id	sid	tid	token	lemma	pos
american_scientific_journal-3270	1	1	213	213	NUM
american_scientific_journal-3270	1	2	american	american	ADJ
american_scientific_journal-3270	1	3	scientific	scientific	ADJ
american_scientific_journal-3270	1	4	research	research	NOUN
american_scientific_journal-3270	1	5	journal	journal	NOUN
american_scientific_journal-3270	1	6	for	for	ADP
american_scientific_journal-3270	1	7	engineering	engineering	NOUN
american_scientific_journal-3270	1	8	,	,	PUNCT
american_scientific_journal-3270	1	9	technology	technology	NOUN
american_scientific_journal-3270	1	10	,	,	PUNCT
american_scientific_journal-3270	1	11	and	and	CCONJ
american_scientific_journal-3270	1	12	sciences	science	NOUN
american_scientific_journal-3270	1	13	(	(	PUNCT
american_scientific_journal-3270	1	14	asrjets	asrjet	NOUN
american_scientific_journal-3270	1	15	)	)	PUNCT
american_scientific_journal-3270	1	16	issn	issn	PROPN
american_scientific_journal-3270	1	17	(	(	PUNCT
american_scientific_journal-3270	1	18	print	print	NOUN
american_scientific_journal-3270	1	19	)	)	PUNCT
american_scientific_journal-3270	1	20	2313	2313	NUM
american_scientific_journal-3270	1	21	-	-	SYM
american_scientific_journal-3270	1	22	4410	4410	NUM
american_scientific_journal-3270	1	23	,	,	PUNCT
american_scientific_journal-3270	1	24	issn	issn	PROPN
american_scientific_journal-3270	1	25	(	(	PUNCT
american_scientific_journal-3270	1	26	online	online	ADJ
american_scientific_journal-3270	1	27	)	)	PUNCT
american_scientific_journal-3270	1	28	2313	2313	NUM
american_scientific_journal-3270	1	29	-	-	SYM
american_scientific_journal-3270	1	30	4402	4402	NUM
american_scientific_journal-3270	1	31	©	©	PROPN
american_scientific_journal-3270	1	32	global	global	ADJ
american_scientific_journal-3270	1	33	society	society	NOUN
american_scientific_journal-3270	1	34	of	of	ADP
american_scientific_journal-3270	1	35	scientific	scientific	ADJ
american_scientific_journal-3270	1	36	research	research	NOUN
american_scientific_journal-3270	1	37	and	and	CCONJ
american_scientific_journal-3270	1	38	researchers	researcher	NOUN
american_scientific_journal-3270	1	39	http://asrjetsjournal.org/	http://asrjetsjournal.org/	VERB
american_scientific_journal-3270	1	40	on	on	ADP
american_scientific_journal-3270	1	41	treating	treating	NOUN
american_scientific_journal-3270	1	42	of	of	ADP
american_scientific_journal-3270	1	43	surface	surface	NOUN
american_scientific_journal-3270	1	44	cracks	crack	NOUN
american_scientific_journal-3270	1	45	in	in	ADP
american_scientific_journal-3270	1	46	finite	finite	ADJ
american_scientific_journal-3270	1	47	layers	layer	NOUN
american_scientific_journal-3270	1	48	of	of	ADP
american_scientific_journal-3270	1	49	fractional	fractional	ADJ
american_scientific_journal-3270	1	50	materials	material	NOUN
american_scientific_journal-3270	1	51	hassan	hassan	PROPN
american_scientific_journal-3270	1	52	khayyat	khayyat	PROPN
american_scientific_journal-3270	1	53	*	*	PROPN
american_scientific_journal-3270	1	54	faculty	faculty	NOUN
american_scientific_journal-3270	1	55	of	of	ADP
american_scientific_journal-3270	1	56	engineering	engineering	NOUN
american_scientific_journal-3270	1	57	,	,	PUNCT
american_scientific_journal-3270	1	58	mechanical	mechanical	ADJ
american_scientific_journal-3270	1	59	engineering	engineering	PROPN
american_scientific_journal-3270	1	60	department	department	PROPN
american_scientific_journal-3270	1	61	shaqra	shaqra	PROPN
american_scientific_journal-3270	1	62	university	university	PROPN
american_scientific_journal-3270	1	63	,	,	PUNCT
american_scientific_journal-3270	1	64	saudi	saudi	PROPN
american_scientific_journal-3270	1	65	arabia	arabia	PROPN
american_scientific_journal-3270	1	66	e	e	PROPN
american_scientific_journal-3270	1	67	-	-	NOUN
american_scientific_journal-3270	1	68	mail	mail	NOUN
american_scientific_journal-3270	1	69	:	:	PUNCT
american_scientific_journal-3270	1	70	hkhayyat@su.edu.sa	hkhayyat@su.edu.sa	PROPN
american_scientific_journal-3270	1	71	abstract	abstract	NOUN
american_scientific_journal-3270	1	72	the	the	DET
american_scientific_journal-3270	1	73	plane	plane	NOUN
american_scientific_journal-3270	1	74	strain	strain	NOUN
american_scientific_journal-3270	1	75	problems	problem	NOUN
american_scientific_journal-3270	1	76	of	of	ADP
american_scientific_journal-3270	1	77	the	the	DET
american_scientific_journal-3270	1	78	bounded	bounded	ADJ
american_scientific_journal-3270	1	79	layer	layer	NOUN
american_scientific_journal-3270	1	80	medium	medium	NOUN
american_scientific_journal-3270	1	81	composed	compose	VERB
american_scientific_journal-3270	1	82	of	of	ADP
american_scientific_journal-3270	1	83	three	three	NUM
american_scientific_journal-3270	1	84	different	different	ADJ
american_scientific_journal-3270	1	85	materials	material	NOUN
american_scientific_journal-3270	1	86	contain	contain	VERB
american_scientific_journal-3270	1	87	a	a	DET
american_scientific_journal-3270	1	88	crack	crack	NOUN
american_scientific_journal-3270	1	89	on	on	ADP
american_scientific_journal-3270	1	90	one	one	NUM
american_scientific_journal-3270	1	91	of	of	ADP
american_scientific_journal-3270	1	92	the	the	DET
american_scientific_journal-3270	1	93	interface	interface	NOUN
american_scientific_journal-3270	1	94	are	be	AUX
american_scientific_journal-3270	1	95	considered	consider	VERB
american_scientific_journal-3270	1	96	.	.	PUNCT
american_scientific_journal-3270	2	1	using	use	VERB
american_scientific_journal-3270	2	2	fourier	fourier	ADJ
american_scientific_journal-3270	2	3	integral	integral	ADJ
american_scientific_journal-3270	2	4	transform	transform	NOUN
american_scientific_journal-3270	2	5	,	,	PUNCT
american_scientific_journal-3270	2	6	the	the	DET
american_scientific_journal-3270	2	7	boundary	boundary	ADJ
american_scientific_journal-3270	2	8	value	value	NOUN
american_scientific_journal-3270	2	9	problem	problem	NOUN
american_scientific_journal-3270	2	10	leads	lead	VERB
american_scientific_journal-3270	2	11	to	to	ADP
american_scientific_journal-3270	2	12	a	a	DET
american_scientific_journal-3270	2	13	mixed	mixed	ADJ
american_scientific_journal-3270	2	14	integral	integral	ADJ
american_scientific_journal-3270	2	15	equation	equation	NOUN
american_scientific_journal-3270	2	16	with	with	ADP
american_scientific_journal-3270	2	17	cauchy	cauchy	ADJ
american_scientific_journal-3270	2	18	kernel	kernel	NOUN
american_scientific_journal-3270	2	19	in	in	ADP
american_scientific_journal-3270	2	20	position	position	NOUN
american_scientific_journal-3270	2	21	and	and	CCONJ
american_scientific_journal-3270	2	22	continuous	continuous	ADJ
american_scientific_journal-3270	2	23	kernel	kernel	NOUN
american_scientific_journal-3270	2	24	in	in	ADP
american_scientific_journal-3270	2	25	time	time	NOUN
american_scientific_journal-3270	2	26	.	.	PUNCT
american_scientific_journal-3270	3	1	in	in	ADP
american_scientific_journal-3270	3	2	addition	addition	NOUN
american_scientific_journal-3270	3	3	,	,	PUNCT
american_scientific_journal-3270	3	4	using	use	VERB
american_scientific_journal-3270	3	5	a	a	DET
american_scientific_journal-3270	3	6	quadratic	quadratic	ADJ
american_scientific_journal-3270	3	7	numerical	numerical	ADJ
american_scientific_journal-3270	3	8	method	method	NOUN
american_scientific_journal-3270	3	9	we	we	PRON
american_scientific_journal-3270	3	10	have	have	VERB
american_scientific_journal-3270	3	11	a	a	DET
american_scientific_journal-3270	3	12	system	system	NOUN
american_scientific_journal-3270	3	13	of	of	ADP
american_scientific_journal-3270	3	14	fredholm	fredholm	ADJ
american_scientific_journal-3270	3	15	integral	integral	ADJ
american_scientific_journal-3270	3	16	equations	equation	NOUN
american_scientific_journal-3270	3	17	with	with	ADP
american_scientific_journal-3270	3	18	cauchy	cauchy	ADJ
american_scientific_journal-3270	3	19	kernel	kernel	NOUN
american_scientific_journal-3270	3	20	in	in	ADP
american_scientific_journal-3270	3	21	position	position	NOUN
american_scientific_journal-3270	3	22	.	.	PUNCT
american_scientific_journal-3270	4	1	then	then	ADV
american_scientific_journal-3270	4	2	,	,	PUNCT
american_scientific_journal-3270	4	3	the	the	DET
american_scientific_journal-3270	4	4	jacobi	jacobi	PROPN
american_scientific_journal-3270	4	5	polynomials	polynomial	NOUN
american_scientific_journal-3270	4	6	method	method	VERB
american_scientific_journal-3270	4	7	,	,	PUNCT
american_scientific_journal-3270	4	8	according	accord	VERB
american_scientific_journal-3270	4	9	to	to	ADP
american_scientific_journal-3270	4	10	the	the	DET
american_scientific_journal-3270	4	11	index	index	NOUN
american_scientific_journal-3270	4	12	of	of	ADP
american_scientific_journal-3270	4	13	integral	integral	ADJ
american_scientific_journal-3270	4	14	equation	equation	NOUN
american_scientific_journal-3270	4	15	,	,	PUNCT
american_scientific_journal-3270	4	16	is	be	AUX
american_scientific_journal-3270	4	17	used	use	VERB
american_scientific_journal-3270	4	18	to	to	PART
american_scientific_journal-3270	4	19	solve	solve	VERB
american_scientific_journal-3270	4	20	the	the	DET
american_scientific_journal-3270	4	21	system	system	NOUN
american_scientific_journal-3270	4	22	of	of	ADP
american_scientific_journal-3270	4	23	fredholm	fredholm	ADJ
american_scientific_journal-3270	4	24	integral	integral	ADJ
american_scientific_journal-3270	4	25	equations	equation	NOUN
american_scientific_journal-3270	4	26	.	.	PUNCT
american_scientific_journal-3270	5	1	moreover	moreover	ADV
american_scientific_journal-3270	5	2	,	,	PUNCT
american_scientific_journal-3270	5	3	the	the	DET
american_scientific_journal-3270	5	4	developing	develop	VERB
american_scientific_journal-3270	5	5	program	program	NOUN
american_scientific_journal-3270	5	6	is	be	AUX
american_scientific_journal-3270	5	7	used	use	VERB
american_scientific_journal-3270	5	8	to	to	ADP
american_scientific_journal-3270	5	9	computing	compute	VERB
american_scientific_journal-3270	5	10	the	the	DET
american_scientific_journal-3270	5	11	approximate	approximate	ADJ
american_scientific_journal-3270	5	12	solution	solution	NOUN
american_scientific_journal-3270	5	13	and	and	CCONJ
american_scientific_journal-3270	5	14	the	the	DET
american_scientific_journal-3270	5	15	estimated	estimate	VERB
american_scientific_journal-3270	5	16	error	error	NOUN
american_scientific_journal-3270	5	17	.	.	PUNCT
american_scientific_journal-3270	6	1	keywords	keyword	NOUN
american_scientific_journal-3270	6	2	:	:	PUNCT
american_scientific_journal-3270	6	3	fracture	fracture	NOUN
american_scientific_journal-3270	6	4	mechanics	mechanic	NOUN
american_scientific_journal-3270	6	5	;	;	PUNCT
american_scientific_journal-3270	6	6	fourier	fourier	ADJ
american_scientific_journal-3270	6	7	integral	integral	ADJ
american_scientific_journal-3270	6	8	transform	transform	NOUN
american_scientific_journal-3270	6	9	;	;	PUNCT
american_scientific_journal-3270	6	10	system	system	NOUN
american_scientific_journal-3270	6	11	of	of	ADP
american_scientific_journal-3270	6	12	fredholm	fredholm	ADJ
american_scientific_journal-3270	6	13	integral	integral	ADJ
american_scientific_journal-3270	6	14	equations	equation	NOUN
american_scientific_journal-3270	6	15	;	;	PUNCT
american_scientific_journal-3270	6	16	cauchy	cauchy	ADJ
american_scientific_journal-3270	6	17	kernel	kernel	PROPN
american_scientific_journal-3270	6	18	;	;	PUNCT
american_scientific_journal-3270	6	19	jacobi	jacobi	PROPN
american_scientific_journal-3270	6	20	polynomial	polynomial	PROPN
american_scientific_journal-3270	6	21	.	.	PUNCT
american_scientific_journal-3270	7	1	1	1	X
american_scientific_journal-3270	7	2	.	.	X
american_scientific_journal-3270	7	3	introduction	introduction	NOUN
american_scientific_journal-3270	7	4	gdoutos	gdoutos	NOUN
american_scientific_journal-3270	7	5	,	,	PUNCT
american_scientific_journal-3270	7	6	in	in	ADP
american_scientific_journal-3270	7	7	his	his	PRON
american_scientific_journal-3270	7	8	work	work	NOUN
american_scientific_journal-3270	7	9	[	[	X
american_scientific_journal-3270	7	10	1	1	NUM
american_scientific_journal-3270	7	11	]	]	PUNCT
american_scientific_journal-3270	7	12	,	,	PUNCT
american_scientific_journal-3270	7	13	stated	state	VERB
american_scientific_journal-3270	7	14	that	that	SCONJ
american_scientific_journal-3270	7	15	,	,	PUNCT
american_scientific_journal-3270	7	16	fracture	fracture	ADJ
american_scientific_journal-3270	7	17	mechanics	mechanic	NOUN
american_scientific_journal-3270	7	18	is	be	AUX
american_scientific_journal-3270	7	19	based	base	VERB
american_scientific_journal-3270	7	20	on	on	ADP
american_scientific_journal-3270	7	21	the	the	DET
american_scientific_journal-3270	7	22	assumption	assumption	NOUN
american_scientific_journal-3270	7	23	that	that	SCONJ
american_scientific_journal-3270	7	24	all	all	DET
american_scientific_journal-3270	7	25	engineering	engineering	NOUN
american_scientific_journal-3270	7	26	materials	material	NOUN
american_scientific_journal-3270	7	27	contain	contain	VERB
american_scientific_journal-3270	7	28	cracks	crack	NOUN
american_scientific_journal-3270	7	29	from	from	ADP
american_scientific_journal-3270	7	30	which	which	DET
american_scientific_journal-3270	7	31	failure	failure	NOUN
american_scientific_journal-3270	7	32	starts	start	VERB
american_scientific_journal-3270	7	33	.	.	PUNCT
american_scientific_journal-3270	8	1	it	it	PRON
american_scientific_journal-3270	8	2	is	be	AUX
american_scientific_journal-3270	8	3	known	know	VERB
american_scientific_journal-3270	8	4	that	that	SCONJ
american_scientific_journal-3270	8	5	,	,	PUNCT
american_scientific_journal-3270	8	6	cracks	crack	NOUN
american_scientific_journal-3270	8	7	lead	lead	VERB
american_scientific_journal-3270	8	8	to	to	ADP
american_scientific_journal-3270	8	9	high	high	ADJ
american_scientific_journal-3270	8	10	stresses	stress	NOUN
american_scientific_journal-3270	8	11	near	near	ADP
american_scientific_journal-3270	8	12	the	the	DET
american_scientific_journal-3270	8	13	crack	crack	NOUN
american_scientific_journal-3270	8	14	growth	growth	NOUN
american_scientific_journal-3270	8	15	takes	take	VERB
american_scientific_journal-3270	8	16	place	place	NOUN
american_scientific_journal-3270	8	17	.	.	PUNCT
american_scientific_journal-3270	9	1	in	in	ADP
american_scientific_journal-3270	9	2	[	[	X
american_scientific_journal-3270	9	3	2	2	NUM
american_scientific_journal-3270	9	4	]	]	PUNCT
american_scientific_journal-3270	9	5	,	,	PUNCT
american_scientific_journal-3270	9	6	erdogen	erdogen	PROPN
american_scientific_journal-3270	9	7	and	and	CCONJ
american_scientific_journal-3270	9	8	kaya	kaya	PROPN
american_scientific_journal-3270	9	9	studied	study	VERB
american_scientific_journal-3270	9	10	the	the	DET
american_scientific_journal-3270	9	11	elasticity	elasticity	NOUN
american_scientific_journal-3270	9	12	problem	problem	NOUN
american_scientific_journal-3270	9	13	for	for	ADP
american_scientific_journal-3270	9	14	an	an	DET
american_scientific_journal-3270	9	15	orthotropic	orthotropic	ADJ
american_scientific_journal-3270	9	16	strip	strip	NOUN
american_scientific_journal-3270	9	17	or	or	CCONJ
american_scientific_journal-3270	9	18	a	a	DET
american_scientific_journal-3270	9	19	beam	beam	NOUN
american_scientific_journal-3270	9	20	with	with	ADP
american_scientific_journal-3270	9	21	an	an	DET
american_scientific_journal-3270	9	22	internal	internal	ADJ
american_scientific_journal-3270	9	23	or	or	CCONJ
american_scientific_journal-3270	9	24	an	an	DET
american_scientific_journal-3270	9	25	edge	edge	NOUN
american_scientific_journal-3270	9	26	crack	crack	NOUN
american_scientific_journal-3270	9	27	under	under	ADP
american_scientific_journal-3270	9	28	general	general	ADJ
american_scientific_journal-3270	9	29	loading	loading	NOUN
american_scientific_journal-3270	9	30	condition	condition	NOUN
american_scientific_journal-3270	9	31	.	.	PUNCT
american_scientific_journal-3270	10	1	in	in	ADP
american_scientific_journal-3270	10	2	[	[	X
american_scientific_journal-3270	10	3	3	3	NUM
american_scientific_journal-3270	10	4	]	]	PUNCT
american_scientific_journal-3270	10	5	,	,	PUNCT
american_scientific_journal-3270	10	6	erdogan	erdogan	PROPN
american_scientific_journal-3270	10	7	discussed	discuss	VERB
american_scientific_journal-3270	10	8	some	some	DET
american_scientific_journal-3270	10	9	different	different	ADJ
american_scientific_journal-3270	10	10	method	method	NOUN
american_scientific_journal-3270	10	11	of	of	ADP
american_scientific_journal-3270	10	12	solution	solution	NOUN
american_scientific_journal-3270	10	13	of	of	ADP
american_scientific_journal-3270	10	14	elastic	elastic	ADJ
american_scientific_journal-3270	10	15	crack	crack	NOUN
american_scientific_journal-3270	10	16	problem	problem	NOUN
american_scientific_journal-3270	10	17	,	,	PUNCT
american_scientific_journal-3270	10	18	and	and	CCONJ
american_scientific_journal-3270	10	19	he	he	PRON
american_scientific_journal-3270	10	20	described	describe	VERB
american_scientific_journal-3270	10	21	number	number	NOUN
american_scientific_journal-3270	10	22	of	of	ADP
american_scientific_journal-3270	10	23	related	relate	VERB
american_scientific_journal-3270	10	24	special	special	ADJ
american_scientific_journal-3270	10	25	mechanics	mechanic	NOUN
american_scientific_journal-3270	10	26	problems	problem	NOUN
american_scientific_journal-3270	10	27	.	.	PUNCT
american_scientific_journal-3270	11	1	in	in	ADP
american_scientific_journal-3270	11	2	[	[	X
american_scientific_journal-3270	11	3	4	4	NUM
american_scientific_journal-3270	11	4	]	]	PUNCT
american_scientific_journal-3270	11	5	,	,	PUNCT
american_scientific_journal-3270	11	6	matbuly	matbuly	ADV
american_scientific_journal-3270	11	7	and	and	CCONJ
american_scientific_journal-3270	11	8	nassar	nassar	PROPN
american_scientific_journal-3270	11	9	analyzed	analyze	VERB
american_scientific_journal-3270	11	10	the	the	DET
american_scientific_journal-3270	11	11	electrostatic	electrostatic	ADJ
american_scientific_journal-3270	11	12	problem	problem	NOUN
american_scientific_journal-3270	11	13	of	of	ADP
american_scientific_journal-3270	11	14	an	an	DET
american_scientific_journal-3270	11	15	edge	edge	NOUN
american_scientific_journal-3270	11	16	cracked	crack	VERB
american_scientific_journal-3270	11	17	orthotropic	orthotropic	ADJ
american_scientific_journal-3270	11	18	strip	strip	NOUN
american_scientific_journal-3270	11	19	.	.	PUNCT
american_scientific_journal-3270	12	1	the	the	DET
american_scientific_journal-3270	12	2	crack	crack	NOUN
american_scientific_journal-3270	12	3	possesses	possess	VERB
american_scientific_journal-3270	12	4	a	a	DET
american_scientific_journal-3270	12	5	semi	semi	ADJ
american_scientific_journal-3270	12	6	-	-	ADJ
american_scientific_journal-3270	12	7	infinite	infinite	ADJ
american_scientific_journal-3270	12	8	length	length	NOUN
american_scientific_journal-3270	12	9	.	.	PUNCT
american_scientific_journal-3270	13	1	moreover	moreover	ADV
american_scientific_journal-3270	13	2	,	,	PUNCT
american_scientific_journal-3270	13	3	the	the	DET
american_scientific_journal-3270	13	4	crack	crack	NOUN
american_scientific_journal-3270	13	5	surfaces	surface	NOUN
american_scientific_journal-3270	13	6	are	be	AUX
american_scientific_journal-3270	13	7	subjected	subject	VERB
american_scientific_journal-3270	13	8	to	to	ADP
american_scientific_journal-3270	13	9	opening	opening	NOUN
american_scientific_journal-3270	13	10	mode	mode	NOUN
american_scientific_journal-3270	13	11	i	i	PRON
american_scientific_journal-3270	13	12	fracture	fracture	VERB
american_scientific_journal-3270	13	13	,	,	PUNCT
american_scientific_journal-3270	13	14	by	by	ADP
american_scientific_journal-3270	13	15	a	a	DET
american_scientific_journal-3270	13	16	concentrated	concentrated	ADJ
american_scientific_journal-3270	13	17	force	force	NOUN
american_scientific_journal-3270	13	18	action	action	NOUN
american_scientific_journal-3270	13	19	.	.	PUNCT
american_scientific_journal-3270	14	1	-----------------------------------------------------------------------	-----------------------------------------------------------------------	PUNCT
american_scientific_journal-3270	15	1	*	*	PUNCT
american_scientific_journal-3270	15	2	corresponding	correspond	VERB
american_scientific_journal-3270	15	3	author	author	NOUN
american_scientific_journal-3270	15	4	.	.	PUNCT
american_scientific_journal-3270	16	1	http://asrjetsjournal.org/	http://asrjetsjournal.org/	PROPN
american_scientific_journal-3270	16	2	american	american	PROPN
american_scientific_journal-3270	16	3	scientific	scientific	PROPN
american_scientific_journal-3270	16	4	research	research	NOUN
american_scientific_journal-3270	16	5	journal	journal	NOUN
american_scientific_journal-3270	16	6	for	for	ADP
american_scientific_journal-3270	16	7	engineering	engineering	NOUN
american_scientific_journal-3270	16	8	,	,	PUNCT
american_scientific_journal-3270	16	9	technology	technology	NOUN
american_scientific_journal-3270	16	10	,	,	PUNCT
american_scientific_journal-3270	16	11	and	and	CCONJ
american_scientific_journal-3270	16	12	sciences	science	NOUN
american_scientific_journal-3270	16	13	(	(	PUNCT
american_scientific_journal-3270	16	14	asrjets	asrjet	NOUN
american_scientific_journal-3270	16	15	)	)	PUNCT
american_scientific_journal-3270	16	16	(	(	PUNCT
american_scientific_journal-3270	16	17	2017	2017	NUM
american_scientific_journal-3270	16	18	)	)	PUNCT
american_scientific_journal-3270	16	19	volume	volume	NOUN
american_scientific_journal-3270	16	20	34	34	NUM
american_scientific_journal-3270	16	21	,	,	PUNCT
american_scientific_journal-3270	16	22	no	no	DET
american_scientific_journal-3270	16	23	1	1	NUM
american_scientific_journal-3270	16	24	,	,	PUNCT
american_scientific_journal-3270	16	25	pp	pp	ADV
american_scientific_journal-3270	16	26	213	213	NUM
american_scientific_journal-3270	16	27	-	-	SYM
american_scientific_journal-3270	16	28	230	230	NUM
american_scientific_journal-3270	16	29	214	214	NUM
american_scientific_journal-3270	16	30	more	more	ADJ
american_scientific_journal-3270	16	31	information	information	NOUN
american_scientific_journal-3270	16	32	for	for	ADP
american_scientific_journal-3270	16	33	treating	treat	VERB
american_scientific_journal-3270	16	34	the	the	DET
american_scientific_journal-3270	16	35	open	open	ADJ
american_scientific_journal-3270	16	36	cracks	crack	NOUN
american_scientific_journal-3270	16	37	of	of	ADP
american_scientific_journal-3270	16	38	the	the	DET
american_scientific_journal-3270	16	39	fracture	fracture	NOUN
american_scientific_journal-3270	16	40	mechanics	mechanic	NOUN
american_scientific_journal-3270	16	41	are	be	AUX
american_scientific_journal-3270	16	42	found	find	VERB
american_scientific_journal-3270	16	43	in	in	ADP
american_scientific_journal-3270	16	44	[	[	PUNCT
american_scientific_journal-3270	16	45	5	5	NUM
american_scientific_journal-3270	16	46	-	-	SYM
american_scientific_journal-3270	16	47	7	7	NUM
american_scientific_journal-3270	16	48	]	]	PUNCT
american_scientific_journal-3270	16	49	.	.	PUNCT
american_scientific_journal-3270	17	1	in	in	ADP
american_scientific_journal-3270	17	2	other	other	ADJ
american_scientific_journal-3270	17	3	side	side	NOUN
american_scientific_journal-3270	17	4	,	,	PUNCT
american_scientific_journal-3270	17	5	many	many	ADJ
american_scientific_journal-3270	17	6	authors	author	NOUN
american_scientific_journal-3270	17	7	have	have	VERB
american_scientific_journal-3270	17	8	interested	interested	ADJ
american_scientific_journal-3270	17	9	in	in	ADP
american_scientific_journal-3270	17	10	solving	solve	VERB
american_scientific_journal-3270	17	11	the	the	DET
american_scientific_journal-3270	17	12	fracture	fracture	NOUN
american_scientific_journal-3270	17	13	mechanics	mechanic	NOUN
american_scientific_journal-3270	17	14	with	with	ADP
american_scientific_journal-3270	17	15	curvilinear	curvilinear	ADJ
american_scientific_journal-3270	17	16	hole	hole	NOUN
american_scientific_journal-3270	17	17	.	.	PUNCT
american_scientific_journal-3270	18	1	some	some	DET
american_scientific_journal-3270	18	2	authors	author	NOUN
american_scientific_journal-3270	18	3	expressed	express	VERB
american_scientific_journal-3270	18	4	the	the	DET
american_scientific_journal-3270	18	5	solution	solution	NOUN
american_scientific_journal-3270	18	6	of	of	ADP
american_scientific_journal-3270	18	7	fractional	fractional	ADJ
american_scientific_journal-3270	18	8	mechanics	mechanic	NOUN
american_scientific_journal-3270	18	9	materials	material	NOUN
american_scientific_journal-3270	18	10	in	in	ADP
american_scientific_journal-3270	18	11	terms	term	NOUN
american_scientific_journal-3270	18	12	of	of	ADP
american_scientific_journal-3270	18	13	two	two	NUM
american_scientific_journal-3270	18	14	complex	complex	ADJ
american_scientific_journal-3270	18	15	potential	potential	ADJ
american_scientific_journal-3270	18	16	functions	function	NOUN
american_scientific_journal-3270	18	17	in	in	ADP
american_scientific_journal-3270	18	18	the	the	DET
american_scientific_journal-3270	18	19	form	form	NOUN
american_scientific_journal-3270	18	20	of	of	ADP
american_scientific_journal-3270	18	21	laurent	laurent	PROPN
american_scientific_journal-3270	18	22	’s	’s	PART
american_scientific_journal-3270	18	23	series	series	NOUN
american_scientific_journal-3270	18	24	,	,	PUNCT
american_scientific_journal-3270	18	25	see	see	VERB
american_scientific_journal-3270	18	26	[	[	X
american_scientific_journal-3270	18	27	8,9,10	8,9,10	NUM
american_scientific_journal-3270	18	28	]	]	X
american_scientific_journal-3270	18	29	.	.	PUNCT
american_scientific_journal-3270	19	1	other	other	ADJ
american_scientific_journal-3270	19	2	used	use	VERB
american_scientific_journal-3270	19	3	complex	complex	ADJ
american_scientific_journal-3270	19	4	variables	variable	NOUN
american_scientific_journal-3270	19	5	method	method	NOUN
american_scientific_journal-3270	19	6	(	(	PUNCT
american_scientific_journal-3270	19	7	cauchy	cauchy	NOUN
american_scientific_journal-3270	19	8	method	method	NOUN
american_scientific_journal-3270	19	9	)	)	PUNCT
american_scientific_journal-3270	19	10	to	to	PART
american_scientific_journal-3270	19	11	obtain	obtain	VERB
american_scientific_journal-3270	19	12	the	the	DET
american_scientific_journal-3270	19	13	solution	solution	NOUN
american_scientific_journal-3270	19	14	of	of	ADP
american_scientific_journal-3270	19	15	fracture	fracture	NOUN
american_scientific_journal-3270	19	16	mechanics	mechanic	NOUN
american_scientific_journal-3270	19	17	with	with	ADP
american_scientific_journal-3270	19	18	curvilinear	curvilinear	ADJ
american_scientific_journal-3270	19	19	hole	hole	NOUN
american_scientific_journal-3270	19	20	in	in	ADP
american_scientific_journal-3270	19	21	the	the	DET
american_scientific_journal-3270	19	22	form	form	NOUN
american_scientific_journal-3270	19	23	of	of	ADP
american_scientific_journal-3270	19	24	two	two	NUM
american_scientific_journal-3270	19	25	gaursat	gaursat	ADJ
american_scientific_journal-3270	19	26	functions	function	NOUN
american_scientific_journal-3270	19	27	,	,	PUNCT
american_scientific_journal-3270	19	28	see	see	VERB
american_scientific_journal-3270	19	29	[	[	X
american_scientific_journal-3270	19	30	11	11	NUM
american_scientific_journal-3270	19	31	-	-	SYM
american_scientific_journal-3270	19	32	16	16	NUM
american_scientific_journal-3270	19	33	]	]	PUNCT
american_scientific_journal-3270	19	34	.	.	PUNCT
american_scientific_journal-3270	20	1	in	in	ADP
american_scientific_journal-3270	20	2	most	most	ADJ
american_scientific_journal-3270	20	3	of	of	ADP
american_scientific_journal-3270	20	4	the	the	DET
american_scientific_journal-3270	20	5	problems	problem	NOUN
american_scientific_journal-3270	20	6	of	of	ADP
american_scientific_journal-3270	20	7	fractional	fractional	ADJ
american_scientific_journal-3270	20	8	mechanics	mechanic	NOUN
american_scientific_journal-3270	20	9	materials	material	NOUN
american_scientific_journal-3270	20	10	,	,	PUNCT
american_scientific_journal-3270	20	11	we	we	PRON
american_scientific_journal-3270	20	12	obtain	obtain	VERB
american_scientific_journal-3270	20	13	a	a	DET
american_scientific_journal-3270	20	14	singular	singular	ADJ
american_scientific_journal-3270	20	15	integral	integral	ADJ
american_scientific_journal-3270	20	16	equation	equation	NOUN
american_scientific_journal-3270	20	17	.	.	PUNCT
american_scientific_journal-3270	21	1	for	for	ADP
american_scientific_journal-3270	21	2	this	this	PRON
american_scientific_journal-3270	21	3	,	,	PUNCT
american_scientific_journal-3270	21	4	many	many	ADJ
american_scientific_journal-3270	21	5	different	different	ADJ
american_scientific_journal-3270	21	6	methods	method	NOUN
american_scientific_journal-3270	21	7	numerical	numerical	ADJ
american_scientific_journal-3270	21	8	and	and	CCONJ
american_scientific_journal-3270	21	9	analytic	analytic	ADJ
american_scientific_journal-3270	21	10	are	be	AUX
american_scientific_journal-3270	21	11	established	establish	VERB
american_scientific_journal-3270	21	12	for	for	ADP
american_scientific_journal-3270	21	13	solving	solve	VERB
american_scientific_journal-3270	21	14	the	the	DET
american_scientific_journal-3270	21	15	contact	contact	NOUN
american_scientific_journal-3270	21	16	problems	problem	NOUN
american_scientific_journal-3270	21	17	.	.	PUNCT
american_scientific_journal-3270	22	1	more	more	ADJ
american_scientific_journal-3270	22	2	information	information	NOUN
american_scientific_journal-3270	22	3	for	for	ADP
american_scientific_journal-3270	22	4	using	use	VERB
american_scientific_journal-3270	22	5	the	the	DET
american_scientific_journal-3270	22	6	different	different	ADJ
american_scientific_journal-3270	22	7	methods	method	NOUN
american_scientific_journal-3270	22	8	for	for	ADP
american_scientific_journal-3270	22	9	solving	solve	VERB
american_scientific_journal-3270	22	10	integral	integral	ADJ
american_scientific_journal-3270	22	11	equations	equation	NOUN
american_scientific_journal-3270	22	12	in	in	ADP
american_scientific_journal-3270	22	13	fractional	fractional	ADJ
american_scientific_journal-3270	22	14	mechanics	mechanic	NOUN
american_scientific_journal-3270	22	15	materials	material	NOUN
american_scientific_journal-3270	22	16	,	,	PUNCT
american_scientific_journal-3270	22	17	see	see	VERB
american_scientific_journal-3270	22	18	[	[	X
american_scientific_journal-3270	22	19	17	17	NUM
american_scientific_journal-3270	22	20	-	-	SYM
american_scientific_journal-3270	22	21	21	21	NUM
american_scientific_journal-3270	22	22	]	]	PUNCT
american_scientific_journal-3270	22	23	.	.	PUNCT
american_scientific_journal-3270	23	1	in	in	ADP
american_scientific_journal-3270	23	2	fractional	fractional	ADJ
american_scientific_journal-3270	23	3	mechanics	mechanic	NOUN
american_scientific_journal-3270	23	4	materials	material	NOUN
american_scientific_journal-3270	23	5	problem	problem	NOUN
american_scientific_journal-3270	23	6	,	,	PUNCT
american_scientific_journal-3270	23	7	the	the	DET
american_scientific_journal-3270	23	8	unknown	unknown	ADJ
american_scientific_journal-3270	23	9	function	function	NOUN
american_scientific_journal-3270	23	10	(	(	PUNCT
american_scientific_journal-3270	23	11	say	say	INTJ
american_scientific_journal-3270	23	12	(	(	PUNCT
american_scientific_journal-3270	23	13	,	,	PUNCT
american_scientific_journal-3270	23	14	)	)	PUNCT
american_scientific_journal-3270	23	15	x	x	SYM
american_scientific_journal-3270	23	16	tφ	tφ	PROPN
american_scientific_journal-3270	23	17	)	)	PUNCT
american_scientific_journal-3270	23	18	may	may	AUX
american_scientific_journal-3270	23	19	be	be	AUX
american_scientific_journal-3270	23	20	either	either	CCONJ
american_scientific_journal-3270	23	21	a	a	DET
american_scientific_journal-3270	23	22	potential	potential	NOUN
american_scientific_journal-3270	23	23	or	or	CCONJ
american_scientific_journal-3270	23	24	a	a	DET
american_scientific_journal-3270	23	25	flux	flux	NOUN
american_scientific_journal-3270	23	26	-	-	PUNCT
american_scientific_journal-3270	23	27	type	type	NOUN
american_scientific_journal-3270	23	28	quantity	quantity	NOUN
american_scientific_journal-3270	23	29	.	.	PUNCT
american_scientific_journal-3270	24	1	in	in	ADP
american_scientific_journal-3270	24	2	this	this	DET
american_scientific_journal-3270	24	3	paper	paper	NOUN
american_scientific_journal-3270	24	4	,	,	PUNCT
american_scientific_journal-3270	24	5	under	under	ADP
american_scientific_journal-3270	24	6	certain	certain	ADJ
american_scientific_journal-3270	24	7	conditions	condition	NOUN
american_scientific_journal-3270	24	8	,	,	PUNCT
american_scientific_journal-3270	24	9	the	the	DET
american_scientific_journal-3270	24	10	problem	problem	NOUN
american_scientific_journal-3270	24	11	of	of	ADP
american_scientific_journal-3270	24	12	fractional	fractional	ADJ
american_scientific_journal-3270	24	13	mechanics	mechanic	NOUN
american_scientific_journal-3270	24	14	materials	material	NOUN
american_scientific_journal-3270	24	15	of	of	ADP
american_scientific_journal-3270	24	16	three	three	NUM
american_scientific_journal-3270	24	17	layers	layer	NOUN
american_scientific_journal-3270	24	18	,	,	PUNCT
american_scientific_journal-3270	24	19	after	after	ADP
american_scientific_journal-3270	24	20	using	use	VERB
american_scientific_journal-3270	24	21	fourier	fourier	NOUN
american_scientific_journal-3270	24	22	transforms	transform	NOUN
american_scientific_journal-3270	24	23	,	,	PUNCT
american_scientific_journal-3270	24	24	leads	lead	VERB
american_scientific_journal-3270	24	25	to	to	ADP
american_scientific_journal-3270	24	26	mixed	mixed	ADJ
american_scientific_journal-3270	24	27	integral	integral	ADJ
american_scientific_journal-3270	24	28	equation	equation	NOUN
american_scientific_journal-3270	24	29	in	in	ADP
american_scientific_journal-3270	24	30	the	the	DET
american_scientific_journal-3270	24	31	space	space	NOUN
american_scientific_journal-3270	24	32	[	[	PUNCT
american_scientific_journal-3270	24	33	]	]	X
american_scientific_journal-3270	24	34	2	2	NUM
american_scientific_journal-3270	24	35	1,1	1,1	NUM
american_scientific_journal-3270	24	36	[	[	X
american_scientific_journal-3270	24	37	0	0	NUM
american_scientific_journal-3270	24	38	,	,	PUNCT
american_scientific_journal-3270	24	39	]	]	X
american_scientific_journal-3270	24	40	,	,	PUNCT
american_scientific_journal-3270	24	41	0	0	NUM
american_scientific_journal-3270	24	42	1.l	1.l	NUM
american_scientific_journal-3270	24	43	c	c	NOUN
american_scientific_journal-3270	24	44	t	t	NOUN
american_scientific_journal-3270	24	45	t	t	PROPN
american_scientific_journal-3270	24	46	t−	t−	PRON
american_scientific_journal-3270	24	47	×	×	NOUN
american_scientific_journal-3270	24	48	≤	≤	ADJ
american_scientific_journal-3270	24	49	≤	≤	NOUN
american_scientific_journal-3270	24	50	<	<	X
american_scientific_journal-3270	24	51	i.e	i.e	X
american_scientific_journal-3270	24	52	,	,	PUNCT
american_scientific_journal-3270	24	53	we	we	PRON
american_scientific_journal-3270	24	54	will	will	AUX
american_scientific_journal-3270	24	55	have	have	VERB
american_scientific_journal-3270	24	56	(	(	PUNCT
american_scientific_journal-3270	24	57	)	)	PUNCT
american_scientific_journal-3270	24	58	1	1	NUM
american_scientific_journal-3270	25	1	1	1	NUM
american_scientific_journal-3270	25	2	1	1	NUM
american_scientific_journal-3270	25	3	1	1	NUM
american_scientific_journal-3270	25	4	0	0	NUM
american_scientific_journal-3270	25	5	(	(	PUNCT
american_scientific_journal-3270	25	6	,	,	PUNCT
american_scientific_journal-3270	25	7	)	)	PUNCT
american_scientific_journal-3270	25	8	(	(	PUNCT
american_scientific_journal-3270	25	9	,	,	PUNCT
american_scientific_journal-3270	25	10	)	)	PUNCT
american_scientific_journal-3270	25	11	(	(	PUNCT
american_scientific_journal-3270	25	12	,	,	PUNCT
american_scientific_journal-3270	25	13	)	)	PUNCT
american_scientific_journal-3270	25	14	,	,	PUNCT
american_scientific_journal-3270	25	15	(	(	PUNCT
american_scientific_journal-3270	25	16	,	,	PUNCT
american_scientific_journal-3270	25	17	)	)	PUNCT
american_scientific_journal-3270	25	18	(	(	PUNCT
american_scientific_journal-3270	25	19	,	,	PUNCT
american_scientific_journal-3270	25	20	)	)	PUNCT
american_scientific_journal-3270	25	21	(	(	PUNCT
american_scientific_journal-3270	25	22	,	,	PUNCT
american_scientific_journal-3270	25	23	)	)	PUNCT
american_scientific_journal-3270	25	24	,	,	PUNCT
american_scientific_journal-3270	25	25	ty	ty	INTJ
american_scientific_journal-3270	25	26	tx	tx	PROPN
american_scientific_journal-3270	25	27	t	t	PROPN
american_scientific_journal-3270	25	28	dy	dy	X
american_scientific_journal-3270	25	29	k	k	PROPN
american_scientific_journal-3270	25	30	x	x	PUNCT
american_scientific_journal-3270	25	31	y	y	VERB
american_scientific_journal-3270	25	32	y	y	PROPN
american_scientific_journal-3270	25	33	t	t	PROPN
american_scientific_journal-3270	25	34	dy	dy	NOUN
american_scientific_journal-3270	25	35	t	t	PROPN
american_scientific_journal-3270	25	36	x	x	PUNCT
american_scientific_journal-3270	26	1	d	d	X
american_scientific_journal-3270	26	2	f	f	X
american_scientific_journal-3270	26	3	x	x	SYM
american_scientific_journal-3270	27	1	t	t	NOUN
american_scientific_journal-3270	27	2	y	y	PROPN
american_scientific_journal-3270	27	3	x	x	PROPN
american_scientific_journal-3270	27	4	λ	λ	X
american_scientific_journal-3270	27	5	φµφ	φµφ	PROPN
american_scientific_journal-3270	27	6	λ	λ	PROPN
american_scientific_journal-3270	27	7	φ	φ	NOUN
american_scientific_journal-3270	27	8	λ	λ	X
american_scientific_journal-3270	27	9	x	x	PROPN
american_scientific_journal-3270	27	10	t	t	PROPN
american_scientific_journal-3270	27	11	φ	φ	PROPN
american_scientific_journal-3270	27	12	t	t	PROPN
american_scientific_journal-3270	27	13	t	t	PROPN
american_scientific_journal-3270	27	14	π	π	X
american_scientific_journal-3270	27	15	−	−	PROPN
american_scientific_journal-3270	27	16	−	−	PROPN
american_scientific_journal-3270	27	17	−	−	PROPN
american_scientific_journal-3270	27	18	−	−	NOUN
american_scientific_journal-3270	27	19	−	−	PROPN
american_scientific_journal-3270	27	20	=	=	PUNCT
american_scientific_journal-3270	27	21	−∫	−∫	NOUN
american_scientific_journal-3270	27	22	∫	∫	PROPN
american_scientific_journal-3270	27	23	∫	∫	PROPN
american_scientific_journal-3270	27	24	(	(	PUNCT
american_scientific_journal-3270	27	25	1.1	1.1	NUM
american_scientific_journal-3270	27	26	)	)	PUNCT
american_scientific_journal-3270	27	27	the	the	DET
american_scientific_journal-3270	27	28	formula	formula	NOUN
american_scientific_journal-3270	27	29	(	(	PUNCT
american_scientific_journal-3270	27	30	1.1	1.1	NUM
american_scientific_journal-3270	27	31	)	)	PUNCT
american_scientific_journal-3270	27	32	is	be	AUX
american_scientific_journal-3270	27	33	called	call	VERB
american_scientific_journal-3270	27	34	mixed	mixed	ADJ
american_scientific_journal-3270	27	35	integral	integral	ADJ
american_scientific_journal-3270	27	36	equation	equation	NOUN
american_scientific_journal-3270	27	37	of	of	ADP
american_scientific_journal-3270	27	38	the	the	DET
american_scientific_journal-3270	27	39	second	second	ADJ
american_scientific_journal-3270	27	40	kind	kind	NOUN
american_scientific_journal-3270	27	41	in	in	ADP
american_scientific_journal-3270	27	42	position	position	NOUN
american_scientific_journal-3270	27	43	and	and	CCONJ
american_scientific_journal-3270	27	44	time	time	NOUN
american_scientific_journal-3270	27	45	,	,	PUNCT
american_scientific_journal-3270	27	46	µ	µ	X
american_scientific_journal-3270	27	47	is	be	AUX
american_scientific_journal-3270	27	48	a	a	DET
american_scientific_journal-3270	27	49	constant	constant	ADJ
american_scientific_journal-3270	27	50	defined	define	VERB
american_scientific_journal-3270	27	51	the	the	DET
american_scientific_journal-3270	27	52	kind	kind	NOUN
american_scientific_journal-3270	27	53	of	of	ADP
american_scientific_journal-3270	27	54	integral	integral	ADJ
american_scientific_journal-3270	27	55	equation	equation	NOUN
american_scientific_journal-3270	27	56	.	.	PUNCT
american_scientific_journal-3270	28	1	if	if	SCONJ
american_scientific_journal-3270	28	2	0,µ	0,µ	NOUN
american_scientific_journal-3270	28	3	=	=	VERB
american_scientific_journal-3270	29	1	we	we	PRON
american_scientific_journal-3270	29	2	have	have	VERB
american_scientific_journal-3270	29	3	the	the	DET
american_scientific_journal-3270	29	4	mixed	mixed	ADJ
american_scientific_journal-3270	29	5	integral	integral	ADJ
american_scientific_journal-3270	29	6	equation	equation	NOUN
american_scientific_journal-3270	29	7	of	of	ADP
american_scientific_journal-3270	29	8	the	the	DET
american_scientific_journal-3270	29	9	first	first	ADJ
american_scientific_journal-3270	29	10	kind	kind	NOUN
american_scientific_journal-3270	29	11	,	,	PUNCT
american_scientific_journal-3270	29	12	if	if	SCONJ
american_scientific_journal-3270	29	13	0,µ	0,µ	PROPN
american_scientific_journal-3270	29	14	≠	≠	PROPN
american_scientific_journal-3270	29	15	we	we	PRON
american_scientific_journal-3270	29	16	have	have	VERB
american_scientific_journal-3270	29	17	integral	integral	ADJ
american_scientific_journal-3270	29	18	equation	equation	NOUN
american_scientific_journal-3270	29	19	of	of	ADP
american_scientific_journal-3270	29	20	the	the	DET
american_scientific_journal-3270	29	21	second	second	ADJ
american_scientific_journal-3270	29	22	kind	kind	NOUN
american_scientific_journal-3270	29	23	.	.	PUNCT
american_scientific_journal-3270	30	1	λ	λ	NOUN
american_scientific_journal-3270	30	2	is	be	AUX
american_scientific_journal-3270	30	3	a	a	DET
american_scientific_journal-3270	30	4	constant	constant	ADJ
american_scientific_journal-3270	30	5	and	and	CCONJ
american_scientific_journal-3270	30	6	has	have	VERB
american_scientific_journal-3270	30	7	physical	physical	ADJ
american_scientific_journal-3270	30	8	meaning	meaning	NOUN
american_scientific_journal-3270	30	9	.	.	PUNCT
american_scientific_journal-3270	31	1	the	the	DET
american_scientific_journal-3270	31	2	given	give	VERB
american_scientific_journal-3270	31	3	function	function	NOUN
american_scientific_journal-3270	31	4	[	[	PUNCT
american_scientific_journal-3270	31	5	]	]	X
american_scientific_journal-3270	31	6	2	2	NUM
american_scientific_journal-3270	31	7	(	(	PUNCT
american_scientific_journal-3270	31	8	,	,	PUNCT
american_scientific_journal-3270	31	9	)	)	PUNCT
american_scientific_journal-3270	31	10	1,1	1,1	NUM
american_scientific_journal-3270	32	1	[	[	X
american_scientific_journal-3270	32	2	0	0	NUM
american_scientific_journal-3270	32	3	,	,	PUNCT
american_scientific_journal-3270	32	4	]	]	X
american_scientific_journal-3270	32	5	f	f	X
american_scientific_journal-3270	32	6	x	x	SYM
american_scientific_journal-3270	32	7	t	t	NOUN
american_scientific_journal-3270	32	8	l	l	NOUN
american_scientific_journal-3270	32	9	c	c	PROPN
american_scientific_journal-3270	32	10	t∈	t∈	VERB
american_scientific_journal-3270	32	11	−	−	PROPN
american_scientific_journal-3270	32	12	×	×	NOUN
american_scientific_journal-3270	32	13	,	,	PUNCT
american_scientific_journal-3270	32	14	and	and	CCONJ
american_scientific_journal-3270	32	15	is	be	AUX
american_scientific_journal-3270	32	16	called	call	VERB
american_scientific_journal-3270	32	17	the	the	DET
american_scientific_journal-3270	32	18	free	free	ADJ
american_scientific_journal-3270	32	19	term	term	NOUN
american_scientific_journal-3270	32	20	.	.	PUNCT
american_scientific_journal-3270	33	1	while	while	SCONJ
american_scientific_journal-3270	33	2	(	(	PUNCT
american_scientific_journal-3270	33	3	,	,	PUNCT
american_scientific_journal-3270	33	4	)	)	PUNCT
american_scientific_journal-3270	33	5	x	x	PROPN
american_scientific_journal-3270	33	6	tφ	tφ	PROPN
american_scientific_journal-3270	33	7	is	be	AUX
american_scientific_journal-3270	33	8	the	the	DET
american_scientific_journal-3270	33	9	unknown	unknown	ADJ
american_scientific_journal-3270	33	10	function	function	NOUN
american_scientific_journal-3270	33	11	.	.	PUNCT
american_scientific_journal-3270	34	1	the	the	DET
american_scientific_journal-3270	34	2	interval	interval	NOUN
american_scientific_journal-3270	34	3	[	[	X
american_scientific_journal-3270	34	4	-1	-1	X
american_scientific_journal-3270	34	5	,	,	PUNCT
american_scientific_journal-3270	34	6	1	1	NUM
american_scientific_journal-3270	34	7	]	]	PUNCT
american_scientific_journal-3270	34	8	is	be	AUX
american_scientific_journal-3270	34	9	the	the	DET
american_scientific_journal-3270	34	10	domain	domain	NOUN
american_scientific_journal-3270	34	11	of	of	ADP
american_scientific_journal-3270	34	12	integration	integration	NOUN
american_scientific_journal-3270	34	13	with	with	ADP
american_scientific_journal-3270	34	14	respect	respect	NOUN
american_scientific_journal-3270	34	15	to	to	ADP
american_scientific_journal-3270	34	16	position	position	NOUN
american_scientific_journal-3270	34	17	x	x	PRON
american_scientific_journal-3270	34	18	,	,	PUNCT
american_scientific_journal-3270	34	19	and	and	CCONJ
american_scientific_journal-3270	34	20	(	(	PUNCT
american_scientific_journal-3270	34	21	,	,	PUNCT
american_scientific_journal-3270	34	22	)	)	PUNCT
american_scientific_journal-3270	34	23	tx	tx	PROPN
american_scientific_journal-3270	34	24	t	t	PROPN
american_scientific_journal-3270	34	25	is	be	AUX
american_scientific_journal-3270	34	26	called	call	VERB
american_scientific_journal-3270	34	27	the	the	DET
american_scientific_journal-3270	34	28	kernel	kernel	NOUN
american_scientific_journal-3270	34	29	of	of	ADP
american_scientific_journal-3270	34	30	volterra	volterra	PROPN
american_scientific_journal-3270	34	31	integral	integral	ADJ
american_scientific_journal-3270	34	32	with	with	ADP
american_scientific_journal-3270	34	33	respect	respect	NOUN
american_scientific_journal-3270	34	34	to	to	ADP
american_scientific_journal-3270	34	35	the	the	DET
american_scientific_journal-3270	34	36	time	time	NOUN
american_scientific_journal-3270	34	37	[	[	X
american_scientific_journal-3270	34	38	0	0	NUM
american_scientific_journal-3270	34	39	,	,	PUNCT
american_scientific_journal-3270	34	40	]	]	X
american_scientific_journal-3270	34	41	;	;	PUNCT
american_scientific_journal-3270	34	42	1	1	NUM
american_scientific_journal-3270	34	43	t	t	NOUN
american_scientific_journal-3270	34	44	t	t	NOUN
american_scientific_journal-3270	34	45	t∈	t∈	X
american_scientific_journal-3270	34	46	<	<	X
american_scientific_journal-3270	34	47	.	.	PUNCT
american_scientific_journal-3270	35	1	then	then	ADV
american_scientific_journal-3270	35	2	using	use	VERB
american_scientific_journal-3270	35	3	chebyshev	chebyshev	PROPN
american_scientific_journal-3270	35	4	-	-	PUNCT
american_scientific_journal-3270	35	5	jacobi	jacobi	PROPN
american_scientific_journal-3270	35	6	polynomials	polynomial	NOUN
american_scientific_journal-3270	35	7	according	accord	VERB
american_scientific_journal-3270	35	8	to	to	ADP
american_scientific_journal-3270	35	9	the	the	DET
american_scientific_journal-3270	35	10	index	index	NOUN
american_scientific_journal-3270	35	11	of	of	ADP
american_scientific_journal-3270	35	12	the	the	DET
american_scientific_journal-3270	35	13	integral	integral	ADJ
american_scientific_journal-3270	35	14	equation	equation	NOUN
american_scientific_journal-3270	35	15	,	,	PUNCT
american_scientific_journal-3270	35	16	the	the	DET
american_scientific_journal-3270	35	17	solution	solution	NOUN
american_scientific_journal-3270	35	18	of	of	ADP
american_scientific_journal-3270	35	19	the	the	DET
american_scientific_journal-3270	35	20	integral	integral	ADJ
american_scientific_journal-3270	35	21	equation	equation	NOUN
american_scientific_journal-3270	35	22	is	be	AUX
american_scientific_journal-3270	35	23	discussed	discuss	VERB
american_scientific_journal-3270	35	24	at	at	ADP
american_scientific_journal-3270	35	25	the	the	DET
american_scientific_journal-3270	35	26	index	index	NOUN
american_scientific_journal-3270	35	27	points	point	NOUN
american_scientific_journal-3270	35	28	.	.	PUNCT
american_scientific_journal-3270	36	1	moreover	moreover	ADV
american_scientific_journal-3270	36	2	,	,	PUNCT
american_scientific_journal-3270	36	3	some	some	DET
american_scientific_journal-3270	36	4	numerical	numerical	ADJ
american_scientific_journal-3270	36	5	methods	method	NOUN
american_scientific_journal-3270	36	6	,	,	PUNCT
american_scientific_journal-3270	36	7	according	accord	VERB
american_scientific_journal-3270	36	8	to	to	ADP
american_scientific_journal-3270	36	9	the	the	DET
american_scientific_journal-3270	36	10	index	index	NOUN
american_scientific_journal-3270	36	11	and	and	CCONJ
american_scientific_journal-3270	36	12	the	the	DET
american_scientific_journal-3270	36	13	kind	kind	NOUN
american_scientific_journal-3270	36	14	of	of	ADP
american_scientific_journal-3270	36	15	chebyshevjacobi	chebyshevjacobi	NOUN
american_scientific_journal-3270	36	16	,	,	PUNCT
american_scientific_journal-3270	36	17	are	be	AUX
american_scientific_journal-3270	36	18	considered	consider	VERB
american_scientific_journal-3270	36	19	and	and	CCONJ
american_scientific_journal-3270	36	20	the	the	DET
american_scientific_journal-3270	36	21	error	error	NOUN
american_scientific_journal-3270	36	22	estimate	estimate	NOUN
american_scientific_journal-3270	36	23	,	,	PUNCT
american_scientific_journal-3270	36	24	in	in	ADP
american_scientific_journal-3270	36	25	each	each	DET
american_scientific_journal-3270	36	26	case	case	NOUN
american_scientific_journal-3270	36	27	,	,	PUNCT
american_scientific_journal-3270	36	28	is	be	AUX
american_scientific_journal-3270	36	29	computed	compute	VERB
american_scientific_journal-3270	36	30	.	.	PUNCT
american_scientific_journal-3270	37	1	2	2	X
american_scientific_journal-3270	37	2	.	.	X
american_scientific_journal-3270	37	3	formulation	formulation	NOUN
american_scientific_journal-3270	37	4	of	of	ADP
american_scientific_journal-3270	37	5	the	the	DET
american_scientific_journal-3270	37	6	generalized	generalized	ADJ
american_scientific_journal-3270	37	7	problem	problem	NOUN
american_scientific_journal-3270	37	8	consider	consider	VERB
american_scientific_journal-3270	37	9	a	a	DET
american_scientific_journal-3270	37	10	plane	plane	NOUN
american_scientific_journal-3270	37	11	strain	strain	NOUN
american_scientific_journal-3270	37	12	problem	problem	NOUN
american_scientific_journal-3270	37	13	of	of	ADP
american_scientific_journal-3270	37	14	the	the	DET
american_scientific_journal-3270	37	15	bounded	bounded	ADJ
american_scientific_journal-3270	37	16	layer	layer	NOUN
american_scientific_journal-3270	37	17	medium	medium	NOUN
american_scientific_journal-3270	37	18	composed	compose	VERB
american_scientific_journal-3270	37	19	of	of	ADP
american_scientific_journal-3270	37	20	three	three	NUM
american_scientific_journal-3270	37	21	different	different	ADJ
american_scientific_journal-3270	37	22	materials	material	NOUN
american_scientific_journal-3270	37	23	,	,	PUNCT
american_scientific_journal-3270	37	24	see	see	VERB
american_scientific_journal-3270	37	25	fig	fig	NOUN
american_scientific_journal-3270	37	26	.	.	PUNCT
american_scientific_journal-3270	38	1	(	(	PUNCT
american_scientific_journal-3270	38	2	1.1	1.1	NUM
american_scientific_journal-3270	38	3	)	)	PUNCT
american_scientific_journal-3270	38	4	.	.	PUNCT
american_scientific_journal-3270	39	1	let	let	VERB
american_scientific_journal-3270	39	2	the	the	DET
american_scientific_journal-3270	39	3	medium	medium	ADJ
american_scientific_journal-3270	39	4	material	material	NOUN
american_scientific_journal-3270	39	5	contains	contain	VERB
american_scientific_journal-3270	39	6	a	a	DET
american_scientific_journal-3270	39	7	crack	crack	NOUN
american_scientific_journal-3270	39	8	on	on	ADP
american_scientific_journal-3270	39	9	one	one	NUM
american_scientific_journal-3270	39	10	of	of	ADP
american_scientific_journal-3270	39	11	the	the	DET
american_scientific_journal-3270	39	12	interface	interface	NOUN
american_scientific_journal-3270	39	13	.	.	PUNCT
american_scientific_journal-3270	40	1	without	without	ADP
american_scientific_journal-3270	40	2	any	any	DET
american_scientific_journal-3270	40	3	loss	loss	NOUN
american_scientific_journal-3270	40	4	in	in	ADP
american_scientific_journal-3270	40	5	generality	generality	NOUN
american_scientific_journal-3270	40	6	,	,	PUNCT
american_scientific_journal-3270	40	7	the	the	DET
american_scientific_journal-3270	40	8	halflength	halflength	NOUN
american_scientific_journal-3270	40	9	of	of	ADP
american_scientific_journal-3270	40	10	the	the	DET
american_scientific_journal-3270	40	11	crack	crack	NOUN
american_scientific_journal-3270	40	12	is	be	AUX
american_scientific_journal-3270	40	13	assumed	assume	VERB
american_scientific_journal-3270	40	14	unity	unity	NOUN
american_scientific_journal-3270	40	15	.	.	PUNCT
american_scientific_journal-3270	41	1	consider	consider	VERB
american_scientific_journal-3270	41	2	with	with	ADP
american_scientific_journal-3270	41	3	the	the	DET
american_scientific_journal-3270	41	4	effect	effect	NOUN
american_scientific_journal-3270	41	5	of	of	ADP
american_scientific_journal-3270	41	6	the	the	DET
american_scientific_journal-3270	41	7	ratio	ratio	NOUN
american_scientific_journal-3270	41	8	of	of	ADP
american_scientific_journal-3270	41	9	the	the	DET
american_scientific_journal-3270	41	10	layer	layer	NOUN
american_scientific_journal-3270	41	11	thickness	thickness	NOUN
american_scientific_journal-3270	41	12	to	to	ADP
american_scientific_journal-3270	41	13	the	the	DET
american_scientific_journal-3270	41	14	crack	crack	NOUN
american_scientific_journal-3270	41	15	length	length	NOUN
american_scientific_journal-3270	41	16	on	on	ADP
american_scientific_journal-3270	41	17	the	the	DET
american_scientific_journal-3270	41	18	stress	stress	NOUN
american_scientific_journal-3270	41	19	intensity	intensity	NOUN
american_scientific_journal-3270	41	20	factors	factor	NOUN
american_scientific_journal-3270	41	21	and	and	CCONJ
american_scientific_journal-3270	41	22	the	the	DET
american_scientific_journal-3270	41	23	strain	strain	ADJ
american_scientific_journal-3270	41	24	energy	energy	NOUN
american_scientific_journal-3270	41	25	release	release	NOUN
american_scientific_journal-3270	41	26	rate	rate	NOUN
american_scientific_journal-3270	41	27	.	.	PUNCT
american_scientific_journal-3270	42	1	for	for	ADP
american_scientific_journal-3270	42	2	interesting	interesting	ADJ
american_scientific_journal-3270	42	3	the	the	DET
american_scientific_journal-3270	42	4	disturbed	disturbed	ADJ
american_scientific_journal-3270	42	5	stress	stress	NOUN
american_scientific_journal-3270	42	6	state	state	NOUN
american_scientific_journal-3270	42	7	,	,	PUNCT
american_scientific_journal-3270	42	8	whiles	while	NOUN
american_scientific_journal-3270	42	9	is	be	AUX
american_scientific_journal-3270	42	10	variable	variable	ADJ
american_scientific_journal-3270	42	11	also	also	ADV
american_scientific_journal-3270	42	12	with	with	ADP
american_scientific_journal-3270	42	13	time	time	NOUN
american_scientific_journal-3270	42	14	,	,	PUNCT
american_scientific_journal-3270	42	15	caused	cause	VERB
american_scientific_journal-3270	42	16	by	by	ADP
american_scientific_journal-3270	42	17	the	the	DET
american_scientific_journal-3270	42	18	crack	crack	NOUN
american_scientific_journal-3270	42	19	.	.	PUNCT
american_scientific_journal-3270	43	1	we	we	PRON
american_scientific_journal-3270	43	2	assume	assume	VERB
american_scientific_journal-3270	43	3	that	that	SCONJ
american_scientific_journal-3270	43	4	the	the	DET
american_scientific_journal-3270	43	5	overall	overall	ADJ
american_scientific_journal-3270	43	6	stress	stress	NOUN
american_scientific_journal-3270	43	7	distribution	distribution	NOUN
american_scientific_journal-3270	43	8	(	(	PUNCT
american_scientific_journal-3270	43	9	0	0	NUM
american_scientific_journal-3270	43	10	)	)	PUNCT
american_scientific_journal-3270	43	11	(	(	PUNCT
american_scientific_journal-3270	43	12	,	,	PUNCT
american_scientific_journal-3270	43	13	,	,	PUNCT
american_scientific_journal-3270	43	14	)	)	PUNCT
american_scientific_journal-3270	43	15	ij	ij	NOUN
american_scientific_journal-3270	43	16	x	x	SYM
american_scientific_journal-3270	43	17	y	y	NOUN
american_scientific_journal-3270	43	18	tσ	tσ	INTJ
american_scientific_journal-3270	43	19	,	,	PUNCT
american_scientific_journal-3270	43	20	in	in	ADP
american_scientific_journal-3270	43	21	the	the	DET
american_scientific_journal-3270	43	22	imperfection	imperfection	NOUN
american_scientific_journal-3270	43	23	free	free	ADJ
american_scientific_journal-3270	43	24	medium	medium	NOUN
american_scientific_journal-3270	43	25	,	,	PUNCT
american_scientific_journal-3270	43	26	is	be	AUX
american_scientific_journal-3270	43	27	known	know	VERB
american_scientific_journal-3270	43	28	.	.	PUNCT
american_scientific_journal-3270	44	1	the	the	DET
american_scientific_journal-3270	44	2	stress	stress	NOUN
american_scientific_journal-3270	44	3	state	state	NOUN
american_scientific_journal-3270	44	4	(	(	PUNCT
american_scientific_journal-3270	44	5	1	1	NUM
american_scientific_journal-3270	44	6	)	)	PUNCT
american_scientific_journal-3270	44	7	(	(	PUNCT
american_scientific_journal-3270	44	8	,	,	PUNCT
american_scientific_journal-3270	44	9	,	,	PUNCT
american_scientific_journal-3270	44	10	)	)	PUNCT
american_scientific_journal-3270	44	11	ij	ij	NOUN
american_scientific_journal-3270	44	12	x	x	SYM
american_scientific_journal-3270	44	13	y	y	NOUN
american_scientific_journal-3270	44	14	tσ	tσ	INTJ
american_scientific_journal-3270	44	15	,	,	PUNCT
american_scientific_journal-3270	44	16	in	in	ADP
american_scientific_journal-3270	44	17	the	the	DET
american_scientific_journal-3270	44	18	cracked	cracked	ADJ
american_scientific_journal-3270	44	19	medium	medium	NOUN
american_scientific_journal-3270	44	20	,	,	PUNCT
american_scientific_journal-3270	44	21	may	may	AUX
american_scientific_journal-3270	44	22	be	be	AUX
american_scientific_journal-3270	44	23	expressed	express	VERB
american_scientific_journal-3270	44	24	as	as	ADP
american_scientific_journal-3270	44	25	american	american	PROPN
american_scientific_journal-3270	44	26	scientific	scientific	PROPN
american_scientific_journal-3270	44	27	research	research	PROPN
american_scientific_journal-3270	44	28	journal	journal	NOUN
american_scientific_journal-3270	44	29	for	for	ADP
american_scientific_journal-3270	44	30	engineering	engineering	NOUN
american_scientific_journal-3270	44	31	,	,	PUNCT
american_scientific_journal-3270	44	32	technology	technology	NOUN
american_scientific_journal-3270	44	33	,	,	PUNCT
american_scientific_journal-3270	44	34	and	and	CCONJ
american_scientific_journal-3270	44	35	sciences	science	NOUN
american_scientific_journal-3270	44	36	(	(	PUNCT
american_scientific_journal-3270	44	37	asrjets	asrjet	NOUN
american_scientific_journal-3270	44	38	)	)	PUNCT
american_scientific_journal-3270	44	39	(	(	PUNCT
american_scientific_journal-3270	44	40	2017	2017	NUM
american_scientific_journal-3270	44	41	)	)	PUNCT
american_scientific_journal-3270	44	42	volume	volume	NOUN
american_scientific_journal-3270	44	43	34	34	NUM
american_scientific_journal-3270	44	44	,	,	PUNCT
american_scientific_journal-3270	44	45	no	no	DET
american_scientific_journal-3270	44	46	1	1	NUM
american_scientific_journal-3270	44	47	,	,	PUNCT
american_scientific_journal-3270	44	48	pp	pp	ADV
american_scientific_journal-3270	44	49	213	213	NUM
american_scientific_journal-3270	44	50	-	-	SYM
american_scientific_journal-3270	44	51	230	230	NUM
american_scientific_journal-3270	44	52	215	215	NUM
american_scientific_journal-3270	44	53	(	(	PUNCT
american_scientific_journal-3270	44	54	1	1	NUM
american_scientific_journal-3270	44	55	)	)	PUNCT
american_scientific_journal-3270	44	56	(	(	PUNCT
american_scientific_journal-3270	44	57	0	0	NUM
american_scientific_journal-3270	44	58	)	)	PUNCT
american_scientific_journal-3270	44	59	(	(	PUNCT
american_scientific_journal-3270	44	60	,	,	PUNCT
american_scientific_journal-3270	44	61	,	,	PUNCT
american_scientific_journal-3270	44	62	)	)	PUNCT
american_scientific_journal-3270	44	63	(	(	PUNCT
american_scientific_journal-3270	44	64	,	,	PUNCT
american_scientific_journal-3270	44	65	,	,	PUNCT
american_scientific_journal-3270	44	66	)	)	PUNCT
american_scientific_journal-3270	44	67	(	(	PUNCT
american_scientific_journal-3270	44	68	,	,	PUNCT
american_scientific_journal-3270	44	69	,	,	PUNCT
american_scientific_journal-3270	44	70	)	)	PUNCT
american_scientific_journal-3270	45	1	ij	ij	INTJ
american_scientific_journal-3270	45	2	ij	ij	INTJ
american_scientific_journal-3270	45	3	ijx	ijx	INTJ
american_scientific_journal-3270	45	4	y	y	PROPN
american_scientific_journal-3270	45	5	t	t	PROPN
american_scientific_journal-3270	45	6	x	x	PUNCT
american_scientific_journal-3270	45	7	y	y	NOUN
american_scientific_journal-3270	45	8	t	t	NOUN
american_scientific_journal-3270	45	9	x	x	X
american_scientific_journal-3270	45	10	y	y	NOUN
american_scientific_journal-3270	45	11	tσ	tσ	PROPN
american_scientific_journal-3270	45	12	σ	σ	NUM
american_scientific_journal-3270	45	13	σ=	σ=	PROPN
american_scientific_journal-3270	45	14	+	+	X
american_scientific_journal-3270	45	15	,	,	PUNCT
american_scientific_journal-3270	45	16	,	,	PUNCT
american_scientific_journal-3270	45	17	,	,	PUNCT
american_scientific_journal-3270	45	18	,	,	PUNCT
american_scientific_journal-3270	45	19	i	i	PRON
american_scientific_journal-3270	45	20	j	j	PROPN
american_scientific_journal-3270	45	21	x	x	VERB
american_scientific_journal-3270	45	22	y	y	PROPN
american_scientific_journal-3270	45	23	z=	z=	PROPN
american_scientific_journal-3270	45	24	(	(	PUNCT
american_scientific_journal-3270	45	25	2.1	2.1	NUM
american_scientific_journal-3270	45	26	)	)	PUNCT
american_scientific_journal-3270	45	27	where	where	SCONJ
american_scientific_journal-3270	45	28	,	,	PUNCT
american_scientific_journal-3270	45	29	ijσ	ijσ	NOUN
american_scientific_journal-3270	45	30	is	be	AUX
american_scientific_journal-3270	45	31	the	the	DET
american_scientific_journal-3270	45	32	disturbed	disturbed	ADJ
american_scientific_journal-3270	45	33	state	state	NOUN
american_scientific_journal-3270	45	34	,	,	PUNCT
american_scientific_journal-3270	45	35	which	which	PRON
american_scientific_journal-3270	45	36	may	may	AUX
american_scientific_journal-3270	45	37	be	be	AUX
american_scientific_journal-3270	45	38	obtained	obtain	VERB
american_scientific_journal-3270	45	39	by	by	ADP
american_scientific_journal-3270	45	40	using	use	VERB
american_scientific_journal-3270	45	41	the	the	DET
american_scientific_journal-3270	45	42	tractions	traction	NOUN
american_scientific_journal-3270	45	43	(	(	PUNCT
american_scientific_journal-3270	45	44	0	0	NUM
american_scientific_journal-3270	45	45	)	)	PUNCT
american_scientific_journal-3270	45	46	1	1	NUM
american_scientific_journal-3270	45	47	(	(	PUNCT
american_scientific_journal-3270	45	48	,	,	PUNCT
american_scientific_journal-3270	45	49	)	)	PUNCT
american_scientific_journal-3270	45	50	(	(	PUNCT
american_scientific_journal-3270	45	51	,	,	PUNCT
american_scientific_journal-3270	45	52	0	0	NUM
american_scientific_journal-3270	45	53	;	;	PUNCT
american_scientific_journal-3270	45	54	)	)	PUNCT
american_scientific_journal-3270	45	55	yyp	yyp	NOUN
american_scientific_journal-3270	46	1	x	x	SYM
american_scientific_journal-3270	46	2	t	t	NOUN
american_scientific_journal-3270	46	3	x	x	PUNCT
american_scientific_journal-3270	46	4	tσ=	tσ=	PROPN
american_scientific_journal-3270	46	5	−	−	NOUN
american_scientific_journal-3270	46	6	;	;	PUNCT
american_scientific_journal-3270	46	7	[	[	PUNCT
american_scientific_journal-3270	46	8	]	]	X
american_scientific_journal-3270	46	9	(	(	PUNCT
american_scientific_journal-3270	46	10	0	0	NUM
american_scientific_journal-3270	46	11	)	)	SYM
american_scientific_journal-3270	46	12	2	2	NUM
american_scientific_journal-3270	46	13	(	(	PUNCT
american_scientific_journal-3270	46	14	,	,	PUNCT
american_scientific_journal-3270	46	15	)	)	PUNCT
american_scientific_journal-3270	46	16	(	(	PUNCT
american_scientific_journal-3270	46	17	,	,	PUNCT
american_scientific_journal-3270	46	18	0	0	NUM
american_scientific_journal-3270	46	19	;	;	PUNCT
american_scientific_journal-3270	46	20	)	)	PUNCT
american_scientific_journal-3270	46	21	,	,	PUNCT
american_scientific_journal-3270	46	22	|	|	ADV
american_scientific_journal-3270	46	23	|	|	ADV
american_scientific_journal-3270	46	24	1	1	NUM
american_scientific_journal-3270	46	25	,	,	PUNCT
american_scientific_journal-3270	46	26	0	0	NUM
american_scientific_journal-3270	46	27	,	,	PUNCT
american_scientific_journal-3270	46	28	;	;	PUNCT
american_scientific_journal-3270	46	29	1.xyp	1.xyp	NUM
american_scientific_journal-3270	46	30	x	x	SYM
american_scientific_journal-3270	46	31	t	t	PROPN
american_scientific_journal-3270	46	32	x	x	SYM
american_scientific_journal-3270	46	33	t	t	PROPN
american_scientific_journal-3270	46	34	x	x	SYM
american_scientific_journal-3270	46	35	t	t	PROPN
american_scientific_journal-3270	46	36	t	t	PROPN
american_scientific_journal-3270	46	37	tσ=	tσ=	PROPN
american_scientific_journal-3270	46	38	−	−	PROPN
american_scientific_journal-3270	46	39	<	<	X
american_scientific_journal-3270	46	40	∈	∈	X
american_scientific_journal-3270	46	41	<	<	X
american_scientific_journal-3270	46	42	(	(	PUNCT
american_scientific_journal-3270	46	43	2.2	2.2	NUM
american_scientific_journal-3270	46	44	)	)	PUNCT
american_scientific_journal-3270	46	45	figure	figure	NOUN
american_scientific_journal-3270	46	46	1.1	1.1	NUM
american_scientific_journal-3270	46	47	which	which	PRON
american_scientific_journal-3270	46	48	are	be	AUX
american_scientific_journal-3270	46	49	the	the	DET
american_scientific_journal-3270	46	50	only	only	ADJ
american_scientific_journal-3270	46	51	external	external	ADJ
american_scientific_journal-3270	46	52	loads	load	NOUN
american_scientific_journal-3270	46	53	applied	apply	VERB
american_scientific_journal-3270	46	54	to	to	ADP
american_scientific_journal-3270	46	55	the	the	DET
american_scientific_journal-3270	46	56	medium	medium	NOUN
american_scientific_journal-3270	46	57	(	(	PUNCT
american_scientific_journal-3270	46	58	the	the	DET
american_scientific_journal-3270	46	59	symmetry	symmetry	NOUN
american_scientific_journal-3270	46	60	is	be	AUX
american_scientific_journal-3270	46	61	considered	consider	VERB
american_scientific_journal-3270	46	62	with	with	ADP
american_scientific_journal-3270	46	63	(	(	PUNCT
american_scientific_journal-3270	46	64	0).x	0).x	PUNCT
american_scientific_journal-3270	46	65	=	=	PUNCT
american_scientific_journal-3270	46	66	the	the	DET
american_scientific_journal-3270	46	67	general	general	ADJ
american_scientific_journal-3270	46	68	problem	problem	NOUN
american_scientific_journal-3270	46	69	can	can	AUX
american_scientific_journal-3270	46	70	always	always	ADV
american_scientific_journal-3270	46	71	be	be	AUX
american_scientific_journal-3270	46	72	expressed	express	VERB
american_scientific_journal-3270	46	73	as	as	ADP
american_scientific_journal-3270	46	74	the	the	DET
american_scientific_journal-3270	46	75	sum	sum	NOUN
american_scientific_journal-3270	46	76	of	of	ADP
american_scientific_journal-3270	46	77	a	a	DET
american_scientific_journal-3270	46	78	symmetric	symmetric	ADJ
american_scientific_journal-3270	46	79	component	component	NOUN
american_scientific_journal-3270	46	80	and	and	CCONJ
american_scientific_journal-3270	46	81	an	an	DET
american_scientific_journal-3270	46	82	anti	anti	ADJ
american_scientific_journal-3270	46	83	-	-	ADJ
american_scientific_journal-3270	46	84	symmetric	symmetric	ADJ
american_scientific_journal-3270	46	85	component	component	NOUN
american_scientific_journal-3270	46	86	.	.	PUNCT
american_scientific_journal-3270	47	1	the	the	DET
american_scientific_journal-3270	47	2	tractions	traction	NOUN
american_scientific_journal-3270	47	3	(	(	PUNCT
american_scientific_journal-3270	47	4	,	,	PUNCT
american_scientific_journal-3270	47	5	)	)	PUNCT
american_scientific_journal-3270	47	6	,	,	PUNCT
american_scientific_journal-3270	47	7	(	(	PUNCT
american_scientific_journal-3270	47	8	1,2)ip	1,2)ip	NUM
american_scientific_journal-3270	47	9	x	x	SYM
american_scientific_journal-3270	47	10	t	t	NOUN
american_scientific_journal-3270	47	11	i	i	PRON
american_scientific_journal-3270	47	12	=	=	PUNCT
american_scientific_journal-3270	47	13	,	,	PUNCT
american_scientific_journal-3270	47	14	have	have	VERB
american_scientific_journal-3270	47	15	the	the	DET
american_scientific_journal-3270	47	16	following	follow	VERB
american_scientific_journal-3270	47	17	properties	property	NOUN
american_scientific_journal-3270	47	18	[	[	PUNCT
american_scientific_journal-3270	47	19	]	]	SYM
american_scientific_journal-3270	47	20	1	1	NUM
american_scientific_journal-3270	47	21	1	1	NUM
american_scientific_journal-3270	47	22	2	2	NUM
american_scientific_journal-3270	47	23	2	2	NUM
american_scientific_journal-3270	47	24	(	(	PUNCT
american_scientific_journal-3270	47	25	,	,	PUNCT
american_scientific_journal-3270	47	26	)	)	PUNCT
american_scientific_journal-3270	47	27	(	(	PUNCT
american_scientific_journal-3270	47	28	,	,	PUNCT
american_scientific_journal-3270	47	29	)	)	PUNCT
american_scientific_journal-3270	47	30	,	,	PUNCT
american_scientific_journal-3270	47	31	(	(	PUNCT
american_scientific_journal-3270	47	32	,	,	PUNCT
american_scientific_journal-3270	47	33	)	)	PUNCT
american_scientific_journal-3270	47	34	(	(	PUNCT
american_scientific_journal-3270	47	35	,	,	PUNCT
american_scientific_journal-3270	47	36	)	)	PUNCT
american_scientific_journal-3270	47	37	,	,	PUNCT
american_scientific_journal-3270	47	38	|	|	ADV
american_scientific_journal-3270	47	39	|	|	ADV
american_scientific_journal-3270	47	40	1	1	NUM
american_scientific_journal-3270	47	41	,	,	PUNCT
american_scientific_journal-3270	47	42	0	0	NUM
american_scientific_journal-3270	47	43	,	,	PUNCT
american_scientific_journal-3270	47	44	;	;	PUNCT
american_scientific_journal-3270	47	45	1.p	1.p	NUM
american_scientific_journal-3270	47	46	x	x	SYM
american_scientific_journal-3270	47	47	t	t	NOUN
american_scientific_journal-3270	47	48	p	p	X
american_scientific_journal-3270	47	49	x	x	X
american_scientific_journal-3270	47	50	t	t	NOUN
american_scientific_journal-3270	47	51	p	p	X
american_scientific_journal-3270	47	52	x	x	X
american_scientific_journal-3270	47	53	t	t	NOUN
american_scientific_journal-3270	47	54	p	p	X
american_scientific_journal-3270	47	55	x	x	X
american_scientific_journal-3270	47	56	t	t	X
american_scientific_journal-3270	47	57	x	x	SYM
american_scientific_journal-3270	47	58	t	t	PROPN
american_scientific_journal-3270	47	59	t	t	PROPN
american_scientific_journal-3270	47	60	t=	t=	NOUN
american_scientific_journal-3270	47	61	−	−	PROPN
american_scientific_journal-3270	47	62	=	=	PUNCT
american_scientific_journal-3270	48	1	−	−	PROPN
american_scientific_journal-3270	48	2	−	−	NOUN
american_scientific_journal-3270	48	3	<	<	X
american_scientific_journal-3270	48	4	∈	∈	PROPN
american_scientific_journal-3270	48	5	<	<	X
american_scientific_journal-3270	48	6	.	.	PUNCT
american_scientific_journal-3270	49	1	(	(	PUNCT
american_scientific_journal-3270	49	2	2.3	2.3	NUM
american_scientific_journal-3270	49	3	)	)	PUNCT
american_scientific_journal-3270	49	4	the	the	DET
american_scientific_journal-3270	49	5	solution	solution	NOUN
american_scientific_journal-3270	49	6	of	of	ADP
american_scientific_journal-3270	49	7	the	the	DET
american_scientific_journal-3270	49	8	anti	anti	ADJ
american_scientific_journal-3270	49	9	-	-	ADJ
american_scientific_journal-3270	49	10	symmetric	symmetric	ADJ
american_scientific_journal-3270	49	11	problem	problem	NOUN
american_scientific_journal-3270	49	12	requires	require	VERB
american_scientific_journal-3270	49	13	only	only	ADV
american_scientific_journal-3270	49	14	a	a	DET
american_scientific_journal-3270	49	15	slight	slight	ADJ
american_scientific_journal-3270	49	16	modification	modification	NOUN
american_scientific_journal-3270	49	17	.	.	PUNCT
american_scientific_journal-3270	50	1	let	let	VERB
american_scientific_journal-3270	50	2	,	,	PUNCT
american_scientific_journal-3270	50	3	i	i	PRON
american_scientific_journal-3270	50	4	iu	iu	ADP
american_scientific_journal-3270	50	5	v	v	PROPN
american_scientific_journal-3270	50	6	be	be	AUX
american_scientific_journal-3270	50	7	the	the	DET
american_scientific_journal-3270	50	8	,	,	PUNCT
american_scientific_journal-3270	50	9	x	x	PROPN
american_scientific_journal-3270	50	10	y	y	NOUN
american_scientific_journal-3270	50	11	components	component	NOUN
american_scientific_journal-3270	50	12	of	of	ADP
american_scientific_journal-3270	50	13	the	the	DET
american_scientific_journal-3270	50	14	displacement	displacement	ADJ
american_scientific_journal-3270	50	15	vector	vector	NOUN
american_scientific_journal-3270	50	16	in	in	ADP
american_scientific_journal-3270	50	17	the	the	DET
american_scientific_journal-3270	50	18	ith	ith	PROPN
american_scientific_journal-3270	50	19	materials	material	NOUN
american_scientific_journal-3270	50	20	and	and	CCONJ
american_scientific_journal-3270	50	21	satisfy	satisfy	VERB
american_scientific_journal-3270	50	22	the	the	DET
american_scientific_journal-3270	50	23	field	field	NOUN
american_scientific_journal-3270	50	24	equations	equation	NOUN
american_scientific_journal-3270	50	25	in	in	ADP
american_scientific_journal-3270	50	26	the	the	DET
american_scientific_journal-3270	50	27	form	form	NOUN
american_scientific_journal-3270	50	28	2	2	NUM
american_scientific_journal-3270	50	29	2	2	NUM
american_scientific_journal-3270	50	30	2	2	NUM
american_scientific_journal-3270	50	31	(	(	PUNCT
american_scientific_journal-3270	50	32	)	)	PUNCT
american_scientific_journal-3270	51	1	i	i	PRON
american_scientific_journal-3270	51	2	i	i	PRON
american_scientific_journal-3270	52	1	i	i	PRON
american_scientific_journal-3270	52	2	i	i	PRON
american_scientific_journal-3270	53	1	i	i	PRON
american_scientific_journal-3270	53	2	i	i	PRON
american_scientific_journal-3270	54	1	i	i	PRON
american_scientific_journal-3270	54	2	u	u	VERB
american_scientific_journal-3270	54	3	v	v	VERB
american_scientific_journal-3270	54	4	d	d	X
american_scientific_journal-3270	54	5	uu	uu	INTJ
american_scientific_journal-3270	54	6	x	x	X
american_scientific_journal-3270	54	7	x	x	SYM
american_scientific_journal-3270	54	8	y	y	VERB
american_scientific_journal-3270	54	9	dt	dt	X
american_scientific_journal-3270	54	10	µ	µ	X
american_scientific_journal-3270	54	11	λ	λ	X
american_scientific_journal-3270	54	12	µ	µ	PROPN
american_scientific_journal-3270	54	13	ρ	ρ	PRON
american_scientific_journal-3270	54	14			PROPN
american_scientific_journal-3270	54	15	∂	∂	PROPN
american_scientific_journal-3270	54	16	∂∂	∂∂	ADJ
american_scientific_journal-3270	54	17	∇	∇	X
american_scientific_journal-3270	54	18	+	+	X
american_scientific_journal-3270	55	1	+	+	PUNCT
american_scientific_journal-3270	55	2	+	+	CCONJ
american_scientific_journal-3270	55	3	=	=	NOUN
american_scientific_journal-3270	55	4			NOUN
american_scientific_journal-3270	55	5	∂	∂	X
american_scientific_journal-3270	55	6	∂	∂	NOUN
american_scientific_journal-3270	55	7	∂	∂	NOUN
american_scientific_journal-3270	55	8			PUNCT
american_scientific_journal-3270	55	9	(	(	PUNCT
american_scientific_journal-3270	55	10	2.4	2.4	NUM
american_scientific_journal-3270	55	11	)	)	SYM
american_scientific_journal-3270	55	12	2	2	NUM
american_scientific_journal-3270	55	13	2	2	NUM
american_scientific_journal-3270	55	14	2	2	NUM
american_scientific_journal-3270	55	15	(	(	PUNCT
american_scientific_journal-3270	55	16	)	)	PUNCT
american_scientific_journal-3270	55	17	i	i	PRON
american_scientific_journal-3270	56	1	i	i	PRON
american_scientific_journal-3270	56	2	i	i	PRON
american_scientific_journal-3270	57	1	i	i	PRON
american_scientific_journal-3270	57	2	i	i	PRON
american_scientific_journal-3270	58	1	i	i	PRON
american_scientific_journal-3270	58	2	i	i	PRON
american_scientific_journal-3270	58	3	u	u	VERB
american_scientific_journal-3270	58	4	v	v	VERB
american_scientific_journal-3270	58	5	d	d	X
american_scientific_journal-3270	58	6	vv	vv	NOUN
american_scientific_journal-3270	59	1	y	y	NOUN
american_scientific_journal-3270	59	2	x	x	SYM
american_scientific_journal-3270	59	3	y	y	VERB
american_scientific_journal-3270	59	4	dt	dt	X
american_scientific_journal-3270	59	5	µ	µ	X
american_scientific_journal-3270	59	6	λ	λ	X
american_scientific_journal-3270	59	7	µ	µ	PROPN
american_scientific_journal-3270	59	8	ρ	ρ	PRON
american_scientific_journal-3270	59	9			PROPN
american_scientific_journal-3270	59	10	∂	∂	PROPN
american_scientific_journal-3270	59	11	∂∂	∂∂	ADJ
american_scientific_journal-3270	59	12	∇	∇	X
american_scientific_journal-3270	59	13	+	+	X
american_scientific_journal-3270	60	1	+	+	PUNCT
american_scientific_journal-3270	60	2	+	+	CCONJ
american_scientific_journal-3270	60	3	=	=	NOUN
american_scientific_journal-3270	60	4			NOUN
american_scientific_journal-3270	60	5	∂	∂	X
american_scientific_journal-3270	60	6	∂	∂	NOUN
american_scientific_journal-3270	60	7	∂	∂	NOUN
american_scientific_journal-3270	60	8			X
american_scientific_journal-3270	60	9	.	.	PUNCT
american_scientific_journal-3270	61	1	(	(	PUNCT
american_scientific_journal-3270	61	2	2.5	2.5	NUM
american_scientific_journal-3270	61	3	)	)	PUNCT
american_scientific_journal-3270	61	4	then	then	ADV
american_scientific_journal-3270	61	5	,	,	PUNCT
american_scientific_journal-3270	61	6	assume	assume	VERB
american_scientific_journal-3270	61	7	the	the	DET
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american_scientific_journal-3270	61	11	the	the	DET
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american_scientific_journal-3270	61	13	x	x	PUNCT
american_scientific_journal-3270	61	14	y	y	NOUN
american_scientific_journal-3270	61	15	2	2	NUM
american_scientific_journal-3270	61	16	2	2	NUM
american_scientific_journal-3270	61	17	(	(	PUNCT
american_scientific_journal-3270	61	18	,	,	PUNCT
american_scientific_journal-3270	61	19	)	)	PUNCT
american_scientific_journal-3270	61	20	ii	ii	PROPN
american_scientific_journal-3270	61	21	µ	µ	PROPN
american_scientific_journal-3270	61	22	υ	υ	PROPN
american_scientific_journal-3270	61	23	3	3	NUM
american_scientific_journal-3270	61	24	3	3	NUM
american_scientific_journal-3270	61	25	(	(	PUNCT
american_scientific_journal-3270	61	26	,	,	PUNCT
american_scientific_journal-3270	61	27	)	)	PUNCT
american_scientific_journal-3270	61	28	iii	iii	PROPN
american_scientific_journal-3270	61	29	µ	µ	NUM
american_scientific_journal-3270	61	30	υ	υ	PRON
american_scientific_journal-3270	61	31	2a	2a	NUM
american_scientific_journal-3270	61	32	2	2	NUM
american_scientific_journal-3270	61	33	2	2	NUM
american_scientific_journal-3270	61	34	(	(	PUNCT
american_scientific_journal-3270	61	35	,	,	PUNCT
american_scientific_journal-3270	61	36	)	)	PUNCT
american_scientific_journal-3270	61	37	ii	ii	PROPN
american_scientific_journal-3270	61	38	µ	µ	PROPN
american_scientific_journal-3270	61	39	υ	υ	NOUN
american_scientific_journal-3270	61	40	1	1	NUM
american_scientific_journal-3270	61	41	1	1	NUM
american_scientific_journal-3270	61	42	(	(	PUNCT
american_scientific_journal-3270	61	43	,	,	PUNCT
american_scientific_journal-3270	61	44	)	)	PUNCT
american_scientific_journal-3270	61	45	i	i	PRON
american_scientific_journal-3270	61	46	µ	µ	VERB
american_scientific_journal-3270	61	47	υ	υ	PRON
american_scientific_journal-3270	61	48	american	american	PROPN
american_scientific_journal-3270	61	49	scientific	scientific	ADJ
american_scientific_journal-3270	61	50	research	research	PROPN
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american_scientific_journal-3270	61	52	for	for	ADP
american_scientific_journal-3270	61	53	engineering	engineering	NOUN
american_scientific_journal-3270	61	54	,	,	PUNCT
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american_scientific_journal-3270	61	56	,	,	PUNCT
american_scientific_journal-3270	61	57	and	and	CCONJ
american_scientific_journal-3270	61	58	sciences	science	NOUN
american_scientific_journal-3270	61	59	(	(	PUNCT
american_scientific_journal-3270	61	60	asrjets	asrjet	NOUN
american_scientific_journal-3270	61	61	)	)	PUNCT
american_scientific_journal-3270	61	62	(	(	PUNCT
american_scientific_journal-3270	61	63	2017	2017	NUM
american_scientific_journal-3270	61	64	)	)	PUNCT
american_scientific_journal-3270	61	65	volume	volume	NOUN
american_scientific_journal-3270	61	66	34	34	NUM
american_scientific_journal-3270	61	67	,	,	PUNCT
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american_scientific_journal-3270	61	69	1	1	NUM
american_scientific_journal-3270	61	70	,	,	PUNCT
american_scientific_journal-3270	61	71	pp	pp	ADV
american_scientific_journal-3270	61	72	213	213	NUM
american_scientific_journal-3270	61	73	-	-	SYM
american_scientific_journal-3270	61	74	230	230	NUM
american_scientific_journal-3270	61	75	216	216	NUM
american_scientific_journal-3270	61	76	(	(	PUNCT
american_scientific_journal-3270	61	77	,	,	PUNCT
american_scientific_journal-3270	61	78	,	,	PUNCT
american_scientific_journal-3270	61	79	)	)	PUNCT
american_scientific_journal-3270	61	80	(	(	PUNCT
american_scientific_journal-3270	61	81	,	,	PUNCT
american_scientific_journal-3270	61	82	)	)	PUNCT
american_scientific_journal-3270	61	83	(	(	PUNCT
american_scientific_journal-3270	61	84	)	)	PUNCT
american_scientific_journal-3270	61	85	i	i	PRON
american_scientific_journal-3270	61	86	iu	iu	VERB
american_scientific_journal-3270	61	87	x	x	VERB
american_scientific_journal-3270	61	88	y	y	NOUN
american_scientific_journal-3270	61	89	t	t	PROPN
american_scientific_journal-3270	61	90	u	u	NOUN
american_scientific_journal-3270	61	91	x	x	VERB
american_scientific_journal-3270	61	92	y	y	NOUN
american_scientific_journal-3270	61	93	f	f	NOUN
american_scientific_journal-3270	61	94	t=	t=	PROPN
american_scientific_journal-3270	62	1	+	+	X
american_scientific_journal-3270	62	2	,	,	PUNCT
american_scientific_journal-3270	62	3	(	(	PUNCT
american_scientific_journal-3270	62	4	2.6	2.6	NUM
american_scientific_journal-3270	62	5	)	)	PUNCT
american_scientific_journal-3270	62	6	(	(	PUNCT
american_scientific_journal-3270	62	7	,	,	PUNCT
american_scientific_journal-3270	62	8	,	,	PUNCT
american_scientific_journal-3270	62	9	)	)	PUNCT
american_scientific_journal-3270	62	10	(	(	PUNCT
american_scientific_journal-3270	62	11	,	,	PUNCT
american_scientific_journal-3270	62	12	)	)	PUNCT
american_scientific_journal-3270	62	13	(	(	PUNCT
american_scientific_journal-3270	62	14	)	)	PUNCT
american_scientific_journal-3270	62	15	i	i	PRON
american_scientific_journal-3270	62	16	iv	iv	VERB
american_scientific_journal-3270	62	17	x	x	PUNCT
american_scientific_journal-3270	62	18	y	y	NOUN
american_scientific_journal-3270	62	19	t	t	PROPN
american_scientific_journal-3270	62	20	v	v	NOUN
american_scientific_journal-3270	62	21	x	x	SYM
american_scientific_journal-3270	62	22	y	y	NOUN
american_scientific_journal-3270	62	23	f	f	NOUN
american_scientific_journal-3270	62	24	t=	t=	PROPN
american_scientific_journal-3270	63	1	+	+	X
american_scientific_journal-3270	63	2	,	,	PUNCT
american_scientific_journal-3270	63	3	(	(	PUNCT
american_scientific_journal-3270	63	4	2.7	2.7	NUM
american_scientific_journal-3270	63	5	)	)	PUNCT
american_scientific_journal-3270	63	6	where	where	SCONJ
american_scientific_journal-3270	63	7	(	(	PUNCT
american_scientific_journal-3270	63	8	)	)	PUNCT
american_scientific_journal-3270	63	9	f	f	PROPN
american_scientific_journal-3270	63	10	t	t	PROPN
american_scientific_journal-3270	63	11	is	be	AUX
american_scientific_journal-3270	63	12	a	a	DET
american_scientific_journal-3270	63	13	function	function	NOUN
american_scientific_journal-3270	63	14	of	of	ADP
american_scientific_journal-3270	63	15	t	t	PROPN
american_scientific_journal-3270	63	16	,	,	PUNCT
american_scientific_journal-3270	63	17	will	will	AUX
american_scientific_journal-3270	63	18	be	be	AUX
american_scientific_journal-3270	63	19	determined	determine	VERB
american_scientific_journal-3270	63	20	.	.	PUNCT
american_scientific_journal-3270	64	1	hence	hence	ADV
american_scientific_journal-3270	64	2	,	,	PUNCT
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american_scientific_journal-3270	64	4	(	(	PUNCT
american_scientific_journal-3270	64	5	2.6	2.6	NUM
american_scientific_journal-3270	64	6	)	)	PUNCT
american_scientific_journal-3270	64	7	and	and	CCONJ
american_scientific_journal-3270	64	8	(	(	PUNCT
american_scientific_journal-3270	64	9	2.7	2.7	NUM
american_scientific_journal-3270	64	10	)	)	PUNCT
american_scientific_journal-3270	64	11	in	in	ADP
american_scientific_journal-3270	64	12	eqs	eqs	PROPN
american_scientific_journal-3270	64	13	.	.	PUNCT
american_scientific_journal-3270	65	1	(	(	PUNCT
american_scientific_journal-3270	65	2	2.4	2.4	NUM
american_scientific_journal-3270	65	3	)	)	PUNCT
american_scientific_journal-3270	65	4	and	and	CCONJ
american_scientific_journal-3270	65	5	(	(	PUNCT
american_scientific_journal-3270	65	6	2.5	2.5	NUM
american_scientific_journal-3270	65	7	)	)	PUNCT
american_scientific_journal-3270	65	8	,	,	PUNCT
american_scientific_journal-3270	65	9	we	we	PRON
american_scientific_journal-3270	65	10	have	have	VERB
american_scientific_journal-3270	65	11	2	2	NUM
american_scientific_journal-3270	65	12	2	2	NUM
american_scientific_journal-3270	65	13	2	2	NUM
american_scientific_journal-3270	65	14	2	2	NUM
american_scientific_journal-3270	65	15	2	2	NUM
american_scientific_journal-3270	65	16	(	(	PUNCT
american_scientific_journal-3270	65	17	2	2	NUM
american_scientific_journal-3270	65	18	)	)	PUNCT
american_scientific_journal-3270	65	19	(	(	PUNCT
american_scientific_journal-3270	65	20	)	)	PUNCT
american_scientific_journal-3270	65	21	0i	0i	NOUN
american_scientific_journal-3270	66	1	i	i	PRON
american_scientific_journal-3270	67	1	i	i	PRON
american_scientific_journal-3270	68	1	i	i	PRON
american_scientific_journal-3270	69	1	i	i	PRON
american_scientific_journal-3270	70	1	i	i	PRON
american_scientific_journal-3270	71	1	i	i	PRON
american_scientific_journal-3270	72	1	i	i	VERB
american_scientific_journal-3270	72	2	u	u	VERB
american_scientific_journal-3270	72	3	u	u	NOUN
american_scientific_journal-3270	72	4	v	v	NOUN
american_scientific_journal-3270	72	5	x	x	SYM
american_scientific_journal-3270	72	6	yx	yx	PROPN
american_scientific_journal-3270	72	7	y	y	PROPN
american_scientific_journal-3270	72	8	λ	λ	PROPN
american_scientific_journal-3270	72	9	µ	µ	X
american_scientific_journal-3270	72	10	µ	µ	X
american_scientific_journal-3270	72	11	λ	λ	X
american_scientific_journal-3270	72	12	µ∂	µ∂	NOUN
american_scientific_journal-3270	72	13	∂	∂	NUM
american_scientific_journal-3270	72	14	∂	∂	NOUN
american_scientific_journal-3270	72	15	+	+	CCONJ
american_scientific_journal-3270	73	1	+	+	PUNCT
american_scientific_journal-3270	73	2	+	+	CCONJ
american_scientific_journal-3270	73	3	+	+	CCONJ
american_scientific_journal-3270	73	4	=	=	SYM
american_scientific_journal-3270	73	5	∂	∂	NUM
american_scientific_journal-3270	73	6	∂∂	∂∂	NOUN
american_scientific_journal-3270	73	7	∂	∂	NUM
american_scientific_journal-3270	73	8	,	,	PUNCT
american_scientific_journal-3270	73	9	(	(	PUNCT
american_scientific_journal-3270	73	10	2.8	2.8	NUM
american_scientific_journal-3270	73	11	)	)	PUNCT
american_scientific_journal-3270	73	12	2	2	NUM
american_scientific_journal-3270	73	13	2	2	NUM
american_scientific_journal-3270	73	14	2	2	NUM
american_scientific_journal-3270	73	15	2	2	NUM
american_scientific_journal-3270	73	16	2	2	NUM
american_scientific_journal-3270	73	17	(	(	PUNCT
american_scientific_journal-3270	73	18	2	2	NUM
american_scientific_journal-3270	73	19	)	)	PUNCT
american_scientific_journal-3270	73	20	(	(	PUNCT
american_scientific_journal-3270	73	21	)	)	PUNCT
american_scientific_journal-3270	73	22	0i	0i	NOUN
american_scientific_journal-3270	73	23	i	i	PRON
american_scientific_journal-3270	74	1	i	i	PRON
american_scientific_journal-3270	74	2	i	i	PRON
american_scientific_journal-3270	75	1	i	i	PRON
american_scientific_journal-3270	75	2	i	i	PRON
american_scientific_journal-3270	76	1	i	i	PRON
american_scientific_journal-3270	76	2	i	i	PRON
american_scientific_journal-3270	76	3	v	v	VERB
american_scientific_journal-3270	76	4	v	v	NUM
american_scientific_journal-3270	76	5	u	u	NOUN
american_scientific_journal-3270	76	6	x	x	NOUN
american_scientific_journal-3270	76	7	yy	yy	INTJ
american_scientific_journal-3270	76	8	x	x	PUNCT
american_scientific_journal-3270	76	9	λ	λ	X
american_scientific_journal-3270	76	10	µ	µ	X
american_scientific_journal-3270	76	11	µ	µ	X
american_scientific_journal-3270	76	12	λ	λ	X
american_scientific_journal-3270	76	13	µ∂	µ∂	NOUN
american_scientific_journal-3270	76	14	∂	∂	NUM
american_scientific_journal-3270	76	15	∂	∂	NOUN
american_scientific_journal-3270	77	1	+	+	CCONJ
american_scientific_journal-3270	77	2	+	+	PUNCT
american_scientific_journal-3270	77	3	+	+	CCONJ
american_scientific_journal-3270	77	4	+	+	CCONJ
american_scientific_journal-3270	77	5	=	=	SYM
american_scientific_journal-3270	77	6	∂	∂	NUM
american_scientific_journal-3270	77	7	∂∂	∂∂	NOUN
american_scientific_journal-3270	77	8	∂	∂	NUM
american_scientific_journal-3270	77	9	,	,	PUNCT
american_scientific_journal-3270	77	10	(	(	PUNCT
american_scientific_journal-3270	77	11	2.9	2.9	NUM
american_scientific_journal-3270	77	12	)	)	PUNCT
american_scientific_journal-3270	77	13	and	and	CCONJ
american_scientific_journal-3270	77	14	2	2	NUM
american_scientific_journal-3270	77	15	2	2	NUM
american_scientific_journal-3270	77	16	(	(	PUNCT
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american_scientific_journal-3270	77	20	i	i	PROPN
american_scientific_journal-3270	78	1	d	d	NOUN
american_scientific_journal-3270	78	2	f	f	PROPN
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american_scientific_journal-3270	79	2	f	f	PROPN
american_scientific_journal-3270	79	3	t	t	PROPN
american_scientific_journal-3270	79	4	dt	dt	X
american_scientific_journal-3270	79	5	µ	µ	X
american_scientific_journal-3270	79	6	ρ	ρ	PROPN
american_scientific_journal-3270	79	7	=	=	PUNCT
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american_scientific_journal-3270	80	2	2.10	2.10	NUM
american_scientific_journal-3270	80	3	)	)	PUNCT
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american_scientific_journal-3270	80	6	(	(	PUNCT
american_scientific_journal-3270	80	7	2.10	2.10	NUM
american_scientific_journal-3270	80	8	)	)	PUNCT
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american_scientific_journal-3270	80	10	a	a	DET
american_scientific_journal-3270	80	11	solution	solution	NOUN
american_scientific_journal-3270	80	12	(	(	PUNCT
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american_scientific_journal-3270	80	14	,	,	PUNCT
american_scientific_journal-3270	80	15	(	(	PUNCT
american_scientific_journal-3270	80	16	(	(	PUNCT
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american_scientific_journal-3270	80	18	0	0	X
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american_scientific_journal-3270	81	1	i	i	PRON
american_scientific_journal-3270	81	2	t	t	VERB
american_scientific_journal-3270	81	3	f	f	PROPN
american_scientific_journal-3270	81	4	t	t	PROPN
american_scientific_journal-3270	81	5	be	be	AUX
american_scientific_journal-3270	81	6	f	f	PROPN
american_scientific_journal-3270	81	7	µ	µ	X
american_scientific_journal-3270	81	8	ρ	ρ	NOUN
american_scientific_journal-3270	81	9	−	−	PROPN
american_scientific_journal-3270	82	1	=	=	SYM
american_scientific_journal-3270	82	2	∞	∞	PROPN
american_scientific_journal-3270	82	3	→	→	PUNCT
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american_scientific_journal-3270	83	1	(	(	PUNCT
american_scientific_journal-3270	83	2	2.11	2.11	NUM
american_scientific_journal-3270	83	3	)	)	PUNCT
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american_scientific_journal-3270	83	5	addition	addition	NOUN
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american_scientific_journal-3270	83	12	(	(	PUNCT
american_scientific_journal-3270	83	13	2.8	2.8	NUM
american_scientific_journal-3270	83	14	)	)	PUNCT
american_scientific_journal-3270	83	15	and	and	CCONJ
american_scientific_journal-3270	83	16	(	(	PUNCT
american_scientific_journal-3270	83	17	2.9	2.9	NUM
american_scientific_journal-3270	83	18	)	)	PUNCT
american_scientific_journal-3270	83	19	,	,	PUNCT
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american_scientific_journal-3270	83	21	use	use	VERB
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american_scientific_journal-3270	83	23	fourier	fourier	ADJ
american_scientific_journal-3270	83	24	integral	integral	ADJ
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american_scientific_journal-3270	83	26	,	,	PUNCT
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american_scientific_journal-3270	83	30	2	2	NUM
american_scientific_journal-3270	83	31	3	3	NUM
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american_scientific_journal-3270	83	33	0	0	NUM
american_scientific_journal-3270	83	34	2	2	NUM
american_scientific_journal-3270	83	35	(	(	PUNCT
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american_scientific_journal-3270	83	40	(	(	PUNCT
american_scientific_journal-3270	83	41	)	)	PUNCT
american_scientific_journal-3270	83	42	siny	siny	NOUN
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american_scientific_journal-3270	85	2	i	i	PRON
american_scientific_journal-3270	85	3	iu	iu	VERB
american_scientific_journal-3270	85	4	x	x	PROPN
american_scientific_journal-3270	85	5	y	y	PROPN
american_scientific_journal-3270	85	6	a	a	PRON
american_scientific_journal-3270	85	7	a	a	DET
american_scientific_journal-3270	85	8	y	y	PROPN
american_scientific_journal-3270	85	9	e	e	PROPN
american_scientific_journal-3270	85	10	a	a	PRON
american_scientific_journal-3270	85	11	a	a	DET
american_scientific_journal-3270	85	12	y	y	PROPN
american_scientific_journal-3270	85	13	e	e	PROPN
american_scientific_journal-3270	85	14	xdα	xdα	PROPN
american_scientific_journal-3270	86	1	α	α	PROPN
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american_scientific_journal-3270	86	7	=	=	PUNCT
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american_scientific_journal-3270	89	9	2	2	NUM
american_scientific_journal-3270	89	10	3	3	NUM
american_scientific_journal-3270	89	11	4	4	NUM
american_scientific_journal-3270	89	12	0	0	NUM
american_scientific_journal-3270	89	13	2	2	NUM
american_scientific_journal-3270	89	14	(	(	PUNCT
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american_scientific_journal-3270	89	18	(	(	PUNCT
american_scientific_journal-3270	89	19	)	)	PUNCT
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american_scientific_journal-3270	90	2	(	(	PUNCT
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american_scientific_journal-3270	90	6	yi	yi	PROPN
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american_scientific_journal-3270	91	2	i	i	PRON
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american_scientific_journal-3270	94	2	k	k	PROPN
american_scientific_journal-3270	95	1	kv	kv	PROPN
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american_scientific_journal-3270	96	4	a	a	DET
american_scientific_journal-3270	96	5	e	e	NOUN
american_scientific_journal-3270	96	6	a	a	DET
american_scientific_journal-3270	96	7	y	y	PROPN
american_scientific_journal-3270	96	8	a	a	DET
american_scientific_journal-3270	96	9	e	e	X
american_scientific_journal-3270	96	10	xdα	xdα	PROPN
american_scientific_journal-3270	96	11	α	α	PROPN
american_scientific_journal-3270	96	12	α	α	NOUN
american_scientific_journal-3270	96	13	α	α	NOUN
american_scientific_journal-3270	97	1	π	π	NOUN
american_scientific_journal-3270	97	2	α	α	NOUN
american_scientific_journal-3270	97	3	α	α	NOUN
american_scientific_journal-3270	97	4	∞	∞	PROPN
american_scientific_journal-3270	97	5	−	−	PUNCT
american_scientific_journal-3270	97	6	=	=	PROPN
american_scientific_journal-3270	98	1	+	+	CCONJ
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american_scientific_journal-3270	99	1	+	+	CCONJ
american_scientific_journal-3270	99	2	−	−	ADP
american_scientific_journal-3270	99	3	+	+	CCONJ
american_scientific_journal-3270	99	4	−	−	PUNCT
american_scientific_journal-3270	99	5			PROPN
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american_scientific_journal-3270	99	7	∫	∫	NOUN
american_scientific_journal-3270	99	8	(	(	PUNCT
american_scientific_journal-3270	99	9	2.13	2.13	NUM
american_scientific_journal-3270	99	10	)	)	PUNCT
american_scientific_journal-3270	99	11	here	here	ADV
american_scientific_journal-3270	99	12	,	,	PUNCT
american_scientific_journal-3270	99	13	ik	ik	PROPN
american_scientific_journal-3270	99	14	have	have	VERB
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american_scientific_journal-3270	99	17	,	,	PUNCT
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american_scientific_journal-3270	99	19	3	3	NUM
american_scientific_journal-3270	99	20	4i	4i	NUM
american_scientific_journal-3270	99	21	ik	ik	PROPN
american_scientific_journal-3270	99	22	υ=	υ=	NOUN
american_scientific_journal-3270	99	23	−	−	PROPN
american_scientific_journal-3270	99	24	for	for	ADP
american_scientific_journal-3270	99	25	plane	plane	NOUN
american_scientific_journal-3270	99	26	strain	strain	NOUN
american_scientific_journal-3270	99	27	and	and	CCONJ
american_scientific_journal-3270	99	28	(	(	PUNCT
american_scientific_journal-3270	99	29	3	3	NUM
american_scientific_journal-3270	99	30	)	)	PUNCT
american_scientific_journal-3270	99	31	/	/	PUNCT
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american_scientific_journal-3270	99	33	1	1	X
american_scientific_journal-3270	99	34	)	)	PUNCT
american_scientific_journal-3270	99	35	i	i	PRON
american_scientific_journal-3270	100	1	i	i	PRON
american_scientific_journal-3270	100	2	ik	ik	VERB
american_scientific_journal-3270	100	3	υ	υ	DET
american_scientific_journal-3270	100	4	υ=	υ=	NOUN
american_scientific_journal-3270	100	5	−	−	PROPN
american_scientific_journal-3270	101	1	+	+	CCONJ
american_scientific_journal-3270	101	2	for	for	ADP
american_scientific_journal-3270	101	3	generalized	generalized	ADJ
american_scientific_journal-3270	101	4	plane	plane	NOUN
american_scientific_journal-3270	101	5	stress	stress	NOUN
american_scientific_journal-3270	101	6	,	,	PUNCT
american_scientific_journal-3270	101	7	iυ	iυ	PROPN
american_scientific_journal-3270	101	8	are	be	AUX
american_scientific_journal-3270	101	9	poisson	poisson	NOUN
american_scientific_journal-3270	101	10	’s	’s	PART
american_scientific_journal-3270	101	11	coefficients	coefficient	NOUN
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american_scientific_journal-3270	101	13	each	each	DET
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american_scientific_journal-3270	101	15	,	,	PUNCT
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american_scientific_journal-3270	101	17	,	,	PUNCT
american_scientific_journal-3270	101	18	,	,	PUNCT
american_scientific_journal-3270	101	19	1,2,3,4i	1,2,3,4i	NUM
american_scientific_journal-3270	101	20	ja	ja	PROPN
american_scientific_journal-3270	101	21	j	j	PROPN
american_scientific_journal-3270	102	1	=	=	PUNCT
american_scientific_journal-3270	102	2	,	,	PUNCT
american_scientific_journal-3270	102	3	are	be	AUX
american_scientific_journal-3270	102	4	functions	function	NOUN
american_scientific_journal-3270	102	5	of	of	ADP
american_scientific_journal-3270	102	6	α	α	PRON
american_scientific_journal-3270	102	7	which	which	PRON
american_scientific_journal-3270	102	8	can	can	AUX
american_scientific_journal-3270	102	9	be	be	AUX
american_scientific_journal-3270	102	10	determined	determine	VERB
american_scientific_journal-3270	102	11	from	from	ADP
american_scientific_journal-3270	102	12	the	the	DET
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american_scientific_journal-3270	102	15	.	.	PUNCT
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american_scientific_journal-3270	103	2	obtaining	obtain	VERB
american_scientific_journal-3270	103	3	the	the	DET
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american_scientific_journal-3270	103	5	of	of	ADP
american_scientific_journal-3270	103	6	,	,	PUNCT
american_scientific_journal-3270	103	7	i	i	PRON
american_scientific_journal-3270	103	8	iu	iu	ADP
american_scientific_journal-3270	103	9	v	v	NUM
american_scientific_journal-3270	103	10	,	,	PUNCT
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american_scientific_journal-3270	103	13	may	may	AUX
american_scientific_journal-3270	103	14	be	be	AUX
american_scientific_journal-3270	103	15	evaluated	evaluate	VERB
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american_scientific_journal-3270	103	17	hook	hook	NOUN
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american_scientific_journal-3270	103	19	law	law	NOUN
american_scientific_journal-3270	103	20	.	.	PUNCT
american_scientific_journal-3270	104	1	in	in	ADP
american_scientific_journal-3270	104	2	particular	particular	ADJ
american_scientific_journal-3270	104	3	,	,	PUNCT
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american_scientific_journal-3270	104	9	vector	vector	NOUN
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american_scientific_journal-3270	104	15	may	may	AUX
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american_scientific_journal-3270	104	18	,	,	PUNCT
american_scientific_journal-3270	104	19	respectively	respectively	ADV
american_scientific_journal-3270	104	20	as	as	ADP
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american_scientific_journal-3270	104	22	1	1	NUM
american_scientific_journal-3270	104	23	2	2	NUM
american_scientific_journal-3270	104	24	2	2	NUM
american_scientific_journal-3270	104	25	3	3	NUM
american_scientific_journal-3270	104	26	4	4	NUM
american_scientific_journal-3270	104	27	4	4	NUM
american_scientific_journal-3270	104	28	0	0	NUM
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american_scientific_journal-3270	106	4	2	2	NUM
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american_scientific_journal-3270	110	3	i	i	PRON
american_scientific_journal-3270	111	1	a	a	DET
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american_scientific_journal-3270	111	3	y	y	NOUN
american_scientific_journal-3270	111	4	a	a	DET
american_scientific_journal-3270	111	5	e	e	NOUN
american_scientific_journal-3270	111	6	a	a	DET
american_scientific_journal-3270	111	7	a	a	DET
american_scientific_journal-3270	111	8	y	y	NOUN
american_scientific_journal-3270	111	9	a	a	DET
american_scientific_journal-3270	111	10	e	e	X
american_scientific_journal-3270	111	11	xdα	xdα	PROPN
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american_scientific_journal-3270	111	18	υ	υ	NOUN
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american_scientific_journal-3270	111	22	∞	∞	NUM
american_scientific_journal-3270	111	23	−=	−=	NOUN
american_scientific_journal-3270	111	24	−	−	PROPN
american_scientific_journal-3270	112	1	+	+	CCONJ
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american_scientific_journal-3270	113	2	−	−	X
american_scientific_journal-3270	114	1	+	+	CCONJ
american_scientific_journal-3270	114	2	−	−	PROPN
american_scientific_journal-3270	114	3	+	+	CCONJ
american_scientific_journal-3270	114	4	+	+	CCONJ
american_scientific_journal-3270	114	5	−∫	−∫	NOUN
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american_scientific_journal-3270	114	14	,	,	PUNCT
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american_scientific_journal-3270	114	28	,	,	PUNCT
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american_scientific_journal-3270	114	31	-	-	SYM
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american_scientific_journal-3270	114	38	1	1	NUM
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american_scientific_journal-3270	114	45	1	1	NUM
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american_scientific_journal-3270	122	1	a	a	DET
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american_scientific_journal-3270	122	3	y	y	NOUN
american_scientific_journal-3270	122	4	a	a	DET
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american_scientific_journal-3270	122	6	a	a	DET
american_scientific_journal-3270	122	7	a	a	DET
american_scientific_journal-3270	122	8	y	y	NOUN
american_scientific_journal-3270	122	9	a	a	X
american_scientific_journal-3270	122	10	e	e	X
american_scientific_journal-3270	122	11	xdα	xdα	PROPN
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american_scientific_journal-3270	122	14	υ	υ	VERB
american_scientific_journal-3270	123	1	α	α	NOUN
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american_scientific_journal-3270	123	5	µ	µ	X
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american_scientific_journal-3270	123	7	∞	∞	PROPN
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american_scientific_journal-3270	126	1	+	+	CCONJ
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american_scientific_journal-3270	126	3	−	−	PROPN
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american_scientific_journal-3270	126	5	(	(	PUNCT
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american_scientific_journal-3270	126	7	)	)	PUNCT
american_scientific_journal-3270	126	8	on	on	ADP
american_scientific_journal-3270	126	9	the	the	DET
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american_scientific_journal-3270	126	11	,	,	PUNCT
american_scientific_journal-3270	126	12	the	the	DET
american_scientific_journal-3270	126	13	medium	medium	NOUN
american_scientific_journal-3270	126	14	may	may	AUX
american_scientific_journal-3270	126	15	have	have	VERB
american_scientific_journal-3270	126	16	formally	formally	ADV
american_scientific_journal-3270	126	17	any	any	DET
american_scientific_journal-3270	126	18	one	one	NUM
american_scientific_journal-3270	126	19	of	of	ADP
american_scientific_journal-3270	126	20	the	the	DET
american_scientific_journal-3270	126	21	following	follow	VERB
american_scientific_journal-3270	126	22	four	four	NUM
american_scientific_journal-3270	126	23	groups	group	NOUN
american_scientific_journal-3270	126	24	of	of	ADP
american_scientific_journal-3270	126	25	homogeneous	homogeneous	ADJ
american_scientific_journal-3270	126	26	boundary	boundary	ADJ
american_scientific_journal-3270	126	27	conditions	condition	NOUN
american_scientific_journal-3270	126	28	(	(	PUNCT
american_scientific_journal-3270	126	29	a	a	X
american_scientific_journal-3270	126	30	)	)	PUNCT
american_scientific_journal-3270	126	31	0i	0i	NOUN
american_scientific_journal-3270	127	1	i	i	PRON
american_scientific_journal-3270	127	2	yy	yy	INTJ
american_scientific_journal-3270	127	3	xyσ	xyσ	PROPN
american_scientific_journal-3270	127	4	σ=	σ=	PROPN
american_scientific_journal-3270	127	5	=	=	PRON
american_scientific_journal-3270	127	6	,	,	PUNCT
american_scientific_journal-3270	127	7	(	(	PUNCT
american_scientific_journal-3270	127	8	b	b	NOUN
american_scientific_journal-3270	127	9	)	)	PUNCT
american_scientific_journal-3270	127	10	0i	0i	NOUN
american_scientific_journal-3270	127	11	iu	iu	ADP
american_scientific_journal-3270	127	12	v=	v=	PROPN
american_scientific_journal-3270	127	13	=	=	PUNCT
american_scientific_journal-3270	127	14	,	,	PUNCT
american_scientific_journal-3270	127	15	(	(	PUNCT
american_scientific_journal-3270	127	16	c	c	X
american_scientific_journal-3270	127	17	)	)	PUNCT
american_scientific_journal-3270	127	18	0i	0i	NOUN
american_scientific_journal-3270	128	1	xy	xy	PROPN
american_scientific_journal-3270	128	2	ivσ	ivσ	PROPN
american_scientific_journal-3270	129	1	=	=	NOUN
american_scientific_journal-3270	129	2	=	=	X
american_scientific_journal-3270	129	3	,	,	PUNCT
american_scientific_journal-3270	129	4	(	(	PUNCT
american_scientific_journal-3270	129	5	d	d	NOUN
american_scientific_journal-3270	129	6	)	)	PUNCT
american_scientific_journal-3270	129	7	0	0	NUM
american_scientific_journal-3270	129	8	,	,	PUNCT
american_scientific_journal-3270	129	9	1,2,3i	1,2,3i	NUM
american_scientific_journal-3270	129	10	yy	yy	INTJ
american_scientific_journal-3270	129	11	iu	iu	ADV
american_scientific_journal-3270	129	12	iσ	iσ	ADV
american_scientific_journal-3270	129	13	=	=	PUNCT
american_scientific_journal-3270	129	14	=	=	SYM
american_scientific_journal-3270	129	15	=	=	SYM
american_scientific_journal-3270	129	16	(	(	PUNCT
american_scientific_journal-3270	129	17	2.16	2.16	NUM
american_scientific_journal-3270	129	18	)	)	PUNCT
american_scientific_journal-3270	129	19	the	the	DET
american_scientific_journal-3270	129	20	continuity	continuity	NOUN
american_scientific_journal-3270	129	21	requires	require	VERB
american_scientific_journal-3270	129	22	that	that	SCONJ
american_scientific_journal-3270	129	23	on	on	ADP
american_scientific_journal-3270	129	24	the	the	DET
american_scientific_journal-3270	129	25	interfaces	interface	NOUN
american_scientific_journal-3270	129	26	the	the	DET
american_scientific_journal-3270	129	27	stress	stress	NOUN
american_scientific_journal-3270	129	28	and	and	CCONJ
american_scientific_journal-3270	129	29	displacement	displacement	ADJ
american_scientific_journal-3270	129	30	vectors	vector	NOUN
american_scientific_journal-3270	129	31	in	in	ADP
american_scientific_journal-3270	129	32	the	the	DET
american_scientific_journal-3270	129	33	adjacent	adjacent	ADJ
american_scientific_journal-3270	129	34	layers	layer	NOUN
american_scientific_journal-3270	129	35	be	be	AUX
american_scientific_journal-3270	129	36	equal	equal	ADJ
american_scientific_journal-3270	129	37	i.e.	i.e.	X
american_scientific_journal-3270	129	38	1	1	NUM
american_scientific_journal-3270	129	39	1	1	NUM
american_scientific_journal-3270	129	40	1	1	NUM
american_scientific_journal-3270	129	41	10	10	NUM
american_scientific_journal-3270	129	42	;	;	PUNCT
american_scientific_journal-3270	129	43	0	0	NUM
american_scientific_journal-3270	129	44	;	;	PUNCT
american_scientific_journal-3270	129	45	0	0	NUM
american_scientific_journal-3270	129	46	;	;	PUNCT
american_scientific_journal-3270	129	47	0i	0i	NOUN
american_scientific_journal-3270	129	48	i	i	PRON
american_scientific_journal-3270	130	1	i	i	PRON
american_scientific_journal-3270	131	1	i	i	PRON
american_scientific_journal-3270	132	1	i	i	PRON
american_scientific_journal-3270	133	1	i	i	PRON
american_scientific_journal-3270	134	1	i	i	PRON
american_scientific_journal-3270	135	1	i	i	PRON
american_scientific_journal-3270	135	2	yy	yy	INTJ
american_scientific_journal-3270	136	1	yy	yy	INTJ
american_scientific_journal-3270	136	2	xy	xy	PROPN
american_scientific_journal-3270	137	1	xyu	xyu	PROPN
american_scientific_journal-3270	137	2	u	u	PROPN
american_scientific_journal-3270	137	3	v	v	PROPN
american_scientific_journal-3270	137	4	v	v	PROPN
american_scientific_journal-3270	137	5	σ	σ	PROPN
american_scientific_journal-3270	137	6	σ	σ	PROPN
american_scientific_journal-3270	137	7	σ	σ	PROPN
american_scientific_journal-3270	137	8	σ+	σ+	X
american_scientific_journal-3270	138	1	+	+	PUNCT
american_scientific_journal-3270	139	1	+	+	PUNCT
american_scientific_journal-3270	139	2	+	+	ADJ
american_scientific_journal-3270	139	3	−	−	NOUN
american_scientific_journal-3270	139	4	=	=	SYM
american_scientific_journal-3270	139	5	−	−	PROPN
american_scientific_journal-3270	139	6	=	=	SYM
american_scientific_journal-3270	139	7	−	−	PROPN
american_scientific_journal-3270	139	8	=	=	SYM
american_scientific_journal-3270	140	1	−	−	PROPN
american_scientific_journal-3270	140	2	=	=	SYM
american_scientific_journal-3270	140	3	,	,	PUNCT
american_scientific_journal-3270	140	4	(	(	PUNCT
american_scientific_journal-3270	140	5	2.17	2.17	NUM
american_scientific_journal-3270	140	6	)	)	PUNCT
american_scientific_journal-3270	140	7	now	now	ADV
american_scientific_journal-3270	140	8	,	,	PUNCT
american_scientific_journal-3270	140	9	to	to	PART
american_scientific_journal-3270	140	10	represent	represent	VERB
american_scientific_journal-3270	140	11	the	the	DET
american_scientific_journal-3270	140	12	problem	problem	NOUN
american_scientific_journal-3270	140	13	in	in	ADP
american_scientific_journal-3270	140	14	the	the	DET
american_scientific_journal-3270	140	15	mixed	mixed	ADJ
american_scientific_journal-3270	140	16	integral	integral	ADJ
american_scientific_journal-3270	140	17	equation	equation	NOUN
american_scientific_journal-3270	140	18	form	form	NOUN
american_scientific_journal-3270	140	19	,	,	PUNCT
american_scientific_journal-3270	140	20	we	we	PRON
american_scientific_journal-3270	140	21	first	first	ADV
american_scientific_journal-3270	140	22	assume	assume	VERB
american_scientific_journal-3270	140	23	that	that	SCONJ
american_scientific_journal-3270	140	24	at	at	ADP
american_scientific_journal-3270	140	25	0y	0y	NUM
american_scientific_journal-3270	140	26	=	=	PUNCT
american_scientific_journal-3270	140	27	the	the	DET
american_scientific_journal-3270	140	28	bond	bond	NOUN
american_scientific_journal-3270	140	29	between	between	ADP
american_scientific_journal-3270	140	30	the	the	DET
american_scientific_journal-3270	140	31	two	two	NUM
american_scientific_journal-3270	140	32	adjacent	adjacent	ADJ
american_scientific_journal-3270	140	33	layers	layer	NOUN
american_scientific_journal-3270	140	34	is	be	AUX
american_scientific_journal-3270	140	35	perfect	perfect	ADJ
american_scientific_journal-3270	140	36	except	except	SCONJ
american_scientific_journal-3270	140	37	for	for	ADP
american_scientific_journal-3270	140	38	the	the	DET
american_scientific_journal-3270	140	39	(	(	PUNCT
american_scientific_journal-3270	140	40	symmetrically	symmetrically	ADV
american_scientific_journal-3270	140	41	located	locate	VERB
american_scientific_journal-3270	140	42	)	)	PUNCT
american_scientific_journal-3270	140	43	dislocations	dislocation	NOUN
american_scientific_journal-3270	140	44	at	at	ADP
american_scientific_journal-3270	140	45	0,y	0,y	NOUN
american_scientific_journal-3270	141	1	x	x	X
american_scientific_journal-3270	141	2	y=	y=	NOUN
american_scientific_journal-3270	141	3	=	=	PUNCT
american_scientific_journal-3270	141	4	defined	define	VERB
american_scientific_journal-3270	141	5	by	by	ADP
american_scientific_journal-3270	141	6	(	(	PUNCT
american_scientific_journal-3270	141	7	)	)	PUNCT
american_scientific_journal-3270	141	8	(	(	PUNCT
american_scientific_journal-3270	141	9	)	)	SYM
american_scientific_journal-3270	141	10	2	2	NUM
american_scientific_journal-3270	141	11	3	3	NUM
american_scientific_journal-3270	141	12	1	1	NUM
american_scientific_journal-3270	141	13	2	2	NUM
american_scientific_journal-3270	141	14	3	3	NUM
american_scientific_journal-3270	141	15	2	2	NUM
american_scientific_journal-3270	141	16	(	(	PUNCT
american_scientific_journal-3270	141	17	,	,	PUNCT
american_scientific_journal-3270	141	18	)	)	PUNCT
american_scientific_journal-3270	141	19	,	,	PUNCT
american_scientific_journal-3270	141	20	(	(	PUNCT
american_scientific_journal-3270	141	21	,	,	PUNCT
american_scientific_journal-3270	141	22	)	)	PUNCT
american_scientific_journal-3270	141	23	u	u	NOUN
american_scientific_journal-3270	141	24	u	u	NOUN
american_scientific_journal-3270	141	25	f	f	PROPN
american_scientific_journal-3270	141	26	x	x	SYM
american_scientific_journal-3270	141	27	t	t	PROPN
american_scientific_journal-3270	141	28	v	v	NUM
american_scientific_journal-3270	141	29	v	v	NOUN
american_scientific_journal-3270	141	30	f	f	PROPN
american_scientific_journal-3270	141	31	x	x	X
american_scientific_journal-3270	141	32	t	t	NOUN
american_scientific_journal-3270	141	33	x	x	PUNCT
american_scientific_journal-3270	141	34	x	x	X
american_scientific_journal-3270	142	1	+	+	CCONJ
american_scientific_journal-3270	142	2	−	−	PROPN
american_scientific_journal-3270	143	1	+	+	CCONJ
american_scientific_journal-3270	143	2	−∂	−∂	PROPN
american_scientific_journal-3270	143	3	∂	∂	NOUN
american_scientific_journal-3270	143	4	−	−	NOUN
american_scientific_journal-3270	144	1	=	=	SYM
american_scientific_journal-3270	144	2	−	−	PROPN
american_scientific_journal-3270	144	3	=	=	SYM
american_scientific_journal-3270	144	4	∂	∂	NUM
american_scientific_journal-3270	144	5	∂	∂	NOUN
american_scientific_journal-3270	144	6	,	,	PUNCT
american_scientific_journal-3270	144	7	(	(	PUNCT
american_scientific_journal-3270	144	8	2.18	2.18	NUM
american_scientific_journal-3270	144	9	)	)	PUNCT
american_scientific_journal-3270	144	10	in	in	ADP
american_scientific_journal-3270	144	11	addition	addition	NOUN
american_scientific_journal-3270	144	12	to	to	ADP
american_scientific_journal-3270	144	13	(	(	PUNCT
american_scientific_journal-3270	144	14	2.18	2.18	NUM
american_scientific_journal-3270	144	15	)	)	PUNCT
american_scientific_journal-3270	144	16	,	,	PUNCT
american_scientific_journal-3270	144	17	on	on	ADP
american_scientific_journal-3270	144	18	the	the	DET
american_scientific_journal-3270	144	19	interface	interface	NOUN
american_scientific_journal-3270	144	20	0,y	0,y	NOUN
american_scientific_journal-3270	145	1	=	=	PUNCT
american_scientific_journal-3270	145	2	we	we	PRON
american_scientific_journal-3270	145	3	have	have	VERB
american_scientific_journal-3270	145	4	the	the	DET
american_scientific_journal-3270	145	5	following	follow	VERB
american_scientific_journal-3270	145	6	conditions	condition	NOUN
american_scientific_journal-3270	145	7	2	2	NUM
american_scientific_journal-3270	145	8	3	3	NUM
american_scientific_journal-3270	145	9	2	2	NUM
american_scientific_journal-3270	145	10	30	30	NUM
american_scientific_journal-3270	145	11	,	,	PUNCT
american_scientific_journal-3270	145	12	0	0	NUM
american_scientific_journal-3270	145	13	,	,	PUNCT
american_scientific_journal-3270	145	14	(	(	PUNCT
american_scientific_journal-3270	145	15	0	0	NUM
american_scientific_journal-3270	145	16	,	,	PUNCT
american_scientific_journal-3270	145	17	0)yy	0)yy	PROPN
american_scientific_journal-3270	146	1	yy	yy	INTJ
american_scientific_journal-3270	147	1	xy	xy	INTJ
american_scientific_journal-3270	147	2	xy	xy	INTJ
american_scientific_journal-3270	148	1	x	x	X
american_scientific_journal-3270	149	1	yσ	yσ	PROPN
american_scientific_journal-3270	149	2	σ	σ	PROPN
american_scientific_journal-3270	149	3	σ	σ	PROPN
american_scientific_journal-3270	149	4	σ−	σ−	PROPN
american_scientific_journal-3270	149	5	=	=	SYM
american_scientific_journal-3270	149	6	−	−	NOUN
american_scientific_journal-3270	149	7	=	=	SYM
american_scientific_journal-3270	149	8	≤	≤	X
american_scientific_journal-3270	149	9	<	<	X
american_scientific_journal-3270	149	10	∞	∞	PROPN
american_scientific_journal-3270	149	11	=	=	PUNCT
american_scientific_journal-3270	149	12	.	.	PUNCT
american_scientific_journal-3270	150	1	(	(	PUNCT
american_scientific_journal-3270	150	2	2.19	2.19	NUM
american_scientific_journal-3270	150	3	)	)	PUNCT
american_scientific_journal-3270	150	4	after	after	ADP
american_scientific_journal-3270	150	5	some	some	DET
american_scientific_journal-3270	150	6	algebraic	algebraic	ADJ
american_scientific_journal-3270	150	7	relations	relation	NOUN
american_scientific_journal-3270	150	8	,	,	PUNCT
american_scientific_journal-3270	150	9	the	the	DET
american_scientific_journal-3270	150	10	components	component	NOUN
american_scientific_journal-3270	150	11	of	of	ADP
american_scientific_journal-3270	150	12	the	the	DET
american_scientific_journal-3270	150	13	stress	stress	NOUN
american_scientific_journal-3270	150	14	vector	vector	NOUN
american_scientific_journal-3270	150	15	at	at	ADP
american_scientific_journal-3270	150	16	0y	0y	NUM
american_scientific_journal-3270	150	17	=	=	SYM
american_scientific_journal-3270	150	18	and	and	CCONJ
american_scientific_journal-3270	150	19	0x	0x	PROPN
american_scientific_journal-3270	150	20	>	>	X
american_scientific_journal-3270	150	21	may	may	AUX
american_scientific_journal-3270	150	22	be	be	AUX
american_scientific_journal-3270	150	23	expressed	express	VERB
american_scientific_journal-3270	150	24	,	,	PUNCT
american_scientific_journal-3270	150	25	respectively	respectively	ADV
american_scientific_journal-3270	150	26	as	as	ADP
american_scientific_journal-3270	150	27	33	33	NUM
american_scientific_journal-3270	150	28	11	11	NUM
american_scientific_journal-3270	150	29	1	1	NUM
american_scientific_journal-3270	150	30	12	12	NUM
american_scientific_journal-3270	150	31	20	20	NUM
american_scientific_journal-3270	150	32	3	3	NUM
american_scientific_journal-3270	150	33	0	0	NUM
american_scientific_journal-3270	150	34	1	1	NUM
american_scientific_journal-3270	150	35	2	2	NUM
american_scientific_journal-3270	150	36	(	(	PUNCT
american_scientific_journal-3270	150	37	,	,	PUNCT
american_scientific_journal-3270	150	38	0	0	NUM
american_scientific_journal-3270	150	39	,	,	PUNCT
american_scientific_journal-3270	150	40	)	)	PUNCT
american_scientific_journal-3270	151	1	lim	lim	PROPN
american_scientific_journal-3270	151	2	{	{	PUNCT
american_scientific_journal-3270	151	3	(	(	PUNCT
american_scientific_journal-3270	151	4	,	,	PUNCT
american_scientific_journal-3270	151	5	)	)	PUNCT
american_scientific_journal-3270	151	6	(	(	PUNCT
american_scientific_journal-3270	151	7	,	,	PUNCT
american_scientific_journal-3270	151	8	)	)	PUNCT
american_scientific_journal-3270	151	9	}	}	PUNCT
american_scientific_journal-3270	151	10	cosx	cosx	PROPN
american_scientific_journal-3270	152	1	yy	yy	PROPN
american_scientific_journal-3270	152	2	y	y	PROPN
american_scientific_journal-3270	152	3	k	k	PROPN
american_scientific_journal-3270	153	1	x	x	PUNCT
american_scientific_journal-3270	153	2	t	t	PROPN
american_scientific_journal-3270	153	3	e	e	PROPN
american_scientific_journal-3270	153	4	a	a	DET
american_scientific_journal-3270	153	5	a	a	PROPN
american_scientific_journal-3270	153	6	t	t	NOUN
american_scientific_journal-3270	153	7	a	a	DET
american_scientific_journal-3270	153	8	a	a	DET
american_scientific_journal-3270	153	9	t	t	NOUN
american_scientific_journal-3270	153	10	xdασ	xdασ	PROPN
american_scientific_journal-3270	153	11	α	α	PROPN
american_scientific_journal-3270	153	12	α	α	NOUN
american_scientific_journal-3270	153	13	α	α	NOUN
american_scientific_journal-3270	153	14	α	α	NOUN
american_scientific_journal-3270	153	15	µ	µ	X
american_scientific_journal-3270	153	16	π−	π−	NOUN
american_scientific_journal-3270	153	17	∞	∞	PROPN
american_scientific_journal-3270	153	18	→	→	PUNCT
american_scientific_journal-3270	154	1	+	+	PUNCT
american_scientific_journal-3270	154	2	=	=	SYM
american_scientific_journal-3270	154	3	+	+	NUM
american_scientific_journal-3270	154	4	∫	∫	PROPN
american_scientific_journal-3270	154	5	+	+	NUM
american_scientific_journal-3270	154	6	11	11	NUM
american_scientific_journal-3270	154	7	1	1	NUM
american_scientific_journal-3270	154	8	12	12	NUM
american_scientific_journal-3270	154	9	2	2	NUM
american_scientific_journal-3270	154	10	0	0	NUM
american_scientific_journal-3270	154	11	0	0	NUM
american_scientific_journal-3270	154	12	2	2	NUM
american_scientific_journal-3270	154	13	{	{	PUNCT
american_scientific_journal-3270	154	14	(	(	PUNCT
american_scientific_journal-3270	154	15	)	)	PUNCT
american_scientific_journal-3270	154	16	(	(	PUNCT
american_scientific_journal-3270	154	17	,	,	PUNCT
american_scientific_journal-3270	154	18	)	)	PUNCT
american_scientific_journal-3270	154	19	(	(	PUNCT
american_scientific_journal-3270	154	20	)	)	PUNCT
american_scientific_journal-3270	154	21	(	(	PUNCT
american_scientific_journal-3270	154	22	,	,	PUNCT
american_scientific_journal-3270	154	23	)	)	PUNCT
american_scientific_journal-3270	154	24	}	}	PUNCT
american_scientific_journal-3270	154	25	cos	cos	PROPN
american_scientific_journal-3270	154	26	(	(	PUNCT
american_scientific_journal-3270	154	27	)	)	PUNCT
american_scientific_journal-3270	154	28	(	(	PUNCT
american_scientific_journal-3270	154	29	,	,	PUNCT
american_scientific_journal-3270	154	30	0	0	NUM
american_scientific_journal-3270	154	31	,	,	PUNCT
american_scientific_journal-3270	154	32	)	)	PUNCT
american_scientific_journal-3270	154	33	t	t	X
american_scientific_journal-3270	154	34	ih	ih	PRON
american_scientific_journal-3270	154	35	a	a	DET
american_scientific_journal-3270	154	36	t	t	NOUN
american_scientific_journal-3270	154	37	h	h	NOUN
american_scientific_journal-3270	154	38	a	a	DET
american_scientific_journal-3270	154	39	t	t	NOUN
american_scientific_journal-3270	155	1	xd	xd	INTJ
american_scientific_journal-3270	155	2	f	f	PROPN
american_scientific_journal-3270	155	3	f	f	PROPN
american_scientific_journal-3270	156	1	x	x	PROPN
american_scientific_journal-3270	156	2	dα	dα	ADP
american_scientific_journal-3270	156	3	α	α	NOUN
american_scientific_journal-3270	156	4	α	α	NOUN
american_scientific_journal-3270	156	5	α	α	NOUN
american_scientific_journal-3270	156	6	α	α	NOUN
american_scientific_journal-3270	157	1	α	α	NOUN
american_scientific_journal-3270	157	2	t	t	PROPN
american_scientific_journal-3270	157	3	t	t	X
american_scientific_journal-3270	157	4	t	t	PROPN
american_scientific_journal-3270	157	5	π	π	X
american_scientific_journal-3270	157	6	∞	∞	PROPN
american_scientific_journal-3270	158	1	+	+	CCONJ
american_scientific_journal-3270	158	2	+	+	NUM
american_scientific_journal-3270	158	3	∫	∫	PROPN
american_scientific_journal-3270	158	4	∫	∫	PROPN
american_scientific_journal-3270	158	5	,	,	PUNCT
american_scientific_journal-3270	158	6	(	(	PUNCT
american_scientific_journal-3270	158	7	2.20	2.20	NUM
american_scientific_journal-3270	158	8	)	)	PUNCT
american_scientific_journal-3270	158	9	33	33	NUM
american_scientific_journal-3270	158	10	21	21	NUM
american_scientific_journal-3270	158	11	1	1	NUM
american_scientific_journal-3270	158	12	22	22	NUM
american_scientific_journal-3270	158	13	20	20	NUM
american_scientific_journal-3270	158	14	3	3	NUM
american_scientific_journal-3270	158	15	0	0	NUM
american_scientific_journal-3270	158	16	1	1	NUM
american_scientific_journal-3270	158	17	2	2	NUM
american_scientific_journal-3270	158	18	(	(	PUNCT
american_scientific_journal-3270	158	19	,	,	PUNCT
american_scientific_journal-3270	158	20	0	0	NUM
american_scientific_journal-3270	158	21	,	,	PUNCT
american_scientific_journal-3270	158	22	)	)	PUNCT
american_scientific_journal-3270	158	23	lim	lim	PROPN
american_scientific_journal-3270	158	24	{	{	PUNCT
american_scientific_journal-3270	158	25	(	(	PUNCT
american_scientific_journal-3270	158	26	,	,	PUNCT
american_scientific_journal-3270	158	27	)	)	PUNCT
american_scientific_journal-3270	158	28	(	(	PUNCT
american_scientific_journal-3270	158	29	,	,	PUNCT
american_scientific_journal-3270	158	30	)	)	PUNCT
american_scientific_journal-3270	158	31	}	}	PUNCT
american_scientific_journal-3270	159	1	sinx	sinx	NOUN
american_scientific_journal-3270	159	2	xy	xy	PROPN
american_scientific_journal-3270	160	1	y	y	PROPN
american_scientific_journal-3270	160	2	k	k	PROPN
american_scientific_journal-3270	161	1	x	x	PUNCT
american_scientific_journal-3270	161	2	t	t	PROPN
american_scientific_journal-3270	161	3	e	e	PROPN
american_scientific_journal-3270	161	4	a	a	DET
american_scientific_journal-3270	161	5	a	a	PROPN
american_scientific_journal-3270	161	6	t	t	NOUN
american_scientific_journal-3270	161	7	a	a	DET
american_scientific_journal-3270	161	8	a	a	DET
american_scientific_journal-3270	161	9	t	t	NOUN
american_scientific_journal-3270	161	10	xdασ	xdασ	PROPN
american_scientific_journal-3270	161	11	α	α	PROPN
american_scientific_journal-3270	161	12	α	α	NOUN
american_scientific_journal-3270	161	13	α	α	NOUN
american_scientific_journal-3270	161	14	α	α	NOUN
american_scientific_journal-3270	161	15	µ	µ	X
american_scientific_journal-3270	161	16	π−	π−	NOUN
american_scientific_journal-3270	161	17	∞	∞	PROPN
american_scientific_journal-3270	161	18	→	→	PUNCT
american_scientific_journal-3270	162	1	+	+	NUM
american_scientific_journal-3270	162	2	−	−	PROPN
american_scientific_journal-3270	162	3	=	=	SYM
american_scientific_journal-3270	163	1	+	+	ADJ
american_scientific_journal-3270	163	2	∫	∫	PROPN
american_scientific_journal-3270	163	3	american	american	PROPN
american_scientific_journal-3270	163	4	scientific	scientific	PROPN
american_scientific_journal-3270	163	5	research	research	PROPN
american_scientific_journal-3270	163	6	journal	journal	NOUN
american_scientific_journal-3270	163	7	for	for	ADP
american_scientific_journal-3270	163	8	engineering	engineering	NOUN
american_scientific_journal-3270	163	9	,	,	PUNCT
american_scientific_journal-3270	163	10	technology	technology	NOUN
american_scientific_journal-3270	163	11	,	,	PUNCT
american_scientific_journal-3270	163	12	and	and	CCONJ
american_scientific_journal-3270	163	13	sciences	science	NOUN
american_scientific_journal-3270	163	14	(	(	PUNCT
american_scientific_journal-3270	163	15	asrjets	asrjet	NOUN
american_scientific_journal-3270	163	16	)	)	PUNCT
american_scientific_journal-3270	163	17	(	(	PUNCT
american_scientific_journal-3270	163	18	2017	2017	NUM
american_scientific_journal-3270	163	19	)	)	PUNCT
american_scientific_journal-3270	163	20	volume	volume	NOUN
american_scientific_journal-3270	163	21	34	34	NUM
american_scientific_journal-3270	163	22	,	,	PUNCT
american_scientific_journal-3270	163	23	no	no	DET
american_scientific_journal-3270	163	24	1	1	NUM
american_scientific_journal-3270	163	25	,	,	PUNCT
american_scientific_journal-3270	163	26	pp	pp	ADV
american_scientific_journal-3270	163	27	213	213	NUM
american_scientific_journal-3270	163	28	-	-	SYM
american_scientific_journal-3270	163	29	230	230	NUM
american_scientific_journal-3270	163	30	218	218	NUM
american_scientific_journal-3270	163	31	+	+	CCONJ
american_scientific_journal-3270	163	32	21	21	NUM
american_scientific_journal-3270	163	33	1	1	NUM
american_scientific_journal-3270	163	34	22	22	NUM
american_scientific_journal-3270	163	35	2	2	NUM
american_scientific_journal-3270	163	36	0	0	NUM
american_scientific_journal-3270	163	37	0	0	NUM
american_scientific_journal-3270	163	38	2	2	NUM
american_scientific_journal-3270	163	39	{	{	PUNCT
american_scientific_journal-3270	163	40	(	(	PUNCT
american_scientific_journal-3270	163	41	)	)	PUNCT
american_scientific_journal-3270	163	42	(	(	PUNCT
american_scientific_journal-3270	163	43	,	,	PUNCT
american_scientific_journal-3270	163	44	)	)	PUNCT
american_scientific_journal-3270	163	45	(	(	PUNCT
american_scientific_journal-3270	163	46	)	)	PUNCT
american_scientific_journal-3270	163	47	(	(	PUNCT
american_scientific_journal-3270	163	48	,	,	PUNCT
american_scientific_journal-3270	163	49	)	)	PUNCT
american_scientific_journal-3270	163	50	}	}	PUNCT
american_scientific_journal-3270	163	51	sin	sin	NOUN
american_scientific_journal-3270	163	52	(	(	PUNCT
american_scientific_journal-3270	163	53	)	)	PUNCT
american_scientific_journal-3270	163	54	(	(	PUNCT
american_scientific_journal-3270	163	55	,	,	PUNCT
american_scientific_journal-3270	163	56	0	0	NUM
american_scientific_journal-3270	163	57	,	,	PUNCT
american_scientific_journal-3270	163	58	)	)	PUNCT
american_scientific_journal-3270	163	59	t	t	X
american_scientific_journal-3270	163	60	ih	ih	PRON
american_scientific_journal-3270	163	61	a	a	DET
american_scientific_journal-3270	163	62	t	t	NOUN
american_scientific_journal-3270	163	63	h	h	NOUN
american_scientific_journal-3270	163	64	a	a	DET
american_scientific_journal-3270	163	65	t	t	NOUN
american_scientific_journal-3270	164	1	xd	xd	INTJ
american_scientific_journal-3270	164	2	f	f	PROPN
american_scientific_journal-3270	164	3	f	f	PROPN
american_scientific_journal-3270	165	1	x	x	PROPN
american_scientific_journal-3270	165	2	dα	dα	ADP
american_scientific_journal-3270	165	3	α	α	NOUN
american_scientific_journal-3270	165	4	α	α	NOUN
american_scientific_journal-3270	165	5	α	α	NOUN
american_scientific_journal-3270	165	6	α	α	NOUN
american_scientific_journal-3270	166	1	α	α	NOUN
american_scientific_journal-3270	166	2	t	t	PROPN
american_scientific_journal-3270	166	3	t	t	X
american_scientific_journal-3270	166	4	t	t	PROPN
american_scientific_journal-3270	166	5	π	π	X
american_scientific_journal-3270	166	6	∞	∞	PROPN
american_scientific_journal-3270	167	1	+	+	CCONJ
american_scientific_journal-3270	168	1	+	+	NUM
american_scientific_journal-3270	168	2	∫	∫	PROPN
american_scientific_journal-3270	168	3	∫	∫	PROPN
american_scientific_journal-3270	168	4	,	,	PUNCT
american_scientific_journal-3270	168	5	(	(	PUNCT
american_scientific_journal-3270	168	6	2.21	2.21	NUM
american_scientific_journal-3270	168	7	)	)	PUNCT
american_scientific_journal-3270	168	8	where	where	SCONJ
american_scientific_journal-3270	168	9	,	,	PUNCT
american_scientific_journal-3270	168	10	(	(	PUNCT
american_scientific_journal-3270	168	11	)	)	PUNCT
american_scientific_journal-3270	168	12	i	i	PRON
american_scientific_journal-3270	168	13	jh	jh	PROPN
american_scientific_journal-3270	168	14	α	α	PROPN
american_scientific_journal-3270	168	15	are	be	AUX
american_scientific_journal-3270	168	16	the	the	DET
american_scientific_journal-3270	168	17	heaviside	heaviside	ADJ
american_scientific_journal-3270	168	18	functions	function	NOUN
american_scientific_journal-3270	168	19	and	and	CCONJ
american_scientific_journal-3270	168	20	ia	ia	PROPN
american_scientific_journal-3270	168	21	are	be	AUX
american_scientific_journal-3270	168	22	the	the	DET
american_scientific_journal-3270	168	23	fourier	fourier	NOUN
american_scientific_journal-3270	168	24	transforms	transform	VERB
american_scientific_journal-3270	168	25	of	of	ADP
american_scientific_journal-3270	168	26	if	if	SCONJ
american_scientific_journal-3270	168	27	defined	define	VERB
american_scientific_journal-3270	168	28	as	as	SCONJ
american_scientific_journal-3270	168	29	follows	follow	VERB
american_scientific_journal-3270	169	1	1	1	NUM
american_scientific_journal-3270	169	2	1	1	NUM
american_scientific_journal-3270	169	3	2	2	NUM
american_scientific_journal-3270	169	4	2	2	NUM
american_scientific_journal-3270	169	5	0	0	NUM
american_scientific_journal-3270	169	6	0	0	NUM
american_scientific_journal-3270	169	7	(	(	PUNCT
american_scientific_journal-3270	169	8	,	,	PUNCT
american_scientific_journal-3270	169	9	)	)	PUNCT
american_scientific_journal-3270	169	10	(	(	PUNCT
american_scientific_journal-3270	169	11	,	,	PUNCT
american_scientific_journal-3270	169	12	)	)	PUNCT
american_scientific_journal-3270	169	13	cos	cos	PROPN
american_scientific_journal-3270	169	14	;	;	PUNCT
american_scientific_journal-3270	169	15	(	(	PUNCT
american_scientific_journal-3270	169	16	,	,	PUNCT
american_scientific_journal-3270	169	17	)	)	PUNCT
american_scientific_journal-3270	169	18	(	(	PUNCT
american_scientific_journal-3270	169	19	,	,	PUNCT
american_scientific_journal-3270	169	20	)	)	PUNCT
american_scientific_journal-3270	169	21	sina	sina	PROPN
american_scientific_journal-3270	169	22	t	t	PROPN
american_scientific_journal-3270	170	1	f	f	PROPN
american_scientific_journal-3270	170	2	z	z	PROPN
american_scientific_journal-3270	170	3	t	t	PROPN
american_scientific_journal-3270	170	4	z	z	PROPN
american_scientific_journal-3270	170	5	dz	dz	PROPN
american_scientific_journal-3270	170	6	a	a	DET
american_scientific_journal-3270	170	7	t	t	NOUN
american_scientific_journal-3270	170	8	f	f	PROPN
american_scientific_journal-3270	170	9	z	z	PROPN
american_scientific_journal-3270	170	10	t	t	PROPN
american_scientific_journal-3270	171	1	zdzα	zdzα	NOUN
american_scientific_journal-3270	171	2	α	α	NOUN
american_scientific_journal-3270	171	3	α	α	NOUN
american_scientific_journal-3270	172	1	α	α	NOUN
american_scientific_journal-3270	172	2	∞	∞	NOUN
american_scientific_journal-3270	172	3	∞	∞	NUM
american_scientific_journal-3270	172	4	=	=	PUNCT
american_scientific_journal-3270	173	1	=	=	NUM
american_scientific_journal-3270	173	2	∫	∫	PROPN
american_scientific_journal-3270	173	3	∫	∫	PROPN
american_scientific_journal-3270	173	4	,	,	PUNCT
american_scientific_journal-3270	173	5	.	.	PUNCT
american_scientific_journal-3270	174	1	(	(	PUNCT
american_scientific_journal-3270	174	2	2.22	2.22	NUM
american_scientific_journal-3270	174	3	)	)	PUNCT
american_scientific_journal-3270	174	4	the	the	DET
american_scientific_journal-3270	174	5	constants	constant	NOUN
american_scientific_journal-3270	174	6	ija	ija	NOUN
american_scientific_journal-3270	174	7	depend	depend	VERB
american_scientific_journal-3270	174	8	on	on	ADP
american_scientific_journal-3270	174	9	the	the	DET
american_scientific_journal-3270	174	10	elastic	elastic	ADJ
american_scientific_journal-3270	174	11	properties	property	NOUN
american_scientific_journal-3270	174	12	of	of	ADP
american_scientific_journal-3270	174	13	the	the	DET
american_scientific_journal-3270	174	14	materials	material	NOUN
american_scientific_journal-3270	174	15	adjacent	adjacent	ADJ
american_scientific_journal-3270	174	16	to	to	ADP
american_scientific_journal-3270	174	17	the	the	DET
american_scientific_journal-3270	174	18	crack	crack	NOUN
american_scientific_journal-3270	174	19	only	only	ADV
american_scientific_journal-3270	174	20	and	and	CCONJ
american_scientific_journal-3270	174	21	are	be	AUX
american_scientific_journal-3270	174	22	given	give	VERB
american_scientific_journal-3270	174	23	by	by	ADP
american_scientific_journal-3270	174	24	11	11	NUM
american_scientific_journal-3270	174	25	22	22	NUM
american_scientific_journal-3270	174	26	2	2	NUM
american_scientific_journal-3270	174	27	4	4	NUM
american_scientific_journal-3270	174	28	4	4	NUM
american_scientific_journal-3270	174	29	12	12	NUM
american_scientific_journal-3270	174	30	21	21	NUM
american_scientific_journal-3270	174	31	4	4	NUM
american_scientific_journal-3270	174	32	2	2	NUM
american_scientific_journal-3270	174	33	4	4	NUM
american_scientific_journal-3270	174	34	4(1	4(1	NOUN
american_scientific_journal-3270	174	35	)	)	PUNCT
american_scientific_journal-3270	174	36	/	/	PUNCT
american_scientific_journal-3270	174	37	,	,	PUNCT
american_scientific_journal-3270	174	38	(	(	PUNCT
american_scientific_journal-3270	174	39	1	1	NUM
american_scientific_journal-3270	174	40	2	2	NUM
american_scientific_journal-3270	174	41	)	)	PUNCT
american_scientific_journal-3270	174	42	/a	/a	PUNCT
american_scientific_journal-3270	175	1	a	a	DET
american_scientific_journal-3270	175	2	a	a	DET
american_scientific_journal-3270	175	3	aλ	aλ	ADP
american_scientific_journal-3270	175	4	λ	λ	X
american_scientific_journal-3270	175	5	λ	λ	NOUN
american_scientific_journal-3270	175	6	λ	λ	X
american_scientific_journal-3270	175	7	λ	λ	X
american_scientific_journal-3270	175	8	λ	λ	X
american_scientific_journal-3270	175	9	λ=	λ=	VERB
american_scientific_journal-3270	175	10	−	−	PROPN
american_scientific_journal-3270	175	11	=	=	SYM
american_scientific_journal-3270	176	1	+	+	NUM
american_scientific_journal-3270	176	2	=	=	SYM
american_scientific_journal-3270	176	3	−	−	PROPN
american_scientific_journal-3270	176	4	=	=	PUNCT
american_scientific_journal-3270	176	5	−	−	PROPN
american_scientific_journal-3270	177	1	+	+	CCONJ
american_scientific_journal-3270	177	2	−	−	PROPN
american_scientific_journal-3270	177	3	,	,	PUNCT
american_scientific_journal-3270	177	4	2	2	NUM
american_scientific_journal-3270	177	5	2	2	NUM
american_scientific_journal-3270	177	6	3	3	NUM
american_scientific_journal-3270	177	7	3	3	NUM
american_scientific_journal-3270	177	8	2	2	NUM
american_scientific_journal-3270	177	9	2	2	NUM
american_scientific_journal-3270	177	10	2	2	NUM
american_scientific_journal-3270	177	11	3	3	NUM
american_scientific_journal-3270	177	12	4	4	NUM
american_scientific_journal-3270	177	13	3	3	NUM
american_scientific_journal-3270	177	14	2	2	NUM
american_scientific_journal-3270	177	15	3	3	NUM
american_scientific_journal-3270	177	16	2	2	NUM
american_scientific_journal-3270	177	17	3	3	NUM
american_scientific_journal-3270	177	18	(	(	PUNCT
american_scientific_journal-3270	177	19	)	)	PUNCT
american_scientific_journal-3270	177	20	/	/	SYM
american_scientific_journal-3270	177	21	(	(	PUNCT
american_scientific_journal-3270	177	22	)	)	PUNCT
american_scientific_journal-3270	177	23	,	,	PUNCT
american_scientific_journal-3270	177	24	(	(	PUNCT
american_scientific_journal-3270	177	25	)	)	PUNCT
american_scientific_journal-3270	177	26	/	/	SYM
american_scientific_journal-3270	177	27	(	(	PUNCT
american_scientific_journal-3270	177	28	)	)	PUNCT
american_scientific_journal-3270	177	29	k	k	PROPN
american_scientific_journal-3270	178	1	k	k	PROPN
american_scientific_journal-3270	178	2	k	k	PROPN
american_scientific_journal-3270	178	3	kλ	kλ	X
american_scientific_journal-3270	178	4	µ	µ	PROPN
american_scientific_journal-3270	178	5	µ	µ	X
american_scientific_journal-3270	178	6	µ	µ	X
american_scientific_journal-3270	178	7	µ	µ	X
american_scientific_journal-3270	178	8	λ	λ	X
american_scientific_journal-3270	178	9	µ	µ	X
american_scientific_journal-3270	178	10	µ	µ	X
american_scientific_journal-3270	178	11	µ	µ	X
american_scientific_journal-3270	178	12	µ=	µ=	NOUN
american_scientific_journal-3270	178	13	−	−	PROPN
american_scientific_journal-3270	179	1	+	+	CCONJ
american_scientific_journal-3270	179	2	=	=	SYM
american_scientific_journal-3270	180	1	+	+	CCONJ
american_scientific_journal-3270	180	2	−	−	PROPN
american_scientific_journal-3270	180	3	.	.	PUNCT
american_scientific_journal-3270	181	1	(	(	PUNCT
american_scientific_journal-3270	181	2	2.23	2.23	NUM
american_scientific_journal-3270	181	3	)	)	PUNCT
american_scientific_journal-3270	181	4	here	here	ADV
american_scientific_journal-3270	181	5	,	,	PUNCT
american_scientific_journal-3270	181	6	iµ	iµ	PROPN
american_scientific_journal-3270	181	7	is	be	AUX
american_scientific_journal-3270	181	8	the	the	DET
american_scientific_journal-3270	181	9	shear	shear	NOUN
american_scientific_journal-3270	181	10	modulus	modulus	NOUN
american_scientific_journal-3270	181	11	and	and	CCONJ
american_scientific_journal-3270	181	12	'	'	PUNCT
american_scientific_journal-3270	181	13	sλ	sλ	NOUN
american_scientific_journal-3270	181	14	are	be	AUX
american_scientific_journal-3270	181	15	lame	lame	NOUN
american_scientific_journal-3270	181	16	’s	’s	PART
american_scientific_journal-3270	181	17	constants	constant	NOUN
american_scientific_journal-3270	181	18	.	.	PUNCT
american_scientific_journal-3270	182	1	the	the	DET
american_scientific_journal-3270	182	2	integrals	integral	NOUN
american_scientific_journal-3270	182	3	on	on	ADP
american_scientific_journal-3270	182	4	the	the	DET
american_scientific_journal-3270	182	5	right	right	ADJ
american_scientific_journal-3270	182	6	hand	hand	NOUN
american_scientific_journal-3270	182	7	side	side	NOUN
american_scientific_journal-3270	182	8	are	be	AUX
american_scientific_journal-3270	182	9	uniformity	uniformity	NOUN
american_scientific_journal-3270	182	10	convergent	convergent	NOUN
american_scientific_journal-3270	182	11	.	.	PUNCT
american_scientific_journal-3270	183	1	the	the	DET
american_scientific_journal-3270	183	2	formulas	formula	NOUN
american_scientific_journal-3270	183	3	(	(	PUNCT
american_scientific_journal-3270	183	4	2.20)-(2.22	2.20)-(2.22	NUM
american_scientific_journal-3270	183	5	)	)	PUNCT
american_scientific_journal-3270	183	6	give	give	VERB
american_scientific_journal-3270	183	7	the	the	DET
american_scientific_journal-3270	183	8	stresses	stress	NOUN
american_scientific_journal-3270	183	9	components	component	NOUN
american_scientific_journal-3270	183	10	for	for	ADP
american_scientific_journal-3270	183	11	all	all	DET
american_scientific_journal-3270	183	12	values	value	NOUN
american_scientific_journal-3270	183	13	of	of	ADP
american_scientific_journal-3270	183	14	x	x	X
american_scientific_journal-3270	183	15	.	.	PUNCT
american_scientific_journal-3270	184	1	the	the	DET
american_scientific_journal-3270	184	2	crack	crack	NOUN
american_scientific_journal-3270	184	3	problem	problem	NOUN
american_scientific_journal-3270	184	4	under	under	ADP
american_scientific_journal-3270	184	5	consideration	consideration	NOUN
american_scientific_journal-3270	184	6	(	(	PUNCT
american_scientific_journal-3270	184	7	,	,	PUNCT
american_scientific_journal-3270	184	8	)	)	PUNCT
american_scientific_journal-3270	184	9	if	if	SCONJ
american_scientific_journal-3270	184	10	x	x	PROPN
american_scientific_journal-3270	184	11	t	t	PROPN
american_scientific_journal-3270	184	12	are	be	AUX
american_scientific_journal-3270	184	13	zero	zero	NUM
american_scientific_journal-3270	184	14	for	for	ADP
american_scientific_journal-3270	184	15	1x	1x	PROPN
american_scientific_journal-3270	184	16	>	>	X
american_scientific_journal-3270	184	17	and	and	CCONJ
american_scientific_journal-3270	184	18	are	be	AUX
american_scientific_journal-3270	184	19	unknown	unknown	ADJ
american_scientific_journal-3270	184	20	for	for	ADP
american_scientific_journal-3270	184	21	1x	1x	NUM
american_scientific_journal-3270	184	22	<	<	X
american_scientific_journal-3270	184	23	.	.	PUNCT
american_scientific_journal-3270	185	1	on	on	ADP
american_scientific_journal-3270	185	2	the	the	DET
american_scientific_journal-3270	185	3	other	other	ADJ
american_scientific_journal-3270	185	4	hand	hand	NOUN
american_scientific_journal-3270	185	5	,	,	PUNCT
american_scientific_journal-3270	185	6	the	the	DET
american_scientific_journal-3270	185	7	stress	stress	NOUN
american_scientific_journal-3270	185	8	vector	vector	NOUN
american_scientific_journal-3270	185	9	on	on	ADP
american_scientific_journal-3270	185	10	the	the	DET
american_scientific_journal-3270	185	11	interface	interface	NOUN
american_scientific_journal-3270	185	12	0y	0y	NOUN
american_scientific_journal-3270	185	13	=	=	PUNCT
american_scientific_journal-3270	185	14	is	be	AUX
american_scientific_journal-3270	185	15	unknown	unknown	ADJ
american_scientific_journal-3270	185	16	for	for	ADP
american_scientific_journal-3270	185	17	1x	1x	NUM
american_scientific_journal-3270	185	18	>	>	PUNCT
american_scientific_journal-3270	185	19	and	and	CCONJ
american_scientific_journal-3270	185	20	is	be	AUX
american_scientific_journal-3270	185	21	given	give	VERB
american_scientific_journal-3270	185	22	as	as	ADP
american_scientific_journal-3270	185	23	known	know	VERB
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american_scientific_journal-3270	185	25	for	for	ADP
american_scientific_journal-3270	185	26	1x	1x	PRON
american_scientific_journal-3270	185	27	<	<	X
american_scientific_journal-3270	185	28	i.e.	i.e.	X
american_scientific_journal-3270	185	29	3	3	NUM
american_scientific_journal-3270	185	30	3	3	NUM
american_scientific_journal-3270	185	31	1	1	NUM
american_scientific_journal-3270	185	32	2	2	NUM
american_scientific_journal-3270	185	33	(	(	PUNCT
american_scientific_journal-3270	185	34	,	,	PUNCT
american_scientific_journal-3270	185	35	0	0	NUM
american_scientific_journal-3270	185	36	,	,	PUNCT
american_scientific_journal-3270	185	37	)	)	PUNCT
american_scientific_journal-3270	185	38	(	(	PUNCT
american_scientific_journal-3270	185	39	,	,	PUNCT
american_scientific_journal-3270	185	40	)	)	PUNCT
american_scientific_journal-3270	185	41	,	,	PUNCT
american_scientific_journal-3270	185	42	(	(	PUNCT
american_scientific_journal-3270	185	43	,	,	PUNCT
american_scientific_journal-3270	185	44	0	0	NUM
american_scientific_journal-3270	185	45	,	,	PUNCT
american_scientific_journal-3270	185	46	)	)	PUNCT
american_scientific_journal-3270	185	47	(	(	PUNCT
american_scientific_journal-3270	185	48	,	,	PUNCT
american_scientific_journal-3270	185	49	)	)	PUNCT
american_scientific_journal-3270	185	50	,	,	PUNCT
american_scientific_journal-3270	185	51	1yy	1yy	PROPN
american_scientific_journal-3270	185	52	xyx	xyx	PROPN
american_scientific_journal-3270	185	53	t	t	PROPN
american_scientific_journal-3270	185	54	p	p	X
american_scientific_journal-3270	185	55	x	x	X
american_scientific_journal-3270	185	56	t	t	X
american_scientific_journal-3270	185	57	x	x	X
american_scientific_journal-3270	185	58	t	t	PROPN
american_scientific_journal-3270	185	59	p	p	X
american_scientific_journal-3270	185	60	x	x	X
american_scientific_journal-3270	185	61	t	t	NOUN
american_scientific_journal-3270	185	62	xσ	xσ	NOUN
american_scientific_journal-3270	185	63	σ=	σ=	X
american_scientific_journal-3270	186	1	=	=	PUNCT
american_scientific_journal-3270	186	2	<	<	X
american_scientific_journal-3270	186	3	.	.	PUNCT
american_scientific_journal-3270	187	1	(	(	PUNCT
american_scientific_journal-3270	187	2	2.24	2.24	NUM
american_scientific_journal-3270	187	3	)	)	PUNCT
american_scientific_journal-3270	187	4	using	use	VERB
american_scientific_journal-3270	187	5	above	above	ADP
american_scientific_journal-3270	187	6	information	information	NOUN
american_scientific_journal-3270	187	7	and	and	CCONJ
american_scientific_journal-3270	187	8	the	the	DET
american_scientific_journal-3270	187	9	following	follow	VERB
american_scientific_journal-3270	187	10	symmetric	symmetric	ADJ
american_scientific_journal-3270	187	11	properties	property	NOUN
american_scientific_journal-3270	187	12	in	in	ADP
american_scientific_journal-3270	187	13	the	the	DET
american_scientific_journal-3270	187	14	presence	presence	NOUN
american_scientific_journal-3270	187	15	of	of	ADP
american_scientific_journal-3270	187	16	time	time	NOUN
american_scientific_journal-3270	187	17	1	1	NUM
american_scientific_journal-3270	187	18	1	1	NUM
american_scientific_journal-3270	187	19	2	2	NUM
american_scientific_journal-3270	187	20	2	2	NUM
american_scientific_journal-3270	187	21	(	(	PUNCT
american_scientific_journal-3270	187	22	,	,	PUNCT
american_scientific_journal-3270	187	23	)	)	PUNCT
american_scientific_journal-3270	187	24	(	(	PUNCT
american_scientific_journal-3270	187	25	,	,	PUNCT
american_scientific_journal-3270	187	26	)	)	PUNCT
american_scientific_journal-3270	187	27	;	;	PUNCT
american_scientific_journal-3270	187	28	(	(	PUNCT
american_scientific_journal-3270	187	29	,	,	PUNCT
american_scientific_journal-3270	187	30	)	)	PUNCT
american_scientific_journal-3270	187	31	(	(	PUNCT
american_scientific_journal-3270	187	32	,	,	PUNCT
american_scientific_journal-3270	187	33	)	)	PUNCT
american_scientific_journal-3270	187	34	f	f	PROPN
american_scientific_journal-3270	188	1	x	x	X
american_scientific_journal-3270	188	2	t	t	NOUN
american_scientific_journal-3270	189	1	f	f	X
american_scientific_journal-3270	189	2	x	x	X
american_scientific_journal-3270	190	1	t	t	NOUN
american_scientific_journal-3270	190	2	f	f	X
american_scientific_journal-3270	191	1	x	x	X
american_scientific_journal-3270	191	2	t	t	NOUN
american_scientific_journal-3270	191	3	f	f	X
american_scientific_journal-3270	191	4	x	x	X
american_scientific_journal-3270	191	5	t=	t=	ADJ
american_scientific_journal-3270	191	6	−	−	PROPN
american_scientific_journal-3270	191	7	=	=	PUNCT
american_scientific_journal-3270	192	1	−	−	PROPN
american_scientific_journal-3270	192	2	−	−	NOUN
american_scientific_journal-3270	192	3	,	,	PUNCT
american_scientific_journal-3270	192	4	we	we	PRON
american_scientific_journal-3270	192	5	get	get	VERB
american_scientific_journal-3270	192	6	1	1	NUM
american_scientific_journal-3270	192	7	1	1	NUM
american_scientific_journal-3270	192	8	3	3	NUM
american_scientific_journal-3270	192	9	11	11	NUM
american_scientific_journal-3270	192	10	12	12	NUM
american_scientific_journal-3270	192	11	1	1	NUM
american_scientific_journal-3270	192	12	1	1	NUM
american_scientific_journal-3270	192	13	20	20	NUM
american_scientific_journal-3270	192	14	3	3	NUM
american_scientific_journal-3270	192	15	1	1	NUM
american_scientific_journal-3270	192	16	0	0	NUM
american_scientific_journal-3270	192	17	1	1	NUM
american_scientific_journal-3270	192	18	1	1	NUM
american_scientific_journal-3270	192	19	(	(	PUNCT
american_scientific_journal-3270	192	20	,	,	PUNCT
american_scientific_journal-3270	192	21	)	)	PUNCT
american_scientific_journal-3270	192	22	lim	lim	PROPN
american_scientific_journal-3270	192	23	(	(	PUNCT
american_scientific_journal-3270	192	24	,	,	PUNCT
american_scientific_journal-3270	192	25	)	)	PUNCT
american_scientific_journal-3270	192	26	cos	cos	PROPN
american_scientific_journal-3270	192	27	(	(	PUNCT
american_scientific_journal-3270	192	28	)	)	PUNCT
american_scientific_journal-3270	192	29	(	(	PUNCT
american_scientific_journal-3270	192	30	,	,	PUNCT
american_scientific_journal-3270	192	31	)	)	PUNCT
american_scientific_journal-3270	193	1	y	y	PROPN
american_scientific_journal-3270	193	2	y	y	PROPN
american_scientific_journal-3270	193	3	k	k	PROPN
american_scientific_journal-3270	193	4	a	a	PROPN
american_scientific_journal-3270	194	1	ap	ap	PROPN
american_scientific_journal-3270	194	2	x	x	PROPN
american_scientific_journal-3270	195	1	t	t	PROPN
american_scientific_journal-3270	195	2	f	f	PROPN
american_scientific_journal-3270	195	3	z	z	PROPN
american_scientific_journal-3270	195	4	t	t	PROPN
american_scientific_journal-3270	195	5	dz	dz	PROPN
american_scientific_journal-3270	195	6	e	e	PROPN
american_scientific_journal-3270	195	7	z	z	NOUN
american_scientific_journal-3270	195	8	x	x	PUNCT
american_scientific_journal-3270	196	1	d	d	NOUN
american_scientific_journal-3270	196	2	f	f	PROPN
american_scientific_journal-3270	196	3	z	z	PROPN
american_scientific_journal-3270	196	4	t	t	PROPN
american_scientific_journal-3270	196	5	dzα	dzα	PROPN
american_scientific_journal-3270	196	6	α	α	PROPN
american_scientific_journal-3270	196	7	α	α	NOUN
american_scientific_journal-3270	196	8	µ	µ	PROPN
american_scientific_journal-3270	196	9	π	π	X
american_scientific_journal-3270	196	10	π−	π−	NOUN
american_scientific_journal-3270	196	11	∞	∞	PROPN
american_scientific_journal-3270	196	12	→	→	SYM
american_scientific_journal-3270	196	13	−	−	PROPN
american_scientific_journal-3270	196	14	−	−	NOUN
american_scientific_journal-3270	196	15	+	+	SYM
american_scientific_journal-3270	196	16	−	−	PROPN
american_scientific_journal-3270	196	17	=	=	SYM
american_scientific_journal-3270	197	1	−	−	PROPN
american_scientific_journal-3270	197	2	+	+	NUM
american_scientific_journal-3270	197	3	×	×	X
american_scientific_journal-3270	197	4			X
american_scientific_journal-3270	198	1	∫	∫	PROPN
american_scientific_journal-3270	198	2	∫	∫	PROPN
american_scientific_journal-3270	198	3	∫	∫	PROPN
american_scientific_journal-3270	199	1	1	1	NUM
american_scientific_journal-3270	199	2	2	2	NUM
american_scientific_journal-3270	199	3	1	1	NUM
american_scientific_journal-3270	199	4	1	1	NUM
american_scientific_journal-3270	199	5	10	10	NUM
american_scientific_journal-3270	199	6	1	1	NUM
american_scientific_journal-3270	199	7	0	0	NUM
american_scientific_journal-3270	199	8	1sin	1sin	NOUN
american_scientific_journal-3270	199	9	(	(	PUNCT
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american_scientific_journal-3270	199	11	(	(	PUNCT
american_scientific_journal-3270	199	12	,	,	PUNCT
american_scientific_journal-3270	199	13	)	)	PUNCT
american_scientific_journal-3270	199	14	(	(	PUNCT
american_scientific_journal-3270	199	15	,	,	PUNCT
american_scientific_journal-3270	199	16	)	)	PUNCT
american_scientific_journal-3270	199	17	(	(	PUNCT
american_scientific_journal-3270	199	18	)	)	PUNCT
american_scientific_journal-3270	199	19	(	(	PUNCT
american_scientific_journal-3270	199	20	,	,	PUNCT
american_scientific_journal-3270	199	21	)	)	PUNCT
american_scientific_journal-3270	199	22	t	t	PROPN
american_scientific_journal-3270	200	1	y	y	PROPN
american_scientific_journal-3270	200	2	j	j	PROPN
american_scientific_journal-3270	200	3	j	j	PROPN
american_scientific_journal-3270	200	4	j	j	PROPN
american_scientific_journal-3270	201	1	e	e	PROPN
american_scientific_journal-3270	201	2	z	z	NOUN
american_scientific_journal-3270	201	3	x	x	PUNCT
american_scientific_journal-3270	202	1	d	d	X
american_scientific_journal-3270	202	2	k	k	X
american_scientific_journal-3270	202	3	x	x	X
american_scientific_journal-3270	202	4	z	z	NOUN
american_scientific_journal-3270	202	5	f	f	PROPN
american_scientific_journal-3270	202	6	z	z	NOUN
american_scientific_journal-3270	202	7	t	t	PROPN
american_scientific_journal-3270	202	8	dz	dz	PROPN
american_scientific_journal-3270	203	1	f	f	PROPN
american_scientific_journal-3270	203	2	f	f	PROPN
american_scientific_journal-3270	203	3	x	x	PROPN
american_scientific_journal-3270	203	4	dα	dα	ADP
american_scientific_journal-3270	203	5	α	α	NOUN
american_scientific_journal-3270	203	6	α	α	NOUN
american_scientific_journal-3270	204	1	t	t	PROPN
american_scientific_journal-3270	204	2	t	t	X
american_scientific_journal-3270	204	3	t	t	PROPN
american_scientific_journal-3270	204	4	π	π	X
american_scientific_journal-3270	204	5	∞	∞	PROPN
american_scientific_journal-3270	204	6	=	=	SYM
american_scientific_journal-3270	204	7	−	−	PROPN
american_scientific_journal-3270	204	8			NUM
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american_scientific_journal-3270	204	10	+	+	CCONJ
american_scientific_journal-3270	204	11	+	+	CCONJ
american_scientific_journal-3270	204	12			PROPN
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american_scientific_journal-3270	204	14	∑∫	∑∫	PROPN
american_scientific_journal-3270	204	15	∫	∫	PROPN
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american_scientific_journal-3270	204	17	,	,	PUNCT
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american_scientific_journal-3270	204	19	1	1	NUM
american_scientific_journal-3270	204	20	1	1	NUM
american_scientific_journal-3270	204	21	3	3	NUM
american_scientific_journal-3270	204	22	21	21	NUM
american_scientific_journal-3270	204	23	22	22	NUM
american_scientific_journal-3270	204	24	3	3	NUM
american_scientific_journal-3270	204	25	1	1	NUM
american_scientific_journal-3270	204	26	20	20	NUM
american_scientific_journal-3270	204	27	3	3	NUM
american_scientific_journal-3270	204	28	1	1	NUM
american_scientific_journal-3270	204	29	0	0	NUM
american_scientific_journal-3270	204	30	1	1	NUM
american_scientific_journal-3270	204	31	0	0	NUM
american_scientific_journal-3270	204	32	1	1	NUM
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american_scientific_journal-3270	204	35	)	)	PUNCT
american_scientific_journal-3270	204	36	lim	lim	PROPN
american_scientific_journal-3270	204	37	(	(	PUNCT
american_scientific_journal-3270	204	38	,	,	PUNCT
american_scientific_journal-3270	204	39	)	)	PUNCT
american_scientific_journal-3270	204	40	sin	sin	NOUN
american_scientific_journal-3270	204	41	(	(	PUNCT
american_scientific_journal-3270	204	42	)	)	PUNCT
american_scientific_journal-3270	204	43	(	(	PUNCT
american_scientific_journal-3270	204	44	,	,	PUNCT
american_scientific_journal-3270	204	45	)	)	PUNCT
american_scientific_journal-3270	204	46	cos	cos	PROPN
american_scientific_journal-3270	204	47	(	(	PUNCT
american_scientific_journal-3270	204	48	)	)	PUNCT
american_scientific_journal-3270	204	49	y	y	PROPN
american_scientific_journal-3270	204	50	y	y	PROPN
american_scientific_journal-3270	204	51	y	y	PROPN
american_scientific_journal-3270	204	52	k	k	PROPN
american_scientific_journal-3270	205	1	a	a	PROPN
american_scientific_journal-3270	205	2	ap	ap	PROPN
american_scientific_journal-3270	206	1	x	x	PROPN
american_scientific_journal-3270	206	2	t	t	PROPN
american_scientific_journal-3270	206	3	f	f	PROPN
american_scientific_journal-3270	206	4	z	z	PROPN
american_scientific_journal-3270	206	5	t	t	PROPN
american_scientific_journal-3270	206	6	dz	dz	PROPN
american_scientific_journal-3270	206	7	e	e	PROPN
american_scientific_journal-3270	206	8	z	z	NOUN
american_scientific_journal-3270	206	9	x	x	PUNCT
american_scientific_journal-3270	207	1	d	d	NOUN
american_scientific_journal-3270	207	2	f	f	PROPN
american_scientific_journal-3270	207	3	z	z	NOUN
american_scientific_journal-3270	207	4	t	t	PROPN
american_scientific_journal-3270	207	5	dz	dz	PROPN
american_scientific_journal-3270	207	6	e	e	PROPN
american_scientific_journal-3270	207	7	z	z	NOUN
american_scientific_journal-3270	207	8	x	x	X
american_scientific_journal-3270	207	9	dxα	dxα	ADJ
american_scientific_journal-3270	207	10	αα	αα	PROPN
american_scientific_journal-3270	207	11	α	α	PROPN
american_scientific_journal-3270	207	12	α	α	NOUN
american_scientific_journal-3270	207	13	µ	µ	PROPN
american_scientific_journal-3270	207	14	π	π	X
american_scientific_journal-3270	207	15	π−	π−	NOUN
american_scientific_journal-3270	207	16	∞	∞	NUM
american_scientific_journal-3270	207	17	∞	∞	NUM
american_scientific_journal-3270	207	18	→	→	SYM
american_scientific_journal-3270	207	19	−	−	PROPN
american_scientific_journal-3270	207	20	−	−	NOUN
american_scientific_journal-3270	207	21	+	+	SYM
american_scientific_journal-3270	207	22	−	−	PROPN
american_scientific_journal-3270	207	23	=	=	SYM
american_scientific_journal-3270	208	1	−	−	PROPN
american_scientific_journal-3270	208	2	+	+	NOUN
american_scientific_journal-3270	208	3	−	−	NUM
american_scientific_journal-3270	208	4			NUM
american_scientific_journal-3270	208	5	∫	∫	PROPN
american_scientific_journal-3270	209	1	∫	∫	PROPN
american_scientific_journal-3270	209	2	∫	∫	PROPN
american_scientific_journal-3270	209	3	∫	∫	PROPN
american_scientific_journal-3270	209	4	american	american	PROPN
american_scientific_journal-3270	209	5	scientific	scientific	PROPN
american_scientific_journal-3270	209	6	research	research	PROPN
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american_scientific_journal-3270	209	8	for	for	ADP
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american_scientific_journal-3270	209	10	,	,	PUNCT
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american_scientific_journal-3270	209	12	,	,	PUNCT
american_scientific_journal-3270	209	13	and	and	CCONJ
american_scientific_journal-3270	209	14	sciences	science	NOUN
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american_scientific_journal-3270	209	18	(	(	PUNCT
american_scientific_journal-3270	209	19	2017	2017	NUM
american_scientific_journal-3270	209	20	)	)	PUNCT
american_scientific_journal-3270	209	21	volume	volume	NOUN
american_scientific_journal-3270	209	22	34	34	NUM
american_scientific_journal-3270	209	23	,	,	PUNCT
american_scientific_journal-3270	209	24	no	no	DET
american_scientific_journal-3270	209	25	1	1	NUM
american_scientific_journal-3270	209	26	,	,	PUNCT
american_scientific_journal-3270	209	27	pp	pp	ADV
american_scientific_journal-3270	209	28	213	213	NUM
american_scientific_journal-3270	209	29	-	-	SYM
american_scientific_journal-3270	209	30	230	230	NUM
american_scientific_journal-3270	209	31	219	219	NUM
american_scientific_journal-3270	209	32	1	1	NUM
american_scientific_journal-3270	209	33	2	2	NUM
american_scientific_journal-3270	209	34	2	2	NUM
american_scientific_journal-3270	209	35	2	2	NUM
american_scientific_journal-3270	209	36	11	11	NUM
american_scientific_journal-3270	209	37	0	0	NUM
american_scientific_journal-3270	209	38	1	1	NUM
american_scientific_journal-3270	209	39	(	(	PUNCT
american_scientific_journal-3270	209	40	,	,	PUNCT
american_scientific_journal-3270	209	41	)	)	PUNCT
american_scientific_journal-3270	209	42	(	(	PUNCT
american_scientific_journal-3270	209	43	,	,	PUNCT
american_scientific_journal-3270	209	44	)	)	PUNCT
american_scientific_journal-3270	209	45	(	(	PUNCT
american_scientific_journal-3270	209	46	)	)	PUNCT
american_scientific_journal-3270	209	47	(	(	PUNCT
american_scientific_journal-3270	209	48	,	,	PUNCT
american_scientific_journal-3270	209	49	)	)	PUNCT
american_scientific_journal-3270	209	50	t	t	PROPN
american_scientific_journal-3270	210	1	j	j	PROPN
american_scientific_journal-3270	211	1	j	j	PROPN
american_scientific_journal-3270	211	2	j	j	PROPN
american_scientific_journal-3270	212	1	k	k	PROPN
american_scientific_journal-3270	212	2	x	x	X
american_scientific_journal-3270	212	3	z	z	NOUN
american_scientific_journal-3270	212	4	f	f	PROPN
american_scientific_journal-3270	212	5	z	z	NOUN
american_scientific_journal-3270	212	6	t	t	PROPN
american_scientific_journal-3270	212	7	dz	dz	PROPN
american_scientific_journal-3270	213	1	f	f	PROPN
american_scientific_journal-3270	213	2	f	f	PROPN
american_scientific_journal-3270	213	3	x	x	X
american_scientific_journal-3270	213	4	dt	dt	X
american_scientific_journal-3270	214	1	t	t	NOUN
american_scientific_journal-3270	214	2	t	t	X
american_scientific_journal-3270	214	3	π	π	PROPN
american_scientific_journal-3270	214	4	=	=	PRON
american_scientific_journal-3270	214	5	−	−	PROPN
american_scientific_journal-3270	214	6			PROPN
american_scientific_journal-3270	214	7	+	+	SYM
american_scientific_journal-3270	214	8	+	+	CCONJ
american_scientific_journal-3270	214	9			PROPN
american_scientific_journal-3270	214	10			PROPN
american_scientific_journal-3270	214	11	∑∫	∑∫	PROPN
american_scientific_journal-3270	214	12	∫	∫	PROPN
american_scientific_journal-3270	214	13	.	.	PUNCT
american_scientific_journal-3270	215	1	(	(	PUNCT
american_scientific_journal-3270	215	2	2.25	2.25	NUM
american_scientific_journal-3270	215	3	)	)	PUNCT
american_scientific_journal-3270	215	4	here	here	ADV
american_scientific_journal-3270	215	5	,	,	PUNCT
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american_scientific_journal-3270	215	8	kernels	kernels	PROPN
american_scientific_journal-3270	215	9	ijk	ijk	PROPN
american_scientific_journal-3270	215	10	are	be	AUX
american_scientific_journal-3270	215	11	given	give	VERB
american_scientific_journal-3270	215	12	by	by	ADP
american_scientific_journal-3270	215	13	11	11	NUM
american_scientific_journal-3270	215	14	11	11	NUM
american_scientific_journal-3270	215	15	12	12	NUM
american_scientific_journal-3270	215	16	12	12	NUM
american_scientific_journal-3270	215	17	0	0	NUM
american_scientific_journal-3270	215	18	0	0	NUM
american_scientific_journal-3270	216	1	(	(	PUNCT
american_scientific_journal-3270	216	2	,	,	PUNCT
american_scientific_journal-3270	216	3	)	)	PUNCT
american_scientific_journal-3270	216	4	(	(	PUNCT
american_scientific_journal-3270	216	5	)	)	PUNCT
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american_scientific_journal-3270	216	7	(	(	PUNCT
american_scientific_journal-3270	216	8	)	)	PUNCT
american_scientific_journal-3270	216	9	;	;	PUNCT
american_scientific_journal-3270	216	10	(	(	PUNCT
american_scientific_journal-3270	216	11	,	,	PUNCT
american_scientific_journal-3270	216	12	)	)	PUNCT
american_scientific_journal-3270	216	13	(	(	PUNCT
american_scientific_journal-3270	216	14	)	)	PUNCT
american_scientific_journal-3270	216	15	sin	sin	NOUN
american_scientific_journal-3270	216	16	(	(	PUNCT
american_scientific_journal-3270	216	17	)	)	PUNCT
american_scientific_journal-3270	216	18	k	k	X
american_scientific_journal-3270	217	1	x	x	PUNCT
american_scientific_journal-3270	217	2	z	z	NOUN
american_scientific_journal-3270	217	3	h	h	NOUN
american_scientific_journal-3270	218	1	z	z	NOUN
american_scientific_journal-3270	218	2	x	x	PUNCT
american_scientific_journal-3270	219	1	d	d	X
american_scientific_journal-3270	219	2	k	k	X
american_scientific_journal-3270	219	3	x	x	X
american_scientific_journal-3270	219	4	z	z	NOUN
american_scientific_journal-3270	219	5	h	h	NOUN
american_scientific_journal-3270	219	6	z	z	NOUN
american_scientific_journal-3270	219	7	x	x	SYM
american_scientific_journal-3270	219	8	dα	dα	ADP
american_scientific_journal-3270	219	9	α	α	NOUN
american_scientific_journal-3270	219	10	α	α	NOUN
american_scientific_journal-3270	219	11	α	α	NOUN
american_scientific_journal-3270	219	12	α	α	NOUN
american_scientific_journal-3270	220	1	α	α	NOUN
american_scientific_journal-3270	220	2	∞	∞	NOUN
american_scientific_journal-3270	220	3	∞	∞	NUM
american_scientific_journal-3270	220	4	=	=	SYM
american_scientific_journal-3270	221	1	−	−	PROPN
american_scientific_journal-3270	221	2	=	=	PUNCT
american_scientific_journal-3270	221	3	−∫	−∫	NOUN
american_scientific_journal-3270	221	4	∫	∫	PROPN
american_scientific_journal-3270	221	5	,	,	PUNCT
american_scientific_journal-3270	221	6	21	21	NUM
american_scientific_journal-3270	221	7	21	21	NUM
american_scientific_journal-3270	221	8	22	22	NUM
american_scientific_journal-3270	221	9	22	22	NUM
american_scientific_journal-3270	221	10	0	0	NUM
american_scientific_journal-3270	221	11	0	0	NUM
american_scientific_journal-3270	222	1	(	(	PUNCT
american_scientific_journal-3270	222	2	,	,	PUNCT
american_scientific_journal-3270	222	3	)	)	PUNCT
american_scientific_journal-3270	222	4	(	(	PUNCT
american_scientific_journal-3270	222	5	)	)	PUNCT
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american_scientific_journal-3270	222	7	(	(	PUNCT
american_scientific_journal-3270	222	8	)	)	PUNCT
american_scientific_journal-3270	222	9	;	;	PUNCT
american_scientific_journal-3270	222	10	(	(	PUNCT
american_scientific_journal-3270	222	11	,	,	PUNCT
american_scientific_journal-3270	222	12	)	)	PUNCT
american_scientific_journal-3270	222	13	(	(	PUNCT
american_scientific_journal-3270	222	14	)	)	PUNCT
american_scientific_journal-3270	222	15	cos	cos	PROPN
american_scientific_journal-3270	222	16	(	(	PUNCT
american_scientific_journal-3270	222	17	)	)	PUNCT
american_scientific_journal-3270	222	18	k	k	X
american_scientific_journal-3270	222	19	x	x	PUNCT
american_scientific_journal-3270	223	1	z	z	NOUN
american_scientific_journal-3270	223	2	h	h	NOUN
american_scientific_journal-3270	224	1	z	z	NOUN
american_scientific_journal-3270	224	2	x	x	PUNCT
american_scientific_journal-3270	225	1	d	d	X
american_scientific_journal-3270	225	2	k	k	X
american_scientific_journal-3270	225	3	x	x	X
american_scientific_journal-3270	225	4	z	z	NOUN
american_scientific_journal-3270	225	5	h	h	NOUN
american_scientific_journal-3270	225	6	z	z	NOUN
american_scientific_journal-3270	225	7	x	x	SYM
american_scientific_journal-3270	225	8	dα	dα	ADP
american_scientific_journal-3270	225	9	α	α	NOUN
american_scientific_journal-3270	225	10	α	α	NOUN
american_scientific_journal-3270	225	11	α	α	NOUN
american_scientific_journal-3270	225	12	α	α	NOUN
american_scientific_journal-3270	226	1	α	α	NOUN
american_scientific_journal-3270	226	2	∞	∞	NOUN
american_scientific_journal-3270	226	3	∞	∞	NUM
american_scientific_journal-3270	226	4	=	=	SYM
american_scientific_journal-3270	227	1	−	−	PROPN
american_scientific_journal-3270	227	2	=	=	PUNCT
american_scientific_journal-3270	227	3	−∫	−∫	NOUN
american_scientific_journal-3270	227	4	∫	∫	PROPN
american_scientific_journal-3270	227	5	,	,	PUNCT
american_scientific_journal-3270	227	6	(	(	PUNCT
american_scientific_journal-3270	227	7	2.26	2.26	NUM
american_scientific_journal-3270	227	8	)	)	PUNCT
american_scientific_journal-3270	227	9	evaluating	evaluate	VERB
american_scientific_journal-3270	227	10	the	the	DET
american_scientific_journal-3270	227	11	infinite	infinite	ADJ
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american_scientific_journal-3270	227	13	in	in	ADP
american_scientific_journal-3270	227	14	(	(	PUNCT
american_scientific_journal-3270	227	15	2.25	2.25	NUM
american_scientific_journal-3270	227	16	)	)	PUNCT
american_scientific_journal-3270	227	17	,	,	PUNCT
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american_scientific_journal-3270	227	26	,	,	PUNCT
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american_scientific_journal-3270	227	29	1	1	NUM
american_scientific_journal-3270	227	30	1	1	NUM
american_scientific_journal-3270	227	31	2	2	NUM
american_scientific_journal-3270	227	32	3	3	NUM
american_scientific_journal-3270	227	33	2	2	NUM
american_scientific_journal-3270	227	34	1	1	NUM
american_scientific_journal-3270	227	35	1	1	NUM
american_scientific_journal-3270	227	36	1	1	NUM
american_scientific_journal-3270	227	37	1	1	NUM
american_scientific_journal-3270	227	38	112	112	NUM
american_scientific_journal-3270	227	39	3	3	NUM
american_scientific_journal-3270	227	40	12	12	NUM
american_scientific_journal-3270	227	41	121	121	NUM
american_scientific_journal-3270	227	42	1	1	NUM
american_scientific_journal-3270	227	43	0	0	NUM
american_scientific_journal-3270	227	44	1	1	NUM
american_scientific_journal-3270	227	45	(	(	PUNCT
american_scientific_journal-3270	227	46	,	,	PUNCT
american_scientific_journal-3270	227	47	)	)	PUNCT
american_scientific_journal-3270	227	48	1	1	NUM
american_scientific_journal-3270	227	49	1	1	NUM
american_scientific_journal-3270	227	50	1	1	NUM
american_scientific_journal-3270	227	51	(	(	PUNCT
american_scientific_journal-3270	227	52	,	,	PUNCT
american_scientific_journal-3270	227	53	)	)	PUNCT
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american_scientific_journal-3270	227	55	,	,	PUNCT
american_scientific_journal-3270	227	56	)	)	PUNCT
american_scientific_journal-3270	227	57	(	(	PUNCT
american_scientific_journal-3270	227	58	,	,	PUNCT
american_scientific_journal-3270	227	59	)	)	PUNCT
american_scientific_journal-3270	227	60	(	(	PUNCT
american_scientific_journal-3270	227	61	,	,	PUNCT
american_scientific_journal-3270	227	62	)	)	PUNCT
american_scientific_journal-3270	227	63	(	(	PUNCT
american_scientific_journal-3270	227	64	)	)	PUNCT
american_scientific_journal-3270	227	65	(	(	PUNCT
american_scientific_journal-3270	227	66	,	,	PUNCT
american_scientific_journal-3270	227	67	)	)	PUNCT
american_scientific_journal-3270	227	68	t	t	PROPN
american_scientific_journal-3270	228	1	j	j	PROPN
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american_scientific_journal-3270	229	2	j	j	PROPN
american_scientific_journal-3270	229	3	k	k	PROPN
american_scientific_journal-3270	229	4	y	y	PROPN
american_scientific_journal-3270	229	5	t	t	PROPN
american_scientific_journal-3270	229	6	dyp	dyp	PROPN
american_scientific_journal-3270	229	7	x	x	SYM
american_scientific_journal-3270	229	8	t	t	PROPN
american_scientific_journal-3270	229	9	x	x	X
american_scientific_journal-3270	230	1	t	t	PROPN
american_scientific_journal-3270	230	2	k	k	NOUN
american_scientific_journal-3270	230	3	x	x	X
american_scientific_journal-3270	230	4	y	y	VERB
american_scientific_journal-3270	230	5	y	y	PROPN
american_scientific_journal-3270	230	6	t	t	PROPN
american_scientific_journal-3270	230	7	dy	dy	X
american_scientific_journal-3270	230	8	f	f	PROPN
american_scientific_journal-3270	230	9	x	x	X
american_scientific_journal-3270	230	10	dt	dt	X
american_scientific_journal-3270	230	11	a	a	X
american_scientific_journal-3270	230	12	x	x	X
american_scientific_journal-3270	230	13	y	y	PROPN
american_scientific_journal-3270	230	14	a	a	DET
american_scientific_journal-3270	230	15	a	a	DET
american_scientific_journal-3270	230	16	φ	φ	NOUN
american_scientific_journal-3270	230	17	γφ	γφ	ADP
american_scientific_journal-3270	230	18	φ	φ	PROPN
american_scientific_journal-3270	230	19	t	t	PROPN
american_scientific_journal-3270	230	20	φ	φ	PROPN
american_scientific_journal-3270	230	21	t	t	PROPN
american_scientific_journal-3270	230	22	µ	µ	PROPN
american_scientific_journal-3270	230	23	π	π	X
american_scientific_journal-3270	230	24	π	π	X
american_scientific_journal-3270	230	25	=	=	PUNCT
american_scientific_journal-3270	230	26	−	−	PROPN
american_scientific_journal-3270	230	27	−	−	PROPN
american_scientific_journal-3270	231	1	+	+	CCONJ
american_scientific_journal-3270	231	2	=	=	SYM
american_scientific_journal-3270	232	1	+	+	NUM
american_scientific_journal-3270	232	2	−	−	PROPN
american_scientific_journal-3270	233	1	+	+	CCONJ
american_scientific_journal-3270	233	2	−	−	PROPN
american_scientific_journal-3270	233	3	∑∫	∑∫	PROPN
american_scientific_journal-3270	233	4	∫	∫	PROPN
american_scientific_journal-3270	233	5	∫	∫	PROPN
american_scientific_journal-3270	233	6	(	(	PUNCT
american_scientific_journal-3270	233	7	2.27	2.27	NUM
american_scientific_journal-3270	233	8	)	)	PUNCT
american_scientific_journal-3270	233	9	,	,	PUNCT
american_scientific_journal-3270	233	10	1	1	NUM
american_scientific_journal-3270	233	11	1	1	NUM
american_scientific_journal-3270	233	12	2	2	NUM
american_scientific_journal-3270	233	13	3	3	NUM
american_scientific_journal-3270	233	14	1	1	NUM
american_scientific_journal-3270	233	15	2	2	NUM
american_scientific_journal-3270	233	16	2	2	NUM
american_scientific_journal-3270	233	17	2	2	NUM
american_scientific_journal-3270	233	18	2	2	NUM
american_scientific_journal-3270	233	19	121	121	NUM
american_scientific_journal-3270	233	20	3	3	NUM
american_scientific_journal-3270	233	21	21	21	NUM
american_scientific_journal-3270	233	22	211	211	NUM
american_scientific_journal-3270	233	23	1	1	NUM
american_scientific_journal-3270	233	24	0	0	NUM
american_scientific_journal-3270	233	25	1	1	NUM
american_scientific_journal-3270	233	26	(	(	PUNCT
american_scientific_journal-3270	233	27	,	,	PUNCT
american_scientific_journal-3270	233	28	)	)	PUNCT
american_scientific_journal-3270	233	29	1	1	NUM
american_scientific_journal-3270	233	30	1	1	NUM
american_scientific_journal-3270	233	31	1	1	NUM
american_scientific_journal-3270	233	32	(	(	PUNCT
american_scientific_journal-3270	233	33	,	,	PUNCT
american_scientific_journal-3270	233	34	)	)	PUNCT
american_scientific_journal-3270	233	35	(	(	PUNCT
american_scientific_journal-3270	233	36	,	,	PUNCT
american_scientific_journal-3270	233	37	)	)	PUNCT
american_scientific_journal-3270	233	38	(	(	PUNCT
american_scientific_journal-3270	233	39	,	,	PUNCT
american_scientific_journal-3270	233	40	)	)	PUNCT
american_scientific_journal-3270	233	41	(	(	PUNCT
american_scientific_journal-3270	233	42	,	,	PUNCT
american_scientific_journal-3270	233	43	)	)	PUNCT
american_scientific_journal-3270	233	44	(	(	PUNCT
american_scientific_journal-3270	233	45	)	)	PUNCT
american_scientific_journal-3270	233	46	(	(	PUNCT
american_scientific_journal-3270	233	47	,	,	PUNCT
american_scientific_journal-3270	233	48	)	)	PUNCT
american_scientific_journal-3270	233	49	t	t	PROPN
american_scientific_journal-3270	234	1	j	j	PROPN
american_scientific_journal-3270	234	2	j	j	PROPN
american_scientific_journal-3270	234	3	j	j	PROPN
american_scientific_journal-3270	234	4	k	k	PROPN
american_scientific_journal-3270	234	5	y	y	PROPN
american_scientific_journal-3270	234	6	t	t	PROPN
american_scientific_journal-3270	234	7	dyp	dyp	PROPN
american_scientific_journal-3270	234	8	x	x	SYM
american_scientific_journal-3270	234	9	t	t	PROPN
american_scientific_journal-3270	234	10	x	x	X
american_scientific_journal-3270	235	1	t	t	PROPN
american_scientific_journal-3270	235	2	k	k	NOUN
american_scientific_journal-3270	235	3	x	x	X
american_scientific_journal-3270	235	4	y	y	VERB
american_scientific_journal-3270	235	5	y	y	PROPN
american_scientific_journal-3270	235	6	t	t	PROPN
american_scientific_journal-3270	235	7	dy	dy	X
american_scientific_journal-3270	235	8	f	f	PROPN
american_scientific_journal-3270	236	1	x	x	PROPN
american_scientific_journal-3270	236	2	d	d	X
american_scientific_journal-3270	236	3	a	a	DET
american_scientific_journal-3270	236	4	y	y	X
american_scientific_journal-3270	236	5	x	x	X
american_scientific_journal-3270	236	6	a	a	DET
american_scientific_journal-3270	236	7	a	a	DET
american_scientific_journal-3270	236	8	φ	φ	NOUN
american_scientific_journal-3270	236	9	γφ	γφ	ADP
american_scientific_journal-3270	236	10	φ	φ	PROPN
american_scientific_journal-3270	236	11	t	t	PROPN
american_scientific_journal-3270	236	12	φ	φ	PROPN
american_scientific_journal-3270	236	13	t	t	PROPN
american_scientific_journal-3270	236	14	t	t	PROPN
american_scientific_journal-3270	236	15	µ	µ	PROPN
american_scientific_journal-3270	236	16	π	π	X
american_scientific_journal-3270	236	17	π	π	X
american_scientific_journal-3270	236	18	=	=	PUNCT
american_scientific_journal-3270	236	19	−	−	PROPN
american_scientific_journal-3270	236	20	−	−	PROPN
american_scientific_journal-3270	237	1	+	+	CCONJ
american_scientific_journal-3270	237	2	=	=	SYM
american_scientific_journal-3270	237	3	−	−	NOUN
american_scientific_journal-3270	237	4	−	−	PROPN
american_scientific_journal-3270	238	1	+	+	CCONJ
american_scientific_journal-3270	238	2	−	−	PROPN
american_scientific_journal-3270	238	3	∑∫	∑∫	PROPN
american_scientific_journal-3270	238	4	∫	∫	PROPN
american_scientific_journal-3270	238	5	∫	∫	PROPN
american_scientific_journal-3270	238	6	(	(	PUNCT
american_scientific_journal-3270	238	7	2.28	2.28	NUM
american_scientific_journal-3270	238	8	)	)	PUNCT
american_scientific_journal-3270	238	9	(	(	PUNCT
american_scientific_journal-3270	238	10	)	)	PUNCT
american_scientific_journal-3270	238	11	(	(	PUNCT
american_scientific_journal-3270	238	12	)	)	PUNCT
american_scientific_journal-3270	238	13	(	(	PUNCT
american_scientific_journal-3270	238	14	)	)	PUNCT
american_scientific_journal-3270	238	15	(	(	PUNCT
american_scientific_journal-3270	238	16	)	)	PUNCT
american_scientific_journal-3270	238	17	3	3	NUM
american_scientific_journal-3270	238	18	3	3	NUM
american_scientific_journal-3270	238	19	2	2	NUM
american_scientific_journal-3270	238	20	2	2	NUM
american_scientific_journal-3270	238	21	2	2	NUM
american_scientific_journal-3270	238	22	311	311	NUM
american_scientific_journal-3270	238	23	22	22	NUM
american_scientific_journal-3270	238	24	12	12	NUM
american_scientific_journal-3270	238	25	21	21	NUM
american_scientific_journal-3270	238	26	2	2	NUM
american_scientific_journal-3270	238	27	2	2	NUM
american_scientific_journal-3270	238	28	3	3	NUM
american_scientific_journal-3270	238	29	3	3	NUM
american_scientific_journal-3270	238	30	3	3	NUM
american_scientific_journal-3270	238	31	2	2	NUM
american_scientific_journal-3270	238	32	k	k	PROPN
american_scientific_journal-3270	238	33	ka	ka	PROPN
american_scientific_journal-3270	239	1	a	a	DET
american_scientific_journal-3270	239	2	a	a	DET
american_scientific_journal-3270	239	3	a	a	DET
american_scientific_journal-3270	239	4	k	k	X
american_scientific_journal-3270	239	5	k	k	PROPN
american_scientific_journal-3270	239	6	µ	µ	PROPN
american_scientific_journal-3270	239	7	µ	µ	X
american_scientific_journal-3270	239	8	µ	µ	X
american_scientific_journal-3270	239	9	µ	µ	X
american_scientific_journal-3270	239	10	γ	γ	X
american_scientific_journal-3270	239	11	µ	µ	X
american_scientific_journal-3270	239	12	µ	µ	X
american_scientific_journal-3270	239	13	µ	µ	X
american_scientific_journal-3270	239	14	µ	µ	X
american_scientific_journal-3270	239	15	+	+	CCONJ
american_scientific_journal-3270	239	16	−	−	PROPN
american_scientific_journal-3270	240	1	+	+	NOUN
american_scientific_journal-3270	240	2	=	=	SYM
american_scientific_journal-3270	240	3	=	=	PUNCT
american_scientific_journal-3270	241	1	=	=	PUNCT
american_scientific_journal-3270	242	1	+	+	PUNCT
american_scientific_journal-3270	242	2	+	+	CCONJ
american_scientific_journal-3270	242	3	+	+	X
american_scientific_journal-3270	242	4	.	.	PUNCT
american_scientific_journal-3270	243	1	(	(	PUNCT
american_scientific_journal-3270	243	2	2.29	2.29	NUM
american_scientific_journal-3270	243	3	)	)	PUNCT
american_scientific_journal-3270	243	4	the	the	DET
american_scientific_journal-3270	243	5	two	two	NUM
american_scientific_journal-3270	243	6	formulas	formula	NOUN
american_scientific_journal-3270	243	7	of	of	ADP
american_scientific_journal-3270	243	8	(	(	PUNCT
american_scientific_journal-3270	243	9	2.27	2.27	NUM
american_scientific_journal-3270	243	10	)	)	PUNCT
american_scientific_journal-3270	243	11	,	,	PUNCT
american_scientific_journal-3270	243	12	(	(	PUNCT
american_scientific_journal-3270	243	13	2.28	2.28	NUM
american_scientific_journal-3270	243	14	)	)	PUNCT
american_scientific_journal-3270	243	15	represent	represent	VERB
american_scientific_journal-3270	243	16	a	a	DET
american_scientific_journal-3270	243	17	system	system	NOUN
american_scientific_journal-3270	243	18	of	of	ADP
american_scientific_journal-3270	243	19	mixed	mixed	ADJ
american_scientific_journal-3270	243	20	integral	integral	ADJ
american_scientific_journal-3270	243	21	equation	equation	NOUN
american_scientific_journal-3270	243	22	with	with	ADP
american_scientific_journal-3270	243	23	cauchy	cauchy	PROPN
american_scientific_journal-3270	243	24	kernel	kernel	PROPN
american_scientific_journal-3270	243	25	.	.	PUNCT
american_scientific_journal-3270	244	1	for	for	ADP
american_scientific_journal-3270	244	2	one	one	NUM
american_scientific_journal-3270	244	3	layer	layer	NOUN
american_scientific_journal-3270	244	4	,	,	PUNCT
american_scientific_journal-3270	244	5	we	we	PRON
american_scientific_journal-3270	244	6	write	write	VERB
american_scientific_journal-3270	244	7	eq	eq	ADP
american_scientific_journal-3270	244	8	.	.	PUNCT
american_scientific_journal-3270	245	1	(	(	PUNCT
american_scientific_journal-3270	245	2	2.27	2.27	NUM
american_scientific_journal-3270	245	3	)	)	PUNCT
american_scientific_journal-3270	245	4	in	in	ADP
american_scientific_journal-3270	245	5	the	the	DET
american_scientific_journal-3270	245	6	following	follow	VERB
american_scientific_journal-3270	245	7	form	form	NOUN
american_scientific_journal-3270	245	8	(	(	PUNCT
american_scientific_journal-3270	245	9	)	)	PUNCT
american_scientific_journal-3270	245	10	(	(	PUNCT
american_scientific_journal-3270	245	11	)	)	PUNCT
american_scientific_journal-3270	245	12	(	(	PUNCT
american_scientific_journal-3270	245	13	)	)	PUNCT
american_scientific_journal-3270	245	14	(	(	PUNCT
american_scientific_journal-3270	245	15	)	)	PUNCT
american_scientific_journal-3270	245	16	(	(	PUNCT
american_scientific_journal-3270	245	17	)	)	PUNCT
american_scientific_journal-3270	245	18	(	(	PUNCT
american_scientific_journal-3270	245	19	)	)	PUNCT
american_scientific_journal-3270	245	20	1	1	NUM
american_scientific_journal-3270	245	21	1	1	NUM
american_scientific_journal-3270	245	22	1	1	NUM
american_scientific_journal-3270	245	23	1	1	NUM
american_scientific_journal-3270	245	24	0	0	NUM
american_scientific_journal-3270	245	25	,	,	PUNCT
american_scientific_journal-3270	245	26	(	(	PUNCT
american_scientific_journal-3270	245	27	)	)	PUNCT
american_scientific_journal-3270	245	28	,	,	PUNCT
american_scientific_journal-3270	245	29	(	(	PUNCT
american_scientific_journal-3270	245	30	,	,	PUNCT
american_scientific_journal-3270	245	31	)	)	PUNCT
american_scientific_journal-3270	245	32	,	,	PUNCT
american_scientific_journal-3270	245	33	,	,	PUNCT
american_scientific_journal-3270	245	34	,	,	PUNCT
american_scientific_journal-3270	245	35	,	,	PUNCT
american_scientific_journal-3270	245	36	,	,	PUNCT
american_scientific_journal-3270	245	37	t	t	PROPN
american_scientific_journal-3270	245	38	x	x	X
american_scientific_journal-3270	246	1	t	t	PROPN
american_scientific_journal-3270	246	2	p	p	X
american_scientific_journal-3270	246	3	y	y	PROPN
american_scientific_journal-3270	246	4	x	x	PROPN
american_scientific_journal-3270	246	5	y	y	PROPN
american_scientific_journal-3270	246	6	t	t	NOUN
american_scientific_journal-3270	246	7	dy	dy	X
american_scientific_journal-3270	246	8	k	k	PROPN
american_scientific_journal-3270	246	9	x	x	PUNCT
american_scientific_journal-3270	246	10	y	y	VERB
american_scientific_journal-3270	246	11	y	y	PROPN
american_scientific_journal-3270	246	12	t	t	PROPN
american_scientific_journal-3270	246	13	dy	dy	NOUN
american_scientific_journal-3270	246	14	t	t	PROPN
american_scientific_journal-3270	246	15	x	x	PUNCT
american_scientific_journal-3270	247	1	d	d	X
american_scientific_journal-3270	247	2	f	f	X
american_scientific_journal-3270	247	3	x	x	PROPN
american_scientific_journal-3270	247	4	tληφ	tληφ	PROPN
american_scientific_journal-3270	247	5	φ	φ	PROPN
american_scientific_journal-3270	247	6	λ	λ	PROPN
american_scientific_journal-3270	247	7	φ	φ	PROPN
american_scientific_journal-3270	247	8	λ	λ	PROPN
american_scientific_journal-3270	247	9	x	x	PROPN
american_scientific_journal-3270	247	10	t	t	PROPN
american_scientific_journal-3270	247	11	φ	φ	PROPN
american_scientific_journal-3270	247	12	t	t	PROPN
american_scientific_journal-3270	247	13	t	t	PROPN
american_scientific_journal-3270	247	14	π	π	X
american_scientific_journal-3270	247	15	−	−	PROPN
american_scientific_journal-3270	247	16	−	−	PROPN
american_scientific_journal-3270	247	17	−	−	PROPN
american_scientific_journal-3270	247	18	−	−	PROPN
american_scientific_journal-3270	247	19	−	−	NOUN
american_scientific_journal-3270	247	20	−	−	PROPN
american_scientific_journal-3270	248	1	=	=	SYM
american_scientific_journal-3270	248	2	∫	∫	PROPN
american_scientific_journal-3270	248	3	∫	∫	PROPN
american_scientific_journal-3270	248	4	∫	∫	PROPN
american_scientific_journal-3270	248	5	{	{	PUNCT
american_scientific_journal-3270	248	6	1	1	NUM
american_scientific_journal-3270	248	7	(	(	PUNCT
american_scientific_journal-3270	248	8	)	)	PUNCT
american_scientific_journal-3270	248	9	p	p	NOUN
american_scientific_journal-3270	248	10	y	y	PROPN
american_scientific_journal-3270	248	11	x	x	SYM
american_scientific_journal-3270	248	12	y	y	NOUN
american_scientific_journal-3270	248	13	x	x	X
american_scientific_journal-3270	248	14	−	−	PROPN
american_scientific_journal-3270	248	15	=	=	SYM
american_scientific_journal-3270	248	16	−	−	PROPN
american_scientific_journal-3270	248	17	}	}	PUNCT
american_scientific_journal-3270	248	18	.	.	PUNCT
american_scientific_journal-3270	249	1	(	(	PUNCT
american_scientific_journal-3270	249	2	2.30	2.30	NUM
american_scientific_journal-3270	249	3	)	)	PUNCT
american_scientific_journal-3270	249	4	the	the	DET
american_scientific_journal-3270	249	5	ends	end	NOUN
american_scientific_journal-3270	249	6	1±	1±	NUM
american_scientific_journal-3270	249	7	are	be	AUX
american_scientific_journal-3270	249	8	points	point	NOUN
american_scientific_journal-3270	249	9	of	of	ADP
american_scientific_journal-3270	249	10	geometric	geometric	ADJ
american_scientific_journal-3270	249	11	singularity	singularity	NOUN
american_scientific_journal-3270	249	12	.	.	PUNCT
american_scientific_journal-3270	250	1	at	at	ADP
american_scientific_journal-3270	250	2	these	these	DET
american_scientific_journal-3270	250	3	points	point	NOUN
american_scientific_journal-3270	250	4	,	,	PUNCT
american_scientific_journal-3270	250	5	and	and	CCONJ
american_scientific_journal-3270	250	6	for	for	ADP
american_scientific_journal-3270	250	7	all	all	DET
american_scientific_journal-3270	250	8	values	value	NOUN
american_scientific_journal-3270	250	9	of	of	ADP
american_scientific_journal-3270	250	10	time	time	NOUN
american_scientific_journal-3270	250	11	,	,	PUNCT
american_scientific_journal-3270	250	12	(	(	PUNCT
american_scientific_journal-3270	250	13	,	,	PUNCT
american_scientific_journal-3270	250	14	)	)	PUNCT
american_scientific_journal-3270	250	15	x	x	X
american_scientific_journal-3270	250	16	tφ	tφ	PROPN
american_scientific_journal-3270	250	17	is	be	AUX
american_scientific_journal-3270	250	18	bounded	bound	VERB
american_scientific_journal-3270	250	19	,	,	PUNCT
american_scientific_journal-3270	250	20	if	if	SCONJ
american_scientific_journal-3270	250	21	it	it	PRON
american_scientific_journal-3270	250	22	is	be	AUX
american_scientific_journal-3270	250	23	a	a	DET
american_scientific_journal-3270	250	24	potential	potential	NOUN
american_scientific_journal-3270	250	25	,	,	PUNCT
american_scientific_journal-3270	250	26	and	and	CCONJ
american_scientific_journal-3270	250	27	(	(	PUNCT
american_scientific_journal-3270	250	28	,	,	PUNCT
american_scientific_journal-3270	250	29	)	)	PUNCT
american_scientific_journal-3270	250	30	x	x	X
american_scientific_journal-3270	250	31	tφ	tφ	PROPN
american_scientific_journal-3270	250	32	has	have	VERB
american_scientific_journal-3270	250	33	a	a	DET
american_scientific_journal-3270	250	34	singularity	singularity	NOUN
american_scientific_journal-3270	250	35	,	,	PUNCT
american_scientific_journal-3270	250	36	if	if	SCONJ
american_scientific_journal-3270	250	37	it	it	PRON
american_scientific_journal-3270	250	38	is	be	AUX
american_scientific_journal-3270	250	39	a	a	DET
american_scientific_journal-3270	250	40	flux	flux	NOUN
american_scientific_journal-3270	250	41	-	-	PUNCT
american_scientific_journal-3270	250	42	type	type	NOUN
american_scientific_journal-3270	250	43	quantity	quantity	NOUN
american_scientific_journal-3270	250	44	of	of	ADP
american_scientific_journal-3270	250	45	system	system	NOUN
american_scientific_journal-3270	250	46	integral	integral	ADJ
american_scientific_journal-3270	250	47	equations	equation	NOUN
american_scientific_journal-3270	250	48	.	.	PUNCT
american_scientific_journal-3270	251	1	this	this	DET
american_scientific_journal-3270	251	2	equation	equation	NOUN
american_scientific_journal-3270	251	3	may	may	AUX
american_scientific_journal-3270	251	4	be	be	AUX
american_scientific_journal-3270	251	5	arising	arise	VERB
american_scientific_journal-3270	251	6	from	from	ADP
american_scientific_journal-3270	251	7	the	the	DET
american_scientific_journal-3270	251	8	formulation	formulation	NOUN
american_scientific_journal-3270	251	9	of	of	ADP
american_scientific_journal-3270	251	10	elasticity	elasticity	NOUN
american_scientific_journal-3270	251	11	problems	problem	NOUN
american_scientific_journal-3270	251	12	for	for	ADP
american_scientific_journal-3270	251	13	the	the	DET
american_scientific_journal-3270	251	14	parallel	parallel	ADJ
american_scientific_journal-3270	251	15	layers	layer	NOUN
american_scientific_journal-3270	251	16	compressed	compress	VERB
american_scientific_journal-3270	251	17	by	by	ADP
american_scientific_journal-3270	251	18	stamps	stamp	NOUN
american_scientific_journal-3270	251	19	with	with	ADP
american_scientific_journal-3270	251	20	arbitrary	arbitrary	ADJ
american_scientific_journal-3270	251	21	profile	profile	NOUN
american_scientific_journal-3270	251	22	.	.	PUNCT
american_scientific_journal-3270	252	1	if	if	SCONJ
american_scientific_journal-3270	252	2	the	the	DET
american_scientific_journal-3270	252	3	contact	contact	NOUN
american_scientific_journal-3270	252	4	between	between	ADP
american_scientific_journal-3270	252	5	the	the	DET
american_scientific_journal-3270	252	6	parallel	parallel	ADJ
american_scientific_journal-3270	252	7	layers	layer	NOUN
american_scientific_journal-3270	252	8	and	and	CCONJ
american_scientific_journal-3270	252	9	the	the	DET
american_scientific_journal-3270	252	10	stamps	stamp	NOUN
american_scientific_journal-3270	252	11	is	be	AUX
american_scientific_journal-3270	252	12	frictionless	frictionless	VERB
american_scientific_journal-3270	252	13	the	the	DET
american_scientific_journal-3270	252	14	corresponding	corresponding	ADJ
american_scientific_journal-3270	252	15	constant	constant	ADJ
american_scientific_journal-3270	252	16	η	η	PROPN
american_scientific_journal-3270	252	17	is	be	AUX
american_scientific_journal-3270	252	18	zero	zero	NUM
american_scientific_journal-3270	252	19	and	and	CCONJ
american_scientific_journal-3270	252	20	the	the	DET
american_scientific_journal-3270	252	21	related	related	ADJ
american_scientific_journal-3270	252	22	system	system	NOUN
american_scientific_journal-3270	252	23	integral	integral	ADJ
american_scientific_journal-3270	252	24	equations	equation	NOUN
american_scientific_journal-3270	252	25	is	be	AUX
american_scientific_journal-3270	252	26	of	of	ADP
american_scientific_journal-3270	252	27	the	the	DET
american_scientific_journal-3270	252	28	first	first	ADJ
american_scientific_journal-3270	252	29	kind	kind	NOUN
american_scientific_journal-3270	252	30	,	,	PUNCT
american_scientific_journal-3270	252	31	while	while	SCONJ
american_scientific_journal-3270	252	32	,	,	PUNCT
american_scientific_journal-3270	252	33	if	if	SCONJ
american_scientific_journal-3270	252	34	the	the	DET
american_scientific_journal-3270	252	35	contact	contact	NOUN
american_scientific_journal-3270	252	36	is	be	AUX
american_scientific_journal-3270	252	37	perfect	perfect	ADJ
american_scientific_journal-3270	252	38	adhesion	adhesion	NOUN
american_scientific_journal-3270	252	39	the	the	DET
american_scientific_journal-3270	252	40	related	related	ADJ
american_scientific_journal-3270	252	41	system	system	NOUN
american_scientific_journal-3270	252	42	integral	integral	ADJ
american_scientific_journal-3270	252	43	equations	equation	NOUN
american_scientific_journal-3270	252	44	is	be	AUX
american_scientific_journal-3270	252	45	of	of	ADP
american_scientific_journal-3270	252	46	the	the	DET
american_scientific_journal-3270	252	47	second	second	ADJ
american_scientific_journal-3270	252	48	kind	kind	NOUN
american_scientific_journal-3270	252	49	,	,	PUNCT
american_scientific_journal-3270	252	50	where	where	SCONJ
american_scientific_journal-3270	252	51	the	the	DET
american_scientific_journal-3270	252	52	lengths	length	NOUN
american_scientific_journal-3270	252	53	of	of	ADP
american_scientific_journal-3270	252	54	the	the	DET
american_scientific_journal-3270	252	55	cracks	crack	NOUN
american_scientific_journal-3270	252	56	or	or	CCONJ
american_scientific_journal-3270	252	57	size	size	NOUN
american_scientific_journal-3270	252	58	of	of	ADP
american_scientific_journal-3270	252	59	the	the	DET
american_scientific_journal-3270	252	60	stamps	stamp	NOUN
american_scientific_journal-3270	252	61	are	be	AUX
american_scientific_journal-3270	252	62	not	not	PART
american_scientific_journal-3270	252	63	equals	equal	NOUN
american_scientific_journal-3270	252	64	.	.	PUNCT
american_scientific_journal-3270	253	1	american	american	ADJ
american_scientific_journal-3270	253	2	scientific	scientific	ADJ
american_scientific_journal-3270	253	3	research	research	PROPN
american_scientific_journal-3270	253	4	journal	journal	NOUN
american_scientific_journal-3270	253	5	for	for	ADP
american_scientific_journal-3270	253	6	engineering	engineering	NOUN
american_scientific_journal-3270	253	7	,	,	PUNCT
american_scientific_journal-3270	253	8	technology	technology	NOUN
american_scientific_journal-3270	253	9	,	,	PUNCT
american_scientific_journal-3270	253	10	and	and	CCONJ
american_scientific_journal-3270	253	11	sciences	science	NOUN
american_scientific_journal-3270	253	12	(	(	PUNCT
american_scientific_journal-3270	253	13	asrjets	asrjet	NOUN
american_scientific_journal-3270	253	14	)	)	PUNCT
american_scientific_journal-3270	253	15	(	(	PUNCT
american_scientific_journal-3270	253	16	2017	2017	NUM
american_scientific_journal-3270	253	17	)	)	PUNCT
american_scientific_journal-3270	253	18	volume	volume	NOUN
american_scientific_journal-3270	253	19	34	34	NUM
american_scientific_journal-3270	253	20	,	,	PUNCT
american_scientific_journal-3270	253	21	no	no	DET
american_scientific_journal-3270	253	22	1	1	NUM
american_scientific_journal-3270	253	23	,	,	PUNCT
american_scientific_journal-3270	253	24	pp	pp	ADV
american_scientific_journal-3270	253	25	213	213	NUM
american_scientific_journal-3270	253	26	-	-	SYM
american_scientific_journal-3270	253	27	230	230	NUM
american_scientific_journal-3270	253	28	220	220	NUM
american_scientific_journal-3270	253	29	3	3	NUM
american_scientific_journal-3270	253	30	.	.	PUNCT
american_scientific_journal-3270	254	1	the	the	DET
american_scientific_journal-3270	254	2	existence	existence	NOUN
american_scientific_journal-3270	254	3	of	of	ADP
american_scientific_journal-3270	254	4	a	a	DET
american_scientific_journal-3270	254	5	unique	unique	ADJ
american_scientific_journal-3270	254	6	solution	solution	NOUN
american_scientific_journal-3270	254	7	of	of	ADP
american_scientific_journal-3270	254	8	mixed	mixed	ADJ
american_scientific_journal-3270	254	9	integral	integral	ADJ
american_scientific_journal-3270	254	10	equation	equation	NOUN
american_scientific_journal-3270	254	11	:	:	PUNCT
american_scientific_journal-3270	254	12	in	in	ADP
american_scientific_journal-3270	254	13	this	this	DET
american_scientific_journal-3270	254	14	section	section	NOUN
american_scientific_journal-3270	254	15	,	,	PUNCT
american_scientific_journal-3270	254	16	we	we	PRON
american_scientific_journal-3270	254	17	use	use	VERB
american_scientific_journal-3270	254	18	banach	banach	ADV
american_scientific_journal-3270	254	19	fixed	fix	VERB
american_scientific_journal-3270	254	20	-	-	PUNCT
american_scientific_journal-3270	254	21	point	point	NOUN
american_scientific_journal-3270	254	22	theorem	theorem	NOUN
american_scientific_journal-3270	254	23	to	to	PART
american_scientific_journal-3270	254	24	prove	prove	VERB
american_scientific_journal-3270	254	25	the	the	DET
american_scientific_journal-3270	254	26	existence	existence	NOUN
american_scientific_journal-3270	254	27	of	of	ADP
american_scientific_journal-3270	254	28	a	a	DET
american_scientific_journal-3270	254	29	unique	unique	ADJ
american_scientific_journal-3270	254	30	solution	solution	NOUN
american_scientific_journal-3270	254	31	of	of	ADP
american_scientific_journal-3270	254	32	mixed	mixed	ADJ
american_scientific_journal-3270	254	33	integral	integral	ADJ
american_scientific_journal-3270	254	34	equation	equation	NOUN
american_scientific_journal-3270	254	35	(	(	PUNCT
american_scientific_journal-3270	254	36	2.30	2.30	NUM
american_scientific_journal-3270	254	37	)	)	PUNCT
american_scientific_journal-3270	254	38	,	,	PUNCT
american_scientific_journal-3270	254	39	under	under	ADP
american_scientific_journal-3270	254	40	certain	certain	ADJ
american_scientific_journal-3270	254	41	conditions	condition	NOUN
american_scientific_journal-3270	254	42	.	.	PUNCT
american_scientific_journal-3270	255	1	for	for	ADP
american_scientific_journal-3270	255	2	this	this	PRON
american_scientific_journal-3270	255	3	,	,	PUNCT
american_scientific_journal-3270	255	4	we	we	PRON
american_scientific_journal-3270	255	5	write	write	VERB
american_scientific_journal-3270	255	6	(	(	PUNCT
american_scientific_journal-3270	255	7	2.30	2.30	NUM
american_scientific_journal-3270	255	8	)	)	PUNCT
american_scientific_journal-3270	255	9	in	in	ADP
american_scientific_journal-3270	255	10	the	the	DET
american_scientific_journal-3270	255	11	integral	integral	ADJ
american_scientific_journal-3270	255	12	operator	operator	NOUN
american_scientific_journal-3270	255	13	form	form	NOUN
american_scientific_journal-3270	255	14	(	(	PUNCT
american_scientific_journal-3270	255	15	)	)	PUNCT
american_scientific_journal-3270	255	16	(	(	PUNCT
american_scientific_journal-3270	255	17	)	)	PUNCT
american_scientific_journal-3270	255	18	(	(	PUNCT
american_scientific_journal-3270	255	19	)	)	PUNCT
american_scientific_journal-3270	255	20	(	(	PUNCT
american_scientific_journal-3270	255	21	)	)	PUNCT
american_scientific_journal-3270	255	22	1	1	NUM
american_scientific_journal-3270	255	23	,	,	PUNCT
american_scientific_journal-3270	255	24	,	,	PUNCT
american_scientific_journal-3270	255	25	,	,	PUNCT
american_scientific_journal-3270	255	26	,	,	PUNCT
american_scientific_journal-3270	255	27	0w	0w	X
american_scientific_journal-3270	255	28	x	x	X
american_scientific_journal-3270	256	1	t	t	NOUN
american_scientific_journal-3270	256	2	f	f	X
american_scientific_journal-3270	256	3	x	x	X
american_scientific_journal-3270	257	1	t	t	PROPN
american_scientific_journal-3270	257	2	w	w	PROPN
american_scientific_journal-3270	257	3	x	x	PROPN
american_scientific_journal-3270	257	4	tφ	tφ	PROPN
american_scientific_journal-3270	257	5	φ	φ	PROPN
american_scientific_journal-3270	257	6	η	η	PROPN
american_scientific_journal-3270	257	7	η	η	PROPN
american_scientific_journal-3270	257	8	=	=	PROPN
american_scientific_journal-3270	257	9	+	+	CCONJ
american_scientific_journal-3270	257	10	≠	≠	PROPN
american_scientific_journal-3270	257	11	,	,	PUNCT
american_scientific_journal-3270	257	12	(	(	PUNCT
american_scientific_journal-3270	257	13	3.1	3.1	NUM
american_scientific_journal-3270	257	14	)	)	PUNCT
american_scientific_journal-3270	257	15	where	where	SCONJ
american_scientific_journal-3270	257	16	w	w	PROPN
american_scientific_journal-3270	257	17	h	h	PROPN
american_scientific_journal-3270	257	18	dφ	dφ	ADP
american_scientific_journal-3270	257	19	φ	φ	PROPN
american_scientific_journal-3270	257	20	φ	φ	PROPN
american_scientific_journal-3270	257	21	xφ=	xφ=	PROPN
american_scientific_journal-3270	258	1	+	+	CCONJ
american_scientific_journal-3270	258	2	+	+	CCONJ
american_scientific_journal-3270	258	3	,	,	PUNCT
american_scientific_journal-3270	258	4	(	(	PUNCT
american_scientific_journal-3270	258	5	3.2	3.2	NUM
american_scientific_journal-3270	258	6	)	)	PUNCT
american_scientific_journal-3270	258	7	and	and	CCONJ
american_scientific_journal-3270	258	8	1	1	NUM
american_scientific_journal-3270	258	9	1	1	NUM
american_scientific_journal-3270	258	10	1	1	NUM
american_scientific_journal-3270	258	11	1	1	NUM
american_scientific_journal-3270	258	12	0	0	NUM
american_scientific_journal-3270	258	13	(	(	PUNCT
american_scientific_journal-3270	258	14	)	)	PUNCT
american_scientific_journal-3270	258	15	(	(	PUNCT
american_scientific_journal-3270	258	16	,	,	PUNCT
american_scientific_journal-3270	258	17	)	)	PUNCT
american_scientific_journal-3270	258	18	,	,	PUNCT
american_scientific_journal-3270	258	19	(	(	PUNCT
american_scientific_journal-3270	258	20	,	,	PUNCT
american_scientific_journal-3270	258	21	)	)	PUNCT
american_scientific_journal-3270	258	22	(	(	PUNCT
american_scientific_journal-3270	258	23	,	,	PUNCT
american_scientific_journal-3270	258	24	)	)	PUNCT
american_scientific_journal-3270	258	25	;	;	PUNCT
american_scientific_journal-3270	258	26	(	(	PUNCT
american_scientific_journal-3270	258	27	,	,	PUNCT
american_scientific_journal-3270	258	28	)	)	PUNCT
american_scientific_journal-3270	258	29	(	(	PUNCT
american_scientific_journal-3270	258	30	,	,	PUNCT
american_scientific_journal-3270	258	31	)	)	PUNCT
american_scientific_journal-3270	258	32	t	t	NOUN
american_scientific_journal-3270	258	33	h	h	NOUN
american_scientific_journal-3270	258	34	p	p	X
american_scientific_journal-3270	258	35	y	y	PROPN
american_scientific_journal-3270	258	36	x	x	PUNCT
american_scientific_journal-3270	258	37	y	y	PROPN
american_scientific_journal-3270	258	38	t	t	NOUN
american_scientific_journal-3270	258	39	dy	dy	X
american_scientific_journal-3270	258	40	d	d	X
american_scientific_journal-3270	258	41	k	k	PROPN
american_scientific_journal-3270	258	42	x	x	VERB
american_scientific_journal-3270	258	43	y	y	VERB
american_scientific_journal-3270	258	44	y	y	PROPN
american_scientific_journal-3270	258	45	t	t	PROPN
american_scientific_journal-3270	258	46	dy	dy	NOUN
american_scientific_journal-3270	258	47	t	t	PROPN
american_scientific_journal-3270	258	48	x	x	X
american_scientific_journal-3270	258	49	dλ	dλ	NOUN
american_scientific_journal-3270	258	50	λ	λ	PROPN
american_scientific_journal-3270	258	51	λφ	λφ	ADP
american_scientific_journal-3270	258	52	φ	φ	PROPN
american_scientific_journal-3270	258	53	φ	φ	PROPN
american_scientific_journal-3270	258	54	φ	φ	PROPN
american_scientific_journal-3270	258	55	xφ	xφ	PROPN
american_scientific_journal-3270	259	1	x	x	SYM
american_scientific_journal-3270	259	2	t	t	PROPN
american_scientific_journal-3270	259	3	φ	φ	PROPN
american_scientific_journal-3270	259	4	t	t	PROPN
american_scientific_journal-3270	259	5	t	t	PROPN
american_scientific_journal-3270	259	6	ηπ	ηπ	PROPN
american_scientific_journal-3270	259	7	η	η	PROPN
american_scientific_journal-3270	259	8	η−	η−	PROPN
american_scientific_journal-3270	260	1	−	−	NOUN
american_scientific_journal-3270	260	2	=	=	SYM
american_scientific_journal-3270	260	3	−	−	PROPN
american_scientific_journal-3270	261	1	=	=	PUNCT
american_scientific_journal-3270	261	2	=	=	NUM
american_scientific_journal-3270	261	3	∫	∫	PROPN
american_scientific_journal-3270	261	4	∫	∫	PROPN
american_scientific_journal-3270	261	5	∫	∫	PROPN
american_scientific_journal-3270	261	6	,	,	PUNCT
american_scientific_journal-3270	261	7	(	(	PUNCT
american_scientific_journal-3270	261	8	3.3	3.3	NUM
american_scientific_journal-3270	261	9	)	)	PUNCT
american_scientific_journal-3270	261	10	then	then	ADV
american_scientific_journal-3270	261	11	,	,	PUNCT
american_scientific_journal-3270	261	12	we	we	PRON
american_scientific_journal-3270	261	13	assume	assume	VERB
american_scientific_journal-3270	261	14	the	the	DET
american_scientific_journal-3270	261	15	following	follow	VERB
american_scientific_journal-3270	261	16	conditions	condition	NOUN
american_scientific_journal-3270	261	17	i	i	PRON
american_scientific_journal-3270	261	18	)	)	PUNCT
american_scientific_journal-3270	261	19	the	the	DET
american_scientific_journal-3270	261	20	two	two	NUM
american_scientific_journal-3270	261	21	kernels	kernel	NOUN
american_scientific_journal-3270	261	22	of	of	ADP
american_scientific_journal-3270	261	23	fredholm	fredholm	ADJ
american_scientific_journal-3270	261	24	integral	integral	ADJ
american_scientific_journal-3270	261	25	term	term	NOUN
american_scientific_journal-3270	261	26	satisfies	satisfie	NOUN
american_scientific_journal-3270	261	27	in	in	ADP
american_scientific_journal-3270	261	28	[	[	PUNCT
american_scientific_journal-3270	261	29	]	]	X
american_scientific_journal-3270	261	30	2	2	NUM
american_scientific_journal-3270	261	31	1,1l	1,1l	NUM
american_scientific_journal-3270	261	32	−	−	NOUN
american_scientific_journal-3270	261	33	,	,	PUNCT
american_scientific_journal-3270	261	34	respectively	respectively	ADV
american_scientific_journal-3270	261	35	,	,	PUNCT
american_scientific_journal-3270	261	36	for	for	ADP
american_scientific_journal-3270	261	37	the	the	DET
american_scientific_journal-3270	261	38	constants	constant	NOUN
american_scientific_journal-3270	261	39	l	l	PROPN
american_scientific_journal-3270	261	40	and	and	CCONJ
american_scientific_journal-3270	261	41	m	m	VERB
american_scientific_journal-3270	261	42	the	the	DET
american_scientific_journal-3270	261	43	following	follow	VERB
american_scientific_journal-3270	261	44	conditions	condition	NOUN
american_scientific_journal-3270	261	45	:	:	PUNCT
american_scientific_journal-3270	261	46	(	(	PUNCT
american_scientific_journal-3270	261	47	i	i	NOUN
american_scientific_journal-3270	261	48	-	-	PUNCT
american_scientific_journal-3270	261	49	a	a	NOUN
american_scientific_journal-3270	261	50	)	)	PUNCT
american_scientific_journal-3270	261	51	(	(	PUNCT
american_scientific_journal-3270	261	52	,	,	PUNCT
american_scientific_journal-3270	261	53	)	)	PUNCT
american_scientific_journal-3270	261	54	k	k	NOUN
american_scientific_journal-3270	262	1	x	x	PUNCT
american_scientific_journal-3270	262	2	y	y	PROPN
american_scientific_journal-3270	262	3	l≤	l≤	ADJ
american_scientific_journal-3270	262	4	,	,	PUNCT
american_scientific_journal-3270	262	5	(	(	PUNCT
american_scientific_journal-3270	262	6	i	i	PROPN
american_scientific_journal-3270	262	7	-	-	PUNCT
american_scientific_journal-3270	262	8	b	b	NOUN
american_scientific_journal-3270	262	9	)	)	PUNCT
american_scientific_journal-3270	262	10	1	1	NUM
american_scientific_journal-3270	262	11	1	1	NUM
american_scientific_journal-3270	262	12	1	1	NUM
american_scientific_journal-3270	262	13	2	2	NUM
american_scientific_journal-3270	262	14	2	2	NUM
american_scientific_journal-3270	262	15	1	1	NUM
american_scientific_journal-3270	262	16	1	1	NUM
american_scientific_journal-3270	262	17	(	(	PUNCT
american_scientific_journal-3270	262	18	)	)	PUNCT
american_scientific_journal-3270	262	19	,	,	PUNCT
american_scientific_journal-3270	262	20	p	p	PROPN
american_scientific_journal-3270	262	21	y	y	PROPN
american_scientific_journal-3270	262	22	x	x	ADJ
american_scientific_journal-3270	262	23	dydx	dydx	PROPN
american_scientific_journal-3270	262	24	m	m	NOUN
american_scientific_journal-3270	262	25	−	−	PROPN
american_scientific_journal-3270	262	26	−	−	PROPN
american_scientific_journal-3270	262	27			NOUN
american_scientific_journal-3270	262	28			NUM
american_scientific_journal-3270	262	29	−	−	NOUN
american_scientific_journal-3270	263	1	=	=	SYM
american_scientific_journal-3270	263	2			ADJ
american_scientific_journal-3270	263	3			PROPN
american_scientific_journal-3270	263	4			SYM
american_scientific_journal-3270	263	5			PROPN
american_scientific_journal-3270	263	6	∫	∫	PROPN
american_scientific_journal-3270	263	7	∫	∫	PROPN
american_scientific_journal-3270	263	8	ii	ii	PROPN
american_scientific_journal-3270	263	9	)	)	PUNCT
american_scientific_journal-3270	263	10	the	the	DET
american_scientific_journal-3270	263	11	kernel	kernel	NOUN
american_scientific_journal-3270	263	12	of	of	ADP
american_scientific_journal-3270	263	13	volterra	volterra	PROPN
american_scientific_journal-3270	263	14	integral	integral	ADJ
american_scientific_journal-3270	263	15	term	term	NOUN
american_scientific_journal-3270	263	16	(	(	PUNCT
american_scientific_journal-3270	263	17	,	,	PUNCT
american_scientific_journal-3270	263	18	)	)	PUNCT
american_scientific_journal-3270	263	19	;	;	PUNCT
american_scientific_journal-3270	263	20	tx	tx	PROPN
american_scientific_journal-3270	263	21	t	t	PROPN
american_scientific_journal-3270	263	22	in	in	ADP
american_scientific_journal-3270	263	23	the	the	DET
american_scientific_journal-3270	263	24	space	space	NOUN
american_scientific_journal-3270	263	25	[	[	PUNCT
american_scientific_journal-3270	263	26	]	]	X
american_scientific_journal-3270	263	27	tc	tc	NUM
american_scientific_journal-3270	263	28	,	,	PUNCT
american_scientific_journal-3270	263	29	0	0	NUM
american_scientific_journal-3270	263	30	,	,	PUNCT
american_scientific_journal-3270	263	31	is	be	AUX
american_scientific_journal-3270	263	32	continuous	continuous	ADJ
american_scientific_journal-3270	263	33	and	and	CCONJ
american_scientific_journal-3270	263	34	satisfies	satisfie	NOUN
american_scientific_journal-3270	263	35	for	for	ADP
american_scientific_journal-3270	263	36	a	a	DET
american_scientific_journal-3270	263	37	constant	constant	ADJ
american_scientific_journal-3270	263	38	n	n	NOUN
american_scientific_journal-3270	263	39	,	,	PUNCT
american_scientific_journal-3270	263	40	the	the	DET
american_scientific_journal-3270	263	41	condition	condition	NOUN
american_scientific_journal-3270	263	42	(	(	PUNCT
american_scientific_journal-3270	263	43	)	)	PUNCT
american_scientific_journal-3270	263	44	,	,	PUNCT
american_scientific_journal-3270	263	45	,	,	PUNCT
american_scientific_journal-3270	263	46	t	t	PROPN
american_scientific_journal-3270	263	47	nx	nx	PROPN
american_scientific_journal-3270	263	48	t	t	PROPN
american_scientific_journal-3270	263	49	≤	≤	PROPN
american_scientific_journal-3270	263	50	[	[	PUNCT
american_scientific_journal-3270	263	51	]	]	X
american_scientific_journal-3270	263	52	,	,	PUNCT
american_scientific_journal-3270	263	53	0,t	0,t	PROPN
american_scientific_journal-3270	263	54	tt∀	tt∀	PROPN
american_scientific_journal-3270	263	55	∈	∈	PROPN
american_scientific_journal-3270	263	56	.	.	PUNCT
american_scientific_journal-3270	264	1	iii	iii	X
american_scientific_journal-3270	264	2	)	)	PUNCT
american_scientific_journal-3270	264	3	the	the	DET
american_scientific_journal-3270	264	4	given	give	VERB
american_scientific_journal-3270	264	5	function	function	NOUN
american_scientific_journal-3270	264	6	(	(	PUNCT
american_scientific_journal-3270	264	7	,	,	PUNCT
american_scientific_journal-3270	264	8	)	)	PUNCT
american_scientific_journal-3270	264	9	f	f	X
american_scientific_journal-3270	265	1	x	x	PUNCT
american_scientific_journal-3270	265	2	t	t	PROPN
american_scientific_journal-3270	265	3	is	be	AUX
american_scientific_journal-3270	265	4	continuous	continuous	ADJ
american_scientific_journal-3270	265	5	in	in	ADP
american_scientific_journal-3270	265	6	the	the	DET
american_scientific_journal-3270	265	7	space	space	NOUN
american_scientific_journal-3270	265	8	[	[	PUNCT
american_scientific_journal-3270	265	9	]	]	X
american_scientific_journal-3270	265	10	2	2	NUM
american_scientific_journal-3270	265	11	1,1	1,1	NUM
american_scientific_journal-3270	265	12	[	[	X
american_scientific_journal-3270	265	13	0	0	NUM
american_scientific_journal-3270	265	14	,	,	PUNCT
american_scientific_journal-3270	265	15	]	]	X
american_scientific_journal-3270	265	16	l	l	NOUN
american_scientific_journal-3270	265	17	c	c	X
american_scientific_journal-3270	265	18	t−	t−	PROPN
american_scientific_journal-3270	265	19	×	×	NOUN
american_scientific_journal-3270	265	20	,	,	PUNCT
american_scientific_journal-3270	265	21	and	and	CCONJ
american_scientific_journal-3270	265	22	its	its	PRON
american_scientific_journal-3270	265	23	norm	norm	NOUN
american_scientific_journal-3270	265	24	is	be	AUX
american_scientific_journal-3270	265	25	1	1	NUM
american_scientific_journal-3270	265	26	1	1	NUM
american_scientific_journal-3270	265	27	2	2	NUM
american_scientific_journal-3270	265	28	2	2	NUM
american_scientific_journal-3270	265	29	0	0	NUM
american_scientific_journal-3270	265	30	0	0	NUM
american_scientific_journal-3270	265	31	1	1	NUM
american_scientific_journal-3270	265	32	(	(	PUNCT
american_scientific_journal-3270	265	33	,	,	PUNCT
american_scientific_journal-3270	265	34	)	)	PUNCT
american_scientific_journal-3270	265	35	(	(	PUNCT
american_scientific_journal-3270	265	36	,	,	PUNCT
american_scientific_journal-3270	265	37	)	)	PUNCT
american_scientific_journal-3270	265	38	,	,	PUNCT
american_scientific_journal-3270	266	1	max	max	PROPN
american_scientific_journal-3270	266	2	t	t	PROPN
american_scientific_journal-3270	266	3	t	t	PROPN
american_scientific_journal-3270	266	4	t	t	PROPN
american_scientific_journal-3270	267	1	f	f	X
american_scientific_journal-3270	267	2	x	x	X
american_scientific_journal-3270	267	3	t	t	NOUN
american_scientific_journal-3270	267	4	f	f	X
american_scientific_journal-3270	267	5	x	x	X
american_scientific_journal-3270	267	6	dx	dx	PROPN
american_scientific_journal-3270	268	1	d	d	PROPN
american_scientific_journal-3270	268	2	rt	rt	PROPN
american_scientific_journal-3270	268	3	t	t	PROPN
american_scientific_journal-3270	268	4	≤	≤	ADJ
american_scientific_journal-3270	268	5	≤	≤	NUM
american_scientific_journal-3270	268	6	−	−	PROPN
american_scientific_journal-3270	268	7			NOUN
american_scientific_journal-3270	268	8			NUM
american_scientific_journal-3270	268	9	=	=	SYM
american_scientific_journal-3270	269	1	=	=	NOUN
american_scientific_journal-3270	269	2			ADJ
american_scientific_journal-3270	269	3			PROPN
american_scientific_journal-3270	269	4			SYM
american_scientific_journal-3270	269	5			PROPN
american_scientific_journal-3270	269	6	∫	∫	PROPN
american_scientific_journal-3270	269	7	∫	∫	PROPN
american_scientific_journal-3270	269	8	.	.	PUNCT
american_scientific_journal-3270	270	1	theorem	theorem	VERB
american_scientific_journal-3270	270	2	1.1	1.1	NUM
american_scientific_journal-3270	270	3	:	:	PUNCT
american_scientific_journal-3270	270	4	the	the	DET
american_scientific_journal-3270	270	5	mixed	mixed	ADJ
american_scientific_journal-3270	270	6	integral	integral	ADJ
american_scientific_journal-3270	270	7	equation	equation	NOUN
american_scientific_journal-3270	270	8	has	have	VERB
american_scientific_journal-3270	270	9	a	a	DET
american_scientific_journal-3270	270	10	unique	unique	ADJ
american_scientific_journal-3270	270	11	solution	solution	NOUN
american_scientific_journal-3270	270	12	in	in	ADP
american_scientific_journal-3270	270	13	the	the	DET
american_scientific_journal-3270	270	14	space	space	NOUN
american_scientific_journal-3270	270	15	[	[	PUNCT
american_scientific_journal-3270	270	16	]	]	X
american_scientific_journal-3270	270	17	2	2	NUM
american_scientific_journal-3270	270	18	1,1	1,1	NUM
american_scientific_journal-3270	270	19	[	[	X
american_scientific_journal-3270	270	20	0	0	NUM
american_scientific_journal-3270	270	21	,	,	PUNCT
american_scientific_journal-3270	270	22	]	]	X
american_scientific_journal-3270	270	23	l	l	NOUN
american_scientific_journal-3270	270	24	c	c	X
american_scientific_journal-3270	270	25	t−	t−	PROPN
american_scientific_journal-3270	270	26	×	×	NOUN
american_scientific_journal-3270	270	27	,	,	PUNCT
american_scientific_journal-3270	270	28	under	under	ADP
american_scientific_journal-3270	270	29	the	the	DET
american_scientific_journal-3270	270	30	condition	condition	NOUN
american_scientific_journal-3270	270	31	0	0	NUM
american_scientific_journal-3270	271	1	(	(	PUNCT
american_scientific_journal-3270	271	2	2	2	NUM
american_scientific_journal-3270	271	3	(	(	PUNCT
american_scientific_journal-3270	271	4	)	)	PUNCT
american_scientific_journal-3270	271	5	)	)	PUNCT
american_scientific_journal-3270	271	6	;	;	PUNCT
american_scientific_journal-3270	272	1	max	max	PROPN
american_scientific_journal-3270	272	2	t	t	PROPN
american_scientific_journal-3270	272	3	m	m	PROPN
american_scientific_journal-3270	272	4	t	t	PROPN
american_scientific_journal-3270	272	5	l	l	NOUN
american_scientific_journal-3270	272	6	n	n	ADP
american_scientific_journal-3270	272	7	t	t	NOUN
american_scientific_journal-3270	273	1	tη	tη	PROPN
american_scientific_journal-3270	273	2	λ	λ	PROPN
american_scientific_journal-3270	273	3	π	π	PROPN
american_scientific_journal-3270	273	4	≤	≤	X
american_scientific_journal-3270	273	5	≤t	≤t	PROPN
american_scientific_journal-3270	273	6	>	>	X
american_scientific_journal-3270	274	1	+	+	PUNCT
american_scientific_journal-3270	275	1	+	+	CCONJ
american_scientific_journal-3270	275	2	=	=	X
american_scientific_journal-3270	275	3	,	,	PUNCT
american_scientific_journal-3270	275	4	.	.	PUNCT
american_scientific_journal-3270	276	1	(	(	PUNCT
american_scientific_journal-3270	276	2	3.4	3.4	NUM
american_scientific_journal-3270	276	3	)	)	PUNCT
american_scientific_journal-3270	276	4	proof	proof	NOUN
american_scientific_journal-3270	276	5	:	:	PUNCT
american_scientific_journal-3270	276	6	to	to	PART
american_scientific_journal-3270	276	7	prove	prove	VERB
american_scientific_journal-3270	276	8	theorem	theorem	VERB
american_scientific_journal-3270	276	9	1.1	1.1	NUM
american_scientific_journal-3270	276	10	,	,	PUNCT
american_scientific_journal-3270	276	11	we	we	PRON
american_scientific_journal-3270	276	12	must	must	AUX
american_scientific_journal-3270	276	13	prove	prove	VERB
american_scientific_journal-3270	276	14	the	the	DET
american_scientific_journal-3270	276	15	following	follow	VERB
american_scientific_journal-3270	276	16	lemmas	lemmas	NOUN
american_scientific_journal-3270	276	17	.	.	PUNCT
american_scientific_journal-3270	277	1	american	american	ADJ
american_scientific_journal-3270	277	2	scientific	scientific	ADJ
american_scientific_journal-3270	277	3	research	research	PROPN
american_scientific_journal-3270	277	4	journal	journal	NOUN
american_scientific_journal-3270	277	5	for	for	ADP
american_scientific_journal-3270	277	6	engineering	engineering	NOUN
american_scientific_journal-3270	277	7	,	,	PUNCT
american_scientific_journal-3270	277	8	technology	technology	NOUN
american_scientific_journal-3270	277	9	,	,	PUNCT
american_scientific_journal-3270	277	10	and	and	CCONJ
american_scientific_journal-3270	277	11	sciences	science	NOUN
american_scientific_journal-3270	277	12	(	(	PUNCT
american_scientific_journal-3270	277	13	asrjets	asrjet	NOUN
american_scientific_journal-3270	277	14	)	)	PUNCT
american_scientific_journal-3270	277	15	(	(	PUNCT
american_scientific_journal-3270	277	16	2017	2017	NUM
american_scientific_journal-3270	277	17	)	)	PUNCT
american_scientific_journal-3270	277	18	volume	volume	NOUN
american_scientific_journal-3270	277	19	34	34	NUM
american_scientific_journal-3270	277	20	,	,	PUNCT
american_scientific_journal-3270	277	21	no	no	DET
american_scientific_journal-3270	277	22	1	1	NUM
american_scientific_journal-3270	277	23	,	,	PUNCT
american_scientific_journal-3270	277	24	pp	pp	ADV
american_scientific_journal-3270	277	25	213	213	NUM
american_scientific_journal-3270	277	26	-	-	SYM
american_scientific_journal-3270	277	27	230	230	NUM
american_scientific_journal-3270	277	28	221	221	NUM
american_scientific_journal-3270	277	29	lemma	lemma	PROPN
american_scientific_journal-3270	277	30	1.1	1.1	NUM
american_scientific_journal-3270	277	31	:	:	PUNCT
american_scientific_journal-3270	277	32	the	the	DET
american_scientific_journal-3270	277	33	integral	integral	ADJ
american_scientific_journal-3270	277	34	operator	operator	NOUN
american_scientific_journal-3270	277	35	w	w	PROPN
american_scientific_journal-3270	277	36	maps	map	NOUN
american_scientific_journal-3270	277	37	[	[	PUNCT
american_scientific_journal-3270	277	38	]	]	SYM
american_scientific_journal-3270	277	39	2	2	NUM
american_scientific_journal-3270	277	40	1,1	1,1	NUM
american_scientific_journal-3270	277	41	[	[	X
american_scientific_journal-3270	277	42	0	0	NUM
american_scientific_journal-3270	277	43	,	,	PUNCT
american_scientific_journal-3270	277	44	]	]	X
american_scientific_journal-3270	277	45	l	l	NOUN
american_scientific_journal-3270	277	46	c	c	X
american_scientific_journal-3270	277	47	t−	t−	DET
american_scientific_journal-3270	277	48	×	×	NOUN
american_scientific_journal-3270	277	49	into	into	ADP
american_scientific_journal-3270	277	50	itself	itself	PRON
american_scientific_journal-3270	277	51	.	.	PUNCT
american_scientific_journal-3270	278	1	proof	proof	NOUN
american_scientific_journal-3270	278	2	:	:	PUNCT
american_scientific_journal-3270	278	3	from	from	ADP
american_scientific_journal-3270	278	4	the	the	DET
american_scientific_journal-3270	278	5	formulas	formula	NOUN
american_scientific_journal-3270	278	6	(	(	PUNCT
american_scientific_journal-3270	278	7	3.1)-(3.3	3.1)-(3.3	NUM
american_scientific_journal-3270	278	8	)	)	PUNCT
american_scientific_journal-3270	278	9	,	,	PUNCT
american_scientific_journal-3270	278	10	the	the	DET
american_scientific_journal-3270	278	11	normality	normality	NOUN
american_scientific_journal-3270	278	12	of	of	ADP
american_scientific_journal-3270	278	13	the	the	DET
american_scientific_journal-3270	278	14	integral	integral	ADJ
american_scientific_journal-3270	278	15	operator	operator	NOUN
american_scientific_journal-3270	278	16	,	,	PUNCT
american_scientific_journal-3270	278	17	and	and	CCONJ
american_scientific_journal-3270	278	18	h	h	NOUN
american_scientific_journal-3270	278	19	dφ	dφ	ADP
american_scientific_journal-3270	278	20	φ	φ	PROPN
american_scientific_journal-3270	278	21	xφ	xφ	PROPN
american_scientific_journal-3270	278	22	will	will	AUX
american_scientific_journal-3270	278	23	take	take	VERB
american_scientific_journal-3270	278	24	the	the	DET
american_scientific_journal-3270	278	25	forms	form	NOUN
american_scientific_journal-3270	278	26	0	0	NUM
american_scientific_journal-3270	278	27	;	;	PUNCT
american_scientific_journal-3270	278	28	2	2	NUM
american_scientific_journal-3270	278	29	;	;	PUNCT
american_scientific_journal-3270	278	30	2	2	NUM
american_scientific_journal-3270	278	31	,	,	PUNCT
american_scientific_journal-3270	278	32	max	max	PROPN
american_scientific_journal-3270	278	33	t	t	PROPN
american_scientific_journal-3270	278	34	h	h	NOUN
american_scientific_journal-3270	278	35	m	m	VERB
american_scientific_journal-3270	278	36	d	d	NOUN
american_scientific_journal-3270	278	37	lt	lt	VERB
american_scientific_journal-3270	278	38	nt	not	PART
american_scientific_journal-3270	278	39	t	t	PROPN
american_scientific_journal-3270	278	40	tλ	tλ	NOUN
american_scientific_journal-3270	278	41	λ	λ	PROPN
american_scientific_journal-3270	278	42	λφ	λφ	ADP
american_scientific_journal-3270	278	43	φ	φ	PROPN
american_scientific_journal-3270	278	44	φ	φ	PROPN
american_scientific_journal-3270	278	45	φ	φ	PROPN
american_scientific_journal-3270	278	46	xφ	xφ	PROPN
american_scientific_journal-3270	278	47	φ	φ	PROPN
american_scientific_journal-3270	278	48	ηπ	ηπ	PROPN
american_scientific_journal-3270	278	49	η	η	PROPN
american_scientific_journal-3270	278	50	η	η	PROPN
american_scientific_journal-3270	278	51	≤	≤	PROPN
american_scientific_journal-3270	278	52	≤t	≤t	NOUN
american_scientific_journal-3270	278	53	≤	≤	ADJ
american_scientific_journal-3270	278	54	≤	≤	NOUN
american_scientific_journal-3270	278	55	≤	≤	NUM
american_scientific_journal-3270	278	56	=	=	PUNCT
american_scientific_journal-3270	278	57	,	,	PUNCT
american_scientific_journal-3270	278	58	(	(	PUNCT
american_scientific_journal-3270	278	59	3.5	3.5	NUM
american_scientific_journal-3270	278	60	)	)	PUNCT
american_scientific_journal-3270	278	61	hence	hence	ADV
american_scientific_journal-3270	278	62	,	,	PUNCT
american_scientific_journal-3270	278	63	with	with	ADP
american_scientific_journal-3270	278	64	the	the	DET
american_scientific_journal-3270	278	65	aid	aid	NOUN
american_scientific_journal-3270	278	66	of	of	ADP
american_scientific_journal-3270	278	67	condition	condition	NOUN
american_scientific_journal-3270	278	68	(	(	PUNCT
american_scientific_journal-3270	278	69	iv	iv	X
american_scientific_journal-3270	278	70	)	)	PUNCT
american_scientific_journal-3270	278	71	and	and	CCONJ
american_scientific_journal-3270	278	72	(	(	PUNCT
american_scientific_journal-3270	278	73	3.5	3.5	NUM
american_scientific_journal-3270	278	74	)	)	PUNCT
american_scientific_journal-3270	278	75	,	,	PUNCT
american_scientific_journal-3270	278	76	we	we	PRON
american_scientific_journal-3270	278	77	get	get	VERB
american_scientific_journal-3270	278	78	(	(	PUNCT
american_scientific_journal-3270	278	79	)	)	PUNCT
american_scientific_journal-3270	278	80	1	1	NUM
american_scientific_journal-3270	278	81	0	0	NUM
american_scientific_journal-3270	278	82	;	;	PUNCT
american_scientific_journal-3270	278	83	2	2	NUM
american_scientific_journal-3270	278	84	,	,	PUNCT
american_scientific_journal-3270	278	85	max	max	PROPN
american_scientific_journal-3270	278	86	t	t	PROPN
american_scientific_journal-3270	278	87	t	t	PROPN
american_scientific_journal-3270	278	88	r	r	NOUN
american_scientific_journal-3270	278	89	mw	mw	PROPN
american_scientific_journal-3270	278	90	t	t	PROPN
american_scientific_journal-3270	278	91	l	l	NOUN
american_scientific_journal-3270	279	1	n	n	ADP
american_scientific_journal-3270	279	2	t	t	X
american_scientific_journal-3270	279	3	tφ	tφ	PROPN
american_scientific_journal-3270	279	4	α	α	PROPN
american_scientific_journal-3270	279	5	φ	φ	PROPN
american_scientific_journal-3270	279	6	α	α	PROPN
american_scientific_journal-3270	279	7	η	η	PROPN
american_scientific_journal-3270	279	8	λ	λ	PROPN
american_scientific_journal-3270	279	9	η	η	PROPN
american_scientific_journal-3270	279	10	π	π	PROPN
american_scientific_journal-3270	279	11	−	−	PROPN
american_scientific_journal-3270	279	12	≤	≤	ADJ
american_scientific_journal-3270	279	13	≤	≤	NUM
american_scientific_journal-3270	279	14			NOUN
american_scientific_journal-3270	279	15			NOUN
american_scientific_journal-3270	279	16	≤	≤	PUNCT
american_scientific_journal-3270	280	1	+	+	PUNCT
american_scientific_journal-3270	280	2	=	=	PUNCT
american_scientific_journal-3270	281	1	+	+	PUNCT
american_scientific_journal-3270	282	1	+	+	CCONJ
american_scientific_journal-3270	282	2	=	=	NOUN
american_scientific_journal-3270	282	3			NOUN
american_scientific_journal-3270	282	4			NOUN
american_scientific_journal-3270	282	5			VERB
american_scientific_journal-3270	282	6			PRON
american_scientific_journal-3270	282	7			VERB
american_scientific_journal-3270	282	8			PUNCT
american_scientific_journal-3270	282	9	,	,	PUNCT
american_scientific_journal-3270	282	10	.	.	PUNCT
american_scientific_journal-3270	283	1	(	(	PUNCT
american_scientific_journal-3270	283	2	3.6	3.6	NUM
american_scientific_journal-3270	283	3	)	)	PUNCT
american_scientific_journal-3270	283	4	the	the	DET
american_scientific_journal-3270	283	5	inequality	inequality	NOUN
american_scientific_journal-3270	283	6	(	(	PUNCT
american_scientific_journal-3270	283	7	3.6	3.6	NUM
american_scientific_journal-3270	283	8	)	)	PUNCT
american_scientific_journal-3270	283	9	yields	yield	NOUN
american_scientific_journal-3270	283	10	that	that	PRON
american_scientific_journal-3270	283	11	,	,	PUNCT
american_scientific_journal-3270	283	12	the	the	DET
american_scientific_journal-3270	283	13	operator	operator	NOUN
american_scientific_journal-3270	283	14	w	w	PROPN
american_scientific_journal-3270	283	15	maps	map	NOUN
american_scientific_journal-3270	283	16	the	the	DET
american_scientific_journal-3270	283	17	ball	ball	NOUN
american_scientific_journal-3270	283	18	s	s	NOUN
american_scientific_journal-3270	283	19	ρ	ρ	NOUN
american_scientific_journal-3270	283	20	in	in	ADP
american_scientific_journal-3270	283	21	[	[	PUNCT
american_scientific_journal-3270	283	22	]	]	X
american_scientific_journal-3270	283	23	2	2	NUM
american_scientific_journal-3270	283	24	1,1	1,1	NUM
american_scientific_journal-3270	284	1	[	[	X
american_scientific_journal-3270	284	2	0	0	NUM
american_scientific_journal-3270	284	3	,	,	PUNCT
american_scientific_journal-3270	284	4	]	]	X
american_scientific_journal-3270	284	5	l	l	NOUN
american_scientific_journal-3270	284	6	c	c	X
american_scientific_journal-3270	284	7	t−	t−	DET
american_scientific_journal-3270	284	8	×	×	NOUN
american_scientific_journal-3270	284	9	into	into	ADP
american_scientific_journal-3270	284	10	itself	itself	PRON
american_scientific_journal-3270	284	11	,	,	PUNCT
american_scientific_journal-3270	284	12	where	where	SCONJ
american_scientific_journal-3270	284	13	1	1	NUM
american_scientific_journal-3270	284	14	1	1	NUM
american_scientific_journal-3270	284	15	rρ	rρ	PROPN
american_scientific_journal-3270	284	16	η	η	PROPN
american_scientific_journal-3270	284	17	α	α	PRON
american_scientific_journal-3270	284	18			NOUN
american_scientific_journal-3270	284	19	=	=	ADP
american_scientific_journal-3270	284	20			PROPN
american_scientific_journal-3270	284	21	−	−	PROPN
american_scientific_journal-3270	284	22			PUNCT
american_scientific_journal-3270	284	23	.	.	PUNCT
american_scientific_journal-3270	285	1	(	(	PUNCT
american_scientific_journal-3270	285	2	3.7	3.7	NUM
american_scientific_journal-3270	285	3	)	)	PUNCT
american_scientific_journal-3270	285	4	since	since	SCONJ
american_scientific_journal-3270	285	5	0	0	NUM
american_scientific_journal-3270	285	6	1	1	NUM
american_scientific_journal-3270	285	7	,	,	PUNCT
american_scientific_journal-3270	285	8	0rρ	0rρ	NOUN
american_scientific_journal-3270	285	9	<	<	X
american_scientific_journal-3270	285	10	<	<	X
american_scientific_journal-3270	285	11	>	>	X
american_scientific_journal-3270	285	12	,	,	PUNCT
american_scientific_journal-3270	285	13	therefore	therefore	ADV
american_scientific_journal-3270	285	14	we	we	PRON
american_scientific_journal-3270	285	15	must	must	AUX
american_scientific_journal-3270	285	16	have	have	VERB
american_scientific_journal-3270	285	17	(	(	PUNCT
american_scientific_journal-3270	285	18	1)α	1)α	NOUN
american_scientific_journal-3270	285	19	<	<	X
american_scientific_journal-3270	285	20	.	.	PUNCT
american_scientific_journal-3270	286	1	moreover	moreover	ADV
american_scientific_journal-3270	286	2	,	,	PUNCT
american_scientific_journal-3270	286	3	the	the	DET
american_scientific_journal-3270	286	4	inequality	inequality	NOUN
american_scientific_journal-3270	286	5	(	(	PUNCT
american_scientific_journal-3270	286	6	3.7	3.7	NUM
american_scientific_journal-3270	286	7	)	)	PUNCT
american_scientific_journal-3270	286	8	involves	involve	VERB
american_scientific_journal-3270	286	9	that	that	SCONJ
american_scientific_journal-3270	286	10	,	,	PUNCT
american_scientific_journal-3270	286	11	the	the	DET
american_scientific_journal-3270	286	12	operators	operator	NOUN
american_scientific_journal-3270	286	13	w	w	PROPN
american_scientific_journal-3270	286	14	and	and	CCONJ
american_scientific_journal-3270	286	15	w	w	PROPN
american_scientific_journal-3270	286	16	are	be	AUX
american_scientific_journal-3270	286	17	bounded	bound	VERB
american_scientific_journal-3270	286	18	lemma	lemma	PROPN
american_scientific_journal-3270	286	19	1.2	1.2	NUM
american_scientific_journal-3270	286	20	:	:	PUNCT
american_scientific_journal-3270	286	21	the	the	DET
american_scientific_journal-3270	286	22	integral	integral	ADJ
american_scientific_journal-3270	286	23	operator	operator	NOUN
american_scientific_journal-3270	286	24	(	(	PUNCT
american_scientific_journal-3270	286	25	3.1	3.1	NUM
american_scientific_journal-3270	286	26	)	)	PUNCT
american_scientific_journal-3270	286	27	,	,	PUNCT
american_scientific_journal-3270	286	28	under	under	ADP
american_scientific_journal-3270	286	29	the	the	DET
american_scientific_journal-3270	286	30	condition	condition	NOUN
american_scientific_journal-3270	286	31	(	(	PUNCT
american_scientific_journal-3270	286	32	3.4	3.4	NUM
american_scientific_journal-3270	286	33	)	)	PUNCT
american_scientific_journal-3270	286	34	is	be	AUX
american_scientific_journal-3270	286	35	continuous	continuous	ADJ
american_scientific_journal-3270	286	36	and	and	CCONJ
american_scientific_journal-3270	286	37	contraction	contraction	NOUN
american_scientific_journal-3270	286	38	operator	operator	NOUN
american_scientific_journal-3270	286	39	.	.	PUNCT
american_scientific_journal-3270	287	1	proof	proof	NOUN
american_scientific_journal-3270	287	2	:	:	PUNCT
american_scientific_journal-3270	287	3	for	for	ADP
american_scientific_journal-3270	287	4	the	the	DET
american_scientific_journal-3270	287	5	two	two	NUM
american_scientific_journal-3270	287	6	functions	function	NOUN
american_scientific_journal-3270	287	7	1	1	NUM
american_scientific_journal-3270	287	8	(	(	PUNCT
american_scientific_journal-3270	287	9	,	,	PUNCT
american_scientific_journal-3270	287	10	)	)	PUNCT
american_scientific_journal-3270	287	11	x	x	SYM
american_scientific_journal-3270	287	12	tφ	tφ	NOUN
american_scientific_journal-3270	287	13	and	and	CCONJ
american_scientific_journal-3270	287	14	2	2	NUM
american_scientific_journal-3270	287	15	(	(	PUNCT
american_scientific_journal-3270	287	16	,	,	PUNCT
american_scientific_journal-3270	287	17	)	)	PUNCT
american_scientific_journal-3270	287	18	x	x	PROPN
american_scientific_journal-3270	287	19	tφ	tφ	NOUN
american_scientific_journal-3270	287	20	in	in	ADP
american_scientific_journal-3270	287	21	the	the	DET
american_scientific_journal-3270	287	22	banach	banach	NOUN
american_scientific_journal-3270	287	23	space	space	NOUN
american_scientific_journal-3270	287	24	(	(	PUNCT
american_scientific_journal-3270	287	25	)	)	PUNCT
american_scientific_journal-3270	287	26	2	2	NUM
american_scientific_journal-3270	287	27	1,1	1,1	NUM
american_scientific_journal-3270	288	1	[	[	X
american_scientific_journal-3270	288	2	0	0	NUM
american_scientific_journal-3270	288	3	,	,	PUNCT
american_scientific_journal-3270	288	4	]	]	X
american_scientific_journal-3270	288	5	l	l	NOUN
american_scientific_journal-3270	288	6	c	c	X
american_scientific_journal-3270	288	7	t−	t−	PROPN
american_scientific_journal-3270	288	8	×	×	VERB
american_scientific_journal-3270	288	9	the	the	DET
american_scientific_journal-3270	288	10	formula	formula	NOUN
american_scientific_journal-3270	288	11	(	(	PUNCT
american_scientific_journal-3270	288	12	3.1	3.1	NUM
american_scientific_journal-3270	288	13	)	)	PUNCT
american_scientific_journal-3270	288	14	after	after	ADP
american_scientific_journal-3270	288	15	using	use	VERB
american_scientific_journal-3270	288	16	the	the	DET
american_scientific_journal-3270	288	17	conditions	condition	NOUN
american_scientific_journal-3270	288	18	(	(	PUNCT
american_scientific_journal-3270	288	19	i),(ii	i),(ii	PROPN
american_scientific_journal-3270	288	20	)	)	PUNCT
american_scientific_journal-3270	288	21	and	and	CCONJ
american_scientific_journal-3270	288	22	(	(	PUNCT
american_scientific_journal-3270	288	23	iii	iii	NOUN
american_scientific_journal-3270	288	24	)	)	PUNCT
american_scientific_journal-3270	288	25	,	,	PUNCT
american_scientific_journal-3270	288	26	then	then	ADV
american_scientific_journal-3270	288	27	applying	apply	VERB
american_scientific_journal-3270	288	28	cauchy	cauchy	NOUN
american_scientific_journal-3270	288	29	–	–	PUNCT
american_scientific_journal-3270	288	30	schwarz	schwarz	PROPN
american_scientific_journal-3270	288	31	inequality	inequality	NOUN
american_scientific_journal-3270	288	32	,	,	PUNCT
american_scientific_journal-3270	288	33	yields	yield	VERB
american_scientific_journal-3270	288	34	1	1	NUM
american_scientific_journal-3270	288	35	1	1	NUM
american_scientific_journal-3270	288	36	2	2	NUM
american_scientific_journal-3270	288	37	1	1	NUM
american_scientific_journal-3270	288	38	2	2	NUM
american_scientific_journal-3270	288	39	,	,	PUNCT
american_scientific_journal-3270	288	40	2	2	NUM
american_scientific_journal-3270	288	41	(	(	PUNCT
american_scientific_journal-3270	288	42	)	)	PUNCT
american_scientific_journal-3270	288	43	mw	mw	PROPN
american_scientific_journal-3270	288	44	w	w	PROPN
american_scientific_journal-3270	288	45	t	t	PROPN
american_scientific_journal-3270	288	46	l	l	PROPN
american_scientific_journal-3270	288	47	nφ	nφ	PROPN
american_scientific_journal-3270	289	1	φ	φ	PROPN
american_scientific_journal-3270	289	2	α	α	PROPN
american_scientific_journal-3270	289	3	φ	φ	PROPN
american_scientific_journal-3270	289	4	φ	φ	PROPN
american_scientific_journal-3270	289	5	α	α	PROPN
american_scientific_journal-3270	289	6	η	η	PROPN
american_scientific_journal-3270	289	7	λ	λ	PROPN
american_scientific_journal-3270	289	8	π	π	PROPN
american_scientific_journal-3270	289	9	−	−	VERB
american_scientific_journal-3270	289	10			NOUN
american_scientific_journal-3270	289	11	−	−	ADJ
american_scientific_journal-3270	289	12	≤	≤	PUNCT
american_scientific_journal-3270	290	1	−	−	PUNCT
american_scientific_journal-3270	291	1	=	=	PUNCT
american_scientific_journal-3270	292	1	+	+	PUNCT
american_scientific_journal-3270	292	2	+	+	ADJ
american_scientific_journal-3270	292	3			ADJ
american_scientific_journal-3270	292	4			NOUN
american_scientific_journal-3270	292	5			VERB
american_scientific_journal-3270	292	6			PRON
american_scientific_journal-3270	292	7			VERB
american_scientific_journal-3270	292	8			PUNCT
american_scientific_journal-3270	292	9	.	.	PUNCT
american_scientific_journal-3270	293	1	(	(	PUNCT
american_scientific_journal-3270	293	2	3.8	3.8	NUM
american_scientific_journal-3270	293	3	)	)	PUNCT
american_scientific_journal-3270	293	4	hence	hence	ADV
american_scientific_journal-3270	293	5	,	,	PUNCT
american_scientific_journal-3270	293	6	w	w	PROPN
american_scientific_journal-3270	293	7	is	be	AUX
american_scientific_journal-3270	293	8	a	a	DET
american_scientific_journal-3270	293	9	continuous	continuous	ADJ
american_scientific_journal-3270	293	10	operator	operator	NOUN
american_scientific_journal-3270	293	11	in	in	ADP
american_scientific_journal-3270	293	12	the	the	DET
american_scientific_journal-3270	293	13	space	space	NOUN
american_scientific_journal-3270	293	14	[	[	PUNCT
american_scientific_journal-3270	293	15	]	]	X
american_scientific_journal-3270	293	16	2	2	NUM
american_scientific_journal-3270	293	17	1,1	1,1	NUM
american_scientific_journal-3270	293	18	[	[	X
american_scientific_journal-3270	293	19	0	0	NUM
american_scientific_journal-3270	293	20	,	,	PUNCT
american_scientific_journal-3270	293	21	]	]	X
american_scientific_journal-3270	293	22	l	l	NOUN
american_scientific_journal-3270	293	23	c	c	X
american_scientific_journal-3270	293	24	t−	t−	PROPN
american_scientific_journal-3270	293	25	×	×	NOUN
american_scientific_journal-3270	293	26	,	,	PUNCT
american_scientific_journal-3270	293	27	and	and	CCONJ
american_scientific_journal-3270	293	28	under	under	ADP
american_scientific_journal-3270	293	29	the	the	DET
american_scientific_journal-3270	293	30	condition	condition	NOUN
american_scientific_journal-3270	293	31	(	(	PUNCT
american_scientific_journal-3270	293	32	1)α	1)α	NUM
american_scientific_journal-3270	293	33	<	<	X
american_scientific_journal-3270	293	34	,	,	PUNCT
american_scientific_journal-3270	293	35	is	be	AUX
american_scientific_journal-3270	293	36	a	a	DET
american_scientific_journal-3270	293	37	contraction	contraction	NOUN
american_scientific_journal-3270	293	38	operator	operator	NOUN
american_scientific_journal-3270	293	39	.	.	PUNCT
american_scientific_journal-3270	294	1	from	from	ADP
american_scientific_journal-3270	294	2	lemma	lemma	PROPN
american_scientific_journal-3270	294	3	1.1	1.1	NUM
american_scientific_journal-3270	294	4	and	and	CCONJ
american_scientific_journal-3270	294	5	lemma	lemma	PROPN
american_scientific_journal-3270	294	6	1.2	1.2	NUM
american_scientific_journal-3270	294	7	and	and	CCONJ
american_scientific_journal-3270	294	8	banach	banach	ADV
american_scientific_journal-3270	294	9	fixed	fix	VERB
american_scientific_journal-3270	294	10	-point	-point	NOUN
american_scientific_journal-3270	294	11	theorem	theorem	NOUN
american_scientific_journal-3270	294	12	,	,	PUNCT
american_scientific_journal-3270	294	13	we	we	PRON
american_scientific_journal-3270	294	14	can	can	AUX
american_scientific_journal-3270	294	15	decide	decide	VERB
american_scientific_journal-3270	294	16	that	that	SCONJ
american_scientific_journal-3270	294	17	the	the	DET
american_scientific_journal-3270	294	18	operator	operator	NOUN
american_scientific_journal-3270	294	19	w	w	NOUN
american_scientific_journal-3270	294	20	has	have	VERB
american_scientific_journal-3270	294	21	a	a	DET
american_scientific_journal-3270	294	22	unique	unique	ADJ
american_scientific_journal-3270	294	23	fixed	fix	VERB
american_scientific_journal-3270	294	24	point	point	NOUN
american_scientific_journal-3270	294	25	which	which	PRON
american_scientific_journal-3270	294	26	is	be	AUX
american_scientific_journal-3270	294	27	the	the	DET
american_scientific_journal-3270	294	28	unique	unique	ADJ
american_scientific_journal-3270	294	29	solution	solution	NOUN
american_scientific_journal-3270	294	30	of	of	ADP
american_scientific_journal-3270	294	31	eq	eq	PROPN
american_scientific_journal-3270	294	32	.	.	PUNCT
american_scientific_journal-3270	295	1	(	(	PUNCT
american_scientific_journal-3270	295	2	.2.30	.2.30	PROPN
american_scientific_journal-3270	295	3	)	)	PUNCT
american_scientific_journal-3270	295	4	.	.	PUNCT
american_scientific_journal-3270	296	1	then	then	ADV
american_scientific_journal-3270	296	2	theorem	theorem	VERB
american_scientific_journal-3270	296	3	1.1	1.1	NUM
american_scientific_journal-3270	296	4	is	be	AUX
american_scientific_journal-3270	296	5	completely	completely	ADV
american_scientific_journal-3270	296	6	proved	prove	VERB
american_scientific_journal-3270	296	7	.	.	PUNCT
american_scientific_journal-3270	297	1	4	4	X
american_scientific_journal-3270	297	2	.	.	X
american_scientific_journal-3270	297	3	the	the	DET
american_scientific_journal-3270	297	4	system	system	NOUN
american_scientific_journal-3270	297	5	of	of	ADP
american_scientific_journal-3270	297	6	fredholm	fredholm	ADJ
american_scientific_journal-3270	297	7	integral	integral	ADJ
american_scientific_journal-3270	297	8	equations	equation	NOUN
american_scientific_journal-3270	297	9	in	in	ADP
american_scientific_journal-3270	297	10	order	order	NOUN
american_scientific_journal-3270	297	11	to	to	PART
american_scientific_journal-3270	297	12	discuss	discuss	VERB
american_scientific_journal-3270	297	13	the	the	DET
american_scientific_journal-3270	297	14	solution	solution	NOUN
american_scientific_journal-3270	297	15	of	of	ADP
american_scientific_journal-3270	297	16	mixed	mixed	ADJ
american_scientific_journal-3270	297	17	integral	integral	ADJ
american_scientific_journal-3270	297	18	equation	equation	NOUN
american_scientific_journal-3270	297	19	(	(	PUNCT
american_scientific_journal-3270	297	20	2.30	2.30	NUM
american_scientific_journal-3270	297	21	)	)	PUNCT
american_scientific_journal-3270	297	22	,	,	PUNCT
american_scientific_journal-3270	297	23	we	we	PRON
american_scientific_journal-3270	297	24	use	use	VERB
american_scientific_journal-3270	297	25	a	a	DET
american_scientific_journal-3270	297	26	quadratic	quadratic	ADJ
american_scientific_journal-3270	297	27	numerical	numerical	ADJ
american_scientific_journal-3270	297	28	method	method	NOUN
american_scientific_journal-3270	297	29	to	to	PART
american_scientific_journal-3270	297	30	transform	transform	VERB
american_scientific_journal-3270	297	31	the	the	DET
american_scientific_journal-3270	297	32	mixed	mixed	ADJ
american_scientific_journal-3270	297	33	integral	integral	ADJ
american_scientific_journal-3270	297	34	equation	equation	NOUN
american_scientific_journal-3270	297	35	in	in	ADP
american_scientific_journal-3270	297	36	position	position	NOUN
american_scientific_journal-3270	297	37	and	and	CCONJ
american_scientific_journal-3270	297	38	time	time	NOUN
american_scientific_journal-3270	297	39	to	to	ADP
american_scientific_journal-3270	297	40	system	system	NOUN
american_scientific_journal-3270	297	41	of	of	ADP
american_scientific_journal-3270	297	42	fredholm	fredholm	ADJ
american_scientific_journal-3270	297	43	integral	integral	ADJ
american_scientific_journal-3270	297	44	equations	equation	NOUN
american_scientific_journal-3270	297	45	.	.	PUNCT
american_scientific_journal-3270	298	1	for	for	ADP
american_scientific_journal-3270	298	2	this	this	PRON
american_scientific_journal-3270	298	3	,	,	PUNCT
american_scientific_journal-3270	298	4	let	let	VERB
american_scientific_journal-3270	298	5	w	w	PROPN
american_scientific_journal-3270	298	6	american	american	ADJ
american_scientific_journal-3270	298	7	scientific	scientific	ADJ
american_scientific_journal-3270	298	8	research	research	NOUN
american_scientific_journal-3270	298	9	journal	journal	NOUN
american_scientific_journal-3270	298	10	for	for	ADP
american_scientific_journal-3270	298	11	engineering	engineering	NOUN
american_scientific_journal-3270	298	12	,	,	PUNCT
american_scientific_journal-3270	298	13	technology	technology	NOUN
american_scientific_journal-3270	298	14	,	,	PUNCT
american_scientific_journal-3270	298	15	and	and	CCONJ
american_scientific_journal-3270	298	16	sciences	science	NOUN
american_scientific_journal-3270	298	17	(	(	PUNCT
american_scientific_journal-3270	298	18	asrjets	asrjet	NOUN
american_scientific_journal-3270	298	19	)	)	PUNCT
american_scientific_journal-3270	298	20	(	(	PUNCT
american_scientific_journal-3270	298	21	2017	2017	NUM
american_scientific_journal-3270	298	22	)	)	PUNCT
american_scientific_journal-3270	298	23	volume	volume	NOUN
american_scientific_journal-3270	298	24	34	34	NUM
american_scientific_journal-3270	298	25	,	,	PUNCT
american_scientific_journal-3270	298	26	no	no	DET
american_scientific_journal-3270	298	27	1	1	NUM
american_scientific_journal-3270	298	28	,	,	PUNCT
american_scientific_journal-3270	298	29	pp	pp	ADV
american_scientific_journal-3270	298	30	213	213	NUM
american_scientific_journal-3270	298	31	-	-	SYM
american_scientific_journal-3270	298	32	230	230	NUM
american_scientific_journal-3270	298	33	222	222	NUM
american_scientific_journal-3270	298	34	it	it	PRON
american_scientific_journal-3270	298	35	t=	t=	PRON
american_scientific_journal-3270	298	36	,	,	PUNCT
american_scientific_journal-3270	298	37	0,1,2,	0,1,2,	NUM
american_scientific_journal-3270	298	38	...	...	PUNCT
american_scientific_journal-3270	298	39	,i	,i	PUNCT
american_scientific_journal-3270	298	40	n=	n=	ADJ
american_scientific_journal-3270	298	41	,	,	PUNCT
american_scientific_journal-3270	298	42	and	and	CCONJ
american_scientific_journal-3270	298	43	follow	follow	VERB
american_scientific_journal-3270	298	44	the	the	DET
american_scientific_journal-3270	298	45	work	work	NOUN
american_scientific_journal-3270	298	46	of	of	ADP
american_scientific_journal-3270	298	47	abdou	abdou	PROPN
american_scientific_journal-3270	298	48	and	and	CCONJ
american_scientific_journal-3270	298	49	mustafa	mustafa	PROPN
american_scientific_journal-3270	299	1	[	[	X
american_scientific_journal-3270	299	2	22	22	NUM
american_scientific_journal-3270	299	3	]	]	PUNCT
american_scientific_journal-3270	299	4	.	.	PUNCT
american_scientific_journal-3270	300	1	hence	hence	ADV
american_scientific_journal-3270	300	2	,	,	PUNCT
american_scientific_journal-3270	300	3	the	the	DET
american_scientific_journal-3270	300	4	volterra	volterra	NOUN
american_scientific_journal-3270	300	5	integral	integral	ADJ
american_scientific_journal-3270	300	6	term	term	NOUN
american_scientific_journal-3270	300	7	,	,	PUNCT
american_scientific_journal-3270	300	8	of	of	ADP
american_scientific_journal-3270	300	9	(	(	PUNCT
american_scientific_journal-3270	300	10	2.30	2.30	NUM
american_scientific_journal-3270	300	11	)	)	PUNCT
american_scientific_journal-3270	300	12	becomes	become	VERB
american_scientific_journal-3270	300	13	(	(	PUNCT
american_scientific_journal-3270	300	14	)	)	PUNCT
american_scientific_journal-3270	300	15	(	(	PUNCT
american_scientific_journal-3270	300	16	)	)	PUNCT
american_scientific_journal-3270	300	17	00	00	PUNCT
american_scientific_journal-3270	301	1	(	(	PUNCT
american_scientific_journal-3270	301	2	,	,	PUNCT
american_scientific_journal-3270	301	3	)	)	PUNCT
american_scientific_journal-3270	301	4	(	(	PUNCT
american_scientific_journal-3270	301	5	,	,	PUNCT
american_scientific_journal-3270	301	6	)	)	PUNCT
american_scientific_journal-3270	301	7	(	(	PUNCT
american_scientific_journal-3270	301	8	,	,	PUNCT
american_scientific_journal-3270	301	9	)	)	PUNCT
american_scientific_journal-3270	301	10	,	,	PUNCT
american_scientific_journal-3270	301	11	,	,	PUNCT
american_scientific_journal-3270	301	12	it	it	PRON
american_scientific_journal-3270	302	1	i	i	PRON
american_scientific_journal-3270	302	2	i	i	PRON
american_scientific_journal-3270	303	1	j	j	VERB
american_scientific_journal-3270	304	1	i	i	PRON
american_scientific_journal-3270	304	2	j	j	PROPN
american_scientific_journal-3270	305	1	j	j	NOUN
american_scientific_journal-3270	306	1	i	i	PRON
american_scientific_journal-3270	306	2	j	j	PROPN
american_scientific_journal-3270	307	1	t	t	NOUN
american_scientific_journal-3270	307	2	x	x	PROPN
american_scientific_journal-3270	307	3	d	d	PROPN
american_scientific_journal-3270	307	4	w	w	PROPN
american_scientific_journal-3270	307	5	t	t	PROPN
american_scientific_journal-3270	307	6	t	t	PROPN
american_scientific_journal-3270	307	7	x	x	SYM
american_scientific_journal-3270	307	8	t	t	NOUN
american_scientific_journal-3270	307	9	r	r	NOUN
american_scientific_journal-3270	307	10	x	x	PUNCT
american_scientific_journal-3270	307	11	tx	tx	PROPN
american_scientific_journal-3270	307	12	t	t	PROPN
american_scientific_journal-3270	308	1	φ	φ	PROPN
american_scientific_journal-3270	308	2	t	t	PROPN
american_scientific_journal-3270	308	3	t	t	PROPN
american_scientific_journal-3270	308	4	x	x	SYM
american_scientific_journal-3270	308	5	φ	φ	PROPN
american_scientific_journal-3270	308	6	=	=	PUNCT
american_scientific_journal-3270	308	7	=	=	PUNCT
american_scientific_journal-3270	309	1	+	+	PROPN
american_scientific_journal-3270	309	2	∑∫	∑∫	PROPN
american_scientific_journal-3270	309	3	.	.	PUNCT
american_scientific_journal-3270	310	1	(	(	PUNCT
american_scientific_journal-3270	310	2	4.1	4.1	NUM
american_scientific_journal-3270	310	3	)	)	PUNCT
american_scientific_journal-3270	310	4	the	the	DET
american_scientific_journal-3270	310	5	values	value	NOUN
american_scientific_journal-3270	310	6	of	of	ADP
american_scientific_journal-3270	310	7	i	i	PRON
american_scientific_journal-3270	310	8	and	and	CCONJ
american_scientific_journal-3270	310	9	the	the	DET
american_scientific_journal-3270	310	10	order	order	NOUN
american_scientific_journal-3270	310	11	of	of	ADP
american_scientific_journal-3270	310	12	the	the	DET
american_scientific_journal-3270	310	13	truncation	truncation	NOUN
american_scientific_journal-3270	310	14	error	error	NOUN
american_scientific_journal-3270	310	15	ir	ir	NOUN
american_scientific_journal-3270	310	16	are	be	AUX
american_scientific_journal-3270	310	17	depending	depend	VERB
american_scientific_journal-3270	310	18	on	on	ADP
american_scientific_journal-3270	310	19	the	the	DET
american_scientific_journal-3270	310	20	number	number	NOUN
american_scientific_journal-3270	310	21	of	of	ADP
american_scientific_journal-3270	310	22	derivatives	derivative	NOUN
american_scientific_journal-3270	310	23	of	of	ADP
american_scientific_journal-3270	310	24	(	(	PUNCT
american_scientific_journal-3270	310	25	,	,	PUNCT
american_scientific_journal-3270	310	26	)	)	PUNCT
american_scientific_journal-3270	310	27	tx	tx	ADP
american_scientific_journal-3270	310	28	t	t	PROPN
american_scientific_journal-3270	310	29	for	for	ADP
american_scientific_journal-3270	310	30	all	all	PRON
american_scientific_journal-3270	310	31	[	[	PUNCT
american_scientific_journal-3270	310	32	]	]	X
american_scientific_journal-3270	310	33	0,tt	0,tt	ADJ
american_scientific_journal-3270	310	34	∈	∈	PROPN
american_scientific_journal-3270	310	35	,	,	PUNCT
american_scientific_journal-3270	310	36	with	with	ADP
american_scientific_journal-3270	310	37	respect	respect	NOUN
american_scientific_journal-3270	310	38	to	to	ADP
american_scientific_journal-3270	310	39	t	t	PROPN
american_scientific_journal-3270	310	40	and	and	CCONJ
american_scientific_journal-3270	310	41	jw	jw	PROPN
american_scientific_journal-3270	310	42	is	be	AUX
american_scientific_journal-3270	310	43	the	the	DET
american_scientific_journal-3270	310	44	weights	weight	NOUN
american_scientific_journal-3270	310	45	,	,	PUNCT
american_scientific_journal-3270	310	46	where	where	SCONJ
american_scientific_journal-3270	310	47	0	0	NUM
american_scientific_journal-3270	310	48	0	0	NUM
american_scientific_journal-3270	310	49	1	1	NUM
american_scientific_journal-3270	310	50	1	1	NUM
american_scientific_journal-3270	310	51	,	,	PUNCT
american_scientific_journal-3270	310	52	2	2	NUM
american_scientific_journal-3270	310	53	2i	2i	NUM
american_scientific_journal-3270	311	1	iw	iw	PROPN
american_scientific_journal-3270	311	2	h	h	PROPN
american_scientific_journal-3270	311	3	w	w	PROPN
american_scientific_journal-3270	311	4	h=	h=	PROPN
american_scientific_journal-3270	311	5	=	=	SYM
american_scientific_journal-3270	312	1	and	and	CCONJ
american_scientific_journal-3270	312	2	j	j	PROPN
american_scientific_journal-3270	312	3	jw	jw	PROPN
american_scientific_journal-3270	312	4	h=	h=	PROPN
american_scientific_journal-3270	312	5	,	,	PUNCT
american_scientific_journal-3270	313	1	0	0	NUM
american_scientific_journal-3270	313	2	j	j	PROPN
american_scientific_journal-3270	313	3	i	i	PRON
american_scientific_journal-3270	313	4	<	<	X
american_scientific_journal-3270	313	5	<	<	X
american_scientific_journal-3270	313	6	,	,	PUNCT
american_scientific_journal-3270	313	7	h	h	PROPN
american_scientific_journal-3270	313	8	denotes	denote	VERB
american_scientific_journal-3270	313	9	the	the	DET
american_scientific_journal-3270	313	10	constant	constant	ADJ
american_scientific_journal-3270	313	11	step	step	NOUN
american_scientific_journal-3270	313	12	size	size	NOUN
american_scientific_journal-3270	313	13	for	for	ADP
american_scientific_journal-3270	313	14	integration	integration	NOUN
american_scientific_journal-3270	313	15	.	.	PUNCT
american_scientific_journal-3270	314	1	using	use	VERB
american_scientific_journal-3270	314	2	(	(	PUNCT
american_scientific_journal-3270	314	3	4.1	4.1	NUM
american_scientific_journal-3270	314	4	)	)	PUNCT
american_scientific_journal-3270	314	5	in	in	ADP
american_scientific_journal-3270	314	6	(	(	PUNCT
american_scientific_journal-3270	314	7	2.30	2.30	NUM
american_scientific_journal-3270	314	8	)	)	PUNCT
american_scientific_journal-3270	314	9	and	and	CCONJ
american_scientific_journal-3270	314	10	then	then	ADV
american_scientific_journal-3270	314	11	after	after	ADP
american_scientific_journal-3270	314	12	using	use	VERB
american_scientific_journal-3270	314	13	the	the	DET
american_scientific_journal-3270	314	14	following	following	ADJ
american_scientific_journal-3270	314	15	notations	notation	NOUN
american_scientific_journal-3270	314	16	:	:	PUNCT
american_scientific_journal-3270	314	17	(	(	PUNCT
american_scientific_journal-3270	314	18	)	)	PUNCT
american_scientific_journal-3270	314	19	(	(	PUNCT
american_scientific_journal-3270	314	20	,	,	PUNCT
american_scientific_journal-3270	314	21	)	)	PUNCT
american_scientific_journal-3270	314	22	,	,	PUNCT
american_scientific_journal-3270	314	23	i	i	PRON
american_scientific_journal-3270	314	24	ix	ix	ADP
american_scientific_journal-3270	314	25	x	x	PUNCT
american_scientific_journal-3270	314	26	tφ	tφ	PROPN
american_scientific_journal-3270	314	27	φ=	φ=	NOUN
american_scientific_journal-3270	314	28	,	,	PUNCT
american_scientific_journal-3270	314	29	(	(	PUNCT
american_scientific_journal-3270	314	30	)	)	PUNCT
american_scientific_journal-3270	314	31	(	(	PUNCT
american_scientific_journal-3270	314	32	,	,	PUNCT
american_scientific_journal-3270	314	33	)	)	PUNCT
american_scientific_journal-3270	314	34	,	,	PUNCT
american_scientific_journal-3270	314	35	(	(	PUNCT
american_scientific_journal-3270	314	36	,	,	PUNCT
american_scientific_journal-3270	314	37	)	)	PUNCT
american_scientific_journal-3270	315	1	i	i	PRON
american_scientific_journal-3270	316	1	i	i	PRON
american_scientific_journal-3270	317	1	i	i	PRON
american_scientific_journal-3270	317	2	j	j	VERB
american_scientific_journal-3270	318	1	i	i	PRON
american_scientific_journal-3270	318	2	jf	jf	VERB
american_scientific_journal-3270	318	3	x	x	X
american_scientific_journal-3270	318	4	f	f	PROPN
american_scientific_journal-3270	318	5	x	x	SYM
american_scientific_journal-3270	318	6	t	t	PROPN
american_scientific_journal-3270	318	7	t	t	PROPN
american_scientific_journal-3270	318	8	tx	tx	PROPN
american_scientific_journal-3270	318	9	x=	x=	PUNCT
american_scientific_journal-3270	319	1	=	=	SYM
american_scientific_journal-3270	319	2	,	,	PUNCT
american_scientific_journal-3270	319	3	0,1,2	0,1,2	NUM
american_scientific_journal-3270	319	4	,	,	PUNCT
american_scientific_journal-3270	319	5	...	...	PUNCT
american_scientific_journal-3270	319	6	,	,	PUNCT
american_scientific_journal-3270	319	7	,	,	PUNCT
american_scientific_journal-3270	319	8	0i	0i	PROPN
american_scientific_journal-3270	319	9	n	n	PROPN
american_scientific_journal-3270	319	10	j	j	PROPN
american_scientific_journal-3270	319	11	i=	i=	PROPN
american_scientific_journal-3270	319	12	≤	≤	PROPN
american_scientific_journal-3270	319	13	≤	≤	NOUN
american_scientific_journal-3270	319	14	,	,	PUNCT
american_scientific_journal-3270	319	15	we	we	PRON
american_scientific_journal-3270	319	16	get	get	VERB
american_scientific_journal-3270	319	17	1	1	NUM
american_scientific_journal-3270	319	18	1	1	NUM
american_scientific_journal-3270	319	19	1	1	NUM
american_scientific_journal-3270	319	20	1	1	NUM
american_scientific_journal-3270	319	21	(	(	PUNCT
american_scientific_journal-3270	319	22	)	)	PUNCT
american_scientific_journal-3270	319	23	(	(	PUNCT
american_scientific_journal-3270	319	24	)	)	PUNCT
american_scientific_journal-3270	319	25	(	(	PUNCT
american_scientific_journal-3270	319	26	)	)	PUNCT
american_scientific_journal-3270	319	27	(	(	PUNCT
american_scientific_journal-3270	319	28	,	,	PUNCT
american_scientific_journal-3270	319	29	)	)	PUNCT
american_scientific_journal-3270	319	30	(	(	PUNCT
american_scientific_journal-3270	319	31	)	)	PUNCT
american_scientific_journal-3270	319	32	(	(	PUNCT
american_scientific_journal-3270	319	33	)	)	PUNCT
american_scientific_journal-3270	320	1	,	,	PUNCT
american_scientific_journal-3270	320	2	i	i	PRON
american_scientific_journal-3270	320	3	i	i	PRON
american_scientific_journal-3270	321	1	i	i	PRON
american_scientific_journal-3270	321	2	i	i	PRON
american_scientific_journal-3270	322	1	ix	ix	ADP
american_scientific_journal-3270	322	2	p	p	PROPN
american_scientific_journal-3270	322	3	y	y	PROPN
american_scientific_journal-3270	322	4	x	x	SYM
american_scientific_journal-3270	322	5	y	y	PROPN
american_scientific_journal-3270	322	6	dy	dy	NOUN
american_scientific_journal-3270	322	7	k	k	PROPN
american_scientific_journal-3270	322	8	x	x	X
american_scientific_journal-3270	322	9	y	y	PROPN
american_scientific_journal-3270	322	10	y	y	PROPN
american_scientific_journal-3270	322	11	dy	dy	PROPN
american_scientific_journal-3270	322	12	xλµ	xλµ	PROPN
american_scientific_journal-3270	322	13	φ	φ	PROPN
american_scientific_journal-3270	322	14	φ	φ	PROPN
american_scientific_journal-3270	323	1	λ	λ	PROPN
american_scientific_journal-3270	323	2	φ	φ	PROPN
american_scientific_journal-3270	323	3	y	y	PROPN
american_scientific_journal-3270	323	4	π	π	PROPN
american_scientific_journal-3270	323	5	−	−	PROPN
american_scientific_journal-3270	323	6	−	−	PROPN
american_scientific_journal-3270	324	1	+	+	CCONJ
american_scientific_journal-3270	324	2	−	−	PROPN
american_scientific_journal-3270	325	1	+	+	CCONJ
american_scientific_journal-3270	325	2	=	=	NUM
american_scientific_journal-3270	325	3	∫	∫	PROPN
american_scientific_journal-3270	325	4	∫	∫	PROPN
american_scientific_journal-3270	325	5	(	(	PUNCT
american_scientific_journal-3270	325	6	4.2	4.2	NUM
american_scientific_journal-3270	325	7	)	)	PUNCT
american_scientific_journal-3270	326	1	where	where	SCONJ
american_scientific_journal-3270	326	2	(	(	PUNCT
american_scientific_journal-3270	326	3	)	)	PUNCT
american_scientific_journal-3270	326	4	,	,	PUNCT
american_scientific_journal-3270	326	5	i	i	PRON
american_scientific_journal-3270	326	6	i	i	PRON
american_scientific_journal-3270	326	7	i	i	PRON
american_scientific_journal-3270	326	8	iwµ	iwµ	VERB
american_scientific_journal-3270	326	9	η	η	PROPN
american_scientific_journal-3270	326	10	λ	λ	X
american_scientific_journal-3270	326	11	x=	x=	PUNCT
american_scientific_journal-3270	327	1	+	+	CCONJ
american_scientific_journal-3270	327	2	,	,	PUNCT
american_scientific_journal-3270	327	3	1	1	NUM
american_scientific_journal-3270	327	4	,	,	PUNCT
american_scientific_journal-3270	327	5	0	0	NUM
american_scientific_journal-3270	328	1	(	(	PUNCT
american_scientific_journal-3270	328	2	)	)	PUNCT
american_scientific_journal-3270	328	3	(	(	PUNCT
american_scientific_journal-3270	328	4	)	)	PUNCT
american_scientific_journal-3270	328	5	i	i	PRON
american_scientific_journal-3270	328	6	i	i	PRON
american_scientific_journal-3270	329	1	i	i	PRON
american_scientific_journal-3270	329	2	j	j	VERB
american_scientific_journal-3270	330	1	i	i	PRON
american_scientific_journal-3270	330	2	j	j	PROPN
american_scientific_journal-3270	331	1	j	j	PROPN
american_scientific_journal-3270	331	2	j	j	PROPN
american_scientific_journal-3270	332	1	f	f	PROPN
american_scientific_journal-3270	333	1	x	x	PROPN
american_scientific_journal-3270	333	2	w	w	NOUN
american_scientific_journal-3270	333	3	xy	xy	PROPN
american_scientific_journal-3270	333	4	λ	λ	X
american_scientific_journal-3270	333	5	x	x	PROPN
american_scientific_journal-3270	333	6	φ	φ	PROPN
american_scientific_journal-3270	333	7	−	−	PROPN
american_scientific_journal-3270	333	8	=	=	PUNCT
american_scientific_journal-3270	333	9			NOUN
american_scientific_journal-3270	333	10	=	=	X
american_scientific_journal-3270	333	11	−	−	PROPN
american_scientific_journal-3270	333	12			NUM
american_scientific_journal-3270	333	13	∑	∑	NOUN
american_scientific_journal-3270	333	14	,	,	PUNCT
american_scientific_journal-3270	333	15	0,1,2,	0,1,2,	NUM
american_scientific_journal-3270	333	16	...	...	PUNCT
american_scientific_journal-3270	333	17	,i	,i	PUNCT
american_scientific_journal-3270	333	18	n=	n=	ADJ
american_scientific_journal-3270	333	19	.	.	PUNCT
american_scientific_journal-3270	334	1	(	(	PUNCT
american_scientific_journal-3270	334	2	4.3	4.3	NUM
american_scientific_journal-3270	334	3	)	)	PUNCT
american_scientific_journal-3270	334	4	the	the	DET
american_scientific_journal-3270	334	5	formula	formula	NOUN
american_scientific_journal-3270	334	6	(	(	PUNCT
american_scientific_journal-3270	334	7	4.2	4.2	NUM
american_scientific_journal-3270	334	8	)	)	PUNCT
american_scientific_journal-3270	334	9	represents	represent	VERB
american_scientific_journal-3270	334	10	system	system	NOUN
american_scientific_journal-3270	334	11	of	of	ADP
american_scientific_journal-3270	334	12	fredholm	fredholm	ADJ
american_scientific_journal-3270	334	13	integral	integral	ADJ
american_scientific_journal-3270	334	14	equations	equation	NOUN
american_scientific_journal-3270	334	15	of	of	ADP
american_scientific_journal-3270	334	16	the	the	DET
american_scientific_journal-3270	334	17	second	second	ADJ
american_scientific_journal-3270	334	18	kind	kind	NOUN
american_scientific_journal-3270	334	19	,	,	PUNCT
american_scientific_journal-3270	334	20	to	to	PART
american_scientific_journal-3270	334	21	prove	prove	VERB
american_scientific_journal-3270	334	22	the	the	DET
american_scientific_journal-3270	334	23	existence	existence	NOUN
american_scientific_journal-3270	334	24	of	of	ADP
american_scientific_journal-3270	334	25	a	a	DET
american_scientific_journal-3270	334	26	unique	unique	ADJ
american_scientific_journal-3270	334	27	solution	solution	NOUN
american_scientific_journal-3270	334	28	of	of	ADP
american_scientific_journal-3270	334	29	(	(	PUNCT
american_scientific_journal-3270	334	30	4.2	4.2	NUM
american_scientific_journal-3270	334	31	)	)	PUNCT
american_scientific_journal-3270	334	32	according	accord	VERB
american_scientific_journal-3270	334	33	to	to	ADP
american_scientific_journal-3270	334	34	the	the	DET
american_scientific_journal-3270	334	35	banach	banach	NOUN
american_scientific_journal-3270	334	36	fixedpoint	fixedpoint	NOUN
american_scientific_journal-3270	334	37	theorem	theorem	NOUN
american_scientific_journal-3270	334	38	,	,	PUNCT
american_scientific_journal-3270	334	39	we	we	PRON
american_scientific_journal-3270	334	40	let	let	VERB
american_scientific_journal-3270	334	41	e	e	PRON
american_scientific_journal-3270	334	42	be	be	AUX
american_scientific_journal-3270	334	43	the	the	DET
american_scientific_journal-3270	334	44	set	set	NOUN
american_scientific_journal-3270	334	45	of	of	ADP
american_scientific_journal-3270	334	46	all	all	DET
american_scientific_journal-3270	334	47	continuous	continuous	ADJ
american_scientific_journal-3270	334	48	functions	function	NOUN
american_scientific_journal-3270	334	49	(	(	PUNCT
american_scientific_journal-3270	334	50	)	)	PUNCT
american_scientific_journal-3270	334	51	p	p	NOUN
american_scientific_journal-3270	334	52	xφ	xφ	PROPN
american_scientific_journal-3270	334	53	in	in	ADP
american_scientific_journal-3270	334	54	the	the	DET
american_scientific_journal-3270	334	55	space	space	NOUN
american_scientific_journal-3270	334	56	[	[	PUNCT
american_scientific_journal-3270	334	57	]	]	X
american_scientific_journal-3270	334	58	2	2	NUM
american_scientific_journal-3270	334	59	1,1l	1,1l	NUM
american_scientific_journal-3270	334	60	−	−	NOUN
american_scientific_journal-3270	334	61	,	,	PUNCT
american_scientific_journal-3270	334	62	where	where	SCONJ
american_scientific_journal-3270	334	63	(	(	PUNCT
american_scientific_journal-3270	334	64	)	)	PUNCT
american_scientific_journal-3270	334	65	(	(	PUNCT
american_scientific_journal-3270	334	66	)	)	PUNCT
american_scientific_journal-3270	334	67	(	(	PUNCT
american_scientific_journal-3270	334	68	)	)	PUNCT
american_scientific_journal-3270	334	69	(	(	PUNCT
american_scientific_journal-3270	334	70	)	)	PUNCT
american_scientific_journal-3270	334	71	{	{	PUNCT
american_scientific_journal-3270	334	72	}	}	PUNCT
american_scientific_journal-3270	334	73	0	0	NUM
american_scientific_journal-3270	334	74	1	1	NUM
american_scientific_journal-3270	334	75	,	,	PUNCT
american_scientific_journal-3270	334	76	,	,	PUNCT
american_scientific_journal-3270	334	77	...	...	PUNCT
american_scientific_journal-3270	334	78	,	,	PUNCT
american_scientific_journal-3270	334	79	,	,	PUNCT
american_scientific_journal-3270	334	80	...	...	PUNCT
american_scientific_journal-3270	335	1	px	px	X
american_scientific_journal-3270	335	2	x	x	PUNCT
american_scientific_journal-3270	335	3	x	x	X
american_scientific_journal-3270	335	4	xφ	xφ	PROPN
american_scientific_journal-3270	335	5	φ	φ	NUM
american_scientific_journal-3270	335	6	φφ	φφ	PROPN
american_scientific_journal-3270	335	7	=	=	PUNCT
american_scientific_journal-3270	335	8	and	and	CCONJ
american_scientific_journal-3270	335	9	define	define	VERB
american_scientific_journal-3270	335	10	the	the	DET
american_scientific_journal-3270	335	11	norm	norm	NOUN
american_scientific_journal-3270	335	12	in	in	ADP
american_scientific_journal-3270	335	13	the	the	DET
american_scientific_journal-3270	335	14	banach	banach	NOUN
american_scientific_journal-3270	335	15	space	space	NOUN
american_scientific_journal-3270	335	16	e	e	X
american_scientific_journal-3270	335	17	by	by	ADP
american_scientific_journal-3270	335	18	(	(	PUNCT
american_scientific_journal-3270	335	19	)	)	SYM
american_scientific_journal-3270	335	20	2	2	NUM
american_scientific_journal-3270	335	21	1,1	1,1	NUM
american_scientific_journal-3270	335	22	(	(	PUNCT
american_scientific_journal-3270	335	23	)	)	PUNCT
american_scientific_journal-3270	335	24	max	max	PROPN
american_scientific_journal-3270	335	25	ie	ie	PROPN
american_scientific_journal-3270	335	26	li	li	PROPN
american_scientific_journal-3270	336	1	xφ	xφ	PROPN
american_scientific_journal-3270	336	2	−	−	PROPN
american_scientific_journal-3270	336	3	φ	φ	PROPN
american_scientific_journal-3270	336	4	=	=	SYM
american_scientific_journal-3270	336	5	and	and	CCONJ
american_scientific_journal-3270	336	6	(	(	PUNCT
american_scientific_journal-3270	336	7	)	)	SYM
american_scientific_journal-3270	336	8	2	2	NUM
american_scientific_journal-3270	336	9	1,1	1,1	NUM
american_scientific_journal-3270	336	10	(	(	PUNCT
american_scientific_journal-3270	336	11	)	)	PUNCT
american_scientific_journal-3270	336	12	max	max	PROPN
american_scientific_journal-3270	336	13	ie	ie	X
american_scientific_journal-3270	336	14	li	li	PROPN
american_scientific_journal-3270	337	1	xy	xy	PROPN
american_scientific_journal-3270	337	2	−	−	PROPN
american_scientific_journal-3270	337	3	ψ	ψ	NOUN
american_scientific_journal-3270	337	4	=	=	X
american_scientific_journal-3270	337	5	.	.	PUNCT
american_scientific_journal-3270	338	1	consider	consider	VERB
american_scientific_journal-3270	338	2	the	the	DET
american_scientific_journal-3270	338	3	following	follow	VERB
american_scientific_journal-3270	338	4	two	two	NUM
american_scientific_journal-3270	338	5	conditions	condition	NOUN
american_scientific_journal-3270	338	6	(	(	PUNCT
american_scientific_journal-3270	338	7	1	1	NUM
american_scientific_journal-3270	338	8	)	)	SYM
american_scientific_journal-3270	338	9	2	2	NUM
american_scientific_journal-3270	338	10	(	(	PUNCT
american_scientific_journal-3270	338	11	)	)	PUNCT
american_scientific_journal-3270	338	12	max	max	PROPN
american_scientific_journal-3270	339	1	i	i	PRON
american_scientific_journal-3270	339	2	li	li	PROPN
american_scientific_journal-3270	340	1	f	f	PROPN
american_scientific_journal-3270	340	2	x	x	INTJ
american_scientific_journal-3270	340	3	q≤	q≤	INTJ
american_scientific_journal-3270	340	4	,	,	PUNCT
american_scientific_journal-3270	340	5	(	(	PUNCT
american_scientific_journal-3270	340	6	2	2	NUM
american_scientific_journal-3270	340	7	)	)	PUNCT
american_scientific_journal-3270	340	8	1	1	NUM
american_scientific_journal-3270	340	9	,	,	PUNCT
american_scientific_journal-3270	340	10	0	0	NUM
american_scientific_journal-3270	340	11	max	max	PROPN
american_scientific_journal-3270	341	1	i	i	PRON
american_scientific_journal-3270	341	2	j	j	PROPN
american_scientific_journal-3270	342	1	i	i	PRON
american_scientific_journal-3270	342	2	j	j	PROPN
american_scientific_journal-3270	342	3	jj	jj	PROPN
american_scientific_journal-3270	342	4	w	w	PROPN
american_scientific_journal-3270	342	5	px	px	PROPN
american_scientific_journal-3270	342	6	−	−	PROPN
american_scientific_journal-3270	342	7	=	=	SYM
american_scientific_journal-3270	342	8	≤∑	≤∑	PROPN
american_scientific_journal-3270	342	9	,	,	PUNCT
american_scientific_journal-3270	342	10	(	(	PUNCT
american_scientific_journal-3270	342	11	q	q	X
american_scientific_journal-3270	342	12	,	,	PUNCT
american_scientific_journal-3270	342	13	p	p	NOUN
american_scientific_journal-3270	342	14	are	be	AUX
american_scientific_journal-3270	342	15	constants	constant	NOUN
american_scientific_journal-3270	342	16	)	)	PUNCT
american_scientific_journal-3270	342	17	.	.	PUNCT
american_scientific_journal-3270	343	1	theorem	theorem	ADJ
american_scientific_journal-3270	343	2	2	2	NUM
american_scientific_journal-3270	343	3	(	(	PUNCT
american_scientific_journal-3270	343	4	without	without	ADP
american_scientific_journal-3270	343	5	proof	proof	NOUN
american_scientific_journal-3270	343	6	):	):	PUNCT
american_scientific_journal-3270	343	7	if	if	SCONJ
american_scientific_journal-3270	343	8	the	the	DET
american_scientific_journal-3270	343	9	conditions	condition	NOUN
american_scientific_journal-3270	343	10	(	(	PUNCT
american_scientific_journal-3270	343	11	i	i	NOUN
american_scientific_journal-3270	343	12	)	)	PUNCT
american_scientific_journal-3270	343	13	,	,	PUNCT
american_scientific_journal-3270	343	14	(	(	PUNCT
american_scientific_journal-3270	343	15	iii	iii	NOUN
american_scientific_journal-3270	343	16	)	)	PUNCT
american_scientific_journal-3270	343	17	,	,	PUNCT
american_scientific_journal-3270	343	18	of	of	ADP
american_scientific_journal-3270	343	19	theorem	theorem	ADJ
american_scientific_journal-3270	343	20	1.1	1.1	NUM
american_scientific_journal-3270	343	21	with	with	ADP
american_scientific_journal-3270	343	22	the	the	DET
american_scientific_journal-3270	343	23	two	two	NUM
american_scientific_journal-3270	343	24	conditions	condition	NOUN
american_scientific_journal-3270	343	25	(	(	PUNCT
american_scientific_journal-3270	343	26	1	1	NUM
american_scientific_journal-3270	343	27	)	)	PUNCT
american_scientific_journal-3270	343	28	and	and	CCONJ
american_scientific_journal-3270	343	29	(	(	PUNCT
american_scientific_journal-3270	343	30	2	2	X
american_scientific_journal-3270	343	31	)	)	PUNCT
american_scientific_journal-3270	343	32	are	be	AUX
american_scientific_journal-3270	343	33	satisfied	satisfied	ADJ
american_scientific_journal-3270	343	34	,	,	PUNCT
american_scientific_journal-3270	343	35	then	then	ADV
american_scientific_journal-3270	343	36	the	the	DET
american_scientific_journal-3270	343	37	formula	formula	NOUN
american_scientific_journal-3270	343	38	(	(	PUNCT
american_scientific_journal-3270	343	39	4.2	4.2	NUM
american_scientific_journal-3270	343	40	)	)	PUNCT
american_scientific_journal-3270	343	41	has	have	VERB
american_scientific_journal-3270	343	42	a	a	DET
american_scientific_journal-3270	343	43	unique	unique	ADJ
american_scientific_journal-3270	343	44	solution	solution	NOUN
american_scientific_journal-3270	343	45	in	in	ADP
american_scientific_journal-3270	343	46	the	the	DET
american_scientific_journal-3270	343	47	space	space	NOUN
american_scientific_journal-3270	343	48	e	e	NOUN
american_scientific_journal-3270	343	49	,	,	PUNCT
american_scientific_journal-3270	343	50	under	under	ADP
american_scientific_journal-3270	343	51	the	the	DET
american_scientific_journal-3270	343	52	condition	condition	NOUN
american_scientific_journal-3270	343	53	:	:	PUNCT
american_scientific_journal-3270	344	1	*	*	PUNCT
american_scientific_journal-3270	344	2	*	*	PUNCT
american_scientific_journal-3270	344	3	2	2	NUM
american_scientific_journal-3270	344	4	,	,	PUNCT
american_scientific_journal-3270	344	5	(	(	PUNCT
american_scientific_journal-3270	344	6	max	max	PROPN
american_scientific_journal-3270	344	7	)	)	PUNCT
american_scientific_journal-3270	344	8	ii	ii	PROPN
american_scientific_journal-3270	344	9	mp	mp	PROPN
american_scientific_journal-3270	344	10	l	l	PROPN
american_scientific_journal-3270	344	11	iλ	iλ	PROPN
american_scientific_journal-3270	344	12	η	η	PROPN
american_scientific_journal-3270	344	13	η	η	PROPN
american_scientific_journal-3270	344	14	µ	µ	X
american_scientific_journal-3270	344	15	π	π	X
american_scientific_journal-3270	344	16			NOUN
american_scientific_journal-3270	344	17	+	+	PUNCT
american_scientific_journal-3270	345	1	+	+	CCONJ
american_scientific_journal-3270	345	2	<	<	X
american_scientific_journal-3270	345	3	=	=	X
american_scientific_journal-3270	345	4	∀	∀	NOUN
american_scientific_journal-3270	345	5			VERB
american_scientific_journal-3270	345	6			PRON
american_scientific_journal-3270	345	7			PUNCT
american_scientific_journal-3270	345	8	.	.	PUNCT
american_scientific_journal-3270	346	1	american	american	PROPN
american_scientific_journal-3270	346	2	scientific	scientific	ADJ
american_scientific_journal-3270	346	3	research	research	PROPN
american_scientific_journal-3270	346	4	journal	journal	NOUN
american_scientific_journal-3270	346	5	for	for	ADP
american_scientific_journal-3270	346	6	engineering	engineering	NOUN
american_scientific_journal-3270	346	7	,	,	PUNCT
american_scientific_journal-3270	346	8	technology	technology	NOUN
american_scientific_journal-3270	346	9	,	,	PUNCT
american_scientific_journal-3270	346	10	and	and	CCONJ
american_scientific_journal-3270	346	11	sciences	science	NOUN
american_scientific_journal-3270	346	12	(	(	PUNCT
american_scientific_journal-3270	346	13	asrjets	asrjet	NOUN
american_scientific_journal-3270	346	14	)	)	PUNCT
american_scientific_journal-3270	346	15	(	(	PUNCT
american_scientific_journal-3270	346	16	2017	2017	NUM
american_scientific_journal-3270	346	17	)	)	PUNCT
american_scientific_journal-3270	346	18	volume	volume	NOUN
american_scientific_journal-3270	346	19	34	34	NUM
american_scientific_journal-3270	346	20	,	,	PUNCT
american_scientific_journal-3270	346	21	no	no	DET
american_scientific_journal-3270	346	22	1	1	NUM
american_scientific_journal-3270	346	23	,	,	PUNCT
american_scientific_journal-3270	346	24	pp	pp	ADV
american_scientific_journal-3270	346	25	213	213	NUM
american_scientific_journal-3270	346	26	-	-	SYM
american_scientific_journal-3270	346	27	230	230	NUM
american_scientific_journal-3270	346	28	223	223	NUM
american_scientific_journal-3270	346	29	5	5	NUM
american_scientific_journal-3270	346	30	.	.	PUNCT
american_scientific_journal-3270	347	1	jacobi	jacobi	PROPN
american_scientific_journal-3270	347	2	polynomials	polynomial	VERB
american_scientific_journal-3270	347	3	method	method	NOUN
american_scientific_journal-3270	347	4	for	for	ADP
american_scientific_journal-3270	347	5	solving	solve	VERB
american_scientific_journal-3270	347	6	system	system	NOUN
american_scientific_journal-3270	347	7	of	of	ADP
american_scientific_journal-3270	347	8	equations	equation	NOUN
american_scientific_journal-3270	347	9	(	(	PUNCT
american_scientific_journal-3270	347	10	4.2	4.2	NUM
american_scientific_journal-3270	347	11	)	)	PUNCT
american_scientific_journal-3270	347	12	the	the	DET
american_scientific_journal-3270	347	13	solution	solution	NOUN
american_scientific_journal-3270	347	14	of	of	ADP
american_scientific_journal-3270	347	15	the	the	DET
american_scientific_journal-3270	347	16	problem	problem	NOUN
american_scientific_journal-3270	347	17	(	(	PUNCT
american_scientific_journal-3270	347	18	4.2	4.2	NUM
american_scientific_journal-3270	347	19	)	)	PUNCT
american_scientific_journal-3270	347	20	can	can	AUX
american_scientific_journal-3270	347	21	be	be	AUX
american_scientific_journal-3270	347	22	written	write	VERB
american_scientific_journal-3270	347	23	as	as	ADP
american_scientific_journal-3270	347	24	(	(	PUNCT
american_scientific_journal-3270	347	25	)	)	PUNCT
american_scientific_journal-3270	347	26	(	(	PUNCT
american_scientific_journal-3270	347	27	)	)	PUNCT
american_scientific_journal-3270	347	28	(	(	PUNCT
american_scientific_journal-3270	347	29	)	)	PUNCT
american_scientific_journal-3270	347	30	y	y	PROPN
american_scientific_journal-3270	347	31	g	g	PROPN
american_scientific_journal-3270	347	32	y	y	PROPN
american_scientific_journal-3270	347	33	w	w	PROPN
american_scientific_journal-3270	347	34	yφ	yφ	PROPN
american_scientific_journal-3270	347	35	=	=	PUNCT
american_scientific_journal-3270	347	36	,	,	PUNCT
american_scientific_journal-3270	347	37	(	(	PUNCT
american_scientific_journal-3270	347	38	)	)	PUNCT
american_scientific_journal-3270	347	39	(	(	PUNCT
american_scientific_journal-3270	347	40	1	1	X
american_scientific_journal-3270	347	41	)	)	PUNCT
american_scientific_journal-3270	347	42	(	(	PUNCT
american_scientific_journal-3270	347	43	1	1	X
american_scientific_journal-3270	347	44	)	)	PUNCT
american_scientific_journal-3270	347	45	w	w	NOUN
american_scientific_journal-3270	347	46	x	x	PUNCT
american_scientific_journal-3270	347	47	x	x	X
american_scientific_journal-3270	347	48	xα	xα	ADJ
american_scientific_journal-3270	347	49	β=	β=	NOUN
american_scientific_journal-3270	348	1	−	−	PROPN
american_scientific_journal-3270	349	1	+	+	CCONJ
american_scientific_journal-3270	349	2	.	.	PUNCT
american_scientific_journal-3270	350	1	(	(	PUNCT
american_scientific_journal-3270	350	2	5.1	5.1	NUM
american_scientific_journal-3270	350	3	)	)	PUNCT
american_scientific_journal-3270	350	4	where	where	SCONJ
american_scientific_journal-3270	350	5	the	the	DET
american_scientific_journal-3270	350	6	unknown	unknown	ADJ
american_scientific_journal-3270	350	7	function	function	NOUN
american_scientific_journal-3270	350	8	(	(	PUNCT
american_scientific_journal-3270	350	9	)	)	PUNCT
american_scientific_journal-3270	350	10	g	g	PROPN
american_scientific_journal-3270	350	11	y	y	PROPN
american_scientific_journal-3270	350	12	is	be	AUX
american_scientific_journal-3270	350	13	regular	regular	ADJ
american_scientific_journal-3270	350	14	on	on	ADP
american_scientific_journal-3270	350	15	1	1	NUM
american_scientific_journal-3270	350	16	1.y−	1.y−	NUM
american_scientific_journal-3270	350	17	≤	≤	PROPN
american_scientific_journal-3270	350	18	≤	≤	NUM
american_scientific_journal-3270	350	19	w(x	w(x	NOUN
american_scientific_journal-3270	350	20	)	)	PUNCT
american_scientific_journal-3270	350	21	is	be	AUX
american_scientific_journal-3270	350	22	the	the	DET
american_scientific_journal-3270	350	23	fundamental	fundamental	ADJ
american_scientific_journal-3270	350	24	function	function	NOUN
american_scientific_journal-3270	350	25	of	of	ADP
american_scientific_journal-3270	350	26	eq	eq	PROPN
american_scientific_journal-3270	350	27	.	.	PUNCT
american_scientific_journal-3270	351	1	(	(	PUNCT
american_scientific_journal-3270	351	2	4.2	4.2	NUM
american_scientific_journal-3270	351	3	)	)	PUNCT
american_scientific_journal-3270	351	4	.	.	PUNCT
american_scientific_journal-3270	352	1	the	the	DET
american_scientific_journal-3270	352	2	singular	singular	ADJ
american_scientific_journal-3270	352	3	behavior	behavior	NOUN
american_scientific_journal-3270	352	4	of	of	ADP
american_scientific_journal-3270	352	5	the	the	DET
american_scientific_journal-3270	352	6	solution	solution	NOUN
american_scientific_journal-3270	352	7	may	may	AUX
american_scientific_journal-3270	352	8	be	be	AUX
american_scientific_journal-3270	352	9	characterized	characterize	VERB
american_scientific_journal-3270	352	10	by	by	ADP
american_scientific_journal-3270	352	11	a	a	DET
american_scientific_journal-3270	352	12	fundamental	fundamental	ADJ
american_scientific_journal-3270	352	13	function	function	NOUN
american_scientific_journal-3270	352	14	and	and	CCONJ
american_scientific_journal-3270	352	15	the	the	DET
american_scientific_journal-3270	352	16	index	index	NOUN
american_scientific_journal-3270	352	17	of	of	ADP
american_scientific_journal-3270	352	18	the	the	DET
american_scientific_journal-3270	352	19	problem	problem	NOUN
american_scientific_journal-3270	352	20	.	.	PUNCT
american_scientific_journal-3270	353	1	where	where	SCONJ
american_scientific_journal-3270	353	2	the	the	DET
american_scientific_journal-3270	353	3	index	index	NOUN
american_scientific_journal-3270	353	4	(	(	PUNCT
american_scientific_journal-3270	353	5	)	)	PUNCT
american_scientific_journal-3270	353	6	k	k	PROPN
american_scientific_journal-3270	353	7	α	α	PROPN
american_scientific_journal-3270	353	8	β=	β=	NOUN
american_scientific_journal-3270	353	9	−	−	PROPN
american_scientific_journal-3270	354	1	+	+	CCONJ
american_scientific_journal-3270	354	2	;	;	PUNCT
american_scientific_journal-3270	354	3	1,0,1.k	1,0,1.k	NUM
american_scientific_journal-3270	354	4	=	=	PUNCT
american_scientific_journal-3270	355	1	−	−	PROPN
american_scientific_journal-3270	355	2	more	more	ADJ
american_scientific_journal-3270	355	3	information	information	NOUN
american_scientific_journal-3270	355	4	for	for	ADP
american_scientific_journal-3270	355	5	the	the	DET
american_scientific_journal-3270	355	6	importance	importance	NOUN
american_scientific_journal-3270	355	7	of	of	ADP
american_scientific_journal-3270	355	8	k	k	PROPN
american_scientific_journal-3270	355	9	can	can	AUX
american_scientific_journal-3270	355	10	be	be	AUX
american_scientific_journal-3270	355	11	founded	found	VERB
american_scientific_journal-3270	355	12	in	in	ADP
american_scientific_journal-3270	355	13	[	[	X
american_scientific_journal-3270	355	14	23	23	NUM
american_scientific_journal-3270	355	15	]	]	PUNCT
american_scientific_journal-3270	355	16	.	.	PUNCT
american_scientific_journal-3270	356	1	the	the	DET
american_scientific_journal-3270	356	2	relation	relation	NOUN
american_scientific_journal-3270	356	3	between	between	ADP
american_scientific_journal-3270	356	4	the	the	DET
american_scientific_journal-3270	356	5	values	value	NOUN
american_scientific_journal-3270	356	6	of	of	ADP
american_scientific_journal-3270	356	7	k	k	PROPN
american_scientific_journal-3270	356	8	and	and	CCONJ
american_scientific_journal-3270	356	9	the	the	DET
american_scientific_journal-3270	356	10	weight	weight	NOUN
american_scientific_journal-3270	356	11	function	function	NOUN
american_scientific_journal-3270	356	12	and	and	CCONJ
american_scientific_journal-3270	356	13	the	the	DET
american_scientific_journal-3270	356	14	unknown	unknown	ADJ
american_scientific_journal-3270	356	15	potential	potential	ADJ
american_scientific_journal-3270	356	16	function	function	NOUN
american_scientific_journal-3270	356	17	can	can	AUX
american_scientific_journal-3270	356	18	be	be	AUX
american_scientific_journal-3270	356	19	discussed	discuss	VERB
american_scientific_journal-3270	356	20	as	as	ADP
american_scientific_journal-3270	356	21	the	the	DET
american_scientific_journal-3270	356	22	following	following	NOUN
american_scientific_journal-3270	356	23	:	:	PUNCT
american_scientific_journal-3270	356	24	(	(	PUNCT
american_scientific_journal-3270	356	25	1	1	NUM
american_scientific_journal-3270	356	26	):	):	PUNCT
american_scientific_journal-3270	356	27	if	if	SCONJ
american_scientific_journal-3270	356	28	1k	1k	NUM
american_scientific_journal-3270	356	29	=	=	SYM
american_scientific_journal-3270	356	30	−	−	PROPN
american_scientific_journal-3270	356	31	.	.	PUNCT
american_scientific_journal-3270	357	1	then	then	ADV
american_scientific_journal-3270	357	2	,	,	PUNCT
american_scientific_journal-3270	357	3	1	1	NUM
american_scientific_journal-3270	357	4	2	2	NUM
american_scientific_journal-3270	357	5	α	α	NOUN
american_scientific_journal-3270	357	6	β=	β=	NOUN
american_scientific_journal-3270	358	1	=	=	PUNCT
american_scientific_journal-3270	358	2	.	.	PUNCT
american_scientific_journal-3270	359	1	in	in	ADP
american_scientific_journal-3270	359	2	this	this	DET
american_scientific_journal-3270	359	3	case	case	NOUN
american_scientific_journal-3270	359	4	,	,	PUNCT
american_scientific_journal-3270	359	5	the	the	DET
american_scientific_journal-3270	359	6	unknown	unknown	ADJ
american_scientific_journal-3270	359	7	function	function	NOUN
american_scientific_journal-3270	359	8	(	(	PUNCT
american_scientific_journal-3270	359	9	)	)	PUNCT
american_scientific_journal-3270	359	10	xφ	xφ	PROPN
american_scientific_journal-3270	359	11	is	be	AUX
american_scientific_journal-3270	359	12	bounded	bound	VERB
american_scientific_journal-3270	359	13	at	at	ADP
american_scientific_journal-3270	359	14	both	both	DET
american_scientific_journal-3270	359	15	ends	end	NOUN
american_scientific_journal-3270	359	16	.	.	PUNCT
american_scientific_journal-3270	360	1	(	(	PUNCT
american_scientific_journal-3270	360	2	2	2	NUM
american_scientific_journal-3270	360	3	):	):	PUNCT
american_scientific_journal-3270	360	4	if	if	SCONJ
american_scientific_journal-3270	360	5	0k	0k	NOUN
american_scientific_journal-3270	360	6	=	=	PRON
american_scientific_journal-3270	360	7	,	,	PUNCT
american_scientific_journal-3270	360	8	this	this	PRON
american_scientific_journal-3270	360	9	means	mean	VERB
american_scientific_journal-3270	360	10	physically	physically	ADV
american_scientific_journal-3270	360	11	that	that	SCONJ
american_scientific_journal-3270	360	12	:	:	PUNCT
american_scientific_journal-3270	360	13	1	1	NUM
american_scientific_journal-3270	360	14	1	1	NUM
american_scientific_journal-3270	360	15	;	;	PUNCT
american_scientific_journal-3270	360	16	,	,	PUNCT
american_scientific_journal-3270	360	17	2	2	NUM
american_scientific_journal-3270	360	18	2	2	NUM
american_scientific_journal-3270	360	19	α	α	NOUN
american_scientific_journal-3270	360	20	β=	β=	NOUN
american_scientific_journal-3270	361	1	−	−	PROPN
american_scientific_journal-3270	361	2	=	=	SYM
american_scientific_journal-3270	361	3	or	or	CCONJ
american_scientific_journal-3270	361	4	1	1	NUM
american_scientific_journal-3270	361	5	1	1	NUM
american_scientific_journal-3270	361	6	;	;	PUNCT
american_scientific_journal-3270	361	7	2	2	NUM
american_scientific_journal-3270	361	8	2	2	NUM
american_scientific_journal-3270	361	9	α	α	NOUN
american_scientific_journal-3270	361	10	β=	β=	NOUN
american_scientific_journal-3270	362	1	=	=	SYM
american_scientific_journal-3270	362	2	−	−	PROPN
american_scientific_journal-3270	362	3	and	and	CCONJ
american_scientific_journal-3270	362	4	the	the	DET
american_scientific_journal-3270	362	5	weight	weight	NOUN
american_scientific_journal-3270	362	6	function	function	NOUN
american_scientific_journal-3270	362	7	,	,	PUNCT
american_scientific_journal-3270	362	8	in	in	ADP
american_scientific_journal-3270	362	9	each	each	DET
american_scientific_journal-3270	362	10	case	case	NOUN
american_scientific_journal-3270	362	11	,	,	PUNCT
american_scientific_journal-3270	362	12	can	can	AUX
american_scientific_journal-3270	362	13	be	be	AUX
american_scientific_journal-3270	362	14	determined	determine	VERB
american_scientific_journal-3270	362	15	.	.	PUNCT
american_scientific_journal-3270	363	1	in	in	ADP
american_scientific_journal-3270	363	2	this	this	DET
american_scientific_journal-3270	363	3	case	case	NOUN
american_scientific_journal-3270	363	4	,	,	PUNCT
american_scientific_journal-3270	363	5	the	the	DET
american_scientific_journal-3270	363	6	unknown	unknown	ADJ
american_scientific_journal-3270	363	7	function	function	NOUN
american_scientific_journal-3270	363	8	(	(	PUNCT
american_scientific_journal-3270	363	9	)	)	PUNCT
american_scientific_journal-3270	363	10	xφ	xφ	PROPN
american_scientific_journal-3270	363	11	is	be	AUX
american_scientific_journal-3270	363	12	bounded	bound	VERB
american_scientific_journal-3270	363	13	at	at	ADP
american_scientific_journal-3270	363	14	one	one	NUM
american_scientific_journal-3270	363	15	end	end	NOUN
american_scientific_journal-3270	363	16	and	and	CCONJ
american_scientific_journal-3270	363	17	has	have	VERB
american_scientific_journal-3270	363	18	an	an	DET
american_scientific_journal-3270	363	19	integrable	integrable	ADJ
american_scientific_journal-3270	363	20	singularity	singularity	NOUN
american_scientific_journal-3270	363	21	at	at	ADP
american_scientific_journal-3270	363	22	the	the	DET
american_scientific_journal-3270	363	23	other	other	ADJ
american_scientific_journal-3270	363	24	one	one	NUM
american_scientific_journal-3270	363	25	.	.	PUNCT
american_scientific_journal-3270	364	1	in	in	ADP
american_scientific_journal-3270	364	2	addition	addition	NOUN
american_scientific_journal-3270	364	3	,	,	PUNCT
american_scientific_journal-3270	364	4	no	no	DET
american_scientific_journal-3270	364	5	extra	extra	ADJ
american_scientific_journal-3270	364	6	condition	condition	NOUN
american_scientific_journal-3270	364	7	is	be	AUX
american_scientific_journal-3270	364	8	needed	need	VERB
american_scientific_journal-3270	364	9	(	(	PUNCT
american_scientific_journal-3270	364	10	the	the	DET
american_scientific_journal-3270	364	11	condition	condition	NOUN
american_scientific_journal-3270	364	12	is	be	AUX
american_scientific_journal-3270	364	13	the	the	DET
american_scientific_journal-3270	364	14	constant	constant	ADJ
american_scientific_journal-3270	364	15	be	be	AUX
american_scientific_journal-3270	364	16	zero	zero	NUM
american_scientific_journal-3270	364	17	)	)	PUNCT
american_scientific_journal-3270	364	18	,	,	PUNCT
american_scientific_journal-3270	364	19	and	and	CCONJ
american_scientific_journal-3270	364	20	the	the	DET
american_scientific_journal-3270	364	21	solution	solution	NOUN
american_scientific_journal-3270	364	22	being	be	AUX
american_scientific_journal-3270	364	23	a	a	DET
american_scientific_journal-3270	364	24	unique	unique	ADJ
american_scientific_journal-3270	364	25	.	.	PUNCT
american_scientific_journal-3270	365	1	(	(	PUNCT
american_scientific_journal-3270	365	2	3	3	NUM
american_scientific_journal-3270	365	3	):	):	PUNCT
american_scientific_journal-3270	365	4	if	if	SCONJ
american_scientific_journal-3270	365	5	1,k	1,k	PROPN
american_scientific_journal-3270	365	6	=	=	PUNCT
american_scientific_journal-3270	365	7	then	then	ADV
american_scientific_journal-3270	365	8	,	,	PUNCT
american_scientific_journal-3270	365	9	1	1	NUM
american_scientific_journal-3270	365	10	2	2	NUM
american_scientific_journal-3270	365	11	α	α	NOUN
american_scientific_journal-3270	365	12	β=	β=	NOUN
american_scientific_journal-3270	366	1	−	−	PROPN
american_scientific_journal-3270	367	1	=	=	PRON
american_scientific_journal-3270	367	2	.	.	PUNCT
american_scientific_journal-3270	368	1	the	the	DET
american_scientific_journal-3270	368	2	function	function	NOUN
american_scientific_journal-3270	368	3	(	(	PUNCT
american_scientific_journal-3270	368	4	)	)	PUNCT
american_scientific_journal-3270	368	5	xφ	xφ	PROPN
american_scientific_journal-3270	368	6	has	have	VERB
american_scientific_journal-3270	368	7	singularities	singularity	NOUN
american_scientific_journal-3270	368	8	at	at	ADP
american_scientific_journal-3270	368	9	both	both	DET
american_scientific_journal-3270	368	10	ends	end	NOUN
american_scientific_journal-3270	368	11	,	,	PUNCT
american_scientific_journal-3270	368	12	and	and	CCONJ
american_scientific_journal-3270	368	13	(	(	PUNCT
american_scientific_journal-3270	368	14	)	)	PUNCT
american_scientific_journal-3270	368	15	xφ	xφ	PROPN
american_scientific_journal-3270	368	16	must	must	AUX
american_scientific_journal-3270	368	17	satisfy	satisfy	VERB
american_scientific_journal-3270	368	18	an	an	DET
american_scientific_journal-3270	368	19	additional	additional	ADJ
american_scientific_journal-3270	368	20	condition	condition	NOUN
american_scientific_journal-3270	368	21	[	[	PUNCT
american_scientific_journal-3270	368	22	]	]	SYM
american_scientific_journal-3270	368	23	1	1	NUM
american_scientific_journal-3270	368	24	1	1	NUM
american_scientific_journal-3270	368	25	(	(	PUNCT
american_scientific_journal-3270	368	26	)	)	PUNCT
american_scientific_journal-3270	368	27	0	0	NUM
american_scientific_journal-3270	369	1	(	(	PUNCT
american_scientific_journal-3270	369	2	)	)	PUNCT
american_scientific_journal-3270	369	3	dxf	dxf	PROPN
american_scientific_journal-3270	369	4	x	x	PUNCT
american_scientific_journal-3270	370	1	w	w	PROPN
american_scientific_journal-3270	370	2	x−	x−	PROPN
american_scientific_journal-3270	370	3	=	=	PRON
american_scientific_journal-3270	370	4	∫	∫	PROPN
american_scientific_journal-3270	370	5	,	,	PUNCT
american_scientific_journal-3270	370	6	1	1	NUM
american_scientific_journal-3270	370	7	1	1	NUM
american_scientific_journal-3270	370	8	(	(	PUNCT
american_scientific_journal-3270	370	9	)	)	PUNCT
american_scientific_journal-3270	370	10	(	(	PUNCT
american_scientific_journal-3270	370	11	)	)	PUNCT
american_scientific_journal-3270	370	12	(	(	PUNCT
american_scientific_journal-3270	370	13	)	)	PUNCT
american_scientific_journal-3270	370	14	(	(	PUNCT
american_scientific_journal-3270	370	15	)	)	PUNCT
american_scientific_journal-3270	370	16	x	x	X
american_scientific_journal-3270	370	17	k	k	NOUN
american_scientific_journal-3270	370	18	y	y	PROPN
american_scientific_journal-3270	370	19	x	x	SYM
american_scientific_journal-3270	370	20	y	y	PROPN
american_scientific_journal-3270	370	21	dy	dy	VERB
american_scientific_journal-3270	370	22	f	f	PROPN
american_scientific_journal-3270	370	23	xλµφ	xλµφ	PROPN
american_scientific_journal-3270	371	1	φ	φ	PROPN
american_scientific_journal-3270	371	2	π	π	PROPN
american_scientific_journal-3270	371	3	−	−	PROPN
american_scientific_journal-3270	372	1	+	+	CCONJ
american_scientific_journal-3270	372	2	−	−	PROPN
american_scientific_journal-3270	373	1	=	=	PRON
american_scientific_journal-3270	373	2	∫	∫	PROPN
american_scientific_journal-3270	373	3	(	(	PUNCT
american_scientific_journal-3270	373	4	5.2	5.2	NUM
american_scientific_journal-3270	373	5	)	)	PUNCT
american_scientific_journal-3270	373	6	once	once	ADV
american_scientific_journal-3270	373	7	,	,	PUNCT
american_scientific_journal-3270	373	8	from	from	ADP
american_scientific_journal-3270	373	9	the	the	DET
american_scientific_journal-3270	373	10	above	above	ADJ
american_scientific_journal-3270	373	11	discuss	discuss	VERB
american_scientific_journal-3270	373	12	the	the	DET
american_scientific_journal-3270	373	13	unknown	unknown	ADJ
american_scientific_journal-3270	373	14	function	function	NOUN
american_scientific_journal-3270	373	15	,	,	PUNCT
american_scientific_journal-3270	373	16	the	the	DET
american_scientific_journal-3270	373	17	fundamental	fundamental	ADJ
american_scientific_journal-3270	373	18	function	function	NOUN
american_scientific_journal-3270	373	19	,	,	PUNCT
american_scientific_journal-3270	373	20	(	(	PUNCT
american_scientific_journal-3270	373	21	)	)	PUNCT
american_scientific_journal-3270	373	22	w	w	PROPN
american_scientific_journal-3270	373	23	y	y	PROPN
american_scientific_journal-3270	373	24	and	and	CCONJ
american_scientific_journal-3270	373	25	he	he	PRON
american_scientific_journal-3270	373	26	index	index	NOUN
american_scientific_journal-3270	373	27	k	k	PROPN
american_scientific_journal-3270	373	28	;	;	PUNCT
american_scientific_journal-3270	373	29	1,0,1k	1,0,1k	NUM
american_scientific_journal-3270	373	30	=	=	SYM
american_scientific_journal-3270	373	31	−	−	PROPN
american_scientific_journal-3270	373	32	can	can	AUX
american_scientific_journal-3270	373	33	be	be	AUX
american_scientific_journal-3270	373	34	connected	connect	VERB
american_scientific_journal-3270	373	35	by	by	ADP
american_scientific_journal-3270	373	36	the	the	DET
american_scientific_journal-3270	373	37	jacobi	jacobi	PROPN
american_scientific_journal-3270	373	38	polynomials	polynomials	PROPN
american_scientific_journal-3270	373	39	(	(	PUNCT
american_scientific_journal-3270	373	40	,	,	PUNCT
american_scientific_journal-3270	373	41	)	)	PUNCT
american_scientific_journal-3270	373	42	(	(	PUNCT
american_scientific_journal-3270	373	43	)	)	PUNCT
american_scientific_journal-3270	373	44	,	,	PUNCT
american_scientific_journal-3270	373	45	(	(	PUNCT
american_scientific_journal-3270	373	46	0,1	0,1	NUM
american_scientific_journal-3270	373	47	,	,	PUNCT
american_scientific_journal-3270	373	48	)	)	PUNCT
american_scientific_journal-3270	374	1	np	np	INTJ
american_scientific_journal-3270	374	2	y	y	PROPN
american_scientific_journal-3270	374	3	nα	nα	VERB
american_scientific_journal-3270	374	4	β	β	X
american_scientific_journal-3270	374	5	=	=	SYM
american_scientific_journal-3270	374	6			NOUN
american_scientific_journal-3270	374	7	in	in	ADP
american_scientific_journal-3270	374	8	the	the	DET
american_scientific_journal-3270	374	9	form	form	NOUN
american_scientific_journal-3270	374	10	(	(	PUNCT
american_scientific_journal-3270	374	11	,	,	PUNCT
american_scientific_journal-3270	374	12	)	)	PUNCT
american_scientific_journal-3270	374	13	0	0	NUM
american_scientific_journal-3270	375	1	(	(	PUNCT
american_scientific_journal-3270	375	2	)	)	PUNCT
american_scientific_journal-3270	375	3	(	(	PUNCT
american_scientific_journal-3270	375	4	)	)	PUNCT
american_scientific_journal-3270	375	5	(	(	PUNCT
american_scientific_journal-3270	375	6	)	)	PUNCT
american_scientific_journal-3270	375	7	n	n	CCONJ
american_scientific_journal-3270	375	8	n	n	CCONJ
american_scientific_journal-3270	375	9	n	n	ADV
american_scientific_journal-3270	375	10	y	y	PROPN
american_scientific_journal-3270	375	11	w	w	PROPN
american_scientific_journal-3270	375	12	y	y	PROPN
american_scientific_journal-3270	375	13	c	c	PROPN
american_scientific_journal-3270	376	1	p	p	NOUN
american_scientific_journal-3270	376	2	yα	yα	VERB
american_scientific_journal-3270	376	3	βφ	βφ	ADP
american_scientific_journal-3270	376	4	∞	∞	NUM
american_scientific_journal-3270	376	5	=	=	PUNCT
american_scientific_journal-3270	377	1	=	=	PUNCT
american_scientific_journal-3270	377	2	∑	∑	PUNCT
american_scientific_journal-3270	377	3	,	,	PUNCT
american_scientific_journal-3270	377	4	(	(	PUNCT
american_scientific_journal-3270	377	5	5.3	5.3	NUM
american_scientific_journal-3270	377	6	)	)	PUNCT
american_scientific_journal-3270	377	7	where	where	SCONJ
american_scientific_journal-3270	377	8	,	,	PUNCT
american_scientific_journal-3270	377	9	(	(	PUNCT
american_scientific_journal-3270	377	10	0,1,	0,1,	NOUN
american_scientific_journal-3270	377	11	...	...	PUNCT
american_scientific_journal-3270	377	12	)nc	)nc	PROPN
american_scientific_journal-3270	378	1	n	n	CCONJ
american_scientific_journal-3270	378	2	=	=	PRON
american_scientific_journal-3270	378	3	are	be	AUX
american_scientific_journal-3270	378	4	undetermined	undetermined	ADJ
american_scientific_journal-3270	378	5	constants	constant	NOUN
american_scientific_journal-3270	378	6	.	.	PUNCT
american_scientific_journal-3270	379	1	hence	hence	ADV
american_scientific_journal-3270	379	2	,	,	PUNCT
american_scientific_journal-3270	379	3	we	we	PRON
american_scientific_journal-3270	379	4	represent	represent	VERB
american_scientific_journal-3270	379	5	the	the	DET
american_scientific_journal-3270	379	6	solution	solution	NOUN
american_scientific_journal-3270	379	7	of	of	ADP
american_scientific_journal-3270	379	8	(	(	PUNCT
american_scientific_journal-3270	379	9	2.30	2.30	NUM
american_scientific_journal-3270	379	10	)	)	PUNCT
american_scientific_journal-3270	379	11	in	in	ADP
american_scientific_journal-3270	379	12	the	the	DET
american_scientific_journal-3270	379	13	form	form	NOUN
american_scientific_journal-3270	379	14	of	of	ADP
american_scientific_journal-3270	379	15	(	(	PUNCT
american_scientific_journal-3270	379	16	5.3	5.3	NUM
american_scientific_journal-3270	379	17	)	)	PUNCT
american_scientific_journal-3270	379	18	.	.	PUNCT
american_scientific_journal-3270	380	1	for	for	ADP
american_scientific_journal-3270	380	2	this	this	PRON
american_scientific_journal-3270	380	3	,	,	PUNCT
american_scientific_journal-3270	380	4	we	we	PRON
american_scientific_journal-3270	380	5	use	use	VERB
american_scientific_journal-3270	380	6	the	the	DET
american_scientific_journal-3270	380	7	following	follow	VERB
american_scientific_journal-3270	380	8	famous	famous	ADJ
american_scientific_journal-3270	380	9	relation	relation	NOUN
american_scientific_journal-3270	380	10	,	,	PUNCT
american_scientific_journal-3270	380	11	see	see	VERB
american_scientific_journal-3270	380	12	szegö	szegö	NOUN
american_scientific_journal-3270	381	1	[	[	X
american_scientific_journal-3270	381	2	24	24	NUM
american_scientific_journal-3270	381	3	]	]	PUNCT
american_scientific_journal-3270	381	4	american	american	ADJ
american_scientific_journal-3270	381	5	scientific	scientific	ADJ
american_scientific_journal-3270	381	6	research	research	PROPN
american_scientific_journal-3270	381	7	journal	journal	NOUN
american_scientific_journal-3270	381	8	for	for	ADP
american_scientific_journal-3270	381	9	engineering	engineering	NOUN
american_scientific_journal-3270	381	10	,	,	PUNCT
american_scientific_journal-3270	381	11	technology	technology	NOUN
american_scientific_journal-3270	381	12	,	,	PUNCT
american_scientific_journal-3270	381	13	and	and	CCONJ
american_scientific_journal-3270	381	14	sciences	science	NOUN
american_scientific_journal-3270	381	15	(	(	PUNCT
american_scientific_journal-3270	381	16	asrjets	asrjet	NOUN
american_scientific_journal-3270	381	17	)	)	PUNCT
american_scientific_journal-3270	381	18	(	(	PUNCT
american_scientific_journal-3270	381	19	2017	2017	NUM
american_scientific_journal-3270	381	20	)	)	PUNCT
american_scientific_journal-3270	381	21	volume	volume	NOUN
american_scientific_journal-3270	381	22	34	34	NUM
american_scientific_journal-3270	381	23	,	,	PUNCT
american_scientific_journal-3270	381	24	no	no	DET
american_scientific_journal-3270	381	25	1	1	NUM
american_scientific_journal-3270	381	26	,	,	PUNCT
american_scientific_journal-3270	381	27	pp	pp	ADV
american_scientific_journal-3270	381	28	213	213	NUM
american_scientific_journal-3270	381	29	-	-	SYM
american_scientific_journal-3270	381	30	230	230	NUM
american_scientific_journal-3270	381	31	224	224	NUM
american_scientific_journal-3270	381	32	1	1	NUM
american_scientific_journal-3270	381	33	(	(	PUNCT
american_scientific_journal-3270	381	34	)	)	PUNCT
american_scientific_journal-3270	381	35	(	(	PUNCT
american_scientific_journal-3270	381	36	,	,	PUNCT
american_scientific_journal-3270	381	37	)	)	PUNCT
american_scientific_journal-3270	381	38	(	(	PUNCT
american_scientific_journal-3270	381	39	,	,	PUNCT
american_scientific_journal-3270	381	40	)	)	PUNCT
american_scientific_journal-3270	381	41	2	2	NUM
american_scientific_journal-3270	381	42	1	1	NUM
american_scientific_journal-3270	381	43	1	1	NUM
american_scientific_journal-3270	381	44	1	1	NUM
american_scientific_journal-3270	381	45	2	2	NUM
american_scientific_journal-3270	381	46	(	(	PUNCT
american_scientific_journal-3270	381	47	)	)	PUNCT
american_scientific_journal-3270	381	48	(	(	PUNCT
american_scientific_journal-3270	381	49	1	1	X
american_scientific_journal-3270	381	50	)	)	PUNCT
american_scientific_journal-3270	381	51	1	1	NUM
american_scientific_journal-3270	381	52	(	(	PUNCT
american_scientific_journal-3270	381	53	)	)	PUNCT
american_scientific_journal-3270	381	54	(	(	PUNCT
american_scientific_journal-3270	381	55	)	)	PUNCT
american_scientific_journal-3270	381	56	cot	cot	NOUN
american_scientific_journal-3270	381	57	(	(	PUNCT
american_scientific_journal-3270	381	58	)	)	PUNCT
american_scientific_journal-3270	381	59	(	(	PUNCT
american_scientific_journal-3270	381	60	)	)	PUNCT
american_scientific_journal-3270	381	61	(	(	PUNCT
american_scientific_journal-3270	381	62	)	)	PUNCT
american_scientific_journal-3270	381	63	1	1	NUM
american_scientific_journal-3270	381	64	,	,	PUNCT
american_scientific_journal-3270	381	65	;	;	PUNCT
american_scientific_journal-3270	381	66	1	1	NUM
american_scientific_journal-3270	381	67	,	,	PUNCT
american_scientific_journal-3270	381	68	(	(	PUNCT
american_scientific_journal-3270	381	69	1	1	NUM
american_scientific_journal-3270	381	70	)	)	PUNCT
american_scientific_journal-3270	381	71	2n	2n	NUM
american_scientific_journal-3270	381	72	n	n	ADP
american_scientific_journal-3270	381	73	dy	dy	NOUN
american_scientific_journal-3270	381	74	n	n	PROPN
american_scientific_journal-3270	381	75	xw	xw	PROPN
american_scientific_journal-3270	382	1	y	y	PROPN
american_scientific_journal-3270	382	2	p	p	PROPN
american_scientific_journal-3270	382	3	y	y	PROPN
american_scientific_journal-3270	382	4	w	w	NOUN
american_scientific_journal-3270	382	5	x	x	X
american_scientific_journal-3270	382	6	p	p	X
american_scientific_journal-3270	382	7	x	x	X
american_scientific_journal-3270	382	8	f	f	PROPN
american_scientific_journal-3270	382	9	n	n	CCONJ
american_scientific_journal-3270	382	10	n	n	CCONJ
american_scientific_journal-3270	382	11	y	y	PROPN
american_scientific_journal-3270	382	12	x	x	PROPN
american_scientific_journal-3270	382	13	n	n	ADP
american_scientific_journal-3270	382	14	α	α	NOUN
american_scientific_journal-3270	382	15	β	β	X
american_scientific_journal-3270	382	16	α	α	X
american_scientific_journal-3270	382	17	β	β	X
american_scientific_journal-3270	382	18	α	α	X
american_scientific_journal-3270	382	19	β	β	X
american_scientific_journal-3270	382	20	α	α	NOUN
american_scientific_journal-3270	382	21	βπα	βπα	NOUN
american_scientific_journal-3270	382	22	α	α	NOUN
american_scientific_journal-3270	382	23	β	β	X
american_scientific_journal-3270	382	24	α	α	X
american_scientific_journal-3270	382	25	π	π	PROPN
american_scientific_journal-3270	382	26	π	π	NOUN
american_scientific_journal-3270	382	27	α	α	X
american_scientific_journal-3270	382	28	β	β	X
american_scientific_journal-3270	382	29	−	−	NOUN
american_scientific_journal-3270	383	1	+	+	CCONJ
american_scientific_journal-3270	383	2	−	−	X
american_scientific_journal-3270	383	3	γ	γ	X
american_scientific_journal-3270	383	4	γ	γ	X
american_scientific_journal-3270	383	5	+	+	X
american_scientific_journal-3270	383	6	+	+	CCONJ
american_scientific_journal-3270	383	7	−	−	VERB
american_scientific_journal-3270	383	8	=	=	ADP
american_scientific_journal-3270	383	9	−	−	NUM
american_scientific_journal-3270	383	10	×	×	NOUN
american_scientific_journal-3270	383	11	+	+	CCONJ
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american_scientific_journal-3270	385	5	+	+	NUM
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american_scientific_journal-3270	385	7	∫	∫	PUNCT
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american_scientific_journal-3270	385	9	(	(	PUNCT
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american_scientific_journal-3270	385	12	,	,	PUNCT
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american_scientific_journal-3270	386	12	,	,	PUNCT
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american_scientific_journal-3270	388	5			PUNCT
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american_scientific_journal-3270	388	7	,	,	PUNCT
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american_scientific_journal-3270	388	22	,	,	PUNCT
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american_scientific_journal-3270	389	9	25	25	NUM
american_scientific_journal-3270	389	10	]	]	PUNCT
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american_scientific_journal-3270	389	16	1	1	NUM
american_scientific_journal-3270	389	17	(	(	PUNCT
american_scientific_journal-3270	389	18	1	1	NUM
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american_scientific_journal-3270	389	23	1	1	NUM
american_scientific_journal-3270	389	24	,	,	PUNCT
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american_scientific_journal-3270	389	34	2n	2n	NUM
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american_scientific_journal-3270	391	4	f	f	PROPN
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american_scientific_journal-3270	391	8	n	n	ADV
american_scientific_journal-3270	391	9	k	k	NOUN
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american_scientific_journal-3270	391	11	β	β	VERB
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american_scientific_journal-3270	393	1	+	+	CCONJ
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american_scientific_journal-3270	396	3	)	)	PUNCT
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american_scientific_journal-3270	396	8	)	)	PUNCT
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american_scientific_journal-3270	397	9	x	x	X
american_scientific_journal-3270	397	10	y	y	NOUN
american_scientific_journal-3270	397	11	x	x	X
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american_scientific_journal-3270	398	2	λ	λ	X
american_scientific_journal-3270	398	3	π	π	X
american_scientific_journal-3270	398	4	−	−	PROPN
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american_scientific_journal-3270	399	7	−	−	PROPN
american_scientific_journal-3270	400	1	−	−	PROPN
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american_scientific_journal-3270	400	3	(	(	PUNCT
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american_scientific_journal-3270	400	5	)	)	PUNCT
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american_scientific_journal-3270	400	8	(	(	PUNCT
american_scientific_journal-3270	400	9	5.6	5.6	NUM
american_scientific_journal-3270	400	10	)	)	PUNCT
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american_scientific_journal-3270	400	20	i	i	PROPN
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american_scientific_journal-3270	400	35	0	0	NUM
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american_scientific_journal-3270	400	37	(	(	PUNCT
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american_scientific_journal-3270	400	42	)	)	PUNCT
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american_scientific_journal-3270	401	1	π	π	X
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american_scientific_journal-3270	401	3	πα	πα	INTJ
american_scientific_journal-3270	401	4	−∞	−∞	X
american_scientific_journal-3270	401	5	−	−	PROPN
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american_scientific_journal-3270	401	9			VERB
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american_scientific_journal-3270	401	11	−	−	VERB
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american_scientific_journal-3270	402	3			PROPN
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american_scientific_journal-3270	402	7	,	,	PUNCT
american_scientific_journal-3270	402	8	(	(	PUNCT
american_scientific_journal-3270	402	9	1	1	NUM
american_scientific_journal-3270	402	10	1)x−	1)x−	PROPN
american_scientific_journal-3270	402	11	<	<	X
american_scientific_journal-3270	402	12	<	<	X
american_scientific_journal-3270	402	13	,	,	PUNCT
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american_scientific_journal-3270	402	15	5.7	5.7	NUM
american_scientific_journal-3270	402	16	)	)	PUNCT
american_scientific_journal-3270	403	1	where	where	SCONJ
american_scientific_journal-3270	403	2	,	,	PUNCT
american_scientific_journal-3270	403	3	1	1	NUM
american_scientific_journal-3270	403	4	(	(	PUNCT
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american_scientific_journal-3270	403	6	)	)	PUNCT
american_scientific_journal-3270	403	7	1	1	NUM
american_scientific_journal-3270	403	8	(	(	PUNCT
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american_scientific_journal-3270	403	17	,	,	PUNCT
american_scientific_journal-3270	403	18	(	(	PUNCT
american_scientific_journal-3270	403	19	1	1	NUM
american_scientific_journal-3270	403	20	1)n	1)n	NUM
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american_scientific_journal-3270	403	22	x	x	PROPN
american_scientific_journal-3270	403	23	w	w	ADP
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american_scientific_journal-3270	404	2	−	−	PROPN
american_scientific_journal-3270	404	3	<	<	X
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american_scientific_journal-3270	404	5	∫	∫	PROPN
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american_scientific_journal-3270	405	1	(	(	PUNCT
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american_scientific_journal-3270	405	7	(	(	PUNCT
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american_scientific_journal-3270	405	9	)	)	PUNCT
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american_scientific_journal-3270	405	17	unknown	unknown	ADJ
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american_scientific_journal-3270	405	19	nc	nc	PROPN
american_scientific_journal-3270	405	20	.	.	PUNCT
american_scientific_journal-3270	406	1	expanding	expand	VERB
american_scientific_journal-3270	406	2	both	both	DET
american_scientific_journal-3270	406	3	sides	side	NOUN
american_scientific_journal-3270	406	4	of	of	ADP
american_scientific_journal-3270	406	5	(	(	PUNCT
american_scientific_journal-3270	406	6	5.7	5.7	NUM
american_scientific_journal-3270	406	7	)	)	PUNCT
american_scientific_journal-3270	406	8	in	in	ADP
american_scientific_journal-3270	406	9	the	the	DET
american_scientific_journal-3270	406	10	form	form	NOUN
american_scientific_journal-3270	406	11	of	of	ADP
american_scientific_journal-3270	406	12	jacobi	jacobi	PROPN
american_scientific_journal-3270	406	13	polynomials	polynomials	PROPN
american_scientific_journal-3270	406	14	(	(	PUNCT
american_scientific_journal-3270	406	15	,	,	PUNCT
american_scientific_journal-3270	406	16	)	)	PUNCT
american_scientific_journal-3270	406	17	(	(	PUNCT
american_scientific_journal-3270	406	18	)	)	PUNCT
american_scientific_journal-3270	406	19	;	;	PUNCT
american_scientific_journal-3270	406	20	(	(	PUNCT
american_scientific_journal-3270	406	21	0,1,	0,1,	NOUN
american_scientific_journal-3270	406	22	...	...	PUNCT
american_scientific_journal-3270	406	23	).kp	).kp	PUNCT
american_scientific_journal-3270	407	1	x	x	X
american_scientific_journal-3270	407	2	kα	kα	NOUN
american_scientific_journal-3270	407	3	β−	β−	PUNCT
american_scientific_journal-3270	408	1	−	−	NOUN
american_scientific_journal-3270	409	1	=	=	SYM
american_scientific_journal-3270	409	2	then	then	ADV
american_scientific_journal-3270	409	3	,	,	PUNCT
american_scientific_journal-3270	409	4	multiplying	multiply	VERB
american_scientific_journal-3270	409	5	both	both	DET
american_scientific_journal-3270	409	6	sides	side	NOUN
american_scientific_journal-3270	409	7	by	by	ADP
american_scientific_journal-3270	409	8	(	(	PUNCT
american_scientific_journal-3270	409	9	)	)	PUNCT
american_scientific_journal-3270	409	10	(	(	PUNCT
american_scientific_journal-3270	409	11	,	,	PUNCT
american_scientific_journal-3270	409	12	)	)	PUNCT
american_scientific_journal-3270	409	13	(	(	PUNCT
american_scientific_journal-3270	409	14	,	,	PUNCT
american_scientific_journal-3270	409	15	)	)	PUNCT
american_scientific_journal-3270	409	16	(	(	PUNCT
american_scientific_journal-3270	409	17	)	)	PUNCT
american_scientific_journal-3270	409	18	,	,	PUNCT
american_scientific_journal-3270	409	19	kw	kw	INTJ
american_scientific_journal-3270	409	20	p	p	X
american_scientific_journal-3270	409	21	xα	xα	INTJ
american_scientific_journal-3270	409	22	βα	βα	X
american_scientific_journal-3270	409	23	β	β	X
american_scientific_journal-3270	409	24	−	−	PROPN
american_scientific_journal-3270	409	25	−−	−−	NOUN
american_scientific_journal-3270	409	26	−	−	NOUN
american_scientific_journal-3270	409	27	,	,	PUNCT
american_scientific_journal-3270	409	28	and	and	CCONJ
american_scientific_journal-3270	409	29	integrating	integrate	VERB
american_scientific_journal-3270	409	30	the	the	DET
american_scientific_journal-3270	409	31	result	result	NOUN
american_scientific_journal-3270	409	32	from	from	ADP
american_scientific_journal-3270	409	33	-1	-1	PUNCT
american_scientific_journal-3270	409	34	to	to	ADP
american_scientific_journal-3270	409	35	1	1	NUM
american_scientific_journal-3270	409	36	and	and	CCONJ
american_scientific_journal-3270	409	37	using	use	VERB
american_scientific_journal-3270	409	38	the	the	DET
american_scientific_journal-3270	409	39	orthogonal	orthogonal	ADJ
american_scientific_journal-3270	409	40	relation	relation	NOUN
american_scientific_journal-3270	409	41	,	,	PUNCT
american_scientific_journal-3270	409	42	see	see	VERB
american_scientific_journal-3270	409	43	erdelyi	erdelyi	NOUN
american_scientific_journal-3270	409	44	[	[	X
american_scientific_journal-3270	409	45	25	25	NUM
american_scientific_journal-3270	409	46	]	]	SYM
american_scientific_journal-3270	409	47	1	1	NUM
american_scientific_journal-3270	409	48	(	(	PUNCT
american_scientific_journal-3270	409	49	,	,	PUNCT
american_scientific_journal-3270	409	50	)	)	PUNCT
american_scientific_journal-3270	409	51	(	(	PUNCT
american_scientific_journal-3270	409	52	,	,	PUNCT
american_scientific_journal-3270	409	53	)	)	PUNCT
american_scientific_journal-3270	409	54	(	(	PUNCT
american_scientific_journal-3270	409	55	,	,	PUNCT
american_scientific_journal-3270	409	56	)	)	PUNCT
american_scientific_journal-3270	409	57	1	1	NUM
american_scientific_journal-3270	409	58	0	0	NUM
american_scientific_journal-3270	409	59	(	(	PUNCT
american_scientific_journal-3270	409	60	)	)	PUNCT
american_scientific_journal-3270	409	61	(	(	PUNCT
american_scientific_journal-3270	409	62	)	)	PUNCT
american_scientific_journal-3270	409	63	(	(	PUNCT
american_scientific_journal-3270	409	64	)	)	PUNCT
american_scientific_journal-3270	409	65	n	n	X
american_scientific_journal-3270	409	66	k	k	PROPN
american_scientific_journal-3270	409	67	k	k	PROPN
american_scientific_journal-3270	410	1	n	n	CCONJ
american_scientific_journal-3270	411	1	k	k	NOUN
american_scientific_journal-3270	411	2	p	p	X
american_scientific_journal-3270	411	3	x	x	X
american_scientific_journal-3270	411	4	p	p	X
american_scientific_journal-3270	411	5	x	x	X
american_scientific_journal-3270	411	6	w	w	PROPN
american_scientific_journal-3270	411	7	x	x	SYM
american_scientific_journal-3270	411	8	dx	dx	PROPN
american_scientific_journal-3270	411	9	n	n	PROPN
american_scientific_journal-3270	411	10	k	k	PROPN
american_scientific_journal-3270	411	11	α	α	X
american_scientific_journal-3270	411	12	β	β	X
american_scientific_journal-3270	411	13	α	α	X
american_scientific_journal-3270	411	14	β	β	X
american_scientific_journal-3270	411	15	α	α	PROPN
american_scientific_journal-3270	411	16	βθ−	βθ−	PUNCT
american_scientific_journal-3270	411	17	≠=	≠=	NOUN
american_scientific_journal-3270	411	18			ADJ
american_scientific_journal-3270	411	19	=	=	NOUN
american_scientific_journal-3270	411	20			NOUN
american_scientific_journal-3270	411	21	∫	∫	NOUN
american_scientific_journal-3270	411	22	,	,	PUNCT
american_scientific_journal-3270	411	23	(	(	PUNCT
american_scientific_journal-3270	411	24	5.9	5.9	NUM
american_scientific_journal-3270	411	25	)	)	PUNCT
american_scientific_journal-3270	411	26	where	where	SCONJ
american_scientific_journal-3270	411	27	american	american	ADJ
american_scientific_journal-3270	411	28	scientific	scientific	ADJ
american_scientific_journal-3270	411	29	research	research	PROPN
american_scientific_journal-3270	411	30	journal	journal	NOUN
american_scientific_journal-3270	411	31	for	for	ADP
american_scientific_journal-3270	411	32	engineering	engineering	NOUN
american_scientific_journal-3270	411	33	,	,	PUNCT
american_scientific_journal-3270	411	34	technology	technology	NOUN
american_scientific_journal-3270	411	35	,	,	PUNCT
american_scientific_journal-3270	411	36	and	and	CCONJ
american_scientific_journal-3270	411	37	sciences	science	NOUN
american_scientific_journal-3270	411	38	(	(	PUNCT
american_scientific_journal-3270	411	39	asrjets	asrjet	NOUN
american_scientific_journal-3270	411	40	)	)	PUNCT
american_scientific_journal-3270	411	41	(	(	PUNCT
american_scientific_journal-3270	411	42	2017	2017	NUM
american_scientific_journal-3270	411	43	)	)	PUNCT
american_scientific_journal-3270	411	44	volume	volume	NOUN
american_scientific_journal-3270	411	45	34	34	NUM
american_scientific_journal-3270	411	46	,	,	PUNCT
american_scientific_journal-3270	411	47	no	no	DET
american_scientific_journal-3270	411	48	1	1	NUM
american_scientific_journal-3270	411	49	,	,	PUNCT
american_scientific_journal-3270	411	50	pp	pp	ADV
american_scientific_journal-3270	411	51	213	213	NUM
american_scientific_journal-3270	411	52	-	-	SYM
american_scientific_journal-3270	411	53	230	230	NUM
american_scientific_journal-3270	411	54	225	225	NUM
american_scientific_journal-3270	411	55	1	1	NUM
american_scientific_journal-3270	411	56	(	(	PUNCT
american_scientific_journal-3270	411	57	,	,	PUNCT
american_scientific_journal-3270	411	58	)	)	PUNCT
american_scientific_journal-3270	411	59	2	2	NUM
american_scientific_journal-3270	411	60	(	(	PUNCT
american_scientific_journal-3270	411	61	1	1	NUM
american_scientific_journal-3270	411	62	)	)	PUNCT
american_scientific_journal-3270	411	63	(	(	PUNCT
american_scientific_journal-3270	411	64	1	1	NUM
american_scientific_journal-3270	411	65	)	)	PUNCT
american_scientific_journal-3270	411	66	,	,	PUNCT
american_scientific_journal-3270	411	67	2	2	NUM
american_scientific_journal-3270	411	68	1	1	NUM
american_scientific_journal-3270	411	69	!	!	PUNCT
american_scientific_journal-3270	412	1	(	(	PUNCT
american_scientific_journal-3270	412	2	1)k	1)k	NUM
american_scientific_journal-3270	412	3	k	k	PROPN
american_scientific_journal-3270	413	1	k	k	PROPN
american_scientific_journal-3270	413	2	k	k	PROPN
american_scientific_journal-3270	414	1	k	k	PROPN
american_scientific_journal-3270	414	2	k	k	PROPN
american_scientific_journal-3270	415	1	α	α	X
american_scientific_journal-3270	415	2	β	β	X
american_scientific_journal-3270	415	3	α	α	X
american_scientific_journal-3270	415	4	β	β	X
american_scientific_journal-3270	415	5	α	α	NOUN
american_scientific_journal-3270	415	6	βθ	βθ	VERB
american_scientific_journal-3270	415	7	α	α	X
american_scientific_journal-3270	415	8	β	β	X
american_scientific_journal-3270	415	9	α	α	X
american_scientific_journal-3270	415	10	β	β	X
american_scientific_journal-3270	416	1	+	+	X
american_scientific_journal-3270	417	1	+	+	CCONJ
american_scientific_journal-3270	417	2	γ	γ	X
american_scientific_journal-3270	417	3	+	+	X
american_scientific_journal-3270	417	4	+	+	CCONJ
american_scientific_journal-3270	417	5	γ	γ	X
american_scientific_journal-3270	417	6	+	+	X
american_scientific_journal-3270	417	7	+	+	PUNCT
american_scientific_journal-3270	417	8	=	=	X
american_scientific_journal-3270	418	1	+	+	PUNCT
american_scientific_journal-3270	418	2	+	+	PUNCT
american_scientific_journal-3270	418	3	+	+	CCONJ
american_scientific_journal-3270	418	4	γ	γ	X
american_scientific_journal-3270	418	5	+	+	X
american_scientific_journal-3270	418	6	+	+	PUNCT
american_scientific_journal-3270	418	7	+	+	CCONJ
american_scientific_journal-3270	418	8	(	(	PUNCT
american_scientific_journal-3270	418	9	0,1,	0,1,	NOUN
american_scientific_journal-3270	418	10	...	...	PUNCT
american_scientific_journal-3270	418	11	)k	)k	X
american_scientific_journal-3270	419	1	=	=	PUNCT
american_scientific_journal-3270	419	2	.	.	PUNCT
american_scientific_journal-3270	420	1	(	(	PUNCT
american_scientific_journal-3270	420	2	5.10	5.10	NUM
american_scientific_journal-3270	420	3	)	)	PUNCT
american_scientific_journal-3270	420	4	hence	hence	ADV
american_scientific_journal-3270	420	5	,	,	PUNCT
american_scientific_journal-3270	420	6	after	after	ADP
american_scientific_journal-3270	420	7	truncating	truncate	VERB
american_scientific_journal-3270	420	8	the	the	DET
american_scientific_journal-3270	420	9	series	series	NOUN
american_scientific_journal-3270	420	10	(	(	PUNCT
american_scientific_journal-3270	420	11	5.7	5.7	NUM
american_scientific_journal-3270	420	12	)	)	PUNCT
american_scientific_journal-3270	420	13	,	,	PUNCT
american_scientific_journal-3270	420	14	we	we	PRON
american_scientific_journal-3270	420	15	have	have	VERB
american_scientific_journal-3270	420	16	(	(	PUNCT
american_scientific_journal-3270	420	17	,	,	PUNCT
american_scientific_journal-3270	420	18	)	)	PUNCT
american_scientific_journal-3270	420	19	0	0	NUM
american_scientific_journal-3270	420	20	2	2	NUM
american_scientific_journal-3270	420	21	,	,	PUNCT
american_scientific_journal-3270	420	22	(	(	PUNCT
american_scientific_journal-3270	420	23	0,1	0,1	NOUN
american_scientific_journal-3270	420	24	,	,	PUNCT
american_scientific_journal-3270	420	25	...	...	PUNCT
american_scientific_journal-3270	420	26	,	,	PUNCT
american_scientific_journal-3270	420	27	)	)	PUNCT
american_scientific_journal-3270	420	28	sin	sin	NOUN
american_scientific_journal-3270	420	29	k	k	PROPN
american_scientific_journal-3270	420	30	n	n	CCONJ
american_scientific_journal-3270	421	1	k	k	PROPN
american_scientific_journal-3270	421	2	k	k	PROPN
american_scientific_journal-3270	421	3	k	k	PROPN
american_scientific_journal-3270	421	4	nk	nk	PROPN
american_scientific_journal-3270	422	1	n	n	PROPN
american_scientific_journal-3270	423	1	k	k	PROPN
american_scientific_journal-3270	424	1	n	n	PROPN
american_scientific_journal-3270	424	2	c	c	NOUN
american_scientific_journal-3270	424	3	d	d	NOUN
american_scientific_journal-3270	424	4	c	c	PROPN
american_scientific_journal-3270	424	5	f	f	PROPN
american_scientific_journal-3270	424	6	k	k	PROPN
american_scientific_journal-3270	424	7	nα	nα	VERB
american_scientific_journal-3270	424	8	βλ	βλ	PROPN
american_scientific_journal-3270	424	9	θ	θ	X
american_scientific_journal-3270	424	10	π	π	NOUN
american_scientific_journal-3270	424	11	πα	πα	INTJ
american_scientific_journal-3270	424	12	−	−	NOUN
american_scientific_journal-3270	424	13	−	−	NOUN
american_scientific_journal-3270	424	14	−	−	PROPN
american_scientific_journal-3270	425	1	+	+	CCONJ
american_scientific_journal-3270	425	2	=	=	SYM
american_scientific_journal-3270	425	3	−	−	PROPN
american_scientific_journal-3270	425	4	+	+	NOUN
american_scientific_journal-3270	425	5	=	=	SYM
american_scientific_journal-3270	425	6	=	=	NOUN
american_scientific_journal-3270	425	7	∑	∑	PROPN
american_scientific_journal-3270	425	8	,	,	PUNCT
american_scientific_journal-3270	425	9	(	(	PUNCT
american_scientific_journal-3270	425	10	5.11	5.11	NUM
american_scientific_journal-3270	425	11	)	)	PUNCT
american_scientific_journal-3270	425	12	where	where	SCONJ
american_scientific_journal-3270	425	13	1	1	NUM
american_scientific_journal-3270	425	14	(	(	PUNCT
american_scientific_journal-3270	425	15	,	,	PUNCT
american_scientific_journal-3270	425	16	)	)	PUNCT
american_scientific_journal-3270	425	17	1	1	NUM
american_scientific_journal-3270	425	18	1	1	NUM
american_scientific_journal-3270	425	19	(	(	PUNCT
american_scientific_journal-3270	425	20	,	,	PUNCT
american_scientific_journal-3270	425	21	)	)	PUNCT
american_scientific_journal-3270	425	22	1	1	NUM
american_scientific_journal-3270	425	23	(	(	PUNCT
american_scientific_journal-3270	425	24	)	)	PUNCT
american_scientific_journal-3270	425	25	(	(	PUNCT
american_scientific_journal-3270	425	26	,	,	PUNCT
american_scientific_journal-3270	425	27	,	,	PUNCT
american_scientific_journal-3270	425	28	)	)	PUNCT
american_scientific_journal-3270	425	29	(	(	PUNCT
american_scientific_journal-3270	425	30	)	)	PUNCT
american_scientific_journal-3270	425	31	(	(	PUNCT
american_scientific_journal-3270	425	32	)	)	PUNCT
american_scientific_journal-3270	425	33	(	(	PUNCT
american_scientific_journal-3270	425	34	,	,	PUNCT
american_scientific_journal-3270	425	35	,	,	PUNCT
american_scientific_journal-3270	425	36	)	)	PUNCT
american_scientific_journal-3270	425	37	(	(	PUNCT
american_scientific_journal-3270	425	38	)	)	PUNCT
american_scientific_journal-3270	425	39	nk	nk	PROPN
american_scientific_journal-3270	425	40	k	k	PROPN
american_scientific_journal-3270	426	1	n	n	PROPN
american_scientific_journal-3270	427	1	k	k	PROPN
american_scientific_journal-3270	427	2	k	k	PROPN
american_scientific_journal-3270	428	1	d	d	PROPN
american_scientific_journal-3270	428	2	p	p	X
american_scientific_journal-3270	428	3	x	x	X
american_scientific_journal-3270	428	4	w	w	NOUN
american_scientific_journal-3270	428	5	x	x	SYM
american_scientific_journal-3270	428	6	h	h	NOUN
american_scientific_journal-3270	428	7	x	x	X
american_scientific_journal-3270	428	8	dx	dx	PROPN
american_scientific_journal-3270	429	1	f	f	PROPN
american_scientific_journal-3270	429	2	p	p	X
american_scientific_journal-3270	429	3	x	x	X
american_scientific_journal-3270	429	4	w	w	NOUN
american_scientific_journal-3270	429	5	x	x	X
american_scientific_journal-3270	429	6	x	x	X
american_scientific_journal-3270	429	7	dx	dx	PROPN
american_scientific_journal-3270	429	8	α	α	PROPN
american_scientific_journal-3270	429	9	β	β	X
american_scientific_journal-3270	429	10	α	α	X
american_scientific_journal-3270	429	11	β	β	X
american_scientific_journal-3270	429	12	α	α	X
american_scientific_journal-3270	429	13	β	β	X
american_scientific_journal-3270	429	14	α	α	X
american_scientific_journal-3270	429	15	β	β	X
american_scientific_journal-3270	429	16	y	y	PROPN
american_scientific_journal-3270	429	17	−	−	PROPN
american_scientific_journal-3270	429	18	−	−	PROPN
american_scientific_journal-3270	429	19	−	−	PROPN
american_scientific_journal-3270	429	20	−	−	PROPN
american_scientific_journal-3270	429	21	−	−	PROPN
american_scientific_journal-3270	429	22	−	−	PROPN
american_scientific_journal-3270	429	23			PROPN
american_scientific_journal-3270	429	24	=	=	PUNCT
american_scientific_journal-3270	430	1	−	−	PROPN
american_scientific_journal-3270	430	2	−	−	PROPN
american_scientific_journal-3270	430	3			PROPN
american_scientific_journal-3270	430	4			NOUN
american_scientific_journal-3270	430	5			PROPN
american_scientific_journal-3270	430	6	=	=	PROPN
american_scientific_journal-3270	431	1	−	−	PROPN
american_scientific_journal-3270	431	2	−	−	PROPN
american_scientific_journal-3270	432	1			PROPN
american_scientific_journal-3270	432	2	∫	∫	PROPN
american_scientific_journal-3270	432	3	∫	∫	PROPN
american_scientific_journal-3270	432	4	.	.	PUNCT
american_scientific_journal-3270	433	1	(	(	PUNCT
american_scientific_journal-3270	433	2	5.12	5.12	NUM
american_scientific_journal-3270	433	3	)	)	PUNCT
american_scientific_journal-3270	433	4	1	1	NUM
american_scientific_journal-3270	433	5	)	)	PUNCT
american_scientific_journal-3270	433	6	in	in	ADP
american_scientific_journal-3270	433	7	the	the	DET
american_scientific_journal-3270	433	8	case	case	NOUN
american_scientific_journal-3270	433	9	k	k	NOUN
american_scientific_journal-3270	433	10	=	=	SYM
american_scientific_journal-3270	433	11	1	1	NUM
american_scientific_journal-3270	433	12	,	,	PUNCT
american_scientific_journal-3270	433	13	we	we	PRON
american_scientific_journal-3270	433	14	note	note	VERB
american_scientific_journal-3270	433	15	that	that	SCONJ
american_scientific_journal-3270	433	16	the	the	DET
american_scientific_journal-3270	433	17	first	first	ADJ
american_scientific_journal-3270	433	18	term	term	NOUN
american_scientific_journal-3270	433	19	in	in	ADP
american_scientific_journal-3270	433	20	the	the	DET
american_scientific_journal-3270	433	21	series	series	NOUN
american_scientific_journal-3270	433	22	(	(	PUNCT
american_scientific_journal-3270	433	23	5.7	5.7	NUM
american_scientific_journal-3270	433	24	)	)	PUNCT
american_scientific_journal-3270	433	25	is	be	AUX
american_scientific_journal-3270	433	26	a	a	DET
american_scientific_journal-3270	433	27	constant	constant	ADJ
american_scientific_journal-3270	433	28	times	time	NOUN
american_scientific_journal-3270	433	29	(	(	PUNCT
american_scientific_journal-3270	433	30	,	,	PUNCT
american_scientific_journal-3270	433	31	)	)	PUNCT
american_scientific_journal-3270	433	32	1	1	NUM
american_scientific_journal-3270	433	33	(	(	PUNCT
american_scientific_journal-3270	433	34	)	)	PUNCT
american_scientific_journal-3270	433	35	.oc	.oc	PUNCT
american_scientific_journal-3270	434	1	p	p	NOUN
american_scientific_journal-3270	435	1	xα	xα	INTJ
american_scientific_journal-3270	435	2	β−	β−	NOUN
american_scientific_journal-3270	436	1	−	−	NOUN
american_scientific_journal-3270	437	1	hence	hence	ADV
american_scientific_journal-3270	437	2	,	,	PUNCT
american_scientific_journal-3270	437	3	in	in	ADP
american_scientific_journal-3270	437	4	solving	solve	VERB
american_scientific_journal-3270	437	5	(	(	PUNCT
american_scientific_journal-3270	437	6	5.11	5.11	NUM
american_scientific_journal-3270	437	7	)	)	PUNCT
american_scientific_journal-3270	437	8	it	it	PRON
american_scientific_journal-3270	437	9	can	can	AUX
american_scientific_journal-3270	437	10	be	be	AUX
american_scientific_journal-3270	437	11	formally	formally	ADV
american_scientific_journal-3270	437	12	assumed	assume	VERB
american_scientific_journal-3270	437	13	that	that	SCONJ
american_scientific_journal-3270	437	14	1	1	NUM
american_scientific_journal-3270	437	15	0.c−	0.c−	NUM
american_scientific_journal-3270	437	16	=	=	PUNCT
american_scientific_journal-3270	437	17	also	also	ADV
american_scientific_journal-3270	437	18	,	,	PUNCT
american_scientific_journal-3270	437	19	from	from	ADP
american_scientific_journal-3270	437	20	(	(	PUNCT
american_scientific_journal-3270	437	21	5.7	5.7	NUM
american_scientific_journal-3270	437	22	)	)	PUNCT
american_scientific_journal-3270	437	23	to	to	ADP
american_scientific_journal-3270	437	24	(	(	PUNCT
american_scientific_journal-3270	437	25	5.12	5.12	NUM
american_scientific_journal-3270	437	26	)	)	PUNCT
american_scientific_journal-3270	437	27	it	it	PRON
american_scientific_journal-3270	437	28	is	be	AUX
american_scientific_journal-3270	437	29	seen	see	VERB
american_scientific_journal-3270	437	30	that	that	SCONJ
american_scientific_journal-3270	437	31	(	(	PUNCT
american_scientific_journal-3270	437	32	,	,	PUNCT
american_scientific_journal-3270	437	33	)	)	PUNCT
american_scientific_journal-3270	437	34	0	0	NUM
american_scientific_journal-3270	438	1	(	(	PUNCT
american_scientific_journal-3270	438	2	)	)	PUNCT
american_scientific_journal-3270	438	3	1p	1p	NUM
american_scientific_journal-3270	438	4	xα	xα	ADP
american_scientific_journal-3270	438	5	β−	β−	PUNCT
american_scientific_journal-3270	439	1	−	−	NOUN
american_scientific_journal-3270	439	2	=	=	PUNCT
american_scientific_journal-3270	439	3	is	be	AUX
american_scientific_journal-3270	439	4	the	the	DET
american_scientific_journal-3270	439	5	first	first	ADJ
american_scientific_journal-3270	439	6	equation	equation	NOUN
american_scientific_journal-3270	439	7	obtained	obtain	VERB
american_scientific_journal-3270	439	8	from	from	ADP
american_scientific_journal-3270	439	9	(	(	PUNCT
american_scientific_journal-3270	439	10	5.11	5.11	NUM
american_scientific_journal-3270	439	11	)	)	PUNCT
american_scientific_journal-3270	439	12	.	.	PUNCT
american_scientific_journal-3270	440	1	2	2	X
american_scientific_journal-3270	440	2	)	)	PUNCT
american_scientific_journal-3270	440	3	in	in	ADP
american_scientific_journal-3270	440	4	the	the	DET
american_scientific_journal-3270	440	5	case	case	NOUN
american_scientific_journal-3270	440	6	k=0	k=0	PROPN
american_scientific_journal-3270	440	7	,	,	PUNCT
american_scientific_journal-3270	440	8	there	there	PRON
american_scientific_journal-3270	440	9	are	be	VERB
american_scientific_journal-3270	440	10	no	no	DET
american_scientific_journal-3270	440	11	additional	additional	ADJ
american_scientific_journal-3270	440	12	arbitrary	arbitrary	ADJ
american_scientific_journal-3270	440	13	constants	constant	NOUN
american_scientific_journal-3270	440	14	or	or	CCONJ
american_scientific_journal-3270	440	15	conditions	condition	NOUN
american_scientific_journal-3270	440	16	,	,	PUNCT
american_scientific_journal-3270	440	17	and	and	CCONJ
american_scientific_journal-3270	440	18	(	(	PUNCT
american_scientific_journal-3270	440	19	5.11	5.11	NUM
american_scientific_journal-3270	440	20	)	)	PUNCT
american_scientific_journal-3270	440	21	provides	provide	VERB
american_scientific_journal-3270	440	22	(	(	PUNCT
american_scientific_journal-3270	440	23	n	n	NOUN
american_scientific_journal-3270	440	24	+	+	CCONJ
american_scientific_journal-3270	440	25	1	1	X
american_scientific_journal-3270	440	26	)	)	PUNCT
american_scientific_journal-3270	440	27	linear	linear	ADJ
american_scientific_journal-3270	440	28	algebraic	algebraic	ADJ
american_scientific_journal-3270	440	29	system	system	NOUN
american_scientific_journal-3270	440	30	for	for	ADP
american_scientific_journal-3270	440	31	the	the	DET
american_scientific_journal-3270	440	32	unknown	unknown	ADJ
american_scientific_journal-3270	440	33	constants	constant	NOUN
american_scientific_journal-3270	440	34	0	0	NUM
american_scientific_journal-3270	440	35	,	,	PUNCT
american_scientific_journal-3270	440	36	...	...	PUNCT
american_scientific_journal-3270	440	37	,	,	PUNCT
american_scientific_journal-3270	440	38	.nc	.nc	PUNCT
american_scientific_journal-3270	441	1	c	c	NOUN
american_scientific_journal-3270	441	2	3	3	NUM
american_scientific_journal-3270	441	3	)	)	PUNCT
american_scientific_journal-3270	441	4	in	in	ADP
american_scientific_journal-3270	441	5	the	the	DET
american_scientific_journal-3270	441	6	case	case	NOUN
american_scientific_journal-3270	441	7	k	k	NOUN
american_scientific_journal-3270	441	8	=	=	SYM
american_scientific_journal-3270	441	9	1	1	NUM
american_scientific_journal-3270	441	10	,	,	PUNCT
american_scientific_journal-3270	441	11	the	the	DET
american_scientific_journal-3270	441	12	n	n	NOUN
american_scientific_journal-3270	441	13	+	+	CCONJ
american_scientific_journal-3270	441	14	1	1	NUM
american_scientific_journal-3270	441	15	equations	equation	NOUN
american_scientific_journal-3270	441	16	given	give	VERB
american_scientific_journal-3270	441	17	by	by	ADP
american_scientific_journal-3270	441	18	(	(	PUNCT
american_scientific_journal-3270	441	19	5.11	5.11	NUM
american_scientific_journal-3270	441	20	)	)	PUNCT
american_scientific_journal-3270	441	21	contains	contain	VERB
american_scientific_journal-3270	441	22	n	n	X
american_scientific_journal-3270	441	23	+	+	CCONJ
american_scientific_journal-3270	441	24	2	2	NUM
american_scientific_journal-3270	441	25	unknown	unknown	ADJ
american_scientific_journal-3270	441	26	constants	constant	NOUN
american_scientific_journal-3270	441	27	,	,	PUNCT
american_scientific_journal-3270	441	28	0	0	NUM
american_scientific_journal-3270	441	29	1	1	NUM
american_scientific_journal-3270	441	30	,	,	PUNCT
american_scientific_journal-3270	441	31	...	...	PUNCT
american_scientific_journal-3270	441	32	,	,	PUNCT
american_scientific_journal-3270	441	33	.nc	.nc	PUNCT
american_scientific_journal-3270	442	1	c	c	X
american_scientific_journal-3270	443	1	+	+	CCONJ
american_scientific_journal-3270	443	2	the	the	DET
american_scientific_journal-3270	443	3	additional	additional	ADJ
american_scientific_journal-3270	443	4	equation	equation	NOUN
american_scientific_journal-3270	443	5	for	for	ADP
american_scientific_journal-3270	443	6	a	a	DET
american_scientific_journal-3270	443	7	unique	unique	ADJ
american_scientific_journal-3270	443	8	solution	solution	NOUN
american_scientific_journal-3270	443	9	is	be	AUX
american_scientific_journal-3270	443	10	provided	provide	VERB
american_scientific_journal-3270	443	11	by	by	ADP
american_scientific_journal-3270	443	12	the	the	DET
american_scientific_journal-3270	443	13	equilibrium	equilibrium	NOUN
american_scientific_journal-3270	443	14	or	or	CCONJ
american_scientific_journal-3270	443	15	compatibility	compatibility	NOUN
american_scientific_journal-3270	443	16	condition	condition	NOUN
american_scientific_journal-3270	443	17	by	by	ADP
american_scientific_journal-3270	443	18	substituting	substitute	VERB
american_scientific_journal-3270	443	19	from	from	ADP
american_scientific_journal-3270	443	20	(	(	PUNCT
american_scientific_journal-3270	443	21	5.10	5.10	NUM
american_scientific_journal-3270	443	22	)	)	PUNCT
american_scientific_journal-3270	443	23	and	and	CCONJ
american_scientific_journal-3270	443	24	using	use	VERB
american_scientific_journal-3270	443	25	the	the	DET
american_scientific_journal-3270	443	26	orthogonal	orthogonal	ADJ
american_scientific_journal-3270	443	27	condition	condition	NOUN
american_scientific_journal-3270	443	28	,	,	PUNCT
american_scientific_journal-3270	443	29	hence	hence	ADV
american_scientific_journal-3270	443	30	eq	eq	NOUN
american_scientific_journal-3270	443	31	.	.	PUNCT
american_scientific_journal-3270	444	1	(	(	PUNCT
american_scientific_journal-3270	444	2	1.7.21	1.7.21	NUM
american_scientific_journal-3270	444	3	)	)	PUNCT
american_scientific_journal-3270	444	4	yields	yield	NOUN
american_scientific_journal-3270	444	5	:	:	PUNCT
american_scientific_journal-3270	444	6	0	0	NUM
american_scientific_journal-3270	444	7	0	0	NUM
american_scientific_journal-3270	444	8	(	(	PUNCT
american_scientific_journal-3270	444	9	,	,	PUNCT
american_scientific_journal-3270	444	10	)	)	PUNCT
american_scientific_journal-3270	445	1	c	c	NOUN
american_scientific_journal-3270	445	2	pθ	pθ	ADP
american_scientific_journal-3270	445	3	α	α	PRON
american_scientific_journal-3270	445	4	β	β	PUNCT
american_scientific_journal-3270	445	5	=	=	PUNCT
american_scientific_journal-3270	445	6	.	.	PUNCT
american_scientific_journal-3270	446	1	(	(	PUNCT
american_scientific_journal-3270	446	2	5.13	5.13	NUM
american_scientific_journal-3270	446	3	)	)	PUNCT
american_scientific_journal-3270	446	4	where	where	SCONJ
american_scientific_journal-3270	446	5	1	1	NUM
american_scientific_journal-3270	446	6	(	(	PUNCT
american_scientific_journal-3270	446	7	,	,	PUNCT
american_scientific_journal-3270	446	8	)	)	PUNCT
american_scientific_journal-3270	446	9	1	1	NUM
american_scientific_journal-3270	446	10	0	0	NUM
american_scientific_journal-3270	446	11	1	1	NUM
american_scientific_journal-3270	446	12	(	(	PUNCT
american_scientific_journal-3270	446	13	1	1	NUM
american_scientific_journal-3270	446	14	)	)	PUNCT
american_scientific_journal-3270	446	15	(	(	PUNCT
american_scientific_journal-3270	446	16	1	1	NUM
american_scientific_journal-3270	446	17	)	)	PUNCT
american_scientific_journal-3270	446	18	(	(	PUNCT
american_scientific_journal-3270	446	19	)	)	PUNCT
american_scientific_journal-3270	446	20	2	2	NUM
american_scientific_journal-3270	446	21	(	(	PUNCT
american_scientific_journal-3270	446	22	2	2	NUM
american_scientific_journal-3270	446	23	)	)	PUNCT
american_scientific_journal-3270	446	24	w	w	PROPN
american_scientific_journal-3270	446	25	t	t	PROPN
american_scientific_journal-3270	446	26	dtα	dtα	NOUN
american_scientific_journal-3270	446	27	β	β	PROPN
american_scientific_journal-3270	446	28	α	α	X
american_scientific_journal-3270	446	29	β	β	X
american_scientific_journal-3270	446	30	α	α	NOUN
american_scientific_journal-3270	446	31	βθ	βθ	VERB
american_scientific_journal-3270	446	32	α	α	X
american_scientific_journal-3270	446	33	β	β	X
american_scientific_journal-3270	447	1	+	+	X
american_scientific_journal-3270	448	1	+	+	CCONJ
american_scientific_journal-3270	448	2	−	−	X
american_scientific_journal-3270	448	3	γ	γ	NOUN
american_scientific_journal-3270	448	4	+	+	NOUN
american_scientific_journal-3270	448	5	γ	γ	X
american_scientific_journal-3270	448	6	+	+	NOUN
american_scientific_journal-3270	448	7	=	=	SYM
american_scientific_journal-3270	448	8	=	=	SYM
american_scientific_journal-3270	448	9	γ	γ	X
american_scientific_journal-3270	448	10	+	+	X
american_scientific_journal-3270	448	11	+	+	NUM
american_scientific_journal-3270	448	12	∫	∫	PROPN
american_scientific_journal-3270	448	13	,	,	PUNCT
american_scientific_journal-3270	448	14	k	k	PROPN
american_scientific_journal-3270	448	15	=	=	PUNCT
american_scientific_journal-3270	448	16	0	0	PROPN
american_scientific_journal-3270	448	17	.	.	PUNCT
american_scientific_journal-3270	448	18	(	(	PUNCT
american_scientific_journal-3270	448	19	5.14	5.14	NUM
american_scientific_journal-3270	448	20	)	)	PUNCT
american_scientific_journal-3270	448	21	6	6	NUM
american_scientific_journal-3270	448	22	.	.	PUNCT
american_scientific_journal-3270	448	23	applications	application	NOUN
american_scientific_journal-3270	448	24	and	and	CCONJ
american_scientific_journal-3270	448	25	discussions	discussion	NOUN
american_scientific_journal-3270	448	26	here	here	ADV
american_scientific_journal-3270	448	27	,	,	PUNCT
american_scientific_journal-3270	448	28	we	we	PRON
american_scientific_journal-3270	448	29	employ	employ	VERB
american_scientific_journal-3270	448	30	the	the	DET
american_scientific_journal-3270	448	31	procedures	procedure	NOUN
american_scientific_journal-3270	448	32	of	of	ADP
american_scientific_journal-3270	448	33	the	the	DET
american_scientific_journal-3270	448	34	jacobi	jacobi	PROPN
american_scientific_journal-3270	448	35	polynomials	polynomial	VERB
american_scientific_journal-3270	448	36	methods	method	NOUN
american_scientific_journal-3270	448	37	to	to	PART
american_scientific_journal-3270	448	38	solve	solve	VERB
american_scientific_journal-3270	448	39	(	(	PUNCT
american_scientific_journal-3270	448	40	2.30	2.30	NUM
american_scientific_journal-3270	448	41	)	)	PUNCT
american_scientific_journal-3270	448	42	with	with	ADP
american_scientific_journal-3270	448	43	1µ	1µ	NUM
american_scientific_journal-3270	448	44	=	=	SYM
american_scientific_journal-3270	449	1	where	where	SCONJ
american_scientific_journal-3270	449	2	the	the	DET
american_scientific_journal-3270	449	3	exact	exact	ADJ
american_scientific_journal-3270	449	4	solution	solution	NOUN
american_scientific_journal-3270	449	5	2	2	NUM
american_scientific_journal-3270	449	6	2	2	NUM
american_scientific_journal-3270	449	7	(	(	PUNCT
american_scientific_journal-3270	449	8	,	,	PUNCT
american_scientific_journal-3270	449	9	)	)	PUNCT
american_scientific_journal-3270	449	10	x	x	SYM
american_scientific_journal-3270	449	11	t	t	NOUN
american_scientific_journal-3270	449	12	x	x	PUNCT
american_scientific_journal-3270	449	13	tφ	tφ	PROPN
american_scientific_journal-3270	449	14	=	=	PUNCT
american_scientific_journal-3270	449	15	,	,	PUNCT
american_scientific_journal-3270	449	16	at	at	ADP
american_scientific_journal-3270	449	17	times	time	NOUN
american_scientific_journal-3270	449	18	0.5	0.5	NUM
american_scientific_journal-3270	449	19	and	and	CCONJ
american_scientific_journal-3270	449	20	0.9	0.9	NUM
american_scientific_journal-3270	449	21	t	t	NOUN
american_scientific_journal-3270	449	22	=	=	PUNCT
american_scientific_journal-3270	449	23	.	.	PUNCT
american_scientific_journal-3270	450	1	in	in	ADP
american_scientific_journal-3270	450	2	addition	addition	NOUN
american_scientific_journal-3270	450	3	,	,	PUNCT
american_scientific_journal-3270	450	4	we	we	PRON
american_scientific_journal-3270	450	5	consider	consider	VERB
american_scientific_journal-3270	450	6	the	the	DET
american_scientific_journal-3270	450	7	continuous	continuous	ADJ
american_scientific_journal-3270	450	8	kernel	kernel	NOUN
american_scientific_journal-3270	450	9	of	of	ADP
american_scientific_journal-3270	450	10	fredholm	fredholm	ADJ
american_scientific_journal-3270	450	11	integral	integral	ADJ
american_scientific_journal-3270	450	12	term	term	NOUN
american_scientific_journal-3270	450	13	1	1	NUM
american_scientific_journal-3270	450	14	(	(	PUNCT
american_scientific_journal-3270	450	15	)	)	PUNCT
american_scientific_journal-3270	450	16	y	y	PROPN
american_scientific_journal-3270	450	17	x−	x−	PROPN
american_scientific_journal-3270	450	18	,	,	PUNCT
american_scientific_journal-3270	450	19	while	while	SCONJ
american_scientific_journal-3270	450	20	the	the	DET
american_scientific_journal-3270	450	21	given	give	VERB
american_scientific_journal-3270	450	22	function	function	NOUN
american_scientific_journal-3270	450	23	(	(	PUNCT
american_scientific_journal-3270	450	24	,	,	PUNCT
american_scientific_journal-3270	450	25	)	)	PUNCT
american_scientific_journal-3270	450	26	t	t	PROPN
american_scientific_journal-3270	450	27	tx	tx	PROPN
american_scientific_journal-3270	450	28	t	t	PROPN
american_scientific_journal-3270	450	29	t=	t=	NUM
american_scientific_journal-3270	450	30	,	,	PUNCT
american_scientific_journal-3270	450	31	with	with	ADP
american_scientific_journal-3270	450	32	2k	2k	NUM
american_scientific_journal-3270	450	33	=	=	SYM
american_scientific_journal-3270	450	34	(	(	PUNCT
american_scientific_journal-3270	450	35	k	k	X
american_scientific_journal-3270	450	36	is	be	AUX
american_scientific_journal-3270	450	37	the	the	DET
american_scientific_journal-3270	450	38	division	division	NOUN
american_scientific_journal-3270	450	39	of	of	ADP
american_scientific_journal-3270	450	40	the	the	DET
american_scientific_journal-3270	450	41	interval	interval	NOUN
american_scientific_journal-3270	450	42	of	of	ADP
american_scientific_journal-3270	450	43	american	american	ADJ
american_scientific_journal-3270	450	44	scientific	scientific	ADJ
american_scientific_journal-3270	450	45	research	research	NOUN
american_scientific_journal-3270	450	46	journal	journal	NOUN
american_scientific_journal-3270	450	47	for	for	ADP
american_scientific_journal-3270	450	48	engineering	engineering	NOUN
american_scientific_journal-3270	450	49	,	,	PUNCT
american_scientific_journal-3270	450	50	technology	technology	NOUN
american_scientific_journal-3270	450	51	,	,	PUNCT
american_scientific_journal-3270	450	52	and	and	CCONJ
american_scientific_journal-3270	450	53	sciences	science	NOUN
american_scientific_journal-3270	450	54	(	(	PUNCT
american_scientific_journal-3270	450	55	asrjets	asrjet	NOUN
american_scientific_journal-3270	450	56	)	)	PUNCT
american_scientific_journal-3270	450	57	(	(	PUNCT
american_scientific_journal-3270	450	58	2017	2017	NUM
american_scientific_journal-3270	450	59	)	)	PUNCT
american_scientific_journal-3270	450	60	volume	volume	NOUN
american_scientific_journal-3270	450	61	34	34	NUM
american_scientific_journal-3270	450	62	,	,	PUNCT
american_scientific_journal-3270	450	63	no	no	DET
american_scientific_journal-3270	450	64	1	1	NUM
american_scientific_journal-3270	450	65	,	,	PUNCT
american_scientific_journal-3270	450	66	pp	pp	ADV
american_scientific_journal-3270	450	67	213	213	NUM
american_scientific_journal-3270	450	68	-	-	SYM
american_scientific_journal-3270	450	69	230	230	NUM
american_scientific_journal-3270	450	70	226	226	NUM
american_scientific_journal-3270	450	71	time	time	NOUN
american_scientific_journal-3270	450	72	[	[	X
american_scientific_journal-3270	450	73	0	0	NUM
american_scientific_journal-3270	450	74	,	,	PUNCT
american_scientific_journal-3270	450	75	t	t	PROPN
american_scientific_journal-3270	450	76	]	]	PUNCT
american_scientific_journal-3270	450	77	.	.	PUNCT
american_scientific_journal-3270	451	1	in	in	ADP
american_scientific_journal-3270	451	2	this	this	DET
american_scientific_journal-3270	451	3	case	case	NOUN
american_scientific_journal-3270	451	4	,	,	PUNCT
american_scientific_journal-3270	451	5	the	the	DET
american_scientific_journal-3270	451	6	free	free	ADJ
american_scientific_journal-3270	451	7	function	function	NOUN
american_scientific_journal-3270	451	8	(	(	PUNCT
american_scientific_journal-3270	451	9	,	,	PUNCT
american_scientific_journal-3270	451	10	)	)	PUNCT
american_scientific_journal-3270	451	11	f	f	X
american_scientific_journal-3270	452	1	x	x	X
american_scientific_journal-3270	452	2	t	t	NOUN
american_scientific_journal-3270	452	3	can	can	AUX
american_scientific_journal-3270	452	4	be	be	AUX
american_scientific_journal-3270	452	5	computed	compute	VERB
american_scientific_journal-3270	452	6	from	from	ADP
american_scientific_journal-3270	452	7	eq	eq	PROPN
american_scientific_journal-3270	452	8	.	.	PUNCT
american_scientific_journal-3270	453	1	(	(	PUNCT
american_scientific_journal-3270	453	2	2.30	2.30	NUM
american_scientific_journal-3270	453	3	)	)	PUNCT
american_scientific_journal-3270	453	4	.	.	PUNCT
american_scientific_journal-3270	454	1	for	for	ADP
american_scientific_journal-3270	454	2	the	the	DET
american_scientific_journal-3270	454	3	polyurethane	polyurethane	NOUN
american_scientific_journal-3270	454	4	and	and	CCONJ
american_scientific_journal-3270	454	5	the	the	DET
american_scientific_journal-3270	454	6	fibber	fibber	NOUN
american_scientific_journal-3270	454	7	materials	material	NOUN
american_scientific_journal-3270	454	8	,	,	PUNCT
american_scientific_journal-3270	454	9	we	we	PRON
american_scientific_journal-3270	454	10	compute	compute	VERB
american_scientific_journal-3270	454	11	(	(	PUNCT
american_scientific_journal-3270	454	12	)	)	PUNCT
american_scientific_journal-3270	454	13	2	2	NUM
american_scientific_journal-3270	454	14	,	,	PUNCT
american_scientific_journal-3270	454	15	1	1	NUM
american_scientific_journal-3270	454	16	2	2	NUM
american_scientific_journal-3270	454	17	gυλ	gυλ	NOUN
american_scientific_journal-3270	454	18	υ	υ	NOUN
american_scientific_journal-3270	454	19	=	=	NOUN
american_scientific_journal-3270	454	20	−	−	PROPN
american_scientific_journal-3270	454	21	that	that	SCONJ
american_scientific_journal-3270	454	22	corresponding	correspond	VERB
american_scientific_journal-3270	454	23	to	to	ADP
american_scientific_journal-3270	454	24	the	the	DET
american_scientific_journal-3270	454	25	value	value	NOUN
american_scientific_journal-3270	454	26	of	of	ADP
american_scientific_journal-3270	454	27	poison	poison	NOUN
american_scientific_journal-3270	454	28	ratio	ratio	NOUN
american_scientific_journal-3270	454	29	0.22	0.22	NUM
american_scientific_journal-3270	454	30	,	,	PUNCT
american_scientific_journal-3270	454	31	0.389υ	0.389υ	PROPN
american_scientific_journal-3270	454	32	=	=	PUNCT
american_scientific_journal-3270	454	33	and	and	CCONJ
american_scientific_journal-3270	454	34	7	7	NUM
american_scientific_journal-3270	454	35	71	71	NUM
american_scientific_journal-3270	454	36	10	10	NUM
american_scientific_journal-3270	454	37	,	,	PUNCT
american_scientific_journal-3270	454	38	0.132	0.132	NUM
american_scientific_journal-3270	454	39	10	10	NUM
american_scientific_journal-3270	454	40	g	g	NOUN
american_scientific_journal-3270	454	41	=	=	SYM
american_scientific_journal-3270	454	42	×	×	PROPN
american_scientific_journal-3270	454	43	×	×	NOUN
american_scientific_journal-3270	454	44	,	,	PUNCT
american_scientific_journal-3270	454	45	respectively	respectively	ADV
american_scientific_journal-3270	454	46	.	.	PUNCT
american_scientific_journal-3270	455	1	in	in	ADP
american_scientific_journal-3270	455	2	our	our	PRON
american_scientific_journal-3270	455	3	applications	application	NOUN
american_scientific_journal-3270	455	4	,	,	PUNCT
american_scientific_journal-3270	455	5	we	we	PRON
american_scientific_journal-3270	455	6	let	let	VERB
american_scientific_journal-3270	455	7	n	n	NOUN
american_scientific_journal-3270	455	8	=	=	SYM
american_scientific_journal-3270	455	9	40	40	NUM
american_scientific_journal-3270	455	10	,	,	PUNCT
american_scientific_journal-3270	455	11	to	to	PART
american_scientific_journal-3270	455	12	get	get	VERB
american_scientific_journal-3270	455	13	the	the	DET
american_scientific_journal-3270	455	14	approximate	approximate	ADJ
american_scientific_journal-3270	455	15	solutions	solution	NOUN
american_scientific_journal-3270	455	16	,	,	PUNCT
american_scientific_journal-3270	455	17	pφ	pφ	INTJ
american_scientific_journal-3270	455	18	,	,	PUNCT
american_scientific_journal-3270	455	19	and	and	CCONJ
american_scientific_journal-3270	455	20	the	the	DET
american_scientific_journal-3270	455	21	corresponding	corresponding	ADJ
american_scientific_journal-3270	455	22	error	error	NOUN
american_scientific_journal-3270	455	23	,	,	PUNCT
american_scientific_journal-3270	455	24	pe	pe	INTJ
american_scientific_journal-3270	455	25	.	.	PUNCT
american_scientific_journal-3270	456	1	in	in	ADP
american_scientific_journal-3270	456	2	the	the	DET
american_scientific_journal-3270	456	3	first	first	ADJ
american_scientific_journal-3270	456	4	case	case	NOUN
american_scientific_journal-3270	456	5	,	,	PUNCT
american_scientific_journal-3270	456	6	let	let	VERB
american_scientific_journal-3270	456	7	k=0	k=0	NOUN
american_scientific_journal-3270	456	8	,	,	PUNCT
american_scientific_journal-3270	456	9	and	and	CCONJ
american_scientific_journal-3270	456	10	write	write	VERB
american_scientific_journal-3270	456	11	in	in	ADP
american_scientific_journal-3270	456	12	(	(	PUNCT
american_scientific_journal-3270	456	13	2.30	2.30	NUM
american_scientific_journal-3270	456	14	)	)	PUNCT
american_scientific_journal-3270	456	15	the	the	DET
american_scientific_journal-3270	456	16	unknown	unknown	ADJ
american_scientific_journal-3270	456	17	function	function	NOUN
american_scientific_journal-3270	456	18	(	(	PUNCT
american_scientific_journal-3270	456	19	)	)	PUNCT
american_scientific_journal-3270	456	20	xφ	xφ	PROPN
american_scientific_journal-3270	456	21	in	in	ADP
american_scientific_journal-3270	456	22	the	the	DET
american_scientific_journal-3270	456	23	jacobi	jacobi	PROPN
american_scientific_journal-3270	456	24	polynomials	polynomial	NOUN
american_scientific_journal-3270	456	25	form	form	VERB
american_scientific_journal-3270	456	26	1	1	NUM
american_scientific_journal-3270	456	27	1	1	NUM
american_scientific_journal-3270	456	28	(	(	PUNCT
american_scientific_journal-3270	456	29	,	,	PUNCT
american_scientific_journal-3270	456	30	)	)	PUNCT
american_scientific_journal-3270	456	31	2	2	NUM
american_scientific_journal-3270	456	32	2	2	NUM
american_scientific_journal-3270	456	33	0	0	NUM
american_scientific_journal-3270	456	34	(	(	PUNCT
american_scientific_journal-3270	456	35	)	)	PUNCT
american_scientific_journal-3270	456	36	(	(	PUNCT
american_scientific_journal-3270	456	37	)	)	PUNCT
american_scientific_journal-3270	456	38	(	(	PUNCT
american_scientific_journal-3270	456	39	)	)	PUNCT
american_scientific_journal-3270	456	40	,	,	PUNCT
american_scientific_journal-3270	456	41	n	n	CCONJ
american_scientific_journal-3270	456	42	n	n	CCONJ
american_scientific_journal-3270	456	43	n	n	CCONJ
american_scientific_journal-3270	456	44	n	n	NOUN
american_scientific_journal-3270	456	45	x	x	NOUN
american_scientific_journal-3270	457	1	c	c	NOUN
american_scientific_journal-3270	457	2	w	w	NOUN
american_scientific_journal-3270	457	3	x	x	X
american_scientific_journal-3270	457	4	p	p	X
american_scientific_journal-3270	457	5	xφ	xφ	NOUN
american_scientific_journal-3270	457	6	−	−	PROPN
american_scientific_journal-3270	458	1	=	=	PUNCT
american_scientific_journal-3270	458	2	=	=	NOUN
american_scientific_journal-3270	458	3	∑	∑	PROPN
american_scientific_journal-3270	458	4	1	1	NUM
american_scientific_journal-3270	458	5	1	1	NUM
american_scientific_journal-3270	458	6	2	2	NUM
american_scientific_journal-3270	458	7	2	2	NUM
american_scientific_journal-3270	458	8	(	(	PUNCT
american_scientific_journal-3270	458	9	)	)	PUNCT
american_scientific_journal-3270	458	10	(	(	PUNCT
american_scientific_journal-3270	458	11	1	1	X
american_scientific_journal-3270	458	12	)	)	PUNCT
american_scientific_journal-3270	458	13	(	(	PUNCT
american_scientific_journal-3270	458	14	1	1	NUM
american_scientific_journal-3270	458	15	)	)	PUNCT
american_scientific_journal-3270	458	16	,	,	PUNCT
american_scientific_journal-3270	458	17	w	w	NOUN
american_scientific_journal-3270	458	18	x	x	PUNCT
american_scientific_journal-3270	458	19	x	x	PUNCT
american_scientific_journal-3270	458	20	x	x	X
american_scientific_journal-3270	458	21	−	−	NOUN
american_scientific_journal-3270	458	22	=	=	SYM
american_scientific_journal-3270	459	1	−	−	PROPN
american_scientific_journal-3270	460	1	+	+	CCONJ
american_scientific_journal-3270	460	2	(	(	PUNCT
american_scientific_journal-3270	460	3	6.1	6.1	NUM
american_scientific_journal-3270	460	4	)	)	PUNCT
american_scientific_journal-3270	460	5	the	the	DET
american_scientific_journal-3270	460	6	unknown	unknown	ADJ
american_scientific_journal-3270	460	7	coefficients	coefficient	NOUN
american_scientific_journal-3270	460	8	1	1	NUM
american_scientific_journal-3270	460	9	,	,	PUNCT
american_scientific_journal-3270	460	10	...	...	PUNCT
american_scientific_journal-3270	460	11	,	,	PUNCT
american_scientific_journal-3270	460	12	nc	nc	PROPN
american_scientific_journal-3270	460	13	c	c	PROPN
american_scientific_journal-3270	460	14	can	can	AUX
american_scientific_journal-3270	460	15	be	be	AUX
american_scientific_journal-3270	460	16	obtained	obtain	VERB
american_scientific_journal-3270	460	17	from	from	ADP
american_scientific_journal-3270	460	18	eq	eq	PROPN
american_scientific_journal-3270	460	19	.	.	PUNCT
american_scientific_journal-3270	461	1	(	(	PUNCT
american_scientific_journal-3270	461	2	5.11	5.11	NUM
american_scientific_journal-3270	461	3	)	)	PUNCT
american_scientific_journal-3270	461	4	and	and	CCONJ
american_scientific_journal-3270	461	5	then	then	ADV
american_scientific_journal-3270	461	6	substituted	substitute	VERB
american_scientific_journal-3270	461	7	into	into	ADP
american_scientific_journal-3270	461	8	eq	eq	PROPN
american_scientific_journal-3270	461	9	.	.	PUNCT
american_scientific_journal-3270	462	1	(	(	PUNCT
american_scientific_journal-3270	462	2	6.1	6.1	NUM
american_scientific_journal-3270	462	3	)	)	PUNCT
american_scientific_journal-3270	462	4	to	to	PART
american_scientific_journal-3270	462	5	get	get	VERB
american_scientific_journal-3270	462	6	the	the	DET
american_scientific_journal-3270	462	7	approximate	approximate	ADJ
american_scientific_journal-3270	462	8	solution	solution	NOUN
american_scientific_journal-3270	462	9	.	.	PUNCT
american_scientific_journal-3270	463	1	secondly	secondly	ADV
american_scientific_journal-3270	463	2	,	,	PUNCT
american_scientific_journal-3270	463	3	if	if	SCONJ
american_scientific_journal-3270	463	4	we	we	PRON
american_scientific_journal-3270	463	5	take	take	VERB
american_scientific_journal-3270	463	6	k=1	k=1	PRON
american_scientific_journal-3270	463	7	,	,	PUNCT
american_scientific_journal-3270	463	8	then	then	ADV
american_scientific_journal-3270	463	9	the	the	DET
american_scientific_journal-3270	463	10	unknown	unknown	ADJ
american_scientific_journal-3270	463	11	function	function	NOUN
american_scientific_journal-3270	463	12	is	be	AUX
american_scientific_journal-3270	463	13	expressed	express	VERB
american_scientific_journal-3270	463	14	in	in	ADP
american_scientific_journal-3270	463	15	cheypshev	cheypshev	NOUN
american_scientific_journal-3270	463	16	polynomials	polynomial	NOUN
american_scientific_journal-3270	463	17	formula	formula	NOUN
american_scientific_journal-3270	463	18	of	of	ADP
american_scientific_journal-3270	463	19	the	the	DET
american_scientific_journal-3270	463	20	first	first	ADJ
american_scientific_journal-3270	463	21	kind	kind	NOUN
american_scientific_journal-3270	463	22	as	as	ADP
american_scientific_journal-3270	463	23	0	0	NUM
american_scientific_journal-3270	463	24	(	(	PUNCT
american_scientific_journal-3270	463	25	)	)	PUNCT
american_scientific_journal-3270	463	26	(	(	PUNCT
american_scientific_journal-3270	463	27	)	)	PUNCT
american_scientific_journal-3270	463	28	(	(	PUNCT
american_scientific_journal-3270	463	29	)	)	PUNCT
american_scientific_journal-3270	463	30	,	,	PUNCT
american_scientific_journal-3270	463	31	n	n	PROPN
american_scientific_journal-3270	463	32	n	n	CCONJ
american_scientific_journal-3270	463	33	nx	nx	PROPN
american_scientific_journal-3270	463	34	c	c	PROPN
american_scientific_journal-3270	463	35	w	w	PROPN
american_scientific_journal-3270	463	36	x	x	X
american_scientific_journal-3270	463	37	t	t	NOUN
american_scientific_journal-3270	463	38	xφ	xφ	PUNCT
american_scientific_journal-3270	464	1	=	=	NOUN
american_scientific_journal-3270	464	2	∑	∑	PROPN
american_scientific_journal-3270	464	3	1	1	NUM
american_scientific_journal-3270	464	4	2	2	NUM
american_scientific_journal-3270	464	5	2	2	NUM
american_scientific_journal-3270	464	6	2	2	NUM
american_scientific_journal-3270	464	7	1	1	NUM
american_scientific_journal-3270	464	8	(	(	PUNCT
american_scientific_journal-3270	464	9	)	)	PUNCT
american_scientific_journal-3270	464	10	(	(	PUNCT
american_scientific_journal-3270	464	11	1	1	X
american_scientific_journal-3270	464	12	)	)	PUNCT
american_scientific_journal-3270	464	13	1	1	NUM
american_scientific_journal-3270	464	14	w	w	NOUN
american_scientific_journal-3270	464	15	x	x	PUNCT
american_scientific_journal-3270	464	16	x	x	PUNCT
american_scientific_journal-3270	464	17	x	x	X
american_scientific_journal-3270	464	18	−	−	NOUN
american_scientific_journal-3270	464	19	=	=	SYM
american_scientific_journal-3270	464	20	−	−	PROPN
american_scientific_journal-3270	464	21	=	=	SYM
american_scientific_journal-3270	464	22	−	−	PROPN
american_scientific_journal-3270	464	23	.	.	PUNCT
american_scientific_journal-3270	465	1	(	(	PUNCT
american_scientific_journal-3270	465	2	6.2	6.2	NUM
american_scientific_journal-3270	465	3	)	)	PUNCT
american_scientific_journal-3270	465	4	the	the	DET
american_scientific_journal-3270	465	5	system	system	NOUN
american_scientific_journal-3270	465	6	of	of	ADP
american_scientific_journal-3270	465	7	ies	ie	NOUN
american_scientific_journal-3270	465	8	(	(	PUNCT
american_scientific_journal-3270	465	9	5.11	5.11	NUM
american_scientific_journal-3270	465	10	)	)	PUNCT
american_scientific_journal-3270	465	11	may	may	AUX
american_scientific_journal-3270	465	12	be	be	AUX
american_scientific_journal-3270	465	13	solved	solve	VERB
american_scientific_journal-3270	465	14	,	,	PUNCT
american_scientific_journal-3270	465	15	after	after	ADP
american_scientific_journal-3270	465	16	determining	determine	VERB
american_scientific_journal-3270	465	17	the	the	DET
american_scientific_journal-3270	465	18	unknown	unknown	ADJ
american_scientific_journal-3270	465	19	coefficients	coefficient	NOUN
american_scientific_journal-3270	465	20	1	1	NUM
american_scientific_journal-3270	465	21	1	1	NUM
american_scientific_journal-3270	465	22	,	,	PUNCT
american_scientific_journal-3270	465	23	...	...	PUNCT
american_scientific_journal-3270	465	24	,	,	PUNCT
american_scientific_journal-3270	465	25	nc	nc	PROPN
american_scientific_journal-3270	465	26	c	c	NOUN
american_scientific_journal-3270	465	27	−	−	PROPN
american_scientific_journal-3270	465	28	.	.	PUNCT
american_scientific_journal-3270	466	1	in	in	ADP
american_scientific_journal-3270	466	2	addition	addition	NOUN
american_scientific_journal-3270	466	3	,	,	PUNCT
american_scientific_journal-3270	466	4	the	the	DET
american_scientific_journal-3270	466	5	physics	physics	NOUN
american_scientific_journal-3270	466	6	of	of	ADP
american_scientific_journal-3270	466	7	the	the	DET
american_scientific_journal-3270	466	8	problem	problem	NOUN
american_scientific_journal-3270	466	9	requires	require	VERB
american_scientific_journal-3270	466	10	that	that	SCONJ
american_scientific_journal-3270	466	11	the	the	DET
american_scientific_journal-3270	466	12	solution	solution	NOUN
american_scientific_journal-3270	466	13	satisfy	satisfy	VERB
american_scientific_journal-3270	466	14	the	the	DET
american_scientific_journal-3270	466	15	compatibility	compatibility	NOUN
american_scientific_journal-3270	466	16	conditions	condition	NOUN
american_scientific_journal-3270	466	17	,	,	PUNCT
american_scientific_journal-3270	466	18	which	which	PRON
american_scientific_journal-3270	466	19	used	use	VERB
american_scientific_journal-3270	466	20	to	to	PART
american_scientific_journal-3270	466	21	determine	determine	VERB
american_scientific_journal-3270	466	22	the	the	DET
american_scientific_journal-3270	466	23	n	n	CCONJ
american_scientific_journal-3270	466	24	arbitrary	arbitrary	ADJ
american_scientific_journal-3270	466	25	constants	constant	NOUN
american_scientific_journal-3270	466	26	in	in	ADP
american_scientific_journal-3270	466	27	the	the	DET
american_scientific_journal-3270	466	28	solution	solution	NOUN
american_scientific_journal-3270	466	29	.	.	PUNCT
american_scientific_journal-3270	467	1	in	in	ADP
american_scientific_journal-3270	467	2	the	the	DET
american_scientific_journal-3270	467	3	later	later	ADJ
american_scientific_journal-3270	467	4	case	case	NOUN
american_scientific_journal-3270	467	5	,	,	PUNCT
american_scientific_journal-3270	467	6	we	we	PRON
american_scientific_journal-3270	467	7	assume	assume	VERB
american_scientific_journal-3270	467	8	k	k	X
american_scientific_journal-3270	467	9	=	=	SYM
american_scientific_journal-3270	468	1	-1	-1	PROPN
american_scientific_journal-3270	468	2	,	,	PUNCT
american_scientific_journal-3270	468	3	then	then	ADV
american_scientific_journal-3270	468	4	the	the	DET
american_scientific_journal-3270	468	5	unknown	unknown	ADJ
american_scientific_journal-3270	468	6	function	function	NOUN
american_scientific_journal-3270	468	7	(	(	PUNCT
american_scientific_journal-3270	468	8	)	)	PUNCT
american_scientific_journal-3270	468	9	xφ	xφ	PROPN
american_scientific_journal-3270	468	10	is	be	AUX
american_scientific_journal-3270	468	11	expressed	express	VERB
american_scientific_journal-3270	468	12	as	as	ADP
american_scientific_journal-3270	468	13	0	0	NUM
american_scientific_journal-3270	468	14	(	(	PUNCT
american_scientific_journal-3270	468	15	)	)	PUNCT
american_scientific_journal-3270	468	16	(	(	PUNCT
american_scientific_journal-3270	468	17	)	)	PUNCT
american_scientific_journal-3270	468	18	(	(	PUNCT
american_scientific_journal-3270	468	19	)	)	PUNCT
american_scientific_journal-3270	468	20	,	,	PUNCT
american_scientific_journal-3270	468	21	n	n	PROPN
american_scientific_journal-3270	468	22	n	n	CCONJ
american_scientific_journal-3270	468	23	nx	nx	PROPN
american_scientific_journal-3270	468	24	c	c	PROPN
american_scientific_journal-3270	468	25	w	w	PROPN
american_scientific_journal-3270	468	26	x	x	PUNCT
american_scientific_journal-3270	468	27	u	u	NOUN
american_scientific_journal-3270	468	28	xφ	xφ	PROPN
american_scientific_journal-3270	469	1	=	=	NOUN
american_scientific_journal-3270	469	2	∑	∑	PROPN
american_scientific_journal-3270	469	3	1	1	NUM
american_scientific_journal-3270	469	4	2	2	NUM
american_scientific_journal-3270	469	5	2	2	NUM
american_scientific_journal-3270	469	6	(	(	PUNCT
american_scientific_journal-3270	469	7	)	)	PUNCT
american_scientific_journal-3270	469	8	(	(	PUNCT
american_scientific_journal-3270	469	9	1	1	X
american_scientific_journal-3270	469	10	)	)	PUNCT
american_scientific_journal-3270	469	11	w	w	NOUN
american_scientific_journal-3270	469	12	x	x	PROPN
american_scientific_journal-3270	469	13	x=	x=	PROPN
american_scientific_journal-3270	469	14	−	−	PROPN
american_scientific_journal-3270	469	15	.	.	PUNCT
american_scientific_journal-3270	470	1	(	(	PUNCT
american_scientific_journal-3270	470	2	6.3	6.3	NUM
american_scientific_journal-3270	470	3	)	)	PUNCT
american_scientific_journal-3270	470	4	in	in	ADP
american_scientific_journal-3270	470	5	the	the	DET
american_scientific_journal-3270	470	6	following	follow	VERB
american_scientific_journal-3270	470	7	tables	table	NOUN
american_scientific_journal-3270	470	8	(	(	PUNCT
american_scientific_journal-3270	470	9	1	1	NUM
american_scientific_journal-3270	470	10	-	-	SYM
american_scientific_journal-3270	470	11	1	1	NUM
american_scientific_journal-3270	470	12	)	)	PUNCT
american_scientific_journal-3270	470	13	-(1	-(1	PROPN
american_scientific_journal-3270	470	14	-	-	PUNCT
american_scientific_journal-3270	470	15	3	3	NUM
american_scientific_journal-3270	470	16	)	)	PUNCT
american_scientific_journal-3270	470	17	,	,	PUNCT
american_scientific_journal-3270	470	18	the	the	DET
american_scientific_journal-3270	470	19	results	result	NOUN
american_scientific_journal-3270	470	20	of	of	ADP
american_scientific_journal-3270	470	21	the	the	DET
american_scientific_journal-3270	470	22	approximate	approximate	ADJ
american_scientific_journal-3270	470	23	solutions	solution	NOUN
american_scientific_journal-3270	470	24	pφ	pφ	ADP
american_scientific_journal-3270	470	25	,	,	PUNCT
american_scientific_journal-3270	470	26	cφ	cφ	PROPN
american_scientific_journal-3270	470	27	and	and	CCONJ
american_scientific_journal-3270	470	28	uφ	uφ	X
american_scientific_journal-3270	470	29	and	and	CCONJ
american_scientific_journal-3270	470	30	the	the	DET
american_scientific_journal-3270	470	31	errors	error	NOUN
american_scientific_journal-3270	470	32	pe	pe	INTJ
american_scientific_journal-3270	470	33	,	,	PUNCT
american_scientific_journal-3270	470	34	ce	ce	PROPN
american_scientific_journal-3270	470	35	and	and	CCONJ
american_scientific_journal-3270	470	36	ue	ue	PROPN
american_scientific_journal-3270	470	37	,	,	PUNCT
american_scientific_journal-3270	470	38	respectively	respectively	ADV
american_scientific_journal-3270	470	39	,	,	PUNCT
american_scientific_journal-3270	470	40	are	be	AUX
american_scientific_journal-3270	470	41	obtained	obtain	VERB
american_scientific_journal-3270	470	42	for	for	ADP
american_scientific_journal-3270	470	43	different	different	ADJ
american_scientific_journal-3270	470	44	cases	case	NOUN
american_scientific_journal-3270	470	45	of	of	ADP
american_scientific_journal-3270	470	46	time	time	NOUN
american_scientific_journal-3270	470	47	0.5	0.5	NUM
american_scientific_journal-3270	470	48	and	and	CCONJ
american_scientific_journal-3270	470	49	0.9	0.9	NUM
american_scientific_journal-3270	470	50	t	t	NOUN
american_scientific_journal-3270	470	51	=	=	PUNCT
american_scientific_journal-3270	470	52	.	.	PUNCT
american_scientific_journal-3270	471	1	in	in	ADP
american_scientific_journal-3270	471	2	this	this	DET
american_scientific_journal-3270	471	3	part	part	NOUN
american_scientific_journal-3270	471	4	,	,	PUNCT
american_scientific_journal-3270	471	5	we	we	PRON
american_scientific_journal-3270	471	6	note	note	VERB
american_scientific_journal-3270	471	7	the	the	DET
american_scientific_journal-3270	471	8	following	follow	VERB
american_scientific_journal-3270	471	9	results	result	NOUN
american_scientific_journal-3270	471	10	:	:	PUNCT
american_scientific_journal-3270	472	1	1	1	X
american_scientific_journal-3270	472	2	.	.	X
american_scientific_journal-3270	472	3	for	for	ADP
american_scientific_journal-3270	472	4	0.5	0.5	NUM
american_scientific_journal-3270	472	5	and	and	CCONJ
american_scientific_journal-3270	472	6	0.9	0.9	NUM
american_scientific_journal-3270	472	7	t	t	NOUN
american_scientific_journal-3270	472	8	=	=	PRON
american_scientific_journal-3270	472	9	,	,	PUNCT
american_scientific_journal-3270	472	10	the	the	DET
american_scientific_journal-3270	472	11	values	value	NOUN
american_scientific_journal-3270	472	12	of	of	ADP
american_scientific_journal-3270	472	13	the	the	DET
american_scientific_journal-3270	472	14	approximate	approximate	ADJ
american_scientific_journal-3270	472	15	solutions	solution	NOUN
american_scientific_journal-3270	472	16	pφ	pφ	ADP
american_scientific_journal-3270	472	17	,	,	PUNCT
american_scientific_journal-3270	472	18	cφ	cφ	PROPN
american_scientific_journal-3270	472	19	and	and	CCONJ
american_scientific_journal-3270	472	20	uφ	uφ	X
american_scientific_journal-3270	472	21	equal	equal	ADJ
american_scientific_journal-3270	472	22	to	to	ADP
american_scientific_journal-3270	472	23	zero	zero	NUM
american_scientific_journal-3270	472	24	at	at	ADP
american_scientific_journal-3270	472	25	1x	1x	NUM
american_scientific_journal-3270	472	26	=	=	SYM
american_scientific_journal-3270	472	27	±	±	NOUN
american_scientific_journal-3270	472	28	,	,	PUNCT
american_scientific_journal-3270	472	29	or	or	CCONJ
american_scientific_journal-3270	472	30	at	at	ADP
american_scientific_journal-3270	472	31	1x	1x	NUM
american_scientific_journal-3270	472	32	=	=	SYM
american_scientific_journal-3270	472	33	±	±	NOUN
american_scientific_journal-3270	472	34	,	,	PUNCT
american_scientific_journal-3270	472	35	the	the	DET
american_scientific_journal-3270	472	36	values	value	NOUN
american_scientific_journal-3270	472	37	of	of	ADP
american_scientific_journal-3270	472	38	the	the	DET
american_scientific_journal-3270	472	39	errors	error	NOUN
american_scientific_journal-3270	472	40	pe	pe	INTJ
american_scientific_journal-3270	472	41	,	,	PUNCT
american_scientific_journal-3270	472	42	ce	ce	PROPN
american_scientific_journal-3270	472	43	and	and	CCONJ
american_scientific_journal-3270	472	44	ue	ue	PROPN
american_scientific_journal-3270	472	45	are	be	AUX
american_scientific_journal-3270	472	46	equal	equal	ADJ
american_scientific_journal-3270	472	47	the	the	DET
american_scientific_journal-3270	472	48	exact	exact	ADJ
american_scientific_journal-3270	472	49	solutions	solution	NOUN
american_scientific_journal-3270	472	50	.	.	PUNCT
american_scientific_journal-3270	473	1	2	2	X
american_scientific_journal-3270	473	2	.	.	X
american_scientific_journal-3270	473	3	the	the	DET
american_scientific_journal-3270	473	4	values	value	NOUN
american_scientific_journal-3270	473	5	of	of	ADP
american_scientific_journal-3270	473	6	ce	ce	PROPN
american_scientific_journal-3270	473	7	are	be	AUX
american_scientific_journal-3270	473	8	less	less	ADJ
american_scientific_journal-3270	473	9	than	than	ADP
american_scientific_journal-3270	473	10	the	the	DET
american_scientific_journal-3270	473	11	other	other	ADJ
american_scientific_journal-3270	473	12	errors	error	NOUN
american_scientific_journal-3270	473	13	pe	pe	INTJ
american_scientific_journal-3270	473	14	and	and	CCONJ
american_scientific_journal-3270	473	15	ue	ue	INTJ
american_scientific_journal-3270	473	16	,	,	PUNCT
american_scientific_journal-3270	473	17	where	where	SCONJ
american_scientific_journal-3270	473	18	we	we	PRON
american_scientific_journal-3270	473	19	have	have	VERB
american_scientific_journal-3270	473	20	.	.	PUNCT
american_scientific_journal-3270	474	1	case	case	NOUN
american_scientific_journal-3270	474	2	1	1	NUM
american_scientific_journal-3270	474	3	:	:	PUNCT
american_scientific_journal-3270	474	4	we	we	PRON
american_scientific_journal-3270	474	5	apply	apply	VERB
american_scientific_journal-3270	474	6	the	the	DET
american_scientific_journal-3270	474	7	jacobi	jacobi	PROPN
american_scientific_journal-3270	474	8	polynomials	polynomial	NOUN
american_scientific_journal-3270	474	9	method	method	VERB
american_scientific_journal-3270	474	10	to	to	PART
american_scientific_journal-3270	474	11	solve	solve	VERB
american_scientific_journal-3270	474	12	eq.(5.6	eq.(5.6	NOUN
american_scientific_journal-3270	474	13	)	)	PUNCT
american_scientific_journal-3270	474	14	c	c	PROPN
american_scientific_journal-3270	475	1	p	p	NOUN
american_scientific_journal-3270	475	2	ue	ue	PROPN
american_scientific_journal-3270	475	3	e	e	X
american_scientific_journal-3270	475	4	e	e	NOUN
american_scientific_journal-3270	475	5	<	<	X
american_scientific_journal-3270	475	6	<	<	X
american_scientific_journal-3270	475	7	american	american	PROPN
american_scientific_journal-3270	475	8	scientific	scientific	ADJ
american_scientific_journal-3270	475	9	research	research	PROPN
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american_scientific_journal-3270	475	11	for	for	ADP
american_scientific_journal-3270	475	12	engineering	engineering	NOUN
american_scientific_journal-3270	475	13	,	,	PUNCT
american_scientific_journal-3270	475	14	technology	technology	NOUN
american_scientific_journal-3270	475	15	,	,	PUNCT
american_scientific_journal-3270	475	16	and	and	CCONJ
american_scientific_journal-3270	475	17	sciences	science	NOUN
american_scientific_journal-3270	475	18	(	(	PUNCT
american_scientific_journal-3270	475	19	asrjets	asrjet	NOUN
american_scientific_journal-3270	475	20	)	)	PUNCT
american_scientific_journal-3270	475	21	(	(	PUNCT
american_scientific_journal-3270	475	22	2017	2017	NUM
american_scientific_journal-3270	475	23	)	)	PUNCT
american_scientific_journal-3270	475	24	volume	volume	NOUN
american_scientific_journal-3270	475	25	34	34	NUM
american_scientific_journal-3270	475	26	,	,	PUNCT
american_scientific_journal-3270	475	27	no	no	DET
american_scientific_journal-3270	475	28	1	1	NUM
american_scientific_journal-3270	475	29	,	,	PUNCT
american_scientific_journal-3270	475	30	pp	pp	ADV
american_scientific_journal-3270	475	31	213	213	NUM
american_scientific_journal-3270	475	32	-	-	SYM
american_scientific_journal-3270	475	33	230	230	NUM
american_scientific_journal-3270	475	34	227	227	NUM
american_scientific_journal-3270	475	35	table	table	NOUN
american_scientific_journal-3270	475	36	1	1	NUM
american_scientific_journal-3270	475	37	-	-	SYM
american_scientific_journal-3270	475	38	1	1	NUM
american_scientific_journal-3270	475	39	t	t	NOUN
american_scientific_journal-3270	475	40	x	x	PUNCT
american_scientific_journal-3270	475	41	exact	exact	ADJ
american_scientific_journal-3270	475	42	jacobi	jacobi	PROPN
american_scientific_journal-3270	475	43	polynomials	polynomial	NOUN
american_scientific_journal-3270	475	44	method	method	VERB
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american_scientific_journal-3270	475	47	polyurethane	polyurethane	NOUN
american_scientific_journal-3270	475	48	v=0.389	v=0.389	NOUN
american_scientific_journal-3270	475	49	appr	appr	PROPN
american_scientific_journal-3270	475	50	.	.	PROPN
american_scientific_journal-3270	475	51	error	error	PROPN
american_scientific_journal-3270	475	52	appr	appr	PROPN
american_scientific_journal-3270	475	53	.	.	PUNCT
american_scientific_journal-3270	475	54	error	error	NOUN
american_scientific_journal-3270	475	55	0.5	0.5	NUM
american_scientific_journal-3270	475	56	-1.00e+00	-1.00e+00	NOUN
american_scientific_journal-3270	475	57	2.500e-01	2.500e-01	NUM
american_scientific_journal-3270	475	58	0.000e+00	0.000e+00	NUM
american_scientific_journal-3270	475	59	2.500e-01	2.500e-01	NUM
american_scientific_journal-3270	475	60	0.00e+00	0.00e+00	NOUN
american_scientific_journal-3270	475	61	2.500e-01	2.500e-01	NUM
american_scientific_journal-3270	475	62	-4.00e-01	-4.00e-01	ADP
american_scientific_journal-3270	475	63	4.000e-02	4.000e-02	NUM
american_scientific_journal-3270	475	64	0	0	NUM
american_scientific_journal-3270	475	65	.	.	PUNCT
american_scientific_journal-3270	476	1	409e-02	409e-02	NOUN
american_scientific_journal-3270	476	2	0.254e-04	0.254e-04	NUM
american_scientific_journal-3270	476	3	2.60101e-02	2.60101e-02	NUM
american_scientific_journal-3270	476	4	0.399e-04	0.399e-04	NUM
american_scientific_journal-3270	476	5	-2.00e-01	-2.00e-01	NOUN
american_scientific_journal-3270	476	6	1.000e-02	1.000e-02	NUM
american_scientific_journal-3270	476	7	0.990e-02	0.990e-02	NUM
american_scientific_journal-3270	476	8	0.858e-05	0.858e-05	NUM
american_scientific_journal-3270	476	9	0.983e-02	0.983e-02	NOUN
american_scientific_journal-3270	476	10	0	0	NUM
american_scientific_journal-3270	476	11	.	.	PUNCT
american_scientific_journal-3270	477	1	817e-05	817e-05	PROPN
american_scientific_journal-3270	477	2	2.00e-01	2.00e-01	NUM
american_scientific_journal-3270	477	3	1.000e-02	1.000e-02	NUM
american_scientific_journal-3270	477	4	0.10047e-02	0.10047e-02	NUM
american_scientific_journal-3270	477	5	0	0	NUM
american_scientific_journal-3270	477	6	.	.	X
american_scientific_journal-3270	478	1	053e-05	053e-05	NUM
american_scientific_journal-3270	478	2	0.2490e-02	0.2490e-02	NUM
american_scientific_journal-3270	479	1	0.0	0.0	NUM
american_scientific_journal-3270	479	2	10e-05	10e-05	NUM
american_scientific_journal-3270	479	3	4.00e-01	4.00e-01	NUM
american_scientific_journal-3270	479	4	4.000e-02	4.000e-02	NUM
american_scientific_journal-3270	479	5	0	0	NUM
american_scientific_journal-3270	479	6	.	.	PUNCT
american_scientific_journal-3270	479	7	428e-02	428e-02	NOUN
american_scientific_journal-3270	479	8	0.057e-05	0.057e-05	NUM
american_scientific_journal-3270	479	9	0.853e-02	0.853e-02	NUM
american_scientific_journal-3270	479	10	0	0	NUM
american_scientific_journal-3270	479	11	.	.	PUNCT
american_scientific_journal-3270	480	1	011e-05	011e-05	PROPN
american_scientific_journal-3270	480	2	1.00e+00	1.00e+00	NUM
american_scientific_journal-3270	480	3	2.500e-01	2.500e-01	NUM
american_scientific_journal-3270	480	4	0.000e+00	0.000e+00	NUM
american_scientific_journal-3270	480	5	2.500e-01	2.500e-01	NUM
american_scientific_journal-3270	480	6	0.000e+00	0.000e+00	NUM
american_scientific_journal-3270	480	7	2.500e-01	2.500e-01	NUM
american_scientific_journal-3270	480	8	0.9	0.9	NUM
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american_scientific_journal-3270	480	10	0.990e-01	0.990e-01	NUM
american_scientific_journal-3270	480	11	0.000e+00	0.000e+00	NUM
american_scientific_journal-3270	480	12	0.990e-01	0.990e-01	NUM
american_scientific_journal-3270	480	13	0.000e+00	0.000e+00	NOUN
american_scientific_journal-3270	480	14	0.990e-01	0.990e-01	NUM
american_scientific_journal-3270	481	1	-6.00e-01	-6.00e-01	X
american_scientific_journal-3270	481	2	2.916e-01	2.916e-01	NUM
american_scientific_journal-3270	481	3	2.916e-01	2.916e-01	NUM
american_scientific_journal-3270	481	4	1.300e-05	1.300e-05	NUM
american_scientific_journal-3270	481	5	2.919e-01	2.919e-01	NUM
american_scientific_journal-3270	481	6	1	1	NUM
american_scientific_journal-3270	481	7	.	.	PUNCT
american_scientific_journal-3270	482	1	275e-05	275e-05	NOUN
american_scientific_journal-3270	482	2	-2.00e-01	-2.00e-01	NOUN
american_scientific_journal-3270	482	3	3.240e-02	3.240e-02	NUM
american_scientific_journal-3270	482	4	3.240e-02	3.240e-02	NUM
american_scientific_journal-3270	482	5	0.5	0.5	NUM
american_scientific_journal-3270	482	6	83e-05	83e-05	NUM
american_scientific_journal-3270	482	7	3.240e-02	3.240e-02	NUM
american_scientific_journal-3270	482	8	0.494e-05	0.494e-05	NUM
american_scientific_journal-3270	483	1	2.00e-01	2.00e-01	NUM
american_scientific_journal-3270	483	2	3.240e-02	3.240e-02	NUM
american_scientific_journal-3270	483	3	3	3	NUM
american_scientific_journal-3270	483	4	.	.	PUNCT
american_scientific_journal-3270	484	1	241e-02	241e-02	NUM
american_scientific_journal-3270	484	2	0.5	0.5	NUM
american_scientific_journal-3270	484	3	04e-05	04e-05	NOUN
american_scientific_journal-3270	484	4	3	3	NUM
american_scientific_journal-3270	484	5	.	.	PUNCT
american_scientific_journal-3270	484	6	241e-03	241e-03	NUM
american_scientific_journal-3270	484	7	0.5	0.5	NUM
american_scientific_journal-3270	484	8	04e-05	04e-05	NOUN
american_scientific_journal-3270	484	9	6.00e-01	6.00e-01	NUM
american_scientific_journal-3270	484	10	2.916e-01	2.916e-01	NUM
american_scientific_journal-3270	484	11	2.917e-02	2.917e-02	NUM
american_scientific_journal-3270	484	12	0.269e-04	0.269e-04	NUM
american_scientific_journal-3270	484	13	2	2	NUM
american_scientific_journal-3270	484	14	.	.	PUNCT
american_scientific_journal-3270	485	1	911e-02	911e-02	NOUN
american_scientific_journal-3270	485	2	0.310e-04	0.310e-04	NUM
american_scientific_journal-3270	486	1	1.00e+00	1.00e+00	NUM
american_scientific_journal-3270	486	2	0.990e-01	0.990e-01	NUM
american_scientific_journal-3270	486	3	0.000e+00	0.000e+00	NUM
american_scientific_journal-3270	486	4	0.990e-01	0.990e-01	NUM
american_scientific_journal-3270	486	5	0.000e+00	0.000e+00	NUM
american_scientific_journal-3270	486	6	0.990e-01	0.990e-01	NUM
american_scientific_journal-3270	486	7	table	table	NOUN
american_scientific_journal-3270	486	8	(	(	PUNCT
american_scientific_journal-3270	486	9	1	1	NUM
american_scientific_journal-3270	486	10	-	-	SYM
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american_scientific_journal-3270	486	13	show	show	VERB
american_scientific_journal-3270	486	14	the	the	DET
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american_scientific_journal-3270	486	18	pe	pe	INTJ
american_scientific_journal-3270	486	19	of	of	ADP
american_scientific_journal-3270	486	20	fibber	fibber	PROPN
american_scientific_journal-3270	486	21	and	and	CCONJ
american_scientific_journal-3270	486	22	polyurethane	polyurethane	NOUN
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american_scientific_journal-3270	487	3	-	-	SYM
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american_scientific_journal-3270	501	10	8.100e-01	8.100e-01	NUM
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american_scientific_journal-3270	502	2	-04	-04	PUNCT
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american_scientific_journal-3270	503	2	2.916e-01	2.916e-01	NUM
american_scientific_journal-3270	503	3	3.244e-01	3.244e-01	NUM
american_scientific_journal-3270	503	4	0.248e-04	0.248e-04	NUM
american_scientific_journal-3270	503	5	3.243e-01	3.243e-01	NUM
american_scientific_journal-3270	503	6	0.102e-04	0.102e-04	NUM
american_scientific_journal-3270	504	1	1.000e+00	1.000e+00	NUM
american_scientific_journal-3270	504	2	8.100e-01	8.100e-01	NUM
american_scientific_journal-3270	504	3	0.000e+00	0.000e+00	NUM
american_scientific_journal-3270	504	4	8.100e-01	8.100e-01	NUM
american_scientific_journal-3270	504	5	0.000e+00	0.000e+00	NUM
american_scientific_journal-3270	504	6	8.100e-01	8.100e-01	NUM
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american_scientific_journal-3270	504	8	scientific	scientific	ADJ
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american_scientific_journal-3270	504	15	,	,	PUNCT
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american_scientific_journal-3270	504	22	2017	2017	NUM
american_scientific_journal-3270	504	23	)	)	PUNCT
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american_scientific_journal-3270	504	26	,	,	PUNCT
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american_scientific_journal-3270	504	28	1	1	NUM
american_scientific_journal-3270	504	29	,	,	PUNCT
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american_scientific_journal-3270	504	31	213	213	NUM
american_scientific_journal-3270	504	32	-	-	SYM
american_scientific_journal-3270	504	33	230	230	NUM
american_scientific_journal-3270	504	34	228	228	NUM
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american_scientific_journal-3270	504	41	show	show	VERB
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american_scientific_journal-3270	504	52	at	at	ADP
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american_scientific_journal-3270	505	10	.	.	PUNCT
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american_scientific_journal-3270	506	4	2.500e-01	2.500e-01	NUM
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american_scientific_journal-3270	506	6	2.500e-01	2.500e-01	NUM
american_scientific_journal-3270	506	7	0.000e+00	0.000e+00	NUM
american_scientific_journal-3270	506	8	2.500e-01	2.500e-01	NUM
american_scientific_journal-3270	506	9	-6.000e-01	-6.000e-01	NUM
american_scientific_journal-3270	506	10	9.000e-02	9.000e-02	NUM
american_scientific_journal-3270	506	11	0.600e-02	0.600e-02	NUM
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american_scientific_journal-3270	506	14	0.873e-04	0.873e-04	NUM
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american_scientific_journal-3270	506	25	0.996e-02	0.996e-02	NUM
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american_scientific_journal-3270	506	77	8.100e-01	8.100e-01	NUM
american_scientific_journal-3270	506	78	0.000e+00	0.000e+00	NUM
american_scientific_journal-3270	506	79	8.100e-01	8.100e-01	NUM
american_scientific_journal-3270	506	80	0.000e+00	0.000e+00	NUM
american_scientific_journal-3270	506	81	8.100e-01	8.100e-01	NUM
american_scientific_journal-3270	506	82	references	reference	NOUN
american_scientific_journal-3270	506	83	[	[	X
american_scientific_journal-3270	506	84	1	1	NUM
american_scientific_journal-3270	506	85	]	]	X
american_scientific_journal-3270	506	86	e.e	e.e	X
american_scientific_journal-3270	506	87	.	.	PUNCT
american_scientific_journal-3270	506	88	gdoutos”fracture	gdoutos”fracture	NOUN
american_scientific_journal-3270	506	89	mechanics	mechanic	NOUN
american_scientific_journal-3270	506	90	”	"	PUNCT
american_scientific_journal-3270	506	91	,	,	PUNCT
american_scientific_journal-3270	506	92	second	second	ADJ
american_scientific_journal-3270	506	93	edition	edition	NOUN
american_scientific_journal-3270	506	94	,	,	PUNCT
american_scientific_journal-3270	506	95	springer	springer	NOUN
american_scientific_journal-3270	506	96	,	,	PUNCT
american_scientific_journal-3270	506	97	2005	2005	NUM
american_scientific_journal-3270	506	98	[	[	X
american_scientific_journal-3270	506	99	2	2	NUM
american_scientific_journal-3270	506	100	]	]	PUNCT
american_scientific_journal-3270	506	101	f.	f.	PROPN
american_scientific_journal-3270	506	102	erdogan	erdogan	PROPN
american_scientific_journal-3270	506	103	,	,	PUNCT
american_scientific_journal-3270	506	104	a.	a.	PROPN
american_scientific_journal-3270	506	105	c.	c.	PROPN
american_scientific_journal-3270	506	106	kaya	kaya	PROPN
american_scientific_journal-3270	506	107	,	,	PUNCT
american_scientific_journal-3270	506	108	”	"	PUNCT
american_scientific_journal-3270	506	109	stress	stress	NOUN
american_scientific_journal-3270	506	110	intensity	intensity	NOUN
american_scientific_journal-3270	506	111	factor	factor	NOUN
american_scientific_journal-3270	506	112	and	and	CCONJ
american_scientific_journal-3270	506	113	cod	cod	NOUN
american_scientific_journal-3270	506	114	in	in	ADP
american_scientific_journal-3270	506	115	an	an	DET
american_scientific_journal-3270	506	116	orthotropic	orthotropic	ADJ
american_scientific_journal-3270	506	117	strip	strip	NOUN
american_scientific_journal-3270	506	118	”	"	PUNCT
american_scientific_journal-3270	506	119	international	international	ADJ
american_scientific_journal-3270	506	120	journal	journal	NOUN
american_scientific_journal-3270	506	121	of	of	ADP
american_scientific_journal-3270	506	122	fracture	fracture	NOUN
american_scientific_journal-3270	506	123	,	,	PUNCT
american_scientific_journal-3270	506	124	vol	vol	NOUN
american_scientific_journal-3270	506	125	.	.	PUNCT
american_scientific_journal-3270	507	1	16(1980)1971	16(1980)1971	NUM
american_scientific_journal-3270	507	2	-	-	SYM
american_scientific_journal-3270	507	3	1980	1980	NUM
american_scientific_journal-3270	507	4	[	[	X
american_scientific_journal-3270	507	5	3	3	NUM
american_scientific_journal-3270	507	6	]	]	X
american_scientific_journal-3270	507	7	f.	f.	PROPN
american_scientific_journal-3270	507	8	erdogan,”stress	erdogan,”stress	PROPN
american_scientific_journal-3270	507	9	intensity	intensity	NOUN
american_scientific_journal-3270	507	10	factors	factor	NOUN
american_scientific_journal-3270	507	11	”	"	PUNCT
american_scientific_journal-3270	508	1	,	,	PUNCT
american_scientific_journal-3270	508	2	asme	asme	PROPN
american_scientific_journal-3270	508	3	applied	apply	VERB
american_scientific_journal-3270	508	4	mechanics	mechanic	NOUN
american_scientific_journal-3270	508	5	,	,	PUNCT
american_scientific_journal-3270	508	6	vol	vol	NOUN
american_scientific_journal-3270	508	7	.	.	PUNCT
american_scientific_journal-3270	509	1	50(1983)276	50(1983)276	NOUN
american_scientific_journal-3270	509	2	-	-	PUNCT
american_scientific_journal-3270	509	3	288	288	NUM
american_scientific_journal-3270	509	4	.	.	PUNCT
american_scientific_journal-3270	510	1	[	[	X
american_scientific_journal-3270	510	2	4	4	X
american_scientific_journal-3270	510	3	]	]	PUNCT
american_scientific_journal-3270	510	4	m.	m.	NOUN
american_scientific_journal-3270	510	5	matbuly	matbuly	ADV
american_scientific_journal-3270	510	6	,	,	PUNCT
american_scientific_journal-3270	510	7	m.s	m.s	PROPN
american_scientific_journal-3270	510	8	.	.	PROPN
american_scientific_journal-3270	510	9	nassr	nassr	PROPN
american_scientific_journal-3270	510	10	,	,	PUNCT
american_scientific_journal-3270	510	11	”	"	PUNCT
american_scientific_journal-3270	510	12	electrostatic	electrostatic	ADJ
american_scientific_journal-3270	510	13	analysis	analysis	NOUN
american_scientific_journal-3270	510	14	of	of	ADP
american_scientific_journal-3270	510	15	edge	edge	NOUN
american_scientific_journal-3270	510	16	cracked	crack	VERB
american_scientific_journal-3270	510	17	orthotropic	orthotropic	ADJ
american_scientific_journal-3270	510	18	plates	plate	NOUN
american_scientific_journal-3270	510	19	”	"	PUNCT
american_scientific_journal-3270	510	20	d.m	d.m	PROPN
american_scientific_journal-3270	510	21	.	.	PROPN
american_scientific_journal-3270	510	22	,j	,j	PROPN
american_scientific_journal-3270	510	23	.	.	PUNCT
american_scientific_journal-3270	511	1	of	of	ADP
american_scientific_journal-3270	511	2	eng	eng	PROPN
american_scientific_journal-3270	511	3	.	.	PROPN
american_scientific_journal-3270	511	4	appl	appl	PROPN
american_scientific_journal-3270	511	5	.	.	PUNCT
american_scientific_journal-3270	512	1	sci	sci	PROPN
american_scientific_journal-3270	512	2	.	.	PUNCT
american_scientific_journal-3270	512	3	vol	vol	NOUN
american_scientific_journal-3270	512	4	.	.	PUNCT
american_scientific_journal-3270	513	1	50(2005)376	50(2005)376	NOUN
american_scientific_journal-3270	513	2	-	-	SYM
american_scientific_journal-3270	513	3	388	388	NUM
american_scientific_journal-3270	513	4	.	.	PUNCT
american_scientific_journal-3270	514	1	[	[	X
american_scientific_journal-3270	514	2	5	5	NUM
american_scientific_journal-3270	514	3	]	]	SYM
american_scientific_journal-3270	514	4	s.y	s.y	PROPN
american_scientific_journal-3270	514	5	.	.	PROPN
american_scientific_journal-3270	514	6	shin	shin	PROPN
american_scientific_journal-3270	514	7	,	,	PUNCT
american_scientific_journal-3270	514	8	h.	h.	PROPN
american_scientific_journal-3270	514	9	lees	lees	PROPN
american_scientific_journal-3270	514	10	,	,	PUNCT
american_scientific_journal-3270	514	11	s.y	s.y	PROPN
american_scientific_journal-3270	514	12	.	.	PROPN
american_scientific_journal-3270	514	13	han	han	PROPN
american_scientific_journal-3270	514	14	,	,	PUNCT
american_scientific_journal-3270	514	15	”	"	PUNCT
american_scientific_journal-3270	514	16	influence	influence	NOUN
american_scientific_journal-3270	514	17	of	of	ADP
american_scientific_journal-3270	514	18	silicon	silicon	NOUN
american_scientific_journal-3270	514	19	in	in	ADP
american_scientific_journal-3270	514	20	low	low	ADJ
american_scientific_journal-3270	514	21	density	density	NOUN
american_scientific_journal-3270	514	22	fe	fe	X
american_scientific_journal-3270	514	23	-	-	PUNCT
american_scientific_journal-3270	514	24	c	c	PROPN
american_scientific_journal-3270	514	25	-	-	PUNCT
american_scientific_journal-3270	514	26	mn	mn	PROPN
american_scientific_journal-3270	514	27	-	-	PUNCT
american_scientific_journal-3270	514	28	al	al	PROPN
american_scientific_journal-3270	514	29	stell	stell	PROPN
american_scientific_journal-3270	514	30	”	"	PUNCT
american_scientific_journal-3270	514	31	metal	metal	NOUN
american_scientific_journal-3270	514	32	.	.	PUNCT
american_scientific_journal-3270	515	1	mat	mat	PROPN
american_scientific_journal-3270	515	2	.	.	PUNCT
american_scientific_journal-3270	515	3	trans	trans	PROPN
american_scientific_journal-3270	515	4	.	.	PUNCT
american_scientific_journal-3270	516	1	a	a	DET
american_scientific_journal-3270	516	2	,	,	PUNCT
american_scientific_journal-3270	516	3	vol	vol	NOUN
american_scientific_journal-3270	516	4	.	.	PUNCT
american_scientific_journal-3270	517	1	41(2010)138	41(2010)138	PROPN
american_scientific_journal-3270	517	2	-	-	PUNCT
american_scientific_journal-3270	517	3	148	148	NUM
american_scientific_journal-3270	517	4	.	.	PUNCT
american_scientific_journal-3270	518	1	american	american	ADJ
american_scientific_journal-3270	518	2	scientific	scientific	ADJ
american_scientific_journal-3270	518	3	research	research	PROPN
american_scientific_journal-3270	518	4	journal	journal	NOUN
american_scientific_journal-3270	518	5	for	for	ADP
american_scientific_journal-3270	518	6	engineering	engineering	NOUN
american_scientific_journal-3270	518	7	,	,	PUNCT
american_scientific_journal-3270	518	8	technology	technology	NOUN
american_scientific_journal-3270	518	9	,	,	PUNCT
american_scientific_journal-3270	518	10	and	and	CCONJ
american_scientific_journal-3270	518	11	sciences	science	NOUN
american_scientific_journal-3270	518	12	(	(	PUNCT
american_scientific_journal-3270	518	13	asrjets	asrjet	NOUN
american_scientific_journal-3270	518	14	)	)	PUNCT
american_scientific_journal-3270	518	15	(	(	PUNCT
american_scientific_journal-3270	518	16	2017	2017	NUM
american_scientific_journal-3270	518	17	)	)	PUNCT
american_scientific_journal-3270	518	18	volume	volume	NOUN
american_scientific_journal-3270	518	19	34	34	NUM
american_scientific_journal-3270	518	20	,	,	PUNCT
american_scientific_journal-3270	518	21	no	no	DET
american_scientific_journal-3270	518	22	1	1	NUM
american_scientific_journal-3270	518	23	,	,	PUNCT
american_scientific_journal-3270	518	24	pp	pp	ADV
american_scientific_journal-3270	518	25	213	213	NUM
american_scientific_journal-3270	518	26	-	-	SYM
american_scientific_journal-3270	518	27	230	230	NUM
american_scientific_journal-3270	518	28	229	229	NUM
american_scientific_journal-3270	519	1	[	[	X
american_scientific_journal-3270	519	2	6	6	NUM
american_scientific_journal-3270	519	3	]	]	PUNCT
american_scientific_journal-3270	519	4	g.	g.	PROPN
american_scientific_journal-3270	519	5	w.	w.	PROPN
american_scientific_journal-3270	519	6	jia	jia	PROPN
american_scientific_journal-3270	519	7	,	,	PUNCT
american_scientific_journal-3270	519	8	l.	l.	PROPN
american_scientific_journal-3270	519	9	hau	hau	PROPN
american_scientific_journal-3270	519	10	,	,	PUNCT
american_scientific_journal-3270	519	11	”	"	PUNCT
american_scientific_journal-3270	519	12	a	a	DET
american_scientific_journal-3270	519	13	note	note	NOUN
american_scientific_journal-3270	519	14	on	on	ADP
american_scientific_journal-3270	519	15	the	the	DET
american_scientific_journal-3270	519	16	discontinuity	discontinuity	NOUN
american_scientific_journal-3270	519	17	problem	problem	NOUN
american_scientific_journal-3270	519	18	in	in	ADP
american_scientific_journal-3270	519	19	heston	heston	PROPN
american_scientific_journal-3270	519	20	's	's	PART
american_scientific_journal-3270	519	21	stochastic	stochastic	ADJ
american_scientific_journal-3270	519	22	volatility	volatility	NOUN
american_scientific_journal-3270	519	23	model	model	NOUN
american_scientific_journal-3270	519	24	”	"	PUNCT
american_scientific_journal-3270	519	25	j.	j.	PROPN
american_scientific_journal-3270	519	26	material	material	PROPN
american_scientific_journal-3270	519	27	process	process	NOUN
american_scientific_journal-3270	519	28	technology	technology	NOUN
american_scientific_journal-3270	519	29	,	,	PUNCT
american_scientific_journal-3270	519	30	vol.187(2007)562	vol.187(2007)562	NOUN
american_scientific_journal-3270	519	31	-	-	PUNCT
american_scientific_journal-3270	519	32	565	565	NUM
american_scientific_journal-3270	519	33	[	[	X
american_scientific_journal-3270	519	34	7]a.a	7]a.a	NUM
american_scientific_journal-3270	519	35	.	.	PUNCT
american_scientific_journal-3270	520	1	rizk	rizk	PROPN
american_scientific_journal-3270	520	2	,	,	PUNCT
american_scientific_journal-3270	520	3	m.	m.	NOUN
american_scientific_journal-3270	520	4	hrairi	hrairi	NOUN
american_scientific_journal-3270	520	5	,	,	PUNCT
american_scientific_journal-3270	520	6	“	"	PUNCT
american_scientific_journal-3270	520	7	edgecracked	edgecracke	VERB
american_scientific_journal-3270	520	8	biomaterial	biomaterial	ADJ
american_scientific_journal-3270	520	9	systems	system	NOUN
american_scientific_journal-3270	520	10	under	under	ADP
american_scientific_journal-3270	520	11	thermal	thermal	ADJ
american_scientific_journal-3270	520	12	heating	heating	NOUN
american_scientific_journal-3270	520	13	”	"	PUNCT
american_scientific_journal-3270	520	14	,	,	PUNCT
american_scientific_journal-3270	520	15	j.	j.	PROPN
american_scientific_journal-3270	520	16	eng.fra	eng.fra	PROPN
american_scientific_journal-3270	520	17	.	.	PROPN
american_scientific_journal-3270	520	18	mech	mech	PROPN
american_scientific_journal-3270	520	19	.	.	PUNCT
american_scientific_journal-3270	521	1	vol.(2009)1648	vol.(2009)1648	PROPN
american_scientific_journal-3270	521	2	-	-	PUNCT
american_scientific_journal-3270	521	3	1653	1653	NUM
american_scientific_journal-3270	521	4	.	.	PUNCT
american_scientific_journal-3270	522	1	[	[	X
american_scientific_journal-3270	522	2	8	8	NUM
american_scientific_journal-3270	522	3	]	]	X
american_scientific_journal-3270	522	4	h.	h.	NOUN
american_scientific_journal-3270	522	5	parkus	parkus	PROPN
american_scientific_journal-3270	522	6	,	,	PUNCT
american_scientific_journal-3270	522	7	thermo	thermo	NOUN
american_scientific_journal-3270	522	8	elasticity	elasticity	NOUN
american_scientific_journal-3270	522	9	,	,	PUNCT
american_scientific_journal-3270	522	10	spring	spring	NOUN
american_scientific_journal-3270	522	11	-	-	PUNCT
american_scientific_journal-3270	522	12	verlag	verlag	NOUN
american_scientific_journal-3270	522	13	,	,	PUNCT
american_scientific_journal-3270	522	14	barlen	barlen	VERB
american_scientific_journal-3270	522	15	,	,	PUNCT
american_scientific_journal-3270	522	16	1976	1976	NUM
american_scientific_journal-3270	522	17	[	[	X
american_scientific_journal-3270	522	18	9	9	NUM
american_scientific_journal-3270	522	19	]	]	X
american_scientific_journal-3270	522	20	n.	n.	PROPN
american_scientific_journal-3270	522	21	noda	noda	PROPN
american_scientific_journal-3270	522	22	,	,	PUNCT
american_scientific_journal-3270	522	23	r.b	r.b	PROPN
american_scientific_journal-3270	522	24	.	.	PROPN
american_scientific_journal-3270	522	25	hetnarski	hetnarski	PROPN
american_scientific_journal-3270	522	26	,	,	PUNCT
american_scientific_journal-3270	522	27	y.	y.	PROPN
american_scientific_journal-3270	522	28	tanigawa	tanigawa	PROPN
american_scientific_journal-3270	522	29	,	,	PUNCT
american_scientific_journal-3270	522	30	thermal	thermal	ADJ
american_scientific_journal-3270	522	31	stress	stress	NOUN
american_scientific_journal-3270	522	32	,	,	PUNCT
american_scientific_journal-3270	522	33	taylor	taylor	PROPN
american_scientific_journal-3270	522	34	and	and	CCONJ
american_scientific_journal-3270	522	35	francis	francis	PROPN
american_scientific_journal-3270	522	36	,	,	PUNCT
american_scientific_journal-3270	522	37	2003	2003	NUM
american_scientific_journal-3270	522	38	.	.	PUNCT
american_scientific_journal-3270	523	1	[	[	X
american_scientific_journal-3270	523	2	10	10	NUM
american_scientific_journal-3270	523	3	]	]	X
american_scientific_journal-3270	523	4	r.b	r.b	PROPN
american_scientific_journal-3270	523	5	.	.	PROPN
american_scientific_journal-3270	523	6	hetnarski	hetnarski	PROPN
american_scientific_journal-3270	523	7	,	,	PUNCT
american_scientific_journal-3270	523	8	j.	j.	PROPN
american_scientific_journal-3270	523	9	ignaczak	ignaczak	PROPN
american_scientific_journal-3270	523	10	,	,	PUNCT
american_scientific_journal-3270	523	11	mathematical	mathematical	ADJ
american_scientific_journal-3270	523	12	theory	theory	NOUN
american_scientific_journal-3270	523	13	of	of	ADP
american_scientific_journal-3270	523	14	elasticity	elasticity	NOUN
american_scientific_journal-3270	523	15	,	,	PUNCT
american_scientific_journal-3270	523	16	taylor	taylor	PROPN
american_scientific_journal-3270	523	17	and	and	CCONJ
american_scientific_journal-3270	523	18	francis	francis	PROPN
american_scientific_journal-3270	523	19	,	,	PUNCT
american_scientific_journal-3270	523	20	2004	2004	NUM
american_scientific_journal-3270	523	21	.	.	PUNCT
american_scientific_journal-3270	524	1	[	[	X
american_scientific_journal-3270	524	2	11	11	NUM
american_scientific_journal-3270	524	3	]	]	PUNCT
american_scientific_journal-3270	524	4	m.	m.	NOUN
american_scientific_journal-3270	524	5	a.	a.	PROPN
american_scientific_journal-3270	524	6	abdou	abdou	PROPN
american_scientific_journal-3270	524	7	,	,	PUNCT
american_scientific_journal-3270	524	8	fundamental	fundamental	ADJ
american_scientific_journal-3270	524	9	problems	problem	NOUN
american_scientific_journal-3270	524	10	for	for	ADP
american_scientific_journal-3270	524	11	finite	finite	ADJ
american_scientific_journal-3270	524	12	plate	plate	NOUN
american_scientific_journal-3270	524	13	with	with	ADP
american_scientific_journal-3270	524	14	a	a	DET
american_scientific_journal-3270	524	15	curvilinear	curvilinear	ADJ
american_scientific_journal-3270	524	16	hole	hole	NOUN
american_scientific_journal-3270	524	17	having	have	VERB
american_scientific_journal-3270	524	18	finite	finite	ADJ
american_scientific_journal-3270	524	19	poles	pole	NOUN
american_scientific_journal-3270	524	20	,	,	PUNCT
american_scientific_journal-3270	524	21	appl	appl	PROPN
american_scientific_journal-3270	524	22	.	.	PROPN
american_scientific_journal-3270	524	23	math	math	PROPN
american_scientific_journal-3270	524	24	.	.	PUNCT
american_scientific_journal-3270	524	25	compute	compute	NOUN
american_scientific_journal-3270	524	26	.	.	PUNCT
american_scientific_journal-3270	525	1	125	125	NUM
american_scientific_journal-3270	525	2	(	(	PUNCT
american_scientific_journal-3270	525	3	2002	2002	NUM
american_scientific_journal-3270	525	4	)	)	PUNCT
american_scientific_journal-3270	525	5	79	79	NUM
american_scientific_journal-3270	525	6	-	-	SYM
american_scientific_journal-3270	525	7	91	91	NUM
american_scientific_journal-3270	526	1	[	[	X
american_scientific_journal-3270	526	2	12	12	NUM
american_scientific_journal-3270	526	3	]	]	PUNCT
american_scientific_journal-3270	526	4	m.	m.	NOUN
american_scientific_journal-3270	526	5	a.	a.	PROPN
american_scientific_journal-3270	526	6	abdou	abdou	PROPN
american_scientific_journal-3270	526	7	,	,	PUNCT
american_scientific_journal-3270	526	8	s.	s.	PROPN
american_scientific_journal-3270	526	9	a.	a.	PROPN
american_scientific_journal-3270	526	10	asseri	asseri	PROPN
american_scientific_journal-3270	526	11	,	,	PUNCT
american_scientific_journal-3270	526	12	gaursat	gaursat	VERB
american_scientific_journal-3270	526	13	functions	function	NOUN
american_scientific_journal-3270	526	14	for	for	ADP
american_scientific_journal-3270	526	15	an	an	DET
american_scientific_journal-3270	526	16	infinite	infinite	ADJ
american_scientific_journal-3270	526	17	plate	plate	NOUN
american_scientific_journal-3270	526	18	with	with	ADP
american_scientific_journal-3270	526	19	a	a	DET
american_scientific_journal-3270	526	20	generalized	generalized	ADJ
american_scientific_journal-3270	526	21	curvilinear	curvilinear	ADJ
american_scientific_journal-3270	526	22	hole	hole	NOUN
american_scientific_journal-3270	526	23	in	in	ADP
american_scientific_journal-3270	526	24	zeta	zeta	PROPN
american_scientific_journal-3270	526	25	plane	plane	NOUN
american_scientific_journal-3270	526	26	,	,	PUNCT
american_scientific_journal-3270	526	27	appl	appl	PROPN
american_scientific_journal-3270	526	28	.	.	PROPN
american_scientific_journal-3270	526	29	math	math	PROPN
american_scientific_journal-3270	526	30	.	.	PUNCT
american_scientific_journal-3270	527	1	compute	compute	PROPN
american_scientific_journal-3270	527	2	.	.	PUNCT
american_scientific_journal-3270	528	1	212	212	NUM
american_scientific_journal-3270	528	2	(	(	PUNCT
american_scientific_journal-3270	528	3	2009	2009	NUM
american_scientific_journal-3270	528	4	)	)	PUNCT
american_scientific_journal-3270	528	5	23	23	NUM
american_scientific_journal-3270	528	6	-	-	SYM
american_scientific_journal-3270	528	7	36	36	NUM
american_scientific_journal-3270	529	1	[	[	SYM
american_scientific_journal-3270	529	2	13	13	NUM
american_scientific_journal-3270	529	3	]	]	PUNCT
american_scientific_journal-3270	529	4	m.	m.	NOUN
american_scientific_journal-3270	529	5	a.	a.	PROPN
american_scientific_journal-3270	529	6	abdou	abdou	PROPN
american_scientific_journal-3270	529	7	,	,	PUNCT
american_scientific_journal-3270	529	8	s.	s.	PROPN
american_scientific_journal-3270	529	9	a.	a.	PROPN
american_scientific_journal-3270	529	10	asseri	asseri	PROPN
american_scientific_journal-3270	529	11	,	,	PUNCT
american_scientific_journal-3270	529	12	closed	close	VERB
american_scientific_journal-3270	529	13	forms	form	NOUN
american_scientific_journal-3270	529	14	of	of	ADP
american_scientific_journal-3270	529	15	gaursat	gaursat	ADJ
american_scientific_journal-3270	529	16	functions	function	NOUN
american_scientific_journal-3270	529	17	in	in	ADP
american_scientific_journal-3270	529	18	presence	presence	NOUN
american_scientific_journal-3270	529	19	of	of	ADP
american_scientific_journal-3270	529	20	heat	heat	NOUN
american_scientific_journal-3270	529	21	for	for	ADP
american_scientific_journal-3270	529	22	curvilinear	curvilinear	ADJ
american_scientific_journal-3270	529	23	holes	hole	NOUN
american_scientific_journal-3270	529	24	,	,	PUNCT
american_scientific_journal-3270	529	25	j.	j.	PROPN
american_scientific_journal-3270	529	26	thermal	thermal	PROPN
american_scientific_journal-3270	529	27	stress	stress	NOUN
american_scientific_journal-3270	529	28	,	,	PUNCT
american_scientific_journal-3270	529	29	vol.32	vol.32	ADV
american_scientific_journal-3270	529	30	,	,	PUNCT
american_scientific_journal-3270	529	31	(	(	PUNCT
american_scientific_journal-3270	529	32	2009	2009	NUM
american_scientific_journal-3270	529	33	)	)	PUNCT
american_scientific_journal-3270	529	34	83	83	NUM
american_scientific_journal-3270	529	35	101	101	NUM
american_scientific_journal-3270	529	36	[	[	X
american_scientific_journal-3270	529	37	14	14	NUM
american_scientific_journal-3270	529	38	]	]	PUNCT
american_scientific_journal-3270	529	39	m.	m.	NOUN
american_scientific_journal-3270	529	40	a.	a.	PROPN
american_scientific_journal-3270	529	41	abdou	abdou	PROPN
american_scientific_journal-3270	529	42	,	,	PUNCT
american_scientific_journal-3270	529	43	s.	s.	PROPN
american_scientific_journal-3270	529	44	j.	j.	PROPN
american_scientific_journal-3270	529	45	monaquel	monaquel	PROPN
american_scientific_journal-3270	529	46	,	,	PUNCT
american_scientific_journal-3270	529	47	integro	integro	PROPN
american_scientific_journal-3270	529	48	differential	differential	ADJ
american_scientific_journal-3270	529	49	equation	equation	NOUN
american_scientific_journal-3270	529	50	and	and	CCONJ
american_scientific_journal-3270	529	51	fundamental	fundamental	ADJ
american_scientific_journal-3270	529	52	problems	problem	NOUN
american_scientific_journal-3270	529	53	of	of	ADP
american_scientific_journal-3270	529	54	an	an	DET
american_scientific_journal-3270	529	55	infinite	infinite	ADJ
american_scientific_journal-3270	529	56	plate	plate	NOUN
american_scientific_journal-3270	529	57	with	with	ADP
american_scientific_journal-3270	529	58	a	a	DET
american_scientific_journal-3270	529	59	curvilinear	curvilinear	ADJ
american_scientific_journal-3270	529	60	hole	hole	NOUN
american_scientific_journal-3270	529	61	having	have	VERB
american_scientific_journal-3270	529	62	a	a	DET
american_scientific_journal-3270	529	63	strong	strong	ADJ
american_scientific_journal-3270	529	64	pole	pole	NOUN
american_scientific_journal-3270	529	65	,	,	PUNCT
american_scientific_journal-3270	529	66	int	int	NOUN
american_scientific_journal-3270	529	67	.	.	PUNCT
american_scientific_journal-3270	530	1	j.	j.	PROPN
american_scientific_journal-3270	530	2	contemp	contemp	PROPN
american_scientific_journal-3270	530	3	.	.	PUNCT
american_scientific_journal-3270	531	1	math	math	NOUN
american_scientific_journal-3270	531	2	.	.	PUNCT
american_scientific_journal-3270	532	1	sciences	science	NOUN
american_scientific_journal-3270	532	2	,	,	PUNCT
american_scientific_journal-3270	532	3	vol	vol	NOUN
american_scientific_journal-3270	532	4	.	.	PROPN
american_scientific_journal-3270	532	5	6	6	NUM
american_scientific_journal-3270	532	6	,	,	PUNCT
american_scientific_journal-3270	532	7	(	(	PUNCT
american_scientific_journal-3270	532	8	2011	2011	NUM
american_scientific_journal-3270	532	9	)	)	PUNCT
american_scientific_journal-3270	532	10	,	,	PUNCT
american_scientific_journal-3270	532	11	no	no	INTJ
american_scientific_journal-3270	532	12	.	.	NOUN
american_scientific_journal-3270	532	13	4	4	NUM
american_scientific_journal-3270	532	14	199	199	NUM
american_scientific_journal-3270	532	15	208	208	NUM
american_scientific_journal-3270	532	16	[	[	X
american_scientific_journal-3270	532	17	15	15	NUM
american_scientific_journal-3270	532	18	]	]	X
american_scientific_journal-3270	532	19	m.	m.	NOUN
american_scientific_journal-3270	532	20	a.	a.	PROPN
american_scientific_journal-3270	532	21	abdou	abdou	PROPN
american_scientific_journal-3270	532	22	,	,	PUNCT
american_scientific_journal-3270	532	23	f.	f.	PROPN
american_scientific_journal-3270	532	24	s.	s.	PROPN
american_scientific_journal-3270	532	25	bayones	bayones	PROPN
american_scientific_journal-3270	532	26	,	,	PUNCT
american_scientific_journal-3270	532	27	integro	integro	ADJ
american_scientific_journal-3270	532	28	–	–	PUNCT
american_scientific_journal-3270	532	29	differential	differential	ADJ
american_scientific_journal-3270	532	30	equation	equation	NOUN
american_scientific_journal-3270	532	31	and	and	CCONJ
american_scientific_journal-3270	532	32	an	an	DET
american_scientific_journal-3270	532	33	infinite	infinite	ADJ
american_scientific_journal-3270	532	34	elastic	elastic	ADJ
american_scientific_journal-3270	532	35	plate	plate	NOUN
american_scientific_journal-3270	532	36	with	with	ADP
american_scientific_journal-3270	532	37	a	a	DET
american_scientific_journal-3270	532	38	curvilinear	curvilinear	ADJ
american_scientific_journal-3270	532	39	hole	hole	NOUN
american_scientific_journal-3270	532	40	in	in	ADP
american_scientific_journal-3270	532	41	s	s	NOUN
american_scientific_journal-3270	532	42	-	-	NOUN
american_scientific_journal-3270	532	43	plane	plane	NOUN
american_scientific_journal-3270	532	44	,	,	PUNCT
american_scientific_journal-3270	532	45	ijrras	ijrras	NOUN
american_scientific_journal-3270	532	46	10	10	NUM
american_scientific_journal-3270	532	47	(	(	PUNCT
american_scientific_journal-3270	532	48	3	3	NUM
american_scientific_journal-3270	532	49	)	)	PUNCT
american_scientific_journal-3270	532	50	march	march	NOUN
american_scientific_journal-3270	532	51	(	(	PUNCT
american_scientific_journal-3270	532	52	2012)1	2012)1	NUM
american_scientific_journal-3270	532	53	-	-	SYM
american_scientific_journal-3270	532	54	10	10	NUM
american_scientific_journal-3270	533	1	[	[	X
american_scientific_journal-3270	533	2	16	16	NUM
american_scientific_journal-3270	533	3	]	]	PUNCT
american_scientific_journal-3270	533	4	m.	m.	NOUN
american_scientific_journal-3270	533	5	a.	a.	PROPN
american_scientific_journal-3270	533	6	abdou	abdou	PROPN
american_scientific_journal-3270	533	7	,	,	PUNCT
american_scientific_journal-3270	533	8	a.	a.	PROPN
american_scientific_journal-3270	533	9	r.	r.	PROPN
american_scientific_journal-3270	533	10	jaan	jaan	PROPN
american_scientific_journal-3270	533	11	,	,	PUNCT
american_scientific_journal-3270	533	12	an	an	DET
american_scientific_journal-3270	533	13	infinite	infinite	ADJ
american_scientific_journal-3270	533	14	elastic	elastic	ADJ
american_scientific_journal-3270	533	15	plate	plate	NOUN
american_scientific_journal-3270	533	16	weakened	weaken	VERB
american_scientific_journal-3270	533	17	by	by	ADP
american_scientific_journal-3270	533	18	a	a	DET
american_scientific_journal-3270	533	19	generalized	generalized	ADJ
american_scientific_journal-3270	533	20	curvilinear	curvilinear	ADJ
american_scientific_journal-3270	533	21	hole	hole	NOUN
american_scientific_journal-3270	533	22	and	and	CCONJ
american_scientific_journal-3270	533	23	gaursat	gaursat	NOUN
american_scientific_journal-3270	533	24	functions	function	NOUN
american_scientific_journal-3270	533	25	,	,	PUNCT
american_scientific_journal-3270	533	26	applied	apply	VERB
american_scientific_journal-3270	533	27	mathematics	mathematic	NOUN
american_scientific_journal-3270	533	28	,	,	PUNCT
american_scientific_journal-3270	533	29	2014	2014	NUM
american_scientific_journal-3270	533	30	,	,	PUNCT
american_scientific_journal-3270	533	31	5	5	NUM
american_scientific_journal-3270	533	32	,	,	PUNCT
american_scientific_journal-3270	533	33	428	428	NUM
american_scientific_journal-3270	533	34	-	-	SYM
american_scientific_journal-3270	533	35	443	443	NUM
american_scientific_journal-3270	533	36	[	[	X
american_scientific_journal-3270	533	37	17	17	NUM
american_scientific_journal-3270	533	38	]	]	PUNCT
american_scientific_journal-3270	533	39	m.	m.	NOUN
american_scientific_journal-3270	533	40	a.	a.	PROPN
american_scientific_journal-3270	533	41	abdou	abdou	PROPN
american_scientific_journal-3270	533	42	,	,	PUNCT
american_scientific_journal-3270	533	43	w.	w.	PROPN
american_scientific_journal-3270	533	44	g.	g.	PROPN
american_scientific_journal-3270	533	45	el	el	PROPN
american_scientific_journal-3270	533	46	said	say	VERB
american_scientific_journal-3270	533	47	,	,	PUNCT
american_scientific_journal-3270	533	48	e.	e.	PROPN
american_scientific_journal-3270	533	49	i.	i.	PROPN
american_scientific_journal-3270	533	50	deebs	deebs	PROPN
american_scientific_journal-3270	533	51	”	"	PUNCT
american_scientific_journal-3270	533	52	a	a	DET
american_scientific_journal-3270	533	53	solution	solution	NOUN
american_scientific_journal-3270	533	54	of	of	ADP
american_scientific_journal-3270	533	55	a	a	DET
american_scientific_journal-3270	533	56	nonlinear	nonlinear	ADJ
american_scientific_journal-3270	533	57	integral	integral	ADJ
american_scientific_journal-3270	533	58	equation	equation	NOUN
american_scientific_journal-3270	533	59	,	,	PUNCT
american_scientific_journal-3270	533	60	appl	appl	PROPN
american_scientific_journal-3270	533	61	.	.	PROPN
american_scientific_journal-3270	533	62	math	math	PROPN
american_scientific_journal-3270	533	63	.	.	PUNCT
american_scientific_journal-3270	534	1	compute	compute	PROPN
american_scientific_journal-3270	534	2	.	.	PUNCT
american_scientific_journal-3270	535	1	160	160	NUM
american_scientific_journal-3270	535	2	(	(	PUNCT
american_scientific_journal-3270	535	3	2005)1	2005)1	NUM
american_scientific_journal-3270	535	4	-	-	SYM
american_scientific_journal-3270	535	5	14	14	NUM
american_scientific_journal-3270	536	1	[	[	SYM
american_scientific_journal-3270	536	2	18	18	NUM
american_scientific_journal-3270	536	3	]	]	PUNCT
american_scientific_journal-3270	536	4	m.	m.	NOUN
american_scientific_journal-3270	536	5	a.	a.	PROPN
american_scientific_journal-3270	536	6	abdou	abdou	PROPN
american_scientific_journal-3270	536	7	,	,	PUNCT
american_scientific_journal-3270	536	8	a.	a.	PROPN
american_scientific_journal-3270	536	9	a.	a.	PROPN
american_scientific_journal-3270	536	10	badr	badr	PROPN
american_scientific_journal-3270	536	11	,	,	PUNCT
american_scientific_journal-3270	536	12	m.	m.	PROPN
american_scientific_journal-3270	536	13	b.	b.	PROPN
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american_scientific_journal-3270	536	15	,	,	PUNCT
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american_scientific_journal-3270	536	18	and	and	CCONJ
american_scientific_journal-3270	536	19	fredholm	fredholm	NOUN
american_scientific_journal-3270	536	20	-	-	PUNCT
american_scientific_journal-3270	536	21	volterra	volterra	NOUN
american_scientific_journal-3270	536	22	integral	integral	ADJ
american_scientific_journal-3270	536	23	equation	equation	NOUN
american_scientific_journal-3270	536	24	,	,	PUNCT
american_scientific_journal-3270	536	25	int	int	NOUN
american_scientific_journal-3270	536	26	.	.	PUNCT
american_scientific_journal-3270	537	1	j.	j.	PROPN
american_scientific_journal-3270	537	2	appl	appl	PROPN
american_scientific_journal-3270	537	3	.	.	PROPN
american_scientific_journal-3270	537	4	and	and	CCONJ
american_scientific_journal-3270	537	5	mech	mech	NOUN
american_scientific_journal-3270	537	6	.	.	PUNCT
american_scientific_journal-3270	538	1	vol.4	vol.4	PROPN
american_scientific_journal-3270	538	2	(	(	PUNCT
american_scientific_journal-3270	538	3	2008	2008	NUM
american_scientific_journal-3270	538	4	)	)	PUNCT
american_scientific_journal-3270	538	5	,	,	PUNCT
american_scientific_journal-3270	538	6	78	78	NUM
american_scientific_journal-3270	538	7	-	-	SYM
american_scientific_journal-3270	538	8	92	92	NUM
american_scientific_journal-3270	538	9	.	.	PUNCT
american_scientific_journal-3270	539	1	[	[	X
american_scientific_journal-3270	539	2	19	19	NUM
american_scientific_journal-3270	539	3	]	]	PUNCT
american_scientific_journal-3270	539	4	m.	m.	NOUN
american_scientific_journal-3270	539	5	a.	a.	PROPN
american_scientific_journal-3270	539	6	abdou	abdou	PROPN
american_scientific_journal-3270	539	7	,	,	PUNCT
american_scientific_journal-3270	539	8	m.	m.	NOUN
american_scientific_journal-3270	539	9	m.	m.	PROPN
american_scientific_journal-3270	539	10	el	el	PROPN
american_scientific_journal-3270	539	11	-	-	PUNCT
american_scientific_journal-3270	539	12	borai	borai	PROPN
american_scientific_journal-3270	539	13	,	,	PUNCT
american_scientific_journal-3270	539	14	m.	m.	NOUN
american_scientific_journal-3270	539	15	m.	m.	PROPN
american_scientific_journal-3270	539	16	el	el	PROPN
american_scientific_journal-3270	539	17	-	-	PUNCT
american_scientific_journal-3270	539	18	kojok	kojok	PROPN
american_scientific_journal-3270	539	19	,	,	PUNCT
american_scientific_journal-3270	539	20	toeplitz	toeplitz	NOUN
american_scientific_journal-3270	539	21	matrix	matrix	NOUN
american_scientific_journal-3270	539	22	method	method	NOUN
american_scientific_journal-3270	539	23	and	and	CCONJ
american_scientific_journal-3270	539	24	nonlinear	nonlinear	ADJ
american_scientific_journal-3270	539	25	integral	integral	ADJ
american_scientific_journal-3270	539	26	equation	equation	NOUN
american_scientific_journal-3270	539	27	of	of	ADP
american_scientific_journal-3270	539	28	hammerstein	hammerstein	PROPN
american_scientific_journal-3270	539	29	type	type	PROPN
american_scientific_journal-3270	539	30	,	,	PUNCT
american_scientific_journal-3270	539	31	j.	j.	PROPN
american_scientific_journal-3270	539	32	comp	comp	PROPN
american_scientific_journal-3270	539	33	.	.	PUNCT
american_scientific_journal-3270	540	1	appl	appl	PROPN
american_scientific_journal-3270	540	2	.	.	PROPN
american_scientific_journal-3270	540	3	math	math	PROPN
american_scientific_journal-3270	540	4	.	.	PUNCT
american_scientific_journal-3270	541	1	vol	vol	NOUN
american_scientific_journal-3270	541	2	.	.	PROPN
american_scientific_journal-3270	541	3	223	223	NUM
american_scientific_journal-3270	541	4	,	,	PUNCT
american_scientific_journal-3270	541	5	(	(	PUNCT
american_scientific_journal-3270	541	6	2009	2009	NUM
american_scientific_journal-3270	541	7	)	)	PUNCT
american_scientific_journal-3270	541	8	765	765	NUM
american_scientific_journal-3270	541	9	–	–	PUNCT
american_scientific_journal-3270	541	10	776	776	NUM
american_scientific_journal-3270	542	1	[	[	X
american_scientific_journal-3270	542	2	20	20	NUM
american_scientific_journal-3270	542	3	]	]	PUNCT
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american_scientific_journal-3270	542	5	a.	a.	PROPN
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american_scientific_journal-3270	542	7	,	,	PUNCT
american_scientific_journal-3270	542	8	a.	a.	PROPN
american_scientific_journal-3270	542	9	a.	a.	PROPN
american_scientific_journal-3270	542	10	badr	badr	PROPN
american_scientific_journal-3270	542	11	,	,	PUNCT
american_scientific_journal-3270	542	12	m.	m.	NOUN
american_scientific_journal-3270	542	13	m.	m.	PROPN
american_scientific_journal-3270	542	14	el	el	PROPN
american_scientific_journal-3270	542	15	-	-	PUNCT
american_scientific_journal-3270	542	16	kojok	kojok	PROPN
american_scientific_journal-3270	542	17	,	,	PUNCT
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american_scientific_journal-3270	542	19	the	the	DET
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american_scientific_journal-3270	542	21	of	of	ADP
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american_scientific_journal-3270	542	23	nonlinear	nonlinear	ADJ
american_scientific_journal-3270	542	24	integral	integral	ADJ
american_scientific_journal-3270	542	25	equation	equation	NOUN
american_scientific_journal-3270	542	26	,	,	PUNCT
american_scientific_journal-3270	542	27	appl	appl	PROPN
american_scientific_journal-3270	542	28	.	.	PROPN
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american_scientific_journal-3270	542	30	.	.	PUNCT
american_scientific_journal-3270	543	1	compute	compute	PROPN
american_scientific_journal-3270	543	2	.	.	PUNCT
american_scientific_journal-3270	544	1	217(2011	217(2011	NUM
american_scientific_journal-3270	544	2	)	)	PUNCT
american_scientific_journal-3270	544	3	5466	5466	NUM
american_scientific_journal-3270	544	4	-	-	SYM
american_scientific_journal-3270	544	5	5475	5475	NUM
american_scientific_journal-3270	544	6	american	american	ADJ
american_scientific_journal-3270	544	7	scientific	scientific	ADJ
american_scientific_journal-3270	544	8	research	research	NOUN
american_scientific_journal-3270	544	9	journal	journal	NOUN
american_scientific_journal-3270	544	10	for	for	ADP
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american_scientific_journal-3270	544	12	,	,	PUNCT
american_scientific_journal-3270	544	13	technology	technology	NOUN
american_scientific_journal-3270	544	14	,	,	PUNCT
american_scientific_journal-3270	544	15	and	and	CCONJ
american_scientific_journal-3270	544	16	sciences	science	NOUN
american_scientific_journal-3270	544	17	(	(	PUNCT
american_scientific_journal-3270	544	18	asrjets	asrjet	NOUN
american_scientific_journal-3270	544	19	)	)	PUNCT
american_scientific_journal-3270	544	20	(	(	PUNCT
american_scientific_journal-3270	544	21	2017	2017	NUM
american_scientific_journal-3270	544	22	)	)	PUNCT
american_scientific_journal-3270	544	23	volume	volume	NOUN
american_scientific_journal-3270	544	24	34	34	NUM
american_scientific_journal-3270	544	25	,	,	PUNCT
american_scientific_journal-3270	544	26	no	no	DET
american_scientific_journal-3270	544	27	1	1	NUM
american_scientific_journal-3270	544	28	,	,	PUNCT
american_scientific_journal-3270	544	29	pp	pp	ADV
american_scientific_journal-3270	544	30	213	213	NUM
american_scientific_journal-3270	544	31	-	-	SYM
american_scientific_journal-3270	544	32	230	230	NUM
american_scientific_journal-3270	544	33	230	230	NUM
american_scientific_journal-3270	544	34	[	[	X
american_scientific_journal-3270	544	35	21	21	NUM
american_scientific_journal-3270	544	36	]	]	PUNCT
american_scientific_journal-3270	544	37	m.	m.	NOUN
american_scientific_journal-3270	544	38	a.	a.	PROPN
american_scientific_journal-3270	544	39	abdou	abdou	PROPN
american_scientific_journal-3270	544	40	,	,	PUNCT
american_scientific_journal-3270	544	41	f.	f.	PROPN
american_scientific_journal-3270	544	42	a.	a.	PROPN
american_scientific_journal-3270	544	43	salama	salama	PROPN
american_scientific_journal-3270	544	44	,	,	PUNCT
american_scientific_journal-3270	544	45	the	the	DET
american_scientific_journal-3270	544	46	solution	solution	NOUN
american_scientific_journal-3270	544	47	of	of	ADP
american_scientific_journal-3270	544	48	mixed	mixed	ADJ
american_scientific_journal-3270	544	49	integral	integral	ADJ
american_scientific_journal-3270	544	50	equation	equation	NOUN
american_scientific_journal-3270	544	51	of	of	ADP
american_scientific_journal-3270	544	52	the	the	DET
american_scientific_journal-3270	544	53	first	first	ADJ
american_scientific_journal-3270	544	54	kind	kind	NOUN
american_scientific_journal-3270	544	55	using	use	VERB
american_scientific_journal-3270	544	56	toeplitz	toeplitz	NOUN
american_scientific_journal-3270	544	57	matrix	matrix	NOUN
american_scientific_journal-3270	544	58	method	method	NOUN
american_scientific_journal-3270	544	59	,	,	PUNCT
american_scientific_journal-3270	544	60	j.	j.	PROPN
american_scientific_journal-3270	544	61	of	of	ADP
american_scientific_journal-3270	544	62	advanced	advanced	PROPN
american_scientific_journal-3270	544	63	in	in	ADP
american_scientific_journal-3270	544	64	mathematics	mathematic	NOUN
american_scientific_journal-3270	544	65	,	,	PUNCT
american_scientific_journal-3270	544	66	vol	vol	NOUN
american_scientific_journal-3270	544	67	.	.	PROPN
american_scientific_journal-3270	544	68	9	9	NUM
american_scientific_journal-3270	544	69	,	,	PUNCT
american_scientific_journal-3270	544	70	no	no	INTJ
american_scientific_journal-3270	544	71	.	.	NOUN
american_scientific_journal-3270	544	72	6	6	NUM
american_scientific_journal-3270	544	73	(	(	PUNCT
american_scientific_journal-3270	544	74	2014)2723	2014)2723	NUM
american_scientific_journal-3270	544	75	-	-	SYM
american_scientific_journal-3270	544	76	2732	2732	NUM
american_scientific_journal-3270	544	77	[	[	X
american_scientific_journal-3270	544	78	22	22	NUM
american_scientific_journal-3270	544	79	]	]	X
american_scientific_journal-3270	544	80	m.a	m.a	PROPN
american_scientific_journal-3270	544	81	.	.	PROPN
american_scientific_journal-3270	544	82	abdou	abdou	PROPN
american_scientific_journal-3270	544	83	,	,	PUNCT
american_scientific_journal-3270	544	84	osama	osama	PROPN
american_scientific_journal-3270	544	85	l.	l.	PROPN
american_scientific_journal-3270	544	86	mustafa	mustafa	PROPN
american_scientific_journal-3270	544	87	,	,	PUNCT
american_scientific_journal-3270	544	88	fredholm	fredholm	PROPN
american_scientific_journal-3270	544	89	–	–	PUNCT
american_scientific_journal-3270	544	90	volterra	volterra	NOUN
american_scientific_journal-3270	544	91	integral	integral	ADJ
american_scientific_journal-3270	544	92	equation	equation	NOUN
american_scientific_journal-3270	544	93	in	in	ADP
american_scientific_journal-3270	544	94	contact	contact	NOUN
american_scientific_journal-3270	544	95	problem	problem	NOUN
american_scientific_journal-3270	544	96	,	,	PUNCT
american_scientific_journal-3270	544	97	j.	j.	PROPN
american_scientific_journal-3270	544	98	appl	appl	PROPN
american_scientific_journal-3270	544	99	.	.	PROPN
american_scientific_journal-3270	544	100	math	math	PROPN
american_scientific_journal-3270	544	101	.	.	PUNCT
american_scientific_journal-3270	545	1	comp.199–215	comp.199–215	PROPN
american_scientific_journal-3270	545	2	,	,	PUNCT
american_scientific_journal-3270	545	3	138	138	NUM
american_scientific_journal-3270	545	4	(	(	PUNCT
american_scientific_journal-3270	545	5	2003	2003	NUM
american_scientific_journal-3270	545	6	)	)	PUNCT
american_scientific_journal-3270	545	7	.	.	PUNCT
american_scientific_journal-3270	546	1	[	[	X
american_scientific_journal-3270	546	2	23	23	NUM
american_scientific_journal-3270	546	3	]	]	PUNCT
american_scientific_journal-3270	546	4	a.	a.	NOUN
american_scientific_journal-3270	546	5	jose	jose	PROPN
american_scientific_journal-3270	546	6	,	,	PUNCT
american_scientific_journal-3270	546	7	cuminato	cuminato	NOUN
american_scientific_journal-3270	546	8	,	,	PUNCT
american_scientific_journal-3270	546	9	numerical	numerical	ADJ
american_scientific_journal-3270	546	10	solution	solution	NOUN
american_scientific_journal-3270	546	11	of	of	ADP
american_scientific_journal-3270	546	12	cauchy	cauchy	ADJ
american_scientific_journal-3270	546	13	type	type	NOUN
american_scientific_journal-3270	546	14	integral	integral	ADJ
american_scientific_journal-3270	546	15	equations	equation	NOUN
american_scientific_journal-3270	546	16	of	of	ADP
american_scientific_journal-3270	546	17	index	index	NOUN
american_scientific_journal-3270	546	18	1	1	NUM
american_scientific_journal-3270	546	19	by	by	ADP
american_scientific_journal-3270	546	20	collocation	collocation	NOUN
american_scientific_journal-3270	546	21	methods	method	NOUN
american_scientific_journal-3270	546	22	,	,	PUNCT
american_scientific_journal-3270	546	23	adv	adv	PROPN
american_scientific_journal-3270	546	24	.	.	PUNCT
american_scientific_journal-3270	546	25	comp	comp	PROPN
american_scientific_journal-3270	546	26	.	.	PUNCT
american_scientific_journal-3270	546	27	math	math	NOUN
american_scientific_journal-3270	546	28	.	.	PUNCT
american_scientific_journal-3270	547	1	6	6	NUM
american_scientific_journal-3270	547	2	(	(	PUNCT
american_scientific_journal-3270	547	3	1996)47	1996)47	NUM
american_scientific_journal-3270	547	4	-	-	SYM
american_scientific_journal-3270	547	5	64	64	NUM
american_scientific_journal-3270	547	6	.	.	PUNCT
american_scientific_journal-3270	548	1	[	[	X
american_scientific_journal-3270	548	2	24	24	NUM
american_scientific_journal-3270	548	3	]	]	X
american_scientific_journal-3270	548	4	g.	g.	PROPN
american_scientific_journal-3270	548	5	szegö	szegö	PROPN
american_scientific_journal-3270	548	6	,	,	PUNCT
american_scientific_journal-3270	548	7	orthogonal	orthogonal	ADJ
american_scientific_journal-3270	548	8	polynomials	polynomial	NOUN
american_scientific_journal-3270	548	9	,	,	PUNCT
american_scientific_journal-3270	548	10	ams	am	NOUN
american_scientific_journal-3270	548	11	colloquium	colloquium	NOUN
american_scientific_journal-3270	548	12	publications	publication	NOUN
american_scientific_journal-3270	548	13	.	.	PUNCT
american_scientific_journal-3270	549	1	23	23	NUM
american_scientific_journal-3270	549	2	,	,	PUNCT
american_scientific_journal-3270	549	3	american	american	PROPN
american_scientific_journal-3270	549	4	mathematical	mathematical	PROPN
american_scientific_journal-3270	549	5	society	society	NOUN
american_scientific_journal-3270	549	6	,	,	PUNCT
american_scientific_journal-3270	549	7	new	new	PROPN
american_scientific_journal-3270	549	8	york	york	PROPN
american_scientific_journal-3270	549	9	,	,	PUNCT
american_scientific_journal-3270	549	10	1999	1999	NUM
american_scientific_journal-3270	549	11	.	.	PUNCT
american_scientific_journal-3270	550	1	[	[	X
american_scientific_journal-3270	550	2	25	25	NUM
american_scientific_journal-3270	550	3	]	]	PUNCT
american_scientific_journal-3270	550	4	a.	a.	NOUN
american_scientific_journal-3270	550	5	erdelyi	erdelyi	NOUN
american_scientific_journal-3270	550	6	,	,	PUNCT
american_scientific_journal-3270	550	7	higher	high	ADJ
american_scientific_journal-3270	550	8	transcendental	transcendental	ADJ
american_scientific_journal-3270	550	9	functions	function	NOUN
american_scientific_journal-3270	550	10	,	,	PUNCT
american_scientific_journal-3270	550	11	vol.2	vol.2	PROPN
american_scientific_journal-3270	550	12	mcgraw	mcgraw	PROPN
american_scientific_journal-3270	550	13	-	-	PUNCT
american_scientific_journal-3270	550	14	hill	hill	NOUN
american_scientific_journal-3270	550	15	.	.	PUNCT
american_scientific_journal-3270	551	1	new	new	PROPN
american_scientific_journal-3270	551	2	york	york	PROPN
american_scientific_journal-3270	551	3	1973	1973	NUM
american_scientific_journal-3270	551	4	.	.	PUNCT