id	sid	tid	token	lemma	pos
ejpam-5617	1	1	european	european	PROPN
ejpam-5617	1	2	journal	journal	PROPN
ejpam-5617	1	3	of	of	ADP
ejpam-5617	1	4	pure	pure	ADJ
ejpam-5617	1	5	and	and	CCONJ
ejpam-5617	1	6	applied	applied	ADJ
ejpam-5617	1	7	mathematics	mathematic	NOUN
ejpam-5617	1	8	2025	2025	NUM
ejpam-5617	1	9	,	,	PUNCT
ejpam-5617	1	10	vol	vol	NOUN
ejpam-5617	1	11	.	.	PROPN
ejpam-5617	1	12	18	18	NUM
ejpam-5617	1	13	,	,	PUNCT
ejpam-5617	1	14	issue	issue	NOUN
ejpam-5617	1	15	1	1	NUM
ejpam-5617	1	16	,	,	PUNCT
ejpam-5617	1	17	article	article	NOUN
ejpam-5617	1	18	number	number	NOUN
ejpam-5617	1	19	5617	5617	NUM
ejpam-5617	1	20	issn	issn	PROPN
ejpam-5617	1	21	1307	1307	NUM
ejpam-5617	1	22	-	-	SYM
ejpam-5617	1	23	5543	5543	NUM
ejpam-5617	1	24	–	–	PUNCT
ejpam-5617	1	25	ejpam.com	ejpam.com	X
ejpam-5617	1	26	published	publish	VERB
ejpam-5617	1	27	by	by	ADP
ejpam-5617	1	28	new	new	PROPN
ejpam-5617	1	29	york	york	PROPN
ejpam-5617	1	30	business	business	PROPN
ejpam-5617	1	31	global	global	ADJ
ejpam-5617	1	32	employing	employ	VERB
ejpam-5617	1	33	the	the	DET
ejpam-5617	1	34	limit	limit	NOUN
ejpam-5617	1	35	residual	residual	ADJ
ejpam-5617	1	36	function	function	NOUN
ejpam-5617	1	37	method	method	NOUN
ejpam-5617	1	38	to	to	PART
ejpam-5617	1	39	solve	solve	VERB
ejpam-5617	1	40	systems	system	NOUN
ejpam-5617	1	41	of	of	ADP
ejpam-5617	1	42	fractional	fractional	ADJ
ejpam-5617	1	43	differential	differential	ADJ
ejpam-5617	1	44	equations	equation	NOUN
ejpam-5617	1	45	ahmad	ahmad	PROPN
ejpam-5617	1	46	el	el	PROPN
ejpam-5617	1	47	-	-	PROPN
ejpam-5617	1	48	ajou1	ajou1	PROPN
ejpam-5617	1	49	,	,	PUNCT
ejpam-5617	1	50	aliaa	aliaa	PROPN
ejpam-5617	1	51	burqan2,∗	burqan2,∗	PROPN
ejpam-5617	1	52	1	1	NUM
ejpam-5617	1	53	department	department	NOUN
ejpam-5617	1	54	of	of	ADP
ejpam-5617	1	55	mathematics	mathematic	NOUN
ejpam-5617	1	56	,	,	PUNCT
ejpam-5617	1	57	faculty	faculty	NOUN
ejpam-5617	1	58	of	of	ADP
ejpam-5617	1	59	science	science	NOUN
ejpam-5617	1	60	,	,	PUNCT
ejpam-5617	1	61	al	al	PROPN
ejpam-5617	1	62	balqa	balqa	NOUN
ejpam-5617	1	63	applied	apply	VERB
ejpam-5617	1	64	university	university	NOUN
ejpam-5617	1	65	,	,	PUNCT
ejpam-5617	1	66	salt	salt	NOUN
ejpam-5617	1	67	19117	19117	NUM
ejpam-5617	1	68	,	,	PUNCT
ejpam-5617	1	69	jordan	jordan	PROPN
ejpam-5617	1	70	2	2	NUM
ejpam-5617	1	71	department	department	NOUN
ejpam-5617	1	72	of	of	ADP
ejpam-5617	1	73	mathematics	mathematic	NOUN
ejpam-5617	1	74	,	,	PUNCT
ejpam-5617	1	75	faculty	faculty	NOUN
ejpam-5617	1	76	of	of	ADP
ejpam-5617	1	77	science	science	NOUN
ejpam-5617	1	78	,	,	PUNCT
ejpam-5617	1	79	zarqa	zarqa	PROPN
ejpam-5617	1	80	university	university	PROPN
ejpam-5617	1	81	,	,	PUNCT
ejpam-5617	1	82	zarqa	zarqa	PROPN
ejpam-5617	1	83	13110	13110	NUM
ejpam-5617	1	84	,	,	PUNCT
ejpam-5617	1	85	jordan	jordan	PROPN
ejpam-5617	1	86	abstract	abstract	PROPN
ejpam-5617	1	87	.	.	PUNCT
ejpam-5617	2	1	this	this	DET
ejpam-5617	2	2	study	study	NOUN
ejpam-5617	2	3	aims	aim	VERB
ejpam-5617	2	4	to	to	PART
ejpam-5617	2	5	solve	solve	VERB
ejpam-5617	2	6	systems	system	NOUN
ejpam-5617	2	7	of	of	ADP
ejpam-5617	2	8	fractional	fractional	ADJ
ejpam-5617	2	9	differential	differential	ADJ
ejpam-5617	2	10	equations	equation	NOUN
ejpam-5617	2	11	analytically	analytically	ADV
ejpam-5617	2	12	using	use	VERB
ejpam-5617	2	13	a	a	DET
ejpam-5617	2	14	simple	simple	ADJ
ejpam-5617	2	15	new	new	ADJ
ejpam-5617	2	16	technique	technique	NOUN
ejpam-5617	2	17	,	,	PUNCT
ejpam-5617	2	18	the	the	DET
ejpam-5617	2	19	limit	limit	NOUN
ejpam-5617	2	20	residual	residual	ADJ
ejpam-5617	2	21	function	function	NOUN
ejpam-5617	2	22	method	method	NOUN
ejpam-5617	2	23	.	.	PUNCT
ejpam-5617	3	1	this	this	DET
ejpam-5617	3	2	method	method	NOUN
ejpam-5617	3	3	relies	rely	VERB
ejpam-5617	3	4	on	on	ADP
ejpam-5617	3	5	coupling	couple	VERB
ejpam-5617	3	6	the	the	DET
ejpam-5617	3	7	residual	residual	ADJ
ejpam-5617	3	8	function	function	NOUN
ejpam-5617	3	9	with	with	ADP
ejpam-5617	3	10	the	the	DET
ejpam-5617	3	11	limit	limit	NOUN
ejpam-5617	3	12	to	to	PART
ejpam-5617	3	13	produce	produce	VERB
ejpam-5617	3	14	analytical	analytical	ADJ
ejpam-5617	3	15	and	and	CCONJ
ejpam-5617	3	16	approximate	approximate	ADJ
ejpam-5617	3	17	solutions	solution	NOUN
ejpam-5617	3	18	within	within	ADP
ejpam-5617	3	19	rapidly	rapidly	ADV
ejpam-5617	3	20	converging	converge	VERB
ejpam-5617	3	21	series	series	NOUN
ejpam-5617	3	22	forms	form	NOUN
ejpam-5617	3	23	.	.	PUNCT
ejpam-5617	4	1	this	this	DET
ejpam-5617	4	2	technique	technique	NOUN
ejpam-5617	4	3	could	could	AUX
ejpam-5617	4	4	be	be	AUX
ejpam-5617	4	5	an	an	DET
ejpam-5617	4	6	alternative	alternative	NOUN
ejpam-5617	4	7	to	to	ADP
ejpam-5617	4	8	the	the	DET
ejpam-5617	4	9	residual	residual	ADJ
ejpam-5617	4	10	power	power	NOUN
ejpam-5617	4	11	series	series	PROPN
ejpam-5617	4	12	method	method	NOUN
ejpam-5617	4	13	which	which	PRON
ejpam-5617	4	14	is	be	AUX
ejpam-5617	4	15	an	an	DET
ejpam-5617	4	16	efficient	efficient	ADJ
ejpam-5617	4	17	and	and	CCONJ
ejpam-5617	4	18	quick	quick	ADJ
ejpam-5617	4	19	-	-	PUNCT
ejpam-5617	4	20	to	to	ADP
ejpam-5617	4	21	-	-	PUNCT
ejpam-5617	4	22	solve	solve	VERB
ejpam-5617	4	23	system	system	NOUN
ejpam-5617	4	24	of	of	ADP
ejpam-5617	4	25	fractional	fractional	ADJ
ejpam-5617	4	26	differential	differential	ADJ
ejpam-5617	4	27	equations	equation	NOUN
ejpam-5617	4	28	,	,	PUNCT
ejpam-5617	4	29	both	both	CCONJ
ejpam-5617	4	30	linear	linear	ADJ
ejpam-5617	4	31	and	and	CCONJ
ejpam-5617	4	32	nonlinear	nonlinear	ADJ
ejpam-5617	4	33	,	,	PUNCT
ejpam-5617	4	34	that	that	PRON
ejpam-5617	4	35	arise	arise	VERB
ejpam-5617	4	36	in	in	ADP
ejpam-5617	4	37	numerous	numerous	ADJ
ejpam-5617	4	38	physical	physical	ADJ
ejpam-5617	4	39	phenomena	phenomenon	NOUN
ejpam-5617	4	40	.	.	PUNCT
ejpam-5617	5	1	to	to	PART
ejpam-5617	5	2	illustrate	illustrate	VERB
ejpam-5617	5	3	the	the	DET
ejpam-5617	5	4	methodology	methodology	NOUN
ejpam-5617	5	5	and	and	CCONJ
ejpam-5617	5	6	confirm	confirm	VERB
ejpam-5617	5	7	its	its	PRON
ejpam-5617	5	8	effectiveness	effectiveness	NOUN
ejpam-5617	5	9	,	,	PUNCT
ejpam-5617	5	10	the	the	DET
ejpam-5617	5	11	study	study	NOUN
ejpam-5617	5	12	explores	explore	VERB
ejpam-5617	5	13	three	three	NUM
ejpam-5617	5	14	different	different	ADJ
ejpam-5617	5	15	applications	application	NOUN
ejpam-5617	5	16	.	.	PUNCT
ejpam-5617	6	1	the	the	DET
ejpam-5617	6	2	proposed	propose	VERB
ejpam-5617	6	3	algorithm	algorithm	NOUN
ejpam-5617	6	4	’s	’s	PART
ejpam-5617	6	5	reliability	reliability	NOUN
ejpam-5617	6	6	and	and	CCONJ
ejpam-5617	6	7	accuracy	accuracy	NOUN
ejpam-5617	6	8	can	can	AUX
ejpam-5617	6	9	be	be	AUX
ejpam-5617	6	10	easily	easily	ADV
ejpam-5617	6	11	described	describe	VERB
ejpam-5617	6	12	by	by	ADP
ejpam-5617	6	13	contrasting	contrast	VERB
ejpam-5617	6	14	the	the	DET
ejpam-5617	6	15	numerical	numerical	ADJ
ejpam-5617	6	16	results	result	NOUN
ejpam-5617	6	17	with	with	ADP
ejpam-5617	6	18	the	the	DET
ejpam-5617	6	19	exact	exact	ADJ
ejpam-5617	6	20	solutions	solution	NOUN
ejpam-5617	6	21	.	.	PUNCT
ejpam-5617	7	1	2020	2020	NUM
ejpam-5617	7	2	mathematics	mathematic	NOUN
ejpam-5617	7	3	subject	subject	NOUN
ejpam-5617	7	4	classifications	classification	NOUN
ejpam-5617	7	5	:	:	PUNCT
ejpam-5617	7	6	26a33	26a33	NUM
ejpam-5617	7	7	,	,	PUNCT
ejpam-5617	7	8	32a05	32a05	NUM
ejpam-5617	7	9	,	,	PUNCT
ejpam-5617	7	10	34a12	34a12	NUM
ejpam-5617	7	11	key	key	ADJ
ejpam-5617	7	12	words	word	NOUN
ejpam-5617	7	13	and	and	CCONJ
ejpam-5617	7	14	phrases	phrase	NOUN
ejpam-5617	7	15	:	:	PUNCT
ejpam-5617	7	16	fractional	fractional	ADJ
ejpam-5617	7	17	initial	initial	ADJ
ejpam-5617	7	18	value	value	NOUN
ejpam-5617	7	19	problems	problem	NOUN
ejpam-5617	7	20	,	,	PUNCT
ejpam-5617	7	21	fractional	fractional	ADJ
ejpam-5617	7	22	power	power	NOUN
ejpam-5617	7	23	series	series	PROPN
ejpam-5617	7	24	,	,	PUNCT
ejpam-5617	7	25	caputo	caputo	PROPN
ejpam-5617	7	26	’s	’s	PART
ejpam-5617	7	27	derivative	derivative	ADJ
ejpam-5617	7	28	operator	operator	NOUN
ejpam-5617	7	29	,	,	PUNCT
ejpam-5617	7	30	residual	residual	ADJ
ejpam-5617	7	31	function	function	NOUN
ejpam-5617	7	32	1	1	NUM
ejpam-5617	7	33	.	.	PUNCT
ejpam-5617	7	34	introduction	introduction	NOUN
ejpam-5617	7	35	in	in	ADP
ejpam-5617	7	36	applied	applied	ADJ
ejpam-5617	7	37	sciences	science	NOUN
ejpam-5617	7	38	such	such	ADJ
ejpam-5617	7	39	as	as	ADP
ejpam-5617	7	40	applied	applied	ADJ
ejpam-5617	7	41	mathematics	mathematic	NOUN
ejpam-5617	7	42	,	,	PUNCT
ejpam-5617	7	43	mathematical	mathematical	ADJ
ejpam-5617	7	44	biology	biology	NOUN
ejpam-5617	7	45	,	,	PUNCT
ejpam-5617	7	46	physics	physics	NOUN
ejpam-5617	7	47	,	,	PUNCT
ejpam-5617	7	48	and	and	CCONJ
ejpam-5617	7	49	engineering	engineering	NOUN
ejpam-5617	7	50	,	,	PUNCT
ejpam-5617	7	51	fractional	fractional	ADJ
ejpam-5617	7	52	calculus	calculus	NOUN
ejpam-5617	7	53	is	be	AUX
ejpam-5617	7	54	currently	currently	ADV
ejpam-5617	7	55	an	an	DET
ejpam-5617	7	56	area	area	NOUN
ejpam-5617	7	57	of	of	ADP
ejpam-5617	7	58	intense	intense	ADJ
ejpam-5617	7	59	study	study	NOUN
ejpam-5617	7	60	.	.	PUNCT
ejpam-5617	8	1	there	there	PRON
ejpam-5617	8	2	are	be	VERB
ejpam-5617	8	3	multiple	multiple	ADJ
ejpam-5617	8	4	definitions	definition	NOUN
ejpam-5617	8	5	for	for	ADP
ejpam-5617	8	6	the	the	DET
ejpam-5617	8	7	fractional	fractional	ADJ
ejpam-5617	8	8	derivative	derivative	NOUN
ejpam-5617	8	9	,	,	PUNCT
ejpam-5617	8	10	making	make	VERB
ejpam-5617	8	11	it	it	PRON
ejpam-5617	8	12	a	a	DET
ejpam-5617	8	13	non	non	ADJ
ejpam-5617	8	14	-	-	ADJ
ejpam-5617	8	15	unique	unique	ADJ
ejpam-5617	8	16	formula	formula	NOUN
ejpam-5617	8	17	now	now	ADV
ejpam-5617	8	18	.	.	PUNCT
ejpam-5617	9	1	the	the	DET
ejpam-5617	9	2	most	most	ADV
ejpam-5617	9	3	commonly	commonly	ADV
ejpam-5617	9	4	used	use	VERB
ejpam-5617	9	5	definition	definition	NOUN
ejpam-5617	9	6	is	be	AUX
ejpam-5617	9	7	the	the	DET
ejpam-5617	9	8	riemann	riemann	PROPN
ejpam-5617	9	9	-	-	PUNCT
ejpam-5617	9	10	liouville	liouville	NOUN
ejpam-5617	9	11	(	(	PUNCT
ejpam-5617	9	12	r	r	NOUN
ejpam-5617	9	13	-	-	PUNCT
ejpam-5617	9	14	l	l	NOUN
ejpam-5617	9	15	)	)	PUNCT
ejpam-5617	9	16	definition	definition	NOUN
ejpam-5617	9	17	,	,	PUNCT
ejpam-5617	9	18	while	while	SCONJ
ejpam-5617	9	19	caputo	caputo	PROPN
ejpam-5617	9	20	’s	’s	PART
ejpam-5617	9	21	definition	definition	NOUN
ejpam-5617	9	22	(	(	PUNCT
ejpam-5617	9	23	1967	1967	NUM
ejpam-5617	9	24	)	)	PUNCT
ejpam-5617	9	25	of	of	ADP
ejpam-5617	9	26	the	the	DET
ejpam-5617	9	27	fractional	fractional	ADJ
ejpam-5617	9	28	derivative	derivative	NOUN
ejpam-5617	9	29	is	be	AUX
ejpam-5617	9	30	also	also	ADV
ejpam-5617	9	31	widely	widely	ADV
ejpam-5617	9	32	used	use	VERB
ejpam-5617	9	33	[	[	PUNCT
ejpam-5617	9	34	6	6	NUM
ejpam-5617	9	35	,	,	PUNCT
ejpam-5617	9	36	12	12	NUM
ejpam-5617	9	37	,	,	PUNCT
ejpam-5617	9	38	13	13	NUM
ejpam-5617	9	39	,	,	PUNCT
ejpam-5617	9	40	29	29	NUM
ejpam-5617	9	41	,	,	PUNCT
ejpam-5617	9	42	31	31	NUM
ejpam-5617	9	43	,	,	PUNCT
ejpam-5617	9	44	32	32	NUM
ejpam-5617	9	45	,	,	PUNCT
ejpam-5617	9	46	37	37	NUM
ejpam-5617	9	47	]	]	PUNCT
ejpam-5617	9	48	.	.	PUNCT
ejpam-5617	10	1	differential	differential	ADJ
ejpam-5617	10	2	equations	equation	NOUN
ejpam-5617	10	3	of	of	ADP
ejpam-5617	10	4	fractional	fractional	ADJ
ejpam-5617	10	5	order	order	NOUN
ejpam-5617	10	6	have	have	AUX
ejpam-5617	10	7	been	be	AUX
ejpam-5617	10	8	the	the	DET
ejpam-5617	10	9	subject	subject	NOUN
ejpam-5617	10	10	of	of	ADP
ejpam-5617	10	11	several	several	ADJ
ejpam-5617	10	12	investigations	investigation	NOUN
ejpam-5617	10	13	due	due	ADP
ejpam-5617	10	14	to	to	ADP
ejpam-5617	10	15	their	their	PRON
ejpam-5617	10	16	frequent	frequent	ADJ
ejpam-5617	10	17	appearance	appearance	NOUN
ejpam-5617	10	18	in	in	ADP
ejpam-5617	10	19	different	different	ADJ
ejpam-5617	10	20	scientific	scientific	ADJ
ejpam-5617	10	21	applications	application	NOUN
ejpam-5617	10	22	.	.	PUNCT
ejpam-5617	11	1	the	the	DET
ejpam-5617	11	2	differential	differential	ADJ
ejpam-5617	11	3	equations	equation	NOUN
ejpam-5617	11	4	in	in	ADP
ejpam-5617	11	5	several	several	ADJ
ejpam-5617	11	6	forms	form	NOUN
ejpam-5617	11	7	of	of	ADP
ejpam-5617	11	8	fractional	fractional	ADJ
ejpam-5617	11	9	derivatives	derivative	NOUN
ejpam-5617	11	10	give	give	VERB
ejpam-5617	11	11	different	different	ADJ
ejpam-5617	11	12	types	type	NOUN
ejpam-5617	11	13	of	of	ADP
ejpam-5617	11	14	solutions	solution	NOUN
ejpam-5617	11	15	.	.	PUNCT
ejpam-5617	12	1	as	as	ADP
ejpam-5617	12	2	a	a	DET
ejpam-5617	12	3	result	result	NOUN
ejpam-5617	12	4	,	,	PUNCT
ejpam-5617	12	5	fractional	fractional	ADJ
ejpam-5617	12	6	differential	differential	ADJ
ejpam-5617	12	7	equations	equation	NOUN
ejpam-5617	12	8	can	can	AUX
ejpam-5617	12	9	not	not	PART
ejpam-5617	12	10	be	be	AUX
ejpam-5617	12	11	solved	solve	VERB
ejpam-5617	12	12	using	use	VERB
ejpam-5617	12	13	a	a	DET
ejpam-5617	12	14	standard	standard	ADJ
ejpam-5617	12	15	approach	approach	NOUN
ejpam-5617	12	16	.	.	PUNCT
ejpam-5617	13	1	therefore	therefore	ADV
ejpam-5617	13	2	,	,	PUNCT
ejpam-5617	13	3	a	a	DET
ejpam-5617	13	4	rapidly	rapidly	ADV
ejpam-5617	13	5	developing	develop	VERB
ejpam-5617	13	6	field	field	NOUN
ejpam-5617	13	7	of	of	ADP
ejpam-5617	13	8	applied	apply	VERB
ejpam-5617	13	9	mathematics	mathematic	NOUN
ejpam-5617	13	10	is	be	AUX
ejpam-5617	13	11	the	the	DET
ejpam-5617	13	12	interpretation	interpretation	NOUN
ejpam-5617	13	13	and	and	CCONJ
ejpam-5617	13	14	solution	solution	NOUN
ejpam-5617	13	15	of	of	ADP
ejpam-5617	13	16	fractional	fractional	ADJ
ejpam-5617	13	17	differential	differential	ADJ
ejpam-5617	13	18	equations	equation	NOUN
ejpam-5617	13	19	.	.	PUNCT
ejpam-5617	14	1	the	the	DET
ejpam-5617	14	2	predictor	predictor	NOUN
ejpam-5617	14	3	-	-	PUNCT
ejpam-5617	14	4	corrector	corrector	NOUN
ejpam-5617	14	5	approach	approach	NOUN
ejpam-5617	14	6	[	[	X
ejpam-5617	14	7	16	16	NUM
ejpam-5617	14	8	]	]	PUNCT
ejpam-5617	14	9	,	,	PUNCT
ejpam-5617	14	10	the	the	DET
ejpam-5617	14	11	variational	variational	ADJ
ejpam-5617	14	12	∗corresponding	∗corresponding	NOUN
ejpam-5617	14	13	author	author	NOUN
ejpam-5617	14	14	.	.	PUNCT
ejpam-5617	15	1	doi	doi	NOUN
ejpam-5617	15	2	:	:	PUNCT
ejpam-5617	15	3	https://doi.org/10.29020/nybg.ejpam.v18i1.5617	https://doi.org/10.29020/nybg.ejpam.v18i1.5617	PROPN
ejpam-5617	15	4	email	email	NOUN
ejpam-5617	15	5	addresses	address	NOUN
ejpam-5617	15	6	:	:	PUNCT
ejpam-5617	15	7	ajou44@bau.edu.jo	ajou44@bau.edu.jo	NUM
ejpam-5617	15	8	(	(	PUNCT
ejpam-5617	15	9	a.	a.	PROPN
ejpam-5617	15	10	el	el	PROPN
ejpam-5617	15	11	-	-	PUNCT
ejpam-5617	15	12	ajou	ajou	ADJ
ejpam-5617	15	13	)	)	PUNCT
ejpam-5617	15	14	,	,	PUNCT
ejpam-5617	15	15	aliaaburqan@zu.edu.jo	aliaaburqan@zu.edu.jo	PROPN
ejpam-5617	15	16	(	(	PUNCT
ejpam-5617	15	17	a.	a.	NOUN
ejpam-5617	15	18	burqan	burqan	PROPN
ejpam-5617	15	19	)	)	PUNCT
ejpam-5617	15	20	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-5617	16	1	1	1	NUM
ejpam-5617	16	2	copyright	copyright	NOUN
ejpam-5617	16	3	:	:	PUNCT
ejpam-5617	16	4	©	©	PROPN
ejpam-5617	16	5	2025	2025	NUM
ejpam-5617	16	6	the	the	DET
ejpam-5617	16	7	author(s	author(s	NOUN
ejpam-5617	16	8	)	)	PUNCT
ejpam-5617	16	9	.	.	PUNCT
ejpam-5617	17	1	(	(	PUNCT
ejpam-5617	17	2	cc	cc	NOUN
ejpam-5617	17	3	by	by	ADP
ejpam-5617	17	4	-	-	PUNCT
ejpam-5617	17	5	nc	nc	PROPN
ejpam-5617	17	6	4.0	4.0	NUM
ejpam-5617	17	7	)	)	PUNCT
ejpam-5617	17	8	a.	a.	PROPN
ejpam-5617	17	9	el	el	PROPN
ejpam-5617	17	10	-	-	PUNCT
ejpam-5617	17	11	ajou	ajou	PROPN
ejpam-5617	17	12	,	,	PUNCT
ejpam-5617	17	13	a.	a.	PROPN
ejpam-5617	17	14	burqan	burqan	PROPN
ejpam-5617	17	15	/	/	SYM
ejpam-5617	17	16	eur	eur	PROPN
ejpam-5617	17	17	.	.	PUNCT
ejpam-5617	18	1	j.	j.	PROPN
ejpam-5617	18	2	pure	pure	PROPN
ejpam-5617	18	3	appl	appl	PROPN
ejpam-5617	18	4	.	.	PROPN
ejpam-5617	18	5	math	math	PROPN
ejpam-5617	18	6	,	,	PUNCT
ejpam-5617	18	7	18	18	NUM
ejpam-5617	18	8	(	(	PUNCT
ejpam-5617	18	9	1	1	NUM
ejpam-5617	18	10	)	)	PUNCT
ejpam-5617	18	11	(	(	PUNCT
ejpam-5617	18	12	2025	2025	NUM
ejpam-5617	18	13	)	)	PUNCT
ejpam-5617	18	14	,	,	PUNCT
ejpam-5617	18	15	5617	5617	NUM
ejpam-5617	18	16	2	2	NUM
ejpam-5617	18	17	of	of	ADP
ejpam-5617	18	18	19	19	NUM
ejpam-5617	18	19	iteration	iteration	NOUN
ejpam-5617	18	20	approach	approach	NOUN
ejpam-5617	18	21	[	[	X
ejpam-5617	18	22	14	14	NUM
ejpam-5617	18	23	,	,	PUNCT
ejpam-5617	18	24	23	23	NUM
ejpam-5617	18	25	]	]	PUNCT
ejpam-5617	18	26	,	,	PUNCT
ejpam-5617	18	27	the	the	DET
ejpam-5617	18	28	homotopy	homotopy	NOUN
ejpam-5617	18	29	perturbation	perturbation	NOUN
ejpam-5617	18	30	approach	approach	NOUN
ejpam-5617	18	31	[	[	X
ejpam-5617	18	32	21	21	NUM
ejpam-5617	18	33	]	]	PUNCT
ejpam-5617	18	34	,	,	PUNCT
ejpam-5617	18	35	the	the	DET
ejpam-5617	18	36	homotopy	homotopy	NOUN
ejpam-5617	18	37	analysis	analysis	NOUN
ejpam-5617	18	38	method	method	NOUN
ejpam-5617	18	39	[	[	X
ejpam-5617	18	40	22	22	NUM
ejpam-5617	18	41	]	]	PUNCT
ejpam-5617	18	42	,	,	PUNCT
ejpam-5617	18	43	the	the	DET
ejpam-5617	18	44	adomian	adomian	NOUN
ejpam-5617	18	45	decomposition	decomposition	NOUN
ejpam-5617	18	46	method	method	NOUN
ejpam-5617	18	47	[	[	X
ejpam-5617	18	48	1	1	NUM
ejpam-5617	18	49	,	,	PUNCT
ejpam-5617	18	50	26	26	NUM
ejpam-5617	18	51	,	,	PUNCT
ejpam-5617	18	52	28	28	NUM
ejpam-5617	18	53	]	]	PUNCT
ejpam-5617	18	54	,	,	PUNCT
ejpam-5617	18	55	the	the	DET
ejpam-5617	18	56	operational	operational	ADJ
ejpam-5617	18	57	matrix	matrix	NOUN
ejpam-5617	18	58	approach	approach	NOUN
ejpam-5617	18	59	[	[	X
ejpam-5617	18	60	34	34	NUM
ejpam-5617	18	61	]	]	PUNCT
ejpam-5617	18	62	,	,	PUNCT
ejpam-5617	18	63	the	the	DET
ejpam-5617	18	64	residual	residual	ADJ
ejpam-5617	18	65	power	power	NOUN
ejpam-5617	18	66	series	series	NOUN
ejpam-5617	18	67	method	method	NOUN
ejpam-5617	18	68	[	[	X
ejpam-5617	18	69	15	15	NUM
ejpam-5617	18	70	,	,	PUNCT
ejpam-5617	18	71	20	20	NUM
ejpam-5617	18	72	,	,	PUNCT
ejpam-5617	18	73	30	30	NUM
ejpam-5617	18	74	]	]	PUNCT
ejpam-5617	18	75	,	,	PUNCT
ejpam-5617	18	76	the	the	DET
ejpam-5617	18	77	laplace	laplace	NOUN
ejpam-5617	18	78	residual	residual	ADJ
ejpam-5617	18	79	power	power	NOUN
ejpam-5617	18	80	series	series	PROPN
ejpam-5617	18	81	method	method	NOUN
ejpam-5617	18	82	[	[	X
ejpam-5617	18	83	3	3	NUM
ejpam-5617	18	84	,	,	PUNCT
ejpam-5617	18	85	9	9	NUM
ejpam-5617	18	86	,	,	PUNCT
ejpam-5617	18	87	10	10	NUM
ejpam-5617	18	88	,	,	PUNCT
ejpam-5617	18	89	27	27	NUM
ejpam-5617	18	90	,	,	PUNCT
ejpam-5617	18	91	36	36	NUM
ejpam-5617	18	92	]	]	PUNCT
ejpam-5617	18	93	,	,	PUNCT
ejpam-5617	18	94	the	the	DET
ejpam-5617	18	95	differential	differential	ADJ
ejpam-5617	18	96	transformation	transformation	NOUN
ejpam-5617	18	97	technique	technique	NOUN
ejpam-5617	18	98	[	[	X
ejpam-5617	18	99	11	11	NUM
ejpam-5617	18	100	]	]	PUNCT
ejpam-5617	18	101	,	,	PUNCT
ejpam-5617	18	102	and	and	CCONJ
ejpam-5617	18	103	the	the	DET
ejpam-5617	18	104	taylor	taylor	PROPN
ejpam-5617	18	105	series	series	PROPN
ejpam-5617	18	106	method	method	NOUN
ejpam-5617	19	1	[	[	X
ejpam-5617	19	2	25	25	NUM
ejpam-5617	19	3	]	]	PUNCT
ejpam-5617	19	4	,	,	PUNCT
ejpam-5617	19	5	are	be	AUX
ejpam-5617	19	6	newly	newly	ADV
ejpam-5617	19	7	employed	employ	VERB
ejpam-5617	19	8	techniques	technique	NOUN
ejpam-5617	19	9	for	for	ADP
ejpam-5617	19	10	solving	solve	VERB
ejpam-5617	19	11	linear	linear	NOUN
ejpam-5617	19	12	and	and	CCONJ
ejpam-5617	19	13	nonlinear	nonlinear	ADJ
ejpam-5617	19	14	differential	differential	ADJ
ejpam-5617	19	15	equations	equation	NOUN
ejpam-5617	19	16	.	.	PUNCT
ejpam-5617	20	1	recently	recently	ADV
ejpam-5617	20	2	,	,	PUNCT
ejpam-5617	20	3	el	el	PROPN
ejpam-5617	20	4	-	-	PUNCT
ejpam-5617	20	5	ajou	ajou	VERB
ejpam-5617	20	6	and	and	CCONJ
ejpam-5617	20	7	burgan	burgan	NOUN
ejpam-5617	20	8	introduced	introduce	VERB
ejpam-5617	20	9	the	the	DET
ejpam-5617	20	10	limit	limit	NOUN
ejpam-5617	20	11	residual	residual	ADJ
ejpam-5617	20	12	function	function	NOUN
ejpam-5617	20	13	(	(	PUNCT
ejpam-5617	20	14	lrf	lrf	NOUN
ejpam-5617	20	15	)	)	PUNCT
ejpam-5617	20	16	method	method	NOUN
ejpam-5617	20	17	[	[	X
ejpam-5617	20	18	18	18	NUM
ejpam-5617	20	19	,	,	PUNCT
ejpam-5617	20	20	19	19	NUM
ejpam-5617	20	21	]	]	PUNCT
ejpam-5617	20	22	to	to	PART
ejpam-5617	20	23	find	find	VERB
ejpam-5617	20	24	analytical	analytical	ADJ
ejpam-5617	20	25	series	series	NOUN
ejpam-5617	20	26	solutions	solution	NOUN
ejpam-5617	20	27	for	for	ADP
ejpam-5617	20	28	linear	linear	ADJ
ejpam-5617	20	29	and	and	CCONJ
ejpam-5617	20	30	nonlinear	nonlinear	ADJ
ejpam-5617	20	31	partial	partial	ADJ
ejpam-5617	20	32	differential	differential	NOUN
ejpam-5617	20	33	equations	equation	NOUN
ejpam-5617	20	34	.	.	PUNCT
ejpam-5617	21	1	the	the	DET
ejpam-5617	21	2	lrf	lrf	NOUN
ejpam-5617	21	3	approach	approach	NOUN
ejpam-5617	21	4	is	be	AUX
ejpam-5617	21	5	a	a	DET
ejpam-5617	21	6	semi	semi	ADJ
ejpam-5617	21	7	-	-	ADJ
ejpam-5617	21	8	analytical	analytical	ADJ
ejpam-5617	21	9	technique	technique	NOUN
ejpam-5617	21	10	that	that	PRON
ejpam-5617	21	11	constructs	construct	VERB
ejpam-5617	21	12	an	an	DET
ejpam-5617	21	13	analytical	analytical	ADJ
ejpam-5617	21	14	solution	solution	NOUN
ejpam-5617	21	15	using	use	VERB
ejpam-5617	21	16	polynomials	polynomial	NOUN
ejpam-5617	21	17	based	base	VERB
ejpam-5617	21	18	on	on	ADP
ejpam-5617	21	19	power	power	NOUN
ejpam-5617	21	20	series	series	PROPN
ejpam-5617	21	21	(	(	PUNCT
ejpam-5617	21	22	ps	ps	NOUN
ejpam-5617	21	23	)	)	PUNCT
ejpam-5617	21	24	expansion	expansion	NOUN
ejpam-5617	21	25	,	,	PUNCT
ejpam-5617	21	26	with	with	ADP
ejpam-5617	21	27	the	the	DET
ejpam-5617	21	28	series	series	NOUN
ejpam-5617	21	29	coefficients	coefficient	NOUN
ejpam-5617	21	30	determined	determine	VERB
ejpam-5617	21	31	by	by	ADP
ejpam-5617	21	32	calculating	calculate	VERB
ejpam-5617	21	33	the	the	DET
ejpam-5617	21	34	limit	limit	NOUN
ejpam-5617	21	35	of	of	ADP
ejpam-5617	21	36	the	the	DET
ejpam-5617	21	37	residual	residual	ADJ
ejpam-5617	21	38	functions	function	NOUN
ejpam-5617	21	39	.	.	PUNCT
ejpam-5617	22	1	indeed	indeed	ADV
ejpam-5617	22	2	,	,	PUNCT
ejpam-5617	22	3	the	the	DET
ejpam-5617	22	4	lrf	lrf	NOUN
ejpam-5617	22	5	offers	offer	VERB
ejpam-5617	22	6	a	a	DET
ejpam-5617	22	7	power	power	NOUN
ejpam-5617	22	8	series	series	NOUN
ejpam-5617	22	9	solution	solution	NOUN
ejpam-5617	22	10	for	for	ADP
ejpam-5617	22	11	differential	differential	ADJ
ejpam-5617	22	12	equations	equation	NOUN
ejpam-5617	22	13	that	that	PRON
ejpam-5617	22	14	is	be	AUX
ejpam-5617	22	15	the	the	DET
ejpam-5617	22	16	same	same	ADJ
ejpam-5617	22	17	as	as	ADP
ejpam-5617	22	18	the	the	DET
ejpam-5617	22	19	taylor	taylor	PROPN
ejpam-5617	22	20	series	series	PROPN
ejpam-5617	22	21	solution	solution	NOUN
ejpam-5617	22	22	.	.	PUNCT
ejpam-5617	23	1	lrf	lrf	NOUN
ejpam-5617	23	2	is	be	AUX
ejpam-5617	23	3	just	just	ADV
ejpam-5617	23	4	a	a	DET
ejpam-5617	23	5	new	new	ADJ
ejpam-5617	23	6	,	,	PUNCT
ejpam-5617	23	7	simple	simple	ADJ
ejpam-5617	23	8	,	,	PUNCT
ejpam-5617	23	9	and	and	CCONJ
ejpam-5617	23	10	efficient	efficient	ADJ
ejpam-5617	23	11	technique	technique	NOUN
ejpam-5617	23	12	for	for	ADP
ejpam-5617	23	13	determining	determine	VERB
ejpam-5617	23	14	the	the	DET
ejpam-5617	23	15	coefficients	coefficient	NOUN
ejpam-5617	23	16	of	of	ADP
ejpam-5617	23	17	the	the	DET
ejpam-5617	23	18	taylor	taylor	PROPN
ejpam-5617	23	19	series	series	PROPN
ejpam-5617	23	20	.	.	PUNCT
ejpam-5617	24	1	on	on	ADP
ejpam-5617	24	2	the	the	DET
ejpam-5617	24	3	other	other	ADJ
ejpam-5617	24	4	hand	hand	NOUN
ejpam-5617	24	5	,	,	PUNCT
ejpam-5617	24	6	much	much	ADJ
ejpam-5617	24	7	literature	literature	NOUN
ejpam-5617	24	8	has	have	AUX
ejpam-5617	24	9	developed	develop	VERB
ejpam-5617	24	10	concerning	concern	VERB
ejpam-5617	24	11	the	the	DET
ejpam-5617	24	12	fractional	fractional	ADJ
ejpam-5617	24	13	system	system	NOUN
ejpam-5617	24	14	of	of	ADP
ejpam-5617	24	15	differential	differential	ADJ
ejpam-5617	24	16	equations	equation	NOUN
ejpam-5617	24	17	and	and	CCONJ
ejpam-5617	24	18	its	its	PRON
ejpam-5617	24	19	applications	application	NOUN
ejpam-5617	24	20	[	[	X
ejpam-5617	24	21	1	1	NUM
ejpam-5617	24	22	,	,	PUNCT
ejpam-5617	24	23	2	2	NUM
ejpam-5617	24	24	,	,	PUNCT
ejpam-5617	24	25	4	4	NUM
ejpam-5617	24	26	,	,	PUNCT
ejpam-5617	24	27	5	5	NUM
ejpam-5617	24	28	,	,	PUNCT
ejpam-5617	24	29	26	26	NUM
ejpam-5617	24	30	,	,	PUNCT
ejpam-5617	24	31	35	35	NUM
ejpam-5617	24	32	]	]	PUNCT
ejpam-5617	24	33	.	.	PUNCT
ejpam-5617	25	1	in	in	ADP
ejpam-5617	25	2	this	this	DET
ejpam-5617	25	3	article	article	NOUN
ejpam-5617	25	4	,	,	PUNCT
ejpam-5617	25	5	we	we	PRON
ejpam-5617	25	6	present	present	VERB
ejpam-5617	25	7	a	a	DET
ejpam-5617	25	8	new	new	ADJ
ejpam-5617	25	9	application	application	NOUN
ejpam-5617	25	10	of	of	ADP
ejpam-5617	25	11	the	the	DET
ejpam-5617	25	12	lrf	lrf	NOUN
ejpam-5617	25	13	technique	technique	NOUN
ejpam-5617	25	14	to	to	PART
ejpam-5617	25	15	yield	yield	VERB
ejpam-5617	25	16	approximate	approximate	ADJ
ejpam-5617	25	17	solutions	solution	NOUN
ejpam-5617	25	18	for	for	ADP
ejpam-5617	25	19	the	the	DET
ejpam-5617	25	20	system	system	NOUN
ejpam-5617	25	21	of	of	ADP
ejpam-5617	25	22	fractional	fractional	ADJ
ejpam-5617	25	23	differential	differential	ADJ
ejpam-5617	25	24	equations	equation	NOUN
ejpam-5617	25	25	on	on	ADP
ejpam-5617	25	26	the	the	DET
ejpam-5617	25	27	form	form	NOUN
ejpam-5617	25	28	dαu1	dαu1	NOUN
ejpam-5617	25	29	(	(	PUNCT
ejpam-5617	25	30	x	x	X
ejpam-5617	25	31	)	)	PUNCT
ejpam-5617	25	32	=	=	SYM
ejpam-5617	25	33	h1	h1	ADJ
ejpam-5617	25	34	(	(	PUNCT
ejpam-5617	25	35	x	x	NOUN
ejpam-5617	25	36	,	,	PUNCT
ejpam-5617	25	37	u1	u1	NOUN
ejpam-5617	25	38	(	(	PUNCT
ejpam-5617	25	39	x	x	NOUN
ejpam-5617	25	40	)	)	PUNCT
ejpam-5617	25	41	,	,	PUNCT
ejpam-5617	25	42	u2	u2	PROPN
ejpam-5617	25	43	(	(	PUNCT
ejpam-5617	25	44	x	x	NOUN
ejpam-5617	25	45	)	)	PUNCT
ejpam-5617	25	46	,	,	PUNCT
ejpam-5617	25	47	.	.	PUNCT
ejpam-5617	25	48	.	.	PUNCT
ejpam-5617	25	49	.	.	PUNCT
ejpam-5617	26	1	,	,	PUNCT
ejpam-5617	26	2	un	un	PROPN
ejpam-5617	26	3	(	(	PUNCT
ejpam-5617	26	4	x	x	NOUN
ejpam-5617	26	5	)	)	PUNCT
ejpam-5617	26	6	)	)	PUNCT
ejpam-5617	26	7	,	,	PUNCT
ejpam-5617	26	8	dαu2	dαu2	PROPN
ejpam-5617	26	9	(	(	PUNCT
ejpam-5617	26	10	x	x	NOUN
ejpam-5617	26	11	)	)	PUNCT
ejpam-5617	26	12	=	=	SYM
ejpam-5617	26	13	h2	h2	NOUN
ejpam-5617	26	14	(	(	PUNCT
ejpam-5617	26	15	x	x	NOUN
ejpam-5617	26	16	,	,	PUNCT
ejpam-5617	26	17	u1	u1	NOUN
ejpam-5617	26	18	(	(	PUNCT
ejpam-5617	26	19	x	x	NOUN
ejpam-5617	26	20	)	)	PUNCT
ejpam-5617	26	21	,	,	PUNCT
ejpam-5617	26	22	u2	u2	PROPN
ejpam-5617	26	23	(	(	PUNCT
ejpam-5617	26	24	x	x	NOUN
ejpam-5617	26	25	)	)	PUNCT
ejpam-5617	26	26	,	,	PUNCT
ejpam-5617	26	27	.	.	PUNCT
ejpam-5617	26	28	.	.	PUNCT
ejpam-5617	26	29	.	.	PUNCT
ejpam-5617	27	1	,	,	PUNCT
ejpam-5617	27	2	un	un	PROPN
ejpam-5617	27	3	(	(	PUNCT
ejpam-5617	27	4	x	x	NOUN
ejpam-5617	27	5	)	)	PUNCT
ejpam-5617	27	6	)	)	PUNCT
ejpam-5617	27	7	,	,	PUNCT
ejpam-5617	27	8	...	...	PUNCT
ejpam-5617	27	9	dαun	dαun	NOUN
ejpam-5617	27	10	(	(	PUNCT
ejpam-5617	27	11	x	x	X
ejpam-5617	27	12	)	)	PUNCT
ejpam-5617	27	13	=	=	SYM
ejpam-5617	27	14	h1	h1	ADJ
ejpam-5617	27	15	(	(	PUNCT
ejpam-5617	27	16	x	x	NOUN
ejpam-5617	27	17	,	,	PUNCT
ejpam-5617	27	18	u1	u1	NOUN
ejpam-5617	27	19	(	(	PUNCT
ejpam-5617	27	20	x	x	NOUN
ejpam-5617	27	21	)	)	PUNCT
ejpam-5617	27	22	,	,	PUNCT
ejpam-5617	27	23	u2	u2	PROPN
ejpam-5617	27	24	(	(	PUNCT
ejpam-5617	27	25	x	x	NOUN
ejpam-5617	27	26	)	)	PUNCT
ejpam-5617	27	27	,	,	PUNCT
ejpam-5617	27	28	.	.	PUNCT
ejpam-5617	27	29	.	.	PUNCT
ejpam-5617	27	30	.	.	PUNCT
ejpam-5617	28	1	,	,	PUNCT
ejpam-5617	28	2	un	un	PROPN
ejpam-5617	28	3	(	(	PUNCT
ejpam-5617	28	4	x	x	NOUN
ejpam-5617	28	5	)	)	PUNCT
ejpam-5617	28	6	)	)	PUNCT
ejpam-5617	28	7	,	,	PUNCT
ejpam-5617	28	8	(	(	PUNCT
ejpam-5617	28	9	1	1	X
ejpam-5617	28	10	)	)	PUNCT
ejpam-5617	28	11	where	where	SCONJ
ejpam-5617	28	12	dα	dα	VERB
ejpam-5617	28	13	,	,	PUNCT
ejpam-5617	28	14	0	0	NUM
ejpam-5617	28	15	<	<	X
ejpam-5617	28	16	α	α	PROPN
ejpam-5617	28	17	≤	≤	ADJ
ejpam-5617	28	18	1	1	NUM
ejpam-5617	28	19	is	be	AUX
ejpam-5617	28	20	the	the	DET
ejpam-5617	28	21	derivative	derivative	NOUN
ejpam-5617	28	22	of	of	ADP
ejpam-5617	28	23	order	order	NOUN
ejpam-5617	28	24	α	α	NOUN
ejpam-5617	28	25	in	in	ADP
ejpam-5617	28	26	the	the	DET
ejpam-5617	28	27	sense	sense	NOUN
ejpam-5617	28	28	of	of	ADP
ejpam-5617	28	29	caputo	caputo	PROPN
ejpam-5617	28	30	,	,	PUNCT
ejpam-5617	28	31	subject	subject	ADJ
ejpam-5617	28	32	to	to	ADP
ejpam-5617	28	33	the	the	DET
ejpam-5617	28	34	initial	initial	ADJ
ejpam-5617	28	35	conditions	condition	NOUN
ejpam-5617	28	36	u1	u1	NOUN
ejpam-5617	28	37	(	(	PUNCT
ejpam-5617	28	38	0	0	NUM
ejpam-5617	28	39	)	)	PUNCT
ejpam-5617	28	40	=	=	SYM
ejpam-5617	29	1	u1,0	u1,0	PROPN
ejpam-5617	29	2	,	,	PUNCT
ejpam-5617	29	3	u2	u2	NOUN
ejpam-5617	29	4	(	(	PUNCT
ejpam-5617	29	5	0	0	NUM
ejpam-5617	29	6	)	)	PUNCT
ejpam-5617	29	7	=	=	SYM
ejpam-5617	29	8	u2,0	u2,0	PROPN
ejpam-5617	29	9	,	,	PUNCT
ejpam-5617	29	10	.	.	PUNCT
ejpam-5617	29	11	.	.	PUNCT
ejpam-5617	29	12	.	.	PUNCT
ejpam-5617	30	1	,	,	PUNCT
ejpam-5617	30	2	un	un	PROPN
ejpam-5617	30	3	(	(	PUNCT
ejpam-5617	30	4	0	0	NUM
ejpam-5617	30	5	)	)	PUNCT
ejpam-5617	30	6	=	=	SYM
ejpam-5617	30	7	un,0	un,0	PROPN
ejpam-5617	30	8	.	.	PUNCT
ejpam-5617	31	1	the	the	DET
ejpam-5617	31	2	structure	structure	NOUN
ejpam-5617	31	3	of	of	ADP
ejpam-5617	31	4	this	this	DET
ejpam-5617	31	5	paper	paper	NOUN
ejpam-5617	31	6	is	be	AUX
ejpam-5617	31	7	as	as	SCONJ
ejpam-5617	31	8	follows	follow	VERB
ejpam-5617	31	9	:	:	PUNCT
ejpam-5617	31	10	section	section	NOUN
ejpam-5617	31	11	2	2	NUM
ejpam-5617	31	12	revisits	revisit	VERB
ejpam-5617	31	13	several	several	ADJ
ejpam-5617	31	14	important	important	ADJ
ejpam-5617	31	15	fundamental	fundamental	ADJ
ejpam-5617	31	16	results	result	NOUN
ejpam-5617	31	17	of	of	ADP
ejpam-5617	31	18	fractional	fractional	ADJ
ejpam-5617	31	19	calculus	calculus	NOUN
ejpam-5617	31	20	and	and	CCONJ
ejpam-5617	31	21	fractional	fractional	ADJ
ejpam-5617	31	22	ps	ps	PROPN
ejpam-5617	31	23	.	.	PROPN
ejpam-5617	31	24	section	section	NOUN
ejpam-5617	31	25	3	3	NUM
ejpam-5617	31	26	provides	provide	VERB
ejpam-5617	31	27	an	an	DET
ejpam-5617	31	28	overview	overview	NOUN
ejpam-5617	31	29	of	of	ADP
ejpam-5617	31	30	the	the	DET
ejpam-5617	31	31	suggested	suggest	VERB
ejpam-5617	31	32	method	method	NOUN
ejpam-5617	31	33	for	for	ADP
ejpam-5617	31	34	solving	solve	VERB
ejpam-5617	31	35	the	the	DET
ejpam-5617	31	36	system	system	NOUN
ejpam-5617	31	37	of	of	ADP
ejpam-5617	31	38	fractional	fractional	ADJ
ejpam-5617	31	39	differential	differential	ADJ
ejpam-5617	31	40	equations	equation	NOUN
ejpam-5617	31	41	.	.	PUNCT
ejpam-5617	32	1	in	in	ADP
ejpam-5617	32	2	section	section	NOUN
ejpam-5617	32	3	4	4	NUM
ejpam-5617	32	4	,	,	PUNCT
ejpam-5617	32	5	three	three	NUM
ejpam-5617	32	6	systems	system	NOUN
ejpam-5617	32	7	of	of	ADP
ejpam-5617	32	8	fractional	fractional	ADJ
ejpam-5617	32	9	initial	initial	ADJ
ejpam-5617	32	10	value	value	NOUN
ejpam-5617	32	11	problems	problem	NOUN
ejpam-5617	32	12	are	be	AUX
ejpam-5617	32	13	solved	solve	VERB
ejpam-5617	32	14	to	to	PART
ejpam-5617	32	15	explore	explore	VERB
ejpam-5617	32	16	the	the	DET
ejpam-5617	32	17	applicability	applicability	NOUN
ejpam-5617	32	18	and	and	CCONJ
ejpam-5617	32	19	simplicity	simplicity	NOUN
ejpam-5617	32	20	of	of	ADP
ejpam-5617	32	21	the	the	DET
ejpam-5617	32	22	lrf	lrf	NOUN
ejpam-5617	32	23	technique	technique	NOUN
ejpam-5617	32	24	.	.	PUNCT
ejpam-5617	33	1	section	section	NOUN
ejpam-5617	33	2	5	5	NUM
ejpam-5617	33	3	provides	provide	VERB
ejpam-5617	33	4	the	the	DET
ejpam-5617	33	5	conclusion	conclusion	NOUN
ejpam-5617	33	6	.	.	PUNCT
ejpam-5617	34	1	2	2	X
ejpam-5617	34	2	.	.	X
ejpam-5617	34	3	essential	essential	ADJ
ejpam-5617	34	4	preliminaries	preliminary	NOUN
ejpam-5617	34	5	and	and	CCONJ
ejpam-5617	34	6	notations	notation	NOUN
ejpam-5617	34	7	this	this	DET
ejpam-5617	34	8	section	section	NOUN
ejpam-5617	34	9	revisits	revisit	VERB
ejpam-5617	34	10	several	several	ADJ
ejpam-5617	34	11	important	important	ADJ
ejpam-5617	34	12	fundamental	fundamental	ADJ
ejpam-5617	34	13	results	result	NOUN
ejpam-5617	34	14	about	about	ADP
ejpam-5617	34	15	the	the	DET
ejpam-5617	34	16	fractional	fractional	ADJ
ejpam-5617	34	17	ps	ps	PROPN
ejpam-5617	34	18	,	,	PUNCT
ejpam-5617	34	19	essential	essential	ADJ
ejpam-5617	34	20	,	,	PUNCT
ejpam-5617	34	21	to	to	ADP
ejpam-5617	34	22	developing	develop	VERB
ejpam-5617	34	23	analytical	analytical	ADJ
ejpam-5617	34	24	solutions	solution	NOUN
ejpam-5617	34	25	for	for	ADP
ejpam-5617	34	26	systems	system	NOUN
ejpam-5617	34	27	of	of	ADP
ejpam-5617	34	28	fractional	fractional	ADJ
ejpam-5617	34	29	differential	differential	ADJ
ejpam-5617	34	30	equations	equation	NOUN
ejpam-5617	34	31	using	use	VERB
ejpam-5617	34	32	the	the	DET
ejpam-5617	34	33	lrf	lrf	NOUN
ejpam-5617	34	34	method	method	NOUN
ejpam-5617	34	35	.	.	PUNCT
ejpam-5617	35	1	there	there	PRON
ejpam-5617	35	2	are	be	VERB
ejpam-5617	35	3	many	many	ADJ
ejpam-5617	35	4	definitions	definition	NOUN
ejpam-5617	35	5	of	of	ADP
ejpam-5617	35	6	fractional	fractional	ADJ
ejpam-5617	35	7	derivatives	derivative	NOUN
ejpam-5617	35	8	in	in	ADP
ejpam-5617	35	9	the	the	DET
ejpam-5617	35	10	mathematical	mathematical	ADJ
ejpam-5617	35	11	literature	literature	NOUN
ejpam-5617	35	12	,	,	PUNCT
ejpam-5617	35	13	such	such	ADJ
ejpam-5617	35	14	as	as	ADP
ejpam-5617	35	15	the	the	DET
ejpam-5617	35	16	riemann	riemann	PROPN
ejpam-5617	35	17	–	–	PUNCT
ejpam-5617	35	18	liouville	liouville	VERB
ejpam-5617	35	19	fractional	fractional	ADJ
ejpam-5617	35	20	derivative	derivative	NOUN
ejpam-5617	35	21	,	,	PUNCT
ejpam-5617	35	22	caputo	caputo	PROPN
ejpam-5617	35	23	fractional	fractional	PROPN
ejpam-5617	35	24	derivative	derivative	ADJ
ejpam-5617	35	25	,	,	PUNCT
ejpam-5617	35	26	grünwald	grünwald	ADJ
ejpam-5617	35	27	–	–	PUNCT
ejpam-5617	35	28	letnikov	letnikov	ADJ
ejpam-5617	35	29	fractional	fractional	ADJ
ejpam-5617	35	30	derivative	derivative	NOUN
ejpam-5617	36	1	[	[	X
ejpam-5617	36	2	12	12	NUM
ejpam-5617	36	3	,	,	PUNCT
ejpam-5617	36	4	31	31	NUM
ejpam-5617	36	5	]	]	PUNCT
ejpam-5617	36	6	,	,	PUNCT
ejpam-5617	36	7	the	the	DET
ejpam-5617	36	8	two	two	NUM
ejpam-5617	36	9	-	-	PUNCT
ejpam-5617	36	10	scale	scale	NOUN
ejpam-5617	36	11	fractal	fractal	ADJ
ejpam-5617	36	12	derivative	derivative	NOUN
ejpam-5617	36	13	[	[	X
ejpam-5617	36	14	7	7	NUM
ejpam-5617	36	15	]	]	PUNCT
ejpam-5617	36	16	,	,	PUNCT
ejpam-5617	36	17	he	he	PRON
ejpam-5617	36	18	’s	’	VERB
ejpam-5617	36	19	fractional	fractional	ADJ
ejpam-5617	36	20	derivative	derivative	ADJ
ejpam-5617	37	1	[	[	X
ejpam-5617	37	2	24	24	NUM
ejpam-5617	37	3	]	]	PUNCT
ejpam-5617	37	4	,	,	PUNCT
ejpam-5617	37	5	conformable	conformable	ADJ
ejpam-5617	37	6	fractional	fractional	ADJ
ejpam-5617	37	7	derivatives	derivative	NOUN
ejpam-5617	37	8	,	,	PUNCT
ejpam-5617	37	9	and	and	CCONJ
ejpam-5617	37	10	atanganabaleanu	atanganabaleanu	PROPN
ejpam-5617	37	11	’s	’s	PART
ejpam-5617	37	12	fractional	fractional	ADJ
ejpam-5617	37	13	derivative	derivative	ADJ
ejpam-5617	37	14	[	[	X
ejpam-5617	37	15	8	8	NUM
ejpam-5617	37	16	]	]	PUNCT
ejpam-5617	37	17	.	.	PUNCT
ejpam-5617	38	1	this	this	DET
ejpam-5617	38	2	article	article	NOUN
ejpam-5617	38	3	focuses	focus	VERB
ejpam-5617	38	4	on	on	ADP
ejpam-5617	38	5	the	the	DET
ejpam-5617	38	6	caputo	caputo	PROPN
ejpam-5617	38	7	derivative	derivative	NOUN
ejpam-5617	38	8	of	of	ADP
ejpam-5617	38	9	order	order	NOUN
ejpam-5617	38	10	α	α	PRON
ejpam-5617	38	11	defined	define	VERB
ejpam-5617	38	12	for	for	ADP
ejpam-5617	38	13	the	the	DET
ejpam-5617	38	14	function	function	NOUN
ejpam-5617	38	15	u(x	u(x	NOUN
ejpam-5617	38	16	)	)	PUNCT
ejpam-5617	38	17	as	as	ADP
ejpam-5617	38	18	in	in	ADP
ejpam-5617	38	19	the	the	DET
ejpam-5617	38	20	next	next	ADJ
ejpam-5617	38	21	definition	definition	NOUN
ejpam-5617	38	22	.	.	PUNCT
ejpam-5617	39	1	in	in	ADP
ejpam-5617	39	2	the	the	DET
ejpam-5617	39	3	future	future	NOUN
ejpam-5617	39	4	,	,	PUNCT
ejpam-5617	39	5	researchers	researcher	NOUN
ejpam-5617	39	6	may	may	AUX
ejpam-5617	39	7	be	be	AUX
ejpam-5617	39	8	a.	a.	PROPN
ejpam-5617	39	9	el	el	PROPN
ejpam-5617	39	10	-	-	PUNCT
ejpam-5617	39	11	ajou	ajou	PROPN
ejpam-5617	39	12	,	,	PUNCT
ejpam-5617	39	13	a.	a.	PROPN
ejpam-5617	39	14	burqan	burqan	PROPN
ejpam-5617	39	15	/	/	SYM
ejpam-5617	39	16	eur	eur	PROPN
ejpam-5617	39	17	.	.	PUNCT
ejpam-5617	40	1	j.	j.	PROPN
ejpam-5617	40	2	pure	pure	PROPN
ejpam-5617	40	3	appl	appl	PROPN
ejpam-5617	40	4	.	.	PROPN
ejpam-5617	40	5	math	math	PROPN
ejpam-5617	40	6	,	,	PUNCT
ejpam-5617	40	7	18	18	NUM
ejpam-5617	40	8	(	(	PUNCT
ejpam-5617	40	9	1	1	NUM
ejpam-5617	40	10	)	)	PUNCT
ejpam-5617	40	11	(	(	PUNCT
ejpam-5617	40	12	2025	2025	NUM
ejpam-5617	40	13	)	)	PUNCT
ejpam-5617	40	14	,	,	PUNCT
ejpam-5617	40	15	5617	5617	NUM
ejpam-5617	40	16	3	3	NUM
ejpam-5617	40	17	of	of	ADP
ejpam-5617	40	18	19	19	NUM
ejpam-5617	40	19	able	able	ADJ
ejpam-5617	40	20	to	to	PART
ejpam-5617	40	21	adapt	adapt	VERB
ejpam-5617	40	22	the	the	DET
ejpam-5617	40	23	lrf	lrf	NOUN
ejpam-5617	40	24	method	method	NOUN
ejpam-5617	40	25	to	to	PART
ejpam-5617	40	26	solve	solve	VERB
ejpam-5617	40	27	fractional	fractional	ADJ
ejpam-5617	40	28	differential	differential	NOUN
ejpam-5617	40	29	equations	equation	NOUN
ejpam-5617	40	30	using	use	VERB
ejpam-5617	40	31	other	other	ADJ
ejpam-5617	40	32	types	type	NOUN
ejpam-5617	40	33	of	of	ADP
ejpam-5617	40	34	fractional	fractional	ADJ
ejpam-5617	40	35	derivatives	derivative	NOUN
ejpam-5617	40	36	.	.	PUNCT
ejpam-5617	41	1	definition	definition	NOUN
ejpam-5617	41	2	2.1	2.1	NUM
ejpam-5617	41	3	.	.	PUNCT
ejpam-5617	42	1	[	[	X
ejpam-5617	42	2	12	12	NUM
ejpam-5617	42	3	,	,	PUNCT
ejpam-5617	42	4	31	31	NUM
ejpam-5617	42	5	]	]	PUNCT
ejpam-5617	42	6	the	the	DET
ejpam-5617	42	7	caputo	caputo	PROPN
ejpam-5617	42	8	derivative	derivative	NOUN
ejpam-5617	42	9	of	of	ADP
ejpam-5617	42	10	order	order	NOUN
ejpam-5617	42	11	α	α	X
ejpam-5617	42	12	∈	∈	PROPN
ejpam-5617	42	13	(	(	PUNCT
ejpam-5617	42	14	m	m	NOUN
ejpam-5617	42	15	−	−	PROPN
ejpam-5617	42	16	1,m	1,m	NOUN
ejpam-5617	42	17	]	]	X
ejpam-5617	42	18	,	,	PUNCT
ejpam-5617	42	19	m∈n	m∈n	NOUN
ejpam-5617	42	20	of	of	ADP
ejpam-5617	42	21	the	the	DET
ejpam-5617	42	22	function	function	NOUN
ejpam-5617	42	23	u	u	NOUN
ejpam-5617	42	24	(	(	PUNCT
ejpam-5617	42	25	x	x	X
ejpam-5617	42	26	)	)	PUNCT
ejpam-5617	42	27	is	be	AUX
ejpam-5617	42	28	defined	define	VERB
ejpam-5617	42	29	as	as	SCONJ
ejpam-5617	42	30	follows	follow	VERB
ejpam-5617	42	31	:	:	PUNCT
ejpam-5617	42	32	dαu	dαu	ADJ
ejpam-5617	42	33	(	(	PUNCT
ejpam-5617	42	34	x	x	X
ejpam-5617	42	35	)	)	PUNCT
ejpam-5617	43	1	=	=	SYM
ejpam-5617	43	2	{	{	PUNCT
ejpam-5617	43	3	1	1	NUM
ejpam-5617	43	4	γ	γ	X
ejpam-5617	43	5	(	(	PUNCT
ejpam-5617	43	6	α	α	NOUN
ejpam-5617	43	7	)	)	PUNCT
ejpam-5617	43	8	∫	∫	NOUN
ejpam-5617	43	9	x	x	SYM
ejpam-5617	44	1	y0	y0	PROPN
ejpam-5617	44	2	(	(	PUNCT
ejpam-5617	44	3	x−	x−	PROPN
ejpam-5617	44	4	y)α−1	y)α−1	PROPN
ejpam-5617	44	5	u(m	u(m	PROPN
ejpam-5617	44	6	)	)	PUNCT
ejpam-5617	44	7	(	(	PUNCT
ejpam-5617	44	8	y	y	X
ejpam-5617	44	9	)	)	PUNCT
ejpam-5617	44	10	dy	dy	PROPN
ejpam-5617	44	11	,	,	PUNCT
ejpam-5617	44	12	m−	m−	PROPN
ejpam-5617	44	13	1	1	NUM
ejpam-5617	44	14	<	<	X
ejpam-5617	44	15	α	α	X
ejpam-5617	44	16	<	<	X
ejpam-5617	44	17	m	m	PROPN
ejpam-5617	44	18	,	,	PUNCT
ejpam-5617	44	19	x	x	SYM
ejpam-5617	44	20	>	>	X
ejpam-5617	44	21	y	y	PROPN
ejpam-5617	44	22	≥	≥	NUM
ejpam-5617	44	23	y0	y0	PROPN
ejpam-5617	44	24	≥	≥	NOUN
ejpam-5617	44	25	0	0	NUM
ejpam-5617	44	26	,	,	PUNCT
ejpam-5617	44	27	u(m	u(m	ADJ
ejpam-5617	44	28	)	)	PUNCT
ejpam-5617	44	29	(	(	PUNCT
ejpam-5617	44	30	x	x	X
ejpam-5617	44	31	)	)	PUNCT
ejpam-5617	44	32	,	,	PUNCT
ejpam-5617	44	33	α	α	NOUN
ejpam-5617	44	34	=	=	PUNCT
ejpam-5617	44	35	m.	m.	NOUN
ejpam-5617	44	36	(	(	PUNCT
ejpam-5617	44	37	2	2	X
ejpam-5617	44	38	)	)	PUNCT
ejpam-5617	44	39	many	many	ADJ
ejpam-5617	44	40	properties	property	NOUN
ejpam-5617	44	41	of	of	ADP
ejpam-5617	44	42	caputo	caputo	PROPN
ejpam-5617	44	43	derivative	derivative	PROPN
ejpam-5617	44	44	can	can	AUX
ejpam-5617	44	45	be	be	AUX
ejpam-5617	44	46	found	find	VERB
ejpam-5617	44	47	in	in	ADP
ejpam-5617	44	48	the	the	DET
ejpam-5617	44	49	refs	ref	NOUN
ejpam-5617	44	50	.	.	PUNCT
ejpam-5617	45	1	[	[	X
ejpam-5617	45	2	12	12	NUM
ejpam-5617	45	3	,	,	PUNCT
ejpam-5617	45	4	31	31	NUM
ejpam-5617	45	5	]	]	PUNCT
ejpam-5617	45	6	.	.	PUNCT
ejpam-5617	46	1	in	in	ADP
ejpam-5617	46	2	the	the	DET
ejpam-5617	46	3	following	following	NOUN
ejpam-5617	46	4	,	,	PUNCT
ejpam-5617	46	5	the	the	DET
ejpam-5617	46	6	definitions	definition	NOUN
ejpam-5617	46	7	and	and	CCONJ
ejpam-5617	46	8	theorems	theorem	NOUN
ejpam-5617	46	9	relevant	relevant	ADJ
ejpam-5617	46	10	to	to	ADP
ejpam-5617	46	11	the	the	DET
ejpam-5617	46	12	classical	classical	ADJ
ejpam-5617	46	13	ps	p	NOUN
ejpam-5617	46	14	are	be	AUX
ejpam-5617	46	15	expanded	expand	VERB
ejpam-5617	46	16	to	to	PART
ejpam-5617	46	17	include	include	VERB
ejpam-5617	46	18	the	the	DET
ejpam-5617	46	19	fractional	fractional	ADJ
ejpam-5617	46	20	case	case	NOUN
ejpam-5617	46	21	in	in	ADP
ejpam-5617	46	22	the	the	DET
ejpam-5617	46	23	caputo	caputo	PROPN
ejpam-5617	46	24	sense	sense	NOUN
ejpam-5617	46	25	.	.	PUNCT
ejpam-5617	47	1	definition	definition	NOUN
ejpam-5617	47	2	2.2	2.2	NUM
ejpam-5617	47	3	.	.	PUNCT
ejpam-5617	48	1	[	[	X
ejpam-5617	48	2	17	17	NUM
ejpam-5617	48	3	]	]	X
ejpam-5617	48	4	a	a	DET
ejpam-5617	48	5	ps	ps	NOUN
ejpam-5617	48	6	representation	representation	NOUN
ejpam-5617	48	7	of	of	ADP
ejpam-5617	48	8	the	the	DET
ejpam-5617	48	9	form	form	NOUN
ejpam-5617	48	10	∞∑	∞∑	NUM
ejpam-5617	48	11	j=0	j=0	PROPN
ejpam-5617	48	12	uj	uj	PROPN
ejpam-5617	48	13	(	(	PUNCT
ejpam-5617	48	14	x−	x−	PROPN
ejpam-5617	48	15	x0	x0	PROPN
ejpam-5617	48	16	)	)	PUNCT
ejpam-5617	48	17	jα	jα	NOUN
ejpam-5617	48	18	=	=	PUNCT
ejpam-5617	48	19	u0	u0	PROPN
ejpam-5617	48	20	+	+	X
ejpam-5617	48	21	u1(x−	u1(x−	ADJ
ejpam-5617	48	22	x0	x0	PROPN
ejpam-5617	48	23	)	)	PUNCT
ejpam-5617	49	1	α	α	PROPN
ejpam-5617	49	2	+	+	X
ejpam-5617	49	3	u2	u2	PROPN
ejpam-5617	49	4	(	(	PUNCT
ejpam-5617	49	5	x−	x−	PROPN
ejpam-5617	49	6	x0	x0	PROPN
ejpam-5617	49	7	)	)	PUNCT
ejpam-5617	49	8	2α	2α	NOUN
ejpam-5617	49	9	+	+	X
ejpam-5617	49	10	.	.	PUNCT
ejpam-5617	49	11	.	.	PUNCT
ejpam-5617	49	12	.	.	PUNCT
ejpam-5617	50	1	,	,	PUNCT
ejpam-5617	50	2	(	(	PUNCT
ejpam-5617	50	3	3	3	X
ejpam-5617	50	4	)	)	PUNCT
ejpam-5617	50	5	where	where	SCONJ
ejpam-5617	50	6	0	0	NUM
ejpam-5617	50	7	≤	≤	NUM
ejpam-5617	50	8	m	m	VERB
ejpam-5617	50	9	−	−	PROPN
ejpam-5617	50	10	1	1	NUM
ejpam-5617	50	11	<	<	X
ejpam-5617	50	12	α	α	PROPN
ejpam-5617	50	13	≤	≤	PUNCT
ejpam-5617	50	14	m	m	PROPN
ejpam-5617	50	15	,	,	PUNCT
ejpam-5617	50	16	x	x	PRON
ejpam-5617	50	17	≥	≥	NOUN
ejpam-5617	50	18	x0	x0	PROPN
ejpam-5617	50	19	is	be	AUX
ejpam-5617	50	20	called	call	VERB
ejpam-5617	50	21	a	a	DET
ejpam-5617	50	22	fractional	fractional	ADJ
ejpam-5617	50	23	ps	ps	NOUN
ejpam-5617	50	24	about	about	ADP
ejpam-5617	50	25	x0	x0	PROPN
ejpam-5617	50	26	where	where	SCONJ
ejpam-5617	50	27	x	x	PRON
ejpam-5617	50	28	is	be	AUX
ejpam-5617	50	29	variable	variable	ADJ
ejpam-5617	50	30	and	and	CCONJ
ejpam-5617	50	31	uj	uj	PROPN
ejpam-5617	50	32	’s	’s	PART
ejpam-5617	50	33	are	be	AUX
ejpam-5617	50	34	constants	constant	NOUN
ejpam-5617	50	35	called	call	VERB
ejpam-5617	50	36	the	the	DET
ejpam-5617	50	37	coefficients	coefficient	NOUN
ejpam-5617	50	38	of	of	ADP
ejpam-5617	50	39	the	the	DET
ejpam-5617	50	40	series	series	NOUN
ejpam-5617	50	41	.	.	PUNCT
ejpam-5617	51	1	theorem	theorem	VERB
ejpam-5617	51	2	2.1	2.1	NUM
ejpam-5617	51	3	.	.	PUNCT
ejpam-5617	52	1	[	[	X
ejpam-5617	52	2	33	33	NUM
ejpam-5617	52	3	]	]	PUNCT
ejpam-5617	52	4	the	the	DET
ejpam-5617	52	5	fractional	fractional	ADJ
ejpam-5617	52	6	ps	ps	PROPN
ejpam-5617	52	7	∑∞	∑∞	X
ejpam-5617	52	8	j=0	j=0	PROPN
ejpam-5617	52	9	uj	uj	PROPN
ejpam-5617	52	10	(	(	PUNCT
ejpam-5617	52	11	x−	x−	PROPN
ejpam-5617	52	12	x0	x0	PROPN
ejpam-5617	52	13	)	)	PUNCT
ejpam-5617	53	1	jα	jα	NOUN
ejpam-5617	53	2	=	=	PUNCT
ejpam-5617	53	3	0	0	NUM
ejpam-5617	53	4	for	for	ADP
ejpam-5617	53	5	all	all	DET
ejpam-5617	53	6	x	x	NOUN
ejpam-5617	53	7	in	in	ADP
ejpam-5617	53	8	|x−	|x−	PROPN
ejpam-5617	53	9	x0|	x0|	PROPN
ejpam-5617	54	1	<	<	X
ejpam-5617	54	2	s	s	X
ejpam-5617	54	3	if	if	SCONJ
ejpam-5617	55	1	and	and	CCONJ
ejpam-5617	55	2	only	only	ADV
ejpam-5617	55	3	if	if	SCONJ
ejpam-5617	55	4	each	each	DET
ejpam-5617	55	5	coefficient	coefficient	NOUN
ejpam-5617	55	6	uj	uj	PROPN
ejpam-5617	55	7	equals	equal	VERB
ejpam-5617	55	8	zero	zero	NUM
ejpam-5617	55	9	.	.	PUNCT
ejpam-5617	56	1	to	to	PART
ejpam-5617	56	2	determine	determine	VERB
ejpam-5617	56	3	the	the	DET
ejpam-5617	56	4	coefficients	coefficient	NOUN
ejpam-5617	56	5	of	of	ADP
ejpam-5617	56	6	the	the	DET
ejpam-5617	56	7	fractional	fractional	ADJ
ejpam-5617	56	8	ps	ps	NOUN
ejpam-5617	56	9	solution	solution	NOUN
ejpam-5617	56	10	,	,	PUNCT
ejpam-5617	56	11	the	the	DET
ejpam-5617	56	12	primary	primary	ADJ
ejpam-5617	56	13	principle	principle	NOUN
ejpam-5617	56	14	for	for	ADP
ejpam-5617	56	15	the	the	DET
ejpam-5617	56	16	lrfd	lrfd	PROPN
ejpam-5617	56	17	approach	approach	NOUN
ejpam-5617	56	18	has	have	AUX
ejpam-5617	56	19	been	be	AUX
ejpam-5617	56	20	presented	present	VERB
ejpam-5617	56	21	and	and	CCONJ
ejpam-5617	56	22	validated	validate	VERB
ejpam-5617	56	23	by	by	ADP
ejpam-5617	56	24	the	the	DET
ejpam-5617	56	25	authors	author	NOUN
ejpam-5617	56	26	in	in	ADP
ejpam-5617	56	27	references	reference	NOUN
ejpam-5617	56	28	[	[	X
ejpam-5617	56	29	18	18	NUM
ejpam-5617	56	30	,	,	PUNCT
ejpam-5617	56	31	19	19	NUM
ejpam-5617	56	32	]	]	PUNCT
ejpam-5617	56	33	,	,	PUNCT
ejpam-5617	56	34	which	which	PRON
ejpam-5617	56	35	is	be	AUX
ejpam-5617	56	36	depicted	depict	VERB
ejpam-5617	56	37	in	in	ADP
ejpam-5617	56	38	the	the	DET
ejpam-5617	56	39	following	follow	VERB
ejpam-5617	56	40	theorem	theorem	PROPN
ejpam-5617	56	41	.	.	PUNCT
ejpam-5617	56	42	theorem	theorem	PROPN
ejpam-5617	56	43	2.2	2.2	NUM
ejpam-5617	56	44	.	.	PUNCT
ejpam-5617	57	1	suppose	suppose	VERB
ejpam-5617	57	2	that	that	SCONJ
ejpam-5617	57	3	u	u	PROPN
ejpam-5617	57	4	(	(	PUNCT
ejpam-5617	57	5	x	x	X
ejpam-5617	57	6	)	)	PUNCT
ejpam-5617	57	7	has	have	VERB
ejpam-5617	57	8	the	the	DET
ejpam-5617	57	9	fractional	fractional	ADJ
ejpam-5617	57	10	ps	ps	NOUN
ejpam-5617	57	11	expansion	expansion	NOUN
ejpam-5617	57	12	u	u	NOUN
ejpam-5617	57	13	(	(	PUNCT
ejpam-5617	57	14	x	x	NOUN
ejpam-5617	57	15	)	)	PUNCT
ejpam-5617	58	1	=	=	NOUN
ejpam-5617	58	2	∑∞	∑∞	X
ejpam-5617	58	3	j=0	j=0	PROPN
ejpam-5617	58	4	uj	uj	PROPN
ejpam-5617	58	5	(	(	PUNCT
ejpam-5617	58	6	x−	x−	PROPN
ejpam-5617	58	7	x0	x0	PROPN
ejpam-5617	58	8	)	)	PUNCT
ejpam-5617	59	1	jα	jα	NOUN
ejpam-5617	59	2	and	and	CCONJ
ejpam-5617	59	3	u	u	PROPN
ejpam-5617	59	4	(	(	PUNCT
ejpam-5617	59	5	x	x	NOUN
ejpam-5617	59	6	)	)	PUNCT
ejpam-5617	59	7	=	=	SYM
ejpam-5617	59	8	0	0	NUM
ejpam-5617	59	9	for	for	ADP
ejpam-5617	59	10	all	all	DET
ejpam-5617	59	11	x	x	NOUN
ejpam-5617	59	12	in	in	ADP
ejpam-5617	59	13	some	some	DET
ejpam-5617	59	14	interval	interval	NOUN
ejpam-5617	59	15	i.	i.	NOUN
ejpam-5617	59	16	then	then	ADV
ejpam-5617	59	17	lim	lim	PROPN
ejpam-5617	59	18	x→x0	x→x0	PROPN
ejpam-5617	59	19	uk(x	uk(x	ADP
ejpam-5617	59	20	)	)	PUNCT
ejpam-5617	59	21	(	(	PUNCT
ejpam-5617	59	22	x−	x−	PROPN
ejpam-5617	59	23	x0	x0	PROPN
ejpam-5617	59	24	)	)	PUNCT
ejpam-5617	59	25	(	(	PUNCT
ejpam-5617	59	26	k−1)α	k−1)α	NOUN
ejpam-5617	59	27	=	=	SYM
ejpam-5617	59	28	0	0	NUM
ejpam-5617	59	29	,	,	PUNCT
ejpam-5617	59	30	k	k	NOUN
ejpam-5617	59	31	=	=	SYM
ejpam-5617	59	32	1	1	NUM
ejpam-5617	59	33	,	,	PUNCT
ejpam-5617	59	34	2	2	NUM
ejpam-5617	59	35	,	,	PUNCT
ejpam-5617	59	36	.	.	PUNCT
ejpam-5617	59	37	.	.	PUNCT
ejpam-5617	59	38	.	.	PUNCT
ejpam-5617	60	1	,	,	PUNCT
ejpam-5617	61	1	x	x	X
ejpam-5617	61	2	̸=	̸=	PROPN
ejpam-5617	61	3	x0	x0	NUM
ejpam-5617	61	4	,	,	PUNCT
ejpam-5617	61	5	(	(	PUNCT
ejpam-5617	61	6	4	4	X
ejpam-5617	61	7	)	)	PUNCT
ejpam-5617	61	8	where	where	SCONJ
ejpam-5617	61	9	uk(x	uk(x	ADP
ejpam-5617	61	10	)	)	PUNCT
ejpam-5617	61	11	=	=	SYM
ejpam-5617	61	12	k∑	k∑	PROPN
ejpam-5617	61	13	j=0	j=0	PROPN
ejpam-5617	61	14	uj	uj	PROPN
ejpam-5617	61	15	(	(	PUNCT
ejpam-5617	61	16	x−	x−	PROPN
ejpam-5617	61	17	x0	x0	PROPN
ejpam-5617	61	18	)	)	PUNCT
ejpam-5617	62	1	jα	jα	PROPN
ejpam-5617	62	2	.	.	PUNCT
ejpam-5617	63	1	(	(	PUNCT
ejpam-5617	63	2	5	5	NUM
ejpam-5617	63	3	)	)	PUNCT
ejpam-5617	63	4	3	3	NUM
ejpam-5617	63	5	.	.	PUNCT
ejpam-5617	64	1	the	the	DET
ejpam-5617	64	2	methodology	methodology	NOUN
ejpam-5617	64	3	of	of	ADP
ejpam-5617	64	4	the	the	DET
ejpam-5617	64	5	lrf	lrf	NOUN
ejpam-5617	64	6	method	method	NOUN
ejpam-5617	64	7	for	for	ADP
ejpam-5617	64	8	solving	solve	VERB
ejpam-5617	64	9	systems	system	NOUN
ejpam-5617	64	10	of	of	ADP
ejpam-5617	64	11	fractional	fractional	ADJ
ejpam-5617	64	12	differential	differential	ADJ
ejpam-5617	64	13	equations	equation	NOUN
ejpam-5617	64	14	this	this	DET
ejpam-5617	64	15	section	section	NOUN
ejpam-5617	64	16	introduces	introduce	VERB
ejpam-5617	64	17	the	the	DET
ejpam-5617	64	18	fundamental	fundamental	ADJ
ejpam-5617	64	19	idea	idea	NOUN
ejpam-5617	64	20	of	of	ADP
ejpam-5617	64	21	the	the	DET
ejpam-5617	64	22	lrf	lrf	NOUN
ejpam-5617	64	23	technique	technique	NOUN
ejpam-5617	64	24	for	for	ADP
ejpam-5617	64	25	analytically	analytically	ADV
ejpam-5617	64	26	solving	solve	VERB
ejpam-5617	64	27	specific	specific	ADJ
ejpam-5617	64	28	systems	system	NOUN
ejpam-5617	64	29	of	of	ADP
ejpam-5617	64	30	linear	linear	PROPN
ejpam-5617	64	31	and	and	CCONJ
ejpam-5617	64	32	non	non	ADJ
ejpam-5617	64	33	-	-	ADJ
ejpam-5617	64	34	linear	linear	ADJ
ejpam-5617	64	35	fractional	fractional	ADJ
ejpam-5617	64	36	differential	differential	ADJ
ejpam-5617	64	37	equations	equation	NOUN
ejpam-5617	64	38	.	.	PUNCT
ejpam-5617	65	1	the	the	DET
ejpam-5617	65	2	a.	a.	PROPN
ejpam-5617	65	3	el	el	PROPN
ejpam-5617	65	4	-	-	PUNCT
ejpam-5617	65	5	ajou	ajou	PROPN
ejpam-5617	65	6	,	,	PUNCT
ejpam-5617	65	7	a.	a.	PROPN
ejpam-5617	65	8	burqan	burqan	PROPN
ejpam-5617	65	9	/	/	SYM
ejpam-5617	65	10	eur	eur	PROPN
ejpam-5617	65	11	.	.	PUNCT
ejpam-5617	66	1	j.	j.	PROPN
ejpam-5617	66	2	pure	pure	PROPN
ejpam-5617	66	3	appl	appl	PROPN
ejpam-5617	66	4	.	.	PROPN
ejpam-5617	66	5	math	math	PROPN
ejpam-5617	66	6	,	,	PUNCT
ejpam-5617	66	7	18	18	NUM
ejpam-5617	66	8	(	(	PUNCT
ejpam-5617	66	9	1	1	NUM
ejpam-5617	66	10	)	)	PUNCT
ejpam-5617	66	11	(	(	PUNCT
ejpam-5617	66	12	2025	2025	NUM
ejpam-5617	66	13	)	)	PUNCT
ejpam-5617	66	14	,	,	PUNCT
ejpam-5617	66	15	5617	5617	NUM
ejpam-5617	66	16	4	4	NUM
ejpam-5617	66	17	of	of	ADP
ejpam-5617	66	18	19	19	NUM
ejpam-5617	66	19	residual	residual	ADJ
ejpam-5617	66	20	function	function	NOUN
ejpam-5617	66	21	and	and	CCONJ
ejpam-5617	66	22	the	the	DET
ejpam-5617	66	23	limit	limit	NOUN
ejpam-5617	66	24	at	at	ADP
ejpam-5617	66	25	zero	zero	NUM
ejpam-5617	66	26	are	be	AUX
ejpam-5617	66	27	the	the	DET
ejpam-5617	66	28	foundational	foundational	ADJ
ejpam-5617	66	29	concepts	concept	NOUN
ejpam-5617	66	30	of	of	ADP
ejpam-5617	66	31	this	this	DET
ejpam-5617	66	32	approach	approach	NOUN
ejpam-5617	66	33	.	.	PUNCT
ejpam-5617	67	1	to	to	PART
ejpam-5617	67	2	demonstrate	demonstrate	VERB
ejpam-5617	67	3	the	the	DET
ejpam-5617	67	4	procedures	procedure	NOUN
ejpam-5617	67	5	of	of	ADP
ejpam-5617	67	6	the	the	DET
ejpam-5617	67	7	lrf	lrf	NOUN
ejpam-5617	67	8	method	method	NOUN
ejpam-5617	67	9	,	,	PUNCT
ejpam-5617	67	10	we	we	PRON
ejpam-5617	67	11	will	will	AUX
ejpam-5617	67	12	be	be	AUX
ejpam-5617	67	13	studying	study	VERB
ejpam-5617	67	14	the	the	DET
ejpam-5617	67	15	following	follow	VERB
ejpam-5617	67	16	class	class	NOUN
ejpam-5617	67	17	of	of	ADP
ejpam-5617	67	18	fractional	fractional	ADJ
ejpam-5617	67	19	differential	differential	NOUN
ejpam-5617	67	20	equation	equation	NOUN
ejpam-5617	67	21	systems	system	NOUN
ejpam-5617	67	22	:	:	PUNCT
ejpam-5617	67	23	dαui	dαui	NOUN
ejpam-5617	67	24	(	(	PUNCT
ejpam-5617	67	25	x	x	NOUN
ejpam-5617	67	26	)	)	PUNCT
ejpam-5617	67	27	=	=	SYM
ejpam-5617	67	28	hi	hi	INTJ
ejpam-5617	67	29	(	(	PUNCT
ejpam-5617	67	30	x	x	NOUN
ejpam-5617	67	31	,	,	PUNCT
ejpam-5617	67	32	u1	u1	NOUN
ejpam-5617	67	33	(	(	PUNCT
ejpam-5617	67	34	x	x	NOUN
ejpam-5617	67	35	)	)	PUNCT
ejpam-5617	67	36	,	,	PUNCT
ejpam-5617	67	37	u2	u2	PROPN
ejpam-5617	67	38	(	(	PUNCT
ejpam-5617	67	39	x	x	NOUN
ejpam-5617	67	40	)	)	PUNCT
ejpam-5617	67	41	,	,	PUNCT
ejpam-5617	67	42	.	.	PUNCT
ejpam-5617	67	43	.	.	PUNCT
ejpam-5617	68	1	.	.	PUNCT
ejpam-5617	69	1	,	,	PUNCT
ejpam-5617	69	2	un	un	PROPN
ejpam-5617	69	3	(	(	PUNCT
ejpam-5617	69	4	x	x	NOUN
ejpam-5617	69	5	)	)	PUNCT
ejpam-5617	69	6	)	)	PUNCT
ejpam-5617	69	7	,	,	PUNCT
ejpam-5617	69	8	x	x	X
ejpam-5617	69	9	≥	≥	NOUN
ejpam-5617	69	10	0	0	NUM
ejpam-5617	69	11	,	,	PUNCT
ejpam-5617	69	12	0	0	NUM
ejpam-5617	69	13	<	<	X
ejpam-5617	69	14	α	α	PROPN
ejpam-5617	69	15	≤	≤	NUM
ejpam-5617	69	16	1	1	NUM
ejpam-5617	69	17	,	,	PUNCT
ejpam-5617	69	18	(	(	PUNCT
ejpam-5617	69	19	6	6	NUM
ejpam-5617	69	20	)	)	PUNCT
ejpam-5617	69	21	with	with	ADP
ejpam-5617	69	22	the	the	DET
ejpam-5617	69	23	initial	initial	ADJ
ejpam-5617	69	24	conditions	condition	NOUN
ejpam-5617	69	25	ui	ui	NOUN
ejpam-5617	69	26	(	(	PUNCT
ejpam-5617	69	27	0	0	NUM
ejpam-5617	69	28	)	)	PUNCT
ejpam-5617	69	29	=	=	SYM
ejpam-5617	70	1	ui,0	ui,0	NOUN
ejpam-5617	70	2	,	,	PUNCT
ejpam-5617	70	3	i	i	PRON
ejpam-5617	70	4	=	=	NOUN
ejpam-5617	70	5	1	1	NUM
ejpam-5617	70	6	,	,	PUNCT
ejpam-5617	70	7	2	2	NUM
ejpam-5617	70	8	,	,	PUNCT
ejpam-5617	70	9	.	.	PUNCT
ejpam-5617	70	10	.	.	PUNCT
ejpam-5617	70	11	.	.	PUNCT
ejpam-5617	71	1	,	,	PUNCT
ejpam-5617	71	2	n.	n.	NOUN
ejpam-5617	71	3	(	(	PUNCT
ejpam-5617	71	4	7	7	NUM
ejpam-5617	71	5	)	)	PUNCT
ejpam-5617	71	6	where	where	SCONJ
ejpam-5617	71	7	α	α	NOUN
ejpam-5617	71	8	is	be	AUX
ejpam-5617	71	9	the	the	DET
ejpam-5617	71	10	order	order	NOUN
ejpam-5617	71	11	of	of	ADP
ejpam-5617	71	12	the	the	DET
ejpam-5617	71	13	caputo	caputo	PROPN
ejpam-5617	71	14	fractional	fractional	PROPN
ejpam-5617	71	15	differential	differential	NOUN
ejpam-5617	71	16	operator	operator	NOUN
ejpam-5617	71	17	dα	dα	NOUN
ejpam-5617	71	18	,	,	PUNCT
ejpam-5617	71	19	hi	hi	INTJ
ejpam-5617	71	20	are	be	AUX
ejpam-5617	71	21	analytic	analytic	ADJ
ejpam-5617	71	22	functions	function	NOUN
ejpam-5617	71	23	,	,	PUNCT
ejpam-5617	71	24	and	and	CCONJ
ejpam-5617	71	25	ui	ui	PROPN
ejpam-5617	71	26	(	(	PUNCT
ejpam-5617	71	27	x	x	X
ejpam-5617	71	28	)	)	PUNCT
ejpam-5617	71	29	are	be	AUX
ejpam-5617	71	30	unknown	unknown	ADJ
ejpam-5617	71	31	analytical	analytical	ADJ
ejpam-5617	71	32	smooth	smooth	ADJ
ejpam-5617	71	33	functions	function	NOUN
ejpam-5617	71	34	that	that	PRON
ejpam-5617	71	35	will	will	AUX
ejpam-5617	71	36	be	be	AUX
ejpam-5617	71	37	identified	identify	VERB
ejpam-5617	71	38	.	.	PUNCT
ejpam-5617	72	1	the	the	DET
ejpam-5617	72	2	lrf	lrf	NOUN
ejpam-5617	72	3	method	method	NOUN
ejpam-5617	72	4	assumes	assume	VERB
ejpam-5617	72	5	writing	write	VERB
ejpam-5617	72	6	the	the	DET
ejpam-5617	72	7	functions	function	NOUN
ejpam-5617	72	8	ui	ui	NOUN
ejpam-5617	73	1	(	(	PUNCT
ejpam-5617	73	2	x	x	X
ejpam-5617	73	3	)	)	PUNCT
ejpam-5617	73	4	using	use	VERB
ejpam-5617	73	5	the	the	DET
ejpam-5617	73	6	following	follow	VERB
ejpam-5617	73	7	fractional	fractional	ADJ
ejpam-5617	73	8	ps	ps	PROPN
ejpam-5617	73	9	expansions	expansion	NOUN
ejpam-5617	73	10	:	:	PUNCT
ejpam-5617	73	11	ui	ui	PROPN
ejpam-5617	73	12	(	(	PUNCT
ejpam-5617	73	13	x	x	X
ejpam-5617	73	14	)	)	PUNCT
ejpam-5617	73	15	=	=	SYM
ejpam-5617	74	1	∞∑	∞∑	NUM
ejpam-5617	74	2	j=0	j=0	PROPN
ejpam-5617	74	3	ui	ui	PROPN
ejpam-5617	74	4	,	,	PUNCT
ejpam-5617	74	5	j	j	PROPN
ejpam-5617	74	6	xjα	xjα	PROPN
ejpam-5617	74	7	,	,	PUNCT
ejpam-5617	74	8	i	i	PRON
ejpam-5617	74	9	=	=	NOUN
ejpam-5617	74	10	1	1	NUM
ejpam-5617	74	11	,	,	PUNCT
ejpam-5617	74	12	2	2	NUM
ejpam-5617	74	13	,	,	PUNCT
ejpam-5617	74	14	.	.	PUNCT
ejpam-5617	74	15	.	.	PUNCT
ejpam-5617	74	16	.	.	PUNCT
ejpam-5617	74	17	,	,	PUNCT
ejpam-5617	74	18	n	n	CCONJ
ejpam-5617	74	19	,	,	PUNCT
ejpam-5617	74	20	x	x	X
ejpam-5617	74	21	≥	≥	NOUN
ejpam-5617	74	22	0	0	NUM
ejpam-5617	74	23	.	.	PUNCT
ejpam-5617	75	1	(	(	PUNCT
ejpam-5617	75	2	8)	8)	NUM
ejpam-5617	75	3	since	since	SCONJ
ejpam-5617	75	4	ui,0	ui,0	PROPN
ejpam-5617	75	5	=	=	SYM
ejpam-5617	75	6	ui	ui	PROPN
ejpam-5617	75	7	(	(	PUNCT
ejpam-5617	75	8	0	0	NUM
ejpam-5617	75	9	)	)	PUNCT
ejpam-5617	75	10	,	,	PUNCT
ejpam-5617	75	11	and	and	CCONJ
ejpam-5617	75	12	by	by	ADP
ejpam-5617	75	13	truncating	truncate	VERB
ejpam-5617	75	14	the	the	DET
ejpam-5617	75	15	series	series	NOUN
ejpam-5617	75	16	(	(	PUNCT
ejpam-5617	75	17	8)	8)	NUM
ejpam-5617	75	18	,	,	PUNCT
ejpam-5617	75	19	we	we	PRON
ejpam-5617	75	20	obtain	obtain	VERB
ejpam-5617	75	21	the	the	DET
ejpam-5617	75	22	kth	kth	PROPN
ejpam-5617	75	23	approximate	approximate	ADJ
ejpam-5617	75	24	solution	solution	NOUN
ejpam-5617	75	25	of	of	ADP
ejpam-5617	75	26	the	the	DET
ejpam-5617	75	27	system	system	NOUN
ejpam-5617	75	28	(	(	PUNCT
ejpam-5617	75	29	6)-(7	6)-(7	NOUN
ejpam-5617	75	30	)	)	PUNCT
ejpam-5617	75	31	as	as	SCONJ
ejpam-5617	75	32	follows	follow	VERB
ejpam-5617	75	33	:	:	PUNCT
ejpam-5617	75	34	uik	uik	NOUN
ejpam-5617	75	35	(	(	PUNCT
ejpam-5617	75	36	x	x	NOUN
ejpam-5617	75	37	)	)	PUNCT
ejpam-5617	75	38	=	=	SYM
ejpam-5617	76	1	ui,0	ui,0	PROPN
ejpam-5617	76	2	+	+	CCONJ
ejpam-5617	76	3	k∑	k∑	ADJ
ejpam-5617	76	4	j=1	j=1	PROPN
ejpam-5617	76	5	ui	ui	PROPN
ejpam-5617	76	6	,	,	PUNCT
ejpam-5617	76	7	j	j	PROPN
ejpam-5617	76	8	xjα	xjα	PROPN
ejpam-5617	76	9	,	,	PUNCT
ejpam-5617	76	10	i	i	PRON
ejpam-5617	76	11	=	=	NOUN
ejpam-5617	76	12	1	1	NUM
ejpam-5617	76	13	,	,	PUNCT
ejpam-5617	76	14	2	2	NUM
ejpam-5617	76	15	,	,	PUNCT
ejpam-5617	76	16	.	.	PUNCT
ejpam-5617	76	17	.	.	PUNCT
ejpam-5617	76	18	.	.	PUNCT
ejpam-5617	76	19	,	,	PUNCT
ejpam-5617	76	20	n	n	CCONJ
ejpam-5617	76	21	,	,	PUNCT
ejpam-5617	76	22	x	x	X
ejpam-5617	76	23	≥	≥	NOUN
ejpam-5617	76	24	0	0	NUM
ejpam-5617	76	25	,	,	PUNCT
ejpam-5617	76	26	(	(	PUNCT
ejpam-5617	76	27	9	9	NUM
ejpam-5617	76	28	)	)	PUNCT
ejpam-5617	76	29	in	in	ADP
ejpam-5617	76	30	which	which	PRON
ejpam-5617	76	31	the	the	DET
ejpam-5617	76	32	constants	constant	NOUN
ejpam-5617	76	33	of	of	ADP
ejpam-5617	76	34	the	the	DET
ejpam-5617	76	35	expansion	expansion	NOUN
ejpam-5617	76	36	series	series	NOUN
ejpam-5617	76	37	,	,	PUNCT
ejpam-5617	76	38	ui	ui	PROPN
ejpam-5617	76	39	,	,	PUNCT
ejpam-5617	76	40	n	n	CCONJ
ejpam-5617	76	41	,	,	PUNCT
ejpam-5617	76	42	can	can	AUX
ejpam-5617	76	43	be	be	AUX
ejpam-5617	76	44	obtained	obtain	VERB
ejpam-5617	76	45	by	by	ADP
ejpam-5617	76	46	identifying	identify	VERB
ejpam-5617	76	47	the	the	DET
ejpam-5617	76	48	residual	residual	ADJ
ejpam-5617	76	49	functions	function	NOUN
ejpam-5617	76	50	as	as	SCONJ
ejpam-5617	76	51	follows	follow	VERB
ejpam-5617	76	52	:	:	PUNCT
ejpam-5617	76	53	rf	rf	NUM
ejpam-5617	76	54	(	(	PUNCT
ejpam-5617	76	55	ui	ui	PROPN
ejpam-5617	76	56	(	(	PUNCT
ejpam-5617	76	57	x	x	NOUN
ejpam-5617	76	58	)	)	PUNCT
ejpam-5617	76	59	)	)	PUNCT
ejpam-5617	77	1	=	=	PRON
ejpam-5617	77	2	dαui	dαui	NOUN
ejpam-5617	77	3	(	(	PUNCT
ejpam-5617	77	4	x)−hi	x)−hi	X
ejpam-5617	77	5	(	(	PUNCT
ejpam-5617	77	6	x	x	NOUN
ejpam-5617	77	7	,	,	PUNCT
ejpam-5617	77	8	u1	u1	NOUN
ejpam-5617	77	9	(	(	PUNCT
ejpam-5617	77	10	x	x	NOUN
ejpam-5617	77	11	)	)	PUNCT
ejpam-5617	77	12	,	,	PUNCT
ejpam-5617	77	13	u2	u2	PROPN
ejpam-5617	77	14	(	(	PUNCT
ejpam-5617	77	15	x	x	NOUN
ejpam-5617	77	16	)	)	PUNCT
ejpam-5617	77	17	,	,	PUNCT
ejpam-5617	77	18	.	.	PUNCT
ejpam-5617	77	19	.	.	PUNCT
ejpam-5617	77	20	.	.	PUNCT
ejpam-5617	78	1	,	,	PUNCT
ejpam-5617	78	2	un	un	PROPN
ejpam-5617	78	3	(	(	PUNCT
ejpam-5617	78	4	x	x	NOUN
ejpam-5617	78	5	)	)	PUNCT
ejpam-5617	78	6	)	)	PUNCT
ejpam-5617	78	7	,	,	PUNCT
ejpam-5617	78	8	i	i	PRON
ejpam-5617	78	9	=	=	NOUN
ejpam-5617	78	10	1	1	NUM
ejpam-5617	78	11	,	,	PUNCT
ejpam-5617	78	12	2	2	NUM
ejpam-5617	78	13	,	,	PUNCT
ejpam-5617	78	14	.	.	PUNCT
ejpam-5617	78	15	.	.	PUNCT
ejpam-5617	79	1	.	.	PUNCT
ejpam-5617	80	1	,	,	PUNCT
ejpam-5617	80	2	n	n	CCONJ
ejpam-5617	80	3	,	,	PUNCT
ejpam-5617	80	4	x	x	X
ejpam-5617	80	5	≥	≥	NOUN
ejpam-5617	80	6	0	0	NUM
ejpam-5617	80	7	.	.	PUNCT
ejpam-5617	81	1	(	(	PUNCT
ejpam-5617	81	2	10	10	NUM
ejpam-5617	81	3	)	)	PUNCT
ejpam-5617	81	4	so	so	ADV
ejpam-5617	81	5	,	,	PUNCT
ejpam-5617	81	6	the	the	DET
ejpam-5617	81	7	kth	kth	PROPN
ejpam-5617	81	8	residual	residual	ADJ
ejpam-5617	81	9	functions	function	NOUN
ejpam-5617	81	10	can	can	AUX
ejpam-5617	81	11	be	be	AUX
ejpam-5617	81	12	written	write	VERB
ejpam-5617	81	13	as	as	ADP
ejpam-5617	81	14	:	:	PUNCT
ejpam-5617	81	15	rf	rf	NUM
ejpam-5617	81	16	(	(	PUNCT
ejpam-5617	81	17	uik	uik	NOUN
ejpam-5617	81	18	(	(	PUNCT
ejpam-5617	81	19	x	x	NOUN
ejpam-5617	81	20	)	)	PUNCT
ejpam-5617	81	21	)	)	PUNCT
ejpam-5617	82	1	=	=	SYM
ejpam-5617	82	2	dαuik	dαuik	NOUN
ejpam-5617	82	3	(	(	PUNCT
ejpam-5617	82	4	x)−hi	x)−hi	X
ejpam-5617	82	5	(	(	PUNCT
ejpam-5617	82	6	x	x	X
ejpam-5617	82	7	,	,	PUNCT
ejpam-5617	82	8	u1k	u1k	PROPN
ejpam-5617	82	9	(	(	PUNCT
ejpam-5617	82	10	x	x	NOUN
ejpam-5617	82	11	)	)	PUNCT
ejpam-5617	82	12	,	,	PUNCT
ejpam-5617	82	13	u2k	u2k	PROPN
ejpam-5617	82	14	(	(	PUNCT
ejpam-5617	82	15	x	x	NOUN
ejpam-5617	82	16	)	)	PUNCT
ejpam-5617	82	17	,	,	PUNCT
ejpam-5617	82	18	.	.	PUNCT
ejpam-5617	82	19	.	.	PUNCT
ejpam-5617	82	20	.	.	PUNCT
ejpam-5617	83	1	,	,	PUNCT
ejpam-5617	83	2	unk	unk	INTJ
ejpam-5617	83	3	(	(	PUNCT
ejpam-5617	83	4	x	x	NOUN
ejpam-5617	83	5	)	)	PUNCT
ejpam-5617	83	6	)	)	PUNCT
ejpam-5617	83	7	,	,	PUNCT
ejpam-5617	83	8	i	i	PRON
ejpam-5617	83	9	=	=	NOUN
ejpam-5617	83	10	1	1	NUM
ejpam-5617	83	11	,	,	PUNCT
ejpam-5617	83	12	2	2	NUM
ejpam-5617	83	13	,	,	PUNCT
ejpam-5617	83	14	.	.	PUNCT
ejpam-5617	83	15	.	.	PUNCT
ejpam-5617	84	1	.	.	PUNCT
ejpam-5617	85	1	,	,	PUNCT
ejpam-5617	85	2	n	n	CCONJ
ejpam-5617	85	3	,	,	PUNCT
ejpam-5617	85	4	x	x	X
ejpam-5617	85	5	≥	≥	NOUN
ejpam-5617	85	6	0	0	NUM
ejpam-5617	85	7	.	.	PUNCT
ejpam-5617	86	1	(	(	PUNCT
ejpam-5617	86	2	11	11	NUM
ejpam-5617	86	3	)	)	PUNCT
ejpam-5617	86	4	to	to	PART
ejpam-5617	86	5	find	find	VERB
ejpam-5617	86	6	the	the	DET
ejpam-5617	86	7	kth	kth	PROPN
ejpam-5617	86	8	approximate	approximate	ADJ
ejpam-5617	86	9	solution	solution	NOUN
ejpam-5617	86	10	of	of	ADP
ejpam-5617	86	11	the	the	DET
ejpam-5617	86	12	system	system	NOUN
ejpam-5617	86	13	(	(	PUNCT
ejpam-5617	86	14	6)-(7	6)-(7	NOUN
ejpam-5617	86	15	)	)	PUNCT
ejpam-5617	86	16	,	,	PUNCT
ejpam-5617	86	17	we	we	PRON
ejpam-5617	86	18	need	need	VERB
ejpam-5617	86	19	to	to	PART
ejpam-5617	86	20	determine	determine	VERB
ejpam-5617	86	21	the	the	DET
ejpam-5617	86	22	value	value	NOUN
ejpam-5617	86	23	of	of	ADP
ejpam-5617	86	24	the	the	DET
ejpam-5617	86	25	coefficients	coefficient	NOUN
ejpam-5617	86	26	,	,	PUNCT
ejpam-5617	86	27	ui	ui	PROPN
ejpam-5617	86	28	,	,	PUNCT
ejpam-5617	86	29	j	j	PROPN
ejpam-5617	86	30	,	,	PUNCT
ejpam-5617	86	31	i	i	PRON
ejpam-5617	86	32	=	=	NOUN
ejpam-5617	86	33	1	1	NUM
ejpam-5617	86	34	,	,	PUNCT
ejpam-5617	86	35	2	2	NUM
ejpam-5617	86	36	,	,	PUNCT
ejpam-5617	86	37	.	.	PUNCT
ejpam-5617	86	38	.	.	PUNCT
ejpam-5617	87	1	.	.	PUNCT
ejpam-5617	88	1	,	,	PUNCT
ejpam-5617	88	2	n	n	CCONJ
ejpam-5617	88	3	,	,	PUNCT
ejpam-5617	89	1	and	and	CCONJ
ejpam-5617	89	2	j	j	PROPN
ejpam-5617	89	3	=	=	SYM
ejpam-5617	89	4	1	1	NUM
ejpam-5617	89	5	,	,	PUNCT
ejpam-5617	89	6	2	2	NUM
ejpam-5617	89	7	,	,	PUNCT
ejpam-5617	89	8	.	.	PUNCT
ejpam-5617	89	9	.	.	PUNCT
ejpam-5617	90	1	.	.	PUNCT
ejpam-5617	91	1	,	,	PUNCT
ejpam-5617	91	2	k	k	X
ejpam-5617	91	3	,	,	PUNCT
ejpam-5617	91	4	in	in	ADP
ejpam-5617	91	5	the	the	DET
ejpam-5617	91	6	series	series	NOUN
ejpam-5617	91	7	(	(	PUNCT
ejpam-5617	91	8	9	9	NUM
ejpam-5617	91	9	)	)	PUNCT
ejpam-5617	91	10	.	.	PUNCT
ejpam-5617	92	1	the	the	DET
ejpam-5617	92	2	essential	essential	ADJ
ejpam-5617	92	3	tool	tool	NOUN
ejpam-5617	92	4	of	of	ADP
ejpam-5617	92	5	the	the	DET
ejpam-5617	92	6	lrf	lrf	NOUN
ejpam-5617	92	7	method	method	NOUN
ejpam-5617	92	8	,	,	PUNCT
ejpam-5617	92	9	which	which	PRON
ejpam-5617	92	10	effectively	effectively	ADV
ejpam-5617	92	11	identifies	identify	VERB
ejpam-5617	92	12	the	the	DET
ejpam-5617	92	13	unknown	unknown	ADJ
ejpam-5617	92	14	coefficients	coefficient	NOUN
ejpam-5617	92	15	,	,	PUNCT
ejpam-5617	92	16	as	as	SCONJ
ejpam-5617	92	17	in	in	ADP
ejpam-5617	92	18	[	[	X
ejpam-5617	92	19	25	25	NUM
ejpam-5617	92	20	]	]	PUNCT
ejpam-5617	92	21	,	,	PUNCT
ejpam-5617	92	22	is	be	AUX
ejpam-5617	92	23	lim	lim	PROPN
ejpam-5617	92	24	x→0	x→0	PROPN
ejpam-5617	92	25	rf	rf	PROPN
ejpam-5617	92	26	(	(	PUNCT
ejpam-5617	92	27	uik	uik	NOUN
ejpam-5617	92	28	(	(	PUNCT
ejpam-5617	92	29	x	x	NOUN
ejpam-5617	92	30	)	)	PUNCT
ejpam-5617	92	31	)	)	PUNCT
ejpam-5617	92	32	x(k−1)α	x(k−1)α	NOUN
ejpam-5617	93	1	=	=	SYM
ejpam-5617	93	2	0	0	NUM
ejpam-5617	93	3	,	,	PUNCT
ejpam-5617	93	4	i	i	PRON
ejpam-5617	93	5	=	=	NOUN
ejpam-5617	93	6	1	1	NUM
ejpam-5617	93	7	,	,	PUNCT
ejpam-5617	93	8	2	2	NUM
ejpam-5617	93	9	,	,	PUNCT
ejpam-5617	93	10	...	...	PUNCT
ejpam-5617	93	11	,	,	PUNCT
ejpam-5617	93	12	n.	n.	NOUN
ejpam-5617	93	13	(	(	PUNCT
ejpam-5617	93	14	12	12	NUM
ejpam-5617	93	15	)	)	PUNCT
ejpam-5617	93	16	to	to	PART
ejpam-5617	93	17	find	find	VERB
ejpam-5617	93	18	the	the	DET
ejpam-5617	93	19	1st	1st	ADJ
ejpam-5617	93	20	approximate	approximate	ADJ
ejpam-5617	93	21	solution	solution	NOUN
ejpam-5617	93	22	,	,	PUNCT
ejpam-5617	93	23	we	we	PRON
ejpam-5617	93	24	must	must	AUX
ejpam-5617	93	25	determine	determine	VERB
ejpam-5617	93	26	the	the	DET
ejpam-5617	93	27	coefficients	coefficient	NOUN
ejpam-5617	93	28	ui,1	ui,1	PROPN
ejpam-5617	93	29	in	in	ADP
ejpam-5617	93	30	the	the	DET
ejpam-5617	93	31	series	series	NOUN
ejpam-5617	93	32	(	(	PUNCT
ejpam-5617	93	33	9	9	NUM
ejpam-5617	93	34	)	)	PUNCT
ejpam-5617	93	35	.	.	PUNCT
ejpam-5617	94	1	we	we	PRON
ejpam-5617	94	2	can	can	AUX
ejpam-5617	94	3	do	do	VERB
ejpam-5617	94	4	this	this	PRON
ejpam-5617	94	5	by	by	ADP
ejpam-5617	94	6	substituting	substitute	VERB
ejpam-5617	94	7	ui1	ui1	PROPN
ejpam-5617	94	8	(	(	PUNCT
ejpam-5617	94	9	x	x	X
ejpam-5617	94	10	)	)	PUNCT
ejpam-5617	94	11	=	=	SYM
ejpam-5617	94	12	ui,0	ui,0	NOUN
ejpam-5617	94	13	+	+	CCONJ
ejpam-5617	94	14	ui,1x	ui,1x	PRON
ejpam-5617	94	15	α	α	NOUN
ejpam-5617	94	16	into	into	ADP
ejpam-5617	94	17	rf	rf	ADJ
ejpam-5617	94	18	(	(	PUNCT
ejpam-5617	94	19	ui1	ui1	PROPN
ejpam-5617	94	20	(	(	PUNCT
ejpam-5617	94	21	x	x	NOUN
ejpam-5617	94	22	)	)	PUNCT
ejpam-5617	94	23	)	)	PUNCT
ejpam-5617	94	24	,	,	PUNCT
ejpam-5617	94	25	i	i	PRON
ejpam-5617	94	26	=	=	NOUN
ejpam-5617	94	27	1	1	NUM
ejpam-5617	94	28	,	,	PUNCT
ejpam-5617	94	29	2	2	NUM
ejpam-5617	94	30	,	,	PUNCT
ejpam-5617	94	31	...	...	PUNCT
ejpam-5617	94	32	,	,	PUNCT
ejpam-5617	94	33	n	n	CCONJ
ejpam-5617	94	34	,	,	PUNCT
ejpam-5617	94	35	and	and	CCONJ
ejpam-5617	94	36	then	then	ADV
ejpam-5617	94	37	solving	solve	VERB
ejpam-5617	94	38	the	the	DET
ejpam-5617	94	39	equations	equation	NOUN
ejpam-5617	94	40	limx→0rf	limx→0rf	VERB
ejpam-5617	94	41	(	(	PUNCT
ejpam-5617	94	42	ui1	ui1	PROPN
ejpam-5617	94	43	(	(	PUNCT
ejpam-5617	94	44	x	x	NOUN
ejpam-5617	94	45	)	)	PUNCT
ejpam-5617	94	46	)	)	PUNCT
ejpam-5617	95	1	=	=	SYM
ejpam-5617	95	2	0	0	NUM
ejpam-5617	96	1	for	for	ADP
ejpam-5617	96	2	ui,1	ui,1	PROPN
ejpam-5617	96	3	,	,	PUNCT
ejpam-5617	96	4	i	i	PRON
ejpam-5617	96	5	=	=	NOUN
ejpam-5617	96	6	1	1	NUM
ejpam-5617	96	7	,	,	PUNCT
ejpam-5617	96	8	2	2	NUM
ejpam-5617	96	9	,	,	PUNCT
ejpam-5617	96	10	.	.	PUNCT
ejpam-5617	96	11	.	.	PUNCT
ejpam-5617	96	12	.	.	PUNCT
ejpam-5617	97	1	,	,	PUNCT
ejpam-5617	97	2	n.	n.	NOUN
ejpam-5617	97	3	this	this	PRON
ejpam-5617	97	4	will	will	AUX
ejpam-5617	97	5	lead	lead	VERB
ejpam-5617	97	6	us	we	PRON
ejpam-5617	97	7	to	to	ADP
ejpam-5617	97	8	our	our	PRON
ejpam-5617	97	9	desire	desire	NOUN
ejpam-5617	97	10	.	.	PUNCT
ejpam-5617	98	1	similarly	similarly	ADV
ejpam-5617	98	2	,	,	PUNCT
ejpam-5617	98	3	we	we	PRON
ejpam-5617	98	4	can	can	AUX
ejpam-5617	98	5	get	get	VERB
ejpam-5617	98	6	the	the	DET
ejpam-5617	98	7	actual	actual	ADJ
ejpam-5617	98	8	2nd	2nd	ADJ
ejpam-5617	98	9	approximate	approximate	ADJ
ejpam-5617	98	10	solution	solution	NOUN
ejpam-5617	98	11	by	by	ADP
ejpam-5617	98	12	substituting	substitute	VERB
ejpam-5617	98	13	ui2	ui2	PROPN
ejpam-5617	98	14	(	(	PUNCT
ejpam-5617	98	15	x	x	X
ejpam-5617	98	16	)	)	PUNCT
ejpam-5617	98	17	=	=	SYM
ejpam-5617	99	1	ui,0	ui,0	NOUN
ejpam-5617	99	2	+	+	CCONJ
ejpam-5617	99	3	ui,1x	ui,1x	PRON
ejpam-5617	99	4	α	α	NOUN
ejpam-5617	99	5	+	+	CCONJ
ejpam-5617	99	6	ui,2x	ui,2x	ADP
ejpam-5617	99	7	2α	2α	NOUN
ejpam-5617	99	8	into	into	ADP
ejpam-5617	99	9	rf	rf	PRON
ejpam-5617	99	10	(	(	PUNCT
ejpam-5617	99	11	ui2	ui2	INTJ
ejpam-5617	99	12	(	(	PUNCT
ejpam-5617	99	13	x	x	NOUN
ejpam-5617	99	14	)	)	PUNCT
ejpam-5617	99	15	)	)	PUNCT
ejpam-5617	99	16	and	and	CCONJ
ejpam-5617	99	17	solving	solve	VERB
ejpam-5617	99	18	the	the	DET
ejpam-5617	99	19	equations	equation	NOUN
ejpam-5617	99	20	limx→0	limx→0	PROPN
ejpam-5617	99	21	rf(ui2(x	rf(ui2(x	PROPN
ejpam-5617	99	22	)	)	PUNCT
ejpam-5617	99	23	)	)	PUNCT
ejpam-5617	100	1	xα	xα	PUNCT
ejpam-5617	101	1	=	=	NOUN
ejpam-5617	101	2	0	0	NUM
ejpam-5617	101	3	for	for	ADP
ejpam-5617	101	4	ui,2	ui,2	PROPN
ejpam-5617	101	5	,	,	PUNCT
ejpam-5617	101	6	i	i	PRON
ejpam-5617	101	7	=	=	NOUN
ejpam-5617	101	8	1	1	NUM
ejpam-5617	101	9	,	,	PUNCT
ejpam-5617	101	10	2	2	NUM
ejpam-5617	101	11	,	,	PUNCT
ejpam-5617	101	12	.	.	PUNCT
ejpam-5617	101	13	.	.	PUNCT
ejpam-5617	101	14	.	.	PUNCT
ejpam-5617	102	1	,	,	PUNCT
ejpam-5617	102	2	n.	n.	PROPN
ejpam-5617	102	3	generally	generally	ADV
ejpam-5617	102	4	,	,	PUNCT
ejpam-5617	102	5	the	the	DET
ejpam-5617	102	6	kth	kth	PROPN
ejpam-5617	102	7	approximate	approximate	ADJ
ejpam-5617	102	8	solution	solution	NOUN
ejpam-5617	102	9	of	of	ADP
ejpam-5617	102	10	the	the	DET
ejpam-5617	102	11	system	system	NOUN
ejpam-5617	102	12	(	(	PUNCT
ejpam-5617	102	13	6)-(7	6)-(7	NOUN
ejpam-5617	102	14	)	)	PUNCT
ejpam-5617	102	15	is	be	AUX
ejpam-5617	102	16	determined	determine	VERB
ejpam-5617	102	17	by	by	ADP
ejpam-5617	102	18	substituting	substitute	VERB
ejpam-5617	102	19	uik	uik	NOUN
ejpam-5617	102	20	(	(	PUNCT
ejpam-5617	102	21	x	x	NOUN
ejpam-5617	102	22	)	)	PUNCT
ejpam-5617	102	23	=	=	SYM
ejpam-5617	102	24	ui(k−1	ui(k−1	NOUN
ejpam-5617	102	25	)	)	PUNCT
ejpam-5617	102	26	(	(	PUNCT
ejpam-5617	102	27	x	x	X
ejpam-5617	102	28	)	)	PUNCT
ejpam-5617	103	1	+	+	CCONJ
ejpam-5617	103	2	ui	ui	PROPN
ejpam-5617	103	3	,	,	PUNCT
ejpam-5617	103	4	kx	kx	PROPN
ejpam-5617	103	5	kα	kα	VERB
ejpam-5617	103	6	into	into	ADP
ejpam-5617	103	7	rf	rf	PROPN
ejpam-5617	103	8	(	(	PUNCT
ejpam-5617	103	9	uik	uik	NOUN
ejpam-5617	103	10	(	(	PUNCT
ejpam-5617	103	11	x	x	NOUN
ejpam-5617	103	12	)	)	PUNCT
ejpam-5617	103	13	)	)	PUNCT
ejpam-5617	103	14	and	and	CCONJ
ejpam-5617	103	15	then	then	ADV
ejpam-5617	103	16	solving	solve	VERB
ejpam-5617	103	17	the	the	DET
ejpam-5617	103	18	algebraic	algebraic	ADJ
ejpam-5617	103	19	equations	equation	NOUN
ejpam-5617	103	20	(	(	PUNCT
ejpam-5617	103	21	12	12	NUM
ejpam-5617	103	22	)	)	PUNCT
ejpam-5617	103	23	for	for	ADP
ejpam-5617	103	24	ui	ui	PROPN
ejpam-5617	103	25	,	,	PUNCT
ejpam-5617	103	26	k.	k.	PROPN
ejpam-5617	103	27	a.	a.	PROPN
ejpam-5617	104	1	el	el	PROPN
ejpam-5617	104	2	-	-	PUNCT
ejpam-5617	104	3	ajou	ajou	PROPN
ejpam-5617	104	4	,	,	PUNCT
ejpam-5617	104	5	a.	a.	PROPN
ejpam-5617	104	6	burqan	burqan	PROPN
ejpam-5617	104	7	/	/	SYM
ejpam-5617	104	8	eur	eur	PROPN
ejpam-5617	104	9	.	.	PUNCT
ejpam-5617	105	1	j.	j.	PROPN
ejpam-5617	105	2	pure	pure	PROPN
ejpam-5617	105	3	appl	appl	PROPN
ejpam-5617	105	4	.	.	PROPN
ejpam-5617	105	5	math	math	PROPN
ejpam-5617	105	6	,	,	PUNCT
ejpam-5617	105	7	18	18	NUM
ejpam-5617	105	8	(	(	PUNCT
ejpam-5617	105	9	1	1	NUM
ejpam-5617	105	10	)	)	PUNCT
ejpam-5617	105	11	(	(	PUNCT
ejpam-5617	105	12	2025	2025	NUM
ejpam-5617	105	13	)	)	PUNCT
ejpam-5617	105	14	,	,	PUNCT
ejpam-5617	105	15	5617	5617	NUM
ejpam-5617	105	16	5	5	NUM
ejpam-5617	105	17	of	of	ADP
ejpam-5617	105	18	19	19	NUM
ejpam-5617	105	19	4	4	NUM
ejpam-5617	105	20	.	.	PUNCT
ejpam-5617	105	21	illustrative	illustrative	ADJ
ejpam-5617	105	22	examples	example	NOUN
ejpam-5617	105	23	this	this	DET
ejpam-5617	105	24	section	section	NOUN
ejpam-5617	105	25	tests	test	VERB
ejpam-5617	105	26	the	the	DET
ejpam-5617	105	27	performance	performance	NOUN
ejpam-5617	105	28	and	and	CCONJ
ejpam-5617	105	29	implementation	implementation	NOUN
ejpam-5617	105	30	of	of	ADP
ejpam-5617	105	31	the	the	DET
ejpam-5617	105	32	suggested	suggest	VERB
ejpam-5617	105	33	method	method	NOUN
ejpam-5617	105	34	on	on	ADP
ejpam-5617	105	35	four	four	NUM
ejpam-5617	105	36	systems	system	NOUN
ejpam-5617	105	37	of	of	ADP
ejpam-5617	105	38	linear	linear	PROPN
ejpam-5617	105	39	and	and	CCONJ
ejpam-5617	105	40	non	non	ADJ
ejpam-5617	105	41	-	-	ADJ
ejpam-5617	105	42	linear	linear	ADJ
ejpam-5617	105	43	fractional	fractional	ADJ
ejpam-5617	105	44	differential	differential	ADJ
ejpam-5617	105	45	equations	equation	NOUN
ejpam-5617	105	46	.	.	PUNCT
ejpam-5617	106	1	the	the	DET
ejpam-5617	106	2	accuracy	accuracy	NOUN
ejpam-5617	106	3	of	of	ADP
ejpam-5617	106	4	the	the	DET
ejpam-5617	106	5	technique	technique	NOUN
ejpam-5617	106	6	will	will	AUX
ejpam-5617	106	7	be	be	AUX
ejpam-5617	106	8	evaluated	evaluate	VERB
ejpam-5617	106	9	by	by	ADP
ejpam-5617	106	10	comparing	compare	VERB
ejpam-5617	106	11	the	the	DET
ejpam-5617	106	12	results	result	NOUN
ejpam-5617	106	13	obtained	obtain	VERB
ejpam-5617	106	14	with	with	ADP
ejpam-5617	106	15	the	the	DET
ejpam-5617	106	16	exact	exact	ADJ
ejpam-5617	106	17	solutions	solution	NOUN
ejpam-5617	106	18	.	.	PUNCT
ejpam-5617	107	1	example	example	NOUN
ejpam-5617	107	2	4.1	4.1	NUM
ejpam-5617	107	3	.	.	PUNCT
ejpam-5617	108	1	consider	consider	VERB
ejpam-5617	108	2	the	the	DET
ejpam-5617	108	3	following	follow	VERB
ejpam-5617	108	4	system	system	NOUN
ejpam-5617	108	5	of	of	ADP
ejpam-5617	108	6	linear	linear	ADJ
ejpam-5617	108	7	fractional	fractional	ADJ
ejpam-5617	108	8	differential	differential	NOUN
ejpam-5617	108	9	equations	equation	NOUN
ejpam-5617	108	10	:	:	PUNCT
ejpam-5617	108	11	dαu1	dαu1	PROPN
ejpam-5617	108	12	(	(	PUNCT
ejpam-5617	108	13	x	x	NOUN
ejpam-5617	108	14	)	)	PUNCT
ejpam-5617	108	15	=	=	SYM
ejpam-5617	108	16	u1	u1	NOUN
ejpam-5617	108	17	(	(	PUNCT
ejpam-5617	108	18	x	x	NOUN
ejpam-5617	108	19	)	)	PUNCT
ejpam-5617	109	1	+	+	CCONJ
ejpam-5617	109	2	u2	u2	PROPN
ejpam-5617	109	3	(	(	PUNCT
ejpam-5617	109	4	x	x	NOUN
ejpam-5617	109	5	)	)	PUNCT
ejpam-5617	109	6	,	,	PUNCT
ejpam-5617	109	7	dαu2	dαu2	PROPN
ejpam-5617	109	8	(	(	PUNCT
ejpam-5617	109	9	x	x	X
ejpam-5617	109	10	)	)	PUNCT
ejpam-5617	109	11	=	=	SYM
ejpam-5617	109	12	−u1	−u1	X
ejpam-5617	109	13	(	(	PUNCT
ejpam-5617	109	14	x	x	X
ejpam-5617	109	15	)	)	PUNCT
ejpam-5617	109	16	+	+	CCONJ
ejpam-5617	109	17	u2	u2	PROPN
ejpam-5617	109	18	(	(	PUNCT
ejpam-5617	109	19	x	x	NOUN
ejpam-5617	109	20	)	)	PUNCT
ejpam-5617	109	21	,	,	PUNCT
ejpam-5617	109	22	(	(	PUNCT
ejpam-5617	109	23	13	13	NUM
ejpam-5617	109	24	)	)	PUNCT
ejpam-5617	109	25	where	where	SCONJ
ejpam-5617	109	26	0	0	NUM
ejpam-5617	109	27	<	<	X
ejpam-5617	109	28	α	α	X
ejpam-5617	109	29	≤	≤	NUM
ejpam-5617	109	30	1	1	NUM
ejpam-5617	109	31	,	,	PUNCT
ejpam-5617	109	32	0	0	NUM
ejpam-5617	109	33	≤	≤	NUM
ejpam-5617	109	34	x	x	PUNCT
ejpam-5617	109	35	with	with	ADP
ejpam-5617	109	36	the	the	DET
ejpam-5617	109	37	initial	initial	ADJ
ejpam-5617	109	38	conditions	condition	NOUN
ejpam-5617	109	39	u1	u1	NOUN
ejpam-5617	109	40	(	(	PUNCT
ejpam-5617	109	41	0	0	NUM
ejpam-5617	109	42	)	)	PUNCT
ejpam-5617	109	43	=	=	SYM
ejpam-5617	109	44	0	0	NUM
ejpam-5617	109	45	,	,	PUNCT
ejpam-5617	109	46	u2	u2	NOUN
ejpam-5617	109	47	(	(	PUNCT
ejpam-5617	109	48	0	0	NUM
ejpam-5617	109	49	)	)	PUNCT
ejpam-5617	109	50	=	=	SYM
ejpam-5617	110	1	1	1	X
ejpam-5617	110	2	.	.	PUNCT
ejpam-5617	110	3	(	(	PUNCT
ejpam-5617	110	4	14	14	NUM
ejpam-5617	110	5	)	)	PUNCT
ejpam-5617	110	6	in	in	ADP
ejpam-5617	110	7	the	the	DET
ejpam-5617	110	8	classical	classical	ADJ
ejpam-5617	110	9	case	case	NOUN
ejpam-5617	110	10	(	(	PUNCT
ejpam-5617	110	11	α	α	NOUN
ejpam-5617	110	12	=	=	NOUN
ejpam-5617	110	13	1	1	NUM
ejpam-5617	110	14	)	)	PUNCT
ejpam-5617	110	15	,	,	PUNCT
ejpam-5617	110	16	the	the	DET
ejpam-5617	110	17	exact	exact	ADJ
ejpam-5617	110	18	solution	solution	NOUN
ejpam-5617	110	19	may	may	AUX
ejpam-5617	110	20	be	be	AUX
ejpam-5617	110	21	obtained	obtain	VERB
ejpam-5617	110	22	analytically	analytically	ADV
ejpam-5617	110	23	and	and	CCONJ
ejpam-5617	110	24	provided	provide	VERB
ejpam-5617	110	25	as	as	SCONJ
ejpam-5617	110	26	follows	follow	VERB
ejpam-5617	110	27	:	:	PUNCT
ejpam-5617	110	28	u1	u1	NOUN
ejpam-5617	110	29	(	(	PUNCT
ejpam-5617	110	30	x	x	NOUN
ejpam-5617	110	31	)	)	PUNCT
ejpam-5617	110	32	=	=	PRON
ejpam-5617	110	33	exsinx	exsinx	NOUN
ejpam-5617	110	34	,	,	PUNCT
ejpam-5617	110	35	u2	u2	PROPN
ejpam-5617	110	36	(	(	PUNCT
ejpam-5617	110	37	x	x	NOUN
ejpam-5617	110	38	)	)	PUNCT
ejpam-5617	110	39	=	=	NOUN
ejpam-5617	110	40	excosx	excosx	NOUN
ejpam-5617	110	41	.	.	PUNCT
ejpam-5617	111	1	(	(	PUNCT
ejpam-5617	111	2	15	15	NUM
ejpam-5617	111	3	)	)	PUNCT
ejpam-5617	111	4	considering	consider	VERB
ejpam-5617	111	5	the	the	DET
ejpam-5617	111	6	lrf	lrf	NOUN
ejpam-5617	111	7	technique	technique	NOUN
ejpam-5617	111	8	to	to	PART
ejpam-5617	111	9	create	create	VERB
ejpam-5617	111	10	an	an	DET
ejpam-5617	111	11	analytical	analytical	ADJ
ejpam-5617	111	12	series	series	NOUN
ejpam-5617	111	13	solution	solution	NOUN
ejpam-5617	111	14	for	for	ADP
ejpam-5617	111	15	system	system	NOUN
ejpam-5617	111	16	(	(	PUNCT
ejpam-5617	111	17	13	13	NUM
ejpam-5617	111	18	)	)	PUNCT
ejpam-5617	111	19	–	–	PUNCT
ejpam-5617	111	20	(	(	PUNCT
ejpam-5617	111	21	14	14	NUM
ejpam-5617	111	22	)	)	PUNCT
ejpam-5617	111	23	,	,	PUNCT
ejpam-5617	111	24	we	we	PRON
ejpam-5617	111	25	start	start	VERB
ejpam-5617	111	26	by	by	ADP
ejpam-5617	111	27	assuming	assume	VERB
ejpam-5617	111	28	that	that	SCONJ
ejpam-5617	111	29	the	the	DET
ejpam-5617	111	30	solution	solution	NOUN
ejpam-5617	111	31	has	have	VERB
ejpam-5617	111	32	the	the	DET
ejpam-5617	111	33	following	follow	VERB
ejpam-5617	111	34	fractional	fractional	ADJ
ejpam-5617	111	35	series	series	NOUN
ejpam-5617	111	36	expansions	expansion	NOUN
ejpam-5617	111	37	:	:	PUNCT
ejpam-5617	111	38	u1	u1	NOUN
ejpam-5617	111	39	(	(	PUNCT
ejpam-5617	111	40	x	x	NOUN
ejpam-5617	111	41	)	)	PUNCT
ejpam-5617	111	42	=	=	SYM
ejpam-5617	112	1	∞∑	∞∑	NUM
ejpam-5617	112	2	n=0	n=0	NUM
ejpam-5617	112	3	u1,n	u1,n	PROPN
ejpam-5617	112	4	xnα	xnα	PROPN
ejpam-5617	112	5	,	,	PUNCT
ejpam-5617	112	6	u2	u2	NOUN
ejpam-5617	112	7	(	(	PUNCT
ejpam-5617	112	8	x	x	NOUN
ejpam-5617	112	9	)	)	PUNCT
ejpam-5617	112	10	=	=	SYM
ejpam-5617	113	1	∞∑	∞∑	NUM
ejpam-5617	113	2	n=0	n=0	NUM
ejpam-5617	113	3	u2,n	u2,n	PROPN
ejpam-5617	113	4	xnα	xnα	ADJ
ejpam-5617	113	5	.	.	PUNCT
ejpam-5617	114	1	(	(	PUNCT
ejpam-5617	114	2	16	16	NUM
ejpam-5617	114	3	)	)	PUNCT
ejpam-5617	114	4	based	base	VERB
ejpam-5617	114	5	on	on	ADP
ejpam-5617	114	6	the	the	DET
ejpam-5617	114	7	initial	initial	ADJ
ejpam-5617	114	8	conditions	condition	NOUN
ejpam-5617	114	9	specified	specify	VERB
ejpam-5617	114	10	in	in	ADP
ejpam-5617	114	11	equation	equation	NOUN
ejpam-5617	114	12	(	(	PUNCT
ejpam-5617	114	13	14	14	NUM
ejpam-5617	114	14	)	)	PUNCT
ejpam-5617	114	15	,	,	PUNCT
ejpam-5617	114	16	we	we	PRON
ejpam-5617	114	17	have	have	VERB
ejpam-5617	114	18	u1,0	u1,0	PROPN
ejpam-5617	114	19	=	=	SYM
ejpam-5617	114	20	0	0	NUM
ejpam-5617	114	21	,	,	PUNCT
ejpam-5617	114	22	u2,0	u2,0	PROPN
ejpam-5617	114	23	=	=	SYM
ejpam-5617	114	24	1	1	NUM
ejpam-5617	114	25	.	.	PUNCT
ejpam-5617	115	1	thus	thus	ADV
ejpam-5617	115	2	,	,	PUNCT
ejpam-5617	115	3	the	the	DET
ejpam-5617	115	4	kth	kth	PROPN
ejpam-5617	115	5	approximation	approximation	NOUN
ejpam-5617	115	6	of	of	ADP
ejpam-5617	115	7	u1	u1	NOUN
ejpam-5617	115	8	(	(	PUNCT
ejpam-5617	115	9	x	x	NOUN
ejpam-5617	115	10	)	)	PUNCT
ejpam-5617	115	11	and	and	CCONJ
ejpam-5617	115	12	u2	u2	PROPN
ejpam-5617	115	13	(	(	PUNCT
ejpam-5617	115	14	x	x	NOUN
ejpam-5617	115	15	)	)	PUNCT
ejpam-5617	115	16	can	can	AUX
ejpam-5617	115	17	be	be	AUX
ejpam-5617	115	18	expressed	express	VERB
ejpam-5617	115	19	as	as	ADP
ejpam-5617	115	20	:	:	PUNCT
ejpam-5617	115	21	u1k	u1k	PROPN
ejpam-5617	115	22	(	(	PUNCT
ejpam-5617	115	23	x	x	X
ejpam-5617	115	24	)	)	PUNCT
ejpam-5617	115	25	=	=	SYM
ejpam-5617	115	26	k∑	k∑	VERB
ejpam-5617	115	27	n=1	n=1	PROPN
ejpam-5617	115	28	u1,n	u1,n	PROPN
ejpam-5617	115	29	xnα	xnα	PROPN
ejpam-5617	115	30	,	,	PUNCT
ejpam-5617	115	31	u2k	u2k	PROPN
ejpam-5617	115	32	(	(	PUNCT
ejpam-5617	115	33	x	x	NOUN
ejpam-5617	115	34	)	)	PUNCT
ejpam-5617	115	35	=	=	SYM
ejpam-5617	115	36	1	1	NUM
ejpam-5617	115	37	+	+	CCONJ
ejpam-5617	115	38	k∑	k∑	ADJ
ejpam-5617	115	39	n=1	n=1	PROPN
ejpam-5617	115	40	u2,n	u2,n	PROPN
ejpam-5617	115	41	xnα	xnα	PROPN
ejpam-5617	115	42	.	.	PUNCT
ejpam-5617	116	1	(	(	PUNCT
ejpam-5617	116	2	17	17	NUM
ejpam-5617	116	3	)	)	PUNCT
ejpam-5617	116	4	to	to	PART
ejpam-5617	116	5	identify	identify	VERB
ejpam-5617	116	6	the	the	DET
ejpam-5617	116	7	additional	additional	ADJ
ejpam-5617	116	8	unknown	unknown	ADJ
ejpam-5617	116	9	coefficients	coefficient	NOUN
ejpam-5617	116	10	of	of	ADP
ejpam-5617	116	11	the	the	DET
ejpam-5617	116	12	series	series	NOUN
ejpam-5617	116	13	given	give	VERB
ejpam-5617	116	14	in	in	ADP
ejpam-5617	116	15	equation	equation	NOUN
ejpam-5617	116	16	(	(	PUNCT
ejpam-5617	116	17	16	16	NUM
ejpam-5617	116	18	)	)	PUNCT
ejpam-5617	116	19	,	,	PUNCT
ejpam-5617	116	20	we	we	PRON
ejpam-5617	116	21	proceed	proceed	VERB
ejpam-5617	116	22	with	with	ADP
ejpam-5617	116	23	the	the	DET
ejpam-5617	116	24	second	second	ADJ
ejpam-5617	116	25	step	step	NOUN
ejpam-5617	116	26	of	of	ADP
ejpam-5617	116	27	the	the	DET
ejpam-5617	116	28	lrf	lrf	NOUN
ejpam-5617	116	29	approach	approach	NOUN
ejpam-5617	116	30	by	by	ADP
ejpam-5617	116	31	defining	define	VERB
ejpam-5617	116	32	the	the	DET
ejpam-5617	116	33	residual	residual	ADJ
ejpam-5617	116	34	functions	function	NOUN
ejpam-5617	116	35	of	of	ADP
ejpam-5617	116	36	equations	equation	NOUN
ejpam-5617	116	37	in	in	ADP
ejpam-5617	116	38	(	(	PUNCT
ejpam-5617	116	39	13	13	NUM
ejpam-5617	116	40	)	)	PUNCT
ejpam-5617	116	41	as	as	SCONJ
ejpam-5617	116	42	follows	follow	VERB
ejpam-5617	116	43	:	:	PUNCT
ejpam-5617	116	44	rf	rf	NUM
ejpam-5617	116	45	(	(	PUNCT
ejpam-5617	116	46	u1	u1	PROPN
ejpam-5617	116	47	(	(	PUNCT
ejpam-5617	116	48	x	x	NOUN
ejpam-5617	116	49	)	)	PUNCT
ejpam-5617	116	50	)	)	PUNCT
ejpam-5617	117	1	=	=	SYM
ejpam-5617	117	2	dαu1	dαu1	PROPN
ejpam-5617	117	3	(	(	PUNCT
ejpam-5617	117	4	x)−	x)−	PROPN
ejpam-5617	117	5	u1	u1	PROPN
ejpam-5617	117	6	(	(	PUNCT
ejpam-5617	117	7	x)−	x)−	PROPN
ejpam-5617	117	8	u2	u2	PROPN
ejpam-5617	117	9	(	(	PUNCT
ejpam-5617	117	10	x	x	NOUN
ejpam-5617	117	11	)	)	PUNCT
ejpam-5617	117	12	,	,	PUNCT
ejpam-5617	117	13	rf	rf	PROPN
ejpam-5617	117	14	(	(	PUNCT
ejpam-5617	117	15	u2(x	u2(x	NOUN
ejpam-5617	117	16	)	)	PUNCT
ejpam-5617	117	17	)	)	PUNCT
ejpam-5617	118	1	=	=	PUNCT
ejpam-5617	118	2	dαu2	dαu2	PROPN
ejpam-5617	118	3	(	(	PUNCT
ejpam-5617	118	4	x	x	X
ejpam-5617	118	5	)	)	PUNCT
ejpam-5617	118	6	+	+	NUM
ejpam-5617	118	7	u1	u1	NOUN
ejpam-5617	118	8	(	(	PUNCT
ejpam-5617	118	9	x)−	x)−	PROPN
ejpam-5617	118	10	u2	u2	PROPN
ejpam-5617	118	11	(	(	PUNCT
ejpam-5617	118	12	x	x	NOUN
ejpam-5617	118	13	)	)	PUNCT
ejpam-5617	118	14	,	,	PUNCT
ejpam-5617	118	15	(	(	PUNCT
ejpam-5617	118	16	18	18	NUM
ejpam-5617	118	17	)	)	PUNCT
ejpam-5617	118	18	and	and	CCONJ
ejpam-5617	118	19	the	the	DET
ejpam-5617	118	20	kth	kth	PROPN
ejpam-5617	118	21	residual	residual	ADJ
ejpam-5617	118	22	functions	function	NOUN
ejpam-5617	118	23	are	be	AUX
ejpam-5617	118	24	expressed	express	VERB
ejpam-5617	118	25	as	as	SCONJ
ejpam-5617	118	26	follows	follow	VERB
ejpam-5617	118	27	:	:	PUNCT
ejpam-5617	118	28	rf	rf	NUM
ejpam-5617	118	29	(	(	PUNCT
ejpam-5617	118	30	u1k	u1k	PROPN
ejpam-5617	118	31	(	(	PUNCT
ejpam-5617	118	32	x	x	NOUN
ejpam-5617	118	33	)	)	PUNCT
ejpam-5617	118	34	)	)	PUNCT
ejpam-5617	119	1	=	=	SYM
ejpam-5617	119	2	dαu1k	dαu1k	PROPN
ejpam-5617	119	3	(	(	PUNCT
ejpam-5617	119	4	x)−	x)−	PROPN
ejpam-5617	119	5	u1k	u1k	PROPN
ejpam-5617	119	6	(	(	PUNCT
ejpam-5617	119	7	x)−	x)−	PROPN
ejpam-5617	119	8	u2k	u2k	PROPN
ejpam-5617	119	9	(	(	PUNCT
ejpam-5617	119	10	x	x	NOUN
ejpam-5617	119	11	)	)	PUNCT
ejpam-5617	119	12	,	,	PUNCT
ejpam-5617	119	13	rf	rf	NUM
ejpam-5617	119	14	(	(	PUNCT
ejpam-5617	119	15	u2k	u2k	PROPN
ejpam-5617	119	16	(	(	PUNCT
ejpam-5617	119	17	x	x	NOUN
ejpam-5617	119	18	)	)	PUNCT
ejpam-5617	119	19	)	)	PUNCT
ejpam-5617	120	1	=	=	SYM
ejpam-5617	120	2	dαu2k	dαu2k	X
ejpam-5617	120	3	(	(	PUNCT
ejpam-5617	120	4	x	x	X
ejpam-5617	120	5	)	)	PUNCT
ejpam-5617	120	6	+	+	CCONJ
ejpam-5617	120	7	u1k	u1k	PROPN
ejpam-5617	120	8	(	(	PUNCT
ejpam-5617	120	9	x)−	x)−	PROPN
ejpam-5617	120	10	u2k	u2k	PROPN
ejpam-5617	120	11	(	(	PUNCT
ejpam-5617	120	12	x	x	NOUN
ejpam-5617	120	13	)	)	PUNCT
ejpam-5617	120	14	.	.	PUNCT
ejpam-5617	121	1	(	(	PUNCT
ejpam-5617	121	2	19	19	NUM
ejpam-5617	121	3	)	)	PUNCT
ejpam-5617	121	4	a.	a.	NOUN
ejpam-5617	121	5	el	el	PROPN
ejpam-5617	121	6	-	-	PUNCT
ejpam-5617	121	7	ajou	ajou	PROPN
ejpam-5617	121	8	,	,	PUNCT
ejpam-5617	121	9	a.	a.	PROPN
ejpam-5617	121	10	burqan	burqan	PROPN
ejpam-5617	121	11	/	/	SYM
ejpam-5617	121	12	eur	eur	PROPN
ejpam-5617	121	13	.	.	PUNCT
ejpam-5617	122	1	j.	j.	PROPN
ejpam-5617	122	2	pure	pure	PROPN
ejpam-5617	122	3	appl	appl	PROPN
ejpam-5617	122	4	.	.	PROPN
ejpam-5617	122	5	math	math	PROPN
ejpam-5617	122	6	,	,	PUNCT
ejpam-5617	122	7	18	18	NUM
ejpam-5617	122	8	(	(	PUNCT
ejpam-5617	122	9	1	1	NUM
ejpam-5617	122	10	)	)	PUNCT
ejpam-5617	122	11	(	(	PUNCT
ejpam-5617	122	12	2025	2025	NUM
ejpam-5617	122	13	)	)	PUNCT
ejpam-5617	122	14	,	,	PUNCT
ejpam-5617	122	15	5617	5617	NUM
ejpam-5617	122	16	6	6	NUM
ejpam-5617	122	17	of	of	ADP
ejpam-5617	122	18	19	19	NUM
ejpam-5617	122	19	by	by	ADP
ejpam-5617	122	20	substituting	substitute	VERB
ejpam-5617	122	21	the	the	DET
ejpam-5617	122	22	first	first	ADJ
ejpam-5617	122	23	approximations	approximation	NOUN
ejpam-5617	122	24	u11	u11	INTJ
ejpam-5617	122	25	(	(	PUNCT
ejpam-5617	122	26	x	x	NOUN
ejpam-5617	122	27	)	)	PUNCT
ejpam-5617	122	28	=	=	SYM
ejpam-5617	123	1	u1,1	u1,1	ADJ
ejpam-5617	123	2	xα	xα	ADJ
ejpam-5617	123	3	,	,	PUNCT
ejpam-5617	123	4	u21	u21	PROPN
ejpam-5617	123	5	(	(	PUNCT
ejpam-5617	123	6	x	x	NOUN
ejpam-5617	123	7	)	)	PUNCT
ejpam-5617	123	8	=	=	SYM
ejpam-5617	123	9	1	1	NUM
ejpam-5617	123	10	+	+	NUM
ejpam-5617	123	11	u2,1x	u2,1x	PROPN
ejpam-5617	123	12	α	α	NOUN
ejpam-5617	123	13	into	into	ADP
ejpam-5617	123	14	the	the	DET
ejpam-5617	123	15	first	first	ADJ
ejpam-5617	123	16	residual	residual	ADJ
ejpam-5617	123	17	functions	function	NOUN
ejpam-5617	123	18	,	,	PUNCT
ejpam-5617	123	19	rf	rf	ADJ
ejpam-5617	123	20	(	(	PUNCT
ejpam-5617	123	21	u11	u11	PROPN
ejpam-5617	123	22	(	(	PUNCT
ejpam-5617	123	23	x	x	NOUN
ejpam-5617	123	24	)	)	PUNCT
ejpam-5617	123	25	)	)	PUNCT
ejpam-5617	123	26	,	,	PUNCT
ejpam-5617	123	27	rf	rf	NUM
ejpam-5617	123	28	(	(	PUNCT
ejpam-5617	123	29	u21	u21	PROPN
ejpam-5617	123	30	(	(	PUNCT
ejpam-5617	123	31	x	x	NOUN
ejpam-5617	123	32	)	)	PUNCT
ejpam-5617	123	33	)	)	PUNCT
ejpam-5617	123	34	,	,	PUNCT
ejpam-5617	123	35	we	we	PRON
ejpam-5617	123	36	obtain	obtain	VERB
ejpam-5617	123	37	rf	rf	PRON
ejpam-5617	123	38	(	(	PUNCT
ejpam-5617	123	39	u11	u11	PROPN
ejpam-5617	123	40	(	(	PUNCT
ejpam-5617	123	41	x	x	NOUN
ejpam-5617	123	42	)	)	PUNCT
ejpam-5617	123	43	)	)	PUNCT
ejpam-5617	124	1	=	=	PUNCT
ejpam-5617	124	2	u1,1γ	u1,1γ	PROPN
ejpam-5617	124	3	(	(	PUNCT
ejpam-5617	124	4	α+	α+	PROPN
ejpam-5617	124	5	1)−	1)−	NUM
ejpam-5617	124	6	u1,1x	u1,1x	NOUN
ejpam-5617	124	7	α	α	NOUN
ejpam-5617	124	8	−	−	PROPN
ejpam-5617	124	9	1−	1−	NUM
ejpam-5617	124	10	u2,1x	u2,1x	PROPN
ejpam-5617	124	11	α	α	PROPN
ejpam-5617	124	12	,	,	PUNCT
ejpam-5617	124	13	rf	rf	ADJ
ejpam-5617	124	14	(	(	PUNCT
ejpam-5617	124	15	u21	u21	PROPN
ejpam-5617	124	16	(	(	PUNCT
ejpam-5617	124	17	x	x	NOUN
ejpam-5617	124	18	)	)	PUNCT
ejpam-5617	124	19	)	)	PUNCT
ejpam-5617	125	1	=	=	PUNCT
ejpam-5617	125	2	u2,1γ	u2,1γ	ADJ
ejpam-5617	125	3	(	(	PUNCT
ejpam-5617	125	4	α+	α+	NOUN
ejpam-5617	125	5	1	1	NUM
ejpam-5617	125	6	)	)	PUNCT
ejpam-5617	125	7	+	+	CCONJ
ejpam-5617	125	8	u1,1x	u1,1x	ADJ
ejpam-5617	125	9	α	α	NOUN
ejpam-5617	125	10	−	−	PROPN
ejpam-5617	125	11	1−	1−	NUM
ejpam-5617	125	12	u2,1x	u2,1x	PROPN
ejpam-5617	125	13	α	α	NOUN
ejpam-5617	125	14	.	.	PUNCT
ejpam-5617	126	1	(	(	PUNCT
ejpam-5617	126	2	20	20	X
ejpam-5617	126	3	)	)	PUNCT
ejpam-5617	126	4	solving	solve	VERB
ejpam-5617	126	5	the	the	DET
ejpam-5617	126	6	equations	equation	NOUN
ejpam-5617	126	7	limx→0rf	limx→0rf	PROPN
ejpam-5617	126	8	(	(	PUNCT
ejpam-5617	126	9	u11	u11	PROPN
ejpam-5617	126	10	(	(	PUNCT
ejpam-5617	126	11	x	x	NOUN
ejpam-5617	126	12	)	)	PUNCT
ejpam-5617	126	13	)	)	PUNCT
ejpam-5617	127	1	=	=	SYM
ejpam-5617	127	2	0	0	NUM
ejpam-5617	127	3	,	,	PUNCT
ejpam-5617	127	4	limx→0rf	limx→0rf	PROPN
ejpam-5617	127	5	(	(	PUNCT
ejpam-5617	127	6	u21	u21	PROPN
ejpam-5617	127	7	(	(	PUNCT
ejpam-5617	127	8	x	x	NOUN
ejpam-5617	127	9	)	)	PUNCT
ejpam-5617	127	10	)	)	PUNCT
ejpam-5617	128	1	=	=	SYM
ejpam-5617	128	2	0	0	NUM
ejpam-5617	128	3	for	for	ADP
ejpam-5617	128	4	u1,1	u1,1	PROPN
ejpam-5617	128	5	,	,	PUNCT
ejpam-5617	128	6	u2,1	u2,1	PROPN
ejpam-5617	128	7	,	,	PUNCT
ejpam-5617	128	8	respectively	respectively	ADV
ejpam-5617	128	9	,	,	PUNCT
ejpam-5617	128	10	we	we	PRON
ejpam-5617	128	11	have	have	VERB
ejpam-5617	128	12	u1,1	u1,1	NOUN
ejpam-5617	128	13	=	=	SYM
ejpam-5617	128	14	1	1	NUM
ejpam-5617	128	15	γ	γ	X
ejpam-5617	128	16	(	(	PUNCT
ejpam-5617	128	17	α+	α+	NOUN
ejpam-5617	128	18	1	1	NUM
ejpam-5617	128	19	)	)	PUNCT
ejpam-5617	128	20	,	,	PUNCT
ejpam-5617	128	21	u2,1	u2,1	PROPN
ejpam-5617	129	1	=	=	NOUN
ejpam-5617	129	2	1	1	NUM
ejpam-5617	129	3	γ	γ	X
ejpam-5617	129	4	(	(	PUNCT
ejpam-5617	129	5	α+	α+	NOUN
ejpam-5617	129	6	1	1	NUM
ejpam-5617	129	7	)	)	PUNCT
ejpam-5617	129	8	.	.	PUNCT
ejpam-5617	130	1	(	(	PUNCT
ejpam-5617	130	2	21	21	NUM
ejpam-5617	130	3	)	)	PUNCT
ejpam-5617	130	4	in	in	ADP
ejpam-5617	130	5	order	order	NOUN
ejpam-5617	130	6	to	to	PART
ejpam-5617	130	7	determine	determine	VERB
ejpam-5617	130	8	the	the	DET
ejpam-5617	130	9	second	second	ADJ
ejpam-5617	130	10	coefficients	coefficient	NOUN
ejpam-5617	130	11	u1,2	u1,2	ADJ
ejpam-5617	130	12	and	and	CCONJ
ejpam-5617	130	13	u2,2	u2,2	PROPN
ejpam-5617	130	14	,	,	PUNCT
ejpam-5617	130	15	substitute	substitute	VERB
ejpam-5617	130	16	the	the	DET
ejpam-5617	130	17	second	second	ADJ
ejpam-5617	130	18	approximations	approximation	NOUN
ejpam-5617	130	19	u12	u12	NOUN
ejpam-5617	130	20	(	(	PUNCT
ejpam-5617	130	21	x	x	NOUN
ejpam-5617	130	22	)	)	PUNCT
ejpam-5617	130	23	=	=	SYM
ejpam-5617	131	1	xα	xα	ADP
ejpam-5617	131	2	γ	γ	PROPN
ejpam-5617	131	3	(	(	PUNCT
ejpam-5617	131	4	α+1	α+1	NUM
ejpam-5617	131	5	)	)	PUNCT
ejpam-5617	131	6	+	+	ADJ
ejpam-5617	131	7	u1,2x	u1,2x	ADJ
ejpam-5617	131	8	2α	2α	NOUN
ejpam-5617	131	9	,	,	PUNCT
ejpam-5617	131	10	u22	u22	PROPN
ejpam-5617	131	11	(	(	PUNCT
ejpam-5617	131	12	x	x	X
ejpam-5617	131	13	)	)	PUNCT
ejpam-5617	131	14	=	=	SYM
ejpam-5617	132	1	1	1	NUM
ejpam-5617	132	2	+	+	NUM
ejpam-5617	132	3	xα	xα	PROPN
ejpam-5617	132	4	γ	γ	PROPN
ejpam-5617	132	5	(	(	PUNCT
ejpam-5617	132	6	α+1	α+1	NUM
ejpam-5617	132	7	)	)	PUNCT
ejpam-5617	133	1	+	+	ADJ
ejpam-5617	133	2	u2,2x	u2,2x	PROPN
ejpam-5617	133	3	2α	2α	NOUN
ejpam-5617	133	4	into	into	ADP
ejpam-5617	133	5	rf	rf	PRON
ejpam-5617	133	6	(	(	PUNCT
ejpam-5617	133	7	u12	u12	PROPN
ejpam-5617	133	8	(	(	PUNCT
ejpam-5617	133	9	x	x	NOUN
ejpam-5617	133	10	)	)	PUNCT
ejpam-5617	133	11	)	)	PUNCT
ejpam-5617	133	12	,	,	PUNCT
ejpam-5617	133	13	rf	rf	PRON
ejpam-5617	133	14	(	(	PUNCT
ejpam-5617	133	15	u22	u22	PROPN
ejpam-5617	133	16	(	(	PUNCT
ejpam-5617	133	17	x	x	NOUN
ejpam-5617	133	18	)	)	PUNCT
ejpam-5617	133	19	)	)	PUNCT
ejpam-5617	133	20	to	to	PART
ejpam-5617	133	21	have	have	VERB
ejpam-5617	133	22	rf	rf	NUM
ejpam-5617	133	23	(	(	PUNCT
ejpam-5617	133	24	u12	u12	PROPN
ejpam-5617	133	25	(	(	PUNCT
ejpam-5617	133	26	x	x	NOUN
ejpam-5617	133	27	)	)	PUNCT
ejpam-5617	133	28	)	)	PUNCT
ejpam-5617	134	1	=	=	SYM
ejpam-5617	134	2	1	1	NUM
ejpam-5617	135	1	+	+	CCONJ
ejpam-5617	135	2	u1,2	u1,2	ADJ
ejpam-5617	135	3	γ	γ	NOUN
ejpam-5617	135	4	(	(	PUNCT
ejpam-5617	135	5	2α+	2α+	NUM
ejpam-5617	135	6	1	1	NUM
ejpam-5617	135	7	)	)	PUNCT
ejpam-5617	135	8	xα	xα	ADP
ejpam-5617	135	9	γ	γ	PROPN
ejpam-5617	135	10	(	(	PUNCT
ejpam-5617	135	11	α+	α+	PROPN
ejpam-5617	135	12	1	1	NUM
ejpam-5617	135	13	)	)	PUNCT
ejpam-5617	135	14	−	−	PROPN
ejpam-5617	135	15	(	(	PUNCT
ejpam-5617	135	16	xα	xα	INTJ
ejpam-5617	135	17	γ	γ	X
ejpam-5617	135	18	(	(	PUNCT
ejpam-5617	135	19	α+	α+	PROPN
ejpam-5617	135	20	1	1	NUM
ejpam-5617	135	21	)	)	PUNCT
ejpam-5617	135	22	+	+	CCONJ
ejpam-5617	135	23	u1,2	u1,2	ADJ
ejpam-5617	135	24	x2α	x2α	X
ejpam-5617	135	25	)	)	PUNCT
ejpam-5617	135	26	−	−	PROPN
ejpam-5617	135	27	(	(	PUNCT
ejpam-5617	135	28	1	1	NUM
ejpam-5617	135	29	+	+	CCONJ
ejpam-5617	135	30	xα	xα	ADP
ejpam-5617	135	31	γ	γ	X
ejpam-5617	135	32	(	(	PUNCT
ejpam-5617	135	33	α+	α+	PROPN
ejpam-5617	135	34	1	1	NUM
ejpam-5617	135	35	)	)	PUNCT
ejpam-5617	135	36	+	+	CCONJ
ejpam-5617	135	37	u2,2	u2,2	PROPN
ejpam-5617	135	38	x2α	x2α	PROPN
ejpam-5617	135	39	)	)	PUNCT
ejpam-5617	135	40	,	,	PUNCT
ejpam-5617	135	41	rf	rf	PRON
ejpam-5617	135	42	(	(	PUNCT
ejpam-5617	135	43	u22	u22	PROPN
ejpam-5617	135	44	(	(	PUNCT
ejpam-5617	135	45	x	x	NOUN
ejpam-5617	135	46	)	)	PUNCT
ejpam-5617	135	47	)	)	PUNCT
ejpam-5617	135	48	=	=	SYM
ejpam-5617	136	1	1	1	NUM
ejpam-5617	136	2	+	+	CCONJ
ejpam-5617	136	3	u2,2	u2,2	PROPN
ejpam-5617	136	4	γ	γ	X
ejpam-5617	136	5	(	(	PUNCT
ejpam-5617	136	6	2α+	2α+	NUM
ejpam-5617	136	7	1	1	NUM
ejpam-5617	136	8	)	)	PUNCT
ejpam-5617	136	9	xα	xα	ADP
ejpam-5617	136	10	γ	γ	PROPN
ejpam-5617	136	11	(	(	PUNCT
ejpam-5617	136	12	α+	α+	PROPN
ejpam-5617	136	13	1	1	NUM
ejpam-5617	136	14	)	)	PUNCT
ejpam-5617	136	15	+	+	CCONJ
ejpam-5617	136	16	(	(	PUNCT
ejpam-5617	136	17	xα	xα	INTJ
ejpam-5617	136	18	γ	γ	X
ejpam-5617	136	19	(	(	PUNCT
ejpam-5617	136	20	α+	α+	PROPN
ejpam-5617	136	21	1	1	NUM
ejpam-5617	136	22	)	)	PUNCT
ejpam-5617	137	1	+	+	CCONJ
ejpam-5617	137	2	u1,2	u1,2	ADJ
ejpam-5617	137	3	x2α	x2α	X
ejpam-5617	137	4	)	)	PUNCT
ejpam-5617	137	5	−	−	PROPN
ejpam-5617	138	1	(	(	PUNCT
ejpam-5617	138	2	1	1	NUM
ejpam-5617	138	3	+	+	CCONJ
ejpam-5617	138	4	xα	xα	ADP
ejpam-5617	138	5	γ	γ	X
ejpam-5617	138	6	(	(	PUNCT
ejpam-5617	138	7	α+	α+	PROPN
ejpam-5617	138	8	1	1	NUM
ejpam-5617	138	9	)	)	PUNCT
ejpam-5617	138	10	+	+	CCONJ
ejpam-5617	139	1	u2,2	u2,2	PROPN
ejpam-5617	139	2	x2α	x2α	PROPN
ejpam-5617	139	3	)	)	PUNCT
ejpam-5617	139	4	.	.	PUNCT
ejpam-5617	140	1	(	(	PUNCT
ejpam-5617	140	2	22	22	X
ejpam-5617	140	3	)	)	PUNCT
ejpam-5617	140	4	making	make	VERB
ejpam-5617	140	5	simple	simple	ADJ
ejpam-5617	140	6	calculations	calculation	NOUN
ejpam-5617	140	7	,	,	PUNCT
ejpam-5617	140	8	the	the	DET
ejpam-5617	140	9	limits	limit	NOUN
ejpam-5617	140	10	limx→0	limx→0	ADV
ejpam-5617	140	11	rf(u12(x	rf(u12(x	NOUN
ejpam-5617	140	12	)	)	PUNCT
ejpam-5617	140	13	)	)	PUNCT
ejpam-5617	140	14	xα	xα	PUNCT
ejpam-5617	141	1	=	=	NOUN
ejpam-5617	141	2	0	0	NUM
ejpam-5617	141	3	,	,	PUNCT
ejpam-5617	141	4	limx→0	limx→0	ADJ
ejpam-5617	141	5	rf(u22(x	rf(u22(x	NOUN
ejpam-5617	141	6	)	)	PUNCT
ejpam-5617	141	7	)	)	PUNCT
ejpam-5617	141	8	xα	xα	PUNCT
ejpam-5617	142	1	=	=	NOUN
ejpam-5617	142	2	0	0	NUM
ejpam-5617	142	3	,	,	PUNCT
ejpam-5617	142	4	yield	yield	VERB
ejpam-5617	142	5	u1,2	u1,2	ADJ
ejpam-5617	142	6	=	=	SYM
ejpam-5617	142	7	2	2	NUM
ejpam-5617	142	8	γ	γ	X
ejpam-5617	142	9	(	(	PUNCT
ejpam-5617	142	10	2α+	2α+	NUM
ejpam-5617	142	11	1	1	NUM
ejpam-5617	142	12	)	)	PUNCT
ejpam-5617	142	13	,	,	PUNCT
ejpam-5617	143	1	u2,2	u2,2	PROPN
ejpam-5617	143	2	=	=	SYM
ejpam-5617	143	3	0	0	PROPN
ejpam-5617	143	4	.	.	PUNCT
ejpam-5617	144	1	(	(	PUNCT
ejpam-5617	144	2	23	23	NUM
ejpam-5617	144	3	)	)	PUNCT
ejpam-5617	144	4	the	the	DET
ejpam-5617	144	5	values	value	NOUN
ejpam-5617	144	6	of	of	ADP
ejpam-5617	144	7	the	the	DET
ejpam-5617	144	8	coefficients	coefficient	NOUN
ejpam-5617	144	9	u1,3	u1,3	ADJ
ejpam-5617	144	10	and	and	CCONJ
ejpam-5617	144	11	u2,3	u2,3	PROPN
ejpam-5617	144	12	are	be	AUX
ejpam-5617	144	13	also	also	ADV
ejpam-5617	144	14	obtained	obtain	VERB
ejpam-5617	144	15	by	by	ADP
ejpam-5617	144	16	substituting	substitute	VERB
ejpam-5617	144	17	u13	u13	NOUN
ejpam-5617	144	18	(	(	PUNCT
ejpam-5617	144	19	x	x	NOUN
ejpam-5617	144	20	)	)	PUNCT
ejpam-5617	144	21	=	=	SYM
ejpam-5617	145	1	xα	xα	ADP
ejpam-5617	145	2	γ	γ	PROPN
ejpam-5617	145	3	(	(	PUNCT
ejpam-5617	145	4	α+1	α+1	NUM
ejpam-5617	145	5	)	)	PUNCT
ejpam-5617	145	6	+	+	CCONJ
ejpam-5617	145	7	2	2	NUM
ejpam-5617	145	8	γ	γ	X
ejpam-5617	145	9	(	(	PUNCT
ejpam-5617	145	10	2α+1)x	2α+1)x	NUM
ejpam-5617	145	11	2α	2α	NOUN
ejpam-5617	145	12	+	+	CCONJ
ejpam-5617	145	13	u1,3	u1,3	PROPN
ejpam-5617	145	14	x3α	x3α	PROPN
ejpam-5617	145	15	and	and	CCONJ
ejpam-5617	145	16	u23	u23	PROPN
ejpam-5617	145	17	(	(	PUNCT
ejpam-5617	145	18	x	x	NOUN
ejpam-5617	145	19	)	)	PUNCT
ejpam-5617	145	20	=	=	SYM
ejpam-5617	145	21	1	1	NUM
ejpam-5617	145	22	+	+	CCONJ
ejpam-5617	145	23	xα	xα	ADP
ejpam-5617	145	24	γ	γ	PROPN
ejpam-5617	145	25	(	(	PUNCT
ejpam-5617	145	26	α+1	α+1	NUM
ejpam-5617	145	27	)	)	PUNCT
ejpam-5617	145	28	+	+	CCONJ
ejpam-5617	146	1	u2,3	u2,3	ADJ
ejpam-5617	146	2	x3α	x3α	PROPN
ejpam-5617	146	3	into	into	ADP
ejpam-5617	146	4	rf	rf	ADJ
ejpam-5617	146	5	(	(	PUNCT
ejpam-5617	146	6	u13	u13	PROPN
ejpam-5617	146	7	(	(	PUNCT
ejpam-5617	146	8	x	x	NOUN
ejpam-5617	146	9	)	)	PUNCT
ejpam-5617	146	10	)	)	PUNCT
ejpam-5617	146	11	,	,	PUNCT
ejpam-5617	146	12	rf	rf	NUM
ejpam-5617	146	13	(	(	PUNCT
ejpam-5617	146	14	u23	u23	PROPN
ejpam-5617	146	15	(	(	PUNCT
ejpam-5617	146	16	x	x	NOUN
ejpam-5617	146	17	)	)	PUNCT
ejpam-5617	146	18	)	)	PUNCT
ejpam-5617	146	19	,	,	PUNCT
ejpam-5617	146	20	and	and	CCONJ
ejpam-5617	146	21	then	then	ADV
ejpam-5617	146	22	we	we	PRON
ejpam-5617	146	23	solve	solve	VERB
ejpam-5617	146	24	the	the	DET
ejpam-5617	146	25	following	follow	VERB
ejpam-5617	146	26	equations	equation	NOUN
ejpam-5617	146	27	:	:	PUNCT
ejpam-5617	147	1	lim	lim	PROPN
ejpam-5617	147	2	x→0	x→0	PROPN
ejpam-5617	147	3	rf	rf	PRON
ejpam-5617	147	4	(	(	PUNCT
ejpam-5617	147	5	u13	u13	PROPN
ejpam-5617	147	6	(	(	PUNCT
ejpam-5617	147	7	x	x	NOUN
ejpam-5617	147	8	)	)	PUNCT
ejpam-5617	147	9	)	)	PUNCT
ejpam-5617	147	10	x2α	x2α	PUNCT
ejpam-5617	148	1	=	=	PUNCT
ejpam-5617	148	2	u1,3	u1,3	ADJ
ejpam-5617	148	3	γ	γ	X
ejpam-5617	148	4	(	(	PUNCT
ejpam-5617	148	5	3α+	3α+	NUM
ejpam-5617	148	6	1	1	NUM
ejpam-5617	148	7	)	)	PUNCT
ejpam-5617	148	8	γ	γ	NOUN
ejpam-5617	148	9	(	(	PUNCT
ejpam-5617	148	10	2α+	2α+	NUM
ejpam-5617	148	11	1	1	NUM
ejpam-5617	148	12	)	)	PUNCT
ejpam-5617	148	13	−	−	PROPN
ejpam-5617	148	14	2	2	NUM
ejpam-5617	148	15	γ	γ	X
ejpam-5617	148	16	(	(	PUNCT
ejpam-5617	148	17	2α+	2α+	NUM
ejpam-5617	148	18	1	1	NUM
ejpam-5617	148	19	)	)	PUNCT
ejpam-5617	148	20	=	=	SYM
ejpam-5617	148	21	0	0	PROPN
ejpam-5617	148	22	,	,	PUNCT
ejpam-5617	148	23	lim	lim	NOUN
ejpam-5617	148	24	x→0	x→0	PROPN
ejpam-5617	149	1	rf	rf	PRON
ejpam-5617	149	2	(	(	PUNCT
ejpam-5617	149	3	u23	u23	PROPN
ejpam-5617	149	4	(	(	PUNCT
ejpam-5617	149	5	x	x	NOUN
ejpam-5617	149	6	)	)	PUNCT
ejpam-5617	149	7	)	)	PUNCT
ejpam-5617	149	8	x2α	x2α	X
ejpam-5617	150	1	=	=	PUNCT
ejpam-5617	150	2	u2,3	u2,3	ADJ
ejpam-5617	150	3	γ	γ	X
ejpam-5617	150	4	(	(	PUNCT
ejpam-5617	150	5	3α+	3α+	NUM
ejpam-5617	150	6	1	1	NUM
ejpam-5617	150	7	)	)	PUNCT
ejpam-5617	150	8	γ	γ	NOUN
ejpam-5617	150	9	(	(	PUNCT
ejpam-5617	150	10	2α+	2α+	NUM
ejpam-5617	150	11	1	1	NUM
ejpam-5617	150	12	)	)	PUNCT
ejpam-5617	150	13	+	+	CCONJ
ejpam-5617	150	14	2	2	NUM
ejpam-5617	150	15	γ	γ	X
ejpam-5617	150	16	(	(	PUNCT
ejpam-5617	150	17	2α+	2α+	NUM
ejpam-5617	150	18	1	1	NUM
ejpam-5617	150	19	)	)	PUNCT
ejpam-5617	150	20	=	=	SYM
ejpam-5617	150	21	0	0	X
ejpam-5617	150	22	.	.	PUNCT
ejpam-5617	151	1	(	(	PUNCT
ejpam-5617	151	2	24	24	NUM
ejpam-5617	151	3	)	)	PUNCT
ejpam-5617	151	4	then	then	ADV
ejpam-5617	151	5	we	we	PRON
ejpam-5617	151	6	have	have	VERB
ejpam-5617	151	7	u1,3	u1,3	NOUN
ejpam-5617	151	8	=	=	SYM
ejpam-5617	151	9	2	2	NUM
ejpam-5617	151	10	γ	γ	X
ejpam-5617	151	11	(	(	PUNCT
ejpam-5617	151	12	3α+	3α+	NUM
ejpam-5617	151	13	1	1	NUM
ejpam-5617	151	14	)	)	PUNCT
ejpam-5617	151	15	,	,	PUNCT
ejpam-5617	151	16	u2,3	u2,3	NOUN
ejpam-5617	151	17	=	=	NOUN
ejpam-5617	151	18	−	−	PROPN
ejpam-5617	151	19	2	2	NUM
ejpam-5617	151	20	γ	γ	X
ejpam-5617	151	21	(	(	PUNCT
ejpam-5617	151	22	3α+	3α+	NUM
ejpam-5617	151	23	1	1	NUM
ejpam-5617	151	24	)	)	PUNCT
ejpam-5617	151	25	.	.	PUNCT
ejpam-5617	152	1	(	(	PUNCT
ejpam-5617	152	2	25	25	NUM
ejpam-5617	152	3	)	)	PUNCT
ejpam-5617	152	4	proceeding	proceeding	NOUN
ejpam-5617	152	5	in	in	ADP
ejpam-5617	152	6	the	the	DET
ejpam-5617	152	7	same	same	ADJ
ejpam-5617	152	8	manner	manner	NOUN
ejpam-5617	152	9	,	,	PUNCT
ejpam-5617	152	10	we	we	PRON
ejpam-5617	152	11	get	get	VERB
ejpam-5617	152	12	u1,4	u1,4	ADV
ejpam-5617	152	13	=	=	SYM
ejpam-5617	152	14	0	0	NUM
ejpam-5617	152	15	,	,	PUNCT
ejpam-5617	152	16	u2,4	u2,4	PROPN
ejpam-5617	152	17	=	=	SYM
ejpam-5617	152	18	−	−	PROPN
ejpam-5617	152	19	4	4	NUM
ejpam-5617	152	20	γ	γ	X
ejpam-5617	152	21	(	(	PUNCT
ejpam-5617	152	22	4α+	4α+	NUM
ejpam-5617	152	23	1	1	NUM
ejpam-5617	152	24	)	)	PUNCT
ejpam-5617	152	25	.	.	PUNCT
ejpam-5617	153	1	(	(	PUNCT
ejpam-5617	153	2	26	26	NUM
ejpam-5617	153	3	)	)	PUNCT
ejpam-5617	153	4	a.	a.	NOUN
ejpam-5617	153	5	el	el	PROPN
ejpam-5617	153	6	-	-	PUNCT
ejpam-5617	153	7	ajou	ajou	PROPN
ejpam-5617	153	8	,	,	PUNCT
ejpam-5617	153	9	a.	a.	PROPN
ejpam-5617	153	10	burqan	burqan	PROPN
ejpam-5617	153	11	/	/	SYM
ejpam-5617	153	12	eur	eur	PROPN
ejpam-5617	153	13	.	.	PUNCT
ejpam-5617	154	1	j.	j.	PROPN
ejpam-5617	154	2	pure	pure	PROPN
ejpam-5617	154	3	appl	appl	PROPN
ejpam-5617	154	4	.	.	PROPN
ejpam-5617	154	5	math	math	PROPN
ejpam-5617	154	6	,	,	PUNCT
ejpam-5617	154	7	18	18	NUM
ejpam-5617	154	8	(	(	PUNCT
ejpam-5617	154	9	1	1	NUM
ejpam-5617	154	10	)	)	PUNCT
ejpam-5617	154	11	(	(	PUNCT
ejpam-5617	154	12	2025	2025	NUM
ejpam-5617	154	13	)	)	PUNCT
ejpam-5617	154	14	,	,	PUNCT
ejpam-5617	154	15	5617	5617	NUM
ejpam-5617	154	16	7	7	NUM
ejpam-5617	154	17	of	of	ADP
ejpam-5617	154	18	19	19	NUM
ejpam-5617	154	19	table	table	NOUN
ejpam-5617	154	20	1	1	NUM
ejpam-5617	154	21	:	:	PUNCT
ejpam-5617	154	22	the	the	DET
ejpam-5617	154	23	coefficients	coefficient	NOUN
ejpam-5617	154	24	of	of	ADP
ejpam-5617	154	25	the	the	DET
ejpam-5617	154	26	7th	7th	ADJ
ejpam-5617	154	27	approximation	approximation	NOUN
ejpam-5617	154	28	of	of	ADP
ejpam-5617	154	29	u1	u1	NOUN
ejpam-5617	154	30	(	(	PUNCT
ejpam-5617	154	31	x	x	NOUN
ejpam-5617	154	32	)	)	PUNCT
ejpam-5617	154	33	,	,	PUNCT
ejpam-5617	154	34	u2	u2	PROPN
ejpam-5617	154	35	(	(	PUNCT
ejpam-5617	154	36	x	x	NOUN
ejpam-5617	154	37	)	)	PUNCT
ejpam-5617	154	38	for	for	ADP
ejpam-5617	154	39	the	the	DET
ejpam-5617	154	40	system	system	NOUN
ejpam-5617	154	41	(	(	PUNCT
ejpam-5617	154	42	13)(14	13)(14	NUM
ejpam-5617	154	43	)	)	PUNCT
ejpam-5617	154	44	.	.	PUNCT
ejpam-5617	155	1	k	k	PROPN
ejpam-5617	155	2	u1,k	u1,k	PROPN
ejpam-5617	155	3	u2,k	u2,k	PROPN
ejpam-5617	155	4	0	0	NUM
ejpam-5617	155	5	0	0	NUM
ejpam-5617	155	6	1	1	NUM
ejpam-5617	155	7	1	1	NUM
ejpam-5617	155	8	1	1	NUM
ejpam-5617	155	9	γ	γ	X
ejpam-5617	155	10	(	(	PUNCT
ejpam-5617	155	11	α+1	α+1	NUM
ejpam-5617	155	12	)	)	PUNCT
ejpam-5617	155	13	1	1	NUM
ejpam-5617	155	14	γ	γ	X
ejpam-5617	155	15	(	(	PUNCT
ejpam-5617	155	16	α+1	α+1	NUM
ejpam-5617	155	17	)	)	PUNCT
ejpam-5617	155	18	2	2	NUM
ejpam-5617	155	19	2	2	NUM
ejpam-5617	155	20	γ	γ	X
ejpam-5617	155	21	(	(	PUNCT
ejpam-5617	155	22	2α+1	2α+1	PROPN
ejpam-5617	155	23	)	)	PUNCT
ejpam-5617	155	24	0	0	NUM
ejpam-5617	155	25	3	3	NUM
ejpam-5617	155	26	2	2	NUM
ejpam-5617	155	27	γ	γ	X
ejpam-5617	155	28	(	(	PUNCT
ejpam-5617	155	29	3α+1	3α+1	PROPN
ejpam-5617	155	30	)	)	PUNCT
ejpam-5617	155	31	−	−	PROPN
ejpam-5617	155	32	2	2	NUM
ejpam-5617	155	33	γ	γ	X
ejpam-5617	155	34	(	(	PUNCT
ejpam-5617	155	35	3α+1	3α+1	PROPN
ejpam-5617	155	36	)	)	PUNCT
ejpam-5617	155	37	4	4	NUM
ejpam-5617	155	38	0	0	NUM
ejpam-5617	155	39	−	−	NUM
ejpam-5617	155	40	4	4	NUM
ejpam-5617	155	41	γ	γ	X
ejpam-5617	155	42	(	(	PUNCT
ejpam-5617	155	43	4α+1	4α+1	PROPN
ejpam-5617	155	44	)	)	PUNCT
ejpam-5617	155	45	5	5	NUM
ejpam-5617	155	46	−	−	PROPN
ejpam-5617	155	47	4	4	NUM
ejpam-5617	155	48	γ	γ	X
ejpam-5617	155	49	(	(	PUNCT
ejpam-5617	155	50	5α+1	5α+1	PROPN
ejpam-5617	155	51	)	)	PUNCT
ejpam-5617	155	52	−	−	PROPN
ejpam-5617	155	53	4	4	NUM
ejpam-5617	155	54	γ	γ	X
ejpam-5617	155	55	(	(	PUNCT
ejpam-5617	155	56	5α+1	5α+1	PROPN
ejpam-5617	155	57	)	)	PUNCT
ejpam-5617	155	58	6	6	NUM
ejpam-5617	155	59	−	−	PROPN
ejpam-5617	155	60	8	8	NUM
ejpam-5617	155	61	γ	γ	X
ejpam-5617	155	62	(	(	PUNCT
ejpam-5617	155	63	6α+1	6α+1	PROPN
ejpam-5617	155	64	)	)	PUNCT
ejpam-5617	155	65	0	0	NUM
ejpam-5617	155	66	7	7	NUM
ejpam-5617	155	67	−	−	NUM
ejpam-5617	155	68	8	8	NUM
ejpam-5617	155	69	γ	γ	X
ejpam-5617	155	70	(	(	PUNCT
ejpam-5617	155	71	7α+1	7α+1	PROPN
ejpam-5617	155	72	)	)	PUNCT
ejpam-5617	155	73	8	8	NUM
ejpam-5617	155	74	γ	γ	X
ejpam-5617	155	75	(	(	PUNCT
ejpam-5617	155	76	7α+1	7α+1	PROPN
ejpam-5617	155	77	)	)	PUNCT
ejpam-5617	155	78	for	for	ADP
ejpam-5617	155	79	k	k	PROPN
ejpam-5617	155	80	=	=	SYM
ejpam-5617	155	81	5	5	NUM
ejpam-5617	155	82	,	,	PUNCT
ejpam-5617	155	83	6	6	NUM
ejpam-5617	155	84	,	,	PUNCT
ejpam-5617	155	85	7	7	NUM
ejpam-5617	155	86	,	,	PUNCT
ejpam-5617	155	87	the	the	DET
ejpam-5617	155	88	algebraic	algebraic	ADJ
ejpam-5617	155	89	equations	equation	NOUN
ejpam-5617	155	90	limx→0	limx→0	ADV
ejpam-5617	155	91	rf(u1k(x	rf(u1k(x	VERB
ejpam-5617	155	92	)	)	PUNCT
ejpam-5617	155	93	)	)	PUNCT
ejpam-5617	155	94	x(k−1)α	x(k−1)α	NOUN
ejpam-5617	156	1	=	=	SYM
ejpam-5617	156	2	0	0	NUM
ejpam-5617	156	3	,	,	PUNCT
ejpam-5617	156	4	limx→0	limx→0	ADV
ejpam-5617	156	5	rf(u2k(x	rf(u2k(x	PROPN
ejpam-5617	156	6	)	)	PUNCT
ejpam-5617	156	7	)	)	PUNCT
ejpam-5617	157	1	x(k−1)α	x(k−1)α	NOUN
ejpam-5617	158	1	=	=	SYM
ejpam-5617	158	2	0	0	NUM
ejpam-5617	158	3	can	can	AUX
ejpam-5617	158	4	be	be	AUX
ejpam-5617	158	5	solved	solve	VERB
ejpam-5617	158	6	repeatedly	repeatedly	ADV
ejpam-5617	158	7	to	to	PART
ejpam-5617	158	8	give	give	VERB
ejpam-5617	158	9	the	the	DET
ejpam-5617	158	10	coefficients	coefficient	NOUN
ejpam-5617	158	11	of	of	ADP
ejpam-5617	158	12	the	the	DET
ejpam-5617	158	13	7th	7th	ADJ
ejpam-5617	158	14	approximation	approximation	NOUN
ejpam-5617	158	15	.	.	PUNCT
ejpam-5617	159	1	the	the	DET
ejpam-5617	159	2	needed	need	VERB
ejpam-5617	159	3	coefficients	coefficient	NOUN
ejpam-5617	159	4	are	be	AUX
ejpam-5617	159	5	summarized	summarize	VERB
ejpam-5617	159	6	in	in	ADP
ejpam-5617	159	7	table	table	NOUN
ejpam-5617	159	8	1	1	NUM
ejpam-5617	159	9	.	.	PUNCT
ejpam-5617	160	1	so	so	ADV
ejpam-5617	160	2	,	,	PUNCT
ejpam-5617	160	3	the	the	DET
ejpam-5617	160	4	lrf	lrf	NOUN
ejpam-5617	160	5	solution	solution	NOUN
ejpam-5617	160	6	of	of	ADP
ejpam-5617	160	7	the	the	DET
ejpam-5617	160	8	system	system	NOUN
ejpam-5617	160	9	(	(	PUNCT
ejpam-5617	160	10	13)-(14	13)-(14	NOUN
ejpam-5617	160	11	)	)	PUNCT
ejpam-5617	160	12	has	have	VERB
ejpam-5617	160	13	the	the	DET
ejpam-5617	160	14	following	follow	VERB
ejpam-5617	160	15	series	series	NOUN
ejpam-5617	160	16	expansions	expansion	NOUN
ejpam-5617	160	17	:	:	PUNCT
ejpam-5617	160	18	u1	u1	NOUN
ejpam-5617	160	19	(	(	PUNCT
ejpam-5617	160	20	x	x	NOUN
ejpam-5617	160	21	)	)	PUNCT
ejpam-5617	160	22	=	=	SYM
ejpam-5617	161	1	xα	xα	ADP
ejpam-5617	161	2	γ	γ	X
ejpam-5617	161	3	(	(	PUNCT
ejpam-5617	161	4	α+	α+	PROPN
ejpam-5617	161	5	1	1	NUM
ejpam-5617	161	6	)	)	PUNCT
ejpam-5617	161	7	+	+	NUM
ejpam-5617	161	8	2x2α	2x2α	ADJ
ejpam-5617	161	9	γ	γ	X
ejpam-5617	161	10	(	(	PUNCT
ejpam-5617	161	11	2α+	2α+	NUM
ejpam-5617	161	12	1	1	NUM
ejpam-5617	161	13	)	)	PUNCT
ejpam-5617	161	14	+	+	CCONJ
ejpam-5617	161	15	2x3α	2x3α	NUM
ejpam-5617	161	16	γ	γ	NOUN
ejpam-5617	161	17	(	(	PUNCT
ejpam-5617	161	18	3α+	3α+	NUM
ejpam-5617	161	19	1	1	NUM
ejpam-5617	161	20	)	)	PUNCT
ejpam-5617	161	21	−	−	PROPN
ejpam-5617	161	22	4	4	NUM
ejpam-5617	161	23	x5α	x5α	SYM
ejpam-5617	161	24	γ	γ	X
ejpam-5617	161	25	(	(	PUNCT
ejpam-5617	161	26	5α+	5α+	NUM
ejpam-5617	161	27	1	1	NUM
ejpam-5617	161	28	)	)	PUNCT
ejpam-5617	161	29	−	−	PROPN
ejpam-5617	161	30	8	8	NUM
ejpam-5617	161	31	x6α	x6α	PROPN
ejpam-5617	161	32	γ	γ	X
ejpam-5617	161	33	(	(	PUNCT
ejpam-5617	161	34	6α+	6α+	NUM
ejpam-5617	161	35	1	1	NUM
ejpam-5617	161	36	)	)	PUNCT
ejpam-5617	161	37	−	−	PROPN
ejpam-5617	161	38	8	8	NUM
ejpam-5617	161	39	x7α	x7α	PROPN
ejpam-5617	161	40	γ	γ	X
ejpam-5617	161	41	(	(	PUNCT
ejpam-5617	161	42	7α+	7α+	NUM
ejpam-5617	161	43	1	1	NUM
ejpam-5617	161	44	)	)	PUNCT
ejpam-5617	161	45	+	+	PROPN
ejpam-5617	161	46	.	.	PUNCT
ejpam-5617	161	47	.	.	PUNCT
ejpam-5617	161	48	.	.	PUNCT
ejpam-5617	162	1	,	,	PUNCT
ejpam-5617	162	2	u2	u2	NOUN
ejpam-5617	162	3	(	(	PUNCT
ejpam-5617	162	4	x	x	NOUN
ejpam-5617	162	5	)	)	PUNCT
ejpam-5617	162	6	=	=	SYM
ejpam-5617	162	7	1	1	NUM
ejpam-5617	162	8	+	+	NUM
ejpam-5617	162	9	xα	xα	ADP
ejpam-5617	162	10	γ	γ	X
ejpam-5617	162	11	(	(	PUNCT
ejpam-5617	162	12	α+	α+	PROPN
ejpam-5617	162	13	1	1	NUM
ejpam-5617	162	14	)	)	PUNCT
ejpam-5617	162	15	−	−	PROPN
ejpam-5617	162	16	2x3α	2x3α	NUM
ejpam-5617	162	17	γ	γ	X
ejpam-5617	162	18	(	(	PUNCT
ejpam-5617	162	19	3α+	3α+	NUM
ejpam-5617	162	20	1	1	NUM
ejpam-5617	162	21	)	)	PUNCT
ejpam-5617	162	22	−	−	PROPN
ejpam-5617	162	23	4	4	NUM
ejpam-5617	162	24	x4α	x4α	PROPN
ejpam-5617	162	25	γ	γ	X
ejpam-5617	162	26	(	(	PUNCT
ejpam-5617	162	27	4α+	4α+	NUM
ejpam-5617	162	28	1	1	NUM
ejpam-5617	162	29	)	)	PUNCT
ejpam-5617	162	30	−	−	PROPN
ejpam-5617	162	31	4	4	NUM
ejpam-5617	162	32	x5α	x5α	SYM
ejpam-5617	162	33	γ	γ	X
ejpam-5617	162	34	(	(	PUNCT
ejpam-5617	162	35	5α+	5α+	NUM
ejpam-5617	162	36	1	1	NUM
ejpam-5617	162	37	)	)	PUNCT
ejpam-5617	162	38	+	+	CCONJ
ejpam-5617	162	39	8	8	NUM
ejpam-5617	162	40	x7α	x7α	PROPN
ejpam-5617	162	41	γ	γ	X
ejpam-5617	162	42	(	(	PUNCT
ejpam-5617	162	43	7α+	7α+	NUM
ejpam-5617	162	44	1	1	NUM
ejpam-5617	162	45	)	)	PUNCT
ejpam-5617	162	46	+	+	CCONJ
ejpam-5617	162	47	.	.	PUNCT
ejpam-5617	162	48	.	.	PUNCT
ejpam-5617	162	49	.	.	PUNCT
ejpam-5617	162	50	.	.	PUNCT
ejpam-5617	163	1	(	(	PUNCT
ejpam-5617	163	2	27	27	NUM
ejpam-5617	163	3	)	)	PUNCT
ejpam-5617	163	4	when	when	SCONJ
ejpam-5617	163	5	α	α	NOUN
ejpam-5617	163	6	=	=	SYM
ejpam-5617	163	7	1	1	NUM
ejpam-5617	163	8	,	,	PUNCT
ejpam-5617	163	9	the	the	DET
ejpam-5617	163	10	series	series	NOUN
ejpam-5617	163	11	solution	solution	NOUN
ejpam-5617	163	12	(	(	PUNCT
ejpam-5617	163	13	27	27	NUM
ejpam-5617	163	14	)	)	PUNCT
ejpam-5617	163	15	becomes	become	VERB
ejpam-5617	163	16	as	as	SCONJ
ejpam-5617	163	17	follows	follow	VERB
ejpam-5617	163	18	:	:	PUNCT
ejpam-5617	163	19	u1	u1	NOUN
ejpam-5617	163	20	(	(	PUNCT
ejpam-5617	163	21	x	x	NOUN
ejpam-5617	163	22	)	)	PUNCT
ejpam-5617	163	23	=	=	SYM
ejpam-5617	163	24	x+	x+	PUNCT
ejpam-5617	164	1	x2	x2	INTJ
ejpam-5617	165	1	+	+	CCONJ
ejpam-5617	165	2	x3	x3	ADJ
ejpam-5617	165	3	3	3	NUM
ejpam-5617	165	4	−	−	PROPN
ejpam-5617	165	5	x5	x5	NOUN
ejpam-5617	165	6	30	30	NUM
ejpam-5617	165	7	−	−	PROPN
ejpam-5617	165	8	x6	x6	PROPN
ejpam-5617	165	9	90	90	NUM
ejpam-5617	165	10	−	−	NOUN
ejpam-5617	165	11	x7	x7	NOUN
ejpam-5617	165	12	630	630	NUM
ejpam-5617	165	13	+	+	CCONJ
ejpam-5617	165	14	.	.	PUNCT
ejpam-5617	165	15	.	.	PUNCT
ejpam-5617	165	16	.	.	PUNCT
ejpam-5617	166	1	,	,	PUNCT
ejpam-5617	166	2	u2	u2	NOUN
ejpam-5617	166	3	(	(	PUNCT
ejpam-5617	166	4	x	x	NOUN
ejpam-5617	166	5	)	)	PUNCT
ejpam-5617	166	6	=	=	SYM
ejpam-5617	166	7	1	1	NUM
ejpam-5617	166	8	+	+	CCONJ
ejpam-5617	166	9	x−	x−	PROPN
ejpam-5617	166	10	x3	x3	VERB
ejpam-5617	166	11	3	3	NUM
ejpam-5617	166	12	−	−	NOUN
ejpam-5617	166	13	x4	x4	PROPN
ejpam-5617	166	14	6	6	NUM
ejpam-5617	166	15	−	−	PROPN
ejpam-5617	166	16	x5	x5	NOUN
ejpam-5617	166	17	30	30	NUM
ejpam-5617	166	18	+	+	CCONJ
ejpam-5617	166	19	x7	x7	NOUN
ejpam-5617	166	20	630	630	NUM
ejpam-5617	166	21	+	+	CCONJ
ejpam-5617	166	22	.	.	PUNCT
ejpam-5617	166	23	.	.	PUNCT
ejpam-5617	166	24	.	.	PUNCT
ejpam-5617	167	1	,	,	PUNCT
ejpam-5617	167	2	(	(	PUNCT
ejpam-5617	167	3	28	28	NUM
ejpam-5617	167	4	)	)	PUNCT
ejpam-5617	167	5	which	which	PRON
ejpam-5617	167	6	is	be	AUX
ejpam-5617	167	7	the	the	DET
ejpam-5617	167	8	expansion	expansion	NOUN
ejpam-5617	167	9	of	of	ADP
ejpam-5617	167	10	the	the	DET
ejpam-5617	167	11	exact	exact	ADJ
ejpam-5617	167	12	solution	solution	NOUN
ejpam-5617	167	13	given	give	VERB
ejpam-5617	167	14	in	in	ADP
ejpam-5617	167	15	(	(	PUNCT
ejpam-5617	167	16	15	15	NUM
ejpam-5617	167	17	)	)	PUNCT
ejpam-5617	167	18	.	.	PUNCT
ejpam-5617	168	1	in	in	ADP
ejpam-5617	168	2	figure	figure	NOUN
ejpam-5617	168	3	1	1	NUM
ejpam-5617	168	4	,	,	PUNCT
ejpam-5617	168	5	the	the	DET
ejpam-5617	168	6	graphs	graph	NOUN
ejpam-5617	168	7	show	show	VERB
ejpam-5617	168	8	the	the	DET
ejpam-5617	168	9	7th	7th	ADJ
ejpam-5617	168	10	approximate	approximate	ADJ
ejpam-5617	168	11	solution	solution	NOUN
ejpam-5617	168	12	of	of	ADP
ejpam-5617	168	13	the	the	DET
ejpam-5617	168	14	system	system	NOUN
ejpam-5617	168	15	(	(	PUNCT
ejpam-5617	168	16	13)-(14	13)-(14	NUM
ejpam-5617	168	17	)	)	PUNCT
ejpam-5617	168	18	at	at	ADP
ejpam-5617	168	19	different	different	ADJ
ejpam-5617	168	20	values	value	NOUN
ejpam-5617	168	21	of	of	ADP
ejpam-5617	168	22	α	α	NOUN
ejpam-5617	168	23	,	,	PUNCT
ejpam-5617	168	24	as	as	ADV
ejpam-5617	168	25	well	well	ADV
ejpam-5617	168	26	as	as	ADP
ejpam-5617	168	27	the	the	DET
ejpam-5617	168	28	exact	exact	ADJ
ejpam-5617	168	29	solution	solution	NOUN
ejpam-5617	168	30	at	at	ADP
ejpam-5617	168	31	α	α	NOUN
ejpam-5617	168	32	=	=	SYM
ejpam-5617	168	33	1	1	NUM
ejpam-5617	168	34	.	.	PUNCT
ejpam-5617	169	1	the	the	DET
ejpam-5617	169	2	graph	graph	NOUN
ejpam-5617	169	3	demonstrates	demonstrate	VERB
ejpam-5617	169	4	strong	strong	ADJ
ejpam-5617	169	5	agreement	agreement	NOUN
ejpam-5617	169	6	between	between	ADP
ejpam-5617	169	7	the	the	DET
ejpam-5617	169	8	7th	7th	ADJ
ejpam-5617	169	9	approximate	approximate	ADJ
ejpam-5617	169	10	solution	solution	NOUN
ejpam-5617	169	11	and	and	CCONJ
ejpam-5617	169	12	the	the	DET
ejpam-5617	169	13	exact	exact	ADJ
ejpam-5617	169	14	solution	solution	NOUN
ejpam-5617	169	15	at	at	ADP
ejpam-5617	169	16	α	α	NOUN
ejpam-5617	169	17	=	=	SYM
ejpam-5617	169	18	1	1	X
ejpam-5617	169	19	.	.	PUNCT
ejpam-5617	170	1	furthermore	furthermore	ADV
ejpam-5617	170	2	,	,	PUNCT
ejpam-5617	170	3	it	it	PRON
ejpam-5617	170	4	illustrates	illustrate	VERB
ejpam-5617	170	5	the	the	DET
ejpam-5617	170	6	impact	impact	NOUN
ejpam-5617	170	7	of	of	ADP
ejpam-5617	170	8	the	the	DET
ejpam-5617	170	9	derivative	derivative	ADJ
ejpam-5617	170	10	order	order	NOUN
ejpam-5617	170	11	on	on	ADP
ejpam-5617	170	12	the	the	DET
ejpam-5617	170	13	solution	solution	NOUN
ejpam-5617	170	14	behavior	behavior	NOUN
ejpam-5617	170	15	,	,	PUNCT
ejpam-5617	170	16	revealing	reveal	VERB
ejpam-5617	170	17	that	that	SCONJ
ejpam-5617	170	18	the	the	DET
ejpam-5617	170	19	solution	solution	NOUN
ejpam-5617	170	20	curve	curve	NOUN
ejpam-5617	170	21	decreases	decrease	VERB
ejpam-5617	170	22	as	as	ADP
ejpam-5617	170	23	the	the	DET
ejpam-5617	170	24	order	order	NOUN
ejpam-5617	170	25	of	of	ADP
ejpam-5617	170	26	the	the	DET
ejpam-5617	170	27	fractional	fractional	ADJ
ejpam-5617	170	28	derivative	derivative	ADJ
ejpam-5617	170	29	decreases	decrease	NOUN
ejpam-5617	170	30	.	.	PUNCT
ejpam-5617	171	1	a.	a.	PROPN
ejpam-5617	171	2	el	el	PROPN
ejpam-5617	171	3	-	-	PUNCT
ejpam-5617	171	4	ajou	ajou	PROPN
ejpam-5617	171	5	,	,	PUNCT
ejpam-5617	171	6	a.	a.	PROPN
ejpam-5617	171	7	burqan	burqan	PROPN
ejpam-5617	171	8	/	/	SYM
ejpam-5617	171	9	eur	eur	PROPN
ejpam-5617	171	10	.	.	PUNCT
ejpam-5617	172	1	j.	j.	PROPN
ejpam-5617	172	2	pure	pure	PROPN
ejpam-5617	172	3	appl	appl	PROPN
ejpam-5617	172	4	.	.	PROPN
ejpam-5617	172	5	math	math	PROPN
ejpam-5617	172	6	,	,	PUNCT
ejpam-5617	172	7	18	18	NUM
ejpam-5617	172	8	(	(	PUNCT
ejpam-5617	172	9	1	1	NUM
ejpam-5617	172	10	)	)	PUNCT
ejpam-5617	172	11	(	(	PUNCT
ejpam-5617	172	12	2025	2025	NUM
ejpam-5617	172	13	)	)	PUNCT
ejpam-5617	172	14	,	,	PUNCT
ejpam-5617	172	15	5617	5617	NUM
ejpam-5617	172	16	8	8	NUM
ejpam-5617	172	17	of	of	ADP
ejpam-5617	172	18	19	19	NUM
ejpam-5617	172	19	(	(	PUNCT
ejpam-5617	172	20	a	a	NOUN
ejpam-5617	172	21	)	)	PUNCT
ejpam-5617	172	22	(	(	PUNCT
ejpam-5617	172	23	b	b	X
ejpam-5617	172	24	)	)	PUNCT
ejpam-5617	172	25	figure	figure	NOUN
ejpam-5617	172	26	1	1	NUM
ejpam-5617	172	27	:	:	PUNCT
ejpam-5617	172	28	the	the	DET
ejpam-5617	172	29	curves	curve	NOUN
ejpam-5617	172	30	of	of	ADP
ejpam-5617	172	31	the	the	DET
ejpam-5617	172	32	7th	7th	ADJ
ejpam-5617	172	33	approximate	approximate	ADJ
ejpam-5617	172	34	and	and	CCONJ
ejpam-5617	172	35	exact	exact	ADJ
ejpam-5617	172	36	(	(	PUNCT
ejpam-5617	172	37	solid	solid	ADJ
ejpam-5617	172	38	curve	curve	NOUN
ejpam-5617	172	39	)	)	PUNCT
ejpam-5617	172	40	solutions	solution	NOUN
ejpam-5617	172	41	of	of	ADP
ejpam-5617	172	42	system	system	NOUN
ejpam-5617	172	43	(	(	PUNCT
ejpam-5617	172	44	13)-(14	13)-(14	NUM
ejpam-5617	172	45	)	)	PUNCT
ejpam-5617	172	46	at	at	ADP
ejpam-5617	172	47	different	different	ADJ
ejpam-5617	172	48	values	value	NOUN
ejpam-5617	172	49	of	of	ADP
ejpam-5617	172	50	α	α	PROPN
ejpam-5617	172	51	.	.	PUNCT
ejpam-5617	172	52	example	example	NOUN
ejpam-5617	172	53	4.2	4.2	NUM
ejpam-5617	172	54	.	.	PUNCT
ejpam-5617	173	1	consider	consider	VERB
ejpam-5617	173	2	the	the	DET
ejpam-5617	173	3	following	follow	VERB
ejpam-5617	173	4	system	system	NOUN
ejpam-5617	173	5	of	of	ADP
ejpam-5617	173	6	non	non	ADJ
ejpam-5617	173	7	-	-	ADJ
ejpam-5617	173	8	linear	linear	ADJ
ejpam-5617	173	9	fractional	fractional	ADJ
ejpam-5617	173	10	differential	differential	ADJ
ejpam-5617	173	11	equations	equation	NOUN
ejpam-5617	173	12	dαu1	dαu1	NOUN
ejpam-5617	173	13	(	(	PUNCT
ejpam-5617	173	14	x	x	NOUN
ejpam-5617	173	15	)	)	PUNCT
ejpam-5617	173	16	=	=	SYM
ejpam-5617	173	17	u1	u1	NOUN
ejpam-5617	173	18	(	(	PUNCT
ejpam-5617	173	19	x	x	NOUN
ejpam-5617	173	20	)	)	PUNCT
ejpam-5617	173	21	,	,	PUNCT
ejpam-5617	173	22	dαu2	dαu2	PROPN
ejpam-5617	173	23	(	(	PUNCT
ejpam-5617	173	24	x	x	X
ejpam-5617	173	25	)	)	PUNCT
ejpam-5617	173	26	=	=	SYM
ejpam-5617	173	27	2u21	2u21	NUM
ejpam-5617	173	28	(	(	PUNCT
ejpam-5617	173	29	x	x	X
ejpam-5617	173	30	)	)	PUNCT
ejpam-5617	173	31	,	,	PUNCT
ejpam-5617	173	32	dαu3	dαu3	NOUN
ejpam-5617	173	33	(	(	PUNCT
ejpam-5617	173	34	x	x	X
ejpam-5617	173	35	)	)	PUNCT
ejpam-5617	173	36	=	=	SYM
ejpam-5617	173	37	3u1	3u1	NUM
ejpam-5617	173	38	(	(	PUNCT
ejpam-5617	173	39	x	x	NOUN
ejpam-5617	173	40	)	)	PUNCT
ejpam-5617	173	41	u2	u2	NOUN
ejpam-5617	173	42	(	(	PUNCT
ejpam-5617	173	43	x	x	NOUN
ejpam-5617	173	44	)	)	PUNCT
ejpam-5617	173	45	,	,	PUNCT
ejpam-5617	173	46	(	(	PUNCT
ejpam-5617	173	47	29	29	NUM
ejpam-5617	173	48	)	)	PUNCT
ejpam-5617	173	49	where	where	SCONJ
ejpam-5617	173	50	0	0	NUM
ejpam-5617	173	51	<	<	X
ejpam-5617	173	52	α	α	X
ejpam-5617	173	53	≤	≤	NUM
ejpam-5617	173	54	1	1	NUM
ejpam-5617	173	55	,	,	PUNCT
ejpam-5617	173	56	0	0	NUM
ejpam-5617	173	57	≤	≤	NUM
ejpam-5617	173	58	x	x	PUNCT
ejpam-5617	173	59	with	with	ADP
ejpam-5617	173	60	the	the	DET
ejpam-5617	173	61	initial	initial	ADJ
ejpam-5617	173	62	conditions	condition	NOUN
ejpam-5617	173	63	u1	u1	NOUN
ejpam-5617	173	64	(	(	PUNCT
ejpam-5617	173	65	0	0	NUM
ejpam-5617	173	66	)	)	PUNCT
ejpam-5617	173	67	=	=	SYM
ejpam-5617	173	68	1	1	NUM
ejpam-5617	173	69	,	,	PUNCT
ejpam-5617	173	70	u2	u2	NOUN
ejpam-5617	173	71	(	(	PUNCT
ejpam-5617	173	72	0	0	NUM
ejpam-5617	173	73	)	)	PUNCT
ejpam-5617	173	74	=	=	SYM
ejpam-5617	173	75	1	1	NUM
ejpam-5617	173	76	,	,	PUNCT
ejpam-5617	173	77	u3	u3	NOUN
ejpam-5617	173	78	(	(	PUNCT
ejpam-5617	173	79	0	0	NUM
ejpam-5617	173	80	)	)	PUNCT
ejpam-5617	173	81	=	=	SYM
ejpam-5617	174	1	1	1	X
ejpam-5617	174	2	.	.	PUNCT
ejpam-5617	174	3	(	(	PUNCT
ejpam-5617	174	4	30	30	NUM
ejpam-5617	174	5	)	)	PUNCT
ejpam-5617	174	6	in	in	ADP
ejpam-5617	174	7	the	the	DET
ejpam-5617	174	8	classical	classical	ADJ
ejpam-5617	174	9	case	case	NOUN
ejpam-5617	174	10	(	(	PUNCT
ejpam-5617	174	11	α	α	NOUN
ejpam-5617	174	12	=	=	NOUN
ejpam-5617	174	13	1	1	NUM
ejpam-5617	174	14	)	)	PUNCT
ejpam-5617	174	15	,	,	PUNCT
ejpam-5617	174	16	the	the	DET
ejpam-5617	174	17	exact	exact	ADJ
ejpam-5617	174	18	solution	solution	NOUN
ejpam-5617	174	19	may	may	AUX
ejpam-5617	174	20	be	be	AUX
ejpam-5617	174	21	obtained	obtain	VERB
ejpam-5617	174	22	analytically	analytically	ADV
ejpam-5617	174	23	and	and	CCONJ
ejpam-5617	174	24	provided	provide	VERB
ejpam-5617	174	25	as	as	SCONJ
ejpam-5617	174	26	follows	follow	VERB
ejpam-5617	174	27	:	:	PUNCT
ejpam-5617	174	28	u1	u1	NOUN
ejpam-5617	174	29	(	(	PUNCT
ejpam-5617	174	30	x	x	NOUN
ejpam-5617	174	31	)	)	PUNCT
ejpam-5617	174	32	=	=	SYM
ejpam-5617	174	33	ex	ex	X
ejpam-5617	174	34	,	,	PUNCT
ejpam-5617	174	35	u2	u2	PROPN
ejpam-5617	174	36	(	(	PUNCT
ejpam-5617	174	37	x	x	NOUN
ejpam-5617	174	38	)	)	PUNCT
ejpam-5617	174	39	=	=	SYM
ejpam-5617	174	40	e2x	e2x	X
ejpam-5617	174	41	,	,	PUNCT
ejpam-5617	174	42	u3	u3	NOUN
ejpam-5617	174	43	(	(	PUNCT
ejpam-5617	174	44	x	x	NOUN
ejpam-5617	174	45	)	)	PUNCT
ejpam-5617	174	46	=	=	SYM
ejpam-5617	174	47	e3x	e3x	PROPN
ejpam-5617	174	48	.	.	PUNCT
ejpam-5617	175	1	(	(	PUNCT
ejpam-5617	175	2	31	31	NUM
ejpam-5617	175	3	)	)	PUNCT
ejpam-5617	175	4	assume	assume	VERB
ejpam-5617	175	5	the	the	DET
ejpam-5617	175	6	solution	solution	NOUN
ejpam-5617	175	7	of	of	ADP
ejpam-5617	175	8	the	the	DET
ejpam-5617	175	9	system	system	NOUN
ejpam-5617	175	10	(	(	PUNCT
ejpam-5617	175	11	29)-(30	29)-(30	NUM
ejpam-5617	175	12	)	)	PUNCT
ejpam-5617	175	13	has	have	VERB
ejpam-5617	175	14	the	the	DET
ejpam-5617	175	15	following	follow	VERB
ejpam-5617	175	16	fractional	fractional	ADJ
ejpam-5617	175	17	series	series	NOUN
ejpam-5617	175	18	expansions	expansion	NOUN
ejpam-5617	175	19	:	:	PUNCT
ejpam-5617	175	20	u1	u1	NOUN
ejpam-5617	175	21	(	(	PUNCT
ejpam-5617	175	22	x	x	NOUN
ejpam-5617	175	23	)	)	PUNCT
ejpam-5617	175	24	=	=	SYM
ejpam-5617	176	1	∞∑	∞∑	NUM
ejpam-5617	176	2	n=0	n=0	NUM
ejpam-5617	176	3	u1,n	u1,n	PROPN
ejpam-5617	176	4	xnα	xnα	PROPN
ejpam-5617	176	5	,	,	PUNCT
ejpam-5617	176	6	u2	u2	NOUN
ejpam-5617	176	7	(	(	PUNCT
ejpam-5617	176	8	x	x	NOUN
ejpam-5617	176	9	)	)	PUNCT
ejpam-5617	176	10	=	=	SYM
ejpam-5617	177	1	∞∑	∞∑	NUM
ejpam-5617	177	2	n=0	n=0	NUM
ejpam-5617	177	3	u2,n	u2,n	ADJ
ejpam-5617	177	4	xnα	xnα	ADJ
ejpam-5617	177	5	,	,	PUNCT
ejpam-5617	177	6	u3	u3	NOUN
ejpam-5617	177	7	(	(	PUNCT
ejpam-5617	177	8	x	x	NOUN
ejpam-5617	177	9	)	)	PUNCT
ejpam-5617	177	10	=	=	SYM
ejpam-5617	178	1	∞∑	∞∑	PRON
ejpam-5617	178	2	n=0	n=0	NUM
ejpam-5617	178	3	u3,n	u3,n	ADJ
ejpam-5617	178	4	xnα	xnα	NOUN
ejpam-5617	178	5	.	.	PUNCT
ejpam-5617	179	1	(	(	PUNCT
ejpam-5617	179	2	32	32	NUM
ejpam-5617	179	3	)	)	PUNCT
ejpam-5617	179	4	employing	employ	VERB
ejpam-5617	179	5	the	the	DET
ejpam-5617	179	6	initial	initial	ADJ
ejpam-5617	179	7	conditions	condition	NOUN
ejpam-5617	179	8	(	(	PUNCT
ejpam-5617	179	9	30	30	NUM
ejpam-5617	179	10	)	)	PUNCT
ejpam-5617	179	11	,	,	PUNCT
ejpam-5617	179	12	then	then	ADV
ejpam-5617	179	13	the	the	DET
ejpam-5617	179	14	kth	kth	PROPN
ejpam-5617	179	15	approximate	approximate	ADJ
ejpam-5617	179	16	solution	solution	NOUN
ejpam-5617	179	17	becomes	become	VERB
ejpam-5617	179	18	as	as	SCONJ
ejpam-5617	179	19	follows	follow	VERB
ejpam-5617	179	20	:	:	PUNCT
ejpam-5617	179	21	u1k	u1k	PROPN
ejpam-5617	179	22	(	(	PUNCT
ejpam-5617	179	23	x	x	NOUN
ejpam-5617	179	24	)	)	PUNCT
ejpam-5617	179	25	=	=	SYM
ejpam-5617	180	1	1	1	NUM
ejpam-5617	180	2	+	+	NUM
ejpam-5617	180	3	k∑	k∑	ADJ
ejpam-5617	180	4	n=1	n=1	PROPN
ejpam-5617	180	5	u1,n	u1,n	PROPN
ejpam-5617	180	6	xnα	xnα	PROPN
ejpam-5617	180	7	,	,	PUNCT
ejpam-5617	180	8	u2k	u2k	PROPN
ejpam-5617	180	9	(	(	PUNCT
ejpam-5617	180	10	x	x	NOUN
ejpam-5617	180	11	)	)	PUNCT
ejpam-5617	180	12	=	=	SYM
ejpam-5617	180	13	1	1	NUM
ejpam-5617	180	14	+	+	NUM
ejpam-5617	180	15	k∑	k∑	ADJ
ejpam-5617	180	16	n=1	n=1	PROPN
ejpam-5617	180	17	u2,n	u2,n	PROPN
ejpam-5617	180	18	xnα	xnα	PROPN
ejpam-5617	180	19	,	,	PUNCT
ejpam-5617	180	20	u3k	u3k	PUNCT
ejpam-5617	180	21	(	(	PUNCT
ejpam-5617	180	22	x	x	X
ejpam-5617	180	23	)	)	PUNCT
ejpam-5617	180	24	=	=	SYM
ejpam-5617	181	1	1	1	NUM
ejpam-5617	181	2	+	+	NUM
ejpam-5617	181	3	k∑	k∑	ADJ
ejpam-5617	181	4	n=1	n=1	PUNCT
ejpam-5617	181	5	u3,n	u3,n	PROPN
ejpam-5617	181	6	xnα	xnα	PROPN
ejpam-5617	181	7	.	.	PUNCT
ejpam-5617	182	1	(	(	PUNCT
ejpam-5617	182	2	33	33	NUM
ejpam-5617	182	3	)	)	PUNCT
ejpam-5617	182	4	a.	a.	NOUN
ejpam-5617	182	5	el	el	PROPN
ejpam-5617	182	6	-	-	PUNCT
ejpam-5617	182	7	ajou	ajou	PROPN
ejpam-5617	182	8	,	,	PUNCT
ejpam-5617	182	9	a.	a.	PROPN
ejpam-5617	182	10	burqan	burqan	PROPN
ejpam-5617	182	11	/	/	SYM
ejpam-5617	182	12	eur	eur	PROPN
ejpam-5617	182	13	.	.	PUNCT
ejpam-5617	183	1	j.	j.	PROPN
ejpam-5617	183	2	pure	pure	PROPN
ejpam-5617	183	3	appl	appl	PROPN
ejpam-5617	183	4	.	.	PROPN
ejpam-5617	183	5	math	math	PROPN
ejpam-5617	183	6	,	,	PUNCT
ejpam-5617	183	7	18	18	NUM
ejpam-5617	183	8	(	(	PUNCT
ejpam-5617	183	9	1	1	NUM
ejpam-5617	183	10	)	)	PUNCT
ejpam-5617	183	11	(	(	PUNCT
ejpam-5617	183	12	2025	2025	NUM
ejpam-5617	183	13	)	)	PUNCT
ejpam-5617	183	14	,	,	PUNCT
ejpam-5617	183	15	5617	5617	NUM
ejpam-5617	183	16	9	9	NUM
ejpam-5617	183	17	of	of	ADP
ejpam-5617	183	18	19	19	NUM
ejpam-5617	183	19	to	to	PART
ejpam-5617	183	20	get	get	VERB
ejpam-5617	183	21	the	the	DET
ejpam-5617	183	22	kth	kth	PROPN
ejpam-5617	183	23	approximate	approximate	ADJ
ejpam-5617	183	24	solution	solution	NOUN
ejpam-5617	183	25	of	of	ADP
ejpam-5617	183	26	system	system	NOUN
ejpam-5617	183	27	(	(	PUNCT
ejpam-5617	183	28	29)-(30	29)-(30	NUM
ejpam-5617	183	29	)	)	PUNCT
ejpam-5617	183	30	,	,	PUNCT
ejpam-5617	183	31	we	we	PRON
ejpam-5617	183	32	define	define	VERB
ejpam-5617	183	33	the	the	DET
ejpam-5617	183	34	kth	kth	PROPN
ejpam-5617	183	35	residual	residual	ADJ
ejpam-5617	183	36	functions	function	NOUN
ejpam-5617	183	37	of	of	ADP
ejpam-5617	183	38	equations	equation	NOUN
ejpam-5617	183	39	(	(	PUNCT
ejpam-5617	183	40	29	29	NUM
ejpam-5617	183	41	)	)	PUNCT
ejpam-5617	183	42	as	as	SCONJ
ejpam-5617	183	43	follows	follow	VERB
ejpam-5617	183	44	:	:	PUNCT
ejpam-5617	183	45	rf	rf	NUM
ejpam-5617	183	46	(	(	PUNCT
ejpam-5617	183	47	u1k	u1k	PROPN
ejpam-5617	183	48	(	(	PUNCT
ejpam-5617	183	49	x	x	NOUN
ejpam-5617	183	50	)	)	PUNCT
ejpam-5617	183	51	)	)	PUNCT
ejpam-5617	184	1	=	=	SYM
ejpam-5617	184	2	dαu1k	dαu1k	PROPN
ejpam-5617	184	3	(	(	PUNCT
ejpam-5617	184	4	x)−	x)−	PROPN
ejpam-5617	184	5	u1k	u1k	PROPN
ejpam-5617	184	6	(	(	PUNCT
ejpam-5617	184	7	x	x	NOUN
ejpam-5617	184	8	)	)	PUNCT
ejpam-5617	184	9	,	,	PUNCT
ejpam-5617	184	10	rf	rf	NUM
ejpam-5617	184	11	(	(	PUNCT
ejpam-5617	184	12	u2k	u2k	PROPN
ejpam-5617	184	13	(	(	PUNCT
ejpam-5617	184	14	x	x	NOUN
ejpam-5617	184	15	)	)	PUNCT
ejpam-5617	184	16	)	)	PUNCT
ejpam-5617	185	1	=	=	SYM
ejpam-5617	186	1	dαu2k	dαu2k	NOUN
ejpam-5617	186	2	(	(	PUNCT
ejpam-5617	186	3	x)−	x)−	PROPN
ejpam-5617	186	4	2u21k(x	2u21k(x	PROPN
ejpam-5617	186	5	)	)	PUNCT
ejpam-5617	186	6	,	,	PUNCT
ejpam-5617	186	7	rf	rf	PROPN
ejpam-5617	186	8	(	(	PUNCT
ejpam-5617	186	9	u3k	u3k	PROPN
ejpam-5617	186	10	(	(	PUNCT
ejpam-5617	186	11	x	x	NOUN
ejpam-5617	186	12	)	)	PUNCT
ejpam-5617	186	13	)	)	PUNCT
ejpam-5617	187	1	=	=	SYM
ejpam-5617	187	2	dαu3k	dαu3k	PROPN
ejpam-5617	187	3	(	(	PUNCT
ejpam-5617	187	4	x)−	x)−	PROPN
ejpam-5617	187	5	3u1k	3u1k	PROPN
ejpam-5617	187	6	(	(	PUNCT
ejpam-5617	187	7	x)u2k	x)u2k	PROPN
ejpam-5617	187	8	(	(	PUNCT
ejpam-5617	187	9	x	x	NOUN
ejpam-5617	187	10	)	)	PUNCT
ejpam-5617	187	11	.	.	PUNCT
ejpam-5617	188	1	(	(	PUNCT
ejpam-5617	188	2	34	34	NUM
ejpam-5617	188	3	)	)	PUNCT
ejpam-5617	188	4	after	after	ADP
ejpam-5617	188	5	substituting	substitute	VERB
ejpam-5617	188	6	the	the	DET
ejpam-5617	188	7	kth	kth	PROPN
ejpam-5617	188	8	approximations	approximation	NOUN
ejpam-5617	188	9	(	(	PUNCT
ejpam-5617	188	10	33	33	NUM
ejpam-5617	188	11	)	)	PUNCT
ejpam-5617	188	12	into	into	ADP
ejpam-5617	188	13	equation	equation	NOUN
ejpam-5617	188	14	(	(	PUNCT
ejpam-5617	188	15	34	34	NUM
ejpam-5617	188	16	)	)	PUNCT
ejpam-5617	188	17	,	,	PUNCT
ejpam-5617	188	18	then	then	ADV
ejpam-5617	188	19	the	the	DET
ejpam-5617	188	20	kth	kth	PROPN
ejpam-5617	188	21	residual	residual	ADJ
ejpam-5617	188	22	functions	function	NOUN
ejpam-5617	188	23	becomes	become	VERB
ejpam-5617	188	24	as	as	ADP
ejpam-5617	188	25	:	:	PUNCT
ejpam-5617	188	26	rf	rf	ADJ
ejpam-5617	188	27	(	(	PUNCT
ejpam-5617	188	28	u1k	u1k	PROPN
ejpam-5617	188	29	(	(	PUNCT
ejpam-5617	188	30	x	x	NOUN
ejpam-5617	188	31	)	)	PUNCT
ejpam-5617	188	32	)	)	PUNCT
ejpam-5617	189	1	=	=	SYM
ejpam-5617	189	2	k∑	k∑	VERB
ejpam-5617	189	3	n=1	n=1	PUNCT
ejpam-5617	189	4	u1,n	u1,n	PROPN
ejpam-5617	189	5	γ	γ	X
ejpam-5617	189	6	(	(	PUNCT
ejpam-5617	189	7	nα+	nα+	NOUN
ejpam-5617	189	8	1	1	NUM
ejpam-5617	189	9	)	)	PUNCT
ejpam-5617	189	10	γ	γ	X
ejpam-5617	189	11	(	(	PUNCT
ejpam-5617	189	12	(	(	PUNCT
ejpam-5617	189	13	n−	n−	NOUN
ejpam-5617	189	14	1)α+	1)α+	NUM
ejpam-5617	189	15	1	1	NUM
ejpam-5617	189	16	)	)	PUNCT
ejpam-5617	189	17	x(n−1)α	x(n−1)α	PROPN
ejpam-5617	190	1	−	−	PROPN
ejpam-5617	190	2	k∑	k∑	PROPN
ejpam-5617	190	3	n=1	n=1	PROPN
ejpam-5617	190	4	u1,n	u1,n	PROPN
ejpam-5617	190	5	xnα	xnα	ADV
ejpam-5617	191	1	−	−	PROPN
ejpam-5617	191	2	1	1	NUM
ejpam-5617	191	3	,	,	PUNCT
ejpam-5617	191	4	rf	rf	ADJ
ejpam-5617	191	5	(	(	PUNCT
ejpam-5617	191	6	u2k	u2k	PROPN
ejpam-5617	191	7	(	(	PUNCT
ejpam-5617	191	8	x	x	NOUN
ejpam-5617	191	9	)	)	PUNCT
ejpam-5617	191	10	)	)	PUNCT
ejpam-5617	192	1	=	=	SYM
ejpam-5617	192	2	k∑	k∑	VERB
ejpam-5617	192	3	n=1	n=1	PROPN
ejpam-5617	192	4	u2,n	u2,n	PROPN
ejpam-5617	192	5	γ	γ	NOUN
ejpam-5617	192	6	(	(	PUNCT
ejpam-5617	192	7	nα+	nα+	NOUN
ejpam-5617	192	8	1	1	NUM
ejpam-5617	192	9	)	)	PUNCT
ejpam-5617	192	10	γ	γ	X
ejpam-5617	192	11	(	(	PUNCT
ejpam-5617	192	12	(	(	PUNCT
ejpam-5617	192	13	n−	n−	NOUN
ejpam-5617	192	14	1)α+	1)α+	NUM
ejpam-5617	192	15	1	1	NUM
ejpam-5617	192	16	)	)	PUNCT
ejpam-5617	192	17	x(n−1)α	x(n−1)α	NOUN
ejpam-5617	193	1	−	−	PROPN
ejpam-5617	193	2	2	2	NUM
ejpam-5617	193	3	(	(	PUNCT
ejpam-5617	193	4	k∑	k∑	NOUN
ejpam-5617	193	5	n=1	n=1	PROPN
ejpam-5617	193	6	u1,n	u1,n	PROPN
ejpam-5617	193	7	xnα	xnα	PROPN
ejpam-5617	194	1	+	+	CCONJ
ejpam-5617	194	2	1	1	NUM
ejpam-5617	194	3	)	)	SYM
ejpam-5617	194	4	2	2	NUM
ejpam-5617	194	5	,	,	PUNCT
ejpam-5617	194	6	rf	rf	ADJ
ejpam-5617	194	7	(	(	PUNCT
ejpam-5617	194	8	u3k	u3k	PROPN
ejpam-5617	194	9	(	(	PUNCT
ejpam-5617	194	10	x	x	NOUN
ejpam-5617	194	11	)	)	PUNCT
ejpam-5617	194	12	)	)	PUNCT
ejpam-5617	195	1	=	=	SYM
ejpam-5617	195	2	k∑	k∑	VERB
ejpam-5617	195	3	n=1	n=1	PROPN
ejpam-5617	195	4	u3,n	u3,n	PROPN
ejpam-5617	195	5	γ	γ	X
ejpam-5617	195	6	(	(	PUNCT
ejpam-5617	195	7	nα+	nα+	NOUN
ejpam-5617	195	8	1	1	NUM
ejpam-5617	195	9	)	)	PUNCT
ejpam-5617	195	10	γ	γ	X
ejpam-5617	195	11	(	(	PUNCT
ejpam-5617	195	12	(	(	PUNCT
ejpam-5617	195	13	n−	n−	NOUN
ejpam-5617	195	14	1)α+	1)α+	NUM
ejpam-5617	195	15	1	1	NUM
ejpam-5617	195	16	)	)	PUNCT
ejpam-5617	195	17	x(n−1)α	x(n−1)α	NOUN
ejpam-5617	196	1	−	−	PROPN
ejpam-5617	196	2	3	3	NUM
ejpam-5617	196	3	(	(	PUNCT
ejpam-5617	196	4	1	1	NUM
ejpam-5617	196	5	+	+	CCONJ
ejpam-5617	196	6	k∑	k∑	ADJ
ejpam-5617	196	7	n=1	n=1	PROPN
ejpam-5617	196	8	u1,n	u1,n	PROPN
ejpam-5617	196	9	xnα	xnα	PROPN
ejpam-5617	196	10	)	)	PUNCT
ejpam-5617	196	11	×	×	NOUN
ejpam-5617	196	12	(	(	PUNCT
ejpam-5617	196	13	1	1	NUM
ejpam-5617	196	14	+	+	CCONJ
ejpam-5617	196	15	k∑	k∑	ADJ
ejpam-5617	196	16	n=1	n=1	PROPN
ejpam-5617	196	17	u2,n	u2,n	PROPN
ejpam-5617	196	18	xnα	xnα	PROPN
ejpam-5617	196	19	)	)	PUNCT
ejpam-5617	196	20	.	.	PUNCT
ejpam-5617	197	1	(	(	PUNCT
ejpam-5617	197	2	35	35	NUM
ejpam-5617	197	3	)	)	PUNCT
ejpam-5617	197	4	according	accord	VERB
ejpam-5617	197	5	to	to	ADP
ejpam-5617	197	6	the	the	DET
ejpam-5617	197	7	formulation	formulation	NOUN
ejpam-5617	197	8	used	use	VERB
ejpam-5617	197	9	in	in	ADP
ejpam-5617	197	10	the	the	DET
ejpam-5617	197	11	previous	previous	ADJ
ejpam-5617	197	12	section	section	NOUN
ejpam-5617	197	13	,	,	PUNCT
ejpam-5617	197	14	the	the	DET
ejpam-5617	197	15	kth	kth	PROPN
ejpam-5617	197	16	approximations	approximation	NOUN
ejpam-5617	197	17	can	can	AUX
ejpam-5617	197	18	be	be	AUX
ejpam-5617	197	19	achieved	achieve	VERB
ejpam-5617	197	20	by	by	ADP
ejpam-5617	197	21	obtaining	obtain	VERB
ejpam-5617	197	22	the	the	DET
ejpam-5617	197	23	coefficients	coefficient	NOUN
ejpam-5617	197	24	u1,j	u1,j	NOUN
ejpam-5617	197	25	,	,	PUNCT
ejpam-5617	197	26	u2,j	u2,j	PROPN
ejpam-5617	197	27	,	,	PUNCT
ejpam-5617	197	28	u3,j	u3,j	PROPN
ejpam-5617	197	29	for	for	ADP
ejpam-5617	197	30	j	j	PROPN
ejpam-5617	197	31	=	=	SYM
ejpam-5617	197	32	1	1	PROPN
ejpam-5617	197	33	,	,	PUNCT
ejpam-5617	197	34	.	.	PUNCT
ejpam-5617	197	35	.	.	PUNCT
ejpam-5617	198	1	.	.	PUNCT
ejpam-5617	199	1	,	,	PUNCT
ejpam-5617	199	2	k	k	PROPN
ejpam-5617	199	3	via	via	ADP
ejpam-5617	199	4	solving	solve	VERB
ejpam-5617	199	5	the	the	DET
ejpam-5617	199	6	following	follow	VERB
ejpam-5617	199	7	algebraic	algebraic	ADJ
ejpam-5617	199	8	equations	equation	NOUN
ejpam-5617	199	9	iteratively	iteratively	ADV
ejpam-5617	199	10	:	:	PUNCT
ejpam-5617	199	11	lim	lim	PROPN
ejpam-5617	199	12	x→0	x→0	PROPN
ejpam-5617	200	1	rf	rf	PRON
ejpam-5617	200	2	(	(	PUNCT
ejpam-5617	200	3	u1j	u1j	X
ejpam-5617	200	4	(	(	PUNCT
ejpam-5617	200	5	x	x	NOUN
ejpam-5617	200	6	)	)	PUNCT
ejpam-5617	200	7	)	)	PUNCT
ejpam-5617	201	1	x(j−1)α	x(j−1)α	PUNCT
ejpam-5617	202	1	=	=	SYM
ejpam-5617	202	2	0	0	PROPN
ejpam-5617	202	3	,	,	PUNCT
ejpam-5617	202	4	lim	lim	PROPN
ejpam-5617	202	5	x→0	x→0	PROPN
ejpam-5617	203	1	rf	rf	PROPN
ejpam-5617	203	2	(	(	PUNCT
ejpam-5617	203	3	u2j	u2j	X
ejpam-5617	203	4	(	(	PUNCT
ejpam-5617	203	5	x	x	NOUN
ejpam-5617	203	6	)	)	PUNCT
ejpam-5617	203	7	)	)	PUNCT
ejpam-5617	204	1	x(j−1)α	x(j−1)α	PUNCT
ejpam-5617	205	1	=	=	SYM
ejpam-5617	205	2	0	0	PROPN
ejpam-5617	205	3	,	,	PUNCT
ejpam-5617	205	4	lim	lim	NOUN
ejpam-5617	205	5	x→0	x→0	PROPN
ejpam-5617	205	6	rf	rf	PRON
ejpam-5617	205	7	(	(	PUNCT
ejpam-5617	205	8	u3j	u3j	PROPN
ejpam-5617	205	9	(	(	PUNCT
ejpam-5617	205	10	x	x	NOUN
ejpam-5617	205	11	)	)	PUNCT
ejpam-5617	205	12	)	)	PUNCT
ejpam-5617	206	1	x(j−1)α	x(j−1)α	PUNCT
ejpam-5617	207	1	=	=	SYM
ejpam-5617	207	2	0	0	PROPN
ejpam-5617	207	3	,	,	PUNCT
ejpam-5617	207	4	j	j	PROPN
ejpam-5617	207	5	=	=	SYM
ejpam-5617	207	6	1	1	NUM
ejpam-5617	207	7	,	,	PUNCT
ejpam-5617	207	8	.	.	PUNCT
ejpam-5617	207	9	.	.	PUNCT
ejpam-5617	207	10	.	.	PUNCT
ejpam-5617	208	1	,	,	PUNCT
ejpam-5617	208	2	k.	k.	PROPN
ejpam-5617	208	3	(	(	PUNCT
ejpam-5617	208	4	36	36	NUM
ejpam-5617	208	5	)	)	PUNCT
ejpam-5617	208	6	these	these	DET
ejpam-5617	208	7	coefficients	coefficient	NOUN
ejpam-5617	208	8	are	be	AUX
ejpam-5617	208	9	summarized	summarize	VERB
ejpam-5617	208	10	in	in	ADP
ejpam-5617	208	11	table	table	NOUN
ejpam-5617	208	12	2	2	NUM
ejpam-5617	208	13	.	.	PUNCT
ejpam-5617	209	1	so	so	ADV
ejpam-5617	209	2	,	,	PUNCT
ejpam-5617	209	3	the	the	DET
ejpam-5617	209	4	lrf	lrf	NOUN
ejpam-5617	209	5	solution	solution	NOUN
ejpam-5617	209	6	of	of	ADP
ejpam-5617	209	7	the	the	DET
ejpam-5617	209	8	system	system	NOUN
ejpam-5617	209	9	(	(	PUNCT
ejpam-5617	209	10	29)-(30	29)-(30	NUM
ejpam-5617	209	11	)	)	PUNCT
ejpam-5617	209	12	has	have	VERB
ejpam-5617	209	13	the	the	DET
ejpam-5617	209	14	following	follow	VERB
ejpam-5617	209	15	series	series	NOUN
ejpam-5617	209	16	expansions	expansion	NOUN
ejpam-5617	209	17	:	:	PUNCT
ejpam-5617	209	18	u1	u1	NOUN
ejpam-5617	209	19	(	(	PUNCT
ejpam-5617	209	20	x	x	NOUN
ejpam-5617	209	21	)	)	PUNCT
ejpam-5617	210	1	=	=	SYM
ejpam-5617	210	2	1	1	NUM
ejpam-5617	211	1	+	+	CCONJ
ejpam-5617	211	2	xα	xα	ADP
ejpam-5617	211	3	γ	γ	X
ejpam-5617	211	4	(	(	PUNCT
ejpam-5617	211	5	α+	α+	PROPN
ejpam-5617	211	6	1	1	NUM
ejpam-5617	211	7	)	)	PUNCT
ejpam-5617	211	8	+	+	CCONJ
ejpam-5617	211	9	x2α	x2α	PROPN
ejpam-5617	211	10	γ	γ	X
ejpam-5617	211	11	(	(	PUNCT
ejpam-5617	211	12	2α+	2α+	NUM
ejpam-5617	211	13	1	1	NUM
ejpam-5617	211	14	)	)	PUNCT
ejpam-5617	211	15	+	+	CCONJ
ejpam-5617	211	16	x3α	x3α	PROPN
ejpam-5617	211	17	γ	γ	X
ejpam-5617	211	18	(	(	PUNCT
ejpam-5617	211	19	3α+	3α+	NUM
ejpam-5617	211	20	1	1	NUM
ejpam-5617	211	21	)	)	PUNCT
ejpam-5617	211	22	+	+	CCONJ
ejpam-5617	211	23	x4α	x4α	PROPN
ejpam-5617	211	24	γ	γ	X
ejpam-5617	211	25	(	(	PUNCT
ejpam-5617	211	26	4α+	4α+	NUM
ejpam-5617	211	27	1	1	NUM
ejpam-5617	211	28	)	)	PUNCT
ejpam-5617	211	29	+	+	CCONJ
ejpam-5617	211	30	.	.	PUNCT
ejpam-5617	211	31	.	.	PUNCT
ejpam-5617	211	32	.	.	PUNCT
ejpam-5617	212	1	,	,	PUNCT
ejpam-5617	212	2	u2	u2	NOUN
ejpam-5617	212	3	(	(	PUNCT
ejpam-5617	212	4	x	x	NOUN
ejpam-5617	212	5	)	)	PUNCT
ejpam-5617	212	6	=	=	SYM
ejpam-5617	212	7	1	1	NUM
ejpam-5617	212	8	+	+	CCONJ
ejpam-5617	212	9	2xα	2xα	ADJ
ejpam-5617	212	10	γ	γ	X
ejpam-5617	212	11	(	(	PUNCT
ejpam-5617	212	12	α+	α+	PROPN
ejpam-5617	212	13	1	1	NUM
ejpam-5617	212	14	)	)	PUNCT
ejpam-5617	212	15	+	+	CCONJ
ejpam-5617	212	16	4x2α	4x2α	ADJ
ejpam-5617	212	17	γ	γ	X
ejpam-5617	212	18	(	(	PUNCT
ejpam-5617	212	19	2α+	2α+	NUM
ejpam-5617	212	20	1	1	NUM
ejpam-5617	212	21	)	)	PUNCT
ejpam-5617	212	22	+	+	CCONJ
ejpam-5617	212	23	(	(	PUNCT
ejpam-5617	212	24	4	4	NUM
ejpam-5617	212	25	γ	γ	X
ejpam-5617	212	26	(	(	PUNCT
ejpam-5617	212	27	3α+	3α+	NUM
ejpam-5617	212	28	1	1	NUM
ejpam-5617	212	29	)	)	PUNCT
ejpam-5617	212	30	+	+	CCONJ
ejpam-5617	212	31	2	2	NUM
ejpam-5617	212	32	γ	γ	X
ejpam-5617	212	33	(	(	PUNCT
ejpam-5617	212	34	2α+	2α+	NUM
ejpam-5617	212	35	1	1	NUM
ejpam-5617	212	36	)	)	PUNCT
ejpam-5617	212	37	γ	γ	X
ejpam-5617	212	38	2	2	NUM
ejpam-5617	212	39	(	(	PUNCT
ejpam-5617	212	40	α+	α+	PROPN
ejpam-5617	212	41	1)γ	1)γ	PROPN
ejpam-5617	212	42	(	(	PUNCT
ejpam-5617	212	43	3α+	3α+	NUM
ejpam-5617	212	44	1	1	NUM
ejpam-5617	212	45	)	)	PUNCT
ejpam-5617	212	46	)	)	PUNCT
ejpam-5617	212	47	x3α	x3α	PROPN
ejpam-5617	212	48	,	,	PUNCT
ejpam-5617	212	49	+	+	CCONJ
ejpam-5617	212	50	(	(	PUNCT
ejpam-5617	212	51	4	4	NUM
ejpam-5617	212	52	γ	γ	X
ejpam-5617	212	53	(	(	PUNCT
ejpam-5617	212	54	4α+	4α+	NUM
ejpam-5617	212	55	1	1	NUM
ejpam-5617	212	56	)	)	PUNCT
ejpam-5617	212	57	+	+	CCONJ
ejpam-5617	212	58	4	4	NUM
ejpam-5617	212	59	γ	γ	NOUN
ejpam-5617	212	60	(	(	PUNCT
ejpam-5617	212	61	3α+	3α+	NUM
ejpam-5617	212	62	1	1	NUM
ejpam-5617	212	63	)	)	PUNCT
ejpam-5617	212	64	γ	γ	X
ejpam-5617	212	65	(	(	PUNCT
ejpam-5617	212	66	α+	α+	PROPN
ejpam-5617	212	67	1)γ	1)γ	PROPN
ejpam-5617	212	68	(	(	PUNCT
ejpam-5617	212	69	2α+	2α+	NUM
ejpam-5617	212	70	1)γ	1)γ	PROPN
ejpam-5617	212	71	(	(	PUNCT
ejpam-5617	212	72	4α+	4α+	NUM
ejpam-5617	212	73	1	1	NUM
ejpam-5617	212	74	)	)	PUNCT
ejpam-5617	212	75	)	)	PUNCT
ejpam-5617	212	76	x4α	x4α	PROPN
ejpam-5617	213	1	+	+	CCONJ
ejpam-5617	213	2	.	.	PUNCT
ejpam-5617	213	3	.	.	PUNCT
ejpam-5617	214	1	.	.	PUNCT
ejpam-5617	215	1	,	,	PUNCT
ejpam-5617	215	2	u3	u3	NOUN
ejpam-5617	215	3	(	(	PUNCT
ejpam-5617	215	4	x	x	NOUN
ejpam-5617	215	5	)	)	PUNCT
ejpam-5617	215	6	=	=	SYM
ejpam-5617	215	7	1	1	NUM
ejpam-5617	215	8	+	+	NUM
ejpam-5617	215	9	3xα	3xα	ADJ
ejpam-5617	215	10	γ	γ	X
ejpam-5617	215	11	(	(	PUNCT
ejpam-5617	215	12	α+	α+	NOUN
ejpam-5617	215	13	1	1	NUM
ejpam-5617	215	14	)	)	PUNCT
ejpam-5617	215	15	+	+	CCONJ
ejpam-5617	215	16	9x2α	9x2α	NUM
ejpam-5617	215	17	γ	γ	X
ejpam-5617	215	18	(	(	PUNCT
ejpam-5617	215	19	2α+	2α+	NUM
ejpam-5617	215	20	1	1	NUM
ejpam-5617	215	21	)	)	PUNCT
ejpam-5617	215	22	+	+	CCONJ
ejpam-5617	215	23	(	(	PUNCT
ejpam-5617	215	24	15	15	NUM
ejpam-5617	215	25	γ	γ	X
ejpam-5617	215	26	(	(	PUNCT
ejpam-5617	215	27	3α+	3α+	NUM
ejpam-5617	215	28	1	1	NUM
ejpam-5617	215	29	)	)	PUNCT
ejpam-5617	215	30	+	+	CCONJ
ejpam-5617	215	31	6	6	NUM
ejpam-5617	215	32	γ	γ	NOUN
ejpam-5617	215	33	(	(	PUNCT
ejpam-5617	215	34	2α+	2α+	NUM
ejpam-5617	215	35	1	1	NUM
ejpam-5617	215	36	)	)	PUNCT
ejpam-5617	215	37	γ	γ	X
ejpam-5617	215	38	2	2	NUM
ejpam-5617	215	39	(	(	PUNCT
ejpam-5617	215	40	α+	α+	PROPN
ejpam-5617	215	41	1)γ	1)γ	PROPN
ejpam-5617	215	42	(	(	PUNCT
ejpam-5617	215	43	3α+	3α+	NUM
ejpam-5617	215	44	1	1	NUM
ejpam-5617	215	45	)	)	PUNCT
ejpam-5617	215	46	)	)	PUNCT
ejpam-5617	216	1	x3α	x3α	PROPN
ejpam-5617	216	2	a.	a.	PROPN
ejpam-5617	217	1	el	el	PROPN
ejpam-5617	217	2	-	-	PUNCT
ejpam-5617	217	3	ajou	ajou	PROPN
ejpam-5617	217	4	,	,	PUNCT
ejpam-5617	217	5	a.	a.	PROPN
ejpam-5617	217	6	burqan	burqan	PROPN
ejpam-5617	217	7	/	/	SYM
ejpam-5617	217	8	eur	eur	PROPN
ejpam-5617	217	9	.	.	PUNCT
ejpam-5617	218	1	j.	j.	PROPN
ejpam-5617	218	2	pure	pure	PROPN
ejpam-5617	218	3	appl	appl	PROPN
ejpam-5617	218	4	.	.	PROPN
ejpam-5617	218	5	math	math	PROPN
ejpam-5617	218	6	,	,	PUNCT
ejpam-5617	218	7	18	18	NUM
ejpam-5617	218	8	(	(	PUNCT
ejpam-5617	218	9	1	1	NUM
ejpam-5617	218	10	)	)	PUNCT
ejpam-5617	218	11	(	(	PUNCT
ejpam-5617	218	12	2025	2025	NUM
ejpam-5617	218	13	)	)	PUNCT
ejpam-5617	218	14	,	,	PUNCT
ejpam-5617	218	15	5617	5617	NUM
ejpam-5617	218	16	10	10	NUM
ejpam-5617	218	17	of	of	ADP
ejpam-5617	218	18	19	19	NUM
ejpam-5617	218	19	table	table	NOUN
ejpam-5617	218	20	2	2	NUM
ejpam-5617	218	21	:	:	PUNCT
ejpam-5617	218	22	the	the	DET
ejpam-5617	218	23	coefficients	coefficient	NOUN
ejpam-5617	218	24	of	of	ADP
ejpam-5617	218	25	the	the	DET
ejpam-5617	218	26	4th	4th	ADJ
ejpam-5617	218	27	approximations	approximation	NOUN
ejpam-5617	218	28	of	of	ADP
ejpam-5617	218	29	u1	u1	NOUN
ejpam-5617	218	30	(	(	PUNCT
ejpam-5617	218	31	x	x	NOUN
ejpam-5617	218	32	)	)	PUNCT
ejpam-5617	218	33	,	,	PUNCT
ejpam-5617	218	34	u2	u2	PROPN
ejpam-5617	218	35	(	(	PUNCT
ejpam-5617	218	36	x	x	NOUN
ejpam-5617	218	37	)	)	PUNCT
ejpam-5617	218	38	,	,	PUNCT
ejpam-5617	218	39	u3	u3	NOUN
ejpam-5617	218	40	(	(	PUNCT
ejpam-5617	218	41	x	x	NOUN
ejpam-5617	218	42	)	)	PUNCT
ejpam-5617	218	43	for	for	ADP
ejpam-5617	218	44	the	the	DET
ejpam-5617	218	45	system	system	NOUN
ejpam-5617	218	46	(	(	PUNCT
ejpam-5617	218	47	29)-(30	29)-(30	NUM
ejpam-5617	218	48	)	)	PUNCT
ejpam-5617	218	49	.	.	PUNCT
ejpam-5617	219	1	k	k	PROPN
ejpam-5617	219	2	u1,k	u1,k	PROPN
ejpam-5617	219	3	u2,k	u2,k	PROPN
ejpam-5617	219	4	u3,k	u3,k	NOUN
ejpam-5617	219	5	0	0	NUM
ejpam-5617	219	6	1	1	NUM
ejpam-5617	219	7	1	1	NUM
ejpam-5617	219	8	1	1	NUM
ejpam-5617	219	9	1	1	NUM
ejpam-5617	219	10	1	1	NUM
ejpam-5617	219	11	γ	γ	X
ejpam-5617	219	12	(	(	PUNCT
ejpam-5617	219	13	α+1	α+1	NUM
ejpam-5617	219	14	)	)	PUNCT
ejpam-5617	219	15	2	2	NUM
ejpam-5617	219	16	γ	γ	X
ejpam-5617	219	17	(	(	PUNCT
ejpam-5617	219	18	α+1	α+1	NUM
ejpam-5617	219	19	)	)	PUNCT
ejpam-5617	219	20	3	3	NUM
ejpam-5617	219	21	γ	γ	X
ejpam-5617	219	22	(	(	PUNCT
ejpam-5617	219	23	α+1	α+1	NUM
ejpam-5617	219	24	)	)	PUNCT
ejpam-5617	219	25	2	2	NUM
ejpam-5617	219	26	1	1	NUM
ejpam-5617	219	27	γ	γ	X
ejpam-5617	219	28	(	(	PUNCT
ejpam-5617	219	29	2α+1	2α+1	PROPN
ejpam-5617	219	30	)	)	PUNCT
ejpam-5617	219	31	4	4	NUM
ejpam-5617	219	32	γ	γ	X
ejpam-5617	219	33	(	(	PUNCT
ejpam-5617	219	34	2α+1	2α+1	PROPN
ejpam-5617	219	35	)	)	PUNCT
ejpam-5617	219	36	9	9	NUM
ejpam-5617	219	37	γ	γ	X
ejpam-5617	219	38	(	(	PUNCT
ejpam-5617	219	39	2α+1	2α+1	PROPN
ejpam-5617	219	40	)	)	PUNCT
ejpam-5617	219	41	3	3	NUM
ejpam-5617	219	42	1	1	NUM
ejpam-5617	219	43	γ	γ	X
ejpam-5617	219	44	(	(	PUNCT
ejpam-5617	219	45	3α+1	3α+1	PROPN
ejpam-5617	219	46	)	)	PUNCT
ejpam-5617	219	47	4	4	NUM
ejpam-5617	219	48	γ	γ	X
ejpam-5617	219	49	(	(	PUNCT
ejpam-5617	219	50	3α+1	3α+1	PROPN
ejpam-5617	219	51	)	)	PUNCT
ejpam-5617	219	52	+	+	CCONJ
ejpam-5617	219	53	2	2	NUM
ejpam-5617	219	54	γ(2	γ(2	NOUN
ejpam-5617	219	55	+	+	NOUN
ejpam-5617	219	56	1	1	NUM
ejpam-5617	219	57	)	)	PUNCT
ejpam-5617	219	58	γ2(α+1)γ	γ2(α+1)γ	PROPN
ejpam-5617	219	59	(	(	PUNCT
ejpam-5617	219	60	3α+1	3α+1	PROPN
ejpam-5617	219	61	)	)	PUNCT
ejpam-5617	219	62	15	15	NUM
ejpam-5617	219	63	γ	γ	X
ejpam-5617	219	64	(	(	PUNCT
ejpam-5617	219	65	3α+1	3α+1	PROPN
ejpam-5617	219	66	)	)	PUNCT
ejpam-5617	219	67	+	+	CCONJ
ejpam-5617	219	68	6	6	NUM
ejpam-5617	219	69	γ(2	γ(2	NOUN
ejpam-5617	219	70	+	+	NOUN
ejpam-5617	219	71	1	1	NUM
ejpam-5617	219	72	)	)	PUNCT
ejpam-5617	219	73	γ2(+1)γ	γ2(+1)γ	PROPN
ejpam-5617	219	74	(	(	PUNCT
ejpam-5617	219	75	3α+1	3α+1	PROPN
ejpam-5617	219	76	)	)	PUNCT
ejpam-5617	219	77	4	4	NUM
ejpam-5617	219	78	1	1	NUM
ejpam-5617	219	79	γ	γ	X
ejpam-5617	219	80	(	(	PUNCT
ejpam-5617	219	81	4α+1	4α+1	PROPN
ejpam-5617	219	82	)	)	PUNCT
ejpam-5617	219	83	4	4	NUM
ejpam-5617	219	84	γ	γ	X
ejpam-5617	219	85	(	(	PUNCT
ejpam-5617	219	86	4α+1	4α+1	PROPN
ejpam-5617	219	87	)	)	PUNCT
ejpam-5617	220	1	+	+	CCONJ
ejpam-5617	220	2	4	4	NUM
ejpam-5617	220	3	γ(3	γ(3	NOUN
ejpam-5617	220	4	+	+	ADJ
ejpam-5617	220	5	1	1	NUM
ejpam-5617	220	6	)	)	PUNCT
ejpam-5617	220	7	γ	γ	NOUN
ejpam-5617	220	8	(	(	PUNCT
ejpam-5617	220	9	α+1)γ	α+1)γ	PROPN
ejpam-5617	220	10	(	(	PUNCT
ejpam-5617	220	11	2α+1)γ	2α+1)γ	PROPN
ejpam-5617	220	12	(	(	PUNCT
ejpam-5617	220	13	4α+1	4α+1	NOUN
ejpam-5617	220	14	)	)	PUNCT
ejpam-5617	220	15	15	15	NUM
ejpam-5617	220	16	γ	γ	X
ejpam-5617	220	17	(	(	PUNCT
ejpam-5617	220	18	4α+1	4α+1	PROPN
ejpam-5617	220	19	)	)	PUNCT
ejpam-5617	221	1	+	+	CCONJ
ejpam-5617	221	2	6	6	NUM
ejpam-5617	221	3	γ(2α+1	γ(2α+1	NOUN
ejpam-5617	221	4	)	)	PUNCT
ejpam-5617	221	5	γ2(α+1)γ	γ2(α+1)γ	PUNCT
ejpam-5617	221	6	(	(	PUNCT
ejpam-5617	221	7	4α+1	4α+1	NOUN
ejpam-5617	221	8	)	)	PUNCT
ejpam-5617	222	1	+	+	CCONJ
ejpam-5617	222	2	18	18	NUM
ejpam-5617	222	3	γ	γ	NOUN
ejpam-5617	222	4	(	(	PUNCT
ejpam-5617	222	5	3α+1	3α+1	PROPN
ejpam-5617	222	6	)	)	PUNCT
ejpam-5617	222	7	γ	γ	NOUN
ejpam-5617	222	8	(	(	PUNCT
ejpam-5617	222	9	α+1)γ	α+1)γ	PROPN
ejpam-5617	222	10	(	(	PUNCT
ejpam-5617	222	11	2α+1)γ	2α+1)γ	PROPN
ejpam-5617	222	12	(	(	PUNCT
ejpam-5617	222	13	4α+1	4α+1	NOUN
ejpam-5617	222	14	)	)	PUNCT
ejpam-5617	223	1	+	+	CCONJ
ejpam-5617	223	2	(	(	PUNCT
ejpam-5617	223	3	15	15	NUM
ejpam-5617	223	4	γ	γ	X
ejpam-5617	223	5	(	(	PUNCT
ejpam-5617	223	6	4α+	4α+	NUM
ejpam-5617	223	7	1	1	NUM
ejpam-5617	223	8	)	)	PUNCT
ejpam-5617	223	9	+	+	CCONJ
ejpam-5617	223	10	6	6	NUM
ejpam-5617	223	11	γ	γ	NOUN
ejpam-5617	223	12	(	(	PUNCT
ejpam-5617	223	13	2α+1	2α+1	PROPN
ejpam-5617	223	14	)	)	PUNCT
ejpam-5617	223	15	γ	γ	X
ejpam-5617	223	16	2	2	NUM
ejpam-5617	223	17	(	(	PUNCT
ejpam-5617	223	18	α+	α+	PROPN
ejpam-5617	223	19	1)γ	1)γ	PROPN
ejpam-5617	223	20	(	(	PUNCT
ejpam-5617	223	21	4α+	4α+	NUM
ejpam-5617	223	22	1	1	NUM
ejpam-5617	223	23	)	)	PUNCT
ejpam-5617	223	24	+	+	CCONJ
ejpam-5617	223	25	18	18	NUM
ejpam-5617	223	26	γ	γ	NOUN
ejpam-5617	223	27	(	(	PUNCT
ejpam-5617	223	28	3α+	3α+	NUM
ejpam-5617	223	29	1	1	NUM
ejpam-5617	223	30	)	)	PUNCT
ejpam-5617	223	31	γ	γ	X
ejpam-5617	223	32	(	(	PUNCT
ejpam-5617	223	33	α+	α+	PROPN
ejpam-5617	223	34	1)γ	1)γ	PROPN
ejpam-5617	223	35	(	(	PUNCT
ejpam-5617	223	36	2α+	2α+	NUM
ejpam-5617	223	37	1)γ	1)γ	PROPN
ejpam-5617	223	38	(	(	PUNCT
ejpam-5617	223	39	4α+	4α+	NUM
ejpam-5617	223	40	1	1	NUM
ejpam-5617	223	41	)	)	PUNCT
ejpam-5617	223	42	)	)	PUNCT
ejpam-5617	223	43	x4α	x4α	PROPN
ejpam-5617	224	1	+	+	CCONJ
ejpam-5617	224	2	.	.	PUNCT
ejpam-5617	224	3	.	.	PUNCT
ejpam-5617	224	4	.	.	PUNCT
ejpam-5617	225	1	.	.	PUNCT
ejpam-5617	226	1	(	(	PUNCT
ejpam-5617	226	2	37	37	NUM
ejpam-5617	226	3	)	)	PUNCT
ejpam-5617	226	4	for	for	ADP
ejpam-5617	226	5	α	α	NOUN
ejpam-5617	226	6	=	=	SYM
ejpam-5617	226	7	1	1	NUM
ejpam-5617	226	8	,	,	PUNCT
ejpam-5617	226	9	the	the	DET
ejpam-5617	226	10	expansions	expansion	NOUN
ejpam-5617	226	11	in	in	ADP
ejpam-5617	226	12	(	(	PUNCT
ejpam-5617	226	13	37	37	NUM
ejpam-5617	226	14	)	)	PUNCT
ejpam-5617	226	15	become	become	VERB
ejpam-5617	226	16	as	as	SCONJ
ejpam-5617	226	17	follows	follow	VERB
ejpam-5617	226	18	:	:	PUNCT
ejpam-5617	226	19	u1	u1	NOUN
ejpam-5617	226	20	(	(	PUNCT
ejpam-5617	226	21	x	x	NOUN
ejpam-5617	226	22	)	)	PUNCT
ejpam-5617	226	23	=	=	SYM
ejpam-5617	226	24	1	1	NUM
ejpam-5617	226	25	+	+	CCONJ
ejpam-5617	226	26	x+	x+	ADJ
ejpam-5617	226	27	x2	x2	NOUN
ejpam-5617	226	28	2	2	NUM
ejpam-5617	226	29	+	+	CCONJ
ejpam-5617	226	30	x3	x3	ADJ
ejpam-5617	226	31	3	3	NUM
ejpam-5617	226	32	!	!	PUNCT
ejpam-5617	227	1	+	+	CCONJ
ejpam-5617	227	2	x4	x4	PROPN
ejpam-5617	227	3	4	4	NUM
ejpam-5617	227	4	!	!	PUNCT
ejpam-5617	228	1	+	+	CCONJ
ejpam-5617	228	2	.	.	PUNCT
ejpam-5617	228	3	.	.	PUNCT
ejpam-5617	229	1	.	.	PUNCT
ejpam-5617	230	1	,	,	PUNCT
ejpam-5617	230	2	u2	u2	NOUN
ejpam-5617	230	3	(	(	PUNCT
ejpam-5617	230	4	x	x	NOUN
ejpam-5617	230	5	)	)	PUNCT
ejpam-5617	230	6	=	=	SYM
ejpam-5617	230	7	1	1	NUM
ejpam-5617	230	8	+	+	NUM
ejpam-5617	230	9	2x+	2x+	NUM
ejpam-5617	230	10	2x2	2x2	NUM
ejpam-5617	230	11	+	+	CCONJ
ejpam-5617	230	12	4x3	4x3	NUM
ejpam-5617	230	13	3	3	NUM
ejpam-5617	230	14	+	+	NUM
ejpam-5617	230	15	2x4	2x4	NUM
ejpam-5617	230	16	3	3	NUM
ejpam-5617	230	17	+	+	CCONJ
ejpam-5617	230	18	.	.	PUNCT
ejpam-5617	230	19	.	.	PUNCT
ejpam-5617	230	20	.	.	PUNCT
ejpam-5617	231	1	,	,	PUNCT
ejpam-5617	231	2	u3	u3	NOUN
ejpam-5617	231	3	(	(	PUNCT
ejpam-5617	231	4	x	x	NOUN
ejpam-5617	231	5	)	)	PUNCT
ejpam-5617	231	6	=	=	SYM
ejpam-5617	231	7	1	1	NUM
ejpam-5617	232	1	+	+	CCONJ
ejpam-5617	232	2	3x+	3x+	NUM
ejpam-5617	232	3	9x2	9x2	NUM
ejpam-5617	232	4	2	2	NUM
ejpam-5617	232	5	+	+	SYM
ejpam-5617	232	6	9x3	9x3	NUM
ejpam-5617	232	7	2	2	NUM
ejpam-5617	232	8	+	+	SYM
ejpam-5617	232	9	27x4	27x4	NUM
ejpam-5617	232	10	8	8	NUM
ejpam-5617	232	11	+	+	CCONJ
ejpam-5617	232	12	.	.	PUNCT
ejpam-5617	232	13	.	.	PUNCT
ejpam-5617	232	14	.	.	PUNCT
ejpam-5617	233	1	,	,	PUNCT
ejpam-5617	233	2	(	(	PUNCT
ejpam-5617	233	3	38	38	NUM
ejpam-5617	233	4	)	)	PUNCT
ejpam-5617	233	5	which	which	PRON
ejpam-5617	233	6	are	be	AUX
ejpam-5617	233	7	the	the	DET
ejpam-5617	233	8	expansions	expansion	NOUN
ejpam-5617	233	9	of	of	ADP
ejpam-5617	233	10	the	the	DET
ejpam-5617	233	11	exact	exact	ADJ
ejpam-5617	233	12	solution	solution	NOUN
ejpam-5617	233	13	indicated	indicate	VERB
ejpam-5617	233	14	in	in	ADP
ejpam-5617	233	15	(	(	PUNCT
ejpam-5617	233	16	31	31	NUM
ejpam-5617	233	17	)	)	PUNCT
ejpam-5617	233	18	.	.	PUNCT
ejpam-5617	234	1	figure	figure	NOUN
ejpam-5617	234	2	2	2	NUM
ejpam-5617	234	3	shows	show	VERB
ejpam-5617	234	4	the	the	DET
ejpam-5617	234	5	graphs	graph	NOUN
ejpam-5617	234	6	of	of	ADP
ejpam-5617	234	7	the	the	DET
ejpam-5617	234	8	4th	4th	ADJ
ejpam-5617	234	9	approximate	approximate	ADJ
ejpam-5617	234	10	solution	solution	NOUN
ejpam-5617	234	11	of	of	ADP
ejpam-5617	234	12	the	the	DET
ejpam-5617	234	13	system	system	NOUN
ejpam-5617	234	14	(	(	PUNCT
ejpam-5617	234	15	29)-(30	29)-(30	NUM
ejpam-5617	234	16	)	)	PUNCT
ejpam-5617	234	17	at	at	ADP
ejpam-5617	234	18	different	different	ADJ
ejpam-5617	234	19	values	value	NOUN
ejpam-5617	234	20	of	of	ADP
ejpam-5617	234	21	α	α	NOUN
ejpam-5617	234	22	,	,	PUNCT
ejpam-5617	234	23	as	as	ADV
ejpam-5617	234	24	well	well	ADV
ejpam-5617	234	25	as	as	ADP
ejpam-5617	234	26	the	the	DET
ejpam-5617	234	27	exact	exact	ADJ
ejpam-5617	234	28	solution	solution	NOUN
ejpam-5617	234	29	at	at	ADP
ejpam-5617	234	30	α	α	NOUN
ejpam-5617	234	31	=	=	SYM
ejpam-5617	234	32	1	1	NUM
ejpam-5617	234	33	.	.	PUNCT
ejpam-5617	235	1	the	the	DET
ejpam-5617	235	2	graph	graph	NOUN
ejpam-5617	235	3	shows	show	VERB
ejpam-5617	235	4	agreement	agreement	NOUN
ejpam-5617	235	5	between	between	ADP
ejpam-5617	235	6	the	the	DET
ejpam-5617	235	7	approximate	approximate	ADJ
ejpam-5617	235	8	and	and	CCONJ
ejpam-5617	235	9	actual	actual	ADJ
ejpam-5617	235	10	solutions	solution	NOUN
ejpam-5617	235	11	at	at	ADP
ejpam-5617	235	12	α	α	NOUN
ejpam-5617	235	13	=	=	SYM
ejpam-5617	235	14	1	1	X
ejpam-5617	235	15	.	.	PUNCT
ejpam-5617	236	1	it	it	PRON
ejpam-5617	236	2	also	also	ADV
ejpam-5617	236	3	shows	show	VERB
ejpam-5617	236	4	the	the	DET
ejpam-5617	236	5	effect	effect	NOUN
ejpam-5617	236	6	of	of	ADP
ejpam-5617	236	7	the	the	DET
ejpam-5617	236	8	derivative	derivative	NOUN
ejpam-5617	236	9	’s	’s	PART
ejpam-5617	236	10	order	order	NOUN
ejpam-5617	236	11	on	on	ADP
ejpam-5617	236	12	the	the	DET
ejpam-5617	236	13	solution	solution	NOUN
ejpam-5617	236	14	’s	’s	PART
ejpam-5617	236	15	behavior	behavior	NOUN
ejpam-5617	236	16	.	.	PUNCT
ejpam-5617	237	1	it	it	PRON
ejpam-5617	237	2	is	be	AUX
ejpam-5617	237	3	noticeable	noticeable	ADJ
ejpam-5617	237	4	that	that	SCONJ
ejpam-5617	237	5	the	the	DET
ejpam-5617	237	6	convergence	convergence	NOUN
ejpam-5617	237	7	intervals	interval	NOUN
ejpam-5617	237	8	of	of	ADP
ejpam-5617	237	9	the	the	DET
ejpam-5617	237	10	solution	solution	NOUN
ejpam-5617	237	11	decrease	decrease	NOUN
ejpam-5617	237	12	due	due	ADP
ejpam-5617	237	13	to	to	ADP
ejpam-5617	237	14	the	the	DET
ejpam-5617	237	15	action	action	NOUN
ejpam-5617	237	16	and	and	CCONJ
ejpam-5617	237	17	effects	effect	NOUN
ejpam-5617	237	18	of	of	ADP
ejpam-5617	237	19	nonlinearity	nonlinearity	NOUN
ejpam-5617	237	20	in	in	ADP
ejpam-5617	237	21	the	the	DET
ejpam-5617	237	22	equation	equation	NOUN
ejpam-5617	237	23	defining	define	VERB
ejpam-5617	237	24	the	the	DET
ejpam-5617	237	25	dependent	dependent	ADJ
ejpam-5617	237	26	variables	variable	NOUN
ejpam-5617	237	27	.	.	PUNCT
ejpam-5617	238	1	a.	a.	PROPN
ejpam-5617	238	2	el	el	PROPN
ejpam-5617	238	3	-	-	PUNCT
ejpam-5617	238	4	ajou	ajou	PROPN
ejpam-5617	238	5	,	,	PUNCT
ejpam-5617	238	6	a.	a.	PROPN
ejpam-5617	238	7	burqan	burqan	PROPN
ejpam-5617	238	8	/	/	SYM
ejpam-5617	238	9	eur	eur	PROPN
ejpam-5617	238	10	.	.	PUNCT
ejpam-5617	239	1	j.	j.	PROPN
ejpam-5617	239	2	pure	pure	PROPN
ejpam-5617	239	3	appl	appl	PROPN
ejpam-5617	239	4	.	.	PROPN
ejpam-5617	239	5	math	math	PROPN
ejpam-5617	239	6	,	,	PUNCT
ejpam-5617	239	7	18	18	NUM
ejpam-5617	239	8	(	(	PUNCT
ejpam-5617	239	9	1	1	NUM
ejpam-5617	239	10	)	)	PUNCT
ejpam-5617	239	11	(	(	PUNCT
ejpam-5617	239	12	2025	2025	NUM
ejpam-5617	239	13	)	)	PUNCT
ejpam-5617	239	14	,	,	PUNCT
ejpam-5617	239	15	5617	5617	NUM
ejpam-5617	239	16	11	11	NUM
ejpam-5617	239	17	of	of	ADP
ejpam-5617	239	18	19	19	NUM
ejpam-5617	239	19	(	(	PUNCT
ejpam-5617	239	20	a	a	NOUN
ejpam-5617	239	21	)	)	PUNCT
ejpam-5617	239	22	(	(	PUNCT
ejpam-5617	239	23	b	b	X
ejpam-5617	239	24	)	)	PUNCT
ejpam-5617	239	25	(	(	PUNCT
ejpam-5617	239	26	c	c	X
ejpam-5617	239	27	)	)	PUNCT
ejpam-5617	239	28	figure	figure	NOUN
ejpam-5617	239	29	2	2	NUM
ejpam-5617	239	30	:	:	PUNCT
ejpam-5617	239	31	the	the	DET
ejpam-5617	239	32	curves	curve	NOUN
ejpam-5617	239	33	of	of	ADP
ejpam-5617	239	34	the	the	DET
ejpam-5617	239	35	4th	4th	ADJ
ejpam-5617	239	36	approximate	approximate	ADJ
ejpam-5617	239	37	and	and	CCONJ
ejpam-5617	239	38	exact	exact	ADJ
ejpam-5617	239	39	(	(	PUNCT
ejpam-5617	239	40	solid	solid	ADJ
ejpam-5617	239	41	curve	curve	NOUN
ejpam-5617	239	42	)	)	PUNCT
ejpam-5617	239	43	solutions	solution	NOUN
ejpam-5617	239	44	of	of	ADP
ejpam-5617	239	45	system	system	NOUN
ejpam-5617	239	46	(	(	PUNCT
ejpam-5617	239	47	29)-(30	29)-(30	NUM
ejpam-5617	239	48	)	)	PUNCT
ejpam-5617	239	49	at	at	ADP
ejpam-5617	239	50	different	different	ADJ
ejpam-5617	239	51	values	value	NOUN
ejpam-5617	239	52	of	of	ADP
ejpam-5617	239	53	α	α	PROPN
ejpam-5617	239	54	.	.	PUNCT
ejpam-5617	239	55	example	example	NOUN
ejpam-5617	239	56	4.3	4.3	NUM
ejpam-5617	239	57	.	.	PUNCT
ejpam-5617	239	58	consider	consider	VERB
ejpam-5617	239	59	the	the	DET
ejpam-5617	239	60	following	follow	VERB
ejpam-5617	239	61	system	system	NOUN
ejpam-5617	239	62	of	of	ADP
ejpam-5617	239	63	non	non	ADJ
ejpam-5617	239	64	-	-	ADJ
ejpam-5617	239	65	linear	linear	ADJ
ejpam-5617	239	66	fractional	fractional	ADJ
ejpam-5617	239	67	differential	differential	ADJ
ejpam-5617	239	68	equations	equation	NOUN
ejpam-5617	239	69	dαu1	dαu1	NOUN
ejpam-5617	239	70	(	(	PUNCT
ejpam-5617	239	71	x	x	NOUN
ejpam-5617	239	72	)	)	PUNCT
ejpam-5617	239	73	=	=	SYM
ejpam-5617	239	74	−1002	−1002	ADJ
ejpam-5617	239	75	u1	u1	NOUN
ejpam-5617	239	76	(	(	PUNCT
ejpam-5617	239	77	x	x	NOUN
ejpam-5617	239	78	)	)	PUNCT
ejpam-5617	239	79	+	+	CCONJ
ejpam-5617	239	80	1000	1000	NUM
ejpam-5617	239	81	u22	u22	NOUN
ejpam-5617	239	82	(	(	PUNCT
ejpam-5617	239	83	x	x	NOUN
ejpam-5617	239	84	)	)	PUNCT
ejpam-5617	239	85	,	,	PUNCT
ejpam-5617	239	86	dαu2	dαu2	PROPN
ejpam-5617	239	87	(	(	PUNCT
ejpam-5617	239	88	x	x	NOUN
ejpam-5617	239	89	)	)	PUNCT
ejpam-5617	239	90	=	=	SYM
ejpam-5617	239	91	u1	u1	NOUN
ejpam-5617	239	92	(	(	PUNCT
ejpam-5617	239	93	x)−	x)−	PROPN
ejpam-5617	239	94	u2	u2	PROPN
ejpam-5617	239	95	(	(	PUNCT
ejpam-5617	239	96	x)−	x)−	PROPN
ejpam-5617	239	97	u22	u22	PROPN
ejpam-5617	239	98	(	(	PUNCT
ejpam-5617	239	99	x	x	X
ejpam-5617	239	100	)	)	PUNCT
ejpam-5617	239	101	,	,	PUNCT
ejpam-5617	239	102	(	(	PUNCT
ejpam-5617	239	103	39	39	NUM
ejpam-5617	239	104	)	)	PUNCT
ejpam-5617	239	105	where	where	SCONJ
ejpam-5617	239	106	0	0	NUM
ejpam-5617	239	107	<	<	X
ejpam-5617	239	108	α	α	X
ejpam-5617	239	109	≤	≤	NUM
ejpam-5617	239	110	1	1	NUM
ejpam-5617	239	111	,	,	PUNCT
ejpam-5617	239	112	0	0	NUM
ejpam-5617	239	113	≤	≤	NUM
ejpam-5617	239	114	x	x	PUNCT
ejpam-5617	239	115	with	with	ADP
ejpam-5617	239	116	the	the	DET
ejpam-5617	239	117	initial	initial	ADJ
ejpam-5617	239	118	conditions	condition	NOUN
ejpam-5617	239	119	u1	u1	NOUN
ejpam-5617	239	120	(	(	PUNCT
ejpam-5617	239	121	0	0	NUM
ejpam-5617	239	122	)	)	PUNCT
ejpam-5617	239	123	=	=	SYM
ejpam-5617	239	124	1	1	NUM
ejpam-5617	239	125	,	,	PUNCT
ejpam-5617	239	126	u2	u2	NOUN
ejpam-5617	239	127	(	(	PUNCT
ejpam-5617	239	128	0	0	NUM
ejpam-5617	239	129	)	)	PUNCT
ejpam-5617	239	130	=	=	SYM
ejpam-5617	240	1	1	1	X
ejpam-5617	240	2	.	.	PUNCT
ejpam-5617	240	3	(	(	PUNCT
ejpam-5617	240	4	40	40	NUM
ejpam-5617	240	5	)	)	PUNCT
ejpam-5617	240	6	in	in	ADP
ejpam-5617	240	7	the	the	DET
ejpam-5617	240	8	classical	classical	ADJ
ejpam-5617	240	9	case	case	NOUN
ejpam-5617	240	10	(	(	PUNCT
ejpam-5617	240	11	α	α	NOUN
ejpam-5617	240	12	=	=	NOUN
ejpam-5617	240	13	1	1	NUM
ejpam-5617	240	14	)	)	PUNCT
ejpam-5617	240	15	,	,	PUNCT
ejpam-5617	240	16	the	the	DET
ejpam-5617	240	17	exact	exact	ADJ
ejpam-5617	240	18	solution	solution	NOUN
ejpam-5617	240	19	is	be	AUX
ejpam-5617	240	20	given	give	VERB
ejpam-5617	240	21	as	as	SCONJ
ejpam-5617	240	22	follows	follow	VERB
ejpam-5617	240	23	:	:	PUNCT
ejpam-5617	240	24	u1	u1	NOUN
ejpam-5617	240	25	(	(	PUNCT
ejpam-5617	240	26	x	x	NOUN
ejpam-5617	240	27	)	)	PUNCT
ejpam-5617	240	28	=	=	SYM
ejpam-5617	240	29	e−2x	e−2x	NOUN
ejpam-5617	240	30	,	,	PUNCT
ejpam-5617	240	31	u2	u2	NOUN
ejpam-5617	240	32	(	(	PUNCT
ejpam-5617	240	33	x	x	NOUN
ejpam-5617	240	34	)	)	PUNCT
ejpam-5617	240	35	=	=	SYM
ejpam-5617	240	36	e−x	e−x	PROPN
ejpam-5617	240	37	.	.	PUNCT
ejpam-5617	241	1	(	(	PUNCT
ejpam-5617	241	2	41	41	NUM
ejpam-5617	241	3	)	)	PUNCT
ejpam-5617	241	4	according	accord	VERB
ejpam-5617	241	5	to	to	ADP
ejpam-5617	241	6	the	the	DET
ejpam-5617	241	7	methodology	methodology	NOUN
ejpam-5617	241	8	of	of	ADP
ejpam-5617	241	9	the	the	DET
ejpam-5617	241	10	lrf	lrf	NOUN
ejpam-5617	241	11	method	method	NOUN
ejpam-5617	241	12	,	,	PUNCT
ejpam-5617	241	13	we	we	PRON
ejpam-5617	241	14	assume	assume	VERB
ejpam-5617	241	15	the	the	DET
ejpam-5617	241	16	solution	solution	NOUN
ejpam-5617	241	17	of	of	ADP
ejpam-5617	241	18	the	the	DET
ejpam-5617	241	19	system	system	NOUN
ejpam-5617	241	20	(	(	PUNCT
ejpam-5617	241	21	39)-(40	39)-(40	NUM
ejpam-5617	241	22	)	)	PUNCT
ejpam-5617	241	23	has	have	VERB
ejpam-5617	241	24	fractional	fractional	ADJ
ejpam-5617	241	25	series	series	NOUN
ejpam-5617	241	26	expansions	expansion	NOUN
ejpam-5617	241	27	as	as	ADP
ejpam-5617	241	28	:	:	PUNCT
ejpam-5617	241	29	u1	u1	NOUN
ejpam-5617	241	30	(	(	PUNCT
ejpam-5617	241	31	x	x	NOUN
ejpam-5617	241	32	)	)	PUNCT
ejpam-5617	241	33	=	=	SYM
ejpam-5617	242	1	∞∑	∞∑	NUM
ejpam-5617	242	2	n=0	n=0	NUM
ejpam-5617	242	3	u1,n	u1,n	PROPN
ejpam-5617	242	4	xnα	xnα	PROPN
ejpam-5617	242	5	,	,	PUNCT
ejpam-5617	242	6	u2	u2	NOUN
ejpam-5617	242	7	(	(	PUNCT
ejpam-5617	242	8	x	x	NOUN
ejpam-5617	242	9	)	)	PUNCT
ejpam-5617	242	10	=	=	SYM
ejpam-5617	243	1	∞∑	∞∑	NUM
ejpam-5617	243	2	n=0	n=0	NUM
ejpam-5617	243	3	u2,n	u2,n	PROPN
ejpam-5617	243	4	xnα	xnα	NOUN
ejpam-5617	243	5	.	.	PUNCT
ejpam-5617	244	1	(	(	PUNCT
ejpam-5617	244	2	42	42	NUM
ejpam-5617	244	3	)	)	PUNCT
ejpam-5617	244	4	a.	a.	PROPN
ejpam-5617	244	5	el	el	PROPN
ejpam-5617	244	6	-	-	PUNCT
ejpam-5617	244	7	ajou	ajou	PROPN
ejpam-5617	244	8	,	,	PUNCT
ejpam-5617	244	9	a.	a.	PROPN
ejpam-5617	244	10	burqan	burqan	PROPN
ejpam-5617	244	11	/	/	SYM
ejpam-5617	244	12	eur	eur	PROPN
ejpam-5617	244	13	.	.	PUNCT
ejpam-5617	245	1	j.	j.	PROPN
ejpam-5617	245	2	pure	pure	PROPN
ejpam-5617	245	3	appl	appl	PROPN
ejpam-5617	245	4	.	.	PROPN
ejpam-5617	245	5	math	math	PROPN
ejpam-5617	245	6	,	,	PUNCT
ejpam-5617	245	7	18	18	NUM
ejpam-5617	245	8	(	(	PUNCT
ejpam-5617	245	9	1	1	NUM
ejpam-5617	245	10	)	)	PUNCT
ejpam-5617	245	11	(	(	PUNCT
ejpam-5617	245	12	2025	2025	NUM
ejpam-5617	245	13	)	)	PUNCT
ejpam-5617	245	14	,	,	PUNCT
ejpam-5617	245	15	5617	5617	NUM
ejpam-5617	245	16	12	12	NUM
ejpam-5617	245	17	of	of	ADP
ejpam-5617	245	18	19	19	NUM
ejpam-5617	245	19	based	base	VERB
ejpam-5617	245	20	on	on	ADP
ejpam-5617	245	21	the	the	DET
ejpam-5617	245	22	initial	initial	ADJ
ejpam-5617	245	23	conditions	condition	NOUN
ejpam-5617	245	24	in	in	ADP
ejpam-5617	245	25	equation	equation	NOUN
ejpam-5617	245	26	(	(	PUNCT
ejpam-5617	245	27	40	40	NUM
ejpam-5617	245	28	)	)	PUNCT
ejpam-5617	245	29	,	,	PUNCT
ejpam-5617	245	30	the	the	DET
ejpam-5617	245	31	kth	kth	PROPN
ejpam-5617	245	32	approximate	approximate	ADJ
ejpam-5617	245	33	solution	solution	NOUN
ejpam-5617	245	34	can	can	AUX
ejpam-5617	245	35	be	be	AUX
ejpam-5617	245	36	written	write	VERB
ejpam-5617	245	37	as	as	ADP
ejpam-5617	245	38	u1k	u1k	PROPN
ejpam-5617	245	39	(	(	PUNCT
ejpam-5617	245	40	x	x	NOUN
ejpam-5617	245	41	)	)	PUNCT
ejpam-5617	245	42	=	=	SYM
ejpam-5617	245	43	1	1	NUM
ejpam-5617	245	44	+	+	CCONJ
ejpam-5617	245	45	k∑	k∑	ADJ
ejpam-5617	245	46	n=1	n=1	PROPN
ejpam-5617	245	47	u1,n	u1,n	PROPN
ejpam-5617	245	48	xnα	xnα	PROPN
ejpam-5617	245	49	,	,	PUNCT
ejpam-5617	245	50	u2k	u2k	PROPN
ejpam-5617	245	51	(	(	PUNCT
ejpam-5617	245	52	x	x	NOUN
ejpam-5617	245	53	)	)	PUNCT
ejpam-5617	245	54	=	=	SYM
ejpam-5617	245	55	1	1	NUM
ejpam-5617	245	56	+	+	CCONJ
ejpam-5617	245	57	k∑	k∑	ADJ
ejpam-5617	245	58	n=1	n=1	PROPN
ejpam-5617	245	59	u2,n	u2,n	PROPN
ejpam-5617	245	60	xnα	xnα	PROPN
ejpam-5617	245	61	.	.	PUNCT
ejpam-5617	246	1	(	(	PUNCT
ejpam-5617	246	2	43	43	NUM
ejpam-5617	246	3	)	)	PUNCT
ejpam-5617	246	4	the	the	DET
ejpam-5617	246	5	residual	residual	ADJ
ejpam-5617	246	6	and	and	CCONJ
ejpam-5617	246	7	kth	kth	VERB
ejpam-5617	246	8	residual	residual	ADJ
ejpam-5617	246	9	functions	function	NOUN
ejpam-5617	246	10	of	of	ADP
ejpam-5617	246	11	equation	equation	NOUN
ejpam-5617	246	12	(	(	PUNCT
ejpam-5617	246	13	39	39	NUM
ejpam-5617	246	14	)	)	PUNCT
ejpam-5617	246	15	can	can	AUX
ejpam-5617	246	16	be	be	AUX
ejpam-5617	246	17	given	give	VERB
ejpam-5617	246	18	respectively	respectively	ADV
ejpam-5617	246	19	as	as	SCONJ
ejpam-5617	246	20	follows	follow	VERB
ejpam-5617	246	21	:	:	PUNCT
ejpam-5617	246	22	rf	rf	NUM
ejpam-5617	246	23	(	(	PUNCT
ejpam-5617	246	24	u1	u1	PROPN
ejpam-5617	246	25	(	(	PUNCT
ejpam-5617	246	26	x	x	NOUN
ejpam-5617	246	27	)	)	PUNCT
ejpam-5617	246	28	)	)	PUNCT
ejpam-5617	247	1	=	=	SYM
ejpam-5617	247	2	dαu1	dαu1	NOUN
ejpam-5617	247	3	(	(	PUNCT
ejpam-5617	247	4	x	x	NOUN
ejpam-5617	247	5	)	)	PUNCT
ejpam-5617	247	6	+	+	CCONJ
ejpam-5617	247	7	1002	1002	NUM
ejpam-5617	247	8	u1	u1	NOUN
ejpam-5617	247	9	(	(	PUNCT
ejpam-5617	247	10	x)−	x)−	PROPN
ejpam-5617	247	11	1000	1000	NUM
ejpam-5617	247	12	u22	u22	PROPN
ejpam-5617	247	13	(	(	PUNCT
ejpam-5617	247	14	x	x	X
ejpam-5617	247	15	)	)	PUNCT
ejpam-5617	247	16	,	,	PUNCT
ejpam-5617	247	17	rf	rf	PROPN
ejpam-5617	247	18	(	(	PUNCT
ejpam-5617	247	19	u2	u2	PROPN
ejpam-5617	247	20	(	(	PUNCT
ejpam-5617	247	21	x	x	NOUN
ejpam-5617	247	22	)	)	PUNCT
ejpam-5617	247	23	)	)	PUNCT
ejpam-5617	247	24	=	=	PUNCT
ejpam-5617	247	25	dαu2	dαu2	PROPN
ejpam-5617	247	26	(	(	PUNCT
ejpam-5617	247	27	x)−	x)−	PROPN
ejpam-5617	247	28	u1	u1	PROPN
ejpam-5617	247	29	(	(	PUNCT
ejpam-5617	247	30	x	x	NOUN
ejpam-5617	247	31	)	)	PUNCT
ejpam-5617	247	32	+	+	CCONJ
ejpam-5617	247	33	u2	u2	NOUN
ejpam-5617	247	34	(	(	PUNCT
ejpam-5617	247	35	x	x	NOUN
ejpam-5617	247	36	)	)	PUNCT
ejpam-5617	247	37	+	+	CCONJ
ejpam-5617	247	38	u22	u22	PROPN
ejpam-5617	247	39	(	(	PUNCT
ejpam-5617	247	40	x	x	NOUN
ejpam-5617	247	41	)	)	PUNCT
ejpam-5617	247	42	.	.	PUNCT
ejpam-5617	248	1	(	(	PUNCT
ejpam-5617	248	2	44	44	NUM
ejpam-5617	248	3	)	)	PUNCT
ejpam-5617	248	4	rf	rf	PROPN
ejpam-5617	248	5	(	(	PUNCT
ejpam-5617	248	6	u1k	u1k	PROPN
ejpam-5617	248	7	(	(	PUNCT
ejpam-5617	248	8	x	x	NOUN
ejpam-5617	248	9	)	)	PUNCT
ejpam-5617	248	10	)	)	PUNCT
ejpam-5617	249	1	=	=	SYM
ejpam-5617	249	2	dαu1k	dαu1k	PROPN
ejpam-5617	249	3	(	(	PUNCT
ejpam-5617	249	4	x	x	X
ejpam-5617	249	5	)	)	PUNCT
ejpam-5617	249	6	+	+	CCONJ
ejpam-5617	249	7	1002	1002	NUM
ejpam-5617	249	8	u1k	u1k	PROPN
ejpam-5617	249	9	(	(	PUNCT
ejpam-5617	249	10	x)−	x)−	PROPN
ejpam-5617	249	11	1000	1000	NUM
ejpam-5617	249	12	u22k(x	u22k(x	NOUN
ejpam-5617	249	13	)	)	PUNCT
ejpam-5617	249	14	,	,	PUNCT
ejpam-5617	249	15	rf	rf	NUM
ejpam-5617	249	16	(	(	PUNCT
ejpam-5617	249	17	u2k	u2k	PROPN
ejpam-5617	249	18	(	(	PUNCT
ejpam-5617	249	19	x	x	NOUN
ejpam-5617	249	20	)	)	PUNCT
ejpam-5617	249	21	)	)	PUNCT
ejpam-5617	249	22	=	=	SYM
ejpam-5617	249	23	dαu2k	dαu2k	NOUN
ejpam-5617	249	24	(	(	PUNCT
ejpam-5617	249	25	x)−	x)−	PROPN
ejpam-5617	249	26	u1k	u1k	PROPN
ejpam-5617	249	27	(	(	PUNCT
ejpam-5617	249	28	x	x	NOUN
ejpam-5617	249	29	)	)	PUNCT
ejpam-5617	250	1	+	+	CCONJ
ejpam-5617	250	2	u2k	u2k	PROPN
ejpam-5617	250	3	(	(	PUNCT
ejpam-5617	250	4	x	x	NOUN
ejpam-5617	250	5	)	)	PUNCT
ejpam-5617	250	6	+	+	PUNCT
ejpam-5617	250	7	u22k(x	u22k(x	NOUN
ejpam-5617	250	8	)	)	PUNCT
ejpam-5617	250	9	.	.	PUNCT
ejpam-5617	251	1	(	(	PUNCT
ejpam-5617	251	2	45	45	NUM
ejpam-5617	251	3	)	)	PUNCT
ejpam-5617	251	4	substituting	substitute	VERB
ejpam-5617	251	5	the	the	DET
ejpam-5617	251	6	kth	kth	PROPN
ejpam-5617	251	7	approximation	approximation	NOUN
ejpam-5617	251	8	(	(	PUNCT
ejpam-5617	251	9	43	43	NUM
ejpam-5617	251	10	)	)	PUNCT
ejpam-5617	251	11	into	into	ADP
ejpam-5617	251	12	the	the	DET
ejpam-5617	251	13	kth	kth	PROPN
ejpam-5617	251	14	residual	residual	ADJ
ejpam-5617	251	15	function	function	NOUN
ejpam-5617	251	16	(	(	PUNCT
ejpam-5617	251	17	45	45	NUM
ejpam-5617	251	18	)	)	PUNCT
ejpam-5617	251	19	gives	give	VERB
ejpam-5617	251	20	the	the	DET
ejpam-5617	251	21	series	series	NOUN
ejpam-5617	251	22	form	form	NOUN
ejpam-5617	251	23	of	of	ADP
ejpam-5617	251	24	the	the	DET
ejpam-5617	251	25	kth	kth	PROPN
ejpam-5617	251	26	residual	residual	ADJ
ejpam-5617	251	27	function	function	NOUN
ejpam-5617	251	28	as	as	SCONJ
ejpam-5617	251	29	follows	follow	VERB
ejpam-5617	251	30	:	:	PUNCT
ejpam-5617	251	31	rf	rf	NUM
ejpam-5617	251	32	(	(	PUNCT
ejpam-5617	251	33	u1k	u1k	PROPN
ejpam-5617	251	34	(	(	PUNCT
ejpam-5617	251	35	x	x	NOUN
ejpam-5617	251	36	)	)	PUNCT
ejpam-5617	251	37	)	)	PUNCT
ejpam-5617	252	1	=	=	SYM
ejpam-5617	252	2	k∑	k∑	VERB
ejpam-5617	252	3	n=1	n=1	PUNCT
ejpam-5617	252	4	u1,n	u1,n	PROPN
ejpam-5617	252	5	γ	γ	X
ejpam-5617	252	6	(	(	PUNCT
ejpam-5617	252	7	nα+	nα+	NOUN
ejpam-5617	252	8	1	1	NUM
ejpam-5617	252	9	)	)	PUNCT
ejpam-5617	252	10	γ	γ	X
ejpam-5617	252	11	(	(	PUNCT
ejpam-5617	252	12	(	(	PUNCT
ejpam-5617	252	13	n−	n−	NOUN
ejpam-5617	252	14	1)α+	1)α+	NUM
ejpam-5617	252	15	1	1	NUM
ejpam-5617	252	16	)	)	PUNCT
ejpam-5617	252	17	x(n−1)α	x(n−1)α	PUNCT
ejpam-5617	253	1	+	+	CCONJ
ejpam-5617	253	2	1002	1002	NUM
ejpam-5617	253	3	(	(	PUNCT
ejpam-5617	253	4	1	1	NUM
ejpam-5617	253	5	+	+	CCONJ
ejpam-5617	253	6	k∑	k∑	ADJ
ejpam-5617	253	7	n=1	n=1	PROPN
ejpam-5617	253	8	u1,n	u1,n	PROPN
ejpam-5617	253	9	xnα	xnα	PRON
ejpam-5617	253	10	)	)	PUNCT
ejpam-5617	253	11	−1000	−1000	NOUN
ejpam-5617	253	12	(	(	PUNCT
ejpam-5617	253	13	1	1	NUM
ejpam-5617	253	14	+	+	CCONJ
ejpam-5617	253	15	k∑	k∑	ADJ
ejpam-5617	253	16	n=1	n=1	PROPN
ejpam-5617	253	17	u2,n	u2,n	PROPN
ejpam-5617	253	18	xnα	xnα	NOUN
ejpam-5617	253	19	)	)	PUNCT
ejpam-5617	253	20	2	2	NUM
ejpam-5617	253	21	,	,	PUNCT
ejpam-5617	253	22	rf	rf	ADJ
ejpam-5617	253	23	(	(	PUNCT
ejpam-5617	253	24	u2k	u2k	PROPN
ejpam-5617	253	25	(	(	PUNCT
ejpam-5617	253	26	x	x	NOUN
ejpam-5617	253	27	)	)	PUNCT
ejpam-5617	253	28	)	)	PUNCT
ejpam-5617	254	1	=	=	SYM
ejpam-5617	254	2	k∑	k∑	VERB
ejpam-5617	254	3	n=1	n=1	PROPN
ejpam-5617	254	4	u2,n	u2,n	PROPN
ejpam-5617	254	5	γ	γ	NOUN
ejpam-5617	254	6	(	(	PUNCT
ejpam-5617	254	7	nα+	nα+	NOUN
ejpam-5617	254	8	1	1	NUM
ejpam-5617	254	9	)	)	PUNCT
ejpam-5617	254	10	γ	γ	X
ejpam-5617	254	11	(	(	PUNCT
ejpam-5617	254	12	(	(	PUNCT
ejpam-5617	254	13	n−	n−	NOUN
ejpam-5617	254	14	1)α+	1)α+	NUM
ejpam-5617	254	15	1	1	NUM
ejpam-5617	254	16	)	)	PUNCT
ejpam-5617	254	17	x(n−1)α	x(n−1)α	PROPN
ejpam-5617	255	1	−	−	PROPN
ejpam-5617	255	2	k∑	k∑	PROPN
ejpam-5617	255	3	n=1	n=1	PROPN
ejpam-5617	255	4	u1,n	u1,n	PROPN
ejpam-5617	255	5	xnα	xnα	PROPN
ejpam-5617	256	1	+	+	CCONJ
ejpam-5617	256	2	k∑	k∑	ADJ
ejpam-5617	256	3	n=1	n=1	PROPN
ejpam-5617	256	4	u2,n	u2,n	PROPN
ejpam-5617	256	5	xnα	xnα	NOUN
ejpam-5617	257	1	+	+	CCONJ
ejpam-5617	257	2	(	(	PUNCT
ejpam-5617	257	3	1	1	NUM
ejpam-5617	257	4	+	+	CCONJ
ejpam-5617	257	5	k∑	k∑	ADJ
ejpam-5617	257	6	n=1	n=1	PROPN
ejpam-5617	257	7	u2,n	u2,n	PROPN
ejpam-5617	257	8	xnα	xnα	NOUN
ejpam-5617	257	9	)	)	PUNCT
ejpam-5617	257	10	2	2	NUM
ejpam-5617	257	11	.	.	PUNCT
ejpam-5617	258	1	(	(	PUNCT
ejpam-5617	258	2	46	46	NUM
ejpam-5617	258	3	)	)	PUNCT
ejpam-5617	258	4	according	accord	VERB
ejpam-5617	258	5	to	to	ADP
ejpam-5617	258	6	the	the	DET
ejpam-5617	258	7	formulation	formulation	NOUN
ejpam-5617	258	8	used	use	VERB
ejpam-5617	258	9	in	in	ADP
ejpam-5617	258	10	the	the	DET
ejpam-5617	258	11	previous	previous	ADJ
ejpam-5617	258	12	section	section	NOUN
ejpam-5617	258	13	,	,	PUNCT
ejpam-5617	258	14	the	the	DET
ejpam-5617	258	15	kth	kth	PROPN
ejpam-5617	258	16	approximations	approximation	NOUN
ejpam-5617	258	17	can	can	AUX
ejpam-5617	258	18	be	be	AUX
ejpam-5617	258	19	achieved	achieve	VERB
ejpam-5617	258	20	by	by	ADP
ejpam-5617	258	21	obtaining	obtain	VERB
ejpam-5617	258	22	the	the	DET
ejpam-5617	258	23	coefficients	coefficient	NOUN
ejpam-5617	258	24	u1,j	u1,j	NOUN
ejpam-5617	258	25	,	,	PUNCT
ejpam-5617	258	26	u2,j	u2,j	PROPN
ejpam-5617	258	27	for	for	ADP
ejpam-5617	258	28	j	j	PROPN
ejpam-5617	258	29	=	=	SYM
ejpam-5617	258	30	1	1	PROPN
ejpam-5617	258	31	,	,	PUNCT
ejpam-5617	258	32	.	.	PUNCT
ejpam-5617	258	33	.	.	PUNCT
ejpam-5617	259	1	.	.	PUNCT
ejpam-5617	260	1	,	,	PUNCT
ejpam-5617	260	2	k	k	PROPN
ejpam-5617	260	3	via	via	ADP
ejpam-5617	260	4	solving	solve	VERB
ejpam-5617	260	5	the	the	DET
ejpam-5617	260	6	following	follow	VERB
ejpam-5617	260	7	algebraic	algebraic	ADJ
ejpam-5617	260	8	equations	equation	NOUN
ejpam-5617	260	9	iteratively	iteratively	ADV
ejpam-5617	260	10	:	:	PUNCT
ejpam-5617	260	11	lim	lim	PROPN
ejpam-5617	260	12	x→0	x→0	PROPN
ejpam-5617	261	1	rf	rf	PRON
ejpam-5617	261	2	(	(	PUNCT
ejpam-5617	261	3	u1j	u1j	X
ejpam-5617	261	4	(	(	PUNCT
ejpam-5617	261	5	x	x	NOUN
ejpam-5617	261	6	)	)	PUNCT
ejpam-5617	261	7	)	)	PUNCT
ejpam-5617	262	1	x(j−1)α	x(j−1)α	PUNCT
ejpam-5617	263	1	=	=	SYM
ejpam-5617	263	2	0	0	PROPN
ejpam-5617	263	3	,	,	PUNCT
ejpam-5617	263	4	lim	lim	PROPN
ejpam-5617	263	5	x→0	x→0	PROPN
ejpam-5617	264	1	rf	rf	PROPN
ejpam-5617	264	2	(	(	PUNCT
ejpam-5617	264	3	u2j	u2j	X
ejpam-5617	264	4	(	(	PUNCT
ejpam-5617	264	5	x	x	NOUN
ejpam-5617	264	6	)	)	PUNCT
ejpam-5617	264	7	)	)	PUNCT
ejpam-5617	265	1	x(j−1)α	x(j−1)α	PUNCT
ejpam-5617	266	1	=	=	PUNCT
ejpam-5617	266	2	0	0	X
ejpam-5617	266	3	.	.	PUNCT
ejpam-5617	267	1	(	(	PUNCT
ejpam-5617	267	2	47	47	NUM
ejpam-5617	267	3	)	)	PUNCT
ejpam-5617	267	4	these	these	DET
ejpam-5617	267	5	coefficients	coefficient	NOUN
ejpam-5617	267	6	are	be	AUX
ejpam-5617	267	7	summarized	summarize	VERB
ejpam-5617	267	8	in	in	ADP
ejpam-5617	267	9	table	table	NOUN
ejpam-5617	267	10	3	3	NUM
ejpam-5617	267	11	.	.	PUNCT
ejpam-5617	268	1	so	so	ADV
ejpam-5617	268	2	,	,	PUNCT
ejpam-5617	268	3	the	the	DET
ejpam-5617	268	4	lrf	lrf	NOUN
ejpam-5617	268	5	solution	solution	NOUN
ejpam-5617	268	6	of	of	ADP
ejpam-5617	268	7	the	the	DET
ejpam-5617	268	8	system	system	NOUN
ejpam-5617	268	9	(	(	PUNCT
ejpam-5617	268	10	39)-(40	39)-(40	NUM
ejpam-5617	268	11	)	)	PUNCT
ejpam-5617	268	12	has	have	VERB
ejpam-5617	268	13	the	the	DET
ejpam-5617	268	14	following	follow	VERB
ejpam-5617	268	15	series	series	NOUN
ejpam-5617	268	16	expansions	expansion	NOUN
ejpam-5617	268	17	:	:	PUNCT
ejpam-5617	268	18	u1	u1	NOUN
ejpam-5617	268	19	(	(	PUNCT
ejpam-5617	268	20	x	x	NOUN
ejpam-5617	268	21	)	)	PUNCT
ejpam-5617	268	22	=	=	SYM
ejpam-5617	269	1	1−	1−	NUM
ejpam-5617	269	2	2xα	2xα	NOUN
ejpam-5617	269	3	γ	γ	X
ejpam-5617	269	4	(	(	PUNCT
ejpam-5617	269	5	α+	α+	PROPN
ejpam-5617	269	6	1	1	NUM
ejpam-5617	269	7	)	)	PUNCT
ejpam-5617	269	8	+	+	CCONJ
ejpam-5617	269	9	4x2α	4x2α	ADJ
ejpam-5617	269	10	γ	γ	X
ejpam-5617	269	11	(	(	PUNCT
ejpam-5617	269	12	2α+	2α+	NUM
ejpam-5617	269	13	1	1	NUM
ejpam-5617	269	14	)	)	PUNCT
ejpam-5617	269	15	+	+	CCONJ
ejpam-5617	269	16	(	(	PUNCT
ejpam-5617	269	17	−	−	PROPN
ejpam-5617	269	18	2008	2008	NUM
ejpam-5617	269	19	γ	γ	X
ejpam-5617	269	20	(	(	PUNCT
ejpam-5617	269	21	3α+	3α+	NUM
ejpam-5617	269	22	1	1	NUM
ejpam-5617	269	23	)	)	PUNCT
ejpam-5617	269	24	+	+	CCONJ
ejpam-5617	269	25	1000	1000	NUM
ejpam-5617	269	26	γ	γ	NOUN
ejpam-5617	269	27	(	(	PUNCT
ejpam-5617	269	28	2α+	2α+	NUM
ejpam-5617	269	29	1	1	NUM
ejpam-5617	269	30	)	)	PUNCT
ejpam-5617	269	31	γ	γ	X
ejpam-5617	269	32	2	2	NUM
ejpam-5617	269	33	(	(	PUNCT
ejpam-5617	269	34	α+	α+	PROPN
ejpam-5617	269	35	1)γ	1)γ	PROPN
ejpam-5617	269	36	(	(	PUNCT
ejpam-5617	269	37	3α+	3α+	NUM
ejpam-5617	269	38	1	1	NUM
ejpam-5617	269	39	)	)	PUNCT
ejpam-5617	269	40	)	)	PUNCT
ejpam-5617	270	1	x3α	x3α	PROPN
ejpam-5617	271	1	+	+	PUNCT
ejpam-5617	271	2	(	(	PUNCT
ejpam-5617	271	3	2014016	2014016	NUM
ejpam-5617	271	4	γ	γ	X
ejpam-5617	271	5	(	(	PUNCT
ejpam-5617	271	6	4α+	4α+	NUM
ejpam-5617	271	7	1	1	NUM
ejpam-5617	271	8	)	)	PUNCT
ejpam-5617	271	9	−	−	PROPN
ejpam-5617	271	10	1004000	1004000	NUM
ejpam-5617	271	11	γ	γ	X
ejpam-5617	271	12	(	(	PUNCT
ejpam-5617	271	13	2α+	2α+	NUM
ejpam-5617	271	14	1	1	NUM
ejpam-5617	271	15	)	)	PUNCT
ejpam-5617	271	16	γ	γ	X
ejpam-5617	271	17	2	2	NUM
ejpam-5617	271	18	(	(	PUNCT
ejpam-5617	271	19	α+	α+	PROPN
ejpam-5617	271	20	1)γ	1)γ	PROPN
ejpam-5617	271	21	(	(	PUNCT
ejpam-5617	271	22	4α+	4α+	NUM
ejpam-5617	271	23	1	1	NUM
ejpam-5617	271	24	)	)	PUNCT
ejpam-5617	271	25	−	−	PROPN
ejpam-5617	271	26	2000	2000	NUM
ejpam-5617	271	27	γ	γ	X
ejpam-5617	271	28	(	(	PUNCT
ejpam-5617	271	29	3α+	3α+	NUM
ejpam-5617	271	30	1	1	NUM
ejpam-5617	271	31	)	)	PUNCT
ejpam-5617	271	32	γ	γ	X
ejpam-5617	271	33	(	(	PUNCT
ejpam-5617	271	34	α+	α+	PROPN
ejpam-5617	271	35	1)γ	1)γ	PROPN
ejpam-5617	271	36	(	(	PUNCT
ejpam-5617	271	37	2α+	2α+	NUM
ejpam-5617	271	38	1)γ	1)γ	PROPN
ejpam-5617	271	39	(	(	PUNCT
ejpam-5617	271	40	4α+	4α+	NUM
ejpam-5617	271	41	1	1	NUM
ejpam-5617	271	42	)	)	PUNCT
ejpam-5617	271	43	)	)	PUNCT
ejpam-5617	271	44	x4α	x4α	PROPN
ejpam-5617	272	1	+	+	CCONJ
ejpam-5617	272	2	.	.	PUNCT
ejpam-5617	272	3	.	.	PUNCT
ejpam-5617	273	1	.	.	PUNCT
ejpam-5617	274	1	,	,	PUNCT
ejpam-5617	275	1	a.	a.	PROPN
ejpam-5617	275	2	el	el	PROPN
ejpam-5617	275	3	-	-	PUNCT
ejpam-5617	275	4	ajou	ajou	PROPN
ejpam-5617	275	5	,	,	PUNCT
ejpam-5617	275	6	a.	a.	PROPN
ejpam-5617	275	7	burqan	burqan	PROPN
ejpam-5617	275	8	/	/	SYM
ejpam-5617	275	9	eur	eur	PROPN
ejpam-5617	275	10	.	.	PUNCT
ejpam-5617	276	1	j.	j.	PROPN
ejpam-5617	276	2	pure	pure	PROPN
ejpam-5617	276	3	appl	appl	PROPN
ejpam-5617	276	4	.	.	PROPN
ejpam-5617	276	5	math	math	PROPN
ejpam-5617	276	6	,	,	PUNCT
ejpam-5617	276	7	18	18	NUM
ejpam-5617	276	8	(	(	PUNCT
ejpam-5617	276	9	1	1	NUM
ejpam-5617	276	10	)	)	PUNCT
ejpam-5617	276	11	(	(	PUNCT
ejpam-5617	276	12	2025	2025	NUM
ejpam-5617	276	13	)	)	PUNCT
ejpam-5617	276	14	,	,	PUNCT
ejpam-5617	276	15	5617	5617	NUM
ejpam-5617	276	16	13	13	NUM
ejpam-5617	276	17	of	of	ADP
ejpam-5617	276	18	19	19	NUM
ejpam-5617	276	19	table	table	NOUN
ejpam-5617	276	20	3	3	NUM
ejpam-5617	276	21	:	:	PUNCT
ejpam-5617	276	22	the	the	DET
ejpam-5617	276	23	coefficients	coefficient	NOUN
ejpam-5617	276	24	of	of	ADP
ejpam-5617	276	25	the	the	DET
ejpam-5617	276	26	4th	4th	ADJ
ejpam-5617	276	27	approximations	approximation	NOUN
ejpam-5617	276	28	of	of	ADP
ejpam-5617	276	29	u1	u1	NOUN
ejpam-5617	276	30	(	(	PUNCT
ejpam-5617	276	31	x	x	NOUN
ejpam-5617	276	32	)	)	PUNCT
ejpam-5617	276	33	,	,	PUNCT
ejpam-5617	276	34	u2	u2	PROPN
ejpam-5617	276	35	(	(	PUNCT
ejpam-5617	276	36	x	x	NOUN
ejpam-5617	276	37	)	)	PUNCT
ejpam-5617	276	38	for	for	ADP
ejpam-5617	276	39	the	the	DET
ejpam-5617	276	40	system	system	NOUN
ejpam-5617	276	41	(	(	PUNCT
ejpam-5617	276	42	39)-(40	39)-(40	NUM
ejpam-5617	276	43	)	)	PUNCT
ejpam-5617	276	44	.	.	PUNCT
ejpam-5617	277	1	k	k	PROPN
ejpam-5617	277	2	u1,k	u1,k	PROPN
ejpam-5617	277	3	u2,k	u2,k	PROPN
ejpam-5617	277	4	0	0	NUM
ejpam-5617	277	5	1	1	NUM
ejpam-5617	277	6	1	1	NUM
ejpam-5617	277	7	1	1	NUM
ejpam-5617	277	8	−	−	NUM
ejpam-5617	277	9	2	2	NUM
ejpam-5617	277	10	γ	γ	X
ejpam-5617	277	11	(	(	PUNCT
ejpam-5617	277	12	α+1	α+1	NUM
ejpam-5617	277	13	)	)	PUNCT
ejpam-5617	277	14	−	−	PROPN
ejpam-5617	277	15	1	1	NUM
ejpam-5617	277	16	γ	γ	X
ejpam-5617	277	17	(	(	PUNCT
ejpam-5617	277	18	α+1	α+1	NUM
ejpam-5617	277	19	)	)	PUNCT
ejpam-5617	277	20	2	2	NUM
ejpam-5617	277	21	4	4	NUM
ejpam-5617	277	22	γ	γ	X
ejpam-5617	277	23	(	(	PUNCT
ejpam-5617	277	24	2α+1	2α+1	PROPN
ejpam-5617	277	25	)	)	PUNCT
ejpam-5617	277	26	1	1	NUM
ejpam-5617	277	27	γ	γ	X
ejpam-5617	277	28	(	(	PUNCT
ejpam-5617	277	29	2α+1	2α+1	PROPN
ejpam-5617	277	30	)	)	PUNCT
ejpam-5617	277	31	3	3	NUM
ejpam-5617	277	32	−	−	PROPN
ejpam-5617	277	33	2008	2008	NUM
ejpam-5617	277	34	γ	γ	X
ejpam-5617	277	35	(	(	PUNCT
ejpam-5617	277	36	3α+1	3α+1	PROPN
ejpam-5617	277	37	)	)	PUNCT
ejpam-5617	277	38	+	+	CCONJ
ejpam-5617	277	39	1000	1000	NUM
ejpam-5617	277	40	γ	γ	NOUN
ejpam-5617	277	41	(	(	PUNCT
ejpam-5617	277	42	2α+1	2α+1	PROPN
ejpam-5617	277	43	)	)	PUNCT
ejpam-5617	277	44	γ2(α+1)γ	γ2(α+1)γ	PROPN
ejpam-5617	277	45	(	(	PUNCT
ejpam-5617	277	46	3α+1	3α+1	PROPN
ejpam-5617	277	47	)	)	PUNCT
ejpam-5617	277	48	1	1	NUM
ejpam-5617	277	49	γ	γ	X
ejpam-5617	277	50	(	(	PUNCT
ejpam-5617	277	51	3α+1	3α+1	PROPN
ejpam-5617	277	52	)	)	PUNCT
ejpam-5617	277	53	−	−	PROPN
ejpam-5617	277	54	γ	γ	X
ejpam-5617	277	55	(	(	PUNCT
ejpam-5617	277	56	2α+1	2α+1	PROPN
ejpam-5617	277	57	)	)	PUNCT
ejpam-5617	277	58	γ2(α+1)γ	γ2(α+1)γ	PROPN
ejpam-5617	277	59	(	(	PUNCT
ejpam-5617	277	60	3α+1	3α+1	PROPN
ejpam-5617	277	61	)	)	PUNCT
ejpam-5617	277	62	4	4	NUM
ejpam-5617	277	63	2014016	2014016	NUM
ejpam-5617	277	64	γ	γ	NOUN
ejpam-5617	277	65	(	(	PUNCT
ejpam-5617	277	66	4α+1	4α+1	PROPN
ejpam-5617	277	67	)	)	PUNCT
ejpam-5617	277	68	−	−	NOUN
ejpam-5617	277	69	1004000	1004000	NUM
ejpam-5617	277	70	γ	γ	X
ejpam-5617	277	71	(	(	PUNCT
ejpam-5617	277	72	2α+1	2α+1	PROPN
ejpam-5617	277	73	)	)	PUNCT
ejpam-5617	277	74	γ2(α+1)γ	γ2(α+1)γ	PROPN
ejpam-5617	277	75	(	(	PUNCT
ejpam-5617	277	76	4α+1	4α+1	NOUN
ejpam-5617	277	77	)	)	PUNCT
ejpam-5617	277	78	−2011	−2011	PROPN
ejpam-5617	277	79	γ	γ	X
ejpam-5617	277	80	(	(	PUNCT
ejpam-5617	277	81	4α+1	4α+1	PROPN
ejpam-5617	277	82	)	)	PUNCT
ejpam-5617	278	1	+	+	CCONJ
ejpam-5617	278	2	1003	1003	NUM
ejpam-5617	278	3	γ	γ	NOUN
ejpam-5617	278	4	(	(	PUNCT
ejpam-5617	278	5	2α+1	2α+1	PROPN
ejpam-5617	278	6	)	)	PUNCT
ejpam-5617	278	7	γ2(α+1)γ	γ2(α+1)γ	PROPN
ejpam-5617	278	8	(	(	PUNCT
ejpam-5617	278	9	4α+1	4α+1	PROPN
ejpam-5617	278	10	)	)	PUNCT
ejpam-5617	278	11	−	−	PROPN
ejpam-5617	278	12	2000	2000	NUM
ejpam-5617	278	13	γ	γ	X
ejpam-5617	278	14	(	(	PUNCT
ejpam-5617	278	15	3α+1	3α+1	PROPN
ejpam-5617	278	16	)	)	PUNCT
ejpam-5617	278	17	γ	γ	NOUN
ejpam-5617	278	18	(	(	PUNCT
ejpam-5617	278	19	α+1)γ	α+1)γ	PROPN
ejpam-5617	278	20	(	(	PUNCT
ejpam-5617	278	21	2α+1)γ	2α+1)γ	PROPN
ejpam-5617	278	22	(	(	PUNCT
ejpam-5617	278	23	4α+1	4α+1	NOUN
ejpam-5617	278	24	)	)	PUNCT
ejpam-5617	279	1	+	+	CCONJ
ejpam-5617	279	2	2	2	NUM
ejpam-5617	279	3	γ	γ	X
ejpam-5617	279	4	(	(	PUNCT
ejpam-5617	279	5	3α+1	3α+1	PROPN
ejpam-5617	279	6	)	)	PUNCT
ejpam-5617	279	7	γ	γ	NOUN
ejpam-5617	279	8	(	(	PUNCT
ejpam-5617	279	9	α+1)γ	α+1)γ	PROPN
ejpam-5617	279	10	(	(	PUNCT
ejpam-5617	279	11	2α+1)γ	2α+1)γ	PROPN
ejpam-5617	279	12	(	(	PUNCT
ejpam-5617	279	13	4α+1	4α+1	PROPN
ejpam-5617	279	14	)	)	PUNCT
ejpam-5617	279	15	u2	u2	NOUN
ejpam-5617	279	16	(	(	PUNCT
ejpam-5617	279	17	x	x	NOUN
ejpam-5617	279	18	)	)	PUNCT
ejpam-5617	279	19	=	=	SYM
ejpam-5617	280	1	1−	1−	NUM
ejpam-5617	280	2	xα	xα	INTJ
ejpam-5617	281	1	γ	γ	X
ejpam-5617	281	2	(	(	PUNCT
ejpam-5617	281	3	α+	α+	PROPN
ejpam-5617	281	4	1	1	NUM
ejpam-5617	281	5	)	)	PUNCT
ejpam-5617	281	6	+	+	CCONJ
ejpam-5617	281	7	x2α	x2α	PROPN
ejpam-5617	281	8	γ	γ	X
ejpam-5617	281	9	(	(	PUNCT
ejpam-5617	281	10	2α+	2α+	NUM
ejpam-5617	281	11	1	1	NUM
ejpam-5617	281	12	)	)	PUNCT
ejpam-5617	281	13	+	+	CCONJ
ejpam-5617	281	14	(	(	PUNCT
ejpam-5617	281	15	1	1	NUM
ejpam-5617	281	16	γ	γ	X
ejpam-5617	281	17	(	(	PUNCT
ejpam-5617	281	18	3α+	3α+	NUM
ejpam-5617	281	19	1	1	NUM
ejpam-5617	281	20	)	)	PUNCT
ejpam-5617	281	21	−	−	PROPN
ejpam-5617	281	22	γ	γ	X
ejpam-5617	281	23	(	(	PUNCT
ejpam-5617	281	24	2α+	2α+	NUM
ejpam-5617	281	25	1	1	NUM
ejpam-5617	281	26	)	)	PUNCT
ejpam-5617	281	27	γ	γ	X
ejpam-5617	281	28	2	2	NUM
ejpam-5617	281	29	(	(	PUNCT
ejpam-5617	281	30	α+	α+	PROPN
ejpam-5617	281	31	1)γ	1)γ	PROPN
ejpam-5617	281	32	(	(	PUNCT
ejpam-5617	281	33	3α+	3α+	NUM
ejpam-5617	281	34	1	1	NUM
ejpam-5617	281	35	)	)	PUNCT
ejpam-5617	281	36	)	)	PUNCT
ejpam-5617	282	1	x3α	x3α	PROPN
ejpam-5617	283	1	+	+	CCONJ
ejpam-5617	283	2	(	(	PUNCT
ejpam-5617	283	3	−	−	PROPN
ejpam-5617	283	4	2011	2011	NUM
ejpam-5617	283	5	γ	γ	X
ejpam-5617	283	6	(	(	PUNCT
ejpam-5617	283	7	4α+	4α+	NUM
ejpam-5617	283	8	1	1	NUM
ejpam-5617	283	9	)	)	PUNCT
ejpam-5617	283	10	+	+	CCONJ
ejpam-5617	283	11	1003	1003	NUM
ejpam-5617	283	12	γ	γ	NOUN
ejpam-5617	283	13	(	(	PUNCT
ejpam-5617	283	14	2α+	2α+	NUM
ejpam-5617	283	15	1	1	NUM
ejpam-5617	283	16	)	)	PUNCT
ejpam-5617	283	17	γ	γ	X
ejpam-5617	283	18	2	2	NUM
ejpam-5617	283	19	(	(	PUNCT
ejpam-5617	283	20	α+	α+	PROPN
ejpam-5617	283	21	1)γ	1)γ	PROPN
ejpam-5617	283	22	(	(	PUNCT
ejpam-5617	283	23	4α+	4α+	NUM
ejpam-5617	283	24	1	1	NUM
ejpam-5617	283	25	)	)	PUNCT
ejpam-5617	283	26	+	+	CCONJ
ejpam-5617	283	27	2	2	NUM
ejpam-5617	283	28	γ	γ	X
ejpam-5617	283	29	(	(	PUNCT
ejpam-5617	283	30	3α+	3α+	NUM
ejpam-5617	283	31	1	1	NUM
ejpam-5617	283	32	)	)	PUNCT
ejpam-5617	283	33	γ	γ	X
ejpam-5617	283	34	(	(	PUNCT
ejpam-5617	283	35	α+	α+	PROPN
ejpam-5617	283	36	1)γ	1)γ	PROPN
ejpam-5617	283	37	(	(	PUNCT
ejpam-5617	283	38	2α+	2α+	NUM
ejpam-5617	283	39	1)γ	1)γ	PROPN
ejpam-5617	283	40	(	(	PUNCT
ejpam-5617	283	41	4α+	4α+	NUM
ejpam-5617	283	42	1	1	NUM
ejpam-5617	283	43	)	)	PUNCT
ejpam-5617	283	44	)	)	PUNCT
ejpam-5617	283	45	x4α	x4α	PROPN
ejpam-5617	284	1	+	+	CCONJ
ejpam-5617	284	2	.	.	PUNCT
ejpam-5617	284	3	.	.	PUNCT
ejpam-5617	284	4	.	.	PUNCT
ejpam-5617	285	1	.	.	PUNCT
ejpam-5617	286	1	(	(	PUNCT
ejpam-5617	286	2	48	48	NUM
ejpam-5617	286	3	)	)	PUNCT
ejpam-5617	286	4	(	(	PUNCT
ejpam-5617	286	5	a	a	X
ejpam-5617	286	6	)	)	PUNCT
ejpam-5617	286	7	(	(	PUNCT
ejpam-5617	286	8	b	b	X
ejpam-5617	286	9	)	)	PUNCT
ejpam-5617	286	10	figure	figure	NOUN
ejpam-5617	286	11	3	3	NUM
ejpam-5617	286	12	:	:	PUNCT
ejpam-5617	286	13	the	the	DET
ejpam-5617	286	14	curves	curve	NOUN
ejpam-5617	286	15	of	of	ADP
ejpam-5617	286	16	the	the	DET
ejpam-5617	286	17	4th	4th	ADJ
ejpam-5617	286	18	approximate	approximate	ADJ
ejpam-5617	286	19	and	and	CCONJ
ejpam-5617	286	20	exact	exact	ADJ
ejpam-5617	286	21	(	(	PUNCT
ejpam-5617	286	22	solid	solid	ADJ
ejpam-5617	286	23	curve	curve	NOUN
ejpam-5617	286	24	)	)	PUNCT
ejpam-5617	286	25	solutions	solution	NOUN
ejpam-5617	286	26	of	of	ADP
ejpam-5617	286	27	system	system	NOUN
ejpam-5617	286	28	(	(	PUNCT
ejpam-5617	286	29	39)-(40	39)-(40	NUM
ejpam-5617	286	30	)	)	PUNCT
ejpam-5617	286	31	at	at	ADP
ejpam-5617	286	32	different	different	ADJ
ejpam-5617	286	33	values	value	NOUN
ejpam-5617	286	34	of	of	ADP
ejpam-5617	286	35	α	α	NOUN
ejpam-5617	286	36	.	.	PUNCT
ejpam-5617	287	1	for	for	ADP
ejpam-5617	287	2	α	α	NOUN
ejpam-5617	287	3	=	=	SYM
ejpam-5617	287	4	1	1	NUM
ejpam-5617	287	5	,	,	PUNCT
ejpam-5617	287	6	the	the	DET
ejpam-5617	287	7	expansions	expansion	NOUN
ejpam-5617	287	8	in	in	ADP
ejpam-5617	287	9	(	(	PUNCT
ejpam-5617	287	10	48	48	NUM
ejpam-5617	287	11	)	)	PUNCT
ejpam-5617	287	12	become	become	VERB
ejpam-5617	287	13	as	as	SCONJ
ejpam-5617	287	14	follows	follow	VERB
ejpam-5617	287	15	:	:	PUNCT
ejpam-5617	287	16	u1	u1	NOUN
ejpam-5617	287	17	(	(	PUNCT
ejpam-5617	287	18	x	x	NOUN
ejpam-5617	287	19	)	)	PUNCT
ejpam-5617	287	20	=	=	SYM
ejpam-5617	288	1	1−	1−	NUM
ejpam-5617	288	2	2x+	2x+	NUM
ejpam-5617	288	3	2x2	2x2	NUM
ejpam-5617	288	4	−	−	NUM
ejpam-5617	288	5	4x3	4x3	NUM
ejpam-5617	288	6	3	3	NUM
ejpam-5617	288	7	+	+	CCONJ
ejpam-5617	288	8	2x4	2x4	NUM
ejpam-5617	288	9	3	3	NUM
ejpam-5617	288	10	+	+	CCONJ
ejpam-5617	288	11	.	.	PUNCT
ejpam-5617	288	12	.	.	PUNCT
ejpam-5617	288	13	.	.	PUNCT
ejpam-5617	289	1	,	,	PUNCT
ejpam-5617	289	2	u2	u2	NOUN
ejpam-5617	289	3	(	(	PUNCT
ejpam-5617	289	4	x	x	NOUN
ejpam-5617	289	5	)	)	PUNCT
ejpam-5617	289	6	=	=	SYM
ejpam-5617	289	7	1−	1−	NUM
ejpam-5617	289	8	x+	x+	X
ejpam-5617	289	9	x2	x2	NOUN
ejpam-5617	289	10	2	2	NUM
ejpam-5617	289	11	−	−	NOUN
ejpam-5617	289	12	x3	x3	NOUN
ejpam-5617	289	13	6	6	NUM
ejpam-5617	289	14	+	+	CCONJ
ejpam-5617	289	15	x4	x4	PROPN
ejpam-5617	289	16	24	24	NUM
ejpam-5617	289	17	+	+	CCONJ
ejpam-5617	289	18	.	.	PUNCT
ejpam-5617	289	19	.	.	PUNCT
ejpam-5617	289	20	.	.	PUNCT
ejpam-5617	289	21	.	.	PUNCT
ejpam-5617	290	1	(	(	PUNCT
ejpam-5617	290	2	49	49	NUM
ejpam-5617	290	3	)	)	PUNCT
ejpam-5617	290	4	which	which	PRON
ejpam-5617	290	5	are	be	AUX
ejpam-5617	290	6	the	the	DET
ejpam-5617	290	7	expansions	expansion	NOUN
ejpam-5617	290	8	of	of	ADP
ejpam-5617	290	9	the	the	DET
ejpam-5617	290	10	exact	exact	ADJ
ejpam-5617	290	11	solution	solution	NOUN
ejpam-5617	290	12	indicated	indicate	VERB
ejpam-5617	290	13	in	in	ADP
ejpam-5617	290	14	(	(	PUNCT
ejpam-5617	290	15	41	41	NUM
ejpam-5617	290	16	)	)	PUNCT
ejpam-5617	290	17	.	.	PUNCT
ejpam-5617	291	1	figure	figure	NOUN
ejpam-5617	291	2	3	3	NUM
ejpam-5617	291	3	shows	show	VERB
ejpam-5617	291	4	graphs	graph	NOUN
ejpam-5617	291	5	of	of	ADP
ejpam-5617	291	6	the	the	DET
ejpam-5617	291	7	4th	4th	ADJ
ejpam-5617	291	8	approximate	approximate	ADJ
ejpam-5617	291	9	solution	solution	NOUN
ejpam-5617	291	10	of	of	ADP
ejpam-5617	291	11	the	the	DET
ejpam-5617	291	12	system	system	NOUN
ejpam-5617	291	13	(	(	PUNCT
ejpam-5617	291	14	39)-(40	39)-(40	NUM
ejpam-5617	291	15	)	)	PUNCT
ejpam-5617	291	16	for	for	ADP
ejpam-5617	291	17	different	different	ADJ
ejpam-5617	291	18	values	value	NOUN
ejpam-5617	291	19	of	of	ADP
ejpam-5617	291	20	α	α	NOUN
ejpam-5617	291	21	.	.	PUNCT
ejpam-5617	292	1	the	the	DET
ejpam-5617	292	2	graphs	graph	NOUN
ejpam-5617	292	3	show	show	VERB
ejpam-5617	292	4	the	the	DET
ejpam-5617	292	5	intervals	interval	NOUN
ejpam-5617	292	6	of	of	ADP
ejpam-5617	292	7	convergence	convergence	NOUN
ejpam-5617	292	8	and	and	CCONJ
ejpam-5617	292	9	the	the	DET
ejpam-5617	292	10	effect	effect	NOUN
ejpam-5617	292	11	of	of	ADP
ejpam-5617	292	12	the	the	DET
ejpam-5617	292	13	a.	a.	NOUN
ejpam-5617	292	14	el	el	PROPN
ejpam-5617	292	15	-	-	PUNCT
ejpam-5617	292	16	ajou	ajou	PROPN
ejpam-5617	292	17	,	,	PUNCT
ejpam-5617	292	18	a.	a.	PROPN
ejpam-5617	292	19	burqan	burqan	PROPN
ejpam-5617	292	20	/	/	SYM
ejpam-5617	292	21	eur	eur	PROPN
ejpam-5617	292	22	.	.	PUNCT
ejpam-5617	293	1	j.	j.	PROPN
ejpam-5617	293	2	pure	pure	PROPN
ejpam-5617	293	3	appl	appl	PROPN
ejpam-5617	293	4	.	.	PROPN
ejpam-5617	293	5	math	math	PROPN
ejpam-5617	293	6	,	,	PUNCT
ejpam-5617	293	7	18	18	NUM
ejpam-5617	293	8	(	(	PUNCT
ejpam-5617	293	9	1	1	NUM
ejpam-5617	293	10	)	)	PUNCT
ejpam-5617	293	11	(	(	PUNCT
ejpam-5617	293	12	2025	2025	NUM
ejpam-5617	293	13	)	)	PUNCT
ejpam-5617	293	14	,	,	PUNCT
ejpam-5617	293	15	5617	5617	NUM
ejpam-5617	293	16	14	14	NUM
ejpam-5617	293	17	of	of	ADP
ejpam-5617	293	18	19	19	NUM
ejpam-5617	293	19	order	order	NOUN
ejpam-5617	293	20	of	of	ADP
ejpam-5617	293	21	the	the	DET
ejpam-5617	293	22	derivative	derivative	NOUN
ejpam-5617	293	23	on	on	ADP
ejpam-5617	293	24	the	the	DET
ejpam-5617	293	25	behavior	behavior	NOUN
ejpam-5617	293	26	of	of	ADP
ejpam-5617	293	27	the	the	DET
ejpam-5617	293	28	solution	solution	NOUN
ejpam-5617	293	29	.	.	PUNCT
ejpam-5617	294	1	example	example	NOUN
ejpam-5617	294	2	4.4	4.4	NUM
ejpam-5617	294	3	.	.	PUNCT
ejpam-5617	295	1	consider	consider	VERB
ejpam-5617	295	2	the	the	DET
ejpam-5617	295	3	following	follow	VERB
ejpam-5617	295	4	system	system	NOUN
ejpam-5617	295	5	of	of	ADP
ejpam-5617	295	6	non	non	ADJ
ejpam-5617	295	7	-	-	ADJ
ejpam-5617	295	8	linear	linear	ADJ
ejpam-5617	295	9	fractional	fractional	ADJ
ejpam-5617	295	10	differential	differential	ADJ
ejpam-5617	295	11	equations	equation	NOUN
ejpam-5617	295	12	dαu1	dαu1	NOUN
ejpam-5617	295	13	(	(	PUNCT
ejpam-5617	295	14	x	x	NOUN
ejpam-5617	295	15	)	)	PUNCT
ejpam-5617	295	16	=	=	SYM
ejpam-5617	295	17	u21	u21	PROPN
ejpam-5617	295	18	(	(	PUNCT
ejpam-5617	295	19	x	x	NOUN
ejpam-5617	295	20	)	)	PUNCT
ejpam-5617	295	21	+	+	CCONJ
ejpam-5617	295	22	u2	u2	PROPN
ejpam-5617	295	23	(	(	PUNCT
ejpam-5617	295	24	x	x	NOUN
ejpam-5617	295	25	)	)	PUNCT
ejpam-5617	295	26	,	,	PUNCT
ejpam-5617	295	27	dαu2	dαu2	PROPN
ejpam-5617	295	28	(	(	PUNCT
ejpam-5617	295	29	x	x	NOUN
ejpam-5617	295	30	)	)	PUNCT
ejpam-5617	295	31	=	=	SYM
ejpam-5617	295	32	u2	u2	PROPN
ejpam-5617	295	33	(	(	PUNCT
ejpam-5617	295	34	x	x	NOUN
ejpam-5617	295	35	)	)	PUNCT
ejpam-5617	295	36	cos	cos	PROPN
ejpam-5617	295	37	(	(	PUNCT
ejpam-5617	295	38	u1	u1	PROPN
ejpam-5617	295	39	(	(	PUNCT
ejpam-5617	295	40	x	x	NOUN
ejpam-5617	295	41	)	)	PUNCT
ejpam-5617	295	42	)	)	PUNCT
ejpam-5617	295	43	,	,	PUNCT
ejpam-5617	295	44	(	(	PUNCT
ejpam-5617	295	45	50	50	NUM
ejpam-5617	295	46	)	)	PUNCT
ejpam-5617	295	47	where	where	SCONJ
ejpam-5617	295	48	0	0	NUM
ejpam-5617	295	49	<	<	X
ejpam-5617	295	50	α	α	X
ejpam-5617	295	51	≤	≤	NUM
ejpam-5617	295	52	1	1	NUM
ejpam-5617	295	53	,	,	PUNCT
ejpam-5617	295	54	x	x	X
ejpam-5617	295	55	≥	≥	NOUN
ejpam-5617	295	56	0	0	NUM
ejpam-5617	295	57	,	,	PUNCT
ejpam-5617	295	58	with	with	ADP
ejpam-5617	295	59	the	the	DET
ejpam-5617	295	60	initial	initial	ADJ
ejpam-5617	295	61	conditions	condition	NOUN
ejpam-5617	295	62	u1	u1	NOUN
ejpam-5617	295	63	(	(	PUNCT
ejpam-5617	295	64	0	0	NUM
ejpam-5617	295	65	)	)	PUNCT
ejpam-5617	295	66	=	=	SYM
ejpam-5617	295	67	0	0	NUM
ejpam-5617	295	68	,	,	PUNCT
ejpam-5617	295	69	u2	u2	NOUN
ejpam-5617	295	70	(	(	PUNCT
ejpam-5617	295	71	0	0	NUM
ejpam-5617	295	72	)	)	PUNCT
ejpam-5617	295	73	=	=	SYM
ejpam-5617	296	1	1	1	X
ejpam-5617	296	2	.	.	PUNCT
ejpam-5617	296	3	(	(	PUNCT
ejpam-5617	296	4	51	51	NUM
ejpam-5617	296	5	)	)	PUNCT
ejpam-5617	296	6	according	accord	VERB
ejpam-5617	296	7	to	to	ADP
ejpam-5617	296	8	the	the	DET
ejpam-5617	296	9	methodology	methodology	NOUN
ejpam-5617	296	10	of	of	ADP
ejpam-5617	296	11	the	the	DET
ejpam-5617	296	12	lrf	lrf	NOUN
ejpam-5617	296	13	method	method	NOUN
ejpam-5617	296	14	,	,	PUNCT
ejpam-5617	296	15	we	we	PRON
ejpam-5617	296	16	assume	assume	VERB
ejpam-5617	296	17	the	the	DET
ejpam-5617	296	18	solution	solution	NOUN
ejpam-5617	296	19	of	of	ADP
ejpam-5617	296	20	the	the	DET
ejpam-5617	296	21	system	system	NOUN
ejpam-5617	296	22	(	(	PUNCT
ejpam-5617	296	23	50)-(51	50)-(51	NOUN
ejpam-5617	296	24	)	)	PUNCT
ejpam-5617	296	25	has	have	VERB
ejpam-5617	296	26	fractional	fractional	ADJ
ejpam-5617	296	27	ps	ps	NOUN
ejpam-5617	296	28	expansions	expansion	NOUN
ejpam-5617	296	29	as	as	ADP
ejpam-5617	296	30	:	:	PUNCT
ejpam-5617	296	31	u1	u1	NOUN
ejpam-5617	296	32	(	(	PUNCT
ejpam-5617	296	33	x	x	NOUN
ejpam-5617	296	34	)	)	PUNCT
ejpam-5617	296	35	=	=	SYM
ejpam-5617	297	1	∞∑	∞∑	NUM
ejpam-5617	297	2	n=0	n=0	NUM
ejpam-5617	297	3	u1,n	u1,n	PROPN
ejpam-5617	297	4	xnα	xnα	PROPN
ejpam-5617	297	5	,	,	PUNCT
ejpam-5617	297	6	u2	u2	NOUN
ejpam-5617	297	7	(	(	PUNCT
ejpam-5617	297	8	x	x	NOUN
ejpam-5617	297	9	)	)	PUNCT
ejpam-5617	297	10	=	=	SYM
ejpam-5617	298	1	∞∑	∞∑	NUM
ejpam-5617	298	2	n=0	n=0	NUM
ejpam-5617	298	3	u2,n	u2,n	PROPN
ejpam-5617	298	4	xnα	xnα	ADJ
ejpam-5617	298	5	.	.	PUNCT
ejpam-5617	299	1	(	(	PUNCT
ejpam-5617	299	2	52	52	NUM
ejpam-5617	299	3	)	)	PUNCT
ejpam-5617	299	4	based	base	VERB
ejpam-5617	299	5	on	on	ADP
ejpam-5617	299	6	the	the	DET
ejpam-5617	299	7	initial	initial	ADJ
ejpam-5617	299	8	conditions	condition	NOUN
ejpam-5617	299	9	in	in	ADP
ejpam-5617	299	10	equation	equation	NOUN
ejpam-5617	299	11	(	(	PUNCT
ejpam-5617	299	12	51	51	NUM
ejpam-5617	299	13	)	)	PUNCT
ejpam-5617	299	14	,	,	PUNCT
ejpam-5617	299	15	the	the	DET
ejpam-5617	299	16	kth	kth	PROPN
ejpam-5617	299	17	approximate	approximate	ADJ
ejpam-5617	299	18	solution	solution	NOUN
ejpam-5617	299	19	can	can	AUX
ejpam-5617	299	20	be	be	AUX
ejpam-5617	299	21	written	write	VERB
ejpam-5617	299	22	as	as	ADP
ejpam-5617	299	23	u1k	u1k	PROPN
ejpam-5617	299	24	(	(	PUNCT
ejpam-5617	299	25	x	x	NOUN
ejpam-5617	299	26	)	)	PUNCT
ejpam-5617	299	27	=	=	SYM
ejpam-5617	299	28	k∑	k∑	VERB
ejpam-5617	299	29	n=1	n=1	PROPN
ejpam-5617	299	30	u1,n	u1,n	PROPN
ejpam-5617	299	31	xnα	xnα	PROPN
ejpam-5617	299	32	,	,	PUNCT
ejpam-5617	299	33	u2k	u2k	PROPN
ejpam-5617	299	34	(	(	PUNCT
ejpam-5617	299	35	x	x	NOUN
ejpam-5617	299	36	)	)	PUNCT
ejpam-5617	299	37	=	=	SYM
ejpam-5617	299	38	1	1	NUM
ejpam-5617	299	39	+	+	CCONJ
ejpam-5617	299	40	k∑	k∑	ADJ
ejpam-5617	299	41	n=1	n=1	PROPN
ejpam-5617	299	42	u2,n	u2,n	PROPN
ejpam-5617	299	43	xnα	xnα	PROPN
ejpam-5617	299	44	.	.	PUNCT
ejpam-5617	300	1	(	(	PUNCT
ejpam-5617	300	2	53	53	NUM
ejpam-5617	300	3	)	)	PUNCT
ejpam-5617	300	4	the	the	DET
ejpam-5617	300	5	residual	residual	ADJ
ejpam-5617	300	6	and	and	CCONJ
ejpam-5617	300	7	kth	kth	VERB
ejpam-5617	300	8	residual	residual	ADJ
ejpam-5617	300	9	functions	function	NOUN
ejpam-5617	300	10	of	of	ADP
ejpam-5617	300	11	equation	equation	NOUN
ejpam-5617	300	12	(	(	PUNCT
ejpam-5617	300	13	50	50	NUM
ejpam-5617	300	14	)	)	PUNCT
ejpam-5617	300	15	can	can	AUX
ejpam-5617	300	16	be	be	AUX
ejpam-5617	300	17	given	give	VERB
ejpam-5617	300	18	respectively	respectively	ADV
ejpam-5617	300	19	as	as	SCONJ
ejpam-5617	300	20	follows	follow	VERB
ejpam-5617	300	21	:	:	PUNCT
ejpam-5617	300	22	rf	rf	NUM
ejpam-5617	300	23	(	(	PUNCT
ejpam-5617	300	24	u1	u1	PROPN
ejpam-5617	300	25	(	(	PUNCT
ejpam-5617	300	26	x	x	NOUN
ejpam-5617	300	27	)	)	PUNCT
ejpam-5617	300	28	)	)	PUNCT
ejpam-5617	301	1	=	=	SYM
ejpam-5617	301	2	dαu1	dαu1	PROPN
ejpam-5617	301	3	(	(	PUNCT
ejpam-5617	301	4	x)−	x)−	PROPN
ejpam-5617	301	5	u21	u21	PROPN
ejpam-5617	301	6	(	(	PUNCT
ejpam-5617	301	7	x)−	x)−	PROPN
ejpam-5617	301	8	u2	u2	PROPN
ejpam-5617	301	9	(	(	PUNCT
ejpam-5617	301	10	x	x	NOUN
ejpam-5617	301	11	)	)	PUNCT
ejpam-5617	301	12	,	,	PUNCT
ejpam-5617	301	13	rf	rf	PROPN
ejpam-5617	301	14	(	(	PUNCT
ejpam-5617	301	15	u2	u2	PROPN
ejpam-5617	301	16	(	(	PUNCT
ejpam-5617	301	17	x	x	NOUN
ejpam-5617	301	18	)	)	PUNCT
ejpam-5617	301	19	)	)	PUNCT
ejpam-5617	301	20	=	=	PUNCT
ejpam-5617	302	1	dαu2	dαu2	PROPN
ejpam-5617	302	2	(	(	PUNCT
ejpam-5617	302	3	x)−	x)−	PROPN
ejpam-5617	302	4	u2	u2	PROPN
ejpam-5617	302	5	(	(	PUNCT
ejpam-5617	302	6	x	x	NOUN
ejpam-5617	302	7	)	)	PUNCT
ejpam-5617	302	8	cos	cos	PROPN
ejpam-5617	302	9	(	(	PUNCT
ejpam-5617	302	10	u1	u1	PROPN
ejpam-5617	302	11	(	(	PUNCT
ejpam-5617	302	12	x	x	NOUN
ejpam-5617	302	13	)	)	PUNCT
ejpam-5617	302	14	)	)	PUNCT
ejpam-5617	302	15	.	.	PUNCT
ejpam-5617	303	1	(	(	PUNCT
ejpam-5617	303	2	54	54	NUM
ejpam-5617	303	3	)	)	PUNCT
ejpam-5617	303	4	rf	rf	ADJ
ejpam-5617	303	5	(	(	PUNCT
ejpam-5617	303	6	u1k	u1k	PROPN
ejpam-5617	303	7	(	(	PUNCT
ejpam-5617	303	8	x	x	NOUN
ejpam-5617	303	9	)	)	PUNCT
ejpam-5617	303	10	)	)	PUNCT
ejpam-5617	304	1	=	=	SYM
ejpam-5617	304	2	dαu1k	dαu1k	PROPN
ejpam-5617	304	3	(	(	PUNCT
ejpam-5617	304	4	x)−	x)−	PROPN
ejpam-5617	304	5	u21k	u21k	PROPN
ejpam-5617	304	6	(	(	PUNCT
ejpam-5617	304	7	x)−	x)−	PROPN
ejpam-5617	304	8	u2k	u2k	PROPN
ejpam-5617	304	9	(	(	PUNCT
ejpam-5617	304	10	x	x	NOUN
ejpam-5617	304	11	)	)	PUNCT
ejpam-5617	304	12	,	,	PUNCT
ejpam-5617	304	13	rf	rf	NUM
ejpam-5617	304	14	(	(	PUNCT
ejpam-5617	304	15	u2k	u2k	PROPN
ejpam-5617	304	16	(	(	PUNCT
ejpam-5617	304	17	x	x	NOUN
ejpam-5617	304	18	)	)	PUNCT
ejpam-5617	304	19	)	)	PUNCT
ejpam-5617	305	1	=	=	SYM
ejpam-5617	305	2	dαu2k	dαu2k	NOUN
ejpam-5617	305	3	(	(	PUNCT
ejpam-5617	305	4	x)−	x)−	PROPN
ejpam-5617	305	5	u2k	u2k	PROPN
ejpam-5617	305	6	(	(	PUNCT
ejpam-5617	305	7	x	x	X
ejpam-5617	305	8	)	)	PUNCT
ejpam-5617	305	9	cos	cos	PROPN
ejpam-5617	305	10	(	(	PUNCT
ejpam-5617	305	11	u1k	u1k	PROPN
ejpam-5617	305	12	(	(	PUNCT
ejpam-5617	305	13	x	x	NOUN
ejpam-5617	305	14	)	)	PUNCT
ejpam-5617	305	15	)	)	PUNCT
ejpam-5617	305	16	.	.	PUNCT
ejpam-5617	306	1	(	(	PUNCT
ejpam-5617	306	2	55	55	NUM
ejpam-5617	306	3	)	)	PUNCT
ejpam-5617	306	4	by	by	ADP
ejpam-5617	306	5	substituting	substitute	VERB
ejpam-5617	306	6	the	the	DET
ejpam-5617	306	7	first	first	ADJ
ejpam-5617	306	8	approximations	approximation	NOUN
ejpam-5617	306	9	u11	u11	INTJ
ejpam-5617	306	10	(	(	PUNCT
ejpam-5617	306	11	x	x	NOUN
ejpam-5617	306	12	)	)	PUNCT
ejpam-5617	306	13	=	=	SYM
ejpam-5617	307	1	u1,1	u1,1	ADJ
ejpam-5617	307	2	xα	xα	ADJ
ejpam-5617	307	3	,	,	PUNCT
ejpam-5617	307	4	u21	u21	PROPN
ejpam-5617	307	5	(	(	PUNCT
ejpam-5617	307	6	x	x	NOUN
ejpam-5617	307	7	)	)	PUNCT
ejpam-5617	307	8	=	=	SYM
ejpam-5617	307	9	1	1	NUM
ejpam-5617	307	10	+	+	NUM
ejpam-5617	307	11	u2,1x	u2,1x	PROPN
ejpam-5617	307	12	α	α	NOUN
ejpam-5617	307	13	into	into	ADP
ejpam-5617	307	14	the	the	DET
ejpam-5617	307	15	first	first	ADJ
ejpam-5617	307	16	residual	residual	ADJ
ejpam-5617	307	17	functions	function	NOUN
ejpam-5617	307	18	,	,	PUNCT
ejpam-5617	307	19	rf	rf	ADJ
ejpam-5617	307	20	(	(	PUNCT
ejpam-5617	307	21	u11	u11	PROPN
ejpam-5617	307	22	(	(	PUNCT
ejpam-5617	307	23	x	x	NOUN
ejpam-5617	307	24	)	)	PUNCT
ejpam-5617	307	25	)	)	PUNCT
ejpam-5617	307	26	,	,	PUNCT
ejpam-5617	307	27	rf	rf	NUM
ejpam-5617	307	28	(	(	PUNCT
ejpam-5617	307	29	u21	u21	PROPN
ejpam-5617	307	30	(	(	PUNCT
ejpam-5617	307	31	x	x	NOUN
ejpam-5617	307	32	)	)	PUNCT
ejpam-5617	307	33	)	)	PUNCT
ejpam-5617	307	34	,	,	PUNCT
ejpam-5617	307	35	we	we	PRON
ejpam-5617	307	36	obtain	obtain	VERB
ejpam-5617	307	37	rf	rf	PRON
ejpam-5617	307	38	(	(	PUNCT
ejpam-5617	307	39	u11	u11	PROPN
ejpam-5617	307	40	(	(	PUNCT
ejpam-5617	307	41	x	x	NOUN
ejpam-5617	307	42	)	)	PUNCT
ejpam-5617	307	43	)	)	PUNCT
ejpam-5617	308	1	=	=	PUNCT
ejpam-5617	308	2	u1,1γ	u1,1γ	PROPN
ejpam-5617	308	3	(	(	PUNCT
ejpam-5617	308	4	α+	α+	PROPN
ejpam-5617	308	5	1)−	1)−	PROPN
ejpam-5617	308	6	(	(	PUNCT
ejpam-5617	308	7	u1,1x	u1,1x	ADJ
ejpam-5617	308	8	α)2	α)2	NOUN
ejpam-5617	308	9	−	−	NOUN
ejpam-5617	308	10	1−	1−	NUM
ejpam-5617	308	11	u2,1x	u2,1x	PROPN
ejpam-5617	308	12	α	α	PROPN
ejpam-5617	308	13	,	,	PUNCT
ejpam-5617	308	14	rf	rf	ADJ
ejpam-5617	308	15	(	(	PUNCT
ejpam-5617	308	16	u21	u21	PROPN
ejpam-5617	308	17	(	(	PUNCT
ejpam-5617	308	18	x	x	NOUN
ejpam-5617	308	19	)	)	PUNCT
ejpam-5617	308	20	)	)	PUNCT
ejpam-5617	309	1	=	=	PUNCT
ejpam-5617	309	2	u2,1γ	u2,1γ	ADJ
ejpam-5617	309	3	(	(	PUNCT
ejpam-5617	309	4	α+	α+	PROPN
ejpam-5617	309	5	1)−	1)−	PROPN
ejpam-5617	309	6	(	(	PUNCT
ejpam-5617	309	7	1	1	NUM
ejpam-5617	309	8	+	+	NUM
ejpam-5617	309	9	u2,1x	u2,1x	PROPN
ejpam-5617	309	10	α	α	NOUN
ejpam-5617	309	11	)	)	PUNCT
ejpam-5617	309	12	cos	cos	PROPN
ejpam-5617	309	13	(	(	PUNCT
ejpam-5617	309	14	u1,1	u1,1	PROPN
ejpam-5617	309	15	xα	xα	CCONJ
ejpam-5617	309	16	)	)	PUNCT
ejpam-5617	309	17	.	.	PUNCT
ejpam-5617	310	1	(	(	PUNCT
ejpam-5617	310	2	56	56	X
ejpam-5617	310	3	)	)	PUNCT
ejpam-5617	310	4	solving	solve	VERB
ejpam-5617	310	5	the	the	DET
ejpam-5617	310	6	equations	equation	NOUN
ejpam-5617	310	7	limx→0rf	limx→0rf	PROPN
ejpam-5617	310	8	(	(	PUNCT
ejpam-5617	310	9	u11	u11	PROPN
ejpam-5617	310	10	(	(	PUNCT
ejpam-5617	310	11	x	x	NOUN
ejpam-5617	310	12	)	)	PUNCT
ejpam-5617	310	13	)	)	PUNCT
ejpam-5617	311	1	=	=	SYM
ejpam-5617	311	2	0	0	NUM
ejpam-5617	311	3	,	,	PUNCT
ejpam-5617	311	4	limx→0rf	limx→0rf	PROPN
ejpam-5617	311	5	(	(	PUNCT
ejpam-5617	311	6	u21	u21	PROPN
ejpam-5617	311	7	(	(	PUNCT
ejpam-5617	311	8	x	x	NOUN
ejpam-5617	311	9	)	)	PUNCT
ejpam-5617	311	10	)	)	PUNCT
ejpam-5617	312	1	=	=	SYM
ejpam-5617	312	2	0	0	NUM
ejpam-5617	312	3	for	for	ADP
ejpam-5617	312	4	u1,1	u1,1	PROPN
ejpam-5617	312	5	,	,	PUNCT
ejpam-5617	312	6	u2,1	u2,1	PROPN
ejpam-5617	312	7	,	,	PUNCT
ejpam-5617	312	8	respectively	respectively	ADV
ejpam-5617	312	9	,	,	PUNCT
ejpam-5617	312	10	we	we	PRON
ejpam-5617	312	11	have	have	VERB
ejpam-5617	312	12	u1,1	u1,1	NOUN
ejpam-5617	312	13	=	=	SYM
ejpam-5617	312	14	1	1	NUM
ejpam-5617	312	15	γ	γ	X
ejpam-5617	312	16	(	(	PUNCT
ejpam-5617	312	17	α+	α+	NOUN
ejpam-5617	312	18	1	1	NUM
ejpam-5617	312	19	)	)	PUNCT
ejpam-5617	312	20	,	,	PUNCT
ejpam-5617	312	21	u2,1	u2,1	PROPN
ejpam-5617	313	1	=	=	NOUN
ejpam-5617	313	2	1	1	NUM
ejpam-5617	313	3	γ	γ	X
ejpam-5617	313	4	(	(	PUNCT
ejpam-5617	313	5	α+	α+	NOUN
ejpam-5617	313	6	1	1	NUM
ejpam-5617	313	7	)	)	PUNCT
ejpam-5617	313	8	.	.	PUNCT
ejpam-5617	314	1	(	(	PUNCT
ejpam-5617	314	2	57	57	NUM
ejpam-5617	314	3	)	)	PUNCT
ejpam-5617	314	4	in	in	ADP
ejpam-5617	314	5	order	order	NOUN
ejpam-5617	314	6	to	to	PART
ejpam-5617	314	7	determine	determine	VERB
ejpam-5617	314	8	the	the	DET
ejpam-5617	314	9	second	second	ADJ
ejpam-5617	314	10	coefficients	coefficient	NOUN
ejpam-5617	314	11	u1,2	u1,2	ADJ
ejpam-5617	314	12	and	and	CCONJ
ejpam-5617	314	13	u2,2	u2,2	PROPN
ejpam-5617	314	14	,	,	PUNCT
ejpam-5617	314	15	substitute	substitute	VERB
ejpam-5617	314	16	the	the	DET
ejpam-5617	314	17	second	second	ADJ
ejpam-5617	314	18	approximations	approximation	NOUN
ejpam-5617	314	19	u12	u12	NOUN
ejpam-5617	314	20	(	(	PUNCT
ejpam-5617	314	21	x	x	NOUN
ejpam-5617	314	22	)	)	PUNCT
ejpam-5617	314	23	=	=	SYM
ejpam-5617	315	1	xα	xα	ADP
ejpam-5617	315	2	γ	γ	PROPN
ejpam-5617	315	3	(	(	PUNCT
ejpam-5617	315	4	α+1	α+1	NUM
ejpam-5617	315	5	)	)	PUNCT
ejpam-5617	316	1	+	+	ADJ
ejpam-5617	316	2	u1,2x	u1,2x	ADJ
ejpam-5617	316	3	2α	2α	NOUN
ejpam-5617	316	4	,	,	PUNCT
ejpam-5617	316	5	u22	u22	PROPN
ejpam-5617	316	6	(	(	PUNCT
ejpam-5617	316	7	x	x	X
ejpam-5617	316	8	)	)	PUNCT
ejpam-5617	316	9	=	=	SYM
ejpam-5617	317	1	1	1	NUM
ejpam-5617	317	2	+	+	NUM
ejpam-5617	317	3	xα	xα	PROPN
ejpam-5617	317	4	γ	γ	PROPN
ejpam-5617	317	5	(	(	PUNCT
ejpam-5617	317	6	α+1	α+1	NUM
ejpam-5617	317	7	)	)	PUNCT
ejpam-5617	318	1	+	+	ADJ
ejpam-5617	318	2	u2,2x	u2,2x	PROPN
ejpam-5617	318	3	2α	2α	NOUN
ejpam-5617	318	4	into	into	ADP
ejpam-5617	318	5	rf	rf	PRON
ejpam-5617	318	6	(	(	PUNCT
ejpam-5617	318	7	u12	u12	PROPN
ejpam-5617	318	8	(	(	PUNCT
ejpam-5617	318	9	x	x	NOUN
ejpam-5617	318	10	)	)	PUNCT
ejpam-5617	318	11	)	)	PUNCT
ejpam-5617	318	12	,	,	PUNCT
ejpam-5617	318	13	rf	rf	PRON
ejpam-5617	318	14	(	(	PUNCT
ejpam-5617	318	15	u22	u22	PROPN
ejpam-5617	318	16	(	(	PUNCT
ejpam-5617	318	17	x	x	NOUN
ejpam-5617	318	18	)	)	PUNCT
ejpam-5617	318	19	)	)	PUNCT
ejpam-5617	318	20	to	to	PART
ejpam-5617	318	21	have	have	VERB
ejpam-5617	318	22	rf	rf	NUM
ejpam-5617	318	23	(	(	PUNCT
ejpam-5617	318	24	u12	u12	PROPN
ejpam-5617	318	25	(	(	PUNCT
ejpam-5617	318	26	x	x	NOUN
ejpam-5617	318	27	)	)	PUNCT
ejpam-5617	318	28	)	)	PUNCT
ejpam-5617	319	1	=	=	PUNCT
ejpam-5617	320	1	1	1	NUM
ejpam-5617	320	2	+	+	NUM
ejpam-5617	320	3	u1,2	u1,2	ADJ
ejpam-5617	320	4	γ	γ	NOUN
ejpam-5617	320	5	(	(	PUNCT
ejpam-5617	320	6	2α+	2α+	NUM
ejpam-5617	320	7	1	1	NUM
ejpam-5617	320	8	)	)	PUNCT
ejpam-5617	320	9	xα	xα	ADP
ejpam-5617	320	10	γ	γ	PROPN
ejpam-5617	320	11	(	(	PUNCT
ejpam-5617	320	12	α+	α+	PROPN
ejpam-5617	320	13	1	1	NUM
ejpam-5617	320	14	)	)	PUNCT
ejpam-5617	320	15	−	−	PROPN
ejpam-5617	320	16	(	(	PUNCT
ejpam-5617	320	17	xα	xα	INTJ
ejpam-5617	320	18	γ	γ	X
ejpam-5617	320	19	(	(	PUNCT
ejpam-5617	320	20	α+	α+	PROPN
ejpam-5617	320	21	1	1	NUM
ejpam-5617	320	22	)	)	PUNCT
ejpam-5617	320	23	+	+	CCONJ
ejpam-5617	320	24	u1,2	u1,2	ADJ
ejpam-5617	320	25	x2α	x2α	PROPN
ejpam-5617	320	26	)	)	PUNCT
ejpam-5617	320	27	2	2	NUM
ejpam-5617	320	28	−	−	PROPN
ejpam-5617	320	29	(	(	PUNCT
ejpam-5617	320	30	1	1	NUM
ejpam-5617	320	31	+	+	CCONJ
ejpam-5617	320	32	xα	xα	ADP
ejpam-5617	320	33	γ	γ	X
ejpam-5617	320	34	(	(	PUNCT
ejpam-5617	320	35	α+	α+	PROPN
ejpam-5617	320	36	1	1	NUM
ejpam-5617	320	37	)	)	PUNCT
ejpam-5617	320	38	+	+	CCONJ
ejpam-5617	320	39	u2,2	u2,2	PROPN
ejpam-5617	320	40	x2α	x2α	PROPN
ejpam-5617	320	41	)	)	PUNCT
ejpam-5617	320	42	,	,	PUNCT
ejpam-5617	320	43	a.	a.	PROPN
ejpam-5617	320	44	el	el	PROPN
ejpam-5617	320	45	-	-	PUNCT
ejpam-5617	320	46	ajou	ajou	PROPN
ejpam-5617	320	47	,	,	PUNCT
ejpam-5617	320	48	a.	a.	PROPN
ejpam-5617	320	49	burqan	burqan	PROPN
ejpam-5617	320	50	/	/	SYM
ejpam-5617	320	51	eur	eur	PROPN
ejpam-5617	320	52	.	.	PUNCT
ejpam-5617	321	1	j.	j.	PROPN
ejpam-5617	321	2	pure	pure	PROPN
ejpam-5617	321	3	appl	appl	PROPN
ejpam-5617	321	4	.	.	PROPN
ejpam-5617	321	5	math	math	PROPN
ejpam-5617	321	6	,	,	PUNCT
ejpam-5617	321	7	18	18	NUM
ejpam-5617	321	8	(	(	PUNCT
ejpam-5617	321	9	1	1	NUM
ejpam-5617	321	10	)	)	PUNCT
ejpam-5617	321	11	(	(	PUNCT
ejpam-5617	321	12	2025	2025	NUM
ejpam-5617	321	13	)	)	PUNCT
ejpam-5617	321	14	,	,	PUNCT
ejpam-5617	321	15	5617	5617	NUM
ejpam-5617	321	16	15	15	NUM
ejpam-5617	321	17	of	of	ADP
ejpam-5617	321	18	19	19	NUM
ejpam-5617	321	19	rf	rf	PART
ejpam-5617	321	20	(	(	PUNCT
ejpam-5617	321	21	u22	u22	PROPN
ejpam-5617	321	22	(	(	PUNCT
ejpam-5617	321	23	x	x	NOUN
ejpam-5617	321	24	)	)	PUNCT
ejpam-5617	321	25	)	)	PUNCT
ejpam-5617	322	1	=	=	SYM
ejpam-5617	322	2	1	1	NUM
ejpam-5617	323	1	+	+	CCONJ
ejpam-5617	323	2	u2,2	u2,2	PROPN
ejpam-5617	323	3	γ	γ	X
ejpam-5617	323	4	(	(	PUNCT
ejpam-5617	323	5	2α+	2α+	NUM
ejpam-5617	323	6	1	1	NUM
ejpam-5617	323	7	)	)	PUNCT
ejpam-5617	323	8	xα	xα	ADP
ejpam-5617	323	9	γ	γ	PROPN
ejpam-5617	323	10	(	(	PUNCT
ejpam-5617	323	11	α+	α+	PROPN
ejpam-5617	323	12	1	1	NUM
ejpam-5617	323	13	)	)	PUNCT
ejpam-5617	323	14	−	−	PROPN
ejpam-5617	323	15	(	(	PUNCT
ejpam-5617	323	16	1	1	NUM
ejpam-5617	323	17	+	+	CCONJ
ejpam-5617	323	18	xα	xα	ADP
ejpam-5617	323	19	γ	γ	X
ejpam-5617	323	20	(	(	PUNCT
ejpam-5617	323	21	α+	α+	PROPN
ejpam-5617	323	22	1	1	NUM
ejpam-5617	323	23	)	)	PUNCT
ejpam-5617	323	24	+	+	CCONJ
ejpam-5617	323	25	u2,2x	u2,2x	PROPN
ejpam-5617	323	26	2α	2α	NOUN
ejpam-5617	323	27	)	)	PUNCT
ejpam-5617	323	28	cos	cos	ADP
ejpam-5617	323	29	(	(	PUNCT
ejpam-5617	323	30	xα	xα	INTJ
ejpam-5617	323	31	γ	γ	X
ejpam-5617	323	32	(	(	PUNCT
ejpam-5617	323	33	α+	α+	PROPN
ejpam-5617	323	34	1	1	NUM
ejpam-5617	323	35	)	)	PUNCT
ejpam-5617	323	36	+	+	CCONJ
ejpam-5617	324	1	u1,2x	u1,2x	ADJ
ejpam-5617	324	2	2α	2α	NOUN
ejpam-5617	324	3	)	)	PUNCT
ejpam-5617	324	4	.	.	PUNCT
ejpam-5617	325	1	(	(	PUNCT
ejpam-5617	325	2	58	58	X
ejpam-5617	325	3	)	)	PUNCT
ejpam-5617	325	4	making	make	VERB
ejpam-5617	325	5	simple	simple	ADJ
ejpam-5617	325	6	calculations	calculation	NOUN
ejpam-5617	325	7	,	,	PUNCT
ejpam-5617	325	8	the	the	DET
ejpam-5617	325	9	limits	limit	NOUN
ejpam-5617	325	10	limx→0	limx→0	ADV
ejpam-5617	325	11	rf(u12(x	rf(u12(x	NOUN
ejpam-5617	325	12	)	)	PUNCT
ejpam-5617	325	13	)	)	PUNCT
ejpam-5617	325	14	xα	xα	PUNCT
ejpam-5617	326	1	=	=	NOUN
ejpam-5617	326	2	0	0	NUM
ejpam-5617	326	3	,	,	PUNCT
ejpam-5617	326	4	limx→0	limx→0	ADJ
ejpam-5617	326	5	rf(u22(x	rf(u22(x	NOUN
ejpam-5617	326	6	)	)	PUNCT
ejpam-5617	326	7	)	)	PUNCT
ejpam-5617	326	8	xα	xα	PUNCT
ejpam-5617	327	1	=	=	NOUN
ejpam-5617	327	2	0	0	NUM
ejpam-5617	327	3	,	,	PUNCT
ejpam-5617	327	4	yield	yield	VERB
ejpam-5617	327	5	u1,2	u1,2	ADJ
ejpam-5617	327	6	=	=	SYM
ejpam-5617	327	7	1	1	NUM
ejpam-5617	327	8	γ	γ	X
ejpam-5617	327	9	(	(	PUNCT
ejpam-5617	327	10	2α+	2α+	NUM
ejpam-5617	327	11	1	1	NUM
ejpam-5617	327	12	)	)	PUNCT
ejpam-5617	327	13	,	,	PUNCT
ejpam-5617	328	1	u2,2	u2,2	NOUN
ejpam-5617	328	2	=	=	SYM
ejpam-5617	328	3	1	1	NUM
ejpam-5617	328	4	γ	γ	X
ejpam-5617	328	5	(	(	PUNCT
ejpam-5617	328	6	2α+	2α+	NUM
ejpam-5617	328	7	1	1	NUM
ejpam-5617	328	8	)	)	PUNCT
ejpam-5617	328	9	.	.	PUNCT
ejpam-5617	329	1	(	(	PUNCT
ejpam-5617	329	2	59	59	NUM
ejpam-5617	329	3	)	)	PUNCT
ejpam-5617	329	4	the	the	DET
ejpam-5617	329	5	values	value	NOUN
ejpam-5617	329	6	of	of	ADP
ejpam-5617	329	7	the	the	DET
ejpam-5617	329	8	coefficients	coefficient	NOUN
ejpam-5617	329	9	u1,3	u1,3	ADJ
ejpam-5617	329	10	and	and	CCONJ
ejpam-5617	329	11	u2,3	u2,3	PROPN
ejpam-5617	329	12	are	be	AUX
ejpam-5617	329	13	also	also	ADV
ejpam-5617	329	14	obtained	obtain	VERB
ejpam-5617	329	15	by	by	ADP
ejpam-5617	329	16	substituting	substitute	VERB
ejpam-5617	329	17	u13	u13	NOUN
ejpam-5617	329	18	(	(	PUNCT
ejpam-5617	329	19	x	x	NOUN
ejpam-5617	329	20	)	)	PUNCT
ejpam-5617	329	21	=	=	SYM
ejpam-5617	329	22	xα	xα	ADP
ejpam-5617	329	23	γ(α+1	γ(α+1	NOUN
ejpam-5617	329	24	)	)	PUNCT
ejpam-5617	330	1	+	+	CCONJ
ejpam-5617	330	2	2	2	NUM
ejpam-5617	330	3	γ(2α+1)x	γ(2α+1)x	NOUN
ejpam-5617	330	4	2α	2α	NOUN
ejpam-5617	330	5	+	+	CCONJ
ejpam-5617	330	6	u1,3	u1,3	PROPN
ejpam-5617	330	7	x3α	x3α	PROPN
ejpam-5617	330	8	and	and	CCONJ
ejpam-5617	330	9	u23	u23	PROPN
ejpam-5617	330	10	(	(	PUNCT
ejpam-5617	330	11	x	x	NOUN
ejpam-5617	330	12	)	)	PUNCT
ejpam-5617	330	13	=	=	SYM
ejpam-5617	330	14	1	1	NUM
ejpam-5617	330	15	+	+	CCONJ
ejpam-5617	330	16	xα	xα	ADP
ejpam-5617	330	17	γ(α+1	γ(α+1	NOUN
ejpam-5617	330	18	)	)	PUNCT
ejpam-5617	331	1	+	+	CCONJ
ejpam-5617	332	1	u2,3	u2,3	ADJ
ejpam-5617	332	2	x3α	x3α	PROPN
ejpam-5617	332	3	into	into	ADP
ejpam-5617	332	4	rf	rf	ADJ
ejpam-5617	332	5	(	(	PUNCT
ejpam-5617	332	6	u13	u13	PROPN
ejpam-5617	332	7	(	(	PUNCT
ejpam-5617	332	8	x	x	NOUN
ejpam-5617	332	9	)	)	PUNCT
ejpam-5617	332	10	)	)	PUNCT
ejpam-5617	332	11	,	,	PUNCT
ejpam-5617	332	12	rf	rf	NUM
ejpam-5617	332	13	(	(	PUNCT
ejpam-5617	332	14	u23	u23	PROPN
ejpam-5617	332	15	(	(	PUNCT
ejpam-5617	332	16	x	x	NOUN
ejpam-5617	332	17	)	)	PUNCT
ejpam-5617	332	18	)	)	PUNCT
ejpam-5617	332	19	,	,	PUNCT
ejpam-5617	332	20	and	and	CCONJ
ejpam-5617	332	21	then	then	ADV
ejpam-5617	332	22	we	we	PRON
ejpam-5617	332	23	solve	solve	VERB
ejpam-5617	332	24	the	the	DET
ejpam-5617	332	25	following	follow	VERB
ejpam-5617	332	26	equations	equation	NOUN
ejpam-5617	332	27	:	:	PUNCT
ejpam-5617	333	1	lim	lim	PROPN
ejpam-5617	333	2	x→0	x→0	PROPN
ejpam-5617	333	3	rf	rf	PRON
ejpam-5617	333	4	(	(	PUNCT
ejpam-5617	333	5	u13	u13	PROPN
ejpam-5617	333	6	(	(	PUNCT
ejpam-5617	333	7	x	x	NOUN
ejpam-5617	333	8	)	)	PUNCT
ejpam-5617	333	9	)	)	PUNCT
ejpam-5617	333	10	x2α	x2α	PUNCT
ejpam-5617	334	1	=	=	PUNCT
ejpam-5617	334	2	0	0	PROPN
ejpam-5617	334	3	,	,	PUNCT
ejpam-5617	334	4	lim	lim	NOUN
ejpam-5617	334	5	x→0	x→0	PROPN
ejpam-5617	335	1	rf	rf	PRON
ejpam-5617	335	2	(	(	PUNCT
ejpam-5617	335	3	u23	u23	PROPN
ejpam-5617	335	4	(	(	PUNCT
ejpam-5617	335	5	x	x	NOUN
ejpam-5617	335	6	)	)	PUNCT
ejpam-5617	335	7	)	)	PUNCT
ejpam-5617	335	8	x2α	x2α	PUNCT
ejpam-5617	336	1	=	=	PUNCT
ejpam-5617	336	2	0	0	X
ejpam-5617	336	3	.	.	PUNCT
ejpam-5617	337	1	(	(	PUNCT
ejpam-5617	337	2	60	60	NUM
ejpam-5617	337	3	)	)	PUNCT
ejpam-5617	337	4	then	then	ADV
ejpam-5617	337	5	we	we	PRON
ejpam-5617	337	6	have	have	VERB
ejpam-5617	337	7	u1,3	u1,3	ADJ
ejpam-5617	337	8	=	=	NOUN
ejpam-5617	337	9	γ	γ	X
ejpam-5617	337	10	2	2	NUM
ejpam-5617	337	11	(	(	PUNCT
ejpam-5617	337	12	α+	α+	NOUN
ejpam-5617	337	13	1	1	NUM
ejpam-5617	337	14	)	)	PUNCT
ejpam-5617	337	15	+	+	CCONJ
ejpam-5617	338	1	γ	γ	X
ejpam-5617	338	2	(	(	PUNCT
ejpam-5617	338	3	2α+	2α+	NUM
ejpam-5617	338	4	1	1	NUM
ejpam-5617	338	5	)	)	PUNCT
ejpam-5617	338	6	γ	γ	X
ejpam-5617	338	7	2	2	NUM
ejpam-5617	338	8	(	(	PUNCT
ejpam-5617	338	9	α+	α+	PROPN
ejpam-5617	338	10	1)γ	1)γ	PROPN
ejpam-5617	338	11	(	(	PUNCT
ejpam-5617	338	12	3α+	3α+	NUM
ejpam-5617	338	13	1	1	NUM
ejpam-5617	338	14	)	)	PUNCT
ejpam-5617	338	15	,	,	PUNCT
ejpam-5617	338	16	u2,3	u2,3	ADJ
ejpam-5617	338	17	=	=	NOUN
ejpam-5617	338	18	2γ	2γ	X
ejpam-5617	338	19	2	2	NUM
ejpam-5617	338	20	(	(	PUNCT
ejpam-5617	338	21	α+	α+	PROPN
ejpam-5617	338	22	1)−	1)−	PROPN
ejpam-5617	338	23	γ	γ	X
ejpam-5617	338	24	(	(	PUNCT
ejpam-5617	338	25	2α+	2α+	NUM
ejpam-5617	338	26	1	1	NUM
ejpam-5617	338	27	)	)	PUNCT
ejpam-5617	338	28	2γ	2γ	X
ejpam-5617	338	29	2	2	NUM
ejpam-5617	338	30	(	(	PUNCT
ejpam-5617	338	31	α+	α+	PROPN
ejpam-5617	338	32	1)γ	1)γ	PROPN
ejpam-5617	338	33	(	(	PUNCT
ejpam-5617	338	34	3α+	3α+	NUM
ejpam-5617	338	35	1	1	NUM
ejpam-5617	338	36	)	)	PUNCT
ejpam-5617	338	37	.	.	PUNCT
ejpam-5617	339	1	(	(	PUNCT
ejpam-5617	339	2	61	61	NUM
ejpam-5617	339	3	)	)	PUNCT
ejpam-5617	339	4	similarly	similarly	ADV
ejpam-5617	339	5	,	,	PUNCT
ejpam-5617	339	6	we	we	PRON
ejpam-5617	339	7	can	can	AUX
ejpam-5617	339	8	find	find	VERB
ejpam-5617	339	9	the	the	DET
ejpam-5617	339	10	following	follow	VERB
ejpam-5617	339	11	coefficients	coefficient	NOUN
ejpam-5617	339	12	,	,	PUNCT
ejpam-5617	339	13	which	which	PRON
ejpam-5617	339	14	are	be	AUX
ejpam-5617	339	15	as	as	SCONJ
ejpam-5617	339	16	follows	follow	VERB
ejpam-5617	339	17	:	:	PUNCT
ejpam-5617	339	18	u1,4	u1,4	ADV
ejpam-5617	339	19	=	=	SYM
ejpam-5617	339	20	2γ	2γ	X
ejpam-5617	339	21	2	2	NUM
ejpam-5617	339	22	(	(	PUNCT
ejpam-5617	339	23	α+	α+	PROPN
ejpam-5617	339	24	1)γ	1)γ	PROPN
ejpam-5617	339	25	(	(	PUNCT
ejpam-5617	339	26	2α+	2α+	NUM
ejpam-5617	339	27	1)−	1)−	NUM
ejpam-5617	339	28	γ	γ	X
ejpam-5617	339	29	2	2	NUM
ejpam-5617	339	30	(	(	PUNCT
ejpam-5617	339	31	2α+	2α+	NUM
ejpam-5617	339	32	1	1	NUM
ejpam-5617	339	33	)	)	PUNCT
ejpam-5617	339	34	+	+	NUM
ejpam-5617	339	35	4γ	4γ	NOUN
ejpam-5617	339	36	(	(	PUNCT
ejpam-5617	339	37	α+	α+	PROPN
ejpam-5617	339	38	1)γ	1)γ	PROPN
ejpam-5617	339	39	(	(	PUNCT
ejpam-5617	339	40	3α+	3α+	NUM
ejpam-5617	339	41	1	1	NUM
ejpam-5617	339	42	)	)	PUNCT
ejpam-5617	339	43	2γ	2γ	X
ejpam-5617	339	44	2	2	NUM
ejpam-5617	339	45	(	(	PUNCT
ejpam-5617	339	46	α+	α+	PROPN
ejpam-5617	339	47	1)γ	1)γ	PROPN
ejpam-5617	339	48	(	(	PUNCT
ejpam-5617	339	49	2α+	2α+	NUM
ejpam-5617	339	50	1)γ	1)γ	PROPN
ejpam-5617	339	51	(	(	PUNCT
ejpam-5617	339	52	4α+	4α+	NUM
ejpam-5617	339	53	1	1	NUM
ejpam-5617	339	54	)	)	PUNCT
ejpam-5617	339	55	,	,	PUNCT
ejpam-5617	339	56	u2,4	u2,4	PROPN
ejpam-5617	339	57	=	=	SYM
ejpam-5617	339	58	γ	γ	X
ejpam-5617	339	59	(	(	PUNCT
ejpam-5617	339	60	α+	α+	PROPN
ejpam-5617	339	61	1	1	NUM
ejpam-5617	339	62	)	)	PUNCT
ejpam-5617	339	63	(	(	PUNCT
ejpam-5617	339	64	2γ	2γ	X
ejpam-5617	339	65	2	2	NUM
ejpam-5617	339	66	(	(	PUNCT
ejpam-5617	339	67	α+	α+	PROPN
ejpam-5617	339	68	1)−	1)−	PROPN
ejpam-5617	339	69	γ	γ	X
ejpam-5617	339	70	(	(	PUNCT
ejpam-5617	339	71	2α+	2α+	NUM
ejpam-5617	339	72	1))γ	1))γ	NUM
ejpam-5617	339	73	(	(	PUNCT
ejpam-5617	339	74	2α+	2α+	PROPN
ejpam-5617	339	75	1)−	1)−	PROPN
ejpam-5617	339	76	(	(	PUNCT
ejpam-5617	339	77	2γ	2γ	X
ejpam-5617	339	78	2	2	NUM
ejpam-5617	339	79	(	(	PUNCT
ejpam-5617	339	80	α+	α+	NOUN
ejpam-5617	339	81	1	1	NUM
ejpam-5617	339	82	)	)	PUNCT
ejpam-5617	339	83	+	+	CCONJ
ejpam-5617	339	84	γ	γ	X
ejpam-5617	339	85	(	(	PUNCT
ejpam-5617	339	86	2α+	2α+	NUM
ejpam-5617	339	87	1))γ	1))γ	NUM
ejpam-5617	339	88	(	(	PUNCT
ejpam-5617	339	89	3α+	3α+	NUM
ejpam-5617	339	90	1	1	NUM
ejpam-5617	339	91	)	)	PUNCT
ejpam-5617	339	92	2γ	2γ	X
ejpam-5617	339	93	3	3	NUM
ejpam-5617	339	94	(	(	PUNCT
ejpam-5617	339	95	α+	α+	PROPN
ejpam-5617	339	96	1)γ	1)γ	PROPN
ejpam-5617	339	97	(	(	PUNCT
ejpam-5617	339	98	2α+	2α+	NUM
ejpam-5617	339	99	1)γ	1)γ	PROPN
ejpam-5617	339	100	(	(	PUNCT
ejpam-5617	339	101	4α+	4α+	NUM
ejpam-5617	339	102	1	1	NUM
ejpam-5617	339	103	)	)	PUNCT
ejpam-5617	339	104	.	.	PUNCT
ejpam-5617	340	1	(	(	PUNCT
ejpam-5617	340	2	62	62	NUM
ejpam-5617	340	3	)	)	PUNCT
ejpam-5617	340	4	so	so	ADV
ejpam-5617	340	5	,	,	PUNCT
ejpam-5617	340	6	the	the	DET
ejpam-5617	340	7	lrf	lrf	NOUN
ejpam-5617	340	8	solution	solution	NOUN
ejpam-5617	340	9	of	of	ADP
ejpam-5617	340	10	the	the	DET
ejpam-5617	340	11	system	system	NOUN
ejpam-5617	340	12	(	(	PUNCT
ejpam-5617	340	13	50)-(51	50)-(51	NOUN
ejpam-5617	340	14	)	)	PUNCT
ejpam-5617	340	15	has	have	VERB
ejpam-5617	340	16	the	the	DET
ejpam-5617	340	17	following	follow	VERB
ejpam-5617	340	18	series	series	NOUN
ejpam-5617	340	19	expansions	expansion	NOUN
ejpam-5617	340	20	:	:	PUNCT
ejpam-5617	340	21	u1	u1	NOUN
ejpam-5617	340	22	(	(	PUNCT
ejpam-5617	340	23	x	x	NOUN
ejpam-5617	340	24	)	)	PUNCT
ejpam-5617	340	25	=	=	SYM
ejpam-5617	341	1	xα	xα	ADP
ejpam-5617	341	2	γ	γ	X
ejpam-5617	341	3	(	(	PUNCT
ejpam-5617	341	4	α+	α+	PROPN
ejpam-5617	341	5	1	1	NUM
ejpam-5617	341	6	)	)	PUNCT
ejpam-5617	341	7	+	+	CCONJ
ejpam-5617	341	8	x2α	x2α	PROPN
ejpam-5617	341	9	γ	γ	X
ejpam-5617	341	10	(	(	PUNCT
ejpam-5617	341	11	2α+	2α+	NUM
ejpam-5617	341	12	1	1	NUM
ejpam-5617	341	13	)	)	PUNCT
ejpam-5617	341	14	+	+	CCONJ
ejpam-5617	341	15	γ	γ	X
ejpam-5617	341	16	2	2	NUM
ejpam-5617	341	17	(	(	PUNCT
ejpam-5617	341	18	α+	α+	NOUN
ejpam-5617	341	19	1	1	NUM
ejpam-5617	341	20	)	)	PUNCT
ejpam-5617	341	21	+	+	CCONJ
ejpam-5617	341	22	γ	γ	X
ejpam-5617	341	23	(	(	PUNCT
ejpam-5617	341	24	2α+	2α+	NUM
ejpam-5617	341	25	1	1	NUM
ejpam-5617	341	26	)	)	PUNCT
ejpam-5617	341	27	γ	γ	X
ejpam-5617	341	28	2	2	NUM
ejpam-5617	341	29	(	(	PUNCT
ejpam-5617	341	30	α+	α+	PROPN
ejpam-5617	341	31	1)γ	1)γ	PROPN
ejpam-5617	341	32	(	(	PUNCT
ejpam-5617	341	33	3α+	3α+	NUM
ejpam-5617	341	34	1	1	NUM
ejpam-5617	341	35	)	)	PUNCT
ejpam-5617	341	36	x3α	x3α	PROPN
ejpam-5617	342	1	+	+	CCONJ
ejpam-5617	342	2	2γ	2γ	NUM
ejpam-5617	342	3	2	2	NUM
ejpam-5617	342	4	(	(	PUNCT
ejpam-5617	342	5	α+	α+	PROPN
ejpam-5617	342	6	1)γ	1)γ	PROPN
ejpam-5617	342	7	(	(	PUNCT
ejpam-5617	342	8	2α+	2α+	NUM
ejpam-5617	342	9	1)−	1)−	NUM
ejpam-5617	342	10	γ	γ	X
ejpam-5617	342	11	2	2	NUM
ejpam-5617	342	12	(	(	PUNCT
ejpam-5617	342	13	2α+	2α+	NUM
ejpam-5617	342	14	1	1	NUM
ejpam-5617	342	15	)	)	PUNCT
ejpam-5617	342	16	+	+	NUM
ejpam-5617	342	17	4γ	4γ	NOUN
ejpam-5617	342	18	(	(	PUNCT
ejpam-5617	342	19	α+	α+	PROPN
ejpam-5617	342	20	1)γ	1)γ	PROPN
ejpam-5617	342	21	(	(	PUNCT
ejpam-5617	342	22	3α+	3α+	NUM
ejpam-5617	342	23	1	1	NUM
ejpam-5617	342	24	)	)	PUNCT
ejpam-5617	342	25	2γ	2γ	X
ejpam-5617	342	26	2	2	NUM
ejpam-5617	342	27	(	(	PUNCT
ejpam-5617	342	28	α+	α+	PROPN
ejpam-5617	342	29	1)γ	1)γ	PROPN
ejpam-5617	342	30	(	(	PUNCT
ejpam-5617	342	31	2α+	2α+	NUM
ejpam-5617	342	32	1)γ	1)γ	PROPN
ejpam-5617	342	33	(	(	PUNCT
ejpam-5617	342	34	4α+	4α+	NUM
ejpam-5617	342	35	1	1	NUM
ejpam-5617	342	36	)	)	PUNCT
ejpam-5617	342	37	x4α	x4α	PUNCT
ejpam-5617	343	1	+	+	CCONJ
ejpam-5617	343	2	.	.	PUNCT
ejpam-5617	343	3	.	.	PUNCT
ejpam-5617	344	1	.	.	PUNCT
ejpam-5617	345	1	,	,	PUNCT
ejpam-5617	345	2	u2	u2	NOUN
ejpam-5617	345	3	(	(	PUNCT
ejpam-5617	345	4	x	x	NOUN
ejpam-5617	345	5	)	)	PUNCT
ejpam-5617	345	6	=	=	SYM
ejpam-5617	345	7	1	1	NUM
ejpam-5617	345	8	+	+	NUM
ejpam-5617	345	9	xα	xα	ADP
ejpam-5617	345	10	γ	γ	X
ejpam-5617	345	11	(	(	PUNCT
ejpam-5617	345	12	α+	α+	PROPN
ejpam-5617	345	13	1	1	NUM
ejpam-5617	345	14	)	)	PUNCT
ejpam-5617	345	15	+	+	CCONJ
ejpam-5617	345	16	x2α	x2α	PROPN
ejpam-5617	345	17	γ	γ	X
ejpam-5617	345	18	(	(	PUNCT
ejpam-5617	345	19	2α+	2α+	NUM
ejpam-5617	345	20	1	1	NUM
ejpam-5617	345	21	)	)	PUNCT
ejpam-5617	345	22	+	+	CCONJ
ejpam-5617	345	23	2γ	2γ	X
ejpam-5617	345	24	2	2	NUM
ejpam-5617	345	25	(	(	PUNCT
ejpam-5617	345	26	α+	α+	PROPN
ejpam-5617	345	27	1)−	1)−	PROPN
ejpam-5617	345	28	γ	γ	X
ejpam-5617	345	29	(	(	PUNCT
ejpam-5617	345	30	2α+	2α+	NUM
ejpam-5617	345	31	1	1	NUM
ejpam-5617	345	32	)	)	PUNCT
ejpam-5617	345	33	2γ	2γ	X
ejpam-5617	345	34	2	2	NUM
ejpam-5617	345	35	(	(	PUNCT
ejpam-5617	345	36	α+	α+	PROPN
ejpam-5617	345	37	1)γ	1)γ	PROPN
ejpam-5617	345	38	(	(	PUNCT
ejpam-5617	345	39	3α+	3α+	NUM
ejpam-5617	345	40	1	1	NUM
ejpam-5617	345	41	)	)	PUNCT
ejpam-5617	345	42	x3α	x3α	PROPN
ejpam-5617	346	1	+	+	CCONJ
ejpam-5617	346	2	γ	γ	X
ejpam-5617	346	3	(	(	PUNCT
ejpam-5617	346	4	α+	α+	NOUN
ejpam-5617	346	5	1	1	NUM
ejpam-5617	346	6	)	)	PUNCT
ejpam-5617	346	7	(	(	PUNCT
ejpam-5617	346	8	2γ	2γ	X
ejpam-5617	346	9	2	2	NUM
ejpam-5617	346	10	(	(	PUNCT
ejpam-5617	346	11	α+	α+	PROPN
ejpam-5617	346	12	1)−	1)−	PROPN
ejpam-5617	346	13	γ	γ	X
ejpam-5617	346	14	(	(	PUNCT
ejpam-5617	346	15	2α+	2α+	NUM
ejpam-5617	346	16	1))γ	1))γ	NUM
ejpam-5617	346	17	(	(	PUNCT
ejpam-5617	346	18	2α+	2α+	PROPN
ejpam-5617	346	19	1)−	1)−	PROPN
ejpam-5617	346	20	(	(	PUNCT
ejpam-5617	346	21	2γ	2γ	X
ejpam-5617	346	22	2	2	NUM
ejpam-5617	346	23	(	(	PUNCT
ejpam-5617	346	24	α+	α+	NOUN
ejpam-5617	346	25	1	1	NUM
ejpam-5617	346	26	)	)	PUNCT
ejpam-5617	346	27	+	+	CCONJ
ejpam-5617	346	28	γ	γ	X
ejpam-5617	346	29	(	(	PUNCT
ejpam-5617	346	30	2α+	2α+	NUM
ejpam-5617	346	31	1))γ	1))γ	NUM
ejpam-5617	346	32	(	(	PUNCT
ejpam-5617	346	33	3α+	3α+	NUM
ejpam-5617	346	34	1	1	NUM
ejpam-5617	346	35	)	)	PUNCT
ejpam-5617	346	36	2γ	2γ	X
ejpam-5617	346	37	3	3	NUM
ejpam-5617	346	38	(	(	PUNCT
ejpam-5617	346	39	α+	α+	PROPN
ejpam-5617	346	40	1)γ	1)γ	PROPN
ejpam-5617	346	41	(	(	PUNCT
ejpam-5617	346	42	2α+	2α+	NUM
ejpam-5617	346	43	1)γ	1)γ	PROPN
ejpam-5617	346	44	(	(	PUNCT
ejpam-5617	346	45	4α+	4α+	NUM
ejpam-5617	346	46	1	1	NUM
ejpam-5617	346	47	)	)	PUNCT
ejpam-5617	346	48	x4α+	x4α+	NOUN
ejpam-5617	346	49	.	.	PUNCT
ejpam-5617	346	50	.	.	PUNCT
ejpam-5617	346	51	.	.	PUNCT
ejpam-5617	346	52	.	.	PUNCT
ejpam-5617	347	1	(	(	PUNCT
ejpam-5617	347	2	63	63	NUM
ejpam-5617	347	3	)	)	PUNCT
ejpam-5617	347	4	for	for	ADP
ejpam-5617	347	5	α	α	NOUN
ejpam-5617	347	6	=	=	SYM
ejpam-5617	347	7	1	1	NUM
ejpam-5617	347	8	,	,	PUNCT
ejpam-5617	347	9	the	the	DET
ejpam-5617	347	10	solution	solution	NOUN
ejpam-5617	347	11	(	(	PUNCT
ejpam-5617	347	12	63	63	NUM
ejpam-5617	347	13	)	)	PUNCT
ejpam-5617	347	14	becomes	become	VERB
ejpam-5617	347	15	as	as	SCONJ
ejpam-5617	347	16	follows	follow	VERB
ejpam-5617	347	17	:	:	PUNCT
ejpam-5617	347	18	u1	u1	NOUN
ejpam-5617	347	19	(	(	PUNCT
ejpam-5617	347	20	x	x	NOUN
ejpam-5617	347	21	)	)	PUNCT
ejpam-5617	348	1	=	=	SYM
ejpam-5617	348	2	x+	x+	PUNCT
ejpam-5617	349	1	x2	x2	NOUN
ejpam-5617	349	2	2	2	NUM
ejpam-5617	349	3	+	+	CCONJ
ejpam-5617	349	4	x3	x3	ADJ
ejpam-5617	349	5	2	2	NUM
ejpam-5617	349	6	+	+	CCONJ
ejpam-5617	349	7	x4	x4	PROPN
ejpam-5617	349	8	4	4	NUM
ejpam-5617	349	9	+	+	CCONJ
ejpam-5617	349	10	.	.	PUNCT
ejpam-5617	349	11	.	.	PUNCT
ejpam-5617	349	12	.	.	PUNCT
ejpam-5617	350	1	,	,	PUNCT
ejpam-5617	350	2	u2	u2	NOUN
ejpam-5617	350	3	(	(	PUNCT
ejpam-5617	350	4	x	x	NOUN
ejpam-5617	350	5	)	)	PUNCT
ejpam-5617	350	6	=	=	SYM
ejpam-5617	350	7	1	1	NUM
ejpam-5617	350	8	+	+	CCONJ
ejpam-5617	350	9	x+	x+	ADJ
ejpam-5617	350	10	x2	x2	NOUN
ejpam-5617	350	11	2	2	X
ejpam-5617	350	12	−	−	NOUN
ejpam-5617	350	13	x4	x4	PROPN
ejpam-5617	350	14	4	4	NUM
ejpam-5617	350	15	+	+	CCONJ
ejpam-5617	350	16	.	.	PUNCT
ejpam-5617	350	17	.	.	PUNCT
ejpam-5617	350	18	.	.	PUNCT
ejpam-5617	350	19	.	.	PUNCT
ejpam-5617	351	1	(	(	PUNCT
ejpam-5617	351	2	64	64	NUM
ejpam-5617	351	3	)	)	PUNCT
ejpam-5617	351	4	this	this	DET
ejpam-5617	351	5	solution	solution	NOUN
ejpam-5617	351	6	coincides	coincide	VERB
ejpam-5617	351	7	with	with	ADP
ejpam-5617	351	8	the	the	DET
ejpam-5617	351	9	solution	solution	NOUN
ejpam-5617	351	10	attained	attain	VERB
ejpam-5617	351	11	by	by	ADP
ejpam-5617	351	12	using	use	VERB
ejpam-5617	351	13	the	the	DET
ejpam-5617	351	14	adomian	adomian	NOUN
ejpam-5617	351	15	decomposition	decomposition	NOUN
ejpam-5617	351	16	method	method	NOUN
ejpam-5617	351	17	[	[	X
ejpam-5617	351	18	38	38	NUM
ejpam-5617	351	19	]	]	PUNCT
ejpam-5617	351	20	.	.	PUNCT
ejpam-5617	352	1	a.	a.	PROPN
ejpam-5617	352	2	el	el	PROPN
ejpam-5617	352	3	-	-	PUNCT
ejpam-5617	352	4	ajou	ajou	PROPN
ejpam-5617	352	5	,	,	PUNCT
ejpam-5617	352	6	a.	a.	PROPN
ejpam-5617	352	7	burqan	burqan	PROPN
ejpam-5617	352	8	/	/	SYM
ejpam-5617	352	9	eur	eur	PROPN
ejpam-5617	352	10	.	.	PUNCT
ejpam-5617	353	1	j.	j.	PROPN
ejpam-5617	353	2	pure	pure	PROPN
ejpam-5617	353	3	appl	appl	PROPN
ejpam-5617	353	4	.	.	PROPN
ejpam-5617	353	5	math	math	PROPN
ejpam-5617	353	6	,	,	PUNCT
ejpam-5617	353	7	18	18	NUM
ejpam-5617	353	8	(	(	PUNCT
ejpam-5617	353	9	1	1	NUM
ejpam-5617	353	10	)	)	PUNCT
ejpam-5617	353	11	(	(	PUNCT
ejpam-5617	353	12	2025	2025	NUM
ejpam-5617	353	13	)	)	PUNCT
ejpam-5617	353	14	,	,	PUNCT
ejpam-5617	353	15	5617	5617	NUM
ejpam-5617	353	16	16	16	NUM
ejpam-5617	353	17	of	of	ADP
ejpam-5617	353	18	19	19	NUM
ejpam-5617	353	19	tables	table	NOUN
ejpam-5617	353	20	4	4	NUM
ejpam-5617	353	21	and	and	CCONJ
ejpam-5617	353	22	5	5	NUM
ejpam-5617	353	23	present	present	ADJ
ejpam-5617	353	24	numerical	numerical	ADJ
ejpam-5617	353	25	values	value	NOUN
ejpam-5617	353	26	for	for	ADP
ejpam-5617	353	27	the	the	DET
ejpam-5617	353	28	4th	4th	ADJ
ejpam-5617	353	29	approximation	approximation	NOUN
ejpam-5617	353	30	of	of	ADP
ejpam-5617	353	31	the	the	DET
ejpam-5617	353	32	solution	solution	NOUN
ejpam-5617	353	33	to	to	ADP
ejpam-5617	353	34	the	the	DET
ejpam-5617	353	35	ivp	ivp	NOUN
ejpam-5617	353	36	(	(	PUNCT
ejpam-5617	353	37	50)-(51	50)-(51	NOUN
ejpam-5617	353	38	)	)	PUNCT
ejpam-5617	353	39	and	and	CCONJ
ejpam-5617	353	40	the	the	DET
ejpam-5617	353	41	residual	residual	ADJ
ejpam-5617	353	42	error	error	NOUN
ejpam-5617	353	43	of	of	ADP
ejpam-5617	353	44	the	the	DET
ejpam-5617	353	45	approximate	approximate	ADJ
ejpam-5617	353	46	solution	solution	NOUN
ejpam-5617	353	47	at	at	ADP
ejpam-5617	353	48	various	various	ADJ
ejpam-5617	353	49	α	α	NOUN
ejpam-5617	353	50	values	value	NOUN
ejpam-5617	353	51	.	.	PUNCT
ejpam-5617	354	1	since	since	SCONJ
ejpam-5617	354	2	there	there	PRON
ejpam-5617	354	3	is	be	VERB
ejpam-5617	354	4	no	no	DET
ejpam-5617	354	5	exact	exact	ADJ
ejpam-5617	354	6	solution	solution	NOUN
ejpam-5617	354	7	available	available	ADJ
ejpam-5617	354	8	for	for	ADP
ejpam-5617	354	9	this	this	DET
ejpam-5617	354	10	problem	problem	NOUN
ejpam-5617	354	11	,	,	PUNCT
ejpam-5617	354	12	we	we	PRON
ejpam-5617	354	13	focus	focus	VERB
ejpam-5617	354	14	solely	solely	ADV
ejpam-5617	354	15	on	on	ADP
ejpam-5617	354	16	the	the	DET
ejpam-5617	354	17	residual	residual	ADJ
ejpam-5617	354	18	error	error	NOUN
ejpam-5617	354	19	,	,	PUNCT
ejpam-5617	354	20	which	which	PRON
ejpam-5617	354	21	is	be	AUX
ejpam-5617	354	22	defined	define	VERB
ejpam-5617	354	23	for	for	ADP
ejpam-5617	354	24	the	the	DET
ejpam-5617	354	25	problem	problem	NOUN
ejpam-5617	354	26	as	as	SCONJ
ejpam-5617	354	27	follows	follow	VERB
ejpam-5617	354	28	:	:	PUNCT
ejpam-5617	355	1	rf	rf	NOUN
ejpam-5617	355	2	.	.	PUNCT
ejpam-5617	355	3	err	err	PROPN
ejpam-5617	355	4	.	.	PUNCT
ejpam-5617	356	1	(	(	PUNCT
ejpam-5617	356	2	x	x	X
ejpam-5617	356	3	)	)	PUNCT
ejpam-5617	356	4	=	=	SYM
ejpam-5617	356	5	∣∣dαu1k	∣∣dαu1k	PROPN
ejpam-5617	356	6	(	(	PUNCT
ejpam-5617	356	7	x)−	x)−	PROPN
ejpam-5617	356	8	u2	u2	PROPN
ejpam-5617	356	9	1k	1k	NOUN
ejpam-5617	356	10	(	(	PUNCT
ejpam-5617	356	11	x)−	x)−	PROPN
ejpam-5617	356	12	u2k	u2k	PROPN
ejpam-5617	356	13	(	(	PUNCT
ejpam-5617	356	14	x	x	X
ejpam-5617	356	15	)	)	PUNCT
ejpam-5617	356	16	∣∣	∣∣	NUM
ejpam-5617	356	17	,	,	PUNCT
ejpam-5617	356	18	rf	rf	PROPN
ejpam-5617	356	19	.	.	PUNCT
ejpam-5617	356	20	err	err	PROPN
ejpam-5617	356	21	.	.	PUNCT
ejpam-5617	357	1	(	(	PUNCT
ejpam-5617	357	2	x	x	X
ejpam-5617	357	3	)	)	PUNCT
ejpam-5617	357	4	=	=	SYM
ejpam-5617	357	5	|dαu2k	|dαu2k	NOUN
ejpam-5617	357	6	(	(	PUNCT
ejpam-5617	357	7	x)−	x)−	PROPN
ejpam-5617	357	8	u2k	u2k	PROPN
ejpam-5617	357	9	(	(	PUNCT
ejpam-5617	357	10	x	x	X
ejpam-5617	357	11	)	)	PUNCT
ejpam-5617	357	12	cos	cos	PROPN
ejpam-5617	357	13	(	(	PUNCT
ejpam-5617	357	14	u1k	u1k	PROPN
ejpam-5617	357	15	(	(	PUNCT
ejpam-5617	357	16	x	x	NOUN
ejpam-5617	357	17	)	)	PUNCT
ejpam-5617	357	18	)	)	PUNCT
ejpam-5617	358	1	|	|	ADV
ejpam-5617	358	2	.	.	PUNCT
ejpam-5617	359	1	(	(	PUNCT
ejpam-5617	359	2	65	65	NUM
ejpam-5617	359	3	)	)	PUNCT
ejpam-5617	359	4	table	table	NOUN
ejpam-5617	359	5	4	4	NUM
ejpam-5617	359	6	:	:	PUNCT
ejpam-5617	359	7	the	the	DET
ejpam-5617	359	8	4th	4th	ADJ
ejpam-5617	359	9	approximation	approximation	NOUN
ejpam-5617	359	10	of	of	ADP
ejpam-5617	359	11	u1	u1	NOUN
ejpam-5617	359	12	(	(	PUNCT
ejpam-5617	359	13	x	x	NOUN
ejpam-5617	359	14	)	)	PUNCT
ejpam-5617	359	15	,	,	PUNCT
ejpam-5617	359	16	the	the	DET
ejpam-5617	359	17	ivp	ivp	X
ejpam-5617	359	18	(	(	PUNCT
ejpam-5617	359	19	33)-(34	33)-(34	NUM
ejpam-5617	359	20	)	)	PUNCT
ejpam-5617	359	21	solution	solution	NOUN
ejpam-5617	359	22	,	,	PUNCT
ejpam-5617	359	23	and	and	CCONJ
ejpam-5617	359	24	the	the	DET
ejpam-5617	359	25	residual	residual	ADJ
ejpam-5617	359	26	error	error	NOUN
ejpam-5617	359	27	for	for	ADP
ejpam-5617	359	28	α	α	NOUN
ejpam-5617	359	29	=	=	SYM
ejpam-5617	359	30	1	1	NUM
ejpam-5617	359	31	and	and	CCONJ
ejpam-5617	359	32	α	α	NOUN
ejpam-5617	359	33	=	=	NOUN
ejpam-5617	359	34	0.8	0.8	NUM
ejpam-5617	359	35	.	.	PUNCT
ejpam-5617	360	1	α	α	X
ejpam-5617	360	2	=	=	SYM
ejpam-5617	360	3	1	1	NUM
ejpam-5617	360	4	α	α	NOUN
ejpam-5617	360	5	=	=	SYM
ejpam-5617	360	6	0.8	0.8	NUM
ejpam-5617	360	7	t	t	NOUN
ejpam-5617	360	8	u14	u14	NOUN
ejpam-5617	360	9	(	(	PUNCT
ejpam-5617	360	10	x	x	X
ejpam-5617	360	11	)	)	PUNCT
ejpam-5617	360	12	rf	rf	NOUN
ejpam-5617	360	13	.	.	PUNCT
ejpam-5617	361	1	err	err	PROPN
ejpam-5617	361	2	.	.	PROPN
ejpam-5617	362	1	u14	u14	NOUN
ejpam-5617	362	2	(	(	PUNCT
ejpam-5617	362	3	x	x	X
ejpam-5617	362	4	)	)	PUNCT
ejpam-5617	362	5	rf	rf	NOUN
ejpam-5617	362	6	.	.	PUNCT
ejpam-5617	363	1	err	err	PROPN
ejpam-5617	363	2	.	.	PROPN
ejpam-5617	364	1	0.0	0.0	NUM
ejpam-5617	364	2	0	0	NUM
ejpam-5617	364	3	0	0	NUM
ejpam-5617	364	4	0	0	NUM
ejpam-5617	364	5	0	0	NUM
ejpam-5617	364	6	0.1	0.1	NUM
ejpam-5617	364	7	0.105525	0.105525	NUM
ejpam-5617	364	8	1.10526×10−4	1.10526×10−4	NUM
ejpam-5617	364	9	0.191650	0.191650	NUM
ejpam-5617	364	10	1.47602×10−3	1.47602×10−3	NUM
ejpam-5617	364	11	0.2	0.2	NUM
ejpam-5617	364	12	0.224400	0.224400	NUM
ejpam-5617	364	13	1.95536×10−3	1.95536×10−3	NUM
ejpam-5617	364	14	0.371681	0.371681	NUM
ejpam-5617	364	15	1.58855×10−2	1.58855×10−2	NUM
ejpam-5617	364	16	0.3	0.3	NUM
ejpam-5617	364	17	0.360525	0.360525	NUM
ejpam-5617	364	18	1.09533×10−2	1.09533×10−2	NUM
ejpam-5617	364	19	0.573817	0.573817	NUM
ejpam-5617	364	20	6.71247×10−2	6.71247×10−2	NUM
ejpam-5617	364	21	0.4	0.4	NUM
ejpam-5617	364	22	0.518400	0.518400	NUM
ejpam-5617	364	23	3.83386×10−2	3.83386×10−2	NUM
ejpam-5617	364	24	0.807786	0.807786	NUM
ejpam-5617	364	25	1.92998×10−1	1.92998×10−1	NUM
ejpam-5617	364	26	0.5	0.5	NUM
ejpam-5617	364	27	0.703125	0.703125	NUM
ejpam-5617	364	28	1.0376×10−1	1.0376×10−1	NUM
ejpam-5617	364	29	1.080985	1.080985	NUM
ejpam-5617	364	30	4.48851×10−1	4.48851×10−1	NOUN
ejpam-5617	364	31	the	the	DET
ejpam-5617	364	32	residual	residual	ADJ
ejpam-5617	364	33	error	error	NOUN
ejpam-5617	364	34	serves	serve	VERB
ejpam-5617	364	35	as	as	ADP
ejpam-5617	364	36	an	an	DET
ejpam-5617	364	37	indicator	indicator	NOUN
ejpam-5617	364	38	of	of	ADP
ejpam-5617	364	39	the	the	DET
ejpam-5617	364	40	solution	solution	NOUN
ejpam-5617	364	41	’s	’s	PART
ejpam-5617	364	42	accuracy	accuracy	NOUN
ejpam-5617	364	43	,	,	PUNCT
ejpam-5617	364	44	although	although	SCONJ
ejpam-5617	364	45	it	it	PRON
ejpam-5617	364	46	does	do	AUX
ejpam-5617	364	47	not	not	PART
ejpam-5617	364	48	precisely	precisely	ADV
ejpam-5617	364	49	measure	measure	VERB
ejpam-5617	364	50	the	the	DET
ejpam-5617	364	51	error	error	NOUN
ejpam-5617	364	52	in	in	ADP
ejpam-5617	364	53	the	the	DET
ejpam-5617	364	54	same	same	ADJ
ejpam-5617	364	55	way	way	NOUN
ejpam-5617	364	56	that	that	PRON
ejpam-5617	364	57	absolute	absolute	ADJ
ejpam-5617	364	58	error	error	NOUN
ejpam-5617	364	59	does	do	VERB
ejpam-5617	364	60	.	.	PUNCT
ejpam-5617	365	1	even	even	ADV
ejpam-5617	365	2	though	though	SCONJ
ejpam-5617	365	3	the	the	DET
ejpam-5617	365	4	residual	residual	ADJ
ejpam-5617	365	5	error	error	NOUN
ejpam-5617	365	6	remains	remain	VERB
ejpam-5617	365	7	within	within	ADP
ejpam-5617	365	8	a	a	DET
ejpam-5617	365	9	range	range	NOUN
ejpam-5617	365	10	of	of	ADP
ejpam-5617	365	11	1	1	NUM
ejpam-5617	365	12	to	to	PART
ejpam-5617	365	13	3	3	NUM
ejpam-5617	365	14	and	and	CCONJ
ejpam-5617	365	15	is	be	AUX
ejpam-5617	365	16	concentrated	concentrate	VERB
ejpam-5617	365	17	in	in	ADP
ejpam-5617	365	18	a	a	DET
ejpam-5617	365	19	small	small	ADJ
ejpam-5617	365	20	interval	interval	NOUN
ejpam-5617	365	21	,	,	PUNCT
ejpam-5617	365	22	the	the	DET
ejpam-5617	365	23	solution	solution	NOUN
ejpam-5617	365	24	period	period	NOUN
ejpam-5617	365	25	can	can	AUX
ejpam-5617	365	26	be	be	AUX
ejpam-5617	365	27	extended	extend	VERB
ejpam-5617	365	28	by	by	ADP
ejpam-5617	365	29	employing	employ	VERB
ejpam-5617	365	30	alternative	alternative	ADJ
ejpam-5617	365	31	techniques	technique	NOUN
ejpam-5617	365	32	,	,	PUNCT
ejpam-5617	365	33	such	such	ADJ
ejpam-5617	365	34	as	as	ADP
ejpam-5617	365	35	multi	multi	ADJ
ejpam-5617	365	36	-	-	ADJ
ejpam-5617	365	37	step	step	ADJ
ejpam-5617	365	38	methods	method	NOUN
ejpam-5617	365	39	.	.	PUNCT
ejpam-5617	366	1	table	table	NOUN
ejpam-5617	366	2	5	5	NUM
ejpam-5617	366	3	:	:	PUNCT
ejpam-5617	366	4	the	the	DET
ejpam-5617	366	5	4th	4th	ADJ
ejpam-5617	366	6	approximation	approximation	NOUN
ejpam-5617	366	7	of	of	ADP
ejpam-5617	366	8	u2	u2	NOUN
ejpam-5617	366	9	(	(	PUNCT
ejpam-5617	366	10	x	x	NOUN
ejpam-5617	366	11	)	)	PUNCT
ejpam-5617	366	12	,	,	PUNCT
ejpam-5617	366	13	the	the	DET
ejpam-5617	366	14	ivp	ivp	X
ejpam-5617	366	15	(	(	PUNCT
ejpam-5617	366	16	33)-(34	33)-(34	NUM
ejpam-5617	366	17	)	)	PUNCT
ejpam-5617	366	18	solution	solution	NOUN
ejpam-5617	366	19	,	,	PUNCT
ejpam-5617	366	20	and	and	CCONJ
ejpam-5617	366	21	the	the	DET
ejpam-5617	366	22	residual	residual	ADJ
ejpam-5617	366	23	error	error	NOUN
ejpam-5617	366	24	for	for	ADP
ejpam-5617	366	25	α	α	NOUN
ejpam-5617	366	26	=	=	SYM
ejpam-5617	366	27	1	1	NUM
ejpam-5617	366	28	and	and	CCONJ
ejpam-5617	366	29	α	α	NOUN
ejpam-5617	366	30	=	=	NOUN
ejpam-5617	366	31	0.8	0.8	NUM
ejpam-5617	366	32	.	.	PUNCT
ejpam-5617	367	1	α	α	X
ejpam-5617	367	2	=	=	SYM
ejpam-5617	367	3	1	1	NUM
ejpam-5617	367	4	α	α	NOUN
ejpam-5617	367	5	=	=	SYM
ejpam-5617	367	6	0.8	0.8	NUM
ejpam-5617	367	7	t	t	NOUN
ejpam-5617	367	8	u24	u24	NOUN
ejpam-5617	367	9	(	(	PUNCT
ejpam-5617	367	10	x	x	NOUN
ejpam-5617	367	11	)	)	PUNCT
ejpam-5617	367	12	rf	rf	NOUN
ejpam-5617	367	13	.	.	PUNCT
ejpam-5617	368	1	err	err	PROPN
ejpam-5617	368	2	.	.	PUNCT
ejpam-5617	369	1	u24	u24	PROPN
ejpam-5617	369	2	(	(	PUNCT
ejpam-5617	369	3	x	x	NOUN
ejpam-5617	369	4	)	)	PUNCT
ejpam-5617	369	5	rf	rf	NOUN
ejpam-5617	369	6	.	.	PUNCT
ejpam-5617	369	7	err	err	PROPN
ejpam-5617	369	8	.	.	PROPN
ejpam-5617	370	1	0.0	0.0	NUM
ejpam-5617	370	2	1	1	NUM
ejpam-5617	370	3	0	0	NUM
ejpam-5617	370	4	1	1	NUM
ejpam-5617	370	5	0	0	NUM
ejpam-5617	370	6	0.1	0.1	NUM
ejpam-5617	370	7	1.104975	1.104975	NUM
ejpam-5617	370	8	1.71532×10−4	1.71532×10−4	NUM
ejpam-5617	370	9	1.187653	1.187653	NUM
ejpam-5617	370	10	2.13071×10−3	2.13071×10−3	NUM
ejpam-5617	370	11	0.2	0.2	NUM
ejpam-5617	370	12	1.219600	1.219600	NUM
ejpam-5617	370	13	2.97806×10−3	2.97806×10−3	NUM
ejpam-5617	370	14	1.347857	1.347857	NUM
ejpam-5617	370	15	2.22820×10−2	2.22820×10−2	NUM
ejpam-5617	370	16	0.3	0.3	NUM
ejpam-5617	370	17	1.342975	1.342975	NUM
ejpam-5617	370	18	1.63625×10−2	1.63625×10−2	NUM
ejpam-5617	370	19	1.504286	1.504286	NUM
ejpam-5617	370	20	9.14918×10−2	9.14918×10−2	NUM
ejpam-5617	370	21	0.4	0.4	NUM
ejpam-5617	370	22	1.473600	1.473600	NUM
ejpam-5617	370	23	5.60118×10−2	5.60118×10−2	NUM
ejpam-5617	370	24	1.657010	1.657010	NUM
ejpam-5617	370	25	2.53724×10−1	2.53724×10−1	NUM
ejpam-5617	370	26	0.5	0.5	NUM
ejpam-5617	370	27	1.609375	1.609375	NUM
ejpam-5617	370	28	1.47328×10−1	1.47328×10−1	NUM
ejpam-5617	370	29	1.803767	1.803767	NUM
ejpam-5617	370	30	5.60315×10−1	5.60315×10−1	NUM
ejpam-5617	370	31	5	5	NUM
ejpam-5617	370	32	.	.	PUNCT
ejpam-5617	370	33	conclusion	conclusion	NOUN
ejpam-5617	370	34	in	in	ADP
ejpam-5617	370	35	this	this	DET
ejpam-5617	370	36	article	article	NOUN
ejpam-5617	371	1	,	,	PUNCT
ejpam-5617	371	2	we	we	PRON
ejpam-5617	371	3	introduced	introduce	VERB
ejpam-5617	371	4	a	a	DET
ejpam-5617	371	5	new	new	ADJ
ejpam-5617	371	6	analytical	analytical	ADJ
ejpam-5617	371	7	iterative	iterative	NOUN
ejpam-5617	371	8	technique	technique	NOUN
ejpam-5617	371	9	called	call	VERB
ejpam-5617	371	10	the	the	DET
ejpam-5617	371	11	lrf	lrf	NOUN
ejpam-5617	371	12	method	method	NOUN
ejpam-5617	371	13	,	,	PUNCT
ejpam-5617	371	14	which	which	PRON
ejpam-5617	371	15	we	we	PRON
ejpam-5617	371	16	used	use	VERB
ejpam-5617	371	17	to	to	PART
ejpam-5617	371	18	solve	solve	VERB
ejpam-5617	371	19	linear	linear	ADJ
ejpam-5617	371	20	and	and	CCONJ
ejpam-5617	371	21	nonlinear	nonlinear	ADJ
ejpam-5617	371	22	systems	system	NOUN
ejpam-5617	371	23	of	of	ADP
ejpam-5617	371	24	caputo	caputo	PROPN
ejpam-5617	371	25	-	-	PUNCT
ejpam-5617	371	26	fractional	fractional	ADJ
ejpam-5617	371	27	differential	differential	ADJ
ejpam-5617	371	28	equations	equation	NOUN
ejpam-5617	371	29	.	.	PUNCT
ejpam-5617	372	1	this	this	DET
ejpam-5617	372	2	approach	approach	NOUN
ejpam-5617	372	3	simplifies	simplifie	NOUN
ejpam-5617	372	4	discovering	discover	VERB
ejpam-5617	372	5	exact	exact	ADJ
ejpam-5617	372	6	solution	solution	NOUN
ejpam-5617	372	7	patterns	pattern	NOUN
ejpam-5617	372	8	while	while	SCONJ
ejpam-5617	372	9	reducing	reduce	VERB
ejpam-5617	372	10	the	the	DET
ejpam-5617	372	11	need	need	NOUN
ejpam-5617	372	12	for	for	ADP
ejpam-5617	372	13	complex	complex	ADJ
ejpam-5617	372	14	computational	computational	ADJ
ejpam-5617	372	15	calculations	calculation	NOUN
ejpam-5617	372	16	.	.	PUNCT
ejpam-5617	373	1	the	the	DET
ejpam-5617	373	2	main	main	ADJ
ejpam-5617	373	3	advantage	advantage	NOUN
ejpam-5617	373	4	of	of	ADP
ejpam-5617	373	5	this	this	DET
ejpam-5617	373	6	method	method	NOUN
ejpam-5617	373	7	is	be	AUX
ejpam-5617	373	8	its	its	PRON
ejpam-5617	373	9	straightforwardness	straightforwardness	NOUN
ejpam-5617	373	10	in	in	ADP
ejpam-5617	373	11	computing	compute	VERB
ejpam-5617	373	12	the	the	DET
ejpam-5617	373	13	coefficients	coefficient	NOUN
ejpam-5617	373	14	of	of	ADP
ejpam-5617	373	15	the	the	DET
ejpam-5617	373	16	series	series	NOUN
ejpam-5617	373	17	solution	solution	NOUN
ejpam-5617	373	18	by	by	ADP
ejpam-5617	373	19	evaluating	evaluate	VERB
ejpam-5617	373	20	the	the	DET
ejpam-5617	373	21	limit	limit	NOUN
ejpam-5617	373	22	of	of	ADP
ejpam-5617	373	23	a	a	DET
ejpam-5617	373	24	form	form	NOUN
ejpam-5617	373	25	that	that	PRON
ejpam-5617	373	26	includes	include	VERB
ejpam-5617	373	27	a.	a.	PROPN
ejpam-5617	373	28	el	el	PROPN
ejpam-5617	373	29	-	-	PUNCT
ejpam-5617	373	30	ajou	ajou	PROPN
ejpam-5617	373	31	,	,	PUNCT
ejpam-5617	373	32	a.	a.	PROPN
ejpam-5617	373	33	burqan	burqan	PROPN
ejpam-5617	373	34	/	/	SYM
ejpam-5617	373	35	eur	eur	PROPN
ejpam-5617	373	36	.	.	PUNCT
ejpam-5617	374	1	j.	j.	PROPN
ejpam-5617	374	2	pure	pure	PROPN
ejpam-5617	374	3	appl	appl	PROPN
ejpam-5617	374	4	.	.	PROPN
ejpam-5617	374	5	math	math	PROPN
ejpam-5617	374	6	,	,	PUNCT
ejpam-5617	374	7	18	18	NUM
ejpam-5617	374	8	(	(	PUNCT
ejpam-5617	374	9	1	1	NUM
ejpam-5617	374	10	)	)	PUNCT
ejpam-5617	374	11	(	(	PUNCT
ejpam-5617	374	12	2025	2025	NUM
ejpam-5617	374	13	)	)	PUNCT
ejpam-5617	374	14	,	,	PUNCT
ejpam-5617	374	15	5617	5617	NUM
ejpam-5617	374	16	17	17	NUM
ejpam-5617	374	17	of	of	ADP
ejpam-5617	374	18	19	19	NUM
ejpam-5617	374	19	the	the	DET
ejpam-5617	374	20	residual	residual	ADJ
ejpam-5617	374	21	function	function	NOUN
ejpam-5617	374	22	for	for	ADP
ejpam-5617	374	23	the	the	DET
ejpam-5617	374	24	given	give	VERB
ejpam-5617	374	25	equations	equation	NOUN
ejpam-5617	374	26	.	.	PUNCT
ejpam-5617	375	1	this	this	PRON
ejpam-5617	375	2	is	be	AUX
ejpam-5617	375	3	a	a	DET
ejpam-5617	375	4	departure	departure	NOUN
ejpam-5617	375	5	from	from	ADP
ejpam-5617	375	6	other	other	ADJ
ejpam-5617	375	7	well	well	ADV
ejpam-5617	375	8	-	-	PUNCT
ejpam-5617	375	9	known	know	VERB
ejpam-5617	375	10	analytic	analytic	ADJ
ejpam-5617	375	11	techniques	technique	NOUN
ejpam-5617	375	12	that	that	PRON
ejpam-5617	375	13	rely	rely	VERB
ejpam-5617	375	14	on	on	ADP
ejpam-5617	375	15	differential	differential	ADJ
ejpam-5617	375	16	and	and	CCONJ
ejpam-5617	375	17	integral	integral	ADJ
ejpam-5617	375	18	operators	operator	NOUN
ejpam-5617	375	19	,	,	PUNCT
ejpam-5617	375	20	which	which	PRON
ejpam-5617	375	21	can	can	AUX
ejpam-5617	375	22	be	be	AUX
ejpam-5617	375	23	challenging	challenge	VERB
ejpam-5617	375	24	in	in	ADP
ejpam-5617	375	25	the	the	DET
ejpam-5617	375	26	fractional	fractional	ADJ
ejpam-5617	375	27	case	case	NOUN
ejpam-5617	375	28	.	.	PUNCT
ejpam-5617	376	1	we	we	PRON
ejpam-5617	376	2	plan	plan	VERB
ejpam-5617	376	3	to	to	PART
ejpam-5617	376	4	modify	modify	VERB
ejpam-5617	376	5	our	our	PRON
ejpam-5617	376	6	approach	approach	NOUN
ejpam-5617	376	7	to	to	PART
ejpam-5617	376	8	handle	handle	VERB
ejpam-5617	376	9	more	more	ADJ
ejpam-5617	376	10	complex	complex	ADJ
ejpam-5617	376	11	real	real	ADJ
ejpam-5617	376	12	-	-	PUNCT
ejpam-5617	376	13	world	world	NOUN
ejpam-5617	376	14	applications	application	NOUN
ejpam-5617	376	15	in	in	ADP
ejpam-5617	376	16	future	future	ADJ
ejpam-5617	376	17	work	work	NOUN
ejpam-5617	376	18	.	.	PUNCT
ejpam-5617	377	1	acknowledgements	acknowledgement	VERB
ejpam-5617	377	2	the	the	DET
ejpam-5617	377	3	authors	author	NOUN
ejpam-5617	377	4	express	express	VERB
ejpam-5617	377	5	their	their	PRON
ejpam-5617	377	6	gratitude	gratitude	NOUN
ejpam-5617	377	7	to	to	ADP
ejpam-5617	377	8	the	the	DET
ejpam-5617	377	9	dear	dear	ADJ
ejpam-5617	377	10	referees	referee	NOUN
ejpam-5617	377	11	,	,	PUNCT
ejpam-5617	377	12	who	who	PRON
ejpam-5617	377	13	wish	wish	VERB
ejpam-5617	377	14	to	to	PART
ejpam-5617	377	15	remain	remain	VERB
ejpam-5617	377	16	anonymous	anonymous	ADJ
ejpam-5617	377	17	,	,	PUNCT
ejpam-5617	377	18	and	and	CCONJ
ejpam-5617	377	19	the	the	DET
ejpam-5617	377	20	editor	editor	NOUN
ejpam-5617	377	21	for	for	ADP
ejpam-5617	377	22	their	their	PRON
ejpam-5617	377	23	helpful	helpful	ADJ
ejpam-5617	377	24	suggestions	suggestion	NOUN
ejpam-5617	377	25	that	that	PRON
ejpam-5617	377	26	improved	improve	VERB
ejpam-5617	377	27	the	the	DET
ejpam-5617	377	28	final	final	ADJ
ejpam-5617	377	29	version	version	NOUN
ejpam-5617	377	30	of	of	ADP
ejpam-5617	377	31	this	this	DET
ejpam-5617	377	32	paper	paper	NOUN
ejpam-5617	377	33	.	.	PUNCT
ejpam-5617	378	1	this	this	DET
ejpam-5617	378	2	research	research	NOUN
ejpam-5617	378	3	is	be	AUX
ejpam-5617	378	4	funded	fund	VERB
ejpam-5617	378	5	by	by	ADP
ejpam-5617	378	6	zarqa	zarqa	PROPN
ejpam-5617	378	7	university	university	PROPN
ejpam-5617	378	8	-	-	PUNCT
ejpam-5617	378	9	jordan	jordan	PROPN
ejpam-5617	378	10	.	.	PUNCT
ejpam-5617	379	1	references	reference	NOUN
ejpam-5617	379	2	[	[	X
ejpam-5617	379	3	1	1	NUM
ejpam-5617	379	4	]	]	PUNCT
ejpam-5617	379	5	a.	a.	NOUN
ejpam-5617	379	6	afreen	afreen	PROPN
ejpam-5617	379	7	and	and	CCONJ
ejpam-5617	379	8	a.	a.	NOUN
ejpam-5617	379	9	raheem	raheem	PROPN
ejpam-5617	379	10	.	.	PUNCT
ejpam-5617	380	1	study	study	NOUN
ejpam-5617	380	2	of	of	ADP
ejpam-5617	380	3	a	a	DET
ejpam-5617	380	4	nonlinear	nonlinear	ADJ
ejpam-5617	380	5	system	system	NOUN
ejpam-5617	380	6	of	of	ADP
ejpam-5617	380	7	fractional	fractional	ADJ
ejpam-5617	380	8	differential	differential	ADJ
ejpam-5617	380	9	equations	equation	NOUN
ejpam-5617	380	10	with	with	ADP
ejpam-5617	380	11	deviated	deviate	VERB
ejpam-5617	380	12	arguments	argument	NOUN
ejpam-5617	380	13	via	via	ADP
ejpam-5617	380	14	adomian	adomian	ADJ
ejpam-5617	380	15	decomposition	decomposition	NOUN
ejpam-5617	380	16	method	method	NOUN
ejpam-5617	380	17	.	.	PUNCT
ejpam-5617	381	1	international	international	ADJ
ejpam-5617	381	2	journal	journal	PROPN
ejpam-5617	381	3	of	of	ADP
ejpam-5617	381	4	applied	applied	ADJ
ejpam-5617	381	5	and	and	CCONJ
ejpam-5617	381	6	computational	computational	ADJ
ejpam-5617	381	7	mathematics	mathematic	NOUN
ejpam-5617	381	8	,	,	PUNCT
ejpam-5617	381	9	8(5):269	8(5):269	NUM
ejpam-5617	381	10	,	,	PUNCT
ejpam-5617	381	11	2022	2022	NUM
ejpam-5617	381	12	.	.	PUNCT
ejpam-5617	382	1	[	[	X
ejpam-5617	382	2	2	2	NUM
ejpam-5617	382	3	]	]	PUNCT
ejpam-5617	382	4	k.	k.	PROPN
ejpam-5617	382	5	i.	i.	PROPN
ejpam-5617	382	6	ahmed	ahmed	PROPN
ejpam-5617	382	7	,	,	PUNCT
ejpam-5617	382	8	h.	h.	PROPN
ejpam-5617	382	9	d.	d.	PROPN
ejpam-5617	382	10	adam	adam	PROPN
ejpam-5617	382	11	,	,	PUNCT
ejpam-5617	382	12	n.	n.	PROPN
ejpam-5617	382	13	almutairi	almutairi	NOUN
ejpam-5617	382	14	,	,	PUNCT
ejpam-5617	382	15	and	and	CCONJ
ejpam-5617	382	16	s.	s.	PROPN
ejpam-5617	382	17	saber	saber	PROPN
ejpam-5617	382	18	.	.	PUNCT
ejpam-5617	383	1	analytical	analytical	ADJ
ejpam-5617	383	2	solutions	solution	NOUN
ejpam-5617	383	3	for	for	ADP
ejpam-5617	383	4	a	a	DET
ejpam-5617	383	5	class	class	NOUN
ejpam-5617	383	6	of	of	ADP
ejpam-5617	383	7	variable	variable	ADJ
ejpam-5617	383	8	-	-	PUNCT
ejpam-5617	383	9	order	order	NOUN
ejpam-5617	383	10	fractional	fractional	ADJ
ejpam-5617	383	11	liu	liu	PROPN
ejpam-5617	383	12	system	system	NOUN
ejpam-5617	383	13	under	under	ADP
ejpam-5617	383	14	time	time	NOUN
ejpam-5617	383	15	-	-	PUNCT
ejpam-5617	383	16	dependent	dependent	ADJ
ejpam-5617	383	17	variable	variable	ADJ
ejpam-5617	383	18	coefficients	coefficient	NOUN
ejpam-5617	383	19	.	.	PUNCT
ejpam-5617	384	1	results	result	NOUN
ejpam-5617	384	2	in	in	ADP
ejpam-5617	384	3	physics	physics	NOUN
ejpam-5617	384	4	,	,	PUNCT
ejpam-5617	384	5	56:107311	56:107311	NUM
ejpam-5617	384	6	,	,	PUNCT
ejpam-5617	384	7	2024	2024	NUM
ejpam-5617	384	8	.	.	PUNCT
ejpam-5617	385	1	[	[	X
ejpam-5617	385	2	3	3	X
ejpam-5617	385	3	]	]	PUNCT
ejpam-5617	385	4	m.	m.	NOUN
ejpam-5617	385	5	alaroud	alaroud	PROPN
ejpam-5617	385	6	.	.	PUNCT
ejpam-5617	386	1	application	application	NOUN
ejpam-5617	386	2	of	of	ADP
ejpam-5617	386	3	laplace	laplace	NOUN
ejpam-5617	386	4	residual	residual	ADJ
ejpam-5617	386	5	power	power	NOUN
ejpam-5617	386	6	series	series	PROPN
ejpam-5617	386	7	method	method	NOUN
ejpam-5617	386	8	for	for	ADP
ejpam-5617	386	9	approximate	approximate	ADJ
ejpam-5617	386	10	solutions	solution	NOUN
ejpam-5617	386	11	of	of	ADP
ejpam-5617	386	12	fractional	fractional	ADJ
ejpam-5617	386	13	ivp	ivp	PROPN
ejpam-5617	386	14	’s	’s	NOUN
ejpam-5617	386	15	.	.	PUNCT
ejpam-5617	387	1	alexandria	alexandria	PROPN
ejpam-5617	387	2	engineering	engineering	PROPN
ejpam-5617	387	3	journal	journal	PROPN
ejpam-5617	387	4	,	,	PUNCT
ejpam-5617	387	5	61(2):1585–1595	61(2):1585–1595	NUM
ejpam-5617	387	6	,	,	PUNCT
ejpam-5617	387	7	2022	2022	NUM
ejpam-5617	387	8	.	.	PUNCT
ejpam-5617	388	1	[	[	X
ejpam-5617	388	2	4	4	NUM
ejpam-5617	388	3	]	]	X
ejpam-5617	388	4	n.	n.	NOUN
ejpam-5617	388	5	almutairi	almutairi	PROPN
ejpam-5617	388	6	and	and	CCONJ
ejpam-5617	388	7	s.	s.	PROPN
ejpam-5617	388	8	saber	saber	PROPN
ejpam-5617	388	9	.	.	PUNCT
ejpam-5617	389	1	on	on	ADP
ejpam-5617	389	2	chaos	chaos	NOUN
ejpam-5617	389	3	control	control	NOUN
ejpam-5617	389	4	of	of	ADP
ejpam-5617	389	5	nonlinear	nonlinear	PROPN
ejpam-5617	389	6	fractional	fractional	PROPN
ejpam-5617	389	7	newton	newton	PROPN
ejpam-5617	389	8	-	-	PUNCT
ejpam-5617	389	9	leipnik	leipnik	NOUN
ejpam-5617	389	10	system	system	NOUN
ejpam-5617	389	11	via	via	ADP
ejpam-5617	389	12	fractional	fractional	PROPN
ejpam-5617	389	13	caputo	caputo	PROPN
ejpam-5617	389	14	-	-	PUNCT
ejpam-5617	389	15	fabrizio	fabrizio	PROPN
ejpam-5617	389	16	derivatives	derivative	NOUN
ejpam-5617	389	17	.	.	PUNCT
ejpam-5617	390	1	scientific	scientific	ADJ
ejpam-5617	390	2	reports	report	NOUN
ejpam-5617	390	3	,	,	PUNCT
ejpam-5617	390	4	13(1):22726	13(1):22726	NUM
ejpam-5617	390	5	,	,	PUNCT
ejpam-5617	390	6	2023	2023	NUM
ejpam-5617	390	7	.	.	PUNCT
ejpam-5617	391	1	[	[	X
ejpam-5617	391	2	5	5	NUM
ejpam-5617	391	3	]	]	X
ejpam-5617	391	4	n.	n.	NOUN
ejpam-5617	391	5	almutairi	almutairi	NOUN
ejpam-5617	391	6	and	and	CCONJ
ejpam-5617	391	7	s.	s.	PROPN
ejpam-5617	391	8	saber	saber	PROPN
ejpam-5617	391	9	.	.	PUNCT
ejpam-5617	392	1	application	application	NOUN
ejpam-5617	392	2	of	of	ADP
ejpam-5617	392	3	a	a	DET
ejpam-5617	392	4	time	time	NOUN
ejpam-5617	392	5	-	-	PUNCT
ejpam-5617	392	6	fractal	fractal	ADJ
ejpam-5617	392	7	fractional	fractional	ADJ
ejpam-5617	392	8	derivative	derivative	NOUN
ejpam-5617	392	9	with	with	ADP
ejpam-5617	392	10	a	a	DET
ejpam-5617	392	11	powerlaw	powerlaw	NOUN
ejpam-5617	392	12	kernel	kernel	NOUN
ejpam-5617	392	13	to	to	ADP
ejpam-5617	392	14	the	the	DET
ejpam-5617	392	15	burke	burke	PROPN
ejpam-5617	392	16	-	-	PUNCT
ejpam-5617	392	17	shaw	shaw	PROPN
ejpam-5617	392	18	system	system	NOUN
ejpam-5617	392	19	based	base	VERB
ejpam-5617	392	20	on	on	ADP
ejpam-5617	392	21	newton	newton	PROPN
ejpam-5617	392	22	’s	’s	PART
ejpam-5617	392	23	interpolation	interpolation	NOUN
ejpam-5617	392	24	polynomials	polynomial	NOUN
ejpam-5617	392	25	.	.	PUNCT
ejpam-5617	393	1	methodsx	methodsx	PROPN
ejpam-5617	393	2	,	,	PUNCT
ejpam-5617	393	3	12:102510	12:102510	NUM
ejpam-5617	393	4	,	,	PUNCT
ejpam-5617	393	5	2024	2024	NUM
ejpam-5617	393	6	.	.	PUNCT
ejpam-5617	394	1	[	[	X
ejpam-5617	394	2	6	6	NUM
ejpam-5617	394	3	]	]	PUNCT
ejpam-5617	394	4	m.	m.	NOUN
ejpam-5617	394	5	altalla	altalla	PROPN
ejpam-5617	394	6	,	,	PUNCT
ejpam-5617	394	7	b.	b.	PROPN
ejpam-5617	394	8	shanmukha	shanmukha	PROPN
ejpam-5617	394	9	,	,	PUNCT
ejpam-5617	394	10	a.	a.	PROPN
ejpam-5617	394	11	el	el	PROPN
ejpam-5617	394	12	-	-	PUNCT
ejpam-5617	394	13	ajou	ajou	ADJ
ejpam-5617	394	14	,	,	PUNCT
ejpam-5617	394	15	and	and	CCONJ
ejpam-5617	394	16	m.	m.	NOUN
ejpam-5617	394	17	alkord	alkord	PROPN
ejpam-5617	394	18	.	.	PUNCT
ejpam-5617	395	1	taylor	taylor	PROPN
ejpam-5617	395	2	’s	’s	PART
ejpam-5617	395	3	series	series	NOUN
ejpam-5617	395	4	in	in	ADP
ejpam-5617	395	5	terms	term	NOUN
ejpam-5617	395	6	of	of	ADP
ejpam-5617	395	7	the	the	DET
ejpam-5617	395	8	modified	modify	VERB
ejpam-5617	395	9	conformable	conformable	ADJ
ejpam-5617	395	10	fractional	fractional	ADJ
ejpam-5617	395	11	derivative	derivative	NOUN
ejpam-5617	395	12	with	with	ADP
ejpam-5617	395	13	applications	application	NOUN
ejpam-5617	395	14	.	.	PUNCT
ejpam-5617	396	1	nonlinear	nonlinear	ADJ
ejpam-5617	396	2	functional	functional	ADJ
ejpam-5617	396	3	analysis	analysis	NOUN
ejpam-5617	396	4	and	and	CCONJ
ejpam-5617	396	5	applications	application	NOUN
ejpam-5617	396	6	,	,	PUNCT
ejpam-5617	396	7	2024:435–450	2024:435–450	NOUN
ejpam-5617	396	8	,	,	PUNCT
ejpam-5617	396	9	2024	2024	NUM
ejpam-5617	396	10	.	.	PUNCT
ejpam-5617	397	1	[	[	X
ejpam-5617	397	2	7	7	X
ejpam-5617	397	3	]	]	X
ejpam-5617	397	4	n.	n.	PROPN
ejpam-5617	397	5	anjum	anjum	PROPN
ejpam-5617	397	6	,	,	PUNCT
ejpam-5617	397	7	c.	c.	PROPN
ejpam-5617	397	8	h.	h.	PROPN
ejpam-5617	397	9	he	he	PRON
ejpam-5617	397	10	,	,	PUNCT
ejpam-5617	397	11	and	and	CCONJ
ejpam-5617	397	12	j.	j.	PROPN
ejpam-5617	397	13	h.	h.	PROPN
ejpam-5617	397	14	he	he	PRON
ejpam-5617	397	15	.	.	PUNCT
ejpam-5617	398	1	two	two	NUM
ejpam-5617	398	2	-	-	PUNCT
ejpam-5617	398	3	scale	scale	NOUN
ejpam-5617	398	4	fractal	fractal	ADJ
ejpam-5617	398	5	theory	theory	NOUN
ejpam-5617	398	6	for	for	ADP
ejpam-5617	398	7	the	the	DET
ejpam-5617	398	8	population	population	NOUN
ejpam-5617	398	9	dynamics	dynamic	NOUN
ejpam-5617	398	10	.	.	PUNCT
ejpam-5617	399	1	fractals	fractal	NOUN
ejpam-5617	399	2	,	,	PUNCT
ejpam-5617	399	3	29(07):2150182	29(07):2150182	NUM
ejpam-5617	399	4	,	,	PUNCT
ejpam-5617	399	5	2021	2021	NUM
ejpam-5617	399	6	.	.	PUNCT
ejpam-5617	400	1	[	[	X
ejpam-5617	400	2	8	8	NUM
ejpam-5617	400	3	]	]	PUNCT
ejpam-5617	400	4	a.	a.	NOUN
ejpam-5617	400	5	atangana	atangana	PROPN
ejpam-5617	400	6	and	and	CCONJ
ejpam-5617	400	7	d.	d.	PROPN
ejpam-5617	400	8	baleanu	baleanu	PROPN
ejpam-5617	400	9	.	.	PUNCT
ejpam-5617	401	1	new	new	ADJ
ejpam-5617	401	2	fractional	fractional	ADJ
ejpam-5617	401	3	derivatives	derivative	NOUN
ejpam-5617	401	4	with	with	ADP
ejpam-5617	401	5	nonlocal	nonlocal	ADJ
ejpam-5617	401	6	and	and	CCONJ
ejpam-5617	401	7	non	non	ADJ
ejpam-5617	401	8	-	-	ADJ
ejpam-5617	401	9	singular	singular	ADJ
ejpam-5617	401	10	kernel	kernel	NOUN
ejpam-5617	401	11	:	:	PUNCT
ejpam-5617	401	12	theory	theory	NOUN
ejpam-5617	401	13	and	and	CCONJ
ejpam-5617	401	14	application	application	NOUN
ejpam-5617	401	15	to	to	PART
ejpam-5617	401	16	heat	heat	NOUN
ejpam-5617	401	17	transfer	transfer	NOUN
ejpam-5617	401	18	model	model	NOUN
ejpam-5617	401	19	.	.	PUNCT
ejpam-5617	402	1	thermal	thermal	ADJ
ejpam-5617	402	2	science	science	NOUN
ejpam-5617	402	3	,	,	PUNCT
ejpam-5617	402	4	20:763–769	20:763–769	PROPN
ejpam-5617	402	5	,	,	PUNCT
ejpam-5617	402	6	2016	2016	NUM
ejpam-5617	402	7	.	.	PUNCT
ejpam-5617	403	1	[	[	X
ejpam-5617	403	2	9	9	NUM
ejpam-5617	403	3	]	]	PUNCT
ejpam-5617	403	4	a.	a.	NOUN
ejpam-5617	403	5	burqan	burqan	PROPN
ejpam-5617	403	6	.	.	PUNCT
ejpam-5617	404	1	a	a	DET
ejpam-5617	404	2	novel	novel	ADJ
ejpam-5617	404	3	scheme	scheme	NOUN
ejpam-5617	404	4	of	of	ADP
ejpam-5617	404	5	the	the	DET
ejpam-5617	404	6	ara	ara	NOUN
ejpam-5617	404	7	transform	transform	NOUN
ejpam-5617	404	8	for	for	ADP
ejpam-5617	404	9	solving	solve	VERB
ejpam-5617	404	10	systems	system	NOUN
ejpam-5617	404	11	of	of	ADP
ejpam-5617	404	12	partial	partial	ADJ
ejpam-5617	404	13	fractional	fractional	ADJ
ejpam-5617	404	14	differential	differential	ADJ
ejpam-5617	404	15	equations	equation	NOUN
ejpam-5617	404	16	.	.	PUNCT
ejpam-5617	405	1	fractal	fractal	PROPN
ejpam-5617	405	2	and	and	CCONJ
ejpam-5617	405	3	fractional	fractional	ADJ
ejpam-5617	405	4	,	,	PUNCT
ejpam-5617	405	5	7(4):306	7(4):306	NUM
ejpam-5617	405	6	,	,	PUNCT
ejpam-5617	405	7	2023	2023	NUM
ejpam-5617	405	8	.	.	PUNCT
ejpam-5617	406	1	[	[	X
ejpam-5617	406	2	10	10	NUM
ejpam-5617	406	3	]	]	PUNCT
ejpam-5617	406	4	a.	a.	NOUN
ejpam-5617	406	5	burqan	burqan	PROPN
ejpam-5617	406	6	,	,	PUNCT
ejpam-5617	406	7	m.	m.	NOUN
ejpam-5617	406	8	khandaqji	khandaqji	PROPN
ejpam-5617	406	9	,	,	PUNCT
ejpam-5617	406	10	z.	z.	PROPN
ejpam-5617	406	11	al	al	PROPN
ejpam-5617	406	12	-	-	PUNCT
ejpam-5617	406	13	zhour	zhour	PROPN
ejpam-5617	406	14	,	,	PUNCT
ejpam-5617	406	15	a.	a.	PROPN
ejpam-5617	406	16	el	el	PROPN
ejpam-5617	406	17	-	-	PUNCT
ejpam-5617	406	18	ajou	ajou	ADJ
ejpam-5617	406	19	,	,	PUNCT
ejpam-5617	406	20	and	and	CCONJ
ejpam-5617	406	21	t.	t.	PROPN
ejpam-5617	406	22	alrahamneh	alrahamneh	NOUN
ejpam-5617	406	23	.	.	PUNCT
ejpam-5617	407	1	analytical	analytical	ADJ
ejpam-5617	407	2	approximate	approximate	ADJ
ejpam-5617	407	3	solutions	solution	NOUN
ejpam-5617	407	4	of	of	ADP
ejpam-5617	407	5	caputo	caputo	PROPN
ejpam-5617	407	6	fractional	fractional	PROPN
ejpam-5617	407	7	kdv	kdv	PROPN
ejpam-5617	407	8	-	-	PUNCT
ejpam-5617	407	9	burgers	burger	NOUN
ejpam-5617	407	10	equations	equation	NOUN
ejpam-5617	407	11	using	use	VERB
ejpam-5617	407	12	laplace	laplace	NOUN
ejpam-5617	407	13	residual	residual	ADJ
ejpam-5617	407	14	power	power	NOUN
ejpam-5617	407	15	series	series	NOUN
ejpam-5617	407	16	technique	technique	NOUN
ejpam-5617	407	17	.	.	PUNCT
ejpam-5617	408	1	journal	journal	NOUN
ejpam-5617	408	2	of	of	ADP
ejpam-5617	408	3	applied	apply	VERB
ejpam-5617	408	4	mathematics	mathematic	NOUN
ejpam-5617	408	5	,	,	PUNCT
ejpam-5617	408	6	1:7835548	1:7835548	NUM
ejpam-5617	408	7	,	,	PUNCT
ejpam-5617	408	8	2024	2024	NUM
ejpam-5617	408	9	.	.	PUNCT
ejpam-5617	409	1	[	[	X
ejpam-5617	409	2	11	11	NUM
ejpam-5617	409	3	]	]	PUNCT
ejpam-5617	409	4	a.	a.	NOUN
ejpam-5617	409	5	burqan	burqan	PROPN
ejpam-5617	409	6	,	,	PUNCT
ejpam-5617	409	7	m.	m.	NOUN
ejpam-5617	409	8	shqair	shqair	PROPN
ejpam-5617	409	9	,	,	PUNCT
ejpam-5617	409	10	a.	a.	PROPN
ejpam-5617	409	11	el	el	PROPN
ejpam-5617	409	12	-	-	PUNCT
ejpam-5617	409	13	ajou	ajou	PROPN
ejpam-5617	409	14	,	,	PUNCT
ejpam-5617	409	15	s.	s.	PROPN
ejpam-5617	409	16	ismaeel	ismaeel	PROPN
ejpam-5617	409	17	,	,	PUNCT
ejpam-5617	409	18	and	and	CCONJ
ejpam-5617	409	19	z.	z.	PROPN
ejpam-5617	409	20	al	al	PROPN
ejpam-5617	409	21	-	-	PUNCT
ejpam-5617	409	22	zhour	zhour	PROPN
ejpam-5617	409	23	.	.	PUNCT
ejpam-5617	410	1	analytical	analytical	ADJ
ejpam-5617	410	2	solutions	solution	NOUN
ejpam-5617	410	3	to	to	ADP
ejpam-5617	410	4	the	the	DET
ejpam-5617	410	5	coupled	couple	VERB
ejpam-5617	410	6	fractional	fractional	ADJ
ejpam-5617	410	7	neutron	neutron	NOUN
ejpam-5617	410	8	diffusion	diffusion	NOUN
ejpam-5617	410	9	equations	equation	NOUN
ejpam-5617	410	10	with	with	ADP
ejpam-5617	410	11	delayed	delay	VERB
ejpam-5617	410	12	neutrons	neutron	NOUN
ejpam-5617	410	13	system	system	NOUN
ejpam-5617	410	14	using	use	VERB
ejpam-5617	410	15	laplace	laplace	NOUN
ejpam-5617	410	16	transform	transform	NOUN
ejpam-5617	410	17	method	method	NOUN
ejpam-5617	410	18	.	.	PUNCT
ejpam-5617	411	1	aims	aim	VERB
ejpam-5617	411	2	mathematics	mathematic	NOUN
ejpam-5617	411	3	,	,	PUNCT
ejpam-5617	411	4	8(8):19297–19312	8(8):19297–19312	NUM
ejpam-5617	411	5	,	,	PUNCT
ejpam-5617	411	6	2023	2023	NUM
ejpam-5617	411	7	.	.	PUNCT
ejpam-5617	412	1	[	[	X
ejpam-5617	412	2	12	12	NUM
ejpam-5617	412	3	]	]	PUNCT
ejpam-5617	412	4	m.	m.	PROPN
ejpam-5617	412	5	caputo	caputo	PROPN
ejpam-5617	412	6	.	.	PUNCT
ejpam-5617	412	7	linear	linear	PROPN
ejpam-5617	412	8	models	model	NOUN
ejpam-5617	412	9	of	of	ADP
ejpam-5617	412	10	dissipation	dissipation	NOUN
ejpam-5617	412	11	whose	whose	DET
ejpam-5617	412	12	q	q	NOUN
ejpam-5617	412	13	is	be	AUX
ejpam-5617	412	14	almost	almost	ADV
ejpam-5617	412	15	frequency	frequency	ADJ
ejpam-5617	412	16	independent	independent	ADJ
ejpam-5617	412	17	–	–	PUNCT
ejpam-5617	412	18	ii	ii	NOUN
ejpam-5617	412	19	.	.	PUNCT
ejpam-5617	412	20	geophysical	geophysical	ADJ
ejpam-5617	412	21	journal	journal	PROPN
ejpam-5617	412	22	international	international	PROPN
ejpam-5617	412	23	,	,	PUNCT
ejpam-5617	412	24	13(5):529–539	13(5):529–539	NUM
ejpam-5617	412	25	,	,	PUNCT
ejpam-5617	412	26	1967	1967	NUM
ejpam-5617	412	27	.	.	PUNCT
ejpam-5617	413	1	[	[	X
ejpam-5617	413	2	13	13	NUM
ejpam-5617	413	3	]	]	PUNCT
ejpam-5617	413	4	s.	s.	PROPN
ejpam-5617	413	5	cifani	cifani	PROPN
ejpam-5617	413	6	and	and	CCONJ
ejpam-5617	413	7	e.	e.	PROPN
ejpam-5617	413	8	r.	r.	PROPN
ejpam-5617	413	9	jakobsen	jakobsen	PROPN
ejpam-5617	413	10	.	.	PUNCT
ejpam-5617	414	1	entropy	entropy	PROPN
ejpam-5617	414	2	solution	solution	NOUN
ejpam-5617	414	3	theory	theory	NOUN
ejpam-5617	414	4	for	for	ADP
ejpam-5617	414	5	fractional	fractional	ADJ
ejpam-5617	414	6	degenerate	degenerate	ADJ
ejpam-5617	414	7	convection	convection	NOUN
ejpam-5617	414	8	–	–	PUNCT
ejpam-5617	414	9	diffusion	diffusion	NOUN
ejpam-5617	414	10	equations	equation	NOUN
ejpam-5617	414	11	.	.	PUNCT
ejpam-5617	415	1	annales	annales	PROPN
ejpam-5617	415	2	de	de	ADP
ejpam-5617	415	3	l’ihp	l’ihp	PROPN
ejpam-5617	415	4	analyse	analyse	PROPN
ejpam-5617	415	5	non	non	ADJ
ejpam-5617	415	6	linéaire	linéaire	PROPN
ejpam-5617	415	7	,	,	PUNCT
ejpam-5617	415	8	28(3):413–441	28(3):413–441	PROPN
ejpam-5617	415	9	,	,	PUNCT
ejpam-5617	415	10	2011	2011	NUM
ejpam-5617	415	11	.	.	PUNCT
ejpam-5617	416	1	[	[	X
ejpam-5617	416	2	14	14	NUM
ejpam-5617	416	3	]	]	X
ejpam-5617	416	4	s.	s.	PROPN
ejpam-5617	416	5	das	das	PROPN
ejpam-5617	416	6	.	.	PROPN
ejpam-5617	417	1	analytical	analytical	ADJ
ejpam-5617	417	2	solution	solution	NOUN
ejpam-5617	417	3	of	of	ADP
ejpam-5617	417	4	a	a	DET
ejpam-5617	417	5	fractional	fractional	ADJ
ejpam-5617	417	6	diffusion	diffusion	NOUN
ejpam-5617	417	7	equation	equation	NOUN
ejpam-5617	417	8	by	by	ADP
ejpam-5617	417	9	variational	variational	ADJ
ejpam-5617	417	10	iteration	iteration	NOUN
ejpam-5617	417	11	method	method	NOUN
ejpam-5617	417	12	.	.	PUNCT
ejpam-5617	418	1	computers	computer	NOUN
ejpam-5617	418	2	math	math	PROPN
ejpam-5617	418	3	.	.	PUNCT
ejpam-5617	419	1	appl	appl	PROPN
ejpam-5617	419	2	.	.	PROPN
ejpam-5617	419	3	,	,	PUNCT
ejpam-5617	419	4	57(3):483–487	57(3):483–487	NUM
ejpam-5617	419	5	,	,	PUNCT
ejpam-5617	419	6	2009	2009	NUM
ejpam-5617	419	7	.	.	PUNCT
ejpam-5617	420	1	[	[	X
ejpam-5617	420	2	15	15	NUM
ejpam-5617	420	3	]	]	PUNCT
ejpam-5617	420	4	a.	a.	NOUN
ejpam-5617	420	5	dawar	dawar	PROPN
ejpam-5617	420	6	,	,	PUNCT
ejpam-5617	420	7	h.	h.	PROPN
ejpam-5617	420	8	khan	khan	PROPN
ejpam-5617	420	9	,	,	PUNCT
ejpam-5617	420	10	s.	s.	PROPN
ejpam-5617	420	11	islam	islam	PROPN
ejpam-5617	420	12	,	,	PUNCT
ejpam-5617	420	13	and	and	CCONJ
ejpam-5617	420	14	w.	w.	PROPN
ejpam-5617	420	15	khan	khan	PROPN
ejpam-5617	420	16	.	.	PUNCT
ejpam-5617	421	1	the	the	DET
ejpam-5617	421	2	improved	improve	VERB
ejpam-5617	421	3	residual	residual	ADJ
ejpam-5617	421	4	power	power	NOUN
ejpam-5617	421	5	series	series	NOUN
ejpam-5617	421	6	method	method	NOUN
ejpam-5617	421	7	for	for	ADP
ejpam-5617	421	8	a.	a.	PROPN
ejpam-5617	421	9	el	el	PROPN
ejpam-5617	421	10	-	-	PUNCT
ejpam-5617	421	11	ajou	ajou	PROPN
ejpam-5617	421	12	,	,	PUNCT
ejpam-5617	421	13	a.	a.	PROPN
ejpam-5617	421	14	burqan	burqan	PROPN
ejpam-5617	421	15	/	/	SYM
ejpam-5617	421	16	eur	eur	PROPN
ejpam-5617	421	17	.	.	PUNCT
ejpam-5617	422	1	j.	j.	PROPN
ejpam-5617	422	2	pure	pure	PROPN
ejpam-5617	422	3	appl	appl	PROPN
ejpam-5617	422	4	.	.	PROPN
ejpam-5617	422	5	math	math	PROPN
ejpam-5617	422	6	,	,	PUNCT
ejpam-5617	422	7	18	18	NUM
ejpam-5617	422	8	(	(	PUNCT
ejpam-5617	422	9	1	1	NUM
ejpam-5617	422	10	)	)	PUNCT
ejpam-5617	422	11	(	(	PUNCT
ejpam-5617	422	12	2025	2025	NUM
ejpam-5617	422	13	)	)	PUNCT
ejpam-5617	422	14	,	,	PUNCT
ejpam-5617	422	15	5617	5617	NUM
ejpam-5617	422	16	18	18	NUM
ejpam-5617	422	17	of	of	ADP
ejpam-5617	422	18	19	19	NUM
ejpam-5617	422	19	a	a	DET
ejpam-5617	422	20	system	system	NOUN
ejpam-5617	422	21	of	of	ADP
ejpam-5617	422	22	differential	differential	ADJ
ejpam-5617	422	23	equations	equation	NOUN
ejpam-5617	422	24	:	:	PUNCT
ejpam-5617	422	25	a	a	DET
ejpam-5617	422	26	new	new	ADJ
ejpam-5617	422	27	semi	semi	ADJ
ejpam-5617	422	28	-	-	ADJ
ejpam-5617	422	29	numerical	numerical	ADJ
ejpam-5617	422	30	method	method	NOUN
ejpam-5617	422	31	.	.	PUNCT
ejpam-5617	423	1	international	international	ADJ
ejpam-5617	423	2	journal	journal	NOUN
ejpam-5617	423	3	of	of	ADP
ejpam-5617	423	4	modelling	modelling	NOUN
ejpam-5617	423	5	and	and	CCONJ
ejpam-5617	423	6	simulation	simulation	NOUN
ejpam-5617	423	7	,	,	PUNCT
ejpam-5617	423	8	pages	page	NOUN
ejpam-5617	423	9	1–14	1–14	PROPN
ejpam-5617	423	10	,	,	PUNCT
ejpam-5617	423	11	2023	2023	NUM
ejpam-5617	423	12	.	.	PUNCT
ejpam-5617	424	1	[	[	X
ejpam-5617	424	2	16	16	NUM
ejpam-5617	424	3	]	]	PUNCT
ejpam-5617	424	4	k.	k.	PROPN
ejpam-5617	424	5	diethelm	diethelm	PROPN
ejpam-5617	424	6	,	,	PUNCT
ejpam-5617	424	7	n.	n.	PROPN
ejpam-5617	424	8	j.	j.	PROPN
ejpam-5617	424	9	ford	ford	PROPN
ejpam-5617	424	10	,	,	PUNCT
ejpam-5617	424	11	and	and	CCONJ
ejpam-5617	424	12	a.	a.	PROPN
ejpam-5617	424	13	d.	d.	PROPN
ejpam-5617	424	14	freed	free	VERB
ejpam-5617	424	15	.	.	PUNCT
ejpam-5617	425	1	a	a	DET
ejpam-5617	425	2	predictor	predictor	NOUN
ejpam-5617	425	3	-	-	PUNCT
ejpam-5617	425	4	corrector	corrector	NOUN
ejpam-5617	425	5	approach	approach	NOUN
ejpam-5617	425	6	for	for	ADP
ejpam-5617	425	7	the	the	DET
ejpam-5617	425	8	numerical	numerical	ADJ
ejpam-5617	425	9	solution	solution	NOUN
ejpam-5617	425	10	of	of	ADP
ejpam-5617	425	11	fractional	fractional	ADJ
ejpam-5617	425	12	differential	differential	ADJ
ejpam-5617	425	13	equations	equation	NOUN
ejpam-5617	425	14	.	.	PUNCT
ejpam-5617	426	1	nonlinear	nonlinear	ADJ
ejpam-5617	426	2	dynamics	dynamic	NOUN
ejpam-5617	426	3	,	,	PUNCT
ejpam-5617	426	4	29:3–22	29:3–22	NUM
ejpam-5617	426	5	,	,	PUNCT
ejpam-5617	426	6	2002	2002	NUM
ejpam-5617	426	7	.	.	PUNCT
ejpam-5617	427	1	[	[	X
ejpam-5617	427	2	17	17	NUM
ejpam-5617	427	3	]	]	X
ejpam-5617	427	4	a.	a.	PROPN
ejpam-5617	427	5	el	el	PROPN
ejpam-5617	427	6	-	-	PUNCT
ejpam-5617	427	7	ajou	ajou	PROPN
ejpam-5617	427	8	.	.	PUNCT
ejpam-5617	428	1	taylor	taylor	PROPN
ejpam-5617	428	2	’s	’s	PART
ejpam-5617	428	3	expansion	expansion	NOUN
ejpam-5617	428	4	for	for	ADP
ejpam-5617	428	5	fractional	fractional	ADJ
ejpam-5617	428	6	matrix	matrix	NOUN
ejpam-5617	428	7	functions	function	NOUN
ejpam-5617	428	8	:	:	PUNCT
ejpam-5617	428	9	theory	theory	NOUN
ejpam-5617	428	10	and	and	CCONJ
ejpam-5617	428	11	applications	application	NOUN
ejpam-5617	428	12	.	.	PUNCT
ejpam-5617	429	1	mathematics	mathematic	NOUN
ejpam-5617	429	2	,	,	PUNCT
ejpam-5617	429	3	21(7):1–17	21(7):1–17	NUM
ejpam-5617	429	4	,	,	PUNCT
ejpam-5617	429	5	2020	2020	NUM
ejpam-5617	429	6	.	.	PUNCT
ejpam-5617	430	1	[	[	X
ejpam-5617	430	2	18	18	NUM
ejpam-5617	430	3	]	]	PUNCT
ejpam-5617	430	4	a.	a.	PROPN
ejpam-5617	430	5	el	el	PROPN
ejpam-5617	430	6	-	-	PUNCT
ejpam-5617	430	7	ajou	ajou	PROPN
ejpam-5617	430	8	and	and	CCONJ
ejpam-5617	430	9	a.	a.	NOUN
ejpam-5617	430	10	burqan	burqan	PROPN
ejpam-5617	430	11	.	.	PUNCT
ejpam-5617	431	1	limit	limit	VERB
ejpam-5617	431	2	residual	residual	ADJ
ejpam-5617	431	3	function	function	NOUN
ejpam-5617	431	4	method	method	NOUN
ejpam-5617	431	5	and	and	CCONJ
ejpam-5617	431	6	applications	application	NOUN
ejpam-5617	431	7	to	to	ADP
ejpam-5617	431	8	pde	pde	NOUN
ejpam-5617	431	9	models	model	NOUN
ejpam-5617	431	10	.	.	PUNCT
ejpam-5617	432	1	the	the	DET
ejpam-5617	432	2	european	european	PROPN
ejpam-5617	432	3	physical	physical	PROPN
ejpam-5617	432	4	journal	journal	PROPN
ejpam-5617	432	5	plus	plus	CCONJ
ejpam-5617	432	6	,	,	PUNCT
ejpam-5617	432	7	139(11):973	139(11):973	NUM
ejpam-5617	432	8	,	,	PUNCT
ejpam-5617	432	9	2024	2024	NUM
ejpam-5617	432	10	.	.	PUNCT
ejpam-5617	433	1	[	[	X
ejpam-5617	433	2	19	19	NUM
ejpam-5617	433	3	]	]	X
ejpam-5617	433	4	a.	a.	PROPN
ejpam-5617	433	5	el	el	PROPN
ejpam-5617	433	6	-	-	PROPN
ejpam-5617	433	7	ajou	ajou	PROPN
ejpam-5617	433	8	and	and	CCONJ
ejpam-5617	433	9	a.	a.	NOUN
ejpam-5617	433	10	burqan	burqan	PROPN
ejpam-5617	433	11	.	.	PUNCT
ejpam-5617	434	1	a	a	DET
ejpam-5617	434	2	new	new	ADJ
ejpam-5617	434	3	algorithm	algorithm	NOUN
ejpam-5617	434	4	for	for	ADP
ejpam-5617	434	5	generating	generate	VERB
ejpam-5617	434	6	power	power	NOUN
ejpam-5617	434	7	series	series	NOUN
ejpam-5617	434	8	solutions	solution	NOUN
ejpam-5617	434	9	for	for	ADP
ejpam-5617	434	10	a	a	DET
ejpam-5617	434	11	broad	broad	ADJ
ejpam-5617	434	12	class	class	NOUN
ejpam-5617	434	13	of	of	ADP
ejpam-5617	434	14	fractional	fractional	ADJ
ejpam-5617	434	15	pdes	pde	NOUN
ejpam-5617	434	16	:	:	PUNCT
ejpam-5617	434	17	applications	application	NOUN
ejpam-5617	434	18	to	to	ADP
ejpam-5617	434	19	interesting	interesting	ADJ
ejpam-5617	434	20	problems	problem	NOUN
ejpam-5617	434	21	.	.	PUNCT
ejpam-5617	435	1	fractals	fractal	NOUN
ejpam-5617	435	2	,	,	PUNCT
ejpam-5617	435	3	2450120	2450120	NUM
ejpam-5617	435	4	,	,	PUNCT
ejpam-5617	435	5	2024	2024	NUM
ejpam-5617	435	6	.	.	PUNCT
ejpam-5617	436	1	[	[	X
ejpam-5617	436	2	20	20	NUM
ejpam-5617	436	3	]	]	PUNCT
ejpam-5617	436	4	a.	a.	PROPN
ejpam-5617	436	5	el	el	PROPN
ejpam-5617	436	6	-	-	PUNCT
ejpam-5617	436	7	ajou	ajou	ADJ
ejpam-5617	436	8	,	,	PUNCT
ejpam-5617	436	9	m.	m.	NOUN
ejpam-5617	436	10	shqair	shqair	PROPN
ejpam-5617	436	11	,	,	PUNCT
ejpam-5617	436	12	i.	i.	PROPN
ejpam-5617	436	13	ghabar	ghabar	PROPN
ejpam-5617	436	14	,	,	PUNCT
ejpam-5617	436	15	a.	a.	PROPN
ejpam-5617	436	16	burqan	burqan	PROPN
ejpam-5617	436	17	,	,	PUNCT
ejpam-5617	436	18	and	and	CCONJ
ejpam-5617	436	19	r.	r.	PROPN
ejpam-5617	436	20	saadeh	saadeh	PROPN
ejpam-5617	436	21	.	.	PUNCT
ejpam-5617	437	1	a	a	DET
ejpam-5617	437	2	solution	solution	NOUN
ejpam-5617	437	3	for	for	ADP
ejpam-5617	437	4	the	the	DET
ejpam-5617	437	5	neutron	neutron	NOUN
ejpam-5617	437	6	diffusion	diffusion	NOUN
ejpam-5617	437	7	equation	equation	NOUN
ejpam-5617	437	8	in	in	ADP
ejpam-5617	437	9	the	the	DET
ejpam-5617	437	10	spherical	spherical	ADJ
ejpam-5617	437	11	and	and	CCONJ
ejpam-5617	437	12	hemispherical	hemispherical	ADJ
ejpam-5617	437	13	reactors	reactor	NOUN
ejpam-5617	437	14	using	use	VERB
ejpam-5617	437	15	the	the	DET
ejpam-5617	437	16	residual	residual	ADJ
ejpam-5617	437	17	power	power	NOUN
ejpam-5617	437	18	series	series	NOUN
ejpam-5617	437	19	.	.	PUNCT
ejpam-5617	438	1	frontiers	frontier	NOUN
ejpam-5617	438	2	in	in	ADP
ejpam-5617	438	3	physics	physics	PROPN
ejpam-5617	438	4	,	,	PUNCT
ejpam-5617	438	5	11:1229142	11:1229142	NUM
ejpam-5617	438	6	,	,	PUNCT
ejpam-5617	438	7	2023	2023	NUM
ejpam-5617	438	8	.	.	PUNCT
ejpam-5617	439	1	[	[	X
ejpam-5617	439	2	21	21	NUM
ejpam-5617	439	3	]	]	X
ejpam-5617	439	4	j.	j.	PROPN
ejpam-5617	439	5	he	he	PROPN
ejpam-5617	439	6	.	.	PUNCT
ejpam-5617	440	1	homotopy	homotopy	VERB
ejpam-5617	440	2	perturbation	perturbation	NOUN
ejpam-5617	440	3	method	method	NOUN
ejpam-5617	440	4	:	:	PUNCT
ejpam-5617	440	5	a	a	DET
ejpam-5617	440	6	new	new	ADJ
ejpam-5617	440	7	nonlinear	nonlinear	ADJ
ejpam-5617	440	8	analytical	analytical	ADJ
ejpam-5617	440	9	technique	technique	NOUN
ejpam-5617	440	10	.	.	PUNCT
ejpam-5617	441	1	applied	apply	VERB
ejpam-5617	441	2	mathematics	mathematic	NOUN
ejpam-5617	441	3	and	and	CCONJ
ejpam-5617	441	4	computation	computation	NOUN
ejpam-5617	441	5	,	,	PUNCT
ejpam-5617	441	6	135(1):73–79	135(1):73–79	NUM
ejpam-5617	441	7	,	,	PUNCT
ejpam-5617	441	8	2003	2003	NUM
ejpam-5617	441	9	.	.	PUNCT
ejpam-5617	442	1	[	[	X
ejpam-5617	442	2	22	22	NUM
ejpam-5617	442	3	]	]	PUNCT
ejpam-5617	442	4	j.	j.	PROPN
ejpam-5617	442	5	he	he	PROPN
ejpam-5617	442	6	,	,	PUNCT
ejpam-5617	442	7	m.	m.	PROPN
ejpam-5617	442	8	jiao	jiao	PROPN
ejpam-5617	442	9	,	,	PUNCT
ejpam-5617	442	10	k.	k.	PROPN
ejpam-5617	442	11	a.	a.	PROPN
ejpam-5617	442	12	gepreel	gepreel	PROPN
ejpam-5617	442	13	,	,	PUNCT
ejpam-5617	442	14	and	and	CCONJ
ejpam-5617	442	15	y.	y.	PROPN
ejpam-5617	442	16	khan	khan	PROPN
ejpam-5617	442	17	.	.	PUNCT
ejpam-5617	443	1	homotopy	homotopy	VERB
ejpam-5617	443	2	analysis	analysis	NOUN
ejpam-5617	443	3	method	method	NOUN
ejpam-5617	443	4	:	:	PUNCT
ejpam-5617	443	5	a	a	DET
ejpam-5617	443	6	new	new	ADJ
ejpam-5617	443	7	analytical	analytical	ADJ
ejpam-5617	443	8	technique	technique	NOUN
ejpam-5617	443	9	for	for	ADP
ejpam-5617	443	10	nonlinear	nonlinear	ADJ
ejpam-5617	443	11	problems	problem	NOUN
ejpam-5617	443	12	.	.	PUNCT
ejpam-5617	444	1	mathematics	mathematic	NOUN
ejpam-5617	444	2	and	and	CCONJ
ejpam-5617	444	3	computers	computer	NOUN
ejpam-5617	444	4	in	in	ADP
ejpam-5617	444	5	simulation	simulation	NOUN
ejpam-5617	444	6	,	,	PUNCT
ejpam-5617	444	7	204:243–258	204:243–258	NUM
ejpam-5617	444	8	,	,	PUNCT
ejpam-5617	444	9	2023	2023	NUM
ejpam-5617	444	10	.	.	PUNCT
ejpam-5617	445	1	[	[	X
ejpam-5617	445	2	23	23	NUM
ejpam-5617	445	3	]	]	PUNCT
ejpam-5617	446	1	j.	j.	PROPN
ejpam-5617	446	2	he	he	PROPN
ejpam-5617	446	3	and	and	CCONJ
ejpam-5617	446	4	x.	x.	PROPN
ejpam-5617	446	5	wu	wu	PROPN
ejpam-5617	446	6	.	.	PUNCT
ejpam-5617	447	1	variational	variational	ADJ
ejpam-5617	447	2	iteration	iteration	NOUN
ejpam-5617	447	3	method	method	NOUN
ejpam-5617	447	4	:	:	PUNCT
ejpam-5617	447	5	new	new	ADJ
ejpam-5617	447	6	development	development	NOUN
ejpam-5617	447	7	and	and	CCONJ
ejpam-5617	447	8	applications	application	NOUN
ejpam-5617	447	9	.	.	PUNCT
ejpam-5617	448	1	computers	computer	NOUN
ejpam-5617	448	2	&	&	CCONJ
ejpam-5617	448	3	mathematics	mathematics	PROPN
ejpam-5617	448	4	with	with	ADP
ejpam-5617	448	5	applications	application	NOUN
ejpam-5617	448	6	,	,	PUNCT
ejpam-5617	448	7	54(7	54(7	NOUN
ejpam-5617	448	8	-	-	PUNCT
ejpam-5617	448	9	8):881–894	8):881–894	NUM
ejpam-5617	448	10	,	,	PUNCT
ejpam-5617	448	11	2007	2007	NUM
ejpam-5617	448	12	.	.	PUNCT
ejpam-5617	449	1	[	[	X
ejpam-5617	449	2	24	24	NUM
ejpam-5617	449	3	]	]	PUNCT
ejpam-5617	449	4	j.	j.	PROPN
ejpam-5617	449	5	h.	h.	PROPN
ejpam-5617	449	6	he	he	PROPN
ejpam-5617	449	7	,	,	PUNCT
ejpam-5617	449	8	z.	z.	PROPN
ejpam-5617	449	9	b.	b.	PROPN
ejpam-5617	449	10	li	li	PROPN
ejpam-5617	449	11	,	,	PUNCT
ejpam-5617	449	12	and	and	CCONJ
ejpam-5617	449	13	q.	q.	PROPN
ejpam-5617	449	14	l.	l.	PROPN
ejpam-5617	449	15	wang	wang	PROPN
ejpam-5617	449	16	.	.	PUNCT
ejpam-5617	450	1	a	a	DET
ejpam-5617	450	2	new	new	ADJ
ejpam-5617	450	3	fractional	fractional	ADJ
ejpam-5617	450	4	derivative	derivative	NOUN
ejpam-5617	450	5	and	and	CCONJ
ejpam-5617	450	6	its	its	PRON
ejpam-5617	450	7	application	application	NOUN
ejpam-5617	450	8	to	to	PART
ejpam-5617	450	9	explanation	explanation	NOUN
ejpam-5617	450	10	of	of	ADP
ejpam-5617	450	11	polar	polar	ADJ
ejpam-5617	450	12	bear	bear	NOUN
ejpam-5617	450	13	hairs	hair	NOUN
ejpam-5617	450	14	.	.	PUNCT
ejpam-5617	451	1	journal	journal	PROPN
ejpam-5617	451	2	of	of	ADP
ejpam-5617	451	3	king	king	PROPN
ejpam-5617	451	4	saud	saud	PROPN
ejpam-5617	451	5	university	university	PROPN
ejpam-5617	451	6	-	-	PUNCT
ejpam-5617	451	7	science	science	NOUN
ejpam-5617	451	8	,	,	PUNCT
ejpam-5617	451	9	28(2):190–192	28(2):190–192	PROPN
ejpam-5617	451	10	,	,	PUNCT
ejpam-5617	451	11	2016	2016	NUM
ejpam-5617	451	12	.	.	PUNCT
ejpam-5617	452	1	[	[	X
ejpam-5617	452	2	25	25	NUM
ejpam-5617	452	3	]	]	PUNCT
ejpam-5617	452	4	j.	j.	PROPN
ejpam-5617	452	5	h.	h.	PROPN
ejpam-5617	452	6	he	he	PROPN
ejpam-5617	452	7	,	,	PUNCT
ejpam-5617	452	8	l.	l.	PROPN
ejpam-5617	452	9	verma	verma	PROPN
ejpam-5617	452	10	,	,	PUNCT
ejpam-5617	452	11	b.	b.	PROPN
ejpam-5617	452	12	pandit	pandit	PROPN
ejpam-5617	452	13	,	,	PUNCT
ejpam-5617	452	14	a.	a.	PROPN
ejpam-5617	452	15	k.	k.	PROPN
ejpam-5617	452	16	verma	verma	PROPN
ejpam-5617	452	17	,	,	PUNCT
ejpam-5617	452	18	and	and	CCONJ
ejpam-5617	452	19	r.	r.	PROPN
ejpam-5617	452	20	p.	p.	PROPN
ejpam-5617	452	21	agarwal	agarwal	PROPN
ejpam-5617	452	22	.	.	PUNCT
ejpam-5617	453	1	a	a	DET
ejpam-5617	453	2	new	new	ADJ
ejpam-5617	453	3	taylor	taylor	PROPN
ejpam-5617	453	4	series	series	PROPN
ejpam-5617	453	5	based	base	VERB
ejpam-5617	453	6	numerical	numerical	ADJ
ejpam-5617	453	7	method	method	NOUN
ejpam-5617	453	8	:	:	PUNCT
ejpam-5617	453	9	simple	simple	ADJ
ejpam-5617	453	10	,	,	PUNCT
ejpam-5617	453	11	reliable	reliable	ADJ
ejpam-5617	453	12	,	,	PUNCT
ejpam-5617	453	13	and	and	CCONJ
ejpam-5617	453	14	promising	promise	VERB
ejpam-5617	453	15	.	.	PUNCT
ejpam-5617	454	1	journal	journal	NOUN
ejpam-5617	454	2	of	of	ADP
ejpam-5617	454	3	applied	applied	ADJ
ejpam-5617	454	4	and	and	CCONJ
ejpam-5617	454	5	computational	computational	ADJ
ejpam-5617	454	6	mechanics	mechanic	NOUN
ejpam-5617	454	7	,	,	PUNCT
ejpam-5617	454	8	9(4):1122–1134	9(4):1122–1134	NUM
ejpam-5617	454	9	,	,	PUNCT
ejpam-5617	454	10	2023	2023	NUM
ejpam-5617	454	11	.	.	PUNCT
ejpam-5617	455	1	[	[	X
ejpam-5617	455	2	26	26	NUM
ejpam-5617	455	3	]	]	X
ejpam-5617	455	4	h.	h.	PROPN
ejpam-5617	455	5	jafari	jafari	PROPN
ejpam-5617	455	6	and	and	CCONJ
ejpam-5617	455	7	v.	v.	ADP
ejpam-5617	455	8	daftardar	daftardar	NOUN
ejpam-5617	455	9	-	-	PUNCT
ejpam-5617	455	10	gejji	gejji	NOUN
ejpam-5617	455	11	.	.	PUNCT
ejpam-5617	456	1	solving	solve	VERB
ejpam-5617	456	2	a	a	DET
ejpam-5617	456	3	system	system	NOUN
ejpam-5617	456	4	of	of	ADP
ejpam-5617	456	5	nonlinear	nonlinear	ADJ
ejpam-5617	456	6	fractional	fractional	ADJ
ejpam-5617	456	7	differential	differential	NOUN
ejpam-5617	456	8	equations	equation	NOUN
ejpam-5617	456	9	using	use	VERB
ejpam-5617	456	10	adomian	adomian	NOUN
ejpam-5617	456	11	decomposition	decomposition	NOUN
ejpam-5617	456	12	.	.	PUNCT
ejpam-5617	457	1	journal	journal	NOUN
ejpam-5617	457	2	of	of	ADP
ejpam-5617	457	3	computational	computational	ADJ
ejpam-5617	457	4	and	and	CCONJ
ejpam-5617	457	5	applied	applied	ADJ
ejpam-5617	457	6	mathematics	mathematic	NOUN
ejpam-5617	457	7	,	,	PUNCT
ejpam-5617	457	8	196(2):644–651	196(2):644–651	NUM
ejpam-5617	457	9	,	,	PUNCT
ejpam-5617	457	10	2006	2006	NUM
ejpam-5617	457	11	.	.	PUNCT
ejpam-5617	458	1	[	[	X
ejpam-5617	458	2	27	27	NUM
ejpam-5617	458	3	]	]	X
ejpam-5617	458	4	h.	h.	PROPN
ejpam-5617	458	5	khresat	khresat	PROPN
ejpam-5617	458	6	,	,	PUNCT
ejpam-5617	458	7	a.	a.	PROPN
ejpam-5617	458	8	el	el	PROPN
ejpam-5617	458	9	-	-	PUNCT
ejpam-5617	458	10	ajou	ajou	PROPN
ejpam-5617	458	11	,	,	PUNCT
ejpam-5617	458	12	s.	s.	PROPN
ejpam-5617	458	13	al	al	PROPN
ejpam-5617	458	14	-	-	PUNCT
ejpam-5617	458	15	omari	omari	PROPN
ejpam-5617	458	16	,	,	PUNCT
ejpam-5617	458	17	s.	s.	PROPN
ejpam-5617	458	18	e.	e.	PROPN
ejpam-5617	458	19	alhazmi	alhazmi	PROPN
ejpam-5617	458	20	,	,	PUNCT
ejpam-5617	458	21	and	and	CCONJ
ejpam-5617	458	22	m.	m.	NOUN
ejpam-5617	458	23	n.	n.	PROPN
ejpam-5617	458	24	oqielat	oqielat	PROPN
ejpam-5617	458	25	.	.	PUNCT
ejpam-5617	459	1	exact	exact	ADJ
ejpam-5617	459	2	and	and	CCONJ
ejpam-5617	459	3	approximate	approximate	ADJ
ejpam-5617	459	4	solutions	solution	NOUN
ejpam-5617	459	5	for	for	ADP
ejpam-5617	459	6	linear	linear	ADJ
ejpam-5617	459	7	and	and	CCONJ
ejpam-5617	459	8	nonlinear	nonlinear	ADJ
ejpam-5617	459	9	partial	partial	ADJ
ejpam-5617	459	10	differential	differential	ADJ
ejpam-5617	459	11	equations	equation	NOUN
ejpam-5617	459	12	via	via	ADP
ejpam-5617	459	13	laplace	laplace	PROPN
ejpam-5617	459	14	residual	residual	ADJ
ejpam-5617	459	15	power	power	NOUN
ejpam-5617	459	16	series	series	PROPN
ejpam-5617	459	17	method	method	NOUN
ejpam-5617	459	18	.	.	PUNCT
ejpam-5617	460	1	axioms	axiom	NOUN
ejpam-5617	460	2	,	,	PUNCT
ejpam-5617	460	3	12(7):694	12(7):694	NUM
ejpam-5617	460	4	,	,	PUNCT
ejpam-5617	460	5	2023	2023	NUM
ejpam-5617	460	6	.	.	PUNCT
ejpam-5617	461	1	[	[	X
ejpam-5617	461	2	28	28	NUM
ejpam-5617	461	3	]	]	X
ejpam-5617	461	4	w.	w.	PROPN
ejpam-5617	461	5	li	li	PROPN
ejpam-5617	461	6	and	and	CCONJ
ejpam-5617	461	7	y.	y.	PROPN
ejpam-5617	461	8	pang	pang	PROPN
ejpam-5617	461	9	.	.	PUNCT
ejpam-5617	462	1	application	application	NOUN
ejpam-5617	462	2	of	of	ADP
ejpam-5617	462	3	adomian	adomian	ADJ
ejpam-5617	462	4	decomposition	decomposition	NOUN
ejpam-5617	462	5	method	method	NOUN
ejpam-5617	462	6	to	to	ADP
ejpam-5617	462	7	nonlinear	nonlinear	ADJ
ejpam-5617	462	8	systems	system	NOUN
ejpam-5617	462	9	.	.	PUNCT
ejpam-5617	463	1	adv	adv	PROPN
ejpam-5617	463	2	differ	differ	VERB
ejpam-5617	463	3	equ	equ	PROPN
ejpam-5617	463	4	,	,	PUNCT
ejpam-5617	463	5	67:2020	67:2020	NUM
ejpam-5617	463	6	,	,	PUNCT
ejpam-5617	463	7	2020	2020	NUM
ejpam-5617	463	8	.	.	PUNCT
ejpam-5617	464	1	[	[	X
ejpam-5617	464	2	29	29	NUM
ejpam-5617	464	3	]	]	X
ejpam-5617	464	4	r.	r.	PROPN
ejpam-5617	464	5	l.	l.	PROPN
ejpam-5617	464	6	magin	magin	PROPN
ejpam-5617	464	7	,	,	PUNCT
ejpam-5617	464	8	c.	c.	PROPN
ejpam-5617	464	9	ingo	ingo	PROPN
ejpam-5617	464	10	,	,	PUNCT
ejpam-5617	464	11	l.	l.	PROPN
ejpam-5617	464	12	colon	colon	NOUN
ejpam-5617	464	13	-	-	PUNCT
ejpam-5617	464	14	perez	perez	PROPN
ejpam-5617	464	15	,	,	PUNCT
ejpam-5617	464	16	w.	w.	PROPN
ejpam-5617	464	17	triplett	triplett	PROPN
ejpam-5617	464	18	,	,	PUNCT
ejpam-5617	464	19	and	and	CCONJ
ejpam-5617	464	20	t.	t.	PROPN
ejpam-5617	464	21	h.	h.	PROPN
ejpam-5617	464	22	mareci	mareci	PROPN
ejpam-5617	464	23	.	.	PUNCT
ejpam-5617	464	24	characterization	characterization	NOUN
ejpam-5617	464	25	of	of	ADP
ejpam-5617	464	26	anomalous	anomalous	ADJ
ejpam-5617	464	27	diffusion	diffusion	NOUN
ejpam-5617	464	28	in	in	ADP
ejpam-5617	464	29	porous	porous	ADJ
ejpam-5617	464	30	biological	biological	ADJ
ejpam-5617	464	31	tissues	tissue	NOUN
ejpam-5617	464	32	using	use	VERB
ejpam-5617	464	33	fractional	fractional	ADJ
ejpam-5617	464	34	order	order	NOUN
ejpam-5617	464	35	derivatives	derivative	NOUN
ejpam-5617	464	36	and	and	CCONJ
ejpam-5617	464	37	entropy	entropy	NOUN
ejpam-5617	464	38	.	.	PUNCT
ejpam-5617	465	1	microporous	microporous	ADJ
ejpam-5617	465	2	and	and	CCONJ
ejpam-5617	465	3	mesoporous	mesoporous	ADJ
ejpam-5617	465	4	materials	material	NOUN
ejpam-5617	465	5	,	,	PUNCT
ejpam-5617	465	6	178:39–43	178:39–43	NUM
ejpam-5617	465	7	,	,	PUNCT
ejpam-5617	465	8	2013	2013	NUM
ejpam-5617	465	9	.	.	PUNCT
ejpam-5617	466	1	[	[	X
ejpam-5617	466	2	30	30	NUM
ejpam-5617	466	3	]	]	X
ejpam-5617	466	4	b.	b.	PROPN
ejpam-5617	466	5	a.	a.	PROPN
ejpam-5617	466	6	mahmood	mahmood	PROPN
ejpam-5617	466	7	,	,	PUNCT
ejpam-5617	466	8	m.	m.	NOUN
ejpam-5617	466	9	a.	a.	PROPN
ejpam-5617	466	10	yousif	yousif	PROPN
ejpam-5617	466	11	,	,	PUNCT
ejpam-5617	466	12	and	and	CCONJ
ejpam-5617	466	13	l.	l.	PROPN
ejpam-5617	466	14	liu	liu	PROPN
ejpam-5617	466	15	.	.	PUNCT
ejpam-5617	467	1	a	a	DET
ejpam-5617	467	2	residual	residual	ADJ
ejpam-5617	467	3	power	power	NOUN
ejpam-5617	467	4	series	series	NOUN
ejpam-5617	467	5	technique	technique	NOUN
ejpam-5617	467	6	for	for	ADP
ejpam-5617	467	7	solving	solve	VERB
ejpam-5617	467	8	boussinesq	boussinesq	ADJ
ejpam-5617	467	9	–	–	PUNCT
ejpam-5617	467	10	burgers	burger	NOUN
ejpam-5617	467	11	equations	equation	NOUN
ejpam-5617	467	12	.	.	PUNCT
ejpam-5617	468	1	cogent	cogent	NOUN
ejpam-5617	468	2	mathematics	mathematic	NOUN
ejpam-5617	468	3	,	,	PUNCT
ejpam-5617	468	4	4(1	4(1	NOUN
ejpam-5617	468	5	)	)	PUNCT
ejpam-5617	468	6	,	,	PUNCT
ejpam-5617	468	7	2017	2017	NUM
ejpam-5617	468	8	.	.	PUNCT
ejpam-5617	469	1	[	[	X
ejpam-5617	469	2	31	31	NUM
ejpam-5617	469	3	]	]	PUNCT
ejpam-5617	469	4	f.	f.	PROPN
ejpam-5617	469	5	mainardi	mainardi	PROPN
ejpam-5617	469	6	.	.	PUNCT
ejpam-5617	469	7	fractional	fractional	ADJ
ejpam-5617	469	8	calculus	calculus	NOUN
ejpam-5617	469	9	:	:	PUNCT
ejpam-5617	469	10	some	some	DET
ejpam-5617	469	11	basic	basic	ADJ
ejpam-5617	469	12	problems	problem	NOUN
ejpam-5617	469	13	in	in	ADP
ejpam-5617	469	14	continuum	continuum	ADJ
ejpam-5617	469	15	and	and	CCONJ
ejpam-5617	469	16	statistical	statistical	ADJ
ejpam-5617	469	17	mechanics	mechanic	NOUN
ejpam-5617	469	18	.	.	PUNCT
ejpam-5617	470	1	in	in	ADP
ejpam-5617	470	2	a.	a.	NOUN
ejpam-5617	470	3	carpinteri	carpinteri	PROPN
ejpam-5617	470	4	and	and	CCONJ
ejpam-5617	470	5	f.	f.	PROPN
ejpam-5617	470	6	mainardi	mainardi	PROPN
ejpam-5617	470	7	,	,	PUNCT
ejpam-5617	470	8	editors	editor	NOUN
ejpam-5617	470	9	,	,	PUNCT
ejpam-5617	470	10	fractals	fractal	NOUN
ejpam-5617	470	11	and	and	CCONJ
ejpam-5617	470	12	fractional	fractional	ADJ
ejpam-5617	470	13	calculus	calculus	NOUN
ejpam-5617	470	14	in	in	ADP
ejpam-5617	470	15	continuum	continuum	ADJ
ejpam-5617	470	16	mechanics	mechanic	NOUN
ejpam-5617	470	17	,	,	PUNCT
ejpam-5617	470	18	pages	page	NOUN
ejpam-5617	470	19	291–348	291–348	NUM
ejpam-5617	470	20	.	.	PUNCT
ejpam-5617	470	21	springer	springer	NOUN
ejpam-5617	470	22	-	-	PUNCT
ejpam-5617	470	23	verlag	verlag	PROPN
ejpam-5617	470	24	,	,	PUNCT
ejpam-5617	470	25	1997	1997	NUM
ejpam-5617	470	26	.	.	PUNCT
ejpam-5617	471	1	[	[	X
ejpam-5617	471	2	32	32	NUM
ejpam-5617	471	3	]	]	PUNCT
ejpam-5617	471	4	f.	f.	PROPN
ejpam-5617	471	5	mainardi	mainardi	PROPN
ejpam-5617	471	6	,	,	PUNCT
ejpam-5617	471	7	m.	m.	NOUN
ejpam-5617	471	8	raberto	raberto	PROPN
ejpam-5617	471	9	,	,	PUNCT
ejpam-5617	471	10	r.	r.	PROPN
ejpam-5617	471	11	gorenflo	gorenflo	PROPN
ejpam-5617	471	12	,	,	PUNCT
ejpam-5617	471	13	and	and	CCONJ
ejpam-5617	471	14	e.	e.	PROPN
ejpam-5617	471	15	scalas	scalas	PROPN
ejpam-5617	471	16	.	.	PUNCT
ejpam-5617	471	17	fractional	fractional	ADJ
ejpam-5617	471	18	calculus	calculus	NOUN
ejpam-5617	471	19	and	and	CCONJ
ejpam-5617	471	20	continuous	continuous	ADJ
ejpam-5617	471	21	-	-	PUNCT
ejpam-5617	471	22	time	time	NOUN
ejpam-5617	471	23	finance	finance	PROPN
ejpam-5617	471	24	ii	ii	PROPN
ejpam-5617	471	25	:	:	PUNCT
ejpam-5617	471	26	the	the	DET
ejpam-5617	471	27	waiting	wait	VERB
ejpam-5617	471	28	-	-	PUNCT
ejpam-5617	471	29	time	time	NOUN
ejpam-5617	471	30	distribution	distribution	NOUN
ejpam-5617	471	31	.	.	PUNCT
ejpam-5617	472	1	physica	physica	NOUN
ejpam-5617	472	2	a	a	DET
ejpam-5617	472	3	:	:	PUNCT
ejpam-5617	472	4	statistical	statistical	ADJ
ejpam-5617	472	5	mechanics	mechanic	NOUN
ejpam-5617	472	6	and	and	CCONJ
ejpam-5617	472	7	its	its	PRON
ejpam-5617	472	8	applications	application	NOUN
ejpam-5617	472	9	,	,	PUNCT
ejpam-5617	472	10	287(3	287(3	NUM
ejpam-5617	472	11	-	-	SYM
ejpam-5617	472	12	4):468–481	4):468–481	NUM
ejpam-5617	472	13	,	,	PUNCT
ejpam-5617	472	14	2000	2000	NUM
ejpam-5617	472	15	.	.	PUNCT
ejpam-5617	473	1	[	[	X
ejpam-5617	473	2	33	33	NUM
ejpam-5617	473	3	]	]	PUNCT
ejpam-5617	473	4	r.	r.	PROPN
ejpam-5617	473	5	k.	k.	PROPN
ejpam-5617	473	6	nagle	nagle	PROPN
ejpam-5617	473	7	,	,	PUNCT
ejpam-5617	473	8	e.	e.	PROPN
ejpam-5617	473	9	b.	b.	PROPN
ejpam-5617	473	10	saff	saff	PROPN
ejpam-5617	473	11	,	,	PUNCT
ejpam-5617	473	12	and	and	CCONJ
ejpam-5617	473	13	a.	a.	PROPN
ejpam-5617	473	14	d.	d.	PROPN
ejpam-5617	473	15	snider	snider	PROPN
ejpam-5617	473	16	.	.	PUNCT
ejpam-5617	474	1	fundamentals	fundamental	NOUN
ejpam-5617	474	2	of	of	ADP
ejpam-5617	474	3	differential	differential	ADJ
ejpam-5617	474	4	equations	equation	NOUN
ejpam-5617	474	5	and	and	CCONJ
ejpam-5617	474	6	boundary	boundary	ADJ
ejpam-5617	474	7	value	value	NOUN
ejpam-5617	474	8	problems	problem	NOUN
ejpam-5617	474	9	.	.	PUNCT
ejpam-5617	475	1	pearson	pearson	PROPN
ejpam-5617	475	2	custom	custom	PROPN
ejpam-5617	475	3	publishing	publishing	PROPN
ejpam-5617	475	4	,	,	PUNCT
ejpam-5617	475	5	boston	boston	PROPN
ejpam-5617	475	6	,	,	PUNCT
ejpam-5617	475	7	mass	mass	PROPN
ejpam-5617	475	8	.	.	PROPN
ejpam-5617	475	9	,	,	PUNCT
ejpam-5617	475	10	2012	2012	NUM
ejpam-5617	475	11	.	.	PUNCT
ejpam-5617	476	1	[	[	X
ejpam-5617	476	2	34	34	NUM
ejpam-5617	476	3	]	]	PUNCT
ejpam-5617	476	4	a.	a.	NOUN
ejpam-5617	476	5	saadatmandi	saadatmandi	PROPN
ejpam-5617	476	6	and	and	CCONJ
ejpam-5617	476	7	m.	m.	NOUN
ejpam-5617	476	8	dehghan	dehghan	PROPN
ejpam-5617	476	9	.	.	PUNCT
ejpam-5617	477	1	a	a	DET
ejpam-5617	477	2	new	new	ADJ
ejpam-5617	477	3	operational	operational	ADJ
ejpam-5617	477	4	matrix	matrix	NOUN
ejpam-5617	477	5	for	for	ADP
ejpam-5617	477	6	solving	solve	VERB
ejpam-5617	477	7	fractional	fractional	ADJ
ejpam-5617	477	8	-	-	PUNCT
ejpam-5617	477	9	order	order	NOUN
ejpam-5617	477	10	a.	a.	NOUN
ejpam-5617	477	11	el	el	PROPN
ejpam-5617	477	12	-	-	PUNCT
ejpam-5617	477	13	ajou	ajou	PROPN
ejpam-5617	477	14	,	,	PUNCT
ejpam-5617	477	15	a.	a.	PROPN
ejpam-5617	477	16	burqan	burqan	PROPN
ejpam-5617	477	17	/	/	SYM
ejpam-5617	477	18	eur	eur	PROPN
ejpam-5617	477	19	.	.	PUNCT
ejpam-5617	478	1	j.	j.	PROPN
ejpam-5617	478	2	pure	pure	PROPN
ejpam-5617	478	3	appl	appl	PROPN
ejpam-5617	478	4	.	.	PROPN
ejpam-5617	478	5	math	math	PROPN
ejpam-5617	478	6	,	,	PUNCT
ejpam-5617	478	7	18	18	NUM
ejpam-5617	478	8	(	(	PUNCT
ejpam-5617	478	9	1	1	NUM
ejpam-5617	478	10	)	)	PUNCT
ejpam-5617	478	11	(	(	PUNCT
ejpam-5617	478	12	2025	2025	NUM
ejpam-5617	478	13	)	)	PUNCT
ejpam-5617	478	14	,	,	PUNCT
ejpam-5617	478	15	5617	5617	NUM
ejpam-5617	478	16	19	19	NUM
ejpam-5617	478	17	of	of	ADP
ejpam-5617	478	18	19	19	NUM
ejpam-5617	478	19	differential	differential	ADJ
ejpam-5617	478	20	equations	equation	NOUN
ejpam-5617	478	21	.	.	PUNCT
ejpam-5617	479	1	computers	computer	NOUN
ejpam-5617	479	2	math	math	PROPN
ejpam-5617	479	3	.	.	PUNCT
ejpam-5617	480	1	appl	appl	PROPN
ejpam-5617	480	2	.	.	PROPN
ejpam-5617	480	3	,	,	PUNCT
ejpam-5617	480	4	59(3):1326–1336	59(3):1326–1336	NUM
ejpam-5617	480	5	,	,	PUNCT
ejpam-5617	480	6	2010	2010	NUM
ejpam-5617	480	7	.	.	PUNCT
ejpam-5617	481	1	[	[	X
ejpam-5617	481	2	35	35	NUM
ejpam-5617	481	3	]	]	X
ejpam-5617	481	4	s.	s.	PROPN
ejpam-5617	481	5	saber	saber	PROPN
ejpam-5617	481	6	.	.	PUNCT
ejpam-5617	482	1	control	control	NOUN
ejpam-5617	482	2	of	of	ADP
ejpam-5617	482	3	chaos	chaos	NOUN
ejpam-5617	482	4	in	in	ADP
ejpam-5617	482	5	the	the	DET
ejpam-5617	482	6	burke	burke	PROPN
ejpam-5617	482	7	-	-	PUNCT
ejpam-5617	482	8	shaw	shaw	PROPN
ejpam-5617	482	9	system	system	NOUN
ejpam-5617	482	10	of	of	ADP
ejpam-5617	482	11	fractal	fractal	ADJ
ejpam-5617	482	12	-	-	PUNCT
ejpam-5617	482	13	fractional	fractional	ADJ
ejpam-5617	482	14	order	order	NOUN
ejpam-5617	482	15	in	in	ADP
ejpam-5617	482	16	the	the	DET
ejpam-5617	482	17	sense	sense	NOUN
ejpam-5617	482	18	of	of	ADP
ejpam-5617	482	19	caputo	caputo	PROPN
ejpam-5617	482	20	-	-	PUNCT
ejpam-5617	482	21	fabrizio	fabrizio	PROPN
ejpam-5617	482	22	.	.	PUNCT
ejpam-5617	483	1	journal	journal	PROPN
ejpam-5617	483	2	of	of	ADP
ejpam-5617	483	3	applied	apply	VERB
ejpam-5617	483	4	mathematics	mathematic	NOUN
ejpam-5617	483	5	and	and	CCONJ
ejpam-5617	483	6	computational	computational	ADJ
ejpam-5617	483	7	mechanics	mechanic	NOUN
ejpam-5617	483	8	,	,	PUNCT
ejpam-5617	483	9	23(1):83–96	23(1):83–96	NUM
ejpam-5617	483	10	,	,	PUNCT
ejpam-5617	483	11	2024	2024	NUM
ejpam-5617	483	12	.	.	PUNCT
ejpam-5617	484	1	[	[	X
ejpam-5617	484	2	36	36	NUM
ejpam-5617	484	3	]	]	PUNCT
ejpam-5617	484	4	a.	a.	NOUN
ejpam-5617	484	5	sarhan	sarhan	NOUN
ejpam-5617	484	6	,	,	PUNCT
ejpam-5617	484	7	a.	a.	PROPN
ejpam-5617	484	8	burqan	burqan	PROPN
ejpam-5617	484	9	,	,	PUNCT
ejpam-5617	484	10	r.	r.	PROPN
ejpam-5617	484	11	saadeh	saadeh	PROPN
ejpam-5617	484	12	,	,	PUNCT
ejpam-5617	484	13	and	and	CCONJ
ejpam-5617	484	14	z.	z.	PROPN
ejpam-5617	484	15	al	al	PROPN
ejpam-5617	484	16	-	-	PUNCT
ejpam-5617	484	17	zhour	zhour	PROPN
ejpam-5617	484	18	.	.	PUNCT
ejpam-5617	485	1	analytical	analytical	ADJ
ejpam-5617	485	2	solutions	solution	NOUN
ejpam-5617	485	3	of	of	ADP
ejpam-5617	485	4	the	the	DET
ejpam-5617	485	5	nonlinear	nonlinear	ADJ
ejpam-5617	485	6	timefractional	timefractional	NOUN
ejpam-5617	485	7	coupled	couple	VERB
ejpam-5617	485	8	boussinesq	boussinesq	ADJ
ejpam-5617	485	9	-	-	PUNCT
ejpam-5617	485	10	burger	burger	NOUN
ejpam-5617	485	11	equations	equation	NOUN
ejpam-5617	485	12	using	use	VERB
ejpam-5617	485	13	laplace	laplace	NOUN
ejpam-5617	485	14	residual	residual	ADJ
ejpam-5617	485	15	power	power	NOUN
ejpam-5617	485	16	series	series	NOUN
ejpam-5617	485	17	technique	technique	NOUN
ejpam-5617	485	18	.	.	PUNCT
ejpam-5617	486	1	fractal	fractal	ADJ
ejpam-5617	486	2	and	and	CCONJ
ejpam-5617	486	3	fractional	fractional	ADJ
ejpam-5617	486	4	,	,	PUNCT
ejpam-5617	486	5	6(11):631	6(11):631	PROPN
ejpam-5617	486	6	,	,	PUNCT
ejpam-5617	486	7	2022	2022	NUM
ejpam-5617	486	8	.	.	PUNCT
ejpam-5617	487	1	[	[	X
ejpam-5617	487	2	37	37	NUM
ejpam-5617	487	3	]	]	PUNCT
ejpam-5617	487	4	s.	s.	PROPN
ejpam-5617	487	5	zhang	zhang	PROPN
ejpam-5617	487	6	and	and	CCONJ
ejpam-5617	487	7	h.	h.	PROPN
ejpam-5617	487	8	q.	q.	PROPN
ejpam-5617	487	9	zhang	zhang	PROPN
ejpam-5617	487	10	.	.	PUNCT
ejpam-5617	488	1	fractional	fractional	ADJ
ejpam-5617	488	2	sub	sub	ADJ
ejpam-5617	488	3	-	-	ADJ
ejpam-5617	488	4	equation	equation	NOUN
ejpam-5617	488	5	method	method	NOUN
ejpam-5617	488	6	and	and	CCONJ
ejpam-5617	488	7	its	its	PRON
ejpam-5617	488	8	applications	application	NOUN
ejpam-5617	488	9	to	to	PART
ejpam-5617	488	10	nonlinear	nonlinear	ADJ
ejpam-5617	488	11	fractional	fractional	ADJ
ejpam-5617	488	12	pdes	pde	NOUN
ejpam-5617	488	13	.	.	PUNCT
ejpam-5617	489	1	physics	physics	NOUN
ejpam-5617	489	2	letters	letter	NOUN
ejpam-5617	489	3	a	a	DET
ejpam-5617	489	4	,	,	PUNCT
ejpam-5617	489	5	375(7):1069–1073	375(7):1069–1073	NOUN
ejpam-5617	489	6	,	,	PUNCT
ejpam-5617	489	7	2011	2011	NUM
ejpam-5617	489	8	.	.	PUNCT
ejpam-5617	490	1	[	[	X
ejpam-5617	490	2	38	38	NUM
ejpam-5617	490	3	]	]	PUNCT
ejpam-5617	490	4	e.	e.	PROPN
ejpam-5617	490	5	a.	a.	PROPN
ejpam-5617	490	6	a.	a.	PROPN
ejpam-5617	490	7	ziada	ziada	PROPN
ejpam-5617	490	8	.	.	PUNCT
ejpam-5617	491	1	analytical	analytical	ADJ
ejpam-5617	491	2	solution	solution	NOUN
ejpam-5617	491	3	of	of	ADP
ejpam-5617	491	4	nonlinear	nonlinear	ADJ
ejpam-5617	491	5	system	system	NOUN
ejpam-5617	491	6	of	of	ADP
ejpam-5617	491	7	fractional	fractional	ADJ
ejpam-5617	491	8	differential	differential	ADJ
ejpam-5617	491	9	equations	equation	NOUN
ejpam-5617	491	10	.	.	PUNCT
ejpam-5617	492	1	journal	journal	PROPN
ejpam-5617	492	2	of	of	ADP
ejpam-5617	492	3	applied	apply	VERB
ejpam-5617	492	4	mathematics	mathematic	NOUN
ejpam-5617	492	5	and	and	CCONJ
ejpam-5617	492	6	physics	physics	NOUN
ejpam-5617	492	7	,	,	PUNCT
ejpam-5617	492	8	9(10):2544–2557	9(10):2544–2557	NUM
ejpam-5617	492	9	,	,	PUNCT
ejpam-5617	492	10	2021	2021	NUM
ejpam-5617	492	11	.	.	PUNCT