id	sid	tid	token	lemma	pos
american_scientific_journal-2507	1	1	47	47	NUM
american_scientific_journal-2507	1	2	american	american	ADJ
american_scientific_journal-2507	1	3	scientific	scientific	ADJ
american_scientific_journal-2507	1	4	research	research	NOUN
american_scientific_journal-2507	1	5	journal	journal	NOUN
american_scientific_journal-2507	1	6	for	for	ADP
american_scientific_journal-2507	1	7	engineering	engineering	NOUN
american_scientific_journal-2507	1	8	,	,	PUNCT
american_scientific_journal-2507	1	9	technology	technology	NOUN
american_scientific_journal-2507	1	10	,	,	PUNCT
american_scientific_journal-2507	1	11	and	and	CCONJ
american_scientific_journal-2507	1	12	sciences	science	NOUN
american_scientific_journal-2507	1	13	(	(	PUNCT
american_scientific_journal-2507	1	14	asrjets	asrjet	NOUN
american_scientific_journal-2507	1	15	)	)	PUNCT
american_scientific_journal-2507	1	16	issn	issn	PROPN
american_scientific_journal-2507	1	17	(	(	PUNCT
american_scientific_journal-2507	1	18	print	print	NOUN
american_scientific_journal-2507	1	19	)	)	PUNCT
american_scientific_journal-2507	1	20	2313	2313	NUM
american_scientific_journal-2507	1	21	-	-	SYM
american_scientific_journal-2507	1	22	4410	4410	NUM
american_scientific_journal-2507	1	23	,	,	PUNCT
american_scientific_journal-2507	1	24	issn	issn	PROPN
american_scientific_journal-2507	1	25	(	(	PUNCT
american_scientific_journal-2507	1	26	online	online	ADJ
american_scientific_journal-2507	1	27	)	)	PUNCT
american_scientific_journal-2507	1	28	2313	2313	NUM
american_scientific_journal-2507	1	29	-	-	SYM
american_scientific_journal-2507	1	30	4402	4402	NUM
american_scientific_journal-2507	1	31	©	©	PROPN
american_scientific_journal-2507	1	32	global	global	ADJ
american_scientific_journal-2507	1	33	society	society	NOUN
american_scientific_journal-2507	1	34	of	of	ADP
american_scientific_journal-2507	1	35	scientific	scientific	ADJ
american_scientific_journal-2507	1	36	research	research	NOUN
american_scientific_journal-2507	1	37	and	and	CCONJ
american_scientific_journal-2507	1	38	researchers	researcher	NOUN
american_scientific_journal-2507	1	39	http://asrjetsjournal.org/	http://asrjetsjournal.org/	PROPN
american_scientific_journal-2507	1	40	numerical	numerical	ADJ
american_scientific_journal-2507	1	41	solution	solution	NOUN
american_scientific_journal-2507	1	42	of	of	ADP
american_scientific_journal-2507	1	43	volterra	volterra	PROPN
american_scientific_journal-2507	1	44	integral	integral	ADJ
american_scientific_journal-2507	1	45	equation	equation	NOUN
american_scientific_journal-2507	1	46	and	and	CCONJ
american_scientific_journal-2507	1	47	its	its	PRON
american_scientific_journal-2507	1	48	error	error	NOUN
american_scientific_journal-2507	1	49	estimates	estimate	NOUN
american_scientific_journal-2507	1	50	via	via	ADP
american_scientific_journal-2507	1	51	spectral	spectral	ADJ
american_scientific_journal-2507	1	52	method	method	PROPN
american_scientific_journal-2507	1	53	olagunju	olagunju	PROPN
american_scientific_journal-2507	1	54	adeyemi	adeyemi	ADP
american_scientific_journal-2507	1	55	s.a	s.a	PROPN
american_scientific_journal-2507	1	56	*	*	PROPN
american_scientific_journal-2507	1	57	,	,	PUNCT
american_scientific_journal-2507	1	58	ogunlaran	ogunlaran	ADJ
american_scientific_journal-2507	1	59	matthew	matthew	PROPN
american_scientific_journal-2507	1	60	o.b	o.b	PROPN
american_scientific_journal-2507	1	61	,	,	PUNCT
american_scientific_journal-2507	1	62	ibrahim	ibrahim	PROPN
american_scientific_journal-2507	1	63	adebisi	adebisi	PROPN
american_scientific_journal-2507	1	64	a.c	a.c	PROPN
american_scientific_journal-2507	1	65	adepartment	adepartment	NOUN
american_scientific_journal-2507	1	66	of	of	ADP
american_scientific_journal-2507	1	67	mathematics	mathematic	NOUN
american_scientific_journal-2507	1	68	,	,	PUNCT
american_scientific_journal-2507	1	69	federal	federal	ADJ
american_scientific_journal-2507	1	70	university	university	NOUN
american_scientific_journal-2507	1	71	lafia	lafia	NOUN
american_scientific_journal-2507	1	72	,	,	PUNCT
american_scientific_journal-2507	1	73	950101	950101	NUM
american_scientific_journal-2507	1	74	,	,	PUNCT
american_scientific_journal-2507	1	75	nigeria	nigeria	PROPN
american_scientific_journal-2507	1	76	bdepartment	bdepartment	NOUN
american_scientific_journal-2507	1	77	of	of	ADP
american_scientific_journal-2507	1	78	mathematics	mathematic	NOUN
american_scientific_journal-2507	1	79	and	and	CCONJ
american_scientific_journal-2507	1	80	statistics	statistic	NOUN
american_scientific_journal-2507	1	81	,	,	PUNCT
american_scientific_journal-2507	1	82	bowen	bowen	PROPN
american_scientific_journal-2507	1	83	university	university	PROPN
american_scientific_journal-2507	1	84	iwo	iwo	PROPN
american_scientific_journal-2507	1	85	,	,	PUNCT
american_scientific_journal-2507	1	86	232101	232101	NUM
american_scientific_journal-2507	1	87	,	,	PUNCT
american_scientific_journal-2507	1	88	nigeria	nigeria	PROPN
american_scientific_journal-2507	1	89	cdepartment	cdepartment	NOUN
american_scientific_journal-2507	1	90	of	of	ADP
american_scientific_journal-2507	1	91	mathematical	mathematical	ADJ
american_scientific_journal-2507	1	92	sciences	sciences	PROPN
american_scientific_journal-2507	1	93	,	,	PUNCT
american_scientific_journal-2507	1	94	oduduwa	oduduwa	PROPN
american_scientific_journal-2507	1	95	university	university	NOUN
american_scientific_journal-2507	1	96	ipetumodu	ipetumodu	NOUN
american_scientific_journal-2507	1	97	,	,	PUNCT
american_scientific_journal-2507	1	98	220371	220371	NUM
american_scientific_journal-2507	1	99	,	,	PUNCT
american_scientific_journal-2507	1	100	nigeria	nigeria	PROPN
american_scientific_journal-2507	1	101	aemail	aemail	NOUN
american_scientific_journal-2507	1	102	:	:	PUNCT
american_scientific_journal-2507	1	103	olagunjuas@gmail.com	olagunjuas@gmail.com	X
american_scientific_journal-2507	1	104	bemail	bemail	NOUN
american_scientific_journal-2507	1	105	:	:	PUNCT
american_scientific_journal-2507	1	106	dothew2002@yahoo.com	dothew2002@yahoo.com	X
american_scientific_journal-2507	2	1	cemail	cemail	NOUN
american_scientific_journal-2507	2	2	:	:	PUNCT
american_scientific_journal-2507	3	1	adebisiibrahim@yahoo.com	adebisiibrahim@yahoo.com	X
american_scientific_journal-2507	3	2	abstract	abstract	ADV
american_scientific_journal-2507	3	3	in	in	ADP
american_scientific_journal-2507	3	4	this	this	DET
american_scientific_journal-2507	3	5	article	article	NOUN
american_scientific_journal-2507	3	6	,	,	PUNCT
american_scientific_journal-2507	3	7	numerical	numerical	ADJ
american_scientific_journal-2507	3	8	solution	solution	NOUN
american_scientific_journal-2507	3	9	of	of	ADP
american_scientific_journal-2507	3	10	volterra	volterra	PROPN
american_scientific_journal-2507	3	11	integral	integral	ADJ
american_scientific_journal-2507	3	12	equations	equation	NOUN
american_scientific_journal-2507	3	13	is	be	AUX
american_scientific_journal-2507	3	14	considered	consider	VERB
american_scientific_journal-2507	3	15	.	.	PUNCT
american_scientific_journal-2507	4	1	a	a	DET
american_scientific_journal-2507	4	2	new	new	ADJ
american_scientific_journal-2507	4	3	approach	approach	NOUN
american_scientific_journal-2507	4	4	in	in	ADP
american_scientific_journal-2507	4	5	the	the	DET
american_scientific_journal-2507	4	6	application	application	NOUN
american_scientific_journal-2507	4	7	of	of	ADP
american_scientific_journal-2507	4	8	spectral	spectral	ADJ
american_scientific_journal-2507	4	9	method	method	NOUN
american_scientific_journal-2507	4	10	is	be	AUX
american_scientific_journal-2507	4	11	proposed	propose	VERB
american_scientific_journal-2507	4	12	,	,	PUNCT
american_scientific_journal-2507	4	13	wherein	wherein	SCONJ
american_scientific_journal-2507	4	14	chebyshev	chebyshev	PROPN
american_scientific_journal-2507	4	15	polynomial	polynomial	NOUN
american_scientific_journal-2507	4	16	of	of	ADP
american_scientific_journal-2507	4	17	the	the	DET
american_scientific_journal-2507	4	18	first	first	ADJ
american_scientific_journal-2507	4	19	kind	kind	NOUN
american_scientific_journal-2507	4	20	)	)	PUNCT
american_scientific_journal-2507	4	21	(	(	PUNCT
american_scientific_journal-2507	4	22	xtk	xtk	ADV
american_scientific_journal-2507	4	23	serves	serve	VERB
american_scientific_journal-2507	4	24	as	as	ADP
american_scientific_journal-2507	4	25	the	the	DET
american_scientific_journal-2507	4	26	basis	basis	NOUN
american_scientific_journal-2507	4	27	function	function	NOUN
american_scientific_journal-2507	4	28	.	.	PUNCT
american_scientific_journal-2507	5	1	essentially	essentially	ADV
american_scientific_journal-2507	5	2	,	,	PUNCT
american_scientific_journal-2507	5	3	the	the	DET
american_scientific_journal-2507	5	4	method	method	NOUN
american_scientific_journal-2507	5	5	is	be	AUX
american_scientific_journal-2507	5	6	based	base	VERB
american_scientific_journal-2507	5	7	on	on	ADP
american_scientific_journal-2507	5	8	the	the	DET
american_scientific_journal-2507	5	9	approach	approach	NOUN
american_scientific_journal-2507	5	10	of	of	ADP
american_scientific_journal-2507	5	11	series	series	NOUN
american_scientific_journal-2507	5	12	solution	solution	NOUN
american_scientific_journal-2507	5	13	where	where	SCONJ
american_scientific_journal-2507	5	14	coefficients	coefficient	NOUN
american_scientific_journal-2507	5	15	of	of	ADP
american_scientific_journal-2507	5	16	)	)	PUNCT
american_scientific_journal-2507	5	17	(	(	PUNCT
american_scientific_journal-2507	5	18	xtk	xtk	ADV
american_scientific_journal-2507	5	19	in	in	ADP
american_scientific_journal-2507	5	20	the	the	DET
american_scientific_journal-2507	5	21	residual	residual	ADJ
american_scientific_journal-2507	5	22	equations	equation	NOUN
american_scientific_journal-2507	5	23	are	be	AUX
american_scientific_journal-2507	5	24	correspondingly	correspondingly	ADV
american_scientific_journal-2507	5	25	equated	equate	VERB
american_scientific_journal-2507	5	26	to	to	PART
american_scientific_journal-2507	5	27	yield	yield	VERB
american_scientific_journal-2507	5	28	system	system	NOUN
american_scientific_journal-2507	5	29	of	of	ADP
american_scientific_journal-2507	5	30	equations	equation	NOUN
american_scientific_journal-2507	5	31	.	.	PUNCT
american_scientific_journal-2507	6	1	expression	expression	NOUN
american_scientific_journal-2507	6	2	for	for	ADP
american_scientific_journal-2507	6	3	error	error	NOUN
american_scientific_journal-2507	6	4	estimates	estimate	NOUN
american_scientific_journal-2507	6	5	which	which	PRON
american_scientific_journal-2507	6	6	effectively	effectively	ADV
american_scientific_journal-2507	6	7	serves	serve	VERB
american_scientific_journal-2507	6	8	as	as	ADP
american_scientific_journal-2507	6	9	upper	upper	ADJ
american_scientific_journal-2507	6	10	bound	bind	VERB
american_scientific_journal-2507	6	11	for	for	ADP
american_scientific_journal-2507	6	12	accrued	accrue	VERB
american_scientific_journal-2507	6	13	errors	error	NOUN
american_scientific_journal-2507	6	14	is	be	AUX
american_scientific_journal-2507	6	15	arrived	arrive	VERB
american_scientific_journal-2507	6	16	at	at	ADP
american_scientific_journal-2507	6	17	.	.	PUNCT
american_scientific_journal-2507	7	1	to	to	PART
american_scientific_journal-2507	7	2	illustrate	illustrate	VERB
american_scientific_journal-2507	7	3	the	the	DET
american_scientific_journal-2507	7	4	accuracy	accuracy	NOUN
american_scientific_journal-2507	7	5	and	and	CCONJ
american_scientific_journal-2507	7	6	effectiveness	effectiveness	NOUN
american_scientific_journal-2507	7	7	of	of	ADP
american_scientific_journal-2507	7	8	the	the	DET
american_scientific_journal-2507	7	9	method	method	NOUN
american_scientific_journal-2507	7	10	and	and	CCONJ
american_scientific_journal-2507	7	11	its	its	PRON
american_scientific_journal-2507	7	12	error	error	NOUN
american_scientific_journal-2507	7	13	estimates	estimate	NOUN
american_scientific_journal-2507	7	14	,	,	PUNCT
american_scientific_journal-2507	7	15	numerical	numerical	ADJ
american_scientific_journal-2507	7	16	examples	example	NOUN
american_scientific_journal-2507	7	17	on	on	ADP
american_scientific_journal-2507	7	18	some	some	DET
american_scientific_journal-2507	7	19	standard	standard	ADJ
american_scientific_journal-2507	7	20	integral	integral	ADJ
american_scientific_journal-2507	7	21	equations	equation	NOUN
american_scientific_journal-2507	7	22	are	be	AUX
american_scientific_journal-2507	7	23	given	give	VERB
american_scientific_journal-2507	7	24	.	.	PUNCT
american_scientific_journal-2507	8	1	keywords	keyword	NOUN
american_scientific_journal-2507	8	2	:	:	PUNCT
american_scientific_journal-2507	8	3	spectral	spectral	ADJ
american_scientific_journal-2507	8	4	method	method	NOUN
american_scientific_journal-2507	8	5	;	;	PUNCT
american_scientific_journal-2507	8	6	chebyshev	chebyshev	NOUN
american_scientific_journal-2507	8	7	basis	basis	NOUN
american_scientific_journal-2507	8	8	function	function	NOUN
american_scientific_journal-2507	8	9	;	;	PUNCT
american_scientific_journal-2507	8	10	coefficients	coefficient	NOUN
american_scientific_journal-2507	8	11	;	;	PUNCT
american_scientific_journal-2507	8	12	volterra	volterra	PROPN
american_scientific_journal-2507	8	13	integral	integral	ADJ
american_scientific_journal-2507	8	14	equations;error	equations;error	NOUN
american_scientific_journal-2507	8	15	estimates	estimate	NOUN
american_scientific_journal-2507	8	16	.	.	PUNCT
american_scientific_journal-2507	9	1	1	1	X
american_scientific_journal-2507	9	2	.	.	X
american_scientific_journal-2507	9	3	introduction	introduction	NOUN
american_scientific_journal-2507	9	4	on	on	ADP
american_scientific_journal-2507	9	5	a	a	DET
american_scientific_journal-2507	9	6	general	general	ADJ
american_scientific_journal-2507	9	7	note	note	NOUN
american_scientific_journal-2507	9	8	,	,	PUNCT
american_scientific_journal-2507	9	9	the	the	DET
american_scientific_journal-2507	9	10	term	term	NOUN
american_scientific_journal-2507	9	11	integral	integral	ADJ
american_scientific_journal-2507	9	12	equation	equation	NOUN
american_scientific_journal-2507	9	13	refers	refer	VERB
american_scientific_journal-2507	9	14	to	to	ADP
american_scientific_journal-2507	9	15	an	an	DET
american_scientific_journal-2507	9	16	equation	equation	NOUN
american_scientific_journal-2507	9	17	where	where	SCONJ
american_scientific_journal-2507	9	18	an	an	DET
american_scientific_journal-2507	9	19	unknown	unknown	ADJ
american_scientific_journal-2507	9	20	function	function	NOUN
american_scientific_journal-2507	9	21	occurs	occur	VERB
american_scientific_journal-2507	9	22	under	under	ADP
american_scientific_journal-2507	9	23	an	an	DET
american_scientific_journal-2507	9	24	integral	integral	ADJ
american_scientific_journal-2507	9	25	.	.	PUNCT
american_scientific_journal-2507	10	1	-----------------------------------------------------------------------	-----------------------------------------------------------------------	PUNCT
american_scientific_journal-2507	11	1	*	*	PUNCT
american_scientific_journal-2507	11	2	corresponding	correspond	VERB
american_scientific_journal-2507	11	3	author	author	NOUN
american_scientific_journal-2507	11	4	.	.	PUNCT
american_scientific_journal-2507	12	1	http://asrjetsjournal.org/	http://asrjetsjournal.org/	PROPN
american_scientific_journal-2507	12	2	american	american	PROPN
american_scientific_journal-2507	12	3	scientific	scientific	PROPN
american_scientific_journal-2507	12	4	research	research	NOUN
american_scientific_journal-2507	12	5	journal	journal	NOUN
american_scientific_journal-2507	12	6	for	for	ADP
american_scientific_journal-2507	12	7	engineering	engineering	NOUN
american_scientific_journal-2507	12	8	,	,	PUNCT
american_scientific_journal-2507	12	9	technology	technology	NOUN
american_scientific_journal-2507	12	10	,	,	PUNCT
american_scientific_journal-2507	12	11	and	and	CCONJ
american_scientific_journal-2507	12	12	sciences	science	NOUN
american_scientific_journal-2507	12	13	(	(	PUNCT
american_scientific_journal-2507	12	14	asrjets	asrjet	NOUN
american_scientific_journal-2507	12	15	)	)	PUNCT
american_scientific_journal-2507	12	16	(	(	PUNCT
american_scientific_journal-2507	12	17	2017	2017	NUM
american_scientific_journal-2507	12	18	)	)	PUNCT
american_scientific_journal-2507	12	19	volume	volume	NOUN
american_scientific_journal-2507	12	20	30	30	NUM
american_scientific_journal-2507	12	21	,	,	PUNCT
american_scientific_journal-2507	12	22	no	no	DET
american_scientific_journal-2507	12	23	1	1	NUM
american_scientific_journal-2507	12	24	,	,	PUNCT
american_scientific_journal-2507	12	25	pp	pp	ADV
american_scientific_journal-2507	12	26	47	47	NUM
american_scientific_journal-2507	12	27	-	-	SYM
american_scientific_journal-2507	12	28	56	56	NUM
american_scientific_journal-2507	12	29	48	48	NUM
american_scientific_journal-2507	12	30	the	the	DET
american_scientific_journal-2507	12	31	standard	standard	ADJ
american_scientific_journal-2507	12	32	type	type	NOUN
american_scientific_journal-2507	12	33	of	of	ADP
american_scientific_journal-2507	12	34	such	such	ADJ
american_scientific_journal-2507	12	35	equation	equation	NOUN
american_scientific_journal-2507	12	36	in	in	ADP
american_scientific_journal-2507	12	37	)	)	PUNCT
american_scientific_journal-2507	12	38	(	(	PUNCT
american_scientific_journal-2507	12	39	xu	xu	PROPN
american_scientific_journal-2507	12	40	is	be	AUX
american_scientific_journal-2507	12	41	of	of	ADP
american_scientific_journal-2507	12	42	the	the	DET
american_scientific_journal-2507	12	43	form	form	NOUN
american_scientific_journal-2507	12	44	:	:	PUNCT
american_scientific_journal-2507	12	45	)	)	PUNCT
american_scientific_journal-2507	12	46	1	1	NUM
american_scientific_journal-2507	12	47	(	(	PUNCT
american_scientific_journal-2507	12	48	)	)	PUNCT
american_scientific_journal-2507	12	49	(	(	PUNCT
american_scientific_journal-2507	12	50	)	)	PUNCT
american_scientific_journal-2507	12	51	(	(	PUNCT
american_scientific_journal-2507	12	52	)	)	PUNCT
american_scientific_journal-2507	12	53	,	,	PUNCT
american_scientific_journal-2507	12	54	(	(	PUNCT
american_scientific_journal-2507	12	55	)	)	PUNCT
american_scientific_journal-2507	12	56	(	(	PUNCT
american_scientific_journal-2507	12	57	)	)	PUNCT
american_scientific_journal-2507	12	58	(	(	PUNCT
american_scientific_journal-2507	12	59	∫	∫	PROPN
american_scientific_journal-2507	13	1	=	=	PROPN
american_scientific_journal-2507	13	2	+	+	X
american_scientific_journal-2507	13	3	b	b	NOUN
american_scientific_journal-2507	13	4	a	a	DET
american_scientific_journal-2507	13	5	xfdttutxkxux	xfdttutxkxux	NOUN
american_scientific_journal-2507	13	6	λa	λa	ADP
american_scientific_journal-2507	13	7	where	where	SCONJ
american_scientific_journal-2507	13	8	a	a	PRON
american_scientific_journal-2507	13	9	and	and	CCONJ
american_scientific_journal-2507	13	10	b	b	NOUN
american_scientific_journal-2507	13	11	are	be	AUX
american_scientific_journal-2507	13	12	limits	limit	NOUN
american_scientific_journal-2507	13	13	of	of	ADP
american_scientific_journal-2507	13	14	integration	integration	NOUN
american_scientific_journal-2507	13	15	,	,	PUNCT
american_scientific_journal-2507	13	16	λ	λ	PROPN
american_scientific_journal-2507	13	17	is	be	AUX
american_scientific_journal-2507	13	18	a	a	DET
american_scientific_journal-2507	13	19	constant	constant	ADJ
american_scientific_journal-2507	13	20	parameter	parameter	NOUN
american_scientific_journal-2507	13	21	.	.	PUNCT
american_scientific_journal-2507	13	22	)	)	PUNCT
american_scientific_journal-2507	14	1	,	,	PUNCT
american_scientific_journal-2507	14	2	(	(	PUNCT
american_scientific_journal-2507	14	3	txk	txk	INTJ
american_scientific_journal-2507	14	4	is	be	AUX
american_scientific_journal-2507	14	5	a	a	DET
american_scientific_journal-2507	14	6	known	know	VERB
american_scientific_journal-2507	14	7	function	function	NOUN
american_scientific_journal-2507	14	8	of	of	ADP
american_scientific_journal-2507	14	9	2	2	NUM
american_scientific_journal-2507	14	10	variables	variable	NOUN
american_scientific_journal-2507	14	11	called	call	VERB
american_scientific_journal-2507	14	12	the	the	DET
american_scientific_journal-2507	14	13	kernel	kernel	NOUN
american_scientific_journal-2507	14	14	or	or	CCONJ
american_scientific_journal-2507	14	15	the	the	DET
american_scientific_journal-2507	14	16	nucleus	nucleus	NOUN
american_scientific_journal-2507	14	17	of	of	ADP
american_scientific_journal-2507	14	18	the	the	DET
american_scientific_journal-2507	14	19	integral	integral	ADJ
american_scientific_journal-2507	14	20	equation	equation	NOUN
american_scientific_journal-2507	14	21	.	.	PUNCT
american_scientific_journal-2507	15	1	it	it	PRON
american_scientific_journal-2507	15	2	is	be	AUX
american_scientific_journal-2507	15	3	defined	define	VERB
american_scientific_journal-2507	15	4	in	in	ADP
american_scientific_journal-2507	15	5	the	the	DET
american_scientific_journal-2507	15	6	square	square	NOUN
american_scientific_journal-2507	15	7	:	:	PUNCT
american_scientific_journal-2507	15	8	{	{	PUNCT
american_scientific_journal-2507	15	9	}	}	PUNCT
american_scientific_journal-2507	15	10	btabxatx	btabxatx	NOUN
american_scientific_journal-2507	15	11	≤≤≤≤=π	≤≤≤≤=π	NOUN
american_scientific_journal-2507	15	12	,	,	PUNCT
american_scientific_journal-2507	15	13	:)	:)	INTJ
american_scientific_journal-2507	15	14	,	,	PUNCT
american_scientific_journal-2507	15	15	(	(	PUNCT
american_scientific_journal-2507	15	16	)	)	PUNCT
american_scientific_journal-2507	15	17	(	(	PUNCT
american_scientific_journal-2507	15	18	xf	xf	PROPN
american_scientific_journal-2507	15	19	is	be	AUX
american_scientific_journal-2507	15	20	a	a	DET
american_scientific_journal-2507	15	21	given	give	VERB
american_scientific_journal-2507	15	22	function	function	NOUN
american_scientific_journal-2507	15	23	that	that	PRON
american_scientific_journal-2507	15	24	corresponds	correspond	VERB
american_scientific_journal-2507	15	25	to	to	ADP
american_scientific_journal-2507	15	26	an	an	DET
american_scientific_journal-2507	15	27	external	external	ADJ
american_scientific_journal-2507	15	28	force	force	NOUN
american_scientific_journal-2507	15	29	acting	act	VERB
american_scientific_journal-2507	15	30	on	on	ADP
american_scientific_journal-2507	15	31	the	the	DET
american_scientific_journal-2507	15	32	system	system	NOUN
american_scientific_journal-2507	15	33	.	.	PUNCT
american_scientific_journal-2507	16	1	if	if	SCONJ
american_scientific_journal-2507	16	2	)	)	PUNCT
american_scientific_journal-2507	16	3	(	(	PUNCT
american_scientific_journal-2507	16	4	xf	xf	PROPN
american_scientific_journal-2507	16	5	is	be	AUX
american_scientific_journal-2507	16	6	identically	identically	ADV
american_scientific_journal-2507	16	7	zero	zero	NUM
american_scientific_journal-2507	16	8	,	,	PUNCT
american_scientific_journal-2507	16	9	the	the	DET
american_scientific_journal-2507	16	10	resulting	result	VERB
american_scientific_journal-2507	16	11	equation	equation	NOUN
american_scientific_journal-2507	16	12	is	be	AUX
american_scientific_journal-2507	16	13	called	call	VERB
american_scientific_journal-2507	16	14	homogeneous	homogeneous	ADJ
american_scientific_journal-2507	16	15	.	.	PUNCT
american_scientific_journal-2507	17	1	solving	solve	VERB
american_scientific_journal-2507	17	2	equation	equation	NOUN
american_scientific_journal-2507	17	3	(	(	PUNCT
american_scientific_journal-2507	17	4	1	1	X
american_scientific_journal-2507	17	5	)	)	PUNCT
american_scientific_journal-2507	17	6	amounts	amount	VERB
american_scientific_journal-2507	17	7	to	to	ADP
american_scientific_journal-2507	17	8	determining	determine	VERB
american_scientific_journal-2507	17	9	a	a	DET
american_scientific_journal-2507	17	10	function	function	NOUN
american_scientific_journal-2507	17	11	)	)	PUNCT
american_scientific_journal-2507	17	12	(	(	PUNCT
american_scientific_journal-2507	17	13	xu	xu	INTJ
american_scientific_journal-2507	17	14	such	such	ADJ
american_scientific_journal-2507	17	15	that	that	SCONJ
american_scientific_journal-2507	17	16	(	(	PUNCT
american_scientific_journal-2507	17	17	1	1	X
american_scientific_journal-2507	17	18	)	)	PUNCT
american_scientific_journal-2507	17	19	is	be	AUX
american_scientific_journal-2507	17	20	satisfied	satisfied	ADJ
american_scientific_journal-2507	17	21	for	for	ADP
american_scientific_journal-2507	17	22	all	all	DET
american_scientific_journal-2507	17	23	points	point	NOUN
american_scientific_journal-2507	17	24	within	within	ADP
american_scientific_journal-2507	17	25	the	the	DET
american_scientific_journal-2507	17	26	interval	interval	NOUN
american_scientific_journal-2507	17	27	;	;	PUNCT
american_scientific_journal-2507	17	28	bxa	bxa	NOUN
american_scientific_journal-2507	17	29	≤≤	≤≤	X
american_scientific_journal-2507	17	30	.	.	PUNCT
american_scientific_journal-2507	18	1	(	(	PUNCT
american_scientific_journal-2507	18	2	herman	herman	PROPN
american_scientific_journal-2507	18	3	brunner	brunner	NOUN
american_scientific_journal-2507	19	1	[	[	X
american_scientific_journal-2507	19	2	1	1	NUM
american_scientific_journal-2507	19	3	]	]	PUNCT
american_scientific_journal-2507	19	4	)	)	PUNCT
american_scientific_journal-2507	19	5	.	.	PUNCT
american_scientific_journal-2507	20	1	as	as	SCONJ
american_scientific_journal-2507	20	2	established	establish	VERB
american_scientific_journal-2507	20	3	by	by	ADP
american_scientific_journal-2507	20	4	grewal	grewal	PROPN
american_scientific_journal-2507	21	1	[	[	X
american_scientific_journal-2507	21	2	2	2	NUM
american_scientific_journal-2507	21	3	]	]	PUNCT
american_scientific_journal-2507	21	4	,	,	PUNCT
american_scientific_journal-2507	21	5	as	as	SCONJ
american_scientific_journal-2507	21	6	it	it	PRON
american_scientific_journal-2507	21	7	is	be	AUX
american_scientific_journal-2507	21	8	for	for	ADP
american_scientific_journal-2507	21	9	differential	differential	ADJ
american_scientific_journal-2507	21	10	equations	equation	NOUN
american_scientific_journal-2507	21	11	,	,	PUNCT
american_scientific_journal-2507	21	12	there	there	PRON
american_scientific_journal-2507	21	13	are	be	VERB
american_scientific_journal-2507	21	14	several	several	ADJ
american_scientific_journal-2507	21	15	integral	integral	ADJ
american_scientific_journal-2507	21	16	equations	equation	NOUN
american_scientific_journal-2507	21	17	for	for	ADP
american_scientific_journal-2507	21	18	which	which	PRON
american_scientific_journal-2507	21	19	analytic	analytic	ADJ
american_scientific_journal-2507	21	20	solution	solution	NOUN
american_scientific_journal-2507	21	21	is	be	AUX
american_scientific_journal-2507	21	22	not	not	PART
american_scientific_journal-2507	21	23	feasible	feasible	ADJ
american_scientific_journal-2507	21	24	,	,	PUNCT
american_scientific_journal-2507	21	25	even	even	ADV
american_scientific_journal-2507	21	26	in	in	ADP
american_scientific_journal-2507	21	27	the	the	DET
american_scientific_journal-2507	21	28	availability	availability	NOUN
american_scientific_journal-2507	21	29	of	of	ADP
american_scientific_journal-2507	21	30	such	such	ADJ
american_scientific_journal-2507	21	31	solutions	solution	NOUN
american_scientific_journal-2507	21	32	,	,	PUNCT
american_scientific_journal-2507	21	33	the	the	DET
american_scientific_journal-2507	21	34	computation	computation	NOUN
american_scientific_journal-2507	21	35	cost	cost	NOUN
american_scientific_journal-2507	21	36	may	may	AUX
american_scientific_journal-2507	21	37	be	be	AUX
american_scientific_journal-2507	21	38	so	so	ADV
american_scientific_journal-2507	21	39	enormous	enormous	ADJ
american_scientific_journal-2507	21	40	that	that	SCONJ
american_scientific_journal-2507	21	41	numerical	numerical	ADJ
american_scientific_journal-2507	21	42	approach	approach	NOUN
american_scientific_journal-2507	21	43	becomes	become	VERB
american_scientific_journal-2507	21	44	the	the	DET
american_scientific_journal-2507	21	45	best	good	ADJ
american_scientific_journal-2507	21	46	and	and	CCONJ
american_scientific_journal-2507	21	47	most	most	ADV
american_scientific_journal-2507	21	48	viable	viable	ADJ
american_scientific_journal-2507	21	49	alternative	alternative	NOUN
american_scientific_journal-2507	21	50	.	.	PUNCT
american_scientific_journal-2507	22	1	the	the	DET
american_scientific_journal-2507	22	2	aim	aim	NOUN
american_scientific_journal-2507	22	3	of	of	ADP
american_scientific_journal-2507	22	4	this	this	DET
american_scientific_journal-2507	22	5	work	work	NOUN
american_scientific_journal-2507	22	6	is	be	AUX
american_scientific_journal-2507	22	7	however	however	ADV
american_scientific_journal-2507	22	8	to	to	PART
american_scientific_journal-2507	22	9	introduce	introduce	VERB
american_scientific_journal-2507	22	10	a	a	DET
american_scientific_journal-2507	22	11	new	new	ADJ
american_scientific_journal-2507	22	12	technique	technique	NOUN
american_scientific_journal-2507	22	13	in	in	ADP
american_scientific_journal-2507	22	14	the	the	DET
american_scientific_journal-2507	22	15	application	application	NOUN
american_scientific_journal-2507	22	16	of	of	ADP
american_scientific_journal-2507	22	17	spectral	spectral	ADJ
american_scientific_journal-2507	22	18	methods	method	NOUN
american_scientific_journal-2507	22	19	such	such	ADJ
american_scientific_journal-2507	22	20	that	that	SCONJ
american_scientific_journal-2507	22	21	the	the	DET
american_scientific_journal-2507	22	22	method	method	NOUN
american_scientific_journal-2507	22	23	will	will	AUX
american_scientific_journal-2507	22	24	yield	yield	VERB
american_scientific_journal-2507	22	25	approximate	approximate	ADJ
american_scientific_journal-2507	22	26	solution	solution	NOUN
american_scientific_journal-2507	22	27	that	that	PRON
american_scientific_journal-2507	22	28	is	be	AUX
american_scientific_journal-2507	22	29	efficient	efficient	ADJ
american_scientific_journal-2507	22	30	,	,	PUNCT
american_scientific_journal-2507	22	31	effective	effective	ADJ
american_scientific_journal-2507	22	32	and	and	CCONJ
american_scientific_journal-2507	22	33	with	with	ADP
american_scientific_journal-2507	22	34	minimal	minimal	ADJ
american_scientific_journal-2507	22	35	computational	computational	ADJ
american_scientific_journal-2507	22	36	cost	cost	NOUN
american_scientific_journal-2507	22	37	.	.	PUNCT
american_scientific_journal-2507	23	1	spectral	spectral	ADJ
american_scientific_journal-2507	23	2	methods	method	NOUN
american_scientific_journal-2507	23	3	are	be	AUX
american_scientific_journal-2507	23	4	based	base	VERB
american_scientific_journal-2507	23	5	on	on	ADP
american_scientific_journal-2507	23	6	the	the	DET
american_scientific_journal-2507	23	7	representation	representation	NOUN
american_scientific_journal-2507	23	8	of	of	ADP
american_scientific_journal-2507	23	9	a	a	DET
american_scientific_journal-2507	23	10	real	real	ADJ
american_scientific_journal-2507	23	11	,	,	PUNCT
american_scientific_journal-2507	23	12	continuous	continuous	ADJ
american_scientific_journal-2507	23	13	function	function	NOUN
american_scientific_journal-2507	23	14	)	)	PUNCT
american_scientific_journal-2507	23	15	(	(	PUNCT
american_scientific_journal-2507	23	16	xf	xf	PROPN
american_scientific_journal-2507	23	17	on	on	ADP
american_scientific_journal-2507	23	18	some	some	DET
american_scientific_journal-2507	23	19	interval	interval	NOUN
american_scientific_journal-2507	23	20	as	as	ADP
american_scientific_journal-2507	23	21	an	an	DET
american_scientific_journal-2507	23	22	expansion	expansion	NOUN
american_scientific_journal-2507	23	23	in	in	ADP
american_scientific_journal-2507	23	24	an	an	DET
american_scientific_journal-2507	23	25	orthogonal	orthogonal	ADJ
american_scientific_journal-2507	23	26	set	set	NOUN
american_scientific_journal-2507	23	27	of	of	ADP
american_scientific_journal-2507	23	28	functions	function	NOUN
american_scientific_journal-2507	23	29	)	)	PUNCT
american_scientific_journal-2507	23	30	(	(	PUNCT
american_scientific_journal-2507	23	31	xnφ	xnφ	PROPN
american_scientific_journal-2507	23	32	i.	i.	PROPN
american_scientific_journal-2507	23	33	e	e	PROPN
american_scientific_journal-2507	23	34	)	)	PUNCT
american_scientific_journal-2507	23	35	2	2	NUM
american_scientific_journal-2507	23	36	(	(	PUNCT
american_scientific_journal-2507	23	37	]	]	PUNCT
american_scientific_journal-2507	23	38	,	,	PUNCT
american_scientific_journal-2507	23	39	[	[	X
american_scientific_journal-2507	23	40	,	,	PUNCT
american_scientific_journal-2507	23	41	)	)	PUNCT
american_scientific_journal-2507	23	42	(	(	PUNCT
american_scientific_journal-2507	23	43	)	)	PUNCT
american_scientific_journal-2507	23	44	(	(	PUNCT
american_scientific_journal-2507	23	45	0	0	NUM
american_scientific_journal-2507	23	46	baxxcxf	baxxcxf	PROPN
american_scientific_journal-2507	23	47	k	k	PROPN
american_scientific_journal-2507	24	1	kk∑	kk∑	PROPN
american_scientific_journal-2507	24	2	∞	∞	PROPN
american_scientific_journal-2507	24	3	=	=	PUNCT
american_scientific_journal-2507	24	4	∈=	∈=	PUNCT
american_scientific_journal-2507	24	5	φ	φ	NUM
american_scientific_journal-2507	24	6	where	where	SCONJ
american_scientific_journal-2507	24	7	the	the	DET
american_scientific_journal-2507	24	8	polynomials	polynomial	NOUN
american_scientific_journal-2507	24	9	)	)	PUNCT
american_scientific_journal-2507	24	10	(	(	PUNCT
american_scientific_journal-2507	24	11	xφ	xφ	PROPN
american_scientific_journal-2507	24	12	are	be	AUX
american_scientific_journal-2507	24	13	orthogonal	orthogonal	PROPN
american_scientific_journal-2507	24	14	i.	i.	PROPN
american_scientific_journal-2507	24	15	e.	e.	PROPN
american_scientific_journal-2507	24	16	)	)	PUNCT
american_scientific_journal-2507	25	1	3()()()(∫	3()()()(∫	NUM
american_scientific_journal-2507	26	1	=	=	SYM
american_scientific_journal-2507	26	2	b	b	PROPN
american_scientific_journal-2507	26	3	a	a	DET
american_scientific_journal-2507	26	4	mnmn	mnmn	NOUN
american_scientific_journal-2507	26	5	dxxxxw	dxxxxw	ADJ
american_scientific_journal-2507	26	6	dφφ	dφφ	NOUN
american_scientific_journal-2507	26	7	with	with	ADP
american_scientific_journal-2507	26	8	)	)	PUNCT
american_scientific_journal-2507	26	9	(	(	PUNCT
american_scientific_journal-2507	26	10	xw	xw	PROPN
american_scientific_journal-2507	26	11	as	as	ADP
american_scientific_journal-2507	26	12	the	the	DET
american_scientific_journal-2507	26	13	weight	weight	NOUN
american_scientific_journal-2507	26	14	function	function	NOUN
american_scientific_journal-2507	26	15	and	and	CCONJ
american_scientific_journal-2507	26	16	the	the	DET
american_scientific_journal-2507	26	17	kronecker	kronecker	NOUN
american_scientific_journal-2507	26	18	delta	delta	NOUN
american_scientific_journal-2507	26	19	is	be	AUX
american_scientific_journal-2507	26	20	defined	define	VERB
american_scientific_journal-2507	26	21	by	by	ADP
american_scientific_journal-2507	26	22	:	:	PUNCT
american_scientific_journal-2507	26	23			PROPN
american_scientific_journal-2507	26	24			ADJ
american_scientific_journal-2507	26	25			ADV
american_scientific_journal-2507	26	26			ADP
american_scientific_journal-2507	26	27			NOUN
american_scientific_journal-2507	26	28	≠	≠	NOUN
american_scientific_journal-2507	26	29	=	=	PUNCT
american_scientific_journal-2507	26	30	=	=	PUNCT
american_scientific_journal-2507	26	31	nm	nm	X
american_scientific_journal-2507	26	32	nm	nm	VERB
american_scientific_journal-2507	26	33	mn	mn	PROPN
american_scientific_journal-2507	26	34	,	,	PUNCT
american_scientific_journal-2507	26	35	0	0	NUM
american_scientific_journal-2507	26	36	)	)	PUNCT
american_scientific_journal-2507	26	37	4	4	NUM
american_scientific_journal-2507	26	38	(	(	PUNCT
american_scientific_journal-2507	26	39	,	,	PUNCT
american_scientific_journal-2507	26	40	1	1	NUM
american_scientific_journal-2507	26	41	d	d	NOUN
american_scientific_journal-2507	26	42	as	as	SCONJ
american_scientific_journal-2507	26	43	illustrated	illustrate	VERB
american_scientific_journal-2507	26	44	in	in	ADP
american_scientific_journal-2507	26	45	[	[	X
american_scientific_journal-2507	26	46	3	3	NUM
american_scientific_journal-2507	26	47	]	]	PUNCT
american_scientific_journal-2507	26	48	,	,	PUNCT
american_scientific_journal-2507	26	49	the	the	DET
american_scientific_journal-2507	26	50	function	function	NOUN
american_scientific_journal-2507	26	51	of	of	ADP
american_scientific_journal-2507	26	52	interest	interest	NOUN
american_scientific_journal-2507	26	53	)	)	PUNCT
american_scientific_journal-2507	26	54	(	(	PUNCT
american_scientific_journal-2507	26	55	xu	xu	PROPN
american_scientific_journal-2507	26	56	is	be	AUX
american_scientific_journal-2507	26	57	approximated	approximate	VERB
american_scientific_journal-2507	26	58	with	with	ADP
american_scientific_journal-2507	26	59	the	the	DET
american_scientific_journal-2507	26	60	finite	finite	ADJ
american_scientific_journal-2507	26	61	sum	sum	NOUN
american_scientific_journal-2507	26	62	american	american	PROPN
american_scientific_journal-2507	26	63	scientific	scientific	ADJ
american_scientific_journal-2507	26	64	research	research	NOUN
american_scientific_journal-2507	26	65	journal	journal	NOUN
american_scientific_journal-2507	26	66	for	for	ADP
american_scientific_journal-2507	26	67	engineering	engineering	NOUN
american_scientific_journal-2507	26	68	,	,	PUNCT
american_scientific_journal-2507	26	69	technology	technology	NOUN
american_scientific_journal-2507	26	70	,	,	PUNCT
american_scientific_journal-2507	26	71	and	and	CCONJ
american_scientific_journal-2507	26	72	sciences	science	NOUN
american_scientific_journal-2507	26	73	(	(	PUNCT
american_scientific_journal-2507	26	74	asrjets	asrjet	NOUN
american_scientific_journal-2507	26	75	)	)	PUNCT
american_scientific_journal-2507	26	76	(	(	PUNCT
american_scientific_journal-2507	26	77	2017	2017	NUM
american_scientific_journal-2507	26	78	)	)	PUNCT
american_scientific_journal-2507	26	79	volume	volume	NOUN
american_scientific_journal-2507	26	80	30	30	NUM
american_scientific_journal-2507	26	81	,	,	PUNCT
american_scientific_journal-2507	26	82	no	no	DET
american_scientific_journal-2507	26	83	1	1	NUM
american_scientific_journal-2507	26	84	,	,	PUNCT
american_scientific_journal-2507	26	85	pp	pp	ADV
american_scientific_journal-2507	26	86	47	47	NUM
american_scientific_journal-2507	26	87	-	-	SYM
american_scientific_journal-2507	26	88	56	56	NUM
american_scientific_journal-2507	26	89	49	49	NUM
american_scientific_journal-2507	26	90	)	)	SYM
american_scientific_journal-2507	26	91	5	5	NUM
american_scientific_journal-2507	26	92	(	(	PUNCT
american_scientific_journal-2507	26	93	]	]	PUNCT
american_scientific_journal-2507	26	94	,	,	PUNCT
american_scientific_journal-2507	26	95	[	[	X
american_scientific_journal-2507	26	96	,	,	PUNCT
american_scientific_journal-2507	26	97	)	)	PUNCT
american_scientific_journal-2507	26	98	(	(	PUNCT
american_scientific_journal-2507	26	99	)	)	PUNCT
american_scientific_journal-2507	26	100	(	(	PUNCT
american_scientific_journal-2507	26	101	0	0	NUM
american_scientific_journal-2507	26	102	'	'	PUNCT
american_scientific_journal-2507	26	103	baxxtcxu	baxxtcxu	NOUN
american_scientific_journal-2507	26	104	n	n	NOUN
american_scientific_journal-2507	26	105	k	k	X
american_scientific_journal-2507	26	106	kkn	kkn	ADV
american_scientific_journal-2507	26	107	∑	∑	PROPN
american_scientific_journal-2507	26	108	=	=	PUNCT
american_scientific_journal-2507	26	109	∈=	∈=	ADP
american_scientific_journal-2507	26	110	where	where	SCONJ
american_scientific_journal-2507	26	111	)	)	PUNCT
american_scientific_journal-2507	26	112	(	(	PUNCT
american_scientific_journal-2507	26	113	xtk	xtk	ADV
american_scientific_journal-2507	26	114	is	be	AUX
american_scientific_journal-2507	26	115	the	the	DET
american_scientific_journal-2507	26	116	chebyshev	chebyshev	NOUN
american_scientific_journal-2507	26	117	polynomials	polynomial	NOUN
american_scientific_journal-2507	26	118	of	of	ADP
american_scientific_journal-2507	26	119	the	the	DET
american_scientific_journal-2507	26	120	first	first	ADJ
american_scientific_journal-2507	26	121	kind	kind	NOUN
american_scientific_journal-2507	26	122	and	and	CCONJ
american_scientific_journal-2507	26	123	kc	kc	PROPN
american_scientific_journal-2507	26	124	are	be	AUX
american_scientific_journal-2507	26	125	coefficients	coefficient	NOUN
american_scientific_journal-2507	26	126	of	of	ADP
american_scientific_journal-2507	26	127	expansion	expansion	NOUN
american_scientific_journal-2507	26	128	.	.	PUNCT
american_scientific_journal-2507	27	1	this	this	PRON
american_scientific_journal-2507	27	2	is	be	AUX
american_scientific_journal-2507	27	3	directly	directly	ADV
american_scientific_journal-2507	27	4	obtained	obtain	VERB
american_scientific_journal-2507	27	5	from	from	ADP
american_scientific_journal-2507	27	6	fourier	fourier	ADJ
american_scientific_journal-2507	27	7	cosine	cosine	NOUN
american_scientific_journal-2507	27	8	series	series	NOUN
american_scientific_journal-2507	27	9	in	in	ADP
american_scientific_journal-2507	27	10	chebyshev	chebyshev	NOUN
american_scientific_journal-2507	27	11	polynomial	polynomial	ADJ
american_scientific_journal-2507	27	12	form	form	NOUN
american_scientific_journal-2507	27	13	.	.	PUNCT
american_scientific_journal-2507	28	1	(	(	PUNCT
american_scientific_journal-2507	28	2	see	see	VERB
american_scientific_journal-2507	28	3	ref	ref	NOUN
american_scientific_journal-2507	28	4	[	[	X
american_scientific_journal-2507	28	5	2][3][4][5	2][3][4][5	NUM
american_scientific_journal-2507	28	6	]	]	NUM
american_scientific_journal-2507	28	7	)	)	PUNCT
american_scientific_journal-2507	28	8	.	.	PUNCT
american_scientific_journal-2507	29	1	the	the	DET
american_scientific_journal-2507	29	2	expansion	expansion	NOUN
american_scientific_journal-2507	29	3	coefficients	coefficient	VERB
american_scientific_journal-2507	29	4	kc	kc	PROPN
american_scientific_journal-2507	29	5	are	be	AUX
american_scientific_journal-2507	29	6	occasionally	occasionally	ADV
american_scientific_journal-2507	29	7	referred	refer	VERB
american_scientific_journal-2507	29	8	to	to	ADP
american_scientific_journal-2507	29	9	as	as	ADP
american_scientific_journal-2507	29	10	the	the	DET
american_scientific_journal-2507	29	11	generalized	generalized	ADJ
american_scientific_journal-2507	29	12	fourier	fourier	ADJ
american_scientific_journal-2507	29	13	coefficients	coefficient	NOUN
american_scientific_journal-2507	29	14	.	.	PUNCT
american_scientific_journal-2507	30	1	as	as	SCONJ
american_scientific_journal-2507	30	2	exemplified	exemplify	VERB
american_scientific_journal-2507	30	3	in	in	ADP
american_scientific_journal-2507	30	4	[	[	X
american_scientific_journal-2507	30	5	3	3	NUM
american_scientific_journal-2507	30	6	]	]	PUNCT
american_scientific_journal-2507	30	7	,	,	PUNCT
american_scientific_journal-2507	30	8	one	one	NUM
american_scientific_journal-2507	30	9	clear	clear	ADJ
american_scientific_journal-2507	30	10	advantage	advantage	NOUN
american_scientific_journal-2507	30	11	that	that	SCONJ
american_scientific_journal-2507	30	12	spectral	spectral	ADJ
american_scientific_journal-2507	30	13	methods	method	NOUN
american_scientific_journal-2507	30	14	have	have	VERB
american_scientific_journal-2507	30	15	over	over	ADP
american_scientific_journal-2507	30	16	finite	finite	ADJ
american_scientific_journal-2507	30	17	difference	difference	NOUN
american_scientific_journal-2507	30	18	methods	method	NOUN
american_scientific_journal-2507	30	19	is	be	AUX
american_scientific_journal-2507	30	20	that	that	SCONJ
american_scientific_journal-2507	30	21	once	once	ADV
american_scientific_journal-2507	30	22	approximate	approximate	ADJ
american_scientific_journal-2507	30	23	spectral	spectral	ADJ
american_scientific_journal-2507	30	24	coefficients	coefficient	NOUN
american_scientific_journal-2507	30	25	have	have	AUX
american_scientific_journal-2507	30	26	been	be	AUX
american_scientific_journal-2507	30	27	found	find	VERB
american_scientific_journal-2507	30	28	,	,	PUNCT
american_scientific_journal-2507	30	29	the	the	DET
american_scientific_journal-2507	30	30	approximate	approximate	ADJ
american_scientific_journal-2507	30	31	solution	solution	NOUN
american_scientific_journal-2507	30	32	can	can	AUX
american_scientific_journal-2507	30	33	immediately	immediately	ADV
american_scientific_journal-2507	30	34	be	be	AUX
american_scientific_journal-2507	30	35	evaluated	evaluate	VERB
american_scientific_journal-2507	30	36	at	at	ADP
american_scientific_journal-2507	30	37	any	any	DET
american_scientific_journal-2507	30	38	point	point	NOUN
american_scientific_journal-2507	30	39	in	in	ADP
american_scientific_journal-2507	30	40	the	the	DET
american_scientific_journal-2507	30	41	range	range	NOUN
american_scientific_journal-2507	30	42	of	of	ADP
american_scientific_journal-2507	30	43	integration	integration	NOUN
american_scientific_journal-2507	30	44	,	,	PUNCT
american_scientific_journal-2507	30	45	whereas	whereas	SCONJ
american_scientific_journal-2507	30	46	to	to	PART
american_scientific_journal-2507	30	47	evaluated	evaluated	VERB
american_scientific_journal-2507	30	48	a	a	DET
american_scientific_journal-2507	30	49	finite	finite	ADJ
american_scientific_journal-2507	30	50	-	-	PUNCT
american_scientific_journal-2507	30	51	difference	difference	NOUN
american_scientific_journal-2507	30	52	solution	solution	NOUN
american_scientific_journal-2507	30	53	at	at	ADP
american_scientific_journal-2507	30	54	an	an	DET
american_scientific_journal-2507	30	55	intermediate	intermediate	ADJ
american_scientific_journal-2507	30	56	point	point	NOUN
american_scientific_journal-2507	30	57	requires	require	VERB
american_scientific_journal-2507	30	58	a	a	DET
american_scientific_journal-2507	30	59	further	further	ADJ
american_scientific_journal-2507	30	60	step	step	NOUN
american_scientific_journal-2507	30	61	of	of	ADP
american_scientific_journal-2507	30	62	interpolation	interpolation	NOUN
american_scientific_journal-2507	30	63	.	.	PUNCT
american_scientific_journal-2507	31	1	in	in	ADP
american_scientific_journal-2507	31	2	addition	addition	NOUN
american_scientific_journal-2507	31	3	,	,	PUNCT
american_scientific_journal-2507	31	4	it	it	PRON
american_scientific_journal-2507	31	5	has	have	AUX
american_scientific_journal-2507	31	6	been	be	AUX
american_scientific_journal-2507	31	7	established	establish	VERB
american_scientific_journal-2507	31	8	over	over	ADP
american_scientific_journal-2507	31	9	the	the	DET
american_scientific_journal-2507	31	10	years	year	NOUN
american_scientific_journal-2507	31	11	that	that	SCONJ
american_scientific_journal-2507	31	12	these	these	DET
american_scientific_journal-2507	31	13	methods	method	NOUN
american_scientific_journal-2507	31	14	possess	possess	VERB
american_scientific_journal-2507	31	15	ability	ability	NOUN
american_scientific_journal-2507	31	16	to	to	PART
american_scientific_journal-2507	31	17	tackle	tackle	VERB
american_scientific_journal-2507	31	18	a	a	DET
american_scientific_journal-2507	31	19	wide	wide	ADJ
american_scientific_journal-2507	31	20	variety	variety	NOUN
american_scientific_journal-2507	31	21	of	of	ADP
american_scientific_journal-2507	31	22	problems	problem	NOUN
american_scientific_journal-2507	31	23	.	.	PUNCT
american_scientific_journal-2507	32	1	in	in	ADP
american_scientific_journal-2507	32	2	particular	particular	ADJ
american_scientific_journal-2507	32	3	,	,	PUNCT
american_scientific_journal-2507	32	4	they	they	PRON
american_scientific_journal-2507	32	5	yield	yield	VERB
american_scientific_journal-2507	32	6	accurate	accurate	ADJ
american_scientific_journal-2507	32	7	results	result	NOUN
american_scientific_journal-2507	32	8	with	with	ADP
american_scientific_journal-2507	32	9	only	only	ADJ
american_scientific_journal-2507	32	10	moderate	moderate	ADJ
american_scientific_journal-2507	32	11	computational	computational	ADJ
american_scientific_journal-2507	32	12	resources	resource	NOUN
american_scientific_journal-2507	32	13	.	.	PUNCT
american_scientific_journal-2507	33	1	2	2	X
american_scientific_journal-2507	33	2	.	.	X
american_scientific_journal-2507	33	3	classification	classification	NOUN
american_scientific_journal-2507	33	4	of	of	ADP
american_scientific_journal-2507	33	5	integral	integral	ADJ
american_scientific_journal-2507	33	6	equations	equation	NOUN
american_scientific_journal-2507	33	7	integral	integral	ADJ
american_scientific_journal-2507	33	8	equations	equation	NOUN
american_scientific_journal-2507	33	9	appear	appear	VERB
american_scientific_journal-2507	33	10	in	in	ADP
american_scientific_journal-2507	33	11	many	many	ADJ
american_scientific_journal-2507	33	12	varieties	variety	NOUN
american_scientific_journal-2507	33	13	,	,	PUNCT
american_scientific_journal-2507	33	14	the	the	DET
american_scientific_journal-2507	33	15	types	type	NOUN
american_scientific_journal-2507	33	16	depend	depend	VERB
american_scientific_journal-2507	33	17	mainly	mainly	ADV
american_scientific_journal-2507	33	18	on	on	ADP
american_scientific_journal-2507	33	19	the	the	DET
american_scientific_journal-2507	33	20	limits	limit	NOUN
american_scientific_journal-2507	33	21	of	of	ADP
american_scientific_journal-2507	33	22	integration	integration	NOUN
american_scientific_journal-2507	33	23	,	,	PUNCT
american_scientific_journal-2507	33	24	the	the	DET
american_scientific_journal-2507	33	25	kernel	kernel	NOUN
american_scientific_journal-2507	33	26	of	of	ADP
american_scientific_journal-2507	33	27	the	the	DET
american_scientific_journal-2507	33	28	equation	equation	NOUN
american_scientific_journal-2507	33	29	and	and	CCONJ
american_scientific_journal-2507	33	30	the	the	DET
american_scientific_journal-2507	33	31	appearance	appearance	NOUN
american_scientific_journal-2507	33	32	of	of	ADP
american_scientific_journal-2507	33	33	unknown	unknown	ADJ
american_scientific_journal-2507	33	34	function	function	NOUN
american_scientific_journal-2507	33	35	)	)	PUNCT
american_scientific_journal-2507	33	36	(	(	PUNCT
american_scientific_journal-2507	33	37	xu	xu	INTJ
american_scientific_journal-2507	33	38	.	.	PUNCT
american_scientific_journal-2507	34	1	if	if	SCONJ
american_scientific_journal-2507	34	2	the	the	DET
american_scientific_journal-2507	34	3	limits	limit	NOUN
american_scientific_journal-2507	34	4	of	of	ADP
american_scientific_journal-2507	34	5	integration	integration	NOUN
american_scientific_journal-2507	34	6	are	be	AUX
american_scientific_journal-2507	34	7	fixed	fix	VERB
american_scientific_journal-2507	34	8	,	,	PUNCT
american_scientific_journal-2507	34	9	the	the	DET
american_scientific_journal-2507	34	10	integral	integral	ADJ
american_scientific_journal-2507	34	11	equation	equation	NOUN
american_scientific_journal-2507	34	12	is	be	AUX
american_scientific_journal-2507	34	13	called	call	VERB
american_scientific_journal-2507	34	14	a	a	DET
american_scientific_journal-2507	34	15	fredholm	fredholm	ADJ
american_scientific_journal-2507	34	16	integral	integral	ADJ
american_scientific_journal-2507	34	17	equation	equation	NOUN
american_scientific_journal-2507	34	18	,	,	PUNCT
american_scientific_journal-2507	34	19	a	a	DET
american_scientific_journal-2507	34	20	typical	typical	ADJ
american_scientific_journal-2507	34	21	example	example	NOUN
american_scientific_journal-2507	34	22	is	be	AUX
american_scientific_journal-2507	34	23	given	give	VERB
american_scientific_journal-2507	34	24	in	in	ADP
american_scientific_journal-2507	34	25	equation	equation	NOUN
american_scientific_journal-2507	34	26	(	(	PUNCT
american_scientific_journal-2507	34	27	1	1	NUM
american_scientific_journal-2507	34	28	)	)	PUNCT
american_scientific_journal-2507	34	29	,	,	PUNCT
american_scientific_journal-2507	34	30	where	where	SCONJ
american_scientific_journal-2507	34	31	a	a	PRON
american_scientific_journal-2507	34	32	and	and	CCONJ
american_scientific_journal-2507	34	33	b	b	NOUN
american_scientific_journal-2507	34	34	are	be	AUX
american_scientific_journal-2507	34	35	constants	constant	NOUN
american_scientific_journal-2507	34	36	.	.	PUNCT
american_scientific_journal-2507	35	1	but	but	CCONJ
american_scientific_journal-2507	35	2	if	if	SCONJ
american_scientific_journal-2507	35	3	at	at	ADV
american_scientific_journal-2507	35	4	least	least	ADV
american_scientific_journal-2507	35	5	one	one	NUM
american_scientific_journal-2507	35	6	limit	limit	NOUN
american_scientific_journal-2507	35	7	is	be	AUX
american_scientific_journal-2507	35	8	a	a	DET
american_scientific_journal-2507	35	9	variable	variable	NOUN
american_scientific_journal-2507	35	10	,	,	PUNCT
american_scientific_journal-2507	35	11	the	the	DET
american_scientific_journal-2507	35	12	equation	equation	NOUN
american_scientific_journal-2507	35	13	is	be	AUX
american_scientific_journal-2507	35	14	called	call	VERB
american_scientific_journal-2507	35	15	a	a	DET
american_scientific_journal-2507	35	16	volterra	volterra	NOUN
american_scientific_journal-2507	35	17	integral	integral	ADJ
american_scientific_journal-2507	35	18	equation	equation	NOUN
american_scientific_journal-2507	35	19	given	give	VERB
american_scientific_journal-2507	35	20	in	in	ADP
american_scientific_journal-2507	35	21	the	the	DET
american_scientific_journal-2507	35	22	form	form	NOUN
american_scientific_journal-2507	35	23	:	:	PUNCT
american_scientific_journal-2507	35	24	)	)	PUNCT
american_scientific_journal-2507	35	25	6	6	NUM
american_scientific_journal-2507	35	26	(	(	PUNCT
american_scientific_journal-2507	35	27	)	)	PUNCT
american_scientific_journal-2507	35	28	(	(	PUNCT
american_scientific_journal-2507	35	29	)	)	PUNCT
american_scientific_journal-2507	35	30	(	(	PUNCT
american_scientific_journal-2507	35	31	)	)	PUNCT
american_scientific_journal-2507	35	32	,	,	PUNCT
american_scientific_journal-2507	35	33	(	(	PUNCT
american_scientific_journal-2507	35	34	)	)	PUNCT
american_scientific_journal-2507	35	35	(	(	PUNCT
american_scientific_journal-2507	35	36	)	)	PUNCT
american_scientific_journal-2507	35	37	(	(	PUNCT
american_scientific_journal-2507	35	38	∫	∫	PROPN
american_scientific_journal-2507	35	39	=	=	SYM
american_scientific_journal-2507	35	40	+	+	NOUN
american_scientific_journal-2507	35	41	x	x	SYM
american_scientific_journal-2507	35	42	a	a	DET
american_scientific_journal-2507	35	43	xfdttutxkxux	xfdttutxkxux	NOUN
american_scientific_journal-2507	35	44	λa	λa	X
american_scientific_journal-2507	35	45	in	in	ADP
american_scientific_journal-2507	35	46	addition	addition	NOUN
american_scientific_journal-2507	35	47	to	to	ADP
american_scientific_journal-2507	35	48	this	this	PRON
american_scientific_journal-2507	35	49	,	,	PUNCT
american_scientific_journal-2507	35	50	integral	integral	ADJ
american_scientific_journal-2507	35	51	equations	equation	NOUN
american_scientific_journal-2507	35	52	can	can	AUX
american_scientific_journal-2507	35	53	further	far	ADV
american_scientific_journal-2507	35	54	be	be	AUX
american_scientific_journal-2507	35	55	classified	classify	VERB
american_scientific_journal-2507	35	56	into	into	ADP
american_scientific_journal-2507	35	57	2	2	NUM
american_scientific_journal-2507	35	58	kinds	kind	NOUN
american_scientific_journal-2507	35	59	taking	take	VERB
american_scientific_journal-2507	35	60	the	the	DET
american_scientific_journal-2507	35	61	following	follow	VERB
american_scientific_journal-2507	35	62	generic	generic	ADJ
american_scientific_journal-2507	35	63	forms	form	NOUN
american_scientific_journal-2507	35	64	:	:	PUNCT
american_scientific_journal-2507	35	65	)	)	PUNCT
american_scientific_journal-2507	36	1	7()()(),(∫	7()()(),(∫	NUM
american_scientific_journal-2507	36	2	=	=	SYM
american_scientific_journal-2507	36	3	b	b	PROPN
american_scientific_journal-2507	36	4	a	a	DET
american_scientific_journal-2507	36	5	xfdttutxk	xfdttutxk	NOUN
american_scientific_journal-2507	36	6	that	that	PRON
american_scientific_journal-2507	36	7	is	be	AUX
american_scientific_journal-2507	36	8	0≡a	0≡a	VERB
american_scientific_journal-2507	36	9	in	in	ADP
american_scientific_journal-2507	36	10	equation	equation	NOUN
american_scientific_journal-2507	36	11	(	(	PUNCT
american_scientific_journal-2507	36	12	1	1	X
american_scientific_journal-2507	36	13	)	)	PUNCT
american_scientific_journal-2507	36	14	such	such	ADJ
american_scientific_journal-2507	36	15	that	that	SCONJ
american_scientific_journal-2507	36	16	u	u	PROPN
american_scientific_journal-2507	36	17	appears	appear	VERB
american_scientific_journal-2507	36	18	only	only	ADV
american_scientific_journal-2507	36	19	under	under	ADP
american_scientific_journal-2507	36	20	the	the	DET
american_scientific_journal-2507	36	21	integral	integral	ADJ
american_scientific_journal-2507	36	22	sign	sign	NOUN
american_scientific_journal-2507	36	23	the	the	DET
american_scientific_journal-2507	36	24	integral	integral	ADJ
american_scientific_journal-2507	36	25	equation	equation	NOUN
american_scientific_journal-2507	36	26	is	be	AUX
american_scientific_journal-2507	36	27	called	call	VERB
american_scientific_journal-2507	36	28	a	a	DET
american_scientific_journal-2507	36	29	fredholm	fredholm	ADJ
american_scientific_journal-2507	36	30	integral	integral	ADJ
american_scientific_journal-2507	36	31	equation	equation	NOUN
american_scientific_journal-2507	36	32	of	of	ADP
american_scientific_journal-2507	36	33	the	the	DET
american_scientific_journal-2507	36	34	first	first	ADJ
american_scientific_journal-2507	36	35	kind	kind	NOUN
american_scientific_journal-2507	36	36	.	.	PUNCT
american_scientific_journal-2507	37	1	however	however	ADV
american_scientific_journal-2507	37	2	,	,	PUNCT
american_scientific_journal-2507	37	3	for	for	ADP
american_scientific_journal-2507	37	4	fredholm	fredholm	ADJ
american_scientific_journal-2507	37	5	integral	integral	ADJ
american_scientific_journal-2507	37	6	equations	equation	NOUN
american_scientific_journal-2507	37	7	of	of	ADP
american_scientific_journal-2507	37	8	the	the	DET
american_scientific_journal-2507	37	9	second	second	ADJ
american_scientific_journal-2507	37	10	kind	kind	NOUN
american_scientific_journal-2507	37	11	,	,	PUNCT
american_scientific_journal-2507	37	12	0≠a	0≠a	ADV
american_scientific_journal-2507	37	13	hence	hence	ADV
american_scientific_journal-2507	37	14	the	the	DET
american_scientific_journal-2507	37	15	unknown	unknown	ADJ
american_scientific_journal-2507	37	16	function	function	NOUN
american_scientific_journal-2507	37	17	u	u	NOUN
american_scientific_journal-2507	37	18	appears	appear	VERB
american_scientific_journal-2507	37	19	both	both	PRON
american_scientific_journal-2507	37	20	inside	inside	ADP
american_scientific_journal-2507	37	21	and	and	CCONJ
american_scientific_journal-2507	37	22	outside	outside	ADP
american_scientific_journal-2507	37	23	the	the	DET
american_scientific_journal-2507	37	24	integral	integral	ADJ
american_scientific_journal-2507	37	25	sign	sign	NOUN
american_scientific_journal-2507	37	26	.	.	PUNCT
american_scientific_journal-2507	38	1	this	this	PRON
american_scientific_journal-2507	38	2	therefore	therefore	ADV
american_scientific_journal-2507	38	3	takes	take	VERB
american_scientific_journal-2507	38	4	the	the	DET
american_scientific_journal-2507	38	5	form	form	NOUN
american_scientific_journal-2507	38	6	:	:	PUNCT
american_scientific_journal-2507	38	7	)	)	PUNCT
american_scientific_journal-2507	38	8	8	8	NUM
american_scientific_journal-2507	38	9	(	(	PUNCT
american_scientific_journal-2507	38	10	)	)	PUNCT
american_scientific_journal-2507	38	11	(	(	PUNCT
american_scientific_journal-2507	38	12	)	)	PUNCT
american_scientific_journal-2507	38	13	(	(	PUNCT
american_scientific_journal-2507	38	14	)	)	PUNCT
american_scientific_journal-2507	38	15	,	,	PUNCT
american_scientific_journal-2507	38	16	(	(	PUNCT
american_scientific_journal-2507	38	17	)	)	PUNCT
american_scientific_journal-2507	38	18	(	(	PUNCT
american_scientific_journal-2507	38	19	)	)	PUNCT
american_scientific_journal-2507	38	20	(	(	PUNCT
american_scientific_journal-2507	38	21	∫	∫	PROPN
american_scientific_journal-2507	38	22	=	=	PROPN
american_scientific_journal-2507	38	23	+	+	X
american_scientific_journal-2507	38	24	b	b	NOUN
american_scientific_journal-2507	38	25	a	a	DET
american_scientific_journal-2507	38	26	xfdttutxkxux	xfdttutxkxux	NOUN
american_scientific_journal-2507	38	27	λa	λa	ADP
american_scientific_journal-2507	38	28	american	american	PROPN
american_scientific_journal-2507	38	29	scientific	scientific	PROPN
american_scientific_journal-2507	38	30	research	research	PROPN
american_scientific_journal-2507	38	31	journal	journal	NOUN
american_scientific_journal-2507	38	32	for	for	ADP
american_scientific_journal-2507	38	33	engineering	engineering	NOUN
american_scientific_journal-2507	38	34	,	,	PUNCT
american_scientific_journal-2507	38	35	technology	technology	NOUN
american_scientific_journal-2507	38	36	,	,	PUNCT
american_scientific_journal-2507	38	37	and	and	CCONJ
american_scientific_journal-2507	38	38	sciences	science	NOUN
american_scientific_journal-2507	38	39	(	(	PUNCT
american_scientific_journal-2507	38	40	asrjets	asrjet	NOUN
american_scientific_journal-2507	38	41	)	)	PUNCT
american_scientific_journal-2507	38	42	(	(	PUNCT
american_scientific_journal-2507	38	43	2017	2017	NUM
american_scientific_journal-2507	38	44	)	)	PUNCT
american_scientific_journal-2507	38	45	volume	volume	NOUN
american_scientific_journal-2507	38	46	30	30	NUM
american_scientific_journal-2507	38	47	,	,	PUNCT
american_scientific_journal-2507	38	48	no	no	DET
american_scientific_journal-2507	38	49	1	1	NUM
american_scientific_journal-2507	38	50	,	,	PUNCT
american_scientific_journal-2507	38	51	pp	pp	ADV
american_scientific_journal-2507	38	52	47	47	NUM
american_scientific_journal-2507	38	53	-	-	SYM
american_scientific_journal-2507	38	54	56	56	NUM
american_scientific_journal-2507	38	55	50	50	NUM
american_scientific_journal-2507	38	56	3	3	NUM
american_scientific_journal-2507	38	57	.	.	PUNCT
american_scientific_journal-2507	38	58	evaluation	evaluation	NOUN
american_scientific_journal-2507	38	59	of	of	ADP
american_scientific_journal-2507	38	60	chebyshev	chebyshev	NOUN
american_scientific_journal-2507	38	61	terms	term	NOUN
american_scientific_journal-2507	38	62	throughout	throughout	ADP
american_scientific_journal-2507	38	63	the	the	DET
american_scientific_journal-2507	38	64	course	course	NOUN
american_scientific_journal-2507	38	65	of	of	ADP
american_scientific_journal-2507	38	66	this	this	DET
american_scientific_journal-2507	38	67	work	work	NOUN
american_scientific_journal-2507	38	68	,	,	PUNCT
american_scientific_journal-2507	38	69	we	we	PRON
american_scientific_journal-2507	38	70	constantly	constantly	ADV
american_scientific_journal-2507	38	71	need	need	VERB
american_scientific_journal-2507	38	72	to	to	PART
american_scientific_journal-2507	38	73	express	express	VERB
american_scientific_journal-2507	38	74	product	product	NOUN
american_scientific_journal-2507	38	75	like	like	ADP
american_scientific_journal-2507	38	76	)	)	PUNCT
american_scientific_journal-2507	38	77	(	(	PUNCT
american_scientific_journal-2507	38	78	)	)	PUNCT
american_scientific_journal-2507	38	79	(	(	PUNCT
american_scientific_journal-2507	38	80	xtxf	xtxf	PROPN
american_scientific_journal-2507	38	81	k	k	PROPN
american_scientific_journal-2507	38	82	and	and	CCONJ
american_scientific_journal-2507	38	83	the	the	DET
american_scientific_journal-2507	38	84	integral	integral	ADJ
american_scientific_journal-2507	38	85	of	of	ADP
american_scientific_journal-2507	38	86	)	)	PUNCT
american_scientific_journal-2507	38	87	(	(	PUNCT
american_scientific_journal-2507	38	88	xtk	xtk	ADV
american_scientific_journal-2507	38	89	.	.	PUNCT
american_scientific_journal-2507	39	1	for	for	ADP
american_scientific_journal-2507	39	2	the	the	DET
american_scientific_journal-2507	39	3	evaluation	evaluation	NOUN
american_scientific_journal-2507	39	4	of	of	ADP
american_scientific_journal-2507	39	5	such	such	ADJ
american_scientific_journal-2507	39	6	terms	term	NOUN
american_scientific_journal-2507	39	7	it	it	PRON
american_scientific_journal-2507	39	8	has	have	AUX
american_scientific_journal-2507	39	9	been	be	AUX
american_scientific_journal-2507	39	10	observed	observe	VERB
american_scientific_journal-2507	39	11	that	that	SCONJ
american_scientific_journal-2507	39	12	for	for	ADP
american_scientific_journal-2507	39	13	an	an	DET
american_scientific_journal-2507	39	14	efficient	efficient	ADJ
american_scientific_journal-2507	39	15	and	and	CCONJ
american_scientific_journal-2507	39	16	stable	stable	ADJ
american_scientific_journal-2507	39	17	execution	execution	NOUN
american_scientific_journal-2507	39	18	,	,	PUNCT
american_scientific_journal-2507	39	19	the	the	DET
american_scientific_journal-2507	39	20	secret	secret	NOUN
american_scientific_journal-2507	39	21	is	be	AUX
american_scientific_journal-2507	39	22	to	to	PART
american_scientific_journal-2507	39	23	avoid	avoid	VERB
american_scientific_journal-2507	39	24	rewriting	rewrite	VERB
american_scientific_journal-2507	39	25	chebyshev	chebyshev	NOUN
american_scientific_journal-2507	39	26	polynomials	polynomial	NOUN
american_scientific_journal-2507	39	27	in	in	ADP
american_scientific_journal-2507	39	28	terms	term	NOUN
american_scientific_journal-2507	39	29	of	of	ADP
american_scientific_journal-2507	39	30	powers	power	NOUN
american_scientific_journal-2507	39	31	of	of	ADP
american_scientific_journal-2507	39	32	x	x	X
american_scientific_journal-2507	39	33	and	and	CCONJ
american_scientific_journal-2507	39	34	to	to	PART
american_scientific_journal-2507	39	35	operate	operate	VERB
american_scientific_journal-2507	39	36	wherever	wherever	SCONJ
american_scientific_journal-2507	39	37	possible	possible	ADJ
american_scientific_journal-2507	39	38	with	with	ADP
american_scientific_journal-2507	39	39	the	the	DET
american_scientific_journal-2507	39	40	chebyshev	chebyshev	NOUN
american_scientific_journal-2507	39	41	polynomials	polynomial	NOUN
american_scientific_journal-2507	39	42	themselves	themselves	PRON
american_scientific_journal-2507	39	43	(	(	PUNCT
american_scientific_journal-2507	39	44	clenshaw	clenshaw	ADJ
american_scientific_journal-2507	39	45	[	[	X
american_scientific_journal-2507	39	46	6	6	NUM
american_scientific_journal-2507	39	47	]	]	NUM
american_scientific_journal-2507	39	48	)	)	PUNCT
american_scientific_journal-2507	39	49	.	.	PUNCT
american_scientific_journal-2507	40	1	as	as	ADP
american_scientific_journal-2507	40	2	a	a	DET
american_scientific_journal-2507	40	3	result	result	NOUN
american_scientific_journal-2507	40	4	of	of	ADP
american_scientific_journal-2507	40	5	this	this	PRON
american_scientific_journal-2507	40	6	,	,	PUNCT
american_scientific_journal-2507	40	7	this	this	DET
american_scientific_journal-2507	40	8	work	work	NOUN
american_scientific_journal-2507	40	9	is	be	AUX
american_scientific_journal-2507	40	10	based	base	VERB
american_scientific_journal-2507	40	11	on	on	ADP
american_scientific_journal-2507	40	12	expressing	express	VERB
american_scientific_journal-2507	40	13	all	all	DET
american_scientific_journal-2507	40	14	terms	term	NOUN
american_scientific_journal-2507	40	15	in	in	ADP
american_scientific_journal-2507	40	16	the	the	DET
american_scientific_journal-2507	40	17	equation	equation	NOUN
american_scientific_journal-2507	40	18	in	in	ADP
american_scientific_journal-2507	40	19	series	series	NOUN
american_scientific_journal-2507	40	20	of	of	ADP
american_scientific_journal-2507	40	21	chebyshev	chebyshev	NOUN
american_scientific_journal-2507	40	22	polynomials	polynomial	NOUN
american_scientific_journal-2507	40	23	.	.	PUNCT
american_scientific_journal-2507	41	1	for	for	ADP
american_scientific_journal-2507	41	2	the	the	DET
american_scientific_journal-2507	41	3	integral	integral	NOUN
american_scientific_journal-2507	41	4	of	of	ADP
american_scientific_journal-2507	41	5	)	)	PUNCT
american_scientific_journal-2507	41	6	(	(	PUNCT
american_scientific_journal-2507	41	7	xtk	xtk	ADV
american_scientific_journal-2507	41	8	,	,	PUNCT
american_scientific_journal-2507	41	9	to	to	PART
american_scientific_journal-2507	41	10	allow	allow	VERB
american_scientific_journal-2507	41	11	for	for	ADP
american_scientific_journal-2507	41	12	effective	effective	ADJ
american_scientific_journal-2507	41	13	evaluation	evaluation	NOUN
american_scientific_journal-2507	41	14	,	,	PUNCT
american_scientific_journal-2507	41	15	we	we	PRON
american_scientific_journal-2507	41	16	express	express	VERB
american_scientific_journal-2507	41	17	this	this	PRON
american_scientific_journal-2507	41	18	as	as	SCONJ
american_scientific_journal-2507	41	19	follows	follow	VERB
american_scientific_journal-2507	41	20	:	:	PUNCT
american_scientific_journal-2507	41	21	[	[	PUNCT
american_scientific_journal-2507	41	22	]	]	X
american_scientific_journal-2507	41	23			PROPN
american_scientific_journal-2507	41	24			PROPN
american_scientific_journal-2507	41	25			PROPN
american_scientific_journal-2507	41	26			PROPN
american_scientific_journal-2507	41	27			ADJ
american_scientific_journal-2507	41	28			ADJ
american_scientific_journal-2507	41	29			NUM
american_scientific_journal-2507	41	30			NOUN
american_scientific_journal-2507	41	31	−	−	PROPN
american_scientific_journal-2507	41	32	−	−	PROPN
american_scientific_journal-2507	41	33	−	−	PROPN
american_scientific_journal-2507	42	1	+	+	CCONJ
american_scientific_journal-2507	42	2	+	+	CCONJ
american_scientific_journal-2507	42	3	=	=	SYM
american_scientific_journal-2507	42	4	−−+−=	−−+−=	NOUN
american_scientific_journal-2507	42	5	−=	−=	NOUN
american_scientific_journal-2507	42	6	∫	∫	PROPN
american_scientific_journal-2507	42	7	∫	∫	PROPN
american_scientific_journal-2507	42	8	∫	∫	PROPN
american_scientific_journal-2507	42	9	1	1	NUM
american_scientific_journal-2507	42	10	1cos	1cos	PROPN
american_scientific_journal-2507	42	11	1	1	NUM
american_scientific_journal-2507	42	12	)	)	PUNCT
american_scientific_journal-2507	42	13	1(cos	1(cos	NOUN
american_scientific_journal-2507	42	14	2	2	NUM
american_scientific_journal-2507	42	15	1	1	NUM
american_scientific_journal-2507	42	16	)	)	PUNCT
american_scientific_journal-2507	42	17	1(sin)1(sin	1(sin)1(sin	NUM
american_scientific_journal-2507	42	18	2	2	NUM
american_scientific_journal-2507	42	19	1	1	NUM
american_scientific_journal-2507	42	20	sincos	sinco	NOUN
american_scientific_journal-2507	42	21	)	)	PUNCT
american_scientific_journal-2507	42	22	(	(	PUNCT
american_scientific_journal-2507	42	23	k	k	NOUN
american_scientific_journal-2507	42	24	k	k	PROPN
american_scientific_journal-2507	42	25	k	k	PROPN
american_scientific_journal-2507	42	26	k	k	PROPN
american_scientific_journal-2507	42	27	dkk	dkk	PROPN
american_scientific_journal-2507	42	28	dkdxxtk	dkdxxtk	ADV
american_scientific_journal-2507	42	29	θθ	θθ	VERB
american_scientific_journal-2507	42	30	θθθ	θθθ	PROPN
american_scientific_journal-2507	42	31	θθθ	θθθ	NOUN
american_scientific_journal-2507	42	32	hence	hence	ADV
american_scientific_journal-2507	42	33	,	,	PUNCT
american_scientific_journal-2507	42	34	∫	∫	PROPN
american_scientific_journal-2507	42	35			PROPN
american_scientific_journal-2507	42	36			PROPN
american_scientific_journal-2507	42	37			PROPN
american_scientific_journal-2507	42	38			ADJ
american_scientific_journal-2507	42	39			PROPN
american_scientific_journal-2507	42	40			PROPN
american_scientific_journal-2507	42	41			PROPN
american_scientific_journal-2507	42	42			ADP
american_scientific_journal-2507	42	43			NOUN
american_scientific_journal-2507	42	44	=	=	SYM
american_scientific_journal-2507	42	45	≠	≠	PROPN
american_scientific_journal-2507	42	46			PROPN
american_scientific_journal-2507	42	47			PROPN
american_scientific_journal-2507	42	48			PROPN
american_scientific_journal-2507	42	49			PROPN
american_scientific_journal-2507	42	50			ADJ
american_scientific_journal-2507	42	51			ADJ
american_scientific_journal-2507	42	52			NUM
american_scientific_journal-2507	42	53			NOUN
american_scientific_journal-2507	42	54	−	−	PROPN
american_scientific_journal-2507	42	55	−	−	PROPN
american_scientific_journal-2507	43	1	+	+	CCONJ
american_scientific_journal-2507	43	2	=	=	SYM
american_scientific_journal-2507	43	3	−+	−+	PROPN
american_scientific_journal-2507	43	4	1	1	NUM
american_scientific_journal-2507	43	5	;)	;)	SYM
american_scientific_journal-2507	43	6	(	(	PUNCT
american_scientific_journal-2507	43	7	4	4	NUM
american_scientific_journal-2507	43	8	1	1	NUM
american_scientific_journal-2507	43	9	)	)	PUNCT
american_scientific_journal-2507	43	10	9	9	NUM
american_scientific_journal-2507	43	11	(	(	PUNCT
american_scientific_journal-2507	43	12	1	1	NUM
american_scientific_journal-2507	43	13	;	;	SYM
american_scientific_journal-2507	43	14	1	1	NUM
american_scientific_journal-2507	43	15	)	)	PUNCT
american_scientific_journal-2507	43	16	(	(	PUNCT
american_scientific_journal-2507	43	17	1	1	X
american_scientific_journal-2507	43	18	)	)	PUNCT
american_scientific_journal-2507	43	19	(	(	PUNCT
american_scientific_journal-2507	43	20	2	2	NUM
american_scientific_journal-2507	43	21	1	1	NUM
american_scientific_journal-2507	43	22	)	)	PUNCT
american_scientific_journal-2507	43	23	(	(	PUNCT
american_scientific_journal-2507	43	24	2	2	NUM
american_scientific_journal-2507	43	25	11	11	NUM
american_scientific_journal-2507	43	26	kxt	kxt	NOUN
american_scientific_journal-2507	44	1	k	k	PROPN
american_scientific_journal-2507	44	2	k	k	PROPN
american_scientific_journal-2507	44	3	xt	xt	PROPN
american_scientific_journal-2507	45	1	k	k	PROPN
american_scientific_journal-2507	45	2	xt	xt	PROPN
american_scientific_journal-2507	45	3	dxxt	dxxt	NOUN
american_scientific_journal-2507	45	4	kk	kk	PROPN
american_scientific_journal-2507	45	5	k	k	PROPN
american_scientific_journal-2507	45	6	also	also	ADV
american_scientific_journal-2507	45	7	it	it	PRON
american_scientific_journal-2507	45	8	is	be	AUX
american_scientific_journal-2507	45	9	frequently	frequently	ADV
american_scientific_journal-2507	45	10	necessary	necessary	ADJ
american_scientific_journal-2507	45	11	to	to	PART
american_scientific_journal-2507	45	12	be	be	AUX
american_scientific_journal-2507	45	13	able	able	ADJ
american_scientific_journal-2507	45	14	to	to	PART
american_scientific_journal-2507	45	15	multiply	multiply	VERB
american_scientific_journal-2507	45	16	chebyshev	chebyshev	VERB
american_scientific_journal-2507	45	17	polynomials	polynomial	NOUN
american_scientific_journal-2507	45	18	by	by	ADP
american_scientific_journal-2507	45	19	factors	factor	NOUN
american_scientific_journal-2507	45	20	such	such	ADJ
american_scientific_journal-2507	45	21	as	as	ADP
american_scientific_journal-2507	45	22	211	211	NUM
american_scientific_journal-2507	45	23	,	,	PUNCT
american_scientific_journal-2507	45	24	xandxx	xandxx	PROPN
american_scientific_journal-2507	45	25	−−	−−	PROPN
american_scientific_journal-2507	45	26	and	and	CCONJ
american_scientific_journal-2507	45	27	to	to	PART
american_scientific_journal-2507	45	28	express	express	VERB
american_scientific_journal-2507	45	29	the	the	DET
american_scientific_journal-2507	45	30	result	result	NOUN
american_scientific_journal-2507	45	31	in	in	ADP
american_scientific_journal-2507	45	32	terms	term	NOUN
american_scientific_journal-2507	45	33	of	of	ADP
american_scientific_journal-2507	45	34	chebyshev	chebyshev	NOUN
american_scientific_journal-2507	45	35	polynomials	polynomial	NOUN
american_scientific_journal-2507	45	36	.	.	PUNCT
american_scientific_journal-2507	46	1	[	[	PUNCT
american_scientific_journal-2507	46	2	]	]	X
american_scientific_journal-2507	46	3	(	(	PUNCT
american_scientific_journal-2507	46	4	)	)	PUNCT
american_scientific_journal-2507	46	5	)	)	PUNCT
american_scientific_journal-2507	46	6	10	10	NUM
american_scientific_journal-2507	46	7	(	(	PUNCT
american_scientific_journal-2507	46	8	)	)	PUNCT
american_scientific_journal-2507	46	9	(	(	PUNCT
american_scientific_journal-2507	46	10	)	)	PUNCT
american_scientific_journal-2507	46	11	(	(	PUNCT
american_scientific_journal-2507	46	12	2	2	NUM
american_scientific_journal-2507	46	13	1	1	NUM
american_scientific_journal-2507	46	14	1cos)1(coscoscos	1cos)1(coscoscos	NUM
american_scientific_journal-2507	46	15	)	)	PUNCT
american_scientific_journal-2507	46	16	(	(	PUNCT
american_scientific_journal-2507	46	17	11	11	NUM
american_scientific_journal-2507	46	18	2	2	NUM
american_scientific_journal-2507	46	19	1	1	NUM
american_scientific_journal-2507	46	20	xtxt	xtxt	NOUN
american_scientific_journal-2507	46	21	kkxtx	kkxtx	NOUN
american_scientific_journal-2507	46	22	kk	kk	PROPN
american_scientific_journal-2507	46	23	k	k	PROPN
american_scientific_journal-2507	46	24	−+	−+	PROPN
american_scientific_journal-2507	47	1	+	+	PROPN
american_scientific_journal-2507	47	2	=	=	PROPN
american_scientific_journal-2507	47	3	−++==	−++==	PROPN
american_scientific_journal-2507	47	4	θθθθ	θθθθ	NOUN
american_scientific_journal-2507	47	5	on	on	ADP
american_scientific_journal-2507	47	6	a	a	DET
american_scientific_journal-2507	47	7	general	general	ADJ
american_scientific_journal-2507	47	8	note	note	NOUN
american_scientific_journal-2507	47	9	,	,	PUNCT
american_scientific_journal-2507	47	10	expression	expression	NOUN
american_scientific_journal-2507	47	11	for	for	ADP
american_scientific_journal-2507	47	12	)	)	PUNCT
american_scientific_journal-2507	47	13	(	(	PUNCT
american_scientific_journal-2507	47	14	xtx	xtx	PROPN
american_scientific_journal-2507	47	15	k	k	PROPN
american_scientific_journal-2507	47	16	m	m	PROPN
american_scientific_journal-2507	47	17	,	,	PUNCT
american_scientific_journal-2507	47	18	as	as	SCONJ
american_scientific_journal-2507	47	19	illustrated	illustrate	VERB
american_scientific_journal-2507	47	20	in	in	ADP
american_scientific_journal-2507	47	21	[	[	X
american_scientific_journal-2507	47	22	3	3	NUM
american_scientific_journal-2507	47	23	]	]	PUNCT
american_scientific_journal-2507	47	24	,	,	PUNCT
american_scientific_journal-2507	47	25	is	be	AUX
american_scientific_journal-2507	47	26	given	give	VERB
american_scientific_journal-2507	47	27	by	by	ADP
american_scientific_journal-2507	47	28	:	:	PUNCT
american_scientific_journal-2507	47	29	)	)	PUNCT
american_scientific_journal-2507	47	30	11()()(2	11()()(2	NUM
american_scientific_journal-2507	47	31	)	)	PUNCT
american_scientific_journal-2507	47	32	(	(	PUNCT
american_scientific_journal-2507	47	33	0	0	NUM
american_scientific_journal-2507	47	34	2	2	NUM
american_scientific_journal-2507	47	35	kmxt	kmxt	NOUN
american_scientific_journal-2507	47	36	r	r	NOUN
american_scientific_journal-2507	47	37	m	m	VERB
american_scientific_journal-2507	47	38	xtx	xtx	PROPN
american_scientific_journal-2507	47	39	m	m	PROPN
american_scientific_journal-2507	47	40	r	r	NOUN
american_scientific_journal-2507	47	41	rmk	rmk	NOUN
american_scientific_journal-2507	47	42	m	m	VERB
american_scientific_journal-2507	47	43	k	k	NOUN
american_scientific_journal-2507	47	44	m	m	VERB
american_scientific_journal-2507	47	45	<	<	X
american_scientific_journal-2507	47	46			X
american_scientific_journal-2507	47	47			PUNCT
american_scientific_journal-2507	48	1			PROPN
american_scientific_journal-2507	49	1			INTJ
american_scientific_journal-2507	49	2			NOUN
american_scientific_journal-2507	49	3			VERB
american_scientific_journal-2507	49	4	=	=	SYM
american_scientific_journal-2507	49	5	∑	∑	PUNCT
american_scientific_journal-2507	49	6	=	=	PUNCT
american_scientific_journal-2507	49	7	−−	−−	NOUN
american_scientific_journal-2507	49	8	−	−	PROPN
american_scientific_journal-2507	49	9	in	in	ADP
american_scientific_journal-2507	49	10	circumstances	circumstance	NOUN
american_scientific_journal-2507	49	11	where	where	SCONJ
american_scientific_journal-2507	49	12	the	the	DET
american_scientific_journal-2507	49	13	variable	variable	ADJ
american_scientific_journal-2507	49	14	coefficient	coefficient	NOUN
american_scientific_journal-2507	49	15	is	be	AUX
american_scientific_journal-2507	49	16	a	a	DET
american_scientific_journal-2507	49	17	non	non	ADJ
american_scientific_journal-2507	49	18	-	-	ADJ
american_scientific_journal-2507	49	19	polynomial	polynomial	ADJ
american_scientific_journal-2507	49	20	term	term	NOUN
american_scientific_journal-2507	49	21	,	,	PUNCT
american_scientific_journal-2507	49	22	we	we	PRON
american_scientific_journal-2507	49	23	adopt	adopt	VERB
american_scientific_journal-2507	49	24	a	a	DET
american_scientific_journal-2507	49	25	technique	technique	NOUN
american_scientific_journal-2507	49	26	in	in	ADP
american_scientific_journal-2507	49	27	[	[	X
american_scientific_journal-2507	49	28	4	4	NUM
american_scientific_journal-2507	49	29	]	]	PUNCT
american_scientific_journal-2507	49	30	for	for	ADP
american_scientific_journal-2507	49	31	the	the	DET
american_scientific_journal-2507	49	32	expression	expression	NOUN
american_scientific_journal-2507	49	33	of	of	ADP
american_scientific_journal-2507	49	34	)	)	PUNCT
american_scientific_journal-2507	49	35	(	(	PUNCT
american_scientific_journal-2507	49	36	)	)	PUNCT
american_scientific_journal-2507	49	37	(	(	PUNCT
american_scientific_journal-2507	49	38	xtxf	xtxf	PROPN
american_scientific_journal-2507	49	39	k	k	PROPN
american_scientific_journal-2507	49	40	where	where	SCONJ
american_scientific_journal-2507	49	41	)	)	PUNCT
american_scientific_journal-2507	49	42	(	(	PUNCT
american_scientific_journal-2507	49	43	xf	xf	PROPN
american_scientific_journal-2507	49	44	is	be	AUX
american_scientific_journal-2507	49	45	first	first	ADV
american_scientific_journal-2507	49	46	written	write	VERB
american_scientific_journal-2507	49	47	in	in	ADP
american_scientific_journal-2507	49	48	taylor	taylor	PROPN
american_scientific_journal-2507	49	49	series	series	PROPN
american_scientific_journal-2507	49	50	form	form	NOUN
american_scientific_journal-2507	49	51	.	.	PUNCT
american_scientific_journal-2507	50	1	american	american	ADJ
american_scientific_journal-2507	50	2	scientific	scientific	ADJ
american_scientific_journal-2507	50	3	research	research	PROPN
american_scientific_journal-2507	50	4	journal	journal	NOUN
american_scientific_journal-2507	50	5	for	for	ADP
american_scientific_journal-2507	50	6	engineering	engineering	NOUN
american_scientific_journal-2507	50	7	,	,	PUNCT
american_scientific_journal-2507	50	8	technology	technology	NOUN
american_scientific_journal-2507	50	9	,	,	PUNCT
american_scientific_journal-2507	50	10	and	and	CCONJ
american_scientific_journal-2507	50	11	sciences	science	NOUN
american_scientific_journal-2507	50	12	(	(	PUNCT
american_scientific_journal-2507	50	13	asrjets	asrjet	NOUN
american_scientific_journal-2507	50	14	)	)	PUNCT
american_scientific_journal-2507	50	15	(	(	PUNCT
american_scientific_journal-2507	50	16	2017	2017	NUM
american_scientific_journal-2507	50	17	)	)	PUNCT
american_scientific_journal-2507	50	18	volume	volume	NOUN
american_scientific_journal-2507	50	19	30	30	NUM
american_scientific_journal-2507	50	20	,	,	PUNCT
american_scientific_journal-2507	50	21	no	no	DET
american_scientific_journal-2507	50	22	1	1	NUM
american_scientific_journal-2507	50	23	,	,	PUNCT
american_scientific_journal-2507	50	24	pp	pp	ADV
american_scientific_journal-2507	50	25	47	47	NUM
american_scientific_journal-2507	50	26	-	-	SYM
american_scientific_journal-2507	50	27	56	56	NUM
american_scientific_journal-2507	50	28	51	51	NUM
american_scientific_journal-2507	50	29	also	also	ADV
american_scientific_journal-2507	50	30	,	,	PUNCT
american_scientific_journal-2507	50	31	the	the	DET
american_scientific_journal-2507	50	32	power	power	NOUN
american_scientific_journal-2507	50	33	nx	nx	PROPN
american_scientific_journal-2507	50	34	that	that	PRON
american_scientific_journal-2507	50	35	makes	make	VERB
american_scientific_journal-2507	50	36	up	up	ADP
american_scientific_journal-2507	50	37	)	)	PUNCT
american_scientific_journal-2507	50	38	(	(	PUNCT
american_scientific_journal-2507	50	39	xf	xf	PROPN
american_scientific_journal-2507	50	40	on	on	ADP
american_scientific_journal-2507	50	41	the	the	DET
american_scientific_journal-2507	50	42	lhs	lhs	PROPN
american_scientific_journal-2507	50	43	of	of	ADP
american_scientific_journal-2507	50	44	equation	equation	NOUN
american_scientific_journal-2507	50	45	(	(	PUNCT
american_scientific_journal-2507	50	46	1	1	X
american_scientific_journal-2507	50	47	)	)	PUNCT
american_scientific_journal-2507	50	48	is	be	AUX
american_scientific_journal-2507	50	49	expressed	express	VERB
american_scientific_journal-2507	50	50	in	in	ADP
american_scientific_journal-2507	50	51	terms	term	NOUN
american_scientific_journal-2507	50	52	of	of	ADP
american_scientific_journal-2507	50	53	the	the	DET
american_scientific_journal-2507	50	54	chebyshev	chebyshev	NOUN
american_scientific_journal-2507	50	55	polynomials	polynomial	NOUN
american_scientific_journal-2507	50	56	of	of	ADP
american_scientific_journal-2507	50	57	degrees	degree	NOUN
american_scientific_journal-2507	50	58	up	up	ADP
american_scientific_journal-2507	50	59	to	to	PART
american_scientific_journal-2507	50	60	n.	n.	VERB
american_scientific_journal-2507	50	61	as	as	SCONJ
american_scientific_journal-2507	50	62	established	establish	VERB
american_scientific_journal-2507	50	63	by	by	ADP
american_scientific_journal-2507	50	64	mason	mason	PROPN
american_scientific_journal-2507	50	65	and	and	CCONJ
american_scientific_journal-2507	50	66	handscomb	handscomb	VERB
american_scientific_journal-2507	50	67	[	[	X
american_scientific_journal-2507	50	68	3	3	NUM
american_scientific_journal-2507	50	69	]	]	PUNCT
american_scientific_journal-2507	50	70	,	,	PUNCT
american_scientific_journal-2507	50	71	this	this	PRON
american_scientific_journal-2507	50	72	is	be	AUX
american_scientific_journal-2507	50	73	given	give	VERB
american_scientific_journal-2507	50	74	by	by	ADP
american_scientific_journal-2507	50	75	:	:	PUNCT
american_scientific_journal-2507	50	76			X
american_scientific_journal-2507	50	77			PROPN
american_scientific_journal-2507	50	78	∑	∑	PUNCT
american_scientific_journal-2507	50	79	=	=	SYM
american_scientific_journal-2507	50	80	−	−	PROPN
american_scientific_journal-2507	50	81	−	−	PROPN
american_scientific_journal-2507	50	82			NOUN
american_scientific_journal-2507	50	83			PUNCT
american_scientific_journal-2507	51	1			PROPN
american_scientific_journal-2507	52	1			INTJ
american_scientific_journal-2507	52	2			NOUN
american_scientific_journal-2507	52	3			VERB
american_scientific_journal-2507	52	4	=	=	SYM
american_scientific_journal-2507	52	5	2	2	NUM
american_scientific_journal-2507	52	6	0	0	NUM
american_scientific_journal-2507	52	7	2	2	NUM
american_scientific_journal-2507	52	8	1	1	NUM
american_scientific_journal-2507	52	9	)	)	PUNCT
american_scientific_journal-2507	52	10	12()(2	12()(2	PROPN
american_scientific_journal-2507	53	1	n	n	NUM
american_scientific_journal-2507	53	2	k	k	PROPN
american_scientific_journal-2507	53	3	kn	kn	PROPN
american_scientific_journal-2507	53	4	nn	nn	PROPN
american_scientific_journal-2507	53	5	xt	xt	PROPN
american_scientific_journal-2507	54	1	k	k	PROPN
american_scientific_journal-2507	54	2	n	n	PROPN
american_scientific_journal-2507	54	3	x	x	SYM
american_scientific_journal-2507	54	4	4	4	X
american_scientific_journal-2507	54	5	.	.	PUNCT
american_scientific_journal-2507	54	6	spectral	spectral	ADJ
american_scientific_journal-2507	54	7	methods	method	NOUN
american_scientific_journal-2507	54	8	spectral	spectral	ADJ
american_scientific_journal-2507	54	9	methods	method	NOUN
american_scientific_journal-2507	54	10	are	be	AUX
american_scientific_journal-2507	54	11	part	part	NOUN
american_scientific_journal-2507	54	12	of	of	ADP
american_scientific_journal-2507	54	13	several	several	ADJ
american_scientific_journal-2507	54	14	methods	method	NOUN
american_scientific_journal-2507	54	15	founded	found	VERB
american_scientific_journal-2507	54	16	on	on	ADP
american_scientific_journal-2507	54	17	orthogonal	orthogonal	ADJ
american_scientific_journal-2507	54	18	expansions	expansion	NOUN
american_scientific_journal-2507	54	19	,	,	PUNCT
american_scientific_journal-2507	54	20	in	in	ADP
american_scientific_journal-2507	54	21	this	this	DET
american_scientific_journal-2507	54	22	study	study	NOUN
american_scientific_journal-2507	54	23	we	we	PRON
american_scientific_journal-2507	54	24	consider	consider	VERB
american_scientific_journal-2507	54	25	the	the	DET
american_scientific_journal-2507	54	26	expansions	expansion	NOUN
american_scientific_journal-2507	54	27	in	in	ADP
american_scientific_journal-2507	54	28	chebyshev	chebyshev	NOUN
american_scientific_journal-2507	54	29	polynomials	polynomial	NOUN
american_scientific_journal-2507	54	30	of	of	ADP
american_scientific_journal-2507	54	31	the	the	DET
american_scientific_journal-2507	54	32	first	first	ADJ
american_scientific_journal-2507	54	33	kind	kind	NOUN
american_scientific_journal-2507	54	34	.	.	PUNCT
american_scientific_journal-2507	55	1	in	in	ADP
american_scientific_journal-2507	55	2	this	this	DET
american_scientific_journal-2507	55	3	method	method	NOUN
american_scientific_journal-2507	55	4	,	,	PUNCT
american_scientific_journal-2507	55	5	the	the	DET
american_scientific_journal-2507	55	6	idea	idea	NOUN
american_scientific_journal-2507	55	7	is	be	AUX
american_scientific_journal-2507	55	8	to	to	PART
american_scientific_journal-2507	55	9	write	write	VERB
american_scientific_journal-2507	55	10	the	the	DET
american_scientific_journal-2507	55	11	solution	solution	NOUN
american_scientific_journal-2507	55	12	to	to	ADP
american_scientific_journal-2507	55	13	the	the	DET
american_scientific_journal-2507	55	14	integral	integral	ADJ
american_scientific_journal-2507	55	15	(	(	PUNCT
american_scientific_journal-2507	55	16	1	1	NUM
american_scientific_journal-2507	55	17	)	)	PUNCT
american_scientific_journal-2507	55	18	as	as	ADP
american_scientific_journal-2507	55	19	a	a	DET
american_scientific_journal-2507	55	20	series	series	NOUN
american_scientific_journal-2507	55	21	of	of	ADP
american_scientific_journal-2507	55	22	“	"	PUNCT
american_scientific_journal-2507	55	23	chebyshev	chebyshev	PROPN
american_scientific_journal-2507	55	24	basis	basis	NOUN
american_scientific_journal-2507	55	25	functions	function	NOUN
american_scientific_journal-2507	55	26	”	"	PUNCT
american_scientific_journal-2507	55	27	i.	i.	PROPN
american_scientific_journal-2507	55	28	e.	e.	PROPN
american_scientific_journal-2507	55	29	)	)	PUNCT
american_scientific_journal-2507	55	30	13()()(ˆ	13()()(ˆ	ADP
american_scientific_journal-2507	55	31	1	1	NUM
american_scientific_journal-2507	55	32	'	'	NUM
american_scientific_journal-2507	55	33	02	02	NUM
american_scientific_journal-2507	55	34	1	1	NUM
american_scientific_journal-2507	55	35	∑	∑	PUNCT
american_scientific_journal-2507	55	36	=	=	SYM
american_scientific_journal-2507	55	37	+	+	NOUN
american_scientific_journal-2507	55	38	=	=	SYM
american_scientific_journal-2507	55	39	n	n	SYM
american_scientific_journal-2507	55	40	k	k	PROPN
american_scientific_journal-2507	55	41	kkn	kkn	PROPN
american_scientific_journal-2507	55	42	xtccxu	xtccxu	NOUN
american_scientific_journal-2507	55	43	equation	equation	NOUN
american_scientific_journal-2507	55	44	(	(	PUNCT
american_scientific_journal-2507	55	45	13	13	NUM
american_scientific_journal-2507	55	46	)	)	PUNCT
american_scientific_journal-2507	55	47	is	be	AUX
american_scientific_journal-2507	55	48	referred	refer	VERB
american_scientific_journal-2507	55	49	to	to	ADP
american_scientific_journal-2507	55	50	as	as	ADP
american_scientific_journal-2507	55	51	the	the	DET
american_scientific_journal-2507	55	52	trial	trial	NOUN
american_scientific_journal-2507	55	53	solution	solution	NOUN
american_scientific_journal-2507	55	54	while	while	SCONJ
american_scientific_journal-2507	55	55	the	the	DET
american_scientific_journal-2507	55	56	expansion	expansion	NOUN
american_scientific_journal-2507	55	57	coefficients	coefficient	VERB
american_scientific_journal-2507	55	58	{	{	PUNCT
american_scientific_journal-2507	55	59	}	}	PUNCT
american_scientific_journal-2507	55	60	kc	kc	PROPN
american_scientific_journal-2507	55	61	is	be	AUX
american_scientific_journal-2507	55	62	referred	refer	VERB
american_scientific_journal-2507	55	63	to	to	ADP
american_scientific_journal-2507	55	64	as	as	ADP
american_scientific_journal-2507	55	65	the	the	DET
american_scientific_journal-2507	55	66	spectral	spectral	ADJ
american_scientific_journal-2507	55	67	space	space	NOUN
american_scientific_journal-2507	55	68	representation	representation	NOUN
american_scientific_journal-2507	55	69	of	of	ADP
american_scientific_journal-2507	55	70	the	the	DET
american_scientific_journal-2507	55	71	function	function	NOUN
american_scientific_journal-2507	55	72	.	.	PUNCT
american_scientific_journal-2507	56	1	it	it	PRON
american_scientific_journal-2507	56	2	is	be	AUX
american_scientific_journal-2507	56	3	to	to	PART
american_scientific_journal-2507	56	4	be	be	AUX
american_scientific_journal-2507	56	5	noted	note	VERB
american_scientific_journal-2507	56	6	that	that	SCONJ
american_scientific_journal-2507	56	7	the	the	DET
american_scientific_journal-2507	56	8	implementation	implementation	NOUN
american_scientific_journal-2507	56	9	of	of	ADP
american_scientific_journal-2507	56	10	spectral	spectral	ADJ
american_scientific_journal-2507	56	11	methods	method	NOUN
american_scientific_journal-2507	56	12	is	be	AUX
american_scientific_journal-2507	56	13	normally	normally	ADV
american_scientific_journal-2507	56	14	accomplished	accomplish	VERB
american_scientific_journal-2507	56	15	with	with	ADP
american_scientific_journal-2507	56	16	either	either	DET
american_scientific_journal-2507	56	17	collocation	collocation	NOUN
american_scientific_journal-2507	56	18	,	,	PUNCT
american_scientific_journal-2507	56	19	galerkin	galerkin	ADJ
american_scientific_journal-2507	56	20	or	or	CCONJ
american_scientific_journal-2507	56	21	a	a	DET
american_scientific_journal-2507	56	22	tau	tau	PROPN
american_scientific_journal-2507	56	23	approach	approach	NOUN
american_scientific_journal-2507	56	24	.	.	PUNCT
american_scientific_journal-2507	57	1	(	(	PUNCT
american_scientific_journal-2507	57	2	see	see	VERB
american_scientific_journal-2507	57	3	ref	ref	NOUN
american_scientific_journal-2507	57	4	[	[	X
american_scientific_journal-2507	57	5	1][5][9][10	1][5][9][10	NUM
american_scientific_journal-2507	57	6	]	]	PUNCT
american_scientific_journal-2507	57	7	)	)	PUNCT
american_scientific_journal-2507	57	8	.	.	PUNCT
american_scientific_journal-2507	58	1	but	but	CCONJ
american_scientific_journal-2507	58	2	in	in	ADP
american_scientific_journal-2507	58	3	this	this	DET
american_scientific_journal-2507	58	4	study	study	NOUN
american_scientific_journal-2507	58	5	,	,	PUNCT
american_scientific_journal-2507	58	6	a	a	DET
american_scientific_journal-2507	58	7	new	new	ADJ
american_scientific_journal-2507	58	8	approach	approach	NOUN
american_scientific_journal-2507	58	9	of	of	ADP
american_scientific_journal-2507	58	10	factorizing	factorize	VERB
american_scientific_journal-2507	58	11	the	the	DET
american_scientific_journal-2507	58	12	coefficients	coefficient	NOUN
american_scientific_journal-2507	58	13	is	be	AUX
american_scientific_journal-2507	58	14	applied	apply	VERB
american_scientific_journal-2507	58	15	as	as	ADP
american_scientific_journal-2507	58	16	an	an	DET
american_scientific_journal-2507	58	17	implementation	implementation	NOUN
american_scientific_journal-2507	58	18	technique	technique	NOUN
american_scientific_journal-2507	58	19	.	.	PUNCT
american_scientific_journal-2507	59	1	equation	equation	NOUN
american_scientific_journal-2507	59	2	(	(	PUNCT
american_scientific_journal-2507	59	3	13	13	NUM
american_scientific_journal-2507	59	4	)	)	PUNCT
american_scientific_journal-2507	59	5	is	be	AUX
american_scientific_journal-2507	59	6	substituted	substitute	VERB
american_scientific_journal-2507	59	7	into	into	ADP
american_scientific_journal-2507	59	8	(	(	PUNCT
american_scientific_journal-2507	59	9	1	1	NUM
american_scientific_journal-2507	59	10	)	)	PUNCT
american_scientific_journal-2507	59	11	to	to	PART
american_scientific_journal-2507	59	12	yield	yield	VERB
american_scientific_journal-2507	59	13	:	:	PUNCT
american_scientific_journal-2507	59	14	)	)	PUNCT
american_scientific_journal-2507	60	1	14()()(ˆ),()(ˆ	14()()(ˆ),()(ˆ	X
american_scientific_journal-2507	60	2	)	)	PUNCT
american_scientific_journal-2507	60	3	(	(	PUNCT
american_scientific_journal-2507	60	4	∫	∫	PROPN
american_scientific_journal-2507	61	1	=	=	PROPN
american_scientific_journal-2507	61	2	+	+	X
american_scientific_journal-2507	61	3	b	b	NOUN
american_scientific_journal-2507	61	4	a	a	DET
american_scientific_journal-2507	61	5	xfdttutxkxux	xfdttutxkxux	NOUN
american_scientific_journal-2507	61	6	λa	λa	ADP
american_scientific_journal-2507	61	7	which	which	PRON
american_scientific_journal-2507	61	8	becomes	become	VERB
american_scientific_journal-2507	61	9	)	)	PUNCT
american_scientific_journal-2507	61	10	15	15	NUM
american_scientific_journal-2507	61	11	(	(	PUNCT
american_scientific_journal-2507	61	12	)	)	PUNCT
american_scientific_journal-2507	61	13	(	(	PUNCT
american_scientific_journal-2507	61	14	)	)	PUNCT
american_scientific_journal-2507	61	15	(	(	PUNCT
american_scientific_journal-2507	61	16	2	2	NUM
american_scientific_journal-2507	61	17	1	1	NUM
american_scientific_journal-2507	61	18	)	)	PUNCT
american_scientific_journal-2507	61	19	,	,	PUNCT
american_scientific_journal-2507	61	20	(	(	PUNCT
american_scientific_journal-2507	61	21	)	)	PUNCT
american_scientific_journal-2507	61	22	(	(	PUNCT
american_scientific_journal-2507	61	23	2	2	NUM
american_scientific_journal-2507	61	24	1	1	NUM
american_scientific_journal-2507	61	25	)	)	PUNCT
american_scientific_journal-2507	61	26	(	(	PUNCT
american_scientific_journal-2507	61	27	1	1	NUM
american_scientific_journal-2507	61	28	0	0	NUM
american_scientific_journal-2507	61	29	1	1	NUM
american_scientific_journal-2507	61	30	0	0	NUM
american_scientific_journal-2507	61	31	∫	∫	PROPN
american_scientific_journal-2507	61	32	∑∑	∑∑	PROPN
american_scientific_journal-2507	62	1	≈	≈	PROPN
american_scientific_journal-2507	62	2			PROPN
american_scientific_journal-2507	62	3			PROPN
american_scientific_journal-2507	62	4			ADJ
american_scientific_journal-2507	62	5			NOUN
american_scientific_journal-2507	62	6			NOUN
american_scientific_journal-2507	62	7	+	+	PROPN
american_scientific_journal-2507	62	8	+	+	ADJ
american_scientific_journal-2507	62	9			PROPN
american_scientific_journal-2507	62	10			PROPN
american_scientific_journal-2507	62	11			PROPN
american_scientific_journal-2507	62	12			ADJ
american_scientific_journal-2507	62	13			NUM
american_scientific_journal-2507	62	14			NOUN
american_scientific_journal-2507	62	15	+	+	X
american_scientific_journal-2507	62	16	=	=	SYM
american_scientific_journal-2507	62	17	=	=	SYM
american_scientific_journal-2507	62	18	b	b	PROPN
american_scientific_journal-2507	62	19	a	a	PRON
american_scientific_journal-2507	62	20	n	n	X
american_scientific_journal-2507	62	21	k	k	PROPN
american_scientific_journal-2507	62	22	kk	kk	PROPN
american_scientific_journal-2507	63	1	n	n	CCONJ
american_scientific_journal-2507	63	2	k	k	PROPN
american_scientific_journal-2507	63	3	kk	kk	X
american_scientific_journal-2507	63	4	xfdtxtcctxkxtccx	xfdtxtcctxkxtccx	VERB
american_scientific_journal-2507	63	5	λa	λa	INTJ
american_scientific_journal-2507	63	6	with	with	ADP
american_scientific_journal-2507	63	7	the	the	DET
american_scientific_journal-2507	63	8	aid	aid	NOUN
american_scientific_journal-2507	63	9	of	of	ADP
american_scientific_journal-2507	63	10	approaches	approach	NOUN
american_scientific_journal-2507	63	11	in	in	ADP
american_scientific_journal-2507	63	12	(	(	PUNCT
american_scientific_journal-2507	63	13	[	[	X
american_scientific_journal-2507	63	14	4][6][8	4][6][8	NUM
american_scientific_journal-2507	63	15	]	]	X
american_scientific_journal-2507	63	16	)	)	PUNCT
american_scientific_journal-2507	63	17	products	product	NOUN
american_scientific_journal-2507	63	18	like	like	ADP
american_scientific_journal-2507	63	19	)	)	PUNCT
american_scientific_journal-2507	63	20	(	(	PUNCT
american_scientific_journal-2507	63	21	)	)	PUNCT
american_scientific_journal-2507	63	22	(	(	PUNCT
american_scientific_journal-2507	63	23	xtx	xtx	PROPN
american_scientific_journal-2507	63	24	ka	ka	PROPN
american_scientific_journal-2507	63	25	and	and	CCONJ
american_scientific_journal-2507	63	26	integral	integral	ADJ
american_scientific_journal-2507	63	27	∫	∫	NOUN
american_scientific_journal-2507	63	28	)	)	PUNCT
american_scientific_journal-2507	63	29	(	(	PUNCT
american_scientific_journal-2507	63	30	)	)	PUNCT
american_scientific_journal-2507	63	31	,	,	PUNCT
american_scientific_journal-2507	63	32	(	(	PUNCT
american_scientific_journal-2507	63	33	xttxk	xttxk	PROPN
american_scientific_journal-2507	63	34	k	k	PROPN
american_scientific_journal-2507	63	35	are	be	AUX
american_scientific_journal-2507	63	36	easily	easily	ADV
american_scientific_journal-2507	63	37	resolved	resolve	VERB
american_scientific_journal-2507	63	38	into	into	ADP
american_scientific_journal-2507	63	39	series	series	NOUN
american_scientific_journal-2507	63	40	of	of	ADP
american_scientific_journal-2507	63	41	chebyshev	chebyshev	NOUN
american_scientific_journal-2507	63	42	polynomials	polynomial	NOUN
american_scientific_journal-2507	63	43	.	.	PUNCT
american_scientific_journal-2507	64	1	also	also	ADV
american_scientific_journal-2507	64	2	)	)	PUNCT
american_scientific_journal-2507	64	3	(	(	PUNCT
american_scientific_journal-2507	64	4	xf	xf	PROPN
american_scientific_journal-2507	64	5	whether	whether	SCONJ
american_scientific_journal-2507	64	6	as	as	SCONJ
american_scientific_journal-2507	64	7	polynomials	polynomial	NOUN
american_scientific_journal-2507	64	8	,	,	PUNCT
american_scientific_journal-2507	64	9	trigonometry	trigonometry	NOUN
american_scientific_journal-2507	64	10	,	,	PUNCT
american_scientific_journal-2507	64	11	exponential	exponential	ADJ
american_scientific_journal-2507	64	12	and	and	CCONJ
american_scientific_journal-2507	64	13	logarithmic	logarithmic	ADJ
american_scientific_journal-2507	64	14	function	function	NOUN
american_scientific_journal-2507	64	15	is	be	AUX
american_scientific_journal-2507	64	16	easily	easily	ADV
american_scientific_journal-2507	64	17	resolved	resolve	VERB
american_scientific_journal-2507	64	18	into	into	ADP
american_scientific_journal-2507	64	19	series	series	NOUN
american_scientific_journal-2507	64	20	of	of	ADP
american_scientific_journal-2507	64	21	chebyshev	chebyshev	NOUN
american_scientific_journal-2507	64	22	polynomials	polynomial	NOUN
american_scientific_journal-2507	64	23	.	.	PUNCT
american_scientific_journal-2507	65	1	equation	equation	NOUN
american_scientific_journal-2507	65	2	(	(	PUNCT
american_scientific_journal-2507	65	3	15	15	NUM
american_scientific_journal-2507	65	4	)	)	PUNCT
american_scientific_journal-2507	65	5	therefore	therefore	ADV
american_scientific_journal-2507	65	6	becomes	become	VERB
american_scientific_journal-2507	65	7	an	an	DET
american_scientific_journal-2507	65	8	equation	equation	NOUN
american_scientific_journal-2507	65	9	in	in	ADP
american_scientific_journal-2507	65	10	series	series	NOUN
american_scientific_journal-2507	65	11	of	of	ADP
american_scientific_journal-2507	65	12	chebyshev	chebyshev	NOUN
american_scientific_journal-2507	65	13	polynomials	polynomial	NOUN
american_scientific_journal-2507	65	14	)	)	PUNCT
american_scientific_journal-2507	65	15	(	(	PUNCT
american_scientific_journal-2507	65	16	xtk	xtk	ADV
american_scientific_journal-2507	65	17	of	of	ADP
american_scientific_journal-2507	65	18	varying	vary	VERB
american_scientific_journal-2507	65	19	degree	degree	NOUN
american_scientific_journal-2507	65	20	on	on	ADP
american_scientific_journal-2507	65	21	both	both	DET
american_scientific_journal-2507	65	22	sides	side	NOUN
american_scientific_journal-2507	65	23	.	.	PUNCT
american_scientific_journal-2507	66	1	coefficients	coefficient	NOUN
american_scientific_journal-2507	66	2	of	of	ADP
american_scientific_journal-2507	66	3	each	each	PRON
american_scientific_journal-2507	66	4	)	)	PUNCT
american_scientific_journal-2507	66	5	(	(	PUNCT
american_scientific_journal-2507	66	6	xtk	xtk	ADV
american_scientific_journal-2507	66	7	are	be	AUX
american_scientific_journal-2507	66	8	thereafter	thereafter	ADV
american_scientific_journal-2507	66	9	equated	equate	VERB
american_scientific_journal-2507	66	10	correspondingly	correspondingly	ADV
american_scientific_journal-2507	66	11	to	to	PART
american_scientific_journal-2507	66	12	yield	yield	VERB
american_scientific_journal-2507	66	13	a	a	DET
american_scientific_journal-2507	66	14	system	system	NOUN
american_scientific_journal-2507	66	15	of	of	ADP
american_scientific_journal-2507	66	16	equations	equation	NOUN
american_scientific_journal-2507	66	17	:	:	PUNCT
american_scientific_journal-2507	66	18	)	)	PUNCT
american_scientific_journal-2507	66	19	16(bxa	16(bxa	ADJ
american_scientific_journal-2507	66	20	=	=	SYM
american_scientific_journal-2507	66	21	american	american	ADJ
american_scientific_journal-2507	66	22	scientific	scientific	ADJ
american_scientific_journal-2507	66	23	research	research	NOUN
american_scientific_journal-2507	66	24	journal	journal	NOUN
american_scientific_journal-2507	66	25	for	for	ADP
american_scientific_journal-2507	66	26	engineering	engineering	NOUN
american_scientific_journal-2507	66	27	,	,	PUNCT
american_scientific_journal-2507	66	28	technology	technology	NOUN
american_scientific_journal-2507	66	29	,	,	PUNCT
american_scientific_journal-2507	66	30	and	and	CCONJ
american_scientific_journal-2507	66	31	sciences	science	NOUN
american_scientific_journal-2507	66	32	(	(	PUNCT
american_scientific_journal-2507	66	33	asrjets	asrjet	NOUN
american_scientific_journal-2507	66	34	)	)	PUNCT
american_scientific_journal-2507	66	35	(	(	PUNCT
american_scientific_journal-2507	66	36	2017	2017	NUM
american_scientific_journal-2507	66	37	)	)	PUNCT
american_scientific_journal-2507	66	38	volume	volume	NOUN
american_scientific_journal-2507	66	39	30	30	NUM
american_scientific_journal-2507	66	40	,	,	PUNCT
american_scientific_journal-2507	66	41	no	no	DET
american_scientific_journal-2507	66	42	1	1	NUM
american_scientific_journal-2507	66	43	,	,	PUNCT
american_scientific_journal-2507	66	44	pp	pp	ADV
american_scientific_journal-2507	66	45	47	47	NUM
american_scientific_journal-2507	66	46	-	-	SYM
american_scientific_journal-2507	66	47	56	56	NUM
american_scientific_journal-2507	66	48	52	52	NUM
american_scientific_journal-2507	66	49	where	where	SCONJ
american_scientific_journal-2507	66	50	a	a	PRON
american_scientific_journal-2507	66	51	is	be	AUX
american_scientific_journal-2507	66	52	the	the	DET
american_scientific_journal-2507	66	53	matrix	matrix	NOUN
american_scientific_journal-2507	66	54	of	of	ADP
american_scientific_journal-2507	66	55	coefficients	coefficient	NOUN
american_scientific_journal-2507	66	56	,	,	PUNCT
american_scientific_journal-2507	66	57	x	x	PRON
american_scientific_journal-2507	66	58	is	be	AUX
american_scientific_journal-2507	66	59	the	the	DET
american_scientific_journal-2507	66	60	column	column	NOUN
american_scientific_journal-2507	66	61	vector	vector	NOUN
american_scientific_journal-2507	66	62	containing	contain	VERB
american_scientific_journal-2507	66	63	the	the	DET
american_scientific_journal-2507	66	64	expansion	expansion	NOUN
american_scientific_journal-2507	66	65	coefficients	coefficient	NOUN
american_scientific_journal-2507	66	66	}	}	PUNCT
american_scientific_journal-2507	66	67	{	{	PUNCT
american_scientific_journal-2507	66	68	nc	nc	PROPN
american_scientific_journal-2507	66	69	and	and	CCONJ
american_scientific_journal-2507	66	70	b	b	PROPN
american_scientific_journal-2507	66	71	is	be	AUX
american_scientific_journal-2507	66	72	the	the	DET
american_scientific_journal-2507	66	73	corresponding	corresponding	ADJ
american_scientific_journal-2507	66	74	coefficients	coefficient	NOUN
american_scientific_journal-2507	66	75	of	of	ADP
american_scientific_journal-2507	66	76	)	)	PUNCT
american_scientific_journal-2507	66	77	(	(	PUNCT
american_scientific_journal-2507	66	78	xtk	xtk	ADV
american_scientific_journal-2507	66	79	after	after	ADP
american_scientific_journal-2507	66	80	)	)	PUNCT
american_scientific_journal-2507	66	81	(	(	PUNCT
american_scientific_journal-2507	66	82	xf	xf	PROPN
american_scientific_journal-2507	66	83	has	have	AUX
american_scientific_journal-2507	66	84	been	be	AUX
american_scientific_journal-2507	66	85	converted	convert	VERB
american_scientific_journal-2507	66	86	into	into	ADP
american_scientific_journal-2507	66	87	series	series	NOUN
american_scientific_journal-2507	66	88	of	of	ADP
american_scientific_journal-2507	66	89	chebyshev	chebyshev	NOUN
american_scientific_journal-2507	66	90	polynomials	polynomial	NOUN
american_scientific_journal-2507	66	91	.	.	PUNCT
american_scientific_journal-2507	67	1	solving	solve	VERB
american_scientific_journal-2507	67	2	(	(	PUNCT
american_scientific_journal-2507	67	3	16	16	NUM
american_scientific_journal-2507	67	4	)	)	PUNCT
american_scientific_journal-2507	67	5	using	use	VERB
american_scientific_journal-2507	67	6	any	any	DET
american_scientific_journal-2507	67	7	algebraic	algebraic	ADJ
american_scientific_journal-2507	67	8	solution	solution	NOUN
american_scientific_journal-2507	67	9	methods	method	NOUN
american_scientific_journal-2507	67	10	yields	yield	VERB
american_scientific_journal-2507	67	11	numerical	numerical	ADJ
american_scientific_journal-2507	67	12	values	value	NOUN
american_scientific_journal-2507	67	13	for	for	ADP
american_scientific_journal-2507	67	14	nccc	nccc	PRON
american_scientific_journal-2507	67	15	...	...	PUNCT
american_scientific_journal-2507	67	16	10	10	NUM
american_scientific_journal-2507	67	17	.these	.these	NOUN
american_scientific_journal-2507	67	18	are	be	AUX
american_scientific_journal-2507	67	19	thereafter	thereafter	ADV
american_scientific_journal-2507	67	20	substituted	substitute	VERB
american_scientific_journal-2507	67	21	into	into	ADP
american_scientific_journal-2507	67	22	(	(	PUNCT
american_scientific_journal-2507	67	23	5	5	NUM
american_scientific_journal-2507	67	24	)	)	PUNCT
american_scientific_journal-2507	67	25	to	to	PART
american_scientific_journal-2507	67	26	yield	yield	VERB
american_scientific_journal-2507	67	27	an	an	DET
american_scientific_journal-2507	67	28	approximate	approximate	ADJ
american_scientific_journal-2507	67	29	solution	solution	NOUN
american_scientific_journal-2507	67	30	to	to	ADP
american_scientific_journal-2507	67	31	integral	integral	ADJ
american_scientific_journal-2507	67	32	equation	equation	NOUN
american_scientific_journal-2507	67	33	(	(	PUNCT
american_scientific_journal-2507	67	34	1	1	NUM
american_scientific_journal-2507	67	35	)	)	PUNCT
american_scientific_journal-2507	67	36	.	.	PUNCT
american_scientific_journal-2507	68	1	5	5	X
american_scientific_journal-2507	68	2	.	.	X
american_scientific_journal-2507	68	3	error	error	NOUN
american_scientific_journal-2507	68	4	estimates	estimate	NOUN
american_scientific_journal-2507	68	5	there	there	PRON
american_scientific_journal-2507	68	6	are	be	VERB
american_scientific_journal-2507	68	7	several	several	ADJ
american_scientific_journal-2507	68	8	studies	study	NOUN
american_scientific_journal-2507	68	9	concerning	concern	VERB
american_scientific_journal-2507	68	10	the	the	DET
american_scientific_journal-2507	68	11	convergence	convergence	NOUN
american_scientific_journal-2507	68	12	of	of	ADP
american_scientific_journal-2507	68	13	spectral	spectral	ADJ
american_scientific_journal-2507	68	14	methods	method	NOUN
american_scientific_journal-2507	68	15	.	.	PUNCT
american_scientific_journal-2507	69	1	these	these	PRON
american_scientific_journal-2507	69	2	include	include	VERB
american_scientific_journal-2507	69	3	(	(	PUNCT
american_scientific_journal-2507	69	4	cheney	cheney	NOUN
american_scientific_journal-2507	69	5	[	[	X
american_scientific_journal-2507	69	6	7	7	NUM
american_scientific_journal-2507	69	7	]	]	PUNCT
american_scientific_journal-2507	69	8	,	,	PUNCT
american_scientific_journal-2507	69	9	and	and	CCONJ
american_scientific_journal-2507	69	10	wazwaz	wazwaz	NOUN
american_scientific_journal-2507	70	1	[	[	X
american_scientific_journal-2507	70	2	9	9	NUM
american_scientific_journal-2507	70	3	]	]	SYM
american_scientific_journal-2507	70	4	)	)	PUNCT
american_scientific_journal-2507	70	5	.	.	PUNCT
american_scientific_journal-2507	71	1	discussion	discussion	NOUN
american_scientific_journal-2507	71	2	on	on	ADP
american_scientific_journal-2507	71	3	the	the	DET
american_scientific_journal-2507	71	4	theory	theory	NOUN
american_scientific_journal-2507	71	5	of	of	ADP
american_scientific_journal-2507	71	6	approximation	approximation	NOUN
american_scientific_journal-2507	71	7	from	from	ADP
american_scientific_journal-2507	71	8	an	an	DET
american_scientific_journal-2507	71	9	historical	historical	ADJ
american_scientific_journal-2507	71	10	perspective	perspective	NOUN
american_scientific_journal-2507	71	11	can	can	AUX
american_scientific_journal-2507	71	12	be	be	AUX
american_scientific_journal-2507	71	13	found	find	VERB
american_scientific_journal-2507	71	14	in	in	ADP
american_scientific_journal-2507	71	15	[	[	X
american_scientific_journal-2507	71	16	8	8	NUM
american_scientific_journal-2507	71	17	]	]	PUNCT
american_scientific_journal-2507	71	18	.	.	PUNCT
american_scientific_journal-2507	72	1	the	the	DET
american_scientific_journal-2507	72	2	minimax	minimax	NOUN
american_scientific_journal-2507	72	3	property	property	NOUN
american_scientific_journal-2507	72	4	of	of	ADP
american_scientific_journal-2507	72	5	)	)	PUNCT
american_scientific_journal-2507	72	6	(	(	PUNCT
american_scientific_journal-2507	72	7	xtk	xtk	ADV
american_scientific_journal-2507	72	8	enhances	enhance	VERB
american_scientific_journal-2507	72	9	the	the	DET
american_scientific_journal-2507	72	10	series	series	NOUN
american_scientific_journal-2507	72	11	in	in	ADP
american_scientific_journal-2507	72	12	the	the	DET
american_scientific_journal-2507	72	13	trial	trial	NOUN
american_scientific_journal-2507	72	14	solution	solution	NOUN
american_scientific_journal-2507	72	15	to	to	PART
american_scientific_journal-2507	72	16	provide	provide	VERB
american_scientific_journal-2507	72	17	an	an	DET
american_scientific_journal-2507	72	18	accurate	accurate	ADJ
american_scientific_journal-2507	72	19	approximation	approximation	NOUN
american_scientific_journal-2507	72	20	to	to	ADP
american_scientific_journal-2507	72	21	)	)	PUNCT
american_scientific_journal-2507	72	22	(	(	PUNCT
american_scientific_journal-2507	72	23	xu	xu	INTJ
american_scientific_journal-2507	72	24	with	with	ADP
american_scientific_journal-2507	72	25	small	small	ADJ
american_scientific_journal-2507	72	26	number	number	NOUN
american_scientific_journal-2507	72	27	of	of	ADP
american_scientific_journal-2507	72	28	terms	term	NOUN
american_scientific_journal-2507	72	29	.	.	PUNCT
american_scientific_journal-2507	73	1	however	however	ADV
american_scientific_journal-2507	73	2	,	,	PUNCT
american_scientific_journal-2507	73	3	it	it	PRON
american_scientific_journal-2507	73	4	is	be	AUX
american_scientific_journal-2507	73	5	to	to	PART
american_scientific_journal-2507	73	6	be	be	AUX
american_scientific_journal-2507	73	7	noted	note	VERB
american_scientific_journal-2507	73	8	that	that	SCONJ
american_scientific_journal-2507	73	9	if	if	SCONJ
american_scientific_journal-2507	73	10	the	the	DET
american_scientific_journal-2507	73	11	method	method	NOUN
american_scientific_journal-2507	73	12	is	be	AUX
american_scientific_journal-2507	73	13	efficient	efficient	ADJ
american_scientific_journal-2507	73	14	,	,	PUNCT
american_scientific_journal-2507	73	15	the	the	DET
american_scientific_journal-2507	73	16	absolute	absolute	ADJ
american_scientific_journal-2507	73	17	values	value	NOUN
american_scientific_journal-2507	73	18	of	of	ADP
american_scientific_journal-2507	73	19	the	the	DET
american_scientific_journal-2507	73	20	coefficients	coefficient	NOUN
american_scientific_journal-2507	73	21	nc	nc	PROPN
american_scientific_journal-2507	73	22	decrease	decrease	VERB
american_scientific_journal-2507	73	23	rapidly	rapidly	ADV
american_scientific_journal-2507	73	24	with	with	ADP
american_scientific_journal-2507	73	25	increasing	increase	VERB
american_scientific_journal-2507	73	26	n	n	CCONJ
american_scientific_journal-2507	73	27	,	,	PUNCT
american_scientific_journal-2507	73	28	this	this	PRON
american_scientific_journal-2507	73	29	is	be	AUX
american_scientific_journal-2507	73	30	realised	realise	VERB
american_scientific_journal-2507	73	31	in	in	ADP
american_scientific_journal-2507	73	32	this	this	DET
american_scientific_journal-2507	73	33	work	work	NOUN
american_scientific_journal-2507	73	34	and	and	CCONJ
american_scientific_journal-2507	73	35	error	error	NOUN
american_scientific_journal-2507	73	36	estimate	estimate	NOUN
american_scientific_journal-2507	73	37	based	base	VERB
american_scientific_journal-2507	73	38	on	on	ADP
american_scientific_journal-2507	73	39	the	the	DET
american_scientific_journal-2507	73	40	sizes	size	NOUN
american_scientific_journal-2507	73	41	of	of	ADP
american_scientific_journal-2507	73	42	chebyshev	chebyshev	PROPN
american_scientific_journal-2507	73	43	coefficients	coefficient	NOUN
american_scientific_journal-2507	73	44	is	be	AUX
american_scientific_journal-2507	73	45	established	establish	VERB
american_scientific_journal-2507	73	46	.	.	PUNCT
american_scientific_journal-2507	74	1	it	it	PRON
american_scientific_journal-2507	74	2	is	be	AUX
american_scientific_journal-2507	74	3	vividly	vividly	ADV
american_scientific_journal-2507	74	4	observed	observe	VERB
american_scientific_journal-2507	74	5	in	in	ADP
american_scientific_journal-2507	74	6	the	the	DET
american_scientific_journal-2507	74	7	course	course	NOUN
american_scientific_journal-2507	74	8	of	of	ADP
american_scientific_journal-2507	74	9	this	this	DET
american_scientific_journal-2507	74	10	work	work	NOUN
american_scientific_journal-2507	74	11	that	that	PRON
american_scientific_journal-2507	74	12	the	the	DET
american_scientific_journal-2507	74	13	resulting	result	VERB
american_scientific_journal-2507	74	14	errors	error	NOUN
american_scientific_journal-2507	74	15	from	from	ADP
american_scientific_journal-2507	74	16	the	the	DET
american_scientific_journal-2507	74	17	solved	solve	VERB
american_scientific_journal-2507	74	18	problems	problem	NOUN
american_scientific_journal-2507	74	19	yield	yield	VERB
american_scientific_journal-2507	74	20	error	error	NOUN
american_scientific_journal-2507	74	21	estimate	estimate	NOUN
american_scientific_journal-2507	74	22	that	that	PRON
american_scientific_journal-2507	74	23	is	be	AUX
american_scientific_journal-2507	74	24	governed	govern	VERB
american_scientific_journal-2507	74	25	by	by	ADP
american_scientific_journal-2507	74	26	:	:	PUNCT
american_scientific_journal-2507	74	27	)	)	PUNCT
american_scientific_journal-2507	75	1	17(1	17(1	NOUN
american_scientific_journal-2507	75	2	0	0	NUM
american_scientific_journal-2507	76	1	−≤	−≤	NUM
american_scientific_journal-2507	76	2	ncce	ncce	NOUN
american_scientific_journal-2507	76	3	nn	nn	PROPN
american_scientific_journal-2507	76	4	6	6	NUM
american_scientific_journal-2507	76	5	.	.	PUNCT
american_scientific_journal-2507	76	6	numerical	numerical	PROPN
american_scientific_journal-2507	76	7	experiment	experiment	PROPN
american_scientific_journal-2507	76	8	the	the	DET
american_scientific_journal-2507	76	9	described	describe	VERB
american_scientific_journal-2507	76	10	method	method	NOUN
american_scientific_journal-2507	76	11	with	with	ADP
american_scientific_journal-2507	76	12	our	our	PRON
american_scientific_journal-2507	76	13	new	new	ADJ
american_scientific_journal-2507	76	14	approach	approach	NOUN
american_scientific_journal-2507	76	15	are	be	AUX
american_scientific_journal-2507	76	16	applied	apply	VERB
american_scientific_journal-2507	76	17	to	to	ADP
american_scientific_journal-2507	76	18	six	six	NUM
american_scientific_journal-2507	76	19	test	test	NOUN
american_scientific_journal-2507	76	20	problems	problem	NOUN
american_scientific_journal-2507	76	21	listed	list	VERB
american_scientific_journal-2507	76	22	below	below	ADV
american_scientific_journal-2507	76	23	.	.	PUNCT
american_scientific_journal-2507	77	1	this	this	PRON
american_scientific_journal-2507	77	2	is	be	AUX
american_scientific_journal-2507	77	3	basically	basically	ADV
american_scientific_journal-2507	77	4	to	to	PART
american_scientific_journal-2507	77	5	illustrate	illustrate	VERB
american_scientific_journal-2507	77	6	the	the	DET
american_scientific_journal-2507	77	7	efficiency	efficiency	NOUN
american_scientific_journal-2507	77	8	of	of	ADP
american_scientific_journal-2507	77	9	this	this	DET
american_scientific_journal-2507	77	10	technique	technique	NOUN
american_scientific_journal-2507	77	11	and	and	CCONJ
american_scientific_journal-2507	77	12	also	also	ADV
american_scientific_journal-2507	77	13	to	to	PART
american_scientific_journal-2507	77	14	compute	compute	VERB
american_scientific_journal-2507	77	15	exact	exact	ADJ
american_scientific_journal-2507	77	16	error	error	NOUN
american_scientific_journal-2507	77	17	which	which	PRON
american_scientific_journal-2507	77	18	will	will	AUX
american_scientific_journal-2507	77	19	serve	serve	VERB
american_scientific_journal-2507	77	20	to	to	PART
american_scientific_journal-2507	77	21	determine	determine	VERB
american_scientific_journal-2507	77	22	the	the	DET
american_scientific_journal-2507	77	23	validity	validity	NOUN
american_scientific_journal-2507	77	24	of	of	ADP
american_scientific_journal-2507	77	25	the	the	DET
american_scientific_journal-2507	77	26	formulation	formulation	NOUN
american_scientific_journal-2507	77	27	for	for	ADP
american_scientific_journal-2507	77	28	error	error	NOUN
american_scientific_journal-2507	77	29	estimates	estimate	NOUN
american_scientific_journal-2507	77	30	.	.	PUNCT
american_scientific_journal-2507	78	1	example	example	NOUN
american_scientific_journal-2507	79	1	1	1	NUM
american_scientific_journal-2507	79	2	.	.	PUNCT
american_scientific_journal-2507	79	3	∫	∫	PROPN
american_scientific_journal-2507	79	4	−=+−+	−=+−+	NOUN
american_scientific_journal-2507	79	5	x	x	PROPN
american_scientific_journal-2507	79	6	xx	xx	NUM
american_scientific_journal-2507	79	7	dttytxexex	dttytxexex	ADJ
american_scientific_journal-2507	79	8	0	0	NUM
american_scientific_journal-2507	79	9	)	)	PUNCT
american_scientific_journal-2507	79	10	(	(	PUNCT
american_scientific_journal-2507	79	11	)	)	PUNCT
american_scientific_journal-2507	79	12	(	(	PUNCT
american_scientific_journal-2507	79	13	22	22	NUM
american_scientific_journal-2507	79	14	the	the	DET
american_scientific_journal-2507	79	15	analytical	analytical	ADJ
american_scientific_journal-2507	79	16	solution	solution	NOUN
american_scientific_journal-2507	79	17	is	be	AUX
american_scientific_journal-2507	79	18	xexxy	xexxy	NOUN
american_scientific_journal-2507	80	1	=)	=)	INTJ
american_scientific_journal-2507	80	2	(	(	PUNCT
american_scientific_journal-2507	80	3	example	example	NOUN
american_scientific_journal-2507	80	4	2	2	NUM
american_scientific_journal-2507	80	5	.	.	X
american_scientific_journal-2507	80	6	american	american	PROPN
american_scientific_journal-2507	80	7	scientific	scientific	ADJ
american_scientific_journal-2507	80	8	research	research	PROPN
american_scientific_journal-2507	80	9	journal	journal	NOUN
american_scientific_journal-2507	80	10	for	for	ADP
american_scientific_journal-2507	80	11	engineering	engineering	NOUN
american_scientific_journal-2507	80	12	,	,	PUNCT
american_scientific_journal-2507	80	13	technology	technology	NOUN
american_scientific_journal-2507	80	14	,	,	PUNCT
american_scientific_journal-2507	80	15	and	and	CCONJ
american_scientific_journal-2507	80	16	sciences	science	NOUN
american_scientific_journal-2507	80	17	(	(	PUNCT
american_scientific_journal-2507	80	18	asrjets	asrjet	NOUN
american_scientific_journal-2507	80	19	)	)	PUNCT
american_scientific_journal-2507	80	20	(	(	PUNCT
american_scientific_journal-2507	80	21	2017	2017	NUM
american_scientific_journal-2507	80	22	)	)	PUNCT
american_scientific_journal-2507	80	23	volume	volume	NOUN
american_scientific_journal-2507	80	24	30	30	NUM
american_scientific_journal-2507	80	25	,	,	PUNCT
american_scientific_journal-2507	80	26	no	no	DET
american_scientific_journal-2507	80	27	1	1	NUM
american_scientific_journal-2507	80	28	,	,	PUNCT
american_scientific_journal-2507	80	29	pp	pp	ADV
american_scientific_journal-2507	80	30	47	47	NUM
american_scientific_journal-2507	80	31	-	-	SYM
american_scientific_journal-2507	80	32	56	56	NUM
american_scientific_journal-2507	80	33	53	53	NUM
american_scientific_journal-2507	80	34	∫=+++−−	∫=+++−−	NOUN
american_scientific_journal-2507	80	35	x	x	X
american_scientific_journal-2507	80	36	x	x	SYM
american_scientific_journal-2507	80	37	dttytxxxxx	dttytxxxxx	NOUN
american_scientific_journal-2507	80	38	0	0	NUM
american_scientific_journal-2507	80	39	22	22	NUM
american_scientific_journal-2507	80	40	)	)	PUNCT
american_scientific_journal-2507	80	41	(	(	PUNCT
american_scientific_journal-2507	80	42	2)1(ln)1(ln	2)1(ln)1(ln	PROPN
american_scientific_journal-2507	80	43	2	2	NUM
american_scientific_journal-2507	80	44	1	1	NUM
american_scientific_journal-2507	80	45	the	the	DET
american_scientific_journal-2507	80	46	analytical	analytical	ADJ
american_scientific_journal-2507	80	47	solution	solution	NOUN
american_scientific_journal-2507	80	48	is	be	AUX
american_scientific_journal-2507	80	49	)	)	PUNCT
american_scientific_journal-2507	80	50	1(ln	1(ln	NUM
american_scientific_journal-2507	80	51	)	)	PUNCT
american_scientific_journal-2507	80	52	(	(	PUNCT
american_scientific_journal-2507	80	53	xxy	xxy	PROPN
american_scientific_journal-2507	81	1	+	+	PROPN
american_scientific_journal-2507	81	2	=	=	AUX
american_scientific_journal-2507	81	3	example	example	NOUN
american_scientific_journal-2507	81	4	3	3	X
american_scientific_journal-2507	81	5	.	.	PUNCT
american_scientific_journal-2507	81	6	∫	∫	PROPN
american_scientific_journal-2507	81	7	−+−−=	−+−−=	PROPN
american_scientific_journal-2507	81	8	x	x	PUNCT
american_scientific_journal-2507	81	9	x	x	PUNCT
american_scientific_journal-2507	81	10	dttytxxexy	dttytxxexy	PROPN
american_scientific_journal-2507	81	11	0	0	NUM
american_scientific_journal-2507	81	12	)	)	PUNCT
american_scientific_journal-2507	81	13	(	(	PUNCT
american_scientific_journal-2507	81	14	)	)	PUNCT
american_scientific_journal-2507	81	15	(	(	PUNCT
american_scientific_journal-2507	81	16	22	22	NUM
american_scientific_journal-2507	81	17	)	)	PUNCT
american_scientific_journal-2507	81	18	(	(	PUNCT
american_scientific_journal-2507	81	19	the	the	DET
american_scientific_journal-2507	81	20	analytical	analytical	ADJ
american_scientific_journal-2507	81	21	solution	solution	NOUN
american_scientific_journal-2507	81	22	is	be	AUX
american_scientific_journal-2507	81	23	xexxy	xexxy	NOUN
american_scientific_journal-2507	82	1	=)	=)	INTJ
american_scientific_journal-2507	82	2	(	(	PUNCT
american_scientific_journal-2507	82	3	example	example	NOUN
american_scientific_journal-2507	82	4	4	4	NUM
american_scientific_journal-2507	82	5	.	.	NOUN
american_scientific_journal-2507	82	6	10	10	NUM
american_scientific_journal-2507	82	7	;	;	PUNCT
american_scientific_journal-2507	82	8	22	22	NUM
american_scientific_journal-2507	82	9	31	31	NUM
american_scientific_journal-2507	82	10	)	)	PUNCT
american_scientific_journal-2507	82	11	(	(	PUNCT
american_scientific_journal-2507	82	12	1	1	NUM
american_scientific_journal-2507	82	13	)	)	SYM
american_scientific_journal-2507	82	14	1	1	NUM
american_scientific_journal-2507	82	15	(	(	PUNCT
american_scientific_journal-2507	82	16	)	)	PUNCT
american_scientific_journal-2507	82	17	(	(	PUNCT
american_scientific_journal-2507	82	18	0	0	NUM
american_scientific_journal-2507	82	19	3	3	NUM
american_scientific_journal-2507	82	20	2	2	NUM
american_scientific_journal-2507	82	21	<	<	X
american_scientific_journal-2507	82	22	<	<	X
american_scientific_journal-2507	82	23	+	+	NOUN
american_scientific_journal-2507	82	24	−−=	−−=	NOUN
american_scientific_journal-2507	82	25	+	+	X
american_scientific_journal-2507	82	26	+	+	CCONJ
american_scientific_journal-2507	82	27	−	−	NOUN
american_scientific_journal-2507	82	28	∫	∫	PROPN
american_scientific_journal-2507	82	29	xxxxdtt	xxxxdtt	NOUN
american_scientific_journal-2507	82	30	t	t	NOUN
american_scientific_journal-2507	82	31	x	x	PUNCT
american_scientific_journal-2507	82	32	x	x	PUNCT
american_scientific_journal-2507	82	33	x	x	X
american_scientific_journal-2507	82	34	φφ	φφ	ADP
american_scientific_journal-2507	82	35	the	the	DET
american_scientific_journal-2507	82	36	analytical	analytical	ADJ
american_scientific_journal-2507	82	37	solution	solution	NOUN
american_scientific_journal-2507	82	38	is	be	AUX
american_scientific_journal-2507	82	39	21	21	NUM
american_scientific_journal-2507	82	40	)	)	PUNCT
american_scientific_journal-2507	82	41	(	(	PUNCT
american_scientific_journal-2507	82	42	xx	xx	NUM
american_scientific_journal-2507	82	43	−=φ	−=φ	PRON
american_scientific_journal-2507	82	44	example	example	NOUN
american_scientific_journal-2507	83	1	5	5	NUM
american_scientific_journal-2507	83	2	.	.	PUNCT
american_scientific_journal-2507	83	3	∫	∫	PROPN
american_scientific_journal-2507	83	4	−−=	−−=	INTJ
american_scientific_journal-2507	84	1	−	−	NOUN
american_scientific_journal-2507	84	2	x	x	PUNCT
american_scientific_journal-2507	84	3	x	x	PUNCT
american_scientific_journal-2507	84	4	dttytxexy	dttytxexy	NOUN
american_scientific_journal-2507	84	5	0	0	NUM
american_scientific_journal-2507	84	6	)	)	PUNCT
american_scientific_journal-2507	84	7	(	(	PUNCT
american_scientific_journal-2507	84	8	)	)	PUNCT
american_scientific_journal-2507	84	9	(	(	PUNCT
american_scientific_journal-2507	84	10	cos2	cos2	PROPN
american_scientific_journal-2507	84	11	)	)	PUNCT
american_scientific_journal-2507	84	12	(	(	PUNCT
american_scientific_journal-2507	84	13	the	the	DET
american_scientific_journal-2507	84	14	exact	exact	ADJ
american_scientific_journal-2507	84	15	solution	solution	NOUN
american_scientific_journal-2507	84	16	is	be	AUX
american_scientific_journal-2507	84	17	2)1	2)1	NUM
american_scientific_journal-2507	84	18	(	(	PUNCT
american_scientific_journal-2507	84	19	)	)	PUNCT
american_scientific_journal-2507	84	20	(	(	PUNCT
american_scientific_journal-2507	84	21	xexy	xexy	ADV
american_scientific_journal-2507	84	22	x	x	X
american_scientific_journal-2507	84	23	−=	−=	NOUN
american_scientific_journal-2507	84	24	−	−	DET
american_scientific_journal-2507	84	25	example	example	NOUN
american_scientific_journal-2507	84	26	6	6	NUM
american_scientific_journal-2507	84	27	.	.	PUNCT
american_scientific_journal-2507	84	28	∫	∫	PROPN
american_scientific_journal-2507	85	1	−−=	−−=	PROPN
american_scientific_journal-2507	85	2	x	x	PROPN
american_scientific_journal-2507	85	3	dttxtyxxy	dttxtyxxy	PROPN
american_scientific_journal-2507	85	4	0	0	NUM
american_scientific_journal-2507	85	5	)	)	PUNCT
american_scientific_journal-2507	85	6	(	(	PUNCT
american_scientific_journal-2507	85	7	sin)(34	sin)(34	PROPN
american_scientific_journal-2507	85	8	)	)	PUNCT
american_scientific_journal-2507	85	9	(	(	PUNCT
american_scientific_journal-2507	85	10	the	the	DET
american_scientific_journal-2507	85	11	exact	exact	ADJ
american_scientific_journal-2507	85	12	solution	solution	NOUN
american_scientific_journal-2507	85	13	is	be	AUX
american_scientific_journal-2507	85	14	xxxy	xxxy	PROPN
american_scientific_journal-2507	85	15	2sin	2sin	NUM
american_scientific_journal-2507	85	16	2	2	NUM
american_scientific_journal-2507	85	17	3	3	NUM
american_scientific_journal-2507	85	18	)	)	PUNCT
american_scientific_journal-2507	85	19	(	(	PUNCT
american_scientific_journal-2507	86	1	+	+	NOUN
american_scientific_journal-2507	86	2	=	=	SYM
american_scientific_journal-2507	86	3	7	7	NUM
american_scientific_journal-2507	86	4	.	.	NOUN
american_scientific_journal-2507	86	5	numerical	numerical	ADJ
american_scientific_journal-2507	86	6	solutions	solution	NOUN
american_scientific_journal-2507	86	7	to	to	ADP
american_scientific_journal-2507	86	8	the	the	DET
american_scientific_journal-2507	86	9	problems	problem	NOUN
american_scientific_journal-2507	86	10	in	in	ADP
american_scientific_journal-2507	86	11	this	this	DET
american_scientific_journal-2507	86	12	section	section	NOUN
american_scientific_journal-2507	86	13	,	,	PUNCT
american_scientific_journal-2507	86	14	maximum	maximum	ADJ
american_scientific_journal-2507	86	15	error	error	NOUN
american_scientific_journal-2507	86	16	with	with	ADP
american_scientific_journal-2507	86	17	the	the	DET
american_scientific_journal-2507	86	18	corresponding	corresponding	ADJ
american_scientific_journal-2507	86	19	error	error	NOUN
american_scientific_journal-2507	86	20	estimates	estimate	NOUN
american_scientific_journal-2507	86	21	obtained	obtain	VERB
american_scientific_journal-2507	86	22	by	by	ADP
american_scientific_journal-2507	86	23	the	the	DET
american_scientific_journal-2507	86	24	use	use	NOUN
american_scientific_journal-2507	86	25	of	of	ADP
american_scientific_journal-2507	86	26	equation	equation	NOUN
american_scientific_journal-2507	86	27	(	(	PUNCT
american_scientific_journal-2507	86	28	17	17	NUM
american_scientific_journal-2507	86	29	)	)	PUNCT
american_scientific_journal-2507	86	30	are	be	AUX
american_scientific_journal-2507	86	31	tabulated	tabulate	VERB
american_scientific_journal-2507	86	32	for	for	ADP
american_scientific_journal-2507	86	33	each	each	DET
american_scientific_journal-2507	86	34	solved	solve	VERB
american_scientific_journal-2507	86	35	problem	problem	NOUN
american_scientific_journal-2507	86	36	.	.	PUNCT
american_scientific_journal-2507	87	1	american	american	ADJ
american_scientific_journal-2507	87	2	scientific	scientific	ADJ
american_scientific_journal-2507	87	3	research	research	PROPN
american_scientific_journal-2507	87	4	journal	journal	NOUN
american_scientific_journal-2507	87	5	for	for	ADP
american_scientific_journal-2507	87	6	engineering	engineering	NOUN
american_scientific_journal-2507	87	7	,	,	PUNCT
american_scientific_journal-2507	87	8	technology	technology	NOUN
american_scientific_journal-2507	87	9	,	,	PUNCT
american_scientific_journal-2507	87	10	and	and	CCONJ
american_scientific_journal-2507	87	11	sciences	science	NOUN
american_scientific_journal-2507	87	12	(	(	PUNCT
american_scientific_journal-2507	87	13	asrjets	asrjet	NOUN
american_scientific_journal-2507	87	14	)	)	PUNCT
american_scientific_journal-2507	87	15	(	(	PUNCT
american_scientific_journal-2507	87	16	2017	2017	NUM
american_scientific_journal-2507	87	17	)	)	PUNCT
american_scientific_journal-2507	87	18	volume	volume	NOUN
american_scientific_journal-2507	87	19	30	30	NUM
american_scientific_journal-2507	87	20	,	,	PUNCT
american_scientific_journal-2507	87	21	no	no	DET
american_scientific_journal-2507	87	22	1	1	NUM
american_scientific_journal-2507	87	23	,	,	PUNCT
american_scientific_journal-2507	87	24	pp	pp	ADV
american_scientific_journal-2507	87	25	47	47	NUM
american_scientific_journal-2507	87	26	-	-	SYM
american_scientific_journal-2507	87	27	56	56	NUM
american_scientific_journal-2507	87	28	54	54	NUM
american_scientific_journal-2507	87	29	table	table	NOUN
american_scientific_journal-2507	87	30	7.1	7.1	NUM
american_scientific_journal-2507	87	31	:	:	PUNCT
american_scientific_journal-2507	87	32	table	table	NOUN
american_scientific_journal-2507	87	33	of	of	ADP
american_scientific_journal-2507	87	34	errors	error	NOUN
american_scientific_journal-2507	87	35	for	for	ADP
american_scientific_journal-2507	87	36	example	example	NOUN
american_scientific_journal-2507	87	37	1	1	NUM
american_scientific_journal-2507	87	38	n	n	CCONJ
american_scientific_journal-2507	87	39	maximum	maximum	ADJ
american_scientific_journal-2507	87	40	error	error	NOUN
american_scientific_journal-2507	87	41	error	error	NOUN
american_scientific_journal-2507	87	42	estimates	estimate	VERB
american_scientific_journal-2507	87	43	4	4	NUM
american_scientific_journal-2507	87	44	9.1817e-004	9.1817e-004	NUM
american_scientific_journal-2507	87	45	1.1880e-003	1.1880e-003	NUM
american_scientific_journal-2507	87	46	6	6	NUM
american_scientific_journal-2507	87	47	1.2914e-006	1.2914e-006	PROPN
american_scientific_journal-2507	87	48	2.4433e-006	2.4433e-006	PROPN
american_scientific_journal-2507	87	49	8	8	NUM
american_scientific_journal-2507	87	50	5.0494e-010	5.0494e-010	PROPN
american_scientific_journal-2507	87	51	1.6489e-009	1.6489e-009	NUM
american_scientific_journal-2507	87	52	10	10	NUM
american_scientific_journal-2507	87	53	4.0378e-014	4.0378e-014	NUM
american_scientific_journal-2507	87	54	2.5328e-012	2.5328e-012	PROPN
american_scientific_journal-2507	87	55	table	table	NOUN
american_scientific_journal-2507	87	56	7.2	7.2	NUM
american_scientific_journal-2507	87	57	:	:	PUNCT
american_scientific_journal-2507	87	58	table	table	NOUN
american_scientific_journal-2507	87	59	of	of	ADP
american_scientific_journal-2507	87	60	errors	error	NOUN
american_scientific_journal-2507	87	61	for	for	ADP
american_scientific_journal-2507	87	62	example	example	NOUN
american_scientific_journal-2507	87	63	2	2	NUM
american_scientific_journal-2507	87	64	n	n	PRON
american_scientific_journal-2507	87	65	maximum	maximum	ADJ
american_scientific_journal-2507	87	66	error	error	NOUN
american_scientific_journal-2507	87	67	error	error	NOUN
american_scientific_journal-2507	87	68	estimates	estimate	VERB
american_scientific_journal-2507	87	69	4	4	NUM
american_scientific_journal-2507	87	70	4.5330e-004	4.5330e-004	NUM
american_scientific_journal-2507	87	71	6.1294e-004	6.1294e-004	NUM
american_scientific_journal-2507	87	72	6	6	NUM
american_scientific_journal-2507	87	73	2.0426e-005	2.0426e-005	NUM
american_scientific_journal-2507	87	74	3.5974e-005	3.5974e-005	NUM
american_scientific_journal-2507	87	75	8	8	NUM
american_scientific_journal-2507	88	1	4.8223e-008	4.8223e-008	NOUN
american_scientific_journal-2507	88	2	3.4838e-007	3.4838e-007	NUM
american_scientific_journal-2507	88	3	10	10	NUM
american_scientific_journal-2507	88	4	3.9632e-010	3.9632e-010	PROPN
american_scientific_journal-2507	88	5	5.7352e-009	5.7352e-009	PROPN
american_scientific_journal-2507	88	6	table	table	NOUN
american_scientific_journal-2507	88	7	7.3	7.3	NUM
american_scientific_journal-2507	88	8	:	:	PUNCT
american_scientific_journal-2507	88	9	table	table	NOUN
american_scientific_journal-2507	88	10	of	of	ADP
american_scientific_journal-2507	88	11	errors	error	NOUN
american_scientific_journal-2507	88	12	for	for	ADP
american_scientific_journal-2507	88	13	example	example	NOUN
american_scientific_journal-2507	88	14	3	3	NUM
american_scientific_journal-2507	88	15	n	n	CCONJ
american_scientific_journal-2507	88	16	maximum	maximum	ADJ
american_scientific_journal-2507	88	17	error	error	NOUN
american_scientific_journal-2507	88	18	error	error	NOUN
american_scientific_journal-2507	88	19	estimates	estimate	VERB
american_scientific_journal-2507	88	20	4	4	NUM
american_scientific_journal-2507	88	21	3.0502e-004	3.0502e-004	NUM
american_scientific_journal-2507	88	22	1.2616e-003	1.2616e-003	PROPN
american_scientific_journal-2507	88	23	6	6	NUM
american_scientific_journal-2507	88	24	6.6005e-007	6.6005e-007	NUM
american_scientific_journal-2507	88	25	2.5637e-006	2.5637e-006	PROPN
american_scientific_journal-2507	88	26	8	8	NUM
american_scientific_journal-2507	88	27	5.7364e-010	5.7364e-010	PROPN
american_scientific_journal-2507	88	28	2.8154e-009	2.8154e-009	PROPN
american_scientific_journal-2507	88	29	10	10	NUM
american_scientific_journal-2507	88	30	5.0188e-013	5.0188e-013	PROPN
american_scientific_journal-2507	88	31	1.1451e-012	1.1451e-012	PROPN
american_scientific_journal-2507	88	32	table	table	NOUN
american_scientific_journal-2507	88	33	7.4	7.4	NUM
american_scientific_journal-2507	88	34	:	:	PUNCT
american_scientific_journal-2507	88	35	table	table	NOUN
american_scientific_journal-2507	88	36	of	of	ADP
american_scientific_journal-2507	88	37	errors	error	NOUN
american_scientific_journal-2507	88	38	for	for	ADP
american_scientific_journal-2507	88	39	example	example	NOUN
american_scientific_journal-2507	88	40	4	4	NUM
american_scientific_journal-2507	88	41	n	n	NUM
american_scientific_journal-2507	88	42	maximum	maximum	ADJ
american_scientific_journal-2507	88	43	error	error	NOUN
american_scientific_journal-2507	88	44	error	error	NOUN
american_scientific_journal-2507	88	45	estimates	estimate	VERB
american_scientific_journal-2507	88	46	4	4	NUM
american_scientific_journal-2507	88	47	0	0	NUM
american_scientific_journal-2507	88	48	0	0	NUM
american_scientific_journal-2507	88	49	6	6	NUM
american_scientific_journal-2507	88	50	0	0	NUM
american_scientific_journal-2507	88	51	0	0	NUM
american_scientific_journal-2507	88	52	8	8	NUM
american_scientific_journal-2507	88	53	0	0	NUM
american_scientific_journal-2507	88	54	0	0	NUM
american_scientific_journal-2507	88	55	10	10	NUM
american_scientific_journal-2507	88	56	0	0	NUM
american_scientific_journal-2507	88	57	0	0	NUM
american_scientific_journal-2507	88	58	table	table	NOUN
american_scientific_journal-2507	88	59	7.5	7.5	NUM
american_scientific_journal-2507	88	60	:	:	PUNCT
american_scientific_journal-2507	88	61	table	table	NOUN
american_scientific_journal-2507	88	62	of	of	ADP
american_scientific_journal-2507	88	63	errors	error	NOUN
american_scientific_journal-2507	88	64	for	for	ADP
american_scientific_journal-2507	88	65	example	example	NOUN
american_scientific_journal-2507	88	66	5	5	NUM
american_scientific_journal-2507	88	67	n	n	NUM
american_scientific_journal-2507	88	68	maximum	maximum	ADJ
american_scientific_journal-2507	88	69	error	error	NOUN
american_scientific_journal-2507	88	70	error	error	NOUN
american_scientific_journal-2507	88	71	estimates	estimate	VERB
american_scientific_journal-2507	88	72	4	4	NUM
american_scientific_journal-2507	88	73	5.4303e-004	5.4303e-004	PROPN
american_scientific_journal-2507	88	74	1.2406e-003	1.2406e-003	PROPN
american_scientific_journal-2507	88	75	6	6	NUM
american_scientific_journal-2507	88	76	4.2182e-006	4.2182e-006	NUM
american_scientific_journal-2507	88	77	8.1274e-005	8.1274e-005	NUM
american_scientific_journal-2507	88	78	8	8	NUM
american_scientific_journal-2507	89	1	2.8226e-009	2.8226e-009	NUM
american_scientific_journal-2507	89	2	3.2139e-008	3.2139e-008	NUM
american_scientific_journal-2507	89	3	10	10	NUM
american_scientific_journal-2507	89	4	3.6431e-011	3.6431e-011	NUM
american_scientific_journal-2507	89	5	4.1236e-010	4.1236e-010	PROPN
american_scientific_journal-2507	89	6	american	american	ADJ
american_scientific_journal-2507	89	7	scientific	scientific	ADJ
american_scientific_journal-2507	89	8	research	research	PROPN
american_scientific_journal-2507	89	9	journal	journal	NOUN
american_scientific_journal-2507	89	10	for	for	ADP
american_scientific_journal-2507	89	11	engineering	engineering	NOUN
american_scientific_journal-2507	89	12	,	,	PUNCT
american_scientific_journal-2507	89	13	technology	technology	NOUN
american_scientific_journal-2507	89	14	,	,	PUNCT
american_scientific_journal-2507	89	15	and	and	CCONJ
american_scientific_journal-2507	89	16	sciences	science	NOUN
american_scientific_journal-2507	89	17	(	(	PUNCT
american_scientific_journal-2507	89	18	asrjets	asrjet	NOUN
american_scientific_journal-2507	89	19	)	)	PUNCT
american_scientific_journal-2507	89	20	(	(	PUNCT
american_scientific_journal-2507	89	21	2017	2017	NUM
american_scientific_journal-2507	89	22	)	)	PUNCT
american_scientific_journal-2507	89	23	volume	volume	NOUN
american_scientific_journal-2507	89	24	30	30	NUM
american_scientific_journal-2507	89	25	,	,	PUNCT
american_scientific_journal-2507	89	26	no	no	DET
american_scientific_journal-2507	89	27	1	1	NUM
american_scientific_journal-2507	89	28	,	,	PUNCT
american_scientific_journal-2507	89	29	pp	pp	ADV
american_scientific_journal-2507	89	30	47	47	NUM
american_scientific_journal-2507	89	31	-	-	SYM
american_scientific_journal-2507	89	32	56	56	NUM
american_scientific_journal-2507	89	33	55	55	NUM
american_scientific_journal-2507	89	34	table	table	NOUN
american_scientific_journal-2507	89	35	7.6	7.6	NUM
american_scientific_journal-2507	89	36	:	:	PUNCT
american_scientific_journal-2507	89	37	table	table	NOUN
american_scientific_journal-2507	89	38	of	of	ADP
american_scientific_journal-2507	89	39	errors	error	NOUN
american_scientific_journal-2507	89	40	for	for	ADP
american_scientific_journal-2507	89	41	example	example	NOUN
american_scientific_journal-2507	89	42	6	6	NUM
american_scientific_journal-2507	89	43	n	n	NUM
american_scientific_journal-2507	89	44	maximum	maximum	ADJ
american_scientific_journal-2507	89	45	error	error	NOUN
american_scientific_journal-2507	89	46	error	error	NOUN
american_scientific_journal-2507	89	47	estimates	estimate	VERB
american_scientific_journal-2507	89	48	4	4	NUM
american_scientific_journal-2507	89	49	9.6371e-004	9.6371e-004	PROPN
american_scientific_journal-2507	89	50	4.2969e-002	4.2969e-002	NUM
american_scientific_journal-2507	89	51	6	6	NUM
american_scientific_journal-2507	89	52	5.2162e-006	5.2162e-006	PROPN
american_scientific_journal-2507	89	53	3.8471e-005	3.8471e-005	PROPN
american_scientific_journal-2507	89	54	8	8	NUM
american_scientific_journal-2507	89	55	1.3432e-008	1.3432e-008	PROPN
american_scientific_journal-2507	89	56	3.9476e-007	3.9476e-007	PROPN
american_scientific_journal-2507	89	57	10	10	NUM
american_scientific_journal-2507	89	58	1.4832e-010	1.4832e-010	NUM
american_scientific_journal-2507	89	59	6.4312e-009	6.4312e-009	PROPN
american_scientific_journal-2507	89	60	8	8	NUM
american_scientific_journal-2507	89	61	.	.	PUNCT
american_scientific_journal-2507	90	1	conclusion	conclusion	NOUN
american_scientific_journal-2507	90	2	the	the	DET
american_scientific_journal-2507	90	3	spectral	spectral	ADJ
american_scientific_journal-2507	90	4	method	method	NOUN
american_scientific_journal-2507	90	5	with	with	ADP
american_scientific_journal-2507	90	6	a	a	DET
american_scientific_journal-2507	90	7	new	new	ADJ
american_scientific_journal-2507	90	8	implementation	implementation	NOUN
american_scientific_journal-2507	90	9	technique	technique	NOUN
american_scientific_journal-2507	90	10	has	have	AUX
american_scientific_journal-2507	90	11	been	be	AUX
american_scientific_journal-2507	90	12	proposed	propose	VERB
american_scientific_journal-2507	90	13	and	and	CCONJ
american_scientific_journal-2507	90	14	applied	apply	VERB
american_scientific_journal-2507	90	15	to	to	ADP
american_scientific_journal-2507	90	16	integral	integral	ADJ
american_scientific_journal-2507	90	17	equations	equation	NOUN
american_scientific_journal-2507	90	18	.	.	PUNCT
american_scientific_journal-2507	91	1	formulation	formulation	NOUN
american_scientific_journal-2507	91	2	for	for	ADP
american_scientific_journal-2507	91	3	error	error	NOUN
american_scientific_journal-2507	91	4	estimates	estimate	NOUN
american_scientific_journal-2507	91	5	with	with	ADP
american_scientific_journal-2507	91	6	the	the	DET
american_scientific_journal-2507	91	7	use	use	NOUN
american_scientific_journal-2507	91	8	of	of	ADP
american_scientific_journal-2507	91	9	spectral	spectral	ADJ
american_scientific_journal-2507	91	10	coefficients	coefficient	NOUN
american_scientific_journal-2507	91	11	has	have	AUX
american_scientific_journal-2507	91	12	also	also	ADV
american_scientific_journal-2507	91	13	been	be	AUX
american_scientific_journal-2507	91	14	established	establish	VERB
american_scientific_journal-2507	91	15	.	.	PUNCT
american_scientific_journal-2507	92	1	a	a	DET
american_scientific_journal-2507	92	2	look	look	NOUN
american_scientific_journal-2507	92	3	at	at	ADP
american_scientific_journal-2507	92	4	table	table	NOUN
american_scientific_journal-2507	92	5	7.1	7.1	NUM
american_scientific_journal-2507	92	6	–	–	PUNCT
american_scientific_journal-2507	92	7	7.6	7.6	NUM
american_scientific_journal-2507	92	8	shows	show	VERB
american_scientific_journal-2507	92	9	that	that	SCONJ
american_scientific_journal-2507	92	10	the	the	DET
american_scientific_journal-2507	92	11	technique	technique	NOUN
american_scientific_journal-2507	92	12	performs	perform	VERB
american_scientific_journal-2507	92	13	effectively	effectively	ADV
american_scientific_journal-2507	92	14	well	well	ADV
american_scientific_journal-2507	92	15	in	in	ADP
american_scientific_journal-2507	92	16	the	the	DET
american_scientific_journal-2507	92	17	solution	solution	NOUN
american_scientific_journal-2507	92	18	of	of	ADP
american_scientific_journal-2507	92	19	these	these	DET
american_scientific_journal-2507	92	20	problems	problem	NOUN
american_scientific_journal-2507	92	21	as	as	SCONJ
american_scientific_journal-2507	92	22	the	the	DET
american_scientific_journal-2507	92	23	produced	produce	VERB
american_scientific_journal-2507	92	24	errors	error	NOUN
american_scientific_journal-2507	92	25	are	be	AUX
american_scientific_journal-2507	92	26	very	very	ADV
american_scientific_journal-2507	92	27	minimal	minimal	ADJ
american_scientific_journal-2507	92	28	.	.	PUNCT
american_scientific_journal-2507	93	1	in	in	ADP
american_scientific_journal-2507	93	2	addition	addition	NOUN
american_scientific_journal-2507	93	3	to	to	ADP
american_scientific_journal-2507	93	4	this	this	PRON
american_scientific_journal-2507	93	5	,	,	PUNCT
american_scientific_journal-2507	93	6	a	a	DET
american_scientific_journal-2507	93	7	consideration	consideration	NOUN
american_scientific_journal-2507	93	8	of	of	ADP
american_scientific_journal-2507	93	9	this	this	DET
american_scientific_journal-2507	93	10	technique	technique	NOUN
american_scientific_journal-2507	93	11	depicts	depict	VERB
american_scientific_journal-2507	93	12	the	the	DET
american_scientific_journal-2507	93	13	simplicity	simplicity	NOUN
american_scientific_journal-2507	93	14	in	in	ADP
american_scientific_journal-2507	93	15	its	its	PRON
american_scientific_journal-2507	93	16	application	application	NOUN
american_scientific_journal-2507	93	17	and	and	CCONJ
american_scientific_journal-2507	93	18	a	a	DET
american_scientific_journal-2507	93	19	very	very	ADV
american_scientific_journal-2507	93	20	low	low	ADJ
american_scientific_journal-2507	93	21	computational	computational	ADJ
american_scientific_journal-2507	93	22	cost	cost	NOUN
american_scientific_journal-2507	93	23	.	.	PUNCT
american_scientific_journal-2507	94	1	the	the	DET
american_scientific_journal-2507	94	2	above	above	ADJ
american_scientific_journal-2507	94	3	tables	table	NOUN
american_scientific_journal-2507	94	4	equally	equally	ADV
american_scientific_journal-2507	94	5	depicts	depict	VERB
american_scientific_journal-2507	94	6	that	that	SCONJ
american_scientific_journal-2507	94	7	the	the	DET
american_scientific_journal-2507	94	8	formulation	formulation	NOUN
american_scientific_journal-2507	94	9	for	for	ADP
american_scientific_journal-2507	94	10	error	error	NOUN
american_scientific_journal-2507	94	11	estimates	estimate	NOUN
american_scientific_journal-2507	94	12	is	be	AUX
american_scientific_journal-2507	94	13	very	very	ADV
american_scientific_journal-2507	94	14	efficient	efficient	ADJ
american_scientific_journal-2507	94	15	in	in	ADP
american_scientific_journal-2507	94	16	application	application	NOUN
american_scientific_journal-2507	94	17	as	as	SCONJ
american_scientific_journal-2507	94	18	it	it	PRON
american_scientific_journal-2507	94	19	provides	provide	VERB
american_scientific_journal-2507	94	20	a	a	DET
american_scientific_journal-2507	94	21	reliable	reliable	ADJ
american_scientific_journal-2507	94	22	bound	bind	VERB
american_scientific_journal-2507	94	23	for	for	ADP
american_scientific_journal-2507	94	24	the	the	DET
american_scientific_journal-2507	94	25	computed	compute	VERB
american_scientific_journal-2507	94	26	error	error	NOUN
american_scientific_journal-2507	94	27	.	.	PUNCT
american_scientific_journal-2507	95	1	also	also	ADV
american_scientific_journal-2507	95	2	,	,	PUNCT
american_scientific_journal-2507	95	3	the	the	DET
american_scientific_journal-2507	95	4	assertion	assertion	NOUN
american_scientific_journal-2507	95	5	of	of	ADP
american_scientific_journal-2507	95	6	[	[	X
american_scientific_journal-2507	95	7	9	9	NUM
american_scientific_journal-2507	95	8	]	]	PUNCT
american_scientific_journal-2507	95	9	about	about	SCONJ
american_scientific_journal-2507	95	10	the	the	DET
american_scientific_journal-2507	95	11	convergence	convergence	NOUN
american_scientific_journal-2507	95	12	of	of	ADP
american_scientific_journal-2507	95	13	spectral	spectral	ADJ
american_scientific_journal-2507	95	14	methods	method	NOUN
american_scientific_journal-2507	95	15	is	be	AUX
american_scientific_journal-2507	95	16	equally	equally	ADV
american_scientific_journal-2507	95	17	observed	observe	VERB
american_scientific_journal-2507	95	18	in	in	ADP
american_scientific_journal-2507	95	19	this	this	DET
american_scientific_journal-2507	95	20	technique	technique	NOUN
american_scientific_journal-2507	95	21	as	as	ADP
american_scientific_journal-2507	95	22	values	value	NOUN
american_scientific_journal-2507	95	23	for	for	ADP
american_scientific_journal-2507	95	24	kc	kc	PROPN
american_scientific_journal-2507	95	25	progressively	progressively	ADV
american_scientific_journal-2507	95	26	and	and	CCONJ
american_scientific_journal-2507	95	27	rapidly	rapidly	ADV
american_scientific_journal-2507	95	28	drops	drop	VERB
american_scientific_journal-2507	95	29	as	as	ADP
american_scientific_journal-2507	95	30	k	k	PROPN
american_scientific_journal-2507	95	31	increases	increase	NOUN
american_scientific_journal-2507	95	32	.	.	PUNCT
american_scientific_journal-2507	96	1	references	reference	NOUN
american_scientific_journal-2507	96	2	[	[	X
american_scientific_journal-2507	96	3	1	1	NUM
american_scientific_journal-2507	96	4	]	]	PUNCT
american_scientific_journal-2507	96	5	brunner	brunner	PROPN
american_scientific_journal-2507	96	6	hermann	hermann	PROPN
american_scientific_journal-2507	96	7	.	.	PROPN
american_scientific_journal-2507	96	8	collocation	collocation	NOUN
american_scientific_journal-2507	96	9	methods	method	NOUN
american_scientific_journal-2507	96	10	for	for	ADP
american_scientific_journal-2507	96	11	volterra	volterra	NOUN
american_scientific_journal-2507	96	12	integral	integral	ADJ
american_scientific_journal-2507	96	13	and	and	CCONJ
american_scientific_journal-2507	96	14	related	related	ADJ
american_scientific_journal-2507	96	15	functional	functional	ADJ
american_scientific_journal-2507	96	16	differential	differential	NOUN
american_scientific_journal-2507	96	17	equations	equation	NOUN
american_scientific_journal-2507	96	18	.	.	PUNCT
american_scientific_journal-2507	97	1	new	new	PROPN
american_scientific_journal-2507	97	2	york	york	PROPN
american_scientific_journal-2507	97	3	:	:	PUNCT
american_scientific_journal-2507	97	4	cambridge	cambridge	PROPN
american_scientific_journal-2507	97	5	university	university	PROPN
american_scientific_journal-2507	97	6	press	press	NOUN
american_scientific_journal-2507	97	7	,	,	PUNCT
american_scientific_journal-2507	97	8	2004	2004	NUM
american_scientific_journal-2507	97	9	,	,	PUNCT
american_scientific_journal-2507	97	10	pp	pp	ADJ
american_scientific_journal-2507	97	11	.	.	PUNCT
american_scientific_journal-2507	98	1	53	53	NUM
american_scientific_journal-2507	98	2	-	-	SYM
american_scientific_journal-2507	98	3	143	143	NUM
american_scientific_journal-2507	98	4	.	.	PUNCT
american_scientific_journal-2507	99	1	[	[	X
american_scientific_journal-2507	99	2	2	2	NUM
american_scientific_journal-2507	99	3	]	]	X
american_scientific_journal-2507	99	4	b.	b.	PROPN
american_scientific_journal-2507	99	5	s.	s.	PROPN
american_scientific_journal-2507	99	6	grewal	grewal	PROPN
american_scientific_journal-2507	99	7	.	.	PUNCT
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american_scientific_journal-2507	100	2	methods	method	NOUN
american_scientific_journal-2507	100	3	in	in	ADP
american_scientific_journal-2507	100	4	engineering	engineering	NOUN
american_scientific_journal-2507	100	5	and	and	CCONJ
american_scientific_journal-2507	100	6	science	science	NOUN
american_scientific_journal-2507	100	7	.	.	PUNCT
american_scientific_journal-2507	101	1	delhi	delhi	PROPN
american_scientific_journal-2507	101	2	:	:	PUNCT
american_scientific_journal-2507	101	3	khanna	khanna	PROPN
american_scientific_journal-2507	101	4	publishers	publisher	NOUN
american_scientific_journal-2507	101	5	,	,	PUNCT
american_scientific_journal-2507	101	6	2007	2007	NUM
american_scientific_journal-2507	101	7	.	.	PUNCT
american_scientific_journal-2507	102	1	[	[	X
american_scientific_journal-2507	102	2	3	3	X
american_scientific_journal-2507	102	3	]	]	X
american_scientific_journal-2507	102	4	j.	j.	PROPN
american_scientific_journal-2507	102	5	c.	c.	PROPN
american_scientific_journal-2507	102	6	mason	mason	PROPN
american_scientific_journal-2507	102	7	and	and	CCONJ
american_scientific_journal-2507	102	8	d.	d.	PROPN
american_scientific_journal-2507	102	9	c.	c.	PROPN
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american_scientific_journal-2507	102	11	.	.	PUNCT
american_scientific_journal-2507	103	1	chebyshev	chebyshev	PROPN
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american_scientific_journal-2507	103	3	.	.	PUNCT
american_scientific_journal-2507	104	1	boca	boca	PROPN
american_scientific_journal-2507	104	2	raton	raton	PROPN
american_scientific_journal-2507	104	3	,	,	PUNCT
american_scientific_journal-2507	104	4	london	london	PROPN
american_scientific_journal-2507	104	5	,	,	PUNCT
american_scientific_journal-2507	104	6	new	new	PROPN
american_scientific_journal-2507	104	7	york	york	PROPN
american_scientific_journal-2507	104	8	,	,	PUNCT
american_scientific_journal-2507	104	9	washington	washington	PROPN
american_scientific_journal-2507	104	10	dc	dc	PROPN
american_scientific_journal-2507	104	11	:	:	PUNCT
american_scientific_journal-2507	104	12	chapman	chapman	PROPN
american_scientific_journal-2507	104	13	&	&	CCONJ
american_scientific_journal-2507	104	14	hall	hall	PROPN
american_scientific_journal-2507	104	15	/	/	SYM
american_scientific_journal-2507	104	16	crc	crc	PROPN
american_scientific_journal-2507	104	17	,	,	PUNCT
american_scientific_journal-2507	104	18	2003	2003	NUM
american_scientific_journal-2507	104	19	.	.	PUNCT
american_scientific_journal-2507	105	1	[	[	X
american_scientific_journal-2507	105	2	4	4	NUM
american_scientific_journal-2507	105	3	]	]	PUNCT
american_scientific_journal-2507	105	4	a.	a.	PROPN
american_scientific_journal-2507	105	5	s.	s.	PROPN
american_scientific_journal-2507	105	6	olagunju	olagunju	PROPN
american_scientific_journal-2507	105	7	.	.	PUNCT
american_scientific_journal-2507	106	1	“	"	PUNCT
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american_scientific_journal-2507	106	3	series	series	PROPN
american_scientific_journal-2507	106	4	representation	representation	NOUN
american_scientific_journal-2507	106	5	for	for	ADP
american_scientific_journal-2507	106	6	product	product	NOUN
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american_scientific_journal-2507	106	8	chebyshev	chebyshev	NOUN
american_scientific_journal-2507	106	9	polynomials	polynomial	NOUN
american_scientific_journal-2507	106	10	and	and	CCONJ
american_scientific_journal-2507	106	11	some	some	DET
american_scientific_journal-2507	106	12	notable	notable	ADJ
american_scientific_journal-2507	106	13	functions	function	NOUN
american_scientific_journal-2507	106	14	”	"	PUNCT
american_scientific_journal-2507	106	15	.	.	PUNCT
american_scientific_journal-2507	107	1	iosr	iosr	PROPN
american_scientific_journal-2507	107	2	journal	journal	PROPN
american_scientific_journal-2507	107	3	of	of	ADP
american_scientific_journal-2507	107	4	mathematics	mathematics	PROPN
american_scientific_journal-2507	107	5	vol	vol	NOUN
american_scientific_journal-2507	107	6	.	.	PUNCT
american_scientific_journal-2507	107	7	2(2	2(2	NUM
american_scientific_journal-2507	107	8	)	)	PUNCT
american_scientific_journal-2507	107	9	,	,	PUNCT
american_scientific_journal-2507	107	10	pp	pp	ADP
american_scientific_journal-2507	107	11	9	9	NUM
american_scientific_journal-2507	107	12	-	-	SYM
american_scientific_journal-2507	107	13	13	13	NUM
american_scientific_journal-2507	107	14	,	,	PUNCT
american_scientific_journal-2507	107	15	2012	2012	NUM
american_scientific_journal-2507	107	16	.	.	PUNCT
american_scientific_journal-2507	108	1	[	[	X
american_scientific_journal-2507	108	2	5	5	NUM
american_scientific_journal-2507	108	3	]	]	PUNCT
american_scientific_journal-2507	108	4	a.	a.	NOUN
american_scientific_journal-2507	108	5	o.	o.	PROPN
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american_scientific_journal-2507	108	7	and	and	CCONJ
american_scientific_journal-2507	108	8	a.	a.	NOUN
american_scientific_journal-2507	108	9	s	s	PROPN
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american_scientific_journal-2507	108	11	.	.	PUNCT
american_scientific_journal-2507	109	1	“	"	PUNCT
american_scientific_journal-2507	109	2	chebyshev	chebyshev	NOUN
american_scientific_journal-2507	109	3	methods	method	NOUN
american_scientific_journal-2507	109	4	for	for	ADP
american_scientific_journal-2507	109	5	the	the	DET
american_scientific_journal-2507	109	6	numerical	numerical	ADJ
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american_scientific_journal-2507	109	8	of	of	ADP
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american_scientific_journal-2507	109	11	differential	differential	ADJ
american_scientific_journal-2507	109	12	equations	equation	NOUN
american_scientific_journal-2507	109	13	”	"	PUNCT
american_scientific_journal-2507	109	14	.	.	PUNCT
american_scientific_journal-2507	110	1	international	international	ADJ
american_scientific_journal-2507	110	2	journal	journal	PROPN
american_scientific_journal-2507	110	3	of	of	ADP
american_scientific_journal-2507	110	4	physical	physical	ADJ
american_scientific_journal-2507	110	5	science	science	NOUN
american_scientific_journal-2507	110	6	.	.	PUNCT
american_scientific_journal-2507	111	1	vol	vol	NOUN
american_scientific_journal-2507	111	2	.	.	PUNCT
american_scientific_journal-2507	112	1	7(13	7(13	NUM
american_scientific_journal-2507	112	2	)	)	PUNCT
american_scientific_journal-2507	112	3	,	,	PUNCT
american_scientific_journal-2507	112	4	pp	pp	ADP
american_scientific_journal-2507	112	5	2032	2032	NUM
american_scientific_journal-2507	112	6	-	-	SYM
american_scientific_journal-2507	112	7	2037	2037	NUM
american_scientific_journal-2507	112	8	,	,	PUNCT
american_scientific_journal-2507	112	9	2012	2012	NUM
american_scientific_journal-2507	112	10	.	.	PUNCT
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american_scientific_journal-2507	113	2	6	6	NUM
american_scientific_journal-2507	113	3	]	]	PUNCT
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american_scientific_journal-2507	113	7	.	.	PUNCT
american_scientific_journal-2507	114	1	“	"	PUNCT
american_scientific_journal-2507	114	2	a	a	DET
american_scientific_journal-2507	114	3	note	note	NOUN
american_scientific_journal-2507	114	4	on	on	ADP
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american_scientific_journal-2507	114	7	of	of	ADP
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american_scientific_journal-2507	114	10	”	"	PUNCT
american_scientific_journal-2507	114	11	.	.	PUNCT
american_scientific_journal-2507	115	1	maths	maths	PROPN
american_scientific_journal-2507	115	2	tab	tab	PROPN
american_scientific_journal-2507	115	3	.	.	PUNCT
american_scientific_journal-2507	115	4	wash	wash	PROPN
american_scientific_journal-2507	115	5	.	.	PUNCT
american_scientific_journal-2507	116	1	vol	vol	NOUN
american_scientific_journal-2507	116	2	.	.	PROPN
american_scientific_journal-2507	117	1	9	9	NUM
american_scientific_journal-2507	117	2	,	,	PUNCT
american_scientific_journal-2507	117	3	pp	pp	ADP
american_scientific_journal-2507	117	4	118120	118120	NUM
american_scientific_journal-2507	117	5	,	,	PUNCT
american_scientific_journal-2507	117	6	1955	1955	NUM
american_scientific_journal-2507	117	7	.	.	PUNCT
american_scientific_journal-2507	118	1	american	american	ADJ
american_scientific_journal-2507	118	2	scientific	scientific	ADJ
american_scientific_journal-2507	118	3	research	research	PROPN
american_scientific_journal-2507	118	4	journal	journal	NOUN
american_scientific_journal-2507	118	5	for	for	ADP
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american_scientific_journal-2507	118	7	,	,	PUNCT
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american_scientific_journal-2507	118	9	,	,	PUNCT
american_scientific_journal-2507	118	10	and	and	CCONJ
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american_scientific_journal-2507	118	12	(	(	PUNCT
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american_scientific_journal-2507	118	17	)	)	PUNCT
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american_scientific_journal-2507	118	19	30	30	NUM
american_scientific_journal-2507	118	20	,	,	PUNCT
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american_scientific_journal-2507	118	22	1	1	NUM
american_scientific_journal-2507	118	23	,	,	PUNCT
american_scientific_journal-2507	118	24	pp	pp	ADV
american_scientific_journal-2507	118	25	47	47	NUM
american_scientific_journal-2507	118	26	-	-	SYM
american_scientific_journal-2507	118	27	56	56	NUM
american_scientific_journal-2507	118	28	56	56	NUM
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american_scientific_journal-2507	118	30	7	7	NUM
american_scientific_journal-2507	118	31	]	]	PUNCT
american_scientific_journal-2507	118	32	e.	e.	PROPN
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american_scientific_journal-2507	118	35	.	.	PUNCT
american_scientific_journal-2507	119	1	introduction	introduction	NOUN
american_scientific_journal-2507	119	2	to	to	ADP
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american_scientific_journal-2507	119	4	theory	theory	NOUN
american_scientific_journal-2507	119	5	.	.	PUNCT
american_scientific_journal-2507	120	1	chelsea	chelsea	PROPN
american_scientific_journal-2507	120	2	,	,	PUNCT
american_scientific_journal-2507	120	3	new	new	PROPN
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american_scientific_journal-2507	120	5	:	:	PUNCT
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american_scientific_journal-2507	120	7	-	-	PUNCT
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american_scientific_journal-2507	120	9	,	,	PUNCT
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american_scientific_journal-2507	120	13	.	.	PUNCT
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american_scientific_journal-2507	121	3	]	]	PUNCT
american_scientific_journal-2507	121	4	t.	t.	PROPN
american_scientific_journal-2507	121	5	j.	j.	PROPN
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american_scientific_journal-2507	121	7	.	.	PUNCT
american_scientific_journal-2507	122	1	chebyshev	chebyshev	PROPN
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american_scientific_journal-2507	122	3	;	;	PUNCT
american_scientific_journal-2507	122	4	from	from	ADP
american_scientific_journal-2507	122	5	approximation	approximation	NOUN
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american_scientific_journal-2507	122	7	to	to	ADP
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american_scientific_journal-2507	122	9	and	and	CCONJ
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american_scientific_journal-2507	122	12	.	.	PUNCT
american_scientific_journal-2507	123	1	new	new	PROPN
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american_scientific_journal-2507	123	3	:	:	PUNCT
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american_scientific_journal-2507	124	3	,	,	PUNCT
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american_scientific_journal-2507	124	5	.	.	PUNCT
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american_scientific_journal-2507	125	2	9	9	NUM
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american_scientific_journal-2507	125	7	.	.	PUNCT
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american_scientific_journal-2507	126	10	.	.	PUNCT
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american_scientific_journal-2507	127	2	:	:	PUNCT
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american_scientific_journal-2507	127	6	,	,	PUNCT
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american_scientific_journal-2507	127	10	:	:	PUNCT
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american_scientific_journal-2507	127	12	-	-	PUNCT
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american_scientific_journal-2507	127	14	,	,	PUNCT
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american_scientific_journal-2507	128	7	.	.	PUNCT
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american_scientific_journal-2507	129	3	in	in	ADP
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american_scientific_journal-2507	129	5	.	.	PUNCT
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american_scientific_journal-2507	130	2	:	:	PUNCT
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american_scientific_journal-2507	130	4	,	,	PUNCT
american_scientific_journal-2507	130	5	2000	2000	NUM
american_scientific_journal-2507	130	6	.	.	PUNCT