id	sid	tid	token	lemma	pos
american_scientific_journal-1326	1	1	139	139	NUM
american_scientific_journal-1326	1	2	american	american	ADJ
american_scientific_journal-1326	1	3	scientific	scientific	ADJ
american_scientific_journal-1326	1	4	research	research	NOUN
american_scientific_journal-1326	1	5	journal	journal	NOUN
american_scientific_journal-1326	1	6	for	for	ADP
american_scientific_journal-1326	1	7	engineering	engineering	NOUN
american_scientific_journal-1326	1	8	,	,	PUNCT
american_scientific_journal-1326	1	9	technology	technology	NOUN
american_scientific_journal-1326	1	10	,	,	PUNCT
american_scientific_journal-1326	1	11	and	and	CCONJ
american_scientific_journal-1326	1	12	sciences	science	NOUN
american_scientific_journal-1326	1	13	(	(	PUNCT
american_scientific_journal-1326	1	14	asrjets	asrjet	NOUN
american_scientific_journal-1326	1	15	)	)	PUNCT
american_scientific_journal-1326	1	16	issn	issn	PROPN
american_scientific_journal-1326	1	17	(	(	PUNCT
american_scientific_journal-1326	1	18	print	print	NOUN
american_scientific_journal-1326	1	19	)	)	PUNCT
american_scientific_journal-1326	1	20	2313	2313	NUM
american_scientific_journal-1326	1	21	-	-	SYM
american_scientific_journal-1326	1	22	4410	4410	NUM
american_scientific_journal-1326	1	23	,	,	PUNCT
american_scientific_journal-1326	1	24	issn	issn	PROPN
american_scientific_journal-1326	1	25	(	(	PUNCT
american_scientific_journal-1326	1	26	online	online	ADJ
american_scientific_journal-1326	1	27	)	)	PUNCT
american_scientific_journal-1326	1	28	2313	2313	NUM
american_scientific_journal-1326	1	29	-	-	SYM
american_scientific_journal-1326	1	30	4402	4402	NUM
american_scientific_journal-1326	1	31	©	©	PROPN
american_scientific_journal-1326	1	32	global	global	ADJ
american_scientific_journal-1326	1	33	society	society	NOUN
american_scientific_journal-1326	1	34	of	of	ADP
american_scientific_journal-1326	1	35	scientific	scientific	ADJ
american_scientific_journal-1326	1	36	research	research	NOUN
american_scientific_journal-1326	1	37	and	and	CCONJ
american_scientific_journal-1326	1	38	researchers	researcher	NOUN
american_scientific_journal-1326	1	39	http://asrjetsjournal.org/	http://asrjetsjournal.org/	VERB
american_scientific_journal-1326	1	40	a	a	DET
american_scientific_journal-1326	1	41	high	high	ADJ
american_scientific_journal-1326	1	42	accurate	accurate	ADJ
american_scientific_journal-1326	1	43	approximation	approximation	NOUN
american_scientific_journal-1326	1	44	for	for	ADP
american_scientific_journal-1326	1	45	a	a	DET
american_scientific_journal-1326	1	46	galactic	galactic	ADJ
american_scientific_journal-1326	1	47	newtonian	newtonian	ADJ
american_scientific_journal-1326	1	48	nonlinear	nonlinear	ADJ
american_scientific_journal-1326	1	49	model	model	NOUN
american_scientific_journal-1326	1	50	validated	validate	VERB
american_scientific_journal-1326	1	51	by	by	ADP
american_scientific_journal-1326	1	52	employing	employ	VERB
american_scientific_journal-1326	1	53	observational	observational	ADJ
american_scientific_journal-1326	1	54	data	datum	NOUN
american_scientific_journal-1326	1	55	u.	u.	PROPN
american_scientific_journal-1326	1	56	filobello	filobello	PROPN
american_scientific_journal-1326	1	57	-	-	PUNCT
american_scientific_journal-1326	1	58	ninoa	ninoa	NOUN
american_scientific_journal-1326	1	59	,	,	PUNCT
american_scientific_journal-1326	1	60	h.	h.	PROPN
american_scientific_journal-1326	1	61	vazquez	vazquez	PROPN
american_scientific_journal-1326	1	62	-	-	PUNCT
american_scientific_journal-1326	1	63	lealb	lealb	PROPN
american_scientific_journal-1326	1	64	*	*	NOUN
american_scientific_journal-1326	1	65	,	,	PUNCT
american_scientific_journal-1326	1	66	m.	m.	PROPN
american_scientific_journal-1326	1	67	sandoval	sandoval	PROPN
american_scientific_journal-1326	1	68	-	-	PUNCT
american_scientific_journal-1326	1	69	hernandezc	hernandezc	PROPN
american_scientific_journal-1326	1	70	,	,	PUNCT
american_scientific_journal-1326	1	71	j.	j.	PROPN
american_scientific_journal-1326	1	72	a.	a.	PROPN
american_scientific_journal-1326	1	73	a.	a.	PROPN
american_scientific_journal-1326	1	74	perez	perez	PROPN
american_scientific_journal-1326	1	75	-	-	PUNCT
american_scientific_journal-1326	1	76	sesmad	sesmad	PROPN
american_scientific_journal-1326	1	77	,	,	PUNCT
american_scientific_journal-1326	1	78	a.	a.	PROPN
american_scientific_journal-1326	1	79	perez	perez	PROPN
american_scientific_journal-1326	1	80	-	-	PUNCT
american_scientific_journal-1326	1	81	sesmae	sesmae	NOUN
american_scientific_journal-1326	1	82	,	,	PUNCT
american_scientific_journal-1326	1	83	a.	a.	PROPN
american_scientific_journal-1326	1	84	sarmiento	sarmiento	PROPN
american_scientific_journal-1326	1	85	-	-	PUNCT
american_scientific_journal-1326	1	86	reyesf	reyesf	NOUN
american_scientific_journal-1326	1	87	,	,	PUNCT
american_scientific_journal-1326	1	88	v.	v.	ADP
american_scientific_journal-1326	1	89	m.	m.	PROPN
american_scientific_journal-1326	1	90	jimenezfernandezg	jimenezfernandezg	PROPN
american_scientific_journal-1326	1	91	,	,	PUNCT
american_scientific_journal-1326	1	92	j.	j.	PROPN
american_scientific_journal-1326	1	93	huerta	huerta	PROPN
american_scientific_journal-1326	1	94	-	-	PUNCT
american_scientific_journal-1326	1	95	chuah	chuah	PROPN
american_scientific_journal-1326	1	96	,	,	PUNCT
american_scientific_journal-1326	1	97	d.	d.	PROPN
american_scientific_journal-1326	1	98	pereyra	pereyra	PROPN
american_scientific_journal-1326	1	99	-	-	PUNCT
american_scientific_journal-1326	1	100	diazi	diazi	PROPN
american_scientific_journal-1326	1	101	,	,	PUNCT
american_scientific_journal-1326	1	102	f.	f.	PROPN
american_scientific_journal-1326	1	103	castro	castro	PROPN
american_scientific_journal-1326	1	104	-	-	PUNCT
american_scientific_journal-1326	1	105	gonzalezj	gonzalezj	PROPN
american_scientific_journal-1326	1	106	,	,	PUNCT
american_scientific_journal-1326	1	107	j.	j.	PROPN
american_scientific_journal-1326	1	108	r.	r.	PROPN
american_scientific_journal-1326	1	109	laguna	laguna	PROPN
american_scientific_journal-1326	1	110	-	-	PUNCT
american_scientific_journal-1326	1	111	camachok	camachok	PROPN
american_scientific_journal-1326	1	112	,	,	PUNCT
american_scientific_journal-1326	1	113	a.	a.	PROPN
american_scientific_journal-1326	1	114	e.	e.	PROPN
american_scientific_journal-1326	1	115	gasca	gasca	PROPN
american_scientific_journal-1326	1	116	-	-	PUNCT
american_scientific_journal-1326	1	117	herreral	herreral	NOUN
american_scientific_journal-1326	1	118	,	,	PUNCT
american_scientific_journal-1326	1	119	j.	j.	PROPN
american_scientific_journal-1326	1	120	e.	e.	PROPN
american_scientific_journal-1326	1	121	pretelin	pretelin	PROPN
american_scientific_journal-1326	1	122	canelam	canelam	PROPN
american_scientific_journal-1326	1	123	,	,	PUNCT
american_scientific_journal-1326	1	124	b.	b.	PROPN
american_scientific_journal-1326	1	125	e.	e.	PROPN
american_scientific_journal-1326	1	126	palmagrayebn	palmagrayebn	PROPN
american_scientific_journal-1326	1	127	,	,	PUNCT
american_scientific_journal-1326	1	128	j.	j.	PROPN
american_scientific_journal-1326	1	129	cervantes	cervantes	PROPN
american_scientific_journal-1326	1	130	-	-	PUNCT
american_scientific_journal-1326	1	131	perezo	perezo	NOUN
american_scientific_journal-1326	1	132	,	,	PUNCT
american_scientific_journal-1326	1	133	c.	c.	PROPN
american_scientific_journal-1326	1	134	e.	e.	PROPN
american_scientific_journal-1326	1	135	sampieri	sampieri	PROPN
american_scientific_journal-1326	1	136	-	-	PUNCT
american_scientific_journal-1326	1	137	gonzalezp	gonzalezp	NOUN
american_scientific_journal-1326	1	138	,	,	PUNCT
american_scientific_journal-1326	1	139	l.	l.	PROPN
american_scientific_journal-1326	1	140	cuellar	cuellar	PROPN
american_scientific_journal-1326	1	141	-	-	PUNCT
american_scientific_journal-1326	1	142	hernándezq	hernándezq	PROPN
american_scientific_journal-1326	1	143	,	,	PUNCT
american_scientific_journal-1326	1	144	c.	c.	PROPN
american_scientific_journal-1326	1	145	hoyos	hoyos	PROPN
american_scientific_journal-1326	1	146	-	-	PUNCT
american_scientific_journal-1326	1	147	reyesr	reyesr	PROPN
american_scientific_journal-1326	1	148	,	,	PUNCT
american_scientific_journal-1326	1	149	r.	r.	PROPN
american_scientific_journal-1326	1	150	ruiz	ruiz	PROPN
american_scientific_journal-1326	1	151	-	-	PUNCT
american_scientific_journal-1326	1	152	gomezs	gomezs	PROPN
american_scientific_journal-1326	1	153	,	,	PUNCT
american_scientific_journal-1326	1	154	a.	a.	PROPN
american_scientific_journal-1326	1	155	d.	d.	PROPN
american_scientific_journal-1326	1	156	contreras	contreras	PROPN
american_scientific_journal-1326	1	157	-	-	PUNCT
american_scientific_journal-1326	1	158	hernandezt	hernandezt	PROPN
american_scientific_journal-1326	1	159	,	,	PUNCT
american_scientific_journal-1326	1	160	o.	o.	PROPN
american_scientific_journal-1326	1	161	alvarezgascau	alvarezgascau	PROPN
american_scientific_journal-1326	1	162	,	,	PUNCT
american_scientific_journal-1326	1	163	f.	f.	PROPN
american_scientific_journal-1326	1	164	j.	j.	PROPN
american_scientific_journal-1326	1	165	gonzalez	gonzalez	PROPN
american_scientific_journal-1326	1	166	-	-	PUNCT
american_scientific_journal-1326	1	167	martinezv	martinezv	PROPN
american_scientific_journal-1326	1	168	a	a	PRON
american_scientific_journal-1326	1	169	,	,	PUNCT
american_scientific_journal-1326	1	170	b	b	NOUN
american_scientific_journal-1326	1	171	,	,	PUNCT
american_scientific_journal-1326	1	172	g	g	PROPN
american_scientific_journal-1326	1	173	,	,	PUNCT
american_scientific_journal-1326	1	174	h	h	NOUN
american_scientific_journal-1326	1	175	,	,	PUNCT
american_scientific_journal-1326	1	176	i	i	PRON
american_scientific_journal-1326	1	177	,	,	PUNCT
american_scientific_journal-1326	1	178	j	j	PROPN
american_scientific_journal-1326	1	179	,	,	PUNCT
american_scientific_journal-1326	1	180	k	k	PROPN
american_scientific_journal-1326	1	181	,	,	PUNCT
american_scientific_journal-1326	1	182	l	l	NOUN
american_scientific_journal-1326	1	183	,	,	PUNCT
american_scientific_journal-1326	1	184	m	m	PROPN
american_scientific_journal-1326	1	185	,	,	PUNCT
american_scientific_journal-1326	1	186	n	n	CCONJ
american_scientific_journal-1326	1	187	,	,	PUNCT
american_scientific_journal-1326	1	188	o	o	NOUN
american_scientific_journal-1326	1	189	,	,	PUNCT
american_scientific_journal-1326	1	190	p	p	X
american_scientific_journal-1326	1	191	,	,	PUNCT
american_scientific_journal-1326	1	192	q	q	ADJ
american_scientific_journal-1326	1	193	,	,	PUNCT
american_scientific_journal-1326	1	194	r	r	NOUN
american_scientific_journal-1326	1	195	,	,	PUNCT
american_scientific_journal-1326	1	196	s	s	PROPN
american_scientific_journal-1326	1	197	,	,	PUNCT
american_scientific_journal-1326	1	198	t	t	PROPN
american_scientific_journal-1326	1	199	,	,	PUNCT
american_scientific_journal-1326	1	200	u	u	NOUN
american_scientific_journal-1326	1	201	,	,	PUNCT
american_scientific_journal-1326	1	202	vfacultad	vfacultad	PROPN
american_scientific_journal-1326	1	203	de	de	PROPN
american_scientific_journal-1326	1	204	instrumentación	instrumentación	PROPN
american_scientific_journal-1326	1	205	electrónica	electrónica	PROPN
american_scientific_journal-1326	1	206	,	,	PUNCT
american_scientific_journal-1326	1	207	universidad	universidad	PROPN
american_scientific_journal-1326	1	208	veracruzana	veracruzana	PROPN
american_scientific_journal-1326	1	209	,	,	PUNCT
american_scientific_journal-1326	1	210	circuito	circuito	PROPN
american_scientific_journal-1326	1	211	gonzalo	gonzalo	PROPN
american_scientific_journal-1326	1	212	aguirre	aguirre	PROPN
american_scientific_journal-1326	1	213	beltrán	beltrán	VERB
american_scientific_journal-1326	1	214	s	s	PROPN
american_scientific_journal-1326	1	215	/	/	SYM
american_scientific_journal-1326	1	216	n	n	CCONJ
american_scientific_journal-1326	1	217	,	,	PUNCT
american_scientific_journal-1326	1	218	xalapa	xalapa	PROPN
american_scientific_journal-1326	1	219	,	,	PUNCT
american_scientific_journal-1326	1	220	veracruz	veracruz	PROPN
american_scientific_journal-1326	1	221	,	,	PUNCT
american_scientific_journal-1326	1	222	91000	91000	NUM
american_scientific_journal-1326	1	223	,	,	PUNCT
american_scientific_journal-1326	1	224	méxico	méxico	PROPN
american_scientific_journal-1326	1	225	.	.	PUNCT
american_scientific_journal-1326	2	1	cdoctorado	cdoctorado	VERB
american_scientific_journal-1326	2	2	en	en	ADP
american_scientific_journal-1326	2	3	ciencia	ciencia	PROPN
american_scientific_journal-1326	2	4	,	,	PUNCT
american_scientific_journal-1326	2	5	cultura	cultura	PROPN
american_scientific_journal-1326	2	6	y	y	PROPN
american_scientific_journal-1326	2	7	tecnología	tecnología	PROPN
american_scientific_journal-1326	2	8	,	,	PUNCT
american_scientific_journal-1326	2	9	universidad	universidad	PROPN
american_scientific_journal-1326	2	10	de	de	PROPN
american_scientific_journal-1326	2	11	xalapa	xalapa	PROPN
american_scientific_journal-1326	2	12	,	,	PUNCT
american_scientific_journal-1326	2	13	km	km	PROPN
american_scientific_journal-1326	2	14	2	2	NUM
american_scientific_journal-1326	2	15	carretera	carretera	NOUN
american_scientific_journal-1326	2	16	xalapa	xalapa	PROPN
american_scientific_journal-1326	2	17	-	-	PUNCT
american_scientific_journal-1326	2	18	veracruz	veracruz	PROPN
american_scientific_journal-1326	2	19	,	,	PUNCT
american_scientific_journal-1326	2	20	xalapa	xalapa	PROPN
american_scientific_journal-1326	2	21	91190	91190	NUM
american_scientific_journal-1326	2	22	,	,	PUNCT
american_scientific_journal-1326	2	23	veracruz	veracruz	PROPN
american_scientific_journal-1326	2	24	,	,	PUNCT
american_scientific_journal-1326	2	25	méxico	méxico	PROPN
american_scientific_journal-1326	2	26	.	.	PUNCT
american_scientific_journal-1326	3	1	dfacultad	dfacultad	PROPN
american_scientific_journal-1326	3	2	de	de	PROPN
american_scientific_journal-1326	3	3	ingeniería	ingeniería	PROPN
american_scientific_journal-1326	3	4	electrónica	electrónica	PROPN
american_scientific_journal-1326	3	5	y	y	PROPN
american_scientific_journal-1326	3	6	comunicaciones	comunicaciones	PROPN
american_scientific_journal-1326	3	7	,	,	PUNCT
american_scientific_journal-1326	3	8	universidad	universidad	PROPN
american_scientific_journal-1326	3	9	veracruzana	veracruzana	PROPN
american_scientific_journal-1326	3	10	,	,	PUNCT
american_scientific_journal-1326	3	11	venustiano	venustiano	PROPN
american_scientific_journal-1326	3	12	carranza	carranza	PROPN
american_scientific_journal-1326	3	13	s	s	PROPN
american_scientific_journal-1326	3	14	/	/	SYM
american_scientific_journal-1326	3	15	n	n	CCONJ
american_scientific_journal-1326	3	16	,	,	PUNCT
american_scientific_journal-1326	3	17	col	col	PROPN
american_scientific_journal-1326	3	18	.	.	PROPN
american_scientific_journal-1326	3	19	revolución	revolución	PROPN
american_scientific_journal-1326	3	20	,	,	PUNCT
american_scientific_journal-1326	3	21	93390	93390	NUM
american_scientific_journal-1326	3	22	,	,	PUNCT
american_scientific_journal-1326	3	23	poza	poza	PROPN
american_scientific_journal-1326	3	24	rica	rica	PROPN
american_scientific_journal-1326	3	25	,	,	PUNCT
american_scientific_journal-1326	3	26	veracruz	veracruz	PROPN
american_scientific_journal-1326	3	27	,	,	PUNCT
american_scientific_journal-1326	3	28	méxico	méxico	PROPN
american_scientific_journal-1326	3	29	.	.	PUNCT
american_scientific_journal-1326	4	1	efacultad	efacultad	PROPN
american_scientific_journal-1326	4	2	de	de	PROPN
american_scientific_journal-1326	4	3	ingeniería	ingeniería	PROPN
american_scientific_journal-1326	4	4	mecánica	mecánica	PROPN
american_scientific_journal-1326	4	5	eléctrica	eléctrica	PROPN
american_scientific_journal-1326	4	6	,	,	PUNCT
american_scientific_journal-1326	4	7	universidad	universidad	PROPN
american_scientific_journal-1326	4	8	veracruzana	veracruzana	PROPN
american_scientific_journal-1326	4	9	,	,	PUNCT
american_scientific_journal-1326	4	10	venustiano	venustiano	PROPN
american_scientific_journal-1326	4	11	carranza	carranza	PROPN
american_scientific_journal-1326	4	12	s	s	PROPN
american_scientific_journal-1326	4	13	/	/	SYM
american_scientific_journal-1326	4	14	n	n	CCONJ
american_scientific_journal-1326	4	15	,	,	PUNCT
american_scientific_journal-1326	4	16	col	col	PROPN
american_scientific_journal-1326	4	17	.	.	PROPN
american_scientific_journal-1326	4	18	revolución	revolución	PROPN
american_scientific_journal-1326	4	19	,	,	PUNCT
american_scientific_journal-1326	4	20	93390	93390	NUM
american_scientific_journal-1326	4	21	,	,	PUNCT
american_scientific_journal-1326	4	22	poza	poza	PROPN
american_scientific_journal-1326	4	23	rica	rica	PROPN
american_scientific_journal-1326	4	24	,	,	PUNCT
american_scientific_journal-1326	4	25	veracruz	veracruz	PROPN
american_scientific_journal-1326	4	26	,	,	PUNCT
american_scientific_journal-1326	4	27	méxico	méxico	PROPN
american_scientific_journal-1326	4	28	.	.	PUNCT
american_scientific_journal-1326	5	1	bemail	bemail	PROPN
american_scientific_journal-1326	5	2	:	:	PUNCT
american_scientific_journal-1326	6	1	hvazquez@uv.com	hvazquez@uv.com	X
american_scientific_journal-1326	7	1	abstract	abstract	NOUN
american_scientific_journal-1326	7	2	this	this	DET
american_scientific_journal-1326	7	3	article	article	NOUN
american_scientific_journal-1326	7	4	proposes	propose	VERB
american_scientific_journal-1326	7	5	perturbation	perturbation	NOUN
american_scientific_journal-1326	7	6	method	method	NOUN
american_scientific_journal-1326	7	7	(	(	PUNCT
american_scientific_journal-1326	7	8	pm	pm	NOUN
american_scientific_journal-1326	7	9	)	)	PUNCT
american_scientific_journal-1326	7	10	to	to	PART
american_scientific_journal-1326	7	11	solve	solve	VERB
american_scientific_journal-1326	7	12	nonlinear	nonlinear	ADJ
american_scientific_journal-1326	7	13	problems	problem	NOUN
american_scientific_journal-1326	7	14	.	.	PUNCT
american_scientific_journal-1326	8	1	as	as	SCONJ
american_scientific_journal-1326	8	2	case	case	NOUN
american_scientific_journal-1326	8	3	study	study	NOUN
american_scientific_journal-1326	8	4	pm	pm	NOUN
american_scientific_journal-1326	8	5	is	be	AUX
american_scientific_journal-1326	8	6	employed	employ	VERB
american_scientific_journal-1326	8	7	to	to	PART
american_scientific_journal-1326	8	8	provide	provide	VERB
american_scientific_journal-1326	8	9	a	a	DET
american_scientific_journal-1326	8	10	detailed	detailed	ADJ
american_scientific_journal-1326	8	11	study	study	NOUN
american_scientific_journal-1326	8	12	of	of	ADP
american_scientific_journal-1326	8	13	a	a	DET
american_scientific_journal-1326	8	14	nonlinear	nonlinear	ADJ
american_scientific_journal-1326	8	15	galactic	galactic	ADJ
american_scientific_journal-1326	8	16	model	model	NOUN
american_scientific_journal-1326	8	17	.	.	PUNCT
american_scientific_journal-1326	9	1	our	our	PRON
american_scientific_journal-1326	9	2	approach	approach	NOUN
american_scientific_journal-1326	9	3	is	be	AUX
american_scientific_journal-1326	9	4	rather	rather	ADV
american_scientific_journal-1326	9	5	elementary	elementary	ADJ
american_scientific_journal-1326	9	6	and	and	CCONJ
american_scientific_journal-1326	9	7	seeks	seek	VERB
american_scientific_journal-1326	9	8	to	to	PART
american_scientific_journal-1326	9	9	explain	explain	VERB
american_scientific_journal-1326	9	10	as	as	ADV
american_scientific_journal-1326	9	11	much	much	ADJ
american_scientific_journal-1326	9	12	detail	detail	NOUN
american_scientific_journal-1326	9	13	as	as	ADP
american_scientific_journal-1326	9	14	possible	possible	ADJ
american_scientific_journal-1326	9	15	the	the	DET
american_scientific_journal-1326	9	16	material	material	NOUN
american_scientific_journal-1326	9	17	of	of	ADP
american_scientific_journal-1326	9	18	this	this	DET
american_scientific_journal-1326	9	19	work	work	NOUN
american_scientific_journal-1326	9	20	.	.	PUNCT
american_scientific_journal-1326	10	1	-----------------------------------------------------------------------	-----------------------------------------------------------------------	PUNCT
american_scientific_journal-1326	11	1	*	*	PUNCT
american_scientific_journal-1326	11	2	corresponding	correspond	VERB
american_scientific_journal-1326	11	3	author	author	NOUN
american_scientific_journal-1326	11	4	.	.	PUNCT
american_scientific_journal-1326	12	1	http://asrjetsjournal.org/	http://asrjetsjournal.org/	PROPN
american_scientific_journal-1326	12	2	american	american	PROPN
american_scientific_journal-1326	12	3	scientific	scientific	PROPN
american_scientific_journal-1326	12	4	research	research	NOUN
american_scientific_journal-1326	12	5	journal	journal	NOUN
american_scientific_journal-1326	12	6	for	for	ADP
american_scientific_journal-1326	12	7	engineering	engineering	NOUN
american_scientific_journal-1326	12	8	,	,	PUNCT
american_scientific_journal-1326	12	9	technology	technology	NOUN
american_scientific_journal-1326	12	10	,	,	PUNCT
american_scientific_journal-1326	12	11	and	and	CCONJ
american_scientific_journal-1326	12	12	sciences	science	NOUN
american_scientific_journal-1326	12	13	(	(	PUNCT
american_scientific_journal-1326	12	14	asrjets	asrjet	NOUN
american_scientific_journal-1326	12	15	)	)	PUNCT
american_scientific_journal-1326	12	16	(	(	PUNCT
american_scientific_journal-1326	12	17	2017	2017	NUM
american_scientific_journal-1326	12	18	)	)	PUNCT
american_scientific_journal-1326	12	19	volume	volume	NOUN
american_scientific_journal-1326	12	20	27	27	NUM
american_scientific_journal-1326	12	21	,	,	PUNCT
american_scientific_journal-1326	12	22	no	no	DET
american_scientific_journal-1326	12	23	1	1	NUM
american_scientific_journal-1326	12	24	,	,	PUNCT
american_scientific_journal-1326	12	25	pp	pp	ADV
american_scientific_journal-1326	12	26	139	139	NUM
american_scientific_journal-1326	12	27	-	-	SYM
american_scientific_journal-1326	12	28	150	150	NUM
american_scientific_journal-1326	12	29	140	140	NUM
american_scientific_journal-1326	12	30	in	in	ADP
american_scientific_journal-1326	12	31	particular	particular	ADJ
american_scientific_journal-1326	13	1	,	,	PUNCT
american_scientific_journal-1326	13	2	our	our	PRON
american_scientific_journal-1326	13	3	solution	solution	NOUN
american_scientific_journal-1326	13	4	gives	give	VERB
american_scientific_journal-1326	13	5	rise	rise	NOUN
american_scientific_journal-1326	13	6	qualitatively	qualitatively	ADV
american_scientific_journal-1326	13	7	,	,	PUNCT
american_scientific_journal-1326	13	8	to	to	ADP
american_scientific_journal-1326	13	9	the	the	DET
american_scientific_journal-1326	13	10	known	know	VERB
american_scientific_journal-1326	13	11	flat	flat	ADJ
american_scientific_journal-1326	13	12	rotation	rotation	NOUN
american_scientific_journal-1326	13	13	curves	curve	NOUN
american_scientific_journal-1326	13	14	.	.	PUNCT
american_scientific_journal-1326	14	1	in	in	ADP
american_scientific_journal-1326	14	2	fact	fact	NOUN
american_scientific_journal-1326	14	3	,	,	PUNCT
american_scientific_journal-1326	14	4	we	we	PRON
american_scientific_journal-1326	14	5	compare	compare	VERB
american_scientific_journal-1326	14	6	the	the	DET
american_scientific_journal-1326	14	7	numerical	numerical	ADJ
american_scientific_journal-1326	14	8	solution	solution	NOUN
american_scientific_journal-1326	14	9	and	and	CCONJ
american_scientific_journal-1326	14	10	the	the	DET
american_scientific_journal-1326	14	11	obtained	obtain	VERB
american_scientific_journal-1326	14	12	approximation	approximation	NOUN
american_scientific_journal-1326	14	13	by	by	ADP
american_scientific_journal-1326	14	14	employing	employ	VERB
american_scientific_journal-1326	14	15	observational	observational	ADJ
american_scientific_journal-1326	14	16	data	datum	NOUN
american_scientific_journal-1326	14	17	proving	prove	VERB
american_scientific_journal-1326	14	18	the	the	DET
american_scientific_journal-1326	14	19	validity	validity	NOUN
american_scientific_journal-1326	14	20	and	and	CCONJ
american_scientific_journal-1326	14	21	high	high	ADJ
american_scientific_journal-1326	14	22	accuracy	accuracy	NOUN
american_scientific_journal-1326	14	23	of	of	ADP
american_scientific_journal-1326	14	24	the	the	DET
american_scientific_journal-1326	14	25	model	model	NOUN
american_scientific_journal-1326	14	26	under	under	ADP
american_scientific_journal-1326	14	27	study	study	NOUN
american_scientific_journal-1326	14	28	.	.	PUNCT
american_scientific_journal-1326	15	1	keywords	keyword	NOUN
american_scientific_journal-1326	15	2	:	:	PUNCT
american_scientific_journal-1326	15	3	perturbation	perturbation	NOUN
american_scientific_journal-1326	15	4	method	method	NOUN
american_scientific_journal-1326	15	5	;	;	PUNCT
american_scientific_journal-1326	15	6	nonlinear	nonlinear	ADJ
american_scientific_journal-1326	15	7	galactic	galactic	ADJ
american_scientific_journal-1326	15	8	model	model	NOUN
american_scientific_journal-1326	15	9	;	;	PUNCT
american_scientific_journal-1326	15	10	flat	flat	ADJ
american_scientific_journal-1326	15	11	rotation	rotation	NOUN
american_scientific_journal-1326	15	12	curves	curve	NOUN
american_scientific_journal-1326	15	13	;	;	PUNCT
american_scientific_journal-1326	15	14	approximated	approximate	VERB
american_scientific_journal-1326	15	15	solutions	solution	NOUN
american_scientific_journal-1326	15	16	.	.	PUNCT
american_scientific_journal-1326	16	1	1	1	X
american_scientific_journal-1326	16	2	.	.	X
american_scientific_journal-1326	16	3	introduction	introduction	NOUN
american_scientific_journal-1326	16	4	the	the	DET
american_scientific_journal-1326	16	5	unusual	unusual	ADJ
american_scientific_journal-1326	16	6	behavior	behavior	NOUN
american_scientific_journal-1326	16	7	of	of	ADP
american_scientific_journal-1326	16	8	the	the	DET
american_scientific_journal-1326	16	9	rotation	rotation	NOUN
american_scientific_journal-1326	16	10	curves	curve	NOUN
american_scientific_journal-1326	16	11	in	in	ADP
american_scientific_journal-1326	16	12	spiral	spiral	ADJ
american_scientific_journal-1326	16	13	galaxies	galaxy	NOUN
american_scientific_journal-1326	16	14	is	be	AUX
american_scientific_journal-1326	16	15	a	a	DET
american_scientific_journal-1326	16	16	scientific	scientific	ADJ
american_scientific_journal-1326	16	17	discovery	discovery	NOUN
american_scientific_journal-1326	16	18	of	of	ADP
american_scientific_journal-1326	16	19	paramount	paramount	ADJ
american_scientific_journal-1326	16	20	importance	importance	NOUN
american_scientific_journal-1326	16	21	.	.	PUNCT
american_scientific_journal-1326	17	1	it	it	PRON
american_scientific_journal-1326	17	2	has	have	AUX
american_scientific_journal-1326	17	3	become	become	VERB
american_scientific_journal-1326	17	4	one	one	NUM
american_scientific_journal-1326	17	5	of	of	ADP
american_scientific_journal-1326	17	6	the	the	DET
american_scientific_journal-1326	17	7	strongest	strong	ADJ
american_scientific_journal-1326	17	8	arguments	argument	NOUN
american_scientific_journal-1326	17	9	supporting	support	VERB
american_scientific_journal-1326	17	10	the	the	DET
american_scientific_journal-1326	17	11	existence	existence	NOUN
american_scientific_journal-1326	17	12	of	of	ADP
american_scientific_journal-1326	17	13	dark	dark	ADJ
american_scientific_journal-1326	17	14	matter	matter	NOUN
american_scientific_journal-1326	17	15	and	and	CCONJ
american_scientific_journal-1326	17	16	has	have	AUX
american_scientific_journal-1326	17	17	even	even	ADV
american_scientific_journal-1326	17	18	led	lead	VERB
american_scientific_journal-1326	17	19	to	to	ADP
american_scientific_journal-1326	17	20	proposing	propose	VERB
american_scientific_journal-1326	17	21	modifications	modification	NOUN
american_scientific_journal-1326	17	22	of	of	ADP
american_scientific_journal-1326	17	23	newtonian	newtonian	ADJ
american_scientific_journal-1326	17	24	gravity	gravity	NOUN
american_scientific_journal-1326	17	25	and	and	CCONJ
american_scientific_journal-1326	17	26	general	general	ADJ
american_scientific_journal-1326	17	27	relativity	relativity	NOUN
american_scientific_journal-1326	17	28	theory	theory	NOUN
american_scientific_journal-1326	17	29	.	.	PUNCT
american_scientific_journal-1326	18	1	nevertheless	nevertheless	ADV
american_scientific_journal-1326	18	2	,	,	PUNCT
american_scientific_journal-1326	18	3	instead	instead	ADV
american_scientific_journal-1326	18	4	of	of	ADP
american_scientific_journal-1326	18	5	considering	consider	VERB
american_scientific_journal-1326	18	6	the	the	DET
american_scientific_journal-1326	18	7	above	above	ADJ
american_scientific_journal-1326	18	8	approaches	approach	NOUN
american_scientific_journal-1326	18	9	here	here	ADV
american_scientific_journal-1326	18	10	,	,	PUNCT
american_scientific_journal-1326	18	11	this	this	DET
american_scientific_journal-1326	18	12	paper	paper	NOUN
american_scientific_journal-1326	18	13	considers	consider	VERB
american_scientific_journal-1326	18	14	the	the	DET
american_scientific_journal-1326	18	15	possibility	possibility	NOUN
american_scientific_journal-1326	18	16	to	to	PART
american_scientific_journal-1326	18	17	explain	explain	VERB
american_scientific_journal-1326	18	18	them	they	PRON
american_scientific_journal-1326	18	19	without	without	ADP
american_scientific_journal-1326	18	20	leaving	leave	VERB
american_scientific_journal-1326	18	21	the	the	DET
american_scientific_journal-1326	18	22	scope	scope	NOUN
american_scientific_journal-1326	18	23	of	of	ADP
american_scientific_journal-1326	18	24	newtonian	newtonian	ADJ
american_scientific_journal-1326	18	25	physics	physic	NOUN
american_scientific_journal-1326	18	26	.	.	PUNCT
american_scientific_journal-1326	19	1	essentially	essentially	ADV
american_scientific_journal-1326	19	2	a	a	DET
american_scientific_journal-1326	19	3	spiral	spiral	ADJ
american_scientific_journal-1326	19	4	galaxy	galaxy	NOUN
american_scientific_journal-1326	19	5	consists	consist	VERB
american_scientific_journal-1326	19	6	of	of	ADP
american_scientific_journal-1326	19	7	:	:	PUNCT
american_scientific_journal-1326	19	8	1	1	NUM
american_scientific_journal-1326	19	9	)	)	PUNCT
american_scientific_journal-1326	19	10	disk	disk	NOUN
american_scientific_journal-1326	19	11	.	.	PUNCT
american_scientific_journal-1326	20	1	in	in	ADP
american_scientific_journal-1326	20	2	this	this	DET
american_scientific_journal-1326	20	3	region	region	NOUN
american_scientific_journal-1326	20	4	,	,	PUNCT
american_scientific_journal-1326	20	5	stars	star	NOUN
american_scientific_journal-1326	20	6	and	and	CCONJ
american_scientific_journal-1326	20	7	other	other	ADJ
american_scientific_journal-1326	20	8	components	component	NOUN
american_scientific_journal-1326	20	9	such	such	ADJ
american_scientific_journal-1326	20	10	as	as	ADP
american_scientific_journal-1326	20	11	gases	gas	NOUN
american_scientific_journal-1326	20	12	essentially	essentially	ADV
american_scientific_journal-1326	20	13	move	move	VERB
american_scientific_journal-1326	20	14	in	in	ADP
american_scientific_journal-1326	20	15	circular	circular	ADJ
american_scientific_journal-1326	20	16	orbits	orbit	NOUN
american_scientific_journal-1326	20	17	around	around	ADP
american_scientific_journal-1326	20	18	the	the	DET
american_scientific_journal-1326	20	19	center	center	NOUN
american_scientific_journal-1326	20	20	of	of	ADP
american_scientific_journal-1326	20	21	the	the	DET
american_scientific_journal-1326	20	22	galaxy	galaxy	NOUN
american_scientific_journal-1326	20	23	.	.	PUNCT
american_scientific_journal-1326	21	1	this	this	DET
american_scientific_journal-1326	21	2	part	part	NOUN
american_scientific_journal-1326	21	3	is	be	AUX
american_scientific_journal-1326	21	4	characterized	characterize	VERB
american_scientific_journal-1326	21	5	for	for	ADP
american_scientific_journal-1326	21	6	the	the	DET
american_scientific_journal-1326	21	7	energy	energy	NOUN
american_scientific_journal-1326	21	8	of	of	ADP
american_scientific_journal-1326	21	9	motion	motion	NOUN
american_scientific_journal-1326	21	10	mainly	mainly	ADV
american_scientific_journal-1326	21	11	due	due	ADJ
american_scientific_journal-1326	21	12	to	to	ADP
american_scientific_journal-1326	21	13	rotation	rotation	NOUN
american_scientific_journal-1326	21	14	,	,	PUNCT
american_scientific_journal-1326	21	15	in	in	ADP
american_scientific_journal-1326	21	16	fact	fact	NOUN
american_scientific_journal-1326	21	17	the	the	DET
american_scientific_journal-1326	21	18	random	random	ADJ
american_scientific_journal-1326	21	19	movements	movement	NOUN
american_scientific_journal-1326	21	20	represent	represent	VERB
american_scientific_journal-1326	21	21	only	only	ADV
american_scientific_journal-1326	21	22	10	10	NUM
american_scientific_journal-1326	21	23	%	%	NOUN
american_scientific_journal-1326	21	24	of	of	ADP
american_scientific_journal-1326	21	25	that	that	DET
american_scientific_journal-1326	21	26	value	value	NOUN
american_scientific_journal-1326	21	27	[	[	X
american_scientific_journal-1326	21	28	2	2	NUM
american_scientific_journal-1326	21	29	]	]	PUNCT
american_scientific_journal-1326	21	30	.	.	PUNCT
american_scientific_journal-1326	22	1	2	2	X
american_scientific_journal-1326	22	2	)	)	PUNCT
american_scientific_journal-1326	22	3	stellar	stellar	ADJ
american_scientific_journal-1326	22	4	halo	halo	NOUN
american_scientific_journal-1326	22	5	.	.	PUNCT
american_scientific_journal-1326	22	6	is	be	AUX
american_scientific_journal-1326	22	7	an	an	DET
american_scientific_journal-1326	22	8	extended	extended	ADJ
american_scientific_journal-1326	22	9	,	,	PUNCT
american_scientific_journal-1326	22	10	roughly	roughly	ADV
american_scientific_journal-1326	22	11	spherical	spherical	ADJ
american_scientific_journal-1326	22	12	component	component	NOUN
american_scientific_journal-1326	22	13	of	of	ADP
american_scientific_journal-1326	22	14	a	a	DET
american_scientific_journal-1326	22	15	galaxy	galaxy	NOUN
american_scientific_journal-1326	22	16	which	which	PRON
american_scientific_journal-1326	22	17	extends	extend	VERB
american_scientific_journal-1326	22	18	beyond	beyond	ADP
american_scientific_journal-1326	22	19	the	the	DET
american_scientific_journal-1326	22	20	main	main	ADJ
american_scientific_journal-1326	22	21	,	,	PUNCT
american_scientific_journal-1326	22	22	visible	visible	ADJ
american_scientific_journal-1326	22	23	component	component	NOUN
american_scientific_journal-1326	22	24	[	[	X
american_scientific_journal-1326	22	25	2	2	NUM
american_scientific_journal-1326	22	26	]	]	PUNCT
american_scientific_journal-1326	22	27	.	.	PUNCT
american_scientific_journal-1326	23	1	this	this	DET
american_scientific_journal-1326	23	2	region	region	NOUN
american_scientific_journal-1326	23	3	is	be	AUX
american_scientific_journal-1326	23	4	characterized	characterize	VERB
american_scientific_journal-1326	23	5	by	by	ADP
american_scientific_journal-1326	23	6	disordered	disordered	ADJ
american_scientific_journal-1326	23	7	rotational	rotational	ADJ
american_scientific_journal-1326	23	8	movements	movement	NOUN
american_scientific_journal-1326	23	9	and	and	CCONJ
american_scientific_journal-1326	23	10	large	large	ADJ
american_scientific_journal-1326	23	11	random	random	ADJ
american_scientific_journal-1326	23	12	motions	motion	NOUN
american_scientific_journal-1326	23	13	.	.	PUNCT
american_scientific_journal-1326	24	1	3	3	X
american_scientific_journal-1326	24	2	)	)	PUNCT
american_scientific_journal-1326	24	3	bulge	bulge	NOUN
american_scientific_journal-1326	24	4	.	.	PUNCT
american_scientific_journal-1326	24	5	represents	represent	VERB
american_scientific_journal-1326	24	6	the	the	DET
american_scientific_journal-1326	24	7	central	central	ADJ
american_scientific_journal-1326	24	8	part	part	NOUN
american_scientific_journal-1326	24	9	of	of	ADP
american_scientific_journal-1326	24	10	the	the	DET
american_scientific_journal-1326	24	11	galaxy	galaxy	NOUN
american_scientific_journal-1326	24	12	.	.	PUNCT
american_scientific_journal-1326	25	1	the	the	DET
american_scientific_journal-1326	25	2	most	most	ADV
american_scientific_journal-1326	25	3	significant	significant	ADJ
american_scientific_journal-1326	25	4	fact	fact	NOUN
american_scientific_journal-1326	25	5	of	of	ADP
american_scientific_journal-1326	25	6	this	this	DET
american_scientific_journal-1326	25	7	region	region	NOUN
american_scientific_journal-1326	25	8	is	be	AUX
american_scientific_journal-1326	25	9	that	that	SCONJ
american_scientific_journal-1326	25	10	the	the	DET
american_scientific_journal-1326	25	11	stars	star	NOUN
american_scientific_journal-1326	25	12	that	that	PRON
american_scientific_journal-1326	25	13	compose	compose	VERB
american_scientific_journal-1326	25	14	it	it	PRON
american_scientific_journal-1326	25	15	rigidly	rigidly	ADV
american_scientific_journal-1326	25	16	rotate	rotate	VERB
american_scientific_journal-1326	25	17	with	with	ADP
american_scientific_journal-1326	25	18	constant	constant	ADJ
american_scientific_journal-1326	25	19	angular	angular	ADJ
american_scientific_journal-1326	25	20	velocity	velocity	NOUN
american_scientific_journal-1326	25	21	.	.	PUNCT
american_scientific_journal-1326	26	1	from	from	ADP
american_scientific_journal-1326	26	2	the	the	DET
american_scientific_journal-1326	26	3	above	above	NOUN
american_scientific_journal-1326	26	4	,	,	PUNCT
american_scientific_journal-1326	26	5	we	we	PRON
american_scientific_journal-1326	26	6	highlight	highlight	VERB
american_scientific_journal-1326	26	7	an	an	DET
american_scientific_journal-1326	26	8	important	important	ADJ
american_scientific_journal-1326	26	9	fact	fact	NOUN
american_scientific_journal-1326	26	10	;	;	PUNCT
american_scientific_journal-1326	26	11	the	the	DET
american_scientific_journal-1326	26	12	differential	differential	ADJ
american_scientific_journal-1326	26	13	character	character	NOUN
american_scientific_journal-1326	26	14	of	of	ADP
american_scientific_journal-1326	26	15	the	the	DET
american_scientific_journal-1326	26	16	rotation	rotation	NOUN
american_scientific_journal-1326	26	17	.	.	PUNCT
american_scientific_journal-1326	27	1	it	it	PRON
american_scientific_journal-1326	27	2	is	be	AUX
american_scientific_journal-1326	27	3	not	not	PART
american_scientific_journal-1326	27	4	difficult	difficult	ADJ
american_scientific_journal-1326	27	5	to	to	PART
american_scientific_journal-1326	27	6	deduce	deduce	VERB
american_scientific_journal-1326	27	7	that	that	SCONJ
american_scientific_journal-1326	27	8	the	the	DET
american_scientific_journal-1326	27	9	rotation	rotation	NOUN
american_scientific_journal-1326	27	10	curve	curve	NOUN
american_scientific_journal-1326	27	11	(	(	PUNCT
american_scientific_journal-1326	27	12	i.e	i.e	PROPN
american_scientific_journal-1326	27	13	,	,	PUNCT
american_scientific_journal-1326	27	14	the	the	DET
american_scientific_journal-1326	27	15	curve	curve	NOUN
american_scientific_journal-1326	27	16	representing	represent	VERB
american_scientific_journal-1326	27	17	the	the	DET
american_scientific_journal-1326	27	18	speed	speed	NOUN
american_scientific_journal-1326	27	19	of	of	ADP
american_scientific_journal-1326	27	20	rotation	rotation	NOUN
american_scientific_journal-1326	27	21	as	as	ADP
american_scientific_journal-1326	27	22	a	a	DET
american_scientific_journal-1326	27	23	function	function	NOUN
american_scientific_journal-1326	27	24	of	of	ADP
american_scientific_journal-1326	27	25	distance	distance	NOUN
american_scientific_journal-1326	27	26	from	from	ADP
american_scientific_journal-1326	27	27	the	the	DET
american_scientific_journal-1326	27	28	center	center	NOUN
american_scientific_journal-1326	27	29	of	of	ADP
american_scientific_journal-1326	27	30	mass	mass	NOUN
american_scientific_journal-1326	27	31	of	of	ADP
american_scientific_journal-1326	27	32	the	the	DET
american_scientific_journal-1326	27	33	galaxy	galaxy	NOUN
american_scientific_journal-1326	27	34	)	)	PUNCT
american_scientific_journal-1326	27	35	should	should	AUX
american_scientific_journal-1326	27	36	indicate	indicate	VERB
american_scientific_journal-1326	27	37	that	that	SCONJ
american_scientific_journal-1326	27	38	up	up	ADP
american_scientific_journal-1326	27	39	to	to	ADP
american_scientific_journal-1326	27	40	a	a	DET
american_scientific_journal-1326	27	41	certain	certain	ADJ
american_scientific_journal-1326	27	42	distance	distance	NOUN
american_scientific_journal-1326	27	43	from	from	ADP
american_scientific_journal-1326	27	44	the	the	DET
american_scientific_journal-1326	27	45	center	center	NOUN
american_scientific_journal-1326	27	46	,	,	PUNCT
american_scientific_journal-1326	27	47	the	the	DET
american_scientific_journal-1326	27	48	orbital	orbital	ADJ
american_scientific_journal-1326	27	49	velocity	velocity	NOUN
american_scientific_journal-1326	27	50	,	,	PUNCT
american_scientific_journal-1326	27	51	increases	increase	NOUN
american_scientific_journal-1326	27	52	proportionally	proportionally	ADV
american_scientific_journal-1326	27	53	with	with	ADP
american_scientific_journal-1326	27	54	this	this	PRON
american_scientific_journal-1326	27	55	,	,	PUNCT
american_scientific_journal-1326	27	56	while	while	SCONJ
american_scientific_journal-1326	27	57	away	away	ADV
american_scientific_journal-1326	27	58	from	from	ADP
american_scientific_journal-1326	27	59	the	the	DET
american_scientific_journal-1326	27	60	disk	disk	NOUN
american_scientific_journal-1326	27	61	(	(	PUNCT
american_scientific_journal-1326	27	62	at	at	ADP
american_scientific_journal-1326	27	63	a	a	DET
american_scientific_journal-1326	27	64	distance	distance	NOUN
american_scientific_journal-1326	27	65	at	at	ADP
american_scientific_journal-1326	27	66	which	which	PRON
american_scientific_journal-1326	27	67	it	it	PRON
american_scientific_journal-1326	27	68	is	be	AUX
american_scientific_journal-1326	27	69	not	not	PART
american_scientific_journal-1326	27	70	observed	observe	VERB
american_scientific_journal-1326	27	71	mass	mass	NOUN
american_scientific_journal-1326	27	72	)	)	PUNCT
american_scientific_journal-1326	27	73	should	should	AUX
american_scientific_journal-1326	27	74	occur	occur	VERB
american_scientific_journal-1326	27	75	a	a	DET
american_scientific_journal-1326	27	76	keplerian	keplerian	ADJ
american_scientific_journal-1326	27	77	rotation	rotation	NOUN
american_scientific_journal-1326	27	78	,	,	PUNCT
american_scientific_journal-1326	27	79	that	that	ADV
american_scientific_journal-1326	27	80	is	is	ADV
american_scientific_journal-1326	27	81	,	,	PUNCT
american_scientific_journal-1326	27	82	a	a	DET
american_scientific_journal-1326	27	83	planet	planet	NOUN
american_scientific_journal-1326	27	84	-	-	PUNCT
american_scientific_journal-1326	27	85	like	like	ADJ
american_scientific_journal-1326	27	86	rotation	rotation	NOUN
american_scientific_journal-1326	27	87	[	[	X
american_scientific_journal-1326	27	88	2,7	2,7	NUM
american_scientific_journal-1326	27	89	]	]	PUNCT
american_scientific_journal-1326	27	90	.	.	PUNCT
american_scientific_journal-1326	28	1	instead	instead	ADV
american_scientific_journal-1326	28	2	,	,	PUNCT
american_scientific_journal-1326	28	3	it	it	PRON
american_scientific_journal-1326	28	4	is	be	AUX
american_scientific_journal-1326	28	5	observed	observe	VERB
american_scientific_journal-1326	28	6	that	that	SCONJ
american_scientific_journal-1326	28	7	the	the	DET
american_scientific_journal-1326	28	8	rotational	rotational	ADJ
american_scientific_journal-1326	28	9	speed	speed	NOUN
american_scientific_journal-1326	28	10	remains	remain	VERB
american_scientific_journal-1326	28	11	essentially	essentially	ADV
american_scientific_journal-1326	28	12	constant	constant	ADJ
american_scientific_journal-1326	28	13	,	,	PUNCT
american_scientific_journal-1326	28	14	i.e.	i.e.	X
american_scientific_journal-1326	28	15	the	the	DET
american_scientific_journal-1326	28	16	angular	angular	ADJ
american_scientific_journal-1326	28	17	velocity	velocity	NOUN
american_scientific_journal-1326	28	18	must	must	AUX
american_scientific_journal-1326	28	19	decrease	decrease	VERB
american_scientific_journal-1326	28	20	with	with	ADP
american_scientific_journal-1326	28	21	radius	radius	NOUN
american_scientific_journal-1326	28	22	,	,	PUNCT
american_scientific_journal-1326	28	23	as	as	ADP
american_scientific_journal-1326	28	24	if	if	SCONJ
american_scientific_journal-1326	28	25	the	the	DET
american_scientific_journal-1326	28	26	mass	mass	NOUN
american_scientific_journal-1326	28	27	of	of	ADP
american_scientific_journal-1326	28	28	the	the	DET
american_scientific_journal-1326	28	29	galaxy	galaxy	NOUN
american_scientific_journal-1326	28	30	following	follow	VERB
american_scientific_journal-1326	28	31	increasing	increase	VERB
american_scientific_journal-1326	28	32	with	with	ADP
american_scientific_journal-1326	28	33	distance	distance	NOUN
american_scientific_journal-1326	28	34	from	from	ADP
american_scientific_journal-1326	28	35	the	the	DET
american_scientific_journal-1326	28	36	galactic	galactic	ADJ
american_scientific_journal-1326	28	37	center	center	NOUN
american_scientific_journal-1326	28	38	.	.	PUNCT
american_scientific_journal-1326	29	1	this	this	DET
american_scientific_journal-1326	29	2	matter	matter	NOUN
american_scientific_journal-1326	29	3	,	,	PUNCT
american_scientific_journal-1326	29	4	which	which	PRON
american_scientific_journal-1326	29	5	is	be	AUX
american_scientific_journal-1326	29	6	supposed	suppose	VERB
american_scientific_journal-1326	29	7	does	do	AUX
american_scientific_journal-1326	29	8	not	not	PART
american_scientific_journal-1326	29	9	emit	emit	VERB
american_scientific_journal-1326	29	10	light	light	NOUN
american_scientific_journal-1326	29	11	and	and	CCONJ
american_scientific_journal-1326	29	12	is	be	AUX
american_scientific_journal-1326	29	13	contained	contain	VERB
american_scientific_journal-1326	29	14	in	in	ADP
american_scientific_journal-1326	29	15	the	the	DET
american_scientific_journal-1326	29	16	halo	halo	NOUN
american_scientific_journal-1326	29	17	,	,	PUNCT
american_scientific_journal-1326	29	18	is	be	AUX
american_scientific_journal-1326	29	19	called	call	VERB
american_scientific_journal-1326	29	20	dark	dark	ADJ
american_scientific_journal-1326	29	21	matter	matter	NOUN
american_scientific_journal-1326	29	22	.	.	PUNCT
american_scientific_journal-1326	30	1	although	although	SCONJ
american_scientific_journal-1326	30	2	the	the	DET
american_scientific_journal-1326	30	3	dark	dark	ADJ
american_scientific_journal-1326	30	4	matter	matter	NOUN
american_scientific_journal-1326	30	5	scenario	scenario	NOUN
american_scientific_journal-1326	30	6	in	in	ADP
american_scientific_journal-1326	30	7	astrophysics	astrophysic	NOUN
american_scientific_journal-1326	30	8	has	have	AUX
american_scientific_journal-1326	30	9	been	be	AUX
american_scientific_journal-1326	30	10	widely	widely	ADV
american_scientific_journal-1326	30	11	employed	employ	VERB
american_scientific_journal-1326	30	12	,	,	PUNCT
american_scientific_journal-1326	30	13	[	[	X
american_scientific_journal-1326	30	14	1	1	X
american_scientific_journal-1326	30	15	]	]	PUNCT
american_scientific_journal-1326	30	16	proposed	propose	VERB
american_scientific_journal-1326	30	17	a	a	DET
american_scientific_journal-1326	30	18	nonlinear	nonlinear	ADJ
american_scientific_journal-1326	30	19	model	model	NOUN
american_scientific_journal-1326	30	20	of	of	ADP
american_scientific_journal-1326	30	21	newtonian	newtonian	ADJ
american_scientific_journal-1326	30	22	gravity	gravity	NOUN
american_scientific_journal-1326	30	23	,	,	PUNCT
american_scientific_journal-1326	30	24	without	without	ADP
american_scientific_journal-1326	30	25	resorting	resort	VERB
american_scientific_journal-1326	30	26	to	to	ADP
american_scientific_journal-1326	30	27	dark	dark	ADJ
american_scientific_journal-1326	30	28	matter	matter	NOUN
american_scientific_journal-1326	30	29	and	and	CCONJ
american_scientific_journal-1326	30	30	other	other	ADJ
american_scientific_journal-1326	30	31	theoretical	theoretical	ADJ
american_scientific_journal-1326	30	32	modifications	modification	NOUN
american_scientific_journal-1326	30	33	.	.	PUNCT
american_scientific_journal-1326	31	1	the	the	DET
american_scientific_journal-1326	31	2	aim	aim	NOUN
american_scientific_journal-1326	31	3	of	of	ADP
american_scientific_journal-1326	31	4	our	our	PRON
american_scientific_journal-1326	31	5	approach	approach	NOUN
american_scientific_journal-1326	31	6	is	be	AUX
american_scientific_journal-1326	31	7	reframe	reframe	VERB
american_scientific_journal-1326	31	8	the	the	DET
american_scientific_journal-1326	31	9	mentioned	mention	VERB
american_scientific_journal-1326	31	10	work	work	NOUN
american_scientific_journal-1326	31	11	,	,	PUNCT
american_scientific_journal-1326	31	12	with	with	ADP
american_scientific_journal-1326	31	13	a	a	DET
american_scientific_journal-1326	31	14	rather	rather	ADV
american_scientific_journal-1326	31	15	elementary	elementary	ADJ
american_scientific_journal-1326	31	16	view	view	NOUN
american_scientific_journal-1326	31	17	,	,	PUNCT
american_scientific_journal-1326	31	18	and	and	CCONJ
american_scientific_journal-1326	31	19	seeks	seek	VERB
american_scientific_journal-1326	31	20	to	to	PART
american_scientific_journal-1326	31	21	explain	explain	VERB
american_scientific_journal-1326	31	22	as	as	ADV
american_scientific_journal-1326	31	23	much	much	ADJ
american_scientific_journal-1326	31	24	detail	detail	NOUN
american_scientific_journal-1326	31	25	as	as	ADP
american_scientific_journal-1326	31	26	possible	possible	ADJ
american_scientific_journal-1326	31	27	the	the	DET
american_scientific_journal-1326	31	28	material	material	NOUN
american_scientific_journal-1326	31	29	of	of	ADP
american_scientific_journal-1326	31	30	this	this	DET
american_scientific_journal-1326	31	31	article	article	NOUN
american_scientific_journal-1326	31	32	.	.	PUNCT
american_scientific_journal-1326	32	1	unlike	unlike	ADP
american_scientific_journal-1326	32	2	the	the	DET
american_scientific_journal-1326	32	3	mentioned	mention	VERB
american_scientific_journal-1326	32	4	paper	paper	NOUN
american_scientific_journal-1326	32	5	[	[	X
american_scientific_journal-1326	32	6	1	1	NUM
american_scientific_journal-1326	32	7	]	]	PUNCT
american_scientific_journal-1326	32	8	,	,	PUNCT
american_scientific_journal-1326	32	9	from	from	ADP
american_scientific_journal-1326	32	10	the	the	DET
american_scientific_journal-1326	32	11	beginning	beginning	NOUN
american_scientific_journal-1326	32	12	we	we	PRON
american_scientific_journal-1326	32	13	restrict	restrict	VERB
american_scientific_journal-1326	32	14	the	the	DET
american_scientific_journal-1326	32	15	application	application	NOUN
american_scientific_journal-1326	32	16	of	of	ADP
american_scientific_journal-1326	32	17	the	the	DET
american_scientific_journal-1326	32	18	model	model	NOUN
american_scientific_journal-1326	32	19	,	,	PUNCT
american_scientific_journal-1326	32	20	to	to	ADP
american_scientific_journal-1326	32	21	the	the	DET
american_scientific_journal-1326	32	22	disk	disk	NOUN
american_scientific_journal-1326	32	23	of	of	ADP
american_scientific_journal-1326	32	24	the	the	DET
american_scientific_journal-1326	32	25	galaxy	galaxy	NOUN
american_scientific_journal-1326	32	26	,	,	PUNCT
american_scientific_journal-1326	32	27	emphasizing	emphasize	VERB
american_scientific_journal-1326	32	28	the	the	DET
american_scientific_journal-1326	32	29	perturbative	perturbative	ADJ
american_scientific_journal-1326	32	30	character	character	NOUN
american_scientific_journal-1326	32	31	of	of	ADP
american_scientific_journal-1326	32	32	the	the	DET
american_scientific_journal-1326	32	33	equation	equation	NOUN
american_scientific_journal-1326	32	34	to	to	PART
american_scientific_journal-1326	32	35	solve	solve	VERB
american_scientific_journal-1326	32	36	and	and	CCONJ
american_scientific_journal-1326	32	37	justifying	justify	VERB
american_scientific_journal-1326	32	38	the	the	DET
american_scientific_journal-1326	32	39	accuracy	accuracy	NOUN
american_scientific_journal-1326	32	40	of	of	ADP
american_scientific_journal-1326	32	41	the	the	DET
american_scientific_journal-1326	32	42	obtained	obtain	VERB
american_scientific_journal-1326	32	43	results	result	NOUN
american_scientific_journal-1326	32	44	.	.	PUNCT
american_scientific_journal-1326	33	1	american	american	ADJ
american_scientific_journal-1326	33	2	scientific	scientific	ADJ
american_scientific_journal-1326	33	3	research	research	PROPN
american_scientific_journal-1326	33	4	journal	journal	NOUN
american_scientific_journal-1326	33	5	for	for	ADP
american_scientific_journal-1326	33	6	engineering	engineering	NOUN
american_scientific_journal-1326	33	7	,	,	PUNCT
american_scientific_journal-1326	33	8	technology	technology	NOUN
american_scientific_journal-1326	33	9	,	,	PUNCT
american_scientific_journal-1326	33	10	and	and	CCONJ
american_scientific_journal-1326	33	11	sciences	science	NOUN
american_scientific_journal-1326	33	12	(	(	PUNCT
american_scientific_journal-1326	33	13	asrjets	asrjet	NOUN
american_scientific_journal-1326	33	14	)	)	PUNCT
american_scientific_journal-1326	33	15	(	(	PUNCT
american_scientific_journal-1326	33	16	2017	2017	NUM
american_scientific_journal-1326	33	17	)	)	PUNCT
american_scientific_journal-1326	33	18	volume	volume	NOUN
american_scientific_journal-1326	33	19	27	27	NUM
american_scientific_journal-1326	33	20	,	,	PUNCT
american_scientific_journal-1326	33	21	no	no	DET
american_scientific_journal-1326	33	22	1	1	NUM
american_scientific_journal-1326	33	23	,	,	PUNCT
american_scientific_journal-1326	33	24	pp	pp	ADV
american_scientific_journal-1326	33	25	139	139	NUM
american_scientific_journal-1326	33	26	-	-	SYM
american_scientific_journal-1326	33	27	150	150	NUM
american_scientific_journal-1326	33	28	141	141	NUM
american_scientific_journal-1326	33	29	this	this	DET
american_scientific_journal-1326	33	30	paper	paper	NOUN
american_scientific_journal-1326	33	31	is	be	AUX
american_scientific_journal-1326	33	32	organized	organize	VERB
american_scientific_journal-1326	33	33	as	as	SCONJ
american_scientific_journal-1326	33	34	follows	follow	VERB
american_scientific_journal-1326	33	35	.	.	PUNCT
american_scientific_journal-1326	34	1	in	in	ADP
american_scientific_journal-1326	34	2	section	section	NOUN
american_scientific_journal-1326	34	3	2	2	NUM
american_scientific_journal-1326	34	4	,	,	PUNCT
american_scientific_journal-1326	34	5	we	we	PRON
american_scientific_journal-1326	34	6	introduce	introduce	VERB
american_scientific_journal-1326	34	7	the	the	DET
american_scientific_journal-1326	34	8	basic	basic	ADJ
american_scientific_journal-1326	34	9	idea	idea	NOUN
american_scientific_journal-1326	34	10	of	of	ADP
american_scientific_journal-1326	34	11	pm	pm	NOUN
american_scientific_journal-1326	34	12	method	method	NOUN
american_scientific_journal-1326	34	13	.	.	PUNCT
american_scientific_journal-1326	35	1	for	for	ADP
american_scientific_journal-1326	35	2	section	section	NOUN
american_scientific_journal-1326	35	3	3	3	NUM
american_scientific_journal-1326	35	4	,	,	PUNCT
american_scientific_journal-1326	35	5	we	we	PRON
american_scientific_journal-1326	35	6	provide	provide	VERB
american_scientific_journal-1326	35	7	an	an	DET
american_scientific_journal-1326	35	8	application	application	NOUN
american_scientific_journal-1326	35	9	of	of	ADP
american_scientific_journal-1326	35	10	pm	pm	NOUN
american_scientific_journal-1326	35	11	method	method	NOUN
american_scientific_journal-1326	35	12	,	,	PUNCT
american_scientific_journal-1326	35	13	by	by	ADP
american_scientific_journal-1326	35	14	solving	solve	VERB
american_scientific_journal-1326	35	15	the	the	DET
american_scientific_journal-1326	35	16	differential	differential	ADJ
american_scientific_journal-1326	35	17	equation	equation	NOUN
american_scientific_journal-1326	35	18	which	which	PRON
american_scientific_journal-1326	35	19	describes	describe	VERB
american_scientific_journal-1326	35	20	a	a	DET
american_scientific_journal-1326	35	21	galactic	galactic	ADJ
american_scientific_journal-1326	35	22	nonlinear	nonlinear	ADJ
american_scientific_journal-1326	35	23	model	model	NOUN
american_scientific_journal-1326	35	24	.	.	PUNCT
american_scientific_journal-1326	36	1	section	section	NOUN
american_scientific_journal-1326	36	2	4	4	NUM
american_scientific_journal-1326	36	3	discusses	discuss	VERB
american_scientific_journal-1326	36	4	the	the	DET
american_scientific_journal-1326	36	5	main	main	ADJ
american_scientific_journal-1326	36	6	results	result	NOUN
american_scientific_journal-1326	36	7	obtained	obtain	VERB
american_scientific_journal-1326	36	8	,	,	PUNCT
american_scientific_journal-1326	36	9	while	while	SCONJ
american_scientific_journal-1326	36	10	,	,	PUNCT
american_scientific_journal-1326	36	11	a	a	DET
american_scientific_journal-1326	36	12	brief	brief	ADJ
american_scientific_journal-1326	36	13	conclusion	conclusion	NOUN
american_scientific_journal-1326	36	14	is	be	AUX
american_scientific_journal-1326	36	15	given	give	VERB
american_scientific_journal-1326	36	16	in	in	ADP
american_scientific_journal-1326	36	17	section	section	NOUN
american_scientific_journal-1326	36	18	5	5	NUM
american_scientific_journal-1326	36	19	.	.	PUNCT
american_scientific_journal-1326	37	1	finally	finally	ADV
american_scientific_journal-1326	37	2	,	,	PUNCT
american_scientific_journal-1326	37	3	appendix	appendix	VERB
american_scientific_journal-1326	37	4	a	a	DET
american_scientific_journal-1326	37	5	provides	provide	VERB
american_scientific_journal-1326	37	6	observational	observational	ADJ
american_scientific_journal-1326	37	7	data	datum	NOUN
american_scientific_journal-1326	37	8	,	,	PUNCT
american_scientific_journal-1326	37	9	to	to	PART
american_scientific_journal-1326	37	10	perform	perform	VERB
american_scientific_journal-1326	37	11	numerical	numerical	ADJ
american_scientific_journal-1326	37	12	comparisons	comparison	NOUN
american_scientific_journal-1326	37	13	.	.	PUNCT
american_scientific_journal-1326	38	1	2	2	X
american_scientific_journal-1326	38	2	.	.	X
american_scientific_journal-1326	38	3	basic	basic	ADJ
american_scientific_journal-1326	38	4	idea	idea	NOUN
american_scientific_journal-1326	38	5	of	of	ADP
american_scientific_journal-1326	38	6	perturbation	perturbation	NOUN
american_scientific_journal-1326	38	7	method	method	VERB
american_scientific_journal-1326	38	8	the	the	DET
american_scientific_journal-1326	38	9	perturbation	perturbation	NOUN
american_scientific_journal-1326	38	10	method	method	NOUN
american_scientific_journal-1326	38	11	(	(	PUNCT
american_scientific_journal-1326	38	12	pm	pm	NOUN
american_scientific_journal-1326	38	13	)	)	PUNCT
american_scientific_journal-1326	38	14	is	be	AUX
american_scientific_journal-1326	38	15	a	a	DET
american_scientific_journal-1326	38	16	well	well	ADV
american_scientific_journal-1326	38	17	-	-	PUNCT
american_scientific_journal-1326	38	18	established	establish	VERB
american_scientific_journal-1326	38	19	method	method	NOUN
american_scientific_journal-1326	38	20	;	;	PUNCT
american_scientific_journal-1326	38	21	it	it	PRON
american_scientific_journal-1326	38	22	is	be	AUX
american_scientific_journal-1326	38	23	among	among	ADP
american_scientific_journal-1326	38	24	the	the	DET
american_scientific_journal-1326	38	25	pioneer	pioneer	NOUN
american_scientific_journal-1326	38	26	techniques	technique	NOUN
american_scientific_journal-1326	38	27	to	to	PART
american_scientific_journal-1326	38	28	approach	approach	VERB
american_scientific_journal-1326	38	29	various	various	ADJ
american_scientific_journal-1326	38	30	kinds	kind	NOUN
american_scientific_journal-1326	38	31	of	of	ADP
american_scientific_journal-1326	38	32	nonlinear	nonlinear	ADJ
american_scientific_journal-1326	38	33	problems	problem	NOUN
american_scientific_journal-1326	38	34	.	.	PUNCT
american_scientific_journal-1326	39	1	this	this	DET
american_scientific_journal-1326	39	2	procedure	procedure	NOUN
american_scientific_journal-1326	39	3	was	be	AUX
american_scientific_journal-1326	39	4	originated	originate	VERB
american_scientific_journal-1326	39	5	by	by	ADP
american_scientific_journal-1326	39	6	s.	s.	PROPN
american_scientific_journal-1326	39	7	d.	d.	PROPN
american_scientific_journal-1326	39	8	poisson	poisson	PROPN
american_scientific_journal-1326	39	9	and	and	CCONJ
american_scientific_journal-1326	39	10	extended	extend	VERB
american_scientific_journal-1326	39	11	by	by	ADP
american_scientific_journal-1326	39	12	j.	j.	PROPN
american_scientific_journal-1326	39	13	h.	h.	PROPN
american_scientific_journal-1326	39	14	poincare	poincare	PROPN
american_scientific_journal-1326	39	15	.	.	PUNCT
american_scientific_journal-1326	40	1	although	although	SCONJ
american_scientific_journal-1326	40	2	the	the	DET
american_scientific_journal-1326	40	3	method	method	NOUN
american_scientific_journal-1326	40	4	appeared	appear	VERB
american_scientific_journal-1326	40	5	in	in	ADP
american_scientific_journal-1326	40	6	the	the	DET
american_scientific_journal-1326	40	7	early	early	ADJ
american_scientific_journal-1326	40	8	19th	19th	ADJ
american_scientific_journal-1326	40	9	century	century	NOUN
american_scientific_journal-1326	40	10	,	,	PUNCT
american_scientific_journal-1326	40	11	the	the	DET
american_scientific_journal-1326	40	12	application	application	NOUN
american_scientific_journal-1326	40	13	of	of	ADP
american_scientific_journal-1326	40	14	a	a	DET
american_scientific_journal-1326	40	15	perturbation	perturbation	NOUN
american_scientific_journal-1326	40	16	procedure	procedure	NOUN
american_scientific_journal-1326	40	17	to	to	PART
american_scientific_journal-1326	40	18	solve	solve	VERB
american_scientific_journal-1326	40	19	nonlinear	nonlinear	ADJ
american_scientific_journal-1326	40	20	differential	differential	ADJ
american_scientific_journal-1326	40	21	equations	equation	NOUN
american_scientific_journal-1326	40	22	was	be	AUX
american_scientific_journal-1326	40	23	performed	perform	VERB
american_scientific_journal-1326	40	24	later	later	ADV
american_scientific_journal-1326	40	25	on	on	ADP
american_scientific_journal-1326	40	26	that	that	DET
american_scientific_journal-1326	40	27	century	century	NOUN
american_scientific_journal-1326	40	28	.	.	PUNCT
american_scientific_journal-1326	41	1	the	the	DET
american_scientific_journal-1326	41	2	most	most	ADV
american_scientific_journal-1326	41	3	significant	significant	ADJ
american_scientific_journal-1326	41	4	efforts	effort	NOUN
american_scientific_journal-1326	41	5	were	be	AUX
american_scientific_journal-1326	41	6	focused	focus	VERB
american_scientific_journal-1326	41	7	on	on	ADP
american_scientific_journal-1326	41	8	celestial	celestial	ADJ
american_scientific_journal-1326	41	9	mechanics	mechanic	NOUN
american_scientific_journal-1326	41	10	,	,	PUNCT
american_scientific_journal-1326	41	11	fluid	fluid	ADJ
american_scientific_journal-1326	41	12	mechanics	mechanic	NOUN
american_scientific_journal-1326	41	13	,	,	PUNCT
american_scientific_journal-1326	41	14	and	and	CCONJ
american_scientific_journal-1326	41	15	aerodynamics	aerodynamic	NOUN
american_scientific_journal-1326	41	16	[	[	X
american_scientific_journal-1326	41	17	3	3	NUM
american_scientific_journal-1326	41	18	-	-	SYM
american_scientific_journal-1326	41	19	6	6	NUM
american_scientific_journal-1326	41	20	]	]	PUNCT
american_scientific_journal-1326	41	21	.	.	PUNCT
american_scientific_journal-1326	42	1	let	let	VERB
american_scientific_journal-1326	42	2	the	the	DET
american_scientific_journal-1326	42	3	differential	differential	ADJ
american_scientific_journal-1326	42	4	equation	equation	NOUN
american_scientific_journal-1326	42	5	of	of	ADP
american_scientific_journal-1326	42	6	one	one	NUM
american_scientific_journal-1326	42	7	dimensional	dimensional	ADJ
american_scientific_journal-1326	42	8	nonlinear	nonlinear	ADJ
american_scientific_journal-1326	42	9	system	system	NOUN
american_scientific_journal-1326	42	10	be	be	AUX
american_scientific_journal-1326	42	11	in	in	ADP
american_scientific_journal-1326	42	12	the	the	DET
american_scientific_journal-1326	42	13	form	form	NOUN
american_scientific_journal-1326	42	14	(	(	PUNCT
american_scientific_journal-1326	42	15	)	)	PUNCT
american_scientific_journal-1326	42	16	(	(	PUNCT
american_scientific_journal-1326	42	17	)	)	PUNCT
american_scientific_journal-1326	42	18	0l	0l	NUM
american_scientific_journal-1326	42	19	x	x	PUNCT
american_scientific_journal-1326	43	1	n	n	NUM
american_scientific_journal-1326	43	2	xε+	xε+	NOUN
american_scientific_journal-1326	43	3	=	=	SYM
american_scientific_journal-1326	43	4	,	,	PUNCT
american_scientific_journal-1326	43	5	(	(	PUNCT
american_scientific_journal-1326	43	6	1	1	X
american_scientific_journal-1326	43	7	)	)	PUNCT
american_scientific_journal-1326	43	8	where	where	SCONJ
american_scientific_journal-1326	43	9	we	we	PRON
american_scientific_journal-1326	43	10	assume	assume	VERB
american_scientific_journal-1326	43	11	that	that	SCONJ
american_scientific_journal-1326	43	12	x	x	PRON
american_scientific_journal-1326	43	13	is	be	AUX
american_scientific_journal-1326	43	14	a	a	DET
american_scientific_journal-1326	43	15	function	function	NOUN
american_scientific_journal-1326	43	16	of	of	ADP
american_scientific_journal-1326	43	17	one	one	NUM
american_scientific_journal-1326	43	18	variable	variable	NOUN
american_scientific_journal-1326	43	19	(	(	PUNCT
american_scientific_journal-1326	43	20	)	)	PUNCT
american_scientific_journal-1326	43	21	x	x	PUNCT
american_scientific_journal-1326	43	22	x	x	NOUN
american_scientific_journal-1326	43	23	t=	t=	PRON
american_scientific_journal-1326	43	24	,	,	PUNCT
american_scientific_journal-1326	43	25	(	(	PUNCT
american_scientific_journal-1326	43	26	)	)	PUNCT
american_scientific_journal-1326	43	27	l	l	NOUN
american_scientific_journal-1326	43	28	x	x	PUNCT
american_scientific_journal-1326	43	29	is	be	AUX
american_scientific_journal-1326	43	30	a	a	DET
american_scientific_journal-1326	43	31	linear	linear	ADJ
american_scientific_journal-1326	43	32	operator	operator	NOUN
american_scientific_journal-1326	43	33	which	which	PRON
american_scientific_journal-1326	43	34	,	,	PUNCT
american_scientific_journal-1326	43	35	in	in	ADP
american_scientific_journal-1326	43	36	general	general	ADJ
american_scientific_journal-1326	43	37	,	,	PUNCT
american_scientific_journal-1326	43	38	contains	contain	VERB
american_scientific_journal-1326	43	39	derivatives	derivative	NOUN
american_scientific_journal-1326	43	40	in	in	ADP
american_scientific_journal-1326	43	41	terms	term	NOUN
american_scientific_journal-1326	43	42	of	of	ADP
american_scientific_journal-1326	43	43	t	t	NOUN
american_scientific_journal-1326	43	44	,	,	PUNCT
american_scientific_journal-1326	43	45	(	(	PUNCT
american_scientific_journal-1326	43	46	)	)	PUNCT
american_scientific_journal-1326	43	47	n	n	X
american_scientific_journal-1326	43	48	x	x	X
american_scientific_journal-1326	43	49	is	be	AUX
american_scientific_journal-1326	43	50	a	a	DET
american_scientific_journal-1326	43	51	nonlinear	nonlinear	ADJ
american_scientific_journal-1326	43	52	operator	operator	NOUN
american_scientific_journal-1326	43	53	,	,	PUNCT
american_scientific_journal-1326	43	54	andε	andε	NOUN
american_scientific_journal-1326	43	55	is	be	AUX
american_scientific_journal-1326	43	56	a	a	DET
american_scientific_journal-1326	43	57	small	small	ADJ
american_scientific_journal-1326	43	58	parameter	parameter	NOUN
american_scientific_journal-1326	43	59	.	.	PUNCT
american_scientific_journal-1326	44	1	considering	consider	VERB
american_scientific_journal-1326	44	2	the	the	DET
american_scientific_journal-1326	44	3	nonlinear	nonlinear	ADJ
american_scientific_journal-1326	44	4	term	term	NOUN
american_scientific_journal-1326	44	5	in	in	ADP
american_scientific_journal-1326	44	6	(	(	PUNCT
american_scientific_journal-1326	44	7	1	1	NUM
american_scientific_journal-1326	44	8	)	)	PUNCT
american_scientific_journal-1326	44	9	to	to	PART
american_scientific_journal-1326	44	10	be	be	AUX
american_scientific_journal-1326	44	11	a	a	DET
american_scientific_journal-1326	44	12	small	small	ADJ
american_scientific_journal-1326	44	13	perturbation	perturbation	NOUN
american_scientific_journal-1326	44	14	and	and	CCONJ
american_scientific_journal-1326	44	15	assuming	assume	VERB
american_scientific_journal-1326	44	16	that	that	SCONJ
american_scientific_journal-1326	44	17	the	the	DET
american_scientific_journal-1326	44	18	solution	solution	NOUN
american_scientific_journal-1326	44	19	for	for	ADP
american_scientific_journal-1326	44	20	(	(	PUNCT
american_scientific_journal-1326	44	21	1	1	X
american_scientific_journal-1326	44	22	)	)	PUNCT
american_scientific_journal-1326	44	23	can	can	AUX
american_scientific_journal-1326	44	24	be	be	AUX
american_scientific_journal-1326	44	25	written	write	VERB
american_scientific_journal-1326	44	26	as	as	ADP
american_scientific_journal-1326	44	27	a	a	DET
american_scientific_journal-1326	44	28	power	power	NOUN
american_scientific_journal-1326	44	29	series	series	NOUN
american_scientific_journal-1326	44	30	in	in	ADP
american_scientific_journal-1326	44	31	the	the	DET
american_scientific_journal-1326	44	32	small	small	ADJ
american_scientific_journal-1326	44	33	parameterε	parameterε	NOUN
american_scientific_journal-1326	44	34	,	,	PUNCT
american_scientific_journal-1326	44	35	2	2	NUM
american_scientific_journal-1326	44	36	0	0	NUM
american_scientific_journal-1326	44	37	1	1	NUM
american_scientific_journal-1326	44	38	2	2	NUM
american_scientific_journal-1326	44	39	(	(	PUNCT
american_scientific_journal-1326	44	40	)	)	PUNCT
american_scientific_journal-1326	44	41	(	(	PUNCT
american_scientific_journal-1326	44	42	)	)	PUNCT
american_scientific_journal-1326	44	43	(	(	PUNCT
american_scientific_journal-1326	44	44	)	)	PUNCT
american_scientific_journal-1326	44	45	(	(	PUNCT
american_scientific_journal-1326	44	46	)	)	PUNCT
american_scientific_journal-1326	44	47	...	...	PUNCT
american_scientific_journal-1326	45	1	x	x	SYM
american_scientific_journal-1326	45	2	t	t	NOUN
american_scientific_journal-1326	45	3	x	x	SYM
american_scientific_journal-1326	45	4	t	t	NOUN
american_scientific_journal-1326	45	5	x	x	SYM
american_scientific_journal-1326	45	6	t	t	NOUN
american_scientific_journal-1326	45	7	x	x	PUNCT
american_scientific_journal-1326	45	8	tε	tε	ADP
american_scientific_journal-1326	45	9	ε=	ε=	ADV
american_scientific_journal-1326	45	10	+	+	CCONJ
american_scientific_journal-1326	46	1	+	+	PUNCT
american_scientific_journal-1326	46	2	+	+	CCONJ
american_scientific_journal-1326	46	3	(	(	PUNCT
american_scientific_journal-1326	46	4	2	2	X
american_scientific_journal-1326	46	5	)	)	PUNCT
american_scientific_journal-1326	46	6	substituting	substitute	VERB
american_scientific_journal-1326	46	7	(	(	PUNCT
american_scientific_journal-1326	46	8	2	2	NUM
american_scientific_journal-1326	46	9	)	)	PUNCT
american_scientific_journal-1326	46	10	into	into	ADP
american_scientific_journal-1326	46	11	(	(	PUNCT
american_scientific_journal-1326	46	12	1	1	NUM
american_scientific_journal-1326	46	13	)	)	PUNCT
american_scientific_journal-1326	46	14	and	and	CCONJ
american_scientific_journal-1326	46	15	equating	equate	VERB
american_scientific_journal-1326	46	16	terms	term	NOUN
american_scientific_journal-1326	46	17	having	have	VERB
american_scientific_journal-1326	46	18	identical	identical	ADJ
american_scientific_journal-1326	46	19	powers	power	NOUN
american_scientific_journal-1326	46	20	ofε	ofε	NOUN
american_scientific_journal-1326	46	21	,	,	PUNCT
american_scientific_journal-1326	46	22	we	we	PRON
american_scientific_journal-1326	46	23	obtain	obtain	VERB
american_scientific_journal-1326	46	24	a	a	DET
american_scientific_journal-1326	46	25	number	number	NOUN
american_scientific_journal-1326	46	26	of	of	ADP
american_scientific_journal-1326	46	27	differential	differential	ADJ
american_scientific_journal-1326	46	28	equations	equation	NOUN
american_scientific_journal-1326	46	29	that	that	PRON
american_scientific_journal-1326	46	30	can	can	AUX
american_scientific_journal-1326	46	31	be	be	AUX
american_scientific_journal-1326	46	32	integrated	integrate	VERB
american_scientific_journal-1326	46	33	,	,	PUNCT
american_scientific_journal-1326	46	34	recursively	recursively	ADV
american_scientific_journal-1326	46	35	,	,	PUNCT
american_scientific_journal-1326	46	36	to	to	PART
american_scientific_journal-1326	46	37	find	find	VERB
american_scientific_journal-1326	46	38	the	the	DET
american_scientific_journal-1326	46	39	values	value	NOUN
american_scientific_journal-1326	46	40	for	for	ADP
american_scientific_journal-1326	46	41	the	the	DET
american_scientific_journal-1326	46	42	functions	function	NOUN
american_scientific_journal-1326	46	43	:	:	PUNCT
american_scientific_journal-1326	46	44	0	0	NUM
american_scientific_journal-1326	46	45	(	(	PUNCT
american_scientific_journal-1326	46	46	)	)	PUNCT
american_scientific_journal-1326	46	47	x	x	SYM
american_scientific_journal-1326	46	48	t	t	PROPN
american_scientific_journal-1326	46	49	,	,	PUNCT
american_scientific_journal-1326	46	50	1	1	NUM
american_scientific_journal-1326	46	51	(	(	PUNCT
american_scientific_journal-1326	46	52	)	)	PUNCT
american_scientific_journal-1326	46	53	x	x	SYM
american_scientific_journal-1326	46	54	t	t	PROPN
american_scientific_journal-1326	46	55	,	,	PUNCT
american_scientific_journal-1326	46	56	2	2	NUM
american_scientific_journal-1326	46	57	(	(	PUNCT
american_scientific_journal-1326	46	58	)	)	PUNCT
american_scientific_journal-1326	46	59	x	x	SYM
american_scientific_journal-1326	46	60	t	t	NOUN
american_scientific_journal-1326	46	61	…	…	PUNCT
american_scientific_journal-1326	46	62	3	3	X
american_scientific_journal-1326	46	63	.	.	NOUN
american_scientific_journal-1326	46	64	approximate	approximate	ADJ
american_scientific_journal-1326	46	65	solution	solution	NOUN
american_scientific_journal-1326	46	66	of	of	ADP
american_scientific_journal-1326	46	67	a	a	DET
american_scientific_journal-1326	46	68	nonlinear	nonlinear	ADJ
american_scientific_journal-1326	46	69	differential	differential	ADJ
american_scientific_journal-1326	46	70	equation	equation	NOUN
american_scientific_journal-1326	46	71	which	which	PRON
american_scientific_journal-1326	46	72	describes	describe	VERB
american_scientific_journal-1326	46	73	a	a	DET
american_scientific_journal-1326	46	74	galactic	galactic	ADJ
american_scientific_journal-1326	46	75	nonlinear	nonlinear	ADJ
american_scientific_journal-1326	46	76	model	model	NOUN
american_scientific_journal-1326	46	77	.	.	PUNCT
american_scientific_journal-1326	47	1	we	we	PRON
american_scientific_journal-1326	47	2	start	start	VERB
american_scientific_journal-1326	47	3	from	from	ADP
american_scientific_journal-1326	47	4	the	the	DET
american_scientific_journal-1326	47	5	fundamental	fundamental	ADJ
american_scientific_journal-1326	47	6	consideration	consideration	NOUN
american_scientific_journal-1326	47	7	that	that	SCONJ
american_scientific_journal-1326	47	8	the	the	DET
american_scientific_journal-1326	47	9	speed	speed	NOUN
american_scientific_journal-1326	47	10	of	of	ADP
american_scientific_journal-1326	47	11	rotation	rotation	NOUN
american_scientific_journal-1326	47	12	of	of	ADP
american_scientific_journal-1326	47	13	matter	matter	NOUN
american_scientific_journal-1326	47	14	in	in	ADP
american_scientific_journal-1326	47	15	a	a	DET
american_scientific_journal-1326	47	16	galaxy	galaxy	NOUN
american_scientific_journal-1326	47	17	at	at	ADP
american_scientific_journal-1326	47	18	a	a	DET
american_scientific_journal-1326	47	19	distance	distance	NOUN
american_scientific_journal-1326	47	20	r	r	NOUN
american_scientific_journal-1326	47	21	from	from	ADP
american_scientific_journal-1326	47	22	the	the	DET
american_scientific_journal-1326	47	23	galactic	galactic	ADJ
american_scientific_journal-1326	47	24	center	center	NOUN
american_scientific_journal-1326	47	25	,	,	PUNCT
american_scientific_journal-1326	47	26	must	must	AUX
american_scientific_journal-1326	47	27	be	be	AUX
american_scientific_journal-1326	47	28	related	relate	VERB
american_scientific_journal-1326	47	29	to	to	ADP
american_scientific_journal-1326	47	30	the	the	DET
american_scientific_journal-1326	47	31	potential	potential	NOUN
american_scientific_journal-1326	47	32	acting	act	VERB
american_scientific_journal-1326	47	33	on	on	ADP
american_scientific_journal-1326	47	34	it	it	PRON
american_scientific_journal-1326	47	35	.	.	PUNCT
american_scientific_journal-1326	48	1	thus	thus	ADV
american_scientific_journal-1326	48	2	,	,	PUNCT
american_scientific_journal-1326	48	3	following	follow	VERB
american_scientific_journal-1326	48	4	newtonian	newtonian	ADJ
american_scientific_journal-1326	48	5	theory	theory	NOUN
american_scientific_journal-1326	48	6	,	,	PUNCT
american_scientific_journal-1326	48	7	the	the	DET
american_scientific_journal-1326	48	8	potential	potential	NOUN
american_scientific_journal-1326	48	9	is	be	AUX
american_scientific_journal-1326	48	10	given	give	VERB
american_scientific_journal-1326	48	11	by	by	ADP
american_scientific_journal-1326	48	12	poisson	poisson	NOUN
american_scientific_journal-1326	48	13	equation	equation	NOUN
american_scientific_journal-1326	48	14	2	2	NUM
american_scientific_journal-1326	48	15	(	(	PUNCT
american_scientific_journal-1326	48	16	,	,	PUNCT
american_scientific_journal-1326	48	17	)	)	PUNCT
american_scientific_journal-1326	48	18	4	4	NUM
american_scientific_journal-1326	48	19	(	(	PUNCT
american_scientific_journal-1326	48	20	,	,	PUNCT
american_scientific_journal-1326	48	21	)	)	PUNCT
american_scientific_journal-1326	48	22	v	v	NOUN
american_scientific_journal-1326	48	23	r	r	NOUN
american_scientific_journal-1326	48	24	t	t	NOUN
american_scientific_journal-1326	48	25	g	g	NOUN
american_scientific_journal-1326	48	26	r	r	NOUN
american_scientific_journal-1326	48	27	tπ	tπ	PRON
american_scientific_journal-1326	48	28	ρ∇	ρ∇	PROPN
american_scientific_journal-1326	48	29	=	=	PUNCT
american_scientific_journal-1326	48	30			ADP
american_scientific_journal-1326	48	31			X
american_scientific_journal-1326	48	32	,	,	PUNCT
american_scientific_journal-1326	48	33	(	(	PUNCT
american_scientific_journal-1326	48	34	3	3	X
american_scientific_journal-1326	48	35	)	)	PUNCT
american_scientific_journal-1326	48	36	where	where	SCONJ
american_scientific_journal-1326	48	37	11	11	NUM
american_scientific_journal-1326	48	38	2	2	NUM
american_scientific_journal-1326	48	39	26.67384	26.67384	NUM
american_scientific_journal-1326	48	40	10	10	NUM
american_scientific_journal-1326	48	41	/g	/g	PUNCT
american_scientific_journal-1326	48	42	nm	nm	ADV
american_scientific_journal-1326	48	43	kg−=	kg−=	PROPN
american_scientific_journal-1326	48	44	×	×	NOUN
american_scientific_journal-1326	48	45	,	,	PUNCT
american_scientific_journal-1326	48	46	is	be	AUX
american_scientific_journal-1326	48	47	the	the	DET
american_scientific_journal-1326	48	48	gravitational	gravitational	ADJ
american_scientific_journal-1326	48	49	constant	constant	NOUN
american_scientific_journal-1326	48	50	.	.	PUNCT
american_scientific_journal-1326	49	1	therefore	therefore	ADV
american_scientific_journal-1326	49	2	,	,	PUNCT
american_scientific_journal-1326	49	3	the	the	DET
american_scientific_journal-1326	49	4	rotational	rotational	ADJ
american_scientific_journal-1326	49	5	speed	speed	NOUN
american_scientific_journal-1326	49	6	requires	require	VERB
american_scientific_journal-1326	49	7	through	through	ADP
american_scientific_journal-1326	49	8	(	(	PUNCT
american_scientific_journal-1326	49	9	3	3	X
american_scientific_journal-1326	49	10	)	)	PUNCT
american_scientific_journal-1326	49	11	a	a	DET
american_scientific_journal-1326	49	12	detailed	detailed	ADJ
american_scientific_journal-1326	49	13	knowledge	knowledge	NOUN
american_scientific_journal-1326	49	14	of	of	ADP
american_scientific_journal-1326	49	15	the	the	DET
american_scientific_journal-1326	49	16	mass	mass	NOUN
american_scientific_journal-1326	49	17	density	density	NOUN
american_scientific_journal-1326	49	18	(	(	PUNCT
american_scientific_journal-1326	49	19	,	,	PUNCT
american_scientific_journal-1326	49	20	)	)	PUNCT
american_scientific_journal-1326	49	21	r	r	NOUN
american_scientific_journal-1326	49	22	tρ	tρ	X
american_scientific_journal-1326	49	23			NOUN
american_scientific_journal-1326	49	24	.	.	PUNCT
american_scientific_journal-1326	50	1	american	american	ADJ
american_scientific_journal-1326	50	2	scientific	scientific	ADJ
american_scientific_journal-1326	50	3	research	research	PROPN
american_scientific_journal-1326	50	4	journal	journal	NOUN
american_scientific_journal-1326	50	5	for	for	ADP
american_scientific_journal-1326	50	6	engineering	engineering	NOUN
american_scientific_journal-1326	50	7	,	,	PUNCT
american_scientific_journal-1326	50	8	technology	technology	NOUN
american_scientific_journal-1326	50	9	,	,	PUNCT
american_scientific_journal-1326	50	10	and	and	CCONJ
american_scientific_journal-1326	50	11	sciences	science	NOUN
american_scientific_journal-1326	50	12	(	(	PUNCT
american_scientific_journal-1326	50	13	asrjets	asrjet	NOUN
american_scientific_journal-1326	50	14	)	)	PUNCT
american_scientific_journal-1326	50	15	(	(	PUNCT
american_scientific_journal-1326	50	16	2017	2017	NUM
american_scientific_journal-1326	50	17	)	)	PUNCT
american_scientific_journal-1326	50	18	volume	volume	NOUN
american_scientific_journal-1326	50	19	27	27	NUM
american_scientific_journal-1326	50	20	,	,	PUNCT
american_scientific_journal-1326	50	21	no	no	DET
american_scientific_journal-1326	50	22	1	1	NUM
american_scientific_journal-1326	50	23	,	,	PUNCT
american_scientific_journal-1326	50	24	pp	pp	ADV
american_scientific_journal-1326	50	25	139	139	NUM
american_scientific_journal-1326	50	26	-	-	SYM
american_scientific_journal-1326	50	27	150	150	NUM
american_scientific_journal-1326	50	28	142	142	NUM
american_scientific_journal-1326	50	29	to	to	PART
american_scientific_journal-1326	50	30	have	have	VERB
american_scientific_journal-1326	50	31	an	an	DET
american_scientific_journal-1326	50	32	adequate	adequate	ADJ
american_scientific_journal-1326	50	33	representation	representation	NOUN
american_scientific_journal-1326	50	34	of	of	ADP
american_scientific_journal-1326	50	35	the	the	DET
american_scientific_journal-1326	50	36	galactic	galactic	ADJ
american_scientific_journal-1326	50	37	density	density	NOUN
american_scientific_journal-1326	50	38	,	,	PUNCT
american_scientific_journal-1326	50	39	we	we	PRON
american_scientific_journal-1326	50	40	will	will	AUX
american_scientific_journal-1326	50	41	take	take	VERB
american_scientific_journal-1326	50	42	into	into	ADP
american_scientific_journal-1326	50	43	account	account	NOUN
american_scientific_journal-1326	50	44	that	that	SCONJ
american_scientific_journal-1326	50	45	the	the	DET
american_scientific_journal-1326	50	46	experimental	experimental	ADJ
american_scientific_journal-1326	50	47	data	datum	NOUN
american_scientific_journal-1326	50	48	show	show	VERB
american_scientific_journal-1326	50	49	that	that	SCONJ
american_scientific_journal-1326	50	50	the	the	DET
american_scientific_journal-1326	50	51	mass	mass	ADJ
american_scientific_journal-1326	50	52	distribution	distribution	NOUN
american_scientific_journal-1326	50	53	is	be	AUX
american_scientific_journal-1326	50	54	gaussian	gaussian	ADJ
american_scientific_journal-1326	50	55	in	in	ADP
american_scientific_journal-1326	50	56	the	the	DET
american_scientific_journal-1326	50	57	observed	observed	ADJ
american_scientific_journal-1326	50	58	velocities	velocity	NOUN
american_scientific_journal-1326	50	59	(	(	PUNCT
american_scientific_journal-1326	50	60	that	that	PRON
american_scientific_journal-1326	50	61	is	be	AUX
american_scientific_journal-1326	50	62	2	2	NUM
american_scientific_journal-1326	50	63	,	,	PUNCT
american_scientific_journal-1326	50	64	ve	ve	VERB
american_scientific_journal-1326	50	65	α	α	DET
american_scientific_journal-1326	50	66	α−≈	α−≈	PROPN
american_scientific_journal-1326	50	67	=	=	SYM
american_scientific_journal-1326	50	68	constant	constant	ADJ
american_scientific_journal-1326	50	69	)	)	PUNCT
american_scientific_journal-1326	51	1	[	[	X
american_scientific_journal-1326	51	2	1	1	NUM
american_scientific_journal-1326	51	3	]	]	PUNCT
american_scientific_journal-1326	51	4	.	.	PUNCT
american_scientific_journal-1326	52	1	this	this	PRON
american_scientific_journal-1326	52	2	allows	allow	VERB
american_scientific_journal-1326	52	3	conceive	conceive	VERB
american_scientific_journal-1326	52	4	a	a	DET
american_scientific_journal-1326	52	5	spiral	spiral	ADJ
american_scientific_journal-1326	52	6	galaxy	galaxy	NOUN
american_scientific_journal-1326	52	7	as	as	ADP
american_scientific_journal-1326	52	8	a	a	DET
american_scientific_journal-1326	52	9	fluid	fluid	NOUN
american_scientific_journal-1326	52	10	with	with	ADP
american_scientific_journal-1326	52	11	a	a	DET
american_scientific_journal-1326	52	12	given	give	VERB
american_scientific_journal-1326	52	13	mass	mass	ADJ
american_scientific_journal-1326	52	14	distribution	distribution	NOUN
american_scientific_journal-1326	52	15	in	in	ADP
american_scientific_journal-1326	52	16	the	the	DET
american_scientific_journal-1326	52	17	phase	phase	NOUN
american_scientific_journal-1326	52	18	space	space	NOUN
american_scientific_journal-1326	52	19	,	,	PUNCT
american_scientific_journal-1326	52	20	say	say	VERB
american_scientific_journal-1326	52	21	(	(	PUNCT
american_scientific_journal-1326	52	22	,	,	PUNCT
american_scientific_journal-1326	52	23	)	)	PUNCT
american_scientific_journal-1326	52	24	r	r	NOUN
american_scientific_journal-1326	52	25	tχ	tχ	PROPN
american_scientific_journal-1326	52	26			NOUN
american_scientific_journal-1326	52	27	.	.	PUNCT
american_scientific_journal-1326	53	1	in	in	ADP
american_scientific_journal-1326	53	2	accordance	accordance	NOUN
american_scientific_journal-1326	53	3	with	with	ADP
american_scientific_journal-1326	53	4	[	[	X
american_scientific_journal-1326	53	5	1,8	1,8	NUM
american_scientific_journal-1326	53	6	]	]	X
american_scientific_journal-1326	53	7	,	,	PUNCT
american_scientific_journal-1326	53	8	the	the	DET
american_scientific_journal-1326	53	9	integral	integral	NOUN
american_scientific_journal-1326	53	10	of	of	ADP
american_scientific_journal-1326	53	11	this	this	PRON
american_scientific_journal-1326	53	12	last	last	ADJ
american_scientific_journal-1326	53	13	over	over	ADP
american_scientific_journal-1326	53	14	the	the	DET
american_scientific_journal-1326	53	15	velocities	velocity	NOUN
american_scientific_journal-1326	53	16	is	be	AUX
american_scientific_journal-1326	53	17	related	relate	VERB
american_scientific_journal-1326	53	18	to	to	ADP
american_scientific_journal-1326	53	19	density	density	NOUN
american_scientific_journal-1326	53	20	(	(	PUNCT
american_scientific_journal-1326	53	21	,	,	PUNCT
american_scientific_journal-1326	53	22	)	)	PUNCT
american_scientific_journal-1326	53	23	r	r	NOUN
american_scientific_journal-1326	53	24	tρ	tρ	X
american_scientific_journal-1326	53	25			NOUN
american_scientific_journal-1326	53	26	through	through	ADP
american_scientific_journal-1326	53	27	the	the	DET
american_scientific_journal-1326	53	28	following	follow	VERB
american_scientific_journal-1326	53	29	integral	integral	ADJ
american_scientific_journal-1326	53	30	(	(	PUNCT
american_scientific_journal-1326	53	31	,	,	PUNCT
american_scientific_journal-1326	53	32	)	)	PUNCT
american_scientific_journal-1326	53	33	(	(	PUNCT
american_scientific_journal-1326	53	34	,	,	PUNCT
american_scientific_journal-1326	53	35	,	,	PUNCT
american_scientific_journal-1326	53	36	)	)	PUNCT
american_scientific_journal-1326	53	37	r	r	NOUN
american_scientific_journal-1326	53	38	t	t	NOUN
american_scientific_journal-1326	53	39	m	m	VERB
american_scientific_journal-1326	53	40	r	r	NOUN
american_scientific_journal-1326	53	41	v	v	NOUN
american_scientific_journal-1326	53	42	t	t	NOUN
american_scientific_journal-1326	53	43	dvρ	dvρ	VERB
american_scientific_journal-1326	54	1	χ=	χ=	X
american_scientific_journal-1326	54	2	∫	∫	PROPN
american_scientific_journal-1326	54	3			ADP
american_scientific_journal-1326	54	4			X
american_scientific_journal-1326	54	5			ADP
american_scientific_journal-1326	54	6			NOUN
american_scientific_journal-1326	54	7	,	,	PUNCT
american_scientific_journal-1326	54	8	(	(	PUNCT
american_scientific_journal-1326	54	9	4	4	X
american_scientific_journal-1326	54	10	)	)	PUNCT
american_scientific_journal-1326	54	11	where	where	SCONJ
american_scientific_journal-1326	54	12	m	m	NOUN
american_scientific_journal-1326	54	13	is	be	AUX
american_scientific_journal-1326	54	14	the	the	DET
american_scientific_journal-1326	54	15	mass	mass	NOUN
american_scientific_journal-1326	54	16	of	of	ADP
american_scientific_journal-1326	54	17	a	a	DET
american_scientific_journal-1326	54	18	typical	typical	ADJ
american_scientific_journal-1326	54	19	star	star	NOUN
american_scientific_journal-1326	54	20	.	.	PUNCT
american_scientific_journal-1326	55	1	following	follow	VERB
american_scientific_journal-1326	55	2	[	[	X
american_scientific_journal-1326	55	3	8	8	NUM
american_scientific_journal-1326	55	4	]	]	PUNCT
american_scientific_journal-1326	55	5	,	,	PUNCT
american_scientific_journal-1326	55	6	mass	mass	ADJ
american_scientific_journal-1326	55	7	distribution	distribution	NOUN
american_scientific_journal-1326	55	8	is	be	AUX
american_scientific_journal-1326	55	9	also	also	ADV
american_scientific_journal-1326	55	10	gaussian	gaussian	ADJ
american_scientific_journal-1326	55	11	in	in	ADP
american_scientific_journal-1326	55	12	the	the	DET
american_scientific_journal-1326	55	13	kinetic	kinetic	ADJ
american_scientific_journal-1326	55	14	energy	energy	NOUN
american_scientific_journal-1326	55	15	(	(	PUNCT
american_scientific_journal-1326	55	16	since	since	SCONJ
american_scientific_journal-1326	55	17	kinetic	kinetic	ADJ
american_scientific_journal-1326	55	18	energy	energy	NOUN
american_scientific_journal-1326	55	19	and	and	CCONJ
american_scientific_journal-1326	55	20	2v	2v	PROPN
american_scientific_journal-1326	55	21	differ	differ	VERB
american_scientific_journal-1326	55	22	just	just	ADV
american_scientific_journal-1326	55	23	in	in	ADP
american_scientific_journal-1326	55	24	a	a	DET
american_scientific_journal-1326	55	25	constant	constant	ADJ
american_scientific_journal-1326	55	26	factor	factor	NOUN
american_scientific_journal-1326	55	27	)	)	PUNCT
american_scientific_journal-1326	55	28	,	,	PUNCT
american_scientific_journal-1326	55	29	and	and	CCONJ
american_scientific_journal-1326	55	30	therefore	therefore	ADV
american_scientific_journal-1326	55	31	is	be	AUX
american_scientific_journal-1326	55	32	reasonable	reasonable	ADJ
american_scientific_journal-1326	55	33	to	to	PART
american_scientific_journal-1326	55	34	propose	propose	VERB
american_scientific_journal-1326	55	35	that	that	SCONJ
american_scientific_journal-1326	55	36	the	the	DET
american_scientific_journal-1326	55	37	mass	mass	ADJ
american_scientific_journal-1326	55	38	distribution	distribution	NOUN
american_scientific_journal-1326	55	39	χ	χ	PART
american_scientific_journal-1326	55	40	to	to	PART
american_scientific_journal-1326	55	41	be	be	AUX
american_scientific_journal-1326	55	42	a	a	DET
american_scientific_journal-1326	55	43	boltzmann	boltzmann	NOUN
american_scientific_journal-1326	55	44	distribution	distribution	NOUN
american_scientific_journal-1326	55	45	in	in	ADP
american_scientific_journal-1326	55	46	the	the	DET
american_scientific_journal-1326	55	47	total	total	ADJ
american_scientific_journal-1326	55	48	energy	energy	NOUN
american_scientific_journal-1326	55	49	e	e	NOUN
american_scientific_journal-1326	55	50	[	[	X
american_scientific_journal-1326	55	51	1	1	NUM
american_scientific_journal-1326	55	52	]	]	PUNCT
american_scientific_journal-1326	55	53	.	.	PUNCT
american_scientific_journal-1326	56	1	in	in	ADP
american_scientific_journal-1326	56	2	what	what	PRON
american_scientific_journal-1326	56	3	follows	follow	VERB
american_scientific_journal-1326	56	4	,	,	PUNCT
american_scientific_journal-1326	56	5	we	we	PRON
american_scientific_journal-1326	56	6	will	will	AUX
american_scientific_journal-1326	56	7	focus	focus	VERB
american_scientific_journal-1326	56	8	to	to	ADP
american_scientific_journal-1326	56	9	the	the	DET
american_scientific_journal-1326	56	10	study	study	NOUN
american_scientific_journal-1326	56	11	of	of	ADP
american_scientific_journal-1326	56	12	the	the	DET
american_scientific_journal-1326	56	13	disc	disc	NOUN
american_scientific_journal-1326	56	14	of	of	ADP
american_scientific_journal-1326	56	15	galaxy	galaxy	NOUN
american_scientific_journal-1326	56	16	assuming	assume	VERB
american_scientific_journal-1326	56	17	a	a	DET
american_scientific_journal-1326	56	18	static	static	ADJ
american_scientific_journal-1326	56	19	regime	regime	NOUN
american_scientific_journal-1326	56	20	.	.	PUNCT
american_scientific_journal-1326	57	1	also	also	ADV
american_scientific_journal-1326	57	2	as	as	SCONJ
american_scientific_journal-1326	57	3	we	we	PRON
american_scientific_journal-1326	57	4	will	will	AUX
american_scientific_journal-1326	57	5	see	see	VERB
american_scientific_journal-1326	57	6	later	later	ADV
american_scientific_journal-1326	57	7	,	,	PUNCT
american_scientific_journal-1326	57	8	our	our	PRON
american_scientific_journal-1326	57	9	results	result	NOUN
american_scientific_journal-1326	57	10	will	will	AUX
american_scientific_journal-1326	57	11	be	be	AUX
american_scientific_journal-1326	57	12	consistent	consistent	ADJ
american_scientific_journal-1326	57	13	with	with	ADP
american_scientific_journal-1326	57	14	the	the	DET
american_scientific_journal-1326	57	15	behavior	behavior	NOUN
american_scientific_journal-1326	57	16	of	of	ADP
american_scientific_journal-1326	57	17	the	the	DET
american_scientific_journal-1326	57	18	rotation	rotation	NOUN
american_scientific_journal-1326	57	19	curves	curve	NOUN
american_scientific_journal-1326	57	20	of	of	ADP
american_scientific_journal-1326	57	21	elliptical	elliptical	ADJ
american_scientific_journal-1326	57	22	galaxies	galaxy	NOUN
american_scientific_journal-1326	57	23	.	.	PUNCT
american_scientific_journal-1326	58	1	from	from	ADP
american_scientific_journal-1326	58	2	the	the	DET
american_scientific_journal-1326	58	3	above	above	ADJ
american_scientific_journal-1326	58	4	,	,	PUNCT
american_scientific_journal-1326	58	5	0	0	NUM
american_scientific_journal-1326	58	6	(	(	PUNCT
american_scientific_journal-1326	58	7	)	)	PUNCT
american_scientific_journal-1326	58	8	ee	ee	PROPN
american_scientific_journal-1326	58	9	e	e	PROPN
american_scientific_journal-1326	58	10	βχ	βχ	ADP
american_scientific_journal-1326	58	11	χ	χ	X
american_scientific_journal-1326	58	12	−=	−=	PUNCT
american_scientific_journal-1326	58	13	,	,	PUNCT
american_scientific_journal-1326	58	14	(	(	PUNCT
american_scientific_journal-1326	58	15	5	5	NUM
american_scientific_journal-1326	58	16	)	)	PUNCT
american_scientific_journal-1326	58	17	for	for	ADP
american_scientific_journal-1326	58	18	some	some	DET
american_scientific_journal-1326	58	19	parameters	parameter	NOUN
american_scientific_journal-1326	58	20	0χ	0χ	NOUN
american_scientific_journal-1326	58	21	and	and	CCONJ
american_scientific_journal-1326	58	22	β	β	X
american_scientific_journal-1326	58	23	(	(	PUNCT
american_scientific_journal-1326	58	24	in	in	ADP
american_scientific_journal-1326	58	25	the	the	DET
american_scientific_journal-1326	58	26	context	context	NOUN
american_scientific_journal-1326	58	27	of	of	ADP
american_scientific_journal-1326	58	28	statistical	statistical	ADJ
american_scientific_journal-1326	58	29	mechanics	mechanic	NOUN
american_scientific_journal-1326	58	30	β	β	NOUN
american_scientific_journal-1326	58	31	would	would	AUX
american_scientific_journal-1326	58	32	be	be	AUX
american_scientific_journal-1326	58	33	identified	identify	VERB
american_scientific_journal-1326	58	34	with	with	ADP
american_scientific_journal-1326	58	35	the	the	DET
american_scientific_journal-1326	58	36	so	so	ADV
american_scientific_journal-1326	58	37	called	call	VERB
american_scientific_journal-1326	58	38	,	,	PUNCT
american_scientific_journal-1326	58	39	temperature	temperature	NOUN
american_scientific_journal-1326	58	40	parameter	parameter	NOUN
american_scientific_journal-1326	58	41	[	[	X
american_scientific_journal-1326	58	42	8	8	NUM
american_scientific_journal-1326	58	43	]	]	NUM
american_scientific_journal-1326	58	44	)	)	PUNCT
american_scientific_journal-1326	58	45	.	.	PUNCT
american_scientific_journal-1326	59	1	in	in	ADP
american_scientific_journal-1326	59	2	order	order	NOUN
american_scientific_journal-1326	59	3	to	to	PART
american_scientific_journal-1326	59	4	exploit	exploit	VERB
american_scientific_journal-1326	59	5	the	the	DET
american_scientific_journal-1326	59	6	axial	axial	ADJ
american_scientific_journal-1326	59	7	symmetry	symmetry	NOUN
american_scientific_journal-1326	59	8	of	of	ADP
american_scientific_journal-1326	59	9	the	the	DET
american_scientific_journal-1326	59	10	system	system	NOUN
american_scientific_journal-1326	59	11	,	,	PUNCT
american_scientific_journal-1326	59	12	we	we	PRON
american_scientific_journal-1326	59	13	will	will	AUX
american_scientific_journal-1326	59	14	employ	employ	VERB
american_scientific_journal-1326	59	15	cylindrical	cylindrical	ADJ
american_scientific_journal-1326	59	16	coordinates	coordinate	NOUN
american_scientific_journal-1326	59	17	,	,	PUNCT
american_scientific_journal-1326	59	18	so	so	SCONJ
american_scientific_journal-1326	59	19	that	that	SCONJ
american_scientific_journal-1326	59	20	it	it	PRON
american_scientific_journal-1326	59	21	is	be	AUX
american_scientific_journal-1326	59	22	possible	possible	ADJ
american_scientific_journal-1326	59	23	to	to	PART
american_scientific_journal-1326	59	24	rewrite	rewrite	VERB
american_scientific_journal-1326	59	25	(	(	PUNCT
american_scientific_journal-1326	59	26	5	5	NUM
american_scientific_journal-1326	59	27	)	)	PUNCT
american_scientific_journal-1326	59	28	as	as	ADP
american_scientific_journal-1326	59	29	(	(	PUNCT
american_scientific_journal-1326	59	30	)	)	SYM
american_scientific_journal-1326	59	31	2	2	NUM
american_scientific_journal-1326	59	32	2	2	NUM
american_scientific_journal-1326	59	33	2	2	NUM
american_scientific_journal-1326	59	34	2	2	NUM
american_scientific_journal-1326	59	35	0	0	NUM
american_scientific_journal-1326	59	36	1	1	NUM
american_scientific_journal-1326	59	37	(	(	PUNCT
american_scientific_journal-1326	59	38	)	)	PUNCT
american_scientific_journal-1326	59	39	exp	exp	NOUN
american_scientific_journal-1326	59	40	[	[	PUNCT
american_scientific_journal-1326	59	41	(	(	PUNCT
american_scientific_journal-1326	59	42	,	,	PUNCT
american_scientific_journal-1326	59	43	)	)	PUNCT
american_scientific_journal-1326	59	44	2	2	NUM
american_scientific_journal-1326	59	45	e	e	NOUN
american_scientific_journal-1326	59	46	r	r	NOUN
american_scientific_journal-1326	59	47	r	r	NOUN
american_scientific_journal-1326	59	48	z	z	NOUN
american_scientific_journal-1326	59	49	v	v	NOUN
american_scientific_journal-1326	59	50	r	r	NOUN
american_scientific_journal-1326	59	51	zχ	zχ	X
american_scientific_journal-1326	59	52	χ	χ	NOUN
american_scientific_journal-1326	59	53	β	β	X
american_scientific_journal-1326	59	54	φ	φ	PROPN
american_scientific_journal-1326	60	1	=	=	ADP
american_scientific_journal-1326	60	2	−	−	PROPN
american_scientific_journal-1326	61	1	+	+	CCONJ
american_scientific_journal-1326	62	1	+	+	PUNCT
american_scientific_journal-1326	62	2	+	+	ADJ
american_scientific_journal-1326	62	3			NOUN
american_scientific_journal-1326	62	4			VERB
american_scientific_journal-1326	62	5			NOUN
american_scientific_journal-1326	62	6			PUNCT
american_scientific_journal-1326	62	7			NOUN
american_scientific_journal-1326	62	8			NOUN
american_scientific_journal-1326	62	9	,	,	PUNCT
american_scientific_journal-1326	62	10	(	(	PUNCT
american_scientific_journal-1326	62	11	6	6	NUM
american_scientific_journal-1326	62	12	)	)	PUNCT
american_scientific_journal-1326	62	13	where	where	SCONJ
american_scientific_journal-1326	62	14	it	it	PRON
american_scientific_journal-1326	62	15	was	be	AUX
american_scientific_journal-1326	62	16	considered	consider	VERB
american_scientific_journal-1326	62	17	,	,	PUNCT
american_scientific_journal-1326	62	18	the	the	DET
american_scientific_journal-1326	62	19	energy	energy	NOUN
american_scientific_journal-1326	62	20	per	per	ADP
american_scientific_journal-1326	62	21	unit	unit	NOUN
american_scientific_journal-1326	62	22	mass	mass	PROPN
american_scientific_journal-1326	62	23	,	,	PUNCT
american_scientific_journal-1326	62	24	to	to	PART
american_scientific_journal-1326	62	25	account	account	VERB
american_scientific_journal-1326	62	26	for	for	ADP
american_scientific_journal-1326	62	27	the	the	DET
american_scientific_journal-1326	62	28	presence	presence	NOUN
american_scientific_journal-1326	62	29	of	of	ADP
american_scientific_journal-1326	62	30	potential	potential	NOUN
american_scientific_journal-1326	62	31	rather	rather	ADV
american_scientific_journal-1326	62	32	than	than	ADP
american_scientific_journal-1326	62	33	the	the	DET
american_scientific_journal-1326	62	34	potential	potential	ADJ
american_scientific_journal-1326	62	35	energy	energy	NOUN
american_scientific_journal-1326	62	36	.	.	PUNCT
american_scientific_journal-1326	63	1	similarly	similarly	ADV
american_scientific_journal-1326	63	2	it	it	PRON
american_scientific_journal-1326	63	3	is	be	AUX
american_scientific_journal-1326	63	4	assumed	assume	VERB
american_scientific_journal-1326	63	5	that	that	SCONJ
american_scientific_journal-1326	63	6	the	the	DET
american_scientific_journal-1326	63	7	total	total	ADJ
american_scientific_journal-1326	63	8	energy	energy	NOUN
american_scientific_journal-1326	63	9	is	be	AUX
american_scientific_journal-1326	63	10	mechanical	mechanical	ADJ
american_scientific_journal-1326	63	11	,	,	PUNCT
american_scientific_journal-1326	63	12	due	due	ADP
american_scientific_journal-1326	63	13	to	to	ADP
american_scientific_journal-1326	63	14	conservative	conservative	ADJ
american_scientific_journal-1326	63	15	character	character	NOUN
american_scientific_journal-1326	63	16	of	of	ADP
american_scientific_journal-1326	63	17	gravitational	gravitational	ADJ
american_scientific_journal-1326	63	18	force	force	NOUN
american_scientific_journal-1326	63	19	field	field	NOUN
american_scientific_journal-1326	64	1	[	[	X
american_scientific_journal-1326	64	2	3,7	3,7	NUM
american_scientific_journal-1326	64	3	]	]	PUNCT
american_scientific_journal-1326	64	4	.	.	PUNCT
american_scientific_journal-1326	65	1	thus	thus	ADV
american_scientific_journal-1326	65	2	,	,	PUNCT
american_scientific_journal-1326	65	3	substituting	substitute	VERB
american_scientific_journal-1326	65	4	(	(	PUNCT
american_scientific_journal-1326	65	5	6	6	NUM
american_scientific_journal-1326	65	6	)	)	PUNCT
american_scientific_journal-1326	65	7	into	into	ADP
american_scientific_journal-1326	65	8	(	(	PUNCT
american_scientific_journal-1326	65	9	4	4	NUM
american_scientific_journal-1326	65	10	)	)	PUNCT
american_scientific_journal-1326	65	11	,	,	PUNCT
american_scientific_journal-1326	65	12	we	we	PRON
american_scientific_journal-1326	65	13	obtain	obtain	VERB
american_scientific_journal-1326	65	14	(	(	PUNCT
american_scientific_journal-1326	65	15	)	)	SYM
american_scientific_journal-1326	65	16	2	2	NUM
american_scientific_journal-1326	65	17	2	2	NUM
american_scientific_journal-1326	65	18	2	2	NUM
american_scientific_journal-1326	65	19	2	2	NUM
american_scientific_journal-1326	65	20	0	0	NUM
american_scientific_journal-1326	65	21	1	1	NUM
american_scientific_journal-1326	65	22	(	(	PUNCT
american_scientific_journal-1326	65	23	,	,	PUNCT
american_scientific_journal-1326	65	24	)	)	PUNCT
american_scientific_journal-1326	65	25	exp	exp	NOUN
american_scientific_journal-1326	65	26	(	(	PUNCT
american_scientific_journal-1326	65	27	,	,	PUNCT
american_scientific_journal-1326	65	28	)	)	PUNCT
american_scientific_journal-1326	65	29	2	2	NUM
american_scientific_journal-1326	65	30	r	r	NOUN
american_scientific_journal-1326	65	31	z	z	NOUN
american_scientific_journal-1326	65	32	m	m	VERB
american_scientific_journal-1326	65	33	rdrd	rdrd	ADJ
american_scientific_journal-1326	65	34	dz	dz	X
american_scientific_journal-1326	65	35	r	r	NOUN
american_scientific_journal-1326	65	36	r	r	NOUN
american_scientific_journal-1326	65	37	z	z	NOUN
american_scientific_journal-1326	65	38	v	v	NOUN
american_scientific_journal-1326	65	39	r	r	NOUN
american_scientific_journal-1326	65	40	zρ	zρ	NOUN
american_scientific_journal-1326	65	41	φ	φ	X
american_scientific_journal-1326	65	42	χ	χ	NOUN
american_scientific_journal-1326	65	43	β	β	X
american_scientific_journal-1326	65	44	φ	φ	NUM
american_scientific_journal-1326	65	45			PRON
american_scientific_journal-1326	65	46	=	=	ADP
american_scientific_journal-1326	65	47	−	−	PROPN
american_scientific_journal-1326	66	1	+	+	CCONJ
american_scientific_journal-1326	66	2	+	+	PUNCT
american_scientific_journal-1326	66	3	+	+	NOUN
american_scientific_journal-1326	66	4			NOUN
american_scientific_journal-1326	66	5			VERB
american_scientific_journal-1326	66	6			ADP
american_scientific_journal-1326	66	7			NOUN
american_scientific_journal-1326	66	8			PROPN
american_scientific_journal-1326	66	9	∫	∫	NOUN
american_scientific_journal-1326	66	10			NOUN
american_scientific_journal-1326	66	11			NOUN
american_scientific_journal-1326	66	12			NOUN
american_scientific_journal-1326	66	13			NOUN
american_scientific_journal-1326	66	14	,	,	PUNCT
american_scientific_journal-1326	66	15	(	(	PUNCT
american_scientific_journal-1326	66	16	7	7	X
american_scientific_journal-1326	66	17	)	)	PUNCT
american_scientific_journal-1326	66	18	american	american	ADJ
american_scientific_journal-1326	66	19	scientific	scientific	ADJ
american_scientific_journal-1326	66	20	research	research	NOUN
american_scientific_journal-1326	66	21	journal	journal	NOUN
american_scientific_journal-1326	66	22	for	for	ADP
american_scientific_journal-1326	66	23	engineering	engineering	NOUN
american_scientific_journal-1326	66	24	,	,	PUNCT
american_scientific_journal-1326	66	25	technology	technology	NOUN
american_scientific_journal-1326	66	26	,	,	PUNCT
american_scientific_journal-1326	66	27	and	and	CCONJ
american_scientific_journal-1326	66	28	sciences	science	NOUN
american_scientific_journal-1326	66	29	(	(	PUNCT
american_scientific_journal-1326	66	30	asrjets	asrjet	NOUN
american_scientific_journal-1326	66	31	)	)	PUNCT
american_scientific_journal-1326	66	32	(	(	PUNCT
american_scientific_journal-1326	66	33	2017	2017	NUM
american_scientific_journal-1326	66	34	)	)	PUNCT
american_scientific_journal-1326	66	35	volume	volume	NOUN
american_scientific_journal-1326	66	36	27	27	NUM
american_scientific_journal-1326	66	37	,	,	PUNCT
american_scientific_journal-1326	66	38	no	no	DET
american_scientific_journal-1326	66	39	1	1	NUM
american_scientific_journal-1326	66	40	,	,	PUNCT
american_scientific_journal-1326	66	41	pp	pp	ADV
american_scientific_journal-1326	66	42	139	139	NUM
american_scientific_journal-1326	66	43	-	-	SYM
american_scientific_journal-1326	66	44	150	150	NUM
american_scientific_journal-1326	66	45	143	143	NUM
american_scientific_journal-1326	66	46	to	to	PART
american_scientific_journal-1326	66	47	evaluate	evaluate	VERB
american_scientific_journal-1326	66	48	(	(	PUNCT
american_scientific_journal-1326	66	49	7	7	NUM
american_scientific_journal-1326	66	50	)	)	PUNCT
american_scientific_journal-1326	66	51	over	over	ADP
american_scientific_journal-1326	66	52	the	the	DET
american_scientific_journal-1326	66	53	velocities	velocity	NOUN
american_scientific_journal-1326	66	54	,	,	PUNCT
american_scientific_journal-1326	66	55	we	we	PRON
american_scientific_journal-1326	66	56	employ	employ	VERB
american_scientific_journal-1326	66	57	gaussian	gaussian	ADJ
american_scientific_journal-1326	66	58	integrals	integral	NOUN
american_scientific_journal-1326	66	59	,	,	PUNCT
american_scientific_journal-1326	66	60	so	so	SCONJ
american_scientific_journal-1326	66	61	that	that	SCONJ
american_scientific_journal-1326	66	62	the	the	DET
american_scientific_journal-1326	66	63	sought	seek	VERB
american_scientific_journal-1326	66	64	dependence	dependence	NOUN
american_scientific_journal-1326	66	65	of	of	ADP
american_scientific_journal-1326	66	66	the	the	DET
american_scientific_journal-1326	66	67	mass	mass	ADJ
american_scientific_journal-1326	66	68	density	density	NOUN
american_scientific_journal-1326	66	69	over	over	ADP
american_scientific_journal-1326	66	70	the	the	DET
american_scientific_journal-1326	66	71	gravitational	gravitational	ADJ
american_scientific_journal-1326	66	72	potential	potential	NOUN
american_scientific_journal-1326	66	73	is	be	AUX
american_scientific_journal-1326	66	74	given	give	VERB
american_scientific_journal-1326	66	75	by	by	ADP
american_scientific_journal-1326	66	76	(	(	PUNCT
american_scientific_journal-1326	66	77	)	)	PUNCT
american_scientific_journal-1326	66	78	3/	3/	NUM
american_scientific_journal-1326	66	79	2	2	NUM
american_scientific_journal-1326	66	80	,	,	PUNCT
american_scientific_journal-1326	66	81	0	0	NUM
american_scientific_journal-1326	66	82	2	2	NUM
american_scientific_journal-1326	66	83	(	(	PUNCT
american_scientific_journal-1326	66	84	,	,	PUNCT
american_scientific_journal-1326	66	85	)	)	PUNCT
american_scientific_journal-1326	66	86	v	v	ADP
american_scientific_journal-1326	66	87	r	r	NOUN
american_scientific_journal-1326	66	88	zr	zr	PROPN
american_scientific_journal-1326	66	89	z	z	NOUN
american_scientific_journal-1326	66	90	m	m	VERB
american_scientific_journal-1326	66	91	e	e	NOUN
american_scientific_journal-1326	66	92	βπρ	βπρ	NUM
american_scientific_journal-1326	66	93	χ	χ	X
american_scientific_journal-1326	66	94	β	β	X
american_scientific_journal-1326	66	95	−	−	NUM
american_scientific_journal-1326	66	96			PUNCT
american_scientific_journal-1326	67	1	=	=	NOUN
american_scientific_journal-1326	67	2			NOUN
american_scientific_journal-1326	67	3			VERB
american_scientific_journal-1326	67	4			PRON
american_scientific_journal-1326	67	5			PUNCT
american_scientific_journal-1326	67	6	,	,	PUNCT
american_scientific_journal-1326	67	7	(	(	PUNCT
american_scientific_journal-1326	67	8	8)	8)	NUM
american_scientific_journal-1326	67	9	substituting	substituting	NOUN
american_scientific_journal-1326	67	10	(	(	PUNCT
american_scientific_journal-1326	67	11	8)	8)	NUM
american_scientific_journal-1326	67	12	into	into	ADP
american_scientific_journal-1326	67	13	(	(	PUNCT
american_scientific_journal-1326	67	14	3	3	NUM
american_scientific_journal-1326	67	15	)	)	PUNCT
american_scientific_journal-1326	67	16	,	,	PUNCT
american_scientific_journal-1326	67	17	we	we	PRON
american_scientific_journal-1326	67	18	get	get	VERB
american_scientific_journal-1326	67	19	2	2	NUM
american_scientific_journal-1326	67	20	2	2	NUM
american_scientific_journal-1326	67	21	(	(	PUNCT
american_scientific_journal-1326	67	22	,	,	PUNCT
american_scientific_journal-1326	67	23	)	)	PUNCT
american_scientific_journal-1326	67	24	02	02	NUM
american_scientific_journal-1326	67	25	2	2	NUM
american_scientific_journal-1326	67	26	1	1	NUM
american_scientific_journal-1326	67	27	4	4	NUM
american_scientific_journal-1326	67	28	v	v	NOUN
american_scientific_journal-1326	67	29	r	r	NOUN
american_scientific_journal-1326	67	30	zv	zv	NOUN
american_scientific_journal-1326	67	31	v	v	NOUN
american_scientific_journal-1326	67	32	v	v	NOUN
american_scientific_journal-1326	67	33	g	g	NOUN
american_scientific_journal-1326	67	34	e	e	NOUN
american_scientific_journal-1326	67	35	r	r	NOUN
american_scientific_journal-1326	67	36	r	r	NOUN
american_scientific_journal-1326	67	37	r	r	NOUN
american_scientific_journal-1326	67	38	z	z	NOUN
american_scientific_journal-1326	67	39	βπ	βπ	NOUN
american_scientific_journal-1326	67	40	ρ	ρ	NUM
american_scientific_journal-1326	67	41	−∂	−∂	PROPN
american_scientific_journal-1326	67	42	∂	∂	NUM
american_scientific_journal-1326	67	43	∂	∂	NOUN
american_scientific_journal-1326	68	1	+	+	CCONJ
american_scientific_journal-1326	68	2	+	+	CCONJ
american_scientific_journal-1326	68	3	=	=	SYM
american_scientific_journal-1326	68	4	∂	∂	NUM
american_scientific_journal-1326	68	5	∂	∂	NUM
american_scientific_journal-1326	68	6	∂	∂	NOUN
american_scientific_journal-1326	68	7	,	,	PUNCT
american_scientific_journal-1326	68	8	(	(	PUNCT
american_scientific_journal-1326	68	9	9	9	NUM
american_scientific_journal-1326	68	10	)	)	PUNCT
american_scientific_journal-1326	68	11	where	where	SCONJ
american_scientific_journal-1326	68	12	,	,	PUNCT
american_scientific_journal-1326	68	13	we	we	PRON
american_scientific_journal-1326	68	14	expressed	express	VERB
american_scientific_journal-1326	68	15	the	the	DET
american_scientific_journal-1326	68	16	laplacian	laplacian	NOUN
american_scientific_journal-1326	68	17	in	in	ADP
american_scientific_journal-1326	68	18	cylindrical	cylindrical	ADJ
american_scientific_journal-1326	68	19	coordinates	coordinate	NOUN
american_scientific_journal-1326	68	20	and	and	CCONJ
american_scientific_journal-1326	68	21	defining	define	VERB
american_scientific_journal-1326	68	22	3/	3/	NUM
american_scientific_journal-1326	68	23	2	2	NUM
american_scientific_journal-1326	68	24	0	0	NUM
american_scientific_journal-1326	68	25	0	0	NUM
american_scientific_journal-1326	68	26	2	2	NUM
american_scientific_journal-1326	68	27	m	m	NOUN
american_scientific_journal-1326	68	28	πρ	πρ	NOUN
american_scientific_journal-1326	68	29	χ	χ	X
american_scientific_journal-1326	68	30	β	β	X
american_scientific_journal-1326	68	31			X
american_scientific_journal-1326	68	32			PUNCT
american_scientific_journal-1326	69	1	=	=	NOUN
american_scientific_journal-1326	69	2			NOUN
american_scientific_journal-1326	69	3			VERB
american_scientific_journal-1326	69	4			PRON
american_scientific_journal-1326	69	5			PUNCT
american_scientific_journal-1326	69	6	.	.	PUNCT
american_scientific_journal-1326	70	1	(	(	PUNCT
american_scientific_journal-1326	70	2	10	10	NUM
american_scientific_journal-1326	70	3	)	)	PUNCT
american_scientific_journal-1326	70	4	given	give	VERB
american_scientific_journal-1326	70	5	the	the	DET
american_scientific_journal-1326	70	6	complexity	complexity	NOUN
american_scientific_journal-1326	70	7	of	of	ADP
american_scientific_journal-1326	70	8	nonlinear	nonlinear	ADJ
american_scientific_journal-1326	70	9	partial	partial	ADJ
american_scientific_journal-1326	70	10	differential	differential	NOUN
american_scientific_journal-1326	70	11	equation	equation	NOUN
american_scientific_journal-1326	70	12	(	(	PUNCT
american_scientific_journal-1326	70	13	9	9	NUM
american_scientific_journal-1326	70	14	)	)	PUNCT
american_scientific_journal-1326	70	15	,	,	PUNCT
american_scientific_journal-1326	70	16	reference	reference	NOUN
american_scientific_journal-1326	70	17	[	[	X
american_scientific_journal-1326	70	18	1	1	NUM
american_scientific_journal-1326	70	19	]	]	PUNCT
american_scientific_journal-1326	70	20	studied	study	VERB
american_scientific_journal-1326	70	21	two	two	NUM
american_scientific_journal-1326	70	22	over	over	ADP
american_scientific_journal-1326	70	23	simplified	simplified	ADJ
american_scientific_journal-1326	70	24	models	model	NOUN
american_scientific_journal-1326	70	25	.	.	PUNCT
american_scientific_journal-1326	71	1	the	the	DET
american_scientific_journal-1326	71	2	first	first	ADJ
american_scientific_journal-1326	71	3	case	case	NOUN
american_scientific_journal-1326	71	4	assumed	assume	VERB
american_scientific_journal-1326	71	5	thatv	thatv	PROPN
american_scientific_journal-1326	71	6	varies	vary	VERB
american_scientific_journal-1326	71	7	only	only	ADV
american_scientific_journal-1326	71	8	with	with	ADP
american_scientific_journal-1326	71	9	the	the	DET
american_scientific_journal-1326	71	10	height	height	NOUN
american_scientific_journal-1326	71	11	to	to	ADP
american_scientific_journal-1326	71	12	the	the	DET
american_scientific_journal-1326	71	13	plane	plane	NOUN
american_scientific_journal-1326	71	14	of	of	ADP
american_scientific_journal-1326	71	15	the	the	DET
american_scientific_journal-1326	71	16	disc	disc	NOUN
american_scientific_journal-1326	71	17	,	,	PUNCT
american_scientific_journal-1326	71	18	and	and	CCONJ
american_scientific_journal-1326	71	19	despite	despite	SCONJ
american_scientific_journal-1326	71	20	the	the	DET
american_scientific_journal-1326	71	21	nonlinear	nonlinear	ADJ
american_scientific_journal-1326	71	22	character	character	NOUN
american_scientific_journal-1326	71	23	of	of	ADP
american_scientific_journal-1326	71	24	the	the	DET
american_scientific_journal-1326	71	25	resultant	resultant	NOUN
american_scientific_journal-1326	71	26	equation	equation	NOUN
american_scientific_journal-1326	71	27	,	,	PUNCT
american_scientific_journal-1326	71	28	got	get	VERB
american_scientific_journal-1326	71	29	at	at	ADP
american_scientific_journal-1326	71	30	exact	exact	ADJ
american_scientific_journal-1326	71	31	solution	solution	NOUN
american_scientific_journal-1326	71	32	.	.	PUNCT
american_scientific_journal-1326	72	1	on	on	ADP
american_scientific_journal-1326	72	2	the	the	DET
american_scientific_journal-1326	72	3	other	other	ADJ
american_scientific_journal-1326	72	4	hand	hand	NOUN
american_scientific_journal-1326	72	5	,	,	PUNCT
american_scientific_journal-1326	72	6	the	the	DET
american_scientific_journal-1326	72	7	second	second	ADJ
american_scientific_journal-1326	72	8	case	case	NOUN
american_scientific_journal-1326	72	9	study	study	NOUN
american_scientific_journal-1326	72	10	,	,	PUNCT
american_scientific_journal-1326	72	11	assumed	assume	VERB
american_scientific_journal-1326	72	12	a	a	DET
american_scientific_journal-1326	72	13	variation	variation	NOUN
american_scientific_journal-1326	72	14	only	only	ADV
american_scientific_journal-1326	72	15	in	in	ADP
american_scientific_journal-1326	72	16	the	the	DET
american_scientific_journal-1326	72	17	radial	radial	ADJ
american_scientific_journal-1326	72	18	direction	direction	NOUN
american_scientific_journal-1326	72	19	,	,	PUNCT
american_scientific_journal-1326	72	20	i.e.	i.e.	X
american_scientific_journal-1326	72	21	(	(	PUNCT
american_scientific_journal-1326	72	22	)	)	PUNCT
american_scientific_journal-1326	72	23	.v	.v	PUNCT
american_scientific_journal-1326	73	1	r	r	NOUN
american_scientific_journal-1326	73	2	the	the	DET
american_scientific_journal-1326	73	3	methodology	methodology	NOUN
american_scientific_journal-1326	73	4	used	use	VERB
american_scientific_journal-1326	73	5	,	,	PUNCT
american_scientific_journal-1326	73	6	expressed	express	VERB
american_scientific_journal-1326	73	7	the	the	DET
american_scientific_journal-1326	73	8	resultant	resultant	NOUN
american_scientific_journal-1326	73	9	equation	equation	NOUN
american_scientific_journal-1326	73	10	in	in	ADP
american_scientific_journal-1326	73	11	terms	term	NOUN
american_scientific_journal-1326	73	12	of	of	ADP
american_scientific_journal-1326	73	13	a	a	DET
american_scientific_journal-1326	73	14	volterra	volterra	NOUN
american_scientific_journal-1326	73	15	second	second	ADJ
american_scientific_journal-1326	73	16	order	order	NOUN
american_scientific_journal-1326	73	17	integral	integral	ADJ
american_scientific_journal-1326	73	18	equation	equation	NOUN
american_scientific_journal-1326	73	19	,	,	PUNCT
american_scientific_journal-1326	73	20	which	which	PRON
american_scientific_journal-1326	73	21	was	be	AUX
american_scientific_journal-1326	73	22	solved	solve	VERB
american_scientific_journal-1326	73	23	by	by	ADP
american_scientific_journal-1326	73	24	means	mean	NOUN
american_scientific_journal-1326	73	25	of	of	ADP
american_scientific_journal-1326	73	26	piccard´s	piccard´s	ADJ
american_scientific_journal-1326	73	27	method	method	NOUN
american_scientific_journal-1326	73	28	,	,	PUNCT
american_scientific_journal-1326	73	29	but	but	CCONJ
american_scientific_journal-1326	73	30	[	[	X
american_scientific_journal-1326	73	31	1	1	X
american_scientific_journal-1326	73	32	]	]	PUNCT
american_scientific_journal-1326	73	33	did	do	AUX
american_scientific_journal-1326	73	34	not	not	PART
american_scientific_journal-1326	73	35	discussed	discuss	VERB
american_scientific_journal-1326	73	36	about	about	ADP
american_scientific_journal-1326	73	37	the	the	DET
american_scientific_journal-1326	73	38	perturbative	perturbative	ADJ
american_scientific_journal-1326	73	39	character	character	NOUN
american_scientific_journal-1326	73	40	of	of	ADP
american_scientific_journal-1326	73	41	the	the	DET
american_scientific_journal-1326	73	42	differential	differential	ADJ
american_scientific_journal-1326	73	43	equation	equation	NOUN
american_scientific_journal-1326	73	44	for	for	ADP
american_scientific_journal-1326	73	45	(	(	PUNCT
american_scientific_journal-1326	73	46	)	)	PUNCT
american_scientific_journal-1326	73	47	,	,	PUNCT
american_scientific_journal-1326	73	48	v	v	NOUN
american_scientific_journal-1326	73	49	r	r	NOUN
american_scientific_journal-1326	73	50	and	and	CCONJ
american_scientific_journal-1326	73	51	did	do	AUX
american_scientific_journal-1326	73	52	not	not	PART
american_scientific_journal-1326	73	53	provide	provide	VERB
american_scientific_journal-1326	73	54	a	a	DET
american_scientific_journal-1326	73	55	manner	manner	NOUN
american_scientific_journal-1326	73	56	to	to	PART
american_scientific_journal-1326	73	57	measure	measure	VERB
american_scientific_journal-1326	73	58	the	the	DET
american_scientific_journal-1326	73	59	accuracy	accuracy	NOUN
american_scientific_journal-1326	73	60	of	of	ADP
american_scientific_journal-1326	73	61	the	the	DET
american_scientific_journal-1326	73	62	proposed	propose	VERB
american_scientific_journal-1326	73	63	results	result	NOUN
american_scientific_journal-1326	73	64	.	.	PUNCT
american_scientific_journal-1326	74	1	therefore	therefore	ADV
american_scientific_journal-1326	74	2	,	,	PUNCT
american_scientific_journal-1326	74	3	unlike	unlike	ADP
american_scientific_journal-1326	74	4	the	the	DET
american_scientific_journal-1326	74	5	above	above	ADJ
american_scientific_journal-1326	74	6	methodology	methodology	NOUN
american_scientific_journal-1326	74	7	,	,	PUNCT
american_scientific_journal-1326	74	8	this	this	DET
american_scientific_journal-1326	74	9	work	work	NOUN
american_scientific_journal-1326	74	10	will	will	AUX
american_scientific_journal-1326	74	11	employ	employ	VERB
american_scientific_journal-1326	74	12	an	an	DET
american_scientific_journal-1326	74	13	understandable	understandable	ADJ
american_scientific_journal-1326	74	14	elementary	elementary	ADJ
american_scientific_journal-1326	74	15	procedure	procedure	NOUN
american_scientific_journal-1326	74	16	,	,	PUNCT
american_scientific_journal-1326	74	17	based	base	VERB
american_scientific_journal-1326	74	18	on	on	ADP
american_scientific_journal-1326	74	19	classical	classical	ADJ
american_scientific_journal-1326	74	20	perturbation	perturbation	NOUN
american_scientific_journal-1326	74	21	method	method	NOUN
american_scientific_journal-1326	74	22	(	(	PUNCT
american_scientific_journal-1326	74	23	pm	pm	NOUN
american_scientific_journal-1326	74	24	)	)	PUNCT
american_scientific_journal-1326	74	25	,	,	PUNCT
american_scientific_journal-1326	74	26	in	in	ADP
american_scientific_journal-1326	74	27	order	order	NOUN
american_scientific_journal-1326	74	28	to	to	PART
american_scientific_journal-1326	74	29	find	find	VERB
american_scientific_journal-1326	74	30	an	an	DET
american_scientific_journal-1326	74	31	analytical	analytical	ADJ
american_scientific_journal-1326	74	32	approximate	approximate	ADJ
american_scientific_journal-1326	74	33	solution	solution	NOUN
american_scientific_journal-1326	74	34	for	for	ADP
american_scientific_journal-1326	74	35	the	the	DET
american_scientific_journal-1326	74	36	above	above	ADJ
american_scientific_journal-1326	74	37	mentioned	mention	VERB
american_scientific_journal-1326	74	38	model	model	NOUN
american_scientific_journal-1326	74	39	which	which	PRON
american_scientific_journal-1326	74	40	besides	besides	SCONJ
american_scientific_journal-1326	74	41	,	,	PUNCT
american_scientific_journal-1326	74	42	takes	take	VERB
american_scientific_journal-1326	74	43	into	into	ADP
american_scientific_journal-1326	74	44	account	account	NOUN
american_scientific_journal-1326	74	45	the	the	DET
american_scientific_journal-1326	74	46	perturbative	perturbative	ADJ
american_scientific_journal-1326	74	47	character	character	NOUN
american_scientific_journal-1326	74	48	of	of	ADP
american_scientific_journal-1326	74	49	the	the	DET
american_scientific_journal-1326	74	50	equation	equation	NOUN
american_scientific_journal-1326	74	51	to	to	PART
american_scientific_journal-1326	74	52	solve	solve	VERB
american_scientific_journal-1326	74	53	.	.	PUNCT
american_scientific_journal-1326	75	1	we	we	PRON
american_scientific_journal-1326	75	2	will	will	AUX
american_scientific_journal-1326	75	3	see	see	VERB
american_scientific_journal-1326	75	4	that	that	SCONJ
american_scientific_journal-1326	75	5	our	our	PRON
american_scientific_journal-1326	75	6	results	result	NOUN
american_scientific_journal-1326	75	7	coincide	coincide	VERB
american_scientific_journal-1326	75	8	with	with	ADP
american_scientific_journal-1326	75	9	those	those	PRON
american_scientific_journal-1326	75	10	obtained	obtain	VERB
american_scientific_journal-1326	75	11	in	in	ADP
american_scientific_journal-1326	75	12	[	[	X
american_scientific_journal-1326	75	13	1	1	NUM
american_scientific_journal-1326	75	14	]	]	PUNCT
american_scientific_journal-1326	75	15	but	but	CCONJ
american_scientific_journal-1326	75	16	besides	besides	ADV
american_scientific_journal-1326	75	17	,	,	PUNCT
american_scientific_journal-1326	75	18	we	we	PRON
american_scientific_journal-1326	75	19	will	will	AUX
american_scientific_journal-1326	75	20	provide	provide	VERB
american_scientific_journal-1326	75	21	the	the	DET
american_scientific_journal-1326	75	22	residual	residual	ADJ
american_scientific_journal-1326	75	23	error	error	NOUN
american_scientific_journal-1326	75	24	in	in	ADP
american_scientific_journal-1326	75	25	order	order	NOUN
american_scientific_journal-1326	75	26	to	to	PART
american_scientific_journal-1326	75	27	make	make	VERB
american_scientific_journal-1326	75	28	sure	sure	ADJ
american_scientific_journal-1326	75	29	of	of	ADP
american_scientific_journal-1326	75	30	the	the	DET
american_scientific_journal-1326	75	31	accuracy	accuracy	NOUN
american_scientific_journal-1326	75	32	of	of	ADP
american_scientific_journal-1326	75	33	the	the	DET
american_scientific_journal-1326	75	34	proposed	propose	VERB
american_scientific_journal-1326	75	35	methodology	methodology	NOUN
american_scientific_journal-1326	75	36	.	.	PUNCT
american_scientific_journal-1326	76	1	thus	thus	ADV
american_scientific_journal-1326	76	2	,	,	PUNCT
american_scientific_journal-1326	76	3	(	(	PUNCT
american_scientific_journal-1326	76	4	9	9	X
american_scientific_journal-1326	76	5	)	)	PUNCT
american_scientific_journal-1326	76	6	adopts	adopt	VERB
american_scientific_journal-1326	76	7	the	the	DET
american_scientific_journal-1326	76	8	following	follow	VERB
american_scientific_journal-1326	76	9	form	form	NOUN
american_scientific_journal-1326	76	10	for	for	ADP
american_scientific_journal-1326	76	11	the	the	DET
american_scientific_journal-1326	76	12	case	case	NOUN
american_scientific_journal-1326	76	13	where	where	SCONJ
american_scientific_journal-1326	76	14	the	the	DET
american_scientific_journal-1326	76	15	potential	potential	NOUN
american_scientific_journal-1326	76	16	varies	vary	VERB
american_scientific_journal-1326	76	17	only	only	ADV
american_scientific_journal-1326	76	18	in	in	ADP
american_scientific_journal-1326	76	19	the	the	DET
american_scientific_journal-1326	76	20	radial	radial	ADJ
american_scientific_journal-1326	76	21	direction	direction	NOUN
american_scientific_journal-1326	76	22	.	.	PUNCT
american_scientific_journal-1326	77	1	2	2	NUM
american_scientific_journal-1326	77	2	(	(	PUNCT
american_scientific_journal-1326	77	3	)	)	PUNCT
american_scientific_journal-1326	77	4	02	02	NUM
american_scientific_journal-1326	77	5	1	1	NUM
american_scientific_journal-1326	77	6	4	4	NUM
american_scientific_journal-1326	77	7	v	v	ADP
american_scientific_journal-1326	77	8	rd	rd	NOUN
american_scientific_journal-1326	77	9	v	v	ADP
american_scientific_journal-1326	77	10	dv	dv	PROPN
american_scientific_journal-1326	77	11	g	g	PROPN
american_scientific_journal-1326	77	12	e	e	PROPN
american_scientific_journal-1326	77	13	dr	dr	PROPN
american_scientific_journal-1326	77	14	r	r	PROPN
american_scientific_journal-1326	77	15	dr	dr	PROPN
american_scientific_journal-1326	77	16	βπ	βπ	PROPN
american_scientific_journal-1326	77	17	ρ	ρ	PROPN
american_scientific_journal-1326	77	18	−+	−+	PROPN
american_scientific_journal-1326	77	19	=	=	PUNCT
american_scientific_journal-1326	77	20	.	.	PUNCT
american_scientific_journal-1326	78	1	(	(	PUNCT
american_scientific_journal-1326	78	2	11	11	NUM
american_scientific_journal-1326	78	3	)	)	PUNCT
american_scientific_journal-1326	78	4	it	it	PRON
american_scientific_journal-1326	78	5	's	be	AUX
american_scientific_journal-1326	78	6	well	well	ADV
american_scientific_journal-1326	78	7	-	-	PUNCT
american_scientific_journal-1326	78	8	known	know	VERB
american_scientific_journal-1326	78	9	that	that	SCONJ
american_scientific_journal-1326	78	10	the	the	DET
american_scientific_journal-1326	78	11	typical	typical	ADJ
american_scientific_journal-1326	78	12	density	density	NOUN
american_scientific_journal-1326	78	13	of	of	ADP
american_scientific_journal-1326	78	14	a	a	DET
american_scientific_journal-1326	78	15	galaxy	galaxy	NOUN
american_scientific_journal-1326	78	16	is	be	AUX
american_scientific_journal-1326	78	17	low	low	ADJ
american_scientific_journal-1326	78	18	,	,	PUNCT
american_scientific_journal-1326	78	19	of	of	ADP
american_scientific_journal-1326	78	20	the	the	DET
american_scientific_journal-1326	78	21	order	order	NOUN
american_scientific_journal-1326	78	22	22	22	NUM
american_scientific_journal-1326	78	23	31	31	NUM
american_scientific_journal-1326	78	24	10	10	NUM
american_scientific_journal-1326	78	25	k	k	X
american_scientific_journal-1326	78	26	m−×	m−×	PROPN
american_scientific_journal-1326	78	27	,	,	PUNCT
american_scientific_journal-1326	78	28	and	and	CCONJ
american_scientific_journal-1326	78	29	therefore	therefore	ADV
american_scientific_journal-1326	78	30	american	american	ADJ
american_scientific_journal-1326	78	31	scientific	scientific	ADJ
american_scientific_journal-1326	78	32	research	research	PROPN
american_scientific_journal-1326	78	33	journal	journal	NOUN
american_scientific_journal-1326	78	34	for	for	ADP
american_scientific_journal-1326	78	35	engineering	engineering	NOUN
american_scientific_journal-1326	78	36	,	,	PUNCT
american_scientific_journal-1326	78	37	technology	technology	NOUN
american_scientific_journal-1326	78	38	,	,	PUNCT
american_scientific_journal-1326	78	39	and	and	CCONJ
american_scientific_journal-1326	78	40	sciences	science	NOUN
american_scientific_journal-1326	78	41	(	(	PUNCT
american_scientific_journal-1326	78	42	asrjets	asrjet	NOUN
american_scientific_journal-1326	78	43	)	)	PUNCT
american_scientific_journal-1326	78	44	(	(	PUNCT
american_scientific_journal-1326	78	45	2017	2017	NUM
american_scientific_journal-1326	78	46	)	)	PUNCT
american_scientific_journal-1326	78	47	volume	volume	NOUN
american_scientific_journal-1326	78	48	27	27	NUM
american_scientific_journal-1326	78	49	,	,	PUNCT
american_scientific_journal-1326	78	50	no	no	DET
american_scientific_journal-1326	78	51	1	1	NUM
american_scientific_journal-1326	78	52	,	,	PUNCT
american_scientific_journal-1326	78	53	pp	pp	ADV
american_scientific_journal-1326	78	54	139	139	NUM
american_scientific_journal-1326	78	55	-	-	SYM
american_scientific_journal-1326	78	56	150	150	NUM
american_scientific_journal-1326	78	57	144	144	NUM
american_scientific_journal-1326	78	58	32	32	NUM
american_scientific_journal-1326	78	59	04	04	NUM
american_scientific_journal-1326	78	60	8.38	8.38	NUM
american_scientific_journal-1326	78	61	10gε	10gε	NOUN
american_scientific_journal-1326	79	1	π	π	PROPN
american_scientific_journal-1326	79	2	ρ	ρ	PROPN
american_scientific_journal-1326	79	3	−=	−=	PROPN
american_scientific_journal-1326	79	4	≅	≅	PROPN
american_scientific_journal-1326	79	5	×	×	PROPN
american_scientific_journal-1326	79	6	(	(	PUNCT
american_scientific_journal-1326	79	7	12	12	NUM
american_scientific_journal-1326	79	8	)	)	PUNCT
american_scientific_journal-1326	79	9	thus	thus	ADV
american_scientific_journal-1326	79	10	1ε	1ε	NUM
american_scientific_journal-1326	79	11	<	<	X
american_scientific_journal-1326	79	12	<	<	X
american_scientific_journal-1326	79	13	,	,	PUNCT
american_scientific_journal-1326	79	14	and	and	CCONJ
american_scientific_journal-1326	79	15	it	it	PRON
american_scientific_journal-1326	79	16	works	work	VERB
american_scientific_journal-1326	79	17	as	as	ADP
american_scientific_journal-1326	79	18	perturbation	perturbation	NOUN
american_scientific_journal-1326	79	19	parameter	parameter	NOUN
american_scientific_journal-1326	79	20	;	;	PUNCT
american_scientific_journal-1326	79	21	for	for	ADP
american_scientific_journal-1326	79	22	the	the	DET
american_scientific_journal-1326	79	23	same	same	ADJ
american_scientific_journal-1326	79	24	,	,	PUNCT
american_scientific_journal-1326	79	25	pm	pm	NOUN
american_scientific_journal-1326	79	26	scheme	scheme	NOUN
american_scientific_journal-1326	79	27	explained	explain	VERB
american_scientific_journal-1326	79	28	in	in	ADP
american_scientific_journal-1326	79	29	section	section	NOUN
american_scientific_journal-1326	79	30	2	2	NUM
american_scientific_journal-1326	79	31	is	be	AUX
american_scientific_journal-1326	79	32	adequate	adequate	ADJ
american_scientific_journal-1326	79	33	for	for	ADP
american_scientific_journal-1326	79	34	this	this	DET
american_scientific_journal-1326	79	35	case	case	NOUN
american_scientific_journal-1326	79	36	.	.	PUNCT
american_scientific_journal-1326	80	1	from	from	ADP
american_scientific_journal-1326	80	2	the	the	DET
american_scientific_journal-1326	80	3	above	above	ADJ
american_scientific_journal-1326	80	4	,	,	PUNCT
american_scientific_journal-1326	80	5	(	(	PUNCT
american_scientific_journal-1326	80	6	11	11	NUM
american_scientific_journal-1326	80	7	)	)	PUNCT
american_scientific_journal-1326	80	8	gives	give	VERB
american_scientific_journal-1326	80	9	rise	rise	NOUN
american_scientific_journal-1326	80	10	to	to	ADP
american_scientific_journal-1326	80	11	(	(	PUNCT
american_scientific_journal-1326	80	12	)	)	PUNCT
american_scientific_journal-1326	80	13	1	1	NUM
american_scientific_journal-1326	80	14	(	(	PUNCT
american_scientific_journal-1326	80	15	)	)	PUNCT
american_scientific_journal-1326	80	16	(	(	PUNCT
american_scientific_journal-1326	80	17	)	)	PUNCT
american_scientific_journal-1326	80	18	0v	0v	NOUN
american_scientific_journal-1326	80	19	rv	rv	NOUN
american_scientific_journal-1326	81	1	r	r	NOUN
american_scientific_journal-1326	81	2	v	v	NOUN
american_scientific_journal-1326	81	3	r	r	NOUN
american_scientific_journal-1326	81	4	e	e	NOUN
american_scientific_journal-1326	81	5	r	r	NOUN
american_scientific_journal-1326	81	6	βε	βε	PROPN
american_scientific_journal-1326	81	7	−′′	−′′	NOUN
american_scientific_journal-1326	81	8	′+	′+	PUNCT
american_scientific_journal-1326	81	9	−	−	PROPN
american_scientific_journal-1326	82	1	=	=	PRON
american_scientific_journal-1326	82	2	,	,	PUNCT
american_scientific_journal-1326	82	3	0	0	NUM
american_scientific_journal-1326	82	4	0	0	NUM
american_scientific_journal-1326	82	5	(	(	PUNCT
american_scientific_journal-1326	82	6	)	)	PUNCT
american_scientific_journal-1326	82	7	v	v	NOUN
american_scientific_journal-1326	82	8	r	r	NOUN
american_scientific_journal-1326	82	9	v=	v=	NOUN
american_scientific_journal-1326	82	10	,	,	PUNCT
american_scientific_journal-1326	82	11	0	0	NUM
american_scientific_journal-1326	82	12	(	(	PUNCT
american_scientific_journal-1326	82	13	)	)	PUNCT
american_scientific_journal-1326	82	14	v	v	NOUN
american_scientific_journal-1326	82	15	r	r	NOUN
american_scientific_journal-1326	82	16	b′	b′	NOUN
american_scientific_journal-1326	82	17	=	=	NOUN
american_scientific_journal-1326	82	18	.	.	PUNCT
american_scientific_journal-1326	83	1	(	(	PUNCT
american_scientific_journal-1326	83	2	13	13	NUM
american_scientific_journal-1326	83	3	)	)	PUNCT
american_scientific_journal-1326	83	4	where	where	SCONJ
american_scientific_journal-1326	83	5	prime	prime	ADJ
american_scientific_journal-1326	83	6	denotes	denote	NOUN
american_scientific_journal-1326	83	7	from	from	ADP
american_scientific_journal-1326	83	8	here	here	ADV
american_scientific_journal-1326	83	9	on	on	ADV
american_scientific_journal-1326	83	10	,	,	PUNCT
american_scientific_journal-1326	83	11	differentiation	differentiation	NOUN
american_scientific_journal-1326	83	12	respect	respect	NOUN
american_scientific_journal-1326	83	13	to	to	ADP
american_scientific_journal-1326	83	14	r	r	NOUN
american_scientific_journal-1326	83	15	,	,	PUNCT
american_scientific_journal-1326	83	16	0r	0r	PROPN
american_scientific_journal-1326	83	17	is	be	AUX
american_scientific_journal-1326	83	18	the	the	DET
american_scientific_journal-1326	83	19	radius	radius	NOUN
american_scientific_journal-1326	83	20	of	of	ADP
american_scientific_journal-1326	83	21	the	the	DET
american_scientific_journal-1326	83	22	galactic	galactic	ADJ
american_scientific_journal-1326	83	23	core	core	NOUN
american_scientific_journal-1326	83	24	and	and	CCONJ
american_scientific_journal-1326	83	25	0v	0v	NOUN
american_scientific_journal-1326	83	26	,	,	PUNCT
american_scientific_journal-1326	83	27	b	b	PROPN
american_scientific_journal-1326	83	28	denotes	denote	VERB
american_scientific_journal-1326	83	29	the	the	DET
american_scientific_journal-1326	83	30	initial	initial	ADJ
american_scientific_journal-1326	83	31	conditions	condition	NOUN
american_scientific_journal-1326	83	32	of	of	ADP
american_scientific_journal-1326	83	33	the	the	DET
american_scientific_journal-1326	83	34	problem	problem	NOUN
american_scientific_journal-1326	83	35	(	(	PUNCT
american_scientific_journal-1326	83	36	see	see	VERB
american_scientific_journal-1326	83	37	appendix	appendix	VERB
american_scientific_journal-1326	83	38	a	a	PRON
american_scientific_journal-1326	83	39	for	for	ADP
american_scientific_journal-1326	83	40	more	more	ADJ
american_scientific_journal-1326	83	41	details	detail	NOUN
american_scientific_journal-1326	83	42	)	)	PUNCT
american_scientific_journal-1326	83	43	.	.	PUNCT
american_scientific_journal-1326	84	1	we	we	PRON
american_scientific_journal-1326	84	2	identify	identify	VERB
american_scientific_journal-1326	84	3	(	(	PUNCT
american_scientific_journal-1326	84	4	see	see	VERB
american_scientific_journal-1326	84	5	(	(	PUNCT
american_scientific_journal-1326	84	6	1	1	NUM
american_scientific_journal-1326	84	7	)	)	PUNCT
american_scientific_journal-1326	84	8	)	)	PUNCT
american_scientific_journal-1326	84	9	.	.	PUNCT
american_scientific_journal-1326	85	1	1	1	NUM
american_scientific_journal-1326	85	2	(	(	PUNCT
american_scientific_journal-1326	85	3	)	)	PUNCT
american_scientific_journal-1326	85	4	l	l	NOUN
american_scientific_journal-1326	85	5	r	r	NOUN
american_scientific_journal-1326	85	6	v	v	NOUN
american_scientific_journal-1326	85	7	v	v	NOUN
american_scientific_journal-1326	85	8	r	r	NOUN
american_scientific_journal-1326	85	9	′′	′′	PROPN
american_scientific_journal-1326	85	10	′=	′=	PROPN
american_scientific_journal-1326	85	11	+	+	CCONJ
american_scientific_journal-1326	85	12	;	;	PUNCT
american_scientific_journal-1326	85	13	(	(	PUNCT
american_scientific_journal-1326	85	14	)	)	PUNCT
american_scientific_journal-1326	85	15	(	(	PUNCT
american_scientific_journal-1326	85	16	)	)	PUNCT
american_scientific_journal-1326	85	17	v	v	ADP
american_scientific_journal-1326	85	18	rn	rn	PROPN
american_scientific_journal-1326	85	19	r	r	NOUN
american_scientific_journal-1326	85	20	e	e	X
american_scientific_journal-1326	85	21	β−=	β−=	PROPN
american_scientific_journal-1326	85	22	−	−	PROPN
american_scientific_journal-1326	85	23	.	.	PUNCT
american_scientific_journal-1326	86	1	(	(	PUNCT
american_scientific_journal-1326	86	2	14	14	NUM
american_scientific_journal-1326	86	3	)	)	PUNCT
american_scientific_journal-1326	86	4	identifyingε	identifyingε	NOUN
american_scientific_journal-1326	86	5	with	with	ADP
american_scientific_journal-1326	86	6	the	the	DET
american_scientific_journal-1326	86	7	pm	pm	NOUN
american_scientific_journal-1326	86	8	parameter	parameter	NOUN
american_scientific_journal-1326	86	9	,	,	PUNCT
american_scientific_journal-1326	86	10	we	we	PRON
american_scientific_journal-1326	86	11	assume	assume	VERB
american_scientific_journal-1326	86	12	a	a	DET
american_scientific_journal-1326	86	13	solution	solution	NOUN
american_scientific_journal-1326	86	14	for	for	ADP
american_scientific_journal-1326	86	15	(	(	PUNCT
american_scientific_journal-1326	86	16	13	13	NUM
american_scientific_journal-1326	86	17	)	)	PUNCT
american_scientific_journal-1326	86	18	in	in	ADP
american_scientific_journal-1326	86	19	the	the	DET
american_scientific_journal-1326	86	20	form	form	NOUN
american_scientific_journal-1326	86	21	2	2	NUM
american_scientific_journal-1326	86	22	3	3	NUM
american_scientific_journal-1326	86	23	4	4	NUM
american_scientific_journal-1326	86	24	0	0	NUM
american_scientific_journal-1326	86	25	1	1	NUM
american_scientific_journal-1326	86	26	2	2	NUM
american_scientific_journal-1326	86	27	3	3	NUM
american_scientific_journal-1326	86	28	4	4	NUM
american_scientific_journal-1326	86	29	(	(	PUNCT
american_scientific_journal-1326	86	30	)	)	PUNCT
american_scientific_journal-1326	86	31	(	(	PUNCT
american_scientific_journal-1326	86	32	)	)	PUNCT
american_scientific_journal-1326	86	33	(	(	PUNCT
american_scientific_journal-1326	86	34	)	)	PUNCT
american_scientific_journal-1326	86	35	(	(	PUNCT
american_scientific_journal-1326	86	36	)	)	PUNCT
american_scientific_journal-1326	86	37	(	(	PUNCT
american_scientific_journal-1326	86	38	)	)	PUNCT
american_scientific_journal-1326	86	39	(	(	PUNCT
american_scientific_journal-1326	86	40	)	)	PUNCT
american_scientific_journal-1326	86	41	...	...	PUNCT
american_scientific_journal-1326	87	1	v	v	X
american_scientific_journal-1326	87	2	r	r	NOUN
american_scientific_journal-1326	87	3	r	r	NOUN
american_scientific_journal-1326	87	4	r	r	NOUN
american_scientific_journal-1326	87	5	r	r	NOUN
american_scientific_journal-1326	87	6	r	r	NOUN
american_scientific_journal-1326	87	7	rν	rν	NOUN
american_scientific_journal-1326	87	8	εν	εν	NOUN
american_scientific_journal-1326	87	9	ε	ε	PROPN
american_scientific_journal-1326	87	10	ν	ν	NOUN
american_scientific_journal-1326	87	11	ε	ε	PROPN
american_scientific_journal-1326	87	12	ν	ν	X
american_scientific_journal-1326	87	13	ε	ε	PROPN
american_scientific_journal-1326	87	14	ν=	ν=	VERB
american_scientific_journal-1326	87	15	+	+	PUNCT
american_scientific_journal-1326	88	1	+	+	PUNCT
american_scientific_journal-1326	89	1	+	+	PUNCT
american_scientific_journal-1326	89	2	+	+	CCONJ
american_scientific_journal-1326	89	3	+	+	CCONJ
american_scientific_journal-1326	89	4	,	,	PUNCT
american_scientific_journal-1326	89	5	(	(	PUNCT
american_scientific_journal-1326	89	6	see	see	VERB
american_scientific_journal-1326	89	7	(	(	PUNCT
american_scientific_journal-1326	89	8	2	2	NUM
american_scientific_journal-1326	89	9	)	)	PUNCT
american_scientific_journal-1326	89	10	)	)	PUNCT
american_scientific_journal-1326	89	11	.	.	PUNCT
american_scientific_journal-1326	90	1	(	(	PUNCT
american_scientific_journal-1326	90	2	15	15	NUM
american_scientific_journal-1326	90	3	)	)	PUNCT
american_scientific_journal-1326	90	4	on	on	ADP
american_scientific_journal-1326	90	5	comparing	compare	VERB
american_scientific_journal-1326	90	6	the	the	DET
american_scientific_journal-1326	90	7	coefficients	coefficient	NOUN
american_scientific_journal-1326	90	8	of	of	ADP
american_scientific_journal-1326	90	9	like	like	ADP
american_scientific_journal-1326	90	10	powers	power	NOUN
american_scientific_journal-1326	90	11	ofε	ofε	NOUN
american_scientific_journal-1326	90	12	it	it	PRON
american_scientific_journal-1326	90	13	can	can	AUX
american_scientific_journal-1326	90	14	be	be	AUX
american_scientific_journal-1326	90	15	solved	solve	VERB
american_scientific_journal-1326	90	16	for	for	ADP
american_scientific_journal-1326	90	17	0	0	NUM
american_scientific_journal-1326	90	18	(	(	PUNCT
american_scientific_journal-1326	90	19	)	)	PUNCT
american_scientific_journal-1326	90	20	rν	rν	PROPN
american_scientific_journal-1326	90	21	,	,	PUNCT
american_scientific_journal-1326	90	22	1	1	NUM
american_scientific_journal-1326	90	23	(	(	PUNCT
american_scientific_journal-1326	90	24	)	)	PUNCT
american_scientific_journal-1326	90	25	rν	rν	PROPN
american_scientific_journal-1326	90	26	,	,	PUNCT
american_scientific_journal-1326	90	27	2	2	NUM
american_scientific_journal-1326	90	28	(	(	PUNCT
american_scientific_journal-1326	90	29	)	)	PUNCT
american_scientific_journal-1326	90	30	rν	rν	PROPN
american_scientific_journal-1326	90	31	,	,	PUNCT
american_scientific_journal-1326	90	32	3	3	NUM
american_scientific_journal-1326	90	33	(	(	PUNCT
american_scientific_journal-1326	90	34	)	)	PUNCT
american_scientific_journal-1326	90	35	rν	rν	NOUN
american_scientific_journal-1326	90	36	,	,	PUNCT
american_scientific_journal-1326	90	37	..	..	PUNCT
american_scientific_journal-1326	90	38	and	and	CCONJ
american_scientific_journal-1326	90	39	so	so	ADV
american_scientific_journal-1326	90	40	on	on	ADV
american_scientific_journal-1326	90	41	.	.	PUNCT
american_scientific_journal-1326	91	1	later	later	ADV
american_scientific_journal-1326	91	2	it	it	PRON
american_scientific_journal-1326	91	3	will	will	AUX
american_scientific_journal-1326	91	4	be	be	AUX
american_scientific_journal-1326	91	5	seen	see	VERB
american_scientific_journal-1326	91	6	that	that	SCONJ
american_scientific_journal-1326	91	7	,	,	PUNCT
american_scientific_journal-1326	91	8	a	a	DET
american_scientific_journal-1326	91	9	very	very	ADV
american_scientific_journal-1326	91	10	accurate	accurate	ADJ
american_scientific_journal-1326	91	11	handy	handy	ADJ
american_scientific_journal-1326	91	12	result	result	NOUN
american_scientific_journal-1326	91	13	is	be	AUX
american_scientific_journal-1326	91	14	obtained	obtain	VERB
american_scientific_journal-1326	91	15	,	,	PUNCT
american_scientific_journal-1326	91	16	by	by	ADP
american_scientific_journal-1326	91	17	keeping	keep	VERB
american_scientific_journal-1326	91	18	up	up	ADP
american_scientific_journal-1326	91	19	to	to	ADP
american_scientific_journal-1326	91	20	first	first	ADJ
american_scientific_journal-1326	91	21	order	order	NOUN
american_scientific_journal-1326	91	22	approximation	approximation	NOUN
american_scientific_journal-1326	91	23	.	.	PUNCT
american_scientific_journal-1326	91	24	0	0	NUM
american_scientific_journal-1326	91	25	)	)	PUNCT
american_scientific_journal-1326	91	26	ε	ε	PROPN
american_scientific_journal-1326	91	27	0	0	NUM
american_scientific_journal-1326	91	28	0	0	NUM
american_scientific_journal-1326	91	29	1	1	NUM
american_scientific_journal-1326	91	30	0	0	NUM
american_scientific_journal-1326	91	31	,	,	PUNCT
american_scientific_journal-1326	91	32	r	r	NOUN
american_scientific_journal-1326	91	33	ν	ν	NOUN
american_scientific_journal-1326	91	34	ν′′	ν′′	NOUN
american_scientific_journal-1326	91	35	′+	′+	PUNCT
american_scientific_journal-1326	92	1	=	=	SYM
american_scientific_journal-1326	92	2	0	0	NUM
american_scientific_journal-1326	92	3	0	0	NUM
american_scientific_journal-1326	92	4	0	0	NUM
american_scientific_journal-1326	92	5	(	(	PUNCT
american_scientific_journal-1326	92	6	)	)	PUNCT
american_scientific_journal-1326	92	7	r	r	NOUN
american_scientific_journal-1326	92	8	vν	vν	NOUN
american_scientific_journal-1326	93	1	=	=	NOUN
american_scientific_journal-1326	93	2	,	,	PUNCT
american_scientific_journal-1326	93	3	0	0	NUM
american_scientific_journal-1326	93	4	0	0	NUM
american_scientific_journal-1326	93	5	(	(	PUNCT
american_scientific_journal-1326	93	6	)	)	PUNCT
american_scientific_journal-1326	93	7	r	r	NOUN
american_scientific_journal-1326	93	8	bν	bν	NOUN
american_scientific_journal-1326	93	9	′	′	NOUN
american_scientific_journal-1326	93	10	=	=	PUNCT
american_scientific_journal-1326	93	11	,	,	PUNCT
american_scientific_journal-1326	93	12	(	(	PUNCT
american_scientific_journal-1326	93	13	16	16	NUM
american_scientific_journal-1326	93	14	)	)	PUNCT
american_scientific_journal-1326	93	15	1)ε	1)ε	NUM
american_scientific_journal-1326	93	16	0	0	NUM
american_scientific_journal-1326	93	17	1	1	NUM
american_scientific_journal-1326	93	18	1	1	NUM
american_scientific_journal-1326	93	19	1	1	NUM
american_scientific_journal-1326	93	20	0,e	0,e	NOUN
american_scientific_journal-1326	94	1	r	r	NOUN
american_scientific_journal-1326	94	2	βνν	βνν	NOUN
american_scientific_journal-1326	94	3	ν	ν	X
american_scientific_journal-1326	94	4	−′′	−′′	NOUN
american_scientific_journal-1326	94	5	′+	′+	PUNCT
american_scientific_journal-1326	94	6	−	−	PROPN
american_scientific_journal-1326	95	1	=	=	SYM
american_scientific_journal-1326	95	2	1	1	NUM
american_scientific_journal-1326	95	3	0	0	NUM
american_scientific_journal-1326	95	4	(	(	PUNCT
american_scientific_journal-1326	95	5	)	)	PUNCT
american_scientific_journal-1326	95	6	0rν	0rν	NOUN
american_scientific_journal-1326	96	1	=	=	SYM
american_scientific_journal-1326	96	2	,	,	PUNCT
american_scientific_journal-1326	96	3	1	1	NUM
american_scientific_journal-1326	96	4	0	0	NUM
american_scientific_journal-1326	96	5	(	(	PUNCT
american_scientific_journal-1326	96	6	)	)	PUNCT
american_scientific_journal-1326	96	7	0rν	0rν	NOUN
american_scientific_journal-1326	96	8	′	′	NUM
american_scientific_journal-1326	97	1	=	=	PUNCT
american_scientific_journal-1326	97	2	.	.	PUNCT
american_scientific_journal-1326	98	1	(	(	PUNCT
american_scientific_journal-1326	98	2	17	17	NUM
american_scientific_journal-1326	98	3	)	)	PUNCT
american_scientific_journal-1326	98	4	to	to	PART
american_scientific_journal-1326	98	5	find	find	VERB
american_scientific_journal-1326	98	6	the	the	DET
american_scientific_journal-1326	98	7	solution	solution	NOUN
american_scientific_journal-1326	98	8	of	of	ADP
american_scientific_journal-1326	98	9	(	(	PUNCT
american_scientific_journal-1326	98	10	16	16	NUM
american_scientific_journal-1326	98	11	)	)	PUNCT
american_scientific_journal-1326	98	12	that	that	PRON
american_scientific_journal-1326	98	13	satisfies	satisfy	VERB
american_scientific_journal-1326	98	14	the	the	DET
american_scientific_journal-1326	98	15	initial	initial	ADJ
american_scientific_journal-1326	98	16	conditions	condition	NOUN
american_scientific_journal-1326	98	17	,	,	PUNCT
american_scientific_journal-1326	98	18	we	we	PRON
american_scientific_journal-1326	98	19	note	note	VERB
american_scientific_journal-1326	98	20	that	that	SCONJ
american_scientific_journal-1326	98	21	it	it	PRON
american_scientific_journal-1326	98	22	,	,	PUNCT
american_scientific_journal-1326	98	23	is	be	AUX
american_scientific_journal-1326	98	24	indeed	indeed	ADV
american_scientific_journal-1326	98	25	a	a	DET
american_scientific_journal-1326	98	26	cauchy	cauchy	PROPN
american_scientific_journal-1326	98	27	-	-	PUNCT
american_scientific_journal-1326	98	28	euler	euler	NOUN
american_scientific_journal-1326	98	29	equation	equation	NOUN
american_scientific_journal-1326	99	1	[	[	X
american_scientific_journal-1326	99	2	9	9	NUM
american_scientific_journal-1326	99	3	]	]	SYM
american_scientific_journal-1326	99	4	2	2	NUM
american_scientific_journal-1326	99	5	0	0	NUM
american_scientific_journal-1326	99	6	0	0	NUM
american_scientific_journal-1326	99	7	0,r	0,r	NUM
american_scientific_journal-1326	99	8	rν	rν	PROPN
american_scientific_journal-1326	99	9	ν′′	ν′′	NOUN
american_scientific_journal-1326	99	10	′+	′+	PUNCT
american_scientific_journal-1326	100	1	=	=	SYM
american_scientific_journal-1326	100	2	(	(	PUNCT
american_scientific_journal-1326	100	3	18	18	NUM
american_scientific_journal-1326	100	4	)	)	PUNCT
american_scientific_journal-1326	100	5	therefore	therefore	ADV
american_scientific_journal-1326	100	6	0	0	NUM
american_scientific_journal-1326	100	7	0	0	NUM
american_scientific_journal-1326	100	8	0	0	NUM
american_scientific_journal-1326	100	9	0	0	NUM
american_scientific_journal-1326	100	10	(	(	PUNCT
american_scientific_journal-1326	100	11	)	)	PUNCT
american_scientific_journal-1326	100	12	ln	ln	PROPN
american_scientific_journal-1326	100	13	rr	rr	VERB
american_scientific_journal-1326	100	14	v	v	ADP
american_scientific_journal-1326	100	15	r	r	NOUN
american_scientific_journal-1326	100	16	b	b	NOUN
american_scientific_journal-1326	100	17	r	r	NOUN
american_scientific_journal-1326	100	18	ν	ν	X
american_scientific_journal-1326	100	19			NOUN
american_scientific_journal-1326	100	20			PUNCT
american_scientific_journal-1326	101	1	=	=	PUNCT
american_scientific_journal-1326	102	1	+	+	NUM
american_scientific_journal-1326	102	2			NOUN
american_scientific_journal-1326	102	3			VERB
american_scientific_journal-1326	102	4			PRON
american_scientific_journal-1326	102	5			NOUN
american_scientific_journal-1326	102	6	,	,	PUNCT
american_scientific_journal-1326	102	7	(	(	PUNCT
american_scientific_journal-1326	102	8	19	19	NUM
american_scientific_journal-1326	102	9	)	)	PUNCT
american_scientific_journal-1326	102	10	american	american	ADJ
american_scientific_journal-1326	102	11	scientific	scientific	ADJ
american_scientific_journal-1326	102	12	research	research	NOUN
american_scientific_journal-1326	102	13	journal	journal	NOUN
american_scientific_journal-1326	102	14	for	for	ADP
american_scientific_journal-1326	102	15	engineering	engineering	NOUN
american_scientific_journal-1326	102	16	,	,	PUNCT
american_scientific_journal-1326	102	17	technology	technology	NOUN
american_scientific_journal-1326	102	18	,	,	PUNCT
american_scientific_journal-1326	102	19	and	and	CCONJ
american_scientific_journal-1326	102	20	sciences	science	NOUN
american_scientific_journal-1326	102	21	(	(	PUNCT
american_scientific_journal-1326	102	22	asrjets	asrjet	NOUN
american_scientific_journal-1326	102	23	)	)	PUNCT
american_scientific_journal-1326	102	24	(	(	PUNCT
american_scientific_journal-1326	102	25	2017	2017	NUM
american_scientific_journal-1326	102	26	)	)	PUNCT
american_scientific_journal-1326	102	27	volume	volume	NOUN
american_scientific_journal-1326	102	28	27	27	NUM
american_scientific_journal-1326	102	29	,	,	PUNCT
american_scientific_journal-1326	102	30	no	no	DET
american_scientific_journal-1326	102	31	1	1	NUM
american_scientific_journal-1326	102	32	,	,	PUNCT
american_scientific_journal-1326	102	33	pp	pp	ADV
american_scientific_journal-1326	102	34	139	139	NUM
american_scientific_journal-1326	102	35	-	-	SYM
american_scientific_journal-1326	102	36	150	150	NUM
american_scientific_journal-1326	102	37	145	145	NUM
american_scientific_journal-1326	102	38	substituting	substitute	VERB
american_scientific_journal-1326	102	39	(	(	PUNCT
american_scientific_journal-1326	102	40	19	19	NUM
american_scientific_journal-1326	102	41	)	)	PUNCT
american_scientific_journal-1326	102	42	into	into	ADP
american_scientific_journal-1326	102	43	(	(	PUNCT
american_scientific_journal-1326	102	44	17	17	NUM
american_scientific_journal-1326	102	45	)	)	PUNCT
american_scientific_journal-1326	102	46	is	be	AUX
american_scientific_journal-1326	102	47	obtained	obtain	VERB
american_scientific_journal-1326	102	48	0	0	NUM
american_scientific_journal-1326	102	49	0	0	NUM
american_scientific_journal-1326	102	50	1	1	NUM
american_scientific_journal-1326	102	51	1	1	NUM
american_scientific_journal-1326	102	52	0	0	NUM
american_scientific_journal-1326	102	53	1	1	NUM
american_scientific_journal-1326	102	54	,	,	PUNCT
american_scientific_journal-1326	102	55	r	r	NOUN
american_scientific_journal-1326	102	56	b	b	PROPN
american_scientific_journal-1326	102	57	v	v	X
american_scientific_journal-1326	102	58	re	re	NOUN
american_scientific_journal-1326	102	59	r	r	NOUN
american_scientific_journal-1326	102	60	r	r	NOUN
american_scientific_journal-1326	102	61	β	β	X
american_scientific_journal-1326	102	62	βν	βν	ADP
american_scientific_journal-1326	102	63	ν	ν	X
american_scientific_journal-1326	102	64	−	−	PROPN
american_scientific_journal-1326	102	65	−	−	PROPN
american_scientific_journal-1326	102	66			NOUN
american_scientific_journal-1326	102	67			PUNCT
american_scientific_journal-1326	103	1	′′	′′	NOUN
american_scientific_journal-1326	103	2	′+	′+	PUNCT
american_scientific_journal-1326	103	3	=	=	NOUN
american_scientific_journal-1326	103	4			NOUN
american_scientific_journal-1326	103	5			VERB
american_scientific_journal-1326	103	6			PRON
american_scientific_journal-1326	103	7			PUNCT
american_scientific_journal-1326	104	1	1	1	NUM
american_scientific_journal-1326	104	2	0	0	NUM
american_scientific_journal-1326	104	3	(	(	PUNCT
american_scientific_journal-1326	104	4	)	)	PUNCT
american_scientific_journal-1326	104	5	0rν	0rν	NOUN
american_scientific_journal-1326	104	6	=	=	SYM
american_scientific_journal-1326	104	7	,	,	PUNCT
american_scientific_journal-1326	104	8	1	1	NUM
american_scientific_journal-1326	104	9	0	0	NUM
american_scientific_journal-1326	104	10	(	(	PUNCT
american_scientific_journal-1326	104	11	)	)	PUNCT
american_scientific_journal-1326	104	12	0rν	0rν	NOUN
american_scientific_journal-1326	104	13	′	′	NUM
american_scientific_journal-1326	105	1	=	=	PUNCT
american_scientific_journal-1326	105	2	.	.	PUNCT
american_scientific_journal-1326	106	1	(	(	PUNCT
american_scientific_journal-1326	106	2	20	20	NUM
american_scientific_journal-1326	106	3	)	)	PUNCT
american_scientific_journal-1326	106	4	to	to	PART
american_scientific_journal-1326	106	5	solve	solve	VERB
american_scientific_journal-1326	106	6	(	(	PUNCT
american_scientific_journal-1326	106	7	20	20	NUM
american_scientific_journal-1326	106	8	)	)	PUNCT
american_scientific_journal-1326	106	9	,	,	PUNCT
american_scientific_journal-1326	106	10	we	we	PRON
american_scientific_journal-1326	106	11	employ	employ	VERB
american_scientific_journal-1326	106	12	the	the	DET
american_scientific_journal-1326	106	13	variation	variation	NOUN
american_scientific_journal-1326	106	14	of	of	ADP
american_scientific_journal-1326	106	15	parameters	parameter	NOUN
american_scientific_journal-1326	106	16	method	method	VERB
american_scientific_journal-1326	106	17	[	[	X
american_scientific_journal-1326	106	18	9	9	NUM
american_scientific_journal-1326	106	19	]	]	PUNCT
american_scientific_journal-1326	106	20	which	which	PRON
american_scientific_journal-1326	106	21	requires	require	VERB
american_scientific_journal-1326	106	22	evaluating	evaluate	VERB
american_scientific_journal-1326	106	23	the	the	DET
american_scientific_journal-1326	106	24	following	follow	VERB
american_scientific_journal-1326	106	25	integrals	integral	NOUN
american_scientific_journal-1326	106	26	1	1	NUM
american_scientific_journal-1326	106	27	(	(	PUNCT
american_scientific_journal-1326	106	28	)	)	PUNCT
american_scientific_journal-1326	106	29	lnf	lnf	PROPN
american_scientific_journal-1326	106	30	r	r	NOUN
american_scientific_journal-1326	106	31	rdru	rdru	NOUN
american_scientific_journal-1326	106	32	w	w	NOUN
american_scientific_journal-1326	106	33	=	=	PUNCT
american_scientific_journal-1326	106	34	−∫	−∫	NOUN
american_scientific_journal-1326	106	35	,	,	PUNCT
american_scientific_journal-1326	106	36	2	2	NUM
american_scientific_journal-1326	106	37	(	(	PUNCT
american_scientific_journal-1326	106	38	)	)	PUNCT
american_scientific_journal-1326	106	39	f	f	PROPN
american_scientific_journal-1326	106	40	r	r	NOUN
american_scientific_journal-1326	106	41	dru	dru	PROPN
american_scientific_journal-1326	106	42	w	w	PROPN
american_scientific_journal-1326	106	43	=	=	SYM
american_scientific_journal-1326	106	44	∫	∫	PROPN
american_scientific_journal-1326	106	45	,	,	PUNCT
american_scientific_journal-1326	106	46	(	(	PUNCT
american_scientific_journal-1326	106	47	21	21	NUM
american_scientific_journal-1326	106	48	)	)	PUNCT
american_scientific_journal-1326	106	49	where	where	SCONJ
american_scientific_journal-1326	106	50	1	1	NUM
american_scientific_journal-1326	106	51	1y	1y	NOUN
american_scientific_journal-1326	106	52	=	=	SYM
american_scientific_journal-1326	106	53	and	and	CCONJ
american_scientific_journal-1326	106	54	2	2	NUM
american_scientific_journal-1326	106	55	lny	lny	PROPN
american_scientific_journal-1326	106	56	r=	r=	PROPN
american_scientific_journal-1326	106	57	are	be	AUX
american_scientific_journal-1326	106	58	the	the	DET
american_scientific_journal-1326	106	59	solutions	solution	NOUN
american_scientific_journal-1326	106	60	of	of	ADP
american_scientific_journal-1326	106	61	the	the	DET
american_scientific_journal-1326	106	62	homogeneous	homogeneous	ADJ
american_scientific_journal-1326	106	63	differential	differential	ADJ
american_scientific_journal-1326	106	64	equation	equation	NOUN
american_scientific_journal-1326	106	65	1	1	NUM
american_scientific_journal-1326	106	66	1	1	NUM
american_scientific_journal-1326	106	67	1	1	NUM
american_scientific_journal-1326	106	68	0	0	NUM
american_scientific_journal-1326	106	69	,	,	PUNCT
american_scientific_journal-1326	106	70	r	r	NOUN
american_scientific_journal-1326	106	71	ν	ν	NOUN
american_scientific_journal-1326	106	72	ν′′	ν′′	NOUN
american_scientific_journal-1326	106	73	′+	′+	PUNCT
american_scientific_journal-1326	107	1	=	=	SYM
american_scientific_journal-1326	107	2	(	(	PUNCT
american_scientific_journal-1326	107	3	22	22	NUM
american_scientific_journal-1326	107	4	)	)	PUNCT
american_scientific_journal-1326	107	5	w	w	NOUN
american_scientific_journal-1326	107	6	is	be	AUX
american_scientific_journal-1326	107	7	the	the	DET
american_scientific_journal-1326	107	8	wronskian	wronskian	NOUN
american_scientific_journal-1326	107	9	of	of	ADP
american_scientific_journal-1326	107	10	these	these	DET
american_scientific_journal-1326	107	11	two	two	NUM
american_scientific_journal-1326	107	12	functions	function	NOUN
american_scientific_journal-1326	107	13	,	,	PUNCT
american_scientific_journal-1326	107	14	which	which	PRON
american_scientific_journal-1326	107	15	is	be	AUX
american_scientific_journal-1326	107	16	given	give	VERB
american_scientific_journal-1326	107	17	by	by	ADP
american_scientific_journal-1326	107	18	1	1	NUM
american_scientific_journal-1326	107	19	2	2	NUM
american_scientific_journal-1326	107	20	(	(	PUNCT
american_scientific_journal-1326	107	21	,	,	PUNCT
american_scientific_journal-1326	107	22	)	)	PUNCT
american_scientific_journal-1326	107	23	1w	1w	VERB
american_scientific_journal-1326	107	24	y	y	PROPN
american_scientific_journal-1326	107	25	y	y	PROPN
american_scientific_journal-1326	107	26	r=	r=	ADJ
american_scientific_journal-1326	107	27	,	,	PUNCT
american_scientific_journal-1326	107	28	(	(	PUNCT
american_scientific_journal-1326	107	29	23	23	NUM
american_scientific_journal-1326	107	30	)	)	PUNCT
american_scientific_journal-1326	107	31	and	and	CCONJ
american_scientific_journal-1326	107	32	(	(	PUNCT
american_scientific_journal-1326	107	33	)	)	PUNCT
american_scientific_journal-1326	107	34	f	f	NOUN
american_scientific_journal-1326	107	35	r	r	NOUN
american_scientific_journal-1326	107	36	is	be	AUX
american_scientific_journal-1326	107	37	the	the	DET
american_scientific_journal-1326	107	38	right	right	ADJ
american_scientific_journal-1326	107	39	hand	hand	NOUN
american_scientific_journal-1326	107	40	side	side	NOUN
american_scientific_journal-1326	107	41	of	of	ADP
american_scientific_journal-1326	107	42	(	(	PUNCT
american_scientific_journal-1326	107	43	20	20	NUM
american_scientific_journal-1326	107	44	)	)	PUNCT
american_scientific_journal-1326	107	45	.	.	PUNCT
american_scientific_journal-1326	108	1	by	by	ADP
american_scientific_journal-1326	108	2	substituting	substitute	VERB
american_scientific_journal-1326	108	3	(	(	PUNCT
american_scientific_journal-1326	108	4	)	)	PUNCT
american_scientific_journal-1326	108	5	f	f	NOUN
american_scientific_journal-1326	108	6	r	r	NOUN
american_scientific_journal-1326	108	7	and	and	CCONJ
american_scientific_journal-1326	108	8	(	(	PUNCT
american_scientific_journal-1326	108	9	23	23	NUM
american_scientific_journal-1326	108	10	)	)	PUNCT
american_scientific_journal-1326	108	11	into	into	ADP
american_scientific_journal-1326	108	12	(	(	PUNCT
american_scientific_journal-1326	108	13	21	21	NUM
american_scientific_journal-1326	108	14	)	)	PUNCT
american_scientific_journal-1326	108	15	leads	lead	VERB
american_scientific_journal-1326	108	16	to	to	ADP
american_scientific_journal-1326	108	17	(	(	PUNCT
american_scientific_journal-1326	108	18	)	)	PUNCT
american_scientific_journal-1326	108	19	0	0	NUM
american_scientific_journal-1326	108	20	0	0	NUM
american_scientific_journal-1326	108	21	0	0	NUM
american_scientific_journal-1326	108	22	0	0	NUM
american_scientific_journal-1326	108	23	1	1	NUM
american_scientific_journal-1326	108	24	22	22	NUM
american_scientific_journal-1326	108	25	0	0	NUM
american_scientific_journal-1326	108	26	0	0	NUM
american_scientific_journal-1326	109	1	ln	ln	ADJ
american_scientific_journal-1326	109	2	1	1	NUM
american_scientific_journal-1326	109	3	,	,	PUNCT
american_scientific_journal-1326	109	4	2	2	NUM
american_scientific_journal-1326	109	5	2	2	NUM
american_scientific_journal-1326	109	6	r	r	NOUN
american_scientific_journal-1326	109	7	c	c	NOUN
american_scientific_journal-1326	109	8	v	v	NOUN
american_scientific_journal-1326	109	9	r	r	NOUN
american_scientific_journal-1326	109	10	c	c	NOUN
american_scientific_journal-1326	109	11	r	r	NOUN
american_scientific_journal-1326	109	12	ru	ru	NOUN
american_scientific_journal-1326	109	13	e	e	NOUN
american_scientific_journal-1326	109	14	r	r	NOUN
american_scientific_journal-1326	109	15	r	r	NOUN
american_scientific_journal-1326	109	16	b	b	NOUN
american_scientific_journal-1326	109	17	r	r	NOUN
american_scientific_journal-1326	109	18	b	b	PROPN
american_scientific_journal-1326	109	19	β	β	X
american_scientific_journal-1326	109	20	β	β	X
american_scientific_journal-1326	109	21	β	β	X
american_scientific_journal-1326	109	22	β	β	X
american_scientific_journal-1326	109	23	β	β	X
american_scientific_journal-1326	109	24	−	−	NOUN
american_scientific_journal-1326	109	25	−	−	PROPN
american_scientific_journal-1326	109	26			VERB
american_scientific_journal-1326	109	27	−	−	X
american_scientific_journal-1326	109	28	=	=	SYM
american_scientific_journal-1326	110	1	+	+	PROPN
american_scientific_journal-1326	110	2			ADJ
american_scientific_journal-1326	110	3			PROPN
american_scientific_journal-1326	110	4	−	−	NOUN
american_scientific_journal-1326	110	5	−	−	NUM
american_scientific_journal-1326	110	6			ADJ
american_scientific_journal-1326	110	7			NOUN
american_scientific_journal-1326	110	8	(	(	PUNCT
american_scientific_journal-1326	110	9	24	24	NUM
american_scientific_journal-1326	110	10	)	)	PUNCT
american_scientific_journal-1326	110	11	00	00	NUM
american_scientific_journal-1326	110	12	0	0	NUM
american_scientific_journal-1326	110	13	0	0	NUM
american_scientific_journal-1326	110	14	2	2	NUM
american_scientific_journal-1326	110	15	2	2	NUM
american_scientific_journal-1326	110	16	0	0	NUM
american_scientific_journal-1326	110	17	,	,	PUNCT
american_scientific_journal-1326	110	18	2	2	NUM
american_scientific_journal-1326	110	19	r	r	NOUN
american_scientific_journal-1326	110	20	cv	cv	NOUN
american_scientific_journal-1326	110	21	r	r	NOUN
american_scientific_journal-1326	110	22	c	c	PROPN
american_scientific_journal-1326	110	23	reu	reu	NOUN
american_scientific_journal-1326	110	24	r	r	NOUN
american_scientific_journal-1326	110	25	b	b	PROPN
american_scientific_journal-1326	110	26	r	r	NOUN
american_scientific_journal-1326	110	27	ββ	ββ	NOUN
american_scientific_journal-1326	110	28	ββ	ββ	INTJ
american_scientific_journal-1326	110	29	−	−	PROPN
american_scientific_journal-1326	110	30	−=	−=	NOUN
american_scientific_journal-1326	110	31	−	−	PROPN
american_scientific_journal-1326	110	32	(	(	PUNCT
american_scientific_journal-1326	110	33	25	25	NUM
american_scientific_journal-1326	110	34	)	)	PUNCT
american_scientific_journal-1326	110	35	where	where	SCONJ
american_scientific_journal-1326	110	36	the	the	DET
american_scientific_journal-1326	110	37	above	above	ADJ
american_scientific_journal-1326	110	38	integration	integration	NOUN
american_scientific_journal-1326	110	39	process	process	NOUN
american_scientific_journal-1326	110	40	,	,	PUNCT
american_scientific_journal-1326	110	41	requires	require	VERB
american_scientific_journal-1326	110	42	that	that	SCONJ
american_scientific_journal-1326	110	43	0	0	NUM
american_scientific_journal-1326	110	44	1r	1r	NUM
american_scientific_journal-1326	110	45	bβ−	bβ−	NUM
american_scientific_journal-1326	110	46	≠	≠	PROPN
american_scientific_journal-1326	110	47	−	−	PROPN
american_scientific_journal-1326	110	48	.	.	PUNCT
american_scientific_journal-1326	111	1	therefore	therefore	ADV
american_scientific_journal-1326	111	2	,	,	PUNCT
american_scientific_journal-1326	111	3	the	the	DET
american_scientific_journal-1326	111	4	solution	solution	NOUN
american_scientific_journal-1326	111	5	of	of	ADP
american_scientific_journal-1326	111	6	(	(	PUNCT
american_scientific_journal-1326	111	7	20	20	NUM
american_scientific_journal-1326	111	8	)	)	PUNCT
american_scientific_journal-1326	111	9	is	be	AUX
american_scientific_journal-1326	111	10	written	write	VERB
american_scientific_journal-1326	111	11	according	accord	VERB
american_scientific_journal-1326	111	12	to	to	ADP
american_scientific_journal-1326	111	13	method	method	NOUN
american_scientific_journal-1326	111	14	of	of	ADP
american_scientific_journal-1326	111	15	variation	variation	NOUN
american_scientific_journal-1326	111	16	of	of	ADP
american_scientific_journal-1326	111	17	parameters	parameter	NOUN
american_scientific_journal-1326	111	18	as	as	ADP
american_scientific_journal-1326	111	19	(	(	PUNCT
american_scientific_journal-1326	111	20	)	)	PUNCT
american_scientific_journal-1326	111	21	0	0	NUM
american_scientific_journal-1326	111	22	0	0	NUM
american_scientific_journal-1326	111	23	02	02	NUM
american_scientific_journal-1326	111	24	0	0	NUM
american_scientific_journal-1326	111	25	1	1	NUM
american_scientific_journal-1326	111	26	2	2	NUM
american_scientific_journal-1326	111	27	0	0	NUM
american_scientific_journal-1326	111	28	(	(	PUNCT
american_scientific_journal-1326	111	29	)	)	PUNCT
american_scientific_journal-1326	111	30	ln	ln	NOUN
american_scientific_journal-1326	111	31	2	2	NUM
american_scientific_journal-1326	111	32	r	r	NOUN
american_scientific_journal-1326	111	33	b	b	NOUN
american_scientific_journal-1326	111	34	v	v	NOUN
american_scientific_journal-1326	111	35	r	r	NOUN
american_scientific_journal-1326	111	36	br	br	NOUN
american_scientific_journal-1326	111	37	e	e	NOUN
american_scientific_journal-1326	111	38	rr	rr	VERB
american_scientific_journal-1326	111	39	a	a	DET
american_scientific_journal-1326	111	40	b	b	NOUN
american_scientific_journal-1326	111	41	r	r	NOUN
american_scientific_journal-1326	111	42	r	r	NOUN
american_scientific_journal-1326	111	43	b	b	PROPN
american_scientific_journal-1326	111	44	β	β	X
american_scientific_journal-1326	111	45	β	β	X
american_scientific_journal-1326	111	46	β	β	X
american_scientific_journal-1326	111	47	ν	ν	X
american_scientific_journal-1326	111	48	β	β	X
american_scientific_journal-1326	111	49	−	−	NOUN
american_scientific_journal-1326	111	50	−	−	PROPN
american_scientific_journal-1326	112	1	=	=	PUNCT
american_scientific_journal-1326	113	1	+	+	PROPN
american_scientific_journal-1326	113	2	+	+	CCONJ
american_scientific_journal-1326	113	3	−	−	NOUN
american_scientific_journal-1326	113	4	,	,	PUNCT
american_scientific_journal-1326	113	5	(	(	PUNCT
american_scientific_journal-1326	113	6	26	26	NUM
american_scientific_journal-1326	113	7	)	)	PUNCT
american_scientific_journal-1326	113	8	to	to	PART
american_scientific_journal-1326	113	9	determine	determine	VERB
american_scientific_journal-1326	113	10	the	the	DET
american_scientific_journal-1326	113	11	values	value	NOUN
american_scientific_journal-1326	113	12	of	of	ADP
american_scientific_journal-1326	113	13	a	a	PRON
american_scientific_journal-1326	113	14	and	and	CCONJ
american_scientific_journal-1326	113	15	b	b	NOUN
american_scientific_journal-1326	113	16	,	,	PUNCT
american_scientific_journal-1326	113	17	we	we	PRON
american_scientific_journal-1326	113	18	apply	apply	VERB
american_scientific_journal-1326	113	19	the	the	DET
american_scientific_journal-1326	113	20	boundary	boundary	ADJ
american_scientific_journal-1326	113	21	conditions	condition	NOUN
american_scientific_journal-1326	113	22	1	1	NUM
american_scientific_journal-1326	113	23	0	0	NUM
american_scientific_journal-1326	113	24	(	(	PUNCT
american_scientific_journal-1326	113	25	)	)	PUNCT
american_scientific_journal-1326	113	26	0rν	0rν	NOUN
american_scientific_journal-1326	113	27	=	=	PUNCT
american_scientific_journal-1326	113	28	and	and	CCONJ
american_scientific_journal-1326	113	29	1	1	NUM
american_scientific_journal-1326	113	30	0	0	NUM
american_scientific_journal-1326	113	31	(	(	PUNCT
american_scientific_journal-1326	113	32	)	)	PUNCT
american_scientific_journal-1326	113	33	0rν	0rν	NOUN
american_scientific_journal-1326	114	1	′	′	NUM
american_scientific_journal-1326	115	1	=	=	PUNCT
american_scientific_journal-1326	115	2	to	to	PART
american_scientific_journal-1326	115	3	(	(	PUNCT
american_scientific_journal-1326	115	4	26	26	NUM
american_scientific_journal-1326	115	5	)	)	PUNCT
american_scientific_journal-1326	115	6	to	to	ADP
american_scientific_journal-1326	115	7	american	american	ADJ
american_scientific_journal-1326	115	8	scientific	scientific	ADJ
american_scientific_journal-1326	115	9	research	research	NOUN
american_scientific_journal-1326	115	10	journal	journal	NOUN
american_scientific_journal-1326	115	11	for	for	ADP
american_scientific_journal-1326	115	12	engineering	engineering	NOUN
american_scientific_journal-1326	115	13	,	,	PUNCT
american_scientific_journal-1326	115	14	technology	technology	NOUN
american_scientific_journal-1326	115	15	,	,	PUNCT
american_scientific_journal-1326	115	16	and	and	CCONJ
american_scientific_journal-1326	115	17	sciences	science	NOUN
american_scientific_journal-1326	115	18	(	(	PUNCT
american_scientific_journal-1326	115	19	asrjets	asrjet	NOUN
american_scientific_journal-1326	115	20	)	)	PUNCT
american_scientific_journal-1326	115	21	(	(	PUNCT
american_scientific_journal-1326	115	22	2017	2017	NUM
american_scientific_journal-1326	115	23	)	)	PUNCT
american_scientific_journal-1326	115	24	volume	volume	NOUN
american_scientific_journal-1326	115	25	27	27	NUM
american_scientific_journal-1326	115	26	,	,	PUNCT
american_scientific_journal-1326	115	27	no	no	DET
american_scientific_journal-1326	115	28	1	1	NUM
american_scientific_journal-1326	115	29	,	,	PUNCT
american_scientific_journal-1326	115	30	pp	pp	ADV
american_scientific_journal-1326	115	31	139	139	NUM
american_scientific_journal-1326	115	32	-	-	SYM
american_scientific_journal-1326	115	33	150	150	NUM
american_scientific_journal-1326	115	34	146	146	NUM
american_scientific_journal-1326	115	35	get	get	NOUN
american_scientific_journal-1326	115	36	(	(	PUNCT
american_scientific_journal-1326	115	37	)	)	PUNCT
american_scientific_journal-1326	115	38	02	02	NUM
american_scientific_journal-1326	115	39	0	0	NUM
american_scientific_journal-1326	115	40	0	0	NUM
american_scientific_journal-1326	115	41	2	2	NUM
american_scientific_journal-1326	115	42	0	0	NUM
american_scientific_journal-1326	115	43	0	0	NUM
american_scientific_journal-1326	115	44	ln	ln	ADJ
american_scientific_journal-1326	115	45	1	1	NUM
american_scientific_journal-1326	115	46	,	,	PUNCT
american_scientific_journal-1326	115	47	2	2	NUM
american_scientific_journal-1326	115	48	2	2	NUM
american_scientific_journal-1326	115	49	v	v	NOUN
american_scientific_journal-1326	115	50	ra	ra	NOUN
american_scientific_journal-1326	115	51	r	r	NOUN
american_scientific_journal-1326	115	52	e	e	NOUN
american_scientific_journal-1326	115	53	r	r	NOUN
american_scientific_journal-1326	115	54	b	b	PROPN
american_scientific_journal-1326	115	55	r	r	NOUN
american_scientific_journal-1326	115	56	b	b	PROPN
american_scientific_journal-1326	115	57	β	β	X
american_scientific_journal-1326	115	58	β	β	X
american_scientific_journal-1326	115	59	β	β	X
american_scientific_journal-1326	115	60	−	−	NOUN
american_scientific_journal-1326	115	61			VERB
american_scientific_journal-1326	115	62			NUM
american_scientific_journal-1326	115	63	=	=	SYM
american_scientific_journal-1326	115	64	−	−	NUM
american_scientific_journal-1326	115	65			PROPN
american_scientific_journal-1326	115	66	−	−	NOUN
american_scientific_journal-1326	115	67	−	−	NUM
american_scientific_journal-1326	115	68			ADJ
american_scientific_journal-1326	115	69			NOUN
american_scientific_journal-1326	115	70	(	(	PUNCT
american_scientific_journal-1326	115	71	27	27	NUM
american_scientific_journal-1326	115	72	)	)	PUNCT
american_scientific_journal-1326	115	73	0	0	NUM
american_scientific_journal-1326	115	74	2	2	NUM
american_scientific_journal-1326	115	75	0	0	NUM
american_scientific_journal-1326	115	76	0	0	NUM
american_scientific_journal-1326	115	77	,	,	PUNCT
american_scientific_journal-1326	115	78	2	2	NUM
american_scientific_journal-1326	115	79	ve	ve	NOUN
american_scientific_journal-1326	115	80	rb	rb	NOUN
american_scientific_journal-1326	115	81	r	r	NOUN
american_scientific_journal-1326	115	82	b	b	PROPN
american_scientific_journal-1326	115	83	β	β	X
american_scientific_journal-1326	115	84	β	β	X
american_scientific_journal-1326	115	85	−−	−−	NOUN
american_scientific_journal-1326	115	86	=	=	SYM
american_scientific_journal-1326	115	87	−	−	PROPN
american_scientific_journal-1326	115	88	(	(	PUNCT
american_scientific_journal-1326	115	89	28	28	NUM
american_scientific_journal-1326	115	90	)	)	PUNCT
american_scientific_journal-1326	115	91	thus	thus	ADV
american_scientific_journal-1326	115	92	,	,	PUNCT
american_scientific_journal-1326	115	93	by	by	ADP
american_scientific_journal-1326	115	94	substituting	substitute	VERB
american_scientific_journal-1326	115	95	(	(	PUNCT
american_scientific_journal-1326	115	96	19	19	NUM
american_scientific_journal-1326	115	97	)	)	PUNCT
american_scientific_journal-1326	115	98	and	and	CCONJ
american_scientific_journal-1326	115	99	(	(	PUNCT
american_scientific_journal-1326	115	100	26	26	NUM
american_scientific_journal-1326	115	101	)	)	PUNCT
american_scientific_journal-1326	115	102	into	into	ADP
american_scientific_journal-1326	115	103	(	(	PUNCT
american_scientific_journal-1326	115	104	15	15	NUM
american_scientific_journal-1326	115	105	)	)	PUNCT
american_scientific_journal-1326	115	106	we	we	PRON
american_scientific_journal-1326	115	107	obtain	obtain	VERB
american_scientific_journal-1326	115	108	a	a	DET
american_scientific_journal-1326	115	109	first	first	ADJ
american_scientific_journal-1326	115	110	order	order	NOUN
american_scientific_journal-1326	115	111	approximation	approximation	NOUN
american_scientific_journal-1326	115	112	for	for	ADP
american_scientific_journal-1326	115	113	the	the	DET
american_scientific_journal-1326	115	114	solution	solution	NOUN
american_scientific_journal-1326	115	115	of	of	ADP
american_scientific_journal-1326	115	116	(	(	PUNCT
american_scientific_journal-1326	115	117	13	13	NUM
american_scientific_journal-1326	115	118	)	)	PUNCT
american_scientific_journal-1326	115	119	,	,	PUNCT
american_scientific_journal-1326	115	120	as	as	SCONJ
american_scientific_journal-1326	115	121	it	it	PRON
american_scientific_journal-1326	115	122	is	be	AUX
american_scientific_journal-1326	115	123	shown	show	VERB
american_scientific_journal-1326	115	124	(	(	PUNCT
american_scientific_journal-1326	115	125	)	)	PUNCT
american_scientific_journal-1326	115	126	(	(	PUNCT
american_scientific_journal-1326	115	127	)	)	PUNCT
american_scientific_journal-1326	115	128	0	0	NUM
american_scientific_journal-1326	115	129	0	0	NUM
american_scientific_journal-1326	115	130	0	0	NUM
american_scientific_journal-1326	115	131	0	0	NUM
american_scientific_journal-1326	115	132	0	0	NUM
american_scientific_journal-1326	115	133	2	2	NUM
american_scientific_journal-1326	115	134	2	2	NUM
american_scientific_journal-1326	115	135	20	20	NUM
american_scientific_journal-1326	115	136	0	0	NUM
american_scientific_journal-1326	115	137	0	0	NUM
american_scientific_journal-1326	115	138	0	0	NUM
american_scientific_journal-1326	115	139	02	02	NUM
american_scientific_journal-1326	115	140	0	0	NUM
american_scientific_journal-1326	115	141	0	0	NUM
american_scientific_journal-1326	115	142	0	0	NUM
american_scientific_journal-1326	116	1	(	(	PUNCT
american_scientific_journal-1326	116	2	)	)	PUNCT
american_scientific_journal-1326	116	3	ln	ln	NOUN
american_scientific_journal-1326	116	4	2	2	NUM
american_scientific_journal-1326	116	5	2	2	NUM
american_scientific_journal-1326	116	6	v	v	NOUN
american_scientific_journal-1326	116	7	r	r	NOUN
american_scientific_journal-1326	116	8	b	b	NOUN
american_scientific_journal-1326	116	9	v	v	NOUN
american_scientific_journal-1326	116	10	r	r	NOUN
american_scientific_journal-1326	116	11	b	b	NOUN
american_scientific_journal-1326	116	12	r	r	NOUN
american_scientific_journal-1326	116	13	br	br	NOUN
american_scientific_journal-1326	116	14	e	e	NOUN
american_scientific_journal-1326	116	15	r	r	NOUN
american_scientific_journal-1326	116	16	erv	erv	NOUN
american_scientific_journal-1326	116	17	r	r	NOUN
american_scientific_journal-1326	116	18	v	v	NOUN
american_scientific_journal-1326	116	19	br	br	NOUN
american_scientific_journal-1326	116	20	r	r	NOUN
american_scientific_journal-1326	116	21	r	r	NOUN
american_scientific_journal-1326	116	22	r	r	NOUN
american_scientific_journal-1326	116	23	b	b	NOUN
american_scientific_journal-1326	116	24	r	r	NOUN
american_scientific_journal-1326	116	25	r	r	NOUN
american_scientific_journal-1326	116	26	b	b	PROPN
american_scientific_journal-1326	116	27	β	β	X
american_scientific_journal-1326	116	28	β	β	X
american_scientific_journal-1326	116	29	β	β	X
american_scientific_journal-1326	116	30	β	β	X
american_scientific_journal-1326	116	31	βε	βε	X
american_scientific_journal-1326	116	32	ε	ε	PROPN
american_scientific_journal-1326	116	33	β	β	X
american_scientific_journal-1326	116	34	β	β	X
american_scientific_journal-1326	116	35	−	−	PROPN
american_scientific_journal-1326	117	1	−	−	NOUN
american_scientific_journal-1326	118	1	−	−	NOUN
american_scientific_journal-1326	118	2	−	−	NOUN
american_scientific_journal-1326	118	3			NUM
american_scientific_journal-1326	118	4			NOUN
american_scientific_journal-1326	118	5			PUNCT
american_scientific_journal-1326	119	1	=	=	PUNCT
american_scientific_journal-1326	120	1	+	+	CCONJ
american_scientific_journal-1326	120	2	−	−	NOUN
american_scientific_journal-1326	121	1	+	+	CCONJ
american_scientific_journal-1326	121	2	−	−	PROPN
american_scientific_journal-1326	121	3			VERB
american_scientific_journal-1326	121	4	−	−	ADJ
american_scientific_journal-1326	121	5	−	−	NOUN
american_scientific_journal-1326	121	6			PROPN
american_scientific_journal-1326	121	7			NOUN
american_scientific_journal-1326	121	8			PUNCT
american_scientific_journal-1326	121	9	.	.	PUNCT
american_scientific_journal-1326	122	1	(	(	PUNCT
american_scientific_journal-1326	122	2	29	29	NUM
american_scientific_journal-1326	122	3	)	)	PUNCT
american_scientific_journal-1326	122	4	it	it	PRON
american_scientific_journal-1326	122	5	's	be	AUX
american_scientific_journal-1326	122	6	important	important	ADJ
american_scientific_journal-1326	122	7	to	to	PART
american_scientific_journal-1326	122	8	note	note	VERB
american_scientific_journal-1326	122	9	that	that	SCONJ
american_scientific_journal-1326	122	10	(	(	PUNCT
american_scientific_journal-1326	122	11	29	29	NUM
american_scientific_journal-1326	122	12	)	)	PUNCT
american_scientific_journal-1326	122	13	coincides	coincide	VERB
american_scientific_journal-1326	122	14	with	with	ADP
american_scientific_journal-1326	122	15	the	the	DET
american_scientific_journal-1326	122	16	obtained	obtain	VERB
american_scientific_journal-1326	122	17	solution	solution	NOUN
american_scientific_journal-1326	122	18	from	from	ADP
american_scientific_journal-1326	122	19	[	[	X
american_scientific_journal-1326	122	20	1	1	NUM
american_scientific_journal-1326	122	21	]	]	PUNCT
american_scientific_journal-1326	122	22	,	,	PUNCT
american_scientific_journal-1326	122	23	by	by	ADP
american_scientific_journal-1326	122	24	resorting	resort	VERB
american_scientific_journal-1326	122	25	to	to	ADP
american_scientific_journal-1326	122	26	a	a	DET
american_scientific_journal-1326	122	27	more	more	ADV
american_scientific_journal-1326	122	28	straightforward	straightforward	ADJ
american_scientific_journal-1326	122	29	procedure	procedure	NOUN
american_scientific_journal-1326	122	30	.	.	PUNCT
american_scientific_journal-1326	123	1	in	in	ADP
american_scientific_journal-1326	123	2	order	order	NOUN
american_scientific_journal-1326	123	3	to	to	PART
american_scientific_journal-1326	123	4	show	show	VERB
american_scientific_journal-1326	123	5	that	that	SCONJ
american_scientific_journal-1326	123	6	(	(	PUNCT
american_scientific_journal-1326	123	7	29	29	NUM
american_scientific_journal-1326	123	8	)	)	PUNCT
american_scientific_journal-1326	123	9	gives	give	VERB
american_scientific_journal-1326	123	10	rise	rise	VERB
american_scientific_journal-1326	123	11	qualitatively	qualitatively	ADV
american_scientific_journal-1326	123	12	to	to	ADP
american_scientific_journal-1326	123	13	the	the	DET
american_scientific_journal-1326	123	14	observed	observe	VERB
american_scientific_journal-1326	123	15	galaxy	galaxy	NOUN
american_scientific_journal-1326	123	16	rotation	rotation	NOUN
american_scientific_journal-1326	123	17	curves	curve	NOUN
american_scientific_journal-1326	123	18	;	;	PUNCT
american_scientific_journal-1326	123	19	we	we	PRON
american_scientific_journal-1326	123	20	note	note	VERB
american_scientific_journal-1326	123	21	that	that	SCONJ
american_scientific_journal-1326	123	22	the	the	DET
american_scientific_journal-1326	123	23	speed	speed	NOUN
american_scientific_journal-1326	123	24	of	of	ADP
american_scientific_journal-1326	123	25	rotation	rotation	NOUN
american_scientific_journal-1326	123	26	of	of	ADP
american_scientific_journal-1326	123	27	a	a	DET
american_scientific_journal-1326	123	28	body	body	NOUN
american_scientific_journal-1326	123	29	of	of	ADP
american_scientific_journal-1326	123	30	mass	mass	NOUN
american_scientific_journal-1326	123	31	m	m	PROPN
american_scientific_journal-1326	123	32	in	in	ADP
american_scientific_journal-1326	123	33	a	a	DET
american_scientific_journal-1326	123	34	galaxy	galaxy	NOUN
american_scientific_journal-1326	123	35	at	at	ADP
american_scientific_journal-1326	123	36	a	a	DET
american_scientific_journal-1326	123	37	distance	distance	NOUN
american_scientific_journal-1326	123	38	r	r	NOUN
american_scientific_journal-1326	123	39	from	from	ADP
american_scientific_journal-1326	123	40	the	the	DET
american_scientific_journal-1326	123	41	galactic	galactic	ADJ
american_scientific_journal-1326	123	42	center	center	NOUN
american_scientific_journal-1326	123	43	,	,	PUNCT
american_scientific_journal-1326	123	44	must	must	AUX
american_scientific_journal-1326	123	45	be	be	AUX
american_scientific_journal-1326	123	46	related	relate	VERB
american_scientific_journal-1326	123	47	to	to	ADP
american_scientific_journal-1326	123	48	the	the	DET
american_scientific_journal-1326	123	49	gravitational	gravitational	ADJ
american_scientific_journal-1326	123	50	potential	potential	NOUN
american_scientific_journal-1326	123	51	acting	act	VERB
american_scientific_journal-1326	123	52	on	on	ADP
american_scientific_journal-1326	123	53	it	it	PRON
american_scientific_journal-1326	123	54	.	.	PUNCT
american_scientific_journal-1326	124	1	from	from	ADP
american_scientific_journal-1326	124	2	newtonian	newtonian	PROPN
american_scientific_journal-1326	124	3	theory	theory	NOUN
american_scientific_journal-1326	124	4	,	,	PUNCT
american_scientific_journal-1326	124	5	the	the	DET
american_scientific_journal-1326	124	6	gravitational	gravitational	ADJ
american_scientific_journal-1326	124	7	force	force	NOUN
american_scientific_journal-1326	124	8	gf	gf	PROPN
american_scientific_journal-1326	124	9	,	,	PUNCT
american_scientific_journal-1326	124	10	provides	provide	VERB
american_scientific_journal-1326	124	11	the	the	DET
american_scientific_journal-1326	124	12	centripetal	centripetal	ADJ
american_scientific_journal-1326	124	13	acceleration	acceleration	NOUN
american_scientific_journal-1326	124	14	2	2	NUM
american_scientific_journal-1326	124	15	/	/	SYM
american_scientific_journal-1326	124	16	gmv	gmv	VERB
american_scientific_journal-1326	124	17	r	r	NOUN
american_scientific_journal-1326	124	18	f=	f=	NOUN
american_scientific_journal-1326	124	19	,	,	PUNCT
american_scientific_journal-1326	124	20	or	or	CCONJ
american_scientific_journal-1326	124	21	2v	2v	PROPN
american_scientific_journal-1326	124	22	g	g	PROPN
american_scientific_journal-1326	124	23	r	r	NOUN
american_scientific_journal-1326	124	24	=	=	PUNCT
american_scientific_journal-1326	124	25	,	,	PUNCT
american_scientific_journal-1326	124	26	(	(	PUNCT
american_scientific_journal-1326	124	27	30	30	NUM
american_scientific_journal-1326	124	28	)	)	PUNCT
american_scientific_journal-1326	124	29	where	where	SCONJ
american_scientific_journal-1326	124	30	g	g	NOUN
american_scientific_journal-1326	124	31	,	,	PUNCT
american_scientific_journal-1326	124	32	is	be	AUX
american_scientific_journal-1326	124	33	the	the	DET
american_scientific_journal-1326	124	34	magnitude	magnitude	NOUN
american_scientific_journal-1326	124	35	of	of	ADP
american_scientific_journal-1326	124	36	the	the	DET
american_scientific_journal-1326	124	37	intensity	intensity	NOUN
american_scientific_journal-1326	124	38	of	of	ADP
american_scientific_journal-1326	124	39	gravitational	gravitational	ADJ
american_scientific_journal-1326	124	40	field	field	NOUN
american_scientific_journal-1326	125	1	[	[	X
american_scientific_journal-1326	125	2	2,3,7	2,3,7	NUM
american_scientific_journal-1326	125	3	]	]	X
american_scientific_journal-1326	125	4	.	.	PUNCT
american_scientific_journal-1326	126	1	likewise	likewise	ADV
american_scientific_journal-1326	126	2	g	g	NOUN
american_scientific_journal-1326	126	3	,	,	PUNCT
american_scientific_journal-1326	126	4	is	be	AUX
american_scientific_journal-1326	126	5	related	relate	VERB
american_scientific_journal-1326	126	6	to	to	ADP
american_scientific_journal-1326	126	7	the	the	DET
american_scientific_journal-1326	126	8	gravitational	gravitational	ADJ
american_scientific_journal-1326	126	9	potential	potential	NOUN
american_scientific_journal-1326	126	10	,	,	PUNCT
american_scientific_journal-1326	126	11	according	accord	VERB
american_scientific_journal-1326	126	12	to	to	ADP
american_scientific_journal-1326	126	13	/g	/g	PUNCT
american_scientific_journal-1326	126	14	dv	dv	PROPN
american_scientific_journal-1326	126	15	dr=	dr=	PROPN
american_scientific_journal-1326	126	16	,	,	PUNCT
american_scientific_journal-1326	126	17	so	so	SCONJ
american_scientific_journal-1326	126	18	that	that	SCONJ
american_scientific_journal-1326	127	1	(	(	PUNCT
american_scientific_journal-1326	127	2	)	)	PUNCT
american_scientific_journal-1326	127	3	dv	dv	PROPN
american_scientific_journal-1326	127	4	rv	rv	PROPN
american_scientific_journal-1326	127	5	r	r	PROPN
american_scientific_journal-1326	127	6	dr	dr	PROPN
american_scientific_journal-1326	127	7	=	=	PROPN
american_scientific_journal-1326	127	8	.	.	PUNCT
american_scientific_journal-1326	128	1	(	(	PUNCT
american_scientific_journal-1326	128	2	31	31	NUM
american_scientific_journal-1326	128	3	)	)	PUNCT
american_scientific_journal-1326	128	4	after	after	ADP
american_scientific_journal-1326	128	5	differentiating	differentiate	VERB
american_scientific_journal-1326	128	6	(	(	PUNCT
american_scientific_journal-1326	128	7	29	29	NUM
american_scientific_journal-1326	128	8	)	)	PUNCT
american_scientific_journal-1326	128	9	and	and	CCONJ
american_scientific_journal-1326	128	10	substituting	substitute	VERB
american_scientific_journal-1326	128	11	this	this	DET
american_scientific_journal-1326	128	12	result	result	NOUN
american_scientific_journal-1326	128	13	into	into	ADP
american_scientific_journal-1326	128	14	(	(	PUNCT
american_scientific_journal-1326	128	15	31	31	NUM
american_scientific_journal-1326	128	16	)	)	PUNCT
american_scientific_journal-1326	128	17	,	,	PUNCT
american_scientific_journal-1326	128	18	we	we	PRON
american_scientific_journal-1326	128	19	obtain	obtain	VERB
american_scientific_journal-1326	128	20	0	0	NUM
american_scientific_journal-1326	128	21	0	0	NUM
american_scientific_journal-1326	129	1	22	22	NUM
american_scientific_journal-1326	129	2	0	0	NUM
american_scientific_journal-1326	129	3	0	0	NUM
american_scientific_journal-1326	129	4	0	0	NUM
american_scientific_journal-1326	129	5	0	0	NUM
american_scientific_journal-1326	129	6	1	1	NUM
american_scientific_journal-1326	129	7	2	2	NUM
american_scientific_journal-1326	129	8	r	r	NOUN
american_scientific_journal-1326	129	9	bvr	bvr	NOUN
american_scientific_journal-1326	129	10	e	e	PROPN
american_scientific_journal-1326	129	11	rv	rv	PROPN
american_scientific_journal-1326	129	12	br	br	NOUN
american_scientific_journal-1326	130	1	r	r	NOUN
american_scientific_journal-1326	130	2	b	b	PROPN
american_scientific_journal-1326	130	3	r	r	NOUN
american_scientific_journal-1326	130	4	ββε	ββε	PUNCT
american_scientific_journal-1326	130	5	β	β	PROPN
american_scientific_journal-1326	130	6	−−	−−	PROPN
american_scientific_journal-1326	130	7			VERB
american_scientific_journal-1326	130	8			PRON
american_scientific_journal-1326	130	9			PUNCT
american_scientific_journal-1326	131	1			ADJ
american_scientific_journal-1326	131	2	=	=	NOUN
american_scientific_journal-1326	132	1	+	+	CCONJ
american_scientific_journal-1326	132	2	−	−	INTJ
american_scientific_journal-1326	133	1	−	−	NUM
american_scientific_journal-1326	133	2			ADJ
american_scientific_journal-1326	133	3			NUM
american_scientific_journal-1326	133	4			NOUN
american_scientific_journal-1326	133	5			PROPN
american_scientific_journal-1326	133	6	.	.	PUNCT
american_scientific_journal-1326	134	1	(	(	PUNCT
american_scientific_journal-1326	134	2	32	32	NUM
american_scientific_journal-1326	134	3	)	)	PUNCT
american_scientific_journal-1326	134	4	we	we	PRON
american_scientific_journal-1326	134	5	note	note	VERB
american_scientific_journal-1326	134	6	that	that	SCONJ
american_scientific_journal-1326	134	7	if	if	SCONJ
american_scientific_journal-1326	134	8	0	0	NUM
american_scientific_journal-1326	134	9	2r	2r	NUM
american_scientific_journal-1326	134	10	bβ	bβ	NOUN
american_scientific_journal-1326	134	11	>	>	X
american_scientific_journal-1326	134	12	,	,	PUNCT
american_scientific_journal-1326	134	13	the	the	DET
american_scientific_journal-1326	134	14	model	model	NOUN
american_scientific_journal-1326	134	15	predicts	predict	VERB
american_scientific_journal-1326	134	16	qualitatively	qualitatively	ADV
american_scientific_journal-1326	134	17	,	,	PUNCT
american_scientific_journal-1326	134	18	the	the	DET
american_scientific_journal-1326	134	19	possibility	possibility	NOUN
american_scientific_journal-1326	134	20	of	of	ADP
american_scientific_journal-1326	134	21	flat	flat	ADJ
american_scientific_journal-1326	134	22	rotation	rotation	NOUN
american_scientific_journal-1326	134	23	curves	curve	NOUN
american_scientific_journal-1326	134	24	,	,	PUNCT
american_scientific_journal-1326	134	25	since	since	SCONJ
american_scientific_journal-1326	134	26	in	in	ADP
american_scientific_journal-1326	134	27	this	this	DET
american_scientific_journal-1326	134	28	american	american	ADJ
american_scientific_journal-1326	134	29	scientific	scientific	ADJ
american_scientific_journal-1326	134	30	research	research	NOUN
american_scientific_journal-1326	134	31	journal	journal	NOUN
american_scientific_journal-1326	134	32	for	for	ADP
american_scientific_journal-1326	134	33	engineering	engineering	NOUN
american_scientific_journal-1326	134	34	,	,	PUNCT
american_scientific_journal-1326	134	35	technology	technology	NOUN
american_scientific_journal-1326	134	36	,	,	PUNCT
american_scientific_journal-1326	134	37	and	and	CCONJ
american_scientific_journal-1326	134	38	sciences	science	NOUN
american_scientific_journal-1326	134	39	(	(	PUNCT
american_scientific_journal-1326	134	40	asrjets	asrjet	NOUN
american_scientific_journal-1326	134	41	)	)	PUNCT
american_scientific_journal-1326	134	42	(	(	PUNCT
american_scientific_journal-1326	134	43	2017	2017	NUM
american_scientific_journal-1326	134	44	)	)	PUNCT
american_scientific_journal-1326	134	45	volume	volume	NOUN
american_scientific_journal-1326	134	46	27	27	NUM
american_scientific_journal-1326	134	47	,	,	PUNCT
american_scientific_journal-1326	134	48	no	no	DET
american_scientific_journal-1326	134	49	1	1	NUM
american_scientific_journal-1326	134	50	,	,	PUNCT
american_scientific_journal-1326	134	51	pp	pp	ADV
american_scientific_journal-1326	134	52	139	139	NUM
american_scientific_journal-1326	134	53	-	-	SYM
american_scientific_journal-1326	134	54	150	150	NUM
american_scientific_journal-1326	134	55	147	147	NUM
american_scientific_journal-1326	134	56	case	case	NOUN
american_scientific_journal-1326	134	57	(	(	PUNCT
american_scientific_journal-1326	134	58	)	)	PUNCT
american_scientific_journal-1326	134	59	02	02	NUM
american_scientific_journal-1326	135	1	0	0	NUM
american_scientific_journal-1326	135	2	0,r	0,r	NUM
american_scientific_journal-1326	135	3	br	br	NOUN
american_scientific_journal-1326	135	4	r	r	NOUN
american_scientific_journal-1326	135	5	β−	β−	NUM
american_scientific_journal-1326	135	6	→	→	PUNCT
american_scientific_journal-1326	135	7	if	if	SCONJ
american_scientific_journal-1326	135	8	r	r	NOUN
american_scientific_journal-1326	135	9	→∞	→∞	X
american_scientific_journal-1326	135	10	and	and	CCONJ
american_scientific_journal-1326	135	11	(	(	PUNCT
american_scientific_journal-1326	135	12	32	32	NUM
american_scientific_journal-1326	135	13	)	)	PUNCT
american_scientific_journal-1326	135	14	becomes	become	VERB
american_scientific_journal-1326	135	15	in	in	ADP
american_scientific_journal-1326	135	16	02	02	NUM
american_scientific_journal-1326	135	17	0	0	NUM
american_scientific_journal-1326	135	18	0	0	NUM
american_scientific_journal-1326	135	19	0	0	NUM
american_scientific_journal-1326	135	20	2	2	NUM
american_scientific_journal-1326	135	21	vr	vr	NOUN
american_scientific_journal-1326	135	22	ev	ev	INTJ
american_scientific_journal-1326	135	23	br	br	PROPN
american_scientific_journal-1326	135	24	r	r	PROPN
american_scientific_journal-1326	135	25	b	b	PROPN
american_scientific_journal-1326	135	26	βε	βε	PROPN
american_scientific_journal-1326	135	27	β	β	X
american_scientific_journal-1326	135	28	−	−	NOUN
american_scientific_journal-1326	136	1	→	→	SYM
american_scientific_journal-1326	136	2	+	+	CCONJ
american_scientific_journal-1326	136	3	−	−	PROPN
american_scientific_journal-1326	136	4	.	.	PUNCT
american_scientific_journal-1326	137	1	(	(	PUNCT
american_scientific_journal-1326	137	2	33	33	NUM
american_scientific_journal-1326	137	3	)	)	PUNCT
american_scientific_journal-1326	137	4	we	we	PRON
american_scientific_journal-1326	137	5	see	see	VERB
american_scientific_journal-1326	137	6	that	that	SCONJ
american_scientific_journal-1326	137	7	(	(	PUNCT
american_scientific_journal-1326	137	8	33	33	NUM
american_scientific_journal-1326	137	9	)	)	PUNCT
american_scientific_journal-1326	137	10	is	be	AUX
american_scientific_journal-1326	137	11	consistent	consistent	ADJ
american_scientific_journal-1326	137	12	with	with	ADP
american_scientific_journal-1326	137	13	the	the	DET
american_scientific_journal-1326	137	14	assumption	assumption	NOUN
american_scientific_journal-1326	137	15	0	0	NUM
american_scientific_journal-1326	138	1	1,r	1,r	NUM
american_scientific_journal-1326	138	2	bβ−	bβ−	PUNCT
american_scientific_journal-1326	138	3	≠	≠	PROPN
american_scientific_journal-1326	138	4	−	−	PROPN
american_scientific_journal-1326	138	5	since	since	SCONJ
american_scientific_journal-1326	138	6	we	we	PRON
american_scientific_journal-1326	138	7	have	have	AUX
american_scientific_journal-1326	138	8	assumed	assume	VERB
american_scientific_journal-1326	138	9	that	that	SCONJ
american_scientific_journal-1326	138	10	0	0	NUM
american_scientific_journal-1326	138	11	2r	2r	NUM
american_scientific_journal-1326	138	12	bβ	bβ	NOUN
american_scientific_journal-1326	138	13	>	>	X
american_scientific_journal-1326	138	14	(	(	PUNCT
american_scientific_journal-1326	138	15	see	see	VERB
american_scientific_journal-1326	138	16	below	below	ADP
american_scientific_journal-1326	138	17	equation	equation	NOUN
american_scientific_journal-1326	138	18	(	(	PUNCT
american_scientific_journal-1326	138	19	25	25	NUM
american_scientific_journal-1326	138	20	)	)	PUNCT
american_scientific_journal-1326	138	21	)	)	PUNCT
american_scientific_journal-1326	138	22	.	.	PUNCT
american_scientific_journal-1326	139	1	besides	besides	SCONJ
american_scientific_journal-1326	139	2	such	such	ADJ
american_scientific_journal-1326	139	3	as	as	SCONJ
american_scientific_journal-1326	139	4	we	we	PRON
american_scientific_journal-1326	139	5	mentioned	mention	VERB
american_scientific_journal-1326	139	6	,	,	PUNCT
american_scientific_journal-1326	139	7	we	we	PRON
american_scientific_journal-1326	139	8	observe	observe	VERB
american_scientific_journal-1326	139	9	that	that	SCONJ
american_scientific_journal-1326	139	10	b	b	NOUN
american_scientific_journal-1326	139	11	can	can	AUX
american_scientific_journal-1326	139	12	takes	take	VERB
american_scientific_journal-1326	139	13	a	a	DET
american_scientific_journal-1326	139	14	wide	wide	ADJ
american_scientific_journal-1326	139	15	range	range	NOUN
american_scientific_journal-1326	139	16	of	of	ADP
american_scientific_journal-1326	139	17	values	value	NOUN
american_scientific_journal-1326	139	18	,	,	PUNCT
american_scientific_journal-1326	139	19	without	without	ADP
american_scientific_journal-1326	139	20	modifying	modify	VERB
american_scientific_journal-1326	139	21	both	both	PRON
american_scientific_journal-1326	139	22	,	,	PUNCT
american_scientific_journal-1326	139	23	the	the	DET
american_scientific_journal-1326	139	24	overall	overall	ADJ
american_scientific_journal-1326	139	25	qualitative	qualitative	ADJ
american_scientific_journal-1326	139	26	nature	nature	NOUN
american_scientific_journal-1326	139	27	of	of	ADP
american_scientific_journal-1326	139	28	the	the	DET
american_scientific_journal-1326	139	29	solution	solution	NOUN
american_scientific_journal-1326	139	30	of	of	ADP
american_scientific_journal-1326	139	31	(	(	PUNCT
american_scientific_journal-1326	139	32	13	13	NUM
american_scientific_journal-1326	139	33	)	)	PUNCT
american_scientific_journal-1326	139	34	(	(	PUNCT
american_scientific_journal-1326	139	35	(	(	PUNCT
american_scientific_journal-1326	139	36	29	29	NUM
american_scientific_journal-1326	139	37	)	)	PUNCT
american_scientific_journal-1326	139	38	)	)	PUNCT
american_scientific_journal-1326	139	39	,	,	PUNCT
american_scientific_journal-1326	139	40	neither	neither	CCONJ
american_scientific_journal-1326	139	41	the	the	DET
american_scientific_journal-1326	139	42	limit	limit	NOUN
american_scientific_journal-1326	139	43	(	(	PUNCT
american_scientific_journal-1326	139	44	33	33	NUM
american_scientific_journal-1326	139	45	)	)	PUNCT
american_scientific_journal-1326	139	46	,	,	PUNCT
american_scientific_journal-1326	139	47	assuming	assume	VERB
american_scientific_journal-1326	139	48	that	that	SCONJ
american_scientific_journal-1326	139	49	0	0	NUM
american_scientific_journal-1326	139	50	2r	2r	NUM
american_scientific_journal-1326	139	51	bβ	bβ	NOUN
american_scientific_journal-1326	139	52	>	>	X
american_scientific_journal-1326	139	53	.	.	PUNCT
american_scientific_journal-1326	140	1	4	4	X
american_scientific_journal-1326	140	2	.	.	X
american_scientific_journal-1326	140	3	discussion	discussion	NOUN
american_scientific_journal-1326	140	4	this	this	DET
american_scientific_journal-1326	140	5	work	work	NOUN
american_scientific_journal-1326	140	6	emphasized	emphasize	VERB
american_scientific_journal-1326	140	7	two	two	NUM
american_scientific_journal-1326	140	8	important	important	ADJ
american_scientific_journal-1326	140	9	aspects	aspect	NOUN
american_scientific_journal-1326	140	10	.	.	PUNCT
american_scientific_journal-1326	141	1	from	from	ADP
american_scientific_journal-1326	141	2	the	the	DET
american_scientific_journal-1326	141	3	mathematical	mathematical	ADJ
american_scientific_journal-1326	141	4	point	point	NOUN
american_scientific_journal-1326	141	5	of	of	ADP
american_scientific_journal-1326	141	6	view	view	NOUN
american_scientific_journal-1326	141	7	the	the	DET
american_scientific_journal-1326	141	8	proposed	propose	VERB
american_scientific_journal-1326	141	9	method	method	NOUN
american_scientific_journal-1326	141	10	pm	pm	NOUN
american_scientific_journal-1326	141	11	,	,	PUNCT
american_scientific_journal-1326	141	12	described	describe	VERB
american_scientific_journal-1326	141	13	with	with	ADP
american_scientific_journal-1326	141	14	accuracy	accuracy	NOUN
american_scientific_journal-1326	141	15	the	the	DET
american_scientific_journal-1326	141	16	model	model	NOUN
american_scientific_journal-1326	141	17	described	describe	VERB
american_scientific_journal-1326	141	18	by	by	ADP
american_scientific_journal-1326	141	19	equation	equation	NOUN
american_scientific_journal-1326	141	20	(	(	PUNCT
american_scientific_journal-1326	141	21	14	14	NUM
american_scientific_journal-1326	141	22	)	)	PUNCT
american_scientific_journal-1326	141	23	.	.	PUNCT
american_scientific_journal-1326	142	1	figure	figure	NOUN
american_scientific_journal-1326	142	2	1	1	NUM
american_scientific_journal-1326	142	3	shows	show	VERB
american_scientific_journal-1326	142	4	the	the	DET
american_scientific_journal-1326	142	5	comparison	comparison	NOUN
american_scientific_journal-1326	142	6	between	between	ADP
american_scientific_journal-1326	142	7	approximation	approximation	NOUN
american_scientific_journal-1326	142	8	(	(	PUNCT
american_scientific_journal-1326	142	9	29	29	NUM
american_scientific_journal-1326	142	10	)	)	PUNCT
american_scientific_journal-1326	142	11	for	for	ADP
american_scientific_journal-1326	142	12	(	(	PUNCT
american_scientific_journal-1326	142	13	13	13	NUM
american_scientific_journal-1326	142	14	)	)	PUNCT
american_scientific_journal-1326	142	15	with	with	ADP
american_scientific_journal-1326	142	16	the	the	DET
american_scientific_journal-1326	142	17	numerical	numerical	ADJ
american_scientific_journal-1326	142	18	solution	solution	NOUN
american_scientific_journal-1326	142	19	(	(	PUNCT
american_scientific_journal-1326	142	20	for	for	ADP
american_scientific_journal-1326	142	21	comparison	comparison	NOUN
american_scientific_journal-1326	142	22	purposes	purpose	NOUN
american_scientific_journal-1326	142	23	,	,	PUNCT
american_scientific_journal-1326	142	24	we	we	PRON
american_scientific_journal-1326	142	25	considered	consider	VERB
american_scientific_journal-1326	142	26	that	that	SCONJ
american_scientific_journal-1326	142	27	the	the	DET
american_scientific_journal-1326	142	28	“	"	PUNCT
american_scientific_journal-1326	142	29	exact	exact	ADJ
american_scientific_journal-1326	142	30	”	"	PUNCT
american_scientific_journal-1326	142	31	solution	solution	NOUN
american_scientific_journal-1326	142	32	is	be	AUX
american_scientific_journal-1326	142	33	computed	compute	VERB
american_scientific_journal-1326	142	34	using	use	VERB
american_scientific_journal-1326	142	35	a	a	DET
american_scientific_journal-1326	142	36	fehlberg	fehlberg	NOUN
american_scientific_journal-1326	142	37	fourth	fourth	ADJ
american_scientific_journal-1326	142	38	-	-	PUNCT
american_scientific_journal-1326	142	39	fifth	fifth	ADJ
american_scientific_journal-1326	142	40	order	order	NOUN
american_scientific_journal-1326	142	41	runge	runge	NOUN
american_scientific_journal-1326	142	42	–	–	PUNCT
american_scientific_journal-1326	142	43	kutta	kutta	NOUN
american_scientific_journal-1326	142	44	method	method	NOUN
american_scientific_journal-1326	142	45	with	with	ADP
american_scientific_journal-1326	142	46	degree	degree	NOUN
american_scientific_journal-1326	142	47	four	four	NUM
american_scientific_journal-1326	142	48	interpolant	interpolant	NOUN
american_scientific_journal-1326	142	49	(	(	PUNCT
american_scientific_journal-1326	142	50	rkf45	rkf45	ADJ
american_scientific_journal-1326	142	51	)	)	PUNCT
american_scientific_journal-1326	143	1	[	[	X
american_scientific_journal-1326	143	2	10	10	NUM
american_scientific_journal-1326	143	3	,	,	PUNCT
american_scientific_journal-1326	143	4	11	11	NUM
american_scientific_journal-1326	143	5	]	]	PUNCT
american_scientific_journal-1326	143	6	as	as	ADP
american_scientific_journal-1326	143	7	a	a	DET
american_scientific_journal-1326	143	8	build	build	NOUN
american_scientific_journal-1326	143	9	-	-	PUNCT
american_scientific_journal-1326	143	10	in	in	ADP
american_scientific_journal-1326	143	11	routine	routine	NOUN
american_scientific_journal-1326	143	12	from	from	ADP
american_scientific_journal-1326	143	13	maple	maple	PROPN
american_scientific_journal-1326	143	14	17	17	NUM
american_scientific_journal-1326	143	15	.	.	PUNCT
american_scientific_journal-1326	144	1	moreover	moreover	ADV
american_scientific_journal-1326	144	2	,	,	PUNCT
american_scientific_journal-1326	144	3	the	the	DET
american_scientific_journal-1326	144	4	routine	routine	NOUN
american_scientific_journal-1326	144	5	was	be	AUX
american_scientific_journal-1326	144	6	configured	configure	VERB
american_scientific_journal-1326	144	7	using	use	VERB
american_scientific_journal-1326	144	8	an	an	DET
american_scientific_journal-1326	144	9	absolute	absolute	ADJ
american_scientific_journal-1326	144	10	error	error	NOUN
american_scientific_journal-1326	144	11	(	(	PUNCT
american_scientific_journal-1326	144	12	a.e	a.e	PROPN
american_scientific_journal-1326	144	13	.	.	PUNCT
american_scientific_journal-1326	144	14	)	)	PUNCT
american_scientific_journal-1326	145	1	tolerance	tolerance	NOUN
american_scientific_journal-1326	145	2	of	of	ADP
american_scientific_journal-1326	145	3	121	121	NUM
american_scientific_journal-1326	145	4	10x	10x	NOUN
american_scientific_journal-1326	145	5	−	−	PROPN
american_scientific_journal-1326	145	6	)	)	PUNCT
american_scientific_journal-1326	145	7	,	,	PUNCT
american_scientific_journal-1326	145	8	where	where	SCONJ
american_scientific_journal-1326	145	9	we	we	PRON
american_scientific_journal-1326	145	10	employed	employ	VERB
american_scientific_journal-1326	145	11	typical	typical	ADJ
american_scientific_journal-1326	145	12	observational	observational	ADJ
american_scientific_journal-1326	145	13	values	value	NOUN
american_scientific_journal-1326	145	14	for	for	ADP
american_scientific_journal-1326	145	15	the	the	DET
american_scientific_journal-1326	145	16	parameters	parameter	NOUN
american_scientific_journal-1326	145	17	of	of	ADP
american_scientific_journal-1326	145	18	(	(	PUNCT
american_scientific_journal-1326	145	19	29	29	NUM
american_scientific_journal-1326	145	20	)	)	PUNCT
american_scientific_journal-1326	145	21	(	(	PUNCT
american_scientific_journal-1326	145	22	we	we	PRON
american_scientific_journal-1326	145	23	remit	remit	VERB
american_scientific_journal-1326	145	24	the	the	DET
american_scientific_journal-1326	145	25	above	above	ADJ
american_scientific_journal-1326	145	26	calculations	calculation	NOUN
american_scientific_journal-1326	145	27	to	to	ADP
american_scientific_journal-1326	145	28	the	the	DET
american_scientific_journal-1326	145	29	appendix	appendix	NOUN
american_scientific_journal-1326	145	30	a	a	PRON
american_scientific_journal-1326	145	31	)	)	PUNCT
american_scientific_journal-1326	145	32	.	.	PUNCT
american_scientific_journal-1326	146	1	although	although	SCONJ
american_scientific_journal-1326	146	2	the	the	DET
american_scientific_journal-1326	146	3	figures	figure	NOUN
american_scientific_journal-1326	146	4	are	be	AUX
american_scientific_journal-1326	146	5	in	in	ADP
american_scientific_journal-1326	146	6	good	good	ADJ
american_scientific_journal-1326	146	7	agreement	agreement	NOUN
american_scientific_journal-1326	146	8	,	,	PUNCT
american_scientific_journal-1326	146	9	showing	show	VERB
american_scientific_journal-1326	146	10	the	the	DET
american_scientific_journal-1326	146	11	highly	highly	ADV
american_scientific_journal-1326	146	12	accuracy	accuracy	NOUN
american_scientific_journal-1326	146	13	of	of	ADP
american_scientific_journal-1326	146	14	(	(	PUNCT
american_scientific_journal-1326	146	15	29	29	NUM
american_scientific_journal-1326	146	16	)	)	PUNCT
american_scientific_journal-1326	146	17	,	,	PUNCT
american_scientific_journal-1326	146	18	it	it	PRON
american_scientific_journal-1326	146	19	was	be	AUX
american_scientific_journal-1326	146	20	verified	verify	VERB
american_scientific_journal-1326	146	21	by	by	ADP
american_scientific_journal-1326	146	22	calculating	calculate	VERB
american_scientific_journal-1326	146	23	the	the	DET
american_scientific_journal-1326	146	24	residual	residual	ADJ
american_scientific_journal-1326	146	25	error	error	NOUN
american_scientific_journal-1326	146	26	(	(	PUNCT
american_scientific_journal-1326	146	27	r.e	r.e	PROPN
american_scientific_journal-1326	146	28	)	)	PUNCT
american_scientific_journal-1326	146	29	of	of	ADP
american_scientific_journal-1326	146	30	(	(	PUNCT
american_scientific_journal-1326	146	31	29	29	NUM
american_scientific_journal-1326	146	32	)	)	PUNCT
american_scientific_journal-1326	146	33	.	.	PUNCT
american_scientific_journal-1326	147	1	r.e	r.e	PROPN
american_scientific_journal-1326	147	2	is	be	AUX
american_scientific_journal-1326	147	3	obtained	obtain	VERB
american_scientific_journal-1326	147	4	substituting	substitute	VERB
american_scientific_journal-1326	147	5	(	(	PUNCT
american_scientific_journal-1326	147	6	29	29	NUM
american_scientific_journal-1326	147	7	)	)	PUNCT
american_scientific_journal-1326	147	8	into	into	ADP
american_scientific_journal-1326	147	9	(	(	PUNCT
american_scientific_journal-1326	147	10	13	13	NUM
american_scientific_journal-1326	147	11	)	)	PUNCT
american_scientific_journal-1326	147	12	.	.	PUNCT
american_scientific_journal-1326	148	1	figure	figure	NOUN
american_scientific_journal-1326	148	2	2	2	NUM
american_scientific_journal-1326	148	3	shows	show	VERB
american_scientific_journal-1326	148	4	that	that	SCONJ
american_scientific_journal-1326	148	5	the	the	DET
american_scientific_journal-1326	148	6	maximum	maximum	ADJ
american_scientific_journal-1326	148	7	value	value	NOUN
american_scientific_journal-1326	148	8	of	of	ADP
american_scientific_journal-1326	148	9	r.e	r.e	PROPN
american_scientific_journal-1326	148	10	is	be	AUX
american_scientific_journal-1326	148	11	501	501	NUM
american_scientific_journal-1326	148	12	10−	10−	NOUN
american_scientific_journal-1326	148	13	<	<	X
american_scientific_journal-1326	148	14	<	<	X
american_scientific_journal-1326	148	15	×	×	NOUN
american_scientific_journal-1326	148	16	which	which	PRON
american_scientific_journal-1326	148	17	confirms	confirm	VERB
american_scientific_journal-1326	148	18	quantitatively	quantitatively	ADV
american_scientific_journal-1326	148	19	the	the	DET
american_scientific_journal-1326	148	20	accuracy	accuracy	NOUN
american_scientific_journal-1326	148	21	of	of	ADP
american_scientific_journal-1326	148	22	the	the	DET
american_scientific_journal-1326	148	23	proposed	propose	VERB
american_scientific_journal-1326	148	24	solution	solution	NOUN
american_scientific_journal-1326	148	25	.	.	PUNCT
american_scientific_journal-1326	149	1	although	although	SCONJ
american_scientific_journal-1326	149	2	figure	figure	NOUN
american_scientific_journal-1326	149	3	1	1	NUM
american_scientific_journal-1326	149	4	shows	show	NOUN
american_scientific_journal-1326	149	5	(	(	PUNCT
american_scientific_journal-1326	149	6	29	29	NUM
american_scientific_journal-1326	149	7	)	)	PUNCT
american_scientific_journal-1326	149	8	in	in	ADP
american_scientific_journal-1326	149	9	20	20	NUM
american_scientific_journal-1326	149	10	23[1.42	23[1.42	NUM
american_scientific_journal-1326	149	11	10	10	NUM
american_scientific_journal-1326	149	12	,	,	PUNCT
american_scientific_journal-1326	149	13	10	10	NUM
american_scientific_journal-1326	149	14	]	]	SYM
american_scientific_journal-1326	149	15	×	×	NOUN
american_scientific_journal-1326	149	16	,	,	PUNCT
american_scientific_journal-1326	149	17	from	from	ADP
american_scientific_journal-1326	149	18	the	the	DET
american_scientific_journal-1326	149	19	figure	figure	NOUN
american_scientific_journal-1326	149	20	2	2	NUM
american_scientific_journal-1326	149	21	is	be	AUX
american_scientific_journal-1326	149	22	clear	clear	ADJ
american_scientific_journal-1326	149	23	that	that	SCONJ
american_scientific_journal-1326	149	24	the	the	DET
american_scientific_journal-1326	149	25	high	high	ADJ
american_scientific_journal-1326	149	26	accuracy	accuracy	NOUN
american_scientific_journal-1326	149	27	of	of	ADP
american_scientific_journal-1326	149	28	our	our	PRON
american_scientific_journal-1326	149	29	approximate	approximate	ADJ
american_scientific_journal-1326	149	30	solution	solution	NOUN
american_scientific_journal-1326	149	31	continues	continue	VERB
american_scientific_journal-1326	149	32	beyond	beyond	ADP
american_scientific_journal-1326	149	33	.	.	PUNCT
american_scientific_journal-1326	150	1	the	the	DET
american_scientific_journal-1326	150	2	methodology	methodology	NOUN
american_scientific_journal-1326	150	3	used	use	VERB
american_scientific_journal-1326	150	4	by	by	ADP
american_scientific_journal-1326	150	5	[	[	X
american_scientific_journal-1326	150	6	1	1	NUM
american_scientific_journal-1326	150	7	]	]	PUNCT
american_scientific_journal-1326	150	8	consisted	consist	VERB
american_scientific_journal-1326	150	9	in	in	ADP
american_scientific_journal-1326	150	10	expressing	express	VERB
american_scientific_journal-1326	150	11	the	the	DET
american_scientific_journal-1326	150	12	resulting	result	VERB
american_scientific_journal-1326	150	13	equation	equation	NOUN
american_scientific_journal-1326	150	14	(	(	PUNCT
american_scientific_journal-1326	150	15	11	11	NUM
american_scientific_journal-1326	150	16	)	)	PUNCT
american_scientific_journal-1326	150	17	in	in	ADP
american_scientific_journal-1326	150	18	terms	term	NOUN
american_scientific_journal-1326	150	19	of	of	ADP
american_scientific_journal-1326	150	20	a	a	DET
american_scientific_journal-1326	150	21	volterra	volterra	NOUN
american_scientific_journal-1326	150	22	second	second	ADJ
american_scientific_journal-1326	150	23	order	order	NOUN
american_scientific_journal-1326	150	24	integral	integral	ADJ
american_scientific_journal-1326	150	25	equation	equation	NOUN
american_scientific_journal-1326	150	26	,	,	PUNCT
american_scientific_journal-1326	150	27	which	which	PRON
american_scientific_journal-1326	150	28	was	be	AUX
american_scientific_journal-1326	150	29	solved	solve	VERB
american_scientific_journal-1326	150	30	by	by	ADP
american_scientific_journal-1326	150	31	means	mean	NOUN
american_scientific_journal-1326	150	32	of	of	ADP
american_scientific_journal-1326	150	33	picard	picard	NOUN
american_scientific_journal-1326	150	34	's	's	PART
american_scientific_journal-1326	150	35	method	method	NOUN
american_scientific_journal-1326	150	36	,	,	PUNCT
american_scientific_journal-1326	150	37	but	but	CCONJ
american_scientific_journal-1326	150	38	the	the	DET
american_scientific_journal-1326	150	39	aforementioned	aforementioned	ADJ
american_scientific_journal-1326	150	40	paper	paper	NOUN
american_scientific_journal-1326	150	41	lack	lack	NOUN
american_scientific_journal-1326	150	42	of	of	ADP
american_scientific_journal-1326	150	43	discussion	discussion	NOUN
american_scientific_journal-1326	150	44	about	about	ADP
american_scientific_journal-1326	150	45	the	the	DET
american_scientific_journal-1326	150	46	perturbative	perturbative	ADJ
american_scientific_journal-1326	150	47	character	character	NOUN
american_scientific_journal-1326	150	48	of	of	ADP
american_scientific_journal-1326	150	49	the	the	DET
american_scientific_journal-1326	150	50	differential	differential	ADJ
american_scientific_journal-1326	150	51	equation	equation	NOUN
american_scientific_journal-1326	150	52	for	for	ADP
american_scientific_journal-1326	150	53	(	(	PUNCT
american_scientific_journal-1326	150	54	)	)	PUNCT
american_scientific_journal-1326	150	55	v	v	NOUN
american_scientific_journal-1326	150	56	r	r	NOUN
american_scientific_journal-1326	151	1	and	and	CCONJ
american_scientific_journal-1326	151	2	it	it	PRON
american_scientific_journal-1326	151	3	did	do	AUX
american_scientific_journal-1326	151	4	not	not	PART
american_scientific_journal-1326	151	5	provide	provide	VERB
american_scientific_journal-1326	151	6	a	a	DET
american_scientific_journal-1326	151	7	manner	manner	NOUN
american_scientific_journal-1326	151	8	to	to	PART
american_scientific_journal-1326	151	9	measure	measure	VERB
american_scientific_journal-1326	151	10	the	the	DET
american_scientific_journal-1326	151	11	accuracy	accuracy	NOUN
american_scientific_journal-1326	151	12	of	of	ADP
american_scientific_journal-1326	151	13	the	the	DET
american_scientific_journal-1326	151	14	proposed	propose	VERB
american_scientific_journal-1326	151	15	results	result	NOUN
american_scientific_journal-1326	151	16	,	,	PUNCT
american_scientific_journal-1326	151	17	since	since	SCONJ
american_scientific_journal-1326	151	18	the	the	DET
american_scientific_journal-1326	151	19	observational	observational	ADJ
american_scientific_journal-1326	151	20	data	datum	NOUN
american_scientific_journal-1326	151	21	were	be	AUX
american_scientific_journal-1326	151	22	not	not	PART
american_scientific_journal-1326	151	23	taken	take	VERB
american_scientific_journal-1326	151	24	into	into	ADP
american_scientific_journal-1326	151	25	account	account	NOUN
american_scientific_journal-1326	151	26	.	.	PUNCT
american_scientific_journal-1326	152	1	unlike	unlike	ADP
american_scientific_journal-1326	152	2	the	the	DET
american_scientific_journal-1326	152	3	above	above	ADJ
american_scientific_journal-1326	152	4	methodology	methodology	NOUN
american_scientific_journal-1326	152	5	,	,	PUNCT
american_scientific_journal-1326	152	6	this	this	DET
american_scientific_journal-1326	152	7	work	work	NOUN
american_scientific_journal-1326	152	8	employed	employ	VERB
american_scientific_journal-1326	152	9	an	an	DET
american_scientific_journal-1326	152	10	elementary	elementary	ADJ
american_scientific_journal-1326	152	11	procedure	procedure	NOUN
american_scientific_journal-1326	152	12	based	base	VERB
american_scientific_journal-1326	152	13	on	on	ADP
american_scientific_journal-1326	152	14	classical	classical	ADJ
american_scientific_journal-1326	152	15	perturbation	perturbation	NOUN
american_scientific_journal-1326	152	16	method	method	NOUN
american_scientific_journal-1326	152	17	in	in	ADP
american_scientific_journal-1326	152	18	order	order	NOUN
american_scientific_journal-1326	152	19	to	to	PART
american_scientific_journal-1326	152	20	find	find	VERB
american_scientific_journal-1326	152	21	an	an	DET
american_scientific_journal-1326	152	22	analytical	analytical	ADJ
american_scientific_journal-1326	152	23	approximate	approximate	ADJ
american_scientific_journal-1326	152	24	solution	solution	NOUN
american_scientific_journal-1326	152	25	for	for	ADP
american_scientific_journal-1326	152	26	(	(	PUNCT
american_scientific_journal-1326	152	27	13	13	NUM
american_scientific_journal-1326	152	28	)	)	PUNCT
american_scientific_journal-1326	152	29	.	.	PUNCT
american_scientific_journal-1326	153	1	a	a	DET
american_scientific_journal-1326	153	2	relevant	relevant	ADJ
american_scientific_journal-1326	153	3	fact	fact	NOUN
american_scientific_journal-1326	153	4	of	of	ADP
american_scientific_journal-1326	153	5	the	the	DET
american_scientific_journal-1326	153	6	proposed	propose	VERB
american_scientific_journal-1326	153	7	pm	pm	NOUN
american_scientific_journal-1326	153	8	solution	solution	NOUN
american_scientific_journal-1326	153	9	was	be	AUX
american_scientific_journal-1326	153	10	highlight	highlight	VERB
american_scientific_journal-1326	153	11	the	the	DET
american_scientific_journal-1326	153	12	perturbative	perturbative	ADJ
american_scientific_journal-1326	153	13	character	character	NOUN
american_scientific_journal-1326	153	14	of	of	ADP
american_scientific_journal-1326	153	15	the	the	DET
american_scientific_journal-1326	153	16	equation	equation	NOUN
american_scientific_journal-1326	153	17	to	to	PART
american_scientific_journal-1326	153	18	solve	solve	VERB
american_scientific_journal-1326	153	19	.	.	PUNCT
american_scientific_journal-1326	154	1	although	although	SCONJ
american_scientific_journal-1326	154	2	the	the	DET
american_scientific_journal-1326	154	3	results	result	NOUN
american_scientific_journal-1326	154	4	of	of	ADP
american_scientific_journal-1326	154	5	[	[	X
american_scientific_journal-1326	154	6	1	1	NUM
american_scientific_journal-1326	154	7	]	]	PUNCT
american_scientific_journal-1326	154	8	coincide	coincide	NOUN
american_scientific_journal-1326	154	9	with	with	ADP
american_scientific_journal-1326	154	10	ours	our	NOUN
american_scientific_journal-1326	154	11	,	,	PUNCT
american_scientific_journal-1326	154	12	it	it	PRON
american_scientific_journal-1326	154	13	did	do	AUX
american_scientific_journal-1326	154	14	not	not	PART
american_scientific_journal-1326	154	15	give	give	VERB
american_scientific_journal-1326	154	16	justification	justification	NOUN
american_scientific_journal-1326	154	17	to	to	PART
american_scientific_journal-1326	154	18	truncate	truncate	VERB
american_scientific_journal-1326	154	19	the	the	DET
american_scientific_journal-1326	154	20	solution	solution	NOUN
american_scientific_journal-1326	154	21	by	by	ADP
american_scientific_journal-1326	154	22	keeping	keep	VERB
american_scientific_journal-1326	154	23	just	just	ADV
american_scientific_journal-1326	154	24	the	the	DET
american_scientific_journal-1326	154	25	first	first	ADJ
american_scientific_journal-1326	154	26	picard	picard	NOUN
american_scientific_journal-1326	154	27	iteration	iteration	NOUN
american_scientific_journal-1326	154	28	.	.	PUNCT
american_scientific_journal-1326	155	1	in	in	ADP
american_scientific_journal-1326	155	2	fact	fact	NOUN
american_scientific_journal-1326	155	3	we	we	PRON
american_scientific_journal-1326	155	4	proved	prove	VERB
american_scientific_journal-1326	155	5	the	the	DET
american_scientific_journal-1326	155	6	feasibility	feasibility	NOUN
american_scientific_journal-1326	155	7	of	of	ADP
american_scientific_journal-1326	155	8	the	the	DET
american_scientific_journal-1326	155	9	model	model	NOUN
american_scientific_journal-1326	155	10	given	give	VERB
american_scientific_journal-1326	155	11	by	by	ADP
american_scientific_journal-1326	155	12	(	(	PUNCT
american_scientific_journal-1326	155	13	13	13	NUM
american_scientific_journal-1326	155	14	)	)	PUNCT
american_scientific_journal-1326	155	15	and	and	CCONJ
american_scientific_journal-1326	155	16	(	(	PUNCT
american_scientific_journal-1326	155	17	29	29	NUM
american_scientific_journal-1326	155	18	)	)	PUNCT
american_scientific_journal-1326	155	19	,	,	PUNCT
american_scientific_journal-1326	155	20	by	by	ADP
american_scientific_journal-1326	155	21	showing	show	VERB
american_scientific_journal-1326	155	22	that	that	SCONJ
american_scientific_journal-1326	155	23	it	it	PRON
american_scientific_journal-1326	155	24	works	work	VERB
american_scientific_journal-1326	155	25	employing	employ	VERB
american_scientific_journal-1326	155	26	reasonable	reasonable	ADJ
american_scientific_journal-1326	155	27	observational	observational	ADJ
american_scientific_journal-1326	155	28	data	datum	NOUN
american_scientific_journal-1326	155	29	.	.	PUNCT
american_scientific_journal-1326	156	1	from	from	ADP
american_scientific_journal-1326	156	2	the	the	DET
american_scientific_journal-1326	156	3	astrophysicist	astrophysicist	ADJ
american_scientific_journal-1326	156	4	point	point	NOUN
american_scientific_journal-1326	156	5	of	of	ADP
american_scientific_journal-1326	156	6	view	view	NOUN
american_scientific_journal-1326	156	7	,	,	PUNCT
american_scientific_journal-1326	156	8	this	this	DET
american_scientific_journal-1326	156	9	work	work	NOUN
american_scientific_journal-1326	156	10	is	be	AUX
american_scientific_journal-1326	156	11	important	important	ADJ
american_scientific_journal-1326	156	12	because	because	SCONJ
american_scientific_journal-1326	156	13	it	it	PRON
american_scientific_journal-1326	156	14	shows	show	VERB
american_scientific_journal-1326	156	15	that	that	SCONJ
american_scientific_journal-1326	156	16	the	the	DET
american_scientific_journal-1326	156	17	qualitative	qualitative	ADJ
american_scientific_journal-1326	156	18	behaviour	behaviour	NOUN
american_scientific_journal-1326	156	19	of	of	ADP
american_scientific_journal-1326	156	20	the	the	DET
american_scientific_journal-1326	156	21	elliptical	elliptical	ADJ
american_scientific_journal-1326	156	22	galaxies	galaxy	NOUN
american_scientific_journal-1326	156	23	rotation	rotation	NOUN
american_scientific_journal-1326	156	24	curves	curve	NOUN
american_scientific_journal-1326	156	25	,	,	PUNCT
american_scientific_journal-1326	156	26	can	can	AUX
american_scientific_journal-1326	156	27	be	be	AUX
american_scientific_journal-1326	156	28	explained	explain	VERB
american_scientific_journal-1326	156	29	in	in	ADP
american_scientific_journal-1326	156	30	terms	term	NOUN
american_scientific_journal-1326	156	31	of	of	ADP
american_scientific_journal-1326	156	32	a	a	DET
american_scientific_journal-1326	156	33	nonlinear	nonlinear	ADJ
american_scientific_journal-1326	156	34	model	model	NOUN
american_scientific_journal-1326	156	35	of	of	ADP
american_scientific_journal-1326	156	36	the	the	DET
american_scientific_journal-1326	156	37	gravitational	gravitational	ADJ
american_scientific_journal-1326	156	38	field	field	NOUN
american_scientific_journal-1326	156	39	,	,	PUNCT
american_scientific_journal-1326	156	40	which	which	PRON
american_scientific_journal-1326	156	41	preserves	preserve	VERB
american_scientific_journal-1326	156	42	the	the	DET
american_scientific_journal-1326	156	43	validity	validity	NOUN
american_scientific_journal-1326	156	44	of	of	ADP
american_scientific_journal-1326	156	45	newtonian	newtonian	ADJ
american_scientific_journal-1326	156	46	physics	physics	NOUN
american_scientific_journal-1326	156	47	and	and	CCONJ
american_scientific_journal-1326	156	48	does	do	AUX
american_scientific_journal-1326	156	49	not	not	PART
american_scientific_journal-1326	156	50	require	require	VERB
american_scientific_journal-1326	156	51	the	the	DET
american_scientific_journal-1326	156	52	existence	existence	NOUN
american_scientific_journal-1326	156	53	of	of	ADP
american_scientific_journal-1326	156	54	dark	dark	ADJ
american_scientific_journal-1326	156	55	matter	matter	NOUN
american_scientific_journal-1326	156	56	.	.	PUNCT
american_scientific_journal-1326	157	1	unlike	unlike	ADP
american_scientific_journal-1326	157	2	[	[	X
american_scientific_journal-1326	157	3	1	1	NUM
american_scientific_journal-1326	157	4	]	]	PUNCT
american_scientific_journal-1326	157	5	,	,	PUNCT
american_scientific_journal-1326	157	6	this	this	DET
american_scientific_journal-1326	157	7	paper	paper	NOUN
american_scientific_journal-1326	157	8	used	use	VERB
american_scientific_journal-1326	157	9	basic	basic	ADJ
american_scientific_journal-1326	157	10	physical	physical	ADJ
american_scientific_journal-1326	157	11	concepts	concept	NOUN
american_scientific_journal-1326	157	12	,	,	PUNCT
american_scientific_journal-1326	157	13	to	to	PART
american_scientific_journal-1326	157	14	express	express	VERB
american_scientific_journal-1326	157	15	their	their	PRON
american_scientific_journal-1326	157	16	ideas	idea	NOUN
american_scientific_journal-1326	157	17	like	like	ADP
american_scientific_journal-1326	157	18	mechanical	mechanical	ADJ
american_scientific_journal-1326	157	19	energy	energy	NOUN
american_scientific_journal-1326	157	20	,	,	PUNCT
american_scientific_journal-1326	157	21	centripetal	centripetal	ADJ
american_scientific_journal-1326	157	22	force	force	NOUN
american_scientific_journal-1326	157	23	,	,	PUNCT
american_scientific_journal-1326	157	24	kinetic	kinetic	ADJ
american_scientific_journal-1326	157	25	energy	energy	NOUN
american_scientific_journal-1326	157	26	and	and	CCONJ
american_scientific_journal-1326	157	27	conservative	conservative	ADJ
american_scientific_journal-1326	157	28	field	field	NOUN
american_scientific_journal-1326	157	29	,	,	PUNCT
american_scientific_journal-1326	157	30	so	so	SCONJ
american_scientific_journal-1326	157	31	that	that	SCONJ
american_scientific_journal-1326	157	32	it	it	PRON
american_scientific_journal-1326	157	33	is	be	AUX
american_scientific_journal-1326	157	34	expected	expect	VERB
american_scientific_journal-1326	157	35	be	be	AUX
american_scientific_journal-1326	157	36	more	more	ADV
american_scientific_journal-1326	157	37	understandable	understandable	ADJ
american_scientific_journal-1326	157	38	.	.	PUNCT
american_scientific_journal-1326	158	1	american	american	ADJ
american_scientific_journal-1326	158	2	scientific	scientific	ADJ
american_scientific_journal-1326	158	3	research	research	PROPN
american_scientific_journal-1326	158	4	journal	journal	NOUN
american_scientific_journal-1326	158	5	for	for	ADP
american_scientific_journal-1326	158	6	engineering	engineering	NOUN
american_scientific_journal-1326	158	7	,	,	PUNCT
american_scientific_journal-1326	158	8	technology	technology	NOUN
american_scientific_journal-1326	158	9	,	,	PUNCT
american_scientific_journal-1326	158	10	and	and	CCONJ
american_scientific_journal-1326	158	11	sciences	science	NOUN
american_scientific_journal-1326	158	12	(	(	PUNCT
american_scientific_journal-1326	158	13	asrjets	asrjet	NOUN
american_scientific_journal-1326	158	14	)	)	PUNCT
american_scientific_journal-1326	158	15	(	(	PUNCT
american_scientific_journal-1326	158	16	2017	2017	NUM
american_scientific_journal-1326	158	17	)	)	PUNCT
american_scientific_journal-1326	158	18	volume	volume	NOUN
american_scientific_journal-1326	158	19	27	27	NUM
american_scientific_journal-1326	158	20	,	,	PUNCT
american_scientific_journal-1326	158	21	no	no	DET
american_scientific_journal-1326	158	22	1	1	NUM
american_scientific_journal-1326	158	23	,	,	PUNCT
american_scientific_journal-1326	158	24	pp	pp	ADV
american_scientific_journal-1326	158	25	139	139	NUM
american_scientific_journal-1326	158	26	-	-	SYM
american_scientific_journal-1326	158	27	150	150	NUM
american_scientific_journal-1326	158	28	148	148	NUM
american_scientific_journal-1326	158	29	figure	figure	NOUN
american_scientific_journal-1326	158	30	1	1	NUM
american_scientific_journal-1326	158	31	:	:	PUNCT
american_scientific_journal-1326	158	32	comparison	comparison	NOUN
american_scientific_journal-1326	158	33	numerical	numerical	ADJ
american_scientific_journal-1326	158	34	solution	solution	NOUN
american_scientific_journal-1326	158	35	of	of	ADP
american_scientific_journal-1326	158	36	the	the	DET
american_scientific_journal-1326	158	37	nonlinear	nonlinear	ADJ
american_scientific_journal-1326	158	38	problem	problem	NOUN
american_scientific_journal-1326	158	39	given	give	VERB
american_scientific_journal-1326	158	40	by	by	ADP
american_scientific_journal-1326	158	41	(	(	PUNCT
american_scientific_journal-1326	158	42	13	13	NUM
american_scientific_journal-1326	158	43	)	)	PUNCT
american_scientific_journal-1326	158	44	and	and	CCONJ
american_scientific_journal-1326	158	45	pm	pm	NOUN
american_scientific_journal-1326	158	46	approximation	approximation	NOUN
american_scientific_journal-1326	158	47	(	(	PUNCT
american_scientific_journal-1326	158	48	29	29	NUM
american_scientific_journal-1326	158	49	)	)	PUNCT
american_scientific_journal-1326	158	50	for	for	ADP
american_scientific_journal-1326	158	51	the	the	DET
american_scientific_journal-1326	158	52	values	value	NOUN
american_scientific_journal-1326	158	53	of	of	ADP
american_scientific_journal-1326	158	54	the	the	DET
american_scientific_journal-1326	158	55	parameters	parameter	NOUN
american_scientific_journal-1326	158	56	given	give	VERB
american_scientific_journal-1326	158	57	by	by	ADP
american_scientific_journal-1326	158	58	(	(	PUNCT
american_scientific_journal-1326	158	59	1	1	NUM
american_scientific_journal-1326	158	60	-	-	PUNCT
american_scientific_journal-1326	158	61	a)-(5	a)-(5	NOUN
american_scientific_journal-1326	158	62	-	-	PUNCT
american_scientific_journal-1326	158	63	a	a	NOUN
american_scientific_journal-1326	158	64	)	)	PUNCT
american_scientific_journal-1326	158	65	.	.	PUNCT
american_scientific_journal-1326	159	1	figure	figure	NOUN
american_scientific_journal-1326	159	2	2	2	NUM
american_scientific_journal-1326	159	3	:	:	PUNCT
american_scientific_journal-1326	159	4	residual	residual	ADJ
american_scientific_journal-1326	159	5	error	error	NOUN
american_scientific_journal-1326	159	6	(	(	PUNCT
american_scientific_journal-1326	159	7	r.e	r.e	PROPN
american_scientific_journal-1326	159	8	.	.	PROPN
american_scientific_journal-1326	159	9	)	)	PUNCT
american_scientific_journal-1326	159	10	of	of	ADP
american_scientific_journal-1326	159	11	(	(	PUNCT
american_scientific_journal-1326	159	12	29	29	NUM
american_scientific_journal-1326	159	13	)	)	PUNCT
american_scientific_journal-1326	159	14	for	for	ADP
american_scientific_journal-1326	159	15	the	the	DET
american_scientific_journal-1326	159	16	values	value	NOUN
american_scientific_journal-1326	159	17	of	of	ADP
american_scientific_journal-1326	159	18	the	the	DET
american_scientific_journal-1326	159	19	parameters	parameter	NOUN
american_scientific_journal-1326	159	20	given	give	VERB
american_scientific_journal-1326	159	21	by	by	ADP
american_scientific_journal-1326	159	22	(	(	PUNCT
american_scientific_journal-1326	159	23	1	1	NUM
american_scientific_journal-1326	159	24	-	-	PUNCT
american_scientific_journal-1326	159	25	a)-(5	a)-(5	NOUN
american_scientific_journal-1326	159	26	-	-	PUNCT
american_scientific_journal-1326	159	27	a	a	NOUN
american_scientific_journal-1326	159	28	)	)	PUNCT
american_scientific_journal-1326	159	29	.	.	PUNCT
american_scientific_journal-1326	160	1	5	5	X
american_scientific_journal-1326	160	2	.	.	X
american_scientific_journal-1326	160	3	conclusions	conclusion	NOUN
american_scientific_journal-1326	160	4	this	this	DET
american_scientific_journal-1326	160	5	paper	paper	NOUN
american_scientific_journal-1326	160	6	presented	present	VERB
american_scientific_journal-1326	160	7	a	a	DET
american_scientific_journal-1326	160	8	nonlinear	nonlinear	ADJ
american_scientific_journal-1326	160	9	model	model	NOUN
american_scientific_journal-1326	160	10	for	for	ADP
american_scientific_journal-1326	160	11	the	the	DET
american_scientific_journal-1326	160	12	gravitation	gravitation	NOUN
american_scientific_journal-1326	160	13	field	field	NOUN
american_scientific_journal-1326	160	14	that	that	PRON
american_scientific_journal-1326	160	15	correctly	correctly	ADV
american_scientific_journal-1326	160	16	describes	describe	VERB
american_scientific_journal-1326	160	17	the	the	DET
american_scientific_journal-1326	160	18	behaviour	behaviour	NOUN
american_scientific_journal-1326	160	19	of	of	ADP
american_scientific_journal-1326	160	20	the	the	DET
american_scientific_journal-1326	160	21	galaxies	galaxy	NOUN
american_scientific_journal-1326	160	22	rotation	rotation	NOUN
american_scientific_journal-1326	160	23	curves	curve	NOUN
american_scientific_journal-1326	160	24	and	and	CCONJ
american_scientific_journal-1326	160	25	fits	fit	VERB
american_scientific_journal-1326	160	26	with	with	ADP
american_scientific_journal-1326	160	27	some	some	DET
american_scientific_journal-1326	160	28	typical	typical	ADJ
american_scientific_journal-1326	160	29	observational	observational	ADJ
american_scientific_journal-1326	160	30	data	datum	NOUN
american_scientific_journal-1326	160	31	,	,	PUNCT
american_scientific_journal-1326	160	32	without	without	ADP
american_scientific_journal-1326	160	33	departing	depart	VERB
american_scientific_journal-1326	160	34	from	from	ADP
american_scientific_journal-1326	160	35	the	the	DET
american_scientific_journal-1326	160	36	newtonian	newtonian	ADJ
american_scientific_journal-1326	160	37	scope	scope	NOUN
american_scientific_journal-1326	160	38	known	know	VERB
american_scientific_journal-1326	160	39	.	.	PUNCT
american_scientific_journal-1326	161	1	a	a	DET
american_scientific_journal-1326	161	2	highlight	highlight	NOUN
american_scientific_journal-1326	161	3	of	of	ADP
american_scientific_journal-1326	161	4	this	this	DET
american_scientific_journal-1326	161	5	work	work	NOUN
american_scientific_journal-1326	161	6	is	be	AUX
american_scientific_journal-1326	161	7	that	that	SCONJ
american_scientific_journal-1326	161	8	although	although	SCONJ
american_scientific_journal-1326	161	9	this	this	PRON
american_scientific_journal-1326	161	10	is	be	AUX
american_scientific_journal-1326	161	11	based	base	VERB
american_scientific_journal-1326	161	12	on	on	ADP
american_scientific_journal-1326	161	13	elementary	elementary	ADJ
american_scientific_journal-1326	161	14	mathematics	mathematics	PROPN
american_scientific_journal-1326	161	15	and	and	CCONJ
american_scientific_journal-1326	161	16	physics	physic	NOUN
american_scientific_journal-1326	161	17	,	,	PUNCT
american_scientific_journal-1326	161	18	very	very	ADV
american_scientific_journal-1326	161	19	accurate	accurate	ADJ
american_scientific_journal-1326	161	20	results	result	NOUN
american_scientific_journal-1326	161	21	were	be	AUX
american_scientific_journal-1326	161	22	obtained	obtain	VERB
american_scientific_journal-1326	161	23	.	.	PUNCT
american_scientific_journal-1326	162	1	appendix	appendix	VERB
american_scientific_journal-1326	162	2	a	a	DET
american_scientific_journal-1326	162	3	detailed	detailed	ADJ
american_scientific_journal-1326	162	4	calculations	calculation	NOUN
american_scientific_journal-1326	162	5	for	for	ADP
american_scientific_journal-1326	162	6	numerical	numerical	ADJ
american_scientific_journal-1326	162	7	comparison	comparison	NOUN
american_scientific_journal-1326	162	8	.	.	PUNCT
american_scientific_journal-1326	163	1	such	such	ADJ
american_scientific_journal-1326	163	2	as	as	SCONJ
american_scientific_journal-1326	163	3	it	it	PRON
american_scientific_journal-1326	163	4	was	be	AUX
american_scientific_journal-1326	163	5	already	already	ADV
american_scientific_journal-1326	163	6	deduced	deduce	VERB
american_scientific_journal-1326	163	7	,	,	PUNCT
american_scientific_journal-1326	163	8	the	the	DET
american_scientific_journal-1326	163	9	value	value	NOUN
american_scientific_journal-1326	163	10	of	of	ADP
american_scientific_journal-1326	163	11	the	the	DET
american_scientific_journal-1326	163	12	perturbation	perturbation	NOUN
american_scientific_journal-1326	163	13	parameter	parameter	NOUN
american_scientific_journal-1326	163	14	is	be	AUX
american_scientific_journal-1326	163	15	(	(	PUNCT
american_scientific_journal-1326	163	16	see	see	VERB
american_scientific_journal-1326	163	17	(	(	PUNCT
american_scientific_journal-1326	163	18	12	12	NUM
american_scientific_journal-1326	163	19	)	)	PUNCT
american_scientific_journal-1326	163	20	)	)	PUNCT
american_scientific_journal-1326	163	21	328.38	328.38	NUM
american_scientific_journal-1326	163	22	10ε	10ε	X
american_scientific_journal-1326	163	23	−≅	−≅	X
american_scientific_journal-1326	163	24	×	×	PROPN
american_scientific_journal-1326	163	25	(	(	PUNCT
american_scientific_journal-1326	163	26	1	1	NUM
american_scientific_journal-1326	163	27	-	-	PUNCT
american_scientific_journal-1326	163	28	a	a	NOUN
american_scientific_journal-1326	163	29	)	)	PUNCT
american_scientific_journal-1326	163	30	american	american	ADJ
american_scientific_journal-1326	163	31	scientific	scientific	ADJ
american_scientific_journal-1326	163	32	research	research	NOUN
american_scientific_journal-1326	163	33	journal	journal	NOUN
american_scientific_journal-1326	163	34	for	for	ADP
american_scientific_journal-1326	163	35	engineering	engineering	NOUN
american_scientific_journal-1326	163	36	,	,	PUNCT
american_scientific_journal-1326	163	37	technology	technology	NOUN
american_scientific_journal-1326	163	38	,	,	PUNCT
american_scientific_journal-1326	163	39	and	and	CCONJ
american_scientific_journal-1326	163	40	sciences	science	NOUN
american_scientific_journal-1326	163	41	(	(	PUNCT
american_scientific_journal-1326	163	42	asrjets	asrjet	NOUN
american_scientific_journal-1326	163	43	)	)	PUNCT
american_scientific_journal-1326	163	44	(	(	PUNCT
american_scientific_journal-1326	163	45	2017	2017	NUM
american_scientific_journal-1326	163	46	)	)	PUNCT
american_scientific_journal-1326	163	47	volume	volume	NOUN
american_scientific_journal-1326	163	48	27	27	NUM
american_scientific_journal-1326	163	49	,	,	PUNCT
american_scientific_journal-1326	163	50	no	no	DET
american_scientific_journal-1326	163	51	1	1	NUM
american_scientific_journal-1326	163	52	,	,	PUNCT
american_scientific_journal-1326	163	53	pp	pp	ADV
american_scientific_journal-1326	163	54	139	139	NUM
american_scientific_journal-1326	163	55	-	-	SYM
american_scientific_journal-1326	163	56	150	150	NUM
american_scientific_journal-1326	163	57	149	149	NUM
american_scientific_journal-1326	163	58	in	in	ADP
american_scientific_journal-1326	163	59	order	order	NOUN
american_scientific_journal-1326	163	60	to	to	PART
american_scientific_journal-1326	163	61	get	get	VERB
american_scientific_journal-1326	163	62	an	an	DET
american_scientific_journal-1326	163	63	estimation	estimation	NOUN
american_scientific_journal-1326	163	64	for	for	ADP
american_scientific_journal-1326	163	65	0	0	NUM
american_scientific_journal-1326	163	66	(	(	PUNCT
american_scientific_journal-1326	163	67	)	)	PUNCT
american_scientific_journal-1326	163	68	v	v	NOUN
american_scientific_journal-1326	163	69	r′	r′	NOUN
american_scientific_journal-1326	163	70	we	we	PRON
american_scientific_journal-1326	163	71	rewrite	rewrite	VERB
american_scientific_journal-1326	163	72	(	(	PUNCT
american_scientific_journal-1326	163	73	31	31	NUM
american_scientific_journal-1326	163	74	)	)	PUNCT
american_scientific_journal-1326	163	75	in	in	ADP
american_scientific_journal-1326	163	76	the	the	DET
american_scientific_journal-1326	163	77	following	follow	VERB
american_scientific_journal-1326	163	78	form	form	NOUN
american_scientific_journal-1326	163	79	2	2	NUM
american_scientific_journal-1326	163	80	(	(	PUNCT
american_scientific_journal-1326	163	81	)	)	PUNCT
american_scientific_journal-1326	163	82	v	v	NOUN
american_scientific_journal-1326	163	83	v	v	NOUN
american_scientific_journal-1326	163	84	r	r	NOUN
american_scientific_journal-1326	163	85	r	r	NOUN
american_scientific_journal-1326	163	86	′=	′=	NOUN
american_scientific_journal-1326	163	87	,	,	PUNCT
american_scientific_journal-1326	163	88	taking	take	VERB
american_scientific_journal-1326	163	89	as	as	ADP
american_scientific_journal-1326	163	90	a	a	DET
american_scientific_journal-1326	163	91	typical	typical	ADJ
american_scientific_journal-1326	163	92	values	value	NOUN
american_scientific_journal-1326	163	93	for	for	ADP
american_scientific_journal-1326	163	94	0	0	NUM
american_scientific_journal-1326	163	95	11000r	11000r	NUM
american_scientific_journal-1326	163	96	=	=	SYM
american_scientific_journal-1326	163	97	light	light	ADJ
american_scientific_journal-1326	163	98	years	year	NOUN
american_scientific_journal-1326	163	99	(	(	PUNCT
american_scientific_journal-1326	163	100	)	)	PUNCT
american_scientific_journal-1326	163	101	201.05	201.05	NUM
american_scientific_journal-1326	163	102	10	10	NUM
american_scientific_journal-1326	163	103	mts×	mts×	PROPN
american_scientific_journal-1326	163	104	and	and	CCONJ
american_scientific_journal-1326	163	105	54.6	54.6	NUM
american_scientific_journal-1326	163	106	10	10	NUM
american_scientific_journal-1326	163	107	/v	/v	SYM
american_scientific_journal-1326	164	1	m	m	PROPN
american_scientific_journal-1326	164	2	s=	s=	PROPN
american_scientific_journal-1326	164	3	×	×	NOUN
american_scientific_journal-1326	164	4	(	(	PUNCT
american_scientific_journal-1326	164	5	velocity	velocity	NOUN
american_scientific_journal-1326	164	6	at	at	ADP
american_scientific_journal-1326	164	7	the	the	DET
american_scientific_journal-1326	164	8	bulge	bulge	NOUN
american_scientific_journal-1326	164	9	's	's	PART
american_scientific_journal-1326	164	10	border	border	NOUN
american_scientific_journal-1326	164	11	)	)	PUNCT
american_scientific_journal-1326	164	12	,	,	PUNCT
american_scientific_journal-1326	164	13	we	we	PRON
american_scientific_journal-1326	164	14	obtain	obtain	VERB
american_scientific_journal-1326	164	15	9	9	NUM
american_scientific_journal-1326	164	16	0	0	NUM
american_scientific_journal-1326	164	17	(	(	PUNCT
american_scientific_journal-1326	164	18	)	)	PUNCT
american_scientific_journal-1326	164	19	2	2	NUM
american_scientific_journal-1326	164	20	10	10	NUM
american_scientific_journal-1326	164	21	/b	/b	SYM
american_scientific_journal-1326	164	22	v	v	NOUN
american_scientific_journal-1326	164	23	r	r	NOUN
american_scientific_journal-1326	164	24	j	j	PROPN
american_scientific_journal-1326	164	25	kg	kg	PROPN
american_scientific_journal-1326	164	26	m−′=	m−′=	PROPN
american_scientific_journal-1326	164	27	=	=	SYM
american_scientific_journal-1326	164	28	×	×	PROPN
american_scientific_journal-1326	164	29	⋅	⋅	X
american_scientific_journal-1326	164	30	(	(	PUNCT
american_scientific_journal-1326	164	31	2	2	NUM
american_scientific_journal-1326	164	32	-	-	PUNCT
american_scientific_journal-1326	164	33	a	a	NOUN
american_scientific_journal-1326	164	34	)	)	PUNCT
american_scientific_journal-1326	164	35	from	from	ADP
american_scientific_journal-1326	164	36	the	the	DET
american_scientific_journal-1326	164	37	above	above	ADP
american_scientific_journal-1326	164	38	11	11	NUM
american_scientific_journal-1326	164	39	0	0	NUM
american_scientific_journal-1326	164	40	2.1	2.1	NUM
american_scientific_journal-1326	164	41	10	10	NUM
american_scientific_journal-1326	164	42	/br	/br	PUNCT
american_scientific_journal-1326	165	1	j	j	PROPN
american_scientific_journal-1326	165	2	kg=	kg=	PROPN
american_scientific_journal-1326	165	3	×	×	PROPN
american_scientific_journal-1326	165	4	(	(	PUNCT
american_scientific_journal-1326	165	5	3	3	NUM
american_scientific_journal-1326	165	6	-	-	PUNCT
american_scientific_journal-1326	165	7	a	a	NOUN
american_scientific_journal-1326	165	8	)	)	PUNCT
american_scientific_journal-1326	165	9	on	on	ADP
american_scientific_journal-1326	165	10	the	the	DET
american_scientific_journal-1326	165	11	other	other	ADJ
american_scientific_journal-1326	165	12	hand	hand	NOUN
american_scientific_journal-1326	165	13	,	,	PUNCT
american_scientific_journal-1326	165	14	with	with	ADP
american_scientific_journal-1326	165	15	the	the	DET
american_scientific_journal-1326	165	16	purpose	purpose	NOUN
american_scientific_journal-1326	165	17	of	of	ADP
american_scientific_journal-1326	165	18	providing	provide	VERB
american_scientific_journal-1326	165	19	an	an	DET
american_scientific_journal-1326	165	20	estimation	estimation	NOUN
american_scientific_journal-1326	165	21	of	of	ADP
american_scientific_journal-1326	165	22	0v	0v	NOUN
american_scientific_journal-1326	165	23	,	,	PUNCT
american_scientific_journal-1326	165	24	we	we	PRON
american_scientific_journal-1326	165	25	assume	assume	VERB
american_scientific_journal-1326	165	26	a	a	DET
american_scientific_journal-1326	165	27	body	body	NOUN
american_scientific_journal-1326	165	28	of	of	ADP
american_scientific_journal-1326	165	29	mass	mass	NOUN
american_scientific_journal-1326	165	30	,	,	PUNCT
american_scientific_journal-1326	165	31	m	m	VERB
american_scientific_journal-1326	165	32	to	to	ADP
american_scientific_journal-1326	165	33	a	a	DET
american_scientific_journal-1326	165	34	distance	distance	NOUN
american_scientific_journal-1326	165	35	0r	0r	NUM
american_scientific_journal-1326	165	36	from	from	ADP
american_scientific_journal-1326	165	37	the	the	DET
american_scientific_journal-1326	165	38	center	center	NOUN
american_scientific_journal-1326	165	39	of	of	ADP
american_scientific_journal-1326	165	40	the	the	DET
american_scientific_journal-1326	165	41	galaxy	galaxy	NOUN
american_scientific_journal-1326	165	42	.	.	PUNCT
american_scientific_journal-1326	166	1	from	from	ADP
american_scientific_journal-1326	166	2	newton	newton	PROPN
american_scientific_journal-1326	166	3	second	second	PROPN
american_scientific_journal-1326	166	4	law	law	NOUN
american_scientific_journal-1326	166	5	,	,	PUNCT
american_scientific_journal-1326	166	6	we	we	PRON
american_scientific_journal-1326	166	7	get	get	VERB
american_scientific_journal-1326	166	8	2	2	NUM
american_scientific_journal-1326	166	9	2	2	NUM
american_scientific_journal-1326	166	10	0	0	NUM
american_scientific_journal-1326	166	11	0	0	NUM
american_scientific_journal-1326	166	12	mv	mv	PROPN
american_scientific_journal-1326	166	13	gmm	gmm	PROPN
american_scientific_journal-1326	166	14	r	r	NOUN
american_scientific_journal-1326	166	15	r	r	NOUN
american_scientific_journal-1326	166	16	=	=	PUNCT
american_scientific_journal-1326	166	17	,	,	PUNCT
american_scientific_journal-1326	166	18	or	or	CCONJ
american_scientific_journal-1326	166	19	2	2	NUM
american_scientific_journal-1326	166	20	0	0	NUM
american_scientific_journal-1326	166	21	,	,	PUNCT
american_scientific_journal-1326	166	22	gmv	gmv	VERB
american_scientific_journal-1326	166	23	r	r	NOUN
american_scientific_journal-1326	166	24	=	=	NOUN
american_scientific_journal-1326	166	25	that	that	PRON
american_scientific_journal-1326	166	26	is	be	AUX
american_scientific_journal-1326	166	27	11	11	NUM
american_scientific_journal-1326	166	28	0	0	NUM
american_scientific_journal-1326	166	29	0	0	NUM
american_scientific_journal-1326	166	30	(	(	PUNCT
american_scientific_journal-1326	166	31	)	)	PUNCT
american_scientific_journal-1326	166	32	2.1	2.1	NUM
american_scientific_journal-1326	166	33	10	10	NUM
american_scientific_journal-1326	166	34	/	/	SYM
american_scientific_journal-1326	166	35	.v	.v	NOUN
american_scientific_journal-1326	167	1	v	v	ADP
american_scientific_journal-1326	167	2	r	r	NOUN
american_scientific_journal-1326	167	3	j	j	PROPN
american_scientific_journal-1326	167	4	kg=	kg=	PROPN
american_scientific_journal-1326	167	5	=	=	SYM
american_scientific_journal-1326	167	6	×	×	PROPN
american_scientific_journal-1326	167	7	(	(	PUNCT
american_scientific_journal-1326	167	8	4	4	NUM
american_scientific_journal-1326	167	9	-	-	PUNCT
american_scientific_journal-1326	167	10	a	a	NOUN
american_scientific_journal-1326	167	11	)	)	PUNCT
american_scientific_journal-1326	167	12	finally	finally	ADV
american_scientific_journal-1326	167	13	,	,	PUNCT
american_scientific_journal-1326	167	14	as	as	ADP
american_scientific_journal-1326	167	15	a	a	DET
american_scientific_journal-1326	167	16	illustrative	illustrative	ADJ
american_scientific_journal-1326	167	17	example	example	NOUN
american_scientific_journal-1326	167	18	,	,	PUNCT
american_scientific_journal-1326	167	19	we	we	PRON
american_scientific_journal-1326	167	20	consider	consider	VERB
american_scientific_journal-1326	167	21	1β	1β	NUM
american_scientific_journal-1326	167	22	=	=	SYM
american_scientific_journal-1326	167	23	(	(	PUNCT
american_scientific_journal-1326	167	24	5	5	NUM
american_scientific_journal-1326	167	25	-	-	PUNCT
american_scientific_journal-1326	167	26	a	a	NOUN
american_scientific_journal-1326	167	27	)	)	PUNCT
american_scientific_journal-1326	167	28	thus	thus	ADV
american_scientific_journal-1326	167	29	,	,	PUNCT
american_scientific_journal-1326	167	30	by	by	ADP
american_scientific_journal-1326	167	31	substituting	substitute	VERB
american_scientific_journal-1326	167	32	(	(	PUNCT
american_scientific_journal-1326	167	33	1	1	NUM
american_scientific_journal-1326	167	34	-	-	PUNCT
american_scientific_journal-1326	167	35	a	a	NOUN
american_scientific_journal-1326	167	36	)	)	PUNCT
american_scientific_journal-1326	167	37	–	–	PUNCT
american_scientific_journal-1326	167	38	(	(	PUNCT
american_scientific_journal-1326	167	39	5	5	NUM
american_scientific_journal-1326	167	40	-	-	PUNCT
american_scientific_journal-1326	167	41	a	a	NOUN
american_scientific_journal-1326	167	42	)	)	PUNCT
american_scientific_journal-1326	167	43	into	into	ADP
american_scientific_journal-1326	167	44	(	(	PUNCT
american_scientific_journal-1326	167	45	29	29	NUM
american_scientific_journal-1326	167	46	)	)	PUNCT
american_scientific_journal-1326	167	47	we	we	PRON
american_scientific_journal-1326	167	48	get	get	VERB
american_scientific_journal-1326	167	49	a	a	DET
american_scientific_journal-1326	167	50	first	first	ADJ
american_scientific_journal-1326	167	51	order	order	NOUN
american_scientific_journal-1326	167	52	approximation	approximation	NOUN
american_scientific_journal-1326	167	53	for	for	ADP
american_scientific_journal-1326	167	54	the	the	DET
american_scientific_journal-1326	167	55	solution	solution	NOUN
american_scientific_journal-1326	167	56	of	of	ADP
american_scientific_journal-1326	167	57	(	(	PUNCT
american_scientific_journal-1326	167	58	13	13	NUM
american_scientific_journal-1326	167	59	)	)	PUNCT
american_scientific_journal-1326	167	60	,	,	PUNCT
american_scientific_journal-1326	167	61	valid	valid	ADJ
american_scientific_journal-1326	167	62	for	for	ADP
american_scientific_journal-1326	167	63	the	the	DET
american_scientific_journal-1326	167	64	above	above	ADJ
american_scientific_journal-1326	167	65	values	value	NOUN
american_scientific_journal-1326	167	66	.	.	PUNCT
american_scientific_journal-1326	168	1	acknowledgements	acknowledgement	NOUN
american_scientific_journal-1326	168	2	we	we	PRON
american_scientific_journal-1326	168	3	gratefully	gratefully	ADV
american_scientific_journal-1326	168	4	acknowledge	acknowledge	VERB
american_scientific_journal-1326	168	5	the	the	DET
american_scientific_journal-1326	168	6	financial	financial	ADJ
american_scientific_journal-1326	168	7	support	support	NOUN
american_scientific_journal-1326	168	8	from	from	ADP
american_scientific_journal-1326	168	9	the	the	DET
american_scientific_journal-1326	168	10	national	national	PROPN
american_scientific_journal-1326	168	11	council	council	PROPN
american_scientific_journal-1326	168	12	for	for	ADP
american_scientific_journal-1326	168	13	science	science	NOUN
american_scientific_journal-1326	168	14	and	and	CCONJ
american_scientific_journal-1326	168	15	technology	technology	NOUN
american_scientific_journal-1326	168	16	of	of	ADP
american_scientific_journal-1326	168	17	american	american	ADJ
american_scientific_journal-1326	168	18	scientific	scientific	ADJ
american_scientific_journal-1326	168	19	research	research	NOUN
american_scientific_journal-1326	168	20	journal	journal	NOUN
american_scientific_journal-1326	168	21	for	for	ADP
american_scientific_journal-1326	168	22	engineering	engineering	NOUN
american_scientific_journal-1326	168	23	,	,	PUNCT
american_scientific_journal-1326	168	24	technology	technology	NOUN
american_scientific_journal-1326	168	25	,	,	PUNCT
american_scientific_journal-1326	168	26	and	and	CCONJ
american_scientific_journal-1326	168	27	sciences	science	NOUN
american_scientific_journal-1326	168	28	(	(	PUNCT
american_scientific_journal-1326	168	29	asrjets	asrjet	NOUN
american_scientific_journal-1326	168	30	)	)	PUNCT
american_scientific_journal-1326	168	31	(	(	PUNCT
american_scientific_journal-1326	168	32	2017	2017	NUM
american_scientific_journal-1326	168	33	)	)	PUNCT
american_scientific_journal-1326	168	34	volume	volume	NOUN
american_scientific_journal-1326	168	35	27	27	NUM
american_scientific_journal-1326	168	36	,	,	PUNCT
american_scientific_journal-1326	168	37	no	no	DET
american_scientific_journal-1326	168	38	1	1	NUM
american_scientific_journal-1326	168	39	,	,	PUNCT
american_scientific_journal-1326	168	40	pp	pp	ADV
american_scientific_journal-1326	168	41	139	139	NUM
american_scientific_journal-1326	168	42	-	-	SYM
american_scientific_journal-1326	168	43	150	150	NUM
american_scientific_journal-1326	168	44	150	150	NUM
american_scientific_journal-1326	168	45	mexico	mexico	NOUN
american_scientific_journal-1326	168	46	(	(	PUNCT
american_scientific_journal-1326	168	47	conacyt	conacyt	ADV
american_scientific_journal-1326	168	48	)	)	PUNCT
american_scientific_journal-1326	168	49	through	through	ADP
american_scientific_journal-1326	168	50	grant	grant	PROPN
american_scientific_journal-1326	168	51	cb-2010	cb-2010	PROPN
american_scientific_journal-1326	168	52	-	-	PUNCT
american_scientific_journal-1326	168	53	01	01	NUM
american_scientific_journal-1326	168	54	#	#	SYM
american_scientific_journal-1326	168	55	157024	157024	NUM
american_scientific_journal-1326	168	56	.	.	PUNCT
american_scientific_journal-1326	169	1	references	reference	NOUN
american_scientific_journal-1326	169	2	[	[	X
american_scientific_journal-1326	169	3	1	1	NUM
american_scientific_journal-1326	169	4	]	]	PUNCT
american_scientific_journal-1326	169	5	c.	c.	PROPN
american_scientific_journal-1326	169	6	a.	a.	PROPN
american_scientific_journal-1326	169	7	m.	m.	PROPN
american_scientific_journal-1326	169	8	de	de	PROPN
american_scientific_journal-1326	169	9	melo	melo	PROPN
american_scientific_journal-1326	169	10	and	and	CCONJ
american_scientific_journal-1326	169	11	s.	s.	PROPN
american_scientific_journal-1326	169	12	t.	t.	PROPN
american_scientific_journal-1326	169	13	“	"	PUNCT
american_scientific_journal-1326	169	14	resende	resende	PROPN
american_scientific_journal-1326	169	15	.	.	PUNCT
american_scientific_journal-1326	170	1	galactic	galactic	ADJ
american_scientific_journal-1326	170	2	nonlinear	nonlinear	PROPN
american_scientific_journal-1326	170	3	dynamical	dynamical	ADJ
american_scientific_journal-1326	170	4	model	model	NOUN
american_scientific_journal-1326	170	5	.	.	PUNCT
american_scientific_journal-1326	170	6	”	"	PUNCT
american_scientific_journal-1326	171	1	international	international	ADJ
american_scientific_journal-1326	171	2	journal	journal	NOUN
american_scientific_journal-1326	171	3	of	of	ADP
american_scientific_journal-1326	171	4	modern	modern	ADJ
american_scientific_journal-1326	171	5	physics	physics	PROPN
american_scientific_journal-1326	171	6	a.	a.	PROPN
american_scientific_journal-1326	171	7	world	world	PROPN
american_scientific_journal-1326	171	8	scientific	scientific	ADJ
american_scientific_journal-1326	171	9	,	,	PUNCT
american_scientific_journal-1326	171	10	2009	2009	NUM
american_scientific_journal-1326	171	11	,	,	PUNCT
american_scientific_journal-1326	171	12	[	[	X
american_scientific_journal-1326	171	13	2	2	NUM
american_scientific_journal-1326	171	14	]	]	PUNCT
american_scientific_journal-1326	171	15	almudena	almudena	PROPN
american_scientific_journal-1326	171	16	zurita	zurita	PROPN
american_scientific_journal-1326	171	17	muñoz	muñoz	PROPN
american_scientific_journal-1326	171	18	.	.	PUNCT
american_scientific_journal-1326	172	1	“	"	PUNCT
american_scientific_journal-1326	172	2	curso	curso	PROPN
american_scientific_journal-1326	172	3	cosmología	cosmología	PROPN
american_scientific_journal-1326	172	4	.	.	PUNCT
american_scientific_journal-1326	173	1	curvas	curvas	PROPN
american_scientific_journal-1326	173	2	de	de	PROPN
american_scientific_journal-1326	173	3	rotación	rotación	PROPN
american_scientific_journal-1326	173	4	y	y	PROPN
american_scientific_journal-1326	173	5	materia	materia	PROPN
american_scientific_journal-1326	173	6	oscura	oscura	PROPN
american_scientific_journal-1326	173	7	en	en	PROPN
american_scientific_journal-1326	173	8	galaxias	galaxias	PROPN
american_scientific_journal-1326	173	9	espirales	espirale	NOUN
american_scientific_journal-1326	173	10	.	.	PUNCT
american_scientific_journal-1326	173	11	”	"	PUNCT
american_scientific_journal-1326	174	1	internet	internet	NOUN
american_scientific_journal-1326	174	2	:	:	PUNCT
american_scientific_journal-1326	174	3	http://www.ugr.es/~azurita/docencia/material_docente/cosmologia/cr_dm_clase_06.pdf	http://www.ugr.es/~azurita/docencia/material_docente/cosmologia/cr_dm_clase_06.pdf	NOUN
american_scientific_journal-1326	174	4	,	,	PUNCT
american_scientific_journal-1326	174	5	2007	2007	NUM
american_scientific_journal-1326	174	6	[	[	X
american_scientific_journal-1326	174	7	sep	sep	PROPN
american_scientific_journal-1326	174	8	.	.	PROPN
american_scientific_journal-1326	174	9	2015	2015	NUM
american_scientific_journal-1326	174	10	]	]	PUNCT
american_scientific_journal-1326	175	1	[	[	X
american_scientific_journal-1326	175	2	3	3	NUM
american_scientific_journal-1326	175	3	]	]	X
american_scientific_journal-1326	175	4	t.l	t.l	X
american_scientific_journal-1326	175	5	.	.	NOUN
american_scientific_journal-1326	175	6	chow	chow	PROPN
american_scientific_journal-1326	175	7	.	.	PUNCT
american_scientific_journal-1326	176	1	classical	classical	ADJ
american_scientific_journal-1326	176	2	mechanics	mechanic	NOUN
american_scientific_journal-1326	176	3	.	.	PUNCT
american_scientific_journal-1326	177	1	usa	usa	PROPN
american_scientific_journal-1326	177	2	:	:	PUNCT
american_scientific_journal-1326	177	3	john	john	PROPN
american_scientific_journal-1326	177	4	wiley	wiley	PROPN
american_scientific_journal-1326	177	5	and	and	CCONJ
american_scientific_journal-1326	177	6	sons	sons	PROPN
american_scientific_journal-1326	177	7	inc	inc	PROPN
american_scientific_journal-1326	177	8	.	.	PROPN
american_scientific_journal-1326	177	9	,	,	PUNCT
american_scientific_journal-1326	177	10	1995	1995	NUM
american_scientific_journal-1326	177	11	.	.	PUNCT
american_scientific_journal-1326	178	1	[	[	X
american_scientific_journal-1326	178	2	4	4	X
american_scientific_journal-1326	178	3	]	]	X
american_scientific_journal-1326	178	4	m.h	m.h	PROPN
american_scientific_journal-1326	178	5	.	.	PROPN
american_scientific_journal-1326	178	6	holmes	holmes	PROPN
american_scientific_journal-1326	178	7	.	.	PUNCT
american_scientific_journal-1326	179	1	introduction	introduction	NOUN
american_scientific_journal-1326	179	2	to	to	ADP
american_scientific_journal-1326	179	3	perturbation	perturbation	NOUN
american_scientific_journal-1326	179	4	methods	method	NOUN
american_scientific_journal-1326	179	5	.	.	PUNCT
american_scientific_journal-1326	180	1	new	new	PROPN
american_scientific_journal-1326	180	2	york	york	PROPN
american_scientific_journal-1326	180	3	:	:	PUNCT
american_scientific_journal-1326	180	4	springer	springer	NOUN
american_scientific_journal-1326	180	5	-	-	PUNCT
american_scientific_journal-1326	180	6	verlag	verlag	PROPN
american_scientific_journal-1326	180	7	,	,	PUNCT
american_scientific_journal-1326	180	8	1995	1995	NUM
american_scientific_journal-1326	180	9	.	.	PUNCT
american_scientific_journal-1326	181	1	[	[	X
american_scientific_journal-1326	181	2	5	5	X
american_scientific_journal-1326	181	3	]	]	X
american_scientific_journal-1326	181	4	u.	u.	NOUN
american_scientific_journal-1326	181	5	filobello	filobello	PROPN
american_scientific_journal-1326	181	6	-	-	PUNCT
american_scientific_journal-1326	181	7	niño	niño	PROPN
american_scientific_journal-1326	181	8	,	,	PUNCT
american_scientific_journal-1326	181	9	h.	h.	PROPN
american_scientific_journal-1326	181	10	vazquez	vazquez	PROPN
american_scientific_journal-1326	181	11	-	-	PUNCT
american_scientific_journal-1326	181	12	leal	leal	PROPN
american_scientific_journal-1326	181	13	,	,	PUNCT
american_scientific_journal-1326	181	14	y.	y.	PROPN
american_scientific_journal-1326	181	15	khan	khan	PROPN
american_scientific_journal-1326	181	16	,	,	PUNCT
american_scientific_journal-1326	181	17	a.	a.	PROPN
american_scientific_journal-1326	181	18	yildirim	yildirim	PROPN
american_scientific_journal-1326	181	19	,	,	PUNCT
american_scientific_journal-1326	181	20	v.m	v.m	PROPN
american_scientific_journal-1326	181	21	.	.	PROPN
american_scientific_journal-1326	181	22	jimenez	jimenez	PROPN
american_scientific_journal-1326	181	23	-	-	PUNCT
american_scientific_journal-1326	181	24	fernandez	fernandez	PROPN
american_scientific_journal-1326	181	25	,	,	PUNCT
american_scientific_journal-1326	181	26	a.	a.	NOUN
american_scientific_journal-1326	181	27	l	l	PROPN
american_scientific_journal-1326	181	28	herreramay	herreramay	PROPN
american_scientific_journal-1326	181	29	,	,	PUNCT
american_scientific_journal-1326	181	30	r.	r.	PROPN
american_scientific_journal-1326	181	31	castañeda	castañeda	PROPN
american_scientific_journal-1326	181	32	-	-	PUNCT
american_scientific_journal-1326	181	33	sheissa	sheissa	ADJ
american_scientific_journal-1326	181	34	,	,	PUNCT
american_scientific_journal-1326	181	35	and	and	CCONJ
american_scientific_journal-1326	181	36	j.	j.	PROPN
american_scientific_journal-1326	181	37	cervantes	cervantes	PROPN
american_scientific_journal-1326	181	38	-	-	PUNCT
american_scientific_journal-1326	181	39	perez	perez	PROPN
american_scientific_journal-1326	181	40	.	.	PUNCT
american_scientific_journal-1326	182	1	“	"	PUNCT
american_scientific_journal-1326	182	2	using	use	VERB
american_scientific_journal-1326	182	3	perturbation	perturbation	NOUN
american_scientific_journal-1326	182	4	method	method	NOUN
american_scientific_journal-1326	182	5	and	and	CCONJ
american_scientific_journal-1326	182	6	laplace	laplace	NOUN
american_scientific_journal-1326	182	7	-	-	PUNCT
american_scientific_journal-1326	182	8	padé	padé	NOUN
american_scientific_journal-1326	182	9	approximation	approximation	NOUN
american_scientific_journal-1326	182	10	to	to	PART
american_scientific_journal-1326	182	11	solve	solve	VERB
american_scientific_journal-1326	182	12	nonlinear	nonlinear	ADJ
american_scientific_journal-1326	182	13	problems	problem	NOUN
american_scientific_journal-1326	182	14	.	.	PUNCT
american_scientific_journal-1326	182	15	”	"	PUNCT
american_scientific_journal-1326	183	1	miskolc	miskolc	ADJ
american_scientific_journal-1326	183	2	mathematical	mathematical	ADJ
american_scientific_journal-1326	183	3	notes	note	NOUN
american_scientific_journal-1326	183	4	,	,	PUNCT
american_scientific_journal-1326	183	5	vol	vol	NOUN
american_scientific_journal-1326	183	6	.	.	PUNCT
american_scientific_journal-1326	183	7	14(1	14(1	NUM
american_scientific_journal-1326	183	8	)	)	PUNCT
american_scientific_journal-1326	183	9	,	,	PUNCT
american_scientific_journal-1326	183	10	pp	pp	PROPN
american_scientific_journal-1326	183	11	.	.	PUNCT
american_scientific_journal-1326	183	12	89	89	NUM
american_scientific_journal-1326	183	13	-	-	SYM
american_scientific_journal-1326	183	14	101	101	NUM
american_scientific_journal-1326	183	15	,	,	PUNCT
american_scientific_journal-1326	183	16	2013	2013	NUM
american_scientific_journal-1326	183	17	.	.	PUNCT
american_scientific_journal-1326	184	1	issn	issn	PROPN
american_scientific_journal-1326	184	2	:	:	PUNCT
american_scientific_journal-1326	184	3	1787	1787	NUM
american_scientific_journal-1326	184	4	-	-	SYM
american_scientific_journal-1326	184	5	2405	2405	NUM
american_scientific_journal-1326	184	6	,	,	PUNCT
american_scientific_journal-1326	184	7	[	[	X
american_scientific_journal-1326	184	8	6	6	NUM
american_scientific_journal-1326	184	9	]	]	X
american_scientific_journal-1326	184	10	u.	u.	NOUN
american_scientific_journal-1326	184	11	filobello	filobello	PROPN
american_scientific_journal-1326	184	12	-	-	PUNCT
american_scientific_journal-1326	184	13	niño	niño	PROPN
american_scientific_journal-1326	184	14	,	,	PUNCT
american_scientific_journal-1326	184	15	h.	h.	PROPN
american_scientific_journal-1326	184	16	vazquez	vazquez	PROPN
american_scientific_journal-1326	184	17	-	-	PUNCT
american_scientific_journal-1326	184	18	leal	leal	PROPN
american_scientific_journal-1326	184	19	,	,	PUNCT
american_scientific_journal-1326	184	20	k.	k.	PROPN
american_scientific_journal-1326	184	21	boubaker	boubaker	PROPN
american_scientific_journal-1326	184	22	,	,	PUNCT
american_scientific_journal-1326	184	23	y.	y.	PROPN
american_scientific_journal-1326	184	24	khan	khan	PROPN
american_scientific_journal-1326	184	25	,	,	PUNCT
american_scientific_journal-1326	184	26	a.	a.	PROPN
american_scientific_journal-1326	184	27	perez	perez	PROPN
american_scientific_journal-1326	184	28	-	-	PUNCT
american_scientific_journal-1326	184	29	sesma	sesma	PROPN
american_scientific_journal-1326	184	30	,	,	PUNCT
american_scientific_journal-1326	184	31	a.	a.	PROPN
american_scientific_journal-1326	184	32	sarmiento	sarmiento	PROPN
american_scientific_journal-1326	184	33	reyes	reyes	PROPN
american_scientific_journal-1326	184	34	,	,	PUNCT
american_scientific_journal-1326	184	35	v.m	v.m	PROPN
american_scientific_journal-1326	184	36	.	.	PROPN
american_scientific_journal-1326	184	37	jimenez	jimenez	PROPN
american_scientific_journal-1326	184	38	-	-	PUNCT
american_scientific_journal-1326	184	39	fernandez	fernandez	PROPN
american_scientific_journal-1326	184	40	,	,	PUNCT
american_scientific_journal-1326	184	41	a	a	DET
american_scientific_journal-1326	184	42	diaz	diaz	PROPN
american_scientific_journal-1326	184	43	-	-	PUNCT
american_scientific_journal-1326	184	44	sanchez	sanchez	PROPN
american_scientific_journal-1326	184	45	,	,	PUNCT
american_scientific_journal-1326	184	46	a.	a.	PROPN
american_scientific_journal-1326	184	47	herrera	herrera	PROPN
american_scientific_journal-1326	184	48	-	-	PUNCT
american_scientific_journal-1326	184	49	may	may	PROPN
american_scientific_journal-1326	184	50	,	,	PUNCT
american_scientific_journal-1326	184	51	j.	j.	PROPN
american_scientific_journal-1326	184	52	sanchez	sanchez	PROPN
american_scientific_journal-1326	184	53	-	-	PUNCT
american_scientific_journal-1326	184	54	orea	orea	PROPN
american_scientific_journal-1326	184	55	and	and	CCONJ
american_scientific_journal-1326	184	56	k.	k.	PROPN
american_scientific_journal-1326	184	57	pereyra	pereyra	PROPN
american_scientific_journal-1326	184	58	-	-	PUNCT
american_scientific_journal-1326	184	59	castro	castro	PROPN
american_scientific_journal-1326	184	60	.	.	PUNCT
american_scientific_journal-1326	185	1	“	"	PUNCT
american_scientific_journal-1326	185	2	perturbation	perturbation	NOUN
american_scientific_journal-1326	185	3	method	method	NOUN
american_scientific_journal-1326	185	4	as	as	ADP
american_scientific_journal-1326	185	5	a	a	DET
american_scientific_journal-1326	185	6	powerful	powerful	ADJ
american_scientific_journal-1326	185	7	tool	tool	NOUN
american_scientific_journal-1326	185	8	to	to	PART
american_scientific_journal-1326	185	9	solve	solve	VERB
american_scientific_journal-1326	185	10	highly	highly	ADV
american_scientific_journal-1326	185	11	nonlinear	nonlinear	ADJ
american_scientific_journal-1326	185	12	problems	problem	NOUN
american_scientific_journal-1326	185	13	:	:	PUNCT
american_scientific_journal-1326	185	14	the	the	DET
american_scientific_journal-1326	185	15	case	case	NOUN
american_scientific_journal-1326	185	16	of	of	ADP
american_scientific_journal-1326	185	17	gelfand	gelfand	PROPN
american_scientific_journal-1326	185	18	,	,	PUNCT
american_scientific_journal-1326	185	19	s	s	PART
american_scientific_journal-1326	185	20	equation	equation	NOUN
american_scientific_journal-1326	185	21	.	.	PUNCT
american_scientific_journal-1326	185	22	”	"	PUNCT
american_scientific_journal-1326	186	1	asian	asian	ADJ
american_scientific_journal-1326	186	2	journal	journal	NOUN
american_scientific_journal-1326	186	3	of	of	ADP
american_scientific_journal-1326	186	4	mathematics	mathematic	NOUN
american_scientific_journal-1326	186	5	and	and	CCONJ
american_scientific_journal-1326	186	6	statistics	statistic	NOUN
american_scientific_journal-1326	186	7	,	,	PUNCT
american_scientific_journal-1326	186	8	vol	vol	NOUN
american_scientific_journal-1326	186	9	.	.	PROPN
american_scientific_journal-1326	186	10	2013	2013	NUM
american_scientific_journal-1326	186	11	,	,	PUNCT
american_scientific_journal-1326	186	12	pp	pp	ADJ
american_scientific_journal-1326	186	13	.	.	PUNCT
american_scientific_journal-1326	187	1	7	7	NUM
american_scientific_journal-1326	187	2	,	,	PUNCT
american_scientific_journal-1326	187	3	2013	2013	NUM
american_scientific_journal-1326	187	4	.	.	PUNCT
american_scientific_journal-1326	188	1	doi	doi	NOUN
american_scientific_journal-1326	188	2	:	:	PUNCT
american_scientific_journal-1326	188	3	10.3923	10.3923	NUM
american_scientific_journal-1326	188	4	/ajms.2013	/ajms.2013	NUM
american_scientific_journal-1326	188	5	,	,	PUNCT
american_scientific_journal-1326	188	6	issn	issn	PROPN
american_scientific_journal-1326	188	7	1994	1994	NUM
american_scientific_journal-1326	188	8	-	-	SYM
american_scientific_journal-1326	188	9	5418	5418	NUM
american_scientific_journal-1326	188	10	,	,	PUNCT
american_scientific_journal-1326	188	11	2013	2013	NUM
american_scientific_journal-1326	188	12	.	.	PUNCT
american_scientific_journal-1326	189	1	[	[	X
american_scientific_journal-1326	189	2	7	7	X
american_scientific_journal-1326	189	3	]	]	X
american_scientific_journal-1326	189	4	r.	r.	PROPN
american_scientific_journal-1326	189	5	resnick	resnick	PROPN
american_scientific_journal-1326	189	6	and	and	CCONJ
american_scientific_journal-1326	189	7	d.	d.	PROPN
american_scientific_journal-1326	189	8	halliday	halliday	PROPN
american_scientific_journal-1326	189	9	.	.	PUNCT
american_scientific_journal-1326	190	1	física	física	PROPN
american_scientific_journal-1326	190	2	vol	vol	NOUN
american_scientific_journal-1326	190	3	.	.	PROPN
american_scientific_journal-1326	190	4	1	1	NUM
american_scientific_journal-1326	190	5	,	,	PUNCT
american_scientific_journal-1326	190	6	usa	usa	PROPN
american_scientific_journal-1326	190	7	:	:	PUNCT
american_scientific_journal-1326	190	8	john	john	PROPN
american_scientific_journal-1326	190	9	wiley	wiley	PROPN
american_scientific_journal-1326	190	10	and	and	CCONJ
american_scientific_journal-1326	190	11	sons	son	NOUN
american_scientific_journal-1326	190	12	,	,	PUNCT
american_scientific_journal-1326	190	13	1977	1977	NUM
american_scientific_journal-1326	190	14	.	.	PUNCT
american_scientific_journal-1326	191	1	[	[	X
american_scientific_journal-1326	191	2	8	8	NUM
american_scientific_journal-1326	191	3	]	]	X
american_scientific_journal-1326	191	4	f.	f.	PROPN
american_scientific_journal-1326	191	5	mandl	mandl	PROPN
american_scientific_journal-1326	191	6	.	.	PUNCT
american_scientific_journal-1326	192	1	física	física	PROPN
american_scientific_journal-1326	192	2	estadística	estadística	PROPN
american_scientific_journal-1326	192	3	.	.	PUNCT
american_scientific_journal-1326	193	1	méxico	méxico	PROPN
american_scientific_journal-1326	193	2	:	:	PUNCT
american_scientific_journal-1326	193	3	editorial	editorial	NOUN
american_scientific_journal-1326	193	4	limusa	limusa	NOUN
american_scientific_journal-1326	193	5	,	,	PUNCT
american_scientific_journal-1326	193	6	s.a	s.a	PROPN
american_scientific_journal-1326	193	7	,	,	PUNCT
american_scientific_journal-1326	193	8	1979	1979	NUM
american_scientific_journal-1326	193	9	.	.	PUNCT
american_scientific_journal-1326	194	1	[	[	X
american_scientific_journal-1326	194	2	9	9	NUM
american_scientific_journal-1326	194	3	]	]	PUNCT
american_scientific_journal-1326	194	4	dennis	dennis	PROPN
american_scientific_journal-1326	194	5	zill	zill	PROPN
american_scientific_journal-1326	194	6	.	.	PUNCT
american_scientific_journal-1326	195	1	a	a	DET
american_scientific_journal-1326	195	2	first	first	ADJ
american_scientific_journal-1326	195	3	course	course	NOUN
american_scientific_journal-1326	195	4	in	in	ADP
american_scientific_journal-1326	195	5	differential	differential	ADJ
american_scientific_journal-1326	195	6	equations	equation	NOUN
american_scientific_journal-1326	195	7	with	with	ADP
american_scientific_journal-1326	195	8	modeling	modeling	NOUN
american_scientific_journal-1326	195	9	applications	application	NOUN
american_scientific_journal-1326	195	10	,	,	PUNCT
american_scientific_journal-1326	195	11	usa	usa	PROPN
american_scientific_journal-1326	195	12	:	:	PUNCT
american_scientific_journal-1326	195	13	brooks	brooks	PROPN
american_scientific_journal-1326	195	14	/cole	/cole	PROPN
american_scientific_journal-1326	195	15	cengage	cengage	PROPN
american_scientific_journal-1326	195	16	learning	learning	PROPN
american_scientific_journal-1326	195	17	,	,	PUNCT
american_scientific_journal-1326	195	18	10th	10th	ADJ
american_scientific_journal-1326	195	19	edition	edition	NOUN
american_scientific_journal-1326	195	20	,	,	PUNCT
american_scientific_journal-1326	195	21	2012	2012	NUM
american_scientific_journal-1326	195	22	[	[	X
american_scientific_journal-1326	195	23	10	10	NUM
american_scientific_journal-1326	195	24	]	]	X
american_scientific_journal-1326	195	25	w.	w.	PROPN
american_scientific_journal-1326	195	26	enright	enright	PROPN
american_scientific_journal-1326	195	27	,	,	PUNCT
american_scientific_journal-1326	195	28	k.	k.	PROPN
american_scientific_journal-1326	195	29	jackson	jackson	PROPN
american_scientific_journal-1326	195	30	,	,	PUNCT
american_scientific_journal-1326	195	31	s.a	s.a	PROPN
american_scientific_journal-1326	195	32	.	.	PROPN
american_scientific_journal-1326	195	33	norsett	norsett	PROPN
american_scientific_journal-1326	195	34	,	,	PUNCT
american_scientific_journal-1326	195	35	p.	p.	PROPN
american_scientific_journal-1326	195	36	thomsen	thomsen	PROPN
american_scientific_journal-1326	195	37	.	.	PUNCT
american_scientific_journal-1326	196	1	“	"	PUNCT
american_scientific_journal-1326	196	2	interpolants	interpolant	NOUN
american_scientific_journal-1326	196	3	for	for	ADP
american_scientific_journal-1326	196	4	runge	runge	NOUN
american_scientific_journal-1326	196	5	–	–	PUNCT
american_scientific_journal-1326	196	6	kutta	kutta	NOUN
american_scientific_journal-1326	196	7	formulas	formula	NOUN
american_scientific_journal-1326	196	8	.	.	PUNCT
american_scientific_journal-1326	196	9	”	"	PUNCT
american_scientific_journal-1326	197	1	acm	acm	PROPN
american_scientific_journal-1326	197	2	transactions	transaction	NOUN
american_scientific_journal-1326	197	3	on	on	ADP
american_scientific_journal-1326	197	4	mathematical	mathematical	ADJ
american_scientific_journal-1326	197	5	software	software	NOUN
american_scientific_journal-1326	197	6	(	(	PUNCT
american_scientific_journal-1326	197	7	toms	tom	NOUN
american_scientific_journal-1326	197	8	)	)	PUNCT
american_scientific_journal-1326	197	9	,	,	PUNCT
american_scientific_journal-1326	197	10	vol	vol	NOUN
american_scientific_journal-1326	197	11	.	.	PUNCT
american_scientific_journal-1326	197	12	12(3	12(3	NUM
american_scientific_journal-1326	197	13	)	)	PUNCT
american_scientific_journal-1326	198	1	pp	pp	ADP
american_scientific_journal-1326	198	2	.	.	PUNCT
american_scientific_journal-1326	199	1	193	193	NUM
american_scientific_journal-1326	199	2	-	-	SYM
american_scientific_journal-1326	199	3	218	218	NUM
american_scientific_journal-1326	199	4	,	,	PUNCT
american_scientific_journal-1326	199	5	1986	1986	NUM
american_scientific_journal-1326	199	6	.	.	PUNCT
american_scientific_journal-1326	200	1	[	[	X
american_scientific_journal-1326	200	2	11	11	NUM
american_scientific_journal-1326	200	3	]	]	PUNCT
american_scientific_journal-1326	200	4	e.	e.	PROPN
american_scientific_journal-1326	200	5	fehlberg	fehlberg	PROPN
american_scientific_journal-1326	200	6	.	.	PUNCT
american_scientific_journal-1326	201	1	“	"	PUNCT
american_scientific_journal-1326	201	2	klassische	klassische	NOUN
american_scientific_journal-1326	201	3	runge	runge	NOUN
american_scientific_journal-1326	201	4	–	–	PUNCT
american_scientific_journal-1326	201	5	kutta	kutta	NOUN
american_scientific_journal-1326	201	6	–	–	PUNCT
american_scientific_journal-1326	201	7	formeln	formeln	NOUN
american_scientific_journal-1326	201	8	vierter	vierter	ADV
american_scientific_journal-1326	201	9	und	und	VERB
american_scientific_journal-1326	201	10	niedrigerer	niedrigerer	NOUN
american_scientific_journal-1326	201	11	ordnung	ordnung	ADJ
american_scientific_journal-1326	201	12	mit	mit	PROPN
american_scientific_journal-1326	201	13	schrittweitenkontrolle	schrittweitenkontrolle	NOUN
american_scientific_journal-1326	201	14	und	und	VERB
american_scientific_journal-1326	201	15	ihre	ihre	NOUN
american_scientific_journal-1326	201	16	anwendung	anwendung	PROPN
american_scientific_journal-1326	201	17	auf	auf	PROPN
american_scientific_journal-1326	201	18	waermeleitungsprobleme	waermeleitungsprobleme	NOUN
american_scientific_journal-1326	201	19	.	.	PUNCT
american_scientific_journal-1326	201	20	”	"	PUNCT
american_scientific_journal-1326	202	1	computing	computing	NOUN
american_scientific_journal-1326	202	2	,	,	PUNCT
american_scientific_journal-1326	202	3	vol	vol	NOUN
american_scientific_journal-1326	202	4	.	.	PROPN
american_scientific_journal-1326	202	5	6	6	NUM
american_scientific_journal-1326	202	6	,	,	PUNCT
american_scientific_journal-1326	202	7	pp	pp	ADJ
american_scientific_journal-1326	202	8	.	.	PUNCT
american_scientific_journal-1326	202	9	6171	6171	NUM
american_scientific_journal-1326	202	10	,	,	PUNCT
american_scientific_journal-1326	202	11	1970	1970	NUM
american_scientific_journal-1326	202	12	http://www.ugr.es/%7eazurita/docencia/material_docente/cosmologia/cr_dm_clase_06.pdf	http://www.ugr.es/%7eazurita/docencia/material_docente/cosmologia/cr_dm_clase_06.pdf	NOUN