id	sid	tid	token	lemma	pos
american_scientific_journal-4887	1	1	113	113	NUM
american_scientific_journal-4887	1	2	american	american	ADJ
american_scientific_journal-4887	1	3	scientific	scientific	ADJ
american_scientific_journal-4887	1	4	research	research	NOUN
american_scientific_journal-4887	1	5	journal	journal	NOUN
american_scientific_journal-4887	1	6	for	for	ADP
american_scientific_journal-4887	1	7	engineering	engineering	NOUN
american_scientific_journal-4887	1	8	,	,	PUNCT
american_scientific_journal-4887	1	9	technology	technology	NOUN
american_scientific_journal-4887	1	10	,	,	PUNCT
american_scientific_journal-4887	1	11	and	and	CCONJ
american_scientific_journal-4887	1	12	sciences	science	NOUN
american_scientific_journal-4887	1	13	(	(	PUNCT
american_scientific_journal-4887	1	14	asrjets	asrjet	NOUN
american_scientific_journal-4887	1	15	)	)	PUNCT
american_scientific_journal-4887	1	16	issn	issn	PROPN
american_scientific_journal-4887	1	17	(	(	PUNCT
american_scientific_journal-4887	1	18	print	print	NOUN
american_scientific_journal-4887	1	19	)	)	PUNCT
american_scientific_journal-4887	1	20	2313	2313	NUM
american_scientific_journal-4887	1	21	-	-	SYM
american_scientific_journal-4887	1	22	4410	4410	NUM
american_scientific_journal-4887	1	23	,	,	PUNCT
american_scientific_journal-4887	1	24	issn	issn	PROPN
american_scientific_journal-4887	1	25	(	(	PUNCT
american_scientific_journal-4887	1	26	online	online	ADJ
american_scientific_journal-4887	1	27	)	)	PUNCT
american_scientific_journal-4887	1	28	2313	2313	NUM
american_scientific_journal-4887	1	29	-	-	SYM
american_scientific_journal-4887	1	30	4402	4402	NUM
american_scientific_journal-4887	1	31	©	©	PROPN
american_scientific_journal-4887	1	32	global	global	ADJ
american_scientific_journal-4887	1	33	society	society	NOUN
american_scientific_journal-4887	1	34	of	of	ADP
american_scientific_journal-4887	1	35	scientific	scientific	ADJ
american_scientific_journal-4887	1	36	research	research	NOUN
american_scientific_journal-4887	1	37	and	and	CCONJ
american_scientific_journal-4887	1	38	researchers	researcher	NOUN
american_scientific_journal-4887	1	39	http://asrjetsjournal.org/	http://asrjetsjournal.org/	NOUN
american_scientific_journal-4887	1	40	alternative	alternative	ADJ
american_scientific_journal-4887	1	41	multiplying	multiply	VERB
american_scientific_journal-4887	1	42	triangular	triangular	NOUN
american_scientific_journal-4887	1	43	fuzzy	fuzzy	ADJ
american_scientific_journal-4887	1	44	number	number	NOUN
american_scientific_journal-4887	1	45	and	and	CCONJ
american_scientific_journal-4887	1	46	applied	apply	VERB
american_scientific_journal-4887	1	47	in	in	ADP
american_scientific_journal-4887	1	48	fully	fully	ADV
american_scientific_journal-4887	1	49	fuzzy	fuzzy	ADJ
american_scientific_journal-4887	1	50	linear	linear	ADJ
american_scientific_journal-4887	1	51	system	system	NOUN
american_scientific_journal-4887	1	52	zulya	zulya	NOUN
american_scientific_journal-4887	1	53	desmitaa	desmitaa	PROPN
american_scientific_journal-4887	1	54	*	*	PROPN
american_scientific_journal-4887	1	55	,	,	PUNCT
american_scientific_journal-4887	1	56	mashadib	mashadib	NOUN
american_scientific_journal-4887	1	57	adepartment	adepartment	NOUN
american_scientific_journal-4887	1	58	of	of	ADP
american_scientific_journal-4887	1	59	mathematics	mathematic	NOUN
american_scientific_journal-4887	1	60	,	,	PUNCT
american_scientific_journal-4887	1	61	university	university	NOUN
american_scientific_journal-4887	1	62	of	of	ADP
american_scientific_journal-4887	1	63	riau	riau	PROPN
american_scientific_journal-4887	1	64	,	,	PUNCT
american_scientific_journal-4887	1	65	pekanbaru	pekanbaru	NOUN
american_scientific_journal-4887	1	66	28293	28293	NUM
american_scientific_journal-4887	1	67	,	,	PUNCT
american_scientific_journal-4887	1	68	indonesia	indonesia	PROPN
american_scientific_journal-4887	1	69	bdepartment	bdepartment	NOUN
american_scientific_journal-4887	1	70	of	of	ADP
american_scientific_journal-4887	1	71	mathematics	mathematics	PROPN
american_scientific_journal-4887	1	72	,	,	PUNCT
american_scientific_journal-4887	1	73	university	university	NOUN
american_scientific_journal-4887	1	74	of	of	ADP
american_scientific_journal-4887	1	75	riau	riau	PROPN
american_scientific_journal-4887	1	76	,	,	PUNCT
american_scientific_journal-4887	1	77	pekanbaru	pekanbaru	NOUN
american_scientific_journal-4887	1	78	28293	28293	NUM
american_scientific_journal-4887	1	79	,	,	PUNCT
american_scientific_journal-4887	1	80	indonesia	indonesia	PROPN
american_scientific_journal-4887	1	81	aemail	aemail	NOUN
american_scientific_journal-4887	1	82	:	:	PUNCT
american_scientific_journal-4887	1	83	zulya.desmita7317@grad.unri.ac.id	zulya.desmita7317@grad.unri.ac.id	NUM
american_scientific_journal-4887	1	84	bemail	bemail	NOUN
american_scientific_journal-4887	1	85	:	:	PUNCT
american_scientific_journal-4887	1	86	mash-math@unri.ac.id	mash-math@unri.ac.id	NOUN
american_scientific_journal-4887	1	87	abstract	abstract	ADV
american_scientific_journal-4887	1	88	in	in	ADP
american_scientific_journal-4887	1	89	this	this	DET
american_scientific_journal-4887	1	90	paper	paper	NOUN
american_scientific_journal-4887	1	91	,	,	PUNCT
american_scientific_journal-4887	1	92	a	a	DET
american_scientific_journal-4887	1	93	new	new	ADJ
american_scientific_journal-4887	1	94	concept	concept	NOUN
american_scientific_journal-4887	1	95	of	of	ADP
american_scientific_journal-4887	1	96	arithmetic	arithmetic	ADJ
american_scientific_journal-4887	1	97	fuzzy	fuzzy	ADJ
american_scientific_journal-4887	1	98	number	number	NOUN
american_scientific_journal-4887	1	99	will	will	AUX
american_scientific_journal-4887	1	100	be	be	AUX
american_scientific_journal-4887	1	101	introduced	introduce	VERB
american_scientific_journal-4887	1	102	using	use	VERB
american_scientific_journal-4887	1	103	the	the	DET
american_scientific_journal-4887	1	104	broad	broad	ADJ
american_scientific_journal-4887	1	105	area	area	NOUN
american_scientific_journal-4887	1	106	concept	concept	NOUN
american_scientific_journal-4887	1	107	triangular	triangular	NOUN
american_scientific_journal-4887	1	108	fuzzy	fuzzy	ADJ
american_scientific_journal-4887	1	109	number	number	NOUN
american_scientific_journal-4887	1	110	so	so	SCONJ
american_scientific_journal-4887	1	111	that	that	SCONJ
american_scientific_journal-4887	1	112	we	we	PRON
american_scientific_journal-4887	1	113	will	will	AUX
american_scientific_journal-4887	1	114	get	get	VERB
american_scientific_journal-4887	1	115	the	the	DET
american_scientific_journal-4887	1	116	form	form	NOUN
american_scientific_journal-4887	1	117	of	of	ADP
american_scientific_journal-4887	1	118	multiplying	multiply	VERB
american_scientific_journal-4887	1	119	fuzzy	fuzzy	ADJ
american_scientific_journal-4887	1	120	number	number	NOUN
american_scientific_journal-4887	1	121	in	in	ADP
american_scientific_journal-4887	1	122	some	some	DET
american_scientific_journal-4887	1	123	cases	case	NOUN
american_scientific_journal-4887	1	124	.	.	PUNCT
american_scientific_journal-4887	2	1	new	new	ADJ
american_scientific_journal-4887	2	2	arithmetic	arithmetic	ADJ
american_scientific_journal-4887	2	3	concept	concept	NOUN
american_scientific_journal-4887	2	4	fuzzy	fuzzy	ADJ
american_scientific_journal-4887	2	5	number	number	NOUN
american_scientific_journal-4887	2	6	will	will	AUX
american_scientific_journal-4887	2	7	be	be	AUX
american_scientific_journal-4887	2	8	applied	apply	VERB
american_scientific_journal-4887	2	9	to	to	PART
american_scientific_journal-4887	2	10	solve	solve	VERB
american_scientific_journal-4887	2	11	the	the	DET
american_scientific_journal-4887	2	12	fully	fully	ADV
american_scientific_journal-4887	2	13	fuzzy	fuzzy	ADJ
american_scientific_journal-4887	2	14	linear	linear	ADJ
american_scientific_journal-4887	2	15	system	system	NOUN
american_scientific_journal-4887	2	16	using	use	VERB
american_scientific_journal-4887	2	17	gauss	gauss	PROPN
american_scientific_journal-4887	2	18	seidel	seidel	PROPN
american_scientific_journal-4887	2	19	method	method	NOUN
american_scientific_journal-4887	2	20	and	and	CCONJ
american_scientific_journal-4887	2	21	the	the	DET
american_scientific_journal-4887	2	22	solution	solution	NOUN
american_scientific_journal-4887	2	23	obtained	obtain	VERB
american_scientific_journal-4887	2	24	is	be	AUX
american_scientific_journal-4887	2	25	a	a	DET
american_scientific_journal-4887	2	26	single	single	ADJ
american_scientific_journal-4887	2	27	solution	solution	NOUN
american_scientific_journal-4887	2	28	.	.	PUNCT
american_scientific_journal-4887	3	1	keywords	keyword	NOUN
american_scientific_journal-4887	3	2	:	:	PUNCT
american_scientific_journal-4887	3	3	arithmetic	arithmetic	ADJ
american_scientific_journal-4887	3	4	fuzzy	fuzzy	ADJ
american_scientific_journal-4887	3	5	number	number	NOUN
american_scientific_journal-4887	3	6	,	,	PUNCT
american_scientific_journal-4887	3	7	fully	fully	ADV
american_scientific_journal-4887	3	8	fuzzy	fuzzy	ADJ
american_scientific_journal-4887	3	9	linear	linear	ADJ
american_scientific_journal-4887	3	10	system	system	NOUN
american_scientific_journal-4887	3	11	,	,	PUNCT
american_scientific_journal-4887	3	12	triangular	triangular	VERB
american_scientific_journal-4887	3	13	fuzzy	fuzzy	ADJ
american_scientific_journal-4887	3	14	number	number	NOUN
american_scientific_journal-4887	3	15	.	.	PUNCT
american_scientific_journal-4887	4	1	2010	2010	NUM
american_scientific_journal-4887	4	2	mathematics	mathematic	NOUN
american_scientific_journal-4887	4	3	subject	subject	ADJ
american_scientific_journal-4887	4	4	classification	classification	NOUN
american_scientific_journal-4887	4	5	:	:	PUNCT
american_scientific_journal-4887	4	6	94d05	94d05	NUM
american_scientific_journal-4887	4	7	,	,	PUNCT
american_scientific_journal-4887	4	8	08a72	08a72	NUM
american_scientific_journal-4887	4	9	,	,	PUNCT
american_scientific_journal-4887	4	10	15b15	15b15	NUM
american_scientific_journal-4887	4	11	1	1	NUM
american_scientific_journal-4887	4	12	.	.	PUNCT
american_scientific_journal-4887	5	1	introduction	introduction	NOUN
american_scientific_journal-4887	5	2	system	system	NOUN
american_scientific_journal-4887	5	3	linear	linear	NOUN
american_scientific_journal-4887	5	4	is	be	AUX
american_scientific_journal-4887	5	5	one	one	NUM
american_scientific_journal-4887	5	6	part	part	NOUN
american_scientific_journal-4887	5	7	of	of	ADP
american_scientific_journal-4887	5	8	linear	linear	PROPN
american_scientific_journal-4887	5	9	algebra	algebra	NOUN
american_scientific_journal-4887	5	10	which	which	PRON
american_scientific_journal-4887	5	11	is	be	AUX
american_scientific_journal-4887	5	12	studied	study	VERB
american_scientific_journal-4887	5	13	in	in	ADP
american_scientific_journal-4887	5	14	mathematics	mathematic	NOUN
american_scientific_journal-4887	5	15	.	.	PUNCT
american_scientific_journal-4887	6	1	the	the	DET
american_scientific_journal-4887	6	2	form	form	NOUN
american_scientific_journal-4887	6	3	of	of	ADP
american_scientific_journal-4887	6	4	the	the	DET
american_scientific_journal-4887	6	5	matrix	matrix	NOUN
american_scientific_journal-4887	6	6	equation	equation	NOUN
american_scientific_journal-4887	6	7	the	the	DET
american_scientific_journal-4887	6	8	system	system	NOUN
american_scientific_journal-4887	6	9	linear	linear	NOUN
american_scientific_journal-4887	6	10	is	be	AUX
american_scientific_journal-4887	6	11	𝑨𝑨𝑨𝑨	𝑨𝑨𝑨𝑨	PROPN
american_scientific_journal-4887	6	12	=	=	SYM
american_scientific_journal-4887	6	13	𝒃𝒃	𝒃𝒃	ADJ
american_scientific_journal-4887	6	14	with	with	ADP
american_scientific_journal-4887	6	15	all	all	DET
american_scientific_journal-4887	6	16	entries	entry	NOUN
american_scientific_journal-4887	6	17	real	real	ADJ
american_scientific_journal-4887	6	18	number	number	NOUN
american_scientific_journal-4887	6	19	.	.	PUNCT
american_scientific_journal-4887	7	1	along	along	ADP
american_scientific_journal-4887	7	2	with	with	ADP
american_scientific_journal-4887	7	3	the	the	DET
american_scientific_journal-4887	7	4	development	development	NOUN
american_scientific_journal-4887	7	5	of	of	ADP
american_scientific_journal-4887	7	6	mathematics	mathematic	NOUN
american_scientific_journal-4887	7	7	,	,	PUNCT
american_scientific_journal-4887	7	8	the	the	DET
american_scientific_journal-4887	7	9	system	system	NOUN
american_scientific_journal-4887	7	10	linear	linear	NOUN
american_scientific_journal-4887	7	11	is	be	AUX
american_scientific_journal-4887	7	12	not	not	PART
american_scientific_journal-4887	7	13	only	only	ADV
american_scientific_journal-4887	7	14	used	use	VERB
american_scientific_journal-4887	7	15	in	in	ADP
american_scientific_journal-4887	7	16	real	real	ADJ
american_scientific_journal-4887	7	17	number	number	NOUN
american_scientific_journal-4887	7	18	,	,	PUNCT
american_scientific_journal-4887	7	19	but	but	CCONJ
american_scientific_journal-4887	7	20	variable	variable	ADJ
american_scientific_journal-4887	7	21	and	and	CCONJ
american_scientific_journal-4887	7	22	constant	constant	ADJ
american_scientific_journal-4887	7	23	in	in	ADP
american_scientific_journal-4887	7	24	system	system	NOUN
american_scientific_journal-4887	7	25	linear	linear	NOUN
american_scientific_journal-4887	7	26	can	can	AUX
american_scientific_journal-4887	7	27	be	be	AUX
american_scientific_journal-4887	7	28	fuzzy	fuzzy	ADJ
american_scientific_journal-4887	7	29	number	number	NOUN
american_scientific_journal-4887	7	30	.	.	PUNCT
american_scientific_journal-4887	8	1	fuzzy	fuzzy	ADJ
american_scientific_journal-4887	8	2	in	in	ADP
american_scientific_journal-4887	8	3	introduced	introduce	VERB
american_scientific_journal-4887	8	4	by	by	ADP
american_scientific_journal-4887	8	5	lothfi	lothfi	PROPN
american_scientific_journal-4887	8	6	a.zadeh	a.zadeh	PROPN
american_scientific_journal-4887	8	7	(	(	PUNCT
american_scientific_journal-4887	8	8	1965	1965	NUM
american_scientific_journal-4887	8	9	)	)	PUNCT
american_scientific_journal-4887	8	10	.	.	PUNCT
american_scientific_journal-4887	9	1	the	the	DET
american_scientific_journal-4887	9	2	system	system	NOUN
american_scientific_journal-4887	9	3	linear	linear	NOUN
american_scientific_journal-4887	9	4	using	use	VERB
american_scientific_journal-4887	9	5	fuzzy	fuzzy	ADJ
american_scientific_journal-4887	9	6	number	number	NOUN
american_scientific_journal-4887	9	7	consists	consist	VERB
american_scientific_journal-4887	9	8	of	of	ADP
american_scientific_journal-4887	9	9	the	the	DET
american_scientific_journal-4887	9	10	fuzzy	fuzzy	ADJ
american_scientific_journal-4887	9	11	linear	linear	ADJ
american_scientific_journal-4887	9	12	system	system	NOUN
american_scientific_journal-4887	9	13	of	of	ADP
american_scientific_journal-4887	9	14	equation	equation	NOUN
american_scientific_journal-4887	9	15	,	,	PUNCT
american_scientific_journal-4887	9	16	the	the	DET
american_scientific_journal-4887	9	17	fully	fully	ADV
american_scientific_journal-4887	9	18	fuzzy	fuzzy	ADJ
american_scientific_journal-4887	9	19	linear	linear	ADJ
american_scientific_journal-4887	9	20	system	system	NOUN
american_scientific_journal-4887	9	21	of	of	ADP
american_scientific_journal-4887	9	22	equation	equation	NOUN
american_scientific_journal-4887	9	23	[	[	X
american_scientific_journal-4887	9	24	1	1	NUM
american_scientific_journal-4887	9	25	,	,	PUNCT
american_scientific_journal-4887	9	26	2	2	NUM
american_scientific_journal-4887	9	27	and	and	CCONJ
american_scientific_journal-4887	9	28	3	3	NUM
american_scientific_journal-4887	9	29	]	]	PUNCT
american_scientific_journal-4887	9	30	,	,	PUNCT
american_scientific_journal-4887	9	31	and	and	CCONJ
american_scientific_journal-4887	9	32	the	the	DET
american_scientific_journal-4887	9	33	dual	dual	ADJ
american_scientific_journal-4887	9	34	fully	fully	ADV
american_scientific_journal-4887	9	35	fuzzy	fuzzy	ADJ
american_scientific_journal-4887	9	36	linear	linear	ADJ
american_scientific_journal-4887	9	37	system	system	NOUN
american_scientific_journal-4887	9	38	of	of	ADP
american_scientific_journal-4887	9	39	equation	equation	NOUN
american_scientific_journal-4887	9	40	[	[	X
american_scientific_journal-4887	9	41	4	4	NUM
american_scientific_journal-4887	9	42	,	,	PUNCT
american_scientific_journal-4887	9	43	5	5	NUM
american_scientific_journal-4887	9	44	,	,	PUNCT
american_scientific_journal-4887	9	45	6	6	NUM
american_scientific_journal-4887	9	46	,	,	PUNCT
american_scientific_journal-4887	9	47	and	and	CCONJ
american_scientific_journal-4887	9	48	7	7	NUM
american_scientific_journal-4887	9	49	]	]	PUNCT
american_scientific_journal-4887	9	50	.	.	PUNCT
american_scientific_journal-4887	10	1	many	many	ADJ
american_scientific_journal-4887	10	2	methods	method	NOUN
american_scientific_journal-4887	10	3	are	be	AUX
american_scientific_journal-4887	10	4	to	to	PART
american_scientific_journal-4887	10	5	solve	solve	VERB
american_scientific_journal-4887	10	6	the	the	DET
american_scientific_journal-4887	10	7	fully	fully	ADV
american_scientific_journal-4887	10	8	fuzzy	fuzzy	ADJ
american_scientific_journal-4887	10	9	linear	linear	ADJ
american_scientific_journal-4887	10	10	system	system	NOUN
american_scientific_journal-4887	10	11	of	of	ADP
american_scientific_journal-4887	10	12	equation	equation	NOUN
american_scientific_journal-4887	10	13	that	that	PRON
american_scientific_journal-4887	10	14	has	have	AUX
american_scientific_journal-4887	10	15	been	be	AUX
american_scientific_journal-4887	10	16	discussed	discuss	VERB
american_scientific_journal-4887	10	17	,	,	PUNCT
american_scientific_journal-4887	10	18	using	use	VERB
american_scientific_journal-4887	10	19	the	the	DET
american_scientific_journal-4887	10	20	decomposition	decomposition	NOUN
american_scientific_journal-4887	10	21	[	[	X
american_scientific_journal-4887	10	22	8	8	NUM
american_scientific_journal-4887	10	23	,	,	PUNCT
american_scientific_journal-4887	10	24	9	9	NUM
american_scientific_journal-4887	10	25	,	,	PUNCT
american_scientific_journal-4887	10	26	and	and	CCONJ
american_scientific_journal-4887	10	27	10	10	NUM
american_scientific_journal-4887	10	28	]	]	PUNCT
american_scientific_journal-4887	10	29	,	,	PUNCT
american_scientific_journal-4887	10	30	using	use	VERB
american_scientific_journal-4887	10	31	the	the	DET
american_scientific_journal-4887	10	32	direct	direct	ADJ
american_scientific_journal-4887	10	33	method	method	NOUN
american_scientific_journal-4887	10	34	and	and	CCONJ
american_scientific_journal-4887	10	35	iteration	iteration	NOUN
american_scientific_journal-4887	10	36	method	method	NOUN
american_scientific_journal-4887	10	37	[	[	X
american_scientific_journal-4887	10	38	11	11	NUM
american_scientific_journal-4887	10	39	,	,	PUNCT
american_scientific_journal-4887	10	40	12	12	NUM
american_scientific_journal-4887	10	41	,	,	PUNCT
american_scientific_journal-4887	10	42	and	and	CCONJ
american_scientific_journal-4887	10	43	13	13	NUM
american_scientific_journal-4887	10	44	]	]	PUNCT
american_scientific_journal-4887	10	45	,	,	PUNCT
american_scientific_journal-4887	10	46	huang	huang	PROPN
american_scientific_journal-4887	10	47	’s	’s	PART
american_scientific_journal-4887	10	48	method	method	NOUN
american_scientific_journal-4887	10	49	[	[	X
american_scientific_journal-4887	10	50	14	14	NUM
american_scientific_journal-4887	10	51	]	]	PUNCT
american_scientific_journal-4887	10	52	,	,	PUNCT
american_scientific_journal-4887	10	53	using	use	VERB
american_scientific_journal-4887	10	54	lu	lu	NOUN
american_scientific_journal-4887	10	55	factorization	factorization	NOUN
american_scientific_journal-4887	10	56	of	of	ADP
american_scientific_journal-4887	10	57	the	the	DET
american_scientific_journal-4887	10	58	coefficient	coefficient	NOUN
american_scientific_journal-4887	10	59	matrix	matrix	NOUN
american_scientific_journal-4887	10	60	[	[	X
american_scientific_journal-4887	10	61	4	4	NUM
american_scientific_journal-4887	10	62	and	and	CCONJ
american_scientific_journal-4887	10	63	6	6	NUM
american_scientific_journal-4887	10	64	]	]	PUNCT
american_scientific_journal-4887	10	65	,	,	PUNCT
american_scientific_journal-4887	10	66	and	and	CCONJ
american_scientific_journal-4887	10	67	using	use	VERB
american_scientific_journal-4887	10	68	cramers	cramer	NOUN
american_scientific_journal-4887	10	69	rules	rule	NOUN
american_scientific_journal-4887	10	70	[	[	X
american_scientific_journal-4887	10	71	15	15	NUM
american_scientific_journal-4887	10	72	]	]	PUNCT
american_scientific_journal-4887	10	73	.	.	PUNCT
american_scientific_journal-4887	11	1	in	in	ADP
american_scientific_journal-4887	11	2	this	this	DET
american_scientific_journal-4887	11	3	paper	paper	NOUN
american_scientific_journal-4887	11	4	,	,	PUNCT
american_scientific_journal-4887	11	5	the	the	DET
american_scientific_journal-4887	11	6	system	system	NOUN
american_scientific_journal-4887	11	7	linear	linear	VERB
american_scientific_journal-4887	11	8	to	to	PART
american_scientific_journal-4887	11	9	be	be	AUX
american_scientific_journal-4887	11	10	discussed	discuss	VERB
american_scientific_journal-4887	11	11	is	be	AUX
american_scientific_journal-4887	11	12	the	the	DET
american_scientific_journal-4887	11	13	fully	fully	ADV
american_scientific_journal-4887	11	14	fuzzy	fuzzy	ADJ
american_scientific_journal-4887	11	15	linear	linear	ADJ
american_scientific_journal-4887	11	16	system	system	NOUN
american_scientific_journal-4887	11	17	of	of	ADP
american_scientific_journal-4887	11	18	equation	equation	NOUN
american_scientific_journal-4887	11	19	.	.	PUNCT
american_scientific_journal-4887	12	1	dehghan	dehghan	PROPN
american_scientific_journal-4887	12	2	and	and	CCONJ
american_scientific_journal-4887	12	3	hashemi	hashemi	NOUN
american_scientific_journal-4887	12	4	(	(	PUNCT
american_scientific_journal-4887	12	5	2006	2006	NUM
american_scientific_journal-4887	12	6	)	)	PUNCT
american_scientific_journal-4887	13	1	[	[	X
american_scientific_journal-4887	13	2	8	8	X
american_scientific_journal-4887	13	3	]	]	PUNCT
american_scientific_journal-4887	13	4	the	the	DET
american_scientific_journal-4887	13	5	fully	fully	ADV
american_scientific_journal-4887	13	6	fuzzy	fuzzy	ADJ
american_scientific_journal-4887	13	7	linear	linear	ADJ
american_scientific_journal-4887	13	8	system	system	NOUN
american_scientific_journal-4887	13	9	of	of	ADP
american_scientific_journal-4887	13	10	equation	equation	NOUN
american_scientific_journal-4887	13	11	is	be	AUX
american_scientific_journal-4887	13	12	a	a	DET
american_scientific_journal-4887	13	13	system	system	NOUN
american_scientific_journal-4887	13	14	linear	linear	ADJ
american_scientific_journal-4887	13	15	with	with	ADP
american_scientific_journal-4887	13	16	elements	element	NOUN
american_scientific_journal-4887	13	17	from	from	ADP
american_scientific_journal-4887	13	18	the	the	DET
american_scientific_journal-4887	13	19	matrix	matrix	NOUN
american_scientific_journal-4887	13	20	and	and	CCONJ
american_scientific_journal-4887	13	21	the	the	DET
american_scientific_journal-4887	13	22	vector	vector	NOUN
american_scientific_journal-4887	13	23	is	be	AUX
american_scientific_journal-4887	13	24	in	in	ADP
american_scientific_journal-4887	13	25	the	the	DET
american_scientific_journal-4887	13	26	-----------------------------------------------------------------------	-----------------------------------------------------------------------	PUNCT
american_scientific_journal-4887	13	27	*	*	PUNCT
american_scientific_journal-4887	13	28	corresponding	correspond	VERB
american_scientific_journal-4887	13	29	author	author	NOUN
american_scientific_journal-4887	13	30	.	.	PUNCT
american_scientific_journal-4887	14	1	e	e	X
american_scientific_journal-4887	14	2	-	-	NOUN
american_scientific_journal-4887	14	3	mail	mail	NOUN
american_scientific_journal-4887	14	4	address	address	NOUN
american_scientific_journal-4887	14	5	:	:	PUNCT
american_scientific_journal-4887	14	6	zulya.desmita7317@grad.unri.ac.id	zulya.desmita7317@grad.unri.ac.id	NUM
american_scientific_journal-4887	14	7	http://asrjetsjournal.org/	http://asrjetsjournal.org/	PROPN
american_scientific_journal-4887	14	8	mailto	mailto	NOUN
american_scientific_journal-4887	14	9	:	:	PUNCT
american_scientific_journal-4887	14	10	zulya.desmita7317@grad.unri.ac.id.m	zulya.desmita7317@grad.unri.ac.id.m	PROPN
american_scientific_journal-4887	14	11	american	american	PROPN
american_scientific_journal-4887	14	12	scientific	scientific	PROPN
american_scientific_journal-4887	14	13	research	research	PROPN
american_scientific_journal-4887	14	14	journal	journal	NOUN
american_scientific_journal-4887	14	15	for	for	ADP
american_scientific_journal-4887	14	16	engineering	engineering	NOUN
american_scientific_journal-4887	14	17	,	,	PUNCT
american_scientific_journal-4887	14	18	technology	technology	NOUN
american_scientific_journal-4887	14	19	,	,	PUNCT
american_scientific_journal-4887	14	20	and	and	CCONJ
american_scientific_journal-4887	14	21	sciences	science	NOUN
american_scientific_journal-4887	14	22	(	(	PUNCT
american_scientific_journal-4887	14	23	asrjets	asrjet	NOUN
american_scientific_journal-4887	14	24	)	)	PUNCT
american_scientific_journal-4887	14	25	(	(	PUNCT
american_scientific_journal-4887	14	26	2019	2019	NUM
american_scientific_journal-4887	14	27	)	)	PUNCT
american_scientific_journal-4887	14	28	volume	volume	NOUN
american_scientific_journal-4887	14	29	56	56	NUM
american_scientific_journal-4887	14	30	,	,	PUNCT
american_scientific_journal-4887	14	31	no	no	DET
american_scientific_journal-4887	14	32	1	1	NUM
american_scientific_journal-4887	14	33	,	,	PUNCT
american_scientific_journal-4887	14	34	pp	pp	ADV
american_scientific_journal-4887	14	35	113	113	NUM
american_scientific_journal-4887	14	36	-	-	SYM
american_scientific_journal-4887	14	37	123	123	NUM
american_scientific_journal-4887	14	38	114	114	NUM
american_scientific_journal-4887	14	39	form	form	NOUN
american_scientific_journal-4887	14	40	fuzzy	fuzzy	ADJ
american_scientific_journal-4887	14	41	number	number	NOUN
american_scientific_journal-4887	14	42	.	.	PUNCT
american_scientific_journal-4887	15	1	the	the	DET
american_scientific_journal-4887	15	2	fully	fully	ADV
american_scientific_journal-4887	15	3	fuzzy	fuzzy	ADJ
american_scientific_journal-4887	15	4	linear	linear	ADJ
american_scientific_journal-4887	15	5	system	system	NOUN
american_scientific_journal-4887	15	6	of	of	ADP
american_scientific_journal-4887	15	7	equation	equation	NOUN
american_scientific_journal-4887	15	8	𝑨𝑨	𝑨𝑨	PROPN
american_scientific_journal-4887	15	9	�	�	PROPN
american_scientific_journal-4887	15	10	⊗	⊗	ADJ
american_scientific_journal-4887	15	11	𝑨𝑨	𝑨𝑨	PROPN
american_scientific_journal-4887	15	12	�	�	PROPN
american_scientific_journal-4887	15	13	=	=	PUNCT
american_scientific_journal-4887	15	14	𝒃𝒃	𝒃𝒃	ADP
american_scientific_journal-4887	15	15	�	�	PROPN
american_scientific_journal-4887	15	16	where	where	SCONJ
american_scientific_journal-4887	15	17	𝑨𝑨	𝑨𝑨	PROPN
american_scientific_journal-4887	15	18	�	�	PROPN
american_scientific_journal-4887	15	19	is	be	AUX
american_scientific_journal-4887	15	20	matrix	matrix	NOUN
american_scientific_journal-4887	15	21	with	with	ADP
american_scientific_journal-4887	15	22	fuzzy	fuzzy	ADJ
american_scientific_journal-4887	15	23	number	number	NOUN
american_scientific_journal-4887	15	24	,	,	PUNCT
american_scientific_journal-4887	15	25	𝑨𝑨	𝑨𝑨	PROPN
american_scientific_journal-4887	15	26	�	�	PROPN
american_scientific_journal-4887	15	27	and	and	CCONJ
american_scientific_journal-4887	15	28	𝒃𝒃	𝒃𝒃	ADP
american_scientific_journal-4887	15	29	�	�	PROPN
american_scientific_journal-4887	15	30	are	be	AUX
american_scientific_journal-4887	15	31	vector	vector	NOUN
american_scientific_journal-4887	15	32	with	with	ADP
american_scientific_journal-4887	15	33	fuzzy	fuzzy	ADJ
american_scientific_journal-4887	15	34	number	number	NOUN
american_scientific_journal-4887	15	35	.	.	PUNCT
american_scientific_journal-4887	16	1	in	in	ADP
american_scientific_journal-4887	16	2	this	this	DET
american_scientific_journal-4887	16	3	paper	paper	NOUN
american_scientific_journal-4887	16	4	,	,	PUNCT
american_scientific_journal-4887	16	5	new	new	ADJ
american_scientific_journal-4887	16	6	definition	definition	NOUN
american_scientific_journal-4887	16	7	of	of	ADP
american_scientific_journal-4887	16	8	positive	positive	ADJ
american_scientific_journal-4887	16	9	fuzzy	fuzzy	ADJ
american_scientific_journal-4887	16	10	number	number	NOUN
american_scientific_journal-4887	16	11	and	and	CCONJ
american_scientific_journal-4887	16	12	negative	negative	ADJ
american_scientific_journal-4887	16	13	fuzzy	fuzzy	ADJ
american_scientific_journal-4887	16	14	number	number	NOUN
american_scientific_journal-4887	16	15	will	will	AUX
american_scientific_journal-4887	16	16	be	be	AUX
american_scientific_journal-4887	16	17	given	give	VERB
american_scientific_journal-4887	16	18	in	in	ADP
american_scientific_journal-4887	16	19	some	some	DET
american_scientific_journal-4887	16	20	cases	case	NOUN
american_scientific_journal-4887	16	21	using	use	VERB
american_scientific_journal-4887	16	22	broad	broad	ADJ
american_scientific_journal-4887	16	23	comparison	comparison	NOUN
american_scientific_journal-4887	16	24	,	,	PUNCT
american_scientific_journal-4887	16	25	then	then	ADV
american_scientific_journal-4887	16	26	by	by	ADP
american_scientific_journal-4887	16	27	defining	define	VERB
american_scientific_journal-4887	16	28	new	new	ADJ
american_scientific_journal-4887	16	29	fuzzy	fuzzy	ADJ
american_scientific_journal-4887	16	30	number	number	NOUN
american_scientific_journal-4887	16	31	,	,	PUNCT
american_scientific_journal-4887	16	32	algebra	algebra	NOUN
american_scientific_journal-4887	16	33	will	will	AUX
american_scientific_journal-4887	16	34	be	be	AUX
american_scientific_journal-4887	16	35	constructed	construct	VERB
american_scientific_journal-4887	16	36	from	from	ADP
american_scientific_journal-4887	16	37	fuzzy	fuzzy	ADJ
american_scientific_journal-4887	16	38	number	number	NOUN
american_scientific_journal-4887	16	39	in	in	ADP
american_scientific_journal-4887	16	40	fully	fully	ADV
american_scientific_journal-4887	16	41	fuzzy	fuzzy	ADJ
american_scientific_journal-4887	16	42	linear	linear	ADJ
american_scientific_journal-4887	16	43	system	system	NOUN
american_scientific_journal-4887	16	44	of	of	ADP
american_scientific_journal-4887	16	45	equation	equation	NOUN
american_scientific_journal-4887	16	46	.	.	PUNCT
american_scientific_journal-4887	17	1	fuzzy	fuzzy	ADJ
american_scientific_journal-4887	17	2	number	number	NOUN
american_scientific_journal-4887	17	3	to	to	PART
american_scientific_journal-4887	17	4	be	be	AUX
american_scientific_journal-4887	17	5	used	use	VERB
american_scientific_journal-4887	17	6	in	in	ADP
american_scientific_journal-4887	17	7	this	this	DET
american_scientific_journal-4887	17	8	paper	paper	NOUN
american_scientific_journal-4887	17	9	is	be	AUX
american_scientific_journal-4887	17	10	triangular	triangular	VERB
american_scientific_journal-4887	17	11	fuzzy	fuzzy	ADJ
american_scientific_journal-4887	17	12	number	number	NOUN
american_scientific_journal-4887	17	13	and	and	CCONJ
american_scientific_journal-4887	17	14	to	to	PART
american_scientific_journal-4887	17	15	solve	solve	VERB
american_scientific_journal-4887	17	16	the	the	DET
american_scientific_journal-4887	17	17	fully	fully	ADV
american_scientific_journal-4887	17	18	fuzzy	fuzzy	ADJ
american_scientific_journal-4887	17	19	linear	linear	ADJ
american_scientific_journal-4887	17	20	system	system	NOUN
american_scientific_journal-4887	17	21	of	of	ADP
american_scientific_journal-4887	17	22	equation	equation	NOUN
american_scientific_journal-4887	17	23	using	use	VERB
american_scientific_journal-4887	17	24	the	the	DET
american_scientific_journal-4887	17	25	gauss	gauss	PROPN
american_scientific_journal-4887	17	26	seidel	seidel	PROPN
american_scientific_journal-4887	17	27	method	method	NOUN
american_scientific_journal-4887	17	28	.	.	PUNCT
american_scientific_journal-4887	18	1	2	2	X
american_scientific_journal-4887	18	2	.	.	X
american_scientific_journal-4887	18	3	the	the	DET
american_scientific_journal-4887	18	4	basic	basic	ADJ
american_scientific_journal-4887	18	5	definition	definition	NOUN
american_scientific_journal-4887	18	6	some	some	PRON
american_scientific_journal-4887	18	7	of	of	ADP
american_scientific_journal-4887	18	8	the	the	DET
american_scientific_journal-4887	18	9	basic	basic	ADJ
american_scientific_journal-4887	18	10	definitions	definition	NOUN
american_scientific_journal-4887	18	11	of	of	ADP
american_scientific_journal-4887	18	12	fuzzy	fuzzy	ADJ
american_scientific_journal-4887	18	13	number	number	NOUN
american_scientific_journal-4887	18	14	have	have	AUX
american_scientific_journal-4887	18	15	been	be	AUX
american_scientific_journal-4887	18	16	in	in	ADP
american_scientific_journal-4887	18	17	ming	ming	PROPN
american_scientific_journal-4887	18	18	ma	ma	PROPN
american_scientific_journal-4887	18	19	(	(	PUNCT
american_scientific_journal-4887	18	20	2000	2000	NUM
american_scientific_journal-4887	18	21	)	)	PUNCT
american_scientific_journal-4887	19	1	[	[	X
american_scientific_journal-4887	19	2	16	16	NUM
american_scientific_journal-4887	19	3	]	]	PUNCT
american_scientific_journal-4887	19	4	.	.	PUNCT
american_scientific_journal-4887	20	1	definition	definition	NOUN
american_scientific_journal-4887	20	2	2.1	2.1	NUM
american_scientific_journal-4887	20	3	a	a	DET
american_scientific_journal-4887	20	4	fuzzy	fuzzy	ADJ
american_scientific_journal-4887	20	5	number	number	NOUN
american_scientific_journal-4887	20	6	is	be	AUX
american_scientific_journal-4887	20	7	a	a	DET
american_scientific_journal-4887	20	8	fuzzy	fuzzy	ADJ
american_scientific_journal-4887	20	9	set	set	VERB
american_scientific_journal-4887	20	10	𝑎𝑎	𝑎𝑎	PROPN
american_scientific_journal-4887	20	11	�	�	PROPN
american_scientific_journal-4887	20	12	:𝑅𝑅	:𝑅𝑅	PUNCT
american_scientific_journal-4887	20	13	→	→	SYM
american_scientific_journal-4887	20	14	[	[	X
american_scientific_journal-4887	20	15	0,1	0,1	NUM
american_scientific_journal-4887	20	16	]	]	PUNCT
american_scientific_journal-4887	20	17	which	which	PRON
american_scientific_journal-4887	20	18	satisfies	satisfy	VERB
american_scientific_journal-4887	20	19	:	:	PUNCT
american_scientific_journal-4887	20	20	1	1	X
american_scientific_journal-4887	20	21	.	.	X
american_scientific_journal-4887	20	22	𝑎𝑎	𝑎𝑎	PROPN
american_scientific_journal-4887	20	23	�	�	PROPN
american_scientific_journal-4887	20	24	is	be	AUX
american_scientific_journal-4887	20	25	upper	upper	ADJ
american_scientific_journal-4887	20	26	semicontinuous	semicontinuous	NOUN
american_scientific_journal-4887	20	27	;	;	PUNCT
american_scientific_journal-4887	20	28	2	2	X
american_scientific_journal-4887	20	29	.	.	X
american_scientific_journal-4887	20	30	𝑎𝑎	𝑎𝑎	PROPN
american_scientific_journal-4887	20	31	�	�	PROPN
american_scientific_journal-4887	20	32	(𝑥𝑥	(𝑥𝑥	PUNCT
american_scientific_journal-4887	20	33	)	)	PUNCT
american_scientific_journal-4887	21	1	=	=	SYM
american_scientific_journal-4887	21	2	0	0	NUM
american_scientific_journal-4887	21	3	outside	outside	ADP
american_scientific_journal-4887	21	4	some	some	DET
american_scientific_journal-4887	21	5	interval	interval	NOUN
american_scientific_journal-4887	22	1	[	[	X
american_scientific_journal-4887	22	2	0,1	0,1	NOUN
american_scientific_journal-4887	22	3	]	]	PUNCT
american_scientific_journal-4887	22	4	;	;	PUNCT
american_scientific_journal-4887	22	5	3	3	X
american_scientific_journal-4887	22	6	.	.	X
american_scientific_journal-4887	22	7	there	there	PRON
american_scientific_journal-4887	22	8	are	be	VERB
american_scientific_journal-4887	22	9	real	real	ADJ
american_scientific_journal-4887	22	10	numbers	number	NOUN
american_scientific_journal-4887	22	11	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-4887	22	12	,	,	PUNCT
american_scientific_journal-4887	22	13	𝑏𝑏	𝑏𝑏	NOUN
american_scientific_journal-4887	22	14	in	in	ADP
american_scientific_journal-4887	22	15	[	[	X
american_scientific_journal-4887	22	16	𝑐𝑐,𝑑𝑑	𝑐𝑐,𝑑𝑑	X
american_scientific_journal-4887	22	17	]	]	PUNCT
american_scientific_journal-4887	22	18	for	for	ADP
american_scientific_journal-4887	22	19	which	which	PRON
american_scientific_journal-4887	22	20	,	,	PUNCT
american_scientific_journal-4887	22	21	(	(	PUNCT
american_scientific_journal-4887	22	22	i	i	NOUN
american_scientific_journal-4887	22	23	)	)	PUNCT
american_scientific_journal-4887	22	24	𝑎𝑎	𝑎𝑎	PROPN
american_scientific_journal-4887	22	25	�	�	PROPN
american_scientific_journal-4887	22	26	(𝑥𝑥	(𝑥𝑥	PUNCT
american_scientific_journal-4887	22	27	)	)	PUNCT
american_scientific_journal-4887	22	28	is	be	AUX
american_scientific_journal-4887	22	29	monotonic	monotonic	ADV
american_scientific_journal-4887	22	30	increasing	increase	VERB
american_scientific_journal-4887	22	31	on	on	ADP
american_scientific_journal-4887	22	32	[	[	X
american_scientific_journal-4887	22	33	𝑐𝑐	𝑐𝑐	INTJ
american_scientific_journal-4887	22	34	,	,	PUNCT
american_scientific_journal-4887	22	35	𝑎𝑎	𝑎𝑎	VERB
american_scientific_journal-4887	22	36	]	]	PUNCT
american_scientific_journal-4887	22	37	;	;	PUNCT
american_scientific_journal-4887	22	38	(	(	PUNCT
american_scientific_journal-4887	22	39	ii	ii	NOUN
american_scientific_journal-4887	22	40	)	)	PUNCT
american_scientific_journal-4887	22	41	𝑎𝑎	𝑎𝑎	PROPN
american_scientific_journal-4887	22	42	�	�	PROPN
american_scientific_journal-4887	22	43	(𝑥𝑥	(𝑥𝑥	PUNCT
american_scientific_journal-4887	22	44	)	)	PUNCT
american_scientific_journal-4887	22	45	is	be	AUX
american_scientific_journal-4887	22	46	monotonic	monotonic	ADJ
american_scientific_journal-4887	22	47	decreasing	decrease	VERB
american_scientific_journal-4887	22	48	on	on	ADP
american_scientific_journal-4887	22	49	[	[	X
american_scientific_journal-4887	22	50	𝑏𝑏,𝑑𝑑	𝑏𝑏,𝑑𝑑	NOUN
american_scientific_journal-4887	22	51	]	]	X
american_scientific_journal-4887	22	52	;	;	PUNCT
american_scientific_journal-4887	22	53	(	(	PUNCT
american_scientific_journal-4887	22	54	iii	iii	NOUN
american_scientific_journal-4887	22	55	)	)	PUNCT
american_scientific_journal-4887	22	56	𝑎𝑎	𝑎𝑎	PROPN
american_scientific_journal-4887	22	57	�	�	PROPN
american_scientific_journal-4887	22	58	(𝑥𝑥	(𝑥𝑥	PUNCT
american_scientific_journal-4887	22	59	)	)	PUNCT
american_scientific_journal-4887	22	60	=	=	SYM
american_scientific_journal-4887	22	61	1	1	NUM
american_scientific_journal-4887	22	62	,	,	PUNCT
american_scientific_journal-4887	22	63	for	for	ADP
american_scientific_journal-4887	22	64	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-4887	22	65	≤	≤	NOUN
american_scientific_journal-4887	22	66	𝑥𝑥	𝑥𝑥	ADP
american_scientific_journal-4887	22	67	≤	≤	NUM
american_scientific_journal-4887	22	68	𝑏𝑏.	𝑏𝑏.	NOUN
american_scientific_journal-4887	22	69	an	an	DET
american_scientific_journal-4887	22	70	equivalent	equivalent	ADJ
american_scientific_journal-4887	22	71	parametric	parametric	ADJ
american_scientific_journal-4887	22	72	definition	definition	NOUN
american_scientific_journal-4887	22	73	is	be	AUX
american_scientific_journal-4887	22	74	given	give	VERB
american_scientific_journal-4887	22	75	in	in	ADP
american_scientific_journal-4887	22	76	friedman	friedman	PROPN
american_scientific_journal-4887	22	77	(	(	PUNCT
american_scientific_journal-4887	22	78	1998	1998	NUM
american_scientific_journal-4887	22	79	)	)	PUNCT
american_scientific_journal-4887	23	1	[	[	X
american_scientific_journal-4887	23	2	17	17	NUM
american_scientific_journal-4887	23	3	]	]	PUNCT
american_scientific_journal-4887	23	4	.	.	PUNCT
american_scientific_journal-4887	24	1	definition	definition	NOUN
american_scientific_journal-4887	24	2	2.2	2.2	NUM
american_scientific_journal-4887	24	3	a	a	DET
american_scientific_journal-4887	24	4	fuzzy	fuzzy	ADJ
american_scientific_journal-4887	24	5	number	number	NOUN
american_scientific_journal-4887	24	6	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-4887	24	7	�	�	PROPN
american_scientific_journal-4887	24	8	is	be	AUX
american_scientific_journal-4887	24	9	a	a	DET
american_scientific_journal-4887	24	10	pair	pair	NOUN
american_scientific_journal-4887	24	11	(	(	PUNCT
american_scientific_journal-4887	24	12	𝑎𝑎(𝑟𝑟	𝑎𝑎(𝑟𝑟	PROPN
american_scientific_journal-4887	24	13	)	)	PUNCT
american_scientific_journal-4887	24	14	,	,	PUNCT
american_scientific_journal-4887	24	15	𝑎𝑎(𝑟𝑟	𝑎𝑎(𝑟𝑟	PROPN
american_scientific_journal-4887	24	16	)	)	PUNCT
american_scientific_journal-4887	24	17	)	)	PUNCT
american_scientific_journal-4887	24	18	of	of	ADP
american_scientific_journal-4887	24	19	functions	function	NOUN
american_scientific_journal-4887	24	20	𝑎𝑎(𝑟𝑟	𝑎𝑎(𝑟𝑟	PROPN
american_scientific_journal-4887	24	21	)	)	PUNCT
american_scientific_journal-4887	24	22	,	,	PUNCT
american_scientific_journal-4887	24	23	𝑎𝑎(𝑟𝑟	𝑎𝑎(𝑟𝑟	PROPN
american_scientific_journal-4887	24	24	)	)	PUNCT
american_scientific_journal-4887	24	25	;	;	PUNCT
american_scientific_journal-4887	24	26	0	0	NUM
american_scientific_journal-4887	24	27	≤	≤	NUM
american_scientific_journal-4887	24	28	𝑟𝑟	𝑟𝑟	ADP
american_scientific_journal-4887	24	29	≤	≤	NUM
american_scientific_journal-4887	24	30	1	1	NUM
american_scientific_journal-4887	24	31	which	which	PRON
american_scientific_journal-4887	24	32	satisfy	satisfy	VERB
american_scientific_journal-4887	24	33	the	the	DET
american_scientific_journal-4887	24	34	following	follow	VERB
american_scientific_journal-4887	24	35	requirements	requirement	NOUN
american_scientific_journal-4887	24	36	:	:	PUNCT
american_scientific_journal-4887	24	37	1	1	X
american_scientific_journal-4887	24	38	.	.	PUNCT
american_scientific_journal-4887	24	39	𝑎𝑎(𝑟𝑟	𝑎𝑎(𝑟𝑟	PROPN
american_scientific_journal-4887	24	40	)	)	PUNCT
american_scientific_journal-4887	24	41	is	be	AUX
american_scientific_journal-4887	24	42	a	a	DET
american_scientific_journal-4887	24	43	bounded	bound	VERB
american_scientific_journal-4887	24	44	left	leave	VERB
american_scientific_journal-4887	24	45	continuous	continuous	ADJ
american_scientific_journal-4887	24	46	nondecreasing	nondecreasing	ADJ
american_scientific_journal-4887	24	47	functions	function	NOUN
american_scientific_journal-4887	24	48	over	over	ADP
american_scientific_journal-4887	24	49	[	[	X
american_scientific_journal-4887	24	50	0,1	0,1	NUM
american_scientific_journal-4887	24	51	]	]	PUNCT
american_scientific_journal-4887	24	52	;	;	PUNCT
american_scientific_journal-4887	24	53	2	2	X
american_scientific_journal-4887	24	54	.	.	PUNCT
american_scientific_journal-4887	24	55	𝑎𝑎(𝑟𝑟	𝑎𝑎(𝑟𝑟	PROPN
american_scientific_journal-4887	24	56	)	)	PUNCT
american_scientific_journal-4887	24	57	is	be	AUX
american_scientific_journal-4887	24	58	a	a	DET
american_scientific_journal-4887	24	59	bounded	bound	VERB
american_scientific_journal-4887	24	60	left	leave	VERB
american_scientific_journal-4887	24	61	continuous	continuous	ADJ
american_scientific_journal-4887	24	62	nonincreasing	nonincreasing	NOUN
american_scientific_journal-4887	24	63	functions	function	NOUN
american_scientific_journal-4887	24	64	over	over	ADP
american_scientific_journal-4887	24	65	[	[	X
american_scientific_journal-4887	24	66	0,1	0,1	NUM
american_scientific_journal-4887	24	67	]	]	PUNCT
american_scientific_journal-4887	24	68	;	;	PUNCT
american_scientific_journal-4887	24	69	3	3	X
american_scientific_journal-4887	24	70	.	.	PUNCT
american_scientific_journal-4887	24	71	𝑎𝑎(𝑟𝑟	𝑎𝑎(𝑟𝑟	PROPN
american_scientific_journal-4887	24	72	)	)	PUNCT
american_scientific_journal-4887	24	73	≤	≤	NUM
american_scientific_journal-4887	24	74	𝑎𝑎(𝑟𝑟),0	𝑎𝑎(𝑟𝑟),0	ADP
american_scientific_journal-4887	24	75	≤	≤	NUM
american_scientific_journal-4887	24	76	𝑟𝑟	𝑟𝑟	ADP
american_scientific_journal-4887	24	77	≤	≤	NUM
american_scientific_journal-4887	24	78	1	1	NUM
american_scientific_journal-4887	24	79	.	.	X
american_scientific_journal-4887	24	80	3	3	X
american_scientific_journal-4887	24	81	.	.	X
american_scientific_journal-4887	24	82	triangular	triangular	NOUN
american_scientific_journal-4887	24	83	fuzzy	fuzzy	ADJ
american_scientific_journal-4887	24	84	number	number	NOUN
american_scientific_journal-4887	24	85	in	in	ADP
american_scientific_journal-4887	24	86	this	this	DET
american_scientific_journal-4887	24	87	section	section	NOUN
american_scientific_journal-4887	24	88	,	,	PUNCT
american_scientific_journal-4887	24	89	we	we	PRON
american_scientific_journal-4887	24	90	discuss	discuss	VERB
american_scientific_journal-4887	24	91	the	the	DET
american_scientific_journal-4887	24	92	concept	concept	NOUN
american_scientific_journal-4887	24	93	triangular	triangular	NOUN
american_scientific_journal-4887	24	94	fuzzy	fuzzy	ADJ
american_scientific_journal-4887	24	95	number	number	NOUN
american_scientific_journal-4887	24	96	,	,	PUNCT
american_scientific_journal-4887	24	97	new	new	ADJ
american_scientific_journal-4887	24	98	definitions	definition	NOUN
american_scientific_journal-4887	24	99	for	for	ADP
american_scientific_journal-4887	24	100	positive	positive	ADJ
american_scientific_journal-4887	24	101	triangular	triangular	NOUN
american_scientific_journal-4887	24	102	fuzzy	fuzzy	ADJ
american_scientific_journal-4887	24	103	number	number	NOUN
american_scientific_journal-4887	24	104	and	and	CCONJ
american_scientific_journal-4887	24	105	negative	negative	ADJ
american_scientific_journal-4887	24	106	triangular	triangular	NOUN
american_scientific_journal-4887	24	107	fuzzy	fuzzy	ADJ
american_scientific_journal-4887	24	108	number	number	NOUN
american_scientific_journal-4887	24	109	,	,	PUNCT
american_scientific_journal-4887	24	110	and	and	CCONJ
american_scientific_journal-4887	24	111	arithmetic	arithmetic	ADJ
american_scientific_journal-4887	24	112	algebraic	algebraic	ADJ
american_scientific_journal-4887	24	113	operations	operation	NOUN
american_scientific_journal-4887	24	114	consisting	consist	VERB
american_scientific_journal-4887	24	115	of	of	ADP
american_scientific_journal-4887	24	116	addition	addition	NOUN
american_scientific_journal-4887	24	117	,	,	PUNCT
american_scientific_journal-4887	24	118	subtraction	subtraction	NOUN
american_scientific_journal-4887	24	119	,	,	PUNCT
american_scientific_journal-4887	24	120	scalar	scalar	ADJ
american_scientific_journal-4887	24	121	product	product	NOUN
american_scientific_journal-4887	24	122	,	,	PUNCT
american_scientific_journal-4887	24	123	multiplication	multiplication	NOUN
american_scientific_journal-4887	24	124	of	of	ADP
american_scientific_journal-4887	24	125	two	two	NUM
american_scientific_journal-4887	24	126	fuzzy	fuzzy	ADJ
american_scientific_journal-4887	24	127	number	number	NOUN
american_scientific_journal-4887	24	128	and	and	CCONJ
american_scientific_journal-4887	24	129	inverse	inverse	ADJ
american_scientific_journal-4887	24	130	fuzzy	fuzzy	ADJ
american_scientific_journal-4887	24	131	number	number	NOUN
american_scientific_journal-4887	24	132	.	.	PUNCT
american_scientific_journal-4887	25	1	in	in	ADP
american_scientific_journal-4887	25	2	this	this	DET
american_scientific_journal-4887	25	3	paper	paper	NOUN
american_scientific_journal-4887	25	4	,	,	PUNCT
american_scientific_journal-4887	25	5	we	we	PRON
american_scientific_journal-4887	25	6	write	write	VERB
american_scientific_journal-4887	25	7	a	a	DET
american_scientific_journal-4887	25	8	fuzzy	fuzzy	ADJ
american_scientific_journal-4887	25	9	number	number	NOUN
american_scientific_journal-4887	25	10	in	in	ADP
american_scientific_journal-4887	25	11	the	the	DET
american_scientific_journal-4887	25	12	form	form	NOUN
american_scientific_journal-4887	25	13	of	of	ADP
american_scientific_journal-4887	25	14	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-4887	25	15	�	�	PROPN
american_scientific_journal-4887	25	16	=	=	SYM
american_scientific_journal-4887	25	17	(	(	PUNCT
american_scientific_journal-4887	25	18	𝑎𝑎,𝛼𝛼,𝛽𝛽	𝑎𝑎,𝛼𝛼,𝛽𝛽	PROPN
american_scientific_journal-4887	25	19	)	)	PUNCT
american_scientific_journal-4887	25	20	,	,	PUNCT
american_scientific_journal-4887	25	21	where	where	SCONJ
american_scientific_journal-4887	25	22	𝒂𝒂	𝒂𝒂	PROPN
american_scientific_journal-4887	25	23	is	be	AUX
american_scientific_journal-4887	25	24	the	the	DET
american_scientific_journal-4887	25	25	center	center	NOUN
american_scientific_journal-4887	25	26	,	,	PUNCT
american_scientific_journal-4887	25	27	𝜶𝜶	𝜶𝜶	X
american_scientific_journal-4887	25	28	is	be	AUX
american_scientific_journal-4887	25	29	the	the	DET
american_scientific_journal-4887	25	30	left	left	ADJ
american_scientific_journal-4887	25	31	width	width	NOUN
american_scientific_journal-4887	25	32	,	,	PUNCT
american_scientific_journal-4887	25	33	and	and	CCONJ
american_scientific_journal-4887	25	34	𝜷𝜷	𝜷𝜷	NOUN
american_scientific_journal-4887	25	35	is	be	AUX
american_scientific_journal-4887	25	36	the	the	DET
american_scientific_journal-4887	25	37	right	right	ADJ
american_scientific_journal-4887	25	38	width	width	NOUN
american_scientific_journal-4887	25	39	.	.	PUNCT
american_scientific_journal-4887	26	1	for	for	ADP
american_scientific_journal-4887	26	2	arbitrary	arbitrary	ADJ
american_scientific_journal-4887	26	3	fuzzy	fuzzy	ADJ
american_scientific_journal-4887	26	4	number	number	NOUN
american_scientific_journal-4887	26	5	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-4887	26	6	�	�	PROPN
american_scientific_journal-4887	26	7	=	=	SYM
american_scientific_journal-4887	26	8	(	(	PUNCT
american_scientific_journal-4887	26	9	𝑎𝑎,𝛼𝛼,𝛽𝛽	𝑎𝑎,𝛼𝛼,𝛽𝛽	PROPN
american_scientific_journal-4887	26	10	)	)	PUNCT
american_scientific_journal-4887	26	11	,	,	PUNCT
american_scientific_journal-4887	26	12	the	the	DET
american_scientific_journal-4887	26	13	membership	membership	NOUN
american_scientific_journal-4887	26	14	function	function	NOUN
american_scientific_journal-4887	26	15	is	be	AUX
american_scientific_journal-4887	26	16	of	of	ADP
american_scientific_journal-4887	26	17	the	the	DET
american_scientific_journal-4887	26	18	form	form	NOUN
american_scientific_journal-4887	26	19	:	:	PUNCT
american_scientific_journal-4887	26	20	𝜇𝜇𝑎𝑎	𝜇𝜇𝑎𝑎	PROPN
american_scientific_journal-4887	26	21	�	�	NOUN
american_scientific_journal-4887	26	22	(𝑥𝑥	(𝑥𝑥	PUNCT
american_scientific_journal-4887	26	23	)	)	PUNCT
american_scientific_journal-4887	27	1	=	=	SYM
american_scientific_journal-4887	28	1	⎩	⎩	NUM
american_scientific_journal-4887	28	2	⎪	⎪	NOUN
american_scientific_journal-4887	28	3	⎨	⎨	ADJ
american_scientific_journal-4887	28	4	⎪	⎪	NOUN
american_scientific_journal-4887	28	5	⎧1	⎧1	NOUN
american_scientific_journal-4887	28	6	−	−	NOUN
american_scientific_journal-4887	28	7	𝑎𝑎	𝑎𝑎	VERB
american_scientific_journal-4887	28	8	−	−	PROPN
american_scientific_journal-4887	28	9	𝑥𝑥	𝑥𝑥	ADP
american_scientific_journal-4887	28	10	𝛼𝛼	𝛼𝛼	PROPN
american_scientific_journal-4887	28	11	,	,	PUNCT
american_scientific_journal-4887	28	12	𝑎𝑎	𝑎𝑎	VERB
american_scientific_journal-4887	28	13	−	−	PROPN
american_scientific_journal-4887	28	14	𝛼𝛼	𝛼𝛼	ADP
american_scientific_journal-4887	28	15	≤	≤	NOUN
american_scientific_journal-4887	28	16	𝑥𝑥	𝑥𝑥	ADP
american_scientific_journal-4887	28	17	≤	≤	NUM
american_scientific_journal-4887	28	18	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-4887	28	19	,	,	PUNCT
american_scientific_journal-4887	28	20	1	1	NUM
american_scientific_journal-4887	28	21	−	−	NOUN
american_scientific_journal-4887	28	22	𝑥𝑥	𝑥𝑥	ADP
american_scientific_journal-4887	28	23	−	−	PROPN
american_scientific_journal-4887	28	24	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-4887	28	25	𝛽𝛽	𝛽𝛽	ADP
american_scientific_journal-4887	28	26	,	,	PUNCT
american_scientific_journal-4887	28	27	𝑎𝑎	𝑎𝑎	VERB
american_scientific_journal-4887	28	28	≤	≤	NOUN
american_scientific_journal-4887	28	29	𝑥𝑥	𝑥𝑥	ADP
american_scientific_journal-4887	28	30	≤	≤	NUM
american_scientific_journal-4887	28	31	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-4887	28	32	+	+	CCONJ
american_scientific_journal-4887	28	33	𝛽𝛽	𝛽𝛽	ADJ
american_scientific_journal-4887	28	34	,	,	PUNCT
american_scientific_journal-4887	28	35	0	0	NUM
american_scientific_journal-4887	28	36	,	,	PUNCT
american_scientific_journal-4887	28	37	𝑜𝑜𝑜𝑜ℎ𝑒𝑒𝑟𝑟𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒.	𝑜𝑜𝑜𝑜ℎ𝑒𝑒𝑟𝑟𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒.	NOUN
american_scientific_journal-4887	28	38	on	on	ADP
american_scientific_journal-4887	28	39	the	the	DET
american_scientific_journal-4887	28	40	other	other	ADJ
american_scientific_journal-4887	28	41	hand	hand	NOUN
american_scientific_journal-4887	28	42	,	,	PUNCT
american_scientific_journal-4887	28	43	a	a	DET
american_scientific_journal-4887	28	44	parametric	parametric	ADJ
american_scientific_journal-4887	28	45	fuzzy	fuzzy	ADJ
american_scientific_journal-4887	28	46	number	number	NOUN
american_scientific_journal-4887	28	47	𝑎𝑎	𝑎𝑎	PROPN
american_scientific_journal-4887	28	48	�	�	PROPN
american_scientific_journal-4887	28	49	=	=	SYM
american_scientific_journal-4887	28	50	�	�	PROPN
american_scientific_journal-4887	28	51	𝑎𝑎(𝑟𝑟	𝑎𝑎(𝑟𝑟	PROPN
american_scientific_journal-4887	28	52	)	)	PUNCT
american_scientific_journal-4887	28	53	,	,	PUNCT
american_scientific_journal-4887	28	54	𝑎𝑎(𝑟𝑟	𝑎𝑎(𝑟𝑟	PROPN
american_scientific_journal-4887	28	55	)	)	PUNCT
american_scientific_journal-4887	28	56	�	�	PROPN
american_scientific_journal-4887	28	57	can	can	AUX
american_scientific_journal-4887	28	58	be	be	AUX
american_scientific_journal-4887	28	59	represented	represent	VERB
american_scientific_journal-4887	28	60	as	as	ADP
american_scientific_journal-4887	28	61	:	:	PUNCT
american_scientific_journal-4887	28	62	𝑎𝑎(𝑟𝑟	𝑎𝑎(𝑟𝑟	PROPN
american_scientific_journal-4887	28	63	)	)	PUNCT
american_scientific_journal-4887	29	1	=	=	PUNCT
american_scientific_journal-4887	29	2	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-4887	29	3	−	−	PROPN
american_scientific_journal-4887	29	4	(	(	PUNCT
american_scientific_journal-4887	29	5	1	1	NUM
american_scientific_journal-4887	29	6	−	−	NOUN
american_scientific_journal-4887	29	7	𝑟𝑟)𝛼𝛼	𝑟𝑟)𝛼𝛼	PUNCT
american_scientific_journal-4887	29	8	and	and	CCONJ
american_scientific_journal-4887	29	9	𝑎𝑎(𝑟𝑟	𝑎𝑎(𝑟𝑟	PROPN
american_scientific_journal-4887	29	10	)	)	PUNCT
american_scientific_journal-4887	30	1	=	=	VERB
american_scientific_journal-4887	30	2	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-4887	30	3	+	+	CCONJ
american_scientific_journal-4887	30	4	(	(	PUNCT
american_scientific_journal-4887	30	5	1	1	NUM
american_scientific_journal-4887	30	6	−	−	PROPN
american_scientific_journal-4887	30	7	𝑟𝑟)𝛽𝛽	𝑟𝑟)𝛽𝛽	NUM
american_scientific_journal-4887	30	8	american	american	ADJ
american_scientific_journal-4887	30	9	scientific	scientific	ADJ
american_scientific_journal-4887	30	10	research	research	NOUN
american_scientific_journal-4887	30	11	journal	journal	NOUN
american_scientific_journal-4887	30	12	for	for	ADP
american_scientific_journal-4887	30	13	engineering	engineering	NOUN
american_scientific_journal-4887	30	14	,	,	PUNCT
american_scientific_journal-4887	30	15	technology	technology	NOUN
american_scientific_journal-4887	30	16	,	,	PUNCT
american_scientific_journal-4887	30	17	and	and	CCONJ
american_scientific_journal-4887	30	18	sciences	science	NOUN
american_scientific_journal-4887	30	19	(	(	PUNCT
american_scientific_journal-4887	30	20	asrjets	asrjet	NOUN
american_scientific_journal-4887	30	21	)	)	PUNCT
american_scientific_journal-4887	30	22	(	(	PUNCT
american_scientific_journal-4887	30	23	2019	2019	NUM
american_scientific_journal-4887	30	24	)	)	PUNCT
american_scientific_journal-4887	30	25	volume	volume	NOUN
american_scientific_journal-4887	30	26	56	56	NUM
american_scientific_journal-4887	30	27	,	,	PUNCT
american_scientific_journal-4887	30	28	no	no	DET
american_scientific_journal-4887	30	29	1	1	NUM
american_scientific_journal-4887	30	30	,	,	PUNCT
american_scientific_journal-4887	30	31	pp	pp	ADV
american_scientific_journal-4887	30	32	113	113	NUM
american_scientific_journal-4887	30	33	-	-	SYM
american_scientific_journal-4887	30	34	123	123	NUM
american_scientific_journal-4887	30	35	115	115	NUM
american_scientific_journal-4887	30	36	3.1	3.1	NUM
american_scientific_journal-4887	30	37	.	.	PUNCT
american_scientific_journal-4887	31	1	triangular	triangular	NOUN
american_scientific_journal-4887	31	2	fuzzy	fuzzy	ADJ
american_scientific_journal-4887	31	3	number	number	NOUN
american_scientific_journal-4887	31	4	positive	positive	ADJ
american_scientific_journal-4887	31	5	and	and	CCONJ
american_scientific_journal-4887	31	6	negative	negative	ADJ
american_scientific_journal-4887	31	7	triangular	triangular	NOUN
american_scientific_journal-4887	31	8	fuzzy	fuzzy	ADJ
american_scientific_journal-4887	31	9	number	number	NOUN
american_scientific_journal-4887	31	10	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-4887	31	11	�	�	PROPN
american_scientific_journal-4887	31	12	=	=	SYM
american_scientific_journal-4887	31	13	(	(	PUNCT
american_scientific_journal-4887	31	14	𝑎𝑎,𝛼𝛼,𝛽𝛽	𝑎𝑎,𝛼𝛼,𝛽𝛽	PROPN
american_scientific_journal-4887	31	15	)	)	PUNCT
american_scientific_journal-4887	31	16	is	be	AUX
american_scientific_journal-4887	31	17	said	say	VERB
american_scientific_journal-4887	31	18	to	to	PART
american_scientific_journal-4887	31	19	be	be	AUX
american_scientific_journal-4887	31	20	positive	positive	ADJ
american_scientific_journal-4887	31	21	or	or	CCONJ
american_scientific_journal-4887	31	22	negative	negative	ADJ
american_scientific_journal-4887	31	23	:	:	PUNCT
american_scientific_journal-4887	32	1	1	1	X
american_scientific_journal-4887	32	2	.	.	X
american_scientific_journal-4887	32	3	if	if	SCONJ
american_scientific_journal-4887	32	4	𝑎𝑎	𝑎𝑎	VERB
american_scientific_journal-4887	32	5	−	−	PROPN
american_scientific_journal-4887	32	6	𝛼𝛼	𝛼𝛼	ADP
american_scientific_journal-4887	32	7	≥	≥	NOUN
american_scientific_journal-4887	32	8	0	0	NUM
american_scientific_journal-4887	32	9	,	,	PUNCT
american_scientific_journal-4887	32	10	then	then	ADV
american_scientific_journal-4887	32	11	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-4887	32	12	�	�	PROPN
american_scientific_journal-4887	32	13	is	be	AUX
american_scientific_journal-4887	32	14	said	say	VERB
american_scientific_journal-4887	32	15	to	to	PART
american_scientific_journal-4887	32	16	be	be	AUX
american_scientific_journal-4887	32	17	positive	positive	ADJ
american_scientific_journal-4887	32	18	,	,	PUNCT
american_scientific_journal-4887	32	19	and	and	CCONJ
american_scientific_journal-4887	32	20	if	if	SCONJ
american_scientific_journal-4887	32	21	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-4887	32	22	+	+	CCONJ
american_scientific_journal-4887	32	23	𝛽𝛽	𝛽𝛽	ADP
american_scientific_journal-4887	32	24	≤	≤	NOUN
american_scientific_journal-4887	32	25	0	0	NUM
american_scientific_journal-4887	32	26	,	,	PUNCT
american_scientific_journal-4887	32	27	then	then	ADV
american_scientific_journal-4887	32	28	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-4887	32	29	�	�	PROPN
american_scientific_journal-4887	32	30	is	be	AUX
american_scientific_journal-4887	32	31	said	say	VERB
american_scientific_journal-4887	32	32	to	to	PART
american_scientific_journal-4887	32	33	be	be	AUX
american_scientific_journal-4887	32	34	negative	negative	ADJ
american_scientific_journal-4887	32	35	.	.	PUNCT
american_scientific_journal-4887	33	1	seen	see	VERB
american_scientific_journal-4887	33	2	in	in	ADP
american_scientific_journal-4887	33	3	figure	figure	NOUN
american_scientific_journal-4887	33	4	1	1	NUM
american_scientific_journal-4887	33	5	:	:	PUNCT
american_scientific_journal-4887	33	6	figure	figure	VERB
american_scientific_journal-4887	33	7	1	1	NUM
american_scientific_journal-4887	33	8	:	:	PUNCT
american_scientific_journal-4887	33	9	triangular	triangular	NOUN
american_scientific_journal-4887	33	10	fuzzy	fuzzy	ADJ
american_scientific_journal-4887	33	11	number	number	NOUN
american_scientific_journal-4887	33	12	potitif	potitif	NOUN
american_scientific_journal-4887	33	13	and	and	CCONJ
american_scientific_journal-4887	33	14	negative	negative	ADJ
american_scientific_journal-4887	33	15	2	2	NUM
american_scientific_journal-4887	33	16	.	.	PUNCT
american_scientific_journal-4887	34	1	if	if	SCONJ
american_scientific_journal-4887	34	2	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-4887	34	3	>	>	X
american_scientific_journal-4887	34	4	0	0	NUM
american_scientific_journal-4887	34	5	and	and	CCONJ
american_scientific_journal-4887	34	6	𝑎𝑎	𝑎𝑎	VERB
american_scientific_journal-4887	34	7	−	−	PROPN
american_scientific_journal-4887	34	8	𝛼𝛼	𝛼𝛼	ADP
american_scientific_journal-4887	34	9	<	<	X
american_scientific_journal-4887	34	10	0	0	NUM
american_scientific_journal-4887	34	11	.	.	PUNCT
american_scientific_journal-4887	34	12	seen	see	VERB
american_scientific_journal-4887	34	13	in	in	ADP
american_scientific_journal-4887	34	14	figure	figure	NOUN
american_scientific_journal-4887	34	15	2	2	NUM
american_scientific_journal-4887	34	16	:	:	PUNCT
american_scientific_journal-4887	34	17	figure	figure	NOUN
american_scientific_journal-4887	34	18	2	2	NUM
american_scientific_journal-4887	34	19	:	:	PUNCT
american_scientific_journal-4887	34	20	triangular	triangular	NOUN
american_scientific_journal-4887	34	21	fuzzy	fuzzy	ADJ
american_scientific_journal-4887	34	22	number	number	NOUN
american_scientific_journal-4887	34	23	𝑎𝑎	𝑎𝑎	VERB
american_scientific_journal-4887	34	24	>	>	SYM
american_scientific_journal-4887	34	25	0	0	NUM
american_scientific_journal-4887	34	26	𝑎𝑎	𝑎𝑎	PROPN
american_scientific_journal-4887	34	27	�	�	PROPN
american_scientific_journal-4887	34	28	=	=	SYM
american_scientific_journal-4887	34	29	(	(	PUNCT
american_scientific_journal-4887	34	30	𝑎𝑎,𝛼𝛼,𝛽𝛽	𝑎𝑎,𝛼𝛼,𝛽𝛽	PROPN
american_scientific_journal-4887	34	31	)	)	PUNCT
american_scientific_journal-4887	34	32	is	be	AUX
american_scientific_journal-4887	34	33	said	say	VERB
american_scientific_journal-4887	34	34	to	to	PART
american_scientific_journal-4887	34	35	be	be	AUX
american_scientific_journal-4887	34	36	positive	positive	ADJ
american_scientific_journal-4887	34	37	if	if	SCONJ
american_scientific_journal-4887	34	38	𝑃𝑃	𝑃𝑃	PROPN
american_scientific_journal-4887	34	39	>	>	X
american_scientific_journal-4887	34	40	𝑄𝑄	𝑄𝑄	PROPN
american_scientific_journal-4887	34	41	,	,	PUNCT
american_scientific_journal-4887	34	42	and	and	CCONJ
american_scientific_journal-4887	34	43	said	say	VERB
american_scientific_journal-4887	34	44	to	to	PART
american_scientific_journal-4887	34	45	be	be	AUX
american_scientific_journal-4887	34	46	negative	negative	ADJ
american_scientific_journal-4887	34	47	if	if	SCONJ
american_scientific_journal-4887	34	48	𝑃𝑃	𝑃𝑃	PROPN
american_scientific_journal-4887	34	49	<	<	X
american_scientific_journal-4887	34	50	𝑄𝑄	𝑄𝑄	PROPN
american_scientific_journal-4887	34	51	or	or	CCONJ
american_scientific_journal-4887	34	52	can	can	AUX
american_scientific_journal-4887	34	53	be	be	AUX
american_scientific_journal-4887	34	54	expressed	express	VERB
american_scientific_journal-4887	34	55	in	in	ADP
american_scientific_journal-4887	34	56	form	form	NOUN
american_scientific_journal-4887	34	57	𝑃𝑃	𝑃𝑃	ADV
american_scientific_journal-4887	34	58	=	=	PUNCT
american_scientific_journal-4887	34	59	𝛽𝛽	𝛽𝛽	ADP
american_scientific_journal-4887	34	60	2	2	NUM
american_scientific_journal-4887	34	61	+	+	CCONJ
american_scientific_journal-4887	34	62	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-4887	34	63	+	+	CCONJ
american_scientific_journal-4887	34	64	𝑎𝑎2	𝑎𝑎2	NOUN
american_scientific_journal-4887	34	65	2𝛽𝛽	2𝛽𝛽	NOUN
american_scientific_journal-4887	34	66	>	>	X
american_scientific_journal-4887	35	1	𝛼𝛼	𝛼𝛼	ADP
american_scientific_journal-4887	35	2	2	2	NUM
american_scientific_journal-4887	35	3	−	−	NOUN
american_scientific_journal-4887	35	4	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-4887	35	5	−	−	NOUN
american_scientific_journal-4887	35	6	𝑎𝑎2	𝑎𝑎2	NOUN
american_scientific_journal-4887	35	7	2𝛽𝛽	2𝛽𝛽	NOUN
american_scientific_journal-4887	36	1	=	=	PUNCT
american_scientific_journal-4887	36	2	𝑄𝑄	𝑄𝑄	NOUN
american_scientific_journal-4887	36	3	positive	positive	ADJ
american_scientific_journal-4887	36	4	,	,	PUNCT
american_scientific_journal-4887	36	5	and	and	CCONJ
american_scientific_journal-4887	36	6	𝑃𝑃	𝑃𝑃	ADV
american_scientific_journal-4887	36	7	=	=	PUNCT
american_scientific_journal-4887	36	8	𝛽𝛽	𝛽𝛽	ADP
american_scientific_journal-4887	36	9	2	2	NUM
american_scientific_journal-4887	36	10	+	+	CCONJ
american_scientific_journal-4887	36	11	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-4887	36	12	+	+	CCONJ
american_scientific_journal-4887	36	13	𝑎𝑎2	𝑎𝑎2	NOUN
american_scientific_journal-4887	36	14	2𝛽𝛽	2𝛽𝛽	NOUN
american_scientific_journal-4887	36	15	<	<	X
american_scientific_journal-4887	36	16	𝛼𝛼	𝛼𝛼	ADP
american_scientific_journal-4887	36	17	2	2	NUM
american_scientific_journal-4887	36	18	−	−	NOUN
american_scientific_journal-4887	36	19	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-4887	36	20	−	−	NOUN
american_scientific_journal-4887	36	21	𝑎𝑎2	𝑎𝑎2	NOUN
american_scientific_journal-4887	36	22	2𝛽𝛽	2𝛽𝛽	NOUN
american_scientific_journal-4887	37	1	=	=	SYM
american_scientific_journal-4887	37	2	𝑄𝑄	𝑄𝑄	NOUN
american_scientific_journal-4887	37	3	negative	negative	ADJ
american_scientific_journal-4887	37	4	.	.	PUNCT
american_scientific_journal-4887	38	1	3	3	X
american_scientific_journal-4887	38	2	.	.	X
american_scientific_journal-4887	38	3	if	if	SCONJ
american_scientific_journal-4887	38	4	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-4887	38	5	<	<	X
american_scientific_journal-4887	38	6	0	0	NUM
american_scientific_journal-4887	38	7	and	and	CCONJ
american_scientific_journal-4887	38	8	𝑎𝑎	𝑎𝑎	VERB
american_scientific_journal-4887	38	9	+	+	X
american_scientific_journal-4887	38	10	𝛽𝛽	𝛽𝛽	X
american_scientific_journal-4887	38	11	>	>	X
american_scientific_journal-4887	38	12	0	0	NUM
american_scientific_journal-4887	38	13	.	.	PUNCT
american_scientific_journal-4887	38	14	seen	see	VERB
american_scientific_journal-4887	38	15	in	in	ADP
american_scientific_journal-4887	38	16	figure	figure	NOUN
american_scientific_journal-4887	38	17	3	3	NUM
american_scientific_journal-4887	38	18	:	:	PUNCT
american_scientific_journal-4887	38	19	figure	figure	VERB
american_scientific_journal-4887	38	20	3	3	NUM
american_scientific_journal-4887	38	21	:	:	PUNCT
american_scientific_journal-4887	38	22	triangular	triangular	NOUN
american_scientific_journal-4887	38	23	fuzzy	fuzzy	ADJ
american_scientific_journal-4887	38	24	number	number	NOUN
american_scientific_journal-4887	38	25	𝑎𝑎	𝑎𝑎	VERB
american_scientific_journal-4887	38	26	<	<	X
american_scientific_journal-4887	38	27	0	0	NUM
american_scientific_journal-4887	38	28	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-4887	38	29	�	�	PROPN
american_scientific_journal-4887	38	30	=	=	SYM
american_scientific_journal-4887	38	31	(	(	PUNCT
american_scientific_journal-4887	38	32	𝑎𝑎,𝛼𝛼,𝛽𝛽	𝑎𝑎,𝛼𝛼,𝛽𝛽	PROPN
american_scientific_journal-4887	38	33	)	)	PUNCT
american_scientific_journal-4887	38	34	is	be	AUX
american_scientific_journal-4887	38	35	said	say	VERB
american_scientific_journal-4887	38	36	to	to	PART
american_scientific_journal-4887	38	37	be	be	AUX
american_scientific_journal-4887	38	38	positive	positive	ADJ
american_scientific_journal-4887	38	39	if	if	SCONJ
american_scientific_journal-4887	38	40	𝑃𝑃	𝑃𝑃	PROPN
american_scientific_journal-4887	38	41	>	>	X
american_scientific_journal-4887	38	42	𝑄𝑄	𝑄𝑄	PROPN
american_scientific_journal-4887	38	43	,	,	PUNCT
american_scientific_journal-4887	38	44	and	and	CCONJ
american_scientific_journal-4887	38	45	said	say	VERB
american_scientific_journal-4887	38	46	to	to	PART
american_scientific_journal-4887	38	47	be	be	AUX
american_scientific_journal-4887	38	48	negative	negative	ADJ
american_scientific_journal-4887	38	49	if	if	SCONJ
american_scientific_journal-4887	38	50	𝑃𝑃	𝑃𝑃	PROPN
american_scientific_journal-4887	38	51	<	<	X
american_scientific_journal-4887	38	52	𝑄𝑄	𝑄𝑄	PROPN
american_scientific_journal-4887	38	53	or	or	CCONJ
american_scientific_journal-4887	38	54	can	can	AUX
american_scientific_journal-4887	38	55	be	be	AUX
american_scientific_journal-4887	38	56	expressed	express	VERB
american_scientific_journal-4887	38	57	in	in	ADP
american_scientific_journal-4887	38	58	form	form	NOUN
american_scientific_journal-4887	38	59	𝑃𝑃	𝑃𝑃	ADV
american_scientific_journal-4887	38	60	=	=	PUNCT
american_scientific_journal-4887	38	61	𝛽𝛽	𝛽𝛽	ADP
american_scientific_journal-4887	38	62	2	2	NUM
american_scientific_journal-4887	38	63	+	+	CCONJ
american_scientific_journal-4887	38	64	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-4887	38	65	−	−	PROPN
american_scientific_journal-4887	39	1	𝑎𝑎2	𝑎𝑎2	INTJ
american_scientific_journal-4887	39	2	2𝛼𝛼	2𝛼𝛼	NOUN
american_scientific_journal-4887	39	3	>	>	X
american_scientific_journal-4887	40	1	𝛼𝛼	𝛼𝛼	ADP
american_scientific_journal-4887	40	2	2	2	NUM
american_scientific_journal-4887	40	3	−	−	NOUN
american_scientific_journal-4887	40	4	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-4887	40	5	+	+	CCONJ
american_scientific_journal-4887	40	6	𝑎𝑎2	𝑎𝑎2	X
american_scientific_journal-4887	40	7	2𝛼𝛼	2𝛼𝛼	NOUN
american_scientific_journal-4887	40	8	=	=	PUNCT
american_scientific_journal-4887	41	1	𝑄𝑄	𝑄𝑄	NOUN
american_scientific_journal-4887	41	2	positive	positive	ADJ
american_scientific_journal-4887	41	3	,	,	PUNCT
american_scientific_journal-4887	41	4	and	and	CCONJ
american_scientific_journal-4887	41	5	𝑃𝑃	𝑃𝑃	ADV
american_scientific_journal-4887	41	6	=	=	PUNCT
american_scientific_journal-4887	41	7	𝛽𝛽	𝛽𝛽	ADP
american_scientific_journal-4887	41	8	2	2	NUM
american_scientific_journal-4887	41	9	+	+	CCONJ
american_scientific_journal-4887	41	10	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-4887	41	11	−	−	PROPN
american_scientific_journal-4887	41	12	𝑎𝑎2	𝑎𝑎2	CCONJ
american_scientific_journal-4887	41	13	2𝛼𝛼	2𝛼𝛼	NOUN
american_scientific_journal-4887	41	14	<	<	X
american_scientific_journal-4887	41	15	𝛼𝛼	𝛼𝛼	ADP
american_scientific_journal-4887	41	16	2	2	NUM
american_scientific_journal-4887	41	17	−	−	NOUN
american_scientific_journal-4887	41	18	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-4887	41	19	+	+	CCONJ
american_scientific_journal-4887	41	20	𝑎𝑎2	𝑎𝑎2	X
american_scientific_journal-4887	41	21	2𝛼𝛼	2𝛼𝛼	NOUN
american_scientific_journal-4887	41	22	=	=	PUNCT
american_scientific_journal-4887	42	1	𝑄𝑄	𝑄𝑄	NOUN
american_scientific_journal-4887	42	2	negative	negative	ADJ
american_scientific_journal-4887	42	3	.	.	PUNCT
american_scientific_journal-4887	43	1	4	4	X
american_scientific_journal-4887	43	2	.	.	X
american_scientific_journal-4887	43	3	if	if	SCONJ
american_scientific_journal-4887	43	4	𝑎𝑎	𝑎𝑎	AUX
american_scientific_journal-4887	43	5	=	=	SYM
american_scientific_journal-4887	43	6	0	0	X
american_scientific_journal-4887	43	7	.	.	PUNCT
american_scientific_journal-4887	43	8	seen	see	VERB
american_scientific_journal-4887	43	9	in	in	ADP
american_scientific_journal-4887	43	10	figure	figure	NOUN
american_scientific_journal-4887	43	11	4	4	NUM
american_scientific_journal-4887	43	12	:	:	PUNCT
american_scientific_journal-4887	43	13	figure	figure	VERB
american_scientific_journal-4887	43	14	4	4	NUM
american_scientific_journal-4887	43	15	:	:	PUNCT
american_scientific_journal-4887	43	16	triangular	triangular	NOUN
american_scientific_journal-4887	43	17	fuzzy	fuzzy	ADJ
american_scientific_journal-4887	43	18	number	number	NOUN
american_scientific_journal-4887	43	19	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-4887	43	20	=	=	SYM
american_scientific_journal-4887	43	21	0	0	NUM
american_scientific_journal-4887	43	22	𝑎𝑎	𝑎𝑎	PROPN
american_scientific_journal-4887	43	23	�	�	PROPN
american_scientific_journal-4887	43	24	=	=	SYM
american_scientific_journal-4887	43	25	(	(	PUNCT
american_scientific_journal-4887	43	26	𝑎𝑎,𝛼𝛼,𝛽𝛽	𝑎𝑎,𝛼𝛼,𝛽𝛽	PROPN
american_scientific_journal-4887	43	27	)	)	PUNCT
american_scientific_journal-4887	43	28	is	be	AUX
american_scientific_journal-4887	43	29	said	say	VERB
american_scientific_journal-4887	43	30	to	to	PART
american_scientific_journal-4887	43	31	be	be	AUX
american_scientific_journal-4887	43	32	positive	positive	ADJ
american_scientific_journal-4887	43	33	if	if	SCONJ
american_scientific_journal-4887	43	34	𝑃𝑃	𝑃𝑃	PROPN
american_scientific_journal-4887	43	35	>	>	X
american_scientific_journal-4887	43	36	𝑄𝑄	𝑄𝑄	PROPN
american_scientific_journal-4887	43	37	,	,	PUNCT
american_scientific_journal-4887	43	38	and	and	CCONJ
american_scientific_journal-4887	43	39	is	be	AUX
american_scientific_journal-4887	43	40	said	say	VERB
american_scientific_journal-4887	43	41	to	to	PART
american_scientific_journal-4887	43	42	be	be	AUX
american_scientific_journal-4887	43	43	negative	negative	ADJ
american_scientific_journal-4887	43	44	if	if	SCONJ
american_scientific_journal-4887	43	45	𝑃𝑃	𝑃𝑃	PROPN
american_scientific_journal-4887	43	46	<	<	X
american_scientific_journal-4887	43	47	𝑄𝑄	𝑄𝑄	PROPN
american_scientific_journal-4887	43	48	or	or	CCONJ
american_scientific_journal-4887	43	49	can	can	AUX
american_scientific_journal-4887	43	50	be	be	AUX
american_scientific_journal-4887	43	51	expressed	express	VERB
american_scientific_journal-4887	43	52	in	in	ADP
american_scientific_journal-4887	43	53	form	form	NOUN
american_scientific_journal-4887	43	54	𝑃𝑃	𝑃𝑃	ADV
american_scientific_journal-4887	43	55	=	=	PUNCT
american_scientific_journal-4887	43	56	𝛽𝛽	𝛽𝛽	X
american_scientific_journal-4887	43	57	>	>	X
american_scientific_journal-4887	43	58	𝛼𝛼	𝛼𝛼	PROPN
american_scientific_journal-4887	43	59	=	=	PUNCT
american_scientific_journal-4887	43	60	𝑄𝑄	𝑄𝑄	PROPN
american_scientific_journal-4887	43	61	positive	positive	ADJ
american_scientific_journal-4887	43	62	,	,	PUNCT
american_scientific_journal-4887	43	63	and	and	CCONJ
american_scientific_journal-4887	43	64	𝑃𝑃	𝑃𝑃	ADV
american_scientific_journal-4887	43	65	=	=	PUNCT
american_scientific_journal-4887	43	66	𝛽𝛽	𝛽𝛽	X
american_scientific_journal-4887	43	67	<	<	X
american_scientific_journal-4887	43	68	𝛼𝛼	𝛼𝛼	X
american_scientific_journal-4887	43	69	=	=	NOUN
american_scientific_journal-4887	43	70	𝑄𝑄	𝑄𝑄	NOUN
american_scientific_journal-4887	43	71	negative	negative	ADJ
american_scientific_journal-4887	43	72	.	.	PUNCT
american_scientific_journal-4887	44	1	american	american	ADJ
american_scientific_journal-4887	44	2	scientific	scientific	ADJ
american_scientific_journal-4887	44	3	research	research	PROPN
american_scientific_journal-4887	44	4	journal	journal	NOUN
american_scientific_journal-4887	44	5	for	for	ADP
american_scientific_journal-4887	44	6	engineering	engineering	NOUN
american_scientific_journal-4887	44	7	,	,	PUNCT
american_scientific_journal-4887	44	8	technology	technology	NOUN
american_scientific_journal-4887	44	9	,	,	PUNCT
american_scientific_journal-4887	44	10	and	and	CCONJ
american_scientific_journal-4887	44	11	sciences	science	NOUN
american_scientific_journal-4887	44	12	(	(	PUNCT
american_scientific_journal-4887	44	13	asrjets	asrjet	NOUN
american_scientific_journal-4887	44	14	)	)	PUNCT
american_scientific_journal-4887	44	15	(	(	PUNCT
american_scientific_journal-4887	44	16	2019	2019	NUM
american_scientific_journal-4887	44	17	)	)	PUNCT
american_scientific_journal-4887	44	18	volume	volume	NOUN
american_scientific_journal-4887	44	19	56	56	NUM
american_scientific_journal-4887	44	20	,	,	PUNCT
american_scientific_journal-4887	44	21	no	no	DET
american_scientific_journal-4887	44	22	1	1	NUM
american_scientific_journal-4887	44	23	,	,	PUNCT
american_scientific_journal-4887	44	24	pp	pp	ADV
american_scientific_journal-4887	44	25	113	113	NUM
american_scientific_journal-4887	44	26	-	-	SYM
american_scientific_journal-4887	44	27	123	123	NUM
american_scientific_journal-4887	44	28	116	116	NUM
american_scientific_journal-4887	44	29	3.2	3.2	NUM
american_scientific_journal-4887	44	30	.	.	PUNCT
american_scientific_journal-4887	45	1	new	new	ADJ
american_scientific_journal-4887	45	2	arithmetic	arithmetic	ADJ
american_scientific_journal-4887	45	3	triangular	triangular	NOUN
american_scientific_journal-4887	45	4	fuzzy	fuzzy	ADJ
american_scientific_journal-4887	45	5	number	number	NOUN
american_scientific_journal-4887	45	6	arithmetic	arithmetic	ADJ
american_scientific_journal-4887	45	7	algebraic	algebraic	ADJ
american_scientific_journal-4887	45	8	operations	operation	NOUN
american_scientific_journal-4887	45	9	will	will	AUX
american_scientific_journal-4887	45	10	be	be	AUX
american_scientific_journal-4887	45	11	given	give	VERB
american_scientific_journal-4887	45	12	for	for	ADP
american_scientific_journal-4887	45	13	triangular	triangular	ADJ
american_scientific_journal-4887	45	14	fuzzy	fuzzy	ADJ
american_scientific_journal-4887	45	15	number	number	NOUN
american_scientific_journal-4887	45	16	.	.	PUNCT
american_scientific_journal-4887	46	1	for	for	ADP
american_scientific_journal-4887	46	2	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-4887	46	3	�	�	PROPN
american_scientific_journal-4887	46	4	=	=	SYM
american_scientific_journal-4887	46	5	(	(	PUNCT
american_scientific_journal-4887	46	6	𝑎𝑎,𝛼𝛼,𝛽𝛽	𝑎𝑎,𝛼𝛼,𝛽𝛽	NOUN
american_scientific_journal-4887	46	7	)	)	PUNCT
american_scientific_journal-4887	46	8	and	and	CCONJ
american_scientific_journal-4887	46	9	𝑏𝑏	𝑏𝑏	ADP
american_scientific_journal-4887	46	10	�	�	NOUN
american_scientific_journal-4887	46	11	=	=	SYM
american_scientific_journal-4887	46	12	(	(	PUNCT
american_scientific_journal-4887	46	13	𝑏𝑏	𝑏𝑏	PROPN
american_scientific_journal-4887	46	14	,	,	PUNCT
american_scientific_journal-4887	46	15	𝛾𝛾	𝛾𝛾	PROPN
american_scientific_journal-4887	46	16	,	,	PUNCT
american_scientific_journal-4887	46	17	𝛿𝛿	𝛿𝛿	PROPN
american_scientific_journal-4887	46	18	)	)	PUNCT
american_scientific_journal-4887	46	19	,	,	PUNCT
american_scientific_journal-4887	46	20	then	then	ADV
american_scientific_journal-4887	46	21	the	the	DET
american_scientific_journal-4887	46	22	parametric	parametric	ADJ
american_scientific_journal-4887	46	23	forms	form	NOUN
american_scientific_journal-4887	46	24	are	be	AUX
american_scientific_journal-4887	46	25	as	as	SCONJ
american_scientific_journal-4887	46	26	follows	follow	VERB
american_scientific_journal-4887	46	27	:	:	PUNCT
american_scientific_journal-4887	46	28	𝑎𝑎	𝑎𝑎	PROPN
american_scientific_journal-4887	46	29	�	�	PROPN
american_scientific_journal-4887	46	30	=	=	SYM
american_scientific_journal-4887	46	31	�	�	PROPN
american_scientific_journal-4887	46	32	𝑎𝑎(𝑟𝑟	𝑎𝑎(𝑟𝑟	PROPN
american_scientific_journal-4887	46	33	)	)	PUNCT
american_scientific_journal-4887	46	34	,	,	PUNCT
american_scientific_journal-4887	46	35	𝑎𝑎(𝑟𝑟	𝑎𝑎(𝑟𝑟	PROPN
american_scientific_journal-4887	46	36	)	)	PUNCT
american_scientific_journal-4887	46	37	�	�	PROPN
american_scientific_journal-4887	46	38	=	=	PUNCT
american_scientific_journal-4887	47	1	[	[	X
american_scientific_journal-4887	47	2	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-4887	47	3	−	−	PROPN
american_scientific_journal-4887	47	4	(	(	PUNCT
american_scientific_journal-4887	47	5	1	1	NUM
american_scientific_journal-4887	47	6	−	−	NOUN
american_scientific_journal-4887	47	7	𝑟𝑟)𝛼𝛼	𝑟𝑟)𝛼𝛼	NOUN
american_scientific_journal-4887	47	8	,	,	PUNCT
american_scientific_journal-4887	47	9	𝑎𝑎	𝑎𝑎	VERB
american_scientific_journal-4887	47	10	+	+	CCONJ
american_scientific_journal-4887	47	11	(	(	PUNCT
american_scientific_journal-4887	47	12	1	1	NUM
american_scientific_journal-4887	47	13	−	−	NOUN
american_scientific_journal-4887	47	14	𝑟𝑟)𝛽𝛽	𝑟𝑟)𝛽𝛽	NOUN
american_scientific_journal-4887	47	15	]	]	X
american_scientific_journal-4887	47	16	𝑏𝑏	𝑏𝑏	PRON
american_scientific_journal-4887	47	17	�	�	PROPN
american_scientific_journal-4887	47	18	=	=	SYM
american_scientific_journal-4887	47	19	�	�	PROPN
american_scientific_journal-4887	47	20	𝑏𝑏(𝑟𝑟	𝑏𝑏(𝑟𝑟	PROPN
american_scientific_journal-4887	47	21	)	)	PUNCT
american_scientific_journal-4887	47	22	,	,	PUNCT
american_scientific_journal-4887	47	23	𝑏𝑏(𝑟𝑟	𝑏𝑏(𝑟𝑟	PROPN
american_scientific_journal-4887	47	24	)	)	PUNCT
american_scientific_journal-4887	47	25	�	�	PROPN
american_scientific_journal-4887	47	26	=	=	PUNCT
american_scientific_journal-4887	48	1	[	[	X
american_scientific_journal-4887	48	2	𝑏𝑏	𝑏𝑏	NUM
american_scientific_journal-4887	48	3	−	−	NOUN
american_scientific_journal-4887	48	4	(	(	PUNCT
american_scientific_journal-4887	48	5	1	1	NUM
american_scientific_journal-4887	48	6	−	−	NOUN
american_scientific_journal-4887	48	7	𝑟𝑟)𝛾𝛾	𝑟𝑟)𝛾𝛾	ADP
american_scientific_journal-4887	48	8	,	,	PUNCT
american_scientific_journal-4887	48	9	𝑏𝑏	𝑏𝑏	NOUN
american_scientific_journal-4887	48	10	+	+	CCONJ
american_scientific_journal-4887	48	11	(	(	PUNCT
american_scientific_journal-4887	48	12	1	1	NUM
american_scientific_journal-4887	48	13	−	−	NOUN
american_scientific_journal-4887	48	14	𝑟𝑟)𝛿𝛿	𝑟𝑟)𝛿𝛿	NUM
american_scientific_journal-4887	48	15	]	]	PUNCT
american_scientific_journal-4887	48	16	then	then	ADV
american_scientific_journal-4887	48	17	for	for	ADP
american_scientific_journal-4887	48	18	the	the	DET
american_scientific_journal-4887	48	19	arithmetic	arithmetic	ADJ
american_scientific_journal-4887	48	20	algebraic	algebraic	ADJ
american_scientific_journal-4887	48	21	process	process	NOUN
american_scientific_journal-4887	48	22	the	the	DET
american_scientific_journal-4887	48	23	two	two	NUM
american_scientific_journal-4887	48	24	triangular	triangular	NOUN
american_scientific_journal-4887	48	25	fuzzy	fuzzy	ADJ
american_scientific_journal-4887	48	26	numbers	number	NOUN
american_scientific_journal-4887	48	27	are	be	AUX
american_scientific_journal-4887	48	28	as	as	SCONJ
american_scientific_journal-4887	48	29	follows	follow	VERB
american_scientific_journal-4887	48	30	:	:	PUNCT
american_scientific_journal-4887	48	31	a.	a.	NOUN
american_scientific_journal-4887	48	32	addition	addition	NOUN
american_scientific_journal-4887	48	33	𝑎𝑎	𝑎𝑎	PROPN
american_scientific_journal-4887	48	34	�	�	PROPN
american_scientific_journal-4887	48	35	⊕	⊕	PROPN
american_scientific_journal-4887	48	36	𝑏𝑏	𝑏𝑏	NOUN
american_scientific_journal-4887	48	37	�	�	PROPN
american_scientific_journal-4887	48	38	=	=	SYM
american_scientific_journal-4887	48	39	�	�	PROPN
american_scientific_journal-4887	48	40	𝑎𝑎(𝑟𝑟	𝑎𝑎(𝑟𝑟	PROPN
american_scientific_journal-4887	48	41	)	)	PUNCT
american_scientific_journal-4887	49	1	+	+	CCONJ
american_scientific_journal-4887	49	2	𝑏𝑏(𝑟𝑟	𝑏𝑏(𝑟𝑟	PROPN
american_scientific_journal-4887	49	3	)	)	PUNCT
american_scientific_journal-4887	49	4	,	,	PUNCT
american_scientific_journal-4887	49	5	𝑎𝑎(𝑟𝑟	𝑎𝑎(𝑟𝑟	PROPN
american_scientific_journal-4887	49	6	)	)	PUNCT
american_scientific_journal-4887	49	7	+	+	CCONJ
american_scientific_journal-4887	49	8	𝑏𝑏(𝑟𝑟	𝑏𝑏(𝑟𝑟	PROPN
american_scientific_journal-4887	49	9	)	)	PUNCT
american_scientific_journal-4887	49	10	�	�	PROPN
american_scientific_journal-4887	50	1	=	=	PUNCT
american_scientific_journal-4887	51	1	[	[	X
american_scientific_journal-4887	51	2	(	(	PUNCT
american_scientific_journal-4887	51	3	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-4887	51	4	−	−	PROPN
american_scientific_journal-4887	51	5	(	(	PUNCT
american_scientific_journal-4887	51	6	1	1	NUM
american_scientific_journal-4887	51	7	−	−	NUM
american_scientific_journal-4887	51	8	𝑟𝑟)𝛼𝛼	𝑟𝑟)𝛼𝛼	NUM
american_scientific_journal-4887	51	9	)	)	PUNCT
american_scientific_journal-4887	52	1	+	+	CCONJ
american_scientific_journal-4887	52	2	(	(	PUNCT
american_scientific_journal-4887	52	3	𝑏𝑏	𝑏𝑏	NUM
american_scientific_journal-4887	52	4	−	−	PROPN
american_scientific_journal-4887	52	5	(	(	PUNCT
american_scientific_journal-4887	52	6	1	1	NUM
american_scientific_journal-4887	52	7	−	−	NUM
american_scientific_journal-4887	52	8	𝑟𝑟)𝛾𝛾	𝑟𝑟)𝛾𝛾	ADP
american_scientific_journal-4887	52	9	)	)	PUNCT
american_scientific_journal-4887	52	10	,	,	PUNCT
american_scientific_journal-4887	52	11	(	(	PUNCT
american_scientific_journal-4887	52	12	𝑎𝑎	𝑎𝑎	VERB
american_scientific_journal-4887	52	13	+	+	CCONJ
american_scientific_journal-4887	52	14	(	(	PUNCT
american_scientific_journal-4887	52	15	1	1	NUM
american_scientific_journal-4887	52	16	−	−	NUM
american_scientific_journal-4887	52	17	𝑟𝑟)𝛽𝛽	𝑟𝑟)𝛽𝛽	NOUN
american_scientific_journal-4887	52	18	)	)	PUNCT
american_scientific_journal-4887	53	1	+	+	CCONJ
american_scientific_journal-4887	53	2	(	(	PUNCT
american_scientific_journal-4887	53	3	𝑏𝑏	𝑏𝑏	NOUN
american_scientific_journal-4887	53	4	+	+	CCONJ
american_scientific_journal-4887	53	5	(	(	PUNCT
american_scientific_journal-4887	53	6	1	1	NUM
american_scientific_journal-4887	53	7	−	−	NUM
american_scientific_journal-4887	53	8	𝑟𝑟)𝛿𝛿	𝑟𝑟)𝛿𝛿	NOUN
american_scientific_journal-4887	53	9	)	)	PUNCT
american_scientific_journal-4887	53	10	]	]	PUNCT
american_scientific_journal-4887	54	1	=	=	PUNCT
american_scientific_journal-4887	55	1	[	[	X
american_scientific_journal-4887	55	2	(	(	PUNCT
american_scientific_journal-4887	55	3	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-4887	55	4	+	+	NUM
american_scientific_journal-4887	55	5	𝑏𝑏	𝑏𝑏	NUM
american_scientific_journal-4887	55	6	)	)	PUNCT
american_scientific_journal-4887	55	7	−	−	PROPN
american_scientific_journal-4887	56	1	(	(	PUNCT
american_scientific_journal-4887	56	2	1	1	NUM
american_scientific_journal-4887	56	3	−	−	PART
american_scientific_journal-4887	56	4	𝑟𝑟)(𝛼𝛼	𝑟𝑟)(𝛼𝛼	NUM
american_scientific_journal-4887	56	5	+	+	NUM
american_scientific_journal-4887	56	6	𝛾𝛾	𝛾𝛾	NOUN
american_scientific_journal-4887	56	7	)	)	PUNCT
american_scientific_journal-4887	56	8	,	,	PUNCT
american_scientific_journal-4887	56	9	(	(	PUNCT
american_scientific_journal-4887	56	10	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-4887	56	11	+	+	NUM
american_scientific_journal-4887	56	12	𝑏𝑏	𝑏𝑏	NUM
american_scientific_journal-4887	56	13	)	)	PUNCT
american_scientific_journal-4887	57	1	+	+	CCONJ
american_scientific_journal-4887	57	2	(	(	PUNCT
american_scientific_journal-4887	57	3	1	1	NUM
american_scientific_journal-4887	57	4	−	−	PROPN
american_scientific_journal-4887	57	5	𝑟𝑟)(𝛽𝛽	𝑟𝑟)(𝛽𝛽	NUM
american_scientific_journal-4887	58	1	+	+	CCONJ
american_scientific_journal-4887	58	2	𝛿𝛿	𝛿𝛿	PROPN
american_scientific_journal-4887	58	3	)	)	PUNCT
american_scientific_journal-4887	58	4	]	]	PUNCT
american_scientific_journal-4887	59	1	transforming	transform	VERB
american_scientific_journal-4887	59	2	back	back	ADV
american_scientific_journal-4887	59	3	into	into	ADP
american_scientific_journal-4887	59	4	the	the	DET
american_scientific_journal-4887	59	5	triangular	triangular	NOUN
american_scientific_journal-4887	59	6	form	form	NOUN
american_scientific_journal-4887	59	7	,	,	PUNCT
american_scientific_journal-4887	59	8	we	we	PRON
american_scientific_journal-4887	59	9	have	have	AUX
american_scientific_journal-4887	59	10	:	:	PUNCT
american_scientific_journal-4887	59	11	𝑎𝑎	𝑎𝑎	PROPN
american_scientific_journal-4887	59	12	�	�	PROPN
american_scientific_journal-4887	59	13	⊕	⊕	PROPN
american_scientific_journal-4887	59	14	𝑏𝑏	𝑏𝑏	NOUN
american_scientific_journal-4887	59	15	�	�	PROPN
american_scientific_journal-4887	59	16	=	=	PUNCT
american_scientific_journal-4887	59	17	(	(	PUNCT
american_scientific_journal-4887	59	18	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-4887	59	19	+	+	X
american_scientific_journal-4887	59	20	𝑏𝑏,𝛼𝛼	𝑏𝑏,𝛼𝛼	ADJ
american_scientific_journal-4887	59	21	+	+	CCONJ
american_scientific_journal-4887	59	22	𝛾𝛾,𝛽𝛽	𝛾𝛾,𝛽𝛽	NOUN
american_scientific_journal-4887	59	23	+	+	CCONJ
american_scientific_journal-4887	59	24	𝛿𝛿	𝛿𝛿	PROPN
american_scientific_journal-4887	59	25	)	)	PUNCT
american_scientific_journal-4887	59	26	b.	b.	PROPN
american_scientific_journal-4887	59	27	subtraction	subtraction	PROPN
american_scientific_journal-4887	59	28	𝑎𝑎	𝑎𝑎	PROPN
american_scientific_journal-4887	59	29	�	�	PROPN
american_scientific_journal-4887	59	30	⊖	⊖	NOUN
american_scientific_journal-4887	59	31	𝑏𝑏	𝑏𝑏	ADP
american_scientific_journal-4887	59	32	�	�	PROPN
american_scientific_journal-4887	59	33	=	=	SYM
american_scientific_journal-4887	59	34	�	�	PROPN
american_scientific_journal-4887	59	35	𝑎𝑎(𝑟𝑟	𝑎𝑎(𝑟𝑟	PROPN
american_scientific_journal-4887	59	36	)	)	PUNCT
american_scientific_journal-4887	60	1	−	−	PROPN
american_scientific_journal-4887	60	2	𝑏𝑏(𝑟𝑟	𝑏𝑏(𝑟𝑟	PROPN
american_scientific_journal-4887	60	3	)	)	PUNCT
american_scientific_journal-4887	60	4	,	,	PUNCT
american_scientific_journal-4887	60	5	𝑎𝑎(𝑟𝑟	𝑎𝑎(𝑟𝑟	PROPN
american_scientific_journal-4887	60	6	)	)	PUNCT
american_scientific_journal-4887	60	7	−	−	ADP
american_scientific_journal-4887	60	8	𝑏𝑏(𝑟𝑟	𝑏𝑏(𝑟𝑟	PROPN
american_scientific_journal-4887	60	9	)	)	PUNCT
american_scientific_journal-4887	60	10	�	�	PROPN
american_scientific_journal-4887	60	11	=	=	PUNCT
american_scientific_journal-4887	61	1	[	[	X
american_scientific_journal-4887	61	2	(	(	PUNCT
american_scientific_journal-4887	61	3	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-4887	61	4	−	−	PROPN
american_scientific_journal-4887	61	5	(	(	PUNCT
american_scientific_journal-4887	61	6	1	1	NUM
american_scientific_journal-4887	61	7	−	−	NUM
american_scientific_journal-4887	61	8	𝑟𝑟)𝛼𝛼	𝑟𝑟)𝛼𝛼	NUM
american_scientific_journal-4887	61	9	)	)	PUNCT
american_scientific_journal-4887	61	10	−	−	PROPN
american_scientific_journal-4887	61	11	(	(	PUNCT
american_scientific_journal-4887	61	12	𝑏𝑏	𝑏𝑏	NOUN
american_scientific_journal-4887	61	13	+	+	CCONJ
american_scientific_journal-4887	61	14	(	(	PUNCT
american_scientific_journal-4887	61	15	1	1	NUM
american_scientific_journal-4887	61	16	−	−	NUM
american_scientific_journal-4887	61	17	𝑟𝑟)𝛿𝛿	𝑟𝑟)𝛿𝛿	NUM
american_scientific_journal-4887	61	18	)	)	PUNCT
american_scientific_journal-4887	61	19	,	,	PUNCT
american_scientific_journal-4887	61	20	(	(	PUNCT
american_scientific_journal-4887	61	21	𝑎𝑎	𝑎𝑎	VERB
american_scientific_journal-4887	61	22	+	+	CCONJ
american_scientific_journal-4887	61	23	(	(	PUNCT
american_scientific_journal-4887	61	24	1	1	NUM
american_scientific_journal-4887	61	25	−	−	NUM
american_scientific_journal-4887	61	26	𝑟𝑟)𝛽𝛽	𝑟𝑟)𝛽𝛽	NOUN
american_scientific_journal-4887	61	27	)	)	PUNCT
american_scientific_journal-4887	61	28	−	−	PROPN
american_scientific_journal-4887	61	29	(	(	PUNCT
american_scientific_journal-4887	61	30	𝑏𝑏	𝑏𝑏	NUM
american_scientific_journal-4887	61	31	−	−	PROPN
american_scientific_journal-4887	61	32	(	(	PUNCT
american_scientific_journal-4887	61	33	1	1	NUM
american_scientific_journal-4887	61	34	−	−	NUM
american_scientific_journal-4887	61	35	𝑟𝑟)𝛾𝛾	𝑟𝑟)𝛾𝛾	ADP
american_scientific_journal-4887	61	36	)	)	PUNCT
american_scientific_journal-4887	61	37	]	]	PUNCT
american_scientific_journal-4887	62	1	=	=	PUNCT
american_scientific_journal-4887	63	1	[	[	X
american_scientific_journal-4887	63	2	(	(	PUNCT
american_scientific_journal-4887	63	3	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-4887	63	4	−	−	NOUN
american_scientific_journal-4887	63	5	𝑏𝑏	𝑏𝑏	NOUN
american_scientific_journal-4887	63	6	)	)	PUNCT
american_scientific_journal-4887	63	7	−	−	PROPN
american_scientific_journal-4887	63	8	(	(	PUNCT
american_scientific_journal-4887	63	9	1	1	NUM
american_scientific_journal-4887	63	10	−	−	PART
american_scientific_journal-4887	63	11	𝑟𝑟)(𝛼𝛼	𝑟𝑟)(𝛼𝛼	NUM
american_scientific_journal-4887	63	12	+	+	NUM
american_scientific_journal-4887	63	13	𝛿𝛿	𝛿𝛿	PROPN
american_scientific_journal-4887	63	14	)	)	PUNCT
american_scientific_journal-4887	63	15	,	,	PUNCT
american_scientific_journal-4887	63	16	(	(	PUNCT
american_scientific_journal-4887	63	17	𝑎𝑎	𝑎𝑎	VERB
american_scientific_journal-4887	63	18	−	−	NOUN
american_scientific_journal-4887	63	19	𝑏𝑏	𝑏𝑏	NUM
american_scientific_journal-4887	63	20	)	)	PUNCT
american_scientific_journal-4887	64	1	+	+	CCONJ
american_scientific_journal-4887	64	2	(	(	PUNCT
american_scientific_journal-4887	64	3	1	1	NUM
american_scientific_journal-4887	64	4	−	−	PROPN
american_scientific_journal-4887	64	5	𝑟𝑟)(𝛽𝛽	𝑟𝑟)(𝛽𝛽	NUM
american_scientific_journal-4887	64	6	+	+	NUM
american_scientific_journal-4887	64	7	𝛾𝛾	𝛾𝛾	NOUN
american_scientific_journal-4887	64	8	)	)	PUNCT
american_scientific_journal-4887	64	9	]	]	PUNCT
american_scientific_journal-4887	65	1	transforming	transform	VERB
american_scientific_journal-4887	65	2	back	back	ADV
american_scientific_journal-4887	65	3	into	into	ADP
american_scientific_journal-4887	65	4	the	the	DET
american_scientific_journal-4887	65	5	triangular	triangular	NOUN
american_scientific_journal-4887	65	6	form	form	NOUN
american_scientific_journal-4887	65	7	,	,	PUNCT
american_scientific_journal-4887	65	8	we	we	PRON
american_scientific_journal-4887	65	9	have	have	AUX
american_scientific_journal-4887	65	10	:	:	PUNCT
american_scientific_journal-4887	65	11	𝑎𝑎	𝑎𝑎	PROPN
american_scientific_journal-4887	65	12	�	�	PROPN
american_scientific_journal-4887	65	13	⊖	⊖	NOUN
american_scientific_journal-4887	65	14	𝑏𝑏	𝑏𝑏	ADP
american_scientific_journal-4887	65	15	�	�	PROPN
american_scientific_journal-4887	65	16	=	=	SYM
american_scientific_journal-4887	65	17	(	(	PUNCT
american_scientific_journal-4887	65	18	𝑎𝑎	𝑎𝑎	VERB
american_scientific_journal-4887	65	19	−	−	PROPN
american_scientific_journal-4887	65	20	𝑏𝑏,𝛼𝛼	𝑏𝑏,𝛼𝛼	NOUN
american_scientific_journal-4887	66	1	+	+	CCONJ
american_scientific_journal-4887	66	2	𝛿𝛿,𝛽𝛽	𝛿𝛿,𝛽𝛽	ADJ
american_scientific_journal-4887	66	3	+	+	CCONJ
american_scientific_journal-4887	66	4	𝛾𝛾	𝛾𝛾	ADJ
american_scientific_journal-4887	66	5	)	)	PUNCT
american_scientific_journal-4887	66	6	c.	c.	NOUN
american_scientific_journal-4887	66	7	scalar	scalar	ADJ
american_scientific_journal-4887	66	8	product	product	NOUN
american_scientific_journal-4887	66	9	as	as	ADP
american_scientific_journal-4887	66	10	𝜆𝜆	𝜆𝜆	PROPN
american_scientific_journal-4887	66	11	⊗	⊗	PROPN
american_scientific_journal-4887	66	12	𝑎𝑎	𝑎𝑎	PROPN
american_scientific_journal-4887	66	13	�	�	PROPN
american_scientific_journal-4887	66	14	=	=	SYM
american_scientific_journal-4887	66	15	�	�	PROPN
american_scientific_journal-4887	66	16	(	(	PUNCT
american_scientific_journal-4887	66	17	𝜆𝜆𝑎𝑎	𝜆𝜆𝑎𝑎	PROPN
american_scientific_journal-4887	66	18	,	,	PUNCT
american_scientific_journal-4887	66	19	𝜆𝜆𝛼𝛼	𝜆𝜆𝛼𝛼	NOUN
american_scientific_journal-4887	66	20	,	,	PUNCT
american_scientific_journal-4887	66	21	𝜆𝜆𝛽𝛽	𝜆𝜆𝛽𝛽	PROPN
american_scientific_journal-4887	66	22	)	)	PUNCT
american_scientific_journal-4887	66	23	𝜆𝜆	𝜆𝜆	NUM
american_scientific_journal-4887	66	24	≥	≥	NOUN
american_scientific_journal-4887	66	25	0	0	NUM
american_scientific_journal-4887	66	26	,	,	PUNCT
american_scientific_journal-4887	66	27	(	(	PUNCT
american_scientific_journal-4887	66	28	𝜆𝜆𝑎𝑎,−𝜆𝜆𝛽𝛽,−𝜆𝜆𝛼𝛼	𝜆𝜆𝑎𝑎,−𝜆𝜆𝛽𝛽,−𝜆𝜆𝛼𝛼	ADJ
american_scientific_journal-4887	66	29	)	)	PUNCT
american_scientific_journal-4887	66	30	𝜆𝜆	𝜆𝜆	ADP
american_scientific_journal-4887	66	31	<	<	X
american_scientific_journal-4887	66	32	0	0	X
american_scientific_journal-4887	66	33	.	.	PUNCT
american_scientific_journal-4887	66	34	d.	d.	PROPN
american_scientific_journal-4887	66	35	multiplication	multiplication	PROPN
american_scientific_journal-4887	66	36	if	if	SCONJ
american_scientific_journal-4887	66	37	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-4887	66	38	�	�	PROPN
american_scientific_journal-4887	66	39	=	=	SYM
american_scientific_journal-4887	66	40	�	�	PROPN
american_scientific_journal-4887	66	41	𝑎𝑎(𝑟𝑟	𝑎𝑎(𝑟𝑟	PROPN
american_scientific_journal-4887	66	42	)	)	PUNCT
american_scientific_journal-4887	66	43	,	,	PUNCT
american_scientific_journal-4887	66	44	𝑎𝑎(𝑟𝑟	𝑎𝑎(𝑟𝑟	PROPN
american_scientific_journal-4887	66	45	)	)	PUNCT
american_scientific_journal-4887	66	46	�	�	PROPN
american_scientific_journal-4887	66	47	and	and	CCONJ
american_scientific_journal-4887	66	48	𝑏𝑏	𝑏𝑏	ADP
american_scientific_journal-4887	66	49	�	�	PROPN
american_scientific_journal-4887	66	50	=	=	SYM
american_scientific_journal-4887	66	51	�	�	PROPN
american_scientific_journal-4887	66	52	𝑏𝑏(𝑟𝑟	𝑏𝑏(𝑟𝑟	PROPN
american_scientific_journal-4887	66	53	)	)	PUNCT
american_scientific_journal-4887	66	54	,	,	PUNCT
american_scientific_journal-4887	66	55	𝑏𝑏(𝑟𝑟	𝑏𝑏(𝑟𝑟	PROPN
american_scientific_journal-4887	66	56	)	)	PUNCT
american_scientific_journal-4887	66	57	�	�	PROPN
american_scientific_journal-4887	66	58	are	be	AUX
american_scientific_journal-4887	66	59	two	two	NUM
american_scientific_journal-4887	66	60	positive	positive	ADJ
american_scientific_journal-4887	66	61	fuzzy	fuzzy	ADJ
american_scientific_journal-4887	66	62	numbers	number	NOUN
american_scientific_journal-4887	66	63	,	,	PUNCT
american_scientific_journal-4887	66	64	then	then	ADV
american_scientific_journal-4887	66	65	�	�	PROPN
american_scientific_journal-4887	66	66	̃	̃	PROPN
american_scientific_journal-4887	66	67	�	�	PROPN
american_scientific_journal-4887	66	68	𝑐	𝑐	NOUN
american_scientific_journal-4887	66	69	=	=	SYM
american_scientific_journal-4887	66	70	𝑎𝑎	𝑎𝑎	PROPN
american_scientific_journal-4887	66	71	�	�	PROPN
american_scientific_journal-4887	66	72	⊗	⊗	PROPN
american_scientific_journal-4887	66	73	𝑏𝑏	𝑏𝑏	NUM
american_scientific_journal-4887	66	74	�	�	PROPN
american_scientific_journal-4887	66	75	=	=	SYM
american_scientific_journal-4887	66	76	�	�	PROPN
american_scientific_journal-4887	66	77	𝑐𝑐(𝑟𝑟	𝑐𝑐(𝑟𝑟	PROPN
american_scientific_journal-4887	66	78	)	)	PUNCT
american_scientific_journal-4887	66	79	,	,	PUNCT
american_scientific_journal-4887	66	80	𝑐𝑐(𝑟𝑟	𝑐𝑐(𝑟𝑟	NUM
american_scientific_journal-4887	66	81	)	)	PUNCT
american_scientific_journal-4887	66	82	�	�	PROPN
american_scientific_journal-4887	66	83	for	for	ADP
american_scientific_journal-4887	66	84	every	every	DET
american_scientific_journal-4887	66	85	𝑟𝑟	𝑟𝑟	ADP
american_scientific_journal-4887	66	86	∈	∈	PROPN
american_scientific_journal-4887	67	1	[	[	X
american_scientific_journal-4887	67	2	0,1	0,1	NUM
american_scientific_journal-4887	67	3	]	]	PUNCT
american_scientific_journal-4887	67	4	.	.	PUNCT
american_scientific_journal-4887	68	1	the	the	DET
american_scientific_journal-4887	68	2	following	follow	VERB
american_scientific_journal-4887	68	3	is	be	AUX
american_scientific_journal-4887	68	4	given	give	VERB
american_scientific_journal-4887	68	5	some	some	DET
american_scientific_journal-4887	68	6	cases	case	NOUN
american_scientific_journal-4887	68	7	for	for	ADP
american_scientific_journal-4887	68	8	triangular	triangular	NOUN
american_scientific_journal-4887	68	9	fuzzy	fuzzy	ADJ
american_scientific_journal-4887	68	10	number	number	NOUN
american_scientific_journal-4887	68	11	to	to	ADP
american_scientific_journal-4887	68	12	multiplication	multiplication	NOUN
american_scientific_journal-4887	68	13	operations	operation	NOUN
american_scientific_journal-4887	68	14	.	.	PUNCT
american_scientific_journal-4887	69	1	(	(	PUNCT
american_scientific_journal-4887	69	2	i	i	NOUN
american_scientific_journal-4887	69	3	)	)	PUNCT
american_scientific_journal-4887	69	4	if	if	SCONJ
american_scientific_journal-4887	69	5	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-4887	69	6	�	�	PROPN
american_scientific_journal-4887	69	7	is	be	AUX
american_scientific_journal-4887	69	8	positive	positive	ADJ
american_scientific_journal-4887	69	9	and	and	CCONJ
american_scientific_journal-4887	69	10	𝑏𝑏	𝑏𝑏	NOUN
american_scientific_journal-4887	69	11	�	�	PROPN
american_scientific_journal-4887	69	12	is	be	AUX
american_scientific_journal-4887	69	13	positive	positive	ADJ
american_scientific_journal-4887	69	14	,	,	PUNCT
american_scientific_journal-4887	69	15	then	then	ADV
american_scientific_journal-4887	69	16	:	:	PUNCT
american_scientific_journal-4887	69	17	�	�	PROPN
american_scientific_journal-4887	69	18	𝑐𝑐(𝑟𝑟	𝑐𝑐(𝑟𝑟	PROPN
american_scientific_journal-4887	69	19	)	)	PUNCT
american_scientific_journal-4887	70	1	=	=	SYM
american_scientific_journal-4887	70	2	𝑎𝑎(𝑟𝑟)𝑏𝑏(1	𝑎𝑎(𝑟𝑟)𝑏𝑏(1	PROPN
american_scientific_journal-4887	70	3	)	)	PUNCT
american_scientific_journal-4887	71	1	+	+	CCONJ
american_scientific_journal-4887	71	2	𝑎𝑎(1)𝑏𝑏(𝑟𝑟	𝑎𝑎(1)𝑏𝑏(𝑟𝑟	NOUN
american_scientific_journal-4887	71	3	)	)	PUNCT
american_scientific_journal-4887	71	4	−	−	ADP
american_scientific_journal-4887	71	5	𝑎𝑎(1)𝑏𝑏(1	𝑎𝑎(1)𝑏𝑏(1	PROPN
american_scientific_journal-4887	71	6	)	)	PUNCT
american_scientific_journal-4887	71	7	𝑐𝑐(𝑟𝑟	𝑐𝑐(𝑟𝑟	PROPN
american_scientific_journal-4887	71	8	)	)	PUNCT
american_scientific_journal-4887	71	9	=	=	SYM
american_scientific_journal-4887	71	10	𝑎𝑎(𝑟𝑟)𝑏𝑏(1	𝑎𝑎(𝑟𝑟)𝑏𝑏(1	PROPN
american_scientific_journal-4887	71	11	)	)	PUNCT
american_scientific_journal-4887	72	1	+	+	CCONJ
american_scientific_journal-4887	72	2	𝑎𝑎(1)𝑏𝑏(𝑟𝑟	𝑎𝑎(1)𝑏𝑏(𝑟𝑟	NOUN
american_scientific_journal-4887	72	3	)	)	PUNCT
american_scientific_journal-4887	72	4	−	−	PROPN
american_scientific_journal-4887	72	5	𝑎𝑎(1)𝑏𝑏(1	𝑎𝑎(1)𝑏𝑏(1	PROPN
american_scientific_journal-4887	72	6	)	)	PUNCT
american_scientific_journal-4887	72	7	(	(	PUNCT
american_scientific_journal-4887	72	8	1	1	NUM
american_scientific_journal-4887	72	9	)	)	PUNCT
american_scientific_journal-4887	72	10	from	from	ADP
american_scientific_journal-4887	72	11	equation	equation	NOUN
american_scientific_journal-4887	72	12	(	(	PUNCT
american_scientific_journal-4887	72	13	1	1	NUM
american_scientific_journal-4887	72	14	)	)	PUNCT
american_scientific_journal-4887	72	15	:	:	PUNCT
american_scientific_journal-4887	72	16	�	�	PROPN
american_scientific_journal-4887	72	17	𝑐𝑐(𝑟𝑟	𝑐𝑐(𝑟𝑟	NUM
american_scientific_journal-4887	72	18	)	)	PUNCT
american_scientific_journal-4887	72	19	,	,	PUNCT
american_scientific_journal-4887	72	20	𝑐𝑐(𝑟𝑟	𝑐𝑐(𝑟𝑟	NUM
american_scientific_journal-4887	72	21	)	)	PUNCT
american_scientific_journal-4887	72	22	�	�	PROPN
american_scientific_journal-4887	72	23	=	=	PUNCT
american_scientific_journal-4887	73	1	[	[	X
american_scientific_journal-4887	73	2	(	(	PUNCT
american_scientific_journal-4887	73	3	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-4887	73	4	−	−	PROPN
american_scientific_journal-4887	73	5	(	(	PUNCT
american_scientific_journal-4887	73	6	1	1	NUM
american_scientific_journal-4887	73	7	−	−	PROPN
american_scientific_journal-4887	73	8	𝑟𝑟)𝛼𝛼)𝑏𝑏	𝑟𝑟)𝛼𝛼)𝑏𝑏	PROPN
american_scientific_journal-4887	73	9	+	+	CCONJ
american_scientific_journal-4887	73	10	𝑎𝑎(𝑏𝑏	𝑎𝑎(𝑏𝑏	PROPN
american_scientific_journal-4887	74	1	−	−	NOUN
american_scientific_journal-4887	75	1	(	(	PUNCT
american_scientific_journal-4887	75	2	1	1	NUM
american_scientific_journal-4887	75	3	−	−	NUM
american_scientific_journal-4887	75	4	𝑟𝑟)𝛾𝛾	𝑟𝑟)𝛾𝛾	ADP
american_scientific_journal-4887	75	5	)	)	PUNCT
american_scientific_journal-4887	76	1	−	−	PROPN
american_scientific_journal-4887	76	2	𝑎𝑎𝑏𝑏	𝑎𝑎𝑏𝑏	NOUN
american_scientific_journal-4887	76	3	,	,	PUNCT
american_scientific_journal-4887	76	4	(	(	PUNCT
american_scientific_journal-4887	76	5	𝑎𝑎	𝑎𝑎	VERB
american_scientific_journal-4887	76	6	+	+	CCONJ
american_scientific_journal-4887	76	7	(	(	PUNCT
american_scientific_journal-4887	76	8	1	1	NUM
american_scientific_journal-4887	76	9	−	−	PROPN
american_scientific_journal-4887	76	10	𝑟𝑟)𝛽𝛽)𝑏𝑏	𝑟𝑟)𝛽𝛽)𝑏𝑏	PROPN
american_scientific_journal-4887	76	11	+	+	NUM
american_scientific_journal-4887	76	12	𝑎𝑎(𝑏𝑏	𝑎𝑎(𝑏𝑏	NOUN
american_scientific_journal-4887	77	1	+	+	CCONJ
american_scientific_journal-4887	77	2	(	(	PUNCT
american_scientific_journal-4887	77	3	1	1	NUM
american_scientific_journal-4887	77	4	−	−	NUM
american_scientific_journal-4887	77	5	𝑟𝑟)𝛿𝛿	𝑟𝑟)𝛿𝛿	NUM
american_scientific_journal-4887	77	6	)	)	PUNCT
american_scientific_journal-4887	77	7	−	−	PROPN
american_scientific_journal-4887	77	8	𝑎𝑎𝑏𝑏	𝑎𝑎𝑏𝑏	NOUN
american_scientific_journal-4887	77	9	]	]	PUNCT
american_scientific_journal-4887	77	10	we	we	PRON
american_scientific_journal-4887	77	11	have	have	VERB
american_scientific_journal-4887	77	12	�	�	PROPN
american_scientific_journal-4887	77	13	̃	̃	PROPN
american_scientific_journal-4887	77	14	�	�	PROPN
american_scientific_journal-4887	77	15	𝑐	𝑐	PROPN
american_scientific_journal-4887	77	16	=	=	SYM
american_scientific_journal-4887	77	17	�	�	PROPN
american_scientific_journal-4887	77	18	𝑐𝑐(𝑟𝑟	𝑐𝑐(𝑟𝑟	NUM
american_scientific_journal-4887	77	19	)	)	PUNCT
american_scientific_journal-4887	77	20	,	,	PUNCT
american_scientific_journal-4887	77	21	𝑐𝑐(𝑟𝑟	𝑐𝑐(𝑟𝑟	NUM
american_scientific_journal-4887	77	22	)	)	PUNCT
american_scientific_journal-4887	77	23	�	�	PROPN
american_scientific_journal-4887	77	24	=	=	PUNCT
american_scientific_journal-4887	78	1	[	[	X
american_scientific_journal-4887	78	2	𝑎𝑎𝑏𝑏	𝑎𝑎𝑏𝑏	NOUN
american_scientific_journal-4887	78	3	−	−	X
american_scientific_journal-4887	78	4	(	(	PUNCT
american_scientific_journal-4887	78	5	1	1	NUM
american_scientific_journal-4887	78	6	−	−	PROPN
american_scientific_journal-4887	78	7	𝑟𝑟)(𝑎𝑎𝛾𝛾	𝑟𝑟)(𝑎𝑎𝛾𝛾	SYM
american_scientific_journal-4887	78	8	+	+	CCONJ
american_scientific_journal-4887	78	9	𝑏𝑏𝛼𝛼	𝑏𝑏𝛼𝛼	ADJ
american_scientific_journal-4887	78	10	)	)	PUNCT
american_scientific_journal-4887	78	11	,	,	PUNCT
american_scientific_journal-4887	78	12	𝑎𝑎𝑏𝑏	𝑎𝑎𝑏𝑏	NOUN
american_scientific_journal-4887	78	13	+	+	CCONJ
american_scientific_journal-4887	78	14	(	(	PUNCT
american_scientific_journal-4887	78	15	1	1	NUM
american_scientific_journal-4887	78	16	−	−	NOUN
american_scientific_journal-4887	78	17	𝑟𝑟)(𝑎𝑎𝛿𝛿	𝑟𝑟)(𝑎𝑎𝛿𝛿	NOUN
american_scientific_journal-4887	79	1	+	+	CCONJ
american_scientific_journal-4887	79	2	𝑏𝑏𝛽𝛽	𝑏𝑏𝛽𝛽	ADJ
american_scientific_journal-4887	79	3	)	)	PUNCT
american_scientific_journal-4887	79	4	]	]	PUNCT
american_scientific_journal-4887	79	5	(	(	PUNCT
american_scientific_journal-4887	79	6	2	2	X
american_scientific_journal-4887	79	7	)	)	PUNCT
american_scientific_journal-4887	79	8	if	if	SCONJ
american_scientific_journal-4887	79	9	we	we	PRON
american_scientific_journal-4887	79	10	let	let	VERB
american_scientific_journal-4887	79	11	�	�	PROPN
american_scientific_journal-4887	79	12	̃	̃	PROPN
american_scientific_journal-4887	79	13	�	�	PROPN
american_scientific_journal-4887	79	14	𝑐	𝑐	NOUN
american_scientific_journal-4887	79	15	=	=	SYM
american_scientific_journal-4887	79	16	(	(	PUNCT
american_scientific_journal-4887	79	17	𝑐𝑐	𝑐𝑐	PROPN
american_scientific_journal-4887	79	18	,	,	PUNCT
american_scientific_journal-4887	79	19	𝜉𝜉,𝜓𝜓	𝜉𝜉,𝜓𝜓	ADJ
american_scientific_journal-4887	79	20	)	)	PUNCT
american_scientific_journal-4887	79	21	,	,	PUNCT
american_scientific_journal-4887	79	22	then	then	ADV
american_scientific_journal-4887	79	23	the	the	DET
american_scientific_journal-4887	79	24	parametric	parametric	ADJ
american_scientific_journal-4887	79	25	fuzzy	fuzzy	ADJ
american_scientific_journal-4887	79	26	number	number	NOUN
american_scientific_journal-4887	79	27	is	be	AUX
american_scientific_journal-4887	79	28	of	of	ADP
american_scientific_journal-4887	79	29	the	the	DET
american_scientific_journal-4887	79	30	form	form	NOUN
american_scientific_journal-4887	79	31	:	:	PUNCT
american_scientific_journal-4887	79	32	�	�	PROPN
american_scientific_journal-4887	79	33	̃	̃	PROPN
american_scientific_journal-4887	79	34	�	�	PROPN
american_scientific_journal-4887	79	35	𝑐	𝑐	NOUN
american_scientific_journal-4887	79	36	=	=	PUNCT
american_scientific_journal-4887	80	1	[	[	X
american_scientific_journal-4887	80	2	𝑐𝑐	𝑐𝑐	INTJ
american_scientific_journal-4887	80	3	−	−	PROPN
american_scientific_journal-4887	80	4	(	(	PUNCT
american_scientific_journal-4887	80	5	1	1	NUM
american_scientific_journal-4887	80	6	−	−	PROPN
american_scientific_journal-4887	80	7	𝑟𝑟)𝜉𝜉	𝑟𝑟)𝜉𝜉	PROPN
american_scientific_journal-4887	80	8	,	,	PUNCT
american_scientific_journal-4887	80	9	𝑐𝑐	𝑐𝑐	X
american_scientific_journal-4887	80	10	+	+	CCONJ
american_scientific_journal-4887	80	11	(	(	PUNCT
american_scientific_journal-4887	80	12	1	1	NUM
american_scientific_journal-4887	80	13	−	−	PRON
american_scientific_journal-4887	80	14	𝑟𝑟)𝜓𝜓	𝑟𝑟)𝜓𝜓	NUM
american_scientific_journal-4887	80	15	]	]	X
american_scientific_journal-4887	80	16	(	(	PUNCT
american_scientific_journal-4887	80	17	3	3	NUM
american_scientific_journal-4887	80	18	)	)	PUNCT
american_scientific_journal-4887	80	19	from	from	ADP
american_scientific_journal-4887	80	20	equation	equation	NOUN
american_scientific_journal-4887	80	21	(	(	PUNCT
american_scientific_journal-4887	80	22	2	2	NUM
american_scientific_journal-4887	80	23	)	)	PUNCT
american_scientific_journal-4887	80	24	and	and	CCONJ
american_scientific_journal-4887	80	25	(	(	PUNCT
american_scientific_journal-4887	80	26	3	3	X
american_scientific_journal-4887	80	27	)	)	PUNCT
american_scientific_journal-4887	80	28	we	we	PRON
american_scientific_journal-4887	80	29	have	have	VERB
american_scientific_journal-4887	80	30	:	:	PUNCT
american_scientific_journal-4887	80	31	𝜉𝜉	𝜉𝜉	PROPN
american_scientific_journal-4887	80	32	=	=	SYM
american_scientific_journal-4887	80	33	𝑎𝑎𝛾𝛾	𝑎𝑎𝛾𝛾	NOUN
american_scientific_journal-4887	80	34	+	+	CCONJ
american_scientific_journal-4887	80	35	𝑏𝑏𝛼𝛼	𝑏𝑏𝛼𝛼	ADJ
american_scientific_journal-4887	80	36	𝜓𝜓	𝜓𝜓	X
american_scientific_journal-4887	80	37	=	=	NOUN
american_scientific_journal-4887	80	38	𝑎𝑎𝛿𝛿	𝑎𝑎𝛿𝛿	PROPN
american_scientific_journal-4887	81	1	+	+	CCONJ
american_scientific_journal-4887	81	2	𝑏𝑏𝛽𝛽	𝑏𝑏𝛽𝛽	ADJ
american_scientific_journal-4887	81	3	so	so	ADV
american_scientific_journal-4887	81	4	multiplication	multiplication	NOUN
american_scientific_journal-4887	81	5	𝑎𝑎	𝑎𝑎	PROPN
american_scientific_journal-4887	81	6	�	�	PROPN
american_scientific_journal-4887	81	7	positive	positive	ADJ
american_scientific_journal-4887	81	8	and	and	CCONJ
american_scientific_journal-4887	81	9	𝑏𝑏	𝑏𝑏	ADP
american_scientific_journal-4887	81	10	�	�	PROPN
american_scientific_journal-4887	81	11	positive	positive	ADJ
american_scientific_journal-4887	81	12	can	can	AUX
american_scientific_journal-4887	81	13	be	be	AUX
american_scientific_journal-4887	81	14	written	write	VERB
american_scientific_journal-4887	81	15	as	as	ADP
american_scientific_journal-4887	81	16	�	�	PROPN
american_scientific_journal-4887	81	17	̃	̃	PROPN
american_scientific_journal-4887	81	18	�	�	PROPN
american_scientific_journal-4887	81	19	𝑐	𝑐	NOUN
american_scientific_journal-4887	81	20	=	=	SYM
american_scientific_journal-4887	81	21	𝑎𝑎	𝑎𝑎	PROPN
american_scientific_journal-4887	81	22	�	�	PROPN
american_scientific_journal-4887	81	23	⊗	⊗	PROPN
american_scientific_journal-4887	81	24	𝑏𝑏	𝑏𝑏	NUM
american_scientific_journal-4887	81	25	�	�	PROPN
american_scientific_journal-4887	81	26	=	=	SYM
american_scientific_journal-4887	81	27	(	(	PUNCT
american_scientific_journal-4887	81	28	𝑎𝑎𝑏𝑏	𝑎𝑎𝑏𝑏	NOUN
american_scientific_journal-4887	81	29	,	,	PUNCT
american_scientific_journal-4887	81	30	𝑎𝑎𝛾𝛾	𝑎𝑎𝛾𝛾	NOUN
american_scientific_journal-4887	81	31	+	+	CCONJ
american_scientific_journal-4887	81	32	𝑏𝑏𝛼𝛼	𝑏𝑏𝛼𝛼	ADJ
american_scientific_journal-4887	81	33	,	,	PUNCT
american_scientific_journal-4887	81	34	𝑎𝑎𝛿𝛿	𝑎𝑎𝛿𝛿	ADJ
american_scientific_journal-4887	81	35	+	+	CCONJ
american_scientific_journal-4887	81	36	𝑏𝑏𝛽𝛽	𝑏𝑏𝛽𝛽	ADJ
american_scientific_journal-4887	81	37	)	)	PUNCT
american_scientific_journal-4887	81	38	(	(	PUNCT
american_scientific_journal-4887	81	39	ii	ii	NOUN
american_scientific_journal-4887	81	40	)	)	PUNCT
american_scientific_journal-4887	81	41	if	if	SCONJ
american_scientific_journal-4887	81	42	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-4887	81	43	�	�	PROPN
american_scientific_journal-4887	81	44	is	be	AUX
american_scientific_journal-4887	81	45	positive	positive	ADJ
american_scientific_journal-4887	81	46	and	and	CCONJ
american_scientific_journal-4887	81	47	𝑏𝑏	𝑏𝑏	NOUN
american_scientific_journal-4887	81	48	�	�	PROPN
american_scientific_journal-4887	81	49	is	be	AUX
american_scientific_journal-4887	81	50	negative	negative	ADJ
american_scientific_journal-4887	81	51	,	,	PUNCT
american_scientific_journal-4887	81	52	then	then	ADV
american_scientific_journal-4887	81	53	:	:	PUNCT
american_scientific_journal-4887	81	54	�	�	PROPN
american_scientific_journal-4887	81	55	𝑐𝑐(𝑟𝑟	𝑐𝑐(𝑟𝑟	PROPN
american_scientific_journal-4887	81	56	)	)	PUNCT
american_scientific_journal-4887	81	57	=	=	SYM
american_scientific_journal-4887	81	58	𝑎𝑎(𝑟𝑟)𝑏𝑏(1	𝑎𝑎(𝑟𝑟)𝑏𝑏(1	PROPN
american_scientific_journal-4887	81	59	)	)	PUNCT
american_scientific_journal-4887	82	1	+	+	CCONJ
american_scientific_journal-4887	82	2	𝑎𝑎(1)𝑏𝑏(𝑟𝑟	𝑎𝑎(1)𝑏𝑏(𝑟𝑟	NOUN
american_scientific_journal-4887	82	3	)	)	PUNCT
american_scientific_journal-4887	82	4	−	−	ADP
american_scientific_journal-4887	82	5	𝑎𝑎(1)𝑏𝑏(1	𝑎𝑎(1)𝑏𝑏(1	PROPN
american_scientific_journal-4887	82	6	)	)	PUNCT
american_scientific_journal-4887	82	7	𝑐𝑐(𝑟𝑟	𝑐𝑐(𝑟𝑟	PROPN
american_scientific_journal-4887	82	8	)	)	PUNCT
american_scientific_journal-4887	82	9	=	=	SYM
american_scientific_journal-4887	82	10	𝑎𝑎(𝑟𝑟)𝑏𝑏(1	𝑎𝑎(𝑟𝑟)𝑏𝑏(1	PROPN
american_scientific_journal-4887	82	11	)	)	PUNCT
american_scientific_journal-4887	83	1	+	+	CCONJ
american_scientific_journal-4887	83	2	𝑎𝑎(1)𝑏𝑏(𝑟𝑟	𝑎𝑎(1)𝑏𝑏(𝑟𝑟	NOUN
american_scientific_journal-4887	83	3	)	)	PUNCT
american_scientific_journal-4887	83	4	−	−	PROPN
american_scientific_journal-4887	83	5	𝑎𝑎(1)𝑏𝑏(1	𝑎𝑎(1)𝑏𝑏(1	PROPN
american_scientific_journal-4887	83	6	)	)	PUNCT
american_scientific_journal-4887	83	7	(	(	PUNCT
american_scientific_journal-4887	83	8	4	4	X
american_scientific_journal-4887	83	9	)	)	PUNCT
american_scientific_journal-4887	83	10	american	american	ADJ
american_scientific_journal-4887	83	11	scientific	scientific	ADJ
american_scientific_journal-4887	83	12	research	research	NOUN
american_scientific_journal-4887	83	13	journal	journal	NOUN
american_scientific_journal-4887	83	14	for	for	ADP
american_scientific_journal-4887	83	15	engineering	engineering	NOUN
american_scientific_journal-4887	83	16	,	,	PUNCT
american_scientific_journal-4887	83	17	technology	technology	NOUN
american_scientific_journal-4887	83	18	,	,	PUNCT
american_scientific_journal-4887	83	19	and	and	CCONJ
american_scientific_journal-4887	83	20	sciences	science	NOUN
american_scientific_journal-4887	83	21	(	(	PUNCT
american_scientific_journal-4887	83	22	asrjets	asrjet	NOUN
american_scientific_journal-4887	83	23	)	)	PUNCT
american_scientific_journal-4887	83	24	(	(	PUNCT
american_scientific_journal-4887	83	25	2019	2019	NUM
american_scientific_journal-4887	83	26	)	)	PUNCT
american_scientific_journal-4887	83	27	volume	volume	NOUN
american_scientific_journal-4887	83	28	56	56	NUM
american_scientific_journal-4887	83	29	,	,	PUNCT
american_scientific_journal-4887	83	30	no	no	DET
american_scientific_journal-4887	83	31	1	1	NUM
american_scientific_journal-4887	83	32	,	,	PUNCT
american_scientific_journal-4887	83	33	pp	pp	ADV
american_scientific_journal-4887	83	34	113	113	NUM
american_scientific_journal-4887	83	35	-	-	SYM
american_scientific_journal-4887	83	36	123	123	NUM
american_scientific_journal-4887	83	37	117	117	NUM
american_scientific_journal-4887	83	38	from	from	ADP
american_scientific_journal-4887	83	39	equation	equation	NOUN
american_scientific_journal-4887	83	40	(	(	PUNCT
american_scientific_journal-4887	83	41	4	4	NUM
american_scientific_journal-4887	83	42	)	)	PUNCT
american_scientific_journal-4887	83	43	:	:	PUNCT
american_scientific_journal-4887	83	44	�	�	PROPN
american_scientific_journal-4887	83	45	𝑐𝑐(𝑟𝑟	𝑐𝑐(𝑟𝑟	NUM
american_scientific_journal-4887	83	46	)	)	PUNCT
american_scientific_journal-4887	83	47	,	,	PUNCT
american_scientific_journal-4887	83	48	𝑐𝑐(𝑟𝑟	𝑐𝑐(𝑟𝑟	NUM
american_scientific_journal-4887	83	49	)	)	PUNCT
american_scientific_journal-4887	83	50	�	�	PROPN
american_scientific_journal-4887	83	51	=	=	PUNCT
american_scientific_journal-4887	84	1	[	[	X
american_scientific_journal-4887	84	2	(	(	PUNCT
american_scientific_journal-4887	84	3	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-4887	84	4	+	+	CCONJ
american_scientific_journal-4887	84	5	(	(	PUNCT
american_scientific_journal-4887	84	6	1	1	NUM
american_scientific_journal-4887	84	7	−	−	PROPN
american_scientific_journal-4887	84	8	𝑟𝑟)𝛽𝛽)𝑏𝑏	𝑟𝑟)𝛽𝛽)𝑏𝑏	PROPN
american_scientific_journal-4887	84	9	+	+	NUM
american_scientific_journal-4887	84	10	𝑎𝑎(𝑏𝑏	𝑎𝑎(𝑏𝑏	NOUN
american_scientific_journal-4887	85	1	−	−	NOUN
american_scientific_journal-4887	85	2	(	(	PUNCT
american_scientific_journal-4887	85	3	1	1	NUM
american_scientific_journal-4887	85	4	−	−	NUM
american_scientific_journal-4887	85	5	𝑟𝑟)𝛾𝛾	𝑟𝑟)𝛾𝛾	ADP
american_scientific_journal-4887	85	6	)	)	PUNCT
american_scientific_journal-4887	86	1	−	−	PROPN
american_scientific_journal-4887	86	2	𝑎𝑎𝑏𝑏	𝑎𝑎𝑏𝑏	NOUN
american_scientific_journal-4887	86	3	,	,	PUNCT
american_scientific_journal-4887	86	4	(	(	PUNCT
american_scientific_journal-4887	86	5	𝑎𝑎	𝑎𝑎	VERB
american_scientific_journal-4887	86	6	−	−	PROPN
american_scientific_journal-4887	86	7	(	(	PUNCT
american_scientific_journal-4887	86	8	1	1	NUM
american_scientific_journal-4887	86	9	−	−	PROPN
american_scientific_journal-4887	86	10	𝑟𝑟)𝛼𝛼)𝑏𝑏	𝑟𝑟)𝛼𝛼)𝑏𝑏	PROPN
american_scientific_journal-4887	86	11	+	+	CCONJ
american_scientific_journal-4887	86	12	𝑎𝑎(𝑏𝑏	𝑎𝑎(𝑏𝑏	NOUN
american_scientific_journal-4887	87	1	+	+	CCONJ
american_scientific_journal-4887	87	2	(	(	PUNCT
american_scientific_journal-4887	87	3	1	1	NUM
american_scientific_journal-4887	87	4	−	−	NUM
american_scientific_journal-4887	87	5	𝑟𝑟)𝛿𝛿	𝑟𝑟)𝛿𝛿	NUM
american_scientific_journal-4887	87	6	)	)	PUNCT
american_scientific_journal-4887	87	7	−	−	PROPN
american_scientific_journal-4887	87	8	𝑎𝑎𝑏𝑏	𝑎𝑎𝑏𝑏	NOUN
american_scientific_journal-4887	87	9	]	]	PUNCT
american_scientific_journal-4887	87	10	we	we	PRON
american_scientific_journal-4887	87	11	have	have	VERB
american_scientific_journal-4887	87	12	�	�	PROPN
american_scientific_journal-4887	87	13	̃	̃	PROPN
american_scientific_journal-4887	87	14	�	�	PROPN
american_scientific_journal-4887	87	15	𝑐	𝑐	PROPN
american_scientific_journal-4887	87	16	=	=	SYM
american_scientific_journal-4887	87	17	�	�	PROPN
american_scientific_journal-4887	87	18	𝑐𝑐(𝑟𝑟	𝑐𝑐(𝑟𝑟	NUM
american_scientific_journal-4887	87	19	)	)	PUNCT
american_scientific_journal-4887	87	20	,	,	PUNCT
american_scientific_journal-4887	87	21	𝑐𝑐(𝑟𝑟	𝑐𝑐(𝑟𝑟	NUM
american_scientific_journal-4887	87	22	)	)	PUNCT
american_scientific_journal-4887	87	23	�	�	PROPN
american_scientific_journal-4887	87	24	=	=	PUNCT
american_scientific_journal-4887	88	1	[	[	X
american_scientific_journal-4887	88	2	𝑎𝑎𝑏𝑏	𝑎𝑎𝑏𝑏	NOUN
american_scientific_journal-4887	88	3	−	−	X
american_scientific_journal-4887	88	4	(	(	PUNCT
american_scientific_journal-4887	88	5	1	1	NUM
american_scientific_journal-4887	88	6	−	−	PROPN
american_scientific_journal-4887	88	7	𝑟𝑟)(𝑎𝑎𝛾𝛾	𝑟𝑟)(𝑎𝑎𝛾𝛾	NUM
american_scientific_journal-4887	88	8	−	−	NOUN
american_scientific_journal-4887	88	9	𝑏𝑏𝛽𝛽	𝑏𝑏𝛽𝛽	ADJ
american_scientific_journal-4887	88	10	)	)	PUNCT
american_scientific_journal-4887	88	11	,	,	PUNCT
american_scientific_journal-4887	88	12	𝑎𝑎𝑏𝑏	𝑎𝑎𝑏𝑏	NOUN
american_scientific_journal-4887	88	13	+	+	CCONJ
american_scientific_journal-4887	88	14	(	(	PUNCT
american_scientific_journal-4887	88	15	1	1	NUM
american_scientific_journal-4887	88	16	−	−	NOUN
american_scientific_journal-4887	88	17	𝑟𝑟)(𝑎𝑎𝛿𝛿	𝑟𝑟)(𝑎𝑎𝛿𝛿	X
american_scientific_journal-4887	88	18	−	−	NOUN
american_scientific_journal-4887	88	19	𝑏𝑏𝛼𝛼	𝑏𝑏𝛼𝛼	ADJ
american_scientific_journal-4887	88	20	)	)	PUNCT
american_scientific_journal-4887	88	21	]	]	PUNCT
american_scientific_journal-4887	88	22	(	(	PUNCT
american_scientific_journal-4887	88	23	5	5	NUM
american_scientific_journal-4887	88	24	)	)	PUNCT
american_scientific_journal-4887	88	25	from	from	ADP
american_scientific_journal-4887	88	26	equation	equation	NOUN
american_scientific_journal-4887	88	27	(	(	PUNCT
american_scientific_journal-4887	88	28	5	5	NUM
american_scientific_journal-4887	88	29	)	)	PUNCT
american_scientific_journal-4887	88	30	and	and	CCONJ
american_scientific_journal-4887	88	31	(	(	PUNCT
american_scientific_journal-4887	88	32	3	3	X
american_scientific_journal-4887	88	33	)	)	PUNCT
american_scientific_journal-4887	88	34	we	we	PRON
american_scientific_journal-4887	88	35	have	have	VERB
american_scientific_journal-4887	88	36	:	:	PUNCT
american_scientific_journal-4887	88	37	𝜉𝜉	𝜉𝜉	PROPN
american_scientific_journal-4887	88	38	=	=	SYM
american_scientific_journal-4887	88	39	𝑎𝑎𝛾𝛾	𝑎𝑎𝛾𝛾	NOUN
american_scientific_journal-4887	88	40	−	−	NOUN
american_scientific_journal-4887	88	41	𝑏𝑏𝛽𝛽	𝑏𝑏𝛽𝛽	ADJ
american_scientific_journal-4887	88	42	𝜓𝜓	𝜓𝜓	X
american_scientific_journal-4887	88	43	=	=	PUNCT
american_scientific_journal-4887	88	44	𝑎𝑎𝛿𝛿	𝑎𝑎𝛿𝛿	PROPN
american_scientific_journal-4887	88	45	−	−	NOUN
american_scientific_journal-4887	88	46	𝑏𝑏𝛼𝛼	𝑏𝑏𝛼𝛼	ADJ
american_scientific_journal-4887	88	47	so	so	SCONJ
american_scientific_journal-4887	88	48	multiplication	multiplication	NOUN
american_scientific_journal-4887	88	49	𝑎𝑎	𝑎𝑎	PROPN
american_scientific_journal-4887	88	50	�	�	PROPN
american_scientific_journal-4887	88	51	positive	positive	ADJ
american_scientific_journal-4887	88	52	and	and	CCONJ
american_scientific_journal-4887	88	53	𝑏𝑏	𝑏𝑏	ADP
american_scientific_journal-4887	88	54	�	�	PROPN
american_scientific_journal-4887	88	55	negative	negative	NOUN
american_scientific_journal-4887	88	56	can	can	AUX
american_scientific_journal-4887	88	57	be	be	AUX
american_scientific_journal-4887	88	58	written	write	VERB
american_scientific_journal-4887	88	59	as	as	ADP
american_scientific_journal-4887	88	60	�	�	PROPN
american_scientific_journal-4887	88	61	̃	̃	PROPN
american_scientific_journal-4887	88	62	�	�	PROPN
american_scientific_journal-4887	88	63	𝑐	𝑐	NOUN
american_scientific_journal-4887	88	64	=	=	SYM
american_scientific_journal-4887	88	65	𝑎𝑎	𝑎𝑎	PROPN
american_scientific_journal-4887	88	66	�	�	PROPN
american_scientific_journal-4887	88	67	⊗	⊗	PROPN
american_scientific_journal-4887	88	68	𝑏𝑏	𝑏𝑏	NUM
american_scientific_journal-4887	88	69	�	�	PROPN
american_scientific_journal-4887	88	70	=	=	SYM
american_scientific_journal-4887	88	71	(	(	PUNCT
american_scientific_journal-4887	88	72	𝑎𝑎𝑏𝑏	𝑎𝑎𝑏𝑏	NOUN
american_scientific_journal-4887	88	73	,	,	PUNCT
american_scientific_journal-4887	88	74	𝑎𝑎𝛾𝛾	𝑎𝑎𝛾𝛾	NOUN
american_scientific_journal-4887	88	75	−	−	PROPN
american_scientific_journal-4887	88	76	𝑏𝑏𝛽𝛽	𝑏𝑏𝛽𝛽	ADJ
american_scientific_journal-4887	88	77	,	,	PUNCT
american_scientific_journal-4887	88	78	𝑎𝑎𝛿𝛿	𝑎𝑎𝛿𝛿	VERB
american_scientific_journal-4887	88	79	−	−	NOUN
american_scientific_journal-4887	88	80	𝑏𝑏𝛼𝛼	𝑏𝑏𝛼𝛼	ADJ
american_scientific_journal-4887	88	81	)	)	PUNCT
american_scientific_journal-4887	88	82	(	(	PUNCT
american_scientific_journal-4887	88	83	iii	iii	X
american_scientific_journal-4887	88	84	)	)	PUNCT
american_scientific_journal-4887	88	85	if	if	SCONJ
american_scientific_journal-4887	88	86	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-4887	88	87	�	�	PROPN
american_scientific_journal-4887	88	88	is	be	AUX
american_scientific_journal-4887	88	89	negative	negative	ADJ
american_scientific_journal-4887	88	90	and	and	CCONJ
american_scientific_journal-4887	88	91	𝑏𝑏	𝑏𝑏	NOUN
american_scientific_journal-4887	88	92	�	�	PROPN
american_scientific_journal-4887	88	93	is	be	AUX
american_scientific_journal-4887	88	94	positive	positive	ADJ
american_scientific_journal-4887	88	95	,	,	PUNCT
american_scientific_journal-4887	88	96	then	then	ADV
american_scientific_journal-4887	88	97	:	:	PUNCT
american_scientific_journal-4887	89	1	�	�	PROPN
american_scientific_journal-4887	89	2	𝑐𝑐	𝑐𝑐	PROPN
american_scientific_journal-4887	89	3	(	(	PUNCT
american_scientific_journal-4887	89	4	𝑟𝑟	𝑟𝑟	NOUN
american_scientific_journal-4887	89	5	)	)	PUNCT
american_scientific_journal-4887	89	6	=	=	SYM
american_scientific_journal-4887	89	7	𝑎𝑎(𝑟𝑟)𝑏𝑏(1	𝑎𝑎(𝑟𝑟)𝑏𝑏(1	PROPN
american_scientific_journal-4887	89	8	)	)	PUNCT
american_scientific_journal-4887	90	1	+	+	CCONJ
american_scientific_journal-4887	90	2	𝑎𝑎(1)𝑏𝑏(𝑟𝑟	𝑎𝑎(1)𝑏𝑏(𝑟𝑟	NOUN
american_scientific_journal-4887	90	3	)	)	PUNCT
american_scientific_journal-4887	90	4	−	−	ADP
american_scientific_journal-4887	90	5	𝑎𝑎(1)𝑏𝑏(1	𝑎𝑎(1)𝑏𝑏(1	PROPN
american_scientific_journal-4887	90	6	)	)	PUNCT
american_scientific_journal-4887	90	7	𝑐𝑐(𝑟𝑟	𝑐𝑐(𝑟𝑟	PROPN
american_scientific_journal-4887	90	8	)	)	PUNCT
american_scientific_journal-4887	90	9	=	=	SYM
american_scientific_journal-4887	90	10	𝑎𝑎(𝑟𝑟)𝑏𝑏(1	𝑎𝑎(𝑟𝑟)𝑏𝑏(1	PROPN
american_scientific_journal-4887	90	11	)	)	PUNCT
american_scientific_journal-4887	91	1	+	+	CCONJ
american_scientific_journal-4887	91	2	𝑎𝑎(1)𝑏𝑏(𝑟𝑟	𝑎𝑎(1)𝑏𝑏(𝑟𝑟	NOUN
american_scientific_journal-4887	91	3	)	)	PUNCT
american_scientific_journal-4887	91	4	−	−	PROPN
american_scientific_journal-4887	91	5	𝑎𝑎(1)𝑏𝑏(1	𝑎𝑎(1)𝑏𝑏(1	PROPN
american_scientific_journal-4887	91	6	)	)	PUNCT
american_scientific_journal-4887	91	7	(	(	PUNCT
american_scientific_journal-4887	91	8	6	6	NUM
american_scientific_journal-4887	91	9	)	)	PUNCT
american_scientific_journal-4887	91	10	from	from	ADP
american_scientific_journal-4887	91	11	equation	equation	NOUN
american_scientific_journal-4887	91	12	(	(	PUNCT
american_scientific_journal-4887	91	13	6	6	NUM
american_scientific_journal-4887	91	14	)	)	PUNCT
american_scientific_journal-4887	91	15	:	:	PUNCT
american_scientific_journal-4887	91	16	�	�	PROPN
american_scientific_journal-4887	91	17	𝑐𝑐(𝑟𝑟	𝑐𝑐(𝑟𝑟	NUM
american_scientific_journal-4887	91	18	)	)	PUNCT
american_scientific_journal-4887	91	19	,	,	PUNCT
american_scientific_journal-4887	91	20	𝑐𝑐(𝑟𝑟	𝑐𝑐(𝑟𝑟	NUM
american_scientific_journal-4887	91	21	)	)	PUNCT
american_scientific_journal-4887	91	22	�	�	PROPN
american_scientific_journal-4887	91	23	=	=	PUNCT
american_scientific_journal-4887	92	1	[	[	X
american_scientific_journal-4887	92	2	(	(	PUNCT
american_scientific_journal-4887	92	3	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-4887	92	4	−	−	PROPN
american_scientific_journal-4887	92	5	(	(	PUNCT
american_scientific_journal-4887	92	6	1	1	NUM
american_scientific_journal-4887	92	7	−	−	PROPN
american_scientific_journal-4887	92	8	𝑟𝑟)𝛼𝛼)𝑏𝑏	𝑟𝑟)𝛼𝛼)𝑏𝑏	PROPN
american_scientific_journal-4887	92	9	+	+	CCONJ
american_scientific_journal-4887	92	10	𝑎𝑎(𝑏𝑏	𝑎𝑎(𝑏𝑏	NOUN
american_scientific_journal-4887	93	1	+	+	CCONJ
american_scientific_journal-4887	93	2	(	(	PUNCT
american_scientific_journal-4887	93	3	1	1	NUM
american_scientific_journal-4887	93	4	−	−	NUM
american_scientific_journal-4887	93	5	𝑟𝑟)𝛿𝛿	𝑟𝑟)𝛿𝛿	NUM
american_scientific_journal-4887	93	6	)	)	PUNCT
american_scientific_journal-4887	93	7	−	−	PROPN
american_scientific_journal-4887	93	8	𝑎𝑎𝑏𝑏	𝑎𝑎𝑏𝑏	NOUN
american_scientific_journal-4887	93	9	,	,	PUNCT
american_scientific_journal-4887	93	10	(	(	PUNCT
american_scientific_journal-4887	93	11	𝑎𝑎	𝑎𝑎	VERB
american_scientific_journal-4887	93	12	+	+	CCONJ
american_scientific_journal-4887	93	13	(	(	PUNCT
american_scientific_journal-4887	93	14	1	1	NUM
american_scientific_journal-4887	93	15	−	−	PROPN
american_scientific_journal-4887	93	16	𝑟𝑟)𝛽𝛽)𝑏𝑏	𝑟𝑟)𝛽𝛽)𝑏𝑏	PROPN
american_scientific_journal-4887	93	17	+	+	NUM
american_scientific_journal-4887	93	18	𝑎𝑎(𝑏𝑏	𝑎𝑎(𝑏𝑏	NOUN
american_scientific_journal-4887	94	1	−	−	NOUN
american_scientific_journal-4887	94	2	(	(	PUNCT
american_scientific_journal-4887	94	3	1	1	NUM
american_scientific_journal-4887	94	4	−	−	NUM
american_scientific_journal-4887	94	5	𝑟𝑟)𝛾𝛾	𝑟𝑟)𝛾𝛾	ADP
american_scientific_journal-4887	94	6	)	)	PUNCT
american_scientific_journal-4887	95	1	−	−	PROPN
american_scientific_journal-4887	95	2	𝑎𝑎𝑏𝑏	𝑎𝑎𝑏𝑏	NOUN
american_scientific_journal-4887	95	3	]	]	PUNCT
american_scientific_journal-4887	95	4	we	we	PRON
american_scientific_journal-4887	95	5	have	have	VERB
american_scientific_journal-4887	95	6	�	�	PROPN
american_scientific_journal-4887	95	7	̃	̃	PROPN
american_scientific_journal-4887	95	8	�	�	PROPN
american_scientific_journal-4887	95	9	𝑐	𝑐	PROPN
american_scientific_journal-4887	95	10	=	=	SYM
american_scientific_journal-4887	95	11	�	�	PROPN
american_scientific_journal-4887	95	12	𝑐𝑐(𝑟𝑟	𝑐𝑐(𝑟𝑟	NUM
american_scientific_journal-4887	95	13	)	)	PUNCT
american_scientific_journal-4887	95	14	,	,	PUNCT
american_scientific_journal-4887	95	15	𝑐𝑐(𝑟𝑟	𝑐𝑐(𝑟𝑟	NUM
american_scientific_journal-4887	95	16	)	)	PUNCT
american_scientific_journal-4887	95	17	�	�	PROPN
american_scientific_journal-4887	95	18	=	=	PUNCT
american_scientific_journal-4887	96	1	[	[	X
american_scientific_journal-4887	96	2	𝑎𝑎𝑏𝑏	𝑎𝑎𝑏𝑏	NOUN
american_scientific_journal-4887	96	3	−	−	X
american_scientific_journal-4887	96	4	(	(	PUNCT
american_scientific_journal-4887	96	5	1	1	NUM
american_scientific_journal-4887	96	6	−	−	PROPN
american_scientific_journal-4887	96	7	𝑟𝑟)(−𝑎𝑎𝛿𝛿	𝑟𝑟)(−𝑎𝑎𝛿𝛿	PROPN
american_scientific_journal-4887	96	8	+	+	CCONJ
american_scientific_journal-4887	96	9	𝑏𝑏𝛼𝛼	𝑏𝑏𝛼𝛼	ADJ
american_scientific_journal-4887	96	10	)	)	PUNCT
american_scientific_journal-4887	96	11	,	,	PUNCT
american_scientific_journal-4887	96	12	𝑎𝑎𝑏𝑏	𝑎𝑎𝑏𝑏	NOUN
american_scientific_journal-4887	96	13	+	+	CCONJ
american_scientific_journal-4887	96	14	(	(	PUNCT
american_scientific_journal-4887	96	15	1	1	NUM
american_scientific_journal-4887	96	16	−	−	NUM
american_scientific_journal-4887	96	17	𝑟𝑟)(−𝑎𝑎𝛾𝛾	𝑟𝑟)(−𝑎𝑎𝛾𝛾	PROPN
american_scientific_journal-4887	96	18	+	+	CCONJ
american_scientific_journal-4887	96	19	𝑏𝑏𝛽𝛽	𝑏𝑏𝛽𝛽	ADJ
american_scientific_journal-4887	96	20	)	)	PUNCT
american_scientific_journal-4887	96	21	]	]	PUNCT
american_scientific_journal-4887	96	22	(	(	PUNCT
american_scientific_journal-4887	96	23	7	7	NUM
american_scientific_journal-4887	96	24	)	)	PUNCT
american_scientific_journal-4887	96	25	from	from	ADP
american_scientific_journal-4887	96	26	equation	equation	NOUN
american_scientific_journal-4887	96	27	(	(	PUNCT
american_scientific_journal-4887	96	28	7	7	NUM
american_scientific_journal-4887	96	29	)	)	PUNCT
american_scientific_journal-4887	96	30	and	and	CCONJ
american_scientific_journal-4887	96	31	(	(	PUNCT
american_scientific_journal-4887	96	32	3	3	X
american_scientific_journal-4887	96	33	)	)	PUNCT
american_scientific_journal-4887	96	34	we	we	PRON
american_scientific_journal-4887	96	35	have	have	VERB
american_scientific_journal-4887	96	36	:	:	PUNCT
american_scientific_journal-4887	96	37	𝜉𝜉	𝜉𝜉	PROPN
american_scientific_journal-4887	96	38	=	=	PUNCT
american_scientific_journal-4887	96	39	−𝑎𝑎𝛿𝛿	−𝑎𝑎𝛿𝛿	PUNCT
american_scientific_journal-4887	97	1	+	+	NUM
american_scientific_journal-4887	97	2	𝑏𝑏𝛼𝛼	𝑏𝑏𝛼𝛼	ADJ
american_scientific_journal-4887	97	3	𝜓𝜓	𝜓𝜓	X
american_scientific_journal-4887	97	4	=	=	X
american_scientific_journal-4887	97	5	−𝑎𝑎𝛾𝛾	−𝑎𝑎𝛾𝛾	PROPN
american_scientific_journal-4887	97	6	+	+	CCONJ
american_scientific_journal-4887	97	7	𝑏𝑏𝛽𝛽	𝑏𝑏𝛽𝛽	ADJ
american_scientific_journal-4887	97	8	so	so	ADV
american_scientific_journal-4887	97	9	multiplication	multiplication	NOUN
american_scientific_journal-4887	97	10	𝑎𝑎	𝑎𝑎	PROPN
american_scientific_journal-4887	97	11	�	�	PROPN
american_scientific_journal-4887	97	12	negative	negative	ADJ
american_scientific_journal-4887	97	13	and	and	CCONJ
american_scientific_journal-4887	97	14	𝑏𝑏	𝑏𝑏	ADP
american_scientific_journal-4887	97	15	�	�	PROPN
american_scientific_journal-4887	97	16	positive	positive	ADJ
american_scientific_journal-4887	97	17	can	can	AUX
american_scientific_journal-4887	97	18	be	be	AUX
american_scientific_journal-4887	97	19	written	write	VERB
american_scientific_journal-4887	97	20	as	as	ADP
american_scientific_journal-4887	97	21	�	�	PROPN
american_scientific_journal-4887	97	22	̃	̃	PROPN
american_scientific_journal-4887	97	23	�	�	PROPN
american_scientific_journal-4887	97	24	𝑐	𝑐	NOUN
american_scientific_journal-4887	97	25	=	=	SYM
american_scientific_journal-4887	97	26	𝑎𝑎	𝑎𝑎	PROPN
american_scientific_journal-4887	97	27	�	�	PROPN
american_scientific_journal-4887	97	28	⊗	⊗	PROPN
american_scientific_journal-4887	97	29	𝑏𝑏	𝑏𝑏	NUM
american_scientific_journal-4887	97	30	�	�	PROPN
american_scientific_journal-4887	97	31	=	=	SYM
american_scientific_journal-4887	97	32	(	(	PUNCT
american_scientific_journal-4887	97	33	𝑎𝑎𝑏𝑏,−𝑎𝑎𝛿𝛿	𝑎𝑎𝑏𝑏,−𝑎𝑎𝛿𝛿	PROPN
american_scientific_journal-4887	97	34	+	+	CCONJ
american_scientific_journal-4887	97	35	𝑏𝑏𝛼𝛼,−𝑎𝑎𝛾𝛾	𝑏𝑏𝛼𝛼,−𝑎𝑎𝛾𝛾	ADJ
american_scientific_journal-4887	97	36	+	+	CCONJ
american_scientific_journal-4887	97	37	𝑏𝑏𝛽𝛽	𝑏𝑏𝛽𝛽	ADJ
american_scientific_journal-4887	97	38	)	)	PUNCT
american_scientific_journal-4887	97	39	(	(	PUNCT
american_scientific_journal-4887	97	40	iv	iv	X
american_scientific_journal-4887	97	41	)	)	PUNCT
american_scientific_journal-4887	97	42	if	if	SCONJ
american_scientific_journal-4887	97	43	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-4887	97	44	�	�	PROPN
american_scientific_journal-4887	97	45	is	be	AUX
american_scientific_journal-4887	97	46	negative	negative	ADJ
american_scientific_journal-4887	97	47	and	and	CCONJ
american_scientific_journal-4887	97	48	𝑏𝑏	𝑏𝑏	NOUN
american_scientific_journal-4887	97	49	�	�	PROPN
american_scientific_journal-4887	97	50	is	be	AUX
american_scientific_journal-4887	97	51	negative	negative	ADJ
american_scientific_journal-4887	97	52	,	,	PUNCT
american_scientific_journal-4887	97	53	then	then	ADV
american_scientific_journal-4887	97	54	:	:	PUNCT
american_scientific_journal-4887	97	55	�	�	PROPN
american_scientific_journal-4887	97	56	𝑐𝑐	𝑐𝑐	PROPN
american_scientific_journal-4887	97	57	(	(	PUNCT
american_scientific_journal-4887	97	58	𝑟𝑟	𝑟𝑟	NOUN
american_scientific_journal-4887	97	59	)	)	PUNCT
american_scientific_journal-4887	97	60	=	=	SYM
american_scientific_journal-4887	97	61	𝑎𝑎(𝑟𝑟)𝑏𝑏(1	𝑎𝑎(𝑟𝑟)𝑏𝑏(1	PROPN
american_scientific_journal-4887	97	62	)	)	PUNCT
american_scientific_journal-4887	98	1	+	+	CCONJ
american_scientific_journal-4887	98	2	𝑎𝑎(1)𝑏𝑏(𝑟𝑟	𝑎𝑎(1)𝑏𝑏(𝑟𝑟	NOUN
american_scientific_journal-4887	98	3	)	)	PUNCT
american_scientific_journal-4887	98	4	−	−	ADP
american_scientific_journal-4887	98	5	𝑎𝑎(1)𝑏𝑏(1	𝑎𝑎(1)𝑏𝑏(1	PROPN
american_scientific_journal-4887	98	6	)	)	PUNCT
american_scientific_journal-4887	98	7	𝑐𝑐(𝑟𝑟	𝑐𝑐(𝑟𝑟	PROPN
american_scientific_journal-4887	98	8	)	)	PUNCT
american_scientific_journal-4887	98	9	=	=	SYM
american_scientific_journal-4887	98	10	𝑎𝑎(𝑟𝑟)𝑏𝑏(1	𝑎𝑎(𝑟𝑟)𝑏𝑏(1	PROPN
american_scientific_journal-4887	98	11	)	)	PUNCT
american_scientific_journal-4887	99	1	+	+	CCONJ
american_scientific_journal-4887	99	2	𝑎𝑎(1)𝑏𝑏(𝑟𝑟	𝑎𝑎(1)𝑏𝑏(𝑟𝑟	NOUN
american_scientific_journal-4887	99	3	)	)	PUNCT
american_scientific_journal-4887	99	4	−	−	PROPN
american_scientific_journal-4887	99	5	𝑎𝑎(1)𝑏𝑏(1	𝑎𝑎(1)𝑏𝑏(1	PROPN
american_scientific_journal-4887	99	6	)	)	PUNCT
american_scientific_journal-4887	99	7	(	(	PUNCT
american_scientific_journal-4887	99	8	8)	8)	NUM
american_scientific_journal-4887	99	9	from	from	ADP
american_scientific_journal-4887	99	10	equation	equation	NOUN
american_scientific_journal-4887	99	11	(	(	PUNCT
american_scientific_journal-4887	99	12	8)	8)	NUM
american_scientific_journal-4887	99	13	:	:	PUNCT
american_scientific_journal-4887	99	14	�	�	PROPN
american_scientific_journal-4887	99	15	𝑐𝑐(𝑟𝑟	𝑐𝑐(𝑟𝑟	NOUN
american_scientific_journal-4887	99	16	)	)	PUNCT
american_scientific_journal-4887	99	17	,	,	PUNCT
american_scientific_journal-4887	99	18	𝑐𝑐(𝑟𝑟	𝑐𝑐(𝑟𝑟	NUM
american_scientific_journal-4887	99	19	)	)	PUNCT
american_scientific_journal-4887	99	20	�	�	PROPN
american_scientific_journal-4887	99	21	=	=	PUNCT
american_scientific_journal-4887	100	1	[	[	X
american_scientific_journal-4887	100	2	(	(	PUNCT
american_scientific_journal-4887	100	3	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-4887	100	4	+	+	CCONJ
american_scientific_journal-4887	100	5	(	(	PUNCT
american_scientific_journal-4887	100	6	1	1	NUM
american_scientific_journal-4887	100	7	−	−	PROPN
american_scientific_journal-4887	100	8	𝑟𝑟)𝛽𝛽)𝑏𝑏	𝑟𝑟)𝛽𝛽)𝑏𝑏	PROPN
american_scientific_journal-4887	100	9	+	+	NUM
american_scientific_journal-4887	100	10	𝑎𝑎(𝑏𝑏	𝑎𝑎(𝑏𝑏	NOUN
american_scientific_journal-4887	101	1	+	+	CCONJ
american_scientific_journal-4887	101	2	(	(	PUNCT
american_scientific_journal-4887	101	3	1	1	NUM
american_scientific_journal-4887	101	4	−	−	NUM
american_scientific_journal-4887	101	5	𝑟𝑟)𝛿𝛿	𝑟𝑟)𝛿𝛿	NUM
american_scientific_journal-4887	101	6	)	)	PUNCT
american_scientific_journal-4887	101	7	−	−	PROPN
american_scientific_journal-4887	101	8	𝑎𝑎𝑏𝑏	𝑎𝑎𝑏𝑏	NOUN
american_scientific_journal-4887	101	9	,	,	PUNCT
american_scientific_journal-4887	101	10	(	(	PUNCT
american_scientific_journal-4887	101	11	𝑎𝑎	𝑎𝑎	VERB
american_scientific_journal-4887	101	12	−	−	PROPN
american_scientific_journal-4887	101	13	(	(	PUNCT
american_scientific_journal-4887	101	14	1	1	NUM
american_scientific_journal-4887	101	15	−	−	PROPN
american_scientific_journal-4887	101	16	𝑟𝑟)𝛼𝛼)𝑏𝑏	𝑟𝑟)𝛼𝛼)𝑏𝑏	PROPN
american_scientific_journal-4887	101	17	+	+	CCONJ
american_scientific_journal-4887	101	18	𝑎𝑎(𝑏𝑏	𝑎𝑎(𝑏𝑏	PROPN
american_scientific_journal-4887	101	19	−	−	NOUN
american_scientific_journal-4887	101	20	(	(	PUNCT
american_scientific_journal-4887	101	21	1	1	NUM
american_scientific_journal-4887	101	22	−	−	NUM
american_scientific_journal-4887	102	1	𝑟𝑟)𝛾𝛾	𝑟𝑟)𝛾𝛾	ADP
american_scientific_journal-4887	102	2	)	)	PUNCT
american_scientific_journal-4887	102	3	−	−	PROPN
american_scientific_journal-4887	102	4	𝑎𝑎𝑏𝑏	𝑎𝑎𝑏𝑏	NOUN
american_scientific_journal-4887	102	5	]	]	PUNCT
american_scientific_journal-4887	102	6	we	we	PRON
american_scientific_journal-4887	102	7	have	have	VERB
american_scientific_journal-4887	102	8	�	�	PROPN
american_scientific_journal-4887	102	9	̃	̃	PROPN
american_scientific_journal-4887	102	10	�	�	PROPN
american_scientific_journal-4887	102	11	𝑐	𝑐	PROPN
american_scientific_journal-4887	102	12	=	=	SYM
american_scientific_journal-4887	102	13	�	�	PROPN
american_scientific_journal-4887	102	14	𝑐𝑐(𝑟𝑟	𝑐𝑐(𝑟𝑟	NUM
american_scientific_journal-4887	102	15	)	)	PUNCT
american_scientific_journal-4887	102	16	,	,	PUNCT
american_scientific_journal-4887	102	17	𝑐𝑐(𝑟𝑟	𝑐𝑐(𝑟𝑟	NUM
american_scientific_journal-4887	102	18	)	)	PUNCT
american_scientific_journal-4887	102	19	�	�	PROPN
american_scientific_journal-4887	103	1	=	=	PUNCT
american_scientific_journal-4887	104	1	[	[	X
american_scientific_journal-4887	104	2	𝑎𝑎𝑏𝑏	𝑎𝑎𝑏𝑏	NOUN
american_scientific_journal-4887	104	3	−	−	X
american_scientific_journal-4887	104	4	(	(	PUNCT
american_scientific_journal-4887	104	5	1	1	NUM
american_scientific_journal-4887	104	6	−	−	NOUN
american_scientific_journal-4887	104	7	𝑟𝑟)(−𝑎𝑎𝛿𝛿	𝑟𝑟)(−𝑎𝑎𝛿𝛿	NUM
american_scientific_journal-4887	104	8	−	−	PROPN
american_scientific_journal-4887	104	9	𝑏𝑏𝛽𝛽	𝑏𝑏𝛽𝛽	ADJ
american_scientific_journal-4887	104	10	)	)	PUNCT
american_scientific_journal-4887	104	11	,	,	PUNCT
american_scientific_journal-4887	104	12	𝑎𝑎𝑏𝑏	𝑎𝑎𝑏𝑏	NOUN
american_scientific_journal-4887	104	13	+	+	CCONJ
american_scientific_journal-4887	104	14	(	(	PUNCT
american_scientific_journal-4887	104	15	1	1	NUM
american_scientific_journal-4887	104	16	−	−	NUM
american_scientific_journal-4887	104	17	𝑟𝑟)(−𝑎𝑎𝛾𝛾	𝑟𝑟)(−𝑎𝑎𝛾𝛾	PROPN
american_scientific_journal-4887	104	18	−	−	NOUN
american_scientific_journal-4887	104	19	𝑏𝑏𝛼𝛼	𝑏𝑏𝛼𝛼	ADJ
american_scientific_journal-4887	104	20	)	)	PUNCT
american_scientific_journal-4887	104	21	]	]	PUNCT
american_scientific_journal-4887	104	22	(	(	PUNCT
american_scientific_journal-4887	104	23	9	9	NUM
american_scientific_journal-4887	104	24	)	)	PUNCT
american_scientific_journal-4887	104	25	from	from	ADP
american_scientific_journal-4887	104	26	equation	equation	NOUN
american_scientific_journal-4887	104	27	(	(	PUNCT
american_scientific_journal-4887	104	28	9	9	NUM
american_scientific_journal-4887	104	29	)	)	PUNCT
american_scientific_journal-4887	104	30	and	and	CCONJ
american_scientific_journal-4887	104	31	(	(	PUNCT
american_scientific_journal-4887	104	32	3	3	X
american_scientific_journal-4887	104	33	)	)	PUNCT
american_scientific_journal-4887	104	34	we	we	PRON
american_scientific_journal-4887	104	35	have	have	VERB
american_scientific_journal-4887	104	36	:	:	PUNCT
american_scientific_journal-4887	104	37	𝜉𝜉	𝜉𝜉	PROPN
american_scientific_journal-4887	104	38	=	=	SYM
american_scientific_journal-4887	104	39	−𝑎𝑎𝛿𝛿	−𝑎𝑎𝛿𝛿	PUNCT
american_scientific_journal-4887	105	1	−	−	PROPN
american_scientific_journal-4887	105	2	𝑏𝑏𝛽𝛽	𝑏𝑏𝛽𝛽	ADJ
american_scientific_journal-4887	105	3	𝜓𝜓	𝜓𝜓	X
american_scientific_journal-4887	105	4	=	=	PUNCT
american_scientific_journal-4887	105	5	−𝑎𝑎𝛾𝛾	−𝑎𝑎𝛾𝛾	NOUN
american_scientific_journal-4887	105	6	−	−	ADV
american_scientific_journal-4887	105	7	𝑏𝑏𝛼𝛼	𝑏𝑏𝛼𝛼	ADJ
american_scientific_journal-4887	105	8	so	so	CCONJ
american_scientific_journal-4887	105	9	multiplication	multiplication	NOUN
american_scientific_journal-4887	105	10	𝑎𝑎	𝑎𝑎	PROPN
american_scientific_journal-4887	105	11	�	�	PROPN
american_scientific_journal-4887	105	12	negative	negative	ADJ
american_scientific_journal-4887	105	13	and	and	CCONJ
american_scientific_journal-4887	105	14	𝑏𝑏	𝑏𝑏	ADP
american_scientific_journal-4887	105	15	�	�	PROPN
american_scientific_journal-4887	105	16	negative	negative	NOUN
american_scientific_journal-4887	105	17	can	can	AUX
american_scientific_journal-4887	105	18	be	be	AUX
american_scientific_journal-4887	105	19	written	write	VERB
american_scientific_journal-4887	105	20	as	as	ADP
american_scientific_journal-4887	105	21	�	�	PROPN
american_scientific_journal-4887	105	22	̃	̃	PROPN
american_scientific_journal-4887	105	23	�	�	PROPN
american_scientific_journal-4887	105	24	𝑐	𝑐	NOUN
american_scientific_journal-4887	105	25	=	=	SYM
american_scientific_journal-4887	105	26	𝑎𝑎	𝑎𝑎	PROPN
american_scientific_journal-4887	105	27	�	�	PROPN
american_scientific_journal-4887	105	28	⊗	⊗	PROPN
american_scientific_journal-4887	105	29	𝑏𝑏	𝑏𝑏	NUM
american_scientific_journal-4887	105	30	�	�	PROPN
american_scientific_journal-4887	105	31	=	=	SYM
american_scientific_journal-4887	105	32	(	(	PUNCT
american_scientific_journal-4887	105	33	𝑎𝑎𝑏𝑏,−(𝑎𝑎𝛿𝛿	𝑎𝑎𝑏𝑏,−(𝑎𝑎𝛿𝛿	INTJ
american_scientific_journal-4887	105	34	+	+	CCONJ
american_scientific_journal-4887	105	35	𝑏𝑏𝛽𝛽),−(𝑎𝑎𝛾𝛾	𝑏𝑏𝛽𝛽),−(𝑎𝑎𝛾𝛾	PROPN
american_scientific_journal-4887	105	36	+	+	CCONJ
american_scientific_journal-4887	105	37	𝑏𝑏𝛼𝛼	𝑏𝑏𝛼𝛼	ADJ
american_scientific_journal-4887	105	38	)	)	PUNCT
american_scientific_journal-4887	105	39	e.	e.	PROPN
american_scientific_journal-4887	105	40	inverse	inverse	VERB
american_scientific_journal-4887	105	41	the	the	DET
american_scientific_journal-4887	105	42	identity	identity	NOUN
american_scientific_journal-4887	105	43	element	element	NOUN
american_scientific_journal-4887	105	44	for	for	ADP
american_scientific_journal-4887	105	45	triangular	triangular	NOUN
american_scientific_journal-4887	105	46	fuzzy	fuzzy	ADJ
american_scientific_journal-4887	105	47	number	number	NOUN
american_scientific_journal-4887	105	48	is	be	AUX
american_scientific_journal-4887	105	49	:	:	PUNCT
american_scientific_journal-4887	105	50	𝐼𝐼	𝐼𝐼	PROPN
american_scientific_journal-4887	105	51	=	=	SYM
american_scientific_journal-4887	105	52	(	(	PUNCT
american_scientific_journal-4887	105	53	1,0,0	1,0,0	NUM
american_scientific_journal-4887	105	54	)	)	PUNCT
american_scientific_journal-4887	105	55	where	where	SCONJ
american_scientific_journal-4887	105	56	𝐼𝐼	𝐼𝐼	PROPN
american_scientific_journal-4887	105	57	=	=	SYM
american_scientific_journal-4887	105	58	(	(	PUNCT
american_scientific_journal-4887	105	59	1,0,0	1,0,0	NUM
american_scientific_journal-4887	105	60	)	)	PUNCT
american_scientific_journal-4887	105	61	is	be	AUX
american_scientific_journal-4887	105	62	positive	positive	ADJ
american_scientific_journal-4887	105	63	.	.	PUNCT
american_scientific_journal-4887	106	1	let	let	VERB
american_scientific_journal-4887	106	2	two	two	NUM
american_scientific_journal-4887	106	3	fuzzy	fuzzy	ADJ
american_scientific_journal-4887	106	4	number	number	NOUN
american_scientific_journal-4887	106	5	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-4887	106	6	�	�	PROPN
american_scientific_journal-4887	106	7	=	=	SYM
american_scientific_journal-4887	106	8	(	(	PUNCT
american_scientific_journal-4887	106	9	𝑎𝑎,𝛼𝛼,𝛽𝛽	𝑎𝑎,𝛼𝛼,𝛽𝛽	NOUN
american_scientific_journal-4887	106	10	)	)	PUNCT
american_scientific_journal-4887	106	11	and	and	CCONJ
american_scientific_journal-4887	106	12	𝑏𝑏	𝑏𝑏	ADP
american_scientific_journal-4887	106	13	�	�	NOUN
american_scientific_journal-4887	106	14	=	=	SYM
american_scientific_journal-4887	106	15	(	(	PUNCT
american_scientific_journal-4887	106	16	𝑏𝑏	𝑏𝑏	PROPN
american_scientific_journal-4887	106	17	,	,	PUNCT
american_scientific_journal-4887	106	18	𝛾𝛾	𝛾𝛾	PROPN
american_scientific_journal-4887	106	19	,	,	PUNCT
american_scientific_journal-4887	106	20	𝛿𝛿	𝛿𝛿	PROPN
american_scientific_journal-4887	106	21	)	)	PUNCT
american_scientific_journal-4887	106	22	have	have	AUX
american_scientific_journal-4887	106	23	inverse	inverse	NOUN
american_scientific_journal-4887	106	24	:	:	PUNCT
american_scientific_journal-4887	106	25	𝑏𝑏	𝑏𝑏	NUM
american_scientific_journal-4887	106	26	�	�	PROPN
american_scientific_journal-4887	106	27	=	=	SYM
american_scientific_journal-4887	106	28	1	1	NUM
american_scientific_journal-4887	106	29	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-4887	106	30	�	�	PROPN
american_scientific_journal-4887	106	31	will	will	AUX
american_scientific_journal-4887	106	32	be	be	AUX
american_scientific_journal-4887	106	33	indicated	indicate	VERB
american_scientific_journal-4887	106	34	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-4887	106	35	�	�	PROPN
american_scientific_journal-4887	106	36	⊗	⊗	PROPN
american_scientific_journal-4887	106	37	𝑏𝑏	𝑏𝑏	NUM
american_scientific_journal-4887	106	38	�	�	PROPN
american_scientific_journal-4887	106	39	=	=	SYM
american_scientific_journal-4887	106	40	(	(	PUNCT
american_scientific_journal-4887	106	41	1,0,0	1,0,0	NUM
american_scientific_journal-4887	106	42	)	)	PUNCT
american_scientific_journal-4887	106	43	.	.	PUNCT
american_scientific_journal-4887	107	1	fuzzy	fuzzy	ADJ
american_scientific_journal-4887	107	2	number	number	NOUN
american_scientific_journal-4887	107	3	𝑎𝑎	𝑎𝑎	PROPN
american_scientific_journal-4887	107	4	�	�	PROPN
american_scientific_journal-4887	107	5	=	=	SYM
american_scientific_journal-4887	107	6	(	(	PUNCT
american_scientific_journal-4887	107	7	𝑎𝑎,𝛼𝛼,𝛽𝛽	𝑎𝑎,𝛼𝛼,𝛽𝛽	PROPN
american_scientific_journal-4887	107	8	)	)	PUNCT
american_scientific_journal-4887	107	9	the	the	DET
american_scientific_journal-4887	107	10	condition	condition	NOUN
american_scientific_journal-4887	107	11	for	for	ADP
american_scientific_journal-4887	107	12	having	have	VERB
american_scientific_journal-4887	107	13	inverse	inverse	NOUN
american_scientific_journal-4887	107	14	is	be	AUX
american_scientific_journal-4887	107	15	𝑎𝑎	𝑎𝑎	VERB
american_scientific_journal-4887	107	16	≠	≠	PROPN
american_scientific_journal-4887	107	17	0	0	NUM
american_scientific_journal-4887	107	18	.	.	PUNCT
american_scientific_journal-4887	108	1	therefore	therefore	ADV
american_scientific_journal-4887	108	2	,	,	PUNCT
american_scientific_journal-4887	108	3	inverse	inverse	NOUN
american_scientific_journal-4887	108	4	for	for	ADP
american_scientific_journal-4887	108	5	triangular	triangular	NOUN
american_scientific_journal-4887	108	6	fuzzy	fuzzy	ADJ
american_scientific_journal-4887	108	7	number	number	NOUN
american_scientific_journal-4887	108	8	consist	consist	NOUN
american_scientific_journal-4887	108	9	of	of	ADP
american_scientific_journal-4887	108	10	two	two	NUM
american_scientific_journal-4887	108	11	cases	case	NOUN
american_scientific_journal-4887	108	12	,	,	PUNCT
american_scientific_journal-4887	108	13	as	as	SCONJ
american_scientific_journal-4887	108	14	follows	follow	VERB
american_scientific_journal-4887	108	15	:	:	PUNCT
american_scientific_journal-4887	108	16	(	(	PUNCT
american_scientific_journal-4887	108	17	i	i	NOUN
american_scientific_journal-4887	108	18	)	)	PUNCT
american_scientific_journal-4887	108	19	if	if	SCONJ
american_scientific_journal-4887	108	20	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-4887	108	21	�	�	PROPN
american_scientific_journal-4887	108	22	>	>	SYM
american_scientific_journal-4887	108	23	0	0	NUM
american_scientific_journal-4887	108	24	and	and	CCONJ
american_scientific_journal-4887	108	25	𝑏𝑏	𝑏𝑏	ADP
american_scientific_journal-4887	108	26	�	�	PROPN
american_scientific_journal-4887	108	27	>	>	X
american_scientific_journal-4887	108	28	0	0	NUM
american_scientific_journal-4887	108	29	,	,	PUNCT
american_scientific_journal-4887	108	30	𝑎𝑎	𝑎𝑎	PROPN
american_scientific_journal-4887	108	31	�	�	PROPN
american_scientific_journal-4887	108	32	⊗	⊗	PROPN
american_scientific_journal-4887	108	33	𝑏𝑏	𝑏𝑏	NUM
american_scientific_journal-4887	108	34	�	�	PROPN
american_scientific_journal-4887	108	35	=	=	SYM
american_scientific_journal-4887	108	36	(	(	PUNCT
american_scientific_journal-4887	108	37	𝑎𝑎,𝛼𝛼,𝛽𝛽	𝑎𝑎,𝛼𝛼,𝛽𝛽	PROPN
american_scientific_journal-4887	108	38	)	)	PUNCT
american_scientific_journal-4887	108	39	⊗	⊗	PROPN
american_scientific_journal-4887	108	40	(	(	PUNCT
american_scientific_journal-4887	108	41	𝑏𝑏	𝑏𝑏	PROPN
american_scientific_journal-4887	108	42	,	,	PUNCT
american_scientific_journal-4887	108	43	𝛾𝛾	𝛾𝛾	PROPN
american_scientific_journal-4887	108	44	,	,	PUNCT
american_scientific_journal-4887	108	45	𝛿𝛿	𝛿𝛿	PROPN
american_scientific_journal-4887	108	46	)	)	PUNCT
american_scientific_journal-4887	108	47	=	=	SYM
american_scientific_journal-4887	108	48	(	(	PUNCT
american_scientific_journal-4887	108	49	𝑎𝑎𝑏𝑏	𝑎𝑎𝑏𝑏	NOUN
american_scientific_journal-4887	108	50	,	,	PUNCT
american_scientific_journal-4887	108	51	𝑎𝑎𝛾𝛾	𝑎𝑎𝛾𝛾	NOUN
american_scientific_journal-4887	108	52	+	+	CCONJ
american_scientific_journal-4887	108	53	𝑏𝑏𝛼𝛼	𝑏𝑏𝛼𝛼	ADJ
american_scientific_journal-4887	108	54	,	,	PUNCT
american_scientific_journal-4887	108	55	𝑎𝑎𝛿𝛿	𝑎𝑎𝛿𝛿	ADJ
american_scientific_journal-4887	108	56	+	+	CCONJ
american_scientific_journal-4887	108	57	𝑏𝑏𝛽𝛽	𝑏𝑏𝛽𝛽	ADJ
american_scientific_journal-4887	108	58	)	)	PUNCT
american_scientific_journal-4887	108	59	=	=	PUNCT
american_scientific_journal-4887	108	60	(	(	PUNCT
american_scientific_journal-4887	108	61	1,0,0	1,0,0	NUM
american_scientific_journal-4887	108	62	)	)	PUNCT
american_scientific_journal-4887	108	63	(	(	PUNCT
american_scientific_journal-4887	108	64	ii	ii	NOUN
american_scientific_journal-4887	108	65	)	)	PUNCT
american_scientific_journal-4887	108	66	if	if	SCONJ
american_scientific_journal-4887	108	67	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-4887	108	68	�	�	PROPN
american_scientific_journal-4887	108	69	<	<	X
american_scientific_journal-4887	108	70	0	0	NUM
american_scientific_journal-4887	108	71	and	and	CCONJ
american_scientific_journal-4887	108	72	𝑏𝑏	𝑏𝑏	ADP
american_scientific_journal-4887	108	73	�	�	PROPN
american_scientific_journal-4887	108	74	<	<	X
american_scientific_journal-4887	108	75	0	0	NUM
american_scientific_journal-4887	108	76	,	,	PUNCT
american_scientific_journal-4887	108	77	𝑎𝑎	𝑎𝑎	PROPN
american_scientific_journal-4887	108	78	�	�	PROPN
american_scientific_journal-4887	108	79	⊗	⊗	PROPN
american_scientific_journal-4887	108	80	𝑏𝑏	𝑏𝑏	NUM
american_scientific_journal-4887	108	81	�	�	PROPN
american_scientific_journal-4887	108	82	=	=	SYM
american_scientific_journal-4887	108	83	(	(	PUNCT
american_scientific_journal-4887	108	84	𝑎𝑎,𝛼𝛼,𝛽𝛽	𝑎𝑎,𝛼𝛼,𝛽𝛽	PROPN
american_scientific_journal-4887	108	85	)	)	PUNCT
american_scientific_journal-4887	108	86	⊗	⊗	PROPN
american_scientific_journal-4887	108	87	(	(	PUNCT
american_scientific_journal-4887	108	88	𝑏𝑏	𝑏𝑏	PROPN
american_scientific_journal-4887	108	89	,	,	PUNCT
american_scientific_journal-4887	108	90	𝛾𝛾	𝛾𝛾	PROPN
american_scientific_journal-4887	108	91	,	,	PUNCT
american_scientific_journal-4887	108	92	𝛿𝛿	𝛿𝛿	PROPN
american_scientific_journal-4887	108	93	)	)	PUNCT
american_scientific_journal-4887	108	94	=	=	PUNCT
american_scientific_journal-4887	108	95	(	(	PUNCT
american_scientific_journal-4887	108	96	𝑎𝑎𝑏𝑏,−(𝑎𝑎𝛿𝛿	𝑎𝑎𝑏𝑏,−(𝑎𝑎𝛿𝛿	INTJ
american_scientific_journal-4887	108	97	+	+	CCONJ
american_scientific_journal-4887	108	98	𝑏𝑏𝛽𝛽),−(𝑎𝑎𝛾𝛾	𝑏𝑏𝛽𝛽),−(𝑎𝑎𝛾𝛾	PROPN
american_scientific_journal-4887	108	99	+	+	CCONJ
american_scientific_journal-4887	108	100	𝑏𝑏𝛼𝛼	𝑏𝑏𝛼𝛼	ADJ
american_scientific_journal-4887	108	101	)	)	PUNCT
american_scientific_journal-4887	108	102	=	=	SYM
american_scientific_journal-4887	108	103	(	(	PUNCT
american_scientific_journal-4887	108	104	1,0,0	1,0,0	NUM
american_scientific_journal-4887	108	105	)	)	PUNCT
american_scientific_journal-4887	108	106	so	so	SCONJ
american_scientific_journal-4887	108	107	the	the	DET
american_scientific_journal-4887	108	108	inverse	inverse	NOUN
american_scientific_journal-4887	108	109	for	for	ADP
american_scientific_journal-4887	108	110	triangular	triangular	NOUN
american_scientific_journal-4887	108	111	fuzzy	fuzzy	ADJ
american_scientific_journal-4887	108	112	number	number	NOUN
american_scientific_journal-4887	108	113	is	be	AUX
american_scientific_journal-4887	108	114	:	:	PUNCT
american_scientific_journal-4887	108	115	𝑏𝑏	𝑏𝑏	NUM
american_scientific_journal-4887	108	116	�	�	PROPN
american_scientific_journal-4887	108	117	=	=	SYM
american_scientific_journal-4887	108	118	1	1	NUM
american_scientific_journal-4887	108	119	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-4887	108	120	�	�	PROPN
american_scientific_journal-4887	108	121	=	=	SYM
american_scientific_journal-4887	108	122	�	�	PROPN
american_scientific_journal-4887	108	123	1	1	NUM
american_scientific_journal-4887	108	124	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-4887	108	125	,	,	PUNCT
american_scientific_journal-4887	108	126	𝛽𝛽	𝛽𝛽	ADP
american_scientific_journal-4887	108	127	𝑎𝑎2	𝑎𝑎2	X
american_scientific_journal-4887	108	128	,	,	PUNCT
american_scientific_journal-4887	108	129	𝛼𝛼	𝛼𝛼	ADP
american_scientific_journal-4887	108	130	𝑎𝑎2	𝑎𝑎2	VERB
american_scientific_journal-4887	108	131	�	�	PROPN
american_scientific_journal-4887	108	132	american	american	PROPN
american_scientific_journal-4887	108	133	scientific	scientific	PROPN
american_scientific_journal-4887	108	134	research	research	PROPN
american_scientific_journal-4887	108	135	journal	journal	NOUN
american_scientific_journal-4887	108	136	for	for	ADP
american_scientific_journal-4887	108	137	engineering	engineering	NOUN
american_scientific_journal-4887	108	138	,	,	PUNCT
american_scientific_journal-4887	108	139	technology	technology	NOUN
american_scientific_journal-4887	108	140	,	,	PUNCT
american_scientific_journal-4887	108	141	and	and	CCONJ
american_scientific_journal-4887	108	142	sciences	science	NOUN
american_scientific_journal-4887	108	143	(	(	PUNCT
american_scientific_journal-4887	108	144	asrjets	asrjet	NOUN
american_scientific_journal-4887	108	145	)	)	PUNCT
american_scientific_journal-4887	108	146	(	(	PUNCT
american_scientific_journal-4887	108	147	2019	2019	NUM
american_scientific_journal-4887	108	148	)	)	PUNCT
american_scientific_journal-4887	108	149	volume	volume	NOUN
american_scientific_journal-4887	108	150	56	56	NUM
american_scientific_journal-4887	108	151	,	,	PUNCT
american_scientific_journal-4887	108	152	no	no	DET
american_scientific_journal-4887	108	153	1	1	NUM
american_scientific_journal-4887	108	154	,	,	PUNCT
american_scientific_journal-4887	108	155	pp	pp	ADV
american_scientific_journal-4887	108	156	113	113	NUM
american_scientific_journal-4887	108	157	-	-	SYM
american_scientific_journal-4887	108	158	123	123	NUM
american_scientific_journal-4887	108	159	118	118	NUM
american_scientific_journal-4887	108	160	4	4	NUM
american_scientific_journal-4887	108	161	.	.	PUNCT
american_scientific_journal-4887	108	162	solving	solve	VERB
american_scientific_journal-4887	108	163	fully	fully	ADV
american_scientific_journal-4887	108	164	fuzzy	fuzzy	ADJ
american_scientific_journal-4887	108	165	linear	linear	ADJ
american_scientific_journal-4887	108	166	system	system	NOUN
american_scientific_journal-4887	108	167	of	of	ADP
american_scientific_journal-4887	108	168	equation	equation	NOUN
american_scientific_journal-4887	108	169	let	let	VERB
american_scientific_journal-4887	108	170	the	the	DET
american_scientific_journal-4887	108	171	fully	fully	ADV
american_scientific_journal-4887	108	172	fuzzy	fuzzy	ADJ
american_scientific_journal-4887	108	173	linear	linear	ADJ
american_scientific_journal-4887	108	174	system	system	NOUN
american_scientific_journal-4887	108	175	be	be	VERB
american_scientific_journal-4887	108	176	as	as	SCONJ
american_scientific_journal-4887	108	177	follows	follow	VERB
american_scientific_journal-4887	108	178	:	:	PUNCT
american_scientific_journal-4887	108	179	(	(	PUNCT
american_scientific_journal-4887	108	180	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-4887	108	181	�	�	NOUN
american_scientific_journal-4887	108	182	11⨂	11⨂	NUM
american_scientific_journal-4887	108	183	𝑥𝑥	𝑥𝑥	ADP
american_scientific_journal-4887	108	184	�	�	NOUN
american_scientific_journal-4887	108	185	1	1	NUM
american_scientific_journal-4887	108	186	)	)	PUNCT
american_scientific_journal-4887	108	187	⊕	⊕	PROPN
american_scientific_journal-4887	108	188	(	(	PUNCT
american_scientific_journal-4887	108	189	𝑎𝑎	𝑎𝑎	PROPN
american_scientific_journal-4887	108	190	�	�	PROPN
american_scientific_journal-4887	108	191	12⨂	12⨂	NUM
american_scientific_journal-4887	108	192	𝑥𝑥	𝑥𝑥	ADP
american_scientific_journal-4887	108	193	�	�	NOUN
american_scientific_journal-4887	108	194	2	2	NUM
american_scientific_journal-4887	108	195	)	)	PUNCT
american_scientific_journal-4887	108	196	⊕	⊕	PROPN
american_scientific_journal-4887	108	197	…	…	PUNCT
american_scientific_journal-4887	108	198	⊕	⊕	PROPN
american_scientific_journal-4887	108	199	(	(	PUNCT
american_scientific_journal-4887	108	200	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-4887	108	201	�	�	NOUN
american_scientific_journal-4887	108	202	1𝑛𝑛⨂	1𝑛𝑛⨂	NUM
american_scientific_journal-4887	108	203	𝑥𝑥	𝑥𝑥	ADP
american_scientific_journal-4887	108	204	�	�	NOUN
american_scientific_journal-4887	108	205	𝑛𝑛	𝑛𝑛	NOUN
american_scientific_journal-4887	108	206	)	)	PUNCT
american_scientific_journal-4887	108	207	=	=	PUNCT
american_scientific_journal-4887	108	208	𝑏𝑏	𝑏𝑏	NUM
american_scientific_journal-4887	108	209	�	�	SYM
american_scientific_journal-4887	108	210	1	1	NUM
american_scientific_journal-4887	108	211	(	(	PUNCT
american_scientific_journal-4887	108	212	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-4887	108	213	�	�	PROPN
american_scientific_journal-4887	108	214	21⨂	21⨂	NUM
american_scientific_journal-4887	108	215	𝑥𝑥	𝑥𝑥	ADP
american_scientific_journal-4887	108	216	�	�	NOUN
american_scientific_journal-4887	108	217	1	1	NUM
american_scientific_journal-4887	108	218	)	)	PUNCT
american_scientific_journal-4887	108	219	⊕	⊕	PROPN
american_scientific_journal-4887	108	220	(	(	PUNCT
american_scientific_journal-4887	108	221	𝑎𝑎	𝑎𝑎	PROPN
american_scientific_journal-4887	108	222	�	�	PROPN
american_scientific_journal-4887	108	223	22⨂	22⨂	NUM
american_scientific_journal-4887	108	224	𝑥𝑥	𝑥𝑥	ADP
american_scientific_journal-4887	108	225	�	�	NOUN
american_scientific_journal-4887	108	226	2	2	NUM
american_scientific_journal-4887	108	227	)	)	PUNCT
american_scientific_journal-4887	108	228	⊕	⊕	PROPN
american_scientific_journal-4887	108	229	…	…	PUNCT
american_scientific_journal-4887	108	230	⊕	⊕	PROPN
american_scientific_journal-4887	108	231	(	(	PUNCT
american_scientific_journal-4887	108	232	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-4887	108	233	�	�	NOUN
american_scientific_journal-4887	108	234	2𝑛𝑛⨂	2𝑛𝑛⨂	NOUN
american_scientific_journal-4887	108	235	𝑥𝑥	𝑥𝑥	ADP
american_scientific_journal-4887	108	236	�	�	NOUN
american_scientific_journal-4887	108	237	𝑛𝑛	𝑛𝑛	NOUN
american_scientific_journal-4887	108	238	)	)	PUNCT
american_scientific_journal-4887	108	239	=	=	PUNCT
american_scientific_journal-4887	108	240	𝑏𝑏	𝑏𝑏	NUM
american_scientific_journal-4887	108	241	�	�	NOUN
american_scientific_journal-4887	108	242	2	2	NUM
american_scientific_journal-4887	108	243	⋮	⋮	NOUN
american_scientific_journal-4887	108	244	⋮	⋮	ADJ
american_scientific_journal-4887	108	245	⋮	⋮	ADJ
american_scientific_journal-4887	108	246	⋮	⋮	NOUN
american_scientific_journal-4887	108	247	(	(	PUNCT
american_scientific_journal-4887	108	248	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-4887	108	249	�	�	NOUN
american_scientific_journal-4887	108	250	𝑛𝑛1⨂	𝑛𝑛1⨂	NUM
american_scientific_journal-4887	108	251	𝑥𝑥	𝑥𝑥	ADP
american_scientific_journal-4887	108	252	�	�	NOUN
american_scientific_journal-4887	108	253	1	1	NUM
american_scientific_journal-4887	108	254	)	)	PUNCT
american_scientific_journal-4887	108	255	⊕	⊕	PROPN
american_scientific_journal-4887	108	256	(	(	PUNCT
american_scientific_journal-4887	108	257	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-4887	108	258	�	�	NOUN
american_scientific_journal-4887	108	259	𝑛𝑛2⨂	𝑛𝑛2⨂	NOUN
american_scientific_journal-4887	108	260	𝑥𝑥	𝑥𝑥	ADP
american_scientific_journal-4887	108	261	�	�	NOUN
american_scientific_journal-4887	108	262	2	2	NUM
american_scientific_journal-4887	108	263	)	)	PUNCT
american_scientific_journal-4887	108	264	⊕	⊕	PROPN
american_scientific_journal-4887	108	265	…	…	PUNCT
american_scientific_journal-4887	108	266	⊕	⊕	PROPN
american_scientific_journal-4887	108	267	(	(	PUNCT
american_scientific_journal-4887	108	268	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-4887	108	269	�	�	NOUN
american_scientific_journal-4887	108	270	𝑛𝑛𝑛𝑛⨂	𝑛𝑛𝑛𝑛⨂	NOUN
american_scientific_journal-4887	108	271	𝑥𝑥	𝑥𝑥	ADP
american_scientific_journal-4887	108	272	�	�	NOUN
american_scientific_journal-4887	108	273	𝑛𝑛	𝑛𝑛	PART
american_scientific_journal-4887	108	274	)	)	PUNCT
american_scientific_journal-4887	108	275	=	=	PUNCT
american_scientific_journal-4887	108	276	𝑏𝑏	𝑏𝑏	NUM
american_scientific_journal-4887	108	277	�	�	NOUN
american_scientific_journal-4887	108	278	𝑛𝑛	𝑛𝑛	VERB
american_scientific_journal-4887	108	279	the	the	DET
american_scientific_journal-4887	108	280	matrix	matrix	NOUN
american_scientific_journal-4887	108	281	form	form	VERB
american_scientific_journal-4887	108	282	the	the	DET
american_scientific_journal-4887	108	283	fully	fully	ADV
american_scientific_journal-4887	108	284	fuzzy	fuzzy	ADJ
american_scientific_journal-4887	108	285	linear	linear	ADJ
american_scientific_journal-4887	108	286	system	system	NOUN
american_scientific_journal-4887	108	287	of	of	ADP
american_scientific_journal-4887	108	288	equation	equation	NOUN
american_scientific_journal-4887	108	289	is	be	AUX
american_scientific_journal-4887	108	290	𝑨𝑨	𝑨𝑨	PROPN
american_scientific_journal-4887	108	291	�	�	PROPN
american_scientific_journal-4887	109	1	⊗	⊗	ADJ
american_scientific_journal-4887	109	2	𝑨𝑨	𝑨𝑨	PROPN
american_scientific_journal-4887	109	3	�	�	PROPN
american_scientific_journal-4887	109	4	=	=	SYM
american_scientific_journal-4887	109	5	𝒃𝒃	𝒃𝒃	PROPN
american_scientific_journal-4887	109	6	�	�	PROPN
american_scientific_journal-4887	109	7	,	,	PUNCT
american_scientific_journal-4887	109	8	where	where	SCONJ
american_scientific_journal-4887	109	9	𝑨𝑨	𝑨𝑨	PROPN
american_scientific_journal-4887	109	10	�	�	X
american_scientific_journal-4887	109	11	=	=	SYM
american_scientific_journal-4887	109	12	(	(	PUNCT
american_scientific_journal-4887	109	13	𝒂𝒂	𝒂𝒂	PROPN
american_scientific_journal-4887	109	14	�	�	PROPN
american_scientific_journal-4887	109	15	𝒊𝒊𝒊𝒊	𝒊𝒊𝒊𝒊	NOUN
american_scientific_journal-4887	109	16	)	)	PUNCT
american_scientific_journal-4887	109	17	=	=	SYM
american_scientific_journal-4887	109	18	(	(	PUNCT
american_scientific_journal-4887	109	19	𝑎𝑎𝑖𝑖𝑖𝑖	𝑎𝑎𝑖𝑖𝑖𝑖	NOUN
american_scientific_journal-4887	109	20	,	,	PUNCT
american_scientific_journal-4887	109	21	𝛼𝛼𝑖𝑖𝑖𝑖	𝛼𝛼𝑖𝑖𝑖𝑖	NOUN
american_scientific_journal-4887	109	22	,	,	PUNCT
american_scientific_journal-4887	109	23	𝛽𝛽𝑖𝑖𝑖𝑖	𝛽𝛽𝑖𝑖𝑖𝑖	ADJ
american_scientific_journal-4887	109	24	)	)	PUNCT
american_scientific_journal-4887	109	25	is	be	AUX
american_scientific_journal-4887	109	26	a	a	DET
american_scientific_journal-4887	109	27	fuzzy	fuzzy	ADJ
american_scientific_journal-4887	109	28	matrix	matrix	NOUN
american_scientific_journal-4887	109	29	𝑛𝑛	𝑛𝑛	AUX
american_scientific_journal-4887	109	30	×	×	NOUN
american_scientific_journal-4887	109	31	𝑛𝑛	𝑛𝑛	NOUN
american_scientific_journal-4887	109	32	,	,	PUNCT
american_scientific_journal-4887	109	33	𝑨𝑨	𝑨𝑨	PROPN
american_scientific_journal-4887	109	34	�	�	X
american_scientific_journal-4887	109	35	=	=	SYM
american_scientific_journal-4887	109	36	(	(	PUNCT
american_scientific_journal-4887	109	37	𝑥𝑥	𝑥𝑥	ADP
american_scientific_journal-4887	109	38	�	�	NOUN
american_scientific_journal-4887	109	39	1	1	NUM
american_scientific_journal-4887	109	40	,	,	PUNCT
american_scientific_journal-4887	109	41	…	…	PUNCT
american_scientific_journal-4887	109	42	,	,	PUNCT
american_scientific_journal-4887	109	43	𝑥𝑥	𝑥𝑥	ADP
american_scientific_journal-4887	109	44	�	�	NOUN
american_scientific_journal-4887	109	45	𝑛𝑛	𝑛𝑛	NOUN
american_scientific_journal-4887	109	46	)	)	PUNCT
american_scientific_journal-4887	109	47	and	and	CCONJ
american_scientific_journal-4887	109	48	𝒃𝒃	𝒃𝒃	ADP
american_scientific_journal-4887	109	49	�	�	PROPN
american_scientific_journal-4887	109	50	=	=	SYM
american_scientific_journal-4887	109	51	(	(	PUNCT
american_scientific_journal-4887	109	52	𝑏𝑏	𝑏𝑏	NUM
american_scientific_journal-4887	109	53	�	�	NOUN
american_scientific_journal-4887	109	54	1	1	NUM
american_scientific_journal-4887	109	55	,	,	PUNCT
american_scientific_journal-4887	109	56	…	…	PUNCT
american_scientific_journal-4887	109	57	,	,	PUNCT
american_scientific_journal-4887	109	58	𝑏𝑏	𝑏𝑏	X
american_scientific_journal-4887	109	59	�	�	NOUN
american_scientific_journal-4887	109	60	𝑛𝑛	𝑛𝑛	PART
american_scientific_journal-4887	109	61	)	)	PUNCT
american_scientific_journal-4887	109	62	are	be	AUX
american_scientific_journal-4887	109	63	fuzzy	fuzzy	ADJ
american_scientific_journal-4887	109	64	vectors	vector	NOUN
american_scientific_journal-4887	109	65	𝑛𝑛	𝑛𝑛	NOUN
american_scientific_journal-4887	109	66	×	×	PROPN
american_scientific_journal-4887	109	67	1	1	NUM
american_scientific_journal-4887	109	68	.	.	PUNCT
american_scientific_journal-4887	110	1	a	a	DET
american_scientific_journal-4887	110	2	matrix	matrix	NOUN
american_scientific_journal-4887	110	3	𝑨𝑨	𝑨𝑨	NOUN
american_scientific_journal-4887	110	4	�	�	NOUN
american_scientific_journal-4887	110	5	=	=	SYM
american_scientific_journal-4887	110	6	(	(	PUNCT
american_scientific_journal-4887	110	7	𝒂𝒂	𝒂𝒂	PROPN
american_scientific_journal-4887	110	8	�	�	PROPN
american_scientific_journal-4887	110	9	𝒊𝒊𝒊𝒊	𝒊𝒊𝒊𝒊	NOUN
american_scientific_journal-4887	110	10	)	)	PUNCT
american_scientific_journal-4887	110	11	is	be	AUX
american_scientific_journal-4887	110	12	called	call	VERB
american_scientific_journal-4887	110	13	a	a	DET
american_scientific_journal-4887	110	14	fuzzy	fuzzy	ADJ
american_scientific_journal-4887	110	15	matrix	matrix	NOUN
american_scientific_journal-4887	110	16	,	,	PUNCT
american_scientific_journal-4887	110	17	if	if	SCONJ
american_scientific_journal-4887	110	18	each	each	DET
american_scientific_journal-4887	110	19	element	element	NOUN
american_scientific_journal-4887	110	20	of	of	ADP
american_scientific_journal-4887	110	21	𝑨𝑨	𝑨𝑨	PROPN
american_scientific_journal-4887	110	22	�	�	PROPN
american_scientific_journal-4887	110	23	is	be	AUX
american_scientific_journal-4887	110	24	a	a	DET
american_scientific_journal-4887	110	25	fuzzy	fuzzy	ADJ
american_scientific_journal-4887	110	26	number	number	NOUN
american_scientific_journal-4887	110	27	.	.	PUNCT
american_scientific_journal-4887	111	1	we	we	PRON
american_scientific_journal-4887	111	2	may	may	AUX
american_scientific_journal-4887	111	3	represent	represent	VERB
american_scientific_journal-4887	111	4	fuzzy	fuzzy	ADJ
american_scientific_journal-4887	111	5	matrix	matrix	NOUN
american_scientific_journal-4887	111	6	𝑨𝑨	𝑨𝑨	PROPN
american_scientific_journal-4887	111	7	�	�	PROPN
american_scientific_journal-4887	111	8	=	=	SYM
american_scientific_journal-4887	111	9	�	�	PROPN
american_scientific_journal-4887	111	10	𝒂𝒂	𝒂𝒂	PROPN
american_scientific_journal-4887	111	11	�	�	PROPN
american_scientific_journal-4887	111	12	𝒊𝒊𝒊𝒊	𝒊𝒊𝒊𝒊	NOUN
american_scientific_journal-4887	111	13	�	�	PROPN
american_scientific_journal-4887	111	14	𝑛𝑛×𝑛𝑛	𝑛𝑛×𝑛𝑛	PROPN
american_scientific_journal-4887	111	15	that	that	PRON
american_scientific_journal-4887	111	16	�	�	PROPN
american_scientific_journal-4887	111	17	𝒂𝒂	𝒂𝒂	PROPN
american_scientific_journal-4887	111	18	�	�	PROPN
american_scientific_journal-4887	111	19	𝒊𝒊𝒊𝒊	𝒊𝒊𝒊𝒊	NOUN
american_scientific_journal-4887	111	20	�	�	PROPN
american_scientific_journal-4887	111	21	=	=	SYM
american_scientific_journal-4887	111	22	�	�	PROPN
american_scientific_journal-4887	111	23	𝑎𝑎𝑖𝑖𝑖𝑖	𝑎𝑎𝑖𝑖𝑖𝑖	NOUN
american_scientific_journal-4887	111	24	,	,	PUNCT
american_scientific_journal-4887	111	25	𝛼𝛼𝑖𝑖𝑖𝑖	𝛼𝛼𝑖𝑖𝑖𝑖	NOUN
american_scientific_journal-4887	111	26	,	,	PUNCT
american_scientific_journal-4887	111	27	𝛽𝛽𝑖𝑖𝑖𝑖	𝛽𝛽𝑖𝑖𝑖𝑖	NOUN
american_scientific_journal-4887	111	28	�	�	PROPN
american_scientific_journal-4887	111	29	with	with	ADP
american_scientific_journal-4887	111	30	new	new	ADJ
american_scientific_journal-4887	111	31	notation	notation	NOUN
american_scientific_journal-4887	111	32	𝑨𝑨	𝑨𝑨	PROPN
american_scientific_journal-4887	111	33	�	�	NOUN
american_scientific_journal-4887	111	34	=	=	SYM
american_scientific_journal-4887	111	35	(	(	PUNCT
american_scientific_journal-4887	111	36	𝐴𝐴,𝑀𝑀,𝑁𝑁	𝐴𝐴,𝑀𝑀,𝑁𝑁	PROPN
american_scientific_journal-4887	111	37	)	)	PUNCT
american_scientific_journal-4887	111	38	,	,	PUNCT
american_scientific_journal-4887	111	39	where	where	SCONJ
american_scientific_journal-4887	111	40	𝐴𝐴	𝐴𝐴	PROPN
american_scientific_journal-4887	111	41	=	=	SYM
american_scientific_journal-4887	111	42	�	�	PROPN
american_scientific_journal-4887	111	43	𝑎𝑎𝑖𝑖𝑖𝑖	𝑎𝑎𝑖𝑖𝑖𝑖	NOUN
american_scientific_journal-4887	111	44	�	�	PROPN
american_scientific_journal-4887	111	45	,	,	PUNCT
american_scientific_journal-4887	111	46	𝑀𝑀	𝑀𝑀	PROPN
american_scientific_journal-4887	111	47	=	=	PUNCT
american_scientific_journal-4887	111	48	�	�	PROPN
american_scientific_journal-4887	111	49	𝛼𝛼𝑖𝑖𝑖𝑖	𝛼𝛼𝑖𝑖𝑖𝑖	NOUN
american_scientific_journal-4887	111	50	�	�	PROPN
american_scientific_journal-4887	111	51	,	,	PUNCT
american_scientific_journal-4887	111	52	and	and	CCONJ
american_scientific_journal-4887	111	53	𝑁𝑁	𝑁𝑁	PROPN
american_scientific_journal-4887	111	54	=	=	SYM
american_scientific_journal-4887	111	55	�	�	PROPN
american_scientific_journal-4887	111	56	𝛽𝛽𝑖𝑖𝑖𝑖	𝛽𝛽𝑖𝑖𝑖𝑖	NOUN
american_scientific_journal-4887	111	57	�	�	NOUN
american_scientific_journal-4887	111	58	are	be	AUX
american_scientific_journal-4887	111	59	three	three	NUM
american_scientific_journal-4887	111	60	𝑛𝑛	𝑛𝑛	NOUN
american_scientific_journal-4887	111	61	𝑥𝑥	𝑥𝑥	ADP
american_scientific_journal-4887	111	62	𝑛𝑛	𝑛𝑛	NOUN
american_scientific_journal-4887	111	63	crips	crip	NOUN
american_scientific_journal-4887	111	64	matrices	matrix	NOUN
american_scientific_journal-4887	111	65	.	.	PUNCT
american_scientific_journal-4887	112	1	next	next	ADV
american_scientific_journal-4887	112	2	,	,	PUNCT
american_scientific_journal-4887	112	3	to	to	PART
american_scientific_journal-4887	112	4	get	get	VERB
american_scientific_journal-4887	112	5	a	a	DET
american_scientific_journal-4887	112	6	solution	solution	NOUN
american_scientific_journal-4887	112	7	the	the	DET
american_scientific_journal-4887	112	8	fully	fully	ADV
american_scientific_journal-4887	112	9	fuzzy	fuzzy	ADJ
american_scientific_journal-4887	112	10	linear	linear	ADJ
american_scientific_journal-4887	112	11	system	system	NOUN
american_scientific_journal-4887	112	12	of	of	ADP
american_scientific_journal-4887	112	13	equation	equation	NOUN
american_scientific_journal-4887	112	14	𝑨𝑨	𝑨𝑨	PROPN
american_scientific_journal-4887	112	15	�	�	PROPN
american_scientific_journal-4887	112	16	⊗	⊗	ADJ
american_scientific_journal-4887	112	17	𝑨𝑨	𝑨𝑨	PROPN
american_scientific_journal-4887	112	18	�	�	PROPN
american_scientific_journal-4887	112	19	=	=	SYM
american_scientific_journal-4887	112	20	𝒃𝒃	𝒃𝒃	ADP
american_scientific_journal-4887	112	21	�	�	PROPN
american_scientific_journal-4887	112	22	,	,	PUNCT
american_scientific_journal-4887	112	23	where	where	SCONJ
american_scientific_journal-4887	112	24	𝑨𝑨	𝑨𝑨	PROPN
american_scientific_journal-4887	112	25	�	�	X
american_scientific_journal-4887	112	26	=	=	SYM
american_scientific_journal-4887	112	27	(	(	PUNCT
american_scientific_journal-4887	112	28	𝐴𝐴,𝑀𝑀,𝑁𝑁	𝐴𝐴,𝑀𝑀,𝑁𝑁	PROPN
american_scientific_journal-4887	112	29	)	)	PUNCT
american_scientific_journal-4887	112	30	,	,	PUNCT
american_scientific_journal-4887	112	31	𝑨𝑨	𝑨𝑨	PROPN
american_scientific_journal-4887	112	32	�	�	X
american_scientific_journal-4887	112	33	=	=	SYM
american_scientific_journal-4887	112	34	(	(	PUNCT
american_scientific_journal-4887	112	35	𝑥𝑥,𝑦𝑦	𝑥𝑥,𝑦𝑦	ADJ
american_scientific_journal-4887	112	36	,	,	PUNCT
american_scientific_journal-4887	112	37	𝑧𝑧	𝑧𝑧	NOUN
american_scientific_journal-4887	112	38	)	)	PUNCT
american_scientific_journal-4887	112	39	,	,	PUNCT
american_scientific_journal-4887	112	40	and	and	CCONJ
american_scientific_journal-4887	112	41	𝒃𝒃	𝒃𝒃	ADP
american_scientific_journal-4887	112	42	�	�	PROPN
american_scientific_journal-4887	112	43	=	=	SYM
american_scientific_journal-4887	112	44	(	(	PUNCT
american_scientific_journal-4887	112	45	𝑏𝑏,𝑔𝑔	𝑏𝑏,𝑔𝑔	PROPN
american_scientific_journal-4887	112	46	,	,	PUNCT
american_scientific_journal-4887	112	47	ℎ	ℎ	PROPN
american_scientific_journal-4887	112	48	)	)	PUNCT
american_scientific_journal-4887	112	49	so	so	SCONJ
american_scientific_journal-4887	112	50	that	that	SCONJ
american_scientific_journal-4887	112	51	it	it	PRON
american_scientific_journal-4887	112	52	is	be	AUX
american_scientific_journal-4887	112	53	obtained	obtain	VERB
american_scientific_journal-4887	112	54	:	:	PUNCT
american_scientific_journal-4887	112	55	(	(	PUNCT
american_scientific_journal-4887	113	1	𝐴𝐴,𝑀𝑀,𝑁𝑁	𝐴𝐴,𝑀𝑀,𝑁𝑁	PROPN
american_scientific_journal-4887	113	2	)	)	PUNCT
american_scientific_journal-4887	113	3	⊗	⊗	PROPN
american_scientific_journal-4887	113	4	(	(	PUNCT
american_scientific_journal-4887	113	5	𝑥𝑥,𝑦𝑦	𝑥𝑥,𝑦𝑦	PROPN
american_scientific_journal-4887	113	6	,	,	PUNCT
american_scientific_journal-4887	113	7	𝑧𝑧	𝑧𝑧	NOUN
american_scientific_journal-4887	113	8	)	)	PUNCT
american_scientific_journal-4887	113	9	=	=	SYM
american_scientific_journal-4887	113	10	(	(	PUNCT
american_scientific_journal-4887	113	11	𝑏𝑏,𝑔𝑔,ℎ	𝑏𝑏,𝑔𝑔,ℎ	PROPN
american_scientific_journal-4887	113	12	)	)	PUNCT
american_scientific_journal-4887	113	13	by	by	ADP
american_scientific_journal-4887	113	14	using	use	VERB
american_scientific_journal-4887	113	15	algebra	algebra	NOUN
american_scientific_journal-4887	113	16	multiplication	multiplication	NOUN
american_scientific_journal-4887	113	17	of	of	ADP
american_scientific_journal-4887	113	18	two	two	NUM
american_scientific_journal-4887	113	19	fuzzy	fuzzy	ADJ
american_scientific_journal-4887	113	20	number	number	NOUN
american_scientific_journal-4887	113	21	for	for	ADP
american_scientific_journal-4887	113	22	𝑨𝑨	𝑨𝑨	PROPN
american_scientific_journal-4887	113	23	�	�	PROPN
american_scientific_journal-4887	113	24	>	>	X
american_scientific_journal-4887	113	25	𝟎𝟎	𝟎𝟎	NUM
american_scientific_journal-4887	113	26	,	,	PUNCT
american_scientific_journal-4887	113	27	𝒃𝒃	𝒃𝒃	ADP
american_scientific_journal-4887	113	28	�	�	PROPN
american_scientific_journal-4887	113	29	>	>	X
american_scientific_journal-4887	113	30	𝟎𝟎	𝟎𝟎	NUM
american_scientific_journal-4887	113	31	,	,	PUNCT
american_scientific_journal-4887	113	32	and	and	CCONJ
american_scientific_journal-4887	113	33	𝑨𝑨	𝑨𝑨	PROPN
american_scientific_journal-4887	113	34	�	�	PROPN
american_scientific_journal-4887	113	35	>	>	X
american_scientific_journal-4887	113	36	𝟎𝟎	𝟎𝟎	NUM
american_scientific_journal-4887	113	37	the	the	DET
american_scientific_journal-4887	113	38	formula	formula	NOUN
american_scientific_journal-4887	113	39	that	that	PRON
american_scientific_journal-4887	113	40	applied	apply	VERB
american_scientific_journal-4887	113	41	is	be	AUX
american_scientific_journal-4887	113	42	(	(	PUNCT
american_scientific_journal-4887	113	43	𝐴𝐴𝑥𝑥,𝐴𝐴𝑦𝑦	𝐴𝐴𝑥𝑥,𝐴𝐴𝑦𝑦	NOUN
american_scientific_journal-4887	113	44	+	+	CCONJ
american_scientific_journal-4887	113	45	𝑀𝑀𝑥𝑥,𝐴𝐴𝑧𝑧	𝑀𝑀𝑥𝑥,𝐴𝐴𝑧𝑧	NOUN
american_scientific_journal-4887	113	46	+	+	CCONJ
american_scientific_journal-4887	113	47	𝑁𝑁𝑥𝑥	𝑁𝑁𝑥𝑥	PROPN
american_scientific_journal-4887	113	48	)	)	PUNCT
american_scientific_journal-4887	114	1	=	=	PRON
american_scientific_journal-4887	114	2	(	(	PUNCT
american_scientific_journal-4887	114	3	𝑏𝑏,𝑔𝑔	𝑏𝑏,𝑔𝑔	NOUN
american_scientific_journal-4887	114	4	,	,	PUNCT
american_scientific_journal-4887	114	5	ℎ	ℎ	PROPN
american_scientific_journal-4887	114	6	)	)	PUNCT
american_scientific_journal-4887	114	7	.	.	PUNCT
american_scientific_journal-4887	115	1	therefore	therefore	ADV
american_scientific_journal-4887	115	2	,	,	PUNCT
american_scientific_journal-4887	115	3	it	it	PRON
american_scientific_journal-4887	115	4	can	can	AUX
american_scientific_journal-4887	115	5	be	be	AUX
american_scientific_journal-4887	115	6	concluded	conclude	VERB
american_scientific_journal-4887	115	7	that	that	SCONJ
american_scientific_journal-4887	115	8	:	:	PUNCT
american_scientific_journal-4887	115	9	𝐴𝐴𝑥𝑥	𝐴𝐴𝑥𝑥	PROPN
american_scientific_journal-4887	115	10	=	=	SYM
american_scientific_journal-4887	115	11	𝑏𝑏	𝑏𝑏	NOUN
american_scientific_journal-4887	115	12	𝐴𝐴𝑦𝑦	𝐴𝐴𝑦𝑦	PROPN
american_scientific_journal-4887	115	13	+	+	CCONJ
american_scientific_journal-4887	115	14	𝑀𝑀𝑥𝑥	𝑀𝑀𝑥𝑥	PROPN
american_scientific_journal-4887	116	1	=	=	SYM
american_scientific_journal-4887	116	2	𝑔𝑔	𝑔𝑔	PROPN
american_scientific_journal-4887	116	3	(	(	PUNCT
american_scientific_journal-4887	116	4	11	11	NUM
american_scientific_journal-4887	116	5	)	)	PUNCT
american_scientific_journal-4887	116	6	𝐴𝐴𝑧𝑧	𝐴𝐴𝑧𝑧	PROPN
american_scientific_journal-4887	117	1	+	+	NUM
american_scientific_journal-4887	117	2	𝑁𝑁𝑥𝑥	𝑁𝑁𝑥𝑥	PROPN
american_scientific_journal-4887	117	3	=	=	PUNCT
american_scientific_journal-4887	117	4	ℎ	ℎ	NOUN
american_scientific_journal-4887	117	5	furthermore	furthermore	ADV
american_scientific_journal-4887	117	6	,	,	PUNCT
american_scientific_journal-4887	117	7	proving	prove	VERB
american_scientific_journal-4887	117	8	equation	equation	NOUN
american_scientific_journal-4887	117	9	(	(	PUNCT
american_scientific_journal-4887	117	10	11	11	NUM
american_scientific_journal-4887	117	11	)	)	PUNCT
american_scientific_journal-4887	117	12	satisfies	satisfie	NOUN
american_scientific_journal-4887	117	13	strictly	strictly	ADV
american_scientific_journal-4887	117	14	diagonal	diagonal	ADJ
american_scientific_journal-4887	117	15	dominant	dominant	ADJ
american_scientific_journal-4887	117	16	with	with	ADP
american_scientific_journal-4887	117	17	the	the	DET
american_scientific_journal-4887	117	18	following	follow	VERB
american_scientific_journal-4887	117	19	formula	formula	NOUN
american_scientific_journal-4887	117	20	:	:	PUNCT
american_scientific_journal-4887	117	21	|𝑎𝑎𝑖𝑖𝑖𝑖|	|𝑎𝑎𝑖𝑖𝑖𝑖|	X
american_scientific_journal-4887	117	22	>	>	X
american_scientific_journal-4887	117	23	�	�	PROPN
american_scientific_journal-4887	117	24	�	�	PROPN
american_scientific_journal-4887	117	25	𝑎𝑎𝑖𝑖𝑖𝑖	𝑎𝑎𝑖𝑖𝑖𝑖	PROPN
american_scientific_journal-4887	117	26	�	�	PROPN
american_scientific_journal-4887	117	27	𝑛𝑛	𝑛𝑛	PROPN
american_scientific_journal-4887	117	28	𝑖𝑖=𝑖𝑖,𝑖𝑖≠𝑖𝑖	𝑖𝑖=𝑖𝑖,𝑖𝑖≠𝑖𝑖	PROPN
american_scientific_journal-4887	117	29	𝑒𝑒	𝑒𝑒	ADP
american_scientific_journal-4887	117	30	=	=	SYM
american_scientific_journal-4887	117	31	1,2	1,2	NUM
american_scientific_journal-4887	117	32	,	,	PUNCT
american_scientific_journal-4887	117	33	…	…	PUNCT
american_scientific_journal-4887	117	34	,	,	PUNCT
american_scientific_journal-4887	117	35	𝑛𝑛	𝑛𝑛	VERB
american_scientific_journal-4887	117	36	then	then	ADV
american_scientific_journal-4887	117	37	do	do	VERB
american_scientific_journal-4887	117	38	the	the	DET
american_scientific_journal-4887	117	39	iteration	iteration	NOUN
american_scientific_journal-4887	117	40	process	process	NOUN
american_scientific_journal-4887	117	41	using	use	VERB
american_scientific_journal-4887	117	42	the	the	DET
american_scientific_journal-4887	117	43	intial	intial	ADJ
american_scientific_journal-4887	117	44	value	value	NOUN
american_scientific_journal-4887	117	45	.	.	PUNCT
american_scientific_journal-4887	118	1	gauss	gauss	PROPN
american_scientific_journal-4887	118	2	seidel	seidel	PROPN
american_scientific_journal-4887	118	3	iteration	iteration	PROPN
american_scientific_journal-4887	118	4	stop	stop	VERB
american_scientific_journal-4887	118	5	if	if	SCONJ
american_scientific_journal-4887	118	6	tolerance	tolerance	NOUN
american_scientific_journal-4887	118	7	has	have	AUX
american_scientific_journal-4887	118	8	been	be	AUX
american_scientific_journal-4887	118	9	achieved	achieve	VERB
american_scientific_journal-4887	118	10	:	:	PUNCT
american_scientific_journal-4887	118	11	�	�	X
american_scientific_journal-4887	118	12	𝑥𝑥	𝑥𝑥	ADP
american_scientific_journal-4887	118	13	�	�	PROPN
american_scientific_journal-4887	118	14	𝑖𝑖	𝑖𝑖	INTJ
american_scientific_journal-4887	118	15	(	(	PUNCT
american_scientific_journal-4887	118	16	𝑗𝑗)⊖𝑥𝑥	𝑗𝑗)⊖𝑥𝑥	PROPN
american_scientific_journal-4887	118	17	�	�	X
american_scientific_journal-4887	118	18	𝑖𝑖	𝑖𝑖	X
american_scientific_journal-4887	118	19	(	(	PUNCT
american_scientific_journal-4887	118	20	𝑗𝑗−𝑖𝑖	𝑗𝑗−𝑖𝑖	NOUN
american_scientific_journal-4887	118	21	)	)	PUNCT
american_scientific_journal-4887	118	22	𝑥𝑥	𝑥𝑥	ADP
american_scientific_journal-4887	118	23	�	�	PROPN
american_scientific_journal-4887	118	24	𝑖𝑖	𝑖𝑖	INTJ
american_scientific_journal-4887	118	25	(	(	PUNCT
american_scientific_journal-4887	118	26	𝑗𝑗	𝑗𝑗	ADJ
american_scientific_journal-4887	118	27	)	)	PUNCT
american_scientific_journal-4887	118	28	�	�	PROPN
american_scientific_journal-4887	118	29	(	(	PUNCT
american_scientific_journal-4887	118	30	12	12	NUM
american_scientific_journal-4887	118	31	)	)	PUNCT
american_scientific_journal-4887	118	32	example	example	NOUN
american_scientific_journal-4887	118	33	:	:	PUNCT
american_scientific_journal-4887	118	34	the	the	DET
american_scientific_journal-4887	118	35	fully	fully	ADV
american_scientific_journal-4887	118	36	fuzzy	fuzzy	ADJ
american_scientific_journal-4887	118	37	system	system	NOUN
american_scientific_journal-4887	118	38	linear	linear	NOUN
american_scientific_journal-4887	118	39	of	of	ADP
american_scientific_journal-4887	118	40	equation	equation	NOUN
american_scientific_journal-4887	118	41	with	with	ADP
american_scientific_journal-4887	118	42	positive	positive	ADJ
american_scientific_journal-4887	118	43	and	and	CCONJ
american_scientific_journal-4887	118	44	positive	positive	ADJ
american_scientific_journal-4887	118	45	multiplication	multiplication	NOUN
american_scientific_journal-4887	118	46	operations	operation	NOUN
american_scientific_journal-4887	118	47	as	as	SCONJ
american_scientific_journal-4887	118	48	follows	follow	VERB
american_scientific_journal-4887	118	49	:	:	PUNCT
american_scientific_journal-4887	118	50	(	(	PUNCT
american_scientific_journal-4887	118	51	)	)	PUNCT
american_scientific_journal-4887	118	52	(	(	PUNCT
american_scientific_journal-4887	118	53	)	)	PUNCT
american_scientific_journal-4887	118	54	(	(	PUNCT
american_scientific_journal-4887	118	55	)	)	PUNCT
american_scientific_journal-4887	118	56	(	(	PUNCT
american_scientific_journal-4887	118	57	)	)	PUNCT
american_scientific_journal-4887	118	58	(	(	PUNCT
american_scientific_journal-4887	118	59	)	)	PUNCT
american_scientific_journal-4887	118	60	(	(	PUNCT
american_scientific_journal-4887	118	61	)	)	PUNCT
american_scientific_journal-4887	118	62	(	(	PUNCT
american_scientific_journal-4887	118	63	)	)	PUNCT
american_scientific_journal-4887	118	64	(	(	PUNCT
american_scientific_journal-4887	118	65	)	)	PUNCT
american_scientific_journal-4887	118	66	(	(	PUNCT
american_scientific_journal-4887	118	67	)	)	PUNCT
american_scientific_journal-4887	118	68	(	(	PUNCT
american_scientific_journal-4887	118	69	)	)	PUNCT
american_scientific_journal-4887	118	70	(	(	PUNCT
american_scientific_journal-4887	118	71	)	)	PUNCT
american_scientific_journal-4887	118	72	(	(	PUNCT
american_scientific_journal-4887	118	73	)	)	PUNCT
american_scientific_journal-4887	118	74	(	(	PUNCT
american_scientific_journal-4887	118	75	)	)	PUNCT
american_scientific_journal-4887	118	76	(	(	PUNCT
american_scientific_journal-4887	118	77	)	)	PUNCT
american_scientific_journal-4887	118	78	(	(	PUNCT
american_scientific_journal-4887	118	79	)	)	PUNCT
american_scientific_journal-4887	118	80	(	(	PUNCT
american_scientific_journal-4887	118	81	)	)	PUNCT
american_scientific_journal-4887	118	82	(	(	PUNCT
american_scientific_journal-4887	118	83	)	)	PUNCT
american_scientific_journal-4887	118	84	(	(	PUNCT
american_scientific_journal-4887	118	85	)	)	PUNCT
american_scientific_journal-4887	118	86	(	(	PUNCT
american_scientific_journal-4887	118	87	)	)	PUNCT
american_scientific_journal-4887	118	88	(	(	PUNCT
american_scientific_journal-4887	118	89	)	)	PUNCT
american_scientific_journal-4887	118	90	(	(	PUNCT
american_scientific_journal-4887	118	91	)	)	PUNCT
american_scientific_journal-4887	118	92	9.131,3.88,5.535,,1.0,1.0,5.4,,3.0,1.0,2,,2.0,1.0,2	9.131,3.88,5.535,,1.0,1.0,5.4,,3.0,1.0,2,,2.0,1.0,2	NUM
american_scientific_journal-4887	119	1	3.109,2.76,5.434,,2.0,2.0,5.1,,4.0,1.0,4,,1.0,1.0,2	3.109,2.76,5.434,,2.0,2.0,5.1,,4.0,1.0,4,,1.0,1.0,2	NUM
american_scientific_journal-4887	119	2	2.536,7.427,1897,,2.0,5.0,6,,5.1,5.1,12,,1,1,19	2.536,7.427,1897,,2.0,5.0,6,,5.1,5.1,12,,1,1,19	NUM
american_scientific_journal-4887	119	3	333222111	333222111	NUM
american_scientific_journal-4887	119	4	333222111	333222111	NUM
american_scientific_journal-4887	119	5	333222111	333222111	NUM
american_scientific_journal-4887	119	6	=	=	SYM
american_scientific_journal-4887	119	7	⊗⊕⊗⊕⊗	⊗⊕⊗⊕⊗	NOUN
american_scientific_journal-4887	119	8	=	=	NOUN
american_scientific_journal-4887	119	9	⊗⊕⊗⊕⊗	⊗⊕⊗⊕⊗	NOUN
american_scientific_journal-4887	119	10	=	=	NOUN
american_scientific_journal-4887	119	11	⊗⊕⊗⊕⊗	⊗⊕⊗⊕⊗	NOUN
american_scientific_journal-4887	119	12	zyxzyxzyx	zyxzyxzyx	NOUN
american_scientific_journal-4887	119	13	zyxzyxzyx	zyxzyxzyx	NOUN
american_scientific_journal-4887	119	14	zyxzyxzyx	zyxzyxzyx	NOUN
american_scientific_journal-4887	119	15	solution	solution	NOUN
american_scientific_journal-4887	119	16	:	:	PUNCT
american_scientific_journal-4887	119	17	the	the	DET
american_scientific_journal-4887	119	18	steps	step	NOUN
american_scientific_journal-4887	119	19	to	to	PART
american_scientific_journal-4887	119	20	solve	solve	VERB
american_scientific_journal-4887	119	21	the	the	DET
american_scientific_journal-4887	119	22	fully	fully	ADV
american_scientific_journal-4887	119	23	fuzzy	fuzzy	ADJ
american_scientific_journal-4887	119	24	linear	linear	ADJ
american_scientific_journal-4887	119	25	system	system	NOUN
american_scientific_journal-4887	119	26	of	of	ADP
american_scientific_journal-4887	119	27	equation	equation	NOUN
american_scientific_journal-4887	119	28	as	as	ADP
american_scientific_journal-4887	119	29	follow	follow	VERB
american_scientific_journal-4887	119	30	:	:	PUNCT
american_scientific_journal-4887	119	31	change	change	VERB
american_scientific_journal-4887	119	32	the	the	DET
american_scientific_journal-4887	119	33	form	form	NOUN
american_scientific_journal-4887	119	34	of	of	ADP
american_scientific_journal-4887	119	35	equations	equation	NOUN
american_scientific_journal-4887	119	36	into	into	ADP
american_scientific_journal-4887	119	37	the	the	DET
american_scientific_journal-4887	119	38	matrix	matrix	NOUN
american_scientific_journal-4887	119	39	𝑨𝑨	𝑨𝑨	NOUN
american_scientific_journal-4887	119	40	�	�	NOUN
american_scientific_journal-4887	119	41	=	=	SYM
american_scientific_journal-4887	119	42	(	(	PUNCT
american_scientific_journal-4887	119	43	𝐴𝐴,𝑀𝑀,𝑁𝑁	𝐴𝐴,𝑀𝑀,𝑁𝑁	PROPN
american_scientific_journal-4887	119	44	)	)	PUNCT
american_scientific_journal-4887	119	45	and	and	CCONJ
american_scientific_journal-4887	119	46	𝒃𝒃	𝒃𝒃	ADP
american_scientific_journal-4887	119	47	�	�	PROPN
american_scientific_journal-4887	119	48	=	=	SYM
american_scientific_journal-4887	119	49	(	(	PUNCT
american_scientific_journal-4887	119	50	𝑏𝑏,𝑔𝑔	𝑏𝑏,𝑔𝑔	PROPN
american_scientific_journal-4887	119	51	,	,	PUNCT
american_scientific_journal-4887	119	52	ℎ	ℎ	PROPN
american_scientific_journal-4887	119	53	)	)	PUNCT
american_scientific_journal-4887	119	54	are	be	AUX
american_scientific_journal-4887	119	55	:	:	PUNCT
american_scientific_journal-4887	119	56	𝐴𝐴	𝐴𝐴	PROPN
american_scientific_journal-4887	119	57	=	=	SYM
american_scientific_journal-4887	119	58	�	�	PROPN
american_scientific_journal-4887	119	59	19	19	NUM
american_scientific_journal-4887	119	60	12	12	NUM
american_scientific_journal-4887	119	61	6	6	NUM
american_scientific_journal-4887	119	62	2	2	NUM
american_scientific_journal-4887	119	63	4	4	NUM
american_scientific_journal-4887	119	64	1.5	1.5	NUM
american_scientific_journal-4887	119	65	2	2	NUM
american_scientific_journal-4887	119	66	2	2	NUM
american_scientific_journal-4887	119	67	4.5	4.5	NUM
american_scientific_journal-4887	119	68	�	�	PROPN
american_scientific_journal-4887	119	69	𝑀𝑀	𝑀𝑀	PROPN
american_scientific_journal-4887	119	70	=	=	SYM
american_scientific_journal-4887	119	71	�	�	PROPN
american_scientific_journal-4887	119	72	1	1	NUM
american_scientific_journal-4887	119	73	1.5	1.5	NUM
american_scientific_journal-4887	119	74	0.5	0.5	NUM
american_scientific_journal-4887	119	75	0.1	0.1	NUM
american_scientific_journal-4887	119	76	0.1	0.1	NUM
american_scientific_journal-4887	119	77	0.2	0.2	NUM
american_scientific_journal-4887	119	78	0.1	0.1	NUM
american_scientific_journal-4887	119	79	0.1	0.1	NUM
american_scientific_journal-4887	119	80	0.1	0.1	NUM
american_scientific_journal-4887	119	81	�	�	PROPN
american_scientific_journal-4887	119	82	𝑁𝑁	𝑁𝑁	PROPN
american_scientific_journal-4887	119	83	=	=	SYM
american_scientific_journal-4887	119	84	�	�	PROPN
american_scientific_journal-4887	119	85	1	1	NUM
american_scientific_journal-4887	119	86	1.5	1.5	NUM
american_scientific_journal-4887	119	87	0.2	0.2	NUM
american_scientific_journal-4887	119	88	0.1	0.1	NUM
american_scientific_journal-4887	119	89	0.4	0.4	NUM
american_scientific_journal-4887	119	90	0.2	0.2	NUM
american_scientific_journal-4887	119	91	0.2	0.2	NUM
american_scientific_journal-4887	119	92	0.3	0.3	NUM
american_scientific_journal-4887	119	93	0.1	0.1	NUM
american_scientific_journal-4887	119	94	�	�	PROPN
american_scientific_journal-4887	119	95	american	american	PROPN
american_scientific_journal-4887	119	96	scientific	scientific	ADJ
american_scientific_journal-4887	119	97	research	research	NOUN
american_scientific_journal-4887	119	98	journal	journal	NOUN
american_scientific_journal-4887	119	99	for	for	ADP
american_scientific_journal-4887	119	100	engineering	engineering	NOUN
american_scientific_journal-4887	119	101	,	,	PUNCT
american_scientific_journal-4887	119	102	technology	technology	NOUN
american_scientific_journal-4887	119	103	,	,	PUNCT
american_scientific_journal-4887	119	104	and	and	CCONJ
american_scientific_journal-4887	119	105	sciences	science	NOUN
american_scientific_journal-4887	119	106	(	(	PUNCT
american_scientific_journal-4887	119	107	asrjets	asrjet	NOUN
american_scientific_journal-4887	119	108	)	)	PUNCT
american_scientific_journal-4887	119	109	(	(	PUNCT
american_scientific_journal-4887	119	110	2019	2019	NUM
american_scientific_journal-4887	119	111	)	)	PUNCT
american_scientific_journal-4887	119	112	volume	volume	NOUN
american_scientific_journal-4887	119	113	56	56	NUM
american_scientific_journal-4887	119	114	,	,	PUNCT
american_scientific_journal-4887	119	115	no	no	DET
american_scientific_journal-4887	119	116	1	1	NUM
american_scientific_journal-4887	119	117	,	,	PUNCT
american_scientific_journal-4887	119	118	pp	pp	ADV
american_scientific_journal-4887	119	119	113	113	NUM
american_scientific_journal-4887	119	120	-	-	SYM
american_scientific_journal-4887	119	121	123	123	NUM
american_scientific_journal-4887	119	122	119	119	NUM
american_scientific_journal-4887	119	123	𝑏𝑏	𝑏𝑏	NOUN
american_scientific_journal-4887	119	124	=	=	SYM
american_scientific_journal-4887	119	125	�	�	PROPN
american_scientific_journal-4887	119	126	1897	1897	NUM
american_scientific_journal-4887	119	127	434.5	434.5	NUM
american_scientific_journal-4887	119	128	535.5	535.5	NUM
american_scientific_journal-4887	119	129	�	�	NOUN
american_scientific_journal-4887	119	130	𝑔𝑔	𝑔𝑔	PROPN
american_scientific_journal-4887	119	131	=	=	PUNCT
american_scientific_journal-4887	119	132	�	�	PROPN
american_scientific_journal-4887	119	133	427.7	427.7	NUM
american_scientific_journal-4887	119	134	76.2	76.2	NUM
american_scientific_journal-4887	119	135	88.3	88.3	NUM
american_scientific_journal-4887	119	136	�	�	NOUN
american_scientific_journal-4887	119	137	ℎ	ℎ	PROPN
american_scientific_journal-4887	119	138	=	=	SYM
american_scientific_journal-4887	119	139	�	�	PROPN
american_scientific_journal-4887	119	140	536.2	536.2	NUM
american_scientific_journal-4887	119	141	109.3	109.3	NUM
american_scientific_journal-4887	119	142	131.9	131.9	NUM
american_scientific_journal-4887	119	143	�	�	NOUN
american_scientific_journal-4887	119	144	because	because	SCONJ
american_scientific_journal-4887	119	145	𝑨𝑨	𝑨𝑨	PROPN
american_scientific_journal-4887	119	146	�	�	PROPN
american_scientific_journal-4887	119	147	>	>	X
american_scientific_journal-4887	119	148	𝟎𝟎	𝟎𝟎	NUM
american_scientific_journal-4887	119	149	,	,	PUNCT
american_scientific_journal-4887	119	150	𝒃𝒃	𝒃𝒃	ADP
american_scientific_journal-4887	119	151	�	�	PROPN
american_scientific_journal-4887	119	152	>	>	X
american_scientific_journal-4887	119	153	𝟎𝟎	𝟎𝟎	NUM
american_scientific_journal-4887	119	154	,	,	PUNCT
american_scientific_journal-4887	119	155	and	and	CCONJ
american_scientific_journal-4887	119	156	𝑨𝑨	𝑨𝑨	PROPN
american_scientific_journal-4887	119	157	�	�	PROPN
american_scientific_journal-4887	119	158	>	>	X
american_scientific_journal-4887	119	159	𝟎𝟎	𝟎𝟎	NUM
american_scientific_journal-4887	119	160	,	,	PUNCT
american_scientific_journal-4887	119	161	the	the	DET
american_scientific_journal-4887	119	162	formula	formula	NOUN
american_scientific_journal-4887	119	163	that	that	PRON
american_scientific_journal-4887	119	164	applied	apply	VERB
american_scientific_journal-4887	119	165	in	in	ADP
american_scientific_journal-4887	119	166	equation	equation	NOUN
american_scientific_journal-4887	119	167	(	(	PUNCT
american_scientific_journal-4887	119	168	11	11	NUM
american_scientific_journal-4887	119	169	)	)	PUNCT
american_scientific_journal-4887	119	170	.	.	PUNCT
american_scientific_journal-4887	120	1	next	next	ADV
american_scientific_journal-4887	120	2	,	,	PUNCT
american_scientific_journal-4887	120	3	change	change	VERB
american_scientific_journal-4887	120	4	the	the	DET
american_scientific_journal-4887	120	5	matrix	matrix	NOUN
american_scientific_journal-4887	120	6	into	into	ADP
american_scientific_journal-4887	120	7	system	system	NOUN
american_scientific_journal-4887	120	8	linear	linear	NOUN
american_scientific_journal-4887	120	9	of	of	ADP
american_scientific_journal-4887	120	10	equation	equation	NOUN
american_scientific_journal-4887	120	11	as	as	SCONJ
american_scientific_journal-4887	120	12	follows	follow	VERB
american_scientific_journal-4887	120	13	:	:	PUNCT
american_scientific_journal-4887	120	14	𝐴𝐴𝑥𝑥	𝐴𝐴𝑥𝑥	PROPN
american_scientific_journal-4887	120	15	=	=	SYM
american_scientific_journal-4887	120	16	𝑏𝑏	𝑏𝑏	NUM
american_scientific_journal-4887	120	17	�	�	PROPN
american_scientific_journal-4887	120	18	19	19	NUM
american_scientific_journal-4887	120	19	12	12	NUM
american_scientific_journal-4887	120	20	6	6	NUM
american_scientific_journal-4887	120	21	2	2	NUM
american_scientific_journal-4887	120	22	4	4	NUM
american_scientific_journal-4887	120	23	1.5	1.5	NUM
american_scientific_journal-4887	120	24	2	2	NUM
american_scientific_journal-4887	120	25	2	2	NUM
american_scientific_journal-4887	120	26	4.5	4.5	NUM
american_scientific_journal-4887	120	27	�	�	PROPN
american_scientific_journal-4887	120	28	�	�	PROPN
american_scientific_journal-4887	120	29	𝑥𝑥1	𝑥𝑥1	PROPN
american_scientific_journal-4887	120	30	𝑥𝑥2	𝑥𝑥2	ADV
american_scientific_journal-4887	120	31	𝑥𝑥3	𝑥𝑥3	PROPN
american_scientific_journal-4887	120	32	�	�	PROPN
american_scientific_journal-4887	120	33	=	=	SYM
american_scientific_journal-4887	120	34	�	�	PROPN
american_scientific_journal-4887	120	35	1897	1897	NUM
american_scientific_journal-4887	120	36	434.5	434.5	NUM
american_scientific_journal-4887	120	37	535.5	535.5	NUM
american_scientific_journal-4887	120	38	�	�	PROPN
american_scientific_journal-4887	120	39	(	(	PUNCT
american_scientific_journal-4887	120	40	13	13	NUM
american_scientific_journal-4887	120	41	)	)	PUNCT
american_scientific_journal-4887	120	42	𝑀𝑀𝑥𝑥	𝑀𝑀𝑥𝑥	PROPN
american_scientific_journal-4887	121	1	+	+	PUNCT
american_scientific_journal-4887	121	2	𝐴𝐴𝑦𝑦	𝐴𝐴𝑦𝑦	PROPN
american_scientific_journal-4887	121	3	=	=	SYM
american_scientific_journal-4887	121	4	𝑔𝑔	𝑔𝑔	PROPN
american_scientific_journal-4887	121	5	�	�	PROPN
american_scientific_journal-4887	121	6	1	1	NUM
american_scientific_journal-4887	121	7	1.5	1.5	NUM
american_scientific_journal-4887	121	8	0.5	0.5	NUM
american_scientific_journal-4887	121	9	0.1	0.1	NUM
american_scientific_journal-4887	121	10	0.1	0.1	NUM
american_scientific_journal-4887	121	11	0.2	0.2	NUM
american_scientific_journal-4887	121	12	0.1	0.1	NUM
american_scientific_journal-4887	121	13	0.1	0.1	NUM
american_scientific_journal-4887	121	14	0.1	0.1	NUM
american_scientific_journal-4887	121	15	�	�	PROPN
american_scientific_journal-4887	121	16	�	�	PROPN
american_scientific_journal-4887	121	17	𝑥𝑥1	𝑥𝑥1	PROPN
american_scientific_journal-4887	121	18	𝑥𝑥2	𝑥𝑥2	ADV
american_scientific_journal-4887	121	19	𝑥𝑥3	𝑥𝑥3	PROPN
american_scientific_journal-4887	121	20	�	�	PROPN
american_scientific_journal-4887	121	21	+	+	CCONJ
american_scientific_journal-4887	121	22	�	�	PROPN
american_scientific_journal-4887	121	23	19	19	NUM
american_scientific_journal-4887	121	24	12	12	NUM
american_scientific_journal-4887	121	25	6	6	NUM
american_scientific_journal-4887	121	26	2	2	NUM
american_scientific_journal-4887	121	27	4	4	NUM
american_scientific_journal-4887	121	28	1.5	1.5	NUM
american_scientific_journal-4887	121	29	2	2	NUM
american_scientific_journal-4887	121	30	2	2	NUM
american_scientific_journal-4887	121	31	4.5	4.5	NUM
american_scientific_journal-4887	121	32	�	�	PROPN
american_scientific_journal-4887	121	33	�	�	PROPN
american_scientific_journal-4887	121	34	𝑦𝑦1	𝑦𝑦1	PROPN
american_scientific_journal-4887	121	35	𝑦𝑦2	𝑦𝑦2	VERB
american_scientific_journal-4887	121	36	𝑦𝑦3	𝑦𝑦3	PROPN
american_scientific_journal-4887	121	37	�	�	PROPN
american_scientific_journal-4887	121	38	=	=	SYM
american_scientific_journal-4887	121	39	�	�	PROPN
american_scientific_journal-4887	121	40	427.7	427.7	NUM
american_scientific_journal-4887	121	41	76.2	76.2	NUM
american_scientific_journal-4887	121	42	88.3	88.3	NUM
american_scientific_journal-4887	121	43	�	�	PROPN
american_scientific_journal-4887	121	44	(	(	PUNCT
american_scientific_journal-4887	121	45	14	14	NUM
american_scientific_journal-4887	121	46	)	)	PUNCT
american_scientific_journal-4887	121	47	𝐴𝐴𝑧𝑧	𝐴𝐴𝑧𝑧	PROPN
american_scientific_journal-4887	122	1	+	+	NUM
american_scientific_journal-4887	122	2	𝑁𝑁𝑥𝑥	𝑁𝑁𝑥𝑥	PROPN
american_scientific_journal-4887	122	3	=	=	PUNCT
american_scientific_journal-4887	122	4	ℎ	ℎ	PART
american_scientific_journal-4887	122	5	�	�	PROPN
american_scientific_journal-4887	122	6	19	19	NUM
american_scientific_journal-4887	122	7	12	12	NUM
american_scientific_journal-4887	122	8	6	6	NUM
american_scientific_journal-4887	122	9	2	2	NUM
american_scientific_journal-4887	122	10	4	4	NUM
american_scientific_journal-4887	122	11	1.5	1.5	NUM
american_scientific_journal-4887	122	12	2	2	NUM
american_scientific_journal-4887	122	13	2	2	NUM
american_scientific_journal-4887	122	14	4.5	4.5	NUM
american_scientific_journal-4887	122	15	�	�	PROPN
american_scientific_journal-4887	122	16	�	�	PROPN
american_scientific_journal-4887	122	17	𝑧𝑧1	𝑧𝑧1	ADV
american_scientific_journal-4887	122	18	𝑧𝑧2	𝑧𝑧2	VERB
american_scientific_journal-4887	122	19	𝑧𝑧3	𝑧𝑧3	X
american_scientific_journal-4887	122	20	�	�	PROPN
american_scientific_journal-4887	122	21	+	+	CCONJ
american_scientific_journal-4887	122	22	�	�	PROPN
american_scientific_journal-4887	122	23	1	1	NUM
american_scientific_journal-4887	122	24	1.5	1.5	NUM
american_scientific_journal-4887	122	25	0.2	0.2	NUM
american_scientific_journal-4887	122	26	0.1	0.1	NUM
american_scientific_journal-4887	122	27	0.4	0.4	NUM
american_scientific_journal-4887	122	28	0.2	0.2	NUM
american_scientific_journal-4887	122	29	0.2	0.2	NUM
american_scientific_journal-4887	122	30	0.3	0.3	NUM
american_scientific_journal-4887	122	31	0.1	0.1	NUM
american_scientific_journal-4887	122	32	�	�	PROPN
american_scientific_journal-4887	122	33	�	�	PROPN
american_scientific_journal-4887	122	34	𝑥𝑥1	𝑥𝑥1	PROPN
american_scientific_journal-4887	122	35	𝑥𝑥2	𝑥𝑥2	ADV
american_scientific_journal-4887	122	36	𝑥𝑥3	𝑥𝑥3	PROPN
american_scientific_journal-4887	122	37	�	�	PROPN
american_scientific_journal-4887	122	38	=	=	SYM
american_scientific_journal-4887	122	39	�	�	PROPN
american_scientific_journal-4887	122	40	536.2	536.2	NUM
american_scientific_journal-4887	122	41	109.3	109.3	NUM
american_scientific_journal-4887	122	42	131.9	131.9	NUM
american_scientific_journal-4887	122	43	�	�	PROPN
american_scientific_journal-4887	122	44	(	(	PUNCT
american_scientific_journal-4887	122	45	15	15	NUM
american_scientific_journal-4887	122	46	)	)	PUNCT
american_scientific_journal-4887	122	47	for	for	ADP
american_scientific_journal-4887	122	48	equation	equation	NOUN
american_scientific_journal-4887	122	49	(	(	PUNCT
american_scientific_journal-4887	122	50	13	13	NUM
american_scientific_journal-4887	122	51	)	)	PUNCT
american_scientific_journal-4887	122	52	,	,	PUNCT
american_scientific_journal-4887	122	53	the	the	DET
american_scientific_journal-4887	122	54	equation	equation	NOUN
american_scientific_journal-4887	122	55	obtained	obtain	VERB
american_scientific_journal-4887	122	56	is	be	AUX
american_scientific_journal-4887	122	57	as	as	SCONJ
american_scientific_journal-4887	122	58	follows	follow	VERB
american_scientific_journal-4887	122	59	:	:	PUNCT
american_scientific_journal-4887	122	60	19𝑥𝑥1	19𝑥𝑥1	NUM
american_scientific_journal-4887	122	61	+	+	CCONJ
american_scientific_journal-4887	122	62	12𝑥𝑥2	12𝑥𝑥2	NUM
american_scientific_journal-4887	122	63	+	+	NUM
american_scientific_journal-4887	122	64	6𝑥𝑥3	6𝑥𝑥3	NUM
american_scientific_journal-4887	122	65	=	=	SYM
american_scientific_journal-4887	122	66	1897	1897	NUM
american_scientific_journal-4887	122	67	2𝑥𝑥1	2𝑥𝑥1	NUM
american_scientific_journal-4887	123	1	+	+	CCONJ
american_scientific_journal-4887	123	2	4𝑥𝑥2	4𝑥𝑥2	PUNCT
american_scientific_journal-4887	124	1	+	+	NUM
american_scientific_journal-4887	124	2	1.5𝑥𝑥3	1.5𝑥𝑥3	NUM
american_scientific_journal-4887	124	3	=	=	SYM
american_scientific_journal-4887	124	4	434.5	434.5	NUM
american_scientific_journal-4887	124	5	2𝑥𝑥1	2𝑥𝑥1	NUM
american_scientific_journal-4887	124	6	+	+	CCONJ
american_scientific_journal-4887	124	7	2𝑥𝑥2	2𝑥𝑥2	NUM
american_scientific_journal-4887	124	8	+	+	NUM
american_scientific_journal-4887	124	9	4.5𝑥𝑥3	4.5𝑥𝑥3	NUM
american_scientific_journal-4887	124	10	=	=	SYM
american_scientific_journal-4887	124	11	535.5	535.5	NUM
american_scientific_journal-4887	124	12	to	to	PART
american_scientific_journal-4887	124	13	get	get	VERB
american_scientific_journal-4887	124	14	the	the	DET
american_scientific_journal-4887	124	15	values	value	NOUN
american_scientific_journal-4887	124	16	𝑥𝑥1	𝑥𝑥1	NOUN
american_scientific_journal-4887	124	17	,	,	PUNCT
american_scientific_journal-4887	124	18	𝑥𝑥2	𝑥𝑥2	PRON
american_scientific_journal-4887	124	19	and	and	CCONJ
american_scientific_journal-4887	124	20	𝑥𝑥3	𝑥𝑥3	PRON
american_scientific_journal-4887	124	21	it	it	PRON
american_scientific_journal-4887	124	22	must	must	AUX
american_scientific_journal-4887	124	23	first	first	ADV
american_scientific_journal-4887	124	24	be	be	AUX
american_scientific_journal-4887	124	25	proven	prove	VERB
american_scientific_journal-4887	124	26	that	that	SCONJ
american_scientific_journal-4887	124	27	equation	equation	NOUN
american_scientific_journal-4887	124	28	(	(	PUNCT
american_scientific_journal-4887	124	29	13	13	NUM
american_scientific_journal-4887	124	30	)	)	PUNCT
american_scientific_journal-4887	124	31	strictly	strictly	ADV
american_scientific_journal-4887	124	32	diagonally	diagonally	ADV
american_scientific_journal-4887	124	33	dominant	dominant	ADJ
american_scientific_journal-4887	124	34	in	in	ADP
american_scientific_journal-4887	124	35	the	the	DET
american_scientific_journal-4887	124	36	following	following	NOUN
american_scientific_journal-4887	124	37	:	:	PUNCT
american_scientific_journal-4887	124	38	|𝑎𝑎11|	|𝑎𝑎11|	NOUN
american_scientific_journal-4887	124	39	≥	≥	NUM
american_scientific_journal-4887	124	40	|𝑎𝑎12|	|𝑎𝑎12|	PROPN
american_scientific_journal-4887	124	41	+	+	ADJ
american_scientific_journal-4887	124	42	|𝑎𝑎13|	|𝑎𝑎13|	PROPN
american_scientific_journal-4887	124	43	→	→	SYM
american_scientific_journal-4887	124	44	|19|	|19|	X
american_scientific_journal-4887	124	45	≥	≥	NOUN
american_scientific_journal-4887	124	46	|12|	|12|	NOUN
american_scientific_journal-4887	124	47	+	+	CCONJ
american_scientific_journal-4887	125	1	|6|	|6|	NOUN
american_scientific_journal-4887	125	2	=	=	SYM
american_scientific_journal-4887	125	3	19	19	NUM
american_scientific_journal-4887	125	4	≥	≥	NOUN
american_scientific_journal-4887	125	5	18	18	NUM
american_scientific_journal-4887	125	6	|𝑎𝑎22|	|𝑎𝑎22|	PROPN
american_scientific_journal-4887	125	7	≥	≥	NOUN
american_scientific_journal-4887	125	8	|𝑎𝑎21|	|𝑎𝑎21|	VERB
american_scientific_journal-4887	125	9	+	+	CCONJ
american_scientific_journal-4887	125	10	|𝑎𝑎23|	|𝑎𝑎23|	ADJ
american_scientific_journal-4887	125	11	→	→	SYM
american_scientific_journal-4887	125	12	|4|	|4|	NOUN
american_scientific_journal-4887	125	13	≥	≥	NOUN
american_scientific_journal-4887	125	14	|2|	|2|	PROPN
american_scientific_journal-4887	125	15	+	+	NUM
american_scientific_journal-4887	125	16	|1.5|	|1.5|	NOUN
american_scientific_journal-4887	125	17	=	=	SYM
american_scientific_journal-4887	125	18	4	4	NUM
american_scientific_journal-4887	125	19	≥	≥	NOUN
american_scientific_journal-4887	125	20	3.5	3.5	NUM
american_scientific_journal-4887	125	21	|𝑎𝑎33|	|𝑎𝑎33|	NOUN
american_scientific_journal-4887	125	22	≥	≥	NOUN
american_scientific_journal-4887	125	23	|𝑎𝑎31|	|𝑎𝑎31|	ADJ
american_scientific_journal-4887	125	24	+	+	CCONJ
american_scientific_journal-4887	125	25	|𝑎𝑎32|	|𝑎𝑎32|	NUM
american_scientific_journal-4887	125	26	→	→	SYM
american_scientific_journal-4887	125	27	|4.5|	|4.5|	PRON
american_scientific_journal-4887	125	28	≥	≥	NOUN
american_scientific_journal-4887	125	29	|2|	|2|	PROPN
american_scientific_journal-4887	125	30	+	+	CCONJ
american_scientific_journal-4887	125	31	|2|	|2|	PROPN
american_scientific_journal-4887	125	32	=	=	SYM
american_scientific_journal-4887	125	33	4.5	4.5	NUM
american_scientific_journal-4887	125	34	≥	≥	NOUN
american_scientific_journal-4887	125	35	4	4	NUM
american_scientific_journal-4887	125	36	all	all	DET
american_scientific_journal-4887	125	37	equations	equation	NOUN
american_scientific_journal-4887	125	38	(	(	PUNCT
american_scientific_journal-4887	125	39	13	13	NUM
american_scientific_journal-4887	125	40	)	)	PUNCT
american_scientific_journal-4887	125	41	are	be	AUX
american_scientific_journal-4887	125	42	proven	prove	VERB
american_scientific_journal-4887	125	43	to	to	PART
american_scientific_journal-4887	125	44	be	be	AUX
american_scientific_journal-4887	125	45	diagonally	diagonally	ADV
american_scientific_journal-4887	125	46	dominant	dominant	ADJ
american_scientific_journal-4887	125	47	,	,	PUNCT
american_scientific_journal-4887	125	48	so	so	ADV
american_scientific_journal-4887	125	49	obtained	obtain	VERB
american_scientific_journal-4887	125	50	:	:	PUNCT
american_scientific_journal-4887	125	51	𝑥𝑥1	𝑥𝑥1	NOUN
american_scientific_journal-4887	125	52	=	=	SYM
american_scientific_journal-4887	125	53	1	1	NUM
american_scientific_journal-4887	125	54	19	19	NUM
american_scientific_journal-4887	125	55	(	(	PUNCT
american_scientific_journal-4887	125	56	1897	1897	NUM
american_scientific_journal-4887	125	57	−	−	NOUN
american_scientific_journal-4887	125	58	12𝑥𝑥2	12𝑥𝑥2	NUM
american_scientific_journal-4887	125	59	−	−	NOUN
american_scientific_journal-4887	125	60	6𝑥𝑥3	6𝑥𝑥3	NUM
american_scientific_journal-4887	125	61	)	)	PUNCT
american_scientific_journal-4887	125	62	𝑥𝑥2	𝑥𝑥2	ADV
american_scientific_journal-4887	126	1	=	=	SYM
american_scientific_journal-4887	126	2	1	1	NUM
american_scientific_journal-4887	126	3	4	4	NUM
american_scientific_journal-4887	126	4	(	(	PUNCT
american_scientific_journal-4887	126	5	434.5	434.5	NUM
american_scientific_journal-4887	126	6	−	−	NOUN
american_scientific_journal-4887	126	7	2𝑥𝑥1	2𝑥𝑥1	NUM
american_scientific_journal-4887	126	8	–	–	PUNCT
american_scientific_journal-4887	126	9	1.5𝑥𝑥3	1.5𝑥𝑥3	NUM
american_scientific_journal-4887	126	10	)	)	PUNCT
american_scientific_journal-4887	126	11	𝑥𝑥3	𝑥𝑥3	PROPN
american_scientific_journal-4887	126	12	=	=	NOUN
american_scientific_journal-4887	126	13	1	1	NUM
american_scientific_journal-4887	126	14	4.5	4.5	NUM
american_scientific_journal-4887	126	15	(	(	PUNCT
american_scientific_journal-4887	126	16	535.5	535.5	NUM
american_scientific_journal-4887	126	17	−	−	PROPN
american_scientific_journal-4887	126	18	2𝑥𝑥1	2𝑥𝑥1	NUM
american_scientific_journal-4887	126	19	−	−	NOUN
american_scientific_journal-4887	126	20	2𝑥𝑥2	2𝑥𝑥2	NUM
american_scientific_journal-4887	126	21	)	)	PUNCT
american_scientific_journal-4887	126	22	then	then	ADV
american_scientific_journal-4887	126	23	the	the	DET
american_scientific_journal-4887	126	24	iteration	iteration	NOUN
american_scientific_journal-4887	126	25	process	process	NOUN
american_scientific_journal-4887	126	26	starts	start	VERB
american_scientific_journal-4887	126	27	with	with	ADP
american_scientific_journal-4887	126	28	the	the	DET
american_scientific_journal-4887	126	29	intial	intial	ADJ
american_scientific_journal-4887	126	30	value	value	NOUN
american_scientific_journal-4887	126	31	(	(	PUNCT
american_scientific_journal-4887	126	32	0	0	NUM
american_scientific_journal-4887	126	33	,	,	PUNCT
american_scientific_journal-4887	126	34	0	0	NUM
american_scientific_journal-4887	126	35	,	,	PUNCT
american_scientific_journal-4887	126	36	0	0	NUM
american_scientific_journal-4887	126	37	)	)	PUNCT
american_scientific_journal-4887	126	38	,	,	PUNCT
american_scientific_journal-4887	126	39	which	which	PRON
american_scientific_journal-4887	126	40	is	be	AUX
american_scientific_journal-4887	126	41	as	as	SCONJ
american_scientific_journal-4887	126	42	follows	follow	VERB
american_scientific_journal-4887	126	43	:	:	PUNCT
american_scientific_journal-4887	126	44	first	first	ADJ
american_scientific_journal-4887	126	45	iteration	iteration	NOUN
american_scientific_journal-4887	126	46	𝑥𝑥1(1	𝑥𝑥1(1	NOUN
american_scientific_journal-4887	126	47	)	)	PUNCT
american_scientific_journal-4887	126	48	=	=	SYM
american_scientific_journal-4887	127	1	1	1	NUM
american_scientific_journal-4887	127	2	19	19	NUM
american_scientific_journal-4887	127	3	(	(	PUNCT
american_scientific_journal-4887	127	4	1897	1897	NUM
american_scientific_journal-4887	127	5	–	–	PUNCT
american_scientific_journal-4887	127	6	12(0	12(0	NUM
american_scientific_journal-4887	127	7	)	)	PUNCT
american_scientific_journal-4887	127	8	–	–	PUNCT
american_scientific_journal-4887	127	9	6(0	6(0	NUM
american_scientific_journal-4887	127	10	)	)	PUNCT
american_scientific_journal-4887	127	11	)	)	PUNCT
american_scientific_journal-4887	128	1	=	=	SYM
american_scientific_journal-4887	128	2	1	1	NUM
american_scientific_journal-4887	128	3	19	19	NUM
american_scientific_journal-4887	128	4	(	(	PUNCT
american_scientific_journal-4887	128	5	1897	1897	NUM
american_scientific_journal-4887	128	6	)	)	PUNCT
american_scientific_journal-4887	128	7	=	=	NOUN
american_scientific_journal-4887	128	8	99.8421	99.8421	NUM
american_scientific_journal-4887	128	9	𝑥𝑥2(1	𝑥𝑥2(1	NOUN
american_scientific_journal-4887	128	10	)	)	PUNCT
american_scientific_journal-4887	128	11	=	=	SYM
american_scientific_journal-4887	129	1	1	1	NUM
american_scientific_journal-4887	129	2	4	4	NUM
american_scientific_journal-4887	129	3	(	(	PUNCT
american_scientific_journal-4887	129	4	434.5	434.5	NUM
american_scientific_journal-4887	129	5	–	–	PUNCT
american_scientific_journal-4887	129	6	2(99.8421	2(99.8421	NUM
american_scientific_journal-4887	129	7	)	)	PUNCT
american_scientific_journal-4887	129	8	–	–	PUNCT
american_scientific_journal-4887	129	9	1.5(0	1.5(0	NUM
american_scientific_journal-4887	129	10	)	)	PUNCT
american_scientific_journal-4887	129	11	)	)	PUNCT
american_scientific_journal-4887	129	12	=	=	SYM
american_scientific_journal-4887	130	1	1	1	NUM
american_scientific_journal-4887	130	2	4	4	NUM
american_scientific_journal-4887	130	3	(	(	PUNCT
american_scientific_journal-4887	130	4	234.8158	234.8158	NUM
american_scientific_journal-4887	130	5	)	)	PUNCT
american_scientific_journal-4887	130	6	=	=	SYM
american_scientific_journal-4887	130	7	58.7039	58.7039	NUM
american_scientific_journal-4887	130	8	𝑥𝑥3(1	𝑥𝑥3(1	NOUN
american_scientific_journal-4887	130	9	)	)	PUNCT
american_scientific_journal-4887	130	10	=	=	SYM
american_scientific_journal-4887	130	11	1	1	NUM
american_scientific_journal-4887	130	12	4.5	4.5	NUM
american_scientific_journal-4887	130	13	(	(	PUNCT
american_scientific_journal-4887	130	14	535.5	535.5	NUM
american_scientific_journal-4887	130	15	–	–	SYM
american_scientific_journal-4887	130	16	2(99.8421	2(99.8421	NUM
american_scientific_journal-4887	130	17	)	)	PUNCT
american_scientific_journal-4887	130	18	–	–	PUNCT
american_scientific_journal-4887	130	19	2(58.7039	2(58.7039	NUM
american_scientific_journal-4887	130	20	)	)	PUNCT
american_scientific_journal-4887	130	21	)	)	PUNCT
american_scientific_journal-4887	131	1	=	=	PUNCT
american_scientific_journal-4887	131	2	1	1	NUM
american_scientific_journal-4887	131	3	4.5	4.5	NUM
american_scientific_journal-4887	131	4	(	(	PUNCT
american_scientific_journal-4887	131	5	218.408	218.408	NUM
american_scientific_journal-4887	131	6	)	)	PUNCT
american_scientific_journal-4887	131	7	=	=	SYM
american_scientific_journal-4887	131	8	48.5351	48.5351	NUM
american_scientific_journal-4887	131	9	second	second	ADJ
american_scientific_journal-4887	131	10	iteration	iteration	NOUN
american_scientific_journal-4887	131	11	𝑥𝑥1(2	𝑥𝑥1(2	NOUN
american_scientific_journal-4887	131	12	)	)	PUNCT
american_scientific_journal-4887	131	13	=	=	SYM
american_scientific_journal-4887	132	1	1	1	NUM
american_scientific_journal-4887	132	2	19	19	NUM
american_scientific_journal-4887	132	3	(	(	PUNCT
american_scientific_journal-4887	132	4	1897	1897	NUM
american_scientific_journal-4887	132	5	–	–	PUNCT
american_scientific_journal-4887	132	6	12(58.7039	12(58.7039	NUM
american_scientific_journal-4887	132	7	)	)	PUNCT
american_scientific_journal-4887	132	8	–	–	PUNCT
american_scientific_journal-4887	132	9	6(48.5351	6(48.5351	NOUN
american_scientific_journal-4887	132	10	)	)	PUNCT
american_scientific_journal-4887	132	11	)	)	PUNCT
american_scientific_journal-4887	133	1	=	=	SYM
american_scientific_journal-4887	134	1	1	1	NUM
american_scientific_journal-4887	134	2	19	19	NUM
american_scientific_journal-4887	134	3	(	(	PUNCT
american_scientific_journal-4887	134	4	901.3426	901.3426	NUM
american_scientific_journal-4887	134	5	)	)	PUNCT
american_scientific_journal-4887	134	6	=	=	SYM
american_scientific_journal-4887	134	7	47.4390	47.4390	NUM
american_scientific_journal-4887	134	8	𝑥𝑥2(2	𝑥𝑥2(2	NOUN
american_scientific_journal-4887	134	9	)	)	PUNCT
american_scientific_journal-4887	134	10	=	=	SYM
american_scientific_journal-4887	134	11	1	1	NUM
american_scientific_journal-4887	134	12	4	4	NUM
american_scientific_journal-4887	134	13	(	(	PUNCT
american_scientific_journal-4887	134	14	434.5	434.5	NUM
american_scientific_journal-4887	134	15	–	–	PUNCT
american_scientific_journal-4887	134	16	2(47.4390	2(47.4390	NUM
american_scientific_journal-4887	134	17	)	)	PUNCT
american_scientific_journal-4887	134	18	–	–	PUNCT
american_scientific_journal-4887	134	19	1.5(48.5351	1.5(48.5351	NOUN
american_scientific_journal-4887	134	20	)	)	PUNCT
american_scientific_journal-4887	134	21	=	=	SYM
american_scientific_journal-4887	135	1	1	1	NUM
american_scientific_journal-4887	135	2	4	4	NUM
american_scientific_journal-4887	135	3	(	(	PUNCT
american_scientific_journal-4887	135	4	266.8194	266.8194	NUM
american_scientific_journal-4887	135	5	)	)	PUNCT
american_scientific_journal-4887	135	6	=	=	PUNCT
american_scientific_journal-4887	135	7	66.7048	66.7048	NUM
american_scientific_journal-4887	135	8	american	american	ADJ
american_scientific_journal-4887	135	9	scientific	scientific	ADJ
american_scientific_journal-4887	135	10	research	research	NOUN
american_scientific_journal-4887	135	11	journal	journal	NOUN
american_scientific_journal-4887	135	12	for	for	ADP
american_scientific_journal-4887	135	13	engineering	engineering	NOUN
american_scientific_journal-4887	135	14	,	,	PUNCT
american_scientific_journal-4887	135	15	technology	technology	NOUN
american_scientific_journal-4887	135	16	,	,	PUNCT
american_scientific_journal-4887	135	17	and	and	CCONJ
american_scientific_journal-4887	135	18	sciences	science	NOUN
american_scientific_journal-4887	135	19	(	(	PUNCT
american_scientific_journal-4887	135	20	asrjets	asrjet	NOUN
american_scientific_journal-4887	135	21	)	)	PUNCT
american_scientific_journal-4887	135	22	(	(	PUNCT
american_scientific_journal-4887	135	23	2019	2019	NUM
american_scientific_journal-4887	135	24	)	)	PUNCT
american_scientific_journal-4887	135	25	volume	volume	NOUN
american_scientific_journal-4887	135	26	56	56	NUM
american_scientific_journal-4887	135	27	,	,	PUNCT
american_scientific_journal-4887	135	28	no	no	DET
american_scientific_journal-4887	135	29	1	1	NUM
american_scientific_journal-4887	135	30	,	,	PUNCT
american_scientific_journal-4887	135	31	pp	pp	ADV
american_scientific_journal-4887	135	32	113	113	NUM
american_scientific_journal-4887	135	33	-	-	SYM
american_scientific_journal-4887	135	34	123	123	NUM
american_scientific_journal-4887	135	35	120	120	NUM
american_scientific_journal-4887	135	36	𝑥𝑥3(2	𝑥𝑥3(2	NOUN
american_scientific_journal-4887	135	37	)	)	PUNCT
american_scientific_journal-4887	135	38	=	=	SYM
american_scientific_journal-4887	135	39	1	1	NUM
american_scientific_journal-4887	135	40	4.5	4.5	NUM
american_scientific_journal-4887	135	41	(	(	PUNCT
american_scientific_journal-4887	135	42	535.5	535.5	NUM
american_scientific_journal-4887	135	43	–	–	PUNCT
american_scientific_journal-4887	135	44	2(47.4390	2(47.4390	NUM
american_scientific_journal-4887	135	45	)	)	PUNCT
american_scientific_journal-4887	135	46	–	–	PUNCT
american_scientific_journal-4887	135	47	2(66.7048	2(66.7048	NUM
american_scientific_journal-4887	135	48	)	)	PUNCT
american_scientific_journal-4887	135	49	)	)	PUNCT
american_scientific_journal-4887	135	50	=	=	PUNCT
american_scientific_journal-4887	136	1	1	1	NUM
american_scientific_journal-4887	136	2	4.5	4.5	NUM
american_scientific_journal-4887	136	3	(	(	PUNCT
american_scientific_journal-4887	136	4	307.2124	307.2124	NUM
american_scientific_journal-4887	136	5	)	)	PUNCT
american_scientific_journal-4887	136	6	=	=	SYM
american_scientific_journal-4887	136	7	68.2694	68.2694	NUM
american_scientific_journal-4887	136	8	based	base	VERB
american_scientific_journal-4887	136	9	on	on	ADP
american_scientific_journal-4887	136	10	equation	equation	NOUN
american_scientific_journal-4887	136	11	(	(	PUNCT
american_scientific_journal-4887	136	12	12	12	NUM
american_scientific_journal-4887	136	13	)	)	PUNCT
american_scientific_journal-4887	136	14	,	,	PUNCT
american_scientific_journal-4887	136	15	the	the	DET
american_scientific_journal-4887	136	16	iteration	iteration	NOUN
american_scientific_journal-4887	136	17	process	process	NOUN
american_scientific_journal-4887	136	18	until	until	SCONJ
american_scientific_journal-4887	136	19	10th	10th	ADJ
american_scientific_journal-4887	136	20	iteration	iteration	NOUN
american_scientific_journal-4887	136	21	is	be	AUX
american_scientific_journal-4887	136	22	obtained	obtain	VERB
american_scientific_journal-4887	136	23	the	the	DET
american_scientific_journal-4887	136	24	value	value	NOUN
american_scientific_journal-4887	136	25	𝑥𝑥1	𝑥𝑥1	NOUN
american_scientific_journal-4887	136	26	=	=	SYM
american_scientific_journal-4887	136	27	37.0021	37.0021	NUM
american_scientific_journal-4887	136	28	,	,	PUNCT
american_scientific_journal-4887	136	29	𝑥𝑥2	𝑥𝑥2	ADV
american_scientific_journal-4887	136	30	=	=	SYM
american_scientific_journal-4887	136	31	61.9987	61.9987	NUM
american_scientific_journal-4887	136	32	,	,	PUNCT
american_scientific_journal-4887	136	33	𝑥𝑥3	𝑥𝑥3	PROPN
american_scientific_journal-4887	136	34	=	=	SYM
american_scientific_journal-4887	136	35	74.9996	74.9996	NUM
american_scientific_journal-4887	136	36	.	.	PUNCT
american_scientific_journal-4887	137	1	for	for	ADP
american_scientific_journal-4887	137	2	equation	equation	NOUN
american_scientific_journal-4887	137	3	(	(	PUNCT
american_scientific_journal-4887	137	4	14	14	NUM
american_scientific_journal-4887	137	5	)	)	PUNCT
american_scientific_journal-4887	137	6	,	,	PUNCT
american_scientific_journal-4887	137	7	the	the	DET
american_scientific_journal-4887	137	8	equation	equation	NOUN
american_scientific_journal-4887	137	9	obtained	obtain	VERB
american_scientific_journal-4887	137	10	is	be	AUX
american_scientific_journal-4887	137	11	as	as	SCONJ
american_scientific_journal-4887	137	12	follows	follow	VERB
american_scientific_journal-4887	137	13	:	:	PUNCT
american_scientific_journal-4887	137	14	𝑥𝑥1	𝑥𝑥1	NOUN
american_scientific_journal-4887	137	15	+	+	CCONJ
american_scientific_journal-4887	137	16	1.5𝑥𝑥2	1.5𝑥𝑥2	NUM
american_scientific_journal-4887	137	17	+	+	NUM
american_scientific_journal-4887	137	18	0.5𝑥𝑥3	0.5𝑥𝑥3	NUM
american_scientific_journal-4887	138	1	+	+	CCONJ
american_scientific_journal-4887	138	2	19𝑦𝑦1	19𝑦𝑦1	NUM
american_scientific_journal-4887	139	1	+	+	CCONJ
american_scientific_journal-4887	139	2	12𝑦𝑦2	12𝑦𝑦2	ADJ
american_scientific_journal-4887	139	3	+	+	CCONJ
american_scientific_journal-4887	139	4	6𝑦𝑦3	6𝑦𝑦3	NUM
american_scientific_journal-4887	139	5	=	=	VERB
american_scientific_journal-4887	139	6	427.7	427.7	NUM
american_scientific_journal-4887	139	7	0.1	0.1	NUM
american_scientific_journal-4887	139	8	𝑥𝑥1	𝑥𝑥1	NOUN
american_scientific_journal-4887	139	9	+	+	CCONJ
american_scientific_journal-4887	139	10	0.1𝑥𝑥2	0.1𝑥𝑥2	NUM
american_scientific_journal-4887	139	11	+	+	NUM
american_scientific_journal-4887	139	12	0.2𝑥𝑥3	0.2𝑥𝑥3	NOUN
american_scientific_journal-4887	139	13	+	+	CCONJ
american_scientific_journal-4887	139	14	2𝑦𝑦1	2𝑦𝑦1	NUM
american_scientific_journal-4887	139	15	+	+	CCONJ
american_scientific_journal-4887	139	16	4𝑦𝑦2	4𝑦𝑦2	NUM
american_scientific_journal-4887	140	1	+	+	CCONJ
american_scientific_journal-4887	140	2	1.5𝑦𝑦3	1.5𝑦𝑦3	NUM
american_scientific_journal-4887	140	3	=	=	NOUN
american_scientific_journal-4887	140	4	76.2	76.2	NUM
american_scientific_journal-4887	140	5	0.1	0.1	NUM
american_scientific_journal-4887	140	6	𝑥𝑥1	𝑥𝑥1	NOUN
american_scientific_journal-4887	140	7	+	+	CCONJ
american_scientific_journal-4887	140	8	0.1𝑥𝑥2	0.1𝑥𝑥2	NUM
american_scientific_journal-4887	140	9	+	+	NUM
american_scientific_journal-4887	140	10	0.1𝑥𝑥3	0.1𝑥𝑥3	NOUN
american_scientific_journal-4887	140	11	+	+	SYM
american_scientific_journal-4887	140	12	2𝑦𝑦1	2𝑦𝑦1	NUM
american_scientific_journal-4887	140	13	+	+	CCONJ
american_scientific_journal-4887	140	14	2𝑦𝑦2	2𝑦𝑦2	NUM
american_scientific_journal-4887	140	15	+	+	CCONJ
american_scientific_journal-4887	140	16	4.5𝑦𝑦3	4.5𝑦𝑦3	NOUN
american_scientific_journal-4887	140	17	=	=	SYM
american_scientific_journal-4887	140	18	88.3	88.3	NUM
american_scientific_journal-4887	140	19	because	because	SCONJ
american_scientific_journal-4887	140	20	the	the	DET
american_scientific_journal-4887	140	21	value	value	NOUN
american_scientific_journal-4887	140	22	𝑥𝑥1	𝑥𝑥1	NOUN
american_scientific_journal-4887	140	23	,	,	PUNCT
american_scientific_journal-4887	140	24	𝑥𝑥2	𝑥𝑥2	PROPN
american_scientific_journal-4887	140	25	,	,	PUNCT
american_scientific_journal-4887	140	26	𝑥𝑥3	𝑥𝑥3	PROPN
american_scientific_journal-4887	140	27	has	have	AUX
american_scientific_journal-4887	140	28	been	be	AUX
american_scientific_journal-4887	140	29	obtained	obtain	VERB
american_scientific_journal-4887	140	30	,	,	PUNCT
american_scientific_journal-4887	140	31	substitution	substitution	NOUN
american_scientific_journal-4887	140	32	value	value	NOUN
american_scientific_journal-4887	140	33	is	be	AUX
american_scientific_journal-4887	140	34	put	put	VERB
american_scientific_journal-4887	140	35	into	into	ADP
american_scientific_journal-4887	140	36	equation	equation	NOUN
american_scientific_journal-4887	140	37	(	(	PUNCT
american_scientific_journal-4887	140	38	14	14	NUM
american_scientific_journal-4887	140	39	)	)	PUNCT
american_scientific_journal-4887	140	40	so	so	SCONJ
american_scientific_journal-4887	140	41	that	that	SCONJ
american_scientific_journal-4887	140	42	the	the	DET
american_scientific_journal-4887	140	43	new	new	ADJ
american_scientific_journal-4887	140	44	equation	equation	NOUN
american_scientific_journal-4887	140	45	is	be	AUX
american_scientific_journal-4887	140	46	obtained	obtain	VERB
american_scientific_journal-4887	140	47	as	as	ADP
american_scientific_journal-4887	140	48	follows	follow	VERB
american_scientific_journal-4887	140	49	:	:	PUNCT
american_scientific_journal-4887	140	50	19𝑦𝑦1	19𝑦𝑦1	PROPN
american_scientific_journal-4887	141	1	+	+	CCONJ
american_scientific_journal-4887	141	2	12𝑦𝑦2	12𝑦𝑦2	ADJ
american_scientific_journal-4887	141	3	+	+	CCONJ
american_scientific_journal-4887	141	4	6𝑦𝑦3	6𝑦𝑦3	NUM
american_scientific_journal-4887	141	5	=	=	SYM
american_scientific_journal-4887	141	6	260.2	260.2	NUM
american_scientific_journal-4887	141	7	2𝑦𝑦1	2𝑦𝑦1	NUM
american_scientific_journal-4887	141	8	+	+	CCONJ
american_scientific_journal-4887	141	9	4𝑦𝑦2	4𝑦𝑦2	NUM
american_scientific_journal-4887	142	1	+	+	CCONJ
american_scientific_journal-4887	142	2	1.5𝑦𝑦3	1.5𝑦𝑦3	NUM
american_scientific_journal-4887	142	3	=	=	SYM
american_scientific_journal-4887	142	4	51.3	51.3	NUM
american_scientific_journal-4887	142	5	2𝑦𝑦1	2𝑦𝑦1	NUM
american_scientific_journal-4887	143	1	+	+	CCONJ
american_scientific_journal-4887	143	2	2𝑦𝑦2	2𝑦𝑦2	NUM
american_scientific_journal-4887	143	3	+	+	CCONJ
american_scientific_journal-4887	143	4	4.5𝑦𝑦3	4.5𝑦𝑦3	NOUN
american_scientific_journal-4887	143	5	=	=	SYM
american_scientific_journal-4887	143	6	70.9	70.9	NUM
american_scientific_journal-4887	143	7	to	to	PART
american_scientific_journal-4887	143	8	get	get	VERB
american_scientific_journal-4887	143	9	the	the	DET
american_scientific_journal-4887	143	10	values	value	NOUN
american_scientific_journal-4887	143	11	𝑦𝑦1,𝑦𝑦2	𝑦𝑦1,𝑦𝑦2	PROPN
american_scientific_journal-4887	143	12	and	and	CCONJ
american_scientific_journal-4887	143	13	𝑦𝑦3	𝑦𝑦3	PROPN
american_scientific_journal-4887	143	14	,	,	PUNCT
american_scientific_journal-4887	143	15	it	it	PRON
american_scientific_journal-4887	143	16	must	must	AUX
american_scientific_journal-4887	143	17	first	first	ADV
american_scientific_journal-4887	143	18	be	be	AUX
american_scientific_journal-4887	143	19	proven	prove	VERB
american_scientific_journal-4887	143	20	that	that	SCONJ
american_scientific_journal-4887	143	21	equation	equation	NOUN
american_scientific_journal-4887	143	22	(	(	PUNCT
american_scientific_journal-4887	143	23	14	14	NUM
american_scientific_journal-4887	143	24	)	)	PUNCT
american_scientific_journal-4887	143	25	strictly	strictly	ADV
american_scientific_journal-4887	143	26	diagonally	diagonally	ADV
american_scientific_journal-4887	143	27	dominant	dominant	ADJ
american_scientific_journal-4887	143	28	in	in	ADP
american_scientific_journal-4887	143	29	the	the	DET
american_scientific_journal-4887	143	30	following	following	NOUN
american_scientific_journal-4887	143	31	:	:	PUNCT
american_scientific_journal-4887	143	32	|𝑎𝑎11|	|𝑎𝑎11|	NOUN
american_scientific_journal-4887	143	33	≥	≥	NUM
american_scientific_journal-4887	143	34	|𝑎𝑎12|	|𝑎𝑎12|	PROPN
american_scientific_journal-4887	143	35	+	+	ADJ
american_scientific_journal-4887	143	36	|𝑎𝑎13|	|𝑎𝑎13|	PROPN
american_scientific_journal-4887	143	37	→	→	SYM
american_scientific_journal-4887	143	38	|19|	|19|	X
american_scientific_journal-4887	143	39	≥	≥	NOUN
american_scientific_journal-4887	143	40	|12|	|12|	NOUN
american_scientific_journal-4887	143	41	+	+	CCONJ
american_scientific_journal-4887	144	1	|6|	|6|	NOUN
american_scientific_journal-4887	144	2	=	=	SYM
american_scientific_journal-4887	144	3	19	19	NUM
american_scientific_journal-4887	144	4	≥	≥	NOUN
american_scientific_journal-4887	144	5	18	18	NUM
american_scientific_journal-4887	144	6	|𝑎𝑎22|	|𝑎𝑎22|	PROPN
american_scientific_journal-4887	144	7	≥	≥	NOUN
american_scientific_journal-4887	144	8	|𝑎𝑎21|	|𝑎𝑎21|	VERB
american_scientific_journal-4887	144	9	+	+	CCONJ
american_scientific_journal-4887	144	10	|𝑎𝑎23|	|𝑎𝑎23|	ADJ
american_scientific_journal-4887	144	11	→	→	SYM
american_scientific_journal-4887	144	12	|4|	|4|	NOUN
american_scientific_journal-4887	144	13	≥	≥	NOUN
american_scientific_journal-4887	144	14	|2|	|2|	PROPN
american_scientific_journal-4887	144	15	+	+	NUM
american_scientific_journal-4887	144	16	|1.5|	|1.5|	NOUN
american_scientific_journal-4887	144	17	=	=	SYM
american_scientific_journal-4887	144	18	4	4	NUM
american_scientific_journal-4887	144	19	≥	≥	NOUN
american_scientific_journal-4887	144	20	3.5	3.5	NUM
american_scientific_journal-4887	144	21	|𝑎𝑎33|	|𝑎𝑎33|	NOUN
american_scientific_journal-4887	144	22	≥	≥	NOUN
american_scientific_journal-4887	144	23	|𝑎𝑎31|	|𝑎𝑎31|	ADJ
american_scientific_journal-4887	144	24	+	+	CCONJ
american_scientific_journal-4887	144	25	|𝑎𝑎32|	|𝑎𝑎32|	NUM
american_scientific_journal-4887	144	26	→	→	SYM
american_scientific_journal-4887	144	27	|4.5|	|4.5|	PRON
american_scientific_journal-4887	144	28	≥	≥	NOUN
american_scientific_journal-4887	144	29	|2|	|2|	PROPN
american_scientific_journal-4887	144	30	+	+	CCONJ
american_scientific_journal-4887	144	31	|2|	|2|	PROPN
american_scientific_journal-4887	144	32	=	=	SYM
american_scientific_journal-4887	144	33	4.5	4.5	NUM
american_scientific_journal-4887	144	34	≥	≥	NOUN
american_scientific_journal-4887	144	35	4	4	NUM
american_scientific_journal-4887	144	36	all	all	DET
american_scientific_journal-4887	144	37	equations	equation	NOUN
american_scientific_journal-4887	144	38	(	(	PUNCT
american_scientific_journal-4887	144	39	14	14	NUM
american_scientific_journal-4887	144	40	)	)	PUNCT
american_scientific_journal-4887	144	41	are	be	AUX
american_scientific_journal-4887	144	42	proven	prove	VERB
american_scientific_journal-4887	144	43	to	to	PART
american_scientific_journal-4887	144	44	be	be	AUX
american_scientific_journal-4887	144	45	diagonally	diagonally	ADV
american_scientific_journal-4887	144	46	dominant	dominant	ADJ
american_scientific_journal-4887	144	47	,	,	PUNCT
american_scientific_journal-4887	144	48	so	so	ADV
american_scientific_journal-4887	144	49	obtained	obtain	VERB
american_scientific_journal-4887	144	50	:	:	PUNCT
american_scientific_journal-4887	145	1	𝑦𝑦1	𝑦𝑦1	PROPN
american_scientific_journal-4887	145	2	=	=	SYM
american_scientific_journal-4887	145	3	1	1	NUM
american_scientific_journal-4887	145	4	19	19	NUM
american_scientific_journal-4887	145	5	(	(	PUNCT
american_scientific_journal-4887	145	6	260.2	260.2	NUM
american_scientific_journal-4887	145	7	−	−	NOUN
american_scientific_journal-4887	145	8	12𝑦𝑦2	12𝑦𝑦2	NUM
american_scientific_journal-4887	145	9	−	−	NOUN
american_scientific_journal-4887	145	10	6𝑦𝑦3	6𝑦𝑦3	NUM
american_scientific_journal-4887	145	11	)	)	PUNCT
american_scientific_journal-4887	145	12	𝑦𝑦2	𝑦𝑦2	NOUN
american_scientific_journal-4887	145	13	=	=	SYM
american_scientific_journal-4887	145	14	1	1	NUM
american_scientific_journal-4887	145	15	4	4	NUM
american_scientific_journal-4887	145	16	(	(	PUNCT
american_scientific_journal-4887	145	17	51.3	51.3	NUM
american_scientific_journal-4887	145	18	−	−	NOUN
american_scientific_journal-4887	145	19	2𝑦𝑦1	2𝑦𝑦1	NUM
american_scientific_journal-4887	145	20	–	–	PUNCT
american_scientific_journal-4887	145	21	1.5𝑦𝑦3	1.5𝑦𝑦3	NUM
american_scientific_journal-4887	145	22	)	)	PUNCT
american_scientific_journal-4887	145	23	𝑦𝑦3	𝑦𝑦3	NOUN
american_scientific_journal-4887	145	24	=	=	SYM
american_scientific_journal-4887	145	25	1	1	NUM
american_scientific_journal-4887	145	26	4.5	4.5	NUM
american_scientific_journal-4887	145	27	(	(	PUNCT
american_scientific_journal-4887	145	28	70.9	70.9	NUM
american_scientific_journal-4887	145	29	−	−	NUM
american_scientific_journal-4887	145	30	2𝑦𝑦1	2𝑦𝑦1	NUM
american_scientific_journal-4887	145	31	−	−	PROPN
american_scientific_journal-4887	145	32	2𝑦𝑦2	2𝑦𝑦2	NUM
american_scientific_journal-4887	145	33	)	)	PUNCT
american_scientific_journal-4887	145	34	then	then	ADV
american_scientific_journal-4887	145	35	the	the	DET
american_scientific_journal-4887	145	36	iteration	iteration	NOUN
american_scientific_journal-4887	145	37	process	process	NOUN
american_scientific_journal-4887	145	38	starts	start	VERB
american_scientific_journal-4887	145	39	with	with	ADP
american_scientific_journal-4887	145	40	the	the	DET
american_scientific_journal-4887	145	41	intial	intial	ADJ
american_scientific_journal-4887	145	42	value	value	NOUN
american_scientific_journal-4887	145	43	(	(	PUNCT
american_scientific_journal-4887	145	44	0	0	NUM
american_scientific_journal-4887	145	45	,	,	PUNCT
american_scientific_journal-4887	145	46	0	0	NUM
american_scientific_journal-4887	145	47	,	,	PUNCT
american_scientific_journal-4887	145	48	0	0	NUM
american_scientific_journal-4887	145	49	)	)	PUNCT
american_scientific_journal-4887	145	50	,	,	PUNCT
american_scientific_journal-4887	145	51	which	which	PRON
american_scientific_journal-4887	145	52	is	be	AUX
american_scientific_journal-4887	145	53	as	as	SCONJ
american_scientific_journal-4887	145	54	follows	follow	VERB
american_scientific_journal-4887	145	55	:	:	PUNCT
american_scientific_journal-4887	145	56	first	first	ADJ
american_scientific_journal-4887	145	57	iteration	iteration	NOUN
american_scientific_journal-4887	145	58	𝑦𝑦1(1	𝑦𝑦1(1	ADV
american_scientific_journal-4887	145	59	)	)	PUNCT
american_scientific_journal-4887	145	60	=	=	SYM
american_scientific_journal-4887	145	61	1	1	NUM
american_scientific_journal-4887	145	62	19	19	NUM
american_scientific_journal-4887	145	63	(	(	PUNCT
american_scientific_journal-4887	145	64	260.2	260.2	NUM
american_scientific_journal-4887	145	65	–	–	PUNCT
american_scientific_journal-4887	145	66	12(0	12(0	NUM
american_scientific_journal-4887	145	67	)	)	PUNCT
american_scientific_journal-4887	145	68	–	–	PUNCT
american_scientific_journal-4887	145	69	6(0	6(0	NUM
american_scientific_journal-4887	145	70	)	)	PUNCT
american_scientific_journal-4887	145	71	)	)	PUNCT
american_scientific_journal-4887	146	1	=	=	SYM
american_scientific_journal-4887	146	2	1	1	NUM
american_scientific_journal-4887	146	3	19	19	NUM
american_scientific_journal-4887	146	4	(	(	PUNCT
american_scientific_journal-4887	146	5	260.2	260.2	NUM
american_scientific_journal-4887	146	6	)	)	PUNCT
american_scientific_journal-4887	146	7	=	=	NOUN
american_scientific_journal-4887	146	8	13.6947	13.6947	NUM
american_scientific_journal-4887	146	9	𝑦𝑦2(1	𝑦𝑦2(1	NOUN
american_scientific_journal-4887	146	10	)	)	PUNCT
american_scientific_journal-4887	146	11	=	=	SYM
american_scientific_journal-4887	147	1	1	1	NUM
american_scientific_journal-4887	147	2	4	4	NUM
american_scientific_journal-4887	147	3	(	(	PUNCT
american_scientific_journal-4887	147	4	51.3	51.3	NUM
american_scientific_journal-4887	147	5	–	–	PUNCT
american_scientific_journal-4887	147	6	2(13.6947	2(13.6947	NUM
american_scientific_journal-4887	147	7	)	)	PUNCT
american_scientific_journal-4887	147	8	–	–	PUNCT
american_scientific_journal-4887	147	9	1.5(0	1.5(0	NUM
american_scientific_journal-4887	147	10	)	)	PUNCT
american_scientific_journal-4887	147	11	)	)	PUNCT
american_scientific_journal-4887	147	12	=	=	SYM
american_scientific_journal-4887	147	13	1	1	NUM
american_scientific_journal-4887	147	14	4	4	NUM
american_scientific_journal-4887	147	15	(	(	PUNCT
american_scientific_journal-4887	147	16	23.9106	23.9106	NUM
american_scientific_journal-4887	147	17	)	)	PUNCT
american_scientific_journal-4887	147	18	=	=	PUNCT
american_scientific_journal-4887	147	19	5.9776	5.9776	NUM
american_scientific_journal-4887	147	20	𝑦𝑦3(1	𝑦𝑦3(1	NOUN
american_scientific_journal-4887	147	21	)	)	PUNCT
american_scientific_journal-4887	147	22	=	=	SYM
american_scientific_journal-4887	147	23	1	1	NUM
american_scientific_journal-4887	147	24	4.5	4.5	NUM
american_scientific_journal-4887	147	25	(	(	PUNCT
american_scientific_journal-4887	147	26	70.9	70.9	NUM
american_scientific_journal-4887	147	27	–	–	PUNCT
american_scientific_journal-4887	147	28	2(13.6947	2(13.6947	NUM
american_scientific_journal-4887	147	29	)	)	PUNCT
american_scientific_journal-4887	147	30	–	–	PUNCT
american_scientific_journal-4887	147	31	2(5.9776	2(5.9776	NUM
american_scientific_journal-4887	147	32	)	)	PUNCT
american_scientific_journal-4887	147	33	)	)	PUNCT
american_scientific_journal-4887	148	1	=	=	PUNCT
american_scientific_journal-4887	148	2	1	1	NUM
american_scientific_journal-4887	148	3	4.5	4.5	NUM
american_scientific_journal-4887	148	4	(	(	PUNCT
american_scientific_journal-4887	148	5	31.5554	31.5554	NUM
american_scientific_journal-4887	148	6	)	)	PUNCT
american_scientific_journal-4887	148	7	=	=	SYM
american_scientific_journal-4887	149	1	7.0123	7.0123	NUM
american_scientific_journal-4887	149	2	second	second	ADJ
american_scientific_journal-4887	149	3	iteration	iteration	NOUN
american_scientific_journal-4887	149	4	𝑦𝑦1(2	𝑦𝑦1(2	NUM
american_scientific_journal-4887	149	5	)	)	PUNCT
american_scientific_journal-4887	149	6	=	=	SYM
american_scientific_journal-4887	149	7	1	1	NUM
american_scientific_journal-4887	149	8	19	19	NUM
american_scientific_journal-4887	149	9	(	(	PUNCT
american_scientific_journal-4887	149	10	260.2	260.2	NUM
american_scientific_journal-4887	149	11	–	–	PUNCT
american_scientific_journal-4887	149	12	12(5.9776	12(5.9776	NUM
american_scientific_journal-4887	149	13	)	)	PUNCT
american_scientific_journal-4887	149	14	–	–	PUNCT
american_scientific_journal-4887	149	15	6(7.0123	6(7.0123	NUM
american_scientific_journal-4887	149	16	)	)	PUNCT
american_scientific_journal-4887	149	17	)	)	PUNCT
american_scientific_journal-4887	149	18	=	=	SYM
american_scientific_journal-4887	149	19	1	1	NUM
american_scientific_journal-4887	149	20	19	19	NUM
american_scientific_journal-4887	149	21	(	(	PUNCT
american_scientific_journal-4887	149	22	146.395	146.395	NUM
american_scientific_journal-4887	149	23	)	)	PUNCT
american_scientific_journal-4887	149	24	=	=	SYM
american_scientific_journal-4887	149	25	7.705	7.705	NUM
american_scientific_journal-4887	149	26	𝑦𝑦2(2	𝑦𝑦2(2	NUM
american_scientific_journal-4887	149	27	)	)	PUNCT
american_scientific_journal-4887	149	28	=	=	SYM
american_scientific_journal-4887	149	29	1	1	NUM
american_scientific_journal-4887	149	30	4	4	NUM
american_scientific_journal-4887	149	31	(	(	PUNCT
american_scientific_journal-4887	149	32	51.3	51.3	NUM
american_scientific_journal-4887	149	33	–	–	PUNCT
american_scientific_journal-4887	149	34	2(7.705	2(7.705	NUM
american_scientific_journal-4887	149	35	)	)	PUNCT
american_scientific_journal-4887	149	36	–	–	PUNCT
american_scientific_journal-4887	149	37	1.5(7.0123	1.5(7.0123	NUM
american_scientific_journal-4887	149	38	)	)	PUNCT
american_scientific_journal-4887	149	39	)	)	PUNCT
american_scientific_journal-4887	149	40	=	=	SYM
american_scientific_journal-4887	150	1	1	1	NUM
american_scientific_journal-4887	150	2	4	4	NUM
american_scientific_journal-4887	150	3	(	(	PUNCT
american_scientific_journal-4887	150	4	25.3716	25.3716	NUM
american_scientific_journal-4887	150	5	)	)	PUNCT
american_scientific_journal-4887	150	6	=	=	PUNCT
american_scientific_journal-4887	151	1	6.3429	6.3429	NUM
american_scientific_journal-4887	151	2	american	american	ADJ
american_scientific_journal-4887	151	3	scientific	scientific	ADJ
american_scientific_journal-4887	151	4	research	research	NOUN
american_scientific_journal-4887	151	5	journal	journal	NOUN
american_scientific_journal-4887	151	6	for	for	ADP
american_scientific_journal-4887	151	7	engineering	engineering	NOUN
american_scientific_journal-4887	151	8	,	,	PUNCT
american_scientific_journal-4887	151	9	technology	technology	NOUN
american_scientific_journal-4887	151	10	,	,	PUNCT
american_scientific_journal-4887	151	11	and	and	CCONJ
american_scientific_journal-4887	151	12	sciences	science	NOUN
american_scientific_journal-4887	151	13	(	(	PUNCT
american_scientific_journal-4887	151	14	asrjets	asrjet	NOUN
american_scientific_journal-4887	151	15	)	)	PUNCT
american_scientific_journal-4887	151	16	(	(	PUNCT
american_scientific_journal-4887	151	17	2019	2019	NUM
american_scientific_journal-4887	151	18	)	)	PUNCT
american_scientific_journal-4887	151	19	volume	volume	NOUN
american_scientific_journal-4887	151	20	56	56	NUM
american_scientific_journal-4887	151	21	,	,	PUNCT
american_scientific_journal-4887	151	22	no	no	DET
american_scientific_journal-4887	151	23	1	1	NUM
american_scientific_journal-4887	151	24	,	,	PUNCT
american_scientific_journal-4887	151	25	pp	pp	ADV
american_scientific_journal-4887	151	26	113	113	NUM
american_scientific_journal-4887	151	27	-	-	SYM
american_scientific_journal-4887	151	28	123	123	NUM
american_scientific_journal-4887	151	29	121	121	NUM
american_scientific_journal-4887	151	30	𝑦𝑦3(2	𝑦𝑦3(2	NOUN
american_scientific_journal-4887	151	31	)	)	PUNCT
american_scientific_journal-4887	151	32	=	=	PUNCT
american_scientific_journal-4887	151	33	1	1	NUM
american_scientific_journal-4887	151	34	4.5	4.5	NUM
american_scientific_journal-4887	151	35	(	(	PUNCT
american_scientific_journal-4887	151	36	70.9	70.9	NUM
american_scientific_journal-4887	151	37	–	–	PUNCT
american_scientific_journal-4887	151	38	2(7.705	2(7.705	NUM
american_scientific_journal-4887	151	39	)	)	PUNCT
american_scientific_journal-4887	151	40	–	–	PUNCT
american_scientific_journal-4887	151	41	2(6.3429	2(6.3429	NUM
american_scientific_journal-4887	151	42	)	)	PUNCT
american_scientific_journal-4887	151	43	)	)	PUNCT
american_scientific_journal-4887	151	44	=	=	PUNCT
american_scientific_journal-4887	151	45	1	1	NUM
american_scientific_journal-4887	151	46	4.5	4.5	NUM
american_scientific_journal-4887	151	47	(	(	PUNCT
american_scientific_journal-4887	151	48	42.8042	42.8042	NUM
american_scientific_journal-4887	151	49	)	)	PUNCT
american_scientific_journal-4887	151	50	=	=	PUNCT
american_scientific_journal-4887	151	51	9.5120	9.5120	NUM
american_scientific_journal-4887	151	52	based	base	VERB
american_scientific_journal-4887	151	53	on	on	ADP
american_scientific_journal-4887	151	54	equation	equation	NOUN
american_scientific_journal-4887	151	55	(	(	PUNCT
american_scientific_journal-4887	151	56	12	12	NUM
american_scientific_journal-4887	151	57	)	)	PUNCT
american_scientific_journal-4887	151	58	,	,	PUNCT
american_scientific_journal-4887	151	59	the	the	DET
american_scientific_journal-4887	151	60	iteration	iteration	NOUN
american_scientific_journal-4887	151	61	process	process	NOUN
american_scientific_journal-4887	151	62	until	until	SCONJ
american_scientific_journal-4887	151	63	10th	10th	ADJ
american_scientific_journal-4887	151	64	iteration	iteration	NOUN
american_scientific_journal-4887	151	65	is	be	AUX
american_scientific_journal-4887	151	66	obtained	obtain	VERB
american_scientific_journal-4887	151	67	the	the	DET
american_scientific_journal-4887	151	68	value	value	NOUN
american_scientific_journal-4887	151	69	𝑦𝑦1	𝑦𝑦1	PROPN
american_scientific_journal-4887	151	70	=	=	SYM
american_scientific_journal-4887	151	71	7.00029	7.00029	NUM
american_scientific_journal-4887	151	72	,	,	PUNCT
american_scientific_journal-4887	151	73	𝑦𝑦2	𝑦𝑦2	NOUN
american_scientific_journal-4887	151	74	=	=	PUNCT
american_scientific_journal-4887	151	75	5.49987	5.49987	NUM
american_scientific_journal-4887	151	76	,	,	PUNCT
american_scientific_journal-4887	151	77	𝑦𝑦3	𝑦𝑦3	PROPN
american_scientific_journal-4887	151	78	=	=	SYM
american_scientific_journal-4887	151	79	10.1998	10.1998	NUM
american_scientific_journal-4887	151	80	.	.	PUNCT
american_scientific_journal-4887	152	1	for	for	ADP
american_scientific_journal-4887	152	2	equation	equation	NOUN
american_scientific_journal-4887	152	3	(	(	PUNCT
american_scientific_journal-4887	152	4	15	15	NUM
american_scientific_journal-4887	152	5	)	)	PUNCT
american_scientific_journal-4887	152	6	,	,	PUNCT
american_scientific_journal-4887	152	7	the	the	DET
american_scientific_journal-4887	152	8	equation	equation	NOUN
american_scientific_journal-4887	152	9	obtained	obtain	VERB
american_scientific_journal-4887	152	10	is	be	AUX
american_scientific_journal-4887	152	11	as	as	SCONJ
american_scientific_journal-4887	152	12	follows	follow	VERB
american_scientific_journal-4887	152	13	:	:	PUNCT
american_scientific_journal-4887	152	14	19𝑧𝑧1	19𝑧𝑧1	ADJ
american_scientific_journal-4887	152	15	+	+	CCONJ
american_scientific_journal-4887	152	16	12𝑧𝑧2	12𝑧𝑧2	NUM
american_scientific_journal-4887	152	17	+	+	CCONJ
american_scientific_journal-4887	152	18	6𝑧𝑧3	6𝑧𝑧3	NUM
american_scientific_journal-4887	153	1	+	+	CCONJ
american_scientific_journal-4887	153	2	𝑥𝑥1	𝑥𝑥1	NOUN
american_scientific_journal-4887	153	3	+	+	CCONJ
american_scientific_journal-4887	153	4	1.5𝑥𝑥2	1.5𝑥𝑥2	NUM
american_scientific_journal-4887	153	5	+0.2𝑥𝑥3	+0.2𝑥𝑥3	NOUN
american_scientific_journal-4887	153	6	=	=	PUNCT
american_scientific_journal-4887	153	7	536.2	536.2	NUM
american_scientific_journal-4887	153	8	2	2	NUM
american_scientific_journal-4887	153	9	𝑧𝑧1	𝑧𝑧1	NOUN
american_scientific_journal-4887	153	10	+	+	CCONJ
american_scientific_journal-4887	153	11	4𝑧𝑧2	4𝑧𝑧2	NUM
american_scientific_journal-4887	153	12	+	+	CCONJ
american_scientific_journal-4887	153	13	1.5𝑧𝑧3	1.5𝑧𝑧3	NUM
american_scientific_journal-4887	153	14	+0.1𝑥𝑥1	+0.1𝑥𝑥1	NOUN
american_scientific_journal-4887	153	15	+	+	X
american_scientific_journal-4887	153	16	0.4𝑥𝑥2	0.4𝑥𝑥2	X
american_scientific_journal-4887	153	17	+	+	NUM
american_scientific_journal-4887	153	18	0.2𝑥𝑥3	0.2𝑥𝑥3	NOUN
american_scientific_journal-4887	153	19	=	=	SYM
american_scientific_journal-4887	153	20	109.3	109.3	NUM
american_scientific_journal-4887	153	21	2	2	NUM
american_scientific_journal-4887	153	22	𝑧𝑧1	𝑧𝑧1	NOUN
american_scientific_journal-4887	153	23	+	+	NOUN
american_scientific_journal-4887	153	24	2𝑧𝑧2	2𝑧𝑧2	NUM
american_scientific_journal-4887	153	25	+	+	NUM
american_scientific_journal-4887	153	26	4.5𝑧𝑧3	4.5𝑧𝑧3	NUM
american_scientific_journal-4887	154	1	+	+	CCONJ
american_scientific_journal-4887	154	2	0.2𝑥𝑥1	0.2𝑥𝑥1	ADJ
american_scientific_journal-4887	154	3	+	+	CCONJ
american_scientific_journal-4887	154	4	0.3𝑥𝑥2	0.3𝑥𝑥2	NUM
american_scientific_journal-4887	154	5	+	+	NUM
american_scientific_journal-4887	154	6	0.1𝑥𝑥3	0.1𝑥𝑥3	NOUN
american_scientific_journal-4887	154	7	=	=	SYM
american_scientific_journal-4887	154	8	131.9	131.9	NUM
american_scientific_journal-4887	155	1	because	because	SCONJ
american_scientific_journal-4887	155	2	the	the	DET
american_scientific_journal-4887	155	3	value	value	NOUN
american_scientific_journal-4887	155	4	of	of	ADP
american_scientific_journal-4887	155	5	𝑥𝑥1	𝑥𝑥1	NOUN
american_scientific_journal-4887	155	6	,	,	PUNCT
american_scientific_journal-4887	155	7	𝑥𝑥2	𝑥𝑥2	PROPN
american_scientific_journal-4887	155	8	,	,	PUNCT
american_scientific_journal-4887	155	9	𝑥𝑥3	𝑥𝑥3	PROPN
american_scientific_journal-4887	155	10	has	have	AUX
american_scientific_journal-4887	155	11	been	be	AUX
american_scientific_journal-4887	155	12	obtained	obtain	VERB
american_scientific_journal-4887	155	13	,	,	PUNCT
american_scientific_journal-4887	155	14	substitution	substitution	NOUN
american_scientific_journal-4887	155	15	value	value	NOUN
american_scientific_journal-4887	155	16	is	be	AUX
american_scientific_journal-4887	155	17	put	put	VERB
american_scientific_journal-4887	155	18	into	into	ADP
american_scientific_journal-4887	155	19	equation	equation	NOUN
american_scientific_journal-4887	155	20	(	(	PUNCT
american_scientific_journal-4887	155	21	15	15	NUM
american_scientific_journal-4887	155	22	)	)	PUNCT
american_scientific_journal-4887	155	23	so	so	SCONJ
american_scientific_journal-4887	155	24	that	that	SCONJ
american_scientific_journal-4887	155	25	the	the	DET
american_scientific_journal-4887	155	26	new	new	ADJ
american_scientific_journal-4887	155	27	equation	equation	NOUN
american_scientific_journal-4887	155	28	is	be	AUX
american_scientific_journal-4887	155	29	obtained	obtain	VERB
american_scientific_journal-4887	155	30	as	as	ADP
american_scientific_journal-4887	155	31	follows	follow	VERB
american_scientific_journal-4887	155	32	:	:	PUNCT
american_scientific_journal-4887	155	33	19𝑧𝑧1	19𝑧𝑧1	ADJ
american_scientific_journal-4887	156	1	+	+	CCONJ
american_scientific_journal-4887	156	2	12𝑧𝑧2	12𝑧𝑧2	NUM
american_scientific_journal-4887	156	3	+	+	CCONJ
american_scientific_journal-4887	156	4	6𝑧𝑧3	6𝑧𝑧3	NUM
american_scientific_journal-4887	156	5	=	=	SYM
american_scientific_journal-4887	156	6	391.2	391.2	NUM
american_scientific_journal-4887	156	7	2	2	NUM
american_scientific_journal-4887	156	8	𝑧𝑧1	𝑧𝑧1	ADV
american_scientific_journal-4887	156	9	+	+	CCONJ
american_scientific_journal-4887	156	10	4𝑧𝑧2	4𝑧𝑧2	NUM
american_scientific_journal-4887	157	1	+	+	CCONJ
american_scientific_journal-4887	157	2	1.5𝑧𝑧3	1.5𝑧𝑧3	NUM
american_scientific_journal-4887	157	3	=	=	SYM
american_scientific_journal-4887	157	4	65.8	65.8	NUM
american_scientific_journal-4887	157	5	2	2	NUM
american_scientific_journal-4887	157	6	𝑧𝑧1	𝑧𝑧1	NOUN
american_scientific_journal-4887	157	7	+	+	NOUN
american_scientific_journal-4887	157	8	2𝑧𝑧2	2𝑧𝑧2	NUM
american_scientific_journal-4887	157	9	+	+	NUM
american_scientific_journal-4887	157	10	4.5𝑧𝑧3	4.5𝑧𝑧3	NUM
american_scientific_journal-4887	157	11	=	=	SYM
american_scientific_journal-4887	157	12	98.4	98.4	NUM
american_scientific_journal-4887	157	13	to	to	PART
american_scientific_journal-4887	157	14	get	get	VERB
american_scientific_journal-4887	157	15	the	the	DET
american_scientific_journal-4887	157	16	values	value	NOUN
american_scientific_journal-4887	157	17	𝑧𝑧1	𝑧𝑧1	ADV
american_scientific_journal-4887	157	18	,	,	PUNCT
american_scientific_journal-4887	157	19	𝑧𝑧2	𝑧𝑧2	NOUN
american_scientific_journal-4887	157	20	and	and	CCONJ
american_scientific_journal-4887	157	21	𝑧𝑧3	𝑧𝑧3	NOUN
american_scientific_journal-4887	157	22	,	,	PUNCT
american_scientific_journal-4887	157	23	it	it	PRON
american_scientific_journal-4887	157	24	must	must	AUX
american_scientific_journal-4887	157	25	first	first	ADV
american_scientific_journal-4887	157	26	be	be	AUX
american_scientific_journal-4887	157	27	proven	prove	VERB
american_scientific_journal-4887	157	28	that	that	SCONJ
american_scientific_journal-4887	157	29	equation	equation	NOUN
american_scientific_journal-4887	157	30	(	(	PUNCT
american_scientific_journal-4887	157	31	15	15	NUM
american_scientific_journal-4887	157	32	)	)	PUNCT
american_scientific_journal-4887	157	33	strictly	strictly	ADV
american_scientific_journal-4887	157	34	diagonally	diagonally	ADV
american_scientific_journal-4887	157	35	dominant	dominant	ADJ
american_scientific_journal-4887	157	36	in	in	ADP
american_scientific_journal-4887	157	37	the	the	DET
american_scientific_journal-4887	157	38	following	following	NOUN
american_scientific_journal-4887	157	39	:	:	PUNCT
american_scientific_journal-4887	157	40	|𝑎𝑎11|	|𝑎𝑎11|	NOUN
american_scientific_journal-4887	157	41	≥	≥	NUM
american_scientific_journal-4887	157	42	|𝑎𝑎12|	|𝑎𝑎12|	PROPN
american_scientific_journal-4887	157	43	+	+	ADJ
american_scientific_journal-4887	157	44	|𝑎𝑎13|	|𝑎𝑎13|	PROPN
american_scientific_journal-4887	157	45	→	→	SYM
american_scientific_journal-4887	157	46	|19|	|19|	X
american_scientific_journal-4887	157	47	≥	≥	NOUN
american_scientific_journal-4887	157	48	|12|	|12|	NOUN
american_scientific_journal-4887	157	49	+	+	CCONJ
american_scientific_journal-4887	158	1	|6|	|6|	NOUN
american_scientific_journal-4887	158	2	=	=	SYM
american_scientific_journal-4887	158	3	19	19	NUM
american_scientific_journal-4887	158	4	≥	≥	NOUN
american_scientific_journal-4887	158	5	18	18	NUM
american_scientific_journal-4887	158	6	|𝑎𝑎22|	|𝑎𝑎22|	PROPN
american_scientific_journal-4887	158	7	≥	≥	NOUN
american_scientific_journal-4887	158	8	|𝑎𝑎21|	|𝑎𝑎21|	VERB
american_scientific_journal-4887	158	9	+	+	CCONJ
american_scientific_journal-4887	158	10	|𝑎𝑎23|	|𝑎𝑎23|	ADJ
american_scientific_journal-4887	158	11	→	→	SYM
american_scientific_journal-4887	158	12	|4|	|4|	NOUN
american_scientific_journal-4887	158	13	≥	≥	NOUN
american_scientific_journal-4887	158	14	|2|	|2|	PROPN
american_scientific_journal-4887	158	15	+	+	NUM
american_scientific_journal-4887	158	16	|1.5|	|1.5|	NOUN
american_scientific_journal-4887	158	17	=	=	SYM
american_scientific_journal-4887	158	18	4	4	NUM
american_scientific_journal-4887	158	19	≥	≥	NOUN
american_scientific_journal-4887	158	20	3.5	3.5	NUM
american_scientific_journal-4887	158	21	|𝑎𝑎33|	|𝑎𝑎33|	NOUN
american_scientific_journal-4887	158	22	≥	≥	NOUN
american_scientific_journal-4887	158	23	|𝑎𝑎31|	|𝑎𝑎31|	ADJ
american_scientific_journal-4887	158	24	+	+	CCONJ
american_scientific_journal-4887	158	25	|𝑎𝑎32|	|𝑎𝑎32|	NUM
american_scientific_journal-4887	158	26	→	→	SYM
american_scientific_journal-4887	158	27	|4.5|	|4.5|	PRON
american_scientific_journal-4887	158	28	≥	≥	NOUN
american_scientific_journal-4887	158	29	|2|	|2|	PROPN
american_scientific_journal-4887	158	30	+	+	CCONJ
american_scientific_journal-4887	158	31	|2|	|2|	PROPN
american_scientific_journal-4887	158	32	=	=	SYM
american_scientific_journal-4887	158	33	4.5	4.5	NUM
american_scientific_journal-4887	158	34	≥	≥	NOUN
american_scientific_journal-4887	158	35	4	4	NUM
american_scientific_journal-4887	158	36	all	all	DET
american_scientific_journal-4887	158	37	equations	equation	NOUN
american_scientific_journal-4887	158	38	(	(	PUNCT
american_scientific_journal-4887	158	39	15	15	NUM
american_scientific_journal-4887	158	40	)	)	PUNCT
american_scientific_journal-4887	158	41	are	be	AUX
american_scientific_journal-4887	158	42	proven	prove	VERB
american_scientific_journal-4887	158	43	to	to	PART
american_scientific_journal-4887	158	44	be	be	AUX
american_scientific_journal-4887	158	45	diagonally	diagonally	ADV
american_scientific_journal-4887	158	46	dominant	dominant	ADJ
american_scientific_journal-4887	158	47	,	,	PUNCT
american_scientific_journal-4887	158	48	so	so	ADV
american_scientific_journal-4887	158	49	obtained	obtain	VERB
american_scientific_journal-4887	158	50	:	:	PUNCT
american_scientific_journal-4887	158	51	𝑧𝑧1	𝑧𝑧1	PROPN
american_scientific_journal-4887	158	52	=	=	NOUN
american_scientific_journal-4887	158	53	1	1	NUM
american_scientific_journal-4887	158	54	19	19	NUM
american_scientific_journal-4887	158	55	(	(	PUNCT
american_scientific_journal-4887	158	56	391.2	391.2	NUM
american_scientific_journal-4887	158	57	−	−	NOUN
american_scientific_journal-4887	158	58	12𝑧𝑧1	12𝑧𝑧1	NOUN
american_scientific_journal-4887	158	59	−	−	PROPN
american_scientific_journal-4887	158	60	6𝑧𝑧3	6𝑧𝑧3	NUM
american_scientific_journal-4887	158	61	)	)	PUNCT
american_scientific_journal-4887	158	62	𝑧𝑧2	𝑧𝑧2	NOUN
american_scientific_journal-4887	158	63	=	=	SYM
american_scientific_journal-4887	158	64	1	1	NUM
american_scientific_journal-4887	158	65	4	4	NUM
american_scientific_journal-4887	158	66	(	(	PUNCT
american_scientific_journal-4887	158	67	65.8	65.8	NUM
american_scientific_journal-4887	158	68	−	−	NOUN
american_scientific_journal-4887	158	69	2𝑧𝑧1	2𝑧𝑧1	NUM
american_scientific_journal-4887	158	70	–	–	PUNCT
american_scientific_journal-4887	158	71	1.5𝑧𝑧3	1.5𝑧𝑧3	NUM
american_scientific_journal-4887	158	72	)	)	PUNCT
american_scientific_journal-4887	158	73	𝑧𝑧3	𝑧𝑧3	NOUN
american_scientific_journal-4887	159	1	=	=	SYM
american_scientific_journal-4887	159	2	1	1	NUM
american_scientific_journal-4887	159	3	4.5	4.5	NUM
american_scientific_journal-4887	159	4	(	(	PUNCT
american_scientific_journal-4887	159	5	98.4	98.4	NUM
american_scientific_journal-4887	159	6	−	−	NOUN
american_scientific_journal-4887	159	7	2𝑧𝑧1	2𝑧𝑧1	NUM
american_scientific_journal-4887	159	8	−	−	NOUN
american_scientific_journal-4887	159	9	2𝑧𝑧2	2𝑧𝑧2	NUM
american_scientific_journal-4887	159	10	)	)	PUNCT
american_scientific_journal-4887	159	11	then	then	ADV
american_scientific_journal-4887	159	12	the	the	DET
american_scientific_journal-4887	159	13	iteration	iteration	NOUN
american_scientific_journal-4887	159	14	process	process	NOUN
american_scientific_journal-4887	159	15	starts	start	VERB
american_scientific_journal-4887	159	16	with	with	ADP
american_scientific_journal-4887	159	17	the	the	DET
american_scientific_journal-4887	159	18	intial	intial	ADJ
american_scientific_journal-4887	159	19	value	value	NOUN
american_scientific_journal-4887	159	20	(	(	PUNCT
american_scientific_journal-4887	159	21	0	0	NUM
american_scientific_journal-4887	159	22	,	,	PUNCT
american_scientific_journal-4887	159	23	0	0	NUM
american_scientific_journal-4887	159	24	,	,	PUNCT
american_scientific_journal-4887	159	25	0	0	NUM
american_scientific_journal-4887	159	26	)	)	PUNCT
american_scientific_journal-4887	159	27	,	,	PUNCT
american_scientific_journal-4887	159	28	which	which	PRON
american_scientific_journal-4887	159	29	is	be	AUX
american_scientific_journal-4887	159	30	as	as	SCONJ
american_scientific_journal-4887	159	31	follows	follow	VERB
american_scientific_journal-4887	159	32	:	:	PUNCT
american_scientific_journal-4887	159	33	first	first	ADJ
american_scientific_journal-4887	159	34	iteration	iteration	NOUN
american_scientific_journal-4887	159	35	𝑧𝑧1(1	𝑧𝑧1(1	ADJ
american_scientific_journal-4887	159	36	)	)	PUNCT
american_scientific_journal-4887	159	37	=	=	SYM
american_scientific_journal-4887	159	38	1	1	NUM
american_scientific_journal-4887	159	39	19	19	NUM
american_scientific_journal-4887	159	40	(	(	PUNCT
american_scientific_journal-4887	159	41	391.2	391.2	NUM
american_scientific_journal-4887	159	42	–	–	PUNCT
american_scientific_journal-4887	159	43	12(0	12(0	NUM
american_scientific_journal-4887	159	44	)	)	PUNCT
american_scientific_journal-4887	159	45	–	–	PUNCT
american_scientific_journal-4887	159	46	6(0	6(0	NUM
american_scientific_journal-4887	159	47	)	)	PUNCT
american_scientific_journal-4887	159	48	)	)	PUNCT
american_scientific_journal-4887	160	1	=	=	SYM
american_scientific_journal-4887	161	1	1	1	NUM
american_scientific_journal-4887	161	2	19	19	NUM
american_scientific_journal-4887	161	3	(	(	PUNCT
american_scientific_journal-4887	161	4	391.2	391.2	NUM
american_scientific_journal-4887	161	5	)	)	PUNCT
american_scientific_journal-4887	161	6	=	=	NOUN
american_scientific_journal-4887	161	7	20.5895	20.5895	NUM
american_scientific_journal-4887	161	8	𝑧𝑧2(1	𝑧𝑧2(1	NOUN
american_scientific_journal-4887	161	9	)	)	PUNCT
american_scientific_journal-4887	161	10	=	=	SYM
american_scientific_journal-4887	161	11	1	1	NUM
american_scientific_journal-4887	161	12	4	4	NUM
american_scientific_journal-4887	161	13	(	(	PUNCT
american_scientific_journal-4887	161	14	65.8	65.8	NUM
american_scientific_journal-4887	161	15	–	–	PUNCT
american_scientific_journal-4887	161	16	2(20.5895	2(20.5895	NUM
american_scientific_journal-4887	161	17	)	)	PUNCT
american_scientific_journal-4887	161	18	–	–	PUNCT
american_scientific_journal-4887	161	19	1.5(0	1.5(0	NUM
american_scientific_journal-4887	161	20	)	)	PUNCT
american_scientific_journal-4887	161	21	)	)	PUNCT
american_scientific_journal-4887	161	22	=	=	SYM
american_scientific_journal-4887	162	1	1	1	NUM
american_scientific_journal-4887	162	2	4	4	NUM
american_scientific_journal-4887	162	3	(	(	PUNCT
american_scientific_journal-4887	162	4	24.621	24.621	NUM
american_scientific_journal-4887	162	5	)	)	PUNCT
american_scientific_journal-4887	162	6	=	=	NOUN
american_scientific_journal-4887	163	1	6.1553	6.1553	NUM
american_scientific_journal-4887	163	2	𝑧𝑧3(1	𝑧𝑧3(1	NOUN
american_scientific_journal-4887	163	3	)	)	PUNCT
american_scientific_journal-4887	163	4	=	=	SYM
american_scientific_journal-4887	163	5	1	1	NUM
american_scientific_journal-4887	163	6	4.5	4.5	NUM
american_scientific_journal-4887	163	7	(	(	PUNCT
american_scientific_journal-4887	163	8	98.4	98.4	NUM
american_scientific_journal-4887	163	9	–	–	SYM
american_scientific_journal-4887	163	10	2(20.5895	2(20.5895	NUM
american_scientific_journal-4887	163	11	)	)	PUNCT
american_scientific_journal-4887	163	12	–	–	PUNCT
american_scientific_journal-4887	163	13	2(6.1553	2(6.1553	NOUN
american_scientific_journal-4887	163	14	)	)	PUNCT
american_scientific_journal-4887	163	15	)	)	PUNCT
american_scientific_journal-4887	163	16	=	=	PUNCT
american_scientific_journal-4887	164	1	1	1	NUM
american_scientific_journal-4887	164	2	4.5	4.5	NUM
american_scientific_journal-4887	164	3	(	(	PUNCT
american_scientific_journal-4887	164	4	44.9104	44.9104	NUM
american_scientific_journal-4887	164	5	)	)	PUNCT
american_scientific_journal-4887	164	6	=	=	NOUN
american_scientific_journal-4887	165	1	9.9801	9.9801	NUM
american_scientific_journal-4887	165	2	second	second	ADJ
american_scientific_journal-4887	165	3	iteration	iteration	NOUN
american_scientific_journal-4887	165	4	𝑧𝑧1(2	𝑧𝑧1(2	NOUN
american_scientific_journal-4887	165	5	)	)	PUNCT
american_scientific_journal-4887	165	6	=	=	SYM
american_scientific_journal-4887	165	7	1	1	NUM
american_scientific_journal-4887	165	8	19	19	NUM
american_scientific_journal-4887	165	9	(	(	PUNCT
american_scientific_journal-4887	165	10	391.2	391.2	NUM
american_scientific_journal-4887	165	11	–	–	PUNCT
american_scientific_journal-4887	165	12	12(6.1553	12(6.1553	NUM
american_scientific_journal-4887	165	13	)	)	PUNCT
american_scientific_journal-4887	165	14	–	–	PUNCT
american_scientific_journal-4887	165	15	6(9.9801	6(9.9801	NUM
american_scientific_journal-4887	165	16	)	)	PUNCT
american_scientific_journal-4887	165	17	)	)	PUNCT
american_scientific_journal-4887	165	18	=	=	SYM
american_scientific_journal-4887	165	19	1	1	NUM
american_scientific_journal-4887	165	20	19	19	NUM
american_scientific_journal-4887	165	21	(	(	PUNCT
american_scientific_journal-4887	165	22	257.4558	257.4558	NUM
american_scientific_journal-4887	165	23	)	)	PUNCT
american_scientific_journal-4887	165	24	=	=	SYM
american_scientific_journal-4887	165	25	13.5503	13.5503	NUM
american_scientific_journal-4887	165	26	𝑧𝑧2(2	𝑧𝑧2(2	NOUN
american_scientific_journal-4887	165	27	)	)	PUNCT
american_scientific_journal-4887	165	28	=	=	SYM
american_scientific_journal-4887	165	29	1	1	NUM
american_scientific_journal-4887	165	30	4	4	NUM
american_scientific_journal-4887	165	31	(	(	PUNCT
american_scientific_journal-4887	165	32	65.8	65.8	NUM
american_scientific_journal-4887	165	33	–	–	PUNCT
american_scientific_journal-4887	165	34	2(13.5503	2(13.5503	NUM
american_scientific_journal-4887	165	35	)	)	PUNCT
american_scientific_journal-4887	165	36	–	–	PUNCT
american_scientific_journal-4887	165	37	1.5(9.9801	1.5(9.9801	NUM
american_scientific_journal-4887	165	38	)	)	PUNCT
american_scientific_journal-4887	165	39	)	)	PUNCT
american_scientific_journal-4887	165	40	=	=	SYM
american_scientific_journal-4887	165	41	1	1	NUM
american_scientific_journal-4887	165	42	4	4	NUM
american_scientific_journal-4887	165	43	(	(	PUNCT
american_scientific_journal-4887	165	44	23.7292	23.7292	NUM
american_scientific_journal-4887	165	45	)	)	PUNCT
american_scientific_journal-4887	165	46	=	=	SYM
american_scientific_journal-4887	165	47	5.9323	5.9323	NUM
american_scientific_journal-4887	165	48	𝑧𝑧3(2	𝑧𝑧3(2	NOUN
american_scientific_journal-4887	165	49	)	)	PUNCT
american_scientific_journal-4887	165	50	=	=	SYM
american_scientific_journal-4887	165	51	1	1	NUM
american_scientific_journal-4887	165	52	4.5	4.5	NUM
american_scientific_journal-4887	165	53	(	(	PUNCT
american_scientific_journal-4887	165	54	98.4	98.4	NUM
american_scientific_journal-4887	165	55	–	–	PUNCT
american_scientific_journal-4887	165	56	2(13.5503	2(13.5503	NUM
american_scientific_journal-4887	165	57	)	)	PUNCT
american_scientific_journal-4887	165	58	–	–	PUNCT
american_scientific_journal-4887	165	59	2(5.9323	2(5.9323	NUM
american_scientific_journal-4887	165	60	)	)	PUNCT
american_scientific_journal-4887	165	61	)	)	PUNCT
american_scientific_journal-4887	165	62	=	=	PUNCT
american_scientific_journal-4887	165	63	1	1	NUM
american_scientific_journal-4887	165	64	4.5	4.5	NUM
american_scientific_journal-4887	165	65	(	(	PUNCT
american_scientific_journal-4887	165	66	59.4348	59.4348	NUM
american_scientific_journal-4887	165	67	)	)	PUNCT
american_scientific_journal-4887	165	68	=	=	PUNCT
american_scientific_journal-4887	165	69	13.2077	13.2077	NUM
american_scientific_journal-4887	165	70	based	base	VERB
american_scientific_journal-4887	165	71	on	on	ADP
american_scientific_journal-4887	165	72	equation	equation	NOUN
american_scientific_journal-4887	165	73	(	(	PUNCT
american_scientific_journal-4887	165	74	12	12	NUM
american_scientific_journal-4887	165	75	)	)	PUNCT
american_scientific_journal-4887	165	76	,	,	PUNCT
american_scientific_journal-4887	165	77	the	the	DET
american_scientific_journal-4887	165	78	iteration	iteration	NOUN
american_scientific_journal-4887	165	79	process	process	NOUN
american_scientific_journal-4887	165	80	until	until	ADP
american_scientific_journal-4887	165	81	13th	13th	ADJ
american_scientific_journal-4887	165	82	iteration	iteration	NOUN
american_scientific_journal-4887	165	83	is	be	AUX
american_scientific_journal-4887	165	84	obtained	obtain	VERB
american_scientific_journal-4887	165	85	the	the	DET
american_scientific_journal-4887	165	86	value	value	NOUN
american_scientific_journal-4887	165	87	𝑧𝑧1	𝑧𝑧1	NOUN
american_scientific_journal-4887	165	88	=	=	SYM
american_scientific_journal-4887	165	89	13.3016	13.3016	NUM
american_scientific_journal-4887	165	90	,	,	PUNCT
american_scientific_journal-4887	165	91	𝑧𝑧2	𝑧𝑧2	VERB
american_scientific_journal-4887	165	92	=	=	NOUN
american_scientific_journal-4887	165	93	4.5794	4.5794	NUM
american_scientific_journal-4887	165	94	,	,	PUNCT
american_scientific_journal-4887	165	95	𝑧𝑧3	𝑧𝑧3	X
american_scientific_journal-4887	165	96	=	=	SYM
american_scientific_journal-4887	165	97	13.9195	13.9195	NUM
american_scientific_journal-4887	165	98	.	.	PUNCT
american_scientific_journal-4887	166	1	american	american	ADJ
american_scientific_journal-4887	166	2	scientific	scientific	ADJ
american_scientific_journal-4887	166	3	research	research	PROPN
american_scientific_journal-4887	166	4	journal	journal	NOUN
american_scientific_journal-4887	166	5	for	for	ADP
american_scientific_journal-4887	166	6	engineering	engineering	NOUN
american_scientific_journal-4887	166	7	,	,	PUNCT
american_scientific_journal-4887	166	8	technology	technology	NOUN
american_scientific_journal-4887	166	9	,	,	PUNCT
american_scientific_journal-4887	166	10	and	and	CCONJ
american_scientific_journal-4887	166	11	sciences	science	NOUN
american_scientific_journal-4887	166	12	(	(	PUNCT
american_scientific_journal-4887	166	13	asrjets	asrjet	NOUN
american_scientific_journal-4887	166	14	)	)	PUNCT
american_scientific_journal-4887	166	15	(	(	PUNCT
american_scientific_journal-4887	166	16	2019	2019	NUM
american_scientific_journal-4887	166	17	)	)	PUNCT
american_scientific_journal-4887	166	18	volume	volume	NOUN
american_scientific_journal-4887	166	19	56	56	NUM
american_scientific_journal-4887	166	20	,	,	PUNCT
american_scientific_journal-4887	166	21	no	no	DET
american_scientific_journal-4887	166	22	1	1	NUM
american_scientific_journal-4887	166	23	,	,	PUNCT
american_scientific_journal-4887	166	24	pp	pp	ADV
american_scientific_journal-4887	166	25	113	113	NUM
american_scientific_journal-4887	166	26	-	-	SYM
american_scientific_journal-4887	166	27	123	123	NUM
american_scientific_journal-4887	166	28	122	122	NUM
american_scientific_journal-4887	166	29	5	5	NUM
american_scientific_journal-4887	166	30	.	.	PUNCT
american_scientific_journal-4887	166	31	conclusion	conclusion	NOUN
american_scientific_journal-4887	166	32	in	in	ADP
american_scientific_journal-4887	166	33	this	this	DET
american_scientific_journal-4887	166	34	paper	paper	NOUN
american_scientific_journal-4887	166	35	,	,	PUNCT
american_scientific_journal-4887	166	36	it	it	PRON
american_scientific_journal-4887	166	37	can	can	AUX
american_scientific_journal-4887	166	38	be	be	AUX
american_scientific_journal-4887	166	39	concluded	conclude	VERB
american_scientific_journal-4887	166	40	that	that	SCONJ
american_scientific_journal-4887	166	41	the	the	DET
american_scientific_journal-4887	166	42	fully	fully	ADV
american_scientific_journal-4887	166	43	fuzzy	fuzzy	ADJ
american_scientific_journal-4887	166	44	linear	linear	ADJ
american_scientific_journal-4887	166	45	system	system	NOUN
american_scientific_journal-4887	166	46	of	of	ADP
american_scientific_journal-4887	166	47	equation	equation	NOUN
american_scientific_journal-4887	166	48	𝑨𝑨	𝑨𝑨	PROPN
american_scientific_journal-4887	166	49	�	�	PROPN
american_scientific_journal-4887	166	50	⊗	⊗	ADJ
american_scientific_journal-4887	166	51	𝑨𝑨	𝑨𝑨	PROPN
american_scientific_journal-4887	166	52	�	�	PROPN
american_scientific_journal-4887	166	53	=	=	SYM
american_scientific_journal-4887	166	54	𝒃𝒃	𝒃𝒃	ADP
american_scientific_journal-4887	166	55	�	�	PROPN
american_scientific_journal-4887	166	56	solved	solve	VERB
american_scientific_journal-4887	166	57	by	by	ADP
american_scientific_journal-4887	166	58	changing	change	VERB
american_scientific_journal-4887	166	59	it	it	PRON
american_scientific_journal-4887	166	60	into	into	ADP
american_scientific_journal-4887	166	61	(	(	PUNCT
american_scientific_journal-4887	166	62	𝐴𝐴,𝑀𝑀,𝑁𝑁	𝐴𝐴,𝑀𝑀,𝑁𝑁	PROPN
american_scientific_journal-4887	166	63	)	)	PUNCT
american_scientific_journal-4887	166	64	⊗	⊗	PROPN
american_scientific_journal-4887	166	65	(	(	PUNCT
american_scientific_journal-4887	166	66	𝑥𝑥,𝑦𝑦	𝑥𝑥,𝑦𝑦	PROPN
american_scientific_journal-4887	166	67	,	,	PUNCT
american_scientific_journal-4887	166	68	𝑧𝑧	𝑧𝑧	NOUN
american_scientific_journal-4887	166	69	)	)	PUNCT
american_scientific_journal-4887	166	70	=	=	SYM
american_scientific_journal-4887	166	71	(	(	PUNCT
american_scientific_journal-4887	166	72	𝑏𝑏,𝑔𝑔	𝑏𝑏,𝑔𝑔	PROPN
american_scientific_journal-4887	166	73	,	,	PUNCT
american_scientific_journal-4887	166	74	ℎ	ℎ	PROPN
american_scientific_journal-4887	166	75	)	)	PUNCT
american_scientific_journal-4887	166	76	,	,	PUNCT
american_scientific_journal-4887	166	77	so	so	SCONJ
american_scientific_journal-4887	166	78	we	we	PRON
american_scientific_journal-4887	166	79	will	will	AUX
american_scientific_journal-4887	166	80	get	get	VERB
american_scientific_journal-4887	166	81	three	three	NUM
american_scientific_journal-4887	166	82	system	system	NOUN
american_scientific_journal-4887	166	83	linear	linear	NOUN
american_scientific_journal-4887	166	84	of	of	ADP
american_scientific_journal-4887	166	85	equation	equation	NOUN
american_scientific_journal-4887	166	86	.	.	PUNCT
american_scientific_journal-4887	167	1	based	base	VERB
american_scientific_journal-4887	167	2	on	on	ADP
american_scientific_journal-4887	167	3	the	the	DET
american_scientific_journal-4887	167	4	results	result	NOUN
american_scientific_journal-4887	167	5	from	from	ADP
american_scientific_journal-4887	167	6	the	the	DET
american_scientific_journal-4887	167	7	example	example	NOUN
american_scientific_journal-4887	167	8	,	,	PUNCT
american_scientific_journal-4887	167	9	the	the	DET
american_scientific_journal-4887	167	10	value	value	NOUN
american_scientific_journal-4887	167	11	obtained	obtain	VERB
american_scientific_journal-4887	167	12	with	with	ADP
american_scientific_journal-4887	167	13	relatively	relatively	ADV
american_scientific_journal-4887	167	14	small	small	ADJ
american_scientific_journal-4887	167	15	errors	error	NOUN
american_scientific_journal-4887	167	16	are	be	AUX
american_scientific_journal-4887	167	17	as	as	ADV
american_scientific_journal-4887	167	18	follow	follow	NOUN
american_scientific_journal-4887	167	19	:	:	PUNCT
american_scientific_journal-4887	167	20	𝑥𝑥	𝑥𝑥	ADP
american_scientific_journal-4887	167	21	�	�	PROPN
american_scientific_journal-4887	167	22	=	=	SYM
american_scientific_journal-4887	167	23	�	�	PROPN
american_scientific_journal-4887	167	24	𝑥𝑥	𝑥𝑥	ADP
american_scientific_journal-4887	167	25	�	�	PROPN
american_scientific_journal-4887	167	26	1	1	NUM
american_scientific_journal-4887	167	27	𝑥𝑥	𝑥𝑥	ADP
american_scientific_journal-4887	167	28	�	�	NOUN
american_scientific_journal-4887	167	29	2	2	NUM
american_scientific_journal-4887	167	30	𝑥𝑥	𝑥𝑥	ADP
american_scientific_journal-4887	167	31	�	�	PROPN
american_scientific_journal-4887	167	32	3	3	NUM
american_scientific_journal-4887	167	33	�	�	PROPN
american_scientific_journal-4887	167	34	=	=	SYM
american_scientific_journal-4887	167	35	�	�	PROPN
american_scientific_journal-4887	167	36	37,7,13.4	37,7,13.4	NUM
american_scientific_journal-4887	167	37	62,5.5,4.6	62,5.5,4.6	NUM
american_scientific_journal-4887	167	38	75,10.2,14	75,10.2,14	NUM
american_scientific_journal-4887	167	39	�	�	PROPN
american_scientific_journal-4887	167	40	references	reference	NOUN
american_scientific_journal-4887	167	41	[	[	X
american_scientific_journal-4887	167	42	1	1	NUM
american_scientific_journal-4887	167	43	]	]	PUNCT
american_scientific_journal-4887	167	44	a.	a.	NOUN
american_scientific_journal-4887	167	45	kumar	kumar	PROPN
american_scientific_journal-4887	167	46	,	,	PUNCT
american_scientific_journal-4887	167	47	a.	a.	NOUN
american_scientific_journal-4887	167	48	bansal	bansal	NOUN
american_scientific_journal-4887	167	49	and	and	CCONJ
american_scientific_journal-4887	167	50	neetu	neetu	NOUN
american_scientific_journal-4887	167	51	.	.	PUNCT
american_scientific_journal-4887	168	1	”	"	PUNCT
american_scientific_journal-4887	168	2	a	a	DET
american_scientific_journal-4887	168	3	method	method	NOUN
american_scientific_journal-4887	168	4	for	for	ADP
american_scientific_journal-4887	168	5	solving	solve	VERB
american_scientific_journal-4887	168	6	fully	fully	ADV
american_scientific_journal-4887	168	7	fuzzy	fuzzy	ADJ
american_scientific_journal-4887	168	8	linear	linear	ADJ
american_scientific_journal-4887	168	9	system	system	NOUN
american_scientific_journal-4887	168	10	with	with	ADP
american_scientific_journal-4887	168	11	trapezoidal	trapezoidal	ADJ
american_scientific_journal-4887	168	12	fuzzy	fuzzy	ADJ
american_scientific_journal-4887	168	13	numbers	number	NOUN
american_scientific_journal-4887	168	14	”	"	PUNCT
american_scientific_journal-4887	168	15	,	,	PUNCT
american_scientific_journal-4887	168	16	iranian	iranian	ADJ
american_scientific_journal-4887	168	17	journal	journal	NOUN
american_scientific_journal-4887	168	18	of	of	ADP
american_scientific_journal-4887	168	19	optimization	optimization	NOUN
american_scientific_journal-4887	168	20	,	,	PUNCT
american_scientific_journal-4887	168	21	vol.2	vol.2	PROPN
american_scientific_journal-4887	168	22	,	,	PUNCT
american_scientific_journal-4887	168	23	pp	pp	ADJ
american_scientific_journal-4887	168	24	.	.	PUNCT
american_scientific_journal-4887	169	1	359	359	NUM
american_scientific_journal-4887	169	2	-	-	SYM
american_scientific_journal-4887	169	3	374	374	NUM
american_scientific_journal-4887	169	4	.	.	PUNCT
american_scientific_journal-4887	170	1	2010	2010	NUM
american_scientific_journal-4887	170	2	.	.	PUNCT
american_scientific_journal-4887	171	1	[	[	X
american_scientific_journal-4887	171	2	2	2	NUM
american_scientific_journal-4887	171	3	]	]	PUNCT
american_scientific_journal-4887	171	4	a.	a.	NOUN
american_scientific_journal-4887	171	5	kumar	kumar	PROPN
american_scientific_journal-4887	171	6	,	,	PUNCT
american_scientific_journal-4887	171	7	neetu	neetu	NOUN
american_scientific_journal-4887	171	8	and	and	CCONJ
american_scientific_journal-4887	171	9	a.	a.	NOUN
american_scientific_journal-4887	171	10	bansal	bansal	NOUN
american_scientific_journal-4887	171	11	.	.	PUNCT
american_scientific_journal-4887	172	1	“	"	PUNCT
american_scientific_journal-4887	172	2	a	a	DET
american_scientific_journal-4887	172	3	new	new	ADJ
american_scientific_journal-4887	172	4	approach	approach	NOUN
american_scientific_journal-4887	172	5	for	for	ADP
american_scientific_journal-4887	172	6	solving	solve	VERB
american_scientific_journal-4887	172	7	fully	fully	ADV
american_scientific_journal-4887	172	8	fuzzy	fuzzy	ADJ
american_scientific_journal-4887	172	9	linear	linear	NOUN
american_scientific_journal-4887	172	10	systems	system	NOUN
american_scientific_journal-4887	172	11	”	"	PUNCT
american_scientific_journal-4887	172	12	,	,	PUNCT
american_scientific_journal-4887	172	13	advances	advance	NOUN
american_scientific_journal-4887	172	14	in	in	ADP
american_scientific_journal-4887	172	15	fuzzy	fuzzy	ADJ
american_scientific_journal-4887	172	16	systems	system	NOUN
american_scientific_journal-4887	172	17	,	,	PUNCT
american_scientific_journal-4887	172	18	pp	pp	ADJ
american_scientific_journal-4887	172	19	.	.	PUNCT
american_scientific_journal-4887	173	1	1	1	NUM
american_scientific_journal-4887	173	2	-	-	SYM
american_scientific_journal-4887	173	3	8	8	NUM
american_scientific_journal-4887	173	4	.	.	PUNCT
american_scientific_journal-4887	174	1	2011	2011	NUM
american_scientific_journal-4887	174	2	.	.	PUNCT
american_scientific_journal-4887	175	1	[	[	X
american_scientific_journal-4887	175	2	3	3	NUM
american_scientific_journal-4887	175	3	]	]	X
american_scientific_journal-4887	175	4	n.	n.	PROPN
american_scientific_journal-4887	175	5	babbar	babbar	PROPN
american_scientific_journal-4887	175	6	,	,	PUNCT
american_scientific_journal-4887	175	7	a.	a.	PROPN
american_scientific_journal-4887	175	8	kumar	kumar	PROPN
american_scientific_journal-4887	175	9	and	and	CCONJ
american_scientific_journal-4887	175	10	a.	a.	NOUN
american_scientific_journal-4887	175	11	bansal	bansal	NOUN
american_scientific_journal-4887	175	12	.	.	PUNCT
american_scientific_journal-4887	176	1	“	"	PUNCT
american_scientific_journal-4887	176	2	solving	solve	VERB
american_scientific_journal-4887	176	3	fully	fully	ADV
american_scientific_journal-4887	176	4	fuzzy	fuzzy	ADJ
american_scientific_journal-4887	176	5	linear	linear	ADJ
american_scientific_journal-4887	176	6	system	system	NOUN
american_scientific_journal-4887	176	7	with	with	ADP
american_scientific_journal-4887	176	8	arbitrary	arbitrary	ADJ
american_scientific_journal-4887	176	9	triangular	triangular	NOUN
american_scientific_journal-4887	176	10	fuzzy	fuzzy	ADJ
american_scientific_journal-4887	176	11	numbers	number	NOUN
american_scientific_journal-4887	176	12	(	(	PUNCT
american_scientific_journal-4887	176	13	𝑚𝑚,𝛼𝛼,𝛽𝛽	𝑚𝑚,𝛼𝛼,𝛽𝛽	NOUN
american_scientific_journal-4887	176	14	)	)	PUNCT
american_scientific_journal-4887	176	15	”	"	PUNCT
american_scientific_journal-4887	176	16	,	,	PUNCT
american_scientific_journal-4887	176	17	soft	soft	ADJ
american_scientific_journal-4887	176	18	comput	comput	NOUN
american_scientific_journal-4887	176	19	,	,	PUNCT
american_scientific_journal-4887	176	20	vol	vol	NOUN
american_scientific_journal-4887	176	21	.	.	PROPN
american_scientific_journal-4887	176	22	17	17	NUM
american_scientific_journal-4887	176	23	.	.	PUNCT
american_scientific_journal-4887	177	1	pp	pp	ADJ
american_scientific_journal-4887	177	2	.	.	PUNCT
american_scientific_journal-4887	178	1	691	691	NUM
american_scientific_journal-4887	178	2	-	-	SYM
american_scientific_journal-4887	178	3	702	702	NUM
american_scientific_journal-4887	178	4	.	.	NOUN
american_scientific_journal-4887	178	5	2013	2013	NUM
american_scientific_journal-4887	178	6	.	.	PUNCT
american_scientific_journal-4887	179	1	[	[	X
american_scientific_journal-4887	179	2	4	4	NUM
american_scientific_journal-4887	179	3	]	]	X
american_scientific_journal-4887	179	4	mashadi	mashadi	NOUN
american_scientific_journal-4887	179	5	.	.	PUNCT
american_scientific_journal-4887	180	1	“	"	PUNCT
american_scientific_journal-4887	180	2	a	a	DET
american_scientific_journal-4887	180	3	new	new	ADJ
american_scientific_journal-4887	180	4	method	method	NOUN
american_scientific_journal-4887	180	5	for	for	ADP
american_scientific_journal-4887	180	6	dual	dual	ADJ
american_scientific_journal-4887	180	7	fully	fully	ADV
american_scientific_journal-4887	180	8	fuzzy	fuzzy	ADJ
american_scientific_journal-4887	180	9	linear	linear	ADJ
american_scientific_journal-4887	180	10	system	system	NOUN
american_scientific_journal-4887	180	11	by	by	ADP
american_scientific_journal-4887	180	12	use	use	NOUN
american_scientific_journal-4887	180	13	lu	lu	NOUN
american_scientific_journal-4887	180	14	factorizations	factorization	NOUN
american_scientific_journal-4887	180	15	of	of	ADP
american_scientific_journal-4887	180	16	the	the	DET
american_scientific_journal-4887	180	17	coefficient	coefficient	NOUN
american_scientific_journal-4887	180	18	matrix	matrix	NOUN
american_scientific_journal-4887	180	19	”	"	PUNCT
american_scientific_journal-4887	180	20	,	,	PUNCT
american_scientific_journal-4887	180	21	jurnal	jurnal	ADJ
american_scientific_journal-4887	180	22	matematika	matematika	PROPN
american_scientific_journal-4887	180	23	dan	dan	PROPN
american_scientific_journal-4887	180	24	sains	sains	PROPN
american_scientific_journal-4887	180	25	,	,	PUNCT
american_scientific_journal-4887	180	26	vol	vol	NOUN
american_scientific_journal-4887	180	27	.	.	PROPN
american_scientific_journal-4887	180	28	15	15	NUM
american_scientific_journal-4887	180	29	.	.	PUNCT
american_scientific_journal-4887	181	1	pp	pp	ADJ
american_scientific_journal-4887	181	2	.	.	PUNCT
american_scientific_journal-4887	182	1	101	101	NUM
american_scientific_journal-4887	182	2	-	-	SYM
american_scientific_journal-4887	182	3	106	106	NUM
american_scientific_journal-4887	182	4	.	.	PUNCT
american_scientific_journal-4887	183	1	2010	2010	NUM
american_scientific_journal-4887	183	2	.	.	PUNCT
american_scientific_journal-4887	184	1	[	[	X
american_scientific_journal-4887	184	2	5	5	X
american_scientific_journal-4887	184	3	]	]	PUNCT
american_scientific_journal-4887	184	4	s.	s.	PROPN
american_scientific_journal-4887	184	5	gemawati	gemawati	PROPN
american_scientific_journal-4887	184	6	,	,	PUNCT
american_scientific_journal-4887	184	7	i.	i.	PROPN
american_scientific_journal-4887	184	8	nasfianti	nasfianti	PROPN
american_scientific_journal-4887	184	9	,	,	PUNCT
american_scientific_journal-4887	184	10	mashadi	mashadi	NOUN
american_scientific_journal-4887	184	11	and	and	CCONJ
american_scientific_journal-4887	184	12	a.	a.	NOUN
american_scientific_journal-4887	184	13	hadi	hadi	PROPN
american_scientific_journal-4887	184	14	.	.	PUNCT
american_scientific_journal-4887	185	1	“	"	PUNCT
american_scientific_journal-4887	185	2	a	a	DET
american_scientific_journal-4887	185	3	new	new	ADJ
american_scientific_journal-4887	185	4	method	method	NOUN
american_scientific_journal-4887	185	5	for	for	ADP
american_scientific_journal-4887	185	6	dual	dual	ADJ
american_scientific_journal-4887	185	7	fully	fully	ADV
american_scientific_journal-4887	185	8	fuzzy	fuzzy	ADJ
american_scientific_journal-4887	185	9	linear	linear	ADJ
american_scientific_journal-4887	185	10	system	system	NOUN
american_scientific_journal-4887	185	11	with	with	ADP
american_scientific_journal-4887	185	12	trapezoidal	trapezoidal	ADJ
american_scientific_journal-4887	185	13	fuzzy	fuzzy	ADJ
american_scientific_journal-4887	185	14	number	number	NOUN
american_scientific_journal-4887	185	15	by	by	ADP
american_scientific_journal-4887	185	16	qr	qr	NOUN
american_scientific_journal-4887	185	17	decomposition	decomposition	NOUN
american_scientific_journal-4887	185	18	”	"	PUNCT
american_scientific_journal-4887	185	19	,	,	PUNCT
american_scientific_journal-4887	185	20	semirata	semirata	NOUN
american_scientific_journal-4887	185	21	-	-	PUNCT
american_scientific_journal-4887	185	22	international	international	ADJ
american_scientific_journal-4887	185	23	conference	conference	NOUN
american_scientific_journal-4887	185	24	on	on	ADP
american_scientific_journal-4887	185	25	science	science	NOUN
american_scientific_journal-4887	185	26	and	and	CCONJ
american_scientific_journal-4887	185	27	technology	technology	NOUN
american_scientific_journal-4887	185	28	,	,	PUNCT
american_scientific_journal-4887	185	29	vol	vol	NOUN
american_scientific_journal-4887	185	30	.	.	PROPN
american_scientific_journal-4887	185	31	1116	1116	NUM
american_scientific_journal-4887	185	32	.	.	PUNCT
american_scientific_journal-4887	186	1	pp	pp	ADJ
american_scientific_journal-4887	186	2	.	.	PUNCT
american_scientific_journal-4887	187	1	1	1	NUM
american_scientific_journal-4887	187	2	-	-	SYM
american_scientific_journal-4887	187	3	5	5	NUM
american_scientific_journal-4887	187	4	.	.	NOUN
american_scientific_journal-4887	187	5	2018	2018	NUM
american_scientific_journal-4887	187	6	.	.	PUNCT
american_scientific_journal-4887	188	1	[	[	X
american_scientific_journal-4887	188	2	6	6	NUM
american_scientific_journal-4887	188	3	]	]	PUNCT
american_scientific_journal-4887	188	4	s.	s.	PROPN
american_scientific_journal-4887	188	5	i.	i.	PROPN
american_scientific_journal-4887	188	6	marni	marni	PROPN
american_scientific_journal-4887	188	7	,	,	PUNCT
american_scientific_journal-4887	188	8	mashadi	mashadi	NOUN
american_scientific_journal-4887	188	9	and	and	CCONJ
american_scientific_journal-4887	188	10	s.	s.	PROPN
american_scientific_journal-4887	188	11	gemawati	gemawati	PROPN
american_scientific_journal-4887	188	12	.	.	PUNCT
american_scientific_journal-4887	189	1	“	"	PUNCT
american_scientific_journal-4887	189	2	solving	solve	VERB
american_scientific_journal-4887	189	3	dual	dual	ADJ
american_scientific_journal-4887	189	4	fully	fully	ADV
american_scientific_journal-4887	189	5	fuzzy	fuzzy	ADJ
american_scientific_journal-4887	189	6	linear	linear	ADJ
american_scientific_journal-4887	189	7	system	system	NOUN
american_scientific_journal-4887	189	8	by	by	ADP
american_scientific_journal-4887	189	9	use	use	NOUN
american_scientific_journal-4887	189	10	factorizations	factorization	NOUN
american_scientific_journal-4887	189	11	of	of	ADP
american_scientific_journal-4887	189	12	the	the	DET
american_scientific_journal-4887	189	13	coefficient	coefficient	NOUN
american_scientific_journal-4887	189	14	matrix	matrix	NOUN
american_scientific_journal-4887	189	15	for	for	ADP
american_scientific_journal-4887	189	16	trapezoidal	trapezoidal	ADJ
american_scientific_journal-4887	189	17	fuzzy	fuzzy	ADJ
american_scientific_journal-4887	189	18	number	number	NOUN
american_scientific_journal-4887	189	19	”	"	PUNCT
american_scientific_journal-4887	189	20	,	,	PUNCT
american_scientific_journal-4887	189	21	bulletin	bulletin	NOUN
american_scientific_journal-4887	189	22	of	of	ADP
american_scientific_journal-4887	189	23	mathematics	mathematic	NOUN
american_scientific_journal-4887	189	24	,	,	PUNCT
american_scientific_journal-4887	189	25	vol	vol	NOUN
american_scientific_journal-4887	189	26	.	.	PROPN
american_scientific_journal-4887	189	27	10	10	NUM
american_scientific_journal-4887	189	28	.	.	PUNCT
american_scientific_journal-4887	190	1	pp	pp	ADJ
american_scientific_journal-4887	190	2	.	.	PUNCT
american_scientific_journal-4887	191	1	145	145	NUM
american_scientific_journal-4887	191	2	-	-	SYM
american_scientific_journal-4887	191	3	56	56	NUM
american_scientific_journal-4887	191	4	.	.	NOUN
american_scientific_journal-4887	191	5	2018	2018	NUM
american_scientific_journal-4887	191	6	.	.	PUNCT
american_scientific_journal-4887	192	1	[	[	X
american_scientific_journal-4887	192	2	7	7	X
american_scientific_journal-4887	192	3	]	]	X
american_scientific_journal-4887	192	4	y.	y.	PROPN
american_scientific_journal-4887	192	5	safitri	safitri	PROPN
american_scientific_journal-4887	192	6	and	and	CCONJ
american_scientific_journal-4887	192	7	mashadi	mashadi	NOUN
american_scientific_journal-4887	192	8	.	.	PUNCT
american_scientific_journal-4887	193	1	“	"	PUNCT
american_scientific_journal-4887	193	2	alternative	alternative	ADJ
american_scientific_journal-4887	193	3	fuzzy	fuzzy	ADJ
american_scientific_journal-4887	193	4	algebra	algebra	NOUN
american_scientific_journal-4887	193	5	to	to	PART
american_scientific_journal-4887	193	6	solve	solve	VERB
american_scientific_journal-4887	193	7	dual	dual	ADV
american_scientific_journal-4887	193	8	fully	fully	ADV
american_scientific_journal-4887	193	9	fuzzy	fuzzy	ADJ
american_scientific_journal-4887	193	10	linear	linear	ADJ
american_scientific_journal-4887	193	11	system	system	NOUN
american_scientific_journal-4887	193	12	using	use	VERB
american_scientific_journal-4887	193	13	st	st	NOUN
american_scientific_journal-4887	193	14	decomposition	decomposition	NOUN
american_scientific_journal-4887	193	15	”	"	PUNCT
american_scientific_journal-4887	193	16	,	,	PUNCT
american_scientific_journal-4887	193	17	iosr	iosr	ADJ
american_scientific_journal-4887	193	18	journal	journal	NOUN
american_scientific_journal-4887	193	19	of	of	ADP
american_scientific_journal-4887	193	20	mathematics	mathematic	NOUN
american_scientific_journal-4887	193	21	,	,	PUNCT
american_scientific_journal-4887	193	22	vol	vol	NOUN
american_scientific_journal-4887	193	23	.	.	PROPN
american_scientific_journal-4887	194	1	15	15	NUM
american_scientific_journal-4887	194	2	.	.	PUNCT
american_scientific_journal-4887	195	1	pp	pp	ADJ
american_scientific_journal-4887	195	2	.	.	PUNCT
american_scientific_journal-4887	196	1	32	32	NUM
american_scientific_journal-4887	196	2	-	-	SYM
american_scientific_journal-4887	196	3	38	38	NUM
american_scientific_journal-4887	196	4	.	.	PUNCT
american_scientific_journal-4887	197	1	2019	2019	NUM
american_scientific_journal-4887	197	2	.	.	PUNCT
american_scientific_journal-4887	198	1	[	[	X
american_scientific_journal-4887	198	2	8	8	NUM
american_scientific_journal-4887	198	3	]	]	X
american_scientific_journal-4887	198	4	m.	m.	NOUN
american_scientific_journal-4887	198	5	dehghan	dehghan	PROPN
american_scientific_journal-4887	198	6	and	and	CCONJ
american_scientific_journal-4887	198	7	b.	b.	PROPN
american_scientific_journal-4887	198	8	hashemi	hashemi	PROPN
american_scientific_journal-4887	198	9	.	.	PUNCT
american_scientific_journal-4887	199	1	“	"	PUNCT
american_scientific_journal-4887	199	2	solution	solution	NOUN
american_scientific_journal-4887	199	3	of	of	ADP
american_scientific_journal-4887	199	4	the	the	DET
american_scientific_journal-4887	199	5	fully	fully	ADV
american_scientific_journal-4887	199	6	fuzzy	fuzzy	ADJ
american_scientific_journal-4887	199	7	linear	linear	ADJ
american_scientific_journal-4887	199	8	systems	system	NOUN
american_scientific_journal-4887	199	9	using	use	VERB
american_scientific_journal-4887	199	10	the	the	DET
american_scientific_journal-4887	199	11	decompositions	decomposition	NOUN
american_scientific_journal-4887	199	12	procedure	procedure	NOUN
american_scientific_journal-4887	199	13	”	"	PUNCT
american_scientific_journal-4887	199	14	,	,	PUNCT
american_scientific_journal-4887	199	15	applied	apply	VERB
american_scientific_journal-4887	199	16	mathematics	mathematic	NOUN
american_scientific_journal-4887	199	17	computation	computation	NOUN
american_scientific_journal-4887	199	18	,	,	PUNCT
american_scientific_journal-4887	199	19	vol	vol	NOUN
american_scientific_journal-4887	199	20	.	.	PROPN
american_scientific_journal-4887	199	21	182	182	NUM
american_scientific_journal-4887	199	22	.	.	PUNCT
american_scientific_journal-4887	200	1	pp	pp	ADJ
american_scientific_journal-4887	200	2	.	.	PUNCT
american_scientific_journal-4887	201	1	1568	1568	NUM
american_scientific_journal-4887	201	2	-	-	SYM
american_scientific_journal-4887	201	3	1580	1580	NUM
american_scientific_journal-4887	201	4	.	.	PUNCT
american_scientific_journal-4887	202	1	2006	2006	NUM
american_scientific_journal-4887	202	2	.	.	PUNCT
american_scientific_journal-4887	203	1	[	[	X
american_scientific_journal-4887	203	2	9	9	NUM
american_scientific_journal-4887	203	3	]	]	X
american_scientific_journal-4887	203	4	s.h	s.h	PROPN
american_scientific_journal-4887	203	5	.	.	PROPN
american_scientific_journal-4887	203	6	nasseri	nasseri	PROPN
american_scientific_journal-4887	203	7	,	,	PUNCT
american_scientific_journal-4887	203	8	m.	m.	NOUN
american_scientific_journal-4887	203	9	sohrabi	sohrabi	NOUN
american_scientific_journal-4887	203	10	and	and	CCONJ
american_scientific_journal-4887	203	11	e.	e.	PROPN
american_scientific_journal-4887	203	12	ardil	ardil	PROPN
american_scientific_journal-4887	203	13	.	.	PUNCT
american_scientific_journal-4887	204	1	“	"	PUNCT
american_scientific_journal-4887	204	2	solving	solve	VERB
american_scientific_journal-4887	204	3	fully	fully	ADV
american_scientific_journal-4887	204	4	fuzzy	fuzzy	ADJ
american_scientific_journal-4887	204	5	linear	linear	ADJ
american_scientific_journal-4887	204	6	systems	system	NOUN
american_scientific_journal-4887	204	7	by	by	ADP
american_scientific_journal-4887	204	8	use	use	NOUN
american_scientific_journal-4887	204	9	of	of	ADP
american_scientific_journal-4887	204	10	a	a	DET
american_scientific_journal-4887	204	11	certain	certain	ADJ
american_scientific_journal-4887	204	12	decomposition	decomposition	NOUN
american_scientific_journal-4887	204	13	of	of	ADP
american_scientific_journal-4887	204	14	the	the	DET
american_scientific_journal-4887	204	15	coefficient	coefficient	NOUN
american_scientific_journal-4887	204	16	matrix	matrix	NOUN
american_scientific_journal-4887	204	17	”	"	PUNCT
american_scientific_journal-4887	204	18	,	,	PUNCT
american_scientific_journal-4887	204	19	international	international	ADJ
american_scientific_journal-4887	204	20	journal	journal	NOUN
american_scientific_journal-4887	204	21	of	of	ADP
american_scientific_journal-4887	204	22	computional	computional	ADJ
american_scientific_journal-4887	204	23	and	and	CCONJ
american_scientific_journal-4887	204	24	mathematical	mathematical	ADJ
american_scientific_journal-4887	204	25	sciences	science	NOUN
american_scientific_journal-4887	204	26	,	,	PUNCT
american_scientific_journal-4887	204	27	vol	vol	NOUN
american_scientific_journal-4887	204	28	.	.	PROPN
american_scientific_journal-4887	205	1	2	2	NUM
american_scientific_journal-4887	205	2	.	.	X
american_scientific_journal-4887	205	3	pp	pp	ADJ
american_scientific_journal-4887	205	4	.	.	PUNCT
american_scientific_journal-4887	206	1	140	140	NUM
american_scientific_journal-4887	206	2	-	-	SYM
american_scientific_journal-4887	206	3	142	142	NUM
american_scientific_journal-4887	206	4	.	.	PUNCT
american_scientific_journal-4887	207	1	2008	2008	NUM
american_scientific_journal-4887	207	2	.	.	PUNCT
american_scientific_journal-4887	208	1	[	[	X
american_scientific_journal-4887	208	2	10	10	NUM
american_scientific_journal-4887	208	3	]	]	X
american_scientific_journal-4887	208	4	t.	t.	NOUN
american_scientific_journal-4887	208	5	allahviranloo	allahviranloo	NOUN
american_scientific_journal-4887	208	6	,	,	PUNCT
american_scientific_journal-4887	208	7	n.	n.	PROPN
american_scientific_journal-4887	208	8	mikaeilvand	mikaeilvand	PROPN
american_scientific_journal-4887	208	9	,	,	PUNCT
american_scientific_journal-4887	208	10	n.	n.	PROPN
american_scientific_journal-4887	208	11	a.	a.	PROPN
american_scientific_journal-4887	208	12	kiani	kiani	PROPN
american_scientific_journal-4887	208	13	and	and	CCONJ
american_scientific_journal-4887	208	14	r.	r.	PROPN
american_scientific_journal-4887	208	15	m.	m.	PROPN
american_scientific_journal-4887	208	16	shastari	shastari	PROPN
american_scientific_journal-4887	208	17	.	.	PUNCT
american_scientific_journal-4887	209	1	“	"	PUNCT
american_scientific_journal-4887	209	2	signed	sign	VERB
american_scientific_journal-4887	209	3	decomposition	decomposition	NOUN
american_scientific_journal-4887	209	4	of	of	ADP
american_scientific_journal-4887	209	5	fully	fully	ADV
american_scientific_journal-4887	209	6	fuzzy	fuzzy	ADJ
american_scientific_journal-4887	209	7	linear	linear	ADJ
american_scientific_journal-4887	209	8	systems	system	NOUN
american_scientific_journal-4887	209	9	”	"	PUNCT
american_scientific_journal-4887	209	10	,	,	PUNCT
american_scientific_journal-4887	209	11	applications	application	NOUN
american_scientific_journal-4887	209	12	and	and	CCONJ
american_scientific_journal-4887	209	13	applied	apply	VERB
american_scientific_journal-4887	209	14	mathematics	mathematic	NOUN
american_scientific_journal-4887	209	15	,	,	PUNCT
american_scientific_journal-4887	209	16	vol	vol	NOUN
american_scientific_journal-4887	209	17	.	.	PROPN
american_scientific_journal-4887	210	1	3	3	X
american_scientific_journal-4887	210	2	.	.	X
american_scientific_journal-4887	210	3	pp	pp	ADJ
american_scientific_journal-4887	210	4	.	.	PUNCT
american_scientific_journal-4887	211	1	77	77	NUM
american_scientific_journal-4887	211	2	-	-	SYM
american_scientific_journal-4887	211	3	88	88	NUM
american_scientific_journal-4887	211	4	.	.	PUNCT
american_scientific_journal-4887	212	1	2008	2008	NUM
american_scientific_journal-4887	212	2	.	.	PUNCT
american_scientific_journal-4887	213	1	[	[	X
american_scientific_journal-4887	213	2	11	11	NUM
american_scientific_journal-4887	213	3	]	]	PUNCT
american_scientific_journal-4887	213	4	m.	m.	NOUN
american_scientific_journal-4887	213	5	dehghan	dehghan	PROPN
american_scientific_journal-4887	213	6	,	,	PUNCT
american_scientific_journal-4887	213	7	b.	b.	PROPN
american_scientific_journal-4887	213	8	hashemi	hashemi	PROPN
american_scientific_journal-4887	213	9	and	and	CCONJ
american_scientific_journal-4887	213	10	m.	m.	NOUN
american_scientific_journal-4887	213	11	ghatee	ghatee	NOUN
american_scientific_journal-4887	213	12	.	.	PUNCT
american_scientific_journal-4887	214	1	“	"	PUNCT
american_scientific_journal-4887	214	2	computational	computational	ADJ
american_scientific_journal-4887	214	3	methods	method	NOUN
american_scientific_journal-4887	214	4	for	for	ADP
american_scientific_journal-4887	214	5	solving	solve	VERB
american_scientific_journal-4887	214	6	fully	fully	ADV
american_scientific_journal-4887	214	7	fuzzy	fuzzy	ADJ
american_scientific_journal-4887	214	8	linear	linear	ADJ
american_scientific_journal-4887	214	9	systems	system	NOUN
american_scientific_journal-4887	214	10	”	"	PUNCT
american_scientific_journal-4887	214	11	,	,	PUNCT
american_scientific_journal-4887	214	12	applied	apply	VERB
american_scientific_journal-4887	214	13	mathematics	mathematic	NOUN
american_scientific_journal-4887	214	14	computation	computation	NOUN
american_scientific_journal-4887	214	15	,	,	PUNCT
american_scientific_journal-4887	214	16	vol	vol	NOUN
american_scientific_journal-4887	214	17	.	.	PROPN
american_scientific_journal-4887	214	18	179	179	NUM
american_scientific_journal-4887	214	19	.	.	PUNCT
american_scientific_journal-4887	215	1	pp	pp	ADJ
american_scientific_journal-4887	215	2	.	.	PUNCT
american_scientific_journal-4887	216	1	328	328	NUM
american_scientific_journal-4887	216	2	-	-	SYM
american_scientific_journal-4887	216	3	343	343	NUM
american_scientific_journal-4887	216	4	.	.	PUNCT
american_scientific_journal-4887	217	1	2006	2006	NUM
american_scientific_journal-4887	217	2	.	.	PUNCT
american_scientific_journal-4887	218	1	[	[	X
american_scientific_journal-4887	218	2	12	12	NUM
american_scientific_journal-4887	218	3	]	]	PUNCT
american_scientific_journal-4887	218	4	m.	m.	NOUN
american_scientific_journal-4887	218	5	dehghan	dehghan	PROPN
american_scientific_journal-4887	218	6	,	,	PUNCT
american_scientific_journal-4887	218	7	b.	b.	PROPN
american_scientific_journal-4887	218	8	hashemi	hashemi	PROPN
american_scientific_journal-4887	218	9	and	and	CCONJ
american_scientific_journal-4887	218	10	m.	m.	NOUN
american_scientific_journal-4887	218	11	ghatee	ghatee	NOUN
american_scientific_journal-4887	218	12	.	.	PUNCT
american_scientific_journal-4887	219	1	“	"	PUNCT
american_scientific_journal-4887	219	2	solution	solution	NOUN
american_scientific_journal-4887	219	3	of	of	ADP
american_scientific_journal-4887	219	4	the	the	DET
american_scientific_journal-4887	219	5	fully	fully	ADV
american_scientific_journal-4887	219	6	fuzzy	fuzzy	ADJ
american_scientific_journal-4887	219	7	linear	linear	ADJ
american_scientific_journal-4887	219	8	systems	system	NOUN
american_scientific_journal-4887	219	9	using	use	VERB
american_scientific_journal-4887	219	10	iterative	iterative	NOUN
american_scientific_journal-4887	219	11	techniques	technique	NOUN
american_scientific_journal-4887	219	12	”	"	PUNCT
american_scientific_journal-4887	219	13	,	,	PUNCT
american_scientific_journal-4887	219	14	chao	chao	PROPN
american_scientific_journal-4887	219	15	,	,	PUNCT
american_scientific_journal-4887	219	16	solitons	soliton	NOUN
american_scientific_journal-4887	219	17	and	and	CCONJ
american_scientific_journal-4887	219	18	fractals	fractal	NOUN
american_scientific_journal-4887	219	19	,	,	PUNCT
american_scientific_journal-4887	219	20	vol	vol	NOUN
american_scientific_journal-4887	219	21	.	.	PUNCT
american_scientific_journal-4887	220	1	34	34	NUM
american_scientific_journal-4887	220	2	.	.	PUNCT
american_scientific_journal-4887	221	1	pp	pp	ADJ
american_scientific_journal-4887	221	2	.	.	PUNCT
american_scientific_journal-4887	222	1	316	316	NUM
american_scientific_journal-4887	222	2	-	-	SYM
american_scientific_journal-4887	222	3	336	336	NUM
american_scientific_journal-4887	222	4	.	.	PUNCT
american_scientific_journal-4887	223	1	2007	2007	NUM
american_scientific_journal-4887	223	2	.	.	PUNCT
american_scientific_journal-4887	224	1	[	[	X
american_scientific_journal-4887	224	2	13	13	NUM
american_scientific_journal-4887	224	3	]	]	X
american_scientific_journal-4887	224	4	g.	g.	PROPN
american_scientific_journal-4887	224	5	gupta	gupta	PROPN
american_scientific_journal-4887	224	6	.	.	PUNCT
american_scientific_journal-4887	225	1	“	"	PUNCT
american_scientific_journal-4887	225	2	some	some	DET
american_scientific_journal-4887	225	3	methods	method	NOUN
american_scientific_journal-4887	225	4	for	for	ADP
american_scientific_journal-4887	225	5	solving	solve	VERB
american_scientific_journal-4887	225	6	fully	fully	ADV
american_scientific_journal-4887	225	7	fuzzy	fuzzy	ADJ
american_scientific_journal-4887	225	8	linear	linear	ADJ
american_scientific_journal-4887	225	9	system	system	NOUN
american_scientific_journal-4887	225	10	of	of	ADP
american_scientific_journal-4887	225	11	equations	equation	NOUN
american_scientific_journal-4887	225	12	”	"	PUNCT
american_scientific_journal-4887	225	13	,	,	PUNCT
american_scientific_journal-4887	225	14	thesis	thesis	NOUN
american_scientific_journal-4887	225	15	,	,	PUNCT
american_scientific_journal-4887	225	16	school	school	NOUN
american_scientific_journal-4887	225	17	of	of	ADP
american_scientific_journal-4887	225	18	mathematics	mathematic	NOUN
american_scientific_journal-4887	225	19	and	and	CCONJ
american_scientific_journal-4887	225	20	computer	computer	NOUN
american_scientific_journal-4887	225	21	applications	application	NOUN
american_scientific_journal-4887	225	22	thapar	thapar	PROPN
american_scientific_journal-4887	225	23	university	university	NOUN
american_scientific_journal-4887	225	24	patiala-147004	patiala-147004	NOUN
american_scientific_journal-4887	225	25	(	(	PUNCT
american_scientific_journal-4887	225	26	punjab	punjab	ADJ
american_scientific_journal-4887	225	27	)	)	PUNCT
american_scientific_journal-4887	225	28	india	india	PROPN
american_scientific_journal-4887	225	29	.	.	PUNCT
american_scientific_journal-4887	225	30	2010	2010	NUM
american_scientific_journal-4887	225	31	.	.	PUNCT
american_scientific_journal-4887	226	1	american	american	ADJ
american_scientific_journal-4887	226	2	scientific	scientific	ADJ
american_scientific_journal-4887	226	3	research	research	PROPN
american_scientific_journal-4887	226	4	journal	journal	NOUN
american_scientific_journal-4887	226	5	for	for	ADP
american_scientific_journal-4887	226	6	engineering	engineering	NOUN
american_scientific_journal-4887	226	7	,	,	PUNCT
american_scientific_journal-4887	226	8	technology	technology	NOUN
american_scientific_journal-4887	226	9	,	,	PUNCT
american_scientific_journal-4887	226	10	and	and	CCONJ
american_scientific_journal-4887	226	11	sciences	science	NOUN
american_scientific_journal-4887	226	12	(	(	PUNCT
american_scientific_journal-4887	226	13	asrjets	asrjet	NOUN
american_scientific_journal-4887	226	14	)	)	PUNCT
american_scientific_journal-4887	226	15	(	(	PUNCT
american_scientific_journal-4887	226	16	2019	2019	NUM
american_scientific_journal-4887	226	17	)	)	PUNCT
american_scientific_journal-4887	226	18	volume	volume	NOUN
american_scientific_journal-4887	226	19	56	56	NUM
american_scientific_journal-4887	226	20	,	,	PUNCT
american_scientific_journal-4887	226	21	no	no	DET
american_scientific_journal-4887	226	22	1	1	NUM
american_scientific_journal-4887	226	23	,	,	PUNCT
american_scientific_journal-4887	226	24	pp	pp	ADV
american_scientific_journal-4887	226	25	113	113	NUM
american_scientific_journal-4887	226	26	-	-	SYM
american_scientific_journal-4887	226	27	123	123	NUM
american_scientific_journal-4887	226	28	123	123	NUM
american_scientific_journal-4887	226	29	[	[	X
american_scientific_journal-4887	226	30	14	14	NUM
american_scientific_journal-4887	226	31	]	]	X
american_scientific_journal-4887	226	32	s.h	s.h	PROPN
american_scientific_journal-4887	226	33	.	.	PROPN
american_scientific_journal-4887	226	34	nasseri	nasseri	PROPN
american_scientific_journal-4887	226	35	and	and	CCONJ
american_scientific_journal-4887	226	36	f.	f.	PROPN
american_scientific_journal-4887	226	37	zahmatkesh	zahmatkesh	PROPN
american_scientific_journal-4887	226	38	.	.	PUNCT
american_scientific_journal-4887	227	1	“	"	PUNCT
american_scientific_journal-4887	227	2	huang	huang	PROPN
american_scientific_journal-4887	227	3	method	method	NOUN
american_scientific_journal-4887	227	4	for	for	ADP
american_scientific_journal-4887	227	5	solving	solve	VERB
american_scientific_journal-4887	227	6	fully	fully	ADV
american_scientific_journal-4887	227	7	fuzzy	fuzzy	ADJ
american_scientific_journal-4887	227	8	linear	linear	ADJ
american_scientific_journal-4887	227	9	system	system	NOUN
american_scientific_journal-4887	227	10	of	of	ADP
american_scientific_journal-4887	227	11	equations	equation	NOUN
american_scientific_journal-4887	227	12	”	"	PUNCT
american_scientific_journal-4887	227	13	,	,	PUNCT
american_scientific_journal-4887	227	14	the	the	DET
american_scientific_journal-4887	227	15	journal	journal	NOUN
american_scientific_journal-4887	227	16	of	of	ADP
american_scientific_journal-4887	227	17	mathematics	mathematic	NOUN
american_scientific_journal-4887	227	18	and	and	CCONJ
american_scientific_journal-4887	227	19	computer	computer	NOUN
american_scientific_journal-4887	227	20	science	science	NOUN
american_scientific_journal-4887	227	21	,	,	PUNCT
american_scientific_journal-4887	227	22	vol	vol	NOUN
american_scientific_journal-4887	227	23	.	.	PROPN
american_scientific_journal-4887	228	1	1	1	NUM
american_scientific_journal-4887	228	2	.	.	X
american_scientific_journal-4887	229	1	pp	pp	ADJ
american_scientific_journal-4887	229	2	.	.	PUNCT
american_scientific_journal-4887	230	1	1	1	NUM
american_scientific_journal-4887	230	2	-	-	SYM
american_scientific_journal-4887	230	3	5	5	NUM
american_scientific_journal-4887	230	4	.	.	NUM
american_scientific_journal-4887	230	5	2010	2010	NUM
american_scientific_journal-4887	230	6	.	.	PUNCT
american_scientific_journal-4887	231	1	[	[	X
american_scientific_journal-4887	231	2	15	15	NUM
american_scientific_journal-4887	231	3	]	]	X
american_scientific_journal-4887	231	4	h.	h.	PROPN
american_scientific_journal-4887	231	5	kholida	kholida	PROPN
american_scientific_journal-4887	231	6	and	and	CCONJ
american_scientific_journal-4887	231	7	mashadi	mashadi	NOUN
american_scientific_journal-4887	231	8	.	.	PUNCT
american_scientific_journal-4887	232	1	“	"	PUNCT
american_scientific_journal-4887	232	2	alternative	alternative	ADJ
american_scientific_journal-4887	232	3	fuzzy	fuzzy	ADJ
american_scientific_journal-4887	232	4	algebra	algebra	NOUN
american_scientific_journal-4887	232	5	for	for	ADP
american_scientific_journal-4887	232	6	fuzzy	fuzzy	ADJ
american_scientific_journal-4887	232	7	linear	linear	NOUN
american_scientific_journal-4887	232	8	system	system	NOUN
american_scientific_journal-4887	232	9	using	use	VERB
american_scientific_journal-4887	232	10	cramers	cramer	NOUN
american_scientific_journal-4887	232	11	rules	rule	NOUN
american_scientific_journal-4887	232	12	on	on	ADP
american_scientific_journal-4887	232	13	fuzzy	fuzzy	ADJ
american_scientific_journal-4887	232	14	trapezoidal	trapezoidal	ADJ
american_scientific_journal-4887	232	15	number	number	NOUN
american_scientific_journal-4887	232	16	”	"	PUNCT
american_scientific_journal-4887	232	17	,	,	PUNCT
american_scientific_journal-4887	232	18	international	international	ADJ
american_scientific_journal-4887	232	19	journal	journal	NOUN
american_scientific_journal-4887	232	20	of	of	ADP
american_scientific_journal-4887	232	21	innovative	innovative	ADJ
american_scientific_journal-4887	232	22	science	science	NOUN
american_scientific_journal-4887	232	23	and	and	CCONJ
american_scientific_journal-4887	232	24	research	research	NOUN
american_scientific_journal-4887	232	25	technology	technology	NOUN
american_scientific_journal-4887	232	26	,	,	PUNCT
american_scientific_journal-4887	232	27	vol	vol	NOUN
american_scientific_journal-4887	232	28	.	.	PROPN
american_scientific_journal-4887	233	1	4	4	X
american_scientific_journal-4887	233	2	.	.	X
american_scientific_journal-4887	233	3	pp	pp	ADJ
american_scientific_journal-4887	233	4	.	.	PUNCT
american_scientific_journal-4887	234	1	494	494	NUM
american_scientific_journal-4887	234	2	-	-	SYM
american_scientific_journal-4887	234	3	500	500	NUM
american_scientific_journal-4887	234	4	.	.	PUNCT
american_scientific_journal-4887	235	1	2019	2019	NUM
american_scientific_journal-4887	235	2	.	.	PUNCT
american_scientific_journal-4887	236	1	[	[	X
american_scientific_journal-4887	236	2	16	16	NUM
american_scientific_journal-4887	236	3	]	]	PUNCT
american_scientific_journal-4887	236	4	m.	m.	PROPN
american_scientific_journal-4887	236	5	ma	ma	PROPN
american_scientific_journal-4887	236	6	,	,	PUNCT
american_scientific_journal-4887	236	7	m.	m.	NOUN
american_scientific_journal-4887	236	8	friedman	friedman	PROPN
american_scientific_journal-4887	236	9	and	and	CCONJ
american_scientific_journal-4887	236	10	a.	a.	NOUN
american_scientific_journal-4887	236	11	kandel	kandel	PROPN
american_scientific_journal-4887	236	12	.	.	PUNCT
american_scientific_journal-4887	237	1	“	"	PUNCT
american_scientific_journal-4887	237	2	duality	duality	NOUN
american_scientific_journal-4887	237	3	in	in	ADP
american_scientific_journal-4887	237	4	fuzzy	fuzzy	ADJ
american_scientific_journal-4887	237	5	linear	linear	PROPN
american_scientific_journal-4887	237	6	systems	system	NOUN
american_scientific_journal-4887	237	7	”	"	PUNCT
american_scientific_journal-4887	237	8	,	,	PUNCT
american_scientific_journal-4887	237	9	fuzzy	fuzzy	ADJ
american_scientific_journal-4887	237	10	sets	set	NOUN
american_scientific_journal-4887	237	11	and	and	CCONJ
american_scientific_journal-4887	237	12	systems	system	NOUN
american_scientific_journal-4887	237	13	,	,	PUNCT
american_scientific_journal-4887	237	14	vol	vol	NOUN
american_scientific_journal-4887	237	15	109	109	NUM
american_scientific_journal-4887	237	16	.	.	PUNCT
american_scientific_journal-4887	238	1	pp	pp	ADJ
american_scientific_journal-4887	238	2	.	.	PUNCT
american_scientific_journal-4887	239	1	55	55	NUM
american_scientific_journal-4887	239	2	-	-	SYM
american_scientific_journal-4887	239	3	58	58	NUM
american_scientific_journal-4887	239	4	.	.	PUNCT
american_scientific_journal-4887	240	1	2000	2000	NUM
american_scientific_journal-4887	240	2	.	.	PUNCT
american_scientific_journal-4887	241	1	[	[	X
american_scientific_journal-4887	241	2	17	17	NUM
american_scientific_journal-4887	241	3	]	]	PUNCT
american_scientific_journal-4887	241	4	m.	m.	NOUN
american_scientific_journal-4887	241	5	friedman	friedman	PROPN
american_scientific_journal-4887	241	6	,	,	PUNCT
american_scientific_journal-4887	241	7	m.	m.	NOUN
american_scientific_journal-4887	241	8	ming	ming	PROPN
american_scientific_journal-4887	241	9	and	and	CCONJ
american_scientific_journal-4887	241	10	a.	a.	PROPN
american_scientific_journal-4887	241	11	kandel	kandel	PROPN
american_scientific_journal-4887	241	12	.	.	PUNCT
american_scientific_journal-4887	242	1	“	"	PUNCT
american_scientific_journal-4887	242	2	fuzzy	fuzzy	ADJ
american_scientific_journal-4887	242	3	linear	linear	PROPN
american_scientific_journal-4887	242	4	systems	system	NOUN
american_scientific_journal-4887	242	5	”	"	PUNCT
american_scientific_journal-4887	242	6	,	,	PUNCT
american_scientific_journal-4887	242	7	fuzzy	fuzzy	ADJ
american_scientific_journal-4887	242	8	sets	set	NOUN
american_scientific_journal-4887	242	9	and	and	CCONJ
american_scientific_journal-4887	242	10	systems	system	NOUN
american_scientific_journal-4887	242	11	,	,	PUNCT
american_scientific_journal-4887	242	12	vol	vol	NOUN
american_scientific_journal-4887	242	13	.	.	PROPN
american_scientific_journal-4887	243	1	96	96	NUM
american_scientific_journal-4887	243	2	.	.	PUNCT
american_scientific_journal-4887	244	1	pp	pp	ADJ
american_scientific_journal-4887	244	2	.	.	PUNCT
american_scientific_journal-4887	245	1	201209	201209	NUM
american_scientific_journal-4887	245	2	.	.	PUNCT
american_scientific_journal-4887	246	1	1998	1998	NUM
american_scientific_journal-4887	246	2	.	.	PUNCT