147	10	min{e(xi	min{e(xi	PROPN
ejpam-5776	147	11	)	)	PUNCT
ejpam-5776	147	12	,	,	PUNCT
ejpam-5776	147	13	e(xj	e(xj	PROPN
ejpam-5776	147	14	)	)	PUNCT
ejpam-5776	147	15	}	}	PUNCT
ejpam-5776	147	16	=	=	SYM
ejpam-5776	147	17	2	2	NUM
ejpam-5776	147	18	;	;	PUNCT
ejpam-5776	147	19	(	(	PUNCT
ejpam-5776	147	20	d	d	X
ejpam-5776	147	21	)	)	PUNCT
ejpam-5776	147	22	for	for	ADP
ejpam-5776	147	23	i	i	PRON
ejpam-5776	147	24	,	,	PUNCT
ejpam-5776	147	25	j	j	PROPN
ejpam-5776	147	26	=	=	SYM
ejpam-5776	147	27	n	n	CCONJ
ejpam-5776	147	28	−	−	PROPN
ejpam-5776	147	29	1	1	NUM
ejpam-5776	147	30	,	,	PUNCT
ejpam-5776	147	31	n	n	CCONJ
ejpam-5776	147	32	,	,	PUNCT
ejpam-5776	147	33	n	n	PROPN
ejpam-5776	147	34	+	+	NOUN
ejpam-5776	147	35	1	1	NUM
ejpam-5776	147	36	,	,	PUNCT
ejpam-5776	147	37	.	.	PUNCT
ejpam-5776	147	38	.	.	PUNCT
ejpam-5776	148	1	.	.	PUNCT
ejpam-5776	149	1	,	,	PUNCT
ejpam-5776	149	2	2n	2n	NUM
ejpam-5776	149	3	−	−	NOUN
ejpam-5776	149	4	2	2	NUM
ejpam-5776	149	5	,	,	PUNCT
ejpam-5776	149	6	ϵij	ϵij	NOUN
ejpam-5776	149	7	=	=	SYM
ejpam-5776	149	8	1	1	NUM
ejpam-5776	149	9	except	except	SCONJ
ejpam-5776	149	10	(	(	PUNCT
ejpam-5776	149	11	i	i	NOUN
ejpam-5776	149	12	=	=	SYM
ejpam-5776	149	13	n	n	CCONJ
ejpam-5776	149	14	−	−	NUM
ejpam-5776	149	15	2	2	NUM
ejpam-5776	149	16	+	+	CCONJ
ejpam-5776	149	17	p	p	NOUN
ejpam-5776	149	18	and	and	CCONJ
ejpam-5776	149	19	j	j	PROPN
ejpam-5776	149	20	=	=	SYM
ejpam-5776	149	21	n	n	CCONJ
ejpam-5776	149	22	−	−	NUM
ejpam-5776	149	23	2	2	NUM
ejpam-5776	149	24	+	+	CCONJ
ejpam-5776	149	25	n	n	DET
ejpam-5776	149	26	2	2	NUM
ejpam-5776	150	1	+	+	CCONJ
ejpam-5776	150	2	p	p	NOUN
ejpam-5776	150	3	for	for	ADP
ejpam-5776	150	4	p	p	NOUN
ejpam-5776	150	5	=	=	SYM
ejpam-5776	150	6	1	1	NUM
ejpam-5776	150	7	,	,	PUNCT
ejpam-5776	150	8	2	2	NUM
ejpam-5776	150	9	,	,	PUNCT
ejpam-5776	150	10	.	.	PUNCT
ejpam-5776	150	11	.	.	PUNCT
ejpam-5776	151	1	.	.	PUNCT
ejpam-5776	152	1	,	,	PUNCT
ejpam-5776	152	2	n2	n2	PROPN
ejpam-5776	152	3	)	)	PUNCT
ejpam-5776	152	4	or	or	CCONJ
ejpam-5776	152	5	vice	vice	NOUN
ejpam-5776	152	6	versa	versa	ADV
ejpam-5776	152	7	,	,	PUNCT
ejpam-5776	152	8	and	and	CCONJ
ejpam-5776	152	9	i	i	PRON
ejpam-5776	152	10	̸=	̸=	PROPN
ejpam-5776	152	11	j	j	PROPN
ejpam-5776	152	12	,	,	PUNCT
ejpam-5776	152	13	ϵij	ϵij	NOUN
ejpam-5776	152	14	=	=	PUNCT
ejpam-5776	152	15	0	0	PUNCT
ejpam-5776	153	1	since	since	SCONJ
ejpam-5776	153	2	dxixj1	dxixj1	PROPN
ejpam-5776	153	3	<	<	X
ejpam-5776	153	4	min{e(xi	min{e(xi	PROPN
ejpam-5776	153	5	)	)	PUNCT
ejpam-5776	153	6	,	,	PUNCT
ejpam-5776	153	7	e(xj	e(xj	PROPN
ejpam-5776	153	8	)	)	PUNCT
ejpam-5776	153	9	}	}	PUNCT
ejpam-5776	153	10	=	=	SYM
ejpam-5776	153	11	2	2	NUM
ejpam-5776	153	12	;	;	PUNCT
ejpam-5776	153	13	(	(	PUNCT
ejpam-5776	153	14	e	e	NOUN
ejpam-5776	153	15	)	)	PUNCT
ejpam-5776	153	16	for	for	ADP
ejpam-5776	153	17	i	i	PROPN
ejpam-5776	153	18	=	=	SYM
ejpam-5776	153	19	j	j	PROPN
ejpam-5776	153	20	,	,	PUNCT
ejpam-5776	153	21	ϵij	ϵij	NOUN
ejpam-5776	153	22	=	=	PUNCT
ejpam-5776	153	23	0	0	X
ejpam-5776	153	24	.	.	PUNCT
ejpam-5776	154	1	this	this	PRON
ejpam-5776	154	2	implies	imply	VERB
ejpam-5776	154	3	that	that	SCONJ
ejpam-5776	154	4	e(ωd2n	e(ωd2n	X
ejpam-5776	154	5	)	)	PUNCT
ejpam-5776	154	6	is	be	AUX
ejpam-5776	154	7	a	a	DET
ejpam-5776	154	8	a2	a2	PROPN
ejpam-5776	154	9	.	.	PUNCT
ejpam-5776	154	10	.	.	PUNCT
ejpam-5776	154	11	.	.	PUNCT
ejpam-5776	155	1	an−1	an−1	PROPN
ejpam-5776	155	2	b	b	PROPN
ejpam-5776	155	3	ab	ab	PROPN
ejpam-5776	155	4	.	.	PUNCT
ejpam-5776	155	5	.	.	PUNCT
ejpam-5776	155	6	.	.	PUNCT
ejpam-5776	156	1	a	a	DET
ejpam-5776	156	2	n	n	NOUN
ejpam-5776	156	3	2	2	NUM
ejpam-5776	156	4	−1b	−1b	X
ejpam-5776	156	5	a	a	PRON
ejpam-5776	156	6	n	n	NUM
ejpam-5776	156	7	2	2	NUM
ejpam-5776	156	8	b	b	PROPN
ejpam-5776	156	9	a	a	DET
ejpam-5776	156	10	n	n	PRON
ejpam-5776	156	11	2	2	NUM
ejpam-5776	156	12	+1b	+1b	NUM
ejpam-5776	156	13	.	.	PUNCT
ejpam-5776	156	14	.	.	PUNCT
ejpam-5776	156	15	.	.	PUNCT
ejpam-5776	157	1	an−1b	an−1b	PROPN
ejpam-5776	157	2			PUNCT
ejpam-5776	158	1	a	a	DET
ejpam-5776	158	2	0	0	NUM
ejpam-5776	158	3	2	2	NUM
ejpam-5776	158	4	.	.	PUNCT
ejpam-5776	158	5	.	.	PUNCT
ejpam-5776	158	6	.	.	PUNCT
ejpam-5776	159	1	2	2	NUM
ejpam-5776	159	2	0	0	NUM
ejpam-5776	159	3	0	0	NUM
ejpam-5776	159	4	.	.	PUNCT
ejpam-5776	159	5	.	.	PUNCT
ejpam-5776	159	6	.	.	PUNCT
ejpam-5776	160	1	0	0	NUM
ejpam-5776	161	1	0	0	NUM
ejpam-5776	161	2	0	0	NUM
ejpam-5776	161	3	.	.	PUNCT
ejpam-5776	161	4	.	.	PUNCT
ejpam-5776	162	1	.	.	PUNCT
ejpam-5776	163	1	0	0	NUM
ejpam-5776	163	2	a2	a2	PROPN
ejpam-5776	163	3	2	2	NUM
ejpam-5776	163	4	0	0	NUM
ejpam-5776	163	5	.	.	PUNCT
ejpam-5776	163	6	.	.	PUNCT
ejpam-5776	163	7	.	.	PUNCT
ejpam-5776	164	1	2	2	NUM
ejpam-5776	164	2	0	0	NUM
ejpam-5776	164	3	0	0	NUM
ejpam-5776	164	4	.	.	PUNCT
ejpam-5776	164	5	.	.	PUNCT
ejpam-5776	164	6	.	.	PUNCT
ejpam-5776	165	1	0	0	NUM
ejpam-5776	166	1	0	0	NUM
ejpam-5776	166	2	0	0	NUM
ejpam-5776	166	3	.	.	PUNCT
ejpam-5776	166	4	.	.	PUNCT
ejpam-5776	167	1	.	.	PUNCT
ejpam-5776	168	1	0	0	NUM
ejpam-5776	168	2	...	...	PUNCT
ejpam-5776	168	3	...	...	PUNCT
ejpam-5776	168	4	.	.	PUNCT
ejpam-5776	168	5	.	.	PUNCT
ejpam-5776	169	1	.	.	PUNCT
ejpam-5776	169	2	...	...	PUNCT
ejpam-5776	170	1	...	...	PUNCT
ejpam-5776	170	2	...	...	PUNCT
ejpam-5776	170	3	.	.	PUNCT
ejpam-5776	170	4	.	.	PUNCT
ejpam-5776	171	1	.	.	PUNCT
ejpam-5776	171	2	...	...	PUNCT
ejpam-5776	172	1	...	...	PUNCT
ejpam-5776	172	2	...	...	PUNCT
ejpam-5776	172	3	.	.	PUNCT
ejpam-5776	172	4	.	.	PUNCT
ejpam-5776	173	1	.	.	PUNCT
ejpam-5776	174	1	...	...	PUNCT
ejpam-5776	175	1	an−1	an−1	ADJ
ejpam-5776	175	2	2	2	NUM
ejpam-5776	175	3	2	2	NUM
ejpam-5776	175	4	.	.	PUNCT
ejpam-5776	175	5	.	.	PUNCT
ejpam-5776	175	6	.	.	PUNCT
ejpam-5776	176	1	0	0	NUM
ejpam-5776	177	1	0	0	NUM
ejpam-5776	177	2	0	0	NUM
ejpam-5776	177	3	.	.	PUNCT
ejpam-5776	177	4	.	.	PUNCT
ejpam-5776	177	5	.	.	PUNCT
ejpam-5776	178	1	0	0	NUM
ejpam-5776	179	1	0	0	NUM
ejpam-5776	179	2	0	0	NUM
ejpam-5776	179	3	.	.	PUNCT
ejpam-5776	179	4	.	.	PUNCT
ejpam-5776	179	5	.	.	PUNCT
ejpam-5776	180	1	0	0	NUM
ejpam-5776	181	1	b	b	X
ejpam-5776	181	2	0	0	NUM
ejpam-5776	181	3	0	0	NUM
ejpam-5776	181	4	.	.	PUNCT
ejpam-5776	181	5	.	.	PUNCT
ejpam-5776	181	6	.	.	PUNCT
ejpam-5776	182	1	0	0	NUM
ejpam-5776	183	1	0	0	NUM
ejpam-5776	183	2	0	0	NUM
ejpam-5776	183	3	.	.	PUNCT
ejpam-5776	183	4	.	.	PUNCT
ejpam-5776	183	5	.	.	PUNCT
ejpam-5776	184	1	0	0	NUM
ejpam-5776	185	1	2	2	NUM
ejpam-5776	185	2	0	0	NUM
ejpam-5776	185	3	.	.	PUNCT
ejpam-5776	185	4	.	.	PUNCT
ejpam-5776	186	1	.	.	PUNCT
ejpam-5776	186	2	0	0	PUNCT
ejpam-5776	187	1	ab	ab	NOUN
ejpam-5776	187	2	0	0	NUM
ejpam-5776	187	3	0	0	NUM
ejpam-5776	187	4	.	.	PUNCT
ejpam-5776	187	5	.	.	PUNCT
ejpam-5776	187	6	.	.	PUNCT
ejpam-5776	188	1	0	0	NUM
ejpam-5776	189	1	0	0	NUM
ejpam-5776	189	2	0	0	NUM
ejpam-5776	189	3	.	.	PUNCT
ejpam-5776	189	4	.	.	PUNCT
ejpam-5776	189	5	.	.	PUNCT
ejpam-5776	190	1	0	0	NUM
ejpam-5776	190	2	0	0	NUM
ejpam-5776	190	3	2	2	NUM
ejpam-5776	190	4	.	.	PUNCT
ejpam-5776	190	5	.	.	PUNCT
ejpam-5776	190	6	.	.	PUNCT
ejpam-5776	191	1	0	0	NUM
ejpam-5776	191	2	...	...	PUNCT
ejpam-5776	191	3	...	...	PUNCT
ejpam-5776	191	4	.	.	PUNCT
ejpam-5776	191	5	.	.	PUNCT
ejpam-5776	192	1	.	.	PUNCT
ejpam-5776	192	2	...	...	PUNCT
ejpam-5776	193	1	...	...	PUNCT
ejpam-5776	193	2	...	...	PUNCT
ejpam-5776	193	3	.	.	PUNCT
ejpam-5776	193	4	.	.	PUNCT
ejpam-5776	194	1	.	.	PUNCT
ejpam-5776	194	2	...	...	PUNCT
ejpam-5776	195	1	...	...	PUNCT
ejpam-5776	195	2	...	...	PUNCT
ejpam-5776	195	3	.	.	PUNCT
ejpam-5776	195	4	.	.	PUNCT
ejpam-5776	196	1	.	.	PUNCT
ejpam-5776	197	1	...	...	PUNCT
ejpam-5776	198	1	a	a	DET
ejpam-5776	198	2	n	n	NOUN
ejpam-5776	198	3	2	2	NUM
ejpam-5776	198	4	−1b	−1b	X
ejpam-5776	198	5	0	0	NUM
ejpam-5776	198	6	0	0	NUM
ejpam-5776	198	7	.	.	PUNCT
ejpam-5776	198	8	.	.	PUNCT
ejpam-5776	198	9	.	.	PUNCT
ejpam-5776	199	1	0	0	NUM
ejpam-5776	200	1	0	0	NUM
ejpam-5776	200	2	0	0	NUM
ejpam-5776	200	3	.	.	PUNCT
ejpam-5776	200	4	.	.	PUNCT
ejpam-5776	200	5	.	.	PUNCT
ejpam-5776	201	1	0	0	NUM
ejpam-5776	202	1	0	0	NUM
ejpam-5776	202	2	0	0	NUM
ejpam-5776	202	3	.	.	PUNCT
ejpam-5776	202	4	.	.	PUNCT
ejpam-5776	203	1	.	.	PUNCT
ejpam-5776	204	1	2	2	NUM
ejpam-5776	204	2	a	a	PRON
ejpam-5776	204	3	n	n	NUM
ejpam-5776	204	4	2	2	NUM
ejpam-5776	204	5	b	b	NOUN
ejpam-5776	204	6	0	0	NUM
ejpam-5776	204	7	0	0	NUM
ejpam-5776	204	8	.	.	PUNCT
ejpam-5776	204	9	.	.	PUNCT
ejpam-5776	204	10	.	.	PUNCT
ejpam-5776	205	1	0	0	NUM
ejpam-5776	206	1	2	2	NUM
ejpam-5776	206	2	0	0	NUM
ejpam-5776	206	3	.	.	PUNCT
ejpam-5776	206	4	.	.	PUNCT
ejpam-5776	206	5	.	.	PUNCT
ejpam-5776	207	1	0	0	NUM
ejpam-5776	208	1	0	0	NUM
ejpam-5776	208	2	0	0	NUM
ejpam-5776	208	3	.	.	PUNCT
ejpam-5776	208	4	.	.	PUNCT
ejpam-5776	209	1	.	.	PUNCT
ejpam-5776	209	2	0	0	PUNCT
ejpam-5776	210	1	a	a	DET
ejpam-5776	210	2	n	n	NOUN
ejpam-5776	210	3	2	2	NUM
ejpam-5776	210	4	+1b	+1b	NUM
ejpam-5776	210	5	0	0	NUM
ejpam-5776	210	6	0	0	NUM
ejpam-5776	210	7	.	.	PUNCT
ejpam-5776	210	8	.	.	PUNCT
ejpam-5776	210	9	.	.	PUNCT
ejpam-5776	211	1	0	0	NUM
ejpam-5776	211	2	0	0	NUM
ejpam-5776	211	3	2	2	NUM
ejpam-5776	211	4	.	.	PUNCT
ejpam-5776	211	5	.	.	PUNCT
ejpam-5776	211	6	.	.	PUNCT
ejpam-5776	212	1	0	0	NUM
ejpam-5776	213	1	0	0	NUM
ejpam-5776	213	2	0	0	NUM
ejpam-5776	213	3	.	.	PUNCT
ejpam-5776	213	4	.	.	PUNCT
ejpam-5776	214	1	.	.	PUNCT
ejpam-5776	215	1	0	0	NUM
ejpam-5776	215	2	...	...	PUNCT
ejpam-5776	215	3	...	...	PUNCT
ejpam-5776	215	4	.	.	PUNCT
ejpam-5776	215	5	.	.	PUNCT
ejpam-5776	216	1	.	.	PUNCT
ejpam-5776	216	2	...	...	PUNCT
ejpam-5776	217	1	...	...	PUNCT
ejpam-5776	217	2	...	...	PUNCT
ejpam-5776	217	3	.	.	PUNCT
ejpam-5776	217	4	.	.	PUNCT
ejpam-5776	218	1	.	.	PUNCT
ejpam-5776	218	2	...	...	PUNCT
ejpam-5776	219	1	...	...	PUNCT
ejpam-5776	219	2	...	...	PUNCT
ejpam-5776	219	3	.	.	PUNCT
ejpam-5776	219	4	.	.	PUNCT
ejpam-5776	219	5	.	.	PUNCT
ejpam-5776	220	1	...	...	PUNCT
ejpam-5776	221	1	an−1b	an−1b	PUNCT
ejpam-5776	221	2	0	0	NUM
ejpam-5776	221	3	0	0	NUM
ejpam-5776	221	4	.	.	PUNCT
ejpam-5776	221	5	.	.	PUNCT
ejpam-5776	221	6	.	.	PUNCT
ejpam-5776	222	1	0	0	NUM
ejpam-5776	223	1	0	0	NUM
ejpam-5776	223	2	0	0	NUM
ejpam-5776	223	3	.	.	PUNCT
ejpam-5776	223	4	.	.	PUNCT
ejpam-5776	223	5	.	.	PUNCT
ejpam-5776	224	1	2	2	NUM
ejpam-5776	224	2	0	0	NUM
ejpam-5776	224	3	0	0	NUM
ejpam-5776	224	4	.	.	PUNCT
ejpam-5776	224	5	.	.	PUNCT
ejpam-5776	224	6	.	.	PUNCT
ejpam-5776	224	7	0	0	PUNCT
ejpam-5776	224	8	.	.	PUNCT
ejpam-5776	225	1	based	base	VERB
ejpam-5776	225	2	on	on	ADP
ejpam-5776	225	3	theorem	theorem	NOUN
ejpam-5776	225	4	4	4	NUM
ejpam-5776	225	5	with	with	ADP
ejpam-5776	225	6	a	a	DET
ejpam-5776	225	7	=	=	SYM
ejpam-5776	225	8	b	b	NOUN
ejpam-5776	225	9	=	=	SYM
ejpam-5776	225	10	2	2	NUM
ejpam-5776	225	11	,	,	PUNCT
ejpam-5776	225	12	c	c	NOUN
ejpam-5776	225	13	=	=	SYM
ejpam-5776	225	14	d	d	PROPN
ejpam-5776	225	15	=	=	SYM
ejpam-5776	225	16	0	0	NUM
ejpam-5776	225	17	,	,	PUNCT
ejpam-5776	225	18	then	then	ADV
ejpam-5776	225	19	we	we	PRON
ejpam-5776	225	20	have	have	VERB
ejpam-5776	225	21	pe(ωd2n	pe(ωd2n	NOUN
ejpam-5776	225	22	)	)	PUNCT
ejpam-5776	225	23	(	(	PUNCT
ejpam-5776	225	24	λ	λ	NOUN
ejpam-5776	225	25	)	)	PUNCT
ejpam-5776	225	26	=	=	PUNCT
ejpam-5776	225	27	(	(	PUNCT
ejpam-5776	225	28	λ+	λ+	NUM
ejpam-5776	225	29	2	2	X
ejpam-5776	225	30	)	)	PUNCT
ejpam-5776	225	31	3(n−2	3(n−2	ADJ
ejpam-5776	225	32	)	)	PUNCT
ejpam-5776	225	33	2	2	NUM
ejpam-5776	225	34	(	(	PUNCT
ejpam-5776	225	35	λ−	λ−	PROPN
ejpam-5776	225	36	2	2	NUM
ejpam-5776	225	37	)	)	PUNCT
ejpam-5776	225	38	n	n	PRON
ejpam-5776	225	39	2	2	NUM
ejpam-5776	225	40	−1	−1	NOUN
ejpam-5776	225	41	(	(	PUNCT
ejpam-5776	225	42	λ2	λ2	NOUN
ejpam-5776	225	43	−	−	PROPN
ejpam-5776	225	44	2	2	NUM
ejpam-5776	225	45	(	(	PUNCT
ejpam-5776	225	46	n−	n−	NOUN
ejpam-5776	225	47	2)λ+	2)λ+	NUM
ejpam-5776	225	48	4(n−	4(n−	NUM
ejpam-5776	225	49	3	3	NUM
ejpam-5776	225	50	)	)	PUNCT
ejpam-5776	225	51	)	)	PUNCT
ejpam-5776	225	52	.	.	PUNCT
ejpam-5776	226	1	the	the	DET
ejpam-5776	226	2	roots	root	NOUN
ejpam-5776	226	3	of	of	ADP
ejpam-5776	226	4	pe(ωd2n	pe(ωd2n	NOUN
ejpam-5776	226	5	)	)	PUNCT
ejpam-5776	226	6	(	(	PUNCT
ejpam-5776	226	7	λ	λ	X
ejpam-5776	226	8	)	)	PUNCT
ejpam-5776	226	9	give	give	VERB
ejpam-5776	226	10	the	the	DET
ejpam-5776	226	11	eigenvalues	eigenvalue	NOUN
ejpam-5776	226	12	of	of	ADP
ejpam-5776	226	13	ωd2n	ωd2n	PROPN
ejpam-5776	226	14	.	.	PUNCT
ejpam-5776	227	1	therefore	therefore	ADV
ejpam-5776	227	2	,	,	PUNCT
ejpam-5776	227	3	the	the	DET
ejpam-5776	227	4	eccentricity	eccentricity	NOUN
ejpam-5776	227	5	energy	energy	NOUN
ejpam-5776	227	6	of	of	ADP
ejpam-5776	227	7	ωd2n	ωd2n	PROPN
ejpam-5776	227	8	is	be	AUX
ejpam-5776	227	9	εe(ωd2n	εe(ωd2n	ADJ
ejpam-5776	227	10	)	)	PUNCT
ejpam-5776	227	11	=	=	PUNCT
ejpam-5776	228	1	(	(	PUNCT
ejpam-5776	228	2	3(n−	3(n−	NUM
ejpam-5776	228	3	2	2	NUM
ejpam-5776	228	4	)	)	SYM
ejpam-5776	228	5	2	2	NUM
ejpam-5776	228	6	)	)	PUNCT
ejpam-5776	228	7	|−2|+	|−2|+	PROPN
ejpam-5776	228	8	(	(	PUNCT
ejpam-5776	228	9	n	n	NOUN
ejpam-5776	228	10	2	2	NUM
ejpam-5776	228	11	−	−	NOUN
ejpam-5776	228	12	1	1	NUM
ejpam-5776	228	13	)	)	PUNCT
ejpam-5776	228	14	|2|+	|2|+	PROPN
ejpam-5776	228	15	|n−	|n−	NOUN
ejpam-5776	228	16	2±	2±	NUM
ejpam-5776	228	17	(	(	PUNCT
ejpam-5776	228	18	n−	n−	NOUN
ejpam-5776	228	19	4)|	4)|	NOUN
ejpam-5776	228	20	=	=	PUNCT
ejpam-5776	229	1	6(n−	6(n−	NUM
ejpam-5776	229	2	2	2	NUM
ejpam-5776	229	3	)	)	PUNCT
ejpam-5776	229	4	.	.	PUNCT
ejpam-5776	230	1	3.2	3.2	NUM
ejpam-5776	230	2	.	.	PUNCT
ejpam-5776	230	3	sum	sum	NOUN
ejpam-5776	230	4	eccentricity	eccentricity	NOUN
ejpam-5776	230	5	energy	energy	NOUN
ejpam-5776	230	6	this	this	DET
ejpam-5776	230	7	part	part	NOUN
ejpam-5776	230	8	focuses	focus	VERB
ejpam-5776	230	9	on	on	ADP
ejpam-5776	230	10	ωd2n	ωd2n	PROPN
ejpam-5776	230	11	’s	’s	PART
ejpam-5776	230	12	sum	sum	NOUN
ejpam-5776	230	13	eccentricity	eccentricity	NOUN
ejpam-5776	230	14	matrix	matrix	NOUN
ejpam-5776	230	15	for	for	ADP
ejpam-5776	230	16	odd	odd	ADJ
ejpam-5776	230	17	and	and	CCONJ
ejpam-5776	230	18	even	even	ADV
ejpam-5776	230	19	n.	n.	PROPN
ejpam-5776	230	20	theorem	theorem	ADJ
ejpam-5776	230	21	6	6	NUM
ejpam-5776	230	22	.	.	PUNCT
ejpam-5776	231	1	in	in	ADP
ejpam-5776	231	2	ωd2n	ωd2n	PROPN
ejpam-5776	231	3	,	,	PUNCT
ejpam-5776	231	4	the	the	DET
ejpam-5776	231	5	sum	sum	NOUN
ejpam-5776	231	6	eccentricity	eccentricity	NOUN
ejpam-5776	231	7	spectral	spectral	ADJ
ejpam-5776	231	8	radius	radius	NOUN
ejpam-5776	231	9	of	of	ADP
ejpam-5776	231	10	ωd2n	ωd2n	PROPN
ejpam-5776	231	11	is	be	AUX
ejpam-5776	231	12	ρse(ωd2n	ρse(ωd2n	NOUN
ejpam-5776	231	13	)	)	PUNCT
ejpam-5776	232	1	=	=	PRON
ejpam-5776	232	2	{	{	PUNCT
ejpam-5776	232	3	n−	n−	NOUN
ejpam-5776	232	4	1	1	NUM
ejpam-5776	232	5	+	+	CCONJ
ejpam-5776	232	6	√	√	PROPN
ejpam-5776	232	7	(	(	PUNCT
ejpam-5776	232	8	n−	n−	NOUN
ejpam-5776	232	9	1)(10n−	1)(10n−	PROPN
ejpam-5776	232	10	1	1	NUM
ejpam-5776	232	11	)	)	PUNCT
ejpam-5776	232	12	,	,	PUNCT
ejpam-5776	232	13	if	if	SCONJ
ejpam-5776	232	14	n	n	PRON
ejpam-5776	232	15	is	be	AUX
ejpam-5776	232	16	odd	odd	ADJ
ejpam-5776	232	17	2	2	NUM
ejpam-5776	232	18	(	(	PUNCT
ejpam-5776	232	19	n−	n−	NOUN
ejpam-5776	232	20	2	2	NUM
ejpam-5776	232	21	+	+	CCONJ
ejpam-5776	232	22	√	√	PROPN
ejpam-5776	232	23	(	(	PUNCT
ejpam-5776	232	24	n−	n−	NOUN
ejpam-5776	232	25	2)(5n−	2)(5n−	NUM
ejpam-5776	232	26	2	2	NUM
ejpam-5776	232	27	)	)	PUNCT
ejpam-5776	232	28	)	)	PUNCT
ejpam-5776	232	29	,	,	PUNCT
ejpam-5776	232	30	if	if	SCONJ
ejpam-5776	232	31	n	n	PRON
ejpam-5776	232	32	is	be	AUX
ejpam-5776	232	33	even	even	ADV
ejpam-5776	232	34	.	.	PUNCT
ejpam-5776	233	1	proof	proof	NOUN
ejpam-5776	233	2	.	.	PUNCT
ejpam-5776	234	1	m.	m.	NOUN
ejpam-5776	234	2	u.	u.	PROPN
ejpam-5776	234	3	romdhini	romdhini	PROPN
ejpam-5776	234	4	et	et	PROPN
ejpam-5776	234	5	al	al	PROPN
ejpam-5776	234	6	.	.	PUNCT
ejpam-5776	234	7	/	/	SYM
ejpam-5776	234	8	eur	eur	PROPN
ejpam-5776	234	9	.	.	PUNCT
ejpam-5776	235	1	j.	j.	PROPN
ejpam-5776	235	2	pure	pure	PROPN
ejpam-5776	235	3	appl	appl	PROPN
ejpam-5776	235	4	.	.	PROPN
ejpam-5776	235	5	math	math	PROPN
ejpam-5776	235	6	,	,	PUNCT
ejpam-5776	235	7	18	18	NUM
ejpam-5776	235	8	(	(	PUNCT
ejpam-5776	235	9	2	2	NUM
ejpam-5776	235	10	)	)	PUNCT
ejpam-5776	235	11	(	(	PUNCT
ejpam-5776	235	12	2025	2025	NUM
ejpam-5776	235	13	)	)	PUNCT
ejpam-5776	235	14	,	,	PUNCT
ejpam-5776	235	15	5776	5776	NUM
ejpam-5776	235	16	7	7	NUM
ejpam-5776	235	17	of	of	ADP
ejpam-5776	235	18	13	13	NUM
ejpam-5776	235	19	(	(	PUNCT
ejpam-5776	235	20	i	i	NOUN
ejpam-5776	235	21	)	)	PUNCT
ejpam-5776	235	22	let	let	VERB
ejpam-5776	235	23	n	n	PRON
ejpam-5776	235	24	be	be	AUX
ejpam-5776	235	25	odd	odd	ADJ
ejpam-5776	235	26	.	.	PUNCT
ejpam-5776	236	1	according	accord	VERB
ejpam-5776	236	2	to	to	ADP
ejpam-5776	236	3	theorem	theorem	ADJ
ejpam-5776	236	4	3	3	NUM
ejpam-5776	236	5	and	and	CCONJ
ejpam-5776	236	6	definition	definition	NOUN
ejpam-5776	236	7	3	3	NUM
ejpam-5776	236	8	,	,	PUNCT
ejpam-5776	236	9	we	we	PRON
ejpam-5776	236	10	can	can	AUX
ejpam-5776	236	11	construct	construct	VERB
ejpam-5776	236	12	the	the	DET
ejpam-5776	236	13	sum	sum	NOUN
ejpam-5776	236	14	eccentricity	eccentricity	NOUN
ejpam-5776	236	15	matrix	matrix	NOUN
ejpam-5776	236	16	of	of	ADP
ejpam-5776	236	17	ωd2n	ωd2n	PROPN
ejpam-5776	236	18	.	.	PUNCT
ejpam-5776	237	1	the	the	DET
ejpam-5776	237	2	entries	entry	NOUN
ejpam-5776	237	3	of	of	ADP
ejpam-5776	237	4	se(ωd2n	se(ωd2n	NOUN
ejpam-5776	237	5	)	)	PUNCT
ejpam-5776	237	6	=	=	PUNCT
ejpam-5776	238	1	[	[	X
ejpam-5776	238	2	sij	sij	X
ejpam-5776	238	3	]	]	X
ejpam-5776	238	4	are	be	AUX
ejpam-5776	238	5	(	(	PUNCT
ejpam-5776	238	6	a	a	NOUN
ejpam-5776	238	7	)	)	PUNCT
ejpam-5776	238	8	for	for	ADP
ejpam-5776	238	9	1	1	NUM
ejpam-5776	238	10	≤	≤	NOUN
ejpam-5776	238	11	i	i	PRON
ejpam-5776	238	12	,	,	PUNCT
ejpam-5776	238	13	j	j	PROPN
ejpam-5776	238	14	≤	≤	PROPN
ejpam-5776	238	15	n−	n−	PROPN
ejpam-5776	238	16	1	1	NUM
ejpam-5776	238	17	and	and	CCONJ
ejpam-5776	238	18	i	i	PRON
ejpam-5776	238	19	̸=	̸=	PROPN
ejpam-5776	238	20	j	j	PROPN
ejpam-5776	238	21	,	,	PUNCT
ejpam-5776	238	22	then	then	ADV
ejpam-5776	238	23	sij	sij	PROPN
ejpam-5776	238	24	=	=	PROPN
ejpam-5776	238	25	0	0	NUM
ejpam-5776	238	26	;	;	PUNCT
ejpam-5776	238	27	(	(	PUNCT
ejpam-5776	238	28	b	b	X
ejpam-5776	238	29	)	)	PUNCT
ejpam-5776	238	30	for	for	ADP
ejpam-5776	238	31	1	1	NUM
ejpam-5776	238	32	≤	≤	NUM
ejpam-5776	238	33	i	i	PRON
ejpam-5776	238	34	≤	≤	NOUN
ejpam-5776	238	35	n	n	CCONJ
ejpam-5776	238	36	−	−	PROPN
ejpam-5776	238	37	1	1	NUM
ejpam-5776	238	38	and	and	CCONJ
ejpam-5776	238	39	j	j	PROPN
ejpam-5776	238	40	=	=	SYM
ejpam-5776	238	41	n	n	CCONJ
ejpam-5776	238	42	,	,	PUNCT
ejpam-5776	238	43	n	n	PROPN
ejpam-5776	238	44	+	+	NOUN
ejpam-5776	238	45	1	1	NUM
ejpam-5776	238	46	,	,	PUNCT
ejpam-5776	238	47	.	.	PUNCT
ejpam-5776	238	48	.	.	PUNCT
ejpam-5776	238	49	.	.	PUNCT
ejpam-5776	239	1	,	,	PUNCT
ejpam-5776	239	2	2n	2n	NUM
ejpam-5776	239	3	−	−	NOUN
ejpam-5776	239	4	1	1	NUM
ejpam-5776	239	5	or	or	CCONJ
ejpam-5776	239	6	vice	vice	NOUN
ejpam-5776	239	7	versa	versa	ADV
ejpam-5776	240	1	and	and	CCONJ
ejpam-5776	240	2	i	i	PRON
ejpam-5776	240	3	̸=	̸=	PROPN
ejpam-5776	240	4	j	j	PROPN
ejpam-5776	240	5	,	,	PUNCT
ejpam-5776	240	6	then	then	ADV
ejpam-5776	240	7	sij	sij	PROPN
ejpam-5776	240	8	=	=	SYM
ejpam-5776	240	9	2	2	NUM
ejpam-5776	240	10	+	+	SYM
ejpam-5776	240	11	1	1	NUM
ejpam-5776	240	12	=	=	SYM
ejpam-5776	240	13	3	3	NUM
ejpam-5776	240	14	since	since	SCONJ
ejpam-5776	240	15	dxixj	dxixj	PROPN
ejpam-5776	240	16	=	=	SYM
ejpam-5776	240	17	min{e(xi	min{e(xi	PROPN
ejpam-5776	240	18	)	)	PUNCT
ejpam-5776	240	19	,	,	PUNCT
ejpam-5776	240	20	e(xj	e(xj	PROPN
ejpam-5776	240	21	)	)	PUNCT
ejpam-5776	240	22	}	}	PUNCT
ejpam-5776	240	23	=	=	SYM
ejpam-5776	240	24	1	1	NUM
ejpam-5776	240	25	;	;	PUNCT
ejpam-5776	240	26	(	(	PUNCT
ejpam-5776	240	27	c	c	X
ejpam-5776	240	28	)	)	PUNCT
ejpam-5776	240	29	for	for	ADP
ejpam-5776	240	30	i	i	PRON
ejpam-5776	240	31	,	,	PUNCT
ejpam-5776	240	32	j	j	PROPN
ejpam-5776	240	33	=	=	SYM
ejpam-5776	240	34	n	n	CCONJ
ejpam-5776	240	35	,	,	PUNCT
ejpam-5776	240	36	n+	n+	ADP
ejpam-5776	240	37	1	1	NUM
ejpam-5776	240	38	,	,	PUNCT
ejpam-5776	240	39	.	.	PUNCT
ejpam-5776	240	40	.	.	PUNCT
ejpam-5776	241	1	.	.	PUNCT
ejpam-5776	242	1	,	,	PUNCT
ejpam-5776	242	2	2n−	2n−	PROPN
ejpam-5776	242	3	1	1	NUM
ejpam-5776	242	4	and	and	CCONJ
ejpam-5776	242	5	i	i	PRON
ejpam-5776	242	6	̸=	̸=	PROPN
ejpam-5776	242	7	j	j	PROPN
ejpam-5776	242	8	,	,	PUNCT
ejpam-5776	242	9	then	then	ADV
ejpam-5776	242	10	sij	sij	PROPN
ejpam-5776	242	11	=	=	PUNCT
ejpam-5776	243	1	1	1	NUM
ejpam-5776	243	2	+	+	SYM
ejpam-5776	243	3	1	1	NUM
ejpam-5776	243	4	=	=	SYM
ejpam-5776	243	5	2	2	NUM
ejpam-5776	243	6	;	;	PUNCT
ejpam-5776	243	7	(	(	PUNCT
ejpam-5776	243	8	d	d	X
ejpam-5776	243	9	)	)	PUNCT
ejpam-5776	243	10	for	for	ADP
ejpam-5776	243	11	i	i	PROPN
ejpam-5776	243	12	=	=	SYM
ejpam-5776	243	13	j	j	PROPN
ejpam-5776	243	14	,	,	PUNCT
ejpam-5776	243	15	sij	sij	PROPN
ejpam-5776	243	16	=	=	SYM
ejpam-5776	243	17	0	0	PROPN
ejpam-5776	243	18	then	then	ADV
ejpam-5776	243	19	se(ωd2n	se(ωd2n	PROPN
ejpam-5776	243	20	)	)	PUNCT
ejpam-5776	243	21	is	be	AUX
ejpam-5776	243	22	as	as	SCONJ
ejpam-5776	243	23	follows	follow	VERB
ejpam-5776	243	24	:	:	PUNCT
ejpam-5776	243	25	se(ωd2n	se(ωd2n	PROPN
ejpam-5776	243	26	)	)	PUNCT
ejpam-5776	243	27	=	=	PUNCT
ejpam-5776	243	28	a	a	DET
ejpam-5776	243	29	a2	a2	PROPN
ejpam-5776	243	30	.	.	PUNCT
ejpam-5776	243	31	.	.	PUNCT
ejpam-5776	243	32	.	.	PUNCT
ejpam-5776	244	1	an−1	an−1	PROPN
ejpam-5776	244	2	b	b	PROPN
ejpam-5776	244	3	ab	ab	PROPN
ejpam-5776	244	4	.	.	PUNCT
ejpam-5776	244	5	.	.	PUNCT
ejpam-5776	244	6	.	.	PUNCT
ejpam-5776	245	1	an−1b	an−1b	PROPN
ejpam-5776	245	2			PROPN
ejpam-5776	246	1	a	a	DET
ejpam-5776	246	2	0	0	NUM
ejpam-5776	246	3	0	0	NUM
ejpam-5776	246	4	.	.	PUNCT
ejpam-5776	246	5	.	.	PUNCT
ejpam-5776	246	6	.	.	PUNCT
ejpam-5776	247	1	0	0	NUM
ejpam-5776	247	2	3	3	NUM
ejpam-5776	247	3	3	3	NUM
ejpam-5776	247	4	.	.	PUNCT
ejpam-5776	247	5	.	.	PUNCT
ejpam-5776	247	6	.	.	PUNCT
ejpam-5776	248	1	3	3	NUM
ejpam-5776	248	2	a2	a2	PROPN
ejpam-5776	248	3	0	0	NUM
ejpam-5776	248	4	0	0	NUM
ejpam-5776	248	5	.	.	PUNCT
ejpam-5776	248	6	.	.	PUNCT
ejpam-5776	248	7	.	.	PUNCT
ejpam-5776	249	1	0	0	NUM
ejpam-5776	249	2	3	3	NUM
ejpam-5776	249	3	3	3	NUM
ejpam-5776	249	4	.	.	PUNCT
ejpam-5776	249	5	.	.	PUNCT
ejpam-5776	249	6	.	.	PUNCT
ejpam-5776	250	1	3	3	NUM
ejpam-5776	250	2	...	...	PUNCT
ejpam-5776	250	3	...	...	PUNCT
ejpam-5776	250	4	...	...	PUNCT
ejpam-5776	250	5	.	.	PUNCT
ejpam-5776	250	6	.	.	PUNCT
ejpam-5776	250	7	.	.	PUNCT
ejpam-5776	251	1	...	...	PUNCT
ejpam-5776	251	2	...	...	PUNCT
ejpam-5776	251	3	...	...	PUNCT
ejpam-5776	251	4	.	.	PUNCT
ejpam-5776	251	5	.	.	PUNCT
ejpam-5776	252	1	.	.	PUNCT
ejpam-5776	253	1	...	...	PUNCT
ejpam-5776	254	1	an−1	an−1	ADJ
ejpam-5776	254	2	0	0	NUM
ejpam-5776	254	3	0	0	NUM
ejpam-5776	254	4	.	.	PUNCT
ejpam-5776	254	5	.	.	PUNCT
ejpam-5776	255	1	.	.	PUNCT
ejpam-5776	256	1	0	0	NUM
ejpam-5776	256	2	3	3	NUM
ejpam-5776	256	3	3	3	NUM
ejpam-5776	256	4	.	.	PUNCT
ejpam-5776	256	5	.	.	PUNCT
ejpam-5776	256	6	.	.	PUNCT
ejpam-5776	257	1	3	3	NUM
ejpam-5776	257	2	b	b	SYM
ejpam-5776	257	3	3	3	NUM
ejpam-5776	257	4	3	3	NUM
ejpam-5776	257	5	.	.	PUNCT
ejpam-5776	257	6	.	.	PUNCT
ejpam-5776	257	7	.	.	PUNCT
ejpam-5776	258	1	3	3	NUM
ejpam-5776	258	2	0	0	NUM
ejpam-5776	258	3	2	2	NUM
ejpam-5776	258	4	.	.	PUNCT
ejpam-5776	258	5	.	.	PUNCT
ejpam-5776	258	6	.	.	PUNCT
ejpam-5776	259	1	2	2	NUM
ejpam-5776	259	2	ab	ab	PROPN
ejpam-5776	259	3	3	3	NUM
ejpam-5776	259	4	3	3	NUM
ejpam-5776	259	5	.	.	PUNCT
ejpam-5776	259	6	.	.	PUNCT
ejpam-5776	259	7	.	.	PUNCT
ejpam-5776	260	1	3	3	NUM
ejpam-5776	260	2	2	2	NUM
ejpam-5776	260	3	0	0	NUM
ejpam-5776	260	4	.	.	PUNCT
ejpam-5776	260	5	.	.	PUNCT
ejpam-5776	260	6	.	.	PUNCT
ejpam-5776	261	1	2	2	NUM
ejpam-5776	261	2	...	...	PUNCT
ejpam-5776	261	3	...	...	PUNCT
ejpam-5776	261	4	...	...	PUNCT
ejpam-5776	261	5	.	.	PUNCT
ejpam-5776	261	6	.	.	PUNCT
ejpam-5776	261	7	.	.	PUNCT
ejpam-5776	262	1	...	...	PUNCT
ejpam-5776	262	2	...	...	PUNCT
ejpam-5776	262	3	...	...	PUNCT
ejpam-5776	262	4	.	.	PUNCT
ejpam-5776	262	5	.	.	PUNCT
ejpam-5776	263	1	.	.	PUNCT
ejpam-5776	264	1	...	...	PUNCT
ejpam-5776	265	1	an−1b	an−1b	PUNCT
ejpam-5776	265	2	3	3	NUM
ejpam-5776	265	3	3	3	NUM
ejpam-5776	265	4	.	.	PUNCT
ejpam-5776	265	5	.	.	PUNCT
ejpam-5776	265	6	.	.	PUNCT
ejpam-5776	266	1	3	3	NUM
ejpam-5776	266	2	2	2	NUM
ejpam-5776	266	3	2	2	NUM
ejpam-5776	266	4	.	.	PUNCT
ejpam-5776	266	5	.	.	PUNCT
ejpam-5776	266	6	.	.	PUNCT
ejpam-5776	267	1	0	0	PUNCT
ejpam-5776	267	2	.	.	PUNCT
ejpam-5776	268	1	se	se	ADJ
ejpam-5776	268	2	-	-	NOUN
ejpam-5776	268	3	matrix	matrix	NOUN
ejpam-5776	268	4	of	of	ADP
ejpam-5776	268	5	ωd2n	ωd2n	PROPN
ejpam-5776	268	6	can	can	AUX
ejpam-5776	268	7	be	be	AUX
ejpam-5776	268	8	written	write	VERB
ejpam-5776	268	9	as	as	ADP
ejpam-5776	268	10	given	give	VERB
ejpam-5776	268	11	below	below	ADP
ejpam-5776	268	12	se(ωd2n	se(ωd2n	NOUN
ejpam-5776	268	13	)	)	PUNCT
ejpam-5776	269	1	=	=	PUNCT
ejpam-5776	269	2	(	(	PUNCT
ejpam-5776	269	3	0n−1	0n−1	PROPN
ejpam-5776	269	4	3j(n−1)×n	3j(n−1)×n	PROPN
ejpam-5776	269	5	3jn×(n−1	3jn×(n−1	NUM
ejpam-5776	269	6	)	)	PUNCT
ejpam-5776	269	7	2(j	2(j	NUM
ejpam-5776	269	8	−	−	NOUN
ejpam-5776	269	9	i)n	i)n	NUM
ejpam-5776	269	10	)	)	PUNCT
ejpam-5776	269	11	,	,	PUNCT
ejpam-5776	269	12	and	and	CCONJ
ejpam-5776	269	13	the	the	DET
ejpam-5776	269	14	characteristic	characteristic	ADJ
ejpam-5776	269	15	formula	formula	NOUN
ejpam-5776	269	16	of	of	ADP
ejpam-5776	269	17	se(ωd2n	se(ωd2n	NOUN
ejpam-5776	269	18	)	)	PUNCT
ejpam-5776	269	19	,	,	PUNCT
ejpam-5776	269	20	pse(ωd2n	pse(ωd2n	NOUN
ejpam-5776	269	21	)	)	PUNCT
ejpam-5776	269	22	(	(	PUNCT
ejpam-5776	269	23	µ	µ	NOUN
ejpam-5776	269	24	)	)	PUNCT
ejpam-5776	269	25	=	=	SYM
ejpam-5776	269	26	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5776	269	27	µin−1	µin−1	PROPN
ejpam-5776	269	28	−3j(n−1)×n	−3j(n−1)×n	ADJ
ejpam-5776	269	29	−3jn×(n−1	−3jn×(n−1	NOUN
ejpam-5776	269	30	)	)	PUNCT
ejpam-5776	269	31	(	(	PUNCT
ejpam-5776	269	32	µ+	µ+	X
ejpam-5776	269	33	2)in	2)in	NUM
ejpam-5776	269	34	−	−	PROPN
ejpam-5776	269	35	2jn	2jn	NOUN
ejpam-5776	269	36	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5776	269	37	.	.	PUNCT
ejpam-5776	270	1	by	by	ADP
ejpam-5776	270	2	lemma	lemma	PROPN
ejpam-5776	270	3	1	1	NUM
ejpam-5776	270	4	,	,	PUNCT
ejpam-5776	270	5	with	with	ADP
ejpam-5776	270	6	a	a	PRON
ejpam-5776	270	7	=	=	SYM
ejpam-5776	270	8	0	0	NUM
ejpam-5776	270	9	,	,	PUNCT
ejpam-5776	270	10	b	b	NOUN
ejpam-5776	270	11	=	=	SYM
ejpam-5776	270	12	2	2	NUM
ejpam-5776	270	13	,	,	PUNCT
ejpam-5776	270	14	c	c	NOUN
ejpam-5776	270	15	=	=	SYM
ejpam-5776	270	16	d	d	PROPN
ejpam-5776	270	17	=	=	SYM
ejpam-5776	270	18	3	3	NUM
ejpam-5776	270	19	,	,	PUNCT
ejpam-5776	270	20	n1	n1	NOUN
ejpam-5776	270	21	=	=	SYM
ejpam-5776	270	22	n−	n−	NOUN
ejpam-5776	270	23	1	1	NUM
ejpam-5776	270	24	and	and	CCONJ
ejpam-5776	270	25	n2	n2	ADJ
ejpam-5776	270	26	=	=	SYM
ejpam-5776	270	27	n	n	CCONJ
ejpam-5776	270	28	,	,	PUNCT
ejpam-5776	270	29	we	we	PRON
ejpam-5776	270	30	obtain	obtain	VERB
ejpam-5776	270	31	pse(ωd2n	pse(ωd2n	NOUN
ejpam-5776	270	32	)	)	PUNCT
ejpam-5776	270	33	(	(	PUNCT
ejpam-5776	270	34	µ	µ	NOUN
ejpam-5776	270	35	)	)	PUNCT
ejpam-5776	270	36	=	=	SYM
ejpam-5776	270	37	µn−2(µ+	µn−2(µ+	NUM
ejpam-5776	270	38	2)n−1	2)n−1	NUM
ejpam-5776	270	39	(	(	PUNCT
ejpam-5776	270	40	µ2	µ2	PROPN
ejpam-5776	270	41	−	−	PROPN
ejpam-5776	270	42	2(n−	2(n−	NUM
ejpam-5776	270	43	1)µ−	1)µ−	NUM
ejpam-5776	270	44	9n(n−	9n(n−	NUM
ejpam-5776	270	45	1	1	NUM
ejpam-5776	270	46	)	)	PUNCT
ejpam-5776	270	47	)	)	PUNCT
ejpam-5776	270	48	.	.	PUNCT
ejpam-5776	271	1	the	the	DET
ejpam-5776	271	2	eigenvalues	eigenvalue	NOUN
ejpam-5776	271	3	of	of	ADP
ejpam-5776	271	4	ωd2n	ωd2n	PROPN
ejpam-5776	271	5	are	be	AUX
ejpam-5776	271	6	µ1	µ1	NOUN
ejpam-5776	271	7	=	=	SYM
ejpam-5776	271	8	0	0	NUM
ejpam-5776	271	9	of	of	ADP
ejpam-5776	271	10	multiplicity	multiplicity	NOUN
ejpam-5776	271	11	n	n	CCONJ
ejpam-5776	271	12	−	−	PROPN
ejpam-5776	271	13	2	2	NUM
ejpam-5776	271	14	,	,	PUNCT
ejpam-5776	271	15	µ2	µ2	PROPN
ejpam-5776	271	16	=	=	PUNCT
ejpam-5776	271	17	−2	−2	NOUN
ejpam-5776	271	18	of	of	ADP
ejpam-5776	271	19	multiplicity	multiplicity	NOUN
ejpam-5776	271	20	n−	n−	NOUN
ejpam-5776	271	21	1	1	NUM
ejpam-5776	271	22	,	,	PUNCT
ejpam-5776	271	23	and	and	CCONJ
ejpam-5776	271	24	µ3,4	µ3,4	ADJ
ejpam-5776	271	25	=	=	SYM
ejpam-5776	271	26	n−	n−	NUM
ejpam-5776	271	27	1±	1±	NUM
ejpam-5776	271	28	√	√	NUM
ejpam-5776	271	29	(	(	PUNCT
ejpam-5776	271	30	n−	n−	NOUN
ejpam-5776	271	31	1)(10n−	1)(10n−	PROPN
ejpam-5776	271	32	1	1	NUM
ejpam-5776	271	33	)	)	PUNCT
ejpam-5776	271	34	.	.	PUNCT
ejpam-5776	272	1	therefore	therefore	ADV
ejpam-5776	272	2	,	,	PUNCT
ejpam-5776	272	3	the	the	DET
ejpam-5776	272	4	se	se	ADJ
ejpam-5776	272	5	-	-	ADJ
ejpam-5776	272	6	spectral	spectral	ADJ
ejpam-5776	272	7	radius	radius	NOUN
ejpam-5776	272	8	of	of	ADP
ejpam-5776	272	9	ωd2n	ωd2n	PROPN
ejpam-5776	272	10	is	be	AUX
ejpam-5776	272	11	ρse(ωd2n	ρse(ωd2n	NOUN
ejpam-5776	272	12	)	)	PUNCT
ejpam-5776	273	1	=	=	PUNCT
ejpam-5776	273	2	n−	n−	NOUN
ejpam-5776	273	3	1	1	NUM
ejpam-5776	273	4	+	+	CCONJ
ejpam-5776	273	5	√	√	PROPN
ejpam-5776	273	6	(	(	PUNCT
ejpam-5776	273	7	n−	n−	NOUN
ejpam-5776	273	8	1)(10n−	1)(10n−	PROPN
ejpam-5776	273	9	1	1	NUM
ejpam-5776	273	10	)	)	PUNCT
ejpam-5776	273	11	.	.	PUNCT
ejpam-5776	274	1	(	(	PUNCT
ejpam-5776	274	2	ii	ii	NOUN
ejpam-5776	274	3	)	)	PUNCT
ejpam-5776	274	4	let	let	VERB
ejpam-5776	274	5	n	n	PRON
ejpam-5776	274	6	be	be	AUX
ejpam-5776	274	7	even	even	ADV
ejpam-5776	274	8	.	.	PUNCT
ejpam-5776	275	1	the	the	DET
ejpam-5776	275	2	entries	entry	NOUN
ejpam-5776	275	3	of	of	ADP
ejpam-5776	275	4	se(ωd2n	se(ωd2n	NOUN
ejpam-5776	275	5	)	)	PUNCT
ejpam-5776	275	6	=	=	PUNCT
ejpam-5776	276	1	[	[	X
ejpam-5776	276	2	sij	sij	X
ejpam-5776	276	3	]	]	X
ejpam-5776	276	4	are	be	AUX
ejpam-5776	276	5	(	(	PUNCT
ejpam-5776	276	6	a	a	NOUN
ejpam-5776	276	7	)	)	PUNCT
ejpam-5776	276	8	for	for	ADP
ejpam-5776	276	9	1	1	NUM
ejpam-5776	276	10	≤	≤	NOUN
ejpam-5776	276	11	i	i	PRON
ejpam-5776	276	12	,	,	PUNCT
ejpam-5776	276	13	j	j	PROPN
ejpam-5776	276	14	≤	≤	PROPN
ejpam-5776	276	15	n−	n−	PROPN
ejpam-5776	276	16	2	2	NUM
ejpam-5776	276	17	and	and	CCONJ
ejpam-5776	276	18	i	i	PRON
ejpam-5776	276	19	̸=	̸=	PROPN
ejpam-5776	276	20	i	i	PRON
ejpam-5776	276	21	,	,	PUNCT
ejpam-5776	276	22	sij	sij	PROPN
ejpam-5776	276	23	=	=	SYM
ejpam-5776	276	24	0	0	NUM
ejpam-5776	276	25	;	;	PUNCT
ejpam-5776	277	1	m.	m.	PROPN
ejpam-5776	277	2	u.	u.	PROPN
ejpam-5776	277	3	romdhini	romdhini	PROPN
ejpam-5776	277	4	et	et	PROPN
ejpam-5776	277	5	al	al	PROPN
ejpam-5776	277	6	.	.	PUNCT
ejpam-5776	277	7	/	/	SYM
ejpam-5776	277	8	eur	eur	PROPN
ejpam-5776	277	9	.	.	PUNCT
ejpam-5776	278	1	j.	j.	PROPN
ejpam-5776	278	2	pure	pure	PROPN
ejpam-5776	278	3	appl	appl	PROPN
ejpam-5776	278	4	.	.	PROPN
ejpam-5776	278	5	math	math	PROPN
ejpam-5776	278	6	,	,	PUNCT
ejpam-5776	278	7	18	18	NUM
ejpam-5776	278	8	(	(	PUNCT
ejpam-5776	278	9	2	2	NUM
ejpam-5776	278	10	)	)	PUNCT
ejpam-5776	278	11	(	(	PUNCT
ejpam-5776	278	12	2025	2025	NUM
ejpam-5776	278	13	)	)	PUNCT
ejpam-5776	278	14	,	,	PUNCT
ejpam-5776	278	15	5776	5776	NUM
ejpam-5776	278	16	8	8	NUM
ejpam-5776	278	17	of	of	ADP
ejpam-5776	278	18	13	13	NUM
ejpam-5776	278	19	(	(	PUNCT
ejpam-5776	278	20	b	b	NOUN
ejpam-5776	278	21	)	)	PUNCT
ejpam-5776	278	22	for	for	ADP
ejpam-5776	278	23	1	1	NUM
ejpam-5776	278	24	≤	≤	NUM
ejpam-5776	278	25	i	i	PRON
ejpam-5776	278	26	≤	≤	ADJ
ejpam-5776	278	27	n−	n−	NOUN
ejpam-5776	278	28	2	2	NUM
ejpam-5776	278	29	,	,	PUNCT
ejpam-5776	278	30	n−	n−	NOUN
ejpam-5776	278	31	1	1	NUM
ejpam-5776	278	32	≤	≤	NUM
ejpam-5776	278	33	j	j	PROPN
ejpam-5776	278	34	≤	≤	PROPN
ejpam-5776	279	1	2n−	2n−	NUM
ejpam-5776	279	2	2	2	NUM
ejpam-5776	279	3	or	or	CCONJ
ejpam-5776	279	4	vice	vice	NOUN
ejpam-5776	279	5	versa	versa	ADV
ejpam-5776	279	6	,	,	PUNCT
ejpam-5776	279	7	sij	sij	PROPN
ejpam-5776	279	8	=	=	PUNCT
ejpam-5776	279	9	2	2	NUM
ejpam-5776	279	10	+	+	NUM
ejpam-5776	279	11	2	2	NUM
ejpam-5776	279	12	=	=	SYM
ejpam-5776	279	13	4	4	NUM
ejpam-5776	279	14	;	;	PUNCT
ejpam-5776	279	15	(	(	PUNCT
ejpam-5776	279	16	c	c	X
ejpam-5776	279	17	)	)	PUNCT
ejpam-5776	279	18	for	for	ADP
ejpam-5776	279	19	n−	n−	NOUN
ejpam-5776	279	20	1	1	NUM
ejpam-5776	279	21	≤	≤	NUM
ejpam-5776	279	22	i	i	PRON
ejpam-5776	279	23	≤	≤	PROPN
ejpam-5776	279	24	n+	n+	PUNCT
ejpam-5776	279	25	n	n	CCONJ
ejpam-5776	279	26	2	2	NUM
ejpam-5776	279	27	−	−	NUM
ejpam-5776	279	28	2	2	NUM
ejpam-5776	279	29	and	and	CCONJ
ejpam-5776	279	30	n+	n+	PUNCT
ejpam-5776	279	31	n	n	CCONJ
ejpam-5776	279	32	2	2	NUM
ejpam-5776	279	33	−	−	PROPN
ejpam-5776	279	34	1	1	NUM
ejpam-5776	279	35	≤	≤	NUM
ejpam-5776	279	36	j	j	PROPN
ejpam-5776	279	37	≤	≤	PROPN
ejpam-5776	280	1	2n−	2n−	PROPN
ejpam-5776	280	2	2	2	NUM
ejpam-5776	280	3	where	where	SCONJ
ejpam-5776	280	4	j	j	PROPN
ejpam-5776	280	5	̸=	̸=	PROPN
ejpam-5776	280	6	n−	n−	NOUN
ejpam-5776	280	7	2	2	NUM
ejpam-5776	280	8	+	+	CCONJ
ejpam-5776	280	9	n	n	PRON
ejpam-5776	280	10	2	2	NUM
ejpam-5776	280	11	+	+	CCONJ
ejpam-5776	280	12	i	i	PRON
ejpam-5776	280	13	or	or	CCONJ
ejpam-5776	280	14	vice	vice	NOUN
ejpam-5776	280	15	versa	versa	ADV
ejpam-5776	280	16	,	,	PUNCT
ejpam-5776	280	17	sij	sij	PROPN
ejpam-5776	280	18	=	=	PUNCT
ejpam-5776	280	19	2	2	NUM
ejpam-5776	280	20	+	+	NUM
ejpam-5776	280	21	2	2	NUM
ejpam-5776	280	22	=	=	SYM
ejpam-5776	280	23	4	4	NUM
ejpam-5776	280	24	;	;	PUNCT
ejpam-5776	280	25	(	(	PUNCT
ejpam-5776	280	26	d	d	X
ejpam-5776	280	27	)	)	PUNCT
ejpam-5776	280	28	for	for	ADP
ejpam-5776	280	29	n−1	n−1	PROPN
ejpam-5776	280	30	≤	≤	PROPN
ejpam-5776	281	1	i	i	PROPN
ejpam-5776	281	2	,	,	PUNCT
ejpam-5776	281	3	j	j	PROPN
ejpam-5776	281	4	≤	≤	PROPN
ejpam-5776	281	5	n+	n+	PUNCT
ejpam-5776	281	6	n	n	CCONJ
ejpam-5776	281	7	2	2	NUM
ejpam-5776	281	8	−2	−2	NOUN
ejpam-5776	281	9	,	,	PUNCT
ejpam-5776	281	10	n+	n+	NUM
ejpam-5776	281	11	n	n	CCONJ
ejpam-5776	281	12	2	2	NUM
ejpam-5776	281	13	−2	−2	NOUN
ejpam-5776	281	14	≤	≤	PUNCT
ejpam-5776	282	1	i	i	PROPN
ejpam-5776	282	2	,	,	PUNCT
ejpam-5776	282	3	j	j	PROPN
ejpam-5776	282	4	≤	≤	PROPN
ejpam-5776	282	5	2n−2	2n−2	NUM
ejpam-5776	282	6	,	,	PUNCT
ejpam-5776	282	7	and	and	CCONJ
ejpam-5776	282	8	i	i	PRON
ejpam-5776	282	9	̸=	̸=	PROPN
ejpam-5776	282	10	j	j	PROPN
ejpam-5776	282	11	,	,	PUNCT
ejpam-5776	282	12	sij	sij	PROPN
ejpam-5776	282	13	=	=	PUNCT
ejpam-5776	282	14	2	2	NUM
ejpam-5776	282	15	+	+	SYM
ejpam-5776	282	16	2	2	NUM
ejpam-5776	282	17	=	=	SYM
ejpam-5776	282	18	4	4	NUM
ejpam-5776	282	19	;	;	PUNCT
ejpam-5776	282	20	(	(	PUNCT
ejpam-5776	282	21	e	e	NOUN
ejpam-5776	282	22	)	)	PUNCT
ejpam-5776	282	23	for	for	ADP
ejpam-5776	282	24	i	i	PROPN
ejpam-5776	282	25	=	=	SYM
ejpam-5776	282	26	j	j	PROPN
ejpam-5776	282	27	,	,	PUNCT
ejpam-5776	282	28	j	j	X
ejpam-5776	282	29	=	=	PUNCT
ejpam-5776	282	30	n−	n−	NOUN
ejpam-5776	282	31	2	2	NUM
ejpam-5776	282	32	+	+	CCONJ
ejpam-5776	282	33	n	n	PRON
ejpam-5776	282	34	2	2	NUM
ejpam-5776	283	1	+	+	CCONJ
ejpam-5776	284	1	i	i	PRON
ejpam-5776	284	2	,	,	PUNCT
ejpam-5776	284	3	i	i	PRON
ejpam-5776	284	4	=	=	VERB
ejpam-5776	284	5	n−	n−	NOUN
ejpam-5776	284	6	2	2	NUM
ejpam-5776	284	7	+	+	CCONJ
ejpam-5776	284	8	n	n	CCONJ
ejpam-5776	284	9	2	2	NUM
ejpam-5776	284	10	+	+	CCONJ
ejpam-5776	284	11	j	j	PROPN
ejpam-5776	284	12	,	,	PUNCT
ejpam-5776	284	13	sij	sij	PROPN
ejpam-5776	284	14	=	=	SYM
ejpam-5776	284	15	0	0	X
ejpam-5776	284	16	.	.	PUNCT
ejpam-5776	285	1	hence	hence	ADV
ejpam-5776	285	2	,	,	PUNCT
ejpam-5776	285	3	the	the	DET
ejpam-5776	285	4	matrix	matrix	NOUN
ejpam-5776	285	5	construction	construction	NOUN
ejpam-5776	285	6	is	be	AUX
ejpam-5776	285	7	as	as	SCONJ
ejpam-5776	285	8	follows	follow	VERB
ejpam-5776	285	9	.	.	PUNCT
ejpam-5776	286	1	se(ωd2n	se(ωd2n	PROPN
ejpam-5776	286	2	)	)	PUNCT
ejpam-5776	286	3	=	=	SYM
ejpam-5776	287	1	a	a	PRON
ejpam-5776	287	2	.	.	PUNCT
ejpam-5776	287	3	.	.	PUNCT
ejpam-5776	287	4	.	.	PUNCT
ejpam-5776	288	1	an−1	an−1	PROPN
ejpam-5776	288	2	b	b	PROPN
ejpam-5776	288	3	.	.	PUNCT
ejpam-5776	288	4	.	.	PUNCT
ejpam-5776	288	5	.	.	PUNCT
ejpam-5776	289	1	a	a	DET
ejpam-5776	289	2	n	n	NOUN
ejpam-5776	289	3	2	2	NUM
ejpam-5776	289	4	−1b	−1b	X
ejpam-5776	289	5	a	a	PRON
ejpam-5776	289	6	n	n	NUM
ejpam-5776	289	7	2	2	NUM
ejpam-5776	289	8	b	b	NOUN
ejpam-5776	289	9	.	.	PUNCT
ejpam-5776	289	10	.	.	PUNCT
ejpam-5776	289	11	.	.	PUNCT
ejpam-5776	290	1	an−1b	an−1b	PROPN
ejpam-5776	290	2			PROPN
ejpam-5776	291	1	a	a	DET
ejpam-5776	291	2	0	0	NUM
ejpam-5776	291	3	.	.	PUNCT
ejpam-5776	291	4	.	.	PUNCT
ejpam-5776	292	1	.	.	PUNCT
ejpam-5776	293	1	0	0	NUM
ejpam-5776	294	1	4	4	NUM
ejpam-5776	294	2	.	.	PUNCT
ejpam-5776	294	3	.	.	PUNCT
ejpam-5776	294	4	.	.	PUNCT
ejpam-5776	295	1	4	4	NUM
ejpam-5776	295	2	4	4	NUM
ejpam-5776	295	3	.	.	PUNCT
ejpam-5776	295	4	.	.	PUNCT
ejpam-5776	295	5	.	.	PUNCT
ejpam-5776	296	1	4	4	NUM
ejpam-5776	296	2	...	...	PUNCT
ejpam-5776	296	3	...	...	PUNCT
ejpam-5776	296	4	.	.	PUNCT
ejpam-5776	296	5	.	.	PUNCT
ejpam-5776	296	6	.	.	PUNCT
ejpam-5776	297	1	...	...	PUNCT
ejpam-5776	297	2	...	...	PUNCT
ejpam-5776	297	3	.	.	PUNCT
ejpam-5776	297	4	.	.	PUNCT
ejpam-5776	298	1	.	.	PUNCT
ejpam-5776	299	1	...	...	PUNCT
ejpam-5776	300	1	...	...	PUNCT
ejpam-5776	301	1	.	.	PUNCT
ejpam-5776	302	1	.	.	PUNCT
ejpam-5776	303	1	.	.	PUNCT
ejpam-5776	304	1	...	...	PUNCT
ejpam-5776	305	1	an−1	an−1	ADJ
ejpam-5776	305	2	0	0	NUM
ejpam-5776	305	3	.	.	PUNCT
ejpam-5776	305	4	.	.	PUNCT
ejpam-5776	305	5	.	.	PUNCT
ejpam-5776	306	1	0	0	NUM
ejpam-5776	307	1	4	4	NUM
ejpam-5776	307	2	.	.	PUNCT
ejpam-5776	307	3	.	.	PUNCT
ejpam-5776	307	4	.	.	PUNCT
ejpam-5776	308	1	4	4	NUM
ejpam-5776	308	2	4	4	NUM
ejpam-5776	308	3	.	.	PUNCT
ejpam-5776	308	4	.	.	PUNCT
ejpam-5776	308	5	.	.	PUNCT
ejpam-5776	309	1	4	4	NUM
ejpam-5776	309	2	b	b	SYM
ejpam-5776	309	3	4	4	NUM
ejpam-5776	309	4	.	.	PUNCT
ejpam-5776	309	5	.	.	PUNCT
ejpam-5776	309	6	.	.	PUNCT
ejpam-5776	310	1	4	4	NUM
ejpam-5776	310	2	0	0	NUM
ejpam-5776	310	3	.	.	PUNCT
ejpam-5776	310	4	.	.	PUNCT
ejpam-5776	310	5	.	.	PUNCT
ejpam-5776	311	1	4	4	NUM
ejpam-5776	311	2	0	0	NUM
ejpam-5776	311	3	.	.	PUNCT
ejpam-5776	311	4	.	.	PUNCT
ejpam-5776	311	5	.	.	PUNCT
ejpam-5776	312	1	4	4	NUM
ejpam-5776	312	2	...	...	PUNCT
ejpam-5776	312	3	...	...	PUNCT
ejpam-5776	312	4	.	.	PUNCT
ejpam-5776	312	5	.	.	PUNCT
ejpam-5776	312	6	.	.	PUNCT
ejpam-5776	313	1	...	...	PUNCT
ejpam-5776	313	2	...	...	PUNCT
ejpam-5776	313	3	.	.	PUNCT
ejpam-5776	313	4	.	.	PUNCT
ejpam-5776	314	1	.	.	PUNCT
ejpam-5776	315	1	...	...	PUNCT
ejpam-5776	316	1	...	...	PUNCT
ejpam-5776	317	1	.	.	PUNCT
ejpam-5776	318	1	.	.	PUNCT
ejpam-5776	319	1	.	.	PUNCT
ejpam-5776	320	1	...	...	PUNCT
ejpam-5776	321	1	a	a	DET
ejpam-5776	321	2	n	n	NOUN
ejpam-5776	321	3	2	2	NUM
ejpam-5776	321	4	−1b	−1b	PROPN
ejpam-5776	321	5	4	4	NUM
ejpam-5776	321	6	.	.	PUNCT
ejpam-5776	321	7	.	.	PUNCT
ejpam-5776	321	8	.	.	PUNCT
ejpam-5776	322	1	4	4	NUM
ejpam-5776	322	2	4	4	NUM
ejpam-5776	322	3	.	.	PUNCT
ejpam-5776	322	4	.	.	PUNCT
ejpam-5776	322	5	.	.	PUNCT
ejpam-5776	323	1	0	0	NUM
ejpam-5776	324	1	4	4	NUM
ejpam-5776	324	2	.	.	PUNCT
ejpam-5776	324	3	.	.	PUNCT
ejpam-5776	324	4	.	.	PUNCT
ejpam-5776	325	1	0	0	PUNCT
ejpam-5776	326	1	a	a	PRON
ejpam-5776	326	2	n	n	NUM
ejpam-5776	326	3	2	2	NUM
ejpam-5776	326	4	b	b	SYM
ejpam-5776	326	5	4	4	NUM
ejpam-5776	326	6	.	.	PUNCT
ejpam-5776	326	7	.	.	PUNCT
ejpam-5776	326	8	.	.	PUNCT
ejpam-5776	327	1	4	4	NUM
ejpam-5776	327	2	0	0	NUM
ejpam-5776	327	3	.	.	PUNCT
ejpam-5776	327	4	.	.	PUNCT
ejpam-5776	327	5	.	.	PUNCT
ejpam-5776	328	1	4	4	NUM
ejpam-5776	328	2	0	0	NUM
ejpam-5776	328	3	.	.	PUNCT
ejpam-5776	328	4	.	.	PUNCT
ejpam-5776	328	5	.	.	PUNCT
ejpam-5776	329	1	4	4	NUM
ejpam-5776	329	2	...	...	PUNCT
ejpam-5776	329	3	...	...	PUNCT
ejpam-5776	329	4	.	.	PUNCT
ejpam-5776	329	5	.	.	PUNCT
ejpam-5776	329	6	.	.	PUNCT
ejpam-5776	330	1	...	...	PUNCT
ejpam-5776	330	2	...	...	PUNCT
ejpam-5776	330	3	.	.	PUNCT
ejpam-5776	330	4	.	.	PUNCT
ejpam-5776	331	1	.	.	PUNCT
ejpam-5776	332	1	...	...	PUNCT
ejpam-5776	333	1	...	...	PUNCT
ejpam-5776	334	1	.	.	PUNCT
ejpam-5776	335	1	.	.	PUNCT
ejpam-5776	336	1	.	.	PUNCT
ejpam-5776	337	1	...	...	PUNCT
ejpam-5776	338	1	an−1b	an−1b	PUNCT
ejpam-5776	338	2	4	4	NUM
ejpam-5776	338	3	.	.	PUNCT
ejpam-5776	338	4	.	.	PUNCT
ejpam-5776	338	5	.	.	PUNCT
ejpam-5776	339	1	4	4	NUM
ejpam-5776	339	2	4	4	NUM
ejpam-5776	339	3	.	.	PUNCT
ejpam-5776	339	4	.	.	PUNCT
ejpam-5776	339	5	.	.	PUNCT
ejpam-5776	340	1	0	0	NUM
ejpam-5776	341	1	4	4	NUM
ejpam-5776	341	2	.	.	PUNCT
ejpam-5776	341	3	.	.	PUNCT
ejpam-5776	341	4	.	.	PUNCT
ejpam-5776	341	5	0	0	PUNCT
ejpam-5776	341	6	.	.	PUNCT
ejpam-5776	342	1	in	in	ADP
ejpam-5776	342	2	other	other	ADJ
ejpam-5776	342	3	words	word	NOUN
ejpam-5776	342	4	,	,	PUNCT
ejpam-5776	342	5	se(ωd2n	se(ωd2n	NOUN
ejpam-5776	342	6	)	)	PUNCT
ejpam-5776	342	7	is	be	AUX
ejpam-5776	342	8	as	as	SCONJ
ejpam-5776	342	9	follows	follow	VERB
ejpam-5776	342	10	:	:	PUNCT
ejpam-5776	342	11	se(ωd2n	se(ωd2n	ADJ
ejpam-5776	342	12	)	)	PUNCT
ejpam-5776	343	1	=	=	PRON
ejpam-5776	343	2			NOUN
ejpam-5776	343	3	0n−2	0n−2	NOUN
ejpam-5776	343	4	4j(n−2)×n	4j(n−2)×n	NUM
ejpam-5776	343	5	2	2	NUM
ejpam-5776	343	6	4j(n−2)×n	4j(n−2)×n	NUM
ejpam-5776	343	7	2	2	NUM
ejpam-5776	343	8	4jn	4jn	NOUN
ejpam-5776	343	9	2	2	NUM
ejpam-5776	343	10	×(n−2	×(n−2	NOUN
ejpam-5776	343	11	)	)	PUNCT
ejpam-5776	343	12	4(j	4(j	NUM
ejpam-5776	343	13	−	−	NOUN
ejpam-5776	343	14	i)n	i)n	NOUN
ejpam-5776	343	15	2	2	NUM
ejpam-5776	343	16	4(j	4(j	NUM
ejpam-5776	343	17	−	−	NOUN
ejpam-5776	343	18	i)n	i)n	NOUN
ejpam-5776	343	19	2	2	NUM
ejpam-5776	343	20	4jn	4jn	ADJ
ejpam-5776	343	21	2	2	NUM
ejpam-5776	343	22	×(n−2	×(n−2	NOUN
ejpam-5776	343	23	)	)	PUNCT
ejpam-5776	343	24	4(j	4(j	NUM
ejpam-5776	343	25	−	−	NOUN
ejpam-5776	343	26	i)n	i)n	NOUN
ejpam-5776	343	27	2	2	NUM
ejpam-5776	343	28	4(j	4(j	NUM
ejpam-5776	343	29	−	−	NOUN
ejpam-5776	343	30	i)n	i)n	NOUN
ejpam-5776	343	31	2	2	NUM
ejpam-5776	343	32			PROPN
ejpam-5776	343	33	.	.	PUNCT
ejpam-5776	344	1	based	base	VERB
ejpam-5776	344	2	on	on	ADP
ejpam-5776	344	3	theorem	theorem	NOUN
ejpam-5776	344	4	4	4	NUM
ejpam-5776	344	5	with	with	ADP
ejpam-5776	344	6	a	a	DET
ejpam-5776	344	7	=	=	SYM
ejpam-5776	344	8	b	b	NOUN
ejpam-5776	344	9	=	=	SYM
ejpam-5776	344	10	0	0	NUM
ejpam-5776	344	11	,	,	PUNCT
ejpam-5776	344	12	c	c	NOUN
ejpam-5776	344	13	=	=	SYM
ejpam-5776	344	14	d	d	NOUN
ejpam-5776	344	15	=	=	SYM
ejpam-5776	344	16	4	4	NUM
ejpam-5776	344	17	,	,	PUNCT
ejpam-5776	344	18	then	then	ADV
ejpam-5776	344	19	pse(ωd2n	pse(ωd2n	VERB
ejpam-5776	344	20	)	)	PUNCT
ejpam-5776	344	21	(	(	PUNCT
ejpam-5776	344	22	µ	µ	NOUN
ejpam-5776	344	23	)	)	PUNCT
ejpam-5776	344	24	=	=	SYM
ejpam-5776	344	25	µ	µ	PRON
ejpam-5776	344	26	3(n−2	3(n−2	NUM
ejpam-5776	344	27	)	)	PUNCT
ejpam-5776	344	28	2	2	NUM
ejpam-5776	344	29	(	(	PUNCT
ejpam-5776	344	30	µ+	µ+	X
ejpam-5776	344	31	8)	8)	NUM
ejpam-5776	344	32	n	n	PRON
ejpam-5776	344	33	2	2	NUM
ejpam-5776	344	34	−1	−1	NOUN
ejpam-5776	344	35	(	(	PUNCT
ejpam-5776	344	36	µ2	µ2	PROPN
ejpam-5776	344	37	−	−	PROPN
ejpam-5776	344	38	4(n−	4(n−	NUM
ejpam-5776	344	39	2)µ−	2)µ−	NUM
ejpam-5776	344	40	16n(n−	16n(n−	NUM
ejpam-5776	344	41	2	2	NUM
ejpam-5776	344	42	)	)	PUNCT
ejpam-5776	344	43	)	)	PUNCT
ejpam-5776	344	44	.	.	PUNCT
ejpam-5776	345	1	the	the	DET
ejpam-5776	345	2	eigenvalues	eigenvalue	NOUN
ejpam-5776	345	3	of	of	ADP
ejpam-5776	345	4	ωd2n	ωd2n	PROPN
ejpam-5776	345	5	are	be	AUX
ejpam-5776	345	6	µ1	µ1	NOUN
ejpam-5776	345	7	=	=	SYM
ejpam-5776	345	8	0	0	NUM
ejpam-5776	345	9	of	of	ADP
ejpam-5776	345	10	multiplicity	multiplicity	NOUN
ejpam-5776	345	11	3(n−2	3(n−2	PROPN
ejpam-5776	345	12	)	)	PUNCT
ejpam-5776	345	13	2	2	NUM
ejpam-5776	345	14	,	,	PUNCT
ejpam-5776	345	15	µ2	µ2	PROPN
ejpam-5776	345	16	=	=	PUNCT
ejpam-5776	345	17	−8	−8	X
ejpam-5776	345	18	of	of	ADP
ejpam-5776	345	19	multiplicity	multiplicity	NOUN
ejpam-5776	345	20	n	n	CCONJ
ejpam-5776	345	21	2	2	NUM
ejpam-5776	345	22	−	−	NUM
ejpam-5776	345	23	1	1	NUM
ejpam-5776	345	24	,	,	PUNCT
ejpam-5776	345	25	and	and	CCONJ
ejpam-5776	345	26	µ3,4	µ3,4	ADJ
ejpam-5776	345	27	=	=	SYM
ejpam-5776	345	28	2	2	NUM
ejpam-5776	345	29	(	(	PUNCT
ejpam-5776	345	30	n−	n−	NOUN
ejpam-5776	345	31	2±	2±	NOUN
ejpam-5776	345	32	√	√	NUM
ejpam-5776	346	1	(	(	PUNCT
ejpam-5776	346	2	n−	n−	NOUN
ejpam-5776	346	3	2)(5n−	2)(5n−	NUM
ejpam-5776	346	4	2	2	NUM
ejpam-5776	346	5	)	)	PUNCT
ejpam-5776	346	6	)	)	PUNCT
ejpam-5776	346	7	.	.	PUNCT
ejpam-5776	347	1	therefore	therefore	ADV
ejpam-5776	347	2	,	,	PUNCT
ejpam-5776	347	3	the	the	DET
ejpam-5776	347	4	se	se	ADJ
ejpam-5776	347	5	-	-	ADJ
ejpam-5776	347	6	spectral	spectral	ADJ
ejpam-5776	347	7	radius	radius	NOUN
ejpam-5776	347	8	of	of	ADP
ejpam-5776	347	9	ωd2n	ωd2n	PROPN
ejpam-5776	347	10	is	be	AUX
ejpam-5776	347	11	ρse(ωd2n	ρse(ωd2n	NOUN
ejpam-5776	347	12	)	)	PUNCT
ejpam-5776	348	1	=	=	SYM
ejpam-5776	348	2	2	2	NUM
ejpam-5776	348	3	(	(	PUNCT
ejpam-5776	348	4	n−	n−	NOUN
ejpam-5776	348	5	2	2	NUM
ejpam-5776	348	6	+	+	CCONJ
ejpam-5776	348	7	√	√	PROPN
ejpam-5776	348	8	(	(	PUNCT
ejpam-5776	348	9	n−	n−	NOUN
ejpam-5776	348	10	2)(5n−	2)(5n−	NUM
ejpam-5776	348	11	2	2	NUM
ejpam-5776	348	12	)	)	PUNCT
ejpam-5776	348	13	)	)	PUNCT
ejpam-5776	348	14	.	.	PUNCT
ejpam-5776	349	1	theorem	theorem	VERB
ejpam-5776	349	2	7	7	NUM
ejpam-5776	349	3	.	.	PUNCT
ejpam-5776	350	1	in	in	ADP
ejpam-5776	350	2	ωd2n	ωd2n	PROPN
ejpam-5776	350	3	,	,	PUNCT
ejpam-5776	350	4	the	the	DET
ejpam-5776	350	5	sum	sum	NOUN
ejpam-5776	350	6	eccentricity	eccentricity	NOUN
ejpam-5776	350	7	energy	energy	NOUN
ejpam-5776	350	8	of	of	ADP
ejpam-5776	350	9	ωd2n	ωd2n	PROPN
ejpam-5776	350	10	is	be	AUX
ejpam-5776	350	11	εse(ωd2n	εse(ωd2n	ADJ
ejpam-5776	350	12	)	)	PUNCT
ejpam-5776	351	1	=	=	PUNCT
ejpam-5776	351	2			PROPN
ejpam-5776	351	3	2	2	NUM
ejpam-5776	351	4	(	(	PUNCT
ejpam-5776	351	5	n−	n−	NOUN
ejpam-5776	351	6	1	1	NUM
ejpam-5776	351	7	+	+	CCONJ
ejpam-5776	351	8	√	√	PROPN
ejpam-5776	351	9	(	(	PUNCT
ejpam-5776	351	10	n−	n−	NOUN
ejpam-5776	351	11	1)(10n−	1)(10n−	NOUN
ejpam-5776	351	12	1	1	NUM
ejpam-5776	351	13	)	)	PUNCT
ejpam-5776	351	14	)	)	PUNCT
ejpam-5776	351	15	,	,	PUNCT
ejpam-5776	351	16	if	if	SCONJ
ejpam-5776	351	17	n	n	PRON
ejpam-5776	351	18	is	be	AUX
ejpam-5776	351	19	odd	odd	ADJ
ejpam-5776	351	20	4	4	NUM
ejpam-5776	351	21	(	(	PUNCT
ejpam-5776	351	22	n−	n−	NOUN
ejpam-5776	351	23	2	2	NUM
ejpam-5776	351	24	+	+	CCONJ
ejpam-5776	351	25	√	√	PROPN
ejpam-5776	351	26	(	(	PUNCT
ejpam-5776	351	27	n−	n−	NOUN
ejpam-5776	351	28	2)(5n−	2)(5n−	NUM
ejpam-5776	351	29	2	2	NUM
ejpam-5776	351	30	)	)	PUNCT
ejpam-5776	351	31	)	)	PUNCT
ejpam-5776	351	32	,	,	PUNCT
ejpam-5776	351	33	if	if	SCONJ
ejpam-5776	351	34	n	n	PRON
ejpam-5776	351	35	is	be	AUX
ejpam-5776	351	36	even	even	ADV
ejpam-5776	351	37	.	.	PUNCT
ejpam-5776	352	1	m.	m.	NOUN
ejpam-5776	352	2	u.	u.	PROPN
ejpam-5776	352	3	romdhini	romdhini	PROPN
ejpam-5776	352	4	et	et	PROPN
ejpam-5776	352	5	al	al	PROPN
ejpam-5776	352	6	.	.	PUNCT
ejpam-5776	352	7	/	/	SYM
ejpam-5776	352	8	eur	eur	PROPN
ejpam-5776	352	9	.	.	PUNCT
ejpam-5776	353	1	j.	j.	PROPN
ejpam-5776	353	2	pure	pure	PROPN
ejpam-5776	353	3	appl	appl	PROPN
ejpam-5776	353	4	.	.	PROPN
ejpam-5776	353	5	math	math	PROPN
ejpam-5776	353	6	,	,	PUNCT
ejpam-5776	353	7	18	18	NUM
ejpam-5776	353	8	(	(	PUNCT
ejpam-5776	353	9	2	2	NUM
ejpam-5776	353	10	)	)	PUNCT
ejpam-5776	353	11	(	(	PUNCT
ejpam-5776	353	12	2025	2025	NUM
ejpam-5776	353	13	)	)	PUNCT
ejpam-5776	353	14	,	,	PUNCT
ejpam-5776	353	15	5776	5776	NUM
ejpam-5776	353	16	9	9	NUM
ejpam-5776	353	17	of	of	ADP
ejpam-5776	353	18	13	13	NUM
ejpam-5776	353	19	proof	proof	NOUN
ejpam-5776	353	20	.	.	PUNCT
ejpam-5776	354	1	(	(	PUNCT
ejpam-5776	354	2	i	i	NOUN
ejpam-5776	354	3	)	)	PUNCT
ejpam-5776	354	4	let	let	VERB
ejpam-5776	354	5	n	n	PRON
ejpam-5776	354	6	be	be	AUX
ejpam-5776	354	7	odd	odd	ADJ
ejpam-5776	354	8	.	.	PUNCT
ejpam-5776	355	1	according	accord	VERB
ejpam-5776	355	2	to	to	ADP
ejpam-5776	355	3	theorem	theorem	ADJ
ejpam-5776	355	4	6	6	NUM
ejpam-5776	355	5	,	,	PUNCT
ejpam-5776	355	6	se	se	NOUN
ejpam-5776	355	7	-	-	NOUN
ejpam-5776	355	8	energy	energy	NOUN
ejpam-5776	355	9	of	of	ADP
ejpam-5776	355	10	ωd2n	ωd2n	PROPN
ejpam-5776	355	11	is	be	AUX
ejpam-5776	355	12	εse(ωd2n	εse(ωd2n	ADJ
ejpam-5776	355	13	)	)	PUNCT
ejpam-5776	356	1	=	=	SYM
ejpam-5776	356	2	(	(	PUNCT
ejpam-5776	356	3	n−	n−	NOUN
ejpam-5776	356	4	2	2	NUM
ejpam-5776	356	5	)	)	PUNCT
ejpam-5776	356	6	|0|+	|0|+	PROPN
ejpam-5776	356	7	(	(	PUNCT
ejpam-5776	356	8	n−	n−	NOUN
ejpam-5776	356	9	1	1	NUM
ejpam-5776	356	10	)	)	PUNCT
ejpam-5776	356	11	|−2|+	|−2|+	PROPN
ejpam-5776	356	12	∣∣∣n−	∣∣∣n−	SYM
ejpam-5776	356	13	1±	1±	NUM
ejpam-5776	356	14	√	√	NUM
ejpam-5776	356	15	(	(	PUNCT
ejpam-5776	356	16	n−	n−	NOUN
ejpam-5776	356	17	1)(10n−	1)(10n−	NOUN
ejpam-5776	356	18	1	1	NUM
ejpam-5776	356	19	)	)	PUNCT
ejpam-5776	356	20	∣∣∣	∣∣∣	NOUN
ejpam-5776	356	21	=	=	SYM
ejpam-5776	356	22	2	2	NUM
ejpam-5776	356	23	(	(	PUNCT
ejpam-5776	356	24	n−	n−	NOUN
ejpam-5776	356	25	1	1	NUM
ejpam-5776	356	26	+	+	CCONJ
ejpam-5776	356	27	√	√	PROPN
ejpam-5776	356	28	(	(	PUNCT
ejpam-5776	356	29	n−	n−	NOUN
ejpam-5776	356	30	1)(10n−	1)(10n−	NOUN
ejpam-5776	356	31	1	1	NUM
ejpam-5776	356	32	)	)	PUNCT
ejpam-5776	356	33	)	)	PUNCT
ejpam-5776	356	34	.	.	PUNCT
ejpam-5776	357	1	(	(	PUNCT
ejpam-5776	357	2	ii	ii	NOUN
ejpam-5776	357	3	)	)	PUNCT
ejpam-5776	357	4	let	let	VERB
ejpam-5776	357	5	n	n	PRON
ejpam-5776	357	6	be	be	AUX
ejpam-5776	357	7	even	even	ADV
ejpam-5776	357	8	.	.	PUNCT
ejpam-5776	358	1	according	accord	VERB
ejpam-5776	358	2	to	to	ADP
ejpam-5776	358	3	theorem	theorem	NOUN
ejpam-5776	358	4	6	6	NUM
ejpam-5776	358	5	,	,	PUNCT
ejpam-5776	358	6	the	the	DET
ejpam-5776	358	7	se	se	NOUN
ejpam-5776	358	8	-	-	NOUN
ejpam-5776	358	9	energy	energy	NOUN
ejpam-5776	358	10	of	of	ADP
ejpam-5776	358	11	ωd2n	ωd2n	PROPN
ejpam-5776	358	12	is	be	AUX
ejpam-5776	358	13	εse(ωd2n	εse(ωd2n	ADJ
ejpam-5776	358	14	)	)	PUNCT
ejpam-5776	359	1	=	=	PUNCT
ejpam-5776	359	2	(	(	PUNCT
ejpam-5776	359	3	3(n−	3(n−	NUM
ejpam-5776	359	4	2	2	NUM
ejpam-5776	359	5	)	)	SYM
ejpam-5776	359	6	2	2	NUM
ejpam-5776	359	7	)	)	PUNCT
ejpam-5776	359	8	|0|+	|0|+	PROPN
ejpam-5776	359	9	(	(	PUNCT
ejpam-5776	359	10	n	n	NOUN
ejpam-5776	359	11	2	2	NUM
ejpam-5776	359	12	−	−	NOUN
ejpam-5776	359	13	1	1	NUM
ejpam-5776	359	14	)	)	PUNCT
ejpam-5776	360	1	|−8|+	|−8|+	PROPN
ejpam-5776	360	2	∣∣∣2(n−	∣∣∣2(n−	PROPN
ejpam-5776	360	3	2)±	2)±	NUM
ejpam-5776	360	4	2	2	NUM
ejpam-5776	360	5	√	√	NUM
ejpam-5776	360	6	(	(	PUNCT
ejpam-5776	360	7	n−	n−	NOUN
ejpam-5776	360	8	2)(5n−	2)(5n−	NUM
ejpam-5776	360	9	2	2	NUM
ejpam-5776	360	10	)	)	PUNCT
ejpam-5776	360	11	∣∣∣	∣∣∣	NOUN
ejpam-5776	360	12	=	=	SYM
ejpam-5776	360	13	4	4	NUM
ejpam-5776	360	14	(	(	PUNCT
ejpam-5776	360	15	n−	n−	NOUN
ejpam-5776	360	16	2	2	NUM
ejpam-5776	360	17	+	+	CCONJ
ejpam-5776	360	18	√	√	PROPN
ejpam-5776	360	19	(	(	PUNCT
ejpam-5776	360	20	n−	n−	NOUN
ejpam-5776	360	21	2)(5n−	2)(5n−	NUM
ejpam-5776	360	22	2	2	NUM
ejpam-5776	360	23	)	)	PUNCT
ejpam-5776	360	24	)	)	PUNCT
ejpam-5776	360	25	.	.	PUNCT
ejpam-5776	361	1	3.3	3.3	NUM
ejpam-5776	361	2	.	.	PUNCT
ejpam-5776	362	1	average	average	ADJ
ejpam-5776	362	2	degree	degree	NOUN
ejpam-5776	362	3	-	-	PUNCT
ejpam-5776	362	4	eccentricity	eccentricity	NOUN
ejpam-5776	362	5	matrix	matrix	NOUN
ejpam-5776	362	6	next	next	ADV
ejpam-5776	362	7	,	,	PUNCT
ejpam-5776	362	8	we	we	PRON
ejpam-5776	362	9	show	show	VERB
ejpam-5776	362	10	the	the	DET
ejpam-5776	362	11	energy	energy	NOUN
ejpam-5776	362	12	of	of	ADP
ejpam-5776	362	13	ωd2n	ωd2n	PROPN
ejpam-5776	362	14	concerning	concern	VERB
ejpam-5776	362	15	the	the	DET
ejpam-5776	362	16	average	average	ADJ
ejpam-5776	362	17	degree	degree	NOUN
ejpam-5776	362	18	-	-	PUNCT
ejpam-5776	362	19	eccentricity	eccentricity	NOUN
ejpam-5776	362	20	matrix	matrix	NOUN
ejpam-5776	362	21	for	for	ADP
ejpam-5776	362	22	odd	odd	ADJ
ejpam-5776	362	23	and	and	CCONJ
ejpam-5776	362	24	even	even	ADV
ejpam-5776	362	25	n.	n.	PROPN
ejpam-5776	362	26	theorem	theorem	ADJ
ejpam-5776	362	27	8	8	NUM
ejpam-5776	362	28	.	.	PUNCT
ejpam-5776	363	1	in	in	ADP
ejpam-5776	363	2	ωd2n	ωd2n	PROPN
ejpam-5776	363	3	,	,	PUNCT
ejpam-5776	363	4	the	the	DET
ejpam-5776	363	5	average	average	ADJ
ejpam-5776	363	6	degree	degree	NOUN
ejpam-5776	363	7	-	-	PUNCT
ejpam-5776	363	8	eccentricity	eccentricity	NOUN
ejpam-5776	363	9	spectral	spectral	ADJ
ejpam-5776	363	10	radius	radius	NOUN
ejpam-5776	363	11	of	of	ADP
ejpam-5776	363	12	ωd2n	ωd2n	PROPN
ejpam-5776	363	13	is	be	AUX
ejpam-5776	363	14	ρade(ωd2n	ρade(ωd2n	NOUN
ejpam-5776	363	15	)	)	PUNCT
ejpam-5776	364	1	=	=	PUNCT
ejpam-5776	365	1			NOUN
ejpam-5776	365	2	1	1	NUM
ejpam-5776	365	3	2	2	NUM
ejpam-5776	365	4	(	(	PUNCT
ejpam-5776	365	5	(	(	PUNCT
ejpam-5776	365	6	n−	n−	NOUN
ejpam-5776	365	7	1	1	NUM
ejpam-5776	365	8	)	)	PUNCT
ejpam-5776	365	9	(	(	PUNCT
ejpam-5776	365	10	n−	n−	NOUN
ejpam-5776	365	11	1	1	NUM
ejpam-5776	365	12	2	2	NUM
ejpam-5776	365	13	)	)	PUNCT
ejpam-5776	366	1	+	+	CCONJ
ejpam-5776	366	2	√	√	INTJ
ejpam-5776	366	3	(	(	PUNCT
ejpam-5776	366	4	n−	n−	NOUN
ejpam-5776	366	5	1)2	1)2	NUM
ejpam-5776	366	6	(	(	PUNCT
ejpam-5776	366	7	n−	n−	NOUN
ejpam-5776	366	8	1	1	NUM
ejpam-5776	366	9	2	2	NUM
ejpam-5776	366	10	)	)	PUNCT
ejpam-5776	366	11	2	2	NUM
ejpam-5776	366	12	+	+	SYM
ejpam-5776	366	13	1	1	NUM
ejpam-5776	366	14	4n(n−	4n(n−	NUM
ejpam-5776	366	15	1)(3n+	1)(3n+	NUM
ejpam-5776	366	16	1)2	1)2	NUM
ejpam-5776	366	17	)	)	PUNCT
ejpam-5776	366	18	,	,	PUNCT
ejpam-5776	366	19	if	if	SCONJ
ejpam-5776	366	20	n	n	PRON
ejpam-5776	366	21	is	be	AUX
ejpam-5776	366	22	odd	odd	ADJ
ejpam-5776	366	23	1	1	NUM
ejpam-5776	366	24	2	2	NUM
ejpam-5776	366	25	(	(	PUNCT
ejpam-5776	366	26	(	(	PUNCT
ejpam-5776	366	27	n−	n−	NOUN
ejpam-5776	366	28	2)(n−	2)(n−	NUM
ejpam-5776	366	29	1	1	NUM
ejpam-5776	366	30	)	)	PUNCT
ejpam-5776	366	31	+	+	CCONJ
ejpam-5776	366	32	√	√	INTJ
ejpam-5776	366	33	(	(	PUNCT
ejpam-5776	366	34	n−	n−	NOUN
ejpam-5776	366	35	2)2(n−	2)2(n−	NUM
ejpam-5776	366	36	1)2	1)2	NUM
ejpam-5776	366	37	+	+	CCONJ
ejpam-5776	366	38	9	9	NUM
ejpam-5776	366	39	4n	4n	NOUN
ejpam-5776	366	40	3(n−	3(n−	NUM
ejpam-5776	366	41	2	2	NUM
ejpam-5776	366	42	)	)	PUNCT
ejpam-5776	366	43	)	)	PUNCT
ejpam-5776	366	44	,	,	PUNCT
ejpam-5776	366	45	if	if	SCONJ
ejpam-5776	366	46	n	n	PRON
ejpam-5776	366	47	is	be	AUX
ejpam-5776	366	48	even	even	ADV
ejpam-5776	366	49	.	.	PUNCT
ejpam-5776	367	1	proof	proof	NOUN
ejpam-5776	367	2	.	.	PUNCT
ejpam-5776	368	1	(	(	PUNCT
ejpam-5776	368	2	i	i	NOUN
ejpam-5776	368	3	)	)	PUNCT
ejpam-5776	368	4	let	let	VERB
ejpam-5776	368	5	n	n	PRON
ejpam-5776	368	6	be	be	AUX
ejpam-5776	368	7	odd	odd	ADJ
ejpam-5776	368	8	.	.	PUNCT
ejpam-5776	369	1	based	base	VERB
ejpam-5776	369	2	on	on	ADP
ejpam-5776	369	3	theorems	theorem	NOUN
ejpam-5776	369	4	2	2	NUM
ejpam-5776	369	5	and	and	CCONJ
ejpam-5776	369	6	3	3	NUM
ejpam-5776	369	7	,	,	PUNCT
ejpam-5776	369	8	and	and	CCONJ
ejpam-5776	369	9	definition	definition	NOUN
ejpam-5776	369	10	4	4	NUM
ejpam-5776	369	11	,	,	PUNCT
ejpam-5776	369	12	we	we	PRON
ejpam-5776	369	13	have	have	VERB
ejpam-5776	369	14	the	the	DET
ejpam-5776	369	15	average	average	ADJ
ejpam-5776	369	16	degree	degree	NOUN
ejpam-5776	369	17	-	-	PUNCT
ejpam-5776	369	18	eccentricity	eccentricity	NOUN
ejpam-5776	369	19	matrix	matrix	NOUN
ejpam-5776	369	20	with	with	ADP
ejpam-5776	369	21	entries	entry	NOUN
ejpam-5776	369	22	of	of	ADP
ejpam-5776	369	23	[	[	X
ejpam-5776	369	24	aij	aij	X
ejpam-5776	369	25	]	]	X
ejpam-5776	369	26	are	be	AUX
ejpam-5776	369	27	(	(	PUNCT
ejpam-5776	369	28	a	a	NOUN
ejpam-5776	369	29	)	)	PUNCT
ejpam-5776	369	30	for	for	ADP
ejpam-5776	369	31	i	i	PRON
ejpam-5776	369	32	,	,	PUNCT
ejpam-5776	369	33	j	j	PROPN
ejpam-5776	369	34	=	=	SYM
ejpam-5776	369	35	1	1	NUM
ejpam-5776	369	36	,	,	PUNCT
ejpam-5776	369	37	2	2	NUM
ejpam-5776	369	38	,	,	PUNCT
ejpam-5776	369	39	.	.	PUNCT
ejpam-5776	369	40	.	.	PUNCT
ejpam-5776	370	1	.	.	PUNCT
ejpam-5776	371	1	,	,	PUNCT
ejpam-5776	371	2	n−	n−	NOUN
ejpam-5776	371	3	1	1	NUM
ejpam-5776	371	4	and	and	CCONJ
ejpam-5776	371	5	i	i	PRON
ejpam-5776	371	6	̸=	̸=	PROPN
ejpam-5776	371	7	j	j	PROPN
ejpam-5776	371	8	,	,	PUNCT
ejpam-5776	371	9	then	then	ADV
ejpam-5776	371	10	aij	aij	PROPN
ejpam-5776	371	11	=	=	SYM
ejpam-5776	371	12	0	0	NUM
ejpam-5776	371	13	;	;	PUNCT
ejpam-5776	371	14	(	(	PUNCT
ejpam-5776	371	15	b	b	X
ejpam-5776	371	16	)	)	PUNCT
ejpam-5776	371	17	for	for	ADP
ejpam-5776	371	18	i	i	PROPN
ejpam-5776	371	19	=	=	NOUN
ejpam-5776	371	20	1	1	NUM
ejpam-5776	371	21	,	,	PUNCT
ejpam-5776	371	22	2	2	NUM
ejpam-5776	371	23	,	,	PUNCT
ejpam-5776	371	24	.	.	PUNCT
ejpam-5776	371	25	.	.	PUNCT
ejpam-5776	372	1	.	.	PUNCT
ejpam-5776	373	1	,	,	PUNCT
ejpam-5776	373	2	n−	n−	NOUN
ejpam-5776	373	3	1	1	NUM
ejpam-5776	373	4	and	and	CCONJ
ejpam-5776	373	5	j	j	PROPN
ejpam-5776	373	6	=	=	SYM
ejpam-5776	373	7	n	n	CCONJ
ejpam-5776	373	8	,	,	PUNCT
ejpam-5776	373	9	n+	n+	ADP
ejpam-5776	373	10	1	1	NUM
ejpam-5776	373	11	,	,	PUNCT
ejpam-5776	373	12	.	.	PUNCT
ejpam-5776	373	13	.	.	PUNCT
ejpam-5776	374	1	.	.	PUNCT
ejpam-5776	375	1	,	,	PUNCT
ejpam-5776	375	2	2n−	2n−	PROPN
ejpam-5776	375	3	1	1	NUM
ejpam-5776	375	4	or	or	CCONJ
ejpam-5776	375	5	vice	vice	NOUN
ejpam-5776	375	6	versa	versa	ADV
ejpam-5776	375	7	and	and	CCONJ
ejpam-5776	375	8	i	i	PRON
ejpam-5776	375	9	̸=	̸=	PROPN
ejpam-5776	375	10	j	j	PROPN
ejpam-5776	375	11	,	,	PUNCT
ejpam-5776	375	12	then	then	ADV
ejpam-5776	375	13	aij	aij	PROPN
ejpam-5776	375	14	=	=	PROPN
ejpam-5776	375	15	1	1	NUM
ejpam-5776	375	16	4(n+	4(n+	PROPN
ejpam-5776	375	17	2(n−	2(n−	NUM
ejpam-5776	375	18	1	1	NUM
ejpam-5776	375	19	)	)	PUNCT
ejpam-5776	376	1	+	+	CCONJ
ejpam-5776	376	2	2	2	NUM
ejpam-5776	376	3	+	+	NUM
ejpam-5776	376	4	1	1	NUM
ejpam-5776	376	5	)	)	PUNCT
ejpam-5776	376	6	=	=	SYM
ejpam-5776	377	1	3n+1	3n+1	PROPN
ejpam-5776	377	2	4	4	NUM
ejpam-5776	377	3	;	;	PUNCT
ejpam-5776	377	4	(	(	PUNCT
ejpam-5776	377	5	c	c	X
ejpam-5776	377	6	)	)	PUNCT
ejpam-5776	377	7	for	for	ADP
ejpam-5776	377	8	i	i	PRON
ejpam-5776	377	9	,	,	PUNCT
ejpam-5776	377	10	j	j	PROPN
ejpam-5776	377	11	=	=	SYM
ejpam-5776	377	12	n	n	CCONJ
ejpam-5776	377	13	,	,	PUNCT
ejpam-5776	377	14	n+1	n+1	PROPN
ejpam-5776	377	15	,	,	PUNCT
ejpam-5776	377	16	.	.	PUNCT
ejpam-5776	377	17	.	.	PUNCT
ejpam-5776	377	18	.	.	PUNCT
ejpam-5776	378	1	,	,	PUNCT
ejpam-5776	378	2	2n−1	2n−1	NUM
ejpam-5776	378	3	and	and	CCONJ
ejpam-5776	378	4	i	i	PRON
ejpam-5776	378	5	̸=	̸=	PROPN
ejpam-5776	378	6	j	j	PROPN
ejpam-5776	378	7	,	,	PUNCT
ejpam-5776	378	8	then	then	ADV
ejpam-5776	378	9	aij	aij	PROPN
ejpam-5776	378	10	=	=	SYM
ejpam-5776	378	11	1	1	NUM
ejpam-5776	378	12	4(2(n−1)+2(n−1)+1	4(2(n−1)+2(n−1)+1	NUM
ejpam-5776	378	13	+	+	NOUN
ejpam-5776	378	14	1	1	NUM
ejpam-5776	378	15	)	)	PUNCT
ejpam-5776	378	16	=	=	PUNCT
ejpam-5776	378	17	n−	n−	NOUN
ejpam-5776	378	18	1	1	NUM
ejpam-5776	378	19	2	2	NUM
ejpam-5776	378	20	;	;	PUNCT
ejpam-5776	378	21	(	(	PUNCT
ejpam-5776	378	22	d	d	X
ejpam-5776	378	23	)	)	PUNCT
ejpam-5776	378	24	for	for	ADP
ejpam-5776	378	25	i	i	PROPN
ejpam-5776	378	26	=	=	SYM
ejpam-5776	378	27	j	j	PROPN
ejpam-5776	378	28	,	,	PUNCT
ejpam-5776	378	29	aij	aij	PROPN
ejpam-5776	378	30	=	=	SYM
ejpam-5776	378	31	0	0	NUM
ejpam-5776	378	32	m.	m.	NOUN
ejpam-5776	378	33	u.	u.	PROPN
ejpam-5776	378	34	romdhini	romdhini	PROPN
ejpam-5776	378	35	et	et	PROPN
ejpam-5776	378	36	al	al	PROPN
ejpam-5776	378	37	.	.	PUNCT
ejpam-5776	378	38	/	/	SYM
ejpam-5776	378	39	eur	eur	PROPN
ejpam-5776	378	40	.	.	PUNCT
ejpam-5776	379	1	j.	j.	PROPN
ejpam-5776	379	2	pure	pure	PROPN
ejpam-5776	379	3	appl	appl	PROPN
ejpam-5776	379	4	.	.	PROPN
ejpam-5776	379	5	math	math	PROPN
ejpam-5776	379	6	,	,	PUNCT
ejpam-5776	379	7	18	18	NUM
ejpam-5776	379	8	(	(	PUNCT
ejpam-5776	379	9	2	2	NUM
ejpam-5776	379	10	)	)	PUNCT
ejpam-5776	379	11	(	(	PUNCT
ejpam-5776	379	12	2025	2025	NUM
ejpam-5776	379	13	)	)	PUNCT
ejpam-5776	379	14	,	,	PUNCT
ejpam-5776	379	15	5776	5776	NUM
ejpam-5776	379	16	10	10	NUM
ejpam-5776	379	17	of	of	ADP
ejpam-5776	379	18	13	13	NUM
ejpam-5776	379	19	then	then	ADV
ejpam-5776	379	20	ade(ωd2n	ade(ωd2n	NOUN
ejpam-5776	379	21	)	)	PUNCT
ejpam-5776	379	22	is	be	AUX
ejpam-5776	379	23	as	as	SCONJ
ejpam-5776	379	24	follows	follow	VERB
ejpam-5776	379	25	:	:	PUNCT
ejpam-5776	379	26	ade(ωd2n	ade(ωd2n	NOUN
ejpam-5776	379	27	)	)	PUNCT
ejpam-5776	379	28	=	=	PUNCT
ejpam-5776	379	29	a	a	DET
ejpam-5776	379	30	a2	a2	PROPN
ejpam-5776	379	31	.	.	PUNCT
ejpam-5776	379	32	.	.	PUNCT
ejpam-5776	379	33	.	.	PUNCT
ejpam-5776	380	1	an−1	an−1	PROPN
ejpam-5776	380	2	b	b	PROPN
ejpam-5776	380	3	ab	ab	PROPN
ejpam-5776	380	4	.	.	PUNCT
ejpam-5776	380	5	.	.	PUNCT
ejpam-5776	380	6	.	.	PUNCT
ejpam-5776	381	1	an−1b	an−1b	PROPN
ejpam-5776	381	2			PROPN
ejpam-5776	382	1	a	a	DET
ejpam-5776	382	2	0	0	NUM
ejpam-5776	382	3	0	0	NUM
ejpam-5776	382	4	.	.	PUNCT
ejpam-5776	382	5	.	.	PUNCT
ejpam-5776	382	6	.	.	PUNCT
ejpam-5776	383	1	0	0	PUNCT
ejpam-5776	384	1	3n+1	3n+1	NUM
ejpam-5776	384	2	4	4	NUM
ejpam-5776	384	3	3n+1	3n+1	NOUN
ejpam-5776	384	4	4	4	NUM
ejpam-5776	384	5	.	.	PUNCT
ejpam-5776	384	6	.	.	PUNCT
ejpam-5776	384	7	.	.	PUNCT
ejpam-5776	385	1	3n+1	3n+1	NOUN
ejpam-5776	385	2	4	4	NUM
ejpam-5776	385	3	a2	a2	PROPN
ejpam-5776	385	4	0	0	NUM
ejpam-5776	385	5	0	0	NUM
ejpam-5776	385	6	.	.	PUNCT
ejpam-5776	385	7	.	.	PUNCT
ejpam-5776	385	8	.	.	PUNCT
ejpam-5776	386	1	0	0	PUNCT
ejpam-5776	387	1	3n+1	3n+1	NUM
ejpam-5776	387	2	4	4	NUM
ejpam-5776	387	3	3n+1	3n+1	NOUN
ejpam-5776	387	4	4	4	NUM
ejpam-5776	387	5	.	.	PUNCT
ejpam-5776	387	6	.	.	PUNCT
ejpam-5776	387	7	.	.	PUNCT
ejpam-5776	388	1	3n+1	3n+1	NOUN
ejpam-5776	388	2	4	4	NUM
ejpam-5776	388	3	...	...	PUNCT
ejpam-5776	388	4	...	...	PUNCT
ejpam-5776	388	5	...	...	PUNCT
ejpam-5776	388	6	.	.	PUNCT
ejpam-5776	388	7	.	.	PUNCT
ejpam-5776	388	8	.	.	PUNCT
ejpam-5776	389	1	...	...	PUNCT
ejpam-5776	389	2	...	...	PUNCT
ejpam-5776	389	3	...	...	PUNCT
ejpam-5776	389	4	.	.	PUNCT
ejpam-5776	389	5	.	.	PUNCT
ejpam-5776	390	1	.	.	PUNCT
ejpam-5776	391	1	...	...	PUNCT
ejpam-5776	392	1	an−1	an−1	ADJ
ejpam-5776	392	2	0	0	NUM
ejpam-5776	392	3	0	0	NUM
ejpam-5776	392	4	.	.	PUNCT
ejpam-5776	392	5	.	.	PUNCT
ejpam-5776	392	6	.	.	PUNCT
ejpam-5776	393	1	0	0	PUNCT
ejpam-5776	394	1	3n+1	3n+1	NUM
ejpam-5776	394	2	4	4	NUM
ejpam-5776	394	3	3n+1	3n+1	NOUN
ejpam-5776	394	4	4	4	NUM
ejpam-5776	394	5	.	.	PUNCT
ejpam-5776	394	6	.	.	PUNCT
ejpam-5776	394	7	.	.	PUNCT
ejpam-5776	395	1	3n+1	3n+1	NOUN
ejpam-5776	395	2	4	4	NUM
ejpam-5776	395	3	b	b	NOUN
ejpam-5776	395	4	3n+1	3n+1	NOUN
ejpam-5776	395	5	4	4	NUM
ejpam-5776	395	6	3n+1	3n+1	NOUN
ejpam-5776	395	7	4	4	NUM
ejpam-5776	395	8	.	.	PUNCT
ejpam-5776	395	9	.	.	PUNCT
ejpam-5776	395	10	.	.	PUNCT
ejpam-5776	396	1	3n+1	3n+1	NOUN
ejpam-5776	396	2	4	4	NUM
ejpam-5776	396	3	0	0	NUM
ejpam-5776	396	4	n−	n−	NOUN
ejpam-5776	396	5	1	1	NUM
ejpam-5776	396	6	2	2	NUM
ejpam-5776	396	7	.	.	PUNCT
ejpam-5776	396	8	.	.	PUNCT
ejpam-5776	396	9	.	.	PUNCT
ejpam-5776	397	1	n−	n−	NOUN
ejpam-5776	397	2	1	1	NUM
ejpam-5776	397	3	2	2	NUM
ejpam-5776	397	4	ab	ab	NOUN
ejpam-5776	397	5	3n+1	3n+1	PROPN
ejpam-5776	397	6	4	4	NUM
ejpam-5776	397	7	3n+1	3n+1	NOUN
ejpam-5776	397	8	4	4	NUM
ejpam-5776	397	9	.	.	PUNCT
ejpam-5776	397	10	.	.	PUNCT
ejpam-5776	397	11	.	.	PUNCT
ejpam-5776	398	1	3n+1	3n+1	NOUN
ejpam-5776	398	2	4	4	NUM
ejpam-5776	398	3	n−	n−	NOUN
ejpam-5776	398	4	1	1	NUM
ejpam-5776	398	5	2	2	NUM
ejpam-5776	398	6	0	0	NUM
ejpam-5776	398	7	.	.	PUNCT
ejpam-5776	398	8	.	.	PUNCT
ejpam-5776	398	9	.	.	PUNCT
ejpam-5776	399	1	n−	n−	NOUN
ejpam-5776	399	2	1	1	NUM
ejpam-5776	399	3	2	2	NUM
ejpam-5776	399	4	...	...	PUNCT
ejpam-5776	399	5	...	...	PUNCT
ejpam-5776	399	6	...	...	PUNCT
ejpam-5776	399	7	.	.	PUNCT
ejpam-5776	399	8	.	.	PUNCT
ejpam-5776	399	9	.	.	PUNCT
ejpam-5776	400	1	...	...	PUNCT
ejpam-5776	400	2	...	...	PUNCT
ejpam-5776	400	3	...	...	PUNCT
ejpam-5776	400	4	.	.	PUNCT
ejpam-5776	400	5	.	.	PUNCT
ejpam-5776	401	1	.	.	PUNCT
ejpam-5776	402	1	...	...	PUNCT
ejpam-5776	403	1	an−1b	an−1b	PUNCT
ejpam-5776	404	1	3n+1	3n+1	NOUN
ejpam-5776	404	2	4	4	NUM
ejpam-5776	404	3	3n+1	3n+1	NOUN
ejpam-5776	404	4	4	4	NUM
ejpam-5776	404	5	.	.	PUNCT
ejpam-5776	404	6	.	.	PUNCT
ejpam-5776	404	7	.	.	PUNCT
ejpam-5776	405	1	3n+1	3n+1	NOUN
ejpam-5776	405	2	4	4	NUM
ejpam-5776	405	3	n−	n−	NOUN
ejpam-5776	405	4	1	1	NUM
ejpam-5776	405	5	2	2	NUM
ejpam-5776	405	6	n−	n−	NOUN
ejpam-5776	405	7	1	1	NUM
ejpam-5776	405	8	2	2	NUM
ejpam-5776	405	9	.	.	PUNCT
ejpam-5776	405	10	.	.	PUNCT
ejpam-5776	406	1	.	.	PUNCT
ejpam-5776	406	2	0	0	PUNCT
ejpam-5776	406	3	.	.	PUNCT
ejpam-5776	407	1	ade	ade	NOUN
ejpam-5776	407	2	-	-	PUNCT
ejpam-5776	407	3	matrix	matrix	NOUN
ejpam-5776	407	4	of	of	ADP
ejpam-5776	407	5	ωd2n	ωd2n	PROPN
ejpam-5776	407	6	can	can	AUX
ejpam-5776	407	7	be	be	AUX
ejpam-5776	407	8	written	write	VERB
ejpam-5776	407	9	as	as	ADP
ejpam-5776	407	10	given	give	VERB
ejpam-5776	407	11	below	below	ADP
ejpam-5776	407	12	ade(ωd2n	ade(ωd2n	NOUN
ejpam-5776	407	13	)	)	PUNCT
ejpam-5776	408	1	=	=	PRON
ejpam-5776	408	2	(	(	PUNCT
ejpam-5776	408	3	0n−1	0n−1	PROPN
ejpam-5776	408	4	(	(	PUNCT
ejpam-5776	408	5	3n+1	3n+1	PROPN
ejpam-5776	408	6	4	4	NUM
ejpam-5776	408	7	)	)	PUNCT
ejpam-5776	408	8	j(n−1)×n	j(n−1)×n	PROPN
ejpam-5776	408	9	(	(	PUNCT
ejpam-5776	408	10	3n+1	3n+1	NUM
ejpam-5776	408	11	4	4	NUM
ejpam-5776	408	12	)	)	PUNCT
ejpam-5776	408	13	jn×(n−1	jn×(n−1	PROPN
ejpam-5776	408	14	)	)	PUNCT
ejpam-5776	408	15	(	(	PUNCT
ejpam-5776	408	16	n−	n−	NOUN
ejpam-5776	408	17	1	1	NUM
ejpam-5776	408	18	2	2	NUM
ejpam-5776	408	19	)	)	PUNCT
ejpam-5776	408	20	(	(	PUNCT
ejpam-5776	408	21	j	j	PROPN
ejpam-5776	408	22	−	−	PROPN
ejpam-5776	408	23	i)n	i)n	PROPN
ejpam-5776	408	24	)	)	PUNCT
ejpam-5776	408	25	,	,	PUNCT
ejpam-5776	408	26	and	and	CCONJ
ejpam-5776	408	27	the	the	DET
ejpam-5776	408	28	characteristic	characteristic	ADJ
ejpam-5776	408	29	formula	formula	NOUN
ejpam-5776	408	30	of	of	ADP
ejpam-5776	408	31	ade(ωd2n	ade(ωd2n	NOUN
ejpam-5776	408	32	)	)	PUNCT
ejpam-5776	408	33	,	,	PUNCT
ejpam-5776	408	34	pade(ωd2n	pade(ωd2n	PROPN
ejpam-5776	408	35	)	)	PUNCT
ejpam-5776	408	36	(	(	PUNCT
ejpam-5776	408	37	µ	µ	NOUN
ejpam-5776	408	38	)	)	PUNCT
ejpam-5776	408	39	=	=	SYM
ejpam-5776	408	40	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5776	408	41	µin−1	µin−1	PROPN
ejpam-5776	408	42	−	−	PROPN
ejpam-5776	408	43	(	(	PUNCT
ejpam-5776	408	44	3n+1	3n+1	PROPN
ejpam-5776	408	45	4	4	NUM
ejpam-5776	408	46	)	)	PUNCT
ejpam-5776	408	47	j(n−1)×n	j(n−1)×n	PROPN
ejpam-5776	409	1	−	−	PROPN
ejpam-5776	409	2	(	(	PUNCT
ejpam-5776	409	3	3n+1	3n+1	PROPN
ejpam-5776	409	4	4	4	NUM
ejpam-5776	409	5	)	)	PUNCT
ejpam-5776	409	6	jn×(n−1	jn×(n−1	PROPN
ejpam-5776	409	7	)	)	PUNCT
ejpam-5776	409	8	(	(	PUNCT
ejpam-5776	409	9	µ+	µ+	X
ejpam-5776	409	10	n−	n−	NOUN
ejpam-5776	409	11	1	1	NUM
ejpam-5776	409	12	2	2	NUM
ejpam-5776	409	13	)	)	PUNCT
ejpam-5776	409	14	in	in	ADP
ejpam-5776	409	15	−	−	PROPN
ejpam-5776	409	16	(	(	PUNCT
ejpam-5776	409	17	n−	n−	NOUN
ejpam-5776	409	18	1	1	NUM
ejpam-5776	409	19	2	2	NUM
ejpam-5776	409	20	)	)	PUNCT
ejpam-5776	409	21	jn	jn	PROPN
ejpam-5776	409	22	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5776	409	23	.	.	PUNCT
ejpam-5776	410	1	by	by	ADP
ejpam-5776	410	2	lemma	lemma	PROPN
ejpam-5776	410	3	1	1	NUM
ejpam-5776	410	4	,	,	PUNCT
ejpam-5776	410	5	with	with	ADP
ejpam-5776	410	6	a	a	PRON
ejpam-5776	410	7	=	=	SYM
ejpam-5776	410	8	0	0	NUM
ejpam-5776	410	9	,	,	PUNCT
ejpam-5776	410	10	b	b	X
ejpam-5776	410	11	=	=	SYM
ejpam-5776	410	12	n	n	CCONJ
ejpam-5776	410	13	−	−	PROPN
ejpam-5776	410	14	1	1	NUM
ejpam-5776	410	15	2	2	NUM
ejpam-5776	410	16	,	,	PUNCT
ejpam-5776	410	17	c	c	NOUN
ejpam-5776	410	18	=	=	SYM
ejpam-5776	410	19	d	d	NOUN
ejpam-5776	410	20	=	=	SYM
ejpam-5776	410	21	3n+1	3n+1	PROPN
ejpam-5776	410	22	4	4	NUM
ejpam-5776	410	23	,	,	PUNCT
ejpam-5776	410	24	n1	n1	NOUN
ejpam-5776	410	25	=	=	SYM
ejpam-5776	410	26	n	n	CCONJ
ejpam-5776	410	27	−	−	NUM
ejpam-5776	410	28	1	1	NUM
ejpam-5776	410	29	and	and	CCONJ
ejpam-5776	410	30	n2	n2	ADJ
ejpam-5776	410	31	=	=	SYM
ejpam-5776	410	32	n	n	CCONJ
ejpam-5776	410	33	,	,	PUNCT
ejpam-5776	410	34	we	we	PRON
ejpam-5776	410	35	obtain	obtain	VERB
ejpam-5776	410	36	pade(ωd2n	pade(ωd2n	PROPN
ejpam-5776	410	37	)	)	PUNCT
ejpam-5776	410	38	(	(	PUNCT
ejpam-5776	410	39	µ	µ	NOUN
ejpam-5776	410	40	)	)	PUNCT
ejpam-5776	410	41	=	=	SYM
ejpam-5776	410	42	µn−2	µn−2	PROPN
ejpam-5776	410	43	(	(	PUNCT
ejpam-5776	410	44	µ+	µ+	X
ejpam-5776	410	45	n−	n−	NOUN
ejpam-5776	410	46	1	1	NUM
ejpam-5776	410	47	2	2	NUM
ejpam-5776	410	48	)	)	PUNCT
ejpam-5776	410	49	n−1	n−1	PROPN
ejpam-5776	410	50	(	(	PUNCT
ejpam-5776	410	51	µ2	µ2	PROPN
ejpam-5776	410	52	−	−	PROPN
ejpam-5776	410	53	(	(	PUNCT
ejpam-5776	410	54	n−	n−	NOUN
ejpam-5776	410	55	1	1	NUM
ejpam-5776	410	56	)	)	PUNCT
ejpam-5776	410	57	(	(	PUNCT
ejpam-5776	410	58	n−	n−	NOUN
ejpam-5776	410	59	1	1	NUM
ejpam-5776	410	60	2	2	NUM
ejpam-5776	410	61	)	)	PUNCT
ejpam-5776	410	62	µ−	µ−	PROPN
ejpam-5776	410	63	1	1	NUM
ejpam-5776	410	64	16	16	NUM
ejpam-5776	410	65	n(n−	n(n−	NOUN
ejpam-5776	410	66	1)(3n+	1)(3n+	PROPN
ejpam-5776	410	67	1)2	1)2	NUM
ejpam-5776	410	68	)	)	PUNCT
ejpam-5776	410	69	.	.	PUNCT
ejpam-5776	411	1	the	the	DET
ejpam-5776	411	2	eigenvalues	eigenvalue	NOUN
ejpam-5776	411	3	of	of	ADP
ejpam-5776	411	4	ωd2n	ωd2n	PROPN
ejpam-5776	411	5	are	be	AUX
ejpam-5776	411	6	µ1	µ1	NOUN
ejpam-5776	411	7	=	=	SYM
ejpam-5776	411	8	0	0	NUM
ejpam-5776	411	9	of	of	ADP
ejpam-5776	411	10	multiplicity	multiplicity	NOUN
ejpam-5776	411	11	n−	n−	NOUN
ejpam-5776	411	12	2	2	NUM
ejpam-5776	411	13	,	,	PUNCT
ejpam-5776	411	14	µ2	µ2	PROPN
ejpam-5776	411	15	=	=	NOUN
ejpam-5776	411	16	1	1	NUM
ejpam-5776	411	17	2	2	NUM
ejpam-5776	411	18	−	−	NOUN
ejpam-5776	411	19	n	n	PROPN
ejpam-5776	411	20	of	of	ADP
ejpam-5776	411	21	multiplicity	multiplicity	NOUN
ejpam-5776	411	22	n	n	CCONJ
ejpam-5776	411	23	−	−	PROPN
ejpam-5776	411	24	1	1	NUM
ejpam-5776	411	25	,	,	PUNCT
ejpam-5776	411	26	and	and	CCONJ
ejpam-5776	411	27	µ3,4	µ3,4	ADJ
ejpam-5776	411	28	=	=	SYM
ejpam-5776	411	29	1	1	NUM
ejpam-5776	411	30	2	2	NUM
ejpam-5776	411	31	(	(	PUNCT
ejpam-5776	411	32	(	(	PUNCT
ejpam-5776	411	33	n−	n−	NOUN
ejpam-5776	411	34	1	1	NUM
ejpam-5776	411	35	)	)	PUNCT
ejpam-5776	411	36	(	(	PUNCT
ejpam-5776	411	37	n−	n−	NOUN
ejpam-5776	411	38	1	1	NUM
ejpam-5776	411	39	2	2	NUM
ejpam-5776	411	40	)	)	PUNCT
ejpam-5776	411	41	±	±	NOUN
ejpam-5776	411	42	√	√	NUM
ejpam-5776	411	43	(	(	PUNCT
ejpam-5776	411	44	n−	n−	PROPN
ejpam-5776	411	45	1)2	1)2	NUM
ejpam-5776	411	46	(	(	PUNCT
ejpam-5776	411	47	n−	n−	NOUN
ejpam-5776	411	48	1	1	NUM
ejpam-5776	411	49	2	2	NUM
ejpam-5776	411	50	)	)	PUNCT
ejpam-5776	411	51	2	2	NUM
ejpam-5776	411	52	+	+	SYM
ejpam-5776	411	53	1	1	NUM
ejpam-5776	411	54	4n(n−	4n(n−	NUM
ejpam-5776	411	55	1)(3n+	1)(3n+	NUM
ejpam-5776	411	56	1)2	1)2	NUM
ejpam-5776	411	57	)	)	PUNCT
ejpam-5776	411	58	.	.	PUNCT
ejpam-5776	412	1	therefore	therefore	ADV
ejpam-5776	412	2	,	,	PUNCT
ejpam-5776	412	3	the	the	DET
ejpam-5776	412	4	ade	ade	PROPN
ejpam-5776	412	5	-	-	PUNCT
ejpam-5776	412	6	spectral	spectral	ADJ
ejpam-5776	412	7	radius	radius	NOUN
ejpam-5776	412	8	of	of	ADP
ejpam-5776	412	9	ωd2n	ωd2n	PROPN
ejpam-5776	412	10	is	be	AUX
ejpam-5776	412	11	ρade(ωd2n	ρade(ωd2n	PROPN
ejpam-5776	412	12	)	)	PUNCT
ejpam-5776	412	13	=	=	SYM
ejpam-5776	413	1	1	1	NUM
ejpam-5776	413	2	2	2	NUM
ejpam-5776	413	3	(n−	(n−	NUM
ejpam-5776	413	4	1	1	NUM
ejpam-5776	413	5	)	)	PUNCT
ejpam-5776	413	6	(	(	PUNCT
ejpam-5776	413	7	n−	n−	NOUN
ejpam-5776	413	8	1	1	NUM
ejpam-5776	413	9	2	2	NUM
ejpam-5776	413	10	)	)	PUNCT
ejpam-5776	413	11	+	+	CCONJ
ejpam-5776	413	12	√	√	INTJ
ejpam-5776	413	13	(	(	PUNCT
ejpam-5776	413	14	n−	n−	NOUN
ejpam-5776	413	15	1)2	1)2	NUM
ejpam-5776	413	16	(	(	PUNCT
ejpam-5776	413	17	n−	n−	NOUN
ejpam-5776	413	18	1	1	NUM
ejpam-5776	413	19	2	2	NUM
ejpam-5776	413	20	)	)	PUNCT
ejpam-5776	413	21	2	2	NUM
ejpam-5776	413	22	+	+	CCONJ
ejpam-5776	413	23	1	1	NUM
ejpam-5776	413	24	4	4	NUM
ejpam-5776	413	25	n(n−	n(n−	NOUN
ejpam-5776	413	26	1)(3n+	1)(3n+	PROPN
ejpam-5776	413	27	1)2	1)2	NUM
ejpam-5776	413	28			PROPN
ejpam-5776	413	29	.	.	PUNCT
ejpam-5776	414	1	(	(	PUNCT
ejpam-5776	414	2	ii	ii	NOUN
ejpam-5776	414	3	)	)	PUNCT
ejpam-5776	414	4	let	let	VERB
ejpam-5776	414	5	n	n	PRON
ejpam-5776	414	6	be	be	AUX
ejpam-5776	414	7	even	even	ADV
ejpam-5776	414	8	.	.	PUNCT
ejpam-5776	415	1	the	the	DET
ejpam-5776	415	2	entries	entry	NOUN
ejpam-5776	415	3	of	of	ADP
ejpam-5776	415	4	ade(ωd2n	ade(ωd2n	NOUN
ejpam-5776	415	5	)	)	PUNCT
ejpam-5776	415	6	=	=	PUNCT
ejpam-5776	416	1	[	[	X
ejpam-5776	416	2	aij	aij	X
ejpam-5776	416	3	]	]	X
ejpam-5776	416	4	are	be	AUX
ejpam-5776	416	5	(	(	PUNCT
ejpam-5776	416	6	a	a	NOUN
ejpam-5776	416	7	)	)	PUNCT
ejpam-5776	416	8	for	for	ADP
ejpam-5776	416	9	1	1	NUM
ejpam-5776	416	10	≤	≤	NOUN
ejpam-5776	416	11	i	i	PRON
ejpam-5776	416	12	,	,	PUNCT
ejpam-5776	416	13	j	j	PROPN
ejpam-5776	416	14	≤	≤	PROPN
ejpam-5776	416	15	n−	n−	PROPN
ejpam-5776	416	16	2	2	NUM
ejpam-5776	416	17	and	and	CCONJ
ejpam-5776	416	18	i	i	PRON
ejpam-5776	416	19	̸=	̸=	PROPN
ejpam-5776	416	20	i	i	PRON
ejpam-5776	416	21	,	,	PUNCT
ejpam-5776	416	22	aij	aij	PROPN
ejpam-5776	416	23	=	=	SYM
ejpam-5776	416	24	0	0	NUM
ejpam-5776	416	25	;	;	PUNCT
ejpam-5776	416	26	(	(	PUNCT
ejpam-5776	416	27	b	b	X
ejpam-5776	416	28	)	)	PUNCT
ejpam-5776	416	29	for	for	ADP
ejpam-5776	416	30	1	1	NUM
ejpam-5776	416	31	≤	≤	NUM
ejpam-5776	416	32	i	i	PRON
ejpam-5776	416	33	≤	≤	PROPN
ejpam-5776	416	34	n−2	n−2	PROPN
ejpam-5776	416	35	,	,	PUNCT
ejpam-5776	416	36	n−1	n−1	PROPN
ejpam-5776	416	37	≤	≤	PROPN
ejpam-5776	416	38	j	j	PROPN
ejpam-5776	416	39	≤	≤	PROPN
ejpam-5776	416	40	2n−2	2n−2	NUM
ejpam-5776	416	41	or	or	CCONJ
ejpam-5776	416	42	vice	vice	NOUN
ejpam-5776	416	43	versa	versa	ADV
ejpam-5776	416	44	,	,	PUNCT
ejpam-5776	416	45	aij	aij	PROPN
ejpam-5776	416	46	=	=	SYM
ejpam-5776	416	47	1	1	NUM
ejpam-5776	416	48	4	4	NUM
ejpam-5776	416	49	(	(	PUNCT
ejpam-5776	416	50	n+	n+	NUM
ejpam-5776	416	51	2(n−	2(n−	NUM
ejpam-5776	416	52	2	2	NUM
ejpam-5776	416	53	)	)	PUNCT
ejpam-5776	416	54	+	+	CCONJ
ejpam-5776	416	55	2	2	NUM
ejpam-5776	416	56	+	+	CCONJ
ejpam-5776	416	57	2	2	NUM
ejpam-5776	416	58	)	)	PUNCT
ejpam-5776	416	59	=	=	SYM
ejpam-5776	416	60	3n	3n	NUM
ejpam-5776	416	61	4	4	NUM
ejpam-5776	416	62	;	;	PUNCT
ejpam-5776	416	63	(	(	PUNCT
ejpam-5776	416	64	c	c	X
ejpam-5776	416	65	)	)	PUNCT
ejpam-5776	416	66	for	for	ADP
ejpam-5776	416	67	n−	n−	NOUN
ejpam-5776	416	68	1	1	NUM
ejpam-5776	416	69	≤	≤	NUM
ejpam-5776	416	70	i	i	PRON
ejpam-5776	416	71	≤	≤	PROPN
ejpam-5776	416	72	n+	n+	PUNCT
ejpam-5776	416	73	n	n	CCONJ
ejpam-5776	416	74	2	2	NUM
ejpam-5776	416	75	−	−	NUM
ejpam-5776	416	76	2	2	NUM
ejpam-5776	416	77	and	and	CCONJ
ejpam-5776	416	78	n+	n+	PUNCT
ejpam-5776	416	79	n	n	CCONJ
ejpam-5776	416	80	2	2	NUM
ejpam-5776	416	81	−	−	PROPN
ejpam-5776	416	82	1	1	NUM
ejpam-5776	416	83	≤	≤	NUM
ejpam-5776	417	1	j	j	PROPN
ejpam-5776	417	2	≤	≤	PROPN
ejpam-5776	418	1	2n−	2n−	PROPN
ejpam-5776	418	2	2	2	NUM
ejpam-5776	418	3	where	where	SCONJ
ejpam-5776	418	4	j	j	PROPN
ejpam-5776	418	5	̸=	̸=	PROPN
ejpam-5776	418	6	n−	n−	NOUN
ejpam-5776	418	7	2	2	NUM
ejpam-5776	418	8	+	+	CCONJ
ejpam-5776	418	9	n	n	PRON
ejpam-5776	418	10	2	2	NUM
ejpam-5776	418	11	+	+	CCONJ
ejpam-5776	418	12	i	i	PRON
ejpam-5776	418	13	or	or	CCONJ
ejpam-5776	418	14	vice	vice	NOUN
ejpam-5776	418	15	versa	versa	ADV
ejpam-5776	418	16	,	,	PUNCT
ejpam-5776	418	17	aij	aij	PROPN
ejpam-5776	418	18	=	=	SYM
ejpam-5776	418	19	1	1	NUM
ejpam-5776	418	20	4	4	NUM
ejpam-5776	418	21	(	(	PUNCT
ejpam-5776	418	22	2(n−	2(n−	NUM
ejpam-5776	418	23	2	2	NUM
ejpam-5776	418	24	)	)	PUNCT
ejpam-5776	418	25	+	+	CCONJ
ejpam-5776	419	1	2(n−	2(n−	NUM
ejpam-5776	419	2	2	2	NUM
ejpam-5776	419	3	)	)	PUNCT
ejpam-5776	419	4	+	+	CCONJ
ejpam-5776	419	5	2	2	NUM
ejpam-5776	419	6	+	+	CCONJ
ejpam-5776	419	7	2	2	NUM
ejpam-5776	419	8	)	)	PUNCT
ejpam-5776	419	9	=	=	SYM
ejpam-5776	419	10	n−	n−	NOUN
ejpam-5776	419	11	1	1	NUM
ejpam-5776	419	12	;	;	PUNCT
ejpam-5776	419	13	m.	m.	PROPN
ejpam-5776	419	14	u.	u.	PROPN
ejpam-5776	419	15	romdhini	romdhini	PROPN
ejpam-5776	419	16	et	et	PROPN
ejpam-5776	419	17	al	al	PROPN
ejpam-5776	419	18	.	.	PUNCT
ejpam-5776	419	19	/	/	SYM
ejpam-5776	419	20	eur	eur	PROPN
ejpam-5776	419	21	.	.	PUNCT
ejpam-5776	420	1	j.	j.	PROPN
ejpam-5776	420	2	pure	pure	PROPN
ejpam-5776	420	3	appl	appl	PROPN
ejpam-5776	420	4	.	.	PROPN
ejpam-5776	420	5	math	math	PROPN
ejpam-5776	420	6	,	,	PUNCT
ejpam-5776	420	7	18	18	NUM
ejpam-5776	420	8	(	(	PUNCT
ejpam-5776	420	9	2	2	NUM
ejpam-5776	420	10	)	)	PUNCT
ejpam-5776	420	11	(	(	PUNCT
ejpam-5776	420	12	2025	2025	NUM
ejpam-5776	420	13	)	)	PUNCT
ejpam-5776	420	14	,	,	PUNCT
ejpam-5776	420	15	5776	5776	NUM
ejpam-5776	420	16	11	11	NUM
ejpam-5776	420	17	of	of	ADP
ejpam-5776	420	18	13	13	NUM
ejpam-5776	420	19	(	(	PUNCT
ejpam-5776	420	20	d	d	NOUN
ejpam-5776	420	21	)	)	PUNCT
ejpam-5776	420	22	for	for	ADP
ejpam-5776	420	23	n	n	NUM
ejpam-5776	420	24	−	−	PROPN
ejpam-5776	420	25	1	1	NUM
ejpam-5776	420	26	≤	≤	PUNCT
ejpam-5776	421	1	i	i	PRON
ejpam-5776	421	2	,	,	PUNCT
ejpam-5776	421	3	j	j	PROPN
ejpam-5776	421	4	≤	≤	PROPN
ejpam-5776	421	5	n	n	PRON
ejpam-5776	421	6	+	+	CCONJ
ejpam-5776	421	7	n	n	NUM
ejpam-5776	421	8	2	2	NUM
ejpam-5776	421	9	−	−	NUM
ejpam-5776	421	10	2	2	NUM
ejpam-5776	421	11	,	,	PUNCT
ejpam-5776	421	12	n	n	PROPN
ejpam-5776	421	13	+	+	CCONJ
ejpam-5776	421	14	n	n	NUM
ejpam-5776	421	15	2	2	NUM
ejpam-5776	421	16	−	−	PROPN
ejpam-5776	421	17	2	2	NUM
ejpam-5776	421	18	≤	≤	NOUN
ejpam-5776	421	19	i	i	PRON
ejpam-5776	421	20	,	,	PUNCT
ejpam-5776	421	21	j	j	PROPN
ejpam-5776	421	22	≤	≤	PROPN
ejpam-5776	421	23	2n	2n	NUM
ejpam-5776	421	24	−	−	ADP
ejpam-5776	421	25	2	2	NUM
ejpam-5776	421	26	,	,	PUNCT
ejpam-5776	421	27	and	and	CCONJ
ejpam-5776	421	28	i	i	PRON
ejpam-5776	421	29	̸=	̸=	PROPN
ejpam-5776	421	30	j	j	PROPN
ejpam-5776	421	31	,	,	PUNCT
ejpam-5776	421	32	aij	aij	PROPN
ejpam-5776	421	33	=	=	SYM
ejpam-5776	421	34	1	1	NUM
ejpam-5776	421	35	4	4	NUM
ejpam-5776	421	36	(	(	PUNCT
ejpam-5776	421	37	2(n−	2(n−	NUM
ejpam-5776	421	38	2	2	NUM
ejpam-5776	421	39	)	)	PUNCT
ejpam-5776	421	40	+	+	CCONJ
ejpam-5776	421	41	2(n−	2(n−	NUM
ejpam-5776	421	42	2	2	NUM
ejpam-5776	421	43	)	)	PUNCT
ejpam-5776	421	44	+	+	CCONJ
ejpam-5776	421	45	2	2	NUM
ejpam-5776	421	46	+	+	CCONJ
ejpam-5776	421	47	2	2	NUM
ejpam-5776	421	48	)	)	PUNCT
ejpam-5776	421	49	=	=	SYM
ejpam-5776	421	50	n−	n−	NOUN
ejpam-5776	421	51	1	1	NUM
ejpam-5776	421	52	;	;	PUNCT
ejpam-5776	421	53	(	(	PUNCT
ejpam-5776	421	54	e	e	NOUN
ejpam-5776	421	55	)	)	PUNCT
ejpam-5776	421	56	for	for	ADP
ejpam-5776	421	57	i	i	PROPN
ejpam-5776	421	58	=	=	SYM
ejpam-5776	421	59	j	j	PROPN
ejpam-5776	421	60	,	,	PUNCT
ejpam-5776	421	61	j	j	X
ejpam-5776	421	62	=	=	PUNCT
ejpam-5776	421	63	n−	n−	NOUN
ejpam-5776	421	64	2	2	NUM
ejpam-5776	421	65	+	+	CCONJ
ejpam-5776	421	66	n	n	PRON
ejpam-5776	421	67	2	2	NUM
ejpam-5776	422	1	+	+	CCONJ
ejpam-5776	423	1	i	i	PRON
ejpam-5776	423	2	,	,	PUNCT
ejpam-5776	423	3	i	i	PRON
ejpam-5776	423	4	=	=	VERB
ejpam-5776	423	5	n−	n−	NOUN
ejpam-5776	423	6	2	2	NUM
ejpam-5776	423	7	+	+	CCONJ
ejpam-5776	423	8	n	n	CCONJ
ejpam-5776	423	9	2	2	NUM
ejpam-5776	423	10	+	+	CCONJ
ejpam-5776	423	11	j	j	PROPN
ejpam-5776	423	12	,	,	PUNCT
ejpam-5776	423	13	aij	aij	PROPN
ejpam-5776	423	14	=	=	SYM
ejpam-5776	423	15	0	0	PROPN
ejpam-5776	423	16	.	.	PUNCT
ejpam-5776	424	1	thus	thus	ADV
ejpam-5776	424	2	,	,	PUNCT
ejpam-5776	424	3	ade(ωd2n	ade(ωd2n	NOUN
ejpam-5776	424	4	)	)	PUNCT
ejpam-5776	425	1	=	=	PUNCT
ejpam-5776	425	2	a	a	PRON
ejpam-5776	425	3	.	.	PUNCT
ejpam-5776	425	4	.	.	PUNCT
ejpam-5776	425	5	.	.	PUNCT
ejpam-5776	426	1	an−1	an−1	PROPN
ejpam-5776	426	2	b	b	PROPN
ejpam-5776	426	3	.	.	PUNCT
ejpam-5776	426	4	.	.	PUNCT
ejpam-5776	426	5	.	.	PUNCT
ejpam-5776	427	1	a	a	DET
ejpam-5776	427	2	n	n	NOUN
ejpam-5776	427	3	2	2	NUM
ejpam-5776	427	4	−1b	−1b	X
ejpam-5776	427	5	a	a	PRON
ejpam-5776	427	6	n	n	NUM
ejpam-5776	427	7	2	2	NUM
ejpam-5776	427	8	b	b	NOUN
ejpam-5776	427	9	.	.	PUNCT
ejpam-5776	427	10	.	.	PUNCT
ejpam-5776	427	11	.	.	PUNCT
ejpam-5776	428	1	an−1b	an−1b	PROPN
ejpam-5776	428	2			PROPN
ejpam-5776	429	1	a	a	DET
ejpam-5776	429	2	0	0	NUM
ejpam-5776	429	3	.	.	PUNCT
ejpam-5776	429	4	.	.	PUNCT
ejpam-5776	430	1	.	.	PUNCT
ejpam-5776	431	1	0	0	NUM
ejpam-5776	432	1	3n	3n	NUM
ejpam-5776	432	2	4	4	NUM
ejpam-5776	432	3	.	.	PUNCT
ejpam-5776	432	4	.	.	PUNCT
ejpam-5776	432	5	.	.	PUNCT
ejpam-5776	433	1	3n	3n	NUM
ejpam-5776	433	2	4	4	NUM
ejpam-5776	433	3	3n	3n	NUM
ejpam-5776	433	4	4	4	NUM
ejpam-5776	433	5	.	.	PUNCT
ejpam-5776	433	6	.	.	PUNCT
ejpam-5776	433	7	.	.	PUNCT
ejpam-5776	434	1	3n	3n	NUM
ejpam-5776	434	2	4	4	NUM
ejpam-5776	434	3	...	...	PUNCT
ejpam-5776	434	4	...	...	PUNCT
ejpam-5776	434	5	.	.	PUNCT
ejpam-5776	434	6	.	.	PUNCT
ejpam-5776	434	7	.	.	PUNCT
ejpam-5776	435	1	...	...	PUNCT
ejpam-5776	435	2	...	...	PUNCT
ejpam-5776	435	3	.	.	PUNCT
ejpam-5776	435	4	.	.	PUNCT
ejpam-5776	436	1	.	.	PUNCT
ejpam-5776	437	1	...	...	PUNCT
ejpam-5776	438	1	...	...	PUNCT
ejpam-5776	439	1	.	.	PUNCT
ejpam-5776	440	1	.	.	PUNCT
ejpam-5776	441	1	.	.	PUNCT
ejpam-5776	442	1	...	...	PUNCT
ejpam-5776	443	1	an−1	an−1	ADJ
ejpam-5776	443	2	0	0	NUM
ejpam-5776	443	3	.	.	PUNCT
ejpam-5776	443	4	.	.	PUNCT
ejpam-5776	443	5	.	.	PUNCT
ejpam-5776	444	1	0	0	NUM
ejpam-5776	445	1	3n	3n	NUM
ejpam-5776	445	2	4	4	NUM
ejpam-5776	445	3	.	.	PUNCT
ejpam-5776	445	4	.	.	PUNCT
ejpam-5776	445	5	.	.	PUNCT
ejpam-5776	446	1	3n	3n	NUM
ejpam-5776	446	2	4	4	NUM
ejpam-5776	446	3	3n	3n	NUM
ejpam-5776	446	4	4	4	NUM
ejpam-5776	446	5	.	.	PUNCT
ejpam-5776	446	6	.	.	PUNCT
ejpam-5776	446	7	.	.	PUNCT
ejpam-5776	447	1	3n	3n	NUM
ejpam-5776	447	2	4	4	NUM
ejpam-5776	447	3	b	b	NOUN
ejpam-5776	447	4	3n	3n	NUM
ejpam-5776	447	5	4	4	NUM
ejpam-5776	447	6	.	.	PUNCT
ejpam-5776	447	7	.	.	PUNCT
ejpam-5776	447	8	.	.	PUNCT
ejpam-5776	448	1	3n	3n	NUM
ejpam-5776	448	2	4	4	NUM
ejpam-5776	448	3	0	0	NUM
ejpam-5776	448	4	.	.	PUNCT
ejpam-5776	448	5	.	.	PUNCT
ejpam-5776	448	6	.	.	PUNCT
ejpam-5776	449	1	n−	n−	NOUN
ejpam-5776	449	2	1	1	NUM
ejpam-5776	449	3	0	0	NUM
ejpam-5776	449	4	.	.	PUNCT
ejpam-5776	449	5	.	.	PUNCT
ejpam-5776	449	6	.	.	PUNCT
ejpam-5776	450	1	n−	n−	NOUN
ejpam-5776	450	2	1	1	NUM
ejpam-5776	450	3	...	...	PUNCT
ejpam-5776	450	4	...	...	PUNCT
ejpam-5776	450	5	.	.	PUNCT
ejpam-5776	450	6	.	.	PUNCT
ejpam-5776	450	7	.	.	PUNCT
ejpam-5776	451	1	...	...	PUNCT
ejpam-5776	451	2	...	...	PUNCT
ejpam-5776	451	3	.	.	PUNCT
ejpam-5776	451	4	.	.	PUNCT
ejpam-5776	452	1	.	.	PUNCT
ejpam-5776	453	1	...	...	PUNCT
ejpam-5776	454	1	...	...	PUNCT
ejpam-5776	455	1	.	.	PUNCT
ejpam-5776	456	1	.	.	PUNCT
ejpam-5776	457	1	.	.	PUNCT
ejpam-5776	458	1	...	...	PUNCT
ejpam-5776	459	1	a	a	DET
ejpam-5776	459	2	n	n	NOUN
ejpam-5776	459	3	2	2	NUM
ejpam-5776	459	4	−1b	−1b	NUM
ejpam-5776	459	5	3n	3n	NUM
ejpam-5776	459	6	4	4	NUM
ejpam-5776	459	7	.	.	PUNCT
ejpam-5776	459	8	.	.	PUNCT
ejpam-5776	459	9	.	.	PUNCT
ejpam-5776	460	1	3n	3n	NUM
ejpam-5776	460	2	4	4	NUM
ejpam-5776	460	3	n−	n−	NOUN
ejpam-5776	460	4	1	1	NUM
ejpam-5776	460	5	.	.	PUNCT
ejpam-5776	460	6	.	.	PUNCT
ejpam-5776	461	1	.	.	PUNCT
ejpam-5776	462	1	0	0	NUM
ejpam-5776	463	1	n−	n−	NOUN
ejpam-5776	463	2	1	1	NUM
ejpam-5776	463	3	.	.	PUNCT
ejpam-5776	463	4	.	.	PUNCT
ejpam-5776	464	1	.	.	PUNCT
ejpam-5776	464	2	0	0	PUNCT
ejpam-5776	465	1	a	a	PRON
ejpam-5776	465	2	n	n	NUM
ejpam-5776	465	3	2	2	NUM
ejpam-5776	465	4	b	b	NOUN
ejpam-5776	465	5	3n	3n	NUM
ejpam-5776	465	6	4	4	NUM
ejpam-5776	465	7	.	.	PUNCT
ejpam-5776	465	8	.	.	PUNCT
ejpam-5776	465	9	.	.	PUNCT
ejpam-5776	466	1	3n	3n	NUM
ejpam-5776	466	2	4	4	NUM
ejpam-5776	466	3	0	0	NUM
ejpam-5776	466	4	.	.	PUNCT
ejpam-5776	466	5	.	.	PUNCT
ejpam-5776	466	6	.	.	PUNCT
ejpam-5776	467	1	n−	n−	NOUN
ejpam-5776	467	2	1	1	NUM
ejpam-5776	467	3	0	0	NUM
ejpam-5776	467	4	.	.	PUNCT
ejpam-5776	467	5	.	.	PUNCT
ejpam-5776	467	6	.	.	PUNCT
ejpam-5776	468	1	n−	n−	NOUN
ejpam-5776	468	2	1	1	NUM
ejpam-5776	468	3	...	...	PUNCT
ejpam-5776	468	4	...	...	PUNCT
ejpam-5776	468	5	.	.	PUNCT
ejpam-5776	468	6	.	.	PUNCT
ejpam-5776	468	7	.	.	PUNCT
ejpam-5776	469	1	...	...	PUNCT
ejpam-5776	469	2	...	...	PUNCT
ejpam-5776	469	3	.	.	PUNCT
ejpam-5776	469	4	.	.	PUNCT
ejpam-5776	470	1	.	.	PUNCT
ejpam-5776	471	1	...	...	PUNCT
ejpam-5776	472	1	...	...	PUNCT
ejpam-5776	473	1	.	.	PUNCT
ejpam-5776	474	1	.	.	PUNCT
ejpam-5776	475	1	.	.	PUNCT
ejpam-5776	476	1	...	...	PUNCT
ejpam-5776	477	1	an−1b	an−1b	PUNCT
ejpam-5776	477	2	3n	3n	NUM
ejpam-5776	477	3	4	4	NUM
ejpam-5776	477	4	.	.	PUNCT
ejpam-5776	477	5	.	.	PUNCT
ejpam-5776	477	6	.	.	PUNCT
ejpam-5776	478	1	3n	3n	NUM
ejpam-5776	478	2	4	4	NUM
ejpam-5776	478	3	n−	n−	NOUN
ejpam-5776	478	4	1	1	NUM
ejpam-5776	478	5	.	.	PUNCT
ejpam-5776	478	6	.	.	PUNCT
ejpam-5776	479	1	.	.	PUNCT
ejpam-5776	480	1	0	0	NUM
ejpam-5776	481	1	n−	n−	NOUN
ejpam-5776	481	2	1	1	NUM
ejpam-5776	481	3	.	.	PUNCT
ejpam-5776	481	4	.	.	PUNCT
ejpam-5776	481	5	.	.	PUNCT
ejpam-5776	482	1	0	0	PUNCT
ejpam-5776	482	2	.	.	PUNCT
ejpam-5776	483	1	in	in	ADP
ejpam-5776	483	2	other	other	ADJ
ejpam-5776	483	3	words	word	NOUN
ejpam-5776	483	4	,	,	PUNCT
ejpam-5776	483	5	ade(ωd2n	ade(ωd2n	NOUN
ejpam-5776	483	6	)	)	PUNCT
ejpam-5776	483	7	is	be	AUX
ejpam-5776	483	8	as	as	SCONJ
ejpam-5776	483	9	follows	follow	VERB
ejpam-5776	483	10	:	:	PUNCT
ejpam-5776	483	11	ade(ωd2n	ade(ωd2n	NOUN
ejpam-5776	483	12	)	)	PUNCT
ejpam-5776	484	1	=	=	PRON
ejpam-5776	485	1			X
ejpam-5776	485	2	0n−2	0n−2	NOUN
ejpam-5776	485	3	3n	3n	NUM
ejpam-5776	485	4	4	4	NUM
ejpam-5776	485	5	j(n−2)×n	j(n−2)×n	SYM
ejpam-5776	485	6	2	2	NUM
ejpam-5776	485	7	3n	3n	NUM
ejpam-5776	485	8	4	4	NUM
ejpam-5776	485	9	j(n−2)×n	j(n−2)×n	SYM
ejpam-5776	485	10	2	2	NUM
ejpam-5776	485	11	3n	3n	NUM
ejpam-5776	485	12	4	4	NUM
ejpam-5776	485	13	jn	jn	PROPN
ejpam-5776	485	14	2	2	NUM
ejpam-5776	485	15	×(n−2	×(n−2	PROPN
ejpam-5776	485	16	)	)	PUNCT
ejpam-5776	485	17	(	(	PUNCT
ejpam-5776	485	18	n−	n−	NOUN
ejpam-5776	485	19	1)(j	1)(j	NUM
ejpam-5776	485	20	−	−	NOUN
ejpam-5776	485	21	i)n	i)n	NOUN
ejpam-5776	485	22	2	2	NUM
ejpam-5776	485	23	(	(	PUNCT
ejpam-5776	485	24	n−	n−	NOUN
ejpam-5776	485	25	1)(j	1)(j	NUM
ejpam-5776	485	26	−	−	NOUN
ejpam-5776	485	27	i)n	i)n	NOUN
ejpam-5776	485	28	2	2	NUM
ejpam-5776	485	29	3n	3n	NUM
ejpam-5776	485	30	4	4	NUM
ejpam-5776	485	31	jn	jn	PROPN
ejpam-5776	485	32	2	2	NUM
ejpam-5776	485	33	×(n−2	×(n−2	PROPN
ejpam-5776	485	34	)	)	PUNCT
ejpam-5776	485	35	(	(	PUNCT
ejpam-5776	485	36	n−	n−	NOUN
ejpam-5776	485	37	1)(j	1)(j	NUM
ejpam-5776	485	38	−	−	NOUN
ejpam-5776	485	39	i)n	i)n	NOUN
ejpam-5776	485	40	2	2	NUM
ejpam-5776	485	41	(	(	PUNCT
ejpam-5776	485	42	n−	n−	NOUN
ejpam-5776	485	43	1)(j	1)(j	NUM
ejpam-5776	485	44	−	−	NOUN
ejpam-5776	485	45	i)n	i)n	NOUN
ejpam-5776	485	46	2	2	NUM
ejpam-5776	485	47			NOUN
ejpam-5776	485	48	.	.	PUNCT
ejpam-5776	486	1	based	base	VERB
ejpam-5776	486	2	on	on	ADP
ejpam-5776	486	3	theorem	theorem	NOUN
ejpam-5776	486	4	4	4	NUM
ejpam-5776	486	5	with	with	ADP
ejpam-5776	486	6	a	a	DET
ejpam-5776	486	7	=	=	SYM
ejpam-5776	486	8	b	b	NOUN
ejpam-5776	486	9	=	=	SYM
ejpam-5776	486	10	0	0	NUM
ejpam-5776	486	11	,	,	PUNCT
ejpam-5776	486	12	c	c	NOUN
ejpam-5776	486	13	=	=	SYM
ejpam-5776	486	14	3n	3n	NUM
ejpam-5776	486	15	4	4	NUM
ejpam-5776	486	16	,	,	PUNCT
ejpam-5776	486	17	d	d	NOUN
ejpam-5776	486	18	=	=	PUNCT
ejpam-5776	486	19	n−	n−	NOUN
ejpam-5776	486	20	1	1	NUM
ejpam-5776	486	21	,	,	PUNCT
ejpam-5776	486	22	then	then	ADV
ejpam-5776	486	23	pade(ωd2n	pade(ωd2n	PROPN
ejpam-5776	486	24	)	)	PUNCT
ejpam-5776	486	25	(	(	PUNCT
ejpam-5776	486	26	µ	µ	NOUN
ejpam-5776	486	27	)	)	PUNCT
ejpam-5776	486	28	=	=	SYM
ejpam-5776	486	29	µ	µ	DET
ejpam-5776	486	30	3(n−2	3(n−2	NUM
ejpam-5776	486	31	)	)	PUNCT
ejpam-5776	486	32	2	2	NUM
ejpam-5776	486	33	(	(	PUNCT
ejpam-5776	486	34	µ+	µ+	X
ejpam-5776	486	35	2(n−	2(n−	NUM
ejpam-5776	486	36	1	1	NUM
ejpam-5776	486	37	)	)	PUNCT
ejpam-5776	486	38	)	)	PUNCT
ejpam-5776	486	39	n	n	PRON
ejpam-5776	486	40	2	2	NUM
ejpam-5776	486	41	−1	−1	NOUN
ejpam-5776	486	42	(	(	PUNCT
ejpam-5776	486	43	µ2	µ2	PROPN
ejpam-5776	486	44	−	−	PROPN
ejpam-5776	486	45	(	(	PUNCT
ejpam-5776	486	46	n−	n−	NOUN
ejpam-5776	486	47	1)(n−	1)(n−	NUM
ejpam-5776	486	48	2)µ−	2)µ−	NUM
ejpam-5776	486	49	9n2	9n2	NUM
ejpam-5776	486	50	16	16	NUM
ejpam-5776	486	51	n(n−	n(n−	NOUN
ejpam-5776	486	52	2	2	NUM
ejpam-5776	486	53	)	)	PUNCT
ejpam-5776	486	54	)	)	PUNCT
ejpam-5776	486	55	.	.	PUNCT
ejpam-5776	487	1	the	the	DET
ejpam-5776	487	2	eigenvalues	eigenvalue	NOUN
ejpam-5776	487	3	of	of	ADP
ejpam-5776	487	4	ωd2n	ωd2n	PROPN
ejpam-5776	487	5	are	be	AUX
ejpam-5776	487	6	µ1	µ1	NOUN
ejpam-5776	487	7	=	=	SYM
ejpam-5776	487	8	0	0	NUM
ejpam-5776	487	9	of	of	ADP
ejpam-5776	487	10	multiplicity	multiplicity	NOUN
ejpam-5776	487	11	3(n−2	3(n−2	PROPN
ejpam-5776	487	12	)	)	PUNCT
ejpam-5776	487	13	2	2	NUM
ejpam-5776	487	14	,	,	PUNCT
ejpam-5776	487	15	µ2	µ2	PROPN
ejpam-5776	487	16	=	=	PUNCT
ejpam-5776	487	17	−2(n	−2(n	VERB
ejpam-5776	487	18	−	−	PROPN
ejpam-5776	487	19	1	1	NUM
ejpam-5776	487	20	)	)	PUNCT
ejpam-5776	487	21	of	of	ADP
ejpam-5776	487	22	multiplicity	multiplicity	NOUN
ejpam-5776	487	23	n	n	CCONJ
ejpam-5776	487	24	2	2	NUM
ejpam-5776	487	25	−	−	NUM
ejpam-5776	487	26	1	1	NUM
ejpam-5776	487	27	,	,	PUNCT
ejpam-5776	487	28	and	and	CCONJ
ejpam-5776	487	29	µ3,4	µ3,4	ADJ
ejpam-5776	487	30	=	=	SYM
ejpam-5776	487	31	1	1	NUM
ejpam-5776	487	32	2	2	NUM
ejpam-5776	487	33	(	(	PUNCT
ejpam-5776	487	34	(	(	PUNCT
ejpam-5776	487	35	n−	n−	NOUN
ejpam-5776	487	36	2)(n−	2)(n−	NUM
ejpam-5776	487	37	1)±	1)±	NUM
ejpam-5776	487	38	√	√	NUM
ejpam-5776	487	39	(	(	PUNCT
ejpam-5776	487	40	n−	n−	NOUN
ejpam-5776	487	41	2)2(n−	2)2(n−	NUM
ejpam-5776	487	42	1)2	1)2	NUM
ejpam-5776	488	1	+	+	CCONJ
ejpam-5776	488	2	9	9	NUM
ejpam-5776	488	3	4n	4n	NOUN
ejpam-5776	488	4	3(n−	3(n−	NUM
ejpam-5776	488	5	2	2	NUM
ejpam-5776	488	6	)	)	PUNCT
ejpam-5776	488	7	)	)	PUNCT
ejpam-5776	488	8	.	.	PUNCT
ejpam-5776	489	1	therefore	therefore	ADV
ejpam-5776	489	2	,	,	PUNCT
ejpam-5776	489	3	the	the	DET
ejpam-5776	489	4	adespectral	adespectral	ADJ
ejpam-5776	489	5	radius	radius	NOUN
ejpam-5776	489	6	of	of	ADP
ejpam-5776	489	7	ωd2n	ωd2n	PROPN
ejpam-5776	489	8	is	be	AUX
ejpam-5776	489	9	ρade(ωd2n	ρade(ωd2n	PROPN
ejpam-5776	489	10	)	)	PUNCT
ejpam-5776	490	1	=	=	SYM
ejpam-5776	490	2	1	1	NUM
ejpam-5776	490	3	2	2	NUM
ejpam-5776	490	4	(	(	PUNCT
ejpam-5776	490	5	(	(	PUNCT
ejpam-5776	490	6	n−	n−	NOUN
ejpam-5776	490	7	2)(n−	2)(n−	NUM
ejpam-5776	490	8	1	1	NUM
ejpam-5776	490	9	)	)	PUNCT
ejpam-5776	490	10	+	+	CCONJ
ejpam-5776	490	11	√	√	INTJ
ejpam-5776	490	12	(	(	PUNCT
ejpam-5776	490	13	n−	n−	NOUN
ejpam-5776	490	14	2)2(n−	2)2(n−	NUM
ejpam-5776	490	15	1)2	1)2	NUM
ejpam-5776	490	16	+	+	CCONJ
ejpam-5776	490	17	9	9	NUM
ejpam-5776	490	18	4	4	NUM
ejpam-5776	490	19	n3(n−	n3(n−	NOUN
ejpam-5776	490	20	2	2	NUM
ejpam-5776	490	21	)	)	PUNCT
ejpam-5776	490	22	)	)	PUNCT
ejpam-5776	490	23	.	.	PUNCT
ejpam-5776	491	1	theorem	theorem	VERB
ejpam-5776	491	2	9	9	NUM
ejpam-5776	491	3	.	.	PUNCT
ejpam-5776	492	1	in	in	ADP
ejpam-5776	492	2	ωd2n	ωd2n	PROPN
ejpam-5776	492	3	,	,	PUNCT
ejpam-5776	492	4	the	the	DET
ejpam-5776	492	5	average	average	ADJ
ejpam-5776	492	6	degree	degree	NOUN
ejpam-5776	492	7	-	-	PUNCT
ejpam-5776	492	8	eccentricity	eccentricity	NOUN
ejpam-5776	492	9	energy	energy	NOUN
ejpam-5776	492	10	of	of	ADP
ejpam-5776	492	11	ωd2n	ωd2n	PROPN
ejpam-5776	492	12	is	be	AUX
ejpam-5776	492	13	εade(ωd2n	εade(ωd2n	PROPN
ejpam-5776	492	14	)	)	PUNCT
ejpam-5776	493	1	=	=	PUNCT
ejpam-5776	493	2			PUNCT
ejpam-5776	493	3	(	(	PUNCT
ejpam-5776	493	4	n−	n−	NOUN
ejpam-5776	493	5	1	1	NUM
ejpam-5776	493	6	)	)	PUNCT
ejpam-5776	493	7	(	(	PUNCT
ejpam-5776	493	8	n−	n−	NOUN
ejpam-5776	493	9	1	1	NUM
ejpam-5776	493	10	2	2	NUM
ejpam-5776	493	11	)	)	PUNCT
ejpam-5776	493	12	+	+	CCONJ
ejpam-5776	493	13	√	√	INTJ
ejpam-5776	493	14	(	(	PUNCT
ejpam-5776	493	15	n−	n−	NOUN
ejpam-5776	493	16	1)2	1)2	NUM
ejpam-5776	493	17	(	(	PUNCT
ejpam-5776	493	18	n−	n−	NOUN
ejpam-5776	493	19	1	1	NUM
ejpam-5776	493	20	2	2	NUM
ejpam-5776	493	21	)	)	PUNCT
ejpam-5776	493	22	2	2	NUM
ejpam-5776	493	23	+	+	SYM
ejpam-5776	493	24	1	1	NUM
ejpam-5776	493	25	4n(n−	4n(n−	NUM
ejpam-5776	493	26	1)(3n+	1)(3n+	NUM
ejpam-5776	494	1	1)2	1)2	NUM
ejpam-5776	494	2	,	,	PUNCT
ejpam-5776	494	3	if	if	SCONJ
ejpam-5776	494	4	n	n	PRON
ejpam-5776	494	5	is	be	AUX
ejpam-5776	494	6	odd	odd	ADJ
ejpam-5776	494	7	(	(	PUNCT
ejpam-5776	494	8	n−	n−	NOUN
ejpam-5776	494	9	2)(n−	2)(n−	NUM
ejpam-5776	494	10	1	1	NUM
ejpam-5776	494	11	)	)	PUNCT
ejpam-5776	495	1	+	+	CCONJ
ejpam-5776	495	2	√	√	INTJ
ejpam-5776	495	3	(	(	PUNCT
ejpam-5776	495	4	n−	n−	NOUN
ejpam-5776	495	5	2)2(n−	2)2(n−	NUM
ejpam-5776	496	1	1)2	1)2	NUM
ejpam-5776	496	2	+	+	CCONJ
ejpam-5776	496	3	9	9	NUM
ejpam-5776	496	4	4n	4n	NOUN
ejpam-5776	496	5	3(n−	3(n−	NUM
ejpam-5776	496	6	2	2	NUM
ejpam-5776	496	7	)	)	PUNCT
ejpam-5776	496	8	,	,	PUNCT
ejpam-5776	496	9	if	if	SCONJ
ejpam-5776	496	10	n	n	PRON
ejpam-5776	496	11	is	be	AUX
ejpam-5776	496	12	even	even	ADV
ejpam-5776	496	13	.	.	PUNCT
ejpam-5776	497	1	proof	proof	NOUN
ejpam-5776	497	2	.	.	PUNCT
ejpam-5776	498	1	m.	m.	NOUN
ejpam-5776	498	2	u.	u.	PROPN
ejpam-5776	498	3	romdhini	romdhini	PROPN
ejpam-5776	498	4	et	et	PROPN
ejpam-5776	498	5	al	al	PROPN
ejpam-5776	498	6	.	.	PUNCT
ejpam-5776	498	7	/	/	SYM
ejpam-5776	498	8	eur	eur	PROPN
ejpam-5776	498	9	.	.	PUNCT
ejpam-5776	499	1	j.	j.	PROPN
ejpam-5776	499	2	pure	pure	PROPN
ejpam-5776	499	3	appl	appl	PROPN
ejpam-5776	499	4	.	.	PROPN
ejpam-5776	499	5	math	math	PROPN
ejpam-5776	499	6	,	,	PUNCT
ejpam-5776	499	7	18	18	NUM
ejpam-5776	499	8	(	(	PUNCT
ejpam-5776	499	9	2	2	NUM
ejpam-5776	499	10	)	)	PUNCT
ejpam-5776	499	11	(	(	PUNCT
ejpam-5776	499	12	2025	2025	NUM
ejpam-5776	499	13	)	)	PUNCT
ejpam-5776	499	14	,	,	PUNCT
ejpam-5776	499	15	5776	5776	NUM
ejpam-5776	499	16	12	12	NUM
ejpam-5776	499	17	of	of	ADP
ejpam-5776	499	18	13	13	NUM
ejpam-5776	499	19	(	(	PUNCT
ejpam-5776	499	20	i	i	NOUN
ejpam-5776	499	21	)	)	PUNCT
ejpam-5776	499	22	let	let	VERB
ejpam-5776	499	23	n	n	PRON
ejpam-5776	499	24	be	be	AUX
ejpam-5776	499	25	odd	odd	ADJ
ejpam-5776	499	26	.	.	PUNCT
ejpam-5776	500	1	based	base	VERB
ejpam-5776	500	2	on	on	ADP
ejpam-5776	500	3	theorems	theorem	NOUN
ejpam-5776	500	4	8	8	NUM
ejpam-5776	500	5	,	,	PUNCT
ejpam-5776	500	6	the	the	DET
ejpam-5776	500	7	ade	ade	NOUN
ejpam-5776	500	8	-	-	PUNCT
ejpam-5776	500	9	energy	energy	NOUN
ejpam-5776	500	10	of	of	ADP
ejpam-5776	500	11	ωd2n	ωd2n	PROPN
ejpam-5776	500	12	is	be	AUX
ejpam-5776	500	13	εade(ωd2n	εade(ωd2n	PROPN
ejpam-5776	500	14	)	)	PUNCT
ejpam-5776	501	1	=	=	PUNCT
ejpam-5776	501	2	(	(	PUNCT
ejpam-5776	501	3	n−	n−	NOUN
ejpam-5776	501	4	2	2	NUM
ejpam-5776	501	5	)	)	PUNCT
ejpam-5776	501	6	|0|+	|0|+	PROPN
ejpam-5776	501	7	(	(	PUNCT
ejpam-5776	501	8	n−	n−	NOUN
ejpam-5776	501	9	1	1	NUM
ejpam-5776	501	10	)	)	PUNCT
ejpam-5776	501	11	∣∣∣∣12	∣∣∣∣12	NOUN
ejpam-5776	501	12	−	−	PROPN
ejpam-5776	501	13	n	n	NUM
ejpam-5776	501	14	∣∣∣∣+∣∣∣∣∣∣12	∣∣∣∣+∣∣∣∣∣∣12	NOUN
ejpam-5776	501	15	(n−	(n−	NUM
ejpam-5776	501	16	1	1	NUM
ejpam-5776	501	17	)	)	PUNCT
ejpam-5776	501	18	(	(	PUNCT
ejpam-5776	501	19	n−	n−	NOUN
ejpam-5776	501	20	1	1	NUM
ejpam-5776	501	21	2	2	NUM
ejpam-5776	501	22	)	)	PUNCT
ejpam-5776	501	23	±	±	NOUN
ejpam-5776	501	24	√	√	NUM
ejpam-5776	501	25	(	(	PUNCT
ejpam-5776	501	26	n−	n−	PROPN
ejpam-5776	501	27	1)2	1)2	NUM
ejpam-5776	501	28	(	(	PUNCT
ejpam-5776	501	29	n−	n−	NOUN
ejpam-5776	501	30	1	1	NUM
ejpam-5776	501	31	2	2	NUM
ejpam-5776	501	32	)	)	PUNCT
ejpam-5776	501	33	2	2	NUM
ejpam-5776	501	34	+	+	CCONJ
ejpam-5776	501	35	1	1	NUM
ejpam-5776	501	36	4	4	NUM
ejpam-5776	501	37	n(n−	n(n−	NOUN
ejpam-5776	501	38	1)(3n+	1)(3n+	PROPN
ejpam-5776	502	1	1)2	1)2	NUM
ejpam-5776	502	2	∣∣∣∣∣∣	∣∣∣∣∣∣	PUNCT
ejpam-5776	502	3	=(	=(	ADJ
ejpam-5776	502	4	n−	n−	PROPN
ejpam-5776	502	5	1	1	NUM
ejpam-5776	502	6	)	)	PUNCT
ejpam-5776	502	7	(	(	PUNCT
ejpam-5776	502	8	n−	n−	NOUN
ejpam-5776	502	9	1	1	NUM
ejpam-5776	502	10	2	2	NUM
ejpam-5776	502	11	)	)	PUNCT
ejpam-5776	503	1	+	+	CCONJ
ejpam-5776	503	2	√	√	INTJ
ejpam-5776	503	3	(	(	PUNCT
ejpam-5776	503	4	n−	n−	NOUN
ejpam-5776	503	5	1)2	1)2	NUM
ejpam-5776	503	6	(	(	PUNCT
ejpam-5776	503	7	n−	n−	NOUN
ejpam-5776	503	8	1	1	NUM
ejpam-5776	503	9	2	2	NUM
ejpam-5776	503	10	)	)	PUNCT
ejpam-5776	503	11	2	2	NUM
ejpam-5776	503	12	+	+	CCONJ
ejpam-5776	503	13	1	1	NUM
ejpam-5776	503	14	4	4	NUM
ejpam-5776	503	15	n(n−	n(n−	NOUN
ejpam-5776	503	16	1)(3n+	1)(3n+	NOUN
ejpam-5776	503	17	1)2	1)2	NUM
ejpam-5776	503	18	.	.	PUNCT
ejpam-5776	504	1	(	(	PUNCT
ejpam-5776	504	2	ii	ii	NOUN
ejpam-5776	504	3	)	)	PUNCT
ejpam-5776	504	4	let	let	VERB
ejpam-5776	504	5	n	n	PRON
ejpam-5776	504	6	be	be	AUX
ejpam-5776	504	7	even	even	ADV
ejpam-5776	504	8	.	.	PUNCT
ejpam-5776	505	1	based	base	VERB
ejpam-5776	505	2	on	on	ADP
ejpam-5776	505	3	theorem	theorem	NOUN
ejpam-5776	505	4	8	8	NUM
ejpam-5776	505	5	,	,	PUNCT
ejpam-5776	505	6	the	the	DET
ejpam-5776	505	7	ade	ade	NOUN
ejpam-5776	505	8	-	-	PUNCT
ejpam-5776	505	9	energy	energy	NOUN
ejpam-5776	505	10	of	of	ADP
ejpam-5776	505	11	ωd2n	ωd2n	PROPN
ejpam-5776	505	12	is	be	AUX
ejpam-5776	505	13	εade(ωd2n	εade(ωd2n	PROPN
ejpam-5776	505	14	)	)	PUNCT
ejpam-5776	506	1	=	=	PRON
ejpam-5776	506	2	(	(	PUNCT
ejpam-5776	506	3	3(n−	3(n−	NUM
ejpam-5776	506	4	2	2	NUM
ejpam-5776	506	5	)	)	SYM
ejpam-5776	506	6	2	2	NUM
ejpam-5776	506	7	)	)	PUNCT
ejpam-5776	506	8	|0|+	|0|+	PROPN
ejpam-5776	506	9	(	(	PUNCT
ejpam-5776	506	10	n	n	NOUN
ejpam-5776	506	11	2	2	NUM
ejpam-5776	506	12	−	−	NOUN
ejpam-5776	506	13	1	1	NUM
ejpam-5776	506	14	)	)	PUNCT
ejpam-5776	506	15	|−2(n−	|−2(n−	X
ejpam-5776	506	16	1)|+∣∣∣∣∣12	1)|+∣∣∣∣∣12	NOUN
ejpam-5776	506	17	(	(	PUNCT
ejpam-5776	506	18	(	(	PUNCT
ejpam-5776	506	19	n−	n−	NOUN
ejpam-5776	506	20	2)(n−	2)(n−	NUM
ejpam-5776	506	21	1)±	1)±	NUM
ejpam-5776	507	1	√	√	NUM
ejpam-5776	507	2	(	(	PUNCT
ejpam-5776	507	3	n−	n−	NOUN
ejpam-5776	507	4	2)2(n−	2)2(n−	NUM
ejpam-5776	508	1	1)2	1)2	NUM
ejpam-5776	509	1	+	+	CCONJ
ejpam-5776	509	2	9	9	NUM
ejpam-5776	509	3	4	4	NUM
ejpam-5776	509	4	n3(n−	n3(n−	NOUN
ejpam-5776	509	5	2	2	NUM
ejpam-5776	509	6	)	)	PUNCT
ejpam-5776	509	7	)	)	PUNCT
ejpam-5776	510	1	∣∣∣∣∣	∣∣∣∣∣	ADP
ejpam-5776	510	2	=(	=(	PROPN
ejpam-5776	510	3	n−	n−	NOUN
ejpam-5776	510	4	2)(n−	2)(n−	NUM
ejpam-5776	510	5	1	1	NUM
ejpam-5776	510	6	)	)	PUNCT
ejpam-5776	511	1	+	+	CCONJ
ejpam-5776	511	2	√	√	INTJ
ejpam-5776	511	3	(	(	PUNCT
ejpam-5776	511	4	n−	n−	NOUN
ejpam-5776	511	5	2)2(n−	2)2(n−	NUM
ejpam-5776	512	1	1)2	1)2	NUM
ejpam-5776	513	1	+	+	CCONJ
ejpam-5776	513	2	9	9	NUM
ejpam-5776	513	3	4	4	NUM
ejpam-5776	513	4	n3(n−	n3(n−	NOUN
ejpam-5776	513	5	2	2	NUM
ejpam-5776	513	6	)	)	PUNCT
ejpam-5776	513	7	.	.	PUNCT
ejpam-5776	514	1	4	4	X
ejpam-5776	514	2	.	.	X
ejpam-5776	514	3	discussion	discussion	NOUN
ejpam-5776	514	4	we	we	PRON
ejpam-5776	514	5	can	can	AUX
ejpam-5776	514	6	conclude	conclude	VERB
ejpam-5776	514	7	several	several	ADJ
ejpam-5776	514	8	interesting	interesting	ADJ
ejpam-5776	514	9	statements	statement	NOUN
ejpam-5776	514	10	from	from	ADP
ejpam-5776	514	11	the	the	DET
ejpam-5776	514	12	results	result	NOUN
ejpam-5776	514	13	of	of	ADP
ejpam-5776	514	14	the	the	DET
ejpam-5776	514	15	previous	previous	ADJ
ejpam-5776	514	16	section	section	NOUN
ejpam-5776	514	17	.	.	PUNCT
ejpam-5776	515	1	corollary	corollary	ADJ
ejpam-5776	515	2	1	1	NUM
ejpam-5776	515	3	.	.	PUNCT
ejpam-5776	516	1	the	the	DET
ejpam-5776	516	2	eccentricity	eccentricity	NOUN
ejpam-5776	516	3	energy	energy	NOUN
ejpam-5776	516	4	of	of	ADP
ejpam-5776	516	5	ωd2n	ωd2n	PROPN
ejpam-5776	516	6	is	be	AUX
ejpam-5776	516	7	always	always	ADV
ejpam-5776	516	8	an	an	DET
ejpam-5776	516	9	even	even	ADV
ejpam-5776	516	10	integer	integer	NOUN
ejpam-5776	516	11	.	.	PUNCT
ejpam-5776	517	1	corollary	corollary	ADJ
ejpam-5776	517	2	2	2	NUM
ejpam-5776	517	3	.	.	PUNCT
ejpam-5776	518	1	the	the	DET
ejpam-5776	518	2	energy	energy	NOUN
ejpam-5776	518	3	of	of	ADP
ejpam-5776	518	4	ωd2n	ωd2n	PROPN
ejpam-5776	518	5	is	be	AUX
ejpam-5776	518	6	never	never	ADV
ejpam-5776	518	7	an	an	DET
ejpam-5776	518	8	odd	odd	ADJ
ejpam-5776	518	9	integer	integer	NOUN
ejpam-5776	518	10	associated	associate	VERB
ejpam-5776	518	11	with	with	ADP
ejpam-5776	518	12	the	the	DET
ejpam-5776	518	13	sum	sum	NOUN
ejpam-5776	518	14	eccentricity	eccentricity	NOUN
ejpam-5776	518	15	and	and	CCONJ
ejpam-5776	518	16	average	average	ADJ
ejpam-5776	518	17	degree	degree	NOUN
ejpam-5776	518	18	eccentricity	eccentricity	NOUN
ejpam-5776	518	19	matrices	matrix	NOUN
ejpam-5776	518	20	.	.	PUNCT
ejpam-5776	519	1	corollary	corollary	ADJ
ejpam-5776	519	2	3	3	NUM
ejpam-5776	519	3	.	.	PUNCT
ejpam-5776	520	1	ωd2n	ωd2n	PROPN
ejpam-5776	520	2	is	be	AUX
ejpam-5776	520	3	hyperenergetic	hyperenergetic	ADJ
ejpam-5776	520	4	associated	associate	VERB
ejpam-5776	520	5	with	with	ADP
ejpam-5776	520	6	the	the	DET
ejpam-5776	520	7	eccentricity	eccentricity	NOUN
ejpam-5776	520	8	-	-	PUNCT
ejpam-5776	520	9	based	base	VERB
ejpam-5776	520	10	matrices	matrix	NOUN
ejpam-5776	520	11	.	.	PUNCT
ejpam-5776	521	1	acknowledgements	acknowledgement	NOUN
ejpam-5776	521	2	the	the	DET
ejpam-5776	521	3	authors	author	NOUN
ejpam-5776	521	4	thank	thank	VERB
ejpam-5776	521	5	the	the	DET
ejpam-5776	521	6	referees	referee	NOUN
ejpam-5776	521	7	for	for	ADP
ejpam-5776	521	8	their	their	PRON
ejpam-5776	521	9	helpful	helpful	ADJ
ejpam-5776	521	10	comments	comment	NOUN
ejpam-5776	521	11	or	or	CCONJ
ejpam-5776	521	12	recommendations	recommendation	NOUN
ejpam-5776	521	13	on	on	ADP
ejpam-5776	521	14	this	this	DET
ejpam-5776	521	15	article	article	NOUN
ejpam-5776	521	16	.	.	PUNCT
ejpam-5776	522	1	we	we	PRON
ejpam-5776	522	2	also	also	ADV
ejpam-5776	522	3	thank	thank	VERB
ejpam-5776	522	4	the	the	DET
ejpam-5776	522	5	university	university	PROPN
ejpam-5776	522	6	of	of	ADP
ejpam-5776	522	7	mataram	mataram	PROPN
ejpam-5776	522	8	,	,	PUNCT
ejpam-5776	522	9	indonesia	indonesia	PROPN
ejpam-5776	522	10	,	,	PUNCT
ejpam-5776	522	11	for	for	ADP
ejpam-5776	522	12	funding	fund	VERB
ejpam-5776	522	13	assistance	assistance	NOUN
ejpam-5776	522	14	through	through	ADP
ejpam-5776	522	15	the	the	DET
ejpam-5776	522	16	overseas	overseas	PROPN
ejpam-5776	522	17	collaborative	collaborative	PROPN
ejpam-5776	522	18	research	research	NOUN
ejpam-5776	522	19	scheme	scheme	NOUN
ejpam-5776	522	20	no.2490	no.2490	PROPN
ejpam-5776	522	21	/	/	SYM
ejpam-5776	522	22	un18.l1	un18.l1	PROPN
ejpam-5776	522	23	/	/	SYM
ejpam-5776	522	24	pp/2025	pp/2025	NOUN
ejpam-5776	522	25	.	.	NOUN
ejpam-5776	523	1	references	reference	NOUN
ejpam-5776	523	2	[	[	X
ejpam-5776	523	3	1	1	NUM
ejpam-5776	523	4	]	]	X
ejpam-5776	523	5	j	j	PROPN
ejpam-5776	523	6	wang	wang	PROPN
ejpam-5776	523	7	,	,	PUNCT
ejpam-5776	523	8	m	m	VERB
ejpam-5776	523	9	lu	lu	PROPN
ejpam-5776	523	10	,	,	PUNCT
ejpam-5776	523	11	f	f	PROPN
ejpam-5776	523	12	belardo	belardo	PROPN
ejpam-5776	523	13	,	,	PUNCT
ejpam-5776	523	14	and	and	CCONJ
ejpam-5776	523	15	m	m	PROPN
ejpam-5776	523	16	randic	randic	ADJ
ejpam-5776	523	17	.	.	PUNCT
ejpam-5776	524	1	the	the	DET
ejpam-5776	524	2	anti	anti	ADJ
ejpam-5776	524	3	-	-	ADJ
ejpam-5776	524	4	adjacency	adjacency	ADJ
ejpam-5776	524	5	matrix	matrix	NOUN
ejpam-5776	524	6	of	of	ADP
ejpam-5776	524	7	a	a	DET
ejpam-5776	524	8	graph	graph	NOUN
ejpam-5776	524	9	:	:	PUNCT
ejpam-5776	524	10	eccentricity	eccentricity	NOUN
ejpam-5776	524	11	matrix	matrix	NOUN
ejpam-5776	524	12	.	.	PUNCT
ejpam-5776	525	1	discrete	discrete	ADJ
ejpam-5776	525	2	applied	apply	VERB
ejpam-5776	525	3	mathematics	mathematic	NOUN
ejpam-5776	525	4	,	,	PUNCT
ejpam-5776	525	5	251:299–309	251:299–309	NUM
ejpam-5776	525	6	,	,	PUNCT
ejpam-5776	525	7	2018	2018	NUM
ejpam-5776	525	8	.	.	PUNCT
ejpam-5776	526	1	[	[	X
ejpam-5776	526	2	2	2	NUM
ejpam-5776	526	3	]	]	PUNCT
ejpam-5776	526	4	m	m	VERB
ejpam-5776	526	5	randic	randic	ADJ
ejpam-5776	526	6	.	.	PUNCT
ejpam-5776	527	1	dmax	dmax	PROPN
ejpam-5776	527	2	-matrix	-matrix	NOUN
ejpam-5776	527	3	of	of	ADP
ejpam-5776	527	4	dominant	dominant	ADJ
ejpam-5776	527	5	distances	distance	NOUN
ejpam-5776	527	6	in	in	ADP
ejpam-5776	527	7	a	a	DET
ejpam-5776	527	8	graph	graph	NOUN
ejpam-5776	527	9	.	.	PUNCT
ejpam-5776	528	1	match	match	NOUN
ejpam-5776	528	2	communications	communication	NOUN
ejpam-5776	528	3	in	in	ADP
ejpam-5776	528	4	mathematical	mathematical	ADJ
ejpam-5776	528	5	and	and	CCONJ
ejpam-5776	528	6	in	in	ADP
ejpam-5776	528	7	computer	computer	NOUN
ejpam-5776	528	8	chemistry	chemistry	NOUN
ejpam-5776	528	9	,	,	PUNCT
ejpam-5776	528	10	70:221–238	70:221–238	PROPN
ejpam-5776	528	11	,	,	PUNCT
ejpam-5776	528	12	2013	2013	NUM
ejpam-5776	528	13	.	.	PUNCT
ejpam-5776	529	1	m.	m.	PROPN
ejpam-5776	529	2	u.	u.	PROPN
ejpam-5776	529	3	romdhini	romdhini	PROPN
ejpam-5776	529	4	et	et	PROPN
ejpam-5776	529	5	al	al	PROPN
ejpam-5776	529	6	.	.	PUNCT
ejpam-5776	529	7	/	/	SYM
ejpam-5776	529	8	eur	eur	PROPN
ejpam-5776	529	9	.	.	PUNCT
ejpam-5776	530	1	j.	j.	PROPN
ejpam-5776	530	2	pure	pure	PROPN
ejpam-5776	530	3	appl	appl	PROPN
ejpam-5776	530	4	.	.	PROPN
ejpam-5776	530	5	math	math	PROPN
ejpam-5776	530	6	,	,	PUNCT
ejpam-5776	530	7	18	18	NUM
ejpam-5776	530	8	(	(	PUNCT
ejpam-5776	530	9	2	2	NUM
ejpam-5776	530	10	)	)	PUNCT
ejpam-5776	530	11	(	(	PUNCT
ejpam-5776	530	12	2025	2025	NUM
ejpam-5776	530	13	)	)	PUNCT
ejpam-5776	530	14	,	,	PUNCT
ejpam-5776	530	15	5776	5776	NUM
ejpam-5776	530	16	13	13	NUM
ejpam-5776	530	17	of	of	ADP
ejpam-5776	530	18	13	13	NUM
ejpam-5776	530	19	[	[	X
ejpam-5776	530	20	3	3	X
ejpam-5776	530	21	]	]	X
ejpam-5776	530	22	i	i	PRON
ejpam-5776	530	23	mahato	mahato	VERB
ejpam-5776	530	24	,	,	PUNCT
ejpam-5776	530	25	r	r	NOUN
ejpam-5776	530	26	gurusamy	gurusamy	NOUN
ejpam-5776	530	27	,	,	PUNCT
ejpam-5776	530	28	m	m	VERB
ejpam-5776	530	29	r	r	NOUN
ejpam-5776	530	30	kannan	kannan	PROPN
ejpam-5776	530	31	,	,	PUNCT
ejpam-5776	530	32	and	and	CCONJ
ejpam-5776	530	33	s	s	AUX
ejpam-5776	530	34	arockiaraj	arockiaraj	VERB
ejpam-5776	530	35	.	.	PUNCT
ejpam-5776	531	1	spectra	spectra	NOUN
ejpam-5776	531	2	of	of	ADP
ejpam-5776	531	3	eccentricity	eccentricity	NOUN
ejpam-5776	531	4	matrices	matrix	NOUN
ejpam-5776	531	5	of	of	ADP
ejpam-5776	531	6	graphs	graph	NOUN
ejpam-5776	531	7	.	.	PUNCT
ejpam-5776	532	1	discrete	discrete	ADJ
ejpam-5776	532	2	applied	applied	ADJ
ejpam-5776	532	3	mathematics	mathematic	NOUN
ejpam-5776	532	4	,	,	PUNCT
ejpam-5776	532	5	285:252–260	285:252–260	NUM
ejpam-5776	532	6	,	,	PUNCT
ejpam-5776	532	7	2020	2020	NUM
ejpam-5776	532	8	.	.	PUNCT
ejpam-5776	533	1	[	[	X
ejpam-5776	533	2	4	4	X
ejpam-5776	533	3	]	]	SYM
ejpam-5776	533	4	m	m	VERB
ejpam-5776	533	5	i	i	NOUN
ejpam-5776	533	6	sowaity	sowaity	NOUN
ejpam-5776	533	7	and	and	CCONJ
ejpam-5776	533	8	b	b	NOUN
ejpam-5776	533	9	sharada	sharada	PROPN
ejpam-5776	533	10	.	.	PUNCT
ejpam-5776	534	1	the	the	DET
ejpam-5776	534	2	sum	sum	NOUN
ejpam-5776	534	3	-	-	PUNCT
ejpam-5776	534	4	eccentricity	eccentricity	NOUN
ejpam-5776	534	5	energy	energy	NOUN
ejpam-5776	534	6	of	of	ADP
ejpam-5776	534	7	a	a	DET
ejpam-5776	534	8	graph	graph	NOUN
ejpam-5776	534	9	.	.	PUNCT
ejpam-5776	535	1	international	international	ADJ
ejpam-5776	535	2	journal	journal	PROPN
ejpam-5776	535	3	on	on	ADP
ejpam-5776	535	4	recent	recent	ADJ
ejpam-5776	535	5	and	and	CCONJ
ejpam-5776	535	6	innovation	innovation	NOUN
ejpam-5776	535	7	trends	trend	NOUN
ejpam-5776	535	8	in	in	ADP
ejpam-5776	535	9	computing	computing	NOUN
ejpam-5776	535	10	and	and	CCONJ
ejpam-5776	535	11	communication	communication	NOUN
ejpam-5776	535	12	,	,	PUNCT
ejpam-5776	535	13	5:293	5:293	NUM
ejpam-5776	535	14	–	–	PUNCT
ejpam-5776	535	15	304	304	NUM
ejpam-5776	535	16	,	,	PUNCT
ejpam-5776	535	17	2017	2017	NUM
ejpam-5776	535	18	.	.	PUNCT
ejpam-5776	536	1	[	[	X
ejpam-5776	536	2	5	5	NUM
ejpam-5776	536	3	]	]	SYM
ejpam-5776	536	4	v	v	NOUN
ejpam-5776	536	5	mathad	mathad	VERB
ejpam-5776	536	6	,	,	PUNCT
ejpam-5776	536	7	s	s	VERB
ejpam-5776	536	8	i	i	PROPN
ejpam-5776	536	9	khalaf	khalaf	PROPN
ejpam-5776	536	10	,	,	PUNCT
ejpam-5776	536	11	s	s	PART
ejpam-5776	536	12	s	s	NOUN
ejpam-5776	536	13	mahde	mahde	NOUN
ejpam-5776	536	14	,	,	PUNCT
ejpam-5776	536	15	and	and	CCONJ
ejpam-5776	536	16	i	i	PROPN
ejpam-5776	536	17	gutman	gutman	NOUN
ejpam-5776	536	18	.	.	PUNCT
ejpam-5776	537	1	average	average	ADJ
ejpam-5776	537	2	degree	degree	NOUN
ejpam-5776	537	3	-	-	PUNCT
ejpam-5776	537	4	eccentricity	eccentricity	NOUN
ejpam-5776	537	5	energy	energy	NOUN
ejpam-5776	537	6	of	of	ADP
ejpam-5776	537	7	graphs	graph	NOUN
ejpam-5776	537	8	.	.	PUNCT
ejpam-5776	538	1	mathematics	mathematic	NOUN
ejpam-5776	538	2	interdisciplinary	interdisciplinary	ADJ
ejpam-5776	538	3	research	research	NOUN
ejpam-5776	538	4	,	,	PUNCT
ejpam-5776	538	5	1:45–54	1:45–54	NUM
ejpam-5776	538	6	,	,	PUNCT
ejpam-5776	538	7	2018	2018	NUM
ejpam-5776	538	8	.	.	PUNCT
ejpam-5776	539	1	[	[	X
ejpam-5776	539	2	6	6	NUM
ejpam-5776	539	3	]	]	PUNCT
ejpam-5776	539	4	i	i	PROPN
ejpam-5776	539	5	gutman	gutman	PROPN
ejpam-5776	539	6	.	.	PUNCT
ejpam-5776	540	1	the	the	DET
ejpam-5776	540	2	energy	energy	NOUN
ejpam-5776	540	3	of	of	ADP
ejpam-5776	540	4	graph	graph	NOUN
ejpam-5776	540	5	.	.	PUNCT
ejpam-5776	541	1	ber	ber	NOUN
ejpam-5776	541	2	.	.	PUNCT
ejpam-5776	541	3	math.-stat	math.-stat	PROPN
ejpam-5776	541	4	.	.	PROPN
ejpam-5776	541	5	sekt	sekt	PROPN
ejpam-5776	541	6	.	.	PUNCT
ejpam-5776	542	1	forschungsz	forschungsz	PROPN
ejpam-5776	542	2	.	.	PUNCT
ejpam-5776	543	1	graz	graz	PROPN
ejpam-5776	543	2	,	,	PUNCT
ejpam-5776	543	3	103:1–2	103:1–2	NUM
ejpam-5776	543	4	,	,	PUNCT
ejpam-5776	543	5	1978	1978	NUM
ejpam-5776	543	6	.	.	PUNCT
ejpam-5776	544	1	[	[	X
ejpam-5776	544	2	7	7	X
ejpam-5776	544	3	]	]	X
ejpam-5776	544	4	r	r	NOUN
ejpam-5776	544	5	b	b	X
ejpam-5776	544	6	bapat	bapat	PROPN
ejpam-5776	544	7	and	and	CCONJ
ejpam-5776	544	8	s	s	NOUN
ejpam-5776	544	9	pati	pati	NOUN
ejpam-5776	544	10	.	.	PUNCT
ejpam-5776	545	1	energy	energy	NOUN
ejpam-5776	545	2	of	of	ADP
ejpam-5776	545	3	a	a	DET
ejpam-5776	545	4	graph	graph	NOUN
ejpam-5776	545	5	is	be	AUX
ejpam-5776	545	6	never	never	ADV
ejpam-5776	545	7	an	an	DET
ejpam-5776	545	8	odd	odd	ADJ
ejpam-5776	545	9	integer	integer	NOUN
ejpam-5776	545	10	.	.	PUNCT
ejpam-5776	546	1	bulletin	bulletin	NOUN
ejpam-5776	546	2	of	of	ADP
ejpam-5776	546	3	kerala	kerala	PROPN
ejpam-5776	546	4	mathematics	mathematics	PROPN
ejpam-5776	546	5	association	association	PROPN
ejpam-5776	546	6	,	,	PUNCT
ejpam-5776	546	7	1:129–132	1:129–132	NUM
ejpam-5776	546	8	,	,	PUNCT
ejpam-5776	546	9	2004	2004	NUM
ejpam-5776	546	10	.	.	PUNCT
ejpam-5776	547	1	[	[	X
ejpam-5776	547	2	8	8	NUM
ejpam-5776	547	3	]	]	SYM
ejpam-5776	547	4	s	s	PART
ejpam-5776	547	5	pirzada	pirzada	NOUN
ejpam-5776	547	6	and	and	CCONJ
ejpam-5776	547	7	i	i	PROPN
ejpam-5776	547	8	gutman	gutman	PROPN
ejpam-5776	547	9	.	.	PUNCT
ejpam-5776	548	1	energy	energy	NOUN
ejpam-5776	548	2	of	of	ADP
ejpam-5776	548	3	a	a	DET
ejpam-5776	548	4	graph	graph	NOUN
ejpam-5776	548	5	is	be	AUX
ejpam-5776	548	6	never	never	ADV
ejpam-5776	548	7	the	the	DET
ejpam-5776	548	8	square	square	ADJ
ejpam-5776	548	9	root	root	NOUN
ejpam-5776	548	10	of	of	ADP
ejpam-5776	548	11	an	an	DET
ejpam-5776	548	12	odd	odd	ADJ
ejpam-5776	548	13	integer	integer	NOUN
ejpam-5776	548	14	.	.	PUNCT
ejpam-5776	549	1	applicable	applicable	ADJ
ejpam-5776	549	2	analysis	analysis	NOUN
ejpam-5776	549	3	and	and	CCONJ
ejpam-5776	549	4	discrete	discrete	ADJ
ejpam-5776	549	5	mathematics	mathematic	NOUN
ejpam-5776	549	6	,	,	PUNCT
ejpam-5776	549	7	2:118–121	2:118–121	NUM
ejpam-5776	549	8	,	,	PUNCT
ejpam-5776	549	9	2008	2008	NUM
ejpam-5776	549	10	.	.	PUNCT
ejpam-5776	550	1	[	[	X
ejpam-5776	550	2	9	9	NUM
ejpam-5776	550	3	]	]	SYM
ejpam-5776	550	4	m	m	VERB
ejpam-5776	550	5	u	u	NOUN
ejpam-5776	550	6	romdhini	romdhini	NOUN
ejpam-5776	550	7	,	,	PUNCT
ejpam-5776	550	8	a	a	DET
ejpam-5776	550	9	nawawi	nawawi	NOUN
ejpam-5776	550	10	,	,	PUNCT
ejpam-5776	550	11	f	f	PROPN
ejpam-5776	550	12	al	al	PROPN
ejpam-5776	550	13	-	-	PUNCT
ejpam-5776	550	14	sharqi	sharqi	PROPN
ejpam-5776	550	15	,	,	PUNCT
ejpam-5776	550	16	a	a	DET
ejpam-5776	550	17	al	al	PROPN
ejpam-5776	550	18	-	-	PUNCT
ejpam-5776	550	19	quran	quran	PROPN
ejpam-5776	550	20	,	,	PUNCT
ejpam-5776	550	21	and	and	CCONJ
ejpam-5776	550	22	s	s	NOUN
ejpam-5776	550	23	r	r	NOUN
ejpam-5776	550	24	kamali	kamali	X
ejpam-5776	550	25	.	.	PUNCT
ejpam-5776	551	1	wienerhosoya	wienerhosoya	PROPN
ejpam-5776	551	2	energy	energy	NOUN
ejpam-5776	551	3	of	of	ADP
ejpam-5776	551	4	non	non	ADJ
ejpam-5776	551	5	-	-	ADJ
ejpam-5776	551	6	commuting	commuting	ADJ
ejpam-5776	551	7	graph	graph	NOUN
ejpam-5776	551	8	for	for	ADP
ejpam-5776	551	9	dihedral	dihedral	ADJ
ejpam-5776	551	10	groups	group	NOUN
ejpam-5776	551	11	.	.	PUNCT
ejpam-5776	552	1	asia	asia	PROPN
ejpam-5776	552	2	pacific	pacific	PROPN
ejpam-5776	552	3	journal	journal	PROPN
ejpam-5776	552	4	of	of	ADP
ejpam-5776	552	5	mathematics	mathematic	NOUN
ejpam-5776	552	6	,	,	PUNCT
ejpam-5776	552	7	11(9):1–9	11(9):1–9	NUM
ejpam-5776	552	8	,	,	PUNCT
ejpam-5776	552	9	2024	2024	NUM
ejpam-5776	552	10	.	.	PUNCT
ejpam-5776	553	1	[	[	X
ejpam-5776	553	2	10	10	NUM
ejpam-5776	553	3	]	]	X
ejpam-5776	553	4	m	m	VERB
ejpam-5776	553	5	u	u	NOUN
ejpam-5776	553	6	romdhini	romdhini	NOUN
ejpam-5776	553	7	and	and	CCONJ
ejpam-5776	553	8	a	a	DET
ejpam-5776	553	9	nawawi	nawawi	NOUN
ejpam-5776	553	10	.	.	PUNCT
ejpam-5776	554	1	on	on	ADP
ejpam-5776	554	2	the	the	DET
ejpam-5776	554	3	spectral	spectral	ADJ
ejpam-5776	554	4	radius	radius	NOUN
ejpam-5776	554	5	and	and	CCONJ
ejpam-5776	554	6	sombor	sombor	NOUN
ejpam-5776	554	7	energy	energy	NOUN
ejpam-5776	554	8	of	of	ADP
ejpam-5776	554	9	the	the	DET
ejpam-5776	554	10	non	non	ADJ
ejpam-5776	554	11	-	-	ADJ
ejpam-5776	554	12	commuting	commuting	ADJ
ejpam-5776	554	13	graph	graph	NOUN
ejpam-5776	554	14	for	for	ADP
ejpam-5776	554	15	dihedral	dihedral	ADJ
ejpam-5776	554	16	groups	group	NOUN
ejpam-5776	554	17	.	.	PUNCT
ejpam-5776	555	1	malaysian	malaysian	ADJ
ejpam-5776	555	2	journal	journal	PROPN
ejpam-5776	555	3	of	of	ADP
ejpam-5776	555	4	fundamental	fundamental	ADJ
ejpam-5776	555	5	and	and	CCONJ
ejpam-5776	555	6	applied	applied	ADJ
ejpam-5776	555	7	sciences	science	NOUN
ejpam-5776	555	8	,	,	PUNCT
ejpam-5776	555	9	20:65–73	20:65–73	NUM
ejpam-5776	555	10	,	,	PUNCT
ejpam-5776	555	11	2024	2024	NUM
ejpam-5776	555	12	.	.	PUNCT
ejpam-5776	556	1	[	[	X
ejpam-5776	556	2	11	11	NUM
ejpam-5776	556	3	]	]	X
ejpam-5776	556	4	m	m	VERB
ejpam-5776	556	5	u	u	NOUN
ejpam-5776	556	6	romdhini	romdhini	NOUN
ejpam-5776	556	7	,	,	PUNCT
ejpam-5776	556	8	f	f	PROPN
ejpam-5776	556	9	al	al	PROPN
ejpam-5776	556	10	-	-	PUNCT
ejpam-5776	556	11	sharqi	sharqi	PROPN
ejpam-5776	556	12	,	,	PUNCT
ejpam-5776	556	13	a	a	DET
ejpam-5776	556	14	al	al	PROPN
ejpam-5776	556	15	-	-	PUNCT
ejpam-5776	556	16	quran	quran	PROPN
ejpam-5776	556	17	,	,	PUNCT
ejpam-5776	556	18	m	m	PROPN
ejpam-5776	556	19	k	k	NOUN
ejpam-5776	556	20	tahat	tahat	PROPN
ejpam-5776	556	21	,	,	PUNCT
ejpam-5776	556	22	and	and	CCONJ
ejpam-5776	556	23	a	a	DET
ejpam-5776	556	24	lutfi	lutfi	NOUN
ejpam-5776	556	25	.	.	PUNCT
ejpam-5776	556	26	exploring	explore	VERB
ejpam-5776	556	27	the	the	DET
ejpam-5776	556	28	algebraic	algebraic	ADJ
ejpam-5776	556	29	structures	structure	NOUN
ejpam-5776	556	30	of	of	ADP
ejpam-5776	556	31	q	q	ADJ
ejpam-5776	556	32	-	-	PUNCT
ejpam-5776	556	33	complex	complex	ADJ
ejpam-5776	556	34	neutrosophic	neutrosophic	ADJ
ejpam-5776	556	35	soft	soft	ADJ
ejpam-5776	556	36	fields	field	NOUN
ejpam-5776	556	37	.	.	PUNCT
ejpam-5776	557	1	international	international	ADJ
ejpam-5776	557	2	journal	journal	PROPN
ejpam-5776	557	3	of	of	ADP
ejpam-5776	557	4	neutrosophic	neutrosophic	ADJ
ejpam-5776	557	5	science	science	NOUN
ejpam-5776	557	6	,	,	PUNCT
ejpam-5776	557	7	22(4):93–105	22(4):93–105	NUM
ejpam-5776	557	8	,	,	PUNCT
ejpam-5776	557	9	2023	2023	NUM
ejpam-5776	557	10	.	.	PUNCT
ejpam-5776	558	1	[	[	X
ejpam-5776	558	2	12	12	NUM
ejpam-5776	558	3	]	]	X
ejpam-5776	558	4	f	f	PROPN
ejpam-5776	558	5	al	al	PROPN
ejpam-5776	558	6	-	-	PUNCT
ejpam-5776	558	7	sharqi	sharqi	PROPN
ejpam-5776	558	8	,	,	PUNCT
ejpam-5776	558	9	a	a	DET
ejpam-5776	558	10	al	al	PROPN
ejpam-5776	558	11	-	-	PUNCT
ejpam-5776	558	12	quran	quran	PROPN
ejpam-5776	558	13	,	,	PUNCT
ejpam-5776	558	14	and	and	CCONJ
ejpam-5776	558	15	z	z	NOUN
ejpam-5776	558	16	m	m	VERB
ejpam-5776	558	17	rodzi	rodzi	NOUN
ejpam-5776	558	18	.	.	PUNCT
ejpam-5776	559	1	multi	multi	ADJ
ejpam-5776	559	2	-	-	ADJ
ejpam-5776	559	3	attribute	attribute	NOUN
ejpam-5776	559	4	group	group	NOUN
ejpam-5776	559	5	decision	decision	NOUN
ejpam-5776	559	6	-	-	PUNCT
ejpam-5776	559	7	making	making	NOUN
ejpam-5776	559	8	based	base	VERB
ejpam-5776	559	9	on	on	ADP
ejpam-5776	559	10	aggregation	aggregation	NOUN
ejpam-5776	559	11	operator	operator	NOUN
ejpam-5776	559	12	and	and	CCONJ
ejpam-5776	559	13	score	score	NOUN
ejpam-5776	559	14	function	function	NOUN
ejpam-5776	559	15	of	of	ADP
ejpam-5776	559	16	bipolar	bipolar	ADJ
ejpam-5776	559	17	neutrosophic	neutrosophic	ADJ
ejpam-5776	559	18	hypersoft	hypersoft	PROPN
ejpam-5776	559	19	environment	environment	NOUN
ejpam-5776	559	20	.	.	PUNCT
ejpam-5776	560	1	neutrosophic	neutrosophic	ADJ
ejpam-5776	560	2	sets	set	NOUN
ejpam-5776	560	3	and	and	CCONJ
ejpam-5776	560	4	systems	system	NOUN
ejpam-5776	560	5	,	,	PUNCT
ejpam-5776	560	6	61(1):465–492	61(1):465–492	NUM
ejpam-5776	560	7	,	,	PUNCT
ejpam-5776	560	8	2023	2023	NUM
ejpam-5776	560	9	.	.	PUNCT
ejpam-5776	561	1	[	[	X
ejpam-5776	561	2	13	13	NUM
ejpam-5776	561	3	]	]	X
ejpam-5776	561	4	a	a	DET
ejpam-5776	561	5	abdollahi	abdollahi	NOUN
ejpam-5776	561	6	,	,	PUNCT
ejpam-5776	561	7	s	s	NOUN
ejpam-5776	561	8	akbari	akbari	PROPN
ejpam-5776	561	9	,	,	PUNCT
ejpam-5776	561	10	and	and	CCONJ
ejpam-5776	561	11	h	h	NOUN
ejpam-5776	561	12	r	r	NOUN
ejpam-5776	561	13	maimani	maimani	NOUN
ejpam-5776	561	14	.	.	PUNCT
ejpam-5776	562	1	non	non	ADJ
ejpam-5776	562	2	-	-	ADJ
ejpam-5776	562	3	commuting	commuting	ADJ
ejpam-5776	562	4	graph	graph	NOUN
ejpam-5776	562	5	of	of	ADP
ejpam-5776	562	6	a	a	DET
ejpam-5776	562	7	group	group	NOUN
ejpam-5776	562	8	.	.	PUNCT
ejpam-5776	563	1	journal	journal	PROPN
ejpam-5776	563	2	of	of	ADP
ejpam-5776	563	3	algebra	algebra	PROPN
ejpam-5776	563	4	,	,	PUNCT
ejpam-5776	563	5	298(2):468–492	298(2):468–492	NUM
ejpam-5776	563	6	,	,	PUNCT
ejpam-5776	563	7	2006	2006	NUM
ejpam-5776	563	8	.	.	PUNCT
ejpam-5776	564	1	[	[	X
ejpam-5776	564	2	14	14	NUM
ejpam-5776	564	3	]	]	X
ejpam-5776	564	4	r	r	NOUN
ejpam-5776	564	5	a	a	DET
ejpam-5776	564	6	horn	horn	NOUN
ejpam-5776	564	7	and	and	CCONJ
ejpam-5776	564	8	c	c	X
ejpam-5776	564	9	a	a	DET
ejpam-5776	564	10	johnson	johnson	PROPN
ejpam-5776	564	11	.	.	PUNCT
ejpam-5776	564	12	matrix	matrix	NOUN
ejpam-5776	564	13	analysis	analysis	NOUN
ejpam-5776	564	14	.	.	PUNCT
ejpam-5776	565	1	cambridge	cambridge	PROPN
ejpam-5776	565	2	university	university	PROPN
ejpam-5776	565	3	press	press	PROPN
ejpam-5776	565	4	,	,	PUNCT
ejpam-5776	565	5	cambridge	cambridge	PROPN
ejpam-5776	565	6	,	,	PUNCT
ejpam-5776	565	7	1985	1985	NUM
ejpam-5776	565	8	.	.	PUNCT
ejpam-5776	566	1	[	[	X
ejpam-5776	566	2	15	15	NUM
ejpam-5776	566	3	]	]	X
ejpam-5776	566	4	x	x	X
ejpam-5776	566	5	li	li	PROPN
ejpam-5776	566	6	,	,	PUNCT
ejpam-5776	566	7	y	y	PROPN
ejpam-5776	566	8	shi	shi	PROPN
ejpam-5776	566	9	,	,	PUNCT
ejpam-5776	566	10	and	and	CCONJ
ejpam-5776	566	11	i	i	PROPN
ejpam-5776	566	12	gutman	gutman	NOUN
ejpam-5776	566	13	.	.	PUNCT
ejpam-5776	567	1	graph	graph	NOUN
ejpam-5776	567	2	energy	energy	NOUN
ejpam-5776	567	3	.	.	PUNCT
ejpam-5776	568	1	springer	springer	NOUN
ejpam-5776	568	2	,	,	PUNCT
ejpam-5776	568	3	new	new	PROPN
ejpam-5776	568	4	york	york	PROPN
ejpam-5776	568	5	,	,	PUNCT
ejpam-5776	568	6	2012	2012	NUM
ejpam-5776	568	7	.	.	PUNCT
ejpam-5776	569	1	[	[	X
ejpam-5776	569	2	16	16	NUM
ejpam-5776	569	3	]	]	X
ejpam-5776	569	4	m	m	VERB
ejpam-5776	569	5	u	u	NOUN
ejpam-5776	569	6	romdhini	romdhini	NOUN
ejpam-5776	569	7	,	,	PUNCT
ejpam-5776	569	8	a	a	DET
ejpam-5776	569	9	nawawi	nawawi	NOUN
ejpam-5776	569	10	,	,	PUNCT
ejpam-5776	569	11	f	f	PROPN
ejpam-5776	569	12	al	al	PROPN
ejpam-5776	569	13	-	-	PUNCT
ejpam-5776	569	14	sharqi	sharqi	PROPN
ejpam-5776	569	15	,	,	PUNCT
ejpam-5776	569	16	and	and	CCONJ
ejpam-5776	569	17	a	a	DET
ejpam-5776	569	18	al	al	PROPN
ejpam-5776	569	19	-	-	PUNCT
ejpam-5776	569	20	quran	quran	PROPN
ejpam-5776	569	21	.	.	PUNCT
ejpam-5776	570	1	closeness	closeness	NOUN
ejpam-5776	570	2	energy	energy	NOUN
ejpam-5776	570	3	of	of	ADP
ejpam-5776	570	4	noncommuting	noncommute	VERB
ejpam-5776	570	5	graph	graph	NOUN
ejpam-5776	570	6	for	for	ADP
ejpam-5776	570	7	dihedral	dihedral	ADJ
ejpam-5776	570	8	groups	group	NOUN
ejpam-5776	570	9	.	.	PUNCT
ejpam-5776	571	1	european	european	ADJ
ejpam-5776	571	2	journal	journal	PROPN
ejpam-5776	571	3	of	of	ADP
ejpam-5776	571	4	pure	pure	ADJ
ejpam-5776	571	5	and	and	CCONJ
ejpam-5776	571	6	applied	applied	ADJ
ejpam-5776	571	7	mathematics	mathematic	NOUN
ejpam-5776	571	8	,	,	PUNCT
ejpam-5776	571	9	17(1):212–221	17(1):212–221	NUM
ejpam-5776	571	10	,	,	PUNCT
ejpam-5776	571	11	2024	2024	NUM
ejpam-5776	571	12	.	.	PUNCT
ejpam-5776	572	1	[	[	X
ejpam-5776	572	2	17	17	NUM
ejpam-5776	572	3	]	]	X
ejpam-5776	572	4	s	s	VERB
ejpam-5776	572	5	m	m	PROPN
ejpam-5776	572	6	s	s	PROPN
ejpam-5776	572	7	khasraw	khasraw	PROPN
ejpam-5776	572	8	,	,	PUNCT
ejpam-5776	572	9	i	i	PROPN
ejpam-5776	572	10	d	d	PROPN
ejpam-5776	572	11	ali	ali	PROPN
ejpam-5776	572	12	,	,	PUNCT
ejpam-5776	572	13	and	and	CCONJ
ejpam-5776	572	14	r	r	NOUN
ejpam-5776	572	15	r	r	NOUN
ejpam-5776	572	16	haji	haji	PROPN
ejpam-5776	572	17	.	.	PUNCT
ejpam-5776	573	1	on	on	ADP
ejpam-5776	573	2	the	the	DET
ejpam-5776	573	3	non	non	ADJ
ejpam-5776	573	4	-	-	ADJ
ejpam-5776	573	5	commuting	commuting	ADJ
ejpam-5776	573	6	graph	graph	NOUN
ejpam-5776	573	7	of	of	ADP
ejpam-5776	573	8	dihedral	dihedral	ADJ
ejpam-5776	573	9	group	group	NOUN
ejpam-5776	573	10	.	.	PUNCT
ejpam-5776	574	1	electronic	electronic	ADJ
ejpam-5776	574	2	journal	journal	NOUN
ejpam-5776	574	3	of	of	ADP
ejpam-5776	574	4	graph	graph	NOUN
ejpam-5776	574	5	theory	theory	NOUN
ejpam-5776	574	6	and	and	CCONJ
ejpam-5776	574	7	applications	application	NOUN
ejpam-5776	574	8	,	,	PUNCT
ejpam-5776	574	9	8(2):233–239	8(2):233–239	NUM
ejpam-5776	574	10	,	,	PUNCT
ejpam-5776	574	11	2020	2020	NUM
ejpam-5776	574	12	.	.	PUNCT
ejpam-5776	575	1	[	[	X
ejpam-5776	575	2	18	18	NUM
ejpam-5776	575	3	]	]	X
ejpam-5776	575	4	m	m	VERB
ejpam-5776	575	5	u	u	NOUN
ejpam-5776	575	6	romdhini	romdhini	NOUN
ejpam-5776	575	7	and	and	CCONJ
ejpam-5776	575	8	a	a	DET
ejpam-5776	575	9	nawawi	nawawi	ADJ
ejpam-5776	575	10	.	.	PUNCT
ejpam-5776	575	11	degree	degree	NOUN
ejpam-5776	575	12	subtraction	subtraction	NOUN
ejpam-5776	575	13	energy	energy	NOUN
ejpam-5776	575	14	of	of	ADP
ejpam-5776	575	15	commuting	commute	VERB
ejpam-5776	575	16	and	and	CCONJ
ejpam-5776	575	17	noncommuting	noncommute	VERB
ejpam-5776	575	18	graphs	graph	NOUN
ejpam-5776	575	19	for	for	ADP
ejpam-5776	575	20	dihedral	dihedral	ADJ
ejpam-5776	575	21	groups	group	NOUN
ejpam-5776	575	22	.	.	PUNCT
ejpam-5776	576	1	international	international	ADJ
ejpam-5776	576	2	journal	journal	PROPN
ejpam-5776	576	3	of	of	ADP
ejpam-5776	576	4	mathematical	mathematical	ADJ
ejpam-5776	576	5	and	and	CCONJ
ejpam-5776	576	6	computational	computational	ADJ
ejpam-5776	576	7	science	science	NOUN
ejpam-5776	576	8	,	,	PUNCT
ejpam-5776	576	9	18(3):497–508	18(3):497–508	NUM
ejpam-5776	576	10	,	,	PUNCT
ejpam-5776	576	11	2023	2023	NUM
ejpam-5776	576	12	.	.	PUNCT
ejpam-5776	577	1	[	[	X
ejpam-5776	577	2	19	19	NUM
ejpam-5776	577	3	]	]	X
ejpam-5776	577	4	h	h	NOUN
ejpam-5776	577	5	s	s	PROPN
ejpam-5776	577	6	ramane	ramane	NOUN
ejpam-5776	577	7	and	and	CCONJ
ejpam-5776	577	8	s	s	NOUN
ejpam-5776	577	9	s	s	NOUN
ejpam-5776	577	10	shinde	shinde	PROPN
ejpam-5776	577	11	.	.	PUNCT
ejpam-5776	577	12	degree	degree	NOUN
ejpam-5776	577	13	exponent	exponent	NOUN
ejpam-5776	577	14	polynomial	polynomial	NOUN
ejpam-5776	577	15	of	of	ADP
ejpam-5776	577	16	graphs	graph	NOUN
ejpam-5776	577	17	obtained	obtain	VERB
ejpam-5776	577	18	by	by	ADP
ejpam-5776	577	19	some	some	DET
ejpam-5776	577	20	graph	graph	NOUN
ejpam-5776	577	21	operations	operation	NOUN
ejpam-5776	577	22	.	.	PUNCT
ejpam-5776	578	1	electronic	electronic	ADJ
ejpam-5776	578	2	journal	journal	NOUN
ejpam-5776	578	3	of	of	ADP
ejpam-5776	578	4	graph	graph	NOUN
ejpam-5776	578	5	theory	theory	NOUN
ejpam-5776	578	6	and	and	CCONJ
ejpam-5776	578	7	application	application	NOUN
ejpam-5776	578	8	,	,	PUNCT
ejpam-5776	578	9	63:161–168	63:161–168	PROPN
ejpam-5776	578	10	,	,	PUNCT
ejpam-5776	578	11	2017	2017	NUM
ejpam-5776	578	12	.	.	PUNCT