id	sid	tid	token	lemma	pos
ejpam-4792	1	1	european	european	PROPN
ejpam-4792	1	2	journal	journal	PROPN
ejpam-4792	1	3	of	of	ADP
ejpam-4792	1	4	pure	pure	ADJ
ejpam-4792	1	5	and	and	CCONJ
ejpam-4792	1	6	applied	apply	VERB
ejpam-4792	1	7	mathematics	mathematic	NOUN
ejpam-4792	1	8	vol	vol	NOUN
ejpam-4792	1	9	.	.	PUNCT
ejpam-4792	2	1	16	16	NUM
ejpam-4792	2	2	,	,	PUNCT
ejpam-4792	2	3	no	no	INTJ
ejpam-4792	2	4	.	.	NOUN
ejpam-4792	2	5	3	3	NUM
ejpam-4792	2	6	,	,	PUNCT
ejpam-4792	2	7	2023	2023	NUM
ejpam-4792	2	8	,	,	PUNCT
ejpam-4792	2	9	1389	1389	NUM
ejpam-4792	2	10	-	-	SYM
ejpam-4792	2	11	1405	1405	NUM
ejpam-4792	2	12	issn	issn	PROPN
ejpam-4792	2	13	1307	1307	NUM
ejpam-4792	2	14	-	-	SYM
ejpam-4792	2	15	5543	5543	NUM
ejpam-4792	2	16	–	–	PUNCT
ejpam-4792	3	1	ejpam.com	ejpam.com	X
ejpam-4792	3	2	published	publish	VERB
ejpam-4792	3	3	by	by	ADP
ejpam-4792	3	4	new	new	PROPN
ejpam-4792	3	5	york	york	PROPN
ejpam-4792	3	6	business	business	PROPN
ejpam-4792	3	7	global	global	ADJ
ejpam-4792	3	8	using	use	VERB
ejpam-4792	3	9	gα	gα	NOUN
ejpam-4792	3	10	-	-	PUNCT
ejpam-4792	3	11	transform	transform	NOUN
ejpam-4792	3	12	to	to	PART
ejpam-4792	3	13	study	study	VERB
ejpam-4792	3	14	higher	high	ADJ
ejpam-4792	3	15	-	-	PUNCT
ejpam-4792	3	16	order	order	NOUN
ejpam-4792	3	17	differential	differential	ADJ
ejpam-4792	3	18	equations	equation	NOUN
ejpam-4792	3	19	with	with	ADP
ejpam-4792	3	20	polynomial	polynomial	ADJ
ejpam-4792	3	21	coefficients	coefficient	NOUN
ejpam-4792	3	22	supaknaree	supaknaree	ADJ
ejpam-4792	3	23	sattaso1	sattaso1	NOUN
ejpam-4792	3	24	,	,	PUNCT
ejpam-4792	3	25	patarawadee	patarawadee	PROPN
ejpam-4792	3	26	prasertsang1,∗	prasertsang1,∗	PROPN
ejpam-4792	3	27	,	,	PUNCT
ejpam-4792	3	28	torsak	torsak	ADJ
ejpam-4792	3	29	prasertsang1	prasertsang1	NOUN
ejpam-4792	3	30	1	1	NUM
ejpam-4792	3	31	faculty	faculty	NOUN
ejpam-4792	3	32	of	of	ADP
ejpam-4792	3	33	science	science	NOUN
ejpam-4792	3	34	and	and	CCONJ
ejpam-4792	3	35	engineering	engineering	NOUN
ejpam-4792	3	36	,	,	PUNCT
ejpam-4792	3	37	kasetsart	kasetsart	PROPN
ejpam-4792	3	38	university	university	PROPN
ejpam-4792	3	39	,	,	PUNCT
ejpam-4792	3	40	chalermphrakiat	chalermphrakiat	PROPN
ejpam-4792	3	41	sakon	sakon	PROPN
ejpam-4792	3	42	nakhon	nakhon	PROPN
ejpam-4792	3	43	province	province	PROPN
ejpam-4792	3	44	campus	campus	PROPN
ejpam-4792	3	45	,	,	PUNCT
ejpam-4792	3	46	sakon	sakon	PROPN
ejpam-4792	3	47	nakhon	nakhon	PROPN
ejpam-4792	3	48	,	,	PUNCT
ejpam-4792	3	49	thailand	thailand	PROPN
ejpam-4792	3	50	abstract	abstract	NOUN
ejpam-4792	3	51	.	.	PUNCT
ejpam-4792	4	1	in	in	ADP
ejpam-4792	4	2	this	this	DET
ejpam-4792	4	3	study	study	NOUN
ejpam-4792	4	4	,	,	PUNCT
ejpam-4792	4	5	solutions	solution	NOUN
ejpam-4792	4	6	of	of	ADP
ejpam-4792	4	7	higher	high	ADJ
ejpam-4792	4	8	-	-	PUNCT
ejpam-4792	4	9	order	order	NOUN
ejpam-4792	4	10	differential	differential	ADJ
ejpam-4792	4	11	equations	equation	NOUN
ejpam-4792	4	12	with	with	ADP
ejpam-4792	4	13	polynomial	polynomial	ADJ
ejpam-4792	4	14	coefficients	coefficient	NOUN
ejpam-4792	4	15	(	(	PUNCT
ejpam-4792	4	16	hodepcs	hodepc	NOUN
ejpam-4792	4	17	)	)	PUNCT
ejpam-4792	4	18	were	be	AUX
ejpam-4792	4	19	obtained	obtain	VERB
ejpam-4792	4	20	by	by	ADP
ejpam-4792	4	21	applying	apply	VERB
ejpam-4792	4	22	the	the	DET
ejpam-4792	4	23	gα	gα	NOUN
ejpam-4792	4	24	-	-	PUNCT
ejpam-4792	4	25	transform	transform	NOUN
ejpam-4792	4	26	.	.	PUNCT
ejpam-4792	5	1	based	base	VERB
ejpam-4792	5	2	on	on	ADP
ejpam-4792	5	3	some	some	DET
ejpam-4792	5	4	characterizations	characterization	NOUN
ejpam-4792	5	5	,	,	PUNCT
ejpam-4792	5	6	the	the	DET
ejpam-4792	5	7	solutions	solution	NOUN
ejpam-4792	5	8	of	of	ADP
ejpam-4792	5	9	hodepcs	hodepc	NOUN
ejpam-4792	5	10	were	be	AUX
ejpam-4792	5	11	investigated	investigate	VERB
ejpam-4792	5	12	.	.	PUNCT
ejpam-4792	6	1	with	with	ADP
ejpam-4792	6	2	the	the	DET
ejpam-4792	6	3	general	general	ADJ
ejpam-4792	6	4	solution	solution	NOUN
ejpam-4792	6	5	of	of	ADP
ejpam-4792	6	6	the	the	DET
ejpam-4792	6	7	hodepcs	hodepc	NOUN
ejpam-4792	6	8	,	,	PUNCT
ejpam-4792	6	9	the	the	DET
ejpam-4792	6	10	curves	curve	NOUN
ejpam-4792	6	11	of	of	ADP
ejpam-4792	6	12	the	the	DET
ejpam-4792	6	13	general	general	ADJ
ejpam-4792	6	14	solution	solution	NOUN
ejpam-4792	6	15	can	can	AUX
ejpam-4792	6	16	be	be	AUX
ejpam-4792	6	17	shown	show	VERB
ejpam-4792	6	18	in	in	ADP
ejpam-4792	6	19	several	several	ADJ
ejpam-4792	6	20	examples	example	NOUN
ejpam-4792	6	21	.	.	PUNCT
ejpam-4792	7	1	2020	2020	NUM
ejpam-4792	7	2	mathematics	mathematic	NOUN
ejpam-4792	7	3	subject	subject	NOUN
ejpam-4792	7	4	classifications	classification	NOUN
ejpam-4792	7	5	:	:	PUNCT
ejpam-4792	7	6	34a25	34a25	NUM
ejpam-4792	7	7	,	,	PUNCT
ejpam-4792	7	8	34a26	34a26	NUM
ejpam-4792	7	9	,	,	PUNCT
ejpam-4792	7	10	34c20	34c20	NUM
ejpam-4792	7	11	,	,	PUNCT
ejpam-4792	7	12	44a10	44a10	NUM
ejpam-4792	7	13	key	key	ADJ
ejpam-4792	7	14	words	word	NOUN
ejpam-4792	7	15	and	and	CCONJ
ejpam-4792	7	16	phrases	phrase	NOUN
ejpam-4792	7	17	:	:	PUNCT
ejpam-4792	7	18	laplace	laplace	NOUN
ejpam-4792	7	19	-	-	PUNCT
ejpam-4792	7	20	type	type	NOUN
ejpam-4792	7	21	integral	integral	ADJ
ejpam-4792	7	22	transforms	transform	NOUN
ejpam-4792	7	23	,	,	PUNCT
ejpam-4792	7	24	gα	gα	NOUN
ejpam-4792	7	25	-	-	PUNCT
ejpam-4792	7	26	transform	transform	NOUN
ejpam-4792	7	27	,	,	PUNCT
ejpam-4792	7	28	higher	high	ADJ
ejpam-4792	7	29	-	-	PUNCT
ejpam-4792	7	30	order	order	NOUN
ejpam-4792	7	31	differential	differential	ADJ
ejpam-4792	7	32	equation	equation	NOUN
ejpam-4792	7	33	with	with	ADP
ejpam-4792	7	34	polynomial	polynomial	ADJ
ejpam-4792	7	35	coefficients	coefficient	NOUN
ejpam-4792	7	36	1	1	NUM
ejpam-4792	7	37	.	.	PUNCT
ejpam-4792	8	1	introduction	introduction	NOUN
ejpam-4792	8	2	differential	differential	NOUN
ejpam-4792	8	3	equations	equation	NOUN
ejpam-4792	8	4	can	can	AUX
ejpam-4792	8	5	be	be	AUX
ejpam-4792	8	6	used	use	VERB
ejpam-4792	8	7	to	to	PART
ejpam-4792	8	8	express	express	VERB
ejpam-4792	8	9	a	a	DET
ejpam-4792	8	10	wide	wide	ADJ
ejpam-4792	8	11	range	range	NOUN
ejpam-4792	8	12	of	of	ADP
ejpam-4792	8	13	physical	physical	ADJ
ejpam-4792	8	14	laws	law	NOUN
ejpam-4792	8	15	and	and	CCONJ
ejpam-4792	8	16	relationships	relationship	NOUN
ejpam-4792	8	17	.	.	PUNCT
ejpam-4792	9	1	consequently	consequently	ADV
ejpam-4792	9	2	,	,	PUNCT
ejpam-4792	9	3	differential	differential	ADJ
ejpam-4792	9	4	equations	equation	NOUN
ejpam-4792	9	5	play	play	VERB
ejpam-4792	9	6	a	a	DET
ejpam-4792	9	7	vital	vital	ADJ
ejpam-4792	9	8	role	role	NOUN
ejpam-4792	9	9	in	in	ADP
ejpam-4792	9	10	a	a	DET
ejpam-4792	9	11	variety	variety	NOUN
ejpam-4792	9	12	of	of	ADP
ejpam-4792	9	13	complicated	complicated	ADJ
ejpam-4792	9	14	events	event	NOUN
ejpam-4792	9	15	that	that	PRON
ejpam-4792	9	16	occur	occur	VERB
ejpam-4792	9	17	all	all	ADV
ejpam-4792	9	18	over	over	ADP
ejpam-4792	9	19	the	the	DET
ejpam-4792	9	20	world	world	NOUN
ejpam-4792	9	21	.	.	PUNCT
ejpam-4792	10	1	mathematics	mathematic	NOUN
ejpam-4792	10	2	can	can	AUX
ejpam-4792	10	3	be	be	AUX
ejpam-4792	10	4	used	use	VERB
ejpam-4792	10	5	to	to	PART
ejpam-4792	10	6	model	model	VERB
ejpam-4792	10	7	any	any	DET
ejpam-4792	10	8	physical	physical	ADJ
ejpam-4792	10	9	phenomenon	phenomenon	NOUN
ejpam-4792	10	10	.	.	PUNCT
ejpam-4792	11	1	modeling	modeling	NOUN
ejpam-4792	11	2	is	be	AUX
ejpam-4792	11	3	a	a	DET
ejpam-4792	11	4	generic	generic	ADJ
ejpam-4792	11	5	method	method	NOUN
ejpam-4792	11	6	used	use	VERB
ejpam-4792	11	7	in	in	ADP
ejpam-4792	11	8	engineering	engineering	NOUN
ejpam-4792	11	9	,	,	PUNCT
ejpam-4792	11	10	science	science	NOUN
ejpam-4792	11	11	,	,	PUNCT
ejpam-4792	11	12	and	and	CCONJ
ejpam-4792	11	13	other	other	ADJ
ejpam-4792	11	14	professions	profession	NOUN
ejpam-4792	11	15	to	to	PART
ejpam-4792	11	16	convert	convert	VERB
ejpam-4792	11	17	physical	physical	ADJ
ejpam-4792	11	18	situations	situation	NOUN
ejpam-4792	11	19	or	or	CCONJ
ejpam-4792	11	20	other	other	ADJ
ejpam-4792	11	21	data	datum	NOUN
ejpam-4792	11	22	into	into	ADP
ejpam-4792	11	23	mathematical	mathematical	ADJ
ejpam-4792	11	24	models	model	NOUN
ejpam-4792	11	25	.	.	PUNCT
ejpam-4792	12	1	subsequently	subsequently	ADV
ejpam-4792	12	2	,	,	PUNCT
ejpam-4792	12	3	the	the	DET
ejpam-4792	12	4	differential	differential	ADJ
ejpam-4792	12	5	equations	equation	NOUN
ejpam-4792	12	6	in	in	ADP
ejpam-4792	12	7	the	the	DET
ejpam-4792	12	8	models	model	NOUN
ejpam-4792	12	9	must	must	AUX
ejpam-4792	12	10	be	be	AUX
ejpam-4792	12	11	solved	solve	VERB
ejpam-4792	12	12	.	.	PUNCT
ejpam-4792	13	1	in	in	ADP
ejpam-4792	13	2	recent	recent	ADJ
ejpam-4792	13	3	years	year	NOUN
ejpam-4792	13	4	,	,	PUNCT
ejpam-4792	13	5	many	many	ADJ
ejpam-4792	13	6	authors	author	NOUN
ejpam-4792	13	7	have	have	AUX
ejpam-4792	13	8	studied	study	VERB
ejpam-4792	13	9	solutions	solution	NOUN
ejpam-4792	13	10	to	to	PART
ejpam-4792	13	11	differential	differential	VERB
ejpam-4792	13	12	equations	equation	NOUN
ejpam-4792	13	13	using	use	VERB
ejpam-4792	13	14	various	various	ADJ
ejpam-4792	13	15	methods	method	NOUN
ejpam-4792	13	16	.	.	PUNCT
ejpam-4792	14	1	in	in	ADP
ejpam-4792	14	2	general	general	ADJ
ejpam-4792	14	3	,	,	PUNCT
ejpam-4792	14	4	it	it	PRON
ejpam-4792	14	5	is	be	AUX
ejpam-4792	14	6	still	still	ADV
ejpam-4792	14	7	very	very	ADV
ejpam-4792	14	8	difficult	difficult	ADJ
ejpam-4792	14	9	to	to	PART
ejpam-4792	14	10	obtain	obtain	VERB
ejpam-4792	14	11	closed	closed	ADJ
ejpam-4792	14	12	-	-	PUNCT
ejpam-4792	14	13	form	form	NOUN
ejpam-4792	14	14	solutions	solution	NOUN
ejpam-4792	14	15	for	for	ADP
ejpam-4792	14	16	differential	differential	ADJ
ejpam-4792	14	17	equations	equation	NOUN
ejpam-4792	14	18	for	for	ADP
ejpam-4792	14	19	most	most	ADJ
ejpam-4792	14	20	models	model	NOUN
ejpam-4792	14	21	of	of	ADP
ejpam-4792	14	22	real	real	ADJ
ejpam-4792	14	23	-	-	PUNCT
ejpam-4792	14	24	life	life	NOUN
ejpam-4792	14	25	problems	problem	NOUN
ejpam-4792	14	26	,	,	PUNCT
ejpam-4792	14	27	but	but	CCONJ
ejpam-4792	14	28	several	several	ADJ
ejpam-4792	14	29	techniques	technique	NOUN
ejpam-4792	14	30	have	have	AUX
ejpam-4792	14	31	been	be	AUX
ejpam-4792	14	32	developed	develop	VERB
ejpam-4792	14	33	to	to	PART
ejpam-4792	14	34	make	make	VERB
ejpam-4792	14	35	it	it	PRON
ejpam-4792	14	36	easier	easy	ADJ
ejpam-4792	14	37	to	to	PART
ejpam-4792	14	38	find	find	VERB
ejpam-4792	14	39	these	these	DET
ejpam-4792	14	40	solutions	solution	NOUN
ejpam-4792	14	41	.	.	PUNCT
ejpam-4792	15	1	integral	integral	ADJ
ejpam-4792	15	2	transforms	transform	NOUN
ejpam-4792	15	3	have	have	AUX
ejpam-4792	15	4	been	be	AUX
ejpam-4792	15	5	widely	widely	ADV
ejpam-4792	15	6	applied	apply	VERB
ejpam-4792	15	7	to	to	PART
ejpam-4792	15	8	solve	solve	VERB
ejpam-4792	15	9	several	several	ADJ
ejpam-4792	15	10	different	different	ADJ
ejpam-4792	15	11	types	type	NOUN
ejpam-4792	15	12	of	of	ADP
ejpam-4792	15	13	differential	differential	ADJ
ejpam-4792	15	14	equations	equation	NOUN
ejpam-4792	15	15	.	.	PUNCT
ejpam-4792	16	1	there	there	PRON
ejpam-4792	16	2	are	be	VERB
ejpam-4792	16	3	many	many	ADJ
ejpam-4792	16	4	publications	publication	NOUN
ejpam-4792	16	5	in	in	ADP
ejpam-4792	16	6	the	the	DET
ejpam-4792	16	7	literature	literature	NOUN
ejpam-4792	16	8	on	on	ADP
ejpam-4792	16	9	the	the	DET
ejpam-4792	16	10	theory	theory	NOUN
ejpam-4792	16	11	and	and	CCONJ
ejpam-4792	16	12	application	application	NOUN
ejpam-4792	16	13	of	of	ADP
ejpam-4792	16	14	integral	integral	ADJ
ejpam-4792	16	15	transform	transform	NOUN
ejpam-4792	16	16	for	for	ADP
ejpam-4792	16	17	solving	solve	VERB
ejpam-4792	16	18	differential	differential	ADJ
ejpam-4792	16	19	equations	equation	NOUN
ejpam-4792	16	20	,	,	PUNCT
ejpam-4792	16	21	including	include	VERB
ejpam-4792	16	22	contributions	contribution	NOUN
ejpam-4792	16	23	by	by	ADP
ejpam-4792	16	24	laplace	laplace	NOUN
ejpam-4792	16	25	[	[	X
ejpam-4792	16	26	3	3	NUM
ejpam-4792	16	27	,	,	PUNCT
ejpam-4792	16	28	4	4	NUM
ejpam-4792	16	29	,	,	PUNCT
ejpam-4792	16	30	6	6	NUM
ejpam-4792	16	31	,	,	PUNCT
ejpam-4792	16	32	14	14	NUM
ejpam-4792	16	33	,	,	PUNCT
ejpam-4792	16	34	20	20	NUM
ejpam-4792	16	35	,	,	PUNCT
ejpam-4792	16	36	21	21	NUM
ejpam-4792	16	37	,	,	PUNCT
ejpam-4792	16	38	27	27	NUM
ejpam-4792	16	39	]	]	PUNCT
ejpam-4792	16	40	,	,	PUNCT
ejpam-4792	16	41	sumudu	sumudu	NOUN
ejpam-4792	16	42	[	[	X
ejpam-4792	16	43	1	1	NUM
ejpam-4792	16	44	,	,	PUNCT
ejpam-4792	16	45	5	5	NUM
ejpam-4792	16	46	,	,	PUNCT
ejpam-4792	16	47	7	7	NUM
ejpam-4792	16	48	,	,	PUNCT
ejpam-4792	16	49	15	15	NUM
ejpam-4792	16	50	,	,	PUNCT
ejpam-4792	16	51	28–30	28–30	PROPN
ejpam-4792	16	52	]	]	PUNCT
ejpam-4792	16	53	,	,	PUNCT
ejpam-4792	16	54	and	and	CCONJ
ejpam-4792	16	55	elzaki	elzaki	VERB
ejpam-4792	16	56	[	[	X
ejpam-4792	16	57	8–13	8–13	NOUN
ejpam-4792	16	58	,	,	PUNCT
ejpam-4792	16	59	26	26	NUM
ejpam-4792	16	60	]	]	PUNCT
ejpam-4792	16	61	.	.	PUNCT
ejpam-4792	17	1	∗corresponding	∗corresponde	VERB
ejpam-4792	17	2	author	author	NOUN
ejpam-4792	17	3	.	.	PUNCT
ejpam-4792	18	1	doi	doi	NOUN
ejpam-4792	18	2	:	:	PUNCT
ejpam-4792	18	3	https://doi.org/10.29020/nybg.ejpam.v16i3.4792	https://doi.org/10.29020/nybg.ejpam.v16i3.4792	PRON
ejpam-4792	18	4	email	email	NOUN
ejpam-4792	18	5	addresses	address	NOUN
ejpam-4792	18	6	:	:	PUNCT
ejpam-4792	18	7	supaknaree.s@ku.th	supaknaree.s@ku.th	PROPN
ejpam-4792	18	8	(	(	PUNCT
ejpam-4792	18	9	s.	s.	PROPN
ejpam-4792	18	10	sattaso	sattaso	PROPN
ejpam-4792	18	11	)	)	PUNCT
ejpam-4792	18	12	,	,	PUNCT
ejpam-4792	18	13	patarawadee.s@ku.th	patarawadee.s@ku.th	PROPN
ejpam-4792	18	14	(	(	PUNCT
ejpam-4792	18	15	p.	p.	PROPN
ejpam-4792	18	16	prasertsang	prasertsang	PROPN
ejpam-4792	18	17	)	)	PUNCT
ejpam-4792	18	18	,	,	PUNCT
ejpam-4792	18	19	torsak.p@ku.th	torsak.p@ku.th	PROPN
ejpam-4792	18	20	(	(	PUNCT
ejpam-4792	18	21	t.	t.	PROPN
ejpam-4792	18	22	prasertsang	prasertsang	PROPN
ejpam-4792	18	23	)	)	PUNCT
ejpam-4792	18	24	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-4792	18	25	1389	1389	NUM
ejpam-4792	18	26	©	©	PROPN
ejpam-4792	18	27	2023	2023	NUM
ejpam-4792	18	28	ejpam	ejpam	NOUN
ejpam-4792	18	29	all	all	DET
ejpam-4792	18	30	rights	right	NOUN
ejpam-4792	18	31	reserved	reserve	VERB
ejpam-4792	18	32	.	.	PUNCT
ejpam-4792	19	1	s.	s.	PROPN
ejpam-4792	19	2	sattaso	sattaso	PROPN
ejpam-4792	19	3	,	,	PUNCT
ejpam-4792	19	4	p.	p.	PROPN
ejpam-4792	19	5	prasertsang	prasertsang	PROPN
ejpam-4792	19	6	,	,	PUNCT
ejpam-4792	19	7	t.	t.	PROPN
ejpam-4792	19	8	prasertsang	prasertsang	PROPN
ejpam-4792	19	9	/	/	SYM
ejpam-4792	19	10	eur	eur	PROPN
ejpam-4792	19	11	.	.	PUNCT
ejpam-4792	20	1	j.	j.	PROPN
ejpam-4792	20	2	pure	pure	PROPN
ejpam-4792	20	3	appl	appl	PROPN
ejpam-4792	20	4	.	.	PROPN
ejpam-4792	20	5	math	math	PROPN
ejpam-4792	20	6	,	,	PUNCT
ejpam-4792	20	7	16	16	NUM
ejpam-4792	20	8	(	(	PUNCT
ejpam-4792	20	9	3	3	NUM
ejpam-4792	20	10	)	)	PUNCT
ejpam-4792	20	11	(	(	PUNCT
ejpam-4792	20	12	2023	2023	NUM
ejpam-4792	20	13	)	)	PUNCT
ejpam-4792	20	14	,	,	PUNCT
ejpam-4792	20	15	1389	1389	NUM
ejpam-4792	20	16	-	-	SYM
ejpam-4792	20	17	1405	1405	NUM
ejpam-4792	20	18	1390	1390	NUM
ejpam-4792	20	19	recently	recently	ADV
ejpam-4792	20	20	,	,	PUNCT
ejpam-4792	20	21	an	an	DET
ejpam-4792	20	22	extended	extended	ADJ
ejpam-4792	20	23	laplace	laplace	NOUN
ejpam-4792	20	24	transform	transform	NOUN
ejpam-4792	20	25	,	,	PUNCT
ejpam-4792	20	26	called	call	VERB
ejpam-4792	20	27	the	the	DET
ejpam-4792	20	28	laplace	laplace	NOUN
ejpam-4792	20	29	-	-	PUNCT
ejpam-4792	20	30	typed	type	VERB
ejpam-4792	20	31	integral	integral	ADJ
ejpam-4792	20	32	transform	transform	NOUN
ejpam-4792	20	33	,	,	PUNCT
ejpam-4792	20	34	or	or	CCONJ
ejpam-4792	20	35	the	the	DET
ejpam-4792	20	36	gα	gα	NOUN
ejpam-4792	20	37	-	-	PUNCT
ejpam-4792	20	38	transform	transform	NOUN
ejpam-4792	20	39	,	,	PUNCT
ejpam-4792	20	40	or	or	CCONJ
ejpam-4792	20	41	the	the	DET
ejpam-4792	20	42	generalized	generalized	ADJ
ejpam-4792	20	43	laplace	laplace	NOUN
ejpam-4792	20	44	-	-	PUNCT
ejpam-4792	20	45	typed	type	VERB
ejpam-4792	20	46	integral	integral	ADJ
ejpam-4792	20	47	transforms	transform	NOUN
ejpam-4792	20	48	,	,	PUNCT
ejpam-4792	20	49	has	have	AUX
ejpam-4792	20	50	been	be	AUX
ejpam-4792	20	51	introduced	introduce	VERB
ejpam-4792	20	52	in	in	ADP
ejpam-4792	20	53	[	[	X
ejpam-4792	20	54	16	16	NUM
ejpam-4792	20	55	]	]	PUNCT
ejpam-4792	20	56	and	and	CCONJ
ejpam-4792	20	57	some	some	PRON
ejpam-4792	20	58	of	of	ADP
ejpam-4792	20	59	its	its	PRON
ejpam-4792	20	60	properties	property	NOUN
ejpam-4792	20	61	have	have	AUX
ejpam-4792	20	62	been	be	AUX
ejpam-4792	20	63	investigated	investigate	VERB
ejpam-4792	20	64	.	.	PUNCT
ejpam-4792	21	1	the	the	DET
ejpam-4792	21	2	gα	gα	NOUN
ejpam-4792	21	3	-	-	PUNCT
ejpam-4792	21	4	transform	transform	NOUN
ejpam-4792	21	5	is	be	AUX
ejpam-4792	21	6	defined	define	VERB
ejpam-4792	21	7	by	by	ADP
ejpam-4792	21	8	the	the	DET
ejpam-4792	21	9	formula	formula	NOUN
ejpam-4792	21	10	gα{f(τ	gα{f(τ	NOUN
ejpam-4792	21	11	)	)	PUNCT
ejpam-4792	21	12	}	}	PUNCT
ejpam-4792	21	13	=	=	SYM
ejpam-4792	21	14	wα	wα	NOUN
ejpam-4792	21	15	∫	∫	PROPN
ejpam-4792	21	16	∞	∞	PROPN
ejpam-4792	21	17	0	0	NUM
ejpam-4792	21	18	e−τ	e−τ	NOUN
ejpam-4792	21	19	/	/	SYM
ejpam-4792	21	20	wf(τ)dτ	wf(τ)dτ	NOUN
ejpam-4792	21	21	,	,	PUNCT
ejpam-4792	21	22	where	where	SCONJ
ejpam-4792	21	23	α	α	PROPN
ejpam-4792	21	24	∈	∈	PROPN
ejpam-4792	21	25	z	z	PROPN
ejpam-4792	21	26	and	and	CCONJ
ejpam-4792	21	27	w	w	PROPN
ejpam-4792	21	28	is	be	AUX
ejpam-4792	21	29	a	a	DET
ejpam-4792	21	30	complex	complex	ADJ
ejpam-4792	21	31	variable	variable	NOUN
ejpam-4792	21	32	.	.	PUNCT
ejpam-4792	22	1	by	by	ADP
ejpam-4792	22	2	selecting	select	VERB
ejpam-4792	22	3	the	the	DET
ejpam-4792	22	4	appropriate	appropriate	ADJ
ejpam-4792	22	5	α	α	NOUN
ejpam-4792	22	6	,	,	PUNCT
ejpam-4792	22	7	thegα	thegα	NOUN
ejpam-4792	22	8	-	-	PUNCT
ejpam-4792	22	9	transform	transform	NOUN
ejpam-4792	22	10	can	can	AUX
ejpam-4792	22	11	be	be	AUX
ejpam-4792	22	12	applied	apply	VERB
ejpam-4792	22	13	immediately	immediately	ADV
ejpam-4792	22	14	to	to	ADP
ejpam-4792	22	15	any	any	DET
ejpam-4792	22	16	situations	situation	NOUN
ejpam-4792	22	17	.	.	PUNCT
ejpam-4792	23	1	table	table	NOUN
ejpam-4792	23	2	1	1	NUM
ejpam-4792	23	3	lists	list	NOUN
ejpam-4792	23	4	some	some	PRON
ejpam-4792	23	5	of	of	ADP
ejpam-4792	23	6	the	the	DET
ejpam-4792	23	7	transforms	transform	NOUN
ejpam-4792	23	8	along	along	ADV
ejpam-4792	23	9	with	with	ADP
ejpam-4792	23	10	their	their	PRON
ejpam-4792	23	11	definitions	definition	NOUN
ejpam-4792	23	12	,	,	PUNCT
ejpam-4792	23	13	and	and	CCONJ
ejpam-4792	23	14	we	we	PRON
ejpam-4792	23	15	use	use	VERB
ejpam-4792	23	16	α	α	NOUN
ejpam-4792	23	17	to	to	PART
ejpam-4792	23	18	convert	convert	VERB
ejpam-4792	23	19	the	the	DET
ejpam-4792	23	20	gα	gα	NOUN
ejpam-4792	23	21	-	-	PUNCT
ejpam-4792	23	22	transform	transform	NOUN
ejpam-4792	23	23	as	as	ADP
ejpam-4792	23	24	appropriate	appropriate	ADJ
ejpam-4792	23	25	.	.	PUNCT
ejpam-4792	24	1	table	table	NOUN
ejpam-4792	24	2	1	1	NUM
ejpam-4792	24	3	:	:	PUNCT
ejpam-4792	24	4	some	some	DET
ejpam-4792	24	5	integral	integral	ADJ
ejpam-4792	24	6	transform	transform	NOUN
ejpam-4792	24	7	definitions	definition	NOUN
ejpam-4792	24	8	transform	transform	VERB
ejpam-4792	24	9	definition	definition	NOUN
ejpam-4792	24	10	gα	gα	NOUN
ejpam-4792	24	11	-	-	PUNCT
ejpam-4792	24	12	transform	transform	NOUN
ejpam-4792	24	13	laplace	laplace	NOUN
ejpam-4792	24	14	∫∞	∫∞	NOUN
ejpam-4792	24	15	0	0	NUM
ejpam-4792	24	16	e−τ	e−τ	NOUN
ejpam-4792	24	17	/	/	SYM
ejpam-4792	24	18	wf(τ)dτ	wf(τ)dτ	ADJ
ejpam-4792	24	19	α	α	NOUN
ejpam-4792	24	20	=	=	NOUN
ejpam-4792	24	21	0	0	NUM
ejpam-4792	24	22	and	and	CCONJ
ejpam-4792	24	23	1	1	NUM
ejpam-4792	24	24	/	/	SYM
ejpam-4792	24	25	s	s	NOUN
ejpam-4792	24	26	=	=	NOUN
ejpam-4792	24	27	w	w	NOUN
ejpam-4792	24	28	sumudu	sumudu	NOUN
ejpam-4792	24	29	1	1	NUM
ejpam-4792	24	30	w	w	NOUN
ejpam-4792	24	31	∫∞	∫∞	NOUN
ejpam-4792	24	32	0	0	NUM
ejpam-4792	24	33	e−τ	e−τ	NOUN
ejpam-4792	24	34	/	/	SYM
ejpam-4792	24	35	wf(τ)dτ	wf(τ)dτ	ADJ
ejpam-4792	24	36	α	α	NOUN
ejpam-4792	24	37	=	=	PUNCT
ejpam-4792	24	38	−1	−1	NOUN
ejpam-4792	25	1	elzaki	elzaki	NOUN
ejpam-4792	25	2	w	w	PROPN
ejpam-4792	25	3	∫∞	∫∞	NOUN
ejpam-4792	25	4	0	0	PUNCT
ejpam-4792	25	5	e−τ	e−τ	NOUN
ejpam-4792	25	6	/	/	SYM
ejpam-4792	25	7	wf(τ)dτ	wf(τ)dτ	ADJ
ejpam-4792	25	8	α	α	NOUN
ejpam-4792	25	9	=	=	SYM
ejpam-4792	25	10	1	1	NUM
ejpam-4792	25	11	furthermore	furthermore	ADV
ejpam-4792	25	12	,	,	PUNCT
ejpam-4792	25	13	the	the	DET
ejpam-4792	25	14	laplace	laplace	NOUN
ejpam-4792	25	15	transform	transform	NOUN
ejpam-4792	25	16	is	be	AUX
ejpam-4792	25	17	well	well	ADV
ejpam-4792	25	18	-	-	PUNCT
ejpam-4792	25	19	known	know	VERB
ejpam-4792	25	20	with	with	ADP
ejpam-4792	25	21	a	a	DET
ejpam-4792	25	22	strong	strong	ADJ
ejpam-4792	25	23	application	application	NOUN
ejpam-4792	25	24	in	in	ADP
ejpam-4792	25	25	derivative	derivative	ADJ
ejpam-4792	25	26	transforms	transform	NOUN
ejpam-4792	25	27	.	.	PUNCT
ejpam-4792	26	1	to	to	PART
ejpam-4792	26	2	select	select	VERB
ejpam-4792	26	3	a	a	DET
ejpam-4792	26	4	transform	transform	NOUN
ejpam-4792	26	5	that	that	PRON
ejpam-4792	26	6	provides	provide	VERB
ejpam-4792	26	7	a	a	DET
ejpam-4792	26	8	simple	simple	ADJ
ejpam-4792	26	9	tool	tool	NOUN
ejpam-4792	26	10	for	for	ADP
ejpam-4792	26	11	integral	integral	ADJ
ejpam-4792	26	12	transforms	transform	NOUN
ejpam-4792	26	13	,	,	PUNCT
ejpam-4792	26	14	one	one	PRON
ejpam-4792	26	15	has	have	VERB
ejpam-4792	26	16	the	the	DET
ejpam-4792	26	17	option	option	NOUN
ejpam-4792	26	18	to	to	PART
ejpam-4792	26	19	choose	choose	VERB
ejpam-4792	26	20	α	α	NOUN
ejpam-4792	26	21	=	=	PUNCT
ejpam-4792	26	22	−2	−2	NOUN
ejpam-4792	26	23	and	and	CCONJ
ejpam-4792	26	24	obtain	obtain	VERB
ejpam-4792	26	25	g−2{f(τ	g−2{f(τ	NOUN
ejpam-4792	26	26	)	)	PUNCT
ejpam-4792	26	27	}	}	PUNCT
ejpam-4792	26	28	=	=	SYM
ejpam-4792	26	29	1	1	NUM
ejpam-4792	26	30	w2	w2	NOUN
ejpam-4792	26	31	∫	∫	PROPN
ejpam-4792	26	32	∞	∞	PROPN
ejpam-4792	26	33	0	0	NUM
ejpam-4792	26	34	e−τ	e−τ	NOUN
ejpam-4792	26	35	/	/	SYM
ejpam-4792	26	36	wf(τ)dτ	wf(τ)dτ	ADJ
ejpam-4792	26	37	;	;	PUNCT
ejpam-4792	26	38	see	see	VERB
ejpam-4792	26	39	[	[	X
ejpam-4792	26	40	17	17	NUM
ejpam-4792	26	41	]	]	PUNCT
ejpam-4792	26	42	for	for	ADP
ejpam-4792	26	43	more	more	ADJ
ejpam-4792	26	44	details	detail	NOUN
ejpam-4792	26	45	.	.	PUNCT
ejpam-4792	27	1	kim	kim	PROPN
ejpam-4792	27	2	hj	hj	PROPN
ejpam-4792	27	3	.	.	PUNCT
ejpam-4792	28	1	[	[	X
ejpam-4792	28	2	18	18	NUM
ejpam-4792	28	3	]	]	PUNCT
ejpam-4792	28	4	used	use	VERB
ejpam-4792	28	5	theg−2	theg−2	ADJ
ejpam-4792	28	6	-	-	PUNCT
ejpam-4792	28	7	transform	transform	NOUN
ejpam-4792	28	8	to	to	PART
ejpam-4792	28	9	solve	solve	VERB
ejpam-4792	28	10	laguerre	laguerre	NOUN
ejpam-4792	28	11	’s	’s	PART
ejpam-4792	28	12	equation	equation	NOUN
ejpam-4792	28	13	.	.	PUNCT
ejpam-4792	29	1	recently	recently	ADV
ejpam-4792	29	2	,	,	PUNCT
ejpam-4792	29	3	sattaso	sattaso	PROPN
ejpam-4792	29	4	s.	s.	PROPN
ejpam-4792	29	5	et	et	PROPN
ejpam-4792	29	6	al	al	PROPN
ejpam-4792	29	7	.	.	PUNCT
ejpam-4792	30	1	[	[	X
ejpam-4792	30	2	24	24	NUM
ejpam-4792	30	3	]	]	PUNCT
ejpam-4792	30	4	explored	explore	VERB
ejpam-4792	30	5	the	the	DET
ejpam-4792	30	6	properties	property	NOUN
ejpam-4792	30	7	of	of	ADP
ejpam-4792	30	8	the	the	DET
ejpam-4792	30	9	gα	gα	NOUN
ejpam-4792	30	10	-	-	PUNCT
ejpam-4792	30	11	transform	transform	NOUN
ejpam-4792	30	12	and	and	CCONJ
ejpam-4792	30	13	offered	offer	VERB
ejpam-4792	30	14	various	various	ADJ
ejpam-4792	30	15	examples	example	NOUN
ejpam-4792	30	16	to	to	PART
ejpam-4792	30	17	demonstrate	demonstrate	VERB
ejpam-4792	30	18	its	its	PRON
ejpam-4792	30	19	usefulness	usefulness	NOUN
ejpam-4792	30	20	.	.	PUNCT
ejpam-4792	31	1	some	some	DET
ejpam-4792	31	2	examples	example	NOUN
ejpam-4792	31	3	can	can	AUX
ejpam-4792	31	4	be	be	AUX
ejpam-4792	31	5	easily	easily	ADV
ejpam-4792	31	6	solved	solve	VERB
ejpam-4792	31	7	with	with	ADP
ejpam-4792	31	8	the	the	DET
ejpam-4792	31	9	gα	gα	NOUN
ejpam-4792	31	10	-	-	PUNCT
ejpam-4792	31	11	transform	transform	NOUN
ejpam-4792	31	12	but	but	CCONJ
ejpam-4792	31	13	not	not	PART
ejpam-4792	31	14	with	with	ADP
ejpam-4792	31	15	the	the	DET
ejpam-4792	31	16	sumudu	sumudu	NOUN
ejpam-4792	31	17	or	or	CCONJ
ejpam-4792	31	18	elzaki	elzaki	NOUN
ejpam-4792	31	19	transforms	transform	VERB
ejpam-4792	31	20	.	.	PUNCT
ejpam-4792	32	1	furthermore	furthermore	ADV
ejpam-4792	32	2	,	,	PUNCT
ejpam-4792	32	3	the	the	DET
ejpam-4792	32	4	application	application	NOUN
ejpam-4792	32	5	of	of	ADP
ejpam-4792	32	6	the	the	DET
ejpam-4792	32	7	n	n	CCONJ
ejpam-4792	32	8	-	-	PUNCT
ejpam-4792	32	9	th	th	X
ejpam-4792	32	10	partial	partial	ADJ
ejpam-4792	32	11	derivatives	derivative	NOUN
ejpam-4792	32	12	to	to	ADP
ejpam-4792	32	13	the	the	DET
ejpam-4792	32	14	gα	gα	NOUN
ejpam-4792	32	15	-	-	PUNCT
ejpam-4792	32	16	transform	transform	NOUN
ejpam-4792	32	17	in	in	ADP
ejpam-4792	32	18	partial	partial	ADJ
ejpam-4792	32	19	differential	differential	ADJ
ejpam-4792	32	20	equations	equation	NOUN
ejpam-4792	32	21	was	be	AUX
ejpam-4792	32	22	presented	present	VERB
ejpam-4792	32	23	by	by	ADP
ejpam-4792	32	24	kim	kim	PROPN
ejpam-4792	32	25	hj	hj	PROPN
ejpam-4792	32	26	.	.	PROPN
ejpam-4792	32	27	et	et	PROPN
ejpam-4792	32	28	al	al	PROPN
ejpam-4792	32	29	.	.	PUNCT
ejpam-4792	33	1	[	[	X
ejpam-4792	33	2	22	22	NUM
ejpam-4792	33	3	]	]	PUNCT
ejpam-4792	33	4	.	.	PUNCT
ejpam-4792	34	1	kim	kim	PROPN
ejpam-4792	34	2	hj	hj	PROPN
ejpam-4792	34	3	.	.	PUNCT
ejpam-4792	35	1	[	[	X
ejpam-4792	35	2	2	2	NUM
ejpam-4792	35	3	]	]	PUNCT
ejpam-4792	35	4	investigated	investigate	VERB
ejpam-4792	35	5	the	the	DET
ejpam-4792	35	6	existence	existence	NOUN
ejpam-4792	35	7	and	and	CCONJ
ejpam-4792	35	8	uniqueness	uniqueness	NOUN
ejpam-4792	35	9	of	of	ADP
ejpam-4792	35	10	theorems	theorem	NOUN
ejpam-4792	35	11	for	for	ADP
ejpam-4792	35	12	a	a	DET
ejpam-4792	35	13	variant	variant	NOUN
ejpam-4792	35	14	of	of	ADP
ejpam-4792	35	15	a	a	DET
ejpam-4792	35	16	generalized	generalized	ADJ
ejpam-4792	35	17	laplace	laplace	NOUN
ejpam-4792	35	18	transform	transform	NOUN
ejpam-4792	35	19	represented	represent	VERB
ejpam-4792	35	20	by	by	ADP
ejpam-4792	35	21	a	a	DET
ejpam-4792	35	22	logarithmic	logarithmic	ADJ
ejpam-4792	35	23	function	function	NOUN
ejpam-4792	35	24	.	.	PUNCT
ejpam-4792	36	1	in	in	ADP
ejpam-4792	36	2	addition	addition	NOUN
ejpam-4792	36	3	,	,	PUNCT
ejpam-4792	36	4	kim	kim	PROPN
ejpam-4792	36	5	hj	hj	PROPN
ejpam-4792	36	6	.	.	PUNCT
ejpam-4792	37	1	[	[	X
ejpam-4792	37	2	19	19	NUM
ejpam-4792	37	3	]	]	PUNCT
ejpam-4792	37	4	considered	consider	VERB
ejpam-4792	37	5	an	an	DET
ejpam-4792	37	6	argument	argument	NOUN
ejpam-4792	37	7	based	base	VERB
ejpam-4792	37	8	on	on	ADP
ejpam-4792	37	9	the	the	DET
ejpam-4792	37	10	rigor	rigor	NOUN
ejpam-4792	37	11	of	of	ADP
ejpam-4792	37	12	mathematical	mathematical	ADJ
ejpam-4792	37	13	induction	induction	NOUN
ejpam-4792	37	14	for	for	ADP
ejpam-4792	37	15	the	the	DET
ejpam-4792	37	16	laplace	laplace	NOUN
ejpam-4792	37	17	transform	transform	NOUN
ejpam-4792	37	18	of	of	ADP
ejpam-4792	37	19	the	the	DET
ejpam-4792	37	20	n	n	ADV
ejpam-4792	37	21	-	-	PUNCT
ejpam-4792	37	22	th	th	X
ejpam-4792	37	23	derivative	derivative	NOUN
ejpam-4792	37	24	of	of	ADP
ejpam-4792	37	25	any	any	DET
ejpam-4792	37	26	order	order	NOUN
ejpam-4792	37	27	.	.	PUNCT
ejpam-4792	38	1	the	the	DET
ejpam-4792	38	2	results	result	NOUN
ejpam-4792	38	3	can	can	AUX
ejpam-4792	38	4	be	be	AUX
ejpam-4792	38	5	extended	extend	VERB
ejpam-4792	38	6	to	to	ADP
ejpam-4792	38	7	the	the	DET
ejpam-4792	38	8	generalized	generalized	ADJ
ejpam-4792	38	9	laplace	laplace	NOUN
ejpam-4792	38	10	transform	transform	NOUN
ejpam-4792	38	11	.	.	PUNCT
ejpam-4792	39	1	geum	geum	NOUN
ejpam-4792	39	2	y.	y.	PROPN
ejpam-4792	39	3	h.	h.	PROPN
ejpam-4792	39	4	et	et	PROPN
ejpam-4792	39	5	al	al	PROPN
ejpam-4792	39	6	.	.	PUNCT
ejpam-4792	40	1	[	[	X
ejpam-4792	40	2	25	25	NUM
ejpam-4792	40	3	]	]	PUNCT
ejpam-4792	40	4	showed	show	VERB
ejpam-4792	40	5	the	the	DET
ejpam-4792	40	6	matrix	matrix	NOUN
ejpam-4792	40	7	representation	representation	NOUN
ejpam-4792	40	8	of	of	ADP
ejpam-4792	40	9	convolution	convolution	NOUN
ejpam-4792	40	10	and	and	CCONJ
ejpam-4792	40	11	related	relate	VERB
ejpam-4792	40	12	the	the	DET
ejpam-4792	40	13	mathematical	mathematical	ADJ
ejpam-4792	40	14	notion	notion	NOUN
ejpam-4792	40	15	of	of	ADP
ejpam-4792	40	16	convolution	convolution	NOUN
ejpam-4792	40	17	to	to	ADP
ejpam-4792	40	18	the	the	DET
ejpam-4792	40	19	concept	concept	NOUN
ejpam-4792	40	20	of	of	ADP
ejpam-4792	40	21	convolution	convolution	NOUN
ejpam-4792	40	22	in	in	ADP
ejpam-4792	40	23	a	a	DET
ejpam-4792	40	24	convolutional	convolutional	ADJ
ejpam-4792	40	25	neural	neural	ADJ
ejpam-4792	40	26	network	network	NOUN
ejpam-4792	40	27	.	.	PUNCT
ejpam-4792	41	1	most	most	ADV
ejpam-4792	41	2	recently	recently	ADV
ejpam-4792	41	3	,	,	PUNCT
ejpam-4792	41	4	the	the	DET
ejpam-4792	41	5	range	range	NOUN
ejpam-4792	41	6	of	of	ADP
ejpam-4792	41	7	gα	gα	NOUN
ejpam-4792	41	8	-	-	PUNCT
ejpam-4792	41	9	transforms	transform	NOUN
ejpam-4792	41	10	that	that	PRON
ejpam-4792	41	11	can	can	AUX
ejpam-4792	41	12	be	be	AUX
ejpam-4792	41	13	used	use	VERB
ejpam-4792	41	14	to	to	PART
ejpam-4792	41	15	solve	solve	VERB
ejpam-4792	41	16	second	second	ADJ
ejpam-4792	41	17	-	-	PUNCT
ejpam-4792	41	18	order	order	NOUN
ejpam-4792	41	19	and	and	CCONJ
ejpam-4792	41	20	third	third	ADJ
ejpam-4792	41	21	-	-	PUNCT
ejpam-4792	41	22	order	order	NOUN
ejpam-4792	41	23	ordinary	ordinary	ADJ
ejpam-4792	41	24	differential	differential	ADJ
ejpam-4792	41	25	equations	equation	NOUN
ejpam-4792	41	26	with	with	ADP
ejpam-4792	41	27	variable	variable	ADJ
ejpam-4792	41	28	coefficients	coefficient	NOUN
ejpam-4792	41	29	was	be	AUX
ejpam-4792	41	30	addressed	address	VERB
ejpam-4792	41	31	by	by	ADP
ejpam-4792	41	32	prasertsang	prasertsang	PROPN
ejpam-4792	41	33	p.	p.	PROPN
ejpam-4792	41	34	et	et	PROPN
ejpam-4792	41	35	al	al	PROPN
ejpam-4792	41	36	.	.	PUNCT
ejpam-4792	42	1	[	[	X
ejpam-4792	42	2	23	23	NUM
ejpam-4792	42	3	]	]	PUNCT
ejpam-4792	42	4	.	.	PUNCT
ejpam-4792	42	5	motivated	motivate	VERB
ejpam-4792	42	6	by	by	ADP
ejpam-4792	42	7	this	this	DET
ejpam-4792	42	8	discussion	discussion	NOUN
ejpam-4792	42	9	,	,	PUNCT
ejpam-4792	42	10	the	the	DET
ejpam-4792	42	11	current	current	ADJ
ejpam-4792	42	12	paper	paper	NOUN
ejpam-4792	42	13	will	will	AUX
ejpam-4792	42	14	extend	extend	VERB
ejpam-4792	42	15	the	the	DET
ejpam-4792	42	16	variable	variable	ADJ
ejpam-4792	42	17	coefficients	coefficient	NOUN
ejpam-4792	42	18	in	in	ADP
ejpam-4792	42	19	general	general	ADJ
ejpam-4792	42	20	form	form	NOUN
ejpam-4792	42	21	and	and	CCONJ
ejpam-4792	42	22	identify	identify	VERB
ejpam-4792	42	23	some	some	DET
ejpam-4792	42	24	characterizations	characterization	NOUN
ejpam-4792	42	25	among	among	ADP
ejpam-4792	42	26	them	they	PRON
ejpam-4792	42	27	.	.	PUNCT
ejpam-4792	43	1	s.	s.	PROPN
ejpam-4792	43	2	sattaso	sattaso	PROPN
ejpam-4792	43	3	,	,	PUNCT
ejpam-4792	43	4	p.	p.	PROPN
ejpam-4792	43	5	prasertsang	prasertsang	PROPN
ejpam-4792	43	6	,	,	PUNCT
ejpam-4792	43	7	t.	t.	PROPN
ejpam-4792	43	8	prasertsang	prasertsang	PROPN
ejpam-4792	43	9	/	/	SYM
ejpam-4792	43	10	eur	eur	PROPN
ejpam-4792	43	11	.	.	PUNCT
ejpam-4792	44	1	j.	j.	PROPN
ejpam-4792	44	2	pure	pure	PROPN
ejpam-4792	44	3	appl	appl	PROPN
ejpam-4792	44	4	.	.	PROPN
ejpam-4792	44	5	math	math	PROPN
ejpam-4792	44	6	,	,	PUNCT
ejpam-4792	44	7	16	16	NUM
ejpam-4792	44	8	(	(	PUNCT
ejpam-4792	44	9	3	3	NUM
ejpam-4792	44	10	)	)	PUNCT
ejpam-4792	44	11	(	(	PUNCT
ejpam-4792	44	12	2023	2023	NUM
ejpam-4792	44	13	)	)	PUNCT
ejpam-4792	44	14	,	,	PUNCT
ejpam-4792	44	15	1389	1389	NUM
ejpam-4792	44	16	-	-	SYM
ejpam-4792	44	17	1405	1405	NUM
ejpam-4792	44	18	1391	1391	NUM
ejpam-4792	44	19	the	the	DET
ejpam-4792	44	20	remaining	remain	VERB
ejpam-4792	44	21	sections	section	NOUN
ejpam-4792	44	22	of	of	ADP
ejpam-4792	44	23	the	the	DET
ejpam-4792	44	24	paper	paper	NOUN
ejpam-4792	44	25	are	be	AUX
ejpam-4792	44	26	organized	organize	VERB
ejpam-4792	44	27	as	as	SCONJ
ejpam-4792	44	28	follows	follow	VERB
ejpam-4792	44	29	.	.	PUNCT
ejpam-4792	45	1	section	section	NOUN
ejpam-4792	45	2	2	2	NUM
ejpam-4792	45	3	introduces	introduce	VERB
ejpam-4792	45	4	a	a	DET
ejpam-4792	45	5	definition	definition	NOUN
ejpam-4792	45	6	and	and	CCONJ
ejpam-4792	45	7	lemmas	lemmas	PROPN
ejpam-4792	45	8	to	to	PART
ejpam-4792	45	9	prove	prove	VERB
ejpam-4792	45	10	the	the	DET
ejpam-4792	45	11	theorem	theorem	PROPN
ejpam-4792	45	12	.	.	PROPN
ejpam-4792	45	13	section	section	NOUN
ejpam-4792	45	14	3	3	NUM
ejpam-4792	45	15	derives	derive	VERB
ejpam-4792	45	16	the	the	DET
ejpam-4792	45	17	solutions	solution	NOUN
ejpam-4792	45	18	of	of	ADP
ejpam-4792	45	19	hodepcs	hodepc	NOUN
ejpam-4792	45	20	via	via	ADP
ejpam-4792	45	21	the	the	DET
ejpam-4792	45	22	gα	gα	NOUN
ejpam-4792	45	23	-	-	PUNCT
ejpam-4792	45	24	transform	transform	NOUN
ejpam-4792	45	25	and	and	CCONJ
ejpam-4792	45	26	obtains	obtain	VERB
ejpam-4792	45	27	some	some	DET
ejpam-4792	45	28	theorem	theorem	NOUN
ejpam-4792	45	29	and	and	CCONJ
ejpam-4792	45	30	corollary	corollary	ADJ
ejpam-4792	45	31	.	.	PUNCT
ejpam-4792	46	1	some	some	DET
ejpam-4792	46	2	applications	application	NOUN
ejpam-4792	46	3	and	and	CCONJ
ejpam-4792	46	4	conclusions	conclusion	NOUN
ejpam-4792	46	5	are	be	AUX
ejpam-4792	46	6	given	give	VERB
ejpam-4792	46	7	in	in	ADP
ejpam-4792	46	8	sections	section	NOUN
ejpam-4792	46	9	4	4	NUM
ejpam-4792	46	10	and	and	CCONJ
ejpam-4792	46	11	5	5	NUM
ejpam-4792	46	12	,	,	PUNCT
ejpam-4792	46	13	respectively	respectively	ADV
ejpam-4792	46	14	.	.	PUNCT
ejpam-4792	47	1	2	2	X
ejpam-4792	47	2	.	.	X
ejpam-4792	47	3	preliminaries	preliminary	NOUN
ejpam-4792	47	4	to	to	PART
ejpam-4792	47	5	analyze	analyze	VERB
ejpam-4792	47	6	the	the	DET
ejpam-4792	47	7	study	study	NOUN
ejpam-4792	47	8	for	for	ADP
ejpam-4792	47	9	hodepcs	hodepc	NOUN
ejpam-4792	47	10	via	via	ADP
ejpam-4792	47	11	the	the	DET
ejpam-4792	47	12	gα	gα	NOUN
ejpam-4792	47	13	-	-	PUNCT
ejpam-4792	47	14	transform	transform	NOUN
ejpam-4792	47	15	,	,	PUNCT
ejpam-4792	47	16	a	a	DET
ejpam-4792	47	17	definition	definition	NOUN
ejpam-4792	47	18	and	and	CCONJ
ejpam-4792	47	19	lemmas	lemma	NOUN
ejpam-4792	47	20	are	be	AUX
ejpam-4792	47	21	given	give	VERB
ejpam-4792	47	22	,	,	PUNCT
ejpam-4792	47	23	as	as	SCONJ
ejpam-4792	47	24	follows	follow	VERB
ejpam-4792	47	25	definition	definition	NOUN
ejpam-4792	47	26	1	1	NUM
ejpam-4792	47	27	.	.	PUNCT
ejpam-4792	48	1	[	[	X
ejpam-4792	48	2	24	24	NUM
ejpam-4792	48	3	]	]	PUNCT
ejpam-4792	48	4	let	let	VERB
ejpam-4792	48	5	f(τ	f(τ	NOUN
ejpam-4792	48	6	)	)	PUNCT
ejpam-4792	48	7	be	be	AUX
ejpam-4792	48	8	a	a	DET
ejpam-4792	48	9	piecewise	piecewise	NOUN
ejpam-4792	48	10	continuous	continuous	ADJ
ejpam-4792	48	11	function	function	NOUN
ejpam-4792	48	12	on	on	ADP
ejpam-4792	48	13	τ	τ	PROPN
ejpam-4792	48	14	≥	≥	X
ejpam-4792	48	15	0	0	NUM
ejpam-4792	48	16	and	and	CCONJ
ejpam-4792	48	17	has	have	VERB
ejpam-4792	48	18	an	an	DET
ejpam-4792	48	19	exponential	exponential	ADJ
ejpam-4792	48	20	order	order	NOUN
ejpam-4792	48	21	k.	k.	NOUN
ejpam-4792	49	1	the	the	DET
ejpam-4792	49	2	gα	gα	NOUN
ejpam-4792	49	3	-	-	PUNCT
ejpam-4792	49	4	transform	transform	NOUN
ejpam-4792	49	5	of	of	ADP
ejpam-4792	49	6	f(τ	f(τ	NOUN
ejpam-4792	49	7	)	)	PUNCT
ejpam-4792	49	8	,	,	PUNCT
ejpam-4792	49	9	briefly	briefly	NOUN
ejpam-4792	49	10	gα{f(τ	gα{f(τ	NOUN
ejpam-4792	49	11	)	)	PUNCT
ejpam-4792	49	12	}	}	PUNCT
ejpam-4792	49	13	,	,	PUNCT
ejpam-4792	49	14	is	be	AUX
ejpam-4792	49	15	characterized	characterize	VERB
ejpam-4792	49	16	with	with	ADP
ejpam-4792	49	17	the	the	DET
ejpam-4792	49	18	formula	formula	NOUN
ejpam-4792	49	19	gα{f(τ	gα{f(τ	NOUN
ejpam-4792	49	20	)	)	PUNCT
ejpam-4792	49	21	}	}	PUNCT
ejpam-4792	49	22	=	=	SYM
ejpam-4792	49	23	wα	wα	NOUN
ejpam-4792	49	24	∫	∫	PROPN
ejpam-4792	49	25	∞	∞	PROPN
ejpam-4792	49	26	0	0	NUM
ejpam-4792	49	27	e−τ	e−τ	NOUN
ejpam-4792	49	28	/	/	SYM
ejpam-4792	49	29	wf(τ)dτ	wf(τ)dτ	NOUN
ejpam-4792	49	30	,	,	PUNCT
ejpam-4792	49	31	where	where	SCONJ
ejpam-4792	49	32	α	α	PROPN
ejpam-4792	49	33	∈	∈	PROPN
ejpam-4792	49	34	z	z	PROPN
ejpam-4792	49	35	and	and	CCONJ
ejpam-4792	49	36	w	w	PROPN
ejpam-4792	49	37	>	>	X
ejpam-4792	49	38	0	0	PUNCT
ejpam-4792	49	39	is	be	AUX
ejpam-4792	49	40	a	a	DET
ejpam-4792	49	41	complex	complex	ADJ
ejpam-4792	49	42	variable	variable	NOUN
ejpam-4792	49	43	and	and	CCONJ
ejpam-4792	49	44	gα{f(τ	gα{f(τ	NOUN
ejpam-4792	49	45	)	)	PUNCT
ejpam-4792	49	46	}	}	PUNCT
ejpam-4792	49	47	exists	exist	VERB
ejpam-4792	49	48	for	for	ADP
ejpam-4792	49	49	w	w	PROPN
ejpam-4792	49	50	<	<	X
ejpam-4792	49	51	1	1	NUM
ejpam-4792	49	52	/	/	SYM
ejpam-4792	49	53	k.	k.	NOUN
ejpam-4792	49	54	lemma	lemma	PROPN
ejpam-4792	50	1	1	1	NUM
ejpam-4792	50	2	.	.	PUNCT
ejpam-4792	51	1	[	[	X
ejpam-4792	51	2	24	24	NUM
ejpam-4792	51	3	]	]	X
ejpam-4792	51	4	if	if	SCONJ
ejpam-4792	51	5	y(m)(τ	y(m)(τ	PROPN
ejpam-4792	51	6	)	)	PUNCT
ejpam-4792	51	7	is	be	AUX
ejpam-4792	51	8	a	a	DET
ejpam-4792	51	9	piecewise	piecewise	NOUN
ejpam-4792	51	10	continuous	continuous	ADJ
ejpam-4792	51	11	function	function	NOUN
ejpam-4792	51	12	on	on	ADP
ejpam-4792	51	13	[	[	X
ejpam-4792	51	14	0,∞	0,∞	NOUN
ejpam-4792	51	15	)	)	PUNCT
ejpam-4792	51	16	for	for	ADP
ejpam-4792	51	17	m	m	PROPN
ejpam-4792	51	18	∈	∈	PROPN
ejpam-4792	51	19	n	n	ADV
ejpam-4792	51	20	∪	∪	X
ejpam-4792	51	21	{	{	PUNCT
ejpam-4792	51	22	0	0	NUM
ejpam-4792	51	23	}	}	PUNCT
ejpam-4792	51	24	and	and	CCONJ
ejpam-4792	51	25	has	have	VERB
ejpam-4792	51	26	an	an	DET
ejpam-4792	51	27	exponential	exponential	ADJ
ejpam-4792	51	28	order	order	NOUN
ejpam-4792	51	29	k	k	PROPN
ejpam-4792	51	30	for	for	ADP
ejpam-4792	51	31	w	w	PROPN
ejpam-4792	51	32	<	<	X
ejpam-4792	51	33	1	1	NUM
ejpam-4792	51	34	k	k	NOUN
ejpam-4792	51	35	,	,	PUNCT
ejpam-4792	51	36	then	then	ADV
ejpam-4792	51	37	gα{τny(m)(τ	gα{τny(m)(τ	NOUN
ejpam-4792	51	38	)	)	PUNCT
ejpam-4792	51	39	}	}	PUNCT
ejpam-4792	52	1	=	=	SYM
ejpam-4792	52	2	w2nd	w2nd	PUNCT
ejpam-4792	52	3	ngα{y(m)(τ	ngα{y(m)(τ	PROPN
ejpam-4792	52	4	)	)	PUNCT
ejpam-4792	52	5	}	}	PUNCT
ejpam-4792	52	6	dwn	dwn	VERB
ejpam-4792	52	7	−	−	PROPN
ejpam-4792	52	8	(	(	PUNCT
ejpam-4792	52	9	n	n	NOUN
ejpam-4792	52	10	1	1	NUM
ejpam-4792	52	11	)	)	PUNCT
ejpam-4792	53	1	[	[	X
ejpam-4792	53	2	α−	α−	X
ejpam-4792	53	3	(	(	PUNCT
ejpam-4792	53	4	n−	n−	PROPN
ejpam-4792	53	5	1)]w2n−1d	1)]w2n−1d	PROPN
ejpam-4792	53	6	n−1gα{y(m)(τ	n−1gα{y(m)(τ	NUM
ejpam-4792	53	7	)	)	PUNCT
ejpam-4792	53	8	}	}	PUNCT
ejpam-4792	53	9	dwn−1	dwn−1	PROPN
ejpam-4792	53	10	+	+	NUM
ejpam-4792	53	11	·	·	PUNCT
ejpam-4792	53	12	·	·	PUNCT
ejpam-4792	53	13	·	·	PUNCT
ejpam-4792	54	1	−	−	PUNCT
ejpam-4792	54	2	(	(	PUNCT
ejpam-4792	54	3	n	n	NUM
ejpam-4792	54	4	n−	n−	NOUN
ejpam-4792	54	5	1	1	NUM
ejpam-4792	54	6	)	)	PUNCT
ejpam-4792	55	1	[	[	X
ejpam-4792	55	2	α−	α−	X
ejpam-4792	55	3	(	(	PUNCT
ejpam-4792	55	4	n−	n−	NOUN
ejpam-4792	55	5	1	1	NUM
ejpam-4792	55	6	)	)	PUNCT
ejpam-4792	55	7	]	]	PUNCT
ejpam-4792	56	1	[	[	X
ejpam-4792	56	2	α−	α−	X
ejpam-4792	56	3	(	(	PUNCT
ejpam-4792	56	4	n−	n−	NOUN
ejpam-4792	56	5	2	2	NUM
ejpam-4792	56	6	)	)	PUNCT
ejpam-4792	56	7	]	]	PUNCT
ejpam-4792	56	8	·	·	PUNCT
ejpam-4792	56	9	·	·	PUNCT
ejpam-4792	56	10	·	·	PUNCT
ejpam-4792	56	11	(	(	PUNCT
ejpam-4792	56	12	α−	α−	ADP
ejpam-4792	56	13	1)wn+1dgα{y(m)(τ	1)wn+1dgα{y(m)(τ	NUM
ejpam-4792	56	14	)	)	PUNCT
ejpam-4792	56	15	}	}	PUNCT
ejpam-4792	56	16	dw	dw	NOUN
ejpam-4792	56	17	+	+	CCONJ
ejpam-4792	56	18	[	[	X
ejpam-4792	56	19	α−	α−	ADP
ejpam-4792	56	20	(	(	PUNCT
ejpam-4792	56	21	n−	n−	NOUN
ejpam-4792	56	22	1	1	NUM
ejpam-4792	56	23	)	)	PUNCT
ejpam-4792	56	24	]	]	PUNCT
ejpam-4792	57	1	[	[	X
ejpam-4792	57	2	α−	α−	X
ejpam-4792	57	3	(	(	PUNCT
ejpam-4792	57	4	n−	n−	NOUN
ejpam-4792	57	5	2	2	NUM
ejpam-4792	57	6	)	)	PUNCT
ejpam-4792	57	7	]	]	PUNCT
ejpam-4792	57	8	·	·	PUNCT
ejpam-4792	57	9	·	·	PUNCT
ejpam-4792	57	10	·	·	PUNCT
ejpam-4792	57	11	αwngα{y(m)(τ	αwngα{y(m)(τ	NUM
ejpam-4792	57	12	)	)	PUNCT
ejpam-4792	57	13	}	}	PUNCT
ejpam-4792	57	14	.	.	PUNCT
ejpam-4792	58	1	(	(	PUNCT
ejpam-4792	58	2	1	1	X
ejpam-4792	58	3	)	)	PUNCT
ejpam-4792	58	4	from	from	ADP
ejpam-4792	58	5	lemma	lemma	PROPN
ejpam-4792	58	6	1	1	NUM
ejpam-4792	58	7	,	,	PUNCT
ejpam-4792	58	8	eq	eq	NOUN
ejpam-4792	58	9	.	.	PUNCT
ejpam-4792	59	1	(	(	PUNCT
ejpam-4792	59	2	1	1	X
ejpam-4792	59	3	)	)	PUNCT
ejpam-4792	59	4	can	can	AUX
ejpam-4792	59	5	be	be	AUX
ejpam-4792	59	6	rewritten	rewrite	VERB
ejpam-4792	59	7	as	as	ADP
ejpam-4792	59	8	the	the	DET
ejpam-4792	59	9	following	following	NOUN
ejpam-4792	59	10	,	,	PUNCT
ejpam-4792	59	11	gα{τny(m)(τ	gα{τny(m)(τ	NOUN
ejpam-4792	59	12	)	)	PUNCT
ejpam-4792	59	13	}	}	PUNCT
ejpam-4792	60	1	=	=	PUNCT
ejpam-4792	60	2	n∑	n∑	NOUN
ejpam-4792	60	3	l=0	l=0	PROPN
ejpam-4792	60	4	(	(	PUNCT
ejpam-4792	60	5	−1)n−l	−1)n−l	X
ejpam-4792	60	6	(	(	PUNCT
ejpam-4792	60	7	n	n	X
ejpam-4792	60	8	l	l	NOUN
ejpam-4792	60	9	)	)	PUNCT
ejpam-4792	61	1	n−1∏	n−1∏	PROPN
ejpam-4792	61	2	s	s	PROPN
ejpam-4792	61	3	=	=	NOUN
ejpam-4792	61	4	l	l	NOUN
ejpam-4792	61	5	(	(	PUNCT
ejpam-4792	61	6	m+	m+	NUM
ejpam-4792	61	7	α−	α−	ADP
ejpam-4792	61	8	s	s	NOUN
ejpam-4792	61	9	)	)	PUNCT
ejpam-4792	61	10	y	y	PROPN
ejpam-4792	61	11	(	(	PUNCT
ejpam-4792	61	12	l)(w	l)(w	NOUN
ejpam-4792	61	13	)	)	PUNCT
ejpam-4792	61	14	wm−n−l	wm−n−l	NOUN
ejpam-4792	61	15	−	−	PROPN
ejpam-4792	61	16	m−1∑	m−1∑	PROPN
ejpam-4792	61	17	k=0	k=0	PROPN
ejpam-4792	61	18	n∏	n∏	PROPN
ejpam-4792	62	1	l=1	l=1	PROPN
ejpam-4792	62	2	(	(	PUNCT
ejpam-4792	62	3	−m+	−m+	NOUN
ejpam-4792	62	4	k	k	X
ejpam-4792	62	5	+	+	PROPN
ejpam-4792	62	6	l)wα−m+k+l+1y(k)(0	l)wα−m+k+l+1y(k)(0	PROPN
ejpam-4792	62	7	)	)	PUNCT
ejpam-4792	62	8	.	.	PUNCT
ejpam-4792	63	1	(	(	PUNCT
ejpam-4792	63	2	2	2	X
ejpam-4792	63	3	)	)	PUNCT
ejpam-4792	63	4	if	if	SCONJ
ejpam-4792	63	5	m	m	ADV
ejpam-4792	63	6	=	=	NOUN
ejpam-4792	63	7	0	0	NUM
ejpam-4792	63	8	in	in	ADP
ejpam-4792	63	9	eq	eq	ADP
ejpam-4792	63	10	.	.	PUNCT
ejpam-4792	64	1	(	(	PUNCT
ejpam-4792	64	2	2	2	NUM
ejpam-4792	64	3	)	)	PUNCT
ejpam-4792	64	4	,	,	PUNCT
ejpam-4792	64	5	gα{τny(τ	gα{τny(τ	PROPN
ejpam-4792	64	6	)	)	PUNCT
ejpam-4792	64	7	}	}	PUNCT
ejpam-4792	65	1	=	=	PUNCT
ejpam-4792	65	2	n∑	n∑	NOUN
ejpam-4792	65	3	l=0	l=0	PROPN
ejpam-4792	65	4	(	(	PUNCT
ejpam-4792	65	5	−1)n−l	−1)n−l	X
ejpam-4792	65	6	(	(	PUNCT
ejpam-4792	65	7	n	n	X
ejpam-4792	65	8	l	l	NOUN
ejpam-4792	65	9	)	)	PUNCT
ejpam-4792	66	1	n−1∏	n−1∏	PROPN
ejpam-4792	66	2	s	s	PROPN
ejpam-4792	66	3	=	=	NOUN
ejpam-4792	66	4	l	l	NOUN
ejpam-4792	66	5	(	(	PUNCT
ejpam-4792	66	6	α−	α−	ADP
ejpam-4792	66	7	s	s	NOUN
ejpam-4792	66	8	)	)	PUNCT
ejpam-4792	66	9	y	y	PROPN
ejpam-4792	66	10	(	(	PUNCT
ejpam-4792	66	11	l)(w	l)(w	NOUN
ejpam-4792	66	12	)	)	PUNCT
ejpam-4792	66	13	w−n−l	w−n−l	X
ejpam-4792	66	14	.	.	PUNCT
ejpam-4792	67	1	if	if	SCONJ
ejpam-4792	67	2	n	n	ADV
ejpam-4792	67	3	=	=	SYM
ejpam-4792	67	4	0	0	NUM
ejpam-4792	67	5	in	in	ADP
ejpam-4792	67	6	eq	eq	ADP
ejpam-4792	67	7	.	.	PUNCT
ejpam-4792	68	1	(	(	PUNCT
ejpam-4792	68	2	2	2	NUM
ejpam-4792	68	3	)	)	PUNCT
ejpam-4792	68	4	,	,	PUNCT
ejpam-4792	68	5	gα{y(m)(τ	gα{y(m)(τ	NOUN
ejpam-4792	68	6	)	)	PUNCT
ejpam-4792	68	7	}	}	PUNCT
ejpam-4792	69	1	=	=	SYM
ejpam-4792	69	2	y	y	PROPN
ejpam-4792	69	3	(	(	PUNCT
ejpam-4792	69	4	w	w	NOUN
ejpam-4792	69	5	)	)	PUNCT
ejpam-4792	69	6	wm	wm	PROPN
ejpam-4792	69	7	−	−	PROPN
ejpam-4792	69	8	m−1∑	m−1∑	PRON
ejpam-4792	69	9	k=0	k=0	PROPN
ejpam-4792	69	10	wα−m+k+1y(k)(0	wα−m+k+1y(k)(0	PROPN
ejpam-4792	69	11	)	)	PUNCT
ejpam-4792	69	12	,	,	PUNCT
ejpam-4792	69	13	where	where	SCONJ
ejpam-4792	69	14	y	y	PROPN
ejpam-4792	69	15	(	(	PUNCT
ejpam-4792	69	16	w	w	PROPN
ejpam-4792	69	17	)	)	PUNCT
ejpam-4792	69	18	=	=	SYM
ejpam-4792	69	19	gα{y(τ	gα{y(τ	NOUN
ejpam-4792	69	20	)	)	PUNCT
ejpam-4792	69	21	}	}	PUNCT
ejpam-4792	69	22	.	.	PUNCT
ejpam-4792	70	1	s.	s.	PROPN
ejpam-4792	70	2	sattaso	sattaso	PROPN
ejpam-4792	70	3	,	,	PUNCT
ejpam-4792	70	4	p.	p.	PROPN
ejpam-4792	70	5	prasertsang	prasertsang	PROPN
ejpam-4792	70	6	,	,	PUNCT
ejpam-4792	70	7	t.	t.	PROPN
ejpam-4792	70	8	prasertsang	prasertsang	PROPN
ejpam-4792	70	9	/	/	SYM
ejpam-4792	70	10	eur	eur	PROPN
ejpam-4792	70	11	.	.	PUNCT
ejpam-4792	71	1	j.	j.	PROPN
ejpam-4792	71	2	pure	pure	PROPN
ejpam-4792	71	3	appl	appl	PROPN
ejpam-4792	71	4	.	.	PROPN
ejpam-4792	71	5	math	math	PROPN
ejpam-4792	71	6	,	,	PUNCT
ejpam-4792	71	7	16	16	NUM
ejpam-4792	71	8	(	(	PUNCT
ejpam-4792	71	9	3	3	NUM
ejpam-4792	71	10	)	)	PUNCT
ejpam-4792	71	11	(	(	PUNCT
ejpam-4792	71	12	2023	2023	NUM
ejpam-4792	71	13	)	)	PUNCT
ejpam-4792	71	14	,	,	PUNCT
ejpam-4792	71	15	1389	1389	NUM
ejpam-4792	71	16	-	-	SYM
ejpam-4792	71	17	1405	1405	NUM
ejpam-4792	71	18	1392	1392	NUM
ejpam-4792	71	19	lemma	lemma	PROPN
ejpam-4792	71	20	2	2	NUM
ejpam-4792	71	21	.	.	PUNCT
ejpam-4792	72	1	[	[	X
ejpam-4792	72	2	24	24	NUM
ejpam-4792	72	3	]	]	PUNCT
ejpam-4792	72	4	assume	assume	VERB
ejpam-4792	72	5	that	that	SCONJ
ejpam-4792	72	6	y(τ	y(τ	PROPN
ejpam-4792	72	7	)	)	PUNCT
ejpam-4792	72	8	=	=	NOUN
ejpam-4792	73	1	∑∞	∑∞	NOUN
ejpam-4792	73	2	n=0	n=0	PUNCT
ejpam-4792	74	1	anτ	anτ	NOUN
ejpam-4792	74	2	n	n	PRON
ejpam-4792	74	3	is	be	AUX
ejpam-4792	74	4	a	a	DET
ejpam-4792	74	5	piecewise	piecewise	NOUN
ejpam-4792	74	6	continuous	continuous	ADJ
ejpam-4792	74	7	function	function	NOUN
ejpam-4792	74	8	on	on	ADP
ejpam-4792	74	9	[	[	X
ejpam-4792	74	10	0,∞	0,∞	NOUN
ejpam-4792	74	11	)	)	PUNCT
ejpam-4792	74	12	and	and	CCONJ
ejpam-4792	74	13	has	have	VERB
ejpam-4792	74	14	an	an	DET
ejpam-4792	74	15	exponential	exponential	ADJ
ejpam-4792	74	16	order	order	NOUN
ejpam-4792	74	17	at	at	ADP
ejpam-4792	74	18	infinity	infinity	NOUN
ejpam-4792	74	19	with	with	ADP
ejpam-4792	74	20	the	the	DET
ejpam-4792	74	21	function	function	NOUN
ejpam-4792	74	22	on	on	ADP
ejpam-4792	74	23	|f(τ)|	|f(τ)|	PROPN
ejpam-4792	74	24	≤	≤	NUM
ejpam-4792	74	25	mekτ	mekτ	NOUN
ejpam-4792	74	26	for	for	ADP
ejpam-4792	74	27	τ	τ	PROPN
ejpam-4792	74	28	≥	≥	X
ejpam-4792	74	29	c̄	c̄	VERB
ejpam-4792	74	30	where	where	SCONJ
ejpam-4792	74	31	c̄	c̄	PROPN
ejpam-4792	74	32	is	be	AUX
ejpam-4792	74	33	a	a	DET
ejpam-4792	74	34	constant	constant	ADJ
ejpam-4792	74	35	,	,	PUNCT
ejpam-4792	74	36	then	then	ADV
ejpam-4792	74	37	gα{f(τ	gα{f(τ	NOUN
ejpam-4792	74	38	)	)	PUNCT
ejpam-4792	74	39	}	}	PUNCT
ejpam-4792	75	1	=	=	PUNCT
ejpam-4792	75	2	∞∑	∞∑	NUM
ejpam-4792	75	3	n=0	n=0	SYM
ejpam-4792	75	4	n!anw	n!anw	PROPN
ejpam-4792	75	5	α+n+1	α+n+1	NOUN
ejpam-4792	75	6	.	.	PUNCT
ejpam-4792	76	1	3	3	X
ejpam-4792	76	2	.	.	X
ejpam-4792	76	3	analytical	analytical	ADJ
ejpam-4792	76	4	study	study	NOUN
ejpam-4792	76	5	for	for	ADP
ejpam-4792	76	6	hodepcs	hodepc	NOUN
ejpam-4792	76	7	via	via	ADP
ejpam-4792	76	8	gα	gα	NOUN
ejpam-4792	76	9	-	-	PUNCT
ejpam-4792	76	10	transform	transform	NOUN
ejpam-4792	76	11	denote	denote	NOUN
ejpam-4792	76	12	n	n	CCONJ
ejpam-4792	76	13	,	,	PUNCT
ejpam-4792	76	14	m	m	VERB
ejpam-4792	76	15	∈	∈	NOUN
ejpam-4792	76	16	n	n	ADV
ejpam-4792	76	17	∪	∪	X
ejpam-4792	76	18	{	{	PUNCT
ejpam-4792	76	19	0	0	NUM
ejpam-4792	76	20	}	}	PUNCT
ejpam-4792	76	21	and	and	CCONJ
ejpam-4792	76	22	m	m	PROPN
ejpam-4792	76	23	≥	≥	NOUN
ejpam-4792	76	24	n	n	CCONJ
ejpam-4792	76	25	,	,	PUNCT
ejpam-4792	76	26	ϱ	ϱ	X
ejpam-4792	76	27	=	=	SYM
ejpam-4792	76	28	2	2	NUM
ejpam-4792	76	29	,	,	PUNCT
ejpam-4792	76	30	3	3	NUM
ejpam-4792	76	31	,	,	PUNCT
ejpam-4792	76	32	4	4	NUM
ejpam-4792	76	33	,	,	PUNCT
ejpam-4792	76	34	.	.	PUNCT
ejpam-4792	76	35	.	.	PUNCT
ejpam-4792	77	1	.	.	PUNCT
ejpam-4792	78	1	,	,	PUNCT
ejpam-4792	78	2	n	n	CCONJ
ejpam-4792	78	3	,	,	PUNCT
ejpam-4792	78	4	ϱ1	ϱ1	NOUN
ejpam-4792	78	5	=	=	SYM
ejpam-4792	78	6	0	0	NUM
ejpam-4792	78	7	,	,	PUNCT
ejpam-4792	78	8	1	1	NUM
ejpam-4792	78	9	,	,	PUNCT
ejpam-4792	78	10	2	2	NUM
ejpam-4792	78	11	,	,	PUNCT
ejpam-4792	78	12	.	.	PUNCT
ejpam-4792	78	13	.	.	PUNCT
ejpam-4792	79	1	.	.	PUNCT
ejpam-4792	80	1	,	,	PUNCT
ejpam-4792	80	2	n−	n−	NOUN
ejpam-4792	80	3	1	1	NUM
ejpam-4792	80	4	,	,	PUNCT
ejpam-4792	80	5	ϱ2	ϱ2	NOUN
ejpam-4792	80	6	=	=	SYM
ejpam-4792	80	7	0	0	NUM
ejpam-4792	80	8	,	,	PUNCT
ejpam-4792	80	9	1	1	NUM
ejpam-4792	80	10	,	,	PUNCT
ejpam-4792	80	11	2	2	NUM
ejpam-4792	80	12	,	,	PUNCT
ejpam-4792	80	13	.	.	PUNCT
ejpam-4792	80	14	.	.	PUNCT
ejpam-4792	81	1	.	.	PUNCT
ejpam-4792	82	1	,	,	PUNCT
ejpam-4792	82	2	n	n	CCONJ
ejpam-4792	82	3	,	,	PUNCT
ejpam-4792	82	4	ρ	ρ	PROPN
ejpam-4792	82	5	=	=	SYM
ejpam-4792	82	6	0	0	NUM
ejpam-4792	82	7	,	,	PUNCT
ejpam-4792	82	8	1	1	NUM
ejpam-4792	82	9	,	,	PUNCT
ejpam-4792	82	10	2	2	NUM
ejpam-4792	82	11	,	,	PUNCT
ejpam-4792	82	12	.	.	PUNCT
ejpam-4792	83	1	.	.	PUNCT
ejpam-4792	83	2	.	.	PUNCT
ejpam-4792	84	1	,	,	PUNCT
ejpam-4792	84	2	m	m	PROPN
ejpam-4792	84	3	,	,	PUNCT
ejpam-4792	84	4	ρ1	ρ1	NOUN
ejpam-4792	84	5	=	=	PUNCT
ejpam-4792	84	6	m−	m−	PROPN
ejpam-4792	84	7	(	(	PUNCT
ejpam-4792	84	8	n−	n−	NOUN
ejpam-4792	84	9	ϱ1	ϱ1	NOUN
ejpam-4792	84	10	−	−	PROPN
ejpam-4792	84	11	1),m−	1),m−	NUM
ejpam-4792	84	12	(	(	PUNCT
ejpam-4792	84	13	n−	n−	NOUN
ejpam-4792	84	14	ϱ1	ϱ1	NOUN
ejpam-4792	84	15	−	−	PROPN
ejpam-4792	84	16	2),m−	2),m−	PROPN
ejpam-4792	84	17	(	(	PUNCT
ejpam-4792	84	18	n−	n−	NOUN
ejpam-4792	84	19	ϱ1	ϱ1	NOUN
ejpam-4792	84	20	−	−	PROPN
ejpam-4792	84	21	3	3	NUM
ejpam-4792	84	22	)	)	PUNCT
ejpam-4792	84	23	,	,	PUNCT
ejpam-4792	84	24	.	.	PUNCT
ejpam-4792	84	25	.	.	PUNCT
ejpam-4792	85	1	.	.	PUNCT
ejpam-4792	86	1	,	,	PUNCT
ejpam-4792	86	2	m−	m−	PROPN
ejpam-4792	86	3	2,m−	2,m−	NUM
ejpam-4792	86	4	1,m	1,m	NOUN
ejpam-4792	86	5	,	,	PUNCT
ejpam-4792	86	6	ρ2	ρ2	NOUN
ejpam-4792	86	7	=	=	SYM
ejpam-4792	86	8	ϱ1	ϱ1	PROPN
ejpam-4792	86	9	+	+	CCONJ
ejpam-4792	86	10	1	1	NUM
ejpam-4792	86	11	,	,	PUNCT
ejpam-4792	86	12	ϱ1	ϱ1	NOUN
ejpam-4792	86	13	+	+	CCONJ
ejpam-4792	86	14	2	2	NUM
ejpam-4792	86	15	,	,	PUNCT
ejpam-4792	86	16	ϱ1	ϱ1	NOUN
ejpam-4792	86	17	+	+	CCONJ
ejpam-4792	86	18	3	3	NUM
ejpam-4792	86	19	,	,	PUNCT
ejpam-4792	86	20	.	.	PUNCT
ejpam-4792	86	21	.	.	PUNCT
ejpam-4792	87	1	.	.	PUNCT
ejpam-4792	88	1	,	,	PUNCT
ejpam-4792	88	2	n−	n−	NOUN
ejpam-4792	88	3	2	2	NUM
ejpam-4792	88	4	,	,	PUNCT
ejpam-4792	88	5	n−	n−	NOUN
ejpam-4792	88	6	1	1	NUM
ejpam-4792	88	7	,	,	PUNCT
ejpam-4792	88	8	n	n	CCONJ
ejpam-4792	88	9	,	,	PUNCT
ejpam-4792	88	10	ρ3	ρ3	NOUN
ejpam-4792	88	11	=	=	SYM
ejpam-4792	88	12	0	0	NUM
ejpam-4792	88	13	,	,	PUNCT
ejpam-4792	88	14	1	1	NUM
ejpam-4792	88	15	,	,	PUNCT
ejpam-4792	88	16	2	2	NUM
ejpam-4792	88	17	,	,	PUNCT
ejpam-4792	88	18	.	.	PUNCT
ejpam-4792	88	19	.	.	PUNCT
ejpam-4792	89	1	.	.	PUNCT
ejpam-4792	90	1	,	,	PUNCT
ejpam-4792	90	2	m−	m−	PROPN
ejpam-4792	90	3	(	(	PUNCT
ejpam-4792	90	4	n−	n−	NOUN
ejpam-4792	90	5	ϱ1	ϱ1	NOUN
ejpam-4792	90	6	+	+	CCONJ
ejpam-4792	90	7	2),m−	2),m−	NUM
ejpam-4792	90	8	(	(	PUNCT
ejpam-4792	90	9	n−	n−	NOUN
ejpam-4792	90	10	ϱ1	ϱ1	NOUN
ejpam-4792	90	11	+	+	CCONJ
ejpam-4792	90	12	1),m−	1),m−	NUM
ejpam-4792	90	13	(	(	PUNCT
ejpam-4792	90	14	n−	n−	NOUN
ejpam-4792	90	15	ϱ1	ϱ1	PROPN
ejpam-4792	90	16	)	)	PUNCT
ejpam-4792	90	17	,	,	PUNCT
ejpam-4792	90	18	υ(u	υ(u	NUM
ejpam-4792	90	19	)	)	PUNCT
ejpam-4792	90	20	=	=	SYM
ejpam-4792	90	21	aρ,0	aρ,0	PROPN
ejpam-4792	90	22	ρ−1∑	ρ−1∑	NUM
ejpam-4792	90	23	k=0	k=0	PROPN
ejpam-4792	90	24	uα−ρ+k+1y(k)(0	uα−ρ+k+1y(k)(0	ADJ
ejpam-4792	90	25	)	)	PUNCT
ejpam-4792	91	1	+	+	NUM
ejpam-4792	91	2	aρ,1	aρ,1	NOUN
ejpam-4792	91	3	ρ−1∑	ρ−1∑	NUM
ejpam-4792	91	4	k=0	k=0	PROPN
ejpam-4792	91	5	(	(	PUNCT
ejpam-4792	91	6	−ρ+	−ρ+	PROPN
ejpam-4792	91	7	k	k	PROPN
ejpam-4792	91	8	+	+	PROPN
ejpam-4792	91	9	1)uα−ρ+k+2y(k)(0	1)uα−ρ+k+2y(k)(0	NUM
ejpam-4792	91	10	)	)	PUNCT
ejpam-4792	91	11	+	+	NOUN
ejpam-4792	91	12	aρ,ϱ	aρ,ϱ	X
ejpam-4792	91	13	ρ−1∑	ρ−1∑	PRON
ejpam-4792	91	14	k=0	k=0	PUNCT
ejpam-4792	91	15	ϱ∏	ϱ∏	PROPN
ejpam-4792	92	1	l=1	l=1	PROPN
ejpam-4792	92	2	(	(	PUNCT
ejpam-4792	92	3	−ρ+	−ρ+	PROPN
ejpam-4792	92	4	k	k	PROPN
ejpam-4792	92	5	+	+	PROPN
ejpam-4792	92	6	l)uα−ρ+k+l+1y(k)(0	l)uα−ρ+k+l+1y(k)(0	PROPN
ejpam-4792	92	7	)	)	PUNCT
ejpam-4792	92	8	,	,	PUNCT
ejpam-4792	92	9	θϱ2(u	θϱ2(u	NOUN
ejpam-4792	92	10	)	)	PUNCT
ejpam-4792	92	11	=	=	PUNCT
ejpam-4792	92	12	m∑	m∑	NOUN
ejpam-4792	92	13	ρ=0	ρ=0	PUNCT
ejpam-4792	92	14	aρ,ϱ2	aρ,ϱ2	NOUN
ejpam-4792	92	15	uρ−2ϱ2	uρ−2ϱ2	NOUN
ejpam-4792	92	16	−	−	PROPN
ejpam-4792	92	17	(	(	PUNCT
ejpam-4792	92	18	ϱ2	ϱ2	NOUN
ejpam-4792	92	19	+	+	CCONJ
ejpam-4792	92	20	1	1	NUM
ejpam-4792	92	21	ϱ2	ϱ2	NOUN
ejpam-4792	92	22	)	)	PUNCT
ejpam-4792	92	23	m∑	m∑	CCONJ
ejpam-4792	92	24	ρ=0	ρ=0	PUNCT
ejpam-4792	92	25	(	(	PUNCT
ejpam-4792	92	26	ρ+	ρ+	NOUN
ejpam-4792	92	27	α−	α−	ADP
ejpam-4792	92	28	ϱ2	ϱ2	NOUN
ejpam-4792	92	29	)	)	PUNCT
ejpam-4792	92	30	aρ,ϱ2	aρ,ϱ2	PROPN
ejpam-4792	93	1	+	+	ADJ
ejpam-4792	93	2	1	1	NUM
ejpam-4792	93	3	uρ−ϱ2−(ϱ2	uρ−ϱ2−(ϱ2	ADJ
ejpam-4792	93	4	+	+	NOUN
ejpam-4792	93	5	1	1	NUM
ejpam-4792	93	6	)	)	PUNCT
ejpam-4792	93	7	+	+	CCONJ
ejpam-4792	93	8	(	(	PUNCT
ejpam-4792	93	9	ϱ2	ϱ2	NOUN
ejpam-4792	93	10	+	+	CCONJ
ejpam-4792	93	11	2	2	NUM
ejpam-4792	93	12	ϱ2	ϱ2	NOUN
ejpam-4792	93	13	)	)	PUNCT
ejpam-4792	93	14	m∑	m∑	VERB
ejpam-4792	94	1	ρ=0	ρ=0	ADJ
ejpam-4792	94	2	ϱ2	ϱ2	ADJ
ejpam-4792	94	3	+	+	ADJ
ejpam-4792	94	4	1∏	1∏	NUM
ejpam-4792	94	5	s=ϱ2	s=ϱ2	NOUN
ejpam-4792	94	6	(	(	PUNCT
ejpam-4792	94	7	ρ+	ρ+	NOUN
ejpam-4792	94	8	α−	α−	ADP
ejpam-4792	94	9	s	s	NOUN
ejpam-4792	94	10	)	)	PUNCT
ejpam-4792	94	11	aρ,ϱ2	aρ,ϱ2	PROPN
ejpam-4792	94	12	+	+	ADJ
ejpam-4792	94	13	2	2	NUM
ejpam-4792	94	14	uρ−ϱ2−(ϱ1	uρ−ϱ2−(ϱ1	NOUN
ejpam-4792	94	15	+	+	NOUN
ejpam-4792	94	16	2	2	NUM
ejpam-4792	94	17	)	)	PUNCT
ejpam-4792	94	18	−	−	PROPN
ejpam-4792	95	1	(	(	PUNCT
ejpam-4792	95	2	ϱ2	ϱ2	NOUN
ejpam-4792	95	3	+	+	CCONJ
ejpam-4792	95	4	3	3	NUM
ejpam-4792	95	5	ϱ2	ϱ2	NOUN
ejpam-4792	95	6	)	)	PUNCT
ejpam-4792	95	7	m∑	m∑	VERB
ejpam-4792	96	1	ρ=0	ρ=0	ADJ
ejpam-4792	96	2	ϱ2	ϱ2	ADJ
ejpam-4792	96	3	+	+	NOUN
ejpam-4792	96	4	2∏	2∏	NUM
ejpam-4792	96	5	s=ϱ2	s=ϱ2	NOUN
ejpam-4792	96	6	(	(	PUNCT
ejpam-4792	96	7	ρ+	ρ+	NOUN
ejpam-4792	96	8	α−	α−	ADP
ejpam-4792	96	9	s	s	NOUN
ejpam-4792	96	10	)	)	PUNCT
ejpam-4792	96	11	aρ,ϱ2	aρ,ϱ2	PROPN
ejpam-4792	97	1	+	+	NOUN
ejpam-4792	97	2	3	3	NUM
ejpam-4792	97	3	uρ−ϱ2−(ϱ2	uρ−ϱ2−(ϱ2	ADJ
ejpam-4792	97	4	+	+	NOUN
ejpam-4792	97	5	3	3	NUM
ejpam-4792	97	6	)	)	PUNCT
ejpam-4792	98	1	+	+	PUNCT
ejpam-4792	98	2	·	·	PUNCT
ejpam-4792	98	3	·	·	PUNCT
ejpam-4792	98	4	·	·	PUNCT
ejpam-4792	99	1	+	+	X
ejpam-4792	99	2	(	(	PUNCT
ejpam-4792	99	3	−1)n−2−ϱ2	−1)n−2−ϱ2	PROPN
ejpam-4792	99	4	(	(	PUNCT
ejpam-4792	99	5	n−	n−	NOUN
ejpam-4792	99	6	2	2	NUM
ejpam-4792	99	7	ϱ2	ϱ2	NOUN
ejpam-4792	99	8	)	)	PUNCT
ejpam-4792	99	9	m∑	m∑	PRON
ejpam-4792	99	10	ρ=ϱ2	ρ=ϱ2	PROPN
ejpam-4792	99	11	n−3∏	n−3∏	PROPN
ejpam-4792	99	12	s=ϱ2	s=ϱ2	NOUN
ejpam-4792	99	13	(	(	PUNCT
ejpam-4792	99	14	ρ+	ρ+	NOUN
ejpam-4792	99	15	α−	α−	ADP
ejpam-4792	99	16	s	s	NOUN
ejpam-4792	99	17	)	)	PUNCT
ejpam-4792	99	18	aρ	aρ	NOUN
ejpam-4792	99	19	,	,	PUNCT
ejpam-4792	99	20	n−2	n−2	PROPN
ejpam-4792	99	21	uρ−ϱ2−n+2	uρ−ϱ2−n+2	ADJ
ejpam-4792	99	22	+	+	PROPN
ejpam-4792	99	23	(	(	PUNCT
ejpam-4792	99	24	−1)n−1−ϱ2	−1)n−1−ϱ2	PROPN
ejpam-4792	99	25	(	(	PUNCT
ejpam-4792	99	26	n−	n−	PROPN
ejpam-4792	99	27	1	1	NUM
ejpam-4792	99	28	ϱ2	ϱ2	NOUN
ejpam-4792	99	29	)	)	PUNCT
ejpam-4792	99	30	m∑	m∑	SCONJ
ejpam-4792	99	31	ρ=ϱ2	ρ=ϱ2	PROPN
ejpam-4792	99	32	n−2∏	n−2∏	ADJ
ejpam-4792	99	33	s=ϱ2	s=ϱ2	NOUN
ejpam-4792	99	34	(	(	PUNCT
ejpam-4792	99	35	ρ+	ρ+	NOUN
ejpam-4792	99	36	α−	α−	ADP
ejpam-4792	99	37	s	s	NOUN
ejpam-4792	99	38	)	)	PUNCT
ejpam-4792	99	39	aρ,ϱ2+n−1	aρ,ϱ2+n−1	PUNCT
ejpam-4792	99	40	uρ−ϱ2−n+1	uρ−ϱ2−n+1	PUNCT
ejpam-4792	100	1	+	+	NOUN
ejpam-4792	100	2	(	(	PUNCT
ejpam-4792	100	3	−1)n−ϱ2	−1)n−ϱ2	ADJ
ejpam-4792	100	4	(	(	PUNCT
ejpam-4792	100	5	n	n	X
ejpam-4792	100	6	ϱ2	ϱ2	NOUN
ejpam-4792	100	7	)	)	PUNCT
ejpam-4792	100	8	m∑	m∑	CCONJ
ejpam-4792	100	9	ρ=ϱ1	ρ=ϱ1	PROPN
ejpam-4792	100	10	n−1∏	n−1∏	ADV
ejpam-4792	100	11	s=ϱ2	s=ϱ2	NOUN
ejpam-4792	100	12	(	(	PUNCT
ejpam-4792	100	13	ρ+	ρ+	NOUN
ejpam-4792	100	14	α−	α−	ADP
ejpam-4792	100	15	s	s	NOUN
ejpam-4792	100	16	)	)	PUNCT
ejpam-4792	100	17	aρ	aρ	NOUN
ejpam-4792	100	18	,	,	PUNCT
ejpam-4792	100	19	n	n	CCONJ
ejpam-4792	100	20	uρ−ϱ2−n	uρ−ϱ2−n	PUNCT
ejpam-4792	100	21	.	.	PUNCT
ejpam-4792	101	1	theorem	theorem	NOUN
ejpam-4792	101	2	1	1	X
ejpam-4792	101	3	.	.	PUNCT
ejpam-4792	101	4	consider	consider	VERB
ejpam-4792	101	5	the	the	DET
ejpam-4792	101	6	higher	high	ADJ
ejpam-4792	101	7	-	-	PUNCT
ejpam-4792	101	8	order	order	NOUN
ejpam-4792	101	9	differential	differential	ADJ
ejpam-4792	101	10	equation	equation	NOUN
ejpam-4792	101	11	in	in	ADP
ejpam-4792	101	12	the	the	DET
ejpam-4792	101	13	form	form	NOUN
ejpam-4792	101	14	m∑	m∑	X
ejpam-4792	101	15	i=0	i=0	PROPN
ejpam-4792	101	16	(	(	PUNCT
ejpam-4792	101	17	n∑	n∑	NOUN
ejpam-4792	101	18	j=0	j=0	PROPN
ejpam-4792	101	19	ai	ai	VERB
ejpam-4792	101	20	,	,	PUNCT
ejpam-4792	101	21	jτ	jτ	PROPN
ejpam-4792	101	22	j)y(i)(τ	j)y(i)(τ	PROPN
ejpam-4792	101	23	)	)	PUNCT
ejpam-4792	102	1	=	=	SYM
ejpam-4792	102	2	φ(τ	φ(τ	NOUN
ejpam-4792	102	3	)	)	PUNCT
ejpam-4792	102	4	,	,	PUNCT
ejpam-4792	102	5	(	(	PUNCT
ejpam-4792	102	6	3	3	X
ejpam-4792	102	7	)	)	PUNCT
ejpam-4792	102	8	s.	s.	PROPN
ejpam-4792	102	9	sattaso	sattaso	PROPN
ejpam-4792	102	10	,	,	PUNCT
ejpam-4792	102	11	p.	p.	PROPN
ejpam-4792	102	12	prasertsang	prasertsang	PROPN
ejpam-4792	102	13	,	,	PUNCT
ejpam-4792	102	14	t.	t.	PROPN
ejpam-4792	102	15	prasertsang	prasertsang	PROPN
ejpam-4792	102	16	/	/	SYM
ejpam-4792	102	17	eur	eur	PROPN
ejpam-4792	102	18	.	.	PUNCT
ejpam-4792	103	1	j.	j.	PROPN
ejpam-4792	103	2	pure	pure	PROPN
ejpam-4792	103	3	appl	appl	PROPN
ejpam-4792	103	4	.	.	PROPN
ejpam-4792	103	5	math	math	PROPN
ejpam-4792	103	6	,	,	PUNCT
ejpam-4792	103	7	16	16	NUM
ejpam-4792	103	8	(	(	PUNCT
ejpam-4792	103	9	3	3	NUM
ejpam-4792	103	10	)	)	PUNCT
ejpam-4792	103	11	(	(	PUNCT
ejpam-4792	103	12	2023	2023	NUM
ejpam-4792	103	13	)	)	PUNCT
ejpam-4792	103	14	,	,	PUNCT
ejpam-4792	103	15	1389	1389	NUM
ejpam-4792	103	16	-	-	SYM
ejpam-4792	103	17	1405	1405	NUM
ejpam-4792	103	18	1393	1393	NUM
ejpam-4792	103	19	where	where	SCONJ
ejpam-4792	103	20	∑n	∑n	PROPN
ejpam-4792	103	21	j=0	j=0	PROPN
ejpam-4792	103	22	ai	ai	VERB
ejpam-4792	103	23	,	,	PUNCT
ejpam-4792	103	24	jτ	jτ	PROPN
ejpam-4792	103	25	j	j	PROPN
ejpam-4792	103	26	are	be	AUX
ejpam-4792	103	27	polynomial	polynomial	ADJ
ejpam-4792	103	28	functions	function	NOUN
ejpam-4792	103	29	with	with	ADP
ejpam-4792	103	30	degree	degree	NOUN
ejpam-4792	103	31	n	n	CCONJ
ejpam-4792	103	32	in	in	ADP
ejpam-4792	103	33	terms	term	NOUN
ejpam-4792	103	34	of	of	ADP
ejpam-4792	103	35	τ	τ	PROPN
ejpam-4792	103	36	where	where	SCONJ
ejpam-4792	103	37	i	i	PRON
ejpam-4792	103	38	=	=	NOUN
ejpam-4792	103	39	0	0	NUM
ejpam-4792	103	40	,	,	PUNCT
ejpam-4792	103	41	1	1	NUM
ejpam-4792	103	42	,	,	PUNCT
ejpam-4792	103	43	2	2	NUM
ejpam-4792	103	44	,	,	PUNCT
ejpam-4792	103	45	.	.	PUNCT
ejpam-4792	103	46	.	.	PUNCT
ejpam-4792	103	47	.	.	PUNCT
ejpam-4792	104	1	,	,	PUNCT
ejpam-4792	104	2	m	m	PROPN
ejpam-4792	104	3	,	,	PUNCT
ejpam-4792	104	4	j	j	PROPN
ejpam-4792	104	5	=	=	SYM
ejpam-4792	104	6	0	0	NUM
ejpam-4792	104	7	,	,	PUNCT
ejpam-4792	104	8	1	1	NUM
ejpam-4792	104	9	,	,	PUNCT
ejpam-4792	104	10	2	2	NUM
ejpam-4792	104	11	,	,	PUNCT
ejpam-4792	104	12	.	.	PUNCT
ejpam-4792	104	13	.	.	PUNCT
ejpam-4792	105	1	.	.	PUNCT
ejpam-4792	106	1	,	,	PUNCT
ejpam-4792	106	2	n	n	CCONJ
ejpam-4792	106	3	,	,	PUNCT
ejpam-4792	106	4	where	where	SCONJ
ejpam-4792	106	5	m	m	VERB
ejpam-4792	106	6	≥	≥	NOUN
ejpam-4792	106	7	n	n	ADV
ejpam-4792	106	8	and	and	CCONJ
ejpam-4792	106	9	ai	ai	VERB
ejpam-4792	106	10	,	,	PUNCT
ejpam-4792	106	11	j	j	PROPN
ejpam-4792	106	12	are	be	AUX
ejpam-4792	106	13	polynomial	polynomial	ADJ
ejpam-4792	106	14	coefficients	coefficient	NOUN
ejpam-4792	106	15	with	with	ADP
ejpam-4792	106	16	am	am	NOUN
ejpam-4792	106	17	,	,	PUNCT
ejpam-4792	106	18	n	n	PRON
ejpam-4792	106	19	̸=	̸=	PROPN
ejpam-4792	106	20	0	0	NUM
ejpam-4792	106	21	and	and	CCONJ
ejpam-4792	106	22	φ(τ	φ(τ	NOUN
ejpam-4792	106	23	)	)	PUNCT
ejpam-4792	107	1	is	be	AUX
ejpam-4792	107	2	an	an	DET
ejpam-4792	107	3	unknown	unknown	ADJ
ejpam-4792	107	4	function	function	NOUN
ejpam-4792	107	5	.	.	PUNCT
ejpam-4792	108	1	if	if	SCONJ
ejpam-4792	108	2	eq	eq	ADJ
ejpam-4792	108	3	.	.	PUNCT
ejpam-4792	109	1	(	(	PUNCT
ejpam-4792	109	2	3	3	X
ejpam-4792	109	3	)	)	PUNCT
ejpam-4792	109	4	satisfies	satisfy	VERB
ejpam-4792	109	5	the	the	DET
ejpam-4792	109	6	following	follow	VERB
ejpam-4792	109	7	conditions	condition	NOUN
ejpam-4792	109	8	aρ1,ϱ1	aρ1,ϱ1	VERB
ejpam-4792	109	9	=	=	SYM
ejpam-4792	109	10	0	0	NUM
ejpam-4792	109	11	,	,	PUNCT
ejpam-4792	109	12	(	(	PUNCT
ejpam-4792	109	13	4	4	NUM
ejpam-4792	109	14	)	)	PUNCT
ejpam-4792	109	15	n∑	n∑	NOUN
ejpam-4792	109	16	j	j	PROPN
ejpam-4792	110	1	=	=	X
ejpam-4792	110	2	ρ2	ρ2	PROPN
ejpam-4792	110	3	(	(	PUNCT
ejpam-4792	110	4	−1)j−ϱ1	−1)j−ϱ1	NUM
ejpam-4792	110	5	(	(	PUNCT
ejpam-4792	110	6	j	j	PROPN
ejpam-4792	110	7	ϱ1	ϱ1	PROPN
ejpam-4792	110	8	)	)	PUNCT
ejpam-4792	111	1	j−1∏	j−1∏	ADP
ejpam-4792	111	2	s=ϱ1	s=ϱ1	PROPN
ejpam-4792	111	3	(	(	PUNCT
ejpam-4792	111	4	−ρ2	−ρ2	PROPN
ejpam-4792	111	5	+	+	NUM
ejpam-4792	111	6	j	j	PROPN
ejpam-4792	111	7	+	+	CCONJ
ejpam-4792	111	8	α−	α−	ADP
ejpam-4792	111	9	s)a−ρ2+j	s)a−ρ2+j	NOUN
ejpam-4792	111	10	,	,	PUNCT
ejpam-4792	111	11	j	j	PROPN
ejpam-4792	111	12	=	=	SYM
ejpam-4792	111	13	0	0	PROPN
ejpam-4792	111	14	,	,	PUNCT
ejpam-4792	111	15	(	(	PUNCT
ejpam-4792	111	16	5	5	NUM
ejpam-4792	111	17	)	)	PUNCT
ejpam-4792	111	18	aρ3,ϱ1	aρ3,ϱ1	VERB
ejpam-4792	112	1	+	+	CCONJ
ejpam-4792	113	1	n∑	n∑	PROPN
ejpam-4792	113	2	j=ϱ1	j=ϱ1	NOUN
ejpam-4792	113	3	+	+	NOUN
ejpam-4792	113	4	1	1	NUM
ejpam-4792	113	5	(	(	PUNCT
ejpam-4792	113	6	−1)j−ϱ1	−1)j−ϱ1	NUM
ejpam-4792	113	7	(	(	PUNCT
ejpam-4792	113	8	j	j	PROPN
ejpam-4792	113	9	ϱ1	ϱ1	PROPN
ejpam-4792	113	10	)	)	PUNCT
ejpam-4792	114	1	j−1∏	j−1∏	ADP
ejpam-4792	114	2	s=ϱ1	s=ϱ1	PROPN
ejpam-4792	114	3	(	(	PUNCT
ejpam-4792	114	4	ρ3	ρ3	NOUN
ejpam-4792	114	5	−	−	PROPN
ejpam-4792	114	6	ϱ1	ϱ1	NOUN
ejpam-4792	114	7	+	+	CCONJ
ejpam-4792	114	8	j	j	PROPN
ejpam-4792	114	9	+	+	CCONJ
ejpam-4792	114	10	α−	α−	ADP
ejpam-4792	114	11	s)aρ3−ϱ1+j	s)aρ3−ϱ1+j	NOUN
ejpam-4792	114	12	,	,	PUNCT
ejpam-4792	114	13	j	j	PROPN
ejpam-4792	114	14	=	=	SYM
ejpam-4792	114	15	0	0	PROPN
ejpam-4792	114	16	,	,	PUNCT
ejpam-4792	114	17	(	(	PUNCT
ejpam-4792	114	18	6	6	NUM
ejpam-4792	114	19	)	)	PUNCT
ejpam-4792	114	20	then	then	ADV
ejpam-4792	114	21	,	,	PUNCT
ejpam-4792	114	22	it	it	PRON
ejpam-4792	114	23	is	be	AUX
ejpam-4792	114	24	appropriately	appropriately	ADV
ejpam-4792	114	25	solved	solve	VERB
ejpam-4792	114	26	using	use	VERB
ejpam-4792	114	27	the	the	DET
ejpam-4792	114	28	gα	gα	NOUN
ejpam-4792	114	29	-	-	PUNCT
ejpam-4792	114	30	transform	transform	NOUN
ejpam-4792	114	31	.	.	PUNCT
ejpam-4792	115	1	proof	proof	NOUN
ejpam-4792	115	2	.	.	PUNCT
ejpam-4792	116	1	taking	take	VERB
ejpam-4792	116	2	the	the	DET
ejpam-4792	116	3	gα	gα	NOUN
ejpam-4792	116	4	-	-	PUNCT
ejpam-4792	116	5	transform	transform	NOUN
ejpam-4792	116	6	along	along	ADP
ejpam-4792	116	7	both	both	DET
ejpam-4792	116	8	sides	side	NOUN
ejpam-4792	116	9	of	of	ADP
ejpam-4792	116	10	(	(	PUNCT
ejpam-4792	116	11	3	3	NUM
ejpam-4792	116	12	)	)	PUNCT
ejpam-4792	116	13	and	and	CCONJ
ejpam-4792	116	14	applying	apply	VERB
ejpam-4792	116	15	eq	eq	ADP
ejpam-4792	116	16	.	.	PUNCT
ejpam-4792	117	1	(	(	PUNCT
ejpam-4792	117	2	2	2	NUM
ejpam-4792	117	3	)	)	PUNCT
ejpam-4792	117	4	,	,	PUNCT
ejpam-4792	117	5	it	it	PRON
ejpam-4792	117	6	follows	follow	VERB
ejpam-4792	117	7	that	that	SCONJ
ejpam-4792	117	8	,	,	PUNCT
ejpam-4792	117	9	m∑	m∑	CCONJ
ejpam-4792	117	10	ρ=0	ρ=0	PRON
ejpam-4792	117	11	aρ,ϱ2	aρ,ϱ2	NOUN
ejpam-4792	118	1	ϱ2∑	ϱ2∑	PRON
ejpam-4792	119	1	l=0	l=0	PROPN
ejpam-4792	119	2	(	(	PUNCT
ejpam-4792	119	3	−1)n−l	−1)n−l	PROPN
ejpam-4792	119	4	(	(	PUNCT
ejpam-4792	119	5	ϱ2	ϱ2	PROPN
ejpam-4792	119	6	l	l	NOUN
ejpam-4792	119	7	)	)	PUNCT
ejpam-4792	119	8	ϱ2−1∏	ϱ2−1∏	PROPN
ejpam-4792	119	9	s	s	PROPN
ejpam-4792	119	10	=	=	PROPN
ejpam-4792	119	11	l	l	X
ejpam-4792	119	12	(	(	PUNCT
ejpam-4792	119	13	ρ+	ρ+	NOUN
ejpam-4792	119	14	α−	α−	ADP
ejpam-4792	119	15	s	s	NOUN
ejpam-4792	119	16	)	)	PUNCT
ejpam-4792	119	17	y	y	PROPN
ejpam-4792	119	18	(	(	PUNCT
ejpam-4792	119	19	l)(u	l)(u	PROPN
ejpam-4792	119	20	)	)	PUNCT
ejpam-4792	119	21	uρ−ϱ2−l	uρ−ϱ2−l	NUM
ejpam-4792	120	1	−	−	PROPN
ejpam-4792	120	2	m∑	m∑	ADV
ejpam-4792	120	3	ρ=0	ρ=0	PRON
ejpam-4792	120	4	aρ,ϱ2	aρ,ϱ2	NOUN
ejpam-4792	120	5	ρ−1∑	ρ−1∑	NUM
ejpam-4792	121	1	k=0	k=0	PRON
ejpam-4792	121	2	ϱ2∏	ϱ2∏	PROPN
ejpam-4792	122	1	l=1	l=1	PROPN
ejpam-4792	122	2	(	(	PUNCT
ejpam-4792	122	3	−ρ+	−ρ+	PROPN
ejpam-4792	122	4	k	k	PROPN
ejpam-4792	122	5	+	+	PROPN
ejpam-4792	122	6	l)uα−ρ+k+l+1y(k)(0	l)uα−ρ+k+l+1y(k)(0	PROPN
ejpam-4792	122	7	)	)	PUNCT
ejpam-4792	122	8	=	=	VERB
ejpam-4792	123	1	gα	gα	ADP
ejpam-4792	123	2	[	[	NOUN
ejpam-4792	123	3	φ(τ	φ(τ	NOUN
ejpam-4792	123	4	)	)	PUNCT
ejpam-4792	123	5	]	]	PUNCT
ejpam-4792	123	6	,	,	PUNCT
ejpam-4792	123	7	(	(	PUNCT
ejpam-4792	123	8	7	7	X
ejpam-4792	123	9	)	)	PUNCT
ejpam-4792	123	10	for	for	ADP
ejpam-4792	123	11	ϱ2	ϱ2	NOUN
ejpam-4792	123	12	=	=	SYM
ejpam-4792	123	13	0	0	NUM
ejpam-4792	123	14	,	,	PUNCT
ejpam-4792	123	15	1	1	NUM
ejpam-4792	123	16	,	,	PUNCT
ejpam-4792	123	17	2	2	NUM
ejpam-4792	123	18	,	,	PUNCT
ejpam-4792	123	19	.	.	PUNCT
ejpam-4792	123	20	.	.	PUNCT
ejpam-4792	123	21	.	.	PUNCT
ejpam-4792	124	1	,	,	PUNCT
ejpam-4792	124	2	n.	n.	PROPN
ejpam-4792	124	3	therefore	therefore	ADV
ejpam-4792	124	4	,	,	PUNCT
ejpam-4792	124	5	eq	eq	ADJ
ejpam-4792	124	6	.	.	PUNCT
ejpam-4792	125	1	(	(	PUNCT
ejpam-4792	125	2	7	7	X
ejpam-4792	125	3	)	)	PUNCT
ejpam-4792	125	4	can	can	AUX
ejpam-4792	125	5	be	be	AUX
ejpam-4792	125	6	represented	represent	VERB
ejpam-4792	125	7	in	in	ADP
ejpam-4792	125	8	terms	term	NOUN
ejpam-4792	125	9	of	of	ADP
ejpam-4792	125	10	all	all	DET
ejpam-4792	125	11	derivatives	derivative	NOUN
ejpam-4792	125	12	of	of	ADP
ejpam-4792	125	13	y	y	PROPN
ejpam-4792	125	14	(	(	PUNCT
ejpam-4792	125	15	u	u	NOUN
ejpam-4792	125	16	)	)	PUNCT
ejpam-4792	125	17	as	as	SCONJ
ejpam-4792	125	18	follows	follow	VERB
ejpam-4792	125	19	n∑	n∑	PROPN
ejpam-4792	125	20	ϱ2=0	ϱ2=0	PROPN
ejpam-4792	125	21	y	y	PROPN
ejpam-4792	125	22	(	(	PUNCT
ejpam-4792	125	23	ϱ2)(u)θϱ2(u	ϱ2)(u)θϱ2(u	NUM
ejpam-4792	125	24	)	)	PUNCT
ejpam-4792	125	25	=	=	NOUN
ejpam-4792	126	1	gα	gα	ADP
ejpam-4792	126	2	[	[	NOUN
ejpam-4792	126	3	φ(τ	φ(τ	NOUN
ejpam-4792	126	4	)	)	PUNCT
ejpam-4792	126	5	]	]	PUNCT
ejpam-4792	127	1	+	+	CCONJ
ejpam-4792	127	2	υ(u	υ(u	NUM
ejpam-4792	127	3	)	)	PUNCT
ejpam-4792	127	4	.	.	PUNCT
ejpam-4792	128	1	(	(	PUNCT
ejpam-4792	128	2	8)	8)	NUM
ejpam-4792	128	3	solving	solve	VERB
ejpam-4792	128	4	the	the	DET
ejpam-4792	128	5	equation	equation	NOUN
ejpam-4792	128	6	(	(	PUNCT
ejpam-4792	128	7	8)	8)	NUM
ejpam-4792	128	8	using	use	VERB
ejpam-4792	128	9	the	the	DET
ejpam-4792	128	10	gα	gα	NOUN
ejpam-4792	128	11	-	-	PUNCT
ejpam-4792	128	12	transform	transform	NOUN
ejpam-4792	128	13	method	method	NOUN
ejpam-4792	128	14	,	,	PUNCT
ejpam-4792	128	15	means	mean	VERB
ejpam-4792	128	16	that	that	SCONJ
ejpam-4792	128	17	the	the	DET
ejpam-4792	128	18	coefficients	coefficient	NOUN
ejpam-4792	128	19	of	of	ADP
ejpam-4792	128	20	y	y	PROPN
ejpam-4792	128	21	(	(	PUNCT
ejpam-4792	128	22	u	u	NOUN
ejpam-4792	128	23	)	)	PUNCT
ejpam-4792	128	24	,	,	PUNCT
ejpam-4792	128	25	y	y	PROPN
ejpam-4792	128	26	′(u	′(u	NOUN
ejpam-4792	128	27	)	)	PUNCT
ejpam-4792	128	28	,	,	PUNCT
ejpam-4792	128	29	y	y	PROPN
ejpam-4792	128	30	′′(u	′′(u	PROPN
ejpam-4792	128	31	)	)	PUNCT
ejpam-4792	128	32	,	,	PUNCT
ejpam-4792	128	33	·	·	PUNCT
ejpam-4792	128	34	·	·	PUNCT
ejpam-4792	128	35	·	·	PUNCT
ejpam-4792	128	36	,	,	PUNCT
ejpam-4792	128	37	y	y	PROPN
ejpam-4792	128	38	(	(	PUNCT
ejpam-4792	128	39	n−3)(u	n−3)(u	PROPN
ejpam-4792	128	40	)	)	PUNCT
ejpam-4792	128	41	,	,	PUNCT
ejpam-4792	128	42	y	y	PROPN
ejpam-4792	128	43	(	(	PUNCT
ejpam-4792	128	44	n−2)(u	n−2)(u	PROPN
ejpam-4792	128	45	)	)	PUNCT
ejpam-4792	128	46	,	,	PUNCT
ejpam-4792	128	47	y	y	PROPN
ejpam-4792	128	48	(	(	PUNCT
ejpam-4792	128	49	n−1)(u	n−1)(u	PROPN
ejpam-4792	128	50	)	)	PUNCT
ejpam-4792	128	51	are	be	AUX
ejpam-4792	128	52	equal	equal	ADJ
ejpam-4792	128	53	to	to	ADP
ejpam-4792	128	54	zero	zero	NUM
ejpam-4792	128	55	.	.	PUNCT
ejpam-4792	129	1	that	that	PRON
ejpam-4792	129	2	is	be	AUX
ejpam-4792	129	3	,	,	PUNCT
ejpam-4792	129	4	θϱ2(u	θϱ2(u	NOUN
ejpam-4792	129	5	)	)	PUNCT
ejpam-4792	129	6	=	=	SYM
ejpam-4792	129	7	0	0	NUM
ejpam-4792	129	8	for	for	ADP
ejpam-4792	129	9	all	all	DET
ejpam-4792	129	10	ϱ2	ϱ2	NOUN
ejpam-4792	129	11	except	except	SCONJ
ejpam-4792	129	12	ϱ2	ϱ2	PROPN
ejpam-4792	129	13	=	=	SYM
ejpam-4792	129	14	n.	n.	PROPN
ejpam-4792	129	15	let	let	VERB
ejpam-4792	129	16	us	we	PRON
ejpam-4792	129	17	consider	consider	VERB
ejpam-4792	129	18	the	the	DET
ejpam-4792	129	19	coefficient	coefficient	NOUN
ejpam-4792	129	20	of	of	ADP
ejpam-4792	129	21	y	y	PROPN
ejpam-4792	129	22	(	(	PUNCT
ejpam-4792	129	23	u	u	NOUN
ejpam-4792	129	24	)	)	PUNCT
ejpam-4792	129	25	is	be	AUX
ejpam-4792	129	26	zero	zero	NUM
ejpam-4792	129	27	,	,	PUNCT
ejpam-4792	129	28	or	or	CCONJ
ejpam-4792	129	29	θ0(u	θ0(u	NUM
ejpam-4792	129	30	)	)	PUNCT
ejpam-4792	129	31	=	=	SYM
ejpam-4792	129	32	0	0	NUM
ejpam-4792	129	33	,	,	PUNCT
ejpam-4792	129	34	by	by	ADP
ejpam-4792	129	35	setting	set	VERB
ejpam-4792	129	36	γ1,0	γ1,0	PROPN
ejpam-4792	129	37	=	=	SYM
ejpam-4792	129	38	1	1	NUM
ejpam-4792	129	39	,	,	PUNCT
ejpam-4792	129	40	2	2	NUM
ejpam-4792	129	41	,	,	PUNCT
ejpam-4792	129	42	3	3	NUM
ejpam-4792	129	43	,	,	PUNCT
ejpam-4792	129	44	.	.	PUNCT
ejpam-4792	129	45	.	.	PUNCT
ejpam-4792	130	1	.	.	PUNCT
ejpam-4792	131	1	,	,	PUNCT
ejpam-4792	131	2	n−	n−	NOUN
ejpam-4792	131	3	1	1	NUM
ejpam-4792	131	4	,	,	PUNCT
ejpam-4792	131	5	γ2,0	γ2,0	PROPN
ejpam-4792	131	6	=	=	SYM
ejpam-4792	131	7	n	n	CCONJ
ejpam-4792	131	8	,	,	PUNCT
ejpam-4792	131	9	n+	n+	ADP
ejpam-4792	131	10	1	1	NUM
ejpam-4792	131	11	,	,	PUNCT
ejpam-4792	131	12	n+	n+	X
ejpam-4792	131	13	2	2	NUM
ejpam-4792	131	14	,	,	PUNCT
ejpam-4792	131	15	.	.	PUNCT
ejpam-4792	131	16	.	.	PUNCT
ejpam-4792	132	1	.	.	PUNCT
ejpam-4792	133	1	,	,	PUNCT
ejpam-4792	133	2	m	m	PROPN
ejpam-4792	133	3	,	,	PUNCT
ejpam-4792	133	4	and	and	CCONJ
ejpam-4792	133	5	γ3,0	γ3,0	PROPN
ejpam-4792	133	6	=	=	SYM
ejpam-4792	133	7	m+	m+	NUM
ejpam-4792	133	8	1,m+	1,m+	NUM
ejpam-4792	133	9	2,m+	2,m+	NOUN
ejpam-4792	133	10	3	3	NUM
ejpam-4792	133	11	,	,	PUNCT
ejpam-4792	133	12	.	.	PUNCT
ejpam-4792	133	13	.	.	PUNCT
ejpam-4792	134	1	.	.	PUNCT
ejpam-4792	135	1	,	,	PUNCT
ejpam-4792	135	2	m+	m+	NUM
ejpam-4792	135	3	n	n	CCONJ
ejpam-4792	135	4	,	,	PUNCT
ejpam-4792	135	5	yields	yield	VERB
ejpam-4792	135	6	um	um	INTJ
ejpam-4792	135	7	→	→	SYM
ejpam-4792	135	8	am,0	am,0	PROPN
ejpam-4792	135	9	=	=	SYM
ejpam-4792	135	10	0	0	NUM
ejpam-4792	135	11	,	,	PUNCT
ejpam-4792	135	12	(	(	PUNCT
ejpam-4792	135	13	9	9	X
ejpam-4792	135	14	)	)	PUNCT
ejpam-4792	135	15	um−γ1,0	um−γ1,0	NOUN
ejpam-4792	135	16	→	→	SYM
ejpam-4792	135	17	am−γ1,0,0	am−γ1,0,0	NOUN
ejpam-4792	135	18	+	+	SYM
ejpam-4792	135	19	γ1,0∑	γ1,0∑	ADJ
ejpam-4792	135	20	j=1	j=1	NOUN
ejpam-4792	135	21	(	(	PUNCT
ejpam-4792	135	22	−1)j−0	−1)j−0	NOUN
ejpam-4792	135	23	(	(	PUNCT
ejpam-4792	135	24	j	j	PROPN
ejpam-4792	135	25	0	0	NUM
ejpam-4792	135	26	)	)	PUNCT
ejpam-4792	136	1	j−1∏	j−1∏	ADP
ejpam-4792	136	2	s=0	s=0	PROPN
ejpam-4792	136	3	(	(	PUNCT
ejpam-4792	136	4	m−	m−	PROPN
ejpam-4792	136	5	γ1,0	γ1,0	PROPN
ejpam-4792	137	1	+	+	NUM
ejpam-4792	137	2	j	j	PROPN
ejpam-4792	137	3	+	+	CCONJ
ejpam-4792	137	4	α−	α−	ADP
ejpam-4792	137	5	s)am−γ1,0+j	s)am−γ1,0+j	NOUN
ejpam-4792	137	6	,	,	PUNCT
ejpam-4792	137	7	j	j	PROPN
ejpam-4792	137	8	=	=	SYM
ejpam-4792	137	9	0	0	PROPN
ejpam-4792	137	10	,	,	PUNCT
ejpam-4792	137	11	(	(	PUNCT
ejpam-4792	137	12	10	10	NUM
ejpam-4792	137	13	)	)	PUNCT
ejpam-4792	137	14	um−γ2,0	um−γ2,0	NOUN
ejpam-4792	137	15	→	→	SYM
ejpam-4792	137	16	am−γ2,0,0	am−γ2,0,0	PROPN
ejpam-4792	138	1	+	+	CCONJ
ejpam-4792	138	2	n∑	n∑	ADJ
ejpam-4792	138	3	j=1	j=1	NOUN
ejpam-4792	138	4	(	(	PUNCT
ejpam-4792	138	5	−1)j−0	−1)j−0	NOUN
ejpam-4792	138	6	(	(	PUNCT
ejpam-4792	138	7	j	j	PROPN
ejpam-4792	138	8	0	0	NUM
ejpam-4792	138	9	)	)	PUNCT
ejpam-4792	139	1	j−1∏	j−1∏	ADP
ejpam-4792	139	2	s=0	s=0	PROPN
ejpam-4792	139	3	(	(	PUNCT
ejpam-4792	139	4	m−	m−	PROPN
ejpam-4792	139	5	γ2,0	γ2,0	PROPN
ejpam-4792	139	6	+	+	NUM
ejpam-4792	139	7	j	j	PROPN
ejpam-4792	139	8	+	+	CCONJ
ejpam-4792	139	9	α−	α−	ADP
ejpam-4792	139	10	s)am−γ2,0+j	s)am−γ2,0+j	ADJ
ejpam-4792	139	11	,	,	PUNCT
ejpam-4792	139	12	j	j	PROPN
ejpam-4792	139	13	=	=	SYM
ejpam-4792	139	14	0	0	PROPN
ejpam-4792	139	15	,	,	PUNCT
ejpam-4792	139	16	(	(	PUNCT
ejpam-4792	139	17	11	11	NUM
ejpam-4792	139	18	)	)	PUNCT
ejpam-4792	139	19	s.	s.	PROPN
ejpam-4792	139	20	sattaso	sattaso	PROPN
ejpam-4792	139	21	,	,	PUNCT
ejpam-4792	139	22	p.	p.	PROPN
ejpam-4792	139	23	prasertsang	prasertsang	PROPN
ejpam-4792	139	24	,	,	PUNCT
ejpam-4792	139	25	t.	t.	PROPN
ejpam-4792	139	26	prasertsang	prasertsang	PROPN
ejpam-4792	139	27	/	/	SYM
ejpam-4792	139	28	eur	eur	PROPN
ejpam-4792	139	29	.	.	PUNCT
ejpam-4792	140	1	j.	j.	PROPN
ejpam-4792	140	2	pure	pure	PROPN
ejpam-4792	140	3	appl	appl	PROPN
ejpam-4792	140	4	.	.	PROPN
ejpam-4792	140	5	math	math	PROPN
ejpam-4792	140	6	,	,	PUNCT
ejpam-4792	140	7	16	16	NUM
ejpam-4792	140	8	(	(	PUNCT
ejpam-4792	140	9	3	3	NUM
ejpam-4792	140	10	)	)	PUNCT
ejpam-4792	140	11	(	(	PUNCT
ejpam-4792	140	12	2023	2023	NUM
ejpam-4792	140	13	)	)	PUNCT
ejpam-4792	140	14	,	,	PUNCT
ejpam-4792	140	15	1389	1389	NUM
ejpam-4792	140	16	-	-	SYM
ejpam-4792	140	17	1405	1405	NUM
ejpam-4792	140	18	1394	1394	NUM
ejpam-4792	140	19	um−γ3,0	um−γ3,0	PROPN
ejpam-4792	140	20	→	→	SYM
ejpam-4792	140	21	n∑	n∑	PROPN
ejpam-4792	140	22	j	j	PROPN
ejpam-4792	141	1	=	=	PROPN
ejpam-4792	141	2	γ3,0−m	γ3,0−m	PROPN
ejpam-4792	141	3	(	(	PUNCT
ejpam-4792	141	4	−1)j−0	−1)j−0	NOUN
ejpam-4792	141	5	(	(	PUNCT
ejpam-4792	141	6	j	j	PROPN
ejpam-4792	141	7	0	0	NUM
ejpam-4792	141	8	)	)	PUNCT
ejpam-4792	141	9	j−1∏	j−1∏	ADP
ejpam-4792	141	10	s=0	s=0	PROPN
ejpam-4792	141	11	(	(	PUNCT
ejpam-4792	141	12	m−	m−	PROPN
ejpam-4792	141	13	γ3,0	γ3,0	PROPN
ejpam-4792	141	14	+	+	NUM
ejpam-4792	141	15	j	j	PROPN
ejpam-4792	141	16	+	+	CCONJ
ejpam-4792	141	17	α−	α−	ADP
ejpam-4792	141	18	s)am−γ3,0+j	s)am−γ3,0+j	PROPN
ejpam-4792	141	19	,	,	PUNCT
ejpam-4792	141	20	j	j	PROPN
ejpam-4792	141	21	=	=	SYM
ejpam-4792	141	22	0	0	PROPN
ejpam-4792	141	23	.	.	PUNCT
ejpam-4792	142	1	(	(	PUNCT
ejpam-4792	142	2	12	12	NUM
ejpam-4792	142	3	)	)	PUNCT
ejpam-4792	142	4	let	let	VERB
ejpam-4792	142	5	us	we	PRON
ejpam-4792	142	6	consider	consider	VERB
ejpam-4792	142	7	the	the	DET
ejpam-4792	142	8	coefficient	coefficient	NOUN
ejpam-4792	142	9	of	of	ADP
ejpam-4792	142	10	y	y	PROPN
ejpam-4792	142	11	′(u	′(u	NOUN
ejpam-4792	142	12	)	)	PUNCT
ejpam-4792	142	13	is	be	AUX
ejpam-4792	142	14	zero	zero	NUM
ejpam-4792	142	15	,	,	PUNCT
ejpam-4792	142	16	or	or	CCONJ
ejpam-4792	142	17	θ1(u	θ1(u	PROPN
ejpam-4792	142	18	)	)	PUNCT
ejpam-4792	142	19	=	=	SYM
ejpam-4792	142	20	0	0	NUM
ejpam-4792	142	21	,	,	PUNCT
ejpam-4792	142	22	by	by	ADP
ejpam-4792	142	23	setting	set	VERB
ejpam-4792	142	24	γ1,1	γ1,1	NOUN
ejpam-4792	142	25	=	=	SYM
ejpam-4792	142	26	1	1	NUM
ejpam-4792	142	27	,	,	PUNCT
ejpam-4792	142	28	2	2	NUM
ejpam-4792	142	29	,	,	PUNCT
ejpam-4792	142	30	3	3	NUM
ejpam-4792	142	31	,	,	PUNCT
ejpam-4792	142	32	.	.	PUNCT
ejpam-4792	142	33	.	.	PUNCT
ejpam-4792	143	1	.	.	PUNCT
ejpam-4792	144	1	,	,	PUNCT
ejpam-4792	144	2	n−2	n−2	PROPN
ejpam-4792	144	3	,	,	PUNCT
ejpam-4792	144	4	γ2,1	γ2,1	PROPN
ejpam-4792	144	5	=	=	SYM
ejpam-4792	144	6	n−1	n−1	PROPN
ejpam-4792	144	7	,	,	PUNCT
ejpam-4792	144	8	n	n	CCONJ
ejpam-4792	144	9	,	,	PUNCT
ejpam-4792	144	10	n+1	n+1	PROPN
ejpam-4792	144	11	,	,	PUNCT
ejpam-4792	144	12	.	.	PUNCT
ejpam-4792	144	13	.	.	PUNCT
ejpam-4792	144	14	.	.	PUNCT
ejpam-4792	145	1	,	,	PUNCT
ejpam-4792	145	2	m	m	PROPN
ejpam-4792	145	3	,	,	PUNCT
ejpam-4792	145	4	and	and	CCONJ
ejpam-4792	145	5	γ3,1	γ3,1	PROPN
ejpam-4792	145	6	=	=	SYM
ejpam-4792	145	7	m+1,m+2,m+3	m+1,m+2,m+3	PROPN
ejpam-4792	145	8	,	,	PUNCT
ejpam-4792	145	9	.	.	PUNCT
ejpam-4792	145	10	.	.	PUNCT
ejpam-4792	146	1	.	.	PUNCT
ejpam-4792	147	1	,	,	PUNCT
ejpam-4792	147	2	m+n−1	m+n−1	PROPN
ejpam-4792	147	3	,	,	PUNCT
ejpam-4792	147	4	we	we	PRON
ejpam-4792	147	5	obtain	obtain	VERB
ejpam-4792	147	6	um−2	um−2	PROPN
ejpam-4792	147	7	→	→	SYM
ejpam-4792	147	8	am,1	am,1	PROPN
ejpam-4792	147	9	=	=	SYM
ejpam-4792	147	10	0	0	PROPN
ejpam-4792	147	11	,	,	PUNCT
ejpam-4792	147	12	(	(	PUNCT
ejpam-4792	147	13	13	13	NUM
ejpam-4792	147	14	)	)	PUNCT
ejpam-4792	147	15	um−γ1,1−2	um−γ1,1−2	PROPN
ejpam-4792	147	16	→	→	SYM
ejpam-4792	147	17	am−γ1,1,1	am−γ1,1,1	PROPN
ejpam-4792	147	18	+	+	PUNCT
ejpam-4792	147	19	γ1,1	γ1,1	NUM
ejpam-4792	147	20	+	+	ADJ
ejpam-4792	147	21	1∑	1∑	PROPN
ejpam-4792	147	22	j=2	j=2	PROPN
ejpam-4792	147	23	(	(	PUNCT
ejpam-4792	147	24	−1)j−1	−1)j−1	PROPN
ejpam-4792	147	25	(	(	PUNCT
ejpam-4792	147	26	j	j	PROPN
ejpam-4792	147	27	1	1	NUM
ejpam-4792	147	28	)	)	PUNCT
ejpam-4792	148	1	j−1∏	j−1∏	ADV
ejpam-4792	148	2	s=1	s=1	X
ejpam-4792	148	3	(	(	PUNCT
ejpam-4792	148	4	m−	m−	PROPN
ejpam-4792	148	5	1−	1−	NUM
ejpam-4792	148	6	γ1,1	γ1,1	NOUN
ejpam-4792	148	7	+	+	CCONJ
ejpam-4792	148	8	j	j	PROPN
ejpam-4792	149	1	+	+	CCONJ
ejpam-4792	149	2	α−	α−	ADP
ejpam-4792	149	3	s)×	s)×	NOUN
ejpam-4792	149	4	(	(	PUNCT
ejpam-4792	149	5	14	14	NUM
ejpam-4792	149	6	)	)	PUNCT
ejpam-4792	149	7	am−1−γ1,1+j	am−1−γ1,1+j	PROPN
ejpam-4792	149	8	,	,	PUNCT
ejpam-4792	149	9	j	j	NOUN
ejpam-4792	149	10	=	=	SYM
ejpam-4792	149	11	0	0	PROPN
ejpam-4792	149	12	,	,	PUNCT
ejpam-4792	149	13	(	(	PUNCT
ejpam-4792	149	14	15	15	NUM
ejpam-4792	149	15	)	)	PUNCT
ejpam-4792	149	16	um−γ2,1−2	um−γ2,1−2	PROPN
ejpam-4792	149	17	→	→	SYM
ejpam-4792	149	18	am−γ2,1,1	am−γ2,1,1	PROPN
ejpam-4792	150	1	+	+	CCONJ
ejpam-4792	150	2	n∑	n∑	PROPN
ejpam-4792	150	3	j=2	j=2	PROPN
ejpam-4792	150	4	(	(	PUNCT
ejpam-4792	150	5	−1)j−1	−1)j−1	PROPN
ejpam-4792	150	6	(	(	PUNCT
ejpam-4792	150	7	j	j	PROPN
ejpam-4792	150	8	1	1	NUM
ejpam-4792	150	9	)	)	PUNCT
ejpam-4792	151	1	j−1∏	j−1∏	ADV
ejpam-4792	151	2	s=1	s=1	X
ejpam-4792	151	3	(	(	PUNCT
ejpam-4792	151	4	m−	m−	PROPN
ejpam-4792	151	5	1−	1−	NUM
ejpam-4792	151	6	γ2,1	γ2,1	PROPN
ejpam-4792	152	1	+	+	CCONJ
ejpam-4792	152	2	j	j	PROPN
ejpam-4792	153	1	+	+	CCONJ
ejpam-4792	153	2	α−	α−	ADP
ejpam-4792	153	3	s)×	s)×	NOUN
ejpam-4792	153	4	(	(	PUNCT
ejpam-4792	153	5	16	16	NUM
ejpam-4792	153	6	)	)	PUNCT
ejpam-4792	153	7	am−1−γ2,1+j	am−1−γ2,1+j	PROPN
ejpam-4792	153	8	,	,	PUNCT
ejpam-4792	153	9	j	j	PROPN
ejpam-4792	153	10	=	=	SYM
ejpam-4792	153	11	0	0	PROPN
ejpam-4792	153	12	,	,	PUNCT
ejpam-4792	153	13	(	(	PUNCT
ejpam-4792	153	14	17	17	NUM
ejpam-4792	153	15	)	)	PUNCT
ejpam-4792	153	16	um−γ3,1−2	um−γ3,1−2	PROPN
ejpam-4792	153	17	→	→	SYM
ejpam-4792	153	18	n∑	n∑	PROPN
ejpam-4792	153	19	j	j	PROPN
ejpam-4792	153	20	=	=	PROPN
ejpam-4792	153	21	γ3,1−m+1	γ3,1−m+1	PROPN
ejpam-4792	153	22	(	(	PUNCT
ejpam-4792	153	23	−1)j−1	−1)j−1	PROPN
ejpam-4792	153	24	(	(	PUNCT
ejpam-4792	153	25	j	j	PROPN
ejpam-4792	153	26	1	1	NUM
ejpam-4792	153	27	)	)	PUNCT
ejpam-4792	154	1	j−1∏	j−1∏	ADV
ejpam-4792	154	2	s=1	s=1	X
ejpam-4792	154	3	(	(	PUNCT
ejpam-4792	154	4	m−	m−	PROPN
ejpam-4792	154	5	1−	1−	NUM
ejpam-4792	154	6	γ3,1	γ3,1	PROPN
ejpam-4792	154	7	+	+	CCONJ
ejpam-4792	154	8	j	j	PROPN
ejpam-4792	155	1	+	+	CCONJ
ejpam-4792	155	2	α−	α−	ADP
ejpam-4792	155	3	s)×	s)×	NOUN
ejpam-4792	155	4	(	(	PUNCT
ejpam-4792	155	5	18	18	NUM
ejpam-4792	155	6	)	)	PUNCT
ejpam-4792	155	7	am−1−γ3,1+j	am−1−γ3,1+j	PROPN
ejpam-4792	155	8	,	,	PUNCT
ejpam-4792	155	9	j	j	NOUN
ejpam-4792	155	10	=	=	SYM
ejpam-4792	155	11	0	0	PROPN
ejpam-4792	155	12	.	.	PUNCT
ejpam-4792	156	1	(	(	PUNCT
ejpam-4792	156	2	19	19	NUM
ejpam-4792	156	3	)	)	PUNCT
ejpam-4792	156	4	let	let	VERB
ejpam-4792	156	5	us	we	PRON
ejpam-4792	156	6	consider	consider	VERB
ejpam-4792	156	7	the	the	DET
ejpam-4792	156	8	coefficient	coefficient	NOUN
ejpam-4792	156	9	of	of	ADP
ejpam-4792	156	10	y	y	PROPN
ejpam-4792	156	11	′′(u	′′(u	PROPN
ejpam-4792	156	12	)	)	PUNCT
ejpam-4792	156	13	is	be	AUX
ejpam-4792	156	14	zero	zero	NUM
ejpam-4792	156	15	,	,	PUNCT
ejpam-4792	156	16	or	or	CCONJ
ejpam-4792	156	17	θ2(u	θ2(u	NOUN
ejpam-4792	156	18	)	)	PUNCT
ejpam-4792	157	1	=	=	SYM
ejpam-4792	157	2	0	0	NUM
ejpam-4792	157	3	,	,	PUNCT
ejpam-4792	157	4	by	by	ADP
ejpam-4792	157	5	setting	set	VERB
ejpam-4792	157	6	γ1,2	γ1,2	ADJ
ejpam-4792	157	7	=	=	SYM
ejpam-4792	157	8	1	1	NUM
ejpam-4792	157	9	,	,	PUNCT
ejpam-4792	157	10	2	2	NUM
ejpam-4792	157	11	,	,	PUNCT
ejpam-4792	157	12	3	3	NUM
ejpam-4792	157	13	,	,	PUNCT
ejpam-4792	157	14	.	.	PUNCT
ejpam-4792	157	15	.	.	PUNCT
ejpam-4792	158	1	.	.	PUNCT
ejpam-4792	159	1	,	,	PUNCT
ejpam-4792	159	2	n−3	n−3	PROPN
ejpam-4792	159	3	,	,	PUNCT
ejpam-4792	159	4	γ2,2	γ2,2	PROPN
ejpam-4792	159	5	=	=	SYM
ejpam-4792	159	6	n−2	n−2	PROPN
ejpam-4792	159	7	,	,	PUNCT
ejpam-4792	159	8	n−1	n−1	PROPN
ejpam-4792	159	9	,	,	PUNCT
ejpam-4792	159	10	n	n	CCONJ
ejpam-4792	159	11	,	,	PUNCT
ejpam-4792	159	12	.	.	PUNCT
ejpam-4792	159	13	.	.	PUNCT
ejpam-4792	159	14	.	.	PUNCT
ejpam-4792	160	1	,	,	PUNCT
ejpam-4792	160	2	m	m	PROPN
ejpam-4792	160	3	,	,	PUNCT
ejpam-4792	160	4	and	and	CCONJ
ejpam-4792	160	5	γ3,2	γ3,2	PROPN
ejpam-4792	160	6	=	=	PUNCT
ejpam-4792	160	7	m+1,m+2,m+3	m+1,m+2,m+3	PROPN
ejpam-4792	160	8	,	,	PUNCT
ejpam-4792	160	9	.	.	PUNCT
ejpam-4792	160	10	.	.	PUNCT
ejpam-4792	161	1	.	.	PUNCT
ejpam-4792	162	1	,	,	PUNCT
ejpam-4792	162	2	m+n−2	m+n−2	PROPN
ejpam-4792	162	3	,	,	PUNCT
ejpam-4792	162	4	we	we	PRON
ejpam-4792	162	5	have	have	VERB
ejpam-4792	162	6	um−4	um−4	PROPN
ejpam-4792	162	7	→	→	SYM
ejpam-4792	162	8	am,2	am,2	PROPN
ejpam-4792	162	9	=	=	SYM
ejpam-4792	162	10	0	0	NUM
ejpam-4792	162	11	,	,	PUNCT
ejpam-4792	162	12	(	(	PUNCT
ejpam-4792	162	13	20	20	NUM
ejpam-4792	162	14	)	)	PUNCT
ejpam-4792	162	15	um−γ1,2−4	um−γ1,2−4	PROPN
ejpam-4792	162	16	→	→	PUNCT
ejpam-4792	163	1	am−γ1,2,2	am−γ1,2,2	PROPN
ejpam-4792	163	2	+	+	PUNCT
ejpam-4792	164	1	γ1,2	γ1,2	ADJ
ejpam-4792	164	2	+	+	ADJ
ejpam-4792	164	3	2∑	2∑	NUM
ejpam-4792	164	4	j=3	j=3	PROPN
ejpam-4792	164	5	(	(	PUNCT
ejpam-4792	164	6	−1)j−2	−1)j−2	X
ejpam-4792	164	7	(	(	PUNCT
ejpam-4792	164	8	j	j	PROPN
ejpam-4792	164	9	2	2	NUM
ejpam-4792	164	10	)	)	PUNCT
ejpam-4792	165	1	j−1∏	j−1∏	ADV
ejpam-4792	165	2	s=2	s=2	PUNCT
ejpam-4792	165	3	(	(	PUNCT
ejpam-4792	165	4	m−	m−	PROPN
ejpam-4792	165	5	2−	2−	NUM
ejpam-4792	165	6	γ1,2	γ1,2	PROPN
ejpam-4792	166	1	+	+	CCONJ
ejpam-4792	166	2	j	j	PROPN
ejpam-4792	166	3	+	+	CCONJ
ejpam-4792	166	4	α−	α−	ADP
ejpam-4792	166	5	s)am−2−γ1,2+j	s)am−2−γ1,2+j	PROPN
ejpam-4792	166	6	,	,	PUNCT
ejpam-4792	166	7	j	j	PROPN
ejpam-4792	166	8	=	=	SYM
ejpam-4792	166	9	0	0	PROPN
ejpam-4792	166	10	,	,	PUNCT
ejpam-4792	166	11	(	(	PUNCT
ejpam-4792	166	12	21	21	NUM
ejpam-4792	166	13	)	)	PUNCT
ejpam-4792	166	14	um−γ2,2−4	um−γ2,2−4	PROPN
ejpam-4792	167	1	→	→	PUNCT
ejpam-4792	167	2	am−γ2,2,2	am−γ2,2,2	PROPN
ejpam-4792	168	1	+	+	CCONJ
ejpam-4792	168	2	n∑	n∑	PROPN
ejpam-4792	169	1	j=3	j=3	PROPN
ejpam-4792	169	2	(	(	PUNCT
ejpam-4792	169	3	−1)j−2	−1)j−2	X
ejpam-4792	169	4	(	(	PUNCT
ejpam-4792	169	5	j	j	PROPN
ejpam-4792	169	6	2	2	NUM
ejpam-4792	169	7	)	)	PUNCT
ejpam-4792	170	1	j−1∏	j−1∏	ADV
ejpam-4792	170	2	s=2	s=2	PUNCT
ejpam-4792	170	3	(	(	PUNCT
ejpam-4792	170	4	m−	m−	PROPN
ejpam-4792	170	5	2−	2−	NUM
ejpam-4792	170	6	γ2,2	γ2,2	PROPN
ejpam-4792	170	7	+	+	CCONJ
ejpam-4792	170	8	j	j	PROPN
ejpam-4792	170	9	+	+	CCONJ
ejpam-4792	170	10	α−	α−	ADP
ejpam-4792	170	11	s)am−2−γ2,2+j	s)am−2−γ2,2+j	PROPN
ejpam-4792	170	12	,	,	PUNCT
ejpam-4792	170	13	j	j	PROPN
ejpam-4792	170	14	=	=	SYM
ejpam-4792	170	15	0	0	PROPN
ejpam-4792	170	16	,	,	PUNCT
ejpam-4792	170	17	(	(	PUNCT
ejpam-4792	170	18	22	22	NUM
ejpam-4792	170	19	)	)	PUNCT
ejpam-4792	170	20	um−γ3,2−4	um−γ3,2−4	PROPN
ejpam-4792	170	21	→	→	SYM
ejpam-4792	170	22	n∑	n∑	PROPN
ejpam-4792	170	23	j	j	PROPN
ejpam-4792	170	24	=	=	PRON
ejpam-4792	170	25	γ3,2−m+2	γ3,2−m+2	PROPN
ejpam-4792	170	26	(	(	PUNCT
ejpam-4792	170	27	−1)j−2	−1)j−2	X
ejpam-4792	170	28	(	(	PUNCT
ejpam-4792	170	29	j	j	PROPN
ejpam-4792	170	30	2	2	NUM
ejpam-4792	170	31	)	)	PUNCT
ejpam-4792	170	32	j−1∏	j−1∏	ADV
ejpam-4792	170	33	s=2	s=2	PUNCT
ejpam-4792	170	34	(	(	PUNCT
ejpam-4792	170	35	m−	m−	PROPN
ejpam-4792	170	36	2−	2−	NUM
ejpam-4792	170	37	γ3,2	γ3,2	PROPN
ejpam-4792	170	38	+	+	CCONJ
ejpam-4792	170	39	j	j	PROPN
ejpam-4792	171	1	+	+	CCONJ
ejpam-4792	171	2	α−	α−	ADP
ejpam-4792	171	3	s)am−2−γ3,2+j	s)am−2−γ3,2+j	PROPN
ejpam-4792	171	4	,	,	PUNCT
ejpam-4792	171	5	j	j	PROPN
ejpam-4792	171	6	=	=	NOUN
ejpam-4792	171	7	0	0	PROPN
ejpam-4792	171	8	.	.	PUNCT
ejpam-4792	172	1	(	(	PUNCT
ejpam-4792	172	2	23	23	NUM
ejpam-4792	172	3	)	)	PUNCT
ejpam-4792	172	4	similarly	similarly	ADV
ejpam-4792	172	5	,	,	PUNCT
ejpam-4792	172	6	the	the	DET
ejpam-4792	172	7	coefficients	coefficient	NOUN
ejpam-4792	172	8	of	of	ADP
ejpam-4792	172	9	y	y	PROPN
ejpam-4792	172	10	′′′(u	′′′(u	PROPN
ejpam-4792	172	11	)	)	PUNCT
ejpam-4792	172	12	,	,	PUNCT
ejpam-4792	172	13	y	y	PROPN
ejpam-4792	172	14	(	(	PUNCT
ejpam-4792	172	15	4)(u	4)(u	NUM
ejpam-4792	172	16	)	)	PUNCT
ejpam-4792	172	17	,	,	PUNCT
ejpam-4792	172	18	y	y	PROPN
ejpam-4792	172	19	(	(	PUNCT
ejpam-4792	172	20	5)(u	5)(u	NUM
ejpam-4792	172	21	)	)	PUNCT
ejpam-4792	172	22	,	,	PUNCT
ejpam-4792	172	23	.	.	PUNCT
ejpam-4792	172	24	.	.	PUNCT
ejpam-4792	173	1	.	.	PUNCT
ejpam-4792	174	1	,	,	PUNCT
ejpam-4792	174	2	y	y	PROPN
ejpam-4792	174	3	(	(	PUNCT
ejpam-4792	174	4	n−3)(u	n−3)(u	PROPN
ejpam-4792	174	5	)	)	PUNCT
ejpam-4792	174	6	,	,	PUNCT
ejpam-4792	174	7	y	y	PROPN
ejpam-4792	174	8	(	(	PUNCT
ejpam-4792	174	9	n−2)(u	n−2)(u	PROPN
ejpam-4792	174	10	)	)	PUNCT
ejpam-4792	174	11	,	,	PUNCT
ejpam-4792	174	12	y	y	PROPN
ejpam-4792	174	13	(	(	PUNCT
ejpam-4792	174	14	n−1)(u	n−1)(u	PROPN
ejpam-4792	174	15	)	)	PUNCT
ejpam-4792	174	16	are	be	AUX
ejpam-4792	174	17	equal	equal	ADJ
ejpam-4792	174	18	to	to	ADP
ejpam-4792	174	19	zero	zero	NUM
ejpam-4792	174	20	.	.	PUNCT
ejpam-4792	175	1	next	next	ADV
ejpam-4792	175	2	,	,	PUNCT
ejpam-4792	175	3	we	we	PRON
ejpam-4792	175	4	will	will	AUX
ejpam-4792	175	5	state	state	VERB
ejpam-4792	175	6	the	the	DET
ejpam-4792	175	7	following	follow	VERB
ejpam-4792	175	8	equations	equation	NOUN
ejpam-4792	175	9	from	from	ADP
ejpam-4792	175	10	the	the	DET
ejpam-4792	175	11	coefficient	coefficient	NOUN
ejpam-4792	175	12	of	of	ADP
ejpam-4792	175	13	y	y	PROPN
ejpam-4792	175	14	(	(	PUNCT
ejpam-4792	175	15	n−3)(u	n−3)(u	PROPN
ejpam-4792	175	16	)	)	PUNCT
ejpam-4792	175	17	=	=	SYM
ejpam-4792	175	18	y	y	PROPN
ejpam-4792	175	19	(	(	PUNCT
ejpam-4792	175	20	n−2)(u	n−2)(u	PROPN
ejpam-4792	175	21	)	)	PUNCT
ejpam-4792	175	22	=	=	SYM
ejpam-4792	175	23	y	y	PROPN
ejpam-4792	175	24	(	(	PUNCT
ejpam-4792	175	25	n−1)(u	n−1)(u	PROPN
ejpam-4792	175	26	)	)	PUNCT
ejpam-4792	175	27	=	=	SYM
ejpam-4792	175	28	0	0	NUM
ejpam-4792	175	29	,	,	PUNCT
ejpam-4792	175	30	by	by	ADP
ejpam-4792	175	31	letting	let	VERB
ejpam-4792	175	32	γ1,n−3	γ1,n−3	PROPN
ejpam-4792	175	33	=	=	SYM
ejpam-4792	175	34	1	1	NUM
ejpam-4792	175	35	,	,	PUNCT
ejpam-4792	175	36	2	2	NUM
ejpam-4792	175	37	,	,	PUNCT
ejpam-4792	175	38	γ2,n−3	γ2,n−3	ADJ
ejpam-4792	175	39	=	=	PUNCT
ejpam-4792	175	40	s.	s.	PROPN
ejpam-4792	175	41	sattaso	sattaso	PROPN
ejpam-4792	175	42	,	,	PUNCT
ejpam-4792	175	43	p.	p.	PROPN
ejpam-4792	175	44	prasertsang	prasertsang	PROPN
ejpam-4792	175	45	,	,	PUNCT
ejpam-4792	175	46	t.	t.	PROPN
ejpam-4792	175	47	prasertsang	prasertsang	PROPN
ejpam-4792	175	48	/	/	SYM
ejpam-4792	175	49	eur	eur	PROPN
ejpam-4792	175	50	.	.	PUNCT
ejpam-4792	176	1	j.	j.	PROPN
ejpam-4792	176	2	pure	pure	PROPN
ejpam-4792	176	3	appl	appl	PROPN
ejpam-4792	176	4	.	.	PROPN
ejpam-4792	176	5	math	math	PROPN
ejpam-4792	176	6	,	,	PUNCT
ejpam-4792	176	7	16	16	NUM
ejpam-4792	176	8	(	(	PUNCT
ejpam-4792	176	9	3	3	NUM
ejpam-4792	176	10	)	)	PUNCT
ejpam-4792	176	11	(	(	PUNCT
ejpam-4792	176	12	2023	2023	NUM
ejpam-4792	176	13	)	)	PUNCT
ejpam-4792	176	14	,	,	PUNCT
ejpam-4792	176	15	1389	1389	NUM
ejpam-4792	176	16	-	-	SYM
ejpam-4792	176	17	1405	1405	NUM
ejpam-4792	176	18	1395	1395	NUM
ejpam-4792	176	19	3	3	NUM
ejpam-4792	176	20	,	,	PUNCT
ejpam-4792	176	21	4	4	NUM
ejpam-4792	176	22	,	,	PUNCT
ejpam-4792	176	23	5	5	NUM
ejpam-4792	176	24	,	,	PUNCT
ejpam-4792	176	25	.	.	PUNCT
ejpam-4792	176	26	.	.	PUNCT
ejpam-4792	176	27	.	.	PUNCT
ejpam-4792	177	1	,	,	PUNCT
ejpam-4792	177	2	m	m	PROPN
ejpam-4792	177	3	,	,	PUNCT
ejpam-4792	177	4	γ3,n−3	γ3,n−3	PROPN
ejpam-4792	177	5	=	=	SYM
ejpam-4792	177	6	m+1,m+2,m+3	m+1,m+2,m+3	NUM
ejpam-4792	177	7	,	,	PUNCT
ejpam-4792	177	8	γ2,n−2	γ2,n−2	NOUN
ejpam-4792	177	9	=	=	SYM
ejpam-4792	177	10	2	2	NUM
ejpam-4792	177	11	,	,	PUNCT
ejpam-4792	177	12	3	3	NUM
ejpam-4792	177	13	,	,	PUNCT
ejpam-4792	177	14	4	4	NUM
ejpam-4792	177	15	,	,	PUNCT
ejpam-4792	177	16	.	.	PUNCT
ejpam-4792	177	17	.	.	PUNCT
ejpam-4792	178	1	.	.	PUNCT
ejpam-4792	179	1	,	,	PUNCT
ejpam-4792	179	2	m	m	PROPN
ejpam-4792	179	3	,	,	PUNCT
ejpam-4792	179	4	γ3,n−2	γ3,n−2	ADJ
ejpam-4792	179	5	=	=	SYM
ejpam-4792	179	6	m+1,m+2	m+1,m+2	NOUN
ejpam-4792	179	7	,	,	PUNCT
ejpam-4792	179	8	and	and	CCONJ
ejpam-4792	179	9	γ2,n−1	γ2,n−1	ADJ
ejpam-4792	179	10	=	=	SYM
ejpam-4792	179	11	1	1	NUM
ejpam-4792	179	12	,	,	PUNCT
ejpam-4792	179	13	2	2	NUM
ejpam-4792	179	14	,	,	PUNCT
ejpam-4792	179	15	3	3	NUM
ejpam-4792	179	16	,	,	PUNCT
ejpam-4792	179	17	.	.	PUNCT
ejpam-4792	179	18	.	.	PUNCT
ejpam-4792	180	1	.	.	PUNCT
ejpam-4792	181	1	,	,	PUNCT
ejpam-4792	181	2	m	m	X
ejpam-4792	181	3	,	,	PUNCT
ejpam-4792	181	4	it	it	PRON
ejpam-4792	181	5	follows	follow	VERB
ejpam-4792	181	6	that	that	SCONJ
ejpam-4792	181	7	um−2(n−3	um−2(n−3	PROPN
ejpam-4792	181	8	)	)	PUNCT
ejpam-4792	181	9	→	→	SYM
ejpam-4792	181	10	am	be	AUX
ejpam-4792	181	11	,	,	PUNCT
ejpam-4792	181	12	n−3	n−3	PROPN
ejpam-4792	181	13	=	=	SYM
ejpam-4792	181	14	0	0	NUM
ejpam-4792	181	15	,	,	PUNCT
ejpam-4792	181	16	(	(	PUNCT
ejpam-4792	181	17	24	24	NUM
ejpam-4792	181	18	)	)	PUNCT
ejpam-4792	181	19	um−γ1,n−3−2(n−3	um−γ1,n−3−2(n−3	ADJ
ejpam-4792	181	20	)	)	PUNCT
ejpam-4792	181	21	→	→	SYM
ejpam-4792	181	22	am−γ1,n−3,n−3	am−γ1,n−3,n−3	PROPN
ejpam-4792	182	1	+	+	CCONJ
ejpam-4792	182	2	γ1,n−3+n−3∑	γ1,n−3+n−3∑	PROPN
ejpam-4792	182	3	j	j	PROPN
ejpam-4792	182	4	=	=	PROPN
ejpam-4792	182	5	n−2	n−2	PROPN
ejpam-4792	182	6	(	(	PUNCT
ejpam-4792	182	7	−1)j−(n−3	−1)j−(n−3	PROPN
ejpam-4792	182	8	)	)	PUNCT
ejpam-4792	182	9	(	(	PUNCT
ejpam-4792	182	10	j	j	PROPN
ejpam-4792	182	11	n−	n−	NOUN
ejpam-4792	182	12	3	3	NUM
ejpam-4792	182	13	)	)	PUNCT
ejpam-4792	182	14	×	×	NOUN
ejpam-4792	182	15	j−1∏	j−1∏	PROPN
ejpam-4792	182	16	s	s	PROPN
ejpam-4792	182	17	=	=	PROPN
ejpam-4792	182	18	n−3	n−3	PROPN
ejpam-4792	182	19	(	(	PUNCT
ejpam-4792	182	20	m−	m−	PROPN
ejpam-4792	182	21	(	(	PUNCT
ejpam-4792	182	22	n−	n−	NOUN
ejpam-4792	182	23	3)−	3)−	PROPN
ejpam-4792	182	24	γ1,n−3	γ1,n−3	PROPN
ejpam-4792	182	25	+	+	CCONJ
ejpam-4792	182	26	j	j	PROPN
ejpam-4792	182	27	+	+	CCONJ
ejpam-4792	182	28	α−	α−	ADP
ejpam-4792	182	29	s)×	s)×	NUM
ejpam-4792	182	30	am−(n−3)−γ1,n−3+j	am−(n−3)−γ1,n−3+j	PROPN
ejpam-4792	182	31	,	,	PUNCT
ejpam-4792	182	32	j	j	PROPN
ejpam-4792	182	33	=	=	SYM
ejpam-4792	182	34	0	0	PROPN
ejpam-4792	182	35	,	,	PUNCT
ejpam-4792	182	36	(	(	PUNCT
ejpam-4792	182	37	25	25	NUM
ejpam-4792	182	38	)	)	PUNCT
ejpam-4792	182	39	um−γ2,n−3−2(n−3	um−γ2,n−3−2(n−3	PROPN
ejpam-4792	182	40	)	)	PUNCT
ejpam-4792	182	41	→	→	SYM
ejpam-4792	182	42	am−γ2,n−3,n−3	am−γ2,n−3,n−3	PROPN
ejpam-4792	182	43	+	+	SYM
ejpam-4792	182	44	n∑	n∑	PROPN
ejpam-4792	182	45	j	j	PROPN
ejpam-4792	182	46	=	=	PROPN
ejpam-4792	182	47	n−2	n−2	PROPN
ejpam-4792	182	48	(	(	PUNCT
ejpam-4792	182	49	−1)j−(n−3	−1)j−(n−3	PROPN
ejpam-4792	182	50	)	)	PUNCT
ejpam-4792	182	51	(	(	PUNCT
ejpam-4792	182	52	j	j	PROPN
ejpam-4792	182	53	n−	n−	NOUN
ejpam-4792	182	54	3	3	NUM
ejpam-4792	182	55	)	)	PUNCT
ejpam-4792	182	56	×	×	NOUN
ejpam-4792	182	57	j−1∏	j−1∏	PROPN
ejpam-4792	182	58	s	s	PROPN
ejpam-4792	182	59	=	=	PROPN
ejpam-4792	182	60	n−3	n−3	PROPN
ejpam-4792	182	61	(	(	PUNCT
ejpam-4792	182	62	m−	m−	PROPN
ejpam-4792	182	63	(	(	PUNCT
ejpam-4792	182	64	n−	n−	NOUN
ejpam-4792	182	65	3)−	3)−	NUM
ejpam-4792	182	66	γ2,n−3	γ2,n−3	PROPN
ejpam-4792	182	67	+	+	NUM
ejpam-4792	182	68	j	j	NOUN
ejpam-4792	182	69	+	+	CCONJ
ejpam-4792	182	70	α−	α−	ADP
ejpam-4792	182	71	s)×	s)×	NOUN
ejpam-4792	182	72	am−(n−3)−γ2+j	am−(n−3)−γ2+j	NOUN
ejpam-4792	182	73	,	,	PUNCT
ejpam-4792	182	74	j	j	PROPN
ejpam-4792	182	75	=	=	SYM
ejpam-4792	182	76	0	0	PROPN
ejpam-4792	182	77	,	,	PUNCT
ejpam-4792	182	78	(	(	PUNCT
ejpam-4792	182	79	26	26	NUM
ejpam-4792	182	80	)	)	PUNCT
ejpam-4792	182	81	um−γ3,n−3−2(n−3	um−γ3,n−3−2(n−3	PROPN
ejpam-4792	182	82	)	)	PUNCT
ejpam-4792	182	83	→	→	PUNCT
ejpam-4792	182	84	n∑	n∑	PROPN
ejpam-4792	182	85	j	j	PROPN
ejpam-4792	182	86	=	=	PROPN
ejpam-4792	182	87	γ3,n−3−m+(n−3	γ3,n−3−m+(n−3	PROPN
ejpam-4792	182	88	)	)	PUNCT
ejpam-4792	182	89	(	(	PUNCT
ejpam-4792	182	90	−1)j−(n−3	−1)j−(n−3	PROPN
ejpam-4792	182	91	)	)	PUNCT
ejpam-4792	182	92	(	(	PUNCT
ejpam-4792	182	93	j	j	PROPN
ejpam-4792	182	94	n−	n−	NOUN
ejpam-4792	182	95	3	3	NUM
ejpam-4792	182	96	)	)	PUNCT
ejpam-4792	182	97	×	×	NOUN
ejpam-4792	182	98	j−1∏	j−1∏	PROPN
ejpam-4792	182	99	s	s	PROPN
ejpam-4792	182	100	=	=	PROPN
ejpam-4792	182	101	n−3	n−3	PROPN
ejpam-4792	182	102	(	(	PUNCT
ejpam-4792	182	103	m−	m−	PROPN
ejpam-4792	182	104	(	(	PUNCT
ejpam-4792	182	105	n−	n−	NOUN
ejpam-4792	182	106	3)−	3)−	NUM
ejpam-4792	182	107	γ3,n−3	γ3,n−3	PROPN
ejpam-4792	182	108	+	+	PROPN
ejpam-4792	182	109	j	j	PROPN
ejpam-4792	182	110	+	+	CCONJ
ejpam-4792	182	111	α−	α−	ADP
ejpam-4792	182	112	s)×	s)×	NOUN
ejpam-4792	182	113	am−(n−3)−γ3,n−3+j	am−(n−3)−γ3,n−3+j	PROPN
ejpam-4792	182	114	,	,	PUNCT
ejpam-4792	182	115	j	j	PROPN
ejpam-4792	182	116	=	=	SYM
ejpam-4792	182	117	0	0	PROPN
ejpam-4792	182	118	,	,	PUNCT
ejpam-4792	182	119	(	(	PUNCT
ejpam-4792	182	120	27	27	NUM
ejpam-4792	182	121	)	)	PUNCT
ejpam-4792	182	122	um−2(n−2	um−2(n−2	NOUN
ejpam-4792	182	123	)	)	PUNCT
ejpam-4792	182	124	→	→	SYM
ejpam-4792	182	125	am	be	AUX
ejpam-4792	182	126	,	,	PUNCT
ejpam-4792	182	127	n−2	n−2	PROPN
ejpam-4792	182	128	=	=	SYM
ejpam-4792	182	129	0	0	NUM
ejpam-4792	182	130	,	,	PUNCT
ejpam-4792	182	131	(	(	PUNCT
ejpam-4792	182	132	28	28	NUM
ejpam-4792	182	133	)	)	PUNCT
ejpam-4792	182	134	um−2(n−2)−1	um−2(n−2)−1	NOUN
ejpam-4792	182	135	→	→	PUNCT
ejpam-4792	182	136	am−1,n−2	am−1,n−2	NOUN
ejpam-4792	182	137	+	+	CCONJ
ejpam-4792	182	138	n−1∑	n−1∑	PROPN
ejpam-4792	182	139	j	j	PROPN
ejpam-4792	182	140	=	=	SYM
ejpam-4792	182	141	n−1	n−1	PROPN
ejpam-4792	182	142	(	(	PUNCT
ejpam-4792	182	143	−1)j−(n−2	−1)j−(n−2	PROPN
ejpam-4792	182	144	)	)	PUNCT
ejpam-4792	182	145	(	(	PUNCT
ejpam-4792	182	146	j	j	PROPN
ejpam-4792	182	147	n−	n−	NOUN
ejpam-4792	182	148	2	2	NUM
ejpam-4792	182	149	)	)	PUNCT
ejpam-4792	182	150	×	×	NOUN
ejpam-4792	182	151	j−1∏	j−1∏	PROPN
ejpam-4792	182	152	s	s	PROPN
ejpam-4792	182	153	=	=	PROPN
ejpam-4792	182	154	n−2	n−2	PROPN
ejpam-4792	182	155	(	(	PUNCT
ejpam-4792	182	156	m−	m−	PROPN
ejpam-4792	182	157	(	(	PUNCT
ejpam-4792	182	158	n−	n−	NOUN
ejpam-4792	182	159	1	1	NUM
ejpam-4792	182	160	)	)	PUNCT
ejpam-4792	183	1	+	+	NUM
ejpam-4792	183	2	j	j	PROPN
ejpam-4792	183	3	+	+	CCONJ
ejpam-4792	183	4	α−	α−	ADP
ejpam-4792	183	5	s)am−(n−1)+j	s)am−(n−1)+j	PROPN
ejpam-4792	183	6	,	,	PUNCT
ejpam-4792	183	7	j	j	PROPN
ejpam-4792	183	8	=	=	SYM
ejpam-4792	183	9	0	0	PROPN
ejpam-4792	183	10	,	,	PUNCT
ejpam-4792	183	11	(	(	PUNCT
ejpam-4792	183	12	29	29	NUM
ejpam-4792	183	13	)	)	PUNCT
ejpam-4792	183	14	um−γ2,n−2−2(n−2	um−γ2,n−2−2(n−2	PROPN
ejpam-4792	183	15	)	)	PUNCT
ejpam-4792	183	16	→	→	SYM
ejpam-4792	183	17	am−γ2,n−2,n−2	am−γ2,n−2,n−2	PROPN
ejpam-4792	184	1	+	+	SYM
ejpam-4792	184	2	n∑	n∑	PROPN
ejpam-4792	184	3	j	j	PROPN
ejpam-4792	185	1	=	=	PROPN
ejpam-4792	185	2	n−1	n−1	PROPN
ejpam-4792	185	3	(	(	PUNCT
ejpam-4792	185	4	−1)j−(n−2	−1)j−(n−2	PROPN
ejpam-4792	185	5	)	)	PUNCT
ejpam-4792	185	6	(	(	PUNCT
ejpam-4792	185	7	j	j	PROPN
ejpam-4792	185	8	n−	n−	NOUN
ejpam-4792	185	9	2	2	NUM
ejpam-4792	185	10	)	)	PUNCT
ejpam-4792	185	11	×	×	NOUN
ejpam-4792	185	12	j−1∏	j−1∏	PROPN
ejpam-4792	185	13	s	s	PROPN
ejpam-4792	185	14	=	=	PROPN
ejpam-4792	185	15	n−2	n−2	PROPN
ejpam-4792	185	16	(	(	PUNCT
ejpam-4792	185	17	m−	m−	PROPN
ejpam-4792	185	18	(	(	PUNCT
ejpam-4792	185	19	n−	n−	PROPN
ejpam-4792	185	20	2)−	2)−	PROPN
ejpam-4792	185	21	γ2,n−2	γ2,n−2	PROPN
ejpam-4792	185	22	+	+	NUM
ejpam-4792	185	23	j	j	NOUN
ejpam-4792	185	24	+	+	CCONJ
ejpam-4792	185	25	α−	α−	ADP
ejpam-4792	185	26	s)×	s)×	NOUN
ejpam-4792	185	27	am−(n−2)−γ2,n−2+j	am−(n−2)−γ2,n−2+j	NUM
ejpam-4792	185	28	,	,	PUNCT
ejpam-4792	185	29	j	j	PROPN
ejpam-4792	185	30	=	=	SYM
ejpam-4792	185	31	0	0	PROPN
ejpam-4792	185	32	,	,	PUNCT
ejpam-4792	185	33	(	(	PUNCT
ejpam-4792	185	34	30	30	NUM
ejpam-4792	185	35	)	)	PUNCT
ejpam-4792	185	36	um−γ3,n−2−2(n−2	um−γ3,n−2−2(n−2	PROPN
ejpam-4792	185	37	)	)	PUNCT
ejpam-4792	185	38	→	→	SYM
ejpam-4792	185	39	n∑	n∑	PROPN
ejpam-4792	185	40	j	j	PROPN
ejpam-4792	185	41	=	=	PUNCT
ejpam-4792	185	42	γ3,n−2−m+(n−2	γ3,n−2−m+(n−2	PROPN
ejpam-4792	185	43	)	)	PUNCT
ejpam-4792	185	44	(	(	PUNCT
ejpam-4792	185	45	−1)j−(n−2	−1)j−(n−2	PROPN
ejpam-4792	185	46	)	)	PUNCT
ejpam-4792	185	47	(	(	PUNCT
ejpam-4792	185	48	j	j	PROPN
ejpam-4792	185	49	n−	n−	NOUN
ejpam-4792	185	50	2	2	NUM
ejpam-4792	185	51	)	)	PUNCT
ejpam-4792	185	52	×	×	PROPN
ejpam-4792	185	53	s.	s.	PROPN
ejpam-4792	185	54	sattaso	sattaso	PROPN
ejpam-4792	185	55	,	,	PUNCT
ejpam-4792	185	56	p.	p.	PROPN
ejpam-4792	185	57	prasertsang	prasertsang	PROPN
ejpam-4792	185	58	,	,	PUNCT
ejpam-4792	185	59	t.	t.	PROPN
ejpam-4792	185	60	prasertsang	prasertsang	PROPN
ejpam-4792	185	61	/	/	SYM
ejpam-4792	185	62	eur	eur	PROPN
ejpam-4792	185	63	.	.	PUNCT
ejpam-4792	186	1	j.	j.	PROPN
ejpam-4792	186	2	pure	pure	PROPN
ejpam-4792	186	3	appl	appl	PROPN
ejpam-4792	186	4	.	.	PROPN
ejpam-4792	186	5	math	math	PROPN
ejpam-4792	186	6	,	,	PUNCT
ejpam-4792	186	7	16	16	NUM
ejpam-4792	186	8	(	(	PUNCT
ejpam-4792	186	9	3	3	NUM
ejpam-4792	186	10	)	)	PUNCT
ejpam-4792	186	11	(	(	PUNCT
ejpam-4792	186	12	2023	2023	NUM
ejpam-4792	186	13	)	)	PUNCT
ejpam-4792	186	14	,	,	PUNCT
ejpam-4792	186	15	1389	1389	NUM
ejpam-4792	186	16	-	-	SYM
ejpam-4792	186	17	1405	1405	NUM
ejpam-4792	186	18	1396	1396	NUM
ejpam-4792	186	19	j−1∏	j−1∏	PROPN
ejpam-4792	186	20	s	s	PROPN
ejpam-4792	186	21	=	=	PROPN
ejpam-4792	186	22	n−2	n−2	PROPN
ejpam-4792	186	23	(	(	PUNCT
ejpam-4792	186	24	m−	m−	PROPN
ejpam-4792	186	25	(	(	PUNCT
ejpam-4792	186	26	n−	n−	NOUN
ejpam-4792	186	27	2)−	2)−	NUM
ejpam-4792	186	28	γ3,n−2	γ3,n−2	PROPN
ejpam-4792	186	29	+	+	NUM
ejpam-4792	186	30	j	j	PROPN
ejpam-4792	187	1	+	+	CCONJ
ejpam-4792	187	2	α−	α−	ADP
ejpam-4792	187	3	s)×	s)×	CCONJ
ejpam-4792	187	4	am−(n−2)−γ3,n−2+j	am−(n−2)−γ3,n−2+j	NOUN
ejpam-4792	187	5	,	,	PUNCT
ejpam-4792	187	6	j	j	PROPN
ejpam-4792	187	7	=	=	SYM
ejpam-4792	187	8	0	0	PROPN
ejpam-4792	187	9	,	,	PUNCT
ejpam-4792	187	10	(	(	PUNCT
ejpam-4792	187	11	31	31	NUM
ejpam-4792	187	12	)	)	PUNCT
ejpam-4792	187	13	um−2(n−1	um−2(n−1	PROPN
ejpam-4792	187	14	)	)	PUNCT
ejpam-4792	187	15	→	→	SYM
ejpam-4792	187	16	am	be	AUX
ejpam-4792	187	17	,	,	PUNCT
ejpam-4792	187	18	n−1	n−1	PROPN
ejpam-4792	187	19	=	=	SYM
ejpam-4792	187	20	0	0	NUM
ejpam-4792	187	21	,	,	PUNCT
ejpam-4792	187	22	(	(	PUNCT
ejpam-4792	187	23	32	32	NUM
ejpam-4792	187	24	)	)	PUNCT
ejpam-4792	187	25	um−γ2,n−1−2(n−1	um−γ2,n−1−2(n−1	PROPN
ejpam-4792	187	26	)	)	PUNCT
ejpam-4792	187	27	→	→	SYM
ejpam-4792	187	28	am−γ2,n−1,n−1	am−γ2,n−1,n−1	NUM
ejpam-4792	187	29	−	−	PROPN
ejpam-4792	187	30	n	n	CCONJ
ejpam-4792	187	31	j−1∏	j−1∏	PROPN
ejpam-4792	187	32	s	s	PROPN
ejpam-4792	187	33	=	=	SYM
ejpam-4792	187	34	n−1	n−1	PROPN
ejpam-4792	187	35	(	(	PUNCT
ejpam-4792	187	36	m−	m−	PROPN
ejpam-4792	187	37	(	(	PUNCT
ejpam-4792	187	38	n−	n−	NOUN
ejpam-4792	187	39	1)−	1)−	NUM
ejpam-4792	187	40	γ2,n−1	γ2,n−1	ADJ
ejpam-4792	188	1	+	+	CCONJ
ejpam-4792	188	2	j	j	PROPN
ejpam-4792	188	3	+	+	CCONJ
ejpam-4792	188	4	α−	α−	ADP
ejpam-4792	188	5	s)×	s)×	NOUN
ejpam-4792	188	6	am−(n−1)−γ2,n−1+j	am−(n−1)−γ2,n−1+j	PROPN
ejpam-4792	188	7	,	,	PUNCT
ejpam-4792	188	8	j	j	PROPN
ejpam-4792	188	9	=	=	SYM
ejpam-4792	188	10	0	0	PROPN
ejpam-4792	188	11	,	,	PUNCT
ejpam-4792	188	12	(	(	PUNCT
ejpam-4792	188	13	33	33	NUM
ejpam-4792	188	14	)	)	PUNCT
ejpam-4792	188	15	um−(m+1)−2(n−1	um−(m+1)−2(n−1	PROPN
ejpam-4792	188	16	)	)	PUNCT
ejpam-4792	188	17	→	→	PUNCT
ejpam-4792	189	1	−n	−n	ADP
ejpam-4792	189	2	j−1∏	j−1∏	PROPN
ejpam-4792	189	3	s	s	PROPN
ejpam-4792	189	4	=	=	SYM
ejpam-4792	189	5	n−1	n−1	PROPN
ejpam-4792	189	6	(	(	PUNCT
ejpam-4792	189	7	−n+	−n+	INTJ
ejpam-4792	189	8	j	j	PROPN
ejpam-4792	189	9	+	+	CCONJ
ejpam-4792	189	10	α−	α−	ADP
ejpam-4792	189	11	s)a−n+j	s)a−n+j	PROPN
ejpam-4792	189	12	,	,	PUNCT
ejpam-4792	189	13	j	j	PROPN
ejpam-4792	189	14	=	=	SYM
ejpam-4792	189	15	0	0	PROPN
ejpam-4792	189	16	.	.	PUNCT
ejpam-4792	190	1	(	(	PUNCT
ejpam-4792	190	2	34	34	NUM
ejpam-4792	190	3	)	)	PUNCT
ejpam-4792	190	4	hence	hence	ADV
ejpam-4792	190	5	,	,	PUNCT
ejpam-4792	190	6	according	accord	VERB
ejpam-4792	190	7	to	to	ADP
ejpam-4792	190	8	eqs	eqs	PROPN
ejpam-4792	190	9	.	.	PUNCT
ejpam-4792	191	1	(	(	PUNCT
ejpam-4792	191	2	9	9	NUM
ejpam-4792	191	3	)	)	PUNCT
ejpam-4792	191	4	,	,	PUNCT
ejpam-4792	191	5	(	(	PUNCT
ejpam-4792	191	6	10	10	NUM
ejpam-4792	191	7	)	)	PUNCT
ejpam-4792	191	8	,	,	PUNCT
ejpam-4792	191	9	(	(	PUNCT
ejpam-4792	191	10	13	13	NUM
ejpam-4792	191	11	)	)	PUNCT
ejpam-4792	191	12	,	,	PUNCT
ejpam-4792	191	13	(	(	PUNCT
ejpam-4792	191	14	14	14	NUM
ejpam-4792	191	15	)	)	PUNCT
ejpam-4792	191	16	,	,	PUNCT
ejpam-4792	191	17	(	(	PUNCT
ejpam-4792	191	18	17	17	NUM
ejpam-4792	191	19	)	)	PUNCT
ejpam-4792	191	20	,	,	PUNCT
ejpam-4792	191	21	(	(	PUNCT
ejpam-4792	191	22	18	18	NUM
ejpam-4792	191	23	)	)	PUNCT
ejpam-4792	191	24	,	,	PUNCT
ejpam-4792	191	25	(	(	PUNCT
ejpam-4792	191	26	21	21	NUM
ejpam-4792	191	27	)	)	PUNCT
ejpam-4792	191	28	,	,	PUNCT
ejpam-4792	191	29	(	(	PUNCT
ejpam-4792	191	30	22	22	NUM
ejpam-4792	191	31	)	)	PUNCT
ejpam-4792	191	32	,	,	PUNCT
ejpam-4792	191	33	(	(	PUNCT
ejpam-4792	191	34	25	25	NUM
ejpam-4792	191	35	)	)	PUNCT
ejpam-4792	191	36	,	,	PUNCT
ejpam-4792	191	37	(	(	PUNCT
ejpam-4792	191	38	26	26	NUM
ejpam-4792	191	39	)	)	PUNCT
ejpam-4792	191	40	,	,	PUNCT
ejpam-4792	191	41	and	and	CCONJ
ejpam-4792	191	42	(	(	PUNCT
ejpam-4792	191	43	29	29	NUM
ejpam-4792	191	44	)	)	PUNCT
ejpam-4792	191	45	,	,	PUNCT
ejpam-4792	191	46	it	it	PRON
ejpam-4792	191	47	can	can	AUX
ejpam-4792	191	48	be	be	AUX
ejpam-4792	191	49	reduced	reduce	VERB
ejpam-4792	191	50	to	to	ADP
ejpam-4792	191	51	the	the	DET
ejpam-4792	191	52	following	follow	VERB
ejpam-4792	191	53	forms	form	NOUN
ejpam-4792	191	54	,	,	PUNCT
ejpam-4792	191	55	am,ϱ	am,ϱ	PROPN
ejpam-4792	191	56	=	=	SYM
ejpam-4792	191	57	0	0	NUM
ejpam-4792	191	58	;	;	PUNCT
ejpam-4792	191	59	ϱ	ϱ	X
ejpam-4792	191	60	=	=	SYM
ejpam-4792	191	61	0	0	NUM
ejpam-4792	191	62	,	,	PUNCT
ejpam-4792	191	63	1	1	NUM
ejpam-4792	191	64	,	,	PUNCT
ejpam-4792	191	65	2	2	NUM
ejpam-4792	191	66	,	,	PUNCT
ejpam-4792	191	67	.	.	PUNCT
ejpam-4792	191	68	.	.	PUNCT
ejpam-4792	192	1	.	.	PUNCT
ejpam-4792	193	1	,	,	PUNCT
ejpam-4792	193	2	n−	n−	NOUN
ejpam-4792	193	3	1	1	NUM
ejpam-4792	193	4	,	,	PUNCT
ejpam-4792	193	5	am−1,ϱ	am−1,ϱ	NOUN
ejpam-4792	193	6	=	=	PUNCT
ejpam-4792	193	7	0	0	NUM
ejpam-4792	193	8	;	;	PUNCT
ejpam-4792	193	9	ϱ	ϱ	X
ejpam-4792	193	10	=	=	SYM
ejpam-4792	193	11	0	0	NUM
ejpam-4792	193	12	,	,	PUNCT
ejpam-4792	193	13	1	1	NUM
ejpam-4792	193	14	,	,	PUNCT
ejpam-4792	193	15	2	2	NUM
ejpam-4792	193	16	,	,	PUNCT
ejpam-4792	193	17	.	.	PUNCT
ejpam-4792	193	18	.	.	PUNCT
ejpam-4792	194	1	.	.	PUNCT
ejpam-4792	195	1	,	,	PUNCT
ejpam-4792	195	2	n−	n−	NOUN
ejpam-4792	195	3	2	2	NUM
ejpam-4792	195	4	,	,	PUNCT
ejpam-4792	195	5	am−2,ϱ	am−2,ϱ	PUNCT
ejpam-4792	195	6	=	=	PUNCT
ejpam-4792	195	7	0	0	NUM
ejpam-4792	195	8	;	;	PUNCT
ejpam-4792	195	9	ϱ	ϱ	X
ejpam-4792	195	10	=	=	SYM
ejpam-4792	195	11	0	0	NUM
ejpam-4792	195	12	,	,	PUNCT
ejpam-4792	195	13	1	1	NUM
ejpam-4792	195	14	,	,	PUNCT
ejpam-4792	195	15	2	2	NUM
ejpam-4792	195	16	,	,	PUNCT
ejpam-4792	195	17	.	.	PUNCT
ejpam-4792	195	18	.	.	PUNCT
ejpam-4792	196	1	.	.	PUNCT
ejpam-4792	197	1	,	,	PUNCT
ejpam-4792	197	2	n−	n−	NOUN
ejpam-4792	197	3	3	3	NUM
ejpam-4792	197	4	,	,	PUNCT
ejpam-4792	197	5	...	...	PUNCT
ejpam-4792	198	1	am−(n−3),ϱ	am−(n−3),ϱ	NUM
ejpam-4792	198	2	=	=	SYM
ejpam-4792	198	3	0	0	NUM
ejpam-4792	198	4	;	;	PUNCT
ejpam-4792	198	5	ϱ	ϱ	X
ejpam-4792	198	6	=	=	SYM
ejpam-4792	198	7	0	0	NUM
ejpam-4792	198	8	,	,	PUNCT
ejpam-4792	198	9	1	1	NUM
ejpam-4792	198	10	,	,	PUNCT
ejpam-4792	198	11	2	2	NUM
ejpam-4792	198	12	,	,	PUNCT
ejpam-4792	198	13	am−(n−2),ϱ	am−(n−2),ϱ	PROPN
ejpam-4792	198	14	=	=	SYM
ejpam-4792	198	15	0	0	NUM
ejpam-4792	198	16	;	;	PUNCT
ejpam-4792	198	17	ϱ	ϱ	X
ejpam-4792	198	18	=	=	SYM
ejpam-4792	198	19	0	0	NUM
ejpam-4792	198	20	,	,	PUNCT
ejpam-4792	198	21	1	1	NUM
ejpam-4792	198	22	am−(n−1),0	am−(n−1),0	PROPN
ejpam-4792	198	23	=	=	SYM
ejpam-4792	198	24	0	0	NUM
ejpam-4792	198	25	,	,	PUNCT
ejpam-4792	198	26	then	then	ADV
ejpam-4792	198	27	,	,	PUNCT
ejpam-4792	198	28	condition	condition	NOUN
ejpam-4792	198	29	(	(	PUNCT
ejpam-4792	198	30	4	4	NUM
ejpam-4792	198	31	)	)	PUNCT
ejpam-4792	198	32	becomes	become	VERB
ejpam-4792	198	33	true	true	ADJ
ejpam-4792	198	34	.	.	PUNCT
ejpam-4792	199	1	from	from	ADP
ejpam-4792	199	2	eqs	eqs	PROPN
ejpam-4792	199	3	.	.	PUNCT
ejpam-4792	200	1	(	(	PUNCT
ejpam-4792	200	2	12	12	NUM
ejpam-4792	200	3	)	)	PUNCT
ejpam-4792	200	4	,	,	PUNCT
ejpam-4792	200	5	(	(	PUNCT
ejpam-4792	200	6	16	16	NUM
ejpam-4792	200	7	)	)	PUNCT
ejpam-4792	200	8	,	,	PUNCT
ejpam-4792	200	9	(	(	PUNCT
ejpam-4792	200	10	20	20	NUM
ejpam-4792	200	11	)	)	PUNCT
ejpam-4792	200	12	,	,	PUNCT
ejpam-4792	200	13	(	(	PUNCT
ejpam-4792	200	14	24	24	NUM
ejpam-4792	200	15	)	)	PUNCT
ejpam-4792	200	16	,	,	PUNCT
ejpam-4792	200	17	(	(	PUNCT
ejpam-4792	200	18	28	28	NUM
ejpam-4792	200	19	)	)	PUNCT
ejpam-4792	200	20	and	and	CCONJ
ejpam-4792	200	21	(	(	PUNCT
ejpam-4792	200	22	31	31	NUM
ejpam-4792	200	23	)	)	PUNCT
ejpam-4792	200	24	can	can	AUX
ejpam-4792	200	25	be	be	AUX
ejpam-4792	200	26	rewritten	rewrite	VERB
ejpam-4792	200	27	as	as	ADP
ejpam-4792	200	28	n∑	n∑	PROPN
ejpam-4792	200	29	j	j	PROPN
ejpam-4792	200	30	=	=	SYM
ejpam-4792	200	31	γ3−m+ϱ1	γ3−m+ϱ1	X
ejpam-4792	200	32	(	(	PUNCT
ejpam-4792	200	33	−1)j−ϱ1	−1)j−ϱ1	NUM
ejpam-4792	200	34	(	(	PUNCT
ejpam-4792	200	35	j	j	PROPN
ejpam-4792	200	36	ϱ1	ϱ1	PROPN
ejpam-4792	200	37	)	)	PUNCT
ejpam-4792	201	1	j−1∏	j−1∏	ADP
ejpam-4792	201	2	s=ϱ1	s=ϱ1	PROPN
ejpam-4792	201	3	(	(	PUNCT
ejpam-4792	201	4	m−	m−	PROPN
ejpam-4792	201	5	ϱ1	ϱ1	PROPN
ejpam-4792	201	6	−	−	PROPN
ejpam-4792	202	1	γ3	γ3	NOUN
ejpam-4792	203	1	+	+	CCONJ
ejpam-4792	203	2	j	j	PROPN
ejpam-4792	203	3	+	+	CCONJ
ejpam-4792	203	4	α−	α−	ADP
ejpam-4792	203	5	s)am−ϱ1−γ3+j	s)am−ϱ1−γ3+j	NOUN
ejpam-4792	203	6	,	,	PUNCT
ejpam-4792	203	7	j	j	NOUN
ejpam-4792	203	8	=	=	SYM
ejpam-4792	203	9	0	0	PROPN
ejpam-4792	203	10	,	,	PUNCT
ejpam-4792	203	11	for	for	ADP
ejpam-4792	203	12	ϱ1	ϱ1	PROPN
ejpam-4792	203	13	=	=	SYM
ejpam-4792	203	14	0	0	NUM
ejpam-4792	203	15	,	,	PUNCT
ejpam-4792	203	16	1	1	NUM
ejpam-4792	203	17	,	,	PUNCT
ejpam-4792	203	18	2	2	NUM
ejpam-4792	203	19	,	,	PUNCT
ejpam-4792	203	20	.	.	PUNCT
ejpam-4792	203	21	.	.	PUNCT
ejpam-4792	204	1	.	.	PUNCT
ejpam-4792	205	1	,	,	PUNCT
ejpam-4792	206	1	n−1	n−1	PROPN
ejpam-4792	206	2	and	and	CCONJ
ejpam-4792	206	3	γ3	γ3	NOUN
ejpam-4792	206	4	=	=	SYM
ejpam-4792	206	5	0	0	NUM
ejpam-4792	206	6	,	,	PUNCT
ejpam-4792	206	7	1	1	NUM
ejpam-4792	206	8	,	,	PUNCT
ejpam-4792	206	9	2	2	NUM
ejpam-4792	206	10	,	,	PUNCT
ejpam-4792	206	11	.	.	PUNCT
ejpam-4792	206	12	.	.	PUNCT
ejpam-4792	207	1	.	.	PUNCT
ejpam-4792	208	1	,	,	PUNCT
ejpam-4792	208	2	m−(n−ϱ1	m−(n−ϱ1	PROPN
ejpam-4792	208	3	+	+	PROPN
ejpam-4792	208	4	2),m−(n−ϱ1	2),m−(n−ϱ1	PROPN
ejpam-4792	208	5	+	+	NOUN
ejpam-4792	208	6	1),m−(n−ϱ1	1),m−(n−ϱ1	NUM
ejpam-4792	208	7	)	)	PUNCT
ejpam-4792	208	8	.	.	PUNCT
ejpam-4792	209	1	thus	thus	ADV
ejpam-4792	209	2	,	,	PUNCT
ejpam-4792	209	3	condition	condition	NOUN
ejpam-4792	209	4	(	(	PUNCT
ejpam-4792	209	5	5	5	NUM
ejpam-4792	209	6	)	)	PUNCT
ejpam-4792	209	7	holds	hold	VERB
ejpam-4792	209	8	by	by	ADP
ejpam-4792	209	9	replacing	replace	VERB
ejpam-4792	209	10	γ3	γ3	NOUN
ejpam-4792	209	11	−m+	−m+	NOUN
ejpam-4792	209	12	ϱ1	ϱ1	NOUN
ejpam-4792	209	13	=	=	SYM
ejpam-4792	209	14	ρ2	ρ2	PROPN
ejpam-4792	209	15	.	.	PUNCT
ejpam-4792	210	1	finally	finally	ADV
ejpam-4792	210	2	,	,	PUNCT
ejpam-4792	210	3	the	the	DET
ejpam-4792	210	4	conditions	condition	NOUN
ejpam-4792	210	5	as	as	SCONJ
ejpam-4792	210	6	stated	state	VERB
ejpam-4792	210	7	in	in	ADP
ejpam-4792	210	8	eqs	eqs	PROPN
ejpam-4792	210	9	.	.	PUNCT
ejpam-4792	211	1	(	(	PUNCT
ejpam-4792	211	2	11	11	NUM
ejpam-4792	211	3	)	)	PUNCT
ejpam-4792	211	4	,	,	PUNCT
ejpam-4792	211	5	(	(	PUNCT
ejpam-4792	211	6	15	15	NUM
ejpam-4792	211	7	)	)	PUNCT
ejpam-4792	211	8	,	,	PUNCT
ejpam-4792	211	9	(	(	PUNCT
ejpam-4792	211	10	19	19	NUM
ejpam-4792	211	11	)	)	PUNCT
ejpam-4792	211	12	,	,	PUNCT
ejpam-4792	211	13	(	(	PUNCT
ejpam-4792	211	14	23	23	NUM
ejpam-4792	211	15	)	)	PUNCT
ejpam-4792	211	16	,	,	PUNCT
ejpam-4792	211	17	(	(	PUNCT
ejpam-4792	211	18	27	27	NUM
ejpam-4792	211	19	)	)	PUNCT
ejpam-4792	211	20	,	,	PUNCT
ejpam-4792	211	21	and	and	CCONJ
ejpam-4792	211	22	(	(	PUNCT
ejpam-4792	211	23	30	30	NUM
ejpam-4792	211	24	)	)	PUNCT
ejpam-4792	211	25	are	be	AUX
ejpam-4792	211	26	properly	properly	ADV
ejpam-4792	211	27	equated	equate	VERB
ejpam-4792	211	28	to	to	ADP
ejpam-4792	211	29	condition	condition	NOUN
ejpam-4792	211	30	(	(	PUNCT
ejpam-4792	211	31	6	6	NUM
ejpam-4792	211	32	)	)	PUNCT
ejpam-4792	211	33	.	.	PUNCT
ejpam-4792	212	1	the	the	DET
ejpam-4792	212	2	proof	proof	NOUN
ejpam-4792	212	3	is	be	AUX
ejpam-4792	212	4	completed	complete	VERB
ejpam-4792	212	5	.	.	PUNCT
ejpam-4792	213	1	note	note	VERB
ejpam-4792	213	2	that	that	SCONJ
ejpam-4792	213	3	(	(	PUNCT
ejpam-4792	213	4	i	i	NOUN
ejpam-4792	213	5	)	)	PUNCT
ejpam-4792	213	6	no	no	INTJ
ejpam-4792	213	7	.	.	PUNCT
ejpam-4792	214	1	coes	coes	PROPN
ejpam-4792	214	2	is	be	AUX
ejpam-4792	214	3	the	the	DET
ejpam-4792	214	4	number	number	NOUN
ejpam-4792	214	5	of	of	ADP
ejpam-4792	214	6	polynomial	polynomial	ADJ
ejpam-4792	214	7	coefficients	coefficient	NOUN
ejpam-4792	214	8	in	in	ADP
ejpam-4792	214	9	eq	eq	ADP
ejpam-4792	214	10	.	.	PUNCT
ejpam-4792	215	1	(	(	PUNCT
ejpam-4792	215	2	3	3	NUM
ejpam-4792	215	3	)	)	PUNCT
ejpam-4792	215	4	and	and	CCONJ
ejpam-4792	215	5	(	(	PUNCT
ejpam-4792	215	6	ii	ii	NOUN
ejpam-4792	215	7	)	)	PUNCT
ejpam-4792	215	8	no	no	NOUN
ejpam-4792	215	9	.	.	PUNCT
ejpam-4792	216	1	cons	con	NOUN
ejpam-4792	216	2	is	be	AUX
ejpam-4792	216	3	the	the	DET
ejpam-4792	216	4	number	number	NOUN
ejpam-4792	216	5	of	of	ADP
ejpam-4792	216	6	conditions	condition	NOUN
ejpam-4792	216	7	according	accord	VERB
ejpam-4792	216	8	to	to	ADP
ejpam-4792	216	9	conditions	condition	NOUN
ejpam-4792	216	10	(	(	PUNCT
ejpam-4792	216	11	4)-(6	4)-(6	NUM
ejpam-4792	216	12	)	)	PUNCT
ejpam-4792	216	13	for	for	ADP
ejpam-4792	216	14	solving	solve	VERB
ejpam-4792	216	15	eq	eq	ADJ
ejpam-4792	216	16	.	.	PUNCT
ejpam-4792	217	1	(	(	PUNCT
ejpam-4792	217	2	3	3	X
ejpam-4792	217	3	)	)	PUNCT
ejpam-4792	217	4	using	use	VERB
ejpam-4792	217	5	the	the	DET
ejpam-4792	217	6	gα	gα	NOUN
ejpam-4792	217	7	-	-	PUNCT
ejpam-4792	217	8	transform	transform	NOUN
ejpam-4792	217	9	.	.	PUNCT
ejpam-4792	218	1	corollary	corollary	ADJ
ejpam-4792	218	2	1	1	NUM
ejpam-4792	218	3	.	.	PUNCT
ejpam-4792	219	1	given	give	VERB
ejpam-4792	219	2	i	i	PRON
ejpam-4792	219	3	=	=	NOUN
ejpam-4792	219	4	0	0	NUM
ejpam-4792	219	5	,	,	PUNCT
ejpam-4792	219	6	1	1	NUM
ejpam-4792	219	7	,	,	PUNCT
ejpam-4792	219	8	2	2	NUM
ejpam-4792	219	9	,	,	PUNCT
ejpam-4792	219	10	.	.	PUNCT
ejpam-4792	219	11	.	.	PUNCT
ejpam-4792	219	12	.	.	PUNCT
ejpam-4792	220	1	,	,	PUNCT
ejpam-4792	220	2	m	m	PROPN
ejpam-4792	220	3	,	,	PUNCT
ejpam-4792	220	4	j	j	PROPN
ejpam-4792	220	5	=	=	SYM
ejpam-4792	220	6	0	0	NUM
ejpam-4792	220	7	,	,	PUNCT
ejpam-4792	220	8	1	1	NUM
ejpam-4792	220	9	,	,	PUNCT
ejpam-4792	220	10	2	2	NUM
ejpam-4792	220	11	,	,	PUNCT
ejpam-4792	220	12	.	.	PUNCT
ejpam-4792	220	13	.	.	PUNCT
ejpam-4792	221	1	.	.	PUNCT
ejpam-4792	222	1	,	,	PUNCT
ejpam-4792	222	2	n	n	CCONJ
ejpam-4792	222	3	,	,	PUNCT
ejpam-4792	222	4	where	where	SCONJ
ejpam-4792	222	5	m	m	PROPN
ejpam-4792	222	6	≥	≥	NOUN
ejpam-4792	222	7	n	n	CCONJ
ejpam-4792	222	8	,	,	PUNCT
ejpam-4792	222	9	ai	ai	VERB
ejpam-4792	222	10	,	,	PUNCT
ejpam-4792	222	11	j	j	PROPN
ejpam-4792	222	12	are	be	AUX
ejpam-4792	222	13	the	the	DET
ejpam-4792	222	14	polynomial	polynomial	ADJ
ejpam-4792	222	15	coefficients	coefficient	NOUN
ejpam-4792	222	16	of	of	ADP
ejpam-4792	222	17	∑n	∑n	PROPN
ejpam-4792	222	18	j=0	j=0	PROPN
ejpam-4792	222	19	ai	ai	VERB
ejpam-4792	222	20	,	,	PUNCT
ejpam-4792	222	21	jτ	jτ	PROPN
ejpam-4792	222	22	j	j	PROPN
ejpam-4792	222	23	with	with	ADP
ejpam-4792	222	24	am	am	PROPN
ejpam-4792	222	25	,	,	PUNCT
ejpam-4792	222	26	n	n	PRON
ejpam-4792	222	27	̸=	̸=	PROPN
ejpam-4792	222	28	0	0	NUM
ejpam-4792	222	29	in	in	ADP
ejpam-4792	222	30	eq	eq	ADP
ejpam-4792	222	31	.	.	PUNCT
ejpam-4792	223	1	(	(	PUNCT
ejpam-4792	223	2	3	3	NUM
ejpam-4792	223	3	)	)	PUNCT
ejpam-4792	223	4	,	,	PUNCT
ejpam-4792	223	5	the	the	DET
ejpam-4792	223	6	following	follow	VERB
ejpam-4792	223	7	statements	statement	NOUN
ejpam-4792	223	8	hold	hold	VERB
ejpam-4792	223	9	:	:	PUNCT
ejpam-4792	223	10	(	(	PUNCT
ejpam-4792	223	11	i	i	NOUN
ejpam-4792	223	12	)	)	PUNCT
ejpam-4792	223	13	no	no	INTJ
ejpam-4792	223	14	.	.	PUNCT
ejpam-4792	224	1	coes	coes	PROPN
ejpam-4792	224	2	is	be	AUX
ejpam-4792	224	3	(	(	PUNCT
ejpam-4792	224	4	m+	m+	NUM
ejpam-4792	224	5	1)(n+	1)(n+	NUM
ejpam-4792	224	6	1	1	NUM
ejpam-4792	224	7	)	)	PUNCT
ejpam-4792	224	8	,	,	PUNCT
ejpam-4792	224	9	s.	s.	PROPN
ejpam-4792	224	10	sattaso	sattaso	PROPN
ejpam-4792	224	11	,	,	PUNCT
ejpam-4792	224	12	p.	p.	PROPN
ejpam-4792	224	13	prasertsang	prasertsang	PROPN
ejpam-4792	224	14	,	,	PUNCT
ejpam-4792	224	15	t.	t.	PROPN
ejpam-4792	224	16	prasertsang	prasertsang	PROPN
ejpam-4792	224	17	/	/	SYM
ejpam-4792	224	18	eur	eur	PROPN
ejpam-4792	224	19	.	.	PUNCT
ejpam-4792	225	1	j.	j.	PROPN
ejpam-4792	225	2	pure	pure	PROPN
ejpam-4792	225	3	appl	appl	PROPN
ejpam-4792	225	4	.	.	PROPN
ejpam-4792	225	5	math	math	PROPN
ejpam-4792	225	6	,	,	PUNCT
ejpam-4792	225	7	16	16	NUM
ejpam-4792	225	8	(	(	PUNCT
ejpam-4792	225	9	3	3	NUM
ejpam-4792	225	10	)	)	PUNCT
ejpam-4792	225	11	(	(	PUNCT
ejpam-4792	225	12	2023	2023	NUM
ejpam-4792	225	13	)	)	PUNCT
ejpam-4792	225	14	,	,	PUNCT
ejpam-4792	225	15	1389	1389	NUM
ejpam-4792	225	16	-	-	SYM
ejpam-4792	225	17	1405	1405	NUM
ejpam-4792	225	18	1397	1397	NUM
ejpam-4792	225	19	(	(	PUNCT
ejpam-4792	225	20	ii	ii	NOUN
ejpam-4792	225	21	)	)	PUNCT
ejpam-4792	225	22	no	no	INTJ
ejpam-4792	225	23	.	.	PUNCT
ejpam-4792	226	1	cons	con	NOUN
ejpam-4792	226	2	is	be	AUX
ejpam-4792	226	3	mn+	mn+	NOUN
ejpam-4792	226	4	n(n+3	n(n+3	PROPN
ejpam-4792	226	5	)	)	PUNCT
ejpam-4792	226	6	2	2	NUM
ejpam-4792	226	7	,	,	PUNCT
ejpam-4792	226	8	(	(	PUNCT
ejpam-4792	226	9	iii	iii	NOUN
ejpam-4792	226	10	)	)	PUNCT
ejpam-4792	226	11	no	no	NOUN
ejpam-4792	226	12	.	.	PUNCT
ejpam-4792	227	1	coes	coes	PROPN
ejpam-4792	227	2	=	=	PUNCT
ejpam-4792	228	1	no	no	INTJ
ejpam-4792	228	2	.	.	PUNCT
ejpam-4792	229	1	cons	con	NOUN
ejpam-4792	229	2	iff	iff	VERB
ejpam-4792	229	3	m	m	PROPN
ejpam-4792	229	4	=	=	SYM
ejpam-4792	229	5	(	(	PUNCT
ejpam-4792	229	6	n−1)(n+2	n−1)(n+2	NOUN
ejpam-4792	229	7	)	)	PUNCT
ejpam-4792	229	8	2	2	NUM
ejpam-4792	229	9	.	.	PUNCT
ejpam-4792	230	1	proof	proof	NOUN
ejpam-4792	230	2	.	.	PUNCT
ejpam-4792	231	1	assume	assume	VERB
ejpam-4792	231	2	that	that	SCONJ
ejpam-4792	231	3	i	i	PRON
ejpam-4792	231	4	=	=	NOUN
ejpam-4792	231	5	0	0	NUM
ejpam-4792	231	6	,	,	PUNCT
ejpam-4792	231	7	1	1	NUM
ejpam-4792	231	8	,	,	PUNCT
ejpam-4792	231	9	2	2	NUM
ejpam-4792	231	10	,	,	PUNCT
ejpam-4792	231	11	.	.	PUNCT
ejpam-4792	231	12	.	.	PUNCT
ejpam-4792	232	1	.	.	PUNCT
ejpam-4792	233	1	,	,	PUNCT
ejpam-4792	233	2	m	m	PROPN
ejpam-4792	233	3	,	,	PUNCT
ejpam-4792	233	4	j	j	PROPN
ejpam-4792	233	5	=	=	SYM
ejpam-4792	233	6	0	0	NUM
ejpam-4792	233	7	,	,	PUNCT
ejpam-4792	233	8	1	1	NUM
ejpam-4792	233	9	,	,	PUNCT
ejpam-4792	233	10	2	2	NUM
ejpam-4792	233	11	,	,	PUNCT
ejpam-4792	233	12	.	.	PUNCT
ejpam-4792	233	13	.	.	PUNCT
ejpam-4792	234	1	.	.	PUNCT
ejpam-4792	235	1	,	,	PUNCT
ejpam-4792	235	2	n	n	CCONJ
ejpam-4792	235	3	,	,	PUNCT
ejpam-4792	235	4	where	where	SCONJ
ejpam-4792	235	5	m	m	PROPN
ejpam-4792	235	6	≥	≥	NOUN
ejpam-4792	235	7	n	n	CCONJ
ejpam-4792	235	8	,	,	PUNCT
ejpam-4792	235	9	ai	ai	VERB
ejpam-4792	235	10	,	,	PUNCT
ejpam-4792	235	11	j	j	PROPN
ejpam-4792	235	12	are	be	AUX
ejpam-4792	235	13	the	the	DET
ejpam-4792	235	14	polynomial	polynomial	ADJ
ejpam-4792	235	15	coefficients	coefficient	NOUN
ejpam-4792	235	16	of	of	ADP
ejpam-4792	235	17	∑n	∑n	PROPN
ejpam-4792	235	18	j=0	j=0	PROPN
ejpam-4792	235	19	ai	ai	VERB
ejpam-4792	235	20	,	,	PUNCT
ejpam-4792	235	21	jτ	jτ	PROPN
ejpam-4792	235	22	j	j	PROPN
ejpam-4792	235	23	with	with	ADP
ejpam-4792	235	24	am	am	PROPN
ejpam-4792	235	25	,	,	PUNCT
ejpam-4792	235	26	n	n	PRON
ejpam-4792	235	27	̸=	̸=	PROPN
ejpam-4792	235	28	0	0	NUM
ejpam-4792	235	29	in	in	ADP
ejpam-4792	235	30	eq	eq	ADP
ejpam-4792	235	31	.	.	PUNCT
ejpam-4792	236	1	(	(	PUNCT
ejpam-4792	236	2	3	3	NUM
ejpam-4792	236	3	)	)	PUNCT
ejpam-4792	236	4	and	and	CCONJ
ejpam-4792	236	5	by	by	ADP
ejpam-4792	236	6	letting	let	VERB
ejpam-4792	236	7	ϱ1	ϱ1	PROPN
ejpam-4792	236	8	=	=	SYM
ejpam-4792	236	9	0	0	NUM
ejpam-4792	236	10	,	,	PUNCT
ejpam-4792	236	11	1	1	NUM
ejpam-4792	236	12	,	,	PUNCT
ejpam-4792	236	13	2	2	NUM
ejpam-4792	236	14	,	,	PUNCT
ejpam-4792	236	15	.	.	PUNCT
ejpam-4792	236	16	.	.	PUNCT
ejpam-4792	236	17	.	.	PUNCT
ejpam-4792	237	1	,	,	PUNCT
ejpam-4792	237	2	n−	n−	NOUN
ejpam-4792	237	3	1	1	NUM
ejpam-4792	237	4	,	,	PUNCT
ejpam-4792	237	5	and	and	CCONJ
ejpam-4792	237	6	ρ1	ρ1	NOUN
ejpam-4792	237	7	=	=	SYM
ejpam-4792	237	8	m−	m−	PROPN
ejpam-4792	237	9	(	(	PUNCT
ejpam-4792	237	10	n−	n−	NOUN
ejpam-4792	237	11	ϱ1	ϱ1	NOUN
ejpam-4792	237	12	−	−	PROPN
ejpam-4792	237	13	1),m−	1),m−	NUM
ejpam-4792	237	14	(	(	PUNCT
ejpam-4792	237	15	n−	n−	NOUN
ejpam-4792	237	16	ϱ1	ϱ1	NOUN
ejpam-4792	237	17	−	−	PROPN
ejpam-4792	237	18	2),m−	2),m−	PROPN
ejpam-4792	237	19	(	(	PUNCT
ejpam-4792	237	20	n−	n−	NOUN
ejpam-4792	237	21	ϱ1	ϱ1	NOUN
ejpam-4792	237	22	−	−	PROPN
ejpam-4792	237	23	3	3	NUM
ejpam-4792	237	24	)	)	PUNCT
ejpam-4792	237	25	,	,	PUNCT
ejpam-4792	237	26	.	.	PUNCT
ejpam-4792	237	27	.	.	PUNCT
ejpam-4792	238	1	.	.	PUNCT
ejpam-4792	239	1	,	,	PUNCT
ejpam-4792	239	2	m−	m−	PROPN
ejpam-4792	239	3	2,m	2,m	NOUN
ejpam-4792	239	4	−	−	ADP
ejpam-4792	239	5	1,m	1,m	NOUN
ejpam-4792	239	6	,	,	PUNCT
ejpam-4792	239	7	ρ2	ρ2	NOUN
ejpam-4792	239	8	=	=	SYM
ejpam-4792	239	9	ϱ1	ϱ1	PROPN
ejpam-4792	239	10	+	+	CCONJ
ejpam-4792	239	11	1	1	NUM
ejpam-4792	239	12	,	,	PUNCT
ejpam-4792	239	13	ϱ1	ϱ1	NOUN
ejpam-4792	239	14	+	+	CCONJ
ejpam-4792	239	15	2	2	NUM
ejpam-4792	239	16	,	,	PUNCT
ejpam-4792	239	17	ϱ1	ϱ1	NOUN
ejpam-4792	239	18	+	+	CCONJ
ejpam-4792	239	19	3	3	NUM
ejpam-4792	239	20	,	,	PUNCT
ejpam-4792	239	21	.	.	PUNCT
ejpam-4792	239	22	.	.	PUNCT
ejpam-4792	239	23	.	.	PUNCT
ejpam-4792	240	1	,	,	PUNCT
ejpam-4792	241	1	n	n	CCONJ
ejpam-4792	241	2	−	−	PROPN
ejpam-4792	241	3	2	2	NUM
ejpam-4792	241	4	,	,	PUNCT
ejpam-4792	241	5	n	n	CCONJ
ejpam-4792	241	6	−	−	PROPN
ejpam-4792	241	7	1	1	NUM
ejpam-4792	241	8	,	,	PUNCT
ejpam-4792	241	9	n	n	CCONJ
ejpam-4792	241	10	,	,	PUNCT
ejpam-4792	241	11	ρ3	ρ3	NOUN
ejpam-4792	241	12	=	=	SYM
ejpam-4792	241	13	0	0	NUM
ejpam-4792	241	14	,	,	PUNCT
ejpam-4792	241	15	1	1	NUM
ejpam-4792	241	16	,	,	PUNCT
ejpam-4792	241	17	2	2	NUM
ejpam-4792	241	18	,	,	PUNCT
ejpam-4792	241	19	.	.	PUNCT
ejpam-4792	241	20	.	.	PUNCT
ejpam-4792	241	21	.	.	PUNCT
ejpam-4792	242	1	,	,	PUNCT
ejpam-4792	242	2	m	m	VERB
ejpam-4792	242	3	−	−	PROPN
ejpam-4792	242	4	(	(	PUNCT
ejpam-4792	242	5	n	n	CCONJ
ejpam-4792	242	6	−	−	PROPN
ejpam-4792	242	7	ϱ1	ϱ1	PROPN
ejpam-4792	243	1	+	+	CCONJ
ejpam-4792	243	2	2),m−	2),m−	NUM
ejpam-4792	243	3	(	(	PUNCT
ejpam-4792	243	4	n−	n−	NOUN
ejpam-4792	243	5	ϱ1	ϱ1	NOUN
ejpam-4792	243	6	+	+	CCONJ
ejpam-4792	243	7	1),m−	1),m−	NUM
ejpam-4792	243	8	(	(	PUNCT
ejpam-4792	243	9	n−	n−	NOUN
ejpam-4792	243	10	ϱ1	ϱ1	NOUN
ejpam-4792	243	11	)	)	PUNCT
ejpam-4792	243	12	.	.	PUNCT
ejpam-4792	244	1	(	(	PUNCT
ejpam-4792	244	2	i	i	NOUN
ejpam-4792	244	3	)	)	PUNCT
ejpam-4792	244	4	for	for	ADP
ejpam-4792	244	5	each	each	DET
ejpam-4792	244	6	i	i	NOUN
ejpam-4792	244	7	=	=	NOUN
ejpam-4792	244	8	0	0	NUM
ejpam-4792	244	9	,	,	PUNCT
ejpam-4792	244	10	1	1	NUM
ejpam-4792	244	11	,	,	PUNCT
ejpam-4792	244	12	2	2	NUM
ejpam-4792	244	13	,	,	PUNCT
ejpam-4792	244	14	.	.	PUNCT
ejpam-4792	244	15	.	.	PUNCT
ejpam-4792	244	16	.	.	PUNCT
ejpam-4792	245	1	,	,	PUNCT
ejpam-4792	245	2	m	m	PROPN
ejpam-4792	245	3	,	,	PUNCT
ejpam-4792	245	4	the	the	DET
ejpam-4792	245	5	numbers	number	NOUN
ejpam-4792	245	6	of	of	ADP
ejpam-4792	245	7	polynomial	polynomial	ADJ
ejpam-4792	245	8	coefficients	coefficient	NOUN
ejpam-4792	245	9	of	of	ADP
ejpam-4792	245	10	all	all	DET
ejpam-4792	245	11	orders	order	NOUN
ejpam-4792	245	12	of	of	ADP
ejpam-4792	245	13	differential	differential	ADJ
ejpam-4792	245	14	equations	equation	NOUN
ejpam-4792	245	15	are	be	AUX
ejpam-4792	245	16	equal	equal	ADJ
ejpam-4792	245	17	to	to	ADP
ejpam-4792	245	18	n+	n+	PRON
ejpam-4792	245	19	1	1	NUM
ejpam-4792	245	20	,	,	PUNCT
ejpam-4792	245	21	then	then	ADV
ejpam-4792	245	22	no	no	INTJ
ejpam-4792	245	23	.	.	PUNCT
ejpam-4792	245	24	coes	coes	PROPN
ejpam-4792	245	25	is	be	AUX
ejpam-4792	245	26	(	(	PUNCT
ejpam-4792	245	27	m+	m+	NUM
ejpam-4792	245	28	1)(n+	1)(n+	NUM
ejpam-4792	245	29	1	1	NUM
ejpam-4792	245	30	)	)	PUNCT
ejpam-4792	245	31	.	.	PUNCT
ejpam-4792	246	1	(	(	PUNCT
ejpam-4792	246	2	ii	ii	NOUN
ejpam-4792	246	3	)	)	PUNCT
ejpam-4792	246	4	from	from	ADP
ejpam-4792	246	5	condition	condition	NOUN
ejpam-4792	246	6	(	(	PUNCT
ejpam-4792	246	7	4	4	NUM
ejpam-4792	246	8	)	)	PUNCT
ejpam-4792	246	9	,	,	PUNCT
ejpam-4792	246	10	we	we	PRON
ejpam-4792	246	11	obtain	obtain	VERB
ejpam-4792	246	12	if	if	SCONJ
ejpam-4792	246	13	ϱ1	ϱ1	NOUN
ejpam-4792	246	14	=	=	SYM
ejpam-4792	246	15	0	0	NUM
ejpam-4792	246	16	,	,	PUNCT
ejpam-4792	246	17	then	then	ADV
ejpam-4792	246	18	ρ1	ρ1	VERB
ejpam-4792	246	19	=	=	PROPN
ejpam-4792	246	20	m−	m−	PROPN
ejpam-4792	246	21	(	(	PUNCT
ejpam-4792	246	22	n−	n−	NOUN
ejpam-4792	246	23	1),m−	1),m−	NUM
ejpam-4792	246	24	(	(	PUNCT
ejpam-4792	246	25	n−	n−	PROPN
ejpam-4792	246	26	2),m−	2),m−	NUM
ejpam-4792	246	27	(	(	PUNCT
ejpam-4792	246	28	n−	n−	NOUN
ejpam-4792	246	29	3	3	NUM
ejpam-4792	246	30	)	)	PUNCT
ejpam-4792	246	31	,	,	PUNCT
ejpam-4792	246	32	.	.	PUNCT
ejpam-4792	246	33	.	.	PUNCT
ejpam-4792	247	1	.	.	PUNCT
ejpam-4792	248	1	,	,	PUNCT
ejpam-4792	248	2	m−	m−	PROPN
ejpam-4792	248	3	2,m−	2,m−	NUM
ejpam-4792	248	4	1,m	1,m	NOUN
ejpam-4792	248	5	,	,	PUNCT
ejpam-4792	248	6	no	no	INTJ
ejpam-4792	248	7	.	.	PUNCT
ejpam-4792	249	1	cons	con	NOUN
ejpam-4792	249	2	is	be	AUX
ejpam-4792	249	3	n	n	CCONJ
ejpam-4792	249	4	,	,	PUNCT
ejpam-4792	249	5	if	if	SCONJ
ejpam-4792	249	6	ϱ1	ϱ1	NOUN
ejpam-4792	249	7	=	=	SYM
ejpam-4792	249	8	1	1	NUM
ejpam-4792	249	9	,	,	PUNCT
ejpam-4792	249	10	then	then	ADV
ejpam-4792	249	11	ρ1	ρ1	VERB
ejpam-4792	249	12	=	=	PROPN
ejpam-4792	249	13	m−	m−	PROPN
ejpam-4792	249	14	(	(	PUNCT
ejpam-4792	249	15	n−	n−	PROPN
ejpam-4792	249	16	2),m−	2),m−	NUM
ejpam-4792	249	17	(	(	PUNCT
ejpam-4792	249	18	n−	n−	NOUN
ejpam-4792	249	19	3),m−	3),m−	NUM
ejpam-4792	249	20	(	(	PUNCT
ejpam-4792	249	21	n−	n−	NOUN
ejpam-4792	249	22	4	4	NUM
ejpam-4792	249	23	)	)	PUNCT
ejpam-4792	249	24	,	,	PUNCT
ejpam-4792	249	25	.	.	PUNCT
ejpam-4792	249	26	.	.	PUNCT
ejpam-4792	250	1	.	.	PUNCT
ejpam-4792	251	1	,	,	PUNCT
ejpam-4792	251	2	m−	m−	PROPN
ejpam-4792	251	3	2,m−	2,m−	NUM
ejpam-4792	251	4	1,m	1,m	NOUN
ejpam-4792	251	5	,	,	PUNCT
ejpam-4792	251	6	no	no	INTJ
ejpam-4792	251	7	.	.	PUNCT
ejpam-4792	252	1	cons	con	NOUN
ejpam-4792	252	2	is	be	AUX
ejpam-4792	252	3	n−	n−	NOUN
ejpam-4792	252	4	1	1	NUM
ejpam-4792	252	5	,	,	PUNCT
ejpam-4792	252	6	if	if	SCONJ
ejpam-4792	252	7	ϱ1	ϱ1	NOUN
ejpam-4792	252	8	=	=	SYM
ejpam-4792	252	9	2	2	NUM
ejpam-4792	252	10	,	,	PUNCT
ejpam-4792	252	11	then	then	ADV
ejpam-4792	252	12	ρ1	ρ1	VERB
ejpam-4792	252	13	=	=	PROPN
ejpam-4792	252	14	m−	m−	PROPN
ejpam-4792	252	15	(	(	PUNCT
ejpam-4792	252	16	n−	n−	PROPN
ejpam-4792	252	17	3),m−	3),m−	NUM
ejpam-4792	252	18	(	(	PUNCT
ejpam-4792	252	19	n−	n−	NOUN
ejpam-4792	252	20	4),m−	4),m−	NUM
ejpam-4792	252	21	(	(	PUNCT
ejpam-4792	252	22	n−	n−	NOUN
ejpam-4792	252	23	5	5	NUM
ejpam-4792	252	24	)	)	PUNCT
ejpam-4792	252	25	,	,	PUNCT
ejpam-4792	252	26	.	.	PUNCT
ejpam-4792	252	27	.	.	PUNCT
ejpam-4792	253	1	.	.	PUNCT
ejpam-4792	254	1	,	,	PUNCT
ejpam-4792	254	2	m−	m−	PROPN
ejpam-4792	254	3	2,m−	2,m−	NUM
ejpam-4792	254	4	1,m	1,m	NOUN
ejpam-4792	254	5	,	,	PUNCT
ejpam-4792	254	6	no	no	INTJ
ejpam-4792	254	7	.	.	PUNCT
ejpam-4792	255	1	cons	con	NOUN
ejpam-4792	255	2	is	be	AUX
ejpam-4792	255	3	n−	n−	NOUN
ejpam-4792	255	4	2	2	NUM
ejpam-4792	255	5	,	,	PUNCT
ejpam-4792	255	6	...	...	PUNCT
ejpam-4792	255	7	if	if	SCONJ
ejpam-4792	255	8	ϱ1	ϱ1	NOUN
ejpam-4792	255	9	=	=	SYM
ejpam-4792	255	10	n−	n−	NOUN
ejpam-4792	255	11	3	3	NUM
ejpam-4792	255	12	,	,	PUNCT
ejpam-4792	255	13	then	then	ADV
ejpam-4792	255	14	ρ1	ρ1	VERB
ejpam-4792	255	15	=	=	SYM
ejpam-4792	255	16	m−	m−	PROPN
ejpam-4792	255	17	2,m−	2,m−	NUM
ejpam-4792	255	18	1,m	1,m	NOUN
ejpam-4792	255	19	,	,	PUNCT
ejpam-4792	255	20	no	no	INTJ
ejpam-4792	255	21	.	.	PUNCT
ejpam-4792	256	1	cons	con	NOUN
ejpam-4792	256	2	is	be	AUX
ejpam-4792	256	3	3	3	NUM
ejpam-4792	256	4	,	,	PUNCT
ejpam-4792	256	5	if	if	SCONJ
ejpam-4792	256	6	ϱ1	ϱ1	NOUN
ejpam-4792	256	7	=	=	SYM
ejpam-4792	256	8	n−	n−	NOUN
ejpam-4792	256	9	2	2	NUM
ejpam-4792	256	10	,	,	PUNCT
ejpam-4792	256	11	then	then	ADV
ejpam-4792	256	12	ρ1	ρ1	VERB
ejpam-4792	256	13	=	=	PROPN
ejpam-4792	257	1	m−	m−	PROPN
ejpam-4792	257	2	1,m	1,m	PROPN
ejpam-4792	257	3	,	,	PUNCT
ejpam-4792	257	4	no	no	INTJ
ejpam-4792	257	5	.	.	PUNCT
ejpam-4792	258	1	cons	con	NOUN
ejpam-4792	258	2	is	be	AUX
ejpam-4792	258	3	2	2	NUM
ejpam-4792	258	4	,	,	PUNCT
ejpam-4792	258	5	if	if	SCONJ
ejpam-4792	258	6	ϱ1	ϱ1	NOUN
ejpam-4792	258	7	=	=	VERB
ejpam-4792	258	8	n−	n−	NOUN
ejpam-4792	258	9	1	1	NUM
ejpam-4792	258	10	,	,	PUNCT
ejpam-4792	258	11	then	then	ADV
ejpam-4792	258	12	ρ1	ρ1	VERB
ejpam-4792	258	13	=	=	SYM
ejpam-4792	258	14	m	m	PROPN
ejpam-4792	258	15	,	,	PUNCT
ejpam-4792	258	16	no	no	INTJ
ejpam-4792	258	17	.	.	PUNCT
ejpam-4792	259	1	cons	con	NOUN
ejpam-4792	259	2	is	be	AUX
ejpam-4792	259	3	1	1	NUM
ejpam-4792	259	4	.	.	PUNCT
ejpam-4792	260	1	consequently	consequently	ADV
ejpam-4792	260	2	,	,	PUNCT
ejpam-4792	260	3	the	the	DET
ejpam-4792	260	4	number	number	NOUN
ejpam-4792	260	5	of	of	ADP
ejpam-4792	260	6	conditions	condition	NOUN
ejpam-4792	260	7	in	in	ADP
ejpam-4792	260	8	conditon	conditon	PROPN
ejpam-4792	260	9	(	(	PUNCT
ejpam-4792	260	10	4	4	NUM
ejpam-4792	260	11	)	)	PUNCT
ejpam-4792	260	12	is	be	AUX
ejpam-4792	260	13	n(n+1	n(n+1	NOUN
ejpam-4792	260	14	)	)	PUNCT
ejpam-4792	260	15	2	2	NUM
ejpam-4792	260	16	.	.	PUNCT
ejpam-4792	261	1	from	from	ADP
ejpam-4792	261	2	condition	condition	NOUN
ejpam-4792	261	3	(	(	PUNCT
ejpam-4792	261	4	5	5	NUM
ejpam-4792	261	5	)	)	PUNCT
ejpam-4792	261	6	,	,	PUNCT
ejpam-4792	261	7	we	we	PRON
ejpam-4792	261	8	have	have	VERB
ejpam-4792	261	9	if	if	SCONJ
ejpam-4792	261	10	ϱ1	ϱ1	PROPN
ejpam-4792	261	11	=	=	SYM
ejpam-4792	261	12	0	0	NUM
ejpam-4792	261	13	,	,	PUNCT
ejpam-4792	261	14	then	then	ADV
ejpam-4792	261	15	ρ2	ρ2	NOUN
ejpam-4792	261	16	=	=	SYM
ejpam-4792	261	17	1	1	NUM
ejpam-4792	261	18	,	,	PUNCT
ejpam-4792	261	19	2	2	NUM
ejpam-4792	261	20	,	,	PUNCT
ejpam-4792	261	21	3	3	NUM
ejpam-4792	261	22	,	,	PUNCT
ejpam-4792	261	23	.	.	PUNCT
ejpam-4792	261	24	.	.	PUNCT
ejpam-4792	262	1	.	.	PUNCT
ejpam-4792	263	1	,	,	PUNCT
ejpam-4792	263	2	n−	n−	NOUN
ejpam-4792	263	3	2	2	NUM
ejpam-4792	263	4	,	,	PUNCT
ejpam-4792	263	5	n−	n−	NOUN
ejpam-4792	263	6	1	1	NUM
ejpam-4792	263	7	,	,	PUNCT
ejpam-4792	263	8	n	n	CCONJ
ejpam-4792	263	9	,	,	PUNCT
ejpam-4792	263	10	no	no	INTJ
ejpam-4792	263	11	.	.	PUNCT
ejpam-4792	264	1	cons	con	NOUN
ejpam-4792	264	2	is	be	AUX
ejpam-4792	264	3	n	n	CCONJ
ejpam-4792	264	4	,	,	PUNCT
ejpam-4792	264	5	if	if	SCONJ
ejpam-4792	264	6	ϱ1	ϱ1	NOUN
ejpam-4792	264	7	=	=	SYM
ejpam-4792	264	8	1	1	NUM
ejpam-4792	264	9	,	,	PUNCT
ejpam-4792	264	10	then	then	ADV
ejpam-4792	264	11	ρ2	ρ2	NOUN
ejpam-4792	264	12	=	=	SYM
ejpam-4792	264	13	2	2	NUM
ejpam-4792	264	14	,	,	PUNCT
ejpam-4792	264	15	3	3	NUM
ejpam-4792	264	16	,	,	PUNCT
ejpam-4792	264	17	.	.	PUNCT
ejpam-4792	264	18	.	.	PUNCT
ejpam-4792	265	1	.	.	PUNCT
ejpam-4792	266	1	,	,	PUNCT
ejpam-4792	266	2	n−	n−	NOUN
ejpam-4792	266	3	2	2	NUM
ejpam-4792	266	4	,	,	PUNCT
ejpam-4792	266	5	n−	n−	NOUN
ejpam-4792	266	6	1	1	NUM
ejpam-4792	266	7	,	,	PUNCT
ejpam-4792	266	8	n	n	CCONJ
ejpam-4792	266	9	,	,	PUNCT
ejpam-4792	266	10	no	no	INTJ
ejpam-4792	266	11	.	.	PUNCT
ejpam-4792	267	1	cons	con	NOUN
ejpam-4792	267	2	is	be	AUX
ejpam-4792	267	3	n−	n−	NOUN
ejpam-4792	267	4	1	1	NUM
ejpam-4792	267	5	,	,	PUNCT
ejpam-4792	267	6	if	if	SCONJ
ejpam-4792	267	7	ϱ1	ϱ1	NOUN
ejpam-4792	267	8	=	=	SYM
ejpam-4792	267	9	2	2	NUM
ejpam-4792	267	10	,	,	PUNCT
ejpam-4792	267	11	then	then	ADV
ejpam-4792	267	12	ρ2	ρ2	NOUN
ejpam-4792	267	13	=	=	SYM
ejpam-4792	267	14	3	3	NUM
ejpam-4792	267	15	,	,	PUNCT
ejpam-4792	267	16	.	.	PUNCT
ejpam-4792	267	17	.	.	PUNCT
ejpam-4792	268	1	.	.	PUNCT
ejpam-4792	269	1	,	,	PUNCT
ejpam-4792	269	2	n−	n−	NOUN
ejpam-4792	269	3	2	2	NUM
ejpam-4792	269	4	,	,	PUNCT
ejpam-4792	269	5	n−	n−	NOUN
ejpam-4792	269	6	1	1	NUM
ejpam-4792	269	7	,	,	PUNCT
ejpam-4792	269	8	n	n	CCONJ
ejpam-4792	269	9	,	,	PUNCT
ejpam-4792	269	10	no	no	INTJ
ejpam-4792	269	11	.	.	PUNCT
ejpam-4792	270	1	cons	con	NOUN
ejpam-4792	270	2	is	be	AUX
ejpam-4792	270	3	n−	n−	NOUN
ejpam-4792	270	4	2	2	NUM
ejpam-4792	270	5	,	,	PUNCT
ejpam-4792	270	6	...	...	PUNCT
ejpam-4792	270	7	if	if	SCONJ
ejpam-4792	270	8	ϱ1	ϱ1	NOUN
ejpam-4792	270	9	=	=	SYM
ejpam-4792	270	10	n−	n−	NOUN
ejpam-4792	270	11	3	3	NUM
ejpam-4792	270	12	,	,	PUNCT
ejpam-4792	270	13	then	then	ADV
ejpam-4792	270	14	ρ2	ρ2	NOUN
ejpam-4792	270	15	=	=	SYM
ejpam-4792	270	16	n−	n−	NOUN
ejpam-4792	270	17	2	2	NUM
ejpam-4792	270	18	,	,	PUNCT
ejpam-4792	270	19	n−	n−	NOUN
ejpam-4792	270	20	1	1	NUM
ejpam-4792	270	21	,	,	PUNCT
ejpam-4792	270	22	n	n	CCONJ
ejpam-4792	270	23	,	,	PUNCT
ejpam-4792	270	24	no	no	INTJ
ejpam-4792	270	25	.	.	PUNCT
ejpam-4792	271	1	cons	con	NOUN
ejpam-4792	271	2	is	be	AUX
ejpam-4792	271	3	3	3	NUM
ejpam-4792	271	4	,	,	PUNCT
ejpam-4792	271	5	if	if	SCONJ
ejpam-4792	271	6	ϱ1	ϱ1	NOUN
ejpam-4792	271	7	=	=	SYM
ejpam-4792	271	8	n−	n−	NOUN
ejpam-4792	271	9	2	2	NUM
ejpam-4792	271	10	,	,	PUNCT
ejpam-4792	271	11	then	then	ADV
ejpam-4792	271	12	ρ2	ρ2	NOUN
ejpam-4792	271	13	=	=	SYM
ejpam-4792	271	14	n−	n−	NOUN
ejpam-4792	271	15	1	1	NUM
ejpam-4792	271	16	,	,	PUNCT
ejpam-4792	271	17	n	n	CCONJ
ejpam-4792	271	18	,	,	PUNCT
ejpam-4792	271	19	no	no	INTJ
ejpam-4792	271	20	.	.	PUNCT
ejpam-4792	272	1	cons	con	NOUN
ejpam-4792	272	2	is	be	AUX
ejpam-4792	272	3	2	2	NUM
ejpam-4792	272	4	,	,	PUNCT
ejpam-4792	272	5	if	if	SCONJ
ejpam-4792	272	6	ϱ1	ϱ1	NOUN
ejpam-4792	272	7	=	=	VERB
ejpam-4792	272	8	n−	n−	NOUN
ejpam-4792	272	9	1	1	NUM
ejpam-4792	272	10	,	,	PUNCT
ejpam-4792	272	11	then	then	ADV
ejpam-4792	272	12	ρ2	ρ2	NOUN
ejpam-4792	272	13	=	=	SYM
ejpam-4792	272	14	n	n	CCONJ
ejpam-4792	272	15	,	,	PUNCT
ejpam-4792	272	16	no	no	INTJ
ejpam-4792	272	17	.	.	PUNCT
ejpam-4792	273	1	cons	con	NOUN
ejpam-4792	273	2	is	be	AUX
ejpam-4792	273	3	1	1	NUM
ejpam-4792	273	4	,	,	PUNCT
ejpam-4792	273	5	consequently	consequently	ADV
ejpam-4792	273	6	,	,	PUNCT
ejpam-4792	273	7	no	no	INTJ
ejpam-4792	273	8	.	.	PUNCT
ejpam-4792	274	1	cons	con	NOUN
ejpam-4792	274	2	in	in	ADP
ejpam-4792	274	3	condition	condition	NOUN
ejpam-4792	274	4	(	(	PUNCT
ejpam-4792	274	5	5	5	NUM
ejpam-4792	274	6	)	)	PUNCT
ejpam-4792	274	7	is	be	AUX
ejpam-4792	274	8	n(n+1	n(n+1	NOUN
ejpam-4792	274	9	)	)	PUNCT
ejpam-4792	274	10	2	2	NUM
ejpam-4792	274	11	,	,	PUNCT
ejpam-4792	274	12	from	from	ADP
ejpam-4792	274	13	eq	eq	ADP
ejpam-4792	274	14	.	.	PUNCT
ejpam-4792	275	1	(	(	PUNCT
ejpam-4792	275	2	6	6	NUM
ejpam-4792	275	3	)	)	PUNCT
ejpam-4792	275	4	,	,	PUNCT
ejpam-4792	275	5	we	we	PRON
ejpam-4792	275	6	get	get	VERB
ejpam-4792	275	7	if	if	SCONJ
ejpam-4792	275	8	ϱ1	ϱ1	NOUN
ejpam-4792	275	9	=	=	SYM
ejpam-4792	275	10	0	0	NUM
ejpam-4792	275	11	,	,	PUNCT
ejpam-4792	275	12	then	then	ADV
ejpam-4792	275	13	ρ3	ρ3	NOUN
ejpam-4792	275	14	=	=	SYM
ejpam-4792	275	15	0	0	NUM
ejpam-4792	275	16	,	,	PUNCT
ejpam-4792	275	17	1	1	NUM
ejpam-4792	275	18	,	,	PUNCT
ejpam-4792	275	19	2	2	NUM
ejpam-4792	275	20	,	,	PUNCT
ejpam-4792	275	21	.	.	PUNCT
ejpam-4792	275	22	.	.	PUNCT
ejpam-4792	276	1	.	.	PUNCT
ejpam-4792	277	1	,	,	PUNCT
ejpam-4792	277	2	m−	m−	PROPN
ejpam-4792	277	3	n−	n−	PROPN
ejpam-4792	277	4	2,m−	2,m−	NUM
ejpam-4792	277	5	n−	n−	NOUN
ejpam-4792	277	6	1,m−	1,m−	NUM
ejpam-4792	277	7	n	n	CCONJ
ejpam-4792	277	8	,	,	PUNCT
ejpam-4792	277	9	no	no	INTJ
ejpam-4792	277	10	.	.	PUNCT
ejpam-4792	278	1	cons	con	NOUN
ejpam-4792	278	2	is	be	AUX
ejpam-4792	278	3	m−	m−	PROPN
ejpam-4792	278	4	n+	n+	PUNCT
ejpam-4792	279	1	1	1	NUM
ejpam-4792	279	2	,	,	PUNCT
ejpam-4792	279	3	if	if	SCONJ
ejpam-4792	279	4	ϱ1	ϱ1	NOUN
ejpam-4792	279	5	=	=	SYM
ejpam-4792	279	6	1	1	NUM
ejpam-4792	279	7	,	,	PUNCT
ejpam-4792	279	8	then	then	ADV
ejpam-4792	279	9	ρ3	ρ3	NOUN
ejpam-4792	279	10	=	=	SYM
ejpam-4792	279	11	0	0	NUM
ejpam-4792	279	12	,	,	PUNCT
ejpam-4792	279	13	1	1	NUM
ejpam-4792	279	14	,	,	PUNCT
ejpam-4792	279	15	2	2	NUM
ejpam-4792	279	16	,	,	PUNCT
ejpam-4792	279	17	.	.	PUNCT
ejpam-4792	279	18	.	.	PUNCT
ejpam-4792	279	19	.	.	PUNCT
ejpam-4792	280	1	,	,	PUNCT
ejpam-4792	280	2	m−	m−	PROPN
ejpam-4792	280	3	n−	n−	VERB
ejpam-4792	280	4	3,m−	3,m−	NUM
ejpam-4792	280	5	n−	n−	NOUN
ejpam-4792	280	6	2,m−	2,m−	NUM
ejpam-4792	280	7	n−	n−	NOUN
ejpam-4792	280	8	1	1	NUM
ejpam-4792	280	9	,	,	PUNCT
ejpam-4792	280	10	no	no	INTJ
ejpam-4792	280	11	.	.	PUNCT
ejpam-4792	281	1	cons	con	NOUN
ejpam-4792	281	2	is	be	AUX
ejpam-4792	281	3	m−	m−	PROPN
ejpam-4792	281	4	n+	n+	PUNCT
ejpam-4792	282	1	2	2	NUM
ejpam-4792	282	2	,	,	PUNCT
ejpam-4792	282	3	if	if	SCONJ
ejpam-4792	282	4	ϱ1	ϱ1	NOUN
ejpam-4792	282	5	=	=	SYM
ejpam-4792	282	6	2	2	NUM
ejpam-4792	282	7	,	,	PUNCT
ejpam-4792	282	8	then	then	ADV
ejpam-4792	282	9	ρ3	ρ3	NOUN
ejpam-4792	282	10	=	=	SYM
ejpam-4792	282	11	0	0	NUM
ejpam-4792	282	12	,	,	PUNCT
ejpam-4792	282	13	1	1	NUM
ejpam-4792	282	14	,	,	PUNCT
ejpam-4792	282	15	2	2	NUM
ejpam-4792	282	16	,	,	PUNCT
ejpam-4792	282	17	.	.	PUNCT
ejpam-4792	282	18	.	.	PUNCT
ejpam-4792	282	19	.	.	PUNCT
ejpam-4792	283	1	,	,	PUNCT
ejpam-4792	283	2	m−	m−	PROPN
ejpam-4792	283	3	n−	n−	VERB
ejpam-4792	283	4	4,m−	4,m−	NUM
ejpam-4792	283	5	n−	n−	NOUN
ejpam-4792	283	6	3,m−	3,m−	NUM
ejpam-4792	283	7	n−	n−	NOUN
ejpam-4792	283	8	2	2	NUM
ejpam-4792	283	9	,	,	PUNCT
ejpam-4792	283	10	no	no	INTJ
ejpam-4792	283	11	.	.	PUNCT
ejpam-4792	284	1	cons	con	NOUN
ejpam-4792	284	2	is	be	AUX
ejpam-4792	284	3	m−	m−	PROPN
ejpam-4792	284	4	n+	n+	PUNCT
ejpam-4792	284	5	3	3	NUM
ejpam-4792	284	6	,	,	PUNCT
ejpam-4792	284	7	...	...	PUNCT
ejpam-4792	284	8	if	if	SCONJ
ejpam-4792	284	9	ϱ1	ϱ1	NOUN
ejpam-4792	284	10	=	=	SYM
ejpam-4792	284	11	n−	n−	NOUN
ejpam-4792	284	12	3	3	NUM
ejpam-4792	284	13	,	,	PUNCT
ejpam-4792	284	14	then	then	ADV
ejpam-4792	284	15	ρ3	ρ3	NOUN
ejpam-4792	284	16	=	=	SYM
ejpam-4792	284	17	0	0	NUM
ejpam-4792	284	18	,	,	PUNCT
ejpam-4792	284	19	1	1	NUM
ejpam-4792	284	20	,	,	PUNCT
ejpam-4792	284	21	2	2	NUM
ejpam-4792	284	22	,	,	PUNCT
ejpam-4792	284	23	.	.	PUNCT
ejpam-4792	284	24	.	.	PUNCT
ejpam-4792	285	1	.	.	PUNCT
ejpam-4792	286	1	,	,	PUNCT
ejpam-4792	286	2	m−	m−	PROPN
ejpam-4792	286	3	5,m−	5,m−	NUM
ejpam-4792	286	4	4,m−	4,m−	NUM
ejpam-4792	286	5	3	3	NUM
ejpam-4792	286	6	,	,	PUNCT
ejpam-4792	286	7	no	no	INTJ
ejpam-4792	286	8	.	.	PUNCT
ejpam-4792	287	1	cons	con	NOUN
ejpam-4792	287	2	is	be	AUX
ejpam-4792	287	3	m−	m−	PROPN
ejpam-4792	287	4	2	2	NUM
ejpam-4792	287	5	,	,	PUNCT
ejpam-4792	287	6	if	if	SCONJ
ejpam-4792	287	7	ϱ1	ϱ1	NOUN
ejpam-4792	287	8	=	=	SYM
ejpam-4792	287	9	n−	n−	NOUN
ejpam-4792	287	10	2	2	NUM
ejpam-4792	287	11	,	,	PUNCT
ejpam-4792	287	12	then	then	ADV
ejpam-4792	287	13	ρ3	ρ3	NOUN
ejpam-4792	287	14	=	=	SYM
ejpam-4792	287	15	0	0	NUM
ejpam-4792	287	16	,	,	PUNCT
ejpam-4792	287	17	1	1	NUM
ejpam-4792	287	18	,	,	PUNCT
ejpam-4792	287	19	2	2	NUM
ejpam-4792	287	20	,	,	PUNCT
ejpam-4792	287	21	.	.	PUNCT
ejpam-4792	287	22	.	.	PUNCT
ejpam-4792	288	1	.	.	PUNCT
ejpam-4792	289	1	,	,	PUNCT
ejpam-4792	289	2	m−	m−	PROPN
ejpam-4792	289	3	4,m−	4,m−	NUM
ejpam-4792	289	4	3,m−	3,m−	NUM
ejpam-4792	289	5	2	2	NUM
ejpam-4792	289	6	,	,	PUNCT
ejpam-4792	289	7	no	no	INTJ
ejpam-4792	289	8	.	.	PUNCT
ejpam-4792	290	1	cons	con	NOUN
ejpam-4792	290	2	is	be	AUX
ejpam-4792	290	3	m−	m−	PROPN
ejpam-4792	290	4	1	1	NUM
ejpam-4792	290	5	,	,	PUNCT
ejpam-4792	290	6	if	if	SCONJ
ejpam-4792	290	7	ϱ1	ϱ1	NOUN
ejpam-4792	290	8	=	=	VERB
ejpam-4792	290	9	n−	n−	NOUN
ejpam-4792	290	10	1	1	NUM
ejpam-4792	290	11	,	,	PUNCT
ejpam-4792	290	12	then	then	ADV
ejpam-4792	290	13	ρ3	ρ3	NOUN
ejpam-4792	290	14	=	=	SYM
ejpam-4792	290	15	0	0	NUM
ejpam-4792	290	16	,	,	PUNCT
ejpam-4792	290	17	1	1	NUM
ejpam-4792	290	18	,	,	PUNCT
ejpam-4792	290	19	2	2	NUM
ejpam-4792	290	20	,	,	PUNCT
ejpam-4792	290	21	.	.	PUNCT
ejpam-4792	290	22	.	.	PUNCT
ejpam-4792	291	1	.	.	PUNCT
ejpam-4792	292	1	,	,	PUNCT
ejpam-4792	292	2	m−	m−	PROPN
ejpam-4792	292	3	3,m−	3,m−	NUM
ejpam-4792	292	4	2,m−	2,m−	NUM
ejpam-4792	292	5	1	1	NUM
ejpam-4792	292	6	,	,	PUNCT
ejpam-4792	292	7	no	no	INTJ
ejpam-4792	292	8	.	.	PUNCT
ejpam-4792	293	1	cons	con	NOUN
ejpam-4792	293	2	is	be	AUX
ejpam-4792	293	3	m.	m.	NOUN
ejpam-4792	293	4	consequently	consequently	ADV
ejpam-4792	293	5	,	,	PUNCT
ejpam-4792	293	6	the	the	DET
ejpam-4792	293	7	number	number	NOUN
ejpam-4792	293	8	of	of	ADP
ejpam-4792	293	9	conditions	condition	NOUN
ejpam-4792	293	10	in	in	ADP
ejpam-4792	293	11	eq	eq	ADP
ejpam-4792	293	12	.	.	PUNCT
ejpam-4792	294	1	(	(	PUNCT
ejpam-4792	294	2	6	6	NUM
ejpam-4792	294	3	)	)	PUNCT
ejpam-4792	294	4	is	be	AUX
ejpam-4792	294	5	mn	mn	PROPN
ejpam-4792	294	6	−	−	PROPN
ejpam-4792	294	7	(	(	PUNCT
ejpam-4792	294	8	n−1)n	n−1)n	PROPN
ejpam-4792	294	9	2	2	NUM
ejpam-4792	294	10	,	,	PUNCT
ejpam-4792	294	11	it	it	PRON
ejpam-4792	294	12	follows	follow	VERB
ejpam-4792	294	13	that	that	SCONJ
ejpam-4792	294	14	no	no	INTJ
ejpam-4792	294	15	.	.	PUNCT
ejpam-4792	295	1	cons	con	NOUN
ejpam-4792	295	2	is	be	AUX
ejpam-4792	295	3	mn+	mn+	NOUN
ejpam-4792	295	4	n(n+3	n(n+3	PROPN
ejpam-4792	295	5	)	)	PUNCT
ejpam-4792	295	6	2	2	NUM
ejpam-4792	295	7	.	.	PUNCT
ejpam-4792	296	1	(	(	PUNCT
ejpam-4792	296	2	iii)(⇒	iii)(⇒	PROPN
ejpam-4792	296	3	)	)	PUNCT
ejpam-4792	296	4	if	if	SCONJ
ejpam-4792	296	5	no	no	INTJ
ejpam-4792	296	6	.	.	PUNCT
ejpam-4792	296	7	coes	coes	PROPN
ejpam-4792	297	1	=	=	PUNCT
ejpam-4792	297	2	no	no	INTJ
ejpam-4792	297	3	.	.	PUNCT
ejpam-4792	298	1	cons	con	NOUN
ejpam-4792	298	2	,	,	PUNCT
ejpam-4792	298	3	then	then	ADV
ejpam-4792	298	4	form	form	NOUN
ejpam-4792	298	5	(	(	PUNCT
ejpam-4792	298	6	i	i	NOUN
ejpam-4792	298	7	)	)	PUNCT
ejpam-4792	298	8	and	and	CCONJ
ejpam-4792	298	9	(	(	PUNCT
ejpam-4792	298	10	ii	ii	NOUN
ejpam-4792	298	11	)	)	PUNCT
ejpam-4792	298	12	,	,	PUNCT
ejpam-4792	298	13	we	we	PRON
ejpam-4792	298	14	have	have	VERB
ejpam-4792	298	15	(	(	PUNCT
ejpam-4792	298	16	m	m	VERB
ejpam-4792	298	17	+	+	NOUN
ejpam-4792	298	18	1)(n	1)(n	NUM
ejpam-4792	298	19	+	+	CCONJ
ejpam-4792	298	20	1	1	NUM
ejpam-4792	298	21	)	)	PUNCT
ejpam-4792	298	22	=	=	PUNCT
ejpam-4792	299	1	s.	s.	PROPN
ejpam-4792	299	2	sattaso	sattaso	PROPN
ejpam-4792	299	3	,	,	PUNCT
ejpam-4792	299	4	p.	p.	PROPN
ejpam-4792	299	5	prasertsang	prasertsang	PROPN
ejpam-4792	299	6	,	,	PUNCT
ejpam-4792	299	7	t.	t.	PROPN
ejpam-4792	299	8	prasertsang	prasertsang	PROPN
ejpam-4792	299	9	/	/	SYM
ejpam-4792	299	10	eur	eur	PROPN
ejpam-4792	299	11	.	.	PUNCT
ejpam-4792	300	1	j.	j.	PROPN
ejpam-4792	300	2	pure	pure	PROPN
ejpam-4792	300	3	appl	appl	PROPN
ejpam-4792	300	4	.	.	PROPN
ejpam-4792	300	5	math	math	PROPN
ejpam-4792	300	6	,	,	PUNCT
ejpam-4792	300	7	16	16	NUM
ejpam-4792	300	8	(	(	PUNCT
ejpam-4792	300	9	3	3	NUM
ejpam-4792	300	10	)	)	PUNCT
ejpam-4792	300	11	(	(	PUNCT
ejpam-4792	300	12	2023	2023	NUM
ejpam-4792	300	13	)	)	PUNCT
ejpam-4792	300	14	,	,	PUNCT
ejpam-4792	300	15	1389	1389	NUM
ejpam-4792	300	16	-	-	SYM
ejpam-4792	300	17	1405	1405	NUM
ejpam-4792	300	18	1398	1398	NUM
ejpam-4792	300	19	mn+	mn+	NOUN
ejpam-4792	300	20	n(n+3	n(n+3	PROPN
ejpam-4792	300	21	)	)	PUNCT
ejpam-4792	300	22	2	2	NUM
ejpam-4792	300	23	,	,	PUNCT
ejpam-4792	300	24	it	it	PRON
ejpam-4792	300	25	can	can	AUX
ejpam-4792	300	26	be	be	AUX
ejpam-4792	300	27	rewritten	rewrite	VERB
ejpam-4792	300	28	as	as	ADP
ejpam-4792	300	29	m	m	NOUN
ejpam-4792	300	30	=	=	SYM
ejpam-4792	300	31	(	(	PUNCT
ejpam-4792	300	32	n−1)(n+2	n−1)(n+2	NOUN
ejpam-4792	300	33	)	)	PUNCT
ejpam-4792	300	34	2	2	NUM
ejpam-4792	300	35	.	.	PUNCT
ejpam-4792	301	1	(	(	PUNCT
ejpam-4792	301	2	⇐	⇐	NOUN
ejpam-4792	301	3	)	)	PUNCT
ejpam-4792	301	4	let	let	VERB
ejpam-4792	301	5	m	m	VERB
ejpam-4792	301	6	=	=	SYM
ejpam-4792	301	7	(	(	PUNCT
ejpam-4792	301	8	n−1)(n+2	n−1)(n+2	NOUN
ejpam-4792	301	9	)	)	PUNCT
ejpam-4792	301	10	2	2	NUM
ejpam-4792	301	11	,	,	PUNCT
ejpam-4792	301	12	suppose	suppose	VERB
ejpam-4792	301	13	that	that	SCONJ
ejpam-4792	301	14	no	no	INTJ
ejpam-4792	301	15	.	.	PUNCT
ejpam-4792	301	16	coes	coes	PROPN
ejpam-4792	301	17	is	be	AUX
ejpam-4792	301	18	not	not	PART
ejpam-4792	301	19	equal	equal	ADJ
ejpam-4792	301	20	to	to	ADP
ejpam-4792	301	21	no	no	PROPN
ejpam-4792	301	22	.	.	PUNCT
ejpam-4792	302	1	cons	con	NOUN
ejpam-4792	302	2	,	,	PUNCT
ejpam-4792	302	3	that	that	ADV
ejpam-4792	302	4	is	is	ADV
ejpam-4792	302	5	(	(	PUNCT
ejpam-4792	302	6	m	m	VERB
ejpam-4792	302	7	+	+	NOUN
ejpam-4792	302	8	1)(n	1)(n	NUM
ejpam-4792	302	9	+	+	CCONJ
ejpam-4792	302	10	1	1	NUM
ejpam-4792	302	11	)	)	PUNCT
ejpam-4792	302	12	̸=	̸=	PROPN
ejpam-4792	302	13	mn	mn	PROPN
ejpam-4792	302	14	+	+	PROPN
ejpam-4792	302	15	n(n+3	n(n+3	PROPN
ejpam-4792	302	16	)	)	PUNCT
ejpam-4792	302	17	2	2	NUM
ejpam-4792	302	18	,	,	PUNCT
ejpam-4792	302	19	implying	imply	VERB
ejpam-4792	302	20	that	that	SCONJ
ejpam-4792	302	21	m	m	VERB
ejpam-4792	302	22	̸=	̸=	PROPN
ejpam-4792	302	23	(	(	PUNCT
ejpam-4792	302	24	n−1)(n+2	n−1)(n+2	NOUN
ejpam-4792	302	25	)	)	PUNCT
ejpam-4792	302	26	2	2	NUM
ejpam-4792	302	27	,	,	PUNCT
ejpam-4792	302	28	which	which	PRON
ejpam-4792	302	29	is	be	AUX
ejpam-4792	302	30	a	a	DET
ejpam-4792	302	31	contradiction	contradiction	NOUN
ejpam-4792	302	32	.	.	PUNCT
ejpam-4792	303	1	therefore	therefore	ADV
ejpam-4792	303	2	,	,	PUNCT
ejpam-4792	303	3	no	no	INTJ
ejpam-4792	303	4	.	.	PUNCT
ejpam-4792	303	5	coes	coes	PROPN
ejpam-4792	303	6	=	=	PUNCT
ejpam-4792	304	1	no	no	INTJ
ejpam-4792	304	2	.	.	PUNCT
ejpam-4792	305	1	cons	con	NOUN
ejpam-4792	305	2	.	.	PUNCT
ejpam-4792	306	1	4	4	X
ejpam-4792	306	2	.	.	X
ejpam-4792	306	3	applications	application	NOUN
ejpam-4792	306	4	according	accord	VERB
ejpam-4792	306	5	to	to	ADP
ejpam-4792	306	6	theorem	theorem	NOUN
ejpam-4792	306	7	1	1	NUM
ejpam-4792	306	8	,	,	PUNCT
ejpam-4792	306	9	the	the	DET
ejpam-4792	306	10	solutions	solution	NOUN
ejpam-4792	306	11	of	of	ADP
ejpam-4792	306	12	the	the	DET
ejpam-4792	306	13	higher	high	ADJ
ejpam-4792	306	14	-	-	PUNCT
ejpam-4792	306	15	order	order	NOUN
ejpam-4792	306	16	differential	differential	ADJ
ejpam-4792	306	17	equations	equation	NOUN
ejpam-4792	306	18	with	with	ADP
ejpam-4792	306	19	polynomial	polynomial	ADJ
ejpam-4792	306	20	coefficients	coefficient	NOUN
ejpam-4792	306	21	through	through	ADP
ejpam-4792	306	22	the	the	DET
ejpam-4792	306	23	gα	gα	NOUN
ejpam-4792	306	24	-	-	PUNCT
ejpam-4792	306	25	transform	transform	NOUN
ejpam-4792	306	26	can	can	AUX
ejpam-4792	306	27	be	be	AUX
ejpam-4792	306	28	solved	solve	VERB
ejpam-4792	306	29	,	,	PUNCT
ejpam-4792	306	30	as	as	SCONJ
ejpam-4792	306	31	follows	follow	VERB
ejpam-4792	306	32	:	:	PUNCT
ejpam-4792	306	33	4.1	4.1	NUM
ejpam-4792	306	34	.	.	PUNCT
ejpam-4792	307	1	the	the	DET
ejpam-4792	307	2	application	application	NOUN
ejpam-4792	307	3	of	of	ADP
ejpam-4792	307	4	fifth	fifth	ADJ
ejpam-4792	307	5	-	-	PUNCT
ejpam-4792	307	6	order	order	NOUN
ejpam-4792	307	7	differential	differential	ADJ
ejpam-4792	307	8	equation	equation	NOUN
ejpam-4792	307	9	with	with	ADP
ejpam-4792	307	10	polynomial	polynomial	ADJ
ejpam-4792	307	11	coefficients	coefficient	NOUN
ejpam-4792	307	12	where	where	SCONJ
ejpam-4792	307	13	α	α	NOUN
ejpam-4792	307	14	=	=	SYM
ejpam-4792	307	15	3	3	NUM
ejpam-4792	307	16	4.1.1	4.1.1	NUM
ejpam-4792	307	17	.	.	PUNCT
ejpam-4792	307	18	process	process	NOUN
ejpam-4792	307	19	of	of	ADP
ejpam-4792	307	20	general	general	ADJ
ejpam-4792	307	21	solution	solution	NOUN
ejpam-4792	307	22	example	example	NOUN
ejpam-4792	307	23	1	1	X
ejpam-4792	307	24	.	.	PUNCT
ejpam-4792	308	1	let	let	VERB
ejpam-4792	308	2	us	we	PRON
ejpam-4792	308	3	consider	consider	VERB
ejpam-4792	308	4	the	the	DET
ejpam-4792	308	5	fifth	fifth	ADJ
ejpam-4792	308	6	-	-	PUNCT
ejpam-4792	308	7	order	order	NOUN
ejpam-4792	308	8	differential	differential	ADJ
ejpam-4792	308	9	equation	equation	NOUN
ejpam-4792	308	10	with	with	ADP
ejpam-4792	308	11	polynomial	polynomial	ADJ
ejpam-4792	308	12	coefficients	coefficient	NOUN
ejpam-4792	308	13	in	in	ADP
ejpam-4792	308	14	the	the	DET
ejpam-4792	308	15	form	form	NOUN
ejpam-4792	308	16	of	of	ADP
ejpam-4792	308	17	t5y(5)(t	t5y(5)(t	NOUN
ejpam-4792	308	18	)	)	PUNCT
ejpam-4792	308	19	+	+	NUM
ejpam-4792	308	20	20t4y(4)(t	20t4y(4)(t	NUM
ejpam-4792	308	21	)	)	PUNCT
ejpam-4792	309	1	+	+	NUM
ejpam-4792	309	2	120t3y′′′(t	120t3y′′′(t	VERB
ejpam-4792	309	3	)	)	PUNCT
ejpam-4792	309	4	+	+	NUM
ejpam-4792	309	5	240t2y′′(t	240t2y′′(t	NUM
ejpam-4792	309	6	)	)	PUNCT
ejpam-4792	310	1	+	+	NUM
ejpam-4792	310	2	120ty′(t	120ty′(t	NUM
ejpam-4792	310	3	)	)	PUNCT
ejpam-4792	310	4	=	=	SYM
ejpam-4792	310	5	t	t	PROPN
ejpam-4792	310	6	,	,	PUNCT
ejpam-4792	310	7	t	t	PROPN
ejpam-4792	310	8	≥	≥	PROPN
ejpam-4792	310	9	0	0	NUM
ejpam-4792	310	10	.	.	PUNCT
ejpam-4792	311	1	(	(	PUNCT
ejpam-4792	311	2	35	35	NUM
ejpam-4792	311	3	)	)	PUNCT
ejpam-4792	311	4	from	from	ADP
ejpam-4792	311	5	eqs	eqs	PROPN
ejpam-4792	311	6	.	.	PUNCT
ejpam-4792	312	1	(	(	PUNCT
ejpam-4792	312	2	3	3	NUM
ejpam-4792	312	3	)	)	PUNCT
ejpam-4792	312	4	and	and	CCONJ
ejpam-4792	312	5	eq	eq	NOUN
ejpam-4792	312	6	.	.	PUNCT
ejpam-4792	313	1	(	(	PUNCT
ejpam-4792	313	2	35	35	NUM
ejpam-4792	313	3	)	)	PUNCT
ejpam-4792	313	4	,	,	PUNCT
ejpam-4792	313	5	we	we	PRON
ejpam-4792	313	6	have	have	VERB
ejpam-4792	313	7	a5,5	a5,5	PROPN
ejpam-4792	313	8	=	=	SYM
ejpam-4792	313	9	1	1	NUM
ejpam-4792	313	10	,	,	PUNCT
ejpam-4792	313	11	a4,4	a4,4	PROPN
ejpam-4792	313	12	=	=	PUNCT
ejpam-4792	313	13	20	20	NUM
ejpam-4792	313	14	,	,	PUNCT
ejpam-4792	313	15	a3,3	a3,3	ADP
ejpam-4792	313	16	=	=	NOUN
ejpam-4792	313	17	120	120	NUM
ejpam-4792	313	18	,	,	PUNCT
ejpam-4792	313	19	a2,2	a2,2	PROPN
ejpam-4792	313	20	=	=	SYM
ejpam-4792	313	21	240	240	NUM
ejpam-4792	313	22	,	,	PUNCT
ejpam-4792	313	23	a1,1	a1,1	NOUN
ejpam-4792	313	24	=	=	SYM
ejpam-4792	313	25	120	120	NUM
ejpam-4792	313	26	,	,	PUNCT
ejpam-4792	313	27	and	and	CCONJ
ejpam-4792	313	28	we	we	PRON
ejpam-4792	313	29	determine	determine	VERB
ejpam-4792	313	30	α	α	PROPN
ejpam-4792	313	31	=	=	NOUN
ejpam-4792	313	32	3	3	NUM
ejpam-4792	313	33	according	accord	VERB
ejpam-4792	313	34	to	to	ADP
ejpam-4792	313	35	the	the	DET
ejpam-4792	313	36	conditions	condition	NOUN
ejpam-4792	313	37	of	of	ADP
ejpam-4792	313	38	theorem	theorem	NOUN
ejpam-4792	313	39	1	1	NUM
ejpam-4792	313	40	,	,	PUNCT
ejpam-4792	313	41	then	then	ADV
ejpam-4792	313	42	applying	apply	VERB
ejpam-4792	313	43	the	the	DET
ejpam-4792	313	44	g3transform	g3transform	NOUN
ejpam-4792	313	45	leads	lead	VERB
ejpam-4792	313	46	to	to	ADP
ejpam-4792	313	47	finding	find	VERB
ejpam-4792	313	48	the	the	DET
ejpam-4792	313	49	solution	solution	NOUN
ejpam-4792	313	50	of	of	ADP
ejpam-4792	313	51	(	(	PUNCT
ejpam-4792	313	52	35	35	NUM
ejpam-4792	313	53	)	)	PUNCT
ejpam-4792	313	54	.	.	PUNCT
ejpam-4792	314	1	by	by	ADP
ejpam-4792	314	2	using	use	VERB
ejpam-4792	314	3	the	the	DET
ejpam-4792	314	4	g3	g3	NOUN
ejpam-4792	314	5	-	-	PUNCT
ejpam-4792	314	6	transform	transform	NOUN
ejpam-4792	314	7	to	to	ADP
ejpam-4792	314	8	(	(	PUNCT
ejpam-4792	314	9	35	35	NUM
ejpam-4792	314	10	)	)	PUNCT
ejpam-4792	314	11	,	,	PUNCT
ejpam-4792	314	12	we	we	PRON
ejpam-4792	314	13	have	have	VERB
ejpam-4792	314	14	g3{t5y(5)(t)}+g3{20t4y(4)(t)}+g3{120t3y′′′(t)}+g3{240t2y′′(t)}+g3{120ty′(t	g3{t5y(5)(t)}+g3{20t4y(4)(t)}+g3{120t3y′′′(t)}+g3{240t2y′′(t)}+g3{120ty′(t	NOUN
ejpam-4792	314	15	)	)	PUNCT
ejpam-4792	314	16	}	}	PUNCT
ejpam-4792	314	17	=	=	SYM
ejpam-4792	314	18	g3{t	g3{t	NOUN
ejpam-4792	314	19	}	}	PUNCT
ejpam-4792	314	20	.	.	PUNCT
ejpam-4792	315	1	using	use	VERB
ejpam-4792	315	2	lemma	lemma	PROPN
ejpam-4792	315	3	1	1	NUM
ejpam-4792	315	4	and	and	CCONJ
ejpam-4792	315	5	a	a	DET
ejpam-4792	315	6	little	little	ADJ
ejpam-4792	315	7	rewriting	rewrite	VERB
ejpam-4792	315	8	yields	yield	NOUN
ejpam-4792	315	9	u5f	u5f	PROPN
ejpam-4792	315	10	(	(	PUNCT
ejpam-4792	315	11	5)(u	5)(u	NUM
ejpam-4792	315	12	)	)	PUNCT
ejpam-4792	315	13	=	=	SYM
ejpam-4792	315	14	u5	u5	PROPN
ejpam-4792	315	15	,	,	PUNCT
ejpam-4792	315	16	f	f	PROPN
ejpam-4792	315	17	(	(	PUNCT
ejpam-4792	315	18	5)(u	5)(u	NUM
ejpam-4792	315	19	)	)	PUNCT
ejpam-4792	315	20	=	=	SYM
ejpam-4792	315	21	1	1	X
ejpam-4792	315	22	.	.	PUNCT
ejpam-4792	316	1	it	it	PRON
ejpam-4792	316	2	follows	follow	VERB
ejpam-4792	316	3	that	that	SCONJ
ejpam-4792	317	1	f	f	PROPN
ejpam-4792	317	2	(	(	PUNCT
ejpam-4792	317	3	u	u	NOUN
ejpam-4792	317	4	)	)	PUNCT
ejpam-4792	317	5	=	=	SYM
ejpam-4792	317	6	u5	u5	PROPN
ejpam-4792	317	7	120	120	NUM
ejpam-4792	317	8	+	+	NUM
ejpam-4792	317	9	c1	c1	PROPN
ejpam-4792	317	10	u4	u4	PROPN
ejpam-4792	317	11	24	24	NUM
ejpam-4792	317	12	+	+	PROPN
ejpam-4792	317	13	c2	c2	PROPN
ejpam-4792	317	14	u3	u3	NOUN
ejpam-4792	317	15	6	6	NUM
ejpam-4792	317	16	+	+	NUM
ejpam-4792	317	17	c3	c3	PROPN
ejpam-4792	317	18	u2	u2	PROPN
ejpam-4792	317	19	2	2	NUM
ejpam-4792	317	20	+	+	CCONJ
ejpam-4792	317	21	c4u+	c4u+	PROPN
ejpam-4792	317	22	c5	c5	PROPN
ejpam-4792	317	23	,	,	PUNCT
ejpam-4792	317	24	(	(	PUNCT
ejpam-4792	317	25	36	36	NUM
ejpam-4792	317	26	)	)	PUNCT
ejpam-4792	317	27	where	where	SCONJ
ejpam-4792	317	28	c1	c1	PROPN
ejpam-4792	317	29	,	,	PUNCT
ejpam-4792	317	30	c2	c2	PROPN
ejpam-4792	317	31	,	,	PUNCT
ejpam-4792	317	32	c3	c3	PROPN
ejpam-4792	317	33	,	,	PUNCT
ejpam-4792	317	34	c4	c4	NOUN
ejpam-4792	317	35	,	,	PUNCT
ejpam-4792	317	36	and	and	CCONJ
ejpam-4792	317	37	c5	c5	PROPN
ejpam-4792	317	38	are	be	AUX
ejpam-4792	317	39	constants	constant	NOUN
ejpam-4792	317	40	.	.	PUNCT
ejpam-4792	318	1	s.	s.	PROPN
ejpam-4792	318	2	sattaso	sattaso	PROPN
ejpam-4792	318	3	,	,	PUNCT
ejpam-4792	318	4	p.	p.	PROPN
ejpam-4792	318	5	prasertsang	prasertsang	PROPN
ejpam-4792	318	6	,	,	PUNCT
ejpam-4792	318	7	t.	t.	PROPN
ejpam-4792	318	8	prasertsang	prasertsang	PROPN
ejpam-4792	318	9	/	/	SYM
ejpam-4792	318	10	eur	eur	PROPN
ejpam-4792	318	11	.	.	PUNCT
ejpam-4792	319	1	j.	j.	PROPN
ejpam-4792	319	2	pure	pure	PROPN
ejpam-4792	319	3	appl	appl	PROPN
ejpam-4792	319	4	.	.	PROPN
ejpam-4792	319	5	math	math	PROPN
ejpam-4792	319	6	,	,	PUNCT
ejpam-4792	319	7	16	16	NUM
ejpam-4792	319	8	(	(	PUNCT
ejpam-4792	319	9	3	3	NUM
ejpam-4792	319	10	)	)	PUNCT
ejpam-4792	319	11	(	(	PUNCT
ejpam-4792	319	12	2023	2023	NUM
ejpam-4792	319	13	)	)	PUNCT
ejpam-4792	319	14	,	,	PUNCT
ejpam-4792	319	15	1389	1389	NUM
ejpam-4792	319	16	-	-	SYM
ejpam-4792	319	17	1405	1405	NUM
ejpam-4792	319	18	1399	1399	NUM
ejpam-4792	319	19	4.1.2	4.1.2	NUM
ejpam-4792	319	20	.	.	PUNCT
ejpam-4792	319	21	graphical	graphical	ADJ
ejpam-4792	319	22	analysis	analysis	NOUN
ejpam-4792	319	23	from	from	ADP
ejpam-4792	319	24	matlab	matlab	PROPN
ejpam-4792	319	25	,	,	PUNCT
ejpam-4792	319	26	figure	figure	NOUN
ejpam-4792	319	27	1	1	NUM
ejpam-4792	319	28	shows	show	VERB
ejpam-4792	319	29	the	the	DET
ejpam-4792	319	30	curves	curve	NOUN
ejpam-4792	319	31	of	of	ADP
ejpam-4792	319	32	general	general	ADJ
ejpam-4792	319	33	solutions	solution	NOUN
ejpam-4792	319	34	y(t	y(t	NUM
ejpam-4792	319	35	)	)	PUNCT
ejpam-4792	319	36	by	by	ADP
ejpam-4792	319	37	applying	apply	VERB
ejpam-4792	319	38	lemma	lemma	PROPN
ejpam-4792	319	39	2	2	NUM
ejpam-4792	319	40	and	and	CCONJ
ejpam-4792	319	41	the	the	DET
ejpam-4792	319	42	inverse	inverse	NOUN
ejpam-4792	319	43	g3	g3	NOUN
ejpam-4792	319	44	-	-	PUNCT
ejpam-4792	319	45	transform	transform	NOUN
ejpam-4792	319	46	.	.	PUNCT
ejpam-4792	320	1	for	for	ADP
ejpam-4792	320	2	the	the	DET
ejpam-4792	320	3	classical	classical	ADJ
ejpam-4792	320	4	solutions	solution	NOUN
ejpam-4792	320	5	,	,	PUNCT
ejpam-4792	320	6	we	we	PRON
ejpam-4792	320	7	have	have	VERB
ejpam-4792	320	8	to	to	PART
ejpam-4792	320	9	set	set	VERB
ejpam-4792	320	10	c2	c2	PROPN
ejpam-4792	320	11	=	=	SYM
ejpam-4792	320	12	c3	c3	PROPN
ejpam-4792	320	13	=	=	PROPN
ejpam-4792	320	14	c4	c4	PROPN
ejpam-4792	320	15	=	=	SYM
ejpam-4792	320	16	c5	c5	PROPN
ejpam-4792	320	17	=	=	PUNCT
ejpam-4792	320	18	0	0	NUM
ejpam-4792	320	19	and	and	CCONJ
ejpam-4792	320	20	various	various	ADJ
ejpam-4792	320	21	cases	case	NOUN
ejpam-4792	320	22	of	of	ADP
ejpam-4792	320	23	c1	c1	PROPN
ejpam-4792	320	24	in	in	ADP
ejpam-4792	320	25	eq	eq	PROPN
ejpam-4792	320	26	.	.	PUNCT
ejpam-4792	321	1	(	(	PUNCT
ejpam-4792	321	2	36	36	NUM
ejpam-4792	321	3	)	)	PUNCT
ejpam-4792	321	4	,	,	PUNCT
ejpam-4792	321	5	(	(	PUNCT
ejpam-4792	321	6	i	i	NOUN
ejpam-4792	321	7	)	)	PUNCT
ejpam-4792	321	8	when	when	SCONJ
ejpam-4792	321	9	c1	c1	PROPN
ejpam-4792	321	10	=	=	PROPN
ejpam-4792	321	11	1	1	NUM
ejpam-4792	321	12	,	,	PUNCT
ejpam-4792	321	13	we	we	PRON
ejpam-4792	321	14	get	get	VERB
ejpam-4792	321	15	y(t	y(t	NUM
ejpam-4792	321	16	)	)	PUNCT
ejpam-4792	322	1	=	=	PUNCT
ejpam-4792	322	2	t	t	PROPN
ejpam-4792	322	3	120	120	NUM
ejpam-4792	323	1	+	+	CCONJ
ejpam-4792	323	2	1	1	NUM
ejpam-4792	323	3	24	24	NUM
ejpam-4792	323	4	as	as	ADP
ejpam-4792	323	5	a	a	DET
ejpam-4792	323	6	solution	solution	NOUN
ejpam-4792	323	7	to	to	ADP
ejpam-4792	323	8	eq	eq	PROPN
ejpam-4792	323	9	.	.	PUNCT
ejpam-4792	324	1	(	(	PUNCT
ejpam-4792	324	2	35	35	NUM
ejpam-4792	324	3	)	)	PUNCT
ejpam-4792	324	4	,	,	PUNCT
ejpam-4792	324	5	(	(	PUNCT
ejpam-4792	324	6	ii	ii	NOUN
ejpam-4792	324	7	)	)	PUNCT
ejpam-4792	324	8	when	when	SCONJ
ejpam-4792	324	9	c1	c1	PROPN
ejpam-4792	324	10	=	=	PROPN
ejpam-4792	324	11	3	3	NUM
ejpam-4792	324	12	,	,	PUNCT
ejpam-4792	324	13	we	we	PRON
ejpam-4792	324	14	get	get	VERB
ejpam-4792	324	15	y(t	y(t	NUM
ejpam-4792	324	16	)	)	PUNCT
ejpam-4792	325	1	=	=	PUNCT
ejpam-4792	325	2	t	t	PROPN
ejpam-4792	325	3	120	120	NUM
ejpam-4792	326	1	+	+	CCONJ
ejpam-4792	326	2	1	1	NUM
ejpam-4792	326	3	8	8	NUM
ejpam-4792	326	4	as	as	ADP
ejpam-4792	326	5	a	a	DET
ejpam-4792	326	6	solution	solution	NOUN
ejpam-4792	326	7	to	to	ADP
ejpam-4792	326	8	eq	eq	PROPN
ejpam-4792	326	9	.	.	PUNCT
ejpam-4792	327	1	(	(	PUNCT
ejpam-4792	327	2	35	35	NUM
ejpam-4792	327	3	)	)	PUNCT
ejpam-4792	327	4	,	,	PUNCT
ejpam-4792	327	5	(	(	PUNCT
ejpam-4792	327	6	iii	iii	X
ejpam-4792	327	7	)	)	PUNCT
ejpam-4792	327	8	when	when	SCONJ
ejpam-4792	327	9	c1	c1	PROPN
ejpam-4792	327	10	=	=	PROPN
ejpam-4792	327	11	24	24	NUM
ejpam-4792	327	12	,	,	PUNCT
ejpam-4792	327	13	we	we	PRON
ejpam-4792	327	14	get	get	VERB
ejpam-4792	327	15	y(t	y(t	NUM
ejpam-4792	327	16	)	)	PUNCT
ejpam-4792	328	1	=	=	PUNCT
ejpam-4792	328	2	t	t	PROPN
ejpam-4792	328	3	120	120	NUM
ejpam-4792	329	1	+	+	CCONJ
ejpam-4792	329	2	1	1	NUM
ejpam-4792	329	3	as	as	ADP
ejpam-4792	329	4	a	a	DET
ejpam-4792	329	5	solution	solution	NOUN
ejpam-4792	329	6	to	to	ADP
ejpam-4792	329	7	eq	eq	PROPN
ejpam-4792	329	8	.	.	PUNCT
ejpam-4792	330	1	(	(	PUNCT
ejpam-4792	330	2	35	35	NUM
ejpam-4792	330	3	)	)	PUNCT
ejpam-4792	330	4	.	.	PUNCT
ejpam-4792	331	1	we	we	PRON
ejpam-4792	331	2	can	can	AUX
ejpam-4792	331	3	summarize	summarize	VERB
ejpam-4792	331	4	that	that	SCONJ
ejpam-4792	331	5	the	the	DET
ejpam-4792	331	6	general	general	ADJ
ejpam-4792	331	7	solutions	solution	NOUN
ejpam-4792	331	8	are	be	AUX
ejpam-4792	331	9	line	line	NOUN
ejpam-4792	331	10	graphs	graph	NOUN
ejpam-4792	331	11	with	with	ADP
ejpam-4792	331	12	intercept	intercept	ADJ
ejpam-4792	331	13	y	y	NOUN
ejpam-4792	331	14	-	-	NOUN
ejpam-4792	331	15	axis	axis	NOUN
ejpam-4792	331	16	at	at	ADP
ejpam-4792	331	17	several	several	ADJ
ejpam-4792	331	18	points	point	NOUN
ejpam-4792	331	19	depending	depend	VERB
ejpam-4792	331	20	on	on	ADP
ejpam-4792	331	21	c1	c1	PROPN
ejpam-4792	331	22	.	.	PUNCT
ejpam-4792	332	1	0	0	NUM
ejpam-4792	333	1	1	1	NUM
ejpam-4792	333	2	2	2	NUM
ejpam-4792	333	3	3	3	NUM
ejpam-4792	333	4	4	4	NUM
ejpam-4792	333	5	5	5	NUM
ejpam-4792	333	6	6	6	NUM
ejpam-4792	333	7	7	7	NUM
ejpam-4792	333	8	8	8	NUM
ejpam-4792	333	9	9	9	NUM
ejpam-4792	333	10	10	10	NUM
ejpam-4792	333	11	t	t	NOUN
ejpam-4792	333	12	0	0	NUM
ejpam-4792	333	13	0.2	0.2	NUM
ejpam-4792	333	14	0.4	0.4	NUM
ejpam-4792	333	15	0.6	0.6	NUM
ejpam-4792	333	16	0.8	0.8	NUM
ejpam-4792	333	17	1	1	NUM
ejpam-4792	333	18	1.2	1.2	NUM
ejpam-4792	333	19	y	y	PROPN
ejpam-4792	333	20	(	(	PUNCT
ejpam-4792	333	21	t	t	PROPN
ejpam-4792	333	22	)	)	PUNCT
ejpam-4792	333	23	c	c	NOUN
ejpam-4792	333	24	1	1	NUM
ejpam-4792	333	25	=	=	SYM
ejpam-4792	333	26	1	1	NUM
ejpam-4792	333	27	,	,	PUNCT
ejpam-4792	333	28	c	c	NOUN
ejpam-4792	333	29	2	2	NUM
ejpam-4792	333	30	=	=	SYM
ejpam-4792	333	31	c	c	NOUN
ejpam-4792	333	32	3	3	NUM
ejpam-4792	333	33	=	=	SYM
ejpam-4792	333	34	c	c	NOUN
ejpam-4792	333	35	4	4	NUM
ejpam-4792	333	36	=	=	SYM
ejpam-4792	333	37	c	c	NOUN
ejpam-4792	333	38	5	5	NUM
ejpam-4792	333	39	=	=	SYM
ejpam-4792	333	40	0	0	PUNCT
ejpam-4792	333	41	c	c	NOUN
ejpam-4792	333	42	1	1	NUM
ejpam-4792	333	43	=	=	SYM
ejpam-4792	333	44	3	3	NUM
ejpam-4792	333	45	,	,	PUNCT
ejpam-4792	333	46	c	c	NOUN
ejpam-4792	333	47	2	2	NUM
ejpam-4792	333	48	=	=	SYM
ejpam-4792	333	49	c	c	NOUN
ejpam-4792	333	50	3	3	NUM
ejpam-4792	333	51	=	=	SYM
ejpam-4792	333	52	c	c	NOUN
ejpam-4792	333	53	4	4	NUM
ejpam-4792	333	54	=	=	SYM
ejpam-4792	333	55	c	c	NOUN
ejpam-4792	333	56	5	5	NUM
ejpam-4792	333	57	=	=	SYM
ejpam-4792	333	58	0	0	PUNCT
ejpam-4792	333	59	c	c	NOUN
ejpam-4792	333	60	1	1	NUM
ejpam-4792	333	61	=	=	SYM
ejpam-4792	333	62	24	24	NUM
ejpam-4792	333	63	,	,	PUNCT
ejpam-4792	333	64	c	c	NOUN
ejpam-4792	333	65	2	2	NUM
ejpam-4792	333	66	=	=	SYM
ejpam-4792	333	67	c	c	NOUN
ejpam-4792	333	68	3	3	NUM
ejpam-4792	333	69	=	=	SYM
ejpam-4792	333	70	c	c	NOUN
ejpam-4792	333	71	4	4	NUM
ejpam-4792	333	72	=	=	SYM
ejpam-4792	333	73	c	c	NOUN
ejpam-4792	333	74	5	5	NUM
ejpam-4792	333	75	=	=	SYM
ejpam-4792	333	76	0	0	NUM
ejpam-4792	333	77	figure	figure	NOUN
ejpam-4792	333	78	1	1	NUM
ejpam-4792	333	79	:	:	PUNCT
ejpam-4792	333	80	general	general	ADJ
ejpam-4792	333	81	solutions	solution	NOUN
ejpam-4792	333	82	of	of	ADP
ejpam-4792	333	83	example	example	NOUN
ejpam-4792	333	84	1	1	NUM
ejpam-4792	333	85	.	.	NOUN
ejpam-4792	333	86	4.2	4.2	NUM
ejpam-4792	333	87	.	.	PUNCT
ejpam-4792	334	1	the	the	DET
ejpam-4792	334	2	application	application	NOUN
ejpam-4792	334	3	of	of	ADP
ejpam-4792	334	4	fifth	fifth	ADJ
ejpam-4792	334	5	-	-	PUNCT
ejpam-4792	334	6	order	order	NOUN
ejpam-4792	334	7	differential	differential	ADJ
ejpam-4792	334	8	equation	equation	NOUN
ejpam-4792	334	9	with	with	ADP
ejpam-4792	334	10	polynomial	polynomial	ADJ
ejpam-4792	334	11	coefficients	coefficient	NOUN
ejpam-4792	334	12	where	where	SCONJ
ejpam-4792	334	13	α	α	NOUN
ejpam-4792	334	14	=	=	NOUN
ejpam-4792	334	15	−1	−1	NOUN
ejpam-4792	334	16	4.2.1	4.2.1	NUM
ejpam-4792	334	17	.	.	PUNCT
ejpam-4792	334	18	process	process	NOUN
ejpam-4792	334	19	of	of	ADP
ejpam-4792	334	20	general	general	ADJ
ejpam-4792	334	21	solution	solution	NOUN
ejpam-4792	334	22	example	example	NOUN
ejpam-4792	334	23	2	2	X
ejpam-4792	334	24	.	.	PUNCT
ejpam-4792	335	1	let	let	VERB
ejpam-4792	335	2	us	we	PRON
ejpam-4792	335	3	consider	consider	VERB
ejpam-4792	335	4	the	the	DET
ejpam-4792	335	5	fifth	fifth	ADJ
ejpam-4792	335	6	-	-	PUNCT
ejpam-4792	335	7	order	order	NOUN
ejpam-4792	335	8	differential	differential	ADJ
ejpam-4792	335	9	equation	equation	NOUN
ejpam-4792	335	10	with	with	ADP
ejpam-4792	335	11	polynomial	polynomial	ADJ
ejpam-4792	335	12	coefficients	coefficient	NOUN
ejpam-4792	335	13	in	in	ADP
ejpam-4792	335	14	the	the	DET
ejpam-4792	335	15	form	form	NOUN
ejpam-4792	335	16	of	of	ADP
ejpam-4792	335	17	t3y(5)(t	t3y(5)(t	VERB
ejpam-4792	335	18	)	)	PUNCT
ejpam-4792	336	1	+	+	CCONJ
ejpam-4792	336	2	(	(	PUNCT
ejpam-4792	336	3	t3	t3	PROPN
ejpam-4792	336	4	+	+	NOUN
ejpam-4792	336	5	6t2)y(4)(t	6t2)y(4)(t	NUM
ejpam-4792	336	6	)	)	PUNCT
ejpam-4792	337	1	+	+	CCONJ
ejpam-4792	337	2	(	(	PUNCT
ejpam-4792	337	3	3t2	3t2	NUM
ejpam-4792	337	4	+	+	SYM
ejpam-4792	337	5	6t)y′′′(t	6t)y′′′(t	NUM
ejpam-4792	337	6	)	)	PUNCT
ejpam-4792	337	7	=	=	SYM
ejpam-4792	337	8	t2	t2	NOUN
ejpam-4792	337	9	2	2	NUM
ejpam-4792	337	10	+	+	SYM
ejpam-4792	337	11	t	t	PROPN
ejpam-4792	337	12	,	,	PUNCT
ejpam-4792	337	13	t	t	PROPN
ejpam-4792	337	14	≥	≥	PROPN
ejpam-4792	337	15	0	0	NUM
ejpam-4792	337	16	.	.	PUNCT
ejpam-4792	338	1	(	(	PUNCT
ejpam-4792	338	2	37	37	NUM
ejpam-4792	338	3	)	)	PUNCT
ejpam-4792	338	4	from	from	ADP
ejpam-4792	338	5	eqs.(3	eqs.(3	PROPN
ejpam-4792	338	6	)	)	PUNCT
ejpam-4792	338	7	and	and	CCONJ
ejpam-4792	338	8	(	(	PUNCT
ejpam-4792	338	9	37	37	NUM
ejpam-4792	338	10	)	)	PUNCT
ejpam-4792	338	11	,	,	PUNCT
ejpam-4792	338	12	we	we	PRON
ejpam-4792	338	13	have	have	VERB
ejpam-4792	338	14	a5,3	a5,3	PROPN
ejpam-4792	338	15	=	=	NOUN
ejpam-4792	338	16	1	1	NUM
ejpam-4792	338	17	,	,	PUNCT
ejpam-4792	338	18	a4,3	a4,3	PROPN
ejpam-4792	338	19	=	=	SYM
ejpam-4792	338	20	1	1	NUM
ejpam-4792	338	21	,	,	PUNCT
ejpam-4792	338	22	a4,2	a4,2	PROPN
ejpam-4792	338	23	=	=	NOUN
ejpam-4792	338	24	6	6	NUM
ejpam-4792	338	25	,	,	PUNCT
ejpam-4792	338	26	a3,2	a3,2	NOUN
ejpam-4792	338	27	=	=	SYM
ejpam-4792	338	28	3	3	NUM
ejpam-4792	338	29	,	,	PUNCT
ejpam-4792	338	30	a3,1	a3,1	PROPN
ejpam-4792	338	31	=	=	SYM
ejpam-4792	338	32	6	6	NUM
ejpam-4792	338	33	,	,	PUNCT
ejpam-4792	338	34	and	and	CCONJ
ejpam-4792	338	35	we	we	PRON
ejpam-4792	338	36	determine	determine	VERB
ejpam-4792	338	37	α	α	NOUN
ejpam-4792	338	38	=	=	SYM
ejpam-4792	338	39	−1	−1	NOUN
ejpam-4792	338	40	according	accord	VERB
ejpam-4792	338	41	to	to	ADP
ejpam-4792	338	42	the	the	DET
ejpam-4792	338	43	conditions	condition	NOUN
ejpam-4792	338	44	of	of	ADP
ejpam-4792	338	45	theorem	theorem	NOUN
ejpam-4792	338	46	1	1	NUM
ejpam-4792	338	47	,	,	PUNCT
ejpam-4792	338	48	so	so	ADV
ejpam-4792	338	49	applying	apply	VERB
ejpam-4792	338	50	the	the	DET
ejpam-4792	338	51	g−1transform	g−1transform	NOUN
ejpam-4792	338	52	leads	lead	VERB
ejpam-4792	338	53	to	to	ADP
ejpam-4792	338	54	finding	find	VERB
ejpam-4792	338	55	the	the	DET
ejpam-4792	338	56	solution	solution	NOUN
ejpam-4792	338	57	of	of	ADP
ejpam-4792	338	58	eq	eq	PROPN
ejpam-4792	338	59	.	.	PUNCT
ejpam-4792	339	1	(	(	PUNCT
ejpam-4792	339	2	37	37	NUM
ejpam-4792	339	3	)	)	PUNCT
ejpam-4792	339	4	.	.	PUNCT
ejpam-4792	340	1	by	by	ADP
ejpam-4792	340	2	using	use	VERB
ejpam-4792	340	3	the	the	DET
ejpam-4792	340	4	g−1	g−1	NOUN
ejpam-4792	340	5	-	-	PUNCT
ejpam-4792	340	6	transform	transform	NOUN
ejpam-4792	340	7	to	to	ADP
ejpam-4792	340	8	(	(	PUNCT
ejpam-4792	340	9	37	37	NUM
ejpam-4792	340	10	)	)	PUNCT
ejpam-4792	340	11	,	,	PUNCT
ejpam-4792	340	12	we	we	PRON
ejpam-4792	340	13	have	have	VERB
ejpam-4792	340	14	g−1{t3y(5)(t)}+g−1{t3y(4)(t)}+g−1{6t2y(4)(t)}+g−1{3t2y′′′(t)}+g−1{6ty′′′(t	g−1{t3y(5)(t)}+g−1{t3y(4)(t)}+g−1{6t2y(4)(t)}+g−1{3t2y′′′(t)}+g−1{6ty′′′(t	NOUN
ejpam-4792	340	15	)	)	PUNCT
ejpam-4792	340	16	}	}	PUNCT
ejpam-4792	340	17	=	=	SYM
ejpam-4792	340	18	g−1	g−1	X
ejpam-4792	340	19	{	{	PUNCT
ejpam-4792	340	20	t2	t2	NOUN
ejpam-4792	340	21	2	2	NUM
ejpam-4792	340	22	}	}	PUNCT
ejpam-4792	340	23	+	+	NOUN
ejpam-4792	340	24	g−1{t	g−1{t	NOUN
ejpam-4792	340	25	}	}	PUNCT
ejpam-4792	340	26	.	.	PUNCT
ejpam-4792	341	1	s.	s.	PROPN
ejpam-4792	341	2	sattaso	sattaso	PROPN
ejpam-4792	341	3	,	,	PUNCT
ejpam-4792	341	4	p.	p.	PROPN
ejpam-4792	341	5	prasertsang	prasertsang	PROPN
ejpam-4792	341	6	,	,	PUNCT
ejpam-4792	341	7	t.	t.	PROPN
ejpam-4792	341	8	prasertsang	prasertsang	PROPN
ejpam-4792	341	9	/	/	SYM
ejpam-4792	341	10	eur	eur	PROPN
ejpam-4792	341	11	.	.	PUNCT
ejpam-4792	342	1	j.	j.	PROPN
ejpam-4792	342	2	pure	pure	PROPN
ejpam-4792	342	3	appl	appl	PROPN
ejpam-4792	342	4	.	.	PROPN
ejpam-4792	342	5	math	math	PROPN
ejpam-4792	342	6	,	,	PUNCT
ejpam-4792	342	7	16	16	NUM
ejpam-4792	342	8	(	(	PUNCT
ejpam-4792	342	9	3	3	NUM
ejpam-4792	342	10	)	)	PUNCT
ejpam-4792	342	11	(	(	PUNCT
ejpam-4792	342	12	2023	2023	NUM
ejpam-4792	342	13	)	)	PUNCT
ejpam-4792	342	14	,	,	PUNCT
ejpam-4792	342	15	1389	1389	NUM
ejpam-4792	342	16	-	-	SYM
ejpam-4792	342	17	1405	1405	NUM
ejpam-4792	342	18	1400	1400	NUM
ejpam-4792	342	19	using	use	VERB
ejpam-4792	342	20	lemma	lemma	PROPN
ejpam-4792	342	21	1	1	NUM
ejpam-4792	342	22	and	and	CCONJ
ejpam-4792	342	23	simplifying	simplify	VERB
ejpam-4792	342	24	the	the	DET
ejpam-4792	342	25	above	above	ADJ
ejpam-4792	342	26	equation	equation	NOUN
ejpam-4792	342	27	,	,	PUNCT
ejpam-4792	342	28	we	we	PRON
ejpam-4792	342	29	have	have	VERB
ejpam-4792	342	30	the	the	DET
ejpam-4792	342	31	following	follow	VERB
ejpam-4792	342	32	(	(	PUNCT
ejpam-4792	342	33	u2	u2	PROPN
ejpam-4792	342	34	+	+	CCONJ
ejpam-4792	342	35	u)f	u)f	ADJ
ejpam-4792	342	36	′′′(u	′′′(u	PROPN
ejpam-4792	342	37	)	)	PUNCT
ejpam-4792	342	38	=	=	SYM
ejpam-4792	342	39	u2	u2	PROPN
ejpam-4792	342	40	+	+	CCONJ
ejpam-4792	342	41	u	u	PROPN
ejpam-4792	342	42	,	,	PUNCT
ejpam-4792	342	43	f	f	PROPN
ejpam-4792	342	44	′′′(u	′′′(u	PROPN
ejpam-4792	342	45	)	)	PUNCT
ejpam-4792	342	46	=	=	SYM
ejpam-4792	343	1	1	1	X
ejpam-4792	343	2	.	.	PUNCT
ejpam-4792	344	1	then	then	ADV
ejpam-4792	344	2	,	,	PUNCT
ejpam-4792	344	3	we	we	PRON
ejpam-4792	344	4	have	have	VERB
ejpam-4792	344	5	f	f	PROPN
ejpam-4792	344	6	(	(	PUNCT
ejpam-4792	344	7	u	u	NOUN
ejpam-4792	344	8	)	)	PUNCT
ejpam-4792	344	9	=	=	SYM
ejpam-4792	344	10	u3	u3	NOUN
ejpam-4792	344	11	6	6	NUM
ejpam-4792	344	12	+	+	NUM
ejpam-4792	344	13	c1	c1	NOUN
ejpam-4792	344	14	u2	u2	PROPN
ejpam-4792	344	15	2	2	NUM
ejpam-4792	344	16	+	+	CCONJ
ejpam-4792	344	17	c2u+	c2u+	PROPN
ejpam-4792	344	18	c3	c3	NOUN
ejpam-4792	344	19	,	,	PUNCT
ejpam-4792	344	20	(	(	PUNCT
ejpam-4792	344	21	38	38	NUM
ejpam-4792	344	22	)	)	PUNCT
ejpam-4792	344	23	where	where	SCONJ
ejpam-4792	344	24	c1	c1	PROPN
ejpam-4792	344	25	,	,	PUNCT
ejpam-4792	344	26	c2	c2	PROPN
ejpam-4792	344	27	,	,	PUNCT
ejpam-4792	344	28	and	and	CCONJ
ejpam-4792	344	29	c3	c3	PROPN
ejpam-4792	344	30	are	be	AUX
ejpam-4792	344	31	constants	constant	NOUN
ejpam-4792	344	32	.	.	PUNCT
ejpam-4792	345	1	4.2.2	4.2.2	X
ejpam-4792	345	2	.	.	PUNCT
ejpam-4792	345	3	graphical	graphical	ADJ
ejpam-4792	345	4	analysis	analysis	NOUN
ejpam-4792	345	5	from	from	ADP
ejpam-4792	345	6	matlab	matlab	PROPN
ejpam-4792	345	7	,	,	PUNCT
ejpam-4792	345	8	figure	figure	NOUN
ejpam-4792	345	9	2	2	NUM
ejpam-4792	345	10	draws	draw	VERB
ejpam-4792	345	11	the	the	DET
ejpam-4792	345	12	curve	curve	NOUN
ejpam-4792	345	13	of	of	ADP
ejpam-4792	345	14	general	general	ADJ
ejpam-4792	345	15	solution	solution	NOUN
ejpam-4792	345	16	y(t	y(t	NUM
ejpam-4792	345	17	)	)	PUNCT
ejpam-4792	345	18	by	by	ADP
ejpam-4792	345	19	applying	apply	VERB
ejpam-4792	345	20	lemma	lemma	PROPN
ejpam-4792	345	21	2	2	NUM
ejpam-4792	345	22	and	and	CCONJ
ejpam-4792	345	23	the	the	DET
ejpam-4792	345	24	inverse	inverse	NOUN
ejpam-4792	345	25	g−1	g−1	NOUN
ejpam-4792	345	26	-	-	PUNCT
ejpam-4792	345	27	transform	transform	NOUN
ejpam-4792	345	28	.	.	PUNCT
ejpam-4792	346	1	for	for	ADP
ejpam-4792	346	2	the	the	DET
ejpam-4792	346	3	classical	classical	ADJ
ejpam-4792	346	4	solutions	solution	NOUN
ejpam-4792	346	5	,	,	PUNCT
ejpam-4792	346	6	we	we	PRON
ejpam-4792	346	7	have	have	VERB
ejpam-4792	346	8	to	to	PART
ejpam-4792	346	9	set	set	VERB
ejpam-4792	346	10	c1	c1	PROPN
ejpam-4792	346	11	=	=	PROPN
ejpam-4792	346	12	c2	c2	PROPN
ejpam-4792	346	13	=	=	PROPN
ejpam-4792	346	14	c3	c3	PROPN
ejpam-4792	346	15	=	=	PUNCT
ejpam-4792	346	16	0	0	NUM
ejpam-4792	346	17	in	in	ADP
ejpam-4792	346	18	eq	eq	ADP
ejpam-4792	346	19	.	.	PUNCT
ejpam-4792	347	1	(	(	PUNCT
ejpam-4792	347	2	38	38	NUM
ejpam-4792	347	3	)	)	PUNCT
ejpam-4792	347	4	.	.	PUNCT
ejpam-4792	348	1	it	it	PRON
ejpam-4792	348	2	is	be	AUX
ejpam-4792	348	3	straightforward	straightforward	ADJ
ejpam-4792	348	4	to	to	PART
ejpam-4792	348	5	illustrate	illustrate	VERB
ejpam-4792	348	6	that	that	PRON
ejpam-4792	348	7	y(t	y(t	NOUN
ejpam-4792	348	8	)	)	PUNCT
ejpam-4792	349	1	=	=	SYM
ejpam-4792	349	2	t3	t3	NOUN
ejpam-4792	349	3	36	36	NUM
ejpam-4792	349	4	satisfies	satisfie	NOUN
ejpam-4792	349	5	eq	eq	ADJ
ejpam-4792	349	6	.	.	PUNCT
ejpam-4792	350	1	(	(	PUNCT
ejpam-4792	350	2	37	37	NUM
ejpam-4792	350	3	)	)	PUNCT
ejpam-4792	350	4	.	.	PUNCT
ejpam-4792	351	1	0	0	NUM
ejpam-4792	352	1	1	1	NUM
ejpam-4792	352	2	2	2	NUM
ejpam-4792	352	3	3	3	NUM
ejpam-4792	352	4	4	4	NUM
ejpam-4792	352	5	5	5	NUM
ejpam-4792	352	6	6	6	NUM
ejpam-4792	352	7	7	7	NUM
ejpam-4792	352	8	8	8	NUM
ejpam-4792	352	9	9	9	NUM
ejpam-4792	352	10	10	10	NUM
ejpam-4792	352	11	t	t	NOUN
ejpam-4792	352	12	0	0	NUM
ejpam-4792	352	13	5	5	NUM
ejpam-4792	352	14	10	10	NUM
ejpam-4792	352	15	15	15	NUM
ejpam-4792	352	16	20	20	NUM
ejpam-4792	352	17	25	25	NUM
ejpam-4792	352	18	30	30	NUM
ejpam-4792	352	19	y	y	PROPN
ejpam-4792	352	20	(	(	PUNCT
ejpam-4792	352	21	t	t	PROPN
ejpam-4792	352	22	)	)	PUNCT
ejpam-4792	352	23	c	c	NOUN
ejpam-4792	352	24	1	1	NUM
ejpam-4792	352	25	=	=	SYM
ejpam-4792	352	26	c	c	NOUN
ejpam-4792	352	27	2	2	NUM
ejpam-4792	352	28	=	=	SYM
ejpam-4792	352	29	c	c	NOUN
ejpam-4792	352	30	3	3	NUM
ejpam-4792	352	31	=	=	SYM
ejpam-4792	352	32	0	0	NUM
ejpam-4792	352	33	figure	figure	NOUN
ejpam-4792	352	34	2	2	NUM
ejpam-4792	352	35	:	:	PUNCT
ejpam-4792	352	36	general	general	ADJ
ejpam-4792	352	37	solutions	solution	NOUN
ejpam-4792	352	38	of	of	ADP
ejpam-4792	352	39	example	example	NOUN
ejpam-4792	352	40	2	2	NUM
ejpam-4792	352	41	.	.	NUM
ejpam-4792	352	42	4.3	4.3	NUM
ejpam-4792	352	43	.	.	PUNCT
ejpam-4792	353	1	the	the	DET
ejpam-4792	353	2	application	application	NOUN
ejpam-4792	353	3	of	of	ADP
ejpam-4792	353	4	seventh	seventh	ADJ
ejpam-4792	353	5	-	-	PUNCT
ejpam-4792	353	6	order	order	NOUN
ejpam-4792	353	7	differential	differential	ADJ
ejpam-4792	353	8	equation	equation	NOUN
ejpam-4792	353	9	with	with	ADP
ejpam-4792	353	10	polynomial	polynomial	ADJ
ejpam-4792	353	11	coefficients	coefficient	NOUN
ejpam-4792	353	12	where	where	SCONJ
ejpam-4792	353	13	α	α	NOUN
ejpam-4792	353	14	=	=	PUNCT
ejpam-4792	353	15	−5	−5	ADP
ejpam-4792	353	16	4.3.1	4.3.1	X
ejpam-4792	353	17	.	.	NOUN
ejpam-4792	353	18	process	process	NOUN
ejpam-4792	353	19	of	of	ADP
ejpam-4792	353	20	general	general	ADJ
ejpam-4792	353	21	solution	solution	NOUN
ejpam-4792	353	22	example	example	NOUN
ejpam-4792	353	23	3	3	X
ejpam-4792	353	24	.	.	PUNCT
ejpam-4792	354	1	let	let	VERB
ejpam-4792	354	2	us	we	PRON
ejpam-4792	354	3	consider	consider	VERB
ejpam-4792	354	4	the	the	DET
ejpam-4792	354	5	seventh	seventh	ADJ
ejpam-4792	354	6	-	-	PUNCT
ejpam-4792	354	7	order	order	NOUN
ejpam-4792	354	8	differential	differential	ADJ
ejpam-4792	354	9	equation	equation	NOUN
ejpam-4792	354	10	with	with	ADP
ejpam-4792	354	11	polynomial	polynomial	ADJ
ejpam-4792	354	12	coefficients	coefficient	NOUN
ejpam-4792	354	13	in	in	ADP
ejpam-4792	354	14	the	the	DET
ejpam-4792	354	15	form	form	NOUN
ejpam-4792	354	16	of	of	ADP
ejpam-4792	354	17	t4y(7)(t)−	t4y(7)(t)−	PROPN
ejpam-4792	354	18	4t3y(6)(t	4t3y(6)(t	PROPN
ejpam-4792	354	19	)	)	PUNCT
ejpam-4792	355	1	+	+	NUM
ejpam-4792	356	1	12t2y(5)(t	12t2y(5)(t	NUM
ejpam-4792	356	2	)	)	PUNCT
ejpam-4792	357	1	+	+	CCONJ
ejpam-4792	357	2	(	(	PUNCT
ejpam-4792	357	3	t4	t4	PROPN
ejpam-4792	357	4	−	−	PROPN
ejpam-4792	357	5	24t)y(4)(t	24t)y(4)(t	NUM
ejpam-4792	357	6	)	)	PUNCT
ejpam-4792	358	1	+	+	CCONJ
ejpam-4792	358	2	(	(	PUNCT
ejpam-4792	358	3	−16t3	−16t3	NUM
ejpam-4792	358	4	+	+	NUM
ejpam-4792	358	5	24)y′′′(t	24)y′′′(t	NUM
ejpam-4792	358	6	)	)	PUNCT
ejpam-4792	358	7	+	+	NUM
ejpam-4792	358	8	120t2y′′(t	120t2y′′(t	X
ejpam-4792	358	9	)	)	PUNCT
ejpam-4792	358	10	−	−	ADP
ejpam-4792	359	1	480ty′(t	480ty′(t	NUM
ejpam-4792	359	2	)	)	PUNCT
ejpam-4792	360	1	+	+	CCONJ
ejpam-4792	360	2	840y(t	840y(t	NUM
ejpam-4792	360	3	)	)	PUNCT
ejpam-4792	361	1	=	=	NOUN
ejpam-4792	361	2	t8	t8	NOUN
ejpam-4792	361	3	+	+	CCONJ
ejpam-4792	361	4	336t5	336t5	NUM
ejpam-4792	361	5	,	,	PUNCT
ejpam-4792	361	6	t	t	PROPN
ejpam-4792	361	7	≥	≥	PROPN
ejpam-4792	361	8	0	0	NUM
ejpam-4792	361	9	.	.	PUNCT
ejpam-4792	361	10	(	(	PUNCT
ejpam-4792	361	11	39	39	NUM
ejpam-4792	361	12	)	)	PUNCT
ejpam-4792	361	13	from	from	ADP
ejpam-4792	361	14	eqs	eqs	PROPN
ejpam-4792	361	15	.	.	PUNCT
ejpam-4792	362	1	(	(	PUNCT
ejpam-4792	362	2	3	3	X
ejpam-4792	362	3	)	)	PUNCT
ejpam-4792	362	4	and	and	CCONJ
ejpam-4792	362	5	(	(	PUNCT
ejpam-4792	362	6	39	39	NUM
ejpam-4792	362	7	)	)	PUNCT
ejpam-4792	362	8	,	,	PUNCT
ejpam-4792	362	9	we	we	PRON
ejpam-4792	362	10	have	have	VERB
ejpam-4792	362	11	a7,4	a7,4	NOUN
ejpam-4792	362	12	=	=	SYM
ejpam-4792	362	13	1	1	NUM
ejpam-4792	362	14	,	,	PUNCT
ejpam-4792	363	1	a6,3	a6,3	PROPN
ejpam-4792	363	2	=	=	SYM
ejpam-4792	363	3	−4	−4	PROPN
ejpam-4792	363	4	,	,	PUNCT
ejpam-4792	363	5	a5,2	a5,2	NOUN
ejpam-4792	363	6	=	=	NOUN
ejpam-4792	363	7	12	12	NUM
ejpam-4792	363	8	,	,	PUNCT
ejpam-4792	363	9	a4,4	a4,4	PROPN
ejpam-4792	363	10	=	=	PUNCT
ejpam-4792	363	11	1	1	NUM
ejpam-4792	363	12	,	,	PUNCT
ejpam-4792	363	13	a4,1	a4,1	PROPN
ejpam-4792	363	14	=	=	SYM
ejpam-4792	363	15	−24	−24	ADV
ejpam-4792	363	16	,	,	PUNCT
ejpam-4792	363	17	a3,3	a3,3	NOUN
ejpam-4792	363	18	=	=	SYM
ejpam-4792	363	19	−16	−16	PROPN
ejpam-4792	363	20	,	,	PUNCT
ejpam-4792	363	21	a3,0	a3,0	PROPN
ejpam-4792	363	22	=	=	SYM
ejpam-4792	363	23	24	24	NUM
ejpam-4792	363	24	,	,	PUNCT
ejpam-4792	363	25	a2,2	a2,2	PROPN
ejpam-4792	363	26	=	=	SYM
ejpam-4792	363	27	120	120	NUM
ejpam-4792	363	28	,	,	PUNCT
ejpam-4792	363	29	a1,1	a1,1	NOUN
ejpam-4792	363	30	=	=	SYM
ejpam-4792	363	31	−480	−480	PROPN
ejpam-4792	363	32	,	,	PUNCT
ejpam-4792	363	33	a0,0	a0,0	NOUN
ejpam-4792	363	34	=	=	SYM
ejpam-4792	363	35	840	840	NUM
ejpam-4792	363	36	,	,	PUNCT
ejpam-4792	363	37	s.	s.	PROPN
ejpam-4792	363	38	sattaso	sattaso	PROPN
ejpam-4792	363	39	,	,	PUNCT
ejpam-4792	364	1	p.	p.	PROPN
ejpam-4792	364	2	prasertsang	prasertsang	PROPN
ejpam-4792	364	3	,	,	PUNCT
ejpam-4792	364	4	t.	t.	PROPN
ejpam-4792	364	5	prasertsang	prasertsang	PROPN
ejpam-4792	364	6	/	/	SYM
ejpam-4792	364	7	eur	eur	PROPN
ejpam-4792	364	8	.	.	PUNCT
ejpam-4792	365	1	j.	j.	PROPN
ejpam-4792	365	2	pure	pure	PROPN
ejpam-4792	365	3	appl	appl	PROPN
ejpam-4792	365	4	.	.	PROPN
ejpam-4792	365	5	math	math	PROPN
ejpam-4792	365	6	,	,	PUNCT
ejpam-4792	365	7	16	16	NUM
ejpam-4792	365	8	(	(	PUNCT
ejpam-4792	365	9	3	3	NUM
ejpam-4792	365	10	)	)	PUNCT
ejpam-4792	365	11	(	(	PUNCT
ejpam-4792	365	12	2023	2023	NUM
ejpam-4792	365	13	)	)	PUNCT
ejpam-4792	365	14	,	,	PUNCT
ejpam-4792	365	15	1389	1389	NUM
ejpam-4792	365	16	-	-	SYM
ejpam-4792	365	17	1405	1405	NUM
ejpam-4792	365	18	1401	1401	NUM
ejpam-4792	365	19	and	and	CCONJ
ejpam-4792	365	20	we	we	PRON
ejpam-4792	365	21	determine	determine	VERB
ejpam-4792	365	22	α	α	NOUN
ejpam-4792	365	23	=	=	SYM
ejpam-4792	365	24	−5	−5	ADP
ejpam-4792	365	25	according	accord	VERB
ejpam-4792	365	26	to	to	ADP
ejpam-4792	365	27	the	the	DET
ejpam-4792	365	28	conditions	condition	NOUN
ejpam-4792	365	29	of	of	ADP
ejpam-4792	365	30	theorem	theorem	NOUN
ejpam-4792	365	31	1	1	NUM
ejpam-4792	365	32	,	,	PUNCT
ejpam-4792	365	33	so	so	ADV
ejpam-4792	365	34	applying	apply	VERB
ejpam-4792	365	35	the	the	DET
ejpam-4792	365	36	g−5transform	g−5transform	NOUN
ejpam-4792	365	37	leads	lead	VERB
ejpam-4792	365	38	to	to	ADP
ejpam-4792	365	39	finding	find	VERB
ejpam-4792	365	40	the	the	DET
ejpam-4792	365	41	solution	solution	NOUN
ejpam-4792	365	42	of	of	ADP
ejpam-4792	365	43	eq	eq	PROPN
ejpam-4792	365	44	.	.	PUNCT
ejpam-4792	366	1	(	(	PUNCT
ejpam-4792	366	2	39	39	NUM
ejpam-4792	366	3	)	)	PUNCT
ejpam-4792	366	4	.	.	PUNCT
ejpam-4792	367	1	by	by	ADP
ejpam-4792	367	2	using	use	VERB
ejpam-4792	367	3	the	the	DET
ejpam-4792	367	4	g−5	g−5	PROPN
ejpam-4792	367	5	-	-	PUNCT
ejpam-4792	367	6	transform	transform	NOUN
ejpam-4792	367	7	to	to	ADP
ejpam-4792	367	8	(	(	PUNCT
ejpam-4792	367	9	39	39	NUM
ejpam-4792	367	10	)	)	PUNCT
ejpam-4792	367	11	,	,	PUNCT
ejpam-4792	367	12	we	we	PRON
ejpam-4792	367	13	have	have	VERB
ejpam-4792	367	14	g−5{t4y(7)(t	g−5{t4y(7)(t	VERB
ejpam-4792	367	15	)	)	PUNCT
ejpam-4792	367	16	}	}	PUNCT
ejpam-4792	367	17	−g−5{4t3y(6)(t)}+g−5{12t2y(5)(t)}+g−5{t4y(4)(t	−g−5{4t3y(6)(t)}+g−5{12t2y(5)(t)}+g−5{t4y(4)(t	PROPN
ejpam-4792	367	18	)	)	PUNCT
ejpam-4792	367	19	}	}	PUNCT
ejpam-4792	367	20	−g−5{24ty(4)(t	−g−5{24ty(4)(t	NOUN
ejpam-4792	367	21	)	)	PUNCT
ejpam-4792	367	22	}	}	PUNCT
ejpam-4792	367	23	−g−5{16t3y′′′(t)}+g−5{24y′′′(t)}+g−5{120t2y′′(t	−g−5{16t3y′′′(t)}+g−5{24y′′′(t)}+g−5{120t2y′′(t	VERB
ejpam-4792	367	24	)	)	PUNCT
ejpam-4792	367	25	}	}	PUNCT
ejpam-4792	367	26	−g−5{480ty′(t)}+g−5{840y(t	−g−5{480ty′(t)}+g−5{840y(t	ADP
ejpam-4792	367	27	)	)	PUNCT
ejpam-4792	367	28	}	}	PUNCT
ejpam-4792	368	1	=	=	SYM
ejpam-4792	368	2	g−5{t8}+g−5{336t5	g−5{t8}+g−5{336t5	NOUN
ejpam-4792	368	3	}	}	PUNCT
ejpam-4792	368	4	.	.	PUNCT
ejpam-4792	369	1	using	use	VERB
ejpam-4792	369	2	lemma	lemma	PROPN
ejpam-4792	369	3	1	1	NUM
ejpam-4792	369	4	and	and	CCONJ
ejpam-4792	369	5	the	the	DET
ejpam-4792	369	6	above	above	ADJ
ejpam-4792	369	7	equation	equation	NOUN
ejpam-4792	369	8	,	,	PUNCT
ejpam-4792	369	9	this	this	PRON
ejpam-4792	369	10	can	can	AUX
ejpam-4792	369	11	be	be	AUX
ejpam-4792	369	12	rewritten	rewrite	VERB
ejpam-4792	369	13	as	as	ADP
ejpam-4792	369	14	(	(	PUNCT
ejpam-4792	369	15	u4	u4	PROPN
ejpam-4792	369	16	+	+	X
ejpam-4792	369	17	u)f	u)f	ADJ
ejpam-4792	369	18	(	(	PUNCT
ejpam-4792	369	19	4)(u	4)(u	NUM
ejpam-4792	369	20	)	)	PUNCT
ejpam-4792	369	21	=	=	SYM
ejpam-4792	369	22	8!(u4	8!(u4	NUM
ejpam-4792	369	23	+	+	NUM
ejpam-4792	369	24	u	u	NOUN
ejpam-4792	369	25	)	)	PUNCT
ejpam-4792	369	26	,	,	PUNCT
ejpam-4792	369	27	f	f	PROPN
ejpam-4792	369	28	(	(	PUNCT
ejpam-4792	369	29	4)(u	4)(u	NUM
ejpam-4792	369	30	)	)	PUNCT
ejpam-4792	369	31	=	=	SYM
ejpam-4792	369	32	8	8	NUM
ejpam-4792	369	33	!	!	PUNCT
ejpam-4792	369	34	.	.	PUNCT
ejpam-4792	370	1	then	then	ADV
ejpam-4792	370	2	,	,	PUNCT
ejpam-4792	370	3	we	we	PRON
ejpam-4792	370	4	have	have	VERB
ejpam-4792	370	5	f	f	PROPN
ejpam-4792	370	6	(	(	PUNCT
ejpam-4792	370	7	u	u	NOUN
ejpam-4792	370	8	)	)	PUNCT
ejpam-4792	370	9	=	=	SYM
ejpam-4792	370	10	8	8	X
ejpam-4792	370	11	!	!	PUNCT
ejpam-4792	371	1	u4	u4	PROPN
ejpam-4792	371	2	24	24	NUM
ejpam-4792	371	3	+	+	PROPN
ejpam-4792	371	4	c1	c1	NOUN
ejpam-4792	371	5	u3	u3	NOUN
ejpam-4792	371	6	6	6	NUM
ejpam-4792	371	7	+	+	NUM
ejpam-4792	371	8	c2	c2	PROPN
ejpam-4792	371	9	u2	u2	PROPN
ejpam-4792	371	10	2	2	NUM
ejpam-4792	371	11	+	+	CCONJ
ejpam-4792	371	12	c3u+	c3u+	NOUN
ejpam-4792	371	13	c4	c4	NOUN
ejpam-4792	371	14	,	,	PUNCT
ejpam-4792	371	15	(	(	PUNCT
ejpam-4792	371	16	40	40	NUM
ejpam-4792	371	17	)	)	PUNCT
ejpam-4792	371	18	where	where	SCONJ
ejpam-4792	371	19	c1	c1	PROPN
ejpam-4792	371	20	,	,	PUNCT
ejpam-4792	371	21	c2	c2	PROPN
ejpam-4792	371	22	,	,	PUNCT
ejpam-4792	371	23	c3	c3	PROPN
ejpam-4792	371	24	,	,	PUNCT
ejpam-4792	371	25	and	and	CCONJ
ejpam-4792	371	26	c4	c4	NOUN
ejpam-4792	371	27	are	be	AUX
ejpam-4792	371	28	constants	constant	NOUN
ejpam-4792	371	29	.	.	PUNCT
ejpam-4792	372	1	4.3.2	4.3.2	X
ejpam-4792	372	2	.	.	PUNCT
ejpam-4792	372	3	graphical	graphical	ADJ
ejpam-4792	372	4	analysis	analysis	NOUN
ejpam-4792	372	5	from	from	ADP
ejpam-4792	372	6	matlab	matlab	PROPN
ejpam-4792	372	7	,	,	PUNCT
ejpam-4792	372	8	figure	figure	NOUN
ejpam-4792	372	9	3	3	NUM
ejpam-4792	372	10	shows	show	VERB
ejpam-4792	372	11	the	the	DET
ejpam-4792	372	12	curves	curve	NOUN
ejpam-4792	372	13	of	of	ADP
ejpam-4792	372	14	general	general	ADJ
ejpam-4792	372	15	solutions	solution	NOUN
ejpam-4792	372	16	y(t	y(t	NUM
ejpam-4792	372	17	)	)	PUNCT
ejpam-4792	372	18	by	by	ADP
ejpam-4792	372	19	applying	apply	VERB
ejpam-4792	372	20	lemma	lemma	PROPN
ejpam-4792	372	21	2	2	NUM
ejpam-4792	372	22	and	and	CCONJ
ejpam-4792	372	23	the	the	DET
ejpam-4792	372	24	inverse	inverse	NOUN
ejpam-4792	372	25	g−5	g−5	PROPN
ejpam-4792	372	26	-	-	PUNCT
ejpam-4792	372	27	transform	transform	NOUN
ejpam-4792	372	28	.	.	PUNCT
ejpam-4792	373	1	we	we	PRON
ejpam-4792	373	2	let	let	VERB
ejpam-4792	373	3	c1	c1	PROPN
ejpam-4792	373	4	,	,	PUNCT
ejpam-4792	373	5	c2	c2	PROPN
ejpam-4792	373	6	,	,	PUNCT
ejpam-4792	373	7	c3	c3	PROPN
ejpam-4792	373	8	,	,	PUNCT
ejpam-4792	373	9	and	and	CCONJ
ejpam-4792	373	10	c4	c4	NOUN
ejpam-4792	373	11	in	in	ADP
ejpam-4792	373	12	eq	eq	ADP
ejpam-4792	373	13	.	.	PUNCT
ejpam-4792	374	1	(	(	PUNCT
ejpam-4792	374	2	40	40	NUM
ejpam-4792	374	3	)	)	PUNCT
ejpam-4792	374	4	in	in	ADP
ejpam-4792	374	5	various	various	ADJ
ejpam-4792	374	6	ways	way	NOUN
ejpam-4792	374	7	as	as	SCONJ
ejpam-4792	374	8	follows	follow	VERB
ejpam-4792	374	9	:	:	PUNCT
ejpam-4792	374	10	(	(	PUNCT
ejpam-4792	374	11	i	i	NOUN
ejpam-4792	374	12	)	)	PUNCT
ejpam-4792	374	13	when	when	SCONJ
ejpam-4792	374	14	c1	c1	PROPN
ejpam-4792	374	15	=	=	PROPN
ejpam-4792	374	16	c2	c2	PROPN
ejpam-4792	374	17	=	=	SYM
ejpam-4792	374	18	c3	c3	PROPN
ejpam-4792	374	19	=	=	PROPN
ejpam-4792	374	20	c4	c4	PROPN
ejpam-4792	374	21	=	=	SYM
ejpam-4792	374	22	0	0	NUM
ejpam-4792	374	23	,	,	PUNCT
ejpam-4792	374	24	we	we	PRON
ejpam-4792	374	25	get	get	VERB
ejpam-4792	374	26	y(t	y(t	NUM
ejpam-4792	374	27	)	)	PUNCT
ejpam-4792	375	1	=	=	NOUN
ejpam-4792	375	2	t8	t8	VERB
ejpam-4792	375	3	24	24	NUM
ejpam-4792	375	4	as	as	ADP
ejpam-4792	375	5	a	a	DET
ejpam-4792	375	6	solution	solution	NOUN
ejpam-4792	375	7	of	of	ADP
ejpam-4792	375	8	eq	eq	PROPN
ejpam-4792	375	9	.	.	PUNCT
ejpam-4792	376	1	(	(	PUNCT
ejpam-4792	376	2	39	39	NUM
ejpam-4792	376	3	)	)	PUNCT
ejpam-4792	376	4	,	,	PUNCT
ejpam-4792	376	5	(	(	PUNCT
ejpam-4792	376	6	ii	ii	NOUN
ejpam-4792	376	7	)	)	PUNCT
ejpam-4792	376	8	when	when	SCONJ
ejpam-4792	376	9	c1	c1	PROPN
ejpam-4792	376	10	=	=	PROPN
ejpam-4792	377	1	7	7	X
ejpam-4792	377	2	!	!	NUM
ejpam-4792	377	3	,	,	PUNCT
ejpam-4792	377	4	c2	c2	PROPN
ejpam-4792	377	5	=	=	PUNCT
ejpam-4792	377	6	6	6	NUM
ejpam-4792	377	7	!	!	NUM
ejpam-4792	377	8	,	,	PUNCT
ejpam-4792	377	9	c3	c3	X
ejpam-4792	377	10	=	=	PUNCT
ejpam-4792	377	11	5	5	NUM
ejpam-4792	377	12	!	!	NUM
ejpam-4792	377	13	,	,	PUNCT
ejpam-4792	377	14	c4	c4	NOUN
ejpam-4792	377	15	=	=	NOUN
ejpam-4792	377	16	4	4	NUM
ejpam-4792	377	17	!	!	NUM
ejpam-4792	377	18	,	,	PUNCT
ejpam-4792	377	19	we	we	PRON
ejpam-4792	377	20	get	get	VERB
ejpam-4792	377	21	y(t	y(t	NUM
ejpam-4792	377	22	)	)	PUNCT
ejpam-4792	378	1	=	=	NOUN
ejpam-4792	378	2	t8	t8	VERB
ejpam-4792	378	3	24	24	NUM
ejpam-4792	378	4	+	+	NUM
ejpam-4792	378	5	t7	t7	PROPN
ejpam-4792	378	6	6	6	NUM
ejpam-4792	378	7	+	+	CCONJ
ejpam-4792	378	8	t6	t6	PROPN
ejpam-4792	378	9	2	2	NUM
ejpam-4792	378	10	+	+	CCONJ
ejpam-4792	378	11	t5	t5	PROPN
ejpam-4792	378	12	+	+	CCONJ
ejpam-4792	378	13	t4	t4	PROPN
ejpam-4792	378	14	as	as	ADP
ejpam-4792	378	15	a	a	DET
ejpam-4792	378	16	solution	solution	NOUN
ejpam-4792	378	17	of	of	ADP
ejpam-4792	378	18	eq	eq	PROPN
ejpam-4792	378	19	.	.	PUNCT
ejpam-4792	379	1	(	(	PUNCT
ejpam-4792	379	2	39	39	NUM
ejpam-4792	379	3	)	)	PUNCT
ejpam-4792	379	4	,	,	PUNCT
ejpam-4792	379	5	(	(	PUNCT
ejpam-4792	379	6	iii	iii	X
ejpam-4792	379	7	)	)	PUNCT
ejpam-4792	379	8	when	when	SCONJ
ejpam-4792	379	9	c1	c1	PROPN
ejpam-4792	379	10	=	=	PROPN
ejpam-4792	380	1	6×	6×	NUM
ejpam-4792	380	2	7	7	NUM
ejpam-4792	380	3	!	!	PUNCT
ejpam-4792	380	4	,	,	PUNCT
ejpam-4792	380	5	c2	c2	PROPN
ejpam-4792	380	6	=	=	SYM
ejpam-4792	380	7	2×	2×	NUM
ejpam-4792	380	8	6	6	NUM
ejpam-4792	380	9	!	!	PUNCT
ejpam-4792	380	10	,	,	PUNCT
ejpam-4792	380	11	c3	c3	X
ejpam-4792	380	12	=	=	PUNCT
ejpam-4792	380	13	5	5	NUM
ejpam-4792	380	14	!	!	NUM
ejpam-4792	380	15	,	,	PUNCT
ejpam-4792	380	16	c4	c4	NOUN
ejpam-4792	380	17	=	=	NOUN
ejpam-4792	380	18	4	4	NUM
ejpam-4792	380	19	!	!	NUM
ejpam-4792	380	20	,	,	PUNCT
ejpam-4792	380	21	we	we	PRON
ejpam-4792	380	22	get	get	VERB
ejpam-4792	380	23	y(t	y(t	NUM
ejpam-4792	380	24	)	)	PUNCT
ejpam-4792	381	1	=	=	NOUN
ejpam-4792	381	2	t8	t8	VERB
ejpam-4792	381	3	24	24	NUM
ejpam-4792	381	4	+	+	CCONJ
ejpam-4792	381	5	t7	t7	PROPN
ejpam-4792	381	6	+	+	CCONJ
ejpam-4792	381	7	t6	t6	PROPN
ejpam-4792	381	8	+	+	CCONJ
ejpam-4792	381	9	t5	t5	PROPN
ejpam-4792	381	10	+	+	CCONJ
ejpam-4792	381	11	t4	t4	PROPN
ejpam-4792	381	12	as	as	ADP
ejpam-4792	381	13	a	a	DET
ejpam-4792	381	14	solution	solution	NOUN
ejpam-4792	381	15	of	of	ADP
ejpam-4792	381	16	eq	eq	PROPN
ejpam-4792	381	17	.	.	PUNCT
ejpam-4792	382	1	(	(	PUNCT
ejpam-4792	382	2	39	39	NUM
ejpam-4792	382	3	)	)	PUNCT
ejpam-4792	382	4	.	.	PUNCT
ejpam-4792	383	1	0	0	NUM
ejpam-4792	384	1	1	1	NUM
ejpam-4792	384	2	2	2	NUM
ejpam-4792	384	3	3	3	NUM
ejpam-4792	384	4	4	4	NUM
ejpam-4792	384	5	5	5	NUM
ejpam-4792	384	6	6	6	NUM
ejpam-4792	384	7	7	7	NUM
ejpam-4792	384	8	8	8	NUM
ejpam-4792	384	9	9	9	NUM
ejpam-4792	384	10	10	10	NUM
ejpam-4792	384	11	t	t	NOUN
ejpam-4792	384	12	0	0	NUM
ejpam-4792	384	13	0.5	0.5	NUM
ejpam-4792	384	14	1	1	NUM
ejpam-4792	384	15	1.5	1.5	NUM
ejpam-4792	384	16	2	2	NUM
ejpam-4792	384	17	y	y	PROPN
ejpam-4792	384	18	(	(	PUNCT
ejpam-4792	384	19	t	t	PROPN
ejpam-4792	384	20	)	)	PUNCT
ejpam-4792	384	21	×10	×10	PROPN
ejpam-4792	384	22	7	7	NUM
ejpam-4792	384	23	c	c	NOUN
ejpam-4792	384	24	1	1	NUM
ejpam-4792	384	25	=	=	SYM
ejpam-4792	384	26	c	c	NOUN
ejpam-4792	384	27	2	2	NUM
ejpam-4792	384	28	=	=	SYM
ejpam-4792	384	29	c	c	NOUN
ejpam-4792	384	30	3	3	NUM
ejpam-4792	384	31	=	=	SYM
ejpam-4792	384	32	c	c	NOUN
ejpam-4792	384	33	4	4	NUM
ejpam-4792	384	34	=	=	SYM
ejpam-4792	384	35	0	0	PUNCT
ejpam-4792	384	36	c	c	NOUN
ejpam-4792	384	37	1	1	NUM
ejpam-4792	384	38	=	=	SYM
ejpam-4792	384	39	7	7	NUM
ejpam-4792	384	40	!	!	NUM
ejpam-4792	384	41	,	,	PUNCT
ejpam-4792	384	42	c	c	NOUN
ejpam-4792	384	43	2	2	NUM
ejpam-4792	384	44	=	=	SYM
ejpam-4792	384	45	6	6	NUM
ejpam-4792	384	46	!	!	NUM
ejpam-4792	384	47	,	,	PUNCT
ejpam-4792	384	48	c	c	NOUN
ejpam-4792	384	49	3	3	NUM
ejpam-4792	384	50	=	=	SYM
ejpam-4792	384	51	5	5	NUM
ejpam-4792	384	52	!	!	NUM
ejpam-4792	384	53	,	,	PUNCT
ejpam-4792	384	54	c	c	NOUN
ejpam-4792	384	55	4	4	NUM
ejpam-4792	384	56	=	=	SYM
ejpam-4792	384	57	4	4	NUM
ejpam-4792	384	58	!	!	X
ejpam-4792	385	1	c	c	NOUN
ejpam-4792	385	2	1	1	NUM
ejpam-4792	385	3	=	=	SYM
ejpam-4792	385	4	6	6	NUM
ejpam-4792	385	5	*	*	SYM
ejpam-4792	385	6	7	7	NUM
ejpam-4792	385	7	!	!	NUM
ejpam-4792	385	8	,	,	PUNCT
ejpam-4792	385	9	c	c	NOUN
ejpam-4792	385	10	2	2	NUM
ejpam-4792	385	11	=	=	SYM
ejpam-4792	385	12	2	2	NUM
ejpam-4792	385	13	*	*	SYM
ejpam-4792	385	14	6	6	NUM
ejpam-4792	385	15	!	!	PUNCT
ejpam-4792	385	16	,	,	PUNCT
ejpam-4792	385	17	c	c	NOUN
ejpam-4792	385	18	3	3	NUM
ejpam-4792	385	19	=	=	SYM
ejpam-4792	385	20	5	5	NUM
ejpam-4792	385	21	!	!	NUM
ejpam-4792	385	22	,	,	PUNCT
ejpam-4792	385	23	c	c	NOUN
ejpam-4792	385	24	4	4	NUM
ejpam-4792	385	25	=	=	SYM
ejpam-4792	385	26	4	4	X
ejpam-4792	385	27	!	!	X
ejpam-4792	385	28	figure	figure	VERB
ejpam-4792	385	29	3	3	NUM
ejpam-4792	385	30	:	:	PUNCT
ejpam-4792	385	31	general	general	ADJ
ejpam-4792	385	32	solutions	solution	NOUN
ejpam-4792	385	33	of	of	ADP
ejpam-4792	385	34	example	example	NOUN
ejpam-4792	386	1	3	3	X
ejpam-4792	386	2	.	.	PUNCT
ejpam-4792	386	3	s.	s.	PROPN
ejpam-4792	386	4	sattaso	sattaso	PROPN
ejpam-4792	386	5	,	,	PUNCT
ejpam-4792	386	6	p.	p.	PROPN
ejpam-4792	386	7	prasertsang	prasertsang	PROPN
ejpam-4792	386	8	,	,	PUNCT
ejpam-4792	386	9	t.	t.	PROPN
ejpam-4792	386	10	prasertsang	prasertsang	PROPN
ejpam-4792	386	11	/	/	SYM
ejpam-4792	386	12	eur	eur	PROPN
ejpam-4792	386	13	.	.	PUNCT
ejpam-4792	387	1	j.	j.	PROPN
ejpam-4792	387	2	pure	pure	PROPN
ejpam-4792	387	3	appl	appl	PROPN
ejpam-4792	387	4	.	.	PROPN
ejpam-4792	387	5	math	math	PROPN
ejpam-4792	387	6	,	,	PUNCT
ejpam-4792	387	7	16	16	NUM
ejpam-4792	387	8	(	(	PUNCT
ejpam-4792	387	9	3	3	NUM
ejpam-4792	387	10	)	)	PUNCT
ejpam-4792	387	11	(	(	PUNCT
ejpam-4792	387	12	2023	2023	NUM
ejpam-4792	387	13	)	)	PUNCT
ejpam-4792	387	14	,	,	PUNCT
ejpam-4792	387	15	1389	1389	NUM
ejpam-4792	387	16	-	-	SYM
ejpam-4792	387	17	1405	1405	NUM
ejpam-4792	387	18	1402	1402	NUM
ejpam-4792	387	19	remark	remark	NOUN
ejpam-4792	387	20	1	1	NUM
ejpam-4792	387	21	.	.	PUNCT
ejpam-4792	388	1	(	(	PUNCT
ejpam-4792	388	2	i	i	NOUN
ejpam-4792	388	3	)	)	PUNCT
ejpam-4792	388	4	for	for	ADP
ejpam-4792	388	5	m	m	PROPN
ejpam-4792	388	6	=	=	SYM
ejpam-4792	388	7	5	5	NUM
ejpam-4792	388	8	and	and	CCONJ
ejpam-4792	388	9	n	n	CCONJ
ejpam-4792	388	10	=	=	SYM
ejpam-4792	388	11	5	5	NUM
ejpam-4792	388	12	,	,	PUNCT
ejpam-4792	388	13	by	by	ADP
ejpam-4792	388	14	corollary	corollary	ADJ
ejpam-4792	388	15	1	1	NUM
ejpam-4792	388	16	,	,	PUNCT
ejpam-4792	388	17	no	no	INTJ
ejpam-4792	388	18	.	.	PUNCT
ejpam-4792	388	19	coes	coes	PROPN
ejpam-4792	388	20	=	=	PUNCT
ejpam-4792	389	1	36	36	NUM
ejpam-4792	389	2	and	and	CCONJ
ejpam-4792	389	3	no	no	INTJ
ejpam-4792	389	4	.	.	PUNCT
ejpam-4792	390	1	cons	con	NOUN
ejpam-4792	390	2	=	=	PUNCT
ejpam-4792	390	3	45	45	NUM
ejpam-4792	390	4	that	that	PRON
ejpam-4792	390	5	is	be	AUX
ejpam-4792	390	6	no	no	INTJ
ejpam-4792	390	7	.	.	PUNCT
ejpam-4792	390	8	coes	coe	VERB
ejpam-4792	390	9	̸=	̸=	PROPN
ejpam-4792	390	10	no	no	NOUN
ejpam-4792	390	11	.	.	PUNCT
ejpam-4792	391	1	cons	con	NOUN
ejpam-4792	391	2	.	.	PUNCT
ejpam-4792	392	1	the	the	DET
ejpam-4792	392	2	solutions	solution	NOUN
ejpam-4792	392	3	of	of	ADP
ejpam-4792	392	4	hodepcs	hodepc	NOUN
ejpam-4792	392	5	under	under	ADP
ejpam-4792	392	6	conditions	condition	NOUN
ejpam-4792	392	7	(	(	PUNCT
ejpam-4792	392	8	4)-(5	4)-(5	NUM
ejpam-4792	392	9	)	)	PUNCT
ejpam-4792	392	10	by	by	ADP
ejpam-4792	392	11	the	the	DET
ejpam-4792	392	12	g3	g3	NOUN
ejpam-4792	392	13	-	-	PUNCT
ejpam-4792	392	14	transform	transform	NOUN
ejpam-4792	392	15	are	be	AUX
ejpam-4792	392	16	infinite	infinite	ADJ
ejpam-4792	392	17	solutions	solution	NOUN
ejpam-4792	392	18	.	.	PUNCT
ejpam-4792	393	1	in	in	ADP
ejpam-4792	393	2	particular	particular	ADJ
ejpam-4792	393	3	,	,	PUNCT
ejpam-4792	393	4	in	in	ADP
ejpam-4792	393	5	example	example	NOUN
ejpam-4792	393	6	1	1	NUM
ejpam-4792	393	7	.	.	NUM
ejpam-4792	393	8	,	,	PUNCT
ejpam-4792	393	9	the	the	DET
ejpam-4792	393	10	polynomial	polynomial	ADJ
ejpam-4792	393	11	coefficients	coefficient	NOUN
ejpam-4792	393	12	a5,5	a5,5	PROPN
ejpam-4792	394	1	=	=	PUNCT
ejpam-4792	394	2	1	1	NUM
ejpam-4792	394	3	,	,	PUNCT
ejpam-4792	394	4	a4,4	a4,4	PROPN
ejpam-4792	394	5	=	=	PUNCT
ejpam-4792	394	6	20	20	NUM
ejpam-4792	394	7	,	,	PUNCT
ejpam-4792	394	8	a3,3	a3,3	ADP
ejpam-4792	394	9	=	=	NOUN
ejpam-4792	394	10	120	120	NUM
ejpam-4792	394	11	,	,	PUNCT
ejpam-4792	394	12	a2,2	a2,2	PROPN
ejpam-4792	394	13	=	=	SYM
ejpam-4792	394	14	240	240	NUM
ejpam-4792	394	15	,	,	PUNCT
ejpam-4792	394	16	a1,1	a1,1	NOUN
ejpam-4792	394	17	=	=	SYM
ejpam-4792	394	18	120	120	NUM
ejpam-4792	394	19	,	,	PUNCT
ejpam-4792	394	20	otherwise	otherwise	ADV
ejpam-4792	394	21	,	,	PUNCT
ejpam-4792	394	22	0	0	NUM
ejpam-4792	394	23	can	can	AUX
ejpam-4792	394	24	be	be	AUX
ejpam-4792	394	25	solved	solve	VERB
ejpam-4792	394	26	.	.	PUNCT
ejpam-4792	395	1	(	(	PUNCT
ejpam-4792	395	2	ii	ii	NOUN
ejpam-4792	395	3	)	)	PUNCT
ejpam-4792	395	4	for	for	ADP
ejpam-4792	395	5	m	m	PROPN
ejpam-4792	395	6	=	=	SYM
ejpam-4792	395	7	5	5	NUM
ejpam-4792	395	8	and	and	CCONJ
ejpam-4792	395	9	n	n	CCONJ
ejpam-4792	395	10	=	=	SYM
ejpam-4792	395	11	3	3	NUM
ejpam-4792	395	12	,	,	PUNCT
ejpam-4792	395	13	by	by	ADP
ejpam-4792	395	14	corollary	corollary	ADJ
ejpam-4792	395	15	1	1	NUM
ejpam-4792	395	16	,	,	PUNCT
ejpam-4792	395	17	no	no	INTJ
ejpam-4792	395	18	.	.	PUNCT
ejpam-4792	395	19	coes	coes	PROPN
ejpam-4792	395	20	=	=	PUNCT
ejpam-4792	396	1	no	no	INTJ
ejpam-4792	396	2	.	.	PUNCT
ejpam-4792	397	1	cons	con	NOUN
ejpam-4792	397	2	=	=	SYM
ejpam-4792	397	3	24	24	NUM
ejpam-4792	397	4	.	.	PUNCT
ejpam-4792	397	5	example	example	NOUN
ejpam-4792	398	1	2	2	NUM
ejpam-4792	398	2	.	.	PUNCT
ejpam-4792	398	3	is	be	AUX
ejpam-4792	398	4	one	one	NUM
ejpam-4792	398	5	of	of	ADP
ejpam-4792	398	6	the	the	DET
ejpam-4792	398	7	solutions	solution	NOUN
ejpam-4792	398	8	under	under	ADP
ejpam-4792	398	9	conditions	condition	NOUN
ejpam-4792	398	10	(	(	PUNCT
ejpam-4792	398	11	4)-(5	4)-(5	NUM
ejpam-4792	398	12	)	)	PUNCT
ejpam-4792	398	13	which	which	PRON
ejpam-4792	398	14	can	can	AUX
ejpam-4792	398	15	be	be	AUX
ejpam-4792	398	16	solved	solve	VERB
ejpam-4792	398	17	by	by	ADP
ejpam-4792	398	18	the	the	DET
ejpam-4792	398	19	g−1	g−1	PROPN
ejpam-4792	398	20	-	-	PUNCT
ejpam-4792	398	21	transform	transform	NOUN
ejpam-4792	398	22	.	.	PUNCT
ejpam-4792	399	1	(	(	PUNCT
ejpam-4792	399	2	iii	iii	NOUN
ejpam-4792	399	3	)	)	PUNCT
ejpam-4792	399	4	for	for	ADP
ejpam-4792	399	5	m	m	PROPN
ejpam-4792	399	6	=	=	SYM
ejpam-4792	399	7	7	7	NUM
ejpam-4792	399	8	and	and	CCONJ
ejpam-4792	399	9	n	n	CCONJ
ejpam-4792	399	10	=	=	NUM
ejpam-4792	399	11	4	4	NUM
ejpam-4792	399	12	,	,	PUNCT
ejpam-4792	399	13	by	by	ADP
ejpam-4792	399	14	corollary	corollary	ADJ
ejpam-4792	399	15	1	1	NUM
ejpam-4792	399	16	,	,	PUNCT
ejpam-4792	399	17	no	no	INTJ
ejpam-4792	399	18	.	.	PUNCT
ejpam-4792	399	19	coes	coes	PROPN
ejpam-4792	399	20	=	=	PUNCT
ejpam-4792	399	21	40	40	NUM
ejpam-4792	399	22	and	and	CCONJ
ejpam-4792	399	23	no	no	INTJ
ejpam-4792	399	24	.	.	PUNCT
ejpam-4792	400	1	cons	con	NOUN
ejpam-4792	400	2	=	=	PUNCT
ejpam-4792	400	3	42	42	NUM
ejpam-4792	400	4	that	that	PRON
ejpam-4792	400	5	is	be	AUX
ejpam-4792	400	6	no	no	INTJ
ejpam-4792	400	7	.	.	PUNCT
ejpam-4792	400	8	coes	coe	VERB
ejpam-4792	400	9	̸=	̸=	PROPN
ejpam-4792	400	10	no	no	PROPN
ejpam-4792	400	11	.	.	PUNCT
ejpam-4792	401	1	cons	con	NOUN
ejpam-4792	401	2	.	.	PUNCT
ejpam-4792	402	1	in	in	ADP
ejpam-4792	402	2	example	example	NOUN
ejpam-4792	402	3	3	3	NUM
ejpam-4792	402	4	.	.	NUM
ejpam-4792	402	5	,	,	PUNCT
ejpam-4792	402	6	the	the	DET
ejpam-4792	402	7	polynomial	polynomial	ADJ
ejpam-4792	402	8	coefficients	coefficient	NOUN
ejpam-4792	402	9	a7,4	a7,4	PROPN
ejpam-4792	402	10	=	=	SYM
ejpam-4792	402	11	1	1	NUM
ejpam-4792	402	12	,	,	PUNCT
ejpam-4792	402	13	a6,3	a6,3	PROPN
ejpam-4792	402	14	=	=	SYM
ejpam-4792	402	15	−4	−4	PROPN
ejpam-4792	402	16	,	,	PUNCT
ejpam-4792	402	17	a5,2	a5,2	NOUN
ejpam-4792	402	18	=	=	NOUN
ejpam-4792	402	19	12	12	NUM
ejpam-4792	402	20	,	,	PUNCT
ejpam-4792	402	21	a4,4	a4,4	PROPN
ejpam-4792	402	22	=	=	PUNCT
ejpam-4792	402	23	1	1	NUM
ejpam-4792	402	24	,	,	PUNCT
ejpam-4792	402	25	a4,1	a4,1	PROPN
ejpam-4792	402	26	=	=	SYM
ejpam-4792	402	27	−24	−24	ADV
ejpam-4792	402	28	,	,	PUNCT
ejpam-4792	402	29	a3,3	a3,3	NOUN
ejpam-4792	402	30	=	=	SYM
ejpam-4792	402	31	−16	−16	PROPN
ejpam-4792	402	32	,	,	PUNCT
ejpam-4792	402	33	a3,0	a3,0	PROPN
ejpam-4792	402	34	=	=	SYM
ejpam-4792	402	35	24	24	NUM
ejpam-4792	402	36	,	,	PUNCT
ejpam-4792	402	37	a2,2	a2,2	PROPN
ejpam-4792	402	38	=	=	SYM
ejpam-4792	402	39	120	120	NUM
ejpam-4792	402	40	,	,	PUNCT
ejpam-4792	402	41	a1,1	a1,1	NOUN
ejpam-4792	402	42	=	=	SYM
ejpam-4792	402	43	−480	−480	PROPN
ejpam-4792	402	44	,	,	PUNCT
ejpam-4792	402	45	a0,0	a0,0	NOUN
ejpam-4792	402	46	=	=	SYM
ejpam-4792	402	47	840	840	NUM
ejpam-4792	402	48	,	,	PUNCT
ejpam-4792	402	49	otherwise	otherwise	ADV
ejpam-4792	402	50	,	,	PUNCT
ejpam-4792	402	51	0	0	NUM
ejpam-4792	402	52	which	which	PRON
ejpam-4792	402	53	can	can	AUX
ejpam-4792	402	54	be	be	AUX
ejpam-4792	402	55	solved	solve	VERB
ejpam-4792	402	56	using	use	VERB
ejpam-4792	402	57	the	the	DET
ejpam-4792	402	58	solutions	solution	NOUN
ejpam-4792	402	59	of	of	ADP
ejpam-4792	402	60	hodepcs	hodepc	NOUN
ejpam-4792	402	61	under	under	ADP
ejpam-4792	402	62	conditions	condition	NOUN
ejpam-4792	402	63	(	(	PUNCT
ejpam-4792	402	64	4)-(5	4)-(5	NUM
ejpam-4792	402	65	)	)	PUNCT
ejpam-4792	402	66	by	by	ADP
ejpam-4792	402	67	the	the	DET
ejpam-4792	402	68	g−5	g−5	PROPN
ejpam-4792	402	69	-	-	PUNCT
ejpam-4792	402	70	transform	transform	NOUN
ejpam-4792	402	71	.	.	PUNCT
ejpam-4792	403	1	in	in	ADP
ejpam-4792	403	2	fact	fact	NOUN
ejpam-4792	403	3	,	,	PUNCT
ejpam-4792	403	4	the	the	DET
ejpam-4792	403	5	solutions	solution	NOUN
ejpam-4792	403	6	of	of	ADP
ejpam-4792	403	7	hodepcs	hodepc	NOUN
ejpam-4792	403	8	under	under	ADP
ejpam-4792	403	9	conditions	condition	NOUN
ejpam-4792	403	10	(	(	PUNCT
ejpam-4792	403	11	4)-(5	4)-(5	NUM
ejpam-4792	403	12	)	)	PUNCT
ejpam-4792	403	13	by	by	ADP
ejpam-4792	403	14	the	the	DET
ejpam-4792	403	15	gα	gα	NOUN
ejpam-4792	403	16	-	-	PUNCT
ejpam-4792	403	17	transform	transform	NOUN
ejpam-4792	403	18	can	can	AUX
ejpam-4792	403	19	be	be	AUX
ejpam-4792	403	20	solved	solve	VERB
ejpam-4792	403	21	using	use	VERB
ejpam-4792	403	22	in	in	ADP
ejpam-4792	403	23	various	various	ADJ
ejpam-4792	403	24	examples	example	NOUN
ejpam-4792	403	25	.	.	PUNCT
ejpam-4792	404	1	if	if	SCONJ
ejpam-4792	404	2	not	not	PART
ejpam-4792	404	3	,	,	PUNCT
ejpam-4792	404	4	the	the	DET
ejpam-4792	404	5	hodepcs	hodepc	NOUN
ejpam-4792	404	6	can	can	AUX
ejpam-4792	404	7	not	not	PART
ejpam-4792	404	8	find	find	VERB
ejpam-4792	404	9	the	the	DET
ejpam-4792	404	10	solutions	solution	NOUN
ejpam-4792	404	11	.	.	PUNCT
ejpam-4792	405	1	remark	remark	PROPN
ejpam-4792	405	2	2	2	NUM
ejpam-4792	405	3	.	.	PUNCT
ejpam-4792	406	1	from	from	ADP
ejpam-4792	406	2	example	example	NOUN
ejpam-4792	406	3	2	2	NUM
ejpam-4792	406	4	.	.	PUNCT
ejpam-4792	407	1	if	if	SCONJ
ejpam-4792	407	2	a3,1	a3,1	PROPN
ejpam-4792	407	3	is	be	AUX
ejpam-4792	407	4	equal	equal	ADJ
ejpam-4792	407	5	to	to	ADP
ejpam-4792	407	6	1	1	NUM
ejpam-4792	407	7	,	,	PUNCT
ejpam-4792	407	8	then	then	ADV
ejpam-4792	407	9	we	we	PRON
ejpam-4792	407	10	have	have	VERB
ejpam-4792	407	11	t3y(5)(t	t3y(5)(t	VERB
ejpam-4792	407	12	)	)	PUNCT
ejpam-4792	408	1	+	+	CCONJ
ejpam-4792	408	2	(	(	PUNCT
ejpam-4792	408	3	t3	t3	PROPN
ejpam-4792	408	4	+	+	NOUN
ejpam-4792	408	5	6t2)y(4)(t	6t2)y(4)(t	NUM
ejpam-4792	408	6	)	)	PUNCT
ejpam-4792	409	1	+	+	CCONJ
ejpam-4792	409	2	(	(	PUNCT
ejpam-4792	409	3	3t2	3t2	NUM
ejpam-4792	409	4	+	+	CCONJ
ejpam-4792	409	5	t)y′′′(t	t)y′′′(t	NOUN
ejpam-4792	409	6	)	)	PUNCT
ejpam-4792	409	7	=	=	SYM
ejpam-4792	409	8	t2	t2	NOUN
ejpam-4792	409	9	2	2	NUM
ejpam-4792	409	10	+	+	SYM
ejpam-4792	409	11	t	t	PROPN
ejpam-4792	409	12	,	,	PUNCT
ejpam-4792	409	13	t	t	PROPN
ejpam-4792	409	14	≥	≥	PROPN
ejpam-4792	409	15	0	0	NUM
ejpam-4792	409	16	.	.	PUNCT
ejpam-4792	410	1	(	(	PUNCT
ejpam-4792	410	2	41	41	NUM
ejpam-4792	410	3	)	)	PUNCT
ejpam-4792	410	4	the	the	DET
ejpam-4792	410	5	conditions	condition	NOUN
ejpam-4792	410	6	do	do	AUX
ejpam-4792	410	7	not	not	PART
ejpam-4792	410	8	satisfy	satisfy	VERB
ejpam-4792	410	9	theorem	theorem	ADJ
ejpam-4792	411	1	1	1	X
ejpam-4792	411	2	.	.	PUNCT
ejpam-4792	412	1	if	if	SCONJ
ejpam-4792	412	2	we	we	PRON
ejpam-4792	412	3	take	take	VERB
ejpam-4792	412	4	g−1	g−1	NOUN
ejpam-4792	412	5	-	-	PUNCT
ejpam-4792	412	6	transform	transform	VERB
ejpam-4792	412	7	both	both	DET
ejpam-4792	412	8	sides	side	NOUN
ejpam-4792	412	9	of	of	ADP
ejpam-4792	412	10	eq	eq	PROPN
ejpam-4792	412	11	.	.	PUNCT
ejpam-4792	413	1	(	(	PUNCT
ejpam-4792	413	2	41	41	NUM
ejpam-4792	413	3	)	)	PUNCT
ejpam-4792	413	4	,	,	PUNCT
ejpam-4792	413	5	we	we	PRON
ejpam-4792	413	6	obtain	obtain	VERB
ejpam-4792	413	7	(	(	PUNCT
ejpam-4792	413	8	u2	u2	NOUN
ejpam-4792	413	9	+	+	CCONJ
ejpam-4792	413	10	u)y	u)y	ADJ
ejpam-4792	414	1	′′′(u)−	′′′(u)−	ADP
ejpam-4792	414	2	5	5	NUM
ejpam-4792	414	3	y	y	PROPN
ejpam-4792	414	4	′(u	′(u	NOUN
ejpam-4792	414	5	)	)	PUNCT
ejpam-4792	414	6	u	u	NOUN
ejpam-4792	414	7	+	+	NOUN
ejpam-4792	414	8	10	10	NUM
ejpam-4792	414	9	y	y	PROPN
ejpam-4792	414	10	(	(	PUNCT
ejpam-4792	414	11	u	u	NOUN
ejpam-4792	414	12	)	)	PUNCT
ejpam-4792	414	13	u2	u2	NOUN
ejpam-4792	414	14	=	=	PROPN
ejpam-4792	414	15	u2	u2	PROPN
ejpam-4792	414	16	+	+	CCONJ
ejpam-4792	414	17	u.	u.	PROPN
ejpam-4792	414	18	observe	observe	VERB
ejpam-4792	414	19	that	that	SCONJ
ejpam-4792	414	20	eq	eq	ADP
ejpam-4792	414	21	.	.	PUNCT
ejpam-4792	415	1	(	(	PUNCT
ejpam-4792	415	2	41	41	NUM
ejpam-4792	415	3	)	)	PUNCT
ejpam-4792	415	4	transformed	transform	VERB
ejpam-4792	415	5	into	into	ADP
ejpam-4792	415	6	a	a	DET
ejpam-4792	415	7	third	third	ADJ
ejpam-4792	415	8	-	-	PUNCT
ejpam-4792	415	9	order	order	NOUN
ejpam-4792	415	10	differential	differential	ADJ
ejpam-4792	415	11	equation	equation	NOUN
ejpam-4792	415	12	with	with	ADP
ejpam-4792	415	13	variable	variable	ADJ
ejpam-4792	415	14	coefficients	coefficient	NOUN
ejpam-4792	415	15	.	.	PUNCT
ejpam-4792	416	1	as	as	ADP
ejpam-4792	416	2	a	a	DET
ejpam-4792	416	3	result	result	NOUN
ejpam-4792	416	4	,	,	PUNCT
ejpam-4792	416	5	setting	set	VERB
ejpam-4792	416	6	α	α	NOUN
ejpam-4792	416	7	=	=	NOUN
ejpam-4792	416	8	−1	−1	NOUN
ejpam-4792	416	9	did	do	AUX
ejpam-4792	416	10	not	not	PART
ejpam-4792	416	11	lead	lead	VERB
ejpam-4792	416	12	to	to	ADP
ejpam-4792	416	13	the	the	DET
ejpam-4792	416	14	solution	solution	NOUN
ejpam-4792	416	15	of	of	ADP
ejpam-4792	416	16	(	(	PUNCT
ejpam-4792	416	17	41	41	NUM
ejpam-4792	416	18	)	)	PUNCT
ejpam-4792	416	19	,	,	PUNCT
ejpam-4792	416	20	including	include	VERB
ejpam-4792	416	21	for	for	ADP
ejpam-4792	416	22	α	α	PRON
ejpam-4792	416	23	equaling	equal	VERB
ejpam-4792	416	24	all	all	DET
ejpam-4792	416	25	other	other	ADJ
ejpam-4792	416	26	values	value	NOUN
ejpam-4792	416	27	.	.	PUNCT
ejpam-4792	417	1	5	5	X
ejpam-4792	417	2	.	.	X
ejpam-4792	417	3	conclusions	conclusion	NOUN
ejpam-4792	417	4	solutions	solution	NOUN
ejpam-4792	417	5	to	to	ADP
ejpam-4792	417	6	higher	high	ADJ
ejpam-4792	417	7	-	-	PUNCT
ejpam-4792	417	8	order	order	NOUN
ejpam-4792	417	9	differential	differential	ADJ
ejpam-4792	417	10	equations	equation	NOUN
ejpam-4792	417	11	with	with	ADP
ejpam-4792	417	12	polynomial	polynomial	ADJ
ejpam-4792	417	13	coefficients	coefficient	NOUN
ejpam-4792	417	14	(	(	PUNCT
ejpam-4792	417	15	hodepcs	hodepc	NOUN
ejpam-4792	417	16	)	)	PUNCT
ejpam-4792	417	17	were	be	AUX
ejpam-4792	417	18	introduced	introduce	VERB
ejpam-4792	417	19	using	use	VERB
ejpam-4792	417	20	the	the	DET
ejpam-4792	417	21	gα	gα	NOUN
ejpam-4792	417	22	-	-	PUNCT
ejpam-4792	417	23	transform	transform	NOUN
ejpam-4792	417	24	.	.	PUNCT
ejpam-4792	418	1	the	the	DET
ejpam-4792	418	2	theorem	theorem	NOUN
ejpam-4792	418	3	and	and	CCONJ
ejpam-4792	418	4	corollary	corollary	NOUN
ejpam-4792	418	5	of	of	ADP
ejpam-4792	418	6	the	the	DET
ejpam-4792	418	7	hodepcs	hodepc	NOUN
ejpam-4792	418	8	were	be	AUX
ejpam-4792	418	9	obtained	obtain	VERB
ejpam-4792	418	10	to	to	PART
ejpam-4792	418	11	guarantee	guarantee	VERB
ejpam-4792	418	12	that	that	SCONJ
ejpam-4792	418	13	they	they	PRON
ejpam-4792	418	14	can	can	AUX
ejpam-4792	418	15	be	be	AUX
ejpam-4792	418	16	corrected	correct	VERB
ejpam-4792	418	17	by	by	ADP
ejpam-4792	418	18	the	the	DET
ejpam-4792	418	19	gα	gα	NOUN
ejpam-4792	418	20	-	-	PUNCT
ejpam-4792	418	21	transform	transform	NOUN
ejpam-4792	418	22	.	.	PUNCT
ejpam-4792	419	1	next	next	ADV
ejpam-4792	419	2	,	,	PUNCT
ejpam-4792	419	3	we	we	PRON
ejpam-4792	419	4	showed	show	VERB
ejpam-4792	419	5	some	some	DET
ejpam-4792	419	6	examples	example	NOUN
ejpam-4792	419	7	according	accord	VERB
ejpam-4792	419	8	to	to	ADP
ejpam-4792	419	9	the	the	DET
ejpam-4792	419	10	theorem	theorem	NOUN
ejpam-4792	419	11	which	which	PRON
ejpam-4792	419	12	is	be	AUX
ejpam-4792	419	13	a	a	DET
ejpam-4792	419	14	strength	strength	NOUN
ejpam-4792	419	15	of	of	ADP
ejpam-4792	419	16	the	the	DET
ejpam-4792	419	17	gα	gα	NOUN
ejpam-4792	419	18	-	-	PUNCT
ejpam-4792	419	19	transform	transform	NOUN
ejpam-4792	419	20	in	in	ADP
ejpam-4792	419	21	solving	solve	VERB
ejpam-4792	419	22	the	the	DET
ejpam-4792	419	23	hodepcs	hodepc	NOUN
ejpam-4792	419	24	by	by	ADP
ejpam-4792	419	25	selecting	select	VERB
ejpam-4792	419	26	an	an	DET
ejpam-4792	419	27	appropriate	appropriate	ADJ
ejpam-4792	419	28	value	value	NOUN
ejpam-4792	419	29	for	for	ADP
ejpam-4792	419	30	α	α	NOUN
ejpam-4792	419	31	and	and	CCONJ
ejpam-4792	419	32	proper	proper	ADJ
ejpam-4792	419	33	coefficients	coefficient	NOUN
ejpam-4792	419	34	of	of	ADP
ejpam-4792	419	35	the	the	DET
ejpam-4792	419	36	polynomial	polynomial	NOUN
ejpam-4792	419	37	.	.	PUNCT
ejpam-4792	420	1	acknowledgements	acknowledgement	NOUN
ejpam-4792	420	2	this	this	DET
ejpam-4792	420	3	research	research	NOUN
ejpam-4792	420	4	was	be	AUX
ejpam-4792	420	5	funded	fund	VERB
ejpam-4792	420	6	by	by	ADP
ejpam-4792	420	7	the	the	DET
ejpam-4792	420	8	following	following	ADJ
ejpam-4792	420	9	individuals	individual	NOUN
ejpam-4792	420	10	:	:	PUNCT
ejpam-4792	420	11	research	research	NOUN
ejpam-4792	420	12	and	and	CCONJ
ejpam-4792	420	13	academic	academic	ADJ
ejpam-4792	420	14	service	service	NOUN
ejpam-4792	420	15	division	division	NOUN
ejpam-4792	420	16	and	and	CCONJ
ejpam-4792	420	17	faculty	faculty	NOUN
ejpam-4792	420	18	of	of	ADP
ejpam-4792	420	19	science	science	NOUN
ejpam-4792	420	20	and	and	CCONJ
ejpam-4792	420	21	engineering	engineering	NOUN
ejpam-4792	420	22	,	,	PUNCT
ejpam-4792	420	23	kasetsart	kasetsart	PROPN
ejpam-4792	420	24	university	university	PROPN
ejpam-4792	420	25	,	,	PUNCT
ejpam-4792	420	26	chalermprakiat	chalermprakiat	PROPN
ejpam-4792	420	27	sakon	sakon	PROPN
ejpam-4792	420	28	nakhon	nakhon	PROPN
ejpam-4792	420	29	province	province	PROPN
ejpam-4792	420	30	campus	campus	PROPN
ejpam-4792	420	31	,	,	PUNCT
ejpam-4792	420	32	sakon	sakon	PROPN
ejpam-4792	420	33	nakhon	nakhon	PROPN
ejpam-4792	420	34	,	,	PUNCT
ejpam-4792	420	35	thailand	thailand	PROPN
ejpam-4792	420	36	.	.	PUNCT
ejpam-4792	421	1	references	reference	NOUN
ejpam-4792	421	2	1403	1403	NUM
ejpam-4792	421	3	references	reference	NOUN
ejpam-4792	421	4	[	[	X
ejpam-4792	421	5	1	1	NUM
ejpam-4792	421	6	]	]	X
ejpam-4792	421	7	m.a	m.a	PROPN
ejpam-4792	421	8	.	.	PROPN
ejpam-4792	421	9	asiru	asiru	PROPN
ejpam-4792	421	10	.	.	PUNCT
ejpam-4792	422	1	further	further	ADJ
ejpam-4792	422	2	properties	property	NOUN
ejpam-4792	422	3	of	of	ADP
ejpam-4792	422	4	the	the	DET
ejpam-4792	422	5	sumudu	sumudu	NOUN
ejpam-4792	422	6	transform	transform	NOUN
ejpam-4792	422	7	and	and	CCONJ
ejpam-4792	422	8	its	its	PRON
ejpam-4792	422	9	applications	application	NOUN
ejpam-4792	422	10	.	.	PUNCT
ejpam-4792	423	1	international	international	ADJ
ejpam-4792	423	2	journal	journal	PROPN
ejpam-4792	423	3	of	of	ADP
ejpam-4792	423	4	mathematical	mathematical	ADJ
ejpam-4792	423	5	education	education	NOUN
ejpam-4792	423	6	in	in	ADP
ejpam-4792	423	7	science	science	NOUN
ejpam-4792	423	8	and	and	CCONJ
ejpam-4792	423	9	technology	technology	NOUN
ejpam-4792	423	10	,	,	PUNCT
ejpam-4792	423	11	33(3):441–449	33(3):441–449	PROPN
ejpam-4792	423	12	,	,	PUNCT
ejpam-4792	423	13	2002	2002	NUM
ejpam-4792	423	14	.	.	PUNCT
ejpam-4792	424	1	[	[	X
ejpam-4792	424	2	2	2	NUM
ejpam-4792	424	3	]	]	PUNCT
ejpam-4792	424	4	hj	hj	PROPN
ejpam-4792	424	5	.	.	PUNCT
ejpam-4792	424	6	kim	kim	PROPN
ejpam-4792	424	7	,	,	PUNCT
ejpam-4792	424	8	s.	s.	PROPN
ejpam-4792	424	9	beak	beak	PROPN
ejpam-4792	424	10	,	,	PUNCT
ejpam-4792	424	11	and	and	CCONJ
ejpam-4792	424	12	j.	j.	PROPN
ejpam-4792	424	13	rho	rho	PROPN
ejpam-4792	424	14	.	.	PUNCT
ejpam-4792	425	1	variant	variant	NOUN
ejpam-4792	425	2	of	of	ADP
ejpam-4792	425	3	laplace	laplace	NOUN
ejpam-4792	425	4	transform	transform	NOUN
ejpam-4792	425	5	represented	represent	VERB
ejpam-4792	425	6	by	by	ADP
ejpam-4792	425	7	a	a	DET
ejpam-4792	425	8	logarithmic	logarithmic	ADJ
ejpam-4792	425	9	function	function	NOUN
ejpam-4792	425	10	.	.	PUNCT
ejpam-4792	426	1	international	international	ADJ
ejpam-4792	426	2	journal	journal	PROPN
ejpam-4792	426	3	of	of	ADP
ejpam-4792	426	4	difference	difference	NOUN
ejpam-4792	426	5	equations	equation	NOUN
ejpam-4792	426	6	,	,	PUNCT
ejpam-4792	426	7	15(1):71–82	15(1):71–82	NUM
ejpam-4792	426	8	,	,	PUNCT
ejpam-4792	426	9	2020	2020	NUM
ejpam-4792	426	10	.	.	PUNCT
ejpam-4792	427	1	[	[	X
ejpam-4792	427	2	3	3	X
ejpam-4792	427	3	]	]	PUNCT
ejpam-4792	427	4	l.	l.	PROPN
ejpam-4792	427	5	debnath	debnath	PROPN
ejpam-4792	427	6	.	.	PUNCT
ejpam-4792	428	1	integral	integral	ADJ
ejpam-4792	428	2	transforms	transform	NOUN
ejpam-4792	428	3	and	and	CCONJ
ejpam-4792	428	4	their	their	PRON
ejpam-4792	428	5	applications	application	NOUN
ejpam-4792	428	6	.	.	PUNCT
ejpam-4792	429	1	crc	crc	PROPN
ejpam-4792	429	2	press	press	PROPN
ejpam-4792	429	3	,	,	PUNCT
ejpam-4792	429	4	florida	florida	PROPN
ejpam-4792	429	5	,	,	PUNCT
ejpam-4792	429	6	boca	boca	PROPN
ejpam-4792	429	7	raton	raton	PROPN
ejpam-4792	429	8	,	,	PUNCT
ejpam-4792	429	9	1995	1995	NUM
ejpam-4792	429	10	.	.	PUNCT
ejpam-4792	430	1	[	[	X
ejpam-4792	430	2	4	4	X
ejpam-4792	430	3	]	]	X
ejpam-4792	430	4	g.	g.	PROPN
ejpam-4792	430	5	doetsch	doetsch	PROPN
ejpam-4792	430	6	.	.	PUNCT
ejpam-4792	431	1	introduction	introduction	NOUN
ejpam-4792	431	2	to	to	ADP
ejpam-4792	431	3	the	the	DET
ejpam-4792	431	4	theory	theory	NOUN
ejpam-4792	431	5	and	and	CCONJ
ejpam-4792	431	6	application	application	NOUN
ejpam-4792	431	7	of	of	ADP
ejpam-4792	431	8	the	the	DET
ejpam-4792	431	9	laplace	laplace	NOUN
ejpam-4792	431	10	transform	transform	NOUN
ejpam-4792	431	11	.	.	PUNCT
ejpam-4792	432	1	springer	springer	NOUN
ejpam-4792	432	2	-	-	PUNCT
ejpam-4792	432	3	verlag	verlag	PROPN
ejpam-4792	432	4	,	,	PUNCT
ejpam-4792	432	5	new	new	PROPN
ejpam-4792	432	6	york	york	PROPN
ejpam-4792	432	7	,	,	PUNCT
ejpam-4792	432	8	usa	usa	PROPN
ejpam-4792	432	9	,	,	PUNCT
ejpam-4792	432	10	1974	1974	NUM
ejpam-4792	432	11	.	.	PUNCT
ejpam-4792	433	1	[	[	X
ejpam-4792	433	2	5	5	NUM
ejpam-4792	433	3	]	]	PUNCT
ejpam-4792	433	4	a.	a.	NOUN
ejpam-4792	433	5	kilicman	kilicman	PROPN
ejpam-4792	433	6	,	,	PUNCT
ejpam-4792	433	7	h.	h.	PROPN
ejpam-4792	433	8	eltayeb	eltayeb	PROPN
ejpam-4792	433	9	,	,	PUNCT
ejpam-4792	433	10	and	and	CCONJ
ejpam-4792	433	11	r.p	r.p	PROPN
ejpam-4792	433	12	.	.	PROPN
ejpam-4792	433	13	agarwal	agarwal	PROPN
ejpam-4792	433	14	.	.	PUNCT
ejpam-4792	434	1	on	on	ADP
ejpam-4792	434	2	sumudu	sumudu	NOUN
ejpam-4792	434	3	transform	transform	NOUN
ejpam-4792	434	4	and	and	CCONJ
ejpam-4792	434	5	system	system	NOUN
ejpam-4792	434	6	of	of	ADP
ejpam-4792	434	7	differential	differential	ADJ
ejpam-4792	434	8	equations	equation	NOUN
ejpam-4792	434	9	.	.	PUNCT
ejpam-4792	435	1	abstract	abstract	ADJ
ejpam-4792	435	2	and	and	CCONJ
ejpam-4792	435	3	applied	apply	VERB
ejpam-4792	435	4	analysis	analysis	NOUN
ejpam-4792	435	5	,	,	PUNCT
ejpam-4792	435	6	2010:11	2010:11	NUM
ejpam-4792	435	7	,	,	PUNCT
ejpam-4792	435	8	2010	2010	NUM
ejpam-4792	435	9	.	.	PUNCT
ejpam-4792	436	1	[	[	X
ejpam-4792	436	2	6	6	NUM
ejpam-4792	436	3	]	]	PUNCT
ejpam-4792	436	4	h.	h.	PROPN
ejpam-4792	436	5	eltayeb	eltayeb	PROPN
ejpam-4792	436	6	and	and	CCONJ
ejpam-4792	436	7	a.	a.	NOUN
ejpam-4792	436	8	kilicman	kilicman	PROPN
ejpam-4792	436	9	.	.	PUNCT
ejpam-4792	437	1	a	a	DET
ejpam-4792	437	2	note	note	NOUN
ejpam-4792	437	3	on	on	ADP
ejpam-4792	437	4	solutions	solution	NOUN
ejpam-4792	437	5	of	of	ADP
ejpam-4792	437	6	wave	wave	NOUN
ejpam-4792	437	7	,	,	PUNCT
ejpam-4792	437	8	laplace	laplace	NOUN
ejpam-4792	437	9	’s	’s	PART
ejpam-4792	437	10	and	and	CCONJ
ejpam-4792	437	11	heat	heat	NOUN
ejpam-4792	437	12	equations	equation	NOUN
ejpam-4792	437	13	with	with	ADP
ejpam-4792	437	14	convolution	convolution	NOUN
ejpam-4792	437	15	terms	term	NOUN
ejpam-4792	437	16	by	by	ADP
ejpam-4792	437	17	using	use	VERB
ejpam-4792	437	18	a	a	DET
ejpam-4792	437	19	double	double	ADJ
ejpam-4792	437	20	laplace	laplace	NOUN
ejpam-4792	437	21	transform	transform	NOUN
ejpam-4792	437	22	.	.	PUNCT
ejpam-4792	438	1	applied	apply	VERB
ejpam-4792	438	2	mathematics	mathematics	NOUN
ejpam-4792	438	3	letters	letter	NOUN
ejpam-4792	438	4	,	,	PUNCT
ejpam-4792	438	5	21(12):1324–1329	21(12):1324–1329	NUM
ejpam-4792	438	6	,	,	PUNCT
ejpam-4792	438	7	2008	2008	NUM
ejpam-4792	438	8	.	.	PUNCT
ejpam-4792	439	1	[	[	X
ejpam-4792	439	2	7	7	X
ejpam-4792	439	3	]	]	X
ejpam-4792	439	4	h.	h.	PROPN
ejpam-4792	439	5	eltayeb	eltayeb	PROPN
ejpam-4792	439	6	and	and	CCONJ
ejpam-4792	439	7	a.	a.	NOUN
ejpam-4792	439	8	kilicman	kilicman	PROPN
ejpam-4792	439	9	.	.	PUNCT
ejpam-4792	440	1	a	a	DET
ejpam-4792	440	2	note	note	NOUN
ejpam-4792	440	3	on	on	ADP
ejpam-4792	440	4	the	the	DET
ejpam-4792	440	5	sumudu	sumudu	NOUN
ejpam-4792	440	6	transforms	transform	VERB
ejpam-4792	440	7	and	and	CCONJ
ejpam-4792	440	8	differential	differential	ADJ
ejpam-4792	440	9	equations	equation	NOUN
ejpam-4792	440	10	.	.	PUNCT
ejpam-4792	441	1	applied	apply	VERB
ejpam-4792	441	2	mathematical	mathematical	ADJ
ejpam-4792	441	3	sciences	sciences	PROPN
ejpam-4792	441	4	,	,	PUNCT
ejpam-4792	441	5	4(22):1089–1098	4(22):1089–1098	NUM
ejpam-4792	441	6	,	,	PUNCT
ejpam-4792	441	7	2010	2010	NUM
ejpam-4792	441	8	.	.	PUNCT
ejpam-4792	442	1	[	[	X
ejpam-4792	442	2	8	8	NUM
ejpam-4792	442	3	]	]	X
ejpam-4792	442	4	t.m	t.m	PROPN
ejpam-4792	442	5	.	.	PROPN
ejpam-4792	442	6	elzaki	elzaki	PROPN
ejpam-4792	442	7	and	and	CCONJ
ejpam-4792	442	8	s.m	s.m	PROPN
ejpam-4792	442	9	.	.	PROPN
ejpam-4792	442	10	elzaki	elzaki	PROPN
ejpam-4792	442	11	.	.	PUNCT
ejpam-4792	443	1	application	application	NOUN
ejpam-4792	443	2	of	of	ADP
ejpam-4792	443	3	new	new	ADJ
ejpam-4792	443	4	transform	transform	NOUN
ejpam-4792	443	5	“	"	PUNCT
ejpam-4792	443	6	elzaki	elzaki	NOUN
ejpam-4792	443	7	transform	transform	NOUN
ejpam-4792	443	8	”	"	PUNCT
ejpam-4792	443	9	to	to	ADP
ejpam-4792	443	10	partial	partial	ADJ
ejpam-4792	443	11	differential	differential	NOUN
ejpam-4792	443	12	equations	equation	NOUN
ejpam-4792	443	13	.	.	PUNCT
ejpam-4792	444	1	global	global	ADJ
ejpam-4792	444	2	journal	journal	PROPN
ejpam-4792	444	3	of	of	ADP
ejpam-4792	444	4	pure	pure	ADJ
ejpam-4792	444	5	and	and	CCONJ
ejpam-4792	444	6	applied	applied	ADJ
ejpam-4792	444	7	mathematics	mathematic	NOUN
ejpam-4792	444	8	,	,	PUNCT
ejpam-4792	444	9	7(1):65	7(1):65	NUM
ejpam-4792	444	10	–	–	PUNCT
ejpam-4792	444	11	70	70	NUM
ejpam-4792	444	12	,	,	PUNCT
ejpam-4792	444	13	2011	2011	NUM
ejpam-4792	444	14	.	.	PUNCT
ejpam-4792	445	1	[	[	X
ejpam-4792	445	2	9	9	NUM
ejpam-4792	445	3	]	]	X
ejpam-4792	445	4	t.m	t.m	PROPN
ejpam-4792	445	5	.	.	PROPN
ejpam-4792	445	6	elzaki	elzaki	PROPN
ejpam-4792	445	7	and	and	CCONJ
ejpam-4792	445	8	s.m	s.m	PROPN
ejpam-4792	445	9	.	.	PROPN
ejpam-4792	445	10	elzaki	elzaki	PROPN
ejpam-4792	445	11	.	.	PUNCT
ejpam-4792	446	1	on	on	ADP
ejpam-4792	446	2	the	the	DET
ejpam-4792	446	3	elzaki	elzaki	NOUN
ejpam-4792	446	4	transform	transform	VERB
ejpam-4792	446	5	and	and	CCONJ
ejpam-4792	446	6	ordinary	ordinary	ADJ
ejpam-4792	446	7	differential	differential	ADJ
ejpam-4792	446	8	equation	equation	NOUN
ejpam-4792	446	9	with	with	ADP
ejpam-4792	446	10	variable	variable	ADJ
ejpam-4792	446	11	coefficients	coefficient	NOUN
ejpam-4792	446	12	.	.	PUNCT
ejpam-4792	447	1	advances	advance	NOUN
ejpam-4792	447	2	in	in	ADP
ejpam-4792	447	3	theoretical	theoretical	ADJ
ejpam-4792	447	4	and	and	CCONJ
ejpam-4792	447	5	applied	applied	ADJ
ejpam-4792	447	6	mathematics	mathematic	NOUN
ejpam-4792	447	7	,	,	PUNCT
ejpam-4792	447	8	6(1):41–46	6(1):41–46	NUM
ejpam-4792	447	9	,	,	PUNCT
ejpam-4792	447	10	2011	2011	NUM
ejpam-4792	447	11	.	.	PUNCT
ejpam-4792	448	1	[	[	X
ejpam-4792	448	2	10	10	NUM
ejpam-4792	448	3	]	]	X
ejpam-4792	448	4	t.m	t.m	PROPN
ejpam-4792	448	5	.	.	PROPN
ejpam-4792	448	6	elzaki	elzaki	PROPN
ejpam-4792	448	7	and	and	CCONJ
ejpam-4792	448	8	s.m	s.m	PROPN
ejpam-4792	448	9	.	.	PROPN
ejpam-4792	448	10	elzaki	elzaki	PROPN
ejpam-4792	448	11	.	.	PUNCT
ejpam-4792	449	1	on	on	ADP
ejpam-4792	449	2	the	the	DET
ejpam-4792	449	3	elzaki	elzaki	NOUN
ejpam-4792	449	4	transform	transform	NOUN
ejpam-4792	449	5	and	and	CCONJ
ejpam-4792	449	6	system	system	NOUN
ejpam-4792	449	7	of	of	ADP
ejpam-4792	449	8	partial	partial	ADJ
ejpam-4792	449	9	differential	differential	ADJ
ejpam-4792	449	10	equations	equation	NOUN
ejpam-4792	449	11	.	.	PUNCT
ejpam-4792	450	1	international	international	ADJ
ejpam-4792	450	2	journal	journal	PROPN
ejpam-4792	450	3	of	of	ADP
ejpam-4792	450	4	mathematical	mathematical	ADJ
ejpam-4792	450	5	education	education	NOUN
ejpam-4792	450	6	in	in	ADP
ejpam-4792	450	7	science	science	NOUN
ejpam-4792	450	8	and	and	CCONJ
ejpam-4792	450	9	technology	technology	NOUN
ejpam-4792	450	10	,	,	PUNCT
ejpam-4792	450	11	6(1):115–123	6(1):115–123	NOUN
ejpam-4792	450	12	,	,	PUNCT
ejpam-4792	450	13	2011	2011	NUM
ejpam-4792	450	14	.	.	PUNCT
ejpam-4792	451	1	[	[	X
ejpam-4792	451	2	11	11	NUM
ejpam-4792	451	3	]	]	X
ejpam-4792	451	4	t.m	t.m	PROPN
ejpam-4792	451	5	.	.	PROPN
ejpam-4792	451	6	elzaki	elzaki	PROPN
ejpam-4792	451	7	,	,	PUNCT
ejpam-4792	451	8	s.m	s.m	PROPN
ejpam-4792	451	9	.	.	PROPN
ejpam-4792	451	10	elzaki	elzaki	PROPN
ejpam-4792	451	11	,	,	PUNCT
ejpam-4792	451	12	and	and	CCONJ
ejpam-4792	451	13	e.a	e.a	PROPN
ejpam-4792	451	14	.	.	PROPN
ejpam-4792	451	15	elnour	elnour	PROPN
ejpam-4792	451	16	.	.	PUNCT
ejpam-4792	452	1	on	on	ADP
ejpam-4792	452	2	some	some	DET
ejpam-4792	452	3	applications	application	NOUN
ejpam-4792	452	4	of	of	ADP
ejpam-4792	452	5	new	new	ADJ
ejpam-4792	452	6	integral	integral	ADJ
ejpam-4792	452	7	transform	transform	NOUN
ejpam-4792	452	8	“	"	PUNCT
ejpam-4792	452	9	elzaki	elzaki	NOUN
ejpam-4792	452	10	transform	transform	NOUN
ejpam-4792	452	11	”	"	PUNCT
ejpam-4792	452	12	.	.	PUNCT
ejpam-4792	453	1	global	global	ADJ
ejpam-4792	453	2	journal	journal	PROPN
ejpam-4792	453	3	of	of	ADP
ejpam-4792	453	4	mathematical	mathematical	ADJ
ejpam-4792	453	5	sciences	science	NOUN
ejpam-4792	453	6	:	:	PUNCT
ejpam-4792	453	7	theory	theory	NOUN
ejpam-4792	453	8	and	and	CCONJ
ejpam-4792	453	9	practical	practical	ADJ
ejpam-4792	453	10	,	,	PUNCT
ejpam-4792	453	11	4(1):15–23	4(1):15–23	NUM
ejpam-4792	453	12	,	,	PUNCT
ejpam-4792	453	13	2012	2012	NUM
ejpam-4792	453	14	.	.	PUNCT
ejpam-4792	454	1	[	[	X
ejpam-4792	454	2	12	12	NUM
ejpam-4792	454	3	]	]	X
ejpam-4792	454	4	t.m	t.m	PROPN
ejpam-4792	454	5	.	.	PROPN
ejpam-4792	454	6	elzaki	elzaki	PROPN
ejpam-4792	454	7	,	,	PUNCT
ejpam-4792	454	8	s.m	s.m	PROPN
ejpam-4792	454	9	.	.	PROPN
ejpam-4792	454	10	elzaki	elzaki	PROPN
ejpam-4792	454	11	,	,	PUNCT
ejpam-4792	454	12	and	and	CCONJ
ejpam-4792	454	13	e.m.a	e.m.a	NOUN
ejpam-4792	454	14	.	.	PUNCT
ejpam-4792	455	1	hilal	hilal	PROPN
ejpam-4792	455	2	.	.	PUNCT
ejpam-4792	456	1	elzaki	elzaki	PROPN
ejpam-4792	456	2	and	and	CCONJ
ejpam-4792	456	3	sumudu	sumudu	NOUN
ejpam-4792	456	4	transforms	transform	VERB
ejpam-4792	456	5	for	for	ADP
ejpam-4792	456	6	solving	solve	VERB
ejpam-4792	456	7	some	some	DET
ejpam-4792	456	8	differential	differential	ADJ
ejpam-4792	456	9	equation	equation	NOUN
ejpam-4792	456	10	.	.	PUNCT
ejpam-4792	457	1	global	global	ADJ
ejpam-4792	457	2	journal	journal	PROPN
ejpam-4792	457	3	of	of	ADP
ejpam-4792	457	4	pure	pure	ADJ
ejpam-4792	457	5	and	and	CCONJ
ejpam-4792	457	6	applied	applied	ADJ
ejpam-4792	457	7	mathematics	mathematic	NOUN
ejpam-4792	457	8	,	,	PUNCT
ejpam-4792	457	9	8(2):167–173	8(2):167–173	NUM
ejpam-4792	457	10	,	,	PUNCT
ejpam-4792	457	11	2012	2012	NUM
ejpam-4792	457	12	.	.	PUNCT
ejpam-4792	458	1	[	[	X
ejpam-4792	458	2	13	13	NUM
ejpam-4792	458	3	]	]	PUNCT
ejpam-4792	458	4	m.	m.	NOUN
ejpam-4792	458	5	eslaminasab	eslaminasab	PROPN
ejpam-4792	458	6	and	and	CCONJ
ejpam-4792	458	7	s.	s.	PROPN
ejpam-4792	458	8	abbasbandy	abbasbandy	PROPN
ejpam-4792	458	9	.	.	PUNCT
ejpam-4792	459	1	study	study	NOUN
ejpam-4792	459	2	on	on	ADP
ejpam-4792	459	3	usage	usage	NOUN
ejpam-4792	459	4	of	of	ADP
ejpam-4792	459	5	elzaki	elzaki	NOUN
ejpam-4792	459	6	transform	transform	NOUN
ejpam-4792	459	7	for	for	ADP
ejpam-4792	459	8	the	the	DET
ejpam-4792	459	9	ordinary	ordinary	ADJ
ejpam-4792	459	10	differential	differential	ADJ
ejpam-4792	459	11	equations	equation	NOUN
ejpam-4792	459	12	with	with	ADP
ejpam-4792	459	13	non	non	ADJ
ejpam-4792	459	14	-	-	ADJ
ejpam-4792	459	15	constant	constant	ADJ
ejpam-4792	459	16	coefficients	coefficient	NOUN
ejpam-4792	459	17	.	.	PUNCT
ejpam-4792	460	1	international	international	ADJ
ejpam-4792	460	2	journal	journal	PROPN
ejpam-4792	460	3	of	of	ADP
ejpam-4792	460	4	industrial	industrial	ADJ
ejpam-4792	460	5	mathematics	mathematic	NOUN
ejpam-4792	460	6	,	,	PUNCT
ejpam-4792	460	7	7(3):277–281	7(3):277–281	NUM
ejpam-4792	460	8	,	,	PUNCT
ejpam-4792	460	9	2015	2015	NUM
ejpam-4792	460	10	.	.	PUNCT
ejpam-4792	461	1	references	reference	NOUN
ejpam-4792	461	2	1404	1404	NUM
ejpam-4792	461	3	[	[	X
ejpam-4792	461	4	14	14	NUM
ejpam-4792	461	5	]	]	X
ejpam-4792	461	6	b.	b.	PROPN
ejpam-4792	461	7	ghil	ghil	PROPN
ejpam-4792	461	8	.	.	PUNCT
ejpam-4792	462	1	the	the	DET
ejpam-4792	462	2	solution	solution	NOUN
ejpam-4792	462	3	of	of	ADP
ejpam-4792	462	4	euler	euler	PROPN
ejpam-4792	462	5	-	-	PUNCT
ejpam-4792	462	6	cauchy	cauchy	NOUN
ejpam-4792	462	7	equation	equation	NOUN
ejpam-4792	462	8	using	use	VERB
ejpam-4792	462	9	laplace	laplace	NOUN
ejpam-4792	462	10	transform	transform	NOUN
ejpam-4792	462	11	.	.	PUNCT
ejpam-4792	463	1	international	international	ADJ
ejpam-4792	463	2	journal	journal	PROPN
ejpam-4792	463	3	of	of	ADP
ejpam-4792	463	4	mathematical	mathematical	ADJ
ejpam-4792	463	5	analysis	analysis	NOUN
ejpam-4792	463	6	,	,	PUNCT
ejpam-4792	463	7	9(53):2611–2618	9(53):2611–2618	NUM
ejpam-4792	463	8	,	,	PUNCT
ejpam-4792	463	9	2015	2015	NUM
ejpam-4792	463	10	.	.	PUNCT
ejpam-4792	464	1	[	[	X
ejpam-4792	464	2	15	15	NUM
ejpam-4792	464	3	]	]	X
ejpam-4792	464	4	a.	a.	NOUN
ejpam-4792	464	5	kadem	kadem	PROPN
ejpam-4792	464	6	and	and	CCONJ
ejpam-4792	464	7	a.	a.	NOUN
ejpam-4792	464	8	kilicman	kilicman	PROPN
ejpam-4792	464	9	.	.	PUNCT
ejpam-4792	465	1	note	note	NOUN
ejpam-4792	465	2	on	on	ADP
ejpam-4792	465	3	transport	transport	NOUN
ejpam-4792	465	4	equation	equation	NOUN
ejpam-4792	465	5	and	and	CCONJ
ejpam-4792	465	6	fractional	fractional	ADJ
ejpam-4792	465	7	sumudu	sumudu	NOUN
ejpam-4792	465	8	transform	transform	NOUN
ejpam-4792	465	9	.	.	PUNCT
ejpam-4792	466	1	computers	computer	NOUN
ejpam-4792	466	2	and	and	CCONJ
ejpam-4792	466	3	mathematics	mathematic	NOUN
ejpam-4792	466	4	with	with	ADP
ejpam-4792	466	5	applications	application	NOUN
ejpam-4792	466	6	,	,	PUNCT
ejpam-4792	466	7	62(8):2995–3003	62(8):2995–3003	NUM
ejpam-4792	466	8	,	,	PUNCT
ejpam-4792	466	9	2011	2011	NUM
ejpam-4792	466	10	.	.	PUNCT
ejpam-4792	467	1	[	[	X
ejpam-4792	467	2	16	16	NUM
ejpam-4792	467	3	]	]	PUNCT
ejpam-4792	467	4	hj	hj	PROPN
ejpam-4792	467	5	.	.	PUNCT
ejpam-4792	467	6	kim	kim	PROPN
ejpam-4792	467	7	.	.	PUNCT
ejpam-4792	468	1	the	the	DET
ejpam-4792	468	2	intrinsic	intrinsic	ADJ
ejpam-4792	468	3	structure	structure	NOUN
ejpam-4792	468	4	and	and	CCONJ
ejpam-4792	468	5	properties	property	NOUN
ejpam-4792	468	6	of	of	ADP
ejpam-4792	468	7	laplace	laplace	NOUN
ejpam-4792	468	8	-	-	PUNCT
ejpam-4792	468	9	typed	type	VERB
ejpam-4792	468	10	integral	integral	ADJ
ejpam-4792	468	11	transforms	transform	NOUN
ejpam-4792	468	12	.	.	PUNCT
ejpam-4792	469	1	mathematical	mathematical	ADJ
ejpam-4792	469	2	problems	problem	NOUN
ejpam-4792	469	3	in	in	ADP
ejpam-4792	469	4	engineering	engineering	NOUN
ejpam-4792	469	5	,	,	PUNCT
ejpam-4792	469	6	2017:8	2017:8	NUM
ejpam-4792	469	7	,	,	PUNCT
ejpam-4792	469	8	2017	2017	NUM
ejpam-4792	469	9	.	.	PUNCT
ejpam-4792	470	1	[	[	X
ejpam-4792	470	2	17	17	NUM
ejpam-4792	470	3	]	]	SYM
ejpam-4792	470	4	hj	hj	PROPN
ejpam-4792	470	5	.	.	PUNCT
ejpam-4792	470	6	kim	kim	PROPN
ejpam-4792	470	7	.	.	PUNCT
ejpam-4792	471	1	on	on	ADP
ejpam-4792	471	2	the	the	DET
ejpam-4792	471	3	form	form	NOUN
ejpam-4792	471	4	and	and	CCONJ
ejpam-4792	471	5	properties	property	NOUN
ejpam-4792	471	6	of	of	ADP
ejpam-4792	471	7	an	an	DET
ejpam-4792	471	8	integral	integral	ADJ
ejpam-4792	471	9	transform	transform	NOUN
ejpam-4792	471	10	with	with	ADP
ejpam-4792	471	11	strength	strength	NOUN
ejpam-4792	471	12	in	in	ADP
ejpam-4792	471	13	integral	integral	ADJ
ejpam-4792	471	14	transforms	transform	NOUN
ejpam-4792	471	15	.	.	PUNCT
ejpam-4792	472	1	far	far	PROPN
ejpam-4792	472	2	east	east	PROPN
ejpam-4792	472	3	journal	journal	PROPN
ejpam-4792	472	4	of	of	ADP
ejpam-4792	472	5	mathematical	mathematical	ADJ
ejpam-4792	472	6	sciences	science	NOUN
ejpam-4792	472	7	,	,	PUNCT
ejpam-4792	472	8	102(11):2831–2844	102(11):2831–2844	NUM
ejpam-4792	472	9	,	,	PUNCT
ejpam-4792	472	10	2017	2017	NUM
ejpam-4792	472	11	.	.	PUNCT
ejpam-4792	473	1	[	[	X
ejpam-4792	473	2	18	18	NUM
ejpam-4792	473	3	]	]	SYM
ejpam-4792	473	4	hj	hj	PROPN
ejpam-4792	473	5	.	.	PUNCT
ejpam-4792	473	6	kim	kim	PROPN
ejpam-4792	473	7	.	.	PUNCT
ejpam-4792	474	1	the	the	DET
ejpam-4792	474	2	solution	solution	NOUN
ejpam-4792	474	3	of	of	ADP
ejpam-4792	474	4	laguerre	laguerre	NOUN
ejpam-4792	474	5	’s	’s	PART
ejpam-4792	474	6	equation	equation	NOUN
ejpam-4792	474	7	by	by	ADP
ejpam-4792	474	8	using	use	VERB
ejpam-4792	474	9	g	g	NOUN
ejpam-4792	474	10	-	-	PUNCT
ejpam-4792	474	11	transform	transform	NOUN
ejpam-4792	474	12	.	.	PUNCT
ejpam-4792	475	1	international	international	ADJ
ejpam-4792	475	2	journal	journal	NOUN
ejpam-4792	475	3	of	of	ADP
ejpam-4792	475	4	applied	apply	VERB
ejpam-4792	475	5	engineering	engineering	NOUN
ejpam-4792	475	6	research	research	NOUN
ejpam-4792	475	7	,	,	PUNCT
ejpam-4792	475	8	12(24):16083–16086	12(24):16083–16086	NUM
ejpam-4792	475	9	,	,	PUNCT
ejpam-4792	475	10	2017	2017	NUM
ejpam-4792	475	11	.	.	PUNCT
ejpam-4792	476	1	[	[	X
ejpam-4792	476	2	19	19	NUM
ejpam-4792	476	3	]	]	SYM
ejpam-4792	476	4	hj	hj	PROPN
ejpam-4792	476	5	.	.	PUNCT
ejpam-4792	477	1	kim	kim	PROPN
ejpam-4792	477	2	.	.	PUNCT
ejpam-4792	478	1	a	a	DET
ejpam-4792	478	2	proof	proof	NOUN
ejpam-4792	478	3	with	with	ADP
ejpam-4792	478	4	respect	respect	NOUN
ejpam-4792	478	5	to	to	ADP
ejpam-4792	478	6	laplace	laplace	NOUN
ejpam-4792	478	7	transform	transform	NOUN
ejpam-4792	478	8	of	of	ADP
ejpam-4792	478	9	the	the	DET
ejpam-4792	478	10	n	n	ADV
ejpam-4792	478	11	-	-	PUNCT
ejpam-4792	478	12	th	th	X
ejpam-4792	478	13	derivative	derivative	NOUN
ejpam-4792	478	14	by	by	ADP
ejpam-4792	478	15	mathematical	mathematical	ADJ
ejpam-4792	478	16	induction	induction	NOUN
ejpam-4792	478	17	.	.	PUNCT
ejpam-4792	479	1	advances	advance	NOUN
ejpam-4792	479	2	in	in	ADP
ejpam-4792	479	3	dynamical	dynamical	ADJ
ejpam-4792	479	4	systems	system	NOUN
ejpam-4792	479	5	and	and	CCONJ
ejpam-4792	479	6	applications	application	NOUN
ejpam-4792	479	7	,	,	PUNCT
ejpam-4792	479	8	15(1):29–33	15(1):29–33	NUM
ejpam-4792	479	9	,	,	PUNCT
ejpam-4792	479	10	2020	2020	NUM
ejpam-4792	479	11	.	.	PUNCT
ejpam-4792	480	1	[	[	X
ejpam-4792	480	2	20	20	NUM
ejpam-4792	480	3	]	]	X
ejpam-4792	480	4	g.a	g.a	PROPN
ejpam-4792	480	5	.	.	PROPN
ejpam-4792	480	6	korn	korn	PROPN
ejpam-4792	480	7	and	and	CCONJ
ejpam-4792	480	8	t.m	t.m	PROPN
ejpam-4792	480	9	.	.	PROPN
ejpam-4792	480	10	korn	korn	PROPN
ejpam-4792	480	11	.	.	PUNCT
ejpam-4792	481	1	mathematical	mathematical	ADJ
ejpam-4792	481	2	handbook	handbook	NOUN
ejpam-4792	481	3	for	for	ADP
ejpam-4792	481	4	scientists	scientist	NOUN
ejpam-4792	481	5	and	and	CCONJ
ejpam-4792	481	6	engineers	engineer	NOUN
ejpam-4792	481	7	(	(	PUNCT
ejpam-4792	481	8	2nd	2nd	ADJ
ejpam-4792	481	9	ed	ed	NOUN
ejpam-4792	481	10	.	.	PUNCT
ejpam-4792	481	11	)	)	PUNCT
ejpam-4792	481	12	.	.	PUNCT
ejpam-4792	482	1	mcgraw	mcgraw	PROPN
ejpam-4792	482	2	-	-	PUNCT
ejpam-4792	482	3	hill	hill	NOUN
ejpam-4792	482	4	companies	company	NOUN
ejpam-4792	482	5	,	,	PUNCT
ejpam-4792	482	6	mineola	mineola	PROPN
ejpam-4792	482	7	,	,	PUNCT
ejpam-4792	482	8	new	new	PROPN
ejpam-4792	482	9	york	york	PROPN
ejpam-4792	482	10	,	,	PUNCT
ejpam-4792	482	11	1968	1968	NUM
ejpam-4792	482	12	.	.	PUNCT
ejpam-4792	483	1	[	[	X
ejpam-4792	483	2	21	21	NUM
ejpam-4792	483	3	]	]	X
ejpam-4792	483	4	e.	e.	PROPN
ejpam-4792	483	5	kreyszig	kreyszig	PROPN
ejpam-4792	483	6	.	.	PUNCT
ejpam-4792	484	1	advanced	advanced	ADJ
ejpam-4792	484	2	engineering	engineering	NOUN
ejpam-4792	484	3	mathematics	mathematic	NOUN
ejpam-4792	484	4	.	.	PUNCT
ejpam-4792	485	1	john	john	PROPN
ejpam-4792	485	2	wiley	wiley	PROPN
ejpam-4792	485	3	and	and	CCONJ
ejpam-4792	485	4	sons	son	NOUN
ejpam-4792	485	5	,	,	PUNCT
ejpam-4792	485	6	hoboken	hoboken	PROPN
ejpam-4792	485	7	,	,	PUNCT
ejpam-4792	485	8	new	new	PROPN
ejpam-4792	485	9	york	york	PROPN
ejpam-4792	485	10	,	,	PUNCT
ejpam-4792	485	11	1999	1999	NUM
ejpam-4792	485	12	.	.	PUNCT
ejpam-4792	486	1	[	[	X
ejpam-4792	486	2	22	22	NUM
ejpam-4792	486	3	]	]	PUNCT
ejpam-4792	486	4	hj	hj	PROPN
ejpam-4792	486	5	.	.	PUNCT
ejpam-4792	487	1	kim	kim	PROPN
ejpam-4792	487	2	,	,	PUNCT
ejpam-4792	487	3	s.	s.	PROPN
ejpam-4792	487	4	sattaso	sattaso	PROPN
ejpam-4792	487	5	,	,	PUNCT
ejpam-4792	487	6	k.	k.	PROPN
ejpam-4792	487	7	nonlaopon	nonlaopon	NOUN
ejpam-4792	487	8	,	,	PUNCT
ejpam-4792	487	9	and	and	CCONJ
ejpam-4792	487	10	k.	k.	PROPN
ejpam-4792	487	11	kaewnimit	kaewnimit	PROPN
ejpam-4792	487	12	.	.	PUNCT
ejpam-4792	488	1	an	an	DET
ejpam-4792	488	2	application	application	NOUN
ejpam-4792	488	3	of	of	ADP
ejpam-4792	488	4	generalized	generalized	ADJ
ejpam-4792	488	5	laplace	laplace	NOUN
ejpam-4792	488	6	transform	transform	NOUN
ejpam-4792	488	7	in	in	ADP
ejpam-4792	488	8	pdes	pde	NOUN
ejpam-4792	488	9	.	.	PUNCT
ejpam-4792	489	1	advances	advance	NOUN
ejpam-4792	489	2	in	in	ADP
ejpam-4792	489	3	dynamical	dynamical	ADJ
ejpam-4792	489	4	systems	system	NOUN
ejpam-4792	489	5	and	and	CCONJ
ejpam-4792	489	6	applications	application	NOUN
ejpam-4792	489	7	,	,	PUNCT
ejpam-4792	489	8	14(2):257–265	14(2):257–265	NOUN
ejpam-4792	489	9	,	,	PUNCT
ejpam-4792	489	10	2019	2019	NUM
ejpam-4792	489	11	.	.	PUNCT
ejpam-4792	490	1	[	[	X
ejpam-4792	490	2	23	23	NUM
ejpam-4792	490	3	]	]	X
ejpam-4792	490	4	p.	p.	PROPN
ejpam-4792	490	5	prasertsang	prasertsang	PROPN
ejpam-4792	490	6	,	,	PUNCT
ejpam-4792	490	7	s.	s.	PROPN
ejpam-4792	490	8	sattaso	sattaso	PROPN
ejpam-4792	490	9	,	,	PUNCT
ejpam-4792	490	10	k.	k.	PROPN
ejpam-4792	490	11	nonlaopon	nonlaopon	NOUN
ejpam-4792	490	12	,	,	PUNCT
ejpam-4792	490	13	and	and	CCONJ
ejpam-4792	490	14	hj	hj	PROPN
ejpam-4792	490	15	.	.	PUNCT
ejpam-4792	491	1	kim	kim	PROPN
ejpam-4792	491	2	.	.	PUNCT
ejpam-4792	492	1	analytical	analytical	ADJ
ejpam-4792	492	2	study	study	NOUN
ejpam-4792	492	3	for	for	ADP
ejpam-4792	492	4	certain	certain	ADJ
ejpam-4792	492	5	ordinary	ordinary	ADJ
ejpam-4792	492	6	differential	differential	ADJ
ejpam-4792	492	7	equations	equation	NOUN
ejpam-4792	492	8	with	with	ADP
ejpam-4792	492	9	variable	variable	ADJ
ejpam-4792	492	10	coefficients	coefficient	NOUN
ejpam-4792	492	11	via	via	ADP
ejpam-4792	492	12	gα	gα	NOUN
ejpam-4792	492	13	-	-	PUNCT
ejpam-4792	492	14	transform	transform	NOUN
ejpam-4792	492	15	.	.	PUNCT
ejpam-4792	493	1	european	european	ADJ
ejpam-4792	493	2	journal	journal	PROPN
ejpam-4792	493	3	of	of	ADP
ejpam-4792	493	4	pure	pure	ADJ
ejpam-4792	493	5	and	and	CCONJ
ejpam-4792	493	6	applied	applied	ADJ
ejpam-4792	493	7	mathematics	mathematic	NOUN
ejpam-4792	493	8	,	,	PUNCT
ejpam-4792	493	9	14(4):1184–1199	14(4):1184–1199	NUM
ejpam-4792	493	10	,	,	PUNCT
ejpam-4792	493	11	2021	2021	NUM
ejpam-4792	493	12	.	.	PUNCT
ejpam-4792	494	1	[	[	X
ejpam-4792	494	2	24	24	NUM
ejpam-4792	494	3	]	]	X
ejpam-4792	494	4	s.	s.	PROPN
ejpam-4792	494	5	sattaso	sattaso	PROPN
ejpam-4792	494	6	,	,	PUNCT
ejpam-4792	494	7	k.	k.	PROPN
ejpam-4792	494	8	nonlaopon	nonlaopon	NOUN
ejpam-4792	494	9	,	,	PUNCT
ejpam-4792	494	10	and	and	CCONJ
ejpam-4792	494	11	hj	hj	PROPN
ejpam-4792	494	12	.	.	PUNCT
ejpam-4792	495	1	kim	kim	PROPN
ejpam-4792	495	2	.	.	PUNCT
ejpam-4792	496	1	further	further	ADJ
ejpam-4792	496	2	properties	property	NOUN
ejpam-4792	496	3	of	of	ADP
ejpam-4792	496	4	laplace	laplace	NOUN
ejpam-4792	496	5	-	-	PUNCT
ejpam-4792	496	6	typed	type	VERB
ejpam-4792	496	7	integral	integral	ADJ
ejpam-4792	496	8	transforms	transform	NOUN
ejpam-4792	496	9	.	.	PUNCT
ejpam-4792	497	1	dynamic	dynamic	ADJ
ejpam-4792	497	2	systems	system	NOUN
ejpam-4792	497	3	and	and	CCONJ
ejpam-4792	497	4	applications	application	NOUN
ejpam-4792	497	5	,	,	PUNCT
ejpam-4792	497	6	28(1):195–215	28(1):195–215	PROPN
ejpam-4792	497	7	,	,	PUNCT
ejpam-4792	497	8	2019	2019	NUM
ejpam-4792	497	9	.	.	PUNCT
ejpam-4792	498	1	[	[	X
ejpam-4792	498	2	25	25	NUM
ejpam-4792	498	3	]	]	X
ejpam-4792	498	4	y.h	y.h	PROPN
ejpam-4792	498	5	.	.	PROPN
ejpam-4792	498	6	geum	geum	PROPN
ejpam-4792	498	7	,	,	PUNCT
ejpam-4792	498	8	a.k	a.k	PROPN
ejpam-4792	498	9	.	.	PROPN
ejpam-4792	498	10	rathie	rathie	NOUN
ejpam-4792	498	11	,	,	PUNCT
ejpam-4792	498	12	and	and	CCONJ
ejpam-4792	498	13	hj	hj	PROPN
ejpam-4792	498	14	.	.	PUNCT
ejpam-4792	499	1	kim	kim	PROPN
ejpam-4792	499	2	.	.	PROPN
ejpam-4792	499	3	matrix	matrix	NOUN
ejpam-4792	499	4	expression	expression	NOUN
ejpam-4792	499	5	of	of	ADP
ejpam-4792	499	6	convolution	convolution	NOUN
ejpam-4792	499	7	and	and	CCONJ
ejpam-4792	499	8	its	its	PRON
ejpam-4792	499	9	generalized	generalized	ADJ
ejpam-4792	499	10	continuous	continuous	ADJ
ejpam-4792	499	11	form	form	NOUN
ejpam-4792	499	12	.	.	PUNCT
ejpam-4792	500	1	symmetry	symmetry	NOUN
ejpam-4792	500	2	,	,	PUNCT
ejpam-4792	500	3	12(11):1791	12(11):1791	NUM
ejpam-4792	500	4	,	,	PUNCT
ejpam-4792	500	5	2020	2020	NUM
ejpam-4792	500	6	.	.	PUNCT
ejpam-4792	501	1	[	[	X
ejpam-4792	501	2	26	26	NUM
ejpam-4792	501	3	]	]	PUNCT
ejpam-4792	501	4	a.	a.	NOUN
ejpam-4792	501	5	devi	devi	PROPN
ejpam-4792	501	6	,	,	PUNCT
ejpam-4792	501	7	p.	p.	PROPN
ejpam-4792	501	8	roy	roy	PROPN
ejpam-4792	501	9	,	,	PUNCT
ejpam-4792	501	10	and	and	CCONJ
ejpam-4792	501	11	v.	v.	ADP
ejpam-4792	501	12	gill	gill	NOUN
ejpam-4792	501	13	.	.	PUNCT
ejpam-4792	502	1	solution	solution	NOUN
ejpam-4792	502	2	of	of	ADP
ejpam-4792	502	3	ordinary	ordinary	ADJ
ejpam-4792	502	4	differential	differential	ADJ
ejpam-4792	502	5	equations	equation	NOUN
ejpam-4792	502	6	with	with	ADP
ejpam-4792	502	7	variable	variable	ADJ
ejpam-4792	502	8	coefficients	coefficient	NOUN
ejpam-4792	502	9	using	use	VERB
ejpam-4792	502	10	elzaki	elzaki	NOUN
ejpam-4792	502	11	transform	transform	NOUN
ejpam-4792	502	12	.	.	PUNCT
ejpam-4792	503	1	asian	asian	ADJ
ejpam-4792	503	2	journal	journal	PROPN
ejpam-4792	503	3	of	of	ADP
ejpam-4792	503	4	applied	apply	VERB
ejpam-4792	503	5	science	science	NOUN
ejpam-4792	503	6	and	and	CCONJ
ejpam-4792	503	7	technology	technology	NOUN
ejpam-4792	503	8	,	,	PUNCT
ejpam-4792	503	9	1(9):186–194	1(9):186–194	PROPN
ejpam-4792	503	10	,	,	PUNCT
ejpam-4792	503	11	2017	2017	NUM
ejpam-4792	503	12	.	.	PUNCT
ejpam-4792	504	1	[	[	X
ejpam-4792	504	2	27	27	NUM
ejpam-4792	504	3	]	]	PUNCT
ejpam-4792	504	4	a.	a.	NOUN
ejpam-4792	504	5	tagliani	tagliani	NOUN
ejpam-4792	504	6	and	and	CCONJ
ejpam-4792	504	7	m.	m.	NOUN
ejpam-4792	504	8	milev	milev	NOUN
ejpam-4792	504	9	.	.	PUNCT
ejpam-4792	505	1	laplace	laplace	PROPN
ejpam-4792	505	2	transform	transform	VERB
ejpam-4792	505	3	and	and	CCONJ
ejpam-4792	505	4	finite	finite	ADJ
ejpam-4792	505	5	difference	difference	NOUN
ejpam-4792	505	6	methods	method	NOUN
ejpam-4792	505	7	for	for	ADP
ejpam-4792	505	8	the	the	DET
ejpam-4792	505	9	black	black	ADJ
ejpam-4792	505	10	-	-	PUNCT
ejpam-4792	505	11	scholes	schole	NOUN
ejpam-4792	505	12	equation	equation	NOUN
ejpam-4792	505	13	.	.	PUNCT
ejpam-4792	506	1	applied	apply	VERB
ejpam-4792	506	2	mathematics	mathematic	NOUN
ejpam-4792	506	3	and	and	CCONJ
ejpam-4792	506	4	computation	computation	NOUN
ejpam-4792	506	5	,	,	PUNCT
ejpam-4792	506	6	220:649–658	220:649–658	NUM
ejpam-4792	506	7	,	,	PUNCT
ejpam-4792	506	8	2013	2013	NUM
ejpam-4792	506	9	.	.	PUNCT
ejpam-4792	507	1	[	[	X
ejpam-4792	507	2	28	28	NUM
ejpam-4792	507	3	]	]	X
ejpam-4792	507	4	g.k	g.k	PROPN
ejpam-4792	507	5	.	.	PROPN
ejpam-4792	507	6	watugala	watugala	PROPN
ejpam-4792	507	7	.	.	PUNCT
ejpam-4792	508	1	sumudu	sumudu	NOUN
ejpam-4792	508	2	transform	transform	NOUN
ejpam-4792	508	3	:	:	PUNCT
ejpam-4792	508	4	a	a	DET
ejpam-4792	508	5	new	new	ADJ
ejpam-4792	508	6	integral	integral	ADJ
ejpam-4792	508	7	transform	transform	NOUN
ejpam-4792	508	8	to	to	PART
ejpam-4792	508	9	solve	solve	VERB
ejpam-4792	508	10	differential	differential	ADJ
ejpam-4792	508	11	equations	equation	NOUN
ejpam-4792	508	12	and	and	CCONJ
ejpam-4792	508	13	control	control	NOUN
ejpam-4792	508	14	engineering	engineering	NOUN
ejpam-4792	508	15	problems	problem	NOUN
ejpam-4792	508	16	.	.	PUNCT
ejpam-4792	509	1	international	international	ADJ
ejpam-4792	509	2	journal	journal	PROPN
ejpam-4792	509	3	of	of	ADP
ejpam-4792	509	4	mathematical	mathematical	ADJ
ejpam-4792	509	5	education	education	NOUN
ejpam-4792	509	6	in	in	ADP
ejpam-4792	509	7	science	science	NOUN
ejpam-4792	509	8	and	and	CCONJ
ejpam-4792	509	9	technology	technology	NOUN
ejpam-4792	509	10	,	,	PUNCT
ejpam-4792	509	11	24(1):35–43	24(1):35–43	NUM
ejpam-4792	509	12	,	,	PUNCT
ejpam-4792	509	13	1993	1993	NUM
ejpam-4792	509	14	.	.	PUNCT
ejpam-4792	510	1	references	reference	NOUN
ejpam-4792	510	2	1405	1405	NUM
ejpam-4792	511	1	[	[	X
ejpam-4792	511	2	29	29	NUM
ejpam-4792	511	3	]	]	PUNCT
ejpam-4792	511	4	s.	s.	PROPN
ejpam-4792	511	5	weerakoon	weerakoon	PROPN
ejpam-4792	511	6	.	.	PUNCT
ejpam-4792	512	1	application	application	NOUN
ejpam-4792	512	2	of	of	ADP
ejpam-4792	512	3	sumudu	sumudu	NOUN
ejpam-4792	512	4	transform	transform	NOUN
ejpam-4792	512	5	to	to	ADP
ejpam-4792	512	6	partial	partial	ADJ
ejpam-4792	512	7	differential	differential	NOUN
ejpam-4792	512	8	equations	equation	NOUN
ejpam-4792	512	9	.	.	PUNCT
ejpam-4792	513	1	international	international	ADJ
ejpam-4792	513	2	journal	journal	PROPN
ejpam-4792	513	3	of	of	ADP
ejpam-4792	513	4	mathematical	mathematical	ADJ
ejpam-4792	513	5	education	education	NOUN
ejpam-4792	513	6	in	in	ADP
ejpam-4792	513	7	science	science	NOUN
ejpam-4792	513	8	and	and	CCONJ
ejpam-4792	513	9	technology	technology	NOUN
ejpam-4792	513	10	,	,	PUNCT
ejpam-4792	513	11	25(2):277	25(2):277	NOUN
ejpam-4792	513	12	–	–	PUNCT
ejpam-4792	513	13	283	283	NUM
ejpam-4792	513	14	,	,	PUNCT
ejpam-4792	513	15	1994	1994	NUM
ejpam-4792	513	16	.	.	PUNCT
ejpam-4792	514	1	[	[	X
ejpam-4792	514	2	30	30	NUM
ejpam-4792	514	3	]	]	PUNCT
ejpam-4792	514	4	j.	j.	PROPN
ejpam-4792	514	5	zhang	zhang	PROPN
ejpam-4792	514	6	.	.	PUNCT
ejpam-4792	515	1	a	a	DET
ejpam-4792	515	2	sumudu	sumudu	NOUN
ejpam-4792	515	3	based	base	VERB
ejpam-4792	515	4	algorithm	algorithm	NOUN
ejpam-4792	515	5	for	for	ADP
ejpam-4792	515	6	solving	solve	VERB
ejpam-4792	515	7	differential	differential	ADJ
ejpam-4792	515	8	equation	equation	NOUN
ejpam-4792	515	9	.	.	PUNCT
ejpam-4792	516	1	computer	computer	NOUN
ejpam-4792	516	2	science	science	PROPN
ejpam-4792	516	3	journal	journal	PROPN
ejpam-4792	516	4	of	of	ADP
ejpam-4792	516	5	moldova	moldova	PROPN
ejpam-4792	516	6	,	,	PUNCT
ejpam-4792	516	7	15(3):303–313	15(3):303–313	NUM
ejpam-4792	516	8	,	,	PUNCT
ejpam-4792	516	9	2007	2007	NUM
ejpam-4792	516	10	.	.	PUNCT