id	sid	tid	token	lemma	pos
american_scientific_journal-1767	1	1	163	163	NUM
american_scientific_journal-1767	1	2	american	american	ADJ
american_scientific_journal-1767	1	3	scientific	scientific	ADJ
american_scientific_journal-1767	1	4	research	research	NOUN
american_scientific_journal-1767	1	5	journal	journal	NOUN
american_scientific_journal-1767	1	6	for	for	ADP
american_scientific_journal-1767	1	7	engineering	engineering	NOUN
american_scientific_journal-1767	1	8	,	,	PUNCT
american_scientific_journal-1767	1	9	technology	technology	NOUN
american_scientific_journal-1767	1	10	,	,	PUNCT
american_scientific_journal-1767	1	11	and	and	CCONJ
american_scientific_journal-1767	1	12	sciences	science	NOUN
american_scientific_journal-1767	1	13	(	(	PUNCT
american_scientific_journal-1767	1	14	asrjets	asrjet	NOUN
american_scientific_journal-1767	1	15	)	)	PUNCT
american_scientific_journal-1767	1	16	issn	issn	PROPN
american_scientific_journal-1767	1	17	(	(	PUNCT
american_scientific_journal-1767	1	18	print	print	NOUN
american_scientific_journal-1767	1	19	)	)	PUNCT
american_scientific_journal-1767	1	20	2313	2313	NUM
american_scientific_journal-1767	1	21	-	-	SYM
american_scientific_journal-1767	1	22	4410	4410	NUM
american_scientific_journal-1767	1	23	,	,	PUNCT
american_scientific_journal-1767	1	24	issn	issn	PROPN
american_scientific_journal-1767	1	25	(	(	PUNCT
american_scientific_journal-1767	1	26	online	online	ADJ
american_scientific_journal-1767	1	27	)	)	PUNCT
american_scientific_journal-1767	1	28	2313	2313	NUM
american_scientific_journal-1767	1	29	-	-	SYM
american_scientific_journal-1767	1	30	4402	4402	NUM
american_scientific_journal-1767	1	31	©	©	PROPN
american_scientific_journal-1767	1	32	global	global	ADJ
american_scientific_journal-1767	1	33	society	society	NOUN
american_scientific_journal-1767	1	34	of	of	ADP
american_scientific_journal-1767	1	35	scientific	scientific	ADJ
american_scientific_journal-1767	1	36	research	research	NOUN
american_scientific_journal-1767	1	37	and	and	CCONJ
american_scientific_journal-1767	1	38	researchers	researcher	NOUN
american_scientific_journal-1767	1	39	http://asrjetsjournal.org/	http://asrjetsjournal.org/	VERB
american_scientific_journal-1767	1	40	a	a	DET
american_scientific_journal-1767	1	41	static	static	ADJ
american_scientific_journal-1767	1	42	solution	solution	NOUN
american_scientific_journal-1767	1	43	to	to	ADP
american_scientific_journal-1767	1	44	einstein	einstein	PROPN
american_scientific_journal-1767	1	45	’s	’s	PART
american_scientific_journal-1767	1	46	field	field	NOUN
american_scientific_journal-1767	1	47	equations	equation	NOUN
american_scientific_journal-1767	1	48	for	for	ADP
american_scientific_journal-1767	1	49	a	a	DET
american_scientific_journal-1767	1	50	spherical	spherical	ADJ
american_scientific_journal-1767	1	51	distribution	distribution	NOUN
american_scientific_journal-1767	1	52	of	of	ADP
american_scientific_journal-1767	1	53	electrically	electrically	ADV
american_scientific_journal-1767	1	54	counterpoised	counterpoise	VERB
american_scientific_journal-1767	1	55	dust	dust	NOUN
american_scientific_journal-1767	1	56	with	with	ADP
american_scientific_journal-1767	1	57	a	a	DET
american_scientific_journal-1767	1	58	set	set	NOUN
american_scientific_journal-1767	1	59	of	of	ADP
american_scientific_journal-1767	1	60	new	new	ADJ
american_scientific_journal-1767	1	61	boundary	boundary	ADJ
american_scientific_journal-1767	1	62	conditions	condition	NOUN
american_scientific_journal-1767	1	63	sashinka	sashinka	NOUN
american_scientific_journal-1767	1	64	wimaladharmaa	wimaladharmaa	VERB
american_scientific_journal-1767	1	65	*	*	PROPN
american_scientific_journal-1767	1	66	,	,	PUNCT
american_scientific_journal-1767	1	67	nalin	nalin	PROPN
american_scientific_journal-1767	1	68	de	de	PROPN
american_scientific_journal-1767	1	69	silvab	silvab	PROPN
american_scientific_journal-1767	1	70	adepartment	adepartment	NOUN
american_scientific_journal-1767	1	71	of	of	ADP
american_scientific_journal-1767	1	72	mathematics	mathematic	NOUN
american_scientific_journal-1767	1	73	,	,	PUNCT
american_scientific_journal-1767	1	74	university	university	NOUN
american_scientific_journal-1767	1	75	of	of	ADP
american_scientific_journal-1767	1	76	kelaniya,11600	kelaniya,11600	PROPN
american_scientific_journal-1767	1	77	,	,	PUNCT
american_scientific_journal-1767	1	78	sri	sri	PROPN
american_scientific_journal-1767	1	79	lanka	lanka	PROPN
american_scientific_journal-1767	1	80	.	.	PUNCT
american_scientific_journal-1767	2	1	bno,109/1,railway	bno,109/1,railway	PROPN
american_scientific_journal-1767	3	1	avenue	avenue	PROPN
american_scientific_journal-1767	3	2	,	,	PUNCT
american_scientific_journal-1767	3	3	maharagama,10280	maharagama,10280	PROPN
american_scientific_journal-1767	3	4	,	,	PUNCT
american_scientific_journal-1767	3	5	sri	sri	PROPN
american_scientific_journal-1767	3	6	lanka	lanka	PROPN
american_scientific_journal-1767	3	7	.	.	PUNCT
american_scientific_journal-1767	4	1	aemail	aemail	PROPN
american_scientific_journal-1767	4	2	:	:	PUNCT
american_scientific_journal-1767	4	3	wimaladharma@kln.ac.lk	wimaladharma@kln.ac.lk	NOUN
american_scientific_journal-1767	4	4	bemail	bemail	NOUN
american_scientific_journal-1767	4	5	:	:	PUNCT
american_scientific_journal-1767	4	6	nalink2003@yahoo.com	nalink2003@yahoo.com	X
american_scientific_journal-1767	5	1	abstract	abstract	ADJ
american_scientific_journal-1767	5	2	a	a	DET
american_scientific_journal-1767	5	3	static	static	ADJ
american_scientific_journal-1767	5	4	spherically	spherically	NOUN
american_scientific_journal-1767	5	5	symmetric	symmetric	ADJ
american_scientific_journal-1767	5	6	solution	solution	NOUN
american_scientific_journal-1767	5	7	to	to	ADP
american_scientific_journal-1767	5	8	einstein	einstein	PROPN
american_scientific_journal-1767	5	9	’s	’s	PART
american_scientific_journal-1767	5	10	field	field	NOUN
american_scientific_journal-1767	5	11	equations	equation	NOUN
american_scientific_journal-1767	5	12	has	have	AUX
american_scientific_journal-1767	5	13	been	be	AUX
american_scientific_journal-1767	5	14	found	find	VERB
american_scientific_journal-1767	5	15	with	with	ADP
american_scientific_journal-1767	5	16	the	the	DET
american_scientific_journal-1767	5	17	standard	standard	ADJ
american_scientific_journal-1767	5	18	boundary	boundary	ADJ
american_scientific_journal-1767	5	19	conditions	condition	NOUN
american_scientific_journal-1767	5	20	for	for	ADP
american_scientific_journal-1767	5	21	a	a	DET
american_scientific_journal-1767	5	22	spherical	spherical	ADJ
american_scientific_journal-1767	5	23	distribution	distribution	NOUN
american_scientific_journal-1767	5	24	of	of	ADP
american_scientific_journal-1767	5	25	electrically	electrically	ADV
american_scientific_journal-1767	5	26	counterpoised	counterpoise	VERB
american_scientific_journal-1767	5	27	dust	dust	NOUN
american_scientific_journal-1767	5	28	in	in	ADP
american_scientific_journal-1767	5	29	sashinka	sashinka	PROPN
american_scientific_journal-1767	5	30	wimaladharma	wimaladharma	PROPN
american_scientific_journal-1767	5	31	and	and	CCONJ
american_scientific_journal-1767	5	32	nalin	nalin	PROPN
american_scientific_journal-1767	5	33	de	de	PROPN
american_scientific_journal-1767	5	34	silva	silva	PROPN
american_scientific_journal-1767	5	35	.	.	PUNCT
american_scientific_journal-1767	6	1	however	however	ADV
american_scientific_journal-1767	6	2	the	the	DET
american_scientific_journal-1767	6	3	solution	solution	NOUN
american_scientific_journal-1767	6	4	obtained	obtain	VERB
american_scientific_journal-1767	6	5	there	there	PRON
american_scientific_journal-1767	6	6	was	be	VERB
american_scientific_journal-1767	6	7	not	not	PART
american_scientific_journal-1767	6	8	lorentzian	lorentzian	ADJ
american_scientific_journal-1767	6	9	at	at	ADP
american_scientific_journal-1767	6	10	infinity	infinity	NOUN
american_scientific_journal-1767	6	11	.	.	PUNCT
american_scientific_journal-1767	7	1	to	to	PART
american_scientific_journal-1767	7	2	overcome	overcome	VERB
american_scientific_journal-1767	7	3	this	this	DET
american_scientific_journal-1767	7	4	problem	problem	NOUN
american_scientific_journal-1767	7	5	,	,	PUNCT
american_scientific_journal-1767	7	6	a	a	DET
american_scientific_journal-1767	7	7	set	set	NOUN
american_scientific_journal-1767	7	8	of	of	ADP
american_scientific_journal-1767	7	9	new	new	ADJ
american_scientific_journal-1767	7	10	boundary	boundary	ADJ
american_scientific_journal-1767	7	11	conditions	condition	NOUN
american_scientific_journal-1767	7	12	has	have	AUX
american_scientific_journal-1767	7	13	been	be	AUX
american_scientific_journal-1767	7	14	introduced	introduce	VERB
american_scientific_journal-1767	7	15	along	along	ADP
american_scientific_journal-1767	7	16	with	with	ADP
american_scientific_journal-1767	7	17	different	different	ADJ
american_scientific_journal-1767	7	18	coordinates	coordinate	NOUN
american_scientific_journal-1767	7	19	for	for	ADP
american_scientific_journal-1767	7	20	different	different	ADJ
american_scientific_journal-1767	7	21	regions	region	NOUN
american_scientific_journal-1767	7	22	of	of	ADP
american_scientific_journal-1767	7	23	the	the	DET
american_scientific_journal-1767	7	24	matter	matter	NOUN
american_scientific_journal-1767	7	25	distribution	distribution	NOUN
american_scientific_journal-1767	7	26	.	.	PUNCT
american_scientific_journal-1767	8	1	keywords	keyword	NOUN
american_scientific_journal-1767	8	2	:	:	PUNCT
american_scientific_journal-1767	8	3	einstein	einstein	PROPN
american_scientific_journal-1767	8	4	’s	’s	PART
american_scientific_journal-1767	8	5	field	field	NOUN
american_scientific_journal-1767	8	6	equations	equation	NOUN
american_scientific_journal-1767	8	7	;	;	PUNCT
american_scientific_journal-1767	8	8	electrically	electrically	ADV
american_scientific_journal-1767	8	9	counterpoised	counterpoise	VERB
american_scientific_journal-1767	8	10	dust	dust	NOUN
american_scientific_journal-1767	8	11	.	.	PUNCT
american_scientific_journal-1767	9	1	1	1	X
american_scientific_journal-1767	9	2	.	.	X
american_scientific_journal-1767	9	3	introduction	introduction	NOUN
american_scientific_journal-1767	9	4	sashinka	sashinka	PROPN
american_scientific_journal-1767	9	5	wimaladharma	wimaladharma	PROPN
american_scientific_journal-1767	9	6	and	and	CCONJ
american_scientific_journal-1767	9	7	nalin	nalin	PROPN
american_scientific_journal-1767	9	8	de	de	PROPN
american_scientific_journal-1767	9	9	silva	silva	PROPN
american_scientific_journal-1767	10	1	[	[	X
american_scientific_journal-1767	10	2	1	1	NUM
american_scientific_journal-1767	10	3	]	]	PUNCT
american_scientific_journal-1767	10	4	considered	consider	VERB
american_scientific_journal-1767	10	5	a	a	DET
american_scientific_journal-1767	10	6	spherically	spherically	NOUN
american_scientific_journal-1767	10	7	symmetric	symmetric	ADJ
american_scientific_journal-1767	10	8	distribution	distribution	NOUN
american_scientific_journal-1767	10	9	of	of	ADP
american_scientific_journal-1767	10	10	electrically	electrically	ADV
american_scientific_journal-1767	10	11	counterpoised	counterpoise	VERB
american_scientific_journal-1767	10	12	dust	dust	NOUN
american_scientific_journal-1767	10	13	and	and	CCONJ
american_scientific_journal-1767	10	14	solved	solve	VERB
american_scientific_journal-1767	10	15	einstein	einstein	PROPN
american_scientific_journal-1767	10	16	-	-	PUNCT
american_scientific_journal-1767	10	17	maxwell	maxwell	PROPN
american_scientific_journal-1767	10	18	field	field	NOUN
american_scientific_journal-1767	10	19	equations	equation	NOUN
american_scientific_journal-1767	10	20	using	use	VERB
american_scientific_journal-1767	10	21	the	the	DET
american_scientific_journal-1767	10	22	standard	standard	ADJ
american_scientific_journal-1767	10	23	boundary	boundary	ADJ
american_scientific_journal-1767	10	24	conditions	condition	NOUN
american_scientific_journal-1767	10	25	which	which	PRON
american_scientific_journal-1767	10	26	says	say	VERB
american_scientific_journal-1767	10	27	that	that	SCONJ
american_scientific_journal-1767	10	28	metric	metric	ADJ
american_scientific_journal-1767	10	29	coefficients	coefficient	NOUN
american_scientific_journal-1767	10	30	and	and	CCONJ
american_scientific_journal-1767	10	31	their	their	PRON
american_scientific_journal-1767	10	32	partial	partial	ADJ
american_scientific_journal-1767	10	33	derivatives	derivative	NOUN
american_scientific_journal-1767	10	34	are	be	AUX
american_scientific_journal-1767	10	35	continuous	continuous	ADJ
american_scientific_journal-1767	10	36	on	on	ADP
american_scientific_journal-1767	10	37	the	the	DET
american_scientific_journal-1767	10	38	boundary	boundary	NOUN
american_scientific_journal-1767	10	39	of	of	ADP
american_scientific_journal-1767	10	40	the	the	DET
american_scientific_journal-1767	10	41	sphere	sphere	NOUN
american_scientific_journal-1767	10	42	.	.	PUNCT
american_scientific_journal-1767	11	1	also	also	ADV
american_scientific_journal-1767	11	2	there	there	ADV
american_scientific_journal-1767	11	3	the	the	DET
american_scientific_journal-1767	11	4	metrics	metric	NOUN
american_scientific_journal-1767	11	5	had	have	VERB
american_scientific_journal-1767	11	6	the	the	DET
american_scientific_journal-1767	11	7	same	same	ADJ
american_scientific_journal-1767	11	8	form	form	NOUN
american_scientific_journal-1767	11	9	for	for	ADP
american_scientific_journal-1767	11	10	the	the	DET
american_scientific_journal-1767	11	11	two	two	NUM
american_scientific_journal-1767	11	12	regions	region	NOUN
american_scientific_journal-1767	11	13	inside	inside	ADP
american_scientific_journal-1767	11	14	and	and	CCONJ
american_scientific_journal-1767	11	15	outside	outside	ADP
american_scientific_journal-1767	11	16	the	the	DET
american_scientific_journal-1767	11	17	sphere	sphere	NOUN
american_scientific_journal-1767	11	18	with	with	ADP
american_scientific_journal-1767	11	19	the	the	DET
american_scientific_journal-1767	11	20	same	same	ADJ
american_scientific_journal-1767	11	21	coordinates	coordinate	NOUN
american_scientific_journal-1767	11	22	(	(	PUNCT
american_scientific_journal-1767	11	23	𝑡𝑡	𝑡𝑡	ADJ
american_scientific_journal-1767	11	24	,	,	PUNCT
american_scientific_journal-1767	11	25	𝑟𝑟	𝑟𝑟	NOUN
american_scientific_journal-1767	11	26	)	)	PUNCT
american_scientific_journal-1767	11	27	both	both	CCONJ
american_scientific_journal-1767	11	28	inside	inside	ADP
american_scientific_journal-1767	11	29	and	and	CCONJ
american_scientific_journal-1767	11	30	outside	outside	ADP
american_scientific_journal-1767	11	31	the	the	DET
american_scientific_journal-1767	11	32	sphere	sphere	NOUN
american_scientific_journal-1767	11	33	.	.	PUNCT
american_scientific_journal-1767	12	1	also	also	ADV
american_scientific_journal-1767	12	2	it	it	PRON
american_scientific_journal-1767	12	3	has	have	AUX
american_scientific_journal-1767	12	4	been	be	AUX
american_scientific_journal-1767	12	5	also	also	ADV
american_scientific_journal-1767	12	6	found	find	VERB
american_scientific_journal-1767	12	7	that	that	SCONJ
american_scientific_journal-1767	12	8	the	the	DET
american_scientific_journal-1767	12	9	metric	metric	NOUN
american_scientific_journal-1767	12	10	in	in	ADP
american_scientific_journal-1767	12	11	the	the	DET
american_scientific_journal-1767	12	12	exterior	exterior	ADJ
american_scientific_journal-1767	12	13	region	region	NOUN
american_scientific_journal-1767	12	14	of	of	ADP
american_scientific_journal-1767	12	15	the	the	DET
american_scientific_journal-1767	12	16	sphere	sphere	NOUN
american_scientific_journal-1767	12	17	is	be	AUX
american_scientific_journal-1767	12	18	not	not	PART
american_scientific_journal-1767	12	19	tending	tend	VERB
american_scientific_journal-1767	12	20	to	to	ADP
american_scientific_journal-1767	12	21	lorentzian	lorentzian	ADJ
american_scientific_journal-1767	12	22	form	form	NOUN
american_scientific_journal-1767	12	23	at	at	ADP
american_scientific_journal-1767	12	24	infinity	infinity	NOUN
american_scientific_journal-1767	12	25	.	.	PUNCT
american_scientific_journal-1767	13	1	-----------------------------------------------------------------------	-----------------------------------------------------------------------	PUNCT
american_scientific_journal-1767	14	1	*	*	PUNCT
american_scientific_journal-1767	14	2	corresponding	correspond	VERB
american_scientific_journal-1767	14	3	author	author	NOUN
american_scientific_journal-1767	14	4	.	.	PUNCT
american_scientific_journal-1767	15	1	http://asrjetsjournal.org/	http://asrjetsjournal.org/	PROPN
american_scientific_journal-1767	15	2	american	american	PROPN
american_scientific_journal-1767	15	3	scientific	scientific	PROPN
american_scientific_journal-1767	15	4	research	research	NOUN
american_scientific_journal-1767	15	5	journal	journal	NOUN
american_scientific_journal-1767	15	6	for	for	ADP
american_scientific_journal-1767	15	7	engineering	engineering	NOUN
american_scientific_journal-1767	15	8	,	,	PUNCT
american_scientific_journal-1767	15	9	technology	technology	NOUN
american_scientific_journal-1767	15	10	,	,	PUNCT
american_scientific_journal-1767	15	11	and	and	CCONJ
american_scientific_journal-1767	15	12	sciences	science	NOUN
american_scientific_journal-1767	15	13	(	(	PUNCT
american_scientific_journal-1767	15	14	asrjets	asrjet	NOUN
american_scientific_journal-1767	15	15	)	)	PUNCT
american_scientific_journal-1767	15	16	(	(	PUNCT
american_scientific_journal-1767	15	17	2016	2016	NUM
american_scientific_journal-1767	15	18	)	)	PUNCT
american_scientific_journal-1767	15	19	volume	volume	NOUN
american_scientific_journal-1767	15	20	21	21	NUM
american_scientific_journal-1767	15	21	,	,	PUNCT
american_scientific_journal-1767	15	22	no	no	DET
american_scientific_journal-1767	15	23	1	1	NUM
american_scientific_journal-1767	15	24	,	,	PUNCT
american_scientific_journal-1767	15	25	pp	pp	ADV
american_scientific_journal-1767	15	26	163	163	NUM
american_scientific_journal-1767	15	27	-	-	SYM
american_scientific_journal-1767	15	28	177	177	NUM
american_scientific_journal-1767	15	29	164	164	NUM
american_scientific_journal-1767	15	30	in	in	ADP
american_scientific_journal-1767	15	31	order	order	NOUN
american_scientific_journal-1767	15	32	to	to	PART
american_scientific_journal-1767	15	33	obtain	obtain	VERB
american_scientific_journal-1767	15	34	a	a	DET
american_scientific_journal-1767	15	35	lorentzian	lorentzian	ADJ
american_scientific_journal-1767	15	36	metric	metric	NOUN
american_scientific_journal-1767	15	37	at	at	ADP
american_scientific_journal-1767	15	38	infinity	infinity	NOUN
american_scientific_journal-1767	15	39	for	for	ADP
american_scientific_journal-1767	15	40	a	a	DET
american_scientific_journal-1767	15	41	spherically	spherically	NOUN
american_scientific_journal-1767	15	42	symmetric	symmetric	ADJ
american_scientific_journal-1767	15	43	distribution	distribution	NOUN
american_scientific_journal-1767	15	44	of	of	ADP
american_scientific_journal-1767	15	45	matter	matter	NOUN
american_scientific_journal-1767	15	46	,	,	PUNCT
american_scientific_journal-1767	15	47	it	it	PRON
american_scientific_journal-1767	15	48	is	be	AUX
american_scientific_journal-1767	15	49	assumed	assume	VERB
american_scientific_journal-1767	15	50	that	that	SCONJ
american_scientific_journal-1767	15	51	the	the	DET
american_scientific_journal-1767	15	52	time	time	NOUN
american_scientific_journal-1767	15	53	and	and	CCONJ
american_scientific_journal-1767	15	54	radial	radial	ADJ
american_scientific_journal-1767	15	55	coordinates	coordinate	NOUN
american_scientific_journal-1767	15	56	are	be	AUX
american_scientific_journal-1767	15	57	different	different	ADJ
american_scientific_journal-1767	15	58	for	for	ADP
american_scientific_journal-1767	15	59	the	the	DET
american_scientific_journal-1767	15	60	two	two	NUM
american_scientific_journal-1767	15	61	regions	region	NOUN
american_scientific_journal-1767	15	62	,	,	PUNCT
american_scientific_journal-1767	15	63	inside	inside	ADP
american_scientific_journal-1767	15	64	and	and	CCONJ
american_scientific_journal-1767	15	65	outside	outside	ADP
american_scientific_journal-1767	15	66	the	the	DET
american_scientific_journal-1767	15	67	sphere	sphere	NOUN
american_scientific_journal-1767	15	68	and	and	CCONJ
american_scientific_journal-1767	15	69	a	a	DET
american_scientific_journal-1767	15	70	new	new	ADJ
american_scientific_journal-1767	15	71	set	set	NOUN
american_scientific_journal-1767	15	72	of	of	ADP
american_scientific_journal-1767	15	73	boundary	boundary	ADJ
american_scientific_journal-1767	15	74	conditions	condition	NOUN
american_scientific_journal-1767	15	75	has	have	AUX
american_scientific_journal-1767	15	76	been	be	AUX
american_scientific_journal-1767	15	77	introduced	introduce	VERB
american_scientific_journal-1767	15	78	to	to	PART
american_scientific_journal-1767	15	79	solve	solve	VERB
american_scientific_journal-1767	15	80	the	the	DET
american_scientific_journal-1767	15	81	einstein	einstein	PROPN
american_scientific_journal-1767	15	82	-	-	PUNCT
american_scientific_journal-1767	15	83	maxwell	maxwell	PROPN
american_scientific_journal-1767	15	84	equations	equation	NOUN
american_scientific_journal-1767	15	85	and	and	CCONJ
american_scientific_journal-1767	15	86	equations	equation	NOUN
american_scientific_journal-1767	15	87	for	for	ADP
american_scientific_journal-1767	15	88	a	a	DET
american_scientific_journal-1767	15	89	distribution	distribution	NOUN
american_scientific_journal-1767	15	90	of	of	ADP
american_scientific_journal-1767	15	91	electrically	electrically	ADV
american_scientific_journal-1767	15	92	counterpoised	counterpoise	VERB
american_scientific_journal-1767	15	93	dust	dust	NOUN
american_scientific_journal-1767	15	94	(	(	PUNCT
american_scientific_journal-1767	15	95	ecd	ecd	PROPN
american_scientific_journal-1767	15	96	)	)	PUNCT
american_scientific_journal-1767	15	97	.	.	PUNCT
american_scientific_journal-1767	16	1	2	2	X
american_scientific_journal-1767	16	2	.	.	X
american_scientific_journal-1767	16	3	material	material	NOUN
american_scientific_journal-1767	16	4	and	and	CCONJ
american_scientific_journal-1767	16	5	the	the	DET
american_scientific_journal-1767	16	6	method	method	NOUN
american_scientific_journal-1767	16	7	closely	closely	ADV
american_scientific_journal-1767	16	8	following	follow	VERB
american_scientific_journal-1767	16	9	the	the	DET
american_scientific_journal-1767	16	10	form	form	NOUN
american_scientific_journal-1767	16	11	of	of	ADP
american_scientific_journal-1767	16	12	the	the	DET
american_scientific_journal-1767	16	13	metric	metric	NOUN
american_scientific_journal-1767	16	14	obtained	obtain	VERB
american_scientific_journal-1767	16	15	in	in	ADP
american_scientific_journal-1767	16	16	sashinka	sashinka	PROPN
american_scientific_journal-1767	16	17	wimaladharma	wimaladharma	NOUN
american_scientific_journal-1767	16	18	and	and	CCONJ
american_scientific_journal-1767	16	19	nalin	nalin	PROPN
american_scientific_journal-1767	16	20	de	de	PROPN
american_scientific_journal-1767	16	21	silva	silva	PROPN
american_scientific_journal-1767	17	1	[	[	X
american_scientific_journal-1767	17	2	1	1	NUM
american_scientific_journal-1767	17	3	]	]	PUNCT
american_scientific_journal-1767	17	4	,	,	PUNCT
american_scientific_journal-1767	17	5	a	a	DET
american_scientific_journal-1767	17	6	metric	metric	NOUN
american_scientific_journal-1767	17	7	for	for	ADP
american_scientific_journal-1767	17	8	exterior	exterior	ADJ
american_scientific_journal-1767	17	9	region	region	NOUN
american_scientific_journal-1767	17	10	of	of	ADP
american_scientific_journal-1767	17	11	the	the	DET
american_scientific_journal-1767	17	12	sphere	sphere	NOUN
american_scientific_journal-1767	17	13	has	have	AUX
american_scientific_journal-1767	17	14	taken	take	VERB
american_scientific_journal-1767	17	15	to	to	PART
american_scientific_journal-1767	17	16	be	be	AUX
american_scientific_journal-1767	17	17	of	of	ADP
american_scientific_journal-1767	17	18	the	the	DET
american_scientific_journal-1767	17	19	form	form	NOUN
american_scientific_journal-1767	17	20	𝑑𝑑𝑑𝑑2	𝑑𝑑𝑑𝑑2	NOUN
american_scientific_journal-1767	18	1	=	=	SYM
american_scientific_journal-1767	18	2	1	1	NUM
american_scientific_journal-1767	18	3	�	�	PROPN
american_scientific_journal-1767	18	4	𝐴𝐴1	𝐴𝐴1	PROPN
american_scientific_journal-1767	18	5	+	+	PROPN
american_scientific_journal-1767	18	6	𝐴𝐴2	𝐴𝐴2	PROPN
american_scientific_journal-1767	18	7	𝑅𝑅	𝑅𝑅	PROPN
american_scientific_journal-1767	18	8	�	�	PROPN
american_scientific_journal-1767	18	9	2	2	NUM
american_scientific_journal-1767	18	10	𝑐𝑐2𝑑𝑑𝑑𝑑2	𝑐𝑐2𝑑𝑑𝑑𝑑2	SYM
american_scientific_journal-1767	18	11	−	−	PROPN
american_scientific_journal-1767	18	12	�	�	PROPN
american_scientific_journal-1767	18	13	𝐴𝐴1	𝐴𝐴1	PROPN
american_scientific_journal-1767	18	14	+	+	CCONJ
american_scientific_journal-1767	18	15	𝐴𝐴2	𝐴𝐴2	PROPN
american_scientific_journal-1767	18	16	𝑅𝑅	𝑅𝑅	PROPN
american_scientific_journal-1767	18	17	�	�	PROPN
american_scientific_journal-1767	18	18	2	2	NUM
american_scientific_journal-1767	18	19	(	(	PUNCT
american_scientific_journal-1767	18	20	𝑑𝑑𝑑𝑑2	𝑑𝑑𝑑𝑑2	PROPN
american_scientific_journal-1767	18	21	+	+	CCONJ
american_scientific_journal-1767	18	22	𝑑𝑑2𝑑𝑑ω2	𝑑𝑑2𝑑𝑑ω2	PROPN
american_scientific_journal-1767	18	23	)	)	PUNCT
american_scientific_journal-1767	18	24	.	.	PUNCT
american_scientific_journal-1767	19	1	the	the	DET
american_scientific_journal-1767	19	2	density	density	NOUN
american_scientific_journal-1767	19	3	of	of	ADP
american_scientific_journal-1767	19	4	a	a	DET
american_scientific_journal-1767	19	5	sphere	sphere	NOUN
american_scientific_journal-1767	19	6	of	of	ADP
american_scientific_journal-1767	19	7	electrically	electrically	ADV
american_scientific_journal-1767	19	8	counterpoised	counterpoise	VERB
american_scientific_journal-1767	19	9	dust	dust	NOUN
american_scientific_journal-1767	19	10	is	be	AUX
american_scientific_journal-1767	19	11	taken	take	VERB
american_scientific_journal-1767	19	12	to	to	PART
american_scientific_journal-1767	19	13	be	be	AUX
american_scientific_journal-1767	19	14	constant	constant	ADJ
american_scientific_journal-1767	19	15	and	and	CCONJ
american_scientific_journal-1767	19	16	equal	equal	ADJ
american_scientific_journal-1767	19	17	to	to	ADP
american_scientific_journal-1767	19	18	24	24	NUM
american_scientific_journal-1767	19	19	1	1	NUM
american_scientific_journal-1767	19	20	lπ	lπ	NOUN
american_scientific_journal-1767	19	21	with	with	ADP
american_scientific_journal-1767	19	22	14	14	NUM
american_scientific_journal-1767	19	23	2	2	NUM
american_scientific_journal-1767	19	24	=	=	NOUN
american_scientific_journal-1767	19	25	lπρ	lπρ	NOUN
american_scientific_journal-1767	19	26	as	as	ADP
american_scientific_journal-1767	19	27	in	in	ADP
american_scientific_journal-1767	19	28	sashinka	sashinka	PROPN
american_scientific_journal-1767	19	29	wimaladharma	wimaladharma	NOUN
american_scientific_journal-1767	19	30	and	and	CCONJ
american_scientific_journal-1767	19	31	nalin	nalin	PROPN
american_scientific_journal-1767	19	32	de	de	PROPN
american_scientific_journal-1767	19	33	silva	silva	PROPN
american_scientific_journal-1767	20	1	[	[	X
american_scientific_journal-1767	20	2	1	1	NUM
american_scientific_journal-1767	20	3	]	]	PUNCT
american_scientific_journal-1767	20	4	.	.	PUNCT
american_scientific_journal-1767	21	1	now	now	ADV
american_scientific_journal-1767	21	2	we	we	PRON
american_scientific_journal-1767	21	3	introduce	introduce	VERB
american_scientific_journal-1767	21	4	two	two	NUM
american_scientific_journal-1767	21	5	sets	set	NOUN
american_scientific_journal-1767	21	6	of	of	ADP
american_scientific_journal-1767	21	7	coordinates	coordinate	NOUN
american_scientific_journal-1767	21	8	(	(	PUNCT
american_scientific_journal-1767	21	9	𝑡𝑡	𝑡𝑡	ADJ
american_scientific_journal-1767	21	10	,	,	PUNCT
american_scientific_journal-1767	21	11	𝑟𝑟	𝑟𝑟	NOUN
american_scientific_journal-1767	21	12	)	)	PUNCT
american_scientific_journal-1767	21	13	and	and	CCONJ
american_scientific_journal-1767	21	14	ω	ω	NUM
american_scientific_journal-1767	21	15	and	and	CCONJ
american_scientific_journal-1767	21	16	(	(	PUNCT
american_scientific_journal-1767	21	17	𝑑𝑑,𝑑𝑑	𝑑𝑑,𝑑𝑑	NOUN
american_scientific_journal-1767	21	18	)	)	PUNCT
american_scientific_journal-1767	21	19	and	and	CCONJ
american_scientific_journal-1767	21	20	ω	ω	NUM
american_scientific_journal-1767	21	21	for	for	ADP
american_scientific_journal-1767	21	22	the	the	DET
american_scientific_journal-1767	21	23	metrics	metric	NOUN
american_scientific_journal-1767	21	24	inside	inside	ADP
american_scientific_journal-1767	21	25	and	and	CCONJ
american_scientific_journal-1767	21	26	outside	outside	ADP
american_scientific_journal-1767	21	27	of	of	ADP
american_scientific_journal-1767	21	28	a	a	DET
american_scientific_journal-1767	21	29	sphere	sphere	NOUN
american_scientific_journal-1767	21	30	of	of	ADP
american_scientific_journal-1767	21	31	constant	constant	ADJ
american_scientific_journal-1767	21	32	density	density	NOUN
american_scientific_journal-1767	21	33	,	,	PUNCT
american_scientific_journal-1767	21	34	respectively	respectively	ADV
american_scientific_journal-1767	21	35	.	.	PUNCT
american_scientific_journal-1767	22	1	then	then	ADV
american_scientific_journal-1767	22	2	the	the	DET
american_scientific_journal-1767	22	3	metrics	metric	NOUN
american_scientific_journal-1767	22	4	for	for	ADP
american_scientific_journal-1767	22	5	the	the	DET
american_scientific_journal-1767	22	6	two	two	NUM
american_scientific_journal-1767	22	7	regions	region	NOUN
american_scientific_journal-1767	22	8	inside	inside	ADP
american_scientific_journal-1767	22	9	and	and	CCONJ
american_scientific_journal-1767	22	10	outside	outside	ADP
american_scientific_journal-1767	22	11	of	of	ADP
american_scientific_journal-1767	22	12	a	a	DET
american_scientific_journal-1767	22	13	sphere	sphere	NOUN
american_scientific_journal-1767	22	14	of	of	ADP
american_scientific_journal-1767	22	15	constant	constant	ADJ
american_scientific_journal-1767	22	16	density	density	NOUN
american_scientific_journal-1767	22	17	24	24	NUM
american_scientific_journal-1767	22	18	1	1	NUM
american_scientific_journal-1767	22	19	lπ	lπ	PROPN
american_scientific_journal-1767	22	20	ρ	ρ	PROPN
american_scientific_journal-1767	22	21	=	=	PUNCT
american_scientific_journal-1767	22	22	can	can	AUX
american_scientific_journal-1767	22	23	be	be	AUX
american_scientific_journal-1767	22	24	written	write	VERB
american_scientific_journal-1767	22	25	in	in	ADP
american_scientific_journal-1767	22	26	the	the	DET
american_scientific_journal-1767	22	27	form	form	NOUN
american_scientific_journal-1767	22	28	𝑑𝑑𝑑𝑑2	𝑑𝑑𝑑𝑑2	NOUN
american_scientific_journal-1767	23	1	=	=	SYM
american_scientific_journal-1767	23	2	1	1	NUM
american_scientific_journal-1767	23	3	�	�	PROPN
american_scientific_journal-1767	23	4	𝜃𝜃	𝜃𝜃	PROPN
american_scientific_journal-1767	23	5	�	�	PROPN
american_scientific_journal-1767	23	6	𝑅𝑅𝑙𝑙	𝑅𝑅𝑙𝑙	ADJ
american_scientific_journal-1767	23	7	�	�	NOUN
american_scientific_journal-1767	23	8	�	�	PROPN
american_scientific_journal-1767	23	9	2	2	NUM
american_scientific_journal-1767	23	10	𝑐𝑐2𝑑𝑑𝑡𝑡2	𝑐𝑐2𝑑𝑑𝑡𝑡2	NOUN
american_scientific_journal-1767	23	11	−	−	PROPN
american_scientific_journal-1767	23	12	�	�	PROPN
american_scientific_journal-1767	23	13	𝜃𝜃	𝜃𝜃	PROPN
american_scientific_journal-1767	23	14	�	�	PROPN
american_scientific_journal-1767	23	15	𝑅𝑅	𝑅𝑅	PROPN
american_scientific_journal-1767	23	16	𝑙𝑙	𝑙𝑙	PROPN
american_scientific_journal-1767	23	17	�	�	PROPN
american_scientific_journal-1767	23	18	�	�	PROPN
american_scientific_journal-1767	23	19	2	2	NUM
american_scientific_journal-1767	23	20	(	(	PUNCT
american_scientific_journal-1767	23	21	𝑑𝑑𝑟𝑟2	𝑑𝑑𝑟𝑟2	X
american_scientific_journal-1767	23	22	+	+	CCONJ
american_scientific_journal-1767	23	23	𝑟𝑟2𝑑𝑑ω2	𝑟𝑟2𝑑𝑑ω2	PROPN
american_scientific_journal-1767	23	24	)	)	PUNCT
american_scientific_journal-1767	23	25	0	0	NUM
american_scientific_journal-1767	24	1	≤	≤	NUM
american_scientific_journal-1767	24	2	𝑟𝑟	𝑟𝑟	ADP
american_scientific_journal-1767	24	3	≤	≤	NUM
american_scientific_journal-1767	24	4	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1767	24	5	𝑑𝑑𝑑𝑑2	𝑑𝑑𝑑𝑑2	PROPN
american_scientific_journal-1767	24	6	=	=	SYM
american_scientific_journal-1767	24	7	1	1	NUM
american_scientific_journal-1767	24	8	�	�	PROPN
american_scientific_journal-1767	24	9	𝐴𝐴1	𝐴𝐴1	PROPN
american_scientific_journal-1767	24	10	+	+	PROPN
american_scientific_journal-1767	24	11	𝐴𝐴2	𝐴𝐴2	PROPN
american_scientific_journal-1767	24	12	𝑅𝑅	𝑅𝑅	PROPN
american_scientific_journal-1767	24	13	�	�	PROPN
american_scientific_journal-1767	24	14	2	2	NUM
american_scientific_journal-1767	24	15	𝑐𝑐2𝑑𝑑𝑑𝑑2	𝑐𝑐2𝑑𝑑𝑑𝑑2	SYM
american_scientific_journal-1767	24	16	−	−	PROPN
american_scientific_journal-1767	24	17	�	�	PROPN
american_scientific_journal-1767	24	18	𝐴𝐴1	𝐴𝐴1	PROPN
american_scientific_journal-1767	24	19	+	+	CCONJ
american_scientific_journal-1767	24	20	𝐴𝐴2	𝐴𝐴2	PROPN
american_scientific_journal-1767	24	21	𝑅𝑅	𝑅𝑅	PROPN
american_scientific_journal-1767	24	22	�	�	PROPN
american_scientific_journal-1767	24	23	2	2	NUM
american_scientific_journal-1767	24	24	�	�	PROPN
american_scientific_journal-1767	24	25	𝑑𝑑𝑑𝑑2	𝑑𝑑𝑑𝑑2	NOUN
american_scientific_journal-1767	24	26	+	+	CCONJ
american_scientific_journal-1767	24	27	𝑑𝑑2𝑑𝑑ω	𝑑𝑑2𝑑𝑑ω	PROPN
american_scientific_journal-1767	24	28	2	2	NUM
american_scientific_journal-1767	24	29	�	�	PROPN
american_scientific_journal-1767	24	30	𝐴𝐴	𝐴𝐴	PROPN
american_scientific_journal-1767	24	31	<	<	X
american_scientific_journal-1767	24	32	𝑑𝑑	𝑑𝑑	PROPN
american_scientific_journal-1767	24	33	.	.	PUNCT
american_scientific_journal-1767	25	1	(	(	PUNCT
american_scientific_journal-1767	25	2	1	1	X
american_scientific_journal-1767	25	3	)	)	PUNCT
american_scientific_journal-1767	25	4	where	where	SCONJ
american_scientific_journal-1767	25	5	𝑑𝑑ω2	𝑑𝑑ω2	NOUN
american_scientific_journal-1767	25	6	=	=	SYM
american_scientific_journal-1767	25	7	𝑑𝑑θ2	𝑑𝑑θ2	PROPN
american_scientific_journal-1767	25	8	+	+	CCONJ
american_scientific_journal-1767	25	9	sin2	sin2	PROPN
american_scientific_journal-1767	25	10	θ	θ	PROPN
american_scientific_journal-1767	25	11	𝑑𝑑φ2	𝑑𝑑φ2	NOUN
american_scientific_journal-1767	25	12	and	and	CCONJ
american_scientific_journal-1767	25	13	𝑑𝑑ω	𝑑𝑑ω	NOUN
american_scientific_journal-1767	25	14	2	2	NUM
american_scientific_journal-1767	25	15	=	=	SYM
american_scientific_journal-1767	25	16	𝑑𝑑θ	𝑑𝑑θ	NOUN
american_scientific_journal-1767	25	17	2	2	NUM
american_scientific_journal-1767	25	18	+	+	CCONJ
american_scientific_journal-1767	25	19	sin2	sin2	NOUN
american_scientific_journal-1767	25	20	θ	θ	PROPN
american_scientific_journal-1767	25	21	𝑑𝑑φ	𝑑𝑑φ	VERB
american_scientific_journal-1767	25	22	2	2	NUM
american_scientific_journal-1767	25	23	,	,	PUNCT
american_scientific_journal-1767	25	24	𝜃𝜃	𝜃𝜃	PROPN
american_scientific_journal-1767	25	25	�	�	PROPN
american_scientific_journal-1767	25	26	𝑅𝑅	𝑅𝑅	PROPN
american_scientific_journal-1767	25	27	𝑙𝑙	𝑙𝑙	PROPN
american_scientific_journal-1767	25	28	�	�	PROPN
american_scientific_journal-1767	25	29	is	be	AUX
american_scientific_journal-1767	25	30	the	the	DET
american_scientific_journal-1767	25	31	emden	emden	ADJ
american_scientific_journal-1767	25	32	function	function	NOUN
american_scientific_journal-1767	25	33	satisfying	satisfy	VERB
american_scientific_journal-1767	25	34	the	the	DET
american_scientific_journal-1767	25	35	emden	emden	ADJ
american_scientific_journal-1767	25	36	equation	equation	NOUN
american_scientific_journal-1767	25	37	[	[	X
american_scientific_journal-1767	25	38	2	2	X
american_scientific_journal-1767	25	39	]	]	PUNCT
american_scientific_journal-1767	25	40	with	with	ADP
american_scientific_journal-1767	25	41	3	3	NUM
american_scientific_journal-1767	25	42	=	=	NOUN
american_scientific_journal-1767	25	43	n	n	NUM
american_scientific_journal-1767	25	44	.	.	PUNCT
american_scientific_journal-1767	26	1	the	the	DET
american_scientific_journal-1767	26	2	metric	metric	NOUN
american_scientific_journal-1767	26	3	for	for	ADP
american_scientific_journal-1767	26	4	the	the	DET
american_scientific_journal-1767	26	5	inside	inside	NOUN
american_scientific_journal-1767	26	6	of	of	ADP
american_scientific_journal-1767	26	7	the	the	DET
american_scientific_journal-1767	26	8	sphere	sphere	NOUN
american_scientific_journal-1767	26	9	is	be	AUX
american_scientific_journal-1767	26	10	taken	take	VERB
american_scientific_journal-1767	26	11	to	to	PART
american_scientific_journal-1767	26	12	be	be	AUX
american_scientific_journal-1767	26	13	of	of	ADP
american_scientific_journal-1767	26	14	the	the	DET
american_scientific_journal-1767	26	15	same	same	ADJ
american_scientific_journal-1767	26	16	form	form	NOUN
american_scientific_journal-1767	26	17	𝑑𝑑𝑑𝑑2	𝑑𝑑𝑑𝑑2	NOUN
american_scientific_journal-1767	27	1	=	=	SYM
american_scientific_journal-1767	27	2	1	1	NUM
american_scientific_journal-1767	27	3	�	�	PROPN
american_scientific_journal-1767	27	4	𝜃𝜃	𝜃𝜃	PROPN
american_scientific_journal-1767	27	5	�	�	PROPN
american_scientific_journal-1767	27	6	𝑅𝑅𝑙𝑙	𝑅𝑅𝑙𝑙	ADJ
american_scientific_journal-1767	27	7	�	�	NOUN
american_scientific_journal-1767	27	8	�	�	PROPN
american_scientific_journal-1767	27	9	2	2	NUM
american_scientific_journal-1767	27	10	𝑐𝑐2𝑑𝑑𝑡𝑡2	𝑐𝑐2𝑑𝑑𝑡𝑡2	NOUN
american_scientific_journal-1767	27	11	−	−	PROPN
american_scientific_journal-1767	27	12	�	�	PROPN
american_scientific_journal-1767	27	13	𝜃𝜃	𝜃𝜃	PROPN
american_scientific_journal-1767	27	14	�	�	PROPN
american_scientific_journal-1767	27	15	𝑅𝑅	𝑅𝑅	PROPN
american_scientific_journal-1767	27	16	𝑙𝑙	𝑙𝑙	PROPN
american_scientific_journal-1767	27	17	�	�	PROPN
american_scientific_journal-1767	27	18	�	�	PROPN
american_scientific_journal-1767	27	19	2	2	NUM
american_scientific_journal-1767	27	20	(	(	PUNCT
american_scientific_journal-1767	27	21	𝑑𝑑𝑟𝑟2	𝑑𝑑𝑟𝑟2	X
american_scientific_journal-1767	27	22	+	+	CCONJ
american_scientific_journal-1767	27	23	𝑟𝑟2𝑑𝑑ω2	𝑟𝑟2𝑑𝑑ω2	PROPN
american_scientific_journal-1767	27	24	)	)	PUNCT
american_scientific_journal-1767	27	25	which	which	PRON
american_scientific_journal-1767	27	26	has	have	AUX
american_scientific_journal-1767	27	27	been	be	AUX
american_scientific_journal-1767	27	28	found	find	VERB
american_scientific_journal-1767	27	29	to	to	PART
american_scientific_journal-1767	27	30	be	be	AUX
american_scientific_journal-1767	27	31	the	the	DET
american_scientific_journal-1767	27	32	metric	metric	NOUN
american_scientific_journal-1767	27	33	inside	inside	ADP
american_scientific_journal-1767	27	34	the	the	DET
american_scientific_journal-1767	27	35	sphere	sphere	NOUN
american_scientific_journal-1767	27	36	in	in	ADP
american_scientific_journal-1767	27	37	sashinka	sashinka	PROPN
american_scientific_journal-1767	27	38	wimaladharma	wimaladharma	PROPN
american_scientific_journal-1767	27	39	and	and	CCONJ
american_scientific_journal-1767	27	40	nalin	nalin	PROPN
american_scientific_journal-1767	27	41	de	de	PROPN
american_scientific_journal-1767	27	42	silva	silva	PROPN
american_scientific_journal-1767	27	43	[	[	X
american_scientific_journal-1767	27	44	1	1	NUM
american_scientific_journal-1767	27	45	]	]	PUNCT
american_scientific_journal-1767	27	46	.	.	PUNCT
american_scientific_journal-1767	27	47	,	,	PUNCT
american_scientific_journal-1767	27	48	as	as	SCONJ
american_scientific_journal-1767	27	49	there	there	PRON
american_scientific_journal-1767	27	50	are	be	VERB
american_scientific_journal-1767	27	51	no	no	DET
american_scientific_journal-1767	27	52	differences	difference	NOUN
american_scientific_journal-1767	27	53	between	between	ADP
american_scientific_journal-1767	27	54	the	the	DET
american_scientific_journal-1767	27	55	coordinates	coordinate	NOUN
american_scientific_journal-1767	27	56	that	that	PRON
american_scientific_journal-1767	27	57	were	be	AUX
american_scientific_journal-1767	27	58	used	use	VERB
american_scientific_journal-1767	27	59	in	in	ADP
american_scientific_journal-1767	27	60	sashinka	sashinka	PROPN
american_scientific_journal-1767	27	61	wimaladharma	wimaladharma	NOUN
american_scientific_journal-1767	27	62	and	and	CCONJ
american_scientific_journal-1767	27	63	nalin	nalin	PROPN
american_scientific_journal-1767	27	64	de	de	PROPN
american_scientific_journal-1767	27	65	silva	silva	PROPN
american_scientific_journal-1767	27	66	[	[	X
american_scientific_journal-1767	27	67	1	1	NUM
american_scientific_journal-1767	27	68	]	]	PUNCT
american_scientific_journal-1767	27	69	,	,	PUNCT
american_scientific_journal-1767	27	70	and	and	CCONJ
american_scientific_journal-1767	27	71	the	the	DET
american_scientific_journal-1767	27	72	present	present	ADJ
american_scientific_journal-1767	27	73	coordinates	coordinate	NOUN
american_scientific_journal-1767	27	74	inside	inside	ADP
american_scientific_journal-1767	27	75	the	the	DET
american_scientific_journal-1767	27	76	sphere	sphere	NOUN
american_scientific_journal-1767	27	77	.	.	PUNCT
american_scientific_journal-1767	28	1	american	american	ADJ
american_scientific_journal-1767	28	2	scientific	scientific	ADJ
american_scientific_journal-1767	28	3	research	research	PROPN
american_scientific_journal-1767	28	4	journal	journal	NOUN
american_scientific_journal-1767	28	5	for	for	ADP
american_scientific_journal-1767	28	6	engineering	engineering	NOUN
american_scientific_journal-1767	28	7	,	,	PUNCT
american_scientific_journal-1767	28	8	technology	technology	NOUN
american_scientific_journal-1767	28	9	,	,	PUNCT
american_scientific_journal-1767	28	10	and	and	CCONJ
american_scientific_journal-1767	28	11	sciences	science	NOUN
american_scientific_journal-1767	28	12	(	(	PUNCT
american_scientific_journal-1767	28	13	asrjets	asrjet	NOUN
american_scientific_journal-1767	28	14	)	)	PUNCT
american_scientific_journal-1767	28	15	(	(	PUNCT
american_scientific_journal-1767	28	16	2016	2016	NUM
american_scientific_journal-1767	28	17	)	)	PUNCT
american_scientific_journal-1767	28	18	volume	volume	NOUN
american_scientific_journal-1767	28	19	21	21	NUM
american_scientific_journal-1767	28	20	,	,	PUNCT
american_scientific_journal-1767	28	21	no	no	DET
american_scientific_journal-1767	28	22	1	1	NUM
american_scientific_journal-1767	28	23	,	,	PUNCT
american_scientific_journal-1767	28	24	pp	pp	ADV
american_scientific_journal-1767	28	25	163	163	NUM
american_scientific_journal-1767	28	26	-	-	SYM
american_scientific_journal-1767	28	27	177	177	NUM
american_scientific_journal-1767	28	28	165	165	NUM
american_scientific_journal-1767	28	29	also	also	ADV
american_scientific_journal-1767	28	30	the	the	DET
american_scientific_journal-1767	28	31	metric	metric	NOUN
american_scientific_journal-1767	28	32	of	of	ADP
american_scientific_journal-1767	28	33	the	the	DET
american_scientific_journal-1767	28	34	space	space	NOUN
american_scientific_journal-1767	28	35	–	–	PUNCT
american_scientific_journal-1767	28	36	time	time	NOUN
american_scientific_journal-1767	28	37	outside	outside	ADP
american_scientific_journal-1767	28	38	the	the	DET
american_scientific_journal-1767	28	39	sphere	sphere	NOUN
american_scientific_journal-1767	28	40	is	be	AUX
american_scientific_journal-1767	28	41	taken	take	VERB
american_scientific_journal-1767	28	42	to	to	PART
american_scientific_journal-1767	28	43	be	be	AUX
american_scientific_journal-1767	28	44	in	in	ADP
american_scientific_journal-1767	28	45	the	the	DET
american_scientific_journal-1767	28	46	form	form	NOUN
american_scientific_journal-1767	28	47	𝑑𝑑𝑑𝑑2	𝑑𝑑𝑑𝑑2	NOUN
american_scientific_journal-1767	29	1	=	=	SYM
american_scientific_journal-1767	29	2	1	1	NUM
american_scientific_journal-1767	29	3	�	�	PROPN
american_scientific_journal-1767	29	4	𝐴𝐴1	𝐴𝐴1	PROPN
american_scientific_journal-1767	29	5	+	+	PROPN
american_scientific_journal-1767	29	6	𝐴𝐴2	𝐴𝐴2	PROPN
american_scientific_journal-1767	29	7	𝑅𝑅	𝑅𝑅	PROPN
american_scientific_journal-1767	29	8	�	�	PROPN
american_scientific_journal-1767	29	9	2	2	NUM
american_scientific_journal-1767	29	10	𝑐𝑐2𝑑𝑑𝑑𝑑2	𝑐𝑐2𝑑𝑑𝑑𝑑2	SYM
american_scientific_journal-1767	29	11	−	−	PROPN
american_scientific_journal-1767	29	12	�	�	PROPN
american_scientific_journal-1767	29	13	𝐴𝐴1	𝐴𝐴1	PROPN
american_scientific_journal-1767	29	14	+	+	CCONJ
american_scientific_journal-1767	29	15	𝐴𝐴2	𝐴𝐴2	PROPN
american_scientific_journal-1767	29	16	𝑅𝑅	𝑅𝑅	PROPN
american_scientific_journal-1767	29	17	�	�	PROPN
american_scientific_journal-1767	29	18	2	2	NUM
american_scientific_journal-1767	29	19	�	�	PROPN
american_scientific_journal-1767	29	20	𝑑𝑑𝑑𝑑2	𝑑𝑑𝑑𝑑2	NOUN
american_scientific_journal-1767	29	21	+	+	CCONJ
american_scientific_journal-1767	29	22	𝑑𝑑2𝑑𝑑ω	𝑑𝑑2𝑑𝑑ω	PROPN
american_scientific_journal-1767	29	23	2	2	NUM
american_scientific_journal-1767	29	24	�	�	PROPN
american_scientific_journal-1767	29	25	(	(	PUNCT
american_scientific_journal-1767	29	26	2	2	NUM
american_scientific_journal-1767	29	27	)	)	PUNCT
american_scientific_journal-1767	29	28	so	so	SCONJ
american_scientific_journal-1767	29	29	that	that	SCONJ
american_scientific_journal-1767	29	30	the	the	DET
american_scientific_journal-1767	29	31	metric	metric	NOUN
american_scientific_journal-1767	29	32	is	be	AUX
american_scientific_journal-1767	29	33	isotropic	isotropic	ADJ
american_scientific_journal-1767	29	34	in	in	ADP
american_scientific_journal-1767	29	35	space	space	NOUN
american_scientific_journal-1767	29	36	coordinates	coordinate	NOUN
american_scientific_journal-1767	29	37	.	.	PUNCT
american_scientific_journal-1767	30	1	since	since	SCONJ
american_scientific_journal-1767	30	2	the	the	DET
american_scientific_journal-1767	30	3	metric	metric	NOUN
american_scientific_journal-1767	30	4	has	have	VERB
american_scientific_journal-1767	30	5	to	to	PART
american_scientific_journal-1767	30	6	be	be	AUX
american_scientific_journal-1767	30	7	lorentzian	lorentzian	ADJ
american_scientific_journal-1767	30	8	at	at	ADP
american_scientific_journal-1767	30	9	infinity	infinity	NOUN
american_scientific_journal-1767	30	10	,	,	PUNCT
american_scientific_journal-1767	30	11	the	the	DET
american_scientific_journal-1767	30	12	constant	constant	ADJ
american_scientific_journal-1767	30	13	𝐴𝐴1	𝐴𝐴1	PROPN
american_scientific_journal-1767	30	14	should	should	AUX
american_scientific_journal-1767	30	15	be	be	AUX
american_scientific_journal-1767	30	16	equal	equal	ADJ
american_scientific_journal-1767	30	17	to	to	ADP
american_scientific_journal-1767	30	18	one	one	NUM
american_scientific_journal-1767	30	19	,	,	PUNCT
american_scientific_journal-1767	30	20	i.e	i.e	PRON
american_scientific_journal-1767	30	21	.𝐴𝐴1	.𝐴𝐴1	NOUN
american_scientific_journal-1767	31	1	=	=	NOUN
american_scientific_journal-1767	31	2	1	1	X
american_scientific_journal-1767	31	3	.	.	X
american_scientific_journal-1767	32	1	in	in	ADP
american_scientific_journal-1767	32	2	general	general	ADJ
american_scientific_journal-1767	32	3	the	the	DET
american_scientific_journal-1767	32	4	coordinates	coordinate	NOUN
american_scientific_journal-1767	32	5	in	in	ADP
american_scientific_journal-1767	32	6	and	and	CCONJ
american_scientific_journal-1767	32	7	outside	outside	ADP
american_scientific_journal-1767	32	8	of	of	ADP
american_scientific_journal-1767	32	9	the	the	DET
american_scientific_journal-1767	32	10	sphere	sphere	NOUN
american_scientific_journal-1767	32	11	do	do	AUX
american_scientific_journal-1767	32	12	not	not	PART
american_scientific_journal-1767	32	13	need	need	VERB
american_scientific_journal-1767	32	14	to	to	PART
american_scientific_journal-1767	32	15	be	be	AUX
american_scientific_journal-1767	32	16	the	the	DET
american_scientific_journal-1767	32	17	same	same	ADJ
american_scientific_journal-1767	32	18	and	and	CCONJ
american_scientific_journal-1767	32	19	we	we	PRON
american_scientific_journal-1767	32	20	take	take	VERB
american_scientific_journal-1767	32	21	this	this	PRON
american_scientific_journal-1767	32	22	to	to	PART
american_scientific_journal-1767	32	23	be	be	AUX
american_scientific_journal-1767	32	24	our	our	PRON
american_scientific_journal-1767	32	25	dissociating	dissociating	NOUN
american_scientific_journal-1767	32	26	point	point	NOUN
american_scientific_journal-1767	32	27	from	from	ADP
american_scientific_journal-1767	32	28	the	the	DET
american_scientific_journal-1767	32	29	work	work	NOUN
american_scientific_journal-1767	32	30	that	that	PRON
american_scientific_journal-1767	32	31	has	have	AUX
american_scientific_journal-1767	32	32	been	be	AUX
american_scientific_journal-1767	32	33	carried	carry	VERB
american_scientific_journal-1767	32	34	out	out	ADP
american_scientific_journal-1767	32	35	previously	previously	ADV
american_scientific_journal-1767	32	36	until	until	ADP
american_scientific_journal-1767	32	37	now	now	ADV
american_scientific_journal-1767	32	38	.	.	PUNCT
american_scientific_journal-1767	33	1	intuitively	intuitively	ADV
american_scientific_journal-1767	33	2	seneviratne	seneviratne	NOUN
american_scientific_journal-1767	33	3	and	and	CCONJ
american_scientific_journal-1767	33	4	de	de	X
american_scientific_journal-1767	33	5	silva[3	silva[3	PROPN
american_scientific_journal-1767	33	6	]	]	X
american_scientific_journal-1767	33	7	have	have	AUX
american_scientific_journal-1767	33	8	also	also	ADV
american_scientific_journal-1767	33	9	used	use	VERB
american_scientific_journal-1767	33	10	different	different	ADJ
american_scientific_journal-1767	33	11	coordinates	coordinate	NOUN
american_scientific_journal-1767	33	12	in	in	ADP
american_scientific_journal-1767	33	13	their	their	PRON
american_scientific_journal-1767	33	14	work	work	NOUN
american_scientific_journal-1767	33	15	.	.	PUNCT
american_scientific_journal-1767	34	1	therefore	therefore	ADV
american_scientific_journal-1767	34	2	in	in	ADP
american_scientific_journal-1767	34	3	this	this	DET
american_scientific_journal-1767	34	4	approach	approach	NOUN
american_scientific_journal-1767	34	5	𝑟𝑟	𝑟𝑟	NOUN
american_scientific_journal-1767	34	6	=	=	PUNCT
american_scientific_journal-1767	34	7	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1767	34	8	in	in	ADP
american_scientific_journal-1767	34	9	the	the	DET
american_scientific_journal-1767	34	10	matter	matter	ADV
american_scientific_journal-1767	34	11	-	-	PUNCT
american_scientific_journal-1767	34	12	filled	fill	VERB
american_scientific_journal-1767	34	13	region	region	NOUN
american_scientific_journal-1767	34	14	corresponds	correspond	VERB
american_scientific_journal-1767	34	15	to	to	ADP
american_scientific_journal-1767	34	16	𝑑𝑑	𝑑𝑑	NOUN
american_scientific_journal-1767	34	17	=	=	SYM
american_scientific_journal-1767	34	18	𝐴𝐴	𝐴𝐴	PROPN
american_scientific_journal-1767	34	19	in	in	ADP
american_scientific_journal-1767	34	20	the	the	DET
american_scientific_journal-1767	34	21	region	region	NOUN
american_scientific_journal-1767	34	22	without	without	ADP
american_scientific_journal-1767	34	23	matter	matter	NOUN
american_scientific_journal-1767	34	24	,	,	PUNCT
american_scientific_journal-1767	34	25	outside	outside	ADP
american_scientific_journal-1767	34	26	the	the	DET
american_scientific_journal-1767	34	27	sphere	sphere	NOUN
american_scientific_journal-1767	34	28	.	.	PUNCT
american_scientific_journal-1767	35	1	a	a	DET
american_scientific_journal-1767	35	2	new	new	ADJ
american_scientific_journal-1767	35	3	set	set	NOUN
american_scientific_journal-1767	35	4	of	of	ADP
american_scientific_journal-1767	35	5	boundary	boundary	ADJ
american_scientific_journal-1767	35	6	conditions	condition	NOUN
american_scientific_journal-1767	35	7	has	have	AUX
american_scientific_journal-1767	35	8	been	be	AUX
american_scientific_journal-1767	35	9	introduced	introduce	VERB
american_scientific_journal-1767	35	10	as	as	ADP
american_scientific_journal-1767	35	11	�	�	PROPN
american_scientific_journal-1767	35	12	�	�	PROPN
american_scientific_journal-1767	35	13	𝑔𝑔𝑖𝑖𝑖𝑖𝛿𝛿𝑥𝑥𝑖𝑖	𝑔𝑔𝑖𝑖𝑖𝑖𝛿𝛿𝑥𝑥𝑖𝑖	PROPN
american_scientific_journal-1767	35	14	�	�	PROPN
american_scientific_journal-1767	35	15	𝑟𝑟=𝑎𝑎	𝑟𝑟=𝑎𝑎	NUM
american_scientific_journal-1767	35	16	=	=	SYM
american_scientific_journal-1767	35	17	�	�	PROPN
american_scientific_journal-1767	35	18	�	�	PROPN
american_scientific_journal-1767	35	19	𝐺𝐺𝑖𝑖𝑖𝑖𝛿𝛿𝑋𝑋𝑖𝑖	𝐺𝐺𝑖𝑖𝑖𝑖𝛿𝛿𝑋𝑋𝑖𝑖	NOUN
american_scientific_journal-1767	35	20	�	�	PROPN
american_scientific_journal-1767	35	21	𝑅𝑅=𝐴𝐴	𝑅𝑅=𝐴𝐴	PUNCT
american_scientific_journal-1767	35	22	(	(	PUNCT
american_scientific_journal-1767	35	23	3	3	NUM
american_scientific_journal-1767	35	24	)	)	PUNCT
american_scientific_journal-1767	35	25	�	�	PROPN
american_scientific_journal-1767	35	26	1	1	NUM
american_scientific_journal-1767	35	27	�	�	PROPN
american_scientific_journal-1767	35	28	𝑔𝑔𝑖𝑖𝑖𝑖	𝑔𝑔𝑖𝑖𝑖𝑖	NOUN
american_scientific_journal-1767	35	29	�	�	PROPN
american_scientific_journal-1767	35	30	𝑑𝑑	𝑑𝑑	PROPN
american_scientific_journal-1767	35	31	𝑑𝑑𝑥𝑥𝑖𝑖	𝑑𝑑𝑥𝑥𝑖𝑖	PROPN
american_scientific_journal-1767	35	32	�	�	PROPN
american_scientific_journal-1767	35	33	�	�	PROPN
american_scientific_journal-1767	35	34	𝑔𝑔𝑖𝑖𝑖𝑖	𝑔𝑔𝑖𝑖𝑖𝑖	PROPN
american_scientific_journal-1767	35	35	�	�	PROPN
american_scientific_journal-1767	35	36	�	�	PROPN
american_scientific_journal-1767	35	37	𝛿𝛿𝑥𝑥𝑖𝑖	𝛿𝛿𝑥𝑥𝑖𝑖	NOUN
american_scientific_journal-1767	35	38	�	�	PROPN
american_scientific_journal-1767	36	1	𝑟𝑟=𝑎𝑎	𝑟𝑟=𝑎𝑎	NUM
american_scientific_journal-1767	36	2	=	=	SYM
american_scientific_journal-1767	36	3	�	�	PROPN
american_scientific_journal-1767	36	4	1	1	NUM
american_scientific_journal-1767	36	5	�	�	PROPN
american_scientific_journal-1767	36	6	𝐺𝐺𝑖𝑖𝑖𝑖	𝐺𝐺𝑖𝑖𝑖𝑖	PROPN
american_scientific_journal-1767	36	7	�	�	PROPN
american_scientific_journal-1767	36	8	𝑑𝑑	𝑑𝑑	VERB
american_scientific_journal-1767	36	9	𝑑𝑑𝑋𝑋𝑖𝑖	𝑑𝑑𝑋𝑋𝑖𝑖	PROPN
american_scientific_journal-1767	36	10	�	�	PROPN
american_scientific_journal-1767	36	11	�	�	PROPN
american_scientific_journal-1767	36	12	𝐺𝐺𝑖𝑖𝑖𝑖	𝐺𝐺𝑖𝑖𝑖𝑖	PROPN
american_scientific_journal-1767	36	13	�	�	PROPN
american_scientific_journal-1767	36	14	�	�	PROPN
american_scientific_journal-1767	36	15	𝛿𝛿𝑋𝑋𝑖𝑖	𝛿𝛿𝑋𝑋𝑖𝑖	NOUN
american_scientific_journal-1767	36	16	�	�	PROPN
american_scientific_journal-1767	36	17	𝑅𝑅=𝐴𝐴	𝑅𝑅=𝐴𝐴	PUNCT
american_scientific_journal-1767	36	18	(	(	PUNCT
american_scientific_journal-1767	36	19	4	4	NUM
american_scientific_journal-1767	36	20	)	)	PUNCT
american_scientific_journal-1767	36	21	instead	instead	ADV
american_scientific_journal-1767	36	22	of	of	ADP
american_scientific_journal-1767	36	23	standard	standard	ADJ
american_scientific_journal-1767	36	24	boundary	boundary	ADJ
american_scientific_journal-1767	36	25	conditions	condition	NOUN
american_scientific_journal-1767	36	26	which	which	PRON
american_scientific_journal-1767	36	27	says	say	VERB
american_scientific_journal-1767	36	28	that	that	SCONJ
american_scientific_journal-1767	36	29	metric	metric	ADJ
american_scientific_journal-1767	36	30	coefficients	coefficient	NOUN
american_scientific_journal-1767	36	31	and	and	CCONJ
american_scientific_journal-1767	36	32	their	their	PRON
american_scientific_journal-1767	36	33	partial	partial	ADJ
american_scientific_journal-1767	36	34	derivatives	derivative	NOUN
american_scientific_journal-1767	36	35	are	be	AUX
american_scientific_journal-1767	36	36	continuous	continuous	ADJ
american_scientific_journal-1767	36	37	across	across	ADP
american_scientific_journal-1767	36	38	the	the	DET
american_scientific_journal-1767	36	39	boundary	boundary	NOUN
american_scientific_journal-1767	36	40	.	.	PUNCT
american_scientific_journal-1767	37	1	here	here	ADV
american_scientific_journal-1767	37	2	𝑔𝑔𝑖𝑖𝑖𝑖	𝑔𝑔𝑖𝑖𝑖𝑖	NOUN
american_scientific_journal-1767	37	3	,	,	PUNCT
american_scientific_journal-1767	37	4	𝑥𝑥𝑖𝑖	𝑥𝑥𝑖𝑖	NOUN
american_scientific_journal-1767	37	5	𝑖𝑖	𝑖𝑖	PUNCT
american_scientific_journal-1767	38	1	=	=	SYM
american_scientific_journal-1767	38	2	0,1,2,3	0,1,2,3	NUM
american_scientific_journal-1767	38	3	and	and	CCONJ
american_scientific_journal-1767	38	4	𝐺𝐺𝑖𝑖𝑖𝑖	𝐺𝐺𝑖𝑖𝑖𝑖	PROPN
american_scientific_journal-1767	38	5	,	,	PUNCT
american_scientific_journal-1767	38	6	𝑋𝑋𝑖𝑖	𝑋𝑋𝑖𝑖	PROPN
american_scientific_journal-1767	38	7	𝑖𝑖	𝑖𝑖	NOUN
american_scientific_journal-1767	39	1	=	=	SYM
american_scientific_journal-1767	39	2	0,1,2,3	0,1,2,3	NUM
american_scientific_journal-1767	39	3	are	be	AUX
american_scientific_journal-1767	39	4	metric	metric	ADJ
american_scientific_journal-1767	39	5	coefficients	coefficient	NOUN
american_scientific_journal-1767	39	6	and	and	CCONJ
american_scientific_journal-1767	39	7	coordinates	coordinate	NOUN
american_scientific_journal-1767	39	8	for	for	ADP
american_scientific_journal-1767	39	9	the	the	DET
american_scientific_journal-1767	39	10	inside	inside	NOUN
american_scientific_journal-1767	39	11	and	and	CCONJ
american_scientific_journal-1767	39	12	the	the	DET
american_scientific_journal-1767	39	13	outside	outside	NOUN
american_scientific_journal-1767	39	14	of	of	ADP
american_scientific_journal-1767	39	15	the	the	DET
american_scientific_journal-1767	39	16	sphere	sphere	NOUN
american_scientific_journal-1767	39	17	,	,	PUNCT
american_scientific_journal-1767	39	18	respectively	respectively	ADV
american_scientific_journal-1767	39	19	.	.	PUNCT
american_scientific_journal-1767	40	1	the	the	DET
american_scientific_journal-1767	40	2	boundary	boundary	ADJ
american_scientific_journal-1767	40	3	condition	condition	NOUN
american_scientific_journal-1767	40	4	(	(	PUNCT
american_scientific_journal-1767	40	5	3	3	X
american_scientific_journal-1767	40	6	)	)	PUNCT
american_scientific_journal-1767	40	7	is	be	AUX
american_scientific_journal-1767	40	8	introduced	introduce	VERB
american_scientific_journal-1767	40	9	guiding	guide	VERB
american_scientific_journal-1767	40	10	by	by	ADP
american_scientific_journal-1767	40	11	the	the	DET
american_scientific_journal-1767	40	12	notion	notion	NOUN
american_scientific_journal-1767	40	13	of	of	ADP
american_scientific_journal-1767	40	14	what	what	PRON
american_scientific_journal-1767	40	15	may	may	AUX
american_scientific_journal-1767	40	16	be	be	AUX
american_scientific_journal-1767	40	17	called	call	VERB
american_scientific_journal-1767	40	18	proper	proper	ADJ
american_scientific_journal-1767	40	19	distances	distance	NOUN
american_scientific_journal-1767	40	20	and	and	CCONJ
american_scientific_journal-1767	40	21	proper	proper	ADJ
american_scientific_journal-1767	40	22	times	time	NOUN
american_scientific_journal-1767	40	23	of	of	ADP
american_scientific_journal-1767	40	24	two	two	NUM
american_scientific_journal-1767	40	25	observers	observer	NOUN
american_scientific_journal-1767	40	26	on	on	ADP
american_scientific_journal-1767	40	27	either	either	DET
american_scientific_journal-1767	40	28	side	side	NOUN
american_scientific_journal-1767	40	29	of	of	ADP
american_scientific_journal-1767	40	30	the	the	DET
american_scientific_journal-1767	40	31	sphere	sphere	NOUN
american_scientific_journal-1767	40	32	.	.	PUNCT
american_scientific_journal-1767	41	1	the	the	DET
american_scientific_journal-1767	41	2	boundary	boundary	ADJ
american_scientific_journal-1767	41	3	condition	condition	NOUN
american_scientific_journal-1767	41	4	(	(	PUNCT
american_scientific_journal-1767	41	5	4	4	X
american_scientific_journal-1767	41	6	)	)	PUNCT
american_scientific_journal-1767	41	7	is	be	AUX
american_scientific_journal-1767	41	8	introduced	introduce	VERB
american_scientific_journal-1767	41	9	replacing	replace	VERB
american_scientific_journal-1767	41	10	ordinary	ordinary	ADJ
american_scientific_journal-1767	41	11	partial	partial	ADJ
american_scientific_journal-1767	41	12	derivatives	derivative	NOUN
american_scientific_journal-1767	41	13	φ∂	φ∂	NOUN
american_scientific_journal-1767	41	14	∂	∂	NUM
american_scientific_journal-1767	41	15	θ∂	θ∂	PROPN
american_scientific_journal-1767	41	16	∂	∂	NUM
american_scientific_journal-1767	41	17	∂	∂	NUM
american_scientific_journal-1767	41	18	∂	∂	NOUN
american_scientific_journal-1767	41	19	,	,	PUNCT
american_scientific_journal-1767	41	20	,	,	PUNCT
american_scientific_journal-1767	41	21	r	r	NOUN
american_scientific_journal-1767	41	22	by	by	ADP
american_scientific_journal-1767	41	23	generalized	generalized	ADJ
american_scientific_journal-1767	41	24	partial	partial	ADJ
american_scientific_journal-1767	41	25	derivatives	derivative	NOUN
american_scientific_journal-1767	41	26	in	in	ADP
american_scientific_journal-1767	41	27	curvilinear	curvilinear	PROPN
american_scientific_journal-1767	41	28	coordinates	coordinate	NOUN
american_scientific_journal-1767	41	29	in	in	ADP
american_scientific_journal-1767	41	30	the	the	DET
american_scientific_journal-1767	41	31	form	form	NOUN
american_scientific_journal-1767	41	32	�	�	PROPN
american_scientific_journal-1767	41	33	1	1	NUM
american_scientific_journal-1767	41	34	�	�	PROPN
american_scientific_journal-1767	41	35	𝑔𝑔𝑖𝑖𝑖𝑖	𝑔𝑔𝑖𝑖𝑖𝑖	NOUN
american_scientific_journal-1767	41	36	�	�	PROPN
american_scientific_journal-1767	41	37	𝑑𝑑	𝑑𝑑	PROPN
american_scientific_journal-1767	41	38	𝑑𝑑𝑥𝑥𝑖𝑖	𝑑𝑑𝑥𝑥𝑖𝑖	PROPN
american_scientific_journal-1767	41	39	�	�	PROPN
american_scientific_journal-1767	41	40	�	�	PROPN
american_scientific_journal-1767	41	41	𝑔𝑔𝑖𝑖𝑖𝑖	𝑔𝑔𝑖𝑖𝑖𝑖	PROPN
american_scientific_journal-1767	41	42	�	�	PROPN
american_scientific_journal-1767	41	43	�	�	PROPN
american_scientific_journal-1767	41	44	𝛿𝛿𝑥𝑥𝑖𝑖	𝛿𝛿𝑥𝑥𝑖𝑖	NOUN
american_scientific_journal-1767	41	45	�	�	PROPN
american_scientific_journal-1767	41	46	𝑟𝑟=𝑎𝑎	𝑟𝑟=𝑎𝑎	NUM
american_scientific_journal-1767	41	47	=	=	SYM
american_scientific_journal-1767	41	48	�	�	PROPN
american_scientific_journal-1767	41	49	1	1	NUM
american_scientific_journal-1767	41	50	�	�	PROPN
american_scientific_journal-1767	41	51	𝐺𝐺𝑖𝑖𝑖𝑖	𝐺𝐺𝑖𝑖𝑖𝑖	PROPN
american_scientific_journal-1767	41	52	�	�	PROPN
american_scientific_journal-1767	41	53	𝑑𝑑	𝑑𝑑	VERB
american_scientific_journal-1767	41	54	𝑑𝑑𝑋𝑋𝑖𝑖	𝑑𝑑𝑋𝑋𝑖𝑖	PROPN
american_scientific_journal-1767	41	55	�	�	PROPN
american_scientific_journal-1767	41	56	�	�	PROPN
american_scientific_journal-1767	41	57	𝐺𝐺𝑖𝑖𝑖𝑖	𝐺𝐺𝑖𝑖𝑖𝑖	PROPN
american_scientific_journal-1767	41	58	�	�	PROPN
american_scientific_journal-1767	41	59	�	�	PROPN
american_scientific_journal-1767	41	60	𝛿𝛿𝑋𝑋𝑖𝑖	𝛿𝛿𝑋𝑋𝑖𝑖	NOUN
american_scientific_journal-1767	41	61	�	�	PROPN
american_scientific_journal-1767	41	62	𝑅𝑅=𝐴𝐴	𝑅𝑅=𝐴𝐴	NOUN
american_scientific_journal-1767	41	63	these	these	DET
american_scientific_journal-1767	41	64	boundary	boundary	ADJ
american_scientific_journal-1767	41	65	conditions	condition	NOUN
american_scientific_journal-1767	41	66	have	have	AUX
american_scientific_journal-1767	41	67	not	not	PART
american_scientific_journal-1767	41	68	been	be	AUX
american_scientific_journal-1767	41	69	used	use	VERB
american_scientific_journal-1767	41	70	previously	previously	ADV
american_scientific_journal-1767	41	71	by	by	ADP
american_scientific_journal-1767	41	72	any	any	DET
american_scientific_journal-1767	41	73	other	other	ADJ
american_scientific_journal-1767	41	74	authors	author	NOUN
american_scientific_journal-1767	41	75	,	,	PUNCT
american_scientific_journal-1767	41	76	but	but	CCONJ
american_scientific_journal-1767	41	77	have	have	AUX
american_scientific_journal-1767	41	78	been	be	AUX
american_scientific_journal-1767	41	79	used	use	VERB
american_scientific_journal-1767	41	80	intuitively	intuitively	ADV
american_scientific_journal-1767	41	81	by	by	ADP
american_scientific_journal-1767	41	82	seneviratne	seneviratne	NOUN
american_scientific_journal-1767	41	83	and	and	CCONJ
american_scientific_journal-1767	41	84	de	de	X
american_scientific_journal-1767	41	85	silva	silva	NOUN
american_scientific_journal-1767	41	86	[	[	X
american_scientific_journal-1767	41	87	3	3	NUM
american_scientific_journal-1767	41	88	]	]	PUNCT
american_scientific_journal-1767	41	89	.	.	PUNCT
american_scientific_journal-1767	42	1	first	first	ADV
american_scientific_journal-1767	42	2	let	let	VERB
american_scientific_journal-1767	42	3	us	we	PRON
american_scientific_journal-1767	42	4	write	write	VERB
american_scientific_journal-1767	42	5	the	the	DET
american_scientific_journal-1767	42	6	metrics	metric	NOUN
american_scientific_journal-1767	42	7	in	in	ADP
american_scientific_journal-1767	42	8	(	(	PUNCT
american_scientific_journal-1767	42	9	1	1	X
american_scientific_journal-1767	42	10	)	)	PUNCT
american_scientific_journal-1767	42	11	at	at	ADP
american_scientific_journal-1767	42	12	the	the	DET
american_scientific_journal-1767	42	13	boundary	boundary	ADJ
american_scientific_journal-1767	42	14	𝑟𝑟	𝑟𝑟	NOUN
american_scientific_journal-1767	42	15	=	=	SYM
american_scientific_journal-1767	42	16	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1767	42	17	and	and	CCONJ
american_scientific_journal-1767	42	18	𝑑𝑑	𝑑𝑑	VERB
american_scientific_journal-1767	42	19	=	=	SYM
american_scientific_journal-1767	42	20	𝐴𝐴	𝐴𝐴	PROPN
american_scientific_journal-1767	42	21	as	as	ADP
american_scientific_journal-1767	42	22	american	american	PROPN
american_scientific_journal-1767	42	23	scientific	scientific	PROPN
american_scientific_journal-1767	42	24	research	research	PROPN
american_scientific_journal-1767	42	25	journal	journal	NOUN
american_scientific_journal-1767	42	26	for	for	ADP
american_scientific_journal-1767	42	27	engineering	engineering	NOUN
american_scientific_journal-1767	42	28	,	,	PUNCT
american_scientific_journal-1767	42	29	technology	technology	NOUN
american_scientific_journal-1767	42	30	,	,	PUNCT
american_scientific_journal-1767	42	31	and	and	CCONJ
american_scientific_journal-1767	42	32	sciences	science	NOUN
american_scientific_journal-1767	42	33	(	(	PUNCT
american_scientific_journal-1767	42	34	asrjets	asrjet	NOUN
american_scientific_journal-1767	42	35	)	)	PUNCT
american_scientific_journal-1767	42	36	(	(	PUNCT
american_scientific_journal-1767	42	37	2016	2016	NUM
american_scientific_journal-1767	42	38	)	)	PUNCT
american_scientific_journal-1767	42	39	volume	volume	NOUN
american_scientific_journal-1767	42	40	21	21	NUM
american_scientific_journal-1767	42	41	,	,	PUNCT
american_scientific_journal-1767	42	42	no	no	DET
american_scientific_journal-1767	42	43	1	1	NUM
american_scientific_journal-1767	42	44	,	,	PUNCT
american_scientific_journal-1767	42	45	pp	pp	ADV
american_scientific_journal-1767	42	46	163	163	NUM
american_scientific_journal-1767	42	47	-	-	SYM
american_scientific_journal-1767	42	48	177	177	NUM
american_scientific_journal-1767	42	49	166	166	NUM
american_scientific_journal-1767	42	50	𝛿𝛿𝑑𝑑2	𝛿𝛿𝑑𝑑2	NOUN
american_scientific_journal-1767	42	51	=	=	SYM
american_scientific_journal-1767	42	52	1	1	NUM
american_scientific_journal-1767	42	53	�	�	PROPN
american_scientific_journal-1767	42	54	𝜃𝜃	𝜃𝜃	PROPN
american_scientific_journal-1767	42	55	�	�	PROPN
american_scientific_journal-1767	42	56	𝑅𝑅𝑙𝑙	𝑅𝑅𝑙𝑙	ADJ
american_scientific_journal-1767	42	57	�	�	NOUN
american_scientific_journal-1767	42	58	�	�	PROPN
american_scientific_journal-1767	42	59	2	2	NUM
american_scientific_journal-1767	42	60	𝑐𝑐2𝛿𝛿𝑡𝑡2	𝑐𝑐2𝛿𝛿𝑡𝑡2	NOUN
american_scientific_journal-1767	42	61	−	−	PROPN
american_scientific_journal-1767	42	62	�	�	PROPN
american_scientific_journal-1767	42	63	𝜃𝜃	𝜃𝜃	PROPN
american_scientific_journal-1767	42	64	�	�	PROPN
american_scientific_journal-1767	42	65	𝑅𝑅	𝑅𝑅	PROPN
american_scientific_journal-1767	42	66	𝑙𝑙	𝑙𝑙	PROPN
american_scientific_journal-1767	42	67	�	�	PROPN
american_scientific_journal-1767	42	68	�	�	PROPN
american_scientific_journal-1767	42	69	2	2	NUM
american_scientific_journal-1767	42	70	�	�	NOUN
american_scientific_journal-1767	42	71	𝛿𝛿𝑟𝑟2	𝛿𝛿𝑟𝑟2	NOUN
american_scientific_journal-1767	42	72	+	+	CCONJ
american_scientific_journal-1767	42	73	𝑟𝑟2(𝛿𝛿θ2	𝑟𝑟2(𝛿𝛿θ2	NUM
american_scientific_journal-1767	42	74	+	+	CCONJ
american_scientific_journal-1767	42	75	sin2	sin2	NOUN
american_scientific_journal-1767	42	76	θ	θ	PROPN
american_scientific_journal-1767	42	77	𝛿𝛿φ2	𝛿𝛿φ2	PROPN
american_scientific_journal-1767	42	78	)	)	PUNCT
american_scientific_journal-1767	42	79	�	�	PROPN
american_scientific_journal-1767	42	80	𝛿𝛿𝑑𝑑2	𝛿𝛿𝑑𝑑2	PROPN
american_scientific_journal-1767	42	81	=	=	SYM
american_scientific_journal-1767	42	82	1	1	NUM
american_scientific_journal-1767	42	83	�	�	PROPN
american_scientific_journal-1767	42	84	𝐴𝐴1	𝐴𝐴1	PROPN
american_scientific_journal-1767	42	85	+	+	PROPN
american_scientific_journal-1767	42	86	𝐴𝐴2	𝐴𝐴2	PROPN
american_scientific_journal-1767	42	87	𝑅𝑅	𝑅𝑅	PROPN
american_scientific_journal-1767	42	88	�	�	PROPN
american_scientific_journal-1767	42	89	2	2	NUM
american_scientific_journal-1767	42	90	𝑐𝑐2𝛿𝛿𝑑𝑑2	𝑐𝑐2𝛿𝛿𝑑𝑑2	NOUN
american_scientific_journal-1767	42	91	−	−	PROPN
american_scientific_journal-1767	42	92	�	�	PROPN
american_scientific_journal-1767	42	93	𝐴𝐴1	𝐴𝐴1	PROPN
american_scientific_journal-1767	42	94	+	+	CCONJ
american_scientific_journal-1767	42	95	𝐴𝐴2	𝐴𝐴2	PROPN
american_scientific_journal-1767	42	96	𝑅𝑅	𝑅𝑅	PROPN
american_scientific_journal-1767	42	97	�	�	PROPN
american_scientific_journal-1767	42	98	2	2	NUM
american_scientific_journal-1767	42	99	�	�	PROPN
american_scientific_journal-1767	42	100	𝛿𝛿𝑑𝑑2	𝛿𝛿𝑑𝑑2	PROPN
american_scientific_journal-1767	42	101	+	+	CCONJ
american_scientific_journal-1767	42	102	𝑑𝑑2	𝑑𝑑2	PROPN
american_scientific_journal-1767	42	103	�	�	NOUN
american_scientific_journal-1767	42	104	𝛿𝛿θ	𝛿𝛿θ	VERB
american_scientific_journal-1767	42	105	2	2	NUM
american_scientific_journal-1767	42	106	+	+	NUM
american_scientific_journal-1767	42	107	sin2	sin2	NOUN
american_scientific_journal-1767	42	108	θ	θ	PROPN
american_scientific_journal-1767	42	109	𝛿𝛿φ	𝛿𝛿φ	VERB
american_scientific_journal-1767	42	110	2	2	NUM
american_scientific_journal-1767	42	111	�	�	PROPN
american_scientific_journal-1767	42	112	�	�	PROPN
american_scientific_journal-1767	42	113	(	(	PUNCT
american_scientific_journal-1767	42	114	5	5	NUM
american_scientific_journal-1767	42	115	)	)	PUNCT
american_scientific_journal-1767	42	116	from	from	ADP
american_scientific_journal-1767	42	117	isotropy	isotropy	NOUN
american_scientific_journal-1767	42	118	θ	θ	PROPN
american_scientific_journal-1767	42	119	has	have	VERB
american_scientific_journal-1767	42	120	to	to	PART
american_scientific_journal-1767	42	121	be	be	AUX
american_scientific_journal-1767	42	122	equal	equal	ADJ
american_scientific_journal-1767	42	123	to	to	ADP
american_scientific_journal-1767	42	124	θ	θ	PROPN
american_scientific_journal-1767	42	125	and	and	CCONJ
american_scientific_journal-1767	42	126	φ	φ	PROPN
american_scientific_journal-1767	42	127	has	have	VERB
american_scientific_journal-1767	42	128	to	to	PART
american_scientific_journal-1767	42	129	be	be	AUX
american_scientific_journal-1767	42	130	equal	equal	ADJ
american_scientific_journal-1767	42	131	to	to	ADP
american_scientific_journal-1767	42	132	φ	φ	NUM
american_scientific_journal-1767	42	133	which	which	PRON
american_scientific_journal-1767	42	134	implies	imply	VERB
american_scientific_journal-1767	42	135	that	that	SCONJ
american_scientific_journal-1767	42	136	ω	ω	PROPN
american_scientific_journal-1767	42	137	=	=	PROPN
american_scientific_journal-1767	42	138	ω	ω	PROPN
american_scientific_journal-1767	42	139	.	.	PUNCT
american_scientific_journal-1767	43	1	hence	hence	ADV
american_scientific_journal-1767	43	2	the	the	DET
american_scientific_journal-1767	43	3	metrics	metric	NOUN
american_scientific_journal-1767	43	4	(	(	PUNCT
american_scientific_journal-1767	43	5	1	1	X
american_scientific_journal-1767	43	6	)	)	PUNCT
american_scientific_journal-1767	43	7	take	take	VERB
american_scientific_journal-1767	43	8	the	the	DET
american_scientific_journal-1767	43	9	form	form	NOUN
american_scientific_journal-1767	43	10	𝑑𝑑𝑑𝑑2	𝑑𝑑𝑑𝑑2	PUNCT
american_scientific_journal-1767	44	1	=	=	SYM
american_scientific_journal-1767	44	2	1	1	NUM
american_scientific_journal-1767	44	3	�	�	PROPN
american_scientific_journal-1767	44	4	𝜃𝜃	𝜃𝜃	PROPN
american_scientific_journal-1767	44	5	�	�	PROPN
american_scientific_journal-1767	44	6	𝑅𝑅𝑙𝑙	𝑅𝑅𝑙𝑙	ADJ
american_scientific_journal-1767	44	7	�	�	NOUN
american_scientific_journal-1767	44	8	�	�	PROPN
american_scientific_journal-1767	44	9	2	2	NUM
american_scientific_journal-1767	44	10	𝑐𝑐2𝑑𝑑𝑡𝑡2	𝑐𝑐2𝑑𝑑𝑡𝑡2	NOUN
american_scientific_journal-1767	44	11	−	−	PROPN
american_scientific_journal-1767	44	12	�	�	PROPN
american_scientific_journal-1767	44	13	𝜃𝜃	𝜃𝜃	PROPN
american_scientific_journal-1767	44	14	�	�	PROPN
american_scientific_journal-1767	44	15	𝑅𝑅	𝑅𝑅	PROPN
american_scientific_journal-1767	44	16	𝑙𝑙	𝑙𝑙	PROPN
american_scientific_journal-1767	44	17	�	�	PROPN
american_scientific_journal-1767	44	18	�	�	PROPN
american_scientific_journal-1767	44	19	2	2	NUM
american_scientific_journal-1767	44	20	(	(	PUNCT
american_scientific_journal-1767	44	21	𝑑𝑑𝑟𝑟2	𝑑𝑑𝑟𝑟2	X
american_scientific_journal-1767	44	22	+	+	CCONJ
american_scientific_journal-1767	44	23	𝑟𝑟2𝑑𝑑ω2	𝑟𝑟2𝑑𝑑ω2	PROPN
american_scientific_journal-1767	44	24	)	)	PUNCT
american_scientific_journal-1767	44	25	0	0	NUM
american_scientific_journal-1767	45	1	≤	≤	NUM
american_scientific_journal-1767	45	2	𝑟𝑟	𝑟𝑟	ADP
american_scientific_journal-1767	45	3	≤	≤	NUM
american_scientific_journal-1767	45	4	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1767	45	5	𝑑𝑑𝑑𝑑2	𝑑𝑑𝑑𝑑2	PROPN
american_scientific_journal-1767	45	6	=	=	SYM
american_scientific_journal-1767	45	7	1	1	NUM
american_scientific_journal-1767	45	8	�	�	PROPN
american_scientific_journal-1767	45	9	1+𝐴𝐴2𝑅𝑅	1+𝐴𝐴2𝑅𝑅	NUM
american_scientific_journal-1767	45	10	�	�	PROPN
american_scientific_journal-1767	45	11	2	2	NUM
american_scientific_journal-1767	45	12	𝑐𝑐2𝑑𝑑𝑑𝑑2	𝑐𝑐2𝑑𝑑𝑑𝑑2	SYM
american_scientific_journal-1767	45	13	−	−	PROPN
american_scientific_journal-1767	45	14	�	�	NOUN
american_scientific_journal-1767	45	15	1	1	NUM
american_scientific_journal-1767	45	16	+	+	NOUN
american_scientific_journal-1767	45	17	𝐴𝐴2	𝐴𝐴2	PROPN
american_scientific_journal-1767	45	18	𝑅𝑅	𝑅𝑅	PROPN
american_scientific_journal-1767	45	19	�	�	PROPN
american_scientific_journal-1767	45	20	2	2	NUM
american_scientific_journal-1767	45	21	(	(	PUNCT
american_scientific_journal-1767	45	22	𝑑𝑑𝑑𝑑2	𝑑𝑑𝑑𝑑2	PROPN
american_scientific_journal-1767	45	23	+	+	CCONJ
american_scientific_journal-1767	45	24	𝑑𝑑2𝑑𝑑ω2	𝑑𝑑2𝑑𝑑ω2	PROPN
american_scientific_journal-1767	45	25	)	)	PUNCT
american_scientific_journal-1767	45	26	𝐴𝐴	𝐴𝐴	PROPN
american_scientific_journal-1767	45	27	<	<	X
american_scientific_journal-1767	45	28	𝑑𝑑	𝑑𝑑	X
american_scientific_journal-1767	45	29	(	(	PUNCT
american_scientific_journal-1767	45	30	6	6	NUM
american_scientific_journal-1767	45	31	)	)	PUNCT
american_scientific_journal-1767	45	32	hence	hence	ADV
american_scientific_journal-1767	45	33	(	(	PUNCT
american_scientific_journal-1767	45	34	5	5	NUM
american_scientific_journal-1767	45	35	)	)	PUNCT
american_scientific_journal-1767	45	36	now	now	ADV
american_scientific_journal-1767	45	37	takes	take	VERB
american_scientific_journal-1767	45	38	the	the	DET
american_scientific_journal-1767	45	39	form	form	NOUN
american_scientific_journal-1767	45	40	𝛿𝛿𝑑𝑑2	𝛿𝛿𝑑𝑑2	PROPN
american_scientific_journal-1767	45	41	=	=	SYM
american_scientific_journal-1767	45	42	1	1	NUM
american_scientific_journal-1767	45	43	�	�	PROPN
american_scientific_journal-1767	45	44	𝜃𝜃	𝜃𝜃	PROPN
american_scientific_journal-1767	45	45	�	�	PROPN
american_scientific_journal-1767	45	46	𝑅𝑅𝑙𝑙	𝑅𝑅𝑙𝑙	ADJ
american_scientific_journal-1767	45	47	�	�	NOUN
american_scientific_journal-1767	45	48	�	�	PROPN
american_scientific_journal-1767	45	49	2	2	NUM
american_scientific_journal-1767	45	50	𝑐𝑐2𝛿𝛿𝑡𝑡2	𝑐𝑐2𝛿𝛿𝑡𝑡2	NOUN
american_scientific_journal-1767	45	51	−	−	PROPN
american_scientific_journal-1767	45	52	�	�	PROPN
american_scientific_journal-1767	45	53	𝜃𝜃	𝜃𝜃	PROPN
american_scientific_journal-1767	45	54	�	�	PROPN
american_scientific_journal-1767	45	55	𝑅𝑅	𝑅𝑅	PROPN
american_scientific_journal-1767	45	56	𝑙𝑙	𝑙𝑙	PROPN
american_scientific_journal-1767	45	57	�	�	PROPN
american_scientific_journal-1767	45	58	�	�	PROPN
american_scientific_journal-1767	45	59	2	2	NUM
american_scientific_journal-1767	45	60	�	�	NOUN
american_scientific_journal-1767	45	61	𝛿𝛿𝑟𝑟2	𝛿𝛿𝑟𝑟2	NOUN
american_scientific_journal-1767	45	62	+	+	CCONJ
american_scientific_journal-1767	45	63	𝑟𝑟2(𝛿𝛿θ2	𝑟𝑟2(𝛿𝛿θ2	NUM
american_scientific_journal-1767	45	64	+	+	CCONJ
american_scientific_journal-1767	45	65	sin2	sin2	NOUN
american_scientific_journal-1767	45	66	θ	θ	PROPN
american_scientific_journal-1767	45	67	𝛿𝛿φ2	𝛿𝛿φ2	PROPN
american_scientific_journal-1767	45	68	)	)	PUNCT
american_scientific_journal-1767	45	69	�	�	PROPN
american_scientific_journal-1767	45	70	𝛿𝛿𝑑𝑑2	𝛿𝛿𝑑𝑑2	PROPN
american_scientific_journal-1767	46	1	=	=	SYM
american_scientific_journal-1767	46	2	1	1	NUM
american_scientific_journal-1767	46	3	�	�	PROPN
american_scientific_journal-1767	46	4	1+𝐴𝐴2𝑅𝑅	1+𝐴𝐴2𝑅𝑅	NUM
american_scientific_journal-1767	46	5	�	�	SYM
american_scientific_journal-1767	46	6	2	2	NUM
american_scientific_journal-1767	46	7	𝑐𝑐2𝛿𝛿𝑑𝑑2	𝑐𝑐2𝛿𝛿𝑑𝑑2	NOUN
american_scientific_journal-1767	46	8	−	−	PROPN
american_scientific_journal-1767	46	9	�	�	PROPN
american_scientific_journal-1767	46	10	1	1	NUM
american_scientific_journal-1767	46	11	+	+	NOUN
american_scientific_journal-1767	46	12	𝐴𝐴2	𝐴𝐴2	PROPN
american_scientific_journal-1767	46	13	𝑅𝑅	𝑅𝑅	PROPN
american_scientific_journal-1767	46	14	�	�	PROPN
american_scientific_journal-1767	46	15	2	2	NUM
american_scientific_journal-1767	46	16	�	�	PROPN
american_scientific_journal-1767	46	17	𝛿𝛿𝑑𝑑2	𝛿𝛿𝑑𝑑2	NOUN
american_scientific_journal-1767	46	18	+	+	CCONJ
american_scientific_journal-1767	46	19	𝑑𝑑2(𝛿𝛿θ2	𝑑𝑑2(𝛿𝛿θ2	PROPN
american_scientific_journal-1767	46	20	+	+	CCONJ
american_scientific_journal-1767	46	21	sin2	sin2	NOUN
american_scientific_journal-1767	46	22	θ	θ	PROPN
american_scientific_journal-1767	46	23	𝛿𝛿φ2	𝛿𝛿φ2	PROPN
american_scientific_journal-1767	46	24	)	)	PUNCT
american_scientific_journal-1767	46	25	�	�	PROPN
american_scientific_journal-1767	46	26	(	(	PUNCT
american_scientific_journal-1767	46	27	7	7	NUM
american_scientific_journal-1767	46	28	)	)	PUNCT
american_scientific_journal-1767	46	29	at	at	ADP
american_scientific_journal-1767	46	30	the	the	DET
american_scientific_journal-1767	46	31	boundary	boundary	NOUN
american_scientific_journal-1767	46	32	of	of	ADP
american_scientific_journal-1767	46	33	the	the	DET
american_scientific_journal-1767	46	34	sphere	sphere	NOUN
american_scientific_journal-1767	46	35	.	.	PUNCT
american_scientific_journal-1767	47	1	application	application	NOUN
american_scientific_journal-1767	47	2	of	of	ADP
american_scientific_journal-1767	47	3	the	the	DET
american_scientific_journal-1767	47	4	first	first	ADJ
american_scientific_journal-1767	47	5	boundary	boundary	ADJ
american_scientific_journal-1767	47	6	condition	condition	NOUN
american_scientific_journal-1767	47	7	(	(	PUNCT
american_scientific_journal-1767	47	8	3	3	NUM
american_scientific_journal-1767	47	9	)	)	PUNCT
american_scientific_journal-1767	47	10	for	for	ADP
american_scientific_journal-1767	47	11	tt	tt	PROPN
american_scientific_journal-1767	47	12	and	and	CCONJ
american_scientific_journal-1767	47	13	on	on	ADP
american_scientific_journal-1767	47	14	the	the	DET
american_scientific_journal-1767	47	15	boundary	boundary	NOUN
american_scientific_journal-1767	47	16	(	(	PUNCT
american_scientific_journal-1767	47	17	𝑟𝑟	𝑟𝑟	NOUN
american_scientific_journal-1767	47	18	=	=	SYM
american_scientific_journal-1767	47	19	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1767	47	20	and	and	CCONJ
american_scientific_journal-1767	47	21	𝑑𝑑	𝑑𝑑	VERB
american_scientific_journal-1767	47	22	=	=	SYM
american_scientific_journal-1767	47	23	𝐴𝐴	𝐴𝐴	PROPN
american_scientific_journal-1767	47	24	)	)	PUNCT
american_scientific_journal-1767	47	25	gives	give	VERB
american_scientific_journal-1767	47	26	1	1	NUM
american_scientific_journal-1767	47	27	𝜃𝜃	𝜃𝜃	PROPN
american_scientific_journal-1767	47	28	�	�	PROPN
american_scientific_journal-1767	47	29	𝑎𝑎𝑙𝑙	𝑎𝑎𝑙𝑙	PROPN
american_scientific_journal-1767	47	30	�	�	PROPN
american_scientific_journal-1767	47	31	𝑐𝑐	𝑐𝑐	PROPN
american_scientific_journal-1767	47	32	𝛿𝛿𝑡𝑡	𝛿𝛿𝑡𝑡	NOUN
american_scientific_journal-1767	47	33	=	=	SYM
american_scientific_journal-1767	47	34	1	1	NUM
american_scientific_journal-1767	47	35	�	�	PROPN
american_scientific_journal-1767	47	36	1+𝐴𝐴2𝐴𝐴	1+𝐴𝐴2𝐴𝐴	NUM
american_scientific_journal-1767	47	37	�	�	PROPN
american_scientific_journal-1767	47	38	𝑐𝑐	𝑐𝑐	PROPN
american_scientific_journal-1767	47	39	𝛿𝛿𝑑𝑑	𝛿𝛿𝑑𝑑	NOUN
american_scientific_journal-1767	47	40	𝛿𝛿𝛿𝛿	𝛿𝛿𝛿𝛿	NOUN
american_scientific_journal-1767	47	41	𝛿𝛿𝛿𝛿	𝛿𝛿𝛿𝛿	PROPN
american_scientific_journal-1767	47	42	=	=	SYM
american_scientific_journal-1767	47	43	𝜃𝜃	𝜃𝜃	PROPN
american_scientific_journal-1767	47	44	�	�	PROPN
american_scientific_journal-1767	47	45	𝑎𝑎𝑙𝑙	𝑎𝑎𝑙𝑙	PROPN
american_scientific_journal-1767	47	46	�	�	PROPN
american_scientific_journal-1767	47	47	�	�	PROPN
american_scientific_journal-1767	47	48	1+𝐴𝐴2𝐴𝐴	1+𝐴𝐴2𝐴𝐴	NUM
american_scientific_journal-1767	47	49	�	�	PROPN
american_scientific_journal-1767	47	50	(	(	PUNCT
american_scientific_journal-1767	47	51	8)	8)	NUM
american_scientific_journal-1767	47	52	application	application	NOUN
american_scientific_journal-1767	47	53	of	of	ADP
american_scientific_journal-1767	47	54	the	the	DET
american_scientific_journal-1767	47	55	second	second	ADJ
american_scientific_journal-1767	47	56	boundary	boundary	ADJ
american_scientific_journal-1767	47	57	condition	condition	NOUN
american_scientific_journal-1767	47	58	(	(	PUNCT
american_scientific_journal-1767	47	59	4	4	NUM
american_scientific_journal-1767	47	60	)	)	PUNCT
american_scientific_journal-1767	47	61	for	for	ADP
american_scientific_journal-1767	47	62	tt	tt	PROPN
american_scientific_journal-1767	47	63	and	and	CCONJ
american_scientific_journal-1767	47	64	on	on	ADP
american_scientific_journal-1767	47	65	the	the	DET
american_scientific_journal-1767	47	66	boundary	boundary	NOUN
american_scientific_journal-1767	47	67	(	(	PUNCT
american_scientific_journal-1767	47	68	𝑟𝑟	𝑟𝑟	NOUN
american_scientific_journal-1767	47	69	=	=	SYM
american_scientific_journal-1767	47	70	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1767	47	71	and	and	CCONJ
american_scientific_journal-1767	47	72	𝑑𝑑	𝑑𝑑	VERB
american_scientific_journal-1767	47	73	=	=	SYM
american_scientific_journal-1767	47	74	𝐴𝐴	𝐴𝐴	PROPN
american_scientific_journal-1767	47	75	)	)	PUNCT
american_scientific_journal-1767	47	76	gives	give	VERB
american_scientific_journal-1767	47	77	1	1	NUM
american_scientific_journal-1767	47	78	𝜃𝜃	𝜃𝜃	PROPN
american_scientific_journal-1767	47	79	�	�	PROPN
american_scientific_journal-1767	47	80	𝑎𝑎𝑙𝑙	𝑎𝑎𝑙𝑙	PROPN
american_scientific_journal-1767	47	81	�	�	PROPN
american_scientific_journal-1767	47	82	�	�	PROPN
american_scientific_journal-1767	47	83	−	−	PROPN
american_scientific_journal-1767	47	84	1	1	NUM
american_scientific_journal-1767	47	85	�	�	PROPN
american_scientific_journal-1767	47	86	𝜃𝜃	𝜃𝜃	PROPN
american_scientific_journal-1767	47	87	�	�	PROPN
american_scientific_journal-1767	47	88	𝑎𝑎𝑙𝑙	𝑎𝑎𝑙𝑙	PROPN
american_scientific_journal-1767	47	89	�	�	PROPN
american_scientific_journal-1767	47	90	�	�	PROPN
american_scientific_journal-1767	47	91	2	2	NUM
american_scientific_journal-1767	47	92	1	1	NUM
american_scientific_journal-1767	47	93	𝑙𝑙	𝑙𝑙	NOUN
american_scientific_journal-1767	47	94	𝜃𝜃′	𝜃𝜃′	NOUN
american_scientific_journal-1767	47	95	�	�	NOUN
american_scientific_journal-1767	47	96	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1767	47	97	𝑙𝑙	𝑙𝑙	PROPN
american_scientific_journal-1767	47	98	�	�	PROPN
american_scientific_journal-1767	47	99	�	�	PROPN
american_scientific_journal-1767	47	100	𝑐𝑐	𝑐𝑐	NOUN
american_scientific_journal-1767	47	101	𝛿𝛿𝑡𝑡	𝛿𝛿𝑡𝑡	NOUN
american_scientific_journal-1767	47	102	=	=	SYM
american_scientific_journal-1767	47	103	1	1	NUM
american_scientific_journal-1767	47	104	�	�	PROPN
american_scientific_journal-1767	47	105	1+𝐴𝐴2𝐴𝐴	1+𝐴𝐴2𝐴𝐴	NUM
american_scientific_journal-1767	47	106	�	�	PROPN
american_scientific_journal-1767	47	107	�	�	PROPN
american_scientific_journal-1767	47	108	−	−	PROPN
american_scientific_journal-1767	47	109	1	1	NUM
american_scientific_journal-1767	47	110	�	�	PROPN
american_scientific_journal-1767	47	111	1+𝐴𝐴2𝐴𝐴	1+𝐴𝐴2𝐴𝐴	NUM
american_scientific_journal-1767	47	112	�	�	PROPN
american_scientific_journal-1767	47	113	2	2	NUM
american_scientific_journal-1767	47	114	�	�	PROPN
american_scientific_journal-1767	47	115	−	−	PROPN
american_scientific_journal-1767	47	116	𝐴𝐴2	𝐴𝐴2	PROPN
american_scientific_journal-1767	47	117	𝐴𝐴2	𝐴𝐴2	PROPN
american_scientific_journal-1767	47	118	�	�	PROPN
american_scientific_journal-1767	47	119	�	�	PROPN
american_scientific_journal-1767	48	1	𝑐𝑐	𝑐𝑐	PROPN
american_scientific_journal-1767	48	2	𝛿𝛿𝑑𝑑	𝛿𝛿𝑑𝑑	NOUN
american_scientific_journal-1767	48	3	𝛿𝛿𝛿𝛿	𝛿𝛿𝛿𝛿	NOUN
american_scientific_journal-1767	48	4	𝛿𝛿𝛿𝛿	𝛿𝛿𝛿𝛿	NOUN
american_scientific_journal-1767	48	5	=	=	PUNCT
american_scientific_journal-1767	48	6	−𝐴𝐴2𝑙𝑙	−𝐴𝐴2𝑙𝑙	PROPN
american_scientific_journal-1767	48	7	�	�	PROPN
american_scientific_journal-1767	48	8	𝜃𝜃	𝜃𝜃	PROPN
american_scientific_journal-1767	48	9	�	�	PROPN
american_scientific_journal-1767	48	10	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1767	48	11	𝑙𝑙	𝑙𝑙	PRON
american_scientific_journal-1767	48	12	�	�	PROPN
american_scientific_journal-1767	48	13	�	�	PROPN
american_scientific_journal-1767	48	14	3	3	NUM
american_scientific_journal-1767	48	15	𝐴𝐴2𝜃𝜃′	𝐴𝐴2𝜃𝜃′	PROPN
american_scientific_journal-1767	48	16	�	�	PROPN
american_scientific_journal-1767	48	17	𝑎𝑎𝑙𝑙	𝑎𝑎𝑙𝑙	PROPN
american_scientific_journal-1767	48	18	�	�	PROPN
american_scientific_journal-1767	48	19	�	�	PROPN
american_scientific_journal-1767	48	20	�	�	PROPN
american_scientific_journal-1767	48	21	1	1	NUM
american_scientific_journal-1767	48	22	+	+	NOUN
american_scientific_journal-1767	48	23	𝐴𝐴2	𝐴𝐴2	PROPN
american_scientific_journal-1767	48	24	𝐴𝐴	𝐴𝐴	PROPN
american_scientific_journal-1767	48	25	�	�	PROPN
american_scientific_journal-1767	48	26	�	�	PROPN
american_scientific_journal-1767	48	27	3	3	NUM
american_scientific_journal-1767	48	28	(	(	PUNCT
american_scientific_journal-1767	48	29	9	9	NUM
american_scientific_journal-1767	48	30	)	)	PUNCT
american_scientific_journal-1767	48	31	american	american	ADJ
american_scientific_journal-1767	48	32	scientific	scientific	ADJ
american_scientific_journal-1767	48	33	research	research	NOUN
american_scientific_journal-1767	48	34	journal	journal	NOUN
american_scientific_journal-1767	48	35	for	for	ADP
american_scientific_journal-1767	48	36	engineering	engineering	NOUN
american_scientific_journal-1767	48	37	,	,	PUNCT
american_scientific_journal-1767	48	38	technology	technology	NOUN
american_scientific_journal-1767	48	39	,	,	PUNCT
american_scientific_journal-1767	48	40	and	and	CCONJ
american_scientific_journal-1767	48	41	sciences	science	NOUN
american_scientific_journal-1767	48	42	(	(	PUNCT
american_scientific_journal-1767	48	43	asrjets	asrjet	NOUN
american_scientific_journal-1767	48	44	)	)	PUNCT
american_scientific_journal-1767	48	45	(	(	PUNCT
american_scientific_journal-1767	48	46	2016	2016	NUM
american_scientific_journal-1767	48	47	)	)	PUNCT
american_scientific_journal-1767	48	48	volume	volume	NOUN
american_scientific_journal-1767	48	49	21	21	NUM
american_scientific_journal-1767	48	50	,	,	PUNCT
american_scientific_journal-1767	48	51	no	no	DET
american_scientific_journal-1767	48	52	1	1	NUM
american_scientific_journal-1767	48	53	,	,	PUNCT
american_scientific_journal-1767	48	54	pp	pp	ADV
american_scientific_journal-1767	48	55	163	163	NUM
american_scientific_journal-1767	48	56	-	-	SYM
american_scientific_journal-1767	48	57	177	177	NUM
american_scientific_journal-1767	48	58	167	167	NUM
american_scientific_journal-1767	48	59	where	where	SCONJ
american_scientific_journal-1767	48	60	“	"	PUNCT
american_scientific_journal-1767	48	61	′	′	NUM
american_scientific_journal-1767	48	62	”	"	PUNCT
american_scientific_journal-1767	48	63	denotes	denote	VERB
american_scientific_journal-1767	48	64	the	the	DET
american_scientific_journal-1767	48	65	differentiation	differentiation	NOUN
american_scientific_journal-1767	48	66	with	with	ADP
american_scientific_journal-1767	48	67	respect	respect	NOUN
american_scientific_journal-1767	48	68	to	to	ADP
american_scientific_journal-1767	48	69	𝑟𝑟	𝑟𝑟	PROPN
american_scientific_journal-1767	48	70	.	.	PUNCT
american_scientific_journal-1767	49	1	application	application	NOUN
american_scientific_journal-1767	49	2	of	of	ADP
american_scientific_journal-1767	49	3	the	the	DET
american_scientific_journal-1767	49	4	first	first	ADJ
american_scientific_journal-1767	49	5	boundary	boundary	ADJ
american_scientific_journal-1767	49	6	condition	condition	NOUN
american_scientific_journal-1767	49	7	(	(	PUNCT
american_scientific_journal-1767	49	8	3	3	NUM
american_scientific_journal-1767	49	9	)	)	PUNCT
american_scientific_journal-1767	49	10	for	for	ADP
american_scientific_journal-1767	49	11	rr	rr	NOUN
american_scientific_journal-1767	49	12	and	and	CCONJ
american_scientific_journal-1767	49	13	on	on	ADP
american_scientific_journal-1767	49	14	the	the	DET
american_scientific_journal-1767	49	15	boundary	boundary	NOUN
american_scientific_journal-1767	49	16	(	(	PUNCT
american_scientific_journal-1767	49	17	𝑟𝑟	𝑟𝑟	NOUN
american_scientific_journal-1767	49	18	=	=	SYM
american_scientific_journal-1767	49	19	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1767	49	20	and	and	CCONJ
american_scientific_journal-1767	49	21	𝑑𝑑	𝑑𝑑	VERB
american_scientific_journal-1767	49	22	=	=	SYM
american_scientific_journal-1767	49	23	𝐴𝐴	𝐴𝐴	PROPN
american_scientific_journal-1767	49	24	)	)	PUNCT
american_scientific_journal-1767	49	25	gives	give	VERB
american_scientific_journal-1767	49	26	𝜃𝜃	𝜃𝜃	PROPN
american_scientific_journal-1767	49	27	�	�	PROPN
american_scientific_journal-1767	49	28	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1767	49	29	𝑙𝑙	𝑙𝑙	PROPN
american_scientific_journal-1767	49	30	�	�	PROPN
american_scientific_journal-1767	49	31	𝛿𝛿𝑟𝑟	𝛿𝛿𝑟𝑟	NOUN
american_scientific_journal-1767	49	32	=	=	SYM
american_scientific_journal-1767	49	33	�	�	PROPN
american_scientific_journal-1767	49	34	1	1	NUM
american_scientific_journal-1767	49	35	+	+	CCONJ
american_scientific_journal-1767	49	36	𝐴𝐴2	𝐴𝐴2	PROPN
american_scientific_journal-1767	49	37	𝐴𝐴	𝐴𝐴	PROPN
american_scientific_journal-1767	49	38	�	�	PROPN
american_scientific_journal-1767	49	39	𝛿𝛿𝑑𝑑	𝛿𝛿𝑑𝑑	PROPN
american_scientific_journal-1767	49	40	𝛿𝛿𝑟𝑟	𝛿𝛿𝑟𝑟	NOUN
american_scientific_journal-1767	49	41	𝛿𝛿𝑅𝑅	𝛿𝛿𝑅𝑅	NOUN
american_scientific_journal-1767	49	42	=	=	SYM
american_scientific_journal-1767	49	43	�	�	PROPN
american_scientific_journal-1767	49	44	1+𝐴𝐴2𝐴𝐴	1+𝐴𝐴2𝐴𝐴	NUM
american_scientific_journal-1767	49	45	�	�	PROPN
american_scientific_journal-1767	49	46	𝜃𝜃	𝜃𝜃	PROPN
american_scientific_journal-1767	49	47	�	�	PROPN
american_scientific_journal-1767	49	48	𝑎𝑎𝑙𝑙	𝑎𝑎𝑙𝑙	PROPN
american_scientific_journal-1767	49	49	�	�	PROPN
american_scientific_journal-1767	49	50	(	(	PUNCT
american_scientific_journal-1767	49	51	10	10	NUM
american_scientific_journal-1767	49	52	)	)	PUNCT
american_scientific_journal-1767	49	53	application	application	NOUN
american_scientific_journal-1767	49	54	of	of	ADP
american_scientific_journal-1767	49	55	the	the	DET
american_scientific_journal-1767	49	56	second	second	ADJ
american_scientific_journal-1767	49	57	boundary	boundary	ADJ
american_scientific_journal-1767	49	58	condition	condition	NOUN
american_scientific_journal-1767	49	59	(	(	PUNCT
american_scientific_journal-1767	49	60	4	4	NUM
american_scientific_journal-1767	49	61	)	)	PUNCT
american_scientific_journal-1767	49	62	for	for	ADP
american_scientific_journal-1767	49	63	rr	rr	NOUN
american_scientific_journal-1767	49	64	and	and	CCONJ
american_scientific_journal-1767	49	65	on	on	ADP
american_scientific_journal-1767	49	66	the	the	DET
american_scientific_journal-1767	49	67	boundary	boundary	NOUN
american_scientific_journal-1767	49	68	(	(	PUNCT
american_scientific_journal-1767	49	69	𝑟𝑟	𝑟𝑟	NOUN
american_scientific_journal-1767	49	70	=	=	SYM
american_scientific_journal-1767	49	71	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1767	49	72	and	and	CCONJ
american_scientific_journal-1767	49	73	𝑑𝑑	𝑑𝑑	VERB
american_scientific_journal-1767	49	74	=	=	SYM
american_scientific_journal-1767	49	75	𝐴𝐴	𝐴𝐴	PROPN
american_scientific_journal-1767	49	76	)	)	PUNCT
american_scientific_journal-1767	49	77	gives	give	VERB
american_scientific_journal-1767	49	78	1	1	NUM
american_scientific_journal-1767	49	79	𝜃𝜃	𝜃𝜃	PROPN
american_scientific_journal-1767	49	80	�	�	PROPN
american_scientific_journal-1767	49	81	𝑎𝑎𝑙𝑙	𝑎𝑎𝑙𝑙	PROPN
american_scientific_journal-1767	49	82	�	�	PROPN
american_scientific_journal-1767	49	83	�	�	PROPN
american_scientific_journal-1767	49	84	1	1	NUM
american_scientific_journal-1767	49	85	𝑙𝑙	𝑙𝑙	NOUN
american_scientific_journal-1767	49	86	𝜃𝜃′	𝜃𝜃′	NOUN
american_scientific_journal-1767	49	87	�	�	NOUN
american_scientific_journal-1767	49	88	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1767	49	89	𝑙𝑙	𝑙𝑙	PROPN
american_scientific_journal-1767	49	90	�	�	PROPN
american_scientific_journal-1767	49	91	�	�	PROPN
american_scientific_journal-1767	49	92	𝛿𝛿𝑟𝑟	𝛿𝛿𝑟𝑟	NOUN
american_scientific_journal-1767	49	93	=	=	SYM
american_scientific_journal-1767	49	94	1	1	NUM
american_scientific_journal-1767	49	95	�	�	PROPN
american_scientific_journal-1767	49	96	1+𝐴𝐴2𝐴𝐴	1+𝐴𝐴2𝐴𝐴	NUM
american_scientific_journal-1767	49	97	�	�	PROPN
american_scientific_journal-1767	49	98	�	�	PROPN
american_scientific_journal-1767	49	99	−	−	PROPN
american_scientific_journal-1767	49	100	𝐴𝐴2	𝐴𝐴2	PROPN
american_scientific_journal-1767	49	101	𝐴𝐴2	𝐴𝐴2	PROPN
american_scientific_journal-1767	49	102	�	�	PROPN
american_scientific_journal-1767	49	103	𝛿𝛿𝑑𝑑	𝛿𝛿𝑑𝑑	PROPN
american_scientific_journal-1767	49	104	𝛿𝛿𝑟𝑟	𝛿𝛿𝑟𝑟	NOUN
american_scientific_journal-1767	49	105	𝛿𝛿𝑅𝑅	𝛿𝛿𝑅𝑅	PROPN
american_scientific_journal-1767	49	106	=	=	SYM
american_scientific_journal-1767	49	107	𝜃𝜃	𝜃𝜃	PROPN
american_scientific_journal-1767	49	108	�	�	PROPN
american_scientific_journal-1767	49	109	𝑎𝑎𝑙𝑙	𝑎𝑎𝑙𝑙	PROPN
american_scientific_journal-1767	49	110	�	�	PROPN
american_scientific_journal-1767	49	111	�	�	PROPN
american_scientific_journal-1767	49	112	1+𝐴𝐴2𝐴𝐴	1+𝐴𝐴2𝐴𝐴	NUM
american_scientific_journal-1767	49	113	�	�	PROPN
american_scientific_journal-1767	49	114	�	�	PROPN
american_scientific_journal-1767	49	115	−𝐴𝐴2𝑙𝑙	−𝐴𝐴2𝑙𝑙	PROPN
american_scientific_journal-1767	49	116	𝐴𝐴2𝜃𝜃′	𝐴𝐴2𝜃𝜃′	PROPN
american_scientific_journal-1767	49	117	�	�	PROPN
american_scientific_journal-1767	49	118	𝑎𝑎𝑙𝑙	𝑎𝑎𝑙𝑙	PROPN
american_scientific_journal-1767	49	119	�	�	PROPN
american_scientific_journal-1767	49	120	�	�	PROPN
american_scientific_journal-1767	49	121	(	(	PUNCT
american_scientific_journal-1767	49	122	11	11	NUM
american_scientific_journal-1767	49	123	)	)	PUNCT
american_scientific_journal-1767	49	124	similarly	similarly	ADV
american_scientific_journal-1767	49	125	application	application	NOUN
american_scientific_journal-1767	49	126	of	of	ADP
american_scientific_journal-1767	49	127	the	the	DET
american_scientific_journal-1767	49	128	same	same	ADJ
american_scientific_journal-1767	49	129	boundary	boundary	ADJ
american_scientific_journal-1767	49	130	conditions	condition	NOUN
american_scientific_journal-1767	49	131	(	(	PUNCT
american_scientific_journal-1767	49	132	3	3	NUM
american_scientific_journal-1767	49	133	)	)	PUNCT
american_scientific_journal-1767	49	134	and	and	CCONJ
american_scientific_journal-1767	49	135	(	(	PUNCT
american_scientific_journal-1767	49	136	4	4	X
american_scientific_journal-1767	49	137	)	)	PUNCT
american_scientific_journal-1767	49	138	for	for	ADP
american_scientific_journal-1767	49	139	the	the	DET
american_scientific_journal-1767	49	140	angular	angular	ADJ
american_scientific_journal-1767	49	141	coordinate	coordinate	NOUN
american_scientific_journal-1767	49	142	ω	ω	PROPN
american_scientific_journal-1767	49	143	in	in	ADP
american_scientific_journal-1767	49	144	the	the	DET
american_scientific_journal-1767	49	145	metric	metric	NOUN
american_scientific_journal-1767	49	146	(	(	PUNCT
american_scientific_journal-1767	49	147	7	7	NUM
american_scientific_journal-1767	49	148	)	)	PUNCT
american_scientific_journal-1767	49	149	on	on	ADP
american_scientific_journal-1767	49	150	the	the	DET
american_scientific_journal-1767	49	151	boundary	boundary	NOUN
american_scientific_journal-1767	49	152	(	(	PUNCT
american_scientific_journal-1767	49	153	𝑟𝑟	𝑟𝑟	NOUN
american_scientific_journal-1767	49	154	=	=	SYM
american_scientific_journal-1767	49	155	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1767	49	156	and	and	CCONJ
american_scientific_journal-1767	49	157	𝑑𝑑	𝑑𝑑	VERB
american_scientific_journal-1767	49	158	=	=	SYM
american_scientific_journal-1767	49	159	𝐴𝐴	𝐴𝐴	PROPN
american_scientific_journal-1767	49	160	)	)	PUNCT
american_scientific_journal-1767	49	161	gives	give	VERB
american_scientific_journal-1767	49	162	𝜃𝜃	𝜃𝜃	PROPN
american_scientific_journal-1767	49	163	�	�	PROPN
american_scientific_journal-1767	49	164	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1767	49	165	𝑙𝑙	𝑙𝑙	NOUN
american_scientific_journal-1767	49	166	�	�	PROPN
american_scientific_journal-1767	49	167	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1767	49	168	=	=	SYM
american_scientific_journal-1767	49	169	�	�	NOUN
american_scientific_journal-1767	49	170	1	1	NUM
american_scientific_journal-1767	49	171	+	+	CCONJ
american_scientific_journal-1767	49	172	𝐴𝐴2	𝐴𝐴2	PROPN
american_scientific_journal-1767	49	173	𝐴𝐴	𝐴𝐴	PROPN
american_scientific_journal-1767	49	174	�	�	PROPN
american_scientific_journal-1767	49	175	𝐴𝐴	𝐴𝐴	PROPN
american_scientific_journal-1767	49	176	(	(	PUNCT
american_scientific_journal-1767	49	177	12	12	NUM
american_scientific_journal-1767	49	178	)	)	PUNCT
american_scientific_journal-1767	49	179	1	1	NUM
american_scientific_journal-1767	49	180	𝜃𝜃	𝜃𝜃	PROPN
american_scientific_journal-1767	49	181	�	�	PROPN
american_scientific_journal-1767	49	182	𝑎𝑎𝑙𝑙	𝑎𝑎𝑙𝑙	PROPN
american_scientific_journal-1767	49	183	�	�	PROPN
american_scientific_journal-1767	49	184	�	�	PROPN
american_scientific_journal-1767	49	185	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1767	49	186	𝑙𝑙	𝑙𝑙	NOUN
american_scientific_journal-1767	49	187	𝜃𝜃′	𝜃𝜃′	NOUN
american_scientific_journal-1767	49	188	�	�	NOUN
american_scientific_journal-1767	49	189	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1767	49	190	𝑙𝑙	𝑙𝑙	PROPN
american_scientific_journal-1767	49	191	�	�	PROPN
american_scientific_journal-1767	49	192	+	+	CCONJ
american_scientific_journal-1767	49	193	𝜃𝜃	𝜃𝜃	PROPN
american_scientific_journal-1767	49	194	�	�	PROPN
american_scientific_journal-1767	49	195	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1767	49	196	𝑙𝑙	𝑙𝑙	PROPN
american_scientific_journal-1767	49	197	�	�	PROPN
american_scientific_journal-1767	49	198	�	�	PROPN
american_scientific_journal-1767	49	199	=	=	SYM
american_scientific_journal-1767	49	200	1	1	NUM
american_scientific_journal-1767	49	201	�	�	PROPN
american_scientific_journal-1767	49	202	1+𝐴𝐴2𝐴𝐴	1+𝐴𝐴2𝐴𝐴	NUM
american_scientific_journal-1767	49	203	�	�	PROPN
american_scientific_journal-1767	49	204	�	�	PROPN
american_scientific_journal-1767	49	205	�	�	PROPN
american_scientific_journal-1767	49	206	1	1	NUM
american_scientific_journal-1767	49	207	+	+	NUM
american_scientific_journal-1767	49	208	𝐴𝐴2	𝐴𝐴2	PROPN
american_scientific_journal-1767	49	209	𝐴𝐴	𝐴𝐴	PROPN
american_scientific_journal-1767	49	210	�	�	PROPN
american_scientific_journal-1767	49	211	+	+	CCONJ
american_scientific_journal-1767	49	212	�	�	PROPN
american_scientific_journal-1767	49	213	−	−	PROPN
american_scientific_journal-1767	49	214	𝐴𝐴2	𝐴𝐴2	PROPN
american_scientific_journal-1767	49	215	𝐴𝐴2	𝐴𝐴2	PROPN
american_scientific_journal-1767	49	216	𝐴𝐴	𝐴𝐴	PROPN
american_scientific_journal-1767	49	217	�	�	PROPN
american_scientific_journal-1767	49	218	�	�	PROPN
american_scientific_journal-1767	49	219	(	(	PUNCT
american_scientific_journal-1767	49	220	13	13	NUM
american_scientific_journal-1767	49	221	)	)	PUNCT
american_scientific_journal-1767	49	222	using	use	VERB
american_scientific_journal-1767	49	223	the	the	DET
american_scientific_journal-1767	49	224	equations	equation	NOUN
american_scientific_journal-1767	49	225	(	(	PUNCT
american_scientific_journal-1767	49	226	8)	8)	NUM
american_scientific_journal-1767	49	227	and	and	CCONJ
american_scientific_journal-1767	49	228	(	(	PUNCT
american_scientific_journal-1767	49	229	9	9	NUM
american_scientific_journal-1767	49	230	)	)	PUNCT
american_scientific_journal-1767	49	231	,	,	PUNCT
american_scientific_journal-1767	49	232	the	the	DET
american_scientific_journal-1767	49	233	constant	constant	ADJ
american_scientific_journal-1767	49	234	𝐴𝐴2	𝐴𝐴2	NOUN
american_scientific_journal-1767	49	235	can	can	AUX
american_scientific_journal-1767	49	236	be	be	AUX
american_scientific_journal-1767	49	237	obtained	obtain	VERB
american_scientific_journal-1767	49	238	as	as	ADP
american_scientific_journal-1767	49	239	𝜃𝜃	𝜃𝜃	PROPN
american_scientific_journal-1767	49	240	�	�	PROPN
american_scientific_journal-1767	49	241	𝑎𝑎𝑙𝑙	𝑎𝑎𝑙𝑙	PROPN
american_scientific_journal-1767	49	242	�	�	PROPN
american_scientific_journal-1767	49	243	�	�	PROPN
american_scientific_journal-1767	49	244	1+𝐴𝐴2𝐴𝐴	1+𝐴𝐴2𝐴𝐴	NUM
american_scientific_journal-1767	49	245	�	�	PROPN
american_scientific_journal-1767	49	246	=	=	SYM
american_scientific_journal-1767	49	247	−𝐴𝐴2𝑙𝑙	−𝐴𝐴2𝑙𝑙	PROPN
american_scientific_journal-1767	49	248	�	�	PROPN
american_scientific_journal-1767	49	249	𝜃𝜃	𝜃𝜃	PROPN
american_scientific_journal-1767	49	250	�	�	PROPN
american_scientific_journal-1767	49	251	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1767	49	252	𝑙𝑙	𝑙𝑙	PRON
american_scientific_journal-1767	49	253	�	�	PROPN
american_scientific_journal-1767	49	254	�	�	PROPN
american_scientific_journal-1767	49	255	3	3	NUM
american_scientific_journal-1767	49	256	𝐴𝐴2𝜃𝜃′	𝐴𝐴2𝜃𝜃′	PROPN
american_scientific_journal-1767	49	257	�	�	PROPN
american_scientific_journal-1767	49	258	𝑎𝑎𝑙𝑙	𝑎𝑎𝑙𝑙	PROPN
american_scientific_journal-1767	49	259	�	�	PROPN
american_scientific_journal-1767	49	260	�	�	PROPN
american_scientific_journal-1767	49	261	�	�	PROPN
american_scientific_journal-1767	49	262	1	1	NUM
american_scientific_journal-1767	49	263	+	+	NOUN
american_scientific_journal-1767	49	264	𝐴𝐴2	𝐴𝐴2	PROPN
american_scientific_journal-1767	49	265	𝐴𝐴	𝐴𝐴	PROPN
american_scientific_journal-1767	49	266	�	�	PROPN
american_scientific_journal-1767	49	267	�	�	PROPN
american_scientific_journal-1767	49	268	3	3	NUM
american_scientific_journal-1767	49	269	i.e	i.e	PRON
american_scientific_journal-1767	49	270	𝐴𝐴2	𝐴𝐴2	PROPN
american_scientific_journal-1767	49	271	=	=	PROPN
american_scientific_journal-1767	49	272	𝐴𝐴2	𝐴𝐴2	PROPN
american_scientific_journal-1767	49	273	𝑙𝑙	𝑙𝑙	PROPN
american_scientific_journal-1767	49	274	�	�	PROPN
american_scientific_journal-1767	49	275	1	1	NUM
american_scientific_journal-1767	49	276	+	+	NUM
american_scientific_journal-1767	49	277	𝐴𝐴2	𝐴𝐴2	PROPN
american_scientific_journal-1767	49	278	𝐴𝐴	𝐴𝐴	PROPN
american_scientific_journal-1767	49	279	�	�	PROPN
american_scientific_journal-1767	49	280	2	2	NUM
american_scientific_journal-1767	49	281	𝜃𝜃′	𝜃𝜃′	PROPN
american_scientific_journal-1767	49	282	�	�	PROPN
american_scientific_journal-1767	49	283	𝑎𝑎𝑙𝑙	𝑎𝑎𝑙𝑙	PROPN
american_scientific_journal-1767	49	284	�	�	PROPN
american_scientific_journal-1767	49	285	�	�	PROPN
american_scientific_journal-1767	49	286	𝜃𝜃	𝜃𝜃	PROPN
american_scientific_journal-1767	49	287	�	�	PROPN
american_scientific_journal-1767	49	288	𝑎𝑎𝑙𝑙	𝑎𝑎𝑙𝑙	PROPN
american_scientific_journal-1767	49	289	�	�	PROPN
american_scientific_journal-1767	49	290	�	�	PROPN
american_scientific_journal-1767	49	291	2	2	NUM
american_scientific_journal-1767	49	292	(	(	PUNCT
american_scientific_journal-1767	49	293	14	14	NUM
american_scientific_journal-1767	49	294	)	)	PUNCT
american_scientific_journal-1767	49	295	the	the	DET
american_scientific_journal-1767	49	296	equation	equation	NOUN
american_scientific_journal-1767	49	297	(	(	PUNCT
american_scientific_journal-1767	49	298	12	12	NUM
american_scientific_journal-1767	49	299	)	)	PUNCT
american_scientific_journal-1767	49	300	can	can	AUX
american_scientific_journal-1767	49	301	be	be	AUX
american_scientific_journal-1767	49	302	rewritten	rewrite	VERB
american_scientific_journal-1767	49	303	in	in	ADP
american_scientific_journal-1767	49	304	the	the	DET
american_scientific_journal-1767	49	305	form	form	NOUN
american_scientific_journal-1767	49	306	�	�	PROPN
american_scientific_journal-1767	49	307	1+𝐴𝐴2𝐴𝐴	1+𝐴𝐴2𝐴𝐴	NUM
american_scientific_journal-1767	49	308	�	�	PROPN
american_scientific_journal-1767	49	309	𝜃𝜃	𝜃𝜃	PROPN
american_scientific_journal-1767	49	310	�	�	PROPN
american_scientific_journal-1767	49	311	𝑎𝑎𝑙𝑙	𝑎𝑎𝑙𝑙	PROPN
american_scientific_journal-1767	49	312	�	�	PROPN
american_scientific_journal-1767	49	313	=	=	PROPN
american_scientific_journal-1767	49	314	𝑎𝑎	𝑎𝑎	VERB
american_scientific_journal-1767	49	315	𝐴𝐴	𝐴𝐴	PROPN
american_scientific_journal-1767	49	316	(	(	PUNCT
american_scientific_journal-1767	49	317	15	15	NUM
american_scientific_journal-1767	49	318	)	)	PUNCT
american_scientific_journal-1767	49	319	then	then	ADV
american_scientific_journal-1767	49	320	using	use	VERB
american_scientific_journal-1767	49	321	equation	equation	NOUN
american_scientific_journal-1767	49	322	(	(	PUNCT
american_scientific_journal-1767	49	323	15	15	NUM
american_scientific_journal-1767	49	324	)	)	PUNCT
american_scientific_journal-1767	49	325	,	,	PUNCT
american_scientific_journal-1767	49	326	equation	equation	NOUN
american_scientific_journal-1767	49	327	(	(	PUNCT
american_scientific_journal-1767	49	328	14	14	NUM
american_scientific_journal-1767	49	329	)	)	PUNCT
american_scientific_journal-1767	49	330	can	can	AUX
american_scientific_journal-1767	49	331	be	be	AUX
american_scientific_journal-1767	49	332	simplified	simplify	VERB
american_scientific_journal-1767	49	333	in	in	ADP
american_scientific_journal-1767	49	334	to	to	ADP
american_scientific_journal-1767	49	335	the	the	DET
american_scientific_journal-1767	49	336	form	form	NOUN
american_scientific_journal-1767	49	337	𝐴𝐴2	𝐴𝐴2	PROPN
american_scientific_journal-1767	49	338	=	=	PROPN
american_scientific_journal-1767	50	1	−𝐴𝐴2	−𝐴𝐴2	PROPN
american_scientific_journal-1767	50	2	𝑙𝑙	𝑙𝑙	NOUN
american_scientific_journal-1767	50	3	�	�	NOUN
american_scientific_journal-1767	50	4	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1767	50	5	2	2	NUM
american_scientific_journal-1767	50	6	𝐴𝐴2	𝐴𝐴2	PROPN
american_scientific_journal-1767	50	7	�	�	PROPN
american_scientific_journal-1767	50	8	𝜃𝜃′	𝜃𝜃′	NOUN
american_scientific_journal-1767	50	9	�	�	NOUN
american_scientific_journal-1767	50	10	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1767	50	11	𝑙𝑙	𝑙𝑙	PRON
american_scientific_journal-1767	50	12	�	�	PROPN
american_scientific_journal-1767	50	13	=	=	SYM
american_scientific_journal-1767	50	14	−𝑎𝑎2	−𝑎𝑎2	ADP
american_scientific_journal-1767	50	15	𝑙𝑙	𝑙𝑙	NOUN
american_scientific_journal-1767	50	16	𝜃𝜃′	𝜃𝜃′	PROPN
american_scientific_journal-1767	50	17	�	�	NOUN
american_scientific_journal-1767	50	18	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1767	50	19	𝑙𝑙	𝑙𝑙	PROPN
american_scientific_journal-1767	50	20	�	�	PROPN
american_scientific_journal-1767	50	21	(	(	PUNCT
american_scientific_journal-1767	50	22	16	16	NUM
american_scientific_journal-1767	50	23	)	)	PUNCT
american_scientific_journal-1767	50	24	american	american	ADJ
american_scientific_journal-1767	50	25	scientific	scientific	ADJ
american_scientific_journal-1767	50	26	research	research	NOUN
american_scientific_journal-1767	50	27	journal	journal	NOUN
american_scientific_journal-1767	50	28	for	for	ADP
american_scientific_journal-1767	50	29	engineering	engineering	NOUN
american_scientific_journal-1767	50	30	,	,	PUNCT
american_scientific_journal-1767	50	31	technology	technology	NOUN
american_scientific_journal-1767	50	32	,	,	PUNCT
american_scientific_journal-1767	50	33	and	and	CCONJ
american_scientific_journal-1767	50	34	sciences	science	NOUN
american_scientific_journal-1767	50	35	(	(	PUNCT
american_scientific_journal-1767	50	36	asrjets	asrjet	NOUN
american_scientific_journal-1767	50	37	)	)	PUNCT
american_scientific_journal-1767	50	38	(	(	PUNCT
american_scientific_journal-1767	50	39	2016	2016	NUM
american_scientific_journal-1767	50	40	)	)	PUNCT
american_scientific_journal-1767	50	41	volume	volume	NOUN
american_scientific_journal-1767	50	42	21	21	NUM
american_scientific_journal-1767	50	43	,	,	PUNCT
american_scientific_journal-1767	50	44	no	no	DET
american_scientific_journal-1767	50	45	1	1	NUM
american_scientific_journal-1767	50	46	,	,	PUNCT
american_scientific_journal-1767	50	47	pp	pp	ADV
american_scientific_journal-1767	50	48	163	163	NUM
american_scientific_journal-1767	50	49	-	-	SYM
american_scientific_journal-1767	50	50	177	177	NUM
american_scientific_journal-1767	50	51	168	168	NUM
american_scientific_journal-1767	50	52	substitution	substitution	NOUN
american_scientific_journal-1767	50	53	of	of	ADP
american_scientific_journal-1767	50	54	the	the	DET
american_scientific_journal-1767	50	55	value	value	NOUN
american_scientific_journal-1767	50	56	of	of	ADP
american_scientific_journal-1767	50	57	2a	2a	NUM
american_scientific_journal-1767	50	58	in	in	ADP
american_scientific_journal-1767	50	59	equation	equation	NOUN
american_scientific_journal-1767	50	60	(	(	PUNCT
american_scientific_journal-1767	50	61	12	12	NUM
american_scientific_journal-1767	50	62	)	)	PUNCT
american_scientific_journal-1767	50	63	gives	give	VERB
american_scientific_journal-1767	50	64	the	the	DET
american_scientific_journal-1767	50	65	value	value	NOUN
american_scientific_journal-1767	50	66	of	of	ADP
american_scientific_journal-1767	50	67	𝐴𝐴	𝐴𝐴	PROPN
american_scientific_journal-1767	50	68	as	as	ADP
american_scientific_journal-1767	50	69	𝐴𝐴	𝐴𝐴	PROPN
american_scientific_journal-1767	50	70	=	=	PUNCT
american_scientific_journal-1767	50	71	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1767	50	72	𝜃𝜃	𝜃𝜃	PROPN
american_scientific_journal-1767	50	73	�	�	PROPN
american_scientific_journal-1767	50	74	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1767	50	75	𝑙𝑙	𝑙𝑙	PRON
american_scientific_journal-1767	50	76	�	�	PROPN
american_scientific_journal-1767	50	77	+	+	CCONJ
american_scientific_journal-1767	50	78	𝑎𝑎2	𝑎𝑎2	X
american_scientific_journal-1767	50	79	𝑙𝑙	𝑙𝑙	NOUN
american_scientific_journal-1767	50	80	𝜃𝜃′	𝜃𝜃′	NOUN
american_scientific_journal-1767	50	81	�	�	NOUN
american_scientific_journal-1767	50	82	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1767	50	83	𝑙𝑙	𝑙𝑙	PROPN
american_scientific_journal-1767	50	84	�	�	PROPN
american_scientific_journal-1767	50	85	(	(	PUNCT
american_scientific_journal-1767	50	86	17	17	NUM
american_scientific_journal-1767	50	87	)	)	PUNCT
american_scientific_journal-1767	50	88	then	then	ADV
american_scientific_journal-1767	50	89	the	the	DET
american_scientific_journal-1767	50	90	metrics	metric	NOUN
american_scientific_journal-1767	50	91	(	(	PUNCT
american_scientific_journal-1767	50	92	6	6	X
american_scientific_journal-1767	50	93	)	)	PUNCT
american_scientific_journal-1767	50	94	become	become	VERB
american_scientific_journal-1767	50	95	𝑑𝑑𝑑𝑑2	𝑑𝑑𝑑𝑑2	NOUN
american_scientific_journal-1767	51	1	=	=	SYM
american_scientific_journal-1767	51	2	1	1	NUM
american_scientific_journal-1767	51	3	�	�	PROPN
american_scientific_journal-1767	51	4	𝜃𝜃	𝜃𝜃	PROPN
american_scientific_journal-1767	51	5	�	�	PROPN
american_scientific_journal-1767	51	6	𝑅𝑅𝑙𝑙	𝑅𝑅𝑙𝑙	ADJ
american_scientific_journal-1767	51	7	�	�	NOUN
american_scientific_journal-1767	51	8	�	�	PROPN
american_scientific_journal-1767	51	9	2	2	NUM
american_scientific_journal-1767	51	10	𝑐𝑐2𝑑𝑑𝑡𝑡2	𝑐𝑐2𝑑𝑑𝑡𝑡2	NOUN
american_scientific_journal-1767	51	11	−	−	PROPN
american_scientific_journal-1767	51	12	�	�	PROPN
american_scientific_journal-1767	51	13	𝜃𝜃	𝜃𝜃	PROPN
american_scientific_journal-1767	51	14	�	�	PROPN
american_scientific_journal-1767	51	15	𝑅𝑅	𝑅𝑅	PROPN
american_scientific_journal-1767	51	16	𝑙𝑙	𝑙𝑙	PROPN
american_scientific_journal-1767	51	17	�	�	PROPN
american_scientific_journal-1767	51	18	�	�	PROPN
american_scientific_journal-1767	51	19	2	2	NUM
american_scientific_journal-1767	51	20	(	(	PUNCT
american_scientific_journal-1767	51	21	𝑑𝑑𝑟𝑟2	𝑑𝑑𝑟𝑟2	X
american_scientific_journal-1767	51	22	+	+	CCONJ
american_scientific_journal-1767	51	23	𝑟𝑟2𝑑𝑑ω2	𝑟𝑟2𝑑𝑑ω2	PROPN
american_scientific_journal-1767	51	24	)	)	PUNCT
american_scientific_journal-1767	51	25	0	0	NUM
american_scientific_journal-1767	52	1	≤	≤	NUM
american_scientific_journal-1767	52	2	𝑟𝑟	𝑟𝑟	ADP
american_scientific_journal-1767	52	3	≤	≤	NUM
american_scientific_journal-1767	52	4	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1767	52	5	𝑑𝑑𝑑𝑑2	𝑑𝑑𝑑𝑑2	PROPN
american_scientific_journal-1767	52	6	=	=	SYM
american_scientific_journal-1767	52	7	1	1	NUM
american_scientific_journal-1767	52	8	�	�	PROPN
american_scientific_journal-1767	52	9	1−1𝑅𝑅	1−1𝑅𝑅	NUM
american_scientific_journal-1767	52	10	�	�	PROPN
american_scientific_journal-1767	52	11	𝑎𝑎2	𝑎𝑎2	X
american_scientific_journal-1767	52	12	𝑙𝑙	𝑙𝑙	NOUN
american_scientific_journal-1767	52	13	𝜃𝜃′	𝜃𝜃′	NOUN
american_scientific_journal-1767	52	14	�	�	PROPN
american_scientific_journal-1767	52	15	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1767	52	16	𝑙𝑙	𝑙𝑙	VERB
american_scientific_journal-1767	52	17	�	�	PROPN
american_scientific_journal-1767	52	18	�	�	NOUN
american_scientific_journal-1767	52	19	�	�	PROPN
american_scientific_journal-1767	52	20	2	2	NUM
american_scientific_journal-1767	52	21	𝑐𝑐2𝑑𝑑𝑑𝑑2	𝑐𝑐2𝑑𝑑𝑑𝑑2	SYM
american_scientific_journal-1767	52	22	−	−	PROPN
american_scientific_journal-1767	52	23	�	�	PROPN
american_scientific_journal-1767	52	24	1	1	NUM
american_scientific_journal-1767	52	25	−	−	PROPN
american_scientific_journal-1767	52	26	1	1	NUM
american_scientific_journal-1767	52	27	𝑅𝑅	𝑅𝑅	PROPN
american_scientific_journal-1767	52	28	�	�	NOUN
american_scientific_journal-1767	52	29	𝑎𝑎	𝑎𝑎	VERB
american_scientific_journal-1767	52	30	2	2	NUM
american_scientific_journal-1767	52	31	𝑙𝑙	𝑙𝑙	NOUN
american_scientific_journal-1767	52	32	𝜃𝜃′	𝜃𝜃′	NOUN
american_scientific_journal-1767	52	33	�	�	NOUN
american_scientific_journal-1767	52	34	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1767	52	35	𝑙𝑙	𝑙𝑙	PROPN
american_scientific_journal-1767	52	36	�	�	PROPN
american_scientific_journal-1767	52	37	�	�	PROPN
american_scientific_journal-1767	52	38	�	�	PROPN
american_scientific_journal-1767	52	39	2	2	NUM
american_scientific_journal-1767	52	40	(	(	PUNCT
american_scientific_journal-1767	52	41	𝑑𝑑𝑑𝑑2	𝑑𝑑𝑑𝑑2	PROPN
american_scientific_journal-1767	52	42	+	+	CCONJ
american_scientific_journal-1767	52	43	𝑑𝑑2𝑑𝑑ω2	𝑑𝑑2𝑑𝑑ω2	PROPN
american_scientific_journal-1767	52	44	)	)	PUNCT
american_scientific_journal-1767	52	45	𝐴𝐴	𝐴𝐴	PROPN
american_scientific_journal-1767	52	46	<	<	X
american_scientific_journal-1767	52	47	𝑑𝑑	𝑑𝑑	X
american_scientific_journal-1767	52	48	(	(	PUNCT
american_scientific_journal-1767	52	49	18	18	NUM
american_scientific_journal-1767	52	50	)	)	PUNCT
american_scientific_journal-1767	52	51	where	where	SCONJ
american_scientific_journal-1767	52	52	we	we	PRON
american_scientific_journal-1767	52	53	have	have	AUX
american_scientific_journal-1767	52	54	replaced	replace	VERB
american_scientific_journal-1767	52	55	𝐴𝐴	𝐴𝐴	PROPN
american_scientific_journal-1767	52	56	by	by	ADP
american_scientific_journal-1767	52	57	(	(	PUNCT
american_scientific_journal-1767	52	58	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1767	52	59	𝜃𝜃	𝜃𝜃	PUNCT
american_scientific_journal-1767	52	60	�	�	PROPN
american_scientific_journal-1767	52	61	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1767	52	62	𝑙𝑙	𝑙𝑙	PRON
american_scientific_journal-1767	52	63	�	�	PROPN
american_scientific_journal-1767	52	64	+	+	CCONJ
american_scientific_journal-1767	52	65	𝑎𝑎2	𝑎𝑎2	X
american_scientific_journal-1767	52	66	𝑙𝑙	𝑙𝑙	NOUN
american_scientific_journal-1767	52	67	𝜃𝜃′	𝜃𝜃′	NOUN
american_scientific_journal-1767	52	68	�	�	NOUN
american_scientific_journal-1767	52	69	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1767	52	70	𝑙𝑙	𝑙𝑙	PROPN
american_scientific_journal-1767	52	71	�	�	PROPN
american_scientific_journal-1767	52	72	)	)	PUNCT
american_scientific_journal-1767	52	73	.	.	PUNCT
american_scientific_journal-1767	53	1	the	the	DET
american_scientific_journal-1767	53	2	values	value	NOUN
american_scientific_journal-1767	53	3	of	of	ADP
american_scientific_journal-1767	53	4	𝐴𝐴	𝐴𝐴	PROPN
american_scientific_journal-1767	53	5	which	which	PRON
american_scientific_journal-1767	53	6	is	be	AUX
american_scientific_journal-1767	53	7	the	the	DET
american_scientific_journal-1767	53	8	radial	radial	ADJ
american_scientific_journal-1767	53	9	coordinate	coordinate	NOUN
american_scientific_journal-1767	53	10	just	just	ADV
american_scientific_journal-1767	53	11	outside	outside	ADP
american_scientific_journal-1767	53	12	the	the	DET
american_scientific_journal-1767	53	13	sphere	sphere	NOUN
american_scientific_journal-1767	53	14	can	can	AUX
american_scientific_journal-1767	53	15	be	be	AUX
american_scientific_journal-1767	53	16	found	find	VERB
american_scientific_journal-1767	53	17	using	use	VERB
american_scientific_journal-1767	53	18	the	the	DET
american_scientific_journal-1767	53	19	values	value	NOUN
american_scientific_journal-1767	53	20	of	of	ADP
american_scientific_journal-1767	53	21	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1767	53	22	𝑙𝑙	𝑙𝑙	PROPN
american_scientific_journal-1767	53	23	.	.	PUNCT
american_scientific_journal-1767	54	1	the	the	DET
american_scientific_journal-1767	54	2	relationship	relationship	NOUN
american_scientific_journal-1767	54	3	between	between	ADP
american_scientific_journal-1767	54	4	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1767	54	5	𝑙𝑙	𝑙𝑙	PROPN
american_scientific_journal-1767	54	6	and	and	CCONJ
american_scientific_journal-1767	54	7	𝐴𝐴	𝐴𝐴	PROPN
american_scientific_journal-1767	54	8	is	be	AUX
american_scientific_journal-1767	54	9	tabulated	tabulate	VERB
american_scientific_journal-1767	54	10	in	in	ADP
american_scientific_journal-1767	54	11	the	the	DET
american_scientific_journal-1767	54	12	table	table	NOUN
american_scientific_journal-1767	54	13	1	1	NUM
american_scientific_journal-1767	54	14	given	give	VERB
american_scientific_journal-1767	54	15	below	below	ADP
american_scientific_journal-1767	54	16	.	.	PUNCT
american_scientific_journal-1767	55	1	table	table	NOUN
american_scientific_journal-1767	55	2	1	1	NUM
american_scientific_journal-1767	55	3	:	:	PUNCT
american_scientific_journal-1767	55	4	the	the	DET
american_scientific_journal-1767	55	5	relationship	relationship	NOUN
american_scientific_journal-1767	55	6	between	between	ADP
american_scientific_journal-1767	55	7	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1767	55	8	𝑙𝑙	𝑙𝑙	PROPN
american_scientific_journal-1767	55	9	and	and	CCONJ
american_scientific_journal-1767	55	10	𝐴𝐴	𝐴𝐴	PROPN
american_scientific_journal-1767	55	11	.	.	PUNCT
american_scientific_journal-1767	56	1	substitution	substitution	NOUN
american_scientific_journal-1767	56	2	of	of	ADP
american_scientific_journal-1767	56	3	the	the	DET
american_scientific_journal-1767	56	4	values	value	NOUN
american_scientific_journal-1767	56	5	for	for	ADP
american_scientific_journal-1767	56	6	𝐴𝐴2	𝐴𝐴2	PROPN
american_scientific_journal-1767	56	7	and	and	CCONJ
american_scientific_journal-1767	56	8	𝐴𝐴	𝐴𝐴	PROPN
american_scientific_journal-1767	56	9	in	in	ADP
american_scientific_journal-1767	56	10	(	(	PUNCT
american_scientific_journal-1767	56	11	8)	8)	NUM
american_scientific_journal-1767	56	12	gives	give	VERB
american_scientific_journal-1767	56	13	𝛿𝛿𝛿𝛿	𝛿𝛿𝛿𝛿	NOUN
american_scientific_journal-1767	56	14	𝛿𝛿𝛿𝛿	𝛿𝛿𝛿𝛿	NOUN
american_scientific_journal-1767	56	15	=	=	SYM
american_scientific_journal-1767	56	16	𝜃𝜃	𝜃𝜃	PROPN
american_scientific_journal-1767	56	17	�	�	PROPN
american_scientific_journal-1767	56	18	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1767	56	19	𝑙𝑙	𝑙𝑙	PRON
american_scientific_journal-1767	56	20	�	�	PROPN
american_scientific_journal-1767	56	21	+	+	CCONJ
american_scientific_journal-1767	56	22	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1767	56	23	𝑙𝑙	𝑙𝑙	NOUN
american_scientific_journal-1767	56	24	𝜃𝜃′	𝜃𝜃′	NOUN
american_scientific_journal-1767	56	25	�	�	NOUN
american_scientific_journal-1767	56	26	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1767	56	27	𝑙𝑙	𝑙𝑙	PROPN
american_scientific_journal-1767	56	28	�	�	PROPN
american_scientific_journal-1767	56	29	(	(	PUNCT
american_scientific_journal-1767	56	30	19	19	NUM
american_scientific_journal-1767	56	31	)	)	PUNCT
american_scientific_journal-1767	56	32	the	the	DET
american_scientific_journal-1767	56	33	values	value	NOUN
american_scientific_journal-1767	56	34	of	of	ADP
american_scientific_journal-1767	56	35	𝛿𝛿𝛿𝛿	𝛿𝛿𝛿𝛿	NOUN
american_scientific_journal-1767	56	36	𝛿𝛿𝛿𝛿	𝛿𝛿𝛿𝛿	NOUN
american_scientific_journal-1767	56	37	for	for	ADP
american_scientific_journal-1767	56	38	few	few	ADJ
american_scientific_journal-1767	56	39	different	different	ADJ
american_scientific_journal-1767	56	40	values	value	NOUN
american_scientific_journal-1767	56	41	of	of	ADP
american_scientific_journal-1767	56	42	l	l	NOUN
american_scientific_journal-1767	56	43	a	a	PRON
american_scientific_journal-1767	56	44	has	have	AUX
american_scientific_journal-1767	56	45	been	be	AUX
american_scientific_journal-1767	56	46	tabulated	tabulate	VERB
american_scientific_journal-1767	56	47	in	in	ADP
american_scientific_journal-1767	56	48	table	table	NOUN
american_scientific_journal-1767	56	49	2	2	NUM
american_scientific_journal-1767	56	50	as	as	SCONJ
american_scientific_journal-1767	56	51	given	give	VERB
american_scientific_journal-1767	56	52	below	below	ADV
american_scientific_journal-1767	56	53	.	.	PUNCT
american_scientific_journal-1767	57	1	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1767	57	2	𝑙𝑙	𝑙𝑙	PRON
american_scientific_journal-1767	57	3	𝐴𝐴	𝐴𝐴	PROPN
american_scientific_journal-1767	57	4	=	=	PUNCT
american_scientific_journal-1767	57	5	(	(	PUNCT
american_scientific_journal-1767	57	6	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1767	57	7	𝜃𝜃	𝜃𝜃	PUNCT
american_scientific_journal-1767	57	8	�	�	PROPN
american_scientific_journal-1767	57	9	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1767	57	10	𝑙𝑙	𝑙𝑙	PRON
american_scientific_journal-1767	57	11	�	�	PROPN
american_scientific_journal-1767	58	1	+	+	CCONJ
american_scientific_journal-1767	58	2	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1767	58	3	2	2	NUM
american_scientific_journal-1767	58	4	𝑙𝑙	𝑙𝑙	NOUN
american_scientific_journal-1767	58	5	𝜃𝜃′	𝜃𝜃′	NOUN
american_scientific_journal-1767	58	6	�	�	NOUN
american_scientific_journal-1767	58	7	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1767	58	8	𝑙𝑙	𝑙𝑙	PROPN
american_scientific_journal-1767	58	9	�	�	PROPN
american_scientific_journal-1767	58	10	)	)	PUNCT
american_scientific_journal-1767	58	11	1	1	NUM
american_scientific_journal-1767	58	12	0.602929	0.602929	NUM
american_scientific_journal-1767	58	13	l	l	NOUN
american_scientific_journal-1767	58	14	2	2	NUM
american_scientific_journal-1767	58	15	0.119738	0.119738	NUM
american_scientific_journal-1767	58	16	l	l	NOUN
american_scientific_journal-1767	58	17	3	3	NUM
american_scientific_journal-1767	58	18	-0.57877	-0.57877	NOUN
american_scientific_journal-1767	58	19	l	l	NOUN
american_scientific_journal-1767	58	20	4	4	NUM
american_scientific_journal-1767	58	21	-1.08588	-1.08588	NOUN
american_scientific_journal-1767	58	22	l	l	NOUN
american_scientific_journal-1767	58	23	5	5	NUM
american_scientific_journal-1767	58	24	-1.44905	-1.44905	VERB
american_scientific_journal-1767	58	25	l	l	NOUN
american_scientific_journal-1767	58	26	6	6	NUM
american_scientific_journal-1767	58	27	-1.75514	-1.75514	NOUN
american_scientific_journal-1767	58	28	l	l	NOUN
american_scientific_journal-1767	58	29	7	7	NUM
american_scientific_journal-1767	58	30	-2.04842	-2.04842	NOUN
american_scientific_journal-1767	58	31	l	l	NOUN
american_scientific_journal-1767	58	32	american	american	PROPN
american_scientific_journal-1767	58	33	scientific	scientific	ADJ
american_scientific_journal-1767	58	34	research	research	NOUN
american_scientific_journal-1767	58	35	journal	journal	NOUN
american_scientific_journal-1767	58	36	for	for	ADP
american_scientific_journal-1767	58	37	engineering	engineering	NOUN
american_scientific_journal-1767	58	38	,	,	PUNCT
american_scientific_journal-1767	58	39	technology	technology	NOUN
american_scientific_journal-1767	58	40	,	,	PUNCT
american_scientific_journal-1767	58	41	and	and	CCONJ
american_scientific_journal-1767	58	42	sciences	science	NOUN
american_scientific_journal-1767	58	43	(	(	PUNCT
american_scientific_journal-1767	58	44	asrjets	asrjet	NOUN
american_scientific_journal-1767	58	45	)	)	PUNCT
american_scientific_journal-1767	58	46	(	(	PUNCT
american_scientific_journal-1767	58	47	2016	2016	NUM
american_scientific_journal-1767	58	48	)	)	PUNCT
american_scientific_journal-1767	58	49	volume	volume	NOUN
american_scientific_journal-1767	58	50	21	21	NUM
american_scientific_journal-1767	58	51	,	,	PUNCT
american_scientific_journal-1767	58	52	no	no	DET
american_scientific_journal-1767	58	53	1	1	NUM
american_scientific_journal-1767	58	54	,	,	PUNCT
american_scientific_journal-1767	58	55	pp	pp	ADV
american_scientific_journal-1767	58	56	163	163	NUM
american_scientific_journal-1767	58	57	-	-	SYM
american_scientific_journal-1767	58	58	177	177	NUM
american_scientific_journal-1767	58	59	169	169	NUM
american_scientific_journal-1767	58	60	table	table	NOUN
american_scientific_journal-1767	58	61	2	2	NUM
american_scientific_journal-1767	58	62	:	:	PUNCT
american_scientific_journal-1767	58	63	few	few	ADJ
american_scientific_journal-1767	58	64	values	value	NOUN
american_scientific_journal-1767	58	65	of	of	ADP
american_scientific_journal-1767	58	66	𝛿𝛿𝛿𝛿	𝛿𝛿𝛿𝛿	NOUN
american_scientific_journal-1767	58	67	𝛿𝛿𝛿𝛿	𝛿𝛿𝛿𝛿	NOUN
american_scientific_journal-1767	58	68	since	since	SCONJ
american_scientific_journal-1767	58	69	𝛿𝛿𝑡𝑡	𝛿𝛿𝑡𝑡	ADJ
american_scientific_journal-1767	58	70	increases	increase	NOUN
american_scientific_journal-1767	58	71	as	as	ADP
american_scientific_journal-1767	58	72	,	,	PUNCT
american_scientific_journal-1767	58	73	𝛿𝛿𝛿𝛿	𝛿𝛿𝛿𝛿	NOUN
american_scientific_journal-1767	58	74	𝛿𝛿𝛿𝛿	𝛿𝛿𝛿𝛿	NOUN
american_scientific_journal-1767	58	75	should	should	AUX
american_scientific_journal-1767	58	76	be	be	AUX
american_scientific_journal-1767	58	77	positive	positive	ADJ
american_scientific_journal-1767	58	78	,	,	PUNCT
american_scientific_journal-1767	58	79	i.e.	i.e.	X
american_scientific_journal-1767	58	80	𝛿𝛿𝛿𝛿	𝛿𝛿𝛿𝛿	NOUN
american_scientific_journal-1767	58	81	𝛿𝛿𝛿𝛿	𝛿𝛿𝛿𝛿	NOUN
american_scientific_journal-1767	58	82	>	>	X
american_scientific_journal-1767	58	83	0	0	X
american_scientific_journal-1767	58	84	.	.	PUNCT
american_scientific_journal-1767	59	1	hence	hence	ADV
american_scientific_journal-1767	59	2	according	accord	VERB
american_scientific_journal-1767	59	3	to	to	ADP
american_scientific_journal-1767	59	4	table	table	NOUN
american_scientific_journal-1767	59	5	2	2	NUM
american_scientific_journal-1767	59	6	,	,	PUNCT
american_scientific_journal-1767	59	7	there	there	PRON
american_scientific_journal-1767	59	8	is	be	VERB
american_scientific_journal-1767	59	9	a	a	DET
american_scientific_journal-1767	59	10	maximum	maximum	ADJ
american_scientific_journal-1767	59	11	value	value	NOUN
american_scientific_journal-1767	59	12	that	that	PRON
american_scientific_journal-1767	59	13	𝑎𝑎	𝑎𝑎	VERB
american_scientific_journal-1767	59	14	𝑙𝑙	𝑙𝑙	PRON
american_scientific_journal-1767	59	15	can	can	AUX
american_scientific_journal-1767	59	16	take	take	VERB
american_scientific_journal-1767	59	17	,	,	PUNCT
american_scientific_journal-1767	59	18	which	which	PRON
american_scientific_journal-1767	59	19	is	be	AUX
american_scientific_journal-1767	59	20	nearly	nearly	ADV
american_scientific_journal-1767	59	21	16.2	16.2	NUM
american_scientific_journal-1767	59	22	.	.	PUNCT
american_scientific_journal-1767	60	1	figure	figure	NOUN
american_scientific_journal-1767	60	2	1	1	NUM
american_scientific_journal-1767	60	3	which	which	PRON
american_scientific_journal-1767	60	4	have	have	VERB
american_scientific_journal-1767	60	5	the	the	DET
american_scientific_journal-1767	60	6	graphs	graph	NOUN
american_scientific_journal-1767	60	7	of	of	ADP
american_scientific_journal-1767	60	8	𝜃𝜃	𝜃𝜃	PROPN
american_scientific_journal-1767	60	9	�	�	PROPN
american_scientific_journal-1767	60	10	𝑅𝑅	𝑅𝑅	PROPN
american_scientific_journal-1767	60	11	𝑙𝑙	𝑙𝑙	PROPN
american_scientific_journal-1767	60	12	�	�	PROPN
american_scientific_journal-1767	60	13	and	and	CCONJ
american_scientific_journal-1767	60	14	𝜃𝜃	𝜃𝜃	PROPN
american_scientific_journal-1767	60	15	�	�	PROPN
american_scientific_journal-1767	60	16	𝑅𝑅	𝑅𝑅	PROPN
american_scientific_journal-1767	60	17	𝑙𝑙	𝑙𝑙	PROPN
american_scientific_journal-1767	60	18	�	�	PROPN
american_scientific_journal-1767	60	19	+	+	CCONJ
american_scientific_journal-1767	60	20	𝑅𝑅	𝑅𝑅	PROPN
american_scientific_journal-1767	60	21	𝑙𝑙	𝑙𝑙	ADJ
american_scientific_journal-1767	60	22	𝜃𝜃′	𝜃𝜃′	NOUN
american_scientific_journal-1767	60	23	�	�	PROPN
american_scientific_journal-1767	60	24	𝑅𝑅	𝑅𝑅	PROPN
american_scientific_journal-1767	60	25	𝑙𝑙	𝑙𝑙	PROPN
american_scientific_journal-1767	60	26	�	�	PROPN
american_scientific_journal-1767	60	27	versus	versus	ADP
american_scientific_journal-1767	60	28	𝑅𝑅	𝑅𝑅	PROPN
american_scientific_journal-1767	60	29	𝑙𝑙	𝑙𝑙	PROPN
american_scientific_journal-1767	60	30	in	in	ADP
american_scientific_journal-1767	60	31	sashinka	sashinka	PROPN
american_scientific_journal-1767	60	32	wimaladharma	wimaladharma	PROPN
american_scientific_journal-1767	60	33	and	and	CCONJ
american_scientific_journal-1767	60	34	nalin	nalin	PROPN
american_scientific_journal-1767	60	35	de	de	PROPN
american_scientific_journal-1767	60	36	silva[1	silva[1	PROPN
american_scientific_journal-1767	60	37	]	]	PUNCT
american_scientific_journal-1767	60	38	also	also	ADV
american_scientific_journal-1767	60	39	confirms	confirm	VERB
american_scientific_journal-1767	60	40	this	this	DET
american_scientific_journal-1767	60	41	result	result	NOUN
american_scientific_journal-1767	60	42	and	and	CCONJ
american_scientific_journal-1767	60	43	a	a	DET
american_scientific_journal-1767	60	44	more	more	ADV
american_scientific_journal-1767	60	45	accurate	accurate	ADJ
american_scientific_journal-1767	60	46	value	value	NOUN
american_scientific_journal-1767	60	47	for	for	ADP
american_scientific_journal-1767	60	48	the	the	DET
american_scientific_journal-1767	60	49	maximum	maximum	NOUN
american_scientific_journal-1767	60	50	of	of	ADP
american_scientific_journal-1767	60	51	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1767	60	52	𝑙𝑙	𝑙𝑙	PROPN
american_scientific_journal-1767	60	53	is	be	AUX
american_scientific_journal-1767	60	54	2.157	2.157	NUM
american_scientific_journal-1767	60	55	as	as	SCONJ
american_scientific_journal-1767	60	56	obtained	obtain	VERB
american_scientific_journal-1767	60	57	using	use	VERB
american_scientific_journal-1767	60	58	the	the	DET
american_scientific_journal-1767	60	59	graph	graph	NOUN
american_scientific_journal-1767	60	60	in	in	ADP
american_scientific_journal-1767	60	61	figure	figure	NOUN
american_scientific_journal-1767	60	62	1	1	NUM
american_scientific_journal-1767	60	63	in	in	ADP
american_scientific_journal-1767	60	64	sashinka	sashinka	PROPN
american_scientific_journal-1767	60	65	wimaladharma	wimaladharma	NOUN
american_scientific_journal-1767	60	66	and	and	CCONJ
american_scientific_journal-1767	60	67	nalin	nalin	PROPN
american_scientific_journal-1767	60	68	de	de	PROPN
american_scientific_journal-1767	60	69	silva	silva	PROPN
american_scientific_journal-1767	61	1	[	[	X
american_scientific_journal-1767	61	2	1	1	NUM
american_scientific_journal-1767	61	3	]	]	PUNCT
american_scientific_journal-1767	61	4	.	.	PUNCT
american_scientific_journal-1767	62	1	considering	consider	VERB
american_scientific_journal-1767	62	2	the	the	DET
american_scientific_journal-1767	62	3	values	value	NOUN
american_scientific_journal-1767	62	4	of	of	ADP
american_scientific_journal-1767	62	5	𝐴𝐴	𝐴𝐴	PROPN
american_scientific_journal-1767	62	6	in	in	ADP
american_scientific_journal-1767	62	7	table	table	NOUN
american_scientific_journal-1767	62	8	1	1	NUM
american_scientific_journal-1767	62	9	,	,	PUNCT
american_scientific_journal-1767	62	10	it	it	PRON
american_scientific_journal-1767	62	11	can	can	AUX
american_scientific_journal-1767	62	12	be	be	AUX
american_scientific_journal-1767	62	13	found	find	VERB
american_scientific_journal-1767	62	14	that	that	SCONJ
american_scientific_journal-1767	62	15	they	they	PRON
american_scientific_journal-1767	62	16	are	be	AUX
american_scientific_journal-1767	62	17	positive	positive	ADJ
american_scientific_journal-1767	62	18	only	only	ADV
american_scientific_journal-1767	62	19	when	when	SCONJ
american_scientific_journal-1767	62	20	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1767	62	21	𝑙𝑙	𝑙𝑙	NOUN
american_scientific_journal-1767	62	22	≤	≤	NUM
american_scientific_journal-1767	62	23	2.16	2.16	NUM
american_scientific_journal-1767	62	24	as	as	SCONJ
american_scientific_journal-1767	62	25	𝐴𝐴	𝐴𝐴	PROPN
american_scientific_journal-1767	62	26	differs	differ	VERB
american_scientific_journal-1767	62	27	from	from	ADP
american_scientific_journal-1767	62	28	𝛿𝛿𝛿𝛿	𝛿𝛿𝛿𝛿	NOUN
american_scientific_journal-1767	62	29	𝛿𝛿𝛿𝛿	𝛿𝛿𝛿𝛿	NOUN
american_scientific_journal-1767	62	30	by	by	ADP
american_scientific_journal-1767	62	31	a	a	DET
american_scientific_journal-1767	62	32	factor	factor	NOUN
american_scientific_journal-1767	62	33	of	of	ADP
american_scientific_journal-1767	62	34	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1767	62	35	which	which	PRON
american_scientific_journal-1767	62	36	is	be	AUX
american_scientific_journal-1767	62	37	positive	positive	ADJ
american_scientific_journal-1767	62	38	being	be	AUX
american_scientific_journal-1767	62	39	the	the	DET
american_scientific_journal-1767	62	40	radial	radial	ADJ
american_scientific_journal-1767	62	41	coordinate	coordinate	NOUN
american_scientific_journal-1767	62	42	as	as	SCONJ
american_scientific_journal-1767	62	43	measured	measure	VERB
american_scientific_journal-1767	62	44	inside	inside	ADP
american_scientific_journal-1767	62	45	the	the	DET
american_scientific_journal-1767	62	46	sphere	sphere	NOUN
american_scientific_journal-1767	62	47	at	at	ADP
american_scientific_journal-1767	62	48	its	its	PRON
american_scientific_journal-1767	62	49	surface	surface	NOUN
american_scientific_journal-1767	62	50	.	.	PUNCT
american_scientific_journal-1767	63	1	therefore	therefore	ADV
american_scientific_journal-1767	63	2	spheres	sphere	VERB
american_scientific_journal-1767	63	3	whose	whose	DET
american_scientific_journal-1767	63	4	radial	radial	ADJ
american_scientific_journal-1767	63	5	coordinate	coordinate	NOUN
american_scientific_journal-1767	63	6	is	be	AUX
american_scientific_journal-1767	63	7	greater	great	ADJ
american_scientific_journal-1767	63	8	than	than	ADP
american_scientific_journal-1767	63	9	2.16	2.16	NUM
american_scientific_journal-1767	63	10	𝑙𝑙	𝑙𝑙	NOUN
american_scientific_journal-1767	63	11	with	with	ADP
american_scientific_journal-1767	63	12	suitable	suitable	ADJ
american_scientific_journal-1767	63	13	units	unit	NOUN
american_scientific_journal-1767	63	14	,	,	PUNCT
american_scientific_journal-1767	63	15	as	as	SCONJ
american_scientific_journal-1767	63	16	measured	measure	VERB
american_scientific_journal-1767	63	17	just	just	ADV
american_scientific_journal-1767	63	18	inside	inside	ADP
american_scientific_journal-1767	63	19	the	the	DET
american_scientific_journal-1767	63	20	spheres	sphere	NOUN
american_scientific_journal-1767	63	21	can	can	AUX
american_scientific_journal-1767	63	22	not	not	PART
american_scientific_journal-1767	63	23	be	be	AUX
american_scientific_journal-1767	63	24	exist	exist	ADJ
american_scientific_journal-1767	63	25	.	.	PUNCT
american_scientific_journal-1767	64	1	now	now	ADV
american_scientific_journal-1767	64	2	the	the	DET
american_scientific_journal-1767	64	3	metric	metric	ADJ
american_scientific_journal-1767	64	4	(	(	PUNCT
american_scientific_journal-1767	64	5	18	18	NUM
american_scientific_journal-1767	64	6	)	)	PUNCT
american_scientific_journal-1767	64	7	outside	outside	ADP
american_scientific_journal-1767	64	8	the	the	DET
american_scientific_journal-1767	64	9	sphere	sphere	NOUN
american_scientific_journal-1767	64	10	can	can	AUX
american_scientific_journal-1767	64	11	be	be	AUX
american_scientific_journal-1767	64	12	written	write	VERB
american_scientific_journal-1767	64	13	as	as	ADP
american_scientific_journal-1767	64	14	𝑑𝑑𝑑𝑑2	𝑑𝑑𝑑𝑑2	PROPN
american_scientific_journal-1767	64	15	=	=	SYM
american_scientific_journal-1767	64	16	1	1	NUM
american_scientific_journal-1767	64	17	�	�	PROPN
american_scientific_journal-1767	64	18	1−1𝑅𝑅	1−1𝑅𝑅	NUM
american_scientific_journal-1767	64	19	�	�	PROPN
american_scientific_journal-1767	64	20	𝑎𝑎2	𝑎𝑎2	X
american_scientific_journal-1767	64	21	𝑙𝑙	𝑙𝑙	NOUN
american_scientific_journal-1767	64	22	𝜃𝜃′	𝜃𝜃′	NOUN
american_scientific_journal-1767	64	23	�	�	PROPN
american_scientific_journal-1767	64	24	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1767	64	25	𝑙𝑙	𝑙𝑙	VERB
american_scientific_journal-1767	64	26	�	�	PROPN
american_scientific_journal-1767	64	27	�	�	NOUN
american_scientific_journal-1767	64	28	�	�	PROPN
american_scientific_journal-1767	64	29	2	2	NUM
american_scientific_journal-1767	64	30	𝑐𝑐2𝑑𝑑𝑑𝑑2	𝑐𝑐2𝑑𝑑𝑑𝑑2	SYM
american_scientific_journal-1767	64	31	−	−	PROPN
american_scientific_journal-1767	64	32	�	�	PROPN
american_scientific_journal-1767	64	33	1	1	NUM
american_scientific_journal-1767	64	34	−	−	PROPN
american_scientific_journal-1767	64	35	1	1	NUM
american_scientific_journal-1767	64	36	𝑅𝑅	𝑅𝑅	PROPN
american_scientific_journal-1767	64	37	�	�	NOUN
american_scientific_journal-1767	64	38	𝑎𝑎	𝑎𝑎	VERB
american_scientific_journal-1767	64	39	2	2	NUM
american_scientific_journal-1767	64	40	𝑙𝑙	𝑙𝑙	NOUN
american_scientific_journal-1767	64	41	𝜃𝜃′	𝜃𝜃′	NOUN
american_scientific_journal-1767	64	42	�	�	NOUN
american_scientific_journal-1767	64	43	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1767	64	44	𝑙𝑙	𝑙𝑙	PROPN
american_scientific_journal-1767	64	45	�	�	PROPN
american_scientific_journal-1767	64	46	�	�	PROPN
american_scientific_journal-1767	64	47	�	�	PROPN
american_scientific_journal-1767	64	48	2	2	NUM
american_scientific_journal-1767	64	49	�	�	PROPN
american_scientific_journal-1767	64	50	𝑑𝑑𝑑𝑑2	𝑑𝑑𝑑𝑑2	NOUN
american_scientific_journal-1767	64	51	+	+	CCONJ
american_scientific_journal-1767	64	52	𝑑𝑑2𝑑𝑑ω	𝑑𝑑2𝑑𝑑ω	PROPN
american_scientific_journal-1767	64	53	2	2	NUM
american_scientific_journal-1767	64	54	�	�	PROPN
american_scientific_journal-1767	64	55	but	but	CCONJ
american_scientific_journal-1767	64	56	in	in	ADP
american_scientific_journal-1767	64	57	wickramasuriya	wickramasuriya	NOUN
american_scientific_journal-1767	64	58	and	and	CCONJ
american_scientific_journal-1767	64	59	bonnar	bonnar	PROPN
american_scientific_journal-1767	65	1	[	[	X
american_scientific_journal-1767	65	2	5	5	NUM
american_scientific_journal-1767	65	3	]	]	PUNCT
american_scientific_journal-1767	65	4	,	,	PUNCT
american_scientific_journal-1767	65	5	it	it	PRON
american_scientific_journal-1767	65	6	has	have	AUX
american_scientific_journal-1767	65	7	been	be	AUX
american_scientific_journal-1767	65	8	shown	show	VERB
american_scientific_journal-1767	65	9	that	that	SCONJ
american_scientific_journal-1767	65	10	𝑚𝑚	𝑚𝑚	ADP
american_scientific_journal-1767	65	11	=	=	PUNCT
american_scientific_journal-1767	65	12	−𝑎𝑎2	−𝑎𝑎2	PROPN
american_scientific_journal-1767	66	1	𝑙𝑙	𝑙𝑙	NOUN
american_scientific_journal-1767	66	2	𝜃𝜃′	𝜃𝜃′	PROPN
american_scientific_journal-1767	66	3	�	�	NOUN
american_scientific_journal-1767	66	4	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1767	66	5	𝑙𝑙	𝑙𝑙	PRON
american_scientific_journal-1767	66	6	�	�	PROPN
american_scientific_journal-1767	66	7	where	where	SCONJ
american_scientific_journal-1767	66	8	𝑚𝑚	𝑚𝑚	ADP
american_scientific_journal-1767	66	9	is	be	AUX
american_scientific_journal-1767	66	10	the	the	DET
american_scientific_journal-1767	66	11	mass	mass	NOUN
american_scientific_journal-1767	66	12	of	of	ADP
american_scientific_journal-1767	66	13	the	the	DET
american_scientific_journal-1767	66	14	sphere	sphere	NOUN
american_scientific_journal-1767	66	15	.	.	PUNCT
american_scientific_journal-1767	67	1	𝑎𝑎	𝑎𝑎	PROPN
american_scientific_journal-1767	67	2	𝑙𝑙	𝑙𝑙	PROPN
american_scientific_journal-1767	67	3	𝛿𝛿𝑡𝑡	𝛿𝛿𝑡𝑡	PROPN
american_scientific_journal-1767	67	4	𝛿𝛿𝑑𝑑	𝛿𝛿𝑑𝑑	PROPN
american_scientific_journal-1767	67	5	=	=	PROPN
american_scientific_journal-1767	67	6	𝜃𝜃	𝜃𝜃	PROPN
american_scientific_journal-1767	67	7	�	�	PROPN
american_scientific_journal-1767	67	8	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1767	67	9	𝑙𝑙	𝑙𝑙	PROPN
american_scientific_journal-1767	67	10	�	�	PROPN
american_scientific_journal-1767	67	11	+	+	CCONJ
american_scientific_journal-1767	67	12	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1767	67	13	𝑙𝑙	𝑙𝑙	NOUN
american_scientific_journal-1767	67	14	𝜃𝜃′	𝜃𝜃′	NOUN
american_scientific_journal-1767	67	15	�	�	PROPN
american_scientific_journal-1767	67	16	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1767	67	17	𝑙𝑙	𝑙𝑙	PROPN
american_scientific_journal-1767	67	18	�	�	PROPN
american_scientific_journal-1767	67	19	1	1	NUM
american_scientific_journal-1767	67	20	0.602929	0.602929	NUM
american_scientific_journal-1767	67	21	2	2	NUM
american_scientific_journal-1767	67	22	0.059869	0.059869	NUM
american_scientific_journal-1767	67	23	3	3	NUM
american_scientific_journal-1767	67	24	-0.19292	-0.19292	NOUN
american_scientific_journal-1767	67	25	4	4	NUM
american_scientific_journal-1767	67	26	-0.27139	-0.27139	ADV
american_scientific_journal-1767	67	27	5	5	NUM
american_scientific_journal-1767	67	28	-0.28981	-0.28981	NOUN
american_scientific_journal-1767	67	29	6	6	NUM
american_scientific_journal-1767	67	30	-0.29252	-0.29252	NOUN
american_scientific_journal-1767	67	31	7	7	NUM
american_scientific_journal-1767	67	32	-0.29252	-0.29252	NOUN
american_scientific_journal-1767	67	33	american	american	PROPN
american_scientific_journal-1767	67	34	scientific	scientific	ADJ
american_scientific_journal-1767	67	35	research	research	PROPN
american_scientific_journal-1767	67	36	journal	journal	NOUN
american_scientific_journal-1767	67	37	for	for	ADP
american_scientific_journal-1767	67	38	engineering	engineering	NOUN
american_scientific_journal-1767	67	39	,	,	PUNCT
american_scientific_journal-1767	67	40	technology	technology	NOUN
american_scientific_journal-1767	67	41	,	,	PUNCT
american_scientific_journal-1767	67	42	and	and	CCONJ
american_scientific_journal-1767	67	43	sciences	science	NOUN
american_scientific_journal-1767	67	44	(	(	PUNCT
american_scientific_journal-1767	67	45	asrjets	asrjet	NOUN
american_scientific_journal-1767	67	46	)	)	PUNCT
american_scientific_journal-1767	67	47	(	(	PUNCT
american_scientific_journal-1767	67	48	2016	2016	NUM
american_scientific_journal-1767	67	49	)	)	PUNCT
american_scientific_journal-1767	67	50	volume	volume	NOUN
american_scientific_journal-1767	67	51	21	21	NUM
american_scientific_journal-1767	67	52	,	,	PUNCT
american_scientific_journal-1767	67	53	no	no	DET
american_scientific_journal-1767	67	54	1	1	NUM
american_scientific_journal-1767	67	55	,	,	PUNCT
american_scientific_journal-1767	67	56	pp	pp	ADV
american_scientific_journal-1767	67	57	163	163	NUM
american_scientific_journal-1767	67	58	-	-	SYM
american_scientific_journal-1767	67	59	177	177	NUM
american_scientific_journal-1767	67	60	170	170	NUM
american_scientific_journal-1767	67	61	hence	hence	ADV
american_scientific_journal-1767	67	62	the	the	DET
american_scientific_journal-1767	67	63	metric	metric	ADJ
american_scientific_journal-1767	67	64	(	(	PUNCT
american_scientific_journal-1767	67	65	18	18	NUM
american_scientific_journal-1767	67	66	)	)	PUNCT
american_scientific_journal-1767	67	67	outside	outside	ADP
american_scientific_journal-1767	67	68	the	the	DET
american_scientific_journal-1767	67	69	sphere	sphere	NOUN
american_scientific_journal-1767	67	70	takes	take	VERB
american_scientific_journal-1767	67	71	the	the	DET
american_scientific_journal-1767	67	72	form	form	NOUN
american_scientific_journal-1767	67	73	𝑑𝑑𝑑𝑑2	𝑑𝑑𝑑𝑑2	NOUN
american_scientific_journal-1767	68	1	=	=	SYM
american_scientific_journal-1767	68	2	1	1	NUM
american_scientific_journal-1767	68	3	�	�	PROPN
american_scientific_journal-1767	68	4	1+𝑚𝑚𝑅𝑅	1+𝑚𝑚𝑅𝑅	NUM
american_scientific_journal-1767	68	5	�	�	PROPN
american_scientific_journal-1767	68	6	2	2	NUM
american_scientific_journal-1767	68	7	𝑐𝑐2𝑑𝑑𝑑𝑑2	𝑐𝑐2𝑑𝑑𝑑𝑑2	SYM
american_scientific_journal-1767	68	8	−	−	PROPN
american_scientific_journal-1767	68	9	�	�	PROPN
american_scientific_journal-1767	68	10	1	1	NUM
american_scientific_journal-1767	68	11	+	+	CCONJ
american_scientific_journal-1767	68	12	𝑚𝑚	𝑚𝑚	ADP
american_scientific_journal-1767	68	13	𝑅𝑅	𝑅𝑅	PROPN
american_scientific_journal-1767	68	14	�	�	PROPN
american_scientific_journal-1767	68	15	2	2	NUM
american_scientific_journal-1767	68	16	(	(	PUNCT
american_scientific_journal-1767	68	17	𝑑𝑑𝑑𝑑2	𝑑𝑑𝑑𝑑2	PROPN
american_scientific_journal-1767	68	18	+	+	CCONJ
american_scientific_journal-1767	68	19	𝑑𝑑2𝑑𝑑ω2	𝑑𝑑2𝑑𝑑ω2	PROPN
american_scientific_journal-1767	68	20	)	)	PUNCT
american_scientific_journal-1767	68	21	thus	thus	ADV
american_scientific_journal-1767	68	22	introducing	introduce	VERB
american_scientific_journal-1767	68	23	different	different	ADJ
american_scientific_journal-1767	68	24	coordinates	coordinate	NOUN
american_scientific_journal-1767	68	25	in	in	ADP
american_scientific_journal-1767	68	26	the	the	DET
american_scientific_journal-1767	68	27	regions	region	NOUN
american_scientific_journal-1767	68	28	inside	inside	ADP
american_scientific_journal-1767	68	29	and	and	CCONJ
american_scientific_journal-1767	68	30	outside	outside	ADP
american_scientific_journal-1767	68	31	the	the	DET
american_scientific_journal-1767	68	32	sphere	sphere	NOUN
american_scientific_journal-1767	68	33	gives	give	VERB
american_scientific_journal-1767	68	34	us	we	PRON
american_scientific_journal-1767	68	35	a	a	DET
american_scientific_journal-1767	68	36	metric	metric	NOUN
american_scientific_journal-1767	68	37	which	which	PRON
american_scientific_journal-1767	68	38	is	be	AUX
american_scientific_journal-1767	68	39	lorentzian	lorentzian	ADJ
american_scientific_journal-1767	68	40	at	at	ADP
american_scientific_journal-1767	68	41	infinity	infinity	NOUN
american_scientific_journal-1767	68	42	,	,	PUNCT
american_scientific_journal-1767	68	43	unlike	unlike	ADP
american_scientific_journal-1767	68	44	in	in	ADP
american_scientific_journal-1767	68	45	sashinka	sashinka	PROPN
american_scientific_journal-1767	68	46	wimaladharma	wimaladharma	NOUN
american_scientific_journal-1767	68	47	and	and	CCONJ
american_scientific_journal-1767	68	48	nalin	nalin	PROPN
american_scientific_journal-1767	68	49	de	de	PROPN
american_scientific_journal-1767	68	50	silva	silva	PROPN
american_scientific_journal-1767	69	1	[	[	X
american_scientific_journal-1767	69	2	1	1	NUM
american_scientific_journal-1767	69	3	]	]	PUNCT
american_scientific_journal-1767	69	4	where	where	SCONJ
american_scientific_journal-1767	69	5	was	be	AUX
american_scientific_journal-1767	69	6	a	a	DET
american_scientific_journal-1767	69	7	metric	metric	NOUN
american_scientific_journal-1767	69	8	that	that	PRON
american_scientific_journal-1767	69	9	was	be	AUX
american_scientific_journal-1767	69	10	not	not	PART
american_scientific_journal-1767	69	11	lorenzian	lorenzian	ADJ
american_scientific_journal-1767	69	12	at	at	ADP
american_scientific_journal-1767	69	13	infinity	infinity	NOUN
american_scientific_journal-1767	69	14	.	.	PUNCT
american_scientific_journal-1767	70	1	now	now	ADV
american_scientific_journal-1767	70	2	considering	consider	VERB
american_scientific_journal-1767	70	3	the	the	DET
american_scientific_journal-1767	70	4	metric	metric	ADJ
american_scientific_journal-1767	70	5	(	(	PUNCT
american_scientific_journal-1767	70	6	1	1	NUM
american_scientific_journal-1767	70	7	)	)	PUNCT
american_scientific_journal-1767	70	8	without	without	ADP
american_scientific_journal-1767	70	9	initially	initially	ADV
american_scientific_journal-1767	70	10	assuming	assume	VERB
american_scientific_journal-1767	70	11	that	that	SCONJ
american_scientific_journal-1767	70	12	it	it	PRON
american_scientific_journal-1767	70	13	becomes	become	VERB
american_scientific_journal-1767	70	14	lorentzian	lorentzian	ADJ
american_scientific_journal-1767	70	15	at	at	ADP
american_scientific_journal-1767	70	16	infinity	infinity	NOUN
american_scientific_journal-1767	70	17	,	,	PUNCT
american_scientific_journal-1767	70	18	and	and	CCONJ
american_scientific_journal-1767	70	19	applying	apply	VERB
american_scientific_journal-1767	70	20	the	the	DET
american_scientific_journal-1767	70	21	same	same	ADJ
american_scientific_journal-1767	70	22	boundary	boundary	ADJ
american_scientific_journal-1767	70	23	conditions	condition	NOUN
american_scientific_journal-1767	70	24	as	as	ADP
american_scientific_journal-1767	70	25	above	above	ADV
american_scientific_journal-1767	70	26	,	,	PUNCT
american_scientific_journal-1767	70	27	it	it	PRON
american_scientific_journal-1767	70	28	can	can	AUX
american_scientific_journal-1767	70	29	be	be	AUX
american_scientific_journal-1767	70	30	shown	show	VERB
american_scientific_journal-1767	70	31	that	that	SCONJ
american_scientific_journal-1767	70	32	the	the	DET
american_scientific_journal-1767	70	33	value	value	NOUN
american_scientific_journal-1767	70	34	of	of	ADP
american_scientific_journal-1767	70	35	the	the	DET
american_scientific_journal-1767	70	36	constant	constant	ADJ
american_scientific_journal-1767	70	37	𝐴𝐴1	𝐴𝐴1	PROPN
american_scientific_journal-1767	70	38	and	and	CCONJ
american_scientific_journal-1767	70	39	𝐴𝐴2	𝐴𝐴2	PROPN
american_scientific_journal-1767	70	40	are	be	AUX
american_scientific_journal-1767	70	41	such	such	ADJ
american_scientific_journal-1767	70	42	that	that	SCONJ
american_scientific_journal-1767	70	43	𝐴𝐴1	𝐴𝐴1	PROPN
american_scientific_journal-1767	70	44	=	=	PUNCT
american_scientific_journal-1767	70	45	𝑎𝑎	𝑎𝑎	VERB
american_scientific_journal-1767	70	46	𝐴𝐴	𝐴𝐴	PROPN
american_scientific_journal-1767	70	47	�	�	PROPN
american_scientific_journal-1767	70	48	𝜃𝜃	𝜃𝜃	PROPN
american_scientific_journal-1767	70	49	�	�	PROPN
american_scientific_journal-1767	70	50	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1767	70	51	𝑙𝑙	𝑙𝑙	PROPN
american_scientific_journal-1767	70	52	�	�	PROPN
american_scientific_journal-1767	70	53	+	+	CCONJ
american_scientific_journal-1767	70	54	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1767	70	55	𝑙𝑙	𝑙𝑙	NOUN
american_scientific_journal-1767	70	56	𝜃𝜃′	𝜃𝜃′	NOUN
american_scientific_journal-1767	70	57	�	�	NOUN
american_scientific_journal-1767	70	58	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1767	70	59	𝑙𝑙	𝑙𝑙	PROPN
american_scientific_journal-1767	70	60	�	�	PROPN
american_scientific_journal-1767	70	61	�	�	PROPN
american_scientific_journal-1767	70	62	(	(	PUNCT
american_scientific_journal-1767	70	63	20	20	NUM
american_scientific_journal-1767	70	64	)	)	PUNCT
american_scientific_journal-1767	70	65	𝐴𝐴2	𝐴𝐴2	NOUN
american_scientific_journal-1767	70	66	=	=	SYM
american_scientific_journal-1767	70	67	−𝑎𝑎2	−𝑎𝑎2	PROPN
american_scientific_journal-1767	70	68	𝑙𝑙	𝑙𝑙	NOUN
american_scientific_journal-1767	70	69	𝜃𝜃′	𝜃𝜃′	PROPN
american_scientific_journal-1767	70	70	�	�	NOUN
american_scientific_journal-1767	70	71	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1767	70	72	𝑙𝑙	𝑙𝑙	PROPN
american_scientific_journal-1767	70	73	�	�	PROPN
american_scientific_journal-1767	70	74	.	.	PUNCT
american_scientific_journal-1767	71	1	(	(	PUNCT
american_scientific_journal-1767	71	2	21	21	NUM
american_scientific_journal-1767	71	3	)	)	PUNCT
american_scientific_journal-1767	71	4	thus	thus	ADV
american_scientific_journal-1767	71	5	it	it	PRON
american_scientific_journal-1767	71	6	is	be	AUX
american_scientific_journal-1767	71	7	found	find	VERB
american_scientific_journal-1767	71	8	that	that	SCONJ
american_scientific_journal-1767	71	9	the	the	DET
american_scientific_journal-1767	71	10	value	value	NOUN
american_scientific_journal-1767	71	11	for	for	ADP
american_scientific_journal-1767	71	12	2a	2a	NUM
american_scientific_journal-1767	71	13	is	be	AUX
american_scientific_journal-1767	71	14	the	the	DET
american_scientific_journal-1767	71	15	same	same	ADJ
american_scientific_journal-1767	71	16	for	for	ADP
american_scientific_journal-1767	71	17	the	the	DET
american_scientific_journal-1767	71	18	metrics	metric	NOUN
american_scientific_journal-1767	71	19	obtained	obtain	VERB
american_scientific_journal-1767	71	20	in	in	ADP
american_scientific_journal-1767	71	21	sashinka	sashinka	PROPN
american_scientific_journal-1767	71	22	wimaladharma	wimaladharma	PROPN
american_scientific_journal-1767	71	23	and	and	CCONJ
american_scientific_journal-1767	71	24	nalin	nalin	PROPN
american_scientific_journal-1767	71	25	de	de	PROPN
american_scientific_journal-1767	71	26	silva	silva	PROPN
american_scientific_journal-1767	72	1	[	[	X
american_scientific_journal-1767	72	2	1	1	NUM
american_scientific_journal-1767	72	3	]	]	PUNCT
american_scientific_journal-1767	72	4	,	,	PUNCT
american_scientific_journal-1767	72	5	(	(	PUNCT
american_scientific_journal-1767	72	6	16	16	NUM
american_scientific_journal-1767	72	7	)	)	PUNCT
american_scientific_journal-1767	72	8	and	and	CCONJ
american_scientific_journal-1767	72	9	(	(	PUNCT
american_scientific_journal-1767	72	10	21	21	NUM
american_scientific_journal-1767	72	11	)	)	PUNCT
american_scientific_journal-1767	72	12	irrespective	irrespective	ADV
american_scientific_journal-1767	72	13	of	of	ADP
american_scientific_journal-1767	72	14	whether	whether	SCONJ
american_scientific_journal-1767	72	15	the	the	DET
american_scientific_journal-1767	72	16	metric	metric	NOUN
american_scientific_journal-1767	72	17	is	be	AUX
american_scientific_journal-1767	72	18	lorentzian	lorentzian	ADJ
american_scientific_journal-1767	72	19	at	at	ADP
american_scientific_journal-1767	72	20	infinity	infinity	NOUN
american_scientific_journal-1767	72	21	.	.	PUNCT
american_scientific_journal-1767	73	1	this	this	PRON
american_scientific_journal-1767	73	2	could	could	AUX
american_scientific_journal-1767	73	3	have	have	AUX
american_scientific_journal-1767	73	4	been	be	AUX
american_scientific_journal-1767	73	5	expected	expect	VERB
american_scientific_journal-1767	73	6	as	as	ADP
american_scientific_journal-1767	73	7	the	the	DET
american_scientific_journal-1767	73	8	expression	expression	NOUN
american_scientific_journal-1767	73	9	for	for	ADP
american_scientific_journal-1767	73	10	2a	2a	NUM
american_scientific_journal-1767	73	11	gives	give	VERB
american_scientific_journal-1767	73	12	the	the	DET
american_scientific_journal-1767	73	13	value	value	NOUN
american_scientific_journal-1767	73	14	of	of	ADP
american_scientific_journal-1767	73	15	m	m	PROPN
american_scientific_journal-1767	73	16	,	,	PUNCT
american_scientific_journal-1767	73	17	the	the	DET
american_scientific_journal-1767	73	18	mass	mass	NOUN
american_scientific_journal-1767	73	19	of	of	ADP
american_scientific_journal-1767	73	20	the	the	DET
american_scientific_journal-1767	73	21	distribution	distribution	NOUN
american_scientific_journal-1767	73	22	as	as	SCONJ
american_scientific_journal-1767	73	23	calculated	calculate	VERB
american_scientific_journal-1767	73	24	inside	inside	ADP
american_scientific_journal-1767	73	25	the	the	DET
american_scientific_journal-1767	73	26	sphere	sphere	NOUN
american_scientific_journal-1767	73	27	by	by	ADP
american_scientific_journal-1767	73	28	integration	integration	NOUN
american_scientific_journal-1767	73	29	as	as	ADP
american_scientific_journal-1767	73	30	in	in	ADP
american_scientific_journal-1767	73	31	wickramasuriya	wickramasuriya	NOUN
american_scientific_journal-1767	73	32	and	and	CCONJ
american_scientific_journal-1767	73	33	bonnar	bonnar	PROPN
american_scientific_journal-1767	74	1	[	[	X
american_scientific_journal-1767	74	2	4	4	NUM
american_scientific_journal-1767	74	3	]	]	PUNCT
american_scientific_journal-1767	74	4	.	.	PUNCT
american_scientific_journal-1767	75	1	if	if	SCONJ
american_scientific_journal-1767	75	2	the	the	DET
american_scientific_journal-1767	75	3	metric	metric	NOUN
american_scientific_journal-1767	75	4	for	for	ADP
american_scientific_journal-1767	75	5	the	the	DET
american_scientific_journal-1767	75	6	outside	outside	NOUN
american_scientific_journal-1767	75	7	of	of	ADP
american_scientific_journal-1767	75	8	the	the	DET
american_scientific_journal-1767	75	9	sphere	sphere	NOUN
american_scientific_journal-1767	75	10	is	be	AUX
american_scientific_journal-1767	75	11	lorentzian	lorentzian	ADJ
american_scientific_journal-1767	75	12	,	,	PUNCT
american_scientific_journal-1767	75	13	then	then	ADV
american_scientific_journal-1767	75	14	then	then	ADV
american_scientific_journal-1767	75	15	the	the	DET
american_scientific_journal-1767	75	16	constant	constant	ADJ
american_scientific_journal-1767	75	17	𝐴𝐴1	𝐴𝐴1	PROPN
american_scientific_journal-1767	75	18	should	should	AUX
american_scientific_journal-1767	75	19	be	be	AUX
american_scientific_journal-1767	75	20	equal	equal	ADJ
american_scientific_journal-1767	75	21	to	to	ADP
american_scientific_journal-1767	75	22	unity	unity	NOUN
american_scientific_journal-1767	75	23	,	,	PUNCT
american_scientific_journal-1767	75	24	i.e	i.e	DET
american_scientific_journal-1767	75	25	𝐴𝐴1	𝐴𝐴1	PROPN
american_scientific_journal-1767	75	26	=	=	PUNCT
american_scientific_journal-1767	75	27	𝑎𝑎	𝑎𝑎	VERB
american_scientific_journal-1767	75	28	𝐴𝐴	𝐴𝐴	PROPN
american_scientific_journal-1767	75	29	�	�	PROPN
american_scientific_journal-1767	75	30	𝜃𝜃	𝜃𝜃	PROPN
american_scientific_journal-1767	75	31	�	�	PROPN
american_scientific_journal-1767	75	32	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1767	75	33	𝑙𝑙	𝑙𝑙	PROPN
american_scientific_journal-1767	75	34	�	�	PROPN
american_scientific_journal-1767	75	35	+	+	CCONJ
american_scientific_journal-1767	75	36	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1767	75	37	𝑙𝑙	𝑙𝑙	NOUN
american_scientific_journal-1767	75	38	𝜃𝜃′	𝜃𝜃′	NOUN
american_scientific_journal-1767	75	39	�	�	NOUN
american_scientific_journal-1767	75	40	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1767	75	41	𝑙𝑙	𝑙𝑙	PROPN
american_scientific_journal-1767	75	42	�	�	PROPN
american_scientific_journal-1767	75	43	�	�	PROPN
american_scientific_journal-1767	75	44	=	=	SYM
american_scientific_journal-1767	75	45	1	1	NUM
american_scientific_journal-1767	75	46	which	which	PRON
american_scientific_journal-1767	75	47	implies	imply	VERB
american_scientific_journal-1767	75	48	that	that	SCONJ
american_scientific_journal-1767	75	49	𝐴𝐴	𝐴𝐴	PROPN
american_scientific_journal-1767	75	50	=	=	PUNCT
american_scientific_journal-1767	75	51	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1767	75	52	�	�	PROPN
american_scientific_journal-1767	75	53	𝜃𝜃	𝜃𝜃	PROPN
american_scientific_journal-1767	75	54	�	�	PROPN
american_scientific_journal-1767	75	55	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1767	75	56	𝑙𝑙	𝑙𝑙	PROPN
american_scientific_journal-1767	75	57	�	�	PROPN
american_scientific_journal-1767	75	58	+	+	CCONJ
american_scientific_journal-1767	75	59	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1767	75	60	𝑙𝑙	𝑙𝑙	NOUN
american_scientific_journal-1767	75	61	𝜃𝜃′	𝜃𝜃′	NOUN
american_scientific_journal-1767	75	62	�	�	NOUN
american_scientific_journal-1767	75	63	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1767	75	64	𝑙𝑙	𝑙𝑙	PROPN
american_scientific_journal-1767	75	65	�	�	PROPN
american_scientific_journal-1767	75	66	�	�	PROPN
american_scientific_journal-1767	75	67	which	which	PRON
american_scientific_journal-1767	75	68	is	be	AUX
american_scientific_journal-1767	75	69	the	the	DET
american_scientific_journal-1767	75	70	value	value	NOUN
american_scientific_journal-1767	75	71	of	of	ADP
american_scientific_journal-1767	75	72	the	the	DET
american_scientific_journal-1767	75	73	radial	radial	ADJ
american_scientific_journal-1767	75	74	coordinate	coordinate	NOUN
american_scientific_journal-1767	75	75	at	at	ADP
american_scientific_journal-1767	75	76	the	the	DET
american_scientific_journal-1767	75	77	surface	surface	NOUN
american_scientific_journal-1767	75	78	of	of	ADP
american_scientific_journal-1767	75	79	the	the	DET
american_scientific_journal-1767	75	80	sphere	sphere	NOUN
american_scientific_journal-1767	75	81	as	as	SCONJ
american_scientific_journal-1767	75	82	measured	measure	VERB
american_scientific_journal-1767	75	83	just	just	ADV
american_scientific_journal-1767	75	84	outside	outside	ADP
american_scientific_journal-1767	75	85	the	the	DET
american_scientific_journal-1767	75	86	sphere	sphere	NOUN
american_scientific_journal-1767	75	87	.	.	PUNCT
american_scientific_journal-1767	76	1	as	as	SCONJ
american_scientific_journal-1767	76	2	before	before	SCONJ
american_scientific_journal-1767	76	3	𝐴𝐴	𝐴𝐴	PROPN
american_scientific_journal-1767	76	4	becomes	become	VERB
american_scientific_journal-1767	76	5	zero	zero	NUM
american_scientific_journal-1767	76	6	when	when	SCONJ
american_scientific_journal-1767	76	7	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1767	76	8	𝑙𝑙	𝑙𝑙	VERB
american_scientific_journal-1767	76	9	is	be	AUX
american_scientific_journal-1767	76	10	nearly	nearly	ADV
american_scientific_journal-1767	76	11	equal	equal	ADJ
american_scientific_journal-1767	76	12	to	to	ADP
american_scientific_journal-1767	76	13	2.16	2.16	NUM
american_scientific_journal-1767	76	14	.	.	PUNCT
american_scientific_journal-1767	77	1	thus	thus	ADV
american_scientific_journal-1767	77	2	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1767	77	3	𝑙𝑙	𝑙𝑙	PROPN
american_scientific_journal-1767	77	4	has	have	AUX
american_scientific_journal-1767	77	5	a	a	DET
american_scientific_journal-1767	77	6	maximum	maximum	ADJ
american_scientific_journal-1767	77	7	value	value	NOUN
american_scientific_journal-1767	77	8	nearly	nearly	ADV
american_scientific_journal-1767	77	9	equal	equal	ADJ
american_scientific_journal-1767	77	10	to	to	ADP
american_scientific_journal-1767	77	11	2.16	2.16	NUM
american_scientific_journal-1767	77	12	.	.	PUNCT
american_scientific_journal-1767	78	1	the	the	DET
american_scientific_journal-1767	78	2	graph	graph	NOUN
american_scientific_journal-1767	78	3	of	of	ADP
american_scientific_journal-1767	78	4	𝐴𝐴𝐴𝐴1	𝐴𝐴𝐴𝐴1	PROPN
american_scientific_journal-1767	78	5	against	against	ADP
american_scientific_journal-1767	78	6	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1767	78	7	𝑙𝑙	𝑙𝑙	PROPN
american_scientific_journal-1767	78	8	is	be	AUX
american_scientific_journal-1767	78	9	plotted	plot	VERB
american_scientific_journal-1767	78	10	in	in	ADP
american_scientific_journal-1767	78	11	figure	figure	NOUN
american_scientific_journal-1767	78	12	1	1	NUM
american_scientific_journal-1767	78	13	.	.	PUNCT
american_scientific_journal-1767	79	1	𝐴𝐴𝐴𝐴1	𝐴𝐴𝐴𝐴1	PROPN
american_scientific_journal-1767	79	2	it	it	PRON
american_scientific_journal-1767	79	3	can	can	AUX
american_scientific_journal-1767	79	4	be	be	AUX
american_scientific_journal-1767	79	5	found	find	VERB
american_scientific_journal-1767	79	6	from	from	ADP
american_scientific_journal-1767	79	7	the	the	DET
american_scientific_journal-1767	79	8	figure	figure	NOUN
american_scientific_journal-1767	79	9	1	1	NUM
american_scientific_journal-1767	79	10	that	that	SCONJ
american_scientific_journal-1767	79	11	𝐴𝐴𝐴𝐴1	𝐴𝐴𝐴𝐴1	PROPN
american_scientific_journal-1767	79	12	has	have	VERB
american_scientific_journal-1767	79	13	a	a	DET
american_scientific_journal-1767	79	14	maximum	maximum	ADJ
american_scientific_journal-1767	79	15	value	value	NOUN
american_scientific_journal-1767	79	16	which	which	PRON
american_scientific_journal-1767	79	17	is	be	AUX
american_scientific_journal-1767	79	18	equal	equal	ADJ
american_scientific_journal-1767	79	19	to	to	ADP
american_scientific_journal-1767	79	20	0.6	0.6	NUM
american_scientific_journal-1767	79	21	𝑙𝑙.	𝑙𝑙.	NOUN
american_scientific_journal-1767	79	22	therefore	therefore	ADV
american_scientific_journal-1767	79	23	when	when	SCONJ
american_scientific_journal-1767	79	24	the	the	DET
american_scientific_journal-1767	79	25	metric	metric	NOUN
american_scientific_journal-1767	79	26	is	be	AUX
american_scientific_journal-1767	79	27	lorentzian	lorentzian	ADJ
american_scientific_journal-1767	79	28	(	(	PUNCT
american_scientific_journal-1767	79	29	𝐴𝐴1	𝐴𝐴1	PROPN
american_scientific_journal-1767	79	30	=	=	NOUN
american_scientific_journal-1767	79	31	1	1	NUM
american_scientific_journal-1767	79	32	)	)	PUNCT
american_scientific_journal-1767	79	33	the	the	DET
american_scientific_journal-1767	79	34	maximum	maximum	ADJ
american_scientific_journal-1767	79	35	value	value	NOUN
american_scientific_journal-1767	79	36	of	of	ADP
american_scientific_journal-1767	79	37	𝐴𝐴	𝐴𝐴	PROPN
american_scientific_journal-1767	79	38	equal	equal	ADJ
american_scientific_journal-1767	79	39	to	to	ADP
american_scientific_journal-1767	79	40	0.6	0.6	NUM
american_scientific_journal-1767	79	41	𝑙𝑙.	𝑙𝑙.	NOUN
american_scientific_journal-1767	79	42	this	this	PRON
american_scientific_journal-1767	79	43	corresponds	correspond	VERB
american_scientific_journal-1767	79	44	to	to	ADP
american_scientific_journal-1767	79	45	a	a	DET
american_scientific_journal-1767	79	46	value	value	NOUN
american_scientific_journal-1767	79	47	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1767	79	48	which	which	PRON
american_scientific_journal-1767	79	49	is	be	AUX
american_scientific_journal-1767	79	50	equal	equal	ADJ
american_scientific_journal-1767	79	51	to	to	ADP
american_scientific_journal-1767	79	52	𝑙𝑙.	𝑙𝑙.	VERB
american_scientific_journal-1767	79	53	thus	thus	ADV
american_scientific_journal-1767	79	54	the	the	DET
american_scientific_journal-1767	79	55	outer	outer	ADJ
american_scientific_journal-1767	79	56	radial	radial	ADJ
american_scientific_journal-1767	79	57	coordinate	coordinate	NOUN
american_scientific_journal-1767	79	58	𝐴𝐴	𝐴𝐴	PROPN
american_scientific_journal-1767	79	59	increases	increase	NOUN
american_scientific_journal-1767	79	60	with	with	ADP
american_scientific_journal-1767	79	61	inner	inner	ADJ
american_scientific_journal-1767	79	62	radial	radial	ADJ
american_scientific_journal-1767	79	63	coordinate	coordinate	NOUN
american_scientific_journal-1767	79	64	𝑎𝑎	𝑎𝑎	VERB
american_scientific_journal-1767	79	65	until	until	ADP
american_scientific_journal-1767	79	66	0.6	0.6	NUM
american_scientific_journal-1767	79	67	𝑙𝑙	𝑙𝑙	NOUN
american_scientific_journal-1767	79	68	.	.	PUNCT
american_scientific_journal-1767	80	1	after	after	SCONJ
american_scientific_journal-1767	80	2	that	that	PRON
american_scientific_journal-1767	80	3	𝐴𝐴	𝐴𝐴	PROPN
american_scientific_journal-1767	80	4	decreases	decrease	VERB
american_scientific_journal-1767	80	5	with	with	ADP
american_scientific_journal-1767	80	6	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1767	80	7	and	and	CCONJ
american_scientific_journal-1767	80	8	becomes	become	VERB
american_scientific_journal-1767	80	9	zero	zero	NUM
american_scientific_journal-1767	80	10	when	when	SCONJ
american_scientific_journal-1767	80	11	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1767	80	12	=	=	SYM
american_scientific_journal-1767	80	13	2.16	2.16	NUM
american_scientific_journal-1767	80	14	𝑙𝑙	𝑙𝑙	NOUN
american_scientific_journal-1767	80	15	.	.	PUNCT
american_scientific_journal-1767	81	1	american	american	PROPN
american_scientific_journal-1767	81	2	scientific	scientific	ADJ
american_scientific_journal-1767	81	3	research	research	PROPN
american_scientific_journal-1767	81	4	journal	journal	NOUN
american_scientific_journal-1767	81	5	for	for	ADP
american_scientific_journal-1767	81	6	engineering	engineering	NOUN
american_scientific_journal-1767	81	7	,	,	PUNCT
american_scientific_journal-1767	81	8	technology	technology	NOUN
american_scientific_journal-1767	81	9	,	,	PUNCT
american_scientific_journal-1767	81	10	and	and	CCONJ
american_scientific_journal-1767	81	11	sciences	science	NOUN
american_scientific_journal-1767	81	12	(	(	PUNCT
american_scientific_journal-1767	81	13	asrjets	asrjet	NOUN
american_scientific_journal-1767	81	14	)	)	PUNCT
american_scientific_journal-1767	81	15	(	(	PUNCT
american_scientific_journal-1767	81	16	2016	2016	NUM
american_scientific_journal-1767	81	17	)	)	PUNCT
american_scientific_journal-1767	81	18	volume	volume	NOUN
american_scientific_journal-1767	81	19	21	21	NUM
american_scientific_journal-1767	81	20	,	,	PUNCT
american_scientific_journal-1767	81	21	no	no	DET
american_scientific_journal-1767	81	22	1	1	NUM
american_scientific_journal-1767	81	23	,	,	PUNCT
american_scientific_journal-1767	81	24	pp	pp	ADV
american_scientific_journal-1767	81	25	163	163	NUM
american_scientific_journal-1767	81	26	-	-	SYM
american_scientific_journal-1767	81	27	177	177	NUM
american_scientific_journal-1767	81	28	171	171	NUM
american_scientific_journal-1767	81	29	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1767	81	30	𝑙𝑙	𝑙𝑙	NOUN
american_scientific_journal-1767	81	31	figure	figure	NOUN
american_scientific_journal-1767	81	32	1	1	NUM
american_scientific_journal-1767	81	33	:	:	PUNCT
american_scientific_journal-1767	81	34	the	the	DET
american_scientific_journal-1767	81	35	graph	graph	NOUN
american_scientific_journal-1767	81	36	of	of	ADP
american_scientific_journal-1767	81	37	𝐴𝐴𝐴𝐴1	𝐴𝐴𝐴𝐴1	PROPN
american_scientific_journal-1767	81	38	against	against	ADP
american_scientific_journal-1767	81	39	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1767	81	40	𝑙𝑙	𝑙𝑙	PROPN
american_scientific_journal-1767	81	41	it	it	PRON
american_scientific_journal-1767	81	42	can	can	AUX
american_scientific_journal-1767	81	43	be	be	AUX
american_scientific_journal-1767	81	44	postulated	postulate	VERB
american_scientific_journal-1767	81	45	that	that	SCONJ
american_scientific_journal-1767	81	46	𝐴𝐴	𝐴𝐴	PROPN
american_scientific_journal-1767	81	47	increases	increase	NOUN
american_scientific_journal-1767	81	48	and	and	CCONJ
american_scientific_journal-1767	81	49	attains	attain	NOUN
american_scientific_journal-1767	81	50	a	a	DET
american_scientific_journal-1767	81	51	maximum	maximum	NOUN
american_scientific_journal-1767	81	52	at	at	ADP
american_scientific_journal-1767	81	53	𝐴𝐴	𝐴𝐴	PROPN
american_scientific_journal-1767	81	54	=	=	SYM
american_scientific_journal-1767	81	55	0.6	0.6	NUM
american_scientific_journal-1767	81	56	𝑙𝑙	𝑙𝑙	INTJ
american_scientific_journal-1767	81	57	when	when	SCONJ
american_scientific_journal-1767	81	58	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1767	81	59	=	=	SYM
american_scientific_journal-1767	81	60	𝑙𝑙	𝑙𝑙	X
american_scientific_journal-1767	81	61	,	,	PUNCT
american_scientific_journal-1767	81	62	and	and	CCONJ
american_scientific_journal-1767	81	63	that	that	SCONJ
american_scientific_journal-1767	81	64	there	there	PRON
american_scientific_journal-1767	81	65	is	be	VERB
american_scientific_journal-1767	81	66	no	no	DET
american_scientific_journal-1767	81	67	decrease	decrease	NOUN
american_scientific_journal-1767	81	68	of	of	ADP
american_scientific_journal-1767	81	69	𝐴𝐴	𝐴𝐴	PROPN
american_scientific_journal-1767	81	70	as	as	ADP
american_scientific_journal-1767	81	71	𝑎𝑎	𝑎𝑎	ADJ
american_scientific_journal-1767	81	72	increases	increase	NOUN
american_scientific_journal-1767	81	73	though	though	SCONJ
american_scientific_journal-1767	81	74	mathematically	mathematically	ADV
american_scientific_journal-1767	81	75	it	it	PRON
american_scientific_journal-1767	81	76	is	be	AUX
american_scientific_journal-1767	81	77	suggested	suggest	VERB
american_scientific_journal-1767	81	78	so	so	ADV
american_scientific_journal-1767	81	79	.	.	PUNCT
american_scientific_journal-1767	82	1	if	if	SCONJ
american_scientific_journal-1767	82	2	𝐴𝐴	𝐴𝐴	PROPN
american_scientific_journal-1767	82	3	decreases	decrease	VERB
american_scientific_journal-1767	82	4	with	with	ADP
american_scientific_journal-1767	82	5	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1767	82	6	after	after	SCONJ
american_scientific_journal-1767	82	7	that	that	SCONJ
american_scientific_journal-1767	82	8	it	it	PRON
american_scientific_journal-1767	82	9	would	would	AUX
american_scientific_journal-1767	82	10	end	end	VERB
american_scientific_journal-1767	82	11	up	up	ADP
american_scientific_journal-1767	82	12	with	with	ADP
american_scientific_journal-1767	82	13	zero	zero	NUM
american_scientific_journal-1767	82	14	and	and	CCONJ
american_scientific_journal-1767	82	15	then	then	ADV
american_scientific_journal-1767	82	16	with	with	ADP
american_scientific_journal-1767	82	17	negative	negative	ADJ
american_scientific_journal-1767	82	18	values	value	NOUN
american_scientific_journal-1767	82	19	that	that	PRON
american_scientific_journal-1767	82	20	have	have	VERB
american_scientific_journal-1767	82	21	no	no	DET
american_scientific_journal-1767	82	22	meaning	meaning	NOUN
american_scientific_journal-1767	82	23	physically	physically	ADV
american_scientific_journal-1767	82	24	.	.	PUNCT
american_scientific_journal-1767	83	1	the	the	DET
american_scientific_journal-1767	83	2	mass	mass	NOUN
american_scientific_journal-1767	83	3	of	of	ADP
american_scientific_journal-1767	83	4	the	the	DET
american_scientific_journal-1767	83	5	sphere	sphere	NOUN
american_scientific_journal-1767	83	6	which	which	PRON
american_scientific_journal-1767	83	7	is	be	AUX
american_scientific_journal-1767	83	8	equal	equal	ADJ
american_scientific_journal-1767	83	9	to	to	ADP
american_scientific_journal-1767	83	10	𝑚𝑚	𝑚𝑚	ADP
american_scientific_journal-1767	83	11	=	=	PUNCT
american_scientific_journal-1767	83	12	−𝑎𝑎2	−𝑎𝑎2	PROPN
american_scientific_journal-1767	83	13	𝑙𝑙	𝑙𝑙	NOUN
american_scientific_journal-1767	83	14	𝜃𝜃′	𝜃𝜃′	PROPN
american_scientific_journal-1767	83	15	�	�	NOUN
american_scientific_journal-1767	83	16	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1767	83	17	𝑙𝑙	𝑙𝑙	PRON
american_scientific_journal-1767	83	18	�	�	PROPN
american_scientific_journal-1767	83	19	is	be	AUX
american_scientific_journal-1767	83	20	plotted	plot	VERB
american_scientific_journal-1767	83	21	against	against	ADP
american_scientific_journal-1767	83	22	𝐴𝐴	𝐴𝐴	PROPN
american_scientific_journal-1767	83	23	in	in	ADP
american_scientific_journal-1767	83	24	the	the	DET
american_scientific_journal-1767	83	25	figure	figure	NOUN
american_scientific_journal-1767	83	26	2	2	NUM
american_scientific_journal-1767	83	27	.	.	PUNCT
american_scientific_journal-1767	84	1	𝑚𝑚	𝑚𝑚	ADP
american_scientific_journal-1767	84	2	=	=	PUNCT
american_scientific_journal-1767	84	3	−𝑎𝑎2	−𝑎𝑎2	PROPN
american_scientific_journal-1767	84	4	𝑙𝑙	𝑙𝑙	NOUN
american_scientific_journal-1767	84	5	𝜃𝜃′	𝜃𝜃′	PROPN
american_scientific_journal-1767	84	6	�	�	NOUN
american_scientific_journal-1767	84	7	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1767	84	8	𝑙𝑙	𝑙𝑙	PROPN
american_scientific_journal-1767	84	9	�	�	PROPN
american_scientific_journal-1767	84	10	𝐴𝐴	𝐴𝐴	PROPN
american_scientific_journal-1767	84	11	figure	figure	NOUN
american_scientific_journal-1767	84	12	2	2	NUM
american_scientific_journal-1767	84	13	:	:	PUNCT
american_scientific_journal-1767	84	14	the	the	DET
american_scientific_journal-1767	84	15	graph	graph	NOUN
american_scientific_journal-1767	84	16	of	of	ADP
american_scientific_journal-1767	84	17	m	m	PRON
american_scientific_journal-1767	84	18	against	against	ADP
american_scientific_journal-1767	84	19	a	a	DET
american_scientific_journal-1767	84	20	figure	figure	NOUN
american_scientific_journal-1767	84	21	2	2	NUM
american_scientific_journal-1767	84	22	suggests	suggest	VERB
american_scientific_journal-1767	84	23	that	that	SCONJ
american_scientific_journal-1767	84	24	𝑚𝑚	𝑚𝑚	ADP
american_scientific_journal-1767	84	25	increases	increase	NOUN
american_scientific_journal-1767	84	26	with	with	ADP
american_scientific_journal-1767	84	27	𝐴𝐴	𝐴𝐴	PROPN
american_scientific_journal-1767	84	28	until	until	SCONJ
american_scientific_journal-1767	84	29	reaches	reach	VERB
american_scientific_journal-1767	84	30	the	the	DET
american_scientific_journal-1767	84	31	value	value	NOUN
american_scientific_journal-1767	84	32	𝐴𝐴	𝐴𝐴	PROPN
american_scientific_journal-1767	84	33	=	=	SYM
american_scientific_journal-1767	84	34	0.6	0.6	NUM
american_scientific_journal-1767	84	35	𝑙𝑙	𝑙𝑙	NOUN
american_scientific_journal-1767	84	36	.after	.after	NOUN
american_scientific_journal-1767	84	37	that	that	SCONJ
american_scientific_journal-1767	84	38	according	accord	VERB
american_scientific_journal-1767	84	39	to	to	ADP
american_scientific_journal-1767	84	40	the	the	DET
american_scientific_journal-1767	84	41	figure	figure	NOUN
american_scientific_journal-1767	84	42	2	2	NUM
american_scientific_journal-1767	84	43	,	,	PUNCT
american_scientific_journal-1767	84	44	𝐴𝐴	𝐴𝐴	PROPN
american_scientific_journal-1767	84	45	decreases	decrease	VERB
american_scientific_journal-1767	84	46	though	though	ADV
american_scientific_journal-1767	84	47	𝑚𝑚	𝑚𝑚	ADP
american_scientific_journal-1767	84	48	increases	increase	NOUN
american_scientific_journal-1767	84	49	,	,	PUNCT
american_scientific_journal-1767	84	50	and	and	CCONJ
american_scientific_journal-1767	84	51	it	it	PRON
american_scientific_journal-1767	84	52	can	can	AUX
american_scientific_journal-1767	84	53	be	be	AUX
american_scientific_journal-1767	84	54	postulated	postulate	VERB
american_scientific_journal-1767	84	55	that	that	SCONJ
american_scientific_journal-1767	84	56	𝑚𝑚	𝑚𝑚	SCONJ
american_scientific_journal-1767	84	57	has	have	VERB
american_scientific_journal-1767	84	58	a	a	DET
american_scientific_journal-1767	84	59	maximum	maximum	ADJ
american_scientific_journal-1767	84	60	1.12	1.12	NUM
american_scientific_journal-1767	84	61	𝑙𝑙	𝑙𝑙	NOUN
american_scientific_journal-1767	84	62	when	when	SCONJ
american_scientific_journal-1767	84	63	𝐴𝐴	𝐴𝐴	PROPN
american_scientific_journal-1767	84	64	=	=	NOUN
american_scientific_journal-1767	84	65	0.6	0.6	NUM
american_scientific_journal-1767	84	66	𝑙𝑙	𝑙𝑙	NOUN
american_scientific_journal-1767	84	67	.	.	PUNCT
american_scientific_journal-1767	85	1	the	the	DET
american_scientific_journal-1767	85	2	maximum	maximum	ADJ
american_scientific_journal-1767	85	3	value	value	NOUN
american_scientific_journal-1767	85	4	of	of	ADP
american_scientific_journal-1767	85	5	𝐴𝐴	𝐴𝐴	PROPN
american_scientific_journal-1767	85	6	is	be	AUX
american_scientific_journal-1767	85	7	the	the	DET
american_scientific_journal-1767	85	8	same	same	ADJ
american_scientific_journal-1767	85	9	for	for	ADP
american_scientific_journal-1767	85	10	both	both	DET
american_scientific_journal-1767	85	11	cases	case	NOUN
american_scientific_journal-1767	85	12	that	that	PRON
american_scientific_journal-1767	85	13	obtained	obtain	VERB
american_scientific_journal-1767	85	14	from	from	ADP
american_scientific_journal-1767	85	15	figure	figure	NOUN
american_scientific_journal-1767	85	16	1	1	NUM
american_scientific_journal-1767	85	17	and	and	CCONJ
american_scientific_journal-1767	85	18	figure	figure	VERB
american_scientific_journal-1767	85	19	2	2	NUM
american_scientific_journal-1767	85	20	.	.	NUM
american_scientific_journal-1767	85	21	0	0	NUM
american_scientific_journal-1767	86	1	0.080.160.240.32	0.080.160.240.32	X
american_scientific_journal-1767	86	2	0.4	0.4	NUM
american_scientific_journal-1767	86	3	0.480.560.640.72	0.480.560.640.72	NOUN
american_scientific_journal-1767	86	4	0.8	0.8	NUM
american_scientific_journal-1767	86	5	0.880.961.041.12	0.880.961.041.12	NUM
american_scientific_journal-1767	86	6	1.2	1.2	NUM
american_scientific_journal-1767	86	7	1.281.361.441.52	1.281.361.441.52	NUM
american_scientific_journal-1767	86	8	1.6	1.6	NUM
american_scientific_journal-1767	86	9	1.681.761.841.92	1.681.761.841.92	NUM
american_scientific_journal-1767	86	10	2	2	NUM
american_scientific_journal-1767	86	11	2.082.162.242.32	2.082.162.242.32	NUM
american_scientific_journal-1767	86	12	2.4	2.4	NUM
american_scientific_journal-1767	86	13	2.48	2.48	NUM
american_scientific_journal-1767	86	14	-0.3	-0.3	PROPN
american_scientific_journal-1767	86	15	-0.2	-0.2	PROPN
american_scientific_journal-1767	86	16	-0.1	-0.1	PROPN
american_scientific_journal-1767	86	17	0	0	NUM
american_scientific_journal-1767	86	18	0.1	0.1	NUM
american_scientific_journal-1767	86	19	0.2	0.2	NUM
american_scientific_journal-1767	86	20	0.3	0.3	NUM
american_scientific_journal-1767	86	21	0.4	0.4	NUM
american_scientific_journal-1767	86	22	0.5	0.5	NUM
american_scientific_journal-1767	86	23	0.6	0.6	NUM
american_scientific_journal-1767	86	24	0.7	0.7	NUM
american_scientific_journal-1767	86	25	a	a	DET
american_scientific_journal-1767	86	26	a	a	DET
american_scientific_journal-1767	86	27	0	0	NUM
american_scientific_journal-1767	86	28	0.1	0.1	NUM
american_scientific_journal-1767	86	29	0.2	0.2	NUM
american_scientific_journal-1767	86	30	0.3	0.3	NUM
american_scientific_journal-1767	86	31	0.4	0.4	NUM
american_scientific_journal-1767	86	32	0.5	0.5	NUM
american_scientific_journal-1767	86	33	0.6	0.6	NUM
american_scientific_journal-1767	86	34	0.7	0.7	NUM
american_scientific_journal-1767	86	35	0	0	NUM
american_scientific_journal-1767	86	36	0.2	0.2	NUM
american_scientific_journal-1767	86	37	0.4	0.4	NUM
american_scientific_journal-1767	86	38	0.6	0.6	NUM
american_scientific_journal-1767	86	39	0.8	0.8	NUM
american_scientific_journal-1767	86	40	1	1	NUM
american_scientific_journal-1767	86	41	1.2	1.2	NUM
american_scientific_journal-1767	86	42	1.4	1.4	NUM
american_scientific_journal-1767	86	43	a	a	DET
american_scientific_journal-1767	86	44	m	m	ADJ
american_scientific_journal-1767	86	45	american	american	ADJ
american_scientific_journal-1767	86	46	scientific	scientific	ADJ
american_scientific_journal-1767	86	47	research	research	NOUN
american_scientific_journal-1767	86	48	journal	journal	NOUN
american_scientific_journal-1767	86	49	for	for	ADP
american_scientific_journal-1767	86	50	engineering	engineering	NOUN
american_scientific_journal-1767	86	51	,	,	PUNCT
american_scientific_journal-1767	86	52	technology	technology	NOUN
american_scientific_journal-1767	86	53	,	,	PUNCT
american_scientific_journal-1767	86	54	and	and	CCONJ
american_scientific_journal-1767	86	55	sciences	science	NOUN
american_scientific_journal-1767	86	56	(	(	PUNCT
american_scientific_journal-1767	86	57	asrjets	asrjet	NOUN
american_scientific_journal-1767	86	58	)	)	PUNCT
american_scientific_journal-1767	86	59	(	(	PUNCT
american_scientific_journal-1767	86	60	2016	2016	NUM
american_scientific_journal-1767	86	61	)	)	PUNCT
american_scientific_journal-1767	86	62	volume	volume	NOUN
american_scientific_journal-1767	86	63	21	21	NUM
american_scientific_journal-1767	86	64	,	,	PUNCT
american_scientific_journal-1767	86	65	no	no	DET
american_scientific_journal-1767	86	66	1	1	NUM
american_scientific_journal-1767	86	67	,	,	PUNCT
american_scientific_journal-1767	86	68	pp	pp	ADV
american_scientific_journal-1767	86	69	163	163	NUM
american_scientific_journal-1767	86	70	-	-	SYM
american_scientific_journal-1767	86	71	177	177	NUM
american_scientific_journal-1767	86	72	172	172	NUM
american_scientific_journal-1767	86	73	the	the	DET
american_scientific_journal-1767	86	74	graph	graph	NOUN
american_scientific_journal-1767	86	75	of	of	ADP
american_scientific_journal-1767	86	76	𝑚𝑚	𝑚𝑚	ADP
american_scientific_journal-1767	86	77	=	=	PUNCT
american_scientific_journal-1767	86	78	−𝑎𝑎2	−𝑎𝑎2	PROPN
american_scientific_journal-1767	86	79	𝑙𝑙	𝑙𝑙	NOUN
american_scientific_journal-1767	86	80	𝜃𝜃′	𝜃𝜃′	PROPN
american_scientific_journal-1767	86	81	�	�	NOUN
american_scientific_journal-1767	86	82	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1767	86	83	𝑙𝑙	𝑙𝑙	PRON
american_scientific_journal-1767	86	84	�	�	PROPN
american_scientific_journal-1767	86	85	versus	versus	ADP
american_scientific_journal-1767	86	86	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1767	86	87	𝑙𝑙	𝑙𝑙	PROPN
american_scientific_journal-1767	86	88	is	be	AUX
american_scientific_journal-1767	86	89	as	as	SCONJ
american_scientific_journal-1767	86	90	shown	show	VERB
american_scientific_journal-1767	86	91	in	in	ADP
american_scientific_journal-1767	86	92	figure	figure	NOUN
american_scientific_journal-1767	86	93	3	3	NUM
american_scientific_journal-1767	86	94	.	.	PUNCT
american_scientific_journal-1767	87	1	𝑚𝑚	𝑚𝑚	ADP
american_scientific_journal-1767	87	2	=	=	PUNCT
american_scientific_journal-1767	87	3	−𝑎𝑎2	−𝑎𝑎2	PROPN
american_scientific_journal-1767	87	4	𝑙𝑙	𝑙𝑙	NOUN
american_scientific_journal-1767	87	5	𝜃𝜃′	𝜃𝜃′	PROPN
american_scientific_journal-1767	87	6	�	�	PROPN
american_scientific_journal-1767	87	7	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1767	87	8	𝑙𝑙	𝑙𝑙	NOUN
american_scientific_journal-1767	87	9	�	�	PROPN
american_scientific_journal-1767	87	10	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1767	87	11	𝑙𝑙	𝑙𝑙	NOUN
american_scientific_journal-1767	87	12	figure	figure	NOUN
american_scientific_journal-1767	87	13	3	3	NUM
american_scientific_journal-1767	87	14	:	:	PUNCT
american_scientific_journal-1767	87	15	the	the	DET
american_scientific_journal-1767	87	16	graph	graph	NOUN
american_scientific_journal-1767	87	17	of	of	ADP
american_scientific_journal-1767	87	18	𝑚𝑚	𝑚𝑚	ADP
american_scientific_journal-1767	87	19	against	against	ADP
american_scientific_journal-1767	87	20	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1767	87	21	𝑙𝑙	𝑙𝑙	PROPN
american_scientific_journal-1767	87	22	in	in	ADP
american_scientific_journal-1767	87	23	figure	figure	NOUN
american_scientific_journal-1767	87	24	3	3	NUM
american_scientific_journal-1767	87	25	,	,	PUNCT
american_scientific_journal-1767	87	26	𝑚𝑚	𝑚𝑚	ADP
american_scientific_journal-1767	87	27	increases	increase	NOUN
american_scientific_journal-1767	87	28	with	with	ADP
american_scientific_journal-1767	87	29	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1767	87	30	𝑙𝑙	𝑙𝑙	PROPN
american_scientific_journal-1767	87	31	without	without	ADP
american_scientific_journal-1767	87	32	a	a	DET
american_scientific_journal-1767	87	33	maximum	maximum	NOUN
american_scientific_journal-1767	87	34	.	.	PUNCT
american_scientific_journal-1767	88	1	however	however	SCONJ
american_scientific_journal-1767	88	2	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1767	88	3	has	have	VERB
american_scientific_journal-1767	88	4	a	a	DET
american_scientific_journal-1767	88	5	maximum	maximum	ADJ
american_scientific_journal-1767	88	6	2.16	2.16	NUM
american_scientific_journal-1767	88	7	𝑙𝑙	𝑙𝑙	NOUN
american_scientific_journal-1767	88	8	and	and	CCONJ
american_scientific_journal-1767	88	9	the	the	DET
american_scientific_journal-1767	88	10	corresponding	corresponding	ADJ
american_scientific_journal-1767	88	11	value	value	NOUN
american_scientific_journal-1767	88	12	of	of	ADP
american_scientific_journal-1767	88	13	𝑚𝑚	𝑚𝑚	ADP
american_scientific_journal-1767	88	14	is	be	AUX
american_scientific_journal-1767	88	15	1.12	1.12	NUM
american_scientific_journal-1767	88	16	𝑙𝑙.	𝑙𝑙.	NOUN
american_scientific_journal-1767	88	17	hence	hence	ADV
american_scientific_journal-1767	88	18	it	it	PRON
american_scientific_journal-1767	88	19	can	can	AUX
american_scientific_journal-1767	88	20	be	be	AUX
american_scientific_journal-1767	88	21	postulated	postulate	VERB
american_scientific_journal-1767	88	22	that	that	SCONJ
american_scientific_journal-1767	88	23	1.12	1.12	NUM
american_scientific_journal-1767	88	24	𝑙𝑙	𝑙𝑙	NOUN
american_scientific_journal-1767	88	25	is	be	AUX
american_scientific_journal-1767	88	26	the	the	DET
american_scientific_journal-1767	88	27	maximum	maximum	ADJ
american_scientific_journal-1767	88	28	value	value	NOUN
american_scientific_journal-1767	88	29	that	that	PRON
american_scientific_journal-1767	88	30	𝑚𝑚	𝑚𝑚	SCONJ
american_scientific_journal-1767	88	31	can	can	AUX
american_scientific_journal-1767	88	32	take	take	VERB
american_scientific_journal-1767	88	33	.	.	PUNCT
american_scientific_journal-1767	89	1	this	this	PRON
american_scientific_journal-1767	89	2	is	be	AUX
american_scientific_journal-1767	89	3	an	an	DET
american_scientific_journal-1767	89	4	interesting	interesting	ADJ
american_scientific_journal-1767	89	5	result	result	NOUN
american_scientific_journal-1767	89	6	as	as	ADP
american_scientific_journal-1767	89	7	in	in	ADP
american_scientific_journal-1767	89	8	the	the	DET
american_scientific_journal-1767	89	9	case	case	NOUN
american_scientific_journal-1767	89	10	of	of	ADP
american_scientific_journal-1767	89	11	electrically	electrically	ADV
american_scientific_journal-1767	89	12	counterpoised	counterpoise	VERB
american_scientific_journal-1767	89	13	dust	dust	NOUN
american_scientific_journal-1767	89	14	distribution	distribution	NOUN
american_scientific_journal-1767	89	15	,	,	PUNCT
american_scientific_journal-1767	89	16	there	there	PRON
american_scientific_journal-1767	89	17	are	be	VERB
american_scientific_journal-1767	89	18	maximum	maximum	ADJ
american_scientific_journal-1767	89	19	values	value	NOUN
american_scientific_journal-1767	89	20	that	that	PRON
american_scientific_journal-1767	89	21	are	be	AUX
american_scientific_journal-1767	89	22	written	write	VERB
american_scientific_journal-1767	89	23	in	in	ADP
american_scientific_journal-1767	89	24	terms	term	NOUN
american_scientific_journal-1767	89	25	of	of	ADP
american_scientific_journal-1767	89	26	𝑙𝑙	𝑙𝑙	PRON
american_scientific_journal-1767	89	27	which	which	PRON
american_scientific_journal-1767	89	28	can	can	AUX
american_scientific_journal-1767	89	29	in	in	ADP
american_scientific_journal-1767	89	30	turn	turn	NOUN
american_scientific_journal-1767	89	31	be	be	AUX
american_scientific_journal-1767	89	32	expressed	express	VERB
american_scientific_journal-1767	89	33	in	in	ADP
american_scientific_journal-1767	89	34	terms	term	NOUN
american_scientific_journal-1767	89	35	of	of	ADP
american_scientific_journal-1767	89	36	density	density	NOUN
american_scientific_journal-1767	89	37	as	as	ADP
american_scientific_journal-1767	89	38	4𝜋𝜋𝜋𝜋𝑙𝑙2	4𝜋𝜋𝜋𝜋𝑙𝑙2	NUM
american_scientific_journal-1767	89	39	=	=	SYM
american_scientific_journal-1767	89	40	1	1	X
american_scientific_journal-1767	89	41	.	.	PUNCT
american_scientific_journal-1767	90	1	this	this	PRON
american_scientific_journal-1767	90	2	implies	imply	VERB
american_scientific_journal-1767	90	3	that	that	SCONJ
american_scientific_journal-1767	90	4	given	give	VERB
american_scientific_journal-1767	90	5	the	the	DET
american_scientific_journal-1767	90	6	constant	constant	ADJ
american_scientific_journal-1767	90	7	density	density	NOUN
american_scientific_journal-1767	90	8	of	of	ADP
american_scientific_journal-1767	90	9	the	the	DET
american_scientific_journal-1767	90	10	distribution	distribution	NOUN
american_scientific_journal-1767	90	11	there	there	PRON
american_scientific_journal-1767	90	12	are	be	VERB
american_scientific_journal-1767	90	13	maximum	maximum	ADJ
american_scientific_journal-1767	90	14	values	value	NOUN
american_scientific_journal-1767	90	15	that	that	PRON
american_scientific_journal-1767	90	16	𝑚𝑚,𝑎𝑎	𝑚𝑚,𝑎𝑎	VERB
american_scientific_journal-1767	90	17	(	(	PUNCT
american_scientific_journal-1767	90	18	and	and	CCONJ
american_scientific_journal-1767	90	19	hence	hence	ADV
american_scientific_journal-1767	90	20	𝐴𝐴	𝐴𝐴	PROPN
american_scientific_journal-1767	90	21	)	)	PUNCT
american_scientific_journal-1767	90	22	can	can	AUX
american_scientific_journal-1767	90	23	take	take	VERB
american_scientific_journal-1767	90	24	.	.	PUNCT
american_scientific_journal-1767	91	1	3	3	X
american_scientific_journal-1767	91	2	.	.	NOUN
american_scientific_journal-1767	91	3	results	result	VERB
american_scientific_journal-1767	91	4	3.1	3.1	NUM
american_scientific_journal-1767	91	5	.	.	PUNCT
american_scientific_journal-1767	92	1	the	the	DET
american_scientific_journal-1767	92	2	red	red	ADJ
american_scientific_journal-1767	92	3	shift	shift	NOUN
american_scientific_journal-1767	92	4	of	of	ADP
american_scientific_journal-1767	92	5	a	a	DET
american_scientific_journal-1767	92	6	pulse	pulse	NOUN
american_scientific_journal-1767	92	7	of	of	ADP
american_scientific_journal-1767	92	8	light	light	NOUN
american_scientific_journal-1767	92	9	an	an	DET
american_scientific_journal-1767	92	10	expression	expression	NOUN
american_scientific_journal-1767	92	11	for	for	ADP
american_scientific_journal-1767	92	12	the	the	DET
american_scientific_journal-1767	92	13	red	red	ADJ
american_scientific_journal-1767	92	14	shift	shift	NOUN
american_scientific_journal-1767	92	15	of	of	ADP
american_scientific_journal-1767	92	16	a	a	DET
american_scientific_journal-1767	92	17	pulse	pulse	NOUN
american_scientific_journal-1767	92	18	of	of	ADP
american_scientific_journal-1767	92	19	light	light	NOUN
american_scientific_journal-1767	92	20	emitted	emit	VERB
american_scientific_journal-1767	92	21	at	at	ADP
american_scientific_journal-1767	92	22	a	a	DET
american_scientific_journal-1767	92	23	point	point	NOUN
american_scientific_journal-1767	92	24	inside	inside	ADP
american_scientific_journal-1767	92	25	of	of	ADP
american_scientific_journal-1767	92	26	the	the	DET
american_scientific_journal-1767	92	27	sphere	sphere	NOUN
american_scientific_journal-1767	92	28	along	along	ADP
american_scientific_journal-1767	92	29	a	a	DET
american_scientific_journal-1767	92	30	radial	radial	ADJ
american_scientific_journal-1767	92	31	direction	direction	NOUN
american_scientific_journal-1767	92	32	as	as	SCONJ
american_scientific_journal-1767	92	33	an	an	DET
american_scientific_journal-1767	92	34	observer	observer	NOUN
american_scientific_journal-1767	92	35	who	who	PRON
american_scientific_journal-1767	92	36	is	be	AUX
american_scientific_journal-1767	92	37	at	at	ADP
american_scientific_journal-1767	92	38	a	a	DET
american_scientific_journal-1767	92	39	large	large	ADJ
american_scientific_journal-1767	92	40	distance	distance	NOUN
american_scientific_journal-1767	92	41	away	away	ADV
american_scientific_journal-1767	92	42	from	from	ADP
american_scientific_journal-1767	92	43	the	the	DET
american_scientific_journal-1767	92	44	sphere	sphere	NOUN
american_scientific_journal-1767	92	45	has	have	AUX
american_scientific_journal-1767	92	46	been	be	AUX
american_scientific_journal-1767	92	47	calculated	calculate	VERB
american_scientific_journal-1767	92	48	.	.	PUNCT
american_scientific_journal-1767	93	1	however	however	ADV
american_scientific_journal-1767	93	2	in	in	ADP
american_scientific_journal-1767	93	3	this	this	DET
american_scientific_journal-1767	93	4	case	case	NOUN
american_scientific_journal-1767	93	5	,	,	PUNCT
american_scientific_journal-1767	93	6	unlike	unlike	ADP
american_scientific_journal-1767	93	7	in	in	ADP
american_scientific_journal-1767	93	8	the	the	DET
american_scientific_journal-1767	93	9	case	case	NOUN
american_scientific_journal-1767	93	10	in	in	ADP
american_scientific_journal-1767	93	11	sashinka	sashinka	PROPN
american_scientific_journal-1767	93	12	wimaladharma	wimaladharma	PROPN
american_scientific_journal-1767	93	13	and	and	CCONJ
american_scientific_journal-1767	93	14	nalin	nalin	PROPN
american_scientific_journal-1767	93	15	de	de	PROPN
american_scientific_journal-1767	93	16	silva	silva	PROPN
american_scientific_journal-1767	93	17	[	[	X
american_scientific_journal-1767	93	18	1	1	NUM
american_scientific_journal-1767	93	19	]	]	PUNCT
american_scientific_journal-1767	93	20	where	where	SCONJ
american_scientific_journal-1767	93	21	we	we	PRON
american_scientific_journal-1767	93	22	used	use	VERB
american_scientific_journal-1767	93	23	standard	standard	ADJ
american_scientific_journal-1767	93	24	lichernowicz	lichernowicz	NOUN
american_scientific_journal-1767	93	25	boundary	boundary	NOUN
american_scientific_journal-1767	93	26	conditions[5	conditions[5	PROPN
american_scientific_journal-1767	93	27	]	]	PUNCT
american_scientific_journal-1767	93	28	,	,	PUNCT
american_scientific_journal-1767	93	29	the	the	DET
american_scientific_journal-1767	93	30	differences	difference	NOUN
american_scientific_journal-1767	93	31	in	in	ADP
american_scientific_journal-1767	93	32	time	time	NOUN
american_scientific_journal-1767	93	33	when	when	SCONJ
american_scientific_journal-1767	93	34	a	a	DET
american_scientific_journal-1767	93	35	light	light	ADJ
american_scientific_journal-1767	93	36	ray	ray	NOUN
american_scientific_journal-1767	93	37	passes	pass	VERB
american_scientific_journal-1767	93	38	through	through	ADP
american_scientific_journal-1767	93	39	the	the	DET
american_scientific_journal-1767	93	40	boundary	boundary	NOUN
american_scientific_journal-1767	93	41	of	of	ADP
american_scientific_journal-1767	93	42	the	the	DET
american_scientific_journal-1767	93	43	sphere	sphere	NOUN
american_scientific_journal-1767	93	44	have	have	AUX
american_scientific_journal-1767	93	45	taken	take	VERB
american_scientific_journal-1767	93	46	into	into	ADP
american_scientific_journal-1767	93	47	consideration	consideration	NOUN
american_scientific_journal-1767	93	48	.	.	PUNCT
american_scientific_journal-1767	94	1	first	first	ADV
american_scientific_journal-1767	94	2	a	a	DET
american_scientific_journal-1767	94	3	pulse	pulse	NOUN
american_scientific_journal-1767	94	4	of	of	ADP
american_scientific_journal-1767	94	5	light	light	NOUN
american_scientific_journal-1767	94	6	with	with	ADP
american_scientific_journal-1767	94	7	front	front	NOUN
american_scientific_journal-1767	94	8	emitted	emit	VERB
american_scientific_journal-1767	94	9	at	at	ADP
american_scientific_journal-1767	94	10	𝑟𝑟	𝑟𝑟	ADV
american_scientific_journal-1767	94	11	=	=	PUNCT
american_scientific_journal-1767	94	12	𝑟𝑟𝑒𝑒	𝑟𝑟𝑒𝑒	NOUN
american_scientific_journal-1767	94	13	at	at	ADP
american_scientific_journal-1767	94	14	𝑡𝑡	𝑡𝑡	NOUN
american_scientific_journal-1767	94	15	=	=	SYM
american_scientific_journal-1767	94	16	𝑡𝑡𝑒𝑒	𝑡𝑡𝑒𝑒	PROPN
american_scientific_journal-1767	94	17	with	with	ADP
american_scientific_journal-1767	94	18	frequency	frequency	NOUN
american_scientific_journal-1767	94	19	𝜈𝜈𝑒𝑒	𝜈𝜈𝑒𝑒	NOUN
american_scientific_journal-1767	94	20	inside	inside	ADP
american_scientific_journal-1767	94	21	the	the	DET
american_scientific_journal-1767	94	22	sphere	sphere	NOUN
american_scientific_journal-1767	94	23	,	,	PUNCT
american_scientific_journal-1767	94	24	and	and	CCONJ
american_scientific_journal-1767	94	25	an	an	DET
american_scientific_journal-1767	94	26	observer	observer	NOUN
american_scientific_journal-1767	94	27	at	at	ADP
american_scientific_journal-1767	94	28	𝑟𝑟	𝑟𝑟	NOUN
american_scientific_journal-1767	94	29	=	=	SYM
american_scientific_journal-1767	94	30	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1767	94	31	,	,	PUNCT
american_scientific_journal-1767	94	32	just	just	ADV
american_scientific_journal-1767	94	33	inside	inside	ADP
american_scientific_journal-1767	94	34	the	the	DET
american_scientific_journal-1767	94	35	boundary	boundary	NOUN
american_scientific_journal-1767	94	36	of	of	ADP
american_scientific_journal-1767	94	37	the	the	DET
american_scientific_journal-1767	94	38	sphere	sphere	NOUN
american_scientific_journal-1767	94	39	receiving	receive	VERB
american_scientific_journal-1767	94	40	it	it	PRON
american_scientific_journal-1767	94	41	at	at	ADP
american_scientific_journal-1767	94	42	𝑡𝑡	𝑡𝑡	PROPN
american_scientific_journal-1767	94	43	=	=	NOUN
american_scientific_journal-1767	94	44	𝑡𝑡𝑒𝑒′	𝑡𝑡𝑒𝑒′	NOUN
american_scientific_journal-1767	94	45	with	with	ADP
american_scientific_journal-1767	94	46	frequency	frequency	NOUN
american_scientific_journal-1767	94	47	𝜈𝜈𝑒𝑒′	𝜈𝜈𝑒𝑒′	NOUN
american_scientific_journal-1767	94	48	has	have	AUX
american_scientific_journal-1767	94	49	been	be	AUX
american_scientific_journal-1767	94	50	considered	consider	VERB
american_scientific_journal-1767	94	51	.	.	PUNCT
american_scientific_journal-1767	95	1	0	0	NUM
american_scientific_journal-1767	95	2	0.5	0.5	NUM
american_scientific_journal-1767	95	3	1	1	NUM
american_scientific_journal-1767	95	4	1.5	1.5	NUM
american_scientific_journal-1767	95	5	2	2	NUM
american_scientific_journal-1767	95	6	0	0	NUM
american_scientific_journal-1767	95	7	0.2	0.2	NUM
american_scientific_journal-1767	95	8	0.4	0.4	NUM
american_scientific_journal-1767	95	9	0.6	0.6	NUM
american_scientific_journal-1767	95	10	0.8	0.8	NUM
american_scientific_journal-1767	95	11	1	1	NUM
american_scientific_journal-1767	95	12	american	american	ADJ
american_scientific_journal-1767	95	13	scientific	scientific	ADJ
american_scientific_journal-1767	95	14	research	research	NOUN
american_scientific_journal-1767	95	15	journal	journal	NOUN
american_scientific_journal-1767	95	16	for	for	ADP
american_scientific_journal-1767	95	17	engineering	engineering	NOUN
american_scientific_journal-1767	95	18	,	,	PUNCT
american_scientific_journal-1767	95	19	technology	technology	NOUN
american_scientific_journal-1767	95	20	,	,	PUNCT
american_scientific_journal-1767	95	21	and	and	CCONJ
american_scientific_journal-1767	95	22	sciences	science	NOUN
american_scientific_journal-1767	95	23	(	(	PUNCT
american_scientific_journal-1767	95	24	asrjets	asrjet	NOUN
american_scientific_journal-1767	95	25	)	)	PUNCT
american_scientific_journal-1767	95	26	(	(	PUNCT
american_scientific_journal-1767	95	27	2016	2016	NUM
american_scientific_journal-1767	95	28	)	)	PUNCT
american_scientific_journal-1767	95	29	volume	volume	NOUN
american_scientific_journal-1767	95	30	21	21	NUM
american_scientific_journal-1767	95	31	,	,	PUNCT
american_scientific_journal-1767	95	32	no	no	DET
american_scientific_journal-1767	95	33	1	1	NUM
american_scientific_journal-1767	95	34	,	,	PUNCT
american_scientific_journal-1767	95	35	pp	pp	ADV
american_scientific_journal-1767	95	36	163	163	NUM
american_scientific_journal-1767	95	37	-	-	SYM
american_scientific_journal-1767	95	38	177	177	NUM
american_scientific_journal-1767	95	39	173	173	NUM
american_scientific_journal-1767	95	40	the	the	DET
american_scientific_journal-1767	95	41	radial	radial	ADJ
american_scientific_journal-1767	95	42	null	null	ADJ
american_scientific_journal-1767	95	43	geodesics	geodesic	NOUN
american_scientific_journal-1767	95	44	within	within	ADP
american_scientific_journal-1767	95	45	the	the	DET
american_scientific_journal-1767	95	46	sphere	sphere	NOUN
american_scientific_journal-1767	95	47	are	be	AUX
american_scientific_journal-1767	95	48	given	give	VERB
american_scientific_journal-1767	95	49	by	by	ADP
american_scientific_journal-1767	95	50	the	the	DET
american_scientific_journal-1767	95	51	metric	metric	ADJ
american_scientific_journal-1767	95	52	(	(	PUNCT
american_scientific_journal-1767	95	53	18	18	NUM
american_scientific_journal-1767	95	54	)	)	PUNCT
american_scientific_journal-1767	95	55	as	as	ADP
american_scientific_journal-1767	95	56	0	0	NUM
american_scientific_journal-1767	95	57	=	=	SYM
american_scientific_journal-1767	95	58	1	1	NUM
american_scientific_journal-1767	95	59	�	�	PROPN
american_scientific_journal-1767	95	60	𝜃𝜃	𝜃𝜃	PROPN
american_scientific_journal-1767	95	61	�	�	PROPN
american_scientific_journal-1767	95	62	𝑟𝑟𝑙𝑙	𝑟𝑟𝑙𝑙	NOUN
american_scientific_journal-1767	95	63	�	�	PROPN
american_scientific_journal-1767	95	64	�	�	PROPN
american_scientific_journal-1767	95	65	2	2	NUM
american_scientific_journal-1767	95	66	𝑐𝑐2𝑑𝑑𝑡𝑡2	𝑐𝑐2𝑑𝑑𝑡𝑡2	NOUN
american_scientific_journal-1767	95	67	−	−	PROPN
american_scientific_journal-1767	95	68	�	�	PROPN
american_scientific_journal-1767	95	69	𝜃𝜃	𝜃𝜃	PROPN
american_scientific_journal-1767	95	70	�	�	PROPN
american_scientific_journal-1767	95	71	𝑟𝑟	𝑟𝑟	ADP
american_scientific_journal-1767	95	72	𝑙𝑙	𝑙𝑙	PROPN
american_scientific_journal-1767	95	73	�	�	PROPN
american_scientific_journal-1767	95	74	�	�	PROPN
american_scientific_journal-1767	95	75	2	2	NUM
american_scientific_journal-1767	95	76	𝑑𝑑𝑟𝑟2	𝑑𝑑𝑟𝑟2	NOUN
american_scientific_journal-1767	95	77	,	,	PUNCT
american_scientific_journal-1767	95	78	taking	take	VERB
american_scientific_journal-1767	95	79	the	the	DET
american_scientific_journal-1767	95	80	plus	plus	ADJ
american_scientific_journal-1767	95	81	sign	sign	NOUN
american_scientific_journal-1767	95	82	since	since	SCONJ
american_scientific_journal-1767	95	83	𝑟𝑟	𝑟𝑟	ADP
american_scientific_journal-1767	95	84	increases	increase	VERB
american_scientific_journal-1767	95	85	with	with	ADP
american_scientific_journal-1767	95	86	time	time	NOUN
american_scientific_journal-1767	95	87	𝑡𝑡	𝑡𝑡	PROPN
american_scientific_journal-1767	95	88	as	as	SCONJ
american_scientific_journal-1767	95	89	the	the	DET
american_scientific_journal-1767	95	90	photons	photon	NOUN
american_scientific_journal-1767	95	91	are	be	AUX
american_scientific_journal-1767	95	92	going	go	VERB
american_scientific_journal-1767	95	93	away	away	ADV
american_scientific_journal-1767	95	94	from	from	ADP
american_scientific_journal-1767	95	95	the	the	DET
american_scientific_journal-1767	95	96	centre	centre	NOUN
american_scientific_journal-1767	95	97	of	of	ADP
american_scientific_journal-1767	95	98	the	the	DET
american_scientific_journal-1767	95	99	sphere	sphere	NOUN
american_scientific_journal-1767	95	100	gives	give	VERB
american_scientific_journal-1767	95	101	𝑑𝑑𝑟𝑟	𝑑𝑑𝑟𝑟	NOUN
american_scientific_journal-1767	95	102	𝑑𝑑𝛿𝛿	𝑑𝑑𝛿𝛿	NOUN
american_scientific_journal-1767	95	103	=	=	PROPN
american_scientific_journal-1767	95	104	𝑐𝑐	𝑐𝑐	PROPN
american_scientific_journal-1767	95	105	�	�	PROPN
american_scientific_journal-1767	95	106	𝜃𝜃	𝜃𝜃	PROPN
american_scientific_journal-1767	95	107	�	�	PROPN
american_scientific_journal-1767	95	108	𝑟𝑟𝑙𝑙	𝑟𝑟𝑙𝑙	NOUN
american_scientific_journal-1767	95	109	�	�	PROPN
american_scientific_journal-1767	95	110	�	�	PROPN
american_scientific_journal-1767	95	111	2	2	NUM
american_scientific_journal-1767	95	112	.	.	PUNCT
american_scientific_journal-1767	96	1	(	(	PUNCT
american_scientific_journal-1767	96	2	28	28	NUM
american_scientific_journal-1767	96	3	)	)	PUNCT
american_scientific_journal-1767	96	4	equation	equation	NOUN
american_scientific_journal-1767	96	5	(	(	PUNCT
american_scientific_journal-1767	96	6	28	28	NUM
american_scientific_journal-1767	96	7	)	)	PUNCT
american_scientific_journal-1767	96	8	can	can	AUX
american_scientific_journal-1767	96	9	be	be	AUX
american_scientific_journal-1767	96	10	integrated	integrate	VERB
american_scientific_journal-1767	96	11	considering	consider	VERB
american_scientific_journal-1767	96	12	the	the	DET
american_scientific_journal-1767	96	13	front	front	NOUN
american_scientific_journal-1767	96	14	of	of	ADP
american_scientific_journal-1767	96	15	the	the	DET
american_scientific_journal-1767	96	16	pulse	pulse	NOUN
american_scientific_journal-1767	96	17	as	as	ADP
american_scientific_journal-1767	96	18	∫	∫	PROPN
american_scientific_journal-1767	96	19	𝑐𝑐	𝑐𝑐	PROPN
american_scientific_journal-1767	96	20	𝑑𝑑𝑡𝑡𝛿𝛿𝑒𝑒′	𝑑𝑑𝑡𝑡𝛿𝛿𝑒𝑒′	NOUN
american_scientific_journal-1767	96	21	𝛿𝛿𝑒𝑒	𝛿𝛿𝑒𝑒	NOUN
american_scientific_journal-1767	97	1	=	=	SYM
american_scientific_journal-1767	97	2	∫	∫	PROPN
american_scientific_journal-1767	97	3	�	�	PROPN
american_scientific_journal-1767	97	4	𝜃𝜃	𝜃𝜃	PROPN
american_scientific_journal-1767	97	5	�	�	PROPN
american_scientific_journal-1767	97	6	𝑟𝑟	𝑟𝑟	ADP
american_scientific_journal-1767	97	7	𝑙𝑙	𝑙𝑙	PROPN
american_scientific_journal-1767	97	8	�	�	PROPN
american_scientific_journal-1767	97	9	�	�	PROPN
american_scientific_journal-1767	97	10	2𝑎𝑎	2𝑎𝑎	PROPN
american_scientific_journal-1767	97	11	𝑟𝑟𝑒𝑒	𝑟𝑟𝑒𝑒	NOUN
american_scientific_journal-1767	97	12	𝑑𝑑𝑟𝑟	𝑑𝑑𝑟𝑟	NOUN
american_scientific_journal-1767	97	13	(	(	PUNCT
american_scientific_journal-1767	97	14	29	29	NUM
american_scientific_journal-1767	97	15	)	)	PUNCT
american_scientific_journal-1767	97	16	assuming	assume	VERB
american_scientific_journal-1767	97	17	that	that	SCONJ
american_scientific_journal-1767	97	18	the	the	DET
american_scientific_journal-1767	97	19	rear	rear	NOUN
american_scientific_journal-1767	97	20	of	of	ADP
american_scientific_journal-1767	97	21	the	the	DET
american_scientific_journal-1767	97	22	pulse	pulse	NOUN
american_scientific_journal-1767	97	23	which	which	PRON
american_scientific_journal-1767	97	24	is	be	AUX
american_scientific_journal-1767	97	25	emitted	emit	VERB
american_scientific_journal-1767	97	26	at	at	ADP
american_scientific_journal-1767	97	27	𝑟𝑟	𝑟𝑟	ADV
american_scientific_journal-1767	97	28	=	=	PUNCT
american_scientific_journal-1767	97	29	𝑟𝑟𝑒𝑒	𝑟𝑟𝑒𝑒	NOUN
american_scientific_journal-1767	97	30	at	at	ADP
american_scientific_journal-1767	97	31	𝑡𝑡	𝑡𝑡	PROPN
american_scientific_journal-1767	97	32	=	=	SYM
american_scientific_journal-1767	97	33	𝑡𝑡𝑒𝑒	𝑡𝑡𝑒𝑒	PROPN
american_scientific_journal-1767	98	1	+	+	CCONJ
american_scientific_journal-1767	98	2	δ𝑡𝑡𝑒𝑒	δ𝑡𝑡𝑒𝑒	NOUN
american_scientific_journal-1767	98	3	with	with	ADP
american_scientific_journal-1767	98	4	frequency	frequency	NOUN
american_scientific_journal-1767	98	5	𝜈𝜈𝑒𝑒	𝜈𝜈𝑒𝑒	NOUN
american_scientific_journal-1767	98	6	will	will	AUX
american_scientific_journal-1767	98	7	observe	observe	VERB
american_scientific_journal-1767	98	8	it	it	PRON
american_scientific_journal-1767	98	9	at	at	ADP
american_scientific_journal-1767	98	10	=	=	NOUN
american_scientific_journal-1767	98	11	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1767	98	12	,	,	PUNCT
american_scientific_journal-1767	98	13	just	just	ADV
american_scientific_journal-1767	98	14	inside	inside	ADP
american_scientific_journal-1767	98	15	the	the	DET
american_scientific_journal-1767	98	16	boundary	boundary	NOUN
american_scientific_journal-1767	98	17	of	of	ADP
american_scientific_journal-1767	98	18	the	the	DET
american_scientific_journal-1767	98	19	sphere	sphere	NOUN
american_scientific_journal-1767	98	20	at	at	ADP
american_scientific_journal-1767	98	21	𝑡𝑡	𝑡𝑡	PROPN
american_scientific_journal-1767	98	22	=	=	SYM
american_scientific_journal-1767	98	23	𝑡𝑡𝑒𝑒′	𝑡𝑡𝑒𝑒′	NOUN
american_scientific_journal-1767	99	1	+	+	CCONJ
american_scientific_journal-1767	99	2	δ𝑡𝑡𝑒𝑒′	δ𝑡𝑡𝑒𝑒′	NOUN
american_scientific_journal-1767	99	3	with	with	ADP
american_scientific_journal-1767	99	4	frequency	frequency	NOUN
american_scientific_journal-1767	99	5	𝜈𝜈𝑒𝑒′	𝜈𝜈𝑒𝑒′	NOUN
american_scientific_journal-1767	99	6	,	,	PUNCT
american_scientific_journal-1767	99	7	equation	equation	NOUN
american_scientific_journal-1767	99	8	(	(	PUNCT
american_scientific_journal-1767	99	9	28	28	NUM
american_scientific_journal-1767	99	10	)	)	PUNCT
american_scientific_journal-1767	99	11	can	can	AUX
american_scientific_journal-1767	99	12	also	also	ADV
american_scientific_journal-1767	99	13	be	be	AUX
american_scientific_journal-1767	99	14	integrated	integrate	VERB
american_scientific_journal-1767	99	15	considering	consider	VERB
american_scientific_journal-1767	99	16	the	the	DET
american_scientific_journal-1767	99	17	rear	rear	NOUN
american_scientific_journal-1767	99	18	of	of	ADP
american_scientific_journal-1767	99	19	the	the	DET
american_scientific_journal-1767	99	20	pulse	pulse	NOUN
american_scientific_journal-1767	99	21	as	as	ADP
american_scientific_journal-1767	99	22	∫	∫	PROPN
american_scientific_journal-1767	99	23	𝑐𝑐	𝑐𝑐	PROPN
american_scientific_journal-1767	99	24	𝑑𝑑𝑡𝑡𝛿𝛿𝑒𝑒′+δ𝛿𝛿𝑒𝑒′	𝑑𝑑𝑡𝑡𝛿𝛿𝑒𝑒′+δ𝛿𝛿𝑒𝑒′	VERB
american_scientific_journal-1767	99	25	𝛿𝛿𝑒𝑒+δ𝛿𝛿𝑒𝑒	𝛿𝛿𝑒𝑒+δ𝛿𝛿𝑒𝑒	PROPN
american_scientific_journal-1767	99	26	=	=	SYM
american_scientific_journal-1767	99	27	∫	∫	PROPN
american_scientific_journal-1767	99	28	�	�	PROPN
american_scientific_journal-1767	99	29	𝜃𝜃	𝜃𝜃	PROPN
american_scientific_journal-1767	99	30	�	�	PROPN
american_scientific_journal-1767	99	31	𝑟𝑟	𝑟𝑟	ADP
american_scientific_journal-1767	99	32	𝑙𝑙	𝑙𝑙	PROPN
american_scientific_journal-1767	99	33	�	�	PROPN
american_scientific_journal-1767	99	34	�	�	PROPN
american_scientific_journal-1767	99	35	2𝑎𝑎	2𝑎𝑎	PROPN
american_scientific_journal-1767	99	36	𝑟𝑟𝑒𝑒	𝑟𝑟𝑒𝑒	NOUN
american_scientific_journal-1767	99	37	𝑑𝑑𝑟𝑟	𝑑𝑑𝑟𝑟	NOUN
american_scientific_journal-1767	99	38	(	(	PUNCT
american_scientific_journal-1767	99	39	30	30	NUM
american_scientific_journal-1767	99	40	)	)	PUNCT
american_scientific_journal-1767	99	41	since	since	SCONJ
american_scientific_journal-1767	99	42	the	the	DET
american_scientific_journal-1767	99	43	right	right	ADJ
american_scientific_journal-1767	99	44	hand	hand	NOUN
american_scientific_journal-1767	99	45	sides	side	NOUN
american_scientific_journal-1767	99	46	of	of	ADP
american_scientific_journal-1767	99	47	equations	equation	NOUN
american_scientific_journal-1767	99	48	(	(	PUNCT
american_scientific_journal-1767	99	49	29	29	NUM
american_scientific_journal-1767	99	50	)	)	PUNCT
american_scientific_journal-1767	99	51	and	and	CCONJ
american_scientific_journal-1767	99	52	(	(	PUNCT
american_scientific_journal-1767	99	53	30	30	NUM
american_scientific_journal-1767	99	54	)	)	PUNCT
american_scientific_journal-1767	99	55	are	be	AUX
american_scientific_journal-1767	99	56	the	the	DET
american_scientific_journal-1767	99	57	same	same	ADJ
american_scientific_journal-1767	99	58	,	,	PUNCT
american_scientific_journal-1767	99	59	it	it	PRON
american_scientific_journal-1767	99	60	can	can	AUX
american_scientific_journal-1767	99	61	be	be	AUX
american_scientific_journal-1767	99	62	obtained	obtain	VERB
american_scientific_journal-1767	99	63	that	that	DET
american_scientific_journal-1767	99	64	∫	∫	PROPN
american_scientific_journal-1767	100	1	𝑐𝑐	𝑐𝑐	NOUN
american_scientific_journal-1767	100	2	𝑑𝑑𝑡𝑡𝛿𝛿𝑒𝑒′	𝑑𝑑𝑡𝑡𝛿𝛿𝑒𝑒′	NOUN
american_scientific_journal-1767	100	3	𝛿𝛿𝑒𝑒	𝛿𝛿𝑒𝑒	NOUN
american_scientific_journal-1767	101	1	=	=	X
american_scientific_journal-1767	101	2	∫	∫	PROPN
american_scientific_journal-1767	101	3	𝑐𝑐	𝑐𝑐	NOUN
american_scientific_journal-1767	101	4	𝑑𝑑𝑡𝑡𝛿𝛿𝑒𝑒′+δ𝛿𝛿𝑒𝑒′	𝑑𝑑𝑡𝑡𝛿𝛿𝑒𝑒′+δ𝛿𝛿𝑒𝑒′	VERB
american_scientific_journal-1767	101	5	𝛿𝛿𝑒𝑒+δ𝛿𝛿𝑒𝑒	𝛿𝛿𝑒𝑒+δ𝛿𝛿𝑒𝑒	PROPN
american_scientific_journal-1767	101	6	.	.	PUNCT
american_scientific_journal-1767	102	1	(	(	PUNCT
american_scientific_journal-1767	102	2	31	31	NUM
american_scientific_journal-1767	102	3	)	)	PUNCT
american_scientific_journal-1767	102	4	rearrangement	rearrangement	NOUN
american_scientific_journal-1767	102	5	and	and	CCONJ
american_scientific_journal-1767	102	6	simplification	simplification	NOUN
american_scientific_journal-1767	102	7	of	of	ADP
american_scientific_journal-1767	102	8	the	the	DET
american_scientific_journal-1767	102	9	equation	equation	NOUN
american_scientific_journal-1767	102	10	(	(	PUNCT
american_scientific_journal-1767	102	11	31	31	NUM
american_scientific_journal-1767	102	12	)	)	PUNCT
american_scientific_journal-1767	102	13	with	with	ADP
american_scientific_journal-1767	102	14	the	the	DET
american_scientific_journal-1767	102	15	assumption	assumption	NOUN
american_scientific_journal-1767	102	16	of	of	ADP
american_scientific_journal-1767	102	17	δ𝑡𝑡𝑒𝑒	δ𝑡𝑡𝑒𝑒	PROPN
american_scientific_journal-1767	102	18	and	and	CCONJ
american_scientific_journal-1767	102	19	δ𝑡𝑡𝑒𝑒′	δ𝑡𝑡𝑒𝑒′	NOUN
american_scientific_journal-1767	102	20	are	be	AUX
american_scientific_journal-1767	102	21	very	very	ADV
american_scientific_journal-1767	102	22	small	small	ADJ
american_scientific_journal-1767	102	23	gives	give	VERB
american_scientific_journal-1767	102	24	δ𝑡𝑡𝑒𝑒	δ𝑡𝑡𝑒𝑒	NOUN
american_scientific_journal-1767	103	1	=	=	SYM
american_scientific_journal-1767	103	2	δ𝑡𝑡𝑒𝑒′	δ𝑡𝑡𝑒𝑒′	NOUN
american_scientific_journal-1767	103	3	(	(	PUNCT
american_scientific_journal-1767	103	4	32	32	NUM
american_scientific_journal-1767	103	5	)	)	PUNCT
american_scientific_journal-1767	103	6	now	now	ADV
american_scientific_journal-1767	103	7	the	the	DET
american_scientific_journal-1767	103	8	proper	proper	ADJ
american_scientific_journal-1767	103	9	time	time	NOUN
american_scientific_journal-1767	103	10	intervals	interval	NOUN
american_scientific_journal-1767	103	11	from	from	ADP
american_scientific_journal-1767	103	12	the	the	DET
american_scientific_journal-1767	103	13	equation	equation	NOUN
american_scientific_journal-1767	103	14	(	(	PUNCT
american_scientific_journal-1767	103	15	18	18	NUM
american_scientific_journal-1767	103	16	)	)	PUNCT
american_scientific_journal-1767	103	17	of	of	ADP
american_scientific_journal-1767	103	18	the	the	DET
american_scientific_journal-1767	103	19	two	two	NUM
american_scientific_journal-1767	103	20	observers	observer	NOUN
american_scientific_journal-1767	103	21	corresponding	correspond	VERB
american_scientific_journal-1767	103	22	to	to	ADP
american_scientific_journal-1767	103	23	δ𝑡𝑡𝑒𝑒	δ𝑡𝑡𝑒𝑒	PROPN
american_scientific_journal-1767	103	24	and	and	CCONJ
american_scientific_journal-1767	103	25	δ𝑡𝑡𝑒𝑒′	δ𝑡𝑡𝑒𝑒′	NOUN
american_scientific_journal-1767	103	26	are	be	AUX
american_scientific_journal-1767	103	27	given	give	VERB
american_scientific_journal-1767	103	28	by	by	ADP
american_scientific_journal-1767	103	29	δ𝜏𝜏𝑒𝑒	δ𝜏𝜏𝑒𝑒	NOUN
american_scientific_journal-1767	103	30	=	=	SYM
american_scientific_journal-1767	103	31	�	�	PROPN
american_scientific_journal-1767	103	32	1	1	NUM
american_scientific_journal-1767	103	33	𝜃𝜃	𝜃𝜃	PROPN
american_scientific_journal-1767	103	34	�	�	PROPN
american_scientific_journal-1767	103	35	𝑟𝑟𝑒𝑒𝑙𝑙	𝑟𝑟𝑒𝑒𝑙𝑙	PROPN
american_scientific_journal-1767	103	36	�	�	PROPN
american_scientific_journal-1767	103	37	�	�	PROPN
american_scientific_journal-1767	103	38	δ𝑡𝑡𝑒𝑒	δ𝑡𝑡𝑒𝑒	PROPN
american_scientific_journal-1767	103	39	and	and	CCONJ
american_scientific_journal-1767	103	40	δ𝜏𝜏𝑒𝑒′	δ𝜏𝜏𝑒𝑒′	NUM
american_scientific_journal-1767	103	41	=	=	SYM
american_scientific_journal-1767	103	42	�	�	PROPN
american_scientific_journal-1767	103	43	1	1	NUM
american_scientific_journal-1767	103	44	𝜃𝜃	𝜃𝜃	PROPN
american_scientific_journal-1767	103	45	�	�	PROPN
american_scientific_journal-1767	103	46	𝑎𝑎𝑙𝑙	𝑎𝑎𝑙𝑙	PROPN
american_scientific_journal-1767	103	47	�	�	PROPN
american_scientific_journal-1767	103	48	�	�	PROPN
american_scientific_journal-1767	103	49	δ𝑡𝑡𝑒𝑒′	δ𝑡𝑡𝑒𝑒′	X
american_scientific_journal-1767	103	50	(	(	PUNCT
american_scientific_journal-1767	103	51	33	33	NUM
american_scientific_journal-1767	103	52	)	)	PUNCT
american_scientific_journal-1767	103	53	where	where	SCONJ
american_scientific_journal-1767	103	54	δ𝜏𝜏𝑒𝑒	δ𝜏𝜏𝑒𝑒	NOUN
american_scientific_journal-1767	103	55	and	and	CCONJ
american_scientific_journal-1767	103	56	δ𝜏𝜏𝑒𝑒′	δ𝜏𝜏𝑒𝑒′	NUM
american_scientific_journal-1767	103	57	are	be	AUX
american_scientific_journal-1767	103	58	the	the	DET
american_scientific_journal-1767	103	59	proper	proper	ADJ
american_scientific_journal-1767	103	60	time	time	NOUN
american_scientific_journal-1767	103	61	intervals	interval	NOUN
american_scientific_journal-1767	103	62	of	of	ADP
american_scientific_journal-1767	103	63	the	the	DET
american_scientific_journal-1767	103	64	two	two	NUM
american_scientific_journal-1767	103	65	observers	observer	NOUN
american_scientific_journal-1767	103	66	at	at	ADP
american_scientific_journal-1767	103	67	𝑟𝑟	𝑟𝑟	ADV
american_scientific_journal-1767	103	68	=	=	SYM
american_scientific_journal-1767	103	69	𝑟𝑟𝑒𝑒	𝑟𝑟𝑒𝑒	NOUN
american_scientific_journal-1767	103	70	and	and	CCONJ
american_scientific_journal-1767	103	71	𝑟𝑟	𝑟𝑟	NOUN
american_scientific_journal-1767	103	72	=	=	NOUN
american_scientific_journal-1767	103	73	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1767	103	74	,	,	PUNCT
american_scientific_journal-1767	103	75	just	just	ADV
american_scientific_journal-1767	103	76	inside	inside	ADP
american_scientific_journal-1767	103	77	the	the	DET
american_scientific_journal-1767	103	78	boundary	boundary	NOUN
american_scientific_journal-1767	103	79	of	of	ADP
american_scientific_journal-1767	103	80	the	the	DET
american_scientific_journal-1767	103	81	sphere	sphere	NOUN
american_scientific_journal-1767	103	82	,	,	PUNCT
american_scientific_journal-1767	103	83	respectively	respectively	ADV
american_scientific_journal-1767	103	84	,	,	PUNCT
american_scientific_journal-1767	103	85	emitting	emit	VERB
american_scientific_journal-1767	103	86	and	and	CCONJ
american_scientific_journal-1767	103	87	receiving	receive	VERB
american_scientific_journal-1767	103	88	the	the	DET
american_scientific_journal-1767	103	89	pulse	pulse	NOUN
american_scientific_journal-1767	103	90	.	.	PUNCT
american_scientific_journal-1767	104	1	the	the	DET
american_scientific_journal-1767	104	2	number	number	NOUN
american_scientific_journal-1767	104	3	of	of	ADP
american_scientific_journal-1767	104	4	cycles	cycle	NOUN
american_scientific_journal-1767	104	5	of	of	ADP
american_scientific_journal-1767	104	6	the	the	DET
american_scientific_journal-1767	104	7	pulse	pulse	NOUN
american_scientific_journal-1767	104	8	remain	remain	VERB
american_scientific_journal-1767	104	9	the	the	DET
american_scientific_journal-1767	104	10	same	same	ADJ
american_scientific_journal-1767	104	11	at	at	ADP
american_scientific_journal-1767	104	12	emission	emission	NOUN
american_scientific_journal-1767	104	13	and	and	CCONJ
american_scientific_journal-1767	104	14	observation	observation	NOUN
american_scientific_journal-1767	104	15	yields	yield	NOUN
american_scientific_journal-1767	104	16	𝜈𝜈𝑒𝑒δ𝜏𝜏𝑒𝑒	𝜈𝜈𝑒𝑒δ𝜏𝜏𝑒𝑒	NOUN
american_scientific_journal-1767	104	17	=	=	PUNCT
american_scientific_journal-1767	104	18	𝜈𝜈𝑒𝑒′δ𝜏𝜏𝑒𝑒′	𝜈𝜈𝑒𝑒′δ𝜏𝜏𝑒𝑒′	PROPN
american_scientific_journal-1767	104	19	american	american	PROPN
american_scientific_journal-1767	104	20	scientific	scientific	PROPN
american_scientific_journal-1767	104	21	research	research	PROPN
american_scientific_journal-1767	104	22	journal	journal	NOUN
american_scientific_journal-1767	104	23	for	for	ADP
american_scientific_journal-1767	104	24	engineering	engineering	NOUN
american_scientific_journal-1767	104	25	,	,	PUNCT
american_scientific_journal-1767	104	26	technology	technology	NOUN
american_scientific_journal-1767	104	27	,	,	PUNCT
american_scientific_journal-1767	104	28	and	and	CCONJ
american_scientific_journal-1767	104	29	sciences	science	NOUN
american_scientific_journal-1767	104	30	(	(	PUNCT
american_scientific_journal-1767	104	31	asrjets	asrjet	NOUN
american_scientific_journal-1767	104	32	)	)	PUNCT
american_scientific_journal-1767	104	33	(	(	PUNCT
american_scientific_journal-1767	104	34	2016	2016	NUM
american_scientific_journal-1767	104	35	)	)	PUNCT
american_scientific_journal-1767	104	36	volume	volume	NOUN
american_scientific_journal-1767	104	37	21	21	NUM
american_scientific_journal-1767	104	38	,	,	PUNCT
american_scientific_journal-1767	104	39	no	no	DET
american_scientific_journal-1767	104	40	1	1	NUM
american_scientific_journal-1767	104	41	,	,	PUNCT
american_scientific_journal-1767	104	42	pp	pp	ADV
american_scientific_journal-1767	104	43	163	163	NUM
american_scientific_journal-1767	104	44	-	-	SYM
american_scientific_journal-1767	104	45	177	177	NUM
american_scientific_journal-1767	104	46	174	174	NUM
american_scientific_journal-1767	104	47	𝜈𝜈𝑒𝑒′	𝜈𝜈𝑒𝑒′	NOUN
american_scientific_journal-1767	104	48	𝜈𝜈𝑒𝑒	𝜈𝜈𝑒𝑒	NOUN
american_scientific_journal-1767	104	49	=	=	SYM
american_scientific_journal-1767	104	50	δ𝜏𝜏𝑒𝑒	δ𝜏𝜏𝑒𝑒	NOUN
american_scientific_journal-1767	104	51	δ𝜏𝜏𝑒𝑒′	δ𝜏𝜏𝑒𝑒′	NUM
american_scientific_journal-1767	104	52	(	(	PUNCT
american_scientific_journal-1767	104	53	34	34	NUM
american_scientific_journal-1767	104	54	)	)	PUNCT
american_scientific_journal-1767	104	55	now	now	ADV
american_scientific_journal-1767	104	56	equation	equation	NOUN
american_scientific_journal-1767	104	57	(	(	PUNCT
american_scientific_journal-1767	104	58	33	33	NUM
american_scientific_journal-1767	104	59	)	)	PUNCT
american_scientific_journal-1767	104	60	and	and	CCONJ
american_scientific_journal-1767	104	61	(	(	PUNCT
american_scientific_journal-1767	104	62	34	34	NUM
american_scientific_journal-1767	104	63	)	)	PUNCT
american_scientific_journal-1767	104	64	give	give	VERB
american_scientific_journal-1767	104	65	𝜈𝜈𝑒𝑒	𝜈𝜈𝑒𝑒	NOUN
american_scientific_journal-1767	104	66	′	′	NOUN
american_scientific_journal-1767	104	67	𝜈𝜈𝑒𝑒	𝜈𝜈𝑒𝑒	NOUN
american_scientific_journal-1767	104	68	=	=	SYM
american_scientific_journal-1767	104	69	𝜃𝜃	𝜃𝜃	PROPN
american_scientific_journal-1767	104	70	�	�	PROPN
american_scientific_journal-1767	104	71	𝑎𝑎𝑙𝑙	𝑎𝑎𝑙𝑙	PROPN
american_scientific_journal-1767	104	72	�	�	PROPN
american_scientific_journal-1767	104	73	𝜃𝜃	𝜃𝜃	PROPN
american_scientific_journal-1767	104	74	�	�	PROPN
american_scientific_journal-1767	104	75	𝑟𝑟𝑒𝑒𝑙𝑙	𝑟𝑟𝑒𝑒𝑙𝑙	PROPN
american_scientific_journal-1767	104	76	�	�	PROPN
american_scientific_journal-1767	104	77	δ𝛿𝛿𝑒𝑒	δ𝛿𝛿𝑒𝑒	PROPN
american_scientific_journal-1767	104	78	δ𝛿𝛿𝑒𝑒′	δ𝛿𝛿𝑒𝑒′	PROPN
american_scientific_journal-1767	104	79	(	(	PUNCT
american_scientific_journal-1767	104	80	35	35	NUM
american_scientific_journal-1767	104	81	)	)	PUNCT
american_scientific_journal-1767	104	82	using	use	VERB
american_scientific_journal-1767	104	83	equation	equation	NOUN
american_scientific_journal-1767	104	84	(	(	PUNCT
american_scientific_journal-1767	104	85	32	32	NUM
american_scientific_journal-1767	104	86	)	)	PUNCT
american_scientific_journal-1767	104	87	,	,	PUNCT
american_scientific_journal-1767	104	88	equation	equation	NOUN
american_scientific_journal-1767	104	89	(	(	PUNCT
american_scientific_journal-1767	104	90	35	35	NUM
american_scientific_journal-1767	104	91	)	)	PUNCT
american_scientific_journal-1767	104	92	can	can	AUX
american_scientific_journal-1767	104	93	be	be	AUX
american_scientific_journal-1767	104	94	simplified	simplify	VERB
american_scientific_journal-1767	104	95	to	to	ADP
american_scientific_journal-1767	104	96	𝜈𝜈𝑒𝑒′	𝜈𝜈𝑒𝑒′	NUM
american_scientific_journal-1767	104	97	𝜈𝜈𝑒𝑒	𝜈𝜈𝑒𝑒	NOUN
american_scientific_journal-1767	104	98	=	=	SYM
american_scientific_journal-1767	104	99	𝜃𝜃	𝜃𝜃	PROPN
american_scientific_journal-1767	104	100	�	�	PROPN
american_scientific_journal-1767	104	101	𝑎𝑎𝑙𝑙	𝑎𝑎𝑙𝑙	PROPN
american_scientific_journal-1767	104	102	�	�	PROPN
american_scientific_journal-1767	104	103	𝜃𝜃	𝜃𝜃	PROPN
american_scientific_journal-1767	104	104	�	�	PROPN
american_scientific_journal-1767	104	105	𝑟𝑟𝑒𝑒𝑙𝑙	𝑟𝑟𝑒𝑒𝑙𝑙	PROPN
american_scientific_journal-1767	104	106	�	�	PROPN
american_scientific_journal-1767	104	107	(	(	PUNCT
american_scientific_journal-1767	104	108	36	36	NUM
american_scientific_journal-1767	104	109	)	)	PUNCT
american_scientific_journal-1767	104	110	now	now	ADV
american_scientific_journal-1767	104	111	consider	consider	VERB
american_scientific_journal-1767	104	112	the	the	DET
american_scientific_journal-1767	104	113	moment	moment	NOUN
american_scientific_journal-1767	104	114	which	which	PRON
american_scientific_journal-1767	104	115	the	the	DET
american_scientific_journal-1767	104	116	pulse	pulse	NOUN
american_scientific_journal-1767	104	117	of	of	ADP
american_scientific_journal-1767	104	118	ray	ray	NOUN
american_scientific_journal-1767	104	119	pass	pass	VERB
american_scientific_journal-1767	104	120	through	through	ADP
american_scientific_journal-1767	104	121	the	the	DET
american_scientific_journal-1767	104	122	boundary	boundary	NOUN
american_scientific_journal-1767	104	123	of	of	ADP
american_scientific_journal-1767	104	124	the	the	DET
american_scientific_journal-1767	104	125	sphere	sphere	NOUN
american_scientific_journal-1767	104	126	.	.	PUNCT
american_scientific_journal-1767	105	1	it	it	PRON
american_scientific_journal-1767	105	2	is	be	AUX
american_scientific_journal-1767	105	3	assumed	assume	VERB
american_scientific_journal-1767	105	4	that	that	SCONJ
american_scientific_journal-1767	105	5	an	an	DET
american_scientific_journal-1767	105	6	observer	observer	NOUN
american_scientific_journal-1767	105	7	at	at	ADP
american_scientific_journal-1767	105	8	𝑑𝑑	𝑑𝑑	PROPN
american_scientific_journal-1767	105	9	=	=	SYM
american_scientific_journal-1767	105	10	𝐴𝐴	𝐴𝐴	PROPN
american_scientific_journal-1767	105	11	but	but	CCONJ
american_scientific_journal-1767	105	12	outside	outside	ADP
american_scientific_journal-1767	105	13	of	of	ADP
american_scientific_journal-1767	105	14	the	the	DET
american_scientific_journal-1767	105	15	sphere	sphere	NOUN
american_scientific_journal-1767	105	16	observed	observe	VERB
american_scientific_journal-1767	105	17	the	the	DET
american_scientific_journal-1767	105	18	pulse	pulse	NOUN
american_scientific_journal-1767	105	19	at	at	ADP
american_scientific_journal-1767	105	20	𝑑𝑑	𝑑𝑑	NOUN
american_scientific_journal-1767	105	21	=	=	PUNCT
american_scientific_journal-1767	105	22	𝑑𝑑0′	𝑑𝑑0′	ADP
american_scientific_journal-1767	105	23	with	with	ADP
american_scientific_journal-1767	105	24	frequency	frequency	NOUN
american_scientific_journal-1767	105	25	𝜈𝜈0′	𝜈𝜈0′	NOUN
american_scientific_journal-1767	105	26	.	.	PUNCT
american_scientific_journal-1767	106	1	then	then	ADV
american_scientific_journal-1767	106	2	the	the	DET
american_scientific_journal-1767	106	3	relationship	relationship	NOUN
american_scientific_journal-1767	106	4	of	of	ADP
american_scientific_journal-1767	106	5	the	the	DET
american_scientific_journal-1767	106	6	time	time	NOUN
american_scientific_journal-1767	106	7	intervals	interval	NOUN
american_scientific_journal-1767	106	8	δ𝑡𝑡𝑒𝑒′	δ𝑡𝑡𝑒𝑒′	NOUN
american_scientific_journal-1767	106	9	and	and	CCONJ
american_scientific_journal-1767	106	10	δ𝑑𝑑0′	δ𝑑𝑑0′	PROPN
american_scientific_journal-1767	106	11	is	be	AUX
american_scientific_journal-1767	106	12	given	give	VERB
american_scientific_journal-1767	106	13	by	by	ADP
american_scientific_journal-1767	106	14	the	the	DET
american_scientific_journal-1767	106	15	equation	equation	NOUN
american_scientific_journal-1767	106	16	(	(	PUNCT
american_scientific_journal-1767	106	17	19	19	NUM
american_scientific_journal-1767	106	18	)	)	PUNCT
american_scientific_journal-1767	106	19	,	,	PUNCT
american_scientific_journal-1767	106	20	which	which	PRON
american_scientific_journal-1767	106	21	is	be	AUX
american_scientific_journal-1767	106	22	δ𝛿𝛿𝑒𝑒′	δ𝛿𝛿𝑒𝑒′	X
american_scientific_journal-1767	106	23	δ𝛿𝛿0′	δ𝛿𝛿0′	PUNCT
american_scientific_journal-1767	107	1	=	=	PRON
american_scientific_journal-1767	107	2	𝜃𝜃	𝜃𝜃	PROPN
american_scientific_journal-1767	107	3	�	�	PROPN
american_scientific_journal-1767	107	4	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1767	107	5	𝑙𝑙	𝑙𝑙	PRON
american_scientific_journal-1767	107	6	�	�	PROPN
american_scientific_journal-1767	107	7	+	+	CCONJ
american_scientific_journal-1767	107	8	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1767	107	9	𝑙𝑙	𝑙𝑙	NOUN
american_scientific_journal-1767	107	10	𝜃𝜃′	𝜃𝜃′	NOUN
american_scientific_journal-1767	107	11	�	�	NOUN
american_scientific_journal-1767	107	12	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1767	107	13	𝑙𝑙	𝑙𝑙	PROPN
american_scientific_journal-1767	107	14	�	�	PROPN
american_scientific_journal-1767	107	15	(	(	PUNCT
american_scientific_journal-1767	107	16	37	37	NUM
american_scientific_journal-1767	107	17	)	)	PUNCT
american_scientific_journal-1767	107	18	then	then	ADV
american_scientific_journal-1767	107	19	using	use	VERB
american_scientific_journal-1767	107	20	the	the	DET
american_scientific_journal-1767	107	21	metrics	metric	NOUN
american_scientific_journal-1767	107	22	in	in	ADP
american_scientific_journal-1767	107	23	(	(	PUNCT
american_scientific_journal-1767	107	24	18	18	NUM
american_scientific_journal-1767	107	25	)	)	PUNCT
american_scientific_journal-1767	107	26	,	,	PUNCT
american_scientific_journal-1767	107	27	the	the	DET
american_scientific_journal-1767	107	28	proper	proper	ADJ
american_scientific_journal-1767	107	29	times	time	NOUN
american_scientific_journal-1767	107	30	of	of	ADP
american_scientific_journal-1767	107	31	the	the	DET
american_scientific_journal-1767	107	32	two	two	NUM
american_scientific_journal-1767	107	33	relevant	relevant	ADJ
american_scientific_journal-1767	107	34	observers	observer	NOUN
american_scientific_journal-1767	107	35	corresponding	correspond	VERB
american_scientific_journal-1767	107	36	to	to	ADP
american_scientific_journal-1767	107	37	δ𝑡𝑡𝑒𝑒′	δ𝑡𝑡𝑒𝑒′	NOUN
american_scientific_journal-1767	107	38	and	and	CCONJ
american_scientific_journal-1767	107	39	δ𝑑𝑑0′	δ𝑑𝑑0′	PROPN
american_scientific_journal-1767	107	40	are	be	AUX
american_scientific_journal-1767	107	41	given	give	VERB
american_scientific_journal-1767	107	42	by	by	ADP
american_scientific_journal-1767	107	43	δ𝜏𝜏𝑒𝑒′	δ𝜏𝜏𝑒𝑒′	NOUN
american_scientific_journal-1767	107	44	=	=	SYM
american_scientific_journal-1767	107	45	�	�	PROPN
american_scientific_journal-1767	107	46	1	1	NUM
american_scientific_journal-1767	107	47	𝜃𝜃	𝜃𝜃	PROPN
american_scientific_journal-1767	107	48	�	�	PROPN
american_scientific_journal-1767	107	49	𝑎𝑎𝑙𝑙	𝑎𝑎𝑙𝑙	PROPN
american_scientific_journal-1767	107	50	�	�	PROPN
american_scientific_journal-1767	107	51	�	�	PROPN
american_scientific_journal-1767	107	52	δ𝑡𝑡𝑒𝑒′	δ𝑡𝑡𝑒𝑒′	NOUN
american_scientific_journal-1767	107	53	and	and	CCONJ
american_scientific_journal-1767	107	54	δ𝜏𝜏0′	δ𝜏𝜏0′	NOUN
american_scientific_journal-1767	107	55	=	=	SYM
american_scientific_journal-1767	107	56	�	�	PROPN
american_scientific_journal-1767	107	57	1	1	NUM
american_scientific_journal-1767	107	58	1−	1−	NUM
american_scientific_journal-1767	107	59	𝑎𝑎2𝜃𝜃′	𝑎𝑎2𝜃𝜃′	PROPN
american_scientific_journal-1767	107	60	�	�	PROPN
american_scientific_journal-1767	107	61	𝑎𝑎𝑙𝑙	𝑎𝑎𝑙𝑙	PROPN
american_scientific_journal-1767	107	62	�	�	PROPN
american_scientific_journal-1767	107	63	𝑙𝑙𝐴𝐴	𝑙𝑙𝐴𝐴	NUM
american_scientific_journal-1767	107	64	�	�	PROPN
american_scientific_journal-1767	107	65	δ𝑑𝑑0′	δ𝑑𝑑0′	PROPN
american_scientific_journal-1767	107	66	(	(	PUNCT
american_scientific_journal-1767	107	67	38	38	NUM
american_scientific_journal-1767	107	68	)	)	PUNCT
american_scientific_journal-1767	107	69	where	where	SCONJ
american_scientific_journal-1767	107	70	δ𝜏𝜏𝑒𝑒′	δ𝜏𝜏𝑒𝑒′	NUM
american_scientific_journal-1767	107	71	and	and	CCONJ
american_scientific_journal-1767	107	72	δ𝜏𝜏0′	δ𝜏𝜏0′	NOUN
american_scientific_journal-1767	107	73	are	be	AUX
american_scientific_journal-1767	107	74	the	the	DET
american_scientific_journal-1767	107	75	proper	proper	ADJ
american_scientific_journal-1767	107	76	time	time	NOUN
american_scientific_journal-1767	107	77	intervals	interval	NOUN
american_scientific_journal-1767	107	78	of	of	ADP
american_scientific_journal-1767	107	79	the	the	DET
american_scientific_journal-1767	107	80	two	two	NUM
american_scientific_journal-1767	107	81	observers	observer	NOUN
american_scientific_journal-1767	107	82	at	at	ADP
american_scientific_journal-1767	107	83	𝑟𝑟	𝑟𝑟	ADV
american_scientific_journal-1767	107	84	=	=	SYM
american_scientific_journal-1767	107	85	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1767	107	86	,	,	PUNCT
american_scientific_journal-1767	107	87	inside	inside	ADP
american_scientific_journal-1767	107	88	the	the	DET
american_scientific_journal-1767	107	89	sphere	sphere	NOUN
american_scientific_journal-1767	107	90	and	and	CCONJ
american_scientific_journal-1767	107	91	𝑑𝑑	𝑑𝑑	VERB
american_scientific_journal-1767	108	1	=	=	SYM
american_scientific_journal-1767	108	2	𝐴𝐴,outside	𝐴𝐴,outside	NOUN
american_scientific_journal-1767	108	3	of	of	ADP
american_scientific_journal-1767	108	4	the	the	DET
american_scientific_journal-1767	108	5	sphere	sphere	NOUN
american_scientific_journal-1767	108	6	respectively	respectively	ADV
american_scientific_journal-1767	108	7	receiving	receive	VERB
american_scientific_journal-1767	108	8	the	the	DET
american_scientific_journal-1767	108	9	pulse	pulse	NOUN
american_scientific_journal-1767	108	10	and	and	CCONJ
american_scientific_journal-1767	108	11	𝐴𝐴	𝐴𝐴	PROPN
american_scientific_journal-1767	108	12	is	be	AUX
american_scientific_journal-1767	108	13	given	give	VERB
american_scientific_journal-1767	108	14	by	by	ADP
american_scientific_journal-1767	108	15	𝐴𝐴	𝐴𝐴	PROPN
american_scientific_journal-1767	108	16	=	=	SYM
american_scientific_journal-1767	108	17	𝑎𝑎𝜃𝜃	𝑎𝑎𝜃𝜃	NOUN
american_scientific_journal-1767	108	18	�	�	NOUN
american_scientific_journal-1767	108	19	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1767	108	20	𝑙𝑙	𝑙𝑙	PRON
american_scientific_journal-1767	108	21	�	�	PROPN
american_scientific_journal-1767	108	22	+	+	CCONJ
american_scientific_journal-1767	108	23	𝑎𝑎2	𝑎𝑎2	X
american_scientific_journal-1767	108	24	𝑙𝑙	𝑙𝑙	NOUN
american_scientific_journal-1767	108	25	𝜃𝜃′	𝜃𝜃′	NOUN
american_scientific_journal-1767	108	26	�	�	NOUN
american_scientific_journal-1767	108	27	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1767	108	28	𝑙𝑙	𝑙𝑙	PROPN
american_scientific_journal-1767	108	29	�	�	PROPN
american_scientific_journal-1767	108	30	.	.	PUNCT
american_scientific_journal-1767	109	1	using	use	VERB
american_scientific_journal-1767	109	2	the	the	DET
american_scientific_journal-1767	109	3	similar	similar	ADJ
american_scientific_journal-1767	109	4	steps	step	NOUN
american_scientific_journal-1767	109	5	in	in	ADP
american_scientific_journal-1767	109	6	equation	equation	NOUN
american_scientific_journal-1767	109	7	(	(	PUNCT
american_scientific_journal-1767	109	8	34),(35	34),(35	NUM
american_scientific_journal-1767	109	9	)	)	PUNCT
american_scientific_journal-1767	109	10	and	and	CCONJ
american_scientific_journal-1767	109	11	(	(	PUNCT
american_scientific_journal-1767	109	12	36	36	NUM
american_scientific_journal-1767	109	13	)	)	PUNCT
american_scientific_journal-1767	109	14	,	,	PUNCT
american_scientific_journal-1767	109	15	the	the	DET
american_scientific_journal-1767	109	16	ratio	ratio	NOUN
american_scientific_journal-1767	109	17	between	between	ADP
american_scientific_journal-1767	109	18	the	the	DET
american_scientific_journal-1767	109	19	frequencies	frequency	NOUN
american_scientific_journal-1767	109	20	𝜈𝜈𝑒𝑒′	𝜈𝜈𝑒𝑒′	NOUN
american_scientific_journal-1767	110	1	and	and	CCONJ
american_scientific_journal-1767	110	2	𝜈𝜈0′	𝜈𝜈0′	NOUN
american_scientific_journal-1767	110	3	can	can	AUX
american_scientific_journal-1767	110	4	be	be	AUX
american_scientific_journal-1767	110	5	obtained	obtain	VERB
american_scientific_journal-1767	110	6	in	in	ADP
american_scientific_journal-1767	110	7	the	the	DET
american_scientific_journal-1767	110	8	form	form	NOUN
american_scientific_journal-1767	110	9	𝜈𝜈𝑒𝑒′	𝜈𝜈𝑒𝑒′	ADP
american_scientific_journal-1767	110	10	𝜈𝜈0′	𝜈𝜈0′	X
american_scientific_journal-1767	110	11	=	=	SYM
american_scientific_journal-1767	110	12	1	1	NUM
american_scientific_journal-1767	110	13	(	(	PUNCT
american_scientific_journal-1767	110	14	39	39	NUM
american_scientific_journal-1767	110	15	)	)	PUNCT
american_scientific_journal-1767	110	16	now	now	ADV
american_scientific_journal-1767	110	17	assuming	assume	VERB
american_scientific_journal-1767	110	18	that	that	SCONJ
american_scientific_journal-1767	110	19	an	an	DET
american_scientific_journal-1767	110	20	observer	observer	NOUN
american_scientific_journal-1767	110	21	at	at	ADP
american_scientific_journal-1767	110	22	a	a	DET
american_scientific_journal-1767	110	23	large	large	ADJ
american_scientific_journal-1767	110	24	distance	distance	NOUN
american_scientific_journal-1767	110	25	𝑑𝑑	𝑑𝑑	NOUN
american_scientific_journal-1767	110	26	=	=	SYM
american_scientific_journal-1767	110	27	𝑑𝑑0	𝑑𝑑0	NOUN
american_scientific_journal-1767	110	28	,	,	PUNCT
american_scientific_journal-1767	110	29	outside	outside	ADP
american_scientific_journal-1767	110	30	of	of	ADP
american_scientific_journal-1767	110	31	the	the	DET
american_scientific_journal-1767	110	32	sphere	sphere	NOUN
american_scientific_journal-1767	110	33	observed	observe	VERB
american_scientific_journal-1767	110	34	the	the	DET
american_scientific_journal-1767	110	35	front	front	NOUN
american_scientific_journal-1767	110	36	of	of	ADP
american_scientific_journal-1767	110	37	the	the	DET
american_scientific_journal-1767	110	38	pulse	pulse	NOUN
american_scientific_journal-1767	110	39	which	which	PRON
american_scientific_journal-1767	110	40	is	be	AUX
american_scientific_journal-1767	110	41	passed	pass	VERB
american_scientific_journal-1767	110	42	through	through	ADP
american_scientific_journal-1767	110	43	the	the	DET
american_scientific_journal-1767	110	44	boundary	boundary	NOUN
american_scientific_journal-1767	110	45	at	at	ADP
american_scientific_journal-1767	110	46	𝑑𝑑	𝑑𝑑	NOUN
american_scientific_journal-1767	110	47	=	=	SYM
american_scientific_journal-1767	110	48	𝑑𝑑0′	𝑑𝑑0′	ADP
american_scientific_journal-1767	110	49	outside	outside	ADP
american_scientific_journal-1767	110	50	the	the	DET
american_scientific_journal-1767	110	51	sphere	sphere	NOUN
american_scientific_journal-1767	110	52	,	,	PUNCT
american_scientific_journal-1767	110	53	the	the	DET
american_scientific_journal-1767	110	54	radial	radial	ADJ
american_scientific_journal-1767	110	55	null	null	ADJ
american_scientific_journal-1767	110	56	geodesic	geodesic	NOUN
american_scientific_journal-1767	110	57	for	for	ADP
american_scientific_journal-1767	110	58	the	the	DET
american_scientific_journal-1767	110	59	exterior	exterior	ADJ
american_scientific_journal-1767	110	60	vacuum	vacuum	NOUN
american_scientific_journal-1767	110	61	region	region	NOUN
american_scientific_journal-1767	110	62	can	can	AUX
american_scientific_journal-1767	110	63	be	be	AUX
american_scientific_journal-1767	110	64	integrated	integrate	VERB
american_scientific_journal-1767	110	65	into	into	ADP
american_scientific_journal-1767	110	66	the	the	DET
american_scientific_journal-1767	110	67	form	form	NOUN
american_scientific_journal-1767	110	68	american	american	PROPN
american_scientific_journal-1767	110	69	scientific	scientific	ADJ
american_scientific_journal-1767	110	70	research	research	NOUN
american_scientific_journal-1767	110	71	journal	journal	NOUN
american_scientific_journal-1767	110	72	for	for	ADP
american_scientific_journal-1767	110	73	engineering	engineering	NOUN
american_scientific_journal-1767	110	74	,	,	PUNCT
american_scientific_journal-1767	110	75	technology	technology	NOUN
american_scientific_journal-1767	110	76	,	,	PUNCT
american_scientific_journal-1767	110	77	and	and	CCONJ
american_scientific_journal-1767	110	78	sciences	science	NOUN
american_scientific_journal-1767	110	79	(	(	PUNCT
american_scientific_journal-1767	110	80	asrjets	asrjet	NOUN
american_scientific_journal-1767	110	81	)	)	PUNCT
american_scientific_journal-1767	110	82	(	(	PUNCT
american_scientific_journal-1767	110	83	2016	2016	NUM
american_scientific_journal-1767	110	84	)	)	PUNCT
american_scientific_journal-1767	110	85	volume	volume	NOUN
american_scientific_journal-1767	110	86	21	21	NUM
american_scientific_journal-1767	110	87	,	,	PUNCT
american_scientific_journal-1767	110	88	no	no	DET
american_scientific_journal-1767	110	89	1	1	NUM
american_scientific_journal-1767	110	90	,	,	PUNCT
american_scientific_journal-1767	110	91	pp	pp	ADV
american_scientific_journal-1767	110	92	163	163	NUM
american_scientific_journal-1767	110	93	-	-	SYM
american_scientific_journal-1767	110	94	177	177	NUM
american_scientific_journal-1767	110	95	175	175	NUM
american_scientific_journal-1767	110	96	∫	∫	NOUN
american_scientific_journal-1767	110	97	𝑐𝑐𝑑𝑑𝑑𝑑𝛿𝛿0	𝑐𝑐𝑑𝑑𝑑𝑑𝛿𝛿0	NOUN
american_scientific_journal-1767	111	1	𝛿𝛿0′	𝛿𝛿0′	NOUN
american_scientific_journal-1767	111	2	=	=	SYM
american_scientific_journal-1767	111	3	∫	∫	PROPN
american_scientific_journal-1767	111	4	�	�	PROPN
american_scientific_journal-1767	111	5	1	1	NUM
american_scientific_journal-1767	111	6	−	−	PROPN
american_scientific_journal-1767	111	7	𝑎𝑎2𝜃𝜃′	𝑎𝑎2𝜃𝜃′	PROPN
american_scientific_journal-1767	111	8	�	�	PROPN
american_scientific_journal-1767	111	9	𝑎𝑎𝑙𝑙	𝑎𝑎𝑙𝑙	PROPN
american_scientific_journal-1767	111	10	�	�	PROPN
american_scientific_journal-1767	111	11	𝑙𝑙𝐴𝐴	𝑙𝑙𝐴𝐴	NUM
american_scientific_journal-1767	111	12	�	�	PROPN
american_scientific_journal-1767	111	13	2	2	NUM
american_scientific_journal-1767	111	14	𝑑𝑑𝑑𝑑𝑅𝑅0	𝑑𝑑𝑑𝑑𝑅𝑅0	NOUN
american_scientific_journal-1767	111	15	𝐴𝐴	𝐴𝐴	PROPN
american_scientific_journal-1767	111	16	(	(	PUNCT
american_scientific_journal-1767	111	17	40	40	NUM
american_scientific_journal-1767	111	18	)	)	PUNCT
american_scientific_journal-1767	111	19	if	if	SCONJ
american_scientific_journal-1767	111	20	the	the	DET
american_scientific_journal-1767	111	21	rear	rear	NOUN
american_scientific_journal-1767	111	22	of	of	ADP
american_scientific_journal-1767	111	23	the	the	DET
american_scientific_journal-1767	111	24	pulse	pulse	NOUN
american_scientific_journal-1767	111	25	is	be	AUX
american_scientific_journal-1767	111	26	observed	observe	VERB
american_scientific_journal-1767	111	27	at	at	ADP
american_scientific_journal-1767	111	28	𝑑𝑑	𝑑𝑑	NOUN
american_scientific_journal-1767	111	29	=	=	SYM
american_scientific_journal-1767	111	30	𝑑𝑑0′	𝑑𝑑0′	ADP
american_scientific_journal-1767	111	31	+	+	CCONJ
american_scientific_journal-1767	111	32	δ𝑑𝑑0′	δ𝑑𝑑0′	NOUN
american_scientific_journal-1767	111	33	at	at	ADP
american_scientific_journal-1767	111	34	𝑑𝑑	𝑑𝑑	NOUN
american_scientific_journal-1767	111	35	=	=	SYM
american_scientific_journal-1767	111	36	𝑑𝑑0	𝑑𝑑0	NOUN
american_scientific_journal-1767	111	37	,	,	PUNCT
american_scientific_journal-1767	111	38	then	then	ADV
american_scientific_journal-1767	111	39	the	the	DET
american_scientific_journal-1767	111	40	radial	radial	ADJ
american_scientific_journal-1767	111	41	null	null	ADJ
american_scientific_journal-1767	111	42	geodesic	geodesic	NOUN
american_scientific_journal-1767	111	43	for	for	ADP
american_scientific_journal-1767	111	44	the	the	DET
american_scientific_journal-1767	111	45	exterior	exterior	ADJ
american_scientific_journal-1767	111	46	vacuum	vacuum	NOUN
american_scientific_journal-1767	111	47	region	region	NOUN
american_scientific_journal-1767	111	48	can	can	AUX
american_scientific_journal-1767	111	49	be	be	AUX
american_scientific_journal-1767	111	50	integrated	integrate	VERB
american_scientific_journal-1767	111	51	into	into	ADP
american_scientific_journal-1767	111	52	the	the	DET
american_scientific_journal-1767	111	53	form	form	NOUN
american_scientific_journal-1767	111	54	∫	∫	PROPN
american_scientific_journal-1767	112	1	𝑐𝑐𝑑𝑑𝑑𝑑𝛿𝛿0+∆𝛿𝛿0	𝑐𝑐𝑑𝑑𝑑𝑑𝛿𝛿0+∆𝛿𝛿0	PRON
american_scientific_journal-1767	112	2	𝛿𝛿0′+∆𝛿𝛿0′	𝛿𝛿0′+∆𝛿𝛿0′	NOUN
american_scientific_journal-1767	112	3	=	=	SYM
american_scientific_journal-1767	112	4	∫	∫	PROPN
american_scientific_journal-1767	112	5	�	�	PROPN
american_scientific_journal-1767	112	6	1	1	NUM
american_scientific_journal-1767	112	7	−	−	PROPN
american_scientific_journal-1767	112	8	𝑎𝑎2𝜃𝜃′	𝑎𝑎2𝜃𝜃′	PROPN
american_scientific_journal-1767	112	9	�	�	PROPN
american_scientific_journal-1767	112	10	𝑎𝑎𝑙𝑙	𝑎𝑎𝑙𝑙	PROPN
american_scientific_journal-1767	112	11	�	�	PROPN
american_scientific_journal-1767	112	12	𝑙𝑙𝐴𝐴	𝑙𝑙𝐴𝐴	NUM
american_scientific_journal-1767	112	13	�	�	PROPN
american_scientific_journal-1767	112	14	2	2	NUM
american_scientific_journal-1767	112	15	𝑑𝑑𝑑𝑑𝑅𝑅0	𝑑𝑑𝑑𝑑𝑅𝑅0	NOUN
american_scientific_journal-1767	112	16	𝐴𝐴	𝐴𝐴	PROPN
american_scientific_journal-1767	112	17	(	(	PUNCT
american_scientific_journal-1767	112	18	41	41	NUM
american_scientific_journal-1767	112	19	)	)	PUNCT
american_scientific_journal-1767	112	20	since	since	SCONJ
american_scientific_journal-1767	112	21	the	the	DET
american_scientific_journal-1767	112	22	right	right	ADJ
american_scientific_journal-1767	112	23	hand	hand	NOUN
american_scientific_journal-1767	112	24	sides	side	NOUN
american_scientific_journal-1767	112	25	of	of	ADP
american_scientific_journal-1767	112	26	(	(	PUNCT
american_scientific_journal-1767	112	27	40	40	NUM
american_scientific_journal-1767	112	28	)	)	PUNCT
american_scientific_journal-1767	112	29	and	and	CCONJ
american_scientific_journal-1767	112	30	(	(	PUNCT
american_scientific_journal-1767	112	31	41	41	NUM
american_scientific_journal-1767	112	32	)	)	PUNCT
american_scientific_journal-1767	112	33	are	be	AUX
american_scientific_journal-1767	112	34	equal	equal	ADJ
american_scientific_journal-1767	112	35	and	and	CCONJ
american_scientific_journal-1767	112	36	hence	hence	ADV
american_scientific_journal-1767	112	37	it	it	PRON
american_scientific_journal-1767	112	38	can	can	AUX
american_scientific_journal-1767	112	39	be	be	AUX
american_scientific_journal-1767	112	40	obtained	obtain	VERB
american_scientific_journal-1767	112	41	∫	∫	PROPN
american_scientific_journal-1767	112	42	𝑐𝑐𝑑𝑑𝑑𝑑𝛿𝛿0	𝑐𝑐𝑑𝑑𝑑𝑑𝛿𝛿0	PROPN
american_scientific_journal-1767	113	1	𝛿𝛿0′	𝛿𝛿0′	NOUN
american_scientific_journal-1767	113	2	=	=	PUNCT
american_scientific_journal-1767	113	3	∫	∫	PROPN
american_scientific_journal-1767	114	1	𝑐𝑐𝑑𝑑𝑑𝑑𝛿𝛿0+∆𝛿𝛿0	𝑐𝑐𝑑𝑑𝑑𝑑𝛿𝛿0+∆𝛿𝛿0	PROPN
american_scientific_journal-1767	114	2	𝛿𝛿0′+∆𝛿𝛿0′	𝛿𝛿0′+∆𝛿𝛿0′	NOUN
american_scientific_journal-1767	114	3	.	.	PUNCT
american_scientific_journal-1767	115	1	rearrangement	rearrangement	NOUN
american_scientific_journal-1767	115	2	and	and	CCONJ
american_scientific_journal-1767	115	3	simplification	simplification	NOUN
american_scientific_journal-1767	115	4	with	with	ADP
american_scientific_journal-1767	115	5	the	the	DET
american_scientific_journal-1767	115	6	assumption	assumption	NOUN
american_scientific_journal-1767	115	7	that	that	SCONJ
american_scientific_journal-1767	115	8	∆𝑑𝑑0	∆𝑑𝑑0	NUM
american_scientific_journal-1767	115	9	and	and	CCONJ
american_scientific_journal-1767	115	10	∆𝑑𝑑0′	∆𝑑𝑑0′	PROPN
american_scientific_journal-1767	115	11	are	be	AUX
american_scientific_journal-1767	115	12	very	very	ADV
american_scientific_journal-1767	115	13	small	small	ADJ
american_scientific_journal-1767	115	14	gives	give	VERB
american_scientific_journal-1767	115	15	∆𝑑𝑑0	∆𝑑𝑑0	PROPN
american_scientific_journal-1767	115	16	=	=	SYM
american_scientific_journal-1767	115	17	∆𝑑𝑑0′	∆𝑑𝑑0′	PROPN
american_scientific_journal-1767	115	18	(	(	PUNCT
american_scientific_journal-1767	115	19	42	42	NUM
american_scientific_journal-1767	115	20	)	)	PUNCT
american_scientific_journal-1767	115	21	now	now	ADV
american_scientific_journal-1767	115	22	using	use	VERB
american_scientific_journal-1767	115	23	the	the	DET
american_scientific_journal-1767	115	24	metrics	metric	NOUN
american_scientific_journal-1767	115	25	in	in	ADP
american_scientific_journal-1767	115	26	(	(	PUNCT
american_scientific_journal-1767	115	27	18	18	NUM
american_scientific_journal-1767	115	28	)	)	PUNCT
american_scientific_journal-1767	115	29	,	,	PUNCT
american_scientific_journal-1767	115	30	the	the	DET
american_scientific_journal-1767	115	31	proper	proper	ADJ
american_scientific_journal-1767	115	32	times	time	NOUN
american_scientific_journal-1767	115	33	of	of	ADP
american_scientific_journal-1767	115	34	the	the	DET
american_scientific_journal-1767	115	35	two	two	NUM
american_scientific_journal-1767	115	36	observers	observer	NOUN
american_scientific_journal-1767	115	37	corresponding	correspond	VERB
american_scientific_journal-1767	115	38	to	to	ADP
american_scientific_journal-1767	115	39	∆𝑑𝑑0′	∆𝑑𝑑0′	PROPN
american_scientific_journal-1767	115	40	and	and	CCONJ
american_scientific_journal-1767	115	41	∆𝑑𝑑0	∆𝑑𝑑0	PROPN
american_scientific_journal-1767	115	42	can	can	AUX
american_scientific_journal-1767	115	43	be	be	AUX
american_scientific_journal-1767	115	44	written	write	VERB
american_scientific_journal-1767	115	45	as	as	ADP
american_scientific_journal-1767	115	46	δ𝜏𝜏0′	δ𝜏𝜏0′	NOUN
american_scientific_journal-1767	115	47	=	=	SYM
american_scientific_journal-1767	115	48	�	�	PROPN
american_scientific_journal-1767	115	49	1	1	NUM
american_scientific_journal-1767	115	50	1−	1−	NUM
american_scientific_journal-1767	115	51	𝑎𝑎2𝜃𝜃′	𝑎𝑎2𝜃𝜃′	PROPN
american_scientific_journal-1767	115	52	�	�	PROPN
american_scientific_journal-1767	115	53	𝑎𝑎𝑙𝑙	𝑎𝑎𝑙𝑙	PROPN
american_scientific_journal-1767	115	54	�	�	PROPN
american_scientific_journal-1767	115	55	𝑙𝑙𝐴𝐴	𝑙𝑙𝐴𝐴	NUM
american_scientific_journal-1767	115	56	�	�	NOUN
american_scientific_journal-1767	115	57	δ𝑑𝑑0′	δ𝑑𝑑0′	PROPN
american_scientific_journal-1767	115	58	and	and	CCONJ
american_scientific_journal-1767	115	59	∆𝜏𝜏0	∆𝜏𝜏0	NUM
american_scientific_journal-1767	115	60	=	=	SYM
american_scientific_journal-1767	115	61	�	�	PROPN
american_scientific_journal-1767	115	62	1	1	NUM
american_scientific_journal-1767	115	63	1−	1−	NUM
american_scientific_journal-1767	115	64	𝑎𝑎2𝜃𝜃′	𝑎𝑎2𝜃𝜃′	PROPN
american_scientific_journal-1767	115	65	�	�	PROPN
american_scientific_journal-1767	115	66	𝑎𝑎𝑙𝑙	𝑎𝑎𝑙𝑙	PROPN
american_scientific_journal-1767	115	67	�	�	PROPN
american_scientific_journal-1767	115	68	𝑙𝑙𝑅𝑅0	𝑙𝑙𝑅𝑅0	PROPN
american_scientific_journal-1767	115	69	�	�	PROPN
american_scientific_journal-1767	115	70	δ𝑑𝑑0	δ𝑑𝑑0	NOUN
american_scientific_journal-1767	115	71	(	(	PUNCT
american_scientific_journal-1767	115	72	43	43	NUM
american_scientific_journal-1767	115	73	)	)	PUNCT
american_scientific_journal-1767	115	74	where	where	SCONJ
american_scientific_journal-1767	115	75	δ𝜏𝜏0′	δ𝜏𝜏0′	X
american_scientific_journal-1767	115	76	and	and	CCONJ
american_scientific_journal-1767	115	77	∆𝜏𝜏0	∆𝜏𝜏0	PRON
american_scientific_journal-1767	115	78	are	be	AUX
american_scientific_journal-1767	115	79	the	the	DET
american_scientific_journal-1767	115	80	proper	proper	ADJ
american_scientific_journal-1767	115	81	time	time	NOUN
american_scientific_journal-1767	115	82	intervals	interval	NOUN
american_scientific_journal-1767	115	83	of	of	ADP
american_scientific_journal-1767	115	84	the	the	DET
american_scientific_journal-1767	115	85	two	two	NUM
american_scientific_journal-1767	115	86	observers	observer	NOUN
american_scientific_journal-1767	115	87	at	at	ADP
american_scientific_journal-1767	115	88	𝐴𝐴,just	𝐴𝐴,just	PROPN
american_scientific_journal-1767	115	89	outside	outside	ADP
american_scientific_journal-1767	115	90	the	the	DET
american_scientific_journal-1767	115	91	boundary	boundary	NOUN
american_scientific_journal-1767	115	92	of	of	ADP
american_scientific_journal-1767	115	93	the	the	DET
american_scientific_journal-1767	115	94	sphere	sphere	NOUN
american_scientific_journal-1767	115	95	and	and	CCONJ
american_scientific_journal-1767	115	96	at	at	ADP
american_scientific_journal-1767	115	97	𝑑𝑑	𝑑𝑑	NOUN
american_scientific_journal-1767	115	98	=	=	SYM
american_scientific_journal-1767	115	99	𝑑𝑑0	𝑑𝑑0	NOUN
american_scientific_journal-1767	115	100	,	,	PUNCT
american_scientific_journal-1767	115	101	a	a	DET
american_scientific_journal-1767	115	102	large	large	ADJ
american_scientific_journal-1767	115	103	distance	distance	NOUN
american_scientific_journal-1767	115	104	outside	outside	ADP
american_scientific_journal-1767	115	105	of	of	ADP
american_scientific_journal-1767	115	106	the	the	DET
american_scientific_journal-1767	115	107	sphere	sphere	NOUN
american_scientific_journal-1767	115	108	respectively	respectively	ADV
american_scientific_journal-1767	115	109	receiving	receive	VERB
american_scientific_journal-1767	115	110	the	the	DET
american_scientific_journal-1767	115	111	pulse	pulse	NOUN
american_scientific_journal-1767	115	112	.	.	PUNCT
american_scientific_journal-1767	116	1	using	use	VERB
american_scientific_journal-1767	116	2	the	the	DET
american_scientific_journal-1767	116	3	fact	fact	NOUN
american_scientific_journal-1767	116	4	that	that	SCONJ
american_scientific_journal-1767	116	5	the	the	DET
american_scientific_journal-1767	116	6	number	number	NOUN
american_scientific_journal-1767	116	7	of	of	ADP
american_scientific_journal-1767	116	8	cycles	cycle	NOUN
american_scientific_journal-1767	116	9	of	of	ADP
american_scientific_journal-1767	116	10	the	the	DET
american_scientific_journal-1767	116	11	pulse	pulse	NOUN
american_scientific_journal-1767	116	12	remain	remain	VERB
american_scientific_journal-1767	116	13	the	the	DET
american_scientific_journal-1767	116	14	same	same	ADJ
american_scientific_journal-1767	116	15	throughout	throughout	ADP
american_scientific_journal-1767	116	16	its	its	PRON
american_scientific_journal-1767	116	17	way	way	NOUN
american_scientific_journal-1767	116	18	and	and	CCONJ
american_scientific_journal-1767	116	19	equation	equation	NOUN
american_scientific_journal-1767	116	20	(	(	PUNCT
american_scientific_journal-1767	116	21	43	43	NUM
american_scientific_journal-1767	116	22	)	)	PUNCT
american_scientific_journal-1767	116	23	,	,	PUNCT
american_scientific_journal-1767	116	24	the	the	DET
american_scientific_journal-1767	116	25	ratio	ratio	NOUN
american_scientific_journal-1767	116	26	between	between	ADP
american_scientific_journal-1767	116	27	the	the	DET
american_scientific_journal-1767	116	28	frequencies	frequency	NOUN
american_scientific_journal-1767	116	29	𝜈𝜈0	𝜈𝜈0	NOUN
american_scientific_journal-1767	116	30	and	and	CCONJ
american_scientific_journal-1767	116	31	𝜈𝜈0′	𝜈𝜈0′	NOUN
american_scientific_journal-1767	116	32	can	can	AUX
american_scientific_journal-1767	116	33	be	be	AUX
american_scientific_journal-1767	116	34	obtained	obtain	VERB
american_scientific_journal-1767	116	35	as	as	ADP
american_scientific_journal-1767	116	36	𝜈𝜈0	𝜈𝜈0	NOUN
american_scientific_journal-1767	116	37	𝜈𝜈0′	𝜈𝜈0′	PROPN
american_scientific_journal-1767	116	38	=	=	SYM
american_scientific_journal-1767	116	39	�	�	PROPN
american_scientific_journal-1767	116	40	1−	1−	NUM
american_scientific_journal-1767	116	41	𝑎𝑎2𝜃𝜃′	𝑎𝑎2𝜃𝜃′	PROPN
american_scientific_journal-1767	116	42	�	�	PROPN
american_scientific_journal-1767	116	43	𝑎𝑎𝑙𝑙	𝑎𝑎𝑙𝑙	PROPN
american_scientific_journal-1767	116	44	�	�	PROPN
american_scientific_journal-1767	116	45	𝑙𝑙𝑅𝑅0	𝑙𝑙𝑅𝑅0	PROPN
american_scientific_journal-1767	116	46	�	�	PROPN
american_scientific_journal-1767	116	47	�	�	PROPN
american_scientific_journal-1767	116	48	1−	1−	NUM
american_scientific_journal-1767	116	49	𝑎𝑎2𝜃𝜃′	𝑎𝑎2𝜃𝜃′	PROPN
american_scientific_journal-1767	116	50	�	�	PROPN
american_scientific_journal-1767	116	51	𝑎𝑎𝑙𝑙	𝑎𝑎𝑙𝑙	PROPN
american_scientific_journal-1767	116	52	�	�	PROPN
american_scientific_journal-1767	116	53	𝑙𝑙𝐴𝐴	𝑙𝑙𝐴𝐴	NUM
american_scientific_journal-1767	116	54	�	�	PROPN
american_scientific_journal-1767	116	55	δ𝛿𝛿0	δ𝛿𝛿0	NOUN
american_scientific_journal-1767	116	56	δ𝛿𝛿0′	δ𝛿𝛿0′	PUNCT
american_scientific_journal-1767	116	57	(	(	PUNCT
american_scientific_journal-1767	116	58	44	44	NUM
american_scientific_journal-1767	116	59	)	)	PUNCT
american_scientific_journal-1767	116	60	equation	equation	NOUN
american_scientific_journal-1767	116	61	(	(	PUNCT
american_scientific_journal-1767	116	62	44	44	NUM
american_scientific_journal-1767	116	63	)	)	PUNCT
american_scientific_journal-1767	116	64	can	can	AUX
american_scientific_journal-1767	116	65	be	be	AUX
american_scientific_journal-1767	116	66	simplified	simplify	VERB
american_scientific_journal-1767	116	67	using	use	VERB
american_scientific_journal-1767	116	68	equation	equation	NOUN
american_scientific_journal-1767	116	69	(	(	PUNCT
american_scientific_journal-1767	116	70	42	42	NUM
american_scientific_journal-1767	116	71	)	)	PUNCT
american_scientific_journal-1767	116	72	into	into	ADP
american_scientific_journal-1767	116	73	the	the	DET
american_scientific_journal-1767	116	74	form	form	NOUN
american_scientific_journal-1767	116	75	𝜈𝜈0	𝜈𝜈0	NOUN
american_scientific_journal-1767	116	76	𝜈𝜈0′	𝜈𝜈0′	NOUN
american_scientific_journal-1767	116	77	=	=	SYM
american_scientific_journal-1767	116	78	�	�	PROPN
american_scientific_journal-1767	116	79	1−	1−	NUM
american_scientific_journal-1767	116	80	𝑎𝑎2𝜃𝜃′	𝑎𝑎2𝜃𝜃′	PROPN
american_scientific_journal-1767	116	81	�	�	PROPN
american_scientific_journal-1767	116	82	𝑎𝑎𝑙𝑙	𝑎𝑎𝑙𝑙	PROPN
american_scientific_journal-1767	116	83	�	�	PROPN
american_scientific_journal-1767	116	84	𝑙𝑙𝑅𝑅0	𝑙𝑙𝑅𝑅0	PROPN
american_scientific_journal-1767	116	85	�	�	PROPN
american_scientific_journal-1767	116	86	�	�	PROPN
american_scientific_journal-1767	116	87	1−	1−	NUM
american_scientific_journal-1767	116	88	𝑎𝑎2𝜃𝜃′	𝑎𝑎2𝜃𝜃′	PROPN
american_scientific_journal-1767	116	89	�	�	PROPN
american_scientific_journal-1767	116	90	𝑎𝑎𝑙𝑙	𝑎𝑎𝑙𝑙	PROPN
american_scientific_journal-1767	116	91	�	�	PROPN
american_scientific_journal-1767	116	92	𝑙𝑙𝐴𝐴	𝑙𝑙𝐴𝐴	NUM
american_scientific_journal-1767	116	93	�	�	PROPN
american_scientific_journal-1767	116	94	(	(	PUNCT
american_scientific_journal-1767	116	95	45	45	NUM
american_scientific_journal-1767	116	96	)	)	PUNCT
american_scientific_journal-1767	116	97	using	use	VERB
american_scientific_journal-1767	116	98	the	the	DET
american_scientific_journal-1767	116	99	fact	fact	NOUN
american_scientific_journal-1767	116	100	that	that	SCONJ
american_scientific_journal-1767	116	101	𝜈𝜈0	𝜈𝜈0	NOUN
american_scientific_journal-1767	116	102	𝜈𝜈𝑒𝑒	𝜈𝜈𝑒𝑒	NOUN
american_scientific_journal-1767	116	103	=	=	SYM
american_scientific_journal-1767	117	1	𝜈𝜈0	𝜈𝜈0	PROPN
american_scientific_journal-1767	117	2	𝜈𝜈0′	𝜈𝜈0′	NOUN
american_scientific_journal-1767	117	3	𝜈𝜈0′	𝜈𝜈0′	PART
american_scientific_journal-1767	117	4	𝜈𝜈𝑒𝑒′	𝜈𝜈𝑒𝑒′	VERB
american_scientific_journal-1767	117	5	𝜈𝜈𝑒𝑒′	𝜈𝜈𝑒𝑒′	X
american_scientific_journal-1767	117	6	𝜈𝜈𝑒𝑒	𝜈𝜈𝑒𝑒	NOUN
american_scientific_journal-1767	117	7	and	and	CCONJ
american_scientific_journal-1767	117	8	equations	equation	NOUN
american_scientific_journal-1767	117	9	(	(	PUNCT
american_scientific_journal-1767	117	10	36),(39	36),(39	NUM
american_scientific_journal-1767	117	11	)	)	PUNCT
american_scientific_journal-1767	117	12	and	and	CCONJ
american_scientific_journal-1767	117	13	(	(	PUNCT
american_scientific_journal-1767	117	14	45	45	NUM
american_scientific_journal-1767	117	15	)	)	PUNCT
american_scientific_journal-1767	117	16	,	,	PUNCT
american_scientific_journal-1767	117	17	it	it	PRON
american_scientific_journal-1767	117	18	can	can	AUX
american_scientific_journal-1767	117	19	be	be	AUX
american_scientific_journal-1767	117	20	obtained	obtain	VERB
american_scientific_journal-1767	117	21	that	that	SCONJ
american_scientific_journal-1767	117	22	american	american	PROPN
american_scientific_journal-1767	117	23	scientific	scientific	ADJ
american_scientific_journal-1767	117	24	research	research	NOUN
american_scientific_journal-1767	117	25	journal	journal	NOUN
american_scientific_journal-1767	117	26	for	for	ADP
american_scientific_journal-1767	117	27	engineering	engineering	NOUN
american_scientific_journal-1767	117	28	,	,	PUNCT
american_scientific_journal-1767	117	29	technology	technology	NOUN
american_scientific_journal-1767	117	30	,	,	PUNCT
american_scientific_journal-1767	117	31	and	and	CCONJ
american_scientific_journal-1767	117	32	sciences	science	NOUN
american_scientific_journal-1767	117	33	(	(	PUNCT
american_scientific_journal-1767	117	34	asrjets	asrjet	NOUN
american_scientific_journal-1767	117	35	)	)	PUNCT
american_scientific_journal-1767	117	36	(	(	PUNCT
american_scientific_journal-1767	117	37	2016	2016	NUM
american_scientific_journal-1767	117	38	)	)	PUNCT
american_scientific_journal-1767	117	39	volume	volume	NOUN
american_scientific_journal-1767	117	40	21	21	NUM
american_scientific_journal-1767	117	41	,	,	PUNCT
american_scientific_journal-1767	117	42	no	no	DET
american_scientific_journal-1767	117	43	1	1	NUM
american_scientific_journal-1767	117	44	,	,	PUNCT
american_scientific_journal-1767	117	45	pp	pp	ADV
american_scientific_journal-1767	117	46	163	163	NUM
american_scientific_journal-1767	117	47	-	-	SYM
american_scientific_journal-1767	117	48	177	177	NUM
american_scientific_journal-1767	117	49	176	176	NUM
american_scientific_journal-1767	117	50	𝜈𝜈0	𝜈𝜈0	NOUN
american_scientific_journal-1767	117	51	𝜈𝜈𝑒𝑒	𝜈𝜈𝑒𝑒	NOUN
american_scientific_journal-1767	117	52	=	=	SYM
american_scientific_journal-1767	117	53	�	�	PROPN
american_scientific_journal-1767	117	54	1−	1−	NUM
american_scientific_journal-1767	117	55	𝑎𝑎2𝜃𝜃′	𝑎𝑎2𝜃𝜃′	PROPN
american_scientific_journal-1767	117	56	�	�	PROPN
american_scientific_journal-1767	117	57	𝑎𝑎𝑙𝑙	𝑎𝑎𝑙𝑙	PROPN
american_scientific_journal-1767	117	58	�	�	PROPN
american_scientific_journal-1767	117	59	𝑙𝑙𝑅𝑅0	𝑙𝑙𝑅𝑅0	PROPN
american_scientific_journal-1767	117	60	1−	1−	NUM
american_scientific_journal-1767	117	61	𝑎𝑎2𝜃𝜃′	𝑎𝑎2𝜃𝜃′	PROPN
american_scientific_journal-1767	117	62	�	�	PROPN
american_scientific_journal-1767	117	63	𝑎𝑎𝑙𝑙	𝑎𝑎𝑙𝑙	PROPN
american_scientific_journal-1767	117	64	�	�	PROPN
american_scientific_journal-1767	117	65	𝑙𝑙𝐴𝐴	𝑙𝑙𝐴𝐴	NUM
american_scientific_journal-1767	117	66	�	�	PROPN
american_scientific_journal-1767	117	67	(	(	PUNCT
american_scientific_journal-1767	117	68	1	1	NUM
american_scientific_journal-1767	117	69	)	)	PUNCT
american_scientific_journal-1767	117	70	�	�	PROPN
american_scientific_journal-1767	117	71	𝜃𝜃	𝜃𝜃	PROPN
american_scientific_journal-1767	117	72	�	�	PROPN
american_scientific_journal-1767	117	73	𝑎𝑎𝑙𝑙	𝑎𝑎𝑙𝑙	PROPN
american_scientific_journal-1767	117	74	�	�	PROPN
american_scientific_journal-1767	117	75	𝜃𝜃	𝜃𝜃	PROPN
american_scientific_journal-1767	117	76	�	�	PROPN
american_scientific_journal-1767	117	77	𝑟𝑟𝑒𝑒𝑙𝑙	𝑟𝑟𝑒𝑒𝑙𝑙	PROPN
american_scientific_journal-1767	117	78	�	�	PROPN
american_scientific_journal-1767	117	79	�	�	PROPN
american_scientific_journal-1767	117	80	(	(	PUNCT
american_scientific_journal-1767	117	81	46	46	NUM
american_scientific_journal-1767	117	82	)	)	PUNCT
american_scientific_journal-1767	117	83	since	since	SCONJ
american_scientific_journal-1767	117	84	the	the	DET
american_scientific_journal-1767	117	85	red	red	ADJ
american_scientific_journal-1767	117	86	shift	shift	NOUN
american_scientific_journal-1767	118	1	𝑧𝑧	𝑧𝑧	ADP
american_scientific_journal-1767	118	2	corresponds	correspond	NOUN
american_scientific_journal-1767	118	3	to	to	ADP
american_scientific_journal-1767	118	4	the	the	DET
american_scientific_journal-1767	118	5	change	change	NOUN
american_scientific_journal-1767	118	6	of	of	ADP
american_scientific_journal-1767	118	7	the	the	DET
american_scientific_journal-1767	118	8	wave	wave	NOUN
american_scientific_journal-1767	118	9	length	length	NOUN
american_scientific_journal-1767	118	10	can	can	AUX
american_scientific_journal-1767	118	11	be	be	AUX
american_scientific_journal-1767	118	12	calculated	calculate	VERB
american_scientific_journal-1767	118	13	as	as	ADP
american_scientific_journal-1767	118	14	1	1	NUM
american_scientific_journal-1767	118	15	+	+	CCONJ
american_scientific_journal-1767	118	16	𝑧𝑧	𝑧𝑧	PROPN
american_scientific_journal-1767	118	17	=	=	ADJ
american_scientific_journal-1767	118	18	𝜆𝜆0	𝜆𝜆0	NOUN
american_scientific_journal-1767	118	19	𝜆𝜆𝑒𝑒	𝜆𝜆𝑒𝑒	NOUN
american_scientific_journal-1767	118	20	=	=	SYM
american_scientific_journal-1767	118	21	�	�	PROPN
american_scientific_journal-1767	118	22	1−	1−	NUM
american_scientific_journal-1767	118	23	𝑎𝑎2𝜃𝜃′	𝑎𝑎2𝜃𝜃′	PROPN
american_scientific_journal-1767	118	24	�	�	PROPN
american_scientific_journal-1767	118	25	𝑎𝑎𝑙𝑙	𝑎𝑎𝑙𝑙	PROPN
american_scientific_journal-1767	118	26	�	�	PROPN
american_scientific_journal-1767	118	27	𝑙𝑙𝐴𝐴	𝑙𝑙𝐴𝐴	NUM
american_scientific_journal-1767	118	28	�	�	PROPN
american_scientific_journal-1767	118	29	𝜃𝜃	𝜃𝜃	PROPN
american_scientific_journal-1767	118	30	�	�	PROPN
american_scientific_journal-1767	118	31	𝑟𝑟𝑒𝑒𝑙𝑙	𝑟𝑟𝑒𝑒𝑙𝑙	PROPN
american_scientific_journal-1767	118	32	�	�	PROPN
american_scientific_journal-1767	118	33	�	�	PROPN
american_scientific_journal-1767	118	34	1−	1−	NUM
american_scientific_journal-1767	118	35	𝑎𝑎2𝜃𝜃′	𝑎𝑎2𝜃𝜃′	PROPN
american_scientific_journal-1767	118	36	�	�	PROPN
american_scientific_journal-1767	118	37	𝑎𝑎𝑙𝑙	𝑎𝑎𝑙𝑙	PROPN
american_scientific_journal-1767	118	38	�	�	PROPN
american_scientific_journal-1767	118	39	𝑙𝑙𝑅𝑅0	𝑙𝑙𝑅𝑅0	PROPN
american_scientific_journal-1767	118	40	�	�	PROPN
american_scientific_journal-1767	118	41	𝜃𝜃	𝜃𝜃	PROPN
american_scientific_journal-1767	118	42	�	�	PROPN
american_scientific_journal-1767	118	43	𝑎𝑎𝑙𝑙	𝑎𝑎𝑙𝑙	PROPN
american_scientific_journal-1767	118	44	�	�	PROPN
american_scientific_journal-1767	118	45	when	when	SCONJ
american_scientific_journal-1767	118	46	𝑑𝑑0	𝑑𝑑0	PROPN
american_scientific_journal-1767	118	47	tends	tend	VERB
american_scientific_journal-1767	118	48	to	to	PART
american_scientific_journal-1767	118	49	infinity	infinity	VERB
american_scientific_journal-1767	118	50	,	,	PUNCT
american_scientific_journal-1767	118	51	the	the	DET
american_scientific_journal-1767	118	52	red	red	ADJ
american_scientific_journal-1767	118	53	shift	shift	NOUN
american_scientific_journal-1767	118	54	is	be	AUX
american_scientific_journal-1767	118	55	equal	equal	ADJ
american_scientific_journal-1767	118	56	to	to	ADP
american_scientific_journal-1767	118	57	1	1	NUM
american_scientific_journal-1767	118	58	+	+	CCONJ
american_scientific_journal-1767	118	59	𝑧𝑧	𝑧𝑧	PROPN
american_scientific_journal-1767	118	60	=	=	PROPN
american_scientific_journal-1767	118	61	�	�	PROPN
american_scientific_journal-1767	118	62	1−	1−	NUM
american_scientific_journal-1767	118	63	𝑎𝑎2𝜃𝜃′	𝑎𝑎2𝜃𝜃′	PROPN
american_scientific_journal-1767	118	64	�	�	PROPN
american_scientific_journal-1767	118	65	𝑎𝑎𝑙𝑙	𝑎𝑎𝑙𝑙	PROPN
american_scientific_journal-1767	118	66	�	�	PROPN
american_scientific_journal-1767	118	67	𝑙𝑙𝐴𝐴	𝑙𝑙𝐴𝐴	NUM
american_scientific_journal-1767	118	68	�	�	PROPN
american_scientific_journal-1767	118	69	𝜃𝜃	𝜃𝜃	PROPN
american_scientific_journal-1767	118	70	�	�	PROPN
american_scientific_journal-1767	118	71	𝑟𝑟𝑒𝑒𝑙𝑙	𝑟𝑟𝑒𝑒𝑙𝑙	PROPN
american_scientific_journal-1767	118	72	�	�	PROPN
american_scientific_journal-1767	118	73	𝜃𝜃	𝜃𝜃	PROPN
american_scientific_journal-1767	118	74	�	�	PROPN
american_scientific_journal-1767	118	75	𝑎𝑎𝑙𝑙	𝑎𝑎𝑙𝑙	PROPN
american_scientific_journal-1767	118	76	�	�	PROPN
american_scientific_journal-1767	118	77	.	.	PUNCT
american_scientific_journal-1767	119	1	when	when	SCONJ
american_scientific_journal-1767	119	2	using	use	VERB
american_scientific_journal-1767	119	3	standard	standard	ADJ
american_scientific_journal-1767	119	4	boundary	boundary	ADJ
american_scientific_journal-1767	119	5	conditions	condition	NOUN
american_scientific_journal-1767	119	6	in	in	ADP
american_scientific_journal-1767	119	7	sashinka	sashinka	PROPN
american_scientific_journal-1767	119	8	wimaladharma	wimaladharma	PROPN
american_scientific_journal-1767	119	9	and	and	CCONJ
american_scientific_journal-1767	119	10	nalin	nalin	PROPN
american_scientific_journal-1767	119	11	de	de	PROPN
american_scientific_journal-1767	119	12	silva[1	silva[1	PROPN
american_scientific_journal-1767	119	13	]	]	PUNCT
american_scientific_journal-1767	119	14	,	,	PUNCT
american_scientific_journal-1767	119	15	the	the	DET
american_scientific_journal-1767	119	16	red	red	ADJ
american_scientific_journal-1767	119	17	shift	shift	NOUN
american_scientific_journal-1767	119	18	was	be	AUX
american_scientific_journal-1767	119	19	calculated	calculate	VERB
american_scientific_journal-1767	119	20	to	to	PART
american_scientific_journal-1767	119	21	be	be	AUX
american_scientific_journal-1767	119	22	1	1	NUM
american_scientific_journal-1767	119	23	+	+	CCONJ
american_scientific_journal-1767	119	24	𝑧𝑧	𝑧𝑧	X
american_scientific_journal-1767	119	25	=	=	PROPN
american_scientific_journal-1767	119	26	𝜃𝜃	𝜃𝜃	PROPN
american_scientific_journal-1767	119	27	�	�	PROPN
american_scientific_journal-1767	119	28	𝑟𝑟𝑒𝑒𝑙𝑙	𝑟𝑟𝑒𝑒𝑙𝑙	PROPN
american_scientific_journal-1767	119	29	�	�	PROPN
american_scientific_journal-1767	119	30	�	�	PROPN
american_scientific_journal-1767	119	31	𝜃𝜃	𝜃𝜃	PROPN
american_scientific_journal-1767	119	32	�	�	PROPN
american_scientific_journal-1767	119	33	𝑎𝑎𝑙𝑙	𝑎𝑎𝑙𝑙	PROPN
american_scientific_journal-1767	119	34	�	�	PROPN
american_scientific_journal-1767	119	35	−	−	VERB
american_scientific_journal-1767	119	36	𝑚𝑚	𝑚𝑚	ADP
american_scientific_journal-1767	119	37	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1767	119	38	�	�	PROPN
american_scientific_journal-1767	119	39	.	.	PUNCT
american_scientific_journal-1767	120	1	the	the	DET
american_scientific_journal-1767	120	2	red	red	ADJ
american_scientific_journal-1767	120	3	shifts	shift	NOUN
american_scientific_journal-1767	120	4	as	as	SCONJ
american_scientific_journal-1767	120	5	observed	observe	VERB
american_scientific_journal-1767	120	6	at	at	ADP
american_scientific_journal-1767	120	7	infinity	infinity	NOUN
american_scientific_journal-1767	120	8	are	be	AUX
american_scientific_journal-1767	120	9	all	all	ADV
american_scientific_journal-1767	120	10	equal	equal	ADJ
american_scientific_journal-1767	120	11	provided	provide	VERB
american_scientific_journal-1767	120	12	that	that	SCONJ
american_scientific_journal-1767	121	1	𝐴𝐴	𝐴𝐴	PROPN
american_scientific_journal-1767	121	2	=	=	PUNCT
american_scientific_journal-1767	121	3	−	−	PROPN
american_scientific_journal-1767	121	4	𝑎𝑎3𝜃𝜃′	𝑎𝑎3𝜃𝜃′	PROPN
american_scientific_journal-1767	121	5	�	�	PROPN
american_scientific_journal-1767	121	6	𝑎𝑎𝑙𝑙	𝑎𝑎𝑙𝑙	PROPN
american_scientific_journal-1767	121	7	�	�	PROPN
american_scientific_journal-1767	121	8	𝑚𝑚𝑙𝑙	𝑚𝑚𝑙𝑙	PROPN
american_scientific_journal-1767	121	9	�	�	PROPN
american_scientific_journal-1767	121	10	𝜃𝜃	𝜃𝜃	PROPN
american_scientific_journal-1767	121	11	�	�	PROPN
american_scientific_journal-1767	121	12	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1767	121	13	𝑙𝑙	𝑙𝑙	PRON
american_scientific_journal-1767	121	14	�	�	PROPN
american_scientific_journal-1767	121	15	−	−	ADP
american_scientific_journal-1767	121	16	𝑚𝑚	𝑚𝑚	ADP
american_scientific_journal-1767	121	17	𝑎𝑎	𝑎𝑎	ADJ
american_scientific_journal-1767	121	18	�	�	PROPN
american_scientific_journal-1767	121	19	.	.	PUNCT
american_scientific_journal-1767	122	1	going	go	VERB
american_scientific_journal-1767	122	2	by	by	ADP
american_scientific_journal-1767	122	3	the	the	DET
american_scientific_journal-1767	122	4	previous	previous	ADJ
american_scientific_journal-1767	122	5	results	result	NOUN
american_scientific_journal-1767	122	6	we	we	PRON
american_scientific_journal-1767	122	7	may	may	AUX
american_scientific_journal-1767	122	8	impose	impose	VERB
american_scientific_journal-1767	122	9	this	this	DET
american_scientific_journal-1767	122	10	condition	condition	NOUN
american_scientific_journal-1767	122	11	on	on	ADP
american_scientific_journal-1767	122	12	𝐴𝐴	𝐴𝐴	PROPN
american_scientific_journal-1767	122	13	so	so	SCONJ
american_scientific_journal-1767	122	14	that	that	SCONJ
american_scientific_journal-1767	122	15	the	the	DET
american_scientific_journal-1767	122	16	red	red	ADJ
american_scientific_journal-1767	122	17	shift	shift	NOUN
american_scientific_journal-1767	122	18	is	be	AUX
american_scientific_journal-1767	122	19	an	an	DET
american_scientific_journal-1767	122	20	invariant	invariant	NOUN
american_scientific_journal-1767	122	21	with	with	ADP
american_scientific_journal-1767	122	22	respect	respect	NOUN
american_scientific_journal-1767	122	23	to	to	ADP
american_scientific_journal-1767	122	24	change	change	NOUN
american_scientific_journal-1767	122	25	of	of	ADP
american_scientific_journal-1767	122	26	coordinates	coordinate	NOUN
american_scientific_journal-1767	122	27	.	.	PUNCT
american_scientific_journal-1767	123	1	4	4	X
american_scientific_journal-1767	123	2	.	.	X
american_scientific_journal-1767	123	3	conclusion	conclusion	NOUN
american_scientific_journal-1767	123	4	a	a	DET
american_scientific_journal-1767	123	5	static	static	ADJ
american_scientific_journal-1767	123	6	spherically	spherically	NOUN
american_scientific_journal-1767	123	7	symmetric	symmetric	ADJ
american_scientific_journal-1767	123	8	solution	solution	NOUN
american_scientific_journal-1767	123	9	to	to	ADP
american_scientific_journal-1767	123	10	einstein	einstein	PROPN
american_scientific_journal-1767	123	11	-	-	PUNCT
american_scientific_journal-1767	123	12	maxwell	maxwell	PROPN
american_scientific_journal-1767	123	13	field	field	NOUN
american_scientific_journal-1767	123	14	equations	equation	NOUN
american_scientific_journal-1767	123	15	for	for	ADP
american_scientific_journal-1767	123	16	a	a	DET
american_scientific_journal-1767	123	17	spherical	spherical	ADJ
american_scientific_journal-1767	123	18	distribution	distribution	NOUN
american_scientific_journal-1767	123	19	of	of	ADP
american_scientific_journal-1767	123	20	electrically	electrically	ADV
american_scientific_journal-1767	123	21	counterpoised	counterpoise	VERB
american_scientific_journal-1767	123	22	dust	dust	NOUN
american_scientific_journal-1767	123	23	distribution	distribution	NOUN
american_scientific_journal-1767	123	24	has	have	AUX
american_scientific_journal-1767	123	25	been	be	AUX
american_scientific_journal-1767	123	26	found	find	VERB
american_scientific_journal-1767	123	27	using	use	VERB
american_scientific_journal-1767	123	28	a	a	DET
american_scientific_journal-1767	123	29	new	new	ADJ
american_scientific_journal-1767	123	30	set	set	NOUN
american_scientific_journal-1767	123	31	of	of	ADP
american_scientific_journal-1767	123	32	boundary	boundary	ADJ
american_scientific_journal-1767	123	33	conditions	condition	NOUN
american_scientific_journal-1767	123	34	with	with	ADP
american_scientific_journal-1767	123	35	the	the	DET
american_scientific_journal-1767	123	36	assumption	assumption	NOUN
american_scientific_journal-1767	123	37	that	that	SCONJ
american_scientific_journal-1767	123	38	the	the	DET
american_scientific_journal-1767	123	39	coordinates	coordinate	NOUN
american_scientific_journal-1767	123	40	in	in	ADP
american_scientific_journal-1767	123	41	inside	inside	ADP
american_scientific_journal-1767	123	42	and	and	CCONJ
american_scientific_journal-1767	123	43	outside	outside	ADP
american_scientific_journal-1767	123	44	of	of	ADP
american_scientific_journal-1767	123	45	the	the	DET
american_scientific_journal-1767	123	46	sphere	sphere	NOUN
american_scientific_journal-1767	123	47	are	be	AUX
american_scientific_journal-1767	123	48	different	different	ADJ
american_scientific_journal-1767	123	49	each	each	DET
american_scientific_journal-1767	123	50	other	other	ADJ
american_scientific_journal-1767	123	51	.	.	PUNCT
american_scientific_journal-1767	124	1	also	also	ADV
american_scientific_journal-1767	124	2	the	the	DET
american_scientific_journal-1767	124	3	new	new	ADJ
american_scientific_journal-1767	124	4	metric	metric	NOUN
american_scientific_journal-1767	124	5	is	be	AUX
american_scientific_journal-1767	124	6	lorentzian	lorentzian	ADJ
american_scientific_journal-1767	124	7	everywhere	everywhere	ADV
american_scientific_journal-1767	124	8	.	.	PUNCT
american_scientific_journal-1767	125	1	it	it	PRON
american_scientific_journal-1767	125	2	is	be	AUX
american_scientific_journal-1767	125	3	also	also	ADV
american_scientific_journal-1767	125	4	found	find	VERB
american_scientific_journal-1767	125	5	that	that	SCONJ
american_scientific_journal-1767	125	6	the	the	DET
american_scientific_journal-1767	125	7	mass	mass	NOUN
american_scientific_journal-1767	125	8	𝑚𝑚	𝑚𝑚	ADP
american_scientific_journal-1767	125	9	,	,	PUNCT
american_scientific_journal-1767	125	10	radial	radial	ADJ
american_scientific_journal-1767	125	11	coordinate	coordinate	NOUN
american_scientific_journal-1767	125	12	just	just	ADV
american_scientific_journal-1767	125	13	inside	inside	ADP
american_scientific_journal-1767	125	14	the	the	DET
american_scientific_journal-1767	125	15	boundary	boundary	ADJ
american_scientific_journal-1767	125	16	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1767	125	17	and	and	CCONJ
american_scientific_journal-1767	125	18	radial	radial	ADJ
american_scientific_journal-1767	125	19	coordinate	coordinate	NOUN
american_scientific_journal-1767	125	20	just	just	ADV
american_scientific_journal-1767	125	21	outside	outside	ADV
american_scientific_journal-1767	125	22	of	of	ADP
american_scientific_journal-1767	125	23	the	the	DET
american_scientific_journal-1767	125	24	boundary	boundary	ADJ
american_scientific_journal-1767	125	25	𝐴𝐴	𝐴𝐴	PROPN
american_scientific_journal-1767	125	26	have	have	VERB
american_scientific_journal-1767	125	27	maximum	maximum	ADJ
american_scientific_journal-1767	125	28	values	value	NOUN
american_scientific_journal-1767	125	29	.	.	PUNCT
american_scientific_journal-1767	126	1	therefore	therefore	ADV
american_scientific_journal-1767	126	2	einstein	einstein	PROPN
american_scientific_journal-1767	126	3	’s	’s	PART
american_scientific_journal-1767	126	4	equations	equation	NOUN
american_scientific_journal-1767	126	5	have	have	AUX
american_scientific_journal-1767	126	6	been	be	AUX
american_scientific_journal-1767	126	7	solved	solve	VERB
american_scientific_journal-1767	126	8	for	for	ADP
american_scientific_journal-1767	126	9	finite	finite	ADJ
american_scientific_journal-1767	126	10	distribution	distribution	NOUN
american_scientific_journal-1767	126	11	of	of	ADP
american_scientific_journal-1767	126	12	matter	matter	NOUN
american_scientific_journal-1767	126	13	.	.	PUNCT
american_scientific_journal-1767	127	1	imposing	impose	VERB
american_scientific_journal-1767	127	2	the	the	DET
american_scientific_journal-1767	127	3	condition	condition	NOUN
american_scientific_journal-1767	127	4	𝐴𝐴	𝐴𝐴	PROPN
american_scientific_journal-1767	127	5	=	=	SYM
american_scientific_journal-1767	127	6	−	−	PROPN
american_scientific_journal-1767	127	7	𝑎𝑎3𝜃𝜃′	𝑎𝑎3𝜃𝜃′	PROPN
american_scientific_journal-1767	127	8	�	�	PROPN
american_scientific_journal-1767	127	9	𝑎𝑎𝑙𝑙	𝑎𝑎𝑙𝑙	PROPN
american_scientific_journal-1767	127	10	�	�	PROPN
american_scientific_journal-1767	127	11	𝑚𝑚𝑙𝑙	𝑚𝑚𝑙𝑙	PROPN
american_scientific_journal-1767	127	12	�	�	PROPN
american_scientific_journal-1767	127	13	𝜃𝜃	𝜃𝜃	PROPN
american_scientific_journal-1767	127	14	�	�	PROPN
american_scientific_journal-1767	127	15	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1767	127	16	𝑙𝑙	𝑙𝑙	PRON
american_scientific_journal-1767	127	17	�	�	PROPN
american_scientific_journal-1767	127	18	−	−	ADP
american_scientific_journal-1767	127	19	𝑚𝑚	𝑚𝑚	ADP
american_scientific_journal-1767	127	20	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-1767	127	21	�	�	PROPN
american_scientific_journal-1767	127	22	on	on	ADP
american_scientific_journal-1767	127	23	𝐴𝐴	𝐴𝐴	PROPN
american_scientific_journal-1767	127	24	,	,	PUNCT
american_scientific_journal-1767	127	25	it	it	PRON
american_scientific_journal-1767	127	26	can	can	AUX
american_scientific_journal-1767	127	27	be	be	AUX
american_scientific_journal-1767	127	28	shown	show	VERB
american_scientific_journal-1767	127	29	that	that	SCONJ
american_scientific_journal-1767	127	30	the	the	DET
american_scientific_journal-1767	127	31	red	red	ADJ
american_scientific_journal-1767	127	32	shift	shift	NOUN
american_scientific_journal-1767	127	33	is	be	AUX
american_scientific_journal-1767	127	34	an	an	DET
american_scientific_journal-1767	127	35	invariant	invariant	NOUN
american_scientific_journal-1767	127	36	with	with	ADP
american_scientific_journal-1767	127	37	respect	respect	NOUN
american_scientific_journal-1767	127	38	to	to	ADP
american_scientific_journal-1767	127	39	change	change	NOUN
american_scientific_journal-1767	127	40	of	of	ADP
american_scientific_journal-1767	127	41	coordinates	coordinate	NOUN
american_scientific_journal-1767	127	42	.	.	PUNCT
american_scientific_journal-1767	128	1	acknowledgement	acknowledgement	NOUN
american_scientific_journal-1767	128	2	i	i	PRON
american_scientific_journal-1767	128	3	express	express	VERB
american_scientific_journal-1767	128	4	my	my	PRON
american_scientific_journal-1767	128	5	sincere	sincere	ADJ
american_scientific_journal-1767	128	6	thanks	thank	NOUN
american_scientific_journal-1767	128	7	and	and	CCONJ
american_scientific_journal-1767	128	8	profound	profound	ADJ
american_scientific_journal-1767	128	9	gratitude	gratitude	NOUN
american_scientific_journal-1767	128	10	to	to	ADP
american_scientific_journal-1767	128	11	my	my	PRON
american_scientific_journal-1767	128	12	research	research	NOUN
american_scientific_journal-1767	128	13	supervisor	supervisor	NOUN
american_scientific_journal-1767	128	14	,	,	PUNCT
american_scientific_journal-1767	128	15	dr	dr	PROPN
american_scientific_journal-1767	128	16	.	.	PROPN
american_scientific_journal-1767	128	17	nalin	nalin	PROPN
american_scientific_journal-1767	128	18	de	de	PROPN
american_scientific_journal-1767	128	19	silva	silva	PROPN
american_scientific_journal-1767	128	20	for	for	ADP
american_scientific_journal-1767	128	21	his	his	PRON
american_scientific_journal-1767	128	22	invaluable	invaluable	ADJ
american_scientific_journal-1767	128	23	advice	advice	NOUN
american_scientific_journal-1767	128	24	,	,	PUNCT
american_scientific_journal-1767	128	25	guidance	guidance	NOUN
american_scientific_journal-1767	128	26	and	and	CCONJ
american_scientific_journal-1767	128	27	encouragement	encouragement	NOUN
american_scientific_journal-1767	128	28	throughout	throughout	ADP
american_scientific_journal-1767	128	29	the	the	DET
american_scientific_journal-1767	128	30	course	course	NOUN
american_scientific_journal-1767	128	31	of	of	ADP
american_scientific_journal-1767	128	32	this	this	DET
american_scientific_journal-1767	128	33	work	work	NOUN
american_scientific_journal-1767	128	34	.	.	PUNCT
american_scientific_journal-1767	129	1	american	american	ADJ
american_scientific_journal-1767	129	2	scientific	scientific	ADJ
american_scientific_journal-1767	129	3	research	research	PROPN
american_scientific_journal-1767	129	4	journal	journal	NOUN
american_scientific_journal-1767	129	5	for	for	ADP
american_scientific_journal-1767	129	6	engineering	engineering	NOUN
american_scientific_journal-1767	129	7	,	,	PUNCT
american_scientific_journal-1767	129	8	technology	technology	NOUN
american_scientific_journal-1767	129	9	,	,	PUNCT
american_scientific_journal-1767	129	10	and	and	CCONJ
american_scientific_journal-1767	129	11	sciences	science	NOUN
american_scientific_journal-1767	129	12	(	(	PUNCT
american_scientific_journal-1767	129	13	asrjets	asrjet	NOUN
american_scientific_journal-1767	129	14	)	)	PUNCT
american_scientific_journal-1767	129	15	(	(	PUNCT
american_scientific_journal-1767	129	16	2016	2016	NUM
american_scientific_journal-1767	129	17	)	)	PUNCT
american_scientific_journal-1767	129	18	volume	volume	NOUN
american_scientific_journal-1767	129	19	21	21	NUM
american_scientific_journal-1767	129	20	,	,	PUNCT
american_scientific_journal-1767	129	21	no	no	DET
american_scientific_journal-1767	129	22	1	1	NUM
american_scientific_journal-1767	129	23	,	,	PUNCT
american_scientific_journal-1767	129	24	pp	pp	ADV
american_scientific_journal-1767	129	25	163	163	NUM
american_scientific_journal-1767	129	26	-	-	SYM
american_scientific_journal-1767	129	27	177	177	NUM
american_scientific_journal-1767	129	28	177	177	NUM
american_scientific_journal-1767	129	29	references	reference	NOUN
american_scientific_journal-1767	129	30	[	[	X
american_scientific_journal-1767	129	31	1	1	NUM
american_scientific_journal-1767	129	32	]	]	PUNCT
american_scientific_journal-1767	129	33	sashinka	sashinka	PROPN
american_scientific_journal-1767	129	34	wimaladharma	wimaladharma	PROPN
american_scientific_journal-1767	129	35	and	and	CCONJ
american_scientific_journal-1767	129	36	nalin	nalin	PROPN
american_scientific_journal-1767	129	37	de	de	PROPN
american_scientific_journal-1767	129	38	silva	silva	PROPN
american_scientific_journal-1767	129	39	.	.	PUNCT
american_scientific_journal-1767	130	1	“	"	PUNCT
american_scientific_journal-1767	130	2	a	a	DET
american_scientific_journal-1767	130	3	static	static	ADJ
american_scientific_journal-1767	130	4	solution	solution	NOUN
american_scientific_journal-1767	130	5	to	to	ADP
american_scientific_journal-1767	130	6	einstein	einstein	PROPN
american_scientific_journal-1767	130	7	’s	’s	PART
american_scientific_journal-1767	130	8	field	field	NOUN
american_scientific_journal-1767	130	9	equations	equation	NOUN
american_scientific_journal-1767	130	10	for	for	ADP
american_scientific_journal-1767	130	11	a	a	DET
american_scientific_journal-1767	130	12	spherical	spherical	ADJ
american_scientific_journal-1767	130	13	distribution	distribution	NOUN
american_scientific_journal-1767	130	14	of	of	ADP
american_scientific_journal-1767	130	15	electrically	electrically	ADV
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american_scientific_journal-1767	130	17	dust”american	dust”american	PROPN
american_scientific_journal-1767	130	18	scientific	scientific	ADJ
american_scientific_journal-1767	130	19	research	research	NOUN
american_scientific_journal-1767	130	20	journal	journal	NOUN
american_scientific_journal-1767	130	21	for	for	ADP
american_scientific_journal-1767	130	22	engineering	engineering	NOUN
american_scientific_journal-1767	130	23	,	,	PUNCT
american_scientific_journal-1767	130	24	technology	technology	NOUN
american_scientific_journal-1767	130	25	(	(	PUNCT
american_scientific_journal-1767	130	26	asrjets	asrjet	NOUN
american_scientific_journal-1767	130	27	)	)	PUNCT
american_scientific_journal-1767	130	28	,	,	PUNCT
american_scientific_journal-1767	130	29	and	and	CCONJ
american_scientific_journal-1767	130	30	sciences	science	NOUN
american_scientific_journal-1767	130	31	,	,	PUNCT
american_scientific_journal-1767	130	32	volume	volume	NOUN
american_scientific_journal-1767	130	33	17,no1	17,no1	NUM
american_scientific_journal-1767	130	34	,	,	PUNCT
american_scientific_journal-1767	130	35	pp	pp	ADV
american_scientific_journal-1767	130	36	155	155	NUM
american_scientific_journal-1767	130	37	-	-	SYM
american_scientific_journal-1767	130	38	164,march,2016	164,march,2016	NUM
american_scientific_journal-1767	130	39	.	.	PUNCT
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american_scientific_journal-1767	131	2	2	2	X
american_scientific_journal-1767	131	3	]	]	PUNCT
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american_scientific_journal-1767	131	5	.	.	PUNCT
american_scientific_journal-1767	132	1	“	"	PUNCT
american_scientific_journal-1767	132	2	study	study	NOUN
american_scientific_journal-1767	132	3	of	of	ADP
american_scientific_journal-1767	132	4	the	the	DET
american_scientific_journal-1767	132	5	lane	lane	NOUN
american_scientific_journal-1767	132	6	emden	emden	ADJ
american_scientific_journal-1767	132	7	equation	equation	NOUN
american_scientific_journal-1767	132	8	and	and	CCONJ
american_scientific_journal-1767	132	9	some	some	PRON
american_scientific_journal-1767	132	10	of	of	ADP
american_scientific_journal-1767	132	11	the	the	DET
american_scientific_journal-1767	132	12	associated	associated	ADJ
american_scientific_journal-1767	132	13	equations	equation	NOUN
american_scientific_journal-1767	132	14	.	.	PUNCT
american_scientific_journal-1767	133	1	”mphil	”mphil	PROPN
american_scientific_journal-1767	133	2	theis	theis	PROPN
american_scientific_journal-1767	133	3	,	,	PUNCT
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american_scientific_journal-1767	133	5	of	of	ADP
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american_scientific_journal-1767	133	7	.	.	PUNCT
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american_scientific_journal-1767	134	2	3	3	X
american_scientific_journal-1767	134	3	]	]	X
american_scientific_journal-1767	134	4	k.w.p.b	k.w.p.b	PROPN
american_scientific_journal-1767	134	5	seneviratne	seneviratne	PROPN
american_scientific_journal-1767	134	6	,	,	PUNCT
american_scientific_journal-1767	134	7	and	and	CCONJ
american_scientific_journal-1767	134	8	nalin	nalin	PROPN
american_scientific_journal-1767	134	9	de	de	PROPN
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american_scientific_journal-1767	134	11	.	.	PUNCT
american_scientific_journal-1767	135	1	“	"	PUNCT
american_scientific_journal-1767	135	2	the	the	DET
american_scientific_journal-1767	135	3	schwarzschild	schwarzschild	NOUN
american_scientific_journal-1767	135	4	space	space	NOUN
american_scientific_journal-1767	135	5	-	-	PUNCT
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american_scientific_journal-1767	135	11	the	the	DET
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american_scientific_journal-1767	135	14	-	-	PUNCT
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american_scientific_journal-1767	135	17	-	-	PUNCT
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american_scientific_journal-1767	135	21	research	research	NOUN
american_scientific_journal-1767	135	22	symposium	symposium	NOUN
american_scientific_journal-1767	135	23	,	,	PUNCT
american_scientific_journal-1767	135	24	university	university	NOUN
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american_scientific_journal-1767	135	27	,	,	PUNCT
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american_scientific_journal-1767	135	30	.	.	PUNCT
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american_scientific_journal-1767	136	3	]	]	X
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american_scientific_journal-1767	136	6	.	.	PUNCT
american_scientific_journal-1767	137	1	“	"	PUNCT
american_scientific_journal-1767	137	2	on	on	ADP
american_scientific_journal-1767	137	3	static	static	ADJ
american_scientific_journal-1767	137	4	distribution	distribution	NOUN
american_scientific_journal-1767	137	5	of	of	ADP
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american_scientific_journal-1767	137	7	in	in	ADP
american_scientific_journal-1767	137	8	general	general	ADJ
american_scientific_journal-1767	137	9	relativity”.phd	relativity”.phd	CCONJ
american_scientific_journal-1767	137	10	thesis	thesis	NOUN
american_scientific_journal-1767	137	11	,	,	PUNCT
american_scientific_journal-1767	137	12	queen	queen	PROPN
american_scientific_journal-1767	137	13	elizabeth	elizabeth	PROPN
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american_scientific_journal-1767	137	17	.	.	PUNCT