id	sid	tid	token	lemma	pos
american_scientific_journal-4187	1	1	1	1	X
american_scientific_journal-4187	1	2	.	.	SYM
american_scientific_journal-4187	1	3	162	162	NUM
american_scientific_journal-4187	1	4	american	american	PROPN
american_scientific_journal-4187	1	5	scientific	scientific	ADJ
american_scientific_journal-4187	1	6	research	research	NOUN
american_scientific_journal-4187	1	7	journal	journal	NOUN
american_scientific_journal-4187	1	8	for	for	ADP
american_scientific_journal-4187	1	9	engineering	engineering	NOUN
american_scientific_journal-4187	1	10	,	,	PUNCT
american_scientific_journal-4187	1	11	technology	technology	NOUN
american_scientific_journal-4187	1	12	,	,	PUNCT
american_scientific_journal-4187	1	13	and	and	CCONJ
american_scientific_journal-4187	1	14	sciences	science	NOUN
american_scientific_journal-4187	1	15	(	(	PUNCT
american_scientific_journal-4187	1	16	asrjets	asrjet	NOUN
american_scientific_journal-4187	1	17	)	)	PUNCT
american_scientific_journal-4187	1	18	issn	issn	PROPN
american_scientific_journal-4187	1	19	(	(	PUNCT
american_scientific_journal-4187	1	20	print	print	NOUN
american_scientific_journal-4187	1	21	)	)	PUNCT
american_scientific_journal-4187	1	22	2313	2313	NUM
american_scientific_journal-4187	1	23	-	-	SYM
american_scientific_journal-4187	1	24	4410	4410	NUM
american_scientific_journal-4187	1	25	,	,	PUNCT
american_scientific_journal-4187	1	26	issn	issn	PROPN
american_scientific_journal-4187	1	27	(	(	PUNCT
american_scientific_journal-4187	1	28	online	online	ADJ
american_scientific_journal-4187	1	29	)	)	PUNCT
american_scientific_journal-4187	1	30	2313	2313	NUM
american_scientific_journal-4187	1	31	-	-	SYM
american_scientific_journal-4187	1	32	4402	4402	NUM
american_scientific_journal-4187	1	33	©	©	PROPN
american_scientific_journal-4187	1	34	global	global	ADJ
american_scientific_journal-4187	1	35	society	society	NOUN
american_scientific_journal-4187	1	36	of	of	ADP
american_scientific_journal-4187	1	37	scientific	scientific	ADJ
american_scientific_journal-4187	1	38	research	research	NOUN
american_scientific_journal-4187	1	39	and	and	CCONJ
american_scientific_journal-4187	1	40	researchers	researcher	NOUN
american_scientific_journal-4187	1	41	http://asrjetsjournal.org/	http://asrjetsjournal.org/	VERB
american_scientific_journal-4187	1	42	a	a	DET
american_scientific_journal-4187	1	43	generalization	generalization	NOUN
american_scientific_journal-4187	1	44	concept	concept	NOUN
american_scientific_journal-4187	1	45	of	of	ADP
american_scientific_journal-4187	1	46	measure	measure	NOUN
american_scientific_journal-4187	1	47	by	by	ADP
american_scientific_journal-4187	1	48	using	use	VERB
american_scientific_journal-4187	1	49	binary	binary	ADJ
american_scientific_journal-4187	1	50	operations	operation	NOUN
american_scientific_journal-4187	1	51	m	m	PROPN
american_scientific_journal-4187	1	52	-	-	ADJ
american_scientific_journal-4187	1	53	hassan	hassan	PROPN
american_scientific_journal-4187	1	54	hadadzadeh	hadadzadeh	PROPN
american_scientific_journal-4187	1	55	naiery	naiery	PROPN
american_scientific_journal-4187	1	56	*	*	PUNCT
american_scientific_journal-4187	1	57	department	department	NOUN
american_scientific_journal-4187	1	58	of	of	ADP
american_scientific_journal-4187	1	59	mathematics	mathematic	NOUN
american_scientific_journal-4187	1	60	,	,	PUNCT
american_scientific_journal-4187	1	61	faculty	faculty	NOUN
american_scientific_journal-4187	1	62	of	of	ADP
american_scientific_journal-4187	1	63	sciences	science	NOUN
american_scientific_journal-4187	1	64	,	,	PUNCT
american_scientific_journal-4187	1	65	semnan	semnan	PROPN
american_scientific_journal-4187	1	66	university	university	PROPN
american_scientific_journal-4187	1	67	,	,	PUNCT
american_scientific_journal-4187	1	68	semnan	semnan	PROPN
american_scientific_journal-4187	1	69	,	,	PUNCT
american_scientific_journal-4187	1	70	iran	iran	PROPN
american_scientific_journal-4187	1	71	email	email	NOUN
american_scientific_journal-4187	1	72	:	:	PUNCT
american_scientific_journal-4187	1	73	center.office323@gmail.com	center.office323@gmail.com	X
american_scientific_journal-4187	1	74	abstract	abstract	NOUN
american_scientific_journal-4187	1	75	in	in	ADP
american_scientific_journal-4187	1	76	this	this	DET
american_scientific_journal-4187	1	77	paper	paper	NOUN
american_scientific_journal-4187	1	78	,	,	PUNCT
american_scientific_journal-4187	1	79	a	a	DET
american_scientific_journal-4187	1	80	generalization	generalization	NOUN
american_scientific_journal-4187	1	81	of	of	ADP
american_scientific_journal-4187	1	82	the	the	DET
american_scientific_journal-4187	1	83	concept	concept	NOUN
american_scientific_journal-4187	1	84	of	of	ADP
american_scientific_journal-4187	1	85	measure	measure	NOUN
american_scientific_journal-4187	1	86	is	be	AUX
american_scientific_journal-4187	1	87	made	make	VERB
american_scientific_journal-4187	1	88	using	use	VERB
american_scientific_journal-4187	1	89	binary	binary	ADJ
american_scientific_journal-4187	1	90	oprations	opration	NOUN
american_scientific_journal-4187	1	91	.	.	PUNCT
american_scientific_journal-4187	2	1	with	with	ADP
american_scientific_journal-4187	2	2	this	this	DET
american_scientific_journal-4187	2	3	generalization	generalization	NOUN
american_scientific_journal-4187	2	4	,	,	PUNCT
american_scientific_journal-4187	2	5	we	we	PRON
american_scientific_journal-4187	2	6	extend	extend	VERB
american_scientific_journal-4187	2	7	the	the	DET
american_scientific_journal-4187	2	8	measure	measure	NOUN
american_scientific_journal-4187	2	9	domain	domain	NOUN
american_scientific_journal-4187	2	10	to	to	PART
american_scientific_journal-4187	2	11	.	.	PUNCT
american_scientific_journal-4187	3	1	in	in	ADP
american_scientific_journal-4187	3	2	the	the	DET
american_scientific_journal-4187	3	3	future	future	NOUN
american_scientific_journal-4187	3	4	,	,	PUNCT
american_scientific_journal-4187	3	5	the	the	DET
american_scientific_journal-4187	3	6	properties	property	NOUN
american_scientific_journal-4187	3	7	of	of	ADP
american_scientific_journal-4187	3	8	this	this	DET
american_scientific_journal-4187	3	9	new	new	ADJ
american_scientific_journal-4187	3	10	concept	concept	NOUN
american_scientific_journal-4187	3	11	will	will	AUX
american_scientific_journal-4187	3	12	be	be	AUX
american_scientific_journal-4187	3	13	examined	examine	VERB
american_scientific_journal-4187	3	14	.	.	PUNCT
american_scientific_journal-4187	4	1	keywords	keyword	NOUN
american_scientific_journal-4187	4	2	:	:	PUNCT
american_scientific_journal-4187	4	3	measure	measure	NOUN
american_scientific_journal-4187	4	4	;	;	PUNCT
american_scientific_journal-4187	4	5	dependable	dependable	ADJ
american_scientific_journal-4187	4	6	value	value	NOUN
american_scientific_journal-4187	4	7	pre	pre	NOUN
american_scientific_journal-4187	4	8	-	-	NOUN
american_scientific_journal-4187	4	9	measure	measure	ADJ
american_scientific_journal-4187	4	10	;	;	PUNCT
american_scientific_journal-4187	4	11	dependable	dependable	ADJ
american_scientific_journal-4187	4	12	value	value	NOUN
american_scientific_journal-4187	4	13	measure	measure	NOUN
american_scientific_journal-4187	4	14	;	;	PUNCT
american_scientific_journal-4187	4	15	dependable	dependable	ADJ
american_scientific_journal-4187	4	16	value	value	NOUN
american_scientific_journal-4187	4	17	measure	measure	NOUN
american_scientific_journal-4187	4	18	under	under	ADP
american_scientific_journal-4187	4	19	binary	binary	ADJ
american_scientific_journal-4187	4	20	oprations	opration	NOUN
american_scientific_journal-4187	4	21	.	.	PUNCT
american_scientific_journal-4187	5	1	1	1	X
american_scientific_journal-4187	5	2	.	.	X
american_scientific_journal-4187	5	3	introduction	introduction	NOUN
american_scientific_journal-4187	5	4	when	when	SCONJ
american_scientific_journal-4187	5	5	we	we	PRON
american_scientific_journal-4187	5	6	study	study	VERB
american_scientific_journal-4187	5	7	of	of	ADP
american_scientific_journal-4187	5	8	measure	measure	NOUN
american_scientific_journal-4187	5	9	theory	theory	NOUN
american_scientific_journal-4187	5	10	,	,	PUNCT
american_scientific_journal-4187	5	11	we	we	PRON
american_scientific_journal-4187	5	12	understand	understand	VERB
american_scientific_journal-4187	5	13	this	this	DET
american_scientific_journal-4187	5	14	formal	formal	ADJ
american_scientific_journal-4187	5	15	theory	theory	NOUN
american_scientific_journal-4187	5	16	is	be	AUX
american_scientific_journal-4187	5	17	using	use	VERB
american_scientific_journal-4187	5	18	in	in	ADP
american_scientific_journal-4187	5	19	lebesgue	lebesgue	NOUN
american_scientific_journal-4187	5	20	and	and	CCONJ
american_scientific_journal-4187	5	21	integral	integral	ADJ
american_scientific_journal-4187	5	22	operation	operation	NOUN
american_scientific_journal-4187	5	23	.	.	PUNCT
american_scientific_journal-4187	6	1	in	in	ADP
american_scientific_journal-4187	6	2	the	the	DET
american_scientific_journal-4187	6	3	following	following	NOUN
american_scientific_journal-4187	6	4	,	,	PUNCT
american_scientific_journal-4187	6	5	the	the	DET
american_scientific_journal-4187	6	6	sigma	sigma	PROPN
american_scientific_journal-4187	6	7	algebra	algebra	NOUN
american_scientific_journal-4187	6	8	structure	structure	NOUN
american_scientific_journal-4187	6	9	is	be	AUX
american_scientific_journal-4187	6	10	proper	proper	ADJ
american_scientific_journal-4187	6	11	to	to	PART
american_scientific_journal-4187	6	12	implement	implement	VERB
american_scientific_journal-4187	6	13	.	.	PUNCT
american_scientific_journal-4187	7	1	as	as	SCONJ
american_scientific_journal-4187	7	2	we	we	PRON
american_scientific_journal-4187	7	3	know	know	VERB
american_scientific_journal-4187	7	4	,	,	PUNCT
american_scientific_journal-4187	7	5	when	when	SCONJ
american_scientific_journal-4187	7	6	we	we	PRON
american_scientific_journal-4187	7	7	talk	talk	VERB
american_scientific_journal-4187	7	8	about	about	ADP
american_scientific_journal-4187	7	9	measure	measure	NOUN
american_scientific_journal-4187	7	10	,	,	PUNCT
american_scientific_journal-4187	7	11	we	we	PRON
american_scientific_journal-4187	7	12	mean	mean	VERB
american_scientific_journal-4187	7	13	the	the	DET
american_scientific_journal-4187	7	14	function	function	NOUN
american_scientific_journal-4187	7	15	such	such	ADJ
american_scientific_journal-4187	7	16	as	as	ADP
american_scientific_journal-4187	7	17	;	;	PUNCT
american_scientific_journal-4187	7	18	which	which	PRON
american_scientific_journal-4187	7	19	has	have	VERB
american_scientific_journal-4187	7	20	the	the	DET
american_scientific_journal-4187	7	21	following	follow	VERB
american_scientific_journal-4187	7	22	properties	property	NOUN
american_scientific_journal-4187	7	23	:	:	PUNCT
american_scientific_journal-4187	7	24	{	{	PUNCT
american_scientific_journal-4187	7	25	(	(	PUNCT
american_scientific_journal-4187	7	26	(	(	PUNCT
american_scientific_journal-4187	7	27	⋃	⋃	PROPN
american_scientific_journal-4187	7	28	)	)	PUNCT
american_scientific_journal-4187	7	29	∑	∑	PUNCT
american_scientific_journal-4187	7	30	(	(	PUNCT
american_scientific_journal-4187	7	31	the	the	DET
american_scientific_journal-4187	7	32	meaning	meaning	NOUN
american_scientific_journal-4187	7	33	of	of	ADP
american_scientific_journal-4187	7	34	is	be	AUX
american_scientific_journal-4187	7	35	the	the	DET
american_scientific_journal-4187	7	36	non	non	ADJ
american_scientific_journal-4187	7	37	-negative	-negative	ADJ
american_scientific_journal-4187	7	38	real	real	ADJ
american_scientific_journal-4187	7	39	numbers	number	NOUN
american_scientific_journal-4187	7	40	.	.	PUNCT
american_scientific_journal-4187	8	1	the	the	DET
american_scientific_journal-4187	8	2	triple	triple	ADJ
american_scientific_journal-4187	8	3	(	(	PUNCT
american_scientific_journal-4187	8	4	is	be	AUX
american_scientific_journal-4187	8	5	which	which	PRON
american_scientific_journal-4187	8	6	is	be	AUX
american_scientific_journal-4187	8	7	an	an	DET
american_scientific_journal-4187	8	8	nonempty	nonempty	ADV
american_scientific_journal-4187	8	9	set	set	VERB
american_scientific_journal-4187	8	10	and	and	CCONJ
american_scientific_journal-4187	8	11	is	be	AUX
american_scientific_journal-4187	8	12	ring	ring	NOUN
american_scientific_journal-4187	8	13	of	of	ADP
american_scientific_journal-4187	8	14	subset	subset	NOUN
american_scientific_journal-4187	8	15	of	of	ADP
american_scientific_journal-4187	8	16	that	that	PRON
american_scientific_journal-4187	8	17	’s	’	VERB
american_scientific_journal-4187	8	18	a	a	DET
american_scientific_journal-4187	8	19	measure	measure	NOUN
american_scientific_journal-4187	8	20	of	of	ADP
american_scientific_journal-4187	8	21	sigma	sigma	PROPN
american_scientific_journal-4187	8	22	algebra	algebra	PROPN
american_scientific_journal-4187	8	23	.	.	PUNCT
american_scientific_journal-4187	9	1	it	it	PRON
american_scientific_journal-4187	9	2	is	be	AUX
american_scientific_journal-4187	9	3	called	call	VERB
american_scientific_journal-4187	9	4	measure	measure	NOUN
american_scientific_journal-4187	9	5	space	space	NOUN
american_scientific_journal-4187	9	6	.	.	PUNCT
american_scientific_journal-4187	10	1	-----------------------------------------------------------------------	-----------------------------------------------------------------------	PUNCT
american_scientific_journal-4187	11	1	*	*	PUNCT
american_scientific_journal-4187	11	2	corresponding	correspond	VERB
american_scientific_journal-4187	11	3	author	author	NOUN
american_scientific_journal-4187	11	4	.	.	PUNCT
american_scientific_journal-4187	12	1	american	american	PROPN
american_scientific_journal-4187	12	2	scientific	scientific	ADJ
american_scientific_journal-4187	12	3	research	research	PROPN
american_scientific_journal-4187	12	4	journal	journal	NOUN
american_scientific_journal-4187	12	5	for	for	ADP
american_scientific_journal-4187	12	6	engineering	engineering	NOUN
american_scientific_journal-4187	12	7	,	,	PUNCT
american_scientific_journal-4187	12	8	technology	technology	NOUN
american_scientific_journal-4187	12	9	,	,	PUNCT
american_scientific_journal-4187	12	10	and	and	CCONJ
american_scientific_journal-4187	12	11	sciences	science	NOUN
american_scientific_journal-4187	12	12	(	(	PUNCT
american_scientific_journal-4187	12	13	asrjets	asrjet	NOUN
american_scientific_journal-4187	12	14	)	)	PUNCT
american_scientific_journal-4187	12	15	(	(	PUNCT
american_scientific_journal-4187	12	16	2019	2019	NUM
american_scientific_journal-4187	12	17	)	)	PUNCT
american_scientific_journal-4187	12	18	volume	volume	NOUN
american_scientific_journal-4187	12	19	59	59	NUM
american_scientific_journal-4187	12	20	,	,	PUNCT
american_scientific_journal-4187	12	21	no	no	DET
american_scientific_journal-4187	12	22	1	1	NUM
american_scientific_journal-4187	12	23	,	,	PUNCT
american_scientific_journal-4187	12	24	pp	pp	ADV
american_scientific_journal-4187	12	25	162	162	NUM
american_scientific_journal-4187	12	26	-	-	SYM
american_scientific_journal-4187	12	27	178	178	NUM
american_scientific_journal-4187	12	28	163	163	NUM
american_scientific_journal-4187	12	29	in	in	ADP
american_scientific_journal-4187	12	30	this	this	DET
american_scientific_journal-4187	12	31	article	article	NOUN
american_scientific_journal-4187	12	32	,	,	PUNCT
american_scientific_journal-4187	12	33	we	we	PRON
american_scientific_journal-4187	12	34	have	have	AUX
american_scientific_journal-4187	12	35	generalized	generalize	VERB
american_scientific_journal-4187	12	36	the	the	DET
american_scientific_journal-4187	12	37	measure	measure	NOUN
american_scientific_journal-4187	12	38	range	range	VERB
american_scientific_journal-4187	12	39	from	from	ADP
american_scientific_journal-4187	12	40	to	to	ADP
american_scientific_journal-4187	12	41	.	.	PUNCT
american_scientific_journal-4187	13	1	the	the	DET
american_scientific_journal-4187	13	2	main	main	ADJ
american_scientific_journal-4187	13	3	principle	principle	NOUN
american_scientific_journal-4187	13	4	,	,	PUNCT
american_scientific_journal-4187	13	5	which	which	PRON
american_scientific_journal-4187	13	6	used	use	VERB
american_scientific_journal-4187	13	7	in	in	ADP
american_scientific_journal-4187	13	8	this	this	DET
american_scientific_journal-4187	13	9	purpose	purpose	NOUN
american_scientific_journal-4187	13	10	,	,	PUNCT
american_scientific_journal-4187	13	11	are	be	AUX
american_scientific_journal-4187	13	12	binary	binary	ADJ
american_scientific_journal-4187	13	13	operations	operation	NOUN
american_scientific_journal-4187	13	14	.	.	PUNCT
american_scientific_journal-4187	14	1	for	for	ADP
american_scientific_journal-4187	14	2	this	this	DET
american_scientific_journal-4187	14	3	purpose	purpose	NOUN
american_scientific_journal-4187	14	4	,	,	PUNCT
american_scientific_journal-4187	14	5	we	we	PRON
american_scientific_journal-4187	14	6	define	define	VERB
american_scientific_journal-4187	14	7	function	function	NOUN
american_scientific_journal-4187	14	8	𝜇	𝜇	ADP
american_scientific_journal-4187	14	9	,	,	PUNCT
american_scientific_journal-4187	14	10	which	which	PRON
american_scientific_journal-4187	14	11	simultaneously	simultaneously	ADV
american_scientific_journal-4187	14	12	satisfies	satisfy	VERB
american_scientific_journal-4187	14	13	the	the	DET
american_scientific_journal-4187	14	14	following	follow	VERB
american_scientific_journal-4187	14	15	two	two	NUM
american_scientific_journal-4187	14	16	conditions	condition	NOUN
american_scientific_journal-4187	14	17	:	:	PUNCT
american_scientific_journal-4187	14	18	𝜇	𝜇	X
american_scientific_journal-4187	14	19	(	(	PUNCT
american_scientific_journal-4187	14	20	⋃	⋃	PROPN
american_scientific_journal-4187	14	21	)	)	PUNCT
american_scientific_journal-4187	14	22	∑	∑	PUNCT
american_scientific_journal-4187	14	23	𝜇	𝜇	ADP
american_scientific_journal-4187	14	24	(	(	PUNCT
american_scientific_journal-4187	14	25	𝜇	𝜇	X
american_scientific_journal-4187	14	26	(	(	PUNCT
american_scientific_journal-4187	14	27	𝜇	𝜇	X
american_scientific_journal-4187	14	28	(	(	PUNCT
american_scientific_journal-4187	14	29	𝜇	𝜇	X
american_scientific_journal-4187	14	30	(	(	PUNCT
american_scientific_journal-4187	14	31	⋃	⋃	PROPN
american_scientific_journal-4187	14	32	)	)	PUNCT
american_scientific_journal-4187	14	33	such	such	ADJ
american_scientific_journal-4187	14	34	that	that	SCONJ
american_scientific_journal-4187	14	35	in	in	ADP
american_scientific_journal-4187	14	36	second	second	ADJ
american_scientific_journal-4187	14	37	condition	condition	NOUN
american_scientific_journal-4187	14	38	are	be	AUX
american_scientific_journal-4187	14	39	binary	binary	ADJ
american_scientific_journal-4187	14	40	operations	operation	NOUN
american_scientific_journal-4187	14	41	.	.	PUNCT
american_scientific_journal-4187	15	1	the	the	DET
american_scientific_journal-4187	15	2	easiest	easy	ADJ
american_scientific_journal-4187	15	3	way	way	NOUN
american_scientific_journal-4187	15	4	to	to	PART
american_scientific_journal-4187	15	5	satisfy	satisfy	VERB
american_scientific_journal-4187	15	6	the	the	DET
american_scientific_journal-4187	15	7	function	function	NOUN
american_scientific_journal-4187	15	8	in	in	ADP
american_scientific_journal-4187	15	9	the	the	DET
american_scientific_journal-4187	15	10	first	first	ADJ
american_scientific_journal-4187	15	11	condition	condition	NOUN
american_scientific_journal-4187	15	12	is	be	AUX
american_scientific_journal-4187	15	13	𝜇	𝜇	ADP
american_scientific_journal-4187	15	14	,	,	PUNCT
american_scientific_journal-4187	15	15	defines	define	NOUN
american_scientific_journal-4187	15	16	as	as	SCONJ
american_scientific_journal-4187	15	17	follow	follow	VERB
american_scientific_journal-4187	15	18	:	:	PUNCT
american_scientific_journal-4187	15	19	𝜇	𝜇	X
american_scientific_journal-4187	15	20	(	(	PUNCT
american_scientific_journal-4187	15	21	(	(	PUNCT
american_scientific_journal-4187	15	22	(	(	PUNCT
american_scientific_journal-4187	15	23	such	such	ADJ
american_scientific_journal-4187	15	24	that	that	PRON
american_scientific_journal-4187	15	25	is	be	AUX
american_scientific_journal-4187	15	26	a	a	DET
american_scientific_journal-4187	15	27	measure	measure	NOUN
american_scientific_journal-4187	15	28	and	and	CCONJ
american_scientific_journal-4187	15	29	is	be	AUX
american_scientific_journal-4187	15	30	a	a	DET
american_scientific_journal-4187	15	31	function	function	NOUN
american_scientific_journal-4187	15	32	.	.	PUNCT
american_scientific_journal-4187	16	1	the	the	DET
american_scientific_journal-4187	16	2	function	function	NOUN
american_scientific_journal-4187	16	3	that	that	PRON
american_scientific_journal-4187	16	4	satisfies	satisfy	VERB
american_scientific_journal-4187	16	5	the	the	DET
american_scientific_journal-4187	16	6	first	first	ADJ
american_scientific_journal-4187	16	7	condition	condition	NOUN
american_scientific_journal-4187	16	8	is	be	AUX
american_scientific_journal-4187	16	9	called	call	VERB
american_scientific_journal-4187	16	10	the	the	DET
american_scientific_journal-4187	16	11	dependable	dependable	ADJ
american_scientific_journal-4187	16	12	value	value	NOUN
american_scientific_journal-4187	16	13	pre	pre	NOUN
american_scientific_journal-4187	16	14	-	-	NOUN
american_scientific_journal-4187	16	15	measure	measure	NOUN
american_scientific_journal-4187	16	16	.	.	PUNCT
american_scientific_journal-4187	17	1	in	in	ADP
american_scientific_journal-4187	17	2	addition	addition	NOUN
american_scientific_journal-4187	17	3	,	,	PUNCT
american_scientific_journal-4187	17	4	when	when	SCONJ
american_scientific_journal-4187	17	5	binary	binary	ADJ
american_scientific_journal-4187	17	6	operations	operation	NOUN
american_scientific_journal-4187	17	7	defined	define	VERB
american_scientific_journal-4187	17	8	as	as	ADP
american_scientific_journal-4187	17	9	the	the	DET
american_scientific_journal-4187	17	10	sum	sum	NOUN
american_scientific_journal-4187	17	11	,	,	PUNCT
american_scientific_journal-4187	17	12	this	this	DET
american_scientific_journal-4187	17	13	measure	measure	NOUN
american_scientific_journal-4187	17	14	is	be	AUX
american_scientific_journal-4187	17	15	called	call	VERB
american_scientific_journal-4187	17	16	dependable	dependable	ADJ
american_scientific_journal-4187	17	17	value	value	NOUN
american_scientific_journal-4187	17	18	measure	measure	NOUN
american_scientific_journal-4187	17	19	.	.	PUNCT
american_scientific_journal-4187	18	1	this	this	DET
american_scientific_journal-4187	18	2	dependable	dependable	ADJ
american_scientific_journal-4187	18	3	value	value	NOUN
american_scientific_journal-4187	18	4	pre	pre	NOUN
american_scientific_journal-4187	18	5	-	-	NOUN
american_scientific_journal-4187	18	6	measure	measure	NOUN
american_scientific_journal-4187	18	7	which	which	PRON
american_scientific_journal-4187	18	8	satisfy	satisfy	VERB
american_scientific_journal-4187	18	9	in	in	ADP
american_scientific_journal-4187	18	10	condition	condition	NOUN
american_scientific_journal-4187	18	11	2	2	NUM
american_scientific_journal-4187	18	12	is	be	AUX
american_scientific_journal-4187	18	13	named	name	VERB
american_scientific_journal-4187	18	14	dependable	dependable	ADJ
american_scientific_journal-4187	18	15	value	value	NOUN
american_scientific_journal-4187	18	16	measure	measure	NOUN
american_scientific_journal-4187	18	17	under	under	ADP
american_scientific_journal-4187	18	18	binary	binary	ADJ
american_scientific_journal-4187	18	19	operations	operation	NOUN
american_scientific_journal-4187	18	20	(	(	PUNCT
american_scientific_journal-4187	18	21	.in	.in	PUNCT
american_scientific_journal-4187	18	22	the	the	DET
american_scientific_journal-4187	18	23	following	following	NOUN
american_scientific_journal-4187	18	24	,	,	PUNCT
american_scientific_journal-4187	18	25	we	we	PRON
american_scientific_journal-4187	18	26	will	will	AUX
american_scientific_journal-4187	18	27	examine	examine	VERB
american_scientific_journal-4187	18	28	the	the	DET
american_scientific_journal-4187	18	29	conditions	condition	NOUN
american_scientific_journal-4187	18	30	which	which	PRON
american_scientific_journal-4187	18	31	dependable	dependable	ADJ
american_scientific_journal-4187	18	32	value	value	NOUN
american_scientific_journal-4187	18	33	pre	pre	NOUN
american_scientific_journal-4187	18	34	-	-	NOUN
american_scientific_journal-4187	18	35	measure	measure	NOUN
american_scientific_journal-4187	18	36	is	be	AUX
american_scientific_journal-4187	18	37	turned	turn	VERB
american_scientific_journal-4187	18	38	to	to	ADP
american_scientific_journal-4187	18	39	the	the	DET
american_scientific_journal-4187	18	40	dependable	dependable	ADJ
american_scientific_journal-4187	18	41	value	value	NOUN
american_scientific_journal-4187	18	42	measure	measure	NOUN
american_scientific_journal-4187	18	43	.	.	PUNCT
american_scientific_journal-4187	19	1	finally	finally	ADV
american_scientific_journal-4187	19	2	,	,	PUNCT
american_scientific_journal-4187	19	3	we	we	PRON
american_scientific_journal-4187	19	4	recognize	recognize	VERB
american_scientific_journal-4187	19	5	some	some	DET
american_scientific_journal-4187	19	6	properties	property	NOUN
american_scientific_journal-4187	19	7	of	of	ADP
american_scientific_journal-4187	19	8	this	this	DET
american_scientific_journal-4187	19	9	type	type	NOUN
american_scientific_journal-4187	19	10	of	of	ADP
american_scientific_journal-4187	19	11	measures	measure	NOUN
american_scientific_journal-4187	19	12	.	.	PUNCT
american_scientific_journal-4187	20	1	it	it	PRON
american_scientific_journal-4187	20	2	seems	seem	VERB
american_scientific_journal-4187	20	3	that	that	SCONJ
american_scientific_journal-4187	20	4	we	we	PRON
american_scientific_journal-4187	20	5	can	can	AUX
american_scientific_journal-4187	20	6	define	define	VERB
american_scientific_journal-4187	20	7	a	a	DET
american_scientific_journal-4187	20	8	numerous	numerous	ADJ
american_scientific_journal-4187	20	9	advantages	advantage	NOUN
american_scientific_journal-4187	20	10	for	for	ADP
american_scientific_journal-4187	20	11	the	the	DET
american_scientific_journal-4187	20	12	generalization	generalization	NOUN
american_scientific_journal-4187	20	13	of	of	ADP
american_scientific_journal-4187	20	14	the	the	DET
american_scientific_journal-4187	20	15	measure	measure	NOUN
american_scientific_journal-4187	20	16	theory	theory	NOUN
american_scientific_journal-4187	20	17	of	of	ADP
american_scientific_journal-4187	20	18	to	to	PART
american_scientific_journal-4187	20	19	.	.	PUNCT
american_scientific_journal-4187	21	1	one	one	NUM
american_scientific_journal-4187	21	2	uses	use	NOUN
american_scientific_journal-4187	21	3	of	of	ADP
american_scientific_journal-4187	21	4	this	this	DET
american_scientific_journal-4187	21	5	type	type	NOUN
american_scientific_journal-4187	21	6	of	of	ADP
american_scientific_journal-4187	21	7	measure	measure	NOUN
american_scientific_journal-4187	21	8	are	be	AUX
american_scientific_journal-4187	21	9	in	in	ADP
american_scientific_journal-4187	21	10	a	a	DET
american_scientific_journal-4187	21	11	nonlinear	nonlinear	ADJ
american_scientific_journal-4187	21	12	analysis	analysis	NOUN
american_scientific_journal-4187	21	13	.	.	PUNCT
american_scientific_journal-4187	22	1	definition1.𝝁	definition1.𝝁	NOUN
american_scientific_journal-4187	22	2	is	be	AUX
american_scientific_journal-4187	22	3	dependable	dependable	ADJ
american_scientific_journal-4187	22	4	value	value	NOUN
american_scientific_journal-4187	22	5	pre	pre	NOUN
american_scientific_journal-4187	22	6	-	-	NOUN
american_scientific_journal-4187	22	7	measure	measure	ADJ
american_scientific_journal-4187	22	8	,	,	PUNCT
american_scientific_journal-4187	22	9	if	if	SCONJ
american_scientific_journal-4187	22	10	𝝁	𝝁	PRON
american_scientific_journal-4187	22	11	is	be	AUX
american_scientific_journal-4187	22	12	a	a	DET
american_scientific_journal-4187	22	13	function	function	NOUN
american_scientific_journal-4187	22	14	that	that	PRON
american_scientific_journal-4187	22	15	we	we	PRON
american_scientific_journal-4187	22	16	define	define	VERB
american_scientific_journal-4187	22	17	as	as	SCONJ
american_scientific_journal-4187	22	18	follows	follow	VERB
american_scientific_journal-4187	22	19	:	:	PUNCT
american_scientific_journal-4187	22	20	𝜇	𝜇	X
american_scientific_journal-4187	22	21	(	(	PUNCT
american_scientific_journal-4187	22	22	⋃	⋃	PROPN
american_scientific_journal-4187	22	23	)	)	PUNCT
american_scientific_journal-4187	22	24	∑	∑	PUNCT
american_scientific_journal-4187	22	25	𝜇	𝜇	ADP
american_scientific_journal-4187	22	26	(	(	PUNCT
american_scientific_journal-4187	22	27	(	(	PUNCT
american_scientific_journal-4187	22	28	the	the	DET
american_scientific_journal-4187	22	29	easiest	easy	ADJ
american_scientific_journal-4187	22	30	way	way	NOUN
american_scientific_journal-4187	22	31	to	to	PART
american_scientific_journal-4187	22	32	make	make	VERB
american_scientific_journal-4187	22	33	a	a	DET
american_scientific_journal-4187	22	34	pre	pre	NOUN
american_scientific_journal-4187	22	35	-	-	NOUN
american_scientific_journal-4187	22	36	measure	measure	NOUN
american_scientific_journal-4187	22	37	is	be	AUX
american_scientific_journal-4187	22	38	that	that	DET
american_scientific_journal-4187	22	39	function	function	NOUN
american_scientific_journal-4187	22	40	𝜇	𝜇	ADP
american_scientific_journal-4187	22	41	define	define	NOUN
american_scientific_journal-4187	22	42	as	as	SCONJ
american_scientific_journal-4187	22	43	follows	follow	VERB
american_scientific_journal-4187	22	44	:	:	PUNCT
american_scientific_journal-4187	22	45	𝜇	𝜇	X
american_scientific_journal-4187	22	46	(	(	PUNCT
american_scientific_journal-4187	22	47	(	(	PUNCT
american_scientific_journal-4187	22	48	(	(	PUNCT
american_scientific_journal-4187	22	49	such	such	ADJ
american_scientific_journal-4187	22	50	that	that	PRON
american_scientific_journal-4187	22	51	is	be	AUX
american_scientific_journal-4187	22	52	measure	measure	NOUN
american_scientific_journal-4187	22	53	and	and	CCONJ
american_scientific_journal-4187	22	54	is	be	AUX
american_scientific_journal-4187	22	55	function	function	NOUN
american_scientific_journal-4187	22	56	.	.	PUNCT
american_scientific_journal-4187	23	1	in	in	ADP
american_scientific_journal-4187	23	2	all	all	PRON
american_scientific_journal-4187	23	3	of	of	ADP
american_scientific_journal-4187	23	4	this	this	DET
american_scientific_journal-4187	23	5	paper	paper	NOUN
american_scientific_journal-4187	23	6	,	,	PUNCT
american_scientific_journal-4187	23	7	it	it	PRON
american_scientific_journal-4187	23	8	’s	’s	AUX
american_scientific_journal-4187	23	9	assumed	assume	VERB
american_scientific_journal-4187	23	10	that	that	SCONJ
american_scientific_journal-4187	23	11	the	the	DET
american_scientific_journal-4187	23	12	function	function	NOUN
american_scientific_journal-4187	23	13	𝜇	𝜇	ADP
american_scientific_journal-4187	23	14	is	be	AUX
american_scientific_journal-4187	23	15	make	make	VERB
american_scientific_journal-4187	23	16	in	in	ADP
american_scientific_journal-4187	23	17	this	this	DET
american_scientific_journal-4187	23	18	way	way	NOUN
american_scientific_journal-4187	23	19	.	.	PUNCT
american_scientific_journal-4187	24	1	dependable	dependable	ADJ
american_scientific_journal-4187	24	2	value	value	NOUN
american_scientific_journal-4187	24	3	pre	pre	NOUN
american_scientific_journal-4187	24	4	-	-	NOUN
american_scientific_journal-4187	24	5	measure	measure	NOUN
american_scientific_journal-4187	24	6	𝜇	𝜇	ADP
american_scientific_journal-4187	24	7	that	that	PRON
american_scientific_journal-4187	24	8	is	be	AUX
american_scientific_journal-4187	24	9	called	call	VERB
american_scientific_journal-4187	24	10	a	a	DET
american_scientific_journal-4187	24	11	dependable	dependable	ADJ
american_scientific_journal-4187	24	12	value	value	NOUN
american_scientific_journal-4187	24	13	measure	measure	NOUN
american_scientific_journal-4187	24	14	under	under	ADP
american_scientific_journal-4187	24	15	binary	binary	ADJ
american_scientific_journal-4187	24	16	operations	operation	NOUN
american_scientific_journal-4187	24	17	(	(	PUNCT
american_scientific_journal-4187	24	18	,	,	PUNCT
american_scientific_journal-4187	24	19	if	if	SCONJ
american_scientific_journal-4187	24	20	𝜇	𝜇	ADV
american_scientific_journal-4187	24	21	is	be	AUX
american_scientific_journal-4187	24	22	function	function	NOUN
american_scientific_journal-4187	24	23	as	as	SCONJ
american_scientific_journal-4187	24	24	follows	follow	VERB
american_scientific_journal-4187	24	25	:	:	PUNCT
american_scientific_journal-4187	24	26	𝜇	𝜇	X
american_scientific_journal-4187	24	27	(	(	PUNCT
american_scientific_journal-4187	24	28	𝜇	𝜇	X
american_scientific_journal-4187	24	29	(	(	PUNCT
american_scientific_journal-4187	24	30	𝜇	𝜇	X
american_scientific_journal-4187	24	31	(	(	PUNCT
american_scientific_journal-4187	24	32	⋃	⋃	PROPN
american_scientific_journal-4187	24	33	)	)	PUNCT
american_scientific_journal-4187	24	34	(	(	PUNCT
american_scientific_journal-4187	24	35	american	american	PROPN
american_scientific_journal-4187	24	36	scientific	scientific	ADJ
american_scientific_journal-4187	24	37	research	research	NOUN
american_scientific_journal-4187	24	38	journal	journal	NOUN
american_scientific_journal-4187	24	39	for	for	ADP
american_scientific_journal-4187	24	40	engineering	engineering	NOUN
american_scientific_journal-4187	24	41	,	,	PUNCT
american_scientific_journal-4187	24	42	technology	technology	NOUN
american_scientific_journal-4187	24	43	,	,	PUNCT
american_scientific_journal-4187	24	44	and	and	CCONJ
american_scientific_journal-4187	24	45	sciences	science	NOUN
american_scientific_journal-4187	24	46	(	(	PUNCT
american_scientific_journal-4187	24	47	asrjets	asrjet	NOUN
american_scientific_journal-4187	24	48	)	)	PUNCT
american_scientific_journal-4187	24	49	(	(	PUNCT
american_scientific_journal-4187	24	50	2019	2019	NUM
american_scientific_journal-4187	24	51	)	)	PUNCT
american_scientific_journal-4187	24	52	volume	volume	NOUN
american_scientific_journal-4187	24	53	59	59	NUM
american_scientific_journal-4187	24	54	,	,	PUNCT
american_scientific_journal-4187	24	55	no	no	DET
american_scientific_journal-4187	24	56	1	1	NUM
american_scientific_journal-4187	24	57	,	,	PUNCT
american_scientific_journal-4187	24	58	pp	pp	ADV
american_scientific_journal-4187	24	59	162	162	NUM
american_scientific_journal-4187	24	60	-	-	SYM
american_scientific_journal-4187	24	61	178	178	NUM
american_scientific_journal-4187	24	62	164	164	NUM
american_scientific_journal-4187	24	63	such	such	ADJ
american_scientific_journal-4187	24	64	that	that	PRON
american_scientific_journal-4187	24	65	are	be	AUX
american_scientific_journal-4187	24	66	binary	binary	ADJ
american_scientific_journal-4187	24	67	oprations	opration	NOUN
american_scientific_journal-4187	24	68	.	.	PUNCT
american_scientific_journal-4187	25	1	if	if	SCONJ
american_scientific_journal-4187	25	2	binary	binary	ADJ
american_scientific_journal-4187	25	3	operations	operation	NOUN
american_scientific_journal-4187	25	4	are	be	AUX
american_scientific_journal-4187	25	5	simple	simple	ADJ
american_scientific_journal-4187	25	6	sum	sum	NOUN
american_scientific_journal-4187	25	7	,	,	PUNCT
american_scientific_journal-4187	25	8	this	this	DET
american_scientific_journal-4187	25	9	function	function	NOUN
american_scientific_journal-4187	25	10	is	be	AUX
american_scientific_journal-4187	25	11	called	call	VERB
american_scientific_journal-4187	25	12	dependable	dependable	ADJ
american_scientific_journal-4187	25	13	value	value	NOUN
american_scientific_journal-4187	25	14	measure	measure	NOUN
american_scientific_journal-4187	25	15	.	.	PUNCT
american_scientific_journal-4187	26	1	in	in	ADP
american_scientific_journal-4187	26	2	other	other	ADJ
american_scientific_journal-4187	26	3	words	word	NOUN
american_scientific_journal-4187	26	4	,	,	PUNCT
american_scientific_journal-4187	26	5	each	each	DET
american_scientific_journal-4187	26	6	dependable	dependable	ADJ
american_scientific_journal-4187	26	7	value	value	NOUN
american_scientific_journal-4187	26	8	measure	measure	NOUN
american_scientific_journal-4187	26	9	is	be	AUX
american_scientific_journal-4187	26	10	a	a	DET
american_scientific_journal-4187	26	11	function	function	NOUN
american_scientific_journal-4187	26	12	,	,	PUNCT
american_scientific_journal-4187	26	13	such	such	ADJ
american_scientific_journal-4187	26	14	as	as	ADP
american_scientific_journal-4187	26	15	which	which	PRON
american_scientific_journal-4187	26	16	satisfies	satisfy	VERB
american_scientific_journal-4187	26	17	to	to	ADP
american_scientific_journal-4187	26	18	the	the	DET
american_scientific_journal-4187	26	19	following	follow	VERB
american_scientific_journal-4187	26	20	properties	property	NOUN
american_scientific_journal-4187	26	21	:	:	PUNCT
american_scientific_journal-4187	26	22	(	(	PUNCT
american_scientific_journal-4187	26	23	⋃	⋃	PROPN
american_scientific_journal-4187	26	24	)	)	PUNCT
american_scientific_journal-4187	26	25	∑	∑	PUNCT
american_scientific_journal-4187	26	26	(	(	PUNCT
american_scientific_journal-4187	26	27	(	(	PUNCT
american_scientific_journal-4187	26	28	(	(	PUNCT
american_scientific_journal-4187	26	29	(	(	PUNCT
american_scientific_journal-4187	26	30	⋃	⋃	PROPN
american_scientific_journal-4187	26	31	)	)	PUNCT
american_scientific_journal-4187	26	32	example	example	NOUN
american_scientific_journal-4187	26	33	1	1	NUM
american_scientific_journal-4187	26	34	:	:	PUNCT
american_scientific_journal-4187	26	35	let	let	VERB
american_scientific_journal-4187	26	36	’s	’s	PRON
american_scientific_journal-4187	26	37	assume	assume	VERB
american_scientific_journal-4187	26	38	that	that	SCONJ
american_scientific_journal-4187	26	39	binary	binary	ADJ
american_scientific_journal-4187	26	40	relations	relation	NOUN
american_scientific_journal-4187	26	41	,	,	PUNCT
american_scientific_journal-4187	26	42	define	define	VERB
american_scientific_journal-4187	26	43	as	as	SCONJ
american_scientific_journal-4187	26	44	follows	follow	VERB
american_scientific_journal-4187	26	45	:	:	PUNCT
american_scientific_journal-4187	26	46	{	{	PUNCT
american_scientific_journal-4187	26	47	}	}	PUNCT
american_scientific_journal-4187	26	48	{	{	PUNCT
american_scientific_journal-4187	26	49	}	}	PUNCT
american_scientific_journal-4187	26	50	in	in	ADP
american_scientific_journal-4187	26	51	addition	addition	NOUN
american_scientific_journal-4187	26	52	,	,	PUNCT
american_scientific_journal-4187	26	53	on	on	ADP
american_scientific_journal-4187	26	54	measure	measure	NOUN
american_scientific_journal-4187	26	55	space	space	NOUN
american_scientific_journal-4187	26	56	can	can	AUX
american_scientific_journal-4187	26	57	define	define	VERB
american_scientific_journal-4187	26	58	as	as	ADP
american_scientific_journal-4187	26	59	(	(	PUNCT
american_scientific_journal-4187	26	60	.	.	PUNCT
american_scientific_journal-4187	27	1	in	in	ADP
american_scientific_journal-4187	27	2	this	this	DET
american_scientific_journal-4187	27	3	case	case	NOUN
american_scientific_journal-4187	27	4	,	,	PUNCT
american_scientific_journal-4187	27	5	the	the	DET
american_scientific_journal-4187	27	6	function	function	NOUN
american_scientific_journal-4187	27	7	𝜇	𝜇	ADP
american_scientific_journal-4187	27	8	which	which	PRON
american_scientific_journal-4187	27	9	is	be	AUX
american_scientific_journal-4187	27	10	define	define	NOUN
american_scientific_journal-4187	27	11	as	as	SCONJ
american_scientific_journal-4187	27	12	follows	follow	VERB
american_scientific_journal-4187	27	13	and	and	CCONJ
american_scientific_journal-4187	27	14	it	it	PRON
american_scientific_journal-4187	27	15	’s	’	VERB
american_scientific_journal-4187	27	16	a	a	DET
american_scientific_journal-4187	27	17	measure	measure	NOUN
american_scientific_journal-4187	27	18	under	under	ADP
american_scientific_journal-4187	27	19	binary	binary	ADJ
american_scientific_journal-4187	27	20	operations	operation	NOUN
american_scientific_journal-4187	27	21	(	(	PUNCT
american_scientific_journal-4187	27	22	.	.	PUNCT
american_scientific_journal-4187	28	1	𝜇	𝜇	X
american_scientific_journal-4187	28	2	(	(	PUNCT
american_scientific_journal-4187	28	3	(	(	PUNCT
american_scientific_journal-4187	28	4	example	example	NOUN
american_scientific_journal-4187	28	5	2	2	NUM
american_scientific_journal-4187	28	6	:	:	PUNCT
american_scientific_journal-4187	28	7	let	let	VERB
american_scientific_journal-4187	28	8	’s	’s	PRON
american_scientific_journal-4187	28	9	assume	assume	VERB
american_scientific_journal-4187	28	10	that	that	SCONJ
american_scientific_journal-4187	28	11	binary	binary	ADJ
american_scientific_journal-4187	28	12	relations	relation	NOUN
american_scientific_journal-4187	28	13	,	,	PUNCT
american_scientific_journal-4187	28	14	define	define	VERB
american_scientific_journal-4187	28	15	as	as	SCONJ
american_scientific_journal-4187	28	16	follows	follow	VERB
american_scientific_journal-4187	28	17	:	:	PUNCT
american_scientific_journal-4187	28	18	in	in	ADP
american_scientific_journal-4187	28	19	addition	addition	NOUN
american_scientific_journal-4187	28	20	,	,	PUNCT
american_scientific_journal-4187	28	21	on	on	ADP
american_scientific_journal-4187	28	22	measure	measure	NOUN
american_scientific_journal-4187	28	23	space	space	NOUN
american_scientific_journal-4187	28	24	can	can	AUX
american_scientific_journal-4187	28	25	define	define	VERB
american_scientific_journal-4187	28	26	as	as	ADP
american_scientific_journal-4187	28	27	(	(	PUNCT
american_scientific_journal-4187	28	28	.	.	PUNCT
american_scientific_journal-4187	29	1	in	in	ADP
american_scientific_journal-4187	29	2	this	this	DET
american_scientific_journal-4187	29	3	case	case	NOUN
american_scientific_journal-4187	29	4	,	,	PUNCT
american_scientific_journal-4187	29	5	the	the	DET
american_scientific_journal-4187	29	6	function	function	NOUN
american_scientific_journal-4187	29	7	is	be	AUX
american_scientific_journal-4187	29	8	𝜇	𝜇	ADP
american_scientific_journal-4187	29	9	which	which	PRON
american_scientific_journal-4187	29	10	is	be	AUX
american_scientific_journal-4187	29	11	define	define	NOUN
american_scientific_journal-4187	29	12	as	as	SCONJ
american_scientific_journal-4187	29	13	follows	follow	VERB
american_scientific_journal-4187	29	14	and	and	CCONJ
american_scientific_journal-4187	29	15	it	it	PRON
american_scientific_journal-4187	29	16	’s	’	VERB
american_scientific_journal-4187	29	17	a	a	DET
american_scientific_journal-4187	29	18	measure	measure	NOUN
american_scientific_journal-4187	29	19	under	under	ADP
american_scientific_journal-4187	29	20	binary	binary	ADJ
american_scientific_journal-4187	29	21	operations	operation	NOUN
american_scientific_journal-4187	29	22	(	(	PUNCT
american_scientific_journal-4187	29	23	.	.	PUNCT
american_scientific_journal-4187	30	1	𝜇	𝜇	X
american_scientific_journal-4187	30	2	(	(	PUNCT
american_scientific_journal-4187	30	3	(	(	PUNCT
american_scientific_journal-4187	30	4	example	example	NOUN
american_scientific_journal-4187	30	5	3	3	NUM
american_scientific_journal-4187	30	6	:	:	PUNCT
american_scientific_journal-4187	30	7	the	the	DET
american_scientific_journal-4187	30	8	function	function	NOUN
american_scientific_journal-4187	30	9	is	be	AUX
american_scientific_journal-4187	30	10	a	a	DET
american_scientific_journal-4187	30	11	dependable	dependable	ADJ
american_scientific_journal-4187	30	12	value	value	NOUN
american_scientific_journal-4187	30	13	measure	measure	NOUN
american_scientific_journal-4187	30	14	.	.	PUNCT
american_scientific_journal-4187	31	1	(	(	PUNCT
american_scientific_journal-4187	31	2	,	,	PUNCT
american_scientific_journal-4187	31	3	theorem1.if	theorem1.if	NOUN
american_scientific_journal-4187	31	4	is	be	AUX
american_scientific_journal-4187	31	5	a	a	DET
american_scientific_journal-4187	31	6	measure	measure	NOUN
american_scientific_journal-4187	31	7	on	on	ADP
american_scientific_journal-4187	31	8	space	space	NOUN
american_scientific_journal-4187	31	9	(	(	PUNCT
american_scientific_journal-4187	31	10	.	.	PUNCT
american_scientific_journal-4187	32	1	in	in	ADP
american_scientific_journal-4187	32	2	addition	addition	NOUN
american_scientific_journal-4187	32	3	,	,	PUNCT
american_scientific_journal-4187	32	4	if	if	SCONJ
american_scientific_journal-4187	32	5	is	be	AUX
american_scientific_journal-4187	32	6	a	a	DET
american_scientific_journal-4187	32	7	function	function	NOUN
american_scientific_journal-4187	32	8	it	it	PRON
american_scientific_journal-4187	32	9	satisfies	satisfy	VERB
american_scientific_journal-4187	32	10	on	on	ADP
american_scientific_journal-4187	32	11	this	this	DET
american_scientific_journal-4187	32	12	condition	condition	NOUN
american_scientific_journal-4187	32	13	:	:	PUNCT
american_scientific_journal-4187	32	14	(	(	PUNCT
american_scientific_journal-4187	32	15	(	(	PUNCT
american_scientific_journal-4187	32	16	(	(	PUNCT
american_scientific_journal-4187	32	17	(	(	PUNCT
american_scientific_journal-4187	32	18	american	american	ADJ
american_scientific_journal-4187	32	19	scientific	scientific	ADJ
american_scientific_journal-4187	32	20	research	research	NOUN
american_scientific_journal-4187	32	21	journal	journal	NOUN
american_scientific_journal-4187	32	22	for	for	ADP
american_scientific_journal-4187	32	23	engineering	engineering	NOUN
american_scientific_journal-4187	32	24	,	,	PUNCT
american_scientific_journal-4187	32	25	technology	technology	NOUN
american_scientific_journal-4187	32	26	,	,	PUNCT
american_scientific_journal-4187	32	27	and	and	CCONJ
american_scientific_journal-4187	32	28	sciences	science	NOUN
american_scientific_journal-4187	32	29	(	(	PUNCT
american_scientific_journal-4187	32	30	asrjets	asrjet	NOUN
american_scientific_journal-4187	32	31	)	)	PUNCT
american_scientific_journal-4187	32	32	(	(	PUNCT
american_scientific_journal-4187	32	33	2019	2019	NUM
american_scientific_journal-4187	32	34	)	)	PUNCT
american_scientific_journal-4187	32	35	volume	volume	NOUN
american_scientific_journal-4187	32	36	59	59	NUM
american_scientific_journal-4187	32	37	,	,	PUNCT
american_scientific_journal-4187	32	38	no	no	DET
american_scientific_journal-4187	32	39	1	1	NUM
american_scientific_journal-4187	32	40	,	,	PUNCT
american_scientific_journal-4187	32	41	pp	pp	ADV
american_scientific_journal-4187	32	42	162	162	NUM
american_scientific_journal-4187	32	43	-	-	SYM
american_scientific_journal-4187	32	44	178	178	NUM
american_scientific_journal-4187	32	45	165	165	NUM
american_scientific_journal-4187	32	46	and	and	CCONJ
american_scientific_journal-4187	32	47	a	a	DET
american_scientific_journal-4187	32	48	binary	binary	ADJ
american_scientific_journal-4187	32	49	operation	operation	NOUN
american_scientific_journal-4187	32	50	should	should	AUX
american_scientific_journal-4187	32	51	be	be	AUX
american_scientific_journal-4187	32	52	like	like	ADP
american_scientific_journal-4187	32	53	for	for	ADP
american_scientific_journal-4187	32	54	any	any	PRON
american_scientific_journal-4187	32	55	,	,	PUNCT
american_scientific_journal-4187	32	56	so	so	CCONJ
american_scientific_journal-4187	32	57	we	we	PRON
american_scientific_journal-4187	32	58	have	have	AUX
american_scientific_journal-4187	32	59	as	as	ADV
american_scientific_journal-4187	32	60	follow	follow	VERB
american_scientific_journal-4187	32	61	:	:	PUNCT
american_scientific_journal-4187	32	62	{	{	PUNCT
american_scientific_journal-4187	32	63	}	}	PUNCT
american_scientific_journal-4187	32	64	(	(	PUNCT
american_scientific_journal-4187	32	65	moreover	moreover	ADV
american_scientific_journal-4187	32	66	,	,	PUNCT
american_scientific_journal-4187	32	67	a	a	DET
american_scientific_journal-4187	32	68	binary	binary	ADJ
american_scientific_journal-4187	32	69	operation	operation	NOUN
american_scientific_journal-4187	32	70	should	should	AUX
american_scientific_journal-4187	32	71	be	be	AUX
american_scientific_journal-4187	32	72	like	like	ADP
american_scientific_journal-4187	32	73	for	for	ADP
american_scientific_journal-4187	32	74	any	any	PRON
american_scientific_journal-4187	32	75	with	with	ADP
american_scientific_journal-4187	32	76	condition	condition	NOUN
american_scientific_journal-4187	32	77	,	,	PUNCT
american_scientific_journal-4187	32	78	so	so	CCONJ
american_scientific_journal-4187	32	79	we	we	PRON
american_scientific_journal-4187	32	80	have	have	AUX
american_scientific_journal-4187	32	81	as	as	ADV
american_scientific_journal-4187	32	82	follow	follow	VERB
american_scientific_journal-4187	32	83	:	:	PUNCT
american_scientific_journal-4187	32	84	(	(	PUNCT
american_scientific_journal-4187	32	85	(	(	PUNCT
american_scientific_journal-4187	32	86	(	(	PUNCT
american_scientific_journal-4187	32	87	(	(	PUNCT
american_scientific_journal-4187	32	88	(	(	PUNCT
american_scientific_journal-4187	32	89	also	also	ADV
american_scientific_journal-4187	32	90	,	,	PUNCT
american_scientific_journal-4187	32	91	if	if	SCONJ
american_scientific_journal-4187	32	92	we	we	PRON
american_scientific_journal-4187	32	93	define	define	VERB
american_scientific_journal-4187	32	94	a	a	DET
american_scientific_journal-4187	32	95	function	function	NOUN
american_scientific_journal-4187	32	96	like	like	ADP
american_scientific_journal-4187	32	97	this	this	PRON
american_scientific_journal-4187	32	98	𝜇	𝜇	ADP
american_scientific_journal-4187	32	99	as	as	ADP
american_scientific_journal-4187	32	100	follow	follow	NOUN
american_scientific_journal-4187	32	101	:	:	PUNCT
american_scientific_journal-4187	32	102	𝜇	𝜇	X
american_scientific_journal-4187	32	103	(	(	PUNCT
american_scientific_journal-4187	32	104	(	(	PUNCT
american_scientific_journal-4187	32	105	(	(	PUNCT
american_scientific_journal-4187	32	106	(	(	PUNCT
american_scientific_journal-4187	32	107	then	then	ADV
american_scientific_journal-4187	32	108	,	,	PUNCT
american_scientific_journal-4187	32	109	𝜇	𝜇	X
american_scientific_journal-4187	32	110	is	be	AUX
american_scientific_journal-4187	32	111	a	a	DET
american_scientific_journal-4187	32	112	dependable	dependable	ADJ
american_scientific_journal-4187	32	113	value	value	NOUN
american_scientific_journal-4187	32	114	measure	measure	NOUN
american_scientific_journal-4187	32	115	under	under	ADP
american_scientific_journal-4187	32	116	binary	binary	ADJ
american_scientific_journal-4187	32	117	operations	operation	NOUN
american_scientific_journal-4187	32	118	(	(	PUNCT
american_scientific_journal-4187	32	119	.	.	PUNCT
american_scientific_journal-4187	33	1	proof.the	proof.the	DET
american_scientific_journal-4187	33	2	proof	proof	NOUN
american_scientific_journal-4187	33	3	that	that	PRON
american_scientific_journal-4187	33	4	function	function	VERB
american_scientific_journal-4187	33	5	𝝁	𝝁	PRON
american_scientific_journal-4187	33	6	is	be	AUX
american_scientific_journal-4187	33	7	dependable	dependable	ADJ
american_scientific_journal-4187	33	8	value	value	NOUN
american_scientific_journal-4187	33	9	pre	pre	NOUN
american_scientific_journal-4187	33	10	-	-	NOUN
american_scientific_journal-4187	33	11	measure	measure	NOUN
american_scientific_journal-4187	33	12	,	,	PUNCT
american_scientific_journal-4187	33	13	it	it	PRON
american_scientific_journal-4187	33	14	is	be	AUX
american_scientific_journal-4187	33	15	easily	easily	ADV
american_scientific_journal-4187	33	16	obtained	obtain	VERB
american_scientific_journal-4187	33	17	by	by	ADP
american_scientific_journal-4187	33	18	using	use	VERB
american_scientific_journal-4187	33	19	(	(	PUNCT
american_scientific_journal-4187	33	20	2	2	NUM
american_scientific_journal-4187	33	21	)	)	PUNCT
american_scientific_journal-4187	33	22	and	and	CCONJ
american_scientific_journal-4187	33	23	(	(	PUNCT
american_scientific_journal-4187	33	24	4	4	NUM
american_scientific_journal-4187	33	25	)	)	PUNCT
american_scientific_journal-4187	33	26	.	.	PUNCT
american_scientific_journal-4187	34	1	in	in	ADP
american_scientific_journal-4187	34	2	order	order	NOUN
american_scientific_journal-4187	34	3	to	to	PART
american_scientific_journal-4187	34	4	proof	proof	NOUN
american_scientific_journal-4187	34	5	that	that	SCONJ
american_scientific_journal-4187	34	6	function	function	NOUN
american_scientific_journal-4187	34	7	is	be	AUX
american_scientific_journal-4187	34	8	dependable	dependable	ADJ
american_scientific_journal-4187	34	9	value	value	NOUN
american_scientific_journal-4187	34	10	measure	measure	NOUN
american_scientific_journal-4187	34	11	under	under	ADP
american_scientific_journal-4187	34	12	binary	binary	ADJ
american_scientific_journal-4187	34	13	operations	operation	NOUN
american_scientific_journal-4187	34	14	(	(	PUNCT
american_scientific_journal-4187	34	15	,	,	PUNCT
american_scientific_journal-4187	34	16	it	it	PRON
american_scientific_journal-4187	34	17	is	be	AUX
american_scientific_journal-4187	34	18	easy	easy	ADJ
american_scientific_journal-4187	34	19	to	to	PART
american_scientific_journal-4187	34	20	write	write	VERB
american_scientific_journal-4187	34	21	down	down	ADP
american_scientific_journal-4187	34	22	the	the	DET
american_scientific_journal-4187	34	23	properties	property	NOUN
american_scientific_journal-4187	34	24	of	of	ADP
american_scientific_journal-4187	34	25	(	(	PUNCT
american_scientific_journal-4187	34	26	*	*	PUNCT
american_scientific_journal-4187	34	27	)	)	PUNCT
american_scientific_journal-4187	34	28	and	and	CCONJ
american_scientific_journal-4187	34	29	(	(	PUNCT
american_scientific_journal-4187	34	30	1	1	X
american_scientific_journal-4187	34	31	)	)	PUNCT
american_scientific_journal-4187	34	32	and	and	CCONJ
american_scientific_journal-4187	34	33	(	(	PUNCT
american_scientific_journal-4187	34	34	3	3	NUM
american_scientific_journal-4187	34	35	):	):	PUNCT
american_scientific_journal-4187	34	36	𝜇	𝜇	X
american_scientific_journal-4187	34	37	(	(	PUNCT
american_scientific_journal-4187	34	38	𝜇	𝜇	X
american_scientific_journal-4187	34	39	(	(	PUNCT
american_scientific_journal-4187	34	40	𝜇	𝜇	X
american_scientific_journal-4187	34	41	(	(	PUNCT
american_scientific_journal-4187	34	42	𝜇	𝜇	X
american_scientific_journal-4187	34	43	(	(	PUNCT
american_scientific_journal-4187	34	44	(	(	PUNCT
american_scientific_journal-4187	34	45	(	(	PUNCT
american_scientific_journal-4187	34	46	(	(	PUNCT
american_scientific_journal-4187	34	47	(	(	PUNCT
american_scientific_journal-4187	34	48	(	(	PUNCT
american_scientific_journal-4187	34	49	{	{	PUNCT
american_scientific_journal-4187	34	50	(	(	PUNCT
american_scientific_journal-4187	34	51	(	(	PUNCT
american_scientific_journal-4187	34	52	}	}	PUNCT
american_scientific_journal-4187	34	53	(	(	PUNCT
american_scientific_journal-4187	34	54	(	(	PUNCT
american_scientific_journal-4187	34	55	{	{	PUNCT
american_scientific_journal-4187	34	56	(	(	PUNCT
american_scientific_journal-4187	34	57	(	(	PUNCT
american_scientific_journal-4187	34	58	}	}	PUNCT
american_scientific_journal-4187	34	59	(	(	PUNCT
american_scientific_journal-4187	34	60	(	(	PUNCT
american_scientific_journal-4187	34	61	(	(	PUNCT
american_scientific_journal-4187	34	62	(	(	PUNCT
american_scientific_journal-4187	34	63	(	(	PUNCT
american_scientific_journal-4187	34	64	(	(	PUNCT
american_scientific_journal-4187	34	65	)	)	PUNCT
american_scientific_journal-4187	34	66	(	(	PUNCT
american_scientific_journal-4187	34	67	(	(	PUNCT
american_scientific_journal-4187	34	68	(	(	PUNCT
american_scientific_journal-4187	34	69	(	(	PUNCT
american_scientific_journal-4187	34	70	(	(	PUNCT
american_scientific_journal-4187	34	71	(	(	PUNCT
american_scientific_journal-4187	34	72	(	(	PUNCT
american_scientific_journal-4187	34	73	(	(	PUNCT
american_scientific_journal-4187	34	74	(	(	PUNCT
american_scientific_journal-4187	34	75	)	)	PUNCT
american_scientific_journal-4187	34	76	(	(	PUNCT
american_scientific_journal-4187	34	77	(	(	PUNCT
american_scientific_journal-4187	34	78	(	(	PUNCT
american_scientific_journal-4187	34	79	(	(	PUNCT
american_scientific_journal-4187	34	80	(	(	PUNCT
american_scientific_journal-4187	34	81	𝜇	𝜇	X
american_scientific_journal-4187	34	82	(	(	PUNCT
american_scientific_journal-4187	34	83	corollary.if	corollary.if	PRON
american_scientific_journal-4187	34	84	is	be	AUX
american_scientific_journal-4187	34	85	a	a	DET
american_scientific_journal-4187	34	86	measure	measure	NOUN
american_scientific_journal-4187	34	87	on	on	ADP
american_scientific_journal-4187	34	88	space	space	NOUN
american_scientific_journal-4187	34	89	(	(	PUNCT
american_scientific_journal-4187	34	90	,	,	PUNCT
american_scientific_journal-4187	34	91	also	also	ADV
american_scientific_journal-4187	34	92	is	be	AUX
american_scientific_journal-4187	34	93	a	a	DET
american_scientific_journal-4187	34	94	function	function	NOUN
american_scientific_journal-4187	34	95	such	such	ADJ
american_scientific_journal-4187	34	96	that	that	SCONJ
american_scientific_journal-4187	34	97	satisfies	satisfie	NOUN
american_scientific_journal-4187	34	98	on	on	ADP
american_scientific_journal-4187	34	99	the	the	DET
american_scientific_journal-4187	34	100	condition	condition	NOUN
american_scientific_journal-4187	34	101	(	(	PUNCT
american_scientific_journal-4187	34	102	(	(	PUNCT
american_scientific_journal-4187	34	103	(	(	PUNCT
american_scientific_journal-4187	34	104	(	(	PUNCT
american_scientific_journal-4187	34	105	in	in	ADP
american_scientific_journal-4187	34	106	addition	addition	NOUN
american_scientific_journal-4187	34	107	,	,	PUNCT
american_scientific_journal-4187	34	108	if	if	SCONJ
american_scientific_journal-4187	34	109	we	we	PRON
american_scientific_journal-4187	34	110	define	define	VERB
american_scientific_journal-4187	34	111	a	a	DET
american_scientific_journal-4187	34	112	function	function	NOUN
american_scientific_journal-4187	34	113	like	like	ADP
american_scientific_journal-4187	34	114	this	this	DET
american_scientific_journal-4187	34	115	ρ	ρ	NOUN
american_scientific_journal-4187	34	116	,	,	PUNCT
american_scientific_journal-4187	34	117	as	as	SCONJ
american_scientific_journal-4187	34	118	follow	follow	VERB
american_scientific_journal-4187	34	119	:	:	PUNCT
american_scientific_journal-4187	34	120	(	(	PUNCT
american_scientific_journal-4187	34	121	(	(	PUNCT
american_scientific_journal-4187	34	122	(	(	PUNCT
american_scientific_journal-4187	34	123	american	american	ADJ
american_scientific_journal-4187	34	124	scientific	scientific	ADJ
american_scientific_journal-4187	34	125	research	research	NOUN
american_scientific_journal-4187	34	126	journal	journal	NOUN
american_scientific_journal-4187	34	127	for	for	ADP
american_scientific_journal-4187	34	128	engineering	engineering	NOUN
american_scientific_journal-4187	34	129	,	,	PUNCT
american_scientific_journal-4187	34	130	technology	technology	NOUN
american_scientific_journal-4187	34	131	,	,	PUNCT
american_scientific_journal-4187	34	132	and	and	CCONJ
american_scientific_journal-4187	34	133	sciences	science	NOUN
american_scientific_journal-4187	34	134	(	(	PUNCT
american_scientific_journal-4187	34	135	asrjets	asrjet	NOUN
american_scientific_journal-4187	34	136	)	)	PUNCT
american_scientific_journal-4187	34	137	(	(	PUNCT
american_scientific_journal-4187	34	138	2019	2019	NUM
american_scientific_journal-4187	34	139	)	)	PUNCT
american_scientific_journal-4187	34	140	volume	volume	NOUN
american_scientific_journal-4187	34	141	59	59	NUM
american_scientific_journal-4187	34	142	,	,	PUNCT
american_scientific_journal-4187	34	143	no	no	DET
american_scientific_journal-4187	34	144	1	1	NUM
american_scientific_journal-4187	34	145	,	,	PUNCT
american_scientific_journal-4187	34	146	pp	pp	ADV
american_scientific_journal-4187	34	147	162	162	NUM
american_scientific_journal-4187	34	148	-	-	SYM
american_scientific_journal-4187	34	149	178	178	NUM
american_scientific_journal-4187	34	150	166	166	NUM
american_scientific_journal-4187	34	151	then	then	ADV
american_scientific_journal-4187	34	152	is	be	AUX
american_scientific_journal-4187	34	153	dependable	dependable	ADJ
american_scientific_journal-4187	34	154	value	value	NOUN
american_scientific_journal-4187	34	155	measure	measure	NOUN
american_scientific_journal-4187	34	156	.	.	PUNCT
american_scientific_journal-4187	35	1	in	in	ADP
american_scientific_journal-4187	35	2	order	order	NOUN
american_scientific_journal-4187	35	3	to	to	PART
american_scientific_journal-4187	35	4	understand	understand	VERB
american_scientific_journal-4187	35	5	the	the	DET
american_scientific_journal-4187	35	6	theorem	theorem	NOUN
american_scientific_journal-4187	35	7	(	(	PUNCT
american_scientific_journal-4187	35	8	1	1	NUM
american_scientific_journal-4187	35	9	)	)	PUNCT
american_scientific_journal-4187	35	10	and	and	CCONJ
american_scientific_journal-4187	35	11	corollary	corollary	ADJ
american_scientific_journal-4187	35	12	,	,	PUNCT
american_scientific_journal-4187	35	13	we	we	PRON
american_scientific_journal-4187	35	14	can	can	AUX
american_scientific_journal-4187	35	15	give	give	VERB
american_scientific_journal-4187	35	16	the	the	DET
american_scientific_journal-4187	35	17	following	follow	VERB
american_scientific_journal-4187	35	18	example	example	NOUN
american_scientific_journal-4187	35	19	.	.	PUNCT
american_scientific_journal-4187	36	1	example	example	NOUN
american_scientific_journal-4187	36	2	4	4	NUM
american_scientific_journal-4187	36	3	:	:	PUNCT
american_scientific_journal-4187	36	4	let	let	VERB
american_scientific_journal-4187	36	5	’s	’s	PRON
american_scientific_journal-4187	36	6	assume	assume	VERB
american_scientific_journal-4187	36	7	that	that	PRON
american_scientific_journal-4187	36	8	is	be	AUX
american_scientific_journal-4187	36	9	a	a	DET
american_scientific_journal-4187	36	10	measure	measure	NOUN
american_scientific_journal-4187	36	11	on	on	ADP
american_scientific_journal-4187	36	12	(	(	PUNCT
american_scientific_journal-4187	36	13	space	space	NOUN
american_scientific_journal-4187	36	14	.	.	PUNCT
american_scientific_journal-4187	37	1	in	in	ADP
american_scientific_journal-4187	37	2	this	this	DET
american_scientific_journal-4187	37	3	case	case	NOUN
american_scientific_journal-4187	37	4	,	,	PUNCT
american_scientific_journal-4187	37	5	which	which	PRON
american_scientific_journal-4187	37	6	define	define	VERB
american_scientific_journal-4187	37	7	below	below	ADV
american_scientific_journal-4187	37	8	,	,	PUNCT
american_scientific_journal-4187	37	9	are	be	AUX
american_scientific_journal-4187	37	10	dependable	dependable	ADJ
american_scientific_journal-4187	37	11	value	value	NOUN
american_scientific_journal-4187	37	12	measures	measure	NOUN
american_scientific_journal-4187	37	13	.	.	PUNCT
american_scientific_journal-4187	38	1	(	(	PUNCT
american_scientific_journal-4187	38	2	(	(	PUNCT
american_scientific_journal-4187	38	3	(	(	PUNCT
american_scientific_journal-4187	38	4	∑	∑	INTJ
american_scientific_journal-4187	38	5	(	(	PUNCT
american_scientific_journal-4187	38	6	solution	solution	NOUN
american_scientific_journal-4187	38	7	.	.	PUNCT
american_scientific_journal-4187	38	8	suppose	suppose	VERB
american_scientific_journal-4187	38	9	that	that	SCONJ
american_scientific_journal-4187	38	10	(	(	PUNCT
american_scientific_journal-4187	38	11	.	.	PUNCT
american_scientific_journal-4187	39	1	in	in	ADP
american_scientific_journal-4187	39	2	order	order	NOUN
american_scientific_journal-4187	39	3	to	to	PART
american_scientific_journal-4187	39	4	measure	measure	VERB
american_scientific_journal-4187	39	5	of	of	ADP
american_scientific_journal-4187	39	6	,	,	PUNCT
american_scientific_journal-4187	39	7	we	we	PRON
american_scientific_journal-4187	39	8	must	must	AUX
american_scientific_journal-4187	39	9	notice	notice	VERB
american_scientific_journal-4187	39	10	that	that	SCONJ
american_scientific_journal-4187	39	11	we	we	PRON
american_scientific_journal-4187	39	12	can	can	AUX
american_scientific_journal-4187	39	13	write	write	VERB
american_scientific_journal-4187	39	14	like	like	ADP
american_scientific_journal-4187	39	15	this	this	PRON
american_scientific_journal-4187	39	16	:	:	PUNCT
american_scientific_journal-4187	39	17	(	(	PUNCT
american_scientific_journal-4187	39	18	(	(	PUNCT
american_scientific_journal-4187	39	19	(	(	PUNCT
american_scientific_journal-4187	39	20	(	(	PUNCT
american_scientific_journal-4187	39	21	(	(	PUNCT
american_scientific_journal-4187	39	22	it	it	PRON
american_scientific_journal-4187	39	23	is	be	AUX
american_scientific_journal-4187	39	24	clear	clear	ADJ
american_scientific_journal-4187	39	25	that	that	SCONJ
american_scientific_journal-4187	39	26	non	non	ADJ
american_scientific_journal-4187	39	27	-	-	ADJ
american_scientific_journal-4187	39	28	negative	negative	ADJ
american_scientific_journal-4187	39	29	of	of	ADP
american_scientific_journal-4187	39	30	the	the	DET
american_scientific_journal-4187	39	31	above	above	ADJ
american_scientific_journal-4187	39	32	fraction	fraction	NOUN
american_scientific_journal-4187	39	33	,	,	PUNCT
american_scientific_journal-4187	39	34	according	accord	VERB
american_scientific_journal-4187	39	35	to	to	ADP
american_scientific_journal-4187	39	36	positive	positive	ADJ
american_scientific_journal-4187	39	37	value	value	NOUN
american_scientific_journal-4187	39	38	of	of	ADP
american_scientific_journal-4187	39	39	.	.	PUNCT
american_scientific_journal-4187	40	1	so	so	ADV
american_scientific_journal-4187	40	2	,	,	PUNCT
american_scientific_journal-4187	40	3	this	this	DET
american_scientific_journal-4187	40	4	function	function	NOUN
american_scientific_journal-4187	40	5	(	(	PUNCT
american_scientific_journal-4187	40	6	is	be	AUX
american_scientific_journal-4187	40	7	satisfies	satisfie	NOUN
american_scientific_journal-4187	40	8	on	on	ADP
american_scientific_journal-4187	40	9	this	this	DET
american_scientific_journal-4187	40	10	condition	condition	NOUN
american_scientific_journal-4187	40	11	)	)	PUNCT
american_scientific_journal-4187	41	1	*	*	PUNCT
american_scientific_journal-4187	42	1	*	*	PUNCT
american_scientific_journal-4187	42	2	(	(	PUNCT
american_scientific_journal-4187	42	3	.	.	PUNCT
american_scientific_journal-4187	43	1	in	in	ADP
american_scientific_journal-4187	43	2	order	order	NOUN
american_scientific_journal-4187	43	3	to	to	PART
american_scientific_journal-4187	43	4	measure	measure	VERB
american_scientific_journal-4187	43	5	,	,	PUNCT
american_scientific_journal-4187	43	6	the	the	DET
american_scientific_journal-4187	43	7	proof	proof	NOUN
american_scientific_journal-4187	43	8	of	of	ADP
american_scientific_journal-4187	43	9	(	(	PUNCT
american_scientific_journal-4187	43	10	∑	∑	ADV
american_scientific_journal-4187	43	11	is	be	AUX
american_scientific_journal-4187	43	12	satisfies	satisfie	NOUN
american_scientific_journal-4187	43	13	on	on	ADP
american_scientific_journal-4187	43	14	this	this	DET
american_scientific_journal-4187	43	15	condition	condition	NOUN
american_scientific_journal-4187	43	16	)	)	PUNCT
american_scientific_journal-4187	44	1	*	*	PUNCT
american_scientific_journal-4187	44	2	*	*	PUNCT
american_scientific_journal-4187	44	3	(	(	PUNCT
american_scientific_journal-4187	44	4	.it	.it	PUNCT
american_scientific_journal-4187	44	5	is	be	AUX
american_scientific_journal-4187	44	6	easy	easy	ADJ
american_scientific_journal-4187	44	7	to	to	PART
american_scientific_journal-4187	44	8	solve	solve	VERB
american_scientific_journal-4187	44	9	,	,	PUNCT
american_scientific_journal-4187	44	10	according	accord	VERB
american_scientific_journal-4187	44	11	to	to	ADP
american_scientific_journal-4187	44	12	the	the	DET
american_scientific_journal-4187	44	13	inequality	inequality	NOUN
american_scientific_journal-4187	44	14	.	.	PUNCT
american_scientific_journal-4187	45	1	(	(	PUNCT
american_scientific_journal-4187	45	2	lemma	lemma	PROPN
american_scientific_journal-4187	45	3	2.let	2.let	PROPN
american_scientific_journal-4187	45	4	’s	’s	PART
american_scientific_journal-4187	45	5	assume	assume	VERB
american_scientific_journal-4187	45	6	that	that	SCONJ
american_scientific_journal-4187	45	7	𝝁	𝝁	PRON
american_scientific_journal-4187	45	8	be	be	AUX
american_scientific_journal-4187	45	9	a	a	DET
american_scientific_journal-4187	45	10	dependable	dependable	ADJ
american_scientific_journal-4187	45	11	value	value	NOUN
american_scientific_journal-4187	45	12	measure	measure	NOUN
american_scientific_journal-4187	45	13	under	under	ADP
american_scientific_journal-4187	45	14	binary	binary	ADJ
american_scientific_journal-4187	45	15	operations	operation	NOUN
american_scientific_journal-4187	45	16	(	(	PUNCT
american_scientific_journal-4187	45	17	.	.	PUNCT
american_scientific_journal-4187	46	1	in	in	ADP
american_scientific_journal-4187	46	2	addition	addition	NOUN
american_scientific_journal-4187	46	3	,	,	PUNCT
american_scientific_journal-4187	46	4	suppose	suppose	VERB
american_scientific_journal-4187	46	5	for	for	ADP
american_scientific_journal-4187	46	6	binary	binary	ADJ
american_scientific_journal-4187	46	7	operations	operation	NOUN
american_scientific_journal-4187	46	8	;	;	PUNCT
american_scientific_journal-4187	46	9	we	we	PRON
american_scientific_journal-4187	46	10	have	have	VERB
american_scientific_journal-4187	46	11	:	:	PUNCT
american_scientific_journal-4187	46	12	moreover	moreover	ADV
american_scientific_journal-4187	46	13	if	if	SCONJ
american_scientific_journal-4187	46	14	are	be	AUX
american_scientific_journal-4187	46	15	non	non	ADJ
american_scientific_journal-4187	46	16	-	-	ADJ
american_scientific_journal-4187	46	17	negative	negative	ADJ
american_scientific_journal-4187	46	18	numbers	number	NOUN
american_scientific_journal-4187	46	19	which	which	PRON
american_scientific_journal-4187	46	20	have	have	VERB
american_scientific_journal-4187	46	21	relation;show	relation;show	NOUN
american_scientific_journal-4187	46	22	that	that	DET
american_scientific_journal-4187	46	23	𝜇	𝜇	X
american_scientific_journal-4187	46	24	(	(	PUNCT
american_scientific_journal-4187	46	25	𝜇	𝜇	X
american_scientific_journal-4187	46	26	(	(	PUNCT
american_scientific_journal-4187	46	27	american	american	ADJ
american_scientific_journal-4187	46	28	scientific	scientific	ADJ
american_scientific_journal-4187	46	29	research	research	NOUN
american_scientific_journal-4187	46	30	journal	journal	NOUN
american_scientific_journal-4187	46	31	for	for	ADP
american_scientific_journal-4187	46	32	engineering	engineering	NOUN
american_scientific_journal-4187	46	33	,	,	PUNCT
american_scientific_journal-4187	46	34	technology	technology	NOUN
american_scientific_journal-4187	46	35	,	,	PUNCT
american_scientific_journal-4187	46	36	and	and	CCONJ
american_scientific_journal-4187	46	37	sciences	science	NOUN
american_scientific_journal-4187	46	38	(	(	PUNCT
american_scientific_journal-4187	46	39	asrjets	asrjet	NOUN
american_scientific_journal-4187	46	40	)	)	PUNCT
american_scientific_journal-4187	46	41	(	(	PUNCT
american_scientific_journal-4187	46	42	2019	2019	NUM
american_scientific_journal-4187	46	43	)	)	PUNCT
american_scientific_journal-4187	46	44	volume	volume	NOUN
american_scientific_journal-4187	46	45	59	59	NUM
american_scientific_journal-4187	46	46	,	,	PUNCT
american_scientific_journal-4187	46	47	no	no	DET
american_scientific_journal-4187	46	48	1	1	NUM
american_scientific_journal-4187	46	49	,	,	PUNCT
american_scientific_journal-4187	46	50	pp	pp	ADV
american_scientific_journal-4187	46	51	162	162	NUM
american_scientific_journal-4187	46	52	-	-	SYM
american_scientific_journal-4187	46	53	178	178	NUM
american_scientific_journal-4187	46	54	167	167	NUM
american_scientific_journal-4187	46	55	proof.due	proof.due	NOUN
american_scientific_journal-4187	46	56	to	to	ADP
american_scientific_journal-4187	46	57	the	the	DET
american_scientific_journal-4187	46	58	feature	feature	NOUN
american_scientific_journal-4187	46	59	of	of	ADP
american_scientific_journal-4187	46	60	,	,	PUNCT
american_scientific_journal-4187	46	61	which	which	PRON
american_scientific_journal-4187	46	62	means	mean	VERB
american_scientific_journal-4187	46	63	dependable	dependable	ADJ
american_scientific_journal-4187	46	64	value	value	NOUN
american_scientific_journal-4187	46	65	measure	measure	NOUN
american_scientific_journal-4187	46	66	under	under	ADP
american_scientific_journal-4187	46	67	binary	binary	ADJ
american_scientific_journal-4187	46	68	operations	operation	NOUN
american_scientific_journal-4187	46	69	(	(	PUNCT
american_scientific_journal-4187	46	70	,	,	PUNCT
american_scientific_journal-4187	46	71	we	we	PRON
american_scientific_journal-4187	46	72	can	can	AUX
american_scientific_journal-4187	46	73	write	write	VERB
american_scientific_journal-4187	46	74	as	as	SCONJ
american_scientific_journal-4187	46	75	follows	follow	VERB
american_scientific_journal-4187	46	76	:	:	PUNCT
american_scientific_journal-4187	46	77	𝜇	𝜇	X
american_scientific_journal-4187	46	78	(	(	PUNCT
american_scientific_journal-4187	46	79	𝜇	𝜇	X
american_scientific_journal-4187	46	80	(	(	PUNCT
american_scientific_journal-4187	46	81	𝜇	𝜇	X
american_scientific_journal-4187	46	82	(	(	PUNCT
american_scientific_journal-4187	46	83	(	(	PUNCT
american_scientific_journal-4187	46	84	𝜇	𝜇	X
american_scientific_journal-4187	46	85	(	(	PUNCT
american_scientific_journal-4187	46	86	now	now	ADV
american_scientific_journal-4187	46	87	,	,	PUNCT
american_scientific_journal-4187	46	88	we	we	PRON
american_scientific_journal-4187	46	89	have	have	AUX
american_scientific_journal-4187	46	90	as	as	ADV
american_scientific_journal-4187	46	91	follow	follow	VERB
american_scientific_journal-4187	46	92	:	:	PUNCT
american_scientific_journal-4187	46	93	𝜇	𝜇	X
american_scientific_journal-4187	46	94	(	(	PUNCT
american_scientific_journal-4187	46	95	𝜇	𝜇	X
american_scientific_journal-4187	46	96	(	(	PUNCT
american_scientific_journal-4187	46	97	𝜇	𝜇	X
american_scientific_journal-4187	46	98	(	(	PUNCT
american_scientific_journal-4187	46	99	therefore	therefore	ADV
american_scientific_journal-4187	46	100	,	,	PUNCT
american_scientific_journal-4187	46	101	we	we	PRON
american_scientific_journal-4187	46	102	get	get	AUX
american_scientific_journal-4187	46	103	desired	desire	VERB
american_scientific_journal-4187	46	104	results	result	NOUN
american_scientific_journal-4187	46	105	corollary.let	corollary.let	X
american_scientific_journal-4187	46	106	’s	’s	PART
american_scientific_journal-4187	46	107	think	think	VERB
american_scientific_journal-4187	46	108	there	there	PRON
american_scientific_journal-4187	46	109	is	be	VERB
american_scientific_journal-4187	46	110	relation	relation	NOUN
american_scientific_journal-4187	46	111	between	between	ADP
american_scientific_journal-4187	46	112	two	two	NUM
american_scientific_journal-4187	46	113	non	non	ADJ
american_scientific_journal-4187	46	114	-	-	ADJ
american_scientific_journal-4187	46	115	negative	negative	ADJ
american_scientific_journal-4187	46	116	numbers	number	NOUN
american_scientific_journal-4187	46	117	.	.	PUNCT
american_scientific_journal-4187	47	1	in	in	ADP
american_scientific_journal-4187	47	2	this	this	DET
american_scientific_journal-4187	47	3	case	case	NOUN
american_scientific_journal-4187	47	4	,	,	PUNCT
american_scientific_journal-4187	47	5	the	the	DET
american_scientific_journal-4187	47	6	following	follow	VERB
american_scientific_journal-4187	47	7	relationship	relationship	NOUN
american_scientific_journal-4187	47	8	is	be	AUX
american_scientific_journal-4187	47	9	established	establish	VERB
american_scientific_journal-4187	47	10	in	in	ADP
american_scientific_journal-4187	47	11	each	each	DET
american_scientific_journal-4187	47	12	dependable	dependable	ADJ
american_scientific_journal-4187	47	13	value	value	NOUN
american_scientific_journal-4187	47	14	measure	measure	NOUN
american_scientific_journal-4187	47	15	𝝆	𝝆	X
american_scientific_journal-4187	47	16	.	.	PUNCT
american_scientific_journal-4187	48	1	(	(	PUNCT
american_scientific_journal-4187	48	2	(	(	PUNCT
american_scientific_journal-4187	48	3	example	example	NOUN
american_scientific_journal-4187	48	4	5	5	NUM
american_scientific_journal-4187	48	5	:	:	PUNCT
american_scientific_journal-4187	48	6	let	let	VERB
american_scientific_journal-4187	48	7	’s	’s	NOUN
american_scientific_journal-4187	48	8	suppose	suppose	VERB
american_scientific_journal-4187	48	9	that	that	SCONJ
american_scientific_journal-4187	48	10	are	be	AUX
american_scientific_journal-4187	48	11	dependable	dependable	ADJ
american_scientific_journal-4187	48	12	value	value	NOUN
american_scientific_journal-4187	48	13	measures	measure	NOUN
american_scientific_journal-4187	48	14	.	.	PUNCT
american_scientific_journal-4187	49	1	in	in	ADP
american_scientific_journal-4187	49	2	this	this	DET
american_scientific_journal-4187	49	3	case	case	NOUN
american_scientific_journal-4187	49	4	,	,	PUNCT
american_scientific_journal-4187	49	5	is	be	AUX
american_scientific_journal-4187	49	6	dependable	dependable	ADJ
american_scientific_journal-4187	49	7	value	value	NOUN
american_scientific_journal-4187	49	8	measure	measure	NOUN
american_scientific_journal-4187	49	9	which	which	PRON
american_scientific_journal-4187	49	10	defined	define	VERB
american_scientific_journal-4187	49	11	by	by	ADP
american_scientific_journal-4187	49	12	the	the	DET
american_scientific_journal-4187	49	13	following	follow	VERB
american_scientific_journal-4187	49	14	criteria	criterion	NOUN
american_scientific_journal-4187	49	15	.	.	PUNCT
american_scientific_journal-4187	50	1	(	(	PUNCT
american_scientific_journal-4187	50	2	(	(	PUNCT
american_scientific_journal-4187	50	3	(	(	PUNCT
american_scientific_journal-4187	50	4	the	the	DET
american_scientific_journal-4187	50	5	research	research	NOUN
american_scientific_journal-4187	50	6	of	of	ADP
american_scientific_journal-4187	50	7	first	first	ADJ
american_scientific_journal-4187	50	8	feature	feature	NOUN
american_scientific_journal-4187	50	9	is	be	AUX
american_scientific_journal-4187	50	10	very	very	ADV
american_scientific_journal-4187	50	11	easy	easy	ADJ
american_scientific_journal-4187	50	12	.	.	PUNCT
american_scientific_journal-4187	51	1	in	in	ADP
american_scientific_journal-4187	51	2	order	order	NOUN
american_scientific_journal-4187	51	3	to	to	PART
american_scientific_journal-4187	51	4	consider	consider	VERB
american_scientific_journal-4187	51	5	of	of	ADP
american_scientific_journal-4187	51	6	the	the	DET
american_scientific_journal-4187	51	7	feature	feature	NOUN
american_scientific_journal-4187	51	8	of	of	ADP
american_scientific_journal-4187	51	9	for	for	ADP
american_scientific_journal-4187	51	10	(	(	PUNCT
american_scientific_journal-4187	51	11	,	,	PUNCT
american_scientific_journal-4187	51	12	we	we	PRON
american_scientific_journal-4187	51	13	have	have	VERB
american_scientific_journal-4187	51	14	to	to	PART
american_scientific_journal-4187	51	15	write	write	VERB
american_scientific_journal-4187	51	16	as	as	ADP
american_scientific_journal-4187	51	17	follow	follow	VERB
american_scientific_journal-4187	51	18	:	:	PUNCT
american_scientific_journal-4187	51	19	(	(	PUNCT
american_scientific_journal-4187	51	20	(	(	PUNCT
american_scientific_journal-4187	51	21	(	(	PUNCT
american_scientific_journal-4187	51	22	(	(	PUNCT
american_scientific_journal-4187	51	23	(	(	PUNCT
american_scientific_journal-4187	51	24	(	(	PUNCT
american_scientific_journal-4187	51	25	)	)	PUNCT
american_scientific_journal-4187	51	26	(	(	PUNCT
american_scientific_journal-4187	51	27	(	(	PUNCT
american_scientific_journal-4187	51	28	(	(	PUNCT
american_scientific_journal-4187	51	29	)	)	PUNCT
american_scientific_journal-4187	51	30	(	(	PUNCT
american_scientific_journal-4187	51	31	(	(	PUNCT
american_scientific_journal-4187	51	32	(	(	PUNCT
american_scientific_journal-4187	51	33	)	)	PUNCT
american_scientific_journal-4187	51	34	due	due	ADP
american_scientific_journal-4187	51	35	to	to	ADP
american_scientific_journal-4187	51	36	the	the	DET
american_scientific_journal-4187	51	37	same	same	ADJ
american_scientific_journal-4187	51	38	operation	operation	NOUN
american_scientific_journal-4187	51	39	in	in	ADP
american_scientific_journal-4187	51	40	this	this	DET
american_scientific_journal-4187	51	41	phrase	phrase	NOUN
american_scientific_journal-4187	51	42	(	(	PUNCT
american_scientific_journal-4187	51	43	,	,	PUNCT
american_scientific_journal-4187	51	44	we	we	PRON
american_scientific_journal-4187	51	45	can	can	AUX
american_scientific_journal-4187	51	46	conclude	conclude	VERB
american_scientific_journal-4187	51	47	as	as	ADP
american_scientific_journal-4187	51	48	follow	follow	VERB
american_scientific_journal-4187	51	49	𝜇	𝜇	ADP
american_scientific_journal-4187	51	50	(	(	PUNCT
american_scientific_journal-4187	51	51	𝜇	𝜇	X
american_scientific_journal-4187	51	52	(	(	PUNCT
american_scientific_journal-4187	51	53	𝜇	𝜇	X
american_scientific_journal-4187	51	54	(	(	PUNCT
american_scientific_journal-4187	51	55	in	in	ADP
american_scientific_journal-4187	51	56	two	two	NUM
american_scientific_journal-4187	51	57	above	above	ADJ
american_scientific_journal-4187	51	58	operations	operation	NOUN
american_scientific_journal-4187	51	59	(	(	PUNCT
american_scientific_journal-4187	51	60	are	be	AUX
american_scientific_journal-4187	51	61	consider	consider	VERB
american_scientific_journal-4187	51	62	as	as	ADP
american_scientific_journal-4187	51	63	an	an	DET
american_scientific_journal-4187	51	64	addition	addition	NOUN
american_scientific_journal-4187	51	65	.	.	PUNCT
american_scientific_journal-4187	52	1	however	however	ADV
american_scientific_journal-4187	52	2	,	,	PUNCT
american_scientific_journal-4187	52	3	if	if	SCONJ
american_scientific_journal-4187	52	4	they	they	PRON
american_scientific_journal-4187	52	5	was	be	AUX
american_scientific_journal-4187	52	6	n’t	not	PART
american_scientific_journal-4187	52	7	an	an	DET
american_scientific_journal-4187	52	8	addition	addition	NOUN
american_scientific_journal-4187	52	9	,	,	PUNCT
american_scientific_journal-4187	52	10	it	it	PRON
american_scientific_journal-4187	52	11	was	be	AUX
american_scientific_journal-4187	52	12	so	so	ADV
american_scientific_journal-4187	52	13	hard	hard	ADJ
american_scientific_journal-4187	52	14	to	to	PART
american_scientific_journal-4187	52	15	solve	solve	VERB
american_scientific_journal-4187	52	16	.	.	PUNCT
american_scientific_journal-4187	53	1	in	in	ADP
american_scientific_journal-4187	53	2	below	below	ADP
american_scientific_journal-4187	53	3	theorem	theorem	PROPN
american_scientific_journal-4187	53	4	,	,	PUNCT
american_scientific_journal-4187	53	5	we	we	PRON
american_scientific_journal-4187	53	6	are	be	AUX
american_scientific_journal-4187	53	7	looking	look	VERB
american_scientific_journal-4187	53	8	for	for	ADP
american_scientific_journal-4187	53	9	functions	function	NOUN
american_scientific_journal-4187	53	10	,	,	PUNCT
american_scientific_journal-4187	53	11	which	which	PRON
american_scientific_journal-4187	53	12	is	be	AUX
american_scientific_journal-4187	53	13	multiplied	multiply	VERB
american_scientific_journal-4187	53	14	by	by	ADP
american_scientific_journal-4187	53	15	their	their	PRON
american_scientific_journal-4187	53	16	dependable	dependable	ADJ
american_scientific_journal-4187	53	17	value	value	NOUN
american_scientific_journal-4187	53	18	measure	measure	NOUN
american_scientific_journal-4187	53	19	,	,	PUNCT
american_scientific_journal-4187	53	20	the	the	DET
american_scientific_journal-4187	53	21	multiplication	multiplication	NOUN
american_scientific_journal-4187	53	22	again	again	ADV
american_scientific_journal-4187	53	23	become	become	VERB
american_scientific_journal-4187	53	24	a	a	DET
american_scientific_journal-4187	53	25	dependable	dependable	ADJ
american_scientific_journal-4187	53	26	value	value	NOUN
american_scientific_journal-4187	53	27	measure	measure	NOUN
american_scientific_journal-4187	53	28	function	function	NOUN
american_scientific_journal-4187	53	29	under	under	ADP
american_scientific_journal-4187	53	30	binary	binary	ADJ
american_scientific_journal-4187	53	31	operations	operation	NOUN
american_scientific_journal-4187	53	32	.	.	PUNCT
american_scientific_journal-4187	54	1	theorem	theorem	VERB
american_scientific_journal-4187	54	2	3.let	3.let	NOUN
american_scientific_journal-4187	54	3	’s	’s	PART
american_scientific_journal-4187	54	4	assume	assume	NOUN
american_scientific_journal-4187	54	5	that	that	PRON
american_scientific_journal-4187	54	6	is	be	AUX
american_scientific_journal-4187	54	7	dependable	dependable	ADJ
american_scientific_journal-4187	54	8	value	value	NOUN
american_scientific_journal-4187	54	9	measure	measure	NOUN
american_scientific_journal-4187	54	10	under	under	ADP
american_scientific_journal-4187	54	11	binary	binary	ADJ
american_scientific_journal-4187	54	12	operations	operation	NOUN
american_scientific_journal-4187	54	13	(	(	PUNCT
american_scientific_journal-4187	54	14	.	.	PUNCT
american_scientific_journal-4187	55	1	in	in	ADP
american_scientific_journal-4187	55	2	addition	addition	NOUN
american_scientific_journal-4187	55	3	,	,	PUNCT
american_scientific_journal-4187	55	4	we	we	PRON
american_scientific_journal-4187	55	5	have	have	VERB
american_scientific_journal-4187	55	6	for	for	ADP
american_scientific_journal-4187	55	7	non	non	ADJ
american_scientific_journal-4187	55	8	-	-	ADJ
american_scientific_journal-4187	55	9	negative	negative	ADJ
american_scientific_journal-4187	55	10	function	function	NOUN
american_scientific_journal-4187	55	11	and	and	CCONJ
american_scientific_journal-4187	55	12	binary	binary	ADJ
american_scientific_journal-4187	55	13	operations	operation	NOUN
american_scientific_journal-4187	55	14	(	(	PUNCT
american_scientific_journal-4187	55	15	:	:	PUNCT
american_scientific_journal-4187	55	16	(	(	PUNCT
american_scientific_journal-4187	55	17	(	(	PUNCT
american_scientific_journal-4187	55	18	(	(	PUNCT
american_scientific_journal-4187	55	19	(	(	PUNCT
american_scientific_journal-4187	55	20	american	american	ADJ
american_scientific_journal-4187	55	21	scientific	scientific	ADJ
american_scientific_journal-4187	55	22	research	research	NOUN
american_scientific_journal-4187	55	23	journal	journal	NOUN
american_scientific_journal-4187	55	24	for	for	ADP
american_scientific_journal-4187	55	25	engineering	engineering	NOUN
american_scientific_journal-4187	55	26	,	,	PUNCT
american_scientific_journal-4187	55	27	technology	technology	NOUN
american_scientific_journal-4187	55	28	,	,	PUNCT
american_scientific_journal-4187	55	29	and	and	CCONJ
american_scientific_journal-4187	55	30	sciences	science	NOUN
american_scientific_journal-4187	55	31	(	(	PUNCT
american_scientific_journal-4187	55	32	asrjets	asrjet	NOUN
american_scientific_journal-4187	55	33	)	)	PUNCT
american_scientific_journal-4187	55	34	(	(	PUNCT
american_scientific_journal-4187	55	35	2019	2019	NUM
american_scientific_journal-4187	55	36	)	)	PUNCT
american_scientific_journal-4187	55	37	volume	volume	NOUN
american_scientific_journal-4187	55	38	59	59	NUM
american_scientific_journal-4187	55	39	,	,	PUNCT
american_scientific_journal-4187	55	40	no	no	DET
american_scientific_journal-4187	55	41	1	1	NUM
american_scientific_journal-4187	55	42	,	,	PUNCT
american_scientific_journal-4187	55	43	pp	pp	ADV
american_scientific_journal-4187	55	44	162	162	NUM
american_scientific_journal-4187	55	45	-	-	SYM
american_scientific_journal-4187	55	46	178	178	NUM
american_scientific_journal-4187	55	47	168	168	NUM
american_scientific_journal-4187	55	48	(	(	PUNCT
american_scientific_journal-4187	55	49	(	(	PUNCT
american_scientific_journal-4187	55	50	(	(	PUNCT
american_scientific_journal-4187	55	51	(	(	PUNCT
american_scientific_journal-4187	55	52	(	(	PUNCT
american_scientific_journal-4187	55	53	then	then	ADV
american_scientific_journal-4187	55	54	function	function	VERB
american_scientific_journal-4187	55	55	𝜇	𝜇	ADP
american_scientific_journal-4187	55	56	is	be	AUX
american_scientific_journal-4187	55	57	dependable	dependable	ADJ
american_scientific_journal-4187	55	58	value	value	NOUN
american_scientific_journal-4187	55	59	measure	measure	NOUN
american_scientific_journal-4187	55	60	under	under	ADP
american_scientific_journal-4187	55	61	binary	binary	ADJ
american_scientific_journal-4187	55	62	operations	operation	NOUN
american_scientific_journal-4187	55	63	(	(	PUNCT
american_scientific_journal-4187	55	64	.	.	PUNCT
american_scientific_journal-4187	56	1	𝜇	𝜇	X
american_scientific_journal-4187	56	2	(	(	PUNCT
american_scientific_journal-4187	56	3	(	(	PUNCT
american_scientific_journal-4187	56	4	(	(	PUNCT
american_scientific_journal-4187	56	5	proof.the	proof.the	DET
american_scientific_journal-4187	56	6	consideration	consideration	NOUN
american_scientific_journal-4187	56	7	of	of	ADP
american_scientific_journal-4187	56	8	dependable	dependable	ADJ
american_scientific_journal-4187	56	9	value	value	NOUN
american_scientific_journal-4187	56	10	pre	pre	ADJ
american_scientific_journal-4187	56	11	-	-	ADJ
american_scientific_journal-4187	56	12	measure	measure	ADJ
american_scientific_journal-4187	56	13	function	function	NOUN
american_scientific_journal-4187	56	14	𝝁	𝝁	PRON
american_scientific_journal-4187	56	15	is	be	AUX
american_scientific_journal-4187	56	16	so	so	ADV
american_scientific_journal-4187	56	17	simple	simple	ADJ
american_scientific_journal-4187	56	18	.	.	PUNCT
american_scientific_journal-4187	57	1	now	now	ADV
american_scientific_journal-4187	57	2	,	,	PUNCT
american_scientific_journal-4187	57	3	by	by	ADP
american_scientific_journal-4187	57	4	using	use	VERB
american_scientific_journal-4187	57	5	the	the	DET
american_scientific_journal-4187	57	6	features	feature	NOUN
american_scientific_journal-4187	57	7	(	(	PUNCT
american_scientific_journal-4187	57	8	5	5	NUM
american_scientific_journal-4187	57	9	)	)	PUNCT
american_scientific_journal-4187	57	10	and	and	CCONJ
american_scientific_journal-4187	57	11	(	(	PUNCT
american_scientific_journal-4187	57	12	6	6	NUM
american_scientific_journal-4187	57	13	)	)	PUNCT
american_scientific_journal-4187	57	14	,	,	PUNCT
american_scientific_journal-4187	57	15	we	we	PRON
american_scientific_journal-4187	57	16	can	can	AUX
american_scientific_journal-4187	57	17	write	write	VERB
american_scientific_journal-4187	57	18	:	:	PUNCT
american_scientific_journal-4187	57	19	𝜇	𝜇	X
american_scientific_journal-4187	57	20	(	(	PUNCT
american_scientific_journal-4187	57	21	𝜇	𝜇	X
american_scientific_journal-4187	57	22	(	(	PUNCT
american_scientific_journal-4187	57	23	(	(	PUNCT
american_scientific_journal-4187	57	24	(	(	PUNCT
american_scientific_journal-4187	57	25	(	(	PUNCT
american_scientific_journal-4187	57	26	(	(	PUNCT
american_scientific_journal-4187	57	27	(	(	PUNCT
american_scientific_journal-4187	57	28	(	(	PUNCT
american_scientific_journal-4187	57	29	(	(	PUNCT
american_scientific_journal-4187	57	30	(	(	PUNCT
american_scientific_journal-4187	57	31	(	(	PUNCT
american_scientific_journal-4187	57	32	(	(	PUNCT
american_scientific_journal-4187	57	33	𝜇	𝜇	X
american_scientific_journal-4187	57	34	(	(	PUNCT
american_scientific_journal-4187	57	35	as	as	SCONJ
american_scientific_journal-4187	57	36	we	we	PRON
american_scientific_journal-4187	57	37	can	can	AUX
american_scientific_journal-4187	57	38	see	see	VERB
american_scientific_journal-4187	57	39	in	in	ADP
american_scientific_journal-4187	57	40	the	the	DET
american_scientific_journal-4187	57	41	above	above	ADJ
american_scientific_journal-4187	57	42	theorem	theorem	NOUN
american_scientific_journal-4187	57	43	,	,	PUNCT
american_scientific_journal-4187	57	44	we	we	PRON
american_scientific_journal-4187	57	45	can	can	AUX
american_scientific_journal-4187	57	46	apply	apply	VERB
american_scientific_journal-4187	57	47	the	the	DET
american_scientific_journal-4187	57	48	conditions	condition	NOUN
american_scientific_journal-4187	57	49	,	,	PUNCT
american_scientific_journal-4187	57	50	which	which	PRON
american_scientific_journal-4187	57	51	are	be	AUX
american_scientific_journal-4187	57	52	possible	possible	ADJ
american_scientific_journal-4187	57	53	to	to	PART
american_scientific_journal-4187	57	54	maintain	maintain	VERB
american_scientific_journal-4187	57	55	the	the	DET
american_scientific_journal-4187	57	56	binary	binary	ADJ
american_scientific_journal-4187	57	57	operations	operation	NOUN
american_scientific_journal-4187	57	58	.	.	PUNCT
american_scientific_journal-4187	58	1	certainly	certainly	ADV
american_scientific_journal-4187	58	2	,	,	PUNCT
american_scientific_journal-4187	58	3	the	the	DET
american_scientific_journal-4187	58	4	condition	condition	NOUN
american_scientific_journal-4187	58	5	is	be	AUX
american_scientific_journal-4187	58	6	n't	not	PART
american_scientific_journal-4187	58	7	always	always	ADV
american_scientific_journal-4187	58	8	like	like	ADP
american_scientific_journal-4187	58	9	that	that	PRON
american_scientific_journal-4187	58	10	.	.	PUNCT
american_scientific_journal-4187	59	1	however	however	ADV
american_scientific_journal-4187	59	2	,	,	PUNCT
american_scientific_journal-4187	59	3	in	in	ADP
american_scientific_journal-4187	59	4	order	order	NOUN
american_scientific_journal-4187	59	5	to	to	PART
american_scientific_journal-4187	59	6	change	change	VERB
american_scientific_journal-4187	59	7	the	the	DET
american_scientific_journal-4187	59	8	condition	condition	NOUN
american_scientific_journal-4187	59	9	,	,	PUNCT
american_scientific_journal-4187	59	10	the	the	DET
american_scientific_journal-4187	59	11	binary	binary	ADJ
american_scientific_journal-4187	59	12	operations	operation	NOUN
american_scientific_journal-4187	59	13	are	be	AUX
american_scientific_journal-4187	59	14	also	also	ADV
american_scientific_journal-4187	59	15	changed	change	VERB
american_scientific_journal-4187	59	16	.	.	PUNCT
american_scientific_journal-4187	60	1	the	the	DET
american_scientific_journal-4187	60	2	following	follow	VERB
american_scientific_journal-4187	60	3	theorem	theorem	NOUN
american_scientific_journal-4187	60	4	has	have	VERB
american_scientific_journal-4187	60	5	this	this	DET
american_scientific_journal-4187	60	6	kind	kind	NOUN
american_scientific_journal-4187	60	7	of	of	ADP
american_scientific_journal-4187	60	8	conditions	condition	NOUN
american_scientific_journal-4187	60	9	.	.	PUNCT
american_scientific_journal-4187	61	1	theorem	theorem	PROPN
american_scientific_journal-4187	61	2	4.let	4.let	PROPN
american_scientific_journal-4187	61	3	’s	’s	PART
american_scientific_journal-4187	61	4	are	be	AUX
american_scientific_journal-4187	61	5	dependable	dependable	ADJ
american_scientific_journal-4187	61	6	value	value	NOUN
american_scientific_journal-4187	61	7	measures	measure	NOUN
american_scientific_journal-4187	61	8	under	under	ADP
american_scientific_journal-4187	61	9	binary	binary	ADJ
american_scientific_journal-4187	61	10	operations	operation	NOUN
american_scientific_journal-4187	61	11	respectively	respectively	ADV
american_scientific_journal-4187	61	12	(	(	PUNCT
american_scientific_journal-4187	61	13	(	(	PUNCT
american_scientific_journal-4187	61	14	̂	̂	PUNCT
american_scientific_journal-4187	61	15	̂	̂	NUM
american_scientific_journal-4187	61	16	;	;	PUNCT
american_scientific_journal-4187	61	17	such	such	ADJ
american_scientific_journal-4187	61	18	that	that	SCONJ
american_scientific_journal-4187	61	19	both	both	DET
american_scientific_journal-4187	61	20	measures	measure	NOUN
american_scientific_journal-4187	61	21	are	be	AUX
american_scientific_journal-4187	61	22	made	make	VERB
american_scientific_journal-4187	61	23	as	as	SCONJ
american_scientific_journal-4187	61	24	follows	follow	VERB
american_scientific_journal-4187	61	25	:	:	PUNCT
american_scientific_journal-4187	61	26	(	(	PUNCT
american_scientific_journal-4187	61	27	(	(	PUNCT
american_scientific_journal-4187	61	28	(	(	PUNCT
american_scientific_journal-4187	61	29	(	(	PUNCT
american_scientific_journal-4187	61	30	(	(	PUNCT
american_scientific_journal-4187	61	31	(	(	PUNCT
american_scientific_journal-4187	61	32	(	(	PUNCT
american_scientific_journal-4187	61	33	(	(	PUNCT
american_scientific_journal-4187	61	34	and	and	CCONJ
american_scientific_journal-4187	61	35	functions	function	NOUN
american_scientific_journal-4187	61	36	have	have	AUX
american_scientific_journal-4187	61	37	)	)	PUNCT
american_scientific_journal-4187	61	38	*	*	PUNCT
american_scientific_journal-4187	62	1	*	*	PUNCT
american_scientific_journal-4187	62	2	(	(	PUNCT
american_scientific_journal-4187	62	3	feature	feature	NOUN
american_scientific_journal-4187	62	4	and	and	CCONJ
american_scientific_journal-4187	62	5	were	be	AUX
american_scientific_journal-4187	62	6	two	two	NUM
american_scientific_journal-4187	62	7	measures	measure	NOUN
american_scientific_journal-4187	62	8	.	.	PUNCT
american_scientific_journal-4187	63	1	in	in	ADP
american_scientific_journal-4187	63	2	addition	addition	NOUN
american_scientific_journal-4187	63	3	,	,	PUNCT
american_scientific_journal-4187	63	4	binary	binary	ADJ
american_scientific_journal-4187	63	5	operations	operation	NOUN
american_scientific_journal-4187	63	6	(	(	PUNCT
american_scientific_journal-4187	63	7	is	be	AUX
american_scientific_journal-4187	63	8	defines	define	NOUN
american_scientific_journal-4187	63	9	as	as	ADP
american_scientific_journal-4187	63	10	follow	follow	NOUN
american_scientific_journal-4187	63	11	:	:	PUNCT
american_scientific_journal-4187	63	12	(	(	PUNCT
american_scientific_journal-4187	63	13	(	(	PUNCT
american_scientific_journal-4187	63	14	̂	̂	X
american_scientific_journal-4187	63	15	)	)	PUNCT
american_scientific_journal-4187	63	16	(	(	PUNCT
american_scientific_journal-4187	63	17	(	(	PUNCT
american_scientific_journal-4187	63	18	(	(	PUNCT
american_scientific_journal-4187	63	19	̂	̂	X
american_scientific_journal-4187	63	20	)	)	PUNCT
american_scientific_journal-4187	63	21	(	(	PUNCT
american_scientific_journal-4187	63	22	then	then	ADV
american_scientific_journal-4187	63	23	𝜇	𝜇	SCONJ
american_scientific_journal-4187	63	24	is	be	AUX
american_scientific_journal-4187	63	25	defines	define	NOUN
american_scientific_journal-4187	63	26	as	as	ADP
american_scientific_journal-4187	63	27	follow	follow	VERB
american_scientific_journal-4187	63	28	,	,	PUNCT
american_scientific_journal-4187	63	29	it	it	PRON
american_scientific_journal-4187	63	30	’s	’	VERB
american_scientific_journal-4187	63	31	a	a	DET
american_scientific_journal-4187	63	32	dependable	dependable	ADJ
american_scientific_journal-4187	63	33	value	value	NOUN
american_scientific_journal-4187	63	34	measure	measure	NOUN
american_scientific_journal-4187	63	35	under	under	ADP
american_scientific_journal-4187	63	36	the	the	DET
american_scientific_journal-4187	63	37	binary	binary	ADJ
american_scientific_journal-4187	63	38	operation	operation	NOUN
american_scientific_journal-4187	63	39	(	(	PUNCT
american_scientific_journal-4187	63	40	.	.	PUNCT
american_scientific_journal-4187	64	1	𝜇	𝜇	X
american_scientific_journal-4187	64	2	(	(	PUNCT
american_scientific_journal-4187	64	3	(	(	PUNCT
american_scientific_journal-4187	64	4	(	(	PUNCT
american_scientific_journal-4187	64	5	)	)	PUNCT
american_scientific_journal-4187	64	6	(	(	PUNCT
american_scientific_journal-4187	64	7	(	(	PUNCT
american_scientific_journal-4187	64	8	proof.the	proof.the	DET
american_scientific_journal-4187	64	9	consideration	consideration	NOUN
american_scientific_journal-4187	64	10	of	of	ADP
american_scientific_journal-4187	64	11	function	function	NOUN
american_scientific_journal-4187	64	12	𝝁	𝝁	PRON
american_scientific_journal-4187	64	13	is	be	AUX
american_scientific_journal-4187	64	14	so	so	ADV
american_scientific_journal-4187	64	15	simple	simple	ADJ
american_scientific_journal-4187	64	16	.	.	PUNCT
american_scientific_journal-4187	65	1	now	now	ADV
american_scientific_journal-4187	65	2	,	,	PUNCT
american_scientific_journal-4187	65	3	we	we	PRON
american_scientific_journal-4187	65	4	are	be	AUX
american_scientific_journal-4187	65	5	going	go	VERB
american_scientific_journal-4187	65	6	to	to	PART
american_scientific_journal-4187	65	7	prove	prove	VERB
american_scientific_journal-4187	65	8	the	the	DET
american_scientific_journal-4187	65	9	second	second	ADJ
american_scientific_journal-4187	65	10	feature	feature	NOUN
american_scientific_journal-4187	65	11	.	.	PUNCT
american_scientific_journal-4187	66	1	according	accord	VERB
american_scientific_journal-4187	66	2	to	to	ADP
american_scientific_journal-4187	66	3	the	the	DET
american_scientific_journal-4187	66	4	hypothesis	hypothesis	NOUN
american_scientific_journal-4187	66	5	of	of	ADP
american_scientific_journal-4187	66	6	the	the	DET
american_scientific_journal-4187	66	7	problem	problem	NOUN
american_scientific_journal-4187	66	8	:	:	PUNCT
american_scientific_journal-4187	66	9	(	(	PUNCT
american_scientific_journal-4187	66	10	(	(	PUNCT
american_scientific_journal-4187	66	11	(	(	PUNCT
american_scientific_journal-4187	66	12	(	(	PUNCT
american_scientific_journal-4187	66	13	̂	̂	X
american_scientific_journal-4187	66	14	(	(	PUNCT
american_scientific_journal-4187	66	15	(	(	PUNCT
american_scientific_journal-4187	66	16	̂	̂	X
american_scientific_journal-4187	66	17	)	)	PUNCT
american_scientific_journal-4187	66	18	as	as	ADP
american_scientific_journal-4187	66	19	a	a	DET
american_scientific_journal-4187	66	20	result	result	NOUN
american_scientific_journal-4187	66	21	,	,	PUNCT
american_scientific_journal-4187	66	22	we	we	PRON
american_scientific_journal-4187	66	23	can	can	AUX
american_scientific_journal-4187	66	24	write	write	VERB
american_scientific_journal-4187	66	25	down	down	ADP
american_scientific_journal-4187	66	26	the	the	DET
american_scientific_journal-4187	66	27	following	follow	VERB
american_scientific_journal-4187	66	28	conditions	condition	NOUN
american_scientific_journal-4187	66	29	:	:	PUNCT
american_scientific_journal-4187	66	30	american	american	ADJ
american_scientific_journal-4187	66	31	scientific	scientific	ADJ
american_scientific_journal-4187	66	32	research	research	PROPN
american_scientific_journal-4187	66	33	journal	journal	NOUN
american_scientific_journal-4187	66	34	for	for	ADP
american_scientific_journal-4187	66	35	engineering	engineering	NOUN
american_scientific_journal-4187	66	36	,	,	PUNCT
american_scientific_journal-4187	66	37	technology	technology	NOUN
american_scientific_journal-4187	66	38	,	,	PUNCT
american_scientific_journal-4187	66	39	and	and	CCONJ
american_scientific_journal-4187	66	40	sciences	science	NOUN
american_scientific_journal-4187	66	41	(	(	PUNCT
american_scientific_journal-4187	66	42	asrjets	asrjet	NOUN
american_scientific_journal-4187	66	43	)	)	PUNCT
american_scientific_journal-4187	66	44	(	(	PUNCT
american_scientific_journal-4187	66	45	2019	2019	NUM
american_scientific_journal-4187	66	46	)	)	PUNCT
american_scientific_journal-4187	66	47	volume	volume	NOUN
american_scientific_journal-4187	66	48	59	59	NUM
american_scientific_journal-4187	66	49	,	,	PUNCT
american_scientific_journal-4187	66	50	no	no	DET
american_scientific_journal-4187	66	51	1	1	NUM
american_scientific_journal-4187	66	52	,	,	PUNCT
american_scientific_journal-4187	66	53	pp	pp	ADV
american_scientific_journal-4187	66	54	162	162	NUM
american_scientific_journal-4187	66	55	-	-	SYM
american_scientific_journal-4187	66	56	178	178	NUM
american_scientific_journal-4187	66	57	169	169	NUM
american_scientific_journal-4187	66	58	(	(	PUNCT
american_scientific_journal-4187	66	59	(	(	PUNCT
american_scientific_journal-4187	66	60	[	[	PUNCT
american_scientific_journal-4187	66	61	(	(	PUNCT
american_scientific_journal-4187	66	62	̂	̂	X
american_scientific_journal-4187	66	63	(	(	PUNCT
american_scientific_journal-4187	66	64	]	]	PUNCT
american_scientific_journal-4187	66	65	(	(	PUNCT
american_scientific_journal-4187	66	66	[	[	PUNCT
american_scientific_journal-4187	66	67	(	(	PUNCT
american_scientific_journal-4187	66	68	̂	̂	X
american_scientific_journal-4187	66	69	)	)	PUNCT
american_scientific_journal-4187	66	70	]	]	PUNCT
american_scientific_journal-4187	66	71	according	accord	VERB
american_scientific_journal-4187	66	72	to	to	ADP
american_scientific_journal-4187	66	73	the	the	DET
american_scientific_journal-4187	66	74	inequality	inequality	NOUN
american_scientific_journal-4187	66	75	and	and	CCONJ
american_scientific_journal-4187	66	76	the	the	DET
american_scientific_journal-4187	66	77	features	feature	NOUN
american_scientific_journal-4187	66	78	of	of	ADP
american_scientific_journal-4187	66	79	(	(	PUNCT
american_scientific_journal-4187	66	80	7	7	NUM
american_scientific_journal-4187	66	81	)	)	PUNCT
american_scientific_journal-4187	66	82	and	and	CCONJ
american_scientific_journal-4187	66	83	(	(	PUNCT
american_scientific_journal-4187	66	84	8)	8)	NUM
american_scientific_journal-4187	66	85	and	and	CCONJ
american_scientific_journal-4187	66	86	(	(	PUNCT
american_scientific_journal-4187	66	87	9	9	NUM
american_scientific_journal-4187	66	88	)	)	PUNCT
american_scientific_journal-4187	66	89	and	and	CCONJ
american_scientific_journal-4187	66	90	(	(	PUNCT
american_scientific_journal-4187	66	91	10	10	NUM
american_scientific_journal-4187	66	92	)	)	PUNCT
american_scientific_journal-4187	66	93	and	and	CCONJ
american_scientific_journal-4187	66	94	due	due	ADP
american_scientific_journal-4187	66	95	to	to	ADP
american_scientific_journal-4187	66	96	the	the	DET
american_scientific_journal-4187	66	97	function	function	NOUN
american_scientific_journal-4187	66	98	has	have	VERB
american_scientific_journal-4187	66	99	*	*	NOUN
american_scientific_journal-4187	66	100	*	*	ADJ
american_scientific_journal-4187	66	101	(	(	PUNCT
american_scientific_journal-4187	66	102	)	)	PUNCT
american_scientific_journal-4187	66	103	feature	feature	NOUN
american_scientific_journal-4187	66	104	,	,	PUNCT
american_scientific_journal-4187	66	105	so	so	SCONJ
american_scientific_journal-4187	66	106	we	we	PRON
american_scientific_journal-4187	66	107	can	can	AUX
american_scientific_journal-4187	66	108	write	write	VERB
american_scientific_journal-4187	66	109	as	as	ADP
american_scientific_journal-4187	66	110	follow	follow	VERB
american_scientific_journal-4187	66	111	:	:	PUNCT
american_scientific_journal-4187	66	112	𝜇	𝜇	X
american_scientific_journal-4187	66	113	(	(	PUNCT
american_scientific_journal-4187	66	114	𝜇	𝜇	X
american_scientific_journal-4187	66	115	(	(	PUNCT
american_scientific_journal-4187	66	116	(	(	PUNCT
american_scientific_journal-4187	66	117	(	(	PUNCT
american_scientific_journal-4187	66	118	[	[	PUNCT
american_scientific_journal-4187	66	119	(	(	PUNCT
american_scientific_journal-4187	66	120	̂	̂	X
american_scientific_journal-4187	66	121	(	(	PUNCT
american_scientific_journal-4187	66	122	]	]	PUNCT
american_scientific_journal-4187	66	123	(	(	PUNCT
american_scientific_journal-4187	66	124	[	[	PUNCT
american_scientific_journal-4187	66	125	(	(	PUNCT
american_scientific_journal-4187	66	126	̂	̂	PROPN
american_scientific_journal-4187	66	127	)	)	PUNCT
american_scientific_journal-4187	66	128	]	]	PUNCT
american_scientific_journal-4187	67	1	(	(	PUNCT
american_scientific_journal-4187	67	2	(	(	PUNCT
american_scientific_journal-4187	67	3	(	(	PUNCT
american_scientific_journal-4187	67	4	̂	̂	X
american_scientific_journal-4187	67	5	)	)	PUNCT
american_scientific_journal-4187	67	6	(	(	PUNCT
american_scientific_journal-4187	67	7	[	[	X
american_scientific_journal-4187	67	8	(	(	PUNCT
american_scientific_journal-4187	67	9	(	(	PUNCT
american_scientific_journal-4187	67	10	(	(	PUNCT
american_scientific_journal-4187	67	11	̂	̂	X
american_scientific_journal-4187	67	12	)	)	PUNCT
american_scientific_journal-4187	67	13	(	(	PUNCT
american_scientific_journal-4187	67	14	(	(	PUNCT
american_scientific_journal-4187	67	15	(	(	PUNCT
american_scientific_journal-4187	67	16	(	(	PUNCT
american_scientific_journal-4187	67	17	̂	̂	X
american_scientific_journal-4187	67	18	)	)	PUNCT
american_scientific_journal-4187	67	19	(	(	PUNCT
american_scientific_journal-4187	67	20	]	]	PUNCT
american_scientific_journal-4187	67	21	*	*	PUNCT
american_scientific_journal-4187	67	22	(	(	PUNCT
american_scientific_journal-4187	67	23	(	(	PUNCT
american_scientific_journal-4187	67	24	(	(	PUNCT
american_scientific_journal-4187	67	25	̂	̂	PROPN
american_scientific_journal-4187	67	26	)	)	PUNCT
american_scientific_journal-4187	67	27	)	)	PUNCT
american_scientific_journal-4187	67	28	(	(	PUNCT
american_scientific_journal-4187	67	29	+	+	X
american_scientific_journal-4187	67	30	(	(	PUNCT
american_scientific_journal-4187	67	31	(	(	PUNCT
american_scientific_journal-4187	67	32	(	(	PUNCT
american_scientific_journal-4187	67	33	̂	̂	PROPN
american_scientific_journal-4187	67	34	)	)	PUNCT
american_scientific_journal-4187	67	35	)	)	PUNCT
american_scientific_journal-4187	67	36	(	(	PUNCT
american_scientific_journal-4187	67	37	(	(	PUNCT
american_scientific_journal-4187	67	38	(	(	PUNCT
american_scientific_journal-4187	67	39	𝜇	𝜇	X
american_scientific_journal-4187	67	40	(	(	PUNCT
american_scientific_journal-4187	67	41	notice.let	notice.let	PROPN
american_scientific_journal-4187	67	42	’s	’s	PART
american_scientific_journal-4187	67	43	think	think	VERB
american_scientific_journal-4187	67	44	𝝆	𝝆	X
american_scientific_journal-4187	67	45	(	(	PUNCT
american_scientific_journal-4187	67	46	(	(	PUNCT
american_scientific_journal-4187	67	47	is	be	AUX
american_scientific_journal-4187	67	48	a	a	DET
american_scientific_journal-4187	67	49	dependable	dependable	ADJ
american_scientific_journal-4187	67	50	value	value	NOUN
american_scientific_journal-4187	67	51	measure	measure	NOUN
american_scientific_journal-4187	67	52	.	.	PUNCT
american_scientific_journal-4187	68	1	in	in	ADP
american_scientific_journal-4187	68	2	this	this	DET
american_scientific_journal-4187	68	3	case	case	NOUN
american_scientific_journal-4187	68	4	,	,	PUNCT
american_scientific_journal-4187	68	5	we	we	PRON
american_scientific_journal-4187	68	6	can	can	AUX
american_scientific_journal-4187	68	7	put	put	VERB
american_scientific_journal-4187	68	8	(	(	PUNCT
american_scientific_journal-4187	68	9	√	√	PUNCT
american_scientific_journal-4187	68	10	function	function	NOUN
american_scientific_journal-4187	68	11	instead	instead	ADV
american_scientific_journal-4187	68	12	of	of	ADP
american_scientific_journal-4187	68	13	.	.	PUNCT
american_scientific_journal-4187	69	1	as	as	ADP
american_scientific_journal-4187	69	2	a	a	DET
american_scientific_journal-4187	69	3	summary	summary	NOUN
american_scientific_journal-4187	69	4	,	,	PUNCT
american_scientific_journal-4187	69	5	the	the	DET
american_scientific_journal-4187	69	6	resulting	result	VERB
american_scientific_journal-4187	69	7	function	function	NOUN
american_scientific_journal-4187	69	8	is	be	AUX
american_scientific_journal-4187	69	9	no	no	DET
american_scientific_journal-4187	69	10	dependable	dependable	ADJ
american_scientific_journal-4187	69	11	value	value	NOUN
american_scientific_journal-4187	69	12	measure	measure	NOUN
american_scientific_journal-4187	69	13	.	.	PUNCT
american_scientific_journal-4187	70	1	(	(	PUNCT
american_scientific_journal-4187	70	2	√	√	NUM
american_scientific_journal-4187	70	3	)	)	PUNCT
american_scientific_journal-4187	70	4	√	√	PROPN
american_scientific_journal-4187	70	5	(	(	PUNCT
american_scientific_journal-4187	70	6	that	that	PRON
american_scientific_journal-4187	70	7	’s	’	VERB
american_scientific_journal-4187	70	8	why	why	SCONJ
american_scientific_journal-4187	70	9	it	it	PRON
american_scientific_journal-4187	70	10	can	can	AUX
american_scientific_journal-4187	70	11	prove	prove	VERB
american_scientific_journal-4187	70	12	easily	easily	ADV
american_scientific_journal-4187	70	13	that	that	SCONJ
american_scientific_journal-4187	70	14	the	the	DET
american_scientific_journal-4187	70	15	following	follow	VERB
american_scientific_journal-4187	70	16	relation	relation	NOUN
american_scientific_journal-4187	70	17	is	be	AUX
american_scientific_journal-4187	70	18	established	establish	VERB
american_scientific_journal-4187	70	19	according	accord	VERB
american_scientific_journal-4187	70	20	to	to	ADP
american_scientific_journal-4187	70	21	the	the	DET
american_scientific_journal-4187	70	22	defined	define	VERB
american_scientific_journal-4187	70	23	function	function	NOUN
american_scientific_journal-4187	70	24	.	.	PUNCT
american_scientific_journal-4187	71	1	(	(	PUNCT
american_scientific_journal-4187	71	2	(	(	PUNCT
american_scientific_journal-4187	71	3	(	(	PUNCT
american_scientific_journal-4187	71	4	(	(	PUNCT
american_scientific_journal-4187	71	5	(	(	PUNCT
american_scientific_journal-4187	71	6	(	(	PUNCT
american_scientific_journal-4187	71	7	therefore	therefore	ADV
american_scientific_journal-4187	71	8	,	,	PUNCT
american_scientific_journal-4187	71	9	as	as	SCONJ
american_scientific_journal-4187	71	10	we	we	PRON
american_scientific_journal-4187	71	11	can	can	AUX
american_scientific_journal-4187	71	12	see	see	VERB
american_scientific_journal-4187	71	13	in	in	ADP
american_scientific_journal-4187	71	14	the	the	DET
american_scientific_journal-4187	71	15	example	example	NOUN
american_scientific_journal-4187	71	16	,	,	PUNCT
american_scientific_journal-4187	71	17	by	by	ADP
american_scientific_journal-4187	71	18	selecting	select	VERB
american_scientific_journal-4187	71	19	a	a	DET
american_scientific_journal-4187	71	20	function	function	NOUN
american_scientific_journal-4187	71	21	we	we	PRON
american_scientific_journal-4187	71	22	can	can	AUX
american_scientific_journal-4187	71	23	change	change	VERB
american_scientific_journal-4187	71	24	the	the	DET
american_scientific_journal-4187	71	25	direction	direction	NOUN
american_scientific_journal-4187	71	26	of	of	ADP
american_scientific_journal-4187	71	27	the	the	DET
american_scientific_journal-4187	71	28	inequality	inequality	NOUN
american_scientific_journal-4187	71	29	.	.	PUNCT
american_scientific_journal-4187	72	1	in	in	ADP
american_scientific_journal-4187	72	2	the	the	DET
american_scientific_journal-4187	72	3	following	following	NOUN
american_scientific_journal-4187	72	4	,	,	PUNCT
american_scientific_journal-4187	72	5	we	we	PRON
american_scientific_journal-4187	72	6	are	be	AUX
american_scientific_journal-4187	72	7	looking	look	VERB
american_scientific_journal-4187	72	8	for	for	ADP
american_scientific_journal-4187	72	9	the	the	DET
american_scientific_journal-4187	72	10	conditions	condition	NOUN
american_scientific_journal-4187	72	11	,	,	PUNCT
american_scientific_journal-4187	72	12	which	which	PRON
american_scientific_journal-4187	72	13	can	can	AUX
american_scientific_journal-4187	72	14	choose	choose	VERB
american_scientific_journal-4187	72	15	the	the	DET
american_scientific_journal-4187	72	16	functions	function	NOUN
american_scientific_journal-4187	72	17	that	that	PRON
american_scientific_journal-4187	72	18	do	do	AUX
american_scientific_journal-4187	72	19	n't	not	PART
american_scientific_journal-4187	72	20	change	change	VERB
american_scientific_journal-4187	72	21	by	by	ADP
american_scientific_journal-4187	72	22	placing	place	VERB
american_scientific_journal-4187	72	23	them	they	PRON
american_scientific_journal-4187	72	24	in	in	ADP
american_scientific_journal-4187	72	25	dependable	dependable	ADJ
american_scientific_journal-4187	72	26	value	value	NOUN
american_scientific_journal-4187	72	27	measure	measure	NOUN
american_scientific_journal-4187	72	28	of	of	ADP
american_scientific_journal-4187	72	29	inequality	inequality	NOUN
american_scientific_journal-4187	72	30	.	.	PUNCT
american_scientific_journal-4187	73	1	theorem	theorem	VERB
american_scientific_journal-4187	73	2	5.let	5.let	PROPN
american_scientific_journal-4187	73	3	’s	’s	PART
american_scientific_journal-4187	73	4	imagine	imagine	NOUN
american_scientific_journal-4187	73	5	is	be	AUX
american_scientific_journal-4187	73	6	dependable	dependable	ADJ
american_scientific_journal-4187	73	7	value	value	NOUN
american_scientific_journal-4187	73	8	measure	measure	NOUN
american_scientific_journal-4187	73	9	under	under	ADP
american_scientific_journal-4187	73	10	binary	binary	ADJ
american_scientific_journal-4187	73	11	operations	operation	NOUN
american_scientific_journal-4187	73	12	(	(	PUNCT
american_scientific_journal-4187	73	13	.	.	PUNCT
american_scientific_journal-4187	74	1	also	also	ADV
american_scientific_journal-4187	74	2	,	,	PUNCT
american_scientific_journal-4187	74	3	if	if	SCONJ
american_scientific_journal-4187	74	4	we	we	PRON
american_scientific_journal-4187	74	5	have	have	VERB
american_scientific_journal-4187	74	6	non	non	ADJ
american_scientific_journal-4187	74	7	-	-	ADJ
american_scientific_journal-4187	74	8	negative	negative	ADJ
american_scientific_journal-4187	74	9	function	function	NOUN
american_scientific_journal-4187	74	10	and	and	CCONJ
american_scientific_journal-4187	74	11	binary	binary	ADJ
american_scientific_journal-4187	74	12	operations	operation	NOUN
american_scientific_journal-4187	74	13	such	such	ADJ
american_scientific_journal-4187	74	14	that	that	PRON
american_scientific_journal-4187	74	15	:	:	PUNCT
american_scientific_journal-4187	74	16	(	(	PUNCT
american_scientific_journal-4187	74	17	(	(	PUNCT
american_scientific_journal-4187	74	18	(	(	PUNCT
american_scientific_journal-4187	74	19	(	(	PUNCT
american_scientific_journal-4187	74	20	(	(	PUNCT
american_scientific_journal-4187	74	21	then	then	ADV
american_scientific_journal-4187	74	22	function	function	VERB
american_scientific_journal-4187	74	23	𝜇	𝜇	ADP
american_scientific_journal-4187	74	24	which	which	PRON
american_scientific_journal-4187	74	25	define	define	NOUN
american_scientific_journal-4187	74	26	as	as	ADP
american_scientific_journal-4187	74	27	follow	follow	NOUN
american_scientific_journal-4187	74	28	is	be	AUX
american_scientific_journal-4187	74	29	also	also	ADV
american_scientific_journal-4187	74	30	dependable	dependable	ADJ
american_scientific_journal-4187	74	31	value	value	NOUN
american_scientific_journal-4187	74	32	measure	measure	NOUN
american_scientific_journal-4187	74	33	under	under	ADP
american_scientific_journal-4187	74	34	binary	binary	ADJ
american_scientific_journal-4187	74	35	operations	operation	NOUN
american_scientific_journal-4187	74	36	(	(	PUNCT
american_scientific_journal-4187	74	37	.	.	PUNCT
american_scientific_journal-4187	75	1	american	american	PROPN
american_scientific_journal-4187	75	2	scientific	scientific	ADJ
american_scientific_journal-4187	75	3	research	research	PROPN
american_scientific_journal-4187	75	4	journal	journal	NOUN
american_scientific_journal-4187	75	5	for	for	ADP
american_scientific_journal-4187	75	6	engineering	engineering	NOUN
american_scientific_journal-4187	75	7	,	,	PUNCT
american_scientific_journal-4187	75	8	technology	technology	NOUN
american_scientific_journal-4187	75	9	,	,	PUNCT
american_scientific_journal-4187	75	10	and	and	CCONJ
american_scientific_journal-4187	75	11	sciences	science	NOUN
american_scientific_journal-4187	75	12	(	(	PUNCT
american_scientific_journal-4187	75	13	asrjets	asrjet	NOUN
american_scientific_journal-4187	75	14	)	)	PUNCT
american_scientific_journal-4187	75	15	(	(	PUNCT
american_scientific_journal-4187	75	16	2019	2019	NUM
american_scientific_journal-4187	75	17	)	)	PUNCT
american_scientific_journal-4187	75	18	volume	volume	NOUN
american_scientific_journal-4187	75	19	59	59	NUM
american_scientific_journal-4187	75	20	,	,	PUNCT
american_scientific_journal-4187	75	21	no	no	DET
american_scientific_journal-4187	75	22	1	1	NUM
american_scientific_journal-4187	75	23	,	,	PUNCT
american_scientific_journal-4187	75	24	pp	pp	ADV
american_scientific_journal-4187	75	25	162	162	NUM
american_scientific_journal-4187	75	26	-	-	SYM
american_scientific_journal-4187	75	27	178	178	NUM
american_scientific_journal-4187	75	28	170	170	NUM
american_scientific_journal-4187	75	29	𝜇	𝜇	ADP
american_scientific_journal-4187	75	30	(	(	PUNCT
american_scientific_journal-4187	75	31	(	(	PUNCT
american_scientific_journal-4187	75	32	(	(	PUNCT
american_scientific_journal-4187	75	33	proof.it	proof.it	PRON
american_scientific_journal-4187	75	34	is	be	AUX
american_scientific_journal-4187	75	35	sufficient	sufficient	ADJ
american_scientific_journal-4187	75	36	to	to	PART
american_scientific_journal-4187	75	37	prove	prove	VERB
american_scientific_journal-4187	75	38	features	feature	NOUN
american_scientific_journal-4187	75	39	.	.	PUNCT
american_scientific_journal-4187	76	1	𝜇	𝜇	ADP
american_scientific_journal-4187	76	2	(	(	PUNCT
american_scientific_journal-4187	76	3	𝜇	𝜇	X
american_scientific_journal-4187	76	4	(	(	PUNCT
american_scientific_journal-4187	76	5	𝜇	𝜇	X
american_scientific_journal-4187	76	6	(	(	PUNCT
american_scientific_journal-4187	76	7	𝜇	𝜇	X
american_scientific_journal-4187	76	8	(	(	PUNCT
american_scientific_journal-4187	76	9	(	(	PUNCT
american_scientific_journal-4187	76	10	(	(	PUNCT
american_scientific_journal-4187	76	11	(	(	PUNCT
american_scientific_journal-4187	76	12	(	(	PUNCT
american_scientific_journal-4187	76	13	(	(	PUNCT
american_scientific_journal-4187	76	14	(	(	PUNCT
american_scientific_journal-4187	76	15	(	(	PUNCT
american_scientific_journal-4187	76	16	(	(	PUNCT
american_scientific_journal-4187	76	17	(	(	PUNCT
american_scientific_journal-4187	76	18	𝜇	𝜇	X
american_scientific_journal-4187	76	19	(	(	PUNCT
american_scientific_journal-4187	76	20	corollary	corollary	ADJ
american_scientific_journal-4187	76	21	.	.	PUNCT
american_scientific_journal-4187	77	1	let	let	VERB
american_scientific_journal-4187	77	2	’s	’s	NOUN
american_scientific_journal-4187	77	3	think	think	VERB
american_scientific_journal-4187	77	4	is	be	AUX
american_scientific_journal-4187	77	5	dependable	dependable	ADJ
american_scientific_journal-4187	77	6	value	value	NOUN
american_scientific_journal-4187	77	7	measure	measure	NOUN
american_scientific_journal-4187	77	8	.	.	PUNCT
american_scientific_journal-4187	78	1	in	in	ADP
american_scientific_journal-4187	78	2	addition	addition	NOUN
american_scientific_journal-4187	78	3	,	,	PUNCT
american_scientific_journal-4187	78	4	the	the	DET
american_scientific_journal-4187	78	5	negative	negative	ADJ
american_scientific_journal-4187	78	6	function	function	NOUN
american_scientific_journal-4187	78	7	satisfies	satisfie	NOUN
american_scientific_journal-4187	78	8	in	in	ADP
american_scientific_journal-4187	78	9	this	this	PRON
american_scientific_journal-4187	78	10	)	)	PUNCT
american_scientific_journal-4187	79	1	*	*	PUNCT
american_scientific_journal-4187	79	2	*	*	PUNCT
american_scientific_journal-4187	79	3	(	(	PUNCT
american_scientific_journal-4187	79	4	condition	condition	NOUN
american_scientific_journal-4187	79	5	.	.	PUNCT
american_scientific_journal-4187	80	1	in	in	ADP
american_scientific_journal-4187	80	2	this	this	DET
american_scientific_journal-4187	80	3	case	case	NOUN
american_scientific_journal-4187	80	4	,	,	PUNCT
american_scientific_journal-4187	80	5	the	the	DET
american_scientific_journal-4187	80	6	function	function	NOUN
american_scientific_journal-4187	80	7	can	can	AUX
american_scientific_journal-4187	80	8	define	define	VERB
american_scientific_journal-4187	80	9	as	as	ADP
american_scientific_journal-4187	80	10	follow	follow	NOUN
american_scientific_journal-4187	80	11	,	,	PUNCT
american_scientific_journal-4187	80	12	which	which	PRON
american_scientific_journal-4187	80	13	is	be	AUX
american_scientific_journal-4187	80	14	a	a	DET
american_scientific_journal-4187	80	15	dependable	dependable	ADJ
american_scientific_journal-4187	80	16	value	value	NOUN
american_scientific_journal-4187	80	17	measure	measure	NOUN
american_scientific_journal-4187	80	18	.	.	PUNCT
american_scientific_journal-4187	81	1	(	(	PUNCT
american_scientific_journal-4187	81	2	(	(	PUNCT
american_scientific_journal-4187	81	3	(	(	PUNCT
american_scientific_journal-4187	81	4	for	for	ADP
american_scientific_journal-4187	81	5	example	example	NOUN
american_scientific_journal-4187	81	6	,	,	PUNCT
american_scientific_journal-4187	81	7	from	from	ADP
american_scientific_journal-4187	81	8	dependable	dependable	ADJ
american_scientific_journal-4187	81	9	value	value	NOUN
american_scientific_journal-4187	81	10	measure	measure	NOUN
american_scientific_journal-4187	81	11	of	of	ADP
american_scientific_journal-4187	81	12	,	,	PUNCT
american_scientific_journal-4187	81	13	we	we	PRON
american_scientific_journal-4187	81	14	can	can	AUX
american_scientific_journal-4187	81	15	make	make	VERB
american_scientific_journal-4187	81	16	following	follow	VERB
american_scientific_journal-4187	81	17	dependable	dependable	ADJ
american_scientific_journal-4187	81	18	value	value	NOUN
american_scientific_journal-4187	81	19	measure	measure	NOUN
american_scientific_journal-4187	81	20	:	:	PUNCT
american_scientific_journal-4187	81	21	(	(	PUNCT
american_scientific_journal-4187	81	22	(	(	PUNCT
american_scientific_journal-4187	81	23	)	)	PUNCT
american_scientific_journal-4187	81	24	we	we	PRON
american_scientific_journal-4187	81	25	can	can	AUX
american_scientific_journal-4187	81	26	easily	easily	ADV
american_scientific_journal-4187	81	27	recognize	recognize	VERB
american_scientific_journal-4187	81	28	that	that	DET
american_scientific_journal-4187	81	29	function	function	NOUN
american_scientific_journal-4187	81	30	(	(	PUNCT
american_scientific_journal-4187	81	31	can	can	AUX
american_scientific_journal-4187	81	32	satisfy	satisfy	VERB
american_scientific_journal-4187	81	33	)	)	PUNCT
american_scientific_journal-4187	81	34	*	*	PUNCT
american_scientific_journal-4187	82	1	*	*	PUNCT
american_scientific_journal-4187	82	2	(	(	PUNCT
american_scientific_journal-4187	82	3	condition	condition	NOUN
american_scientific_journal-4187	82	4	.	.	PUNCT
american_scientific_journal-4187	83	1	therefore	therefore	ADV
american_scientific_journal-4187	83	2	,	,	PUNCT
american_scientific_journal-4187	83	3	we	we	PRON
american_scientific_journal-4187	83	4	can	can	AUX
american_scientific_journal-4187	83	5	conclude	conclude	VERB
american_scientific_journal-4187	83	6	that	that	SCONJ
american_scientific_journal-4187	83	7	the	the	DET
american_scientific_journal-4187	83	8	function	function	NOUN
american_scientific_journal-4187	83	9	is	be	AUX
american_scientific_journal-4187	83	10	dependable	dependable	ADJ
american_scientific_journal-4187	83	11	value	value	NOUN
american_scientific_journal-4187	83	12	measure	measure	NOUN
american_scientific_journal-4187	83	13	.	.	PUNCT
american_scientific_journal-4187	84	1	theorem6.suppose	theorem6.suppose	PROPN
american_scientific_journal-4187	84	2	be	be	VERB
american_scientific_journal-4187	84	3	a	a	DET
american_scientific_journal-4187	84	4	dependable	dependable	ADJ
american_scientific_journal-4187	84	5	value	value	NOUN
american_scientific_journal-4187	84	6	measure	measure	NOUN
american_scientific_journal-4187	84	7	under	under	ADP
american_scientific_journal-4187	84	8	binary	binary	ADJ
american_scientific_journal-4187	84	9	operations	operation	NOUN
american_scientific_journal-4187	84	10	(	(	PUNCT
american_scientific_journal-4187	84	11	and	and	CCONJ
american_scientific_journal-4187	84	12	also	also	ADV
american_scientific_journal-4187	84	13	functions	function	NOUN
american_scientific_journal-4187	84	14	can	can	AUX
american_scientific_journal-4187	84	15	satisfy	satisfy	VERB
american_scientific_journal-4187	84	16	the	the	DET
american_scientific_journal-4187	84	17	condition	condition	NOUN
american_scientific_journal-4187	84	18	(	(	PUNCT
american_scientific_journal-4187	84	19	(	(	PUNCT
american_scientific_journal-4187	84	20	(	(	PUNCT
american_scientific_journal-4187	84	21	(	(	PUNCT
american_scientific_journal-4187	84	22	(	(	PUNCT
american_scientific_journal-4187	84	23	in	in	ADP
american_scientific_journal-4187	84	24	addition	addition	NOUN
american_scientific_journal-4187	84	25	,	,	PUNCT
american_scientific_journal-4187	84	26	due	due	ADP
american_scientific_journal-4187	84	27	to	to	ADP
american_scientific_journal-4187	84	28	the	the	DET
american_scientific_journal-4187	84	29	binary	binary	ADJ
american_scientific_journal-4187	84	30	operations	operation	NOUN
american_scientific_journal-4187	84	31	(	(	PUNCT
american_scientific_journal-4187	84	32	,	,	PUNCT
american_scientific_journal-4187	84	33	we	we	PRON
american_scientific_journal-4187	84	34	have	have	AUX
american_scientific_journal-4187	84	35	the	the	DET
american_scientific_journal-4187	84	36	following	follow	VERB
american_scientific_journal-4187	84	37	relations	relation	NOUN
american_scientific_journal-4187	84	38	:	:	PUNCT
american_scientific_journal-4187	84	39	(	(	PUNCT
american_scientific_journal-4187	84	40	(	(	PUNCT
american_scientific_journal-4187	84	41	(	(	PUNCT
american_scientific_journal-4187	84	42	(	(	PUNCT
american_scientific_journal-4187	84	43	(	(	PUNCT
american_scientific_journal-4187	84	44	(	(	PUNCT
american_scientific_journal-4187	84	45	(	(	PUNCT
american_scientific_journal-4187	84	46	(	(	PUNCT
american_scientific_journal-4187	84	47	(	(	PUNCT
american_scientific_journal-4187	84	48	(	(	PUNCT
american_scientific_journal-4187	84	49	(	(	PUNCT
american_scientific_journal-4187	84	50	)	)	PUNCT
american_scientific_journal-4187	84	51	(	(	PUNCT
american_scientific_journal-4187	84	52	(	(	PUNCT
american_scientific_journal-4187	84	53	(	(	PUNCT
american_scientific_journal-4187	84	54	(	(	PUNCT
american_scientific_journal-4187	84	55	(	(	PUNCT
american_scientific_journal-4187	84	56	(	(	PUNCT
american_scientific_journal-4187	84	57	(	(	PUNCT
american_scientific_journal-4187	84	58	(	(	PUNCT
american_scientific_journal-4187	84	59	(	(	PUNCT
american_scientific_journal-4187	84	60	(	(	PUNCT
american_scientific_journal-4187	84	61	(	(	PUNCT
american_scientific_journal-4187	84	62	)	)	PUNCT
american_scientific_journal-4187	84	63	(	(	PUNCT
american_scientific_journal-4187	84	64	in	in	ADP
american_scientific_journal-4187	84	65	this	this	DET
american_scientific_journal-4187	84	66	case	case	NOUN
american_scientific_journal-4187	84	67	,	,	PUNCT
american_scientific_journal-4187	84	68	function	function	NOUN
american_scientific_journal-4187	84	69	𝜇	𝜇	SCONJ
american_scientific_journal-4187	84	70	can	can	AUX
american_scientific_journal-4187	84	71	define	define	VERB
american_scientific_journal-4187	84	72	as	as	ADP
american_scientific_journal-4187	84	73	follow	follow	NOUN
american_scientific_journal-4187	84	74	which	which	PRON
american_scientific_journal-4187	84	75	is	be	AUX
american_scientific_journal-4187	84	76	a	a	DET
american_scientific_journal-4187	84	77	dependable	dependable	ADJ
american_scientific_journal-4187	84	78	value	value	NOUN
american_scientific_journal-4187	84	79	measure	measure	NOUN
american_scientific_journal-4187	84	80	under	under	ADP
american_scientific_journal-4187	84	81	binary	binary	ADJ
american_scientific_journal-4187	84	82	operations	operation	NOUN
american_scientific_journal-4187	84	83	(	(	PUNCT
american_scientific_journal-4187	84	84	.	.	PUNCT
american_scientific_journal-4187	85	1	𝜇	𝜇	X
american_scientific_journal-4187	85	2	(	(	PUNCT
american_scientific_journal-4187	85	3	(	(	PUNCT
american_scientific_journal-4187	85	4	(	(	PUNCT
american_scientific_journal-4187	85	5	(	(	PUNCT
american_scientific_journal-4187	85	6	(	(	PUNCT
american_scientific_journal-4187	85	7	proof.according	proof.accorde	VERB
american_scientific_journal-4187	85	8	to	to	PART
american_scientific_journal-4187	85	9	feature	feature	VERB
american_scientific_journal-4187	85	10	(	(	PUNCT
american_scientific_journal-4187	85	11	11	11	NUM
american_scientific_journal-4187	85	12	)	)	PUNCT
american_scientific_journal-4187	85	13	,	,	PUNCT
american_scientific_journal-4187	85	14	we	we	PRON
american_scientific_journal-4187	85	15	conclude	conclude	VERB
american_scientific_journal-4187	85	16	as	as	SCONJ
american_scientific_journal-4187	85	17	follow	follow	VERB
american_scientific_journal-4187	85	18	:	:	PUNCT
american_scientific_journal-4187	85	19	𝜇	𝜇	X
american_scientific_journal-4187	85	20	(	(	PUNCT
american_scientific_journal-4187	85	21	(	(	PUNCT
american_scientific_journal-4187	85	22	(	(	PUNCT
american_scientific_journal-4187	85	23	(	(	PUNCT
american_scientific_journal-4187	85	24	(	(	PUNCT
american_scientific_journal-4187	85	25	american	american	ADJ
american_scientific_journal-4187	85	26	scientific	scientific	ADJ
american_scientific_journal-4187	85	27	research	research	NOUN
american_scientific_journal-4187	85	28	journal	journal	NOUN
american_scientific_journal-4187	85	29	for	for	ADP
american_scientific_journal-4187	85	30	engineering	engineering	NOUN
american_scientific_journal-4187	85	31	,	,	PUNCT
american_scientific_journal-4187	85	32	technology	technology	NOUN
american_scientific_journal-4187	85	33	,	,	PUNCT
american_scientific_journal-4187	85	34	and	and	CCONJ
american_scientific_journal-4187	85	35	sciences	science	NOUN
american_scientific_journal-4187	85	36	(	(	PUNCT
american_scientific_journal-4187	85	37	asrjets	asrjet	NOUN
american_scientific_journal-4187	85	38	)	)	PUNCT
american_scientific_journal-4187	85	39	(	(	PUNCT
american_scientific_journal-4187	85	40	2019	2019	NUM
american_scientific_journal-4187	85	41	)	)	PUNCT
american_scientific_journal-4187	85	42	volume	volume	NOUN
american_scientific_journal-4187	85	43	59	59	NUM
american_scientific_journal-4187	85	44	,	,	PUNCT
american_scientific_journal-4187	85	45	no	no	DET
american_scientific_journal-4187	85	46	1	1	NUM
american_scientific_journal-4187	85	47	,	,	PUNCT
american_scientific_journal-4187	85	48	pp	pp	ADV
american_scientific_journal-4187	85	49	162	162	NUM
american_scientific_journal-4187	85	50	-	-	SYM
american_scientific_journal-4187	85	51	178	178	NUM
american_scientific_journal-4187	85	52	171	171	NUM
american_scientific_journal-4187	85	53	now	now	ADV
american_scientific_journal-4187	85	54	to	to	PART
american_scientific_journal-4187	85	55	continue	continue	VERB
american_scientific_journal-4187	85	56	,	,	PUNCT
american_scientific_journal-4187	85	57	we	we	PRON
american_scientific_journal-4187	85	58	prove	prove	VERB
american_scientific_journal-4187	85	59	the	the	DET
american_scientific_journal-4187	85	60	first	first	ADJ
american_scientific_journal-4187	85	61	feature	feature	NOUN
american_scientific_journal-4187	85	62	.	.	PUNCT
american_scientific_journal-4187	86	1	𝜇	𝜇	ADP
american_scientific_journal-4187	86	2	(	(	PUNCT
american_scientific_journal-4187	86	3	(	(	PUNCT
american_scientific_journal-4187	86	4	(	(	PUNCT
american_scientific_journal-4187	86	5	(	(	PUNCT
american_scientific_journal-4187	86	6	(	(	PUNCT
american_scientific_journal-4187	86	7	(	(	PUNCT
american_scientific_journal-4187	86	8	(	(	PUNCT
american_scientific_journal-4187	86	9	(	(	PUNCT
american_scientific_journal-4187	86	10	(	(	PUNCT
american_scientific_journal-4187	86	11	(	(	PUNCT
american_scientific_journal-4187	86	12	(	(	PUNCT
american_scientific_journal-4187	86	13	(	(	PUNCT
american_scientific_journal-4187	86	14	(	(	PUNCT
american_scientific_journal-4187	86	15	(	(	PUNCT
american_scientific_journal-4187	86	16	(	(	PUNCT
american_scientific_journal-4187	86	17	(	(	PUNCT
american_scientific_journal-4187	86	18	(	(	PUNCT
american_scientific_journal-4187	86	19	(	(	PUNCT
american_scientific_journal-4187	86	20	)	)	PUNCT
american_scientific_journal-4187	86	21	(	(	PUNCT
american_scientific_journal-4187	86	22	(	(	PUNCT
american_scientific_journal-4187	86	23	(	(	PUNCT
american_scientific_journal-4187	86	24	(	(	PUNCT
american_scientific_journal-4187	86	25	(	(	PUNCT
american_scientific_journal-4187	86	26	𝜇	𝜇	X
american_scientific_journal-4187	86	27	(	(	PUNCT
american_scientific_journal-4187	86	28	𝜇	𝜇	X
american_scientific_journal-4187	86	29	(	(	PUNCT
american_scientific_journal-4187	86	30	now	now	ADV
american_scientific_journal-4187	86	31	to	to	PART
american_scientific_journal-4187	86	32	prove	prove	VERB
american_scientific_journal-4187	86	33	the	the	DET
american_scientific_journal-4187	86	34	second	second	ADJ
american_scientific_journal-4187	86	35	feature	feature	NOUN
american_scientific_journal-4187	86	36	,	,	PUNCT
american_scientific_journal-4187	86	37	due	due	ADP
american_scientific_journal-4187	86	38	to	to	ADP
american_scientific_journal-4187	86	39	the	the	DET
american_scientific_journal-4187	86	40	inequalities	inequality	NOUN
american_scientific_journal-4187	86	41	(	(	PUNCT
american_scientific_journal-4187	86	42	12	12	NUM
american_scientific_journal-4187	86	43	)	)	PUNCT
american_scientific_journal-4187	86	44	and	and	CCONJ
american_scientific_journal-4187	86	45	(	(	PUNCT
american_scientific_journal-4187	86	46	13	13	NUM
american_scientific_journal-4187	86	47	)	)	PUNCT
american_scientific_journal-4187	86	48	,	,	PUNCT
american_scientific_journal-4187	86	49	we	we	PRON
american_scientific_journal-4187	86	50	have	have	AUX
american_scientific_journal-4187	86	51	as	as	ADV
american_scientific_journal-4187	86	52	follow	follow	AUX
american_scientific_journal-4187	86	53	:	:	PUNCT
american_scientific_journal-4187	86	54	𝜇	𝜇	X
american_scientific_journal-4187	86	55	(	(	PUNCT
american_scientific_journal-4187	86	56	𝜇	𝜇	X
american_scientific_journal-4187	86	57	(	(	PUNCT
american_scientific_journal-4187	86	58	(	(	PUNCT
american_scientific_journal-4187	86	59	(	(	PUNCT
american_scientific_journal-4187	86	60	(	(	PUNCT
american_scientific_journal-4187	86	61	(	(	PUNCT
american_scientific_journal-4187	86	62	(	(	PUNCT
american_scientific_journal-4187	86	63	)	)	PUNCT
american_scientific_journal-4187	86	64	(	(	PUNCT
american_scientific_journal-4187	86	65	(	(	PUNCT
american_scientific_journal-4187	86	66	(	(	PUNCT
american_scientific_journal-4187	86	67	(	(	PUNCT
american_scientific_journal-4187	86	68	(	(	PUNCT
american_scientific_journal-4187	86	69	(	(	PUNCT
american_scientific_journal-4187	86	70	(	(	PUNCT
american_scientific_journal-4187	86	71	(	(	PUNCT
american_scientific_journal-4187	86	72	(	(	PUNCT
american_scientific_journal-4187	86	73	(	(	PUNCT
american_scientific_journal-4187	86	74	(	(	PUNCT
american_scientific_journal-4187	86	75	)	)	PUNCT
american_scientific_journal-4187	86	76	(	(	PUNCT
american_scientific_journal-4187	86	77	(	(	PUNCT
american_scientific_journal-4187	86	78	(	(	PUNCT
american_scientific_journal-4187	86	79	(	(	PUNCT
american_scientific_journal-4187	86	80	(	(	PUNCT
american_scientific_journal-4187	86	81	)	)	PUNCT
american_scientific_journal-4187	86	82	(	(	PUNCT
american_scientific_journal-4187	86	83	(	(	PUNCT
american_scientific_journal-4187	86	84	(	(	PUNCT
american_scientific_journal-4187	86	85	(	(	PUNCT
american_scientific_journal-4187	86	86	(	(	PUNCT
american_scientific_journal-4187	86	87	(	(	PUNCT
american_scientific_journal-4187	86	88	𝜇	𝜇	X
american_scientific_journal-4187	86	89	(	(	PUNCT
american_scientific_journal-4187	86	90	notice.a	notice.a	ADJ
american_scientific_journal-4187	86	91	sufficient	sufficient	ADJ
american_scientific_journal-4187	86	92	condition	condition	NOUN
american_scientific_journal-4187	86	93	for	for	ADP
american_scientific_journal-4187	86	94	the	the	DET
american_scientific_journal-4187	86	95	inequality	inequality	NOUN
american_scientific_journal-4187	86	96	(	(	PUNCT
american_scientific_journal-4187	86	97	13	13	NUM
american_scientific_journal-4187	86	98	)	)	PUNCT
american_scientific_journal-4187	86	99	is	be	AUX
american_scientific_journal-4187	86	100	that	that	SCONJ
american_scientific_journal-4187	86	101	functions	function	NOUN
american_scientific_journal-4187	86	102	has	have	VERB
american_scientific_journal-4187	86	103	the	the	DET
american_scientific_journal-4187	86	104	binary	binary	PROPN
american_scientific_journal-4187	86	105	operations	operation	NOUN
american_scientific_journal-4187	86	106	relations	relation	NOUN
american_scientific_journal-4187	86	107	(	(	PUNCT
american_scientific_journal-4187	86	108	:	:	PUNCT
american_scientific_journal-4187	86	109	(	(	PUNCT
american_scientific_journal-4187	86	110	(	(	PUNCT
american_scientific_journal-4187	86	111	(	(	PUNCT
american_scientific_journal-4187	86	112	(	(	PUNCT
american_scientific_journal-4187	86	113	(	(	PUNCT
american_scientific_journal-4187	86	114	(	(	PUNCT
american_scientific_journal-4187	86	115	)	)	PUNCT
american_scientific_journal-4187	86	116	(	(	PUNCT
american_scientific_journal-4187	86	117	(	(	PUNCT
american_scientific_journal-4187	86	118	(	(	PUNCT
american_scientific_journal-4187	86	119	(	(	PUNCT
american_scientific_journal-4187	86	120	(	(	PUNCT
american_scientific_journal-4187	86	121	(	(	PUNCT
american_scientific_journal-4187	86	122	(	(	PUNCT
american_scientific_journal-4187	86	123	(	(	PUNCT
american_scientific_journal-4187	86	124	(	(	PUNCT
american_scientific_journal-4187	86	125	)	)	PUNCT
american_scientific_journal-4187	87	1	(	(	PUNCT
american_scientific_journal-4187	87	2	(	(	PUNCT
american_scientific_journal-4187	87	3	(	(	PUNCT
american_scientific_journal-4187	87	4	(	(	PUNCT
american_scientific_journal-4187	87	5	theorem7.let	theorem7.let	X
american_scientific_journal-4187	87	6	’s	’s	NOUN
american_scientific_journal-4187	87	7	is	be	AUX
american_scientific_journal-4187	87	8	a	a	DET
american_scientific_journal-4187	87	9	dependable	dependable	ADJ
american_scientific_journal-4187	87	10	value	value	NOUN
american_scientific_journal-4187	87	11	measure	measure	NOUN
american_scientific_journal-4187	87	12	under	under	ADP
american_scientific_journal-4187	87	13	binary	binary	ADJ
american_scientific_journal-4187	87	14	operations	operation	NOUN
american_scientific_journal-4187	87	15	(	(	PUNCT
american_scientific_journal-4187	87	16	and	and	CCONJ
american_scientific_journal-4187	87	17	also	also	ADV
american_scientific_journal-4187	87	18	functions	function	VERB
american_scientific_journal-4187	87	19	satisfy	satisfy	VERB
american_scientific_journal-4187	87	20	on	on	ADP
american_scientific_journal-4187	87	21	(	(	PUNCT
american_scientific_journal-4187	87	22	11	11	NUM
american_scientific_journal-4187	87	23	)	)	PUNCT
american_scientific_journal-4187	87	24	and	and	CCONJ
american_scientific_journal-4187	87	25	(	(	PUNCT
american_scientific_journal-4187	87	26	12	12	NUM
american_scientific_journal-4187	87	27	)	)	PUNCT
american_scientific_journal-4187	87	28	and	and	CCONJ
american_scientific_journal-4187	87	29	(	(	PUNCT
american_scientific_journal-4187	87	30	14	14	NUM
american_scientific_journal-4187	87	31	)	)	PUNCT
american_scientific_journal-4187	87	32	and	and	CCONJ
american_scientific_journal-4187	87	33	(	(	PUNCT
american_scientific_journal-4187	87	34	15	15	NUM
american_scientific_journal-4187	87	35	)	)	PUNCT
american_scientific_journal-4187	87	36	conditions	condition	NOUN
american_scientific_journal-4187	87	37	.then	.then	AUX
american_scientific_journal-4187	87	38	function	function	VERB
american_scientific_journal-4187	87	39	𝝁	𝝁	PRON
american_scientific_journal-4187	87	40	can	can	AUX
american_scientific_journal-4187	87	41	define	define	VERB
american_scientific_journal-4187	87	42	as	as	ADP
american_scientific_journal-4187	87	43	a	a	DET
american_scientific_journal-4187	87	44	dependable	dependable	ADJ
american_scientific_journal-4187	87	45	value	value	NOUN
american_scientific_journal-4187	87	46	measure	measure	NOUN
american_scientific_journal-4187	87	47	under	under	ADP
american_scientific_journal-4187	87	48	binary	binary	ADJ
american_scientific_journal-4187	87	49	operations	operation	NOUN
american_scientific_journal-4187	87	50	(	(	PUNCT
american_scientific_journal-4187	87	51	.	.	PUNCT
american_scientific_journal-4187	88	1	𝜇	𝜇	X
american_scientific_journal-4187	88	2	(	(	PUNCT
american_scientific_journal-4187	88	3	(	(	PUNCT
american_scientific_journal-4187	88	4	(	(	PUNCT
american_scientific_journal-4187	88	5	(	(	PUNCT
american_scientific_journal-4187	88	6	(	(	PUNCT
american_scientific_journal-4187	88	7	example6.let	example6.let	NOUN
american_scientific_journal-4187	88	8	’s	’s	PART
american_scientific_journal-4187	88	9	think	think	VERB
american_scientific_journal-4187	88	10	that	that	PRON
american_scientific_journal-4187	88	11	is	be	AUX
american_scientific_journal-4187	88	12	a	a	DET
american_scientific_journal-4187	88	13	dependable	dependable	ADJ
american_scientific_journal-4187	88	14	value	value	NOUN
american_scientific_journal-4187	88	15	measure	measure	NOUN
american_scientific_journal-4187	88	16	under	under	ADP
american_scientific_journal-4187	88	17	binary	binary	ADJ
american_scientific_journal-4187	88	18	operations	operation	NOUN
american_scientific_journal-4187	88	19	(	(	PUNCT
american_scientific_journal-4187	88	20	which	which	PRON
american_scientific_journal-4187	88	21	define	define	VERB
american_scientific_journal-4187	88	22	by	by	ADP
american_scientific_journal-4187	88	23	following	follow	VERB
american_scientific_journal-4187	88	24	criterion	criterion	NOUN
american_scientific_journal-4187	88	25	.	.	PUNCT
american_scientific_journal-4187	89	1	(	(	PUNCT
american_scientific_journal-4187	89	2	(	(	PUNCT
american_scientific_journal-4187	89	3	in	in	ADP
american_scientific_journal-4187	89	4	addition	addition	NOUN
american_scientific_journal-4187	89	5	,	,	PUNCT
american_scientific_journal-4187	89	6	above	above	ADP
american_scientific_journal-4187	89	7	binary	binary	ADJ
american_scientific_journal-4187	89	8	operation	operation	NOUN
american_scientific_journal-4187	89	9	should	should	AUX
american_scientific_journal-4187	89	10	define	define	VERB
american_scientific_journal-4187	89	11	as	as	ADP
american_scientific_journal-4187	89	12	follow	follow	NOUN
american_scientific_journal-4187	89	13	:	:	PUNCT
american_scientific_journal-4187	89	14	in	in	ADP
american_scientific_journal-4187	89	15	this	this	DET
american_scientific_journal-4187	89	16	case	case	NOUN
american_scientific_journal-4187	89	17	,	,	PUNCT
american_scientific_journal-4187	89	18	𝜇	𝜇	ADP
american_scientific_journal-4187	89	19	which	which	PRON
american_scientific_journal-4187	89	20	define	define	NOUN
american_scientific_journal-4187	89	21	as	as	ADP
american_scientific_journal-4187	89	22	criterion	criterion	NOUN
american_scientific_journal-4187	89	23	is	be	AUX
american_scientific_journal-4187	89	24	a	a	DET
american_scientific_journal-4187	89	25	dependable	dependable	ADJ
american_scientific_journal-4187	89	26	value	value	NOUN
american_scientific_journal-4187	89	27	measure	measure	NOUN
american_scientific_journal-4187	89	28	under	under	ADP
american_scientific_journal-4187	89	29	binary	binary	ADJ
american_scientific_journal-4187	89	30	operations	operation	NOUN
american_scientific_journal-4187	89	31	american	american	PROPN
american_scientific_journal-4187	89	32	scientific	scientific	ADJ
american_scientific_journal-4187	89	33	research	research	NOUN
american_scientific_journal-4187	89	34	journal	journal	NOUN
american_scientific_journal-4187	89	35	for	for	ADP
american_scientific_journal-4187	89	36	engineering	engineering	NOUN
american_scientific_journal-4187	89	37	,	,	PUNCT
american_scientific_journal-4187	89	38	technology	technology	NOUN
american_scientific_journal-4187	89	39	,	,	PUNCT
american_scientific_journal-4187	89	40	and	and	CCONJ
american_scientific_journal-4187	89	41	sciences	science	NOUN
american_scientific_journal-4187	89	42	(	(	PUNCT
american_scientific_journal-4187	89	43	asrjets	asrjet	NOUN
american_scientific_journal-4187	89	44	)	)	PUNCT
american_scientific_journal-4187	89	45	(	(	PUNCT
american_scientific_journal-4187	89	46	2019	2019	NUM
american_scientific_journal-4187	89	47	)	)	PUNCT
american_scientific_journal-4187	89	48	volume	volume	NOUN
american_scientific_journal-4187	89	49	59	59	NUM
american_scientific_journal-4187	89	50	,	,	PUNCT
american_scientific_journal-4187	89	51	no	no	DET
american_scientific_journal-4187	89	52	1	1	NUM
american_scientific_journal-4187	89	53	,	,	PUNCT
american_scientific_journal-4187	89	54	pp	pp	ADV
american_scientific_journal-4187	89	55	162	162	NUM
american_scientific_journal-4187	89	56	-	-	SYM
american_scientific_journal-4187	89	57	178	178	NUM
american_scientific_journal-4187	89	58	172	172	NUM
american_scientific_journal-4187	89	59	(	(	PUNCT
american_scientific_journal-4187	89	60	.	.	PUNCT
american_scientific_journal-4187	90	1	𝜇	𝜇	X
american_scientific_journal-4187	90	2	(	(	PUNCT
american_scientific_journal-4187	90	3	(	(	PUNCT
american_scientific_journal-4187	90	4	(	(	PUNCT
american_scientific_journal-4187	90	5	notice.in	notice.in	X
american_scientific_journal-4187	90	6	the	the	DET
american_scientific_journal-4187	90	7	previous	previous	ADJ
american_scientific_journal-4187	90	8	theorem	theorem	NOUN
american_scientific_journal-4187	90	9	,	,	PUNCT
american_scientific_journal-4187	90	10	both	both	DET
american_scientific_journal-4187	90	11	conditions	condition	NOUN
american_scientific_journal-4187	90	12	are	be	AUX
american_scientific_journal-4187	90	13	compulsory	compulsory	ADJ
american_scientific_journal-4187	90	14	.	.	PUNCT
american_scientific_journal-4187	91	1	for	for	ADP
american_scientific_journal-4187	91	2	example	example	NOUN
american_scientific_journal-4187	91	3	,	,	PUNCT
american_scientific_journal-4187	91	4	you	you	PRON
american_scientific_journal-4187	91	5	can	can	AUX
american_scientific_journal-4187	91	6	consider	consider	VERB
american_scientific_journal-4187	91	7	the	the	DET
american_scientific_journal-4187	91	8	previous	previous	ADJ
american_scientific_journal-4187	91	9	example𝜇	example𝜇	NOUN
american_scientific_journal-4187	91	10	,	,	PUNCT
american_scientific_journal-4187	91	11	which	which	PRON
american_scientific_journal-4187	91	12	defined	define	VERB
american_scientific_journal-4187	91	13	by	by	ADP
american_scientific_journal-4187	91	14	below	below	ADP
american_scientific_journal-4187	91	15	criterion	criterion	NOUN
american_scientific_journal-4187	91	16	:	:	PUNCT
american_scientific_journal-4187	91	17	𝜇	𝜇	X
american_scientific_journal-4187	91	18	(	(	PUNCT
american_scientific_journal-4187	91	19	(	(	PUNCT
american_scientific_journal-4187	91	20	(	(	PUNCT
american_scientific_journal-4187	91	21	according	accord	VERB
american_scientific_journal-4187	91	22	to	to	ADP
american_scientific_journal-4187	91	23	the	the	DET
american_scientific_journal-4187	91	24	defined	define	VERB
american_scientific_journal-4187	91	25	criterion	criterion	NOUN
american_scientific_journal-4187	91	26	,	,	PUNCT
american_scientific_journal-4187	91	27	it	it	PRON
american_scientific_journal-4187	91	28	’s	’	VERB
american_scientific_journal-4187	91	29	clear	clear	ADJ
american_scientific_journal-4187	91	30	that	that	SCONJ
american_scientific_journal-4187	91	31	we	we	PRON
american_scientific_journal-4187	91	32	have	have	VERB
american_scientific_journal-4187	91	33	negative	negative	ADJ
american_scientific_journal-4187	91	34	number	number	NOUN
american_scientific_journal-4187	91	35	for	for	ADP
american_scientific_journal-4187	91	36	which	which	PRON
american_scientific_journal-4187	91	37	is	be	AUX
american_scientific_journal-4187	91	38	a	a	DET
american_scientific_journal-4187	91	39	result	result	NOUN
american_scientific_journal-4187	91	40	of	of	ADP
american_scientific_journal-4187	91	41	𝜇	𝜇	X
american_scientific_journal-4187	91	42	(	(	PUNCT
american_scientific_journal-4187	91	43	.	.	PUNCT
american_scientific_journal-4187	92	1	theorem8.let	theorem8.let	X
american_scientific_journal-4187	92	2	’s	’s	ADV
american_scientific_journal-4187	92	3	think	think	VERB
american_scientific_journal-4187	92	4	(	(	PUNCT
american_scientific_journal-4187	92	5	is	be	AUX
american_scientific_journal-4187	92	6	a	a	DET
american_scientific_journal-4187	92	7	dependable	dependable	ADJ
american_scientific_journal-4187	92	8	value	value	NOUN
american_scientific_journal-4187	92	9	measures	measure	NOUN
american_scientific_journal-4187	92	10	under	under	ADP
american_scientific_journal-4187	92	11	binary	binary	ADJ
american_scientific_journal-4187	92	12	operations	operation	NOUN
american_scientific_journal-4187	92	13	(	(	PUNCT
american_scientific_journal-4187	92	14	and	and	CCONJ
american_scientific_journal-4187	92	15	these	these	DET
american_scientific_journal-4187	92	16	relations	relation	NOUN
american_scientific_journal-4187	92	17	define	define	VERB
american_scientific_journal-4187	92	18	as	as	ADP
american_scientific_journal-4187	92	19	follow	follow	NOUN
american_scientific_journal-4187	92	20	:	:	PUNCT
american_scientific_journal-4187	92	21	(	(	PUNCT
american_scientific_journal-4187	92	22	(	(	PUNCT
american_scientific_journal-4187	92	23	(	(	PUNCT
american_scientific_journal-4187	92	24	in	in	ADP
american_scientific_journal-4187	92	25	addition	addition	NOUN
american_scientific_journal-4187	92	26	,	,	PUNCT
american_scientific_journal-4187	92	27	we	we	PRON
american_scientific_journal-4187	92	28	have	have	VERB
american_scientific_journal-4187	92	29	this	this	PRON
american_scientific_journal-4187	92	30	about	about	ADP
american_scientific_journal-4187	92	31	binary	binary	ADJ
american_scientific_journal-4187	92	32	operations	operation	NOUN
american_scientific_journal-4187	92	33	(	(	PUNCT
american_scientific_journal-4187	92	34	:	:	PUNCT
american_scientific_journal-4187	92	35	(	(	PUNCT
american_scientific_journal-4187	92	36	(	(	PUNCT
american_scientific_journal-4187	92	37	(	(	PUNCT
american_scientific_journal-4187	92	38	(	(	PUNCT
american_scientific_journal-4187	92	39	(	(	PUNCT
american_scientific_journal-4187	92	40	√	√	INTJ
american_scientific_journal-4187	92	41	(	(	PUNCT
american_scientific_journal-4187	92	42	in	in	ADP
american_scientific_journal-4187	92	43	this	this	DET
american_scientific_journal-4187	92	44	case	case	NOUN
american_scientific_journal-4187	92	45	function	function	NOUN
american_scientific_journal-4187	92	46	𝜇	𝜇	SCONJ
american_scientific_journal-4187	92	47	can	can	AUX
american_scientific_journal-4187	92	48	define	define	VERB
american_scientific_journal-4187	92	49	as	as	ADP
american_scientific_journal-4187	92	50	follow	follow	NOUN
american_scientific_journal-4187	92	51	which	which	PRON
american_scientific_journal-4187	92	52	is	be	AUX
american_scientific_journal-4187	92	53	a	a	DET
american_scientific_journal-4187	92	54	dependable	dependable	ADJ
american_scientific_journal-4187	92	55	value	value	NOUN
american_scientific_journal-4187	92	56	measure	measure	NOUN
american_scientific_journal-4187	92	57	under	under	ADP
american_scientific_journal-4187	92	58	binary	binary	ADJ
american_scientific_journal-4187	92	59	operations	operation	NOUN
american_scientific_journal-4187	92	60	(	(	PUNCT
american_scientific_journal-4187	92	61	.	.	PUNCT
american_scientific_journal-4187	93	1	𝜇	𝜇	X
american_scientific_journal-4187	93	2	(	(	PUNCT
american_scientific_journal-4187	93	3	∏	∏	PROPN
american_scientific_journal-4187	93	4	√	√	PROPN
american_scientific_journal-4187	93	5	(	(	PUNCT
american_scientific_journal-4187	93	6	proof.the	proof.the	DET
american_scientific_journal-4187	93	7	consideration	consideration	NOUN
american_scientific_journal-4187	93	8	of	of	ADP
american_scientific_journal-4187	93	9	this	this	DET
american_scientific_journal-4187	93	10	feature	feature	NOUN
american_scientific_journal-4187	93	11	(	(	PUNCT
american_scientific_journal-4187	93	12	,	,	PUNCT
american_scientific_journal-4187	93	13	due	due	ADP
american_scientific_journal-4187	93	14	to	to	ADP
american_scientific_journal-4187	93	15	the	the	DET
american_scientific_journal-4187	93	16	above	above	ADJ
american_scientific_journal-4187	93	17	relations	relation	NOUN
american_scientific_journal-4187	93	18	are	be	AUX
american_scientific_journal-4187	93	19	too	too	ADV
american_scientific_journal-4187	93	20	easy	easy	ADJ
american_scientific_journal-4187	93	21	.	.	PUNCT
american_scientific_journal-4187	94	1	𝜇	𝜇	ADP
american_scientific_journal-4187	94	2	(	(	PUNCT
american_scientific_journal-4187	94	3	∏	∏	PROPN
american_scientific_journal-4187	94	4	√	√	PROPN
american_scientific_journal-4187	94	5	(	(	PUNCT
american_scientific_journal-4187	94	6	∏	∏	PROPN
american_scientific_journal-4187	94	7	√	√	PROPN
american_scientific_journal-4187	94	8	(	(	PUNCT
american_scientific_journal-4187	94	9	(	(	PUNCT
american_scientific_journal-4187	94	10	√(∏	√(∏	PROPN
american_scientific_journal-4187	94	11	(	(	PUNCT
american_scientific_journal-4187	94	12	(	(	PUNCT
american_scientific_journal-4187	94	13	(	(	PUNCT
american_scientific_journal-4187	94	14	∏	∏	NUM
american_scientific_journal-4187	94	15	√	√	PROPN
american_scientific_journal-4187	94	16	(	(	PUNCT
american_scientific_journal-4187	94	17	(	(	PUNCT
american_scientific_journal-4187	94	18	∏	∏	NUM
american_scientific_journal-4187	94	19	√	√	PROPN
american_scientific_journal-4187	94	20	(	(	PUNCT
american_scientific_journal-4187	94	21	(	(	PUNCT
american_scientific_journal-4187	94	22	(	(	PUNCT
american_scientific_journal-4187	94	23	∏	∏	NUM
american_scientific_journal-4187	94	24	√	√	PROPN
american_scientific_journal-4187	94	25	(	(	PUNCT
american_scientific_journal-4187	94	26	(	(	PUNCT
american_scientific_journal-4187	94	27	∏	∏	NUM
american_scientific_journal-4187	94	28	√	√	PROPN
american_scientific_journal-4187	94	29	(	(	PUNCT
american_scientific_journal-4187	94	30	(	(	PUNCT
american_scientific_journal-4187	94	31	√(∏	√(∏	PROPN
american_scientific_journal-4187	94	32	(	(	PUNCT
american_scientific_journal-4187	94	33	(	(	PUNCT
american_scientific_journal-4187	94	34	(	(	PUNCT
american_scientific_journal-4187	94	35	√(∏	√(∏	PROPN
american_scientific_journal-4187	94	36	(	(	PUNCT
american_scientific_journal-4187	94	37	(	(	PUNCT
american_scientific_journal-4187	94	38	(	(	PUNCT
american_scientific_journal-4187	94	39	∏	∏	NUM
american_scientific_journal-4187	94	40	√	√	PROPN
american_scientific_journal-4187	94	41	(	(	PUNCT
american_scientific_journal-4187	94	42	(	(	PUNCT
american_scientific_journal-4187	94	43	∏	∏	NUM
american_scientific_journal-4187	94	44	√	√	PROPN
american_scientific_journal-4187	94	45	(	(	PUNCT
american_scientific_journal-4187	94	46	(	(	PUNCT
american_scientific_journal-4187	94	47	american	american	ADJ
american_scientific_journal-4187	94	48	scientific	scientific	ADJ
american_scientific_journal-4187	94	49	research	research	NOUN
american_scientific_journal-4187	94	50	journal	journal	NOUN
american_scientific_journal-4187	94	51	for	for	ADP
american_scientific_journal-4187	94	52	engineering	engineering	NOUN
american_scientific_journal-4187	94	53	,	,	PUNCT
american_scientific_journal-4187	94	54	technology	technology	NOUN
american_scientific_journal-4187	94	55	,	,	PUNCT
american_scientific_journal-4187	94	56	and	and	CCONJ
american_scientific_journal-4187	94	57	sciences	science	NOUN
american_scientific_journal-4187	94	58	(	(	PUNCT
american_scientific_journal-4187	94	59	asrjets	asrjet	NOUN
american_scientific_journal-4187	94	60	)	)	PUNCT
american_scientific_journal-4187	94	61	(	(	PUNCT
american_scientific_journal-4187	94	62	2019	2019	NUM
american_scientific_journal-4187	94	63	)	)	PUNCT
american_scientific_journal-4187	94	64	volume	volume	NOUN
american_scientific_journal-4187	94	65	59	59	NUM
american_scientific_journal-4187	94	66	,	,	PUNCT
american_scientific_journal-4187	94	67	no	no	DET
american_scientific_journal-4187	94	68	1	1	NUM
american_scientific_journal-4187	94	69	,	,	PUNCT
american_scientific_journal-4187	94	70	pp	pp	ADV
american_scientific_journal-4187	94	71	162	162	NUM
american_scientific_journal-4187	94	72	-	-	SYM
american_scientific_journal-4187	94	73	178	178	NUM
american_scientific_journal-4187	94	74	173	173	NUM
american_scientific_journal-4187	94	75	∏	∏	NUM
american_scientific_journal-4187	94	76	√	√	PROPN
american_scientific_journal-4187	94	77	(	(	PUNCT
american_scientific_journal-4187	94	78	∏	∏	PROPN
american_scientific_journal-4187	94	79	√	√	PROPN
american_scientific_journal-4187	94	80	(	(	PUNCT
american_scientific_journal-4187	94	81	𝜇	𝜇	X
american_scientific_journal-4187	94	82	(	(	PUNCT
american_scientific_journal-4187	94	83	𝜇	𝜇	X
american_scientific_journal-4187	94	84	(	(	PUNCT
american_scientific_journal-4187	94	85	according	accord	VERB
american_scientific_journal-4187	94	86	to	to	ADP
american_scientific_journal-4187	94	87	this	this	DET
american_scientific_journal-4187	94	88	feature	feature	NOUN
american_scientific_journal-4187	94	89	(	(	PUNCT
american_scientific_journal-4187	94	90	about	about	ADP
american_scientific_journal-4187	94	91	(	(	PUNCT
american_scientific_journal-4187	94	92	16	16	NUM
american_scientific_journal-4187	94	93	)	)	PUNCT
american_scientific_journal-4187	94	94	and	and	CCONJ
american_scientific_journal-4187	94	95	(	(	PUNCT
american_scientific_journal-4187	94	96	17	17	NUM
american_scientific_journal-4187	94	97	)	)	PUNCT
american_scientific_journal-4187	94	98	,	,	PUNCT
american_scientific_journal-4187	94	99	we	we	PRON
american_scientific_journal-4187	94	100	can	can	AUX
american_scientific_journal-4187	94	101	write	write	VERB
american_scientific_journal-4187	94	102	as	as	ADP
american_scientific_journal-4187	94	103	follow	follow	VERB
american_scientific_journal-4187	94	104	:	:	PUNCT
american_scientific_journal-4187	94	105	𝜇	𝜇	X
american_scientific_journal-4187	94	106	(	(	PUNCT
american_scientific_journal-4187	94	107	𝜇	𝜇	X
american_scientific_journal-4187	94	108	(	(	PUNCT
american_scientific_journal-4187	94	109	∏	∏	PROPN
american_scientific_journal-4187	94	110	√	√	PROPN
american_scientific_journal-4187	94	111	(	(	PUNCT
american_scientific_journal-4187	94	112	∏	∏	PROPN
american_scientific_journal-4187	94	113	√	√	PROPN
american_scientific_journal-4187	94	114	(	(	PUNCT
american_scientific_journal-4187	94	115	∏	∏	PROPN
american_scientific_journal-4187	94	116	(	(	PUNCT
american_scientific_journal-4187	94	117	√	√	PROPN
american_scientific_journal-4187	94	118	(	(	PUNCT
american_scientific_journal-4187	94	119	√	√	NUM
american_scientific_journal-4187	94	120	(	(	PUNCT
american_scientific_journal-4187	94	121	∏	∏	PROPN
american_scientific_journal-4187	94	122	(	(	PUNCT
american_scientific_journal-4187	94	123	√	√	PROPN
american_scientific_journal-4187	94	124	(	(	PUNCT
american_scientific_journal-4187	94	125	(	(	PUNCT
american_scientific_journal-4187	94	126	∏	∏	NUM
american_scientific_journal-4187	94	127	√	√	PROPN
american_scientific_journal-4187	94	128	(	(	PUNCT
american_scientific_journal-4187	94	129	𝜇	𝜇	X
american_scientific_journal-4187	94	130	(	(	PUNCT
american_scientific_journal-4187	94	131	lemma9.let	lemma9.let	VERB
american_scientific_journal-4187	94	132	’s	’s	ADV
american_scientific_journal-4187	94	133	think	think	VERB
american_scientific_journal-4187	94	134	this	this	DET
american_scientific_journal-4187	94	135	function	function	NOUN
american_scientific_journal-4187	94	136	is	be	AUX
american_scientific_journal-4187	94	137	a	a	DET
american_scientific_journal-4187	94	138	dependable	dependable	ADJ
american_scientific_journal-4187	94	139	value	value	NOUN
american_scientific_journal-4187	94	140	pre	pre	NOUN
american_scientific_journal-4187	94	141	-	-	NOUN
american_scientific_journal-4187	94	142	measure	measure	NOUN
american_scientific_journal-4187	95	1	and	and	CCONJ
american_scientific_journal-4187	95	2	also	also	ADV
american_scientific_journal-4187	95	3	we	we	PRON
american_scientific_journal-4187	95	4	have	have	AUX
american_scientific_journal-4187	95	5	as	as	ADV
american_scientific_journal-4187	95	6	follow	follow	VERB
american_scientific_journal-4187	95	7	:	:	PUNCT
american_scientific_journal-4187	95	8	(	(	PUNCT
american_scientific_journal-4187	95	9	(	(	PUNCT
american_scientific_journal-4187	95	10	(	(	PUNCT
american_scientific_journal-4187	95	11	(	(	PUNCT
american_scientific_journal-4187	95	12	in	in	ADP
american_scientific_journal-4187	95	13	this	this	DET
american_scientific_journal-4187	95	14	case	case	NOUN
american_scientific_journal-4187	95	15	,	,	PUNCT
american_scientific_journal-4187	95	16	is	be	AUX
american_scientific_journal-4187	95	17	a	a	DET
american_scientific_journal-4187	95	18	dependable	dependable	ADJ
american_scientific_journal-4187	95	19	value	value	NOUN
american_scientific_journal-4187	95	20	measure	measure	NOUN
american_scientific_journal-4187	95	21	under	under	ADP
american_scientific_journal-4187	95	22	binary	binary	ADJ
american_scientific_journal-4187	95	23	operation	operation	NOUN
american_scientific_journal-4187	95	24	(	(	PUNCT
american_scientific_journal-4187	95	25	.	.	PUNCT
american_scientific_journal-4187	96	1	proof.let	proof.let	NOUN
american_scientific_journal-4187	96	2	’s	’s	PART
american_scientific_journal-4187	96	3	think	think	VERB
american_scientific_journal-4187	96	4	this	this	DET
american_scientific_journal-4187	96	5	way	way	NOUN
american_scientific_journal-4187	96	6	:	:	PUNCT
american_scientific_journal-4187	96	7	(	(	PUNCT
american_scientific_journal-4187	96	8	(	(	PUNCT
american_scientific_journal-4187	96	9	(	(	PUNCT
american_scientific_journal-4187	96	10	(	(	PUNCT
american_scientific_journal-4187	96	11	(	(	PUNCT
american_scientific_journal-4187	96	12	(	(	PUNCT
american_scientific_journal-4187	96	13	in	in	ADP
american_scientific_journal-4187	96	14	order	order	NOUN
american_scientific_journal-4187	96	15	to	to	PART
american_scientific_journal-4187	96	16	addition	addition	NOUN
american_scientific_journal-4187	96	17	of	of	ADP
american_scientific_journal-4187	96	18	this	this	DET
american_scientific_journal-4187	96	19	relation	relation	NOUN
american_scientific_journal-4187	96	20	,	,	PUNCT
american_scientific_journal-4187	96	21	we	we	PRON
american_scientific_journal-4187	96	22	can	can	AUX
american_scientific_journal-4187	96	23	conclude	conclude	VERB
american_scientific_journal-4187	96	24	as	as	ADP
american_scientific_journal-4187	96	25	follow	follow	VERB
american_scientific_journal-4187	96	26	:	:	PUNCT
american_scientific_journal-4187	96	27	(	(	PUNCT
american_scientific_journal-4187	96	28	(	(	PUNCT
american_scientific_journal-4187	96	29	(	(	PUNCT
american_scientific_journal-4187	96	30	now	now	ADV
american_scientific_journal-4187	96	31	,	,	PUNCT
american_scientific_journal-4187	96	32	other	other	ADJ
american_scientific_journal-4187	96	33	operations	operation	NOUN
american_scientific_journal-4187	96	34	are	be	AUX
american_scientific_journal-4187	96	35	sole	sole	ADJ
american_scientific_journal-4187	96	36	by	by	ADP
american_scientific_journal-4187	96	37	(	(	PUNCT
american_scientific_journal-4187	96	38	18	18	NUM
american_scientific_journal-4187	96	39	)	)	PUNCT
american_scientific_journal-4187	96	40	relation	relation	NOUN
american_scientific_journal-4187	96	41	.	.	PUNCT
american_scientific_journal-4187	97	1	now	now	ADV
american_scientific_journal-4187	97	2	,	,	PUNCT
american_scientific_journal-4187	97	3	let	let	VERB
american_scientific_journal-4187	97	4	's	us	PRON
american_scientific_journal-4187	97	5	talk	talk	VERB
american_scientific_journal-4187	97	6	about	about	ADP
american_scientific_journal-4187	97	7	a	a	DET
american_scientific_journal-4187	97	8	theorem	theorem	NOUN
american_scientific_journal-4187	97	9	which	which	PRON
american_scientific_journal-4187	97	10	gives	give	VERB
american_scientific_journal-4187	97	11	us	we	PRON
american_scientific_journal-4187	97	12	an	an	DET
american_scientific_journal-4187	97	13	impressive	impressive	ADJ
american_scientific_journal-4187	97	14	test	test	NOUN
american_scientific_journal-4187	97	15	for	for	ADP
american_scientific_journal-4187	97	16	examining	examine	VERB
american_scientific_journal-4187	97	17	the	the	DET
american_scientific_journal-4187	97	18	dependable	dependable	ADJ
american_scientific_journal-4187	97	19	value	value	NOUN
american_scientific_journal-4187	97	20	pre	pre	ADJ
american_scientific_journal-4187	97	21	-	-	ADJ
american_scientific_journal-4187	97	22	measure	measure	ADJ
american_scientific_journal-4187	97	23	theorem10.let	theorem10.let	NOUN
american_scientific_journal-4187	97	24	’s	’s	PART
american_scientific_journal-4187	97	25	assume	assume	PROPN
american_scientific_journal-4187	97	26	functions	function	NOUN
american_scientific_journal-4187	97	27	𝝁	𝝁	PRON
american_scientific_journal-4187	97	28	and	and	CCONJ
american_scientific_journal-4187	97	29	also	also	ADV
american_scientific_journal-4187	97	30	suppose	suppose	VERB
american_scientific_journal-4187	97	31	is	be	AUX
american_scientific_journal-4187	97	32	a	a	DET
american_scientific_journal-4187	97	33	dependable	dependable	ADJ
american_scientific_journal-4187	97	34	value	value	NOUN
american_scientific_journal-4187	97	35	pre	pre	NOUN
american_scientific_journal-4187	97	36	-	-	NOUN
american_scientific_journal-4187	97	37	measure	measure	NOUN
american_scientific_journal-4187	97	38	,	,	PUNCT
american_scientific_journal-4187	97	39	such	such	ADJ
american_scientific_journal-4187	97	40	that	that	PRON
american_scientific_journal-4187	97	41	for	for	ADP
american_scientific_journal-4187	97	42	each	each	PRON
american_scientific_journal-4187	97	43	have	have	VERB
american_scientific_journal-4187	97	44	relation	relation	NOUN
american_scientific_journal-4187	97	45	:	:	PUNCT
american_scientific_journal-4187	97	46	(	(	PUNCT
american_scientific_journal-4187	97	47	(	(	PUNCT
american_scientific_journal-4187	97	48	𝜇	𝜇	X
american_scientific_journal-4187	97	49	(	(	PUNCT
american_scientific_journal-4187	97	50	in	in	ADP
american_scientific_journal-4187	97	51	addition	addition	NOUN
american_scientific_journal-4187	97	52	,	,	PUNCT
american_scientific_journal-4187	97	53	we	we	PRON
american_scientific_journal-4187	97	54	have	have	AUX
american_scientific_journal-4187	97	55	as	as	ADV
american_scientific_journal-4187	97	56	follow	follow	VERB
american_scientific_journal-4187	97	57	:	:	PUNCT
american_scientific_journal-4187	97	58	american	american	ADJ
american_scientific_journal-4187	97	59	scientific	scientific	ADJ
american_scientific_journal-4187	97	60	research	research	PROPN
american_scientific_journal-4187	97	61	journal	journal	NOUN
american_scientific_journal-4187	97	62	for	for	ADP
american_scientific_journal-4187	97	63	engineering	engineering	NOUN
american_scientific_journal-4187	97	64	,	,	PUNCT
american_scientific_journal-4187	97	65	technology	technology	NOUN
american_scientific_journal-4187	97	66	,	,	PUNCT
american_scientific_journal-4187	97	67	and	and	CCONJ
american_scientific_journal-4187	97	68	sciences	science	NOUN
american_scientific_journal-4187	97	69	(	(	PUNCT
american_scientific_journal-4187	97	70	asrjets	asrjet	NOUN
american_scientific_journal-4187	97	71	)	)	PUNCT
american_scientific_journal-4187	97	72	(	(	PUNCT
american_scientific_journal-4187	97	73	2019	2019	NUM
american_scientific_journal-4187	97	74	)	)	PUNCT
american_scientific_journal-4187	97	75	volume	volume	NOUN
american_scientific_journal-4187	97	76	59	59	NUM
american_scientific_journal-4187	97	77	,	,	PUNCT
american_scientific_journal-4187	97	78	no	no	DET
american_scientific_journal-4187	97	79	1	1	NUM
american_scientific_journal-4187	97	80	,	,	PUNCT
american_scientific_journal-4187	97	81	pp	pp	ADV
american_scientific_journal-4187	97	82	162	162	NUM
american_scientific_journal-4187	97	83	-	-	SYM
american_scientific_journal-4187	97	84	178	178	NUM
american_scientific_journal-4187	97	85	174	174	NUM
american_scientific_journal-4187	97	86	𝜇	𝜇	X
american_scientific_journal-4187	97	87	(	(	PUNCT
american_scientific_journal-4187	97	88	𝜇	𝜇	X
american_scientific_journal-4187	97	89	(	(	PUNCT
american_scientific_journal-4187	97	90	(	(	PUNCT
american_scientific_journal-4187	97	91	in	in	ADP
american_scientific_journal-4187	97	92	addition	addition	NOUN
american_scientific_journal-4187	97	93	,	,	PUNCT
american_scientific_journal-4187	97	94	there	there	PRON
american_scientific_journal-4187	97	95	should	should	AUX
american_scientific_journal-4187	97	96	be	be	AUX
american_scientific_journal-4187	97	97	binary	binary	ADJ
american_scientific_journal-4187	97	98	operation	operation	NOUN
american_scientific_journal-4187	97	99	for	for	ADP
american_scientific_journal-4187	97	100	(	(	PUNCT
american_scientific_journal-4187	97	101	18	18	NUM
american_scientific_journal-4187	97	102	)	)	PUNCT
american_scientific_journal-4187	97	103	relations	relation	NOUN
american_scientific_journal-4187	97	104	.	.	PUNCT
american_scientific_journal-4187	98	1	then	then	ADV
american_scientific_journal-4187	98	2	is	be	AUX
american_scientific_journal-4187	98	3	a	a	DET
american_scientific_journal-4187	98	4	dependable	dependable	ADJ
american_scientific_journal-4187	98	5	value	value	NOUN
american_scientific_journal-4187	98	6	measure	measure	NOUN
american_scientific_journal-4187	98	7	under	under	ADP
american_scientific_journal-4187	98	8	binary	binary	ADJ
american_scientific_journal-4187	98	9	operations	operation	NOUN
american_scientific_journal-4187	98	10	(	(	PUNCT
american_scientific_journal-4187	98	11	.	.	PUNCT
american_scientific_journal-4187	99	1	proof.it	proof.it	X
american_scientific_journal-4187	99	2	’s	’	VERB
american_scientific_journal-4187	99	3	clear	clear	ADJ
american_scientific_journal-4187	99	4	that	that	SCONJ
american_scientific_journal-4187	99	5	due	due	ADP
american_scientific_journal-4187	99	6	to	to	ADP
american_scientific_journal-4187	99	7	the	the	DET
american_scientific_journal-4187	99	8	assumptions	assumption	NOUN
american_scientific_journal-4187	99	9	and	and	CCONJ
american_scientific_journal-4187	99	10	lemma	lemma	PROPN
american_scientific_journal-4187	99	11	10	10	NUM
american_scientific_journal-4187	99	12	to	to	PART
american_scientific_journal-4187	99	13	prove	prove	VERB
american_scientific_journal-4187	99	14	this	this	DET
american_scientific_journal-4187	99	15	relation	relation	NOUN
american_scientific_journal-4187	99	16	(	(	PUNCT
american_scientific_journal-4187	99	17	(	(	PUNCT
american_scientific_journal-4187	99	18	(	(	PUNCT
american_scientific_journal-4187	99	19	,	,	PUNCT
american_scientific_journal-4187	99	20	it	it	PRON
american_scientific_journal-4187	99	21	’s	’	VERB
american_scientific_journal-4187	99	22	sufficient	sufficient	ADJ
american_scientific_journal-4187	99	23	to	to	PART
american_scientific_journal-4187	99	24	prove	prove	VERB
american_scientific_journal-4187	99	25	that	that	SCONJ
american_scientific_journal-4187	99	26	the	the	DET
american_scientific_journal-4187	99	27	following	follow	VERB
american_scientific_journal-4187	99	28	relation	relation	NOUN
american_scientific_journal-4187	99	29	is	be	AUX
american_scientific_journal-4187	99	30	established	establish	VERB
american_scientific_journal-4187	99	31	.	.	PUNCT
american_scientific_journal-4187	100	1	(	(	PUNCT
american_scientific_journal-4187	100	2	(	(	PUNCT
american_scientific_journal-4187	100	3	(	(	PUNCT
american_scientific_journal-4187	100	4	in	in	ADP
american_scientific_journal-4187	100	5	order	order	NOUN
american_scientific_journal-4187	100	6	to	to	PART
american_scientific_journal-4187	100	7	do	do	AUX
american_scientific_journal-4187	100	8	this	this	PRON
american_scientific_journal-4187	100	9	(	(	PUNCT
american_scientific_journal-4187	100	10	(	(	PUNCT
american_scientific_journal-4187	100	11	we	we	PRON
american_scientific_journal-4187	100	12	have	have	VERB
american_scientific_journal-4187	100	13	to	to	PART
american_scientific_journal-4187	100	14	define	define	VERB
american_scientific_journal-4187	100	15	as	as	ADP
american_scientific_journal-4187	100	16	follow	follow	VERB
american_scientific_journal-4187	100	17	;	;	PUNCT
american_scientific_journal-4187	100	18	(	(	PUNCT
american_scientific_journal-4187	100	19	𝜇	𝜇	X
american_scientific_journal-4187	100	20	(	(	PUNCT
american_scientific_journal-4187	100	21	(	(	PUNCT
american_scientific_journal-4187	100	22	(	(	PUNCT
american_scientific_journal-4187	100	23	𝜇	𝜇	X
american_scientific_journal-4187	100	24	(	(	PUNCT
american_scientific_journal-4187	100	25	(	(	PUNCT
american_scientific_journal-4187	100	26	it	it	PRON
american_scientific_journal-4187	100	27	’s	’	VERB
american_scientific_journal-4187	100	28	clear	clear	ADJ
american_scientific_journal-4187	100	29	that	that	SCONJ
american_scientific_journal-4187	100	30	we	we	PRON
american_scientific_journal-4187	100	31	can	can	AUX
american_scientific_journal-4187	100	32	write	write	VERB
american_scientific_journal-4187	100	33	as	as	ADP
american_scientific_journal-4187	100	34	follow	follow	VERB
american_scientific_journal-4187	100	35	:	:	PUNCT
american_scientific_journal-4187	100	36	(	(	PUNCT
american_scientific_journal-4187	100	37	(	(	PUNCT
american_scientific_journal-4187	100	38	(	(	PUNCT
american_scientific_journal-4187	100	39	𝜇	𝜇	X
american_scientific_journal-4187	100	40	(	(	PUNCT
american_scientific_journal-4187	100	41	(	(	PUNCT
american_scientific_journal-4187	100	42	(	(	PUNCT
american_scientific_journal-4187	100	43	therefore	therefore	ADV
american_scientific_journal-4187	100	44	,	,	PUNCT
american_scientific_journal-4187	100	45	we	we	PRON
american_scientific_journal-4187	100	46	have	have	AUX
american_scientific_journal-4187	100	47	as	as	ADV
american_scientific_journal-4187	100	48	follow	follow	VERB
american_scientific_journal-4187	100	49	:	:	PUNCT
american_scientific_journal-4187	100	50	(	(	PUNCT
american_scientific_journal-4187	100	51	(	(	PUNCT
american_scientific_journal-4187	100	52	(	(	PUNCT
american_scientific_journal-4187	100	53	(	(	PUNCT
american_scientific_journal-4187	100	54	(	(	PUNCT
american_scientific_journal-4187	100	55	so	so	ADV
american_scientific_journal-4187	100	56	,	,	PUNCT
american_scientific_journal-4187	100	57	we	we	PRON
american_scientific_journal-4187	100	58	have	have	AUX
american_scientific_journal-4187	100	59	as	as	ADV
american_scientific_journal-4187	100	60	follow	follow	VERB
american_scientific_journal-4187	100	61	;	;	PUNCT
american_scientific_journal-4187	100	62	(	(	PUNCT
american_scientific_journal-4187	100	63	(	(	PUNCT
american_scientific_journal-4187	100	64	(	(	PUNCT
american_scientific_journal-4187	100	65	(	(	PUNCT
american_scientific_journal-4187	100	66	(	(	PUNCT
american_scientific_journal-4187	100	67	(	(	PUNCT
american_scientific_journal-4187	100	68	(	(	PUNCT
american_scientific_journal-4187	100	69	(	(	PUNCT
american_scientific_journal-4187	100	70	(	(	PUNCT
american_scientific_journal-4187	100	71	as	as	ADP
american_scientific_journal-4187	100	72	a	a	DET
american_scientific_journal-4187	100	73	result	result	NOUN
american_scientific_journal-4187	100	74	,	,	PUNCT
american_scientific_journal-4187	100	75	by	by	ADP
american_scientific_journal-4187	100	76	addition	addition	NOUN
american_scientific_journal-4187	100	77	of	of	ADP
american_scientific_journal-4187	100	78	both	both	CCONJ
american_scientific_journal-4187	100	79	unequal	unequal	ADJ
american_scientific_journal-4187	100	80	sides	side	NOUN
american_scientific_journal-4187	100	81	,	,	PUNCT
american_scientific_journal-4187	100	82	we	we	PRON
american_scientific_journal-4187	100	83	have	have	AUX
american_scientific_journal-4187	100	84	as	as	ADV
american_scientific_journal-4187	100	85	follow	follow	VERB
american_scientific_journal-4187	100	86	:	:	PUNCT
american_scientific_journal-4187	100	87	(	(	PUNCT
american_scientific_journal-4187	100	88	(	(	PUNCT
american_scientific_journal-4187	100	89	(	(	PUNCT
american_scientific_journal-4187	100	90	(	(	PUNCT
american_scientific_journal-4187	100	91	)	)	PUNCT
american_scientific_journal-4187	100	92	[	[	PUNCT
american_scientific_journal-4187	100	93	(	(	PUNCT
american_scientific_journal-4187	100	94	(	(	PUNCT
american_scientific_journal-4187	100	95	(	(	PUNCT
american_scientific_journal-4187	100	96	(	(	X
american_scientific_journal-4187	100	97	)	)	PUNCT
american_scientific_journal-4187	100	98	]	]	PUNCT
american_scientific_journal-4187	101	1	(	(	PUNCT
american_scientific_journal-4187	101	2	(	(	PUNCT
american_scientific_journal-4187	101	3	(	(	PUNCT
american_scientific_journal-4187	101	4	therefore	therefore	ADV
american_scientific_journal-4187	101	5	,	,	PUNCT
american_scientific_journal-4187	101	6	for	for	ADP
american_scientific_journal-4187	101	7	prove	prove	NOUN
american_scientific_journal-4187	101	8	(	(	PUNCT
american_scientific_journal-4187	101	9	(	(	PUNCT
american_scientific_journal-4187	101	10	(	(	PUNCT
american_scientific_journal-4187	101	11	in	in	ADP
american_scientific_journal-4187	101	12	above	above	ADP
american_scientific_journal-4187	101	13	inequality	inequality	NOUN
american_scientific_journal-4187	101	14	,	,	PUNCT
american_scientific_journal-4187	101	15	there	there	PRON
american_scientific_journal-4187	101	16	is	be	VERB
american_scientific_journal-4187	101	17	sufficient	sufficient	ADJ
american_scientific_journal-4187	101	18	condition	condition	NOUN
american_scientific_journal-4187	101	19	to	to	PART
american_scientific_journal-4187	101	20	prove	prove	VERB
american_scientific_journal-4187	101	21	that	that	SCONJ
american_scientific_journal-4187	101	22	:	:	PUNCT
american_scientific_journal-4187	101	23	(	(	PUNCT
american_scientific_journal-4187	101	24	(	(	PUNCT
american_scientific_journal-4187	101	25	(	(	PUNCT
american_scientific_journal-4187	101	26	(	(	PUNCT
american_scientific_journal-4187	101	27	)	)	PUNCT
american_scientific_journal-4187	101	28	[	[	PUNCT
american_scientific_journal-4187	101	29	(	(	PUNCT
american_scientific_journal-4187	101	30	(	(	PUNCT
american_scientific_journal-4187	101	31	(	(	PUNCT
american_scientific_journal-4187	101	32	(	(	PUNCT
american_scientific_journal-4187	101	33	)	)	PUNCT
american_scientific_journal-4187	101	34	]	]	PUNCT
american_scientific_journal-4187	101	35	american	american	PROPN
american_scientific_journal-4187	101	36	scientific	scientific	ADJ
american_scientific_journal-4187	101	37	research	research	PROPN
american_scientific_journal-4187	101	38	journal	journal	NOUN
american_scientific_journal-4187	101	39	for	for	ADP
american_scientific_journal-4187	101	40	engineering	engineering	NOUN
american_scientific_journal-4187	101	41	,	,	PUNCT
american_scientific_journal-4187	101	42	technology	technology	NOUN
american_scientific_journal-4187	101	43	,	,	PUNCT
american_scientific_journal-4187	101	44	and	and	CCONJ
american_scientific_journal-4187	101	45	sciences	science	NOUN
american_scientific_journal-4187	101	46	(	(	PUNCT
american_scientific_journal-4187	101	47	asrjets	asrjet	NOUN
american_scientific_journal-4187	101	48	)	)	PUNCT
american_scientific_journal-4187	101	49	(	(	PUNCT
american_scientific_journal-4187	101	50	2019	2019	NUM
american_scientific_journal-4187	101	51	)	)	PUNCT
american_scientific_journal-4187	101	52	volume	volume	NOUN
american_scientific_journal-4187	101	53	59	59	NUM
american_scientific_journal-4187	101	54	,	,	PUNCT
american_scientific_journal-4187	101	55	no	no	DET
american_scientific_journal-4187	101	56	1	1	NUM
american_scientific_journal-4187	101	57	,	,	PUNCT
american_scientific_journal-4187	101	58	pp	pp	ADV
american_scientific_journal-4187	101	59	162	162	NUM
american_scientific_journal-4187	101	60	-	-	SYM
american_scientific_journal-4187	101	61	178	178	NUM
american_scientific_journal-4187	101	62	175	175	NUM
american_scientific_journal-4187	101	63	in	in	ADP
american_scientific_journal-4187	101	64	order	order	NOUN
american_scientific_journal-4187	101	65	by	by	ADP
american_scientific_journal-4187	101	66	replace	replace	VERB
american_scientific_journal-4187	101	67	the	the	DET
american_scientific_journal-4187	101	68	values	value	NOUN
american_scientific_journal-4187	101	69	,	,	PUNCT
american_scientific_journal-4187	101	70	and	and	CCONJ
american_scientific_journal-4187	101	71	streamline	streamline	VERB
american_scientific_journal-4187	101	72	the	the	DET
american_scientific_journal-4187	101	73	relation	relation	NOUN
american_scientific_journal-4187	101	74	,	,	PUNCT
american_scientific_journal-4187	101	75	we	we	PRON
american_scientific_journal-4187	101	76	can	can	AUX
american_scientific_journal-4187	101	77	easily	easily	ADV
american_scientific_journal-4187	101	78	conclude	conclude	VERB
american_scientific_journal-4187	101	79	as	as	SCONJ
american_scientific_journal-4187	101	80	follow	follow	VERB
american_scientific_journal-4187	101	81	.	.	PUNCT
american_scientific_journal-4187	102	1	𝜇	𝜇	SCONJ
american_scientific_journal-4187	102	2	(	(	PUNCT
american_scientific_journal-4187	102	3	𝜇	𝜇	X
american_scientific_journal-4187	102	4	(	(	PUNCT
american_scientific_journal-4187	102	5	(	(	PUNCT
american_scientific_journal-4187	102	6	for	for	ADP
american_scientific_journal-4187	102	7	example	example	NOUN
american_scientific_journal-4187	102	8	,	,	PUNCT
american_scientific_journal-4187	102	9	if	if	SCONJ
american_scientific_journal-4187	102	10	is	be	AUX
american_scientific_journal-4187	102	11	a	a	DET
american_scientific_journal-4187	102	12	dependable	dependable	ADJ
american_scientific_journal-4187	102	13	value	value	NOUN
american_scientific_journal-4187	102	14	measure	measure	NOUN
american_scientific_journal-4187	102	15	.	.	PUNCT
american_scientific_journal-4187	103	1	such	such	ADJ
american_scientific_journal-4187	103	2	that	that	DET
american_scientific_journal-4187	103	3	relation	relation	NOUN
american_scientific_journal-4187	103	4	is	be	AUX
american_scientific_journal-4187	103	5	stable	stable	ADJ
american_scientific_journal-4187	103	6	in	in	ADP
american_scientific_journal-4187	103	7	order	order	NOUN
american_scientific_journal-4187	103	8	to	to	PART
american_scientific_journal-4187	103	9	𝜇	𝜇	X
american_scientific_journal-4187	103	10	.	.	PUNCT
american_scientific_journal-4187	104	1	it	it	PRON
american_scientific_journal-4187	104	2	can	can	AUX
american_scientific_journal-4187	104	3	define	define	VERB
american_scientific_journal-4187	104	4	as	as	ADP
american_scientific_journal-4187	104	5	follow	follow	VERB
american_scientific_journal-4187	104	6	:	:	PUNCT
american_scientific_journal-4187	104	7	𝜇	𝜇	X
american_scientific_journal-4187	104	8	(	(	PUNCT
american_scientific_journal-4187	104	9	(	(	PUNCT
american_scientific_journal-4187	104	10	(	(	PUNCT
american_scientific_journal-4187	104	11	(	(	PUNCT
american_scientific_journal-4187	104	12	(	(	PUNCT
american_scientific_journal-4187	104	13	(	(	PUNCT
american_scientific_journal-4187	104	14	(	(	PUNCT
american_scientific_journal-4187	104	15	where	where	SCONJ
american_scientific_journal-4187	104	16	(	(	PUNCT
american_scientific_journal-4187	104	17	(	(	PUNCT
american_scientific_journal-4187	104	18	.	.	PUNCT
american_scientific_journal-4187	105	1	the	the	DET
american_scientific_journal-4187	105	2	proof	proof	NOUN
american_scientific_journal-4187	105	3	that	that	SCONJ
american_scientific_journal-4187	105	4	function	function	NOUN
american_scientific_journal-4187	105	5	is	be	AUX
american_scientific_journal-4187	105	6	dependable	dependable	ADJ
american_scientific_journal-4187	105	7	value	value	NOUN
american_scientific_journal-4187	105	8	pre	pre	NOUN
american_scientific_journal-4187	105	9	-	-	NOUN
american_scientific_journal-4187	105	10	measure	measure	NOUN
american_scientific_journal-4187	105	11	,	,	PUNCT
american_scientific_journal-4187	105	12	it	it	PRON
american_scientific_journal-4187	105	13	is	be	AUX
american_scientific_journal-4187	105	14	easily	easily	ADV
american_scientific_journal-4187	105	15	.	.	PUNCT
american_scientific_journal-4187	106	1	according	accord	VERB
american_scientific_journal-4187	106	2	to	to	ADP
american_scientific_journal-4187	106	3	the	the	DET
american_scientific_journal-4187	106	4	theorem	theorem	NOUN
american_scientific_journal-4187	106	5	5	5	NUM
american_scientific_journal-4187	106	6	,	,	PUNCT
american_scientific_journal-4187	106	7	it	it	PRON
american_scientific_journal-4187	106	8	’s	’	VERB
american_scientific_journal-4187	106	9	clear	clear	ADJ
american_scientific_journal-4187	106	10	that	that	SCONJ
american_scientific_journal-4187	106	11	(	(	PUNCT
american_scientific_journal-4187	106	12	has	have	AUX
american_scientific_journal-4187	106	13	this	this	DET
american_scientific_journal-4187	106	14	relation	relation	NOUN
american_scientific_journal-4187	106	15	is	be	AUX
american_scientific_journal-4187	106	16	a	a	DET
american_scientific_journal-4187	106	17	dependable	dependable	ADJ
american_scientific_journal-4187	106	18	value	value	NOUN
american_scientific_journal-4187	106	19	measure	measure	NOUN
american_scientific_journal-4187	106	20	.	.	PUNCT
american_scientific_journal-4187	107	1	in	in	ADP
american_scientific_journal-4187	107	2	addition	addition	NOUN
american_scientific_journal-4187	107	3	,	,	PUNCT
american_scientific_journal-4187	107	4	according	accord	VERB
american_scientific_journal-4187	107	5	to	to	ADP
american_scientific_journal-4187	107	6	the	the	DET
american_scientific_journal-4187	107	7	lemma	lemma	PROPN
american_scientific_journal-4187	107	8	2	2	NUM
american_scientific_journal-4187	107	9	and	and	CCONJ
american_scientific_journal-4187	107	10	criteria	criterion	NOUN
american_scientific_journal-4187	107	11	𝜇	𝜇	ADP
american_scientific_journal-4187	107	12	,	,	PUNCT
american_scientific_journal-4187	107	13	we	we	PRON
american_scientific_journal-4187	107	14	have	have	AUX
american_scientific_journal-4187	107	15	as	as	ADV
american_scientific_journal-4187	107	16	follow	follow	VERB
american_scientific_journal-4187	107	17	;	;	PUNCT
american_scientific_journal-4187	107	18	(	(	PUNCT
american_scientific_journal-4187	107	19	𝜇	𝜇	X
american_scientific_journal-4187	107	20	(	(	PUNCT
american_scientific_journal-4187	107	21	(	(	PUNCT
american_scientific_journal-4187	107	22	on	on	ADP
american_scientific_journal-4187	107	23	the	the	DET
american_scientific_journal-4187	107	24	other	other	ADJ
american_scientific_journal-4187	107	25	hand	hand	NOUN
american_scientific_journal-4187	107	26	,	,	PUNCT
american_scientific_journal-4187	107	27	from	from	ADP
american_scientific_journal-4187	107	28	,	,	PUNCT
american_scientific_journal-4187	107	29	we	we	PRON
american_scientific_journal-4187	107	30	can	can	AUX
american_scientific_journal-4187	107	31	easily	easily	ADV
american_scientific_journal-4187	107	32	conclude	conclude	VERB
american_scientific_journal-4187	107	33	that	that	PRON
american_scientific_journal-4187	107	34	.	.	PUNCT
american_scientific_journal-4187	108	1	so	so	ADV
american_scientific_journal-4187	108	2	,	,	PUNCT
american_scientific_journal-4187	108	3	we	we	PRON
american_scientific_journal-4187	108	4	have	have	AUX
american_scientific_journal-4187	108	5	as	as	ADV
american_scientific_journal-4187	108	6	follow	follow	VERB
american_scientific_journal-4187	108	7	;	;	PUNCT
american_scientific_journal-4187	108	8	(	(	PUNCT
american_scientific_journal-4187	108	9	(	(	PUNCT
american_scientific_journal-4187	108	10	(	(	PUNCT
american_scientific_journal-4187	108	11	(	(	PUNCT
american_scientific_journal-4187	108	12	(	(	PUNCT
american_scientific_journal-4187	108	13	(	(	PUNCT
american_scientific_journal-4187	108	14	(	(	PUNCT
american_scientific_journal-4187	108	15	(	(	PUNCT
american_scientific_journal-4187	108	16	(	(	PUNCT
american_scientific_journal-4187	108	17	(	(	PUNCT
american_scientific_journal-4187	108	18	therefore	therefore	ADV
american_scientific_journal-4187	108	19	,	,	PUNCT
american_scientific_journal-4187	108	20	due	due	ADP
american_scientific_journal-4187	108	21	to	to	ADP
american_scientific_journal-4187	108	22	the	the	DET
american_scientific_journal-4187	108	23	proven	prove	VERB
american_scientific_journal-4187	108	24	theorem	theorem	PROPN
american_scientific_journal-4187	108	25	,	,	PUNCT
american_scientific_journal-4187	108	26	we	we	PRON
american_scientific_journal-4187	108	27	conclude	conclude	VERB
american_scientific_journal-4187	108	28	that	that	SCONJ
american_scientific_journal-4187	108	29	𝜇	𝜇	SCONJ
american_scientific_journal-4187	108	30	is	be	AUX
american_scientific_journal-4187	108	31	dependable	dependable	ADJ
american_scientific_journal-4187	108	32	value	value	NOUN
american_scientific_journal-4187	108	33	measure	measure	NOUN
american_scientific_journal-4187	108	34	.	.	PUNCT
american_scientific_journal-4187	109	1	theorem11.suppose	theorem11.suppose	PRON
american_scientific_journal-4187	109	2	that	that	PRON
american_scientific_journal-4187	109	3	function	function	VERB
american_scientific_journal-4187	109	4	𝜇	𝜇	ADP
american_scientific_journal-4187	109	5	is	be	AUX
american_scientific_journal-4187	109	6	a	a	DET
american_scientific_journal-4187	109	7	dependable	dependable	ADJ
american_scientific_journal-4187	109	8	value	value	NOUN
american_scientific_journal-4187	109	9	pre	pre	NOUN
american_scientific_journal-4187	109	10	-	-	NOUN
american_scientific_journal-4187	109	11	measure	measure	NOUN
american_scientific_journal-4187	109	12	and	and	CCONJ
american_scientific_journal-4187	109	13	also	also	ADV
american_scientific_journal-4187	109	14	we	we	PRON
american_scientific_journal-4187	109	15	have	have	VERB
american_scientific_journal-4187	109	16	this	this	DET
american_scientific_journal-4187	109	17	relation	relation	NOUN
american_scientific_journal-4187	109	18	as	as	ADP
american_scientific_journal-4187	109	19	follow	follow	VERB
american_scientific_journal-4187	109	20	:	:	PUNCT
american_scientific_journal-4187	109	21	𝜇	𝜇	X
american_scientific_journal-4187	109	22	(	(	PUNCT
american_scientific_journal-4187	109	23	𝜇	𝜇	X
american_scientific_journal-4187	109	24	(	(	PUNCT
american_scientific_journal-4187	109	25	in	in	ADP
american_scientific_journal-4187	109	26	this	this	DET
american_scientific_journal-4187	109	27	case	case	NOUN
american_scientific_journal-4187	109	28	,	,	PUNCT
american_scientific_journal-4187	109	29	𝜇	𝜇	X
american_scientific_journal-4187	109	30	is	be	AUX
american_scientific_journal-4187	109	31	dependable	dependable	ADJ
american_scientific_journal-4187	109	32	value	value	NOUN
american_scientific_journal-4187	109	33	measure	measure	NOUN
american_scientific_journal-4187	109	34	.	.	PUNCT
american_scientific_journal-4187	110	1	proof	proof	NOUN
american_scientific_journal-4187	110	2	.	.	PUNCT
american_scientific_journal-4187	111	1	(	(	PUNCT
american_scientific_journal-4187	111	2	(	(	PUNCT
american_scientific_journal-4187	111	3	(	(	PUNCT
american_scientific_journal-4187	111	4	(	(	PUNCT
american_scientific_journal-4187	111	5	(	(	PUNCT
american_scientific_journal-4187	111	6	theorem	theorem	ADJ
american_scientific_journal-4187	111	7	12.let	12.let	PROPN
american_scientific_journal-4187	111	8	’s	’s	PART
american_scientific_journal-4187	111	9	think	think	VERB
american_scientific_journal-4187	111	10	that	that	SCONJ
american_scientific_journal-4187	111	11	the	the	DET
american_scientific_journal-4187	111	12	function	function	NOUN
american_scientific_journal-4187	111	13	is	be	AUX
american_scientific_journal-4187	111	14	a	a	DET
american_scientific_journal-4187	111	15	dependable	dependable	ADJ
american_scientific_journal-4187	111	16	value	value	NOUN
american_scientific_journal-4187	111	17	pre	pre	NOUN
american_scientific_journal-4187	111	18	-	-	NOUN
american_scientific_journal-4187	111	19	measure	measure	NOUN
american_scientific_journal-4187	111	20	and	and	CCONJ
american_scientific_journal-4187	111	21	𝜇	𝜇	NOUN
american_scientific_journal-4187	111	22	is	be	AUX
american_scientific_journal-4187	111	23	dependable	dependable	ADJ
american_scientific_journal-4187	111	24	value	value	NOUN
american_scientific_journal-4187	111	25	measure	measure	NOUN
american_scientific_journal-4187	111	26	and	and	CCONJ
american_scientific_journal-4187	111	27	we	we	PRON
american_scientific_journal-4187	111	28	have	have	VERB
american_scientific_journal-4187	111	29	this	this	DET
american_scientific_journal-4187	111	30	function	function	NOUN
american_scientific_journal-4187	111	31	as	as	ADP
american_scientific_journal-4187	111	32	follow	follow	VERB
american_scientific_journal-4187	111	33	:	:	PUNCT
american_scientific_journal-4187	111	34	𝜇	𝜇	X
american_scientific_journal-4187	111	35	(	(	PUNCT
american_scientific_journal-4187	111	36	(	(	PUNCT
american_scientific_journal-4187	111	37	𝜇	𝜇	X
american_scientific_journal-4187	111	38	(	(	PUNCT
american_scientific_journal-4187	111	39	⋃	⋃	PROPN
american_scientific_journal-4187	111	40	)	)	PUNCT
american_scientific_journal-4187	111	41	(	(	PUNCT
american_scientific_journal-4187	111	42	in	in	ADP
american_scientific_journal-4187	111	43	this	this	DET
american_scientific_journal-4187	111	44	case	case	NOUN
american_scientific_journal-4187	111	45	,	,	PUNCT
american_scientific_journal-4187	111	46	is	be	AUX
american_scientific_journal-4187	111	47	a	a	DET
american_scientific_journal-4187	111	48	dependable	dependable	ADJ
american_scientific_journal-4187	111	49	value	value	NOUN
american_scientific_journal-4187	111	50	measure	measure	NOUN
american_scientific_journal-4187	111	51	.	.	PUNCT
american_scientific_journal-4187	112	1	american	american	ADJ
american_scientific_journal-4187	112	2	scientific	scientific	ADJ
american_scientific_journal-4187	112	3	research	research	PROPN
american_scientific_journal-4187	112	4	journal	journal	NOUN
american_scientific_journal-4187	112	5	for	for	ADP
american_scientific_journal-4187	112	6	engineering	engineering	NOUN
american_scientific_journal-4187	112	7	,	,	PUNCT
american_scientific_journal-4187	112	8	technology	technology	NOUN
american_scientific_journal-4187	112	9	,	,	PUNCT
american_scientific_journal-4187	112	10	and	and	CCONJ
american_scientific_journal-4187	112	11	sciences	science	NOUN
american_scientific_journal-4187	112	12	(	(	PUNCT
american_scientific_journal-4187	112	13	asrjets	asrjet	NOUN
american_scientific_journal-4187	112	14	)	)	PUNCT
american_scientific_journal-4187	112	15	(	(	PUNCT
american_scientific_journal-4187	112	16	2019	2019	NUM
american_scientific_journal-4187	112	17	)	)	PUNCT
american_scientific_journal-4187	112	18	volume	volume	NOUN
american_scientific_journal-4187	112	19	59	59	NUM
american_scientific_journal-4187	112	20	,	,	PUNCT
american_scientific_journal-4187	112	21	no	no	DET
american_scientific_journal-4187	112	22	1	1	NUM
american_scientific_journal-4187	112	23	,	,	PUNCT
american_scientific_journal-4187	112	24	pp	pp	ADV
american_scientific_journal-4187	112	25	162	162	NUM
american_scientific_journal-4187	112	26	-	-	SYM
american_scientific_journal-4187	112	27	178	178	NUM
american_scientific_journal-4187	112	28	176	176	NUM
american_scientific_journal-4187	112	29	proof.it	proof.it	NOUN
american_scientific_journal-4187	112	30	’s	’	VERB
american_scientific_journal-4187	112	31	clear	clear	ADJ
american_scientific_journal-4187	112	32	that	that	SCONJ
american_scientific_journal-4187	112	33	we	we	PRON
american_scientific_journal-4187	112	34	can	can	AUX
american_scientific_journal-4187	112	35	as	as	ADV
american_scientific_journal-4187	112	36	follow	follow	VERB
american_scientific_journal-4187	112	37	:	:	PUNCT
american_scientific_journal-4187	112	38	𝜇	𝜇	ADP
american_scientific_journal-4187	112	39	(	(	PUNCT
american_scientific_journal-4187	112	40	(	(	PUNCT
american_scientific_journal-4187	112	41	𝜇	𝜇	X
american_scientific_journal-4187	112	42	(	(	PUNCT
american_scientific_journal-4187	112	43	⋃	⋃	PROPN
american_scientific_journal-4187	112	44	)	)	PUNCT
american_scientific_journal-4187	112	45	(	(	PUNCT
american_scientific_journal-4187	112	46	⋃	⋃	PROPN
american_scientific_journal-4187	112	47	)	)	PUNCT
american_scientific_journal-4187	112	48	as	as	ADP
american_scientific_journal-4187	112	49	a	a	DET
american_scientific_journal-4187	112	50	result	result	NOUN
american_scientific_journal-4187	112	51	,	,	PUNCT
american_scientific_journal-4187	112	52	has	have	VERB
american_scientific_journal-4187	112	53	one	one	NUM
american_scientific_journal-4187	112	54	-	-	PUNCT
american_scientific_journal-4187	112	55	sided	sided	ADJ
american_scientific_journal-4187	112	56	feature	feature	NOUN
american_scientific_journal-4187	112	57	and	and	CCONJ
american_scientific_journal-4187	112	58	due	due	ADP
american_scientific_journal-4187	112	59	to	to	ADP
american_scientific_journal-4187	112	60	the	the	DET
american_scientific_journal-4187	112	61	previous	previous	ADJ
american_scientific_journal-4187	112	62	theorem	theorem	NOUN
american_scientific_journal-4187	112	63	,	,	PUNCT
american_scientific_journal-4187	112	64	we	we	PRON
american_scientific_journal-4187	112	65	have	have	VERB
american_scientific_journal-4187	112	66	a	a	DET
american_scientific_journal-4187	112	67	dependable	dependable	ADJ
american_scientific_journal-4187	112	68	value	value	NOUN
american_scientific_journal-4187	112	69	measure	measure	NOUN
american_scientific_journal-4187	112	70	.	.	PUNCT
american_scientific_journal-4187	113	1	example7.let	example7.let	VERB
american_scientific_journal-4187	113	2	’s	’s	PART
american_scientific_journal-4187	113	3	think	think	VERB
american_scientific_journal-4187	113	4	about	about	ADP
american_scientific_journal-4187	113	5	the	the	DET
american_scientific_journal-4187	113	6	pre	pre	NOUN
american_scientific_journal-4187	113	7	-	-	NOUN
american_scientific_journal-4187	113	8	measure	measure	NOUN
american_scientific_journal-4187	113	9	that	that	PRON
american_scientific_journal-4187	113	10	can	can	AUX
american_scientific_journal-4187	113	11	satisfy	satisfy	VERB
american_scientific_journal-4187	113	12	for	for	ADP
american_scientific_journal-4187	113	13	any	any	DET
american_scientific_journal-4187	113	14	arbitrary	arbitrary	ADJ
american_scientific_journal-4187	113	15	numbers	number	NOUN
american_scientific_journal-4187	113	16	and	and	CCONJ
american_scientific_journal-4187	113	17	any	any	DET
american_scientific_journal-4187	113	18	sets	set	NOUN
american_scientific_journal-4187	113	19	of	of	ADP
american_scientific_journal-4187	113	20	condition	condition	NOUN
american_scientific_journal-4187	113	21	as	as	ADP
american_scientific_journal-4187	113	22	follow	follow	NOUN
american_scientific_journal-4187	113	23	:	:	PUNCT
american_scientific_journal-4187	113	24	(	(	PUNCT
american_scientific_journal-4187	113	25	(	(	PUNCT
american_scientific_journal-4187	113	26	⋃	⋃	X
american_scientific_journal-4187	113	27	(	(	PUNCT
american_scientific_journal-4187	113	28	such	such	ADJ
american_scientific_journal-4187	113	29	that	that	DET
american_scientific_journal-4187	113	30	and	and	CCONJ
american_scientific_journal-4187	113	31	{	{	PUNCT
american_scientific_journal-4187	113	32	(	(	PUNCT
american_scientific_journal-4187	113	33	(	(	PUNCT
american_scientific_journal-4187	113	34	is	be	AUX
american_scientific_journal-4187	113	35	turning	turn	VERB
american_scientific_journal-4187	113	36	to	to	ADP
american_scientific_journal-4187	113	37	which	which	PRON
american_scientific_journal-4187	113	38	is	be	AUX
american_scientific_journal-4187	113	39	dependable	dependable	ADJ
american_scientific_journal-4187	113	40	value	value	NOUN
american_scientific_journal-4187	113	41	measure	measure	NOUN
american_scientific_journal-4187	113	42	.	.	PUNCT
american_scientific_journal-4187	114	1	solution.suppose	solution.suppose	VERB
american_scientific_journal-4187	114	2	that	that	SCONJ
american_scientific_journal-4187	114	3	hence	hence	ADV
american_scientific_journal-4187	114	4	we	we	PRON
american_scientific_journal-4187	114	5	can	can	AUX
american_scientific_journal-4187	114	6	use	use	VERB
american_scientific_journal-4187	114	7	the	the	DET
american_scientific_journal-4187	114	8	condition	condition	NOUN
american_scientific_journal-4187	114	9	of	of	ADP
american_scientific_journal-4187	114	10	the	the	DET
american_scientific_journal-4187	114	11	problem	problem	NOUN
american_scientific_journal-4187	114	12	,	,	PUNCT
american_scientific_journal-4187	114	13	we	we	PRON
american_scientific_journal-4187	114	14	can	can	AUX
american_scientific_journal-4187	114	15	write	write	VERB
american_scientific_journal-4187	114	16	as	as	ADP
american_scientific_journal-4187	114	17	follow	follow	VERB
american_scientific_journal-4187	114	18	:	:	PUNCT
american_scientific_journal-4187	114	19	(	(	PUNCT
american_scientific_journal-4187	114	20	(	(	PUNCT
american_scientific_journal-4187	114	21	⋃	⋃	X
american_scientific_journal-4187	114	22	due	due	ADP
american_scientific_journal-4187	114	23	to	to	ADP
american_scientific_journal-4187	114	24	,	,	PUNCT
american_scientific_journal-4187	114	25	and	and	CCONJ
american_scientific_journal-4187	114	26	desired	desire	VERB
american_scientific_journal-4187	114	27	numbers	number	NOUN
american_scientific_journal-4187	114	28	and	and	CCONJ
american_scientific_journal-4187	114	29	sets	set	NOUN
american_scientific_journal-4187	114	30	,	,	PUNCT
american_scientific_journal-4187	114	31	we	we	PRON
american_scientific_journal-4187	114	32	have	have	AUX
american_scientific_journal-4187	114	33	as	as	ADV
american_scientific_journal-4187	114	34	follow	follow	VERB
american_scientific_journal-4187	114	35	:	:	PUNCT
american_scientific_journal-4187	114	36	(	(	PUNCT
american_scientific_journal-4187	114	37	(	(	PUNCT
american_scientific_journal-4187	114	38	(	(	PUNCT
american_scientific_journal-4187	114	39	⋃	⋃	PROPN
american_scientific_journal-4187	114	40	)	)	PUNCT
american_scientific_journal-4187	114	41	in	in	ADP
american_scientific_journal-4187	114	42	the	the	DET
american_scientific_journal-4187	114	43	following	following	NOUN
american_scientific_journal-4187	114	44	,	,	PUNCT
american_scientific_journal-4187	114	45	we	we	PRON
american_scientific_journal-4187	114	46	examine	examine	VERB
american_scientific_journal-4187	114	47	the	the	DET
american_scientific_journal-4187	114	48	feature	feature	NOUN
american_scientific_journal-4187	114	49	of	of	ADP
american_scientific_journal-4187	114	50	the	the	DET
american_scientific_journal-4187	114	51	dependable	dependable	ADJ
american_scientific_journal-4187	114	52	value	value	NOUN
american_scientific_journal-4187	114	53	measure	measure	NOUN
american_scientific_journal-4187	114	54	,	,	PUNCT
american_scientific_journal-4187	114	55	which	which	PRON
american_scientific_journal-4187	114	56	can	can	AUX
american_scientific_journal-4187	114	57	help	help	VERB
american_scientific_journal-4187	114	58	us	we	PRON
american_scientific_journal-4187	114	59	to	to	PART
american_scientific_journal-4187	114	60	accurately	accurately	ADV
american_scientific_journal-4187	114	61	get	get	VERB
american_scientific_journal-4187	114	62	the	the	DET
american_scientific_journal-4187	114	63	dependable	dependable	ADJ
american_scientific_journal-4187	114	64	value	value	NOUN
american_scientific_journal-4187	114	65	measure	measure	NOUN
american_scientific_journal-4187	114	66	.	.	PUNCT
american_scientific_journal-4187	115	1	if	if	SCONJ
american_scientific_journal-4187	115	2	then	then	ADV
american_scientific_journal-4187	115	3	we	we	PRON
american_scientific_journal-4187	115	4	have	have	VERB
american_scientific_journal-4187	115	5	as	as	ADV
american_scientific_journal-4187	115	6	follow	follow	VERB
american_scientific_journal-4187	115	7	:	:	PUNCT
american_scientific_journal-4187	115	8	(	(	PUNCT
american_scientific_journal-4187	115	9	(	(	PUNCT
american_scientific_journal-4187	115	10	theorem11	theorem11	NOUN
american_scientific_journal-4187	115	11	completes	complete	VERB
american_scientific_journal-4187	115	12	the	the	DET
american_scientific_journal-4187	115	13	answer	answer	NOUN
american_scientific_journal-4187	115	14	.	.	PUNCT
american_scientific_journal-4187	116	1	definition2.the	definition2.the	DET
american_scientific_journal-4187	116	2	dependable	dependable	ADJ
american_scientific_journal-4187	116	3	value	value	NOUN
american_scientific_journal-4187	116	4	measure	measure	NOUN
american_scientific_journal-4187	116	5	of	of	ADP
american_scientific_journal-4187	116	6	𝜇	𝜇	ADV
american_scientific_journal-4187	116	7	,	,	PUNCT
american_scientific_journal-4187	116	8	we	we	PRON
american_scientific_journal-4187	116	9	call	call	VERB
american_scientific_journal-4187	116	10	it	it	PRON
american_scientific_journal-4187	116	11	has	have	VERB
american_scientific_journal-4187	116	12	a	a	DET
american_scientific_journal-4187	116	13	simple	simple	ADJ
american_scientific_journal-4187	116	14	form	form	NOUN
american_scientific_journal-4187	116	15	;	;	PUNCT
american_scientific_journal-4187	116	16	if	if	SCONJ
american_scientific_journal-4187	116	17	we	we	PRON
american_scientific_journal-4187	116	18	have	have	VERB
american_scientific_journal-4187	116	19	for	for	ADP
american_scientific_journal-4187	116	20	every	every	PRON
american_scientific_journal-4187	116	21	as	as	ADV
american_scientific_journal-4187	116	22	follow	follow	NOUN
american_scientific_journal-4187	116	23	:	:	PUNCT
american_scientific_journal-4187	116	24	𝜇	𝜇	X
american_scientific_journal-4187	116	25	(	(	PUNCT
american_scientific_journal-4187	116	26	(	(	PUNCT
american_scientific_journal-4187	116	27	(	(	PUNCT
american_scientific_journal-4187	116	28	such	such	ADJ
american_scientific_journal-4187	116	29	that	that	PRON
american_scientific_journal-4187	116	30	can	can	AUX
american_scientific_journal-4187	116	31	satisfy	satisfy	VERB
american_scientific_journal-4187	116	32	this	this	DET
american_scientific_journal-4187	116	33	condition	condition	NOUN
american_scientific_journal-4187	116	34	)	)	PUNCT
american_scientific_journal-4187	116	35	*	*	PUNCT
american_scientific_journal-4187	116	36	(	(	PUNCT
american_scientific_journal-4187	116	37	,	,	PUNCT
american_scientific_journal-4187	116	38	and	and	CCONJ
american_scientific_journal-4187	116	39	also	also	ADV
american_scientific_journal-4187	116	40	measure	measure	NOUN
american_scientific_journal-4187	116	41	of	of	ADP
american_scientific_journal-4187	116	42	(	(	PUNCT
american_scientific_journal-4187	116	43	is	be	AUX
american_scientific_journal-4187	116	44	under	under	ADP
american_scientific_journal-4187	116	45	(	(	PUNCT
american_scientific_journal-4187	116	46	.	.	PUNCT
american_scientific_journal-4187	117	1	american	american	PROPN
american_scientific_journal-4187	117	2	scientific	scientific	ADJ
american_scientific_journal-4187	117	3	research	research	PROPN
american_scientific_journal-4187	117	4	journal	journal	NOUN
american_scientific_journal-4187	117	5	for	for	ADP
american_scientific_journal-4187	117	6	engineering	engineering	NOUN
american_scientific_journal-4187	117	7	,	,	PUNCT
american_scientific_journal-4187	117	8	technology	technology	NOUN
american_scientific_journal-4187	117	9	,	,	PUNCT
american_scientific_journal-4187	117	10	and	and	CCONJ
american_scientific_journal-4187	117	11	sciences	science	NOUN
american_scientific_journal-4187	117	12	(	(	PUNCT
american_scientific_journal-4187	117	13	asrjets	asrjet	NOUN
american_scientific_journal-4187	117	14	)	)	PUNCT
american_scientific_journal-4187	117	15	(	(	PUNCT
american_scientific_journal-4187	117	16	2019	2019	NUM
american_scientific_journal-4187	117	17	)	)	PUNCT
american_scientific_journal-4187	117	18	volume	volume	NOUN
american_scientific_journal-4187	117	19	59	59	NUM
american_scientific_journal-4187	117	20	,	,	PUNCT
american_scientific_journal-4187	117	21	no	no	DET
american_scientific_journal-4187	117	22	1	1	NUM
american_scientific_journal-4187	117	23	,	,	PUNCT
american_scientific_journal-4187	117	24	pp	pp	ADV
american_scientific_journal-4187	117	25	162	162	NUM
american_scientific_journal-4187	117	26	-	-	SYM
american_scientific_journal-4187	117	27	178	178	NUM
american_scientific_journal-4187	117	28	177	177	NUM
american_scientific_journal-4187	117	29	theorem13.assume	theorem13.assume	NOUN
american_scientific_journal-4187	117	30	that	that	PRON
american_scientific_journal-4187	117	31	𝜇	𝜇	AUX
american_scientific_journal-4187	117	32	be	be	VERB
american_scientific_journal-4187	117	33	a	a	DET
american_scientific_journal-4187	117	34	dependable	dependable	ADJ
american_scientific_journal-4187	117	35	value	value	NOUN
american_scientific_journal-4187	117	36	measure	measure	NOUN
american_scientific_journal-4187	117	37	such	such	ADJ
american_scientific_journal-4187	117	38	that	that	PRON
american_scientific_journal-4187	117	39	has	have	VERB
american_scientific_journal-4187	117	40	a	a	DET
american_scientific_journal-4187	117	41	simple	simple	ADJ
american_scientific_journal-4187	117	42	form	form	NOUN
american_scientific_journal-4187	117	43	.	.	PUNCT
american_scientific_journal-4187	118	1	also	also	ADV
american_scientific_journal-4187	118	2	,	,	PUNCT
american_scientific_journal-4187	118	3	suppose	suppose	VERB
american_scientific_journal-4187	118	4	given	give	VERB
american_scientific_journal-4187	118	5	deals	deal	NOUN
american_scientific_journal-4187	118	6	𝜇	𝜇	ADP
american_scientific_journal-4187	118	7	(	(	PUNCT
american_scientific_journal-4187	118	8	,	,	PUNCT
american_scientific_journal-4187	118	9	𝜇	𝜇	X
american_scientific_journal-4187	118	10	(	(	PUNCT
american_scientific_journal-4187	118	11	for	for	ADP
american_scientific_journal-4187	118	12	constant	constant	ADJ
american_scientific_journal-4187	118	13	number	number	NOUN
american_scientific_journal-4187	118	14	,	,	PUNCT
american_scientific_journal-4187	118	15	constant	constant	ADJ
american_scientific_journal-4187	118	16	set	set	NOUN
american_scientific_journal-4187	118	17	,	,	PUNCT
american_scientific_journal-4187	118	18	any	any	DET
american_scientific_journal-4187	118	19	numbers	number	NOUN
american_scientific_journal-4187	118	20	and	and	CCONJ
american_scientific_journal-4187	118	21	any	any	DET
american_scientific_journal-4187	118	22	sets	set	NOUN
american_scientific_journal-4187	118	23	such	such	ADJ
american_scientific_journal-4187	118	24	as	as	ADP
american_scientific_journal-4187	118	25	and	and	CCONJ
american_scientific_journal-4187	118	26	also	also	ADV
american_scientific_journal-4187	118	27	𝜇	𝜇	ADP
american_scientific_journal-4187	118	28	(	(	PUNCT
american_scientific_journal-4187	118	29	.then	.then	X
american_scientific_journal-4187	118	30	for	for	ADP
american_scientific_journal-4187	118	31	any	any	DET
american_scientific_journal-4187	118	32	arbitrary	arbitrary	ADJ
american_scientific_journal-4187	118	33	numbers	number	NOUN
american_scientific_journal-4187	118	34	such	such	ADJ
american_scientific_journal-4187	118	35	as	as	ADP
american_scientific_journal-4187	118	36	,	,	PUNCT
american_scientific_journal-4187	118	37	and	and	CCONJ
american_scientific_journal-4187	118	38	any	any	DET
american_scientific_journal-4187	118	39	arbitrary	arbitrary	ADJ
american_scientific_journal-4187	118	40	sets	set	NOUN
american_scientific_journal-4187	118	41	𝜇	𝜇	X
american_scientific_journal-4187	118	42	(	(	PUNCT
american_scientific_journal-4187	118	43	is	be	AUX
american_scientific_journal-4187	118	44	calculable	calculable	ADJ
american_scientific_journal-4187	118	45	.	.	PUNCT
american_scientific_journal-4187	119	1	proof.let	proof.let	NOUN
american_scientific_journal-4187	119	2	’s	’s	PART
american_scientific_journal-4187	119	3	think	think	VERB
american_scientific_journal-4187	119	4	we	we	PRON
american_scientific_journal-4187	119	5	have	have	AUX
american_scientific_journal-4187	119	6	as	as	ADV
american_scientific_journal-4187	119	7	follow	follow	VERB
american_scientific_journal-4187	119	8	:	:	PUNCT
american_scientific_journal-4187	119	9	𝜇	𝜇	X
american_scientific_journal-4187	119	10	(	(	PUNCT
american_scientific_journal-4187	119	11	(	(	PUNCT
american_scientific_journal-4187	119	12	(	(	PUNCT
american_scientific_journal-4187	119	13	in	in	ADP
american_scientific_journal-4187	119	14	this	this	DET
american_scientific_journal-4187	119	15	case	case	NOUN
american_scientific_journal-4187	119	16	,	,	PUNCT
american_scientific_journal-4187	119	17	we	we	PRON
american_scientific_journal-4187	119	18	can	can	AUX
american_scientific_journal-4187	119	19	conclude	conclude	VERB
american_scientific_journal-4187	119	20	from	from	ADP
american_scientific_journal-4187	119	21	this	this	DET
american_scientific_journal-4187	119	22	relation	relation	NOUN
american_scientific_journal-4187	119	23	:	:	PUNCT
american_scientific_journal-4187	119	24	pay	pay	VERB
american_scientific_journal-4187	119	25	attention	attention	NOUN
american_scientific_journal-4187	119	26	that	that	PRON
american_scientific_journal-4187	119	27	𝜇	𝜇	ADV
american_scientific_journal-4187	119	28	(	(	PUNCT
american_scientific_journal-4187	119	29	therefore	therefore	ADV
american_scientific_journal-4187	119	30	,	,	PUNCT
american_scientific_journal-4187	119	31	we	we	PRON
american_scientific_journal-4187	119	32	can	can	AUX
american_scientific_journal-4187	119	33	calculate	calculate	VERB
american_scientific_journal-4187	119	34	this	this	PRON
american_scientific_journal-4187	119	35	𝜇	𝜇	ADP
american_scientific_journal-4187	119	36	(	(	PUNCT
american_scientific_journal-4187	119	37	as	as	ADP
american_scientific_journal-4187	119	38	follow	follow	VERB
american_scientific_journal-4187	119	39	:	:	PUNCT
american_scientific_journal-4187	119	40	𝜇	𝜇	X
american_scientific_journal-4187	119	41	(	(	PUNCT
american_scientific_journal-4187	119	42	𝜇	𝜇	X
american_scientific_journal-4187	119	43	(	(	PUNCT
american_scientific_journal-4187	119	44	𝜇	𝜇	X
american_scientific_journal-4187	119	45	(	(	PUNCT
american_scientific_journal-4187	119	46	𝜇	𝜇	X
american_scientific_journal-4187	119	47	(	(	PUNCT
american_scientific_journal-4187	119	48	(	(	PUNCT
american_scientific_journal-4187	119	49	(	(	PUNCT
american_scientific_journal-4187	119	50	(	(	PUNCT
american_scientific_journal-4187	119	51	(	(	PUNCT
american_scientific_journal-4187	119	52	(	(	PUNCT
american_scientific_journal-4187	119	53	(	(	PUNCT
american_scientific_journal-4187	119	54	𝜇	𝜇	X
american_scientific_journal-4187	119	55	(	(	PUNCT
american_scientific_journal-4187	119	56	(	(	PUNCT
american_scientific_journal-4187	119	57	(	(	PUNCT
american_scientific_journal-4187	119	58	(	(	PUNCT
american_scientific_journal-4187	119	59	(	(	PUNCT
american_scientific_journal-4187	119	60	(	(	PUNCT
american_scientific_journal-4187	119	61	(	(	PUNCT
american_scientific_journal-4187	119	62	𝜇	𝜇	X
american_scientific_journal-4187	119	63	(	(	PUNCT
american_scientific_journal-4187	119	64	𝜇	𝜇	X
american_scientific_journal-4187	119	65	(	(	PUNCT
american_scientific_journal-4187	119	66	𝜇	𝜇	X
american_scientific_journal-4187	119	67	(	(	PUNCT
american_scientific_journal-4187	119	68	𝜇	𝜇	X
american_scientific_journal-4187	119	69	(	(	PUNCT
american_scientific_journal-4187	119	70	this	this	DET
american_scientific_journal-4187	119	71	simple	simple	ADJ
american_scientific_journal-4187	119	72	theorem	theorem	NOUN
american_scientific_journal-4187	119	73	has	have	VERB
american_scientific_journal-4187	119	74	important	important	ADJ
american_scientific_journal-4187	119	75	results	result	NOUN
american_scientific_journal-4187	119	76	.	.	PUNCT
american_scientific_journal-4187	120	1	some	some	PRON
american_scientific_journal-4187	120	2	of	of	ADP
american_scientific_journal-4187	120	3	them	they	PRON
american_scientific_journal-4187	120	4	are	be	AUX
american_scientific_journal-4187	120	5	referred	refer	VERB
american_scientific_journal-4187	120	6	to	to	ADP
american_scientific_journal-4187	120	7	below	below	ADV
american_scientific_journal-4187	120	8	.	.	PUNCT
american_scientific_journal-4187	121	1	theorem	theorem	VERB
american_scientific_journal-4187	121	2	14.suppose	14.suppose	NUM
american_scientific_journal-4187	121	3	that	that	SCONJ
american_scientific_journal-4187	121	4	we	we	PRON
american_scientific_journal-4187	121	5	have	have	VERB
american_scientific_journal-4187	121	6	below	below	ADP
american_scientific_journal-4187	121	7	relation	relation	NOUN
american_scientific_journal-4187	121	8	for	for	ADP
american_scientific_journal-4187	121	9	some	some	PRON
american_scientific_journal-4187	121	10	and	and	CCONJ
american_scientific_journal-4187	121	11	:	:	PUNCT
american_scientific_journal-4187	121	12	{	{	PUNCT
american_scientific_journal-4187	121	13	𝜇	𝜇	X
american_scientific_journal-4187	121	14	(	(	PUNCT
american_scientific_journal-4187	121	15	𝜇	𝜇	X
american_scientific_journal-4187	121	16	(	(	PUNCT
american_scientific_journal-4187	121	17	𝜇	𝜇	X
american_scientific_journal-4187	121	18	(	(	PUNCT
american_scientific_journal-4187	121	19	𝜇	𝜇	X
american_scientific_journal-4187	121	20	(	(	PUNCT
american_scientific_journal-4187	121	21	then	then	ADV
american_scientific_journal-4187	121	22	we	we	PRON
american_scientific_journal-4187	121	23	have	have	AUX
american_scientific_journal-4187	121	24	as	as	ADV
american_scientific_journal-4187	121	25	follow	follow	VERB
american_scientific_journal-4187	121	26	:	:	PUNCT
american_scientific_journal-4187	121	27	𝜇	𝜇	X
american_scientific_journal-4187	121	28	(	(	PUNCT
american_scientific_journal-4187	121	29	𝜇	𝜇	X
american_scientific_journal-4187	121	30	(	(	PUNCT
american_scientific_journal-4187	121	31	proof.according	proof.accorde	VERB
american_scientific_journal-4187	121	32	to	to	ADP
american_scientific_journal-4187	121	33	this	this	PRON
american_scientific_journal-4187	121	34	𝝁	𝝁	PROPN
american_scientific_journal-4187	121	35	(	(	PUNCT
american_scientific_journal-4187	121	36	𝝁	𝝁	NUM
american_scientific_journal-4187	121	37	(	(	PUNCT
american_scientific_journal-4187	121	38	,	,	PUNCT
american_scientific_journal-4187	121	39	we	we	PRON
american_scientific_journal-4187	121	40	can	can	AUX
american_scientific_journal-4187	121	41	use	use	VERB
american_scientific_journal-4187	121	42	above	above	ADP
american_scientific_journal-4187	121	43	theorem	theorem	NOUN
american_scientific_journal-4187	121	44	as	as	ADP
american_scientific_journal-4187	121	45	follow	follow	NOUN
american_scientific_journal-4187	121	46	:	:	PUNCT
american_scientific_journal-4187	121	47	𝜇	𝜇	X
american_scientific_journal-4187	121	48	(	(	PUNCT
american_scientific_journal-4187	121	49	𝜇	𝜇	X
american_scientific_journal-4187	121	50	(	(	PUNCT
american_scientific_journal-4187	121	51	𝜇	𝜇	X
american_scientific_journal-4187	121	52	(	(	PUNCT
american_scientific_journal-4187	121	53	𝜇	𝜇	X
american_scientific_journal-4187	121	54	(	(	PUNCT
american_scientific_journal-4187	121	55	𝜇	𝜇	X
american_scientific_journal-4187	121	56	(	(	PUNCT
american_scientific_journal-4187	121	57	𝜇	𝜇	X
american_scientific_journal-4187	121	58	(	(	PUNCT
american_scientific_journal-4187	121	59	𝜇	𝜇	X
american_scientific_journal-4187	121	60	(	(	PUNCT
american_scientific_journal-4187	121	61	𝜇	𝜇	X
american_scientific_journal-4187	121	62	(	(	PUNCT
american_scientific_journal-4187	121	63	therefore	therefore	ADV
american_scientific_journal-4187	121	64	,	,	PUNCT
american_scientific_journal-4187	121	65	we	we	PRON
american_scientific_journal-4187	121	66	have	have	AUX
american_scientific_journal-4187	121	67	as	as	ADV
american_scientific_journal-4187	121	68	follow	follow	VERB
american_scientific_journal-4187	121	69	:	:	PUNCT
american_scientific_journal-4187	121	70	𝜇	𝜇	X
american_scientific_journal-4187	121	71	(	(	PUNCT
american_scientific_journal-4187	121	72	𝜇	𝜇	X
american_scientific_journal-4187	121	73	(	(	PUNCT
american_scientific_journal-4187	121	74	𝜇	𝜇	X
american_scientific_journal-4187	121	75	(	(	PUNCT
american_scientific_journal-4187	121	76	𝜇	𝜇	X
american_scientific_journal-4187	121	77	(	(	PUNCT
american_scientific_journal-4187	121	78	𝜇	𝜇	X
american_scientific_journal-4187	121	79	(	(	PUNCT
american_scientific_journal-4187	121	80	𝜇	𝜇	X
american_scientific_journal-4187	121	81	(	(	PUNCT
american_scientific_journal-4187	121	82	this	this	DET
american_scientific_journal-4187	121	83	relation	relation	NOUN
american_scientific_journal-4187	121	84	and	and	CCONJ
american_scientific_journal-4187	121	85	hypothesis	hypothesis	NOUN
american_scientific_journal-4187	121	86	of	of	ADP
american_scientific_journal-4187	121	87	theorem	theorem	ADJ
american_scientific_journal-4187	121	88	yield	yield	NOUN
american_scientific_journal-4187	121	89	result	result	NOUN
american_scientific_journal-4187	121	90	.	.	PUNCT
american_scientific_journal-4187	122	1	american	american	ADJ
american_scientific_journal-4187	122	2	scientific	scientific	ADJ
american_scientific_journal-4187	122	3	research	research	PROPN
american_scientific_journal-4187	122	4	journal	journal	NOUN
american_scientific_journal-4187	122	5	for	for	ADP
american_scientific_journal-4187	122	6	engineering	engineering	NOUN
american_scientific_journal-4187	122	7	,	,	PUNCT
american_scientific_journal-4187	122	8	technology	technology	NOUN
american_scientific_journal-4187	122	9	,	,	PUNCT
american_scientific_journal-4187	122	10	and	and	CCONJ
american_scientific_journal-4187	122	11	sciences	science	NOUN
american_scientific_journal-4187	122	12	(	(	PUNCT
american_scientific_journal-4187	122	13	asrjets	asrjet	NOUN
american_scientific_journal-4187	122	14	)	)	PUNCT
american_scientific_journal-4187	122	15	(	(	PUNCT
american_scientific_journal-4187	122	16	2019	2019	NUM
american_scientific_journal-4187	122	17	)	)	PUNCT
american_scientific_journal-4187	122	18	volume	volume	NOUN
american_scientific_journal-4187	122	19	59	59	NUM
american_scientific_journal-4187	122	20	,	,	PUNCT
american_scientific_journal-4187	122	21	no	no	DET
american_scientific_journal-4187	122	22	1	1	NUM
american_scientific_journal-4187	122	23	,	,	PUNCT
american_scientific_journal-4187	122	24	pp	pp	ADV
american_scientific_journal-4187	122	25	162	162	NUM
american_scientific_journal-4187	122	26	-	-	SYM
american_scientific_journal-4187	122	27	178	178	NUM
american_scientific_journal-4187	122	28	178	178	NUM
american_scientific_journal-4187	122	29	theorem15.let	theorem15.let	NOUN
american_scientific_journal-4187	122	30	’s	’s	PART
american_scientific_journal-4187	122	31	think	think	VERB
american_scientific_journal-4187	122	32	𝝁	𝝁	PRON
american_scientific_journal-4187	122	33	is	be	AUX
american_scientific_journal-4187	122	34	dependable	dependable	ADJ
american_scientific_journal-4187	122	35	value	value	NOUN
american_scientific_journal-4187	122	36	pre	pre	NOUN
american_scientific_journal-4187	122	37	-	-	NOUN
american_scientific_journal-4187	122	38	measure	measure	NOUN
american_scientific_journal-4187	122	39	.	.	PUNCT
american_scientific_journal-4187	123	1	if	if	SCONJ
american_scientific_journal-4187	123	2	for	for	ADP
american_scientific_journal-4187	123	3	each	each	DET
american_scientific_journal-4187	123	4	numbers	number	NOUN
american_scientific_journal-4187	123	5	and	and	CCONJ
american_scientific_journal-4187	123	6	for	for	ADP
american_scientific_journal-4187	123	7	each	each	DET
american_scientific_journal-4187	123	8	sets	set	NOUN
american_scientific_journal-4187	123	9	like	like	ADP
american_scientific_journal-4187	123	10	there	there	PRON
american_scientific_journal-4187	123	11	exist	exist	VERB
american_scientific_journal-4187	123	12	and	and	CCONJ
american_scientific_journal-4187	123	13	,	,	PUNCT
american_scientific_journal-4187	123	14	so	so	ADV
american_scientific_journal-4187	123	15	we	we	PRON
american_scientific_journal-4187	123	16	have	have	AUX
american_scientific_journal-4187	123	17	as	as	ADV
american_scientific_journal-4187	123	18	follow	follow	VERB
american_scientific_journal-4187	123	19	:	:	PUNCT
american_scientific_journal-4187	123	20	𝜇	𝜇	X
american_scientific_journal-4187	123	21	(	(	PUNCT
american_scientific_journal-4187	123	22	𝜇	𝜇	X
american_scientific_journal-4187	123	23	(	(	PUNCT
american_scientific_journal-4187	123	24	𝜇	𝜇	X
american_scientific_journal-4187	123	25	(	(	PUNCT
american_scientific_journal-4187	123	26	𝜇	𝜇	X
american_scientific_journal-4187	123	27	(	(	PUNCT
american_scientific_journal-4187	123	28	𝜇	𝜇	X
american_scientific_journal-4187	123	29	(	(	PUNCT
american_scientific_journal-4187	123	30	also	also	ADV
american_scientific_journal-4187	123	31	,	,	PUNCT
american_scientific_journal-4187	123	32	the	the	DET
american_scientific_journal-4187	123	33	additional	additional	ADJ
american_scientific_journal-4187	123	34	of	of	ADP
american_scientific_journal-4187	123	35	𝜇	𝜇	ADP
american_scientific_journal-4187	123	36	(	(	PUNCT
american_scientific_journal-4187	123	37	𝜇	𝜇	X
american_scientific_journal-4187	123	38	(	(	PUNCT
american_scientific_journal-4187	123	39	be	be	AUX
american_scientific_journal-4187	123	40	positive	positive	ADJ
american_scientific_journal-4187	123	41	numbers	number	NOUN
american_scientific_journal-4187	123	42	.	.	PUNCT
american_scientific_journal-4187	124	1	then	then	ADV
american_scientific_journal-4187	124	2	𝜇	𝜇	X
american_scientific_journal-4187	124	3	is	be	AUX
american_scientific_journal-4187	124	4	a	a	DET
american_scientific_journal-4187	124	5	dependable	dependable	ADJ
american_scientific_journal-4187	124	6	value	value	NOUN
american_scientific_journal-4187	124	7	measure	measure	NOUN
american_scientific_journal-4187	124	8	.	.	PUNCT
american_scientific_journal-4187	125	1	proof.according	proof.accorde	VERB
american_scientific_journal-4187	125	2	to	to	ADP
american_scientific_journal-4187	125	3	the	the	DET
american_scientific_journal-4187	125	4	assumptions	assumption	NOUN
american_scientific_journal-4187	125	5	,	,	PUNCT
american_scientific_journal-4187	125	6	we	we	PRON
american_scientific_journal-4187	125	7	can	can	AUX
american_scientific_journal-4187	125	8	write	write	VERB
american_scientific_journal-4187	125	9	as	as	ADP
american_scientific_journal-4187	125	10	follow	follow	VERB
american_scientific_journal-4187	125	11	:	:	PUNCT
american_scientific_journal-4187	125	12	𝜇	𝜇	X
american_scientific_journal-4187	125	13	(	(	PUNCT
american_scientific_journal-4187	125	14	𝜇	𝜇	X
american_scientific_journal-4187	125	15	(	(	PUNCT
american_scientific_journal-4187	125	16	𝜇	𝜇	X
american_scientific_journal-4187	125	17	(	(	PUNCT
american_scientific_journal-4187	125	18	𝜇	𝜇	X
american_scientific_journal-4187	125	19	(	(	PUNCT
american_scientific_journal-4187	125	20	𝜇	𝜇	X
american_scientific_journal-4187	125	21	(	(	PUNCT
american_scientific_journal-4187	125	22	𝜇	𝜇	X
american_scientific_journal-4187	125	23	(	(	PUNCT
american_scientific_journal-4187	125	24	𝜇	𝜇	X
american_scientific_journal-4187	125	25	(	(	PUNCT
american_scientific_journal-4187	125	26	now	now	ADV
american_scientific_journal-4187	125	27	,	,	PUNCT
american_scientific_journal-4187	125	28	due	due	ADP
american_scientific_journal-4187	125	29	to	to	ADP
american_scientific_journal-4187	125	30	the	the	DET
american_scientific_journal-4187	125	31	theorem	theorem	ADJ
american_scientific_journal-4187	125	32	13	13	NUM
american_scientific_journal-4187	125	33	,	,	PUNCT
american_scientific_journal-4187	125	34	we	we	PRON
american_scientific_journal-4187	125	35	can	can	AUX
american_scientific_journal-4187	125	36	write	write	VERB
american_scientific_journal-4187	125	37	as	as	ADP
american_scientific_journal-4187	125	38	follow	follow	VERB
american_scientific_journal-4187	125	39	:	:	PUNCT
american_scientific_journal-4187	125	40	𝜇	𝜇	X
american_scientific_journal-4187	125	41	(	(	PUNCT
american_scientific_journal-4187	125	42	𝜇	𝜇	X
american_scientific_journal-4187	125	43	(	(	PUNCT
american_scientific_journal-4187	125	44	𝜇	𝜇	X
american_scientific_journal-4187	125	45	(	(	PUNCT
american_scientific_journal-4187	125	46	pay	pay	VERB
american_scientific_journal-4187	125	47	attention	attention	NOUN
american_scientific_journal-4187	125	48	that	that	PRON
american_scientific_journal-4187	125	49	assumptions	assumption	NOUN
american_scientific_journal-4187	125	50	are	be	AUX
american_scientific_journal-4187	125	51	for	for	ADP
american_scientific_journal-4187	125	52	and	and	CCONJ
american_scientific_journal-4187	125	53	,	,	PUNCT
american_scientific_journal-4187	125	54	so	so	CCONJ
american_scientific_journal-4187	125	55	this	this	DET
american_scientific_journal-4187	125	56	proof	proof	NOUN
american_scientific_journal-4187	125	57	is	be	AUX
american_scientific_journal-4187	125	58	over	over	ADP
american_scientific_journal-4187	125	59	theorem16.let	theorem16.let	PROPN
american_scientific_journal-4187	125	60	’s	’s	PART
american_scientific_journal-4187	125	61	𝝁	𝝁	PRON
american_scientific_journal-4187	125	62	is	be	AUX
american_scientific_journal-4187	125	63	dependable	dependable	ADJ
american_scientific_journal-4187	125	64	value	value	NOUN
american_scientific_journal-4187	125	65	pre	pre	NOUN
american_scientific_journal-4187	125	66	-	-	NOUN
american_scientific_journal-4187	125	67	measure	measure	NOUN
american_scientific_journal-4187	125	68	and	and	CCONJ
american_scientific_journal-4187	125	69	also	also	ADV
american_scientific_journal-4187	125	70	if	if	SCONJ
american_scientific_journal-4187	125	71	for	for	ADP
american_scientific_journal-4187	125	72	every	every	DET
american_scientific_journal-4187	125	73	numbers	number	NOUN
american_scientific_journal-4187	125	74	and	and	CCONJ
american_scientific_journal-4187	125	75	sets	set	NOUN
american_scientific_journal-4187	125	76	,	,	PUNCT
american_scientific_journal-4187	125	77	there	there	PRON
american_scientific_journal-4187	125	78	exist	exist	VERB
american_scientific_journal-4187	125	79	a	a	DET
american_scientific_journal-4187	125	80	number	number	NOUN
american_scientific_journal-4187	125	81	and	and	CCONJ
american_scientific_journal-4187	125	82	set	set	VERB
american_scientific_journal-4187	125	83	,	,	PUNCT
american_scientific_journal-4187	125	84	such	such	ADJ
american_scientific_journal-4187	125	85	that	that	SCONJ
american_scientific_journal-4187	125	86	:	:	PUNCT
american_scientific_journal-4187	125	87	𝜇	𝜇	X
american_scientific_journal-4187	125	88	(	(	PUNCT
american_scientific_journal-4187	125	89	𝜇	𝜇	X
american_scientific_journal-4187	125	90	(	(	PUNCT
american_scientific_journal-4187	125	91	𝜇	𝜇	X
american_scientific_journal-4187	125	92	(	(	PUNCT
american_scientific_journal-4187	125	93	𝜇	𝜇	X
american_scientific_journal-4187	125	94	(	(	PUNCT
american_scientific_journal-4187	125	95	then	then	ADV
american_scientific_journal-4187	125	96	𝜇	𝜇	ADP
american_scientific_journal-4187	125	97	is	be	AUX
american_scientific_journal-4187	125	98	dependable	dependable	ADJ
american_scientific_journal-4187	125	99	value	value	NOUN
american_scientific_journal-4187	125	100	measure	measure	NOUN
american_scientific_journal-4187	125	101	.	.	PUNCT
american_scientific_journal-4187	126	1	proof	proof	NOUN
american_scientific_journal-4187	126	2	.	.	PUNCT
american_scientific_journal-4187	127	1	according	accord	VERB
american_scientific_journal-4187	127	2	to	to	ADP
american_scientific_journal-4187	127	3	the	the	DET
american_scientific_journal-4187	127	4	assumptions	assumption	NOUN
american_scientific_journal-4187	127	5	,	,	PUNCT
american_scientific_journal-4187	127	6	we	we	PRON
american_scientific_journal-4187	127	7	can	can	AUX
american_scientific_journal-4187	127	8	write	write	VERB
american_scientific_journal-4187	127	9	as	as	ADP
american_scientific_journal-4187	127	10	follow	follow	VERB
american_scientific_journal-4187	127	11	:	:	PUNCT
american_scientific_journal-4187	127	12	𝜇	𝜇	X
american_scientific_journal-4187	127	13	(	(	PUNCT
american_scientific_journal-4187	127	14	now	now	ADV
american_scientific_journal-4187	127	15	,	,	PUNCT
american_scientific_journal-4187	127	16	other	other	ADJ
american_scientific_journal-4187	127	17	operations	operation	NOUN
american_scientific_journal-4187	127	18	by	by	ADP
american_scientific_journal-4187	127	19	theorem	theorem	NOUN
american_scientific_journal-4187	127	20	13	13	NUM
american_scientific_journal-4187	127	21	is	be	AUX
american_scientific_journal-4187	127	22	simple	simple	ADJ
american_scientific_journal-4187	127	23	.	.	PUNCT
american_scientific_journal-4187	128	1	references	reference	NOUN
american_scientific_journal-4187	128	2	[	[	X
american_scientific_journal-4187	128	3	1	1	NUM
american_scientific_journal-4187	128	4	]	]	PUNCT
american_scientific_journal-4187	128	5	.	.	PUNCT
american_scientific_journal-4187	129	1	p.r.halmos	p.r.halmos	PROPN
american_scientific_journal-4187	129	2	,	,	PUNCT
american_scientific_journal-4187	129	3	measure	measure	NOUN
american_scientific_journal-4187	129	4	theory	theory	NOUN
american_scientific_journal-4187	129	5	,	,	PUNCT
american_scientific_journal-4187	129	6	van	van	PROPN
american_scientific_journal-4187	129	7	nostrand	nostrand	PROPN
american_scientific_journal-4187	129	8	,	,	PUNCT
american_scientific_journal-4187	129	9	new	new	PROPN
american_scientific_journal-4187	129	10	york	york	PROPN
american_scientific_journal-4187	129	11	,	,	PUNCT
american_scientific_journal-4187	129	12	1997	1997	NUM
american_scientific_journal-4187	129	13	.	.	PUNCT
american_scientific_journal-4187	130	1	[	[	X
american_scientific_journal-4187	130	2	2	2	NUM
american_scientific_journal-4187	130	3	]	]	PUNCT
american_scientific_journal-4187	130	4	.	.	PUNCT
american_scientific_journal-4187	131	1	d.b	d.b	PROPN
american_scientific_journal-4187	131	2	.	.	PROPN
american_scientific_journal-4187	131	3	finetti	finetti	PROPN
american_scientific_journal-4187	131	4	,	,	PUNCT
american_scientific_journal-4187	131	5	theory	theory	NOUN
american_scientific_journal-4187	131	6	of	of	ADP
american_scientific_journal-4187	131	7	probability	probability	NOUN
american_scientific_journal-4187	131	8	(	(	PUNCT
american_scientific_journal-4187	131	9	i),john	i),john	PROPN
american_scientific_journal-4187	131	10	wiley	wiley	NOUN
american_scientific_journal-4187	131	11	,	,	PUNCT
american_scientific_journal-4187	131	12	new	new	PROPN
american_scientific_journal-4187	131	13	york	york	PROPN
american_scientific_journal-4187	131	14	,	,	PUNCT
american_scientific_journal-4187	131	15	1994	1994	NUM
american_scientific_journal-4187	131	16	.	.	PUNCT
american_scientific_journal-4187	132	1	[	[	X
american_scientific_journal-4187	132	2	3	3	NUM
american_scientific_journal-4187	132	3	]	]	PUNCT
american_scientific_journal-4187	132	4	.	.	PUNCT
american_scientific_journal-4187	133	1	e.hewitt	e.hewitt	PUNCT
american_scientific_journal-4187	133	2	andk.a.ross	andk.a.ross	NOUN
american_scientific_journal-4187	133	3	,	,	PUNCT
american_scientific_journal-4187	133	4	abstract	abstract	ADJ
american_scientific_journal-4187	133	5	harmonic	harmonic	ADJ
american_scientific_journal-4187	133	6	analysis	analysis	NOUN
american_scientific_journal-4187	133	7	,	,	PUNCT
american_scientific_journal-4187	133	8	vol.i	vol.i	PROPN
american_scientific_journal-4187	133	9	,	,	PUNCT
american_scientific_journal-4187	133	10	springer	springer	NOUN
american_scientific_journal-4187	133	11	-	-	PUNCT
american_scientific_journal-4187	133	12	verlag	verlag	PROPN
american_scientific_journal-4187	133	13	,	,	PUNCT
american_scientific_journal-4187	133	14	berlin(1965	berlin(1965	NOUN
american_scientific_journal-4187	133	15	)	)	PUNCT
american_scientific_journal-4187	133	16	.	.	PUNCT
american_scientific_journal-4187	134	1	[	[	X
american_scientific_journal-4187	134	2	4	4	NUM
american_scientific_journal-4187	134	3	]	]	PUNCT
american_scientific_journal-4187	134	4	.	.	PUNCT
american_scientific_journal-4187	135	1	i.n.herstein	i.n.herstein	ADJ
american_scientific_journal-4187	135	2	,	,	PUNCT
american_scientific_journal-4187	135	3	topics	topic	NOUN
american_scientific_journal-4187	135	4	in	in	ADP
american_scientific_journal-4187	135	5	algebra.new	algebra.new	PROPN
american_scientific_journal-4187	135	6	york	york	PROPN
american_scientific_journal-4187	135	7	:	:	PUNCT
american_scientific_journal-4187	135	8	blasdell,1994	blasdell,1994	VERB
american_scientific_journal-4187	135	9	.	.	PUNCT
american_scientific_journal-4187	136	1	[	[	X
american_scientific_journal-4187	136	2	5	5	NUM
american_scientific_journal-4187	136	3	]	]	PUNCT
american_scientific_journal-4187	136	4	.	.	PUNCT
american_scientific_journal-4187	136	5	r.a.dean	r.a.dean	ADJ
american_scientific_journal-4187	136	6	,	,	PUNCT
american_scientific_journal-4187	136	7	elements	element	NOUN
american_scientific_journal-4187	136	8	of	of	ADP
american_scientific_journal-4187	136	9	abstract	abstract	ADJ
american_scientific_journal-4187	136	10	algebra.new	algebra.new	PROPN
american_scientific_journal-4187	136	11	york	york	PROPN
american_scientific_journal-4187	136	12	:	:	PUNCT
american_scientific_journal-4187	136	13	wily	wily	ADJ
american_scientific_journal-4187	136	14	,	,	PUNCT
american_scientific_journal-4187	136	15	1996	1996	NUM
american_scientific_journal-4187	136	16	.	.	PUNCT