id	sid	tid	token	lemma	pos
ejpam-5986	1	1	european	european	PROPN
ejpam-5986	1	2	journal	journal	PROPN
ejpam-5986	1	3	of	of	ADP
ejpam-5986	1	4	pure	pure	ADJ
ejpam-5986	1	5	and	and	CCONJ
ejpam-5986	1	6	applied	applied	ADJ
ejpam-5986	1	7	mathematics	mathematic	NOUN
ejpam-5986	1	8	2025	2025	NUM
ejpam-5986	1	9	,	,	PUNCT
ejpam-5986	1	10	vol	vol	NOUN
ejpam-5986	1	11	.	.	PROPN
ejpam-5986	1	12	18	18	NUM
ejpam-5986	1	13	,	,	PUNCT
ejpam-5986	1	14	issue	issue	NOUN
ejpam-5986	1	15	2	2	NUM
ejpam-5986	1	16	,	,	PUNCT
ejpam-5986	1	17	article	article	NOUN
ejpam-5986	1	18	number	number	NOUN
ejpam-5986	1	19	5986	5986	NUM
ejpam-5986	1	20	issn	issn	VERB
ejpam-5986	1	21	1307	1307	NUM
ejpam-5986	1	22	-	-	SYM
ejpam-5986	1	23	5543	5543	NUM
ejpam-5986	1	24	–	–	PUNCT
ejpam-5986	1	25	ejpam.com	ejpam.com	X
ejpam-5986	1	26	published	publish	VERB
ejpam-5986	1	27	by	by	ADP
ejpam-5986	1	28	new	new	PROPN
ejpam-5986	1	29	york	york	PROPN
ejpam-5986	1	30	business	business	PROPN
ejpam-5986	1	31	global	global	ADJ
ejpam-5986	1	32	modified	modify	VERB
ejpam-5986	1	33	laplace	laplace	NOUN
ejpam-5986	1	34	-	-	PUNCT
ejpam-5986	1	35	type	type	NOUN
ejpam-5986	1	36	transform	transform	NOUN
ejpam-5986	1	37	and	and	CCONJ
ejpam-5986	1	38	its	its	PRON
ejpam-5986	1	39	properties	property	NOUN
ejpam-5986	1	40	i̇nci	i̇nci	PROPN
ejpam-5986	1	41	ege	ege	PROPN
ejpam-5986	1	42	department	department	PROPN
ejpam-5986	1	43	of	of	ADP
ejpam-5986	1	44	mathematics	mathematic	NOUN
ejpam-5986	1	45	,	,	PUNCT
ejpam-5986	1	46	faculty	faculty	NOUN
ejpam-5986	1	47	of	of	ADP
ejpam-5986	1	48	science	science	NOUN
ejpam-5986	1	49	,	,	PUNCT
ejpam-5986	1	50	university	university	NOUN
ejpam-5986	1	51	of	of	ADP
ejpam-5986	1	52	aydın	aydın	PROPN
ejpam-5986	1	53	adnan	adnan	PROPN
ejpam-5986	1	54	menderes	menderes	PROPN
ejpam-5986	1	55	,	,	PUNCT
ejpam-5986	1	56	aydın	aydın	PROPN
ejpam-5986	1	57	,	,	PUNCT
ejpam-5986	1	58	türkiye	türkiye	NOUN
ejpam-5986	1	59	abstract	abstract	NOUN
ejpam-5986	1	60	.	.	PUNCT
ejpam-5986	2	1	in	in	ADP
ejpam-5986	2	2	this	this	DET
ejpam-5986	2	3	article	article	NOUN
ejpam-5986	2	4	,	,	PUNCT
ejpam-5986	2	5	we	we	PRON
ejpam-5986	2	6	introduce	introduce	VERB
ejpam-5986	2	7	the	the	DET
ejpam-5986	2	8	modified	modify	VERB
ejpam-5986	2	9	laplace	laplace	NOUN
ejpam-5986	2	10	-	-	PUNCT
ejpam-5986	2	11	type	type	NOUN
ejpam-5986	2	12	transform	transform	NOUN
ejpam-5986	2	13	,	,	PUNCT
ejpam-5986	2	14	develop	develop	VERB
ejpam-5986	2	15	convergence	convergence	NOUN
ejpam-5986	2	16	properties	property	NOUN
ejpam-5986	2	17	,	,	PUNCT
ejpam-5986	2	18	and	and	CCONJ
ejpam-5986	2	19	obtain	obtain	VERB
ejpam-5986	2	20	fundamental	fundamental	ADJ
ejpam-5986	2	21	formulas	formula	NOUN
ejpam-5986	2	22	of	of	ADP
ejpam-5986	2	23	some	some	DET
ejpam-5986	2	24	elementary	elementary	ADJ
ejpam-5986	2	25	functions	function	NOUN
ejpam-5986	2	26	such	such	ADJ
ejpam-5986	2	27	as	as	ADP
ejpam-5986	2	28	power	power	NOUN
ejpam-5986	2	29	functions	function	NOUN
ejpam-5986	2	30	,	,	PUNCT
ejpam-5986	2	31	sine	sine	NOUN
ejpam-5986	2	32	,	,	PUNCT
ejpam-5986	2	33	cosine	cosine	NOUN
ejpam-5986	2	34	,	,	PUNCT
ejpam-5986	2	35	hyperbolic	hyperbolic	ADJ
ejpam-5986	2	36	sine	sine	NOUN
ejpam-5986	2	37	,	,	PUNCT
ejpam-5986	2	38	hyperbolic	hyperbolic	ADJ
ejpam-5986	2	39	cosine	cosine	NOUN
ejpam-5986	2	40	,	,	PUNCT
ejpam-5986	2	41	and	and	CCONJ
ejpam-5986	2	42	exponential	exponential	ADJ
ejpam-5986	2	43	functions	function	NOUN
ejpam-5986	2	44	.	.	PUNCT
ejpam-5986	3	1	we	we	PRON
ejpam-5986	3	2	derive	derive	VERB
ejpam-5986	3	3	translation	translation	NOUN
ejpam-5986	3	4	theorems	theorem	NOUN
ejpam-5986	3	5	and	and	CCONJ
ejpam-5986	3	6	a	a	DET
ejpam-5986	3	7	scale	scale	NOUN
ejpam-5986	3	8	-	-	PUNCT
ejpam-5986	3	9	preserving	preserve	VERB
ejpam-5986	3	10	theorem	theorem	NOUN
ejpam-5986	3	11	and	and	CCONJ
ejpam-5986	3	12	also	also	ADV
ejpam-5986	3	13	show	show	VERB
ejpam-5986	3	14	the	the	DET
ejpam-5986	3	15	relationship	relationship	NOUN
ejpam-5986	3	16	between	between	ADP
ejpam-5986	3	17	the	the	DET
ejpam-5986	3	18	modified	modify	VERB
ejpam-5986	3	19	laplace	laplace	NOUN
ejpam-5986	3	20	type	type	NOUN
ejpam-5986	3	21	transform	transform	NOUN
ejpam-5986	3	22	and	and	CCONJ
ejpam-5986	3	23	the	the	DET
ejpam-5986	3	24	modified	modify	VERB
ejpam-5986	3	25	degenerate	degenerate	ADJ
ejpam-5986	3	26	gamma	gamma	NOUN
ejpam-5986	3	27	function	function	NOUN
ejpam-5986	3	28	.	.	PUNCT
ejpam-5986	4	1	this	this	DET
ejpam-5986	4	2	integral	integral	ADJ
ejpam-5986	4	3	transform	transform	NOUN
ejpam-5986	4	4	is	be	AUX
ejpam-5986	4	5	applied	apply	VERB
ejpam-5986	4	6	to	to	PART
ejpam-5986	4	7	solve	solve	VERB
ejpam-5986	4	8	linear	linear	ADJ
ejpam-5986	4	9	ordinary	ordinary	ADJ
ejpam-5986	4	10	differential	differential	ADJ
ejpam-5986	4	11	equations	equation	NOUN
ejpam-5986	4	12	with	with	ADP
ejpam-5986	4	13	constant	constant	ADJ
ejpam-5986	4	14	coefficients	coefficient	NOUN
ejpam-5986	4	15	and	and	CCONJ
ejpam-5986	4	16	a	a	DET
ejpam-5986	4	17	volterra	volterra	NOUN
ejpam-5986	4	18	integral	integral	ADJ
ejpam-5986	4	19	equation	equation	NOUN
ejpam-5986	4	20	of	of	ADP
ejpam-5986	4	21	the	the	DET
ejpam-5986	4	22	second	second	ADJ
ejpam-5986	4	23	kind	kind	NOUN
ejpam-5986	4	24	.	.	PUNCT
ejpam-5986	5	1	2020	2020	NUM
ejpam-5986	5	2	mathematics	mathematic	NOUN
ejpam-5986	5	3	subject	subject	NOUN
ejpam-5986	5	4	classifications	classification	NOUN
ejpam-5986	5	5	:	:	PUNCT
ejpam-5986	5	6	44a10	44a10	NUM
ejpam-5986	5	7	,	,	PUNCT
ejpam-5986	5	8	44a20	44a20	NUM
ejpam-5986	5	9	,	,	PUNCT
ejpam-5986	5	10	34a25	34a25	NUM
ejpam-5986	5	11	,	,	PUNCT
ejpam-5986	5	12	44a05	44a05	NUM
ejpam-5986	5	13	key	key	ADJ
ejpam-5986	5	14	words	word	NOUN
ejpam-5986	5	15	and	and	CCONJ
ejpam-5986	5	16	phrases	phrase	NOUN
ejpam-5986	5	17	:	:	PUNCT
ejpam-5986	5	18	laplace	laplace	NOUN
ejpam-5986	5	19	transform	transform	NOUN
ejpam-5986	5	20	,	,	PUNCT
ejpam-5986	5	21	laplace	laplace	NOUN
ejpam-5986	5	22	-	-	PUNCT
ejpam-5986	5	23	type	type	NOUN
ejpam-5986	5	24	integral	integral	ADJ
ejpam-5986	5	25	transform	transform	NOUN
ejpam-5986	5	26	,	,	PUNCT
ejpam-5986	5	27	modified	modify	VERB
ejpam-5986	5	28	degenerate	degenerate	ADJ
ejpam-5986	5	29	gamma	gamma	NOUN
ejpam-5986	5	30	function	function	NOUN
ejpam-5986	5	31	,	,	PUNCT
ejpam-5986	5	32	integral	integral	ADJ
ejpam-5986	5	33	equation	equation	NOUN
ejpam-5986	5	34	1	1	NUM
ejpam-5986	5	35	.	.	PUNCT
ejpam-5986	5	36	introduction	introduction	NOUN
ejpam-5986	5	37	a	a	DET
ejpam-5986	5	38	transformation	transformation	NOUN
ejpam-5986	5	39	is	be	AUX
ejpam-5986	5	40	a	a	DET
ejpam-5986	5	41	mathematical	mathematical	ADJ
ejpam-5986	5	42	technique	technique	NOUN
ejpam-5986	5	43	that	that	PRON
ejpam-5986	5	44	changes	change	VERB
ejpam-5986	5	45	one	one	NUM
ejpam-5986	5	46	function	function	NOUN
ejpam-5986	5	47	into	into	ADP
ejpam-5986	5	48	another	another	PRON
ejpam-5986	5	49	.	.	PUNCT
ejpam-5986	6	1	an	an	DET
ejpam-5986	6	2	integral	integral	ADJ
ejpam-5986	6	3	transform	transform	NOUN
ejpam-5986	6	4	maps	map	VERB
ejpam-5986	6	5	a	a	DET
ejpam-5986	6	6	function	function	NOUN
ejpam-5986	6	7	from	from	ADP
ejpam-5986	6	8	its	its	PRON
ejpam-5986	6	9	original	original	ADJ
ejpam-5986	6	10	function	function	NOUN
ejpam-5986	6	11	space	space	NOUN
ejpam-5986	6	12	into	into	ADP
ejpam-5986	6	13	another	another	DET
ejpam-5986	6	14	function	function	NOUN
ejpam-5986	6	15	space	space	NOUN
ejpam-5986	6	16	by	by	ADP
ejpam-5986	6	17	using	use	VERB
ejpam-5986	6	18	integration	integration	NOUN
ejpam-5986	6	19	as	as	ADP
ejpam-5986	6	20	a	a	DET
ejpam-5986	6	21	tool	tool	NOUN
ejpam-5986	6	22	to	to	PART
ejpam-5986	6	23	solve	solve	VERB
ejpam-5986	6	24	differential	differential	ADJ
ejpam-5986	6	25	and	and	CCONJ
ejpam-5986	6	26	integral	integral	ADJ
ejpam-5986	6	27	equations	equation	NOUN
ejpam-5986	6	28	.	.	PUNCT
ejpam-5986	7	1	its	its	PRON
ejpam-5986	7	2	motivation	motivation	NOUN
ejpam-5986	7	3	comes	come	VERB
ejpam-5986	7	4	from	from	ADP
ejpam-5986	7	5	some	some	DET
ejpam-5986	7	6	classes	class	NOUN
ejpam-5986	7	7	of	of	ADP
ejpam-5986	7	8	problems	problem	NOUN
ejpam-5986	7	9	that	that	PRON
ejpam-5986	7	10	are	be	AUX
ejpam-5986	7	11	difficult	difficult	ADJ
ejpam-5986	7	12	to	to	PART
ejpam-5986	7	13	solve	solve	VERB
ejpam-5986	7	14	in	in	ADP
ejpam-5986	7	15	their	their	PRON
ejpam-5986	7	16	original	original	ADJ
ejpam-5986	7	17	representations	representation	NOUN
ejpam-5986	7	18	.	.	PUNCT
ejpam-5986	8	1	an	an	DET
ejpam-5986	8	2	integral	integral	ADJ
ejpam-5986	8	3	transform	transform	NOUN
ejpam-5986	8	4	takes	take	VERB
ejpam-5986	8	5	a	a	DET
ejpam-5986	8	6	function	function	NOUN
ejpam-5986	8	7	from	from	ADP
ejpam-5986	8	8	its	its	PRON
ejpam-5986	8	9	original	original	ADJ
ejpam-5986	8	10	domain	domain	NOUN
ejpam-5986	8	11	into	into	ADP
ejpam-5986	8	12	another	another	PRON
ejpam-5986	8	13	,	,	PUNCT
ejpam-5986	8	14	which	which	PRON
ejpam-5986	8	15	may	may	AUX
ejpam-5986	8	16	make	make	VERB
ejpam-5986	8	17	solving	solve	VERB
ejpam-5986	8	18	the	the	DET
ejpam-5986	8	19	equation	equation	NOUN
ejpam-5986	8	20	much	much	ADV
ejpam-5986	8	21	easier	easy	ADJ
ejpam-5986	8	22	than	than	ADP
ejpam-5986	8	23	in	in	ADP
ejpam-5986	8	24	the	the	DET
ejpam-5986	8	25	original	original	ADJ
ejpam-5986	8	26	domain	domain	NOUN
ejpam-5986	8	27	.	.	PUNCT
ejpam-5986	9	1	the	the	DET
ejpam-5986	9	2	transformed	transform	VERB
ejpam-5986	9	3	function	function	NOUN
ejpam-5986	9	4	can	can	AUX
ejpam-5986	9	5	generally	generally	ADV
ejpam-5986	9	6	be	be	AUX
ejpam-5986	9	7	mapped	map	VERB
ejpam-5986	9	8	back	back	ADV
ejpam-5986	9	9	to	to	ADP
ejpam-5986	9	10	the	the	DET
ejpam-5986	9	11	original	original	ADJ
ejpam-5986	9	12	function	function	NOUN
ejpam-5986	9	13	space	space	NOUN
ejpam-5986	9	14	using	use	VERB
ejpam-5986	9	15	the	the	DET
ejpam-5986	9	16	inverse	inverse	NOUN
ejpam-5986	9	17	transform	transform	NOUN
ejpam-5986	9	18	.	.	PUNCT
ejpam-5986	10	1	an	an	DET
ejpam-5986	10	2	integral	integral	ADJ
ejpam-5986	10	3	transform	transform	NOUN
ejpam-5986	10	4	t	t	NOUN
ejpam-5986	10	5	is	be	AUX
ejpam-5986	10	6	of	of	ADP
ejpam-5986	10	7	the	the	DET
ejpam-5986	10	8	form	form	NOUN
ejpam-5986	10	9	(	(	PUNCT
ejpam-5986	10	10	tv)(t	tv)(t	PROPN
ejpam-5986	10	11	)	)	PUNCT
ejpam-5986	11	1	=	=	SYM
ejpam-5986	11	2	∫	∫	PROPN
ejpam-5986	12	1	x2	x2	PROPN
ejpam-5986	12	2	x1	x1	PROPN
ejpam-5986	12	3	v(x)k(x	v(x)k(x	NOUN
ejpam-5986	12	4	,	,	PUNCT
ejpam-5986	12	5	t	t	PROPN
ejpam-5986	12	6	)	)	PUNCT
ejpam-5986	12	7	dx	dx	PROPN
ejpam-5986	12	8	,	,	PUNCT
ejpam-5986	12	9	where	where	SCONJ
ejpam-5986	12	10	v	v	NOUN
ejpam-5986	12	11	is	be	AUX
ejpam-5986	12	12	the	the	DET
ejpam-5986	12	13	input	input	NOUN
ejpam-5986	12	14	function	function	NOUN
ejpam-5986	12	15	,	,	PUNCT
ejpam-5986	12	16	tv	tv	NOUN
ejpam-5986	12	17	is	be	AUX
ejpam-5986	12	18	the	the	DET
ejpam-5986	12	19	output	output	NOUN
ejpam-5986	12	20	function	function	NOUN
ejpam-5986	12	21	and	and	CCONJ
ejpam-5986	12	22	k(x	k(x	PROPN
ejpam-5986	12	23	,	,	PUNCT
ejpam-5986	12	24	t	t	PROPN
ejpam-5986	12	25	)	)	PUNCT
ejpam-5986	12	26	is	be	AUX
ejpam-5986	12	27	the	the	DET
ejpam-5986	12	28	kernel	kernel	NOUN
ejpam-5986	12	29	of	of	ADP
ejpam-5986	12	30	the	the	DET
ejpam-5986	12	31	transform	transform	NOUN
ejpam-5986	12	32	.	.	PUNCT
ejpam-5986	13	1	numerous	numerous	ADJ
ejpam-5986	13	2	useful	useful	ADJ
ejpam-5986	13	3	integral	integral	ADJ
ejpam-5986	13	4	transforms	transform	NOUN
ejpam-5986	13	5	have	have	AUX
ejpam-5986	13	6	been	be	AUX
ejpam-5986	13	7	defined	define	VERB
ejpam-5986	13	8	;	;	PUNCT
ejpam-5986	13	9	see	see	VERB
ejpam-5986	13	10	for	for	ADP
ejpam-5986	13	11	example	example	NOUN
ejpam-5986	13	12	[	[	X
ejpam-5986	13	13	1–20	1–20	NUM
ejpam-5986	13	14	]	]	X
ejpam-5986	13	15	.	.	PUNCT
ejpam-5986	14	1	each	each	PRON
ejpam-5986	14	2	is	be	AUX
ejpam-5986	14	3	specified	specify	VERB
ejpam-5986	14	4	by	by	ADP
ejpam-5986	14	5	a	a	DET
ejpam-5986	14	6	choice	choice	NOUN
ejpam-5986	14	7	of	of	ADP
ejpam-5986	14	8	the	the	DET
ejpam-5986	14	9	kernel	kernel	PROPN
ejpam-5986	14	10	function	function	PROPN
ejpam-5986	14	11	k	k	PROPN
ejpam-5986	14	12	of	of	ADP
ejpam-5986	14	13	two	two	NUM
ejpam-5986	14	14	variables	variable	NOUN
ejpam-5986	14	15	.	.	PUNCT
ejpam-5986	15	1	perhaps	perhaps	ADV
ejpam-5986	15	2	the	the	DET
ejpam-5986	15	3	most	most	ADV
ejpam-5986	15	4	wellknown	wellknown	ADJ
ejpam-5986	15	5	integral	integral	ADJ
ejpam-5986	15	6	transform	transform	NOUN
ejpam-5986	15	7	is	be	AUX
ejpam-5986	15	8	the	the	DET
ejpam-5986	15	9	laplace	laplace	NOUN
ejpam-5986	15	10	transform	transform	NOUN
ejpam-5986	15	11	.	.	PUNCT
ejpam-5986	16	1	besides	besides	SCONJ
ejpam-5986	16	2	mathematics	mathematic	NOUN
ejpam-5986	16	3	,	,	PUNCT
ejpam-5986	16	4	it	it	PRON
ejpam-5986	16	5	is	be	AUX
ejpam-5986	16	6	utilized	utilize	VERB
ejpam-5986	16	7	doi	doi	NOUN
ejpam-5986	16	8	:	:	PUNCT
ejpam-5986	16	9	https://doi.org/10.29020/nybg.ejpam.v18i2.5986	https://doi.org/10.29020/nybg.ejpam.v18i2.5986	PRON
ejpam-5986	16	10	email	email	NOUN
ejpam-5986	16	11	address	address	NOUN
ejpam-5986	16	12	:	:	PUNCT
ejpam-5986	16	13	iege@adu.edu.tr	iege@adu.edu.tr	PROPN
ejpam-5986	16	14	(	(	PUNCT
ejpam-5986	16	15	i̇.	i̇.	PROPN
ejpam-5986	16	16	ege	ege	NOUN
ejpam-5986	16	17	)	)	PUNCT
ejpam-5986	16	18	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-5986	17	1	1	1	NUM
ejpam-5986	17	2	copyright	copyright	NOUN
ejpam-5986	17	3	:	:	PUNCT
ejpam-5986	17	4	©	©	PROPN
ejpam-5986	17	5	2025	2025	NUM
ejpam-5986	17	6	the	the	DET
ejpam-5986	17	7	author(s	author(s	NOUN
ejpam-5986	17	8	)	)	PUNCT
ejpam-5986	17	9	.	.	PUNCT
ejpam-5986	18	1	(	(	PUNCT
ejpam-5986	18	2	cc	cc	NOUN
ejpam-5986	18	3	by	by	ADP
ejpam-5986	18	4	-	-	PUNCT
ejpam-5986	18	5	nc	nc	PROPN
ejpam-5986	18	6	4.0	4.0	NUM
ejpam-5986	18	7	)	)	PUNCT
ejpam-5986	18	8	i̇.	i̇.	NOUN
ejpam-5986	18	9	ege	ege	PROPN
ejpam-5986	18	10	/	/	SYM
ejpam-5986	18	11	eur	eur	PROPN
ejpam-5986	18	12	.	.	PUNCT
ejpam-5986	19	1	j.	j.	PROPN
ejpam-5986	19	2	pure	pure	PROPN
ejpam-5986	19	3	appl	appl	PROPN
ejpam-5986	19	4	.	.	PROPN
ejpam-5986	19	5	math	math	PROPN
ejpam-5986	19	6	,	,	PUNCT
ejpam-5986	19	7	18	18	NUM
ejpam-5986	19	8	(	(	PUNCT
ejpam-5986	19	9	2	2	NUM
ejpam-5986	19	10	)	)	PUNCT
ejpam-5986	19	11	(	(	PUNCT
ejpam-5986	19	12	2025	2025	NUM
ejpam-5986	19	13	)	)	PUNCT
ejpam-5986	19	14	,	,	PUNCT
ejpam-5986	19	15	5986	5986	NUM
ejpam-5986	19	16	2	2	NUM
ejpam-5986	19	17	of	of	ADP
ejpam-5986	19	18	20	20	NUM
ejpam-5986	19	19	in	in	ADP
ejpam-5986	19	20	other	other	ADJ
ejpam-5986	19	21	fields	field	NOUN
ejpam-5986	19	22	of	of	ADP
ejpam-5986	19	23	study	study	NOUN
ejpam-5986	19	24	wildly	wildly	ADV
ejpam-5986	19	25	as	as	ADP
ejpam-5986	19	26	engineering	engineering	NOUN
ejpam-5986	19	27	,	,	PUNCT
ejpam-5986	19	28	physics	physics	NOUN
ejpam-5986	19	29	,	,	PUNCT
ejpam-5986	19	30	astronomy	astronomy	NOUN
ejpam-5986	19	31	,	,	PUNCT
ejpam-5986	19	32	etc	etc	X
ejpam-5986	19	33	.	.	X
ejpam-5986	19	34	for	for	ADP
ejpam-5986	19	35	example	example	NOUN
ejpam-5986	19	36	,	,	PUNCT
ejpam-5986	19	37	it	it	PRON
ejpam-5986	19	38	is	be	AUX
ejpam-5986	19	39	used	use	VERB
ejpam-5986	19	40	to	to	PART
ejpam-5986	19	41	solve	solve	VERB
ejpam-5986	19	42	differential	differential	ADJ
ejpam-5986	19	43	equations	equation	NOUN
ejpam-5986	19	44	occurring	occur	VERB
ejpam-5986	19	45	in	in	ADP
ejpam-5986	19	46	the	the	DET
ejpam-5986	19	47	analysis	analysis	NOUN
ejpam-5986	19	48	of	of	ADP
ejpam-5986	19	49	electronic	electronic	ADJ
ejpam-5986	19	50	circuits	circuit	NOUN
ejpam-5986	19	51	.	.	PUNCT
ejpam-5986	20	1	laplace	laplace	NOUN
ejpam-5986	20	2	transform	transform	NOUN
ejpam-5986	20	3	is	be	AUX
ejpam-5986	20	4	defined	define	VERB
ejpam-5986	20	5	by	by	ADP
ejpam-5986	20	6	f	f	PROPN
ejpam-5986	20	7	(	(	PUNCT
ejpam-5986	20	8	u	u	NOUN
ejpam-5986	20	9	)	)	PUNCT
ejpam-5986	20	10	=	=	SYM
ejpam-5986	20	11	l{f(t	l{f(t	NOUN
ejpam-5986	20	12	)	)	PUNCT
ejpam-5986	20	13	}	}	PUNCT
ejpam-5986	21	1	=	=	SYM
ejpam-5986	21	2	∫	∫	PROPN
ejpam-5986	22	1	∞	∞	PROPN
ejpam-5986	22	2	0	0	NUM
ejpam-5986	22	3	e−utf(t	e−utf(t	NUM
ejpam-5986	22	4	)	)	PUNCT
ejpam-5986	22	5	dt	dt	NOUN
ejpam-5986	22	6	(	(	PUNCT
ejpam-5986	22	7	1	1	X
ejpam-5986	22	8	)	)	PUNCT
ejpam-5986	22	9	provided	provide	VERB
ejpam-5986	22	10	that	that	SCONJ
ejpam-5986	22	11	the	the	DET
ejpam-5986	22	12	integral	integral	ADJ
ejpam-5986	22	13	converges	converge	NOUN
ejpam-5986	22	14	[	[	X
ejpam-5986	22	15	10	10	NUM
ejpam-5986	22	16	]	]	PUNCT
ejpam-5986	22	17	.	.	PUNCT
ejpam-5986	23	1	there	there	PRON
ejpam-5986	23	2	are	be	VERB
ejpam-5986	23	3	many	many	ADJ
ejpam-5986	23	4	integral	integral	ADJ
ejpam-5986	23	5	transforms	transform	NOUN
ejpam-5986	23	6	in	in	ADP
ejpam-5986	23	7	the	the	DET
ejpam-5986	23	8	laplace	laplace	NOUN
ejpam-5986	23	9	class	class	NOUN
ejpam-5986	23	10	and	and	CCONJ
ejpam-5986	23	11	most	most	ADJ
ejpam-5986	23	12	of	of	ADP
ejpam-5986	23	13	them	they	PRON
ejpam-5986	23	14	have	have	AUX
ejpam-5986	23	15	been	be	AUX
ejpam-5986	23	16	named	name	VERB
ejpam-5986	23	17	after	after	ADP
ejpam-5986	23	18	the	the	DET
ejpam-5986	23	19	mathematicians	mathematician	NOUN
ejpam-5986	23	20	who	who	PRON
ejpam-5986	23	21	introduced	introduce	VERB
ejpam-5986	23	22	them	they	PRON
ejpam-5986	23	23	.	.	PUNCT
ejpam-5986	24	1	some	some	PRON
ejpam-5986	24	2	of	of	ADP
ejpam-5986	24	3	these	these	PRON
ejpam-5986	24	4	are	be	AUX
ejpam-5986	24	5	the	the	DET
ejpam-5986	24	6	sumudu	sumudu	NOUN
ejpam-5986	24	7	transform	transform	NOUN
ejpam-5986	24	8	[	[	X
ejpam-5986	24	9	21	21	NUM
ejpam-5986	24	10	]	]	PUNCT
ejpam-5986	24	11	,	,	PUNCT
ejpam-5986	24	12	the	the	DET
ejpam-5986	24	13	natural	natural	ADJ
ejpam-5986	24	14	transform	transform	NOUN
ejpam-5986	24	15	[	[	X
ejpam-5986	24	16	22	22	NUM
ejpam-5986	24	17	]	]	PUNCT
ejpam-5986	24	18	,	,	PUNCT
ejpam-5986	24	19	the	the	DET
ejpam-5986	24	20	elzaki	elzaki	NOUN
ejpam-5986	24	21	transform	transform	VERB
ejpam-5986	24	22	[	[	X
ejpam-5986	24	23	23	23	NUM
ejpam-5986	24	24	]	]	PUNCT
ejpam-5986	24	25	,	,	PUNCT
ejpam-5986	24	26	the	the	DET
ejpam-5986	24	27	aboodh	aboodh	NOUN
ejpam-5986	24	28	transform	transform	NOUN
ejpam-5986	24	29	[	[	X
ejpam-5986	24	30	24	24	NUM
ejpam-5986	24	31	]	]	PUNCT
ejpam-5986	24	32	,	,	PUNCT
ejpam-5986	24	33	the	the	DET
ejpam-5986	24	34	zz	zz	PROPN
ejpam-5986	24	35	transform	transform	NOUN
ejpam-5986	24	36	[	[	X
ejpam-5986	24	37	25	25	NUM
ejpam-5986	24	38	]	]	PUNCT
ejpam-5986	24	39	and	and	CCONJ
ejpam-5986	24	40	the	the	DET
ejpam-5986	24	41	polynomial	polynomial	ADJ
ejpam-5986	24	42	integral	integral	ADJ
ejpam-5986	24	43	transform	transform	NOUN
ejpam-5986	24	44	[	[	X
ejpam-5986	24	45	26	26	NUM
ejpam-5986	24	46	]	]	PUNCT
ejpam-5986	24	47	.	.	PUNCT
ejpam-5986	25	1	the	the	DET
ejpam-5986	25	2	sumudu	sumudu	NOUN
ejpam-5986	25	3	[	[	X
ejpam-5986	25	4	21	21	NUM
ejpam-5986	25	5	]	]	PUNCT
ejpam-5986	25	6	and	and	CCONJ
ejpam-5986	25	7	elzaki	elzaki	NOUN
ejpam-5986	25	8	transforms	transform	VERB
ejpam-5986	25	9	[	[	X
ejpam-5986	25	10	23	23	NUM
ejpam-5986	25	11	]	]	PUNCT
ejpam-5986	25	12	are	be	AUX
ejpam-5986	25	13	defined	define	VERB
ejpam-5986	25	14	respectively	respectively	ADV
ejpam-5986	25	15	as	as	ADP
ejpam-5986	25	16	s(u	s(u	NOUN
ejpam-5986	25	17	)	)	PUNCT
ejpam-5986	25	18	=	=	PUNCT
ejpam-5986	25	19	s{f(t	s{f(t	NUM
ejpam-5986	25	20	)	)	PUNCT
ejpam-5986	25	21	}	}	PUNCT
ejpam-5986	25	22	=	=	SYM
ejpam-5986	25	23	1	1	NUM
ejpam-5986	25	24	u	u	NOUN
ejpam-5986	25	25	∫	∫	PROPN
ejpam-5986	25	26	∞	∞	NOUN
ejpam-5986	25	27	0	0	NUM
ejpam-5986	26	1	e−	e−	PROPN
ejpam-5986	26	2	t	t	PROPN
ejpam-5986	26	3	u	u	NOUN
ejpam-5986	26	4	f(t	f(t	PROPN
ejpam-5986	26	5	)	)	PUNCT
ejpam-5986	26	6	dt	dt	X
ejpam-5986	26	7	,	,	PUNCT
ejpam-5986	26	8	(	(	PUNCT
ejpam-5986	26	9	2	2	NUM
ejpam-5986	26	10	)	)	PUNCT
ejpam-5986	26	11	and	and	CCONJ
ejpam-5986	26	12	e(u	e(u	PROPN
ejpam-5986	26	13	)	)	PUNCT
ejpam-5986	27	1	=	=	PUNCT
ejpam-5986	27	2	e{f(t	e{f(t	NOUN
ejpam-5986	27	3	)	)	PUNCT
ejpam-5986	27	4	}	}	PUNCT
ejpam-5986	28	1	=	=	SYM
ejpam-5986	28	2	u	u	NOUN
ejpam-5986	28	3	∫	∫	PROPN
ejpam-5986	28	4	∞	∞	NOUN
ejpam-5986	28	5	0	0	NUM
ejpam-5986	29	1	e−	e−	PROPN
ejpam-5986	29	2	t	t	PROPN
ejpam-5986	29	3	u	u	NOUN
ejpam-5986	29	4	f(t	f(t	PROPN
ejpam-5986	29	5	)	)	PUNCT
ejpam-5986	29	6	dt	dt	X
ejpam-5986	29	7	.	.	PUNCT
ejpam-5986	30	1	(	(	PUNCT
ejpam-5986	30	2	3	3	X
ejpam-5986	30	3	)	)	PUNCT
ejpam-5986	30	4	recently	recently	ADV
ejpam-5986	30	5	,	,	PUNCT
ejpam-5986	30	6	the	the	DET
ejpam-5986	30	7	laplace	laplace	NOUN
ejpam-5986	30	8	-	-	PUNCT
ejpam-5986	30	9	type	type	NOUN
ejpam-5986	30	10	integral	integral	ADJ
ejpam-5986	30	11	transform	transform	NOUN
ejpam-5986	30	12	is	be	AUX
ejpam-5986	30	13	introduced	introduce	VERB
ejpam-5986	30	14	by	by	ADP
ejpam-5986	30	15	kim	kim	PROPN
ejpam-5986	30	16	in	in	ADP
ejpam-5986	30	17	[	[	X
ejpam-5986	30	18	27	27	NUM
ejpam-5986	30	19	]	]	PUNCT
ejpam-5986	30	20	as	as	ADP
ejpam-5986	30	21	fα(u	fα(u	NOUN
ejpam-5986	30	22	)	)	PUNCT
ejpam-5986	30	23	=	=	PUNCT
ejpam-5986	31	1	gα{f(t	gα{f(t	NOUN
ejpam-5986	31	2	)	)	PUNCT
ejpam-5986	31	3	}	}	PUNCT
ejpam-5986	31	4	=	=	PUNCT
ejpam-5986	31	5	uα	uα	PROPN
ejpam-5986	31	6	∫	∫	PROPN
ejpam-5986	31	7	∞	∞	PROPN
ejpam-5986	31	8	0	0	NUM
ejpam-5986	32	1	e−	e−	PROPN
ejpam-5986	32	2	t	t	PROPN
ejpam-5986	32	3	u	u	NOUN
ejpam-5986	32	4	f(t	f(t	PROPN
ejpam-5986	32	5	)	)	PUNCT
ejpam-5986	32	6	dt	dt	X
ejpam-5986	32	7	,	,	PUNCT
ejpam-5986	32	8	(	(	PUNCT
ejpam-5986	32	9	4	4	X
ejpam-5986	32	10	)	)	PUNCT
ejpam-5986	32	11	where	where	SCONJ
ejpam-5986	32	12	f(t	f(t	NOUN
ejpam-5986	32	13	)	)	PUNCT
ejpam-5986	32	14	be	be	VERB
ejpam-5986	32	15	an	an	DET
ejpam-5986	32	16	integrable	integrable	ADJ
ejpam-5986	32	17	function	function	NOUN
ejpam-5986	32	18	on	on	ADP
ejpam-5986	32	19	[	[	X
ejpam-5986	32	20	0.∞	0.∞	NOUN
ejpam-5986	32	21	)	)	PUNCT
ejpam-5986	32	22	,	,	PUNCT
ejpam-5986	32	23	u	u	NOUN
ejpam-5986	32	24	>	>	X
ejpam-5986	32	25	0	0	PUNCT
ejpam-5986	32	26	and	and	CCONJ
ejpam-5986	32	27	α	α	PROPN
ejpam-5986	32	28	∈	∈	PROPN
ejpam-5986	32	29	z.	z.	X
ejpam-5986	33	1	the	the	DET
ejpam-5986	33	2	modified	modify	VERB
ejpam-5986	33	3	degenerate	degenerate	ADJ
ejpam-5986	33	4	gamma	gamma	NOUN
ejpam-5986	33	5	function	function	NOUN
ejpam-5986	33	6	defined	define	VERB
ejpam-5986	33	7	in	in	ADP
ejpam-5986	33	8	[	[	X
ejpam-5986	33	9	28	28	NUM
ejpam-5986	33	10	]	]	PUNCT
ejpam-5986	33	11	as	as	ADP
ejpam-5986	33	12	γ∗	γ∗	PROPN
ejpam-5986	33	13	λ(x	λ(x	PROPN
ejpam-5986	33	14	)	)	PUNCT
ejpam-5986	34	1	=	=	SYM
ejpam-5986	34	2	∫	∫	PROPN
ejpam-5986	35	1	∞	∞	NUM
ejpam-5986	35	2	0	0	NUM
ejpam-5986	35	3	tx−1(1	tx−1(1	SYM
ejpam-5986	35	4	+	+	X
ejpam-5986	35	5	λ)−	λ)−	X
ejpam-5986	35	6	t	t	NOUN
ejpam-5986	35	7	λ	λ	X
ejpam-5986	35	8	dt	dt	PROPN
ejpam-5986	35	9	,	,	PUNCT
ejpam-5986	35	10	λ	λ	PROPN
ejpam-5986	35	11	∈	∈	PROPN
ejpam-5986	35	12	(	(	PUNCT
ejpam-5986	35	13	0	0	NUM
ejpam-5986	35	14	,	,	PUNCT
ejpam-5986	35	15	1	1	NUM
ejpam-5986	35	16	)	)	PUNCT
ejpam-5986	35	17	and	and	CCONJ
ejpam-5986	35	18	re(x	re(x	NOUN
ejpam-5986	35	19	)	)	PUNCT
ejpam-5986	35	20	>	>	X
ejpam-5986	35	21	0	0	NUM
ejpam-5986	35	22	,	,	PUNCT
ejpam-5986	35	23	(	(	PUNCT
ejpam-5986	35	24	5	5	NUM
ejpam-5986	35	25	)	)	PUNCT
ejpam-5986	36	1	and	and	CCONJ
ejpam-5986	36	2	satisfies	satisfy	VERB
ejpam-5986	36	3	the	the	DET
ejpam-5986	36	4	properties	property	NOUN
ejpam-5986	36	5	that	that	PRON
ejpam-5986	36	6	γ∗	γ∗	VERB
ejpam-5986	36	7	λ(x+	λ(x+	ADV
ejpam-5986	36	8	1	1	NUM
ejpam-5986	36	9	)	)	PUNCT
ejpam-5986	36	10	=	=	SYM
ejpam-5986	36	11	λx	λx	PROPN
ejpam-5986	36	12	ln(1	ln(1	PROPN
ejpam-5986	36	13	+	+	CCONJ
ejpam-5986	36	14	λ	λ	PROPN
ejpam-5986	36	15	)	)	PUNCT
ejpam-5986	36	16	γ∗	γ∗	NOUN
ejpam-5986	36	17	λ(x	λ(x	PROPN
ejpam-5986	36	18	)	)	PUNCT
ejpam-5986	36	19	,	,	PUNCT
ejpam-5986	36	20	γ∗	γ∗	VERB
ejpam-5986	36	21	λ(n+	λ(n+	NOUN
ejpam-5986	36	22	1	1	X
ejpam-5986	36	23	)	)	PUNCT
ejpam-5986	36	24	=	=	PUNCT
ejpam-5986	36	25	λn+1n	λn+1n	ADJ
ejpam-5986	36	26	!	!	PUNCT
ejpam-5986	37	1	lnn+1(1	lnn+1(1	PUNCT
ejpam-5986	38	1	+	+	PUNCT
ejpam-5986	38	2	λ	λ	NOUN
ejpam-5986	38	3	)	)	PUNCT
ejpam-5986	38	4	,	,	PUNCT
ejpam-5986	38	5	n	n	NOUN
ejpam-5986	38	6	=	=	SYM
ejpam-5986	38	7	1	1	NUM
ejpam-5986	38	8	,	,	PUNCT
ejpam-5986	38	9	2	2	NUM
ejpam-5986	38	10	,	,	PUNCT
ejpam-5986	38	11	.	.	PUNCT
ejpam-5986	38	12	.	.	PUNCT
ejpam-5986	38	13	.	.	PUNCT
ejpam-5986	38	14	.	.	PUNCT
ejpam-5986	39	1	(	(	PUNCT
ejpam-5986	39	2	6	6	X
ejpam-5986	39	3	)	)	PUNCT
ejpam-5986	39	4	degenerate	degenerate	ADJ
ejpam-5986	39	5	versions	version	NOUN
ejpam-5986	39	6	of	of	ADP
ejpam-5986	39	7	existing	exist	VERB
ejpam-5986	39	8	integral	integral	ADJ
ejpam-5986	39	9	transforms	transform	NOUN
ejpam-5986	39	10	have	have	AUX
ejpam-5986	39	11	also	also	ADV
ejpam-5986	39	12	been	be	AUX
ejpam-5986	39	13	studied	study	VERB
ejpam-5986	39	14	in	in	ADP
ejpam-5986	39	15	the	the	DET
ejpam-5986	39	16	last	last	ADJ
ejpam-5986	39	17	few	few	ADJ
ejpam-5986	39	18	years	year	NOUN
ejpam-5986	39	19	.	.	PUNCT
ejpam-5986	40	1	for	for	ADP
ejpam-5986	40	2	example	example	NOUN
ejpam-5986	40	3	,	,	PUNCT
ejpam-5986	40	4	kim	kim	PROPN
ejpam-5986	40	5	and	and	CCONJ
ejpam-5986	40	6	kim	kim	PROPN
ejpam-5986	40	7	introduced	introduce	VERB
ejpam-5986	40	8	the	the	DET
ejpam-5986	40	9	degenerate	degenerate	ADJ
ejpam-5986	40	10	laplace	laplace	NOUN
ejpam-5986	40	11	transform	transform	NOUN
ejpam-5986	40	12	[	[	X
ejpam-5986	40	13	29	29	NUM
ejpam-5986	40	14	]	]	PUNCT
ejpam-5986	40	15	and	and	CCONJ
ejpam-5986	40	16	upadhyaya	upadhyaya	NOUN
ejpam-5986	40	17	gives	give	VERB
ejpam-5986	40	18	further	further	ADJ
ejpam-5986	40	19	results	result	NOUN
ejpam-5986	40	20	for	for	ADP
ejpam-5986	40	21	the	the	DET
ejpam-5986	40	22	degenerate	degenerate	ADJ
ejpam-5986	40	23	laplace	laplace	NOUN
ejpam-5986	40	24	transform	transform	NOUN
ejpam-5986	40	25	[	[	X
ejpam-5986	40	26	30–32	30–32	NUM
ejpam-5986	40	27	]	]	PUNCT
ejpam-5986	40	28	.	.	PUNCT
ejpam-5986	41	1	campos	campos	AUX
ejpam-5986	41	2	et	et	PROPN
ejpam-5986	41	3	al	al	PROPN
ejpam-5986	41	4	.	.	PROPN
ejpam-5986	41	5	defined	define	VERB
ejpam-5986	41	6	degenerate	degenerate	ADJ
ejpam-5986	41	7	laplace	laplace	NOUN
ejpam-5986	41	8	-	-	PUNCT
ejpam-5986	41	9	type	type	NOUN
ejpam-5986	41	10	integral	integral	ADJ
ejpam-5986	41	11	transform	transform	NOUN
ejpam-5986	41	12	and	and	CCONJ
ejpam-5986	41	13	gave	give	VERB
ejpam-5986	41	14	its	its	PRON
ejpam-5986	41	15	properties	property	NOUN
ejpam-5986	41	16	[	[	X
ejpam-5986	41	17	3	3	NUM
ejpam-5986	41	18	]	]	PUNCT
ejpam-5986	41	19	.	.	PUNCT
ejpam-5986	42	1	also	also	ADV
ejpam-5986	42	2	,	,	PUNCT
ejpam-5986	42	3	duran	duran	PROPN
ejpam-5986	42	4	defined	define	VERB
ejpam-5986	42	5	the	the	DET
ejpam-5986	42	6	degenerate	degenerate	ADJ
ejpam-5986	42	7	sumudu	sumudu	NOUN
ejpam-5986	42	8	transform	transform	NOUN
ejpam-5986	42	9	[	[	X
ejpam-5986	42	10	33	33	NUM
ejpam-5986	42	11	]	]	PUNCT
ejpam-5986	42	12	and	and	CCONJ
ejpam-5986	42	13	kalavathi	kalavathi	PROPN
ejpam-5986	42	14	et	et	PROPN
ejpam-5986	42	15	al	al	PROPN
ejpam-5986	42	16	.	.	PROPN
ejpam-5986	42	17	defined	define	VERB
ejpam-5986	42	18	the	the	DET
ejpam-5986	42	19	degenerate	degenerate	ADJ
ejpam-5986	42	20	elzaki	elzaki	NOUN
ejpam-5986	42	21	transform	transform	VERB
ejpam-5986	42	22	[	[	X
ejpam-5986	42	23	34	34	NUM
ejpam-5986	42	24	]	]	PUNCT
ejpam-5986	42	25	.	.	PUNCT
ejpam-5986	43	1	motivated	motivate	VERB
ejpam-5986	43	2	by	by	ADP
ejpam-5986	43	3	the	the	DET
ejpam-5986	43	4	above	above	ADV
ejpam-5986	43	5	-	-	PUNCT
ejpam-5986	43	6	mentioned	mention	VERB
ejpam-5986	43	7	research	research	NOUN
ejpam-5986	43	8	,	,	PUNCT
ejpam-5986	43	9	in	in	ADP
ejpam-5986	43	10	this	this	DET
ejpam-5986	43	11	paper	paper	NOUN
ejpam-5986	43	12	we	we	PRON
ejpam-5986	43	13	proposed	propose	VERB
ejpam-5986	43	14	the	the	DET
ejpam-5986	43	15	modified	modify	VERB
ejpam-5986	43	16	laplace	laplace	NOUN
ejpam-5986	43	17	-	-	PUNCT
ejpam-5986	43	18	type	type	NOUN
ejpam-5986	43	19	transform	transform	NOUN
ejpam-5986	43	20	.	.	PUNCT
ejpam-5986	44	1	the	the	DET
ejpam-5986	44	2	mentioned	mention	VERB
ejpam-5986	44	3	transform	transform	NOUN
ejpam-5986	44	4	is	be	AUX
ejpam-5986	44	5	indicated	indicate	VERB
ejpam-5986	44	6	by	by	ADP
ejpam-5986	44	7	the	the	DET
ejpam-5986	44	8	operator	operator	NOUN
ejpam-5986	44	9	g∗	g∗	VERB
ejpam-5986	44	10	α	α	NOUN
ejpam-5986	44	11	,	,	PUNCT
ejpam-5986	44	12	λ	λ	PROPN
ejpam-5986	44	13	i̇.	i̇.	NOUN
ejpam-5986	44	14	ege	ege	PROPN
ejpam-5986	44	15	/	/	SYM
ejpam-5986	44	16	eur	eur	PROPN
ejpam-5986	44	17	.	.	PUNCT
ejpam-5986	45	1	j.	j.	PROPN
ejpam-5986	45	2	pure	pure	PROPN
ejpam-5986	45	3	appl	appl	PROPN
ejpam-5986	45	4	.	.	PROPN
ejpam-5986	45	5	math	math	PROPN
ejpam-5986	45	6	,	,	PUNCT
ejpam-5986	45	7	18	18	NUM
ejpam-5986	45	8	(	(	PUNCT
ejpam-5986	45	9	2	2	NUM
ejpam-5986	45	10	)	)	PUNCT
ejpam-5986	45	11	(	(	PUNCT
ejpam-5986	45	12	2025	2025	NUM
ejpam-5986	45	13	)	)	PUNCT
ejpam-5986	45	14	,	,	PUNCT
ejpam-5986	45	15	5986	5986	NUM
ejpam-5986	45	16	3	3	NUM
ejpam-5986	45	17	of	of	ADP
ejpam-5986	45	18	20	20	NUM
ejpam-5986	45	19	through	through	ADP
ejpam-5986	45	20	this	this	DET
ejpam-5986	45	21	research	research	NOUN
ejpam-5986	45	22	.	.	PUNCT
ejpam-5986	46	1	we	we	PRON
ejpam-5986	46	2	define	define	VERB
ejpam-5986	46	3	the	the	DET
ejpam-5986	46	4	modified	modify	VERB
ejpam-5986	46	5	laplace	laplace	NOUN
ejpam-5986	46	6	-	-	PUNCT
ejpam-5986	46	7	type	type	NOUN
ejpam-5986	46	8	transform	transform	NOUN
ejpam-5986	46	9	and	and	CCONJ
ejpam-5986	46	10	provide	provide	VERB
ejpam-5986	46	11	some	some	PRON
ejpam-5986	46	12	of	of	ADP
ejpam-5986	46	13	their	their	PRON
ejpam-5986	46	14	properties	property	NOUN
ejpam-5986	46	15	and	and	CCONJ
ejpam-5986	46	16	relations	relation	NOUN
ejpam-5986	46	17	,	,	PUNCT
ejpam-5986	46	18	and	and	CCONJ
ejpam-5986	46	19	derive	derive	VERB
ejpam-5986	46	20	the	the	DET
ejpam-5986	46	21	modified	modify	VERB
ejpam-5986	46	22	laplace	laplace	NOUN
ejpam-5986	46	23	-	-	PUNCT
ejpam-5986	46	24	type	type	NOUN
ejpam-5986	46	25	transform	transform	NOUN
ejpam-5986	46	26	of	of	ADP
ejpam-5986	46	27	some	some	DET
ejpam-5986	46	28	functions	function	NOUN
ejpam-5986	46	29	such	such	ADJ
ejpam-5986	46	30	as	as	ADP
ejpam-5986	46	31	power	power	NOUN
ejpam-5986	46	32	functions	function	NOUN
ejpam-5986	46	33	,	,	PUNCT
ejpam-5986	46	34	sine	sine	NOUN
ejpam-5986	46	35	,	,	PUNCT
ejpam-5986	46	36	cosine	cosine	NOUN
ejpam-5986	46	37	,	,	PUNCT
ejpam-5986	46	38	hyperbolic	hyperbolic	ADJ
ejpam-5986	46	39	sine	sine	NOUN
ejpam-5986	46	40	,	,	PUNCT
ejpam-5986	46	41	hyperbolic	hyperbolic	ADJ
ejpam-5986	46	42	cosine	cosine	NOUN
ejpam-5986	46	43	,	,	PUNCT
ejpam-5986	46	44	exponential	exponential	ADJ
ejpam-5986	46	45	function	function	NOUN
ejpam-5986	46	46	,	,	PUNCT
ejpam-5986	46	47	and	and	CCONJ
ejpam-5986	46	48	function	function	VERB
ejpam-5986	46	49	derivatives	derivative	NOUN
ejpam-5986	46	50	.	.	PUNCT
ejpam-5986	47	1	moreover	moreover	ADV
ejpam-5986	47	2	,	,	PUNCT
ejpam-5986	47	3	we	we	PRON
ejpam-5986	47	4	attain	attain	VERB
ejpam-5986	47	5	relations	relation	NOUN
ejpam-5986	47	6	between	between	ADP
ejpam-5986	47	7	the	the	DET
ejpam-5986	47	8	laplace	laplace	NOUN
ejpam-5986	47	9	-	-	PUNCT
ejpam-5986	47	10	type	type	NOUN
ejpam-5986	47	11	transform	transform	NOUN
ejpam-5986	47	12	and	and	CCONJ
ejpam-5986	47	13	the	the	DET
ejpam-5986	47	14	modified	modify	VERB
ejpam-5986	47	15	laplace	laplace	NOUN
ejpam-5986	47	16	-	-	PUNCT
ejpam-5986	47	17	type	type	NOUN
ejpam-5986	47	18	transform	transform	NOUN
ejpam-5986	47	19	and	and	CCONJ
ejpam-5986	47	20	also	also	ADV
ejpam-5986	47	21	give	give	VERB
ejpam-5986	47	22	a	a	DET
ejpam-5986	47	23	relation	relation	NOUN
ejpam-5986	47	24	between	between	ADP
ejpam-5986	47	25	the	the	DET
ejpam-5986	47	26	modified	modify	VERB
ejpam-5986	47	27	laplace	laplace	NOUN
ejpam-5986	47	28	-	-	PUNCT
ejpam-5986	47	29	type	type	NOUN
ejpam-5986	47	30	transform	transform	NOUN
ejpam-5986	47	31	and	and	CCONJ
ejpam-5986	47	32	the	the	DET
ejpam-5986	47	33	modified	modify	VERB
ejpam-5986	47	34	degenerate	degenerate	ADJ
ejpam-5986	47	35	gamma	gamma	NOUN
ejpam-5986	47	36	function	function	NOUN
ejpam-5986	47	37	.	.	PUNCT
ejpam-5986	48	1	also	also	ADV
ejpam-5986	48	2	,	,	PUNCT
ejpam-5986	48	3	we	we	PRON
ejpam-5986	48	4	give	give	VERB
ejpam-5986	48	5	some	some	DET
ejpam-5986	48	6	operational	operational	ADJ
ejpam-5986	48	7	properties	property	NOUN
ejpam-5986	48	8	of	of	ADP
ejpam-5986	48	9	modified	modified	ADJ
ejpam-5986	48	10	laplace	laplace	NOUN
ejpam-5986	48	11	-	-	PUNCT
ejpam-5986	48	12	type	type	NOUN
ejpam-5986	48	13	transform	transform	NOUN
ejpam-5986	48	14	.	.	PUNCT
ejpam-5986	49	1	2	2	X
ejpam-5986	49	2	.	.	X
ejpam-5986	49	3	the	the	DET
ejpam-5986	49	4	main	main	ADJ
ejpam-5986	49	5	results	result	NOUN
ejpam-5986	49	6	in	in	ADP
ejpam-5986	49	7	this	this	DET
ejpam-5986	49	8	section	section	NOUN
ejpam-5986	49	9	,	,	PUNCT
ejpam-5986	49	10	we	we	PRON
ejpam-5986	49	11	present	present	VERB
ejpam-5986	49	12	the	the	DET
ejpam-5986	49	13	modified	modify	VERB
ejpam-5986	49	14	laplace	laplace	NOUN
ejpam-5986	49	15	-	-	PUNCT
ejpam-5986	49	16	type	type	NOUN
ejpam-5986	49	17	transform	transform	NOUN
ejpam-5986	49	18	g∗	g∗	NOUN
ejpam-5986	49	19	α	α	NOUN
ejpam-5986	49	20	,	,	PUNCT
ejpam-5986	49	21	λ	λ	X
ejpam-5986	49	22	,	,	PUNCT
ejpam-5986	49	23	give	give	VERB
ejpam-5986	49	24	sufficient	sufficient	ADJ
ejpam-5986	49	25	conditions	condition	NOUN
ejpam-5986	49	26	for	for	ADP
ejpam-5986	49	27	the	the	DET
ejpam-5986	49	28	existence	existence	NOUN
ejpam-5986	49	29	,	,	PUNCT
ejpam-5986	49	30	and	and	CCONJ
ejpam-5986	49	31	calculate	calculate	VERB
ejpam-5986	49	32	the	the	DET
ejpam-5986	49	33	modified	modify	VERB
ejpam-5986	49	34	laplace	laplace	NOUN
ejpam-5986	49	35	-	-	PUNCT
ejpam-5986	49	36	type	type	NOUN
ejpam-5986	49	37	transform	transform	NOUN
ejpam-5986	49	38	of	of	ADP
ejpam-5986	49	39	some	some	DET
ejpam-5986	49	40	frequently	frequently	ADV
ejpam-5986	49	41	used	use	VERB
ejpam-5986	49	42	functions	function	NOUN
ejpam-5986	49	43	.	.	PUNCT
ejpam-5986	50	1	definition	definition	NOUN
ejpam-5986	50	2	1	1	NUM
ejpam-5986	50	3	.	.	PUNCT
ejpam-5986	51	1	let	let	VERB
ejpam-5986	51	2	λ	λ	X
ejpam-5986	51	3	∈	∈	PROPN
ejpam-5986	51	4	(	(	PUNCT
ejpam-5986	51	5	0,∞	0,∞	NOUN
ejpam-5986	51	6	)	)	PUNCT
ejpam-5986	51	7	,	,	PUNCT
ejpam-5986	52	1	α	α	PROPN
ejpam-5986	52	2	∈	∈	PROPN
ejpam-5986	53	1	z	z	PROPN
ejpam-5986	53	2	,	,	PUNCT
ejpam-5986	53	3	u	u	NOUN
ejpam-5986	53	4	>	>	X
ejpam-5986	53	5	0	0	PUNCT
ejpam-5986	53	6	and	and	CCONJ
ejpam-5986	53	7	f(t	f(t	NOUN
ejpam-5986	53	8	)	)	PUNCT
ejpam-5986	53	9	be	be	VERB
ejpam-5986	53	10	an	an	DET
ejpam-5986	53	11	integrable	integrable	ADJ
ejpam-5986	53	12	function	function	NOUN
ejpam-5986	53	13	defined	define	VERB
ejpam-5986	53	14	for	for	ADP
ejpam-5986	53	15	all	all	DET
ejpam-5986	53	16	t	t	PROPN
ejpam-5986	53	17	≥	≥	NOUN
ejpam-5986	53	18	0	0	NUM
ejpam-5986	53	19	.	.	PUNCT
ejpam-5986	54	1	then	then	ADV
ejpam-5986	54	2	the	the	DET
ejpam-5986	54	3	integral	integral	ADJ
ejpam-5986	54	4	g∗	g∗	PROPN
ejpam-5986	54	5	α	α	X
ejpam-5986	54	6	,	,	PUNCT
ejpam-5986	54	7	λ{f(t	λ{f(t	NUM
ejpam-5986	54	8	)	)	PUNCT
ejpam-5986	54	9	}	}	PUNCT
ejpam-5986	54	10	=	=	PUNCT
ejpam-5986	55	1	uα	uα	PROPN
ejpam-5986	55	2	∫	∫	PROPN
ejpam-5986	55	3	∞	∞	PROPN
ejpam-5986	55	4	0	0	NUM
ejpam-5986	56	1	(	(	PUNCT
ejpam-5986	56	2	1	1	NUM
ejpam-5986	56	3	+	+	X
ejpam-5986	56	4	λ)−	λ)−	ADP
ejpam-5986	56	5	t	t	NOUN
ejpam-5986	56	6	uλ	uλ	PRON
ejpam-5986	56	7	f(t	f(t	PROPN
ejpam-5986	56	8	)	)	PUNCT
ejpam-5986	56	9	dt	dt	X
ejpam-5986	56	10	(	(	PUNCT
ejpam-5986	56	11	7	7	X
ejpam-5986	56	12	)	)	PUNCT
ejpam-5986	56	13	is	be	AUX
ejpam-5986	56	14	said	say	VERB
ejpam-5986	56	15	to	to	PART
ejpam-5986	56	16	be	be	AUX
ejpam-5986	56	17	the	the	DET
ejpam-5986	56	18	modified	modify	VERB
ejpam-5986	56	19	laplace	laplace	NOUN
ejpam-5986	56	20	-	-	PUNCT
ejpam-5986	56	21	type	type	NOUN
ejpam-5986	56	22	transform	transform	NOUN
ejpam-5986	56	23	g∗	g∗	NOUN
ejpam-5986	56	24	α	α	NOUN
ejpam-5986	56	25	,	,	PUNCT
ejpam-5986	56	26	λ	λ	PROPN
ejpam-5986	56	27	of	of	ADP
ejpam-5986	56	28	f(t	f(t	PROPN
ejpam-5986	56	29	)	)	PUNCT
ejpam-5986	56	30	provided	provide	VERB
ejpam-5986	56	31	that	that	SCONJ
ejpam-5986	56	32	the	the	DET
ejpam-5986	56	33	integral	integral	ADJ
ejpam-5986	56	34	in	in	ADP
ejpam-5986	56	35	(	(	PUNCT
ejpam-5986	56	36	7	7	NUM
ejpam-5986	56	37	)	)	PUNCT
ejpam-5986	56	38	exists	exist	VERB
ejpam-5986	56	39	.	.	PUNCT
ejpam-5986	57	1	since	since	SCONJ
ejpam-5986	57	2	the	the	DET
ejpam-5986	57	3	function	function	NOUN
ejpam-5986	57	4	g∗	g∗	VERB
ejpam-5986	57	5	α	α	X
ejpam-5986	57	6	,	,	PUNCT
ejpam-5986	57	7	λ{f(t	λ{f(t	NUM
ejpam-5986	57	8	)	)	PUNCT
ejpam-5986	57	9	}	}	PUNCT
ejpam-5986	57	10	is	be	AUX
ejpam-5986	57	11	depend	depend	VERB
ejpam-5986	57	12	on	on	ADP
ejpam-5986	57	13	the	the	DET
ejpam-5986	57	14	variable	variable	ADJ
ejpam-5986	57	15	u	u	NOUN
ejpam-5986	57	16	,	,	PUNCT
ejpam-5986	57	17	it	it	PRON
ejpam-5986	57	18	can	can	AUX
ejpam-5986	57	19	be	be	AUX
ejpam-5986	57	20	denoted	denote	VERB
ejpam-5986	57	21	as	as	ADP
ejpam-5986	57	22	f	f	PROPN
ejpam-5986	57	23	∗	∗	PROPN
ejpam-5986	57	24	α	α	PROPN
ejpam-5986	57	25	,	,	PUNCT
ejpam-5986	57	26	λ(u	λ(u	PROPN
ejpam-5986	57	27	)	)	PUNCT
ejpam-5986	57	28	.	.	PUNCT
ejpam-5986	58	1	we	we	PRON
ejpam-5986	58	2	note	note	VERB
ejpam-5986	58	3	that	that	SCONJ
ejpam-5986	58	4	lim	lim	PROPN
ejpam-5986	58	5	λ→0	λ→0	PROPN
ejpam-5986	58	6	g∗	g∗	VERB
ejpam-5986	58	7	α	α	X
ejpam-5986	58	8	,	,	PUNCT
ejpam-5986	58	9	λ{f(t	λ{f(t	NUM
ejpam-5986	58	10	)	)	PUNCT
ejpam-5986	58	11	}	}	PUNCT
ejpam-5986	58	12	=	=	SYM
ejpam-5986	58	13	gα{f(t	gα{f(t	NOUN
ejpam-5986	58	14	)	)	PUNCT
ejpam-5986	58	15	}	}	PUNCT
ejpam-5986	58	16	,	,	PUNCT
ejpam-5986	58	17	(	(	PUNCT
ejpam-5986	58	18	8)	8)	NUM
ejpam-5986	58	19	lim	lim	NOUN
ejpam-5986	58	20	λ→0	λ→0	PUNCT
ejpam-5986	58	21	α=1	α=1	PUNCT
ejpam-5986	58	22	g∗	g∗	VERB
ejpam-5986	58	23	α	α	X
ejpam-5986	58	24	,	,	PUNCT
ejpam-5986	58	25	λ{f(t	λ{f(t	NUM
ejpam-5986	58	26	)	)	PUNCT
ejpam-5986	58	27	}	}	PUNCT
ejpam-5986	58	28	=	=	PUNCT
ejpam-5986	58	29	e{f(t	e{f(t	NOUN
ejpam-5986	58	30	)	)	PUNCT
ejpam-5986	58	31	}	}	PUNCT
ejpam-5986	58	32	(	(	PUNCT
ejpam-5986	58	33	9	9	NUM
ejpam-5986	58	34	)	)	PUNCT
ejpam-5986	58	35	and	and	CCONJ
ejpam-5986	58	36	lim	lim	PROPN
ejpam-5986	58	37	λ→0	λ→0	PUNCT
ejpam-5986	58	38	α=−1	α=−1	NUM
ejpam-5986	58	39	g∗	g∗	PROPN
ejpam-5986	58	40	α	α	NOUN
ejpam-5986	58	41	,	,	PUNCT
ejpam-5986	58	42	λ{f(t	λ{f(t	NUM
ejpam-5986	58	43	)	)	PUNCT
ejpam-5986	58	44	}	}	PUNCT
ejpam-5986	58	45	=	=	SYM
ejpam-5986	58	46	s{f(t	s{f(t	NUM
ejpam-5986	58	47	)	)	PUNCT
ejpam-5986	58	48	}	}	PUNCT
ejpam-5986	58	49	.	.	PUNCT
ejpam-5986	59	1	(	(	PUNCT
ejpam-5986	59	2	10	10	NUM
ejpam-5986	59	3	)	)	PUNCT
ejpam-5986	59	4	now	now	ADV
ejpam-5986	59	5	we	we	PRON
ejpam-5986	59	6	give	give	VERB
ejpam-5986	59	7	sufficient	sufficient	ADJ
ejpam-5986	59	8	conditions	condition	NOUN
ejpam-5986	59	9	for	for	ADP
ejpam-5986	59	10	the	the	DET
ejpam-5986	59	11	existence	existence	NOUN
ejpam-5986	59	12	of	of	ADP
ejpam-5986	59	13	the	the	DET
ejpam-5986	59	14	new	new	ADJ
ejpam-5986	59	15	integral	integral	ADJ
ejpam-5986	59	16	transform	transform	NOUN
ejpam-5986	59	17	.	.	PUNCT
ejpam-5986	60	1	theorem	theorem	NOUN
ejpam-5986	60	2	1	1	NUM
ejpam-5986	60	3	.	.	PUNCT
ejpam-5986	61	1	(	(	PUNCT
ejpam-5986	61	2	existence	existence	NOUN
ejpam-5986	61	3	property	property	NOUN
ejpam-5986	61	4	of	of	ADP
ejpam-5986	61	5	g∗	g∗	PROPN
ejpam-5986	61	6	α	α	PROPN
ejpam-5986	61	7	,	,	PUNCT
ejpam-5986	61	8	λ	λ	NOUN
ejpam-5986	61	9	)	)	PUNCT
ejpam-5986	61	10	let	let	VERB
ejpam-5986	61	11	f(t	f(t	NOUN
ejpam-5986	61	12	)	)	PUNCT
ejpam-5986	61	13	be	be	AUX
ejpam-5986	61	14	a	a	DET
ejpam-5986	61	15	piecewise	piecewise	NOUN
ejpam-5986	61	16	-	-	PUNCT
ejpam-5986	61	17	continious	continious	ADJ
ejpam-5986	61	18	function	function	NOUN
ejpam-5986	61	19	on	on	ADP
ejpam-5986	61	20	every	every	DET
ejpam-5986	61	21	finite	finite	ADJ
ejpam-5986	61	22	interval	interval	NOUN
ejpam-5986	61	23	[	[	X
ejpam-5986	61	24	0	0	NUM
ejpam-5986	61	25	,	,	PUNCT
ejpam-5986	61	26	a	a	DET
ejpam-5986	61	27	]	]	X
ejpam-5986	61	28	and	and	CCONJ
ejpam-5986	61	29	of	of	ADP
ejpam-5986	61	30	exponential	exponential	ADJ
ejpam-5986	61	31	order	order	NOUN
ejpam-5986	61	32	as	as	SCONJ
ejpam-5986	61	33	t	t	PROPN
ejpam-5986	61	34	goes	go	VERB
ejpam-5986	61	35	to	to	ADP
ejpam-5986	61	36	infinity	infinity	NOUN
ejpam-5986	61	37	with	with	ADP
ejpam-5986	61	38	|f(t)|	|f(t)|	ADJ
ejpam-5986	61	39	≤	≤	ADJ
ejpam-5986	61	40	mekt	mekt	NOUN
ejpam-5986	61	41	for	for	ADP
ejpam-5986	61	42	t	t	PROPN
ejpam-5986	61	43	>	>	X
ejpam-5986	61	44	l	l	PROPN
ejpam-5986	61	45	,	,	PUNCT
ejpam-5986	61	46	where	where	SCONJ
ejpam-5986	61	47	and	and	CCONJ
ejpam-5986	61	48	k	k	NOUN
ejpam-5986	61	49	,	,	PUNCT
ejpam-5986	61	50	l	l	NOUN
ejpam-5986	61	51	,	,	PUNCT
ejpam-5986	61	52	m	m	VERB
ejpam-5986	61	53	are	be	AUX
ejpam-5986	61	54	constants	constant	NOUN
ejpam-5986	61	55	and	and	CCONJ
ejpam-5986	61	56	m	m	VERB
ejpam-5986	61	57	>	>	X
ejpam-5986	61	58	0	0	X
ejpam-5986	61	59	.	.	PUNCT
ejpam-5986	62	1	then	then	ADV
ejpam-5986	62	2	g∗	g∗	VERB
ejpam-5986	62	3	α	α	X
ejpam-5986	62	4	,	,	PUNCT
ejpam-5986	62	5	λ{f(t	λ{f(t	NUM
ejpam-5986	62	6	)	)	PUNCT
ejpam-5986	62	7	}	}	PUNCT
ejpam-5986	62	8	exists	exist	VERB
ejpam-5986	62	9	for	for	ADP
ejpam-5986	62	10	1	1	NUM
ejpam-5986	62	11	u	u	NOUN
ejpam-5986	62	12	>	>	X
ejpam-5986	62	13	kλ	kλ	X
ejpam-5986	62	14	ln(1+λ	ln(1+λ	PROPN
ejpam-5986	62	15	)	)	PUNCT
ejpam-5986	62	16	.	.	PUNCT
ejpam-5986	63	1	proof	proof	NOUN
ejpam-5986	63	2	.	.	PUNCT
ejpam-5986	64	1	we	we	PRON
ejpam-5986	64	2	can	can	AUX
ejpam-5986	64	3	write	write	VERB
ejpam-5986	64	4	uα	uα	PROPN
ejpam-5986	64	5	∫	∫	PROPN
ejpam-5986	64	6	∞	∞	PROPN
ejpam-5986	64	7	0	0	PUNCT
ejpam-5986	65	1	(	(	PUNCT
ejpam-5986	65	2	1	1	NUM
ejpam-5986	65	3	+	+	X
ejpam-5986	65	4	λ)−	λ)−	ADP
ejpam-5986	65	5	t	t	NOUN
ejpam-5986	65	6	uλ	uλ	DET
ejpam-5986	65	7	f(t	f(t	NOUN
ejpam-5986	65	8	)	)	PUNCT
ejpam-5986	66	1	dt	dt	NOUN
ejpam-5986	67	1	=	=	PUNCT
ejpam-5986	67	2	uα	uα	PROPN
ejpam-5986	67	3	∫	∫	PROPN
ejpam-5986	67	4	l	l	NOUN
ejpam-5986	67	5	0	0	PUNCT
ejpam-5986	67	6	(	(	PUNCT
ejpam-5986	67	7	1	1	NUM
ejpam-5986	67	8	+	+	X
ejpam-5986	67	9	λ)−	λ)−	ADP
ejpam-5986	67	10	t	t	NOUN
ejpam-5986	67	11	uλ	uλ	PRON
ejpam-5986	67	12	f(t	f(t	NOUN
ejpam-5986	67	13	)	)	PUNCT
ejpam-5986	67	14	dt+	dt+	NOUN
ejpam-5986	67	15	uα	uα	PROPN
ejpam-5986	67	16	∫	∫	PROPN
ejpam-5986	68	1	∞	∞	PROPN
ejpam-5986	68	2	l	l	NOUN
ejpam-5986	68	3	(	(	PUNCT
ejpam-5986	68	4	1	1	NUM
ejpam-5986	68	5	+	+	X
ejpam-5986	68	6	λ)−	λ)−	ADP
ejpam-5986	68	7	t	t	NOUN
ejpam-5986	68	8	uλ	uλ	PRON
ejpam-5986	68	9	f(t	f(t	PROPN
ejpam-5986	68	10	)	)	PUNCT
ejpam-5986	68	11	dt	dt	X
ejpam-5986	68	12	.	.	PUNCT
ejpam-5986	69	1	(	(	PUNCT
ejpam-5986	69	2	11	11	NUM
ejpam-5986	69	3	)	)	PUNCT
ejpam-5986	69	4	i̇.	i̇.	NOUN
ejpam-5986	69	5	ege	ege	PROPN
ejpam-5986	69	6	/	/	SYM
ejpam-5986	69	7	eur	eur	PROPN
ejpam-5986	69	8	.	.	PUNCT
ejpam-5986	70	1	j.	j.	PROPN
ejpam-5986	70	2	pure	pure	PROPN
ejpam-5986	70	3	appl	appl	PROPN
ejpam-5986	70	4	.	.	PROPN
ejpam-5986	70	5	math	math	PROPN
ejpam-5986	70	6	,	,	PUNCT
ejpam-5986	70	7	18	18	NUM
ejpam-5986	70	8	(	(	PUNCT
ejpam-5986	70	9	2	2	NUM
ejpam-5986	70	10	)	)	PUNCT
ejpam-5986	70	11	(	(	PUNCT
ejpam-5986	70	12	2025	2025	NUM
ejpam-5986	70	13	)	)	PUNCT
ejpam-5986	70	14	,	,	PUNCT
ejpam-5986	70	15	5986	5986	NUM
ejpam-5986	70	16	4	4	NUM
ejpam-5986	70	17	of	of	ADP
ejpam-5986	70	18	20	20	NUM
ejpam-5986	70	19	since	since	SCONJ
ejpam-5986	70	20	the	the	DET
ejpam-5986	70	21	function	function	NOUN
ejpam-5986	70	22	f(t	f(t	NOUN
ejpam-5986	70	23	)	)	PUNCT
ejpam-5986	70	24	is	be	AUX
ejpam-5986	70	25	continuous	continuous	ADJ
ejpam-5986	70	26	on	on	ADP
ejpam-5986	70	27	the	the	DET
ejpam-5986	70	28	interval	interval	NOUN
ejpam-5986	71	1	[	[	X
ejpam-5986	71	2	0	0	NUM
ejpam-5986	71	3	,	,	PUNCT
ejpam-5986	71	4	l	l	NOUN
ejpam-5986	71	5	]	]	X
ejpam-5986	71	6	,	,	PUNCT
ejpam-5986	71	7	there	there	PRON
ejpam-5986	71	8	exist	exist	VERB
ejpam-5986	71	9	an	an	DET
ejpam-5986	71	10	m	m	NOUN
ejpam-5986	71	11	>	>	X
ejpam-5986	71	12	0	0	NUM
ejpam-5986	72	1	such	such	ADJ
ejpam-5986	72	2	that	that	SCONJ
ejpam-5986	72	3	|f(t)|	|f(t)|	PROPN
ejpam-5986	72	4	≤	≤	NOUN
ejpam-5986	72	5	m	m	VERB
ejpam-5986	72	6	.	.	PUNCT
ejpam-5986	73	1	it	it	PRON
ejpam-5986	73	2	gives	give	VERB
ejpam-5986	73	3	that	that	PRON
ejpam-5986	73	4	uα	uα	PROPN
ejpam-5986	73	5	∫	∫	PROPN
ejpam-5986	73	6	l	l	NOUN
ejpam-5986	73	7	0	0	PUNCT
ejpam-5986	74	1	(	(	PUNCT
ejpam-5986	74	2	1	1	NUM
ejpam-5986	74	3	+	+	X
ejpam-5986	74	4	λ)−	λ)−	ADP
ejpam-5986	74	5	t	t	NOUN
ejpam-5986	74	6	uλ	uλ	DET
ejpam-5986	74	7	f(t	f(t	PROPN
ejpam-5986	74	8	)	)	PUNCT
ejpam-5986	75	1	dt	dt	PART
ejpam-5986	75	2	≤	≤	NUM
ejpam-5986	76	1	muα	muα	NOUN
ejpam-5986	76	2	∫	∫	PROPN
ejpam-5986	76	3	l	l	NOUN
ejpam-5986	76	4	0	0	PUNCT
ejpam-5986	77	1	(	(	PUNCT
ejpam-5986	77	2	1	1	NUM
ejpam-5986	77	3	+	+	X
ejpam-5986	77	4	λ)−	λ)−	ADP
ejpam-5986	77	5	t	t	X
ejpam-5986	77	6	uλ	uλ	X
ejpam-5986	77	7	dt	dt	NOUN
ejpam-5986	78	1	=	=	PUNCT
ejpam-5986	78	2	mλuα+1	mλuα+1	NOUN
ejpam-5986	78	3	ln(1	ln(1	PROPN
ejpam-5986	78	4	+	+	CCONJ
ejpam-5986	78	5	λ	λ	NOUN
ejpam-5986	78	6	)	)	PUNCT
ejpam-5986	79	1	[	[	X
ejpam-5986	79	2	1−	1−	NUM
ejpam-5986	79	3	(	(	PUNCT
ejpam-5986	79	4	1	1	NUM
ejpam-5986	79	5	+	+	CCONJ
ejpam-5986	79	6	λ)−	λ)−	ADP
ejpam-5986	79	7	l	l	NOUN
ejpam-5986	79	8	uλ	uλ	X
ejpam-5986	79	9	]	]	PUNCT
ejpam-5986	79	10	<	<	X
ejpam-5986	79	11	∞.	∞.	PROPN
ejpam-5986	79	12	hence	hence	ADV
ejpam-5986	79	13	the	the	DET
ejpam-5986	79	14	first	first	ADJ
ejpam-5986	79	15	integral	integral	NOUN
ejpam-5986	79	16	on	on	ADP
ejpam-5986	79	17	the	the	DET
ejpam-5986	79	18	right	right	ADJ
ejpam-5986	79	19	-	-	PUNCT
ejpam-5986	79	20	hand	hand	NOUN
ejpam-5986	79	21	side	side	NOUN
ejpam-5986	79	22	of	of	ADP
ejpam-5986	79	23	equation	equation	NOUN
ejpam-5986	79	24	(	(	PUNCT
ejpam-5986	79	25	11	11	NUM
ejpam-5986	79	26	)	)	PUNCT
ejpam-5986	79	27	exists	exist	VERB
ejpam-5986	79	28	.	.	PUNCT
ejpam-5986	80	1	also	also	ADV
ejpam-5986	80	2	,	,	PUNCT
ejpam-5986	80	3	since	since	SCONJ
ejpam-5986	80	4	|(1	|(1	PROPN
ejpam-5986	80	5	+	+	PROPN
ejpam-5986	80	6	λ)−	λ)−	PROPN
ejpam-5986	80	7	t	t	PROPN
ejpam-5986	80	8	uλ	uλ	PRON
ejpam-5986	80	9	f(t)|	f(t)|	ADJ
ejpam-5986	80	10	≤	≤	ADJ
ejpam-5986	80	11	m(1	m(1	NOUN
ejpam-5986	80	12	+	+	PROPN
ejpam-5986	81	1	λ)−	λ)−	PROPN
ejpam-5986	81	2	t	t	X
ejpam-5986	81	3	uλ	uλ	X
ejpam-5986	81	4	ekt	ekt	PROPN
ejpam-5986	82	1	=	=	PUNCT
ejpam-5986	82	2	me−	me−	PROPN
ejpam-5986	82	3	t	t	PROPN
ejpam-5986	82	4	uλ	uλ	PRON
ejpam-5986	82	5	ln(1+λ)ekt	ln(1+λ)ekt	PROPN
ejpam-5986	83	1	=	=	PUNCT
ejpam-5986	83	2	me	i	PRON
ejpam-5986	83	3	t	t	PROPN
ejpam-5986	83	4	(	(	PUNCT
ejpam-5986	83	5	k−	k−	PROPN
ejpam-5986	83	6	ln(1+λ	ln(1+λ	ADV
ejpam-5986	83	7	)	)	PUNCT
ejpam-5986	83	8	uλ	uλ	ADP
ejpam-5986	83	9	)	)	PUNCT
ejpam-5986	84	1	we	we	PRON
ejpam-5986	84	2	have	have	VERB
ejpam-5986	84	3	∣∣∣∣uα	∣∣∣∣uα	NOUN
ejpam-5986	84	4	∫	∫	PROPN
ejpam-5986	84	5	∞	∞	PROPN
ejpam-5986	84	6	l	l	NOUN
ejpam-5986	84	7	(	(	PUNCT
ejpam-5986	84	8	1	1	NUM
ejpam-5986	84	9	+	+	X
ejpam-5986	84	10	λ)−	λ)−	ADP
ejpam-5986	84	11	t	t	NOUN
ejpam-5986	84	12	uλ	uλ	DET
ejpam-5986	84	13	f(t	f(t	PROPN
ejpam-5986	84	14	)	)	PUNCT
ejpam-5986	85	1	dt	dt	X
ejpam-5986	85	2	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5986	85	3	≤	≤	PROPN
ejpam-5986	86	1	uα	uα	PROPN
ejpam-5986	86	2	∫	∫	PROPN
ejpam-5986	86	3	∞	∞	NUM
ejpam-5986	86	4	l	l	NOUN
ejpam-5986	86	5	e−	e−	PROPN
ejpam-5986	86	6	t	t	PROPN
ejpam-5986	86	7	uλ	uλ	ADP
ejpam-5986	86	8	ln(1+λ	ln(1+λ	PROPN
ejpam-5986	86	9	)	)	PUNCT
ejpam-5986	87	1	|f(t)|	|f(t)|	ADJ
ejpam-5986	87	2	dt	dt	X
ejpam-5986	87	3	=	=	SYM
ejpam-5986	87	4	muα	muα	PROPN
ejpam-5986	87	5	lim	lim	PROPN
ejpam-5986	87	6	h→∞	h→∞	NUM
ejpam-5986	87	7	∫	∫	PROPN
ejpam-5986	88	1	h	h	PROPN
ejpam-5986	88	2	l	l	PROPN
ejpam-5986	88	3	e	e	PROPN
ejpam-5986	88	4	t	t	PROPN
ejpam-5986	88	5	(	(	PUNCT
ejpam-5986	88	6	k−	k−	PROPN
ejpam-5986	88	7	ln(1+λ	ln(1+λ	ADV
ejpam-5986	88	8	)	)	PUNCT
ejpam-5986	88	9	uλ	uλ	ADV
ejpam-5986	88	10	)	)	PUNCT
ejpam-5986	88	11	dt	dt	PROPN
ejpam-5986	89	1	=	=	PUNCT
ejpam-5986	89	2	mλuα+1	mλuα+1	NOUN
ejpam-5986	90	1	ln(1	ln(1	PROPN
ejpam-5986	90	2	+	+	CCONJ
ejpam-5986	90	3	λ)−	λ)−	PROPN
ejpam-5986	90	4	kuλ	kuλ	NOUN
ejpam-5986	90	5	e	e	NOUN
ejpam-5986	90	6	l	l	X
ejpam-5986	90	7	(	(	PUNCT
ejpam-5986	90	8	k−	k−	PROPN
ejpam-5986	90	9	ln(1+λ	ln(1+λ	ADV
ejpam-5986	90	10	)	)	PUNCT
ejpam-5986	90	11	uλ	uλ	ADP
ejpam-5986	90	12	)	)	PUNCT
ejpam-5986	90	13	<	<	X
ejpam-5986	90	14	∞	∞	PROPN
ejpam-5986	90	15	for	for	ADP
ejpam-5986	90	16	k	k	PROPN
ejpam-5986	90	17	<	<	X
ejpam-5986	90	18	ln(1+λ	ln(1+λ	PROPN
ejpam-5986	90	19	)	)	PUNCT
ejpam-5986	90	20	uλ	uλ	NOUN
ejpam-5986	90	21	.	.	PUNCT
ejpam-5986	91	1	then	then	ADV
ejpam-5986	91	2	we	we	PRON
ejpam-5986	91	3	proved	prove	VERB
ejpam-5986	91	4	that	that	SCONJ
ejpam-5986	91	5	the	the	DET
ejpam-5986	91	6	integral	integral	ADJ
ejpam-5986	91	7	uα	uα	PROPN
ejpam-5986	91	8	∫	∫	PROPN
ejpam-5986	91	9	∞	∞	PROPN
ejpam-5986	91	10	0	0	NUM
ejpam-5986	92	1	(	(	PUNCT
ejpam-5986	92	2	1	1	NUM
ejpam-5986	92	3	+	+	X
ejpam-5986	92	4	λ)−	λ)−	ADP
ejpam-5986	92	5	t	t	NOUN
ejpam-5986	92	6	uλ	uλ	PRON
ejpam-5986	92	7	f(t	f(t	PROPN
ejpam-5986	92	8	)	)	PUNCT
ejpam-5986	92	9	dt	dt	X
ejpam-5986	93	1	(	(	PUNCT
ejpam-5986	93	2	12	12	NUM
ejpam-5986	93	3	)	)	PUNCT
ejpam-5986	93	4	exists	exist	VERB
ejpam-5986	93	5	,	,	PUNCT
ejpam-5986	93	6	and	and	CCONJ
ejpam-5986	93	7	the	the	DET
ejpam-5986	93	8	result	result	NOUN
ejpam-5986	93	9	follows	follow	VERB
ejpam-5986	93	10	.	.	PUNCT
ejpam-5986	94	1	theorem	theorem	NOUN
ejpam-5986	94	2	2	2	NUM
ejpam-5986	94	3	.	.	PUNCT
ejpam-5986	95	1	the	the	DET
ejpam-5986	95	2	modified	modify	VERB
ejpam-5986	95	3	laplace	laplace	NOUN
ejpam-5986	95	4	-	-	PUNCT
ejpam-5986	95	5	type	type	NOUN
ejpam-5986	95	6	transform	transform	NOUN
ejpam-5986	95	7	of	of	ADP
ejpam-5986	95	8	the	the	DET
ejpam-5986	95	9	function	function	NOUN
ejpam-5986	95	10	f(t	f(t	PROPN
ejpam-5986	95	11	)	)	PUNCT
ejpam-5986	95	12	=	=	SYM
ejpam-5986	95	13	tn	tn	PROPN
ejpam-5986	95	14	,	,	PUNCT
ejpam-5986	95	15	n	n	NOUN
ejpam-5986	95	16	=	=	SYM
ejpam-5986	95	17	1	1	NUM
ejpam-5986	95	18	,	,	PUNCT
ejpam-5986	95	19	2	2	NUM
ejpam-5986	95	20	,	,	PUNCT
ejpam-5986	95	21	.	.	PUNCT
ejpam-5986	95	22	.	.	PUNCT
ejpam-5986	95	23	.	.	PUNCT
ejpam-5986	96	1	is	be	AUX
ejpam-5986	96	2	given	give	VERB
ejpam-5986	96	3	by	by	ADP
ejpam-5986	96	4	g∗	g∗	PROPN
ejpam-5986	96	5	α	α	NOUN
ejpam-5986	96	6	,	,	PUNCT
ejpam-5986	96	7	λ{tn	λ{tn	PROPN
ejpam-5986	96	8	}	}	PUNCT
ejpam-5986	96	9	=	=	SYM
ejpam-5986	96	10	n!λn+1uα+n+1	n!λn+1uα+n+1	NOUN
ejpam-5986	96	11	lnn+1(1	lnn+1(1	X
ejpam-5986	96	12	+	+	PUNCT
ejpam-5986	96	13	λ	λ	NOUN
ejpam-5986	96	14	)	)	PUNCT
ejpam-5986	96	15	.	.	PUNCT
ejpam-5986	97	1	proof	proof	NOUN
ejpam-5986	97	2	.	.	PUNCT
ejpam-5986	98	1	by	by	ADP
ejpam-5986	98	2	considering	consider	VERB
ejpam-5986	98	3	the	the	DET
ejpam-5986	98	4	definition	definition	NOUN
ejpam-5986	98	5	1	1	NUM
ejpam-5986	98	6	for	for	ADP
ejpam-5986	98	7	f(t	f(t	NOUN
ejpam-5986	98	8	)	)	PUNCT
ejpam-5986	98	9	=	=	SYM
ejpam-5986	98	10	tn	tn	PROPN
ejpam-5986	98	11	,	,	PUNCT
ejpam-5986	98	12	leads	lead	VERB
ejpam-5986	98	13	to	to	PART
ejpam-5986	98	14	g∗	g∗	VERB
ejpam-5986	98	15	α	α	PRON
ejpam-5986	98	16	,	,	PUNCT
ejpam-5986	98	17	λ{tn	λ{tn	PROPN
ejpam-5986	98	18	}	}	PUNCT
ejpam-5986	98	19	=	=	PUNCT
ejpam-5986	98	20	uα	uα	PROPN
ejpam-5986	98	21	∫	∫	PROPN
ejpam-5986	98	22	∞	∞	PROPN
ejpam-5986	98	23	0	0	NUM
ejpam-5986	99	1	(	(	PUNCT
ejpam-5986	99	2	1	1	NUM
ejpam-5986	99	3	+	+	X
ejpam-5986	99	4	λ)−	λ)−	ADP
ejpam-5986	99	5	t	t	PROPN
ejpam-5986	99	6	uλ	uλ	PRON
ejpam-5986	99	7	tn	tn	PROPN
ejpam-5986	100	1	dt	dt	PROPN
ejpam-5986	101	1	=	=	PUNCT
ejpam-5986	101	2	uα	uα	PROPN
ejpam-5986	101	3	lim	lim	PROPN
ejpam-5986	101	4	h→∞	h→∞	NUM
ejpam-5986	101	5	∫	∫	PROPN
ejpam-5986	101	6	h	h	NOUN
ejpam-5986	101	7	0	0	PUNCT
ejpam-5986	102	1	(	(	PUNCT
ejpam-5986	102	2	1	1	NUM
ejpam-5986	102	3	+	+	X
ejpam-5986	102	4	λ)−	λ)−	ADP
ejpam-5986	102	5	t	t	PROPN
ejpam-5986	102	6	uλ	uλ	X
ejpam-5986	102	7	tn	tn	PROPN
ejpam-5986	102	8	dt	dt	PROPN
ejpam-5986	102	9	.	.	PUNCT
ejpam-5986	103	1	using	use	VERB
ejpam-5986	103	2	integration	integration	NOUN
ejpam-5986	103	3	by	by	ADP
ejpam-5986	103	4	parts	part	NOUN
ejpam-5986	103	5	,	,	PUNCT
ejpam-5986	103	6	we	we	PRON
ejpam-5986	103	7	have	have	AUX
ejpam-5986	103	8	g∗	g∗	PROPN
ejpam-5986	103	9	α	α	PRON
ejpam-5986	103	10	,	,	PUNCT
ejpam-5986	103	11	λ{tn	λ{tn	PROPN
ejpam-5986	103	12	}	}	PUNCT
ejpam-5986	103	13	=	=	SYM
ejpam-5986	103	14	uα	uα	PROPN
ejpam-5986	103	15	lim	lim	PROPN
ejpam-5986	103	16	h→∞	h→∞	PROPN
ejpam-5986	104	1	[	[	PUNCT
ejpam-5986	104	2	−tnuλ(1	−tnuλ(1	PUNCT
ejpam-5986	104	3	+	+	NUM
ejpam-5986	104	4	λ	λ	NOUN
ejpam-5986	104	5	)	)	PUNCT
ejpam-5986	104	6	−t	−t	NOUN
ejpam-5986	104	7	uλ	uλ	NOUN
ejpam-5986	104	8	ln(1	ln(1	PROPN
ejpam-5986	104	9	+	+	CCONJ
ejpam-5986	104	10	λ	λ	NOUN
ejpam-5986	104	11	)	)	PUNCT
ejpam-5986	104	12	∣∣∣∣h	∣∣∣∣h	NOUN
ejpam-5986	104	13	0	0	PUNCT
ejpam-5986	105	1	+	+	CCONJ
ejpam-5986	105	2	nuλ	nuλ	PROPN
ejpam-5986	105	3	ln(1	ln(1	PROPN
ejpam-5986	105	4	+	+	CCONJ
ejpam-5986	105	5	λ	λ	PROPN
ejpam-5986	105	6	)	)	PUNCT
ejpam-5986	105	7	∫	∫	PROPN
ejpam-5986	106	1	h	h	NOUN
ejpam-5986	106	2	0	0	PROPN
ejpam-5986	106	3	tn−1(1	tn−1(1	PRON
ejpam-5986	106	4	+	+	NUM
ejpam-5986	106	5	λ	λ	NOUN
ejpam-5986	106	6	)	)	PUNCT
ejpam-5986	106	7	−t	−t	NOUN
ejpam-5986	106	8	uλ	uλ	ADP
ejpam-5986	106	9	dt	dt	X
ejpam-5986	106	10	]	]	PUNCT
ejpam-5986	106	11	.	.	PUNCT
ejpam-5986	107	1	since	since	SCONJ
ejpam-5986	107	2	for	for	ADP
ejpam-5986	107	3	1	1	NUM
ejpam-5986	107	4	uλ	uλ	NOUN
ejpam-5986	107	5	>	>	X
ejpam-5986	107	6	0	0	NUM
ejpam-5986	107	7	we	we	PRON
ejpam-5986	107	8	have	have	VERB
ejpam-5986	107	9	limh→	limh→	NUM
ejpam-5986	107	10	∞	∞	NUM
ejpam-5986	108	1	hnuλ(1	hnuλ(1	PROPN
ejpam-5986	108	2	+	+	CCONJ
ejpam-5986	108	3	λ	λ	NOUN
ejpam-5986	108	4	)	)	PUNCT
ejpam-5986	108	5	−h	−h	VERB
ejpam-5986	108	6	uλ	uλ	PRON
ejpam-5986	108	7	ln(1	ln(1	PROPN
ejpam-5986	108	8	+	+	CCONJ
ejpam-5986	108	9	λ	λ	NOUN
ejpam-5986	108	10	)	)	PUNCT
ejpam-5986	108	11	=	=	SYM
ejpam-5986	108	12	0	0	NUM
ejpam-5986	108	13	,	,	PUNCT
ejpam-5986	108	14	then	then	ADV
ejpam-5986	108	15	g∗	g∗	VERB
ejpam-5986	108	16	α	α	PRON
ejpam-5986	108	17	,	,	PUNCT
ejpam-5986	108	18	λ{tn	λ{tn	PROPN
ejpam-5986	108	19	}	}	PUNCT
ejpam-5986	108	20	=	=	PUNCT
ejpam-5986	108	21	nuλ	nuλ	PROPN
ejpam-5986	108	22	ln(1	ln(1	PROPN
ejpam-5986	108	23	+	+	CCONJ
ejpam-5986	108	24	λ	λ	NOUN
ejpam-5986	108	25	)	)	PUNCT
ejpam-5986	108	26	g∗	g∗	VERB
ejpam-5986	108	27	α	α	NOUN
ejpam-5986	108	28	,	,	PUNCT
ejpam-5986	108	29	λ{tn−1	λ{tn−1	ADJ
ejpam-5986	108	30	}	}	PUNCT
ejpam-5986	108	31	,	,	PUNCT
ejpam-5986	108	32	and	and	CCONJ
ejpam-5986	108	33	so	so	ADV
ejpam-5986	108	34	g∗	g∗	VERB
ejpam-5986	108	35	α	α	NOUN
ejpam-5986	108	36	,	,	PUNCT
ejpam-5986	108	37	λ{tn−1	λ{tn−1	ADJ
ejpam-5986	108	38	}	}	PUNCT
ejpam-5986	108	39	=	=	SYM
ejpam-5986	108	40	(	(	PUNCT
ejpam-5986	108	41	n−	n−	NOUN
ejpam-5986	108	42	1)uλ	1)uλ	PROPN
ejpam-5986	108	43	ln(1	ln(1	PROPN
ejpam-5986	108	44	+	+	CCONJ
ejpam-5986	108	45	λ	λ	NOUN
ejpam-5986	108	46	)	)	PUNCT
ejpam-5986	108	47	g∗	g∗	PROPN
ejpam-5986	108	48	α	α	NOUN
ejpam-5986	108	49	,	,	PUNCT
ejpam-5986	108	50	λ{tn−2	λ{tn−2	NOUN
ejpam-5986	108	51	}	}	PUNCT
ejpam-5986	108	52	.	.	PUNCT
ejpam-5986	109	1	i̇.	i̇.	PROPN
ejpam-5986	109	2	ege	ege	PROPN
ejpam-5986	109	3	/	/	SYM
ejpam-5986	109	4	eur	eur	PROPN
ejpam-5986	109	5	.	.	PUNCT
ejpam-5986	110	1	j.	j.	PROPN
ejpam-5986	110	2	pure	pure	PROPN
ejpam-5986	110	3	appl	appl	PROPN
ejpam-5986	110	4	.	.	PROPN
ejpam-5986	110	5	math	math	PROPN
ejpam-5986	110	6	,	,	PUNCT
ejpam-5986	110	7	18	18	NUM
ejpam-5986	110	8	(	(	PUNCT
ejpam-5986	110	9	2	2	NUM
ejpam-5986	110	10	)	)	PUNCT
ejpam-5986	110	11	(	(	PUNCT
ejpam-5986	110	12	2025	2025	NUM
ejpam-5986	110	13	)	)	PUNCT
ejpam-5986	110	14	,	,	PUNCT
ejpam-5986	110	15	5986	5986	NUM
ejpam-5986	110	16	5	5	NUM
ejpam-5986	110	17	of	of	ADP
ejpam-5986	110	18	20	20	NUM
ejpam-5986	110	19	hence	hence	ADV
ejpam-5986	110	20	,	,	PUNCT
ejpam-5986	110	21	we	we	PRON
ejpam-5986	110	22	get	get	VERB
ejpam-5986	110	23	g∗	g∗	NOUN
ejpam-5986	110	24	α	α	NOUN
ejpam-5986	110	25	,	,	PUNCT
ejpam-5986	110	26	λ{tn	λ{tn	PROPN
ejpam-5986	110	27	}	}	PUNCT
ejpam-5986	110	28	=	=	SYM
ejpam-5986	110	29	n(n−	n(n−	VERB
ejpam-5986	110	30	1)u2λ2	1)u2λ2	NUM
ejpam-5986	110	31	ln2(1	ln2(1	NOUN
ejpam-5986	110	32	+	+	CCONJ
ejpam-5986	110	33	λ	λ	NOUN
ejpam-5986	110	34	)	)	PUNCT
ejpam-5986	110	35	g∗	g∗	PROPN
ejpam-5986	110	36	α	α	NOUN
ejpam-5986	110	37	,	,	PUNCT
ejpam-5986	110	38	λ{tn−2	λ{tn−2	NOUN
ejpam-5986	110	39	}	}	PUNCT
ejpam-5986	110	40	.	.	PUNCT
ejpam-5986	111	1	continiuting	continiute	VERB
ejpam-5986	111	2	this	this	DET
ejpam-5986	111	3	process	process	NOUN
ejpam-5986	111	4	we	we	PRON
ejpam-5986	111	5	get	get	VERB
ejpam-5986	111	6	g∗	g∗	NOUN
ejpam-5986	111	7	α	α	NOUN
ejpam-5986	111	8	,	,	PUNCT
ejpam-5986	111	9	λ{tn	λ{tn	PROPN
ejpam-5986	111	10	}	}	PUNCT
ejpam-5986	111	11	=	=	SYM
ejpam-5986	111	12	n(n−	n(n−	PRON
ejpam-5986	111	13	1	1	NUM
ejpam-5986	111	14	)	)	PUNCT
ejpam-5986	111	15	.	.	PUNCT
ejpam-5986	111	16	.	.	PUNCT
ejpam-5986	112	1	.	.	PUNCT
ejpam-5986	113	1	2unλn	2unλn	NUM
ejpam-5986	113	2	lnn(1	lnn(1	VERB
ejpam-5986	113	3	+	+	CCONJ
ejpam-5986	113	4	λ	λ	X
ejpam-5986	113	5	)	)	PUNCT
ejpam-5986	113	6	g∗	g∗	VERB
ejpam-5986	113	7	α	α	NUM
ejpam-5986	113	8	,	,	PUNCT
ejpam-5986	113	9	λ{1	λ{1	PROPN
ejpam-5986	113	10	}	}	PUNCT
ejpam-5986	113	11	.	.	PUNCT
ejpam-5986	114	1	also	also	ADV
ejpam-5986	114	2	by	by	ADP
ejpam-5986	114	3	taking	take	VERB
ejpam-5986	114	4	f(t	f(t	NOUN
ejpam-5986	114	5	)	)	PUNCT
ejpam-5986	114	6	=	=	SYM
ejpam-5986	114	7	1	1	NUM
ejpam-5986	114	8	in	in	ADP
ejpam-5986	114	9	the	the	DET
ejpam-5986	114	10	definition	definition	NOUN
ejpam-5986	114	11	1	1	NUM
ejpam-5986	114	12	,	,	PUNCT
ejpam-5986	114	13	we	we	PRON
ejpam-5986	114	14	have	have	AUX
ejpam-5986	114	15	g∗	g∗	PROPN
ejpam-5986	114	16	α	α	PRON
ejpam-5986	114	17	,	,	PUNCT
ejpam-5986	114	18	λ{1	λ{1	PROPN
ejpam-5986	114	19	}	}	PUNCT
ejpam-5986	114	20	=	=	PUNCT
ejpam-5986	114	21	uα	uα	PROPN
ejpam-5986	114	22	∫	∫	PROPN
ejpam-5986	114	23	∞	∞	PROPN
ejpam-5986	114	24	0	0	NUM
ejpam-5986	115	1	(	(	PUNCT
ejpam-5986	115	2	1	1	NUM
ejpam-5986	115	3	+	+	X
ejpam-5986	115	4	λ)−	λ)−	ADP
ejpam-5986	115	5	t	t	X
ejpam-5986	115	6	uλ	uλ	NOUN
ejpam-5986	115	7	dt	dt	PROPN
ejpam-5986	116	1	=	=	PUNCT
ejpam-5986	116	2	uα	uα	PROPN
ejpam-5986	116	3	lim	lim	PROPN
ejpam-5986	116	4	h→∞	h→∞	NUM
ejpam-5986	116	5	∫	∫	PROPN
ejpam-5986	116	6	h	h	NOUN
ejpam-5986	116	7	0	0	PUNCT
ejpam-5986	117	1	(	(	PUNCT
ejpam-5986	117	2	1	1	NUM
ejpam-5986	117	3	+	+	X
ejpam-5986	117	4	λ)−	λ)−	ADP
ejpam-5986	117	5	t	t	X
ejpam-5986	117	6	uλ	uλ	NOUN
ejpam-5986	117	7	dt	dt	NOUN
ejpam-5986	118	1	=	=	PUNCT
ejpam-5986	118	2	λuα+1	λuα+1	NOUN
ejpam-5986	118	3	ln(1	ln(1	PROPN
ejpam-5986	118	4	+	+	NUM
ejpam-5986	118	5	λ	λ	NOUN
ejpam-5986	118	6	)	)	PUNCT
ejpam-5986	118	7	,	,	PUNCT
ejpam-5986	118	8	and	and	CCONJ
ejpam-5986	118	9	the	the	DET
ejpam-5986	118	10	result	result	NOUN
ejpam-5986	118	11	follows	follow	VERB
ejpam-5986	118	12	.	.	PUNCT
ejpam-5986	119	1	note	note	VERB
ejpam-5986	119	2	that	that	SCONJ
ejpam-5986	119	3	,	,	PUNCT
ejpam-5986	119	4	from	from	ADP
ejpam-5986	119	5	the	the	DET
ejpam-5986	119	6	theorem	theorem	NOUN
ejpam-5986	119	7	2	2	NUM
ejpam-5986	119	8	we	we	PRON
ejpam-5986	119	9	have	have	VERB
ejpam-5986	119	10	lim	lim	PROPN
ejpam-5986	119	11	λ→0	λ→0	PROPN
ejpam-5986	119	12	g∗	g∗	VERB
ejpam-5986	119	13	α	α	PRON
ejpam-5986	119	14	,	,	PUNCT
ejpam-5986	119	15	λ{tn	λ{tn	PROPN
ejpam-5986	119	16	}	}	PUNCT
ejpam-5986	119	17	=	=	SYM
ejpam-5986	119	18	lim	lim	PROPN
ejpam-5986	119	19	λ→0	λ→0	PROPN
ejpam-5986	119	20	n!λn+1uα+n+1	n!λn+1uα+n+1	PROPN
ejpam-5986	119	21	lnn+1(1	lnn+1(1	PUNCT
ejpam-5986	120	1	+	+	PUNCT
ejpam-5986	120	2	λ	λ	X
ejpam-5986	120	3	)	)	PUNCT
ejpam-5986	120	4	=	=	SYM
ejpam-5986	120	5	n!uα+n+1	n!uα+n+1	NOUN
ejpam-5986	120	6	=	=	SYM
ejpam-5986	120	7	gα{tn	gα{tn	ADJ
ejpam-5986	120	8	}	}	PUNCT
ejpam-5986	120	9	for	for	ADP
ejpam-5986	120	10	n	n	NOUN
ejpam-5986	120	11	=	=	SYM
ejpam-5986	120	12	0	0	NUM
ejpam-5986	120	13	,	,	PUNCT
ejpam-5986	120	14	1	1	NUM
ejpam-5986	120	15	,	,	PUNCT
ejpam-5986	120	16	2	2	NUM
ejpam-5986	120	17	,	,	PUNCT
ejpam-5986	120	18	.	.	PUNCT
ejpam-5986	120	19	.	.	PUNCT
ejpam-5986	121	1	..	..	PUNCT
ejpam-5986	121	2	also	also	ADV
ejpam-5986	121	3	note	note	VERB
ejpam-5986	121	4	that	that	SCONJ
ejpam-5986	121	5	,	,	PUNCT
ejpam-5986	121	6	by	by	ADP
ejpam-5986	121	7	using	use	VERB
ejpam-5986	121	8	the	the	DET
ejpam-5986	121	9	equation	equation	NOUN
ejpam-5986	121	10	(	(	PUNCT
ejpam-5986	121	11	6	6	NUM
ejpam-5986	121	12	)	)	PUNCT
ejpam-5986	121	13	we	we	PRON
ejpam-5986	121	14	give	give	VERB
ejpam-5986	121	15	the	the	DET
ejpam-5986	121	16	relation	relation	NOUN
ejpam-5986	121	17	between	between	ADP
ejpam-5986	121	18	the	the	DET
ejpam-5986	121	19	modified	modify	VERB
ejpam-5986	121	20	laplacetype	laplacetype	NOUN
ejpam-5986	121	21	transform	transform	NOUN
ejpam-5986	121	22	and	and	CCONJ
ejpam-5986	121	23	the	the	DET
ejpam-5986	121	24	modified	modify	VERB
ejpam-5986	121	25	degenerate	degenerate	ADJ
ejpam-5986	121	26	gamma	gamma	NOUN
ejpam-5986	121	27	function	function	NOUN
ejpam-5986	121	28	γ∗	γ∗	PROPN
ejpam-5986	121	29	λ	λ	PROPN
ejpam-5986	121	30	for	for	ADP
ejpam-5986	121	31	λ	λ	PROPN
ejpam-5986	121	32	∈	∈	PROPN
ejpam-5986	121	33	(	(	PUNCT
ejpam-5986	121	34	0	0	NUM
ejpam-5986	121	35	,	,	PUNCT
ejpam-5986	121	36	1	1	NUM
ejpam-5986	121	37	)	)	PUNCT
ejpam-5986	121	38	as	as	ADP
ejpam-5986	121	39	g∗	g∗	VERB
ejpam-5986	121	40	α	α	NOUN
ejpam-5986	121	41	,	,	PUNCT
ejpam-5986	121	42	λ{tn	λ{tn	PROPN
ejpam-5986	121	43	}	}	PUNCT
ejpam-5986	121	44	=	=	SYM
ejpam-5986	121	45	γ∗	γ∗	PROPN
ejpam-5986	121	46	λ(n+	λ(n+	NOUN
ejpam-5986	121	47	1)uα+n+1	1)uα+n+1	NUM
ejpam-5986	121	48	.	.	PUNCT
ejpam-5986	122	1	theorem	theorem	VERB
ejpam-5986	122	2	3	3	NUM
ejpam-5986	122	3	.	.	PUNCT
ejpam-5986	123	1	the	the	DET
ejpam-5986	123	2	modified	modify	VERB
ejpam-5986	123	3	laplace	laplace	NOUN
ejpam-5986	123	4	-	-	PUNCT
ejpam-5986	123	5	type	type	NOUN
ejpam-5986	123	6	transform	transform	NOUN
ejpam-5986	123	7	of	of	ADP
ejpam-5986	123	8	the	the	DET
ejpam-5986	123	9	function	function	NOUN
ejpam-5986	123	10	f(t	f(t	NOUN
ejpam-5986	123	11	)	)	PUNCT
ejpam-5986	123	12	=	=	PUNCT
ejpam-5986	123	13	eat	eat	NOUN
ejpam-5986	123	14	,	,	PUNCT
ejpam-5986	123	15	is	be	AUX
ejpam-5986	123	16	given	give	VERB
ejpam-5986	123	17	by	by	ADP
ejpam-5986	123	18	g∗	g∗	PROPN
ejpam-5986	123	19	α	α	PROPN
ejpam-5986	123	20	,	,	PUNCT
ejpam-5986	123	21	λ{eat	λ{eat	X
ejpam-5986	123	22	}	}	PUNCT
ejpam-5986	123	23	=	=	PUNCT
ejpam-5986	123	24	λuα+1	λuα+1	AUX
ejpam-5986	123	25	ln(1	ln(1	NOUN
ejpam-5986	123	26	+	+	CCONJ
ejpam-5986	123	27	λ)−	λ)−	PROPN
ejpam-5986	123	28	aλu	aλu	NOUN
ejpam-5986	123	29	for	for	ADP
ejpam-5986	123	30	u	u	NOUN
ejpam-5986	123	31	<	<	X
ejpam-5986	123	32	ln(1	ln(1	PROPN
ejpam-5986	123	33	+	+	CCONJ
ejpam-5986	123	34	λ	λ	NOUN
ejpam-5986	123	35	)	)	PUNCT
ejpam-5986	123	36	aλ	aλ	ADP
ejpam-5986	123	37	and	and	CCONJ
ejpam-5986	123	38	a	a	DET
ejpam-5986	123	39	∈	∈	PROPN
ejpam-5986	123	40	r.	r.	NOUN
ejpam-5986	123	41	proof	proof	NOUN
ejpam-5986	123	42	.	.	PUNCT
ejpam-5986	124	1	using	use	VERB
ejpam-5986	124	2	the	the	DET
ejpam-5986	124	3	equation	equation	NOUN
ejpam-5986	124	4	(	(	PUNCT
ejpam-5986	124	5	7	7	NUM
ejpam-5986	124	6	)	)	PUNCT
ejpam-5986	124	7	for	for	ADP
ejpam-5986	124	8	f(t	f(t	NOUN
ejpam-5986	124	9	)	)	PUNCT
ejpam-5986	124	10	=	=	PRON
ejpam-5986	124	11	eat	eat	VERB
ejpam-5986	124	12	and	and	CCONJ
ejpam-5986	124	13	writing	write	VERB
ejpam-5986	124	14	(	(	PUNCT
ejpam-5986	124	15	1	1	NUM
ejpam-5986	125	1	+	+	X
ejpam-5986	125	2	λ)−	λ)−	ADP
ejpam-5986	125	3	t	t	X
ejpam-5986	125	4	uλ	uλ	NOUN
ejpam-5986	126	1	=	=	PUNCT
ejpam-5986	126	2	e	e	PROPN
ejpam-5986	126	3	−t	−t	PROPN
ejpam-5986	126	4	ln(1+λ	ln(1+λ	ADV
ejpam-5986	126	5	)	)	PUNCT
ejpam-5986	126	6	λu	λu	X
ejpam-5986	126	7	we	we	PRON
ejpam-5986	126	8	obtain	obtain	VERB
ejpam-5986	126	9	g∗	g∗	PROPN
ejpam-5986	126	10	α	α	NOUN
ejpam-5986	126	11	,	,	PUNCT
ejpam-5986	126	12	λ{eat	λ{eat	X
ejpam-5986	126	13	}	}	PUNCT
ejpam-5986	126	14	=	=	PUNCT
ejpam-5986	126	15	uα	uα	PROPN
ejpam-5986	126	16	∫	∫	PROPN
ejpam-5986	126	17	∞	∞	PROPN
ejpam-5986	126	18	0	0	NUM
ejpam-5986	127	1	(	(	PUNCT
ejpam-5986	127	2	1	1	NUM
ejpam-5986	127	3	+	+	X
ejpam-5986	127	4	λ)−	λ)−	ADP
ejpam-5986	127	5	t	t	NOUN
ejpam-5986	127	6	uλ	uλ	DET
ejpam-5986	127	7	eat	eat	NOUN
ejpam-5986	127	8	dt	dt	NOUN
ejpam-5986	127	9	=	=	SYM
ejpam-5986	127	10	uα	uα	PROPN
ejpam-5986	127	11	lim	lim	PROPN
ejpam-5986	128	1	h→∞	h→∞	NUM
ejpam-5986	128	2	∫	∫	PROPN
ejpam-5986	128	3	h	h	NOUN
ejpam-5986	128	4	0	0	NUM
ejpam-5986	128	5	e	e	NOUN
ejpam-5986	128	6	t	t	PROPN
ejpam-5986	128	7	(	(	PUNCT
ejpam-5986	128	8	a−	a−	PROPN
ejpam-5986	128	9	ln(1+λ	ln(1+λ	PROPN
ejpam-5986	128	10	)	)	PUNCT
ejpam-5986	128	11	λu	λu	X
ejpam-5986	128	12	)	)	PUNCT
ejpam-5986	128	13	dt	dt	PROPN
ejpam-5986	129	1	=	=	SYM
ejpam-5986	129	2	lim	lim	PROPN
ejpam-5986	129	3	h→∞	h→∞	NUM
ejpam-5986	129	4	λuα+1	λuα+1	NOUN
ejpam-5986	129	5	aλu−	aλu−	PROPN
ejpam-5986	129	6	ln(1	ln(1	PROPN
ejpam-5986	129	7	+	+	CCONJ
ejpam-5986	129	8	λ	λ	NOUN
ejpam-5986	129	9	)	)	PUNCT
ejpam-5986	129	10	[	[	PUNCT
ejpam-5986	129	11	e	e	NOUN
ejpam-5986	129	12	h	h	PROPN
ejpam-5986	129	13	(	(	PUNCT
ejpam-5986	129	14	a−	a−	PROPN
ejpam-5986	129	15	ln(1+λ	ln(1+λ	PROPN
ejpam-5986	129	16	)	)	PUNCT
ejpam-5986	129	17	λu	λu	X
ejpam-5986	129	18	)	)	PUNCT
ejpam-5986	129	19	−	−	PROPN
ejpam-5986	129	20	1	1	NUM
ejpam-5986	129	21	]	]	PUNCT
ejpam-5986	129	22	=	=	PUNCT
ejpam-5986	129	23	λuα+1	λuα+1	NOUN
ejpam-5986	130	1	ln(1	ln(1	NOUN
ejpam-5986	130	2	+	+	CCONJ
ejpam-5986	130	3	λ)−	λ)−	PROPN
ejpam-5986	130	4	aλu	aλu	NOUN
ejpam-5986	130	5	for	for	ADP
ejpam-5986	130	6	a	a	DET
ejpam-5986	130	7	<	<	X
ejpam-5986	130	8	ln(1+λ	ln(1+λ	PROPN
ejpam-5986	130	9	)	)	PUNCT
ejpam-5986	130	10	λu	λu	X
ejpam-5986	130	11	,	,	PUNCT
ejpam-5986	130	12	and	and	CCONJ
ejpam-5986	130	13	the	the	DET
ejpam-5986	130	14	proof	proof	NOUN
ejpam-5986	130	15	is	be	AUX
ejpam-5986	130	16	completed	complete	VERB
ejpam-5986	130	17	.	.	PUNCT
ejpam-5986	131	1	note	note	VERB
ejpam-5986	131	2	that	that	SCONJ
ejpam-5986	131	3	,	,	PUNCT
ejpam-5986	131	4	from	from	ADP
ejpam-5986	131	5	the	the	DET
ejpam-5986	131	6	theorem	theorem	NOUN
ejpam-5986	131	7	3	3	NUM
ejpam-5986	131	8	we	we	PRON
ejpam-5986	131	9	have	have	VERB
ejpam-5986	131	10	lim	lim	PROPN
ejpam-5986	131	11	λ→0	λ→0	PROPN
ejpam-5986	131	12	g∗	g∗	VERB
ejpam-5986	131	13	α	α	NOUN
ejpam-5986	131	14	,	,	PUNCT
ejpam-5986	131	15	λ{eat	λ{eat	X
ejpam-5986	132	1	}	}	PUNCT
ejpam-5986	132	2	=	=	SYM
ejpam-5986	132	3	lim	lim	PROPN
ejpam-5986	132	4	λ→0	λ→0	PUNCT
ejpam-5986	132	5	λuα+1	λuα+1	NOUN
ejpam-5986	133	1	ln(1	ln(1	PROPN
ejpam-5986	133	2	+	+	CCONJ
ejpam-5986	133	3	λ)−	λ)−	PROPN
ejpam-5986	133	4	aλu	aλu	NOUN
ejpam-5986	133	5	=	=	VERB
ejpam-5986	133	6	uα+1	uα+1	NOUN
ejpam-5986	133	7	1−	1−	NUM
ejpam-5986	133	8	au	au	X
ejpam-5986	133	9	=	=	VERB
ejpam-5986	133	10	gα{eat	gα{eat	NOUN
ejpam-5986	133	11	}	}	PUNCT
ejpam-5986	133	12	.	.	PUNCT
ejpam-5986	134	1	theorem	theorem	NOUN
ejpam-5986	134	2	4	4	NUM
ejpam-5986	134	3	.	.	PUNCT
ejpam-5986	135	1	the	the	DET
ejpam-5986	135	2	modified	modify	VERB
ejpam-5986	135	3	laplace	laplace	NOUN
ejpam-5986	135	4	-	-	PUNCT
ejpam-5986	135	5	type	type	NOUN
ejpam-5986	135	6	transform	transform	NOUN
ejpam-5986	135	7	of	of	ADP
ejpam-5986	135	8	the	the	DET
ejpam-5986	135	9	function	function	NOUN
ejpam-5986	135	10	f(t	f(t	NOUN
ejpam-5986	135	11	)	)	PUNCT
ejpam-5986	136	1	=	=	PUNCT
ejpam-5986	136	2	sin	sin	NOUN
ejpam-5986	136	3	at	at	ADP
ejpam-5986	136	4	is	be	AUX
ejpam-5986	136	5	given	give	VERB
ejpam-5986	136	6	by	by	ADP
ejpam-5986	136	7	g∗	g∗	PROPN
ejpam-5986	136	8	α	α	PROPN
ejpam-5986	136	9	,	,	PUNCT
ejpam-5986	136	10	λ{sin	λ{sin	X
ejpam-5986	136	11	at	at	ADP
ejpam-5986	136	12	}	}	PUNCT
ejpam-5986	136	13	=	=	SYM
ejpam-5986	136	14	aλ2uα+2	aλ2uα+2	PROPN
ejpam-5986	136	15	ln2(1	ln2(1	NOUN
ejpam-5986	136	16	+	+	X
ejpam-5986	136	17	λ	λ	NOUN
ejpam-5986	136	18	)	)	PUNCT
ejpam-5986	136	19	+	+	CCONJ
ejpam-5986	136	20	a2λ2u2	a2λ2u2	PROPN
ejpam-5986	136	21	.	.	PUNCT
ejpam-5986	137	1	(	(	PUNCT
ejpam-5986	137	2	13	13	NUM
ejpam-5986	137	3	)	)	PUNCT
ejpam-5986	137	4	i̇.	i̇.	NOUN
ejpam-5986	137	5	ege	ege	PROPN
ejpam-5986	137	6	/	/	SYM
ejpam-5986	137	7	eur	eur	PROPN
ejpam-5986	137	8	.	.	PUNCT
ejpam-5986	138	1	j.	j.	PROPN
ejpam-5986	138	2	pure	pure	PROPN
ejpam-5986	138	3	appl	appl	PROPN
ejpam-5986	138	4	.	.	PROPN
ejpam-5986	138	5	math	math	PROPN
ejpam-5986	138	6	,	,	PUNCT
ejpam-5986	138	7	18	18	NUM
ejpam-5986	138	8	(	(	PUNCT
ejpam-5986	138	9	2	2	NUM
ejpam-5986	138	10	)	)	PUNCT
ejpam-5986	138	11	(	(	PUNCT
ejpam-5986	138	12	2025	2025	NUM
ejpam-5986	138	13	)	)	PUNCT
ejpam-5986	138	14	,	,	PUNCT
ejpam-5986	138	15	5986	5986	NUM
ejpam-5986	138	16	6	6	NUM
ejpam-5986	138	17	of	of	ADP
ejpam-5986	138	18	20	20	NUM
ejpam-5986	138	19	proof	proof	NOUN
ejpam-5986	138	20	.	.	PUNCT
ejpam-5986	139	1	by	by	ADP
ejpam-5986	139	2	writing	write	VERB
ejpam-5986	139	3	sin	sin	NOUN
ejpam-5986	139	4	at	at	ADP
ejpam-5986	139	5	=	=	SYM
ejpam-5986	139	6	eiat−e−iat	eiat−e−iat	NOUN
ejpam-5986	139	7	2i	2i	NOUN
ejpam-5986	139	8	,	,	PUNCT
ejpam-5986	139	9	we	we	PRON
ejpam-5986	139	10	obtain	obtain	VERB
ejpam-5986	139	11	g∗	g∗	PROPN
ejpam-5986	139	12	α	α	NOUN
ejpam-5986	139	13	,	,	PUNCT
ejpam-5986	139	14	λ{sin	λ{sin	X
ejpam-5986	139	15	at	at	ADP
ejpam-5986	139	16	}	}	PUNCT
ejpam-5986	139	17	=	=	PUNCT
ejpam-5986	139	18	uα	uα	PROPN
ejpam-5986	139	19	∫	∫	PROPN
ejpam-5986	139	20	∞	∞	PROPN
ejpam-5986	139	21	0	0	NUM
ejpam-5986	140	1	(	(	PUNCT
ejpam-5986	140	2	1	1	NUM
ejpam-5986	140	3	+	+	X
ejpam-5986	140	4	λ)−	λ)−	ADP
ejpam-5986	140	5	t	t	PROPN
ejpam-5986	140	6	uλ	uλ	DET
ejpam-5986	140	7	sin	sin	NOUN
ejpam-5986	140	8	at	at	ADP
ejpam-5986	140	9	dt	dt	PROPN
ejpam-5986	140	10	=	=	SYM
ejpam-5986	140	11	uα	uα	PROPN
ejpam-5986	140	12	∫	∫	PROPN
ejpam-5986	140	13	∞	∞	PROPN
ejpam-5986	140	14	0	0	PUNCT
ejpam-5986	140	15	e	e	PROPN
ejpam-5986	140	16	−t	−t	PROPN
ejpam-5986	140	17	ln(1+λ	ln(1+λ	ADV
ejpam-5986	140	18	)	)	PUNCT
ejpam-5986	140	19	λu	λu	X
ejpam-5986	140	20	(	(	PUNCT
ejpam-5986	140	21	eiat	eiat	PROPN
ejpam-5986	140	22	−	−	PROPN
ejpam-5986	140	23	e−iat	e−iat	NOUN
ejpam-5986	140	24	2i	2i	NUM
ejpam-5986	140	25	)	)	PUNCT
ejpam-5986	140	26	dt	dt	X
ejpam-5986	141	1	=	=	PUNCT
ejpam-5986	141	2	uα	uα	PROPN
ejpam-5986	141	3	2i	2i	NUM
ejpam-5986	141	4	lim	lim	PROPN
ejpam-5986	141	5	h→∞	h→∞	NUM
ejpam-5986	141	6	∫	∫	PROPN
ejpam-5986	141	7	h	h	NOUN
ejpam-5986	141	8	0	0	PUNCT
ejpam-5986	142	1	[	[	PUNCT
ejpam-5986	142	2	e	e	X
ejpam-5986	142	3	−t	−t	PROPN
ejpam-5986	142	4	(	(	PUNCT
ejpam-5986	142	5	ln(1+λ	ln(1+λ	PROPN
ejpam-5986	142	6	)	)	PUNCT
ejpam-5986	142	7	λu	λu	X
ejpam-5986	142	8	−ia	−ia	NOUN
ejpam-5986	142	9	)	)	PUNCT
ejpam-5986	142	10	−	−	PROPN
ejpam-5986	142	11	e	e	ADP
ejpam-5986	142	12	−t	−t	PROPN
ejpam-5986	142	13	(	(	PUNCT
ejpam-5986	142	14	ia+	ia+	PROPN
ejpam-5986	142	15	ln(1+λ	ln(1+λ	PROPN
ejpam-5986	142	16	)	)	PUNCT
ejpam-5986	142	17	λu	λu	PROPN
ejpam-5986	142	18	)	)	PUNCT
ejpam-5986	142	19	]	]	PUNCT
ejpam-5986	143	1	dt	dt	X
ejpam-5986	143	2	=	=	PUNCT
ejpam-5986	143	3	uα	uα	PROPN
ejpam-5986	143	4	2i	2i	NUM
ejpam-5986	143	5	lim	lim	PROPN
ejpam-5986	143	6	h→∞	h→∞	PROPN
ejpam-5986	143	7	[	[	PUNCT
ejpam-5986	143	8	λu	λu	AUX
ejpam-5986	143	9	iaλu−	iaλu−	NOUN
ejpam-5986	143	10	ln(1	ln(1	PROPN
ejpam-5986	143	11	+	+	CCONJ
ejpam-5986	143	12	λ	λ	NOUN
ejpam-5986	143	13	)	)	PUNCT
ejpam-5986	143	14	e	e	NOUN
ejpam-5986	143	15	−h	−h	ADV
ejpam-5986	143	16	(	(	PUNCT
ejpam-5986	143	17	ln(1+λ	ln(1+λ	PROPN
ejpam-5986	143	18	)	)	PUNCT
ejpam-5986	143	19	λu	λu	X
ejpam-5986	143	20	−ia	−ia	PROPN
ejpam-5986	143	21	)	)	PUNCT
ejpam-5986	144	1	+	+	CCONJ
ejpam-5986	144	2	λu	λu	X
ejpam-5986	145	1	ln(1	ln(1	NOUN
ejpam-5986	145	2	+	+	PROPN
ejpam-5986	145	3	λ)−	λ)−	PROPN
ejpam-5986	145	4	iaλu	iaλu	NOUN
ejpam-5986	145	5	]	]	PUNCT
ejpam-5986	145	6	−uα	−uα	DET
ejpam-5986	145	7	2i	2i	PROPN
ejpam-5986	145	8	lim	lim	PROPN
ejpam-5986	145	9	h→∞	h→∞	PROPN
ejpam-5986	145	10	[	[	PUNCT
ejpam-5986	145	11	−λu	−λu	NUM
ejpam-5986	145	12	iaλu+	iaλu+	NOUN
ejpam-5986	145	13	ln(1	ln(1	PROPN
ejpam-5986	145	14	+	+	CCONJ
ejpam-5986	145	15	λ	λ	NOUN
ejpam-5986	145	16	)	)	PUNCT
ejpam-5986	145	17	e	e	NOUN
ejpam-5986	145	18	−h	−h	ADV
ejpam-5986	145	19	(	(	PUNCT
ejpam-5986	145	20	ia+	ia+	PROPN
ejpam-5986	145	21	ln(1+λ	ln(1+λ	NOUN
ejpam-5986	145	22	)	)	PUNCT
ejpam-5986	145	23	λu	λu	X
ejpam-5986	145	24	)	)	PUNCT
ejpam-5986	146	1	+	+	CCONJ
ejpam-5986	146	2	λu	λu	X
ejpam-5986	146	3	ln(1	ln(1	NOUN
ejpam-5986	146	4	+	+	NUM
ejpam-5986	146	5	λ	λ	NOUN
ejpam-5986	146	6	)	)	PUNCT
ejpam-5986	146	7	+	+	CCONJ
ejpam-5986	146	8	iaλu	iaλu	NOUN
ejpam-5986	146	9	]	]	X
ejpam-5986	146	10	=	=	SYM
ejpam-5986	146	11	λuα+1	λuα+1	NOUN
ejpam-5986	146	12	2i	2i	VERB
ejpam-5986	146	13	[	[	PUNCT
ejpam-5986	146	14	1	1	NUM
ejpam-5986	146	15	ln(1	ln(1	PROPN
ejpam-5986	146	16	+	+	PROPN
ejpam-5986	146	17	λ)−	λ)−	PROPN
ejpam-5986	146	18	iaλu	iaλu	NOUN
ejpam-5986	146	19	−	−	PROPN
ejpam-5986	146	20	1	1	NUM
ejpam-5986	147	1	ln(1	ln(1	PROPN
ejpam-5986	147	2	+	+	NUM
ejpam-5986	147	3	λ	λ	NOUN
ejpam-5986	147	4	)	)	PUNCT
ejpam-5986	147	5	+	+	CCONJ
ejpam-5986	147	6	iaλu	iaλu	X
ejpam-5986	147	7	]	]	X
ejpam-5986	147	8	=	=	SYM
ejpam-5986	148	1	aλ2uα+2	aλ2uα+2	NUM
ejpam-5986	148	2	ln2(1	ln2(1	NOUN
ejpam-5986	148	3	+	+	X
ejpam-5986	148	4	λ	λ	NOUN
ejpam-5986	148	5	)	)	PUNCT
ejpam-5986	148	6	+	+	CCONJ
ejpam-5986	148	7	a2λ2u2	a2λ2u2	PROPN
ejpam-5986	148	8	for	for	ADP
ejpam-5986	148	9	ia−	ia−	PROPN
ejpam-5986	148	10	ln(1+λ	ln(1+λ	PRON
ejpam-5986	148	11	)	)	PUNCT
ejpam-5986	149	1	λu	λu	X
ejpam-5986	149	2	<	<	X
ejpam-5986	149	3	0	0	NUM
ejpam-5986	150	1	and	and	CCONJ
ejpam-5986	150	2	ia+	ia+	NOUN
ejpam-5986	150	3	ln(1+λ	ln(1+λ	PROPN
ejpam-5986	150	4	)	)	PUNCT
ejpam-5986	151	1	λu	λu	X
ejpam-5986	151	2	>	>	X
ejpam-5986	151	3	0	0	X
ejpam-5986	151	4	.	.	PUNCT
ejpam-5986	152	1	also	also	ADV
ejpam-5986	152	2	since	since	SCONJ
ejpam-5986	152	3	ln(1+λ	ln(1+λ	PROPN
ejpam-5986	152	4	)	)	PUNCT
ejpam-5986	152	5	λ	λ	X
ejpam-5986	152	6	>	>	X
ejpam-5986	152	7	0	0	NUM
ejpam-5986	152	8	,	,	PUNCT
ejpam-5986	152	9	we	we	PRON
ejpam-5986	152	10	get	get	VERB
ejpam-5986	152	11	the	the	DET
ejpam-5986	152	12	result	result	NOUN
ejpam-5986	152	13	.	.	PUNCT
ejpam-5986	153	1	note	note	VERB
ejpam-5986	153	2	that	that	SCONJ
ejpam-5986	153	3	,	,	PUNCT
ejpam-5986	153	4	from	from	ADP
ejpam-5986	153	5	the	the	DET
ejpam-5986	153	6	theorem	theorem	NOUN
ejpam-5986	153	7	4	4	NUM
ejpam-5986	153	8	we	we	PRON
ejpam-5986	153	9	have	have	VERB
ejpam-5986	153	10	lim	lim	PROPN
ejpam-5986	153	11	λ→0	λ→0	PROPN
ejpam-5986	153	12	g∗	g∗	VERB
ejpam-5986	153	13	α	α	NOUN
ejpam-5986	153	14	,	,	PUNCT
ejpam-5986	153	15	λ{sin	λ{sin	X
ejpam-5986	153	16	at	at	ADP
ejpam-5986	153	17	}	}	PUNCT
ejpam-5986	153	18	=	=	SYM
ejpam-5986	153	19	lim	lim	PROPN
ejpam-5986	153	20	λ→0	λ→0	PROPN
ejpam-5986	153	21	=	=	PUNCT
ejpam-5986	153	22	aλ2uα+2	aλ2uα+2	PROPN
ejpam-5986	153	23	ln2(1	ln2(1	NOUN
ejpam-5986	153	24	+	+	X
ejpam-5986	153	25	λ	λ	NOUN
ejpam-5986	153	26	)	)	PUNCT
ejpam-5986	154	1	+	+	NUM
ejpam-5986	154	2	a2λ2u2	a2λ2u2	PROPN
ejpam-5986	154	3	=	=	SYM
ejpam-5986	154	4	auα+2	auα+2	ADJ
ejpam-5986	154	5	1	1	NUM
ejpam-5986	154	6	+	+	CCONJ
ejpam-5986	154	7	a2u2	a2u2	PROPN
ejpam-5986	154	8	=	=	PUNCT
ejpam-5986	154	9	gα{sin	gα{sin	NOUN
ejpam-5986	154	10	at	at	ADP
ejpam-5986	154	11	}	}	PUNCT
ejpam-5986	154	12	.	.	PUNCT
ejpam-5986	155	1	now	now	ADV
ejpam-5986	155	2	,	,	PUNCT
ejpam-5986	155	3	we	we	PRON
ejpam-5986	155	4	give	give	VERB
ejpam-5986	155	5	the	the	DET
ejpam-5986	155	6	transform	transform	NOUN
ejpam-5986	155	7	of	of	ADP
ejpam-5986	155	8	the	the	DET
ejpam-5986	155	9	mathematical	mathematical	ADJ
ejpam-5986	155	10	construct	construct	PROPN
ejpam-5986	155	11	dirac	dirac	PROPN
ejpam-5986	155	12	’s	’s	PART
ejpam-5986	155	13	delta	delta	NOUN
ejpam-5986	155	14	function	function	NOUN
ejpam-5986	155	15	δ	δ	PROPN
ejpam-5986	155	16	defined	define	VERB
ejpam-5986	155	17	as	as	ADP
ejpam-5986	155	18	δ(t	δ(t	NOUN
ejpam-5986	155	19	)	)	PUNCT
ejpam-5986	155	20	=	=	PUNCT
ejpam-5986	155	21	{	{	PUNCT
ejpam-5986	155	22	+	+	NOUN
ejpam-5986	155	23	∞	∞	PROPN
ejpam-5986	155	24	,	,	PUNCT
ejpam-5986	155	25	t	t	NOUN
ejpam-5986	156	1	=	=	SYM
ejpam-5986	156	2	0	0	NUM
ejpam-5986	156	3	0	0	NUM
ejpam-5986	156	4	,	,	PUNCT
ejpam-5986	156	5	otherwise	otherwise	ADV
ejpam-5986	156	6	,	,	PUNCT
ejpam-5986	156	7	∫	∫	PROPN
ejpam-5986	156	8	∞	∞	PROPN
ejpam-5986	156	9	−∞	−∞	ADP
ejpam-5986	156	10	δ(t	δ(t	PROPN
ejpam-5986	156	11	)	)	PUNCT
ejpam-5986	156	12	dt	dt	NOUN
ejpam-5986	157	1	=	=	SYM
ejpam-5986	157	2	1	1	X
ejpam-5986	157	3	.	.	PUNCT
ejpam-5986	157	4	theorem	theorem	NOUN
ejpam-5986	157	5	5	5	NUM
ejpam-5986	157	6	.	.	PUNCT
ejpam-5986	158	1	the	the	DET
ejpam-5986	158	2	modified	modify	VERB
ejpam-5986	158	3	laplace	laplace	NOUN
ejpam-5986	158	4	-	-	PUNCT
ejpam-5986	158	5	type	type	NOUN
ejpam-5986	158	6	transform	transform	NOUN
ejpam-5986	158	7	of	of	ADP
ejpam-5986	158	8	the	the	DET
ejpam-5986	158	9	dirac	dirac	NOUN
ejpam-5986	158	10	’s	’s	PART
ejpam-5986	158	11	delta	delta	NOUN
ejpam-5986	158	12	function	function	NOUN
ejpam-5986	158	13	is	be	AUX
ejpam-5986	158	14	g∗	g∗	NOUN
ejpam-5986	158	15	α	α	NOUN
ejpam-5986	158	16	,	,	PUNCT
ejpam-5986	158	17	λ{δ(t−	λ{δ(t−	NOUN
ejpam-5986	158	18	a	a	NOUN
ejpam-5986	158	19	)	)	PUNCT
ejpam-5986	158	20	}	}	PUNCT
ejpam-5986	158	21	=	=	PUNCT
ejpam-5986	158	22	uα(1	uα(1	PROPN
ejpam-5986	159	1	+	+	CCONJ
ejpam-5986	159	2	λ)−	λ)−	ADP
ejpam-5986	159	3	a	a	DET
ejpam-5986	159	4	λu	λu	X
ejpam-5986	159	5	,	,	PUNCT
ejpam-5986	159	6	a	a	DET
ejpam-5986	159	7	≥	≥	NOUN
ejpam-5986	159	8	0	0	NUM
ejpam-5986	159	9	.	.	PUNCT
ejpam-5986	160	1	proof	proof	NOUN
ejpam-5986	160	2	.	.	PUNCT
ejpam-5986	161	1	let	let	VERB
ejpam-5986	161	2	fh(t−	fh(t−	PROPN
ejpam-5986	161	3	a	a	X
ejpam-5986	161	4	)	)	PUNCT
ejpam-5986	161	5	=	=	SYM
ejpam-5986	161	6	{	{	PUNCT
ejpam-5986	161	7	1	1	NUM
ejpam-5986	161	8	h	h	NOUN
ejpam-5986	161	9	,	,	PUNCT
ejpam-5986	161	10	a	a	DET
ejpam-5986	161	11	≤	≤	NUM
ejpam-5986	161	12	t	t	NOUN
ejpam-5986	161	13	≤	≤	NUM
ejpam-5986	161	14	a+	a+	PUNCT
ejpam-5986	161	15	h	h	NOUN
ejpam-5986	161	16	0	0	NUM
ejpam-5986	161	17	,	,	PUNCT
ejpam-5986	161	18	otherwise	otherwise	ADV
ejpam-5986	161	19	.	.	PUNCT
ejpam-5986	162	1	then	then	ADV
ejpam-5986	162	2	we	we	PRON
ejpam-5986	162	3	have	have	VERB
ejpam-5986	162	4	,	,	PUNCT
ejpam-5986	162	5	g∗	g∗	VERB
ejpam-5986	162	6	α	α	NOUN
ejpam-5986	162	7	,	,	PUNCT
ejpam-5986	162	8	λ{fh(t−	λ{fh(t−	PROPN
ejpam-5986	162	9	a	a	NOUN
ejpam-5986	162	10	)	)	PUNCT
ejpam-5986	162	11	}	}	PUNCT
ejpam-5986	162	12	=	=	PUNCT
ejpam-5986	163	1	uα	uα	PROPN
ejpam-5986	163	2	∫	∫	PROPN
ejpam-5986	163	3	∞	∞	PROPN
ejpam-5986	163	4	0	0	NUM
ejpam-5986	164	1	(	(	PUNCT
ejpam-5986	164	2	1	1	NUM
ejpam-5986	164	3	+	+	X
ejpam-5986	164	4	λ)−	λ)−	ADP
ejpam-5986	164	5	t	t	X
ejpam-5986	164	6	uλ	uλ	X
ejpam-5986	164	7	fh(t−	fh(t−	PROPN
ejpam-5986	164	8	a	a	X
ejpam-5986	164	9	)	)	PUNCT
ejpam-5986	164	10	dt	dt	NOUN
ejpam-5986	165	1	=	=	SYM
ejpam-5986	165	2	uα	uα	PROPN
ejpam-5986	165	3	h	h	NOUN
ejpam-5986	165	4	∫	∫	PROPN
ejpam-5986	165	5	a+h	a+h	X
ejpam-5986	165	6	a	a	DET
ejpam-5986	165	7	(	(	PUNCT
ejpam-5986	165	8	1	1	NUM
ejpam-5986	165	9	+	+	X
ejpam-5986	165	10	λ)−	λ)−	ADP
ejpam-5986	165	11	t	t	X
ejpam-5986	165	12	uλ	uλ	X
ejpam-5986	165	13	dt	dt	NOUN
ejpam-5986	166	1	=	=	SYM
ejpam-5986	166	2	−	−	PROPN
ejpam-5986	166	3	λuα+1	λuα+1	NOUN
ejpam-5986	166	4	ln(1	ln(1	PROPN
ejpam-5986	166	5	+	+	NUM
ejpam-5986	166	6	λ)h	λ)h	X
ejpam-5986	166	7	(	(	PUNCT
ejpam-5986	166	8	1	1	NUM
ejpam-5986	166	9	+	+	X
ejpam-5986	167	1	λ)−	λ)−	ADP
ejpam-5986	167	2	a	a	DET
ejpam-5986	167	3	uλ	uλ	X
ejpam-5986	167	4	[	[	PUNCT
ejpam-5986	167	5	(	(	PUNCT
ejpam-5986	167	6	1	1	NUM
ejpam-5986	167	7	+	+	X
ejpam-5986	167	8	λ)−	λ)−	ADP
ejpam-5986	167	9	h	h	NOUN
ejpam-5986	167	10	uλ	uλ	PRON
ejpam-5986	167	11	−	−	PROPN
ejpam-5986	167	12	1	1	NUM
ejpam-5986	167	13	]	]	PUNCT
ejpam-5986	167	14	.	.	PUNCT
ejpam-5986	168	1	since	since	SCONJ
ejpam-5986	168	2	δ(t−	δ(t−	PROPN
ejpam-5986	168	3	a	a	PRON
ejpam-5986	168	4	)	)	PUNCT
ejpam-5986	168	5	is	be	AUX
ejpam-5986	168	6	the	the	DET
ejpam-5986	168	7	limit	limit	NOUN
ejpam-5986	168	8	of	of	ADP
ejpam-5986	168	9	fh	fh	PROPN
ejpam-5986	168	10	as	as	ADP
ejpam-5986	168	11	h	h	PROPN
ejpam-5986	168	12	→	→	SYM
ejpam-5986	168	13	0	0	NUM
ejpam-5986	168	14	we	we	PRON
ejpam-5986	168	15	get	get	VERB
ejpam-5986	168	16	g∗	g∗	NOUN
ejpam-5986	168	17	α	α	NOUN
ejpam-5986	168	18	,	,	PUNCT
ejpam-5986	168	19	λ{δ(t−	λ{δ(t−	NOUN
ejpam-5986	168	20	a	a	NOUN
ejpam-5986	168	21	)	)	PUNCT
ejpam-5986	168	22	}	}	PUNCT
ejpam-5986	169	1	=	=	SYM
ejpam-5986	169	2	lim	lim	PROPN
ejpam-5986	169	3	h→0	h→0	ADV
ejpam-5986	169	4	g∗	g∗	VERB
ejpam-5986	169	5	α	α	NOUN
ejpam-5986	169	6	,	,	PUNCT
ejpam-5986	169	7	λ{fh(t−	λ{fh(t−	PROPN
ejpam-5986	169	8	a	a	NOUN
ejpam-5986	169	9	)	)	PUNCT
ejpam-5986	169	10	}	}	PUNCT
ejpam-5986	170	1	=	=	PUNCT
ejpam-5986	170	2	uα(1	uα(1	PROPN
ejpam-5986	170	3	+	+	CCONJ
ejpam-5986	171	1	λ)−	λ)−	ADP
ejpam-5986	171	2	a	a	DET
ejpam-5986	171	3	λu	λu	X
ejpam-5986	171	4	by	by	ADP
ejpam-5986	171	5	l’hospital	l’hospital	ADJ
ejpam-5986	171	6	rule	rule	NOUN
ejpam-5986	171	7	,	,	PUNCT
ejpam-5986	171	8	and	and	CCONJ
ejpam-5986	171	9	the	the	DET
ejpam-5986	171	10	result	result	NOUN
ejpam-5986	171	11	follows	follow	VERB
ejpam-5986	171	12	.	.	PUNCT
ejpam-5986	172	1	note	note	VERB
ejpam-5986	172	2	that	that	SCONJ
ejpam-5986	172	3	,	,	PUNCT
ejpam-5986	172	4	from	from	ADP
ejpam-5986	172	5	the	the	DET
ejpam-5986	172	6	theorem	theorem	NOUN
ejpam-5986	172	7	5	5	NUM
ejpam-5986	172	8	we	we	PRON
ejpam-5986	172	9	have	have	VERB
ejpam-5986	172	10	lim	lim	PROPN
ejpam-5986	172	11	λ→0	λ→0	PROPN
ejpam-5986	172	12	g∗	g∗	VERB
ejpam-5986	172	13	α	α	NOUN
ejpam-5986	172	14	,	,	PUNCT
ejpam-5986	172	15	λ{δ(t−	λ{δ(t−	NOUN
ejpam-5986	172	16	a	a	NOUN
ejpam-5986	172	17	)	)	PUNCT
ejpam-5986	172	18	}	}	PUNCT
ejpam-5986	173	1	=	=	SYM
ejpam-5986	173	2	lim	lim	PROPN
ejpam-5986	173	3	λ→0	λ→0	PUNCT
ejpam-5986	173	4	uα(1	uα(1	PROPN
ejpam-5986	174	1	+	+	CCONJ
ejpam-5986	175	1	λ)−	λ)−	ADP
ejpam-5986	175	2	a	a	PRON
ejpam-5986	175	3	λu	λu	X
ejpam-5986	175	4	=	=	SYM
ejpam-5986	175	5	uαe−	uαe−	PROPN
ejpam-5986	175	6	a	a	DET
ejpam-5986	175	7	u	u	NOUN
ejpam-5986	175	8	=	=	X
ejpam-5986	175	9	gα{δ(t−	gα{δ(t−	PROPN
ejpam-5986	175	10	a	a	NOUN
ejpam-5986	175	11	)	)	PUNCT
ejpam-5986	175	12	}	}	PUNCT
ejpam-5986	175	13	.	.	PUNCT
ejpam-5986	176	1	i̇.	i̇.	PROPN
ejpam-5986	176	2	ege	ege	PROPN
ejpam-5986	176	3	/	/	SYM
ejpam-5986	176	4	eur	eur	PROPN
ejpam-5986	176	5	.	.	PUNCT
ejpam-5986	177	1	j.	j.	PROPN
ejpam-5986	177	2	pure	pure	PROPN
ejpam-5986	177	3	appl	appl	PROPN
ejpam-5986	177	4	.	.	PROPN
ejpam-5986	177	5	math	math	PROPN
ejpam-5986	177	6	,	,	PUNCT
ejpam-5986	177	7	18	18	NUM
ejpam-5986	177	8	(	(	PUNCT
ejpam-5986	177	9	2	2	NUM
ejpam-5986	177	10	)	)	PUNCT
ejpam-5986	177	11	(	(	PUNCT
ejpam-5986	177	12	2025	2025	NUM
ejpam-5986	177	13	)	)	PUNCT
ejpam-5986	177	14	,	,	PUNCT
ejpam-5986	177	15	5986	5986	NUM
ejpam-5986	177	16	7	7	NUM
ejpam-5986	177	17	of	of	ADP
ejpam-5986	177	18	20	20	NUM
ejpam-5986	177	19	3	3	NUM
ejpam-5986	177	20	.	.	PUNCT
ejpam-5986	178	1	some	some	DET
ejpam-5986	178	2	operational	operational	ADJ
ejpam-5986	178	3	properties	property	NOUN
ejpam-5986	178	4	in	in	ADP
ejpam-5986	178	5	this	this	DET
ejpam-5986	178	6	section	section	NOUN
ejpam-5986	178	7	,	,	PUNCT
ejpam-5986	178	8	we	we	PRON
ejpam-5986	178	9	present	present	VERB
ejpam-5986	178	10	some	some	DET
ejpam-5986	178	11	useful	useful	ADJ
ejpam-5986	178	12	operational	operational	ADJ
ejpam-5986	178	13	properties	property	NOUN
ejpam-5986	178	14	of	of	ADP
ejpam-5986	178	15	the	the	DET
ejpam-5986	178	16	modified	modify	VERB
ejpam-5986	178	17	laplacetype	laplacetype	NOUN
ejpam-5986	178	18	transform	transform	NOUN
ejpam-5986	178	19	.	.	PUNCT
ejpam-5986	179	1	firstly	firstly	ADV
ejpam-5986	179	2	,	,	PUNCT
ejpam-5986	179	3	the	the	DET
ejpam-5986	179	4	modified	modify	VERB
ejpam-5986	179	5	laplace	laplace	NOUN
ejpam-5986	179	6	-	-	PUNCT
ejpam-5986	179	7	type	type	NOUN
ejpam-5986	179	8	transform	transform	NOUN
ejpam-5986	179	9	satisfies	satisfy	VERB
ejpam-5986	179	10	the	the	DET
ejpam-5986	179	11	following	follow	VERB
ejpam-5986	179	12	linearity	linearity	NOUN
ejpam-5986	179	13	property	property	NOUN
ejpam-5986	179	14	.	.	PUNCT
ejpam-5986	180	1	theorem	theorem	VERB
ejpam-5986	180	2	6	6	NUM
ejpam-5986	180	3	.	.	PUNCT
ejpam-5986	181	1	(	(	PUNCT
ejpam-5986	181	2	linearity	linearity	NOUN
ejpam-5986	181	3	)	)	PUNCT
ejpam-5986	181	4	let	let	VERB
ejpam-5986	181	5	i	i	PRON
ejpam-5986	181	6	=	=	NOUN
ejpam-5986	181	7	1	1	NUM
ejpam-5986	181	8	,	,	PUNCT
ejpam-5986	181	9	2	2	NUM
ejpam-5986	181	10	,	,	PUNCT
ejpam-5986	181	11	.	.	PUNCT
ejpam-5986	181	12	.	.	PUNCT
ejpam-5986	181	13	.	.	PUNCT
ejpam-5986	182	1	n.	n.	PROPN
ejpam-5986	183	1	if	if	SCONJ
ejpam-5986	183	2	fi(t	fi(t	NOUN
ejpam-5986	183	3	)	)	PUNCT
ejpam-5986	183	4	is	be	AUX
ejpam-5986	183	5	a	a	DET
ejpam-5986	183	6	function	function	NOUN
ejpam-5986	183	7	whose	whose	DET
ejpam-5986	183	8	modified	modify	VERB
ejpam-5986	183	9	laplacetype	laplacetype	NOUN
ejpam-5986	183	10	integral	integral	ADJ
ejpam-5986	183	11	transform	transform	NOUN
ejpam-5986	183	12	exists	exist	VERB
ejpam-5986	183	13	,	,	PUNCT
ejpam-5986	183	14	then	then	ADV
ejpam-5986	183	15	for	for	ADP
ejpam-5986	183	16	any	any	DET
ejpam-5986	183	17	constant	constant	ADJ
ejpam-5986	183	18	αi	αi	NOUN
ejpam-5986	183	19	we	we	PRON
ejpam-5986	183	20	have	have	AUX
ejpam-5986	183	21	g∗	g∗	PROPN
ejpam-5986	183	22	α	α	PRON
ejpam-5986	183	23	,	,	PUNCT
ejpam-5986	183	24	λ	λ	PROPN
ejpam-5986	183	25	{	{	PUNCT
ejpam-5986	183	26	n∑	n∑	NOUN
ejpam-5986	183	27	i=1	i=1	PROPN
ejpam-5986	183	28	αifi(t	αifi(t	NOUN
ejpam-5986	183	29	)	)	PUNCT
ejpam-5986	183	30	}	}	PUNCT
ejpam-5986	184	1	=	=	PUNCT
ejpam-5986	184	2	n∑	n∑	PROPN
ejpam-5986	184	3	i=1	i=1	PROPN
ejpam-5986	184	4	αig	αig	NOUN
ejpam-5986	184	5	∗	∗	NOUN
ejpam-5986	184	6	α	α	NOUN
ejpam-5986	184	7	,	,	PUNCT
ejpam-5986	184	8	λ{fi(t	λ{fi(t	NOUN
ejpam-5986	184	9	)	)	PUNCT
ejpam-5986	184	10	}	}	PUNCT
ejpam-5986	184	11	.	.	PUNCT
ejpam-5986	185	1	(	(	PUNCT
ejpam-5986	185	2	14	14	X
ejpam-5986	185	3	)	)	PUNCT
ejpam-5986	185	4	proof	proof	NOUN
ejpam-5986	185	5	.	.	PUNCT
ejpam-5986	186	1	let	let	VERB
ejpam-5986	186	2	fi(t	fi(t	NOUN
ejpam-5986	186	3	)	)	PUNCT
ejpam-5986	186	4	be	be	AUX
ejpam-5986	186	5	any	any	DET
ejpam-5986	186	6	function	function	NOUN
ejpam-5986	186	7	whose	whose	DET
ejpam-5986	186	8	modified	modify	VERB
ejpam-5986	186	9	laplace	laplace	NOUN
ejpam-5986	186	10	-	-	PUNCT
ejpam-5986	186	11	type	type	NOUN
ejpam-5986	186	12	integral	integral	ADJ
ejpam-5986	186	13	transform	transform	NOUN
ejpam-5986	186	14	exists	exist	VERB
ejpam-5986	186	15	for	for	ADP
ejpam-5986	186	16	i	i	PROPN
ejpam-5986	186	17	=	=	SYM
ejpam-5986	186	18	1	1	NUM
ejpam-5986	186	19	,	,	PUNCT
ejpam-5986	186	20	2	2	NUM
ejpam-5986	186	21	,	,	PUNCT
ejpam-5986	186	22	.	.	PUNCT
ejpam-5986	186	23	.	.	PUNCT
ejpam-5986	186	24	.	.	PUNCT
ejpam-5986	187	1	n.	n.	PROPN
ejpam-5986	187	2	then	then	ADV
ejpam-5986	187	3	g∗	g∗	VERB
ejpam-5986	187	4	α	α	PRON
ejpam-5986	187	5	,	,	PUNCT
ejpam-5986	187	6	λ	λ	PROPN
ejpam-5986	187	7	{	{	PUNCT
ejpam-5986	187	8	n∑	n∑	NOUN
ejpam-5986	187	9	i=1	i=1	PROPN
ejpam-5986	187	10	αifi(t	αifi(t	NOUN
ejpam-5986	187	11	)	)	PUNCT
ejpam-5986	187	12	}	}	PUNCT
ejpam-5986	188	1	=	=	PUNCT
ejpam-5986	188	2	uα	uα	PROPN
ejpam-5986	188	3	∫	∫	PROPN
ejpam-5986	188	4	∞	∞	PROPN
ejpam-5986	188	5	0	0	PUNCT
ejpam-5986	189	1	[	[	PUNCT
ejpam-5986	189	2	(	(	PUNCT
ejpam-5986	189	3	1	1	NUM
ejpam-5986	189	4	+	+	X
ejpam-5986	189	5	λ)−	λ)−	ADP
ejpam-5986	189	6	t	t	X
ejpam-5986	189	7	uλ	uλ	INTJ
ejpam-5986	190	1	n∑	n∑	PROPN
ejpam-5986	190	2	i=1	i=1	PROPN
ejpam-5986	191	1	αifi(t	αifi(t	PROPN
ejpam-5986	191	2	)	)	PUNCT
ejpam-5986	191	3	]	]	PUNCT
ejpam-5986	192	1	dt	dt	PROPN
ejpam-5986	193	1	=	=	PUNCT
ejpam-5986	193	2	n∑	n∑	PROPN
ejpam-5986	193	3	i=1	i=1	PROPN
ejpam-5986	193	4	αiu	αiu	ADP
ejpam-5986	193	5	α	α	DET
ejpam-5986	193	6	∫	∫	PROPN
ejpam-5986	193	7	∞	∞	NOUN
ejpam-5986	193	8	0	0	NUM
ejpam-5986	194	1	(	(	PUNCT
ejpam-5986	194	2	1	1	NUM
ejpam-5986	194	3	+	+	X
ejpam-5986	194	4	λ)−	λ)−	ADP
ejpam-5986	194	5	t	t	PROPN
ejpam-5986	194	6	uλ	uλ	ADP
ejpam-5986	194	7	fi(t	fi(t	NOUN
ejpam-5986	194	8	)	)	PUNCT
ejpam-5986	195	1	dt	dt	NOUN
ejpam-5986	196	1	=	=	SYM
ejpam-5986	196	2	n∑	n∑	PROPN
ejpam-5986	196	3	i=1	i=1	PROPN
ejpam-5986	196	4	αig	αig	NOUN
ejpam-5986	196	5	∗	∗	NOUN
ejpam-5986	196	6	α	α	NOUN
ejpam-5986	196	7	,	,	PUNCT
ejpam-5986	196	8	λ{fi(t	λ{fi(t	NOUN
ejpam-5986	196	9	)	)	PUNCT
ejpam-5986	196	10	}	}	PUNCT
ejpam-5986	196	11	,	,	PUNCT
ejpam-5986	196	12	and	and	CCONJ
ejpam-5986	196	13	the	the	DET
ejpam-5986	196	14	result	result	NOUN
ejpam-5986	196	15	follows	follow	VERB
ejpam-5986	196	16	.	.	PUNCT
ejpam-5986	197	1	theorem	theorem	ADJ
ejpam-5986	197	2	7	7	NUM
ejpam-5986	197	3	.	.	PUNCT
ejpam-5986	198	1	the	the	DET
ejpam-5986	198	2	modified	modify	VERB
ejpam-5986	198	3	laplace	laplace	NOUN
ejpam-5986	198	4	-	-	PUNCT
ejpam-5986	198	5	type	type	NOUN
ejpam-5986	198	6	transform	transform	NOUN
ejpam-5986	198	7	of	of	ADP
ejpam-5986	198	8	the	the	DET
ejpam-5986	198	9	function	function	NOUN
ejpam-5986	198	10	f(t	f(t	PROPN
ejpam-5986	198	11	)	)	PUNCT
ejpam-5986	198	12	=	=	VERB
ejpam-5986	198	13	sinh	sinh	NOUN
ejpam-5986	198	14	at	at	ADP
ejpam-5986	198	15	is	be	AUX
ejpam-5986	198	16	given	give	VERB
ejpam-5986	198	17	by	by	ADP
ejpam-5986	198	18	g∗	g∗	PROPN
ejpam-5986	198	19	α	α	PROPN
ejpam-5986	198	20	,	,	PUNCT
ejpam-5986	198	21	λ{sinh	λ{sinh	X
ejpam-5986	198	22	at	at	ADP
ejpam-5986	198	23	}	}	PUNCT
ejpam-5986	198	24	=	=	SYM
ejpam-5986	198	25	aλ2uα+2	aλ2uα+2	PROPN
ejpam-5986	198	26	ln2(1	ln2(1	NOUN
ejpam-5986	199	1	+	+	CCONJ
ejpam-5986	199	2	λ)−	λ)−	ADP
ejpam-5986	199	3	a2λ2u2	a2λ2u2	PROPN
ejpam-5986	199	4	for	for	ADP
ejpam-5986	199	5	u	u	NOUN
ejpam-5986	199	6	<	<	X
ejpam-5986	199	7	ln(1	ln(1	PROPN
ejpam-5986	199	8	+	+	CCONJ
ejpam-5986	199	9	λ	λ	NOUN
ejpam-5986	199	10	)	)	PUNCT
ejpam-5986	199	11	aλ	aλ	ADP
ejpam-5986	199	12	.	.	PUNCT
ejpam-5986	200	1	proof	proof	NOUN
ejpam-5986	200	2	.	.	PUNCT
ejpam-5986	201	1	by	by	ADP
ejpam-5986	201	2	using	use	VERB
ejpam-5986	201	3	the	the	DET
ejpam-5986	201	4	equation	equation	NOUN
ejpam-5986	201	5	sinh	sinh	NOUN
ejpam-5986	201	6	at	at	ADP
ejpam-5986	201	7	=	=	PUNCT
ejpam-5986	201	8	eat	eat	VERB
ejpam-5986	201	9	−	−	PROPN
ejpam-5986	201	10	e−at	e−at	PROPN
ejpam-5986	201	11	2	2	NUM
ejpam-5986	201	12	and	and	CCONJ
ejpam-5986	201	13	the	the	DET
ejpam-5986	201	14	linearity	linearity	NOUN
ejpam-5986	201	15	properity	properity	NOUN
ejpam-5986	201	16	(	(	PUNCT
ejpam-5986	201	17	14	14	NUM
ejpam-5986	201	18	)	)	PUNCT
ejpam-5986	201	19	we	we	PRON
ejpam-5986	201	20	get	get	VERB
ejpam-5986	201	21	g∗	g∗	PROPN
ejpam-5986	201	22	α	α	PRON
ejpam-5986	201	23	,	,	PUNCT
ejpam-5986	201	24	λ{sinh	λ{sinh	X
ejpam-5986	201	25	at	at	ADP
ejpam-5986	201	26	}	}	PUNCT
ejpam-5986	201	27	=	=	SYM
ejpam-5986	201	28	1	1	NUM
ejpam-5986	201	29	2	2	NUM
ejpam-5986	201	30	[	[	PUNCT
ejpam-5986	201	31	g∗	g∗	VERB
ejpam-5986	201	32	α	α	NOUN
ejpam-5986	201	33	,	,	PUNCT
ejpam-5986	201	34	λ{eat	λ{eat	NUM
ejpam-5986	201	35	}	}	PUNCT
ejpam-5986	201	36	−g∗	−g∗	PROPN
ejpam-5986	201	37	α	α	NOUN
ejpam-5986	201	38	,	,	PUNCT
ejpam-5986	201	39	λ{e−at	λ{e−at	PROPN
ejpam-5986	201	40	}	}	PUNCT
ejpam-5986	201	41	]	]	PUNCT
ejpam-5986	201	42	.	.	PUNCT
ejpam-5986	202	1	now	now	ADV
ejpam-5986	202	2	,	,	PUNCT
ejpam-5986	202	3	using	use	VERB
ejpam-5986	202	4	the	the	DET
ejpam-5986	202	5	theorem	theorem	NOUN
ejpam-5986	202	6	3	3	NUM
ejpam-5986	202	7	the	the	DET
ejpam-5986	202	8	result	result	NOUN
ejpam-5986	202	9	follows	follow	VERB
ejpam-5986	202	10	.	.	PUNCT
ejpam-5986	203	1	note	note	VERB
ejpam-5986	203	2	that	that	SCONJ
ejpam-5986	203	3	,	,	PUNCT
ejpam-5986	203	4	lim	lim	PROPN
ejpam-5986	203	5	λ→0	λ→0	PROPN
ejpam-5986	203	6	g∗	g∗	VERB
ejpam-5986	203	7	α	α	PRON
ejpam-5986	203	8	,	,	PUNCT
ejpam-5986	203	9	λ{sinh	λ{sinh	X
ejpam-5986	203	10	at	at	ADP
ejpam-5986	203	11	}	}	PUNCT
ejpam-5986	203	12	=	=	SYM
ejpam-5986	203	13	lim	lim	PROPN
ejpam-5986	203	14	λ→0	λ→0	PUNCT
ejpam-5986	203	15	aλ2uα+2	aλ2uα+2	PROPN
ejpam-5986	203	16	ln2(1	ln2(1	NOUN
ejpam-5986	204	1	+	+	CCONJ
ejpam-5986	204	2	λ)−	λ)−	ADP
ejpam-5986	204	3	a2λ2u2	a2λ2u2	PROPN
ejpam-5986	204	4	=	=	SYM
ejpam-5986	204	5	auα+2	auα+2	ADJ
ejpam-5986	204	6	1−	1−	NUM
ejpam-5986	205	1	a2u2	a2u2	NOUN
ejpam-5986	205	2	=	=	SYM
ejpam-5986	205	3	gα{sinh	gα{sinh	PROPN
ejpam-5986	205	4	at	at	ADP
ejpam-5986	205	5	}	}	PUNCT
ejpam-5986	205	6	.	.	PUNCT
ejpam-5986	206	1	theorem	theorem	ADJ
ejpam-5986	206	2	8	8	NUM
ejpam-5986	206	3	.	.	PUNCT
ejpam-5986	207	1	(	(	PUNCT
ejpam-5986	207	2	transform	transform	NOUN
ejpam-5986	207	3	of	of	ADP
ejpam-5986	207	4	derivatives	derivative	NOUN
ejpam-5986	207	5	)	)	PUNCT
ejpam-5986	207	6	if	if	SCONJ
ejpam-5986	207	7	f(t	f(t	NOUN
ejpam-5986	207	8	)	)	PUNCT
ejpam-5986	207	9	,	,	PUNCT
ejpam-5986	207	10	f	f	PROPN
ejpam-5986	207	11	′	′	NUM
ejpam-5986	207	12	(	(	PUNCT
ejpam-5986	207	13	t	t	PROPN
ejpam-5986	207	14	)	)	PUNCT
ejpam-5986	207	15	,	,	PUNCT
ejpam-5986	207	16	.	.	PUNCT
ejpam-5986	207	17	.	.	PUNCT
ejpam-5986	207	18	.	.	PUNCT
ejpam-5986	208	1	f	f	PROPN
ejpam-5986	208	2	(	(	PUNCT
ejpam-5986	208	3	n−1)(t	n−1)(t	PROPN
ejpam-5986	208	4	)	)	PUNCT
ejpam-5986	208	5	are	be	AUX
ejpam-5986	208	6	continious	continious	ADJ
ejpam-5986	208	7	functions	function	NOUN
ejpam-5986	208	8	on	on	ADP
ejpam-5986	208	9	the	the	DET
ejpam-5986	208	10	interval	interval	NOUN
ejpam-5986	208	11	[	[	X
ejpam-5986	208	12	0	0	NUM
ejpam-5986	208	13	,	,	PUNCT
ejpam-5986	208	14	l	l	NOUN
ejpam-5986	208	15	]	]	X
ejpam-5986	208	16	and	and	CCONJ
ejpam-5986	208	17	of	of	ADP
ejpam-5986	208	18	exponential	exponential	ADJ
ejpam-5986	208	19	order	order	NOUN
ejpam-5986	208	20	as	as	SCONJ
ejpam-5986	208	21	t	t	PROPN
ejpam-5986	208	22	goes	go	VERB
ejpam-5986	208	23	to	to	ADP
ejpam-5986	208	24	infinity	infinity	NOUN
ejpam-5986	208	25	for	for	ADP
ejpam-5986	208	26	t	t	PROPN
ejpam-5986	208	27	>	>	PUNCT
ejpam-5986	208	28	l	l	PROPN
ejpam-5986	208	29	while	while	SCONJ
ejpam-5986	208	30	f	f	PROPN
ejpam-5986	208	31	(	(	PUNCT
ejpam-5986	208	32	n)(t	n)(t	PROPN
ejpam-5986	208	33	)	)	PUNCT
ejpam-5986	208	34	is	be	AUX
ejpam-5986	208	35	piecewise	piecewise	NOUN
ejpam-5986	208	36	-	-	PUNCT
ejpam-5986	208	37	continious	continious	NOUN
ejpam-5986	208	38	on	on	ADP
ejpam-5986	208	39	the	the	DET
ejpam-5986	208	40	interval	interval	NOUN
ejpam-5986	208	41	[	[	X
ejpam-5986	208	42	0	0	NUM
ejpam-5986	208	43	,	,	PUNCT
ejpam-5986	208	44	l	l	NOUN
ejpam-5986	208	45	]	]	PUNCT
ejpam-5986	208	46	,	,	PUNCT
ejpam-5986	208	47	then	then	ADV
ejpam-5986	208	48	g∗	g∗	VERB
ejpam-5986	208	49	α	α	PRON
ejpam-5986	208	50	,	,	PUNCT
ejpam-5986	208	51	λ{f	λ{f	NOUN
ejpam-5986	208	52	(	(	PUNCT
ejpam-5986	208	53	n)(t	n)(t	ADJ
ejpam-5986	208	54	)	)	PUNCT
ejpam-5986	208	55	}	}	PUNCT
ejpam-5986	208	56	=	=	SYM
ejpam-5986	208	57	lnn(1	lnn(1	X
ejpam-5986	209	1	+	+	CCONJ
ejpam-5986	209	2	λ	λ	NOUN
ejpam-5986	209	3	)	)	PUNCT
ejpam-5986	209	4	λnun	λnun	PROPN
ejpam-5986	209	5	g∗	g∗	VERB
ejpam-5986	209	6	α	α	X
ejpam-5986	209	7	,	,	PUNCT
ejpam-5986	209	8	λ{f(t	λ{f(t	NUM
ejpam-5986	209	9	)	)	PUNCT
ejpam-5986	209	10	}	}	PUNCT
ejpam-5986	209	11	−	−	PROPN
ejpam-5986	209	12	uα	uα	NOUN
ejpam-5986	209	13	lnn−1(1	lnn−1(1	VERB
ejpam-5986	209	14	+	+	CCONJ
ejpam-5986	209	15	λ	λ	NOUN
ejpam-5986	209	16	)	)	PUNCT
ejpam-5986	209	17	λn−1un−1	λn−1un−1	X
ejpam-5986	209	18	f(0	f(0	NOUN
ejpam-5986	209	19	)	)	PUNCT
ejpam-5986	210	1	−uα	−uα	NOUN
ejpam-5986	210	2	lnn−2(1	lnn−2(1	PROPN
ejpam-5986	210	3	+	+	CCONJ
ejpam-5986	210	4	λ	λ	NOUN
ejpam-5986	210	5	)	)	PUNCT
ejpam-5986	210	6	λn−2un−2	λn−2un−2	SYM
ejpam-5986	210	7	f	f	NOUN
ejpam-5986	210	8	′	′	NUM
ejpam-5986	210	9	(	(	PUNCT
ejpam-5986	210	10	0)−	0)−	PROPN
ejpam-5986	210	11	.	.	PUNCT
ejpam-5986	210	12	.	.	PUNCT
ejpam-5986	211	1	.−	.−	PUNCT
ejpam-5986	212	1	uαf	uαf	INTJ
ejpam-5986	212	2	(	(	PUNCT
ejpam-5986	212	3	n−1)(0	n−1)(0	NOUN
ejpam-5986	212	4	)	)	PUNCT
ejpam-5986	212	5	,	,	PUNCT
ejpam-5986	212	6	(	(	PUNCT
ejpam-5986	212	7	15	15	NUM
ejpam-5986	212	8	)	)	PUNCT
ejpam-5986	212	9	where	where	SCONJ
ejpam-5986	212	10	f	f	PROPN
ejpam-5986	212	11	(	(	PUNCT
ejpam-5986	212	12	n)(t	n)(t	PROPN
ejpam-5986	212	13	)	)	PUNCT
ejpam-5986	212	14	=	=	PUNCT
ejpam-5986	213	1	dn	dn	PROPN
ejpam-5986	213	2	dtn	dtn	PROPN
ejpam-5986	213	3	f(t	f(t	PROPN
ejpam-5986	213	4	)	)	PUNCT
ejpam-5986	213	5	and	and	CCONJ
ejpam-5986	213	6	n	n	CCONJ
ejpam-5986	213	7	=	=	SYM
ejpam-5986	213	8	1	1	NUM
ejpam-5986	213	9	,	,	PUNCT
ejpam-5986	213	10	2	2	NUM
ejpam-5986	213	11	,	,	PUNCT
ejpam-5986	213	12	3	3	NUM
ejpam-5986	213	13	,	,	PUNCT
ejpam-5986	213	14	.	.	PUNCT
ejpam-5986	213	15	.	.	PUNCT
ejpam-5986	214	1	..	..	PUNCT
ejpam-5986	214	2	i̇.	i̇.	PROPN
ejpam-5986	214	3	ege	ege	PROPN
ejpam-5986	214	4	/	/	SYM
ejpam-5986	214	5	eur	eur	PROPN
ejpam-5986	214	6	.	.	PUNCT
ejpam-5986	215	1	j.	j.	PROPN
ejpam-5986	215	2	pure	pure	PROPN
ejpam-5986	215	3	appl	appl	PROPN
ejpam-5986	215	4	.	.	PROPN
ejpam-5986	215	5	math	math	PROPN
ejpam-5986	215	6	,	,	PUNCT
ejpam-5986	215	7	18	18	NUM
ejpam-5986	215	8	(	(	PUNCT
ejpam-5986	215	9	2	2	NUM
ejpam-5986	215	10	)	)	PUNCT
ejpam-5986	215	11	(	(	PUNCT
ejpam-5986	215	12	2025	2025	NUM
ejpam-5986	215	13	)	)	PUNCT
ejpam-5986	215	14	,	,	PUNCT
ejpam-5986	215	15	5986	5986	NUM
ejpam-5986	215	16	8	8	NUM
ejpam-5986	215	17	of	of	ADP
ejpam-5986	215	18	20	20	NUM
ejpam-5986	215	19	proof	proof	NOUN
ejpam-5986	215	20	.	.	PUNCT
ejpam-5986	216	1	using	use	VERB
ejpam-5986	216	2	the	the	DET
ejpam-5986	216	3	definition	definition	NOUN
ejpam-5986	216	4	(	(	PUNCT
ejpam-5986	216	5	1	1	NUM
ejpam-5986	216	6	)	)	PUNCT
ejpam-5986	216	7	and	and	CCONJ
ejpam-5986	216	8	the	the	DET
ejpam-5986	216	9	integration	integration	NOUN
ejpam-5986	216	10	by	by	ADP
ejpam-5986	216	11	parts	part	NOUN
ejpam-5986	216	12	,	,	PUNCT
ejpam-5986	216	13	we	we	PRON
ejpam-5986	216	14	have	have	AUX
ejpam-5986	216	15	g∗	g∗	NOUN
ejpam-5986	216	16	α	α	PRON
ejpam-5986	216	17	,	,	PUNCT
ejpam-5986	216	18	λ{f	λ{f	NOUN
ejpam-5986	216	19	′	′	NUM
ejpam-5986	216	20	(	(	PUNCT
ejpam-5986	216	21	t	t	NOUN
ejpam-5986	216	22	)	)	PUNCT
ejpam-5986	216	23	}	}	PUNCT
ejpam-5986	217	1	=	=	PUNCT
ejpam-5986	217	2	uα	uα	PROPN
ejpam-5986	217	3	∫	∫	PROPN
ejpam-5986	217	4	∞	∞	PROPN
ejpam-5986	217	5	0	0	NUM
ejpam-5986	218	1	(	(	PUNCT
ejpam-5986	218	2	1	1	NUM
ejpam-5986	218	3	+	+	X
ejpam-5986	218	4	λ)−	λ)−	ADP
ejpam-5986	218	5	t	t	X
ejpam-5986	218	6	uλ	uλ	X
ejpam-5986	218	7	f	f	PROPN
ejpam-5986	219	1	′	′	NUM
ejpam-5986	219	2	(	(	PUNCT
ejpam-5986	219	3	t	t	NOUN
ejpam-5986	219	4	)	)	PUNCT
ejpam-5986	219	5	dt	dt	NOUN
ejpam-5986	220	1	=	=	PUNCT
ejpam-5986	220	2	uα	uα	PROPN
ejpam-5986	220	3	lim	lim	PROPN
ejpam-5986	220	4	h→∞	h→∞	NUM
ejpam-5986	220	5	∫	∫	PROPN
ejpam-5986	220	6	h	h	NOUN
ejpam-5986	220	7	0	0	PUNCT
ejpam-5986	221	1	(	(	PUNCT
ejpam-5986	221	2	1	1	NUM
ejpam-5986	221	3	+	+	X
ejpam-5986	221	4	λ)−	λ)−	ADP
ejpam-5986	221	5	t	t	X
ejpam-5986	221	6	uλ	uλ	X
ejpam-5986	221	7	f	f	PROPN
ejpam-5986	222	1	′	′	NUM
ejpam-5986	222	2	(	(	PUNCT
ejpam-5986	222	3	t	t	NOUN
ejpam-5986	222	4	)	)	PUNCT
ejpam-5986	222	5	dt	dt	NOUN
ejpam-5986	223	1	=	=	PUNCT
ejpam-5986	223	2	uα	uα	PROPN
ejpam-5986	223	3	lim	lim	PROPN
ejpam-5986	223	4	h→∞	h→∞	PROPN
ejpam-5986	223	5	[	[	PUNCT
ejpam-5986	223	6	(	(	PUNCT
ejpam-5986	223	7	1	1	NUM
ejpam-5986	223	8	+	+	X
ejpam-5986	223	9	λ)−	λ)−	ADP
ejpam-5986	223	10	t	t	NOUN
ejpam-5986	223	11	uλ	uλ	DET
ejpam-5986	223	12	f(t	f(t	PROPN
ejpam-5986	223	13	)	)	PUNCT
ejpam-5986	223	14	∣∣∣∣h	∣∣∣∣h	NOUN
ejpam-5986	223	15	0	0	PUNCT
ejpam-5986	224	1	+	+	CCONJ
ejpam-5986	224	2	ln(1	ln(1	PROPN
ejpam-5986	224	3	+	+	CCONJ
ejpam-5986	224	4	λ	λ	NOUN
ejpam-5986	224	5	)	)	PUNCT
ejpam-5986	224	6	λu	λu	X
ejpam-5986	224	7	∫	∫	PROPN
ejpam-5986	224	8	h	h	PROPN
ejpam-5986	224	9	0	0	PUNCT
ejpam-5986	225	1	(	(	PUNCT
ejpam-5986	225	2	1	1	NUM
ejpam-5986	225	3	+	+	X
ejpam-5986	225	4	λ)−	λ)−	ADP
ejpam-5986	225	5	t	t	NOUN
ejpam-5986	225	6	uλ	uλ	DET
ejpam-5986	225	7	f(t	f(t	PROPN
ejpam-5986	225	8	)	)	PUNCT
ejpam-5986	225	9	dt	dt	PUNCT
ejpam-5986	225	10	]	]	PUNCT
ejpam-5986	225	11	(	(	PUNCT
ejpam-5986	225	12	16	16	NUM
ejpam-5986	225	13	)	)	PUNCT
ejpam-5986	225	14	=	=	SYM
ejpam-5986	225	15	−uαf(0	−uαf(0	NOUN
ejpam-5986	225	16	)	)	PUNCT
ejpam-5986	226	1	+	+	PUNCT
ejpam-5986	226	2	ln(1	ln(1	PROPN
ejpam-5986	226	3	+	+	CCONJ
ejpam-5986	226	4	λ	λ	NOUN
ejpam-5986	226	5	)	)	PUNCT
ejpam-5986	226	6	λu	λu	AUX
ejpam-5986	226	7	g∗	g∗	VERB
ejpam-5986	226	8	α	α	X
ejpam-5986	226	9	,	,	PUNCT
ejpam-5986	226	10	λ{f(t	λ{f(t	NUM
ejpam-5986	226	11	)	)	PUNCT
ejpam-5986	226	12	}	}	PUNCT
ejpam-5986	226	13	,	,	PUNCT
ejpam-5986	226	14	and	and	CCONJ
ejpam-5986	226	15	the	the	DET
ejpam-5986	226	16	equation	equation	NOUN
ejpam-5986	226	17	(	(	PUNCT
ejpam-5986	226	18	15	15	NUM
ejpam-5986	226	19	)	)	PUNCT
ejpam-5986	226	20	follows	follow	VERB
ejpam-5986	226	21	for	for	ADP
ejpam-5986	226	22	n	n	NOUN
ejpam-5986	226	23	=	=	SYM
ejpam-5986	226	24	1	1	NUM
ejpam-5986	226	25	.	.	PUNCT
ejpam-5986	227	1	now	now	ADV
ejpam-5986	227	2	for	for	ADP
ejpam-5986	227	3	proving	prove	VERB
ejpam-5986	227	4	the	the	DET
ejpam-5986	227	5	equation	equation	NOUN
ejpam-5986	227	6	(	(	PUNCT
ejpam-5986	227	7	15	15	NUM
ejpam-5986	227	8	)	)	PUNCT
ejpam-5986	227	9	,	,	PUNCT
ejpam-5986	227	10	we	we	PRON
ejpam-5986	227	11	use	use	VERB
ejpam-5986	227	12	induction	induction	NOUN
ejpam-5986	227	13	method	method	NOUN
ejpam-5986	227	14	on	on	ADP
ejpam-5986	227	15	n.	n.	NOUN
ejpam-5986	227	16	the	the	DET
ejpam-5986	227	17	equation	equation	NOUN
ejpam-5986	227	18	(	(	PUNCT
ejpam-5986	227	19	15	15	NUM
ejpam-5986	227	20	)	)	PUNCT
ejpam-5986	227	21	is	be	AUX
ejpam-5986	227	22	true	true	ADJ
ejpam-5986	227	23	for	for	ADP
ejpam-5986	227	24	n	n	NOUN
ejpam-5986	227	25	=	=	SYM
ejpam-5986	227	26	1	1	NUM
ejpam-5986	227	27	.	.	PUNCT
ejpam-5986	227	28	by	by	ADP
ejpam-5986	227	29	using	use	VERB
ejpam-5986	227	30	the	the	DET
ejpam-5986	227	31	equation	equation	NOUN
ejpam-5986	227	32	(	(	PUNCT
ejpam-5986	227	33	16	16	NUM
ejpam-5986	227	34	)	)	PUNCT
ejpam-5986	227	35	we	we	PRON
ejpam-5986	227	36	can	can	AUX
ejpam-5986	227	37	write	write	VERB
ejpam-5986	227	38	g∗	g∗	PROPN
ejpam-5986	227	39	α	α	NOUN
ejpam-5986	227	40	,	,	PUNCT
ejpam-5986	227	41	λ{f	λ{f	NOUN
ejpam-5986	227	42	(	(	PUNCT
ejpam-5986	227	43	k+1)(t	k+1)(t	PROPN
ejpam-5986	227	44	)	)	PUNCT
ejpam-5986	227	45	}	}	PUNCT
ejpam-5986	227	46	=	=	PUNCT
ejpam-5986	227	47	g∗	g∗	VERB
ejpam-5986	227	48	α	α	NOUN
ejpam-5986	227	49	,	,	PUNCT
ejpam-5986	227	50	λ	λ	PROPN
ejpam-5986	227	51	{	{	PUNCT
ejpam-5986	227	52	d	d	X
ejpam-5986	227	53	dt	dt	X
ejpam-5986	227	54	f	f	X
ejpam-5986	227	55	(	(	PUNCT
ejpam-5986	227	56	k)(t	k)(t	PROPN
ejpam-5986	227	57	)	)	PUNCT
ejpam-5986	227	58	}	}	PUNCT
ejpam-5986	228	1	=	=	PUNCT
ejpam-5986	228	2	ln(1	ln(1	PROPN
ejpam-5986	228	3	+	+	NUM
ejpam-5986	228	4	λ	λ	AUX
ejpam-5986	228	5	)	)	PUNCT
ejpam-5986	228	6	λu	λu	AUX
ejpam-5986	228	7	g∗	g∗	VERB
ejpam-5986	228	8	α	α	NOUN
ejpam-5986	228	9	,	,	PUNCT
ejpam-5986	228	10	λ{f	λ{f	NOUN
ejpam-5986	228	11	(	(	PUNCT
ejpam-5986	228	12	k)(t	k)(t	PROPN
ejpam-5986	228	13	)	)	PUNCT
ejpam-5986	228	14	}	}	PUNCT
ejpam-5986	228	15	−	−	PROPN
ejpam-5986	228	16	uαfn(0	uαfn(0	NOUN
ejpam-5986	228	17	)	)	PUNCT
ejpam-5986	228	18	=	=	PUNCT
ejpam-5986	229	1	ln(1	ln(1	NOUN
ejpam-5986	229	2	+	+	NUM
ejpam-5986	229	3	λ	λ	NOUN
ejpam-5986	229	4	)	)	PUNCT
ejpam-5986	229	5	λu	λu	X
ejpam-5986	229	6	[	[	PUNCT
ejpam-5986	229	7	lnk(1	lnk(1	ADJ
ejpam-5986	229	8	+	+	CCONJ
ejpam-5986	229	9	λ	λ	NOUN
ejpam-5986	229	10	)	)	PUNCT
ejpam-5986	229	11	λkuk	λkuk	PROPN
ejpam-5986	229	12	g∗	g∗	PROPN
ejpam-5986	229	13	α	α	X
ejpam-5986	229	14	,	,	PUNCT
ejpam-5986	229	15	λ{f(t	λ{f(t	NUM
ejpam-5986	229	16	)	)	PUNCT
ejpam-5986	229	17	}	}	PUNCT
ejpam-5986	229	18	−	−	PROPN
ejpam-5986	230	1	uα	uα	PROPN
ejpam-5986	230	2	lnk−1(1	lnk−1(1	PROPN
ejpam-5986	230	3	+	+	NOUN
ejpam-5986	230	4	λ	λ	NOUN
ejpam-5986	230	5	)	)	PUNCT
ejpam-5986	230	6	λk−1uk−1	λk−1uk−1	NUM
ejpam-5986	230	7	f(0)−	f(0)−	PROPN
ejpam-5986	230	8	.	.	PUNCT
ejpam-5986	230	9	.	.	PUNCT
ejpam-5986	231	1	.−	.−	PUNCT
ejpam-5986	232	1	uαf	uαf	INTJ
ejpam-5986	232	2	(	(	PUNCT
ejpam-5986	232	3	k−1)(0	k−1)(0	PROPN
ejpam-5986	232	4	)	)	PUNCT
ejpam-5986	232	5	]	]	PUNCT
ejpam-5986	233	1	−	−	PROPN
ejpam-5986	233	2	uαf	uαf	NOUN
ejpam-5986	233	3	(	(	PUNCT
ejpam-5986	233	4	k)(0	k)(0	X
ejpam-5986	233	5	)	)	PUNCT
ejpam-5986	233	6	=	=	SYM
ejpam-5986	233	7	lnk+1(1	lnk+1(1	X
ejpam-5986	233	8	+	+	CCONJ
ejpam-5986	233	9	λ	λ	X
ejpam-5986	233	10	)	)	PUNCT
ejpam-5986	233	11	λkuk	λkuk	PROPN
ejpam-5986	233	12	g∗	g∗	PROPN
ejpam-5986	233	13	α	α	X
ejpam-5986	233	14	,	,	PUNCT
ejpam-5986	233	15	λ{f(t	λ{f(t	NUM
ejpam-5986	233	16	)	)	PUNCT
ejpam-5986	233	17	}	}	PUNCT
ejpam-5986	233	18	−	−	ADP
ejpam-5986	233	19	uα	uα	NOUN
ejpam-5986	233	20	lnk(1	lnk(1	NOUN
ejpam-5986	233	21	+	+	CCONJ
ejpam-5986	233	22	λ	λ	NOUN
ejpam-5986	233	23	)	)	PUNCT
ejpam-5986	233	24	λkuk	λkuk	PROPN
ejpam-5986	233	25	f(0)−	f(0)−	NOUN
ejpam-5986	233	26	.	.	PUNCT
ejpam-5986	233	27	.	.	PUNCT
ejpam-5986	234	1	.−	.−	PUNCT
ejpam-5986	235	1	uα	uα	X
ejpam-5986	235	2	ln(1	ln(1	PROPN
ejpam-5986	235	3	+	+	CCONJ
ejpam-5986	235	4	λ	λ	NOUN
ejpam-5986	235	5	)	)	PUNCT
ejpam-5986	236	1	λu	λu	X
ejpam-5986	236	2	f	f	PROPN
ejpam-5986	236	3	(	(	PUNCT
ejpam-5986	236	4	k−1)(0)−	k−1)(0)−	PROPN
ejpam-5986	236	5	uαf	uαf	NOUN
ejpam-5986	236	6	(	(	PUNCT
ejpam-5986	236	7	k)(0	k)(0	ADJ
ejpam-5986	236	8	)	)	PUNCT
ejpam-5986	236	9	.	.	PUNCT
ejpam-5986	237	1	this	this	PRON
ejpam-5986	237	2	proves	prove	VERB
ejpam-5986	237	3	that	that	SCONJ
ejpam-5986	237	4	the	the	DET
ejpam-5986	237	5	equation	equation	NOUN
ejpam-5986	237	6	(	(	PUNCT
ejpam-5986	237	7	15	15	NUM
ejpam-5986	237	8	)	)	PUNCT
ejpam-5986	237	9	is	be	AUX
ejpam-5986	237	10	true	true	ADJ
ejpam-5986	237	11	for	for	ADP
ejpam-5986	237	12	n	n	NOUN
ejpam-5986	237	13	=	=	SYM
ejpam-5986	237	14	k	k	PROPN
ejpam-5986	238	1	+	+	CCONJ
ejpam-5986	238	2	1	1	NUM
ejpam-5986	238	3	and	and	CCONJ
ejpam-5986	238	4	the	the	DET
ejpam-5986	238	5	equation	equation	NOUN
ejpam-5986	238	6	(	(	PUNCT
ejpam-5986	238	7	15	15	NUM
ejpam-5986	238	8	)	)	PUNCT
ejpam-5986	238	9	follows	follow	VERB
ejpam-5986	238	10	.	.	PUNCT
ejpam-5986	239	1	note	note	VERB
ejpam-5986	239	2	that	that	SCONJ
ejpam-5986	239	3	,	,	PUNCT
ejpam-5986	239	4	by	by	ADP
ejpam-5986	239	5	using	use	VERB
ejpam-5986	239	6	the	the	DET
ejpam-5986	239	7	theorem	theorem	NOUN
ejpam-5986	239	8	8	8	NUM
ejpam-5986	239	9	we	we	PRON
ejpam-5986	239	10	have	have	VERB
ejpam-5986	239	11	lim	lim	PROPN
ejpam-5986	239	12	λ→0	λ→0	PROPN
ejpam-5986	239	13	g∗	g∗	VERB
ejpam-5986	239	14	α	α	NOUN
ejpam-5986	239	15	,	,	PUNCT
ejpam-5986	239	16	λ{f	λ{f	NOUN
ejpam-5986	239	17	(	(	PUNCT
ejpam-5986	239	18	n)(t	n)(t	ADJ
ejpam-5986	239	19	)	)	PUNCT
ejpam-5986	239	20	}	}	PUNCT
ejpam-5986	240	1	=	=	SYM
ejpam-5986	240	2	lim	lim	PROPN
ejpam-5986	240	3	λ→0	λ→0	PUNCT
ejpam-5986	240	4	[	[	PUNCT
ejpam-5986	240	5	lnn(1	lnn(1	X
ejpam-5986	240	6	+	+	CCONJ
ejpam-5986	240	7	λ	λ	NOUN
ejpam-5986	240	8	)	)	PUNCT
ejpam-5986	240	9	λnun	λnun	PROPN
ejpam-5986	240	10	g∗	g∗	VERB
ejpam-5986	240	11	α	α	X
ejpam-5986	240	12	,	,	PUNCT
ejpam-5986	240	13	λ{f(t	λ{f(t	NUM
ejpam-5986	240	14	)	)	PUNCT
ejpam-5986	240	15	}	}	PUNCT
ejpam-5986	240	16	−	−	PROPN
ejpam-5986	241	1	uα	uα	NOUN
ejpam-5986	241	2	lnn−1(1	lnn−1(1	VERB
ejpam-5986	241	3	+	+	CCONJ
ejpam-5986	241	4	λ	λ	NOUN
ejpam-5986	241	5	)	)	PUNCT
ejpam-5986	241	6	λn−1un−1	λn−1un−1	AUX
ejpam-5986	241	7	f(0)−	f(0)−	PROPN
ejpam-5986	241	8	.	.	PUNCT
ejpam-5986	241	9	.	.	PUNCT
ejpam-5986	242	1	.−	.−	PUNCT
ejpam-5986	243	1	uαf	uαf	INTJ
ejpam-5986	243	2	(	(	PUNCT
ejpam-5986	243	3	n−1)(0	n−1)(0	NOUN
ejpam-5986	243	4	)	)	PUNCT
ejpam-5986	243	5	]	]	PUNCT
ejpam-5986	244	1	=	=	SYM
ejpam-5986	244	2	1	1	NUM
ejpam-5986	244	3	un	un	PROPN
ejpam-5986	244	4	gα{f(t	gα{f(t	NOUN
ejpam-5986	244	5	)	)	PUNCT
ejpam-5986	244	6	}	}	PUNCT
ejpam-5986	244	7	−	−	PROPN
ejpam-5986	244	8	1	1	NUM
ejpam-5986	244	9	un−1	un−1	ADJ
ejpam-5986	244	10	f(0)uα	f(0)uα	NOUN
ejpam-5986	244	11	−	−	PROPN
ejpam-5986	244	12	1	1	NUM
ejpam-5986	244	13	un−2	un−2	PROPN
ejpam-5986	244	14	f	f	NOUN
ejpam-5986	244	15	′	′	NUM
ejpam-5986	244	16	(	(	PUNCT
ejpam-5986	244	17	0)uα	0)uα	NOUN
ejpam-5986	244	18	−	−	PROPN
ejpam-5986	244	19	.	.	PUNCT
ejpam-5986	244	20	.	.	PUNCT
ejpam-5986	245	1	.−	.−	PUNCT
ejpam-5986	246	1	uαf	uαf	INTJ
ejpam-5986	246	2	(	(	PUNCT
ejpam-5986	246	3	n−1)(0	n−1)(0	NOUN
ejpam-5986	246	4	)	)	PUNCT
ejpam-5986	246	5	=	=	SYM
ejpam-5986	246	6	gα{f	gα{f	PROPN
ejpam-5986	246	7	(	(	PUNCT
ejpam-5986	246	8	n)(t	n)(t	PROPN
ejpam-5986	246	9	)	)	PUNCT
ejpam-5986	246	10	}	}	PUNCT
ejpam-5986	246	11	.	.	PUNCT
ejpam-5986	247	1	for	for	ADP
ejpam-5986	247	2	n	n	NOUN
ejpam-5986	247	3	=	=	SYM
ejpam-5986	247	4	1	1	NUM
ejpam-5986	247	5	,	,	PUNCT
ejpam-5986	247	6	2	2	NUM
ejpam-5986	247	7	,	,	PUNCT
ejpam-5986	247	8	3	3	NUM
ejpam-5986	247	9	,	,	PUNCT
ejpam-5986	247	10	.	.	PUNCT
ejpam-5986	247	11	.	.	PUNCT
ejpam-5986	248	1	..	..	PUNCT
ejpam-5986	248	2	corollary	corollary	ADJ
ejpam-5986	248	3	1	1	NUM
ejpam-5986	248	4	.	.	PUNCT
ejpam-5986	249	1	the	the	DET
ejpam-5986	249	2	modified	modify	VERB
ejpam-5986	249	3	laplace	laplace	NOUN
ejpam-5986	249	4	-	-	PUNCT
ejpam-5986	249	5	type	type	NOUN
ejpam-5986	249	6	transform	transform	NOUN
ejpam-5986	249	7	of	of	ADP
ejpam-5986	249	8	the	the	DET
ejpam-5986	249	9	function	function	NOUN
ejpam-5986	249	10	f(t	f(t	PROPN
ejpam-5986	249	11	)	)	PUNCT
ejpam-5986	250	1	=	=	PUNCT
ejpam-5986	250	2	cos	cos	PROPN
ejpam-5986	250	3	at	at	ADP
ejpam-5986	250	4	is	be	AUX
ejpam-5986	250	5	given	give	VERB
ejpam-5986	250	6	by	by	ADP
ejpam-5986	250	7	g∗	g∗	PROPN
ejpam-5986	250	8	α	α	PROPN
ejpam-5986	250	9	,	,	PUNCT
ejpam-5986	250	10	λ{cos	λ{cos	ADJ
ejpam-5986	250	11	at	at	ADP
ejpam-5986	250	12	}	}	PUNCT
ejpam-5986	250	13	=	=	PUNCT
ejpam-5986	250	14	λ	λ	X
ejpam-5986	250	15	ln(1	ln(1	NOUN
ejpam-5986	250	16	+	+	CCONJ
ejpam-5986	250	17	λ)uα+1	λ)uα+1	NOUN
ejpam-5986	250	18	ln2(1	ln2(1	NOUN
ejpam-5986	250	19	+	+	X
ejpam-5986	250	20	λ	λ	NOUN
ejpam-5986	250	21	)	)	PUNCT
ejpam-5986	250	22	+	+	CCONJ
ejpam-5986	250	23	a2λ2u2	a2λ2u2	PROPN
ejpam-5986	250	24	.	.	PUNCT
ejpam-5986	251	1	(	(	PUNCT
ejpam-5986	251	2	17	17	NUM
ejpam-5986	251	3	)	)	PUNCT
ejpam-5986	251	4	proof	proof	NOUN
ejpam-5986	251	5	.	.	PUNCT
ejpam-5986	252	1	let	let	VERB
ejpam-5986	252	2	f(t	f(t	NOUN
ejpam-5986	252	3	)	)	PUNCT
ejpam-5986	252	4	=	=	PUNCT
ejpam-5986	253	1	1	1	NUM
ejpam-5986	253	2	a	a	DET
ejpam-5986	253	3	sin	sin	NOUN
ejpam-5986	253	4	at	at	ADP
ejpam-5986	253	5	.	.	PUNCT
ejpam-5986	254	1	then	then	ADV
ejpam-5986	254	2	f	f	PROPN
ejpam-5986	254	3	′	′	NUM
ejpam-5986	254	4	(	(	PUNCT
ejpam-5986	254	5	t	t	NOUN
ejpam-5986	254	6	)	)	PUNCT
ejpam-5986	255	1	=	=	PUNCT
ejpam-5986	255	2	cos	cos	ADP
ejpam-5986	255	3	at	at	ADP
ejpam-5986	255	4	and	and	CCONJ
ejpam-5986	255	5	f(0	f(0	NOUN
ejpam-5986	255	6	)	)	PUNCT
ejpam-5986	255	7	=	=	SYM
ejpam-5986	256	1	0	0	X
ejpam-5986	256	2	.	.	PUNCT
ejpam-5986	256	3	now	now	ADV
ejpam-5986	256	4	using	use	VERB
ejpam-5986	256	5	the	the	DET
ejpam-5986	256	6	linearity	linearity	NOUN
ejpam-5986	256	7	property	property	NOUN
ejpam-5986	256	8	(	(	PUNCT
ejpam-5986	256	9	14	14	NUM
ejpam-5986	256	10	)	)	PUNCT
ejpam-5986	256	11	and	and	CCONJ
ejpam-5986	256	12	the	the	DET
ejpam-5986	256	13	equation	equation	NOUN
ejpam-5986	256	14	(	(	PUNCT
ejpam-5986	256	15	16	16	NUM
ejpam-5986	256	16	)	)	PUNCT
ejpam-5986	256	17	we	we	PRON
ejpam-5986	256	18	get	get	VERB
ejpam-5986	256	19	g∗	g∗	PROPN
ejpam-5986	256	20	α	α	NOUN
ejpam-5986	256	21	,	,	PUNCT
ejpam-5986	256	22	λ{cos	λ{cos	ADJ
ejpam-5986	256	23	at	at	ADP
ejpam-5986	256	24	}	}	PUNCT
ejpam-5986	256	25	=	=	SYM
ejpam-5986	256	26	ln(1	ln(1	PROPN
ejpam-5986	256	27	+	+	NUM
ejpam-5986	256	28	λ	λ	NOUN
ejpam-5986	256	29	)	)	PUNCT
ejpam-5986	256	30	aλu	aλu	VERB
ejpam-5986	256	31	and	and	CCONJ
ejpam-5986	256	32	g∗	g∗	VERB
ejpam-5986	256	33	α	α	PROPN
ejpam-5986	256	34	,	,	PUNCT
ejpam-5986	256	35	λ{sin	λ{sin	X
ejpam-5986	256	36	at	at	ADP
ejpam-5986	256	37	}	}	PUNCT
ejpam-5986	256	38	=	=	PUNCT
ejpam-5986	256	39	λ	λ	X
ejpam-5986	256	40	ln(1	ln(1	NOUN
ejpam-5986	256	41	+	+	CCONJ
ejpam-5986	256	42	λ)uα+1	λ)uα+1	NOUN
ejpam-5986	256	43	ln2(1	ln2(1	NOUN
ejpam-5986	256	44	+	+	X
ejpam-5986	256	45	λ	λ	NOUN
ejpam-5986	256	46	)	)	PUNCT
ejpam-5986	256	47	+	+	CCONJ
ejpam-5986	256	48	a2λ2u2	a2λ2u2	PROPN
ejpam-5986	256	49	.	.	PUNCT
ejpam-5986	257	1	i̇.	i̇.	PROPN
ejpam-5986	257	2	ege	ege	PROPN
ejpam-5986	257	3	/	/	SYM
ejpam-5986	257	4	eur	eur	PROPN
ejpam-5986	257	5	.	.	PUNCT
ejpam-5986	258	1	j.	j.	PROPN
ejpam-5986	258	2	pure	pure	PROPN
ejpam-5986	258	3	appl	appl	PROPN
ejpam-5986	258	4	.	.	PROPN
ejpam-5986	258	5	math	math	PROPN
ejpam-5986	258	6	,	,	PUNCT
ejpam-5986	258	7	18	18	NUM
ejpam-5986	258	8	(	(	PUNCT
ejpam-5986	258	9	2	2	NUM
ejpam-5986	258	10	)	)	PUNCT
ejpam-5986	258	11	(	(	PUNCT
ejpam-5986	258	12	2025	2025	NUM
ejpam-5986	258	13	)	)	PUNCT
ejpam-5986	258	14	,	,	PUNCT
ejpam-5986	258	15	5986	5986	NUM
ejpam-5986	258	16	9	9	NUM
ejpam-5986	258	17	of	of	ADP
ejpam-5986	258	18	20	20	NUM
ejpam-5986	258	19	corollary	corollary	ADJ
ejpam-5986	258	20	2	2	NUM
ejpam-5986	258	21	.	.	PUNCT
ejpam-5986	259	1	the	the	DET
ejpam-5986	259	2	modified	modify	VERB
ejpam-5986	259	3	laplace	laplace	NOUN
ejpam-5986	259	4	-	-	PUNCT
ejpam-5986	259	5	type	type	NOUN
ejpam-5986	259	6	transform	transform	NOUN
ejpam-5986	259	7	of	of	ADP
ejpam-5986	259	8	the	the	DET
ejpam-5986	259	9	function	function	NOUN
ejpam-5986	259	10	f(t	f(t	NOUN
ejpam-5986	259	11	)	)	PUNCT
ejpam-5986	260	1	=	=	VERB
ejpam-5986	260	2	cosh	cosh	NOUN
ejpam-5986	260	3	at	at	ADP
ejpam-5986	260	4	is	be	AUX
ejpam-5986	260	5	given	give	VERB
ejpam-5986	260	6	by	by	ADP
ejpam-5986	260	7	g∗	g∗	PROPN
ejpam-5986	260	8	α	α	PROPN
ejpam-5986	260	9	,	,	PUNCT
ejpam-5986	260	10	λ{cosh	λ{cosh	ADV
ejpam-5986	260	11	at	at	ADP
ejpam-5986	260	12	}	}	PUNCT
ejpam-5986	260	13	=	=	PUNCT
ejpam-5986	260	14	λ	λ	X
ejpam-5986	260	15	ln(1	ln(1	NOUN
ejpam-5986	260	16	+	+	CCONJ
ejpam-5986	260	17	λ)uα+1	λ)uα+1	NOUN
ejpam-5986	260	18	ln2(1	ln2(1	NOUN
ejpam-5986	261	1	+	+	CCONJ
ejpam-5986	261	2	λ)−	λ)−	ADP
ejpam-5986	261	3	a2λ2u2	a2λ2u2	PROPN
ejpam-5986	261	4	for	for	ADP
ejpam-5986	261	5	u	u	NOUN
ejpam-5986	261	6	<	<	X
ejpam-5986	261	7	ln(1	ln(1	PROPN
ejpam-5986	261	8	+	+	CCONJ
ejpam-5986	261	9	λ	λ	NOUN
ejpam-5986	261	10	)	)	PUNCT
ejpam-5986	261	11	aλ	aλ	ADP
ejpam-5986	261	12	.	.	PUNCT
ejpam-5986	262	1	proof	proof	NOUN
ejpam-5986	262	2	.	.	PUNCT
ejpam-5986	263	1	with	with	ADP
ejpam-5986	263	2	the	the	DET
ejpam-5986	263	3	similar	similar	ADJ
ejpam-5986	263	4	proof	proof	NOUN
ejpam-5986	263	5	of	of	ADP
ejpam-5986	263	6	the	the	DET
ejpam-5986	263	7	corollary	corollary	ADJ
ejpam-5986	263	8	1	1	NUM
ejpam-5986	263	9	we	we	PRON
ejpam-5986	263	10	get	get	VERB
ejpam-5986	263	11	the	the	DET
ejpam-5986	263	12	result	result	NOUN
ejpam-5986	263	13	.	.	PUNCT
ejpam-5986	264	1	note	note	VERB
ejpam-5986	264	2	that	that	SCONJ
ejpam-5986	264	3	,	,	PUNCT
ejpam-5986	264	4	from	from	ADP
ejpam-5986	264	5	the	the	DET
ejpam-5986	264	6	corollaries	corollary	NOUN
ejpam-5986	264	7	1	1	NUM
ejpam-5986	264	8	and	and	CCONJ
ejpam-5986	264	9	2	2	NUM
ejpam-5986	264	10	we	we	PRON
ejpam-5986	264	11	have	have	VERB
ejpam-5986	264	12	lim	lim	PROPN
ejpam-5986	264	13	λ→0	λ→0	PROPN
ejpam-5986	264	14	g∗	g∗	VERB
ejpam-5986	264	15	α	α	PRON
ejpam-5986	264	16	,	,	PUNCT
ejpam-5986	264	17	λ{cos	λ{cos	ADJ
ejpam-5986	264	18	at	at	ADP
ejpam-5986	264	19	}	}	PUNCT
ejpam-5986	264	20	=	=	SYM
ejpam-5986	264	21	lim	lim	PROPN
ejpam-5986	264	22	λ→0	λ→0	PUNCT
ejpam-5986	264	23	λ	λ	X
ejpam-5986	264	24	ln(1	ln(1	NOUN
ejpam-5986	264	25	+	+	CCONJ
ejpam-5986	264	26	λ)uα+1	λ)uα+1	NOUN
ejpam-5986	264	27	ln2(1	ln2(1	NOUN
ejpam-5986	264	28	+	+	X
ejpam-5986	264	29	λ	λ	NOUN
ejpam-5986	264	30	)	)	PUNCT
ejpam-5986	265	1	+	+	NUM
ejpam-5986	265	2	a2λ2u2	a2λ2u2	NOUN
ejpam-5986	265	3	=	=	PUNCT
ejpam-5986	265	4	uα+1	uα+1	VERB
ejpam-5986	265	5	1	1	NUM
ejpam-5986	265	6	+	+	CCONJ
ejpam-5986	265	7	a2u2	a2u2	PROPN
ejpam-5986	265	8	=	=	NOUN
ejpam-5986	265	9	gα{cos	gα{cos	ADJ
ejpam-5986	265	10	at	at	ADP
ejpam-5986	265	11	}	}	PUNCT
ejpam-5986	265	12	,	,	PUNCT
ejpam-5986	265	13	lim	lim	PROPN
ejpam-5986	265	14	λ→0	λ→0	PROPN
ejpam-5986	265	15	g∗	g∗	VERB
ejpam-5986	265	16	α	α	PRON
ejpam-5986	265	17	,	,	PUNCT
ejpam-5986	265	18	λ{cosh	λ{cosh	ADV
ejpam-5986	265	19	at	at	ADP
ejpam-5986	265	20	}	}	PUNCT
ejpam-5986	265	21	=	=	SYM
ejpam-5986	265	22	lim	lim	PROPN
ejpam-5986	265	23	λ→0	λ→0	PUNCT
ejpam-5986	265	24	λ	λ	X
ejpam-5986	265	25	ln(1	ln(1	NOUN
ejpam-5986	265	26	+	+	CCONJ
ejpam-5986	265	27	λ)uα+1	λ)uα+1	NOUN
ejpam-5986	265	28	ln2(1	ln2(1	NOUN
ejpam-5986	266	1	+	+	CCONJ
ejpam-5986	266	2	λ)−	λ)−	X
ejpam-5986	266	3	a2λ2u2	a2λ2u2	NOUN
ejpam-5986	266	4	=	=	PUNCT
ejpam-5986	266	5	uα+1	uα+1	NUM
ejpam-5986	266	6	1−	1−	NUM
ejpam-5986	266	7	a2u2	a2u2	PROPN
ejpam-5986	266	8	=	=	NOUN
ejpam-5986	266	9	gα{cosh	gα{cosh	PROPN
ejpam-5986	266	10	at	at	ADP
ejpam-5986	266	11	}	}	PUNCT
ejpam-5986	266	12	.	.	PUNCT
ejpam-5986	267	1	let	let	VERB
ejpam-5986	267	2	fα	fα	VERB
ejpam-5986	267	3	,	,	PUNCT
ejpam-5986	267	4	λ	λ	PRON
ejpam-5986	267	5	be	be	AUX
ejpam-5986	267	6	the	the	DET
ejpam-5986	267	7	modified	modify	VERB
ejpam-5986	267	8	laplace	laplace	NOUN
ejpam-5986	267	9	-	-	PUNCT
ejpam-5986	267	10	type	type	NOUN
ejpam-5986	267	11	transform	transform	NOUN
ejpam-5986	267	12	and	and	CCONJ
ejpam-5986	267	13	fα	fα	PART
ejpam-5986	267	14	be	be	AUX
ejpam-5986	267	15	the	the	DET
ejpam-5986	267	16	the	the	DET
ejpam-5986	267	17	laplace	laplace	NOUN
ejpam-5986	267	18	-	-	PUNCT
ejpam-5986	267	19	type	type	NOUN
ejpam-5986	267	20	integral	integral	ADJ
ejpam-5986	267	21	transform	transform	NOUN
ejpam-5986	267	22	of	of	ADP
ejpam-5986	267	23	f(t	f(t	NOUN
ejpam-5986	267	24	)	)	PUNCT
ejpam-5986	267	25	,	,	PUNCT
ejpam-5986	267	26	g∗	g∗	VERB
ejpam-5986	267	27	α	α	X
ejpam-5986	267	28	,	,	PUNCT
ejpam-5986	267	29	λ{f(t	λ{f(t	NUM
ejpam-5986	267	30	)	)	PUNCT
ejpam-5986	267	31	}	}	PUNCT
ejpam-5986	267	32	=	=	SYM
ejpam-5986	267	33	f	f	PROPN
ejpam-5986	267	34	∗	∗	X
ejpam-5986	267	35	α	α	PROPN
ejpam-5986	267	36	,	,	PUNCT
ejpam-5986	267	37	λ(u	λ(u	PROPN
ejpam-5986	267	38	)	)	PUNCT
ejpam-5986	267	39	and	and	CCONJ
ejpam-5986	267	40	lα{f(t	lα{f(t	NOUN
ejpam-5986	267	41	)	)	PUNCT
ejpam-5986	267	42	}	}	PUNCT
ejpam-5986	267	43	=	=	SYM
ejpam-5986	267	44	fα(u	fα(u	NOUN
ejpam-5986	267	45	)	)	PUNCT
ejpam-5986	267	46	.	.	PUNCT
ejpam-5986	268	1	besides	besides	SCONJ
ejpam-5986	268	2	the	the	DET
ejpam-5986	268	3	relation	relation	NOUN
ejpam-5986	268	4	limλ→0	limλ→0	PROPN
ejpam-5986	268	5	g	g	PROPN
ejpam-5986	268	6	∗	∗	NOUN
ejpam-5986	268	7	α	α	PROPN
ejpam-5986	268	8	,	,	PUNCT
ejpam-5986	268	9	λ{f(t	λ{f(t	NUM
ejpam-5986	268	10	)	)	PUNCT
ejpam-5986	268	11	}	}	PUNCT
ejpam-5986	268	12	=	=	SYM
ejpam-5986	268	13	gα{f(t	gα{f(t	NOUN
ejpam-5986	268	14	)	)	PUNCT
ejpam-5986	268	15	}	}	PUNCT
ejpam-5986	268	16	we	we	PRON
ejpam-5986	268	17	give	give	VERB
ejpam-5986	268	18	the	the	DET
ejpam-5986	268	19	following	follow	VERB
ejpam-5986	268	20	equation	equation	NOUN
ejpam-5986	268	21	relation	relation	NOUN
ejpam-5986	268	22	between	between	ADP
ejpam-5986	268	23	the	the	DET
ejpam-5986	268	24	modified	modify	VERB
ejpam-5986	268	25	laplace	laplace	NOUN
ejpam-5986	268	26	-	-	PUNCT
ejpam-5986	268	27	type	type	NOUN
ejpam-5986	268	28	transform	transform	NOUN
ejpam-5986	268	29	and	and	CCONJ
ejpam-5986	268	30	the	the	DET
ejpam-5986	268	31	laplace	laplace	NOUN
ejpam-5986	268	32	-	-	PUNCT
ejpam-5986	268	33	type	type	NOUN
ejpam-5986	268	34	integral	integral	ADJ
ejpam-5986	268	35	transform	transform	NOUN
ejpam-5986	268	36	.	.	PUNCT
ejpam-5986	269	1	since	since	SCONJ
ejpam-5986	269	2	g∗	g∗	PROPN
ejpam-5986	269	3	α	α	NUM
ejpam-5986	269	4	,	,	PUNCT
ejpam-5986	269	5	λ{f(t	λ{f(t	NUM
ejpam-5986	269	6	)	)	PUNCT
ejpam-5986	269	7	}	}	PUNCT
ejpam-5986	269	8	=	=	PUNCT
ejpam-5986	269	9	uα	uα	PROPN
ejpam-5986	269	10	∫	∫	PROPN
ejpam-5986	269	11	∞	∞	PROPN
ejpam-5986	269	12	0	0	NUM
ejpam-5986	269	13	(	(	PUNCT
ejpam-5986	269	14	1	1	NUM
ejpam-5986	269	15	+	+	X
ejpam-5986	269	16	λ)−	λ)−	ADP
ejpam-5986	269	17	t	t	NOUN
ejpam-5986	269	18	uλ	uλ	DET
ejpam-5986	269	19	f(t	f(t	NOUN
ejpam-5986	269	20	)	)	PUNCT
ejpam-5986	269	21	dt	dt	NOUN
ejpam-5986	270	1	=	=	PUNCT
ejpam-5986	270	2	uα	uα	PROPN
ejpam-5986	270	3	∫	∫	PROPN
ejpam-5986	270	4	∞	∞	PROPN
ejpam-5986	270	5	0	0	PUNCT
ejpam-5986	271	1	e	e	PROPN
ejpam-5986	271	2	−t	−t	PROPN
ejpam-5986	271	3	ln(1+λ	ln(1+λ	ADV
ejpam-5986	271	4	)	)	PUNCT
ejpam-5986	271	5	λu	λu	ADP
ejpam-5986	271	6	f(t	f(t	NOUN
ejpam-5986	271	7	)	)	PUNCT
ejpam-5986	271	8	dt	dt	NOUN
ejpam-5986	272	1	=	=	PUNCT
ejpam-5986	272	2	(	(	PUNCT
ejpam-5986	272	3	ln(1	ln(1	PROPN
ejpam-5986	272	4	+	+	NUM
ejpam-5986	272	5	λ	λ	NOUN
ejpam-5986	272	6	)	)	PUNCT
ejpam-5986	272	7	λ	λ	NOUN
ejpam-5986	272	8	)	)	PUNCT
ejpam-5986	272	9	α	α	NOUN
ejpam-5986	272	10	fα	fα	NOUN
ejpam-5986	272	11	(	(	PUNCT
ejpam-5986	272	12	λu	λu	X
ejpam-5986	272	13	ln(1	ln(1	PROPN
ejpam-5986	272	14	+	+	CCONJ
ejpam-5986	272	15	λ	λ	NOUN
ejpam-5986	272	16	)	)	PUNCT
ejpam-5986	272	17	)	)	PUNCT
ejpam-5986	272	18	,	,	PUNCT
ejpam-5986	272	19	this	this	PRON
ejpam-5986	272	20	implies	imply	VERB
ejpam-5986	272	21	that	that	SCONJ
ejpam-5986	272	22	f	f	PROPN
ejpam-5986	272	23	∗	∗	PROPN
ejpam-5986	272	24	α	α	AUX
ejpam-5986	272	25	,	,	PUNCT
ejpam-5986	272	26	λ(u	λ(u	PROPN
ejpam-5986	272	27	)	)	PUNCT
ejpam-5986	272	28	=	=	PUNCT
ejpam-5986	273	1	(	(	PUNCT
ejpam-5986	273	2	ln(1	ln(1	PROPN
ejpam-5986	273	3	+	+	NUM
ejpam-5986	273	4	λ	λ	NOUN
ejpam-5986	273	5	)	)	PUNCT
ejpam-5986	273	6	λ	λ	NOUN
ejpam-5986	273	7	)	)	PUNCT
ejpam-5986	273	8	α	α	NOUN
ejpam-5986	273	9	fα	fα	NOUN
ejpam-5986	273	10	(	(	PUNCT
ejpam-5986	273	11	λu	λu	X
ejpam-5986	274	1	ln(1	ln(1	PROPN
ejpam-5986	274	2	+	+	CCONJ
ejpam-5986	274	3	λ	λ	NOUN
ejpam-5986	274	4	)	)	PUNCT
ejpam-5986	274	5	)	)	PUNCT
ejpam-5986	274	6	.	.	PUNCT
ejpam-5986	275	1	(	(	PUNCT
ejpam-5986	275	2	18	18	NUM
ejpam-5986	275	3	)	)	PUNCT
ejpam-5986	275	4	now	now	ADV
ejpam-5986	275	5	replace	replace	VERB
ejpam-5986	275	6	u	u	NOUN
ejpam-5986	275	7	by	by	ADP
ejpam-5986	275	8	ln(1	ln(1	PROPN
ejpam-5986	275	9	+	+	CCONJ
ejpam-5986	275	10	λ	λ	NOUN
ejpam-5986	275	11	)	)	PUNCT
ejpam-5986	275	12	λ	λ	X
ejpam-5986	275	13	u	u	NOUN
ejpam-5986	275	14	in	in	ADP
ejpam-5986	275	15	the	the	DET
ejpam-5986	275	16	equation	equation	NOUN
ejpam-5986	275	17	(	(	PUNCT
ejpam-5986	275	18	18	18	NUM
ejpam-5986	275	19	)	)	PUNCT
ejpam-5986	275	20	we	we	PRON
ejpam-5986	275	21	have	have	AUX
ejpam-5986	275	22	the	the	DET
ejpam-5986	275	23	relation	relation	NOUN
ejpam-5986	275	24	fα(u	fα(u	NOUN
ejpam-5986	275	25	)	)	PUNCT
ejpam-5986	275	26	=	=	SYM
ejpam-5986	276	1	(	(	PUNCT
ejpam-5986	276	2	λ	λ	X
ejpam-5986	276	3	ln(1	ln(1	PROPN
ejpam-5986	276	4	+	+	CCONJ
ejpam-5986	276	5	λ	λ	NOUN
ejpam-5986	276	6	)	)	PUNCT
ejpam-5986	276	7	)	)	PUNCT
ejpam-5986	277	1	α	α	PROPN
ejpam-5986	277	2	f	f	PROPN
ejpam-5986	277	3	∗	∗	PROPN
ejpam-5986	277	4	α	α	PROPN
ejpam-5986	277	5	,	,	PUNCT
ejpam-5986	277	6	λ	λ	X
ejpam-5986	277	7	(	(	PUNCT
ejpam-5986	277	8	ln(1	ln(1	PROPN
ejpam-5986	277	9	+	+	CCONJ
ejpam-5986	277	10	λ	λ	NOUN
ejpam-5986	277	11	)	)	PUNCT
ejpam-5986	277	12	λ	λ	NOUN
ejpam-5986	277	13	u	u	NOUN
ejpam-5986	277	14	)	)	PUNCT
ejpam-5986	277	15	.	.	PUNCT
ejpam-5986	278	1	example	example	NOUN
ejpam-5986	279	1	1	1	NUM
ejpam-5986	279	2	.	.	PUNCT
ejpam-5986	279	3	suppose	suppose	VERB
ejpam-5986	279	4	we	we	PRON
ejpam-5986	279	5	want	want	VERB
ejpam-5986	279	6	to	to	PART
ejpam-5986	279	7	find	find	VERB
ejpam-5986	279	8	g∗	g∗	PROPN
ejpam-5986	279	9	α	α	PRON
ejpam-5986	279	10	,	,	PUNCT
ejpam-5986	279	11	λ{cos	λ{cos	PROPN
ejpam-5986	279	12	at	at	ADP
ejpam-5986	279	13	}	}	PUNCT
ejpam-5986	279	14	using	use	VERB
ejpam-5986	279	15	the	the	DET
ejpam-5986	279	16	relation	relation	NOUN
ejpam-5986	279	17	by	by	ADP
ejpam-5986	279	18	the	the	DET
ejpam-5986	279	19	equation	equation	NOUN
ejpam-5986	279	20	(	(	PUNCT
ejpam-5986	279	21	18	18	NUM
ejpam-5986	279	22	)	)	PUNCT
ejpam-5986	279	23	.	.	PUNCT
ejpam-5986	280	1	let	let	AUX
ejpam-5986	280	2	g∗	g∗	VERB
ejpam-5986	280	3	α	α	PRON
ejpam-5986	280	4	,	,	PUNCT
ejpam-5986	280	5	λ{f(t	λ{f(t	NUM
ejpam-5986	280	6	)	)	PUNCT
ejpam-5986	280	7	}	}	PUNCT
ejpam-5986	280	8	=	=	SYM
ejpam-5986	280	9	f	f	PROPN
ejpam-5986	280	10	∗	∗	X
ejpam-5986	280	11	α	α	PROPN
ejpam-5986	280	12	,	,	PUNCT
ejpam-5986	280	13	λ(u	λ(u	PROPN
ejpam-5986	280	14	)	)	PUNCT
ejpam-5986	280	15	and	and	CCONJ
ejpam-5986	280	16	lα{f(t	lα{f(t	NOUN
ejpam-5986	280	17	)	)	PUNCT
ejpam-5986	280	18	}	}	PUNCT
ejpam-5986	280	19	=	=	SYM
ejpam-5986	280	20	fα(u	fα(u	NOUN
ejpam-5986	280	21	)	)	PUNCT
ejpam-5986	280	22	.	.	PUNCT
ejpam-5986	281	1	since	since	SCONJ
ejpam-5986	281	2	lα{cos	lα{co	NOUN
ejpam-5986	281	3	at	at	ADP
ejpam-5986	281	4	}	}	PUNCT
ejpam-5986	281	5	=	=	SYM
ejpam-5986	281	6	fα(u	fα(u	X
ejpam-5986	281	7	)	)	PUNCT
ejpam-5986	281	8	=	=	PUNCT
ejpam-5986	281	9	uα+1	uα+1	VERB
ejpam-5986	281	10	1	1	NUM
ejpam-5986	281	11	+	+	CCONJ
ejpam-5986	281	12	a2u2	a2u2	AUX
ejpam-5986	281	13	,	,	PUNCT
ejpam-5986	281	14	we	we	PRON
ejpam-5986	281	15	get	get	VERB
ejpam-5986	281	16	g∗	g∗	PROPN
ejpam-5986	281	17	α	α	NOUN
ejpam-5986	281	18	,	,	PUNCT
ejpam-5986	281	19	λ{cos	λ{cos	ADJ
ejpam-5986	281	20	at	at	ADP
ejpam-5986	281	21	}	}	PUNCT
ejpam-5986	281	22	=	=	SYM
ejpam-5986	281	23	(	(	PUNCT
ejpam-5986	281	24	ln(1	ln(1	PROPN
ejpam-5986	281	25	+	+	NUM
ejpam-5986	281	26	λ	λ	NOUN
ejpam-5986	281	27	)	)	PUNCT
ejpam-5986	281	28	λ	λ	NOUN
ejpam-5986	281	29	)	)	PUNCT
ejpam-5986	281	30	α	α	NOUN
ejpam-5986	281	31	fα	fα	NOUN
ejpam-5986	281	32	(	(	PUNCT
ejpam-5986	281	33	λu	λu	X
ejpam-5986	281	34	ln(1	ln(1	PROPN
ejpam-5986	281	35	+	+	CCONJ
ejpam-5986	281	36	λ	λ	NOUN
ejpam-5986	281	37	)	)	PUNCT
ejpam-5986	281	38	)	)	PUNCT
ejpam-5986	282	1	=	=	PUNCT
ejpam-5986	282	2	(	(	PUNCT
ejpam-5986	282	3	ln(1	ln(1	PROPN
ejpam-5986	282	4	+	+	NUM
ejpam-5986	282	5	λ	λ	NOUN
ejpam-5986	282	6	)	)	PUNCT
ejpam-5986	282	7	λ	λ	NOUN
ejpam-5986	282	8	)	)	PUNCT
ejpam-5986	282	9	α	α	PROPN
ejpam-5986	282	10	(	(	PUNCT
ejpam-5986	282	11	λu	λu	X
ejpam-5986	282	12	ln(1	ln(1	PROPN
ejpam-5986	282	13	+	+	CCONJ
ejpam-5986	282	14	λ	λ	NOUN
ejpam-5986	282	15	)	)	PUNCT
ejpam-5986	282	16	)	)	PUNCT
ejpam-5986	283	1	α+1	α+1	NUM
ejpam-5986	283	2	1	1	NUM
ejpam-5986	283	3	1	1	NUM
ejpam-5986	283	4	+	+	NUM
ejpam-5986	283	5	a2λ2u2	a2λ2u2	ADJ
ejpam-5986	283	6	ln2(1	ln2(1	NOUN
ejpam-5986	283	7	+	+	CCONJ
ejpam-5986	283	8	λ	λ	NOUN
ejpam-5986	283	9	)	)	PUNCT
ejpam-5986	283	10	=	=	SYM
ejpam-5986	284	1	λ	λ	X
ejpam-5986	284	2	ln(1	ln(1	NOUN
ejpam-5986	284	3	+	+	CCONJ
ejpam-5986	284	4	λ)uα+1	λ)uα+1	NOUN
ejpam-5986	284	5	ln2(1	ln2(1	NOUN
ejpam-5986	284	6	+	+	X
ejpam-5986	284	7	λ	λ	NOUN
ejpam-5986	284	8	)	)	PUNCT
ejpam-5986	284	9	+	+	CCONJ
ejpam-5986	284	10	a2λ2u2	a2λ2u2	PROPN
ejpam-5986	284	11	.	.	PUNCT
ejpam-5986	285	1	i̇.	i̇.	PROPN
ejpam-5986	285	2	ege	ege	PROPN
ejpam-5986	285	3	/	/	SYM
ejpam-5986	285	4	eur	eur	PROPN
ejpam-5986	285	5	.	.	PUNCT
ejpam-5986	286	1	j.	j.	PROPN
ejpam-5986	286	2	pure	pure	PROPN
ejpam-5986	286	3	appl	appl	PROPN
ejpam-5986	286	4	.	.	PROPN
ejpam-5986	286	5	math	math	PROPN
ejpam-5986	286	6	,	,	PUNCT
ejpam-5986	286	7	18	18	NUM
ejpam-5986	286	8	(	(	PUNCT
ejpam-5986	286	9	2	2	NUM
ejpam-5986	286	10	)	)	PUNCT
ejpam-5986	286	11	(	(	PUNCT
ejpam-5986	286	12	2025	2025	NUM
ejpam-5986	286	13	)	)	PUNCT
ejpam-5986	286	14	,	,	PUNCT
ejpam-5986	286	15	5986	5986	NUM
ejpam-5986	286	16	10	10	NUM
ejpam-5986	286	17	of	of	ADP
ejpam-5986	286	18	20	20	NUM
ejpam-5986	286	19	theorem	theorem	NOUN
ejpam-5986	286	20	9	9	NUM
ejpam-5986	286	21	.	.	PUNCT
ejpam-5986	287	1	(	(	PUNCT
ejpam-5986	287	2	the	the	DET
ejpam-5986	287	3	first	first	ADJ
ejpam-5986	287	4	translation	translation	NOUN
ejpam-5986	287	5	)	)	PUNCT
ejpam-5986	287	6	let	let	VERB
ejpam-5986	287	7	gα{f(t	gα{f(t	NOUN
ejpam-5986	287	8	)	)	PUNCT
ejpam-5986	287	9	}	}	PUNCT
ejpam-5986	287	10	=	=	SYM
ejpam-5986	287	11	fα(u	fα(u	NOUN
ejpam-5986	287	12	)	)	PUNCT
ejpam-5986	287	13	.	.	PUNCT
ejpam-5986	288	1	then	then	ADV
ejpam-5986	288	2	g∗	g∗	VERB
ejpam-5986	288	3	α	α	NOUN
ejpam-5986	288	4	,	,	PUNCT
ejpam-5986	288	5	λ{eatf(t	λ{eatf(t	NOUN
ejpam-5986	288	6	)	)	PUNCT
ejpam-5986	288	7	}	}	PUNCT
ejpam-5986	288	8	=	=	SYM
ejpam-5986	289	1	(	(	PUNCT
ejpam-5986	289	2	ln(1	ln(1	ADP
ejpam-5986	289	3	+	+	PROPN
ejpam-5986	289	4	λ)−	λ)−	X
ejpam-5986	289	5	aλu	aλu	ADJ
ejpam-5986	289	6	λ	λ	PROPN
ejpam-5986	289	7	)	)	PUNCT
ejpam-5986	289	8	α	α	NOUN
ejpam-5986	289	9	fα	fα	NOUN
ejpam-5986	289	10	(	(	PUNCT
ejpam-5986	289	11	λu	λu	X
ejpam-5986	289	12	ln(1	ln(1	NOUN
ejpam-5986	289	13	+	+	CCONJ
ejpam-5986	289	14	λ)−	λ)−	PROPN
ejpam-5986	289	15	aλu	aλu	NOUN
ejpam-5986	289	16	)	)	PUNCT
ejpam-5986	289	17	for	for	ADP
ejpam-5986	289	18	u	u	NOUN
ejpam-5986	289	19	<	<	X
ejpam-5986	289	20	ln(1	ln(1	PROPN
ejpam-5986	289	21	+	+	CCONJ
ejpam-5986	289	22	λ	λ	NOUN
ejpam-5986	289	23	)	)	PUNCT
ejpam-5986	289	24	aλ	aλ	ADP
ejpam-5986	289	25	.	.	PUNCT
ejpam-5986	290	1	proof	proof	NOUN
ejpam-5986	290	2	.	.	PUNCT
ejpam-5986	291	1	by	by	ADP
ejpam-5986	291	2	using	use	VERB
ejpam-5986	291	3	the	the	DET
ejpam-5986	291	4	equation	equation	NOUN
ejpam-5986	291	5	(	(	PUNCT
ejpam-5986	291	6	7	7	X
ejpam-5986	291	7	)	)	PUNCT
ejpam-5986	291	8	we	we	PRON
ejpam-5986	291	9	have	have	AUX
ejpam-5986	291	10	g∗	g∗	VERB
ejpam-5986	291	11	α	α	NUM
ejpam-5986	291	12	,	,	PUNCT
ejpam-5986	291	13	λ{eatf(t	λ{eatf(t	NOUN
ejpam-5986	291	14	)	)	PUNCT
ejpam-5986	291	15	}	}	PUNCT
ejpam-5986	292	1	=	=	PUNCT
ejpam-5986	292	2	uα	uα	PROPN
ejpam-5986	292	3	∫	∫	PROPN
ejpam-5986	292	4	∞	∞	PROPN
ejpam-5986	292	5	0	0	NUM
ejpam-5986	293	1	(	(	PUNCT
ejpam-5986	293	2	1	1	NUM
ejpam-5986	293	3	+	+	X
ejpam-5986	293	4	λ)−	λ)−	X
ejpam-5986	293	5	t	t	PROPN
ejpam-5986	293	6	uλ	uλ	PRON
ejpam-5986	293	7	eatf(t	eatf(t	PROPN
ejpam-5986	293	8	)	)	PUNCT
ejpam-5986	293	9	dt	dt	PROPN
ejpam-5986	294	1	=	=	PUNCT
ejpam-5986	294	2	uα	uα	PROPN
ejpam-5986	294	3	∫	∫	PROPN
ejpam-5986	294	4	∞	∞	PROPN
ejpam-5986	294	5	0	0	PUNCT
ejpam-5986	295	1	e	e	PROPN
ejpam-5986	295	2	−t	−t	NOUN
ejpam-5986	295	3	(	(	PUNCT
ejpam-5986	295	4	ln(1+λ	ln(1+λ	PROPN
ejpam-5986	295	5	)	)	PUNCT
ejpam-5986	295	6	λu	λu	X
ejpam-5986	295	7	−a	−a	ADV
ejpam-5986	295	8	)	)	PUNCT
ejpam-5986	295	9	f(t	f(t	PROPN
ejpam-5986	295	10	)	)	PUNCT
ejpam-5986	295	11	dt	dt	NOUN
ejpam-5986	296	1	=	=	SYM
ejpam-5986	296	2	uα	uα	PROPN
ejpam-5986	296	3	(	(	PUNCT
ejpam-5986	296	4	λu	λu	X
ejpam-5986	297	1	ln(1	ln(1	NOUN
ejpam-5986	297	2	+	+	CCONJ
ejpam-5986	297	3	λ)−	λ)−	PROPN
ejpam-5986	297	4	aλu	aλu	NOUN
ejpam-5986	297	5	)	)	PUNCT
ejpam-5986	297	6	α	α	NOUN
ejpam-5986	297	7	(	(	PUNCT
ejpam-5986	297	8	ln(1	ln(1	PROPN
ejpam-5986	297	9	+	+	CCONJ
ejpam-5986	298	1	λ)−	λ)−	PROPN
ejpam-5986	298	2	aλu	aλu	NOUN
ejpam-5986	298	3	λu	λu	X
ejpam-5986	298	4	)	)	PUNCT
ejpam-5986	298	5	α	α	NOUN
ejpam-5986	298	6	∫	∫	PROPN
ejpam-5986	299	1	∞	∞	NOUN
ejpam-5986	299	2	0	0	PUNCT
ejpam-5986	300	1	e	e	X
ejpam-5986	300	2	−	−	PROPN
ejpam-5986	300	3	t	t	PROPN
ejpam-5986	300	4	λu	λu	X
ejpam-5986	301	1	ln(1	ln(1	PROPN
ejpam-5986	301	2	+	+	CCONJ
ejpam-5986	301	3	λ)−	λ)−	PROPN
ejpam-5986	301	4	aλu	aλu	ADJ
ejpam-5986	301	5	f(t	f(t	NOUN
ejpam-5986	301	6	)	)	PUNCT
ejpam-5986	301	7	dt	dt	NOUN
ejpam-5986	302	1	=	=	PUNCT
ejpam-5986	302	2	(	(	PUNCT
ejpam-5986	302	3	ln(1	ln(1	ADP
ejpam-5986	302	4	+	+	CCONJ
ejpam-5986	302	5	λ)−	λ)−	PROPN
ejpam-5986	302	6	aλu	aλu	NOUN
ejpam-5986	302	7	λu	λu	X
ejpam-5986	302	8	)	)	PUNCT
ejpam-5986	302	9	α	α	NOUN
ejpam-5986	302	10	fα	fα	ADV
ejpam-5986	302	11	{	{	PUNCT
ejpam-5986	302	12	λu	λu	X
ejpam-5986	302	13	ln(1	ln(1	NOUN
ejpam-5986	302	14	+	+	CCONJ
ejpam-5986	302	15	λ)−	λ)−	PROPN
ejpam-5986	302	16	aλu	aλu	NOUN
ejpam-5986	302	17	}	}	PUNCT
ejpam-5986	302	18	for	for	ADP
ejpam-5986	302	19	λu	λu	PROPN
ejpam-5986	302	20	ln(1	ln(1	NOUN
ejpam-5986	302	21	+	+	PROPN
ejpam-5986	302	22	λ)−	λ)−	PROPN
ejpam-5986	302	23	aλu	aλu	NOUN
ejpam-5986	302	24	>	>	X
ejpam-5986	302	25	0	0	NUM
ejpam-5986	302	26	,	,	PUNCT
ejpam-5986	302	27	and	and	CCONJ
ejpam-5986	302	28	the	the	DET
ejpam-5986	302	29	result	result	NOUN
ejpam-5986	302	30	follows	follow	VERB
ejpam-5986	302	31	.	.	PUNCT
ejpam-5986	303	1	note	note	VERB
ejpam-5986	303	2	that	that	SCONJ
ejpam-5986	303	3	,	,	PUNCT
ejpam-5986	303	4	by	by	ADP
ejpam-5986	303	5	using	use	VERB
ejpam-5986	303	6	the	the	DET
ejpam-5986	303	7	theorem	theorem	NOUN
ejpam-5986	303	8	9	9	NUM
ejpam-5986	303	9	we	we	PRON
ejpam-5986	303	10	have	have	VERB
ejpam-5986	303	11	lim	lim	PROPN
ejpam-5986	303	12	λ→0	λ→0	PROPN
ejpam-5986	303	13	g∗	g∗	VERB
ejpam-5986	303	14	α	α	NOUN
ejpam-5986	303	15	,	,	PUNCT
ejpam-5986	303	16	λ{eatf(t	λ{eatf(t	NOUN
ejpam-5986	303	17	)	)	PUNCT
ejpam-5986	303	18	}	}	PUNCT
ejpam-5986	304	1	=	=	SYM
ejpam-5986	304	2	lim	lim	PROPN
ejpam-5986	304	3	λ→0	λ→0	PUNCT
ejpam-5986	305	1	[	[	X
ejpam-5986	305	2	(	(	PUNCT
ejpam-5986	305	3	ln(1	ln(1	ADP
ejpam-5986	305	4	+	+	PROPN
ejpam-5986	305	5	λ)−	λ)−	X
ejpam-5986	305	6	aλu	aλu	ADJ
ejpam-5986	305	7	λ	λ	PROPN
ejpam-5986	305	8	)	)	PUNCT
ejpam-5986	305	9	α	α	NOUN
ejpam-5986	305	10	fα	fα	NOUN
ejpam-5986	305	11	(	(	PUNCT
ejpam-5986	305	12	λu	λu	X
ejpam-5986	305	13	ln(1	ln(1	NOUN
ejpam-5986	305	14	+	+	CCONJ
ejpam-5986	305	15	λ)−	λ)−	PROPN
ejpam-5986	305	16	aλu	aλu	NOUN
ejpam-5986	305	17	)	)	PUNCT
ejpam-5986	305	18	]	]	PUNCT
ejpam-5986	306	1	=	=	PUNCT
ejpam-5986	306	2	(	(	PUNCT
ejpam-5986	306	3	1−	1−	NUM
ejpam-5986	306	4	au)α	au)α	NOUN
ejpam-5986	306	5	fα	fα	ADP
ejpam-5986	306	6	{	{	PUNCT
ejpam-5986	306	7	u	u	NOUN
ejpam-5986	306	8	1−	1−	NUM
ejpam-5986	306	9	au	au	PROPN
ejpam-5986	306	10	}	}	PUNCT
ejpam-5986	306	11	=	=	NOUN
ejpam-5986	306	12	gα{eatf(t	gα{eatf(t	NOUN
ejpam-5986	306	13	)	)	PUNCT
ejpam-5986	306	14	}	}	PUNCT
ejpam-5986	306	15	,	,	PUNCT
ejpam-5986	306	16	and	and	CCONJ
ejpam-5986	306	17	since	since	SCONJ
ejpam-5986	306	18	gα{sin	gα{sin	NOUN
ejpam-5986	306	19	bt	bt	NOUN
ejpam-5986	306	20	}	}	PUNCT
ejpam-5986	306	21	=	=	PUNCT
ejpam-5986	306	22	buα+2	buα+2	X
ejpam-5986	306	23	1	1	NUM
ejpam-5986	307	1	+	+	CCONJ
ejpam-5986	307	2	b2u2	b2u2	PROPN
ejpam-5986	307	3	=	=	NOUN
ejpam-5986	307	4	fα(u	fα(u	NOUN
ejpam-5986	307	5	)	)	PUNCT
ejpam-5986	307	6	,	,	PUNCT
ejpam-5986	307	7	gα{cos	gα{cos	ADJ
ejpam-5986	307	8	bt	bt	ADJ
ejpam-5986	307	9	}	}	PUNCT
ejpam-5986	307	10	=	=	PUNCT
ejpam-5986	307	11	uα+1	uα+1	NOUN
ejpam-5986	307	12	1	1	NUM
ejpam-5986	308	1	+	+	CCONJ
ejpam-5986	308	2	b2u2	b2u2	PROPN
ejpam-5986	308	3	=	=	NOUN
ejpam-5986	308	4	fα(u	fα(u	X
ejpam-5986	308	5	)	)	PUNCT
ejpam-5986	308	6	in	in	ADP
ejpam-5986	308	7	[	[	X
ejpam-5986	308	8	27	27	NUM
ejpam-5986	308	9	]	]	PUNCT
ejpam-5986	308	10	,	,	PUNCT
ejpam-5986	308	11	we	we	PRON
ejpam-5986	308	12	get	get	VERB
ejpam-5986	308	13	the	the	DET
ejpam-5986	308	14	following	follow	VERB
ejpam-5986	308	15	results	result	NOUN
ejpam-5986	308	16	:	:	PUNCT
ejpam-5986	308	17	g∗	g∗	VERB
ejpam-5986	308	18	α	α	NOUN
ejpam-5986	308	19	,	,	PUNCT
ejpam-5986	308	20	λ{eat	λ{eat	PROPN
ejpam-5986	308	21	sin	sin	VERB
ejpam-5986	308	22	bt	bt	NOUN
ejpam-5986	308	23	}	}	PUNCT
ejpam-5986	309	1	=	=	SYM
ejpam-5986	309	2	bλ2uα+2	bλ2uα+2	X
ejpam-5986	309	3	(	(	PUNCT
ejpam-5986	309	4	ln(1	ln(1	PROPN
ejpam-5986	309	5	+	+	PROPN
ejpam-5986	309	6	λ)−	λ)−	PROPN
ejpam-5986	309	7	aλu)2	aλu)2	PROPN
ejpam-5986	309	8	+	+	CCONJ
ejpam-5986	309	9	b2λ2u2	b2λ2u2	ADJ
ejpam-5986	309	10	,	,	PUNCT
ejpam-5986	309	11	g∗	g∗	VERB
ejpam-5986	309	12	α	α	PRON
ejpam-5986	309	13	,	,	PUNCT
ejpam-5986	309	14	λ{eat	λ{eat	PROPN
ejpam-5986	309	15	cos	cos	PROPN
ejpam-5986	309	16	bt	bt	PROPN
ejpam-5986	309	17	}	}	PUNCT
ejpam-5986	309	18	=	=	NUM
ejpam-5986	309	19	λuα+1	λuα+1	NOUN
ejpam-5986	309	20	(	(	PUNCT
ejpam-5986	309	21	ln(1	ln(1	NOUN
ejpam-5986	309	22	+	+	CCONJ
ejpam-5986	309	23	λ)−	λ)−	PROPN
ejpam-5986	309	24	aλu	aλu	NOUN
ejpam-5986	309	25	)	)	PUNCT
ejpam-5986	309	26	(	(	PUNCT
ejpam-5986	310	1	ln(1	ln(1	PROPN
ejpam-5986	310	2	+	+	PROPN
ejpam-5986	310	3	λ)−	λ)−	PROPN
ejpam-5986	310	4	aλu)2	aλu)2	PROPN
ejpam-5986	310	5	+	+	CCONJ
ejpam-5986	310	6	b2λ2u2	b2λ2u2	ADJ
ejpam-5986	310	7	.	.	PUNCT
ejpam-5986	311	1	theorem	theorem	ADJ
ejpam-5986	311	2	10	10	NUM
ejpam-5986	311	3	.	.	PUNCT
ejpam-5986	312	1	(	(	PUNCT
ejpam-5986	312	2	the	the	DET
ejpam-5986	312	3	second	second	ADJ
ejpam-5986	312	4	translation	translation	NOUN
ejpam-5986	312	5	)	)	PUNCT
ejpam-5986	312	6	let	let	VERB
ejpam-5986	312	7	g∗	g∗	VERB
ejpam-5986	312	8	α	α	PRON
ejpam-5986	312	9	,	,	PUNCT
ejpam-5986	312	10	λ{f(t	λ{f(t	NUM
ejpam-5986	312	11	)	)	PUNCT
ejpam-5986	312	12	}	}	PUNCT
ejpam-5986	312	13	=	=	SYM
ejpam-5986	312	14	f	f	PROPN
ejpam-5986	312	15	∗	∗	X
ejpam-5986	312	16	α	α	PROPN
ejpam-5986	312	17	,	,	PUNCT
ejpam-5986	312	18	λ(u	λ(u	PROPN
ejpam-5986	312	19	)	)	PUNCT
ejpam-5986	312	20	.	.	PUNCT
ejpam-5986	313	1	then	then	ADV
ejpam-5986	313	2	for	for	ADP
ejpam-5986	313	3	a	a	DET
ejpam-5986	313	4	≥	≥	NOUN
ejpam-5986	313	5	0	0	NUM
ejpam-5986	314	1	we	we	PRON
ejpam-5986	314	2	have	have	AUX
ejpam-5986	314	3	g∗	g∗	PROPN
ejpam-5986	314	4	α	α	PROPN
ejpam-5986	314	5	,	,	PUNCT
ejpam-5986	314	6	λ{f(t−	λ{f(t−	NOUN
ejpam-5986	314	7	a)h(t−	a)h(t−	NOUN
ejpam-5986	315	1	a	a	X
ejpam-5986	315	2	)	)	PUNCT
ejpam-5986	315	3	}	}	PUNCT
ejpam-5986	315	4	=	=	SYM
ejpam-5986	315	5	(	(	PUNCT
ejpam-5986	315	6	1	1	NUM
ejpam-5986	315	7	+	+	NUM
ejpam-5986	315	8	λ	λ	NOUN
ejpam-5986	315	9	)	)	PUNCT
ejpam-5986	315	10	−a	−a	NOUN
ejpam-5986	315	11	λu	λu	X
ejpam-5986	315	12	f	f	PROPN
ejpam-5986	315	13	∗	∗	PROPN
ejpam-5986	315	14	α	α	PROPN
ejpam-5986	315	15	,	,	PUNCT
ejpam-5986	315	16	λ(u	λ(u	PROPN
ejpam-5986	315	17	)	)	PUNCT
ejpam-5986	315	18	,	,	PUNCT
ejpam-5986	315	19	where	where	SCONJ
ejpam-5986	315	20	h(t	h(t	PROPN
ejpam-5986	315	21	)	)	PUNCT
ejpam-5986	315	22	is	be	AUX
ejpam-5986	315	23	the	the	DET
ejpam-5986	315	24	heaviside	heaviside	ADJ
ejpam-5986	315	25	function	function	NOUN
ejpam-5986	315	26	,	,	PUNCT
ejpam-5986	315	27	which	which	PRON
ejpam-5986	315	28	is	be	AUX
ejpam-5986	315	29	defined	define	VERB
ejpam-5986	315	30	by	by	ADP
ejpam-5986	315	31	h(t	h(t	PROPN
ejpam-5986	315	32	)	)	PUNCT
ejpam-5986	316	1	=	=	PUNCT
ejpam-5986	316	2	1	1	NUM
ejpam-5986	316	3	if	if	SCONJ
ejpam-5986	316	4	t	t	PROPN
ejpam-5986	316	5	≥	≥	NOUN
ejpam-5986	316	6	0	0	NUM
ejpam-5986	316	7	and	and	CCONJ
ejpam-5986	316	8	h(t	h(t	NUM
ejpam-5986	316	9	)	)	PUNCT
ejpam-5986	317	1	=	=	SYM
ejpam-5986	317	2	0	0	PUNCT
ejpam-5986	318	1	if	if	SCONJ
ejpam-5986	318	2	t	t	PROPN
ejpam-5986	318	3	<	<	X
ejpam-5986	318	4	0	0	NUM
ejpam-5986	318	5	.	.	PUNCT
ejpam-5986	319	1	in	in	ADP
ejpam-5986	319	2	particular	particular	ADJ
ejpam-5986	319	3	,	,	PUNCT
ejpam-5986	319	4	the	the	DET
ejpam-5986	319	5	modified	modify	VERB
ejpam-5986	319	6	laplace	laplace	NOUN
ejpam-5986	319	7	-	-	PUNCT
ejpam-5986	319	8	type	type	NOUN
ejpam-5986	319	9	transform	transform	NOUN
ejpam-5986	319	10	of	of	ADP
ejpam-5986	319	11	the	the	DET
ejpam-5986	319	12	heaviside	heaviside	ADJ
ejpam-5986	319	13	function	function	NOUN
ejpam-5986	319	14	is	be	AUX
ejpam-5986	319	15	g∗	g∗	NOUN
ejpam-5986	319	16	α	α	PRON
ejpam-5986	319	17	,	,	PUNCT
ejpam-5986	319	18	λ{h(t−	λ{h(t−	PUNCT
ejpam-5986	319	19	a	a	X
ejpam-5986	319	20	)	)	PUNCT
ejpam-5986	319	21	}	}	PUNCT
ejpam-5986	319	22	=	=	PUNCT
ejpam-5986	319	23	λ	λ	X
ejpam-5986	319	24	ln(1	ln(1	PROPN
ejpam-5986	319	25	+	+	NUM
ejpam-5986	319	26	λ	λ	NOUN
ejpam-5986	319	27	)	)	PUNCT
ejpam-5986	319	28	(	(	PUNCT
ejpam-5986	319	29	1	1	NUM
ejpam-5986	319	30	+	+	NUM
ejpam-5986	319	31	λ	λ	NOUN
ejpam-5986	319	32	)	)	PUNCT
ejpam-5986	319	33	−a	−a	NOUN
ejpam-5986	319	34	λu	λu	ADP
ejpam-5986	319	35	uα+1	uα+1	NOUN
ejpam-5986	319	36	.	.	PUNCT
ejpam-5986	320	1	i̇.	i̇.	VERB
ejpam-5986	320	2	ege	ege	PROPN
ejpam-5986	320	3	/	/	SYM
ejpam-5986	320	4	eur	eur	PROPN
ejpam-5986	320	5	.	.	PUNCT
ejpam-5986	321	1	j.	j.	PROPN
ejpam-5986	321	2	pure	pure	PROPN
ejpam-5986	321	3	appl	appl	PROPN
ejpam-5986	321	4	.	.	PROPN
ejpam-5986	321	5	math	math	PROPN
ejpam-5986	321	6	,	,	PUNCT
ejpam-5986	321	7	18	18	NUM
ejpam-5986	321	8	(	(	PUNCT
ejpam-5986	321	9	2	2	NUM
ejpam-5986	321	10	)	)	PUNCT
ejpam-5986	321	11	(	(	PUNCT
ejpam-5986	321	12	2025	2025	NUM
ejpam-5986	321	13	)	)	PUNCT
ejpam-5986	321	14	,	,	PUNCT
ejpam-5986	321	15	5986	5986	NUM
ejpam-5986	321	16	11	11	NUM
ejpam-5986	321	17	of	of	ADP
ejpam-5986	321	18	20	20	NUM
ejpam-5986	321	19	proof	proof	NOUN
ejpam-5986	321	20	.	.	PUNCT
ejpam-5986	322	1	we	we	PRON
ejpam-5986	322	2	have	have	AUX
ejpam-5986	322	3	g∗	g∗	PROPN
ejpam-5986	322	4	α	α	PROPN
ejpam-5986	322	5	,	,	PUNCT
ejpam-5986	322	6	λ{f(t−	λ{f(t−	NOUN
ejpam-5986	322	7	a)h(t−	a)h(t−	NOUN
ejpam-5986	323	1	a	a	X
ejpam-5986	323	2	)	)	PUNCT
ejpam-5986	323	3	}	}	PUNCT
ejpam-5986	323	4	=	=	PUNCT
ejpam-5986	324	1	uα	uα	PROPN
ejpam-5986	324	2	∫	∫	PROPN
ejpam-5986	324	3	∞	∞	PROPN
ejpam-5986	324	4	0	0	NUM
ejpam-5986	325	1	(	(	PUNCT
ejpam-5986	325	2	1	1	NUM
ejpam-5986	325	3	+	+	X
ejpam-5986	325	4	λ)−	λ)−	ADP
ejpam-5986	325	5	t	t	X
ejpam-5986	325	6	uλ	uλ	X
ejpam-5986	326	1	f(t−	f(t−	PROPN
ejpam-5986	327	1	a)h(t−	a)h(t−	NOUN
ejpam-5986	327	2	a	a	NOUN
ejpam-5986	327	3	)	)	PUNCT
ejpam-5986	327	4	dt	dt	NOUN
ejpam-5986	328	1	=	=	PUNCT
ejpam-5986	328	2	uα	uα	PROPN
ejpam-5986	328	3	∫	∫	PROPN
ejpam-5986	328	4	∞	∞	PROPN
ejpam-5986	328	5	a	a	DET
ejpam-5986	328	6	(	(	PUNCT
ejpam-5986	328	7	1	1	NUM
ejpam-5986	328	8	+	+	X
ejpam-5986	328	9	λ)−	λ)−	X
ejpam-5986	328	10	t	t	X
ejpam-5986	328	11	uλ	uλ	X
ejpam-5986	329	1	f(t−	f(t−	PROPN
ejpam-5986	329	2	a	a	PRON
ejpam-5986	329	3	)	)	PUNCT
ejpam-5986	329	4	dt	dt	NOUN
ejpam-5986	329	5	.	.	PUNCT
ejpam-5986	330	1	now	now	ADV
ejpam-5986	330	2	,	,	PUNCT
ejpam-5986	330	3	using	use	VERB
ejpam-5986	330	4	the	the	DET
ejpam-5986	330	5	change	change	NOUN
ejpam-5986	330	6	of	of	ADP
ejpam-5986	330	7	variable	variable	NOUN
ejpam-5986	330	8	t−	t−	ADP
ejpam-5986	330	9	a	a	DET
ejpam-5986	330	10	=	=	X
ejpam-5986	330	11	y	y	NOUN
ejpam-5986	330	12	we	we	PRON
ejpam-5986	330	13	get	get	VERB
ejpam-5986	330	14	g∗	g∗	PROPN
ejpam-5986	330	15	α	α	NOUN
ejpam-5986	330	16	,	,	PUNCT
ejpam-5986	330	17	λ{f(t−	λ{f(t−	NOUN
ejpam-5986	330	18	a)h(t−	a)h(t−	NOUN
ejpam-5986	331	1	a	a	X
ejpam-5986	331	2	)	)	PUNCT
ejpam-5986	331	3	}	}	PUNCT
ejpam-5986	331	4	=	=	PUNCT
ejpam-5986	332	1	uα	uα	PROPN
ejpam-5986	332	2	∫	∫	PROPN
ejpam-5986	332	3	∞	∞	PROPN
ejpam-5986	332	4	0	0	NUM
ejpam-5986	333	1	(	(	PUNCT
ejpam-5986	333	2	1	1	NUM
ejpam-5986	333	3	+	+	CCONJ
ejpam-5986	333	4	λ)−	λ)−	PROPN
ejpam-5986	333	5	(	(	PUNCT
ejpam-5986	333	6	a+y	a+y	NOUN
ejpam-5986	333	7	)	)	PUNCT
ejpam-5986	333	8	uλ	uλ	PRON
ejpam-5986	333	9	f(y	f(y	NOUN
ejpam-5986	333	10	)	)	PUNCT
ejpam-5986	333	11	dy	dy	NOUN
ejpam-5986	333	12	=	=	PUNCT
ejpam-5986	333	13	uα(1	uα(1	PROPN
ejpam-5986	334	1	+	+	CCONJ
ejpam-5986	335	1	λ)−	λ)−	ADP
ejpam-5986	335	2	a	a	PRON
ejpam-5986	335	3	uλ	uλ	X
ejpam-5986	335	4	∫	∫	PROPN
ejpam-5986	335	5	∞	∞	PROPN
ejpam-5986	335	6	0	0	NUM
ejpam-5986	336	1	(	(	PUNCT
ejpam-5986	336	2	1	1	NUM
ejpam-5986	336	3	+	+	X
ejpam-5986	336	4	λ)−	λ)−	PROPN
ejpam-5986	336	5	y	y	PROPN
ejpam-5986	336	6	uλ	uλ	PRON
ejpam-5986	336	7	f(y	f(y	NOUN
ejpam-5986	336	8	)	)	PUNCT
ejpam-5986	336	9	dy	dy	NOUN
ejpam-5986	336	10	=	=	SYM
ejpam-5986	336	11	(	(	PUNCT
ejpam-5986	336	12	1	1	NUM
ejpam-5986	337	1	+	+	X
ejpam-5986	337	2	λ)−	λ)−	ADP
ejpam-5986	337	3	a	a	DET
ejpam-5986	337	4	uλf	uλf	PROPN
ejpam-5986	337	5	∗	∗	NOUN
ejpam-5986	337	6	α	α	PROPN
ejpam-5986	337	7	,	,	PUNCT
ejpam-5986	337	8	λ(u	λ(u	PROPN
ejpam-5986	337	9	)	)	PUNCT
ejpam-5986	337	10	and	and	CCONJ
ejpam-5986	337	11	g∗	g∗	VERB
ejpam-5986	337	12	α	α	NUM
ejpam-5986	337	13	,	,	PUNCT
ejpam-5986	337	14	λ{h(t−	λ{h(t−	PUNCT
ejpam-5986	337	15	a	a	X
ejpam-5986	337	16	)	)	PUNCT
ejpam-5986	337	17	}	}	PUNCT
ejpam-5986	337	18	=	=	PUNCT
ejpam-5986	337	19	uα	uα	PROPN
ejpam-5986	337	20	∫	∫	PROPN
ejpam-5986	337	21	∞	∞	PROPN
ejpam-5986	337	22	0	0	NUM
ejpam-5986	338	1	(	(	PUNCT
ejpam-5986	338	2	1	1	NUM
ejpam-5986	338	3	+	+	X
ejpam-5986	338	4	λ)−	λ)−	PROPN
ejpam-5986	338	5	t	t	PROPN
ejpam-5986	339	1	uλh(t−	uλh(t−	NOUN
ejpam-5986	339	2	a	a	X
ejpam-5986	339	3	)	)	PUNCT
ejpam-5986	339	4	dt	dt	NOUN
ejpam-5986	339	5	=	=	PUNCT
ejpam-5986	340	1	uα	uα	PROPN
ejpam-5986	340	2	∫	∫	PROPN
ejpam-5986	340	3	∞	∞	PROPN
ejpam-5986	341	1	a	a	DET
ejpam-5986	341	2	(	(	PUNCT
ejpam-5986	341	3	1	1	NUM
ejpam-5986	341	4	+	+	X
ejpam-5986	341	5	λ)−	λ)−	X
ejpam-5986	341	6	t	t	NOUN
ejpam-5986	341	7	λu	λu	X
ejpam-5986	341	8	dt	dt	NOUN
ejpam-5986	341	9	=	=	PUNCT
ejpam-5986	341	10	λ	λ	X
ejpam-5986	341	11	ln(1	ln(1	PROPN
ejpam-5986	341	12	+	+	NUM
ejpam-5986	341	13	λ	λ	NOUN
ejpam-5986	341	14	)	)	PUNCT
ejpam-5986	341	15	(	(	PUNCT
ejpam-5986	341	16	1	1	NUM
ejpam-5986	342	1	+	+	X
ejpam-5986	342	2	λ)−	λ)−	ADP
ejpam-5986	342	3	a	a	DET
ejpam-5986	342	4	λuuα+1	λuuα+1	NOUN
ejpam-5986	342	5	.	.	PUNCT
ejpam-5986	343	1	note	note	VERB
ejpam-5986	343	2	that	that	SCONJ
ejpam-5986	343	3	by	by	ADP
ejpam-5986	343	4	using	use	VERB
ejpam-5986	343	5	the	the	DET
ejpam-5986	343	6	theorem	theorem	NOUN
ejpam-5986	343	7	10	10	NUM
ejpam-5986	343	8	we	we	PRON
ejpam-5986	343	9	have	have	VERB
ejpam-5986	343	10	lim	lim	PROPN
ejpam-5986	343	11	λ→0	λ→0	PROPN
ejpam-5986	343	12	g∗	g∗	VERB
ejpam-5986	343	13	α	α	PROPN
ejpam-5986	343	14	,	,	PUNCT
ejpam-5986	343	15	λ{f(t−	λ{f(t−	NOUN
ejpam-5986	343	16	a)h(t−	a)h(t−	NOUN
ejpam-5986	344	1	a	a	X
ejpam-5986	344	2	)	)	PUNCT
ejpam-5986	344	3	}	}	PUNCT
ejpam-5986	344	4	=	=	SYM
ejpam-5986	344	5	lim	lim	PROPN
ejpam-5986	344	6	λ→0	λ→0	PUNCT
ejpam-5986	344	7	(	(	PUNCT
ejpam-5986	344	8	1	1	NUM
ejpam-5986	344	9	+	+	NUM
ejpam-5986	344	10	λ	λ	NOUN
ejpam-5986	344	11	)	)	PUNCT
ejpam-5986	344	12	−a	−a	NOUN
ejpam-5986	344	13	λu	λu	X
ejpam-5986	344	14	f	f	PROPN
ejpam-5986	344	15	∗	∗	PROPN
ejpam-5986	344	16	α	α	PROPN
ejpam-5986	344	17	,	,	PUNCT
ejpam-5986	344	18	λ(u	λ(u	PROPN
ejpam-5986	344	19	)	)	PUNCT
ejpam-5986	344	20	=	=	PUNCT
ejpam-5986	345	1	e−	e−	X
ejpam-5986	345	2	a	a	DET
ejpam-5986	345	3	ufα(u	ufα(u	PROPN
ejpam-5986	345	4	)	)	PUNCT
ejpam-5986	345	5	=	=	SYM
ejpam-5986	346	1	gα{f(t−	gα{f(t−	INTJ
ejpam-5986	346	2	a)h(t−	a)h(t−	NOUN
ejpam-5986	346	3	a	a	X
ejpam-5986	346	4	)	)	PUNCT
ejpam-5986	346	5	}	}	PUNCT
ejpam-5986	346	6	,	,	PUNCT
ejpam-5986	346	7	(	(	PUNCT
ejpam-5986	346	8	19	19	NUM
ejpam-5986	346	9	)	)	PUNCT
ejpam-5986	346	10	and	and	CCONJ
ejpam-5986	346	11	lim	lim	PROPN
ejpam-5986	346	12	λ→0	λ→0	PROPN
ejpam-5986	346	13	g∗	g∗	VERB
ejpam-5986	346	14	α	α	NOUN
ejpam-5986	346	15	,	,	PUNCT
ejpam-5986	346	16	λ{h(t−	λ{h(t−	PUNCT
ejpam-5986	346	17	a	a	X
ejpam-5986	346	18	)	)	PUNCT
ejpam-5986	346	19	}	}	PUNCT
ejpam-5986	347	1	=	=	SYM
ejpam-5986	347	2	lim	lim	PROPN
ejpam-5986	347	3	λ→0	λ→0	PUNCT
ejpam-5986	347	4	λ	λ	X
ejpam-5986	347	5	ln(1	ln(1	PROPN
ejpam-5986	347	6	+	+	NUM
ejpam-5986	347	7	λ	λ	NOUN
ejpam-5986	347	8	)	)	PUNCT
ejpam-5986	347	9	(	(	PUNCT
ejpam-5986	347	10	1	1	NUM
ejpam-5986	347	11	+	+	NUM
ejpam-5986	347	12	λ	λ	NOUN
ejpam-5986	347	13	)	)	PUNCT
ejpam-5986	347	14	−a	−a	NOUN
ejpam-5986	347	15	λu	λu	NOUN
ejpam-5986	347	16	uα+1	uα+1	NOUN
ejpam-5986	347	17	=	=	PRON
ejpam-5986	347	18	e−	e−	X
ejpam-5986	347	19	a	a	DET
ejpam-5986	347	20	uuα+1	uuα+1	NOUN
ejpam-5986	347	21	=	=	SYM
ejpam-5986	347	22	gα{h(t−	gα{h(t−	NOUN
ejpam-5986	347	23	a	a	NOUN
ejpam-5986	347	24	)	)	PUNCT
ejpam-5986	347	25	}	}	PUNCT
ejpam-5986	347	26	.	.	PUNCT
ejpam-5986	348	1	(	(	PUNCT
ejpam-5986	348	2	20	20	NUM
ejpam-5986	348	3	)	)	PUNCT
ejpam-5986	348	4	theorem	theorem	NOUN
ejpam-5986	348	5	11	11	NUM
ejpam-5986	348	6	.	.	PUNCT
ejpam-5986	349	1	(	(	PUNCT
ejpam-5986	349	2	transform	transform	NOUN
ejpam-5986	349	3	of	of	ADP
ejpam-5986	349	4	an	an	DET
ejpam-5986	349	5	integral	integral	ADJ
ejpam-5986	349	6	)	)	PUNCT
ejpam-5986	349	7	let	let	VERB
ejpam-5986	349	8	f(t	f(t	NOUN
ejpam-5986	349	9	)	)	PUNCT
ejpam-5986	349	10	be	be	AUX
ejpam-5986	349	11	a	a	DET
ejpam-5986	349	12	piecewise	piecewise	NOUN
ejpam-5986	349	13	-	-	PUNCT
ejpam-5986	349	14	continious	continious	ADJ
ejpam-5986	349	15	function	function	NOUN
ejpam-5986	349	16	for	for	ADP
ejpam-5986	349	17	t	t	PROPN
ejpam-5986	349	18	≥	≥	NOUN
ejpam-5986	349	19	0	0	NUM
ejpam-5986	349	20	and	and	CCONJ
ejpam-5986	349	21	integrable	integrable	ADJ
ejpam-5986	349	22	.	.	PUNCT
ejpam-5986	350	1	then	then	ADV
ejpam-5986	350	2	if	if	SCONJ
ejpam-5986	350	3	g∗	g∗	VERB
ejpam-5986	350	4	α	α	X
ejpam-5986	350	5	,	,	PUNCT
ejpam-5986	350	6	λ{f(t	λ{f(t	NUM
ejpam-5986	350	7	)	)	PUNCT
ejpam-5986	350	8	}	}	PUNCT
ejpam-5986	350	9	=	=	SYM
ejpam-5986	350	10	f	f	PROPN
ejpam-5986	350	11	∗	∗	X
ejpam-5986	350	12	α	α	PROPN
ejpam-5986	350	13	,	,	PUNCT
ejpam-5986	350	14	λ(u	λ(u	PROPN
ejpam-5986	350	15	)	)	PUNCT
ejpam-5986	350	16	we	we	PRON
ejpam-5986	350	17	have	have	AUX
ejpam-5986	350	18	g∗	g∗	PROPN
ejpam-5986	350	19	α	α	PRON
ejpam-5986	350	20	,	,	PUNCT
ejpam-5986	350	21	λ	λ	PROPN
ejpam-5986	350	22	{	{	PUNCT
ejpam-5986	350	23	∫	∫	PROPN
ejpam-5986	350	24	t	t	PROPN
ejpam-5986	350	25	0	0	NUM
ejpam-5986	350	26	f(s	f(	NOUN
ejpam-5986	350	27	)	)	PUNCT
ejpam-5986	350	28	ds	ds	VERB
ejpam-5986	350	29	}	}	PUNCT
ejpam-5986	350	30	=	=	PUNCT
ejpam-5986	350	31	λu	λu	X
ejpam-5986	350	32	ln(1	ln(1	NOUN
ejpam-5986	350	33	+	+	CCONJ
ejpam-5986	350	34	λ	λ	PROPN
ejpam-5986	350	35	)	)	PUNCT
ejpam-5986	350	36	f	f	PROPN
ejpam-5986	350	37	∗	∗	PROPN
ejpam-5986	350	38	α	α	PROPN
ejpam-5986	350	39	,	,	PUNCT
ejpam-5986	350	40	λ(u	λ(u	PROPN
ejpam-5986	350	41	)	)	PUNCT
ejpam-5986	350	42	.	.	PUNCT
ejpam-5986	351	1	(	(	PUNCT
ejpam-5986	351	2	21	21	NUM
ejpam-5986	351	3	)	)	PUNCT
ejpam-5986	351	4	proof	proof	NOUN
ejpam-5986	351	5	.	.	PUNCT
ejpam-5986	352	1	let	let	VERB
ejpam-5986	352	2	g(t	g(t	PROPN
ejpam-5986	352	3	)	)	PUNCT
ejpam-5986	353	1	=	=	SYM
ejpam-5986	354	1	∫	∫	PROPN
ejpam-5986	354	2	t	t	NOUN
ejpam-5986	354	3	0	0	NUM
ejpam-5986	354	4	f(s	f(	NOUN
ejpam-5986	354	5	)	)	PUNCT
ejpam-5986	354	6	ds	ds	PROPN
ejpam-5986	354	7	.	.	PROPN
ejpam-5986	354	8	then	then	ADV
ejpam-5986	354	9	by	by	ADP
ejpam-5986	354	10	using	use	VERB
ejpam-5986	354	11	the	the	DET
ejpam-5986	354	12	theorem	theorem	NOUN
ejpam-5986	354	13	8	8	NUM
ejpam-5986	354	14	we	we	PRON
ejpam-5986	354	15	get	get	VERB
ejpam-5986	354	16	g∗	g∗	PROPN
ejpam-5986	354	17	α	α	X
ejpam-5986	354	18	,	,	PUNCT
ejpam-5986	354	19	λ{f(t	λ{f(t	NUM
ejpam-5986	354	20	)	)	PUNCT
ejpam-5986	354	21	}	}	PUNCT
ejpam-5986	354	22	=	=	PUNCT
ejpam-5986	354	23	g∗	g∗	VERB
ejpam-5986	354	24	α	α	NOUN
ejpam-5986	354	25	,	,	PUNCT
ejpam-5986	354	26	λ{g	λ{g	X
ejpam-5986	354	27	′	′	NUM
ejpam-5986	354	28	(	(	PUNCT
ejpam-5986	354	29	t	t	NOUN
ejpam-5986	354	30	)	)	PUNCT
ejpam-5986	354	31	}	}	PUNCT
ejpam-5986	355	1	=	=	PUNCT
ejpam-5986	355	2	ln(1	ln(1	PROPN
ejpam-5986	355	3	+	+	NUM
ejpam-5986	355	4	λ	λ	NOUN
ejpam-5986	355	5	)	)	PUNCT
ejpam-5986	355	6	λu	λu	AUX
ejpam-5986	355	7	g∗	g∗	VERB
ejpam-5986	355	8	α	α	NOUN
ejpam-5986	355	9	,	,	PUNCT
ejpam-5986	355	10	λ{g(t	λ{g(t	PROPN
ejpam-5986	355	11	)	)	PUNCT
ejpam-5986	355	12	}	}	PUNCT
ejpam-5986	355	13	−	−	NOUN
ejpam-5986	355	14	uαg(0	uαg(0	NOUN
ejpam-5986	355	15	)	)	PUNCT
ejpam-5986	356	1	=	=	PUNCT
ejpam-5986	357	1	ln(1	ln(1	NOUN
ejpam-5986	357	2	+	+	NUM
ejpam-5986	357	3	λ	λ	NOUN
ejpam-5986	357	4	)	)	PUNCT
ejpam-5986	357	5	λu	λu	AUX
ejpam-5986	357	6	g∗	g∗	VERB
ejpam-5986	357	7	α	α	NOUN
ejpam-5986	357	8	,	,	PUNCT
ejpam-5986	357	9	λ{g(t	λ{g(t	PROPN
ejpam-5986	357	10	)	)	PUNCT
ejpam-5986	357	11	}	}	PUNCT
ejpam-5986	357	12	,	,	PUNCT
ejpam-5986	357	13	since	since	SCONJ
ejpam-5986	357	14	g(0	g(0	PROPN
ejpam-5986	357	15	)	)	PUNCT
ejpam-5986	357	16	=	=	SYM
ejpam-5986	357	17	0	0	X
ejpam-5986	357	18	.	.	PUNCT
ejpam-5986	358	1	hence	hence	ADV
ejpam-5986	358	2	,	,	PUNCT
ejpam-5986	358	3	f	f	PROPN
ejpam-5986	358	4	∗	∗	PROPN
ejpam-5986	358	5	α	α	PROPN
ejpam-5986	358	6	,	,	PUNCT
ejpam-5986	358	7	λ(u	λ(u	PROPN
ejpam-5986	358	8	)	)	PUNCT
ejpam-5986	359	1	=	=	PUNCT
ejpam-5986	360	1	ln(1	ln(1	NOUN
ejpam-5986	360	2	+	+	NUM
ejpam-5986	360	3	λ	λ	NOUN
ejpam-5986	360	4	)	)	PUNCT
ejpam-5986	360	5	λu	λu	AUX
ejpam-5986	360	6	g∗	g∗	VERB
ejpam-5986	360	7	α	α	NOUN
ejpam-5986	360	8	,	,	PUNCT
ejpam-5986	360	9	λ{g(t	λ{g(t	PROPN
ejpam-5986	360	10	)	)	PUNCT
ejpam-5986	360	11	}	}	PUNCT
ejpam-5986	360	12	,	,	PUNCT
ejpam-5986	360	13	and	and	CCONJ
ejpam-5986	360	14	the	the	DET
ejpam-5986	360	15	result	result	NOUN
ejpam-5986	360	16	follows	follow	VERB
ejpam-5986	360	17	.	.	PUNCT
ejpam-5986	361	1	note	note	VERB
ejpam-5986	361	2	that	that	SCONJ
ejpam-5986	361	3	by	by	ADP
ejpam-5986	361	4	using	use	VERB
ejpam-5986	361	5	the	the	DET
ejpam-5986	361	6	theorem	theorem	ADJ
ejpam-5986	361	7	11	11	NUM
ejpam-5986	361	8	we	we	PRON
ejpam-5986	361	9	have	have	VERB
ejpam-5986	361	10	lim	lim	PROPN
ejpam-5986	361	11	λ→0	λ→0	PROPN
ejpam-5986	361	12	g∗	g∗	VERB
ejpam-5986	361	13	α	α	PRON
ejpam-5986	361	14	,	,	PUNCT
ejpam-5986	361	15	λ	λ	PROPN
ejpam-5986	361	16	{	{	PUNCT
ejpam-5986	361	17	∫	∫	PROPN
ejpam-5986	361	18	t	t	PROPN
ejpam-5986	361	19	0	0	NUM
ejpam-5986	361	20	f(s	f(	NOUN
ejpam-5986	361	21	)	)	PUNCT
ejpam-5986	361	22	ds	ds	VERB
ejpam-5986	361	23	}	}	PUNCT
ejpam-5986	361	24	=	=	SYM
ejpam-5986	361	25	lim	lim	PROPN
ejpam-5986	361	26	λ→0	λ→0	PUNCT
ejpam-5986	362	1	λu	λu	PROPN
ejpam-5986	362	2	ln(1	ln(1	PROPN
ejpam-5986	362	3	+	+	CCONJ
ejpam-5986	362	4	λ	λ	PROPN
ejpam-5986	362	5	)	)	PUNCT
ejpam-5986	362	6	f	f	PROPN
ejpam-5986	362	7	∗	∗	PROPN
ejpam-5986	362	8	α	α	PROPN
ejpam-5986	362	9	,	,	PUNCT
ejpam-5986	362	10	λ(u	λ(u	PROPN
ejpam-5986	362	11	)	)	PUNCT
ejpam-5986	363	1	=	=	SYM
ejpam-5986	363	2	uf	uf	PROPN
ejpam-5986	363	3	(	(	PUNCT
ejpam-5986	363	4	u	u	NOUN
ejpam-5986	363	5	)	)	PUNCT
ejpam-5986	363	6	=	=	NOUN
ejpam-5986	363	7	gα	gα	NOUN
ejpam-5986	363	8	{	{	PUNCT
ejpam-5986	363	9	∫	∫	PROPN
ejpam-5986	363	10	t	t	PROPN
ejpam-5986	363	11	0	0	NUM
ejpam-5986	363	12	f(s	f(	NOUN
ejpam-5986	363	13	)	)	PUNCT
ejpam-5986	363	14	ds	ds	VERB
ejpam-5986	363	15	}	}	PUNCT
ejpam-5986	363	16	.	.	PUNCT
ejpam-5986	364	1	i̇.	i̇.	PROPN
ejpam-5986	364	2	ege	ege	PROPN
ejpam-5986	364	3	/	/	SYM
ejpam-5986	364	4	eur	eur	PROPN
ejpam-5986	364	5	.	.	PUNCT
ejpam-5986	365	1	j.	j.	PROPN
ejpam-5986	365	2	pure	pure	PROPN
ejpam-5986	365	3	appl	appl	PROPN
ejpam-5986	365	4	.	.	PROPN
ejpam-5986	365	5	math	math	PROPN
ejpam-5986	365	6	,	,	PUNCT
ejpam-5986	365	7	18	18	NUM
ejpam-5986	365	8	(	(	PUNCT
ejpam-5986	365	9	2	2	NUM
ejpam-5986	365	10	)	)	PUNCT
ejpam-5986	365	11	(	(	PUNCT
ejpam-5986	365	12	2025	2025	NUM
ejpam-5986	365	13	)	)	PUNCT
ejpam-5986	365	14	,	,	PUNCT
ejpam-5986	365	15	5986	5986	NUM
ejpam-5986	365	16	12	12	NUM
ejpam-5986	365	17	of	of	ADP
ejpam-5986	365	18	20	20	NUM
ejpam-5986	365	19	theorem	theorem	NOUN
ejpam-5986	365	20	12	12	NUM
ejpam-5986	365	21	.	.	PUNCT
ejpam-5986	366	1	(	(	PUNCT
ejpam-5986	366	2	change	change	NOUN
ejpam-5986	366	3	of	of	ADP
ejpam-5986	366	4	scale	scale	NOUN
ejpam-5986	366	5	)	)	PUNCT
ejpam-5986	366	6	let	let	VERB
ejpam-5986	366	7	g∗	g∗	VERB
ejpam-5986	366	8	α	α	PRON
ejpam-5986	366	9	,	,	PUNCT
ejpam-5986	366	10	λ{f(t	λ{f(t	NUM
ejpam-5986	366	11	)	)	PUNCT
ejpam-5986	366	12	}	}	PUNCT
ejpam-5986	366	13	=	=	SYM
ejpam-5986	366	14	f	f	PROPN
ejpam-5986	366	15	∗	∗	X
ejpam-5986	366	16	α	α	PROPN
ejpam-5986	366	17	,	,	PUNCT
ejpam-5986	366	18	λ(u	λ(u	PROPN
ejpam-5986	366	19	)	)	PUNCT
ejpam-5986	366	20	.	.	PUNCT
ejpam-5986	367	1	then	then	ADV
ejpam-5986	367	2	g∗	g∗	VERB
ejpam-5986	367	3	α	α	PRON
ejpam-5986	367	4	,	,	PUNCT
ejpam-5986	367	5	λ{f(at	λ{f(at	PROPN
ejpam-5986	367	6	)	)	PUNCT
ejpam-5986	367	7	}	}	PUNCT
ejpam-5986	368	1	=	=	SYM
ejpam-5986	368	2	1	1	NUM
ejpam-5986	368	3	aα+1	aα+1	NOUN
ejpam-5986	368	4	f	f	PROPN
ejpam-5986	368	5	∗	∗	NOUN
ejpam-5986	368	6	α	α	PROPN
ejpam-5986	368	7	,	,	PUNCT
ejpam-5986	368	8	λ(au	λ(au	PROPN
ejpam-5986	368	9	)	)	PUNCT
ejpam-5986	368	10	for	for	ADP
ejpam-5986	368	11	a	a	DET
ejpam-5986	368	12	>	>	X
ejpam-5986	368	13	0	0	NUM
ejpam-5986	368	14	.	.	PUNCT
ejpam-5986	369	1	(	(	PUNCT
ejpam-5986	369	2	22	22	NUM
ejpam-5986	369	3	)	)	PUNCT
ejpam-5986	369	4	proof	proof	NOUN
ejpam-5986	369	5	.	.	PUNCT
ejpam-5986	370	1	let	let	VERB
ejpam-5986	370	2	at	at	ADP
ejpam-5986	370	3	=	=	NOUN
ejpam-5986	370	4	w.	w.	PROPN
ejpam-5986	370	5	then	then	ADV
ejpam-5986	370	6	g∗	g∗	VERB
ejpam-5986	370	7	α	α	PRON
ejpam-5986	370	8	,	,	PUNCT
ejpam-5986	370	9	λ{f(at	λ{f(at	PROPN
ejpam-5986	370	10	)	)	PUNCT
ejpam-5986	370	11	}	}	PUNCT
ejpam-5986	371	1	=	=	PUNCT
ejpam-5986	371	2	uα	uα	PROPN
ejpam-5986	371	3	∫	∫	PROPN
ejpam-5986	371	4	∞	∞	PROPN
ejpam-5986	371	5	0	0	NUM
ejpam-5986	372	1	(	(	PUNCT
ejpam-5986	372	2	1	1	NUM
ejpam-5986	372	3	+	+	X
ejpam-5986	372	4	λ)−	λ)−	ADP
ejpam-5986	372	5	t	t	PROPN
ejpam-5986	372	6	uλ	uλ	DET
ejpam-5986	372	7	f(at	f(at	NOUN
ejpam-5986	372	8	)	)	PUNCT
ejpam-5986	372	9	dt	dt	NOUN
ejpam-5986	373	1	=	=	PUNCT
ejpam-5986	373	2	uα	uα	PROPN
ejpam-5986	373	3	a	a	DET
ejpam-5986	373	4	∫	∫	PROPN
ejpam-5986	373	5	∞	∞	NOUN
ejpam-5986	373	6	0	0	NUM
ejpam-5986	374	1	(	(	PUNCT
ejpam-5986	374	2	1	1	NUM
ejpam-5986	374	3	+	+	NUM
ejpam-5986	374	4	λ	λ	NOUN
ejpam-5986	374	5	)	)	PUNCT
ejpam-5986	374	6	−	−	PROPN
ejpam-5986	374	7	w	w	PROPN
ejpam-5986	374	8	λ(au	λ(au	PROPN
ejpam-5986	374	9	)	)	PUNCT
ejpam-5986	374	10	f(w	f(w	PROPN
ejpam-5986	374	11	)	)	PUNCT
ejpam-5986	374	12	dw	dw	NOUN
ejpam-5986	375	1	=	=	PUNCT
ejpam-5986	375	2	uα	uα	PROPN
ejpam-5986	375	3	a	a	DET
ejpam-5986	375	4	(	(	PUNCT
ejpam-5986	375	5	au)α	au)α	NOUN
ejpam-5986	375	6	(	(	PUNCT
ejpam-5986	375	7	au)α	au)α	PROPN
ejpam-5986	375	8	∫	∫	PROPN
ejpam-5986	375	9	∞	∞	PROPN
ejpam-5986	375	10	0	0	NUM
ejpam-5986	376	1	(	(	PUNCT
ejpam-5986	376	2	1	1	NUM
ejpam-5986	376	3	+	+	NUM
ejpam-5986	376	4	λ	λ	NOUN
ejpam-5986	376	5	)	)	PUNCT
ejpam-5986	376	6	−	−	PROPN
ejpam-5986	376	7	w	w	PROPN
ejpam-5986	376	8	λ(au	λ(au	PROPN
ejpam-5986	376	9	)	)	PUNCT
ejpam-5986	376	10	f(w	f(w	PROPN
ejpam-5986	376	11	)	)	PUNCT
ejpam-5986	376	12	dw	dw	NOUN
ejpam-5986	376	13	=	=	SYM
ejpam-5986	376	14	1	1	NUM
ejpam-5986	376	15	aα+1	aα+1	NUM
ejpam-5986	376	16	f	f	PROPN
ejpam-5986	376	17	∗	∗	NOUN
ejpam-5986	376	18	α	α	PROPN
ejpam-5986	376	19	,	,	PUNCT
ejpam-5986	376	20	λ(au	λ(au	PROPN
ejpam-5986	376	21	)	)	PUNCT
ejpam-5986	376	22	for	for	ADP
ejpam-5986	376	23	a	a	DET
ejpam-5986	376	24	>	>	X
ejpam-5986	376	25	0	0	NUM
ejpam-5986	376	26	,	,	PUNCT
ejpam-5986	376	27	and	and	CCONJ
ejpam-5986	376	28	the	the	DET
ejpam-5986	376	29	result	result	NOUN
ejpam-5986	376	30	follows	follow	VERB
ejpam-5986	376	31	.	.	PUNCT
ejpam-5986	377	1	note	note	VERB
ejpam-5986	377	2	that	that	SCONJ
ejpam-5986	377	3	by	by	ADP
ejpam-5986	377	4	using	use	VERB
ejpam-5986	377	5	the	the	DET
ejpam-5986	377	6	theorem	theorem	NOUN
ejpam-5986	377	7	12	12	NUM
ejpam-5986	377	8	we	we	PRON
ejpam-5986	377	9	have	have	VERB
ejpam-5986	377	10	lim	lim	PROPN
ejpam-5986	377	11	λ→0	λ→0	PROPN
ejpam-5986	377	12	g∗	g∗	VERB
ejpam-5986	377	13	α	α	PROPN
ejpam-5986	377	14	,	,	PUNCT
ejpam-5986	377	15	λ{f(at	λ{f(at	PROPN
ejpam-5986	377	16	)	)	PUNCT
ejpam-5986	377	17	}	}	PUNCT
ejpam-5986	378	1	=	=	SYM
ejpam-5986	378	2	lim	lim	PROPN
ejpam-5986	378	3	λ→0	λ→0	PROPN
ejpam-5986	378	4	1	1	NUM
ejpam-5986	378	5	aα+1	aα+1	NOUN
ejpam-5986	378	6	f	f	PROPN
ejpam-5986	378	7	∗	∗	NOUN
ejpam-5986	378	8	α	α	PROPN
ejpam-5986	378	9	,	,	PUNCT
ejpam-5986	378	10	λ(au	λ(au	PROPN
ejpam-5986	378	11	)	)	PUNCT
ejpam-5986	378	12	=	=	SYM
ejpam-5986	378	13	1	1	NUM
ejpam-5986	378	14	aα+1	aα+1	NUM
ejpam-5986	378	15	fα(au	fα(au	NOUN
ejpam-5986	378	16	)	)	PUNCT
ejpam-5986	378	17	.	.	PUNCT
ejpam-5986	379	1	theorem	theorem	VERB
ejpam-5986	379	2	13	13	NUM
ejpam-5986	379	3	.	.	PUNCT
ejpam-5986	380	1	let	let	AUX
ejpam-5986	380	2	g∗	g∗	VERB
ejpam-5986	380	3	α	α	PRON
ejpam-5986	380	4	,	,	PUNCT
ejpam-5986	380	5	λ{f(t	λ{f(t	NUM
ejpam-5986	380	6	)	)	PUNCT
ejpam-5986	380	7	}	}	PUNCT
ejpam-5986	380	8	=	=	SYM
ejpam-5986	380	9	f	f	PROPN
ejpam-5986	380	10	∗	∗	X
ejpam-5986	380	11	α	α	PROPN
ejpam-5986	380	12	,	,	PUNCT
ejpam-5986	380	13	λ(u	λ(u	PROPN
ejpam-5986	380	14	)	)	PUNCT
ejpam-5986	380	15	and	and	CCONJ
ejpam-5986	380	16	g(t	g(t	PROPN
ejpam-5986	380	17	)	)	PUNCT
ejpam-5986	381	1	=	=	PRON
ejpam-5986	381	2	f(t	f(t	PROPN
ejpam-5986	381	3	−	−	PROPN
ejpam-5986	381	4	a	a	X
ejpam-5986	381	5	)	)	PUNCT
ejpam-5986	381	6	for	for	ADP
ejpam-5986	381	7	t	t	PROPN
ejpam-5986	381	8	≥	≥	NOUN
ejpam-5986	381	9	a	a	PRON
ejpam-5986	381	10	and	and	CCONJ
ejpam-5986	381	11	g(t	g(t	PROPN
ejpam-5986	381	12	)	)	PUNCT
ejpam-5986	382	1	=	=	SYM
ejpam-5986	382	2	0	0	NUM
ejpam-5986	382	3	for	for	ADP
ejpam-5986	382	4	0	0	NUM
ejpam-5986	382	5	≤	≤	NOUN
ejpam-5986	382	6	t	t	PROPN
ejpam-5986	382	7	<	<	X
ejpam-5986	382	8	a	a	X
ejpam-5986	382	9	,	,	PUNCT
ejpam-5986	382	10	a	a	PRON
ejpam-5986	382	11	>	>	X
ejpam-5986	382	12	0	0	X
ejpam-5986	382	13	.	.	PUNCT
ejpam-5986	383	1	then	then	ADV
ejpam-5986	383	2	g∗	g∗	VERB
ejpam-5986	383	3	α	α	NOUN
ejpam-5986	383	4	,	,	PUNCT
ejpam-5986	383	5	λ{g(t	λ{g(t	PROPN
ejpam-5986	383	6	)	)	PUNCT
ejpam-5986	383	7	}	}	PUNCT
ejpam-5986	383	8	=	=	SYM
ejpam-5986	384	1	(	(	PUNCT
ejpam-5986	384	2	1	1	NUM
ejpam-5986	384	3	+	+	X
ejpam-5986	384	4	λ)−	λ)−	ADP
ejpam-5986	384	5	a	a	DET
ejpam-5986	384	6	uλf	uλf	PROPN
ejpam-5986	384	7	∗	∗	NOUN
ejpam-5986	384	8	α	α	PROPN
ejpam-5986	384	9	,	,	PUNCT
ejpam-5986	384	10	λ(u	λ(u	PROPN
ejpam-5986	384	11	)	)	PUNCT
ejpam-5986	384	12	.	.	PUNCT
ejpam-5986	385	1	proof	proof	NOUN
ejpam-5986	385	2	.	.	PUNCT
ejpam-5986	386	1	let	let	VERB
ejpam-5986	386	2	us	we	PRON
ejpam-5986	386	3	write	write	VERB
ejpam-5986	386	4	g∗	g∗	PROPN
ejpam-5986	386	5	α	α	NOUN
ejpam-5986	386	6	,	,	PUNCT
ejpam-5986	386	7	λ{g(t	λ{g(t	PROPN
ejpam-5986	386	8	)	)	PUNCT
ejpam-5986	386	9	}	}	PUNCT
ejpam-5986	387	1	=	=	PUNCT
ejpam-5986	387	2	uα	uα	PROPN
ejpam-5986	387	3	∫	∫	PROPN
ejpam-5986	387	4	∞	∞	PROPN
ejpam-5986	387	5	0	0	NUM
ejpam-5986	388	1	(	(	PUNCT
ejpam-5986	388	2	1	1	NUM
ejpam-5986	388	3	+	+	X
ejpam-5986	388	4	λ)−	λ)−	ADP
ejpam-5986	388	5	t	t	PROPN
ejpam-5986	388	6	uλ	uλ	PRON
ejpam-5986	388	7	g(t	g(t	PROPN
ejpam-5986	388	8	)	)	PUNCT
ejpam-5986	389	1	dt	dt	NOUN
ejpam-5986	390	1	=	=	PUNCT
ejpam-5986	390	2	uα	uα	PROPN
ejpam-5986	390	3	∫	∫	PROPN
ejpam-5986	390	4	∞	∞	PROPN
ejpam-5986	390	5	a	a	DET
ejpam-5986	390	6	(	(	PUNCT
ejpam-5986	390	7	1	1	NUM
ejpam-5986	390	8	+	+	X
ejpam-5986	390	9	λ)−	λ)−	X
ejpam-5986	390	10	t	t	X
ejpam-5986	390	11	uλ	uλ	X
ejpam-5986	391	1	f(t−	f(t−	PROPN
ejpam-5986	391	2	a	a	PRON
ejpam-5986	391	3	)	)	PUNCT
ejpam-5986	391	4	dt	dt	NOUN
ejpam-5986	391	5	.	.	PUNCT
ejpam-5986	392	1	now	now	ADV
ejpam-5986	392	2	let	let	VERB
ejpam-5986	392	3	t−	t−	PROPN
ejpam-5986	392	4	a	a	X
ejpam-5986	392	5	=	=	X
ejpam-5986	392	6	y.	y.	NOUN
ejpam-5986	392	7	then	then	ADV
ejpam-5986	392	8	we	we	PRON
ejpam-5986	392	9	find	find	VERB
ejpam-5986	392	10	g∗	g∗	PROPN
ejpam-5986	392	11	α	α	NOUN
ejpam-5986	392	12	,	,	PUNCT
ejpam-5986	392	13	λ{g(t	λ{g(t	PROPN
ejpam-5986	392	14	)	)	PUNCT
ejpam-5986	392	15	}	}	PUNCT
ejpam-5986	393	1	=	=	PUNCT
ejpam-5986	393	2	uα	uα	PROPN
ejpam-5986	393	3	∫	∫	PROPN
ejpam-5986	393	4	∞	∞	PROPN
ejpam-5986	393	5	0	0	NUM
ejpam-5986	394	1	(	(	PUNCT
ejpam-5986	394	2	1	1	NUM
ejpam-5986	394	3	+	+	X
ejpam-5986	394	4	λ)−	λ)−	X
ejpam-5986	394	5	y+a	y+a	PROPN
ejpam-5986	394	6	uλ	uλ	PRON
ejpam-5986	394	7	f(y	f(y	NOUN
ejpam-5986	394	8	)	)	PUNCT
ejpam-5986	394	9	dy	dy	NOUN
ejpam-5986	394	10	=	=	SYM
ejpam-5986	394	11	(	(	PUNCT
ejpam-5986	394	12	1	1	NUM
ejpam-5986	395	1	+	+	X
ejpam-5986	395	2	λ)−	λ)−	ADP
ejpam-5986	395	3	a	a	DET
ejpam-5986	395	4	uλuα	uλuα	NOUN
ejpam-5986	395	5	∫	∫	PROPN
ejpam-5986	395	6	∞	∞	PROPN
ejpam-5986	395	7	0	0	NUM
ejpam-5986	395	8	(	(	PUNCT
ejpam-5986	395	9	1	1	NUM
ejpam-5986	395	10	+	+	X
ejpam-5986	395	11	λ)−	λ)−	PROPN
ejpam-5986	395	12	y	y	PROPN
ejpam-5986	395	13	uλ	uλ	PRON
ejpam-5986	395	14	f(y	f(y	PROPN
ejpam-5986	395	15	)	)	PUNCT
ejpam-5986	395	16	dy	dy	NOUN
ejpam-5986	395	17	,	,	PUNCT
ejpam-5986	395	18	and	and	CCONJ
ejpam-5986	395	19	the	the	DET
ejpam-5986	395	20	result	result	NOUN
ejpam-5986	395	21	follows	follow	VERB
ejpam-5986	395	22	.	.	PUNCT
ejpam-5986	396	1	now	now	ADV
ejpam-5986	396	2	,	,	PUNCT
ejpam-5986	396	3	we	we	PRON
ejpam-5986	396	4	give	give	VERB
ejpam-5986	396	5	an	an	DET
ejpam-5986	396	6	example	example	NOUN
ejpam-5986	396	7	to	to	PART
ejpam-5986	396	8	illustrate	illustrate	VERB
ejpam-5986	396	9	the	the	DET
ejpam-5986	396	10	last	last	ADJ
ejpam-5986	396	11	theorem	theorem	NOUN
ejpam-5986	396	12	.	.	PROPN
ejpam-5986	396	13	example	example	NOUN
ejpam-5986	396	14	2	2	NUM
ejpam-5986	396	15	.	.	X
ejpam-5986	396	16	for	for	ADP
ejpam-5986	396	17	g(t	g(t	PROPN
ejpam-5986	396	18	)	)	PUNCT
ejpam-5986	397	1	=	=	PRON
ejpam-5986	397	2	{	{	PUNCT
ejpam-5986	397	3	sin	sin	PROPN
ejpam-5986	397	4	t	t	PROPN
ejpam-5986	397	5	,	,	PUNCT
ejpam-5986	397	6	t	t	PROPN
ejpam-5986	397	7	≥	≥	PROPN
ejpam-5986	397	8	π	π	PROPN
ejpam-5986	397	9	2	2	NUM
ejpam-5986	397	10	0	0	NUM
ejpam-5986	397	11	,	,	PUNCT
ejpam-5986	397	12	0	0	NUM
ejpam-5986	397	13	≤	≤	NUM
ejpam-5986	397	14	t	t	X
ejpam-5986	397	15	<	<	X
ejpam-5986	397	16	π	π	PROPN
ejpam-5986	397	17	2	2	NUM
ejpam-5986	397	18	we	we	PRON
ejpam-5986	397	19	want	want	VERB
ejpam-5986	397	20	to	to	PART
ejpam-5986	397	21	find	find	VERB
ejpam-5986	397	22	g∗	g∗	PROPN
ejpam-5986	397	23	α	α	NOUN
ejpam-5986	397	24	,	,	PUNCT
ejpam-5986	397	25	λ{g(t	λ{g(t	PROPN
ejpam-5986	397	26	)	)	PUNCT
ejpam-5986	397	27	}	}	PUNCT
ejpam-5986	397	28	.	.	PUNCT
ejpam-5986	398	1	since	since	SCONJ
ejpam-5986	398	2	cos	cos	PROPN
ejpam-5986	398	3	(	(	PUNCT
ejpam-5986	398	4	t−	t−	PROPN
ejpam-5986	398	5	π	π	PROPN
ejpam-5986	398	6	2	2	NUM
ejpam-5986	398	7	)	)	PUNCT
ejpam-5986	398	8	=	=	VERB
ejpam-5986	398	9	sin	sin	PROPN
ejpam-5986	398	10	t	t	PROPN
ejpam-5986	398	11	,	,	PUNCT
ejpam-5986	398	12	we	we	PRON
ejpam-5986	398	13	have	have	VERB
ejpam-5986	398	14	g(t	g(t	PROPN
ejpam-5986	398	15	)	)	PUNCT
ejpam-5986	399	1	=	=	PRON
ejpam-5986	399	2	{	{	PUNCT
ejpam-5986	399	3	cos	cos	X
ejpam-5986	399	4	(	(	PUNCT
ejpam-5986	399	5	t−	t−	PROPN
ejpam-5986	399	6	π	π	PROPN
ejpam-5986	399	7	2	2	NUM
ejpam-5986	399	8	)	)	PUNCT
ejpam-5986	399	9	,	,	PUNCT
ejpam-5986	399	10	t	t	PROPN
ejpam-5986	399	11	≥	≥	PROPN
ejpam-5986	399	12	π	π	PROPN
ejpam-5986	399	13	2	2	NUM
ejpam-5986	399	14	0	0	NUM
ejpam-5986	399	15	,	,	PUNCT
ejpam-5986	399	16	0	0	NUM
ejpam-5986	399	17	≤	≤	NUM
ejpam-5986	399	18	t	t	X
ejpam-5986	399	19	<	<	X
ejpam-5986	399	20	π	π	PROPN
ejpam-5986	399	21	2	2	NUM
ejpam-5986	399	22	.	.	PUNCT
ejpam-5986	400	1	i̇.	i̇.	PROPN
ejpam-5986	400	2	ege	ege	PROPN
ejpam-5986	400	3	/	/	SYM
ejpam-5986	400	4	eur	eur	PROPN
ejpam-5986	400	5	.	.	PUNCT
ejpam-5986	401	1	j.	j.	PROPN
ejpam-5986	401	2	pure	pure	PROPN
ejpam-5986	401	3	appl	appl	PROPN
ejpam-5986	401	4	.	.	PROPN
ejpam-5986	401	5	math	math	PROPN
ejpam-5986	401	6	,	,	PUNCT
ejpam-5986	401	7	18	18	NUM
ejpam-5986	401	8	(	(	PUNCT
ejpam-5986	401	9	2	2	NUM
ejpam-5986	401	10	)	)	PUNCT
ejpam-5986	401	11	(	(	PUNCT
ejpam-5986	401	12	2025	2025	NUM
ejpam-5986	401	13	)	)	PUNCT
ejpam-5986	401	14	,	,	PUNCT
ejpam-5986	401	15	5986	5986	NUM
ejpam-5986	401	16	13	13	NUM
ejpam-5986	401	17	of	of	ADP
ejpam-5986	401	18	20	20	NUM
ejpam-5986	401	19	then	then	ADV
ejpam-5986	401	20	by	by	ADP
ejpam-5986	401	21	the	the	DET
ejpam-5986	401	22	theorem	theorem	NOUN
ejpam-5986	401	23	13	13	NUM
ejpam-5986	401	24	for	for	ADP
ejpam-5986	401	25	f(t	f(t	NOUN
ejpam-5986	401	26	)	)	PUNCT
ejpam-5986	401	27	=	=	SYM
ejpam-5986	401	28	cos	cos	PROPN
ejpam-5986	401	29	t	t	PROPN
ejpam-5986	401	30	we	we	PRON
ejpam-5986	401	31	have	have	AUX
ejpam-5986	401	32	g∗	g∗	VERB
ejpam-5986	401	33	α	α	PRON
ejpam-5986	401	34	,	,	PUNCT
ejpam-5986	401	35	λ{g(t	λ{g(t	PROPN
ejpam-5986	401	36	)	)	PUNCT
ejpam-5986	401	37	}	}	PUNCT
ejpam-5986	401	38	=	=	SYM
ejpam-5986	401	39	(	(	PUNCT
ejpam-5986	401	40	1	1	NUM
ejpam-5986	402	1	+	+	X
ejpam-5986	402	2	λ)−	λ)−	PROPN
ejpam-5986	402	3	π	π	PROPN
ejpam-5986	402	4	2uλf	2uλf	NUM
ejpam-5986	402	5	∗	∗	NOUN
ejpam-5986	402	6	α	α	NOUN
ejpam-5986	402	7	,	,	PUNCT
ejpam-5986	402	8	λ(u	λ(u	PROPN
ejpam-5986	402	9	)	)	PUNCT
ejpam-5986	402	10	.	.	PUNCT
ejpam-5986	403	1	also	also	ADV
ejpam-5986	403	2	,	,	PUNCT
ejpam-5986	403	3	since	since	SCONJ
ejpam-5986	403	4	g∗	g∗	PROPN
ejpam-5986	403	5	α	α	PRON
ejpam-5986	403	6	,	,	PUNCT
ejpam-5986	403	7	λ{cos	λ{cos	PROPN
ejpam-5986	403	8	t	t	NOUN
ejpam-5986	403	9	}	}	PUNCT
ejpam-5986	403	10	=	=	SYM
ejpam-5986	403	11	f	f	PROPN
ejpam-5986	403	12	∗	∗	X
ejpam-5986	403	13	α	α	PROPN
ejpam-5986	403	14	,	,	PUNCT
ejpam-5986	403	15	λ(u	λ(u	PROPN
ejpam-5986	403	16	)	)	PUNCT
ejpam-5986	403	17	=	=	PUNCT
ejpam-5986	403	18	λ	λ	X
ejpam-5986	403	19	ln(1	ln(1	NOUN
ejpam-5986	403	20	+	+	CCONJ
ejpam-5986	403	21	λ)uα+1	λ)uα+1	NOUN
ejpam-5986	403	22	ln2(1	ln2(1	NOUN
ejpam-5986	403	23	+	+	X
ejpam-5986	403	24	λ	λ	NOUN
ejpam-5986	403	25	)	)	PUNCT
ejpam-5986	404	1	+	+	CCONJ
ejpam-5986	404	2	λ2u2	λ2u2	AUX
ejpam-5986	404	3	,	,	PUNCT
ejpam-5986	404	4	by	by	ADP
ejpam-5986	404	5	the	the	DET
ejpam-5986	404	6	equation	equation	NOUN
ejpam-5986	404	7	(	(	PUNCT
ejpam-5986	404	8	17	17	NUM
ejpam-5986	404	9	)	)	PUNCT
ejpam-5986	404	10	we	we	PRON
ejpam-5986	404	11	have	have	AUX
ejpam-5986	404	12	g∗	g∗	PROPN
ejpam-5986	404	13	α	α	PRON
ejpam-5986	404	14	,	,	PUNCT
ejpam-5986	404	15	λ{g(t	λ{g(t	PROPN
ejpam-5986	404	16	)	)	PUNCT
ejpam-5986	404	17	}	}	PUNCT
ejpam-5986	405	1	=	=	SYM
ejpam-5986	406	1	(	(	PUNCT
ejpam-5986	406	2	1	1	NUM
ejpam-5986	406	3	+	+	X
ejpam-5986	406	4	λ)−	λ)−	ADP
ejpam-5986	406	5	π	π	NUM
ejpam-5986	406	6	2uλ	2uλ	NOUN
ejpam-5986	407	1	λ	λ	X
ejpam-5986	407	2	ln(1	ln(1	NOUN
ejpam-5986	407	3	+	+	CCONJ
ejpam-5986	407	4	λ)uα+1	λ)uα+1	NOUN
ejpam-5986	407	5	ln2(1	ln2(1	NOUN
ejpam-5986	407	6	+	+	X
ejpam-5986	407	7	λ	λ	NOUN
ejpam-5986	407	8	)	)	PUNCT
ejpam-5986	408	1	+	+	CCONJ
ejpam-5986	408	2	λ2u2	λ2u2	AUX
ejpam-5986	408	3	.	.	PUNCT
ejpam-5986	408	4	theorem	theorem	ADJ
ejpam-5986	408	5	14	14	NUM
ejpam-5986	408	6	.	.	PUNCT
ejpam-5986	409	1	(	(	PUNCT
ejpam-5986	409	2	multiplication	multiplication	NOUN
ejpam-5986	409	3	of	of	ADP
ejpam-5986	409	4	powers	power	NOUN
ejpam-5986	409	5	of	of	ADP
ejpam-5986	409	6	the	the	DET
ejpam-5986	409	7	variable	variable	NOUN
ejpam-5986	409	8	)	)	PUNCT
ejpam-5986	409	9	let	let	VERB
ejpam-5986	409	10	g∗	g∗	VERB
ejpam-5986	409	11	α	α	PRON
ejpam-5986	409	12	,	,	PUNCT
ejpam-5986	409	13	λ{f(t	λ{f(t	NUM
ejpam-5986	409	14	)	)	PUNCT
ejpam-5986	409	15	}	}	PUNCT
ejpam-5986	409	16	=	=	SYM
ejpam-5986	409	17	f	f	PROPN
ejpam-5986	409	18	∗	∗	X
ejpam-5986	409	19	α	α	PROPN
ejpam-5986	409	20	,	,	PUNCT
ejpam-5986	409	21	λ(u	λ(u	PROPN
ejpam-5986	409	22	)	)	PUNCT
ejpam-5986	409	23	.	.	PUNCT
ejpam-5986	410	1	then	then	ADV
ejpam-5986	410	2	g∗	g∗	VERB
ejpam-5986	410	3	α	α	PRON
ejpam-5986	410	4	,	,	PUNCT
ejpam-5986	410	5	λ{tnf(t	λ{tnf(t	NOUN
ejpam-5986	410	6	)	)	PUNCT
ejpam-5986	410	7	}	}	PUNCT
ejpam-5986	410	8	=	=	SYM
ejpam-5986	410	9	λn	λn	NOUN
ejpam-5986	410	10	lnn(1	lnn(1	PUNCT
ejpam-5986	411	1	+	+	CCONJ
ejpam-5986	411	2	λ	λ	SYM
ejpam-5986	411	3	)	)	PUNCT
ejpam-5986	411	4	u2n	u2n	PROPN
ejpam-5986	411	5	dn	dn	PROPN
ejpam-5986	411	6	dun	dun	PROPN
ejpam-5986	411	7	f	f	PROPN
ejpam-5986	411	8	∗	∗	PROPN
ejpam-5986	411	9	α	α	PROPN
ejpam-5986	411	10	,	,	PUNCT
ejpam-5986	411	11	λ(u)−	λ(u)−	PROPN
ejpam-5986	411	12	λn	λn	NOUN
ejpam-5986	411	13	lnn(1	lnn(1	VERB
ejpam-5986	411	14	+	+	CCONJ
ejpam-5986	411	15	λ	λ	X
ejpam-5986	411	16	)	)	PUNCT
ejpam-5986	411	17	(	(	PUNCT
ejpam-5986	411	18	n	n	NOUN
ejpam-5986	411	19	1	1	NUM
ejpam-5986	411	20	)	)	PUNCT
ejpam-5986	411	21	(	(	PUNCT
ejpam-5986	411	22	α−	α−	X
ejpam-5986	411	23	(	(	PUNCT
ejpam-5986	411	24	n−	n−	NOUN
ejpam-5986	411	25	1))u2n−1	1))u2n−1	NUM
ejpam-5986	411	26	dn−1	dn−1	PROPN
ejpam-5986	411	27	dun−1	dun−1	PROPN
ejpam-5986	411	28	f	f	PROPN
ejpam-5986	411	29	∗	∗	PROPN
ejpam-5986	411	30	α	α	PROPN
ejpam-5986	411	31	,	,	PUNCT
ejpam-5986	411	32	λ(u	λ(u	PROPN
ejpam-5986	411	33	)	)	PUNCT
ejpam-5986	412	1	+	+	CCONJ
ejpam-5986	412	2	λn	λn	ADP
ejpam-5986	412	3	lnn(1	lnn(1	PUNCT
ejpam-5986	412	4	+	+	CCONJ
ejpam-5986	412	5	λ	λ	X
ejpam-5986	412	6	)	)	PUNCT
ejpam-5986	412	7	(	(	PUNCT
ejpam-5986	412	8	n	n	NOUN
ejpam-5986	412	9	2	2	NUM
ejpam-5986	412	10	)	)	PUNCT
ejpam-5986	412	11	(	(	PUNCT
ejpam-5986	412	12	α−	α−	X
ejpam-5986	412	13	(	(	PUNCT
ejpam-5986	412	14	n−	n−	PROPN
ejpam-5986	412	15	1))(α−	1))(α−	NUM
ejpam-5986	412	16	(	(	PUNCT
ejpam-5986	412	17	n−	n−	NOUN
ejpam-5986	412	18	2))u2n−2	2))u2n−2	NUM
ejpam-5986	412	19	dn−2	dn−2	PROPN
ejpam-5986	412	20	dun−2	dun−2	PROPN
ejpam-5986	412	21	f	f	PROPN
ejpam-5986	412	22	∗	∗	PROPN
ejpam-5986	412	23	α	α	PROPN
ejpam-5986	412	24	,	,	PUNCT
ejpam-5986	412	25	λ(u	λ(u	PROPN
ejpam-5986	412	26	)	)	PUNCT
ejpam-5986	412	27	−	−	PROPN
ejpam-5986	412	28	λn	λn	NOUN
ejpam-5986	412	29	lnn(1	lnn(1	VERB
ejpam-5986	413	1	+	+	CCONJ
ejpam-5986	413	2	λ	λ	X
ejpam-5986	413	3	)	)	PUNCT
ejpam-5986	413	4	(	(	PUNCT
ejpam-5986	413	5	n	n	NOUN
ejpam-5986	413	6	3	3	NUM
ejpam-5986	413	7	)	)	PUNCT
ejpam-5986	413	8	(	(	PUNCT
ejpam-5986	413	9	α−	α−	X
ejpam-5986	413	10	(	(	PUNCT
ejpam-5986	413	11	n−	n−	PROPN
ejpam-5986	413	12	1))(α−	1))(α−	NUM
ejpam-5986	413	13	(	(	PUNCT
ejpam-5986	413	14	n−	n−	NOUN
ejpam-5986	413	15	2))(α−	2))(α−	NUM
ejpam-5986	413	16	(	(	PUNCT
ejpam-5986	413	17	n−	n−	NOUN
ejpam-5986	413	18	3))u2n−3	3))u2n−3	NUM
ejpam-5986	413	19	dn−3	dn−3	VERB
ejpam-5986	413	20	dun−3	dun−3	PROPN
ejpam-5986	413	21	f	f	PROPN
ejpam-5986	413	22	∗	∗	X
ejpam-5986	413	23	α	α	PROPN
ejpam-5986	413	24	,	,	PUNCT
ejpam-5986	413	25	λ(u	λ(u	PROPN
ejpam-5986	413	26	)	)	PUNCT
ejpam-5986	413	27	+	+	CCONJ
ejpam-5986	413	28	.	.	PUNCT
ejpam-5986	413	29	.	.	PUNCT
ejpam-5986	413	30	.	.	PUNCT
ejpam-5986	414	1	+	+	ADV
ejpam-5986	414	2	(	(	PUNCT
ejpam-5986	414	3	−1)n	−1)n	X
ejpam-5986	414	4	λn	λn	PROPN
ejpam-5986	414	5	lnn(1	lnn(1	PUNCT
ejpam-5986	414	6	+	+	CCONJ
ejpam-5986	414	7	λ	λ	X
ejpam-5986	414	8	)	)	PUNCT
ejpam-5986	414	9	(	(	PUNCT
ejpam-5986	414	10	α−	α−	X
ejpam-5986	414	11	(	(	PUNCT
ejpam-5986	414	12	n−	n−	PROPN
ejpam-5986	414	13	1))(α−	1))(α−	NUM
ejpam-5986	414	14	(	(	PUNCT
ejpam-5986	414	15	n−	n−	NOUN
ejpam-5986	414	16	2	2	NUM
ejpam-5986	414	17	)	)	PUNCT
ejpam-5986	414	18	)	)	PUNCT
ejpam-5986	414	19	.	.	PUNCT
ejpam-5986	414	20	.	.	PUNCT
ejpam-5986	414	21	.	.	PUNCT
ejpam-5986	415	1	αunf	αunf	ADJ
ejpam-5986	415	2	∗	∗	PROPN
ejpam-5986	415	3	α	α	PROPN
ejpam-5986	415	4	,	,	PUNCT
ejpam-5986	415	5	λ(u	λ(u	PROPN
ejpam-5986	415	6	)	)	PUNCT
ejpam-5986	415	7	(	(	PUNCT
ejpam-5986	415	8	23	23	NUM
ejpam-5986	415	9	)	)	PUNCT
ejpam-5986	415	10	for	for	ADP
ejpam-5986	415	11	n	n	NOUN
ejpam-5986	415	12	=	=	SYM
ejpam-5986	415	13	1	1	NUM
ejpam-5986	415	14	,	,	PUNCT
ejpam-5986	415	15	2	2	NUM
ejpam-5986	415	16	,	,	PUNCT
ejpam-5986	415	17	3	3	NUM
ejpam-5986	415	18	,	,	PUNCT
ejpam-5986	415	19	.	.	PUNCT
ejpam-5986	415	20	.	.	PUNCT
ejpam-5986	416	1	..	..	PUNCT
ejpam-5986	416	2	proof	proof	NOUN
ejpam-5986	416	3	.	.	PUNCT
ejpam-5986	417	1	we	we	PRON
ejpam-5986	417	2	use	use	VERB
ejpam-5986	417	3	the	the	DET
ejpam-5986	417	4	induction	induction	NOUN
ejpam-5986	417	5	method	method	NOUN
ejpam-5986	417	6	on	on	ADP
ejpam-5986	417	7	n	n	CCONJ
ejpam-5986	417	8	for	for	ADP
ejpam-5986	417	9	proving	prove	VERB
ejpam-5986	417	10	the	the	DET
ejpam-5986	417	11	equation	equation	NOUN
ejpam-5986	417	12	(	(	PUNCT
ejpam-5986	417	13	23	23	NUM
ejpam-5986	417	14	)	)	PUNCT
ejpam-5986	417	15	.	.	PUNCT
ejpam-5986	418	1	since	since	SCONJ
ejpam-5986	418	2	d	d	PROPN
ejpam-5986	418	3	du	du	PROPN
ejpam-5986	418	4	f	f	PROPN
ejpam-5986	418	5	∗	∗	PROPN
ejpam-5986	418	6	α	α	PROPN
ejpam-5986	418	7	,	,	PUNCT
ejpam-5986	418	8	λ(u	λ(u	PROPN
ejpam-5986	418	9	)	)	PUNCT
ejpam-5986	418	10	=	=	PUNCT
ejpam-5986	418	11	αuα−1	αuα−1	NUM
ejpam-5986	418	12	∫	∫	NOUN
ejpam-5986	418	13	∞	∞	NOUN
ejpam-5986	418	14	0	0	NUM
ejpam-5986	418	15	(	(	PUNCT
ejpam-5986	418	16	1	1	NUM
ejpam-5986	418	17	+	+	X
ejpam-5986	418	18	λ)−	λ)−	ADP
ejpam-5986	418	19	t	t	NOUN
ejpam-5986	418	20	uλ	uλ	PRON
ejpam-5986	418	21	f(t	f(t	NOUN
ejpam-5986	418	22	)	)	PUNCT
ejpam-5986	418	23	dt+	dt+	NOUN
ejpam-5986	418	24	uα−2	uα−2	NOUN
ejpam-5986	418	25	ln(1	ln(1	PROPN
ejpam-5986	418	26	+	+	CCONJ
ejpam-5986	418	27	λ	λ	NOUN
ejpam-5986	418	28	)	)	PUNCT
ejpam-5986	418	29	λ	λ	PROPN
ejpam-5986	418	30	∫	∫	PROPN
ejpam-5986	418	31	∞	∞	NUM
ejpam-5986	418	32	0	0	NUM
ejpam-5986	419	1	(	(	PUNCT
ejpam-5986	419	2	1	1	NUM
ejpam-5986	419	3	+	+	X
ejpam-5986	419	4	λ)−	λ)−	X
ejpam-5986	419	5	t	t	NOUN
ejpam-5986	419	6	uλ	uλ	PRON
ejpam-5986	419	7	tf(t	tf(t	NOUN
ejpam-5986	419	8	)	)	PUNCT
ejpam-5986	420	1	dt	dt	NOUN
ejpam-5986	421	1	=	=	SYM
ejpam-5986	421	2	α	α	X
ejpam-5986	421	3	u	u	X
ejpam-5986	421	4	f	f	PROPN
ejpam-5986	421	5	∗	∗	PROPN
ejpam-5986	421	6	α	α	PROPN
ejpam-5986	421	7	,	,	PUNCT
ejpam-5986	421	8	λ(u	λ(u	PROPN
ejpam-5986	421	9	)	)	PUNCT
ejpam-5986	422	1	+	+	PUNCT
ejpam-5986	422	2	ln(1	ln(1	PROPN
ejpam-5986	422	3	+	+	CCONJ
ejpam-5986	422	4	λ	λ	NOUN
ejpam-5986	422	5	)	)	PUNCT
ejpam-5986	422	6	λu2	λu2	AUX
ejpam-5986	422	7	g∗	g∗	VERB
ejpam-5986	422	8	α	α	NUM
ejpam-5986	422	9	,	,	PUNCT
ejpam-5986	422	10	λ{tf(t	λ{tf(t	PROPN
ejpam-5986	422	11	)	)	PUNCT
ejpam-5986	422	12	}	}	PUNCT
ejpam-5986	422	13	,	,	PUNCT
ejpam-5986	422	14	the	the	DET
ejpam-5986	422	15	equation	equation	NOUN
ejpam-5986	422	16	(	(	PUNCT
ejpam-5986	422	17	23	23	NUM
ejpam-5986	422	18	)	)	PUNCT
ejpam-5986	422	19	is	be	AUX
ejpam-5986	422	20	true	true	ADJ
ejpam-5986	422	21	for	for	ADP
ejpam-5986	422	22	n	n	NOUN
ejpam-5986	422	23	=	=	SYM
ejpam-5986	422	24	1	1	NUM
ejpam-5986	422	25	.	.	PUNCT
ejpam-5986	423	1	now	now	ADV
ejpam-5986	423	2	suppose	suppose	VERB
ejpam-5986	423	3	that	that	SCONJ
ejpam-5986	423	4	the	the	DET
ejpam-5986	423	5	equation	equation	NOUN
ejpam-5986	423	6	(	(	PUNCT
ejpam-5986	423	7	23	23	NUM
ejpam-5986	423	8	)	)	PUNCT
ejpam-5986	423	9	is	be	AUX
ejpam-5986	423	10	valid	valid	ADJ
ejpam-5986	423	11	for	for	ADP
ejpam-5986	423	12	n.	n.	NOUN
ejpam-5986	423	13	since	since	SCONJ
ejpam-5986	423	14	g∗	g∗	PROPN
ejpam-5986	423	15	α	α	NUM
ejpam-5986	423	16	,	,	PUNCT
ejpam-5986	423	17	λ{tnf(t	λ{tnf(t	NOUN
ejpam-5986	423	18	)	)	PUNCT
ejpam-5986	423	19	}	}	PUNCT
ejpam-5986	423	20	=	=	PUNCT
ejpam-5986	423	21	uα	uα	PROPN
ejpam-5986	423	22	∫	∫	PROPN
ejpam-5986	423	23	∞	∞	PROPN
ejpam-5986	423	24	0	0	NUM
ejpam-5986	424	1	(	(	PUNCT
ejpam-5986	424	2	1	1	NUM
ejpam-5986	424	3	+	+	X
ejpam-5986	424	4	λ)−	λ)−	ADP
ejpam-5986	424	5	t	t	X
ejpam-5986	424	6	uλ	uλ	PRON
ejpam-5986	424	7	tnf(t	tnf(t	NOUN
ejpam-5986	424	8	)	)	PUNCT
ejpam-5986	425	1	dt	dt	NOUN
ejpam-5986	425	2	we	we	PRON
ejpam-5986	425	3	have	have	VERB
ejpam-5986	425	4	d	d	PART
ejpam-5986	425	5	du	du	PROPN
ejpam-5986	425	6	g∗	g∗	PROPN
ejpam-5986	425	7	α	α	NUM
ejpam-5986	425	8	,	,	PUNCT
ejpam-5986	425	9	λ{tnf(t	λ{tnf(t	NOUN
ejpam-5986	425	10	)	)	PUNCT
ejpam-5986	425	11	}	}	PUNCT
ejpam-5986	425	12	=	=	PUNCT
ejpam-5986	425	13	α	α	NUM
ejpam-5986	425	14	u	u	NOUN
ejpam-5986	425	15	g∗	g∗	VERB
ejpam-5986	425	16	α	α	NOUN
ejpam-5986	425	17	,	,	PUNCT
ejpam-5986	425	18	λ{tnf(t)}+	λ{tnf(t)}+	NOUN
ejpam-5986	426	1	ln(1	ln(1	NOUN
ejpam-5986	426	2	+	+	CCONJ
ejpam-5986	426	3	λ	λ	NOUN
ejpam-5986	426	4	)	)	PUNCT
ejpam-5986	426	5	λu2	λu2	AUX
ejpam-5986	426	6	g∗	g∗	VERB
ejpam-5986	426	7	α	α	PRON
ejpam-5986	426	8	,	,	PUNCT
ejpam-5986	426	9	λ{tn+1f(t	λ{tn+1f(t	NUM
ejpam-5986	426	10	)	)	PUNCT
ejpam-5986	426	11	}	}	PUNCT
ejpam-5986	426	12	.	.	PUNCT
ejpam-5986	427	1	then	then	ADV
ejpam-5986	427	2	g∗	g∗	VERB
ejpam-5986	427	3	α	α	PRON
ejpam-5986	427	4	,	,	PUNCT
ejpam-5986	427	5	λ{tn+1f(t	λ{tn+1f(t	NUM
ejpam-5986	427	6	)	)	PUNCT
ejpam-5986	427	7	}	}	PUNCT
ejpam-5986	427	8	=	=	PUNCT
ejpam-5986	427	9	λu2	λu2	X
ejpam-5986	427	10	ln(1	ln(1	NOUN
ejpam-5986	427	11	+	+	CCONJ
ejpam-5986	427	12	λ	λ	NOUN
ejpam-5986	427	13	)	)	PUNCT
ejpam-5986	427	14	d	d	X
ejpam-5986	427	15	du	du	PROPN
ejpam-5986	427	16	g∗	g∗	PROPN
ejpam-5986	427	17	α	α	NUM
ejpam-5986	427	18	,	,	PUNCT
ejpam-5986	427	19	λ{tnf(t	λ{tnf(t	NOUN
ejpam-5986	427	20	)	)	PUNCT
ejpam-5986	427	21	}	}	PUNCT
ejpam-5986	428	1	−	−	ADP
ejpam-5986	428	2	λαu	λαu	NOUN
ejpam-5986	428	3	ln(1	ln(1	PROPN
ejpam-5986	428	4	+	+	CCONJ
ejpam-5986	428	5	λ	λ	NOUN
ejpam-5986	428	6	)	)	PUNCT
ejpam-5986	428	7	g∗	g∗	PROPN
ejpam-5986	428	8	α	α	X
ejpam-5986	428	9	,	,	PUNCT
ejpam-5986	428	10	λ{tnf(t	λ{tnf(t	PROPN
ejpam-5986	428	11	)	)	PUNCT
ejpam-5986	428	12	}	}	PUNCT
ejpam-5986	428	13	.	.	PUNCT
ejpam-5986	429	1	(	(	PUNCT
ejpam-5986	429	2	24	24	NUM
ejpam-5986	429	3	)	)	PUNCT
ejpam-5986	429	4	now	now	ADV
ejpam-5986	429	5	,	,	PUNCT
ejpam-5986	429	6	by	by	ADP
ejpam-5986	429	7	the	the	DET
ejpam-5986	429	8	inductive	inductive	ADJ
ejpam-5986	429	9	hypothesis	hypothesis	NOUN
ejpam-5986	429	10	,	,	PUNCT
ejpam-5986	429	11	we	we	PRON
ejpam-5986	429	12	get	get	VERB
ejpam-5986	429	13	i̇.	i̇.	PROPN
ejpam-5986	429	14	ege	ege	PROPN
ejpam-5986	429	15	/	/	SYM
ejpam-5986	429	16	eur	eur	PROPN
ejpam-5986	429	17	.	.	PUNCT
ejpam-5986	430	1	j.	j.	PROPN
ejpam-5986	430	2	pure	pure	PROPN
ejpam-5986	430	3	appl	appl	PROPN
ejpam-5986	430	4	.	.	PROPN
ejpam-5986	430	5	math	math	PROPN
ejpam-5986	430	6	,	,	PUNCT
ejpam-5986	430	7	18	18	NUM
ejpam-5986	430	8	(	(	PUNCT
ejpam-5986	430	9	2	2	NUM
ejpam-5986	430	10	)	)	PUNCT
ejpam-5986	430	11	(	(	PUNCT
ejpam-5986	430	12	2025	2025	NUM
ejpam-5986	430	13	)	)	PUNCT
ejpam-5986	430	14	,	,	PUNCT
ejpam-5986	430	15	5986	5986	NUM
ejpam-5986	430	16	14	14	NUM
ejpam-5986	430	17	of	of	ADP
ejpam-5986	430	18	20	20	NUM
ejpam-5986	430	19	g∗	g∗	PROPN
ejpam-5986	430	20	α	α	NOUN
ejpam-5986	430	21	,	,	PUNCT
ejpam-5986	430	22	λ{tn+1f(t	λ{tn+1f(t	NUM
ejpam-5986	430	23	)	)	PUNCT
ejpam-5986	430	24	}	}	PUNCT
ejpam-5986	430	25	=	=	SYM
ejpam-5986	430	26	λn+1	λn+1	X
ejpam-5986	430	27	lnn+1(1	lnn+1(1	X
ejpam-5986	430	28	+	+	CCONJ
ejpam-5986	430	29	λ	λ	X
ejpam-5986	430	30	)	)	PUNCT
ejpam-5986	430	31	[	[	PUNCT
ejpam-5986	430	32	u2n+1	u2n+1	PUNCT
ejpam-5986	430	33	dn+1	dn+1	X
ejpam-5986	430	34	dun+1	dun+1	VERB
ejpam-5986	430	35	f	f	PROPN
ejpam-5986	430	36	∗	∗	NOUN
ejpam-5986	430	37	α	α	PROPN
ejpam-5986	430	38	,	,	PUNCT
ejpam-5986	430	39	λ(u)−	λ(u)−	PROPN
ejpam-5986	430	40	(	(	PUNCT
ejpam-5986	430	41	n+	n+	NUM
ejpam-5986	430	42	1	1	NUM
ejpam-5986	430	43	1	1	NUM
ejpam-5986	430	44	)	)	PUNCT
ejpam-5986	430	45	(	(	PUNCT
ejpam-5986	430	46	α−	α−	ADP
ejpam-5986	430	47	n)u2n+1	n)u2n+1	PROPN
ejpam-5986	430	48	dn	dn	PROPN
ejpam-5986	430	49	dun	dun	PROPN
ejpam-5986	430	50	f	f	PROPN
ejpam-5986	430	51	∗	∗	PROPN
ejpam-5986	430	52	α	α	PROPN
ejpam-5986	430	53	,	,	PUNCT
ejpam-5986	430	54	λ(u	λ(u	PROPN
ejpam-5986	430	55	)	)	PUNCT
ejpam-5986	430	56	]	]	PUNCT
ejpam-5986	431	1	+	+	CCONJ
ejpam-5986	431	2	λn+1	λn+1	X
ejpam-5986	431	3	lnn+1(1	lnn+1(1	X
ejpam-5986	431	4	+	+	X
ejpam-5986	431	5	λ	λ	X
ejpam-5986	431	6	)	)	PUNCT
ejpam-5986	431	7	[	[	X
ejpam-5986	431	8	(	(	PUNCT
ejpam-5986	431	9	n+	n+	SYM
ejpam-5986	431	10	1	1	NUM
ejpam-5986	431	11	2	2	NUM
ejpam-5986	431	12	)	)	PUNCT
ejpam-5986	431	13	(	(	PUNCT
ejpam-5986	431	14	α−	α−	ADP
ejpam-5986	431	15	n	n	CCONJ
ejpam-5986	431	16	)	)	PUNCT
ejpam-5986	431	17	(	(	PUNCT
ejpam-5986	431	18	α−	α−	X
ejpam-5986	431	19	(	(	PUNCT
ejpam-5986	431	20	n−	n−	NOUN
ejpam-5986	431	21	1))u2n	1))u2n	PROPN
ejpam-5986	431	22	dn−1	dn−1	NOUN
ejpam-5986	431	23	dun−1	dun−1	PROPN
ejpam-5986	431	24	f	f	PROPN
ejpam-5986	431	25	∗	∗	PROPN
ejpam-5986	431	26	α	α	PROPN
ejpam-5986	431	27	,	,	PUNCT
ejpam-5986	431	28	λ(u	λ(u	PROPN
ejpam-5986	431	29	)	)	PUNCT
ejpam-5986	431	30	+	+	CCONJ
ejpam-5986	431	31	.	.	PUNCT
ejpam-5986	431	32	.	.	PUNCT
ejpam-5986	431	33	.	.	PUNCT
ejpam-5986	432	1	]	]	PUNCT
ejpam-5986	433	1	+	+	CCONJ
ejpam-5986	433	2	λn+1	λn+1	X
ejpam-5986	433	3	lnn+1(1	lnn+1(1	X
ejpam-5986	433	4	+	+	X
ejpam-5986	433	5	λ	λ	X
ejpam-5986	433	6	)	)	PUNCT
ejpam-5986	433	7	[	[	PUNCT
ejpam-5986	433	8	(	(	PUNCT
ejpam-5986	433	9	−1)n+1(α−	−1)n+1(α−	NOUN
ejpam-5986	433	10	n	n	CCONJ
ejpam-5986	433	11	)	)	PUNCT
ejpam-5986	433	12	(	(	PUNCT
ejpam-5986	433	13	α−	α−	X
ejpam-5986	433	14	(	(	PUNCT
ejpam-5986	433	15	n−	n−	NOUN
ejpam-5986	433	16	1	1	NUM
ejpam-5986	433	17	)	)	PUNCT
ejpam-5986	433	18	)	)	PUNCT
ejpam-5986	433	19	.	.	PUNCT
ejpam-5986	433	20	.	.	PUNCT
ejpam-5986	433	21	.	.	PUNCT
ejpam-5986	434	1	αun+1f	αun+1f	PROPN
ejpam-5986	434	2	∗	∗	PROPN
ejpam-5986	434	3	α	α	PROPN
ejpam-5986	434	4	,	,	PUNCT
ejpam-5986	434	5	λ(u	λ(u	PROPN
ejpam-5986	434	6	)	)	PUNCT
ejpam-5986	434	7	]	]	PUNCT
ejpam-5986	434	8	.	.	PUNCT
ejpam-5986	435	1	hence	hence	ADV
ejpam-5986	435	2	the	the	DET
ejpam-5986	435	3	equation	equation	NOUN
ejpam-5986	435	4	(	(	PUNCT
ejpam-5986	435	5	23	23	NUM
ejpam-5986	435	6	)	)	PUNCT
ejpam-5986	435	7	is	be	AUX
ejpam-5986	435	8	valid	valid	ADJ
ejpam-5986	435	9	for	for	ADP
ejpam-5986	435	10	n+	n+	X
ejpam-5986	435	11	1	1	NUM
ejpam-5986	435	12	,	,	PUNCT
ejpam-5986	435	13	and	and	CCONJ
ejpam-5986	435	14	the	the	DET
ejpam-5986	435	15	result	result	NOUN
ejpam-5986	435	16	follows	follow	VERB
ejpam-5986	435	17	.	.	PUNCT
ejpam-5986	436	1	example	example	NOUN
ejpam-5986	437	1	3	3	X
ejpam-5986	437	2	.	.	X
ejpam-5986	438	1	we	we	PRON
ejpam-5986	438	2	want	want	VERB
ejpam-5986	438	3	to	to	PART
ejpam-5986	438	4	find	find	VERB
ejpam-5986	438	5	g∗	g∗	PROPN
ejpam-5986	438	6	α	α	X
ejpam-5986	438	7	,	,	PUNCT
ejpam-5986	438	8	λ{tet	λ{tet	PROPN
ejpam-5986	438	9	}	}	PUNCT
ejpam-5986	438	10	.	.	PUNCT
ejpam-5986	439	1	by	by	ADP
ejpam-5986	439	2	the	the	DET
ejpam-5986	439	3	theorem	theorem	NOUN
ejpam-5986	439	4	14	14	NUM
ejpam-5986	439	5	we	we	PRON
ejpam-5986	439	6	can	can	AUX
ejpam-5986	439	7	write	write	VERB
ejpam-5986	439	8	g∗	g∗	PROPN
ejpam-5986	439	9	α	α	NOUN
ejpam-5986	439	10	,	,	PUNCT
ejpam-5986	439	11	λ{tet	λ{tet	X
ejpam-5986	439	12	}	}	PUNCT
ejpam-5986	439	13	=	=	PUNCT
ejpam-5986	439	14	λu2	λu2	X
ejpam-5986	439	15	ln(1	ln(1	NOUN
ejpam-5986	439	16	+	+	CCONJ
ejpam-5986	439	17	λ	λ	NOUN
ejpam-5986	439	18	)	)	PUNCT
ejpam-5986	439	19	d	d	X
ejpam-5986	439	20	du	du	PROPN
ejpam-5986	439	21	f	f	PROPN
ejpam-5986	439	22	∗	∗	PROPN
ejpam-5986	439	23	α	α	PROPN
ejpam-5986	439	24	,	,	PUNCT
ejpam-5986	440	1	λ(u)−	λ(u)−	NOUN
ejpam-5986	440	2	λαu	λαu	NOUN
ejpam-5986	440	3	ln(1	ln(1	PROPN
ejpam-5986	440	4	+	+	CCONJ
ejpam-5986	440	5	λ	λ	NOUN
ejpam-5986	440	6	)	)	PUNCT
ejpam-5986	440	7	f	f	PROPN
ejpam-5986	440	8	∗	∗	PROPN
ejpam-5986	440	9	α	α	PROPN
ejpam-5986	440	10	,	,	PUNCT
ejpam-5986	440	11	λ(u	λ(u	PROPN
ejpam-5986	440	12	)	)	PUNCT
ejpam-5986	440	13	,	,	PUNCT
ejpam-5986	440	14	where	where	SCONJ
ejpam-5986	440	15	f	f	PROPN
ejpam-5986	440	16	∗	∗	PROPN
ejpam-5986	440	17	α	α	PROPN
ejpam-5986	440	18	,	,	PUNCT
ejpam-5986	440	19	λ(u	λ(u	PROPN
ejpam-5986	440	20	)	)	PUNCT
ejpam-5986	440	21	=	=	PUNCT
ejpam-5986	440	22	g∗	g∗	VERB
ejpam-5986	440	23	α	α	NUM
ejpam-5986	440	24	,	,	PUNCT
ejpam-5986	440	25	λ{et	λ{et	PROPN
ejpam-5986	440	26	}	}	PUNCT
ejpam-5986	440	27	.	.	PUNCT
ejpam-5986	441	1	since	since	SCONJ
ejpam-5986	441	2	g∗	g∗	PROPN
ejpam-5986	441	3	α	α	NUM
ejpam-5986	441	4	,	,	PUNCT
ejpam-5986	441	5	λ{et	λ{et	PROPN
ejpam-5986	441	6	}	}	PUNCT
ejpam-5986	441	7	=	=	SYM
ejpam-5986	441	8	λuα+1	λuα+1	NOUN
ejpam-5986	441	9	ln(1	ln(1	PROPN
ejpam-5986	441	10	+	+	CCONJ
ejpam-5986	441	11	λ)−	λ)−	X
ejpam-5986	441	12	λu	λu	X
ejpam-5986	441	13	for	for	ADP
ejpam-5986	441	14	u	u	NOUN
ejpam-5986	441	15	<	<	X
ejpam-5986	441	16	ln(1	ln(1	PROPN
ejpam-5986	441	17	+	+	CCONJ
ejpam-5986	441	18	λ	λ	PROPN
ejpam-5986	441	19	)	)	PUNCT
ejpam-5986	441	20	λ	λ	PROPN
ejpam-5986	441	21	,	,	PUNCT
ejpam-5986	441	22	then	then	ADV
ejpam-5986	441	23	g∗	g∗	VERB
ejpam-5986	441	24	α	α	PRON
ejpam-5986	441	25	,	,	PUNCT
ejpam-5986	441	26	λ{tet	λ{tet	X
ejpam-5986	441	27	}	}	PUNCT
ejpam-5986	441	28	=	=	PUNCT
ejpam-5986	441	29	λu2	λu2	NOUN
ejpam-5986	441	30	ln(1+λ	ln(1+λ	ADV
ejpam-5986	441	31	)	)	PUNCT
ejpam-5986	442	1	d	d	X
ejpam-5986	442	2	du	du	X
ejpam-5986	442	3	(	(	PUNCT
ejpam-5986	442	4	λuα+1	λuα+1	NOUN
ejpam-5986	442	5	ln(1	ln(1	PROPN
ejpam-5986	442	6	+	+	CCONJ
ejpam-5986	442	7	λ)−	λ)−	PROPN
ejpam-5986	442	8	λu	λu	X
ejpam-5986	442	9	)	)	PUNCT
ejpam-5986	442	10	−	−	PROPN
ejpam-5986	443	1	λαu	λαu	NOUN
ejpam-5986	443	2	ln(1+λ	ln(1+λ	ADV
ejpam-5986	443	3	)	)	PUNCT
ejpam-5986	443	4	λuα+1	λuα+1	VERB
ejpam-5986	444	1	ln(1	ln(1	PROPN
ejpam-5986	444	2	+	+	X
ejpam-5986	444	3	λ)−	λ)−	PROPN
ejpam-5986	444	4	λu	λu	X
ejpam-5986	444	5	=	=	PUNCT
ejpam-5986	444	6	λ2uα+2	λ2uα+2	X
ejpam-5986	444	7	(	(	PUNCT
ejpam-5986	444	8	ln(1	ln(1	NOUN
ejpam-5986	444	9	+	+	PROPN
ejpam-5986	444	10	λ)−	λ)−	PROPN
ejpam-5986	444	11	λu)2	λu)2	NOUN
ejpam-5986	444	12	.	.	PUNCT
ejpam-5986	445	1	note	note	VERB
ejpam-5986	445	2	that	that	SCONJ
ejpam-5986	445	3	,	,	PUNCT
ejpam-5986	445	4	we	we	PRON
ejpam-5986	445	5	can	can	AUX
ejpam-5986	445	6	find	find	VERB
ejpam-5986	445	7	the	the	DET
ejpam-5986	445	8	same	same	ADJ
ejpam-5986	445	9	result	result	NOUN
ejpam-5986	445	10	for	for	ADP
ejpam-5986	445	11	g∗	g∗	PROPN
ejpam-5986	445	12	α	α	PROPN
ejpam-5986	445	13	,	,	PUNCT
ejpam-5986	445	14	λ{tet	λ{tet	X
ejpam-5986	445	15	}	}	PUNCT
ejpam-5986	445	16	by	by	ADP
ejpam-5986	445	17	using	use	VERB
ejpam-5986	445	18	the	the	DET
ejpam-5986	445	19	theorem	theorem	NOUN
ejpam-5986	445	20	9	9	NUM
ejpam-5986	445	21	as	as	ADP
ejpam-5986	445	22	the	the	DET
ejpam-5986	445	23	following	following	NOUN
ejpam-5986	445	24	:	:	PUNCT
ejpam-5986	445	25	since	since	SCONJ
ejpam-5986	445	26	g∗	g∗	PROPN
ejpam-5986	445	27	α	α	NUM
ejpam-5986	445	28	,	,	PUNCT
ejpam-5986	445	29	λ{ett	λ{ett	X
ejpam-5986	445	30	}	}	PUNCT
ejpam-5986	445	31	=	=	SYM
ejpam-5986	446	1	(	(	PUNCT
ejpam-5986	446	2	ln(1	ln(1	ADP
ejpam-5986	446	3	+	+	PROPN
ejpam-5986	446	4	λ)−	λ)−	X
ejpam-5986	446	5	λu	λu	X
ejpam-5986	446	6	λ	λ	NOUN
ejpam-5986	446	7	)	)	PUNCT
ejpam-5986	446	8	α	α	NOUN
ejpam-5986	446	9	fα	fα	NOUN
ejpam-5986	447	1	(	(	PUNCT
ejpam-5986	447	2	λu	λu	X
ejpam-5986	447	3	ln(1	ln(1	NOUN
ejpam-5986	447	4	+	+	PROPN
ejpam-5986	447	5	λ)−	λ)−	PROPN
ejpam-5986	447	6	λu	λu	X
ejpam-5986	447	7	)	)	PUNCT
ejpam-5986	447	8	where	where	SCONJ
ejpam-5986	447	9	fα(u	fα(u	NOUN
ejpam-5986	447	10	)	)	PUNCT
ejpam-5986	447	11	=	=	SYM
ejpam-5986	447	12	gα{t	gα{t	PROPN
ejpam-5986	447	13	}	}	PUNCT
ejpam-5986	447	14	and	and	CCONJ
ejpam-5986	447	15	gα{t	gα{t	PROPN
ejpam-5986	447	16	}	}	PUNCT
ejpam-5986	447	17	=	=	SYM
ejpam-5986	448	1	uα+2	uα+2	NUM
ejpam-5986	448	2	we	we	PRON
ejpam-5986	448	3	get	get	VERB
ejpam-5986	448	4	g∗	g∗	PROPN
ejpam-5986	448	5	α	α	NOUN
ejpam-5986	448	6	,	,	PUNCT
ejpam-5986	448	7	λ{tet	λ{tet	PROPN
ejpam-5986	448	8	}	}	PUNCT
ejpam-5986	448	9	=	=	SYM
ejpam-5986	449	1	λ2uα+2	λ2uα+2	X
ejpam-5986	449	2	(	(	PUNCT
ejpam-5986	449	3	ln(1	ln(1	NOUN
ejpam-5986	449	4	+	+	PROPN
ejpam-5986	449	5	λ)−	λ)−	PROPN
ejpam-5986	449	6	λu)2	λu)2	NOUN
ejpam-5986	449	7	.	.	PUNCT
ejpam-5986	450	1	theorem	theorem	VERB
ejpam-5986	450	2	15	15	NUM
ejpam-5986	450	3	.	.	PUNCT
ejpam-5986	451	1	(	(	PUNCT
ejpam-5986	451	2	convolution	convolution	NOUN
ejpam-5986	451	3	)	)	PUNCT
ejpam-5986	451	4	let	let	AUX
ejpam-5986	451	5	g∗	g∗	VERB
ejpam-5986	451	6	α	α	PRON
ejpam-5986	451	7	,	,	PUNCT
ejpam-5986	451	8	λ{f(t	λ{f(t	NUM
ejpam-5986	451	9	)	)	PUNCT
ejpam-5986	451	10	}	}	PUNCT
ejpam-5986	451	11	=	=	SYM
ejpam-5986	451	12	f	f	PROPN
ejpam-5986	451	13	∗	∗	X
ejpam-5986	451	14	α	α	PROPN
ejpam-5986	451	15	,	,	PUNCT
ejpam-5986	451	16	λ(u	λ(u	PROPN
ejpam-5986	451	17	)	)	PUNCT
ejpam-5986	451	18	,	,	PUNCT
ejpam-5986	451	19	and	and	CCONJ
ejpam-5986	451	20	g∗	g∗	VERB
ejpam-5986	451	21	α	α	NOUN
ejpam-5986	451	22	,	,	PUNCT
ejpam-5986	451	23	λ{g(t	λ{g(t	PROPN
ejpam-5986	451	24	)	)	PUNCT
ejpam-5986	451	25	}	}	PUNCT
ejpam-5986	451	26	=	=	PUNCT
ejpam-5986	451	27	g∗	g∗	VERB
ejpam-5986	451	28	α	α	NOUN
ejpam-5986	451	29	,	,	PUNCT
ejpam-5986	451	30	λ(u	λ(u	PROPN
ejpam-5986	451	31	)	)	PUNCT
ejpam-5986	451	32	.	.	PUNCT
ejpam-5986	452	1	then	then	ADV
ejpam-5986	452	2	the	the	DET
ejpam-5986	452	3	modified	modified	ADJ
ejpam-5986	452	4	laplace	laplace	NOUN
ejpam-5986	452	5	-	-	PUNCT
ejpam-5986	452	6	type	type	NOUN
ejpam-5986	452	7	transform	transform	NOUN
ejpam-5986	452	8	of	of	ADP
ejpam-5986	452	9	the	the	DET
ejpam-5986	452	10	convolution	convolution	NOUN
ejpam-5986	452	11	is	be	AUX
ejpam-5986	452	12	given	give	VERB
ejpam-5986	452	13	as	as	ADP
ejpam-5986	452	14	g∗	g∗	PROPN
ejpam-5986	452	15	α	α	NOUN
ejpam-5986	452	16	,	,	PUNCT
ejpam-5986	452	17	λ{(f	λ{(f	ADP
ejpam-5986	452	18	∗	∗	NOUN
ejpam-5986	452	19	g)(t	g)(t	NOUN
ejpam-5986	452	20	)	)	PUNCT
ejpam-5986	452	21	}	}	PUNCT
ejpam-5986	452	22	=	=	SYM
ejpam-5986	453	1	1	1	NUM
ejpam-5986	453	2	uα	uα	PROPN
ejpam-5986	453	3	f	f	PROPN
ejpam-5986	453	4	∗	∗	PROPN
ejpam-5986	453	5	α	α	PROPN
ejpam-5986	453	6	,	,	PUNCT
ejpam-5986	453	7	λ(u)g	λ(u)g	PROPN
ejpam-5986	453	8	∗	∗	NOUN
ejpam-5986	453	9	α	α	PROPN
ejpam-5986	453	10	,	,	PUNCT
ejpam-5986	453	11	λ(u	λ(u	PROPN
ejpam-5986	453	12	)	)	PUNCT
ejpam-5986	453	13	,	,	PUNCT
ejpam-5986	453	14	(	(	PUNCT
ejpam-5986	453	15	25	25	NUM
ejpam-5986	453	16	)	)	PUNCT
ejpam-5986	453	17	where	where	SCONJ
ejpam-5986	453	18	f	f	PROPN
ejpam-5986	453	19	∗	∗	VERB
ejpam-5986	453	20	g	g	PROPN
ejpam-5986	453	21	is	be	AUX
ejpam-5986	453	22	the	the	DET
ejpam-5986	453	23	convolution	convolution	NOUN
ejpam-5986	453	24	of	of	ADP
ejpam-5986	453	25	two	two	NUM
ejpam-5986	453	26	functions	function	NOUN
ejpam-5986	453	27	defined	define	VERB
ejpam-5986	453	28	by	by	ADP
ejpam-5986	453	29	(	(	PUNCT
ejpam-5986	453	30	f	f	PROPN
ejpam-5986	453	31	∗	∗	NOUN
ejpam-5986	453	32	g)(t	g)(t	PUNCT
ejpam-5986	453	33	)	)	PUNCT
ejpam-5986	453	34	=	=	SYM
ejpam-5986	454	1	∫	∫	PROPN
ejpam-5986	454	2	t	t	PROPN
ejpam-5986	454	3	0	0	NUM
ejpam-5986	454	4	f(x)g(t−	f(x)g(t−	PROPN
ejpam-5986	454	5	x	x	SYM
ejpam-5986	454	6	)	)	PUNCT
ejpam-5986	454	7	dx	dx	PROPN
ejpam-5986	454	8	.	.	PUNCT
ejpam-5986	455	1	(	(	PUNCT
ejpam-5986	455	2	26	26	NUM
ejpam-5986	455	3	)	)	PUNCT
ejpam-5986	455	4	proof	proof	NOUN
ejpam-5986	455	5	.	.	PUNCT
ejpam-5986	456	1	by	by	ADP
ejpam-5986	456	2	the	the	DET
ejpam-5986	456	3	equations	equation	NOUN
ejpam-5986	456	4	(	(	PUNCT
ejpam-5986	456	5	7	7	NUM
ejpam-5986	456	6	)	)	PUNCT
ejpam-5986	456	7	and	and	CCONJ
ejpam-5986	456	8	(	(	PUNCT
ejpam-5986	456	9	26	26	NUM
ejpam-5986	456	10	)	)	PUNCT
ejpam-5986	456	11	we	we	PRON
ejpam-5986	456	12	have	have	AUX
ejpam-5986	456	13	g∗	g∗	PROPN
ejpam-5986	456	14	α	α	PRON
ejpam-5986	456	15	,	,	PUNCT
ejpam-5986	456	16	λ{(f	λ{(f	ADP
ejpam-5986	456	17	∗	∗	NOUN
ejpam-5986	456	18	g)(t	g)(t	NOUN
ejpam-5986	456	19	)	)	PUNCT
ejpam-5986	456	20	}	}	PUNCT
ejpam-5986	457	1	=	=	PUNCT
ejpam-5986	457	2	uα	uα	PROPN
ejpam-5986	457	3	∫	∫	PROPN
ejpam-5986	457	4	∞	∞	PROPN
ejpam-5986	457	5	0	0	NUM
ejpam-5986	458	1	(	(	PUNCT
ejpam-5986	458	2	1	1	NUM
ejpam-5986	459	1	+	+	X
ejpam-5986	459	2	λ)−	λ)−	ADP
ejpam-5986	459	3	t	t	X
ejpam-5986	459	4	uλ	uλ	X
ejpam-5986	459	5	(	(	PUNCT
ejpam-5986	459	6	∫	∫	PROPN
ejpam-5986	459	7	t	t	PROPN
ejpam-5986	459	8	0	0	NUM
ejpam-5986	459	9	f(x)g(t−	f(x)g(t−	PROPN
ejpam-5986	459	10	x	x	SYM
ejpam-5986	459	11	)	)	PUNCT
ejpam-5986	459	12	dx	dx	PROPN
ejpam-5986	459	13	)	)	PUNCT
ejpam-5986	460	1	dt	dt	PROPN
ejpam-5986	460	2	i̇.	i̇.	PROPN
ejpam-5986	460	3	ege	ege	PROPN
ejpam-5986	460	4	/	/	SYM
ejpam-5986	460	5	eur	eur	PROPN
ejpam-5986	460	6	.	.	PUNCT
ejpam-5986	461	1	j.	j.	PROPN
ejpam-5986	461	2	pure	pure	PROPN
ejpam-5986	461	3	appl	appl	PROPN
ejpam-5986	461	4	.	.	PROPN
ejpam-5986	461	5	math	math	PROPN
ejpam-5986	461	6	,	,	PUNCT
ejpam-5986	461	7	18	18	NUM
ejpam-5986	461	8	(	(	PUNCT
ejpam-5986	461	9	2	2	NUM
ejpam-5986	461	10	)	)	PUNCT
ejpam-5986	461	11	(	(	PUNCT
ejpam-5986	461	12	2025	2025	NUM
ejpam-5986	461	13	)	)	PUNCT
ejpam-5986	461	14	,	,	PUNCT
ejpam-5986	461	15	5986	5986	NUM
ejpam-5986	461	16	15	15	NUM
ejpam-5986	461	17	of	of	ADP
ejpam-5986	461	18	20	20	NUM
ejpam-5986	461	19	=	=	SYM
ejpam-5986	461	20	uα	uα	PROPN
ejpam-5986	461	21	∫	∫	PROPN
ejpam-5986	461	22	∞	∞	PROPN
ejpam-5986	461	23	0	0	NUM
ejpam-5986	462	1	∫	∫	PROPN
ejpam-5986	463	1	∞	∞	NUM
ejpam-5986	463	2	x	x	SYM
ejpam-5986	463	3	(	(	PUNCT
ejpam-5986	463	4	1	1	NUM
ejpam-5986	463	5	+	+	X
ejpam-5986	463	6	λ)−	λ)−	ADP
ejpam-5986	463	7	t	t	PROPN
ejpam-5986	463	8	uλ	uλ	PRON
ejpam-5986	463	9	f(x)g(t−	f(x)g(t−	PROPN
ejpam-5986	463	10	x	x	X
ejpam-5986	463	11	)	)	PUNCT
ejpam-5986	463	12	dt	dt	X
ejpam-5986	464	1	dx	dx	PROPN
ejpam-5986	464	2	.	.	PUNCT
ejpam-5986	464	3	now	now	ADV
ejpam-5986	464	4	putting	put	VERB
ejpam-5986	464	5	t−	t−	NOUN
ejpam-5986	464	6	x	x	PUNCT
ejpam-5986	465	1	=	=	SYM
ejpam-5986	465	2	w	w	NOUN
ejpam-5986	465	3	we	we	PRON
ejpam-5986	465	4	have	have	AUX
ejpam-5986	465	5	g∗	g∗	PROPN
ejpam-5986	465	6	α	α	PRON
ejpam-5986	465	7	,	,	PUNCT
ejpam-5986	465	8	λ{(f	λ{(f	ADP
ejpam-5986	465	9	∗	∗	NOUN
ejpam-5986	465	10	g)(t	g)(t	NOUN
ejpam-5986	465	11	)	)	PUNCT
ejpam-5986	465	12	}	}	PUNCT
ejpam-5986	466	1	=	=	PUNCT
ejpam-5986	466	2	uα	uα	PROPN
ejpam-5986	466	3	∫	∫	PROPN
ejpam-5986	466	4	∞	∞	PROPN
ejpam-5986	466	5	0	0	NUM
ejpam-5986	467	1	∫	∫	PROPN
ejpam-5986	467	2	∞	∞	PROPN
ejpam-5986	467	3	0	0	NUM
ejpam-5986	468	1	(	(	PUNCT
ejpam-5986	468	2	1	1	NUM
ejpam-5986	468	3	+	+	CCONJ
ejpam-5986	468	4	λ)−	λ)−	ADP
ejpam-5986	468	5	w+x	w+x	NUM
ejpam-5986	468	6	uλ	uλ	ADP
ejpam-5986	468	7	f(x)g(w	f(x)g(w	PROPN
ejpam-5986	468	8	)	)	PUNCT
ejpam-5986	468	9	dw	dw	PROPN
ejpam-5986	468	10	dx	dx	PROPN
ejpam-5986	468	11	=	=	SYM
ejpam-5986	468	12	1	1	NUM
ejpam-5986	468	13	uα	uα	PROPN
ejpam-5986	468	14	(	(	PUNCT
ejpam-5986	468	15	uα	uα	PROPN
ejpam-5986	468	16	∫	∫	PROPN
ejpam-5986	468	17	∞	∞	PROPN
ejpam-5986	468	18	0	0	NUM
ejpam-5986	469	1	(	(	PUNCT
ejpam-5986	469	2	1	1	NUM
ejpam-5986	469	3	+	+	CCONJ
ejpam-5986	469	4	λ)−	λ)−	X
ejpam-5986	469	5	w	w	NOUN
ejpam-5986	469	6	uλ	uλ	X
ejpam-5986	469	7	g(w	g(w	PROPN
ejpam-5986	469	8	)	)	PUNCT
ejpam-5986	469	9	)	)	PUNCT
ejpam-5986	470	1	(	(	PUNCT
ejpam-5986	470	2	uα	uα	NOUN
ejpam-5986	470	3	∫	∫	PROPN
ejpam-5986	470	4	∞	∞	PROPN
ejpam-5986	470	5	0	0	NUM
ejpam-5986	470	6	(	(	PUNCT
ejpam-5986	470	7	1	1	NUM
ejpam-5986	471	1	+	+	CCONJ
ejpam-5986	471	2	λ)−	λ)−	X
ejpam-5986	471	3	x	x	SYM
ejpam-5986	471	4	uλ	uλ	PRON
ejpam-5986	471	5	f(x	f(x	PROPN
ejpam-5986	471	6	)	)	PUNCT
ejpam-5986	471	7	dx	dx	PROPN
ejpam-5986	471	8	)	)	PUNCT
ejpam-5986	471	9	,	,	PUNCT
ejpam-5986	471	10	and	and	CCONJ
ejpam-5986	471	11	the	the	DET
ejpam-5986	471	12	result	result	NOUN
ejpam-5986	471	13	follows	follow	VERB
ejpam-5986	471	14	.	.	PUNCT
ejpam-5986	472	1	note	note	VERB
ejpam-5986	472	2	that	that	SCONJ
ejpam-5986	472	3	,	,	PUNCT
ejpam-5986	472	4	the	the	DET
ejpam-5986	472	5	modified	modify	VERB
ejpam-5986	472	6	laplace	laplace	NOUN
ejpam-5986	472	7	-	-	PUNCT
ejpam-5986	472	8	type	type	NOUN
ejpam-5986	472	9	transform	transform	NOUN
ejpam-5986	472	10	preserves	preserve	VERB
ejpam-5986	472	11	the	the	DET
ejpam-5986	472	12	associative	associative	ADJ
ejpam-5986	472	13	property	property	NOUN
ejpam-5986	472	14	concerning	concern	VERB
ejpam-5986	472	15	the	the	DET
ejpam-5986	472	16	convolution	convolution	NOUN
ejpam-5986	472	17	operator	operator	NOUN
ejpam-5986	472	18	:	:	PUNCT
ejpam-5986	472	19	g∗	g∗	VERB
ejpam-5986	472	20	α	α	PRON
ejpam-5986	472	21	,	,	PUNCT
ejpam-5986	472	22	λ{((f	λ{((f	PROPN
ejpam-5986	472	23	∗	∗	NOUN
ejpam-5986	472	24	g	g	NOUN
ejpam-5986	472	25	)	)	PUNCT
ejpam-5986	472	26	∗	∗	NOUN
ejpam-5986	472	27	h)(t	h)(t	PROPN
ejpam-5986	472	28	)	)	PUNCT
ejpam-5986	472	29	}	}	PUNCT
ejpam-5986	472	30	=	=	PUNCT
ejpam-5986	472	31	g∗	g∗	VERB
ejpam-5986	472	32	α	α	NOUN
ejpam-5986	472	33	,	,	PUNCT
ejpam-5986	472	34	λ{(f	λ{(f	X
ejpam-5986	472	35	∗	∗	NOUN
ejpam-5986	472	36	(	(	PUNCT
ejpam-5986	472	37	g	g	PROPN
ejpam-5986	472	38	∗	∗	NOUN
ejpam-5986	472	39	h))(t	h))(t	PART
ejpam-5986	472	40	)	)	PUNCT
ejpam-5986	472	41	}	}	PUNCT
ejpam-5986	472	42	.	.	PUNCT
ejpam-5986	473	1	let	let	AUX
ejpam-5986	473	2	g∗	g∗	VERB
ejpam-5986	473	3	α	α	PRON
ejpam-5986	473	4	,	,	PUNCT
ejpam-5986	473	5	λ{f(t	λ{f(t	NUM
ejpam-5986	473	6	)	)	PUNCT
ejpam-5986	473	7	}	}	PUNCT
ejpam-5986	473	8	=	=	SYM
ejpam-5986	473	9	f	f	PROPN
ejpam-5986	473	10	∗	∗	X
ejpam-5986	473	11	α	α	PROPN
ejpam-5986	473	12	,	,	PUNCT
ejpam-5986	473	13	λ(u	λ(u	PROPN
ejpam-5986	473	14	)	)	PUNCT
ejpam-5986	473	15	.	.	PUNCT
ejpam-5986	474	1	then	then	ADV
ejpam-5986	474	2	f(t	f(t	NOUN
ejpam-5986	474	3	)	)	PUNCT
ejpam-5986	474	4	is	be	AUX
ejpam-5986	474	5	called	call	VERB
ejpam-5986	474	6	as	as	ADP
ejpam-5986	474	7	the	the	DET
ejpam-5986	474	8	inverse	inverse	ADJ
ejpam-5986	474	9	laplace	laplace	NOUN
ejpam-5986	474	10	-	-	PUNCT
ejpam-5986	474	11	type	type	NOUN
ejpam-5986	474	12	transform	transform	NOUN
ejpam-5986	474	13	of	of	ADP
ejpam-5986	474	14	f	f	PROPN
ejpam-5986	474	15	∗	∗	PROPN
ejpam-5986	474	16	α	α	PROPN
ejpam-5986	474	17	,	,	PUNCT
ejpam-5986	474	18	λ(u	λ(u	PROPN
ejpam-5986	474	19	)	)	PUNCT
ejpam-5986	474	20	and	and	CCONJ
ejpam-5986	474	21	defined	define	VERB
ejpam-5986	474	22	by	by	ADP
ejpam-5986	474	23	g∗−1	g∗−1	PROPN
ejpam-5986	474	24	α	α	PROPN
ejpam-5986	474	25	,	,	PUNCT
ejpam-5986	474	26	λ	λ	PROPN
ejpam-5986	474	27	{	{	PUNCT
ejpam-5986	474	28	f	f	PROPN
ejpam-5986	474	29	∗	∗	PROPN
ejpam-5986	474	30	α	α	PROPN
ejpam-5986	474	31	,	,	PUNCT
ejpam-5986	474	32	λ(u	λ(u	PROPN
ejpam-5986	474	33	)	)	PUNCT
ejpam-5986	474	34	}	}	PUNCT
ejpam-5986	475	1	=	=	SYM
ejpam-5986	475	2	f(t	f(t	NOUN
ejpam-5986	475	3	)	)	PUNCT
ejpam-5986	475	4	.	.	PUNCT
ejpam-5986	476	1	also	also	ADV
ejpam-5986	476	2	note	note	VERB
ejpam-5986	476	3	that	that	SCONJ
ejpam-5986	476	4	,	,	PUNCT
ejpam-5986	476	5	the	the	DET
ejpam-5986	476	6	inverse	inverse	NOUN
ejpam-5986	476	7	modified	modify	VERB
ejpam-5986	476	8	laplace	laplace	NOUN
ejpam-5986	476	9	-	-	PUNCT
ejpam-5986	476	10	type	type	NOUN
ejpam-5986	476	11	transform	transform	NOUN
ejpam-5986	476	12	is	be	AUX
ejpam-5986	476	13	linear	linear	ADJ
ejpam-5986	476	14	.	.	PUNCT
ejpam-5986	477	1	namely	namely	ADV
ejpam-5986	477	2	,	,	PUNCT
ejpam-5986	477	3	let	let	VERB
ejpam-5986	477	4	αi	αi	PRON
ejpam-5986	477	5	∈	∈	PROPN
ejpam-5986	477	6	r	r	NOUN
ejpam-5986	477	7	,	,	PUNCT
ejpam-5986	477	8	g∗	g∗	VERB
ejpam-5986	477	9	α	α	NOUN
ejpam-5986	477	10	,	,	PUNCT
ejpam-5986	477	11	λ{fi(t	λ{fi(t	NOUN
ejpam-5986	477	12	)	)	PUNCT
ejpam-5986	477	13	}	}	PUNCT
ejpam-5986	478	1	=	=	SYM
ejpam-5986	478	2	f	f	PROPN
ejpam-5986	478	3	∗	∗	NOUN
ejpam-5986	478	4	i	i	PRON
ejpam-5986	478	5	,	,	PUNCT
ejpam-5986	478	6	α	α	X
ejpam-5986	478	7	,	,	PUNCT
ejpam-5986	478	8	λ(u	λ(u	PROPN
ejpam-5986	478	9	)	)	PUNCT
ejpam-5986	478	10	for	for	ADP
ejpam-5986	478	11	i	i	PROPN
ejpam-5986	478	12	=	=	SYM
ejpam-5986	478	13	1	1	NUM
ejpam-5986	478	14	,	,	PUNCT
ejpam-5986	478	15	2	2	NUM
ejpam-5986	478	16	,	,	PUNCT
ejpam-5986	478	17	.	.	PUNCT
ejpam-5986	478	18	.	.	PUNCT
ejpam-5986	479	1	..	..	PUNCT
ejpam-5986	480	1	then	then	ADV
ejpam-5986	480	2	g∗−1	g∗−1	PROPN
ejpam-5986	480	3	α	α	NOUN
ejpam-5986	480	4	,	,	PUNCT
ejpam-5986	480	5	λ	λ	PROPN
ejpam-5986	480	6	{	{	PUNCT
ejpam-5986	480	7	n∑	n∑	NOUN
ejpam-5986	480	8	i=1	i=1	PROPN
ejpam-5986	480	9	αif	αif	PROPN
ejpam-5986	480	10	∗	∗	NOUN
ejpam-5986	480	11	i	i	PRON
ejpam-5986	480	12	,	,	PUNCT
ejpam-5986	480	13	α	α	X
ejpam-5986	480	14	,	,	PUNCT
ejpam-5986	480	15	λ(u	λ(u	PROPN
ejpam-5986	480	16	)	)	PUNCT
ejpam-5986	480	17	}	}	PUNCT
ejpam-5986	481	1	=	=	PUNCT
ejpam-5986	482	1	n∑	n∑	PROPN
ejpam-5986	482	2	i=1	i=1	PROPN
ejpam-5986	482	3	αig	αig	NOUN
ejpam-5986	482	4	∗−1	∗−1	PROPN
ejpam-5986	482	5	α	α	X
ejpam-5986	482	6	,	,	PUNCT
ejpam-5986	482	7	λ	λ	PROPN
ejpam-5986	482	8	{	{	PUNCT
ejpam-5986	482	9	f	f	PROPN
ejpam-5986	482	10	∗	∗	X
ejpam-5986	482	11	i	i	PRON
ejpam-5986	482	12	,	,	PUNCT
ejpam-5986	482	13	α	α	X
ejpam-5986	482	14	,	,	PUNCT
ejpam-5986	482	15	λ(u	λ(u	PROPN
ejpam-5986	482	16	)	)	PUNCT
ejpam-5986	482	17	}	}	PUNCT
ejpam-5986	482	18	.	.	PUNCT
ejpam-5986	483	1	4	4	X
ejpam-5986	483	2	.	.	X
ejpam-5986	483	3	applications	application	NOUN
ejpam-5986	483	4	in	in	ADP
ejpam-5986	483	5	this	this	DET
ejpam-5986	483	6	section	section	NOUN
ejpam-5986	483	7	,	,	PUNCT
ejpam-5986	483	8	we	we	PRON
ejpam-5986	483	9	give	give	VERB
ejpam-5986	483	10	examples	example	NOUN
ejpam-5986	483	11	to	to	PART
ejpam-5986	483	12	illustrate	illustrate	VERB
ejpam-5986	483	13	the	the	DET
ejpam-5986	483	14	use	use	NOUN
ejpam-5986	483	15	of	of	ADP
ejpam-5986	483	16	the	the	DET
ejpam-5986	483	17	mentioned	mention	VERB
ejpam-5986	483	18	transform	transform	NOUN
ejpam-5986	483	19	in	in	ADP
ejpam-5986	483	20	solving	solve	VERB
ejpam-5986	483	21	certain	certain	ADJ
ejpam-5986	483	22	initial	initial	ADJ
ejpam-5986	483	23	value	value	NOUN
ejpam-5986	483	24	problems	problem	NOUN
ejpam-5986	483	25	described	describe	VERB
ejpam-5986	483	26	by	by	ADP
ejpam-5986	483	27	ordinary	ordinary	ADJ
ejpam-5986	483	28	differential	differential	ADJ
ejpam-5986	483	29	equations	equation	NOUN
ejpam-5986	483	30	and	and	CCONJ
ejpam-5986	483	31	a	a	DET
ejpam-5986	483	32	volterra	volterra	NOUN
ejpam-5986	483	33	integral	integral	ADJ
ejpam-5986	483	34	equation	equation	NOUN
ejpam-5986	483	35	of	of	ADP
ejpam-5986	483	36	the	the	DET
ejpam-5986	483	37	second	second	ADJ
ejpam-5986	483	38	kind	kind	NOUN
ejpam-5986	483	39	.	.	PUNCT
ejpam-5986	484	1	example	example	NOUN
ejpam-5986	484	2	4	4	NUM
ejpam-5986	484	3	.	.	PUNCT
ejpam-5986	485	1	consider	consider	VERB
ejpam-5986	485	2	the	the	DET
ejpam-5986	485	3	first	first	ADJ
ejpam-5986	485	4	order	order	NOUN
ejpam-5986	485	5	differential	differential	NOUN
ejpam-5986	485	6	equation	equation	NOUN
ejpam-5986	485	7	dx	dx	PROPN
ejpam-5986	486	1	dt	dt	PROPN
ejpam-5986	487	1	+	+	CCONJ
ejpam-5986	487	2	x	x	X
ejpam-5986	487	3	=	=	SYM
ejpam-5986	487	4	0	0	NUM
ejpam-5986	487	5	with	with	ADP
ejpam-5986	487	6	the	the	DET
ejpam-5986	487	7	condition	condition	NOUN
ejpam-5986	487	8	x(0	x(0	PROPN
ejpam-5986	487	9	)	)	PUNCT
ejpam-5986	488	1	=	=	PUNCT
ejpam-5986	488	2	1	1	X
ejpam-5986	488	3	.	.	PUNCT
ejpam-5986	488	4	(	(	PUNCT
ejpam-5986	488	5	27	27	NUM
ejpam-5986	488	6	)	)	PUNCT
ejpam-5986	488	7	applying	apply	VERB
ejpam-5986	488	8	the	the	DET
ejpam-5986	488	9	modified	modify	VERB
ejpam-5986	488	10	laplace	laplace	NOUN
ejpam-5986	488	11	-	-	PUNCT
ejpam-5986	488	12	type	type	NOUN
ejpam-5986	488	13	transform	transform	NOUN
ejpam-5986	488	14	to	to	ADP
ejpam-5986	488	15	both	both	DET
ejpam-5986	488	16	sides	side	NOUN
ejpam-5986	488	17	of	of	ADP
ejpam-5986	488	18	the	the	DET
ejpam-5986	488	19	equation	equation	NOUN
ejpam-5986	488	20	(	(	PUNCT
ejpam-5986	488	21	27	27	NUM
ejpam-5986	488	22	)	)	PUNCT
ejpam-5986	488	23	and	and	CCONJ
ejpam-5986	488	24	using	use	VERB
ejpam-5986	488	25	the	the	DET
ejpam-5986	488	26	linearity	linearity	NOUN
ejpam-5986	488	27	property	property	NOUN
ejpam-5986	488	28	we	we	PRON
ejpam-5986	488	29	get	get	VERB
ejpam-5986	488	30	−uαx(0	−uαx(0	NOUN
ejpam-5986	488	31	)	)	PUNCT
ejpam-5986	489	1	+	+	PUNCT
ejpam-5986	489	2	ln(1	ln(1	PROPN
ejpam-5986	489	3	+	+	NUM
ejpam-5986	489	4	λ	λ	NOUN
ejpam-5986	489	5	)	)	PUNCT
ejpam-5986	489	6	λu	λu	AUX
ejpam-5986	489	7	g∗	g∗	VERB
ejpam-5986	489	8	α	α	NOUN
ejpam-5986	489	9	,	,	PUNCT
ejpam-5986	489	10	λ{x(t)}+g∗	λ{x(t)}+g∗	PROPN
ejpam-5986	489	11	α	α	NOUN
ejpam-5986	489	12	,	,	PUNCT
ejpam-5986	489	13	λ{x(t	λ{x(t	PROPN
ejpam-5986	489	14	)	)	PUNCT
ejpam-5986	489	15	}	}	PUNCT
ejpam-5986	490	1	=	=	SYM
ejpam-5986	490	2	0	0	X
ejpam-5986	490	3	.	.	PUNCT
ejpam-5986	491	1	putting	put	VERB
ejpam-5986	491	2	x(0	x(0	PROPN
ejpam-5986	491	3	)	)	PUNCT
ejpam-5986	492	1	=	=	SYM
ejpam-5986	492	2	1	1	NUM
ejpam-5986	492	3	we	we	PRON
ejpam-5986	492	4	have	have	AUX
ejpam-5986	492	5	g∗	g∗	PROPN
ejpam-5986	492	6	α	α	PRON
ejpam-5986	492	7	,	,	PUNCT
ejpam-5986	492	8	λ{x(t	λ{x(t	PROPN
ejpam-5986	492	9	)	)	PUNCT
ejpam-5986	492	10	}	}	PUNCT
ejpam-5986	493	1	=	=	NUM
ejpam-5986	493	2	λuα+1	λuα+1	NOUN
ejpam-5986	493	3	ln(1	ln(1	PROPN
ejpam-5986	493	4	+	+	NUM
ejpam-5986	493	5	λ	λ	NOUN
ejpam-5986	493	6	)	)	PUNCT
ejpam-5986	494	1	+	+	NUM
ejpam-5986	494	2	λu	λu	X
ejpam-5986	494	3	.	.	PUNCT
ejpam-5986	495	1	now	now	ADV
ejpam-5986	495	2	,	,	PUNCT
ejpam-5986	495	3	applying	apply	VERB
ejpam-5986	495	4	the	the	DET
ejpam-5986	495	5	inverse	inverse	NOUN
ejpam-5986	495	6	modified	modify	VERB
ejpam-5986	495	7	laplace	laplace	NOUN
ejpam-5986	495	8	-	-	PUNCT
ejpam-5986	495	9	type	type	NOUN
ejpam-5986	495	10	transform	transform	NOUN
ejpam-5986	495	11	,	,	PUNCT
ejpam-5986	495	12	and	and	CCONJ
ejpam-5986	495	13	using	use	VERB
ejpam-5986	495	14	the	the	DET
ejpam-5986	495	15	theorem	theorem	NOUN
ejpam-5986	495	16	3	3	NUM
ejpam-5986	495	17	gives	give	VERB
ejpam-5986	495	18	the	the	DET
ejpam-5986	495	19	solution	solution	NOUN
ejpam-5986	495	20	x(t	x(t	PROPN
ejpam-5986	495	21	)	)	PUNCT
ejpam-5986	495	22	=	=	SYM
ejpam-5986	495	23	e−t	e−t	NOUN
ejpam-5986	495	24	.	.	PUNCT
ejpam-5986	496	1	i̇.	i̇.	PROPN
ejpam-5986	496	2	ege	ege	PROPN
ejpam-5986	496	3	/	/	SYM
ejpam-5986	496	4	eur	eur	PROPN
ejpam-5986	496	5	.	.	PUNCT
ejpam-5986	497	1	j.	j.	PROPN
ejpam-5986	497	2	pure	pure	PROPN
ejpam-5986	497	3	appl	appl	PROPN
ejpam-5986	497	4	.	.	PROPN
ejpam-5986	497	5	math	math	PROPN
ejpam-5986	497	6	,	,	PUNCT
ejpam-5986	497	7	18	18	NUM
ejpam-5986	497	8	(	(	PUNCT
ejpam-5986	497	9	2	2	NUM
ejpam-5986	497	10	)	)	PUNCT
ejpam-5986	497	11	(	(	PUNCT
ejpam-5986	497	12	2025	2025	NUM
ejpam-5986	497	13	)	)	PUNCT
ejpam-5986	497	14	,	,	PUNCT
ejpam-5986	497	15	5986	5986	NUM
ejpam-5986	497	16	16	16	NUM
ejpam-5986	497	17	of	of	ADP
ejpam-5986	497	18	20	20	NUM
ejpam-5986	497	19	example	example	NOUN
ejpam-5986	497	20	5	5	NUM
ejpam-5986	497	21	.	.	X
ejpam-5986	497	22	consider	consider	VERB
ejpam-5986	497	23	the	the	DET
ejpam-5986	497	24	first	first	ADJ
ejpam-5986	497	25	order	order	NOUN
ejpam-5986	497	26	differential	differential	NOUN
ejpam-5986	497	27	equation	equation	NOUN
ejpam-5986	497	28	dx	dx	PROPN
ejpam-5986	497	29	dt	dt	PROPN
ejpam-5986	498	1	+	+	CCONJ
ejpam-5986	498	2	x	x	SYM
ejpam-5986	498	3	=	=	SYM
ejpam-5986	498	4	3	3	NUM
ejpam-5986	498	5	t	t	NOUN
ejpam-5986	498	6	with	with	ADP
ejpam-5986	498	7	the	the	DET
ejpam-5986	498	8	condition	condition	NOUN
ejpam-5986	498	9	x(0	x(0	PROPN
ejpam-5986	498	10	)	)	PUNCT
ejpam-5986	499	1	=	=	PUNCT
ejpam-5986	499	2	1	1	X
ejpam-5986	499	3	.	.	PUNCT
ejpam-5986	500	1	(	(	PUNCT
ejpam-5986	500	2	28	28	NUM
ejpam-5986	500	3	)	)	PUNCT
ejpam-5986	500	4	applying	apply	VERB
ejpam-5986	500	5	the	the	DET
ejpam-5986	500	6	modified	modify	VERB
ejpam-5986	500	7	laplace	laplace	NOUN
ejpam-5986	500	8	-	-	PUNCT
ejpam-5986	500	9	type	type	NOUN
ejpam-5986	500	10	transform	transform	NOUN
ejpam-5986	500	11	we	we	PRON
ejpam-5986	500	12	have	have	AUX
ejpam-5986	500	13	−uαx(0	−uαx(0	VERB
ejpam-5986	500	14	)	)	PUNCT
ejpam-5986	501	1	+	+	PUNCT
ejpam-5986	501	2	ln(1	ln(1	PROPN
ejpam-5986	501	3	+	+	NUM
ejpam-5986	501	4	λ	λ	NOUN
ejpam-5986	501	5	)	)	PUNCT
ejpam-5986	501	6	λu	λu	AUX
ejpam-5986	501	7	g∗	g∗	VERB
ejpam-5986	501	8	α	α	NOUN
ejpam-5986	501	9	,	,	PUNCT
ejpam-5986	501	10	λ{x(t)}+	λ{x(t)}+	NOUN
ejpam-5986	501	11	2g∗	2g∗	NUM
ejpam-5986	501	12	α	α	NOUN
ejpam-5986	501	13	,	,	PUNCT
ejpam-5986	501	14	λ{x(t	λ{x(t	PROPN
ejpam-5986	501	15	)	)	PUNCT
ejpam-5986	501	16	}	}	PUNCT
ejpam-5986	501	17	=	=	SYM
ejpam-5986	502	1	3λ2uα+2	3λ2uα+2	NUM
ejpam-5986	502	2	ln2(1	ln2(1	NOUN
ejpam-5986	502	3	+	+	CCONJ
ejpam-5986	502	4	λ	λ	NOUN
ejpam-5986	502	5	)	)	PUNCT
ejpam-5986	502	6	.	.	PUNCT
ejpam-5986	503	1	then	then	ADV
ejpam-5986	503	2	by	by	ADP
ejpam-5986	503	3	using	use	VERB
ejpam-5986	503	4	initial	initial	ADJ
ejpam-5986	503	5	condition	condition	NOUN
ejpam-5986	503	6	and	and	CCONJ
ejpam-5986	503	7	partial	partial	ADJ
ejpam-5986	503	8	fraction	fraction	NOUN
ejpam-5986	503	9	we	we	PRON
ejpam-5986	503	10	get	get	VERB
ejpam-5986	503	11	g∗	g∗	PROPN
ejpam-5986	503	12	α	α	NOUN
ejpam-5986	503	13	,	,	PUNCT
ejpam-5986	503	14	λ{x(t	λ{x(t	PROPN
ejpam-5986	503	15	)	)	PUNCT
ejpam-5986	503	16	}	}	PUNCT
ejpam-5986	504	1	=	=	PUNCT
ejpam-5986	504	2	3λ3uα+3	3λ3uα+3	NUM
ejpam-5986	504	3	ln2(1	ln2(1	NOUN
ejpam-5986	504	4	+	+	X
ejpam-5986	504	5	λ	λ	NOUN
ejpam-5986	504	6	)	)	PUNCT
ejpam-5986	505	1	[	[	X
ejpam-5986	505	2	ln(1	ln(1	PROPN
ejpam-5986	505	3	+	+	NUM
ejpam-5986	505	4	λ	λ	NOUN
ejpam-5986	505	5	)	)	PUNCT
ejpam-5986	506	1	+	+	X
ejpam-5986	506	2	λu	λu	X
ejpam-5986	506	3	]	]	X
ejpam-5986	506	4	+	+	NUM
ejpam-5986	506	5	λuα+1	λuα+1	NOUN
ejpam-5986	506	6	ln(1	ln(1	PROPN
ejpam-5986	506	7	+	+	NUM
ejpam-5986	506	8	λ	λ	NOUN
ejpam-5986	506	9	)	)	PUNCT
ejpam-5986	507	1	+	+	NUM
ejpam-5986	507	2	λu	λu	X
ejpam-5986	507	3	=	=	PUNCT
ejpam-5986	508	1	−	−	PROPN
ejpam-5986	508	2	3λuα+1	3λuα+1	NUM
ejpam-5986	509	1	ln(1	ln(1	PROPN
ejpam-5986	509	2	+	+	NUM
ejpam-5986	509	3	λ	λ	NOUN
ejpam-5986	509	4	)	)	PUNCT
ejpam-5986	510	1	+	+	CCONJ
ejpam-5986	510	2	3λ2uα+2	3λ2uα+2	NUM
ejpam-5986	510	3	ln2(1	ln2(1	NOUN
ejpam-5986	510	4	+	+	CCONJ
ejpam-5986	510	5	λ	λ	NOUN
ejpam-5986	510	6	)	)	PUNCT
ejpam-5986	511	1	+	+	NUM
ejpam-5986	511	2	4λuα+1	4λuα+1	NUM
ejpam-5986	511	3	ln(1	ln(1	NOUN
ejpam-5986	511	4	+	+	NUM
ejpam-5986	511	5	λ	λ	NOUN
ejpam-5986	511	6	)	)	PUNCT
ejpam-5986	512	1	+	+	CCONJ
ejpam-5986	512	2	λu	λu	X
ejpam-5986	512	3	.	.	PUNCT
ejpam-5986	513	1	taking	take	VERB
ejpam-5986	513	2	the	the	DET
ejpam-5986	513	3	inverse	inverse	NOUN
ejpam-5986	513	4	modified	modify	VERB
ejpam-5986	513	5	laplace	laplace	NOUN
ejpam-5986	513	6	-	-	PUNCT
ejpam-5986	513	7	type	type	NOUN
ejpam-5986	513	8	transform	transform	NOUN
ejpam-5986	513	9	of	of	ADP
ejpam-5986	513	10	the	the	DET
ejpam-5986	513	11	last	last	ADJ
ejpam-5986	513	12	equation	equation	NOUN
ejpam-5986	513	13	and	and	CCONJ
ejpam-5986	513	14	using	use	VERB
ejpam-5986	513	15	the	the	DET
ejpam-5986	513	16	theorems	theorem	NOUN
ejpam-5986	513	17	2	2	NUM
ejpam-5986	513	18	and	and	CCONJ
ejpam-5986	513	19	3	3	NUM
ejpam-5986	513	20	leads	lead	VERB
ejpam-5986	513	21	to	to	ADP
ejpam-5986	513	22	the	the	DET
ejpam-5986	513	23	solution	solution	NOUN
ejpam-5986	513	24	x(t	x(t	PROPN
ejpam-5986	513	25	)	)	PUNCT
ejpam-5986	513	26	=	=	PUNCT
ejpam-5986	514	1	−3	−3	PROPN
ejpam-5986	515	1	+	+	CCONJ
ejpam-5986	515	2	3t+	3t+	NUM
ejpam-5986	515	3	4e−t	4e−t	NOUN
ejpam-5986	515	4	.	.	PUNCT
ejpam-5986	516	1	now	now	ADV
ejpam-5986	516	2	,	,	PUNCT
ejpam-5986	516	3	we	we	PRON
ejpam-5986	516	4	use	use	VERB
ejpam-5986	516	5	the	the	DET
ejpam-5986	516	6	modified	modify	VERB
ejpam-5986	516	7	laplace	laplace	NOUN
ejpam-5986	516	8	-	-	PUNCT
ejpam-5986	516	9	type	type	NOUN
ejpam-5986	516	10	transform	transform	NOUN
ejpam-5986	516	11	for	for	ADP
ejpam-5986	516	12	solving	solve	VERB
ejpam-5986	516	13	a	a	DET
ejpam-5986	516	14	volterra	volterra	NOUN
ejpam-5986	516	15	integral	integral	ADJ
ejpam-5986	516	16	equation	equation	NOUN
ejpam-5986	516	17	of	of	ADP
ejpam-5986	516	18	the	the	DET
ejpam-5986	516	19	second	second	ADJ
ejpam-5986	516	20	kind	kind	NOUN
ejpam-5986	516	21	.	.	PUNCT
ejpam-5986	516	22	example	example	NOUN
ejpam-5986	517	1	6	6	NUM
ejpam-5986	517	2	.	.	PUNCT
ejpam-5986	517	3	consider	consider	VERB
ejpam-5986	517	4	the	the	DET
ejpam-5986	517	5	integral	integral	ADJ
ejpam-5986	517	6	equation	equation	NOUN
ejpam-5986	517	7	x(t	x(t	PROPN
ejpam-5986	517	8	)	)	PUNCT
ejpam-5986	518	1	=	=	SYM
ejpam-5986	518	2	t2	t2	PROPN
ejpam-5986	518	3	+	+	CCONJ
ejpam-5986	518	4	∫	∫	PROPN
ejpam-5986	518	5	t	t	PROPN
ejpam-5986	518	6	0	0	NUM
ejpam-5986	518	7	x(v	x(v	NUM
ejpam-5986	518	8	)	)	PUNCT
ejpam-5986	519	1	sin(t−	sin(t−	PROPN
ejpam-5986	519	2	v	v	X
ejpam-5986	519	3	)	)	PUNCT
ejpam-5986	519	4	dv	dv	PROPN
ejpam-5986	519	5	.	.	PROPN
ejpam-5986	520	1	(	(	PUNCT
ejpam-5986	520	2	29	29	NUM
ejpam-5986	520	3	)	)	PUNCT
ejpam-5986	520	4	by	by	ADP
ejpam-5986	520	5	the	the	DET
ejpam-5986	520	6	equation	equation	NOUN
ejpam-5986	520	7	(	(	PUNCT
ejpam-5986	520	8	26	26	NUM
ejpam-5986	520	9	)	)	PUNCT
ejpam-5986	520	10	we	we	PRON
ejpam-5986	520	11	write	write	VERB
ejpam-5986	520	12	the	the	DET
ejpam-5986	520	13	equation	equation	NOUN
ejpam-5986	520	14	(	(	PUNCT
ejpam-5986	520	15	29	29	NUM
ejpam-5986	520	16	)	)	PUNCT
ejpam-5986	520	17	as	as	ADP
ejpam-5986	520	18	x(t	x(t	PROPN
ejpam-5986	520	19	)	)	PUNCT
ejpam-5986	520	20	=	=	SYM
ejpam-5986	520	21	t2	t2	NOUN
ejpam-5986	520	22	+	+	CCONJ
ejpam-5986	520	23	(	(	PUNCT
ejpam-5986	520	24	x	x	NOUN
ejpam-5986	520	25	∗	∗	NOUN
ejpam-5986	520	26	sin)(t	sin)(t	NOUN
ejpam-5986	520	27	)	)	PUNCT
ejpam-5986	520	28	.	.	PUNCT
ejpam-5986	521	1	operating	operate	VERB
ejpam-5986	521	2	the	the	DET
ejpam-5986	521	3	modified	modify	VERB
ejpam-5986	521	4	laplace	laplace	NOUN
ejpam-5986	521	5	-	-	PUNCT
ejpam-5986	521	6	type	type	NOUN
ejpam-5986	521	7	transform	transform	NOUN
ejpam-5986	521	8	on	on	ADP
ejpam-5986	521	9	both	both	DET
ejpam-5986	521	10	sides	side	NOUN
ejpam-5986	521	11	to	to	ADP
ejpam-5986	521	12	the	the	DET
ejpam-5986	521	13	last	last	ADJ
ejpam-5986	521	14	equation	equation	NOUN
ejpam-5986	521	15	and	and	CCONJ
ejpam-5986	521	16	using	use	VERB
ejpam-5986	521	17	the	the	DET
ejpam-5986	521	18	convolution	convolution	NOUN
ejpam-5986	521	19	theorem	theorem	VERB
ejpam-5986	521	20	15	15	NUM
ejpam-5986	521	21	we	we	PRON
ejpam-5986	521	22	have	have	AUX
ejpam-5986	521	23	g∗	g∗	VERB
ejpam-5986	521	24	α	α	PRON
ejpam-5986	521	25	,	,	PUNCT
ejpam-5986	521	26	λ{x(t	λ{x(t	PROPN
ejpam-5986	521	27	)	)	PUNCT
ejpam-5986	521	28	}	}	PUNCT
ejpam-5986	521	29	=	=	PUNCT
ejpam-5986	521	30	g∗	g∗	VERB
ejpam-5986	521	31	α	α	NOUN
ejpam-5986	521	32	,	,	PUNCT
ejpam-5986	521	33	λ{t2}+g∗	λ{t2}+g∗	PROPN
ejpam-5986	521	34	α	α	NOUN
ejpam-5986	521	35	,	,	PUNCT
ejpam-5986	521	36	λ{(x	λ{(x	PROPN
ejpam-5986	521	37	∗	∗	NOUN
ejpam-5986	521	38	sin)(t	sin)(t	NOUN
ejpam-5986	521	39	)	)	PUNCT
ejpam-5986	521	40	}	}	PUNCT
ejpam-5986	521	41	=	=	PUNCT
ejpam-5986	521	42	g∗	g∗	VERB
ejpam-5986	521	43	α	α	NOUN
ejpam-5986	521	44	,	,	PUNCT
ejpam-5986	521	45	λ{t2}+	λ{t2}+	PROPN
ejpam-5986	521	46	1	1	NUM
ejpam-5986	521	47	uα	uα	PROPN
ejpam-5986	521	48	g∗	g∗	PROPN
ejpam-5986	521	49	α	α	PRON
ejpam-5986	521	50	,	,	PUNCT
ejpam-5986	521	51	λ{x(t)}g∗	λ{x(t)}g∗	PROPN
ejpam-5986	521	52	α	α	X
ejpam-5986	521	53	,	,	PUNCT
ejpam-5986	521	54	λ{sin	λ{sin	PROPN
ejpam-5986	521	55	t	t	PROPN
ejpam-5986	521	56	}	}	PUNCT
ejpam-5986	521	57	.	.	PUNCT
ejpam-5986	522	1	then	then	ADV
ejpam-5986	522	2	,	,	PUNCT
ejpam-5986	522	3	g∗	g∗	VERB
ejpam-5986	522	4	α	α	PRON
ejpam-5986	522	5	,	,	PUNCT
ejpam-5986	522	6	λ{x(t	λ{x(t	PROPN
ejpam-5986	522	7	)	)	PUNCT
ejpam-5986	522	8	}	}	PUNCT
ejpam-5986	522	9	(	(	PUNCT
ejpam-5986	522	10	1−	1−	NUM
ejpam-5986	522	11	g∗	g∗	PROPN
ejpam-5986	522	12	α	α	NOUN
ejpam-5986	522	13	,	,	PUNCT
ejpam-5986	522	14	λ{sin	λ{sin	PROPN
ejpam-5986	522	15	t	t	PROPN
ejpam-5986	522	16	}	}	PUNCT
ejpam-5986	522	17	uα	uα	PROPN
ejpam-5986	522	18	)	)	PUNCT
ejpam-5986	522	19	=	=	PUNCT
ejpam-5986	522	20	g∗	g∗	VERB
ejpam-5986	522	21	α	α	NOUN
ejpam-5986	522	22	,	,	PUNCT
ejpam-5986	522	23	λ{t2	λ{t2	NUM
ejpam-5986	522	24	}	}	PUNCT
ejpam-5986	522	25	.	.	PUNCT
ejpam-5986	523	1	now	now	ADV
ejpam-5986	523	2	using	use	VERB
ejpam-5986	523	3	the	the	DET
ejpam-5986	523	4	theorems	theorem	NOUN
ejpam-5986	523	5	2	2	NUM
ejpam-5986	523	6	and	and	CCONJ
ejpam-5986	523	7	4	4	NUM
ejpam-5986	523	8	we	we	PRON
ejpam-5986	523	9	get	get	VERB
ejpam-5986	523	10	g∗	g∗	PROPN
ejpam-5986	523	11	α	α	NOUN
ejpam-5986	523	12	,	,	PUNCT
ejpam-5986	523	13	λ{x(t	λ{x(t	PROPN
ejpam-5986	523	14	)	)	PUNCT
ejpam-5986	523	15	}	}	PUNCT
ejpam-5986	524	1	=	=	PUNCT
ejpam-5986	525	1	2λ3uα+3	2λ3uα+3	NUM
ejpam-5986	525	2	ln3(1	ln3(1	VERB
ejpam-5986	525	3	+	+	CCONJ
ejpam-5986	525	4	λ	λ	X
ejpam-5986	525	5	)	)	PUNCT
ejpam-5986	525	6	uα	uα	PROPN
ejpam-5986	525	7	1	1	NUM
ejpam-5986	525	8	uα	uα	NOUN
ejpam-5986	525	9	−	−	PROPN
ejpam-5986	525	10	λ2uα+2	λ2uα+2	NOUN
ejpam-5986	525	11	ln2(1	ln2(1	NOUN
ejpam-5986	525	12	+	+	CCONJ
ejpam-5986	525	13	λ	λ	NOUN
ejpam-5986	525	14	)	)	PUNCT
ejpam-5986	525	15	+	+	CCONJ
ejpam-5986	525	16	λ2u2	λ2u2	X
ejpam-5986	525	17	i̇.	i̇.	PROPN
ejpam-5986	525	18	ege	ege	PROPN
ejpam-5986	525	19	/	/	SYM
ejpam-5986	525	20	eur	eur	PROPN
ejpam-5986	525	21	.	.	PUNCT
ejpam-5986	526	1	j.	j.	PROPN
ejpam-5986	526	2	pure	pure	PROPN
ejpam-5986	526	3	appl	appl	PROPN
ejpam-5986	526	4	.	.	PROPN
ejpam-5986	526	5	math	math	PROPN
ejpam-5986	526	6	,	,	PUNCT
ejpam-5986	526	7	18	18	NUM
ejpam-5986	526	8	(	(	PUNCT
ejpam-5986	526	9	2	2	NUM
ejpam-5986	526	10	)	)	PUNCT
ejpam-5986	526	11	(	(	PUNCT
ejpam-5986	526	12	2025	2025	NUM
ejpam-5986	526	13	)	)	PUNCT
ejpam-5986	526	14	,	,	PUNCT
ejpam-5986	526	15	5986	5986	NUM
ejpam-5986	526	16	17	17	NUM
ejpam-5986	526	17	of	of	ADP
ejpam-5986	526	18	20	20	NUM
ejpam-5986	526	19	=	=	SYM
ejpam-5986	526	20	2λ3uα+3	2λ3uα+3	NUM
ejpam-5986	526	21	ln3(1	ln3(1	PRON
ejpam-5986	526	22	+	+	CCONJ
ejpam-5986	526	23	λ	λ	NOUN
ejpam-5986	526	24	)	)	PUNCT
ejpam-5986	526	25	ln2(1	ln2(1	NOUN
ejpam-5986	526	26	+	+	SYM
ejpam-5986	526	27	λ	λ	NOUN
ejpam-5986	526	28	)	)	PUNCT
ejpam-5986	527	1	+	+	NUM
ejpam-5986	527	2	λ2u2	λ2u2	NOUN
ejpam-5986	527	3	ln2(1	ln2(1	NOUN
ejpam-5986	527	4	+	+	CCONJ
ejpam-5986	527	5	λ	λ	NOUN
ejpam-5986	527	6	)	)	PUNCT
ejpam-5986	527	7	=	=	SYM
ejpam-5986	527	8	2λ3uα+3	2λ3uα+3	NUM
ejpam-5986	527	9	ln3(1	ln3(1	VERB
ejpam-5986	527	10	+	+	CCONJ
ejpam-5986	527	11	λ	λ	X
ejpam-5986	527	12	)	)	PUNCT
ejpam-5986	527	13	2λ5uα+5	2λ5uα+5	NUM
ejpam-5986	527	14	ln5(1	ln5(1	NOUN
ejpam-5986	527	15	+	+	X
ejpam-5986	527	16	λ	λ	NOUN
ejpam-5986	527	17	)	)	PUNCT
ejpam-5986	527	18	.	.	PUNCT
ejpam-5986	528	1	lastly	lastly	ADV
ejpam-5986	528	2	,	,	PUNCT
ejpam-5986	528	3	taking	take	VERB
ejpam-5986	528	4	the	the	DET
ejpam-5986	528	5	inverse	inverse	NOUN
ejpam-5986	528	6	modified	modify	VERB
ejpam-5986	528	7	laplace	laplace	NOUN
ejpam-5986	528	8	-	-	PUNCT
ejpam-5986	528	9	type	type	NOUN
ejpam-5986	528	10	transform	transform	NOUN
ejpam-5986	528	11	of	of	ADP
ejpam-5986	528	12	the	the	DET
ejpam-5986	528	13	last	last	ADJ
ejpam-5986	528	14	equation	equation	NOUN
ejpam-5986	528	15	leads	lead	VERB
ejpam-5986	528	16	to	to	ADP
ejpam-5986	528	17	the	the	DET
ejpam-5986	528	18	solution	solution	NOUN
ejpam-5986	528	19	x(t	x(t	PROPN
ejpam-5986	528	20	)	)	PUNCT
ejpam-5986	529	1	=	=	SYM
ejpam-5986	529	2	t2	t2	NOUN
ejpam-5986	529	3	+	+	CCONJ
ejpam-5986	529	4	1	1	NUM
ejpam-5986	529	5	12	12	NUM
ejpam-5986	529	6	t4	t4	PROPN
ejpam-5986	529	7	.	.	PUNCT
ejpam-5986	529	8	table	table	NOUN
ejpam-5986	529	9	1	1	NUM
ejpam-5986	529	10	:	:	PUNCT
ejpam-5986	529	11	the	the	DET
ejpam-5986	529	12	modified	modify	VERB
ejpam-5986	529	13	laplace	laplace	NOUN
ejpam-5986	529	14	-	-	PUNCT
ejpam-5986	529	15	type	type	NOUN
ejpam-5986	529	16	transform	transform	NOUN
ejpam-5986	529	17	of	of	ADP
ejpam-5986	529	18	some	some	DET
ejpam-5986	529	19	elementary	elementary	ADJ
ejpam-5986	529	20	functions	function	NOUN
ejpam-5986	529	21	.	.	PUNCT
ejpam-5986	530	1	f(t	f(t	NOUN
ejpam-5986	530	2	)	)	PUNCT
ejpam-5986	531	1	=	=	SYM
ejpam-5986	532	1	g∗−1	g∗−1	PROPN
ejpam-5986	532	2	α	α	NOUN
ejpam-5986	532	3	,	,	PUNCT
ejpam-5986	532	4	λ	λ	PROPN
ejpam-5986	532	5	{	{	PUNCT
ejpam-5986	532	6	f	f	PROPN
ejpam-5986	532	7	∗	∗	PROPN
ejpam-5986	532	8	α	α	PROPN
ejpam-5986	532	9	,	,	PUNCT
ejpam-5986	532	10	λ(u	λ(u	PROPN
ejpam-5986	532	11	)	)	PUNCT
ejpam-5986	532	12	}	}	PUNCT
ejpam-5986	532	13	f	f	PROPN
ejpam-5986	532	14	∗	∗	PROPN
ejpam-5986	532	15	α	α	PROPN
ejpam-5986	532	16	,	,	PUNCT
ejpam-5986	532	17	λ(u	λ(u	PROPN
ejpam-5986	532	18	)	)	PUNCT
ejpam-5986	532	19	=	=	PUNCT
ejpam-5986	532	20	g∗	g∗	VERB
ejpam-5986	532	21	α	α	X
ejpam-5986	532	22	,	,	PUNCT
ejpam-5986	532	23	λ{f(t	λ{f(t	NUM
ejpam-5986	532	24	)	)	PUNCT
ejpam-5986	532	25	}	}	PUNCT
ejpam-5986	532	26	1	1	NUM
ejpam-5986	532	27	λuα+1	λuα+1	NOUN
ejpam-5986	532	28	ln(1	ln(1	PROPN
ejpam-5986	532	29	+	+	NUM
ejpam-5986	532	30	λ	λ	NOUN
ejpam-5986	532	31	)	)	PUNCT
ejpam-5986	532	32	t	t	NOUN
ejpam-5986	532	33	λ2	λ2	NOUN
ejpam-5986	532	34	uα+2	uα+2	NUM
ejpam-5986	532	35	ln2(1	ln2(1	NOUN
ejpam-5986	532	36	+	+	CCONJ
ejpam-5986	532	37	λ	λ	NOUN
ejpam-5986	532	38	)	)	PUNCT
ejpam-5986	532	39	tn	tn	PROPN
ejpam-5986	532	40	,	,	PUNCT
ejpam-5986	532	41	(	(	PUNCT
ejpam-5986	532	42	n	n	NOUN
ejpam-5986	532	43	=	=	SYM
ejpam-5986	532	44	1	1	NUM
ejpam-5986	532	45	,	,	PUNCT
ejpam-5986	532	46	2	2	NUM
ejpam-5986	532	47	,	,	PUNCT
ejpam-5986	532	48	.	.	PUNCT
ejpam-5986	532	49	.	.	PUNCT
ejpam-5986	532	50	.	.	PUNCT
ejpam-5986	532	51	)	)	PUNCT
ejpam-5986	533	1	n!λn+1uα+n+1	n!λn+1uα+n+1	PROPN
ejpam-5986	533	2	lnn+1(1	lnn+1(1	PUNCT
ejpam-5986	534	1	+	+	PUNCT
ejpam-5986	534	2	λ	λ	X
ejpam-5986	534	3	)	)	PUNCT
ejpam-5986	534	4	eat	eat	VERB
ejpam-5986	534	5	λuα+1	λuα+1	NOUN
ejpam-5986	534	6	ln(1	ln(1	PROPN
ejpam-5986	534	7	+	+	CCONJ
ejpam-5986	534	8	λ)−	λ)−	PROPN
ejpam-5986	534	9	aλu	aλu	ADJ
ejpam-5986	534	10	sin	sin	NOUN
ejpam-5986	534	11	at	at	ADP
ejpam-5986	534	12	aλ2uα+2	aλ2uα+2	PROPN
ejpam-5986	534	13	ln2(1	ln2(1	NOUN
ejpam-5986	534	14	+	+	CCONJ
ejpam-5986	534	15	λ	λ	NOUN
ejpam-5986	534	16	)	)	PUNCT
ejpam-5986	535	1	+	+	CCONJ
ejpam-5986	535	2	a2λ2u2	a2λ2u2	PROPN
ejpam-5986	535	3	cos	cos	PROPN
ejpam-5986	535	4	at	at	ADP
ejpam-5986	535	5	λ	λ	PROPN
ejpam-5986	535	6	ln(1	ln(1	NOUN
ejpam-5986	535	7	+	+	CCONJ
ejpam-5986	535	8	λ)uα+1	λ)uα+1	NOUN
ejpam-5986	535	9	ln2(1	ln2(1	NOUN
ejpam-5986	535	10	+	+	X
ejpam-5986	535	11	λ	λ	NOUN
ejpam-5986	535	12	)	)	PUNCT
ejpam-5986	535	13	+	+	CCONJ
ejpam-5986	535	14	a2λ2u2	a2λ2u2	PROPN
ejpam-5986	535	15	sinh	sinh	NOUN
ejpam-5986	535	16	at	at	ADP
ejpam-5986	535	17	aλ2uα+2	aλ2uα+2	PROPN
ejpam-5986	535	18	ln2(1	ln2(1	NOUN
ejpam-5986	536	1	+	+	CCONJ
ejpam-5986	536	2	λ)−	λ)−	ADP
ejpam-5986	536	3	a2λ2u2	a2λ2u2	PROPN
ejpam-5986	536	4	cosh	cosh	NOUN
ejpam-5986	536	5	at	at	ADP
ejpam-5986	536	6	λ	λ	PROPN
ejpam-5986	536	7	ln(1	ln(1	NOUN
ejpam-5986	536	8	+	+	CCONJ
ejpam-5986	536	9	λ)uα+1	λ)uα+1	NOUN
ejpam-5986	536	10	ln2(1	ln2(1	NOUN
ejpam-5986	537	1	+	+	CCONJ
ejpam-5986	537	2	λ)−	λ)−	PROPN
ejpam-5986	537	3	a2λ2u2	a2λ2u2	NOUN
ejpam-5986	537	4	eat	eat	VERB
ejpam-5986	537	5	sin	sin	NOUN
ejpam-5986	537	6	bt	bt	X
ejpam-5986	537	7	bλ2uα+2	bλ2uα+2	PROPN
ejpam-5986	538	1	(	(	PUNCT
ejpam-5986	538	2	ln(1	ln(1	PROPN
ejpam-5986	538	3	+	+	PROPN
ejpam-5986	538	4	λ)−	λ)−	PROPN
ejpam-5986	538	5	aλu)2	aλu)2	PROPN
ejpam-5986	538	6	+	+	CCONJ
ejpam-5986	538	7	b2λ2u2	b2λ2u2	ADJ
ejpam-5986	538	8	eat	eat	NOUN
ejpam-5986	538	9	cos	cos	SCONJ
ejpam-5986	538	10	bt	bt	ADJ
ejpam-5986	538	11	λuα+1	λuα+1	NOUN
ejpam-5986	538	12	(	(	PUNCT
ejpam-5986	538	13	ln(1	ln(1	NOUN
ejpam-5986	538	14	+	+	CCONJ
ejpam-5986	538	15	λ)−	λ)−	PROPN
ejpam-5986	538	16	aλu	aλu	NOUN
ejpam-5986	538	17	)	)	PUNCT
ejpam-5986	538	18	(	(	PUNCT
ejpam-5986	538	19	ln(1	ln(1	PROPN
ejpam-5986	538	20	+	+	PROPN
ejpam-5986	538	21	λ)−	λ)−	PROPN
ejpam-5986	538	22	aλu)2	aλu)2	PROPN
ejpam-5986	538	23	+	+	CCONJ
ejpam-5986	538	24	b2λ2u2	b2λ2u2	ADJ
ejpam-5986	538	25	i̇.	i̇.	PROPN
ejpam-5986	538	26	ege	ege	PROPN
ejpam-5986	538	27	/	/	SYM
ejpam-5986	538	28	eur	eur	PROPN
ejpam-5986	538	29	.	.	PUNCT
ejpam-5986	539	1	j.	j.	PROPN
ejpam-5986	539	2	pure	pure	PROPN
ejpam-5986	539	3	appl	appl	PROPN
ejpam-5986	539	4	.	.	PROPN
ejpam-5986	539	5	math	math	PROPN
ejpam-5986	539	6	,	,	PUNCT
ejpam-5986	539	7	18	18	NUM
ejpam-5986	539	8	(	(	PUNCT
ejpam-5986	539	9	2	2	NUM
ejpam-5986	539	10	)	)	PUNCT
ejpam-5986	539	11	(	(	PUNCT
ejpam-5986	539	12	2025	2025	NUM
ejpam-5986	539	13	)	)	PUNCT
ejpam-5986	539	14	,	,	PUNCT
ejpam-5986	539	15	5986	5986	NUM
ejpam-5986	539	16	18	18	NUM
ejpam-5986	539	17	of	of	ADP
ejpam-5986	539	18	20	20	NUM
ejpam-5986	539	19	5	5	NUM
ejpam-5986	539	20	.	.	PUNCT
ejpam-5986	540	1	conclusion	conclusion	NOUN
ejpam-5986	540	2	in	in	ADP
ejpam-5986	540	3	the	the	DET
ejpam-5986	540	4	presented	present	VERB
ejpam-5986	540	5	paper	paper	NOUN
ejpam-5986	540	6	,	,	PUNCT
ejpam-5986	540	7	we	we	PRON
ejpam-5986	540	8	have	have	AUX
ejpam-5986	540	9	considered	consider	VERB
ejpam-5986	540	10	the	the	DET
ejpam-5986	540	11	concept	concept	NOUN
ejpam-5986	540	12	of	of	ADP
ejpam-5986	540	13	the	the	DET
ejpam-5986	540	14	modified	modify	VERB
ejpam-5986	540	15	laplace	laplace	NOUN
ejpam-5986	540	16	-	-	PUNCT
ejpam-5986	540	17	type	type	NOUN
ejpam-5986	540	18	transform	transform	NOUN
ejpam-5986	540	19	and	and	CCONJ
ejpam-5986	540	20	give	give	VERB
ejpam-5986	540	21	relations	relation	NOUN
ejpam-5986	540	22	between	between	ADP
ejpam-5986	540	23	some	some	DET
ejpam-5986	540	24	integral	integral	ADJ
ejpam-5986	540	25	transforms	transform	NOUN
ejpam-5986	540	26	in	in	ADP
ejpam-5986	540	27	the	the	DET
ejpam-5986	540	28	laplace	laplace	NOUN
ejpam-5986	540	29	class	class	NOUN
ejpam-5986	540	30	such	such	ADJ
ejpam-5986	540	31	as	as	ADP
ejpam-5986	540	32	the	the	DET
ejpam-5986	540	33	laplace	laplace	NOUN
ejpam-5986	540	34	-	-	PUNCT
ejpam-5986	540	35	type	type	NOUN
ejpam-5986	540	36	,	,	PUNCT
ejpam-5986	540	37	sumudu	sumudu	NOUN
ejpam-5986	540	38	,	,	PUNCT
ejpam-5986	540	39	and	and	CCONJ
ejpam-5986	540	40	elzaki	elzaki	NOUN
ejpam-5986	540	41	transforms	transform	VERB
ejpam-5986	540	42	.	.	PUNCT
ejpam-5986	541	1	we	we	PRON
ejpam-5986	541	2	have	have	AUX
ejpam-5986	541	3	proved	prove	VERB
ejpam-5986	541	4	some	some	DET
ejpam-5986	541	5	properties	property	NOUN
ejpam-5986	541	6	and	and	CCONJ
ejpam-5986	541	7	derived	derive	VERB
ejpam-5986	541	8	the	the	DET
ejpam-5986	541	9	modified	modify	VERB
ejpam-5986	541	10	laplace	laplace	NOUN
ejpam-5986	541	11	-	-	PUNCT
ejpam-5986	541	12	type	type	NOUN
ejpam-5986	541	13	transform	transform	NOUN
ejpam-5986	541	14	of	of	ADP
ejpam-5986	541	15	power	power	NOUN
ejpam-5986	541	16	functions	function	NOUN
ejpam-5986	541	17	,	,	PUNCT
ejpam-5986	541	18	sine	sine	NOUN
ejpam-5986	541	19	,	,	PUNCT
ejpam-5986	541	20	cosine	cosine	NOUN
ejpam-5986	541	21	,	,	PUNCT
ejpam-5986	541	22	hyperbolic	hyperbolic	ADJ
ejpam-5986	541	23	sine	sine	NOUN
ejpam-5986	541	24	,	,	PUNCT
ejpam-5986	541	25	hyperbolic	hyperbolic	ADJ
ejpam-5986	541	26	cosine	cosine	NOUN
ejpam-5986	541	27	,	,	PUNCT
ejpam-5986	541	28	exponential	exponential	ADJ
ejpam-5986	541	29	function	function	NOUN
ejpam-5986	541	30	,	,	PUNCT
ejpam-5986	541	31	and	and	CCONJ
ejpam-5986	541	32	function	function	VERB
ejpam-5986	541	33	derivatives	derivative	NOUN
ejpam-5986	541	34	.	.	PUNCT
ejpam-5986	542	1	we	we	PRON
ejpam-5986	542	2	give	give	VERB
ejpam-5986	542	3	some	some	DET
ejpam-5986	542	4	operational	operational	ADJ
ejpam-5986	542	5	properties	property	NOUN
ejpam-5986	542	6	such	such	ADJ
ejpam-5986	542	7	as	as	ADP
ejpam-5986	542	8	linearity	linearity	NOUN
ejpam-5986	542	9	,	,	PUNCT
ejpam-5986	542	10	translations	translation	NOUN
ejpam-5986	542	11	,	,	PUNCT
ejpam-5986	542	12	and	and	CCONJ
ejpam-5986	542	13	scale	scale	NOUN
ejpam-5986	542	14	preserving	preserving	NOUN
ejpam-5986	542	15	.	.	PUNCT
ejpam-5986	543	1	besides	besides	SCONJ
ejpam-5986	543	2	these	these	PRON
ejpam-5986	543	3	,	,	PUNCT
ejpam-5986	543	4	we	we	PRON
ejpam-5986	543	5	have	have	AUX
ejpam-5986	543	6	also	also	ADV
ejpam-5986	543	7	examined	examine	VERB
ejpam-5986	543	8	the	the	DET
ejpam-5986	543	9	relation	relation	NOUN
ejpam-5986	543	10	between	between	ADP
ejpam-5986	543	11	the	the	DET
ejpam-5986	543	12	modified	modify	VERB
ejpam-5986	543	13	laplace	laplace	NOUN
ejpam-5986	543	14	-	-	PUNCT
ejpam-5986	543	15	type	type	NOUN
ejpam-5986	543	16	transform	transform	NOUN
ejpam-5986	543	17	and	and	CCONJ
ejpam-5986	543	18	the	the	DET
ejpam-5986	543	19	modified	modify	VERB
ejpam-5986	543	20	degenerate	degenerate	ADJ
ejpam-5986	543	21	gamma	gamma	NOUN
ejpam-5986	543	22	function	function	NOUN
ejpam-5986	543	23	.	.	PUNCT
ejpam-5986	544	1	we	we	PRON
ejpam-5986	544	2	have	have	AUX
ejpam-5986	544	3	applied	apply	VERB
ejpam-5986	544	4	the	the	DET
ejpam-5986	544	5	new	new	ADJ
ejpam-5986	544	6	transform	transform	NOUN
ejpam-5986	544	7	to	to	PART
ejpam-5986	544	8	solve	solve	VERB
ejpam-5986	544	9	some	some	DET
ejpam-5986	544	10	ordinary	ordinary	ADJ
ejpam-5986	544	11	differential	differential	ADJ
ejpam-5986	544	12	equations	equation	NOUN
ejpam-5986	544	13	and	and	CCONJ
ejpam-5986	544	14	a	a	DET
ejpam-5986	544	15	volterra	volterra	NOUN
ejpam-5986	544	16	integral	integral	ADJ
ejpam-5986	544	17	equation	equation	NOUN
ejpam-5986	544	18	.	.	PUNCT
ejpam-5986	545	1	in	in	ADP
ejpam-5986	545	2	the	the	DET
ejpam-5986	545	3	future	future	NOUN
ejpam-5986	545	4	,	,	PUNCT
ejpam-5986	545	5	the	the	DET
ejpam-5986	545	6	presented	present	VERB
ejpam-5986	545	7	transform	transform	NOUN
ejpam-5986	545	8	can	can	AUX
ejpam-5986	545	9	be	be	AUX
ejpam-5986	545	10	used	use	VERB
ejpam-5986	545	11	in	in	ADP
ejpam-5986	545	12	many	many	ADJ
ejpam-5986	545	13	scopes	scope	NOUN
ejpam-5986	545	14	,	,	PUNCT
ejpam-5986	545	15	such	such	ADJ
ejpam-5986	545	16	as	as	ADP
ejpam-5986	545	17	solving	solve	VERB
ejpam-5986	545	18	various	various	ADJ
ejpam-5986	545	19	complicated	complicated	ADJ
ejpam-5986	545	20	problems	problem	NOUN
ejpam-5986	545	21	by	by	ADP
ejpam-5986	545	22	developing	develop	VERB
ejpam-5986	545	23	a	a	DET
ejpam-5986	545	24	mathematical	mathematical	ADJ
ejpam-5986	545	25	model	model	NOUN
ejpam-5986	545	26	using	use	VERB
ejpam-5986	545	27	some	some	DET
ejpam-5986	545	28	differential	differential	ADJ
ejpam-5986	545	29	equations	equation	NOUN
ejpam-5986	545	30	.	.	PUNCT
ejpam-5986	546	1	acknowledgements	acknowledgement	NOUN
ejpam-5986	546	2	the	the	DET
ejpam-5986	546	3	author	author	NOUN
ejpam-5986	546	4	expresses	express	VERB
ejpam-5986	546	5	gratitude	gratitude	NOUN
ejpam-5986	546	6	to	to	ADP
ejpam-5986	546	7	the	the	DET
ejpam-5986	546	8	anonymous	anonymous	ADJ
ejpam-5986	546	9	reviewers	reviewer	NOUN
ejpam-5986	546	10	for	for	ADP
ejpam-5986	546	11	their	their	PRON
ejpam-5986	546	12	valuable	valuable	ADJ
ejpam-5986	546	13	feedback	feedback	NOUN
ejpam-5986	546	14	and	and	CCONJ
ejpam-5986	546	15	constructive	constructive	ADJ
ejpam-5986	546	16	suggestions	suggestion	NOUN
ejpam-5986	546	17	,	,	PUNCT
ejpam-5986	546	18	which	which	PRON
ejpam-5986	546	19	have	have	AUX
ejpam-5986	546	20	enhanced	enhance	VERB
ejpam-5986	546	21	the	the	DET
ejpam-5986	546	22	quality	quality	NOUN
ejpam-5986	546	23	of	of	ADP
ejpam-5986	546	24	this	this	DET
ejpam-5986	546	25	manuscript	manuscript	NOUN
ejpam-5986	546	26	.	.	PUNCT
ejpam-5986	547	1	references	reference	NOUN
ejpam-5986	547	2	[	[	X
ejpam-5986	547	3	1	1	NUM
ejpam-5986	547	4	]	]	X
ejpam-5986	547	5	y.	y.	PROPN
ejpam-5986	547	6	almalki	almalki	PROPN
ejpam-5986	547	7	,	,	PUNCT
ejpam-5986	547	8	m.	m.	NOUN
ejpam-5986	547	9	abdalla	abdalla	PROPN
ejpam-5986	547	10	,	,	PUNCT
ejpam-5986	547	11	and	and	CCONJ
ejpam-5986	547	12	h.	h.	PROPN
ejpam-5986	547	13	abd	abd	PROPN
ejpam-5986	547	14	-	-	PUNCT
ejpam-5986	547	15	elmageed	elmageed	NOUN
ejpam-5986	547	16	.	.	PUNCT
ejpam-5986	548	1	results	result	NOUN
ejpam-5986	548	2	on	on	ADP
ejpam-5986	548	3	the	the	DET
ejpam-5986	548	4	modified	modify	VERB
ejpam-5986	548	5	degenerate	degenerate	ADJ
ejpam-5986	548	6	laplace	laplace	NOUN
ejpam-5986	548	7	-	-	PUNCT
ejpam-5986	548	8	type	type	NOUN
ejpam-5986	548	9	integral	integral	ADJ
ejpam-5986	548	10	associated	associate	VERB
ejpam-5986	548	11	with	with	ADP
ejpam-5986	548	12	applications	application	NOUN
ejpam-5986	548	13	involving	involve	VERB
ejpam-5986	548	14	fractional	fractional	ADJ
ejpam-5986	548	15	kinetic	kinetic	ADJ
ejpam-5986	548	16	equations	equation	NOUN
ejpam-5986	548	17	.	.	PUNCT
ejpam-5986	549	1	demonstratio	demonstratio	PROPN
ejpam-5986	549	2	mathematica	mathematica	PROPN
ejpam-5986	549	3	,	,	PUNCT
ejpam-5986	549	4	56(1):20230112	56(1):20230112	NUM
ejpam-5986	549	5	,	,	PUNCT
ejpam-5986	549	6	2023	2023	NUM
ejpam-5986	549	7	.	.	PUNCT
ejpam-5986	550	1	[	[	X
ejpam-5986	550	2	2	2	NUM
ejpam-5986	550	3	]	]	PUNCT
ejpam-5986	550	4	a.	a.	NOUN
ejpam-5986	550	5	k.	k.	PROPN
ejpam-5986	550	6	alsalihi	alsalihi	PROPN
ejpam-5986	550	7	.	.	PUNCT
ejpam-5986	551	1	modified	modify	VERB
ejpam-5986	551	2	elzaki	elzaki	NOUN
ejpam-5986	551	3	transform	transform	NOUN
ejpam-5986	551	4	and	and	CCONJ
ejpam-5986	551	5	its	its	PRON
ejpam-5986	551	6	applications	application	NOUN
ejpam-5986	551	7	.	.	PUNCT
ejpam-5986	552	1	abhath	abhath	PROPN
ejpam-5986	552	2	journal	journal	PROPN
ejpam-5986	552	3	of	of	ADP
ejpam-5986	552	4	basic	basic	ADJ
ejpam-5986	552	5	and	and	CCONJ
ejpam-5986	552	6	applied	applied	ADJ
ejpam-5986	552	7	sciences	science	NOUN
ejpam-5986	552	8	,	,	PUNCT
ejpam-5986	552	9	1(1):83–102	1(1):83–102	NUM
ejpam-5986	552	10	,	,	PUNCT
ejpam-5986	552	11	2022	2022	NUM
ejpam-5986	552	12	.	.	PUNCT
ejpam-5986	553	1	[	[	X
ejpam-5986	553	2	3	3	X
ejpam-5986	553	3	]	]	X
ejpam-5986	553	4	h.	h.	PROPN
ejpam-5986	553	5	campos	campos	PROPN
ejpam-5986	553	6	,	,	PUNCT
ejpam-5986	553	7	j.	j.	PROPN
ejpam-5986	553	8	fernandez	fernandez	PROPN
ejpam-5986	553	9	,	,	PUNCT
ejpam-5986	553	10	and	and	CCONJ
ejpam-5986	553	11	j.	j.	PROPN
ejpam-5986	553	12	b.	b.	PROPN
ejpam-5986	553	13	natuil	natuil	PROPN
ejpam-5986	553	14	.	.	PUNCT
ejpam-5986	554	1	on	on	ADP
ejpam-5986	554	2	degenerate	degenerate	ADJ
ejpam-5986	554	3	laplace	laplace	NOUN
ejpam-5986	554	4	-	-	PUNCT
ejpam-5986	554	5	type	type	NOUN
ejpam-5986	554	6	integral	integral	ADJ
ejpam-5986	554	7	transform	transform	NOUN
ejpam-5986	554	8	.	.	PUNCT
ejpam-5986	555	1	european	european	ADJ
ejpam-5986	555	2	journal	journal	PROPN
ejpam-5986	555	3	of	of	ADP
ejpam-5986	555	4	pure	pure	ADJ
ejpam-5986	555	5	and	and	CCONJ
ejpam-5986	555	6	applied	applied	ADJ
ejpam-5986	555	7	mathematics	mathematic	NOUN
ejpam-5986	555	8	,	,	PUNCT
ejpam-5986	555	9	16(4):2213–2233	16(4):2213–2233	NUM
ejpam-5986	555	10	,	,	PUNCT
ejpam-5986	555	11	2023	2023	NUM
ejpam-5986	555	12	.	.	PUNCT
ejpam-5986	556	1	[	[	X
ejpam-5986	556	2	4	4	NUM
ejpam-5986	556	3	]	]	PUNCT
ejpam-5986	556	4	a.	a.	PROPN
ejpam-5986	556	5	d.	d.	PROPN
ejpam-5986	556	6	chindhe	chindhe	PROPN
ejpam-5986	556	7	and	and	CCONJ
ejpam-5986	556	8	s.	s.	PROPN
ejpam-5986	556	9	kiwne	kiwne	PROPN
ejpam-5986	556	10	.	.	PUNCT
ejpam-5986	557	1	natural	natural	ADJ
ejpam-5986	557	2	transform	transform	NOUN
ejpam-5986	557	3	and	and	CCONJ
ejpam-5986	557	4	special	special	ADJ
ejpam-5986	557	5	functions	function	NOUN
ejpam-5986	557	6	.	.	PUNCT
ejpam-5986	558	1	journal	journal	NOUN
ejpam-5986	558	2	of	of	ADP
ejpam-5986	558	3	new	new	ADJ
ejpam-5986	558	4	theory	theory	NOUN
ejpam-5986	558	5	,	,	PUNCT
ejpam-5986	558	6	15:39–47	15:39–47	PROPN
ejpam-5986	558	7	,	,	PUNCT
ejpam-5986	558	8	2017	2017	NUM
ejpam-5986	558	9	.	.	PUNCT
ejpam-5986	559	1	[	[	X
ejpam-5986	559	2	5	5	X
ejpam-5986	559	3	]	]	PUNCT
ejpam-5986	559	4	u.	u.	PROPN
ejpam-5986	559	5	duran1	duran1	PROPN
ejpam-5986	559	6	.	.	PUNCT
ejpam-5986	560	1	modified	modify	VERB
ejpam-5986	560	2	sumudu	sumudu	NOUN
ejpam-5986	560	3	transform	transform	NOUN
ejpam-5986	560	4	and	and	CCONJ
ejpam-5986	560	5	its	its	PRON
ejpam-5986	560	6	properties	property	NOUN
ejpam-5986	560	7	.	.	PUNCT
ejpam-5986	561	1	sakarya	sakarya	PROPN
ejpam-5986	561	2	university	university	PROPN
ejpam-5986	561	3	journal	journal	NOUN
ejpam-5986	561	4	of	of	ADP
ejpam-5986	561	5	science	science	NOUN
ejpam-5986	561	6	,	,	PUNCT
ejpam-5986	561	7	25(2):389–396	25(2):389–396	PROPN
ejpam-5986	561	8	,	,	PUNCT
ejpam-5986	561	9	2021	2021	NUM
ejpam-5986	561	10	.	.	PUNCT
ejpam-5986	562	1	[	[	X
ejpam-5986	562	2	6	6	NUM
ejpam-5986	562	3	]	]	PUNCT
ejpam-5986	562	4	s.	s.	PROPN
ejpam-5986	562	5	q.	q.	PROPN
ejpam-5986	562	6	hasan	hasan	PROPN
ejpam-5986	562	7	,	,	PUNCT
ejpam-5986	562	8	u.	u.	PROPN
ejpam-5986	562	9	m.	m.	PROPN
ejpam-5986	562	10	abubakar	abubakar	PROPN
ejpam-5986	562	11	,	,	PUNCT
ejpam-5986	562	12	and	and	CCONJ
ejpam-5986	562	13	m.	m.	PROPN
ejpam-5986	562	14	l.	l.	PROPN
ejpam-5986	562	15	kaurangini	kaurangini	PROPN
ejpam-5986	562	16	.	.	PUNCT
ejpam-5986	563	1	the	the	DET
ejpam-5986	563	2	new	new	ADJ
ejpam-5986	563	3	integral	integral	ADJ
ejpam-5986	563	4	transform	transform	NOUN
ejpam-5986	563	5	”	"	PUNCT
ejpam-5986	563	6	sum	sum	NOUN
ejpam-5986	563	7	transform	transform	NOUN
ejpam-5986	563	8	”	"	PUNCT
ejpam-5986	563	9	and	and	CCONJ
ejpam-5986	563	10	its	its	PRON
ejpam-5986	563	11	properties	property	NOUN
ejpam-5986	563	12	.	.	PUNCT
ejpam-5986	564	1	palastine	palastine	PROPN
ejpam-5986	564	2	journal	journal	PROPN
ejpam-5986	564	3	of	of	ADP
ejpam-5986	564	4	mathematics	mathematic	NOUN
ejpam-5986	564	5	,	,	PUNCT
ejpam-5986	564	6	12(special	12(special	NUM
ejpam-5986	564	7	issue	issue	NOUN
ejpam-5986	564	8	i):30–45	i):30–45	NOUN
ejpam-5986	564	9	,	,	PUNCT
ejpam-5986	564	10	2023	2023	NUM
ejpam-5986	564	11	.	.	PUNCT
ejpam-5986	565	1	[	[	X
ejpam-5986	565	2	7	7	X
ejpam-5986	565	3	]	]	X
ejpam-5986	565	4	h.	h.	PROPN
ejpam-5986	565	5	jafari	jafari	PROPN
ejpam-5986	565	6	.	.	PUNCT
ejpam-5986	566	1	a	a	DET
ejpam-5986	566	2	new	new	ADJ
ejpam-5986	566	3	general	general	ADJ
ejpam-5986	566	4	integral	integral	ADJ
ejpam-5986	566	5	transform	transform	NOUN
ejpam-5986	566	6	for	for	ADP
ejpam-5986	566	7	solving	solve	VERB
ejpam-5986	566	8	integral	integral	ADJ
ejpam-5986	566	9	equations	equation	NOUN
ejpam-5986	566	10	.	.	PUNCT
ejpam-5986	567	1	journal	journal	NOUN
ejpam-5986	567	2	of	of	ADP
ejpam-5986	567	3	advanced	advanced	ADJ
ejpam-5986	567	4	research	research	NOUN
ejpam-5986	567	5	,	,	PUNCT
ejpam-5986	567	6	32:133–138	32:133–138	PROPN
ejpam-5986	567	7	,	,	PUNCT
ejpam-5986	567	8	2021	2021	NUM
ejpam-5986	567	9	.	.	PUNCT
ejpam-5986	568	1	[	[	X
ejpam-5986	568	2	8	8	NUM
ejpam-5986	568	3	]	]	PUNCT
ejpam-5986	568	4	t.	t.	PROPN
ejpam-5986	568	5	kim	kim	PROPN
ejpam-5986	568	6	and	and	CCONJ
ejpam-5986	568	7	d.	d.	PROPN
ejpam-5986	568	8	s.	s.	PROPN
ejpam-5986	568	9	kim	kim	PROPN
ejpam-5986	568	10	.	.	PUNCT
ejpam-5986	569	1	note	note	NOUN
ejpam-5986	569	2	on	on	ADP
ejpam-5986	569	3	the	the	DET
ejpam-5986	569	4	degenerate	degenerate	ADJ
ejpam-5986	569	5	gamma	gamma	NOUN
ejpam-5986	569	6	function	function	NOUN
ejpam-5986	569	7	.	.	PUNCT
ejpam-5986	570	1	russian	russian	ADJ
ejpam-5986	570	2	journal	journal	PROPN
ejpam-5986	570	3	of	of	ADP
ejpam-5986	570	4	mathematical	mathematical	ADJ
ejpam-5986	570	5	physics	physics	NOUN
ejpam-5986	570	6	,	,	PUNCT
ejpam-5986	570	7	27:352–358	27:352–358	PROPN
ejpam-5986	570	8	,	,	PUNCT
ejpam-5986	570	9	2020	2020	NUM
ejpam-5986	570	10	.	.	PUNCT
ejpam-5986	571	1	[	[	X
ejpam-5986	571	2	9	9	NUM
ejpam-5986	571	3	]	]	PUNCT
ejpam-5986	571	4	a.	a.	NOUN
ejpam-5986	571	5	kumar	kumar	PROPN
ejpam-5986	571	6	,	,	PUNCT
ejpam-5986	571	7	b.	b.	PROPN
ejpam-5986	571	8	shikha	shikha	PROPN
ejpam-5986	571	9	,	,	PUNCT
ejpam-5986	571	10	and	and	CCONJ
ejpam-5986	571	11	s.	s.	PROPN
ejpam-5986	571	12	aggarwal	aggarwal	PROPN
ejpam-5986	571	13	.	.	PUNCT
ejpam-5986	572	1	a	a	DET
ejpam-5986	572	2	new	new	ADJ
ejpam-5986	572	3	novel	novel	ADJ
ejpam-5986	572	4	integral	integral	ADJ
ejpam-5986	572	5	transform	transform	NOUN
ejpam-5986	572	6	”	"	PUNCT
ejpam-5986	572	7	anuj	anuj	PROPN
ejpam-5986	572	8	transform	transform	NOUN
ejpam-5986	572	9	”	"	PUNCT
ejpam-5986	572	10	with	with	ADP
ejpam-5986	572	11	application	application	NOUN
ejpam-5986	572	12	.	.	PUNCT
ejpam-5986	573	1	design	design	NOUN
ejpam-5986	573	2	engineering	engineering	NOUN
ejpam-5986	573	3	,	,	PUNCT
ejpam-5986	573	4	9:12741–12751	9:12741–12751	NUM
ejpam-5986	573	5	,	,	PUNCT
ejpam-5986	573	6	2021	2021	NUM
ejpam-5986	573	7	.	.	PUNCT
ejpam-5986	574	1	[	[	X
ejpam-5986	574	2	10	10	NUM
ejpam-5986	574	3	]	]	X
ejpam-5986	574	4	p.	p.	NOUN
ejpam-5986	574	5	s.	s.	PROPN
ejpam-5986	574	6	laplace	laplace	PROPN
ejpam-5986	574	7	.	.	PUNCT
ejpam-5986	575	1	théorie	théorie	ADJ
ejpam-5986	575	2	analytique	analytique	ADJ
ejpam-5986	575	3	des	des	PROPN
ejpam-5986	575	4	probabilités	probabilités	PROPN
ejpam-5986	575	5	.	.	PUNCT
ejpam-5986	576	1	courcier	courcier	PROPN
ejpam-5986	576	2	,	,	PUNCT
ejpam-5986	576	3	1820	1820	NUM
ejpam-5986	576	4	.	.	PUNCT
ejpam-5986	577	1	i̇.	i̇.	PROPN
ejpam-5986	577	2	ege	ege	PROPN
ejpam-5986	577	3	/	/	SYM
ejpam-5986	577	4	eur	eur	PROPN
ejpam-5986	577	5	.	.	PUNCT
ejpam-5986	578	1	j.	j.	PROPN
ejpam-5986	578	2	pure	pure	PROPN
ejpam-5986	578	3	appl	appl	PROPN
ejpam-5986	578	4	.	.	PROPN
ejpam-5986	578	5	math	math	PROPN
ejpam-5986	578	6	,	,	PUNCT
ejpam-5986	578	7	18	18	NUM
ejpam-5986	578	8	(	(	PUNCT
ejpam-5986	578	9	2	2	NUM
ejpam-5986	578	10	)	)	PUNCT
ejpam-5986	578	11	(	(	PUNCT
ejpam-5986	578	12	2025	2025	NUM
ejpam-5986	578	13	)	)	PUNCT
ejpam-5986	578	14	,	,	PUNCT
ejpam-5986	578	15	5986	5986	NUM
ejpam-5986	578	16	19	19	NUM
ejpam-5986	578	17	of	of	ADP
ejpam-5986	578	18	20	20	NUM
ejpam-5986	578	19	[	[	SYM
ejpam-5986	578	20	11	11	NUM
ejpam-5986	578	21	]	]	PUNCT
ejpam-5986	578	22	k.	k.	PROPN
ejpam-5986	578	23	nantomah	nantomah	PROPN
ejpam-5986	578	24	.	.	PUNCT
ejpam-5986	579	1	certain	certain	ADJ
ejpam-5986	579	2	properties	property	NOUN
ejpam-5986	579	3	of	of	ADP
ejpam-5986	579	4	the	the	DET
ejpam-5986	579	5	modified	modify	VERB
ejpam-5986	579	6	degenerate	degenerate	ADJ
ejpam-5986	579	7	gamma	gamma	NOUN
ejpam-5986	579	8	function	function	NOUN
ejpam-5986	579	9	.	.	PUNCT
ejpam-5986	580	1	journal	journal	NOUN
ejpam-5986	580	2	of	of	ADP
ejpam-5986	580	3	mathematics	mathematic	NOUN
ejpam-5986	580	4	,	,	PUNCT
ejpam-5986	580	5	pages	page	NOUN
ejpam-5986	580	6	1–6	1–6	NUM
ejpam-5986	580	7	,	,	PUNCT
ejpam-5986	580	8	2021	2021	NUM
ejpam-5986	580	9	.	.	PUNCT
ejpam-5986	581	1	[	[	X
ejpam-5986	581	2	12	12	NUM
ejpam-5986	581	3	]	]	X
ejpam-5986	581	4	d.	d.	PROPN
ejpam-5986	581	5	patil	patil	PROPN
ejpam-5986	581	6	and	and	CCONJ
ejpam-5986	581	7	s.	s.	PROPN
ejpam-5986	581	8	khakale	khakale	PROPN
ejpam-5986	581	9	.	.	PUNCT
ejpam-5986	582	1	the	the	DET
ejpam-5986	582	2	new	new	ADJ
ejpam-5986	582	3	integral	integral	ADJ
ejpam-5986	582	4	transform	transform	NOUN
ejpam-5986	582	5	”	"	PUNCT
ejpam-5986	582	6	soham	soham	PROPN
ejpam-5986	582	7	transform	transform	NOUN
ejpam-5986	582	8	”	"	PUNCT
ejpam-5986	582	9	.	.	PUNCT
ejpam-5986	583	1	journal	journal	PROPN
ejpam-5986	583	2	of	of	ADP
ejpam-5986	583	3	mathematics	mathematic	NOUN
ejpam-5986	583	4	,	,	PUNCT
ejpam-5986	583	5	3(10):126–132	3(10):126–132	NUM
ejpam-5986	583	6	,	,	PUNCT
ejpam-5986	583	7	2021	2021	NUM
ejpam-5986	583	8	.	.	PUNCT
ejpam-5986	584	1	[	[	X
ejpam-5986	584	2	13	13	NUM
ejpam-5986	584	3	]	]	PUNCT
ejpam-5986	584	4	d.	d.	PROPN
ejpam-5986	584	5	p.	p.	PROPN
ejpam-5986	584	6	patil	patil	PROPN
ejpam-5986	584	7	,	,	PUNCT
ejpam-5986	584	8	d.	d.	PROPN
ejpam-5986	584	9	s.	s.	PROPN
ejpam-5986	584	10	patil	patil	PROPN
ejpam-5986	584	11	,	,	PUNCT
ejpam-5986	584	12	and	and	CCONJ
ejpam-5986	584	13	s.	s.	PROPN
ejpam-5986	584	14	m.	m.	PROPN
ejpam-5986	584	15	kanchan	kanchan	PROPN
ejpam-5986	584	16	.	.	PUNCT
ejpam-5986	585	1	new	new	ADJ
ejpam-5986	585	2	integral	integral	ADJ
ejpam-5986	585	3	transform	transform	NOUN
ejpam-5986	585	4	,	,	PUNCT
ejpam-5986	585	5	”	"	PUNCT
ejpam-5986	585	6	double	double	ADJ
ejpam-5986	585	7	kushare	kushare	NOUN
ejpam-5986	585	8	transform	transform	NOUN
ejpam-5986	585	9	”	"	PUNCT
ejpam-5986	585	10	.	.	PUNCT
ejpam-5986	586	1	ire	ire	ADJ
ejpam-5986	586	2	journals	journal	NOUN
ejpam-5986	586	3	,	,	PUNCT
ejpam-5986	586	4	6(1):45–52	6(1):45–52	NUM
ejpam-5986	586	5	,	,	PUNCT
ejpam-5986	586	6	2022	2022	NUM
ejpam-5986	586	7	.	.	PUNCT
ejpam-5986	587	1	[	[	X
ejpam-5986	587	2	14	14	NUM
ejpam-5986	587	3	]	]	PUNCT
ejpam-5986	587	4	m.	m.	NOUN
ejpam-5986	587	5	saif	saif	PROPN
ejpam-5986	587	6	,	,	PUNCT
ejpam-5986	587	7	f.	f.	PROPN
ejpam-5986	587	8	khan	khan	PROPN
ejpam-5986	587	9	,	,	PUNCT
ejpam-5986	587	10	k.	k.	PROPN
ejpam-5986	587	11	s.	s.	PROPN
ejpam-5986	587	12	nisar	nisar	PROPN
ejpam-5986	587	13	,	,	PUNCT
ejpam-5986	587	14	and	and	CCONJ
ejpam-5986	587	15	s.	s.	PROPN
ejpam-5986	587	16	araci	araci	PROPN
ejpam-5986	587	17	.	.	PUNCT
ejpam-5986	588	1	modified	modify	VERB
ejpam-5986	588	2	laplace	laplace	NOUN
ejpam-5986	588	3	transform	transform	NOUN
ejpam-5986	588	4	and	and	CCONJ
ejpam-5986	588	5	its	its	PRON
ejpam-5986	588	6	properties	property	NOUN
ejpam-5986	588	7	.	.	PUNCT
ejpam-5986	589	1	j.	j.	PROPN
ejpam-5986	589	2	math	math	PROPN
ejpam-5986	589	3	.	.	PUNCT
ejpam-5986	590	1	computer	computer	NOUN
ejpam-5986	590	2	sci	sci	PROPN
ejpam-5986	590	3	.	.	PROPN
ejpam-5986	590	4	,	,	PUNCT
ejpam-5986	590	5	21:127–135	21:127–135	PROPN
ejpam-5986	590	6	,	,	PUNCT
ejpam-5986	590	7	2020	2020	NUM
ejpam-5986	590	8	.	.	PUNCT
ejpam-5986	591	1	[	[	X
ejpam-5986	591	2	15	15	NUM
ejpam-5986	591	3	]	]	X
ejpam-5986	591	4	s.	s.	PROPN
ejpam-5986	591	5	sattaso	sattaso	PROPN
ejpam-5986	591	6	,	,	PUNCT
ejpam-5986	591	7	k.	k.	PROPN
ejpam-5986	591	8	nonlaopon	nonlaopon	NOUN
ejpam-5986	591	9	,	,	PUNCT
ejpam-5986	591	10	and	and	CCONJ
ejpam-5986	591	11	h.	h.	PROPN
ejpam-5986	591	12	kim	kim	PROPN
ejpam-5986	591	13	.	.	PUNCT
ejpam-5986	592	1	further	further	ADJ
ejpam-5986	592	2	properties	property	NOUN
ejpam-5986	592	3	of	of	ADP
ejpam-5986	592	4	laplace	laplace	NOUN
ejpam-5986	592	5	-	-	PUNCT
ejpam-5986	592	6	typed	type	VERB
ejpam-5986	592	7	integral	integral	ADJ
ejpam-5986	592	8	transforms	transform	NOUN
ejpam-5986	592	9	.	.	PUNCT
ejpam-5986	593	1	dyn	dyn	NOUN
ejpam-5986	593	2	.	.	PUNCT
ejpam-5986	594	1	syst	syst	PROPN
ejpam-5986	594	2	.	.	PUNCT
ejpam-5986	595	1	appl	appl	PROPN
ejpam-5986	595	2	.	.	PROPN
ejpam-5986	595	3	,	,	PUNCT
ejpam-5986	596	1	28:195–215	28:195–215	NUM
ejpam-5986	596	2	,	,	PUNCT
ejpam-5986	596	3	2019	2019	NUM
ejpam-5986	596	4	.	.	PUNCT
ejpam-5986	597	1	[	[	X
ejpam-5986	597	2	16	16	NUM
ejpam-5986	597	3	]	]	X
ejpam-5986	597	4	j.	j.	PROPN
ejpam-5986	597	5	l.	l.	PROPN
ejpam-5986	597	6	schiff	schiff	PROPN
ejpam-5986	597	7	.	.	PUNCT
ejpam-5986	598	1	the	the	DET
ejpam-5986	598	2	laplace	laplace	NOUN
ejpam-5986	598	3	transform	transform	NOUN
ejpam-5986	598	4	:	:	PUNCT
ejpam-5986	598	5	theory	theory	NOUN
ejpam-5986	598	6	and	and	CCONJ
ejpam-5986	598	7	applications	application	NOUN
ejpam-5986	598	8	.	.	PUNCT
ejpam-5986	599	1	springer	springer	NOUN
ejpam-5986	599	2	-	-	PUNCT
ejpam-5986	599	3	verlag	verlag	PROPN
ejpam-5986	599	4	,	,	PUNCT
ejpam-5986	599	5	new	new	PROPN
ejpam-5986	599	6	york	york	PROPN
ejpam-5986	599	7	,	,	PUNCT
ejpam-5986	599	8	1999	1999	NUM
ejpam-5986	599	9	.	.	PUNCT
ejpam-5986	600	1	[	[	X
ejpam-5986	600	2	17	17	NUM
ejpam-5986	600	3	]	]	X
ejpam-5986	600	4	l.	l.	PROPN
ejpam-5986	600	5	m.	m.	PROPN
ejpam-5986	600	6	upadhyaya	upadhyaya	PROPN
ejpam-5986	600	7	.	.	PUNCT
ejpam-5986	601	1	introducing	introduce	VERB
ejpam-5986	601	2	the	the	DET
ejpam-5986	601	3	upadhyaya	upadhyaya	NOUN
ejpam-5986	601	4	integral	integral	ADJ
ejpam-5986	601	5	transform	transform	NOUN
ejpam-5986	601	6	.	.	PUNCT
ejpam-5986	602	1	bull	bull	NOUN
ejpam-5986	602	2	.	.	PUNCT
ejpam-5986	603	1	pure	pure	ADJ
ejpam-5986	603	2	appl	appl	PROPN
ejpam-5986	603	3	.	.	PUNCT
ejpam-5986	604	1	sci	sci	PROPN
ejpam-5986	604	2	.	.	PROPN
ejpam-5986	604	3	,	,	PUNCT
ejpam-5986	604	4	38e(1):471–510	38e(1):471–510	NUM
ejpam-5986	604	5	,	,	PUNCT
ejpam-5986	604	6	2019	2019	NUM
ejpam-5986	604	7	.	.	PUNCT
ejpam-5986	605	1	[	[	X
ejpam-5986	605	2	18	18	NUM
ejpam-5986	605	3	]	]	X
ejpam-5986	605	4	l.	l.	PROPN
ejpam-5986	605	5	m.	m.	PROPN
ejpam-5986	605	6	upadhyaya	upadhyaya	PROPN
ejpam-5986	605	7	,	,	PUNCT
ejpam-5986	605	8	a.	a.	NOUN
ejpam-5986	605	9	shehata	shehata	PROPN
ejpam-5986	605	10	,	,	PUNCT
ejpam-5986	605	11	and	and	CCONJ
ejpam-5986	605	12	a.	a.	PROPN
ejpam-5986	605	13	kamal	kamal	PROPN
ejpam-5986	605	14	.	.	PUNCT
ejpam-5986	606	1	an	an	DET
ejpam-5986	606	2	update	update	NOUN
ejpam-5986	606	3	on	on	ADP
ejpam-5986	606	4	the	the	DET
ejpam-5986	606	5	upadhyaya	upadhyaya	NOUN
ejpam-5986	606	6	transform	transform	NOUN
ejpam-5986	606	7	.	.	PUNCT
ejpam-5986	607	1	bull	bull	NOUN
ejpam-5986	607	2	.	.	PUNCT
ejpam-5986	608	1	pure	pure	ADJ
ejpam-5986	608	2	appl	appl	PROPN
ejpam-5986	608	3	.	.	PUNCT
ejpam-5986	609	1	sci	sci	PROPN
ejpam-5986	609	2	.	.	PUNCT
ejpam-5986	609	3	sect	sect	NOUN
ejpam-5986	609	4	.	.	PUNCT
ejpam-5986	610	1	e	e	X
ejpam-5986	610	2	math	math	NOUN
ejpam-5986	610	3	.	.	PUNCT
ejpam-5986	611	1	stat	stat	PROPN
ejpam-5986	611	2	.	.	PUNCT
ejpam-5986	611	3	,	,	PUNCT
ejpam-5986	611	4	40e(1):26–44	40e(1):26–44	NUM
ejpam-5986	611	5	,	,	PUNCT
ejpam-5986	611	6	2021	2021	NUM
ejpam-5986	611	7	.	.	PUNCT
ejpam-5986	612	1	[	[	X
ejpam-5986	612	2	19	19	NUM
ejpam-5986	612	3	]	]	X
ejpam-5986	612	4	e.	e.	PROPN
ejpam-5986	612	5	m.	m.	PROPN
ejpam-5986	612	6	xhaferraj	xhaferraj	PROPN
ejpam-5986	612	7	.	.	PUNCT
ejpam-5986	613	1	the	the	DET
ejpam-5986	613	2	new	new	ADJ
ejpam-5986	613	3	integral	integral	ADJ
ejpam-5986	613	4	transform	transform	NOUN
ejpam-5986	613	5	:	:	PUNCT
ejpam-5986	613	6	”	"	PUNCT
ejpam-5986	613	7	ne	ne	X
ejpam-5986	613	8	transform	transform	NOUN
ejpam-5986	613	9	”	"	PUNCT
ejpam-5986	613	10	and	and	CCONJ
ejpam-5986	613	11	its	its	PRON
ejpam-5986	613	12	applications	application	NOUN
ejpam-5986	613	13	.	.	PUNCT
ejpam-5986	614	1	european	european	ADJ
ejpam-5986	614	2	journal	journal	PROPN
ejpam-5986	614	3	of	of	ADP
ejpam-5986	614	4	formal	formal	ADJ
ejpam-5986	614	5	sciences	science	NOUN
ejpam-5986	614	6	and	and	CCONJ
ejpam-5986	614	7	engineering	engineering	NOUN
ejpam-5986	614	8	,	,	PUNCT
ejpam-5986	614	9	6(1):22–34	6(1):22–34	NUM
ejpam-5986	614	10	,	,	PUNCT
ejpam-5986	614	11	2023	2023	NUM
ejpam-5986	614	12	.	.	PUNCT
ejpam-5986	615	1	[	[	X
ejpam-5986	615	2	20	20	NUM
ejpam-5986	615	3	]	]	X
ejpam-5986	615	4	o.	o.	NOUN
ejpam-5986	615	5	yağcı	yağcı	PROPN
ejpam-5986	615	6	and	and	CCONJ
ejpam-5986	615	7	r.	r.	PROPN
ejpam-5986	615	8	şahin	şahin	PROPN
ejpam-5986	615	9	.	.	PROPN
ejpam-5986	615	10	degenerate	degenerate	ADJ
ejpam-5986	615	11	pochhammer	pochhammer	NOUN
ejpam-5986	615	12	symbol	symbol	NOUN
ejpam-5986	615	13	,	,	PUNCT
ejpam-5986	615	14	degenerate	degenerate	ADJ
ejpam-5986	615	15	sumudu	sumudu	NOUN
ejpam-5986	615	16	transform	transform	NOUN
ejpam-5986	615	17	and	and	CCONJ
ejpam-5986	615	18	degenerate	degenerate	ADJ
ejpam-5986	615	19	hypergeometric	hypergeometric	ADJ
ejpam-5986	615	20	function	function	NOUN
ejpam-5986	615	21	with	with	ADP
ejpam-5986	615	22	applications	application	NOUN
ejpam-5986	615	23	.	.	PUNCT
ejpam-5986	616	1	hacettepe	hacettepe	PROPN
ejpam-5986	616	2	journal	journal	PROPN
ejpam-5986	616	3	of	of	ADP
ejpam-5986	616	4	mathematics	mathematic	NOUN
ejpam-5986	616	5	and	and	CCONJ
ejpam-5986	616	6	statistics	statistic	NOUN
ejpam-5986	616	7	,	,	PUNCT
ejpam-5986	616	8	50(5):1448–1465	50(5):1448–1465	NUM
ejpam-5986	616	9	,	,	PUNCT
ejpam-5986	616	10	2021	2021	NUM
ejpam-5986	616	11	.	.	PUNCT
ejpam-5986	617	1	[	[	X
ejpam-5986	617	2	21	21	NUM
ejpam-5986	617	3	]	]	X
ejpam-5986	617	4	g.	g.	PROPN
ejpam-5986	617	5	k.	k.	PROPN
ejpam-5986	617	6	watugala	watugala	PROPN
ejpam-5986	617	7	.	.	PUNCT
ejpam-5986	618	1	sumudu	sumudu	NOUN
ejpam-5986	618	2	transform	transform	NOUN
ejpam-5986	618	3	:	:	PUNCT
ejpam-5986	618	4	a	a	DET
ejpam-5986	618	5	new	new	ADJ
ejpam-5986	618	6	integral	integral	ADJ
ejpam-5986	618	7	transform	transform	NOUN
ejpam-5986	618	8	to	to	PART
ejpam-5986	618	9	solve	solve	VERB
ejpam-5986	618	10	differential	differential	ADJ
ejpam-5986	618	11	equations	equation	NOUN
ejpam-5986	618	12	and	and	CCONJ
ejpam-5986	618	13	control	control	NOUN
ejpam-5986	618	14	engineering	engineering	NOUN
ejpam-5986	618	15	problems	problem	NOUN
ejpam-5986	618	16	.	.	PUNCT
ejpam-5986	619	1	integrated	integrated	ADJ
ejpam-5986	619	2	education	education	NOUN
ejpam-5986	619	3	,	,	PUNCT
ejpam-5986	619	4	24(1):35–43	24(1):35–43	NUM
ejpam-5986	619	5	,	,	PUNCT
ejpam-5986	619	6	1993	1993	NUM
ejpam-5986	619	7	.	.	PUNCT
ejpam-5986	620	1	[	[	X
ejpam-5986	620	2	22	22	NUM
ejpam-5986	620	3	]	]	PUNCT
ejpam-5986	620	4	z.	z.	PROPN
ejpam-5986	620	5	h.	h.	PROPN
ejpam-5986	620	6	khan	khan	PROPN
ejpam-5986	620	7	and	and	CCONJ
ejpam-5986	620	8	w.	w.	PROPN
ejpam-5986	620	9	a.	a.	PROPN
ejpam-5986	620	10	khan	khan	PROPN
ejpam-5986	620	11	.	.	PUNCT
ejpam-5986	621	1	n	n	CCONJ
ejpam-5986	621	2	-	-	PUNCT
ejpam-5986	621	3	transform	transform	NOUN
ejpam-5986	621	4	-	-	PUNCT
ejpam-5986	621	5	properties	property	NOUN
ejpam-5986	621	6	and	and	CCONJ
ejpam-5986	621	7	applications	application	NOUN
ejpam-5986	621	8	.	.	PUNCT
ejpam-5986	622	1	nust	nust	PROPN
ejpam-5986	622	2	journal	journal	PROPN
ejpam-5986	622	3	of	of	ADP
ejpam-5986	622	4	engineering	engineering	NOUN
ejpam-5986	622	5	sciences	science	NOUN
ejpam-5986	622	6	,	,	PUNCT
ejpam-5986	622	7	1(1):127–133	1(1):127–133	NUM
ejpam-5986	622	8	,	,	PUNCT
ejpam-5986	622	9	2008	2008	NUM
ejpam-5986	622	10	.	.	PUNCT
ejpam-5986	623	1	[	[	X
ejpam-5986	623	2	23	23	NUM
ejpam-5986	623	3	]	]	PUNCT
ejpam-5986	623	4	t.	t.	PROPN
ejpam-5986	623	5	m.	m.	PROPN
ejpam-5986	623	6	elzaki	elzaki	PROPN
ejpam-5986	623	7	,	,	PUNCT
ejpam-5986	623	8	s.	s.	PROPN
ejpam-5986	623	9	m.	m.	PROPN
ejpam-5986	623	10	elzaki	elzaki	PROPN
ejpam-5986	623	11	,	,	PUNCT
ejpam-5986	623	12	and	and	CCONJ
ejpam-5986	623	13	e.	e.	PROPN
ejpam-5986	623	14	a.	a.	PROPN
ejpam-5986	623	15	elnour	elnour	PROPN
ejpam-5986	623	16	.	.	PUNCT
ejpam-5986	624	1	on	on	ADP
ejpam-5986	624	2	some	some	DET
ejpam-5986	624	3	applications	application	NOUN
ejpam-5986	624	4	of	of	ADP
ejpam-5986	624	5	new	new	ADJ
ejpam-5986	624	6	integral	integral	ADJ
ejpam-5986	624	7	transform	transform	NOUN
ejpam-5986	624	8	”	"	PUNCT
ejpam-5986	624	9	elzaki	elzaki	NOUN
ejpam-5986	624	10	transform	transform	NOUN
ejpam-5986	624	11	”	"	PUNCT
ejpam-5986	624	12	.	.	PUNCT
ejpam-5986	625	1	global	global	ADJ
ejpam-5986	625	2	journal	journal	PROPN
ejpam-5986	625	3	of	of	ADP
ejpam-5986	625	4	mathematical	mathematical	ADJ
ejpam-5986	625	5	sciences	science	NOUN
ejpam-5986	625	6	:	:	PUNCT
ejpam-5986	625	7	theory	theory	NOUN
ejpam-5986	625	8	and	and	CCONJ
ejpam-5986	625	9	practical	practical	ADJ
ejpam-5986	625	10	,	,	PUNCT
ejpam-5986	625	11	4(1):15–23	4(1):15–23	NUM
ejpam-5986	625	12	,	,	PUNCT
ejpam-5986	625	13	2012	2012	NUM
ejpam-5986	625	14	.	.	PUNCT
ejpam-5986	626	1	[	[	X
ejpam-5986	626	2	24	24	NUM
ejpam-5986	626	3	]	]	PUNCT
ejpam-5986	626	4	k.	k.	PROPN
ejpam-5986	626	5	s.	s.	PROPN
ejpam-5986	626	6	aboodh	aboodh	PROPN
ejpam-5986	626	7	.	.	PUNCT
ejpam-5986	627	1	the	the	DET
ejpam-5986	627	2	new	new	ADJ
ejpam-5986	627	3	integral	integral	ADJ
ejpam-5986	627	4	transform	transform	NOUN
ejpam-5986	627	5	”	"	PUNCT
ejpam-5986	627	6	aboodh	aboodh	NOUN
ejpam-5986	627	7	transform	transform	NOUN
ejpam-5986	627	8	”	"	PUNCT
ejpam-5986	627	9	.	.	PUNCT
ejpam-5986	628	1	global	global	ADJ
ejpam-5986	628	2	journal	journal	PROPN
ejpam-5986	628	3	of	of	ADP
ejpam-5986	628	4	pure	pure	ADJ
ejpam-5986	628	5	and	and	CCONJ
ejpam-5986	628	6	applied	applied	ADJ
ejpam-5986	628	7	mathematics	mathematic	NOUN
ejpam-5986	628	8	,	,	PUNCT
ejpam-5986	628	9	9(1):35–43	9(1):35–43	NUM
ejpam-5986	628	10	,	,	PUNCT
ejpam-5986	628	11	2013	2013	NUM
ejpam-5986	628	12	.	.	PUNCT
ejpam-5986	629	1	[	[	X
ejpam-5986	629	2	25	25	NUM
ejpam-5986	629	3	]	]	PUNCT
ejpam-5986	629	4	z.	z.	PROPN
ejpam-5986	629	5	u.	u.	PROPN
ejpam-5986	629	6	zafar	zafar	PROPN
ejpam-5986	629	7	.	.	PUNCT
ejpam-5986	630	1	zz	zz	PROPN
ejpam-5986	630	2	transform	transform	VERB
ejpam-5986	630	3	method	method	NOUN
ejpam-5986	630	4	.	.	PUNCT
ejpam-5986	631	1	int	int	NOUN
ejpam-5986	631	2	.	.	PUNCT
ejpam-5986	632	1	j.	j.	PROPN
ejpam-5986	632	2	adv	adv	PROPN
ejpam-5986	632	3	.	.	PUNCT
ejpam-5986	633	1	eng	eng	PROPN
ejpam-5986	633	2	.	.	PUNCT
ejpam-5986	633	3	glob	glob	PROPN
ejpam-5986	633	4	.	.	PUNCT
ejpam-5986	634	1	technol	technol	PROPN
ejpam-5986	634	2	,	,	PUNCT
ejpam-5986	634	3	4(1):1605–1611	4(1):1605–1611	PROPN
ejpam-5986	634	4	,	,	PUNCT
ejpam-5986	634	5	2016	2016	NUM
ejpam-5986	634	6	.	.	PUNCT
ejpam-5986	635	1	[	[	X
ejpam-5986	635	2	26	26	NUM
ejpam-5986	635	3	]	]	X
ejpam-5986	635	4	b.	b.	PROPN
ejpam-5986	635	5	barnes	barnes	PROPN
ejpam-5986	635	6	.	.	PUNCT
ejpam-5986	636	1	polynomial	polynomial	ADJ
ejpam-5986	636	2	integral	integral	ADJ
ejpam-5986	636	3	transform	transform	NOUN
ejpam-5986	636	4	for	for	ADP
ejpam-5986	636	5	solving	solve	VERB
ejpam-5986	636	6	differential	differential	ADJ
ejpam-5986	636	7	equations	equation	NOUN
ejpam-5986	636	8	.	.	PUNCT
ejpam-5986	637	1	european	european	PROPN
ejpam-5986	637	2	journal	journal	PROPN
ejpam-5986	637	3	of	of	ADP
ejpam-5986	637	4	pure	pure	ADJ
ejpam-5986	637	5	and	and	CCONJ
ejpam-5986	637	6	applied	applied	ADJ
ejpam-5986	637	7	mathematics	mathematic	NOUN
ejpam-5986	637	8	,	,	PUNCT
ejpam-5986	637	9	9(2):140–151	9(2):140–151	NUM
ejpam-5986	637	10	,	,	PUNCT
ejpam-5986	637	11	2016	2016	NUM
ejpam-5986	637	12	.	.	PUNCT
ejpam-5986	638	1	[	[	X
ejpam-5986	638	2	27	27	NUM
ejpam-5986	638	3	]	]	X
ejpam-5986	638	4	h.	h.	PROPN
ejpam-5986	638	5	kim	kim	PROPN
ejpam-5986	638	6	.	.	PUNCT
ejpam-5986	639	1	the	the	DET
ejpam-5986	639	2	intrinsic	intrinsic	ADJ
ejpam-5986	639	3	structure	structure	NOUN
ejpam-5986	639	4	and	and	CCONJ
ejpam-5986	639	5	properties	property	NOUN
ejpam-5986	639	6	of	of	ADP
ejpam-5986	639	7	laplace	laplace	NOUN
ejpam-5986	639	8	-	-	PUNCT
ejpam-5986	639	9	typed	type	VERB
ejpam-5986	639	10	integral	integral	ADJ
ejpam-5986	639	11	transforms	transform	NOUN
ejpam-5986	639	12	.	.	PUNCT
ejpam-5986	640	1	mathematical	mathematical	ADJ
ejpam-5986	640	2	problems	problem	NOUN
ejpam-5986	640	3	in	in	ADP
ejpam-5986	640	4	engineering	engineering	NOUN
ejpam-5986	640	5	,	,	PUNCT
ejpam-5986	640	6	2017:1–8	2017:1–8	PROPN
ejpam-5986	640	7	,	,	PUNCT
ejpam-5986	640	8	2017	2017	NUM
ejpam-5986	640	9	.	.	PUNCT
ejpam-5986	641	1	[	[	X
ejpam-5986	641	2	28	28	NUM
ejpam-5986	641	3	]	]	X
ejpam-5986	641	4	y.	y.	PROPN
ejpam-5986	641	5	kim	kim	PROPN
ejpam-5986	641	6	,	,	PUNCT
ejpam-5986	641	7	b.	b.	PROPN
ejpam-5986	641	8	m.	m.	PROPN
ejpam-5986	641	9	kim	kim	PROPN
ejpam-5986	641	10	,	,	PUNCT
ejpam-5986	641	11	l.	l.	PROPN
ejpam-5986	641	12	c.	c.	PROPN
ejpam-5986	641	13	jang	jang	PROPN
ejpam-5986	641	14	,	,	PUNCT
ejpam-5986	641	15	and	and	CCONJ
ejpam-5986	641	16	j.	j.	PROPN
ejpam-5986	641	17	kwon	kwon	PROPN
ejpam-5986	641	18	.	.	PUNCT
ejpam-5986	642	1	a	a	DET
ejpam-5986	642	2	note	note	NOUN
ejpam-5986	642	3	on	on	ADP
ejpam-5986	642	4	modified	modified	ADJ
ejpam-5986	642	5	degenerate	degenerate	ADJ
ejpam-5986	642	6	gamma	gamma	NOUN
ejpam-5986	642	7	and	and	CCONJ
ejpam-5986	642	8	laplace	laplace	PROPN
ejpam-5986	642	9	transformation	transformation	NOUN
ejpam-5986	642	10	.	.	PUNCT
ejpam-5986	643	1	symmetry	symmetry	NOUN
ejpam-5986	643	2	,	,	PUNCT
ejpam-5986	643	3	10(10):471	10(10):471	NUM
ejpam-5986	643	4	,	,	PUNCT
ejpam-5986	643	5	2018	2018	NUM
ejpam-5986	643	6	.	.	PUNCT
ejpam-5986	644	1	[	[	X
ejpam-5986	644	2	29	29	NUM
ejpam-5986	644	3	]	]	PUNCT
ejpam-5986	644	4	t.	t.	PROPN
ejpam-5986	644	5	kim	kim	PROPN
ejpam-5986	644	6	and	and	CCONJ
ejpam-5986	644	7	d.	d.	PROPN
ejpam-5986	644	8	s.	s.	PROPN
ejpam-5986	644	9	kim	kim	PROPN
ejpam-5986	644	10	.	.	PROPN
ejpam-5986	644	11	degenerate	degenerate	ADJ
ejpam-5986	644	12	laplace	laplace	NOUN
ejpam-5986	644	13	transform	transform	NOUN
ejpam-5986	644	14	and	and	CCONJ
ejpam-5986	644	15	degenerate	degenerate	ADJ
ejpam-5986	644	16	gamma	gamma	NOUN
ejpam-5986	644	17	function	function	NOUN
ejpam-5986	644	18	.	.	PUNCT
ejpam-5986	645	1	russian	russian	ADJ
ejpam-5986	645	2	journal	journal	PROPN
ejpam-5986	645	3	of	of	ADP
ejpam-5986	645	4	mathematical	mathematical	ADJ
ejpam-5986	645	5	physics	physics	NOUN
ejpam-5986	645	6	,	,	PUNCT
ejpam-5986	645	7	24:241–248	24:241–248	NUM
ejpam-5986	645	8	,	,	PUNCT
ejpam-5986	645	9	2017	2017	NUM
ejpam-5986	645	10	.	.	PUNCT
ejpam-5986	646	1	[	[	X
ejpam-5986	646	2	30	30	NUM
ejpam-5986	646	3	]	]	X
ejpam-5986	646	4	l.	l.	PROPN
ejpam-5986	646	5	m.	m.	PROPN
ejpam-5986	646	6	upadhyaya	upadhyaya	PROPN
ejpam-5986	646	7	.	.	PUNCT
ejpam-5986	647	1	on	on	ADP
ejpam-5986	647	2	the	the	DET
ejpam-5986	647	3	degenerate	degenerate	ADJ
ejpam-5986	647	4	laplace	laplace	NOUN
ejpam-5986	647	5	transform	transform	NOUN
ejpam-5986	647	6	iii	iii	PROPN
ejpam-5986	647	7	.	.	PUNCT
ejpam-5986	647	8	international	international	ADJ
ejpam-5986	647	9	journal	journal	PROPN
ejpam-5986	647	10	of	of	ADP
ejpam-5986	647	11	engineering	engineering	NOUN
ejpam-5986	647	12	,	,	PUNCT
ejpam-5986	647	13	science	science	NOUN
ejpam-5986	647	14	and	and	CCONJ
ejpam-5986	647	15	mathematics	mathematic	NOUN
ejpam-5986	647	16	,	,	PUNCT
ejpam-5986	647	17	5(12):63–71	5(12):63–71	NUM
ejpam-5986	647	18	,	,	PUNCT
ejpam-5986	647	19	2017	2017	NUM
ejpam-5986	647	20	.	.	PUNCT
ejpam-5986	648	1	[	[	X
ejpam-5986	648	2	31	31	NUM
ejpam-5986	648	3	]	]	PUNCT
ejpam-5986	648	4	l.	l.	PROPN
ejpam-5986	648	5	m.	m.	PROPN
ejpam-5986	648	6	upadhyaya	upadhyaya	PROPN
ejpam-5986	648	7	.	.	PUNCT
ejpam-5986	649	1	on	on	ADP
ejpam-5986	649	2	the	the	DET
ejpam-5986	649	3	degenerate	degenerate	ADJ
ejpam-5986	649	4	laplace	laplace	NOUN
ejpam-5986	649	5	transform	transform	NOUN
ejpam-5986	649	6	i.	i.	NOUN
ejpam-5986	649	7	bulletin	bulletin	NOUN
ejpam-5986	649	8	of	of	ADP
ejpam-5986	649	9	pure	pure	ADJ
ejpam-5986	649	10	and	and	CCONJ
ejpam-5986	649	11	i̇.	i̇.	NOUN
ejpam-5986	649	12	ege	ege	PROPN
ejpam-5986	649	13	/	/	SYM
ejpam-5986	649	14	eur	eur	PROPN
ejpam-5986	649	15	.	.	PUNCT
ejpam-5986	650	1	j.	j.	PROPN
ejpam-5986	650	2	pure	pure	PROPN
ejpam-5986	650	3	appl	appl	PROPN
ejpam-5986	650	4	.	.	PROPN
ejpam-5986	650	5	math	math	PROPN
ejpam-5986	650	6	,	,	PUNCT
ejpam-5986	650	7	18	18	NUM
ejpam-5986	650	8	(	(	PUNCT
ejpam-5986	650	9	2	2	NUM
ejpam-5986	650	10	)	)	PUNCT
ejpam-5986	650	11	(	(	PUNCT
ejpam-5986	650	12	2025	2025	NUM
ejpam-5986	650	13	)	)	PUNCT
ejpam-5986	650	14	,	,	PUNCT
ejpam-5986	650	15	5986	5986	NUM
ejpam-5986	650	16	20	20	NUM
ejpam-5986	650	17	of	of	ADP
ejpam-5986	650	18	20	20	NUM
ejpam-5986	650	19	applied	apply	VERB
ejpam-5986	650	20	sciences	science	NOUN
ejpam-5986	650	21	section	section	NOUN
ejpam-5986	650	22	-	-	PUNCT
ejpam-5986	650	23	e	e	NOUN
ejpam-5986	650	24	-	-	NOUN
ejpam-5986	650	25	mathematics	mathematic	NOUN
ejpam-5986	650	26	and	and	CCONJ
ejpam-5986	650	27	statistics	statistic	NOUN
ejpam-5986	650	28	,	,	PUNCT
ejpam-5986	650	29	37(e):1–8	37(e):1–8	NUM
ejpam-5986	650	30	,	,	PUNCT
ejpam-5986	650	31	2018	2018	NUM
ejpam-5986	650	32	.	.	PUNCT
ejpam-5986	651	1	[	[	X
ejpam-5986	651	2	32	32	NUM
ejpam-5986	651	3	]	]	PUNCT
ejpam-5986	651	4	l.	l.	PROPN
ejpam-5986	651	5	m.	m.	PROPN
ejpam-5986	651	6	upadhyaya	upadhyaya	PROPN
ejpam-5986	651	7	.	.	PUNCT
ejpam-5986	652	1	on	on	ADP
ejpam-5986	652	2	the	the	DET
ejpam-5986	652	3	degenerate	degenerate	ADJ
ejpam-5986	652	4	laplace	laplace	NOUN
ejpam-5986	652	5	transform	transform	NOUN
ejpam-5986	652	6	iii	iii	PROPN
ejpam-5986	652	7	.	.	PUNCT
ejpam-5986	652	8	international	international	ADJ
ejpam-5986	652	9	journal	journal	PROPN
ejpam-5986	652	10	of	of	ADP
ejpam-5986	652	11	engineering	engineering	NOUN
ejpam-5986	652	12	,	,	PUNCT
ejpam-5986	652	13	science	science	NOUN
ejpam-5986	652	14	and	and	CCONJ
ejpam-5986	652	15	mathematics	mathematic	NOUN
ejpam-5986	652	16	,	,	PUNCT
ejpam-5986	652	17	7(1):400–410	7(1):400–410	NUM
ejpam-5986	652	18	,	,	PUNCT
ejpam-5986	652	19	2018	2018	NUM
ejpam-5986	652	20	.	.	PUNCT
ejpam-5986	653	1	[	[	X
ejpam-5986	653	2	33	33	NUM
ejpam-5986	653	3	]	]	X
ejpam-5986	653	4	u.	u.	PROPN
ejpam-5986	653	5	duran	duran	PROPN
ejpam-5986	653	6	.	.	PUNCT
ejpam-5986	654	1	degenerate	degenerate	ADJ
ejpam-5986	654	2	sumudu	sumudu	NOUN
ejpam-5986	654	3	transform	transform	NOUN
ejpam-5986	654	4	and	and	CCONJ
ejpam-5986	654	5	its	its	PRON
ejpam-5986	654	6	properties	property	NOUN
ejpam-5986	654	7	.	.	PUNCT
ejpam-5986	655	1	filomat	filomat	NOUN
ejpam-5986	655	2	,	,	PUNCT
ejpam-5986	655	3	35(14):4731	35(14):4731	NUM
ejpam-5986	655	4	–	–	PUNCT
ejpam-5986	655	5	4741	4741	NUM
ejpam-5986	655	6	,	,	PUNCT
ejpam-5986	655	7	2021	2021	NUM
ejpam-5986	655	8	.	.	PUNCT
ejpam-5986	656	1	[	[	X
ejpam-5986	656	2	34	34	NUM
ejpam-5986	656	3	]	]	PUNCT
ejpam-5986	656	4	a.	a.	NOUN
ejpam-5986	656	5	kalavathi	kalavathi	PROPN
ejpam-5986	656	6	,	,	PUNCT
ejpam-5986	656	7	t.	t.	PROPN
ejpam-5986	656	8	kohila	kohila	PROPN
ejpam-5986	656	9	,	,	PUNCT
ejpam-5986	656	10	and	and	CCONJ
ejpam-5986	656	11	l.	l.	PROPN
ejpam-5986	656	12	m.	m.	PROPN
ejpam-5986	656	13	upadhyaya	upadhyaya	PROPN
ejpam-5986	656	14	.	.	PUNCT
ejpam-5986	657	1	on	on	ADP
ejpam-5986	657	2	the	the	DET
ejpam-5986	657	3	degenerate	degenerate	ADJ
ejpam-5986	657	4	elzaki	elzaki	NOUN
ejpam-5986	657	5	transform	transform	NOUN
ejpam-5986	657	6	.	.	PUNCT
ejpam-5986	658	1	bull	bull	NOUN
ejpam-5986	658	2	.	.	PUNCT
ejpam-5986	659	1	pure	pure	ADJ
ejpam-5986	659	2	appl	appl	PROPN
ejpam-5986	659	3	.	.	PUNCT
ejpam-5986	660	1	sci	sci	PROPN
ejpam-5986	660	2	.	.	PUNCT
ejpam-5986	660	3	sect	sect	NOUN
ejpam-5986	660	4	.	.	PUNCT
ejpam-5986	661	1	e	e	X
ejpam-5986	661	2	math	math	NOUN
ejpam-5986	661	3	.	.	PUNCT
ejpam-5986	662	1	stat	stat	PROPN
ejpam-5986	662	2	.	.	PUNCT
ejpam-5986	662	3	,	,	PUNCT
ejpam-5986	662	4	40e(1):99–107	40e(1):99–107	X
ejpam-5986	662	5	,	,	PUNCT
ejpam-5986	662	6	2021	2021	NUM
ejpam-5986	662	7	.	.	PUNCT