id	sid	tid	token	lemma	pos
ejpam-6136	1	1	european	european	PROPN
ejpam-6136	1	2	journal	journal	PROPN
ejpam-6136	1	3	of	of	ADP
ejpam-6136	1	4	pure	pure	ADJ
ejpam-6136	1	5	and	and	CCONJ
ejpam-6136	1	6	applied	applied	ADJ
ejpam-6136	1	7	mathematics	mathematic	NOUN
ejpam-6136	1	8	2025	2025	NUM
ejpam-6136	1	9	,	,	PUNCT
ejpam-6136	1	10	vol	vol	NOUN
ejpam-6136	1	11	.	.	PROPN
ejpam-6136	1	12	18	18	NUM
ejpam-6136	1	13	,	,	PUNCT
ejpam-6136	1	14	issue	issue	NOUN
ejpam-6136	1	15	3	3	NUM
ejpam-6136	1	16	,	,	PUNCT
ejpam-6136	1	17	article	article	NOUN
ejpam-6136	1	18	number	number	NOUN
ejpam-6136	1	19	6136	6136	NUM
ejpam-6136	1	20	issn	issn	VERB
ejpam-6136	1	21	1307	1307	NUM
ejpam-6136	1	22	-	-	SYM
ejpam-6136	1	23	5543	5543	NUM
ejpam-6136	1	24	–	–	PUNCT
ejpam-6136	1	25	ejpam.com	ejpam.com	X
ejpam-6136	1	26	published	publish	VERB
ejpam-6136	1	27	by	by	ADP
ejpam-6136	1	28	new	new	PROPN
ejpam-6136	1	29	york	york	PROPN
ejpam-6136	1	30	business	business	PROPN
ejpam-6136	1	31	global	global	PROPN
ejpam-6136	1	32	on	on	ADP
ejpam-6136	1	33	the	the	DET
ejpam-6136	1	34	degenerate	degenerate	ADJ
ejpam-6136	1	35	sadik	sadik	PROPN
ejpam-6136	1	36	transform	transform	NOUN
ejpam-6136	1	37	jamilon	jamilon	PROPN
ejpam-6136	1	38	b.	b.	PROPN
ejpam-6136	1	39	mohamadali1,∗	mohamadali1,∗	PROPN
ejpam-6136	1	40	,	,	PUNCT
ejpam-6136	1	41	normalah	normalah	NOUN
ejpam-6136	1	42	s.	s.	PROPN
ejpam-6136	1	43	abdulcarim1	abdulcarim1	PROPN
ejpam-6136	1	44	1	1	NUM
ejpam-6136	1	45	department	department	NOUN
ejpam-6136	1	46	of	of	ADP
ejpam-6136	1	47	mathematics	mathematic	NOUN
ejpam-6136	1	48	,	,	PUNCT
ejpam-6136	1	49	college	college	NOUN
ejpam-6136	1	50	of	of	ADP
ejpam-6136	1	51	natural	natural	ADJ
ejpam-6136	1	52	sciences	science	NOUN
ejpam-6136	1	53	and	and	CCONJ
ejpam-6136	1	54	mathematics	mathematic	NOUN
ejpam-6136	1	55	,	,	PUNCT
ejpam-6136	1	56	mindanao	mindanao	PROPN
ejpam-6136	1	57	state	state	PROPN
ejpam-6136	1	58	university	university	PROPN
ejpam-6136	1	59	main	main	ADJ
ejpam-6136	1	60	campus	campus	NOUN
ejpam-6136	1	61	,	,	PUNCT
ejpam-6136	1	62	9700	9700	NUM
ejpam-6136	1	63	marawi	marawi	PROPN
ejpam-6136	1	64	city	city	PROPN
ejpam-6136	1	65	,	,	PUNCT
ejpam-6136	1	66	philippines	philippine	NOUN
ejpam-6136	1	67	abstract	abstract	ADJ
ejpam-6136	1	68	.	.	PUNCT
ejpam-6136	2	1	in	in	ADP
ejpam-6136	2	2	this	this	DET
ejpam-6136	2	3	paper	paper	NOUN
ejpam-6136	2	4	,	,	PUNCT
ejpam-6136	2	5	the	the	DET
ejpam-6136	2	6	authors	author	NOUN
ejpam-6136	2	7	introduce	introduce	VERB
ejpam-6136	2	8	the	the	DET
ejpam-6136	2	9	degenerate	degenerate	ADJ
ejpam-6136	2	10	sadik	sadik	ADJ
ejpam-6136	2	11	transform	transform	NOUN
ejpam-6136	2	12	and	and	CCONJ
ejpam-6136	2	13	investigates	investigate	VERB
ejpam-6136	2	14	the	the	DET
ejpam-6136	2	15	transform	transform	NOUN
ejpam-6136	2	16	of	of	ADP
ejpam-6136	2	17	some	some	DET
ejpam-6136	2	18	elementary	elementary	ADJ
ejpam-6136	2	19	functions	function	NOUN
ejpam-6136	2	20	.	.	PUNCT
ejpam-6136	3	1	also	also	ADV
ejpam-6136	3	2	,	,	PUNCT
ejpam-6136	3	3	sufficient	sufficient	ADJ
ejpam-6136	3	4	condition	condition	NOUN
ejpam-6136	3	5	for	for	ADP
ejpam-6136	3	6	the	the	DET
ejpam-6136	3	7	existence	existence	NOUN
ejpam-6136	3	8	of	of	ADP
ejpam-6136	3	9	the	the	DET
ejpam-6136	3	10	said	say	VERB
ejpam-6136	3	11	transform	transform	NOUN
ejpam-6136	3	12	is	be	AUX
ejpam-6136	3	13	also	also	ADV
ejpam-6136	3	14	presented	present	VERB
ejpam-6136	3	15	.	.	PUNCT
ejpam-6136	4	1	furthermore	furthermore	ADV
ejpam-6136	4	2	,	,	PUNCT
ejpam-6136	4	3	this	this	DET
ejpam-6136	4	4	paper	paper	NOUN
ejpam-6136	4	5	concludes	conclude	VERB
ejpam-6136	4	6	that	that	SCONJ
ejpam-6136	4	7	degenerate	degenerate	ADJ
ejpam-6136	4	8	sadik	sadik	ADJ
ejpam-6136	4	9	transform	transform	NOUN
ejpam-6136	4	10	is	be	AUX
ejpam-6136	4	11	a	a	DET
ejpam-6136	4	12	unification	unification	NOUN
ejpam-6136	4	13	of	of	ADP
ejpam-6136	4	14	some	some	DET
ejpam-6136	4	15	other	other	ADJ
ejpam-6136	4	16	degenerate	degenerate	NOUN
ejpam-6136	4	17	transforms	transform	VERB
ejpam-6136	4	18	such	such	ADJ
ejpam-6136	4	19	as	as	ADP
ejpam-6136	4	20	degenerate	degenerate	ADJ
ejpam-6136	4	21	laplace	laplace	NOUN
ejpam-6136	4	22	transform	transform	NOUN
ejpam-6136	4	23	,	,	PUNCT
ejpam-6136	4	24	degenerate	degenerate	ADJ
ejpam-6136	4	25	sumudu	sumudu	NOUN
ejpam-6136	4	26	transform	transform	NOUN
ejpam-6136	4	27	,	,	PUNCT
ejpam-6136	4	28	degenerate	degenerate	ADJ
ejpam-6136	4	29	elzaki	elzaki	NOUN
ejpam-6136	4	30	integral	integral	ADJ
ejpam-6136	4	31	transform	transform	NOUN
ejpam-6136	4	32	and	and	CCONJ
ejpam-6136	4	33	laplace	laplace	NOUN
ejpam-6136	4	34	-	-	PUNCT
ejpam-6136	4	35	type	type	NOUN
ejpam-6136	4	36	integral	integral	ADJ
ejpam-6136	4	37	transform	transform	NOUN
ejpam-6136	4	38	.	.	PUNCT
ejpam-6136	5	1	2020	2020	NUM
ejpam-6136	5	2	mathematics	mathematic	NOUN
ejpam-6136	5	3	subject	subject	NOUN
ejpam-6136	5	4	classifications	classification	NOUN
ejpam-6136	5	5	:	:	PUNCT
ejpam-6136	5	6	44a99	44a99	NUM
ejpam-6136	5	7	key	key	ADJ
ejpam-6136	5	8	words	word	NOUN
ejpam-6136	5	9	and	and	CCONJ
ejpam-6136	5	10	phrases	phrase	NOUN
ejpam-6136	5	11	:	:	PUNCT
ejpam-6136	5	12	degenerate	degenerate	ADJ
ejpam-6136	5	13	laplace	laplace	NOUN
ejpam-6136	5	14	transform	transform	NOUN
ejpam-6136	5	15	,	,	PUNCT
ejpam-6136	5	16	degenerate	degenerate	ADJ
ejpam-6136	5	17	elzaki	elzaki	NOUN
ejpam-6136	5	18	transform	transform	NOUN
ejpam-6136	5	19	,	,	PUNCT
ejpam-6136	5	20	degenerate	degenerate	ADJ
ejpam-6136	5	21	tarig	tarig	NOUN
ejpam-6136	5	22	integral	integral	ADJ
ejpam-6136	5	23	transform	transform	NOUN
ejpam-6136	5	24	,	,	PUNCT
ejpam-6136	5	25	degenerate	degenerate	ADJ
ejpam-6136	5	26	sumudu	sumudu	NOUN
ejpam-6136	5	27	transform	transform	NOUN
ejpam-6136	5	28	,	,	PUNCT
ejpam-6136	5	29	degenerate	degenerate	ADJ
ejpam-6136	5	30	laplace	laplace	NOUN
ejpam-6136	5	31	-	-	PUNCT
ejpam-6136	5	32	type	type	NOUN
ejpam-6136	5	33	integral	integral	ADJ
ejpam-6136	5	34	transform	transform	NOUN
ejpam-6136	5	35	1	1	NUM
ejpam-6136	5	36	.	.	PUNCT
ejpam-6136	5	37	introduction	introduction	NOUN
ejpam-6136	5	38	the	the	DET
ejpam-6136	5	39	integral	integral	ADJ
ejpam-6136	5	40	transformation	transformation	NOUN
ejpam-6136	5	41	method	method	NOUN
ejpam-6136	5	42	is	be	AUX
ejpam-6136	5	43	widely	widely	ADV
ejpam-6136	5	44	utilized	utilize	VERB
ejpam-6136	5	45	in	in	ADP
ejpam-6136	5	46	solving	solve	VERB
ejpam-6136	5	47	various	various	ADJ
ejpam-6136	5	48	types	type	NOUN
ejpam-6136	5	49	of	of	ADP
ejpam-6136	5	50	differential	differential	ADJ
ejpam-6136	5	51	equations	equation	NOUN
ejpam-6136	5	52	due	due	ADP
ejpam-6136	5	53	to	to	ADP
ejpam-6136	5	54	its	its	PRON
ejpam-6136	5	55	ability	ability	NOUN
ejpam-6136	5	56	to	to	PART
ejpam-6136	5	57	simplify	simplify	VERB
ejpam-6136	5	58	complex	complex	ADJ
ejpam-6136	5	59	problems	problem	NOUN
ejpam-6136	5	60	.	.	PUNCT
ejpam-6136	6	1	by	by	ADP
ejpam-6136	6	2	converting	convert	VERB
ejpam-6136	6	3	differential	differential	ADJ
ejpam-6136	6	4	equations	equation	NOUN
ejpam-6136	6	5	into	into	ADP
ejpam-6136	6	6	algebraic	algebraic	ADJ
ejpam-6136	6	7	equations	equation	NOUN
ejpam-6136	6	8	,	,	PUNCT
ejpam-6136	6	9	integral	integral	ADJ
ejpam-6136	6	10	transforms	transform	NOUN
ejpam-6136	6	11	streamline	streamline	VERB
ejpam-6136	6	12	the	the	DET
ejpam-6136	6	13	problem	problem	NOUN
ejpam-6136	6	14	-	-	PUNCT
ejpam-6136	6	15	solving	solve	VERB
ejpam-6136	6	16	process	process	NOUN
ejpam-6136	6	17	,	,	PUNCT
ejpam-6136	6	18	making	make	VERB
ejpam-6136	6	19	it	it	PRON
ejpam-6136	6	20	significantly	significantly	ADV
ejpam-6136	6	21	easier	easy	ADJ
ejpam-6136	6	22	and	and	CCONJ
ejpam-6136	6	23	more	more	ADV
ejpam-6136	6	24	efficient	efficient	ADJ
ejpam-6136	6	25	[	[	X
ejpam-6136	6	26	1	1	NUM
ejpam-6136	6	27	]	]	PUNCT
ejpam-6136	6	28	.	.	PUNCT
ejpam-6136	7	1	over	over	ADP
ejpam-6136	7	2	time	time	NOUN
ejpam-6136	7	3	,	,	PUNCT
ejpam-6136	7	4	numerous	numerous	ADJ
ejpam-6136	7	5	integral	integral	ADJ
ejpam-6136	7	6	transforms	transform	NOUN
ejpam-6136	7	7	have	have	AUX
ejpam-6136	7	8	been	be	AUX
ejpam-6136	7	9	developed	develop	VERB
ejpam-6136	7	10	,	,	PUNCT
ejpam-6136	7	11	including	include	VERB
ejpam-6136	7	12	the	the	DET
ejpam-6136	7	13	sumudu	sumudu	NOUN
ejpam-6136	7	14	transform	transform	NOUN
ejpam-6136	7	15	[	[	X
ejpam-6136	7	16	2	2	NUM
ejpam-6136	7	17	]	]	PUNCT
ejpam-6136	7	18	,	,	PUNCT
ejpam-6136	7	19	tarig	tarig	NOUN
ejpam-6136	7	20	transform	transform	VERB
ejpam-6136	7	21	[	[	X
ejpam-6136	7	22	3	3	NUM
ejpam-6136	7	23	]	]	PUNCT
ejpam-6136	7	24	,	,	PUNCT
ejpam-6136	7	25	elzaki	elzaki	NOUN
ejpam-6136	7	26	transform	transform	VERB
ejpam-6136	7	27	[	[	X
ejpam-6136	7	28	4	4	NUM
ejpam-6136	7	29	]	]	PUNCT
ejpam-6136	7	30	,	,	PUNCT
ejpam-6136	7	31	aboodh	aboodh	PROPN
ejpam-6136	7	32	transform	transform	VERB
ejpam-6136	7	33	[	[	X
ejpam-6136	7	34	5	5	NUM
ejpam-6136	7	35	]	]	PUNCT
ejpam-6136	7	36	,	,	PUNCT
ejpam-6136	7	37	kamal	kamal	PROPN
ejpam-6136	7	38	transform	transform	VERB
ejpam-6136	7	39	[	[	X
ejpam-6136	7	40	6	6	NUM
ejpam-6136	7	41	]	]	PUNCT
ejpam-6136	7	42	,	,	PUNCT
ejpam-6136	7	43	and	and	CCONJ
ejpam-6136	7	44	laplace	laplace	PROPN
ejpam-6136	7	45	-	-	PUNCT
ejpam-6136	7	46	carson	carson	PROPN
ejpam-6136	7	47	transform	transform	NOUN
ejpam-6136	7	48	[	[	X
ejpam-6136	7	49	7	7	NUM
ejpam-6136	7	50	]	]	PUNCT
ejpam-6136	7	51	.	.	PUNCT
ejpam-6136	8	1	among	among	ADP
ejpam-6136	8	2	these	these	PRON
ejpam-6136	8	3	,	,	PUNCT
ejpam-6136	8	4	the	the	DET
ejpam-6136	8	5	laplace	laplace	NOUN
ejpam-6136	8	6	transform	transform	NOUN
ejpam-6136	8	7	,	,	PUNCT
ejpam-6136	8	8	introduced	introduce	VERB
ejpam-6136	8	9	by	by	ADP
ejpam-6136	8	10	pierre	pierre	PROPN
ejpam-6136	8	11	-	-	PUNCT
ejpam-6136	8	12	simon	simon	PROPN
ejpam-6136	8	13	laplace	laplace	NOUN
ejpam-6136	8	14	,	,	PUNCT
ejpam-6136	8	15	remains	remain	VERB
ejpam-6136	8	16	one	one	NUM
ejpam-6136	8	17	of	of	ADP
ejpam-6136	8	18	the	the	DET
ejpam-6136	8	19	most	most	ADV
ejpam-6136	8	20	prominent	prominent	ADJ
ejpam-6136	8	21	and	and	CCONJ
ejpam-6136	8	22	widely	widely	ADV
ejpam-6136	8	23	applied	apply	VERB
ejpam-6136	8	24	tools	tool	NOUN
ejpam-6136	8	25	in	in	ADP
ejpam-6136	8	26	mathematics	mathematic	NOUN
ejpam-6136	8	27	,	,	PUNCT
ejpam-6136	8	28	physics	physics	NOUN
ejpam-6136	8	29	,	,	PUNCT
ejpam-6136	8	30	and	and	CCONJ
ejpam-6136	8	31	engineering	engineer	VERB
ejpam-6136	8	32	[	[	X
ejpam-6136	8	33	8	8	NUM
ejpam-6136	8	34	]	]	PUNCT
ejpam-6136	8	35	.	.	PUNCT
ejpam-6136	9	1	the	the	DET
ejpam-6136	9	2	laplace	laplace	NOUN
ejpam-6136	9	3	transform	transform	NOUN
ejpam-6136	9	4	of	of	ADP
ejpam-6136	9	5	a	a	DET
ejpam-6136	9	6	function	function	NOUN
ejpam-6136	9	7	f(t	f(t	PROPN
ejpam-6136	9	8	)	)	PUNCT
ejpam-6136	9	9	,	,	PUNCT
ejpam-6136	9	10	denoted	denote	VERB
ejpam-6136	9	11	by	by	ADP
ejpam-6136	9	12	l{f(t	l{f(t	NOUN
ejpam-6136	9	13	)	)	PUNCT
ejpam-6136	9	14	}	}	PUNCT
ejpam-6136	9	15	is	be	AUX
ejpam-6136	9	16	defined	define	VERB
ejpam-6136	9	17	as	as	ADP
ejpam-6136	9	18	f	f	PROPN
ejpam-6136	9	19	(	(	PUNCT
ejpam-6136	9	20	s	s	NOUN
ejpam-6136	9	21	)	)	PUNCT
ejpam-6136	9	22	=	=	SYM
ejpam-6136	9	23	l	l	NOUN
ejpam-6136	9	24	{	{	PUNCT
ejpam-6136	9	25	f(t	f(t	PROPN
ejpam-6136	9	26	)	)	PUNCT
ejpam-6136	9	27	}	}	PUNCT
ejpam-6136	9	28	=	=	PUNCT
ejpam-6136	10	1	∫	∫	PROPN
ejpam-6136	10	2	∞	∞	PROPN
ejpam-6136	10	3	0	0	NUM
ejpam-6136	11	1	e−stf(t)dt	e−stf(t)dt	PROPN
ejpam-6136	11	2	,	,	PUNCT
ejpam-6136	11	3	for	for	ADP
ejpam-6136	11	4	all	all	DET
ejpam-6136	11	5	real	real	ADJ
ejpam-6136	11	6	numbers	number	NOUN
ejpam-6136	11	7	t	t	PROPN
ejpam-6136	11	8	≥	≥	NOUN
ejpam-6136	11	9	0	0	NUM
ejpam-6136	12	1	where	where	SCONJ
ejpam-6136	12	2	s	s	PROPN
ejpam-6136	12	3	∈	∈	PROPN
ejpam-6136	12	4	c.	c.	PROPN
ejpam-6136	12	5	∗corresponding	∗corresponde	VERB
ejpam-6136	12	6	author	author	NOUN
ejpam-6136	12	7	.	.	PUNCT
ejpam-6136	13	1	doi	doi	NOUN
ejpam-6136	13	2	:	:	PUNCT
ejpam-6136	13	3	https://doi.org/10.29020/nybg.ejpam.v18i3.6136	https://doi.org/10.29020/nybg.ejpam.v18i3.6136	ADJ
ejpam-6136	13	4	email	email	NOUN
ejpam-6136	13	5	addresses	address	NOUN
ejpam-6136	13	6	:	:	PUNCT
ejpam-6136	13	7	mohamadali.jb57@s.msumain.edu.ph	mohamadali.jb57@s.msumain.edu.ph	NUM
ejpam-6136	13	8	(	(	PUNCT
ejpam-6136	13	9	j.	j.	PROPN
ejpam-6136	13	10	mohamadali	mohamadali	PROPN
ejpam-6136	13	11	)	)	PUNCT
ejpam-6136	13	12	,	,	PUNCT
ejpam-6136	13	13	normalah.abdulcarim@msumain.edu.ph	normalah.abdulcarim@msumain.edu.ph	PROPN
ejpam-6136	13	14	(	(	PUNCT
ejpam-6136	13	15	n.	n.	PROPN
ejpam-6136	13	16	abdulcarim	abdulcarim	PROPN
ejpam-6136	13	17	)	)	PUNCT
ejpam-6136	13	18	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-6136	14	1	1	1	NUM
ejpam-6136	14	2	copyright	copyright	NOUN
ejpam-6136	14	3	:	:	PUNCT
ejpam-6136	14	4	©	©	PROPN
ejpam-6136	14	5	2025	2025	NUM
ejpam-6136	14	6	the	the	DET
ejpam-6136	14	7	author(s	author(s	NOUN
ejpam-6136	14	8	)	)	PUNCT
ejpam-6136	14	9	.	.	PUNCT
ejpam-6136	15	1	(	(	PUNCT
ejpam-6136	15	2	cc	cc	NOUN
ejpam-6136	15	3	by	by	ADP
ejpam-6136	15	4	-	-	PUNCT
ejpam-6136	15	5	nc	nc	PROPN
ejpam-6136	15	6	4.0	4.0	NUM
ejpam-6136	15	7	)	)	PUNCT
ejpam-6136	15	8	j.	j.	PROPN
ejpam-6136	15	9	mohamadali	mohamadali	PROPN
ejpam-6136	15	10	,	,	PUNCT
ejpam-6136	15	11	n.	n.	PROPN
ejpam-6136	15	12	abdulcarim	abdulcarim	PROPN
ejpam-6136	15	13	/	/	SYM
ejpam-6136	15	14	eur	eur	PROPN
ejpam-6136	15	15	.	.	PUNCT
ejpam-6136	16	1	j.	j.	PROPN
ejpam-6136	16	2	pure	pure	PROPN
ejpam-6136	16	3	appl	appl	PROPN
ejpam-6136	16	4	.	.	PROPN
ejpam-6136	16	5	math	math	PROPN
ejpam-6136	16	6	,	,	PUNCT
ejpam-6136	16	7	18	18	NUM
ejpam-6136	16	8	(	(	PUNCT
ejpam-6136	16	9	3	3	NUM
ejpam-6136	16	10	)	)	PUNCT
ejpam-6136	16	11	(	(	PUNCT
ejpam-6136	16	12	2025	2025	NUM
ejpam-6136	16	13	)	)	PUNCT
ejpam-6136	16	14	,	,	PUNCT
ejpam-6136	16	15	6136	6136	NUM
ejpam-6136	16	16	2	2	NUM
ejpam-6136	16	17	of	of	ADP
ejpam-6136	16	18	19	19	NUM
ejpam-6136	16	19	throughout	throughout	ADP
ejpam-6136	16	20	the	the	DET
ejpam-6136	16	21	centuries	century	NOUN
ejpam-6136	16	22	,	,	PUNCT
ejpam-6136	16	23	integral	integral	ADJ
ejpam-6136	16	24	transforms	transform	NOUN
ejpam-6136	16	25	have	have	AUX
ejpam-6136	16	26	played	play	VERB
ejpam-6136	16	27	a	a	DET
ejpam-6136	16	28	vital	vital	ADJ
ejpam-6136	16	29	role	role	NOUN
ejpam-6136	16	30	in	in	ADP
ejpam-6136	16	31	the	the	DET
ejpam-6136	16	32	development	development	NOUN
ejpam-6136	16	33	of	of	ADP
ejpam-6136	16	34	new	new	ADJ
ejpam-6136	16	35	mathematical	mathematical	ADJ
ejpam-6136	16	36	tools	tool	NOUN
ejpam-6136	16	37	across	across	ADP
ejpam-6136	16	38	various	various	ADJ
ejpam-6136	16	39	scientific	scientific	ADJ
ejpam-6136	16	40	disciplines	discipline	NOUN
ejpam-6136	16	41	.	.	PUNCT
ejpam-6136	17	1	in	in	ADP
ejpam-6136	17	2	2018	2018	NUM
ejpam-6136	17	3	,	,	PUNCT
ejpam-6136	17	4	mathematician	mathematician	NOUN
ejpam-6136	17	5	sadikali	sadikali	VERB
ejpam-6136	17	6	latif	latif	PROPN
ejpam-6136	17	7	shaikh	shaikh	PROPN
ejpam-6136	17	8	introduced	introduce	VERB
ejpam-6136	17	9	a	a	DET
ejpam-6136	17	10	new	new	ADJ
ejpam-6136	17	11	integral	integral	ADJ
ejpam-6136	17	12	transform	transform	NOUN
ejpam-6136	17	13	,	,	PUNCT
ejpam-6136	17	14	named	name	VERB
ejpam-6136	17	15	the	the	DET
ejpam-6136	17	16	sadik	sadik	PROPN
ejpam-6136	17	17	transform	transform	NOUN
ejpam-6136	17	18	[	[	X
ejpam-6136	17	19	9	9	NUM
ejpam-6136	17	20	]	]	PUNCT
ejpam-6136	17	21	,	,	PUNCT
ejpam-6136	17	22	which	which	PRON
ejpam-6136	17	23	generalizes	generalize	VERB
ejpam-6136	17	24	and	and	CCONJ
ejpam-6136	17	25	unifies	unify	VERB
ejpam-6136	17	26	several	several	ADJ
ejpam-6136	17	27	existing	exist	VERB
ejpam-6136	17	28	integral	integral	ADJ
ejpam-6136	17	29	transforms	transform	NOUN
ejpam-6136	17	30	.	.	PUNCT
ejpam-6136	18	1	this	this	DET
ejpam-6136	18	2	transform	transform	NOUN
ejpam-6136	18	3	is	be	AUX
ejpam-6136	18	4	denoted	denote	VERB
ejpam-6136	18	5	by	by	ADP
ejpam-6136	18	6	s{f(t	s{f(t	NOUN
ejpam-6136	18	7	)	)	PUNCT
ejpam-6136	18	8	}	}	PUNCT
ejpam-6136	18	9	and	and	CCONJ
ejpam-6136	18	10	defined	define	VERB
ejpam-6136	18	11	by	by	ADP
ejpam-6136	18	12	f{(uα	f{(uα	NOUN
ejpam-6136	18	13	,	,	PUNCT
ejpam-6136	18	14	β	β	NOUN
ejpam-6136	18	15	)	)	PUNCT
ejpam-6136	18	16	}	}	PUNCT
ejpam-6136	18	17	=	=	SYM
ejpam-6136	18	18	s{f(t	s{f(t	NUM
ejpam-6136	18	19	)	)	PUNCT
ejpam-6136	18	20	}	}	PUNCT
ejpam-6136	18	21	=	=	SYM
ejpam-6136	19	1	1	1	NUM
ejpam-6136	19	2	uβ	uβ	NOUN
ejpam-6136	19	3	∫	∫	PROPN
ejpam-6136	19	4	∞	∞	PROPN
ejpam-6136	19	5	0	0	NUM
ejpam-6136	19	6	e−uα	e−uα	PROPN
ejpam-6136	19	7	(	(	PUNCT
ejpam-6136	19	8	t)f(t)dt	t)f(t)dt	NOUN
ejpam-6136	19	9	.	.	PUNCT
ejpam-6136	20	1	(	(	PUNCT
ejpam-6136	20	2	1	1	X
ejpam-6136	20	3	)	)	PUNCT
ejpam-6136	20	4	where	where	SCONJ
ejpam-6136	20	5	α	α	X
ejpam-6136	20	6	,	,	PUNCT
ejpam-6136	20	7	β	β	X
ejpam-6136	20	8	∈	∈	NOUN
ejpam-6136	20	9	r	r	NOUN
ejpam-6136	20	10	and	and	CCONJ
ejpam-6136	20	11	u	u	NOUN
ejpam-6136	20	12	is	be	AUX
ejpam-6136	20	13	a	a	DET
ejpam-6136	20	14	parameter	parameter	NOUN
ejpam-6136	20	15	.	.	PUNCT
ejpam-6136	21	1	the	the	DET
ejpam-6136	21	2	sadik	sadik	PROPN
ejpam-6136	21	3	transform	transform	NOUN
ejpam-6136	21	4	provides	provide	VERB
ejpam-6136	21	5	a	a	DET
ejpam-6136	21	6	flexible	flexible	ADJ
ejpam-6136	21	7	framework	framework	NOUN
ejpam-6136	21	8	that	that	PRON
ejpam-6136	21	9	encompasses	encompass	VERB
ejpam-6136	21	10	a	a	DET
ejpam-6136	21	11	wide	wide	ADJ
ejpam-6136	21	12	range	range	NOUN
ejpam-6136	21	13	of	of	ADP
ejpam-6136	21	14	existing	exist	VERB
ejpam-6136	21	15	transforms	transform	NOUN
ejpam-6136	21	16	by	by	ADP
ejpam-6136	21	17	assigning	assign	VERB
ejpam-6136	21	18	specific	specific	ADJ
ejpam-6136	21	19	values	value	NOUN
ejpam-6136	21	20	to	to	ADP
ejpam-6136	21	21	the	the	DET
ejpam-6136	21	22	parameters	parameter	NOUN
ejpam-6136	21	23	α	α	PROPN
ejpam-6136	21	24	and	and	CCONJ
ejpam-6136	21	25	β	β	X
ejpam-6136	21	26	.	.	PUNCT
ejpam-6136	22	1	that	that	PRON
ejpam-6136	22	2	is	be	AUX
ejpam-6136	22	3	,	,	PUNCT
ejpam-6136	22	4	when	when	SCONJ
ejpam-6136	22	5	α	α	PROPN
ejpam-6136	22	6	=	=	NOUN
ejpam-6136	22	7	0	0	NUM
ejpam-6136	22	8	and	and	CCONJ
ejpam-6136	22	9	β	β	X
ejpam-6136	22	10	=	=	SYM
ejpam-6136	22	11	1	1	NUM
ejpam-6136	22	12	,	,	PUNCT
ejpam-6136	22	13	we	we	PRON
ejpam-6136	22	14	get	get	VERB
ejpam-6136	22	15	s{f(t	s{f(t	NOUN
ejpam-6136	22	16	)	)	PUNCT
ejpam-6136	22	17	}	}	PUNCT
ejpam-6136	23	1	=	=	SYM
ejpam-6136	23	2	∫	∫	PROPN
ejpam-6136	24	1	∞	∞	NUM
ejpam-6136	24	2	0	0	PUNCT
ejpam-6136	25	1	f(ut)e−tdt	f(ut)e−tdt	PROPN
ejpam-6136	25	2	,	,	PUNCT
ejpam-6136	25	3	u	u	PROPN
ejpam-6136	25	4	∈	∈	PROPN
ejpam-6136	25	5	(	(	PUNCT
ejpam-6136	25	6	−τ1	−τ1	PROPN
ejpam-6136	25	7	,	,	PUNCT
ejpam-6136	25	8	τ2	τ2	NOUN
ejpam-6136	25	9	)	)	PUNCT
ejpam-6136	25	10	,	,	PUNCT
ejpam-6136	25	11	popularly	popularly	ADV
ejpam-6136	25	12	known	know	VERB
ejpam-6136	25	13	as	as	ADP
ejpam-6136	25	14	the	the	DET
ejpam-6136	25	15	sumudu	sumudu	NOUN
ejpam-6136	25	16	transform	transform	VERB
ejpam-6136	25	17	[	[	X
ejpam-6136	25	18	2	2	NUM
ejpam-6136	25	19	]	]	PUNCT
ejpam-6136	25	20	,	,	PUNCT
ejpam-6136	25	21	when	when	SCONJ
ejpam-6136	25	22	α	α	NOUN
ejpam-6136	25	23	=	=	VERB
ejpam-6136	25	24	−2	−2	NOUN
ejpam-6136	25	25	and	and	CCONJ
ejpam-6136	25	26	β	β	X
ejpam-6136	25	27	=	=	SYM
ejpam-6136	25	28	1	1	NUM
ejpam-6136	25	29	,	,	PUNCT
ejpam-6136	25	30	we	we	PRON
ejpam-6136	25	31	acquire	acquire	VERB
ejpam-6136	25	32	t	t	PROPN
ejpam-6136	25	33	{	{	PUNCT
ejpam-6136	25	34	f(t	f(t	PROPN
ejpam-6136	25	35	)	)	PUNCT
ejpam-6136	25	36	}	}	PUNCT
ejpam-6136	25	37	=	=	SYM
ejpam-6136	25	38	1	1	NUM
ejpam-6136	25	39	u	u	NOUN
ejpam-6136	25	40	∫	∫	PROPN
ejpam-6136	25	41	∞	∞	NOUN
ejpam-6136	25	42	0	0	NUM
ejpam-6136	26	1	e−	e−	PROPN
ejpam-6136	26	2	t	t	PROPN
ejpam-6136	26	3	u2	u2	PROPN
ejpam-6136	26	4	f(t)dt	f(t)dt	PROPN
ejpam-6136	26	5	,	,	PUNCT
ejpam-6136	26	6	commonly	commonly	ADV
ejpam-6136	26	7	called	call	VERB
ejpam-6136	26	8	as	as	ADP
ejpam-6136	26	9	the	the	DET
ejpam-6136	26	10	tarig	tarig	NOUN
ejpam-6136	26	11	integral	integral	ADJ
ejpam-6136	26	12	transform	transform	NOUN
ejpam-6136	26	13	[	[	X
ejpam-6136	26	14	3	3	NUM
ejpam-6136	26	15	]	]	PUNCT
ejpam-6136	26	16	,	,	PUNCT
ejpam-6136	26	17	when	when	SCONJ
ejpam-6136	26	18	α	α	NOUN
ejpam-6136	26	19	=	=	VERB
ejpam-6136	26	20	−1	−1	NOUN
ejpam-6136	26	21	and	and	CCONJ
ejpam-6136	26	22	β	β	NOUN
ejpam-6136	26	23	=	=	SYM
ejpam-6136	26	24	−1	−1	NOUN
ejpam-6136	26	25	,	,	PUNCT
ejpam-6136	26	26	we	we	PRON
ejpam-6136	26	27	obtain	obtain	VERB
ejpam-6136	26	28	ef{(t	ef{(t	NUM
ejpam-6136	26	29	)	)	PUNCT
ejpam-6136	26	30	}	}	PUNCT
ejpam-6136	27	1	=	=	SYM
ejpam-6136	27	2	u	u	NOUN
ejpam-6136	27	3	∫	∫	PROPN
ejpam-6136	27	4	∞	∞	NOUN
ejpam-6136	27	5	0	0	NUM
ejpam-6136	28	1	e−	e−	PROPN
ejpam-6136	28	2	t	t	PROPN
ejpam-6136	28	3	u	u	PROPN
ejpam-6136	28	4	f(t)dt	f(t)dt	PROPN
ejpam-6136	28	5	,	,	PUNCT
ejpam-6136	28	6	t	t	PROPN
ejpam-6136	28	7	≤	≤	NUM
ejpam-6136	28	8	0	0	NUM
ejpam-6136	28	9	,	,	PUNCT
ejpam-6136	28	10	k1	k1	ADJ
ejpam-6136	28	11	≤	≤	NUM
ejpam-6136	28	12	u	u	NOUN
ejpam-6136	28	13	≤	≤	ADJ
ejpam-6136	28	14	k2	k2	ADJ
ejpam-6136	28	15	,	,	PUNCT
ejpam-6136	28	16	well	well	ADV
ejpam-6136	28	17	-	-	PUNCT
ejpam-6136	28	18	known	know	VERB
ejpam-6136	28	19	as	as	ADP
ejpam-6136	28	20	the	the	DET
ejpam-6136	28	21	elzaki	elzaki	NOUN
ejpam-6136	28	22	integral	integral	ADJ
ejpam-6136	28	23	transform	transform	NOUN
ejpam-6136	28	24	[	[	X
ejpam-6136	28	25	10	10	NUM
ejpam-6136	28	26	]	]	PUNCT
ejpam-6136	28	27	,	,	PUNCT
ejpam-6136	28	28	when	when	SCONJ
ejpam-6136	28	29	α	α	PROPN
ejpam-6136	28	30	=	=	SYM
ejpam-6136	28	31	1	1	NUM
ejpam-6136	28	32	and	and	CCONJ
ejpam-6136	28	33	β	β	X
ejpam-6136	28	34	=	=	SYM
ejpam-6136	28	35	1	1	NUM
ejpam-6136	28	36	,	,	PUNCT
ejpam-6136	28	37	we	we	PRON
ejpam-6136	28	38	get	get	VERB
ejpam-6136	28	39	a{f(t	a{f(t	NOUN
ejpam-6136	28	40	)	)	PUNCT
ejpam-6136	28	41	}	}	PUNCT
ejpam-6136	28	42	=	=	SYM
ejpam-6136	28	43	k(u	k(u	X
ejpam-6136	28	44	)	)	PUNCT
ejpam-6136	28	45	=	=	SYM
ejpam-6136	28	46	1	1	NUM
ejpam-6136	28	47	u	u	NOUN
ejpam-6136	28	48	∫	∫	PROPN
ejpam-6136	28	49	∞	∞	NOUN
ejpam-6136	28	50	0	0	NUM
ejpam-6136	29	1	f(t)e−utdt	f(t)e−utdt	PROPN
ejpam-6136	29	2	,	,	PUNCT
ejpam-6136	29	3	t	t	PROPN
ejpam-6136	29	4	≥	≥	NOUN
ejpam-6136	29	5	0	0	NUM
ejpam-6136	29	6	,	,	PUNCT
ejpam-6136	29	7	k1	k1	ADJ
ejpam-6136	29	8	≤	≤	PROPN
ejpam-6136	29	9	u,≤	u,≤	NUM
ejpam-6136	29	10	k2	k2	NOUN
ejpam-6136	29	11	,	,	PUNCT
ejpam-6136	29	12	familiarly	familiarly	ADV
ejpam-6136	29	13	named	name	VERB
ejpam-6136	29	14	as	as	ADP
ejpam-6136	29	15	the	the	DET
ejpam-6136	29	16	aboodh	aboodh	ADJ
ejpam-6136	29	17	transform	transform	NOUN
ejpam-6136	29	18	[	[	X
ejpam-6136	29	19	5	5	NUM
ejpam-6136	29	20	]	]	PUNCT
ejpam-6136	29	21	,	,	PUNCT
ejpam-6136	29	22	when	when	SCONJ
ejpam-6136	29	23	α	α	NOUN
ejpam-6136	29	24	=	=	VERB
ejpam-6136	29	25	−1	−1	NOUN
ejpam-6136	29	26	and	and	CCONJ
ejpam-6136	29	27	β	β	X
ejpam-6136	29	28	=	=	SYM
ejpam-6136	29	29	0	0	NUM
ejpam-6136	29	30	,	,	PUNCT
ejpam-6136	29	31	we	we	PRON
ejpam-6136	29	32	derive	derive	VERB
ejpam-6136	29	33	k{f	k{f	NOUN
ejpam-6136	29	34	(	(	PUNCT
ejpam-6136	29	35	t	t	NOUN
ejpam-6136	29	36	)	)	PUNCT
ejpam-6136	29	37	}	}	PUNCT
ejpam-6136	29	38	=	=	SYM
ejpam-6136	29	39	∫	∫	PROPN
ejpam-6136	29	40	∞	∞	NUM
ejpam-6136	29	41	0	0	NUM
ejpam-6136	30	1	f(t)e	f(t)e	PROPN
ejpam-6136	30	2	−t	−t	PROPN
ejpam-6136	30	3	u	u	NOUN
ejpam-6136	30	4	tdt	tdt	PROPN
ejpam-6136	30	5	=	=	SYM
ejpam-6136	30	6	g(u	g(u	PROPN
ejpam-6136	30	7	)	)	PUNCT
ejpam-6136	30	8	,	,	PUNCT
ejpam-6136	30	9	t	t	PROPN
ejpam-6136	30	10	≥	≥	NUM
ejpam-6136	30	11	0	0	NUM
ejpam-6136	30	12	,	,	PUNCT
ejpam-6136	30	13	k1	k1	ADJ
ejpam-6136	30	14	≤	≤	NUM
ejpam-6136	30	15	u	u	NOUN
ejpam-6136	30	16	≤	≤	NOUN
ejpam-6136	30	17	k2	k2	NOUN
ejpam-6136	30	18	,	,	PUNCT
ejpam-6136	30	19	recognized	recognize	VERB
ejpam-6136	30	20	as	as	ADP
ejpam-6136	30	21	the	the	DET
ejpam-6136	30	22	kamal	kamal	PROPN
ejpam-6136	30	23	transform	transform	NOUN
ejpam-6136	30	24	[	[	X
ejpam-6136	30	25	6	6	NUM
ejpam-6136	30	26	]	]	PUNCT
ejpam-6136	30	27	;	;	PUNCT
ejpam-6136	30	28	and	and	CCONJ
ejpam-6136	30	29	when	when	SCONJ
ejpam-6136	30	30	α	α	PROPN
ejpam-6136	30	31	=	=	SYM
ejpam-6136	30	32	1	1	NUM
ejpam-6136	30	33	and	and	CCONJ
ejpam-6136	30	34	β	β	X
ejpam-6136	30	35	=	=	SYM
ejpam-6136	30	36	−1	−1	NOUN
ejpam-6136	30	37	,	,	PUNCT
ejpam-6136	30	38	we	we	PRON
ejpam-6136	30	39	get	get	VERB
ejpam-6136	30	40	lc{f(t	lc{f(t	NOUN
ejpam-6136	30	41	)	)	PUNCT
ejpam-6136	30	42	}	}	PUNCT
ejpam-6136	31	1	=	=	PUNCT
ejpam-6136	31	2	g{p	g{p	ADJ
ejpam-6136	31	3	}	}	PUNCT
ejpam-6136	31	4	=	=	PUNCT
ejpam-6136	31	5	p	p	NOUN
ejpam-6136	31	6	∫	∫	PROPN
ejpam-6136	31	7	∞	∞	PROPN
ejpam-6136	31	8	0	0	NUM
ejpam-6136	32	1	e−ptg(t)dt	e−ptg(t)dt	PROPN
ejpam-6136	32	2	=	=	SYM
ejpam-6136	32	3	pl{g(t	pl{g(t	NOUN
ejpam-6136	32	4	)	)	PUNCT
ejpam-6136	32	5	}	}	PUNCT
ejpam-6136	32	6	,	,	PUNCT
ejpam-6136	32	7	identified	identify	VERB
ejpam-6136	32	8	as	as	ADP
ejpam-6136	32	9	as	as	ADP
ejpam-6136	32	10	the	the	DET
ejpam-6136	32	11	laplace	laplace	NOUN
ejpam-6136	32	12	-	-	PUNCT
ejpam-6136	32	13	carson	carson	PROPN
ejpam-6136	32	14	transform	transform	NOUN
ejpam-6136	32	15	[	[	X
ejpam-6136	32	16	7	7	NUM
ejpam-6136	32	17	]	]	PUNCT
ejpam-6136	32	18	.	.	PUNCT
ejpam-6136	33	1	these	these	DET
ejpam-6136	33	2	instances	instance	NOUN
ejpam-6136	33	3	illustrate	illustrate	VERB
ejpam-6136	33	4	the	the	DET
ejpam-6136	33	5	remarkable	remarkable	ADJ
ejpam-6136	33	6	generality	generality	NOUN
ejpam-6136	33	7	and	and	CCONJ
ejpam-6136	33	8	versatility	versatility	NOUN
ejpam-6136	33	9	of	of	ADP
ejpam-6136	33	10	the	the	DET
ejpam-6136	33	11	sadik	sadik	PROPN
ejpam-6136	33	12	transform	transform	NOUN
ejpam-6136	33	13	as	as	ADP
ejpam-6136	33	14	a	a	DET
ejpam-6136	33	15	unifying	unifying	ADJ
ejpam-6136	33	16	structure	structure	NOUN
ejpam-6136	33	17	for	for	ADP
ejpam-6136	33	18	various	various	ADJ
ejpam-6136	33	19	wellknown	wellknown	NOUN
ejpam-6136	33	20	transforms	transform	VERB
ejpam-6136	33	21	.	.	PUNCT
ejpam-6136	34	1	in	in	ADP
ejpam-6136	34	2	mathematics	mathematic	NOUN
ejpam-6136	34	3	the	the	DET
ejpam-6136	34	4	degenerate	degenerate	ADJ
ejpam-6136	34	5	refers	refer	VERB
ejpam-6136	34	6	to	to	ADP
ejpam-6136	34	7	the	the	DET
ejpam-6136	34	8	simplification	simplification	NOUN
ejpam-6136	34	9	of	of	ADP
ejpam-6136	34	10	solutions	solution	NOUN
ejpam-6136	34	11	,	,	PUNCT
ejpam-6136	34	12	particularly	particularly	ADV
ejpam-6136	34	13	in	in	ADP
ejpam-6136	34	14	limiting	limit	VERB
ejpam-6136	34	15	scenarios	scenario	NOUN
ejpam-6136	34	16	where	where	SCONJ
ejpam-6136	34	17	specific	specific	ADJ
ejpam-6136	34	18	parameters	parameter	NOUN
ejpam-6136	34	19	,	,	PUNCT
ejpam-6136	34	20	denoted	denote	VERB
ejpam-6136	34	21	as	as	ADP
ejpam-6136	34	22	λ	λ	PROPN
ejpam-6136	34	23	,	,	PUNCT
ejpam-6136	34	24	approach	approach	VERB
ejpam-6136	34	25	critical	critical	ADJ
ejpam-6136	34	26	values	value	NOUN
ejpam-6136	34	27	like	like	ADP
ejpam-6136	34	28	zero	zero	NUM
ejpam-6136	34	29	.	.	PUNCT
ejpam-6136	35	1	recently	recently	ADV
ejpam-6136	35	2	,	,	PUNCT
ejpam-6136	35	3	researchers	researcher	NOUN
ejpam-6136	35	4	have	have	AUX
ejpam-6136	35	5	shown	show	VERB
ejpam-6136	35	6	growing	grow	VERB
ejpam-6136	35	7	interest	interest	NOUN
ejpam-6136	35	8	in	in	ADP
ejpam-6136	35	9	exploring	explore	VERB
ejpam-6136	35	10	degenerate	degenerate	ADJ
ejpam-6136	35	11	versions	version	NOUN
ejpam-6136	35	12	of	of	ADP
ejpam-6136	35	13	classical	classical	ADJ
ejpam-6136	35	14	integral	integral	ADJ
ejpam-6136	35	15	transforms	transform	NOUN
ejpam-6136	35	16	.	.	PUNCT
ejpam-6136	36	1	some	some	PRON
ejpam-6136	36	2	of	of	ADP
ejpam-6136	36	3	these	these	DET
ejpam-6136	36	4	degenerate	degenerate	ADJ
ejpam-6136	36	5	transforms	transform	NOUN
ejpam-6136	36	6	are	be	AUX
ejpam-6136	36	7	the	the	DET
ejpam-6136	36	8	degenerate	degenerate	ADJ
ejpam-6136	36	9	j.	j.	PROPN
ejpam-6136	36	10	mohamadali	mohamadali	PROPN
ejpam-6136	36	11	,	,	PUNCT
ejpam-6136	36	12	n.	n.	PROPN
ejpam-6136	36	13	abdulcarim	abdulcarim	PROPN
ejpam-6136	36	14	/	/	SYM
ejpam-6136	36	15	eur	eur	PROPN
ejpam-6136	36	16	.	.	PUNCT
ejpam-6136	37	1	j.	j.	PROPN
ejpam-6136	37	2	pure	pure	PROPN
ejpam-6136	37	3	appl	appl	PROPN
ejpam-6136	37	4	.	.	PROPN
ejpam-6136	37	5	math	math	PROPN
ejpam-6136	37	6	,	,	PUNCT
ejpam-6136	37	7	18	18	NUM
ejpam-6136	37	8	(	(	PUNCT
ejpam-6136	37	9	3	3	NUM
ejpam-6136	37	10	)	)	PUNCT
ejpam-6136	37	11	(	(	PUNCT
ejpam-6136	37	12	2025	2025	NUM
ejpam-6136	37	13	)	)	PUNCT
ejpam-6136	37	14	,	,	PUNCT
ejpam-6136	37	15	6136	6136	NUM
ejpam-6136	37	16	3	3	NUM
ejpam-6136	37	17	of	of	ADP
ejpam-6136	37	18	19	19	NUM
ejpam-6136	37	19	laplace	laplace	NOUN
ejpam-6136	37	20	integral	integral	ADJ
ejpam-6136	37	21	transform	transform	NOUN
ejpam-6136	37	22	[	[	X
ejpam-6136	37	23	11	11	NUM
ejpam-6136	37	24	]	]	PUNCT
ejpam-6136	37	25	,	,	PUNCT
ejpam-6136	37	26	degenerate	degenerate	ADJ
ejpam-6136	37	27	laplace	laplace	NOUN
ejpam-6136	37	28	-	-	PUNCT
ejpam-6136	37	29	type	type	NOUN
ejpam-6136	37	30	integral	integral	ADJ
ejpam-6136	37	31	transform	transform	NOUN
ejpam-6136	37	32	[	[	X
ejpam-6136	37	33	12	12	NUM
ejpam-6136	37	34	]	]	PUNCT
ejpam-6136	37	35	,	,	PUNCT
ejpam-6136	37	36	degenerate	degenerate	ADJ
ejpam-6136	37	37	elzaki	elzaki	NOUN
ejpam-6136	37	38	integral	integral	ADJ
ejpam-6136	37	39	transform	transform	NOUN
ejpam-6136	37	40	[	[	X
ejpam-6136	37	41	13	13	NUM
ejpam-6136	37	42	]	]	PUNCT
ejpam-6136	37	43	and	and	CCONJ
ejpam-6136	37	44	degenerate	degenerate	ADJ
ejpam-6136	37	45	sumudu	sumudu	NOUN
ejpam-6136	37	46	transform	transform	NOUN
ejpam-6136	37	47	[	[	X
ejpam-6136	37	48	14	14	NUM
ejpam-6136	37	49	]	]	PUNCT
ejpam-6136	37	50	defined	define	VERB
ejpam-6136	37	51	by	by	ADP
ejpam-6136	37	52	lλ{f(t	lλ{f(t	NOUN
ejpam-6136	37	53	)	)	PUNCT
ejpam-6136	37	54	}	}	PUNCT
ejpam-6136	37	55	=	=	SYM
ejpam-6136	37	56	∫	∫	PROPN
ejpam-6136	37	57	∞	∞	NUM
ejpam-6136	37	58	0	0	NUM
ejpam-6136	37	59	e−s	e−s	PROPN
ejpam-6136	37	60	λ	λ	PROPN
ejpam-6136	37	61	(	(	PUNCT
ejpam-6136	37	62	t)f(t)dt	t)f(t)dt	NOUN
ejpam-6136	37	63	=	=	SYM
ejpam-6136	37	64	∫	∫	PROPN
ejpam-6136	37	65	∞	∞	PROPN
ejpam-6136	37	66	0	0	NUM
ejpam-6136	38	1	(	(	PUNCT
ejpam-6136	38	2	1	1	NUM
ejpam-6136	39	1	+	+	CCONJ
ejpam-6136	39	2	λt)−	λt)−	PROPN
ejpam-6136	39	3	s	s	X
ejpam-6136	39	4	λ	λ	X
ejpam-6136	39	5	f(t)dt	f(t)dt	NOUN
ejpam-6136	39	6	,	,	PUNCT
ejpam-6136	39	7	fαλ(u	fαλ(u	PROPN
ejpam-6136	39	8	)	)	PUNCT
ejpam-6136	39	9	=	=	SYM
ejpam-6136	39	10	gαλ{f(t	gαλ{f(t	PROPN
ejpam-6136	39	11	)	)	PUNCT
ejpam-6136	39	12	}	}	PUNCT
ejpam-6136	40	1	=	=	PUNCT
ejpam-6136	40	2	uα	uα	PROPN
ejpam-6136	40	3	∫	∫	PROPN
ejpam-6136	40	4	∞	∞	PROPN
ejpam-6136	40	5	0	0	PUNCT
ejpam-6136	41	1	e	e	NOUN
ejpam-6136	41	2	−	−	PROPN
ejpam-6136	41	3	1	1	NUM
ejpam-6136	41	4	u	u	NOUN
ejpam-6136	41	5	λ	λ	PROPN
ejpam-6136	41	6	(	(	PUNCT
ejpam-6136	41	7	t	t	NOUN
ejpam-6136	41	8	)	)	PUNCT
ejpam-6136	41	9	f(t)dt	f(t)dt	PROPN
ejpam-6136	41	10	=	=	PUNCT
ejpam-6136	41	11	uα	uα	PROPN
ejpam-6136	41	12	∫	∫	PROPN
ejpam-6136	41	13	∞	∞	PROPN
ejpam-6136	41	14	0	0	NUM
ejpam-6136	42	1	(	(	PUNCT
ejpam-6136	42	2	1	1	NUM
ejpam-6136	42	3	+	+	CCONJ
ejpam-6136	42	4	λt)−	λt)−	PROPN
ejpam-6136	42	5	1	1	X
ejpam-6136	42	6	uλ	uλ	ADP
ejpam-6136	42	7	f(t)dt	f(t)dt	PROPN
ejpam-6136	42	8	,	,	PUNCT
ejpam-6136	42	9	eλ{f(t	eλ{f(t	NOUN
ejpam-6136	42	10	)	)	PUNCT
ejpam-6136	42	11	}	}	PUNCT
ejpam-6136	42	12	=	=	SYM
ejpam-6136	42	13	u	u	NOUN
ejpam-6136	42	14	∫	∫	PROPN
ejpam-6136	42	15	∞	∞	PROPN
ejpam-6136	42	16	0	0	PUNCT
ejpam-6136	43	1	e	e	NOUN
ejpam-6136	43	2	−	−	PROPN
ejpam-6136	43	3	1	1	NUM
ejpam-6136	43	4	u	u	NOUN
ejpam-6136	43	5	λ	λ	X
ejpam-6136	43	6	(	(	PUNCT
ejpam-6136	43	7	t)f(t)dt	t)f(t)dt	NOUN
ejpam-6136	43	8	=	=	SYM
ejpam-6136	43	9	u	u	NOUN
ejpam-6136	43	10	∫	∫	PROPN
ejpam-6136	43	11	∞	∞	PROPN
ejpam-6136	43	12	0	0	NUM
ejpam-6136	44	1	(	(	PUNCT
ejpam-6136	44	2	1	1	NUM
ejpam-6136	44	3	+	+	CCONJ
ejpam-6136	44	4	λt	λt	X
ejpam-6136	44	5	)	)	PUNCT
ejpam-6136	44	6	1	1	NUM
ejpam-6136	44	7	uλ	uλ	ADP
ejpam-6136	44	8	f(t)dt	f(t)dt	PROPN
ejpam-6136	44	9	,	,	PUNCT
ejpam-6136	44	10	gλ{(u	gλ{(u	PROPN
ejpam-6136	44	11	)	)	PUNCT
ejpam-6136	44	12	}	}	PUNCT
ejpam-6136	44	13	=	=	SYM
ejpam-6136	44	14	sλ{f(t	sλ{f(t	NOUN
ejpam-6136	44	15	)	)	PUNCT
ejpam-6136	44	16	}	}	PUNCT
ejpam-6136	44	17	=	=	SYM
ejpam-6136	45	1	1	1	NUM
ejpam-6136	45	2	u	u	NOUN
ejpam-6136	45	3	∫	∫	PROPN
ejpam-6136	45	4	∞	∞	NOUN
ejpam-6136	45	5	0	0	PUNCT
ejpam-6136	46	1	e	e	NOUN
ejpam-6136	46	2	−1	−1	NOUN
ejpam-6136	46	3	u	u	X
ejpam-6136	46	4	λ	λ	X
ejpam-6136	46	5	(	(	PUNCT
ejpam-6136	46	6	t)dt	t)dt	PROPN
ejpam-6136	46	7	,	,	PUNCT
ejpam-6136	46	8	u	u	NOUN
ejpam-6136	46	9	∈	∈	PROPN
ejpam-6136	46	10	(	(	PUNCT
ejpam-6136	46	11	−τ1	−τ1	PROPN
ejpam-6136	46	12	,	,	PUNCT
ejpam-6136	46	13	τ2	τ2	NOUN
ejpam-6136	46	14	)	)	PUNCT
ejpam-6136	46	15	,	,	PUNCT
ejpam-6136	46	16	respectively	respectively	ADV
ejpam-6136	46	17	.	.	PUNCT
ejpam-6136	47	1	in	in	ADP
ejpam-6136	47	2	light	light	NOUN
ejpam-6136	47	3	of	of	ADP
ejpam-6136	47	4	these	these	DET
ejpam-6136	47	5	developments	development	NOUN
ejpam-6136	47	6	,	,	PUNCT
ejpam-6136	47	7	the	the	DET
ejpam-6136	47	8	authors	author	NOUN
ejpam-6136	47	9	are	be	AUX
ejpam-6136	47	10	motivated	motivated	ADJ
ejpam-6136	47	11	to	to	PART
ejpam-6136	47	12	introduce	introduce	VERB
ejpam-6136	47	13	and	and	CCONJ
ejpam-6136	47	14	analyze	analyze	VERB
ejpam-6136	47	15	a	a	DET
ejpam-6136	47	16	degenerate	degenerate	ADJ
ejpam-6136	47	17	version	version	NOUN
ejpam-6136	47	18	of	of	ADP
ejpam-6136	47	19	the	the	DET
ejpam-6136	47	20	sadik	sadik	PROPN
ejpam-6136	47	21	transform	transform	NOUN
ejpam-6136	47	22	and	and	CCONJ
ejpam-6136	47	23	investigates	investigate	VERB
ejpam-6136	47	24	the	the	DET
ejpam-6136	47	25	transform	transform	NOUN
ejpam-6136	47	26	of	of	ADP
ejpam-6136	47	27	some	some	DET
ejpam-6136	47	28	elementary	elementary	ADJ
ejpam-6136	47	29	functions	function	NOUN
ejpam-6136	47	30	.	.	PUNCT
ejpam-6136	48	1	also	also	ADV
ejpam-6136	48	2	,	,	PUNCT
ejpam-6136	48	3	sufficient	sufficient	ADJ
ejpam-6136	48	4	condition	condition	NOUN
ejpam-6136	48	5	for	for	ADP
ejpam-6136	48	6	the	the	DET
ejpam-6136	48	7	existence	existence	NOUN
ejpam-6136	48	8	of	of	ADP
ejpam-6136	48	9	the	the	DET
ejpam-6136	48	10	said	say	VERB
ejpam-6136	48	11	transform	transform	NOUN
ejpam-6136	48	12	is	be	AUX
ejpam-6136	48	13	also	also	ADV
ejpam-6136	48	14	presented	present	VERB
ejpam-6136	48	15	.	.	PUNCT
ejpam-6136	49	1	2	2	X
ejpam-6136	49	2	.	.	X
ejpam-6136	49	3	preliminaries	preliminary	NOUN
ejpam-6136	49	4	taekyon	taekyon	VERB
ejpam-6136	49	5	kim	kim	PROPN
ejpam-6136	49	6	and	and	CCONJ
ejpam-6136	49	7	dae	dae	PROPN
ejpam-6136	49	8	s.	s.	PROPN
ejpam-6136	49	9	kim	kim	PROPN
ejpam-6136	50	1	[	[	X
ejpam-6136	50	2	11	11	NUM
ejpam-6136	50	3	]	]	PUNCT
ejpam-6136	50	4	defined	define	VERB
ejpam-6136	50	5	the	the	DET
ejpam-6136	50	6	degenerate	degenerate	ADJ
ejpam-6136	50	7	laplace	laplace	NOUN
ejpam-6136	50	8	transform	transform	NOUN
ejpam-6136	50	9	by	by	ADP
ejpam-6136	50	10	the	the	DET
ejpam-6136	50	11	integral	integral	ADJ
ejpam-6136	50	12	lλf(t	lλf(t	NOUN
ejpam-6136	50	13	)	)	PUNCT
ejpam-6136	50	14	=	=	SYM
ejpam-6136	51	1	∫	∫	PROPN
ejpam-6136	51	2	∞	∞	PROPN
ejpam-6136	51	3	0	0	NUM
ejpam-6136	52	1	e−s	e−s	PROPN
ejpam-6136	52	2	λ	λ	PROPN
ejpam-6136	52	3	(	(	PUNCT
ejpam-6136	52	4	t)f(t)dt	t)f(t)dt	NOUN
ejpam-6136	52	5	=	=	SYM
ejpam-6136	52	6	∫	∫	PROPN
ejpam-6136	52	7	∞	∞	PROPN
ejpam-6136	52	8	0	0	NUM
ejpam-6136	52	9	(	(	PUNCT
ejpam-6136	52	10	1	1	NUM
ejpam-6136	52	11	+	+	CCONJ
ejpam-6136	52	12	λt)−	λt)−	NOUN
ejpam-6136	52	13	s	s	X
ejpam-6136	52	14	λ	λ	NOUN
ejpam-6136	52	15	f(t)dt	f(t)dt	NOUN
ejpam-6136	52	16	if	if	SCONJ
ejpam-6136	52	17	the	the	DET
ejpam-6136	52	18	integral	integral	ADJ
ejpam-6136	52	19	converges	converge	NOUN
ejpam-6136	52	20	.	.	PUNCT
ejpam-6136	53	1	the	the	DET
ejpam-6136	53	2	following	follow	VERB
ejpam-6136	53	3	are	be	AUX
ejpam-6136	53	4	some	some	DET
ejpam-6136	53	5	results	result	NOUN
ejpam-6136	53	6	of	of	ADP
ejpam-6136	53	7	the	the	DET
ejpam-6136	53	8	degenerate	degenerate	ADJ
ejpam-6136	53	9	laplace	laplace	NOUN
ejpam-6136	53	10	integral	integral	ADJ
ejpam-6136	53	11	transform	transform	NOUN
ejpam-6136	53	12	of	of	ADP
ejpam-6136	53	13	some	some	DET
ejpam-6136	53	14	elementary	elementary	ADJ
ejpam-6136	53	15	functions	function	NOUN
ejpam-6136	53	16	f(t	f(t	NOUN
ejpam-6136	53	17	):	):	PUNCT
ejpam-6136	53	18	f(t	f(t	NOUN
ejpam-6136	53	19	)	)	PUNCT
ejpam-6136	53	20	lλ{f(t	lλ{f(t	NOUN
ejpam-6136	53	21	)	)	PUNCT
ejpam-6136	53	22	}	}	PUNCT
ejpam-6136	53	23	1	1	NUM
ejpam-6136	53	24	1	1	NUM
ejpam-6136	53	25	s−λ	s−λ	NOUN
ejpam-6136	53	26	cos	cos	X
ejpam-6136	53	27	(	(	PUNCT
ejpam-6136	53	28	a	a	NOUN
ejpam-6136	53	29	)	)	PUNCT
ejpam-6136	53	30	λ	λ	PROPN
ejpam-6136	53	31	(	(	PUNCT
ejpam-6136	53	32	t	t	NOUN
ejpam-6136	53	33	)	)	PUNCT
ejpam-6136	53	34	s−λ	s−λ	PROPN
ejpam-6136	53	35	(	(	PUNCT
ejpam-6136	53	36	s−λ)2+a2	s−λ)2+a2	PROPN
ejpam-6136	53	37	t	t	PROPN
ejpam-6136	53	38	1	1	NUM
ejpam-6136	53	39	s2−3sλ+2λ2	s2−3sλ+2λ2	NOUN
ejpam-6136	53	40	sinh	sinh	NOUN
ejpam-6136	53	41	(	(	PUNCT
ejpam-6136	53	42	a	a	NOUN
ejpam-6136	53	43	)	)	PUNCT
ejpam-6136	53	44	λ	λ	PROPN
ejpam-6136	53	45	(	(	PUNCT
ejpam-6136	53	46	t	t	PROPN
ejpam-6136	53	47	)	)	PUNCT
ejpam-6136	53	48	a	a	DET
ejpam-6136	53	49	(	(	PUNCT
ejpam-6136	53	50	s−λ)2−a2	s−λ)2−a2	NOUN
ejpam-6136	53	51	f(t	f(t	NOUN
ejpam-6136	53	52	)	)	PUNCT
ejpam-6136	53	53	lλ{f(t	lλ{f(t	NOUN
ejpam-6136	53	54	)	)	PUNCT
ejpam-6136	53	55	}	}	PUNCT
ejpam-6136	53	56	tn(n	tn(n	NUM
ejpam-6136	54	1	=	=	SYM
ejpam-6136	54	2	0	0	NUM
ejpam-6136	54	3	,	,	PUNCT
ejpam-6136	54	4	1	1	NUM
ejpam-6136	54	5	,	,	PUNCT
ejpam-6136	54	6	...	...	PUNCT
ejpam-6136	54	7	)	)	PUNCT
ejpam-6136	55	1	n	n	CCONJ
ejpam-6136	55	2	!	!	X
ejpam-6136	55	3	sn+1	sn+1	NUM
ejpam-6136	55	4	1	1	NUM
ejpam-6136	55	5	(	(	PUNCT
ejpam-6136	55	6	1−λ	1−λ	NUM
ejpam-6136	55	7	s	s	NOUN
ejpam-6136	55	8	)	)	PUNCT
ejpam-6136	55	9	...	...	PUNCT
ejpam-6136	56	1	(	(	PUNCT
ejpam-6136	56	2	1−	1−	NUM
ejpam-6136	56	3	(	(	PUNCT
ejpam-6136	56	4	n+1)λ	n+1)λ	PROPN
ejpam-6136	56	5	s	s	PART
ejpam-6136	56	6	)	)	PUNCT
ejpam-6136	56	7	cosh	cosh	NOUN
ejpam-6136	56	8	(	(	PUNCT
ejpam-6136	56	9	a	a	X
ejpam-6136	56	10	)	)	PUNCT
ejpam-6136	56	11	λ	λ	PROPN
ejpam-6136	56	12	(	(	PUNCT
ejpam-6136	56	13	t	t	NOUN
ejpam-6136	56	14	)	)	PUNCT
ejpam-6136	56	15	s−λ	s−λ	PROPN
ejpam-6136	56	16	(	(	PUNCT
ejpam-6136	56	17	s−λ)2−a2	s−λ)2−a2	NUM
ejpam-6136	56	18	eaλ(t	eaλ(t	PROPN
ejpam-6136	56	19	)	)	PUNCT
ejpam-6136	56	20	1	1	NUM
ejpam-6136	56	21	s−λ−a	s−λ−a	PROPN
ejpam-6136	56	22	sin	sin	NOUN
ejpam-6136	56	23	(	(	PUNCT
ejpam-6136	56	24	a	a	X
ejpam-6136	56	25	)	)	PUNCT
ejpam-6136	56	26	λ	λ	PROPN
ejpam-6136	56	27	(	(	PUNCT
ejpam-6136	56	28	t	t	PROPN
ejpam-6136	56	29	)	)	PUNCT
ejpam-6136	56	30	a	a	PRON
ejpam-6136	56	31	(	(	PUNCT
ejpam-6136	56	32	s−λ)2+a2	s−λ)2+a2	PROPN
ejpam-6136	56	33	now	now	ADV
ejpam-6136	56	34	,	,	PUNCT
ejpam-6136	56	35	letting	let	VERB
ejpam-6136	56	36	s	s	X
ejpam-6136	56	37	=	=	SYM
ejpam-6136	56	38	1	1	NUM
ejpam-6136	56	39	u	u	NOUN
ejpam-6136	56	40	,	,	PUNCT
ejpam-6136	56	41	the	the	DET
ejpam-6136	56	42	degenerate	degenerate	ADJ
ejpam-6136	56	43	laplace	laplace	NOUN
ejpam-6136	56	44	transform	transform	NOUN
ejpam-6136	56	45	can	can	AUX
ejpam-6136	56	46	be	be	AUX
ejpam-6136	56	47	rewritten	rewrite	VERB
ejpam-6136	56	48	as	as	ADP
ejpam-6136	56	49	lλ{f(t	lλ{f(t	NOUN
ejpam-6136	56	50	)	)	PUNCT
ejpam-6136	56	51	}	}	PUNCT
ejpam-6136	57	1	=	=	SYM
ejpam-6136	57	2	∫	∫	PROPN
ejpam-6136	58	1	∞	∞	NUM
ejpam-6136	58	2	0	0	PUNCT
ejpam-6136	59	1	e	e	NOUN
ejpam-6136	59	2	1	1	NUM
ejpam-6136	59	3	u	u	NOUN
ejpam-6136	59	4	λ	λ	PROPN
ejpam-6136	59	5	(	(	PUNCT
ejpam-6136	59	6	t)f(t)dt	t)f(t)dt	NOUN
ejpam-6136	59	7	=	=	SYM
ejpam-6136	59	8	∫	∫	PROPN
ejpam-6136	59	9	∞	∞	PROPN
ejpam-6136	59	10	0	0	NUM
ejpam-6136	59	11	(	(	PUNCT
ejpam-6136	59	12	1	1	NUM
ejpam-6136	59	13	+	+	CCONJ
ejpam-6136	59	14	λt	λt	X
ejpam-6136	59	15	)	)	PUNCT
ejpam-6136	59	16	1	1	NUM
ejpam-6136	59	17	uλ	uλ	ADP
ejpam-6136	59	18	f(t)dt	f(t)dt	PROPN
ejpam-6136	59	19	.	.	PUNCT
ejpam-6136	59	20	consequently	consequently	ADV
ejpam-6136	59	21	,	,	PUNCT
ejpam-6136	59	22	the	the	DET
ejpam-6136	59	23	degenerate	degenerate	ADJ
ejpam-6136	59	24	laplace	laplace	NOUN
ejpam-6136	59	25	integral	integral	ADJ
ejpam-6136	59	26	transform	transform	NOUN
ejpam-6136	59	27	[	[	X
ejpam-6136	59	28	14	14	NUM
ejpam-6136	59	29	]	]	PUNCT
ejpam-6136	59	30	of	of	ADP
ejpam-6136	59	31	some	some	DET
ejpam-6136	59	32	elementary	elementary	ADJ
ejpam-6136	59	33	functions	function	NOUN
ejpam-6136	59	34	f(t	f(t	NOUN
ejpam-6136	59	35	)	)	PUNCT
ejpam-6136	59	36	are	be	AUX
ejpam-6136	59	37	as	as	SCONJ
ejpam-6136	59	38	follows	follow	VERB
ejpam-6136	59	39	:	:	PUNCT
ejpam-6136	59	40	j.	j.	PROPN
ejpam-6136	59	41	mohamadali	mohamadali	PROPN
ejpam-6136	59	42	,	,	PUNCT
ejpam-6136	59	43	n.	n.	PROPN
ejpam-6136	59	44	abdulcarim	abdulcarim	PROPN
ejpam-6136	59	45	/	/	SYM
ejpam-6136	59	46	eur	eur	PROPN
ejpam-6136	59	47	.	.	PUNCT
ejpam-6136	60	1	j.	j.	PROPN
ejpam-6136	60	2	pure	pure	PROPN
ejpam-6136	60	3	appl	appl	PROPN
ejpam-6136	60	4	.	.	PROPN
ejpam-6136	60	5	math	math	PROPN
ejpam-6136	60	6	,	,	PUNCT
ejpam-6136	60	7	18	18	NUM
ejpam-6136	60	8	(	(	PUNCT
ejpam-6136	60	9	3	3	NUM
ejpam-6136	60	10	)	)	PUNCT
ejpam-6136	60	11	(	(	PUNCT
ejpam-6136	60	12	2025	2025	NUM
ejpam-6136	60	13	)	)	PUNCT
ejpam-6136	60	14	,	,	PUNCT
ejpam-6136	60	15	6136	6136	NUM
ejpam-6136	60	16	4	4	NUM
ejpam-6136	60	17	of	of	ADP
ejpam-6136	60	18	19	19	NUM
ejpam-6136	60	19	f(t	f(t	NOUN
ejpam-6136	60	20	)	)	PUNCT
ejpam-6136	60	21	lλ{f(t	lλ{f(t	NOUN
ejpam-6136	60	22	)	)	PUNCT
ejpam-6136	60	23	}	}	PUNCT
ejpam-6136	60	24	1	1	NUM
ejpam-6136	60	25	u	u	NOUN
ejpam-6136	60	26	1−λu	1−λu	PROPN
ejpam-6136	60	27	t	t	PROPN
ejpam-6136	60	28	u2	u2	PROPN
ejpam-6136	60	29	(	(	PUNCT
ejpam-6136	60	30	1−λ)(1−2λu	1−λ)(1−2λu	PROPN
ejpam-6136	60	31	)	)	PUNCT
ejpam-6136	60	32	sinh	sinh	NOUN
ejpam-6136	60	33	(	(	PUNCT
ejpam-6136	60	34	a	a	X
ejpam-6136	60	35	)	)	PUNCT
ejpam-6136	60	36	λ	λ	PROPN
ejpam-6136	60	37	(	(	PUNCT
ejpam-6136	60	38	t	t	PROPN
ejpam-6136	60	39	)	)	PUNCT
ejpam-6136	60	40	au2	au2	NOUN
ejpam-6136	60	41	(	(	PUNCT
ejpam-6136	60	42	1−λu)2−u2a2	1−λu)2−u2a2	NUM
ejpam-6136	60	43	cosh	cosh	NOUN
ejpam-6136	60	44	(	(	PUNCT
ejpam-6136	60	45	a	a	NOUN
ejpam-6136	60	46	)	)	PUNCT
ejpam-6136	60	47	λ	λ	PROPN
ejpam-6136	60	48	(	(	PUNCT
ejpam-6136	60	49	t	t	PROPN
ejpam-6136	60	50	)	)	PUNCT
ejpam-6136	60	51	(	(	PUNCT
ejpam-6136	60	52	1−uλ)u	1−uλ)u	X
ejpam-6136	60	53	(	(	PUNCT
ejpam-6136	60	54	1−λu)2−u2a2	1−λu)2−u2a2	NUM
ejpam-6136	60	55	f(t	f(t	NOUN
ejpam-6136	60	56	)	)	PUNCT
ejpam-6136	60	57	lλ{f(t	lλ{f(t	NOUN
ejpam-6136	60	58	)	)	PUNCT
ejpam-6136	60	59	}	}	PUNCT
ejpam-6136	60	60	tn(n	tn(n	NUM
ejpam-6136	60	61	=	=	SYM
ejpam-6136	60	62	0	0	NUM
ejpam-6136	60	63	,	,	PUNCT
ejpam-6136	60	64	1	1	NUM
ejpam-6136	60	65	,	,	PUNCT
ejpam-6136	60	66	...	...	PUNCT
ejpam-6136	60	67	)	)	PUNCT
ejpam-6136	61	1	n!un+1	n!un+1	PROPN
ejpam-6136	61	2	(	(	PUNCT
ejpam-6136	61	3	1−λu)	1−λu)	NUM
ejpam-6136	61	4	...	...	SYM
ejpam-6136	61	5	(1(n+1)λu	(1(n+1)λu	X
ejpam-6136	61	6	)	)	PUNCT
ejpam-6136	62	1	eaλ(t	eaλ(t	ADV
ejpam-6136	62	2	)	)	PUNCT
ejpam-6136	62	3	u	u	NOUN
ejpam-6136	62	4	1−u(a+λ	1−u(a+λ	NOUN
ejpam-6136	62	5	)	)	PUNCT
ejpam-6136	62	6	cos	cos	PROPN
ejpam-6136	62	7	(	(	PUNCT
ejpam-6136	62	8	a	a	X
ejpam-6136	62	9	)	)	PUNCT
ejpam-6136	62	10	λ	λ	PROPN
ejpam-6136	62	11	(	(	PUNCT
ejpam-6136	62	12	t	t	PROPN
ejpam-6136	62	13	)	)	PUNCT
ejpam-6136	62	14	(	(	PUNCT
ejpam-6136	62	15	1−uλ)u	1−uλ)u	X
ejpam-6136	62	16	(	(	PUNCT
ejpam-6136	62	17	1−uλ)2+u2a2	1−uλ)2+u2a2	NUM
ejpam-6136	62	18	sin	sin	NOUN
ejpam-6136	62	19	(	(	PUNCT
ejpam-6136	62	20	a	a	X
ejpam-6136	62	21	)	)	PUNCT
ejpam-6136	62	22	λ	λ	PROPN
ejpam-6136	62	23	(	(	PUNCT
ejpam-6136	62	24	t	t	PROPN
ejpam-6136	62	25	)	)	PUNCT
ejpam-6136	62	26	au2	au2	NOUN
ejpam-6136	62	27	(	(	PUNCT
ejpam-6136	62	28	1−uλ)2+u2a2	1−uλ)2+u2a2	NUM
ejpam-6136	62	29	note	note	VERB
ejpam-6136	62	30	that	that	SCONJ
ejpam-6136	62	31	lim	lim	PROPN
ejpam-6136	62	32	λ→0	λ→0	ADV
ejpam-6136	62	33	lλ{f(t	lλ{f(t	PUNCT
ejpam-6136	62	34	)	)	PUNCT
ejpam-6136	62	35	}	}	PUNCT
ejpam-6136	62	36	=	=	PUNCT
ejpam-6136	62	37	l{f(t	l{f(t	NOUN
ejpam-6136	62	38	)	)	PUNCT
ejpam-6136	62	39	}	}	PUNCT
ejpam-6136	62	40	.	.	PUNCT
ejpam-6136	63	1	in	in	ADP
ejpam-6136	63	2	2023	2023	NUM
ejpam-6136	63	3	,	,	PUNCT
ejpam-6136	63	4	jade	jade	PROPN
ejpam-6136	63	5	bong	bong	PROPN
ejpam-6136	63	6	m.	m.	PROPN
ejpam-6136	63	7	natuil	natuil	PROPN
ejpam-6136	63	8	,	,	PUNCT
ejpam-6136	63	9	harren	harren	PROPN
ejpam-6136	63	10	j.	j.	PROPN
ejpam-6136	63	11	campos	campos	PROPN
ejpam-6136	63	12	and	and	CCONJ
ejpam-6136	63	13	jezer	jezer	PROPN
ejpam-6136	63	14	c.	c.	PROPN
ejpam-6136	63	15	fernandez	fernandez	PROPN
ejpam-6136	64	1	[	[	X
ejpam-6136	64	2	12	12	NUM
ejpam-6136	64	3	]	]	PUNCT
ejpam-6136	64	4	defined	define	VERB
ejpam-6136	64	5	the	the	DET
ejpam-6136	64	6	degenerate	degenerate	NOUN
ejpam-6136	64	7	of	of	ADP
ejpam-6136	64	8	laplace	laplace	NOUN
ejpam-6136	64	9	-	-	PUNCT
ejpam-6136	64	10	type	type	NOUN
ejpam-6136	64	11	integral	integral	ADJ
ejpam-6136	64	12	transform	transform	NOUN
ejpam-6136	64	13	by	by	ADP
ejpam-6136	64	14	the	the	DET
ejpam-6136	64	15	integral	integral	ADJ
ejpam-6136	64	16	fαλ(u	fαλ(u	NOUN
ejpam-6136	64	17	)	)	PUNCT
ejpam-6136	64	18	=	=	SYM
ejpam-6136	64	19	gαλ{f(t	gαλ{f(t	PROPN
ejpam-6136	64	20	)	)	PUNCT
ejpam-6136	64	21	}	}	PUNCT
ejpam-6136	65	1	=	=	PUNCT
ejpam-6136	65	2	uα	uα	PROPN
ejpam-6136	65	3	∫	∫	PROPN
ejpam-6136	65	4	∞	∞	PROPN
ejpam-6136	65	5	0	0	PUNCT
ejpam-6136	66	1	e	e	NOUN
ejpam-6136	66	2	−	−	PROPN
ejpam-6136	66	3	1	1	NUM
ejpam-6136	66	4	u	u	NOUN
ejpam-6136	66	5	λ	λ	PROPN
ejpam-6136	66	6	(	(	PUNCT
ejpam-6136	66	7	t	t	NOUN
ejpam-6136	66	8	)	)	PUNCT
ejpam-6136	66	9	f(t)dt	f(t)dt	PROPN
ejpam-6136	66	10	=	=	PUNCT
ejpam-6136	66	11	uα	uα	PROPN
ejpam-6136	66	12	∫	∫	PROPN
ejpam-6136	66	13	∞	∞	PROPN
ejpam-6136	66	14	0	0	NUM
ejpam-6136	67	1	(	(	PUNCT
ejpam-6136	67	2	1	1	NUM
ejpam-6136	67	3	+	+	CCONJ
ejpam-6136	67	4	λt)−	λt)−	PROPN
ejpam-6136	67	5	1	1	X
ejpam-6136	67	6	uλ	uλ	ADP
ejpam-6136	67	7	f(t)dt	f(t)dt	PROPN
ejpam-6136	67	8	.	.	PROPN
ejpam-6136	67	9	presented	present	VERB
ejpam-6136	67	10	below	below	ADV
ejpam-6136	67	11	are	be	AUX
ejpam-6136	67	12	the	the	DET
ejpam-6136	67	13	laplace	laplace	NOUN
ejpam-6136	67	14	-	-	PUNCT
ejpam-6136	67	15	type	type	NOUN
ejpam-6136	67	16	integral	integral	ADJ
ejpam-6136	67	17	transform	transform	NOUN
ejpam-6136	67	18	of	of	ADP
ejpam-6136	67	19	some	some	DET
ejpam-6136	67	20	elementary	elementary	ADJ
ejpam-6136	67	21	functions	function	NOUN
ejpam-6136	67	22	that	that	PRON
ejpam-6136	67	23	are	be	AUX
ejpam-6136	67	24	well	well	ADV
ejpam-6136	67	25	-	-	PUNCT
ejpam-6136	67	26	discussed	discuss	VERB
ejpam-6136	67	27	in	in	ADP
ejpam-6136	67	28	:	:	PUNCT
ejpam-6136	67	29	f(t	f(t	NOUN
ejpam-6136	67	30	)	)	PUNCT
ejpam-6136	67	31	gαλ{f(t	gαλ{f(t	PROPN
ejpam-6136	67	32	)	)	PUNCT
ejpam-6136	67	33	}	}	PUNCT
ejpam-6136	67	34	1	1	NUM
ejpam-6136	67	35	uα+1	uα+1	NUM
ejpam-6136	67	36	1−uλ	1−uλ	NUM
ejpam-6136	67	37	tn(0	tn(0	PROPN
ejpam-6136	67	38	,	,	PUNCT
ejpam-6136	67	39	1	1	NUM
ejpam-6136	67	40	,	,	PUNCT
ejpam-6136	67	41	2	2	NUM
ejpam-6136	67	42	,	,	PUNCT
ejpam-6136	67	43	...	...	PUNCT
ejpam-6136	67	44	)	)	PUNCT
ejpam-6136	68	1	n!uα+1+n	n!uα+1+n	INTJ
ejpam-6136	68	2	(	(	PUNCT
ejpam-6136	68	3	1−uλ)	1−uλ)	NUM
ejpam-6136	68	4	...	...	SYM
ejpam-6136	68	5	(1−(n+1)uλ	(1−(n+1)uλ	NUM
ejpam-6136	68	6	)	)	PUNCT
ejpam-6136	69	1	t	t	NOUN
ejpam-6136	69	2	uα+2	uα+2	NUM
ejpam-6136	69	3	(	(	PUNCT
ejpam-6136	69	4	1−uλ)(1−2uλ	1−uλ)(1−2uλ	NUM
ejpam-6136	69	5	)	)	PUNCT
ejpam-6136	69	6	eaλt	eaλt	NOUN
ejpam-6136	69	7	uα+1	uα+1	ADV
ejpam-6136	69	8	1	1	NUM
ejpam-6136	69	9	−u(a+λ	−u(a+λ	NOUN
ejpam-6136	69	10	)	)	PUNCT
ejpam-6136	69	11	f(t	f(t	NOUN
ejpam-6136	69	12	)	)	PUNCT
ejpam-6136	69	13	gαλ{f(t	gαλ{f(t	PROPN
ejpam-6136	69	14	)	)	PUNCT
ejpam-6136	69	15	}	}	PUNCT
ejpam-6136	69	16	sin	sin	NOUN
ejpam-6136	69	17	(	(	PUNCT
ejpam-6136	69	18	a	a	X
ejpam-6136	69	19	)	)	PUNCT
ejpam-6136	69	20	λ	λ	PROPN
ejpam-6136	69	21	t	t	PROPN
ejpam-6136	69	22	auα+2	auα+2	PROPN
ejpam-6136	69	23	(	(	PUNCT
ejpam-6136	69	24	1−λu)2+u2a2	1−λu)2+u2a2	NUM
ejpam-6136	69	25	cos	cos	X
ejpam-6136	69	26	(	(	PUNCT
ejpam-6136	69	27	a	a	X
ejpam-6136	69	28	)	)	PUNCT
ejpam-6136	69	29	λ	λ	PROPN
ejpam-6136	69	30	t	t	PROPN
ejpam-6136	69	31	(	(	PUNCT
ejpam-6136	69	32	1−λu)uα+1	1−λu)uα+1	NUM
ejpam-6136	69	33	(	(	PUNCT
ejpam-6136	69	34	1−λu)2+u2a2	1−λu)2+u2a2	NUM
ejpam-6136	69	35	sinh	sinh	NOUN
ejpam-6136	69	36	(	(	PUNCT
ejpam-6136	69	37	a	a	X
ejpam-6136	69	38	)	)	PUNCT
ejpam-6136	69	39	λ	λ	PROPN
ejpam-6136	69	40	t	t	PROPN
ejpam-6136	69	41	auα+2	auα+2	PROPN
ejpam-6136	69	42	(	(	PUNCT
ejpam-6136	69	43	1−λu)2−u2a2	1−λu)2−u2a2	NUM
ejpam-6136	69	44	cosh	cosh	NOUN
ejpam-6136	69	45	(	(	PUNCT
ejpam-6136	69	46	a	a	X
ejpam-6136	69	47	)	)	PUNCT
ejpam-6136	69	48	λ	λ	PROPN
ejpam-6136	69	49	t	t	PROPN
ejpam-6136	69	50	(	(	PUNCT
ejpam-6136	69	51	1−λu)uα+1	1−λu)uα+1	NUM
ejpam-6136	69	52	(	(	PUNCT
ejpam-6136	69	53	1−λu)2−u2a2	1−λu)2−u2a2	NUM
ejpam-6136	69	54	in	in	ADP
ejpam-6136	69	55	2021	2021	NUM
ejpam-6136	69	56	,	,	PUNCT
ejpam-6136	69	57	a.	a.	NOUN
ejpam-6136	69	58	kalavati	kalavati	PROPN
ejpam-6136	69	59	,	,	PUNCT
ejpam-6136	69	60	t.	t.	PROPN
ejpam-6136	69	61	kohali	kohali	PROPN
ejpam-6136	69	62	,	,	PUNCT
ejpam-6136	69	63	and	and	CCONJ
ejpam-6136	69	64	l.m	l.m	PROPN
ejpam-6136	69	65	.	.	PROPN
ejpam-6136	69	66	upadhyaya	upadhyaya	PROPN
ejpam-6136	70	1	[	[	X
ejpam-6136	70	2	13	13	NUM
ejpam-6136	70	3	]	]	PUNCT
ejpam-6136	70	4	defined	define	VERB
ejpam-6136	70	5	the	the	DET
ejpam-6136	70	6	degenerate	degenerate	NOUN
ejpam-6136	70	7	of	of	ADP
ejpam-6136	70	8	elzaki	elzaki	NOUN
ejpam-6136	70	9	transform	transform	NOUN
ejpam-6136	70	10	by	by	ADP
ejpam-6136	70	11	the	the	DET
ejpam-6136	70	12	integral	integral	ADJ
ejpam-6136	70	13	eλ{f(t	eλ{f(t	NOUN
ejpam-6136	70	14	)	)	PUNCT
ejpam-6136	70	15	}	}	PUNCT
ejpam-6136	71	1	=	=	SYM
ejpam-6136	71	2	u	u	NOUN
ejpam-6136	71	3	∫	∫	PROPN
ejpam-6136	71	4	∞	∞	PROPN
ejpam-6136	71	5	0	0	PUNCT
ejpam-6136	72	1	e	e	NOUN
ejpam-6136	72	2	−	−	PROPN
ejpam-6136	72	3	1	1	NUM
ejpam-6136	72	4	u	u	NOUN
ejpam-6136	72	5	λ	λ	X
ejpam-6136	72	6	(	(	PUNCT
ejpam-6136	72	7	t)f(t)dt	t)f(t)dt	NOUN
ejpam-6136	72	8	=	=	SYM
ejpam-6136	72	9	u	u	NOUN
ejpam-6136	72	10	∫	∫	PROPN
ejpam-6136	72	11	∞	∞	PROPN
ejpam-6136	72	12	0	0	NUM
ejpam-6136	73	1	(	(	PUNCT
ejpam-6136	73	2	1	1	NUM
ejpam-6136	73	3	+	+	CCONJ
ejpam-6136	73	4	λt)−	λt)−	PROPN
ejpam-6136	73	5	1	1	X
ejpam-6136	73	6	uλ	uλ	ADP
ejpam-6136	73	7	f(t)dt	f(t)dt	PROPN
ejpam-6136	73	8	.	.	PROPN
ejpam-6136	73	9	below	below	ADV
ejpam-6136	73	10	are	be	AUX
ejpam-6136	73	11	the	the	DET
ejpam-6136	73	12	degenerate	degenerate	ADJ
ejpam-6136	73	13	elzaki	elzaki	NOUN
ejpam-6136	73	14	integral	integral	ADJ
ejpam-6136	73	15	transform	transform	NOUN
ejpam-6136	73	16	of	of	ADP
ejpam-6136	73	17	some	some	DET
ejpam-6136	73	18	elementary	elementary	ADJ
ejpam-6136	73	19	functions	function	NOUN
ejpam-6136	73	20	f(t	f(t	NOUN
ejpam-6136	73	21	):	):	PUNCT
ejpam-6136	73	22	f(t	f(t	NOUN
ejpam-6136	73	23	)	)	PUNCT
ejpam-6136	73	24	eλ{f(t	eλ{f(t	NOUN
ejpam-6136	73	25	)	)	PUNCT
ejpam-6136	73	26	}	}	PUNCT
ejpam-6136	73	27	1	1	NUM
ejpam-6136	73	28	u2	u2	PROPN
ejpam-6136	73	29	1−λu	1−λu	PROPN
ejpam-6136	73	30	cos	cos	X
ejpam-6136	73	31	(	(	PUNCT
ejpam-6136	73	32	a	a	X
ejpam-6136	73	33	)	)	PUNCT
ejpam-6136	73	34	λ	λ	PROPN
ejpam-6136	73	35	(	(	PUNCT
ejpam-6136	73	36	t	t	PROPN
ejpam-6136	73	37	)	)	PUNCT
ejpam-6136	73	38	(	(	PUNCT
ejpam-6136	73	39	1−uλ)u2	1−uλ)u2	NUM
ejpam-6136	73	40	(	(	PUNCT
ejpam-6136	73	41	1−uλ)2+u2a2	1−uλ)2+u2a2	NUM
ejpam-6136	73	42	t	t	NOUN
ejpam-6136	73	43	u3	u3	NOUN
ejpam-6136	73	44	(	(	PUNCT
ejpam-6136	73	45	1−λ)(1−2λu	1−λ)(1−2λu	NUM
ejpam-6136	73	46	)	)	PUNCT
ejpam-6136	73	47	tn(n	tn(n	NUM
ejpam-6136	74	1	=	=	SYM
ejpam-6136	74	2	0	0	NUM
ejpam-6136	74	3	,	,	PUNCT
ejpam-6136	74	4	1	1	NUM
ejpam-6136	74	5	,	,	PUNCT
ejpam-6136	74	6	...	...	PUNCT
ejpam-6136	74	7	)	)	PUNCT
ejpam-6136	75	1	n!un+2	n!un+2	PRON
ejpam-6136	75	2	(	(	PUNCT
ejpam-6136	75	3	1−λu)	1−λu)	NUM
ejpam-6136	75	4	...	...	SYM
ejpam-6136	75	5	(1−(n+1)λu	(1−(n+1)λu	NOUN
ejpam-6136	75	6	)	)	PUNCT
ejpam-6136	75	7	f(t	f(t	NOUN
ejpam-6136	75	8	)	)	PUNCT
ejpam-6136	75	9	eλ{f(t	eλ{f(t	NOUN
ejpam-6136	75	10	)	)	PUNCT
ejpam-6136	75	11	}	}	PUNCT
ejpam-6136	75	12	cosh	cosh	NOUN
ejpam-6136	75	13	(	(	PUNCT
ejpam-6136	75	14	a	a	X
ejpam-6136	75	15	)	)	PUNCT
ejpam-6136	75	16	λ	λ	PROPN
ejpam-6136	75	17	(	(	PUNCT
ejpam-6136	75	18	t	t	PROPN
ejpam-6136	75	19	)	)	PUNCT
ejpam-6136	75	20	(	(	PUNCT
ejpam-6136	75	21	1−uλ)u2	1−uλ)u2	NUM
ejpam-6136	75	22	(	(	PUNCT
ejpam-6136	75	23	1−λu)2−u2a2	1−λu)2−u2a2	NUM
ejpam-6136	75	24	eaλ(t	eaλ(t	X
ejpam-6136	75	25	)	)	PUNCT
ejpam-6136	75	26	u2	u2	PROPN
ejpam-6136	75	27	1−u(a+λ	1−u(a+λ	NOUN
ejpam-6136	75	28	)	)	PUNCT
ejpam-6136	75	29	sin	sin	NOUN
ejpam-6136	75	30	(	(	PUNCT
ejpam-6136	75	31	a	a	X
ejpam-6136	75	32	)	)	PUNCT
ejpam-6136	75	33	λ	λ	PROPN
ejpam-6136	75	34	(	(	PUNCT
ejpam-6136	75	35	t	t	PROPN
ejpam-6136	75	36	)	)	PUNCT
ejpam-6136	75	37	au3	au3	NOUN
ejpam-6136	75	38	(	(	PUNCT
ejpam-6136	75	39	1−uλ)2+u2a2	1−uλ)2+u2a2	NUM
ejpam-6136	75	40	sinh	sinh	NOUN
ejpam-6136	75	41	(	(	PUNCT
ejpam-6136	75	42	a	a	NOUN
ejpam-6136	75	43	)	)	PUNCT
ejpam-6136	75	44	λ	λ	PROPN
ejpam-6136	75	45	(	(	PUNCT
ejpam-6136	75	46	t	t	PROPN
ejpam-6136	75	47	)	)	PUNCT
ejpam-6136	75	48	au3	au3	NOUN
ejpam-6136	75	49	(	(	PUNCT
ejpam-6136	75	50	1−λu)2−u2a2	1−λu)2−u2a2	NUM
ejpam-6136	75	51	j.	j.	PROPN
ejpam-6136	75	52	mohamadali	mohamadali	PROPN
ejpam-6136	75	53	,	,	PUNCT
ejpam-6136	75	54	n.	n.	PROPN
ejpam-6136	75	55	abdulcarim	abdulcarim	PROPN
ejpam-6136	75	56	/	/	SYM
ejpam-6136	75	57	eur	eur	PROPN
ejpam-6136	75	58	.	.	PUNCT
ejpam-6136	76	1	j.	j.	PROPN
ejpam-6136	76	2	pure	pure	PROPN
ejpam-6136	76	3	appl	appl	PROPN
ejpam-6136	76	4	.	.	PROPN
ejpam-6136	76	5	math	math	PROPN
ejpam-6136	76	6	,	,	PUNCT
ejpam-6136	76	7	18	18	NUM
ejpam-6136	76	8	(	(	PUNCT
ejpam-6136	76	9	3	3	NUM
ejpam-6136	76	10	)	)	PUNCT
ejpam-6136	76	11	(	(	PUNCT
ejpam-6136	76	12	2025	2025	NUM
ejpam-6136	76	13	)	)	PUNCT
ejpam-6136	76	14	,	,	PUNCT
ejpam-6136	76	15	6136	6136	NUM
ejpam-6136	76	16	5	5	NUM
ejpam-6136	76	17	of	of	ADP
ejpam-6136	76	18	19	19	NUM
ejpam-6136	76	19	note	note	NOUN
ejpam-6136	76	20	that	that	SCONJ
ejpam-6136	76	21	limλ→0	limλ→0	PROPN
ejpam-6136	76	22	eλ{f(t	eλ{f(t	PROPN
ejpam-6136	76	23	)	)	PUNCT
ejpam-6136	76	24	}	}	PUNCT
ejpam-6136	76	25	=	=	SYM
ejpam-6136	76	26	e{f(t	e{f(t	NOUN
ejpam-6136	76	27	)	)	PUNCT
ejpam-6136	76	28	}	}	PUNCT
ejpam-6136	76	29	.	.	PUNCT
ejpam-6136	77	1	in	in	ADP
ejpam-6136	77	2	2020	2020	NUM
ejpam-6136	77	3	,	,	PUNCT
ejpam-6136	77	4	duran	duran	NOUN
ejpam-6136	77	5	of	of	ADP
ejpam-6136	77	6	iskenderun	iskenderun	PROPN
ejpam-6136	77	7	technical	technical	ADJ
ejpam-6136	77	8	university	university	NOUN
ejpam-6136	78	1	[	[	X
ejpam-6136	78	2	14	14	NUM
ejpam-6136	78	3	]	]	PUNCT
ejpam-6136	78	4	defined	define	VERB
ejpam-6136	78	5	the	the	DET
ejpam-6136	78	6	degenerate	degenerate	NOUN
ejpam-6136	78	7	of	of	ADP
ejpam-6136	78	8	sumudu	sumudu	NOUN
ejpam-6136	78	9	transform	transform	NOUN
ejpam-6136	78	10	by	by	ADP
ejpam-6136	78	11	the	the	DET
ejpam-6136	78	12	integral	integral	ADJ
ejpam-6136	78	13	gλ{(u	gλ{(u	NOUN
ejpam-6136	78	14	)	)	PUNCT
ejpam-6136	78	15	}	}	PUNCT
ejpam-6136	78	16	=	=	SYM
ejpam-6136	78	17	sλ{f(t	sλ{f(t	NOUN
ejpam-6136	78	18	)	)	PUNCT
ejpam-6136	78	19	}	}	PUNCT
ejpam-6136	78	20	=	=	SYM
ejpam-6136	78	21	1	1	NUM
ejpam-6136	78	22	u	u	NOUN
ejpam-6136	78	23	∫	∫	PROPN
ejpam-6136	78	24	∞	∞	NOUN
ejpam-6136	78	25	0	0	PUNCT
ejpam-6136	79	1	e	e	NOUN
ejpam-6136	79	2	−1	−1	NOUN
ejpam-6136	79	3	u	u	X
ejpam-6136	79	4	λ	λ	X
ejpam-6136	79	5	(	(	PUNCT
ejpam-6136	79	6	t)dt	t)dt	PROPN
ejpam-6136	79	7	,	,	PUNCT
ejpam-6136	79	8	u	u	NOUN
ejpam-6136	79	9	∈	∈	PROPN
ejpam-6136	79	10	(	(	PUNCT
ejpam-6136	79	11	−τ1	−τ1	PROPN
ejpam-6136	79	12	,	,	PUNCT
ejpam-6136	79	13	τ2	τ2	NOUN
ejpam-6136	79	14	)	)	PUNCT
ejpam-6136	79	15	.	.	PUNCT
ejpam-6136	80	1	the	the	DET
ejpam-6136	80	2	degenerate	degenerate	ADJ
ejpam-6136	80	3	sumudu	sumudu	NOUN
ejpam-6136	80	4	transform	transform	NOUN
ejpam-6136	80	5	satisfies	satisfie	NOUN
ejpam-6136	80	6	the	the	DET
ejpam-6136	80	7	following	follow	VERB
ejpam-6136	80	8	operational	operational	ADJ
ejpam-6136	80	9	properties	property	NOUN
ejpam-6136	80	10	and	and	CCONJ
ejpam-6136	80	11	the	the	DET
ejpam-6136	80	12	transform	transform	NOUN
ejpam-6136	80	13	of	of	ADP
ejpam-6136	80	14	some	some	DET
ejpam-6136	80	15	elementary	elementary	ADJ
ejpam-6136	80	16	function	function	NOUN
ejpam-6136	80	17	f(t	f(t	NOUN
ejpam-6136	80	18	):	):	PUNCT
ejpam-6136	80	19	f(t	f(t	NOUN
ejpam-6136	80	20	)	)	PUNCT
ejpam-6136	80	21	sλ{f(t	sλ{f(t	NOUN
ejpam-6136	80	22	)	)	PUNCT
ejpam-6136	80	23	}	}	PUNCT
ejpam-6136	81	1	1	1	NUM
ejpam-6136	81	2	1	1	NUM
ejpam-6136	81	3	1−λu	1−λu	NUM
ejpam-6136	81	4	tn	tn	NOUN
ejpam-6136	81	5	n!un	n!un	NUM
ejpam-6136	81	6	(	(	PUNCT
ejpam-6136	81	7	1−λu)(1−2λu)	1−λu)(1−2λu)	NUM
ejpam-6136	81	8	...	...	SYM
ejpam-6136	81	9	(1−(n+1)λu	(1−(n+1)λu	NOUN
ejpam-6136	81	10	)	)	PUNCT
ejpam-6136	81	11	t	t	PROPN
ejpam-6136	81	12	u	u	PROPN
ejpam-6136	81	13	(	(	PUNCT
ejpam-6136	81	14	1−λu)(1−2λu	1−λu)(1−2λu	NUM
ejpam-6136	81	15	)	)	PUNCT
ejpam-6136	81	16	eaλt	eaλt	NOUN
ejpam-6136	81	17	1	1	NUM
ejpam-6136	81	18	1	1	NUM
ejpam-6136	81	19	−u(a+λ	−u(a+λ	NUM
ejpam-6136	81	20	)	)	PUNCT
ejpam-6136	81	21	f(t	f(t	NOUN
ejpam-6136	81	22	)	)	PUNCT
ejpam-6136	81	23	sλ{f(t	sλ{f(t	NOUN
ejpam-6136	81	24	)	)	PUNCT
ejpam-6136	81	25	}	}	PUNCT
ejpam-6136	81	26	sin	sin	NOUN
ejpam-6136	81	27	(	(	PUNCT
ejpam-6136	81	28	a	a	X
ejpam-6136	81	29	)	)	PUNCT
ejpam-6136	81	30	λ	λ	PROPN
ejpam-6136	81	31	t	t	NOUN
ejpam-6136	81	32	au	au	X
ejpam-6136	82	1	(	(	PUNCT
ejpam-6136	82	2	1−λu)2+u2a2	1−λu)2+u2a2	NUM
ejpam-6136	82	3	cos	cos	X
ejpam-6136	82	4	(	(	PUNCT
ejpam-6136	82	5	a	a	X
ejpam-6136	82	6	)	)	PUNCT
ejpam-6136	82	7	λ	λ	NOUN
ejpam-6136	82	8	t	t	NOUN
ejpam-6136	82	9	1−uλ	1−uλ	NUM
ejpam-6136	82	10	(	(	PUNCT
ejpam-6136	82	11	1−λu)2+u2a2	1−λu)2+u2a2	NUM
ejpam-6136	82	12	sinh	sinh	NOUN
ejpam-6136	82	13	(	(	PUNCT
ejpam-6136	82	14	a	a	X
ejpam-6136	82	15	)	)	PUNCT
ejpam-6136	82	16	λ	λ	PROPN
ejpam-6136	82	17	t	t	PROPN
ejpam-6136	82	18	au	au	X
ejpam-6136	82	19	(	(	PUNCT
ejpam-6136	82	20	1−λu)2−u2a2	1−λu)2−u2a2	NUM
ejpam-6136	82	21	cosh	cosh	NOUN
ejpam-6136	82	22	(	(	PUNCT
ejpam-6136	82	23	a	a	X
ejpam-6136	82	24	)	)	PUNCT
ejpam-6136	82	25	λ	λ	NOUN
ejpam-6136	82	26	t	t	NOUN
ejpam-6136	82	27	1−uλ	1−uλ	NUM
ejpam-6136	82	28	(	(	PUNCT
ejpam-6136	82	29	1−λu)2−u2a2	1−λu)2−u2a2	NUM
ejpam-6136	82	30	furthermore	furthermore	ADV
ejpam-6136	82	31	,	,	PUNCT
ejpam-6136	82	32	in	in	ADP
ejpam-6136	82	33	2017	2017	NUM
ejpam-6136	82	34	,	,	PUNCT
ejpam-6136	82	35	kim	kim	PROPN
ejpam-6136	82	36	et	et	PROPN
ejpam-6136	82	37	al	al	PROPN
ejpam-6136	83	1	[	[	X
ejpam-6136	83	2	15	15	NUM
ejpam-6136	83	3	]	]	PUNCT
ejpam-6136	83	4	defined	define	VERB
ejpam-6136	83	5	the	the	DET
ejpam-6136	83	6	degenerate	degenerate	ADJ
ejpam-6136	83	7	exponential	exponential	ADJ
ejpam-6136	83	8	function	function	NOUN
ejpam-6136	83	9	as	as	ADP
ejpam-6136	83	10	exλ(t	exλ(t	NOUN
ejpam-6136	83	11	)	)	PUNCT
ejpam-6136	83	12	=	=	PUNCT
ejpam-6136	84	1	(	(	PUNCT
ejpam-6136	84	2	1	1	NUM
ejpam-6136	84	3	+	+	CCONJ
ejpam-6136	84	4	λt	λt	X
ejpam-6136	84	5	)	)	PUNCT
ejpam-6136	84	6	x	x	SYM
ejpam-6136	84	7	λ	λ	NOUN
ejpam-6136	84	8	,	,	PUNCT
ejpam-6136	84	9	eλ(t	eλ(t	ADV
ejpam-6136	84	10	)	)	PUNCT
ejpam-6136	84	11	=	=	SYM
ejpam-6136	84	12	e1λ(t	e1λ(t	NOUN
ejpam-6136	84	13	)	)	PUNCT
ejpam-6136	84	14	=	=	PUNCT
ejpam-6136	85	1	(	(	PUNCT
ejpam-6136	85	2	1	1	NUM
ejpam-6136	85	3	+	+	CCONJ
ejpam-6136	85	4	λt	λt	X
ejpam-6136	85	5	)	)	PUNCT
ejpam-6136	85	6	1	1	NUM
ejpam-6136	85	7	λ	λ	X
ejpam-6136	85	8	(	(	PUNCT
ejpam-6136	85	9	2	2	NUM
ejpam-6136	85	10	)	)	PUNCT
ejpam-6136	85	11	for	for	ADP
ejpam-6136	85	12	λ	λ	PROPN
ejpam-6136	85	13	∈	∈	PROPN
ejpam-6136	85	14	r	r	NOUN
ejpam-6136	85	15	,	,	PUNCT
ejpam-6136	85	16	.	.	PUNCT
ejpam-6136	86	1	here	here	ADV
ejpam-6136	86	2	,	,	PUNCT
ejpam-6136	86	3	we	we	PRON
ejpam-6136	86	4	note	note	VERB
ejpam-6136	86	5	that	that	SCONJ
ejpam-6136	86	6	exλ(t	exλ(t	ADV
ejpam-6136	86	7	)	)	PUNCT
ejpam-6136	86	8	=	=	PUNCT
ejpam-6136	87	1	∞∑	∞∑	NUM
ejpam-6136	87	2	n=0	n=0	NUM
ejpam-6136	87	3	(	(	PUNCT
ejpam-6136	87	4	x)n	x)n	PROPN
ejpam-6136	87	5	,	,	PUNCT
ejpam-6136	87	6	λ	λ	PROPN
ejpam-6136	87	7	tn	tn	NOUN
ejpam-6136	87	8	n	n	X
ejpam-6136	87	9	!	!	PROPN
ejpam-6136	87	10	,	,	PUNCT
ejpam-6136	87	11	where	where	SCONJ
ejpam-6136	87	12	(	(	PUNCT
ejpam-6136	87	13	x)0,λ	x)0,λ	NOUN
ejpam-6136	87	14	=	=	SYM
ejpam-6136	87	15	1	1	NUM
ejpam-6136	87	16	,	,	PUNCT
ejpam-6136	87	17	(	(	PUNCT
ejpam-6136	87	18	x)n	x)n	PROPN
ejpam-6136	87	19	,	,	PUNCT
ejpam-6136	87	20	λ	λ	PROPN
ejpam-6136	87	21	=	=	SYM
ejpam-6136	87	22	x(x−	x(x−	PROPN
ejpam-6136	87	23	λ)(x−	λ)(x−	PROPN
ejpam-6136	87	24	2λ	2λ	NUM
ejpam-6136	87	25	)	)	PUNCT
ejpam-6136	87	26	·	·	PUNCT
ejpam-6136	87	27	·	·	PUNCT
ejpam-6136	87	28	·	·	PUNCT
ejpam-6136	87	29	(	(	PUNCT
ejpam-6136	87	30	x−(n−1)λ	x−(n−1)λ	NUM
ejpam-6136	87	31	)	)	PUNCT
ejpam-6136	87	32	for	for	ADP
ejpam-6136	87	33	n	n	NUM
ejpam-6136	87	34	≥	≥	NOUN
ejpam-6136	87	35	1	1	NUM
ejpam-6136	87	36	and	and	CCONJ
ejpam-6136	87	37	that	that	SCONJ
ejpam-6136	87	38	limλ→0	limλ→0	PROPN
ejpam-6136	87	39	e	e	PROPN
ejpam-6136	87	40	x	x	PROPN
ejpam-6136	87	41	λ(t	λ(t	NOUN
ejpam-6136	87	42	)	)	PUNCT
ejpam-6136	87	43	=	=	SYM
ejpam-6136	87	44	limλ→0(1+λt	limλ→0(1+λt	PROPN
ejpam-6136	87	45	)	)	PUNCT
ejpam-6136	87	46	x	x	SYM
ejpam-6136	87	47	λ	λ	NOUN
ejpam-6136	87	48	=	=	NOUN
ejpam-6136	87	49	ext	ext	NOUN
ejpam-6136	87	50	.	.	PUNCT
ejpam-6136	88	1	in	in	ADP
ejpam-6136	88	2	[	[	X
ejpam-6136	88	3	16	16	NUM
ejpam-6136	88	4	]	]	PUNCT
ejpam-6136	88	5	,	,	PUNCT
ejpam-6136	88	6	the	the	DET
ejpam-6136	88	7	degenerate	degenerate	ADJ
ejpam-6136	88	8	sine	sine	NOUN
ejpam-6136	88	9	and	and	CCONJ
ejpam-6136	88	10	degenerate	degenerate	ADJ
ejpam-6136	88	11	cosine	cosine	NOUN
ejpam-6136	88	12	functions	function	NOUN
ejpam-6136	88	13	are	be	AUX
ejpam-6136	88	14	defined	define	VERB
ejpam-6136	88	15	by	by	ADP
ejpam-6136	88	16	the	the	DET
ejpam-6136	88	17	relations	relation	NOUN
ejpam-6136	88	18	sin	sin	NOUN
ejpam-6136	88	19	(	(	PUNCT
ejpam-6136	88	20	x	x	X
ejpam-6136	88	21	)	)	PUNCT
ejpam-6136	88	22	λ	λ	PROPN
ejpam-6136	88	23	(	(	PUNCT
ejpam-6136	88	24	t	t	PROPN
ejpam-6136	88	25	)	)	PUNCT
ejpam-6136	88	26	=	=	SYM
ejpam-6136	88	27	eixλ	eixλ	PROPN
ejpam-6136	88	28	(	(	PUNCT
ejpam-6136	88	29	t)−	t)−	PROPN
ejpam-6136	88	30	e−ix	e−ix	NOUN
ejpam-6136	88	31	λ	λ	PROPN
ejpam-6136	88	32	(	(	PUNCT
ejpam-6136	88	33	t	t	PROPN
ejpam-6136	88	34	)	)	PUNCT
ejpam-6136	88	35	2i	2i	NOUN
ejpam-6136	88	36	=	=	NOUN
ejpam-6136	88	37	sin	sin	NOUN
ejpam-6136	88	38	(	(	PUNCT
ejpam-6136	88	39	x	x	PART
ejpam-6136	88	40	λ	λ	NOUN
ejpam-6136	88	41	log(1	log(1	NOUN
ejpam-6136	88	42	+	+	CCONJ
ejpam-6136	88	43	λt	λt	X
ejpam-6136	88	44	)	)	PUNCT
ejpam-6136	88	45	)	)	PUNCT
ejpam-6136	88	46	,	,	PUNCT
ejpam-6136	88	47	(	(	PUNCT
ejpam-6136	88	48	3	3	X
ejpam-6136	88	49	)	)	PUNCT
ejpam-6136	88	50	cos	cos	NOUN
ejpam-6136	88	51	(	(	PUNCT
ejpam-6136	88	52	x	x	X
ejpam-6136	88	53	)	)	PUNCT
ejpam-6136	88	54	λ	λ	PROPN
ejpam-6136	88	55	(	(	PUNCT
ejpam-6136	88	56	t	t	PROPN
ejpam-6136	88	57	)	)	PUNCT
ejpam-6136	88	58	=	=	SYM
ejpam-6136	88	59	eixλ	eixλ	PROPN
ejpam-6136	88	60	(	(	PUNCT
ejpam-6136	88	61	t	t	PROPN
ejpam-6136	88	62	)	)	PUNCT
ejpam-6136	89	1	+	+	CCONJ
ejpam-6136	89	2	e−ix	e−ix	PROPN
ejpam-6136	89	3	λ	λ	PROPN
ejpam-6136	89	4	(	(	PUNCT
ejpam-6136	89	5	t	t	PROPN
ejpam-6136	89	6	)	)	PUNCT
ejpam-6136	89	7	2	2	NUM
ejpam-6136	89	8	=	=	SYM
ejpam-6136	89	9	cos	cos	X
ejpam-6136	89	10	(	(	PUNCT
ejpam-6136	89	11	x	x	PART
ejpam-6136	89	12	λ	λ	NOUN
ejpam-6136	89	13	log(1	log(1	NOUN
ejpam-6136	89	14	+	+	CCONJ
ejpam-6136	89	15	λt	λt	X
ejpam-6136	89	16	)	)	PUNCT
ejpam-6136	89	17	)	)	PUNCT
ejpam-6136	89	18	,	,	PUNCT
ejpam-6136	89	19	(	(	PUNCT
ejpam-6136	89	20	4	4	X
ejpam-6136	89	21	)	)	PUNCT
ejpam-6136	89	22	respectively	respectively	ADV
ejpam-6136	89	23	,	,	PUNCT
ejpam-6136	89	24	where	where	SCONJ
ejpam-6136	89	25	i	i	PRON
ejpam-6136	89	26	=	=	VERB
ejpam-6136	89	27	√	√	NUM
ejpam-6136	89	28	−1	−1	NOUN
ejpam-6136	89	29	.	.	PUNCT
ejpam-6136	90	1	in	in	ADP
ejpam-6136	90	2	[	[	X
ejpam-6136	90	3	11	11	NUM
ejpam-6136	90	4	]	]	PUNCT
ejpam-6136	90	5	,	,	PUNCT
ejpam-6136	90	6	the	the	DET
ejpam-6136	90	7	degenerate	degenerate	ADJ
ejpam-6136	90	8	euler	euler	NOUN
ejpam-6136	90	9	function	function	NOUN
ejpam-6136	90	10	is	be	AUX
ejpam-6136	90	11	defined	define	VERB
ejpam-6136	90	12	by	by	ADP
ejpam-6136	90	13	the	the	DET
ejpam-6136	90	14	relation	relation	NOUN
ejpam-6136	90	15	eixλ	eixλ	PROPN
ejpam-6136	90	16	(	(	PUNCT
ejpam-6136	90	17	t	t	PROPN
ejpam-6136	90	18	)	)	PUNCT
ejpam-6136	90	19	=	=	SYM
ejpam-6136	90	20	cos	cos	X
ejpam-6136	90	21	(	(	PUNCT
ejpam-6136	90	22	x	x	X
ejpam-6136	90	23	)	)	PUNCT
ejpam-6136	90	24	λ	λ	PROPN
ejpam-6136	90	25	(	(	PUNCT
ejpam-6136	90	26	t	t	PROPN
ejpam-6136	90	27	)	)	PUNCT
ejpam-6136	91	1	+	+	CCONJ
ejpam-6136	91	2	i	i	PRON
ejpam-6136	91	3	sin	sin	VERB
ejpam-6136	91	4	(	(	PUNCT
ejpam-6136	91	5	x	x	X
ejpam-6136	91	6	)	)	PUNCT
ejpam-6136	91	7	λ	λ	PROPN
ejpam-6136	91	8	(	(	PUNCT
ejpam-6136	91	9	t	t	PROPN
ejpam-6136	91	10	)	)	PUNCT
ejpam-6136	91	11	,	,	PUNCT
ejpam-6136	91	12	(	(	PUNCT
ejpam-6136	91	13	5	5	X
ejpam-6136	91	14	)	)	PUNCT
ejpam-6136	92	1	where	where	SCONJ
ejpam-6136	92	2	cos	cos	PROPN
ejpam-6136	92	3	(	(	PUNCT
ejpam-6136	92	4	x	x	X
ejpam-6136	92	5	)	)	PUNCT
ejpam-6136	92	6	λ	λ	PROPN
ejpam-6136	92	7	(	(	PUNCT
ejpam-6136	92	8	t	t	PROPN
ejpam-6136	92	9	)	)	PUNCT
ejpam-6136	92	10	=	=	SYM
ejpam-6136	92	11	cos	cos	PROPN
ejpam-6136	92	12	(	(	PUNCT
ejpam-6136	92	13	x	x	PART
ejpam-6136	92	14	λ	λ	NOUN
ejpam-6136	92	15	log(1	log(1	NOUN
ejpam-6136	92	16	+	+	CCONJ
ejpam-6136	92	17	λt	λt	X
ejpam-6136	92	18	)	)	PUNCT
ejpam-6136	92	19	)	)	PUNCT
ejpam-6136	92	20	and	and	CCONJ
ejpam-6136	92	21	sin	sin	NOUN
ejpam-6136	92	22	(	(	PUNCT
ejpam-6136	92	23	x	x	NOUN
ejpam-6136	92	24	)	)	PUNCT
ejpam-6136	92	25	λ	λ	PROPN
ejpam-6136	92	26	(	(	PUNCT
ejpam-6136	92	27	t	t	PROPN
ejpam-6136	92	28	)	)	PUNCT
ejpam-6136	92	29	=	=	NOUN
ejpam-6136	92	30	sin	sin	NOUN
ejpam-6136	92	31	(	(	PUNCT
ejpam-6136	92	32	x	x	PUNCT
ejpam-6136	92	33	λ	λ	NOUN
ejpam-6136	92	34	log(1	log(1	NOUN
ejpam-6136	92	35	+	+	CCONJ
ejpam-6136	92	36	λt	λt	X
ejpam-6136	92	37	)	)	PUNCT
ejpam-6136	92	38	)	)	PUNCT
ejpam-6136	92	39	.	.	PUNCT
ejpam-6136	93	1	j.	j.	PROPN
ejpam-6136	93	2	mohamadali	mohamadali	PROPN
ejpam-6136	93	3	,	,	PUNCT
ejpam-6136	93	4	n.	n.	PROPN
ejpam-6136	93	5	abdulcarim	abdulcarim	PROPN
ejpam-6136	93	6	/	/	SYM
ejpam-6136	93	7	eur	eur	PROPN
ejpam-6136	93	8	.	.	PUNCT
ejpam-6136	94	1	j.	j.	PROPN
ejpam-6136	94	2	pure	pure	PROPN
ejpam-6136	94	3	appl	appl	PROPN
ejpam-6136	94	4	.	.	PROPN
ejpam-6136	94	5	math	math	PROPN
ejpam-6136	94	6	,	,	PUNCT
ejpam-6136	94	7	18	18	NUM
ejpam-6136	94	8	(	(	PUNCT
ejpam-6136	94	9	3	3	NUM
ejpam-6136	94	10	)	)	PUNCT
ejpam-6136	94	11	(	(	PUNCT
ejpam-6136	94	12	2025	2025	NUM
ejpam-6136	94	13	)	)	PUNCT
ejpam-6136	94	14	,	,	PUNCT
ejpam-6136	94	15	6136	6136	NUM
ejpam-6136	94	16	6	6	NUM
ejpam-6136	94	17	of	of	ADP
ejpam-6136	94	18	19	19	NUM
ejpam-6136	94	19	in	in	ADP
ejpam-6136	94	20	[	[	X
ejpam-6136	94	21	14	14	NUM
ejpam-6136	94	22	]	]	PUNCT
ejpam-6136	94	23	,	,	PUNCT
ejpam-6136	94	24	the	the	DET
ejpam-6136	94	25	degenerate	degenerate	ADJ
ejpam-6136	94	26	hyperbolic	hyperbolic	ADJ
ejpam-6136	94	27	sine	sine	NOUN
ejpam-6136	94	28	and	and	CCONJ
ejpam-6136	94	29	degenerate	degenerate	ADJ
ejpam-6136	94	30	hyperbolic	hyperbolic	ADJ
ejpam-6136	94	31	cosine	cosine	NOUN
ejpam-6136	94	32	functions	function	NOUN
ejpam-6136	94	33	are	be	AUX
ejpam-6136	94	34	defined	define	VERB
ejpam-6136	94	35	by	by	ADP
ejpam-6136	94	36	the	the	DET
ejpam-6136	94	37	relations	relation	NOUN
ejpam-6136	94	38	sinh	sinh	NOUN
ejpam-6136	94	39	(	(	PUNCT
ejpam-6136	94	40	x	x	X
ejpam-6136	94	41	)	)	PUNCT
ejpam-6136	94	42	λ	λ	PROPN
ejpam-6136	94	43	(	(	PUNCT
ejpam-6136	94	44	t	t	PROPN
ejpam-6136	94	45	)	)	PUNCT
ejpam-6136	94	46	=	=	PUNCT
ejpam-6136	94	47	exλ(t)−	exλ(t)−	PROPN
ejpam-6136	94	48	e−x	e−x	PROPN
ejpam-6136	94	49	λ	λ	PROPN
ejpam-6136	94	50	(	(	PUNCT
ejpam-6136	94	51	t	t	PROPN
ejpam-6136	94	52	)	)	PUNCT
ejpam-6136	94	53	2	2	NUM
ejpam-6136	94	54	(	(	PUNCT
ejpam-6136	94	55	6	6	NUM
ejpam-6136	94	56	)	)	PUNCT
ejpam-6136	94	57	cosh	cosh	NOUN
ejpam-6136	94	58	(	(	PUNCT
ejpam-6136	94	59	x	x	X
ejpam-6136	94	60	)	)	PUNCT
ejpam-6136	94	61	λ	λ	PROPN
ejpam-6136	94	62	(	(	PUNCT
ejpam-6136	94	63	t	t	PROPN
ejpam-6136	94	64	)	)	PUNCT
ejpam-6136	94	65	=	=	SYM
ejpam-6136	94	66	exλ(t	exλ(t	PROPN
ejpam-6136	94	67	)	)	PUNCT
ejpam-6136	94	68	+	+	NUM
ejpam-6136	94	69	e−x	e−x	PROPN
ejpam-6136	94	70	λ	λ	PROPN
ejpam-6136	94	71	(	(	PUNCT
ejpam-6136	94	72	t	t	PROPN
ejpam-6136	94	73	)	)	PUNCT
ejpam-6136	94	74	2	2	NUM
ejpam-6136	94	75	,	,	PUNCT
ejpam-6136	94	76	(	(	PUNCT
ejpam-6136	94	77	7	7	X
ejpam-6136	94	78	)	)	PUNCT
ejpam-6136	94	79	respectively	respectively	ADV
ejpam-6136	94	80	.	.	PUNCT
ejpam-6136	95	1	3	3	X
ejpam-6136	95	2	.	.	X
ejpam-6136	95	3	main	main	ADJ
ejpam-6136	95	4	results	result	NOUN
ejpam-6136	95	5	this	this	DET
ejpam-6136	95	6	section	section	NOUN
ejpam-6136	95	7	presents	present	VERB
ejpam-6136	95	8	definition	definition	NOUN
ejpam-6136	95	9	of	of	ADP
ejpam-6136	95	10	the	the	DET
ejpam-6136	95	11	degenerate	degenerate	ADJ
ejpam-6136	95	12	sadik	sadik	PROPN
ejpam-6136	95	13	transform	transform	NOUN
ejpam-6136	95	14	.	.	PUNCT
ejpam-6136	96	1	moreover	moreover	ADV
ejpam-6136	96	2	,	,	PUNCT
ejpam-6136	96	3	discussions	discussion	NOUN
ejpam-6136	96	4	on	on	ADP
ejpam-6136	96	5	some	some	DET
ejpam-6136	96	6	elementary	elementary	ADJ
ejpam-6136	96	7	functions	function	NOUN
ejpam-6136	96	8	of	of	ADP
ejpam-6136	96	9	the	the	DET
ejpam-6136	96	10	degenerate	degenerate	ADJ
ejpam-6136	96	11	sadik	sadik	PROPN
ejpam-6136	96	12	transform	transform	NOUN
ejpam-6136	96	13	are	be	AUX
ejpam-6136	96	14	also	also	ADV
ejpam-6136	96	15	provided	provide	VERB
ejpam-6136	96	16	.	.	PUNCT
ejpam-6136	97	1	definition	definition	NOUN
ejpam-6136	97	2	1	1	NUM
ejpam-6136	97	3	.	.	PUNCT
ejpam-6136	98	1	let	let	VERB
ejpam-6136	98	2	λ	λ	X
ejpam-6136	98	3	∈	∈	PROPN
ejpam-6136	98	4	(	(	PUNCT
ejpam-6136	98	5	0,∞	0,∞	NOUN
ejpam-6136	98	6	)	)	PUNCT
ejpam-6136	98	7	and	and	CCONJ
ejpam-6136	98	8	let	let	VERB
ejpam-6136	98	9	f(t	f(t	NOUN
ejpam-6136	98	10	)	)	PUNCT
ejpam-6136	98	11	be	be	VERB
ejpam-6136	98	12	a	a	DET
ejpam-6136	98	13	function	function	NOUN
ejpam-6136	98	14	defined	define	VERB
ejpam-6136	98	15	for	for	ADP
ejpam-6136	98	16	t	t	PROPN
ejpam-6136	98	17	≥	≥	NOUN
ejpam-6136	98	18	0	0	NUM
ejpam-6136	98	19	.	.	PUNCT
ejpam-6136	99	1	then	then	ADV
ejpam-6136	99	2	the	the	DET
ejpam-6136	99	3	integral	integral	ADJ
ejpam-6136	99	4	fλ(u	fλ(u	PUNCT
ejpam-6136	99	5	α	α	NOUN
ejpam-6136	99	6	,	,	PUNCT
ejpam-6136	99	7	β	β	NOUN
ejpam-6136	99	8	)	)	PUNCT
ejpam-6136	99	9	=	=	SYM
ejpam-6136	99	10	sλ{f(t	sλ{f(t	NOUN
ejpam-6136	99	11	)	)	PUNCT
ejpam-6136	99	12	}	}	PUNCT
ejpam-6136	99	13	=	=	SYM
ejpam-6136	99	14	1	1	NUM
ejpam-6136	99	15	uβ	uβ	NOUN
ejpam-6136	99	16	∫	∫	PROPN
ejpam-6136	99	17	∞	∞	PROPN
ejpam-6136	99	18	0	0	NUM
ejpam-6136	99	19	e−uα	e−uα	PROPN
ejpam-6136	99	20	λ	λ	PROPN
ejpam-6136	99	21	(	(	PUNCT
ejpam-6136	99	22	t)f(t)dt	t)f(t)dt	NOUN
ejpam-6136	99	23	=	=	SYM
ejpam-6136	99	24	1	1	NUM
ejpam-6136	99	25	uβ	uβ	NOUN
ejpam-6136	99	26	∫	∫	PROPN
ejpam-6136	99	27	∞	∞	PROPN
ejpam-6136	99	28	0	0	NUM
ejpam-6136	100	1	(	(	PUNCT
ejpam-6136	100	2	1	1	NUM
ejpam-6136	100	3	+	+	CCONJ
ejpam-6136	100	4	λt)−	λt)−	X
ejpam-6136	100	5	uα	uα	X
ejpam-6136	100	6	λ	λ	X
ejpam-6136	100	7	f(t)dt	f(t)dt	X
ejpam-6136	100	8	(	(	PUNCT
ejpam-6136	100	9	8)	8)	NUM
ejpam-6136	100	10	is	be	AUX
ejpam-6136	100	11	said	say	VERB
ejpam-6136	100	12	to	to	PART
ejpam-6136	100	13	be	be	AUX
ejpam-6136	100	14	the	the	DET
ejpam-6136	100	15	degenerate	degenerate	ADJ
ejpam-6136	100	16	sadik	sadik	ADJ
ejpam-6136	100	17	transform	transform	NOUN
ejpam-6136	100	18	of	of	ADP
ejpam-6136	100	19	f(t	f(t	NOUN
ejpam-6136	100	20	)	)	PUNCT
ejpam-6136	100	21	.	.	PUNCT
ejpam-6136	101	1	if	if	SCONJ
ejpam-6136	101	2	the	the	DET
ejpam-6136	101	3	improper	improper	ADJ
ejpam-6136	101	4	integral	integral	NOUN
ejpam-6136	101	5	is	be	AUX
ejpam-6136	101	6	convergent	convergent	NOUN
ejpam-6136	101	7	,	,	PUNCT
ejpam-6136	101	8	then	then	ADV
ejpam-6136	101	9	we	we	PRON
ejpam-6136	101	10	say	say	VERB
ejpam-6136	101	11	that	that	SCONJ
ejpam-6136	101	12	the	the	DET
ejpam-6136	101	13	function	function	NOUN
ejpam-6136	101	14	f(t	f(t	NOUN
ejpam-6136	101	15	)	)	PUNCT
ejpam-6136	101	16	possesses	possess	VERB
ejpam-6136	101	17	as	as	ADP
ejpam-6136	101	18	a	a	DET
ejpam-6136	101	19	degenerate	degenerate	ADJ
ejpam-6136	101	20	sadik	sadik	PROPN
ejpam-6136	101	21	transform	transform	NOUN
ejpam-6136	101	22	.	.	PUNCT
ejpam-6136	102	1	now	now	ADV
ejpam-6136	102	2	,	,	PUNCT
ejpam-6136	102	3	observe	observe	VERB
ejpam-6136	102	4	that	that	SCONJ
ejpam-6136	102	5	,	,	PUNCT
ejpam-6136	102	6	if	if	SCONJ
ejpam-6136	102	7	the	the	DET
ejpam-6136	102	8	degenerate	degenerate	ADJ
ejpam-6136	102	9	sadik	sadik	ADJ
ejpam-6136	102	10	transform	transform	NOUN
ejpam-6136	102	11	of	of	ADP
ejpam-6136	102	12	f(t	f(t	NOUN
ejpam-6136	102	13	)	)	PUNCT
ejpam-6136	102	14	exists	exist	VERB
ejpam-6136	102	15	,	,	PUNCT
ejpam-6136	102	16	then	then	ADV
ejpam-6136	102	17	from	from	ADP
ejpam-6136	102	18	the	the	DET
ejpam-6136	102	19	above	above	ADJ
ejpam-6136	102	20	definition	definition	NOUN
ejpam-6136	102	21	,	,	PUNCT
ejpam-6136	102	22	lim	lim	NOUN
ejpam-6136	102	23	λ→0	λ→0	ADV
ejpam-6136	102	24	sλ{f(t	sλ{f(t	NOUN
ejpam-6136	102	25	)	)	PUNCT
ejpam-6136	102	26	}	}	PUNCT
ejpam-6136	103	1	=	=	SYM
ejpam-6136	103	2	lim	lim	PROPN
ejpam-6136	103	3	λ→0	λ→0	PUNCT
ejpam-6136	103	4	[	[	PUNCT
ejpam-6136	103	5	1	1	NUM
ejpam-6136	103	6	uβ	uβ	NOUN
ejpam-6136	103	7	∫	∫	PROPN
ejpam-6136	103	8	∞	∞	PROPN
ejpam-6136	103	9	0	0	NUM
ejpam-6136	103	10	e−uα	e−uα	PROPN
ejpam-6136	103	11	λ	λ	PROPN
ejpam-6136	103	12	(	(	PUNCT
ejpam-6136	103	13	t)f(t)dt	t)f(t)dt	NOUN
ejpam-6136	103	14	]	]	X
ejpam-6136	103	15	=	=	SYM
ejpam-6136	103	16	1	1	NUM
ejpam-6136	104	1	uβ	uβ	NOUN
ejpam-6136	104	2	∫	∫	PROPN
ejpam-6136	104	3	∞	∞	PROPN
ejpam-6136	104	4	0	0	NUM
ejpam-6136	105	1	e−uα	e−uα	PROPN
ejpam-6136	105	2	(	(	PUNCT
ejpam-6136	105	3	t)f(t)dt	t)f(t)dt	NOUN
ejpam-6136	105	4	=	=	SYM
ejpam-6136	105	5	s{f(t	s{f(t	NUM
ejpam-6136	105	6	)	)	PUNCT
ejpam-6136	105	7	}	}	PUNCT
ejpam-6136	105	8	.	.	PUNCT
ejpam-6136	106	1	remark	remark	NOUN
ejpam-6136	106	2	1	1	NUM
ejpam-6136	106	3	.	.	PUNCT
ejpam-6136	106	4	m	m	PROPN
ejpam-6136	106	5	1	1	NUM
ejpam-6136	106	6	.	.	PUNCT
ejpam-6136	107	1	when	when	SCONJ
ejpam-6136	107	2	β	β	X
ejpam-6136	107	3	=	=	NOUN
ejpam-6136	107	4	0	0	NUM
ejpam-6136	107	5	and	and	CCONJ
ejpam-6136	107	6	α	α	NOUN
ejpam-6136	107	7	=	=	NOUN
ejpam-6136	107	8	1	1	NUM
ejpam-6136	107	9	in	in	ADP
ejpam-6136	107	10	equation	equation	NOUN
ejpam-6136	107	11	(	(	PUNCT
ejpam-6136	107	12	8)	8)	NUM
ejpam-6136	107	13	,	,	PUNCT
ejpam-6136	107	14	sλ{f(t	sλ{f(t	NOUN
ejpam-6136	107	15	)	)	PUNCT
ejpam-6136	107	16	}	}	PUNCT
ejpam-6136	107	17	=	=	SYM
ejpam-6136	107	18	1	1	NUM
ejpam-6136	107	19	u0	u0	ADJ
ejpam-6136	107	20	∫	∫	PROPN
ejpam-6136	107	21	∞	∞	PROPN
ejpam-6136	107	22	0	0	NUM
ejpam-6136	107	23	e−u	e−u	PROPN
ejpam-6136	107	24	λ	λ	PROPN
ejpam-6136	107	25	(	(	PUNCT
ejpam-6136	107	26	t)f(t	t)f(t	VERB
ejpam-6136	107	27	)	)	PUNCT
ejpam-6136	107	28	dt	dt	NOUN
ejpam-6136	107	29	=	=	SYM
ejpam-6136	107	30	lλ{f(t	lλ{f(t	NOUN
ejpam-6136	107	31	)	)	PUNCT
ejpam-6136	107	32	}	}	PUNCT
ejpam-6136	107	33	.	.	PUNCT
ejpam-6136	108	1	2	2	X
ejpam-6136	108	2	.	.	X
ejpam-6136	108	3	when	when	SCONJ
ejpam-6136	108	4	β	β	X
ejpam-6136	108	5	=	=	VERB
ejpam-6136	108	6	−1	−1	NOUN
ejpam-6136	108	7	and	and	CCONJ
ejpam-6136	108	8	α	α	NOUN
ejpam-6136	108	9	=	=	SYM
ejpam-6136	108	10	−1	−1	NOUN
ejpam-6136	108	11	in	in	ADP
ejpam-6136	108	12	equation	equation	NOUN
ejpam-6136	108	13	(	(	PUNCT
ejpam-6136	108	14	8)	8)	NUM
ejpam-6136	108	15	,	,	PUNCT
ejpam-6136	108	16	sλ{f(t	sλ{f(t	NOUN
ejpam-6136	108	17	)	)	PUNCT
ejpam-6136	108	18	}	}	PUNCT
ejpam-6136	108	19	=	=	SYM
ejpam-6136	108	20	1	1	NUM
ejpam-6136	108	21	u−1	u−1	PROPN
ejpam-6136	108	22	∫	∫	PROPN
ejpam-6136	108	23	∞	∞	NOUN
ejpam-6136	108	24	0	0	NUM
ejpam-6136	109	1	e−u−1	e−u−1	PROPN
ejpam-6136	109	2	λ	λ	PROPN
ejpam-6136	109	3	(	(	PUNCT
ejpam-6136	109	4	t)f(t	t)f(t	VERB
ejpam-6136	109	5	)	)	PUNCT
ejpam-6136	109	6	dt	dt	NOUN
ejpam-6136	109	7	=	=	SYM
ejpam-6136	109	8	eλ{f(t	eλ{f(t	NOUN
ejpam-6136	109	9	)	)	PUNCT
ejpam-6136	109	10	}	}	PUNCT
ejpam-6136	109	11	.	.	PUNCT
ejpam-6136	110	1	3	3	X
ejpam-6136	110	2	.	.	X
ejpam-6136	110	3	when	when	SCONJ
ejpam-6136	110	4	β	β	X
ejpam-6136	110	5	=	=	SYM
ejpam-6136	110	6	1	1	NUM
ejpam-6136	110	7	and	and	CCONJ
ejpam-6136	110	8	α	α	NOUN
ejpam-6136	110	9	=	=	SYM
ejpam-6136	110	10	−1	−1	NOUN
ejpam-6136	110	11	in	in	ADP
ejpam-6136	110	12	equation	equation	NOUN
ejpam-6136	110	13	(	(	PUNCT
ejpam-6136	110	14	8)	8)	NUM
ejpam-6136	110	15	,	,	PUNCT
ejpam-6136	110	16	sλ{f(t	sλ{f(t	NOUN
ejpam-6136	110	17	)	)	PUNCT
ejpam-6136	110	18	}	}	PUNCT
ejpam-6136	110	19	=	=	SYM
ejpam-6136	110	20	1	1	NUM
ejpam-6136	110	21	u1	u1	NOUN
ejpam-6136	110	22	∫	∫	PROPN
ejpam-6136	110	23	∞	∞	NOUN
ejpam-6136	110	24	0	0	NUM
ejpam-6136	111	1	e−u−1	e−u−1	PROPN
ejpam-6136	111	2	λ	λ	PROPN
ejpam-6136	111	3	(	(	PUNCT
ejpam-6136	111	4	t)f(t	t)f(t	VERB
ejpam-6136	111	5	)	)	PUNCT
ejpam-6136	111	6	dt	dt	NOUN
ejpam-6136	111	7	=	=	SYM
ejpam-6136	111	8	sλ{f(t	sλ{f(t	PROPN
ejpam-6136	111	9	)	)	PUNCT
ejpam-6136	111	10	}	}	PUNCT
ejpam-6136	111	11	.	.	PUNCT
ejpam-6136	112	1	j.	j.	PROPN
ejpam-6136	112	2	mohamadali	mohamadali	PROPN
ejpam-6136	112	3	,	,	PUNCT
ejpam-6136	112	4	n.	n.	PROPN
ejpam-6136	112	5	abdulcarim	abdulcarim	PROPN
ejpam-6136	112	6	/	/	SYM
ejpam-6136	112	7	eur	eur	PROPN
ejpam-6136	112	8	.	.	PUNCT
ejpam-6136	113	1	j.	j.	PROPN
ejpam-6136	113	2	pure	pure	PROPN
ejpam-6136	113	3	appl	appl	PROPN
ejpam-6136	113	4	.	.	PROPN
ejpam-6136	113	5	math	math	PROPN
ejpam-6136	113	6	,	,	PUNCT
ejpam-6136	113	7	18	18	NUM
ejpam-6136	113	8	(	(	PUNCT
ejpam-6136	113	9	3	3	NUM
ejpam-6136	113	10	)	)	PUNCT
ejpam-6136	113	11	(	(	PUNCT
ejpam-6136	113	12	2025	2025	NUM
ejpam-6136	113	13	)	)	PUNCT
ejpam-6136	113	14	,	,	PUNCT
ejpam-6136	113	15	6136	6136	NUM
ejpam-6136	113	16	7	7	NUM
ejpam-6136	113	17	of	of	ADP
ejpam-6136	113	18	19	19	NUM
ejpam-6136	113	19	4	4	NUM
ejpam-6136	113	20	.	.	PUNCT
ejpam-6136	114	1	when	when	SCONJ
ejpam-6136	114	2	β	β	X
ejpam-6136	114	3	=	=	SYM
ejpam-6136	114	4	−α	−α	PROPN
ejpam-6136	114	5	and	and	CCONJ
ejpam-6136	114	6	α	α	NOUN
ejpam-6136	114	7	=	=	SYM
ejpam-6136	114	8	−1	−1	NOUN
ejpam-6136	114	9	in	in	ADP
ejpam-6136	114	10	equation	equation	NOUN
ejpam-6136	114	11	(	(	PUNCT
ejpam-6136	114	12	8)	8)	NUM
ejpam-6136	114	13	,	,	PUNCT
ejpam-6136	114	14	gαλ{f(t	gαλ{f(t	PROPN
ejpam-6136	114	15	)	)	PUNCT
ejpam-6136	114	16	}	}	PUNCT
ejpam-6136	115	1	=	=	SYM
ejpam-6136	115	2	1	1	NUM
ejpam-6136	115	3	u−α	u−α	NUM
ejpam-6136	115	4	∫	∫	PROPN
ejpam-6136	115	5	∞	∞	NOUN
ejpam-6136	115	6	0	0	NUM
ejpam-6136	116	1	e−u−1	e−u−1	PROPN
ejpam-6136	116	2	λ	λ	PROPN
ejpam-6136	116	3	(	(	PUNCT
ejpam-6136	116	4	t)f(t	t)f(t	VERB
ejpam-6136	116	5	)	)	PUNCT
ejpam-6136	116	6	dt	dt	NOUN
ejpam-6136	116	7	=	=	PUNCT
ejpam-6136	116	8	gαλ{f(t	gαλ{f(t	PROPN
ejpam-6136	116	9	)	)	PUNCT
ejpam-6136	116	10	}	}	PUNCT
ejpam-6136	116	11	.	.	PUNCT
ejpam-6136	117	1	the	the	DET
ejpam-6136	117	2	following	follow	VERB
ejpam-6136	117	3	theorem	theorem	NOUN
ejpam-6136	117	4	is	be	AUX
ejpam-6136	117	5	a	a	DET
ejpam-6136	117	6	sufficient	sufficient	ADJ
ejpam-6136	117	7	condition	condition	NOUN
ejpam-6136	117	8	for	for	ADP
ejpam-6136	117	9	the	the	DET
ejpam-6136	117	10	existence	existence	NOUN
ejpam-6136	117	11	of	of	ADP
ejpam-6136	117	12	degenerate	degenerate	ADJ
ejpam-6136	117	13	sadik	sadik	PROPN
ejpam-6136	117	14	transform	transform	NOUN
ejpam-6136	117	15	theorem	theorem	NOUN
ejpam-6136	117	16	1	1	X
ejpam-6136	117	17	.	.	PUNCT
ejpam-6136	117	18	suppose	suppose	VERB
ejpam-6136	117	19	that	that	SCONJ
ejpam-6136	117	20	f(t	f(t	PROPN
ejpam-6136	117	21	)	)	PUNCT
ejpam-6136	117	22	is	be	AUX
ejpam-6136	117	23	a	a	DET
ejpam-6136	117	24	piecewise	piecewise	NOUN
ejpam-6136	117	25	-	-	PUNCT
ejpam-6136	117	26	continuous	continuous	ADJ
ejpam-6136	117	27	function	function	NOUN
ejpam-6136	117	28	on	on	ADP
ejpam-6136	117	29	the	the	DET
ejpam-6136	117	30	interval	interval	NOUN
ejpam-6136	117	31	[	[	X
ejpam-6136	117	32	0,∞	0,∞	NOUN
ejpam-6136	117	33	)	)	PUNCT
ejpam-6136	117	34	and	and	CCONJ
ejpam-6136	117	35	of	of	ADP
ejpam-6136	117	36	degenerate	degenerate	ADJ
ejpam-6136	117	37	exponential	exponential	ADJ
ejpam-6136	117	38	order	order	NOUN
ejpam-6136	117	39	at	at	ADP
ejpam-6136	117	40	infinity	infinity	NOUN
ejpam-6136	117	41	with	with	ADP
ejpam-6136	117	42	|f(t)|	|f(t)|	PROPN
ejpam-6136	117	43	≤	≤	ADJ
ejpam-6136	117	44	mecλ(t	mecλ(t	NOUN
ejpam-6136	117	45	)	)	PUNCT
ejpam-6136	117	46	for	for	ADP
ejpam-6136	117	47	t	t	PROPN
ejpam-6136	117	48	>	>	X
ejpam-6136	117	49	p	p	X
ejpam-6136	117	50	,	,	PUNCT
ejpam-6136	117	51	where	where	SCONJ
ejpam-6136	117	52	m	m	PROPN
ejpam-6136	117	53	≥	≥	VERB
ejpam-6136	117	54	0	0	NUM
ejpam-6136	117	55	and	and	CCONJ
ejpam-6136	117	56	p	p	X
ejpam-6136	117	57	,	,	PUNCT
ejpam-6136	117	58	c	c	PROPN
ejpam-6136	117	59	are	be	AUX
ejpam-6136	117	60	constants	constant	NOUN
ejpam-6136	117	61	.	.	PUNCT
ejpam-6136	118	1	then	then	ADV
ejpam-6136	118	2	sλ{f(t	sλ{f(t	NOUN
ejpam-6136	118	3	)	)	PUNCT
ejpam-6136	118	4	}	}	PUNCT
ejpam-6136	118	5	exists	exist	VERB
ejpam-6136	118	6	for	for	ADP
ejpam-6136	118	7	−uα	−uα	PROPN
ejpam-6136	118	8	+	+	PROPN
ejpam-6136	118	9	c	c	NOUN
ejpam-6136	118	10	λ	λ	NOUN
ejpam-6136	119	1	+	+	NOUN
ejpam-6136	119	2	1	1	NUM
ejpam-6136	119	3	<	<	X
ejpam-6136	119	4	0	0	NUM
ejpam-6136	119	5	.	.	PUNCT
ejpam-6136	120	1	proof	proof	NOUN
ejpam-6136	120	2	.	.	PUNCT
ejpam-6136	121	1	suppose	suppose	VERB
ejpam-6136	121	2	that	that	SCONJ
ejpam-6136	121	3	f(t	f(t	PROPN
ejpam-6136	121	4	)	)	PUNCT
ejpam-6136	121	5	is	be	AUX
ejpam-6136	121	6	a	a	DET
ejpam-6136	121	7	piecewise	piecewise	NOUN
ejpam-6136	121	8	-	-	PUNCT
ejpam-6136	121	9	continuous	continuous	ADJ
ejpam-6136	121	10	function	function	NOUN
ejpam-6136	121	11	on	on	ADP
ejpam-6136	121	12	the	the	DET
ejpam-6136	121	13	interval	interval	NOUN
ejpam-6136	121	14	[	[	X
ejpam-6136	121	15	0,∞	0,∞	NOUN
ejpam-6136	121	16	)	)	PUNCT
ejpam-6136	121	17	and	and	CCONJ
ejpam-6136	121	18	has	have	VERB
ejpam-6136	121	19	degenerate	degenerate	ADJ
ejpam-6136	121	20	exponential	exponential	ADJ
ejpam-6136	121	21	order	order	NOUN
ejpam-6136	121	22	at	at	ADP
ejpam-6136	121	23	infinity	infinity	NOUN
ejpam-6136	121	24	with	with	ADP
ejpam-6136	121	25	|f(t)|	|f(t)|	PROPN
ejpam-6136	121	26	≤	≤	ADJ
ejpam-6136	121	27	mecλ(t	mecλ(t	NOUN
ejpam-6136	121	28	)	)	PUNCT
ejpam-6136	121	29	.	.	PUNCT
ejpam-6136	122	1	then	then	ADV
ejpam-6136	122	2	,	,	PUNCT
ejpam-6136	122	3	1	1	NUM
ejpam-6136	122	4	uβ	uβ	NOUN
ejpam-6136	122	5	∫	∫	PROPN
ejpam-6136	122	6	∞	∞	PROPN
ejpam-6136	122	7	0	0	NUM
ejpam-6136	122	8	e−uα	e−uα	PROPN
ejpam-6136	122	9	λ	λ	PROPN
ejpam-6136	122	10	(	(	PUNCT
ejpam-6136	122	11	t)f(t	t)f(t	VERB
ejpam-6136	122	12	)	)	PUNCT
ejpam-6136	122	13	dt	dt	NOUN
ejpam-6136	122	14	=	=	SYM
ejpam-6136	122	15	1	1	NUM
ejpam-6136	123	1	uβ	uβ	NOUN
ejpam-6136	123	2	∫	∫	PROPN
ejpam-6136	124	1	p	p	NOUN
ejpam-6136	124	2	0	0	NUM
ejpam-6136	124	3	e−uα	e−uα	PROPN
ejpam-6136	124	4	λ	λ	PROPN
ejpam-6136	124	5	(	(	PUNCT
ejpam-6136	124	6	t)f(t	t)f(t	VERB
ejpam-6136	124	7	)	)	PUNCT
ejpam-6136	124	8	dt+	dt+	NOUN
ejpam-6136	124	9	1	1	NUM
ejpam-6136	124	10	uβ	uβ	NOUN
ejpam-6136	124	11	∫	∫	PROPN
ejpam-6136	124	12	∞	∞	PROPN
ejpam-6136	124	13	p	p	PROPN
ejpam-6136	124	14	e−uα	e−uα	PROPN
ejpam-6136	124	15	λ	λ	PROPN
ejpam-6136	124	16	(	(	PUNCT
ejpam-6136	124	17	t)f(t	t)f(t	VERB
ejpam-6136	124	18	)	)	PUNCT
ejpam-6136	124	19	dt	dt	NOUN
ejpam-6136	124	20	.	.	PUNCT
ejpam-6136	125	1	(	(	PUNCT
ejpam-6136	125	2	9	9	NUM
ejpam-6136	125	3	)	)	PUNCT
ejpam-6136	125	4	since	since	SCONJ
ejpam-6136	125	5	the	the	DET
ejpam-6136	125	6	function	function	NOUN
ejpam-6136	125	7	f(t	f(t	NOUN
ejpam-6136	125	8	)	)	PUNCT
ejpam-6136	125	9	is	be	AUX
ejpam-6136	125	10	piecewise	piecewise	NOUN
ejpam-6136	125	11	-	-	PUNCT
ejpam-6136	125	12	continuous	continuous	ADJ
ejpam-6136	125	13	in	in	ADP
ejpam-6136	125	14	every	every	DET
ejpam-6136	125	15	finite	finite	ADJ
ejpam-6136	125	16	interval	interval	NOUN
ejpam-6136	125	17	0	0	NUM
ejpam-6136	125	18	≤	≤	NUM
ejpam-6136	125	19	t	t	NOUN
ejpam-6136	125	20	≤	≤	ADJ
ejpam-6136	125	21	p	p	NOUN
ejpam-6136	125	22	,	,	PUNCT
ejpam-6136	125	23	the	the	DET
ejpam-6136	125	24	first	first	ADJ
ejpam-6136	125	25	integral	integral	NOUN
ejpam-6136	125	26	on	on	ADP
ejpam-6136	125	27	the	the	DET
ejpam-6136	125	28	right	right	ADJ
ejpam-6136	125	29	hand	hand	NOUN
ejpam-6136	125	30	side	side	NOUN
ejpam-6136	125	31	of	of	ADP
ejpam-6136	125	32	equation	equation	NOUN
ejpam-6136	125	33	(	(	PUNCT
ejpam-6136	125	34	9	9	X
ejpam-6136	125	35	)	)	PUNCT
ejpam-6136	125	36	exists	exist	VERB
ejpam-6136	125	37	.	.	PUNCT
ejpam-6136	126	1	now	now	ADV
ejpam-6136	126	2	,	,	PUNCT
ejpam-6136	126	3	we	we	PRON
ejpam-6136	126	4	will	will	AUX
ejpam-6136	126	5	show	show	VERB
ejpam-6136	126	6	that	that	SCONJ
ejpam-6136	126	7	the	the	DET
ejpam-6136	126	8	second	second	ADJ
ejpam-6136	126	9	integral	integral	NOUN
ejpam-6136	126	10	on	on	ADP
ejpam-6136	126	11	the	the	DET
ejpam-6136	126	12	right	right	ADJ
ejpam-6136	126	13	hand	hand	NOUN
ejpam-6136	126	14	side	side	NOUN
ejpam-6136	126	15	also	also	ADV
ejpam-6136	126	16	exists	exist	VERB
ejpam-6136	126	17	.	.	PUNCT
ejpam-6136	127	1	note	note	VERB
ejpam-6136	127	2	that	that	SCONJ
ejpam-6136	127	3	for	for	ADP
ejpam-6136	127	4	t	t	PROPN
ejpam-6136	127	5	>	>	PUNCT
ejpam-6136	127	6	p,∣∣e−uα	p,∣∣e−uα	PROPN
ejpam-6136	127	7	λ	λ	PROPN
ejpam-6136	127	8	(	(	PUNCT
ejpam-6136	127	9	t)f(t	t)f(t	VERB
ejpam-6136	127	10	)	)	PUNCT
ejpam-6136	127	11	∣∣	∣∣	NUM
ejpam-6136	127	12	≤	≤	NUM
ejpam-6136	127	13	e−uα	e−uα	PROPN
ejpam-6136	127	14	λ	λ	PROPN
ejpam-6136	127	15	(	(	PUNCT
ejpam-6136	127	16	t	t	PROPN
ejpam-6136	127	17	)	)	PUNCT
ejpam-6136	127	18	mecλ(t	mecλ(t	PROPN
ejpam-6136	127	19	)	)	PUNCT
ejpam-6136	127	20	.	.	PUNCT
ejpam-6136	128	1	thus	thus	ADV
ejpam-6136	128	2	,	,	PUNCT
ejpam-6136	128	3	1	1	NUM
ejpam-6136	128	4	uβ	uβ	NOUN
ejpam-6136	128	5	∫	∫	PROPN
ejpam-6136	128	6	∞	∞	PROPN
ejpam-6136	128	7	p	p	PROPN
ejpam-6136	128	8	∣∣e−uα	∣∣e−uα	PROPN
ejpam-6136	128	9	λ	λ	PROPN
ejpam-6136	128	10	(	(	PUNCT
ejpam-6136	128	11	t)f(t	t)f(t	VERB
ejpam-6136	128	12	)	)	PUNCT
ejpam-6136	128	13	∣∣	∣∣	NUM
ejpam-6136	128	14	dt	dt	X
ejpam-6136	128	15	≤	≤	NUM
ejpam-6136	128	16	1	1	NUM
ejpam-6136	128	17	uβ	uβ	NOUN
ejpam-6136	128	18	∫	∫	PROPN
ejpam-6136	128	19	∞	∞	PROPN
ejpam-6136	129	1	p	p	PROPN
ejpam-6136	129	2	e−uα	e−uα	PROPN
ejpam-6136	129	3	λ	λ	PROPN
ejpam-6136	129	4	(	(	PUNCT
ejpam-6136	129	5	t)mecλ(t	t)mecλ(t	NOUN
ejpam-6136	129	6	)	)	PUNCT
ejpam-6136	129	7	dt	dt	NOUN
ejpam-6136	130	1	=	=	NOUN
ejpam-6136	130	2	m	m	VERB
ejpam-6136	130	3	uβ	uβ	PROPN
ejpam-6136	130	4	lim	lim	PROPN
ejpam-6136	130	5	r→∞	r→∞	PUNCT
ejpam-6136	130	6	∫	∫	PROPN
ejpam-6136	130	7	r	r	PROPN
ejpam-6136	130	8	p	p	PROPN
ejpam-6136	130	9	(	(	PUNCT
ejpam-6136	130	10	1	1	NUM
ejpam-6136	130	11	+	+	CCONJ
ejpam-6136	130	12	λt	λt	X
ejpam-6136	130	13	)	)	PUNCT
ejpam-6136	130	14	−uα+c	−uα+c	NOUN
ejpam-6136	130	15	λ	λ	X
ejpam-6136	131	1	dt	dt	PROPN
ejpam-6136	131	2	.	.	PUNCT
ejpam-6136	131	3	evaluation	evaluation	NOUN
ejpam-6136	131	4	the	the	DET
ejpam-6136	131	5	right	right	ADJ
ejpam-6136	131	6	-	-	PUNCT
ejpam-6136	131	7	hand	hand	NOUN
ejpam-6136	131	8	side	side	NOUN
ejpam-6136	131	9	of	of	ADP
ejpam-6136	131	10	the	the	DET
ejpam-6136	131	11	above	above	ADJ
ejpam-6136	131	12	equation	equation	NOUN
ejpam-6136	131	13	,	,	PUNCT
ejpam-6136	131	14	we	we	PRON
ejpam-6136	131	15	can	can	AUX
ejpam-6136	131	16	see	see	VERB
ejpam-6136	131	17	that	that	SCONJ
ejpam-6136	131	18	the	the	DET
ejpam-6136	131	19	integral	integral	ADJ
ejpam-6136	131	20	converges	converge	NOUN
ejpam-6136	131	21	for	for	ADP
ejpam-6136	131	22	−uα	−uα	PROPN
ejpam-6136	131	23	+	+	PROPN
ejpam-6136	131	24	c	c	NOUN
ejpam-6136	131	25	λ	λ	NOUN
ejpam-6136	132	1	+	+	NOUN
ejpam-6136	132	2	1	1	NUM
ejpam-6136	132	3	<	<	X
ejpam-6136	132	4	0	0	NUM
ejpam-6136	132	5	.	.	PUNCT
ejpam-6136	133	1	since	since	SCONJ
ejpam-6136	133	2	both	both	CCONJ
ejpam-6136	133	3	the	the	DET
ejpam-6136	133	4	integrals	integral	NOUN
ejpam-6136	133	5	on	on	ADP
ejpam-6136	133	6	the	the	DET
ejpam-6136	133	7	right	right	ADJ
ejpam-6136	133	8	hand	hand	NOUN
ejpam-6136	133	9	equation	equation	NOUN
ejpam-6136	133	10	(	(	PUNCT
ejpam-6136	133	11	9	9	X
ejpam-6136	133	12	)	)	PUNCT
ejpam-6136	133	13	converges	converge	NOUN
ejpam-6136	133	14	for	for	ADP
ejpam-6136	133	15	−uα	−uα	PROPN
ejpam-6136	133	16	+	+	PROPN
ejpam-6136	133	17	c	c	NOUN
ejpam-6136	133	18	λ	λ	NOUN
ejpam-6136	133	19	+	+	NOUN
ejpam-6136	133	20	1	1	NUM
ejpam-6136	133	21	<	<	X
ejpam-6136	133	22	0	0	NUM
ejpam-6136	133	23	,	,	PUNCT
ejpam-6136	133	24	f(t	f(t	PROPN
ejpam-6136	133	25	)	)	PUNCT
ejpam-6136	133	26	has	have	VERB
ejpam-6136	133	27	a	a	DET
ejpam-6136	133	28	degenerate	degenerate	ADJ
ejpam-6136	133	29	sadik	sadik	ADJ
ejpam-6136	133	30	transform	transform	NOUN
ejpam-6136	133	31	for	for	ADP
ejpam-6136	133	32	−uα	−uα	PRON
ejpam-6136	133	33	+	+	PROPN
ejpam-6136	133	34	c	c	NOUN
ejpam-6136	133	35	λ	λ	NOUN
ejpam-6136	134	1	+	+	NOUN
ejpam-6136	134	2	1	1	NUM
ejpam-6136	134	3	<	<	X
ejpam-6136	134	4	0	0	NUM
ejpam-6136	134	5	.	.	PUNCT
ejpam-6136	135	1	the	the	DET
ejpam-6136	135	2	following	follow	VERB
ejpam-6136	135	3	theorem	theorem	NOUN
ejpam-6136	135	4	is	be	AUX
ejpam-6136	135	5	the	the	DET
ejpam-6136	135	6	linearity	linearity	NOUN
ejpam-6136	135	7	property	property	NOUN
ejpam-6136	135	8	of	of	ADP
ejpam-6136	135	9	the	the	DET
ejpam-6136	135	10	degenerate	degenerate	ADJ
ejpam-6136	135	11	sadik	sadik	PROPN
ejpam-6136	135	12	transform	transform	NOUN
ejpam-6136	135	13	theorem	theorem	NOUN
ejpam-6136	135	14	2	2	X
ejpam-6136	135	15	.	.	PUNCT
ejpam-6136	136	1	let	let	VERB
ejpam-6136	136	2	a	a	DET
ejpam-6136	136	3	,	,	PUNCT
ejpam-6136	136	4	b	b	X
ejpam-6136	136	5	∈	∈	NOUN
ejpam-6136	136	6	r	r	NOUN
ejpam-6136	136	7	and	and	CCONJ
ejpam-6136	136	8	let	let	VERB
ejpam-6136	136	9	f(t	f(t	NOUN
ejpam-6136	136	10	)	)	PUNCT
ejpam-6136	136	11	and	and	CCONJ
ejpam-6136	136	12	g(t	g(t	PROPN
ejpam-6136	136	13	)	)	PUNCT
ejpam-6136	136	14	be	be	AUX
ejpam-6136	136	15	functions	function	NOUN
ejpam-6136	136	16	whose	whose	DET
ejpam-6136	136	17	degenerate	degenerate	ADJ
ejpam-6136	136	18	sadik	sadik	ADJ
ejpam-6136	136	19	transform	transform	NOUN
ejpam-6136	136	20	exist	exist	VERB
ejpam-6136	136	21	,	,	PUNCT
ejpam-6136	136	22	then	then	ADV
ejpam-6136	136	23	sλ[af(t	sλ[af(t	NUM
ejpam-6136	136	24	)	)	PUNCT
ejpam-6136	136	25	+	+	NUM
ejpam-6136	136	26	bg(t	bg(t	NUM
ejpam-6136	136	27	)	)	PUNCT
ejpam-6136	136	28	]	]	PUNCT
ejpam-6136	137	1	=	=	PUNCT
ejpam-6136	137	2	asλ[f(t	asλ[f(t	NOUN
ejpam-6136	137	3	)	)	PUNCT
ejpam-6136	137	4	]	]	PUNCT
ejpam-6136	138	1	+	+	CCONJ
ejpam-6136	138	2	bsλ[g(t	bsλ[g(t	X
ejpam-6136	138	3	)	)	PUNCT
ejpam-6136	138	4	]	]	PUNCT
ejpam-6136	138	5	proof	proof	NOUN
ejpam-6136	138	6	.	.	PUNCT
ejpam-6136	139	1	let	let	VERB
ejpam-6136	139	2	a	a	DET
ejpam-6136	139	3	,	,	PUNCT
ejpam-6136	139	4	b	b	X
ejpam-6136	139	5	∈	∈	NOUN
ejpam-6136	139	6	r	r	NOUN
ejpam-6136	139	7	and	and	CCONJ
ejpam-6136	139	8	let	let	VERB
ejpam-6136	139	9	f(t	f(t	NOUN
ejpam-6136	139	10	)	)	PUNCT
ejpam-6136	139	11	and	and	CCONJ
ejpam-6136	139	12	g(t	g(t	PROPN
ejpam-6136	139	13	)	)	PUNCT
ejpam-6136	139	14	be	be	VERB
ejpam-6136	139	15	any	any	DET
ejpam-6136	139	16	function	function	NOUN
ejpam-6136	139	17	whose	whose	DET
ejpam-6136	139	18	degenerate	degenerate	ADJ
ejpam-6136	139	19	sadik	sadik	ADJ
ejpam-6136	139	20	transform	transform	NOUN
ejpam-6136	139	21	exist	exist	VERB
ejpam-6136	139	22	,	,	PUNCT
ejpam-6136	139	23	then	then	ADV
ejpam-6136	139	24	sλ{af(t	sλ{af(t	PROPN
ejpam-6136	139	25	)	)	PUNCT
ejpam-6136	139	26	+	+	NUM
ejpam-6136	139	27	bg(t	bg(t	NUM
ejpam-6136	139	28	)	)	PUNCT
ejpam-6136	139	29	}	}	PUNCT
ejpam-6136	139	30	=	=	SYM
ejpam-6136	140	1	1	1	NUM
ejpam-6136	140	2	uβ	uβ	NOUN
ejpam-6136	140	3	∫	∫	PROPN
ejpam-6136	140	4	∞	∞	PROPN
ejpam-6136	140	5	0	0	NUM
ejpam-6136	140	6	e−uα	e−uα	PROPN
ejpam-6136	140	7	λ	λ	PROPN
ejpam-6136	140	8	(	(	PUNCT
ejpam-6136	140	9	t	t	PROPN
ejpam-6136	140	10	)	)	PUNCT
ejpam-6136	140	11	{	{	PUNCT
ejpam-6136	140	12	af(t	af(t	ADV
ejpam-6136	140	13	)	)	PUNCT
ejpam-6136	140	14	+	+	NUM
ejpam-6136	140	15	bg(t	bg(t	NUM
ejpam-6136	140	16	)	)	PUNCT
ejpam-6136	140	17	}	}	PUNCT
ejpam-6136	140	18	dt	dt	ADP
ejpam-6136	140	19	j.	j.	PROPN
ejpam-6136	140	20	mohamadali	mohamadali	PROPN
ejpam-6136	140	21	,	,	PUNCT
ejpam-6136	140	22	n.	n.	PROPN
ejpam-6136	140	23	abdulcarim	abdulcarim	PROPN
ejpam-6136	140	24	/	/	SYM
ejpam-6136	140	25	eur	eur	PROPN
ejpam-6136	140	26	.	.	PUNCT
ejpam-6136	141	1	j.	j.	PROPN
ejpam-6136	141	2	pure	pure	PROPN
ejpam-6136	141	3	appl	appl	PROPN
ejpam-6136	141	4	.	.	PROPN
ejpam-6136	141	5	math	math	PROPN
ejpam-6136	141	6	,	,	PUNCT
ejpam-6136	141	7	18	18	NUM
ejpam-6136	141	8	(	(	PUNCT
ejpam-6136	141	9	3	3	NUM
ejpam-6136	141	10	)	)	PUNCT
ejpam-6136	141	11	(	(	PUNCT
ejpam-6136	141	12	2025	2025	NUM
ejpam-6136	141	13	)	)	PUNCT
ejpam-6136	141	14	,	,	PUNCT
ejpam-6136	141	15	6136	6136	NUM
ejpam-6136	141	16	8	8	NUM
ejpam-6136	141	17	of	of	ADP
ejpam-6136	141	18	19	19	NUM
ejpam-6136	141	19	=	=	NOUN
ejpam-6136	141	20	a	a	DET
ejpam-6136	141	21	1	1	NUM
ejpam-6136	141	22	uβ	uβ	NOUN
ejpam-6136	141	23	∫	∫	PROPN
ejpam-6136	141	24	∞	∞	PROPN
ejpam-6136	141	25	0	0	NUM
ejpam-6136	141	26	e−uα	e−uα	PROPN
ejpam-6136	141	27	λ	λ	PROPN
ejpam-6136	141	28	(	(	PUNCT
ejpam-6136	141	29	t	t	NOUN
ejpam-6136	141	30	)	)	PUNCT
ejpam-6136	141	31	f(t	f(t	NOUN
ejpam-6136	141	32	)	)	PUNCT
ejpam-6136	141	33	dt+	dt+	NOUN
ejpam-6136	141	34	b	b	NOUN
ejpam-6136	141	35	1	1	NUM
ejpam-6136	142	1	uβ	uβ	NOUN
ejpam-6136	142	2	∫	∫	PROPN
ejpam-6136	143	1	∞	∞	PROPN
ejpam-6136	143	2	0	0	NUM
ejpam-6136	143	3	e−uα	e−uα	PROPN
ejpam-6136	143	4	λ	λ	PROPN
ejpam-6136	143	5	(	(	PUNCT
ejpam-6136	143	6	t	t	PROPN
ejpam-6136	143	7	)	)	PUNCT
ejpam-6136	143	8	g(t	g(t	PROPN
ejpam-6136	143	9	)	)	PUNCT
ejpam-6136	143	10	dt	dt	PUNCT
ejpam-6136	144	1	=	=	NOUN
ejpam-6136	144	2	a	a	PRON
ejpam-6136	144	3	sλ{f(t)}+	sλ{f(t)}+	NOUN
ejpam-6136	144	4	b	b	X
ejpam-6136	144	5	sλ{g(t	sλ{g(t	NOUN
ejpam-6136	144	6	)	)	PUNCT
ejpam-6136	144	7	}	}	PUNCT
ejpam-6136	144	8	.	.	PUNCT
ejpam-6136	145	1	the	the	DET
ejpam-6136	145	2	following	follow	VERB
ejpam-6136	145	3	results	result	NOUN
ejpam-6136	145	4	are	be	AUX
ejpam-6136	145	5	some	some	PRON
ejpam-6136	145	6	of	of	ADP
ejpam-6136	145	7	the	the	DET
ejpam-6136	145	8	elementary	elementary	ADJ
ejpam-6136	145	9	functions	function	NOUN
ejpam-6136	145	10	of	of	ADP
ejpam-6136	145	11	the	the	DET
ejpam-6136	145	12	degenerate	degenerate	ADJ
ejpam-6136	145	13	sadik	sadik	PROPN
ejpam-6136	145	14	transform	transform	NOUN
ejpam-6136	145	15	.	.	PUNCT
ejpam-6136	146	1	theorem	theorem	NOUN
ejpam-6136	146	2	3	3	NUM
ejpam-6136	146	3	.	.	PUNCT
ejpam-6136	147	1	the	the	DET
ejpam-6136	147	2	degenerate	degenerate	ADJ
ejpam-6136	147	3	sadik	sadik	PROPN
ejpam-6136	147	4	transform	transform	NOUN
ejpam-6136	147	5	of	of	ADP
ejpam-6136	147	6	the	the	DET
ejpam-6136	147	7	function	function	NOUN
ejpam-6136	147	8	f(t	f(t	NOUN
ejpam-6136	147	9	)	)	PUNCT
ejpam-6136	147	10	=	=	SYM
ejpam-6136	147	11	1	1	NUM
ejpam-6136	147	12	is	be	AUX
ejpam-6136	147	13	given	give	VERB
ejpam-6136	147	14	by	by	ADP
ejpam-6136	147	15	sλ{1	sλ{1	PRON
ejpam-6136	147	16	}	}	PUNCT
ejpam-6136	147	17	=	=	SYM
ejpam-6136	147	18	1	1	NUM
ejpam-6136	147	19	uα+β	uα+β	NOUN
ejpam-6136	147	20	−	−	PROPN
ejpam-6136	147	21	uβλ	uβλ	NOUN
ejpam-6136	147	22	,	,	PUNCT
ejpam-6136	147	23	for	for	ADP
ejpam-6136	147	24	−uα	−uα	DET
ejpam-6136	147	25	λ	λ	PROPN
ejpam-6136	147	26	+	+	PROPN
ejpam-6136	147	27	1	1	NUM
ejpam-6136	147	28	<	<	X
ejpam-6136	147	29	0	0	NUM
ejpam-6136	147	30	.	.	PUNCT
ejpam-6136	148	1	(	(	PUNCT
ejpam-6136	148	2	10	10	NUM
ejpam-6136	148	3	)	)	PUNCT
ejpam-6136	148	4	proof	proof	NOUN
ejpam-6136	148	5	.	.	PUNCT
ejpam-6136	149	1	from	from	ADP
ejpam-6136	149	2	equation	equation	NOUN
ejpam-6136	149	3	(	(	PUNCT
ejpam-6136	149	4	8)	8)	NUM
ejpam-6136	149	5	,	,	PUNCT
ejpam-6136	149	6	when	when	SCONJ
ejpam-6136	149	7	f(t	f(t	NOUN
ejpam-6136	149	8	)	)	PUNCT
ejpam-6136	149	9	=	=	SYM
ejpam-6136	149	10	1	1	NUM
ejpam-6136	149	11	,	,	PUNCT
ejpam-6136	149	12	we	we	PRON
ejpam-6136	149	13	have	have	VERB
ejpam-6136	149	14	sλ{1	sλ{1	NUM
ejpam-6136	149	15	}	}	PUNCT
ejpam-6136	149	16	=	=	SYM
ejpam-6136	150	1	1	1	NUM
ejpam-6136	150	2	uβ	uβ	NOUN
ejpam-6136	150	3	∫	∫	PROPN
ejpam-6136	150	4	∞	∞	PROPN
ejpam-6136	150	5	0	0	NUM
ejpam-6136	150	6	e−uα	e−uα	PROPN
ejpam-6136	150	7	λ	λ	PROPN
ejpam-6136	150	8	(	(	PUNCT
ejpam-6136	150	9	t){1	t){1	PROPN
ejpam-6136	150	10	}	}	PUNCT
ejpam-6136	150	11	dt	dt	NOUN
ejpam-6136	150	12	=	=	SYM
ejpam-6136	151	1	1	1	NUM
ejpam-6136	151	2	uβ	uβ	NOUN
ejpam-6136	151	3	∫	∫	PROPN
ejpam-6136	151	4	∞	∞	PROPN
ejpam-6136	151	5	0	0	NUM
ejpam-6136	152	1	(	(	PUNCT
ejpam-6136	152	2	1	1	NUM
ejpam-6136	152	3	+	+	CCONJ
ejpam-6136	152	4	λt	λt	ADP
ejpam-6136	152	5	)	)	PUNCT
ejpam-6136	152	6	−uα	−uα	PRON
ejpam-6136	152	7	λ	λ	X
ejpam-6136	152	8	dt	dt	NOUN
ejpam-6136	152	9	=	=	SYM
ejpam-6136	152	10	1	1	NUM
ejpam-6136	152	11	uβ	uβ	PROPN
ejpam-6136	152	12	lim	lim	PROPN
ejpam-6136	152	13	r→∞	r→∞	PUNCT
ejpam-6136	152	14	∫	∫	PROPN
ejpam-6136	153	1	r	r	NOUN
ejpam-6136	153	2	0	0	NUM
ejpam-6136	153	3	(	(	PUNCT
ejpam-6136	153	4	1	1	NUM
ejpam-6136	153	5	+	+	CCONJ
ejpam-6136	153	6	λt	λt	ADP
ejpam-6136	153	7	)	)	PUNCT
ejpam-6136	153	8	−uα	−uα	PRON
ejpam-6136	153	9	λ	λ	X
ejpam-6136	153	10	dt	dt	NOUN
ejpam-6136	153	11	=	=	SYM
ejpam-6136	153	12	1	1	NUM
ejpam-6136	153	13	uβ	uβ	NOUN
ejpam-6136	153	14	lim	lim	PROPN
ejpam-6136	153	15	r→∞	r→∞	NUM
ejpam-6136	154	1	[	[	X
ejpam-6136	154	2	(	(	PUNCT
ejpam-6136	154	3	(	(	PUNCT
ejpam-6136	154	4	1	1	NUM
ejpam-6136	154	5	+	+	NUM
ejpam-6136	154	6	λr	λr	NOUN
ejpam-6136	154	7	)	)	PUNCT
ejpam-6136	154	8	−uα	−uα	PROPN
ejpam-6136	155	1	λ	λ	X
ejpam-6136	155	2	+1	+1	PROPN
ejpam-6136	155	3	−uα	−uα	PROPN
ejpam-6136	155	4	+	+	X
ejpam-6136	155	5	λ	λ	PROPN
ejpam-6136	155	6	)	)	PUNCT
ejpam-6136	156	1	−	−	PROPN
ejpam-6136	156	2	(	(	PUNCT
ejpam-6136	156	3	(	(	PUNCT
ejpam-6136	156	4	1	1	X
ejpam-6136	156	5	)	)	PUNCT
ejpam-6136	157	1	−uα	−uα	NOUN
ejpam-6136	158	1	λ	λ	X
ejpam-6136	158	2	+1	+1	PROPN
ejpam-6136	158	3	−uα	−uα	PROPN
ejpam-6136	158	4	+	+	X
ejpam-6136	158	5	λ	λ	PROPN
ejpam-6136	158	6	)	)	PUNCT
ejpam-6136	158	7	]	]	PUNCT
ejpam-6136	159	1	=	=	PUNCT
ejpam-6136	159	2	1	1	NUM
ejpam-6136	159	3	uβ	uβ	NOUN
ejpam-6136	159	4	[	[	PUNCT
ejpam-6136	159	5	−	−	X
ejpam-6136	159	6	(	(	PUNCT
ejpam-6136	159	7	1	1	NUM
ejpam-6136	159	8	−uα	−uα	NOUN
ejpam-6136	159	9	+	+	X
ejpam-6136	159	10	λ	λ	PROPN
ejpam-6136	159	11	)	)	PUNCT
ejpam-6136	159	12	]	]	PUNCT
ejpam-6136	159	13	,	,	PUNCT
ejpam-6136	159	14	for	for	ADP
ejpam-6136	159	15	−uα	−uα	DET
ejpam-6136	159	16	λ	λ	PROPN
ejpam-6136	159	17	+	+	PROPN
ejpam-6136	159	18	1	1	NUM
ejpam-6136	159	19	<	<	SYM
ejpam-6136	159	20	0	0	PUNCT
ejpam-6136	159	21	=	=	SYM
ejpam-6136	159	22	1	1	NUM
ejpam-6136	159	23	uβ	uβ	NOUN
ejpam-6136	159	24	(	(	PUNCT
ejpam-6136	159	25	1	1	NUM
ejpam-6136	159	26	uα	uα	NOUN
ejpam-6136	159	27	−	−	PROPN
ejpam-6136	159	28	λ	λ	PROPN
ejpam-6136	159	29	)	)	PUNCT
ejpam-6136	159	30	=	=	SYM
ejpam-6136	160	1	1	1	NUM
ejpam-6136	160	2	uαuβ	uαuβ	NOUN
ejpam-6136	160	3	−	−	PROPN
ejpam-6136	161	1	uβλ	uβλ	NOUN
ejpam-6136	161	2	.	.	PUNCT
ejpam-6136	162	1	hence	hence	ADV
ejpam-6136	162	2	,	,	PUNCT
ejpam-6136	162	3	the	the	DET
ejpam-6136	162	4	degenerate	degenerate	ADJ
ejpam-6136	162	5	sadik	sadik	ADJ
ejpam-6136	162	6	transform	transform	NOUN
ejpam-6136	162	7	of	of	ADP
ejpam-6136	162	8	the	the	DET
ejpam-6136	162	9	function	function	NOUN
ejpam-6136	162	10	f(t	f(t	NOUN
ejpam-6136	162	11	)	)	PUNCT
ejpam-6136	162	12	=	=	SYM
ejpam-6136	162	13	1	1	NUM
ejpam-6136	162	14	is	be	AUX
ejpam-6136	162	15	given	give	VERB
ejpam-6136	162	16	by	by	ADP
ejpam-6136	162	17	sλ{1	sλ{1	PRON
ejpam-6136	162	18	}	}	PUNCT
ejpam-6136	162	19	=	=	SYM
ejpam-6136	162	20	1	1	NUM
ejpam-6136	162	21	uα+β	uα+β	NOUN
ejpam-6136	162	22	−	−	PROPN
ejpam-6136	162	23	uβλ	uβλ	NOUN
ejpam-6136	162	24	,	,	PUNCT
ejpam-6136	162	25	for	for	ADP
ejpam-6136	162	26	−uα	−uα	DET
ejpam-6136	162	27	λ	λ	PROPN
ejpam-6136	162	28	+	+	PROPN
ejpam-6136	162	29	1	1	NUM
ejpam-6136	162	30	<	<	X
ejpam-6136	162	31	0	0	NUM
ejpam-6136	162	32	.	.	PUNCT
ejpam-6136	162	33	remark	remark	PROPN
ejpam-6136	162	34	2	2	NUM
ejpam-6136	162	35	.	.	X
ejpam-6136	162	36	observe	observe	VERB
ejpam-6136	162	37	that	that	SCONJ
ejpam-6136	162	38	as	as	ADP
ejpam-6136	162	39	λ	λ	PROPN
ejpam-6136	162	40	→	→	SYM
ejpam-6136	162	41	0	0	NUM
ejpam-6136	162	42	,	,	PUNCT
ejpam-6136	162	43	sλ{1	sλ{1	PRON
ejpam-6136	162	44	}	}	PUNCT
ejpam-6136	162	45	tends	tend	VERB
ejpam-6136	162	46	to	to	PART
ejpam-6136	162	47	s{1	s{1	PROPN
ejpam-6136	162	48	}	}	PUNCT
ejpam-6136	162	49	.	.	PUNCT
ejpam-6136	163	1	that	that	PRON
ejpam-6136	163	2	is	is	ADV
ejpam-6136	163	3	,	,	PUNCT
ejpam-6136	163	4	lim	lim	PROPN
ejpam-6136	163	5	λ→0	λ→0	PROPN
ejpam-6136	163	6	sλ{1	sλ{1	PROPN
ejpam-6136	163	7	}	}	PUNCT
ejpam-6136	163	8	=	=	SYM
ejpam-6136	163	9	lim	lim	PROPN
ejpam-6136	163	10	λ→0	λ→0	PUNCT
ejpam-6136	163	11	[	[	PUNCT
ejpam-6136	163	12	1	1	NUM
ejpam-6136	163	13	uα+β	uα+β	NOUN
ejpam-6136	163	14	−	−	PROPN
ejpam-6136	163	15	uβλ	uβλ	NOUN
ejpam-6136	163	16	]	]	X
ejpam-6136	163	17	=	=	SYM
ejpam-6136	163	18	1	1	NUM
ejpam-6136	163	19	uα+β	uα+β	NOUN
ejpam-6136	163	20	=	=	SYM
ejpam-6136	163	21	s{1	s{1	PROPN
ejpam-6136	163	22	}	}	PUNCT
ejpam-6136	163	23	.	.	PUNCT
ejpam-6136	164	1	remark	remark	NOUN
ejpam-6136	164	2	3	3	NUM
ejpam-6136	164	3	.	.	PUNCT
ejpam-6136	164	4	m	m	PROPN
ejpam-6136	164	5	1	1	NUM
ejpam-6136	164	6	.	.	PUNCT
ejpam-6136	165	1	when	when	SCONJ
ejpam-6136	165	2	β	β	X
ejpam-6136	165	3	=	=	NOUN
ejpam-6136	165	4	0	0	NUM
ejpam-6136	165	5	and	and	CCONJ
ejpam-6136	165	6	α	α	NOUN
ejpam-6136	165	7	=	=	NOUN
ejpam-6136	165	8	1	1	NUM
ejpam-6136	165	9	in	in	ADP
ejpam-6136	165	10	equation	equation	NOUN
ejpam-6136	165	11	(	(	PUNCT
ejpam-6136	165	12	10	10	NUM
ejpam-6136	165	13	)	)	PUNCT
ejpam-6136	165	14	,	,	PUNCT
ejpam-6136	165	15	sλ{1	sλ{1	NOUN
ejpam-6136	165	16	}	}	PUNCT
ejpam-6136	165	17	=	=	SYM
ejpam-6136	165	18	1	1	NUM
ejpam-6136	165	19	u1	u1	NOUN
ejpam-6136	165	20	+	+	NOUN
ejpam-6136	165	21	0	0	NUM
ejpam-6136	165	22	−	−	NOUN
ejpam-6136	165	23	u0λ	u0λ	NOUN
ejpam-6136	165	24	=	=	NOUN
ejpam-6136	165	25	1	1	NUM
ejpam-6136	165	26	u−	u−	PROPN
ejpam-6136	165	27	λ	λ	X
ejpam-6136	165	28	=	=	PUNCT
ejpam-6136	165	29	lλ{1	lλ{1	NUM
ejpam-6136	165	30	}	}	PUNCT
ejpam-6136	165	31	.	.	PUNCT
ejpam-6136	166	1	j.	j.	PROPN
ejpam-6136	166	2	mohamadali	mohamadali	PROPN
ejpam-6136	166	3	,	,	PUNCT
ejpam-6136	166	4	n.	n.	PROPN
ejpam-6136	166	5	abdulcarim	abdulcarim	PROPN
ejpam-6136	166	6	/	/	SYM
ejpam-6136	166	7	eur	eur	PROPN
ejpam-6136	166	8	.	.	PUNCT
ejpam-6136	167	1	j.	j.	PROPN
ejpam-6136	167	2	pure	pure	PROPN
ejpam-6136	167	3	appl	appl	PROPN
ejpam-6136	167	4	.	.	PROPN
ejpam-6136	167	5	math	math	PROPN
ejpam-6136	167	6	,	,	PUNCT
ejpam-6136	167	7	18	18	NUM
ejpam-6136	167	8	(	(	PUNCT
ejpam-6136	167	9	3	3	NUM
ejpam-6136	167	10	)	)	PUNCT
ejpam-6136	167	11	(	(	PUNCT
ejpam-6136	167	12	2025	2025	NUM
ejpam-6136	167	13	)	)	PUNCT
ejpam-6136	167	14	,	,	PUNCT
ejpam-6136	167	15	6136	6136	NUM
ejpam-6136	167	16	9	9	NUM
ejpam-6136	167	17	of	of	ADP
ejpam-6136	167	18	19	19	NUM
ejpam-6136	167	19	2	2	NUM
ejpam-6136	167	20	.	.	PUNCT
ejpam-6136	168	1	when	when	SCONJ
ejpam-6136	168	2	β	β	X
ejpam-6136	168	3	=	=	VERB
ejpam-6136	168	4	−1	−1	NOUN
ejpam-6136	168	5	and	and	CCONJ
ejpam-6136	168	6	α	α	NOUN
ejpam-6136	168	7	=	=	SYM
ejpam-6136	168	8	−1	−1	NOUN
ejpam-6136	168	9	in	in	ADP
ejpam-6136	168	10	equation	equation	NOUN
ejpam-6136	168	11	(	(	PUNCT
ejpam-6136	168	12	10	10	NUM
ejpam-6136	168	13	)	)	PUNCT
ejpam-6136	168	14	,	,	PUNCT
ejpam-6136	168	15	sλ{1	sλ{1	NOUN
ejpam-6136	168	16	}	}	PUNCT
ejpam-6136	168	17	=	=	SYM
ejpam-6136	168	18	1	1	NUM
ejpam-6136	168	19	u−1+−1	u−1+−1	NOUN
ejpam-6136	168	20	−	−	NOUN
ejpam-6136	168	21	u−1λ	u−1λ	NOUN
ejpam-6136	168	22	=	=	PROPN
ejpam-6136	168	23	u2	u2	PROPN
ejpam-6136	168	24	1−	1−	NUM
ejpam-6136	168	25	uλ	uλ	NOUN
ejpam-6136	168	26	=	=	PUNCT
ejpam-6136	168	27	eλ{1	eλ{1	NUM
ejpam-6136	168	28	}	}	PUNCT
ejpam-6136	168	29	.	.	PUNCT
ejpam-6136	169	1	3	3	X
ejpam-6136	169	2	.	.	X
ejpam-6136	169	3	when	when	SCONJ
ejpam-6136	169	4	β	β	X
ejpam-6136	169	5	=	=	SYM
ejpam-6136	169	6	1	1	NUM
ejpam-6136	169	7	and	and	CCONJ
ejpam-6136	169	8	α	α	NOUN
ejpam-6136	169	9	=	=	SYM
ejpam-6136	169	10	−1	−1	NOUN
ejpam-6136	169	11	in	in	ADP
ejpam-6136	169	12	equation	equation	NOUN
ejpam-6136	169	13	(	(	PUNCT
ejpam-6136	169	14	10	10	NUM
ejpam-6136	169	15	)	)	PUNCT
ejpam-6136	169	16	,	,	PUNCT
ejpam-6136	169	17	sλ{1	sλ{1	NOUN
ejpam-6136	169	18	}	}	PUNCT
ejpam-6136	169	19	=	=	SYM
ejpam-6136	169	20	1	1	NUM
ejpam-6136	169	21	u−1	u−1	PROPN
ejpam-6136	169	22	+	+	PROPN
ejpam-6136	169	23	1	1	NUM
ejpam-6136	169	24	−	−	PROPN
ejpam-6136	169	25	u1λ	u1λ	PROPN
ejpam-6136	169	26	=	=	SYM
ejpam-6136	170	1	1	1	NUM
ejpam-6136	170	2	1−	1−	NUM
ejpam-6136	170	3	uλ	uλ	NOUN
ejpam-6136	170	4	=	=	PUNCT
ejpam-6136	170	5	sλ{1	sλ{1	NOUN
ejpam-6136	170	6	}	}	PUNCT
ejpam-6136	170	7	.	.	PUNCT
ejpam-6136	171	1	4	4	X
ejpam-6136	171	2	.	.	X
ejpam-6136	171	3	when	when	SCONJ
ejpam-6136	171	4	β	β	X
ejpam-6136	171	5	=	=	SYM
ejpam-6136	171	6	−α	−α	PROPN
ejpam-6136	171	7	and	and	CCONJ
ejpam-6136	171	8	α	α	NOUN
ejpam-6136	171	9	=	=	SYM
ejpam-6136	171	10	−1	−1	NOUN
ejpam-6136	171	11	in	in	ADP
ejpam-6136	171	12	equation	equation	NOUN
ejpam-6136	171	13	(	(	PUNCT
ejpam-6136	171	14	10	10	NUM
ejpam-6136	171	15	)	)	PUNCT
ejpam-6136	171	16	,	,	PUNCT
ejpam-6136	171	17	sλ{1	sλ{1	NOUN
ejpam-6136	171	18	}	}	PUNCT
ejpam-6136	171	19	=	=	SYM
ejpam-6136	171	20	1	1	NUM
ejpam-6136	171	21	u−1+(−α	u−1+(−α	NOUN
ejpam-6136	171	22	)	)	PUNCT
ejpam-6136	172	1	−	−	NOUN
ejpam-6136	173	1	u−αλ	u−αλ	NOUN
ejpam-6136	173	2	=	=	PUNCT
ejpam-6136	173	3	u(α+1	u(α+1	NOUN
ejpam-6136	173	4	)	)	PUNCT
ejpam-6136	173	5	1−	1−	NUM
ejpam-6136	173	6	uλ	uλ	X
ejpam-6136	173	7	=	=	SYM
ejpam-6136	173	8	gαλ{1	gαλ{1	PROPN
ejpam-6136	173	9	}	}	PUNCT
ejpam-6136	173	10	.	.	PUNCT
ejpam-6136	174	1	theorem	theorem	VERB
ejpam-6136	174	2	4	4	NUM
ejpam-6136	174	3	.	.	PUNCT
ejpam-6136	175	1	the	the	DET
ejpam-6136	175	2	degenerate	degenerate	ADJ
ejpam-6136	175	3	sadik	sadik	PROPN
ejpam-6136	175	4	transform	transform	NOUN
ejpam-6136	175	5	of	of	ADP
ejpam-6136	175	6	the	the	DET
ejpam-6136	175	7	function	function	NOUN
ejpam-6136	175	8	f(t	f(t	PROPN
ejpam-6136	175	9	)	)	PUNCT
ejpam-6136	176	1	=	=	SYM
ejpam-6136	176	2	t	t	PROPN
ejpam-6136	176	3	is	be	AUX
ejpam-6136	176	4	given	give	VERB
ejpam-6136	176	5	by	by	ADP
ejpam-6136	176	6	sλ{t	sλ{t	PROPN
ejpam-6136	176	7	}	}	PUNCT
ejpam-6136	176	8	=	=	SYM
ejpam-6136	176	9	u−β	u−β	NOUN
ejpam-6136	176	10	(	(	PUNCT
ejpam-6136	176	11	uα	uα	PROPN
ejpam-6136	176	12	−	−	PROPN
ejpam-6136	176	13	2λ)(uα	2λ)(uα	NUM
ejpam-6136	176	14	−	−	PROPN
ejpam-6136	176	15	λ	λ	NOUN
ejpam-6136	176	16	)	)	PUNCT
ejpam-6136	176	17	,	,	PUNCT
ejpam-6136	176	18	for	for	ADP
ejpam-6136	176	19	−uα	−uα	DET
ejpam-6136	176	20	λ	λ	PROPN
ejpam-6136	176	21	+	+	PROPN
ejpam-6136	176	22	2	2	NUM
ejpam-6136	176	23	<	<	X
ejpam-6136	176	24	0	0	NUM
ejpam-6136	176	25	.	.	PUNCT
ejpam-6136	177	1	(	(	PUNCT
ejpam-6136	177	2	11	11	NUM
ejpam-6136	177	3	)	)	PUNCT
ejpam-6136	177	4	proof	proof	NOUN
ejpam-6136	177	5	.	.	PUNCT
ejpam-6136	178	1	by	by	ADP
ejpam-6136	178	2	definition	definition	NOUN
ejpam-6136	178	3	for	for	ADP
ejpam-6136	178	4	f(t	f(t	NOUN
ejpam-6136	178	5	)	)	PUNCT
ejpam-6136	178	6	=	=	SYM
ejpam-6136	178	7	t	t	PROPN
ejpam-6136	178	8	,	,	PUNCT
ejpam-6136	178	9	we	we	PRON
ejpam-6136	178	10	have	have	VERB
ejpam-6136	178	11	sλ{t	sλ{t	VERB
ejpam-6136	178	12	}	}	PUNCT
ejpam-6136	178	13	=	=	SYM
ejpam-6136	179	1	1	1	NUM
ejpam-6136	179	2	uβ	uβ	NOUN
ejpam-6136	179	3	∫	∫	PROPN
ejpam-6136	179	4	∞	∞	PROPN
ejpam-6136	179	5	0	0	NUM
ejpam-6136	179	6	e−uα	e−uα	PROPN
ejpam-6136	179	7	λ	λ	PROPN
ejpam-6136	179	8	(	(	PUNCT
ejpam-6136	179	9	t	t	PROPN
ejpam-6136	179	10	)	)	PUNCT
ejpam-6136	179	11	{	{	PUNCT
ejpam-6136	179	12	t	t	NOUN
ejpam-6136	179	13	}	}	PUNCT
ejpam-6136	179	14	dt	dt	NOUN
ejpam-6136	179	15	=	=	SYM
ejpam-6136	179	16	1	1	NUM
ejpam-6136	179	17	uβ	uβ	PROPN
ejpam-6136	179	18	lim	lim	PROPN
ejpam-6136	179	19	r→∞	r→∞	PUNCT
ejpam-6136	179	20	∫	∫	PROPN
ejpam-6136	180	1	r	r	NOUN
ejpam-6136	180	2	0	0	NUM
ejpam-6136	180	3	(	(	PUNCT
ejpam-6136	180	4	1	1	NUM
ejpam-6136	180	5	+	+	CCONJ
ejpam-6136	180	6	λt	λt	ADP
ejpam-6136	180	7	)	)	PUNCT
ejpam-6136	180	8	−uα	−uα	PROPN
ejpam-6136	180	9	λ	λ	PROPN
ejpam-6136	180	10	t	t	NOUN
ejpam-6136	180	11	dt	dt	X
ejpam-6136	180	12	.	.	PUNCT
ejpam-6136	181	1	=	=	SYM
ejpam-6136	181	2	1	1	NUM
ejpam-6136	181	3	uβλ	uβλ	NOUN
ejpam-6136	181	4	lim	lim	PROPN
ejpam-6136	181	5	r→∞	r→∞	NUM
ejpam-6136	182	1	[	[	X
ejpam-6136	182	2	(	(	PUNCT
ejpam-6136	182	3	(	(	PUNCT
ejpam-6136	182	4	1	1	NUM
ejpam-6136	182	5	+	+	CCONJ
ejpam-6136	182	6	λ(r	λ(r	NOUN
ejpam-6136	182	7	)	)	PUNCT
ejpam-6136	182	8	)	)	PUNCT
ejpam-6136	183	1	−uα	−uα	PROPN
ejpam-6136	183	2	λ	λ	PROPN
ejpam-6136	183	3	+2	+2	PROPN
ejpam-6136	183	4	−uα	−uα	PROPN
ejpam-6136	183	5	+	+	PROPN
ejpam-6136	183	6	2λ	2λ	NUM
ejpam-6136	183	7	−	−	NOUN
ejpam-6136	184	1	(	(	PUNCT
ejpam-6136	184	2	1	1	NUM
ejpam-6136	184	3	+	+	CCONJ
ejpam-6136	184	4	λ(r	λ(r	NOUN
ejpam-6136	184	5	)	)	PUNCT
ejpam-6136	184	6	)	)	PUNCT
ejpam-6136	185	1	−uα	−uα	PROPN
ejpam-6136	186	1	λ	λ	X
ejpam-6136	186	2	+1	+1	PROPN
ejpam-6136	186	3	−uα	−uα	PROPN
ejpam-6136	186	4	+	+	X
ejpam-6136	186	5	λ	λ	PROPN
ejpam-6136	186	6	)	)	PUNCT
ejpam-6136	187	1	−	−	PROPN
ejpam-6136	188	1	(	(	PUNCT
ejpam-6136	188	2	(	(	PUNCT
ejpam-6136	188	3	1	1	X
ejpam-6136	188	4	)	)	PUNCT
ejpam-6136	188	5	−uα	−uα	NOUN
ejpam-6136	188	6	λ	λ	PROPN
ejpam-6136	188	7	+2	+2	PROPN
ejpam-6136	188	8	−uα	−uα	PROPN
ejpam-6136	188	9	+	+	PROPN
ejpam-6136	188	10	2λ	2λ	NUM
ejpam-6136	189	1	−	−	NOUN
ejpam-6136	189	2	(	(	PUNCT
ejpam-6136	189	3	1	1	X
ejpam-6136	189	4	)	)	PUNCT
ejpam-6136	189	5	−uα	−uα	NOUN
ejpam-6136	189	6	λ	λ	X
ejpam-6136	189	7	+1	+1	PROPN
ejpam-6136	189	8	−uα	−uα	PROPN
ejpam-6136	189	9	+	+	X
ejpam-6136	189	10	λ	λ	PROPN
ejpam-6136	189	11	)	)	PUNCT
ejpam-6136	189	12	]	]	PUNCT
ejpam-6136	190	1	=	=	SYM
ejpam-6136	190	2	1	1	NUM
ejpam-6136	190	3	uβλ	uβλ	NOUN
ejpam-6136	190	4	−	−	PROPN
ejpam-6136	191	1	(	(	PUNCT
ejpam-6136	191	2	1	1	NUM
ejpam-6136	191	3	−uα	−uα	NOUN
ejpam-6136	191	4	+	+	NUM
ejpam-6136	191	5	2λ	2λ	NUM
ejpam-6136	192	1	−	−	NOUN
ejpam-6136	192	2	1	1	NUM
ejpam-6136	192	3	−uα	−uα	NOUN
ejpam-6136	192	4	+	+	X
ejpam-6136	192	5	λ	λ	PROPN
ejpam-6136	192	6	)	)	PUNCT
ejpam-6136	192	7	for	for	ADP
ejpam-6136	192	8	−uα	−uα	PRON
ejpam-6136	192	9	λ	λ	PROPN
ejpam-6136	192	10	+	+	CCONJ
ejpam-6136	192	11	2	2	NUM
ejpam-6136	192	12	<	<	SYM
ejpam-6136	192	13	0	0	NUM
ejpam-6136	192	14	=	=	SYM
ejpam-6136	192	15	1	1	NUM
ejpam-6136	192	16	uβλ	uβλ	NOUN
ejpam-6136	192	17	(	(	PUNCT
ejpam-6136	192	18	1	1	NUM
ejpam-6136	192	19	uα	uα	PROPN
ejpam-6136	192	20	−	−	PROPN
ejpam-6136	192	21	2λ	2λ	NOUN
ejpam-6136	192	22	−	−	NOUN
ejpam-6136	192	23	1	1	NUM
ejpam-6136	192	24	uα	uα	PROPN
ejpam-6136	192	25	−	−	PROPN
ejpam-6136	192	26	λ	λ	PROPN
ejpam-6136	192	27	)	)	PUNCT
ejpam-6136	192	28	=	=	SYM
ejpam-6136	192	29	u−β	u−β	NOUN
ejpam-6136	192	30	(	(	PUNCT
ejpam-6136	192	31	uα	uα	PROPN
ejpam-6136	192	32	−	−	PROPN
ejpam-6136	192	33	2λ)(uα	2λ)(uα	NUM
ejpam-6136	192	34	−	−	PROPN
ejpam-6136	192	35	λ	λ	NOUN
ejpam-6136	192	36	)	)	PUNCT
ejpam-6136	192	37	.	.	PUNCT
ejpam-6136	193	1	remark	remark	NOUN
ejpam-6136	193	2	4	4	NUM
ejpam-6136	193	3	.	.	PUNCT
ejpam-6136	193	4	observe	observe	VERB
ejpam-6136	193	5	that	that	SCONJ
ejpam-6136	193	6	as	as	ADP
ejpam-6136	193	7	λ	λ	PROPN
ejpam-6136	193	8	→	→	SYM
ejpam-6136	193	9	0	0	NUM
ejpam-6136	193	10	,	,	PUNCT
ejpam-6136	193	11	sλ{t	sλ{t	PROPN
ejpam-6136	193	12	}	}	PUNCT
ejpam-6136	193	13	tends	tend	VERB
ejpam-6136	193	14	to	to	PART
ejpam-6136	193	15	s{t	s{t	VERB
ejpam-6136	193	16	}	}	PUNCT
ejpam-6136	193	17	.	.	PUNCT
ejpam-6136	194	1	that	that	PRON
ejpam-6136	194	2	is	is	ADV
ejpam-6136	194	3	,	,	PUNCT
ejpam-6136	194	4	lim	lim	PROPN
ejpam-6136	194	5	λ→0	λ→0	PUNCT
ejpam-6136	194	6	sλ{t	sλ{t	PROPN
ejpam-6136	194	7	}	}	PUNCT
ejpam-6136	194	8	=	=	SYM
ejpam-6136	194	9	u−β	u−β	NOUN
ejpam-6136	194	10	(	(	PUNCT
ejpam-6136	194	11	uα)(uα	uα)(uα	NOUN
ejpam-6136	194	12	)	)	PUNCT
ejpam-6136	194	13	=	=	SYM
ejpam-6136	194	14	u−β	u−β	NOUN
ejpam-6136	194	15	u2α	u2α	NOUN
ejpam-6136	194	16	=	=	PUNCT
ejpam-6136	194	17	s{t	s{t	VERB
ejpam-6136	194	18	}	}	PUNCT
ejpam-6136	194	19	.	.	PUNCT
ejpam-6136	195	1	remark	remark	NOUN
ejpam-6136	195	2	5	5	NUM
ejpam-6136	195	3	.	.	PUNCT
ejpam-6136	195	4	m	m	PROPN
ejpam-6136	195	5	1	1	NUM
ejpam-6136	195	6	.	.	PUNCT
ejpam-6136	196	1	when	when	SCONJ
ejpam-6136	196	2	β	β	X
ejpam-6136	196	3	=	=	NOUN
ejpam-6136	196	4	0	0	NUM
ejpam-6136	196	5	and	and	CCONJ
ejpam-6136	196	6	α	α	NOUN
ejpam-6136	196	7	=	=	NOUN
ejpam-6136	196	8	1	1	NUM
ejpam-6136	196	9	in	in	ADP
ejpam-6136	196	10	equation	equation	NOUN
ejpam-6136	196	11	(	(	PUNCT
ejpam-6136	196	12	11	11	NUM
ejpam-6136	196	13	)	)	PUNCT
ejpam-6136	196	14	,	,	PUNCT
ejpam-6136	196	15	sλ{t	sλ{t	PROPN
ejpam-6136	196	16	}	}	PUNCT
ejpam-6136	196	17	=	=	SYM
ejpam-6136	196	18	u−0	u−0	PROPN
ejpam-6136	196	19	(	(	PUNCT
ejpam-6136	196	20	u1	u1	NOUN
ejpam-6136	196	21	−	−	PROPN
ejpam-6136	196	22	2λ)(u1	2λ)(u1	NUM
ejpam-6136	196	23	−	−	ADP
ejpam-6136	196	24	λ	λ	NOUN
ejpam-6136	196	25	)	)	PUNCT
ejpam-6136	196	26	=	=	SYM
ejpam-6136	196	27	1	1	NUM
ejpam-6136	196	28	u2	u2	NOUN
ejpam-6136	196	29	−	−	PROPN
ejpam-6136	196	30	3uλ+	3uλ+	NUM
ejpam-6136	196	31	2λ2	2λ2	NUM
ejpam-6136	196	32	=	=	SYM
ejpam-6136	196	33	lλ{t	lλ{t	PROPN
ejpam-6136	196	34	}	}	PUNCT
ejpam-6136	196	35	.	.	PUNCT
ejpam-6136	197	1	j.	j.	PROPN
ejpam-6136	197	2	mohamadali	mohamadali	PROPN
ejpam-6136	197	3	,	,	PUNCT
ejpam-6136	197	4	n.	n.	PROPN
ejpam-6136	197	5	abdulcarim	abdulcarim	PROPN
ejpam-6136	197	6	/	/	SYM
ejpam-6136	197	7	eur	eur	PROPN
ejpam-6136	197	8	.	.	PUNCT
ejpam-6136	198	1	j.	j.	PROPN
ejpam-6136	198	2	pure	pure	PROPN
ejpam-6136	198	3	appl	appl	PROPN
ejpam-6136	198	4	.	.	PROPN
ejpam-6136	198	5	math	math	PROPN
ejpam-6136	198	6	,	,	PUNCT
ejpam-6136	198	7	18	18	NUM
ejpam-6136	198	8	(	(	PUNCT
ejpam-6136	198	9	3	3	NUM
ejpam-6136	198	10	)	)	PUNCT
ejpam-6136	198	11	(	(	PUNCT
ejpam-6136	198	12	2025	2025	NUM
ejpam-6136	198	13	)	)	PUNCT
ejpam-6136	198	14	,	,	PUNCT
ejpam-6136	198	15	6136	6136	NUM
ejpam-6136	198	16	10	10	NUM
ejpam-6136	198	17	of	of	ADP
ejpam-6136	198	18	19	19	NUM
ejpam-6136	198	19	2	2	NUM
ejpam-6136	198	20	.	.	PUNCT
ejpam-6136	199	1	when	when	SCONJ
ejpam-6136	199	2	β	β	X
ejpam-6136	199	3	=	=	VERB
ejpam-6136	199	4	−1	−1	NOUN
ejpam-6136	199	5	and	and	CCONJ
ejpam-6136	199	6	α	α	NOUN
ejpam-6136	199	7	=	=	SYM
ejpam-6136	199	8	−1	−1	NOUN
ejpam-6136	199	9	in	in	ADP
ejpam-6136	199	10	equation	equation	NOUN
ejpam-6136	199	11	(	(	PUNCT
ejpam-6136	199	12	11	11	NUM
ejpam-6136	199	13	)	)	PUNCT
ejpam-6136	199	14	,	,	PUNCT
ejpam-6136	199	15	sλ{t	sλ{t	PROPN
ejpam-6136	199	16	}	}	PUNCT
ejpam-6136	199	17	=	=	SYM
ejpam-6136	199	18	u−(−1	u−(−1	X
ejpam-6136	199	19	)	)	PUNCT
ejpam-6136	200	1	(	(	PUNCT
ejpam-6136	200	2	u−1	u−1	PROPN
ejpam-6136	200	3	−	−	PROPN
ejpam-6136	200	4	2λ)(u−1	2λ)(u−1	ADJ
ejpam-6136	200	5	−	−	PROPN
ejpam-6136	200	6	λ	λ	NOUN
ejpam-6136	200	7	)	)	PUNCT
ejpam-6136	200	8	=	=	SYM
ejpam-6136	200	9	u3	u3	NOUN
ejpam-6136	200	10	(	(	PUNCT
ejpam-6136	200	11	1−	1−	NUM
ejpam-6136	200	12	uλ)(1−	uλ)(1−	ADJ
ejpam-6136	200	13	2uλ	2uλ	NOUN
ejpam-6136	200	14	)	)	PUNCT
ejpam-6136	200	15	=	=	SYM
ejpam-6136	200	16	eλ{t	eλ{t	PROPN
ejpam-6136	200	17	}	}	PUNCT
ejpam-6136	200	18	.	.	PUNCT
ejpam-6136	201	1	3	3	X
ejpam-6136	201	2	.	.	X
ejpam-6136	201	3	when	when	SCONJ
ejpam-6136	201	4	β	β	X
ejpam-6136	201	5	=	=	SYM
ejpam-6136	201	6	1	1	NUM
ejpam-6136	201	7	and	and	CCONJ
ejpam-6136	201	8	α	α	NOUN
ejpam-6136	201	9	=	=	SYM
ejpam-6136	201	10	−1	−1	NOUN
ejpam-6136	201	11	in	in	ADP
ejpam-6136	201	12	equation	equation	NOUN
ejpam-6136	201	13	(	(	PUNCT
ejpam-6136	201	14	11	11	NUM
ejpam-6136	201	15	)	)	PUNCT
ejpam-6136	201	16	,	,	PUNCT
ejpam-6136	201	17	sλ{t	sλ{t	PROPN
ejpam-6136	201	18	}	}	PUNCT
ejpam-6136	201	19	=	=	SYM
ejpam-6136	201	20	u−1	u−1	PROPN
ejpam-6136	201	21	(	(	PUNCT
ejpam-6136	201	22	u−1	u−1	PROPN
ejpam-6136	201	23	−	−	PROPN
ejpam-6136	201	24	2λ)(u−1	2λ)(u−1	ADJ
ejpam-6136	201	25	−	−	PROPN
ejpam-6136	201	26	λ	λ	NOUN
ejpam-6136	201	27	)	)	PUNCT
ejpam-6136	201	28	=	=	SYM
ejpam-6136	201	29	u	u	NOUN
ejpam-6136	201	30	(	(	PUNCT
ejpam-6136	201	31	1−	1−	NUM
ejpam-6136	201	32	uλ)(1−	uλ)(1−	ADJ
ejpam-6136	201	33	2uλ	2uλ	NOUN
ejpam-6136	201	34	)	)	PUNCT
ejpam-6136	201	35	=	=	SYM
ejpam-6136	202	1	sλ{t	sλ{t	PROPN
ejpam-6136	202	2	}	}	PUNCT
ejpam-6136	202	3	.	.	PUNCT
ejpam-6136	203	1	4	4	X
ejpam-6136	203	2	.	.	X
ejpam-6136	203	3	when	when	SCONJ
ejpam-6136	203	4	β	β	X
ejpam-6136	203	5	=	=	SYM
ejpam-6136	203	6	−α	−α	PROPN
ejpam-6136	203	7	and	and	CCONJ
ejpam-6136	203	8	α	α	NOUN
ejpam-6136	203	9	=	=	SYM
ejpam-6136	203	10	−1	−1	NOUN
ejpam-6136	203	11	in	in	ADP
ejpam-6136	203	12	equation	equation	NOUN
ejpam-6136	203	13	(	(	PUNCT
ejpam-6136	203	14	11	11	NUM
ejpam-6136	203	15	)	)	PUNCT
ejpam-6136	203	16	,	,	PUNCT
ejpam-6136	203	17	sλ{t	sλ{t	PROPN
ejpam-6136	203	18	}	}	PUNCT
ejpam-6136	203	19	=	=	SYM
ejpam-6136	203	20	u−(−α	u−(−α	NUM
ejpam-6136	203	21	)	)	PUNCT
ejpam-6136	204	1	(	(	PUNCT
ejpam-6136	204	2	u−1	u−1	PROPN
ejpam-6136	204	3	−	−	PROPN
ejpam-6136	204	4	2λ)(u−1	2λ)(u−1	ADJ
ejpam-6136	204	5	−	−	PROPN
ejpam-6136	204	6	λ	λ	NOUN
ejpam-6136	204	7	)	)	PUNCT
ejpam-6136	204	8	=	=	SYM
ejpam-6136	204	9	uα+2	uα+2	PROPN
ejpam-6136	204	10	(	(	PUNCT
ejpam-6136	204	11	1−	1−	NUM
ejpam-6136	204	12	uλ)(1−	uλ)(1−	ADJ
ejpam-6136	204	13	2uλ	2uλ	NOUN
ejpam-6136	204	14	)	)	PUNCT
ejpam-6136	204	15	=	=	SYM
ejpam-6136	204	16	gαλ{t	gαλ{t	PROPN
ejpam-6136	204	17	}	}	PUNCT
ejpam-6136	204	18	.	.	PUNCT
ejpam-6136	205	1	theorem	theorem	NOUN
ejpam-6136	205	2	5	5	NUM
ejpam-6136	205	3	.	.	PUNCT
ejpam-6136	206	1	the	the	DET
ejpam-6136	206	2	degenerate	degenerate	ADJ
ejpam-6136	206	3	sadik	sadik	PROPN
ejpam-6136	206	4	transform	transform	NOUN
ejpam-6136	206	5	of	of	ADP
ejpam-6136	206	6	the	the	DET
ejpam-6136	206	7	function	function	NOUN
ejpam-6136	206	8	f(t	f(t	PROPN
ejpam-6136	206	9	)	)	PUNCT
ejpam-6136	206	10	=	=	SYM
ejpam-6136	206	11	eaλ(t	eaλ(t	PROPN
ejpam-6136	206	12	)	)	PUNCT
ejpam-6136	206	13	is	be	AUX
ejpam-6136	206	14	given	give	VERB
ejpam-6136	206	15	by	by	ADP
ejpam-6136	206	16	sλ{eaλ(t	sλ{eaλ(t	NOUN
ejpam-6136	206	17	)	)	PUNCT
ejpam-6136	206	18	}	}	PUNCT
ejpam-6136	206	19	=	=	SYM
ejpam-6136	207	1	u−β	u−β	NOUN
ejpam-6136	207	2	uα	uα	NOUN
ejpam-6136	207	3	−	−	PROPN
ejpam-6136	207	4	a−	a−	PROPN
ejpam-6136	207	5	λ	λ	PROPN
ejpam-6136	207	6	for	for	ADP
ejpam-6136	207	7	−uα	−uα	PRON
ejpam-6136	207	8	+	+	NUM
ejpam-6136	207	9	a	a	DET
ejpam-6136	207	10	λ	λ	NOUN
ejpam-6136	207	11	+	+	ADP
ejpam-6136	207	12	1	1	NUM
ejpam-6136	207	13	<	<	X
ejpam-6136	207	14	0	0	NUM
ejpam-6136	207	15	.	.	PUNCT
ejpam-6136	208	1	(	(	PUNCT
ejpam-6136	208	2	12	12	NUM
ejpam-6136	208	3	)	)	PUNCT
ejpam-6136	208	4	proof	proof	NOUN
ejpam-6136	208	5	.	.	PUNCT
ejpam-6136	209	1	from	from	ADP
ejpam-6136	209	2	equation	equation	NOUN
ejpam-6136	209	3	(	(	PUNCT
ejpam-6136	209	4	8)	8)	NUM
ejpam-6136	209	5	,	,	PUNCT
ejpam-6136	209	6	when	when	SCONJ
ejpam-6136	209	7	f(t	f(t	NOUN
ejpam-6136	209	8	)	)	PUNCT
ejpam-6136	209	9	=	=	SYM
ejpam-6136	209	10	eaλ(t	eaλ(t	PROPN
ejpam-6136	209	11	)	)	PUNCT
ejpam-6136	209	12	,	,	PUNCT
ejpam-6136	209	13	we	we	PRON
ejpam-6136	209	14	have	have	AUX
ejpam-6136	209	15	sλ{eaλ(t	sλ{eaλ(t	X
ejpam-6136	209	16	)	)	PUNCT
ejpam-6136	209	17	}	}	PUNCT
ejpam-6136	209	18	=	=	SYM
ejpam-6136	210	1	1	1	NUM
ejpam-6136	210	2	uβ	uβ	NOUN
ejpam-6136	210	3	∫	∫	PROPN
ejpam-6136	210	4	∞	∞	PROPN
ejpam-6136	210	5	0	0	NUM
ejpam-6136	210	6	e−uα	e−uα	PROPN
ejpam-6136	210	7	λ	λ	PROPN
ejpam-6136	210	8	(	(	PUNCT
ejpam-6136	210	9	t	t	PROPN
ejpam-6136	210	10	)	)	PUNCT
ejpam-6136	210	11	eaλ(t	eaλ(t	PROPN
ejpam-6136	210	12	)	)	PUNCT
ejpam-6136	210	13	dt	dt	NOUN
ejpam-6136	211	1	=	=	SYM
ejpam-6136	211	2	1	1	NUM
ejpam-6136	211	3	uβ	uβ	PROPN
ejpam-6136	211	4	lim	lim	PROPN
ejpam-6136	211	5	r→∞	r→∞	PUNCT
ejpam-6136	211	6	∫	∫	PROPN
ejpam-6136	212	1	r	r	NOUN
ejpam-6136	212	2	0	0	NUM
ejpam-6136	212	3	(	(	PUNCT
ejpam-6136	212	4	1	1	NUM
ejpam-6136	212	5	+	+	CCONJ
ejpam-6136	212	6	λt	λt	X
ejpam-6136	212	7	)	)	PUNCT
ejpam-6136	212	8	−uα+a	−uα+a	PROPN
ejpam-6136	213	1	λ	λ	X
ejpam-6136	213	2	dt	dt	NOUN
ejpam-6136	213	3	.	.	PUNCT
ejpam-6136	214	1	=	=	SYM
ejpam-6136	214	2	1	1	NUM
ejpam-6136	214	3	uβ	uβ	NOUN
ejpam-6136	214	4	lim	lim	PROPN
ejpam-6136	214	5	r→∞	r→∞	NUM
ejpam-6136	215	1	[	[	X
ejpam-6136	215	2	(	(	PUNCT
ejpam-6136	215	3	(	(	PUNCT
ejpam-6136	215	4	1	1	NUM
ejpam-6136	215	5	+	+	NUM
ejpam-6136	215	6	λr	λr	NOUN
ejpam-6136	215	7	)	)	PUNCT
ejpam-6136	215	8	−uα+a	−uα+a	VERB
ejpam-6136	216	1	λ	λ	X
ejpam-6136	216	2	+1	+1	NOUN
ejpam-6136	216	3	−uα	−uα	PROPN
ejpam-6136	216	4	+	+	CCONJ
ejpam-6136	216	5	a+	a+	PUNCT
ejpam-6136	216	6	λ	λ	PROPN
ejpam-6136	216	7	)	)	PUNCT
ejpam-6136	216	8	−	−	PROPN
ejpam-6136	217	1	(	(	PUNCT
ejpam-6136	217	2	(	(	PUNCT
ejpam-6136	217	3	1	1	X
ejpam-6136	217	4	)	)	PUNCT
ejpam-6136	217	5	−uα+a	−uα+a	PART
ejpam-6136	218	1	λ	λ	X
ejpam-6136	218	2	+1	+1	NOUN
ejpam-6136	218	3	−uα	−uα	PROPN
ejpam-6136	218	4	+	+	X
ejpam-6136	218	5	a+	a+	PUNCT
ejpam-6136	218	6	λ	λ	NOUN
ejpam-6136	218	7	)	)	PUNCT
ejpam-6136	218	8	]	]	PUNCT
ejpam-6136	219	1	=	=	PUNCT
ejpam-6136	219	2	1	1	NUM
ejpam-6136	219	3	uβ	uβ	NOUN
ejpam-6136	219	4	[	[	PUNCT
ejpam-6136	219	5	−	−	X
ejpam-6136	219	6	(	(	PUNCT
ejpam-6136	219	7	1	1	NUM
ejpam-6136	219	8	−uα	−uα	NOUN
ejpam-6136	219	9	+	+	CCONJ
ejpam-6136	219	10	a+	a+	PUNCT
ejpam-6136	219	11	λ	λ	PROPN
ejpam-6136	219	12	)	)	PUNCT
ejpam-6136	219	13	]	]	PUNCT
ejpam-6136	219	14	,	,	PUNCT
ejpam-6136	219	15	for	for	ADP
ejpam-6136	219	16	−uα	−uα	PRON
ejpam-6136	219	17	+	+	NUM
ejpam-6136	219	18	a	a	DET
ejpam-6136	219	19	λ	λ	NOUN
ejpam-6136	219	20	+	+	ADP
ejpam-6136	219	21	1	1	NUM
ejpam-6136	219	22	<	<	SYM
ejpam-6136	219	23	0	0	PUNCT
ejpam-6136	219	24	=	=	SYM
ejpam-6136	219	25	1	1	NUM
ejpam-6136	219	26	uβ	uβ	NOUN
ejpam-6136	219	27	(	(	PUNCT
ejpam-6136	219	28	1	1	NUM
ejpam-6136	219	29	uα	uα	NOUN
ejpam-6136	219	30	−	−	PROPN
ejpam-6136	219	31	a−	a−	PROPN
ejpam-6136	219	32	λ	λ	PROPN
ejpam-6136	219	33	)	)	PUNCT
ejpam-6136	219	34	=	=	SYM
ejpam-6136	220	1	u−β	u−β	NOUN
ejpam-6136	220	2	uα	uα	NOUN
ejpam-6136	220	3	−	−	PROPN
ejpam-6136	220	4	a−	a−	PROPN
ejpam-6136	220	5	λ	λ	PROPN
ejpam-6136	220	6	.	.	PUNCT
ejpam-6136	221	1	remark	remark	PROPN
ejpam-6136	221	2	6	6	NUM
ejpam-6136	221	3	.	.	PUNCT
ejpam-6136	222	1	observe	observe	VERB
ejpam-6136	222	2	that	that	SCONJ
ejpam-6136	222	3	as	as	ADP
ejpam-6136	222	4	λ	λ	PROPN
ejpam-6136	222	5	→	→	SYM
ejpam-6136	222	6	0	0	NUM
ejpam-6136	222	7	,	,	PUNCT
ejpam-6136	222	8	sλ{eaλ(t	sλ{eaλ(t	X
ejpam-6136	222	9	)	)	PUNCT
ejpam-6136	222	10	}	}	PUNCT
ejpam-6136	222	11	tends	tend	VERB
ejpam-6136	222	12	to	to	PART
ejpam-6136	222	13	s{ea(t	s{ea(t	VERB
ejpam-6136	222	14	)	)	PUNCT
ejpam-6136	222	15	}	}	PUNCT
ejpam-6136	222	16	.	.	PUNCT
ejpam-6136	223	1	that	that	PRON
ejpam-6136	223	2	is	is	ADV
ejpam-6136	223	3	,	,	PUNCT
ejpam-6136	223	4	lim	lim	PROPN
ejpam-6136	223	5	λ→0	λ→0	ADV
ejpam-6136	223	6	sλ{eaλ(t	sλ{eaλ(t	PROPN
ejpam-6136	223	7	)	)	PUNCT
ejpam-6136	223	8	}	}	PUNCT
ejpam-6136	223	9	=	=	SYM
ejpam-6136	224	1	u−β	u−β	NOUN
ejpam-6136	224	2	uα	uα	NOUN
ejpam-6136	224	3	−	−	PROPN
ejpam-6136	224	4	a−	a−	PROPN
ejpam-6136	224	5	0	0	NUM
ejpam-6136	224	6	=	=	SYM
ejpam-6136	224	7	s{ea(t	s{ea(t	PROPN
ejpam-6136	224	8	)	)	PUNCT
ejpam-6136	224	9	}	}	PUNCT
ejpam-6136	224	10	.	.	PUNCT
ejpam-6136	225	1	remark	remark	NOUN
ejpam-6136	225	2	7	7	NUM
ejpam-6136	225	3	.	.	PUNCT
ejpam-6136	225	4	m	m	PROPN
ejpam-6136	225	5	1	1	NUM
ejpam-6136	225	6	.	.	PUNCT
ejpam-6136	226	1	when	when	SCONJ
ejpam-6136	226	2	β	β	X
ejpam-6136	226	3	=	=	NOUN
ejpam-6136	226	4	0	0	NUM
ejpam-6136	226	5	and	and	CCONJ
ejpam-6136	226	6	α	α	NOUN
ejpam-6136	226	7	=	=	NOUN
ejpam-6136	226	8	1	1	NUM
ejpam-6136	226	9	in	in	ADP
ejpam-6136	226	10	equation	equation	NOUN
ejpam-6136	226	11	(	(	PUNCT
ejpam-6136	226	12	12	12	NUM
ejpam-6136	226	13	)	)	PUNCT
ejpam-6136	226	14	,	,	PUNCT
ejpam-6136	226	15	sλ{eaλ(t	sλ{eaλ(t	X
ejpam-6136	226	16	)	)	PUNCT
ejpam-6136	226	17	}	}	PUNCT
ejpam-6136	226	18	=	=	SYM
ejpam-6136	226	19	u−0	u−0	PROPN
ejpam-6136	226	20	u1	u1	NOUN
ejpam-6136	226	21	−	−	NOUN
ejpam-6136	226	22	a−	a−	PROPN
ejpam-6136	226	23	λ	λ	NOUN
ejpam-6136	226	24	=	=	SYM
ejpam-6136	226	25	1	1	NUM
ejpam-6136	226	26	u−	u−	PROPN
ejpam-6136	226	27	a−	a−	PROPN
ejpam-6136	226	28	λ	λ	NOUN
ejpam-6136	226	29	=	=	SYM
ejpam-6136	226	30	lλ{eaλ(t	lλ{eaλ(t	NOUN
ejpam-6136	226	31	)	)	PUNCT
ejpam-6136	226	32	}	}	PUNCT
ejpam-6136	226	33	.	.	PUNCT
ejpam-6136	227	1	j.	j.	PROPN
ejpam-6136	227	2	mohamadali	mohamadali	PROPN
ejpam-6136	227	3	,	,	PUNCT
ejpam-6136	227	4	n.	n.	PROPN
ejpam-6136	227	5	abdulcarim	abdulcarim	PROPN
ejpam-6136	227	6	/	/	SYM
ejpam-6136	227	7	eur	eur	PROPN
ejpam-6136	227	8	.	.	PUNCT
ejpam-6136	228	1	j.	j.	PROPN
ejpam-6136	228	2	pure	pure	PROPN
ejpam-6136	228	3	appl	appl	PROPN
ejpam-6136	228	4	.	.	PROPN
ejpam-6136	228	5	math	math	PROPN
ejpam-6136	228	6	,	,	PUNCT
ejpam-6136	228	7	18	18	NUM
ejpam-6136	228	8	(	(	PUNCT
ejpam-6136	228	9	3	3	NUM
ejpam-6136	228	10	)	)	PUNCT
ejpam-6136	228	11	(	(	PUNCT
ejpam-6136	228	12	2025	2025	NUM
ejpam-6136	228	13	)	)	PUNCT
ejpam-6136	228	14	,	,	PUNCT
ejpam-6136	228	15	6136	6136	NUM
ejpam-6136	228	16	11	11	NUM
ejpam-6136	228	17	of	of	ADP
ejpam-6136	228	18	19	19	NUM
ejpam-6136	228	19	2	2	NUM
ejpam-6136	228	20	.	.	PUNCT
ejpam-6136	229	1	when	when	SCONJ
ejpam-6136	229	2	β	β	X
ejpam-6136	229	3	=	=	VERB
ejpam-6136	229	4	−1	−1	NOUN
ejpam-6136	229	5	and	and	CCONJ
ejpam-6136	229	6	α	α	NOUN
ejpam-6136	229	7	=	=	SYM
ejpam-6136	229	8	−1	−1	NOUN
ejpam-6136	229	9	in	in	ADP
ejpam-6136	229	10	equation	equation	NOUN
ejpam-6136	229	11	(	(	PUNCT
ejpam-6136	229	12	12	12	NUM
ejpam-6136	229	13	)	)	PUNCT
ejpam-6136	229	14	,	,	PUNCT
ejpam-6136	229	15	sλ{eaλ(t	sλ{eaλ(t	X
ejpam-6136	229	16	)	)	PUNCT
ejpam-6136	229	17	}	}	PUNCT
ejpam-6136	229	18	=	=	SYM
ejpam-6136	229	19	u−(−1	u−(−1	X
ejpam-6136	229	20	)	)	PUNCT
ejpam-6136	230	1	u−1	u−1	PROPN
ejpam-6136	230	2	−	−	PROPN
ejpam-6136	230	3	a−	a−	PROPN
ejpam-6136	230	4	λ	λ	NOUN
ejpam-6136	230	5	=	=	SYM
ejpam-6136	230	6	u2	u2	PROPN
ejpam-6136	230	7	1−	1−	NUM
ejpam-6136	230	8	u(a+	u(a+	PROPN
ejpam-6136	230	9	λ	λ	NOUN
ejpam-6136	230	10	)	)	PUNCT
ejpam-6136	230	11	=	=	NUM
ejpam-6136	230	12	eλ{eaλ(t	eλ{eaλ(t	NOUN
ejpam-6136	230	13	)	)	PUNCT
ejpam-6136	230	14	}	}	PUNCT
ejpam-6136	230	15	.	.	PUNCT
ejpam-6136	231	1	3	3	X
ejpam-6136	231	2	.	.	X
ejpam-6136	231	3	when	when	SCONJ
ejpam-6136	231	4	β	β	X
ejpam-6136	231	5	=	=	SYM
ejpam-6136	231	6	1	1	NUM
ejpam-6136	231	7	and	and	CCONJ
ejpam-6136	231	8	α	α	NOUN
ejpam-6136	231	9	=	=	SYM
ejpam-6136	231	10	−1	−1	NOUN
ejpam-6136	231	11	in	in	ADP
ejpam-6136	231	12	equation	equation	NOUN
ejpam-6136	231	13	(	(	PUNCT
ejpam-6136	231	14	12	12	NUM
ejpam-6136	231	15	)	)	PUNCT
ejpam-6136	231	16	,	,	PUNCT
ejpam-6136	231	17	sλ{eaλ(t	sλ{eaλ(t	X
ejpam-6136	231	18	)	)	PUNCT
ejpam-6136	231	19	}	}	PUNCT
ejpam-6136	232	1	=	=	PUNCT
ejpam-6136	232	2	u−1	u−1	PROPN
ejpam-6136	232	3	u−1	u−1	PROPN
ejpam-6136	232	4	−	−	PROPN
ejpam-6136	232	5	a−	a−	PROPN
ejpam-6136	232	6	λ	λ	NOUN
ejpam-6136	232	7	=	=	SYM
ejpam-6136	232	8	1	1	NUM
ejpam-6136	232	9	1−	1−	NUM
ejpam-6136	232	10	u(a+	u(a+	PROPN
ejpam-6136	232	11	λ	λ	NOUN
ejpam-6136	232	12	)	)	PUNCT
ejpam-6136	232	13	=	=	SYM
ejpam-6136	232	14	sλ{eaλ(t	sλ{eaλ(t	PROPN
ejpam-6136	232	15	)	)	PUNCT
ejpam-6136	232	16	}	}	PUNCT
ejpam-6136	232	17	.	.	PUNCT
ejpam-6136	233	1	4	4	X
ejpam-6136	233	2	.	.	X
ejpam-6136	233	3	when	when	SCONJ
ejpam-6136	233	4	β	β	X
ejpam-6136	233	5	=	=	SYM
ejpam-6136	233	6	−α	−α	PROPN
ejpam-6136	233	7	and	and	CCONJ
ejpam-6136	233	8	α	α	NOUN
ejpam-6136	233	9	=	=	SYM
ejpam-6136	233	10	−1	−1	NOUN
ejpam-6136	233	11	in	in	ADP
ejpam-6136	233	12	equation	equation	NOUN
ejpam-6136	233	13	(	(	PUNCT
ejpam-6136	233	14	12	12	NUM
ejpam-6136	233	15	)	)	PUNCT
ejpam-6136	233	16	,	,	PUNCT
ejpam-6136	233	17	sλ{eaλ(t	sλ{eaλ(t	X
ejpam-6136	233	18	)	)	PUNCT
ejpam-6136	233	19	}	}	PUNCT
ejpam-6136	233	20	=	=	SYM
ejpam-6136	233	21	u−(−α	u−(−α	NUM
ejpam-6136	233	22	)	)	PUNCT
ejpam-6136	234	1	u−1	u−1	PROPN
ejpam-6136	234	2	−	−	PROPN
ejpam-6136	234	3	a−	a−	PROPN
ejpam-6136	234	4	λ	λ	NOUN
ejpam-6136	234	5	=	=	PUNCT
ejpam-6136	234	6	uα+1	uα+1	NOUN
ejpam-6136	234	7	1−	1−	NUM
ejpam-6136	234	8	u(a+	u(a+	ADJ
ejpam-6136	234	9	λ	λ	NOUN
ejpam-6136	234	10	)	)	PUNCT
ejpam-6136	234	11	=	=	SYM
ejpam-6136	234	12	gαλ{eaλ(t	gαλ{eaλ(t	PROPN
ejpam-6136	234	13	)	)	PUNCT
ejpam-6136	234	14	}	}	PUNCT
ejpam-6136	234	15	.	.	PUNCT
ejpam-6136	235	1	corollary	corollary	ADJ
ejpam-6136	235	2	1	1	NUM
ejpam-6136	235	3	.	.	PUNCT
ejpam-6136	236	1	the	the	DET
ejpam-6136	236	2	degenerate	degenerate	ADJ
ejpam-6136	236	3	sadik	sadik	PROPN
ejpam-6136	236	4	transform	transform	NOUN
ejpam-6136	236	5	of	of	ADP
ejpam-6136	236	6	the	the	DET
ejpam-6136	236	7	function	function	NOUN
ejpam-6136	236	8	is	be	AUX
ejpam-6136	236	9	f(t	f(t	NOUN
ejpam-6136	236	10	)	)	PUNCT
ejpam-6136	236	11	=	=	SYM
ejpam-6136	236	12	e−a	e−a	NUM
ejpam-6136	236	13	λ	λ	PROPN
ejpam-6136	236	14	(	(	PUNCT
ejpam-6136	236	15	t	t	PROPN
ejpam-6136	236	16	)	)	PUNCT
ejpam-6136	236	17	is	be	AUX
ejpam-6136	236	18	given	give	VERB
ejpam-6136	236	19	by	by	ADP
ejpam-6136	236	20	sλ{e−a	sλ{e−a	X
ejpam-6136	236	21	λ	λ	PROPN
ejpam-6136	236	22	(	(	PUNCT
ejpam-6136	236	23	t	t	NOUN
ejpam-6136	236	24	)	)	PUNCT
ejpam-6136	236	25	}	}	PUNCT
ejpam-6136	236	26	=	=	SYM
ejpam-6136	236	27	u−β	u−β	NOUN
ejpam-6136	236	28	uα	uα	PROPN
ejpam-6136	236	29	+	+	CCONJ
ejpam-6136	236	30	a−	a−	PROPN
ejpam-6136	236	31	λ	λ	PROPN
ejpam-6136	236	32	,	,	PUNCT
ejpam-6136	236	33	for	for	ADP
ejpam-6136	236	34	−uα	−uα	PRON
ejpam-6136	236	35	−	−	PROPN
ejpam-6136	236	36	a	a	DET
ejpam-6136	236	37	λ	λ	NOUN
ejpam-6136	236	38	+	+	ADP
ejpam-6136	236	39	1	1	NUM
ejpam-6136	236	40	<	<	X
ejpam-6136	236	41	0	0	NUM
ejpam-6136	236	42	.	.	PUNCT
ejpam-6136	237	1	(	(	PUNCT
ejpam-6136	237	2	13	13	NUM
ejpam-6136	237	3	)	)	PUNCT
ejpam-6136	237	4	theorem	theorem	NOUN
ejpam-6136	237	5	6	6	NUM
ejpam-6136	237	6	.	.	PUNCT
ejpam-6136	238	1	the	the	DET
ejpam-6136	238	2	degenerate	degenerate	ADJ
ejpam-6136	238	3	sadik	sadik	PROPN
ejpam-6136	238	4	transform	transform	NOUN
ejpam-6136	238	5	of	of	ADP
ejpam-6136	238	6	the	the	DET
ejpam-6136	238	7	function	function	NOUN
ejpam-6136	238	8	f(t	f(t	NOUN
ejpam-6136	238	9	)	)	PUNCT
ejpam-6136	238	10	=	=	SYM
ejpam-6136	238	11	eiaλ	eiaλ	NOUN
ejpam-6136	238	12	(	(	PUNCT
ejpam-6136	238	13	t	t	NOUN
ejpam-6136	238	14	)	)	PUNCT
ejpam-6136	238	15	is	be	AUX
ejpam-6136	238	16	given	give	VERB
ejpam-6136	238	17	by	by	ADP
ejpam-6136	238	18	sλ{eiaλ	sλ{eiaλ	X
ejpam-6136	238	19	(	(	PUNCT
ejpam-6136	238	20	t	t	NOUN
ejpam-6136	238	21	)	)	PUNCT
ejpam-6136	238	22	}	}	PUNCT
ejpam-6136	239	1	=	=	SYM
ejpam-6136	239	2	u−β	u−β	NOUN
ejpam-6136	239	3	uα	uα	NOUN
ejpam-6136	239	4	−	−	PROPN
ejpam-6136	239	5	ia−	ia−	PROPN
ejpam-6136	239	6	λ	λ	PROPN
ejpam-6136	239	7	,	,	PUNCT
ejpam-6136	239	8	for	for	ADP
ejpam-6136	239	9	0	0	NUM
ejpam-6136	239	10	<	<	X
ejpam-6136	239	11	u−αλ	u−αλ	NOUN
ejpam-6136	239	12	<	<	X
ejpam-6136	239	13	1	1	NUM
ejpam-6136	239	14	.	.	PUNCT
ejpam-6136	239	15	(	(	PUNCT
ejpam-6136	239	16	14	14	NUM
ejpam-6136	239	17	)	)	PUNCT
ejpam-6136	239	18	proof	proof	NOUN
ejpam-6136	239	19	.	.	PUNCT
ejpam-6136	240	1	when	when	SCONJ
ejpam-6136	240	2	f(t	f(t	NOUN
ejpam-6136	240	3	)	)	PUNCT
ejpam-6136	240	4	=	=	SYM
ejpam-6136	240	5	eiaλ	eiaλ	NOUN
ejpam-6136	240	6	(	(	PUNCT
ejpam-6136	240	7	t	t	NOUN
ejpam-6136	240	8	)	)	PUNCT
ejpam-6136	240	9	in	in	ADP
ejpam-6136	240	10	equation	equation	NOUN
ejpam-6136	240	11	(	(	PUNCT
ejpam-6136	240	12	8)	8)	NUM
ejpam-6136	240	13	,	,	PUNCT
ejpam-6136	240	14	we	we	PRON
ejpam-6136	240	15	have	have	VERB
ejpam-6136	240	16	sλ{eiaλ	sλ{eiaλ	NOUN
ejpam-6136	240	17	(	(	PUNCT
ejpam-6136	240	18	t	t	NOUN
ejpam-6136	240	19	)	)	PUNCT
ejpam-6136	240	20	}	}	PUNCT
ejpam-6136	240	21	=	=	SYM
ejpam-6136	241	1	1	1	NUM
ejpam-6136	241	2	uβ	uβ	NOUN
ejpam-6136	241	3	∫	∫	PROPN
ejpam-6136	241	4	∞	∞	PROPN
ejpam-6136	241	5	0	0	NUM
ejpam-6136	241	6	e−uα	e−uα	PROPN
ejpam-6136	241	7	λ	λ	PROPN
ejpam-6136	241	8	(	(	PUNCT
ejpam-6136	241	9	t	t	PROPN
ejpam-6136	241	10	)	)	PUNCT
ejpam-6136	241	11	{	{	PUNCT
ejpam-6136	241	12	eiaλ	eiaλ	NOUN
ejpam-6136	241	13	(	(	PUNCT
ejpam-6136	241	14	t	t	NOUN
ejpam-6136	241	15	)	)	PUNCT
ejpam-6136	241	16	}	}	PUNCT
ejpam-6136	241	17	dt	dt	NOUN
ejpam-6136	241	18	=	=	SYM
ejpam-6136	241	19	1	1	NUM
ejpam-6136	241	20	uβ	uβ	PROPN
ejpam-6136	241	21	lim	lim	PROPN
ejpam-6136	241	22	r→∞	r→∞	PUNCT
ejpam-6136	241	23	∫	∫	PROPN
ejpam-6136	242	1	r	r	NOUN
ejpam-6136	242	2	0	0	NUM
ejpam-6136	242	3	(	(	PUNCT
ejpam-6136	242	4	1	1	NUM
ejpam-6136	242	5	+	+	CCONJ
ejpam-6136	242	6	λt	λt	X
ejpam-6136	242	7	)	)	PUNCT
ejpam-6136	242	8	−uα+ia	−uα+ia	PROPN
ejpam-6136	242	9	λ	λ	INTJ
ejpam-6136	242	10	dt	dt	NOUN
ejpam-6136	242	11	.	.	PUNCT
ejpam-6136	243	1	=	=	SYM
ejpam-6136	243	2	1	1	NUM
ejpam-6136	243	3	uβ	uβ	NOUN
ejpam-6136	243	4	lim	lim	PROPN
ejpam-6136	243	5	r→∞	r→∞	NUM
ejpam-6136	243	6	[	[	PUNCT
ejpam-6136	243	7	(	(	PUNCT
ejpam-6136	243	8	1	1	NUM
ejpam-6136	243	9	+	+	NUM
ejpam-6136	243	10	λr	λr	NOUN
ejpam-6136	243	11	)	)	PUNCT
ejpam-6136	243	12	−uα+λ	−uα+λ	NOUN
ejpam-6136	243	13	λ	λ	PROPN
ejpam-6136	243	14	(	(	PUNCT
ejpam-6136	243	15	1	1	NUM
ejpam-6136	243	16	+	+	NUM
ejpam-6136	243	17	λr	λr	NOUN
ejpam-6136	243	18	)	)	PUNCT
ejpam-6136	243	19	ia	ia	PROPN
ejpam-6136	243	20	λ	λ	PROPN
ejpam-6136	243	21	−uα	−uα	PROPN
ejpam-6136	243	22	+	+	CCONJ
ejpam-6136	243	23	ia+	ia+	PROPN
ejpam-6136	243	24	λ	λ	X
ejpam-6136	243	25	−	−	PROPN
ejpam-6136	243	26	(	(	PUNCT
ejpam-6136	243	27	1	1	NUM
ejpam-6136	243	28	)	)	PUNCT
ejpam-6136	243	29	−uα+λ	−uα+λ	NOUN
ejpam-6136	243	30	λ	λ	PROPN
ejpam-6136	243	31	(	(	PUNCT
ejpam-6136	243	32	1	1	NUM
ejpam-6136	243	33	)	)	PUNCT
ejpam-6136	243	34	ia	ia	NOUN
ejpam-6136	243	35	λ	λ	X
ejpam-6136	243	36	−uα	−uα	PROPN
ejpam-6136	243	37	+	+	CCONJ
ejpam-6136	243	38	ia+	ia+	NOUN
ejpam-6136	243	39	λ	λ	X
ejpam-6136	243	40	]	]	X
ejpam-6136	243	41	=	=	SYM
ejpam-6136	243	42	1	1	NUM
ejpam-6136	243	43	uβ	uβ	NOUN
ejpam-6136	243	44	lim	lim	PROPN
ejpam-6136	243	45	r→∞	r→∞	NUM
ejpam-6136	243	46	[	[	PUNCT
ejpam-6136	243	47	(	(	PUNCT
ejpam-6136	243	48	1	1	NUM
ejpam-6136	243	49	+	+	NUM
ejpam-6136	243	50	λr	λr	NOUN
ejpam-6136	243	51	)	)	PUNCT
ejpam-6136	243	52	−uα+λ	−uα+λ	NOUN
ejpam-6136	243	53	λ	λ	PROPN
ejpam-6136	243	54	eiaλ	eiaλ	NOUN
ejpam-6136	243	55	r	r	NOUN
ejpam-6136	243	56	−uα	−uα	NOUN
ejpam-6136	243	57	+	+	CCONJ
ejpam-6136	243	58	ia+	ia+	PROPN
ejpam-6136	243	59	λ	λ	NOUN
ejpam-6136	243	60	−	−	PROPN
ejpam-6136	243	61	1	1	NUM
ejpam-6136	243	62	−uα	−uα	PROPN
ejpam-6136	243	63	+	+	CCONJ
ejpam-6136	243	64	ia+	ia+	NOUN
ejpam-6136	243	65	λ	λ	X
ejpam-6136	243	66	]	]	X
ejpam-6136	243	67	=	=	SYM
ejpam-6136	243	68	1	1	NUM
ejpam-6136	243	69	uβ	uβ	NOUN
ejpam-6136	243	70	lim	lim	PROPN
ejpam-6136	243	71	r→∞	r→∞	NUM
ejpam-6136	244	1	[	[	X
ejpam-6136	244	2	(	(	PUNCT
ejpam-6136	244	3	1	1	NUM
ejpam-6136	244	4	+	+	NUM
ejpam-6136	244	5	λr	λr	NOUN
ejpam-6136	244	6	)	)	PUNCT
ejpam-6136	244	7	−uα+λ	−uα+λ	NOUN
ejpam-6136	244	8	λ	λ	PROPN
ejpam-6136	244	9	(	(	PUNCT
ejpam-6136	244	10	cos	cos	X
ejpam-6136	244	11	(	(	PUNCT
ejpam-6136	244	12	a	a	DET
ejpam-6136	244	13	λ	λ	X
ejpam-6136	244	14	log(1	log(1	NOUN
ejpam-6136	244	15	+	+	CCONJ
ejpam-6136	244	16	λr	λr	NOUN
ejpam-6136	244	17	)	)	PUNCT
ejpam-6136	244	18	)	)	PUNCT
ejpam-6136	245	1	+	+	CCONJ
ejpam-6136	245	2	i	i	PRON
ejpam-6136	245	3	sin	sin	VERB
ejpam-6136	245	4	(	(	PUNCT
ejpam-6136	245	5	a	a	DET
ejpam-6136	245	6	λ	λ	X
ejpam-6136	245	7	log(1	log(1	NOUN
ejpam-6136	245	8	+	+	CCONJ
ejpam-6136	245	9	λr	λr	NOUN
ejpam-6136	245	10	)	)	PUNCT
ejpam-6136	245	11	)	)	PUNCT
ejpam-6136	245	12	)	)	PUNCT
ejpam-6136	246	1	−uα	−uα	PROPN
ejpam-6136	246	2	+	+	CCONJ
ejpam-6136	246	3	ia+	ia+	PROPN
ejpam-6136	246	4	λ	λ	X
ejpam-6136	246	5	]	]	PUNCT
ejpam-6136	246	6	−	−	PROPN
ejpam-6136	247	1	[	[	PUNCT
ejpam-6136	247	2	1	1	NUM
ejpam-6136	247	3	−uα	−uα	NOUN
ejpam-6136	247	4	+	+	CCONJ
ejpam-6136	247	5	ia+	ia+	NOUN
ejpam-6136	247	6	λ	λ	X
ejpam-6136	247	7	]	]	PUNCT
ejpam-6136	247	8	if	if	SCONJ
ejpam-6136	247	9	u−αλ	u−αλ	NOUN
ejpam-6136	247	10	=	=	NOUN
ejpam-6136	247	11	1	1	NUM
ejpam-6136	247	12	,	,	PUNCT
ejpam-6136	247	13	then	then	ADV
ejpam-6136	247	14	the	the	DET
ejpam-6136	247	15	first	first	ADJ
ejpam-6136	247	16	limit	limit	NOUN
ejpam-6136	247	17	on	on	ADP
ejpam-6136	247	18	the	the	DET
ejpam-6136	247	19	right	right	ADJ
ejpam-6136	247	20	-	-	PUNCT
ejpam-6136	247	21	hand	hand	NOUN
ejpam-6136	247	22	side	side	NOUN
ejpam-6136	247	23	of	of	ADP
ejpam-6136	247	24	the	the	DET
ejpam-6136	247	25	above	above	ADJ
ejpam-6136	247	26	equation	equation	NOUN
ejpam-6136	247	27	does	do	AUX
ejpam-6136	247	28	not	not	PART
ejpam-6136	247	29	exist	exist	VERB
ejpam-6136	247	30	since	since	SCONJ
ejpam-6136	247	31	the	the	DET
ejpam-6136	247	32	value	value	NOUN
ejpam-6136	247	33	of	of	ADP
ejpam-6136	247	34	the	the	DET
ejpam-6136	247	35	function	function	NOUN
ejpam-6136	247	36	j.	j.	PROPN
ejpam-6136	247	37	mohamadali	mohamadali	PROPN
ejpam-6136	247	38	,	,	PUNCT
ejpam-6136	247	39	n.	n.	PROPN
ejpam-6136	247	40	abdulcarim	abdulcarim	PROPN
ejpam-6136	247	41	/	/	SYM
ejpam-6136	247	42	eur	eur	PROPN
ejpam-6136	247	43	.	.	PUNCT
ejpam-6136	248	1	j.	j.	PROPN
ejpam-6136	248	2	pure	pure	PROPN
ejpam-6136	248	3	appl	appl	PROPN
ejpam-6136	248	4	.	.	PROPN
ejpam-6136	248	5	math	math	PROPN
ejpam-6136	248	6	,	,	PUNCT
ejpam-6136	248	7	18	18	NUM
ejpam-6136	248	8	(	(	PUNCT
ejpam-6136	248	9	3	3	NUM
ejpam-6136	248	10	)	)	PUNCT
ejpam-6136	248	11	(	(	PUNCT
ejpam-6136	248	12	2025	2025	NUM
ejpam-6136	248	13	)	)	PUNCT
ejpam-6136	248	14	,	,	PUNCT
ejpam-6136	248	15	6136	6136	NUM
ejpam-6136	248	16	12	12	NUM
ejpam-6136	248	17	of	of	ADP
ejpam-6136	248	18	19	19	NUM
ejpam-6136	248	19	cos	co	NOUN
ejpam-6136	248	20	(	(	PUNCT
ejpam-6136	248	21	a	a	DET
ejpam-6136	248	22	λ	λ	X
ejpam-6136	248	23	log(1	log(1	NOUN
ejpam-6136	248	24	+	+	CCONJ
ejpam-6136	248	25	λr	λr	NOUN
ejpam-6136	248	26	)	)	PUNCT
ejpam-6136	248	27	)	)	PUNCT
ejpam-6136	249	1	and	and	CCONJ
ejpam-6136	249	2	i	i	PRON
ejpam-6136	249	3	sin	sin	VERB
ejpam-6136	249	4	(	(	PUNCT
ejpam-6136	249	5	a	a	DET
ejpam-6136	249	6	λ	λ	X
ejpam-6136	249	7	log(1	log(1	NOUN
ejpam-6136	249	8	+	+	CCONJ
ejpam-6136	249	9	λr	λr	NOUN
ejpam-6136	249	10	)	)	PUNCT
ejpam-6136	249	11	)	)	PUNCT
ejpam-6136	249	12	is	be	AUX
ejpam-6136	249	13	oscillate	oscillate	ADJ
ejpam-6136	249	14	between	between	ADP
ejpam-6136	249	15	1	1	NUM
ejpam-6136	249	16	and	and	CCONJ
ejpam-6136	249	17	−1	−1	NOUN
ejpam-6136	249	18	.	.	PUNCT
ejpam-6136	250	1	thus	thus	ADV
ejpam-6136	250	2	,	,	PUNCT
ejpam-6136	250	3	sλ{eiaλ	sλ{eiaλ	NOUN
ejpam-6136	250	4	}	}	PUNCT
ejpam-6136	250	5	is	be	AUX
ejpam-6136	250	6	not	not	PART
ejpam-6136	250	7	defined	define	VERB
ejpam-6136	250	8	.	.	PUNCT
ejpam-6136	251	1	similarly	similarly	ADV
ejpam-6136	251	2	,	,	PUNCT
ejpam-6136	251	3	sλ{eiaλ	sλ{eiaλ	NOUN
ejpam-6136	251	4	}	}	PUNCT
ejpam-6136	251	5	is	be	AUX
ejpam-6136	251	6	not	not	PART
ejpam-6136	251	7	defined	define	VERB
ejpam-6136	251	8	for	for	ADP
ejpam-6136	251	9	u−αλ	u−αλ	NOUN
ejpam-6136	251	10	>	>	X
ejpam-6136	251	11	1	1	X
ejpam-6136	251	12	.	.	PUNCT
ejpam-6136	252	1	however	however	ADV
ejpam-6136	252	2	,	,	PUNCT
ejpam-6136	252	3	observe	observe	VERB
ejpam-6136	252	4	that	that	SCONJ
ejpam-6136	252	5	for	for	ADP
ejpam-6136	252	6	0	0	NUM
ejpam-6136	252	7	<	<	X
ejpam-6136	252	8	u−αλ	u−αλ	NOUN
ejpam-6136	252	9	<	<	X
ejpam-6136	252	10	1	1	NUM
ejpam-6136	252	11	,	,	PUNCT
ejpam-6136	252	12	(	(	PUNCT
ejpam-6136	252	13	1+λ(r	1+λ(r	NOUN
ejpam-6136	252	14	)	)	PUNCT
ejpam-6136	252	15	)	)	PUNCT
ejpam-6136	253	1	−uα+λ	−uα+λ	NOUN
ejpam-6136	253	2	λ	λ	PROPN
ejpam-6136	253	3	approaches	approach	VERB
ejpam-6136	253	4	to	to	ADP
ejpam-6136	253	5	0	0	NUM
ejpam-6136	253	6	as	as	SCONJ
ejpam-6136	253	7	r	r	NOUN
ejpam-6136	253	8	approaches	approach	NOUN
ejpam-6136	253	9	to	to	ADP
ejpam-6136	253	10	∞.	∞.	PROPN
ejpam-6136	253	11	hence	hence	ADV
ejpam-6136	253	12	,	,	PUNCT
ejpam-6136	253	13	sλ{eiaλ	sλ{eiaλ	NOUN
ejpam-6136	253	14	}	}	PUNCT
ejpam-6136	253	15	=	=	SYM
ejpam-6136	253	16	1	1	NUM
ejpam-6136	253	17	uβ	uβ	NOUN
ejpam-6136	253	18	[	[	PUNCT
ejpam-6136	253	19	−	−	X
ejpam-6136	253	20	(	(	PUNCT
ejpam-6136	253	21	1	1	NUM
ejpam-6136	253	22	−uα	−uα	NOUN
ejpam-6136	253	23	+	+	CCONJ
ejpam-6136	253	24	ia+	ia+	PROPN
ejpam-6136	253	25	λ	λ	PROPN
ejpam-6136	253	26	)	)	PUNCT
ejpam-6136	253	27	]	]	PUNCT
ejpam-6136	254	1	=	=	PUNCT
ejpam-6136	254	2	u−β	u−β	NOUN
ejpam-6136	254	3	uα	uα	NOUN
ejpam-6136	254	4	−	−	PROPN
ejpam-6136	254	5	ia−	ia−	PROPN
ejpam-6136	254	6	λ	λ	PROPN
ejpam-6136	254	7	,	,	PUNCT
ejpam-6136	254	8	for	for	ADP
ejpam-6136	254	9	u−αλ	u−αλ	NOUN
ejpam-6136	254	10	<	<	X
ejpam-6136	254	11	1	1	NUM
ejpam-6136	254	12	.	.	PUNCT
ejpam-6136	254	13	corollary	corollary	ADJ
ejpam-6136	254	14	2	2	NUM
ejpam-6136	254	15	.	.	PUNCT
ejpam-6136	255	1	the	the	DET
ejpam-6136	255	2	degenerate	degenerate	ADJ
ejpam-6136	255	3	sadik	sadik	PROPN
ejpam-6136	255	4	transform	transform	NOUN
ejpam-6136	255	5	of	of	ADP
ejpam-6136	255	6	the	the	DET
ejpam-6136	255	7	function	function	NOUN
ejpam-6136	255	8	f(t	f(t	NOUN
ejpam-6136	255	9	)	)	PUNCT
ejpam-6136	256	1	=	=	NOUN
ejpam-6136	256	2	e−ia	e−ia	PROPN
ejpam-6136	256	3	λ	λ	PROPN
ejpam-6136	256	4	(	(	PUNCT
ejpam-6136	256	5	t	t	PROPN
ejpam-6136	256	6	)	)	PUNCT
ejpam-6136	256	7	is	be	AUX
ejpam-6136	256	8	given	give	VERB
ejpam-6136	256	9	by	by	ADP
ejpam-6136	256	10	sλ{e−ia	sλ{e−ia	PROPN
ejpam-6136	256	11	λ	λ	PROPN
ejpam-6136	256	12	(	(	PUNCT
ejpam-6136	256	13	t	t	NOUN
ejpam-6136	256	14	)	)	PUNCT
ejpam-6136	256	15	}	}	PUNCT
ejpam-6136	257	1	=	=	SYM
ejpam-6136	257	2	u−β	u−β	NOUN
ejpam-6136	257	3	uα	uα	PROPN
ejpam-6136	257	4	+	+	CCONJ
ejpam-6136	257	5	ia−	ia−	PROPN
ejpam-6136	257	6	λ	λ	NOUN
ejpam-6136	257	7	,	,	PUNCT
ejpam-6136	257	8	for	for	ADP
ejpam-6136	257	9	0	0	NUM
ejpam-6136	257	10	<	<	X
ejpam-6136	257	11	u−αλ	u−αλ	NOUN
ejpam-6136	257	12	<	<	X
ejpam-6136	257	13	1	1	NUM
ejpam-6136	257	14	.	.	PUNCT
ejpam-6136	257	15	(	(	PUNCT
ejpam-6136	257	16	15	15	NUM
ejpam-6136	257	17	)	)	PUNCT
ejpam-6136	257	18	theorem	theorem	NOUN
ejpam-6136	257	19	7	7	NUM
ejpam-6136	257	20	.	.	PUNCT
ejpam-6136	258	1	the	the	DET
ejpam-6136	258	2	degenerate	degenerate	ADJ
ejpam-6136	258	3	sadik	sadik	PROPN
ejpam-6136	258	4	transform	transform	NOUN
ejpam-6136	258	5	of	of	ADP
ejpam-6136	258	6	the	the	DET
ejpam-6136	258	7	function	function	NOUN
ejpam-6136	258	8	f(t	f(t	PROPN
ejpam-6136	258	9	)	)	PUNCT
ejpam-6136	259	1	=	=	SYM
ejpam-6136	259	2	sinaλ(t	sinaλ(t	NOUN
ejpam-6136	259	3	)	)	PUNCT
ejpam-6136	259	4	is	be	AUX
ejpam-6136	259	5	given	give	VERB
ejpam-6136	259	6	by	by	ADP
ejpam-6136	259	7	sλ{sinaλ(t	sλ{sinaλ(t	NOUN
ejpam-6136	259	8	)	)	PUNCT
ejpam-6136	259	9	}	}	PUNCT
ejpam-6136	260	1	=	=	SYM
ejpam-6136	260	2	au−β	au−β	ADJ
ejpam-6136	260	3	u2α	u2α	NOUN
ejpam-6136	260	4	−	−	PROPN
ejpam-6136	260	5	2uαλ+	2uαλ+	NUM
ejpam-6136	260	6	a2	a2	PROPN
ejpam-6136	260	7	+	+	CCONJ
ejpam-6136	260	8	λ2	λ2	NOUN
ejpam-6136	260	9	.	.	PUNCT
ejpam-6136	261	1	(	(	PUNCT
ejpam-6136	261	2	16	16	X
ejpam-6136	261	3	)	)	PUNCT
ejpam-6136	261	4	proof	proof	NOUN
ejpam-6136	261	5	.	.	PUNCT
ejpam-6136	262	1	note	note	VERB
ejpam-6136	262	2	that	that	SCONJ
ejpam-6136	262	3	from	from	ADP
ejpam-6136	262	4	definition	definition	NOUN
ejpam-6136	262	5	3	3	NUM
ejpam-6136	262	6	for	for	ADP
ejpam-6136	262	7	f(t	f(t	NOUN
ejpam-6136	262	8	)	)	PUNCT
ejpam-6136	262	9	=	=	SYM
ejpam-6136	262	10	sin	sin	NOUN
ejpam-6136	262	11	(	(	PUNCT
ejpam-6136	262	12	a	a	X
ejpam-6136	262	13	)	)	PUNCT
ejpam-6136	262	14	λ	λ	PROPN
ejpam-6136	262	15	(	(	PUNCT
ejpam-6136	262	16	t	t	PROPN
ejpam-6136	262	17	)	)	PUNCT
ejpam-6136	262	18	,	,	PUNCT
ejpam-6136	262	19	we	we	PRON
ejpam-6136	262	20	have	have	VERB
ejpam-6136	262	21	sλ{sinaλ(t	sλ{sinaλ(t	NOUN
ejpam-6136	262	22	)	)	PUNCT
ejpam-6136	262	23	}	}	PUNCT
ejpam-6136	262	24	=	=	SYM
ejpam-6136	262	25	sλ	sλ	NOUN
ejpam-6136	262	26	{	{	PUNCT
ejpam-6136	262	27	eiaλ	eiaλ	NOUN
ejpam-6136	262	28	(	(	PUNCT
ejpam-6136	262	29	t)−	t)−	PROPN
ejpam-6136	262	30	e−ia	e−ia	PRON
ejpam-6136	262	31	λ	λ	PROPN
ejpam-6136	262	32	(	(	PUNCT
ejpam-6136	262	33	t	t	PROPN
ejpam-6136	262	34	)	)	PUNCT
ejpam-6136	262	35	2i	2i	NOUN
ejpam-6136	262	36	}	}	PUNCT
ejpam-6136	262	37	.	.	PUNCT
ejpam-6136	263	1	(	(	PUNCT
ejpam-6136	263	2	17	17	NUM
ejpam-6136	263	3	)	)	PUNCT
ejpam-6136	263	4	now	now	ADV
ejpam-6136	263	5	,	,	PUNCT
ejpam-6136	263	6	applying	apply	VERB
ejpam-6136	263	7	theorems	theorem	NOUN
ejpam-6136	263	8	2	2	NUM
ejpam-6136	263	9	,	,	PUNCT
ejpam-6136	263	10	6	6	NUM
ejpam-6136	263	11	and	and	CCONJ
ejpam-6136	263	12	corollary	corollary	ADJ
ejpam-6136	263	13	2	2	NUM
ejpam-6136	263	14	equation	equation	NOUN
ejpam-6136	263	15	(	(	PUNCT
ejpam-6136	263	16	17	17	NUM
ejpam-6136	263	17	)	)	PUNCT
ejpam-6136	263	18	deduces	deduce	VERB
ejpam-6136	263	19	sλ{sinaλ(t	sλ{sinaλ(t	NOUN
ejpam-6136	263	20	)	)	PUNCT
ejpam-6136	263	21	}	}	PUNCT
ejpam-6136	263	22	=	=	PUNCT
ejpam-6136	264	1	(	(	PUNCT
ejpam-6136	264	2	1	1	NUM
ejpam-6136	264	3	2i	2i	NUM
ejpam-6136	264	4	)	)	PUNCT
ejpam-6136	265	1	[	[	PUNCT
ejpam-6136	265	2	sλ	sλ	NOUN
ejpam-6136	265	3	{	{	PUNCT
ejpam-6136	265	4	eiaλ	eiaλ	NOUN
ejpam-6136	265	5	(	(	PUNCT
ejpam-6136	265	6	t	t	NOUN
ejpam-6136	265	7	)	)	PUNCT
ejpam-6136	265	8	}	}	PUNCT
ejpam-6136	265	9	−	−	ADP
ejpam-6136	265	10	sλ	sλ	NOUN
ejpam-6136	265	11	{	{	PUNCT
ejpam-6136	265	12	e−ia	e−ia	ADP
ejpam-6136	265	13	λ	λ	PROPN
ejpam-6136	265	14	(	(	PUNCT
ejpam-6136	265	15	t	t	PROPN
ejpam-6136	265	16	)	)	PUNCT
ejpam-6136	265	17	}	}	PUNCT
ejpam-6136	265	18	]	]	PUNCT
ejpam-6136	266	1	=	=	PUNCT
ejpam-6136	266	2	(	(	PUNCT
ejpam-6136	266	3	1	1	NUM
ejpam-6136	266	4	2i	2i	NUM
ejpam-6136	266	5	)	)	PUNCT
ejpam-6136	266	6	[	[	PUNCT
ejpam-6136	266	7	u−β	u−β	NOUN
ejpam-6136	266	8	uα	uα	NOUN
ejpam-6136	266	9	−	−	PROPN
ejpam-6136	266	10	ia−	ia−	PROPN
ejpam-6136	266	11	λ	λ	PROPN
ejpam-6136	266	12	−	−	PROPN
ejpam-6136	266	13	u−β	u−β	PROPN
ejpam-6136	266	14	uα	uα	PROPN
ejpam-6136	266	15	+	+	CCONJ
ejpam-6136	266	16	ia−	ia−	PROPN
ejpam-6136	266	17	λ	λ	X
ejpam-6136	266	18	]	]	X
ejpam-6136	266	19	=	=	PUNCT
ejpam-6136	266	20	(	(	PUNCT
ejpam-6136	266	21	u−β	u−β	NOUN
ejpam-6136	266	22	2i	2i	NUM
ejpam-6136	266	23	)	)	PUNCT
ejpam-6136	266	24	[	[	PUNCT
ejpam-6136	266	25	uα	uα	X
ejpam-6136	266	26	+	+	CCONJ
ejpam-6136	266	27	ia−	ia−	PROPN
ejpam-6136	266	28	λ−	λ−	PROPN
ejpam-6136	266	29	uα	uα	PROPN
ejpam-6136	266	30	+	+	CCONJ
ejpam-6136	266	31	ia+	ia+	PROPN
ejpam-6136	266	32	λ	λ	PROPN
ejpam-6136	266	33	(	(	PUNCT
ejpam-6136	266	34	uα)2	uα)2	NOUN
ejpam-6136	266	35	+	+	CCONJ
ejpam-6136	266	36	uαia−	uαia−	NOUN
ejpam-6136	266	37	uαλ−	uαλ−	PROPN
ejpam-6136	266	38	uαia−	uαia−	NOUN
ejpam-6136	266	39	(	(	PUNCT
ejpam-6136	266	40	ia)2	ia)2	PROPN
ejpam-6136	266	41	+	+	CCONJ
ejpam-6136	266	42	iaλ−	iaλ−	PROPN
ejpam-6136	266	43	uαλ−	uαλ−	PROPN
ejpam-6136	266	44	iaλ+	iaλ+	PROPN
ejpam-6136	266	45	λ2	λ2	NOUN
ejpam-6136	266	46	]	]	PUNCT
ejpam-6136	266	47	=	=	PUNCT
ejpam-6136	266	48	(	(	PUNCT
ejpam-6136	266	49	u−β	u−β	NOUN
ejpam-6136	266	50	2i	2i	NUM
ejpam-6136	266	51	)	)	PUNCT
ejpam-6136	266	52	[	[	PUNCT
ejpam-6136	266	53	2ia	2ia	ADJ
ejpam-6136	266	54	u2α	u2α	ADJ
ejpam-6136	266	55	−	−	PROPN
ejpam-6136	266	56	2uαλ+	2uαλ+	NUM
ejpam-6136	266	57	a2	a2	PROPN
ejpam-6136	266	58	+	+	CCONJ
ejpam-6136	266	59	λ2	λ2	NOUN
ejpam-6136	266	60	]	]	PUNCT
ejpam-6136	266	61	=	=	PUNCT
ejpam-6136	266	62	[	[	PUNCT
ejpam-6136	266	63	au−β	au−β	ADJ
ejpam-6136	266	64	u2α	u2α	NOUN
ejpam-6136	266	65	−	−	PROPN
ejpam-6136	266	66	2uαλ+	2uαλ+	NUM
ejpam-6136	266	67	a2	a2	PROPN
ejpam-6136	266	68	+	+	CCONJ
ejpam-6136	266	69	λ2	λ2	NOUN
ejpam-6136	266	70	]	]	PUNCT
ejpam-6136	266	71	.	.	PUNCT
ejpam-6136	267	1	therefore	therefore	ADV
ejpam-6136	267	2	,	,	PUNCT
ejpam-6136	267	3	the	the	DET
ejpam-6136	267	4	degenerate	degenerate	ADJ
ejpam-6136	267	5	sadik	sadik	ADJ
ejpam-6136	267	6	transform	transform	NOUN
ejpam-6136	267	7	of	of	ADP
ejpam-6136	267	8	the	the	DET
ejpam-6136	267	9	function	function	NOUN
ejpam-6136	267	10	f(t	f(t	NOUN
ejpam-6136	267	11	)	)	PUNCT
ejpam-6136	267	12	=	=	SYM
ejpam-6136	267	13	sin	sin	NOUN
ejpam-6136	267	14	(	(	PUNCT
ejpam-6136	267	15	a	a	X
ejpam-6136	267	16	)	)	PUNCT
ejpam-6136	267	17	λ	λ	PROPN
ejpam-6136	267	18	(	(	PUNCT
ejpam-6136	267	19	t	t	PROPN
ejpam-6136	267	20	)	)	PUNCT
ejpam-6136	267	21	is	be	AUX
ejpam-6136	267	22	given	give	VERB
ejpam-6136	267	23	by	by	ADP
ejpam-6136	267	24	sλ{sinaλ(t	sλ{sinaλ(t	NOUN
ejpam-6136	267	25	)	)	PUNCT
ejpam-6136	267	26	}	}	PUNCT
ejpam-6136	268	1	=	=	SYM
ejpam-6136	268	2	au−β	au−β	ADJ
ejpam-6136	268	3	u2α	u2α	NOUN
ejpam-6136	268	4	−	−	PROPN
ejpam-6136	268	5	2uαλ+	2uαλ+	NUM
ejpam-6136	268	6	a2	a2	PROPN
ejpam-6136	268	7	+	+	CCONJ
ejpam-6136	268	8	λ2	λ2	NOUN
ejpam-6136	268	9	.	.	PUNCT
ejpam-6136	269	1	j.	j.	PROPN
ejpam-6136	269	2	mohamadali	mohamadali	PROPN
ejpam-6136	269	3	,	,	PUNCT
ejpam-6136	269	4	n.	n.	PROPN
ejpam-6136	269	5	abdulcarim	abdulcarim	PROPN
ejpam-6136	269	6	/	/	SYM
ejpam-6136	269	7	eur	eur	PROPN
ejpam-6136	269	8	.	.	PUNCT
ejpam-6136	270	1	j.	j.	PROPN
ejpam-6136	270	2	pure	pure	PROPN
ejpam-6136	270	3	appl	appl	PROPN
ejpam-6136	270	4	.	.	PROPN
ejpam-6136	270	5	math	math	PROPN
ejpam-6136	270	6	,	,	PUNCT
ejpam-6136	270	7	18	18	NUM
ejpam-6136	270	8	(	(	PUNCT
ejpam-6136	270	9	3	3	NUM
ejpam-6136	270	10	)	)	PUNCT
ejpam-6136	270	11	(	(	PUNCT
ejpam-6136	270	12	2025	2025	NUM
ejpam-6136	270	13	)	)	PUNCT
ejpam-6136	270	14	,	,	PUNCT
ejpam-6136	270	15	6136	6136	NUM
ejpam-6136	270	16	13	13	NUM
ejpam-6136	270	17	of	of	ADP
ejpam-6136	270	18	19	19	NUM
ejpam-6136	270	19	remark	remark	NOUN
ejpam-6136	270	20	8	8	NUM
ejpam-6136	270	21	.	.	PUNCT
ejpam-6136	270	22	observe	observe	VERB
ejpam-6136	270	23	that	that	SCONJ
ejpam-6136	270	24	as	as	ADP
ejpam-6136	270	25	λ	λ	PROPN
ejpam-6136	270	26	→	→	SYM
ejpam-6136	270	27	0	0	NUM
ejpam-6136	270	28	,	,	PUNCT
ejpam-6136	270	29	sλ{sin	sλ{sin	NOUN
ejpam-6136	270	30	(	(	PUNCT
ejpam-6136	270	31	a	a	NOUN
ejpam-6136	270	32	)	)	PUNCT
ejpam-6136	270	33	λ	λ	PROPN
ejpam-6136	270	34	(	(	PUNCT
ejpam-6136	270	35	t	t	NOUN
ejpam-6136	270	36	)	)	PUNCT
ejpam-6136	270	37	}	}	PUNCT
ejpam-6136	270	38	tends	tend	VERB
ejpam-6136	270	39	to	to	PART
ejpam-6136	270	40	s{sin	s{sin	VERB
ejpam-6136	270	41	at	at	ADP
ejpam-6136	270	42	}	}	PUNCT
ejpam-6136	270	43	.	.	PUNCT
ejpam-6136	271	1	that	that	PRON
ejpam-6136	271	2	is	is	ADV
ejpam-6136	271	3	,	,	PUNCT
ejpam-6136	271	4	lim	lim	PROPN
ejpam-6136	271	5	λ→0	λ→0	PUNCT
ejpam-6136	271	6	sλ{sinaλ(t	sλ{sinaλ(t	NOUN
ejpam-6136	271	7	)	)	PUNCT
ejpam-6136	271	8	}	}	PUNCT
ejpam-6136	272	1	=	=	SYM
ejpam-6136	272	2	lim	lim	PROPN
ejpam-6136	272	3	λ→0	λ→0	PUNCT
ejpam-6136	272	4	[	[	PUNCT
ejpam-6136	272	5	au−β	au−β	ADJ
ejpam-6136	272	6	u2α	u2α	NOUN
ejpam-6136	272	7	−	−	PROPN
ejpam-6136	272	8	2uαλ+	2uαλ+	NUM
ejpam-6136	272	9	a2	a2	PROPN
ejpam-6136	272	10	+	+	CCONJ
ejpam-6136	272	11	λ2	λ2	NOUN
ejpam-6136	272	12	]	]	PUNCT
ejpam-6136	272	13	=	=	SYM
ejpam-6136	272	14	au−β	au−β	ADJ
ejpam-6136	272	15	u2α	u2α	NOUN
ejpam-6136	272	16	+	+	NUM
ejpam-6136	272	17	a2	a2	PROPN
ejpam-6136	272	18	=	=	SYM
ejpam-6136	272	19	s{sin(at	s{sin(at	PROPN
ejpam-6136	272	20	)	)	PUNCT
ejpam-6136	272	21	}	}	PUNCT
ejpam-6136	272	22	.	.	PUNCT
ejpam-6136	273	1	remark	remark	NOUN
ejpam-6136	273	2	9	9	NUM
ejpam-6136	273	3	.	.	PUNCT
ejpam-6136	273	4	m	m	PROPN
ejpam-6136	273	5	1	1	NUM
ejpam-6136	273	6	.	.	PUNCT
ejpam-6136	274	1	when	when	SCONJ
ejpam-6136	274	2	β	β	X
ejpam-6136	274	3	=	=	NOUN
ejpam-6136	274	4	0	0	NUM
ejpam-6136	274	5	and	and	CCONJ
ejpam-6136	274	6	α	α	NOUN
ejpam-6136	274	7	=	=	NOUN
ejpam-6136	274	8	1	1	NUM
ejpam-6136	274	9	in	in	ADP
ejpam-6136	274	10	equation	equation	NOUN
ejpam-6136	274	11	(	(	PUNCT
ejpam-6136	274	12	16	16	NUM
ejpam-6136	274	13	)	)	PUNCT
ejpam-6136	274	14	,	,	PUNCT
ejpam-6136	274	15	sλ{sinaλ(t	sλ{sinaλ(t	NOUN
ejpam-6136	274	16	)	)	PUNCT
ejpam-6136	274	17	}	}	PUNCT
ejpam-6136	275	1	=	=	PUNCT
ejpam-6136	275	2	au−0	au−0	PROPN
ejpam-6136	275	3	u2(1	u2(1	NOUN
ejpam-6136	275	4	)	)	PUNCT
ejpam-6136	276	1	−	−	PROPN
ejpam-6136	276	2	2u1λ+	2u1λ+	NUM
ejpam-6136	276	3	a2	a2	PROPN
ejpam-6136	276	4	+	+	CCONJ
ejpam-6136	276	5	λ2	λ2	NOUN
ejpam-6136	276	6	=	=	SYM
ejpam-6136	276	7	a	a	PRON
ejpam-6136	276	8	(	(	PUNCT
ejpam-6136	276	9	u−	u−	ADJ
ejpam-6136	276	10	λ)2	λ)2	NOUN
ejpam-6136	276	11	+	+	NUM
ejpam-6136	276	12	a2	a2	PROPN
ejpam-6136	276	13	=	=	PUNCT
ejpam-6136	276	14	lλ{sinaλ(t	lλ{sinaλ(t	PROPN
ejpam-6136	276	15	)	)	PUNCT
ejpam-6136	276	16	}	}	PUNCT
ejpam-6136	276	17	.	.	PUNCT
ejpam-6136	277	1	2	2	X
ejpam-6136	277	2	.	.	X
ejpam-6136	277	3	when	when	SCONJ
ejpam-6136	277	4	β	β	X
ejpam-6136	277	5	=	=	VERB
ejpam-6136	277	6	−1	−1	NOUN
ejpam-6136	277	7	and	and	CCONJ
ejpam-6136	277	8	α	α	NOUN
ejpam-6136	277	9	=	=	SYM
ejpam-6136	277	10	−1	−1	NOUN
ejpam-6136	277	11	in	in	ADP
ejpam-6136	277	12	equation	equation	NOUN
ejpam-6136	277	13	(	(	PUNCT
ejpam-6136	277	14	16	16	NUM
ejpam-6136	277	15	)	)	PUNCT
ejpam-6136	277	16	,	,	PUNCT
ejpam-6136	277	17	sλ{sinaλ(t	sλ{sinaλ(t	NOUN
ejpam-6136	277	18	)	)	PUNCT
ejpam-6136	277	19	}	}	PUNCT
ejpam-6136	277	20	=	=	SYM
ejpam-6136	277	21	au−(−1	au−(−1	PROPN
ejpam-6136	277	22	)	)	PUNCT
ejpam-6136	277	23	u2(−1	u2(−1	NOUN
ejpam-6136	277	24	)	)	PUNCT
ejpam-6136	278	1	−	−	PROPN
ejpam-6136	278	2	2u−1λ+	2u−1λ+	NUM
ejpam-6136	278	3	a2	a2	PROPN
ejpam-6136	278	4	+	+	CCONJ
ejpam-6136	278	5	λ2	λ2	NOUN
ejpam-6136	278	6	=	=	SYM
ejpam-6136	278	7	au3	au3	X
ejpam-6136	278	8	(	(	PUNCT
ejpam-6136	278	9	1−	1−	NUM
ejpam-6136	279	1	λu)2	λu)2	NOUN
ejpam-6136	279	2	+	+	CCONJ
ejpam-6136	279	3	a2u2	a2u2	PROPN
ejpam-6136	279	4	=	=	NOUN
ejpam-6136	279	5	eλ{sinaλ(t	eλ{sinaλ(t	PROPN
ejpam-6136	279	6	)	)	PUNCT
ejpam-6136	279	7	}	}	PUNCT
ejpam-6136	279	8	.	.	PUNCT
ejpam-6136	280	1	3	3	X
ejpam-6136	280	2	.	.	X
ejpam-6136	280	3	when	when	SCONJ
ejpam-6136	280	4	β	β	X
ejpam-6136	280	5	=	=	SYM
ejpam-6136	280	6	1	1	NUM
ejpam-6136	280	7	and	and	CCONJ
ejpam-6136	280	8	α	α	NOUN
ejpam-6136	280	9	=	=	SYM
ejpam-6136	280	10	−1	−1	NOUN
ejpam-6136	280	11	in	in	ADP
ejpam-6136	280	12	equation	equation	NOUN
ejpam-6136	280	13	(	(	PUNCT
ejpam-6136	280	14	16	16	NUM
ejpam-6136	280	15	)	)	PUNCT
ejpam-6136	280	16	,	,	PUNCT
ejpam-6136	280	17	sλ{sinaλ(t	sλ{sinaλ(t	NOUN
ejpam-6136	280	18	)	)	PUNCT
ejpam-6136	280	19	}	}	PUNCT
ejpam-6136	281	1	=	=	SYM
ejpam-6136	281	2	au−1	au−1	ADJ
ejpam-6136	281	3	u2(−1	u2(−1	NOUN
ejpam-6136	281	4	)	)	PUNCT
ejpam-6136	281	5	−	−	PROPN
ejpam-6136	281	6	2u−1λ+	2u−1λ+	NUM
ejpam-6136	281	7	a2	a2	PROPN
ejpam-6136	281	8	+	+	CCONJ
ejpam-6136	281	9	λ2	λ2	NOUN
ejpam-6136	281	10	=	=	SYM
ejpam-6136	281	11	au	au	X
ejpam-6136	281	12	(	(	PUNCT
ejpam-6136	281	13	1−	1−	NUM
ejpam-6136	281	14	λu)2	λu)2	NOUN
ejpam-6136	281	15	+	+	CCONJ
ejpam-6136	281	16	a2u2	a2u2	NOUN
ejpam-6136	281	17	=	=	NOUN
ejpam-6136	281	18	sλ{sinaλ(t	sλ{sinaλ(t	NOUN
ejpam-6136	281	19	)	)	PUNCT
ejpam-6136	281	20	}	}	PUNCT
ejpam-6136	281	21	.	.	PUNCT
ejpam-6136	282	1	4	4	X
ejpam-6136	282	2	.	.	X
ejpam-6136	282	3	when	when	SCONJ
ejpam-6136	282	4	β	β	X
ejpam-6136	282	5	=	=	SYM
ejpam-6136	282	6	−α	−α	PROPN
ejpam-6136	282	7	and	and	CCONJ
ejpam-6136	282	8	α	α	NOUN
ejpam-6136	282	9	=	=	SYM
ejpam-6136	282	10	−1	−1	NOUN
ejpam-6136	282	11	in	in	ADP
ejpam-6136	282	12	equation	equation	NOUN
ejpam-6136	282	13	(	(	PUNCT
ejpam-6136	282	14	16	16	NUM
ejpam-6136	282	15	)	)	PUNCT
ejpam-6136	282	16	,	,	PUNCT
ejpam-6136	282	17	sλ{sinaλ(t	sλ{sinaλ(t	NOUN
ejpam-6136	282	18	)	)	PUNCT
ejpam-6136	282	19	}	}	PUNCT
ejpam-6136	282	20	=	=	SYM
ejpam-6136	282	21	au−(−α	au−(−α	X
ejpam-6136	282	22	)	)	PUNCT
ejpam-6136	282	23	u2(−1	u2(−1	NOUN
ejpam-6136	282	24	)	)	PUNCT
ejpam-6136	283	1	−	−	PROPN
ejpam-6136	283	2	2u−1λ+	2u−1λ+	NUM
ejpam-6136	283	3	a2	a2	PROPN
ejpam-6136	283	4	+	+	CCONJ
ejpam-6136	283	5	λ2	λ2	NOUN
ejpam-6136	283	6	=	=	SYM
ejpam-6136	283	7	auα+2	auα+2	PROPN
ejpam-6136	283	8	(	(	PUNCT
ejpam-6136	283	9	1−	1−	NUM
ejpam-6136	283	10	λu)2	λu)2	NOUN
ejpam-6136	283	11	+	+	CCONJ
ejpam-6136	283	12	a2u2	a2u2	PROPN
ejpam-6136	283	13	=	=	PUNCT
ejpam-6136	283	14	gαλ{sinaλ(t	gαλ{sinaλ(t	PROPN
ejpam-6136	283	15	)	)	PUNCT
ejpam-6136	283	16	}	}	PUNCT
ejpam-6136	283	17	.	.	PUNCT
ejpam-6136	284	1	theorem	theorem	VERB
ejpam-6136	284	2	8	8	NUM
ejpam-6136	284	3	.	.	PUNCT
ejpam-6136	285	1	the	the	DET
ejpam-6136	285	2	degenerate	degenerate	ADJ
ejpam-6136	285	3	sadik	sadik	PROPN
ejpam-6136	285	4	transform	transform	NOUN
ejpam-6136	285	5	of	of	ADP
ejpam-6136	285	6	the	the	DET
ejpam-6136	285	7	function	function	NOUN
ejpam-6136	285	8	f(t	f(t	NOUN
ejpam-6136	285	9	)	)	PUNCT
ejpam-6136	285	10	=	=	SYM
ejpam-6136	285	11	cosaλ(t	cosaλ(t	NOUN
ejpam-6136	285	12	)	)	PUNCT
ejpam-6136	285	13	is	be	AUX
ejpam-6136	285	14	given	give	VERB
ejpam-6136	285	15	by	by	ADP
ejpam-6136	285	16	sλ{cosaλ(t	sλ{cosaλ(t	NOUN
ejpam-6136	285	17	)	)	PUNCT
ejpam-6136	285	18	}	}	PUNCT
ejpam-6136	286	1	=	=	SYM
ejpam-6136	286	2	auα−β	auα−β	PROPN
ejpam-6136	286	3	−	−	PROPN
ejpam-6136	286	4	u−βλ	u−βλ	VERB
ejpam-6136	286	5	u2α	u2α	NOUN
ejpam-6136	286	6	−	−	PROPN
ejpam-6136	286	7	2uαλ+	2uαλ+	NUM
ejpam-6136	286	8	a2	a2	PROPN
ejpam-6136	286	9	+	+	CCONJ
ejpam-6136	286	10	λ2	λ2	NOUN
ejpam-6136	286	11	(	(	PUNCT
ejpam-6136	286	12	18	18	NUM
ejpam-6136	286	13	)	)	PUNCT
ejpam-6136	286	14	remark	remark	NOUN
ejpam-6136	286	15	10	10	NUM
ejpam-6136	286	16	.	.	PUNCT
ejpam-6136	287	1	observe	observe	VERB
ejpam-6136	287	2	that	that	SCONJ
ejpam-6136	287	3	as	as	ADP
ejpam-6136	287	4	λ	λ	PROPN
ejpam-6136	287	5	→	→	SYM
ejpam-6136	287	6	0	0	NUM
ejpam-6136	287	7	,	,	PUNCT
ejpam-6136	287	8	sλ{cos	sλ{co	NOUN
ejpam-6136	287	9	(	(	PUNCT
ejpam-6136	287	10	a	a	X
ejpam-6136	287	11	)	)	PUNCT
ejpam-6136	287	12	λ	λ	PROPN
ejpam-6136	287	13	(	(	PUNCT
ejpam-6136	287	14	t	t	NOUN
ejpam-6136	287	15	)	)	PUNCT
ejpam-6136	287	16	}	}	PUNCT
ejpam-6136	287	17	tends	tend	VERB
ejpam-6136	287	18	to	to	ADP
ejpam-6136	287	19	s{cos	s{cos	NOUN
ejpam-6136	287	20	at	at	ADP
ejpam-6136	287	21	}	}	PUNCT
ejpam-6136	287	22	.	.	PUNCT
ejpam-6136	288	1	that	that	PRON
ejpam-6136	288	2	is	is	ADV
ejpam-6136	288	3	,	,	PUNCT
ejpam-6136	288	4	lim	lim	PROPN
ejpam-6136	288	5	λ→0	λ→0	PUNCT
ejpam-6136	288	6	sλ{cosaλ(t	sλ{cosaλ(t	PROPN
ejpam-6136	288	7	)	)	PUNCT
ejpam-6136	288	8	}	}	PUNCT
ejpam-6136	289	1	=	=	SYM
ejpam-6136	289	2	uα−β	uα−β	NOUN
ejpam-6136	289	3	−	−	NOUN
ejpam-6136	289	4	u−β(0	u−β(0	ADJ
ejpam-6136	289	5	)	)	PUNCT
ejpam-6136	289	6	u2α	u2α	NOUN
ejpam-6136	289	7	−	−	PROPN
ejpam-6136	289	8	2uα(0	2uα(0	NUM
ejpam-6136	289	9	)	)	PUNCT
ejpam-6136	290	1	+	+	NUM
ejpam-6136	290	2	a2	a2	PROPN
ejpam-6136	290	3	+	+	CCONJ
ejpam-6136	290	4	(	(	PUNCT
ejpam-6136	290	5	0)2	0)2	NUM
ejpam-6136	290	6	=	=	SYM
ejpam-6136	290	7	s{cos(at	s{cos(at	PROPN
ejpam-6136	290	8	)	)	PUNCT
ejpam-6136	290	9	}	}	PUNCT
ejpam-6136	290	10	.	.	PUNCT
ejpam-6136	291	1	remark	remark	NOUN
ejpam-6136	291	2	11	11	NUM
ejpam-6136	291	3	.	.	PUNCT
ejpam-6136	292	1	m	m	PROPN
ejpam-6136	292	2	1	1	NUM
ejpam-6136	292	3	.	.	PUNCT
ejpam-6136	293	1	when	when	SCONJ
ejpam-6136	293	2	β	β	X
ejpam-6136	293	3	=	=	NOUN
ejpam-6136	293	4	0	0	NUM
ejpam-6136	293	5	and	and	CCONJ
ejpam-6136	293	6	α	α	NOUN
ejpam-6136	293	7	=	=	NOUN
ejpam-6136	293	8	1	1	NUM
ejpam-6136	293	9	in	in	ADP
ejpam-6136	293	10	equation	equation	NOUN
ejpam-6136	293	11	(	(	PUNCT
ejpam-6136	293	12	18	18	NUM
ejpam-6136	293	13	)	)	PUNCT
ejpam-6136	293	14	,	,	PUNCT
ejpam-6136	293	15	sλ{cosaλ(t	sλ{cosaλ(t	NOUN
ejpam-6136	293	16	)	)	PUNCT
ejpam-6136	293	17	}	}	PUNCT
ejpam-6136	293	18	=	=	SYM
ejpam-6136	293	19	u1−0	u1−0	PROPN
ejpam-6136	293	20	−	−	PROPN
ejpam-6136	293	21	u−(1)λ	u−(1)λ	PROPN
ejpam-6136	293	22	u2(1	u2(1	PROPN
ejpam-6136	293	23	)	)	PUNCT
ejpam-6136	293	24	−	−	PROPN
ejpam-6136	293	25	2u1λ+	2u1λ+	NUM
ejpam-6136	293	26	a2	a2	PROPN
ejpam-6136	293	27	+	+	CCONJ
ejpam-6136	293	28	λ2	λ2	NOUN
ejpam-6136	293	29	=	=	SYM
ejpam-6136	293	30	u−	u−	PROPN
ejpam-6136	293	31	λ	λ	PROPN
ejpam-6136	293	32	u2	u2	NOUN
ejpam-6136	293	33	−	−	PROPN
ejpam-6136	293	34	2uλ+	2uλ+	NUM
ejpam-6136	293	35	λ2	λ2	NOUN
ejpam-6136	293	36	+	+	NUM
ejpam-6136	293	37	a2	a2	NOUN
ejpam-6136	293	38	=	=	PUNCT
ejpam-6136	293	39	lλ{cosaλ(t	lλ{cosaλ(t	NOUN
ejpam-6136	293	40	)	)	PUNCT
ejpam-6136	293	41	}	}	PUNCT
ejpam-6136	293	42	.	.	PUNCT
ejpam-6136	294	1	2	2	X
ejpam-6136	294	2	.	.	X
ejpam-6136	294	3	when	when	SCONJ
ejpam-6136	294	4	β	β	X
ejpam-6136	294	5	=	=	VERB
ejpam-6136	294	6	−1	−1	NOUN
ejpam-6136	294	7	and	and	CCONJ
ejpam-6136	294	8	α	α	NOUN
ejpam-6136	294	9	=	=	SYM
ejpam-6136	294	10	−1	−1	NOUN
ejpam-6136	294	11	in	in	ADP
ejpam-6136	294	12	equation	equation	NOUN
ejpam-6136	294	13	(	(	PUNCT
ejpam-6136	294	14	18	18	NUM
ejpam-6136	294	15	)	)	PUNCT
ejpam-6136	294	16	,	,	PUNCT
ejpam-6136	294	17	sλ{cosaλ(t	sλ{cosaλ(t	NOUN
ejpam-6136	294	18	)	)	PUNCT
ejpam-6136	294	19	}	}	PUNCT
ejpam-6136	294	20	=	=	SYM
ejpam-6136	294	21	u1−(−1	u1−(−1	PROPN
ejpam-6136	294	22	)	)	PUNCT
ejpam-6136	294	23	−	−	PROPN
ejpam-6136	294	24	u−(−1)λ	u−(−1)λ	NUM
ejpam-6136	294	25	u2(−1	u2(−1	NOUN
ejpam-6136	294	26	)	)	PUNCT
ejpam-6136	295	1	−	−	PROPN
ejpam-6136	295	2	2u−1λ+	2u−1λ+	NUM
ejpam-6136	295	3	a2	a2	PROPN
ejpam-6136	295	4	+	+	CCONJ
ejpam-6136	295	5	λ2	λ2	NOUN
ejpam-6136	295	6	=	=	SYM
ejpam-6136	295	7	(	(	PUNCT
ejpam-6136	295	8	1−	1−	NUM
ejpam-6136	295	9	uλ)u2	uλ)u2	PROPN
ejpam-6136	295	10	(	(	PUNCT
ejpam-6136	295	11	1−	1−	NUM
ejpam-6136	295	12	λ)2	λ)2	NOUN
ejpam-6136	295	13	+	+	CCONJ
ejpam-6136	295	14	a2u2	a2u2	NOUN
ejpam-6136	295	15	=	=	PUNCT
ejpam-6136	295	16	eλ{cosaλ(t	eλ{cosaλ(t	NOUN
ejpam-6136	295	17	)	)	PUNCT
ejpam-6136	295	18	}	}	PUNCT
ejpam-6136	295	19	.	.	PUNCT
ejpam-6136	296	1	j.	j.	PROPN
ejpam-6136	296	2	mohamadali	mohamadali	PROPN
ejpam-6136	296	3	,	,	PUNCT
ejpam-6136	296	4	n.	n.	PROPN
ejpam-6136	296	5	abdulcarim	abdulcarim	PROPN
ejpam-6136	296	6	/	/	SYM
ejpam-6136	296	7	eur	eur	PROPN
ejpam-6136	296	8	.	.	PUNCT
ejpam-6136	297	1	j.	j.	PROPN
ejpam-6136	297	2	pure	pure	PROPN
ejpam-6136	297	3	appl	appl	PROPN
ejpam-6136	297	4	.	.	PROPN
ejpam-6136	297	5	math	math	PROPN
ejpam-6136	297	6	,	,	PUNCT
ejpam-6136	297	7	18	18	NUM
ejpam-6136	297	8	(	(	PUNCT
ejpam-6136	297	9	3	3	NUM
ejpam-6136	297	10	)	)	PUNCT
ejpam-6136	297	11	(	(	PUNCT
ejpam-6136	297	12	2025	2025	NUM
ejpam-6136	297	13	)	)	PUNCT
ejpam-6136	297	14	,	,	PUNCT
ejpam-6136	297	15	6136	6136	NUM
ejpam-6136	297	16	14	14	NUM
ejpam-6136	297	17	of	of	ADP
ejpam-6136	297	18	19	19	NUM
ejpam-6136	297	19	3	3	NUM
ejpam-6136	297	20	.	.	PUNCT
ejpam-6136	298	1	when	when	SCONJ
ejpam-6136	298	2	β	β	X
ejpam-6136	298	3	=	=	SYM
ejpam-6136	298	4	1	1	NUM
ejpam-6136	298	5	and	and	CCONJ
ejpam-6136	298	6	α	α	NOUN
ejpam-6136	298	7	=	=	SYM
ejpam-6136	298	8	−1	−1	NOUN
ejpam-6136	298	9	in	in	ADP
ejpam-6136	298	10	equation	equation	NOUN
ejpam-6136	298	11	(	(	PUNCT
ejpam-6136	298	12	18	18	NUM
ejpam-6136	298	13	)	)	PUNCT
ejpam-6136	298	14	,	,	PUNCT
ejpam-6136	298	15	sλ{cosaλ(t	sλ{cosaλ(t	NOUN
ejpam-6136	298	16	)	)	PUNCT
ejpam-6136	298	17	}	}	PUNCT
ejpam-6136	298	18	=	=	SYM
ejpam-6136	298	19	u−1−(1	u−1−(1	NOUN
ejpam-6136	298	20	)	)	PUNCT
ejpam-6136	298	21	−	−	PROPN
ejpam-6136	299	1	u−(1)λ	u−(1)λ	PROPN
ejpam-6136	299	2	u2(−1	u2(−1	PROPN
ejpam-6136	299	3	)	)	PUNCT
ejpam-6136	300	1	−	−	PROPN
ejpam-6136	300	2	2u−1λ+	2u−1λ+	NUM
ejpam-6136	300	3	a2	a2	PROPN
ejpam-6136	300	4	+	+	CCONJ
ejpam-6136	300	5	λ2	λ2	NOUN
ejpam-6136	300	6	=	=	SYM
ejpam-6136	300	7	(	(	PUNCT
ejpam-6136	300	8	u−2	u−2	INTJ
ejpam-6136	300	9	−	−	PROPN
ejpam-6136	300	10	u−1λ)(u2	u−1λ)(u2	PROPN
ejpam-6136	300	11	)	)	PUNCT
ejpam-6136	300	12	1−	1−	NUM
ejpam-6136	300	13	2uλ+	2uλ+	NUM
ejpam-6136	300	14	λ2u2	λ2u2	AUX
ejpam-6136	301	1	+	+	CCONJ
ejpam-6136	301	2	a2u2	a2u2	PROPN
ejpam-6136	301	3	=	=	SYM
ejpam-6136	301	4	1−	1−	NUM
ejpam-6136	301	5	uλ	uλ	NOUN
ejpam-6136	301	6	(	(	PUNCT
ejpam-6136	301	7	1−	1−	NUM
ejpam-6136	301	8	λu)2	λu)2	NOUN
ejpam-6136	301	9	+	+	CCONJ
ejpam-6136	301	10	a2u2	a2u2	PROPN
ejpam-6136	301	11	=	=	NOUN
ejpam-6136	301	12	sλ{cosaλ(t	sλ{cosaλ(t	NOUN
ejpam-6136	301	13	)	)	PUNCT
ejpam-6136	301	14	}	}	PUNCT
ejpam-6136	301	15	.	.	PUNCT
ejpam-6136	302	1	4	4	X
ejpam-6136	302	2	.	.	X
ejpam-6136	302	3	when	when	SCONJ
ejpam-6136	302	4	β	β	X
ejpam-6136	302	5	=	=	SYM
ejpam-6136	302	6	−α	−α	PROPN
ejpam-6136	302	7	and	and	CCONJ
ejpam-6136	302	8	α	α	NOUN
ejpam-6136	302	9	=	=	SYM
ejpam-6136	302	10	−1	−1	NOUN
ejpam-6136	302	11	in	in	ADP
ejpam-6136	302	12	equation	equation	NOUN
ejpam-6136	302	13	(	(	PUNCT
ejpam-6136	302	14	18	18	NUM
ejpam-6136	302	15	)	)	PUNCT
ejpam-6136	302	16	,	,	PUNCT
ejpam-6136	302	17	sλ{cosaλ(t	sλ{cosaλ(t	NOUN
ejpam-6136	302	18	)	)	PUNCT
ejpam-6136	302	19	}	}	PUNCT
ejpam-6136	302	20	=	=	SYM
ejpam-6136	302	21	u−1−(−α	u−1−(−α	NOUN
ejpam-6136	302	22	)	)	PUNCT
ejpam-6136	302	23	−	−	PROPN
ejpam-6136	302	24	u−(−α)λ	u−(−α)λ	ADP
ejpam-6136	302	25	u2(−1	u2(−1	NOUN
ejpam-6136	302	26	)	)	PUNCT
ejpam-6136	303	1	−	−	PROPN
ejpam-6136	303	2	2u−1λ+	2u−1λ+	NUM
ejpam-6136	303	3	a2	a2	PROPN
ejpam-6136	303	4	+	+	CCONJ
ejpam-6136	303	5	λ2	λ2	NOUN
ejpam-6136	303	6	=	=	SYM
ejpam-6136	303	7	(	(	PUNCT
ejpam-6136	303	8	1−	1−	NUM
ejpam-6136	303	9	uλ)u1+α	uλ)u1+α	NOUN
ejpam-6136	303	10	(	(	PUNCT
ejpam-6136	303	11	1−	1−	NUM
ejpam-6136	303	12	λu)2	λu)2	NOUN
ejpam-6136	303	13	+	+	CCONJ
ejpam-6136	303	14	a2u2	a2u2	PROPN
ejpam-6136	303	15	=	=	PUNCT
ejpam-6136	303	16	gαλ{cosaλ(t	gαλ{cosaλ(t	PROPN
ejpam-6136	303	17	)	)	PUNCT
ejpam-6136	303	18	}	}	PUNCT
ejpam-6136	303	19	.	.	PUNCT
ejpam-6136	304	1	theorem	theorem	VERB
ejpam-6136	304	2	9	9	NUM
ejpam-6136	304	3	.	.	PUNCT
ejpam-6136	305	1	the	the	DET
ejpam-6136	305	2	degenerate	degenerate	ADJ
ejpam-6136	305	3	sadik	sadik	PROPN
ejpam-6136	305	4	transform	transform	NOUN
ejpam-6136	305	5	of	of	ADP
ejpam-6136	305	6	the	the	DET
ejpam-6136	305	7	function	function	NOUN
ejpam-6136	305	8	f(t	f(t	PROPN
ejpam-6136	305	9	)	)	PUNCT
ejpam-6136	305	10	defined	define	VERB
ejpam-6136	305	11	by	by	ADP
ejpam-6136	305	12	f(t	f(t	NOUN
ejpam-6136	305	13	)	)	PUNCT
ejpam-6136	305	14	=	=	SYM
ejpam-6136	305	15	sinh	sinh	NOUN
ejpam-6136	305	16	(	(	PUNCT
ejpam-6136	305	17	a	a	NOUN
ejpam-6136	305	18	)	)	PUNCT
ejpam-6136	305	19	λ	λ	PROPN
ejpam-6136	305	20	(	(	PUNCT
ejpam-6136	305	21	t	t	PROPN
ejpam-6136	305	22	)	)	PUNCT
ejpam-6136	305	23	is	be	AUX
ejpam-6136	305	24	given	give	VERB
ejpam-6136	305	25	by	by	ADP
ejpam-6136	305	26	sλ{sinhaλ(t	sλ{sinhaλ(t	NOUN
ejpam-6136	305	27	)	)	PUNCT
ejpam-6136	305	28	}	}	PUNCT
ejpam-6136	305	29	=	=	SYM
ejpam-6136	305	30	au−β	au−β	ADJ
ejpam-6136	305	31	u2α	u2α	NOUN
ejpam-6136	305	32	−	−	PROPN
ejpam-6136	305	33	2uαλ−	2uαλ−	NUM
ejpam-6136	305	34	a2	a2	PROPN
ejpam-6136	305	35	+	+	CCONJ
ejpam-6136	305	36	λ2	λ2	NOUN
ejpam-6136	305	37	.	.	PUNCT
ejpam-6136	306	1	(	(	PUNCT
ejpam-6136	306	2	19	19	NUM
ejpam-6136	306	3	)	)	PUNCT
ejpam-6136	306	4	remark	remark	NOUN
ejpam-6136	306	5	12	12	NUM
ejpam-6136	306	6	.	.	PUNCT
ejpam-6136	307	1	observe	observe	VERB
ejpam-6136	307	2	that	that	SCONJ
ejpam-6136	307	3	as	as	ADP
ejpam-6136	307	4	λ	λ	PROPN
ejpam-6136	307	5	→	→	SYM
ejpam-6136	307	6	0	0	NUM
ejpam-6136	307	7	,	,	PUNCT
ejpam-6136	307	8	sλ{sinh	sλ{sinh	X
ejpam-6136	307	9	(	(	PUNCT
ejpam-6136	307	10	a	a	X
ejpam-6136	307	11	)	)	PUNCT
ejpam-6136	307	12	λ	λ	PROPN
ejpam-6136	307	13	(	(	PUNCT
ejpam-6136	307	14	t	t	NOUN
ejpam-6136	307	15	)	)	PUNCT
ejpam-6136	307	16	}	}	PUNCT
ejpam-6136	307	17	tends	tend	VERB
ejpam-6136	307	18	to	to	PART
ejpam-6136	307	19	s{sinh	s{sinh	VERB
ejpam-6136	307	20	at	at	ADP
ejpam-6136	307	21	}	}	PUNCT
ejpam-6136	307	22	.	.	PUNCT
ejpam-6136	308	1	that	that	PRON
ejpam-6136	308	2	is	is	ADV
ejpam-6136	308	3	,	,	PUNCT
ejpam-6136	308	4	lim	lim	PROPN
ejpam-6136	308	5	λ→0	λ→0	PROPN
ejpam-6136	308	6	sλ{sinhaλ(t	sλ{sinhaλ(t	PROPN
ejpam-6136	308	7	)	)	PUNCT
ejpam-6136	308	8	}	}	PUNCT
ejpam-6136	309	1	=	=	SYM
ejpam-6136	309	2	lim	lim	PROPN
ejpam-6136	309	3	λ→0	λ→0	PUNCT
ejpam-6136	309	4	[	[	PUNCT
ejpam-6136	309	5	au−β	au−β	ADJ
ejpam-6136	309	6	u2α	u2α	NOUN
ejpam-6136	309	7	−	−	PROPN
ejpam-6136	309	8	2uαλ−	2uαλ−	NUM
ejpam-6136	309	9	a2	a2	PROPN
ejpam-6136	309	10	+	+	CCONJ
ejpam-6136	309	11	λ2	λ2	NOUN
ejpam-6136	309	12	]	]	X
ejpam-6136	309	13	=	=	SYM
ejpam-6136	309	14	s{sinh(at	s{sinh(at	PROPN
ejpam-6136	309	15	)	)	PUNCT
ejpam-6136	309	16	}	}	PUNCT
ejpam-6136	309	17	.	.	PUNCT
ejpam-6136	310	1	remark	remark	NOUN
ejpam-6136	310	2	13	13	NUM
ejpam-6136	310	3	.	.	PUNCT
ejpam-6136	311	1	m	m	PROPN
ejpam-6136	311	2	1	1	NUM
ejpam-6136	311	3	.	.	PUNCT
ejpam-6136	312	1	when	when	SCONJ
ejpam-6136	312	2	β	β	X
ejpam-6136	312	3	=	=	NOUN
ejpam-6136	312	4	0	0	NUM
ejpam-6136	312	5	and	and	CCONJ
ejpam-6136	312	6	α	α	NOUN
ejpam-6136	312	7	=	=	NOUN
ejpam-6136	312	8	1	1	NUM
ejpam-6136	312	9	in	in	ADP
ejpam-6136	312	10	equation	equation	NOUN
ejpam-6136	312	11	(	(	PUNCT
ejpam-6136	312	12	19	19	NUM
ejpam-6136	312	13	)	)	PUNCT
ejpam-6136	312	14	,	,	PUNCT
ejpam-6136	312	15	sλ{sinhaλ(t	sλ{sinhaλ(t	NOUN
ejpam-6136	312	16	)	)	PUNCT
ejpam-6136	312	17	}	}	PUNCT
ejpam-6136	313	1	=	=	PUNCT
ejpam-6136	313	2	au−0	au−0	PROPN
ejpam-6136	313	3	u2(1	u2(1	NOUN
ejpam-6136	313	4	)	)	PUNCT
ejpam-6136	314	1	−	−	PROPN
ejpam-6136	314	2	2u1λ−	2u1λ−	NUM
ejpam-6136	314	3	a2	a2	PROPN
ejpam-6136	314	4	+	+	CCONJ
ejpam-6136	314	5	λ2	λ2	NOUN
ejpam-6136	314	6	=	=	SYM
ejpam-6136	314	7	a	a	PRON
ejpam-6136	314	8	(	(	PUNCT
ejpam-6136	314	9	u−	u−	ADJ
ejpam-6136	314	10	λ)2	λ)2	NOUN
ejpam-6136	314	11	−	−	PROPN
ejpam-6136	314	12	a2	a2	NOUN
ejpam-6136	314	13	=	=	PUNCT
ejpam-6136	314	14	lλ{sinhaλ(t	lλ{sinhaλ(t	PROPN
ejpam-6136	314	15	)	)	PUNCT
ejpam-6136	314	16	}	}	PUNCT
ejpam-6136	314	17	.	.	PUNCT
ejpam-6136	315	1	2	2	X
ejpam-6136	315	2	.	.	X
ejpam-6136	315	3	when	when	SCONJ
ejpam-6136	315	4	β	β	X
ejpam-6136	315	5	=	=	VERB
ejpam-6136	315	6	−1	−1	NOUN
ejpam-6136	315	7	and	and	CCONJ
ejpam-6136	315	8	α	α	NOUN
ejpam-6136	315	9	=	=	SYM
ejpam-6136	315	10	−1	−1	NOUN
ejpam-6136	315	11	in	in	ADP
ejpam-6136	315	12	equation	equation	NOUN
ejpam-6136	315	13	(	(	PUNCT
ejpam-6136	315	14	19	19	NUM
ejpam-6136	315	15	)	)	PUNCT
ejpam-6136	315	16	,	,	PUNCT
ejpam-6136	315	17	sλ{sinhaλ(t	sλ{sinhaλ(t	NOUN
ejpam-6136	315	18	)	)	PUNCT
ejpam-6136	315	19	}	}	PUNCT
ejpam-6136	315	20	=	=	SYM
ejpam-6136	315	21	au−(−1	au−(−1	PROPN
ejpam-6136	315	22	)	)	PUNCT
ejpam-6136	315	23	u2(−1	u2(−1	NOUN
ejpam-6136	315	24	)	)	PUNCT
ejpam-6136	316	1	−	−	PROPN
ejpam-6136	316	2	2u−1λ−	2u−1λ−	NUM
ejpam-6136	316	3	a2	a2	PROPN
ejpam-6136	316	4	+	+	CCONJ
ejpam-6136	316	5	λ2	λ2	NOUN
ejpam-6136	316	6	=	=	SYM
ejpam-6136	316	7	au3	au3	X
ejpam-6136	316	8	(	(	PUNCT
ejpam-6136	316	9	1−	1−	NUM
ejpam-6136	316	10	λu)2	λu)2	NOUN
ejpam-6136	316	11	−	−	PROPN
ejpam-6136	316	12	a2u2	a2u2	NOUN
ejpam-6136	316	13	=	=	NOUN
ejpam-6136	316	14	eλ{sinhaλ(t	eλ{sinhaλ(t	NOUN
ejpam-6136	316	15	)	)	PUNCT
ejpam-6136	316	16	}	}	PUNCT
ejpam-6136	316	17	.	.	PUNCT
ejpam-6136	317	1	3	3	X
ejpam-6136	317	2	.	.	X
ejpam-6136	317	3	when	when	SCONJ
ejpam-6136	317	4	β	β	X
ejpam-6136	317	5	=	=	SYM
ejpam-6136	317	6	1	1	NUM
ejpam-6136	317	7	and	and	CCONJ
ejpam-6136	317	8	α	α	NOUN
ejpam-6136	317	9	=	=	SYM
ejpam-6136	317	10	−1	−1	NOUN
ejpam-6136	317	11	in	in	ADP
ejpam-6136	317	12	equation	equation	NOUN
ejpam-6136	317	13	(	(	PUNCT
ejpam-6136	317	14	19	19	NUM
ejpam-6136	317	15	)	)	PUNCT
ejpam-6136	317	16	,	,	PUNCT
ejpam-6136	317	17	=	=	SYM
ejpam-6136	317	18	au−1	au−1	ADJ
ejpam-6136	317	19	u2(−1	u2(−1	NOUN
ejpam-6136	317	20	)	)	PUNCT
ejpam-6136	317	21	−	−	PROPN
ejpam-6136	318	1	2u−1λ−	2u−1λ−	NUM
ejpam-6136	318	2	a2	a2	PROPN
ejpam-6136	318	3	+	+	CCONJ
ejpam-6136	318	4	λ2	λ2	NOUN
ejpam-6136	318	5	=	=	SYM
ejpam-6136	318	6	au	au	X
ejpam-6136	318	7	(	(	PUNCT
ejpam-6136	318	8	1−	1−	NUM
ejpam-6136	318	9	λu)2	λu)2	NOUN
ejpam-6136	318	10	−	−	PROPN
ejpam-6136	319	1	a2u2	a2u2	NOUN
ejpam-6136	319	2	=	=	SYM
ejpam-6136	319	3	sλ{sinhaλ(t	sλ{sinhaλ(t	NOUN
ejpam-6136	319	4	)	)	PUNCT
ejpam-6136	319	5	}	}	PUNCT
ejpam-6136	319	6	.	.	PUNCT
ejpam-6136	320	1	4	4	X
ejpam-6136	320	2	.	.	X
ejpam-6136	320	3	when	when	SCONJ
ejpam-6136	320	4	β	β	X
ejpam-6136	320	5	=	=	SYM
ejpam-6136	320	6	−α	−α	PROPN
ejpam-6136	320	7	and	and	CCONJ
ejpam-6136	320	8	α	α	NOUN
ejpam-6136	320	9	=	=	SYM
ejpam-6136	320	10	−1	−1	NOUN
ejpam-6136	320	11	in	in	ADP
ejpam-6136	320	12	equation	equation	NOUN
ejpam-6136	320	13	(	(	PUNCT
ejpam-6136	320	14	19	19	NUM
ejpam-6136	320	15	)	)	PUNCT
ejpam-6136	320	16	,	,	PUNCT
ejpam-6136	320	17	=	=	PUNCT
ejpam-6136	320	18	au−(−α	au−(−α	ADJ
ejpam-6136	320	19	)	)	PUNCT
ejpam-6136	320	20	u2(−1	u2(−1	NOUN
ejpam-6136	320	21	)	)	PUNCT
ejpam-6136	321	1	−	−	PROPN
ejpam-6136	321	2	2u−1λ−	2u−1λ−	NUM
ejpam-6136	321	3	a2	a2	PROPN
ejpam-6136	321	4	+	+	CCONJ
ejpam-6136	321	5	λ2	λ2	NOUN
ejpam-6136	321	6	=	=	SYM
ejpam-6136	321	7	auα+2	auα+2	PROPN
ejpam-6136	321	8	(	(	PUNCT
ejpam-6136	321	9	1−	1−	NUM
ejpam-6136	321	10	λu)2	λu)2	NOUN
ejpam-6136	321	11	−	−	PROPN
ejpam-6136	322	1	a2u2	a2u2	PROPN
ejpam-6136	322	2	=	=	SYM
ejpam-6136	322	3	gαλ{sinhaλ(t	gαλ{sinhaλ(t	PROPN
ejpam-6136	322	4	)	)	PUNCT
ejpam-6136	322	5	}	}	PUNCT
ejpam-6136	322	6	.	.	PUNCT
ejpam-6136	323	1	j.	j.	PROPN
ejpam-6136	323	2	mohamadali	mohamadali	PROPN
ejpam-6136	323	3	,	,	PUNCT
ejpam-6136	323	4	n.	n.	PROPN
ejpam-6136	323	5	abdulcarim	abdulcarim	PROPN
ejpam-6136	323	6	/	/	SYM
ejpam-6136	323	7	eur	eur	PROPN
ejpam-6136	323	8	.	.	PUNCT
ejpam-6136	324	1	j.	j.	PROPN
ejpam-6136	324	2	pure	pure	PROPN
ejpam-6136	324	3	appl	appl	PROPN
ejpam-6136	324	4	.	.	PROPN
ejpam-6136	324	5	math	math	PROPN
ejpam-6136	324	6	,	,	PUNCT
ejpam-6136	324	7	18	18	NUM
ejpam-6136	324	8	(	(	PUNCT
ejpam-6136	324	9	3	3	NUM
ejpam-6136	324	10	)	)	PUNCT
ejpam-6136	324	11	(	(	PUNCT
ejpam-6136	324	12	2025	2025	NUM
ejpam-6136	324	13	)	)	PUNCT
ejpam-6136	324	14	,	,	PUNCT
ejpam-6136	324	15	6136	6136	NUM
ejpam-6136	324	16	15	15	NUM
ejpam-6136	324	17	of	of	ADP
ejpam-6136	324	18	19	19	NUM
ejpam-6136	324	19	theorem	theorem	VERB
ejpam-6136	324	20	10	10	NUM
ejpam-6136	324	21	.	.	PUNCT
ejpam-6136	325	1	the	the	DET
ejpam-6136	325	2	degenerate	degenerate	ADJ
ejpam-6136	325	3	sadik	sadik	PROPN
ejpam-6136	325	4	transform	transform	NOUN
ejpam-6136	325	5	of	of	ADP
ejpam-6136	325	6	the	the	DET
ejpam-6136	325	7	function	function	NOUN
ejpam-6136	325	8	f(t	f(t	PROPN
ejpam-6136	325	9	)	)	PUNCT
ejpam-6136	325	10	defined	define	VERB
ejpam-6136	325	11	by	by	ADP
ejpam-6136	325	12	f(t	f(t	NOUN
ejpam-6136	325	13	)	)	PUNCT
ejpam-6136	325	14	=	=	SYM
ejpam-6136	325	15	cosh	cosh	NOUN
ejpam-6136	325	16	(	(	PUNCT
ejpam-6136	325	17	a	a	X
ejpam-6136	325	18	)	)	PUNCT
ejpam-6136	325	19	λ	λ	PROPN
ejpam-6136	325	20	(	(	PUNCT
ejpam-6136	325	21	t	t	PROPN
ejpam-6136	325	22	)	)	PUNCT
ejpam-6136	325	23	is	be	AUX
ejpam-6136	325	24	given	give	VERB
ejpam-6136	325	25	by	by	ADP
ejpam-6136	325	26	sλ{coshaλ(t	sλ{coshaλ(t	NOUN
ejpam-6136	325	27	)	)	PUNCT
ejpam-6136	325	28	}	}	PUNCT
ejpam-6136	325	29	=	=	SYM
ejpam-6136	325	30	uα−β	uα−β	NOUN
ejpam-6136	325	31	−	−	NOUN
ejpam-6136	325	32	u−βλ	u−βλ	PROPN
ejpam-6136	325	33	u2α	u2α	NOUN
ejpam-6136	325	34	−	−	PROPN
ejpam-6136	325	35	2uαλ−	2uαλ−	NUM
ejpam-6136	325	36	a2	a2	PROPN
ejpam-6136	325	37	+	+	CCONJ
ejpam-6136	325	38	λ2	λ2	NOUN
ejpam-6136	325	39	.	.	PUNCT
ejpam-6136	326	1	(	(	PUNCT
ejpam-6136	326	2	20	20	NUM
ejpam-6136	326	3	)	)	PUNCT
ejpam-6136	326	4	proof	proof	NOUN
ejpam-6136	326	5	.	.	PUNCT
ejpam-6136	327	1	observe	observe	VERB
ejpam-6136	327	2	that	that	SCONJ
ejpam-6136	327	3	by	by	ADP
ejpam-6136	327	4	definition	definition	NOUN
ejpam-6136	327	5	7	7	NUM
ejpam-6136	327	6	,	,	PUNCT
ejpam-6136	327	7	for	for	ADP
ejpam-6136	327	8	f(t	f(t	NOUN
ejpam-6136	327	9	)	)	PUNCT
ejpam-6136	327	10	=	=	SYM
ejpam-6136	327	11	cosh	cosh	NOUN
ejpam-6136	327	12	(	(	PUNCT
ejpam-6136	327	13	a	a	X
ejpam-6136	327	14	)	)	PUNCT
ejpam-6136	327	15	λ	λ	PROPN
ejpam-6136	327	16	(	(	PUNCT
ejpam-6136	327	17	t	t	PROPN
ejpam-6136	327	18	)	)	PUNCT
ejpam-6136	327	19	,	,	PUNCT
ejpam-6136	327	20	we	we	PRON
ejpam-6136	327	21	have	have	VERB
ejpam-6136	327	22	sλ{cosh	sλ{cosh	ADV
ejpam-6136	327	23	(	(	PUNCT
ejpam-6136	327	24	a	a	X
ejpam-6136	327	25	)	)	PUNCT
ejpam-6136	327	26	λ	λ	PROPN
ejpam-6136	327	27	(	(	PUNCT
ejpam-6136	327	28	t	t	NOUN
ejpam-6136	327	29	)	)	PUNCT
ejpam-6136	327	30	}	}	PUNCT
ejpam-6136	328	1	=	=	SYM
ejpam-6136	328	2	sλ	sλ	NOUN
ejpam-6136	328	3	{	{	PUNCT
ejpam-6136	328	4	eaλ(t	eaλ(t	PROPN
ejpam-6136	328	5	)	)	PUNCT
ejpam-6136	329	1	+	+	NUM
ejpam-6136	329	2	e−a	e−a	NUM
ejpam-6136	329	3	λ	λ	PROPN
ejpam-6136	329	4	(	(	PUNCT
ejpam-6136	329	5	t	t	PROPN
ejpam-6136	329	6	)	)	PUNCT
ejpam-6136	329	7	2	2	NUM
ejpam-6136	329	8	}	}	PUNCT
ejpam-6136	329	9	.	.	PUNCT
ejpam-6136	330	1	next	next	ADV
ejpam-6136	330	2	,	,	PUNCT
ejpam-6136	330	3	applying	apply	VERB
ejpam-6136	330	4	theorems	theorem	NOUN
ejpam-6136	330	5	2	2	NUM
ejpam-6136	330	6	,	,	PUNCT
ejpam-6136	330	7	5	5	NUM
ejpam-6136	330	8	and	and	CCONJ
ejpam-6136	330	9	corollary	corollary	ADJ
ejpam-6136	330	10	1	1	NUM
ejpam-6136	330	11	,	,	PUNCT
ejpam-6136	330	12	simplifying	simplify	VERB
ejpam-6136	330	13	the	the	DET
ejpam-6136	330	14	resulting	result	VERB
ejpam-6136	330	15	equation	equation	NOUN
ejpam-6136	330	16	resulted	result	VERB
ejpam-6136	330	17	to	to	ADP
ejpam-6136	330	18	sλ{coshaλ(t	sλ{coshaλ(t	NOUN
ejpam-6136	330	19	)	)	PUNCT
ejpam-6136	330	20	}	}	PUNCT
ejpam-6136	331	1	=	=	X
ejpam-6136	331	2	sλ	sλ	X
ejpam-6136	331	3	{	{	PUNCT
ejpam-6136	331	4	eaλ(t	eaλ(t	PROPN
ejpam-6136	331	5	)	)	PUNCT
ejpam-6136	331	6	+	+	NUM
ejpam-6136	331	7	e−a	e−a	NUM
ejpam-6136	331	8	λ	λ	PROPN
ejpam-6136	331	9	(	(	PUNCT
ejpam-6136	331	10	t	t	PROPN
ejpam-6136	331	11	)	)	PUNCT
ejpam-6136	331	12	2	2	NUM
ejpam-6136	331	13	}	}	PUNCT
ejpam-6136	331	14	=	=	SYM
ejpam-6136	331	15	(	(	PUNCT
ejpam-6136	331	16	1	1	NUM
ejpam-6136	331	17	2	2	NUM
ejpam-6136	331	18	)	)	PUNCT
ejpam-6136	331	19	[	[	PUNCT
ejpam-6136	331	20	sλ	sλ	X
ejpam-6136	331	21	{	{	PUNCT
ejpam-6136	331	22	eaλ(t	eaλ(t	PROPN
ejpam-6136	331	23	)	)	PUNCT
ejpam-6136	331	24	}	}	PUNCT
ejpam-6136	332	1	+	+	CCONJ
ejpam-6136	332	2	sλ	sλ	NOUN
ejpam-6136	332	3	{	{	PUNCT
ejpam-6136	332	4	e−a	e−a	PROPN
ejpam-6136	332	5	λ	λ	PROPN
ejpam-6136	332	6	(	(	PUNCT
ejpam-6136	332	7	t	t	PROPN
ejpam-6136	332	8	)	)	PUNCT
ejpam-6136	332	9	}	}	PUNCT
ejpam-6136	332	10	]	]	PUNCT
ejpam-6136	333	1	=	=	PUNCT
ejpam-6136	333	2	(	(	PUNCT
ejpam-6136	333	3	1	1	NUM
ejpam-6136	333	4	2	2	NUM
ejpam-6136	333	5	)	)	PUNCT
ejpam-6136	333	6	[	[	PUNCT
ejpam-6136	333	7	u−β	u−β	NOUN
ejpam-6136	333	8	uα	uα	NOUN
ejpam-6136	333	9	−	−	PROPN
ejpam-6136	333	10	a−	a−	PROPN
ejpam-6136	333	11	λ	λ	PROPN
ejpam-6136	333	12	+	+	CCONJ
ejpam-6136	333	13	u−β	u−β	NOUN
ejpam-6136	333	14	uα	uα	NOUN
ejpam-6136	333	15	+	+	CCONJ
ejpam-6136	333	16	a−	a−	PROPN
ejpam-6136	333	17	λ	λ	X
ejpam-6136	333	18	]	]	X
ejpam-6136	333	19	=	=	PUNCT
ejpam-6136	333	20	(	(	PUNCT
ejpam-6136	333	21	u−β	u−β	NOUN
ejpam-6136	333	22	2	2	NUM
ejpam-6136	333	23	)	)	PUNCT
ejpam-6136	333	24	[	[	PUNCT
ejpam-6136	333	25	2uα	2uα	ADJ
ejpam-6136	333	26	−	−	PROPN
ejpam-6136	333	27	2λ	2λ	NOUN
ejpam-6136	333	28	u2α	u2α	NOUN
ejpam-6136	333	29	−	−	PROPN
ejpam-6136	333	30	2uαλ−	2uαλ−	NUM
ejpam-6136	333	31	a2	a2	PROPN
ejpam-6136	333	32	+	+	CCONJ
ejpam-6136	333	33	λ2	λ2	NOUN
ejpam-6136	333	34	]	]	PUNCT
ejpam-6136	333	35	=	=	PUNCT
ejpam-6136	333	36	u−βuα	u−βuα	NOUN
ejpam-6136	333	37	−	−	PROPN
ejpam-6136	334	1	u−βλ	u−βλ	PROPN
ejpam-6136	334	2	u2α	u2α	NOUN
ejpam-6136	334	3	−	−	PROPN
ejpam-6136	334	4	2uαλ−	2uαλ−	NUM
ejpam-6136	334	5	a2	a2	PROPN
ejpam-6136	334	6	+	+	CCONJ
ejpam-6136	334	7	λ2	λ2	NOUN
ejpam-6136	334	8	=	=	SYM
ejpam-6136	334	9	uα−β	uα−β	NOUN
ejpam-6136	334	10	−	−	NOUN
ejpam-6136	334	11	u−βλ	u−βλ	PROPN
ejpam-6136	334	12	u2α	u2α	NOUN
ejpam-6136	334	13	−	−	PROPN
ejpam-6136	334	14	2uαλ−	2uαλ−	NUM
ejpam-6136	334	15	a2	a2	PROPN
ejpam-6136	334	16	+	+	CCONJ
ejpam-6136	334	17	λ2	λ2	NOUN
ejpam-6136	334	18	.	.	PUNCT
ejpam-6136	335	1	remark	remark	PROPN
ejpam-6136	335	2	14	14	NUM
ejpam-6136	335	3	.	.	PUNCT
ejpam-6136	336	1	observe	observe	VERB
ejpam-6136	336	2	that	that	SCONJ
ejpam-6136	336	3	as	as	ADP
ejpam-6136	336	4	λ	λ	PROPN
ejpam-6136	336	5	→	→	SYM
ejpam-6136	336	6	0	0	NUM
ejpam-6136	336	7	,	,	PUNCT
ejpam-6136	336	8	sλ{cosh(a	sλ{cosh(a	NOUN
ejpam-6136	336	9	)	)	PUNCT
ejpam-6136	336	10	λ(t	λ(t	NOUN
ejpam-6136	336	11	)	)	PUNCT
ejpam-6136	336	12	}	}	PUNCT
ejpam-6136	336	13	tends	tend	VERB
ejpam-6136	336	14	to	to	PART
ejpam-6136	336	15	s{cosh	s{cosh	VERB
ejpam-6136	336	16	at	at	ADP
ejpam-6136	336	17	}	}	PUNCT
ejpam-6136	336	18	.	.	PUNCT
ejpam-6136	337	1	that	that	PRON
ejpam-6136	337	2	is	is	ADV
ejpam-6136	337	3	,	,	PUNCT
ejpam-6136	337	4	lim	lim	PROPN
ejpam-6136	337	5	λ→0	λ→0	PUNCT
ejpam-6136	337	6	sλ{coshaλ(t	sλ{coshaλ(t	PROPN
ejpam-6136	337	7	)	)	PUNCT
ejpam-6136	337	8	}	}	PUNCT
ejpam-6136	338	1	=	=	SYM
ejpam-6136	338	2	lim	lim	PROPN
ejpam-6136	338	3	λ→0	λ→0	PUNCT
ejpam-6136	338	4	[	[	PUNCT
ejpam-6136	338	5	uα−β	uα−β	NOUN
ejpam-6136	338	6	−	−	NOUN
ejpam-6136	338	7	u−βλ	u−βλ	PROPN
ejpam-6136	338	8	u2α	u2α	NOUN
ejpam-6136	338	9	−	−	PROPN
ejpam-6136	338	10	2uαλ−	2uαλ−	NUM
ejpam-6136	338	11	a2	a2	PROPN
ejpam-6136	339	1	+	+	CCONJ
ejpam-6136	340	1	λ2	λ2	NOUN
ejpam-6136	340	2	]	]	PUNCT
ejpam-6136	340	3	=	=	PUNCT
ejpam-6136	341	1	[	[	PUNCT
ejpam-6136	341	2	uα−β	uα−β	NOUN
ejpam-6136	341	3	−	−	NOUN
ejpam-6136	341	4	u−β(0	u−β(0	ADJ
ejpam-6136	341	5	)	)	PUNCT
ejpam-6136	341	6	u2α	u2α	NOUN
ejpam-6136	341	7	−	−	PROPN
ejpam-6136	341	8	2uα(0)−	2uα(0)−	PROPN
ejpam-6136	341	9	a2	a2	PROPN
ejpam-6136	341	10	+	+	CCONJ
ejpam-6136	341	11	(	(	PUNCT
ejpam-6136	341	12	0)2	0)2	NOUN
ejpam-6136	341	13	]	]	PUNCT
ejpam-6136	341	14	=	=	SYM
ejpam-6136	341	15	s{cosh(at	s{cosh(at	NOUN
ejpam-6136	341	16	)	)	PUNCT
ejpam-6136	341	17	}	}	PUNCT
ejpam-6136	341	18	.	.	PUNCT
ejpam-6136	342	1	remark	remark	PROPN
ejpam-6136	342	2	15	15	NUM
ejpam-6136	342	3	.	.	PUNCT
ejpam-6136	343	1	m	m	PROPN
ejpam-6136	343	2	1	1	NUM
ejpam-6136	343	3	.	.	PUNCT
ejpam-6136	344	1	when	when	SCONJ
ejpam-6136	344	2	β	β	X
ejpam-6136	344	3	=	=	NOUN
ejpam-6136	344	4	0	0	NUM
ejpam-6136	344	5	and	and	CCONJ
ejpam-6136	344	6	α	α	NOUN
ejpam-6136	344	7	=	=	NOUN
ejpam-6136	344	8	1	1	NUM
ejpam-6136	344	9	in	in	ADP
ejpam-6136	344	10	equation	equation	NOUN
ejpam-6136	344	11	(	(	PUNCT
ejpam-6136	344	12	20	20	NUM
ejpam-6136	344	13	)	)	PUNCT
ejpam-6136	344	14	,	,	PUNCT
ejpam-6136	344	15	sλ{coshaλ(t	sλ{coshaλ(t	NOUN
ejpam-6136	344	16	)	)	PUNCT
ejpam-6136	344	17	}	}	PUNCT
ejpam-6136	344	18	=	=	SYM
ejpam-6136	344	19	u1−0	u1−0	PROPN
ejpam-6136	344	20	−	−	PROPN
ejpam-6136	344	21	u−0λ	u−0λ	INTJ
ejpam-6136	344	22	u2(1	u2(1	PROPN
ejpam-6136	344	23	)	)	PUNCT
ejpam-6136	344	24	−	−	PROPN
ejpam-6136	344	25	2u1λ−	2u1λ−	NUM
ejpam-6136	344	26	a2	a2	PROPN
ejpam-6136	344	27	+	+	CCONJ
ejpam-6136	344	28	λ2	λ2	NOUN
ejpam-6136	344	29	=	=	SYM
ejpam-6136	344	30	u−	u−	PROPN
ejpam-6136	344	31	λ	λ	PROPN
ejpam-6136	344	32	u2	u2	NOUN
ejpam-6136	344	33	−	−	PROPN
ejpam-6136	344	34	2uλ+	2uλ+	NUM
ejpam-6136	344	35	λ2	λ2	NOUN
ejpam-6136	344	36	−	−	PROPN
ejpam-6136	344	37	a2	a2	NOUN
ejpam-6136	344	38	=	=	PUNCT
ejpam-6136	344	39	lλ{coshaλ(t	lλ{coshaλ(t	NOUN
ejpam-6136	344	40	)	)	PUNCT
ejpam-6136	344	41	}	}	PUNCT
ejpam-6136	344	42	.	.	PUNCT
ejpam-6136	345	1	2	2	X
ejpam-6136	345	2	.	.	X
ejpam-6136	345	3	when	when	SCONJ
ejpam-6136	345	4	β	β	X
ejpam-6136	345	5	=	=	VERB
ejpam-6136	345	6	−1	−1	NOUN
ejpam-6136	345	7	and	and	CCONJ
ejpam-6136	345	8	α	α	NOUN
ejpam-6136	345	9	=	=	SYM
ejpam-6136	345	10	−1	−1	NOUN
ejpam-6136	345	11	in	in	ADP
ejpam-6136	345	12	equation	equation	NOUN
ejpam-6136	345	13	(	(	PUNCT
ejpam-6136	345	14	20	20	NUM
ejpam-6136	345	15	)	)	PUNCT
ejpam-6136	345	16	,	,	PUNCT
ejpam-6136	345	17	sλ{coshaλ(t	sλ{coshaλ(t	NOUN
ejpam-6136	345	18	)	)	PUNCT
ejpam-6136	345	19	}	}	PUNCT
ejpam-6136	345	20	=	=	SYM
ejpam-6136	345	21	u−1−(−1	u−1−(−1	PROPN
ejpam-6136	345	22	)	)	PUNCT
ejpam-6136	346	1	−	−	PROPN
ejpam-6136	346	2	u−(−1)λ	u−(−1)λ	NUM
ejpam-6136	346	3	u2(−1	u2(−1	NOUN
ejpam-6136	346	4	)	)	PUNCT
ejpam-6136	347	1	−	−	PROPN
ejpam-6136	347	2	2u−1λ−	2u−1λ−	NUM
ejpam-6136	347	3	a2	a2	PROPN
ejpam-6136	347	4	+	+	CCONJ
ejpam-6136	347	5	λ2	λ2	NOUN
ejpam-6136	347	6	=	=	SYM
ejpam-6136	347	7	(	(	PUNCT
ejpam-6136	347	8	1−	1−	NUM
ejpam-6136	347	9	uλ)u2	uλ)u2	NOUN
ejpam-6136	347	10	1−	1−	NUM
ejpam-6136	347	11	2uλ+	2uλ+	NUM
ejpam-6136	347	12	λ2u2	λ2u2	NOUN
ejpam-6136	347	13	−	−	PROPN
ejpam-6136	348	1	a2u2	a2u2	NOUN
ejpam-6136	348	2	=	=	NOUN
ejpam-6136	348	3	eλ{coshaλ(t	eλ{coshaλ(t	PROPN
ejpam-6136	348	4	)	)	PUNCT
ejpam-6136	348	5	}	}	PUNCT
ejpam-6136	348	6	.	.	PUNCT
ejpam-6136	349	1	j.	j.	PROPN
ejpam-6136	349	2	mohamadali	mohamadali	PROPN
ejpam-6136	349	3	,	,	PUNCT
ejpam-6136	349	4	n.	n.	PROPN
ejpam-6136	349	5	abdulcarim	abdulcarim	PROPN
ejpam-6136	349	6	/	/	SYM
ejpam-6136	349	7	eur	eur	PROPN
ejpam-6136	349	8	.	.	PUNCT
ejpam-6136	350	1	j.	j.	PROPN
ejpam-6136	350	2	pure	pure	PROPN
ejpam-6136	350	3	appl	appl	PROPN
ejpam-6136	350	4	.	.	PROPN
ejpam-6136	350	5	math	math	PROPN
ejpam-6136	350	6	,	,	PUNCT
ejpam-6136	350	7	18	18	NUM
ejpam-6136	350	8	(	(	PUNCT
ejpam-6136	350	9	3	3	NUM
ejpam-6136	350	10	)	)	PUNCT
ejpam-6136	350	11	(	(	PUNCT
ejpam-6136	350	12	2025	2025	NUM
ejpam-6136	350	13	)	)	PUNCT
ejpam-6136	350	14	,	,	PUNCT
ejpam-6136	350	15	6136	6136	NUM
ejpam-6136	350	16	16	16	NUM
ejpam-6136	350	17	of	of	ADP
ejpam-6136	350	18	19	19	NUM
ejpam-6136	350	19	3	3	NUM
ejpam-6136	350	20	.	.	PUNCT
ejpam-6136	351	1	when	when	SCONJ
ejpam-6136	351	2	β	β	X
ejpam-6136	351	3	=	=	SYM
ejpam-6136	351	4	1	1	NUM
ejpam-6136	351	5	and	and	CCONJ
ejpam-6136	351	6	α	α	NOUN
ejpam-6136	351	7	=	=	SYM
ejpam-6136	351	8	−1	−1	NOUN
ejpam-6136	351	9	in	in	ADP
ejpam-6136	351	10	equation	equation	NOUN
ejpam-6136	351	11	(	(	PUNCT
ejpam-6136	351	12	20	20	NUM
ejpam-6136	351	13	)	)	PUNCT
ejpam-6136	351	14	,	,	PUNCT
ejpam-6136	351	15	sλ{coshaλ(t	sλ{coshaλ(t	NOUN
ejpam-6136	351	16	)	)	PUNCT
ejpam-6136	351	17	}	}	PUNCT
ejpam-6136	352	1	=	=	PUNCT
ejpam-6136	352	2	u−1−1	u−1−1	PROPN
ejpam-6136	352	3	−	−	PROPN
ejpam-6136	352	4	u−1λ	u−1λ	NOUN
ejpam-6136	352	5	u2(−1	u2(−1	PROPN
ejpam-6136	352	6	)	)	PUNCT
ejpam-6136	353	1	−	−	PROPN
ejpam-6136	353	2	2u−1λ−	2u−1λ−	NUM
ejpam-6136	353	3	a2	a2	PROPN
ejpam-6136	353	4	+	+	CCONJ
ejpam-6136	353	5	λ2	λ2	NOUN
ejpam-6136	353	6	=	=	SYM
ejpam-6136	353	7	1−	1−	NUM
ejpam-6136	353	8	uλ	uλ	NOUN
ejpam-6136	353	9	(	(	PUNCT
ejpam-6136	353	10	1−	1−	NUM
ejpam-6136	353	11	λu)2	λu)2	NOUN
ejpam-6136	353	12	−	−	PROPN
ejpam-6136	353	13	a2u2	a2u2	NOUN
ejpam-6136	353	14	=	=	NOUN
ejpam-6136	353	15	sλ{coshaλ(t	sλ{coshaλ(t	NOUN
ejpam-6136	353	16	)	)	PUNCT
ejpam-6136	353	17	}	}	PUNCT
ejpam-6136	353	18	.	.	PUNCT
ejpam-6136	354	1	4	4	X
ejpam-6136	354	2	.	.	X
ejpam-6136	354	3	when	when	SCONJ
ejpam-6136	354	4	β	β	X
ejpam-6136	354	5	=	=	SYM
ejpam-6136	354	6	−α	−α	PROPN
ejpam-6136	354	7	and	and	CCONJ
ejpam-6136	354	8	α	α	NOUN
ejpam-6136	354	9	=	=	SYM
ejpam-6136	354	10	−1	−1	NOUN
ejpam-6136	354	11	in	in	ADP
ejpam-6136	354	12	equation	equation	NOUN
ejpam-6136	354	13	(	(	PUNCT
ejpam-6136	354	14	20	20	NUM
ejpam-6136	354	15	)	)	PUNCT
ejpam-6136	354	16	,	,	PUNCT
ejpam-6136	354	17	sλ{coshaλ(t	sλ{coshaλ(t	NOUN
ejpam-6136	354	18	)	)	PUNCT
ejpam-6136	354	19	}	}	PUNCT
ejpam-6136	354	20	=	=	SYM
ejpam-6136	354	21	u−1−(−α	u−1−(−α	NOUN
ejpam-6136	354	22	)	)	PUNCT
ejpam-6136	354	23	−	−	PROPN
ejpam-6136	354	24	u−(−α)λ	u−(−α)λ	ADP
ejpam-6136	354	25	u2(−1	u2(−1	NOUN
ejpam-6136	354	26	)	)	PUNCT
ejpam-6136	355	1	−	−	PROPN
ejpam-6136	355	2	2u−1λ−	2u−1λ−	NUM
ejpam-6136	355	3	a2	a2	PROPN
ejpam-6136	355	4	+	+	CCONJ
ejpam-6136	355	5	λ2	λ2	NOUN
ejpam-6136	355	6	=	=	SYM
ejpam-6136	355	7	(	(	PUNCT
ejpam-6136	355	8	1−	1−	NUM
ejpam-6136	355	9	uλ)uα+1	uλ)uα+1	NOUN
ejpam-6136	355	10	(	(	PUNCT
ejpam-6136	355	11	1−	1−	NUM
ejpam-6136	355	12	λu)2	λu)2	NOUN
ejpam-6136	355	13	−	−	PROPN
ejpam-6136	356	1	a2u2	a2u2	NOUN
ejpam-6136	356	2	=	=	SYM
ejpam-6136	356	3	gαλ{coshaλ(t	gαλ{coshaλ(t	NOUN
ejpam-6136	356	4	)	)	PUNCT
ejpam-6136	356	5	}	}	PUNCT
ejpam-6136	356	6	.	.	PUNCT
ejpam-6136	357	1	theorem	theorem	VERB
ejpam-6136	357	2	11	11	NUM
ejpam-6136	357	3	.	.	PUNCT
ejpam-6136	358	1	the	the	DET
ejpam-6136	358	2	degenerate	degenerate	ADJ
ejpam-6136	358	3	sadik	sadik	PROPN
ejpam-6136	358	4	transform	transform	NOUN
ejpam-6136	358	5	of	of	ADP
ejpam-6136	358	6	the	the	DET
ejpam-6136	358	7	function	function	NOUN
ejpam-6136	358	8	f(t	f(t	PROPN
ejpam-6136	358	9	)	)	PUNCT
ejpam-6136	358	10	=	=	SYM
ejpam-6136	358	11	tn	tn	NOUN
ejpam-6136	358	12	is	be	AUX
ejpam-6136	358	13	given	give	VERB
ejpam-6136	358	14	by	by	ADP
ejpam-6136	358	15	,	,	PUNCT
ejpam-6136	358	16	sλ{tn	sλ{tn	PROPN
ejpam-6136	358	17	}	}	PUNCT
ejpam-6136	358	18	=	=	SYM
ejpam-6136	358	19	n	n	X
ejpam-6136	358	20	!	!	PUNCT
ejpam-6136	359	1	uβ(uα	uβ(uα	NOUN
ejpam-6136	359	2	−	−	NOUN
ejpam-6136	359	3	λ)(uα	λ)(uα	NOUN
ejpam-6136	359	4	−	−	PROPN
ejpam-6136	359	5	2λ)	2λ)	PROPN
ejpam-6136	359	6	....	....	PUNCT
ejpam-6136	359	7	(uα	(uα	PUNCT
ejpam-6136	359	8	−	−	PROPN
ejpam-6136	359	9	nλ)(uα	nλ)(uα	PUNCT
ejpam-6136	359	10	−	−	PROPN
ejpam-6136	359	11	(	(	PUNCT
ejpam-6136	359	12	n+	n+	NOUN
ejpam-6136	359	13	1)λ	1)λ	NUM
ejpam-6136	359	14	)	)	PUNCT
ejpam-6136	359	15	(	(	PUNCT
ejpam-6136	359	16	21	21	NUM
ejpam-6136	359	17	)	)	PUNCT
ejpam-6136	359	18	for	for	ADP
ejpam-6136	359	19	(	(	PUNCT
ejpam-6136	359	20	n−	n−	NOUN
ejpam-6136	359	21	k	k	NOUN
ejpam-6136	360	1	+	+	CCONJ
ejpam-6136	361	1	1)λ−	1)λ−	NUM
ejpam-6136	361	2	uα	uα	ADP
ejpam-6136	362	1	λ	λ	X
ejpam-6136	362	2	<	<	X
ejpam-6136	362	3	0	0	NUM
ejpam-6136	362	4	.	.	PUNCT
ejpam-6136	362	5	proof	proof	NOUN
ejpam-6136	362	6	.	.	PUNCT
ejpam-6136	363	1	directly	directly	ADV
ejpam-6136	363	2	from	from	ADP
ejpam-6136	363	3	the	the	DET
ejpam-6136	363	4	definition	definition	NOUN
ejpam-6136	363	5	1	1	NUM
ejpam-6136	363	6	,	,	PUNCT
ejpam-6136	363	7	for	for	ADP
ejpam-6136	363	8	f(t	f(t	NOUN
ejpam-6136	363	9	)	)	PUNCT
ejpam-6136	363	10	=	=	SYM
ejpam-6136	363	11	tn	tn	PROPN
ejpam-6136	363	12	,	,	PUNCT
ejpam-6136	363	13	we	we	PRON
ejpam-6136	363	14	have	have	AUX
ejpam-6136	363	15	sλ{tn	sλ{tn	ADJ
ejpam-6136	363	16	}	}	PUNCT
ejpam-6136	363	17	=	=	SYM
ejpam-6136	363	18	1	1	NUM
ejpam-6136	364	1	uβ	uβ	NOUN
ejpam-6136	364	2	∫	∫	PROPN
ejpam-6136	364	3	∞	∞	PROPN
ejpam-6136	364	4	0	0	NUM
ejpam-6136	364	5	e−uα	e−uα	PROPN
ejpam-6136	364	6	λ	λ	PROPN
ejpam-6136	364	7	(	(	PUNCT
ejpam-6136	364	8	t	t	PROPN
ejpam-6136	364	9	)	)	PUNCT
ejpam-6136	364	10	tn	tn	PROPN
ejpam-6136	364	11	dt	dt	NOUN
ejpam-6136	364	12	=	=	SYM
ejpam-6136	364	13	1	1	NUM
ejpam-6136	364	14	uβλn+1	uβλn+1	PROPN
ejpam-6136	364	15	n∑	n∑	NOUN
ejpam-6136	364	16	k=0	k=0	PROPN
ejpam-6136	364	17	(	(	PUNCT
ejpam-6136	364	18	n	n	X
ejpam-6136	364	19	k	k	NOUN
ejpam-6136	364	20	)	)	PUNCT
ejpam-6136	364	21	(	(	PUNCT
ejpam-6136	364	22	−1)k	−1)k	PROPN
ejpam-6136	364	23	lim	lim	PROPN
ejpam-6136	364	24	r→∞	r→∞	X
ejpam-6136	365	1	[	[	PUNCT
ejpam-6136	365	2	λ	λ	X
ejpam-6136	365	3	v	v	ADP
ejpam-6136	365	4	−uα+λn−λk+λ	−uα+λn−λk+λ	PROPN
ejpam-6136	365	5	λ	λ	PROPN
ejpam-6136	365	6	−uα	−uα	PROPN
ejpam-6136	365	7	+	+	X
ejpam-6136	365	8	λn−	λn−	PUNCT
ejpam-6136	365	9	λk	λk	X
ejpam-6136	365	10	+	+	NUM
ejpam-6136	365	11	λ	λ	X
ejpam-6136	365	12	]	]	PUNCT
ejpam-6136	365	13	∣∣∣∣1+λr	∣∣∣∣1+λr	PROPN
ejpam-6136	365	14	1	1	NUM
ejpam-6136	365	15	=	=	SYM
ejpam-6136	365	16	1	1	NUM
ejpam-6136	365	17	uβλn	uβλn	NOUN
ejpam-6136	365	18	n∑	n∑	NOUN
ejpam-6136	365	19	k=0	k=0	PROPN
ejpam-6136	365	20	(	(	PUNCT
ejpam-6136	365	21	n	n	X
ejpam-6136	365	22	k	k	NOUN
ejpam-6136	365	23	)	)	PUNCT
ejpam-6136	365	24	(	(	PUNCT
ejpam-6136	365	25	−1)k	−1)k	PROPN
ejpam-6136	365	26	[	[	PUNCT
ejpam-6136	365	27	−	−	PROPN
ejpam-6136	365	28	1	1	NUM
ejpam-6136	365	29	−uα	−uα	NOUN
ejpam-6136	366	1	+	+	X
ejpam-6136	366	2	λ(n−	λ(n−	X
ejpam-6136	366	3	k	k	NOUN
ejpam-6136	366	4	+	+	PROPN
ejpam-6136	366	5	1	1	NUM
ejpam-6136	366	6	)	)	PUNCT
ejpam-6136	366	7	]	]	PUNCT
ejpam-6136	366	8	,	,	PUNCT
ejpam-6136	366	9	for	for	ADP
ejpam-6136	366	10	(	(	PUNCT
ejpam-6136	366	11	n−	n−	NOUN
ejpam-6136	366	12	k	k	NOUN
ejpam-6136	366	13	+	+	CCONJ
ejpam-6136	366	14	1)λ−	1)λ−	NUM
ejpam-6136	366	15	uα	uα	ADP
ejpam-6136	367	1	λ	λ	X
ejpam-6136	367	2	<	<	X
ejpam-6136	367	3	0	0	PUNCT
ejpam-6136	367	4	=	=	SYM
ejpam-6136	367	5	1	1	NUM
ejpam-6136	367	6	uβλn	uβλn	NOUN
ejpam-6136	367	7	[	[	PUNCT
ejpam-6136	367	8	1	1	NUM
ejpam-6136	367	9	uα	uα	NOUN
ejpam-6136	367	10	−	−	NOUN
ejpam-6136	367	11	λ(n+	λ(n+	NOUN
ejpam-6136	367	12	1	1	NUM
ejpam-6136	367	13	)	)	PUNCT
ejpam-6136	367	14	−	−	PROPN
ejpam-6136	368	1	n	n	PRON
ejpam-6136	368	2	uα	uα	NOUN
ejpam-6136	368	3	−	−	PROPN
ejpam-6136	368	4	nλ	nλ	NOUN
ejpam-6136	369	1	+	+	CCONJ
ejpam-6136	369	2	...	...	PUNCT
ejpam-6136	370	1	+	+	CCONJ
ejpam-6136	370	2	n(−1)n−1	n(−1)n−1	ADP
ejpam-6136	370	3	(	(	PUNCT
ejpam-6136	370	4	1	1	NUM
ejpam-6136	370	5	uα	uα	PROPN
ejpam-6136	370	6	−	−	PROPN
ejpam-6136	370	7	2λ	2λ	PROPN
ejpam-6136	370	8	)	)	PUNCT
ejpam-6136	370	9	+	+	CCONJ
ejpam-6136	370	10	(	(	PUNCT
ejpam-6136	370	11	−1)n	−1)n	X
ejpam-6136	370	12	(	(	PUNCT
ejpam-6136	370	13	1	1	NUM
ejpam-6136	370	14	uα	uα	NOUN
ejpam-6136	370	15	−	−	PROPN
ejpam-6136	370	16	λ	λ	PROPN
ejpam-6136	370	17	)	)	PUNCT
ejpam-6136	370	18	]	]	PUNCT
ejpam-6136	371	1	=	=	PUNCT
ejpam-6136	371	2	n!λn	n!λn	ADP
ejpam-6136	371	3	uβλn(uα	uβλn(uα	NOUN
ejpam-6136	371	4	−	−	NOUN
ejpam-6136	371	5	λ)(uα	λ)(uα	NOUN
ejpam-6136	371	6	−	−	PROPN
ejpam-6136	372	1	2λ)	2λ)	PROPN
ejpam-6136	372	2	....	....	PUNCT
ejpam-6136	372	3	(uα	(uα	PUNCT
ejpam-6136	372	4	−	−	PROPN
ejpam-6136	372	5	nλ)(uα	nλ)(uα	PUNCT
ejpam-6136	372	6	−	−	PROPN
ejpam-6136	372	7	(	(	PUNCT
ejpam-6136	372	8	n+	n+	NOUN
ejpam-6136	372	9	1)λ	1)λ	NOUN
ejpam-6136	372	10	)	)	PUNCT
ejpam-6136	372	11	=	=	SYM
ejpam-6136	372	12	n	n	X
ejpam-6136	372	13	!	!	PUNCT
ejpam-6136	373	1	uβ(uα	uβ(uα	NOUN
ejpam-6136	373	2	−	−	NOUN
ejpam-6136	373	3	λ)(uα	λ)(uα	NOUN
ejpam-6136	373	4	−	−	PROPN
ejpam-6136	373	5	2λ)	2λ)	PROPN
ejpam-6136	373	6	....	....	PUNCT
ejpam-6136	373	7	(uα	(uα	PUNCT
ejpam-6136	373	8	−	−	PROPN
ejpam-6136	373	9	nλ)(uα	nλ)(uα	PUNCT
ejpam-6136	373	10	−	−	PROPN
ejpam-6136	373	11	(	(	PUNCT
ejpam-6136	373	12	n+	n+	NOUN
ejpam-6136	373	13	1)λ	1)λ	NOUN
ejpam-6136	373	14	)	)	PUNCT
ejpam-6136	373	15	for	for	ADP
ejpam-6136	373	16	(	(	PUNCT
ejpam-6136	373	17	n−	n−	NOUN
ejpam-6136	373	18	k	k	NOUN
ejpam-6136	374	1	+	+	CCONJ
ejpam-6136	375	1	1)λ−	1)λ−	NUM
ejpam-6136	375	2	uα	uα	ADP
ejpam-6136	376	1	λ	λ	X
ejpam-6136	376	2	<	<	X
ejpam-6136	376	3	0	0	PROPN
ejpam-6136	376	4	.	.	PROPN
ejpam-6136	376	5	remark	remark	PROPN
ejpam-6136	376	6	16	16	NUM
ejpam-6136	376	7	.	.	PUNCT
ejpam-6136	377	1	observe	observe	VERB
ejpam-6136	377	2	that	that	SCONJ
ejpam-6136	377	3	as	as	ADP
ejpam-6136	377	4	λ	λ	PROPN
ejpam-6136	377	5	→	→	SYM
ejpam-6136	377	6	0	0	NUM
ejpam-6136	377	7	,	,	PUNCT
ejpam-6136	377	8	sλ{tn	sλ{tn	PROPN
ejpam-6136	377	9	}	}	PUNCT
ejpam-6136	377	10	tends	tend	VERB
ejpam-6136	377	11	to	to	ADP
ejpam-6136	377	12	s{tn	s{tn	PROPN
ejpam-6136	377	13	}	}	PUNCT
ejpam-6136	377	14	.	.	PUNCT
ejpam-6136	378	1	that	that	PRON
ejpam-6136	378	2	is	is	ADV
ejpam-6136	378	3	,	,	PUNCT
ejpam-6136	378	4	lim	lim	PROPN
ejpam-6136	378	5	λ→0	λ→0	PUNCT
ejpam-6136	378	6	sλ{tn	sλ{tn	PROPN
ejpam-6136	378	7	}	}	PUNCT
ejpam-6136	378	8	=	=	SYM
ejpam-6136	378	9	lim	lim	PROPN
ejpam-6136	378	10	λ→0	λ→0	PUNCT
ejpam-6136	378	11	[	[	PUNCT
ejpam-6136	378	12	n	n	X
ejpam-6136	378	13	!	!	PUNCT
ejpam-6136	379	1	uβ(uα	uβ(uα	NOUN
ejpam-6136	379	2	−	−	NOUN
ejpam-6136	379	3	λ)(uα	λ)(uα	NOUN
ejpam-6136	379	4	−	−	PROPN
ejpam-6136	379	5	2λ)	2λ)	PROPN
ejpam-6136	379	6	....	....	PUNCT
ejpam-6136	379	7	(uα	(uα	PUNCT
ejpam-6136	379	8	−	−	PROPN
ejpam-6136	379	9	nλ)(uα	nλ)(uα	PUNCT
ejpam-6136	379	10	−	−	PROPN
ejpam-6136	379	11	(	(	PUNCT
ejpam-6136	379	12	n+	n+	NOUN
ejpam-6136	379	13	1)λ	1)λ	NUM
ejpam-6136	379	14	)	)	PUNCT
ejpam-6136	379	15	]	]	PUNCT
ejpam-6136	380	1	=	=	PUNCT
ejpam-6136	380	2	s{tn	s{tn	PROPN
ejpam-6136	380	3	}	}	PUNCT
ejpam-6136	380	4	.	.	PUNCT
ejpam-6136	381	1	remark	remark	PROPN
ejpam-6136	381	2	17	17	NUM
ejpam-6136	381	3	.	.	PUNCT
ejpam-6136	382	1	m	m	PROPN
ejpam-6136	382	2	j.	j.	PROPN
ejpam-6136	382	3	mohamadali	mohamadali	PROPN
ejpam-6136	382	4	,	,	PUNCT
ejpam-6136	382	5	n.	n.	PROPN
ejpam-6136	382	6	abdulcarim	abdulcarim	PROPN
ejpam-6136	382	7	/	/	SYM
ejpam-6136	382	8	eur	eur	PROPN
ejpam-6136	382	9	.	.	PUNCT
ejpam-6136	383	1	j.	j.	PROPN
ejpam-6136	383	2	pure	pure	PROPN
ejpam-6136	383	3	appl	appl	PROPN
ejpam-6136	383	4	.	.	PROPN
ejpam-6136	383	5	math	math	PROPN
ejpam-6136	383	6	,	,	PUNCT
ejpam-6136	383	7	18	18	NUM
ejpam-6136	383	8	(	(	PUNCT
ejpam-6136	383	9	3	3	NUM
ejpam-6136	383	10	)	)	PUNCT
ejpam-6136	383	11	(	(	PUNCT
ejpam-6136	383	12	2025	2025	NUM
ejpam-6136	383	13	)	)	PUNCT
ejpam-6136	383	14	,	,	PUNCT
ejpam-6136	383	15	6136	6136	NUM
ejpam-6136	383	16	17	17	NUM
ejpam-6136	383	17	of	of	ADP
ejpam-6136	383	18	19	19	NUM
ejpam-6136	383	19	1	1	NUM
ejpam-6136	383	20	.	.	PUNCT
ejpam-6136	384	1	when	when	SCONJ
ejpam-6136	384	2	β	β	X
ejpam-6136	384	3	=	=	NOUN
ejpam-6136	384	4	0	0	NUM
ejpam-6136	384	5	and	and	CCONJ
ejpam-6136	384	6	α	α	NOUN
ejpam-6136	384	7	=	=	NOUN
ejpam-6136	384	8	1	1	NUM
ejpam-6136	384	9	in	in	ADP
ejpam-6136	384	10	equation	equation	NOUN
ejpam-6136	384	11	(	(	PUNCT
ejpam-6136	384	12	21	21	NUM
ejpam-6136	384	13	)	)	PUNCT
ejpam-6136	384	14	,	,	PUNCT
ejpam-6136	384	15	sλ{tn	sλ{tn	PROPN
ejpam-6136	384	16	}	}	PUNCT
ejpam-6136	384	17	=	=	SYM
ejpam-6136	384	18	n	n	X
ejpam-6136	384	19	!	!	PUNCT
ejpam-6136	385	1	u0(u1	u0(u1	NOUN
ejpam-6136	385	2	−	−	PROPN
ejpam-6136	385	3	λ)(u1	λ)(u1	NOUN
ejpam-6136	386	1	−	−	PROPN
ejpam-6136	386	2	2λ)	2λ)	PROPN
ejpam-6136	386	3	....	....	PUNCT
ejpam-6136	387	1	(u1	(u1	PUNCT
ejpam-6136	387	2	−	−	X
ejpam-6136	387	3	nλ)(u1	nλ)(u1	NOUN
ejpam-6136	387	4	−	−	PROPN
ejpam-6136	388	1	(	(	PUNCT
ejpam-6136	388	2	n+	n+	NOUN
ejpam-6136	388	3	1)λ	1)λ	NOUN
ejpam-6136	388	4	)	)	PUNCT
ejpam-6136	388	5	=	=	SYM
ejpam-6136	389	1	n	n	X
ejpam-6136	389	2	!	!	PUNCT
ejpam-6136	390	1	un+1(1−	un+1(1−	ADJ
ejpam-6136	391	1	λ	λ	X
ejpam-6136	391	2	u)(1−	u)(1−	PROPN
ejpam-6136	391	3	2λ	2λ	NUM
ejpam-6136	391	4	u	u	NOUN
ejpam-6136	391	5	)	)	PUNCT
ejpam-6136	391	6	....	....	PUNCT
ejpam-6136	391	7	(	(	PUNCT
ejpam-6136	391	8	1−	1−	NUM
ejpam-6136	391	9	nλ	nλ	NOUN
ejpam-6136	391	10	u	u	NOUN
ejpam-6136	391	11	)	)	PUNCT
ejpam-6136	391	12	(	(	PUNCT
ejpam-6136	391	13	1−	1−	NUM
ejpam-6136	391	14	(	(	PUNCT
ejpam-6136	391	15	n+1)λ	n+1)λ	PROPN
ejpam-6136	391	16	u	u	NOUN
ejpam-6136	391	17	)	)	PUNCT
ejpam-6136	391	18	=	=	SYM
ejpam-6136	391	19	lλ{tn	lλ{tn	PROPN
ejpam-6136	391	20	}	}	PUNCT
ejpam-6136	391	21	.	.	PUNCT
ejpam-6136	392	1	2	2	X
ejpam-6136	392	2	.	.	X
ejpam-6136	392	3	when	when	SCONJ
ejpam-6136	392	4	β	β	X
ejpam-6136	392	5	=	=	VERB
ejpam-6136	392	6	−1	−1	NOUN
ejpam-6136	392	7	and	and	CCONJ
ejpam-6136	392	8	α	α	NOUN
ejpam-6136	392	9	=	=	SYM
ejpam-6136	392	10	−1	−1	NOUN
ejpam-6136	392	11	in	in	ADP
ejpam-6136	392	12	equation	equation	NOUN
ejpam-6136	392	13	(	(	PUNCT
ejpam-6136	392	14	21	21	NUM
ejpam-6136	392	15	)	)	PUNCT
ejpam-6136	392	16	,	,	PUNCT
ejpam-6136	392	17	sλ{tn	sλ{tn	PROPN
ejpam-6136	392	18	}	}	PUNCT
ejpam-6136	392	19	=	=	SYM
ejpam-6136	392	20	n	n	X
ejpam-6136	392	21	!	!	PUNCT
ejpam-6136	393	1	u−1(u−1	u−1(u−1	INTJ
ejpam-6136	393	2	−	−	PROPN
ejpam-6136	393	3	λ)(u−1	λ)(u−1	PROPN
ejpam-6136	393	4	−	−	PROPN
ejpam-6136	393	5	2λ)	2λ)	PROPN
ejpam-6136	393	6	....	....	PUNCT
ejpam-6136	394	1	(u−1	(u−1	PRON
ejpam-6136	394	2	−	−	PROPN
ejpam-6136	394	3	nλ)(u−1	nλ)(u−1	ADV
ejpam-6136	394	4	−	−	PROPN
ejpam-6136	394	5	(	(	PUNCT
ejpam-6136	394	6	n+	n+	NOUN
ejpam-6136	394	7	1)λ	1)λ	NOUN
ejpam-6136	394	8	)	)	PUNCT
ejpam-6136	394	9	=	=	SYM
ejpam-6136	395	1	n!un+2	n!un+2	NOUN
ejpam-6136	395	2	(	(	PUNCT
ejpam-6136	395	3	1−	1−	NUM
ejpam-6136	395	4	uλ)(1−	uλ)(1−	PROPN
ejpam-6136	395	5	2uλ)	2uλ)	NUM
ejpam-6136	395	6	....	....	PUNCT
ejpam-6136	395	7	(1−	(1−	PROPN
ejpam-6136	395	8	nuλ)(1−	nuλ)(1−	PROPN
ejpam-6136	395	9	(	(	PUNCT
ejpam-6136	395	10	n+	n+	NUM
ejpam-6136	395	11	1)uλ	1)uλ	NUM
ejpam-6136	395	12	)	)	PUNCT
ejpam-6136	395	13	=	=	NOUN
ejpam-6136	395	14	eλ{tn	eλ{tn	ADJ
ejpam-6136	395	15	}	}	PUNCT
ejpam-6136	395	16	.	.	PUNCT
ejpam-6136	396	1	3	3	X
ejpam-6136	396	2	.	.	X
ejpam-6136	396	3	when	when	SCONJ
ejpam-6136	396	4	β	β	X
ejpam-6136	396	5	=	=	SYM
ejpam-6136	396	6	1	1	NUM
ejpam-6136	396	7	and	and	CCONJ
ejpam-6136	396	8	α	α	NOUN
ejpam-6136	396	9	=	=	SYM
ejpam-6136	396	10	−1	−1	NOUN
ejpam-6136	396	11	in	in	ADP
ejpam-6136	396	12	equation	equation	NOUN
ejpam-6136	396	13	(	(	PUNCT
ejpam-6136	396	14	21	21	NUM
ejpam-6136	396	15	)	)	PUNCT
ejpam-6136	396	16	,	,	PUNCT
ejpam-6136	396	17	sλ{tn	sλ{tn	PROPN
ejpam-6136	396	18	}	}	PUNCT
ejpam-6136	396	19	=	=	SYM
ejpam-6136	396	20	n	n	X
ejpam-6136	396	21	!	!	PUNCT
ejpam-6136	396	22	u1(u−1	u1(u−1	PROPN
ejpam-6136	397	1	−	−	PROPN
ejpam-6136	397	2	λ)(u−1	λ)(u−1	PROPN
ejpam-6136	397	3	−	−	PROPN
ejpam-6136	397	4	2λ)	2λ)	PROPN
ejpam-6136	397	5	....	....	PUNCT
ejpam-6136	398	1	(u−1	(u−1	PRON
ejpam-6136	398	2	−	−	PROPN
ejpam-6136	398	3	nλ)(u−1	nλ)(u−1	ADV
ejpam-6136	398	4	−	−	PROPN
ejpam-6136	398	5	(	(	PUNCT
ejpam-6136	398	6	n+	n+	NOUN
ejpam-6136	398	7	1)λ	1)λ	NOUN
ejpam-6136	398	8	)	)	PUNCT
ejpam-6136	399	1	=	=	SYM
ejpam-6136	399	2	n!un	n!un	NOUN
ejpam-6136	399	3	(	(	PUNCT
ejpam-6136	399	4	1−	1−	NUM
ejpam-6136	399	5	uλ)(1−	uλ)(1−	PROPN
ejpam-6136	399	6	2uλ)	2uλ)	NUM
ejpam-6136	399	7	....	....	PUNCT
ejpam-6136	399	8	(1−	(1−	PROPN
ejpam-6136	399	9	nuλ)(1−	nuλ)(1−	PROPN
ejpam-6136	399	10	(	(	PUNCT
ejpam-6136	399	11	n+	n+	NUM
ejpam-6136	399	12	1)uλ	1)uλ	NUM
ejpam-6136	399	13	)	)	PUNCT
ejpam-6136	399	14	=	=	SYM
ejpam-6136	399	15	sλ{tn	sλ{tn	PROPN
ejpam-6136	399	16	}	}	PUNCT
ejpam-6136	399	17	.	.	PUNCT
ejpam-6136	400	1	4	4	X
ejpam-6136	400	2	.	.	X
ejpam-6136	400	3	when	when	SCONJ
ejpam-6136	400	4	β	β	X
ejpam-6136	400	5	=	=	SYM
ejpam-6136	400	6	−α	−α	PROPN
ejpam-6136	400	7	and	and	CCONJ
ejpam-6136	400	8	α	α	NOUN
ejpam-6136	400	9	=	=	SYM
ejpam-6136	400	10	−1	−1	NOUN
ejpam-6136	400	11	in	in	ADP
ejpam-6136	400	12	equation	equation	NOUN
ejpam-6136	400	13	(	(	PUNCT
ejpam-6136	400	14	21	21	NUM
ejpam-6136	400	15	)	)	PUNCT
ejpam-6136	400	16	,	,	PUNCT
ejpam-6136	400	17	sλ{tn	sλ{tn	PROPN
ejpam-6136	400	18	}	}	PUNCT
ejpam-6136	400	19	=	=	SYM
ejpam-6136	400	20	n	n	X
ejpam-6136	400	21	!	!	NOUN
ejpam-6136	400	22	u−α(u−1	u−α(u−1	ADJ
ejpam-6136	401	1	−	−	PUNCT
ejpam-6136	401	2	λ)(u−1	λ)(u−1	VERB
ejpam-6136	401	3	−	−	PROPN
ejpam-6136	401	4	2λ)	2λ)	PROPN
ejpam-6136	401	5	....	....	PUNCT
ejpam-6136	402	1	(u−1	(u−1	PRON
ejpam-6136	402	2	−	−	PROPN
ejpam-6136	402	3	nλ)(u−1	nλ)(u−1	ADV
ejpam-6136	402	4	−	−	PROPN
ejpam-6136	402	5	(	(	PUNCT
ejpam-6136	402	6	n+	n+	NOUN
ejpam-6136	402	7	1)λ	1)λ	NOUN
ejpam-6136	402	8	)	)	PUNCT
ejpam-6136	402	9	=	=	SYM
ejpam-6136	402	10	n!u−α+(n+1	n!u−α+(n+1	NOUN
ejpam-6136	402	11	)	)	PUNCT
ejpam-6136	402	12	(	(	PUNCT
ejpam-6136	402	13	1−	1−	NUM
ejpam-6136	402	14	uλ)(1−	uλ)(1−	PROPN
ejpam-6136	402	15	2uλ)	2uλ)	NUM
ejpam-6136	402	16	....	....	PUNCT
ejpam-6136	403	1	(1−	(1−	PROPN
ejpam-6136	403	2	nuλ)(1−	nuλ)(1−	PROPN
ejpam-6136	403	3	(	(	PUNCT
ejpam-6136	403	4	n+	n+	NUM
ejpam-6136	403	5	1)uλ	1)uλ	NUM
ejpam-6136	403	6	)	)	PUNCT
ejpam-6136	403	7	=	=	PRON
ejpam-6136	403	8	gαλ{tn	gαλ{tn	PUNCT
ejpam-6136	403	9	}	}	PUNCT
ejpam-6136	403	10	.	.	PUNCT
ejpam-6136	404	1	conclusion	conclusion	NOUN
ejpam-6136	404	2	this	this	DET
ejpam-6136	404	3	study	study	NOUN
ejpam-6136	404	4	introduced	introduce	VERB
ejpam-6136	404	5	the	the	DET
ejpam-6136	404	6	degenerate	degenerate	ADJ
ejpam-6136	404	7	version	version	NOUN
ejpam-6136	404	8	of	of	ADP
ejpam-6136	404	9	sadik	sadik	PROPN
ejpam-6136	404	10	transform	transform	PROPN
ejpam-6136	404	11	,	,	PUNCT
ejpam-6136	404	12	a	a	DET
ejpam-6136	404	13	generalization	generalization	NOUN
ejpam-6136	404	14	of	of	ADP
ejpam-6136	404	15	the	the	DET
ejpam-6136	404	16	sadik	sadik	PROPN
ejpam-6136	404	17	transform	transform	NOUN
ejpam-6136	404	18	that	that	PRON
ejpam-6136	404	19	sum	sum	VERB
ejpam-6136	404	20	up	up	ADP
ejpam-6136	404	21	some	some	DET
ejpam-6136	404	22	known	know	VERB
ejpam-6136	404	23	degenerate	degenerate	ADJ
ejpam-6136	404	24	transforms	transform	NOUN
ejpam-6136	404	25	,	,	PUNCT
ejpam-6136	404	26	including	include	VERB
ejpam-6136	404	27	the	the	DET
ejpam-6136	404	28	degenerate	degenerate	ADJ
ejpam-6136	404	29	laplace	laplace	NOUN
ejpam-6136	404	30	,	,	PUNCT
ejpam-6136	404	31	sumudu	sumudu	NOUN
ejpam-6136	404	32	,	,	PUNCT
ejpam-6136	404	33	tarig	tarig	NOUN
ejpam-6136	404	34	,	,	PUNCT
ejpam-6136	404	35	elzaki	elzaki	NOUN
ejpam-6136	404	36	,	,	PUNCT
ejpam-6136	404	37	and	and	CCONJ
ejpam-6136	404	38	laplace	laplace	NOUN
ejpam-6136	404	39	-	-	PUNCT
ejpam-6136	404	40	type	type	NOUN
ejpam-6136	404	41	integral	integral	ADJ
ejpam-6136	404	42	transforms	transform	NOUN
ejpam-6136	404	43	.	.	PUNCT
ejpam-6136	405	1	by	by	ADP
ejpam-6136	405	2	defining	define	VERB
ejpam-6136	405	3	the	the	DET
ejpam-6136	405	4	degenerate	degenerate	ADJ
ejpam-6136	405	5	sadik	sadik	PROPN
ejpam-6136	405	6	transform	transform	NOUN
ejpam-6136	405	7	and	and	CCONJ
ejpam-6136	405	8	establishing	establish	VERB
ejpam-6136	405	9	its	its	PRON
ejpam-6136	405	10	existence	existence	NOUN
ejpam-6136	405	11	under	under	ADP
ejpam-6136	405	12	specific	specific	ADJ
ejpam-6136	405	13	conditions	condition	NOUN
ejpam-6136	405	14	,	,	PUNCT
ejpam-6136	405	15	the	the	DET
ejpam-6136	405	16	paper	paper	NOUN
ejpam-6136	405	17	demonstrated	demonstrate	VERB
ejpam-6136	405	18	its	its	PRON
ejpam-6136	405	19	capacity	capacity	NOUN
ejpam-6136	405	20	to	to	PART
ejpam-6136	405	21	serve	serve	VERB
ejpam-6136	405	22	as	as	ADP
ejpam-6136	405	23	a	a	DET
ejpam-6136	405	24	unifying	unifying	ADJ
ejpam-6136	405	25	framework	framework	NOUN
ejpam-6136	405	26	for	for	ADP
ejpam-6136	405	27	multiple	multiple	ADJ
ejpam-6136	405	28	degenerate	degenerate	ADJ
ejpam-6136	405	29	transforms	transform	NOUN
ejpam-6136	405	30	.	.	PUNCT
ejpam-6136	406	1	the	the	DET
ejpam-6136	406	2	transform	transform	NOUN
ejpam-6136	406	3	of	of	ADP
ejpam-6136	406	4	several	several	ADJ
ejpam-6136	406	5	elementary	elementary	ADJ
ejpam-6136	406	6	functions	function	NOUN
ejpam-6136	406	7	was	be	AUX
ejpam-6136	406	8	derived	derive	VERB
ejpam-6136	406	9	,	,	PUNCT
ejpam-6136	406	10	and	and	CCONJ
ejpam-6136	406	11	the	the	DET
ejpam-6136	406	12	results	result	NOUN
ejpam-6136	406	13	validated	validate	VERB
ejpam-6136	406	14	that	that	PRON
ejpam-6136	406	15	degenerate	degenerate	ADJ
ejpam-6136	406	16	sadik	sadik	PROPN
ejpam-6136	406	17	transform	transform	NOUN
ejpam-6136	406	18	certainly	certainly	ADV
ejpam-6136	406	19	converges	converge	VERB
ejpam-6136	406	20	to	to	ADP
ejpam-6136	406	21	the	the	DET
ejpam-6136	406	22	natural	natural	ADJ
ejpam-6136	406	23	sadik	sadik	PROPN
ejpam-6136	406	24	transform	transform	NOUN
ejpam-6136	406	25	as	as	SCONJ
ejpam-6136	406	26	the	the	DET
ejpam-6136	406	27	degeneracy	degeneracy	PROPN
ejpam-6136	406	28	parameter	parameter	PROPN
ejpam-6136	406	29	approaches	approach	VERB
ejpam-6136	406	30	zero	zero	NUM
ejpam-6136	406	31	.	.	PUNCT
ejpam-6136	407	1	this	this	DET
ejpam-6136	407	2	highlights	highlight	VERB
ejpam-6136	407	3	the	the	DET
ejpam-6136	407	4	degenerate	degenerate	ADJ
ejpam-6136	407	5	sadik	sadik	PROPN
ejpam-6136	407	6	transform	transform	NOUN
ejpam-6136	407	7	’s	’s	PART
ejpam-6136	407	8	flexibility	flexibility	NOUN
ejpam-6136	407	9	,	,	PUNCT
ejpam-6136	407	10	depth	depth	NOUN
ejpam-6136	407	11	,	,	PUNCT
ejpam-6136	407	12	and	and	CCONJ
ejpam-6136	407	13	potential	potential	NOUN
ejpam-6136	407	14	for	for	ADP
ejpam-6136	407	15	broader	broad	ADJ
ejpam-6136	407	16	application	application	NOUN
ejpam-6136	407	17	across	across	ADP
ejpam-6136	407	18	various	various	ADJ
ejpam-6136	407	19	mathematical	mathematical	ADJ
ejpam-6136	407	20	and	and	CCONJ
ejpam-6136	407	21	applied	applied	ADJ
ejpam-6136	407	22	areas	area	NOUN
ejpam-6136	407	23	.	.	PUNCT
ejpam-6136	408	1	j.	j.	PROPN
ejpam-6136	408	2	mohamadali	mohamadali	PROPN
ejpam-6136	408	3	,	,	PUNCT
ejpam-6136	408	4	n.	n.	PROPN
ejpam-6136	408	5	abdulcarim	abdulcarim	PROPN
ejpam-6136	408	6	/	/	SYM
ejpam-6136	408	7	eur	eur	PROPN
ejpam-6136	408	8	.	.	PUNCT
ejpam-6136	409	1	j.	j.	PROPN
ejpam-6136	409	2	pure	pure	PROPN
ejpam-6136	409	3	appl	appl	PROPN
ejpam-6136	409	4	.	.	PROPN
ejpam-6136	409	5	math	math	PROPN
ejpam-6136	409	6	,	,	PUNCT
ejpam-6136	409	7	18	18	NUM
ejpam-6136	409	8	(	(	PUNCT
ejpam-6136	409	9	3	3	NUM
ejpam-6136	409	10	)	)	PUNCT
ejpam-6136	409	11	(	(	PUNCT
ejpam-6136	409	12	2025	2025	NUM
ejpam-6136	409	13	)	)	PUNCT
ejpam-6136	409	14	,	,	PUNCT
ejpam-6136	409	15	6136	6136	NUM
ejpam-6136	409	16	18	18	NUM
ejpam-6136	409	17	of	of	ADP
ejpam-6136	409	18	19	19	NUM
ejpam-6136	409	19	recommendation	recommendation	NOUN
ejpam-6136	409	20	the	the	DET
ejpam-6136	409	21	following	follow	VERB
ejpam-6136	409	22	are	be	AUX
ejpam-6136	409	23	recommended	recommend	VERB
ejpam-6136	409	24	for	for	ADP
ejpam-6136	409	25	further	further	ADJ
ejpam-6136	409	26	investigations	investigation	NOUN
ejpam-6136	409	27	:	:	PUNCT
ejpam-6136	410	1	1	1	X
ejpam-6136	410	2	.	.	X
ejpam-6136	410	3	to	to	PART
ejpam-6136	410	4	define	define	VERB
ejpam-6136	410	5	degenerate	degenerate	ADJ
ejpam-6136	410	6	versions	version	NOUN
ejpam-6136	410	7	of	of	ADP
ejpam-6136	410	8	other	other	ADJ
ejpam-6136	410	9	well	well	ADV
ejpam-6136	410	10	-	-	PUNCT
ejpam-6136	410	11	known	know	VERB
ejpam-6136	410	12	transforms	transform	NOUN
ejpam-6136	410	13	,	,	PUNCT
ejpam-6136	410	14	such	such	ADJ
ejpam-6136	410	15	as	as	ADP
ejpam-6136	410	16	the	the	DET
ejpam-6136	410	17	aboodh	aboodh	NOUN
ejpam-6136	410	18	and	and	CCONJ
ejpam-6136	410	19	kamal	kamal	PROPN
ejpam-6136	410	20	transforms	transform	VERB
ejpam-6136	410	21	,	,	PUNCT
ejpam-6136	410	22	and	and	CCONJ
ejpam-6136	410	23	derive	derive	VERB
ejpam-6136	410	24	their	their	PRON
ejpam-6136	410	25	forms	form	NOUN
ejpam-6136	410	26	when	when	SCONJ
ejpam-6136	410	27	applied	apply	VERB
ejpam-6136	410	28	to	to	ADP
ejpam-6136	410	29	elementary	elementary	ADJ
ejpam-6136	410	30	functions	function	NOUN
ejpam-6136	410	31	.	.	PUNCT
ejpam-6136	411	1	2	2	X
ejpam-6136	411	2	.	.	X
ejpam-6136	411	3	to	to	PART
ejpam-6136	411	4	derive	derive	VERB
ejpam-6136	411	5	and	and	CCONJ
ejpam-6136	411	6	analyze	analyze	VERB
ejpam-6136	411	7	the	the	DET
ejpam-6136	411	8	degenerate	degenerate	ADJ
ejpam-6136	411	9	sadik	sadik	ADJ
ejpam-6136	411	10	transform	transform	NOUN
ejpam-6136	411	11	of	of	ADP
ejpam-6136	411	12	derivatives	derivative	NOUN
ejpam-6136	411	13	and	and	CCONJ
ejpam-6136	411	14	integrals	integral	NOUN
ejpam-6136	411	15	of	of	ADP
ejpam-6136	411	16	elementary	elementary	ADJ
ejpam-6136	411	17	functions	function	NOUN
ejpam-6136	411	18	,	,	PUNCT
ejpam-6136	411	19	helping	help	VERB
ejpam-6136	411	20	to	to	PART
ejpam-6136	411	21	understand	understand	VERB
ejpam-6136	411	22	how	how	SCONJ
ejpam-6136	411	23	it	it	PRON
ejpam-6136	411	24	behaves	behave	VERB
ejpam-6136	411	25	under	under	ADP
ejpam-6136	411	26	basic	basic	ADJ
ejpam-6136	411	27	calculus	calculus	NOUN
ejpam-6136	411	28	operations	operation	NOUN
ejpam-6136	411	29	.	.	PUNCT
ejpam-6136	412	1	3	3	X
ejpam-6136	412	2	.	.	PUNCT
ejpam-6136	412	3	to	to	PART
ejpam-6136	412	4	explore	explore	VERB
ejpam-6136	412	5	the	the	DET
ejpam-6136	412	6	inverse	inverse	NOUN
ejpam-6136	412	7	of	of	ADP
ejpam-6136	412	8	the	the	DET
ejpam-6136	412	9	degenerate	degenerate	ADJ
ejpam-6136	412	10	sadik	sadik	PROPN
ejpam-6136	412	11	transform	transform	NOUN
ejpam-6136	412	12	,	,	PUNCT
ejpam-6136	412	13	which	which	PRON
ejpam-6136	412	14	is	be	AUX
ejpam-6136	412	15	a	a	DET
ejpam-6136	412	16	key	key	ADJ
ejpam-6136	412	17	step	step	NOUN
ejpam-6136	412	18	for	for	ADP
ejpam-6136	412	19	reconstructing	reconstruct	VERB
ejpam-6136	412	20	original	original	ADJ
ejpam-6136	412	21	functions	function	NOUN
ejpam-6136	412	22	and	and	CCONJ
ejpam-6136	412	23	solving	solve	VERB
ejpam-6136	412	24	applied	apply	VERB
ejpam-6136	412	25	problems	problem	NOUN
ejpam-6136	412	26	effectively	effectively	ADV
ejpam-6136	412	27	.	.	PUNCT
ejpam-6136	413	1	acknowledgements	acknowledgement	NOUN
ejpam-6136	413	2	this	this	DET
ejpam-6136	413	3	research	research	NOUN
ejpam-6136	413	4	is	be	AUX
ejpam-6136	413	5	funded	fund	VERB
ejpam-6136	413	6	by	by	ADP
ejpam-6136	413	7	the	the	DET
ejpam-6136	413	8	department	department	PROPN
ejpam-6136	413	9	of	of	ADP
ejpam-6136	413	10	science	science	NOUN
ejpam-6136	413	11	and	and	CCONJ
ejpam-6136	413	12	technology	technology	NOUN
ejpam-6136	413	13	(	(	PUNCT
ejpam-6136	413	14	dost	dost	NOUN
ejpam-6136	413	15	)	)	PUNCT
ejpam-6136	413	16	and	and	CCONJ
ejpam-6136	413	17	the	the	DET
ejpam-6136	413	18	mindanao	mindanao	PROPN
ejpam-6136	413	19	state	state	PROPN
ejpam-6136	413	20	university	university	PROPN
ejpam-6136	413	21	main	main	ADJ
ejpam-6136	413	22	campus	campus	NOUN
ejpam-6136	413	23	,	,	PUNCT
ejpam-6136	413	24	marawi	marawi	PROPN
ejpam-6136	413	25	city	city	PROPN
ejpam-6136	413	26	.	.	PUNCT
ejpam-6136	414	1	references	reference	NOUN
ejpam-6136	414	2	[	[	X
ejpam-6136	414	3	1	1	NUM
ejpam-6136	414	4	]	]	PUNCT
ejpam-6136	414	5	c.	c.	PROPN
ejpam-6136	414	6	chen	chen	PROPN
ejpam-6136	414	7	and	and	CCONJ
ejpam-6136	414	8	k.	k.	PROPN
ejpam-6136	414	9	koh	koh	PROPN
ejpam-6136	414	10	.	.	PUNCT
ejpam-6136	415	1	principles	principle	NOUN
ejpam-6136	415	2	and	and	CCONJ
ejpam-6136	415	3	techniques	technique	NOUN
ejpam-6136	415	4	in	in	ADP
ejpam-6136	415	5	combinatorics	combinatoric	NOUN
ejpam-6136	415	6	.	.	PUNCT
ejpam-6136	416	1	world	world	PROPN
ejpam-6136	416	2	scientific	scientific	PROPN
ejpam-6136	416	3	publishing	publishing	PROPN
ejpam-6136	416	4	co.	co.	PROPN
ejpam-6136	416	5	pte	pte	PROPN
ejpam-6136	416	6	.	.	PROPN
ejpam-6136	416	7	ltd	ltd	PROPN
ejpam-6136	416	8	.	.	PROPN
ejpam-6136	416	9	,	,	PUNCT
ejpam-6136	416	10	1992	1992	NUM
ejpam-6136	416	11	.	.	PUNCT
ejpam-6136	417	1	[	[	X
ejpam-6136	417	2	2	2	NUM
ejpam-6136	417	3	]	]	PUNCT
ejpam-6136	417	4	f.	f.	PROPN
ejpam-6136	417	5	b.	b.	PROPN
ejpam-6136	417	6	m.	m.	PROPN
ejpam-6136	417	7	belgacem	belgacem	NOUN
ejpam-6136	417	8	and	and	CCONJ
ejpam-6136	417	9	a.	a.	NOUN
ejpam-6136	417	10	a.	a.	PROPN
ejpam-6136	417	11	karaballi	karaballi	PROPN
ejpam-6136	417	12	.	.	PUNCT
ejpam-6136	418	1	sumudu	sumudu	NOUN
ejpam-6136	418	2	transform	transform	VERB
ejpam-6136	418	3	fundamental	fundamental	ADJ
ejpam-6136	418	4	properties	property	NOUN
ejpam-6136	418	5	investigations	investigation	NOUN
ejpam-6136	418	6	and	and	CCONJ
ejpam-6136	418	7	applications	application	NOUN
ejpam-6136	418	8	.	.	PUNCT
ejpam-6136	419	1	2006	2006	NUM
ejpam-6136	419	2	.	.	PUNCT
ejpam-6136	420	1	[	[	X
ejpam-6136	420	2	3	3	X
ejpam-6136	420	3	]	]	X
ejpam-6136	420	4	t.	t.	PROPN
ejpam-6136	420	5	m.	m.	NOUN
ejpam-6136	420	6	elzaki	elzaki	PROPN
ejpam-6136	420	7	and	and	CCONJ
ejpam-6136	420	8	m.	m.	PROPN
ejpam-6136	420	9	e.	e.	PROPN
ejpam-6136	420	10	salih	salih	PROPN
ejpam-6136	420	11	.	.	PUNCT
ejpam-6136	421	1	on	on	ADP
ejpam-6136	421	2	the	the	DET
ejpam-6136	421	3	relationship	relationship	NOUN
ejpam-6136	421	4	between	between	ADP
ejpam-6136	421	5	laplace	laplace	NOUN
ejpam-6136	421	6	transform	transform	NOUN
ejpam-6136	421	7	and	and	CCONJ
ejpam-6136	421	8	new	new	ADJ
ejpam-6136	421	9	integral	integral	ADJ
ejpam-6136	421	10	transform	transform	NOUN
ejpam-6136	421	11	tarig	tarig	NOUN
ejpam-6136	421	12	transform	transform	NOUN
ejpam-6136	421	13	.	.	PUNCT
ejpam-6136	421	14	elixir	elixir	NOUN
ejpam-6136	421	15	applied	apply	VERB
ejpam-6136	421	16	mathematics	mathematic	NOUN
ejpam-6136	421	17	,	,	PUNCT
ejpam-6136	421	18	36:3230–3233	36:3230–3233	NUM
ejpam-6136	421	19	,	,	PUNCT
ejpam-6136	421	20	2011	2011	NUM
ejpam-6136	421	21	.	.	PUNCT
ejpam-6136	422	1	[	[	X
ejpam-6136	422	2	4	4	NUM
ejpam-6136	422	3	]	]	PUNCT
ejpam-6136	422	4	m.	m.	NOUN
ejpam-6136	422	5	t.	t.	PROPN
ejpam-6136	422	6	elzaki	elzaki	PROPN
ejpam-6136	422	7	.	.	PUNCT
ejpam-6136	423	1	the	the	DET
ejpam-6136	423	2	new	new	ADJ
ejpam-6136	423	3	integral	integral	ADJ
ejpam-6136	423	4	transform	transform	NOUN
ejpam-6136	423	5	:	:	PUNCT
ejpam-6136	423	6	”	"	PUNCT
ejpam-6136	423	7	elzaki	elzaki	NOUN
ejpam-6136	423	8	transform	transform	NOUN
ejpam-6136	423	9	”	"	PUNCT
ejpam-6136	423	10	.	.	PUNCT
ejpam-6136	424	1	global	global	ADJ
ejpam-6136	424	2	journal	journal	PROPN
ejpam-6136	424	3	of	of	ADP
ejpam-6136	424	4	pure	pure	ADJ
ejpam-6136	424	5	and	and	CCONJ
ejpam-6136	424	6	applied	applied	ADJ
ejpam-6136	424	7	mathematics	mathematic	NOUN
ejpam-6136	424	8	,	,	PUNCT
ejpam-6136	424	9	2011	2011	NUM
ejpam-6136	424	10	.	.	PUNCT
ejpam-6136	425	1	[	[	X
ejpam-6136	425	2	5	5	X
ejpam-6136	425	3	]	]	X
ejpam-6136	425	4	khalid	khalid	PROPN
ejpam-6136	425	5	suliman	suliman	PROPN
ejpam-6136	425	6	aboodh	aboodh	PROPN
ejpam-6136	425	7	.	.	PUNCT
ejpam-6136	426	1	the	the	DET
ejpam-6136	426	2	new	new	ADJ
ejpam-6136	426	3	integral	integral	ADJ
ejpam-6136	426	4	transform	transform	NOUN
ejpam-6136	426	5	:	:	PUNCT
ejpam-6136	426	6	”	"	PUNCT
ejpam-6136	426	7	aboodh	aboodh	PROPN
ejpam-6136	426	8	transform	transform	NOUN
ejpam-6136	426	9	”	"	PUNCT
ejpam-6136	426	10	.	.	PUNCT
ejpam-6136	427	1	global	global	ADJ
ejpam-6136	427	2	journal	journal	PROPN
ejpam-6136	427	3	of	of	ADP
ejpam-6136	427	4	pure	pure	ADJ
ejpam-6136	427	5	and	and	CCONJ
ejpam-6136	427	6	applied	applied	ADJ
ejpam-6136	427	7	mathematics	mathematic	NOUN
ejpam-6136	427	8	,	,	PUNCT
ejpam-6136	427	9	9:35–43	9:35–43	PROPN
ejpam-6136	427	10	,	,	PUNCT
ejpam-6136	427	11	2013	2013	NUM
ejpam-6136	427	12	.	.	PUNCT
ejpam-6136	428	1	[	[	X
ejpam-6136	428	2	6	6	NUM
ejpam-6136	428	3	]	]	PUNCT
ejpam-6136	428	4	sudhanshu	sudhanshu	NOUN
ejpam-6136	428	5	aggarwal	aggarwal	PROPN
ejpam-6136	428	6	,	,	PUNCT
ejpam-6136	428	7	nidhi	nidhi	PROPN
ejpam-6136	428	8	sharma	sharma	PROPN
ejpam-6136	428	9	,	,	PUNCT
ejpam-6136	428	10	and	and	CCONJ
ejpam-6136	428	11	raman	raman	NOUN
ejpam-6136	428	12	chauhan	chauhan	PROPN
ejpam-6136	428	13	.	.	PUNCT
ejpam-6136	428	14	application	application	NOUN
ejpam-6136	428	15	of	of	ADP
ejpam-6136	428	16	kamal	kamal	PROPN
ejpam-6136	428	17	transform	transform	NOUN
ejpam-6136	428	18	for	for	ADP
ejpam-6136	428	19	solving	solve	VERB
ejpam-6136	428	20	linear	linear	PROPN
ejpam-6136	428	21	volterra	volterra	NOUN
ejpam-6136	428	22	integral	integral	ADJ
ejpam-6136	428	23	equations	equation	NOUN
ejpam-6136	428	24	of	of	ADP
ejpam-6136	428	25	first	first	ADJ
ejpam-6136	428	26	kind	kind	NOUN
ejpam-6136	428	27	.	.	PUNCT
ejpam-6136	429	1	international	international	ADJ
ejpam-6136	429	2	journal	journal	PROPN
ejpam-6136	429	3	of	of	ADP
ejpam-6136	429	4	research	research	NOUN
ejpam-6136	429	5	in	in	ADP
ejpam-6136	429	6	advent	advent	ADJ
ejpam-6136	429	7	technology	technology	NOUN
ejpam-6136	429	8	,	,	PUNCT
ejpam-6136	429	9	6(8	6(8	NUM
ejpam-6136	429	10	)	)	PUNCT
ejpam-6136	429	11	,	,	PUNCT
ejpam-6136	429	12	2018	2018	NUM
ejpam-6136	429	13	.	.	PUNCT
ejpam-6136	430	1	[	[	X
ejpam-6136	430	2	7	7	X
ejpam-6136	430	3	]	]	X
ejpam-6136	430	4	prem	prem	PROPN
ejpam-6136	430	5	kumar	kumar	PROPN
ejpam-6136	430	6	and	and	CCONJ
ejpam-6136	430	7	sania	sania	PROPN
ejpam-6136	430	8	qureshi	qureshi	PROPN
ejpam-6136	430	9	.	.	PUNCT
ejpam-6136	430	10	laplace	laplace	PROPN
ejpam-6136	430	11	-	-	PUNCT
ejpam-6136	430	12	carson	carson	PROPN
ejpam-6136	430	13	integral	integral	ADJ
ejpam-6136	430	14	transform	transform	NOUN
ejpam-6136	430	15	for	for	ADP
ejpam-6136	430	16	exact	exact	ADJ
ejpam-6136	430	17	solution	solution	NOUN
ejpam-6136	430	18	of	of	ADP
ejpam-6136	430	19	non	non	ADJ
ejpam-6136	430	20	-	-	ADJ
ejpam-6136	430	21	integer	integer	ADJ
ejpam-6136	430	22	order	order	NOUN
ejpam-6136	430	23	initial	initial	ADJ
ejpam-6136	430	24	value	value	NOUN
ejpam-6136	430	25	problems	problem	NOUN
ejpam-6136	430	26	with	with	ADP
ejpam-6136	430	27	caputo	caputo	PROPN
ejpam-6136	430	28	operator	operator	PROPN
ejpam-6136	430	29	.	.	PUNCT
ejpam-6136	431	1	journal	journal	PROPN
ejpam-6136	431	2	of	of	ADP
ejpam-6136	431	3	applied	apply	VERB
ejpam-6136	431	4	mathematics	mathematic	NOUN
ejpam-6136	431	5	and	and	CCONJ
ejpam-6136	431	6	computational	computational	ADJ
ejpam-6136	431	7	mechanics	mechanic	NOUN
ejpam-6136	431	8	,	,	PUNCT
ejpam-6136	431	9	19(1):57–66	19(1):57–66	NUM
ejpam-6136	431	10	,	,	PUNCT
ejpam-6136	431	11	2020	2020	NUM
ejpam-6136	431	12	.	.	PUNCT
ejpam-6136	432	1	[	[	X
ejpam-6136	432	2	8	8	NUM
ejpam-6136	432	3	]	]	X
ejpam-6136	432	4	l.	l.	PROPN
ejpam-6136	432	5	debnath	debnath	PROPN
ejpam-6136	432	6	and	and	CCONJ
ejpam-6136	432	7	dabaru	dabaru	PROPN
ejpam-6136	432	8	.	.	PUNCT
ejpam-6136	433	1	integral	integral	ADJ
ejpam-6136	433	2	-	-	PUNCT
ejpam-6136	433	3	transforms	transform	NOUN
ejpam-6136	433	4	and	and	CCONJ
ejpam-6136	433	5	their	their	PRON
ejpam-6136	433	6	applications	application	NOUN
ejpam-6136	433	7	,	,	PUNCT
ejpam-6136	433	8	3rd	3rd	ADJ
ejpam-6136	433	9	edition	edition	NOUN
ejpam-6136	433	10	.	.	PUNCT
ejpam-6136	434	1	[	[	X
ejpam-6136	434	2	9	9	NUM
ejpam-6136	434	3	]	]	PUNCT
ejpam-6136	434	4	sadikali	sadikali	VERB
ejpam-6136	434	5	latif	latif	PROPN
ejpam-6136	434	6	shaik	shaik	PROPN
ejpam-6136	434	7	.	.	PUNCT
ejpam-6136	435	1	introducing	introduce	VERB
ejpam-6136	435	2	a	a	DET
ejpam-6136	435	3	new	new	ADJ
ejpam-6136	435	4	integral	integral	ADJ
ejpam-6136	435	5	transform	transform	NOUN
ejpam-6136	435	6	:	:	PUNCT
ejpam-6136	435	7	sadik	sadik	ADJ
ejpam-6136	435	8	transform	transform	NOUN
ejpam-6136	435	9	.	.	PUNCT
ejpam-6136	436	1	american	american	PROPN
ejpam-6136	436	2	international	international	PROPN
ejpam-6136	436	3	journal	journal	PROPN
ejpam-6136	436	4	of	of	ADP
ejpam-6136	436	5	research	research	NOUN
ejpam-6136	436	6	in	in	ADP
ejpam-6136	436	7	science	science	NOUN
ejpam-6136	436	8	,	,	PUNCT
ejpam-6136	436	9	technology	technology	NOUN
ejpam-6136	436	10	,	,	PUNCT
ejpam-6136	436	11	engineering	engineering	NOUN
ejpam-6136	436	12	and	and	CCONJ
ejpam-6136	436	13	mathematics	mathematic	NOUN
ejpam-6136	436	14	,	,	PUNCT
ejpam-6136	436	15	2018	2018	NUM
ejpam-6136	436	16	.	.	PUNCT
ejpam-6136	437	1	[	[	X
ejpam-6136	437	2	10	10	NUM
ejpam-6136	437	3	]	]	X
ejpam-6136	437	4	j.	j.	PROPN
ejpam-6136	437	5	stewart	stewart	PROPN
ejpam-6136	437	6	.	.	PUNCT
ejpam-6136	438	1	single	single	ADJ
ejpam-6136	438	2	variable	variable	ADJ
ejpam-6136	438	3	calculus	calculus	NOUN
ejpam-6136	438	4	:	:	PUNCT
ejpam-6136	438	5	early	early	ADJ
ejpam-6136	438	6	transcendentals	transcendental	NOUN
ejpam-6136	438	7	,	,	PUNCT
ejpam-6136	438	8	2nd	2nd	PROPN
ejpam-6136	438	9	edition	edition	NOUN
ejpam-6136	438	10	.	.	PUNCT
ejpam-6136	439	1	thomson	thomson	PROPN
ejpam-6136	439	2	brooks	brooks	PROPN
ejpam-6136	439	3	/	/	SYM
ejpam-6136	439	4	cole	cole	PROPN
ejpam-6136	439	5	,	,	PUNCT
ejpam-6136	439	6	2003	2003	NUM
ejpam-6136	439	7	.	.	PUNCT
ejpam-6136	440	1	j.	j.	PROPN
ejpam-6136	440	2	mohamadali	mohamadali	PROPN
ejpam-6136	440	3	,	,	PUNCT
ejpam-6136	440	4	n.	n.	PROPN
ejpam-6136	440	5	abdulcarim	abdulcarim	PROPN
ejpam-6136	440	6	/	/	SYM
ejpam-6136	440	7	eur	eur	PROPN
ejpam-6136	440	8	.	.	PUNCT
ejpam-6136	441	1	j.	j.	PROPN
ejpam-6136	441	2	pure	pure	PROPN
ejpam-6136	441	3	appl	appl	PROPN
ejpam-6136	441	4	.	.	PROPN
ejpam-6136	441	5	math	math	PROPN
ejpam-6136	441	6	,	,	PUNCT
ejpam-6136	441	7	18	18	NUM
ejpam-6136	441	8	(	(	PUNCT
ejpam-6136	441	9	3	3	NUM
ejpam-6136	441	10	)	)	PUNCT
ejpam-6136	441	11	(	(	PUNCT
ejpam-6136	441	12	2025	2025	NUM
ejpam-6136	441	13	)	)	PUNCT
ejpam-6136	441	14	,	,	PUNCT
ejpam-6136	441	15	6136	6136	NUM
ejpam-6136	441	16	19	19	NUM
ejpam-6136	441	17	of	of	ADP
ejpam-6136	441	18	19	19	NUM
ejpam-6136	442	1	[	[	SYM
ejpam-6136	442	2	11	11	NUM
ejpam-6136	442	3	]	]	PUNCT
ejpam-6136	442	4	t.	t.	PROPN
ejpam-6136	442	5	kim	kim	PROPN
ejpam-6136	442	6	and	and	CCONJ
ejpam-6136	442	7	d.	d.	PROPN
ejpam-6136	442	8	s.	s.	PROPN
ejpam-6136	442	9	kim	kim	PROPN
ejpam-6136	442	10	.	.	PROPN
ejpam-6136	443	1	degenerate	degenerate	ADJ
ejpam-6136	443	2	laplace	laplace	NOUN
ejpam-6136	443	3	transform	transform	NOUN
ejpam-6136	443	4	and	and	CCONJ
ejpam-6136	443	5	degenerate	degenerate	ADJ
ejpam-6136	443	6	gamma	gamma	NOUN
ejpam-6136	443	7	function	function	NOUN
ejpam-6136	443	8	.	.	PUNCT
ejpam-6136	444	1	russian	russian	ADJ
ejpam-6136	444	2	journal	journal	PROPN
ejpam-6136	444	3	of	of	ADP
ejpam-6136	444	4	mathematical	mathematical	ADJ
ejpam-6136	444	5	physics	physics	NOUN
ejpam-6136	444	6	,	,	PUNCT
ejpam-6136	444	7	pages	page	VERB
ejpam-6136	444	8	241–248	241–248	NUM
ejpam-6136	444	9	.	.	PUNCT
ejpam-6136	445	1	[	[	X
ejpam-6136	445	2	12	12	NUM
ejpam-6136	445	3	]	]	PUNCT
ejpam-6136	445	4	j.	j.	PROPN
ejpam-6136	445	5	b.	b.	PROPN
ejpam-6136	445	6	natuil	natuil	PROPN
ejpam-6136	445	7	,	,	PUNCT
ejpam-6136	445	8	h.	h.	PROPN
ejpam-6136	445	9	campos	campos	PROPN
ejpam-6136	445	10	,	,	PUNCT
ejpam-6136	445	11	and	and	CCONJ
ejpam-6136	445	12	j.	j.	PROPN
ejpam-6136	445	13	fernandez	fernandez	PROPN
ejpam-6136	445	14	.	.	PUNCT
ejpam-6136	446	1	on	on	ADP
ejpam-6136	446	2	degenerate	degenerate	ADJ
ejpam-6136	446	3	laplace	laplace	NOUN
ejpam-6136	446	4	-	-	PUNCT
ejpam-6136	446	5	type	type	NOUN
ejpam-6136	446	6	integral	integral	ADJ
ejpam-6136	446	7	transform	transform	NOUN
ejpam-6136	446	8	.	.	PUNCT
ejpam-6136	447	1	european	european	ADJ
ejpam-6136	447	2	journal	journal	PROPN
ejpam-6136	447	3	of	of	ADP
ejpam-6136	447	4	pure	pure	ADJ
ejpam-6136	447	5	and	and	CCONJ
ejpam-6136	447	6	applied	applied	ADJ
ejpam-6136	447	7	mathematics	mathematic	NOUN
ejpam-6136	447	8	,	,	PUNCT
ejpam-6136	447	9	16(4):2213–2233	16(4):2213–2233	NUM
ejpam-6136	447	10	,	,	PUNCT
ejpam-6136	447	11	2023	2023	NUM
ejpam-6136	447	12	.	.	PUNCT
ejpam-6136	448	1	[	[	X
ejpam-6136	448	2	13	13	NUM
ejpam-6136	448	3	]	]	PUNCT
ejpam-6136	448	4	a.	a.	NOUN
ejpam-6136	448	5	kalavathi	kalavathi	PROPN
ejpam-6136	448	6	,	,	PUNCT
ejpam-6136	448	7	t.	t.	PROPN
ejpam-6136	448	8	kohila	kohila	PROPN
ejpam-6136	448	9	,	,	PUNCT
ejpam-6136	448	10	and	and	CCONJ
ejpam-6136	448	11	l.	l.	PROPN
ejpam-6136	448	12	m.	m.	PROPN
ejpam-6136	448	13	upadhyaya	upadhyaya	PROPN
ejpam-6136	448	14	.	.	PUNCT
ejpam-6136	449	1	on	on	ADP
ejpam-6136	449	2	degenerate	degenerate	ADJ
ejpam-6136	449	3	elzaki	elzaki	NOUN
ejpam-6136	449	4	transform	transform	NOUN
ejpam-6136	449	5	.	.	PUNCT
ejpam-6136	450	1	bulletin	bulletin	NOUN
ejpam-6136	450	2	of	of	ADP
ejpam-6136	450	3	pure	pure	ADJ
ejpam-6136	450	4	and	and	CCONJ
ejpam-6136	450	5	applied	apply	VERB
ejpam-6136	450	6	sciences	science	NOUN
ejpam-6136	450	7	section	section	NOUN
ejpam-6136	450	8	e	e	NOUN
ejpam-6136	450	9	-	-	NOUN
ejpam-6136	450	10	mathematics	mathematic	NOUN
ejpam-6136	450	11	&	&	CCONJ
ejpam-6136	450	12	statistics	statistic	NOUN
ejpam-6136	450	13	,	,	PUNCT
ejpam-6136	450	14	40e(1):99–107	40e(1):99–107	X
ejpam-6136	450	15	,	,	PUNCT
ejpam-6136	450	16	2021	2021	NUM
ejpam-6136	450	17	.	.	PUNCT
ejpam-6136	451	1	[	[	X
ejpam-6136	451	2	14	14	NUM
ejpam-6136	451	3	]	]	X
ejpam-6136	451	4	u.	u.	PROPN
ejpam-6136	451	5	duran	duran	PROPN
ejpam-6136	451	6	.	.	PUNCT
ejpam-6136	452	1	degenerate	degenerate	PROPN
ejpam-6136	452	2	sumudo	sumudo	PROPN
ejpam-6136	452	3	transform	transform	NOUN
ejpam-6136	452	4	and	and	CCONJ
ejpam-6136	452	5	its	its	PRON
ejpam-6136	452	6	properties	property	NOUN
ejpam-6136	452	7	.	.	PUNCT
ejpam-6136	453	1	preprints	preprint	NOUN
ejpam-6136	453	2	,	,	PUNCT
ejpam-6136	453	3	2020	2020	NUM
ejpam-6136	453	4	.	.	PUNCT
ejpam-6136	454	1	doi	doi	NOUN
ejpam-6136	454	2	:	:	PUNCT
ejpam-6136	454	3	10.20944	10.20944	NUM
ejpam-6136	454	4	/	/	SYM
ejpam-6136	454	5	preprints202012.0626.v1	preprints202012.0626.v1	NOUN
ejpam-6136	454	6	.	.	PUNCT
ejpam-6136	455	1	[	[	X
ejpam-6136	455	2	15	15	NUM
ejpam-6136	455	3	]	]	PUNCT
ejpam-6136	455	4	t.	t.	PROPN
ejpam-6136	455	5	kim	kim	PROPN
ejpam-6136	455	6	,	,	PUNCT
ejpam-6136	455	7	d.	d.	PROPN
ejpam-6136	455	8	s.	s.	PROPN
ejpam-6136	455	9	kim	kim	PROPN
ejpam-6136	455	10	,	,	PUNCT
ejpam-6136	455	11	and	and	CCONJ
ejpam-6136	455	12	g.	g.	PROPN
ejpam-6136	455	13	w.	w.	PROPN
ejpam-6136	455	14	jang	jang	PROPN
ejpam-6136	455	15	.	.	PUNCT
ejpam-6136	456	1	a	a	DET
ejpam-6136	456	2	note	note	NOUN
ejpam-6136	456	3	on	on	ADP
ejpam-6136	456	4	degenerate	degenerate	ADJ
ejpam-6136	456	5	fubini	fubini	ADJ
ejpam-6136	456	6	polynomials	polynomial	NOUN
ejpam-6136	456	7	.	.	PUNCT
ejpam-6136	457	1	proceedings	proceeding	NOUN
ejpam-6136	457	2	of	of	ADP
ejpam-6136	457	3	the	the	DET
ejpam-6136	457	4	jangjeon	jangjeon	PROPN
ejpam-6136	457	5	mathematical	mathematical	PROPN
ejpam-6136	457	6	society	society	NOUN
ejpam-6136	457	7	,	,	PUNCT
ejpam-6136	457	8	(	(	PUNCT
ejpam-6136	457	9	4):521–531	4):521–531	NUM
ejpam-6136	457	10	,	,	PUNCT
ejpam-6136	457	11	2017	2017	NUM
ejpam-6136	457	12	.	.	PUNCT
ejpam-6136	458	1	[	[	X
ejpam-6136	458	2	16	16	NUM
ejpam-6136	458	3	]	]	PUNCT
ejpam-6136	458	4	t.	t.	PROPN
ejpam-6136	458	5	kim	kim	PROPN
ejpam-6136	458	6	,	,	PUNCT
ejpam-6136	458	7	d.	d.	PROPN
ejpam-6136	458	8	s.	s.	PROPN
ejpam-6136	458	9	kim	kim	PROPN
ejpam-6136	458	10	,	,	PUNCT
ejpam-6136	458	11	and	and	CCONJ
ejpam-6136	458	12	h.	h.	PROPN
ejpam-6136	458	13	lee	lee	PROPN
ejpam-6136	458	14	.	.	PUNCT
ejpam-6136	459	1	a	a	DET
ejpam-6136	459	2	note	note	NOUN
ejpam-6136	459	3	on	on	ADP
ejpam-6136	459	4	degenerate	degenerate	ADJ
ejpam-6136	459	5	euler	euler	NOUN
ejpam-6136	459	6	and	and	CCONJ
ejpam-6136	459	7	bernoulli	bernoulli	NOUN
ejpam-6136	459	8	polynomials	polynomial	NOUN
ejpam-6136	459	9	of	of	ADP
ejpam-6136	459	10	complex	complex	ADJ
ejpam-6136	459	11	variable	variable	NOUN
ejpam-6136	459	12	.	.	PUNCT
ejpam-6136	460	1	symmetry	symmetry	NOUN
ejpam-6136	460	2	,	,	PUNCT
ejpam-6136	460	3	11:1339	11:1339	NUM
ejpam-6136	460	4	,	,	PUNCT
ejpam-6136	460	5	2019	2019	NUM
ejpam-6136	460	6	.	.	PUNCT