id	sid	tid	token	lemma	pos
american_scientific_journal-1402	1	1	american	american	PROPN
american_scientific_journal-1402	1	2	scientific	scientific	ADJ
american_scientific_journal-1402	1	3	research	research	NOUN
american_scientific_journal-1402	1	4	journal	journal	NOUN
american_scientific_journal-1402	1	5	for	for	ADP
american_scientific_journal-1402	1	6	engineering	engineering	NOUN
american_scientific_journal-1402	1	7	,	,	PUNCT
american_scientific_journal-1402	1	8	technology	technology	NOUN
american_scientific_journal-1402	1	9	,	,	PUNCT
american_scientific_journal-1402	1	10	and	and	CCONJ
american_scientific_journal-1402	1	11	sciences	science	NOUN
american_scientific_journal-1402	1	12	(	(	PUNCT
american_scientific_journal-1402	1	13	asrjets	asrjet	NOUN
american_scientific_journal-1402	1	14	)	)	PUNCT
american_scientific_journal-1402	1	15	issn	issn	PROPN
american_scientific_journal-1402	1	16	(	(	PUNCT
american_scientific_journal-1402	1	17	print	print	NOUN
american_scientific_journal-1402	1	18	)	)	PUNCT
american_scientific_journal-1402	1	19	2313	2313	NUM
american_scientific_journal-1402	1	20	-	-	SYM
american_scientific_journal-1402	1	21	4410	4410	NUM
american_scientific_journal-1402	1	22	,	,	PUNCT
american_scientific_journal-1402	1	23	issn	issn	PROPN
american_scientific_journal-1402	1	24	(	(	PUNCT
american_scientific_journal-1402	1	25	online	online	ADJ
american_scientific_journal-1402	1	26	)	)	PUNCT
american_scientific_journal-1402	1	27	2313	2313	NUM
american_scientific_journal-1402	1	28	-	-	SYM
american_scientific_journal-1402	1	29	4402	4402	NUM
american_scientific_journal-1402	1	30	©	©	PROPN
american_scientific_journal-1402	1	31	global	global	ADJ
american_scientific_journal-1402	1	32	society	society	NOUN
american_scientific_journal-1402	1	33	of	of	ADP
american_scientific_journal-1402	1	34	scientific	scientific	ADJ
american_scientific_journal-1402	1	35	research	research	NOUN
american_scientific_journal-1402	1	36	and	and	CCONJ
american_scientific_journal-1402	1	37	researchers	researcher	NOUN
american_scientific_journal-1402	1	38	http://asrjetsjournal.org/	http://asrjetsjournal.org/	VERB
american_scientific_journal-1402	1	39	a	a	DET
american_scientific_journal-1402	1	40	static	static	ADJ
american_scientific_journal-1402	1	41	solution	solution	NOUN
american_scientific_journal-1402	1	42	to	to	ADP
american_scientific_journal-1402	1	43	einstein	einstein	PROPN
american_scientific_journal-1402	1	44	’s	’s	PART
american_scientific_journal-1402	1	45	field	field	NOUN
american_scientific_journal-1402	1	46	equations	equation	NOUN
american_scientific_journal-1402	1	47	for	for	ADP
american_scientific_journal-1402	1	48	a	a	DET
american_scientific_journal-1402	1	49	spherical	spherical	ADJ
american_scientific_journal-1402	1	50	distribution	distribution	NOUN
american_scientific_journal-1402	1	51	of	of	ADP
american_scientific_journal-1402	1	52	electrically	electrically	ADV
american_scientific_journal-1402	1	53	counterpoised	counterpoise	VERB
american_scientific_journal-1402	1	54	dust	dust	NOUN
american_scientific_journal-1402	1	55	sashinka	sashinka	NOUN
american_scientific_journal-1402	1	56	wimaladharmaa	wimaladharmaa	VERB
american_scientific_journal-1402	1	57	*	*	PROPN
american_scientific_journal-1402	1	58	,	,	PUNCT
american_scientific_journal-1402	1	59	nalin	nalin	PROPN
american_scientific_journal-1402	1	60	de	de	PROPN
american_scientific_journal-1402	1	61	silvab	silvab	PROPN
american_scientific_journal-1402	1	62	adepartment	adepartment	NOUN
american_scientific_journal-1402	1	63	of	of	ADP
american_scientific_journal-1402	1	64	mathematics	mathematic	NOUN
american_scientific_journal-1402	1	65	,	,	PUNCT
american_scientific_journal-1402	1	66	university	university	NOUN
american_scientific_journal-1402	1	67	of	of	ADP
american_scientific_journal-1402	1	68	kelaniya	kelaniya	PROPN
american_scientific_journal-1402	1	69	,	,	PUNCT
american_scientific_journal-1402	1	70	11600	11600	NUM
american_scientific_journal-1402	1	71	,	,	PUNCT
american_scientific_journal-1402	1	72	sri	sri	PROPN
american_scientific_journal-1402	1	73	lanka	lanka	PROPN
american_scientific_journal-1402	1	74	.	.	PUNCT
american_scientific_journal-1402	2	1	bno.109/1	bno.109/1	PROPN
american_scientific_journal-1402	2	2	,	,	PUNCT
american_scientific_journal-1402	2	3	railway	railway	NOUN
american_scientific_journal-1402	2	4	avenue	avenue	PROPN
american_scientific_journal-1402	2	5	,	,	PUNCT
american_scientific_journal-1402	2	6	maharagama	maharagama	NOUN
american_scientific_journal-1402	2	7	,	,	PUNCT
american_scientific_journal-1402	2	8	10280	10280	NUM
american_scientific_journal-1402	2	9	,	,	PUNCT
american_scientific_journal-1402	2	10	sri	sri	PROPN
american_scientific_journal-1402	2	11	lanka	lanka	PROPN
american_scientific_journal-1402	2	12	.	.	PUNCT
american_scientific_journal-1402	3	1	aemail	aemail	PROPN
american_scientific_journal-1402	3	2	:	:	PUNCT
american_scientific_journal-1402	3	3	wimaladharma@kln.ac.lk	wimaladharma@kln.ac.lk	NOUN
american_scientific_journal-1402	3	4	bemail	bemail	NOUN
american_scientific_journal-1402	3	5	:	:	PUNCT
american_scientific_journal-1402	3	6	nalink2003@yahoo.com	nalink2003@yahoo.com	X
american_scientific_journal-1402	4	1	abstract	abstract	ADJ
american_scientific_journal-1402	4	2	the	the	DET
american_scientific_journal-1402	4	3	work	work	NOUN
american_scientific_journal-1402	4	4	on	on	ADP
american_scientific_journal-1402	4	5	einstein	einstein	PROPN
american_scientific_journal-1402	4	6	-	-	PUNCT
american_scientific_journal-1402	4	7	maxwell	maxwell	PROPN
american_scientific_journal-1402	4	8	equations	equation	NOUN
american_scientific_journal-1402	4	9	for	for	ADP
american_scientific_journal-1402	4	10	a	a	DET
american_scientific_journal-1402	4	11	sphere	sphere	NOUN
american_scientific_journal-1402	4	12	composed	compose	VERB
american_scientific_journal-1402	4	13	of	of	ADP
american_scientific_journal-1402	4	14	a	a	DET
american_scientific_journal-1402	4	15	special	special	ADJ
american_scientific_journal-1402	4	16	kind	kind	NOUN
american_scientific_journal-1402	4	17	of	of	ADP
american_scientific_journal-1402	4	18	matter	matter	NOUN
american_scientific_journal-1402	4	19	distribution	distribution	NOUN
american_scientific_journal-1402	4	20	called	call	VERB
american_scientific_journal-1402	4	21	electrically	electrically	ADV
american_scientific_journal-1402	4	22	counterpoised	counterpoise	VERB
american_scientific_journal-1402	4	23	dust	dust	NOUN
american_scientific_journal-1402	4	24	(	(	PUNCT
american_scientific_journal-1402	4	25	ecd	ecd	PROPN
american_scientific_journal-1402	4	26	)	)	PUNCT
american_scientific_journal-1402	4	27	with	with	ADP
american_scientific_journal-1402	4	28	constant	constant	ADJ
american_scientific_journal-1402	4	29	density	density	NOUN
american_scientific_journal-1402	4	30	has	have	AUX
american_scientific_journal-1402	4	31	been	be	AUX
american_scientific_journal-1402	4	32	discussed	discuss	VERB
american_scientific_journal-1402	4	33	.	.	PUNCT
american_scientific_journal-1402	5	1	the	the	DET
american_scientific_journal-1402	5	2	better	well	ADJ
american_scientific_journal-1402	5	3	understanding	understanding	NOUN
american_scientific_journal-1402	5	4	of	of	ADP
american_scientific_journal-1402	5	5	the	the	DET
american_scientific_journal-1402	5	6	electrically	electrically	ADV
american_scientific_journal-1402	5	7	counterpoised	counterpoise	VERB
american_scientific_journal-1402	5	8	dust	dust	NOUN
american_scientific_journal-1402	5	9	model	model	NOUN
american_scientific_journal-1402	5	10	in	in	ADP
american_scientific_journal-1402	5	11	detail	detail	NOUN
american_scientific_journal-1402	5	12	will	will	AUX
american_scientific_journal-1402	5	13	helps	help	VERB
american_scientific_journal-1402	5	14	scientists	scientist	NOUN
american_scientific_journal-1402	5	15	to	to	PART
american_scientific_journal-1402	5	16	understand	understand	VERB
american_scientific_journal-1402	5	17	the	the	DET
american_scientific_journal-1402	5	18	universe	universe	NOUN
american_scientific_journal-1402	5	19	in	in	ADP
american_scientific_journal-1402	5	20	better	well	ADJ
american_scientific_journal-1402	5	21	way	way	NOUN
american_scientific_journal-1402	5	22	.	.	PUNCT
american_scientific_journal-1402	6	1	along	along	ADP
american_scientific_journal-1402	6	2	this	this	DET
american_scientific_journal-1402	6	3	line	line	NOUN
american_scientific_journal-1402	6	4	,	,	PUNCT
american_scientific_journal-1402	6	5	the	the	DET
american_scientific_journal-1402	6	6	understanding	understanding	NOUN
american_scientific_journal-1402	6	7	of	of	ADP
american_scientific_journal-1402	6	8	static	static	ADJ
american_scientific_journal-1402	6	9	solutions	solution	NOUN
american_scientific_journal-1402	6	10	for	for	ADP
american_scientific_journal-1402	6	11	the	the	DET
american_scientific_journal-1402	6	12	electrically	electrically	ADV
american_scientific_journal-1402	6	13	counterpoised	counterpoise	VERB
american_scientific_journal-1402	6	14	dust	dust	NOUN
american_scientific_journal-1402	6	15	will	will	AUX
american_scientific_journal-1402	6	16	be	be	AUX
american_scientific_journal-1402	6	17	a	a	DET
american_scientific_journal-1402	6	18	crucial	crucial	ADJ
american_scientific_journal-1402	6	19	factor	factor	NOUN
american_scientific_journal-1402	6	20	.	.	PUNCT
american_scientific_journal-1402	7	1	to	to	PART
american_scientific_journal-1402	7	2	understand	understand	VERB
american_scientific_journal-1402	7	3	the	the	DET
american_scientific_journal-1402	7	4	static	static	ADJ
american_scientific_journal-1402	7	5	solutions	solution	NOUN
american_scientific_journal-1402	7	6	for	for	ADP
american_scientific_journal-1402	7	7	the	the	DET
american_scientific_journal-1402	7	8	electrically	electrically	ADV
american_scientific_journal-1402	7	9	counterpoised	counterpoise	VERB
american_scientific_journal-1402	7	10	dust	dust	NOUN
american_scientific_journal-1402	7	11	,	,	PUNCT
american_scientific_journal-1402	7	12	static	static	ADJ
american_scientific_journal-1402	7	13	solutions	solution	NOUN
american_scientific_journal-1402	7	14	for	for	ADP
american_scientific_journal-1402	7	15	the	the	DET
american_scientific_journal-1402	7	16	einsteinmaxwell	einsteinmaxwell	NOUN
american_scientific_journal-1402	7	17	equations	equation	NOUN
american_scientific_journal-1402	7	18	have	have	AUX
american_scientific_journal-1402	7	19	been	be	AUX
american_scientific_journal-1402	7	20	found	find	VERB
american_scientific_journal-1402	7	21	.	.	PUNCT
american_scientific_journal-1402	8	1	in	in	ADP
american_scientific_journal-1402	8	2	particular	particular	ADJ
american_scientific_journal-1402	8	3	,	,	PUNCT
american_scientific_journal-1402	8	4	static	static	ADJ
american_scientific_journal-1402	8	5	solutions	solution	NOUN
american_scientific_journal-1402	8	6	for	for	ADP
american_scientific_journal-1402	8	7	a	a	DET
american_scientific_journal-1402	8	8	sphere	sphere	NOUN
american_scientific_journal-1402	8	9	composed	compose	VERB
american_scientific_journal-1402	8	10	of	of	ADP
american_scientific_journal-1402	8	11	electrically	electrically	ADV
american_scientific_journal-1402	8	12	counterpoised	counterpoise	VERB
american_scientific_journal-1402	8	13	dust	dust	NOUN
american_scientific_journal-1402	8	14	matter	matter	NOUN
american_scientific_journal-1402	8	15	using	use	VERB
american_scientific_journal-1402	8	16	standard	standard	ADJ
american_scientific_journal-1402	8	17	boundary	boundary	ADJ
american_scientific_journal-1402	8	18	conditions	condition	NOUN
american_scientific_journal-1402	8	19	tested	test	VERB
american_scientific_journal-1402	8	20	.	.	PUNCT
american_scientific_journal-1402	9	1	in	in	ADP
american_scientific_journal-1402	9	2	addition	addition	NOUN
american_scientific_journal-1402	9	3	to	to	ADP
american_scientific_journal-1402	9	4	that	that	SCONJ
american_scientific_journal-1402	9	5	the	the	DET
american_scientific_journal-1402	9	6	expressions	expression	NOUN
american_scientific_journal-1402	9	7	for	for	ADP
american_scientific_journal-1402	9	8	the	the	DET
american_scientific_journal-1402	9	9	redshift	redshift	NOUN
american_scientific_journal-1402	9	10	moving	move	VERB
american_scientific_journal-1402	9	11	along	along	ADP
american_scientific_journal-1402	9	12	a	a	DET
american_scientific_journal-1402	9	13	radial	radial	ADJ
american_scientific_journal-1402	9	14	geodesic	geodesic	NOUN
american_scientific_journal-1402	9	15	have	have	AUX
american_scientific_journal-1402	9	16	been	be	AUX
american_scientific_journal-1402	9	17	obtained	obtain	VERB
american_scientific_journal-1402	9	18	.	.	PUNCT
american_scientific_journal-1402	10	1	keywords	keyword	NOUN
american_scientific_journal-1402	10	2	:	:	PUNCT
american_scientific_journal-1402	10	3	einstein	einstein	ADJ
american_scientific_journal-1402	10	4	field	field	NOUN
american_scientific_journal-1402	10	5	equations	equation	NOUN
american_scientific_journal-1402	10	6	;	;	PUNCT
american_scientific_journal-1402	10	7	electrically	electrically	ADV
american_scientific_journal-1402	10	8	counterpoised	counterpoise	VERB
american_scientific_journal-1402	10	9	dust	dust	NOUN
american_scientific_journal-1402	10	10	.	.	PUNCT
american_scientific_journal-1402	11	1	1	1	X
american_scientific_journal-1402	11	2	.	.	X
american_scientific_journal-1402	11	3	introduction	introduction	NOUN
american_scientific_journal-1402	11	4	in	in	ADP
american_scientific_journal-1402	11	5	a	a	DET
american_scientific_journal-1402	11	6	distribution	distribution	NOUN
american_scientific_journal-1402	11	7	of	of	ADP
american_scientific_journal-1402	11	8	electrically	electrically	ADV
american_scientific_journal-1402	11	9	counterpoised	counterpoise	VERB
american_scientific_journal-1402	11	10	dust	dust	NOUN
american_scientific_journal-1402	11	11	,	,	PUNCT
american_scientific_journal-1402	11	12	there	there	PRON
american_scientific_journal-1402	11	13	are	be	VERB
american_scientific_journal-1402	11	14	no	no	DET
american_scientific_journal-1402	11	15	resultant	resultant	NOUN
american_scientific_journal-1402	11	16	force	force	NOUN
american_scientific_journal-1402	11	17	between	between	ADP
american_scientific_journal-1402	11	18	each	each	DET
american_scientific_journal-1402	11	19	particle	particle	NOUN
american_scientific_journal-1402	11	20	since	since	SCONJ
american_scientific_journal-1402	11	21	all	all	DET
american_scientific_journal-1402	11	22	the	the	DET
american_scientific_journal-1402	11	23	forces	force	NOUN
american_scientific_journal-1402	11	24	between	between	ADP
american_scientific_journal-1402	11	25	particles	particle	NOUN
american_scientific_journal-1402	11	26	in	in	ADP
american_scientific_journal-1402	11	27	such	such	DET
american_scientific_journal-1402	11	28	a	a	DET
american_scientific_journal-1402	11	29	distribution	distribution	NOUN
american_scientific_journal-1402	11	30	have	have	AUX
american_scientific_journal-1402	11	31	been	be	AUX
american_scientific_journal-1402	11	32	balanced	balance	VERB
american_scientific_journal-1402	11	33	.	.	PUNCT
american_scientific_journal-1402	12	1	wickramasuriya	wickramasuriya	X
american_scientific_journal-1402	13	1	[	[	X
american_scientific_journal-1402	13	2	1	1	X
american_scientific_journal-1402	13	3	]	]	PUNCT
american_scientific_journal-1402	13	4	considered	consider	VERB
american_scientific_journal-1402	13	5	a	a	DET
american_scientific_journal-1402	13	6	spherical	spherical	ADJ
american_scientific_journal-1402	13	7	distribution	distribution	NOUN
american_scientific_journal-1402	13	8	of	of	ADP
american_scientific_journal-1402	13	9	electrically	electrically	ADV
american_scientific_journal-1402	13	10	counterpoised	counterpoise	VERB
american_scientific_journal-1402	13	11	dust	dust	NOUN
american_scientific_journal-1402	13	12	(	(	PUNCT
american_scientific_journal-1402	13	13	ecd	ecd	PROPN
american_scientific_journal-1402	13	14	)	)	PUNCT
american_scientific_journal-1402	13	15	and	and	CCONJ
american_scientific_journal-1402	13	16	proved	prove	VERB
american_scientific_journal-1402	13	17	that	that	SCONJ
american_scientific_journal-1402	13	18	einstein	einstein	PROPN
american_scientific_journal-1402	13	19	’s	’s	PART
american_scientific_journal-1402	13	20	field	field	NOUN
american_scientific_journal-1402	13	21	equations	equation	NOUN
american_scientific_journal-1402	13	22	can	can	AUX
american_scientific_journal-1402	13	23	be	be	AUX
american_scientific_journal-1402	13	24	written	write	VERB
american_scientific_journal-1402	13	25	in	in	ADP
american_scientific_journal-1402	13	26	a	a	DET
american_scientific_journal-1402	13	27	simple	simple	ADJ
american_scientific_journal-1402	13	28	form	form	NOUN
american_scientific_journal-1402	13	29	for	for	ADP
american_scientific_journal-1402	13	30	such	such	DET
american_scientific_journal-1402	13	31	a	a	DET
american_scientific_journal-1402	13	32	distribution	distribution	NOUN
american_scientific_journal-1402	13	33	.	.	PUNCT
american_scientific_journal-1402	14	1	using	use	VERB
american_scientific_journal-1402	14	2	this	this	DET
american_scientific_journal-1402	14	3	form	form	NOUN
american_scientific_journal-1402	14	4	,	,	PUNCT
american_scientific_journal-1402	14	5	a	a	DET
american_scientific_journal-1402	14	6	static	static	ADJ
american_scientific_journal-1402	14	7	solution	solution	NOUN
american_scientific_journal-1402	14	8	to	to	ADP
american_scientific_journal-1402	14	9	einstein	einstein	PROPN
american_scientific_journal-1402	14	10	’s	’s	PART
american_scientific_journal-1402	14	11	field	field	NOUN
american_scientific_journal-1402	14	12	equations	equation	NOUN
american_scientific_journal-1402	14	13	has	have	AUX
american_scientific_journal-1402	14	14	been	be	AUX
american_scientific_journal-1402	14	15	found	find	VERB
american_scientific_journal-1402	14	16	with	with	ADP
american_scientific_journal-1402	14	17	the	the	DET
american_scientific_journal-1402	14	18	application	application	NOUN
american_scientific_journal-1402	14	19	of	of	ADP
american_scientific_journal-1402	14	20	standard	standard	ADJ
american_scientific_journal-1402	14	21	boundary	boundary	ADJ
american_scientific_journal-1402	14	22	conditions	condition	NOUN
american_scientific_journal-1402	14	23	.	.	PUNCT
american_scientific_journal-1402	15	1	-----------------------------------------------------------------------	-----------------------------------------------------------------------	PUNCT
american_scientific_journal-1402	16	1	*	*	PUNCT
american_scientific_journal-1402	16	2	corresponding	correspond	VERB
american_scientific_journal-1402	16	3	author	author	NOUN
american_scientific_journal-1402	16	4	.	.	PUNCT
american_scientific_journal-1402	17	1	155	155	NUM
american_scientific_journal-1402	17	2	http://asrjetsjournal.org/	http://asrjetsjournal.org/	PROPN
american_scientific_journal-1402	17	3	american	american	ADJ
american_scientific_journal-1402	17	4	scientific	scientific	ADJ
american_scientific_journal-1402	17	5	research	research	NOUN
american_scientific_journal-1402	17	6	journal	journal	NOUN
american_scientific_journal-1402	17	7	for	for	ADP
american_scientific_journal-1402	17	8	engineering	engineering	NOUN
american_scientific_journal-1402	17	9	,	,	PUNCT
american_scientific_journal-1402	17	10	technology	technology	NOUN
american_scientific_journal-1402	17	11	,	,	PUNCT
american_scientific_journal-1402	17	12	and	and	CCONJ
american_scientific_journal-1402	17	13	sciences	science	NOUN
american_scientific_journal-1402	17	14	(	(	PUNCT
american_scientific_journal-1402	17	15	asrjets	asrjet	NOUN
american_scientific_journal-1402	17	16	)	)	PUNCT
american_scientific_journal-1402	17	17	(	(	PUNCT
american_scientific_journal-1402	17	18	2016	2016	NUM
american_scientific_journal-1402	17	19	)	)	PUNCT
american_scientific_journal-1402	17	20	volume	volume	NOUN
american_scientific_journal-1402	17	21	17	17	NUM
american_scientific_journal-1402	17	22	,	,	PUNCT
american_scientific_journal-1402	17	23	no	no	DET
american_scientific_journal-1402	17	24	1	1	NUM
american_scientific_journal-1402	17	25	,	,	PUNCT
american_scientific_journal-1402	17	26	pp	pp	ADV
american_scientific_journal-1402	17	27	155	155	NUM
american_scientific_journal-1402	17	28	-	-	SYM
american_scientific_journal-1402	17	29	164	164	NUM
american_scientific_journal-1402	17	30	the	the	DET
american_scientific_journal-1402	17	31	red	red	ADJ
american_scientific_journal-1402	17	32	shift	shift	NOUN
american_scientific_journal-1402	17	33	of	of	ADP
american_scientific_journal-1402	17	34	a	a	DET
american_scientific_journal-1402	17	35	pulse	pulse	NOUN
american_scientific_journal-1402	17	36	of	of	ADP
american_scientific_journal-1402	17	37	light	light	NOUN
american_scientific_journal-1402	17	38	which	which	PRON
american_scientific_journal-1402	17	39	is	be	AUX
american_scientific_journal-1402	17	40	emitted	emit	VERB
american_scientific_journal-1402	17	41	at	at	ADP
american_scientific_journal-1402	17	42	a	a	DET
american_scientific_journal-1402	17	43	point	point	NOUN
american_scientific_journal-1402	17	44	inside	inside	ADP
american_scientific_journal-1402	17	45	the	the	DET
american_scientific_journal-1402	17	46	sphere	sphere	NOUN
american_scientific_journal-1402	17	47	as	as	SCONJ
american_scientific_journal-1402	17	48	observed	observe	VERB
american_scientific_journal-1402	17	49	by	by	ADP
american_scientific_journal-1402	17	50	an	an	DET
american_scientific_journal-1402	17	51	observer	observer	NOUN
american_scientific_journal-1402	17	52	who	who	PRON
american_scientific_journal-1402	17	53	is	be	AUX
american_scientific_journal-1402	17	54	at	at	ADP
american_scientific_journal-1402	17	55	a	a	DET
american_scientific_journal-1402	17	56	large	large	ADJ
american_scientific_journal-1402	17	57	distance	distance	NOUN
american_scientific_journal-1402	17	58	in	in	ADP
american_scientific_journal-1402	17	59	the	the	DET
american_scientific_journal-1402	17	60	exterior	exterior	ADJ
american_scientific_journal-1402	17	61	region	region	NOUN
american_scientific_journal-1402	17	62	is	be	AUX
american_scientific_journal-1402	17	63	also	also	ADV
american_scientific_journal-1402	17	64	calculated	calculate	VERB
american_scientific_journal-1402	17	65	.	.	PUNCT
american_scientific_journal-1402	18	1	2	2	X
american_scientific_journal-1402	18	2	.	.	X
american_scientific_journal-1402	18	3	material	material	NOUN
american_scientific_journal-1402	18	4	and	and	CCONJ
american_scientific_journal-1402	18	5	the	the	DET
american_scientific_journal-1402	18	6	method	method	NOUN
american_scientific_journal-1402	18	7	wickramasuriya	wickramasuriya	NOUN
american_scientific_journal-1402	19	1	[	[	X
american_scientific_journal-1402	19	2	1	1	X
american_scientific_journal-1402	19	3	]	]	PUNCT
american_scientific_journal-1402	19	4	consider	consider	VERB
american_scientific_journal-1402	19	5	a	a	DET
american_scientific_journal-1402	19	6	spherically	spherically	NOUN
american_scientific_journal-1402	19	7	metric	metric	NOUN
american_scientific_journal-1402	19	8	in	in	ADP
american_scientific_journal-1402	19	9	the	the	DET
american_scientific_journal-1402	19	10	form	form	NOUN
american_scientific_journal-1402	19	11	𝒅𝒅𝒅𝒅𝟐𝟐	𝒅𝒅𝒅𝒅𝟐𝟐	NOUN
american_scientific_journal-1402	19	12	=	=	PUNCT
american_scientific_journal-1402	20	1	𝒆𝒆𝟐𝟐𝑼𝑼𝒄𝒄𝟐𝟐𝒅𝒅𝒅𝒅𝟐𝟐	𝒆𝒆𝟐𝟐𝑼𝑼𝒄𝒄𝟐𝟐𝒅𝒅𝒅𝒅𝟐𝟐	X
american_scientific_journal-1402	21	1	−	−	NOUN
american_scientific_journal-1402	21	2	𝒆𝒆−𝟐𝟐𝑼𝑼(𝒅𝒅𝒅𝒅𝟐𝟐	𝒆𝒆−𝟐𝟐𝑼𝑼(𝒅𝒅𝒅𝒅𝟐𝟐	NOUN
american_scientific_journal-1402	21	3	+	+	NUM
american_scientific_journal-1402	21	4	𝒅𝒅𝟐𝟐𝒅𝒅𝒅𝒅𝟐𝟐	𝒅𝒅𝟐𝟐𝒅𝒅𝒅𝒅𝟐𝟐	NOUN
american_scientific_journal-1402	21	5	+	+	CCONJ
american_scientific_journal-1402	21	6	𝒅𝒅𝟐𝟐	𝒅𝒅𝟐𝟐	PROPN
american_scientific_journal-1402	21	7	𝐬𝐬𝐬𝐬𝐬𝐬𝟐𝟐	𝐬𝐬𝐬𝐬𝐬𝐬𝟐𝟐	NOUN
american_scientific_journal-1402	21	8	𝒅𝒅𝒅𝒅𝒅𝒅𝟐𝟐	𝒅𝒅𝒅𝒅𝒅𝒅𝟐𝟐	NOUN
american_scientific_journal-1402	21	9	)	)	PUNCT
american_scientific_journal-1402	21	10	(	(	PUNCT
american_scientific_journal-1402	21	11	1	1	X
american_scientific_journal-1402	21	12	)	)	PUNCT
american_scientific_journal-1402	22	1	and	and	CCONJ
american_scientific_journal-1402	22	2	proved	prove	VERB
american_scientific_journal-1402	22	3	that	that	SCONJ
american_scientific_journal-1402	22	4	einstein	einstein	PROPN
american_scientific_journal-1402	22	5	’s	’s	PART
american_scientific_journal-1402	22	6	field	field	NOUN
american_scientific_journal-1402	22	7	equations	equation	NOUN
american_scientific_journal-1402	22	8	for	for	ADP
american_scientific_journal-1402	22	9	a	a	DET
american_scientific_journal-1402	22	10	spherically	spherically	NOUN
american_scientific_journal-1402	22	11	symmetric	symmetric	ADJ
american_scientific_journal-1402	22	12	distribution	distribution	NOUN
american_scientific_journal-1402	22	13	of	of	ADP
american_scientific_journal-1402	22	14	electrically	electrically	ADV
american_scientific_journal-1402	22	15	counterpoised	counterpoise	VERB
american_scientific_journal-1402	22	16	dust	dust	NOUN
american_scientific_journal-1402	22	17	(	(	PUNCT
american_scientific_journal-1402	22	18	ecd	ecd	PROPN
american_scientific_journal-1402	22	19	)	)	PUNCT
american_scientific_journal-1402	22	20	can	can	AUX
american_scientific_journal-1402	22	21	be	be	AUX
american_scientific_journal-1402	22	22	written	write	VERB
american_scientific_journal-1402	22	23	in	in	ADP
american_scientific_journal-1402	22	24	the	the	DET
american_scientific_journal-1402	22	25	form	form	NOUN
american_scientific_journal-1402	22	26	𝟏𝟏	𝟏𝟏	NUM
american_scientific_journal-1402	22	27	𝒅𝒅𝟐𝟐	𝒅𝒅𝟐𝟐	PROPN
american_scientific_journal-1402	22	28	𝒅𝒅	𝒅𝒅	PROPN
american_scientific_journal-1402	22	29	𝒅𝒅𝒅𝒅	𝒅𝒅𝒅𝒅	PROPN
american_scientific_journal-1402	22	30	�	�	PROPN
american_scientific_journal-1402	23	1	𝒅𝒅𝟐𝟐	𝒅𝒅𝟐𝟐	PROPN
american_scientific_journal-1402	23	2	𝒅𝒅𝒆𝒆	𝒅𝒅𝒆𝒆	NOUN
american_scientific_journal-1402	23	3	−𝑼𝑼	−𝑼𝑼	PROPN
american_scientific_journal-1402	23	4	𝒅𝒅𝒅𝒅	𝒅𝒅𝒅𝒅	PROPN
american_scientific_journal-1402	23	5	�	�	PROPN
american_scientific_journal-1402	23	6	=	=	SYM
american_scientific_journal-1402	23	7	−𝟒𝟒𝝅𝝅𝝅𝝅𝒆𝒆−𝟑𝟑𝑼𝑼	−𝟒𝟒𝝅𝝅𝝅𝝅𝒆𝒆−𝟑𝟑𝑼𝑼	PROPN
american_scientific_journal-1402	23	8	(	(	PUNCT
american_scientific_journal-1402	23	9	2	2	NUM
american_scientific_journal-1402	23	10	)	)	PUNCT
american_scientific_journal-1402	23	11	where	where	SCONJ
american_scientific_journal-1402	23	12	𝝅𝝅	𝝅𝝅	PROPN
american_scientific_journal-1402	23	13	is	be	AUX
american_scientific_journal-1402	23	14	the	the	DET
american_scientific_journal-1402	23	15	density	density	NOUN
american_scientific_journal-1402	23	16	of	of	ADP
american_scientific_journal-1402	23	17	the	the	DET
american_scientific_journal-1402	23	18	sphere	sphere	NOUN
american_scientific_journal-1402	23	19	.	.	PUNCT
american_scientific_journal-1402	24	1	using	use	VERB
american_scientific_journal-1402	24	2	the	the	DET
american_scientific_journal-1402	24	3	transformations	transformation	NOUN
american_scientific_journal-1402	24	4	𝒚𝒚	𝒚𝒚	NOUN
american_scientific_journal-1402	24	5	=	=	SYM
american_scientific_journal-1402	24	6	𝒆𝒆−𝑼𝑼	𝒆𝒆−𝑼𝑼	PROPN
american_scientific_journal-1402	24	7	and	and	CCONJ
american_scientific_journal-1402	24	8	𝒅𝒅	𝒅𝒅	NOUN
american_scientific_journal-1402	24	9	=	=	PUNCT
american_scientific_journal-1402	24	10	𝒍𝒍𝒍𝒍	𝒍𝒍𝒍𝒍	PROPN
american_scientific_journal-1402	24	11	,	,	PUNCT
american_scientific_journal-1402	24	12	equation	equation	NOUN
american_scientific_journal-1402	24	13	(	(	PUNCT
american_scientific_journal-1402	24	14	2	2	X
american_scientific_journal-1402	24	15	)	)	PUNCT
american_scientific_journal-1402	24	16	can	can	AUX
american_scientific_journal-1402	24	17	be	be	AUX
american_scientific_journal-1402	24	18	written	write	VERB
american_scientific_journal-1402	24	19	in	in	ADP
american_scientific_journal-1402	24	20	the	the	DET
american_scientific_journal-1402	24	21	form	form	NOUN
american_scientific_journal-1402	24	22	𝟏𝟏	𝟏𝟏	NUM
american_scientific_journal-1402	24	23	𝒍𝒍𝟐𝟐	𝒍𝒍𝟐𝟐	PROPN
american_scientific_journal-1402	24	24	𝒅𝒅	𝒅𝒅	PROPN
american_scientific_journal-1402	24	25	𝒅𝒅𝒍𝒍	𝒅𝒅𝒍𝒍	PROPN
american_scientific_journal-1402	24	26	�	�	PROPN
american_scientific_journal-1402	24	27	𝒍𝒍𝟐𝟐	𝒍𝒍𝟐𝟐	PROPN
american_scientific_journal-1402	24	28	𝒅𝒅𝒚𝒚	𝒅𝒅𝒚𝒚	VERB
american_scientific_journal-1402	24	29	𝒅𝒅𝒍𝒍	𝒅𝒅𝒍𝒍	PROPN
american_scientific_journal-1402	24	30	�	�	PROPN
american_scientific_journal-1402	24	31	=	=	SYM
american_scientific_journal-1402	24	32	−𝟒𝟒𝝅𝝅𝝅𝝅𝒍𝒍𝟐𝟐𝒚𝒚𝟑𝟑	−𝟒𝟒𝝅𝝅𝝅𝝅𝒍𝒍𝟐𝟐𝒚𝒚𝟑𝟑	PROPN
american_scientific_journal-1402	24	33	(	(	PUNCT
american_scientific_journal-1402	24	34	3	3	NUM
american_scientific_journal-1402	24	35	)	)	PUNCT
american_scientific_journal-1402	24	36	where	where	SCONJ
american_scientific_journal-1402	24	37	𝒚𝒚	𝒚𝒚	ADV
american_scientific_journal-1402	24	38	=	=	SYM
american_scientific_journal-1402	24	39	𝒚𝒚(𝒍𝒍	𝒚𝒚(𝒍𝒍	NOUN
american_scientific_journal-1402	24	40	)	)	PUNCT
american_scientific_journal-1402	24	41	and	and	CCONJ
american_scientific_journal-1402	24	42	𝒚𝒚′	𝒚𝒚′	X
american_scientific_journal-1402	24	43	=	=	PUNCT
american_scientific_journal-1402	24	44	𝒅𝒅𝒚𝒚	𝒅𝒅𝒚𝒚	VERB
american_scientific_journal-1402	24	45	𝒅𝒅𝒍𝒍	𝒅𝒅𝒍𝒍	NOUN
american_scientific_journal-1402	24	46	.	.	PUNCT
american_scientific_journal-1402	25	1	now	now	ADV
american_scientific_journal-1402	25	2	choose	choose	VERB
american_scientific_journal-1402	25	3	𝒍𝒍	𝒍𝒍	NOUN
american_scientific_journal-1402	26	1	such	such	ADJ
american_scientific_journal-1402	26	2	that	that	SCONJ
american_scientific_journal-1402	26	3	𝟒𝟒𝝅𝝅𝝅𝝅𝒍𝒍𝟐𝟐	𝟒𝟒𝝅𝝅𝝅𝝅𝒍𝒍𝟐𝟐	PROPN
american_scientific_journal-1402	26	4	=	=	SYM
american_scientific_journal-1402	26	5	𝟏𝟏.	𝟏𝟏.	NOUN
american_scientific_journal-1402	26	6	then	then	ADV
american_scientific_journal-1402	26	7	(	(	PUNCT
american_scientific_journal-1402	26	8	3	3	X
american_scientific_journal-1402	26	9	)	)	PUNCT
american_scientific_journal-1402	26	10	reduces	reduce	VERB
american_scientific_journal-1402	26	11	to	to	ADP
american_scientific_journal-1402	26	12	𝟏𝟏	𝟏𝟏	NUM
american_scientific_journal-1402	26	13	𝒍𝒍𝟐𝟐	𝒍𝒍𝟐𝟐	PROPN
american_scientific_journal-1402	26	14	𝒅𝒅	𝒅𝒅	PROPN
american_scientific_journal-1402	26	15	𝒅𝒅𝒍𝒍	𝒅𝒅𝒍𝒍	PROPN
american_scientific_journal-1402	26	16	�	�	PROPN
american_scientific_journal-1402	26	17	𝒍𝒍𝟐𝟐	𝒍𝒍𝟐𝟐	PROPN
american_scientific_journal-1402	26	18	𝒅𝒅𝒚𝒚	𝒅𝒅𝒚𝒚	VERB
american_scientific_journal-1402	26	19	𝒅𝒅𝒍𝒍	𝒅𝒅𝒍𝒍	PROPN
american_scientific_journal-1402	26	20	�	�	PROPN
american_scientific_journal-1402	26	21	=	=	SYM
american_scientific_journal-1402	26	22	−𝒚𝒚𝟑𝟑	−𝒚𝒚𝟑𝟑	PROPN
american_scientific_journal-1402	26	23	(	(	PUNCT
american_scientific_journal-1402	26	24	4	4	X
american_scientific_journal-1402	26	25	)	)	PUNCT
american_scientific_journal-1402	26	26	equation	equation	NOUN
american_scientific_journal-1402	26	27	(	(	PUNCT
american_scientific_journal-1402	26	28	4	4	X
american_scientific_journal-1402	26	29	)	)	PUNCT
american_scientific_journal-1402	26	30	is	be	AUX
american_scientific_journal-1402	26	31	in	in	ADP
american_scientific_journal-1402	26	32	the	the	DET
american_scientific_journal-1402	26	33	form	form	NOUN
american_scientific_journal-1402	26	34	of	of	ADP
american_scientific_journal-1402	26	35	lane	lane	NOUN
american_scientific_journal-1402	26	36	emden	emden	PROPN
american_scientific_journal-1402	26	37	equation	equation	NOUN
american_scientific_journal-1402	26	38	,	,	PUNCT
american_scientific_journal-1402	26	39	the	the	DET
american_scientific_journal-1402	26	40	solution	solution	NOUN
american_scientific_journal-1402	26	41	of	of	ADP
american_scientific_journal-1402	26	42	which	which	PRON
american_scientific_journal-1402	26	43	is	be	AUX
american_scientific_journal-1402	26	44	𝒚𝒚	𝒚𝒚	NOUN
american_scientific_journal-1402	26	45	,	,	PUNCT
american_scientific_journal-1402	26	46	which	which	PRON
american_scientific_journal-1402	26	47	we	we	PRON
american_scientific_journal-1402	26	48	write	write	VERB
american_scientific_journal-1402	26	49	as	as	ADP
american_scientific_journal-1402	26	50	𝒅𝒅(𝒍𝒍	𝒅𝒅(𝒍𝒍	PROPN
american_scientific_journal-1402	26	51	)	)	PUNCT
american_scientific_journal-1402	26	52	since	since	SCONJ
american_scientific_journal-1402	26	53	the	the	DET
american_scientific_journal-1402	26	54	solution	solution	NOUN
american_scientific_journal-1402	26	55	of	of	ADP
american_scientific_journal-1402	26	56	𝟏𝟏	𝟏𝟏	NUM
american_scientific_journal-1402	26	57	𝒍𝒍𝟐𝟐	𝒍𝒍𝟐𝟐	PROPN
american_scientific_journal-1402	26	58	𝒅𝒅	𝒅𝒅	PROPN
american_scientific_journal-1402	26	59	𝒅𝒅𝒍𝒍	𝒅𝒅𝒍𝒍	PROPN
american_scientific_journal-1402	26	60	�	�	PROPN
american_scientific_journal-1402	26	61	𝒍𝒍𝟐𝟐	𝒍𝒍𝟐𝟐	PROPN
american_scientific_journal-1402	26	62	𝒅𝒅𝒚𝒚	𝒅𝒅𝒚𝒚	VERB
american_scientific_journal-1402	26	63	𝒅𝒅𝒍𝒍	𝒅𝒅𝒍𝒍	PROPN
american_scientific_journal-1402	26	64	�	�	PROPN
american_scientific_journal-1402	27	1	=	=	PUNCT
american_scientific_journal-1402	27	2	−𝒚𝒚𝟑𝟑	−𝒚𝒚𝟑𝟑	PROPN
american_scientific_journal-1402	27	3	is	be	AUX
american_scientific_journal-1402	27	4	usually	usually	ADV
american_scientific_journal-1402	27	5	written	write	VERB
american_scientific_journal-1402	27	6	as	as	ADP
american_scientific_journal-1402	27	7	𝒅𝒅(𝒍𝒍	𝒅𝒅(𝒍𝒍	PROPN
american_scientific_journal-1402	27	8	)	)	PUNCT
american_scientific_journal-1402	27	9	,	,	PUNCT
american_scientific_journal-1402	27	10	the	the	DET
american_scientific_journal-1402	27	11	so	so	ADV
american_scientific_journal-1402	27	12	called	call	VERB
american_scientific_journal-1402	27	13	lane	lane	PROPN
american_scientific_journal-1402	27	14	emden	emden	PROPN
american_scientific_journal-1402	27	15	function	function	NOUN
american_scientific_journal-1402	27	16	.	.	PUNCT
american_scientific_journal-1402	28	1	lane	lane	PROPN
american_scientific_journal-1402	28	2	emden	emden	PROPN
american_scientific_journal-1402	28	3	function	function	NOUN
american_scientific_journal-1402	28	4	has	have	AUX
american_scientific_journal-1402	28	5	been	be	AUX
american_scientific_journal-1402	28	6	expressed	express	VERB
american_scientific_journal-1402	28	7	as	as	ADP
american_scientific_journal-1402	28	8	a	a	DET
american_scientific_journal-1402	28	9	power	power	NOUN
american_scientific_journal-1402	28	10	series	series	NOUN
american_scientific_journal-1402	28	11	in	in	ADP
american_scientific_journal-1402	28	12	even	even	ADV
american_scientific_journal-1402	28	13	powers	power	NOUN
american_scientific_journal-1402	28	14	of	of	ADP
american_scientific_journal-1402	28	15	𝒍𝒍	𝒍𝒍	NOUN
american_scientific_journal-1402	28	16	.the	.the	PUNCT
american_scientific_journal-1402	29	1	power	power	PROPN
american_scientific_journal-1402	29	2	series	series	PROPN
american_scientific_journal-1402	29	3	converges	converge	VERB
american_scientific_journal-1402	29	4	slowly	slowly	ADV
american_scientific_journal-1402	29	5	,	,	PUNCT
american_scientific_journal-1402	29	6	and	and	CCONJ
american_scientific_journal-1402	29	7	it	it	PRON
american_scientific_journal-1402	29	8	is	be	AUX
american_scientific_journal-1402	29	9	more	more	ADV
american_scientific_journal-1402	29	10	advantageous	advantageous	ADJ
american_scientific_journal-1402	29	11	to	to	PART
american_scientific_journal-1402	29	12	obtain	obtain	VERB
american_scientific_journal-1402	29	13	the	the	DET
american_scientific_journal-1402	29	14	solution	solution	NOUN
american_scientific_journal-1402	29	15	in	in	ADP
american_scientific_journal-1402	29	16	terms	term	NOUN
american_scientific_journal-1402	29	17	of	of	ADP
american_scientific_journal-1402	29	18	a	a	DET
american_scientific_journal-1402	29	19	table	table	NOUN
american_scientific_journal-1402	29	20	of	of	ADP
american_scientific_journal-1402	29	21	values	value	NOUN
american_scientific_journal-1402	29	22	according	accord	VERB
american_scientific_journal-1402	29	23	to	to	ADP
american_scientific_journal-1402	29	24	dharmawardane	dharmawardane	NOUN
american_scientific_journal-1402	29	25	[	[	X
american_scientific_journal-1402	29	26	2	2	NUM
american_scientific_journal-1402	29	27	]	]	PUNCT
american_scientific_journal-1402	29	28	.	.	PUNCT
american_scientific_journal-1402	30	1	he	he	PRON
american_scientific_journal-1402	30	2	has	have	AUX
american_scientific_journal-1402	30	3	plotted	plot	VERB
american_scientific_journal-1402	30	4	the	the	DET
american_scientific_journal-1402	30	5	graph	graph	NOUN
american_scientific_journal-1402	30	6	of	of	ADP
american_scientific_journal-1402	30	7	𝒅𝒅	𝒅𝒅	PROPN
american_scientific_journal-1402	30	8	�	�	PROPN
american_scientific_journal-1402	30	9	𝒅𝒅	𝒅𝒅	PROPN
american_scientific_journal-1402	30	10	𝒍𝒍	𝒍𝒍	PROPN
american_scientific_journal-1402	30	11	�	�	PROPN
american_scientific_journal-1402	30	12	and	and	CCONJ
american_scientific_journal-1402	30	13	𝒅𝒅	𝒅𝒅	PROPN
american_scientific_journal-1402	30	14	�	�	PROPN
american_scientific_journal-1402	30	15	𝒅𝒅	𝒅𝒅	NOUN
american_scientific_journal-1402	30	16	𝒍𝒍	𝒍𝒍	PROPN
american_scientific_journal-1402	30	17	�	�	PROPN
american_scientific_journal-1402	31	1	+	+	CCONJ
american_scientific_journal-1402	31	2	𝒅𝒅	𝒅𝒅	PROPN
american_scientific_journal-1402	31	3	𝒍𝒍	𝒍𝒍	NOUN
american_scientific_journal-1402	31	4	𝒅𝒅′	𝒅𝒅′	PROPN
american_scientific_journal-1402	31	5	�	�	PROPN
american_scientific_journal-1402	31	6	𝒅𝒅	𝒅𝒅	PROPN
american_scientific_journal-1402	31	7	𝒍𝒍	𝒍𝒍	NOUN
american_scientific_journal-1402	31	8	�	�	PROPN
american_scientific_journal-1402	31	9	against	against	ADP
american_scientific_journal-1402	31	10	𝒅𝒅	𝒅𝒅	PROPN
american_scientific_journal-1402	31	11	𝒍𝒍	𝒍𝒍	NOUN
american_scientific_journal-1402	31	12	which	which	PRON
american_scientific_journal-1402	31	13	is	be	AUX
american_scientific_journal-1402	31	14	reproduced	reproduce	VERB
american_scientific_journal-1402	31	15	in	in	ADP
american_scientific_journal-1402	31	16	figure	figure	NOUN
american_scientific_journal-1402	31	17	1	1	NUM
american_scientific_journal-1402	31	18	,	,	PUNCT
american_scientific_journal-1402	31	19	where	where	SCONJ
american_scientific_journal-1402	31	20	𝒍𝒍	𝒍𝒍	NOUN
american_scientific_journal-1402	31	21	=	=	SYM
american_scientific_journal-1402	31	22	𝒅𝒅	𝒅𝒅	PROPN
american_scientific_journal-1402	31	23	𝒍𝒍	𝒍𝒍	VERB
american_scientific_journal-1402	31	24	now	now	ADV
american_scientific_journal-1402	31	25	as	as	SCONJ
american_scientific_journal-1402	31	26	it	it	PRON
american_scientific_journal-1402	31	27	has	have	AUX
american_scientific_journal-1402	31	28	been	be	AUX
american_scientific_journal-1402	31	29	shown	show	VERB
american_scientific_journal-1402	31	30	in	in	ADP
american_scientific_journal-1402	31	31	wimaladharma	wimaladharma	NOUN
american_scientific_journal-1402	32	1	[	[	X
american_scientific_journal-1402	32	2	3	3	X
american_scientific_journal-1402	32	3	]	]	PUNCT
american_scientific_journal-1402	32	4	that	that	SCONJ
american_scientific_journal-1402	32	5	𝑒𝑒𝑈𝑈(𝑅𝑅	𝑒𝑒𝑈𝑈(𝑅𝑅	NOUN
american_scientific_journal-1402	32	6	)	)	PUNCT
american_scientific_journal-1402	32	7	=	=	SYM
american_scientific_journal-1402	32	8	1	1	NUM
american_scientific_journal-1402	32	9	±	±	NUM
american_scientific_journal-1402	32	10	φ(𝑅𝑅	φ(𝑅𝑅	PROPN
american_scientific_journal-1402	32	11	)	)	PUNCT
american_scientific_journal-1402	32	12	,	,	PUNCT
american_scientific_journal-1402	32	13	where	where	SCONJ
american_scientific_journal-1402	32	14	φ(𝑅𝑅	φ(𝑅𝑅	NOUN
american_scientific_journal-1402	32	15	)	)	PUNCT
american_scientific_journal-1402	32	16	is	be	AUX
american_scientific_journal-1402	32	17	the	the	DET
american_scientific_journal-1402	32	18	newtonian	newtonian	ADJ
american_scientific_journal-1402	32	19	potential	potential	NOUN
american_scientific_journal-1402	32	20	divided	divide	VERB
american_scientific_journal-1402	32	21	by	by	ADP
american_scientific_journal-1402	32	22	𝑐𝑐2	𝑐𝑐2	PROPN
american_scientific_journal-1402	32	23	,	,	PUNCT
american_scientific_journal-1402	32	24	where	where	SCONJ
american_scientific_journal-1402	32	25	𝑐𝑐	𝑐𝑐	PROPN
american_scientific_journal-1402	32	26	is	be	AUX
american_scientific_journal-1402	32	27	the	the	DET
american_scientific_journal-1402	32	28	velocity	velocity	NOUN
american_scientific_journal-1402	32	29	of	of	ADP
american_scientific_journal-1402	32	30	light	light	NOUN
american_scientific_journal-1402	32	31	.	.	PUNCT
american_scientific_journal-1402	33	1	assuming	assume	VERB
american_scientific_journal-1402	33	2	that	that	SCONJ
american_scientific_journal-1402	33	3	when	when	SCONJ
american_scientific_journal-1402	33	4	𝑅𝑅	𝑅𝑅	PROPN
american_scientific_journal-1402	33	5	=	=	SYM
american_scientific_journal-1402	33	6	0	0	PROPN
american_scientific_journal-1402	33	7	,	,	PUNCT
american_scientific_journal-1402	33	8	φ	φ	NOUN
american_scientific_journal-1402	33	9	and	and	CCONJ
american_scientific_journal-1402	33	10	𝜕𝜕φ	𝜕𝜕φ	ADJ
american_scientific_journal-1402	33	11	𝜕𝜕𝑅𝑅	𝜕𝜕𝑅𝑅	PROPN
american_scientific_journal-1402	33	12	to	to	PART
american_scientific_journal-1402	33	13	be	be	AUX
american_scientific_journal-1402	33	14	equal	equal	ADJ
american_scientific_journal-1402	33	15	to	to	ADP
american_scientific_journal-1402	33	16	zero	zero	NUM
american_scientific_journal-1402	33	17	,	,	PUNCT
american_scientific_journal-1402	33	18	due	due	ADJ
american_scientific_journal-1402	33	19	to	to	ADP
american_scientific_journal-1402	33	20	physical	physical	ADJ
american_scientific_journal-1402	33	21	conditions	condition	NOUN
american_scientific_journal-1402	33	22	,	,	PUNCT
american_scientific_journal-1402	33	23	it	it	PRON
american_scientific_journal-1402	33	24	can	can	AUX
american_scientific_journal-1402	33	25	be	be	AUX
american_scientific_journal-1402	33	26	proved	prove	VERB
american_scientific_journal-1402	33	27	that	that	SCONJ
american_scientific_journal-1402	33	28	𝑦𝑦(0	𝑦𝑦(0	NOUN
american_scientific_journal-1402	33	29	)	)	PUNCT
american_scientific_journal-1402	33	30	=	=	SYM
american_scientific_journal-1402	33	31	1	1	NUM
american_scientific_journal-1402	33	32	and	and	CCONJ
american_scientific_journal-1402	33	33	𝑦𝑦′(0	𝑦𝑦′(0	NUM
american_scientific_journal-1402	33	34	)	)	PUNCT
american_scientific_journal-1402	34	1	=	=	SYM
american_scientific_journal-1402	35	1	0	0	X
american_scientific_journal-1402	35	2	.	.	PUNCT
american_scientific_journal-1402	36	1	𝑦𝑦	𝑦𝑦	PROPN
american_scientific_journal-1402	36	2	156	156	NUM
american_scientific_journal-1402	36	3	american	american	ADJ
american_scientific_journal-1402	36	4	scientific	scientific	ADJ
american_scientific_journal-1402	36	5	research	research	NOUN
american_scientific_journal-1402	36	6	journal	journal	NOUN
american_scientific_journal-1402	36	7	for	for	ADP
american_scientific_journal-1402	36	8	engineering	engineering	NOUN
american_scientific_journal-1402	36	9	,	,	PUNCT
american_scientific_journal-1402	36	10	technology	technology	NOUN
american_scientific_journal-1402	36	11	,	,	PUNCT
american_scientific_journal-1402	36	12	and	and	CCONJ
american_scientific_journal-1402	36	13	sciences	science	NOUN
american_scientific_journal-1402	36	14	(	(	PUNCT
american_scientific_journal-1402	36	15	asrjets	asrjet	NOUN
american_scientific_journal-1402	36	16	)	)	PUNCT
american_scientific_journal-1402	36	17	(	(	PUNCT
american_scientific_journal-1402	36	18	2016	2016	NUM
american_scientific_journal-1402	36	19	)	)	PUNCT
american_scientific_journal-1402	36	20	volume	volume	NOUN
american_scientific_journal-1402	36	21	17	17	NUM
american_scientific_journal-1402	36	22	,	,	PUNCT
american_scientific_journal-1402	36	23	no	no	DET
american_scientific_journal-1402	36	24	1	1	NUM
american_scientific_journal-1402	36	25	,	,	PUNCT
american_scientific_journal-1402	36	26	pp	pp	ADV
american_scientific_journal-1402	36	27	155	155	NUM
american_scientific_journal-1402	36	28	-	-	SYM
american_scientific_journal-1402	36	29	164	164	NUM
american_scientific_journal-1402	36	30	therefore	therefore	ADV
american_scientific_journal-1402	36	31	the	the	DET
american_scientific_journal-1402	36	32	initial	initial	NOUN
american_scientific_journal-1402	36	33	of	of	ADP
american_scientific_journal-1402	36	34	the	the	DET
american_scientific_journal-1402	36	35	equation	equation	NOUN
american_scientific_journal-1402	36	36	(	(	PUNCT
american_scientific_journal-1402	36	37	3	3	X
american_scientific_journal-1402	36	38	)	)	PUNCT
american_scientific_journal-1402	36	39	are	be	AUX
american_scientific_journal-1402	36	40	the	the	DET
american_scientific_journal-1402	36	41	same	same	ADJ
american_scientific_journal-1402	36	42	as	as	ADP
american_scientific_journal-1402	36	43	the	the	DET
american_scientific_journal-1402	36	44	initial	initial	ADJ
american_scientific_journal-1402	36	45	conditions	condition	NOUN
american_scientific_journal-1402	36	46	of	of	ADP
american_scientific_journal-1402	36	47	lane	lane	NOUN
american_scientific_journal-1402	36	48	emden	emden	ADJ
american_scientific_journal-1402	36	49	equation	equation	NOUN
american_scientific_journal-1402	36	50	.	.	PUNCT
american_scientific_journal-1402	37	1	as	as	ADP
american_scientific_journal-1402	37	2	an	an	DET
american_scientific_journal-1402	37	3	illustration	illustration	NOUN
american_scientific_journal-1402	37	4	we	we	PRON
american_scientific_journal-1402	37	5	have	have	VERB
american_scientific_journal-1402	37	6	,	,	PUNCT
american_scientific_journal-1402	37	7	for	for	ADP
american_scientific_journal-1402	37	8	a	a	DET
american_scientific_journal-1402	37	9	few	few	ADJ
american_scientific_journal-1402	37	10	values	value	NOUN
american_scientific_journal-1402	37	11	of	of	ADP
american_scientific_journal-1402	37	12	𝑥𝑥	𝑥𝑥	ADP
american_scientific_journal-1402	37	13	,	,	PUNCT
american_scientific_journal-1402	37	14	the	the	DET
american_scientific_journal-1402	37	15	values	value	NOUN
american_scientific_journal-1402	37	16	of	of	ADP
american_scientific_journal-1402	37	17	the	the	DET
american_scientific_journal-1402	37	18	emden	emden	ADJ
american_scientific_journal-1402	37	19	function	function	NOUN
american_scientific_journal-1402	37	20	𝜃𝜃(𝑥𝑥	𝜃𝜃(𝑥𝑥	PROPN
american_scientific_journal-1402	37	21	)	)	PUNCT
american_scientific_journal-1402	37	22	given	give	VERB
american_scientific_journal-1402	37	23	by	by	ADP
american_scientific_journal-1402	37	24	dharmawardane	dharmawardane	NOUN
american_scientific_journal-1402	38	1	[	[	X
american_scientific_journal-1402	38	2	2	2	NUM
american_scientific_journal-1402	38	3	]	]	PUNCT
american_scientific_journal-1402	38	4	.	.	PUNCT
american_scientific_journal-1402	39	1	figure	figure	NOUN
american_scientific_journal-1402	39	2	1	1	NUM
american_scientific_journal-1402	39	3	:	:	PUNCT
american_scientific_journal-1402	39	4	the	the	DET
american_scientific_journal-1402	39	5	graph	graph	NOUN
american_scientific_journal-1402	39	6	of	of	ADP
american_scientific_journal-1402	39	7	𝜃𝜃	𝜃𝜃	PROPN
american_scientific_journal-1402	39	8	�	�	PROPN
american_scientific_journal-1402	39	9	𝑅𝑅	𝑅𝑅	PROPN
american_scientific_journal-1402	39	10	𝑙𝑙	𝑙𝑙	PROPN
american_scientific_journal-1402	39	11	�	�	PROPN
american_scientific_journal-1402	39	12	and	and	CCONJ
american_scientific_journal-1402	39	13	𝜃𝜃	𝜃𝜃	PROPN
american_scientific_journal-1402	39	14	�	�	PROPN
american_scientific_journal-1402	39	15	𝑅𝑅	𝑅𝑅	PROPN
american_scientific_journal-1402	39	16	𝑙𝑙	𝑙𝑙	PROPN
american_scientific_journal-1402	39	17	�	�	PROPN
american_scientific_journal-1402	39	18	+	+	CCONJ
american_scientific_journal-1402	39	19	𝑅𝑅	𝑅𝑅	PROPN
american_scientific_journal-1402	39	20	𝑙𝑙	𝑙𝑙	ADJ
american_scientific_journal-1402	39	21	𝜃𝜃′	𝜃𝜃′	NOUN
american_scientific_journal-1402	39	22	�	�	PROPN
american_scientific_journal-1402	39	23	𝑅𝑅	𝑅𝑅	PROPN
american_scientific_journal-1402	39	24	𝑙𝑙	𝑙𝑙	PUNCT
american_scientific_journal-1402	39	25	�	�	PROPN
american_scientific_journal-1402	39	26	against	against	ADP
american_scientific_journal-1402	39	27	𝑅𝑅	𝑅𝑅	PROPN
american_scientific_journal-1402	39	28	𝑙𝑙	𝑙𝑙	PROPN
american_scientific_journal-1402	39	29	in	in	ADP
american_scientific_journal-1402	39	30	figure	figure	NOUN
american_scientific_journal-1402	39	31	2	2	NUM
american_scientific_journal-1402	39	32	a	a	DET
american_scientific_journal-1402	39	33	graph	graph	NOUN
american_scientific_journal-1402	39	34	of	of	ADP
american_scientific_journal-1402	39	35	�	�	PROPN
american_scientific_journal-1402	39	36	−	−	PROPN
american_scientific_journal-1402	39	37	�	�	PROPN
american_scientific_journal-1402	39	38	𝑅𝑅	𝑅𝑅	PROPN
american_scientific_journal-1402	39	39	𝑙𝑙	𝑙𝑙	PUNCT
american_scientific_journal-1402	39	40	�	�	PROPN
american_scientific_journal-1402	39	41	2	2	NUM
american_scientific_journal-1402	39	42	𝜃𝜃′	𝜃𝜃′	NOUN
american_scientific_journal-1402	39	43	�	�	NOUN
american_scientific_journal-1402	39	44	𝑅𝑅	𝑅𝑅	PROPN
american_scientific_journal-1402	39	45	𝑙𝑙	𝑙𝑙	PROPN
american_scientific_journal-1402	39	46	�	�	PROPN
american_scientific_journal-1402	39	47	�	�	PROPN
american_scientific_journal-1402	39	48	is	be	AUX
american_scientific_journal-1402	39	49	reproduced	reproduce	VERB
american_scientific_journal-1402	39	50	against	against	ADP
american_scientific_journal-1402	39	51	𝑅𝑅	𝑅𝑅	PROPN
american_scientific_journal-1402	39	52	𝑙𝑙	𝑙𝑙	PROPN
american_scientific_journal-1402	39	53	.	.	PUNCT
american_scientific_journal-1402	40	1	𝑅𝑅	𝑅𝑅	PROPN
american_scientific_journal-1402	40	2	𝑙𝑙	𝑙𝑙	PROPN
american_scientific_journal-1402	40	3	figure	figure	NOUN
american_scientific_journal-1402	40	4	2	2	NUM
american_scientific_journal-1402	40	5	:	:	PUNCT
american_scientific_journal-1402	40	6	the	the	DET
american_scientific_journal-1402	40	7	graph	graph	NOUN
american_scientific_journal-1402	40	8	of	of	ADP
american_scientific_journal-1402	40	9	�	�	PROPN
american_scientific_journal-1402	40	10	−	−	PROPN
american_scientific_journal-1402	40	11	�	�	PROPN
american_scientific_journal-1402	40	12	𝑅𝑅	𝑅𝑅	PROPN
american_scientific_journal-1402	40	13	𝑙𝑙	𝑙𝑙	PUNCT
american_scientific_journal-1402	40	14	�	�	PROPN
american_scientific_journal-1402	40	15	2	2	NUM
american_scientific_journal-1402	40	16	𝜃𝜃′	𝜃𝜃′	NOUN
american_scientific_journal-1402	40	17	�	�	NOUN
american_scientific_journal-1402	40	18	𝑅𝑅	𝑅𝑅	PROPN
american_scientific_journal-1402	40	19	𝑙𝑙	𝑙𝑙	PROPN
american_scientific_journal-1402	40	20	�	�	PROPN
american_scientific_journal-1402	40	21	�	�	PROPN
american_scientific_journal-1402	40	22	since	since	SCONJ
american_scientific_journal-1402	40	23	𝜃𝜃(𝑥𝑥	𝜃𝜃(𝑥𝑥	PROPN
american_scientific_journal-1402	40	24	)	)	PUNCT
american_scientific_journal-1402	40	25	=	=	SYM
american_scientific_journal-1402	40	26	𝑦𝑦(𝑥𝑥	𝑦𝑦(𝑥𝑥	PROPN
american_scientific_journal-1402	40	27	)	)	PUNCT
american_scientific_journal-1402	40	28	,	,	PUNCT
american_scientific_journal-1402	40	29	the	the	DET
american_scientific_journal-1402	40	30	interior	interior	ADJ
american_scientific_journal-1402	40	31	solution	solution	NOUN
american_scientific_journal-1402	40	32	for	for	ADP
american_scientific_journal-1402	40	33	the	the	DET
american_scientific_journal-1402	40	34	above	above	ADJ
american_scientific_journal-1402	40	35	distribution	distribution	NOUN
american_scientific_journal-1402	40	36	of	of	ADP
american_scientific_journal-1402	40	37	electrically	electrically	ADV
american_scientific_journal-1402	40	38	counterpoised	counterpoise	VERB
american_scientific_journal-1402	40	39	dust	dust	NOUN
american_scientific_journal-1402	40	40	(	(	PUNCT
american_scientific_journal-1402	40	41	ecd	ecd	PROPN
american_scientific_journal-1402	40	42	)	)	PUNCT
american_scientific_journal-1402	40	43	can	can	AUX
american_scientific_journal-1402	40	44	be	be	AUX
american_scientific_journal-1402	40	45	written	write	VERB
american_scientific_journal-1402	40	46	as	as	ADP
american_scientific_journal-1402	40	47	𝑒𝑒−𝑈𝑈	𝑒𝑒−𝑈𝑈	PROPN
american_scientific_journal-1402	40	48	=	=	PROPN
american_scientific_journal-1402	40	49	𝜃𝜃	𝜃𝜃	PROPN
american_scientific_journal-1402	40	50	�	�	PROPN
american_scientific_journal-1402	40	51	𝑅𝑅	𝑅𝑅	PROPN
american_scientific_journal-1402	40	52	𝑙𝑙	𝑙𝑙	PROPN
american_scientific_journal-1402	40	53	�	�	PROPN
american_scientific_journal-1402	40	54	,	,	PUNCT
american_scientific_journal-1402	40	55	where	where	SCONJ
american_scientific_journal-1402	40	56	𝑥𝑥	𝑥𝑥	ADP
american_scientific_journal-1402	40	57	=	=	PUNCT
american_scientific_journal-1402	40	58	𝑅𝑅	𝑅𝑅	PROPN
american_scientific_journal-1402	40	59	𝑙𝑙	𝑙𝑙	X
american_scientific_journal-1402	40	60	.	.	PUNCT
american_scientific_journal-1402	40	61	0	0	NUM
american_scientific_journal-1402	40	62	0.5	0.5	NUM
american_scientific_journal-1402	40	63	1	1	NUM
american_scientific_journal-1402	40	64	1.5	1.5	NUM
american_scientific_journal-1402	40	65	2	2	NUM
american_scientific_journal-1402	40	66	0	0	NUM
american_scientific_journal-1402	40	67	0.2	0.2	NUM
american_scientific_journal-1402	40	68	0.4	0.4	NUM
american_scientific_journal-1402	40	69	0.6	0.6	NUM
american_scientific_journal-1402	40	70	0.8	0.8	NUM
american_scientific_journal-1402	40	71	1	1	NUM
american_scientific_journal-1402	40	72	0	0	NUM
american_scientific_journal-1402	40	73	2	2	NUM
american_scientific_journal-1402	40	74	4	4	NUM
american_scientific_journal-1402	40	75	6	6	NUM
american_scientific_journal-1402	40	76	8	8	NUM
american_scientific_journal-1402	40	77	0	0	NUM
american_scientific_journal-1402	40	78	0.2	0.2	NUM
american_scientific_journal-1402	40	79	0.6	0.6	NUM
american_scientific_journal-1402	40	80	0.8	0.8	NUM
american_scientific_journal-1402	40	81	1	1	NUM
american_scientific_journal-1402	40	82	(	(	PUNCT
american_scientific_journal-1402	40	83	)	)	PUNCT
american_scientific_journal-1402	40	84	ry	ry	NOUN
american_scientific_journal-1402	40	85	θ=	θ=	NOUN
american_scientific_journal-1402	40	86			NOUN
american_scientific_journal-1402	40	87			PUNCT
american_scientific_journal-1402	41	1			PROPN
american_scientific_journal-1402	41	2			NOUN
american_scientific_journal-1402	42	1			PROPN
american_scientific_journal-1402	42	2	=	=	PROPN
american_scientific_journal-1402	42	3	l	l	X
american_scientific_journal-1402	42	4	ry	ry	NOUN
american_scientific_journal-1402	42	5	θ	θ	PROPN
american_scientific_journal-1402	42	6	𝑦𝑦	𝑦𝑦	PROPN
american_scientific_journal-1402	42	7	157	157	NUM
american_scientific_journal-1402	42	8	american	american	ADJ
american_scientific_journal-1402	42	9	scientific	scientific	ADJ
american_scientific_journal-1402	42	10	research	research	NOUN
american_scientific_journal-1402	42	11	journal	journal	NOUN
american_scientific_journal-1402	42	12	for	for	ADP
american_scientific_journal-1402	42	13	engineering	engineering	NOUN
american_scientific_journal-1402	42	14	,	,	PUNCT
american_scientific_journal-1402	42	15	technology	technology	NOUN
american_scientific_journal-1402	42	16	,	,	PUNCT
american_scientific_journal-1402	42	17	and	and	CCONJ
american_scientific_journal-1402	42	18	sciences	science	NOUN
american_scientific_journal-1402	42	19	(	(	PUNCT
american_scientific_journal-1402	42	20	asrjets	asrjet	NOUN
american_scientific_journal-1402	42	21	)	)	PUNCT
american_scientific_journal-1402	42	22	(	(	PUNCT
american_scientific_journal-1402	42	23	2016	2016	NUM
american_scientific_journal-1402	42	24	)	)	PUNCT
american_scientific_journal-1402	42	25	volume	volume	NOUN
american_scientific_journal-1402	42	26	17	17	NUM
american_scientific_journal-1402	42	27	,	,	PUNCT
american_scientific_journal-1402	42	28	no	no	DET
american_scientific_journal-1402	42	29	1	1	NUM
american_scientific_journal-1402	42	30	,	,	PUNCT
american_scientific_journal-1402	42	31	pp	pp	ADV
american_scientific_journal-1402	42	32	155	155	NUM
american_scientific_journal-1402	42	33	-	-	SYM
american_scientific_journal-1402	42	34	164	164	NUM
american_scientific_journal-1402	42	35	therefore	therefore	ADV
american_scientific_journal-1402	42	36	the	the	DET
american_scientific_journal-1402	42	37	metric	metric	NOUN
american_scientific_journal-1402	42	38	for	for	ADP
american_scientific_journal-1402	42	39	the	the	DET
american_scientific_journal-1402	42	40	interior	interior	ADJ
american_scientific_journal-1402	42	41	region	region	NOUN
american_scientific_journal-1402	42	42	comprising	comprise	VERB
american_scientific_journal-1402	42	43	electrically	electrically	ADV
american_scientific_journal-1402	42	44	counterpoised	counterpoise	VERB
american_scientific_journal-1402	42	45	dust	dust	NOUN
american_scientific_journal-1402	42	46	(	(	PUNCT
american_scientific_journal-1402	42	47	ecd	ecd	PROPN
american_scientific_journal-1402	42	48	)	)	PUNCT
american_scientific_journal-1402	42	49	can	can	AUX
american_scientific_journal-1402	42	50	be	be	AUX
american_scientific_journal-1402	42	51	written	write	VERB
american_scientific_journal-1402	42	52	in	in	ADP
american_scientific_journal-1402	42	53	the	the	DET
american_scientific_journal-1402	42	54	form	form	NOUN
american_scientific_journal-1402	42	55	table	table	NOUN
american_scientific_journal-1402	42	56	1	1	NUM
american_scientific_journal-1402	42	57	:	:	PUNCT
american_scientific_journal-1402	42	58	the	the	DET
american_scientific_journal-1402	42	59	values	value	NOUN
american_scientific_journal-1402	42	60	of	of	ADP
american_scientific_journal-1402	42	61	the	the	DET
american_scientific_journal-1402	42	62	emden	emden	ADJ
american_scientific_journal-1402	42	63	function	function	NOUN
american_scientific_journal-1402	42	64	𝜃𝜃(𝑥𝑥	𝜃𝜃(𝑥𝑥	PROPN
american_scientific_journal-1402	42	65	)	)	PUNCT
american_scientific_journal-1402	42	66	𝑥𝑥	𝑥𝑥	ADP
american_scientific_journal-1402	42	67	𝜃𝜃(𝑥𝑥	𝜃𝜃(𝑥𝑥	PROPN
american_scientific_journal-1402	42	68	)	)	PUNCT
american_scientific_journal-1402	42	69	0.0	0.0	NUM
american_scientific_journal-1402	42	70	1.000000	1.000000	NUM
american_scientific_journal-1402	42	71	1.0	1.0	NUM
american_scientific_journal-1402	42	72	0.855058	0.855058	NUM
american_scientific_journal-1402	42	73	2.0	2.0	NUM
american_scientific_journal-1402	42	74	0.582851	0.582851	NUM
american_scientific_journal-1402	42	75	3.0	3.0	NUM
american_scientific_journal-1402	42	76	0.359227	0.359227	NUM
american_scientific_journal-1402	42	77	4.0	4.0	NUM
american_scientific_journal-1402	42	78	0.209282	0.209282	NUM
american_scientific_journal-1402	42	79	5.0	5.0	NUM
american_scientific_journal-1402	42	80	0.11082	0.11082	NUM
american_scientific_journal-1402	42	81	6.0	6.0	NUM
american_scientific_journal-1402	42	82	0.043738	0.043738	NUM
american_scientific_journal-1402	42	83	7.0	7.0	NUM
american_scientific_journal-1402	42	84	-0.0043122	-0.0043122	NOUN
american_scientific_journal-1402	42	85	𝑑𝑑𝑑𝑑2	𝑑𝑑𝑑𝑑2	PUNCT
american_scientific_journal-1402	43	1	=	=	SYM
american_scientific_journal-1402	43	2	1	1	NUM
american_scientific_journal-1402	43	3	�	�	PROPN
american_scientific_journal-1402	43	4	𝜃𝜃	𝜃𝜃	PROPN
american_scientific_journal-1402	43	5	�	�	PROPN
american_scientific_journal-1402	43	6	𝑅𝑅𝑙𝑙	𝑅𝑅𝑙𝑙	ADJ
american_scientific_journal-1402	43	7	�	�	NOUN
american_scientific_journal-1402	43	8	�	�	PROPN
american_scientific_journal-1402	43	9	2	2	NUM
american_scientific_journal-1402	43	10	𝑐𝑐2𝑑𝑑𝑑𝑑2	𝑐𝑐2𝑑𝑑𝑑𝑑2	SYM
american_scientific_journal-1402	43	11	−	−	PROPN
american_scientific_journal-1402	43	12	�	�	PROPN
american_scientific_journal-1402	43	13	𝜃𝜃	𝜃𝜃	PROPN
american_scientific_journal-1402	43	14	�	�	PROPN
american_scientific_journal-1402	43	15	𝑅𝑅	𝑅𝑅	PROPN
american_scientific_journal-1402	43	16	𝑙𝑙	𝑙𝑙	PROPN
american_scientific_journal-1402	43	17	�	�	PROPN
american_scientific_journal-1402	43	18	�	�	PROPN
american_scientific_journal-1402	43	19	2	2	NUM
american_scientific_journal-1402	43	20	(	(	PUNCT
american_scientific_journal-1402	43	21	𝑑𝑑𝑅𝑅2	𝑑𝑑𝑅𝑅2	NOUN
american_scientific_journal-1402	43	22	+	+	X
american_scientific_journal-1402	43	23	𝑅𝑅2𝑑𝑑𝜃𝜃2	𝑅𝑅2𝑑𝑑𝜃𝜃2	X
american_scientific_journal-1402	43	24	+	+	CCONJ
american_scientific_journal-1402	43	25	𝑅𝑅2	𝑅𝑅2	ADJ
american_scientific_journal-1402	43	26	sin2	sin2	NOUN
american_scientific_journal-1402	43	27	𝜃𝜃	𝜃𝜃	PROPN
american_scientific_journal-1402	43	28	𝑑𝑑𝑑𝑑2	𝑑𝑑𝑑𝑑2	PROPN
american_scientific_journal-1402	43	29	)	)	PUNCT
american_scientific_journal-1402	43	30	,	,	PUNCT
american_scientific_journal-1402	43	31	𝑅𝑅	𝑅𝑅	PROPN
american_scientific_journal-1402	43	32	≤	≤	NUM
american_scientific_journal-1402	43	33	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1402	43	34	(	(	PUNCT
american_scientific_journal-1402	43	35	5	5	NUM
american_scientific_journal-1402	43	36	)	)	PUNCT
american_scientific_journal-1402	43	37	where	where	SCONJ
american_scientific_journal-1402	43	38	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1402	43	39	is	be	AUX
american_scientific_journal-1402	43	40	the	the	DET
american_scientific_journal-1402	43	41	radius	radius	NOUN
american_scientific_journal-1402	43	42	of	of	ADP
american_scientific_journal-1402	43	43	the	the	DET
american_scientific_journal-1402	43	44	sphere	sphere	NOUN
american_scientific_journal-1402	43	45	.	.	PUNCT
american_scientific_journal-1402	44	1	now	now	ADV
american_scientific_journal-1402	44	2	for	for	ADP
american_scientific_journal-1402	44	3	the	the	DET
american_scientific_journal-1402	44	4	exterior	exterior	ADJ
american_scientific_journal-1402	44	5	vacuum	vacuum	NOUN
american_scientific_journal-1402	44	6	region	region	NOUN
american_scientific_journal-1402	44	7	,	,	PUNCT
american_scientific_journal-1402	44	8	the	the	DET
american_scientific_journal-1402	44	9	matter	matter	NOUN
american_scientific_journal-1402	44	10	density	density	NOUN
american_scientific_journal-1402	44	11	𝜌𝜌	𝜌𝜌	NOUN
american_scientific_journal-1402	44	12	is	be	AUX
american_scientific_journal-1402	44	13	equal	equal	ADJ
american_scientific_journal-1402	44	14	to	to	ADP
american_scientific_journal-1402	44	15	zero	zero	NUM
american_scientific_journal-1402	44	16	since	since	SCONJ
american_scientific_journal-1402	44	17	there	there	PRON
american_scientific_journal-1402	44	18	is	be	VERB
american_scientific_journal-1402	44	19	no	no	DET
american_scientific_journal-1402	44	20	matter	matter	NOUN
american_scientific_journal-1402	44	21	present	present	ADJ
american_scientific_journal-1402	44	22	there	there	ADV
american_scientific_journal-1402	44	23	.	.	PUNCT
american_scientific_journal-1402	45	1	therefore	therefore	ADV
american_scientific_journal-1402	45	2	,	,	PUNCT
american_scientific_journal-1402	45	3	for	for	ADP
american_scientific_journal-1402	45	4	the	the	DET
american_scientific_journal-1402	45	5	exterior	exterior	ADJ
american_scientific_journal-1402	45	6	vacuum	vacuum	NOUN
american_scientific_journal-1402	45	7	region	region	NOUN
american_scientific_journal-1402	45	8	(	(	PUNCT
american_scientific_journal-1402	45	9	2	2	X
american_scientific_journal-1402	45	10	)	)	PUNCT
american_scientific_journal-1402	45	11	becomes	become	VERB
american_scientific_journal-1402	45	12	1	1	NUM
american_scientific_journal-1402	45	13	𝑅𝑅2	𝑅𝑅2	NOUN
american_scientific_journal-1402	45	14	𝑑𝑑	𝑑𝑑	VERB
american_scientific_journal-1402	45	15	𝑑𝑑𝑅𝑅	𝑑𝑑𝑅𝑅	NOUN
american_scientific_journal-1402	45	16	�	�	NOUN
american_scientific_journal-1402	45	17	𝑅𝑅2	𝑅𝑅2	NOUN
american_scientific_journal-1402	45	18	𝑑𝑑𝑒𝑒	𝑑𝑑𝑒𝑒	ADJ
american_scientific_journal-1402	45	19	−𝑈𝑈	−𝑈𝑈	PROPN
american_scientific_journal-1402	45	20	𝑑𝑑𝑅𝑅	𝑑𝑑𝑅𝑅	NOUN
american_scientific_journal-1402	45	21	�	�	PROPN
american_scientific_journal-1402	45	22	=	=	SYM
american_scientific_journal-1402	45	23	0	0	NUM
american_scientific_journal-1402	46	1	(	(	PUNCT
american_scientific_journal-1402	46	2	6	6	NUM
american_scientific_journal-1402	46	3	)	)	PUNCT
american_scientific_journal-1402	46	4	the	the	DET
american_scientific_journal-1402	46	5	solution	solution	NOUN
american_scientific_journal-1402	46	6	of	of	ADP
american_scientific_journal-1402	46	7	the	the	DET
american_scientific_journal-1402	46	8	differential	differential	ADJ
american_scientific_journal-1402	46	9	equation	equation	NOUN
american_scientific_journal-1402	46	10	(	(	PUNCT
american_scientific_journal-1402	46	11	6	6	NUM
american_scientific_journal-1402	46	12	)	)	PUNCT
american_scientific_journal-1402	46	13	takes	take	VERB
american_scientific_journal-1402	46	14	the	the	DET
american_scientific_journal-1402	46	15	form	form	NOUN
american_scientific_journal-1402	46	16	𝑒𝑒−𝑈𝑈	𝑒𝑒−𝑈𝑈	NOUN
american_scientific_journal-1402	46	17	=	=	PUNCT
american_scientific_journal-1402	46	18	𝐴𝐴1	𝐴𝐴1	PROPN
american_scientific_journal-1402	46	19	+	+	CCONJ
american_scientific_journal-1402	46	20	𝐴𝐴2	𝐴𝐴2	PROPN
american_scientific_journal-1402	46	21	𝑅𝑅	𝑅𝑅	PROPN
american_scientific_journal-1402	46	22	(	(	PUNCT
american_scientific_journal-1402	46	23	7	7	NUM
american_scientific_journal-1402	46	24	)	)	PUNCT
american_scientific_journal-1402	46	25	where	where	SCONJ
american_scientific_journal-1402	46	26	𝐴𝐴1	𝐴𝐴1	PROPN
american_scientific_journal-1402	46	27	is	be	AUX
american_scientific_journal-1402	46	28	a	a	DET
american_scientific_journal-1402	46	29	constant	constant	ADJ
american_scientific_journal-1402	46	30	.	.	PUNCT
american_scientific_journal-1402	47	1	therefore	therefore	ADV
american_scientific_journal-1402	47	2	the	the	DET
american_scientific_journal-1402	47	3	corresponding	correspond	VERB
american_scientific_journal-1402	47	4	exterior	exterior	ADJ
american_scientific_journal-1402	47	5	metric	metric	NOUN
american_scientific_journal-1402	47	6	can	can	AUX
american_scientific_journal-1402	47	7	be	be	AUX
american_scientific_journal-1402	47	8	written	write	VERB
american_scientific_journal-1402	47	9	as	as	ADP
american_scientific_journal-1402	47	10	𝑑𝑑𝑑𝑑2	𝑑𝑑𝑑𝑑2	PROPN
american_scientific_journal-1402	47	11	=	=	SYM
american_scientific_journal-1402	47	12	𝑒𝑒2𝑈𝑈𝑐𝑐2𝑑𝑑𝑑𝑑2	𝑒𝑒2𝑈𝑈𝑐𝑐2𝑑𝑑𝑑𝑑2	PROPN
american_scientific_journal-1402	47	13	−	−	PROPN
american_scientific_journal-1402	47	14	𝑒𝑒−2𝑈𝑈(𝑑𝑑𝑅𝑅2	𝑒𝑒−2𝑈𝑈(𝑑𝑑𝑅𝑅2	NOUN
american_scientific_journal-1402	47	15	+	+	CCONJ
american_scientific_journal-1402	47	16	𝑅𝑅2𝑑𝑑𝜃𝜃2	𝑅𝑅2𝑑𝑑𝜃𝜃2	X
american_scientific_journal-1402	47	17	+	+	CCONJ
american_scientific_journal-1402	47	18	𝑅𝑅2	𝑅𝑅2	ADJ
american_scientific_journal-1402	47	19	sin2	sin2	NOUN
american_scientific_journal-1402	47	20	𝜃𝜃	𝜃𝜃	PROPN
american_scientific_journal-1402	47	21	𝑑𝑑𝑑𝑑2	𝑑𝑑𝑑𝑑2	PROPN
american_scientific_journal-1402	47	22	)	)	PUNCT
american_scientific_journal-1402	48	1	(	(	PUNCT
american_scientific_journal-1402	48	2	8)	8)	NUM
american_scientific_journal-1402	48	3	where	where	SCONJ
american_scientific_journal-1402	48	4	𝑒𝑒−𝑈𝑈	𝑒𝑒−𝑈𝑈	PROPN
american_scientific_journal-1402	48	5	=	=	PUNCT
american_scientific_journal-1402	48	6	𝐴𝐴1	𝐴𝐴1	PROPN
american_scientific_journal-1402	48	7	+	+	CCONJ
american_scientific_journal-1402	48	8	𝐴𝐴2	𝐴𝐴2	PROPN
american_scientific_journal-1402	48	9	𝑅𝑅	𝑅𝑅	PROPN
american_scientific_journal-1402	48	10	,	,	PUNCT
american_scientific_journal-1402	48	11	𝑅𝑅	𝑅𝑅	PROPN
american_scientific_journal-1402	48	12	>	>	X
american_scientific_journal-1402	48	13	𝑎𝑎.	𝑎𝑎.	PROPN
american_scientific_journal-1402	48	14	now	now	ADV
american_scientific_journal-1402	48	15	,	,	PUNCT
american_scientific_journal-1402	48	16	from	from	ADP
american_scientific_journal-1402	48	17	(	(	PUNCT
american_scientific_journal-1402	48	18	5	5	NUM
american_scientific_journal-1402	48	19	)	)	PUNCT
american_scientific_journal-1402	48	20	and	and	CCONJ
american_scientific_journal-1402	48	21	(	(	PUNCT
american_scientific_journal-1402	48	22	8)	8)	NUM
american_scientific_journal-1402	48	23	the	the	DET
american_scientific_journal-1402	48	24	metric	metric	NOUN
american_scientific_journal-1402	48	25	for	for	ADP
american_scientific_journal-1402	48	26	the	the	DET
american_scientific_journal-1402	48	27	whole	whole	ADJ
american_scientific_journal-1402	48	28	distribution	distribution	NOUN
american_scientific_journal-1402	48	29	of	of	ADP
american_scientific_journal-1402	48	30	matter	matter	NOUN
american_scientific_journal-1402	48	31	can	can	AUX
american_scientific_journal-1402	48	32	be	be	AUX
american_scientific_journal-1402	48	33	written	write	VERB
american_scientific_journal-1402	48	34	as	as	ADP
american_scientific_journal-1402	48	35	158	158	NUM
american_scientific_journal-1402	48	36	american	american	ADJ
american_scientific_journal-1402	48	37	scientific	scientific	ADJ
american_scientific_journal-1402	48	38	research	research	NOUN
american_scientific_journal-1402	48	39	journal	journal	NOUN
american_scientific_journal-1402	48	40	for	for	ADP
american_scientific_journal-1402	48	41	engineering	engineering	NOUN
american_scientific_journal-1402	48	42	,	,	PUNCT
american_scientific_journal-1402	48	43	technology	technology	NOUN
american_scientific_journal-1402	48	44	,	,	PUNCT
american_scientific_journal-1402	48	45	and	and	CCONJ
american_scientific_journal-1402	48	46	sciences	science	NOUN
american_scientific_journal-1402	48	47	(	(	PUNCT
american_scientific_journal-1402	48	48	asrjets	asrjet	NOUN
american_scientific_journal-1402	48	49	)	)	PUNCT
american_scientific_journal-1402	48	50	(	(	PUNCT
american_scientific_journal-1402	48	51	2016	2016	NUM
american_scientific_journal-1402	48	52	)	)	PUNCT
american_scientific_journal-1402	48	53	volume	volume	NOUN
american_scientific_journal-1402	48	54	17	17	NUM
american_scientific_journal-1402	48	55	,	,	PUNCT
american_scientific_journal-1402	48	56	no	no	DET
american_scientific_journal-1402	48	57	1	1	NUM
american_scientific_journal-1402	48	58	,	,	PUNCT
american_scientific_journal-1402	48	59	pp	pp	ADV
american_scientific_journal-1402	48	60	155	155	NUM
american_scientific_journal-1402	48	61	-	-	SYM
american_scientific_journal-1402	48	62	164	164	NUM
american_scientific_journal-1402	48	63	𝑑𝑑𝑑𝑑2	𝑑𝑑𝑑𝑑2	NOUN
american_scientific_journal-1402	48	64	=	=	SYM
american_scientific_journal-1402	48	65	1	1	NUM
american_scientific_journal-1402	48	66	�	�	PROPN
american_scientific_journal-1402	48	67	𝜃𝜃	𝜃𝜃	PROPN
american_scientific_journal-1402	48	68	�	�	PROPN
american_scientific_journal-1402	48	69	𝑅𝑅𝑙𝑙	𝑅𝑅𝑙𝑙	PROPN
american_scientific_journal-1402	48	70	�	�	PROPN
american_scientific_journal-1402	48	71	�	�	PROPN
american_scientific_journal-1402	48	72	2	2	NUM
american_scientific_journal-1402	48	73	𝑐𝑐	𝑐𝑐	NOUN
american_scientific_journal-1402	48	74	2𝑑𝑑𝑑𝑑2	2𝑑𝑑𝑑𝑑2	NUM
american_scientific_journal-1402	48	75	−	−	PROPN
american_scientific_journal-1402	48	76	�	�	PROPN
american_scientific_journal-1402	48	77	𝜃𝜃	𝜃𝜃	PROPN
american_scientific_journal-1402	48	78	�	�	PROPN
american_scientific_journal-1402	48	79	𝑅𝑅	𝑅𝑅	PROPN
american_scientific_journal-1402	48	80	𝑙𝑙	𝑙𝑙	PROPN
american_scientific_journal-1402	48	81	�	�	PROPN
american_scientific_journal-1402	48	82	�	�	PROPN
american_scientific_journal-1402	48	83	2	2	NUM
american_scientific_journal-1402	48	84	(	(	PUNCT
american_scientific_journal-1402	48	85	𝑑𝑑𝑅𝑅2	𝑑𝑑𝑅𝑅2	NOUN
american_scientific_journal-1402	48	86	+	+	CCONJ
american_scientific_journal-1402	48	87	𝑅𝑅2𝑑𝑑ω2	𝑅𝑅2𝑑𝑑ω2	PROPN
american_scientific_journal-1402	48	88	)	)	PUNCT
american_scientific_journal-1402	48	89	,	,	PUNCT
american_scientific_journal-1402	48	90	𝑅𝑅	𝑅𝑅	PROPN
american_scientific_journal-1402	48	91	≤	≤	NUM
american_scientific_journal-1402	48	92	𝑎𝑎	𝑎𝑎	VERB
american_scientific_journal-1402	48	93	𝑑𝑑𝑑𝑑2	𝑑𝑑𝑑𝑑2	PROPN
american_scientific_journal-1402	48	94	=	=	SYM
american_scientific_journal-1402	48	95	1	1	NUM
american_scientific_journal-1402	48	96	�	�	PROPN
american_scientific_journal-1402	48	97	𝐴𝐴1	𝐴𝐴1	PROPN
american_scientific_journal-1402	48	98	+	+	PROPN
american_scientific_journal-1402	48	99	𝐴𝐴2	𝐴𝐴2	PROPN
american_scientific_journal-1402	48	100	𝑅𝑅	𝑅𝑅	PROPN
american_scientific_journal-1402	48	101	�	�	PROPN
american_scientific_journal-1402	48	102	2	2	NUM
american_scientific_journal-1402	48	103	𝑐𝑐2𝑑𝑑𝑑𝑑2	𝑐𝑐2𝑑𝑑𝑑𝑑2	SYM
american_scientific_journal-1402	48	104	−	−	PROPN
american_scientific_journal-1402	48	105	�	�	PROPN
american_scientific_journal-1402	48	106	𝐴𝐴1	𝐴𝐴1	PROPN
american_scientific_journal-1402	48	107	+	+	CCONJ
american_scientific_journal-1402	48	108	𝐴𝐴2	𝐴𝐴2	PROPN
american_scientific_journal-1402	48	109	𝑅𝑅	𝑅𝑅	PROPN
american_scientific_journal-1402	48	110	�	�	PROPN
american_scientific_journal-1402	48	111	2	2	NUM
american_scientific_journal-1402	48	112	(	(	PUNCT
american_scientific_journal-1402	48	113	𝑑𝑑𝑅𝑅2	𝑑𝑑𝑅𝑅2	NOUN
american_scientific_journal-1402	48	114	+	+	CCONJ
american_scientific_journal-1402	48	115	𝑅𝑅2𝑑𝑑ω2	𝑅𝑅2𝑑𝑑ω2	PROPN
american_scientific_journal-1402	48	116	)	)	PUNCT
american_scientific_journal-1402	48	117	𝑎𝑎	𝑎𝑎	VERB
american_scientific_journal-1402	48	118	<	<	X
american_scientific_journal-1402	48	119	𝑅𝑅	𝑅𝑅	PROPN
american_scientific_journal-1402	48	120	(	(	PUNCT
american_scientific_journal-1402	48	121	9	9	NUM
american_scientific_journal-1402	48	122	)	)	PUNCT
american_scientific_journal-1402	48	123	where	where	SCONJ
american_scientific_journal-1402	48	124	𝑑𝑑ω2	𝑑𝑑ω2	NOUN
american_scientific_journal-1402	48	125	=	=	SYM
american_scientific_journal-1402	48	126	𝑑𝑑𝜃𝜃2	𝑑𝑑𝜃𝜃2	X
american_scientific_journal-1402	49	1	+	+	CCONJ
american_scientific_journal-1402	49	2	𝑅𝑅2	𝑅𝑅2	PROPN
american_scientific_journal-1402	49	3	sin2	sin2	NOUN
american_scientific_journal-1402	49	4	𝜃𝜃	𝜃𝜃	PROPN
american_scientific_journal-1402	49	5	𝑑𝑑𝑑𝑑2	𝑑𝑑𝑑𝑑2	PROPN
american_scientific_journal-1402	49	6	.	.	PUNCT
american_scientific_journal-1402	50	1	here	here	ADV
american_scientific_journal-1402	50	2	we	we	PRON
american_scientific_journal-1402	50	3	apply	apply	VERB
american_scientific_journal-1402	50	4	the	the	DET
american_scientific_journal-1402	50	5	standard	standard	ADJ
american_scientific_journal-1402	50	6	boundary	boundary	ADJ
american_scientific_journal-1402	50	7	conditions	condition	NOUN
american_scientific_journal-1402	50	8	,	,	PUNCT
american_scientific_journal-1402	50	9	known	know	VERB
american_scientific_journal-1402	50	10	as	as	ADP
american_scientific_journal-1402	50	11	lichernowicz	lichernowicz	NOUN
american_scientific_journal-1402	50	12	’s	’s	PART
american_scientific_journal-1402	50	13	boundary	boundary	ADJ
american_scientific_journal-1402	50	14	conditions	condition	NOUN
american_scientific_journal-1402	50	15	which	which	PRON
american_scientific_journal-1402	50	16	says	say	VERB
american_scientific_journal-1402	50	17	that	that	SCONJ
american_scientific_journal-1402	50	18	metric	metric	ADJ
american_scientific_journal-1402	50	19	coefficients	coefficient	NOUN
american_scientific_journal-1402	50	20	and	and	CCONJ
american_scientific_journal-1402	50	21	their	their	PRON
american_scientific_journal-1402	50	22	derivatives	derivative	NOUN
american_scientific_journal-1402	50	23	are	be	AUX
american_scientific_journal-1402	50	24	continuous	continuous	ADJ
american_scientific_journal-1402	50	25	at	at	ADP
american_scientific_journal-1402	50	26	the	the	DET
american_scientific_journal-1402	50	27	boundary	boundary	NOUN
american_scientific_journal-1402	50	28	,	,	PUNCT
american_scientific_journal-1402	50	29	𝑅𝑅	𝑅𝑅	PROPN
american_scientific_journal-1402	50	30	=	=	PUNCT
american_scientific_journal-1402	50	31	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1402	50	32	.	.	PUNCT
american_scientific_journal-1402	51	1	then	then	ADV
american_scientific_journal-1402	51	2	we	we	PRON
american_scientific_journal-1402	51	3	obtain	obtain	VERB
american_scientific_journal-1402	51	4	1	1	NUM
american_scientific_journal-1402	51	5	𝜃𝜃	𝜃𝜃	PROPN
american_scientific_journal-1402	51	6	�	�	PROPN
american_scientific_journal-1402	51	7	𝑎𝑎𝑙𝑙	𝑎𝑎𝑙𝑙	NOUN
american_scientific_journal-1402	51	8	�	�	PROPN
american_scientific_journal-1402	51	9	=	=	SYM
american_scientific_journal-1402	51	10	1	1	NUM
american_scientific_journal-1402	51	11	�	�	PROPN
american_scientific_journal-1402	51	12	𝐴𝐴1	𝐴𝐴1	PROPN
american_scientific_journal-1402	51	13	+	+	PROPN
american_scientific_journal-1402	51	14	𝐴𝐴2	𝐴𝐴2	PROPN
american_scientific_journal-1402	51	15	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1402	51	16	�	�	PROPN
american_scientific_journal-1402	51	17	(	(	PUNCT
american_scientific_journal-1402	51	18	10	10	NUM
american_scientific_journal-1402	51	19	)	)	PUNCT
american_scientific_journal-1402	51	20	−	−	PROPN
american_scientific_journal-1402	51	21	1	1	NUM
american_scientific_journal-1402	51	22	�	�	PROPN
american_scientific_journal-1402	51	23	𝜃𝜃	𝜃𝜃	PROPN
american_scientific_journal-1402	51	24	�	�	PROPN
american_scientific_journal-1402	51	25	𝑎𝑎𝑙𝑙	𝑎𝑎𝑙𝑙	PROPN
american_scientific_journal-1402	51	26	�	�	PROPN
american_scientific_journal-1402	51	27	�	�	PROPN
american_scientific_journal-1402	51	28	3	3	NUM
american_scientific_journal-1402	51	29	�	�	PROPN
american_scientific_journal-1402	51	30	1	1	NUM
american_scientific_journal-1402	51	31	𝑙𝑙	𝑙𝑙	NOUN
american_scientific_journal-1402	51	32	𝜃𝜃′	𝜃𝜃′	NOUN
american_scientific_journal-1402	51	33	�	�	NOUN
american_scientific_journal-1402	51	34	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1402	51	35	𝑙𝑙	𝑙𝑙	NOUN
american_scientific_journal-1402	51	36	�	�	NOUN
american_scientific_journal-1402	51	37	�	�	PROPN
american_scientific_journal-1402	51	38	=	=	SYM
american_scientific_journal-1402	51	39	−	−	PROPN
american_scientific_journal-1402	51	40	1	1	NUM
american_scientific_journal-1402	51	41	�	�	PROPN
american_scientific_journal-1402	51	42	𝐴𝐴1	𝐴𝐴1	PROPN
american_scientific_journal-1402	51	43	+	+	PROPN
american_scientific_journal-1402	51	44	𝐴𝐴2	𝐴𝐴2	PROPN
american_scientific_journal-1402	51	45	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1402	51	46	�	�	PROPN
american_scientific_journal-1402	51	47	3	3	NUM
american_scientific_journal-1402	51	48	�	�	PROPN
american_scientific_journal-1402	51	49	−	−	PROPN
american_scientific_journal-1402	51	50	𝐴𝐴2	𝐴𝐴2	PROPN
american_scientific_journal-1402	51	51	𝑎𝑎2	𝑎𝑎2	X
american_scientific_journal-1402	51	52	�	�	PROPN
american_scientific_journal-1402	51	53	(	(	PUNCT
american_scientific_journal-1402	51	54	11	11	NUM
american_scientific_journal-1402	51	55	)	)	PUNCT
american_scientific_journal-1402	51	56	substituting	substitute	VERB
american_scientific_journal-1402	51	57	(	(	PUNCT
american_scientific_journal-1402	51	58	10	10	NUM
american_scientific_journal-1402	51	59	)	)	PUNCT
american_scientific_journal-1402	51	60	in	in	ADP
american_scientific_journal-1402	51	61	(	(	PUNCT
american_scientific_journal-1402	51	62	11	11	NUM
american_scientific_journal-1402	51	63	)	)	PUNCT
american_scientific_journal-1402	51	64	,	,	PUNCT
american_scientific_journal-1402	51	65	we	we	PRON
american_scientific_journal-1402	51	66	obtain	obtain	VERB
american_scientific_journal-1402	51	67	𝐴𝐴2	𝐴𝐴2	PROPN
american_scientific_journal-1402	51	68	=	=	SYM
american_scientific_journal-1402	51	69	−𝑎𝑎2	−𝑎𝑎2	ADP
american_scientific_journal-1402	51	70	𝑙𝑙	𝑙𝑙	NOUN
american_scientific_journal-1402	51	71	𝜃𝜃′	𝜃𝜃′	PROPN
american_scientific_journal-1402	51	72	�	�	NOUN
american_scientific_journal-1402	51	73	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1402	51	74	𝑙𝑙	𝑙𝑙	PROPN
american_scientific_journal-1402	51	75	�	�	PROPN
american_scientific_journal-1402	51	76	.	.	PUNCT
american_scientific_journal-1402	52	1	(	(	PUNCT
american_scientific_journal-1402	52	2	12	12	NUM
american_scientific_journal-1402	52	3	)	)	PUNCT
american_scientific_journal-1402	52	4	using	use	VERB
american_scientific_journal-1402	52	5	the	the	DET
american_scientific_journal-1402	52	6	fact	fact	NOUN
american_scientific_journal-1402	52	7	that	that	SCONJ
american_scientific_journal-1402	52	8	𝐴𝐴2	𝐴𝐴2	PROPN
american_scientific_journal-1402	52	9	=	=	PUNCT
american_scientific_journal-1402	52	10	𝑚𝑚	𝑚𝑚	ADP
american_scientific_journal-1402	52	11	according	accord	VERB
american_scientific_journal-1402	52	12	to	to	ADP
american_scientific_journal-1402	52	13	wickramasuriya	wickramasuriya	PROPN
american_scientific_journal-1402	52	14	[	[	X
american_scientific_journal-1402	52	15	1	1	NUM
american_scientific_journal-1402	52	16	]	]	PUNCT
american_scientific_journal-1402	52	17	,	,	PUNCT
american_scientific_journal-1402	52	18	the	the	DET
american_scientific_journal-1402	52	19	value	value	NOUN
american_scientific_journal-1402	52	20	of	of	ADP
american_scientific_journal-1402	52	21	the	the	DET
american_scientific_journal-1402	52	22	mass	mass	NOUN
american_scientific_journal-1402	52	23	of	of	ADP
american_scientific_journal-1402	52	24	the	the	DET
american_scientific_journal-1402	52	25	sphere	sphere	NOUN
american_scientific_journal-1402	52	26	of	of	ADP
american_scientific_journal-1402	52	27	electrically	electrically	ADV
american_scientific_journal-1402	52	28	counterpoised	counterpoise	VERB
american_scientific_journal-1402	52	29	dust	dust	NOUN
american_scientific_journal-1402	52	30	is	be	AUX
american_scientific_journal-1402	52	31	found	find	VERB
american_scientific_journal-1402	52	32	as	as	ADP
american_scientific_journal-1402	52	33	𝑚𝑚	𝑚𝑚	ADP
american_scientific_journal-1402	52	34	=	=	PROPN
american_scientific_journal-1402	52	35	𝐴𝐴2	𝐴𝐴2	PROPN
american_scientific_journal-1402	52	36	=	=	SYM
american_scientific_journal-1402	52	37	−𝑎𝑎2	−𝑎𝑎2	PROPN
american_scientific_journal-1402	52	38	𝑙𝑙	𝑙𝑙	NOUN
american_scientific_journal-1402	52	39	𝜃𝜃′	𝜃𝜃′	PROPN
american_scientific_journal-1402	52	40	�	�	NOUN
american_scientific_journal-1402	52	41	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1402	52	42	𝑙𝑙	𝑙𝑙	PROPN
american_scientific_journal-1402	52	43	�	�	PROPN
american_scientific_journal-1402	52	44	(	(	PUNCT
american_scientific_journal-1402	52	45	13	13	NUM
american_scientific_journal-1402	52	46	)	)	PUNCT
american_scientific_journal-1402	52	47	substitution	substitution	NOUN
american_scientific_journal-1402	52	48	of	of	ADP
american_scientific_journal-1402	52	49	(	(	PUNCT
american_scientific_journal-1402	52	50	13	13	NUM
american_scientific_journal-1402	52	51	)	)	PUNCT
american_scientific_journal-1402	52	52	in	in	ADP
american_scientific_journal-1402	52	53	(	(	PUNCT
american_scientific_journal-1402	52	54	10	10	NUM
american_scientific_journal-1402	52	55	)	)	PUNCT
american_scientific_journal-1402	52	56	gives	give	VERB
american_scientific_journal-1402	52	57	𝐴𝐴1	𝐴𝐴1	PROPN
american_scientific_journal-1402	52	58	=	=	SYM
american_scientific_journal-1402	52	59	𝜃𝜃	𝜃𝜃	PROPN
american_scientific_journal-1402	52	60	�	�	PROPN
american_scientific_journal-1402	52	61	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1402	52	62	𝑙𝑙	𝑙𝑙	VERB
american_scientific_journal-1402	52	63	�	�	PROPN
american_scientific_journal-1402	52	64	−	−	ADP
american_scientific_journal-1402	52	65	𝑚𝑚	𝑚𝑚	ADP
american_scientific_journal-1402	52	66	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1402	52	67	.	.	PUNCT
american_scientific_journal-1402	53	1	(	(	PUNCT
american_scientific_journal-1402	53	2	14	14	NUM
american_scientific_journal-1402	53	3	)	)	PUNCT
american_scientific_journal-1402	53	4	now	now	ADV
american_scientific_journal-1402	53	5	the	the	DET
american_scientific_journal-1402	53	6	metric	metric	NOUN
american_scientific_journal-1402	53	7	for	for	ADP
american_scientific_journal-1402	53	8	the	the	DET
american_scientific_journal-1402	53	9	entire	entire	ADJ
american_scientific_journal-1402	53	10	spherical	spherical	ADJ
american_scientific_journal-1402	53	11	distribution	distribution	NOUN
american_scientific_journal-1402	53	12	takes	take	VERB
american_scientific_journal-1402	53	13	the	the	DET
american_scientific_journal-1402	53	14	form	form	NOUN
american_scientific_journal-1402	53	15	𝑑𝑑𝑑𝑑2	𝑑𝑑𝑑𝑑2	PUNCT
american_scientific_journal-1402	54	1	=	=	SYM
american_scientific_journal-1402	54	2	1	1	NUM
american_scientific_journal-1402	54	3	�	�	PROPN
american_scientific_journal-1402	54	4	𝜃𝜃	𝜃𝜃	PROPN
american_scientific_journal-1402	54	5	�	�	PROPN
american_scientific_journal-1402	54	6	𝑅𝑅𝑙𝑙	𝑅𝑅𝑙𝑙	PROPN
american_scientific_journal-1402	54	7	�	�	PROPN
american_scientific_journal-1402	54	8	�	�	PROPN
american_scientific_journal-1402	54	9	2	2	NUM
american_scientific_journal-1402	54	10	𝑐𝑐	𝑐𝑐	NOUN
american_scientific_journal-1402	54	11	2𝑑𝑑𝑑𝑑2	2𝑑𝑑𝑑𝑑2	NUM
american_scientific_journal-1402	54	12	−	−	PROPN
american_scientific_journal-1402	54	13	�	�	PROPN
american_scientific_journal-1402	54	14	𝜃𝜃	𝜃𝜃	PROPN
american_scientific_journal-1402	54	15	�	�	PROPN
american_scientific_journal-1402	54	16	𝑅𝑅	𝑅𝑅	PROPN
american_scientific_journal-1402	54	17	𝑙𝑙	𝑙𝑙	PROPN
american_scientific_journal-1402	54	18	�	�	PROPN
american_scientific_journal-1402	54	19	�	�	PROPN
american_scientific_journal-1402	54	20	2	2	NUM
american_scientific_journal-1402	54	21	(	(	PUNCT
american_scientific_journal-1402	54	22	𝑑𝑑𝑅𝑅2	𝑑𝑑𝑅𝑅2	NOUN
american_scientific_journal-1402	54	23	+	+	CCONJ
american_scientific_journal-1402	54	24	𝑅𝑅2𝑑𝑑ω2	𝑅𝑅2𝑑𝑑ω2	PROPN
american_scientific_journal-1402	54	25	)	)	PUNCT
american_scientific_journal-1402	54	26	,	,	PUNCT
american_scientific_journal-1402	54	27	0	0	NUM
american_scientific_journal-1402	54	28	≤	≤	NUM
american_scientific_journal-1402	54	29	𝑅𝑅	𝑅𝑅	PROPN
american_scientific_journal-1402	54	30	≤	≤	NUM
american_scientific_journal-1402	54	31	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1402	54	32	𝑑𝑑𝑑𝑑2	𝑑𝑑𝑑𝑑2	PROPN
american_scientific_journal-1402	54	33	=	=	SYM
american_scientific_journal-1402	54	34	1	1	NUM
american_scientific_journal-1402	54	35	�	�	PROPN
american_scientific_journal-1402	54	36	𝜃𝜃	𝜃𝜃	PROPN
american_scientific_journal-1402	54	37	�	�	PROPN
american_scientific_journal-1402	54	38	𝑎𝑎𝑙𝑙	𝑎𝑎𝑙𝑙	PROPN
american_scientific_journal-1402	54	39	�	�	PROPN
american_scientific_journal-1402	54	40	−	−	PUNCT
american_scientific_journal-1402	54	41	𝑚𝑚	𝑚𝑚	ADP
american_scientific_journal-1402	54	42	𝑎𝑎+	𝑎𝑎+	PROPN
american_scientific_journal-1402	54	43	𝑚𝑚	𝑚𝑚	ADP
american_scientific_journal-1402	54	44	𝑅𝑅	𝑅𝑅	PROPN
american_scientific_journal-1402	54	45	�	�	PROPN
american_scientific_journal-1402	54	46	2	2	NUM
american_scientific_journal-1402	54	47	𝑐𝑐2𝑑𝑑𝑑𝑑2	𝑐𝑐2𝑑𝑑𝑑𝑑2	SYM
american_scientific_journal-1402	54	48	−	−	PROPN
american_scientific_journal-1402	54	49	�	�	PROPN
american_scientific_journal-1402	54	50	𝜃𝜃	𝜃𝜃	PROPN
american_scientific_journal-1402	54	51	�	�	PROPN
american_scientific_journal-1402	54	52	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1402	54	53	𝑙𝑙	𝑙𝑙	PRON
american_scientific_journal-1402	54	54	�	�	PROPN
american_scientific_journal-1402	54	55	−	−	ADP
american_scientific_journal-1402	54	56	𝑚𝑚	𝑚𝑚	ADP
american_scientific_journal-1402	54	57	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1402	54	58	+	+	CCONJ
american_scientific_journal-1402	54	59	𝑚𝑚	𝑚𝑚	ADP
american_scientific_journal-1402	54	60	𝑅𝑅	𝑅𝑅	PROPN
american_scientific_journal-1402	54	61	�	�	PROPN
american_scientific_journal-1402	54	62	2	2	NUM
american_scientific_journal-1402	54	63	(	(	PUNCT
american_scientific_journal-1402	54	64	𝑑𝑑𝑅𝑅2	𝑑𝑑𝑅𝑅2	NOUN
american_scientific_journal-1402	54	65	+	+	CCONJ
american_scientific_journal-1402	54	66	𝑅𝑅2𝑑𝑑ω2	𝑅𝑅2𝑑𝑑ω2	PROPN
american_scientific_journal-1402	54	67	)	)	PUNCT
american_scientific_journal-1402	54	68	𝑎𝑎	𝑎𝑎	VERB
american_scientific_journal-1402	54	69	<	<	X
american_scientific_journal-1402	54	70	𝑅𝑅	𝑅𝑅	PROPN
american_scientific_journal-1402	54	71	(	(	PUNCT
american_scientific_journal-1402	54	72	15	15	NUM
american_scientific_journal-1402	54	73	)	)	PUNCT
american_scientific_journal-1402	54	74	159	159	NUM
american_scientific_journal-1402	54	75	american	american	ADJ
american_scientific_journal-1402	54	76	scientific	scientific	ADJ
american_scientific_journal-1402	54	77	research	research	NOUN
american_scientific_journal-1402	54	78	journal	journal	NOUN
american_scientific_journal-1402	54	79	for	for	ADP
american_scientific_journal-1402	54	80	engineering	engineering	NOUN
american_scientific_journal-1402	54	81	,	,	PUNCT
american_scientific_journal-1402	54	82	technology	technology	NOUN
american_scientific_journal-1402	54	83	,	,	PUNCT
american_scientific_journal-1402	54	84	and	and	CCONJ
american_scientific_journal-1402	54	85	sciences	science	NOUN
american_scientific_journal-1402	54	86	(	(	PUNCT
american_scientific_journal-1402	54	87	asrjets	asrjet	NOUN
american_scientific_journal-1402	54	88	)	)	PUNCT
american_scientific_journal-1402	54	89	(	(	PUNCT
american_scientific_journal-1402	54	90	2016	2016	NUM
american_scientific_journal-1402	54	91	)	)	PUNCT
american_scientific_journal-1402	54	92	volume	volume	NOUN
american_scientific_journal-1402	54	93	17	17	NUM
american_scientific_journal-1402	54	94	,	,	PUNCT
american_scientific_journal-1402	54	95	no	no	DET
american_scientific_journal-1402	54	96	1	1	NUM
american_scientific_journal-1402	54	97	,	,	PUNCT
american_scientific_journal-1402	54	98	pp	pp	ADV
american_scientific_journal-1402	54	99	155	155	NUM
american_scientific_journal-1402	54	100	-	-	SYM
american_scientific_journal-1402	54	101	164	164	NUM
american_scientific_journal-1402	54	102	according	accord	VERB
american_scientific_journal-1402	54	103	to	to	ADP
american_scientific_journal-1402	54	104	the	the	DET
american_scientific_journal-1402	54	105	figure	figure	NOUN
american_scientific_journal-1402	54	106	1	1	NUM
american_scientific_journal-1402	54	107	,	,	PUNCT
american_scientific_journal-1402	54	108	𝜃𝜃	𝜃𝜃	PROPN
american_scientific_journal-1402	54	109	�	�	PROPN
american_scientific_journal-1402	54	110	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1402	54	111	𝑙𝑙	𝑙𝑙	VERB
american_scientific_journal-1402	54	112	�	�	PROPN
american_scientific_journal-1402	54	113	−	−	ADP
american_scientific_journal-1402	54	114	𝑚𝑚	𝑚𝑚	ADP
american_scientific_journal-1402	54	115	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1402	54	116	=	=	SYM
american_scientific_journal-1402	54	117	𝜃𝜃	𝜃𝜃	PROPN
american_scientific_journal-1402	54	118	�	�	PROPN
american_scientific_journal-1402	54	119	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1402	54	120	𝑙𝑙	𝑙𝑙	PRON
american_scientific_journal-1402	54	121	�	�	PROPN
american_scientific_journal-1402	54	122	+	+	CCONJ
american_scientific_journal-1402	54	123	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1402	54	124	𝑙𝑙	𝑙𝑙	NOUN
american_scientific_journal-1402	54	125	𝜃𝜃′	𝜃𝜃′	NOUN
american_scientific_journal-1402	54	126	�	�	NOUN
american_scientific_journal-1402	54	127	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1402	54	128	𝑙𝑙	𝑙𝑙	PRON
american_scientific_journal-1402	54	129	�	�	PROPN
american_scientific_journal-1402	54	130	=	=	NOUN
american_scientific_journal-1402	54	131	1	1	NUM
american_scientific_journal-1402	54	132	only	only	ADV
american_scientific_journal-1402	54	133	when	when	SCONJ
american_scientific_journal-1402	54	134	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1402	54	135	𝑙𝑙	𝑙𝑙	NOUN
american_scientific_journal-1402	54	136	=	=	SYM
american_scientific_journal-1402	54	137	0	0	NUM
american_scientific_journal-1402	54	138	which	which	PRON
american_scientific_journal-1402	54	139	implies	imply	VERB
american_scientific_journal-1402	54	140	that	that	SCONJ
american_scientific_journal-1402	54	141	𝑎𝑎	𝑎𝑎	VERB
american_scientific_journal-1402	54	142	=	=	SYM
american_scientific_journal-1402	54	143	0	0	NUM
american_scientific_journal-1402	54	144	and	and	CCONJ
american_scientific_journal-1402	54	145	𝑚𝑚	𝑚𝑚	ADP
american_scientific_journal-1402	54	146	=	=	NOUN
american_scientific_journal-1402	54	147	0	0	PROPN
american_scientific_journal-1402	54	148	.	.	PUNCT
american_scientific_journal-1402	55	1	thus	thus	ADV
american_scientific_journal-1402	55	2	the	the	DET
american_scientific_journal-1402	55	3	metric	metric	NOUN
american_scientific_journal-1402	55	4	is	be	AUX
american_scientific_journal-1402	55	5	lorentzian	lorentzian	ADJ
american_scientific_journal-1402	55	6	at	at	ADP
american_scientific_journal-1402	55	7	large	large	ADJ
american_scientific_journal-1402	55	8	distances	distance	NOUN
american_scientific_journal-1402	55	9	only	only	ADV
american_scientific_journal-1402	55	10	if	if	SCONJ
american_scientific_journal-1402	55	11	a=0	a=0	PRON
american_scientific_journal-1402	55	12	and	and	CCONJ
american_scientific_journal-1402	55	13	m=0	m=0	PROPN
american_scientific_journal-1402	55	14	,	,	PUNCT
american_scientific_journal-1402	55	15	which	which	PRON
american_scientific_journal-1402	55	16	makes	make	VERB
american_scientific_journal-1402	55	17	the	the	DET
american_scientific_journal-1402	55	18	distribution	distribution	NOUN
american_scientific_journal-1402	55	19	devoid	devoid	ADJ
american_scientific_journal-1402	55	20	of	of	ADP
american_scientific_journal-1402	55	21	matter	matter	NOUN
american_scientific_journal-1402	55	22	.	.	PUNCT
american_scientific_journal-1402	56	1	it	it	PRON
american_scientific_journal-1402	56	2	is	be	AUX
american_scientific_journal-1402	56	3	the	the	DET
american_scientific_journal-1402	56	4	flat	flat	ADJ
american_scientific_journal-1402	56	5	space	space	NOUN
american_scientific_journal-1402	56	6	time	time	NOUN
american_scientific_journal-1402	56	7	without	without	ADP
american_scientific_journal-1402	56	8	matter	matter	NOUN
american_scientific_journal-1402	56	9	which	which	PRON
american_scientific_journal-1402	56	10	is	be	AUX
american_scientific_journal-1402	56	11	of	of	ADP
american_scientific_journal-1402	56	12	no	no	DET
american_scientific_journal-1402	56	13	interest	interest	NOUN
american_scientific_journal-1402	56	14	.	.	PUNCT
american_scientific_journal-1402	57	1	3	3	X
american_scientific_journal-1402	57	2	.	.	NOUN
american_scientific_journal-1402	57	3	results	result	VERB
american_scientific_journal-1402	57	4	3.1	3.1	NUM
american_scientific_journal-1402	57	5	the	the	DET
american_scientific_journal-1402	57	6	red	red	ADJ
american_scientific_journal-1402	57	7	shift	shift	NOUN
american_scientific_journal-1402	57	8	of	of	ADP
american_scientific_journal-1402	57	9	a	a	DET
american_scientific_journal-1402	57	10	pulse	pulse	NOUN
american_scientific_journal-1402	57	11	of	of	ADP
american_scientific_journal-1402	57	12	light	light	NOUN
american_scientific_journal-1402	57	13	here	here	ADV
american_scientific_journal-1402	57	14	we	we	PRON
american_scientific_journal-1402	57	15	consider	consider	VERB
american_scientific_journal-1402	57	16	the	the	DET
american_scientific_journal-1402	57	17	red	red	ADJ
american_scientific_journal-1402	57	18	shift	shift	NOUN
american_scientific_journal-1402	57	19	of	of	ADP
american_scientific_journal-1402	57	20	a	a	DET
american_scientific_journal-1402	57	21	pulse	pulse	NOUN
american_scientific_journal-1402	57	22	of	of	ADP
american_scientific_journal-1402	57	23	light	light	NOUN
american_scientific_journal-1402	57	24	which	which	PRON
american_scientific_journal-1402	57	25	is	be	AUX
american_scientific_journal-1402	57	26	emitted	emit	VERB
american_scientific_journal-1402	57	27	at	at	ADP
american_scientific_journal-1402	57	28	a	a	DET
american_scientific_journal-1402	57	29	point	point	NOUN
american_scientific_journal-1402	57	30	inside	inside	ADP
american_scientific_journal-1402	57	31	of	of	ADP
american_scientific_journal-1402	57	32	the	the	DET
american_scientific_journal-1402	57	33	sphere	sphere	NOUN
american_scientific_journal-1402	57	34	as	as	SCONJ
american_scientific_journal-1402	57	35	observed	observe	VERB
american_scientific_journal-1402	57	36	by	by	ADP
american_scientific_journal-1402	57	37	an	an	DET
american_scientific_journal-1402	57	38	observer	observer	NOUN
american_scientific_journal-1402	57	39	who	who	PRON
american_scientific_journal-1402	57	40	is	be	AUX
american_scientific_journal-1402	57	41	at	at	ADP
american_scientific_journal-1402	57	42	a	a	DET
american_scientific_journal-1402	57	43	large	large	ADJ
american_scientific_journal-1402	57	44	distance	distance	NOUN
american_scientific_journal-1402	57	45	away	away	ADV
american_scientific_journal-1402	57	46	in	in	ADP
american_scientific_journal-1402	57	47	the	the	DET
american_scientific_journal-1402	57	48	exterior	exterior	ADJ
american_scientific_journal-1402	57	49	region	region	NOUN
american_scientific_journal-1402	57	50	using	use	VERB
american_scientific_journal-1402	57	51	expressions	expression	NOUN
american_scientific_journal-1402	57	52	for	for	ADP
american_scientific_journal-1402	57	53	null	null	ADJ
american_scientific_journal-1402	57	54	geodesics	geodesic	NOUN
american_scientific_journal-1402	57	55	in	in	ADP
american_scientific_journal-1402	57	56	general	general	ADJ
american_scientific_journal-1402	57	57	relativity	relativity	NOUN
american_scientific_journal-1402	57	58	.	.	PUNCT
american_scientific_journal-1402	58	1	consider	consider	VERB
american_scientific_journal-1402	58	2	a	a	DET
american_scientific_journal-1402	58	3	pulse	pulse	NOUN
american_scientific_journal-1402	58	4	of	of	ADP
american_scientific_journal-1402	58	5	light	light	NOUN
american_scientific_journal-1402	58	6	with	with	ADP
american_scientific_journal-1402	58	7	front	front	NOUN
american_scientific_journal-1402	58	8	emitted	emit	VERB
american_scientific_journal-1402	58	9	at	at	ADP
american_scientific_journal-1402	58	10	𝑅𝑅	𝑅𝑅	PROPN
american_scientific_journal-1402	58	11	=	=	SYM
american_scientific_journal-1402	58	12	𝑅𝑅𝑒𝑒	𝑅𝑅𝑒𝑒	PROPN
american_scientific_journal-1402	58	13	at	at	ADP
american_scientific_journal-1402	58	14	𝑑𝑑	𝑑𝑑	NOUN
american_scientific_journal-1402	58	15	=	=	SYM
american_scientific_journal-1402	58	16	𝑑𝑑𝑒𝑒	𝑑𝑑𝑒𝑒	ADJ
american_scientific_journal-1402	58	17	with	with	ADP
american_scientific_journal-1402	58	18	frequency	frequency	NOUN
american_scientific_journal-1402	58	19	𝜈𝜈𝑒𝑒	𝜈𝜈𝑒𝑒	NOUN
american_scientific_journal-1402	58	20	inside	inside	ADP
american_scientific_journal-1402	58	21	the	the	DET
american_scientific_journal-1402	58	22	sphere	sphere	NOUN
american_scientific_journal-1402	58	23	and	and	CCONJ
american_scientific_journal-1402	58	24	an	an	DET
american_scientific_journal-1402	58	25	observer	observer	NOUN
american_scientific_journal-1402	58	26	at	at	ADP
american_scientific_journal-1402	58	27	𝑅𝑅	𝑅𝑅	PROPN
american_scientific_journal-1402	58	28	=	=	PUNCT
american_scientific_journal-1402	58	29	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1402	58	30	,	,	PUNCT
american_scientific_journal-1402	58	31	just	just	ADV
american_scientific_journal-1402	58	32	inside	inside	ADP
american_scientific_journal-1402	58	33	the	the	DET
american_scientific_journal-1402	58	34	surface	surface	NOUN
american_scientific_journal-1402	58	35	of	of	ADP
american_scientific_journal-1402	58	36	the	the	DET
american_scientific_journal-1402	58	37	sphere	sphere	NOUN
american_scientific_journal-1402	58	38	receiving	receive	VERB
american_scientific_journal-1402	58	39	it	it	PRON
american_scientific_journal-1402	58	40	at	at	ADP
american_scientific_journal-1402	58	41	𝑑𝑑	𝑑𝑑	NOUN
american_scientific_journal-1402	58	42	=	=	NOUN
american_scientific_journal-1402	58	43	𝑑𝑑𝑒𝑒′	𝑑𝑑𝑒𝑒′	NOUN
american_scientific_journal-1402	58	44	with	with	ADP
american_scientific_journal-1402	58	45	frequency	frequency	PROPN
american_scientific_journal-1402	58	46	𝜈𝜈𝑒𝑒′.	𝜈𝜈𝑒𝑒′.	NOUN
american_scientific_journal-1402	58	47	now	now	ADV
american_scientific_journal-1402	58	48	consider	consider	VERB
american_scientific_journal-1402	58	49	the	the	DET
american_scientific_journal-1402	58	50	radial	radial	ADJ
american_scientific_journal-1402	58	51	null	null	ADJ
american_scientific_journal-1402	58	52	geodesics	geodesic	NOUN
american_scientific_journal-1402	58	53	within	within	ADP
american_scientific_journal-1402	58	54	the	the	DET
american_scientific_journal-1402	58	55	sphere	sphere	NOUN
american_scientific_journal-1402	58	56	.	.	PUNCT
american_scientific_journal-1402	58	57	0	0	PUNCT
american_scientific_journal-1402	59	1	=	=	SYM
american_scientific_journal-1402	59	2	1	1	NUM
american_scientific_journal-1402	59	3	�	�	PROPN
american_scientific_journal-1402	59	4	𝜃𝜃	𝜃𝜃	PROPN
american_scientific_journal-1402	59	5	�	�	PROPN
american_scientific_journal-1402	59	6	𝑅𝑅𝑙𝑙	𝑅𝑅𝑙𝑙	PROPN
american_scientific_journal-1402	59	7	�	�	PROPN
american_scientific_journal-1402	59	8	�	�	PROPN
american_scientific_journal-1402	59	9	2	2	NUM
american_scientific_journal-1402	59	10	𝑐𝑐	𝑐𝑐	NOUN
american_scientific_journal-1402	59	11	2𝑑𝑑𝑑𝑑2	2𝑑𝑑𝑑𝑑2	NUM
american_scientific_journal-1402	59	12	−	−	PROPN
american_scientific_journal-1402	59	13	�	�	PROPN
american_scientific_journal-1402	59	14	𝜃𝜃	𝜃𝜃	PROPN
american_scientific_journal-1402	59	15	�	�	PROPN
american_scientific_journal-1402	59	16	𝑅𝑅	𝑅𝑅	PROPN
american_scientific_journal-1402	59	17	𝑙𝑙	𝑙𝑙	PROPN
american_scientific_journal-1402	59	18	�	�	PROPN
american_scientific_journal-1402	59	19	�	�	PROPN
american_scientific_journal-1402	59	20	2	2	NUM
american_scientific_journal-1402	59	21	𝑑𝑑𝑅𝑅2	𝑑𝑑𝑅𝑅2	NOUN
american_scientific_journal-1402	59	22	from	from	ADP
american_scientific_journal-1402	59	23	which	which	PRON
american_scientific_journal-1402	59	24	we	we	PRON
american_scientific_journal-1402	59	25	obtain	obtain	VERB
american_scientific_journal-1402	59	26	𝑑𝑑𝑅𝑅	𝑑𝑑𝑅𝑅	NOUN
american_scientific_journal-1402	59	27	𝑑𝑑𝑑𝑑	𝑑𝑑𝑑𝑑	NOUN
american_scientific_journal-1402	60	1	=	=	PUNCT
american_scientific_journal-1402	60	2	𝑐𝑐	𝑐𝑐	PROPN
american_scientific_journal-1402	60	3	�	�	PROPN
american_scientific_journal-1402	60	4	𝜃𝜃	𝜃𝜃	PART
american_scientific_journal-1402	60	5	�	�	PROPN
american_scientific_journal-1402	60	6	𝑅𝑅𝑙𝑙	𝑅𝑅𝑙𝑙	ADJ
american_scientific_journal-1402	60	7	�	�	NOUN
american_scientific_journal-1402	60	8	�	�	PROPN
american_scientific_journal-1402	60	9	2	2	NUM
american_scientific_journal-1402	60	10	.	.	PUNCT
american_scientific_journal-1402	61	1	(	(	PUNCT
american_scientific_journal-1402	61	2	16	16	NUM
american_scientific_journal-1402	61	3	)	)	PUNCT
american_scientific_journal-1402	61	4	(	(	PUNCT
american_scientific_journal-1402	61	5	the	the	DET
american_scientific_journal-1402	61	6	plus	plus	ADJ
american_scientific_journal-1402	61	7	sign	sign	NOUN
american_scientific_journal-1402	61	8	is	be	AUX
american_scientific_journal-1402	61	9	taken	take	VERB
american_scientific_journal-1402	61	10	since	since	SCONJ
american_scientific_journal-1402	61	11	𝑅𝑅	𝑅𝑅	PROPN
american_scientific_journal-1402	61	12	increases	increase	NOUN
american_scientific_journal-1402	61	13	with	with	ADP
american_scientific_journal-1402	61	14	time	time	NOUN
american_scientific_journal-1402	61	15	𝑑𝑑	𝑑𝑑	PROPN
american_scientific_journal-1402	61	16	as	as	SCONJ
american_scientific_journal-1402	61	17	the	the	DET
american_scientific_journal-1402	61	18	photons	photon	NOUN
american_scientific_journal-1402	61	19	are	be	AUX
american_scientific_journal-1402	61	20	going	go	VERB
american_scientific_journal-1402	61	21	away	away	ADV
american_scientific_journal-1402	61	22	from	from	ADP
american_scientific_journal-1402	61	23	the	the	DET
american_scientific_journal-1402	61	24	centre	centre	NOUN
american_scientific_journal-1402	61	25	of	of	ADP
american_scientific_journal-1402	61	26	the	the	DET
american_scientific_journal-1402	61	27	sphere	sphere	NOUN
american_scientific_journal-1402	61	28	)	)	PUNCT
american_scientific_journal-1402	61	29	now	now	ADV
american_scientific_journal-1402	61	30	integration	integration	NOUN
american_scientific_journal-1402	61	31	of	of	ADP
american_scientific_journal-1402	61	32	(	(	PUNCT
american_scientific_journal-1402	61	33	16	16	NUM
american_scientific_journal-1402	61	34	)	)	PUNCT
american_scientific_journal-1402	61	35	gives	give	VERB
american_scientific_journal-1402	61	36	∫	∫	PROPN
american_scientific_journal-1402	62	1	𝑐𝑐	𝑐𝑐	NOUN
american_scientific_journal-1402	62	2	𝑑𝑑𝑑𝑑𝑑𝑑𝑒𝑒′	𝑑𝑑𝑑𝑑𝑑𝑑𝑒𝑒′	PRON
american_scientific_journal-1402	62	3	𝑑𝑑𝑒𝑒	𝑑𝑑𝑒𝑒	PROPN
american_scientific_journal-1402	63	1	=	=	SYM
american_scientific_journal-1402	63	2	∫	∫	PROPN
american_scientific_journal-1402	63	3	�	�	PROPN
american_scientific_journal-1402	63	4	𝜃𝜃	𝜃𝜃	PROPN
american_scientific_journal-1402	63	5	�	�	PROPN
american_scientific_journal-1402	63	6	𝑅𝑅	𝑅𝑅	PROPN
american_scientific_journal-1402	63	7	𝑙𝑙	𝑙𝑙	PROPN
american_scientific_journal-1402	63	8	�	�	PROPN
american_scientific_journal-1402	63	9	�	�	PROPN
american_scientific_journal-1402	63	10	2	2	NUM
american_scientific_journal-1402	63	11	𝑑𝑑𝑅𝑅𝑅𝑅𝑒𝑒′	𝑑𝑑𝑅𝑅𝑅𝑅𝑒𝑒′	ADP
american_scientific_journal-1402	63	12	𝑅𝑅𝑒𝑒	𝑅𝑅𝑒𝑒	PROPN
american_scientific_journal-1402	63	13	(	(	PUNCT
american_scientific_journal-1402	63	14	17	17	NUM
american_scientific_journal-1402	63	15	)	)	PUNCT
american_scientific_journal-1402	63	16	now	now	ADV
american_scientific_journal-1402	63	17	consider	consider	VERB
american_scientific_journal-1402	63	18	the	the	DET
american_scientific_journal-1402	63	19	rear	rear	NOUN
american_scientific_journal-1402	63	20	of	of	ADP
american_scientific_journal-1402	63	21	the	the	DET
american_scientific_journal-1402	63	22	pulse	pulse	NOUN
american_scientific_journal-1402	63	23	emitted	emit	VERB
american_scientific_journal-1402	63	24	at	at	ADP
american_scientific_journal-1402	63	25	𝑅𝑅	𝑅𝑅	PROPN
american_scientific_journal-1402	63	26	=	=	SYM
american_scientific_journal-1402	63	27	𝑅𝑅𝑒𝑒	𝑅𝑅𝑒𝑒	PROPN
american_scientific_journal-1402	63	28	at	at	ADP
american_scientific_journal-1402	63	29	𝑑𝑑	𝑑𝑑	NOUN
american_scientific_journal-1402	63	30	=	=	SYM
american_scientific_journal-1402	63	31	𝑑𝑑𝑒𝑒	𝑑𝑑𝑒𝑒	PROPN
american_scientific_journal-1402	63	32	+	+	CCONJ
american_scientific_journal-1402	63	33	δ𝑑𝑑𝑒𝑒	δ𝑑𝑑𝑒𝑒	NOUN
american_scientific_journal-1402	63	34	with	with	ADP
american_scientific_journal-1402	63	35	frequency	frequency	NOUN
american_scientific_journal-1402	63	36	𝜈𝜈𝑒𝑒	𝜈𝜈𝑒𝑒	NOUN
american_scientific_journal-1402	63	37	.	.	PUNCT
american_scientific_journal-1402	64	1	let	let	VERB
american_scientific_journal-1402	64	2	us	we	PRON
american_scientific_journal-1402	64	3	assume	assume	VERB
american_scientific_journal-1402	64	4	that	that	SCONJ
american_scientific_journal-1402	64	5	the	the	DET
american_scientific_journal-1402	64	6	rear	rear	NOUN
american_scientific_journal-1402	64	7	of	of	ADP
american_scientific_journal-1402	64	8	the	the	DET
american_scientific_journal-1402	64	9	pulse	pulse	NOUN
american_scientific_journal-1402	64	10	is	be	AUX
american_scientific_journal-1402	64	11	observed	observe	VERB
american_scientific_journal-1402	64	12	at	at	ADP
american_scientific_journal-1402	64	13	𝑅𝑅	𝑅𝑅	PROPN
american_scientific_journal-1402	64	14	=	=	PUNCT
american_scientific_journal-1402	64	15	𝑎𝑎	𝑎𝑎	PROPN
american_scientific_journal-1402	64	16	,	,	PUNCT
american_scientific_journal-1402	64	17	the	the	DET
american_scientific_journal-1402	64	18	boundary	boundary	NOUN
american_scientific_journal-1402	64	19	of	of	ADP
american_scientific_journal-1402	64	20	the	the	DET
american_scientific_journal-1402	64	21	sphere	sphere	NOUN
american_scientific_journal-1402	64	22	at	at	ADP
american_scientific_journal-1402	64	23	𝑑𝑑	𝑑𝑑	NOUN
american_scientific_journal-1402	64	24	=	=	NOUN
american_scientific_journal-1402	64	25	𝑑𝑑𝑒𝑒′	𝑑𝑑𝑒𝑒′	NOUN
american_scientific_journal-1402	65	1	+	+	CCONJ
american_scientific_journal-1402	65	2	δ𝑑𝑑𝑒𝑒′	δ𝑑𝑑𝑒𝑒′	NOUN
american_scientific_journal-1402	65	3	with	with	ADP
american_scientific_journal-1402	65	4	frequency	frequency	NOUN
american_scientific_journal-1402	65	5	𝜈𝜈𝑒𝑒′.	𝜈𝜈𝑒𝑒′.	ADJ
american_scientific_journal-1402	65	6	integration	integration	NOUN
american_scientific_journal-1402	65	7	of	of	ADP
american_scientific_journal-1402	65	8	(	(	PUNCT
american_scientific_journal-1402	65	9	17	17	NUM
american_scientific_journal-1402	65	10	)	)	PUNCT
american_scientific_journal-1402	65	11	for	for	ADP
american_scientific_journal-1402	65	12	the	the	DET
american_scientific_journal-1402	65	13	rear	rear	NOUN
american_scientific_journal-1402	65	14	of	of	ADP
american_scientific_journal-1402	65	15	the	the	DET
american_scientific_journal-1402	65	16	pulse	pulse	NOUN
american_scientific_journal-1402	65	17	gives	give	VERB
american_scientific_journal-1402	65	18	160	160	NUM
american_scientific_journal-1402	65	19	american	american	ADJ
american_scientific_journal-1402	65	20	scientific	scientific	ADJ
american_scientific_journal-1402	65	21	research	research	NOUN
american_scientific_journal-1402	65	22	journal	journal	NOUN
american_scientific_journal-1402	65	23	for	for	ADP
american_scientific_journal-1402	65	24	engineering	engineering	NOUN
american_scientific_journal-1402	65	25	,	,	PUNCT
american_scientific_journal-1402	65	26	technology	technology	NOUN
american_scientific_journal-1402	65	27	,	,	PUNCT
american_scientific_journal-1402	65	28	and	and	CCONJ
american_scientific_journal-1402	65	29	sciences	science	NOUN
american_scientific_journal-1402	65	30	(	(	PUNCT
american_scientific_journal-1402	65	31	asrjets	asrjet	NOUN
american_scientific_journal-1402	65	32	)	)	PUNCT
american_scientific_journal-1402	65	33	(	(	PUNCT
american_scientific_journal-1402	65	34	2016	2016	NUM
american_scientific_journal-1402	65	35	)	)	PUNCT
american_scientific_journal-1402	65	36	volume	volume	NOUN
american_scientific_journal-1402	65	37	17	17	NUM
american_scientific_journal-1402	65	38	,	,	PUNCT
american_scientific_journal-1402	65	39	no	no	DET
american_scientific_journal-1402	65	40	1	1	NUM
american_scientific_journal-1402	65	41	,	,	PUNCT
american_scientific_journal-1402	65	42	pp	pp	ADV
american_scientific_journal-1402	65	43	155	155	NUM
american_scientific_journal-1402	65	44	-	-	SYM
american_scientific_journal-1402	65	45	164	164	NUM
american_scientific_journal-1402	65	46	∫	∫	NOUN
american_scientific_journal-1402	66	1	𝑐𝑐	𝑐𝑐	NOUN
american_scientific_journal-1402	66	2	𝑑𝑑𝑑𝑑𝑑𝑑𝑒𝑒′+δ𝑑𝑑𝑒𝑒′	𝑑𝑑𝑑𝑑𝑑𝑑𝑒𝑒′+δ𝑑𝑑𝑒𝑒′	PROPN
american_scientific_journal-1402	66	3	𝑑𝑑𝑒𝑒+δ𝑑𝑑𝑒𝑒	𝑑𝑑𝑒𝑒+δ𝑑𝑑𝑒𝑒	PROPN
american_scientific_journal-1402	66	4	=	=	SYM
american_scientific_journal-1402	66	5	∫	∫	PROPN
american_scientific_journal-1402	66	6	�	�	PROPN
american_scientific_journal-1402	66	7	𝜃𝜃	𝜃𝜃	PROPN
american_scientific_journal-1402	66	8	�	�	PROPN
american_scientific_journal-1402	66	9	𝑅𝑅	𝑅𝑅	PROPN
american_scientific_journal-1402	66	10	𝑙𝑙	𝑙𝑙	PROPN
american_scientific_journal-1402	66	11	�	�	PROPN
american_scientific_journal-1402	66	12	�	�	PROPN
american_scientific_journal-1402	66	13	2	2	NUM
american_scientific_journal-1402	66	14	𝑑𝑑𝑅𝑅𝑅𝑅𝑒𝑒′	𝑑𝑑𝑅𝑅𝑅𝑅𝑒𝑒′	ADP
american_scientific_journal-1402	66	15	𝑅𝑅𝑒𝑒	𝑅𝑅𝑒𝑒	PROPN
american_scientific_journal-1402	66	16	(	(	PUNCT
american_scientific_journal-1402	66	17	18	18	NUM
american_scientific_journal-1402	66	18	)	)	PUNCT
american_scientific_journal-1402	66	19	from	from	ADP
american_scientific_journal-1402	66	20	(	(	PUNCT
american_scientific_journal-1402	66	21	17	17	NUM
american_scientific_journal-1402	66	22	)	)	PUNCT
american_scientific_journal-1402	66	23	and	and	CCONJ
american_scientific_journal-1402	66	24	(	(	PUNCT
american_scientific_journal-1402	66	25	18	18	NUM
american_scientific_journal-1402	66	26	)	)	PUNCT
american_scientific_journal-1402	66	27	we	we	PRON
american_scientific_journal-1402	66	28	obtain	obtain	VERB
american_scientific_journal-1402	66	29	δ𝑑𝑑𝑒𝑒	δ𝑑𝑑𝑒𝑒	NOUN
american_scientific_journal-1402	66	30	=	=	SYM
american_scientific_journal-1402	66	31	δ𝑑𝑑𝑒𝑒′	δ𝑑𝑑𝑒𝑒′	X
american_scientific_journal-1402	67	1	(	(	PUNCT
american_scientific_journal-1402	67	2	19	19	NUM
american_scientific_journal-1402	67	3	)	)	PUNCT
american_scientific_journal-1402	67	4	now	now	ADV
american_scientific_journal-1402	67	5	from	from	ADP
american_scientific_journal-1402	67	6	the	the	DET
american_scientific_journal-1402	67	7	metric	metric	ADJ
american_scientific_journal-1402	67	8	(	(	PUNCT
american_scientific_journal-1402	67	9	15	15	NUM
american_scientific_journal-1402	67	10	)	)	PUNCT
american_scientific_journal-1402	67	11	the	the	DET
american_scientific_journal-1402	67	12	proper	proper	ADJ
american_scientific_journal-1402	67	13	time	time	NOUN
american_scientific_journal-1402	67	14	intervals	interval	NOUN
american_scientific_journal-1402	67	15	of	of	ADP
american_scientific_journal-1402	67	16	the	the	DET
american_scientific_journal-1402	67	17	two	two	NUM
american_scientific_journal-1402	67	18	observers	observer	NOUN
american_scientific_journal-1402	67	19	corresponding	correspond	VERB
american_scientific_journal-1402	67	20	to	to	ADP
american_scientific_journal-1402	67	21	δ𝑑𝑑𝑒𝑒	δ𝑑𝑑𝑒𝑒	NOUN
american_scientific_journal-1402	67	22	and	and	CCONJ
american_scientific_journal-1402	67	23	δ𝑑𝑑𝑒𝑒′	δ𝑑𝑑𝑒𝑒′	NOUN
american_scientific_journal-1402	67	24	are	be	AUX
american_scientific_journal-1402	67	25	given	give	VERB
american_scientific_journal-1402	67	26	by	by	ADP
american_scientific_journal-1402	67	27	δ𝜏𝜏𝑒𝑒	δ𝜏𝜏𝑒𝑒	NOUN
american_scientific_journal-1402	67	28	=	=	SYM
american_scientific_journal-1402	67	29	�	�	PROPN
american_scientific_journal-1402	67	30	1	1	NUM
american_scientific_journal-1402	67	31	𝜃𝜃	𝜃𝜃	PROPN
american_scientific_journal-1402	67	32	�	�	PROPN
american_scientific_journal-1402	67	33	𝑅𝑅𝑒𝑒𝑙𝑙	𝑅𝑅𝑒𝑒𝑙𝑙	PROPN
american_scientific_journal-1402	67	34	�	�	PROPN
american_scientific_journal-1402	67	35	�	�	PROPN
american_scientific_journal-1402	67	36	δ𝑑𝑑𝑒𝑒	δ𝑑𝑑𝑒𝑒	PROPN
american_scientific_journal-1402	67	37	and	and	CCONJ
american_scientific_journal-1402	67	38	δ𝜏𝜏𝑒𝑒′	δ𝜏𝜏𝑒𝑒′	NUM
american_scientific_journal-1402	67	39	=	=	SYM
american_scientific_journal-1402	67	40	�	�	PROPN
american_scientific_journal-1402	67	41	1	1	NUM
american_scientific_journal-1402	67	42	𝜃𝜃	𝜃𝜃	PROPN
american_scientific_journal-1402	67	43	�	�	PROPN
american_scientific_journal-1402	67	44	𝑎𝑎𝑙𝑙	𝑎𝑎𝑙𝑙	PROPN
american_scientific_journal-1402	67	45	�	�	PROPN
american_scientific_journal-1402	67	46	�	�	PROPN
american_scientific_journal-1402	67	47	δ𝑑𝑑𝑒𝑒′	δ𝑑𝑑𝑒𝑒′	X
american_scientific_journal-1402	67	48	(	(	PUNCT
american_scientific_journal-1402	67	49	20	20	NUM
american_scientific_journal-1402	67	50	)	)	PUNCT
american_scientific_journal-1402	67	51	where	where	SCONJ
american_scientific_journal-1402	67	52	δ𝜏𝜏𝑒𝑒	δ𝜏𝜏𝑒𝑒	NOUN
american_scientific_journal-1402	67	53	and	and	CCONJ
american_scientific_journal-1402	67	54	δ𝜏𝜏𝑒𝑒′	δ𝜏𝜏𝑒𝑒′	NUM
american_scientific_journal-1402	67	55	are	be	AUX
american_scientific_journal-1402	67	56	the	the	DET
american_scientific_journal-1402	67	57	proper	proper	ADJ
american_scientific_journal-1402	67	58	time	time	NOUN
american_scientific_journal-1402	67	59	intervals	interval	NOUN
american_scientific_journal-1402	67	60	of	of	ADP
american_scientific_journal-1402	67	61	the	the	DET
american_scientific_journal-1402	67	62	two	two	NUM
american_scientific_journal-1402	67	63	observers	observer	NOUN
american_scientific_journal-1402	67	64	at	at	ADP
american_scientific_journal-1402	67	65	𝑅𝑅	𝑅𝑅	PROPN
american_scientific_journal-1402	67	66	=	=	SYM
american_scientific_journal-1402	67	67	𝑅𝑅𝑒𝑒	𝑅𝑅𝑒𝑒	PROPN
american_scientific_journal-1402	67	68	and	and	CCONJ
american_scientific_journal-1402	67	69	𝑅𝑅	𝑅𝑅	PROPN
american_scientific_journal-1402	67	70	=	=	PUNCT
american_scientific_journal-1402	67	71	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1402	67	72	,	,	PUNCT
american_scientific_journal-1402	67	73	just	just	ADV
american_scientific_journal-1402	67	74	inside	inside	ADP
american_scientific_journal-1402	67	75	the	the	DET
american_scientific_journal-1402	67	76	surface	surface	NOUN
american_scientific_journal-1402	67	77	of	of	ADP
american_scientific_journal-1402	67	78	the	the	DET
american_scientific_journal-1402	67	79	sphere	sphere	NOUN
american_scientific_journal-1402	67	80	,	,	PUNCT
american_scientific_journal-1402	67	81	respectively	respectively	ADV
american_scientific_journal-1402	67	82	,	,	PUNCT
american_scientific_journal-1402	67	83	emitting	emit	VERB
american_scientific_journal-1402	67	84	and	and	CCONJ
american_scientific_journal-1402	67	85	receiving	receive	VERB
american_scientific_journal-1402	67	86	the	the	DET
american_scientific_journal-1402	67	87	pulse	pulse	NOUN
american_scientific_journal-1402	67	88	.	.	PUNCT
american_scientific_journal-1402	68	1	since	since	SCONJ
american_scientific_journal-1402	68	2	the	the	DET
american_scientific_journal-1402	68	3	number	number	NOUN
american_scientific_journal-1402	68	4	of	of	ADP
american_scientific_journal-1402	68	5	cycles	cycle	NOUN
american_scientific_journal-1402	68	6	of	of	ADP
american_scientific_journal-1402	68	7	the	the	DET
american_scientific_journal-1402	68	8	pulse	pulse	NOUN
american_scientific_journal-1402	68	9	remain	remain	VERB
american_scientific_journal-1402	68	10	the	the	DET
american_scientific_journal-1402	68	11	same	same	ADJ
american_scientific_journal-1402	68	12	at	at	ADP
american_scientific_journal-1402	68	13	emission	emission	NOUN
american_scientific_journal-1402	68	14	and	and	CCONJ
american_scientific_journal-1402	68	15	observation	observation	NOUN
american_scientific_journal-1402	68	16	,	,	PUNCT
american_scientific_journal-1402	68	17	we	we	PRON
american_scientific_journal-1402	68	18	have	have	VERB
american_scientific_journal-1402	68	19	𝜈𝜈𝑒𝑒δ𝜏𝜏𝑒𝑒	𝜈𝜈𝑒𝑒δ𝜏𝜏𝑒𝑒	NOUN
american_scientific_journal-1402	68	20	=	=	PUNCT
american_scientific_journal-1402	68	21	𝜈𝜈𝑒𝑒′	𝜈𝜈𝑒𝑒′	PRON
american_scientific_journal-1402	68	22	δ𝜏𝜏𝑒𝑒′	δ𝜏𝜏𝑒𝑒′	NUM
american_scientific_journal-1402	68	23	(	(	PUNCT
american_scientific_journal-1402	68	24	21	21	NUM
american_scientific_journal-1402	68	25	)	)	PUNCT
american_scientific_journal-1402	68	26	where	where	SCONJ
american_scientific_journal-1402	68	27	𝜈𝜈𝑒𝑒	𝜈𝜈𝑒𝑒	NOUN
american_scientific_journal-1402	68	28	and	and	CCONJ
american_scientific_journal-1402	68	29	𝜈𝜈𝑒𝑒′	𝜈𝜈𝑒𝑒′	NOUN
american_scientific_journal-1402	68	30	are	be	AUX
american_scientific_journal-1402	68	31	the	the	DET
american_scientific_journal-1402	68	32	emitted	emitted	ADJ
american_scientific_journal-1402	68	33	and	and	CCONJ
american_scientific_journal-1402	68	34	observed	observed	ADJ
american_scientific_journal-1402	68	35	frequencies	frequency	NOUN
american_scientific_journal-1402	68	36	respectively	respectively	ADV
american_scientific_journal-1402	68	37	.	.	PUNCT
american_scientific_journal-1402	69	1	then	then	ADV
american_scientific_journal-1402	69	2	the	the	DET
american_scientific_journal-1402	69	3	equations	equation	NOUN
american_scientific_journal-1402	69	4	(	(	PUNCT
american_scientific_journal-1402	69	5	20	20	NUM
american_scientific_journal-1402	69	6	)	)	PUNCT
american_scientific_journal-1402	69	7	and	and	CCONJ
american_scientific_journal-1402	69	8	(	(	PUNCT
american_scientific_journal-1402	69	9	21	21	NUM
american_scientific_journal-1402	69	10	)	)	PUNCT
american_scientific_journal-1402	69	11	give	give	VERB
american_scientific_journal-1402	69	12	𝜈𝜈𝑒𝑒′	𝜈𝜈𝑒𝑒′	PRON
american_scientific_journal-1402	69	13	𝜈𝜈𝑒𝑒	𝜈𝜈𝑒𝑒	NOUN
american_scientific_journal-1402	69	14	=	=	SYM
american_scientific_journal-1402	69	15	δ𝜏𝜏𝑒𝑒	δ𝜏𝜏𝑒𝑒	NOUN
american_scientific_journal-1402	69	16	δ𝜏𝜏𝑒𝑒′	δ𝜏𝜏𝑒𝑒′	NUM
american_scientific_journal-1402	70	1	=	=	SYM
american_scientific_journal-1402	70	2	𝜃𝜃	𝜃𝜃	PROPN
american_scientific_journal-1402	70	3	�	�	PROPN
american_scientific_journal-1402	70	4	𝑎𝑎𝑙𝑙	𝑎𝑎𝑙𝑙	PROPN
american_scientific_journal-1402	70	5	�	�	PROPN
american_scientific_journal-1402	70	6	𝜃𝜃	𝜃𝜃	PROPN
american_scientific_journal-1402	70	7	�	�	PROPN
american_scientific_journal-1402	70	8	𝑅𝑅𝑒𝑒𝑙𝑙	𝑅𝑅𝑒𝑒𝑙𝑙	PROPN
american_scientific_journal-1402	70	9	�	�	PROPN
american_scientific_journal-1402	70	10	�	�	PROPN
american_scientific_journal-1402	70	11	δ𝑑𝑑𝑒𝑒	δ𝑑𝑑𝑒𝑒	PROPN
american_scientific_journal-1402	70	12	δ𝑑𝑑𝑒𝑒′	δ𝑑𝑑𝑒𝑒′	NUM
american_scientific_journal-1402	70	13	�	�	PROPN
american_scientific_journal-1402	70	14	(	(	PUNCT
american_scientific_journal-1402	70	15	22	22	NUM
american_scientific_journal-1402	70	16	)	)	PUNCT
american_scientific_journal-1402	70	17	the	the	DET
american_scientific_journal-1402	70	18	equation	equation	NOUN
american_scientific_journal-1402	70	19	(	(	PUNCT
american_scientific_journal-1402	70	20	19	19	NUM
american_scientific_journal-1402	70	21	)	)	PUNCT
american_scientific_journal-1402	70	22	leads	lead	VERB
american_scientific_journal-1402	70	23	the	the	DET
american_scientific_journal-1402	70	24	equation	equation	NOUN
american_scientific_journal-1402	70	25	(	(	PUNCT
american_scientific_journal-1402	70	26	22	22	NUM
american_scientific_journal-1402	70	27	)	)	PUNCT
american_scientific_journal-1402	70	28	to	to	ADP
american_scientific_journal-1402	70	29	𝜈𝜈𝑒𝑒′	𝜈𝜈𝑒𝑒′	NUM
american_scientific_journal-1402	70	30	𝜈𝜈𝑒𝑒	𝜈𝜈𝑒𝑒	NOUN
american_scientific_journal-1402	70	31	=	=	SYM
american_scientific_journal-1402	70	32	𝜃𝜃	𝜃𝜃	PROPN
american_scientific_journal-1402	70	33	�	�	PROPN
american_scientific_journal-1402	70	34	𝑎𝑎𝑙𝑙	𝑎𝑎𝑙𝑙	PROPN
american_scientific_journal-1402	70	35	�	�	PROPN
american_scientific_journal-1402	70	36	𝜃𝜃	𝜃𝜃	PROPN
american_scientific_journal-1402	70	37	�	�	PROPN
american_scientific_journal-1402	70	38	𝑅𝑅𝑒𝑒𝑙𝑙	𝑅𝑅𝑒𝑒𝑙𝑙	PROPN
american_scientific_journal-1402	70	39	�	�	PROPN
american_scientific_journal-1402	70	40	(	(	PUNCT
american_scientific_journal-1402	70	41	23	23	NUM
american_scientific_journal-1402	70	42	)	)	PUNCT
american_scientific_journal-1402	70	43	now	now	ADV
american_scientific_journal-1402	70	44	consider	consider	VERB
american_scientific_journal-1402	70	45	the	the	DET
american_scientific_journal-1402	70	46	moment	moment	NOUN
american_scientific_journal-1402	70	47	at	at	ADP
american_scientific_journal-1402	70	48	which	which	PRON
american_scientific_journal-1402	70	49	the	the	DET
american_scientific_journal-1402	70	50	pulse	pulse	NOUN
american_scientific_journal-1402	70	51	of	of	ADP
american_scientific_journal-1402	70	52	light	light	NOUN
american_scientific_journal-1402	70	53	passes	pass	VERB
american_scientific_journal-1402	70	54	through	through	ADP
american_scientific_journal-1402	70	55	the	the	DET
american_scientific_journal-1402	70	56	boundary	boundary	NOUN
american_scientific_journal-1402	70	57	.	.	PUNCT
american_scientific_journal-1402	71	1	earlier	early	ADV
american_scientific_journal-1402	71	2	in	in	ADP
american_scientific_journal-1402	71	3	this	this	DET
american_scientific_journal-1402	71	4	section	section	NOUN
american_scientific_journal-1402	71	5	,	,	PUNCT
american_scientific_journal-1402	71	6	we	we	PRON
american_scientific_journal-1402	71	7	assumed	assume	VERB
american_scientific_journal-1402	71	8	that	that	SCONJ
american_scientific_journal-1402	71	9	the	the	DET
american_scientific_journal-1402	71	10	observer	observer	NOUN
american_scientific_journal-1402	71	11	at	at	ADP
american_scientific_journal-1402	71	12	𝑅𝑅	𝑅𝑅	PROPN
american_scientific_journal-1402	71	13	=	=	PUNCT
american_scientific_journal-1402	71	14	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1402	71	15	,	,	PUNCT
american_scientific_journal-1402	71	16	at	at	ADP
american_scientific_journal-1402	71	17	the	the	DET
american_scientific_journal-1402	71	18	boundary	boundary	NOUN
american_scientific_journal-1402	71	19	of	of	ADP
american_scientific_journal-1402	71	20	the	the	DET
american_scientific_journal-1402	71	21	sphere	sphere	NOUN
american_scientific_journal-1402	71	22	but	but	CCONJ
american_scientific_journal-1402	71	23	inside	inside	ADV
american_scientific_journal-1402	71	24	it	it	PRON
american_scientific_journal-1402	71	25	observed	observe	VERB
american_scientific_journal-1402	71	26	the	the	DET
american_scientific_journal-1402	71	27	pulse	pulse	NOUN
american_scientific_journal-1402	71	28	at	at	ADP
american_scientific_journal-1402	71	29	𝑑𝑑	𝑑𝑑	NOUN
american_scientific_journal-1402	71	30	=	=	NOUN
american_scientific_journal-1402	71	31	𝑑𝑑𝑒𝑒′	𝑑𝑑𝑒𝑒′	NOUN
american_scientific_journal-1402	71	32	with	with	ADP
american_scientific_journal-1402	71	33	frequency	frequency	NOUN
american_scientific_journal-1402	71	34	𝜈𝜈𝑒𝑒′.	𝜈𝜈𝑒𝑒′.	NOUN
american_scientific_journal-1402	71	35	now	now	ADV
american_scientific_journal-1402	71	36	our	our	PRON
american_scientific_journal-1402	71	37	assumption	assumption	NOUN
american_scientific_journal-1402	71	38	is	be	AUX
american_scientific_journal-1402	71	39	that	that	SCONJ
american_scientific_journal-1402	71	40	an	an	DET
american_scientific_journal-1402	71	41	observer	observer	NOUN
american_scientific_journal-1402	71	42	at	at	ADP
american_scientific_journal-1402	71	43	𝑅𝑅	𝑅𝑅	PROPN
american_scientific_journal-1402	71	44	=	=	PUNCT
american_scientific_journal-1402	71	45	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1402	71	46	but	but	CCONJ
american_scientific_journal-1402	71	47	outside	outside	ADP
american_scientific_journal-1402	71	48	of	of	ADP
american_scientific_journal-1402	71	49	the	the	DET
american_scientific_journal-1402	71	50	sphere	sphere	NOUN
american_scientific_journal-1402	71	51	observed	observe	VERB
american_scientific_journal-1402	71	52	the	the	DET
american_scientific_journal-1402	71	53	pulse	pulse	NOUN
american_scientific_journal-1402	71	54	at	at	ADP
american_scientific_journal-1402	71	55	𝑑𝑑	𝑑𝑑	NOUN
american_scientific_journal-1402	71	56	=	=	PUNCT
american_scientific_journal-1402	71	57	𝑑𝑑0′	𝑑𝑑0′	ADP
american_scientific_journal-1402	71	58	with	with	ADP
american_scientific_journal-1402	71	59	frequency	frequency	NOUN
american_scientific_journal-1402	71	60	𝜈𝜈0′.	𝜈𝜈0′.	NOUN
american_scientific_journal-1402	71	61	then	then	ADV
american_scientific_journal-1402	71	62	using	use	VERB
american_scientific_journal-1402	71	63	the	the	DET
american_scientific_journal-1402	71	64	metrics	metric	NOUN
american_scientific_journal-1402	71	65	in	in	ADP
american_scientific_journal-1402	71	66	(	(	PUNCT
american_scientific_journal-1402	71	67	15	15	NUM
american_scientific_journal-1402	71	68	)	)	PUNCT
american_scientific_journal-1402	71	69	,	,	PUNCT
american_scientific_journal-1402	71	70	the	the	DET
american_scientific_journal-1402	71	71	proper	proper	ADJ
american_scientific_journal-1402	71	72	times	time	NOUN
american_scientific_journal-1402	71	73	of	of	ADP
american_scientific_journal-1402	71	74	the	the	DET
american_scientific_journal-1402	71	75	two	two	NUM
american_scientific_journal-1402	71	76	observers	observer	NOUN
american_scientific_journal-1402	71	77	corresponding	correspond	VERB
american_scientific_journal-1402	71	78	to	to	ADP
american_scientific_journal-1402	71	79	δ𝜏𝜏𝑒𝑒′	δ𝜏𝜏𝑒𝑒′	NUM
american_scientific_journal-1402	71	80	and	and	CCONJ
american_scientific_journal-1402	71	81	δ𝜏𝜏0′	δ𝜏𝜏0′	NOUN
american_scientific_journal-1402	71	82	can	can	AUX
american_scientific_journal-1402	71	83	be	be	AUX
american_scientific_journal-1402	71	84	written	write	VERB
american_scientific_journal-1402	71	85	as	as	ADP
american_scientific_journal-1402	71	86	δ𝜏𝜏𝑒𝑒′	δ𝜏𝜏𝑒𝑒′	NOUN
american_scientific_journal-1402	71	87	=	=	SYM
american_scientific_journal-1402	71	88	�	�	PROPN
american_scientific_journal-1402	71	89	1	1	NUM
american_scientific_journal-1402	71	90	𝜃𝜃	𝜃𝜃	PROPN
american_scientific_journal-1402	71	91	�	�	PROPN
american_scientific_journal-1402	71	92	𝑎𝑎𝑙𝑙	𝑎𝑎𝑙𝑙	PROPN
american_scientific_journal-1402	71	93	�	�	PROPN
american_scientific_journal-1402	71	94	�	�	PROPN
american_scientific_journal-1402	71	95	δ𝑑𝑑𝑒𝑒′	δ𝑑𝑑𝑒𝑒′	NUM
american_scientific_journal-1402	71	96	and	and	CCONJ
american_scientific_journal-1402	71	97	δ𝜏𝜏0′	δ𝜏𝜏0′	PROPN
american_scientific_journal-1402	71	98	=	=	SYM
american_scientific_journal-1402	71	99	�	�	PROPN
american_scientific_journal-1402	71	100	1	1	NUM
american_scientific_journal-1402	71	101	𝜃𝜃	𝜃𝜃	PROPN
american_scientific_journal-1402	71	102	�	�	PROPN
american_scientific_journal-1402	71	103	𝑎𝑎𝑙𝑙	𝑎𝑎𝑙𝑙	PROPN
american_scientific_journal-1402	71	104	�	�	PROPN
american_scientific_journal-1402	71	105	−	−	PUNCT
american_scientific_journal-1402	71	106	𝑚𝑚	𝑚𝑚	ADP
american_scientific_journal-1402	71	107	𝑎𝑎+	𝑎𝑎+	VERB
american_scientific_journal-1402	71	108	𝑚𝑚	𝑚𝑚	ADP
american_scientific_journal-1402	71	109	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1402	71	110	�	�	PROPN
american_scientific_journal-1402	71	111	δ𝑑𝑑0′	δ𝑑𝑑0′	PROPN
american_scientific_journal-1402	71	112	=	=	SYM
american_scientific_journal-1402	71	113	�	�	PROPN
american_scientific_journal-1402	71	114	1	1	NUM
american_scientific_journal-1402	71	115	𝜃𝜃	𝜃𝜃	PROPN
american_scientific_journal-1402	71	116	�	�	PROPN
american_scientific_journal-1402	71	117	𝑎𝑎𝑙𝑙	𝑎𝑎𝑙𝑙	PROPN
american_scientific_journal-1402	71	118	�	�	PROPN
american_scientific_journal-1402	71	119	�	�	PROPN
american_scientific_journal-1402	71	120	δ𝑑𝑑0′	δ𝑑𝑑0′	PROPN
american_scientific_journal-1402	71	121	(	(	PUNCT
american_scientific_journal-1402	71	122	24	24	NUM
american_scientific_journal-1402	71	123	)	)	PUNCT
american_scientific_journal-1402	71	124	161	161	NUM
american_scientific_journal-1402	71	125	american	american	ADJ
american_scientific_journal-1402	71	126	scientific	scientific	ADJ
american_scientific_journal-1402	71	127	research	research	NOUN
american_scientific_journal-1402	71	128	journal	journal	NOUN
american_scientific_journal-1402	71	129	for	for	ADP
american_scientific_journal-1402	71	130	engineering	engineering	NOUN
american_scientific_journal-1402	71	131	,	,	PUNCT
american_scientific_journal-1402	71	132	technology	technology	NOUN
american_scientific_journal-1402	71	133	,	,	PUNCT
american_scientific_journal-1402	71	134	and	and	CCONJ
american_scientific_journal-1402	71	135	sciences	science	NOUN
american_scientific_journal-1402	71	136	(	(	PUNCT
american_scientific_journal-1402	71	137	asrjets	asrjet	NOUN
american_scientific_journal-1402	71	138	)	)	PUNCT
american_scientific_journal-1402	71	139	(	(	PUNCT
american_scientific_journal-1402	71	140	2016	2016	NUM
american_scientific_journal-1402	71	141	)	)	PUNCT
american_scientific_journal-1402	71	142	volume	volume	NOUN
american_scientific_journal-1402	71	143	17	17	NUM
american_scientific_journal-1402	71	144	,	,	PUNCT
american_scientific_journal-1402	71	145	no	no	DET
american_scientific_journal-1402	71	146	1	1	NUM
american_scientific_journal-1402	71	147	,	,	PUNCT
american_scientific_journal-1402	71	148	pp	pp	ADV
american_scientific_journal-1402	71	149	155	155	NUM
american_scientific_journal-1402	71	150	-	-	SYM
american_scientific_journal-1402	71	151	164	164	NUM
american_scientific_journal-1402	71	152	where	where	SCONJ
american_scientific_journal-1402	71	153	δ𝜏𝜏0′	δ𝜏𝜏0′	X
american_scientific_journal-1402	71	154	and	and	CCONJ
american_scientific_journal-1402	71	155	δ𝜏𝜏𝑒𝑒′	δ𝜏𝜏𝑒𝑒′	NUM
american_scientific_journal-1402	71	156	are	be	AUX
american_scientific_journal-1402	71	157	the	the	DET
american_scientific_journal-1402	71	158	proper	proper	ADJ
american_scientific_journal-1402	71	159	time	time	NOUN
american_scientific_journal-1402	71	160	intervals	interval	NOUN
american_scientific_journal-1402	71	161	of	of	ADP
american_scientific_journal-1402	71	162	the	the	DET
american_scientific_journal-1402	71	163	two	two	NUM
american_scientific_journal-1402	71	164	observers	observer	NOUN
american_scientific_journal-1402	71	165	at	at	ADP
american_scientific_journal-1402	71	166	𝑅𝑅	𝑅𝑅	PROPN
american_scientific_journal-1402	71	167	=	=	PUNCT
american_scientific_journal-1402	71	168	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1402	71	169	,	,	PUNCT
american_scientific_journal-1402	71	170	inside	inside	ADP
american_scientific_journal-1402	71	171	the	the	DET
american_scientific_journal-1402	71	172	sphere	sphere	NOUN
american_scientific_journal-1402	71	173	and	and	CCONJ
american_scientific_journal-1402	71	174	outside	outside	ADP
american_scientific_journal-1402	71	175	the	the	DET
american_scientific_journal-1402	71	176	sphere	sphere	NOUN
american_scientific_journal-1402	71	177	respectively	respectively	ADV
american_scientific_journal-1402	71	178	observing	observe	VERB
american_scientific_journal-1402	71	179	the	the	DET
american_scientific_journal-1402	71	180	pulse	pulse	NOUN
american_scientific_journal-1402	71	181	.	.	PUNCT
american_scientific_journal-1402	72	1	since	since	SCONJ
american_scientific_journal-1402	72	2	the	the	DET
american_scientific_journal-1402	72	3	number	number	NOUN
american_scientific_journal-1402	72	4	of	of	ADP
american_scientific_journal-1402	72	5	cycles	cycle	NOUN
american_scientific_journal-1402	72	6	in	in	ADP
american_scientific_journal-1402	72	7	the	the	DET
american_scientific_journal-1402	72	8	pulse	pulse	NOUN
american_scientific_journal-1402	72	9	remain	remain	VERB
american_scientific_journal-1402	72	10	the	the	DET
american_scientific_journal-1402	72	11	same	same	ADJ
american_scientific_journal-1402	72	12	as	as	SCONJ
american_scientific_journal-1402	72	13	it	it	PRON
american_scientific_journal-1402	72	14	crosses	cross	VERB
american_scientific_journal-1402	72	15	the	the	DET
american_scientific_journal-1402	72	16	boundary	boundary	NOUN
american_scientific_journal-1402	72	17	,	,	PUNCT
american_scientific_journal-1402	72	18	from	from	ADP
american_scientific_journal-1402	72	19	the	the	DET
american_scientific_journal-1402	72	20	equation	equation	NOUN
american_scientific_journal-1402	72	21	(	(	PUNCT
american_scientific_journal-1402	72	22	24	24	NUM
american_scientific_journal-1402	72	23	)	)	PUNCT
american_scientific_journal-1402	72	24	we	we	PRON
american_scientific_journal-1402	72	25	obtain	obtain	VERB
american_scientific_journal-1402	72	26	𝜐𝜐𝑒𝑒′	𝜐𝜐𝑒𝑒′	NUM
american_scientific_journal-1402	72	27	𝜐𝜐0′	𝜐𝜐0′	X
american_scientific_journal-1402	72	28	=	=	PUNCT
american_scientific_journal-1402	72	29	δ𝜏𝜏0′	δ𝜏𝜏0′	X
american_scientific_journal-1402	72	30	δ𝜏𝜏𝑒𝑒′	δ𝜏𝜏𝑒𝑒′	NUM
american_scientific_journal-1402	72	31	=	=	SYM
american_scientific_journal-1402	72	32	δ𝑑𝑑0′	δ𝑑𝑑0′	PROPN
american_scientific_journal-1402	72	33	δ𝑑𝑑𝑒𝑒′	δ𝑑𝑑𝑒𝑒′	SYM
american_scientific_journal-1402	72	34	(	(	PUNCT
american_scientific_journal-1402	72	35	25	25	NUM
american_scientific_journal-1402	72	36	)	)	PUNCT
american_scientific_journal-1402	72	37	according	accord	VERB
american_scientific_journal-1402	72	38	to	to	ADP
american_scientific_journal-1402	72	39	the	the	DET
american_scientific_journal-1402	72	40	standard	standard	ADJ
american_scientific_journal-1402	72	41	boundary	boundary	ADJ
american_scientific_journal-1402	72	42	conditions	condition	NOUN
american_scientific_journal-1402	72	43	,	,	PUNCT
american_scientific_journal-1402	72	44	the	the	DET
american_scientific_journal-1402	72	45	coordinate	coordinate	NOUN
american_scientific_journal-1402	72	46	time	time	NOUN
american_scientific_journal-1402	72	47	intervals	interval	NOUN
american_scientific_journal-1402	72	48	do	do	AUX
american_scientific_journal-1402	72	49	not	not	PART
american_scientific_journal-1402	72	50	vary	vary	VERB
american_scientific_journal-1402	72	51	across	across	ADP
american_scientific_journal-1402	72	52	the	the	DET
american_scientific_journal-1402	72	53	boundary	boundary	NOUN
american_scientific_journal-1402	72	54	.	.	PUNCT
american_scientific_journal-1402	73	1	then	then	ADV
american_scientific_journal-1402	73	2	the	the	DET
american_scientific_journal-1402	73	3	equation	equation	NOUN
american_scientific_journal-1402	73	4	(	(	PUNCT
american_scientific_journal-1402	73	5	25	25	NUM
american_scientific_journal-1402	73	6	)	)	PUNCT
american_scientific_journal-1402	73	7	simplifies	simplifie	NOUN
american_scientific_journal-1402	73	8	to	to	ADP
american_scientific_journal-1402	73	9	𝜐𝜐𝑒𝑒′	𝜐𝜐𝑒𝑒′	NUM
american_scientific_journal-1402	73	10	𝜐𝜐0′	𝜐𝜐0′	X
american_scientific_journal-1402	73	11	=	=	SYM
american_scientific_journal-1402	73	12	1	1	NUM
american_scientific_journal-1402	73	13	(	(	PUNCT
american_scientific_journal-1402	73	14	26	26	NUM
american_scientific_journal-1402	73	15	)	)	PUNCT
american_scientific_journal-1402	73	16	now	now	ADV
american_scientific_journal-1402	73	17	assume	assume	VERB
american_scientific_journal-1402	73	18	that	that	SCONJ
american_scientific_journal-1402	73	19	an	an	DET
american_scientific_journal-1402	73	20	observer	observer	NOUN
american_scientific_journal-1402	73	21	at	at	ADP
american_scientific_journal-1402	73	22	a	a	DET
american_scientific_journal-1402	73	23	large	large	ADJ
american_scientific_journal-1402	73	24	distance	distance	NOUN
american_scientific_journal-1402	73	25	𝑅𝑅	𝑅𝑅	PROPN
american_scientific_journal-1402	73	26	=	=	SYM
american_scientific_journal-1402	73	27	𝑅𝑅0	𝑅𝑅0	PROPN
american_scientific_journal-1402	73	28	,	,	PUNCT
american_scientific_journal-1402	73	29	outside	outside	ADP
american_scientific_journal-1402	73	30	of	of	ADP
american_scientific_journal-1402	73	31	the	the	DET
american_scientific_journal-1402	73	32	sphere	sphere	NOUN
american_scientific_journal-1402	73	33	observed	observe	VERB
american_scientific_journal-1402	73	34	the	the	DET
american_scientific_journal-1402	73	35	front	front	NOUN
american_scientific_journal-1402	73	36	of	of	ADP
american_scientific_journal-1402	73	37	the	the	DET
american_scientific_journal-1402	73	38	pulse	pulse	NOUN
american_scientific_journal-1402	73	39	which	which	PRON
american_scientific_journal-1402	73	40	is	be	AUX
american_scientific_journal-1402	73	41	passed	pass	VERB
american_scientific_journal-1402	73	42	through	through	ADP
american_scientific_journal-1402	73	43	the	the	DET
american_scientific_journal-1402	73	44	boundary	boundary	NOUN
american_scientific_journal-1402	73	45	at	at	ADP
american_scientific_journal-1402	73	46	𝑑𝑑	𝑑𝑑	NOUN
american_scientific_journal-1402	73	47	=	=	SYM
american_scientific_journal-1402	73	48	𝑑𝑑0′	𝑑𝑑0′	ADP
american_scientific_journal-1402	73	49	outside	outside	ADP
american_scientific_journal-1402	73	50	the	the	DET
american_scientific_journal-1402	73	51	sphere	sphere	NOUN
american_scientific_journal-1402	73	52	at	at	ADP
american_scientific_journal-1402	73	53	𝑑𝑑	𝑑𝑑	NOUN
american_scientific_journal-1402	73	54	=	=	SYM
american_scientific_journal-1402	73	55	𝑑𝑑0	𝑑𝑑0	NOUN
american_scientific_journal-1402	73	56	,	,	PUNCT
american_scientific_journal-1402	73	57	and	and	CCONJ
american_scientific_journal-1402	73	58	the	the	DET
american_scientific_journal-1402	73	59	rear	rear	NOUN
american_scientific_journal-1402	73	60	of	of	ADP
american_scientific_journal-1402	73	61	the	the	DET
american_scientific_journal-1402	73	62	pulse	pulse	NOUN
american_scientific_journal-1402	73	63	which	which	PRON
american_scientific_journal-1402	73	64	is	be	AUX
american_scientific_journal-1402	73	65	passed	pass	VERB
american_scientific_journal-1402	73	66	through	through	ADP
american_scientific_journal-1402	73	67	the	the	DET
american_scientific_journal-1402	73	68	boundary	boundary	NOUN
american_scientific_journal-1402	73	69	at	at	ADP
american_scientific_journal-1402	73	70	𝑑𝑑	𝑑𝑑	NOUN
american_scientific_journal-1402	73	71	=	=	SYM
american_scientific_journal-1402	73	72	𝑑𝑑0′	𝑑𝑑0′	ADP
american_scientific_journal-1402	73	73	+	+	CCONJ
american_scientific_journal-1402	73	74	δ𝑑𝑑0′	δ𝑑𝑑0′	NOUN
american_scientific_journal-1402	73	75	outside	outside	ADP
american_scientific_journal-1402	73	76	the	the	DET
american_scientific_journal-1402	73	77	sphere	sphere	NOUN
american_scientific_journal-1402	73	78	,	,	PUNCT
american_scientific_journal-1402	73	79	at	at	ADP
american_scientific_journal-1402	73	80	𝑑𝑑	𝑑𝑑	NOUN
american_scientific_journal-1402	73	81	=	=	PUNCT
american_scientific_journal-1402	73	82	𝑑𝑑0	𝑑𝑑0	NOUN
american_scientific_journal-1402	73	83	+	+	CCONJ
american_scientific_journal-1402	73	84	δ𝑑𝑑0	δ𝑑𝑑0	NOUN
american_scientific_journal-1402	73	85	respectively	respectively	ADV
american_scientific_journal-1402	73	86	with	with	ADP
american_scientific_journal-1402	73	87	the	the	DET
american_scientific_journal-1402	73	88	frequency	frequency	NOUN
american_scientific_journal-1402	73	89	𝜐𝜐0	𝜐𝜐0	NOUN
american_scientific_journal-1402	73	90	.	.	PUNCT
american_scientific_journal-1402	74	1	now	now	ADV
american_scientific_journal-1402	74	2	we	we	PRON
american_scientific_journal-1402	74	3	have	have	VERB
american_scientific_journal-1402	74	4	to	to	PART
american_scientific_journal-1402	74	5	consider	consider	VERB
american_scientific_journal-1402	74	6	the	the	DET
american_scientific_journal-1402	74	7	exterior	exterior	ADJ
american_scientific_journal-1402	74	8	metric	metric	ADJ
american_scientific_journal-1402	74	9	in	in	ADP
american_scientific_journal-1402	74	10	(	(	PUNCT
american_scientific_journal-1402	74	11	15	15	NUM
american_scientific_journal-1402	74	12	)	)	PUNCT
american_scientific_journal-1402	74	13	which	which	PRON
american_scientific_journal-1402	74	14	is	be	AUX
american_scientific_journal-1402	74	15	𝑑𝑑𝑑𝑑2	𝑑𝑑𝑑𝑑2	NOUN
american_scientific_journal-1402	74	16	=	=	SYM
american_scientific_journal-1402	74	17	1	1	NUM
american_scientific_journal-1402	74	18	�	�	PROPN
american_scientific_journal-1402	74	19	𝜃𝜃	𝜃𝜃	PROPN
american_scientific_journal-1402	74	20	�	�	PROPN
american_scientific_journal-1402	74	21	𝑎𝑎𝑙𝑙	𝑎𝑎𝑙𝑙	PROPN
american_scientific_journal-1402	74	22	�	�	PROPN
american_scientific_journal-1402	74	23	−	−	PUNCT
american_scientific_journal-1402	74	24	𝑚𝑚	𝑚𝑚	ADP
american_scientific_journal-1402	74	25	𝑎𝑎+	𝑎𝑎+	PROPN
american_scientific_journal-1402	74	26	𝑚𝑚	𝑚𝑚	ADP
american_scientific_journal-1402	74	27	𝑅𝑅	𝑅𝑅	PROPN
american_scientific_journal-1402	74	28	�	�	PROPN
american_scientific_journal-1402	74	29	2	2	NUM
american_scientific_journal-1402	74	30	𝑐𝑐2𝑑𝑑𝑑𝑑2	𝑐𝑐2𝑑𝑑𝑑𝑑2	SYM
american_scientific_journal-1402	74	31	−	−	PROPN
american_scientific_journal-1402	74	32	�	�	PROPN
american_scientific_journal-1402	74	33	𝜃𝜃	𝜃𝜃	PROPN
american_scientific_journal-1402	74	34	�	�	PROPN
american_scientific_journal-1402	74	35	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1402	74	36	𝑙𝑙	𝑙𝑙	PRON
american_scientific_journal-1402	74	37	�	�	PROPN
american_scientific_journal-1402	74	38	−	−	ADP
american_scientific_journal-1402	74	39	𝑚𝑚	𝑚𝑚	ADP
american_scientific_journal-1402	74	40	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1402	74	41	+	+	CCONJ
american_scientific_journal-1402	74	42	𝑚𝑚	𝑚𝑚	ADP
american_scientific_journal-1402	74	43	𝑅𝑅	𝑅𝑅	PROPN
american_scientific_journal-1402	74	44	�	�	PROPN
american_scientific_journal-1402	74	45	2	2	NUM
american_scientific_journal-1402	74	46	(	(	PUNCT
american_scientific_journal-1402	74	47	𝑑𝑑𝑅𝑅2	𝑑𝑑𝑅𝑅2	NOUN
american_scientific_journal-1402	74	48	+	+	CCONJ
american_scientific_journal-1402	74	49	𝑅𝑅2𝑑𝑑ω2	𝑅𝑅2𝑑𝑑ω2	PROPN
american_scientific_journal-1402	74	50	)	)	PUNCT
american_scientific_journal-1402	74	51	.	.	PUNCT
american_scientific_journal-1402	75	1	considering	consider	VERB
american_scientific_journal-1402	75	2	the	the	DET
american_scientific_journal-1402	75	3	null	null	ADJ
american_scientific_journal-1402	75	4	geodesics	geodesic	NOUN
american_scientific_journal-1402	75	5	of	of	ADP
american_scientific_journal-1402	75	6	the	the	DET
american_scientific_journal-1402	75	7	metric	metric	NOUN
american_scientific_journal-1402	75	8	we	we	PRON
american_scientific_journal-1402	75	9	obtain	obtain	VERB
american_scientific_journal-1402	75	10	𝑐𝑐	𝑐𝑐	PRON
american_scientific_journal-1402	75	11	𝑑𝑑𝑑𝑑	𝑑𝑑𝑑𝑑	NOUN
american_scientific_journal-1402	76	1	=	=	PUNCT
american_scientific_journal-1402	76	2	�	�	PROPN
american_scientific_journal-1402	76	3	𝜃𝜃	𝜃𝜃	PROPN
american_scientific_journal-1402	76	4	�	�	PROPN
american_scientific_journal-1402	76	5	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1402	76	6	𝑙𝑙	𝑙𝑙	PRON
american_scientific_journal-1402	76	7	�	�	PROPN
american_scientific_journal-1402	77	1	−	−	ADP
american_scientific_journal-1402	77	2	𝑚𝑚	𝑚𝑚	ADP
american_scientific_journal-1402	77	3	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1402	77	4	+	+	CCONJ
american_scientific_journal-1402	77	5	𝑚𝑚	𝑚𝑚	ADP
american_scientific_journal-1402	77	6	𝑅𝑅	𝑅𝑅	PROPN
american_scientific_journal-1402	77	7	�	�	PROPN
american_scientific_journal-1402	77	8	2	2	NUM
american_scientific_journal-1402	77	9	𝑑𝑑𝑅𝑅	𝑑𝑑𝑅𝑅	NOUN
american_scientific_journal-1402	77	10	(	(	PUNCT
american_scientific_journal-1402	77	11	27	27	NUM
american_scientific_journal-1402	77	12	)	)	PUNCT
american_scientific_journal-1402	77	13	(	(	PUNCT
american_scientific_journal-1402	77	14	plus	plus	CCONJ
american_scientific_journal-1402	77	15	sign	sign	NOUN
american_scientific_journal-1402	77	16	is	be	AUX
american_scientific_journal-1402	77	17	taken	take	VERB
american_scientific_journal-1402	77	18	since	since	SCONJ
american_scientific_journal-1402	77	19	the	the	DET
american_scientific_journal-1402	77	20	null	null	ADJ
american_scientific_journal-1402	77	21	ray	ray	NOUN
american_scientific_journal-1402	77	22	is	be	AUX
american_scientific_journal-1402	77	23	away	away	ADV
american_scientific_journal-1402	77	24	from	from	ADP
american_scientific_journal-1402	77	25	the	the	DET
american_scientific_journal-1402	77	26	centre	centre	NOUN
american_scientific_journal-1402	77	27	of	of	ADP
american_scientific_journal-1402	77	28	the	the	DET
american_scientific_journal-1402	77	29	sphere	sphere	NOUN
american_scientific_journal-1402	77	30	.	.	PUNCT
american_scientific_journal-1402	77	31	)	)	PUNCT
american_scientific_journal-1402	78	1	integration	integration	NOUN
american_scientific_journal-1402	78	2	of	of	ADP
american_scientific_journal-1402	78	3	(	(	PUNCT
american_scientific_journal-1402	78	4	27	27	NUM
american_scientific_journal-1402	78	5	)	)	PUNCT
american_scientific_journal-1402	78	6	gives	give	VERB
american_scientific_journal-1402	78	7	∫	∫	PROPN
american_scientific_journal-1402	78	8	𝑐𝑐	𝑐𝑐	NOUN
american_scientific_journal-1402	78	9	𝑑𝑑𝑑𝑑𝑑𝑑0	𝑑𝑑𝑑𝑑𝑑𝑑0	ADJ
american_scientific_journal-1402	78	10	𝑑𝑑0′	𝑑𝑑0′	ADP
american_scientific_journal-1402	78	11	=	=	SYM
american_scientific_journal-1402	78	12	∫	∫	PROPN
american_scientific_journal-1402	78	13	�	�	PROPN
american_scientific_journal-1402	78	14	𝜃𝜃	𝜃𝜃	PROPN
american_scientific_journal-1402	78	15	�	�	PROPN
american_scientific_journal-1402	78	16	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1402	78	17	𝑙𝑙	𝑙𝑙	PRON
american_scientific_journal-1402	78	18	�	�	PROPN
american_scientific_journal-1402	78	19	−	−	ADP
american_scientific_journal-1402	78	20	𝑚𝑚	𝑚𝑚	ADP
american_scientific_journal-1402	78	21	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1402	78	22	+	+	CCONJ
american_scientific_journal-1402	78	23	𝑚𝑚	𝑚𝑚	ADP
american_scientific_journal-1402	78	24	𝑅𝑅	𝑅𝑅	PROPN
american_scientific_journal-1402	78	25	�	�	PROPN
american_scientific_journal-1402	78	26	2	2	NUM
american_scientific_journal-1402	78	27	𝑑𝑑𝑅𝑅𝑅𝑅0	𝑑𝑑𝑅𝑅𝑅𝑅0	NOUN
american_scientific_journal-1402	78	28	𝑅𝑅=𝑎𝑎	𝑅𝑅=𝑎𝑎	PROPN
american_scientific_journal-1402	78	29	(	(	PUNCT
american_scientific_journal-1402	78	30	28	28	NUM
american_scientific_journal-1402	78	31	)	)	PUNCT
american_scientific_journal-1402	78	32	if	if	SCONJ
american_scientific_journal-1402	78	33	the	the	DET
american_scientific_journal-1402	78	34	rear	rear	NOUN
american_scientific_journal-1402	78	35	of	of	ADP
american_scientific_journal-1402	78	36	the	the	DET
american_scientific_journal-1402	78	37	pulse	pulse	NOUN
american_scientific_journal-1402	78	38	is	be	AUX
american_scientific_journal-1402	78	39	observed	observe	VERB
american_scientific_journal-1402	78	40	at	at	ADP
american_scientific_journal-1402	78	41	𝑑𝑑0	𝑑𝑑0	NOUN
american_scientific_journal-1402	78	42	+	+	CCONJ
american_scientific_journal-1402	78	43	δ𝑑𝑑0	δ𝑑𝑑0	NOUN
american_scientific_journal-1402	78	44	at	at	ADP
american_scientific_journal-1402	78	45	𝑅𝑅	𝑅𝑅	PROPN
american_scientific_journal-1402	78	46	=	=	SYM
american_scientific_journal-1402	78	47	𝑅𝑅0	𝑅𝑅0	PROPN
american_scientific_journal-1402	78	48	,	,	PUNCT
american_scientific_journal-1402	78	49	then	then	ADV
american_scientific_journal-1402	78	50	integration	integration	NOUN
american_scientific_journal-1402	78	51	of	of	ADP
american_scientific_journal-1402	78	52	(	(	PUNCT
american_scientific_journal-1402	78	53	27	27	NUM
american_scientific_journal-1402	78	54	)	)	PUNCT
american_scientific_journal-1402	78	55	gives	give	VERB
american_scientific_journal-1402	78	56	∫	∫	PROPN
american_scientific_journal-1402	78	57	𝑐𝑐	𝑐𝑐	NOUN
american_scientific_journal-1402	78	58	𝑑𝑑𝑑𝑑𝑑𝑑0+δ𝑑𝑑0	𝑑𝑑𝑑𝑑𝑑𝑑0+δ𝑑𝑑0	NOUN
american_scientific_journal-1402	78	59	𝑑𝑑0′+δ𝑑𝑑0′	𝑑𝑑0′+δ𝑑𝑑0′	PROPN
american_scientific_journal-1402	78	60	=	=	SYM
american_scientific_journal-1402	78	61	∫	∫	PROPN
american_scientific_journal-1402	78	62	�	�	PROPN
american_scientific_journal-1402	78	63	𝜃𝜃	𝜃𝜃	PROPN
american_scientific_journal-1402	78	64	�	�	PROPN
american_scientific_journal-1402	78	65	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1402	78	66	𝑙𝑙	𝑙𝑙	PRON
american_scientific_journal-1402	78	67	�	�	PROPN
american_scientific_journal-1402	78	68	−	−	ADP
american_scientific_journal-1402	78	69	𝑚𝑚	𝑚𝑚	ADP
american_scientific_journal-1402	78	70	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1402	78	71	+	+	CCONJ
american_scientific_journal-1402	78	72	𝑚𝑚	𝑚𝑚	ADP
american_scientific_journal-1402	78	73	𝑅𝑅	𝑅𝑅	PROPN
american_scientific_journal-1402	78	74	�	�	PROPN
american_scientific_journal-1402	78	75	2	2	NUM
american_scientific_journal-1402	78	76	𝑑𝑑𝑅𝑅𝑅𝑅0	𝑑𝑑𝑅𝑅𝑅𝑅0	NOUN
american_scientific_journal-1402	78	77	𝑅𝑅=𝑎𝑎	𝑅𝑅=𝑎𝑎	PROPN
american_scientific_journal-1402	78	78	(	(	PUNCT
american_scientific_journal-1402	78	79	29	29	NUM
american_scientific_journal-1402	78	80	)	)	PUNCT
american_scientific_journal-1402	78	81	from	from	ADP
american_scientific_journal-1402	78	82	the	the	DET
american_scientific_journal-1402	78	83	equations	equation	NOUN
american_scientific_journal-1402	78	84	(	(	PUNCT
american_scientific_journal-1402	78	85	28	28	NUM
american_scientific_journal-1402	78	86	)	)	PUNCT
american_scientific_journal-1402	78	87	and	and	CCONJ
american_scientific_journal-1402	78	88	(	(	PUNCT
american_scientific_journal-1402	78	89	29	29	NUM
american_scientific_journal-1402	78	90	)	)	PUNCT
american_scientific_journal-1402	78	91	we	we	PRON
american_scientific_journal-1402	78	92	obtain	obtain	VERB
american_scientific_journal-1402	78	93	162	162	NUM
american_scientific_journal-1402	78	94	american	american	ADJ
american_scientific_journal-1402	78	95	scientific	scientific	ADJ
american_scientific_journal-1402	78	96	research	research	NOUN
american_scientific_journal-1402	78	97	journal	journal	NOUN
american_scientific_journal-1402	78	98	for	for	ADP
american_scientific_journal-1402	78	99	engineering	engineering	NOUN
american_scientific_journal-1402	78	100	,	,	PUNCT
american_scientific_journal-1402	78	101	technology	technology	NOUN
american_scientific_journal-1402	78	102	,	,	PUNCT
american_scientific_journal-1402	78	103	and	and	CCONJ
american_scientific_journal-1402	78	104	sciences	science	NOUN
american_scientific_journal-1402	78	105	(	(	PUNCT
american_scientific_journal-1402	78	106	asrjets	asrjet	NOUN
american_scientific_journal-1402	78	107	)	)	PUNCT
american_scientific_journal-1402	78	108	(	(	PUNCT
american_scientific_journal-1402	78	109	2016	2016	NUM
american_scientific_journal-1402	78	110	)	)	PUNCT
american_scientific_journal-1402	78	111	volume	volume	NOUN
american_scientific_journal-1402	78	112	17	17	NUM
american_scientific_journal-1402	78	113	,	,	PUNCT
american_scientific_journal-1402	78	114	no	no	DET
american_scientific_journal-1402	78	115	1	1	NUM
american_scientific_journal-1402	78	116	,	,	PUNCT
american_scientific_journal-1402	78	117	pp	pp	ADV
american_scientific_journal-1402	78	118	155	155	NUM
american_scientific_journal-1402	78	119	-	-	SYM
american_scientific_journal-1402	78	120	164	164	NUM
american_scientific_journal-1402	78	121	δ𝑑𝑑0′	δ𝑑𝑑0′	NOUN
american_scientific_journal-1402	78	122	=	=	SYM
american_scientific_journal-1402	78	123	δ𝑑𝑑0	δ𝑑𝑑0	PROPN
american_scientific_journal-1402	78	124	(	(	PUNCT
american_scientific_journal-1402	78	125	30	30	NUM
american_scientific_journal-1402	78	126	)	)	PUNCT
american_scientific_journal-1402	78	127	then	then	ADV
american_scientific_journal-1402	78	128	using	use	VERB
american_scientific_journal-1402	78	129	the	the	DET
american_scientific_journal-1402	78	130	metrics	metric	NOUN
american_scientific_journal-1402	78	131	in	in	ADP
american_scientific_journal-1402	78	132	(	(	PUNCT
american_scientific_journal-1402	78	133	15	15	NUM
american_scientific_journal-1402	78	134	)	)	PUNCT
american_scientific_journal-1402	78	135	,	,	PUNCT
american_scientific_journal-1402	78	136	the	the	DET
american_scientific_journal-1402	78	137	proper	proper	ADJ
american_scientific_journal-1402	78	138	times	time	NOUN
american_scientific_journal-1402	78	139	of	of	ADP
american_scientific_journal-1402	78	140	the	the	DET
american_scientific_journal-1402	78	141	two	two	NUM
american_scientific_journal-1402	78	142	observers	observer	NOUN
american_scientific_journal-1402	78	143	corresponding	correspond	VERB
american_scientific_journal-1402	78	144	to	to	ADP
american_scientific_journal-1402	78	145	δ𝑑𝑑0′	δ𝑑𝑑0′	PROPN
american_scientific_journal-1402	78	146	and	and	CCONJ
american_scientific_journal-1402	78	147	δ𝑑𝑑0	δ𝑑𝑑0	NOUN
american_scientific_journal-1402	78	148	can	can	AUX
american_scientific_journal-1402	78	149	be	be	AUX
american_scientific_journal-1402	78	150	written	write	VERB
american_scientific_journal-1402	78	151	as	as	ADP
american_scientific_journal-1402	78	152	δ𝜏𝜏0′	δ𝜏𝜏0′	NOUN
american_scientific_journal-1402	78	153	=	=	SYM
american_scientific_journal-1402	78	154	�	�	PROPN
american_scientific_journal-1402	78	155	1	1	NUM
american_scientific_journal-1402	78	156	𝜃𝜃	𝜃𝜃	PROPN
american_scientific_journal-1402	78	157	�	�	PROPN
american_scientific_journal-1402	78	158	𝑎𝑎𝑙𝑙	𝑎𝑎𝑙𝑙	PROPN
american_scientific_journal-1402	78	159	�	�	PROPN
american_scientific_journal-1402	78	160	�	�	PROPN
american_scientific_journal-1402	78	161	δ𝑑𝑑0′	δ𝑑𝑑0′	PROPN
american_scientific_journal-1402	78	162	and	and	CCONJ
american_scientific_journal-1402	78	163	δ𝜏𝜏0	δ𝜏𝜏0	PROPN
american_scientific_journal-1402	78	164	=	=	SYM
american_scientific_journal-1402	78	165	�	�	PROPN
american_scientific_journal-1402	78	166	1	1	NUM
american_scientific_journal-1402	78	167	𝜃𝜃	𝜃𝜃	PROPN
american_scientific_journal-1402	78	168	�	�	PROPN
american_scientific_journal-1402	78	169	𝑎𝑎𝑙𝑙	𝑎𝑎𝑙𝑙	PROPN
american_scientific_journal-1402	78	170	�	�	PROPN
american_scientific_journal-1402	78	171	−	−	PUNCT
american_scientific_journal-1402	78	172	𝑚𝑚	𝑚𝑚	ADP
american_scientific_journal-1402	78	173	𝑎𝑎+	𝑎𝑎+	PROPN
american_scientific_journal-1402	78	174	𝑚𝑚	𝑚𝑚	ADP
american_scientific_journal-1402	78	175	𝑅𝑅0	𝑅𝑅0	PROPN
american_scientific_journal-1402	78	176	�	�	PROPN
american_scientific_journal-1402	78	177	δ𝑑𝑑0	δ𝑑𝑑0	PROPN
american_scientific_journal-1402	78	178	(	(	PUNCT
american_scientific_journal-1402	78	179	31	31	NUM
american_scientific_journal-1402	78	180	)	)	PUNCT
american_scientific_journal-1402	78	181	where	where	SCONJ
american_scientific_journal-1402	78	182	δ𝜏𝜏0′	δ𝜏𝜏0′	NOUN
american_scientific_journal-1402	78	183	and	and	CCONJ
american_scientific_journal-1402	78	184	δ𝜏𝜏0	δ𝜏𝜏0	NOUN
american_scientific_journal-1402	78	185	respectively	respectively	ADV
american_scientific_journal-1402	78	186	are	be	AUX
american_scientific_journal-1402	78	187	the	the	DET
american_scientific_journal-1402	78	188	proper	proper	ADJ
american_scientific_journal-1402	78	189	time	time	NOUN
american_scientific_journal-1402	78	190	intervals	interval	NOUN
american_scientific_journal-1402	78	191	of	of	ADP
american_scientific_journal-1402	78	192	the	the	DET
american_scientific_journal-1402	78	193	two	two	NUM
american_scientific_journal-1402	78	194	observers	observer	NOUN
american_scientific_journal-1402	78	195	at	at	ADP
american_scientific_journal-1402	78	196	𝑅𝑅	𝑅𝑅	PROPN
american_scientific_journal-1402	78	197	=	=	PUNCT
american_scientific_journal-1402	78	198	𝑎𝑎,outside	𝑎𝑎,outside	PROPN
american_scientific_journal-1402	78	199	the	the	DET
american_scientific_journal-1402	78	200	sphere	sphere	NOUN
american_scientific_journal-1402	78	201	,	,	PUNCT
american_scientific_journal-1402	78	202	and	and	CCONJ
american_scientific_journal-1402	78	203	at	at	ADP
american_scientific_journal-1402	78	204	𝑅𝑅	𝑅𝑅	PROPN
american_scientific_journal-1402	78	205	=	=	SYM
american_scientific_journal-1402	78	206	𝑅𝑅0	𝑅𝑅0	PROPN
american_scientific_journal-1402	78	207	,	,	PUNCT
american_scientific_journal-1402	78	208	a	a	DET
american_scientific_journal-1402	78	209	large	large	ADJ
american_scientific_journal-1402	78	210	distance	distance	NOUN
american_scientific_journal-1402	78	211	outside	outside	ADP
american_scientific_journal-1402	78	212	of	of	ADP
american_scientific_journal-1402	78	213	the	the	DET
american_scientific_journal-1402	78	214	sphere	sphere	NOUN
american_scientific_journal-1402	78	215	observing	observe	VERB
american_scientific_journal-1402	78	216	the	the	DET
american_scientific_journal-1402	78	217	pulse	pulse	NOUN
american_scientific_journal-1402	78	218	.	.	PUNCT
american_scientific_journal-1402	79	1	since	since	SCONJ
american_scientific_journal-1402	79	2	the	the	DET
american_scientific_journal-1402	79	3	number	number	NOUN
american_scientific_journal-1402	79	4	of	of	ADP
american_scientific_journal-1402	79	5	cycles	cycle	NOUN
american_scientific_journal-1402	79	6	of	of	ADP
american_scientific_journal-1402	79	7	the	the	DET
american_scientific_journal-1402	79	8	pulse	pulse	NOUN
american_scientific_journal-1402	79	9	remain	remain	VERB
american_scientific_journal-1402	79	10	the	the	DET
american_scientific_journal-1402	79	11	same	same	ADJ
american_scientific_journal-1402	79	12	throughout	throughout	ADP
american_scientific_journal-1402	79	13	its	its	PRON
american_scientific_journal-1402	79	14	way	way	NOUN
american_scientific_journal-1402	79	15	,	,	PUNCT
american_scientific_journal-1402	79	16	we	we	PRON
american_scientific_journal-1402	79	17	obtain	obtain	VERB
american_scientific_journal-1402	79	18	𝜐𝜐0	𝜐𝜐0	ADV
american_scientific_journal-1402	79	19	𝜐𝜐0′	𝜐𝜐0′	X
american_scientific_journal-1402	80	1	=	=	PUNCT
american_scientific_journal-1402	81	1	δ𝜏𝜏0′	δ𝜏𝜏0′	NOUN
american_scientific_journal-1402	81	2	δ𝜏𝜏0	δ𝜏𝜏0	NOUN
american_scientific_journal-1402	81	3	(	(	PUNCT
american_scientific_journal-1402	81	4	32	32	NUM
american_scientific_journal-1402	81	5	)	)	PUNCT
american_scientific_journal-1402	81	6	substitution	substitution	NOUN
american_scientific_journal-1402	81	7	(	(	PUNCT
american_scientific_journal-1402	81	8	31	31	NUM
american_scientific_journal-1402	81	9	)	)	PUNCT
american_scientific_journal-1402	81	10	in	in	ADP
american_scientific_journal-1402	81	11	(	(	PUNCT
american_scientific_journal-1402	81	12	32	32	NUM
american_scientific_journal-1402	81	13	)	)	PUNCT
american_scientific_journal-1402	81	14	gives	give	VERB
american_scientific_journal-1402	81	15	𝜐𝜐0	𝜐𝜐0	PRON
american_scientific_journal-1402	81	16	𝜐𝜐0′	𝜐𝜐0′	PROPN
american_scientific_journal-1402	81	17	=	=	PROPN
american_scientific_journal-1402	81	18	�	�	PROPN
american_scientific_journal-1402	81	19	𝜃𝜃	𝜃𝜃	PROPN
american_scientific_journal-1402	81	20	�	�	PROPN
american_scientific_journal-1402	81	21	𝑎𝑎𝑙𝑙	𝑎𝑎𝑙𝑙	PROPN
american_scientific_journal-1402	81	22	�	�	PROPN
american_scientific_journal-1402	81	23	−	−	PUNCT
american_scientific_journal-1402	81	24	𝑚𝑚	𝑚𝑚	ADP
american_scientific_journal-1402	81	25	𝑎𝑎+	𝑎𝑎+	PROPN
american_scientific_journal-1402	81	26	𝑚𝑚	𝑚𝑚	ADP
american_scientific_journal-1402	81	27	𝑅𝑅0	𝑅𝑅0	PROPN
american_scientific_journal-1402	81	28	�	�	PROPN
american_scientific_journal-1402	81	29	�	�	PROPN
american_scientific_journal-1402	81	30	𝜃𝜃	𝜃𝜃	PROPN
american_scientific_journal-1402	81	31	�	�	PROPN
american_scientific_journal-1402	81	32	𝑎𝑎𝑙𝑙	𝑎𝑎𝑙𝑙	PROPN
american_scientific_journal-1402	81	33	�	�	PROPN
american_scientific_journal-1402	81	34	�	�	PROPN
american_scientific_journal-1402	81	35	�	�	PROPN
american_scientific_journal-1402	81	36	δ𝑑𝑑0	δ𝑑𝑑0	ADJ
american_scientific_journal-1402	81	37	′	′	NUM
american_scientific_journal-1402	81	38	δ𝑑𝑑0	δ𝑑𝑑0	ADJ
american_scientific_journal-1402	81	39	�	�	PROPN
american_scientific_journal-1402	81	40	(	(	PUNCT
american_scientific_journal-1402	81	41	33	33	NUM
american_scientific_journal-1402	81	42	)	)	PUNCT
american_scientific_journal-1402	81	43	substituting	substitute	VERB
american_scientific_journal-1402	81	44	δ𝑑𝑑0′	δ𝑑𝑑0′	NOUN
american_scientific_journal-1402	81	45	=	=	SYM
american_scientific_journal-1402	81	46	δ𝑑𝑑0	δ𝑑𝑑0	ADJ
american_scientific_journal-1402	81	47	in	in	ADP
american_scientific_journal-1402	81	48	(	(	PUNCT
american_scientific_journal-1402	81	49	33	33	NUM
american_scientific_journal-1402	81	50	)	)	PUNCT
american_scientific_journal-1402	81	51	,	,	PUNCT
american_scientific_journal-1402	81	52	we	we	PRON
american_scientific_journal-1402	81	53	obtain	obtain	VERB
american_scientific_journal-1402	81	54	𝜐𝜐0	𝜐𝜐0	DET
american_scientific_journal-1402	81	55	𝜐𝜐0′	𝜐𝜐0′	PROPN
american_scientific_journal-1402	81	56	=	=	SYM
american_scientific_journal-1402	81	57	�	�	PROPN
american_scientific_journal-1402	81	58	𝜃𝜃	𝜃𝜃	PROPN
american_scientific_journal-1402	81	59	�	�	PROPN
american_scientific_journal-1402	81	60	𝑎𝑎𝑙𝑙	𝑎𝑎𝑙𝑙	PROPN
american_scientific_journal-1402	81	61	�	�	PROPN
american_scientific_journal-1402	81	62	−	−	PUNCT
american_scientific_journal-1402	81	63	𝑚𝑚	𝑚𝑚	ADP
american_scientific_journal-1402	81	64	𝑎𝑎+	𝑎𝑎+	PROPN
american_scientific_journal-1402	81	65	𝑚𝑚	𝑚𝑚	ADP
american_scientific_journal-1402	81	66	𝑅𝑅0	𝑅𝑅0	PROPN
american_scientific_journal-1402	81	67	�	�	PROPN
american_scientific_journal-1402	81	68	�	�	PROPN
american_scientific_journal-1402	81	69	𝜃𝜃	𝜃𝜃	PROPN
american_scientific_journal-1402	81	70	�	�	PROPN
american_scientific_journal-1402	81	71	𝑎𝑎𝑙𝑙	𝑎𝑎𝑙𝑙	PROPN
american_scientific_journal-1402	81	72	�	�	PROPN
american_scientific_journal-1402	81	73	�	�	PROPN
american_scientific_journal-1402	81	74	(	(	PUNCT
american_scientific_journal-1402	81	75	34	34	NUM
american_scientific_journal-1402	81	76	)	)	PUNCT
american_scientific_journal-1402	81	77	using	use	VERB
american_scientific_journal-1402	81	78	the	the	DET
american_scientific_journal-1402	81	79	fact	fact	NOUN
american_scientific_journal-1402	81	80	𝜈𝜈0	𝜈𝜈0	NOUN
american_scientific_journal-1402	81	81	𝜈𝜈𝑒𝑒	𝜈𝜈𝑒𝑒	NOUN
american_scientific_journal-1402	81	82	=	=	SYM
american_scientific_journal-1402	81	83	𝜐𝜐0	𝜐𝜐0	ADP
american_scientific_journal-1402	81	84	𝜐𝜐0′	𝜐𝜐0′	PROPN
american_scientific_journal-1402	82	1	𝜐𝜐0′	𝜐𝜐0′	PROPN
american_scientific_journal-1402	82	2	𝜐𝜐𝑒𝑒′	𝜐𝜐𝑒𝑒′	NOUN
american_scientific_journal-1402	82	3	𝜈𝜈𝑒𝑒′	𝜈𝜈𝑒𝑒′	ADP
american_scientific_journal-1402	82	4	𝜈𝜈𝑒𝑒	𝜈𝜈𝑒𝑒	NOUN
american_scientific_journal-1402	82	5	and	and	CCONJ
american_scientific_journal-1402	82	6	the	the	DET
american_scientific_journal-1402	82	7	equations	equation	NOUN
american_scientific_journal-1402	82	8	(	(	PUNCT
american_scientific_journal-1402	82	9	23	23	NUM
american_scientific_journal-1402	82	10	)	)	PUNCT
american_scientific_journal-1402	82	11	,	,	PUNCT
american_scientific_journal-1402	82	12	(	(	PUNCT
american_scientific_journal-1402	82	13	26	26	NUM
american_scientific_journal-1402	82	14	)	)	PUNCT
american_scientific_journal-1402	82	15	and	and	CCONJ
american_scientific_journal-1402	82	16	(	(	PUNCT
american_scientific_journal-1402	82	17	34	34	NUM
american_scientific_journal-1402	82	18	)	)	PUNCT
american_scientific_journal-1402	82	19	,	,	PUNCT
american_scientific_journal-1402	82	20	we	we	PRON
american_scientific_journal-1402	82	21	obtain	obtain	VERB
american_scientific_journal-1402	82	22	𝜈𝜈0	𝜈𝜈0	NOUN
american_scientific_journal-1402	82	23	𝜈𝜈𝑒𝑒	𝜈𝜈𝑒𝑒	NOUN
american_scientific_journal-1402	82	24	=	=	SYM
american_scientific_journal-1402	82	25	�	�	PROPN
american_scientific_journal-1402	82	26	𝜃𝜃	𝜃𝜃	PROPN
american_scientific_journal-1402	82	27	�	�	PROPN
american_scientific_journal-1402	82	28	𝑎𝑎𝑙𝑙	𝑎𝑎𝑙𝑙	PROPN
american_scientific_journal-1402	82	29	�	�	PROPN
american_scientific_journal-1402	82	30	−	−	PUNCT
american_scientific_journal-1402	82	31	𝑚𝑚	𝑚𝑚	ADP
american_scientific_journal-1402	82	32	𝑎𝑎+	𝑎𝑎+	PROPN
american_scientific_journal-1402	82	33	𝑚𝑚	𝑚𝑚	ADP
american_scientific_journal-1402	82	34	𝑅𝑅0	𝑅𝑅0	PROPN
american_scientific_journal-1402	82	35	�	�	PROPN
american_scientific_journal-1402	82	36	�	�	PROPN
american_scientific_journal-1402	82	37	𝜃𝜃	𝜃𝜃	PROPN
american_scientific_journal-1402	82	38	�	�	PROPN
american_scientific_journal-1402	82	39	𝑎𝑎𝑙𝑙	𝑎𝑎𝑙𝑙	PROPN
american_scientific_journal-1402	82	40	�	�	PROPN
american_scientific_journal-1402	82	41	�	�	PROPN
american_scientific_journal-1402	82	42	�	�	PROPN
american_scientific_journal-1402	82	43	𝜃𝜃	𝜃𝜃	PROPN
american_scientific_journal-1402	82	44	�	�	PROPN
american_scientific_journal-1402	82	45	𝑎𝑎𝑙𝑙	𝑎𝑎𝑙𝑙	PROPN
american_scientific_journal-1402	82	46	�	�	PROPN
american_scientific_journal-1402	82	47	�	�	PROPN
american_scientific_journal-1402	82	48	�	�	PROPN
american_scientific_journal-1402	82	49	𝜃𝜃	𝜃𝜃	PROPN
american_scientific_journal-1402	82	50	�	�	PROPN
american_scientific_journal-1402	82	51	𝑅𝑅𝑒𝑒𝑙𝑙	𝑅𝑅𝑒𝑒𝑙𝑙	PROPN
american_scientific_journal-1402	82	52	�	�	PROPN
american_scientific_journal-1402	82	53	�	�	PROPN
american_scientific_journal-1402	82	54	(	(	PUNCT
american_scientific_journal-1402	82	55	35	35	NUM
american_scientific_journal-1402	82	56	)	)	PUNCT
american_scientific_journal-1402	82	57	since	since	SCONJ
american_scientific_journal-1402	82	58	the	the	DET
american_scientific_journal-1402	82	59	red	red	ADJ
american_scientific_journal-1402	82	60	shift	shift	NOUN
american_scientific_journal-1402	82	61	z	z	NOUN
american_scientific_journal-1402	82	62	corresponds	correspond	VERB
american_scientific_journal-1402	82	63	to	to	ADP
american_scientific_journal-1402	82	64	the	the	DET
american_scientific_journal-1402	82	65	change	change	NOUN
american_scientific_journal-1402	82	66	of	of	ADP
american_scientific_journal-1402	82	67	the	the	DET
american_scientific_journal-1402	82	68	wave	wave	NOUN
american_scientific_journal-1402	82	69	length	length	NOUN
american_scientific_journal-1402	82	70	,	,	PUNCT
american_scientific_journal-1402	82	71	we	we	PRON
american_scientific_journal-1402	82	72	have	have	VERB
american_scientific_journal-1402	82	73	1	1	NUM
american_scientific_journal-1402	82	74	+	+	ADJ
american_scientific_journal-1402	82	75	𝑧𝑧	𝑧𝑧	X
american_scientific_journal-1402	82	76	=	=	ADJ
american_scientific_journal-1402	82	77	𝜆𝜆0	𝜆𝜆0	NOUN
american_scientific_journal-1402	82	78	𝜆𝜆𝑒𝑒	𝜆𝜆𝑒𝑒	NOUN
american_scientific_journal-1402	82	79	=	=	SYM
american_scientific_journal-1402	82	80	𝜃𝜃	𝜃𝜃	PROPN
american_scientific_journal-1402	82	81	�	�	PROPN
american_scientific_journal-1402	82	82	𝑅𝑅𝑒𝑒𝑙𝑙	𝑅𝑅𝑒𝑒𝑙𝑙	PROPN
american_scientific_journal-1402	82	83	�	�	PROPN
american_scientific_journal-1402	82	84	�	�	PROPN
american_scientific_journal-1402	82	85	𝜃𝜃	𝜃𝜃	PROPN
american_scientific_journal-1402	82	86	�	�	PROPN
american_scientific_journal-1402	82	87	𝑎𝑎𝑙𝑙	𝑎𝑎𝑙𝑙	PROPN
american_scientific_journal-1402	82	88	�	�	PROPN
american_scientific_journal-1402	82	89	−	−	PUNCT
american_scientific_journal-1402	82	90	𝑚𝑚	𝑚𝑚	ADP
american_scientific_journal-1402	82	91	𝑎𝑎+	𝑎𝑎+	PROPN
american_scientific_journal-1402	82	92	𝑚𝑚	𝑚𝑚	ADP
american_scientific_journal-1402	82	93	𝑅𝑅0	𝑅𝑅0	PROPN
american_scientific_journal-1402	82	94	�	�	PROPN
american_scientific_journal-1402	82	95	(	(	PUNCT
american_scientific_journal-1402	82	96	36	36	NUM
american_scientific_journal-1402	82	97	)	)	PUNCT
american_scientific_journal-1402	82	98	it	it	PRON
american_scientific_journal-1402	82	99	is	be	AUX
american_scientific_journal-1402	82	100	clear	clear	ADJ
american_scientific_journal-1402	82	101	that	that	SCONJ
american_scientific_journal-1402	82	102	the	the	DET
american_scientific_journal-1402	82	103	red	red	ADJ
american_scientific_journal-1402	82	104	shift	shift	NOUN
american_scientific_journal-1402	82	105	as	as	SCONJ
american_scientific_journal-1402	82	106	observed	observe	VERB
american_scientific_journal-1402	82	107	by	by	ADP
american_scientific_journal-1402	82	108	an	an	DET
american_scientific_journal-1402	82	109	observer	observer	NOUN
american_scientific_journal-1402	82	110	at	at	ADP
american_scientific_journal-1402	82	111	infinity	infinity	NOUN
american_scientific_journal-1402	82	112	is	be	AUX
american_scientific_journal-1402	82	113	given	give	VERB
american_scientific_journal-1402	82	114	by	by	ADP
american_scientific_journal-1402	82	115	1	1	NUM
american_scientific_journal-1402	82	116	+	+	NOUN
american_scientific_journal-1402	82	117	𝑧𝑧	𝑧𝑧	PROPN
american_scientific_journal-1402	82	118	=	=	ADJ
american_scientific_journal-1402	82	119	𝜆𝜆0	𝜆𝜆0	NOUN
american_scientific_journal-1402	82	120	𝜆𝜆𝑒𝑒	𝜆𝜆𝑒𝑒	NOUN
american_scientific_journal-1402	83	1	=	=	SYM
american_scientific_journal-1402	83	2	𝜃𝜃	𝜃𝜃	PROPN
american_scientific_journal-1402	83	3	�	�	PROPN
american_scientific_journal-1402	83	4	𝑅𝑅𝑒𝑒𝑙𝑙	𝑅𝑅𝑒𝑒𝑙𝑙	PROPN
american_scientific_journal-1402	83	5	�	�	PROPN
american_scientific_journal-1402	83	6	�	�	PROPN
american_scientific_journal-1402	83	7	𝜃𝜃	𝜃𝜃	PROPN
american_scientific_journal-1402	83	8	�	�	PROPN
american_scientific_journal-1402	83	9	𝑎𝑎𝑙𝑙	𝑎𝑎𝑙𝑙	PROPN
american_scientific_journal-1402	83	10	�	�	PROPN
american_scientific_journal-1402	83	11	−	−	VERB
american_scientific_journal-1402	83	12	𝑚𝑚	𝑚𝑚	ADP
american_scientific_journal-1402	83	13	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1402	83	14	�	�	PROPN
american_scientific_journal-1402	83	15	(	(	PUNCT
american_scientific_journal-1402	83	16	37	37	NUM
american_scientific_journal-1402	83	17	)	)	PUNCT
american_scientific_journal-1402	83	18	since	since	SCONJ
american_scientific_journal-1402	83	19	𝑅𝑅𝑒𝑒	𝑅𝑅𝑒𝑒	PROPN
american_scientific_journal-1402	83	20	<	<	X
american_scientific_journal-1402	83	21	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1402	83	22	and	and	CCONJ
american_scientific_journal-1402	83	23	𝜃𝜃	𝜃𝜃	PROPN
american_scientific_journal-1402	83	24	�	�	PROPN
american_scientific_journal-1402	83	25	𝑅𝑅	𝑅𝑅	PROPN
american_scientific_journal-1402	83	26	𝑙𝑙	𝑙𝑙	PROPN
american_scientific_journal-1402	83	27	�	�	PROPN
american_scientific_journal-1402	83	28	is	be	AUX
american_scientific_journal-1402	83	29	a	a	DET
american_scientific_journal-1402	83	30	decreasing	decrease	VERB
american_scientific_journal-1402	83	31	function	function	NOUN
american_scientific_journal-1402	83	32	,	,	PUNCT
american_scientific_journal-1402	83	33	it	it	PRON
american_scientific_journal-1402	83	34	can	can	AUX
american_scientific_journal-1402	83	35	be	be	AUX
american_scientific_journal-1402	83	36	shown	show	VERB
american_scientific_journal-1402	83	37	that	that	SCONJ
american_scientific_journal-1402	83	38	the	the	DET
american_scientific_journal-1402	83	39	pulse	pulse	NOUN
american_scientific_journal-1402	83	40	of	of	ADP
american_scientific_journal-1402	83	41	light	light	NOUN
american_scientific_journal-1402	83	42	is	be	AUX
american_scientific_journal-1402	83	43	red	red	ADJ
american_scientific_journal-1402	83	44	shifted	shift	VERB
american_scientific_journal-1402	83	45	.	.	PUNCT
american_scientific_journal-1402	84	1	163	163	NUM
american_scientific_journal-1402	84	2	american	american	ADJ
american_scientific_journal-1402	84	3	scientific	scientific	ADJ
american_scientific_journal-1402	84	4	research	research	NOUN
american_scientific_journal-1402	84	5	journal	journal	NOUN
american_scientific_journal-1402	84	6	for	for	ADP
american_scientific_journal-1402	84	7	engineering	engineering	NOUN
american_scientific_journal-1402	84	8	,	,	PUNCT
american_scientific_journal-1402	84	9	technology	technology	NOUN
american_scientific_journal-1402	84	10	,	,	PUNCT
american_scientific_journal-1402	84	11	and	and	CCONJ
american_scientific_journal-1402	84	12	sciences	science	NOUN
american_scientific_journal-1402	84	13	(	(	PUNCT
american_scientific_journal-1402	84	14	asrjets	asrjet	NOUN
american_scientific_journal-1402	84	15	)	)	PUNCT
american_scientific_journal-1402	84	16	(	(	PUNCT
american_scientific_journal-1402	84	17	2016	2016	NUM
american_scientific_journal-1402	84	18	)	)	PUNCT
american_scientific_journal-1402	84	19	volume	volume	NOUN
american_scientific_journal-1402	84	20	17	17	NUM
american_scientific_journal-1402	84	21	,	,	PUNCT
american_scientific_journal-1402	84	22	no	no	DET
american_scientific_journal-1402	84	23	1	1	NUM
american_scientific_journal-1402	84	24	,	,	PUNCT
american_scientific_journal-1402	84	25	pp	pp	ADV
american_scientific_journal-1402	84	26	155	155	NUM
american_scientific_journal-1402	84	27	-	-	SYM
american_scientific_journal-1402	84	28	164	164	NUM
american_scientific_journal-1402	84	29	4	4	NUM
american_scientific_journal-1402	84	30	.	.	PUNCT
american_scientific_journal-1402	85	1	conclusion	conclusion	NOUN
american_scientific_journal-1402	85	2	we	we	PRON
american_scientific_journal-1402	85	3	obtained	obtain	VERB
american_scientific_journal-1402	85	4	the	the	DET
american_scientific_journal-1402	85	5	metrics	metric	NOUN
american_scientific_journal-1402	85	6	for	for	ADP
american_scientific_journal-1402	85	7	an	an	DET
american_scientific_journal-1402	85	8	electrically	electrically	ADV
american_scientific_journal-1402	85	9	counterpoised	counterpoise	VERB
american_scientific_journal-1402	85	10	dust	dust	NOUN
american_scientific_journal-1402	85	11	sphere	sphere	ADV
american_scientific_journal-1402	85	12	using	use	VERB
american_scientific_journal-1402	85	13	what	what	PRON
american_scientific_journal-1402	85	14	are	be	AUX
american_scientific_journal-1402	85	15	known	know	VERB
american_scientific_journal-1402	85	16	as	as	ADP
american_scientific_journal-1402	85	17	standard	standard	ADJ
american_scientific_journal-1402	85	18	boundary	boundary	ADJ
american_scientific_journal-1402	85	19	conditions	condition	NOUN
american_scientific_journal-1402	85	20	.	.	PUNCT
american_scientific_journal-1402	86	1	in	in	ADP
american_scientific_journal-1402	86	2	this	this	DET
american_scientific_journal-1402	86	3	formalism	formalism	NOUN
american_scientific_journal-1402	86	4	we	we	PRON
american_scientific_journal-1402	86	5	use	use	VERB
american_scientific_journal-1402	86	6	the	the	DET
american_scientific_journal-1402	86	7	same	same	ADJ
american_scientific_journal-1402	86	8	coordinates	coordinate	NOUN
american_scientific_journal-1402	86	9	in	in	ADP
american_scientific_journal-1402	86	10	the	the	DET
american_scientific_journal-1402	86	11	two	two	NUM
american_scientific_journal-1402	86	12	regions	region	NOUN
american_scientific_journal-1402	86	13	inside	inside	ADP
american_scientific_journal-1402	86	14	the	the	DET
american_scientific_journal-1402	86	15	spherical	spherical	ADJ
american_scientific_journal-1402	86	16	distribution	distribution	NOUN
american_scientific_journal-1402	86	17	of	of	ADP
american_scientific_journal-1402	86	18	matter	matter	NOUN
american_scientific_journal-1402	86	19	as	as	ADV
american_scientific_journal-1402	86	20	well	well	ADV
american_scientific_journal-1402	86	21	as	as	ADP
american_scientific_journal-1402	86	22	outside	outside	ADV
american_scientific_journal-1402	86	23	.	.	PUNCT
american_scientific_journal-1402	87	1	also	also	ADV
american_scientific_journal-1402	87	2	it	it	PRON
american_scientific_journal-1402	87	3	is	be	AUX
american_scientific_journal-1402	87	4	shown	show	VERB
american_scientific_journal-1402	87	5	that	that	SCONJ
american_scientific_journal-1402	87	6	a	a	DET
american_scientific_journal-1402	87	7	pulse	pulse	NOUN
american_scientific_journal-1402	87	8	of	of	ADP
american_scientific_journal-1402	87	9	light	light	NOUN
american_scientific_journal-1402	87	10	which	which	PRON
american_scientific_journal-1402	87	11	is	be	AUX
american_scientific_journal-1402	87	12	emitted	emit	VERB
american_scientific_journal-1402	87	13	from	from	ADP
american_scientific_journal-1402	87	14	the	the	DET
american_scientific_journal-1402	87	15	inside	inside	NOUN
american_scientific_journal-1402	87	16	of	of	ADP
american_scientific_journal-1402	87	17	the	the	DET
american_scientific_journal-1402	87	18	sphere	sphere	NOUN
american_scientific_journal-1402	87	19	as	as	SCONJ
american_scientific_journal-1402	87	20	observed	observe	VERB
american_scientific_journal-1402	87	21	by	by	ADP
american_scientific_journal-1402	87	22	an	an	DET
american_scientific_journal-1402	87	23	observer	observer	NOUN
american_scientific_journal-1402	87	24	at	at	ADP
american_scientific_journal-1402	87	25	infinity	infinity	NOUN
american_scientific_journal-1402	87	26	is	be	AUX
american_scientific_journal-1402	87	27	red	red	ADJ
american_scientific_journal-1402	87	28	shifted	shift	VERB
american_scientific_journal-1402	87	29	.	.	PUNCT
american_scientific_journal-1402	88	1	so	so	ADV
american_scientific_journal-1402	88	2	the	the	DET
american_scientific_journal-1402	88	3	solution	solution	NOUN
american_scientific_journal-1402	88	4	obtained	obtain	VERB
american_scientific_journal-1402	88	5	for	for	ADP
american_scientific_journal-1402	88	6	the	the	DET
american_scientific_journal-1402	88	7	einstein	einstein	PROPN
american_scientific_journal-1402	88	8	’s	’s	PART
american_scientific_journal-1402	88	9	field	field	NOUN
american_scientific_journal-1402	88	10	equations	equation	NOUN
american_scientific_journal-1402	88	11	is	be	AUX
american_scientific_journal-1402	88	12	physically	physically	ADV
american_scientific_journal-1402	88	13	acceptable	acceptable	ADJ
american_scientific_journal-1402	88	14	.	.	PUNCT
american_scientific_journal-1402	89	1	however	however	ADV
american_scientific_journal-1402	89	2	,	,	PUNCT
american_scientific_journal-1402	89	3	the	the	DET
american_scientific_journal-1402	89	4	metric	metric	NOUN
american_scientific_journal-1402	89	5	we	we	PRON
american_scientific_journal-1402	89	6	obtained	obtain	VERB
american_scientific_journal-1402	89	7	for	for	ADP
american_scientific_journal-1402	89	8	the	the	DET
american_scientific_journal-1402	89	9	external	external	ADJ
american_scientific_journal-1402	89	10	region	region	NOUN
american_scientific_journal-1402	89	11	is	be	AUX
american_scientific_journal-1402	89	12	not	not	PART
american_scientific_journal-1402	89	13	lorentzian	lorentzian	ADJ
american_scientific_journal-1402	89	14	at	at	ADP
american_scientific_journal-1402	89	15	infinity	infinity	NOUN
american_scientific_journal-1402	89	16	(	(	PUNCT
american_scientific_journal-1402	89	17	large	large	ADJ
american_scientific_journal-1402	89	18	distances	distance	NOUN
american_scientific_journal-1402	89	19	)	)	PUNCT
american_scientific_journal-1402	89	20	in	in	ADP
american_scientific_journal-1402	89	21	general	general	ADJ
american_scientific_journal-1402	89	22	and	and	CCONJ
american_scientific_journal-1402	89	23	it	it	PRON
american_scientific_journal-1402	89	24	becomes	become	VERB
american_scientific_journal-1402	89	25	lorentzian	lorentzian	ADJ
american_scientific_journal-1402	89	26	only	only	ADV
american_scientific_journal-1402	89	27	when	when	SCONJ
american_scientific_journal-1402	89	28	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1402	89	29	,	,	PUNCT
american_scientific_journal-1402	89	30	the	the	DET
american_scientific_journal-1402	89	31	radial	radial	ADJ
american_scientific_journal-1402	89	32	coordinate	coordinate	NOUN
american_scientific_journal-1402	89	33	and	and	CCONJ
american_scientific_journal-1402	89	34	𝑚𝑚	𝑚𝑚	ADP
american_scientific_journal-1402	89	35	,	,	PUNCT
american_scientific_journal-1402	89	36	the	the	DET
american_scientific_journal-1402	89	37	mass	mass	NOUN
american_scientific_journal-1402	89	38	of	of	ADP
american_scientific_journal-1402	89	39	the	the	DET
american_scientific_journal-1402	89	40	ecd	ecd	PROPN
american_scientific_journal-1402	89	41	distribution	distribution	NOUN
american_scientific_journal-1402	89	42	becomes	become	VERB
american_scientific_journal-1402	89	43	zero	zero	NUM
american_scientific_journal-1402	89	44	.	.	PUNCT
american_scientific_journal-1402	90	1	that	that	PRON
american_scientific_journal-1402	90	2	is	be	AUX
american_scientific_journal-1402	90	3	when	when	SCONJ
american_scientific_journal-1402	90	4	there	there	PRON
american_scientific_journal-1402	90	5	is	be	VERB
american_scientific_journal-1402	90	6	no	no	PRON
american_scientific_journal-1402	90	7	matter	matter	NOUN
american_scientific_journal-1402	90	8	distribution	distribution	NOUN
american_scientific_journal-1402	90	9	and	and	CCONJ
american_scientific_journal-1402	90	10	which	which	PRON
american_scientific_journal-1402	90	11	makes	make	VERB
american_scientific_journal-1402	90	12	the	the	DET
american_scientific_journal-1402	90	13	space	space	NOUN
american_scientific_journal-1402	90	14	time	time	NOUN
american_scientific_journal-1402	90	15	flat	flat	ADJ
american_scientific_journal-1402	90	16	and	and	CCONJ
american_scientific_journal-1402	90	17	lorentzian	lorentzian	ADJ
american_scientific_journal-1402	90	18	throughout	throughout	NOUN
american_scientific_journal-1402	90	19	.	.	PUNCT
american_scientific_journal-1402	91	1	in	in	ADP
american_scientific_journal-1402	91	2	our	our	PRON
american_scientific_journal-1402	91	3	next	next	ADJ
american_scientific_journal-1402	91	4	article	article	NOUN
american_scientific_journal-1402	91	5	,	,	PUNCT
american_scientific_journal-1402	91	6	we	we	PRON
american_scientific_journal-1402	91	7	will	will	AUX
american_scientific_journal-1402	91	8	overcome	overcome	VERB
american_scientific_journal-1402	91	9	this	this	DET
american_scientific_journal-1402	91	10	difficulty	difficulty	NOUN
american_scientific_journal-1402	91	11	by	by	ADP
american_scientific_journal-1402	91	12	using	use	VERB
american_scientific_journal-1402	91	13	different	different	ADJ
american_scientific_journal-1402	91	14	coordinates	coordinate	NOUN
american_scientific_journal-1402	91	15	for	for	ADP
american_scientific_journal-1402	91	16	the	the	DET
american_scientific_journal-1402	91	17	two	two	NUM
american_scientific_journal-1402	91	18	regions	region	NOUN
american_scientific_journal-1402	91	19	,	,	PUNCT
american_scientific_journal-1402	91	20	inside	inside	ADP
american_scientific_journal-1402	91	21	of	of	ADP
american_scientific_journal-1402	91	22	the	the	DET
american_scientific_journal-1402	91	23	sphere	sphere	NOUN
american_scientific_journal-1402	91	24	and	and	CCONJ
american_scientific_journal-1402	91	25	outside	outside	ADP
american_scientific_journal-1402	91	26	of	of	ADP
american_scientific_journal-1402	91	27	the	the	DET
american_scientific_journal-1402	91	28	sphere	sphere	NOUN
american_scientific_journal-1402	91	29	.	.	PUNCT
american_scientific_journal-1402	92	1	then	then	ADV
american_scientific_journal-1402	92	2	we	we	PRON
american_scientific_journal-1402	92	3	will	will	AUX
american_scientific_journal-1402	92	4	require	require	VERB
american_scientific_journal-1402	92	5	more	more	ADJ
american_scientific_journal-1402	92	6	equations	equation	NOUN
american_scientific_journal-1402	92	7	to	to	PART
american_scientific_journal-1402	92	8	solve	solve	VERB
american_scientific_journal-1402	92	9	einstein	einstein	PROPN
american_scientific_journal-1402	92	10	’s	’s	PART
american_scientific_journal-1402	92	11	field	field	NOUN
american_scientific_journal-1402	92	12	equations	equation	NOUN
american_scientific_journal-1402	92	13	.	.	PUNCT
american_scientific_journal-1402	93	1	therefore	therefore	ADV
american_scientific_journal-1402	93	2	we	we	PRON
american_scientific_journal-1402	93	3	will	will	AUX
american_scientific_journal-1402	93	4	apply	apply	VERB
american_scientific_journal-1402	93	5	a	a	DET
american_scientific_journal-1402	93	6	new	new	ADJ
american_scientific_journal-1402	93	7	set	set	NOUN
american_scientific_journal-1402	93	8	of	of	ADP
american_scientific_journal-1402	93	9	boundary	boundary	ADJ
american_scientific_journal-1402	93	10	conditions	condition	NOUN
american_scientific_journal-1402	93	11	other	other	ADJ
american_scientific_journal-1402	93	12	than	than	ADP
american_scientific_journal-1402	93	13	standard	standard	ADJ
american_scientific_journal-1402	93	14	boundary	boundary	ADJ
american_scientific_journal-1402	93	15	conditions	condition	NOUN
american_scientific_journal-1402	93	16	to	to	PART
american_scientific_journal-1402	93	17	find	find	VERB
american_scientific_journal-1402	93	18	exact	exact	ADJ
american_scientific_journal-1402	93	19	solutions	solution	NOUN
american_scientific_journal-1402	93	20	to	to	ADP
american_scientific_journal-1402	93	21	einstein	einstein	PROPN
american_scientific_journal-1402	93	22	’s	’s	PART
american_scientific_journal-1402	93	23	field	field	NOUN
american_scientific_journal-1402	93	24	equations	equation	NOUN
american_scientific_journal-1402	93	25	.	.	PUNCT
american_scientific_journal-1402	94	1	also	also	ADV
american_scientific_journal-1402	94	2	we	we	PRON
american_scientific_journal-1402	94	3	are	be	AUX
american_scientific_journal-1402	94	4	going	go	VERB
american_scientific_journal-1402	94	5	to	to	PART
american_scientific_journal-1402	94	6	compare	compare	VERB
american_scientific_journal-1402	94	7	the	the	DET
american_scientific_journal-1402	94	8	results	result	NOUN
american_scientific_journal-1402	94	9	obtained	obtain	VERB
american_scientific_journal-1402	94	10	in	in	ADP
american_scientific_journal-1402	94	11	this	this	DET
american_scientific_journal-1402	94	12	article	article	NOUN
american_scientific_journal-1402	94	13	with	with	ADP
american_scientific_journal-1402	94	14	the	the	DET
american_scientific_journal-1402	94	15	results	result	NOUN
american_scientific_journal-1402	94	16	which	which	PRON
american_scientific_journal-1402	94	17	will	will	AUX
american_scientific_journal-1402	94	18	be	be	AUX
american_scientific_journal-1402	94	19	obtained	obtain	VERB
american_scientific_journal-1402	94	20	using	use	VERB
american_scientific_journal-1402	94	21	new	new	ADJ
american_scientific_journal-1402	94	22	set	set	NOUN
american_scientific_journal-1402	94	23	of	of	ADP
american_scientific_journal-1402	94	24	boundary	boundary	ADJ
american_scientific_journal-1402	94	25	conditions	condition	NOUN
american_scientific_journal-1402	94	26	.	.	PUNCT
american_scientific_journal-1402	95	1	acknowledgements	acknowledgement	NOUN
american_scientific_journal-1402	95	2	i	i	PRON
american_scientific_journal-1402	95	3	express	express	VERB
american_scientific_journal-1402	95	4	my	my	PRON
american_scientific_journal-1402	95	5	sincere	sincere	ADJ
american_scientific_journal-1402	95	6	thanks	thank	NOUN
american_scientific_journal-1402	95	7	and	and	CCONJ
american_scientific_journal-1402	95	8	profound	profound	ADJ
american_scientific_journal-1402	95	9	gratitude	gratitude	NOUN
american_scientific_journal-1402	95	10	to	to	ADP
american_scientific_journal-1402	95	11	my	my	PRON
american_scientific_journal-1402	95	12	research	research	NOUN
american_scientific_journal-1402	95	13	supervisors	supervisor	NOUN
american_scientific_journal-1402	95	14	,	,	PUNCT
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american_scientific_journal-1402	95	18	de	de	X
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american_scientific_journal-1402	95	20	and	and	CCONJ
american_scientific_journal-1402	95	21	late	late	ADJ
american_scientific_journal-1402	95	22	prof	prof	PROPN
american_scientific_journal-1402	95	23	.	.	PUNCT
american_scientific_journal-1402	96	1	s.b.p	s.b.p	PROPN
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american_scientific_journal-1402	96	3	,	,	PUNCT
american_scientific_journal-1402	96	4	for	for	ADP
american_scientific_journal-1402	96	5	their	their	PRON
american_scientific_journal-1402	96	6	invaluable	invaluable	ADJ
american_scientific_journal-1402	96	7	advice	advice	NOUN
american_scientific_journal-1402	96	8	,	,	PUNCT
american_scientific_journal-1402	96	9	guidance	guidance	NOUN
american_scientific_journal-1402	96	10	and	and	CCONJ
american_scientific_journal-1402	96	11	encouragement	encouragement	NOUN
american_scientific_journal-1402	96	12	throughout	throughout	ADP
american_scientific_journal-1402	96	13	the	the	DET
american_scientific_journal-1402	96	14	course	course	NOUN
american_scientific_journal-1402	96	15	of	of	ADP
american_scientific_journal-1402	96	16	this	this	DET
american_scientific_journal-1402	96	17	work	work	NOUN
american_scientific_journal-1402	96	18	.	.	PUNCT
american_scientific_journal-1402	97	1	references	reference	NOUN
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american_scientific_journal-1402	97	6	.	.	PROPN
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american_scientific_journal-1402	97	8	.	.	PUNCT
american_scientific_journal-1402	98	1	“	"	PUNCT
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american_scientific_journal-1402	98	3	static	static	ADJ
american_scientific_journal-1402	98	4	distribution	distribution	NOUN
american_scientific_journal-1402	98	5	of	of	ADP
american_scientific_journal-1402	98	6	matter	matter	NOUN
american_scientific_journal-1402	98	7	in	in	ADP
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american_scientific_journal-1402	98	9	relativity	relativity	NOUN
american_scientific_journal-1402	98	10	.	.	PUNCT
american_scientific_journal-1402	98	11	”	"	PUNCT
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american_scientific_journal-1402	99	2	thesis	thesis	NOUN
american_scientific_journal-1402	99	3	,	,	PUNCT
american_scientific_journal-1402	99	4	queen	queen	PROPN
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american_scientific_journal-1402	99	9	,	,	PUNCT
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american_scientific_journal-1402	99	11	.	.	PUNCT
american_scientific_journal-1402	100	1	[	[	X
american_scientific_journal-1402	100	2	2	2	NUM
american_scientific_journal-1402	100	3	]	]	X
american_scientific_journal-1402	100	4	p.m.n	p.m.n	PROPN
american_scientific_journal-1402	100	5	.	.	PUNCT
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american_scientific_journal-1402	100	7	.	.	PUNCT
american_scientific_journal-1402	101	1	“	"	PUNCT
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american_scientific_journal-1402	101	11	the	the	DET
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american_scientific_journal-1402	101	14	.	.	PUNCT
american_scientific_journal-1402	101	15	”	"	PUNCT
american_scientific_journal-1402	102	1	mphil	mphil	PROPN
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american_scientific_journal-1402	102	3	,	,	PUNCT
american_scientific_journal-1402	102	4	university	university	NOUN
american_scientific_journal-1402	102	5	of	of	ADP
american_scientific_journal-1402	102	6	kelaniya	kelaniya	PROPN
american_scientific_journal-1402	102	7	,	,	PUNCT
american_scientific_journal-1402	102	8	sri	sri	PROPN
american_scientific_journal-1402	102	9	lanka	lanka	PROPN
american_scientific_journal-1402	102	10	,	,	PUNCT
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american_scientific_journal-1402	102	12	.	.	PUNCT
american_scientific_journal-1402	103	1	[	[	X
american_scientific_journal-1402	103	2	3	3	X
american_scientific_journal-1402	103	3	]	]	PUNCT
american_scientific_journal-1402	103	4	n.a.s.n	n.a.s.n	PROPN
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american_scientific_journal-1402	103	6	.	.	PUNCT
american_scientific_journal-1402	104	1	“	"	PUNCT
american_scientific_journal-1402	104	2	a	a	DET
american_scientific_journal-1402	104	3	study	study	NOUN
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american_scientific_journal-1402	104	5	static	static	ADJ
american_scientific_journal-1402	104	6	relativistic	relativistic	ADJ
american_scientific_journal-1402	104	7	electrically	electrically	ADV
american_scientific_journal-1402	104	8	charged	charge	VERB
american_scientific_journal-1402	104	9	spherical	spherical	ADJ
american_scientific_journal-1402	104	10	distributions	distribution	NOUN
american_scientific_journal-1402	104	11	with	with	ADP
american_scientific_journal-1402	104	12	old	old	ADJ
american_scientific_journal-1402	104	13	and	and	CCONJ
american_scientific_journal-1402	104	14	new	new	ADJ
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american_scientific_journal-1402	104	17	.	.	PUNCT
american_scientific_journal-1402	104	18	”	"	PUNCT
american_scientific_journal-1402	105	1	mphil	mphil	PROPN
american_scientific_journal-1402	105	2	thesis	thesis	NOUN
american_scientific_journal-1402	105	3	,	,	PUNCT
american_scientific_journal-1402	105	4	university	university	NOUN
american_scientific_journal-1402	105	5	of	of	ADP
american_scientific_journal-1402	105	6	kelaniya	kelaniya	PROPN
american_scientific_journal-1402	105	7	,	,	PUNCT
american_scientific_journal-1402	105	8	sri	sri	PROPN
american_scientific_journal-1402	105	9	lanka	lanka	PROPN
american_scientific_journal-1402	105	10	,	,	PUNCT
american_scientific_journal-1402	105	11	2013	2013	NUM
american_scientific_journal-1402	105	12	.	.	PUNCT
american_scientific_journal-1402	106	1	164	164	NUM