id	sid	tid	token	lemma	pos
ejpam-4226	1	1	european	european	PROPN
ejpam-4226	1	2	journal	journal	PROPN
ejpam-4226	1	3	of	of	ADP
ejpam-4226	1	4	pure	pure	ADJ
ejpam-4226	1	5	and	and	CCONJ
ejpam-4226	1	6	applied	apply	VERB
ejpam-4226	1	7	mathematics	mathematic	NOUN
ejpam-4226	1	8	vol	vol	NOUN
ejpam-4226	1	9	.	.	PROPN
ejpam-4226	2	1	15	15	NUM
ejpam-4226	2	2	,	,	PUNCT
ejpam-4226	2	3	no	no	INTJ
ejpam-4226	2	4	.	.	NOUN
ejpam-4226	2	5	1	1	NUM
ejpam-4226	2	6	,	,	PUNCT
ejpam-4226	2	7	2022	2022	NUM
ejpam-4226	2	8	,	,	PUNCT
ejpam-4226	2	9	106	106	NUM
ejpam-4226	2	10	-	-	SYM
ejpam-4226	2	11	125	125	NUM
ejpam-4226	2	12	issn	issn	PROPN
ejpam-4226	2	13	1307	1307	NUM
ejpam-4226	2	14	-	-	SYM
ejpam-4226	2	15	5543	5543	NUM
ejpam-4226	2	16	–	–	PUNCT
ejpam-4226	2	17	ejpam.com	ejpam.com	X
ejpam-4226	2	18	published	publish	VERB
ejpam-4226	2	19	by	by	ADP
ejpam-4226	2	20	new	new	PROPN
ejpam-4226	2	21	york	york	PROPN
ejpam-4226	2	22	business	business	PROPN
ejpam-4226	2	23	global	global	ADJ
ejpam-4226	2	24	atomic	atomic	ADJ
ejpam-4226	2	25	solution	solution	NOUN
ejpam-4226	2	26	of	of	ADP
ejpam-4226	2	27	fractional	fractional	ADJ
ejpam-4226	2	28	abstract	abstract	ADJ
ejpam-4226	2	29	cauchy	cauchy	ADJ
ejpam-4226	2	30	problem	problem	NOUN
ejpam-4226	2	31	of	of	ADP
ejpam-4226	2	32	high	high	ADJ
ejpam-4226	2	33	order	order	NOUN
ejpam-4226	2	34	in	in	ADP
ejpam-4226	2	35	banach	banach	NOUN
ejpam-4226	2	36	spaces	space	NOUN
ejpam-4226	2	37	fatema	fatema	PROPN
ejpam-4226	2	38	bekraoui1	bekraoui1	PROPN
ejpam-4226	2	39	,	,	PUNCT
ejpam-4226	2	40	mohammed	mohammed	PROPN
ejpam-4226	2	41	al	al	PROPN
ejpam-4226	2	42	horani2	horani2	PROPN
ejpam-4226	2	43	,	,	PUNCT
ejpam-4226	2	44	roshdi	roshdi	ADJ
ejpam-4226	2	45	khalil3,∗	khalil3,∗	NOUN
ejpam-4226	2	46	1	1	NUM
ejpam-4226	2	47	department	department	NOUN
ejpam-4226	2	48	of	of	ADP
ejpam-4226	2	49	mathematics	mathematic	NOUN
ejpam-4226	2	50	,	,	PUNCT
ejpam-4226	2	51	school	school	NOUN
ejpam-4226	2	52	of	of	ADP
ejpam-4226	2	53	science	science	NOUN
ejpam-4226	2	54	,	,	PUNCT
ejpam-4226	2	55	the	the	DET
ejpam-4226	2	56	university	university	PROPN
ejpam-4226	2	57	of	of	ADP
ejpam-4226	2	58	jordan	jordan	PROPN
ejpam-4226	2	59	,	,	PUNCT
ejpam-4226	2	60	amman	amman	PROPN
ejpam-4226	2	61	,	,	PUNCT
ejpam-4226	2	62	jordan	jordan	PROPN
ejpam-4226	2	63	abstract	abstract	PROPN
ejpam-4226	2	64	.	.	PUNCT
ejpam-4226	3	1	the	the	DET
ejpam-4226	3	2	abstract	abstract	ADJ
ejpam-4226	3	3	cauchy	cauchy	PROPN
ejpam-4226	3	4	problem	problem	NOUN
ejpam-4226	3	5	,	,	PUNCT
ejpam-4226	3	6	which	which	PRON
ejpam-4226	3	7	is	be	AUX
ejpam-4226	3	8	a	a	DET
ejpam-4226	3	9	vector	vector	NOUN
ejpam-4226	3	10	valued	value	VERB
ejpam-4226	3	11	differential	differential	NOUN
ejpam-4226	3	12	equation	equation	NOUN
ejpam-4226	3	13	is	be	AUX
ejpam-4226	3	14	an	an	DET
ejpam-4226	3	15	important	important	ADJ
ejpam-4226	3	16	equation	equation	NOUN
ejpam-4226	3	17	in	in	ADP
ejpam-4226	3	18	many	many	ADJ
ejpam-4226	3	19	branches	branch	NOUN
ejpam-4226	3	20	of	of	ADP
ejpam-4226	3	21	science	science	NOUN
ejpam-4226	3	22	.	.	PUNCT
ejpam-4226	4	1	authors	author	NOUN
ejpam-4226	4	2	usually	usually	ADV
ejpam-4226	4	3	study	study	VERB
ejpam-4226	4	4	and	and	CCONJ
ejpam-4226	4	5	discuss	discuss	VERB
ejpam-4226	4	6	first	first	ADJ
ejpam-4226	4	7	and	and	CCONJ
ejpam-4226	4	8	second	second	ADJ
ejpam-4226	4	9	order	order	NOUN
ejpam-4226	4	10	abstract	abstract	ADJ
ejpam-4226	4	11	cauchy	cauchy	PROPN
ejpam-4226	4	12	problem	problem	NOUN
ejpam-4226	4	13	.	.	PUNCT
ejpam-4226	5	1	in	in	ADP
ejpam-4226	5	2	this	this	DET
ejpam-4226	5	3	paper	paper	NOUN
ejpam-4226	5	4	,	,	PUNCT
ejpam-4226	5	5	we	we	PRON
ejpam-4226	5	6	try	try	VERB
ejpam-4226	5	7	to	to	PART
ejpam-4226	5	8	find	find	VERB
ejpam-4226	5	9	atomic	atomic	ADJ
ejpam-4226	5	10	solutions	solution	NOUN
ejpam-4226	5	11	of	of	ADP
ejpam-4226	5	12	the	the	DET
ejpam-4226	5	13	fractional	fractional	ADJ
ejpam-4226	5	14	abstract	abstract	ADJ
ejpam-4226	5	15	cauchy	cauchy	ADJ
ejpam-4226	5	16	problem	problem	NOUN
ejpam-4226	5	17	with	with	ADP
ejpam-4226	5	18	order	order	NOUN
ejpam-4226	5	19	3α	3α	NOUN
ejpam-4226	5	20	,	,	PUNCT
ejpam-4226	5	21	where	where	SCONJ
ejpam-4226	5	22	α	α	PRON
ejpam-4226	5	23	∈	∈	PROPN
ejpam-4226	5	24	(	(	PUNCT
ejpam-4226	5	25	0	0	NUM
ejpam-4226	5	26	,	,	PUNCT
ejpam-4226	5	27	1	1	NUM
ejpam-4226	5	28	)	)	PUNCT
ejpam-4226	5	29	.	.	PUNCT
ejpam-4226	6	1	it	it	PRON
ejpam-4226	6	2	turned	turn	VERB
ejpam-4226	6	3	out	out	ADP
ejpam-4226	6	4	that	that	SCONJ
ejpam-4226	6	5	there	there	PRON
ejpam-4226	6	6	are	be	VERB
ejpam-4226	6	7	so	so	ADV
ejpam-4226	6	8	many	many	ADJ
ejpam-4226	6	9	cases	case	NOUN
ejpam-4226	6	10	to	to	PART
ejpam-4226	6	11	consider	consider	VERB
ejpam-4226	6	12	in	in	ADP
ejpam-4226	6	13	order	order	NOUN
ejpam-4226	6	14	to	to	PART
ejpam-4226	6	15	determine	determine	VERB
ejpam-4226	6	16	atomic	atomic	ADJ
ejpam-4226	6	17	solution	solution	NOUN
ejpam-4226	6	18	.	.	PUNCT
ejpam-4226	7	1	2020	2020	NUM
ejpam-4226	7	2	mathematics	mathematic	NOUN
ejpam-4226	7	3	subject	subject	NOUN
ejpam-4226	7	4	classifications	classification	NOUN
ejpam-4226	7	5	:	:	PUNCT
ejpam-4226	7	6	26a33	26a33	NUM
ejpam-4226	7	7	key	key	ADJ
ejpam-4226	7	8	words	word	NOUN
ejpam-4226	7	9	and	and	CCONJ
ejpam-4226	7	10	phrases	phrase	NOUN
ejpam-4226	7	11	:	:	PUNCT
ejpam-4226	7	12	tensor	tensor	NOUN
ejpam-4226	7	13	product	product	NOUN
ejpam-4226	7	14	of	of	ADP
ejpam-4226	7	15	banach	banach	NOUN
ejpam-4226	7	16	spaces	space	NOUN
ejpam-4226	7	17	,	,	PUNCT
ejpam-4226	7	18	atomic	atomic	ADJ
ejpam-4226	7	19	solution	solution	NOUN
ejpam-4226	7	20	,	,	PUNCT
ejpam-4226	7	21	conformable	conformable	ADJ
ejpam-4226	7	22	derivative	derivative	ADJ
ejpam-4226	7	23	,	,	PUNCT
ejpam-4226	7	24	abstract	abstract	ADJ
ejpam-4226	7	25	cauchy	cauchy	PROPN
ejpam-4226	7	26	problem	problem	NOUN
ejpam-4226	7	27	.	.	PUNCT
ejpam-4226	8	1	1	1	X
ejpam-4226	8	2	.	.	X
ejpam-4226	8	3	introduction	introduction	NOUN
ejpam-4226	8	4	let	let	VERB
ejpam-4226	8	5	x	x	PRON
ejpam-4226	8	6	be	be	AUX
ejpam-4226	8	7	a	a	DET
ejpam-4226	8	8	banach	banach	NOUN
ejpam-4226	8	9	space	space	NOUN
ejpam-4226	9	1	and	and	CCONJ
ejpam-4226	9	2	i	i	PRON
ejpam-4226	9	3	=	=	PUNCT
ejpam-4226	10	1	[	[	X
ejpam-4226	10	2	0	0	NUM
ejpam-4226	10	3	,	,	PUNCT
ejpam-4226	10	4	1	1	NUM
ejpam-4226	10	5	]	]	PUNCT
ejpam-4226	10	6	.	.	PUNCT
ejpam-4226	11	1	let	let	AUX
ejpam-4226	11	2	c(i	c(i	NOUN
ejpam-4226	11	3	)	)	PUNCT
ejpam-4226	11	4	be	be	AUX
ejpam-4226	11	5	the	the	DET
ejpam-4226	11	6	banach	banach	NOUN
ejpam-4226	11	7	space	space	NOUN
ejpam-4226	11	8	of	of	ADP
ejpam-4226	11	9	all	all	DET
ejpam-4226	11	10	real	real	ADV
ejpam-4226	11	11	valued	value	VERB
ejpam-4226	11	12	continuous	continuous	ADJ
ejpam-4226	11	13	functions	function	NOUN
ejpam-4226	11	14	on	on	ADP
ejpam-4226	11	15	i	i	PRON
ejpam-4226	11	16	under	under	ADP
ejpam-4226	11	17	the	the	DET
ejpam-4226	11	18	sup	sup	NOUN
ejpam-4226	11	19	-	-	PUNCT
ejpam-4226	11	20	norm	norm	NOUN
ejpam-4226	11	21	,	,	PUNCT
ejpam-4226	11	22	and	and	CCONJ
ejpam-4226	11	23	c(i	c(i	NOUN
ejpam-4226	11	24	,	,	PUNCT
ejpam-4226	11	25	x	x	PRON
ejpam-4226	11	26	)	)	PUNCT
ejpam-4226	11	27	be	be	AUX
ejpam-4226	11	28	the	the	DET
ejpam-4226	11	29	banach	banach	NOUN
ejpam-4226	11	30	space	space	NOUN
ejpam-4226	11	31	of	of	ADP
ejpam-4226	11	32	all	all	DET
ejpam-4226	11	33	continuous	continuous	ADJ
ejpam-4226	11	34	functions	function	NOUN
ejpam-4226	11	35	defined	define	VERB
ejpam-4226	11	36	on	on	ADP
ejpam-4226	11	37	i	i	PRON
ejpam-4226	11	38	with	with	ADP
ejpam-4226	11	39	values	value	NOUN
ejpam-4226	11	40	in	in	ADP
ejpam-4226	11	41	x.	x.	NOUN
ejpam-4226	11	42	a	a	DET
ejpam-4226	11	43	classical	classical	ADJ
ejpam-4226	11	44	and	and	CCONJ
ejpam-4226	11	45	important	important	ADJ
ejpam-4226	11	46	differential	differential	ADJ
ejpam-4226	11	47	equation	equation	NOUN
ejpam-4226	11	48	that	that	PRON
ejpam-4226	11	49	appears	appear	VERB
ejpam-4226	11	50	in	in	ADP
ejpam-4226	11	51	physics	physics	NOUN
ejpam-4226	11	52	and	and	CCONJ
ejpam-4226	11	53	other	other	ADJ
ejpam-4226	11	54	branches	branch	NOUN
ejpam-4226	11	55	of	of	ADP
ejpam-4226	11	56	applied	apply	VERB
ejpam-4226	11	57	sciences	science	NOUN
ejpam-4226	11	58	is	be	AUX
ejpam-4226	11	59	the	the	DET
ejpam-4226	11	60	so	so	ADV
ejpam-4226	11	61	called	call	VERB
ejpam-4226	11	62	abstract	abstract	ADJ
ejpam-4226	11	63	cauchy	cauchy	ADJ
ejpam-4226	11	64	problem	problem	NOUN
ejpam-4226	11	65	of	of	ADP
ejpam-4226	11	66	the	the	DET
ejpam-4226	11	67	first	first	ADJ
ejpam-4226	11	68	order	order	NOUN
ejpam-4226	11	69	.	.	PUNCT
ejpam-4226	12	1	one	one	NUM
ejpam-4226	12	2	form	form	NOUN
ejpam-4226	12	3	of	of	ADP
ejpam-4226	12	4	such	such	ADJ
ejpam-4226	12	5	equation	equation	NOUN
ejpam-4226	12	6	is	be	AUX
ejpam-4226	12	7	bu	bu	ADP
ejpam-4226	12	8	′	′	NUM
ejpam-4226	12	9	=	=	NOUN
ejpam-4226	12	10	au(t	au(t	NUM
ejpam-4226	12	11	)	)	PUNCT
ejpam-4226	13	1	+	+	NUM
ejpam-4226	13	2	f(t)z	f(t)z	PROPN
ejpam-4226	13	3	u(0	u(0	PROPN
ejpam-4226	13	4	)	)	PUNCT
ejpam-4226	13	5	=	=	SYM
ejpam-4226	14	1	x0	x0	PROPN
ejpam-4226	14	2	.	.	PUNCT
ejpam-4226	15	1	here	here	ADV
ejpam-4226	15	2	u	u	NOUN
ejpam-4226	15	3	is	be	AUX
ejpam-4226	15	4	a	a	DET
ejpam-4226	15	5	continuously	continuously	ADV
ejpam-4226	15	6	differentiable	differentiable	ADJ
ejpam-4226	15	7	function	function	NOUN
ejpam-4226	15	8	in	in	ADP
ejpam-4226	15	9	c(i	c(i	NOUN
ejpam-4226	15	10	,	,	PUNCT
ejpam-4226	15	11	x	x	NOUN
ejpam-4226	15	12	)	)	PUNCT
ejpam-4226	15	13	and	and	CCONJ
ejpam-4226	15	14	a	a	DET
ejpam-4226	15	15	,	,	PUNCT
ejpam-4226	15	16	b	b	NOUN
ejpam-4226	15	17	are	be	AUX
ejpam-4226	15	18	densely	densely	ADV
ejpam-4226	15	19	defined	define	VERB
ejpam-4226	15	20	linear	linear	ADJ
ejpam-4226	15	21	operators	operator	NOUN
ejpam-4226	15	22	on	on	ADP
ejpam-4226	15	23	the	the	DET
ejpam-4226	15	24	codomain	codomain	NOUN
ejpam-4226	15	25	of	of	ADP
ejpam-4226	15	26	u.	u.	NOUN
ejpam-4226	15	27	if	if	SCONJ
ejpam-4226	15	28	f	f	PROPN
ejpam-4226	15	29	=	=	SYM
ejpam-4226	15	30	0	0	PROPN
ejpam-4226	15	31	or	or	CCONJ
ejpam-4226	15	32	z	z	NOUN
ejpam-4226	15	33	=	=	SYM
ejpam-4226	15	34	0	0	NUM
ejpam-4226	15	35	,	,	PUNCT
ejpam-4226	15	36	then	then	ADV
ejpam-4226	15	37	the	the	DET
ejpam-4226	15	38	equation	equation	NOUN
ejpam-4226	15	39	is	be	AUX
ejpam-4226	15	40	homogeneous	homogeneous	ADJ
ejpam-4226	15	41	otherwise	otherwise	ADV
ejpam-4226	15	42	it	it	PRON
ejpam-4226	15	43	is	be	AUX
ejpam-4226	15	44	called	call	VERB
ejpam-4226	15	45	nonhomogeneous	nonhomogeneous	ADJ
ejpam-4226	15	46	.	.	PUNCT
ejpam-4226	16	1	now	now	ADV
ejpam-4226	16	2	in	in	ADP
ejpam-4226	16	3	the	the	DET
ejpam-4226	16	4	non	non	ADJ
ejpam-4226	16	5	-	-	ADJ
ejpam-4226	16	6	homogeneous	homogeneous	ADJ
ejpam-4226	16	7	problem	problem	NOUN
ejpam-4226	16	8	we	we	PRON
ejpam-4226	16	9	have	have	VERB
ejpam-4226	16	10	two	two	NUM
ejpam-4226	16	11	cases	case	NOUN
ejpam-4226	16	12	.	.	PUNCT
ejpam-4226	17	1	the	the	DET
ejpam-4226	17	2	first	first	ADJ
ejpam-4226	17	3	type	type	NOUN
ejpam-4226	17	4	,	,	PUNCT
ejpam-4226	17	5	if	if	SCONJ
ejpam-4226	17	6	u	u	NOUN
ejpam-4226	17	7	is	be	AUX
ejpam-4226	17	8	unknown	unknown	ADJ
ejpam-4226	17	9	and	and	CCONJ
ejpam-4226	17	10	f	f	PROPN
ejpam-4226	17	11	is	be	AUX
ejpam-4226	17	12	given	give	VERB
ejpam-4226	17	13	and	and	CCONJ
ejpam-4226	17	14	this	this	PRON
ejpam-4226	17	15	is	be	AUX
ejpam-4226	17	16	called	call	VERB
ejpam-4226	17	17	the	the	DET
ejpam-4226	17	18	direct	direct	ADJ
ejpam-4226	17	19	problem	problem	NOUN
ejpam-4226	17	20	.	.	PUNCT
ejpam-4226	18	1	the	the	DET
ejpam-4226	18	2	second	second	ADJ
ejpam-4226	18	3	type	type	NOUN
ejpam-4226	18	4	,	,	PUNCT
ejpam-4226	18	5	u	u	NOUN
ejpam-4226	18	6	∗corresponding	∗corresponde	VERB
ejpam-4226	18	7	author	author	NOUN
ejpam-4226	18	8	.	.	PUNCT
ejpam-4226	19	1	doi	doi	NOUN
ejpam-4226	19	2	:	:	PUNCT
ejpam-4226	19	3	https://doi.org/10.29020/nybg.ejpam.v15i1.4226	https://doi.org/10.29020/nybg.ejpam.v15i1.4226	PROPN
ejpam-4226	19	4	email	email	NOUN
ejpam-4226	19	5	addresses	address	NOUN
ejpam-4226	19	6	:	:	PUNCT
ejpam-4226	19	7	fat9180303@ju.edu.jo	fat9180303@ju.edu.jo	PROPN
ejpam-4226	19	8	(	(	PUNCT
ejpam-4226	19	9	f.	f.	PROPN
ejpam-4226	19	10	bekraoui	bekraoui	PROPN
ejpam-4226	19	11	)	)	PUNCT
ejpam-4226	19	12	,	,	PUNCT
ejpam-4226	20	1	horani@ju.edu.jo	horani@ju.edu.jo	NOUN
ejpam-4226	20	2	(	(	PUNCT
ejpam-4226	20	3	m.	m.	NOUN
ejpam-4226	20	4	al	al	PROPN
ejpam-4226	20	5	horani	horani	PROPN
ejpam-4226	20	6	)	)	PUNCT
ejpam-4226	20	7	,	,	PUNCT
ejpam-4226	20	8	roshdi@ju.edu.jo	roshdi@ju.edu.jo	PROPN
ejpam-4226	20	9	(	(	PUNCT
ejpam-4226	20	10	r.	r.	PROPN
ejpam-4226	20	11	khalil	khalil	PROPN
ejpam-4226	20	12	)	)	PUNCT
ejpam-4226	20	13	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-4226	21	1	106	106	NUM
ejpam-4226	22	1	©	©	PROPN
ejpam-4226	22	2	2022	2022	NUM
ejpam-4226	22	3	ejpam	ejpam	VERB
ejpam-4226	22	4	all	all	DET
ejpam-4226	22	5	rights	right	NOUN
ejpam-4226	22	6	reserved	reserve	VERB
ejpam-4226	22	7	.	.	PUNCT
ejpam-4226	23	1	f.	f.	PROPN
ejpam-4226	23	2	bekraoui	bekraoui	PROPN
ejpam-4226	23	3	,	,	PUNCT
ejpam-4226	23	4	m.	m.	PROPN
ejpam-4226	23	5	al	al	PROPN
ejpam-4226	23	6	horani	horani	PROPN
ejpam-4226	23	7	,	,	PUNCT
ejpam-4226	23	8	r.	r.	PROPN
ejpam-4226	23	9	khalil	khalil	PROPN
ejpam-4226	23	10	/	/	SYM
ejpam-4226	23	11	eur	eur	PROPN
ejpam-4226	23	12	.	.	PUNCT
ejpam-4226	24	1	j.	j.	PROPN
ejpam-4226	24	2	pure	pure	PROPN
ejpam-4226	24	3	appl	appl	PROPN
ejpam-4226	24	4	.	.	PROPN
ejpam-4226	24	5	math	math	PROPN
ejpam-4226	24	6	,	,	PUNCT
ejpam-4226	24	7	15	15	NUM
ejpam-4226	24	8	(	(	PUNCT
ejpam-4226	24	9	1	1	NUM
ejpam-4226	24	10	)	)	PUNCT
ejpam-4226	24	11	(	(	PUNCT
ejpam-4226	24	12	2022	2022	NUM
ejpam-4226	24	13	)	)	PUNCT
ejpam-4226	24	14	,	,	PUNCT
ejpam-4226	24	15	106	106	NUM
ejpam-4226	24	16	-	-	SYM
ejpam-4226	24	17	125	125	NUM
ejpam-4226	24	18	107	107	NUM
ejpam-4226	24	19	and	and	CCONJ
ejpam-4226	24	20	f	f	PROPN
ejpam-4226	24	21	are	be	AUX
ejpam-4226	24	22	unknowns	unknown	NOUN
ejpam-4226	24	23	and	and	CCONJ
ejpam-4226	24	24	it	it	PRON
ejpam-4226	24	25	is	be	AUX
ejpam-4226	24	26	called	call	VERB
ejpam-4226	24	27	the	the	DET
ejpam-4226	24	28	inverse	inverse	NOUN
ejpam-4226	24	29	problem	problem	NOUN
ejpam-4226	24	30	.	.	PUNCT
ejpam-4226	25	1	if	if	SCONJ
ejpam-4226	25	2	b	b	NOUN
ejpam-4226	25	3	is	be	AUX
ejpam-4226	25	4	not	not	PART
ejpam-4226	25	5	invertible	invertible	ADJ
ejpam-4226	25	6	,	,	PUNCT
ejpam-4226	25	7	then	then	ADV
ejpam-4226	25	8	the	the	DET
ejpam-4226	25	9	equation	equation	NOUN
ejpam-4226	25	10	is	be	AUX
ejpam-4226	25	11	called	call	VERB
ejpam-4226	25	12	degenerate	degenerate	ADJ
ejpam-4226	25	13	otherwise	otherwise	ADV
ejpam-4226	25	14	it	it	PRON
ejpam-4226	25	15	is	be	AUX
ejpam-4226	25	16	called	call	VERB
ejpam-4226	25	17	nondegenerate	nondegenerate	ADJ
ejpam-4226	25	18	.	.	PUNCT
ejpam-4226	26	1	it	it	PRON
ejpam-4226	26	2	was	be	AUX
ejpam-4226	26	3	hille	hille	PROPN
ejpam-4226	26	4	,	,	PUNCT
ejpam-4226	26	5	in	in	ADP
ejpam-4226	26	6	1952	1952	NUM
ejpam-4226	26	7	who	who	PRON
ejpam-4226	26	8	introduced	introduce	VERB
ejpam-4226	26	9	the	the	DET
ejpam-4226	26	10	abstract	abstract	ADJ
ejpam-4226	26	11	cauchy	cauchy	PROPN
ejpam-4226	26	12	problem	problem	NOUN
ejpam-4226	26	13	.	.	PUNCT
ejpam-4226	27	1	all	all	DET
ejpam-4226	27	2	the	the	DET
ejpam-4226	27	3	work	work	NOUN
ejpam-4226	27	4	since	since	SCONJ
ejpam-4226	27	5	then	then	ADV
ejpam-4226	27	6	was	be	AUX
ejpam-4226	27	7	trying	try	VERB
ejpam-4226	27	8	to	to	PART
ejpam-4226	27	9	solve	solve	VERB
ejpam-4226	27	10	the	the	DET
ejpam-4226	27	11	abstract	abstract	ADJ
ejpam-4226	27	12	cauchy	cauchy	ADJ
ejpam-4226	27	13	problem	problem	NOUN
ejpam-4226	27	14	of	of	ADP
ejpam-4226	27	15	the	the	DET
ejpam-4226	27	16	first	first	ADJ
ejpam-4226	27	17	order	order	NOUN
ejpam-4226	27	18	or	or	CCONJ
ejpam-4226	27	19	second	second	ADJ
ejpam-4226	27	20	order	order	NOUN
ejpam-4226	27	21	.	.	PUNCT
ejpam-4226	28	1	most	most	ADJ
ejpam-4226	28	2	of	of	ADP
ejpam-4226	28	3	the	the	DET
ejpam-4226	28	4	analysis	analysis	NOUN
ejpam-4226	28	5	of	of	ADP
ejpam-4226	28	6	the	the	DET
ejpam-4226	28	7	abstract	abstract	ADJ
ejpam-4226	28	8	cauchy	cauchy	ADJ
ejpam-4226	28	9	problem	problem	NOUN
ejpam-4226	28	10	was	be	AUX
ejpam-4226	28	11	using	use	VERB
ejpam-4226	28	12	theory	theory	NOUN
ejpam-4226	28	13	of	of	ADP
ejpam-4226	28	14	semigroups	semigroup	NOUN
ejpam-4226	28	15	of	of	ADP
ejpam-4226	28	16	operators	operator	NOUN
ejpam-4226	28	17	.	.	PUNCT
ejpam-4226	29	1	we	we	PRON
ejpam-4226	29	2	refer	refer	VERB
ejpam-4226	29	3	to	to	ADP
ejpam-4226	29	4	[	[	X
ejpam-4226	29	5	1	1	NUM
ejpam-4226	29	6	]	]	PUNCT
ejpam-4226	29	7	,	,	PUNCT
ejpam-4226	29	8	[	[	X
ejpam-4226	29	9	2]-[4	2]-[4	X
ejpam-4226	29	10	]	]	X
ejpam-4226	29	11	,	,	PUNCT
ejpam-4226	29	12	for	for	ADP
ejpam-4226	29	13	more	more	ADJ
ejpam-4226	29	14	on	on	ADP
ejpam-4226	29	15	the	the	DET
ejpam-4226	29	16	abstract	abstract	ADJ
ejpam-4226	29	17	cauchy	cauchy	PROPN
ejpam-4226	29	18	problem	problem	NOUN
ejpam-4226	29	19	.	.	PUNCT
ejpam-4226	30	1	in	in	ADP
ejpam-4226	30	2	this	this	DET
ejpam-4226	30	3	paper	paper	NOUN
ejpam-4226	30	4	,	,	PUNCT
ejpam-4226	30	5	we	we	PRON
ejpam-4226	30	6	will	will	AUX
ejpam-4226	30	7	use	use	VERB
ejpam-4226	30	8	tensor	tensor	NOUN
ejpam-4226	30	9	product	product	NOUN
ejpam-4226	30	10	technique	technique	NOUN
ejpam-4226	30	11	to	to	PART
ejpam-4226	30	12	find	find	VERB
ejpam-4226	30	13	what	what	PRON
ejpam-4226	30	14	is	be	AUX
ejpam-4226	30	15	called	call	VERB
ejpam-4226	30	16	atomic	atomic	ADJ
ejpam-4226	30	17	solution	solution	NOUN
ejpam-4226	30	18	for	for	ADP
ejpam-4226	30	19	the	the	DET
ejpam-4226	30	20	fractional	fractional	ADJ
ejpam-4226	30	21	abstract	abstract	ADJ
ejpam-4226	30	22	cauchy	cauchy	PROPN
ejpam-4226	30	23	problem	problem	NOUN
ejpam-4226	30	24	,	,	PUNCT
ejpam-4226	30	25	of	of	ADP
ejpam-4226	30	26	the	the	DET
ejpam-4226	30	27	third	third	ADJ
ejpam-4226	30	28	order	order	NOUN
ejpam-4226	30	29	.	.	PUNCT
ejpam-4226	31	1	indeed	indeed	ADV
ejpam-4226	31	2	,	,	PUNCT
ejpam-4226	31	3	we	we	PRON
ejpam-4226	31	4	will	will	AUX
ejpam-4226	31	5	study	study	VERB
ejpam-4226	31	6	the	the	DET
ejpam-4226	31	7	fractional	fractional	ADJ
ejpam-4226	31	8	abstract	abstract	ADJ
ejpam-4226	31	9	cauchy	cauchy	ADJ
ejpam-4226	31	10	problem	problem	NOUN
ejpam-4226	31	11	of	of	ADP
ejpam-4226	31	12	the	the	DET
ejpam-4226	31	13	form	form	NOUN
ejpam-4226	31	14	:	:	PUNCT
ejpam-4226	31	15	{	{	PUNCT
ejpam-4226	31	16	u(3α)(t	u(3α)(t	NOUN
ejpam-4226	31	17	)	)	PUNCT
ejpam-4226	31	18	+	+	NOUN
ejpam-4226	31	19	au(2α)(t	au(2α)(t	X
ejpam-4226	31	20	)	)	PUNCT
ejpam-4226	31	21	+	+	NOUN
ejpam-4226	31	22	bu(α)(t	bu(α)(t	NUM
ejpam-4226	31	23	)	)	PUNCT
ejpam-4226	31	24	+	+	NOUN
ejpam-4226	31	25	cu(t	cu(t	X
ejpam-4226	31	26	)	)	PUNCT
ejpam-4226	31	27	=	=	SYM
ejpam-4226	31	28	f(t	f(t	NOUN
ejpam-4226	31	29	)	)	PUNCT
ejpam-4226	31	30	u(0	u(0	NOUN
ejpam-4226	31	31	)	)	PUNCT
ejpam-4226	31	32	=	=	SYM
ejpam-4226	31	33	x0	x0	PROPN
ejpam-4226	31	34	,	,	PUNCT
ejpam-4226	31	35	u(α)(0	u(α)(0	PROPN
ejpam-4226	31	36	)	)	PUNCT
ejpam-4226	31	37	=	=	SYM
ejpam-4226	32	1	x1	x1	PROPN
ejpam-4226	32	2	,	,	PUNCT
ejpam-4226	32	3	u(2α)(0	u(2α)(0	ADJ
ejpam-4226	32	4	)	)	PUNCT
ejpam-4226	32	5	=	=	SYM
ejpam-4226	32	6	x2	x2	PROPN
ejpam-4226	32	7	.	.	PUNCT
ejpam-4226	33	1	(	(	PUNCT
ejpam-4226	33	2	1	1	X
ejpam-4226	33	3	)	)	PUNCT
ejpam-4226	33	4	where	where	SCONJ
ejpam-4226	33	5	,	,	PUNCT
ejpam-4226	33	6	a	a	DET
ejpam-4226	33	7	,	,	PUNCT
ejpam-4226	33	8	b	b	NOUN
ejpam-4226	33	9	,	,	PUNCT
ejpam-4226	33	10	c	c	PROPN
ejpam-4226	33	11	are	be	AUX
ejpam-4226	33	12	closed	close	VERB
ejpam-4226	33	13	operators	operator	NOUN
ejpam-4226	33	14	with	with	ADP
ejpam-4226	33	15	domain	domain	NOUN
ejpam-4226	33	16	in	in	ADP
ejpam-4226	33	17	range	range	NOUN
ejpam-4226	33	18	of	of	ADP
ejpam-4226	33	19	u	u	NOUN
ejpam-4226	33	20	,	,	PUNCT
ejpam-4226	33	21	and	and	CCONJ
ejpam-4226	33	22	f	f	PROPN
ejpam-4226	33	23	is	be	AUX
ejpam-4226	33	24	a	a	DET
ejpam-4226	33	25	given	give	VERB
ejpam-4226	33	26	vector	vector	NOUN
ejpam-4226	33	27	valued	value	VERB
ejpam-4226	33	28	function	function	NOUN
ejpam-4226	33	29	with	with	ADP
ejpam-4226	33	30	range	range	NOUN
ejpam-4226	33	31	in	in	ADP
ejpam-4226	33	32	x.	x.	NOUN
ejpam-4226	33	33	here	here	ADV
ejpam-4226	33	34	u(α	u(α	NOUN
ejpam-4226	33	35	)	)	PUNCT
ejpam-4226	33	36	denotes	denote	VERB
ejpam-4226	33	37	the	the	DET
ejpam-4226	33	38	α−conformable	α−conformable	ADJ
ejpam-4226	33	39	derivative	derivative	NOUN
ejpam-4226	33	40	of	of	ADP
ejpam-4226	33	41	u.	u.	NOUN
ejpam-4226	33	42	here	here	ADV
ejpam-4226	33	43	is	be	AUX
ejpam-4226	33	44	the	the	DET
ejpam-4226	33	45	definition	definition	NOUN
ejpam-4226	33	46	of	of	ADP
ejpam-4226	33	47	the	the	DET
ejpam-4226	33	48	conformable	conformable	ADJ
ejpam-4226	33	49	derivative	derivative	NOUN
ejpam-4226	33	50	given	give	VERB
ejpam-4226	33	51	in	in	ADP
ejpam-4226	33	52	[	[	X
ejpam-4226	33	53	5	5	NUM
ejpam-4226	33	54	]	]	PUNCT
ejpam-4226	33	55	:	:	PUNCT
ejpam-4226	33	56	for	for	ADP
ejpam-4226	33	57	g	g	NOUN
ejpam-4226	33	58	:	:	PUNCT
ejpam-4226	34	1	[	[	X
ejpam-4226	34	2	0;∞	0;∞	NOUN
ejpam-4226	34	3	)	)	PUNCT
ejpam-4226	34	4	→	→	SYM
ejpam-4226	34	5	r	r	NOUN
ejpam-4226	34	6	and	and	CCONJ
ejpam-4226	34	7	0	0	NUM
ejpam-4226	34	8	<	<	X
ejpam-4226	34	9	α	α	PROPN
ejpam-4226	34	10	≤	≤	NUM
ejpam-4226	34	11	1	1	NUM
ejpam-4226	34	12	,	,	PUNCT
ejpam-4226	34	13	the	the	DET
ejpam-4226	34	14	conformable	conformable	ADJ
ejpam-4226	34	15	fractional	fractional	ADJ
ejpam-4226	34	16	derivative	derivative	NOUN
ejpam-4226	34	17	of	of	ADP
ejpam-4226	34	18	g	g	NOUN
ejpam-4226	34	19	of	of	ADP
ejpam-4226	34	20	order	order	NOUN
ejpam-4226	34	21	α	α	NOUN
ejpam-4226	34	22	is	be	AUX
ejpam-4226	34	23	defined	define	VERB
ejpam-4226	34	24	by	by	ADP
ejpam-4226	34	25	dα(g)(t	dα(g)(t	NOUN
ejpam-4226	34	26	)	)	PUNCT
ejpam-4226	35	1	=	=	SYM
ejpam-4226	35	2	lim	lim	PROPN
ejpam-4226	35	3	ε→0	ε→0	NOUN
ejpam-4226	35	4	g(t+	g(t+	PROPN
ejpam-4226	35	5	εt1−α)−	εt1−α)−	PROPN
ejpam-4226	35	6	g(t	g(t	PROPN
ejpam-4226	35	7	)	)	PUNCT
ejpam-4226	36	1	ε	ε	PROPN
ejpam-4226	36	2	we	we	PRON
ejpam-4226	36	3	often	often	ADV
ejpam-4226	36	4	write	write	VERB
ejpam-4226	36	5	u(α	u(α	NOUN
ejpam-4226	36	6	)	)	PUNCT
ejpam-4226	36	7	for	for	ADP
ejpam-4226	36	8	dαu	dαu	NOUN
ejpam-4226	36	9	for	for	ADP
ejpam-4226	36	10	all	all	DET
ejpam-4226	36	11	t	t	PROPN
ejpam-4226	36	12	>	>	X
ejpam-4226	36	13	0	0	NUM
ejpam-4226	36	14	,	,	PUNCT
ejpam-4226	36	15	if	if	SCONJ
ejpam-4226	36	16	g	g	PROPN
ejpam-4226	36	17	is	be	AUX
ejpam-4226	36	18	α	α	PRON
ejpam-4226	36	19	differentiable	differentiable	ADJ
ejpam-4226	36	20	on	on	ADP
ejpam-4226	36	21	(	(	PUNCT
ejpam-4226	36	22	0	0	NUM
ejpam-4226	36	23	;	;	PUNCT
ejpam-4226	36	24	b	b	X
ejpam-4226	36	25	)	)	PUNCT
ejpam-4226	36	26	where	where	SCONJ
ejpam-4226	36	27	b	b	X
ejpam-4226	36	28	>	>	X
ejpam-4226	36	29	0	0	NUM
ejpam-4226	36	30	and	and	CCONJ
ejpam-4226	36	31	limt→0	limt→0	PROPN
ejpam-4226	36	32	+	+	CCONJ
ejpam-4226	36	33	g(α)(t	g(α)(t	NOUN
ejpam-4226	36	34	)	)	PUNCT
ejpam-4226	36	35	exists	exist	VERB
ejpam-4226	36	36	,	,	PUNCT
ejpam-4226	36	37	then	then	ADV
ejpam-4226	36	38	one	one	PRON
ejpam-4226	36	39	can	can	AUX
ejpam-4226	36	40	define	define	VERB
ejpam-4226	36	41	g(α)(0	g(α)(0	PROPN
ejpam-4226	36	42	)	)	PUNCT
ejpam-4226	37	1	=	=	SYM
ejpam-4226	37	2	limt→0	limt→0	PROPN
ejpam-4226	37	3	+	+	CCONJ
ejpam-4226	37	4	g(α)(t	g(α)(t	NOUN
ejpam-4226	37	5	)	)	PUNCT
ejpam-4226	37	6	.	.	PUNCT
ejpam-4226	38	1	the	the	DET
ejpam-4226	38	2	α	α	PROPN
ejpam-4226	38	3	fractional	fractional	ADJ
ejpam-4226	38	4	integral	integral	ADJ
ejpam-4226	38	5	of	of	ADP
ejpam-4226	38	6	a	a	DET
ejpam-4226	38	7	function	function	NOUN
ejpam-4226	38	8	f	f	X
ejpam-4226	38	9	starting	start	VERB
ejpam-4226	38	10	from	from	ADP
ejpam-4226	38	11	a	a	DET
ejpam-4226	38	12	≥	≥	NOUN
ejpam-4226	38	13	0	0	NUM
ejpam-4226	38	14	is	be	AUX
ejpam-4226	38	15	:	:	PUNCT
ejpam-4226	38	16	iaα(f(t	iaα(f(t	NOUN
ejpam-4226	38	17	)	)	PUNCT
ejpam-4226	38	18	)	)	PUNCT
ejpam-4226	39	1	=	=	SYM
ejpam-4226	39	2	ia(t1−αf(t	ia(t1−αf(t	NOUN
ejpam-4226	39	3	)	)	PUNCT
ejpam-4226	39	4	)	)	PUNCT
ejpam-4226	40	1	=	=	SYM
ejpam-4226	40	2	∫	∫	PROPN
ejpam-4226	40	3	t	t	PROPN
ejpam-4226	40	4	a	a	DET
ejpam-4226	40	5	f(s	f(	NOUN
ejpam-4226	40	6	)	)	PUNCT
ejpam-4226	41	1	s1−α	s1−α	PROPN
ejpam-4226	41	2	ds	ds	NOUN
ejpam-4226	41	3	for	for	ADP
ejpam-4226	41	4	more	more	ADV
ejpam-4226	41	5	on	on	ADP
ejpam-4226	41	6	conformable	conformable	ADJ
ejpam-4226	41	7	fractional	fractional	ADJ
ejpam-4226	41	8	derivative	derivative	NOUN
ejpam-4226	41	9	we	we	PRON
ejpam-4226	41	10	refer	refer	VERB
ejpam-4226	41	11	to	to	ADP
ejpam-4226	41	12	[	[	X
ejpam-4226	41	13	6]-[19	6]-[19	NOUN
ejpam-4226	41	14	]	]	PUNCT
ejpam-4226	41	15	.	.	PUNCT
ejpam-4226	42	1	now	now	ADV
ejpam-4226	42	2	,	,	PUNCT
ejpam-4226	42	3	we	we	PRON
ejpam-4226	42	4	need	need	VERB
ejpam-4226	42	5	some	some	DET
ejpam-4226	42	6	basic	basic	ADJ
ejpam-4226	42	7	facts	fact	NOUN
ejpam-4226	42	8	from	from	ADP
ejpam-4226	42	9	theory	theory	NOUN
ejpam-4226	42	10	of	of	ADP
ejpam-4226	42	11	tensor	tensor	NOUN
ejpam-4226	42	12	product	product	NOUN
ejpam-4226	42	13	of	of	ADP
ejpam-4226	42	14	banach	banach	NOUN
ejpam-4226	42	15	spaces	space	NOUN
ejpam-4226	42	16	.	.	PUNCT
ejpam-4226	43	1	let	let	VERB
ejpam-4226	43	2	x	x	PRON
ejpam-4226	43	3	and	and	CCONJ
ejpam-4226	43	4	y	y	PROPN
ejpam-4226	43	5	be	be	VERB
ejpam-4226	43	6	banach	banach	ADV
ejpam-4226	43	7	spaces	space	NOUN
ejpam-4226	43	8	,	,	PUNCT
ejpam-4226	43	9	x∗	x∗	PROPN
ejpam-4226	43	10	denote	denote	VERB
ejpam-4226	43	11	the	the	DET
ejpam-4226	43	12	dual	dual	ADJ
ejpam-4226	43	13	of	of	ADP
ejpam-4226	43	14	x.	x.	NOUN
ejpam-4226	43	15	for	for	ADP
ejpam-4226	43	16	x	x	SYM
ejpam-4226	43	17	∈	∈	PROPN
ejpam-4226	43	18	x	x	X
ejpam-4226	43	19	and	and	CCONJ
ejpam-4226	43	20	y	y	PROPN
ejpam-4226	43	21	∈	∈	PROPN
ejpam-4226	44	1	y	y	PROPN
ejpam-4226	44	2	define	define	VERB
ejpam-4226	44	3	the	the	DET
ejpam-4226	44	4	map	map	NOUN
ejpam-4226	44	5	x⊗	x⊗	VERB
ejpam-4226	44	6	y	y	PROPN
ejpam-4226	44	7	:	:	PUNCT
ejpam-4226	44	8	x∗	x∗	PROPN
ejpam-4226	44	9	→	→	SYM
ejpam-4226	44	10	y	y	PROPN
ejpam-4226	44	11	as	as	ADP
ejpam-4226	44	12	:	:	PUNCT
ejpam-4226	44	13	x⊗	x⊗	PROPN
ejpam-4226	44	14	y(x∗	y(x∗	PROPN
ejpam-4226	44	15	)	)	PUNCT
ejpam-4226	44	16	=	=	PUNCT
ejpam-4226	44	17	⟨x	⟨x	VERB
ejpam-4226	44	18	,	,	PUNCT
ejpam-4226	44	19	x∗⟩y	x∗⟩y	PROPN
ejpam-4226	44	20	,	,	PUNCT
ejpam-4226	44	21	for	for	ADP
ejpam-4226	44	22	all	all	DET
ejpam-4226	44	23	x∗	x∗	PROPN
ejpam-4226	44	24	∈	∈	PROPN
ejpam-4226	44	25	x∗.	x∗.	PUNCT
ejpam-4226	45	1	clearly	clearly	ADV
ejpam-4226	45	2	,	,	PUNCT
ejpam-4226	45	3	x	x	PROPN
ejpam-4226	45	4	⊗	⊗	PROPN
ejpam-4226	45	5	y	y	PROPN
ejpam-4226	45	6	is	be	AUX
ejpam-4226	45	7	a	a	DET
ejpam-4226	45	8	bounded	bounded	ADJ
ejpam-4226	45	9	linear	linear	ADJ
ejpam-4226	45	10	operator	operator	NOUN
ejpam-4226	45	11	and	and	CCONJ
ejpam-4226	45	12	∥	∥	NUM
ejpam-4226	45	13	x	x	PUNCT
ejpam-4226	46	1	⊗	⊗	PROPN
ejpam-4226	46	2	y	y	PROPN
ejpam-4226	46	3	∥=∥	∥=∥	PROPN
ejpam-4226	46	4	x	x	X
ejpam-4226	46	5	∥∥	∥∥	X
ejpam-4226	46	6	y	y	PROPN
ejpam-4226	46	7	∥	∥	PROPN
ejpam-4226	46	8	,	,	PUNCT
ejpam-4226	46	9	[	[	PUNCT
ejpam-4226	46	10	18	18	NUM
ejpam-4226	46	11	]	]	PUNCT
ejpam-4226	46	12	.	.	PUNCT
ejpam-4226	47	1	such	such	DET
ejpam-4226	47	2	an	an	DET
ejpam-4226	47	3	operator	operator	NOUN
ejpam-4226	47	4	x	x	PUNCT
ejpam-4226	47	5	⊗	⊗	PROPN
ejpam-4226	47	6	y	y	PROPN
ejpam-4226	47	7	is	be	AUX
ejpam-4226	47	8	called	call	VERB
ejpam-4226	47	9	an	an	DET
ejpam-4226	47	10	atom	atom	NOUN
ejpam-4226	47	11	.	.	PUNCT
ejpam-4226	48	1	the	the	DET
ejpam-4226	48	2	set	set	NOUN
ejpam-4226	48	3	x	x	PUNCT
ejpam-4226	48	4	⊗	⊗	PROPN
ejpam-4226	48	5	y	y	PROPN
ejpam-4226	48	6	=	=	PUNCT
ejpam-4226	48	7	span{x	span{x	VERB
ejpam-4226	48	8	⊗	⊗	ADJ
ejpam-4226	48	9	y	y	NOUN
ejpam-4226	48	10	:	:	PUNCT
ejpam-4226	48	11	x	x	PUNCT
ejpam-4226	48	12	∈	∈	NOUN
ejpam-4226	48	13	x	x	X
ejpam-4226	48	14	and	and	CCONJ
ejpam-4226	48	15	y	y	PROPN
ejpam-4226	48	16	∈	∈	PROPN
ejpam-4226	48	17	y	y	PROPN
ejpam-4226	48	18	}	}	PUNCT
ejpam-4226	48	19	is	be	AUX
ejpam-4226	48	20	a	a	DET
ejpam-4226	48	21	subspace	subspace	NOUN
ejpam-4226	48	22	of	of	ADP
ejpam-4226	48	23	l(x∗	l(x∗	NOUN
ejpam-4226	48	24	,	,	PUNCT
ejpam-4226	48	25	y	y	PROPN
ejpam-4226	48	26	)	)	PUNCT
ejpam-4226	48	27	.	.	PUNCT
ejpam-4226	49	1	the	the	DET
ejpam-4226	49	2	following	follow	VERB
ejpam-4226	49	3	lemma	lemma	PROPN
ejpam-4226	49	4	,	,	PUNCT
ejpam-4226	49	5	see	see	VERB
ejpam-4226	49	6	[	[	X
ejpam-4226	49	7	20]-[22	20]-[22	PROPN
ejpam-4226	49	8	]	]	PUNCT
ejpam-4226	49	9	,	,	PUNCT
ejpam-4226	49	10	is	be	AUX
ejpam-4226	49	11	needed	need	VERB
ejpam-4226	49	12	in	in	ADP
ejpam-4226	49	13	our	our	PRON
ejpam-4226	49	14	paper	paper	NOUN
ejpam-4226	49	15	.	.	PUNCT
ejpam-4226	50	1	theorem	theorem	NOUN
ejpam-4226	50	2	1	1	NUM
ejpam-4226	50	3	.	.	PUNCT
ejpam-4226	51	1	let	let	VERB
ejpam-4226	51	2	x1	x1	PROPN
ejpam-4226	51	3	⊗	⊗	PROPN
ejpam-4226	51	4	y1	y1	PROPN
ejpam-4226	52	1	and	and	CCONJ
ejpam-4226	53	1	x2	x2	PROPN
ejpam-4226	53	2	⊗	⊗	PROPN
ejpam-4226	53	3	y2	y2	INTJ
ejpam-4226	53	4	be	be	VERB
ejpam-4226	53	5	two	two	NUM
ejpam-4226	53	6	nonzero	nonzero	NOUN
ejpam-4226	53	7	atoms	atom	NOUN
ejpam-4226	53	8	in	in	ADP
ejpam-4226	53	9	x	x	PROPN
ejpam-4226	53	10	⊗	⊗	PROPN
ejpam-4226	53	11	y	y	PROPN
ejpam-4226	53	12	such	such	ADJ
ejpam-4226	53	13	that	that	SCONJ
ejpam-4226	53	14	x1	x1	PROPN
ejpam-4226	53	15	⊗	⊗	PROPN
ejpam-4226	53	16	y1	y1	PROPN
ejpam-4226	54	1	+	+	CCONJ
ejpam-4226	54	2	x2	x2	PROPN
ejpam-4226	55	1	⊗	⊗	ADJ
ejpam-4226	55	2	y2	y2	PROPN
ejpam-4226	55	3	=	=	SYM
ejpam-4226	56	1	x3	x3	ADJ
ejpam-4226	56	2	⊗	⊗	PROPN
ejpam-4226	56	3	y3	y3	PROPN
ejpam-4226	56	4	f.	f.	PROPN
ejpam-4226	56	5	bekraoui	bekraoui	PROPN
ejpam-4226	56	6	,	,	PUNCT
ejpam-4226	56	7	m.	m.	PROPN
ejpam-4226	56	8	al	al	PROPN
ejpam-4226	56	9	horani	horani	PROPN
ejpam-4226	56	10	,	,	PUNCT
ejpam-4226	56	11	r.	r.	PROPN
ejpam-4226	56	12	khalil	khalil	PROPN
ejpam-4226	56	13	/	/	SYM
ejpam-4226	56	14	eur	eur	PROPN
ejpam-4226	56	15	.	.	PUNCT
ejpam-4226	57	1	j.	j.	PROPN
ejpam-4226	57	2	pure	pure	PROPN
ejpam-4226	57	3	appl	appl	PROPN
ejpam-4226	57	4	.	.	PROPN
ejpam-4226	57	5	math	math	PROPN
ejpam-4226	57	6	,	,	PUNCT
ejpam-4226	57	7	15	15	NUM
ejpam-4226	57	8	(	(	PUNCT
ejpam-4226	57	9	1	1	NUM
ejpam-4226	57	10	)	)	PUNCT
ejpam-4226	57	11	(	(	PUNCT
ejpam-4226	57	12	2022	2022	NUM
ejpam-4226	57	13	)	)	PUNCT
ejpam-4226	57	14	,	,	PUNCT
ejpam-4226	57	15	106	106	NUM
ejpam-4226	57	16	-	-	SYM
ejpam-4226	57	17	125	125	NUM
ejpam-4226	57	18	108	108	NUM
ejpam-4226	57	19	then	then	ADV
ejpam-4226	57	20	either	either	CCONJ
ejpam-4226	57	21	x1	x1	PROPN
ejpam-4226	57	22	,	,	PUNCT
ejpam-4226	57	23	x2	x2	PROPN
ejpam-4226	57	24	or	or	CCONJ
ejpam-4226	57	25	y1	y1	NOUN
ejpam-4226	57	26	,	,	PUNCT
ejpam-4226	57	27	y2	y2	PROPN
ejpam-4226	57	28	are	be	AUX
ejpam-4226	57	29	linearly	linearly	ADV
ejpam-4226	57	30	dependent	dependent	ADJ
ejpam-4226	57	31	.	.	PUNCT
ejpam-4226	58	1	one	one	PRON
ejpam-4226	58	2	can	can	AUX
ejpam-4226	58	3	easily	easily	ADV
ejpam-4226	58	4	prove	prove	VERB
ejpam-4226	58	5	that	that	SCONJ
ejpam-4226	58	6	:	:	PUNCT
ejpam-4226	58	7	lemma	lemma	PROPN
ejpam-4226	58	8	1	1	X
ejpam-4226	58	9	.	.	PUNCT
ejpam-4226	59	1	if	if	SCONJ
ejpam-4226	59	2	x1	x1	PROPN
ejpam-4226	59	3	⊗	⊗	PROPN
ejpam-4226	59	4	y1	y1	PROPN
ejpam-4226	59	5	=	=	SYM
ejpam-4226	60	1	x2	x2	PROPN
ejpam-4226	61	1	⊗	⊗	PROPN
ejpam-4226	61	2	y2	y2	PROPN
ejpam-4226	61	3	,	,	PUNCT
ejpam-4226	61	4	then	then	ADV
ejpam-4226	61	5	x1	x1	NUM
ejpam-4226	61	6	,	,	PUNCT
ejpam-4226	61	7	x2	x2	PRON
ejpam-4226	61	8	are	be	AUX
ejpam-4226	61	9	dependent	dependent	ADJ
ejpam-4226	61	10	and	and	CCONJ
ejpam-4226	61	11	y1	y1	ADJ
ejpam-4226	61	12	,	,	PUNCT
ejpam-4226	61	13	y2	y2	PROPN
ejpam-4226	61	14	are	be	AUX
ejpam-4226	61	15	dependent	dependent	ADJ
ejpam-4226	61	16	too	too	ADV
ejpam-4226	61	17	.	.	PUNCT
ejpam-4226	62	1	2	2	X
ejpam-4226	62	2	.	.	X
ejpam-4226	62	3	main	main	ADJ
ejpam-4226	62	4	result	result	NOUN
ejpam-4226	62	5	now	now	ADV
ejpam-4226	62	6	we	we	PRON
ejpam-4226	62	7	are	be	AUX
ejpam-4226	62	8	interested	interested	ADJ
ejpam-4226	62	9	in	in	ADP
ejpam-4226	62	10	finding	find	VERB
ejpam-4226	62	11	atomic	atomic	ADJ
ejpam-4226	62	12	solution	solution	NOUN
ejpam-4226	62	13	of	of	ADP
ejpam-4226	62	14	problem	problem	NOUN
ejpam-4226	62	15	(	(	PUNCT
ejpam-4226	62	16	1).that	1).that	PRON
ejpam-4226	62	17	is	be	AUX
ejpam-4226	62	18	a	a	DET
ejpam-4226	62	19	solution	solution	NOUN
ejpam-4226	62	20	of	of	ADP
ejpam-4226	62	21	the	the	DET
ejpam-4226	62	22	form	form	NOUN
ejpam-4226	62	23	v	v	ADP
ejpam-4226	62	24	⊗	⊗	PROPN
ejpam-4226	62	25	x	x	X
ejpam-4226	62	26	,	,	PUNCT
ejpam-4226	62	27	with	with	ADP
ejpam-4226	62	28	v(t	v(t	ADJ
ejpam-4226	62	29	)	)	PUNCT
ejpam-4226	62	30	∈	∈	PROPN
ejpam-4226	62	31	r	r	NOUN
ejpam-4226	62	32	,	,	PUNCT
ejpam-4226	62	33	and	and	CCONJ
ejpam-4226	62	34	x	x	PUNCT
ejpam-4226	62	35	∈	∈	NOUN
ejpam-4226	62	36	x.	x.	NOUN
ejpam-4226	62	37	also	also	ADV
ejpam-4226	62	38	,	,	PUNCT
ejpam-4226	62	39	we	we	PRON
ejpam-4226	62	40	assume	assume	VERB
ejpam-4226	62	41	f	f	X
ejpam-4226	62	42	=	=	SYM
ejpam-4226	62	43	g	g	PROPN
ejpam-4226	62	44	⊗	⊗	PROPN
ejpam-4226	62	45	z.	z.	PROPN
ejpam-4226	62	46	substitute	substitute	PROPN
ejpam-4226	62	47	in	in	ADP
ejpam-4226	62	48	(	(	PUNCT
ejpam-4226	62	49	1	1	NUM
ejpam-4226	62	50	)	)	PUNCT
ejpam-4226	62	51	to	to	PART
ejpam-4226	62	52	get	get	VERB
ejpam-4226	62	53	:	:	PUNCT
ejpam-4226	62	54	v(3α)(t)⊗	v(3α)(t)⊗	ADJ
ejpam-4226	62	55	x+	x+	NUM
ejpam-4226	62	56	v(2α)(t)⊗ax+	v(2α)(t)⊗ax+	PROPN
ejpam-4226	62	57	v(α)(t)⊗bx+	v(α)(t)⊗bx+	NOUN
ejpam-4226	62	58	v(t)⊗	v(t)⊗	NOUN
ejpam-4226	62	59	cx	cx	NOUN
ejpam-4226	62	60	=	=	SYM
ejpam-4226	62	61	g(t)⊗	g(t)⊗	PROPN
ejpam-4226	62	62	z	z	NOUN
ejpam-4226	62	63	.	.	PUNCT
ejpam-4226	63	1	(	(	PUNCT
ejpam-4226	63	2	2	2	X
ejpam-4226	63	3	)	)	PUNCT
ejpam-4226	63	4	we	we	PRON
ejpam-4226	63	5	assume	assume	VERB
ejpam-4226	63	6	the	the	DET
ejpam-4226	63	7	conditions	condition	NOUN
ejpam-4226	63	8	v(0	v(0	NOUN
ejpam-4226	63	9	)	)	PUNCT
ejpam-4226	63	10	=	=	SYM
ejpam-4226	64	1	1	1	NUM
ejpam-4226	64	2	,	,	PUNCT
ejpam-4226	64	3	v(α)(0	v(α)(0	PROPN
ejpam-4226	64	4	)	)	PUNCT
ejpam-4226	64	5	=	=	SYM
ejpam-4226	65	1	1	1	NUM
ejpam-4226	65	2	,	,	PUNCT
ejpam-4226	65	3	v(2α)(0	v(2α)(0	NUM
ejpam-4226	65	4	)	)	PUNCT
ejpam-4226	65	5	=	=	SYM
ejpam-4226	66	1	1	1	X
ejpam-4226	66	2	.	.	X
ejpam-4226	66	3	there	there	PRON
ejpam-4226	66	4	are	be	VERB
ejpam-4226	66	5	many	many	ADJ
ejpam-4226	66	6	cases	case	NOUN
ejpam-4226	66	7	to	to	PART
ejpam-4226	66	8	consider	consider	VERB
ejpam-4226	66	9	.	.	PUNCT
ejpam-4226	67	1	once	once	ADV
ejpam-4226	67	2	again	again	ADV
ejpam-4226	67	3	,	,	PUNCT
ejpam-4226	67	4	the	the	DET
ejpam-4226	67	5	general	general	ADJ
ejpam-4226	67	6	form	form	NOUN
ejpam-4226	67	7	of	of	ADP
ejpam-4226	67	8	third	third	ADJ
ejpam-4226	67	9	-	-	PUNCT
ejpam-4226	67	10	order	order	NOUN
ejpam-4226	67	11	fractional	fractional	ADJ
ejpam-4226	67	12	abstract	abstract	ADJ
ejpam-4226	67	13	cauchy	cauchy	ADJ
ejpam-4226	67	14	problem	problem	NOUN
ejpam-4226	67	15	is	be	AUX
ejpam-4226	67	16	{	{	PUNCT
ejpam-4226	67	17	u(3α)(t	u(3α)(t	NOUN
ejpam-4226	67	18	)	)	PUNCT
ejpam-4226	67	19	+	+	NOUN
ejpam-4226	67	20	au(2α)(t	au(2α)(t	X
ejpam-4226	67	21	)	)	PUNCT
ejpam-4226	67	22	+	+	NOUN
ejpam-4226	67	23	bu(α)(t	bu(α)(t	NUM
ejpam-4226	67	24	)	)	PUNCT
ejpam-4226	67	25	+	+	NOUN
ejpam-4226	67	26	cu(t	cu(t	X
ejpam-4226	67	27	)	)	PUNCT
ejpam-4226	67	28	=	=	SYM
ejpam-4226	67	29	h(t	h(t	X
ejpam-4226	67	30	)	)	PUNCT
ejpam-4226	67	31	u(0	u(0	NOUN
ejpam-4226	67	32	)	)	PUNCT
ejpam-4226	67	33	=	=	SYM
ejpam-4226	67	34	x0	x0	PROPN
ejpam-4226	67	35	,	,	PUNCT
ejpam-4226	67	36	u(α)(0	u(α)(0	PROPN
ejpam-4226	67	37	)	)	PUNCT
ejpam-4226	67	38	=	=	SYM
ejpam-4226	68	1	x1	x1	PROPN
ejpam-4226	68	2	,	,	PUNCT
ejpam-4226	68	3	u(2α)(0	u(2α)(0	ADJ
ejpam-4226	68	4	)	)	PUNCT
ejpam-4226	68	5	=	=	SYM
ejpam-4226	68	6	x2	x2	PROPN
ejpam-4226	68	7	.	.	PUNCT
ejpam-4226	69	1	where	where	SCONJ
ejpam-4226	69	2	u	u	NOUN
ejpam-4226	69	3	is	be	AUX
ejpam-4226	69	4	3αdifferentiable	3αdifferentiable	NUM
ejpam-4226	69	5	function	function	NOUN
ejpam-4226	69	6	from	from	ADP
ejpam-4226	69	7	i	i	PRON
ejpam-4226	69	8	to	to	ADP
ejpam-4226	69	9	x	x	PROPN
ejpam-4226	69	10	and	and	CCONJ
ejpam-4226	69	11	a	a	DET
ejpam-4226	69	12	,	,	PUNCT
ejpam-4226	69	13	b	b	NOUN
ejpam-4226	69	14	,	,	PUNCT
ejpam-4226	69	15	and	and	CCONJ
ejpam-4226	69	16	c	c	PROPN
ejpam-4226	69	17	are	be	AUX
ejpam-4226	69	18	closed	close	VERB
ejpam-4226	69	19	linear	linear	ADJ
ejpam-4226	69	20	operator	operator	NOUN
ejpam-4226	69	21	on	on	ADP
ejpam-4226	69	22	x.	x.	NOUN
ejpam-4226	69	23	notice	notice	PROPN
ejpam-4226	69	24	,	,	PUNCT
ejpam-4226	69	25	we	we	PRON
ejpam-4226	69	26	use	use	VERB
ejpam-4226	69	27	u(3α	u(3α	NOUN
ejpam-4226	69	28	)	)	PUNCT
ejpam-4226	69	29	to	to	PART
ejpam-4226	69	30	denote	denote	VERB
ejpam-4226	69	31	dαdαdαu	dαdαdαu	PROPN
ejpam-4226	69	32	we	we	PRON
ejpam-4226	69	33	are	be	AUX
ejpam-4226	69	34	interested	interested	ADJ
ejpam-4226	69	35	in	in	ADP
ejpam-4226	69	36	finding	find	VERB
ejpam-4226	69	37	an	an	DET
ejpam-4226	69	38	atomic	atomic	ADJ
ejpam-4226	69	39	solution	solution	NOUN
ejpam-4226	69	40	of	of	ADP
ejpam-4226	69	41	equation	equation	NOUN
ejpam-4226	69	42	(	(	PUNCT
ejpam-4226	69	43	1	1	NUM
ejpam-4226	69	44	)	)	PUNCT
ejpam-4226	69	45	,	,	PUNCT
ejpam-4226	69	46	where	where	SCONJ
ejpam-4226	69	47	the	the	DET
ejpam-4226	69	48	right	right	ADJ
ejpam-4226	69	49	hand	hand	NOUN
ejpam-4226	69	50	side	side	NOUN
ejpam-4226	69	51	of	of	ADP
ejpam-4226	69	52	the	the	DET
ejpam-4226	69	53	equation	equation	NOUN
ejpam-4226	69	54	is	be	AUX
ejpam-4226	69	55	an	an	DET
ejpam-4226	69	56	atom	atom	NOUN
ejpam-4226	69	57	.	.	PUNCT
ejpam-4226	70	1	now	now	ADV
ejpam-4226	70	2	let	let	VERB
ejpam-4226	70	3	the	the	DET
ejpam-4226	70	4	atomic	atomic	ADJ
ejpam-4226	70	5	solution	solution	NOUN
ejpam-4226	70	6	we	we	PRON
ejpam-4226	70	7	are	be	AUX
ejpam-4226	70	8	looking	look	VERB
ejpam-4226	70	9	for	for	ADP
ejpam-4226	70	10	be	be	AUX
ejpam-4226	70	11	u(t	u(t	NOUN
ejpam-4226	70	12	)	)	PUNCT
ejpam-4226	70	13	=	=	SYM
ejpam-4226	71	1	v(t)x	v(t)x	PROPN
ejpam-4226	71	2	=	=	SYM
ejpam-4226	71	3	v	v	ADP
ejpam-4226	71	4	⊗	⊗	PROPN
ejpam-4226	71	5	x.	x.	NOUN
ejpam-4226	71	6	in	in	ADP
ejpam-4226	71	7	this	this	DET
ejpam-4226	71	8	case	case	NOUN
ejpam-4226	71	9	we	we	PRON
ejpam-4226	71	10	let	let	VERB
ejpam-4226	71	11	h(t	h(t	PRON
ejpam-4226	71	12	)	)	PUNCT
ejpam-4226	72	1	=	=	SYM
ejpam-4226	72	2	f(t)z	f(t)z	NOUN
ejpam-4226	72	3	=	=	SYM
ejpam-4226	73	1	f	f	PROPN
ejpam-4226	74	1	⊗	⊗	PROPN
ejpam-4226	74	2	z	z	PROPN
ejpam-4226	74	3	,	,	PUNCT
ejpam-4226	74	4	f	f	PROPN
ejpam-4226	74	5	is	be	AUX
ejpam-4226	74	6	a	a	DET
ejpam-4226	74	7	scalar	scalar	ADJ
ejpam-4226	74	8	valued	value	VERB
ejpam-4226	74	9	function	function	NOUN
ejpam-4226	74	10	.	.	PUNCT
ejpam-4226	75	1	here	here	ADV
ejpam-4226	75	2	v	v	NOUN
ejpam-4226	75	3	,	,	PUNCT
ejpam-4226	75	4	x	x	PRON
ejpam-4226	75	5	are	be	AUX
ejpam-4226	75	6	unknowns	unknown	NOUN
ejpam-4226	75	7	and	and	CCONJ
ejpam-4226	75	8	f	f	X
ejpam-4226	75	9	,	,	PUNCT
ejpam-4226	75	10	z	z	PROPN
ejpam-4226	75	11	are	be	AUX
ejpam-4226	75	12	given	give	VERB
ejpam-4226	75	13	let	let	VERB
ejpam-4226	75	14	us	we	PRON
ejpam-4226	75	15	rewrite	rewrite	VERB
ejpam-4226	75	16	(	(	PUNCT
ejpam-4226	75	17	2	2	NUM
ejpam-4226	75	18	)	)	PUNCT
ejpam-4226	75	19	in	in	ADP
ejpam-4226	75	20	the	the	DET
ejpam-4226	75	21	form	form	NOUN
ejpam-4226	75	22	v(3α)(t)⊗	v(3α)(t)⊗	ADJ
ejpam-4226	75	23	x+	x+	NUM
ejpam-4226	75	24	v(2α)(t)⊗ax+	v(2α)(t)⊗ax+	PROPN
ejpam-4226	75	25	v(α)(t)⊗bx+	v(α)(t)⊗bx+	NOUN
ejpam-4226	75	26	v(t)⊗	v(t)⊗	NOUN
ejpam-4226	75	27	cx	cx	NOUN
ejpam-4226	75	28	=	=	SYM
ejpam-4226	75	29	f(t)⊗	f(t)⊗	PROPN
ejpam-4226	75	30	z	z	NOUN
ejpam-4226	75	31	,	,	PUNCT
ejpam-4226	75	32	(	(	PUNCT
ejpam-4226	75	33	∗	∗	NOUN
ejpam-4226	75	34	)	)	PUNCT
ejpam-4226	75	35	v(0	v(0	NOUN
ejpam-4226	75	36	)	)	PUNCT
ejpam-4226	75	37	=	=	SYM
ejpam-4226	75	38	v(α)(0	v(α)(0	NOUN
ejpam-4226	75	39	)	)	PUNCT
ejpam-4226	76	1	=	=	SYM
ejpam-4226	76	2	v(2α)(0	v(2α)(0	NOUN
ejpam-4226	76	3	)	)	PUNCT
ejpam-4226	76	4	=	=	SYM
ejpam-4226	77	1	1	1	X
ejpam-4226	77	2	.	.	PUNCT
ejpam-4226	78	1	(	(	PUNCT
ejpam-4226	78	2	∗∗	∗∗	X
ejpam-4226	78	3	)	)	PUNCT
ejpam-4226	78	4	there	there	PRON
ejpam-4226	78	5	are	be	VERB
ejpam-4226	78	6	many	many	ADJ
ejpam-4226	78	7	cases	case	NOUN
ejpam-4226	78	8	to	to	PART
ejpam-4226	78	9	consider	consider	VERB
ejpam-4226	78	10	.	.	PUNCT
ejpam-4226	79	1	a.	a.	NOUN
ejpam-4226	79	2	the	the	DET
ejpam-4226	79	3	first	first	PROPN
ejpam-4226	79	4	case	case	PROPN
ejpam-4226	79	5	(	(	PUNCT
ejpam-4226	79	6	a	a	NOUN
ejpam-4226	79	7	)	)	PUNCT
ejpam-4226	79	8	v(3α	v(3α	NOUN
ejpam-4226	79	9	)	)	PUNCT
ejpam-4226	79	10	=	=	SYM
ejpam-4226	80	1	v(2α	v(2α	X
ejpam-4226	80	2	)	)	PUNCT
ejpam-4226	80	3	=	=	SYM
ejpam-4226	80	4	v(α	v(α	PROPN
ejpam-4226	80	5	)	)	PUNCT
ejpam-4226	80	6	=	=	SYM
ejpam-4226	81	1	v.	v.	ADP
ejpam-4226	81	2	or	or	CCONJ
ejpam-4226	81	3	(	(	PUNCT
ejpam-4226	81	4	b	b	NOUN
ejpam-4226	81	5	)	)	PUNCT
ejpam-4226	81	6	x	x	X
ejpam-4226	82	1	=	=	PUNCT
ejpam-4226	82	2	ax	ax	NOUN
ejpam-4226	82	3	=	=	PUNCT
ejpam-4226	82	4	bx	bx	PROPN
ejpam-4226	82	5	=	=	PROPN
ejpam-4226	82	6	cx	cx	PROPN
ejpam-4226	82	7	f.	f.	PROPN
ejpam-4226	82	8	bekraoui	bekraoui	PROPN
ejpam-4226	82	9	,	,	PUNCT
ejpam-4226	82	10	m.	m.	PROPN
ejpam-4226	82	11	al	al	PROPN
ejpam-4226	82	12	horani	horani	PROPN
ejpam-4226	82	13	,	,	PUNCT
ejpam-4226	82	14	r.	r.	PROPN
ejpam-4226	82	15	khalil	khalil	PROPN
ejpam-4226	82	16	/	/	SYM
ejpam-4226	82	17	eur	eur	PROPN
ejpam-4226	82	18	.	.	PUNCT
ejpam-4226	83	1	j.	j.	PROPN
ejpam-4226	83	2	pure	pure	PROPN
ejpam-4226	83	3	appl	appl	PROPN
ejpam-4226	83	4	.	.	PROPN
ejpam-4226	83	5	math	math	PROPN
ejpam-4226	83	6	,	,	PUNCT
ejpam-4226	83	7	15	15	NUM
ejpam-4226	83	8	(	(	PUNCT
ejpam-4226	83	9	1	1	NUM
ejpam-4226	83	10	)	)	PUNCT
ejpam-4226	83	11	(	(	PUNCT
ejpam-4226	83	12	2022	2022	NUM
ejpam-4226	83	13	)	)	PUNCT
ejpam-4226	83	14	,	,	PUNCT
ejpam-4226	83	15	106	106	NUM
ejpam-4226	83	16	-	-	SYM
ejpam-4226	83	17	125	125	NUM
ejpam-4226	83	18	109	109	NUM
ejpam-4226	83	19	let	let	VERB
ejpam-4226	83	20	us	we	PRON
ejpam-4226	83	21	consider	consider	VERB
ejpam-4226	83	22	the	the	DET
ejpam-4226	83	23	case	case	NOUN
ejpam-4226	83	24	where	where	SCONJ
ejpam-4226	83	25	v(3α	v(3α	NOUN
ejpam-4226	83	26	)	)	PUNCT
ejpam-4226	83	27	=	=	SYM
ejpam-4226	83	28	v(2α	v(2α	X
ejpam-4226	83	29	)	)	PUNCT
ejpam-4226	83	30	=	=	SYM
ejpam-4226	83	31	v(α	v(α	PROPN
ejpam-4226	83	32	)	)	PUNCT
ejpam-4226	83	33	=	=	SYM
ejpam-4226	83	34	v	v	NOUN
ejpam-4226	83	35	.	.	PUNCT
ejpam-4226	84	1	(	(	PUNCT
ejpam-4226	84	2	3	3	X
ejpam-4226	84	3	)	)	PUNCT
ejpam-4226	84	4	now	now	ADV
ejpam-4226	84	5	we	we	PRON
ejpam-4226	84	6	are	be	AUX
ejpam-4226	84	7	looking	look	VERB
ejpam-4226	84	8	for	for	ADP
ejpam-4226	84	9	v	v	NOUN
ejpam-4226	84	10	that	that	SCONJ
ejpam-4226	84	11	satisfies	satisfie	NOUN
ejpam-4226	84	12	(	(	PUNCT
ejpam-4226	84	13	1	1	NUM
ejpam-4226	84	14	)	)	PUNCT
ejpam-4226	84	15	.	.	PUNCT
ejpam-4226	85	1	from	from	ADP
ejpam-4226	85	2	(	(	PUNCT
ejpam-4226	85	3	3	3	X
ejpam-4226	85	4	)	)	PUNCT
ejpam-4226	85	5	we	we	PRON
ejpam-4226	85	6	have	have	VERB
ejpam-4226	85	7	the	the	DET
ejpam-4226	85	8	following	follow	VERB
ejpam-4226	85	9	situations	situation	NOUN
ejpam-4226	85	10	:	:	PUNCT
ejpam-4226	85	11	1	1	NUM
ejpam-4226	85	12	.	.	X
ejpam-4226	85	13	v(3α	v(3α	NOUN
ejpam-4226	85	14	)	)	PUNCT
ejpam-4226	85	15	=	=	SYM
ejpam-4226	85	16	v(2α	v(2α	NOUN
ejpam-4226	85	17	)	)	PUNCT
ejpam-4226	85	18	,	,	PUNCT
ejpam-4226	85	19	2	2	NUM
ejpam-4226	85	20	.	.	NOUN
ejpam-4226	85	21	v(2α	v(2α	NOUN
ejpam-4226	85	22	)	)	PUNCT
ejpam-4226	85	23	=	=	SYM
ejpam-4226	86	1	v(α	v(α	PROPN
ejpam-4226	86	2	)	)	PUNCT
ejpam-4226	86	3	,	,	PUNCT
ejpam-4226	86	4	3	3	X
ejpam-4226	86	5	.	.	PUNCT
ejpam-4226	87	1	v(α	v(α	PROPN
ejpam-4226	87	2	)	)	PUNCT
ejpam-4226	87	3	=	=	SYM
ejpam-4226	87	4	v	v	NOUN
ejpam-4226	87	5	,	,	PUNCT
ejpam-4226	87	6	4	4	NUM
ejpam-4226	87	7	.	.	PUNCT
ejpam-4226	87	8	v(3α	v(3α	NOUN
ejpam-4226	87	9	)	)	PUNCT
ejpam-4226	87	10	=	=	SYM
ejpam-4226	88	1	v(α	v(α	NOUN
ejpam-4226	88	2	)	)	PUNCT
ejpam-4226	88	3	,	,	PUNCT
ejpam-4226	88	4	5	5	NUM
ejpam-4226	88	5	.	.	PUNCT
ejpam-4226	88	6	v(3α	v(3α	NOUN
ejpam-4226	88	7	)	)	PUNCT
ejpam-4226	88	8	=	=	SYM
ejpam-4226	88	9	v	v	NOUN
ejpam-4226	88	10	,	,	PUNCT
ejpam-4226	88	11	6	6	NUM
ejpam-4226	88	12	.	.	PUNCT
ejpam-4226	88	13	v(2α	v(2α	NOUN
ejpam-4226	88	14	)	)	PUNCT
ejpam-4226	88	15	=	=	SYM
ejpam-4226	88	16	v	v	NOUN
ejpam-4226	88	17	,	,	PUNCT
ejpam-4226	88	18	situation	situation	NOUN
ejpam-4226	88	19	1	1	NUM
ejpam-4226	88	20	.	.	PUNCT
ejpam-4226	88	21	v(3α	v(3α	NOUN
ejpam-4226	88	22	)	)	PUNCT
ejpam-4226	88	23	=	=	SYM
ejpam-4226	88	24	v(2α	v(2α	NOUN
ejpam-4226	88	25	)	)	PUNCT
ejpam-4226	88	26	by	by	ADP
ejpam-4226	88	27	the	the	DET
ejpam-4226	88	28	results	result	NOUN
ejpam-4226	88	29	in	in	ADP
ejpam-4226	88	30	[	[	X
ejpam-4226	88	31	12	12	NUM
ejpam-4226	88	32	]	]	PUNCT
ejpam-4226	88	33	,	,	PUNCT
ejpam-4226	88	34	the	the	DET
ejpam-4226	88	35	associated	associated	ADJ
ejpam-4226	88	36	characteristic	characteristic	ADJ
ejpam-4226	88	37	equation	equation	NOUN
ejpam-4226	88	38	is	be	AUX
ejpam-4226	88	39	r2(r	r2(r	VERB
ejpam-4226	88	40	−	−	NOUN
ejpam-4226	88	41	1	1	NUM
ejpam-4226	88	42	)	)	PUNCT
ejpam-4226	88	43	=	=	SYM
ejpam-4226	89	1	0	0	X
ejpam-4226	89	2	.	.	PUNCT
ejpam-4226	90	1	hence	hence	ADV
ejpam-4226	90	2	r	r	NOUN
ejpam-4226	90	3	=	=	SYM
ejpam-4226	90	4	0	0	NUM
ejpam-4226	90	5	,	,	PUNCT
ejpam-4226	90	6	0	0	NUM
ejpam-4226	90	7	,	,	PUNCT
ejpam-4226	90	8	1	1	NUM
ejpam-4226	90	9	thus	thus	ADV
ejpam-4226	90	10	v(t	v(t	VERB
ejpam-4226	90	11	)	)	PUNCT
ejpam-4226	91	1	=	=	PROPN
ejpam-4226	91	2	c1	c1	PROPN
ejpam-4226	91	3	+	+	CCONJ
ejpam-4226	91	4	c2	c2	PROPN
ejpam-4226	91	5	1	1	NUM
ejpam-4226	91	6	α	α	NOUN
ejpam-4226	91	7	tα	tα	PROPN
ejpam-4226	91	8	+	+	CCONJ
ejpam-4226	91	9	c3	c3	PROPN
ejpam-4226	91	10	exp	exp	NOUN
ejpam-4226	91	11	1	1	NUM
ejpam-4226	91	12	α	α	NOUN
ejpam-4226	91	13	tα	tα	NOUN
ejpam-4226	91	14	from	from	ADP
ejpam-4226	91	15	(	(	PUNCT
ejpam-4226	91	16	∗∗	∗∗	PROPN
ejpam-4226	91	17	)	)	PUNCT
ejpam-4226	91	18	,	,	PUNCT
ejpam-4226	91	19	we	we	PRON
ejpam-4226	91	20	obtain	obtain	VERB
ejpam-4226	91	21			PUNCT
ejpam-4226	91	22	c1	c1	PROPN
ejpam-4226	91	23	+	+	CCONJ
ejpam-4226	91	24	c2	c2	PROPN
ejpam-4226	91	25	+	+	CCONJ
ejpam-4226	91	26	c3	c3	X
ejpam-4226	91	27	=	=	SYM
ejpam-4226	91	28	1	1	NUM
ejpam-4226	91	29	c2	c2	PROPN
ejpam-4226	91	30	+	+	CCONJ
ejpam-4226	91	31	c3	c3	X
ejpam-4226	91	32	=	=	SYM
ejpam-4226	91	33	1	1	NUM
ejpam-4226	91	34	c3	c3	NOUN
ejpam-4226	91	35	=	=	SYM
ejpam-4226	91	36	1	1	NUM
ejpam-4226	91	37	.	.	PUNCT
ejpam-4226	91	38	thus	thus	ADV
ejpam-4226	91	39	c1	c1	PROPN
ejpam-4226	91	40	=	=	PUNCT
ejpam-4226	91	41	0	0	PROPN
ejpam-4226	91	42	,	,	PUNCT
ejpam-4226	91	43	c2	c2	PROPN
ejpam-4226	91	44	=	=	SYM
ejpam-4226	91	45	0	0	PROPN
ejpam-4226	91	46	,	,	PUNCT
ejpam-4226	91	47	c3	c3	NOUN
ejpam-4226	91	48	=	=	PUNCT
ejpam-4226	91	49	1	1	X
ejpam-4226	91	50	.	.	PUNCT
ejpam-4226	91	51	hence	hence	ADV
ejpam-4226	91	52	v(t	v(t	NOUN
ejpam-4226	91	53	)	)	PUNCT
ejpam-4226	91	54	=	=	SYM
ejpam-4226	91	55	exp	exp	NOUN
ejpam-4226	91	56	1	1	NUM
ejpam-4226	91	57	α	α	NOUN
ejpam-4226	91	58	tα	tα	PROPN
ejpam-4226	91	59	.	.	PUNCT
ejpam-4226	92	1	(	(	PUNCT
ejpam-4226	92	2	4	4	X
ejpam-4226	92	3	)	)	PUNCT
ejpam-4226	92	4	situation	situation	NOUN
ejpam-4226	92	5	4	4	NUM
ejpam-4226	92	6	.	.	PUNCT
ejpam-4226	92	7	v(3α	v(3α	NOUN
ejpam-4226	92	8	)	)	PUNCT
ejpam-4226	92	9	=	=	SYM
ejpam-4226	92	10	v(α	v(α	NOUN
ejpam-4226	92	11	)	)	PUNCT
ejpam-4226	92	12	.	.	PUNCT
ejpam-4226	93	1	again	again	ADV
ejpam-4226	93	2	using	use	VERB
ejpam-4226	93	3	the	the	DET
ejpam-4226	93	4	results	result	NOUN
ejpam-4226	93	5	in	in	ADP
ejpam-4226	93	6	[	[	X
ejpam-4226	93	7	12	12	NUM
ejpam-4226	93	8	]	]	PUNCT
ejpam-4226	93	9	,	,	PUNCT
ejpam-4226	93	10	the	the	DET
ejpam-4226	93	11	associated	associated	ADJ
ejpam-4226	93	12	characteristic	characteristic	ADJ
ejpam-4226	93	13	equation	equation	NOUN
ejpam-4226	93	14	is	be	AUX
ejpam-4226	93	15	r(r2	r(r2	NOUN
ejpam-4226	93	16	−	−	NOUN
ejpam-4226	93	17	1	1	NUM
ejpam-4226	93	18	)	)	PUNCT
ejpam-4226	93	19	=	=	SYM
ejpam-4226	94	1	0	0	X
ejpam-4226	94	2	.	.	PUNCT
ejpam-4226	95	1	hence	hence	ADV
ejpam-4226	95	2	r	r	NOUN
ejpam-4226	95	3	=	=	SYM
ejpam-4226	95	4	0	0	NUM
ejpam-4226	95	5	,	,	PUNCT
ejpam-4226	95	6	1,−1	1,−1	NUM
ejpam-4226	95	7	.	.	PUNCT
ejpam-4226	96	1	so	so	ADV
ejpam-4226	96	2	v(t	v(t	ADJ
ejpam-4226	96	3	)	)	PUNCT
ejpam-4226	96	4	=	=	PROPN
ejpam-4226	96	5	c1	c1	PROPN
ejpam-4226	96	6	+	+	CCONJ
ejpam-4226	96	7	c2	c2	PROPN
ejpam-4226	96	8	exp	exp	NOUN
ejpam-4226	96	9	(	(	PUNCT
ejpam-4226	96	10	−	−	PROPN
ejpam-4226	96	11	1	1	NUM
ejpam-4226	96	12	α	α	NOUN
ejpam-4226	96	13	tα	tα	PROPN
ejpam-4226	96	14	)	)	PUNCT
ejpam-4226	97	1	+	+	CCONJ
ejpam-4226	97	2	c3	c3	PROPN
ejpam-4226	97	3	exp	exp	NOUN
ejpam-4226	97	4	1	1	NUM
ejpam-4226	97	5	α	α	NOUN
ejpam-4226	97	6	tα	tα	NOUN
ejpam-4226	97	7	using	use	VERB
ejpam-4226	97	8	the	the	DET
ejpam-4226	97	9	conditions	condition	NOUN
ejpam-4226	97	10	in	in	ADP
ejpam-4226	97	11	(	(	PUNCT
ejpam-4226	97	12	∗∗	∗∗	X
ejpam-4226	97	13	)	)	PUNCT
ejpam-4226	97	14	we	we	PRON
ejpam-4226	97	15	get	get	VERB
ejpam-4226	97	16	c1	c1	PROPN
ejpam-4226	97	17	+	+	CCONJ
ejpam-4226	97	18	c2	c2	PROPN
ejpam-4226	97	19	+	+	CCONJ
ejpam-4226	97	20	c3	c3	X
ejpam-4226	97	21	=	=	SYM
ejpam-4226	97	22	1	1	NUM
ejpam-4226	97	23	,	,	PUNCT
ejpam-4226	97	24	−c2	−c2	PROPN
ejpam-4226	97	25	+	+	CCONJ
ejpam-4226	97	26	c3	c3	X
ejpam-4226	97	27	=	=	SYM
ejpam-4226	97	28	1	1	NUM
ejpam-4226	97	29	,	,	PUNCT
ejpam-4226	97	30	c2	c2	PROPN
ejpam-4226	97	31	+	+	CCONJ
ejpam-4226	97	32	c3	c3	X
ejpam-4226	97	33	=	=	PUNCT
ejpam-4226	97	34	1	1	NUM
ejpam-4226	97	35	.	.	PUNCT
ejpam-4226	98	1	thus	thus	ADV
ejpam-4226	98	2	,	,	PUNCT
ejpam-4226	98	3	c1	c1	PROPN
ejpam-4226	98	4	=	=	PROPN
ejpam-4226	98	5	0	0	PROPN
ejpam-4226	98	6	,	,	PUNCT
ejpam-4226	98	7	c2	c2	PROPN
ejpam-4226	98	8	=	=	SYM
ejpam-4226	98	9	0	0	NUM
ejpam-4226	98	10	,	,	PUNCT
ejpam-4226	98	11	and	and	CCONJ
ejpam-4226	98	12	c3	c3	X
ejpam-4226	98	13	=	=	PUNCT
ejpam-4226	98	14	1	1	X
ejpam-4226	98	15	.	.	PUNCT
ejpam-4226	99	1	so	so	ADV
ejpam-4226	99	2	v(t	v(t	ADJ
ejpam-4226	99	3	)	)	PUNCT
ejpam-4226	99	4	=	=	SYM
ejpam-4226	99	5	exp	exp	NOUN
ejpam-4226	99	6	1	1	NUM
ejpam-4226	99	7	α	α	NOUN
ejpam-4226	99	8	tα	tα	PROPN
ejpam-4226	99	9	f.	f.	PROPN
ejpam-4226	99	10	bekraoui	bekraoui	PROPN
ejpam-4226	99	11	,	,	PUNCT
ejpam-4226	99	12	m.	m.	PROPN
ejpam-4226	99	13	al	al	PROPN
ejpam-4226	99	14	horani	horani	PROPN
ejpam-4226	99	15	,	,	PUNCT
ejpam-4226	99	16	r.	r.	PROPN
ejpam-4226	99	17	khalil	khalil	PROPN
ejpam-4226	99	18	/	/	SYM
ejpam-4226	99	19	eur	eur	PROPN
ejpam-4226	99	20	.	.	PUNCT
ejpam-4226	100	1	j.	j.	PROPN
ejpam-4226	100	2	pure	pure	PROPN
ejpam-4226	100	3	appl	appl	PROPN
ejpam-4226	100	4	.	.	PROPN
ejpam-4226	100	5	math	math	PROPN
ejpam-4226	100	6	,	,	PUNCT
ejpam-4226	100	7	15	15	NUM
ejpam-4226	100	8	(	(	PUNCT
ejpam-4226	100	9	1	1	NUM
ejpam-4226	100	10	)	)	PUNCT
ejpam-4226	100	11	(	(	PUNCT
ejpam-4226	100	12	2022	2022	NUM
ejpam-4226	100	13	)	)	PUNCT
ejpam-4226	100	14	,	,	PUNCT
ejpam-4226	100	15	106	106	NUM
ejpam-4226	100	16	-	-	SYM
ejpam-4226	100	17	125	125	NUM
ejpam-4226	100	18	110	110	NUM
ejpam-4226	100	19	situation	situation	NOUN
ejpam-4226	100	20	5	5	NUM
ejpam-4226	100	21	.	.	PUNCT
ejpam-4226	100	22	v(3α	v(3α	NOUN
ejpam-4226	100	23	)	)	PUNCT
ejpam-4226	100	24	=	=	PRON
ejpam-4226	101	1	v	v	ADP
ejpam-4226	101	2	another	another	DET
ejpam-4226	101	3	use	use	NOUN
ejpam-4226	101	4	of	of	ADP
ejpam-4226	101	5	the	the	DET
ejpam-4226	101	6	result	result	NOUN
ejpam-4226	102	1	[	[	X
ejpam-4226	102	2	12	12	NUM
ejpam-4226	102	3	]	]	PUNCT
ejpam-4226	102	4	,	,	PUNCT
ejpam-4226	102	5	the	the	DET
ejpam-4226	102	6	associated	associated	ADJ
ejpam-4226	102	7	characteristic	characteristic	ADJ
ejpam-4226	102	8	equation	equation	NOUN
ejpam-4226	102	9	is	be	AUX
ejpam-4226	102	10	r3	r3	NOUN
ejpam-4226	102	11	−	−	NOUN
ejpam-4226	102	12	1	1	NUM
ejpam-4226	102	13	=	=	SYM
ejpam-4226	102	14	0	0	NUM
ejpam-4226	102	15	,	,	PUNCT
ejpam-4226	102	16	so	so	ADV
ejpam-4226	102	17	(	(	PUNCT
ejpam-4226	102	18	r	r	NOUN
ejpam-4226	102	19	−	−	PROPN
ejpam-4226	102	20	1)(r2	1)(r2	NUM
ejpam-4226	103	1	+	+	NOUN
ejpam-4226	103	2	r	r	NOUN
ejpam-4226	103	3	+	+	NOUN
ejpam-4226	103	4	1	1	NUM
ejpam-4226	103	5	)	)	PUNCT
ejpam-4226	103	6	=	=	SYM
ejpam-4226	103	7	0	0	X
ejpam-4226	103	8	.	.	PUNCT
ejpam-4226	103	9	hence	hence	ADV
ejpam-4226	103	10	r1	r1	PROPN
ejpam-4226	103	11	=	=	SYM
ejpam-4226	104	1	1,r2	1,r2	NUM
ejpam-4226	104	2	=	=	SYM
ejpam-4226	105	1	−1	−1	NOUN
ejpam-4226	106	1	+	+	CCONJ
ejpam-4226	106	2	i	i	PRON
ejpam-4226	106	3	√	√	VERB
ejpam-4226	106	4	3	3	NUM
ejpam-4226	106	5	2	2	NUM
ejpam-4226	106	6	and	and	CCONJ
ejpam-4226	106	7	r3	r3	PROPN
ejpam-4226	106	8	=	=	SYM
ejpam-4226	107	1	−1−	−1−	PROPN
ejpam-4226	108	1	i	i	PRON
ejpam-4226	108	2	√	√	VERB
ejpam-4226	108	3	3	3	NUM
ejpam-4226	108	4	2	2	NUM
ejpam-4226	108	5	.	.	PUNCT
ejpam-4226	109	1	so	so	ADV
ejpam-4226	109	2	v(t	v(t	ADJ
ejpam-4226	109	3	)	)	PUNCT
ejpam-4226	109	4	=	=	SYM
ejpam-4226	109	5	exp	exp	NOUN
ejpam-4226	109	6	(	(	PUNCT
ejpam-4226	109	7	−	−	PROPN
ejpam-4226	109	8	1	1	NUM
ejpam-4226	109	9	2α	2α	NOUN
ejpam-4226	109	10	tα	tα	PROPN
ejpam-4226	109	11	)	)	PUNCT
ejpam-4226	109	12	(	(	PUNCT
ejpam-4226	109	13	c1	c1	PROPN
ejpam-4226	109	14	cos	cos	PROPN
ejpam-4226	109	15	√	√	PROPN
ejpam-4226	109	16	3tα	3tα	ADJ
ejpam-4226	109	17	2α	2α	NOUN
ejpam-4226	109	18	+	+	CCONJ
ejpam-4226	109	19	c2	c2	PROPN
ejpam-4226	109	20	sin	sin	VERB
ejpam-4226	109	21	√	√	NUM
ejpam-4226	109	22	3tα	3tα	ADJ
ejpam-4226	109	23	2α	2α	NOUN
ejpam-4226	109	24	)	)	PUNCT
ejpam-4226	110	1	+	+	CCONJ
ejpam-4226	110	2	c3	c3	PROPN
ejpam-4226	110	3	exp	exp	NOUN
ejpam-4226	110	4	1	1	NUM
ejpam-4226	110	5	α	α	PROPN
ejpam-4226	110	6	tα	tα	PROPN
ejpam-4226	110	7	.	.	PUNCT
ejpam-4226	111	1	using	use	VERB
ejpam-4226	111	2	(	(	PUNCT
ejpam-4226	111	3	∗∗	∗∗	NOUN
ejpam-4226	111	4	)	)	PUNCT
ejpam-4226	111	5	to	to	PART
ejpam-4226	111	6	get	get	VERB
ejpam-4226	111	7			PROPN
ejpam-4226	111	8	c1	c1	PROPN
ejpam-4226	111	9	+	+	CCONJ
ejpam-4226	111	10	c3	c3	X
ejpam-4226	111	11	=	=	SYM
ejpam-4226	111	12	1	1	NUM
ejpam-4226	111	13	−1	−1	NOUN
ejpam-4226	111	14	2	2	NUM
ejpam-4226	111	15	c1	c1	NOUN
ejpam-4226	111	16	+	+	CCONJ
ejpam-4226	111	17	c2	c2	PROPN
ejpam-4226	111	18	+	+	CCONJ
ejpam-4226	111	19	c3	c3	X
ejpam-4226	111	20	=	=	PUNCT
ejpam-4226	111	21	1	1	NUM
ejpam-4226	111	22	−3	−3	NOUN
ejpam-4226	111	23	4c1	4c1	NUM
ejpam-4226	111	24	−	−	PROPN
ejpam-4226	112	1	c2	c2	PROPN
ejpam-4226	112	2	+	+	CCONJ
ejpam-4226	112	3	c3	c3	X
ejpam-4226	112	4	=	=	SYM
ejpam-4226	112	5	1	1	NUM
ejpam-4226	112	6	,	,	PUNCT
ejpam-4226	112	7	from	from	ADP
ejpam-4226	112	8	which	which	PRON
ejpam-4226	112	9	we	we	PRON
ejpam-4226	112	10	get	get	VERB
ejpam-4226	112	11	c1	c1	PROPN
ejpam-4226	112	12	=	=	PUNCT
ejpam-4226	112	13	0	0	PROPN
ejpam-4226	112	14	,	,	PUNCT
ejpam-4226	112	15	c2	c2	PROPN
ejpam-4226	112	16	=	=	SYM
ejpam-4226	112	17	0	0	NUM
ejpam-4226	112	18	,	,	PUNCT
ejpam-4226	112	19	and	and	CCONJ
ejpam-4226	112	20	c3	c3	X
ejpam-4226	112	21	=	=	PUNCT
ejpam-4226	112	22	1	1	X
ejpam-4226	112	23	.	.	PUNCT
ejpam-4226	112	24	thus	thus	ADV
ejpam-4226	112	25	v(t	v(t	VERB
ejpam-4226	112	26	)	)	PUNCT
ejpam-4226	112	27	=	=	SYM
ejpam-4226	112	28	exp	exp	NOUN
ejpam-4226	112	29	1	1	NUM
ejpam-4226	112	30	α	α	NOUN
ejpam-4226	112	31	tα	tα	PROPN
ejpam-4226	112	32	.	.	PUNCT
ejpam-4226	113	1	if	if	SCONJ
ejpam-4226	113	2	we	we	PRON
ejpam-4226	113	3	do	do	VERB
ejpam-4226	113	4	the	the	DET
ejpam-4226	113	5	other	other	ADJ
ejpam-4226	113	6	situations	situation	NOUN
ejpam-4226	113	7	we	we	PRON
ejpam-4226	113	8	get	get	VERB
ejpam-4226	113	9	the	the	DET
ejpam-4226	113	10	same	same	ADJ
ejpam-4226	113	11	solution	solution	NOUN
ejpam-4226	113	12	:	:	PUNCT
ejpam-4226	113	13	v(t	v(t	NUM
ejpam-4226	113	14	)	)	PUNCT
ejpam-4226	113	15	=	=	SYM
ejpam-4226	113	16	exp	exp	NOUN
ejpam-4226	113	17	1	1	NUM
ejpam-4226	113	18	α	α	NOUN
ejpam-4226	113	19	t	t	NOUN
ejpam-4226	113	20	α	α	NOUN
ejpam-4226	113	21	.	.	PUNCT
ejpam-4226	114	1	thus	thus	ADV
ejpam-4226	114	2	if	if	SCONJ
ejpam-4226	114	3	there	there	PRON
ejpam-4226	114	4	is	be	VERB
ejpam-4226	114	5	an	an	DET
ejpam-4226	114	6	atomic	atomic	ADJ
ejpam-4226	114	7	solution	solution	NOUN
ejpam-4226	114	8	for	for	ADP
ejpam-4226	114	9	this	this	DET
ejpam-4226	114	10	case	case	NOUN
ejpam-4226	114	11	,	,	PUNCT
ejpam-4226	114	12	then	then	ADV
ejpam-4226	114	13	v	v	NOUN
ejpam-4226	114	14	must	must	AUX
ejpam-4226	114	15	equal	equal	VERB
ejpam-4226	114	16	to	to	ADP
ejpam-4226	114	17	exp	exp	NOUN
ejpam-4226	114	18	1	1	NUM
ejpam-4226	114	19	α	α	NOUN
ejpam-4226	114	20	t	t	NOUN
ejpam-4226	114	21	α	α	NOUN
ejpam-4226	114	22	.	.	PUNCT
ejpam-4226	115	1	but	but	CCONJ
ejpam-4226	115	2	from	from	ADP
ejpam-4226	115	3	lemma	lemma	PROPN
ejpam-4226	115	4	1	1	NUM
ejpam-4226	115	5	,	,	PUNCT
ejpam-4226	115	6	we	we	PRON
ejpam-4226	115	7	must	must	AUX
ejpam-4226	115	8	have	have	VERB
ejpam-4226	115	9	f(t	f(t	NOUN
ejpam-4226	115	10	)	)	PUNCT
ejpam-4226	116	1	=	=	SYM
ejpam-4226	116	2	exp	exp	NOUN
ejpam-4226	116	3	1	1	NUM
ejpam-4226	116	4	α	α	NOUN
ejpam-4226	116	5	t	t	NOUN
ejpam-4226	116	6	α	α	NOUN
ejpam-4226	116	7	in	in	ADP
ejpam-4226	116	8	order	order	NOUN
ejpam-4226	116	9	to	to	PART
ejpam-4226	116	10	get	get	VERB
ejpam-4226	116	11	an	an	DET
ejpam-4226	116	12	atomic	atomic	ADJ
ejpam-4226	116	13	solution	solution	NOUN
ejpam-4226	116	14	.	.	PUNCT
ejpam-4226	117	1	now	now	ADV
ejpam-4226	117	2	,	,	PUNCT
ejpam-4226	117	3	substitute	substitute	NOUN
ejpam-4226	117	4	v(t	v(t	NOUN
ejpam-4226	117	5	)	)	PUNCT
ejpam-4226	117	6	=	=	SYM
ejpam-4226	117	7	exp	exp	NOUN
ejpam-4226	117	8	1	1	NUM
ejpam-4226	117	9	α	α	NOUN
ejpam-4226	117	10	t	t	NOUN
ejpam-4226	117	11	α	α	X
ejpam-4226	117	12	in	in	ADP
ejpam-4226	117	13	(	(	PUNCT
ejpam-4226	117	14	∗	∗	NOUN
ejpam-4226	117	15	)	)	PUNCT
ejpam-4226	117	16	,	,	PUNCT
ejpam-4226	117	17	we	we	PRON
ejpam-4226	117	18	get	get	VERB
ejpam-4226	117	19	exp	exp	NOUN
ejpam-4226	117	20	1	1	NUM
ejpam-4226	117	21	α	α	NOUN
ejpam-4226	117	22	tα	tα	NOUN
ejpam-4226	118	1	[	[	X
ejpam-4226	118	2	x+ax+bx+	x+ax+bx+	PROPN
ejpam-4226	118	3	cx	cx	X
ejpam-4226	118	4	]	]	X
ejpam-4226	118	5	=	=	SYM
ejpam-4226	118	6	f(t)⊗	f(t)⊗	PROPN
ejpam-4226	118	7	z	z	NOUN
ejpam-4226	118	8	.	.	PUNCT
ejpam-4226	119	1	(	(	PUNCT
ejpam-4226	119	2	∗	∗	NOUN
ejpam-4226	119	3	∗	∗	NOUN
ejpam-4226	119	4	∗	∗	NOUN
ejpam-4226	119	5	)	)	PUNCT
ejpam-4226	119	6	it	it	PRON
ejpam-4226	119	7	remains	remain	VERB
ejpam-4226	119	8	to	to	PART
ejpam-4226	119	9	find	find	VERB
ejpam-4226	119	10	x.	x.	NOUN
ejpam-4226	119	11	from	from	ADP
ejpam-4226	119	12	equation	equation	NOUN
ejpam-4226	119	13	(	(	PUNCT
ejpam-4226	119	14	∗	∗	NOUN
ejpam-4226	119	15	∗	∗	NOUN
ejpam-4226	119	16	∗	∗	NOUN
ejpam-4226	119	17	)	)	PUNCT
ejpam-4226	119	18	,	,	PUNCT
ejpam-4226	119	19	we	we	PRON
ejpam-4226	119	20	have	have	VERB
ejpam-4226	119	21	two	two	NUM
ejpam-4226	119	22	atoms	atom	NOUN
ejpam-4226	119	23	are	be	AUX
ejpam-4226	119	24	equal	equal	ADJ
ejpam-4226	119	25	.	.	PUNCT
ejpam-4226	120	1	thus	thus	ADV
ejpam-4226	120	2	the	the	DET
ejpam-4226	120	3	first	first	ADJ
ejpam-4226	120	4	coordinates	coordinate	NOUN
ejpam-4226	120	5	are	be	AUX
ejpam-4226	120	6	equal	equal	ADJ
ejpam-4226	120	7	and	and	CCONJ
ejpam-4226	120	8	the	the	DET
ejpam-4226	120	9	second	second	ADJ
ejpam-4226	120	10	coordinates	coordinate	NOUN
ejpam-4226	120	11	are	be	AUX
ejpam-4226	120	12	equal	equal	ADJ
ejpam-4226	120	13	by	by	ADP
ejpam-4226	120	14	lemma	lemma	PROPN
ejpam-4226	120	15	1	1	NUM
ejpam-4226	120	16	.	.	PUNCT
ejpam-4226	121	1	thus	thus	ADV
ejpam-4226	121	2	we	we	PRON
ejpam-4226	121	3	get	get	VERB
ejpam-4226	121	4	x+ax+bx+	x+ax+bx+	PROPN
ejpam-4226	121	5	cx	cx	PROPN
ejpam-4226	122	1	=	=	PUNCT
ejpam-4226	122	2	z	z	PROPN
ejpam-4226	122	3	.	.	PUNCT
ejpam-4226	123	1	this	this	PRON
ejpam-4226	123	2	is	be	AUX
ejpam-4226	123	3	(	(	PUNCT
ejpam-4226	123	4	i	i	PRON
ejpam-4226	123	5	+	+	VERB
ejpam-4226	123	6	a+b	a+b	NUM
ejpam-4226	123	7	+	+	X
ejpam-4226	123	8	c)x	c)x	X
ejpam-4226	124	1	=	=	SYM
ejpam-4226	124	2	z	z	NOUN
ejpam-4226	124	3	.	.	PUNCT
ejpam-4226	125	1	(	(	PUNCT
ejpam-4226	125	2	5	5	NUM
ejpam-4226	125	3	)	)	PUNCT
ejpam-4226	125	4	hence	hence	ADV
ejpam-4226	125	5	,	,	PUNCT
ejpam-4226	125	6	for	for	ADP
ejpam-4226	125	7	the	the	DET
ejpam-4226	125	8	atomic	atomic	ADJ
ejpam-4226	125	9	solution	solution	NOUN
ejpam-4226	125	10	to	to	PART
ejpam-4226	125	11	exist	exist	VERB
ejpam-4226	125	12	we	we	PRON
ejpam-4226	125	13	must	must	AUX
ejpam-4226	125	14	have	have	VERB
ejpam-4226	125	15	x	x	PART
ejpam-4226	125	16	to	to	PART
ejpam-4226	125	17	satisfy	satisfy	VERB
ejpam-4226	125	18	(	(	PUNCT
ejpam-4226	125	19	5	5	NUM
ejpam-4226	125	20	)	)	PUNCT
ejpam-4226	125	21	,	,	PUNCT
ejpam-4226	125	22	noting	note	VERB
ejpam-4226	125	23	that	that	SCONJ
ejpam-4226	125	24	z	z	PROPN
ejpam-4226	125	25	is	be	AUX
ejpam-4226	125	26	given	give	VERB
ejpam-4226	125	27	.	.	PUNCT
ejpam-4226	126	1	so	so	ADV
ejpam-4226	126	2	the	the	DET
ejpam-4226	126	3	image	image	NOUN
ejpam-4226	126	4	of	of	ADP
ejpam-4226	126	5	x	x	PUNCT
ejpam-4226	126	6	under	under	ADP
ejpam-4226	126	7	i	i	PRON
ejpam-4226	126	8	+	+	PROPN
ejpam-4226	126	9	a+b	a+b	NUM
ejpam-4226	126	10	+	+	CCONJ
ejpam-4226	126	11	c	c	NOUN
ejpam-4226	126	12	must	must	AUX
ejpam-4226	126	13	be	be	AUX
ejpam-4226	126	14	z.	z.	NOUN
ejpam-4226	126	15	let	let	VERB
ejpam-4226	126	16	x	x	SYM
ejpam-4226	126	17	=	=	PUNCT
ejpam-4226	126	18	ax	ax	NOUN
ejpam-4226	126	19	=	=	PUNCT
ejpam-4226	126	20	bx	bx	NOUN
ejpam-4226	126	21	=	=	PUNCT
ejpam-4226	126	22	cx	cx	PROPN
ejpam-4226	127	1	=	=	PUNCT
ejpam-4226	127	2	z	z	PROPN
ejpam-4226	127	3	.	.	PUNCT
ejpam-4226	128	1	(	(	PUNCT
ejpam-4226	128	2	6	6	NUM
ejpam-4226	128	3	)	)	PUNCT
ejpam-4226	128	4	so	so	ADV
ejpam-4226	128	5	,	,	PUNCT
ejpam-4226	128	6	x	x	PUNCT
ejpam-4226	128	7	=	=	PUNCT
ejpam-4226	128	8	z	z	NOUN
ejpam-4226	129	1	and	and	CCONJ
ejpam-4226	129	2	it	it	PRON
ejpam-4226	129	3	is	be	AUX
ejpam-4226	129	4	an	an	DET
ejpam-4226	129	5	eigenvector	eigenvector	NOUN
ejpam-4226	129	6	(	(	PUNCT
ejpam-4226	129	7	a	a	DET
ejpam-4226	129	8	fixed	fixed	ADJ
ejpam-4226	129	9	point	point	NOUN
ejpam-4226	129	10	)	)	PUNCT
ejpam-4226	129	11	for	for	ADP
ejpam-4226	129	12	a	a	DET
ejpam-4226	129	13	,	,	PUNCT
ejpam-4226	129	14	b	b	NOUN
ejpam-4226	129	15	,	,	PUNCT
ejpam-4226	129	16	and	and	CCONJ
ejpam-4226	129	17	c.	c.	PROPN
ejpam-4226	129	18	now	now	ADV
ejpam-4226	129	19	substitute	substitute	VERB
ejpam-4226	129	20	in	in	ADP
ejpam-4226	129	21	equation	equation	NOUN
ejpam-4226	129	22	(	(	PUNCT
ejpam-4226	129	23	∗	∗	NOUN
ejpam-4226	129	24	)	)	PUNCT
ejpam-4226	129	25	to	to	PART
ejpam-4226	129	26	get	get	VERB
ejpam-4226	129	27	[	[	PUNCT
ejpam-4226	129	28	v(3α)(t	v(3α)(t	NOUN
ejpam-4226	129	29	)	)	PUNCT
ejpam-4226	130	1	+	+	CCONJ
ejpam-4226	130	2	v(2α)(t	v(2α)(t	X
ejpam-4226	130	3	)	)	PUNCT
ejpam-4226	130	4	+	+	PUNCT
ejpam-4226	130	5	v(α)(t	v(α)(t	NUM
ejpam-4226	130	6	)	)	PUNCT
ejpam-4226	131	1	+	+	CCONJ
ejpam-4226	131	2	v(t	v(t	NOUN
ejpam-4226	131	3	)	)	PUNCT
ejpam-4226	131	4	]	]	PUNCT
ejpam-4226	132	1	⊗	⊗	PROPN
ejpam-4226	132	2	x	x	X
ejpam-4226	132	3	=	=	SYM
ejpam-4226	132	4	f(t)⊗	f(t)⊗	PROPN
ejpam-4226	132	5	z	z	NOUN
ejpam-4226	132	6	.	.	PUNCT
ejpam-4226	133	1	(	(	PUNCT
ejpam-4226	133	2	7	7	X
ejpam-4226	133	3	)	)	PUNCT
ejpam-4226	133	4	f.	f.	PROPN
ejpam-4226	133	5	bekraoui	bekraoui	PROPN
ejpam-4226	133	6	,	,	PUNCT
ejpam-4226	133	7	m.	m.	PROPN
ejpam-4226	133	8	al	al	PROPN
ejpam-4226	133	9	horani	horani	PROPN
ejpam-4226	133	10	,	,	PUNCT
ejpam-4226	133	11	r.	r.	PROPN
ejpam-4226	133	12	khalil	khalil	PROPN
ejpam-4226	133	13	/	/	SYM
ejpam-4226	133	14	eur	eur	PROPN
ejpam-4226	133	15	.	.	PUNCT
ejpam-4226	134	1	j.	j.	PROPN
ejpam-4226	134	2	pure	pure	PROPN
ejpam-4226	134	3	appl	appl	PROPN
ejpam-4226	134	4	.	.	PROPN
ejpam-4226	134	5	math	math	PROPN
ejpam-4226	134	6	,	,	PUNCT
ejpam-4226	134	7	15	15	NUM
ejpam-4226	134	8	(	(	PUNCT
ejpam-4226	134	9	1	1	NUM
ejpam-4226	134	10	)	)	PUNCT
ejpam-4226	134	11	(	(	PUNCT
ejpam-4226	134	12	2022	2022	NUM
ejpam-4226	134	13	)	)	PUNCT
ejpam-4226	134	14	,	,	PUNCT
ejpam-4226	134	15	106	106	NUM
ejpam-4226	134	16	-	-	SYM
ejpam-4226	134	17	125	125	NUM
ejpam-4226	134	18	111	111	NUM
ejpam-4226	134	19	from	from	ADP
ejpam-4226	134	20	equation	equation	NOUN
ejpam-4226	134	21	(	(	PUNCT
ejpam-4226	134	22	7	7	NUM
ejpam-4226	134	23	)	)	PUNCT
ejpam-4226	134	24	,	,	PUNCT
ejpam-4226	134	25	since	since	SCONJ
ejpam-4226	134	26	x	x	PROPN
ejpam-4226	134	27	=	=	SYM
ejpam-4226	134	28	z	z	X
ejpam-4226	134	29	,	,	PUNCT
ejpam-4226	134	30	we	we	PRON
ejpam-4226	134	31	get	get	VERB
ejpam-4226	134	32	v(3α	v(3α	NOUN
ejpam-4226	134	33	)	)	PUNCT
ejpam-4226	134	34	+	+	NUM
ejpam-4226	134	35	v(2α	v(2α	NOUN
ejpam-4226	134	36	)	)	PUNCT
ejpam-4226	134	37	+	+	CCONJ
ejpam-4226	134	38	v(α	v(α	NOUN
ejpam-4226	134	39	)	)	PUNCT
ejpam-4226	135	1	+	+	X
ejpam-4226	135	2	v	v	NOUN
ejpam-4226	135	3	=	=	SYM
ejpam-4226	135	4	f	f	PROPN
ejpam-4226	135	5	.	.	PUNCT
ejpam-4226	136	1	(	(	PUNCT
ejpam-4226	136	2	8)	8)	NUM
ejpam-4226	136	3	this	this	PRON
ejpam-4226	136	4	is	be	AUX
ejpam-4226	136	5	a	a	DET
ejpam-4226	136	6	linear	linear	ADJ
ejpam-4226	136	7	fractional	fractional	ADJ
ejpam-4226	136	8	non	non	ADJ
ejpam-4226	136	9	-	-	ADJ
ejpam-4226	136	10	homogenous	homogenous	ADJ
ejpam-4226	136	11	differential	differential	NOUN
ejpam-4226	136	12	equation	equation	NOUN
ejpam-4226	136	13	.	.	PUNCT
ejpam-4226	137	1	thus	thus	ADV
ejpam-4226	137	2	using	use	VERB
ejpam-4226	137	3	result	result	NOUN
ejpam-4226	137	4	in	in	ADP
ejpam-4226	137	5	[	[	X
ejpam-4226	137	6	12	12	NUM
ejpam-4226	137	7	]	]	PUNCT
ejpam-4226	137	8	,	,	PUNCT
ejpam-4226	137	9	we	we	PRON
ejpam-4226	137	10	find	find	VERB
ejpam-4226	137	11	the	the	DET
ejpam-4226	137	12	homogenous	homogenous	ADJ
ejpam-4226	137	13	solution	solution	NOUN
ejpam-4226	137	14	vh	vh	PROPN
ejpam-4226	137	15	and	and	CCONJ
ejpam-4226	137	16	a	a	DET
ejpam-4226	137	17	particular	particular	ADJ
ejpam-4226	137	18	solution	solution	NOUN
ejpam-4226	137	19	vp	vp	NOUN
ejpam-4226	137	20	,	,	PUNCT
ejpam-4226	137	21	and	and	CCONJ
ejpam-4226	137	22	so	so	ADV
ejpam-4226	137	23	,	,	PUNCT
ejpam-4226	137	24	the	the	DET
ejpam-4226	137	25	general	general	ADJ
ejpam-4226	137	26	solution	solution	NOUN
ejpam-4226	137	27	will	will	AUX
ejpam-4226	137	28	be	be	AUX
ejpam-4226	137	29	vg	vg	NOUN
ejpam-4226	137	30	=	=	SYM
ejpam-4226	137	31	vh	vh	PROPN
ejpam-4226	137	32	+	+	CCONJ
ejpam-4226	137	33	vp	vp	PROPN
ejpam-4226	137	34	.	.	PUNCT
ejpam-4226	138	1	now	now	ADV
ejpam-4226	138	2	for	for	ADP
ejpam-4226	138	3	vh	vh	PROPN
ejpam-4226	138	4	,	,	PUNCT
ejpam-4226	138	5	the	the	DET
ejpam-4226	138	6	associated	associated	ADJ
ejpam-4226	138	7	characteristic	characteristic	ADJ
ejpam-4226	138	8	equation	equation	NOUN
ejpam-4226	138	9	is	be	AUX
ejpam-4226	138	10	(	(	PUNCT
ejpam-4226	138	11	r	r	NOUN
ejpam-4226	138	12	+	+	NOUN
ejpam-4226	138	13	1	1	NUM
ejpam-4226	138	14	)	)	PUNCT
ejpam-4226	138	15	(	(	PUNCT
ejpam-4226	138	16	r2	r2	NOUN
ejpam-4226	138	17	+	+	CCONJ
ejpam-4226	138	18	1	1	NUM
ejpam-4226	138	19	)	)	PUNCT
ejpam-4226	138	20	=	=	SYM
ejpam-4226	138	21	0	0	NUM
ejpam-4226	138	22	,	,	PUNCT
ejpam-4226	138	23	which	which	PRON
ejpam-4226	138	24	has	have	VERB
ejpam-4226	138	25	the	the	DET
ejpam-4226	138	26	roots	root	NOUN
ejpam-4226	138	27	−1,±i	−1,±i	VERB
ejpam-4226	138	28	.	.	PUNCT
ejpam-4226	139	1	then	then	ADV
ejpam-4226	139	2	vh(t	vh(t	PUNCT
ejpam-4226	139	3	)	)	PUNCT
ejpam-4226	140	1	=	=	SYM
ejpam-4226	140	2	c1	c1	PROPN
ejpam-4226	140	3	exp	exp	NOUN
ejpam-4226	140	4	(	(	PUNCT
ejpam-4226	140	5	−	−	PROPN
ejpam-4226	140	6	1	1	NUM
ejpam-4226	140	7	α	α	NOUN
ejpam-4226	140	8	tα	tα	PROPN
ejpam-4226	140	9	)	)	PUNCT
ejpam-4226	141	1	+	+	CCONJ
ejpam-4226	141	2	c2	c2	PROPN
ejpam-4226	141	3	cos	cos	PROPN
ejpam-4226	141	4	1	1	NUM
ejpam-4226	141	5	α	α	NOUN
ejpam-4226	141	6	tα	tα	PROPN
ejpam-4226	141	7	+	+	CCONJ
ejpam-4226	141	8	c3	c3	PROPN
ejpam-4226	141	9	sin	sin	NOUN
ejpam-4226	141	10	1	1	NUM
ejpam-4226	141	11	α	α	NOUN
ejpam-4226	141	12	tα	tα	PROPN
ejpam-4226	141	13	.	.	PUNCT
ejpam-4226	142	1	for	for	ADP
ejpam-4226	142	2	the	the	DET
ejpam-4226	142	3	particular	particular	ADJ
ejpam-4226	142	4	solution	solution	NOUN
ejpam-4226	142	5	,	,	PUNCT
ejpam-4226	142	6	we	we	PRON
ejpam-4226	142	7	use	use	VERB
ejpam-4226	142	8	variation	variation	NOUN
ejpam-4226	142	9	of	of	ADP
ejpam-4226	142	10	parameters	parameter	NOUN
ejpam-4226	142	11	introduced	introduce	VERB
ejpam-4226	142	12	in	in	ADP
ejpam-4226	142	13	[	[	X
ejpam-4226	142	14	12	12	NUM
ejpam-4226	142	15	]	]	PUNCT
ejpam-4226	142	16	.	.	PUNCT
ejpam-4226	143	1	let	let	AUX
ejpam-4226	143	2	v1	v1	NOUN
ejpam-4226	143	3	=	=	SYM
ejpam-4226	143	4	exp	exp	NOUN
ejpam-4226	143	5	(	(	PUNCT
ejpam-4226	143	6	−	−	PROPN
ejpam-4226	143	7	1	1	NUM
ejpam-4226	143	8	α	α	NOUN
ejpam-4226	143	9	t	t	NOUN
ejpam-4226	143	10	α	α	NOUN
ejpam-4226	143	11	)	)	PUNCT
ejpam-4226	143	12	,	,	PUNCT
ejpam-4226	143	13	v2	v2	PROPN
ejpam-4226	143	14	=	=	SYM
ejpam-4226	143	15	cos	cos	PROPN
ejpam-4226	143	16	1	1	NUM
ejpam-4226	143	17	α	α	NOUN
ejpam-4226	143	18	t	t	NOUN
ejpam-4226	143	19	α	α	NOUN
ejpam-4226	143	20	and	and	CCONJ
ejpam-4226	143	21	v3	v3	PROPN
ejpam-4226	143	22	=	=	PUNCT
ejpam-4226	143	23	sin	sin	NOUN
ejpam-4226	143	24	1	1	NUM
ejpam-4226	143	25	α	α	NOUN
ejpam-4226	143	26	t	t	NOUN
ejpam-4226	143	27	α	α	NOUN
ejpam-4226	143	28	.	.	PUNCT
ejpam-4226	144	1	so	so	ADV
ejpam-4226	144	2	vp(t	vp(t	PUNCT
ejpam-4226	144	3	)	)	PUNCT
ejpam-4226	144	4	=	=	SYM
ejpam-4226	144	5	3∑	3∑	NUM
ejpam-4226	144	6	m=1	m=1	X
ejpam-4226	144	7	vm(t	vm(t	NOUN
ejpam-4226	144	8	)	)	PUNCT
ejpam-4226	145	1	∫	∫	PROPN
ejpam-4226	145	2	t	t	PROPN
ejpam-4226	145	3	a	a	DET
ejpam-4226	145	4	f(s)wα	f(s)wα	PROPN
ejpam-4226	145	5	m(s	m(s	PROPN
ejpam-4226	145	6	)	)	PUNCT
ejpam-4226	145	7	wα(s)s1−α	wα(s)s1−α	PROPN
ejpam-4226	145	8	ds	ds	NOUN
ejpam-4226	145	9	=	=	PUNCT
ejpam-4226	145	10	exp	exp	NOUN
ejpam-4226	145	11	(	(	PUNCT
ejpam-4226	145	12	−	−	PROPN
ejpam-4226	145	13	1	1	NUM
ejpam-4226	145	14	α	α	NOUN
ejpam-4226	145	15	tα	tα	PROPN
ejpam-4226	145	16	)	)	PUNCT
ejpam-4226	146	1	∫	∫	PROPN
ejpam-4226	146	2	t	t	PROPN
ejpam-4226	146	3	a	a	DET
ejpam-4226	146	4	f(s)wα	f(s)wα	PROPN
ejpam-4226	146	5	1	1	NUM
ejpam-4226	146	6	(	(	PUNCT
ejpam-4226	146	7	s	s	NOUN
ejpam-4226	146	8	)	)	PUNCT
ejpam-4226	146	9	wα(s)s1−α	wα(s)s1−α	PROPN
ejpam-4226	146	10	ds+	ds+	NOUN
ejpam-4226	146	11	cos	cos	PROPN
ejpam-4226	146	12	1	1	NUM
ejpam-4226	146	13	α	α	NOUN
ejpam-4226	146	14	tα	tα	PROPN
ejpam-4226	146	15	∫	∫	PROPN
ejpam-4226	146	16	t	t	PROPN
ejpam-4226	146	17	a	a	DET
ejpam-4226	146	18	f(s)wα	f(s)wα	PROPN
ejpam-4226	146	19	2	2	NUM
ejpam-4226	146	20	(	(	PUNCT
ejpam-4226	146	21	s	s	NOUN
ejpam-4226	146	22	)	)	PUNCT
ejpam-4226	146	23	wα(s)s1−α	wα(s)s1−α	PROPN
ejpam-4226	147	1	ds	ds	PRON
ejpam-4226	147	2	+	+	NOUN
ejpam-4226	147	3	sin	sin	NOUN
ejpam-4226	147	4	1	1	NUM
ejpam-4226	147	5	α	α	NOUN
ejpam-4226	147	6	tα	tα	PROPN
ejpam-4226	147	7	∫	∫	PROPN
ejpam-4226	147	8	t	t	PROPN
ejpam-4226	147	9	a	a	DET
ejpam-4226	147	10	f(s)wα	f(s)wα	PROPN
ejpam-4226	147	11	3	3	NUM
ejpam-4226	147	12	(	(	PUNCT
ejpam-4226	147	13	s	s	NOUN
ejpam-4226	147	14	)	)	PUNCT
ejpam-4226	147	15	wα(s)s1−α	wα(s)s1−α	PUNCT
ejpam-4226	147	16	ds	ds	INTJ
ejpam-4226	147	17	where	where	SCONJ
ejpam-4226	147	18	wα	wα	NOUN
ejpam-4226	147	19	=	=	SYM
ejpam-4226	147	20	∣∣∣∣∣∣∣	∣∣∣∣∣∣∣	PROPN
ejpam-4226	147	21	v1	v1	PROPN
ejpam-4226	147	22	v2	v2	PROPN
ejpam-4226	147	23	v3	v3	PROPN
ejpam-4226	147	24	v	v	PROPN
ejpam-4226	147	25	(	(	PUNCT
ejpam-4226	147	26	α	α	NOUN
ejpam-4226	147	27	)	)	PUNCT
ejpam-4226	147	28	1	1	NUM
ejpam-4226	147	29	v	v	NOUN
ejpam-4226	147	30	(	(	PUNCT
ejpam-4226	147	31	α	α	NOUN
ejpam-4226	147	32	)	)	PUNCT
ejpam-4226	147	33	2	2	NUM
ejpam-4226	147	34	v	v	NOUN
ejpam-4226	147	35	(	(	PUNCT
ejpam-4226	147	36	α	α	NOUN
ejpam-4226	147	37	)	)	PUNCT
ejpam-4226	147	38	3	3	NUM
ejpam-4226	147	39	v	v	NOUN
ejpam-4226	147	40	(	(	PUNCT
ejpam-4226	147	41	2α	2α	NOUN
ejpam-4226	147	42	)	)	PUNCT
ejpam-4226	147	43	1	1	NUM
ejpam-4226	147	44	v	v	NOUN
ejpam-4226	147	45	(	(	PUNCT
ejpam-4226	147	46	2α	2α	NOUN
ejpam-4226	147	47	)	)	PUNCT
ejpam-4226	147	48	2	2	NUM
ejpam-4226	147	49	v	v	NOUN
ejpam-4226	147	50	(	(	PUNCT
ejpam-4226	147	51	2α	2α	NOUN
ejpam-4226	147	52	)	)	PUNCT
ejpam-4226	147	53	3	3	NUM
ejpam-4226	147	54	∣∣∣∣∣∣∣	∣∣∣∣∣∣∣	PROPN
ejpam-4226	147	55	and	and	CCONJ
ejpam-4226	147	56	wα	wα	NOUN
ejpam-4226	147	57	m	m	NOUN
ejpam-4226	147	58	is	be	AUX
ejpam-4226	147	59	the	the	DET
ejpam-4226	147	60	determinant	determinant	ADJ
ejpam-4226	147	61	obtained	obtain	VERB
ejpam-4226	147	62	from	from	ADP
ejpam-4226	147	63	wα	wα	NOUN
ejpam-4226	147	64	by	by	ADP
ejpam-4226	147	65	replacing	replace	VERB
ejpam-4226	147	66	mth	mth	NOUN
ejpam-4226	147	67	column	column	NOUN
ejpam-4226	147	68	by	by	ADP
ejpam-4226	147	69	the	the	DET
ejpam-4226	147	70	column	column	NOUN
ejpam-4226	147	71	(	(	PUNCT
ejpam-4226	147	72	0	0	NUM
ejpam-4226	147	73	,	,	PUNCT
ejpam-4226	147	74	0	0	NUM
ejpam-4226	147	75	,	,	PUNCT
ejpam-4226	147	76	1)t	1)t	NUM
ejpam-4226	147	77	,	,	PUNCT
ejpam-4226	147	78	m	m	VERB
ejpam-4226	147	79	=	=	NOUN
ejpam-4226	147	80	1	1	NUM
ejpam-4226	147	81	,	,	PUNCT
ejpam-4226	147	82	2	2	NUM
ejpam-4226	147	83	,	,	PUNCT
ejpam-4226	147	84	3	3	NUM
ejpam-4226	147	85	.	.	PUNCT
ejpam-4226	148	1	thus	thus	ADV
ejpam-4226	148	2	vp(t	vp(t	PUNCT
ejpam-4226	148	3	)	)	PUNCT
ejpam-4226	148	4	=	=	SYM
ejpam-4226	148	5	exp	exp	NOUN
ejpam-4226	148	6	(	(	PUNCT
ejpam-4226	148	7	−	−	PROPN
ejpam-4226	148	8	1	1	NUM
ejpam-4226	148	9	α	α	NOUN
ejpam-4226	148	10	tα	tα	PROPN
ejpam-4226	148	11	)	)	PUNCT
ejpam-4226	148	12	∫	∫	PROPN
ejpam-4226	148	13	t	t	PROPN
ejpam-4226	148	14	a	a	DET
ejpam-4226	148	15	f(s	f(	NOUN
ejpam-4226	148	16	)	)	PUNCT
ejpam-4226	148	17	2	2	NUM
ejpam-4226	148	18	exp	exp	NOUN
ejpam-4226	148	19	(	(	PUNCT
ejpam-4226	148	20	−	−	PROPN
ejpam-4226	148	21	1	1	NUM
ejpam-4226	148	22	αs	αs	PROPN
ejpam-4226	148	23	α	α	NOUN
ejpam-4226	148	24	)	)	PUNCT
ejpam-4226	149	1	s1−α	s1−α	PROPN
ejpam-4226	149	2	ds−	ds−	PROPN
ejpam-4226	149	3	cos	cos	ADP
ejpam-4226	149	4	1	1	NUM
ejpam-4226	149	5	α	α	NOUN
ejpam-4226	149	6	tα	tα	PROPN
ejpam-4226	149	7	∫	∫	PROPN
ejpam-4226	149	8	t	t	PROPN
ejpam-4226	149	9	a	a	DET
ejpam-4226	149	10	f(s	f(	NOUN
ejpam-4226	149	11	)	)	PUNCT
ejpam-4226	149	12	(	(	PUNCT
ejpam-4226	149	13	cos	cos	PROPN
ejpam-4226	149	14	s+	s+	ADV
ejpam-4226	149	15	sin	sin	PROPN
ejpam-4226	149	16	s	s	PROPN
ejpam-4226	149	17	)	)	PUNCT
ejpam-4226	149	18	2s1−α	2s1−α	NUM
ejpam-4226	149	19	ds	ds	PRON
ejpam-4226	149	20	+	+	ADJ
ejpam-4226	149	21	sin	sin	NOUN
ejpam-4226	149	22	1	1	NUM
ejpam-4226	149	23	α	α	NOUN
ejpam-4226	149	24	tα	tα	PROPN
ejpam-4226	149	25	∫	∫	PROPN
ejpam-4226	149	26	t	t	PROPN
ejpam-4226	149	27	a	a	DET
ejpam-4226	149	28	f(s	f(	NOUN
ejpam-4226	149	29	)	)	PUNCT
ejpam-4226	149	30	(	(	PUNCT
ejpam-4226	149	31	cos	cos	PROPN
ejpam-4226	149	32	s−	s−	PROPN
ejpam-4226	149	33	sin	sin	VERB
ejpam-4226	149	34	s	s	NOUN
ejpam-4226	149	35	)	)	PUNCT
ejpam-4226	149	36	2s1−α	2s1−α	NUM
ejpam-4226	149	37	ds	ds	ADJ
ejpam-4226	149	38	=	=	PUNCT
ejpam-4226	149	39	exp	exp	NOUN
ejpam-4226	149	40	(	(	PUNCT
ejpam-4226	149	41	−	−	PROPN
ejpam-4226	149	42	1	1	NUM
ejpam-4226	149	43	α	α	NOUN
ejpam-4226	149	44	tα	tα	PROPN
ejpam-4226	149	45	)	)	PUNCT
ejpam-4226	149	46	iaα	iaα	PROPN
ejpam-4226	149	47	(	(	PUNCT
ejpam-4226	149	48	f(t	f(t	PROPN
ejpam-4226	149	49	)	)	PUNCT
ejpam-4226	149	50	2	2	NUM
ejpam-4226	149	51	exp	exp	NOUN
ejpam-4226	149	52	(	(	PUNCT
ejpam-4226	149	53	−	−	PROPN
ejpam-4226	149	54	1	1	NUM
ejpam-4226	149	55	α	α	NOUN
ejpam-4226	149	56	t	t	NOUN
ejpam-4226	149	57	α	α	NOUN
ejpam-4226	149	58	)	)	PUNCT
ejpam-4226	149	59	)	)	PUNCT
ejpam-4226	150	1	−	−	PROPN
ejpam-4226	150	2	cos	cos	PROPN
ejpam-4226	150	3	1	1	NUM
ejpam-4226	150	4	α	α	NOUN
ejpam-4226	150	5	tαiaα	tαiaα	NOUN
ejpam-4226	150	6	(	(	PUNCT
ejpam-4226	150	7	f(t	f(t	PROPN
ejpam-4226	150	8	)	)	PUNCT
ejpam-4226	150	9	(	(	PUNCT
ejpam-4226	150	10	cos	cos	X
ejpam-4226	150	11	t+	t+	PROPN
ejpam-4226	150	12	sin	sin	NOUN
ejpam-4226	150	13	t	t	PROPN
ejpam-4226	150	14	)	)	PUNCT
ejpam-4226	150	15	2	2	NUM
ejpam-4226	150	16	)	)	PUNCT
ejpam-4226	151	1	+	+	VERB
ejpam-4226	151	2	sin	sin	NOUN
ejpam-4226	151	3	1	1	NUM
ejpam-4226	151	4	α	α	NOUN
ejpam-4226	151	5	tαiaα	tαiaα	NOUN
ejpam-4226	151	6	(	(	PUNCT
ejpam-4226	151	7	f(t	f(t	PROPN
ejpam-4226	151	8	)	)	PUNCT
ejpam-4226	151	9	(	(	PUNCT
ejpam-4226	151	10	cos	cos	PROPN
ejpam-4226	151	11	s−	s−	PROPN
ejpam-4226	151	12	sin	sin	VERB
ejpam-4226	151	13	t	t	PROPN
ejpam-4226	151	14	)	)	PUNCT
ejpam-4226	151	15	2	2	NUM
ejpam-4226	151	16	)	)	PUNCT
ejpam-4226	151	17	hence	hence	ADV
ejpam-4226	151	18	v(t	v(t	NOUN
ejpam-4226	151	19	)	)	PUNCT
ejpam-4226	151	20	=	=	PUNCT
ejpam-4226	151	21	vh(t	vh(t	X
ejpam-4226	151	22	)	)	PUNCT
ejpam-4226	151	23	+	+	CCONJ
ejpam-4226	151	24	vp(t	vp(t	X
ejpam-4226	151	25	)	)	PUNCT
ejpam-4226	151	26	=	=	SYM
ejpam-4226	151	27	c1	c1	PROPN
ejpam-4226	151	28	exp	exp	NOUN
ejpam-4226	151	29	(	(	PUNCT
ejpam-4226	151	30	−	−	PROPN
ejpam-4226	151	31	1	1	NUM
ejpam-4226	151	32	α	α	NOUN
ejpam-4226	151	33	tα	tα	PROPN
ejpam-4226	151	34	)	)	PUNCT
ejpam-4226	152	1	+	+	CCONJ
ejpam-4226	152	2	c2	c2	PROPN
ejpam-4226	152	3	cos	cos	PROPN
ejpam-4226	152	4	1	1	NUM
ejpam-4226	152	5	α	α	NOUN
ejpam-4226	152	6	tα	tα	PROPN
ejpam-4226	152	7	+	+	CCONJ
ejpam-4226	152	8	c3	c3	PROPN
ejpam-4226	152	9	sin	sin	NOUN
ejpam-4226	152	10	1	1	NUM
ejpam-4226	152	11	α	α	NOUN
ejpam-4226	152	12	tα	tα	PROPN
ejpam-4226	152	13	+	+	CCONJ
ejpam-4226	152	14	exp	exp	NOUN
ejpam-4226	152	15	(	(	PUNCT
ejpam-4226	152	16	−	−	PROPN
ejpam-4226	152	17	1	1	NUM
ejpam-4226	152	18	α	α	NOUN
ejpam-4226	152	19	tα	tα	PROPN
ejpam-4226	152	20	)	)	PUNCT
ejpam-4226	152	21	iaα	iaα	PROPN
ejpam-4226	152	22	(	(	PUNCT
ejpam-4226	152	23	f(t	f(t	PROPN
ejpam-4226	152	24	)	)	PUNCT
ejpam-4226	152	25	2	2	NUM
ejpam-4226	152	26	exp	exp	NOUN
ejpam-4226	152	27	(	(	PUNCT
ejpam-4226	152	28	−	−	PROPN
ejpam-4226	152	29	1	1	NUM
ejpam-4226	152	30	α	α	NOUN
ejpam-4226	152	31	t	t	NOUN
ejpam-4226	152	32	α	α	NOUN
ejpam-4226	152	33	)	)	PUNCT
ejpam-4226	152	34	)	)	PUNCT
ejpam-4226	153	1	f.	f.	PROPN
ejpam-4226	153	2	bekraoui	bekraoui	PROPN
ejpam-4226	153	3	,	,	PUNCT
ejpam-4226	153	4	m.	m.	PROPN
ejpam-4226	153	5	al	al	PROPN
ejpam-4226	153	6	horani	horani	PROPN
ejpam-4226	153	7	,	,	PUNCT
ejpam-4226	153	8	r.	r.	PROPN
ejpam-4226	153	9	khalil	khalil	PROPN
ejpam-4226	153	10	/	/	SYM
ejpam-4226	153	11	eur	eur	PROPN
ejpam-4226	153	12	.	.	PUNCT
ejpam-4226	154	1	j.	j.	PROPN
ejpam-4226	154	2	pure	pure	PROPN
ejpam-4226	154	3	appl	appl	PROPN
ejpam-4226	154	4	.	.	PROPN
ejpam-4226	154	5	math	math	PROPN
ejpam-4226	154	6	,	,	PUNCT
ejpam-4226	154	7	15	15	NUM
ejpam-4226	154	8	(	(	PUNCT
ejpam-4226	154	9	1	1	NUM
ejpam-4226	154	10	)	)	PUNCT
ejpam-4226	154	11	(	(	PUNCT
ejpam-4226	154	12	2022	2022	NUM
ejpam-4226	154	13	)	)	PUNCT
ejpam-4226	154	14	,	,	PUNCT
ejpam-4226	154	15	106	106	NUM
ejpam-4226	154	16	-	-	SYM
ejpam-4226	154	17	125	125	NUM
ejpam-4226	154	18	112	112	NUM
ejpam-4226	154	19	−	−	NOUN
ejpam-4226	154	20	cos	cos	PROPN
ejpam-4226	154	21	1	1	NUM
ejpam-4226	154	22	α	α	NOUN
ejpam-4226	154	23	tαiaα	tαiaα	NOUN
ejpam-4226	154	24	(	(	PUNCT
ejpam-4226	154	25	f(t	f(t	PROPN
ejpam-4226	154	26	)	)	PUNCT
ejpam-4226	154	27	(	(	PUNCT
ejpam-4226	154	28	cos	cos	X
ejpam-4226	154	29	t+	t+	PROPN
ejpam-4226	154	30	sin	sin	NOUN
ejpam-4226	154	31	t	t	PROPN
ejpam-4226	154	32	)	)	PUNCT
ejpam-4226	154	33	2	2	NUM
ejpam-4226	154	34	)	)	PUNCT
ejpam-4226	154	35	+	+	CCONJ
ejpam-4226	154	36	sin	sin	NOUN
ejpam-4226	154	37	1	1	NUM
ejpam-4226	154	38	α	α	NOUN
ejpam-4226	154	39	tαiaα	tαiaα	NOUN
ejpam-4226	154	40	(	(	PUNCT
ejpam-4226	154	41	f(t	f(t	PROPN
ejpam-4226	154	42	)	)	PUNCT
ejpam-4226	154	43	(	(	PUNCT
ejpam-4226	154	44	cos	cos	ADP
ejpam-4226	154	45	t−	t−	PROPN
ejpam-4226	154	46	sin	sin	NOUN
ejpam-4226	154	47	t	t	PROPN
ejpam-4226	154	48	)	)	PUNCT
ejpam-4226	154	49	2	2	NUM
ejpam-4226	154	50	)	)	PUNCT
ejpam-4226	154	51	v(α	v(α	PROPN
ejpam-4226	154	52	)	)	PUNCT
ejpam-4226	154	53	=	=	SYM
ejpam-4226	154	54	−c1	−c1	NOUN
ejpam-4226	154	55	exp	exp	NOUN
ejpam-4226	154	56	(	(	PUNCT
ejpam-4226	154	57	−	−	PROPN
ejpam-4226	154	58	1	1	NUM
ejpam-4226	154	59	α	α	NOUN
ejpam-4226	154	60	tα	tα	PROPN
ejpam-4226	154	61	)	)	PUNCT
ejpam-4226	155	1	−	−	PROPN
ejpam-4226	155	2	c2	c2	PROPN
ejpam-4226	155	3	sin	sin	VERB
ejpam-4226	155	4	1	1	NUM
ejpam-4226	155	5	α	α	NOUN
ejpam-4226	155	6	tα	tα	PROPN
ejpam-4226	155	7	+	+	CCONJ
ejpam-4226	155	8	c3	c3	X
ejpam-4226	155	9	cos	cos	PROPN
ejpam-4226	155	10	1	1	NUM
ejpam-4226	155	11	α	α	NOUN
ejpam-4226	155	12	tα	tα	VERB
ejpam-4226	155	13	+	+	NOUN
ejpam-4226	155	14	exp	exp	NOUN
ejpam-4226	155	15	(	(	PUNCT
ejpam-4226	155	16	−	−	PROPN
ejpam-4226	155	17	1	1	NUM
ejpam-4226	155	18	α	α	NOUN
ejpam-4226	155	19	tα	tα	PROPN
ejpam-4226	155	20	)	)	PUNCT
ejpam-4226	155	21	[	[	PUNCT
ejpam-4226	155	22	−iaα	−iaα	PROPN
ejpam-4226	155	23	(	(	PUNCT
ejpam-4226	155	24	f(t	f(t	PROPN
ejpam-4226	155	25	)	)	PUNCT
ejpam-4226	155	26	2	2	NUM
ejpam-4226	155	27	exp	exp	NOUN
ejpam-4226	155	28	(	(	PUNCT
ejpam-4226	155	29	−	−	PROPN
ejpam-4226	155	30	1	1	NUM
ejpam-4226	155	31	α	α	NOUN
ejpam-4226	155	32	t	t	NOUN
ejpam-4226	155	33	α	α	NOUN
ejpam-4226	155	34	)	)	PUNCT
ejpam-4226	155	35	)	)	PUNCT
ejpam-4226	156	1	+	+	CCONJ
ejpam-4226	156	2	f(t	f(t	NOUN
ejpam-4226	156	3	)	)	PUNCT
ejpam-4226	156	4	2	2	NUM
ejpam-4226	156	5	exp	exp	NOUN
ejpam-4226	156	6	(	(	PUNCT
ejpam-4226	156	7	−	−	PROPN
ejpam-4226	156	8	1	1	NUM
ejpam-4226	156	9	α	α	NOUN
ejpam-4226	156	10	t	t	NOUN
ejpam-4226	156	11	α	α	NOUN
ejpam-4226	156	12	)	)	PUNCT
ejpam-4226	156	13	]	]	PUNCT
ejpam-4226	157	1	+	+	PUNCT
ejpam-4226	157	2	sin	sin	NOUN
ejpam-4226	157	3	1	1	NUM
ejpam-4226	157	4	α	α	NOUN
ejpam-4226	157	5	tα	tα	PROPN
ejpam-4226	157	6	[	[	PUNCT
ejpam-4226	157	7	iaα	iaα	NOUN
ejpam-4226	157	8	(	(	PUNCT
ejpam-4226	157	9	f(t	f(t	PROPN
ejpam-4226	157	10	)	)	PUNCT
ejpam-4226	157	11	(	(	PUNCT
ejpam-4226	157	12	cos	cos	X
ejpam-4226	157	13	t+	t+	PROPN
ejpam-4226	157	14	sin	sin	NOUN
ejpam-4226	157	15	t	t	PROPN
ejpam-4226	157	16	)	)	PUNCT
ejpam-4226	157	17	2	2	NUM
ejpam-4226	157	18	)	)	PUNCT
ejpam-4226	157	19	+	+	CCONJ
ejpam-4226	157	20	f(t	f(t	NOUN
ejpam-4226	157	21	)	)	PUNCT
ejpam-4226	157	22	(	(	PUNCT
ejpam-4226	157	23	cos	cos	ADP
ejpam-4226	157	24	t−	t−	PROPN
ejpam-4226	157	25	sin	sin	NOUN
ejpam-4226	157	26	t	t	PROPN
ejpam-4226	157	27	)	)	PUNCT
ejpam-4226	157	28	2	2	NUM
ejpam-4226	157	29	]	]	PUNCT
ejpam-4226	157	30	+	+	ADJ
ejpam-4226	157	31	cos	cos	ADJ
ejpam-4226	157	32	1	1	NUM
ejpam-4226	157	33	α	α	NOUN
ejpam-4226	157	34	tα	tα	PROPN
ejpam-4226	157	35	[	[	PUNCT
ejpam-4226	157	36	iaα	iaα	NOUN
ejpam-4226	157	37	(	(	PUNCT
ejpam-4226	157	38	f(t	f(t	PROPN
ejpam-4226	157	39	)	)	PUNCT
ejpam-4226	157	40	(	(	PUNCT
ejpam-4226	157	41	cos	cos	ADP
ejpam-4226	157	42	t−	t−	PROPN
ejpam-4226	157	43	sin	sin	NOUN
ejpam-4226	157	44	t	t	PROPN
ejpam-4226	157	45	)	)	PUNCT
ejpam-4226	157	46	2	2	NUM
ejpam-4226	157	47	)	)	PUNCT
ejpam-4226	157	48	−	−	PRON
ejpam-4226	157	49	f(t	f(t	NOUN
ejpam-4226	157	50	)	)	PUNCT
ejpam-4226	157	51	(	(	PUNCT
ejpam-4226	157	52	cos	cos	X
ejpam-4226	157	53	t+	t+	PROPN
ejpam-4226	157	54	sin	sin	NOUN
ejpam-4226	157	55	t	t	PROPN
ejpam-4226	157	56	)	)	PUNCT
ejpam-4226	157	57	2	2	NUM
ejpam-4226	157	58	]	]	PUNCT
ejpam-4226	157	59	u(2α	u(2α	X
ejpam-4226	157	60	)	)	PUNCT
ejpam-4226	157	61	=	=	SYM
ejpam-4226	157	62	c1	c1	PROPN
ejpam-4226	157	63	exp	exp	NOUN
ejpam-4226	157	64	(	(	PUNCT
ejpam-4226	157	65	−	−	PROPN
ejpam-4226	157	66	1	1	NUM
ejpam-4226	157	67	α	α	NOUN
ejpam-4226	157	68	tα	tα	PROPN
ejpam-4226	157	69	)	)	PUNCT
ejpam-4226	157	70	−	−	PROPN
ejpam-4226	157	71	c2	c2	PROPN
ejpam-4226	157	72	cos	cos	PROPN
ejpam-4226	157	73	1	1	NUM
ejpam-4226	157	74	α	α	NOUN
ejpam-4226	157	75	tα	tα	PROPN
ejpam-4226	157	76	−	−	PROPN
ejpam-4226	157	77	c3	c3	PROPN
ejpam-4226	157	78	sin	sin	NOUN
ejpam-4226	157	79	1	1	NUM
ejpam-4226	157	80	α	α	NOUN
ejpam-4226	157	81	tα	tα	VERB
ejpam-4226	157	82	+	+	NOUN
ejpam-4226	157	83	exp	exp	NOUN
ejpam-4226	157	84	(	(	PUNCT
ejpam-4226	157	85	−	−	PROPN
ejpam-4226	157	86	1	1	NUM
ejpam-4226	157	87	α	α	NOUN
ejpam-4226	157	88	tα	tα	PROPN
ejpam-4226	157	89	)	)	PUNCT
ejpam-4226	158	1	[	[	PUNCT
ejpam-4226	158	2	iaα	iaα	NOUN
ejpam-4226	158	3	(	(	PUNCT
ejpam-4226	158	4	f(t	f(t	PROPN
ejpam-4226	158	5	)	)	PUNCT
ejpam-4226	158	6	2	2	NUM
ejpam-4226	158	7	exp	exp	NOUN
ejpam-4226	158	8	(	(	PUNCT
ejpam-4226	158	9	−	−	PROPN
ejpam-4226	158	10	1	1	NUM
ejpam-4226	158	11	α	α	NOUN
ejpam-4226	158	12	t	t	NOUN
ejpam-4226	158	13	α	α	NOUN
ejpam-4226	158	14	)	)	PUNCT
ejpam-4226	158	15	)	)	PUNCT
ejpam-4226	159	1	+	+	CCONJ
ejpam-4226	159	2	f	f	X
ejpam-4226	159	3	(	(	PUNCT
ejpam-4226	159	4	α)(t	α)(t	PROPN
ejpam-4226	159	5	)	)	PUNCT
ejpam-4226	159	6	exp	exp	NOUN
ejpam-4226	159	7	(	(	PUNCT
ejpam-4226	159	8	−	−	PROPN
ejpam-4226	159	9	1	1	NUM
ejpam-4226	159	10	α	α	NOUN
ejpam-4226	159	11	t	t	NOUN
ejpam-4226	159	12	α	α	NOUN
ejpam-4226	159	13	)	)	PUNCT
ejpam-4226	160	1	+	+	CCONJ
ejpam-4226	160	2	f(t	f(t	NOUN
ejpam-4226	160	3	)	)	PUNCT
ejpam-4226	160	4	exp	exp	NOUN
ejpam-4226	160	5	(	(	PUNCT
ejpam-4226	160	6	−	−	PROPN
ejpam-4226	160	7	1	1	NUM
ejpam-4226	160	8	α	α	NOUN
ejpam-4226	160	9	t	t	NOUN
ejpam-4226	160	10	α	α	NOUN
ejpam-4226	160	11	)	)	PUNCT
ejpam-4226	160	12	2	2	NUM
ejpam-4226	160	13	exp	exp	NOUN
ejpam-4226	160	14	(	(	PUNCT
ejpam-4226	160	15	−	−	PROPN
ejpam-4226	160	16	2	2	NUM
ejpam-4226	160	17	α	α	NOUN
ejpam-4226	160	18	t	t	NOUN
ejpam-4226	160	19	α	α	NOUN
ejpam-4226	160	20	)	)	PUNCT
ejpam-4226	160	21	]	]	PUNCT
ejpam-4226	160	22	−	−	PRON
ejpam-4226	160	23	f(t	f(t	NOUN
ejpam-4226	160	24	)	)	PUNCT
ejpam-4226	161	1	+	+	CCONJ
ejpam-4226	161	2	cos	cos	ADP
ejpam-4226	161	3	1	1	NUM
ejpam-4226	161	4	α	α	NOUN
ejpam-4226	161	5	tα	tα	PROPN
ejpam-4226	161	6	[	[	PUNCT
ejpam-4226	161	7	iaα	iaα	NOUN
ejpam-4226	161	8	(	(	PUNCT
ejpam-4226	161	9	f(t	f(t	PROPN
ejpam-4226	161	10	)	)	PUNCT
ejpam-4226	161	11	(	(	PUNCT
ejpam-4226	161	12	cos	cos	X
ejpam-4226	161	13	t+	t+	PROPN
ejpam-4226	161	14	sin	sin	NOUN
ejpam-4226	161	15	t	t	PROPN
ejpam-4226	161	16	)	)	PUNCT
ejpam-4226	161	17	2	2	NUM
ejpam-4226	161	18	)	)	PUNCT
ejpam-4226	161	19	+	+	CCONJ
ejpam-4226	161	20	f(t	f(t	NOUN
ejpam-4226	161	21	)	)	PUNCT
ejpam-4226	161	22	(	(	PUNCT
ejpam-4226	161	23	cos	cos	ADP
ejpam-4226	161	24	t−	t−	PROPN
ejpam-4226	161	25	sin	sin	NOUN
ejpam-4226	161	26	t	t	PROPN
ejpam-4226	161	27	)	)	PUNCT
ejpam-4226	161	28	2	2	NUM
ejpam-4226	161	29	−	−	PROPN
ejpam-4226	161	30	f	f	PROPN
ejpam-4226	161	31	(	(	PUNCT
ejpam-4226	161	32	α)(t	α)(t	PROPN
ejpam-4226	161	33	)	)	PUNCT
ejpam-4226	161	34	(	(	PUNCT
ejpam-4226	161	35	cos	cos	X
ejpam-4226	161	36	t+	t+	PROPN
ejpam-4226	161	37	sin	sin	NOUN
ejpam-4226	161	38	t	t	PROPN
ejpam-4226	161	39	)	)	PUNCT
ejpam-4226	161	40	2	2	NUM
ejpam-4226	161	41	]	]	PUNCT
ejpam-4226	161	42	−	−	PROPN
ejpam-4226	161	43	sin	sin	NOUN
ejpam-4226	161	44	1	1	NUM
ejpam-4226	161	45	α	α	NOUN
ejpam-4226	161	46	tα	tα	PROPN
ejpam-4226	161	47	[	[	PUNCT
ejpam-4226	161	48	iaα	iaα	NOUN
ejpam-4226	161	49	(	(	PUNCT
ejpam-4226	161	50	f(t	f(t	PROPN
ejpam-4226	161	51	)	)	PUNCT
ejpam-4226	161	52	(	(	PUNCT
ejpam-4226	161	53	cos	cos	ADP
ejpam-4226	161	54	t−	t−	PROPN
ejpam-4226	161	55	sin	sin	NOUN
ejpam-4226	161	56	t	t	PROPN
ejpam-4226	161	57	)	)	PUNCT
ejpam-4226	161	58	2	2	NUM
ejpam-4226	161	59	)	)	PUNCT
ejpam-4226	161	60	−	−	PRON
ejpam-4226	161	61	f(t	f(t	NOUN
ejpam-4226	161	62	)	)	PUNCT
ejpam-4226	161	63	(	(	PUNCT
ejpam-4226	161	64	cos	cos	X
ejpam-4226	161	65	t+	t+	PROPN
ejpam-4226	161	66	sin	sin	NOUN
ejpam-4226	161	67	t	t	PROPN
ejpam-4226	161	68	)	)	PUNCT
ejpam-4226	161	69	2	2	NUM
ejpam-4226	161	70	−	−	PROPN
ejpam-4226	161	71	f	f	PROPN
ejpam-4226	161	72	(	(	PUNCT
ejpam-4226	161	73	α)(t	α)(t	PROPN
ejpam-4226	161	74	)	)	PUNCT
ejpam-4226	161	75	(	(	PUNCT
ejpam-4226	161	76	cos	cos	ADP
ejpam-4226	161	77	t−	t−	PROPN
ejpam-4226	161	78	sin	sin	NOUN
ejpam-4226	161	79	t	t	PROPN
ejpam-4226	161	80	)	)	PUNCT
ejpam-4226	161	81	2	2	NUM
ejpam-4226	161	82	]	]	PUNCT
ejpam-4226	161	83	but	but	CCONJ
ejpam-4226	161	84	v(0	v(0	X
ejpam-4226	161	85	)	)	PUNCT
ejpam-4226	161	86	=	=	SYM
ejpam-4226	161	87	1	1	NUM
ejpam-4226	161	88	,	,	PUNCT
ejpam-4226	161	89	v(α)(0	v(α)(0	PROPN
ejpam-4226	161	90	)	)	PUNCT
ejpam-4226	161	91	=	=	SYM
ejpam-4226	161	92	1	1	NUM
ejpam-4226	161	93	and	and	CCONJ
ejpam-4226	161	94	v(2α)(0	v(2α)(0	NUM
ejpam-4226	161	95	)	)	PUNCT
ejpam-4226	162	1	=	=	SYM
ejpam-4226	162	2	1	1	X
ejpam-4226	162	3	.	.	PUNCT
ejpam-4226	162	4	thus	thus	NUM
ejpam-4226	163	1	c1	c1	PROPN
ejpam-4226	163	2	+	+	CCONJ
ejpam-4226	163	3	c2	c2	PROPN
ejpam-4226	163	4	=	=	SYM
ejpam-4226	163	5	1	1	NUM
ejpam-4226	163	6	c3	c3	PROPN
ejpam-4226	163	7	−	−	PROPN
ejpam-4226	163	8	c1	c1	PROPN
ejpam-4226	163	9	=	=	PROPN
ejpam-4226	163	10	1	1	NUM
ejpam-4226	163	11	c1	c1	PROPN
ejpam-4226	163	12	−	−	PROPN
ejpam-4226	163	13	c2	c2	PROPN
ejpam-4226	163	14	+	+	CCONJ
ejpam-4226	163	15	iaα	iaα	PROPN
ejpam-4226	163	16	(	(	PUNCT
ejpam-4226	163	17	f(0	f(0	NOUN
ejpam-4226	163	18	)	)	PUNCT
ejpam-4226	163	19	)	)	PUNCT
ejpam-4226	164	1	=	=	SYM
ejpam-4226	165	1	1	1	NUM
ejpam-4226	165	2	⇐	⇐	ADJ
ejpam-4226	165	3	⇒	⇒	PROPN
ejpam-4226	165	4			PUNCT
ejpam-4226	165	5	c1	c1	NOUN
ejpam-4226	165	6	=	=	PROPN
ejpam-4226	165	7	1−	1−	NUM
ejpam-4226	165	8	1	1	NUM
ejpam-4226	165	9	2i	2i	NOUN
ejpam-4226	165	10	a	a	DET
ejpam-4226	165	11	α	α	PROPN
ejpam-4226	165	12	(	(	PUNCT
ejpam-4226	165	13	f(0	f(0	NOUN
ejpam-4226	165	14	)	)	PUNCT
ejpam-4226	165	15	)	)	PUNCT
ejpam-4226	165	16	c2	c2	PROPN
ejpam-4226	165	17	=	=	SYM
ejpam-4226	165	18	1	1	NUM
ejpam-4226	165	19	2i	2i	NUM
ejpam-4226	165	20	a	a	DET
ejpam-4226	165	21	α	α	PROPN
ejpam-4226	165	22	(	(	PUNCT
ejpam-4226	165	23	f(0	f(0	NOUN
ejpam-4226	165	24	)	)	PUNCT
ejpam-4226	165	25	)	)	PUNCT
ejpam-4226	166	1	c3	c3	NOUN
ejpam-4226	166	2	=	=	PUNCT
ejpam-4226	166	3	2−	2−	NUM
ejpam-4226	166	4	1	1	NUM
ejpam-4226	166	5	2i	2i	NOUN
ejpam-4226	166	6	a	a	DET
ejpam-4226	166	7	α	α	PROPN
ejpam-4226	166	8	(	(	PUNCT
ejpam-4226	166	9	f(0	f(0	NOUN
ejpam-4226	166	10	)	)	PUNCT
ejpam-4226	166	11	)	)	PUNCT
ejpam-4226	166	12	hence	hence	ADV
ejpam-4226	166	13	v(t	v(t	X
ejpam-4226	166	14	)	)	PUNCT
ejpam-4226	166	15	=	=	PUNCT
ejpam-4226	167	1	(	(	PUNCT
ejpam-4226	167	2	1−	1−	NUM
ejpam-4226	167	3	1	1	NUM
ejpam-4226	167	4	2	2	NUM
ejpam-4226	167	5	iaα	iaα	NOUN
ejpam-4226	167	6	(	(	PUNCT
ejpam-4226	167	7	f(0	f(0	NOUN
ejpam-4226	167	8	)	)	PUNCT
ejpam-4226	167	9	)	)	PUNCT
ejpam-4226	167	10	)	)	PUNCT
ejpam-4226	167	11	exp	exp	NOUN
ejpam-4226	167	12	(	(	PUNCT
ejpam-4226	167	13	−	−	PROPN
ejpam-4226	167	14	1	1	NUM
ejpam-4226	167	15	α	α	NOUN
ejpam-4226	167	16	tα	tα	PROPN
ejpam-4226	167	17	)	)	PUNCT
ejpam-4226	168	1	+	+	CCONJ
ejpam-4226	168	2	1	1	NUM
ejpam-4226	168	3	2	2	NUM
ejpam-4226	168	4	iaα	iaα	NOUN
ejpam-4226	168	5	(	(	PUNCT
ejpam-4226	168	6	f(0	f(0	NOUN
ejpam-4226	168	7	)	)	PUNCT
ejpam-4226	168	8	)	)	PUNCT
ejpam-4226	169	1	cos	cos	ADP
ejpam-4226	169	2	1	1	NUM
ejpam-4226	169	3	α	α	NOUN
ejpam-4226	169	4	tα	tα	PROPN
ejpam-4226	169	5	+	+	CCONJ
ejpam-4226	169	6	(	(	PUNCT
ejpam-4226	169	7	2−	2−	NUM
ejpam-4226	169	8	1	1	NUM
ejpam-4226	169	9	2	2	NUM
ejpam-4226	169	10	iaα	iaα	NOUN
ejpam-4226	169	11	(	(	PUNCT
ejpam-4226	169	12	f(0	f(0	NOUN
ejpam-4226	169	13	)	)	PUNCT
ejpam-4226	169	14	)	)	PUNCT
ejpam-4226	169	15	)	)	PUNCT
ejpam-4226	169	16	sin	sin	NOUN
ejpam-4226	169	17	1	1	NUM
ejpam-4226	169	18	α	α	NOUN
ejpam-4226	169	19	tα	tα	PROPN
ejpam-4226	169	20	+	+	CCONJ
ejpam-4226	169	21	exp	exp	NOUN
ejpam-4226	169	22	(	(	PUNCT
ejpam-4226	169	23	−	−	PROPN
ejpam-4226	169	24	1	1	NUM
ejpam-4226	169	25	α	α	NOUN
ejpam-4226	169	26	tα	tα	PROPN
ejpam-4226	169	27	)	)	PUNCT
ejpam-4226	170	1	iaα	iaα	PROPN
ejpam-4226	170	2	(	(	PUNCT
ejpam-4226	170	3	f(t	f(t	PROPN
ejpam-4226	170	4	)	)	PUNCT
ejpam-4226	170	5	2	2	NUM
ejpam-4226	170	6	exp	exp	NOUN
ejpam-4226	170	7	(	(	PUNCT
ejpam-4226	170	8	−	−	PROPN
ejpam-4226	170	9	1	1	NUM
ejpam-4226	170	10	α	α	NOUN
ejpam-4226	170	11	t	t	NOUN
ejpam-4226	170	12	α	α	NOUN
ejpam-4226	170	13	)	)	PUNCT
ejpam-4226	170	14	)	)	PUNCT
ejpam-4226	170	15	−	−	PROPN
ejpam-4226	171	1	cos	cos	PROPN
ejpam-4226	171	2	1	1	NUM
ejpam-4226	171	3	α	α	NOUN
ejpam-4226	171	4	tαiaα	tαiaα	NOUN
ejpam-4226	171	5	(	(	PUNCT
ejpam-4226	171	6	f(t	f(t	PROPN
ejpam-4226	171	7	)	)	PUNCT
ejpam-4226	171	8	(	(	PUNCT
ejpam-4226	171	9	cos	cos	X
ejpam-4226	171	10	t+	t+	PROPN
ejpam-4226	171	11	sin	sin	NOUN
ejpam-4226	171	12	t	t	PROPN
ejpam-4226	171	13	)	)	PUNCT
ejpam-4226	171	14	2	2	NUM
ejpam-4226	171	15	)	)	PUNCT
ejpam-4226	172	1	+	+	VERB
ejpam-4226	172	2	sin	sin	NOUN
ejpam-4226	172	3	1	1	NUM
ejpam-4226	172	4	α	α	NOUN
ejpam-4226	172	5	tαiaα	tαiaα	NOUN
ejpam-4226	172	6	(	(	PUNCT
ejpam-4226	172	7	f(t	f(t	PROPN
ejpam-4226	172	8	)	)	PUNCT
ejpam-4226	172	9	(	(	PUNCT
ejpam-4226	172	10	cos	cos	ADP
ejpam-4226	172	11	t−	t−	PROPN
ejpam-4226	172	12	sin	sin	NOUN
ejpam-4226	172	13	t	t	PROPN
ejpam-4226	172	14	)	)	PUNCT
ejpam-4226	172	15	2	2	NUM
ejpam-4226	172	16	)	)	PUNCT
ejpam-4226	172	17	hence	hence	ADV
ejpam-4226	172	18	,	,	PUNCT
ejpam-4226	172	19	the	the	DET
ejpam-4226	172	20	atomic	atomic	ADJ
ejpam-4226	172	21	solution	solution	NOUN
ejpam-4226	172	22	that	that	PRON
ejpam-4226	172	23	satisfies	satisfy	VERB
ejpam-4226	172	24	the	the	DET
ejpam-4226	172	25	conditions	condition	NOUN
ejpam-4226	172	26	is	be	AUX
ejpam-4226	172	27	f.	f.	PROPN
ejpam-4226	172	28	bekraoui	bekraoui	PROPN
ejpam-4226	172	29	,	,	PUNCT
ejpam-4226	172	30	m.	m.	PROPN
ejpam-4226	172	31	al	al	PROPN
ejpam-4226	172	32	horani	horani	PROPN
ejpam-4226	172	33	,	,	PUNCT
ejpam-4226	172	34	r.	r.	PROPN
ejpam-4226	172	35	khalil	khalil	PROPN
ejpam-4226	172	36	/	/	SYM
ejpam-4226	172	37	eur	eur	PROPN
ejpam-4226	172	38	.	.	PUNCT
ejpam-4226	173	1	j.	j.	PROPN
ejpam-4226	173	2	pure	pure	PROPN
ejpam-4226	173	3	appl	appl	PROPN
ejpam-4226	173	4	.	.	PROPN
ejpam-4226	173	5	math	math	PROPN
ejpam-4226	173	6	,	,	PUNCT
ejpam-4226	173	7	15	15	NUM
ejpam-4226	173	8	(	(	PUNCT
ejpam-4226	173	9	1	1	NUM
ejpam-4226	173	10	)	)	PUNCT
ejpam-4226	173	11	(	(	PUNCT
ejpam-4226	173	12	2022	2022	NUM
ejpam-4226	173	13	)	)	PUNCT
ejpam-4226	173	14	,	,	PUNCT
ejpam-4226	173	15	106	106	NUM
ejpam-4226	173	16	-	-	SYM
ejpam-4226	173	17	125	125	NUM
ejpam-4226	173	18	113	113	NUM
ejpam-4226	173	19	[	[	X
ejpam-4226	173	20	(	(	PUNCT
ejpam-4226	173	21	1−	1−	NUM
ejpam-4226	173	22	1	1	NUM
ejpam-4226	173	23	2	2	NUM
ejpam-4226	173	24	iaα	iaα	NOUN
ejpam-4226	173	25	(	(	PUNCT
ejpam-4226	173	26	f(0	f(0	NOUN
ejpam-4226	173	27	)	)	PUNCT
ejpam-4226	173	28	)	)	PUNCT
ejpam-4226	173	29	)	)	PUNCT
ejpam-4226	173	30	exp	exp	NOUN
ejpam-4226	173	31	(	(	PUNCT
ejpam-4226	173	32	−	−	PROPN
ejpam-4226	173	33	1	1	NUM
ejpam-4226	173	34	α	α	NOUN
ejpam-4226	173	35	tα	tα	PROPN
ejpam-4226	173	36	)	)	PUNCT
ejpam-4226	174	1	+	+	CCONJ
ejpam-4226	174	2	1	1	NUM
ejpam-4226	174	3	2	2	NUM
ejpam-4226	174	4	iaα	iaα	NOUN
ejpam-4226	174	5	(	(	PUNCT
ejpam-4226	174	6	f(0	f(0	NOUN
ejpam-4226	174	7	)	)	PUNCT
ejpam-4226	174	8	)	)	PUNCT
ejpam-4226	175	1	cos	cos	ADP
ejpam-4226	175	2	1	1	NUM
ejpam-4226	175	3	α	α	NOUN
ejpam-4226	175	4	tα	tα	PROPN
ejpam-4226	175	5	+	+	CCONJ
ejpam-4226	175	6	(	(	PUNCT
ejpam-4226	175	7	2−	2−	NUM
ejpam-4226	175	8	1	1	NUM
ejpam-4226	175	9	2	2	NUM
ejpam-4226	175	10	iaα	iaα	NOUN
ejpam-4226	175	11	(	(	PUNCT
ejpam-4226	175	12	f(0	f(0	NOUN
ejpam-4226	175	13	)	)	PUNCT
ejpam-4226	175	14	)	)	PUNCT
ejpam-4226	175	15	)	)	PUNCT
ejpam-4226	175	16	sin	sin	NOUN
ejpam-4226	175	17	1	1	NUM
ejpam-4226	175	18	α	α	NOUN
ejpam-4226	175	19	tα	tα	PROPN
ejpam-4226	175	20	]	]	PUNCT
ejpam-4226	176	1	⊗	⊗	PROPN
ejpam-4226	176	2	z	z	PROPN
ejpam-4226	177	1	+	+	CCONJ
ejpam-4226	177	2	[	[	PUNCT
ejpam-4226	177	3	exp	exp	NOUN
ejpam-4226	177	4	(	(	PUNCT
ejpam-4226	177	5	−	−	PROPN
ejpam-4226	177	6	1	1	NUM
ejpam-4226	177	7	α	α	NOUN
ejpam-4226	177	8	tα	tα	PROPN
ejpam-4226	177	9	)	)	PUNCT
ejpam-4226	177	10	iaα	iaα	PROPN
ejpam-4226	177	11	(	(	PUNCT
ejpam-4226	177	12	f(t	f(t	PROPN
ejpam-4226	177	13	)	)	PUNCT
ejpam-4226	177	14	2	2	NUM
ejpam-4226	177	15	exp	exp	NOUN
ejpam-4226	177	16	(	(	PUNCT
ejpam-4226	177	17	−	−	PROPN
ejpam-4226	177	18	1	1	NUM
ejpam-4226	177	19	α	α	NOUN
ejpam-4226	177	20	t	t	NOUN
ejpam-4226	177	21	α	α	NOUN
ejpam-4226	177	22	)	)	PUNCT
ejpam-4226	177	23	)	)	PUNCT
ejpam-4226	177	24	−	−	PROPN
ejpam-4226	178	1	cos	cos	PROPN
ejpam-4226	178	2	1	1	NUM
ejpam-4226	178	3	α	α	NOUN
ejpam-4226	178	4	tαiaα	tαiaα	NOUN
ejpam-4226	178	5	(	(	PUNCT
ejpam-4226	178	6	f(t	f(t	PROPN
ejpam-4226	178	7	)	)	PUNCT
ejpam-4226	178	8	(	(	PUNCT
ejpam-4226	178	9	cos	cos	X
ejpam-4226	178	10	t+	t+	PROPN
ejpam-4226	178	11	sin	sin	NOUN
ejpam-4226	178	12	t	t	PROPN
ejpam-4226	178	13	)	)	PUNCT
ejpam-4226	178	14	2	2	NUM
ejpam-4226	178	15	)	)	PUNCT
ejpam-4226	179	1	+	+	VERB
ejpam-4226	179	2	sin	sin	NOUN
ejpam-4226	179	3	1	1	NUM
ejpam-4226	179	4	α	α	NOUN
ejpam-4226	179	5	tαiaα	tαiaα	NOUN
ejpam-4226	179	6	(	(	PUNCT
ejpam-4226	179	7	f(t	f(t	PROPN
ejpam-4226	179	8	)	)	PUNCT
ejpam-4226	179	9	(	(	PUNCT
ejpam-4226	179	10	cos	cos	ADP
ejpam-4226	179	11	t−	t−	PROPN
ejpam-4226	179	12	sin	sin	NOUN
ejpam-4226	179	13	t	t	PROPN
ejpam-4226	179	14	)	)	PUNCT
ejpam-4226	179	15	2	2	NUM
ejpam-4226	179	16	)	)	PUNCT
ejpam-4226	179	17	]	]	PUNCT
ejpam-4226	180	1	⊗	⊗	PROPN
ejpam-4226	180	2	z	z	NOUN
ejpam-4226	180	3	.	.	PUNCT
ejpam-4226	181	1	all	all	DET
ejpam-4226	181	2	other	other	ADJ
ejpam-4226	181	3	situations	situation	NOUN
ejpam-4226	181	4	are	be	AUX
ejpam-4226	181	5	handled	handle	VERB
ejpam-4226	181	6	in	in	ADP
ejpam-4226	181	7	the	the	DET
ejpam-4226	181	8	same	same	ADJ
ejpam-4226	181	9	way	way	NOUN
ejpam-4226	181	10	.	.	PUNCT
ejpam-4226	182	1	b.	b.	VERB
ejpam-4226	182	2	the	the	DET
ejpam-4226	182	3	second	second	ADJ
ejpam-4226	182	4	case	case	NOUN
ejpam-4226	182	5	.	.	PUNCT
ejpam-4226	183	1			PROPN
ejpam-4226	183	2	(	(	PUNCT
ejpam-4226	183	3	i	i	NOUN
ejpam-4226	183	4	)	)	PUNCT
ejpam-4226	183	5	v(3α)(t)⊗	v(3α)(t)⊗	VERB
ejpam-4226	183	6	x+	x+	X
ejpam-4226	183	7	v(2α)(t)⊗ax	v(2α)(t)⊗ax	PROPN
ejpam-4226	183	8	=	=	NOUN
ejpam-4226	183	9	v1(t)⊗	v1(t)⊗	ADJ
ejpam-4226	183	10	y1	y1	NOUN
ejpam-4226	183	11	and	and	CCONJ
ejpam-4226	183	12	(	(	PUNCT
ejpam-4226	183	13	ii	ii	NOUN
ejpam-4226	183	14	)	)	PUNCT
ejpam-4226	183	15	v(α)(t)⊗bx+	v(α)(t)⊗bx+	PROPN
ejpam-4226	183	16	v(t)⊗	v(t)⊗	NOUN
ejpam-4226	183	17	cx	cx	NOUN
ejpam-4226	183	18	=	=	PUNCT
ejpam-4226	183	19	v2(t)⊗	v2(t)⊗	PROPN
ejpam-4226	183	20	y2	y2	PROPN
ejpam-4226	183	21	,	,	PUNCT
ejpam-4226	183	22	this	this	PRON
ejpam-4226	183	23	has	have	VERB
ejpam-4226	183	24	the	the	DET
ejpam-4226	183	25	following	follow	VERB
ejpam-4226	183	26	situations	situation	NOUN
ejpam-4226	183	27	:	:	PUNCT
ejpam-4226	183	28	which	which	PRON
ejpam-4226	183	29	gives	give	VERB
ejpam-4226	183	30	four	four	NUM
ejpam-4226	183	31	situations	situation	NOUN
ejpam-4226	183	32	.	.	PUNCT
ejpam-4226	184	1	situation	situation	NOUN
ejpam-4226	184	2	1	1	NUM
ejpam-4226	184	3	.	.	PUNCT
ejpam-4226	184	4			PUNCT
ejpam-4226	184	5	v(3α	v(3α	NOUN
ejpam-4226	184	6	)	)	PUNCT
ejpam-4226	184	7	=	=	SYM
ejpam-4226	184	8	v(2α	v(2α	X
ejpam-4226	184	9	)	)	PUNCT
ejpam-4226	184	10	=	=	SYM
ejpam-4226	184	11	v1(t	v1(t	PROPN
ejpam-4226	184	12	)	)	PUNCT
ejpam-4226	184	13	and	and	CCONJ
ejpam-4226	184	14	v(α	v(α	PROPN
ejpam-4226	184	15	)	)	PUNCT
ejpam-4226	184	16	=	=	SYM
ejpam-4226	184	17	v	v	NOUN
ejpam-4226	184	18	=	=	SYM
ejpam-4226	184	19	v2(t	v2(t	NOUN
ejpam-4226	184	20	)	)	PUNCT
ejpam-4226	184	21	now	now	ADV
ejpam-4226	184	22	for	for	ADP
ejpam-4226	184	23	v(3α	v(3α	NOUN
ejpam-4226	184	24	)	)	PUNCT
ejpam-4226	184	25	=	=	SYM
ejpam-4226	184	26	v(2α	v(2α	NOUN
ejpam-4226	184	27	)	)	PUNCT
ejpam-4226	184	28	,	,	PUNCT
ejpam-4226	184	29	the	the	DET
ejpam-4226	184	30	associated	associated	ADJ
ejpam-4226	184	31	characteristic	characteristic	ADJ
ejpam-4226	184	32	equation	equation	NOUN
ejpam-4226	184	33	is	be	AUX
ejpam-4226	184	34	r3	r3	PROPN
ejpam-4226	184	35	−	−	NOUN
ejpam-4226	184	36	r2	r2	PROPN
ejpam-4226	184	37	=	=	PUNCT
ejpam-4226	185	1	0	0	X
ejpam-4226	185	2	.	.	PUNCT
ejpam-4226	185	3	hence	hence	ADV
ejpam-4226	185	4	using	use	VERB
ejpam-4226	185	5	[	[	X
ejpam-4226	185	6	12	12	NUM
ejpam-4226	185	7	]	]	PUNCT
ejpam-4226	185	8	,	,	PUNCT
ejpam-4226	185	9	we	we	PRON
ejpam-4226	185	10	get	get	VERB
ejpam-4226	185	11	v(t	v(t	NOUN
ejpam-4226	185	12	)	)	PUNCT
ejpam-4226	186	1	=	=	SYM
ejpam-4226	186	2	c1	c1	PROPN
ejpam-4226	186	3	+	+	CCONJ
ejpam-4226	186	4	c2	c2	PROPN
ejpam-4226	186	5	tα	tα	VERB
ejpam-4226	186	6	α	α	PROPN
ejpam-4226	187	1	+	+	PROPN
ejpam-4226	187	2	c3	c3	PROPN
ejpam-4226	187	3	exp	exp	NOUN
ejpam-4226	187	4	1	1	NUM
ejpam-4226	187	5	α	α	NOUN
ejpam-4226	187	6	tα	tα	VERB
ejpam-4226	187	7	using	use	VERB
ejpam-4226	187	8	conditions	condition	NOUN
ejpam-4226	187	9	in	in	ADP
ejpam-4226	187	10	(	(	PUNCT
ejpam-4226	187	11	∗∗	∗∗	X
ejpam-4226	187	12	)	)	PUNCT
ejpam-4226	187	13	we	we	PRON
ejpam-4226	187	14	get	get	VERB
ejpam-4226	187	15	v(t	v(t	NOUN
ejpam-4226	187	16	)	)	PUNCT
ejpam-4226	187	17	=	=	SYM
ejpam-4226	187	18	exp	exp	NOUN
ejpam-4226	187	19	1	1	NUM
ejpam-4226	187	20	α	α	NOUN
ejpam-4226	187	21	tα	tα	PROPN
ejpam-4226	187	22	for	for	ADP
ejpam-4226	187	23	v(α	v(α	PROPN
ejpam-4226	187	24	)	)	PUNCT
ejpam-4226	187	25	=	=	SYM
ejpam-4226	187	26	v	v	NOUN
ejpam-4226	187	27	,	,	PUNCT
ejpam-4226	187	28	the	the	DET
ejpam-4226	187	29	associated	associated	ADJ
ejpam-4226	187	30	characteristic	characteristic	ADJ
ejpam-4226	187	31	equation	equation	NOUN
ejpam-4226	187	32	is	be	AUX
ejpam-4226	187	33	r−	r−	PROPN
ejpam-4226	187	34	1	1	NUM
ejpam-4226	187	35	=	=	SYM
ejpam-4226	187	36	0	0	NUM
ejpam-4226	187	37	.	.	PUNCT
ejpam-4226	188	1	hence	hence	ADV
ejpam-4226	188	2	using	use	VERB
ejpam-4226	188	3	[	[	X
ejpam-4226	188	4	6	6	NUM
ejpam-4226	188	5	]	]	PUNCT
ejpam-4226	188	6	,	,	PUNCT
ejpam-4226	188	7	we	we	PRON
ejpam-4226	188	8	get	get	VERB
ejpam-4226	188	9	v(t	v(t	VERB
ejpam-4226	188	10	)	)	PUNCT
ejpam-4226	188	11	=	=	PUNCT
ejpam-4226	189	1	c	c	NOUN
ejpam-4226	189	2	exp	exp	NOUN
ejpam-4226	189	3	1	1	NUM
ejpam-4226	189	4	α	α	NOUN
ejpam-4226	189	5	tα	tα	VERB
ejpam-4226	189	6	using	use	VERB
ejpam-4226	189	7	conditions	condition	NOUN
ejpam-4226	189	8	in	in	ADP
ejpam-4226	189	9	(	(	PUNCT
ejpam-4226	189	10	∗∗	∗∗	X
ejpam-4226	189	11	)	)	PUNCT
ejpam-4226	189	12	we	we	PRON
ejpam-4226	189	13	get	get	VERB
ejpam-4226	189	14	v(t	v(t	NOUN
ejpam-4226	189	15	)	)	PUNCT
ejpam-4226	189	16	=	=	SYM
ejpam-4226	189	17	exp	exp	NOUN
ejpam-4226	189	18	1	1	NUM
ejpam-4226	189	19	α	α	NOUN
ejpam-4226	189	20	tα	tα	PROPN
ejpam-4226	189	21	f.	f.	PROPN
ejpam-4226	189	22	bekraoui	bekraoui	PROPN
ejpam-4226	189	23	,	,	PUNCT
ejpam-4226	189	24	m.	m.	PROPN
ejpam-4226	189	25	al	al	PROPN
ejpam-4226	189	26	horani	horani	PROPN
ejpam-4226	189	27	,	,	PUNCT
ejpam-4226	189	28	r.	r.	PROPN
ejpam-4226	189	29	khalil	khalil	PROPN
ejpam-4226	189	30	/	/	SYM
ejpam-4226	189	31	eur	eur	PROPN
ejpam-4226	189	32	.	.	PUNCT
ejpam-4226	190	1	j.	j.	PROPN
ejpam-4226	190	2	pure	pure	PROPN
ejpam-4226	190	3	appl	appl	PROPN
ejpam-4226	190	4	.	.	PROPN
ejpam-4226	190	5	math	math	PROPN
ejpam-4226	190	6	,	,	PUNCT
ejpam-4226	190	7	15	15	NUM
ejpam-4226	190	8	(	(	PUNCT
ejpam-4226	190	9	1	1	NUM
ejpam-4226	190	10	)	)	PUNCT
ejpam-4226	190	11	(	(	PUNCT
ejpam-4226	190	12	2022	2022	NUM
ejpam-4226	190	13	)	)	PUNCT
ejpam-4226	190	14	,	,	PUNCT
ejpam-4226	190	15	106	106	NUM
ejpam-4226	190	16	-	-	SYM
ejpam-4226	190	17	125	125	NUM
ejpam-4226	190	18	114	114	NUM
ejpam-4226	190	19	similarly	similarly	ADV
ejpam-4226	190	20	for	for	ADP
ejpam-4226	190	21	v(3α	v(3α	NOUN
ejpam-4226	190	22	)	)	PUNCT
ejpam-4226	190	23	=	=	SYM
ejpam-4226	191	1	v	v	NOUN
ejpam-4226	191	2	so	so	ADV
ejpam-4226	191	3			PUNCT
ejpam-4226	191	4	x+ax	x+ax	VERB
ejpam-4226	192	1	=	=	SYM
ejpam-4226	192	2	y1	y1	NOUN
ejpam-4226	192	3	and	and	CCONJ
ejpam-4226	192	4	bx+	bx+	NOUN
ejpam-4226	192	5	cx	cx	PROPN
ejpam-4226	193	1	=	=	PUNCT
ejpam-4226	193	2	y2	y2	PROPN
ejpam-4226	193	3	hence	hence	ADV
ejpam-4226	193	4			PUNCT
ejpam-4226	193	5	(	(	PUNCT
ejpam-4226	193	6	i	i	PRON
ejpam-4226	193	7	+	+	NOUN
ejpam-4226	193	8	a)x	a)x	X
ejpam-4226	193	9	=	=	SYM
ejpam-4226	193	10	y1	y1	INTJ
ejpam-4226	193	11	and	and	CCONJ
ejpam-4226	193	12	(	(	PUNCT
ejpam-4226	193	13	b	b	NOUN
ejpam-4226	193	14	+	+	X
ejpam-4226	193	15	c)x	c)x	X
ejpam-4226	194	1	=	=	SYM
ejpam-4226	194	2	y2	y2	INTJ
ejpam-4226	194	3	now	now	ADV
ejpam-4226	194	4	we	we	PRON
ejpam-4226	194	5	go	go	VERB
ejpam-4226	194	6	to	to	ADP
ejpam-4226	194	7	our	our	PRON
ejpam-4226	194	8	equation	equation	NOUN
ejpam-4226	194	9	exp	exp	NOUN
ejpam-4226	194	10	1	1	NUM
ejpam-4226	194	11	α	α	NOUN
ejpam-4226	194	12	tα	tα	PROPN
ejpam-4226	195	1	⊗	⊗	PROPN
ejpam-4226	196	1	[	[	X
ejpam-4226	196	2	x+ax+bx+	x+ax+bx+	X
ejpam-4226	196	3	cx	cx	X
ejpam-4226	196	4	]	]	X
ejpam-4226	196	5	=	=	PUNCT
ejpam-4226	196	6	f(t)⊗	f(t)⊗	PROPN
ejpam-4226	196	7	z	z	NOUN
ejpam-4226	197	1	so	so	ADV
ejpam-4226	197	2	,	,	PUNCT
ejpam-4226	197	3	f	f	PROPN
ejpam-4226	197	4	must	must	AUX
ejpam-4226	197	5	be	be	AUX
ejpam-4226	197	6	equal	equal	ADJ
ejpam-4226	197	7	to	to	ADP
ejpam-4226	197	8	exp	exp	NOUN
ejpam-4226	197	9	1	1	NUM
ejpam-4226	197	10	α	α	NOUN
ejpam-4226	197	11	t	t	NOUN
ejpam-4226	197	12	α	α	NOUN
ejpam-4226	197	13	for	for	ADP
ejpam-4226	197	14	the	the	DET
ejpam-4226	197	15	atomic	atomic	ADJ
ejpam-4226	197	16	solution	solution	NOUN
ejpam-4226	197	17	to	to	PART
ejpam-4226	197	18	exist	exist	VERB
ejpam-4226	197	19	and	and	CCONJ
ejpam-4226	197	20	the	the	DET
ejpam-4226	197	21	image	image	NOUN
ejpam-4226	197	22	of	of	ADP
ejpam-4226	197	23	x	x	PUNCT
ejpam-4226	197	24	under	under	ADP
ejpam-4226	197	25	[	[	X
ejpam-4226	197	26	i	i	PRON
ejpam-4226	197	27	+	+	PROPN
ejpam-4226	197	28	a+b	a+b	NUM
ejpam-4226	197	29	+	+	CCONJ
ejpam-4226	197	30	c]x	c]x	NOUN
ejpam-4226	197	31	=	=	SYM
ejpam-4226	197	32	z.	z.	PROPN
ejpam-4226	197	33	situation	situation	NOUN
ejpam-4226	197	34	2	2	NUM
ejpam-4226	197	35	.	.	NUM
ejpam-4226	197	36			PUNCT
ejpam-4226	197	37	v(3α	v(3α	NOUN
ejpam-4226	197	38	)	)	PUNCT
ejpam-4226	197	39	=	=	SYM
ejpam-4226	197	40	v(2α	v(2α	X
ejpam-4226	197	41	)	)	PUNCT
ejpam-4226	197	42	=	=	SYM
ejpam-4226	197	43	v1(t	v1(t	X
ejpam-4226	197	44	)	)	PUNCT
ejpam-4226	197	45	and	and	CCONJ
ejpam-4226	197	46	bx	bx	X
ejpam-4226	197	47	=	=	SYM
ejpam-4226	197	48	cx	cx	PROPN
ejpam-4226	198	1	=	=	PUNCT
ejpam-4226	198	2	y2	y2	PROPN
ejpam-4226	198	3	now	now	ADV
ejpam-4226	198	4	for	for	ADP
ejpam-4226	198	5	v(3α	v(3α	NOUN
ejpam-4226	198	6	)	)	PUNCT
ejpam-4226	198	7	=	=	SYM
ejpam-4226	198	8	v(2α	v(2α	X
ejpam-4226	198	9	)	)	PUNCT
ejpam-4226	198	10	=	=	SYM
ejpam-4226	199	1	v1(t	v1(t	PROPN
ejpam-4226	199	2	)	)	PUNCT
ejpam-4226	200	1	,	,	PUNCT
ejpam-4226	200	2	then	then	ADV
ejpam-4226	200	3	v(t	v(t	NOUN
ejpam-4226	200	4	)	)	PUNCT
ejpam-4226	200	5	=	=	SYM
ejpam-4226	200	6	exp	exp	NOUN
ejpam-4226	200	7	1	1	NUM
ejpam-4226	200	8	α	α	NOUN
ejpam-4226	200	9	tα	tα	PROPN
ejpam-4226	200	10	substitute	substitute	NOUN
ejpam-4226	200	11	in	in	ADP
ejpam-4226	200	12	the	the	DET
ejpam-4226	200	13	main	main	ADJ
ejpam-4226	200	14	equation	equation	NOUN
ejpam-4226	200	15	we	we	PRON
ejpam-4226	200	16	get	get	VERB
ejpam-4226	200	17	exp	exp	NOUN
ejpam-4226	200	18	1	1	NUM
ejpam-4226	200	19	α	α	NOUN
ejpam-4226	200	20	tα	tα	PROPN
ejpam-4226	201	1	⊗	⊗	PROPN
ejpam-4226	202	1	[	[	X
ejpam-4226	202	2	x+ax	x+ax	X
ejpam-4226	202	3	]	]	X
ejpam-4226	202	4	+	+	CCONJ
ejpam-4226	202	5	2	2	NUM
ejpam-4226	202	6	exp	exp	NOUN
ejpam-4226	202	7	1	1	NUM
ejpam-4226	202	8	α	α	NOUN
ejpam-4226	202	9	tα	tα	PROPN
ejpam-4226	202	10	⊗bx	⊗bx	NOUN
ejpam-4226	202	11	=	=	SYM
ejpam-4226	202	12	f(t)⊗	f(t)⊗	PROPN
ejpam-4226	202	13	z	z	NOUN
ejpam-4226	202	14	exp	exp	NOUN
ejpam-4226	202	15	1	1	NUM
ejpam-4226	202	16	α	α	NOUN
ejpam-4226	202	17	tα	tα	VERB
ejpam-4226	202	18	⊗	⊗	PROPN
ejpam-4226	203	1	[	[	X
ejpam-4226	203	2	x+ax+	x+ax+	ADJ
ejpam-4226	203	3	2bx	2bx	ADJ
ejpam-4226	203	4	]	]	X
ejpam-4226	203	5	=	=	SYM
ejpam-4226	203	6	f(t)⊗	f(t)⊗	PROPN
ejpam-4226	203	7	z	z	VERB
ejpam-4226	203	8	then	then	ADV
ejpam-4226	203	9	for	for	SCONJ
ejpam-4226	203	10	the	the	DET
ejpam-4226	203	11	atomic	atomic	ADJ
ejpam-4226	203	12	solution	solution	NOUN
ejpam-4226	203	13	to	to	PART
ejpam-4226	203	14	exist	exist	VERB
ejpam-4226	203	15	,	,	PUNCT
ejpam-4226	203	16	f	f	PROPN
ejpam-4226	203	17	=	=	SYM
ejpam-4226	203	18	exp	exp	NOUN
ejpam-4226	203	19	1	1	NUM
ejpam-4226	203	20	α	α	NOUN
ejpam-4226	203	21	t	t	NOUN
ejpam-4226	203	22	α	α	NOUN
ejpam-4226	203	23	,	,	PUNCT
ejpam-4226	203	24	and	and	CCONJ
ejpam-4226	203	25	[	[	X
ejpam-4226	203	26	i	i	X
ejpam-4226	203	27	+	+	NOUN
ejpam-4226	203	28	a+	a+	X
ejpam-4226	203	29	2b]x	2b]x	NUM
ejpam-4226	203	30	=	=	SYM
ejpam-4226	203	31	z.	z.	PROPN
ejpam-4226	203	32	situation	situation	NOUN
ejpam-4226	203	33	3	3	NUM
ejpam-4226	203	34	.	.	PUNCT
ejpam-4226	204	1			PUNCT
ejpam-4226	204	2	x	x	X
ejpam-4226	204	3	=	=	PUNCT
ejpam-4226	204	4	ax	ax	NOUN
ejpam-4226	204	5	=	=	SYM
ejpam-4226	204	6	y1	y1	NOUN
ejpam-4226	204	7	and	and	CCONJ
ejpam-4226	204	8	v(α	v(α	PROPN
ejpam-4226	204	9	)	)	PUNCT
ejpam-4226	204	10	=	=	SYM
ejpam-4226	204	11	v	v	NOUN
ejpam-4226	204	12	=	=	SYM
ejpam-4226	204	13	v2	v2	PROPN
ejpam-4226	204	14	now	now	ADV
ejpam-4226	204	15	,	,	PUNCT
ejpam-4226	204	16	v(α	v(α	PROPN
ejpam-4226	204	17	)	)	PUNCT
ejpam-4226	204	18	=	=	SYM
ejpam-4226	204	19	v	v	NOUN
ejpam-4226	204	20	gives	give	VERB
ejpam-4226	204	21	v(t	v(t	NOUN
ejpam-4226	204	22	)	)	PUNCT
ejpam-4226	204	23	=	=	SYM
ejpam-4226	204	24	exp	exp	NOUN
ejpam-4226	204	25	1	1	NUM
ejpam-4226	204	26	α	α	NOUN
ejpam-4226	204	27	tα	tα	VERB
ejpam-4226	204	28	so	so	ADV
ejpam-4226	204	29	exp	exp	NOUN
ejpam-4226	204	30	1	1	NUM
ejpam-4226	204	31	α	α	NOUN
ejpam-4226	204	32	tα	tα	PROPN
ejpam-4226	205	1	⊗	⊗	PROPN
ejpam-4226	206	1	[	[	X
ejpam-4226	206	2	x+ax+bx+	x+ax+bx+	X
ejpam-4226	206	3	cx	cx	X
ejpam-4226	206	4	]	]	X
ejpam-4226	206	5	=	=	SYM
ejpam-4226	206	6	f(t)⊗	f(t)⊗	PROPN
ejpam-4226	206	7	z	z	NOUN
ejpam-4226	206	8	exp	exp	NOUN
ejpam-4226	206	9	1	1	NUM
ejpam-4226	206	10	α	α	NOUN
ejpam-4226	206	11	tα	tα	VERB
ejpam-4226	206	12	⊗	⊗	PROPN
ejpam-4226	207	1	[	[	X
ejpam-4226	207	2	2ax+bx+	2ax+bx+	NUM
ejpam-4226	207	3	cx	cx	NOUN
ejpam-4226	207	4	]	]	X
ejpam-4226	207	5	=	=	SYM
ejpam-4226	207	6	f(t)⊗	f(t)⊗	PROPN
ejpam-4226	207	7	z	z	PROPN
ejpam-4226	207	8	f.	f.	PROPN
ejpam-4226	207	9	bekraoui	bekraoui	PROPN
ejpam-4226	207	10	,	,	PUNCT
ejpam-4226	207	11	m.	m.	PROPN
ejpam-4226	207	12	al	al	PROPN
ejpam-4226	207	13	horani	horani	PROPN
ejpam-4226	207	14	,	,	PUNCT
ejpam-4226	207	15	r.	r.	PROPN
ejpam-4226	207	16	khalil	khalil	PROPN
ejpam-4226	207	17	/	/	SYM
ejpam-4226	207	18	eur	eur	PROPN
ejpam-4226	207	19	.	.	PUNCT
ejpam-4226	208	1	j.	j.	PROPN
ejpam-4226	208	2	pure	pure	PROPN
ejpam-4226	208	3	appl	appl	PROPN
ejpam-4226	208	4	.	.	PROPN
ejpam-4226	208	5	math	math	PROPN
ejpam-4226	208	6	,	,	PUNCT
ejpam-4226	208	7	15	15	NUM
ejpam-4226	208	8	(	(	PUNCT
ejpam-4226	208	9	1	1	NUM
ejpam-4226	208	10	)	)	PUNCT
ejpam-4226	208	11	(	(	PUNCT
ejpam-4226	208	12	2022	2022	NUM
ejpam-4226	208	13	)	)	PUNCT
ejpam-4226	208	14	,	,	PUNCT
ejpam-4226	208	15	106	106	NUM
ejpam-4226	208	16	-	-	SYM
ejpam-4226	208	17	125	125	NUM
ejpam-4226	208	18	115	115	NUM
ejpam-4226	208	19	hence	hence	ADV
ejpam-4226	208	20	f	f	PROPN
ejpam-4226	208	21	must	must	AUX
ejpam-4226	208	22	equal	equal	VERB
ejpam-4226	208	23	exp	exp	NOUN
ejpam-4226	208	24	1	1	NUM
ejpam-4226	208	25	α	α	NOUN
ejpam-4226	208	26	t	t	NOUN
ejpam-4226	208	27	α	α	NOUN
ejpam-4226	208	28	and	and	CCONJ
ejpam-4226	209	1	[	[	X
ejpam-4226	209	2	2a+b	2a+b	NUM
ejpam-4226	209	3	+	+	CCONJ
ejpam-4226	209	4	c]x	c]x	NOUN
ejpam-4226	209	5	=	=	SYM
ejpam-4226	209	6	z.	z.	PROPN
ejpam-4226	209	7	situation	situation	NOUN
ejpam-4226	209	8	4	4	NUM
ejpam-4226	209	9	.	.	PUNCT
ejpam-4226	210	1			PUNCT
ejpam-4226	210	2	x	x	X
ejpam-4226	210	3	=	=	PUNCT
ejpam-4226	210	4	ax	ax	NOUN
ejpam-4226	210	5	=	=	PUNCT
ejpam-4226	210	6	y1	y1	PROPN
ejpam-4226	210	7	and	and	CCONJ
ejpam-4226	210	8	bx	bx	NOUN
ejpam-4226	210	9	=	=	SYM
ejpam-4226	210	10	cx	cx	PROPN
ejpam-4226	211	1	=	=	PUNCT
ejpam-4226	211	2	y2	y2	INTJ
ejpam-4226	212	1	so	so	ADV
ejpam-4226	212	2	[	[	PUNCT
ejpam-4226	212	3	v(3α	v(3α	NOUN
ejpam-4226	212	4	)	)	PUNCT
ejpam-4226	212	5	+	+	NOUN
ejpam-4226	212	6	v(2α	v(2α	NOUN
ejpam-4226	212	7	)	)	PUNCT
ejpam-4226	212	8	]	]	PUNCT
ejpam-4226	213	1	⊗	⊗	ADJ
ejpam-4226	213	2	x+	x+	PUNCT
ejpam-4226	213	3	[	[	PUNCT
ejpam-4226	213	4	v(α	v(α	PROPN
ejpam-4226	213	5	)	)	PUNCT
ejpam-4226	213	6	+	+	NUM
ejpam-4226	213	7	v	v	X
ejpam-4226	213	8	]	]	PUNCT
ejpam-4226	213	9	⊗bx	⊗bx	NOUN
ejpam-4226	213	10	=	=	SYM
ejpam-4226	213	11	f	f	PROPN
ejpam-4226	213	12	⊗	⊗	PROPN
ejpam-4226	213	13	z.	z.	PROPN
ejpam-4226	213	14	hence	hence	ADV
ejpam-4226	213	15	we	we	PRON
ejpam-4226	213	16	have	have	VERB
ejpam-4226	213	17	two	two	NUM
ejpam-4226	213	18	subcases	subcase	NOUN
ejpam-4226	213	19	:	:	PUNCT
ejpam-4226	213	20	1.v(3α	1.v(3α	NUM
ejpam-4226	213	21	)	)	PUNCT
ejpam-4226	214	1	+	+	NUM
ejpam-4226	215	1	v(2α	v(2α	X
ejpam-4226	215	2	)	)	PUNCT
ejpam-4226	215	3	=	=	SYM
ejpam-4226	215	4	v(α	v(α	PROPN
ejpam-4226	215	5	)	)	PUNCT
ejpam-4226	216	1	+	+	CCONJ
ejpam-4226	216	2	v	v	NOUN
ejpam-4226	216	3	or	or	CCONJ
ejpam-4226	216	4	2	2	NUM
ejpam-4226	216	5	.	.	X
ejpam-4226	216	6	bx	bx	NOUN
ejpam-4226	216	7	=	=	PUNCT
ejpam-4226	217	1	x.	x.	NOUN
ejpam-4226	217	2	if	if	SCONJ
ejpam-4226	217	3	bx	bx	X
ejpam-4226	217	4	=	=	SYM
ejpam-4226	217	5	x	x	NOUN
ejpam-4226	217	6	,	,	PUNCT
ejpam-4226	217	7	then	then	ADV
ejpam-4226	217	8	[	[	PUNCT
ejpam-4226	217	9	v(3α	v(3α	NOUN
ejpam-4226	217	10	)	)	PUNCT
ejpam-4226	217	11	+	+	NUM
ejpam-4226	217	12	v(2α	v(2α	NOUN
ejpam-4226	217	13	)	)	PUNCT
ejpam-4226	217	14	+	+	CCONJ
ejpam-4226	217	15	v(α	v(α	NOUN
ejpam-4226	217	16	)	)	PUNCT
ejpam-4226	218	1	+	+	X
ejpam-4226	218	2	v	v	ADP
ejpam-4226	218	3	]	]	PUNCT
ejpam-4226	218	4	⊗	⊗	PROPN
ejpam-4226	218	5	x	x	X
ejpam-4226	219	1	=	=	SYM
ejpam-4226	219	2	f	f	PROPN
ejpam-4226	219	3	⊗	⊗	PROPN
ejpam-4226	219	4	z.	z.	PROPN
ejpam-4226	219	5	hence	hence	ADV
ejpam-4226	219	6	x	x	X
ejpam-4226	220	1	=	=	PUNCT
ejpam-4226	220	2	z.	z.	PROPN
ejpam-4226	221	1	now	now	ADV
ejpam-4226	221	2	we	we	PRON
ejpam-4226	221	3	solve	solve	VERB
ejpam-4226	221	4	v(3α	v(3α	NOUN
ejpam-4226	221	5	)	)	PUNCT
ejpam-4226	221	6	+	+	NUM
ejpam-4226	221	7	v(2α	v(2α	NOUN
ejpam-4226	221	8	)	)	PUNCT
ejpam-4226	221	9	+	+	CCONJ
ejpam-4226	221	10	v(α	v(α	NOUN
ejpam-4226	221	11	)	)	PUNCT
ejpam-4226	222	1	+	+	NUM
ejpam-4226	222	2	v	v	X
ejpam-4226	222	3	=	=	PUNCT
ejpam-4226	222	4	f.	f.	NOUN
ejpam-4226	222	5	this	this	PRON
ejpam-4226	222	6	is	be	AUX
ejpam-4226	222	7	a	a	DET
ejpam-4226	222	8	linear	linear	ADJ
ejpam-4226	222	9	fractional	fractional	ADJ
ejpam-4226	222	10	differential	differential	ADJ
ejpam-4226	222	11	equation	equation	NOUN
ejpam-4226	222	12	of	of	ADP
ejpam-4226	222	13	order	order	NOUN
ejpam-4226	222	14	3α	3α	NOUN
ejpam-4226	222	15	.	.	PUNCT
ejpam-4226	223	1	using	use	VERB
ejpam-4226	223	2	[	[	X
ejpam-4226	223	3	12	12	NUM
ejpam-4226	223	4	]	]	PUNCT
ejpam-4226	223	5	,	,	PUNCT
ejpam-4226	223	6	we	we	PRON
ejpam-4226	223	7	get	get	VERB
ejpam-4226	223	8	the	the	DET
ejpam-4226	223	9	general	general	ADJ
ejpam-4226	223	10	solution	solution	NOUN
ejpam-4226	223	11	vg	vg	ADP
ejpam-4226	223	12	=	=	SYM
ejpam-4226	223	13	vh+vp	vh+vp	PROPN
ejpam-4226	223	14	,	,	PUNCT
ejpam-4226	223	15	the	the	DET
ejpam-4226	223	16	sum	sum	NOUN
ejpam-4226	223	17	of	of	ADP
ejpam-4226	223	18	the	the	DET
ejpam-4226	223	19	homogenous	homogenous	ADJ
ejpam-4226	223	20	solution	solution	NOUN
ejpam-4226	223	21	and	and	CCONJ
ejpam-4226	223	22	the	the	DET
ejpam-4226	223	23	particular	particular	ADJ
ejpam-4226	223	24	solution	solution	NOUN
ejpam-4226	223	25	.	.	PUNCT
ejpam-4226	224	1	for	for	ADP
ejpam-4226	224	2	homogenous	homogenous	ADJ
ejpam-4226	224	3	solution	solution	NOUN
ejpam-4226	224	4	vh	vh	PROPN
ejpam-4226	224	5	,	,	PUNCT
ejpam-4226	224	6	the	the	DET
ejpam-4226	224	7	associated	associated	ADJ
ejpam-4226	224	8	characteristic	characteristic	ADJ
ejpam-4226	224	9	equation	equation	NOUN
ejpam-4226	224	10	is	be	AUX
ejpam-4226	224	11	r3+r2+r+1	r3+r2+r+1	PROPN
ejpam-4226	224	12	=	=	SYM
ejpam-4226	224	13	0	0	PROPN
ejpam-4226	224	14	,	,	PUNCT
ejpam-4226	224	15	which	which	PRON
ejpam-4226	224	16	has	have	VERB
ejpam-4226	224	17	the	the	DET
ejpam-4226	224	18	roots	root	NOUN
ejpam-4226	224	19	i,−i	i,−i	NOUN
ejpam-4226	224	20	and	and	CCONJ
ejpam-4226	224	21	−1	−1	NOUN
ejpam-4226	224	22	.	.	PUNCT
ejpam-4226	225	1	then	then	ADV
ejpam-4226	225	2	vh(t	vh(t	PUNCT
ejpam-4226	225	3	)	)	PUNCT
ejpam-4226	226	1	=	=	SYM
ejpam-4226	226	2	c1	c1	PROPN
ejpam-4226	226	3	exp	exp	NOUN
ejpam-4226	226	4	(	(	PUNCT
ejpam-4226	226	5	−	−	PROPN
ejpam-4226	226	6	1	1	NUM
ejpam-4226	226	7	α	α	NOUN
ejpam-4226	226	8	tα	tα	PROPN
ejpam-4226	226	9	)	)	PUNCT
ejpam-4226	227	1	+	+	CCONJ
ejpam-4226	227	2	c2	c2	PROPN
ejpam-4226	227	3	cos	cos	PROPN
ejpam-4226	227	4	1	1	NUM
ejpam-4226	227	5	α	α	NOUN
ejpam-4226	227	6	tα	tα	PROPN
ejpam-4226	227	7	+	+	CCONJ
ejpam-4226	227	8	c3	c3	PROPN
ejpam-4226	227	9	sin	sin	NOUN
ejpam-4226	227	10	1	1	NUM
ejpam-4226	227	11	α	α	NOUN
ejpam-4226	227	12	tα	tα	PROPN
ejpam-4226	227	13	for	for	ADP
ejpam-4226	227	14	the	the	DET
ejpam-4226	227	15	particular	particular	ADJ
ejpam-4226	227	16	solution	solution	NOUN
ejpam-4226	227	17	,	,	PUNCT
ejpam-4226	227	18	we	we	PRON
ejpam-4226	227	19	use	use	VERB
ejpam-4226	227	20	variation	variation	NOUN
ejpam-4226	227	21	of	of	ADP
ejpam-4226	227	22	parameters	parameter	NOUN
ejpam-4226	227	23	introduced	introduce	VERB
ejpam-4226	227	24	in	in	ADP
ejpam-4226	227	25	[	[	X
ejpam-4226	227	26	12	12	NUM
ejpam-4226	227	27	]	]	PUNCT
ejpam-4226	227	28	.	.	PUNCT
ejpam-4226	228	1	let	let	VERB
ejpam-4226	228	2	u1	u1	NOUN
ejpam-4226	228	3	=	=	PUNCT
ejpam-4226	228	4	exp	exp	NOUN
ejpam-4226	228	5	(	(	PUNCT
ejpam-4226	228	6	−	−	PROPN
ejpam-4226	228	7	1	1	NUM
ejpam-4226	228	8	α	α	NOUN
ejpam-4226	228	9	t	t	NOUN
ejpam-4226	228	10	α	α	NOUN
ejpam-4226	228	11	)	)	PUNCT
ejpam-4226	228	12	,	,	PUNCT
ejpam-4226	228	13	u2	u2	PROPN
ejpam-4226	228	14	=	=	SYM
ejpam-4226	228	15	cos	cos	PROPN
ejpam-4226	228	16	1	1	NUM
ejpam-4226	228	17	α	α	NOUN
ejpam-4226	228	18	t	t	NOUN
ejpam-4226	228	19	α	α	NOUN
ejpam-4226	228	20	and	and	CCONJ
ejpam-4226	228	21	u3	u3	NOUN
ejpam-4226	228	22	=	=	SYM
ejpam-4226	228	23	sin	sin	NOUN
ejpam-4226	228	24	1	1	NUM
ejpam-4226	228	25	α	α	NOUN
ejpam-4226	228	26	t	t	NOUN
ejpam-4226	228	27	α	α	NOUN
ejpam-4226	228	28	so	so	ADV
ejpam-4226	228	29	vp(t	vp(t	PUNCT
ejpam-4226	228	30	)	)	PUNCT
ejpam-4226	228	31	=	=	SYM
ejpam-4226	228	32	3∑	3∑	NUM
ejpam-4226	228	33	m=1	m=1	X
ejpam-4226	228	34	um(t	um(t	NUM
ejpam-4226	228	35	)	)	PUNCT
ejpam-4226	229	1	∫	∫	PROPN
ejpam-4226	229	2	t	t	PROPN
ejpam-4226	229	3	a	a	DET
ejpam-4226	229	4	f(s)wα	f(s)wα	PROPN
ejpam-4226	229	5	m(s	m(s	PROPN
ejpam-4226	229	6	)	)	PUNCT
ejpam-4226	229	7	wα(s)s1−α	wα(s)s1−α	PROPN
ejpam-4226	229	8	ds	ds	NOUN
ejpam-4226	229	9	=	=	PUNCT
ejpam-4226	229	10	exp	exp	NOUN
ejpam-4226	229	11	(	(	PUNCT
ejpam-4226	229	12	−	−	PROPN
ejpam-4226	229	13	1	1	NUM
ejpam-4226	229	14	α	α	NOUN
ejpam-4226	229	15	tα	tα	PROPN
ejpam-4226	229	16	)	)	PUNCT
ejpam-4226	230	1	∫	∫	PROPN
ejpam-4226	230	2	t	t	PROPN
ejpam-4226	230	3	a	a	DET
ejpam-4226	230	4	f(s)wα	f(s)wα	PROPN
ejpam-4226	230	5	1	1	NUM
ejpam-4226	230	6	(	(	PUNCT
ejpam-4226	230	7	s	s	NOUN
ejpam-4226	230	8	)	)	PUNCT
ejpam-4226	230	9	wα(s)s1−α	wα(s)s1−α	PROPN
ejpam-4226	230	10	ds+	ds+	NOUN
ejpam-4226	230	11	cos	cos	PROPN
ejpam-4226	230	12	1	1	NUM
ejpam-4226	230	13	α	α	NOUN
ejpam-4226	230	14	tα	tα	PROPN
ejpam-4226	230	15	∫	∫	PROPN
ejpam-4226	230	16	t	t	PROPN
ejpam-4226	230	17	a	a	DET
ejpam-4226	230	18	f(s)wα	f(s)wα	PROPN
ejpam-4226	230	19	2	2	NUM
ejpam-4226	230	20	(	(	PUNCT
ejpam-4226	230	21	s	s	NOUN
ejpam-4226	230	22	)	)	PUNCT
ejpam-4226	230	23	wα(s)s1−α	wα(s)s1−α	PROPN
ejpam-4226	230	24	ds+	ds+	ADJ
ejpam-4226	230	25	sin	sin	NOUN
ejpam-4226	230	26	1	1	NUM
ejpam-4226	230	27	α	α	NOUN
ejpam-4226	230	28	tα	tα	PROPN
ejpam-4226	230	29	∫	∫	PROPN
ejpam-4226	230	30	t	t	PROPN
ejpam-4226	230	31	a	a	DET
ejpam-4226	230	32	f(s)wα	f(s)wα	PROPN
ejpam-4226	230	33	3	3	NUM
ejpam-4226	230	34	(	(	PUNCT
ejpam-4226	230	35	s	s	NOUN
ejpam-4226	230	36	)	)	PUNCT
ejpam-4226	230	37	wα(s)s1−α	wα(s)s1−α	PUNCT
ejpam-4226	231	1	ds	ds	INTJ
ejpam-4226	231	2	where	where	SCONJ
ejpam-4226	231	3	wα	wα	NOUN
ejpam-4226	231	4	=	=	SYM
ejpam-4226	231	5	∣∣∣∣∣∣∣	∣∣∣∣∣∣∣	PROPN
ejpam-4226	231	6	u1	u1	PROPN
ejpam-4226	231	7	u2	u2	PROPN
ejpam-4226	231	8	u3	u3	PROPN
ejpam-4226	231	9	u	u	PROPN
ejpam-4226	231	10	(	(	PUNCT
ejpam-4226	231	11	α	α	NOUN
ejpam-4226	231	12	)	)	PUNCT
ejpam-4226	231	13	1	1	NUM
ejpam-4226	231	14	u	u	NOUN
ejpam-4226	231	15	(	(	PUNCT
ejpam-4226	231	16	α	α	NOUN
ejpam-4226	231	17	)	)	PUNCT
ejpam-4226	231	18	2	2	NUM
ejpam-4226	231	19	u	u	NOUN
ejpam-4226	231	20	(	(	PUNCT
ejpam-4226	231	21	α	α	NOUN
ejpam-4226	231	22	)	)	PUNCT
ejpam-4226	231	23	3	3	NUM
ejpam-4226	231	24	u	u	NOUN
ejpam-4226	231	25	(	(	PUNCT
ejpam-4226	231	26	2α	2α	NOUN
ejpam-4226	231	27	)	)	PUNCT
ejpam-4226	231	28	1	1	NUM
ejpam-4226	231	29	u	u	NOUN
ejpam-4226	231	30	(	(	PUNCT
ejpam-4226	231	31	2α	2α	NOUN
ejpam-4226	231	32	)	)	PUNCT
ejpam-4226	231	33	2	2	NUM
ejpam-4226	231	34	u	u	NOUN
ejpam-4226	231	35	(	(	PUNCT
ejpam-4226	231	36	2α	2α	NOUN
ejpam-4226	231	37	)	)	PUNCT
ejpam-4226	231	38	3	3	NUM
ejpam-4226	231	39	∣∣∣∣∣∣∣	∣∣∣∣∣∣∣	PROPN
ejpam-4226	231	40	and	and	CCONJ
ejpam-4226	231	41	wα	wα	NOUN
ejpam-4226	231	42	m	m	NOUN
ejpam-4226	231	43	is	be	AUX
ejpam-4226	231	44	the	the	DET
ejpam-4226	231	45	determinant	determinant	ADJ
ejpam-4226	231	46	obtained	obtain	VERB
ejpam-4226	231	47	from	from	ADP
ejpam-4226	231	48	wα	wα	NOUN
ejpam-4226	231	49	by	by	ADP
ejpam-4226	231	50	replacing	replace	VERB
ejpam-4226	231	51	mth	mth	NOUN
ejpam-4226	231	52	column	column	NOUN
ejpam-4226	231	53	by	by	ADP
ejpam-4226	231	54	the	the	DET
ejpam-4226	231	55	column	column	NOUN
ejpam-4226	231	56	(	(	PUNCT
ejpam-4226	231	57	0	0	NUM
ejpam-4226	231	58	,	,	PUNCT
ejpam-4226	231	59	0	0	NUM
ejpam-4226	231	60	,	,	PUNCT
ejpam-4226	231	61	1	1	NUM
ejpam-4226	231	62	)	)	PUNCT
ejpam-4226	231	63	,	,	PUNCT
ejpam-4226	231	64	m	m	VERB
ejpam-4226	231	65	=	=	NOUN
ejpam-4226	231	66	1	1	NUM
ejpam-4226	231	67	,	,	PUNCT
ejpam-4226	231	68	2	2	NUM
ejpam-4226	231	69	,	,	PUNCT
ejpam-4226	231	70	3.thus	3.thus	NUM
ejpam-4226	231	71	vp(t	vp(t	NOUN
ejpam-4226	231	72	)	)	PUNCT
ejpam-4226	231	73	=	=	SYM
ejpam-4226	231	74	exp	exp	NOUN
ejpam-4226	231	75	(	(	PUNCT
ejpam-4226	231	76	−	−	PROPN
ejpam-4226	231	77	1	1	NUM
ejpam-4226	231	78	α	α	NOUN
ejpam-4226	231	79	tα	tα	PROPN
ejpam-4226	231	80	)	)	PUNCT
ejpam-4226	231	81	∫	∫	PROPN
ejpam-4226	231	82	t	t	PROPN
ejpam-4226	231	83	a	a	DET
ejpam-4226	231	84	f(s	f(	NOUN
ejpam-4226	231	85	)	)	PUNCT
ejpam-4226	231	86	2	2	NUM
ejpam-4226	231	87	exp	exp	NOUN
ejpam-4226	231	88	(	(	PUNCT
ejpam-4226	231	89	−	−	PROPN
ejpam-4226	231	90	1	1	NUM
ejpam-4226	231	91	αs	αs	PROPN
ejpam-4226	231	92	α	α	NOUN
ejpam-4226	231	93	)	)	PUNCT
ejpam-4226	232	1	s1−α	s1−α	PROPN
ejpam-4226	232	2	ds−	ds−	PROPN
ejpam-4226	232	3	cos	cos	ADP
ejpam-4226	232	4	1	1	NUM
ejpam-4226	232	5	α	α	NOUN
ejpam-4226	232	6	tα	tα	PROPN
ejpam-4226	232	7	∫	∫	PROPN
ejpam-4226	232	8	t	t	PROPN
ejpam-4226	232	9	a	a	DET
ejpam-4226	232	10	f(s	f(	NOUN
ejpam-4226	232	11	)	)	PUNCT
ejpam-4226	232	12	(	(	PUNCT
ejpam-4226	232	13	cos	cos	PROPN
ejpam-4226	232	14	s+	s+	ADV
ejpam-4226	232	15	sin	sin	PROPN
ejpam-4226	232	16	s	s	PROPN
ejpam-4226	232	17	)	)	PUNCT
ejpam-4226	232	18	2s1−α	2s1−α	NUM
ejpam-4226	232	19	ds	ds	PROPN
ejpam-4226	232	20	f.	f.	PROPN
ejpam-4226	232	21	bekraoui	bekraoui	PROPN
ejpam-4226	232	22	,	,	PUNCT
ejpam-4226	232	23	m.	m.	PROPN
ejpam-4226	232	24	al	al	PROPN
ejpam-4226	232	25	horani	horani	PROPN
ejpam-4226	232	26	,	,	PUNCT
ejpam-4226	232	27	r.	r.	PROPN
ejpam-4226	232	28	khalil	khalil	PROPN
ejpam-4226	232	29	/	/	SYM
ejpam-4226	232	30	eur	eur	PROPN
ejpam-4226	232	31	.	.	PUNCT
ejpam-4226	233	1	j.	j.	PROPN
ejpam-4226	233	2	pure	pure	PROPN
ejpam-4226	233	3	appl	appl	PROPN
ejpam-4226	233	4	.	.	PROPN
ejpam-4226	233	5	math	math	PROPN
ejpam-4226	233	6	,	,	PUNCT
ejpam-4226	233	7	15	15	NUM
ejpam-4226	233	8	(	(	PUNCT
ejpam-4226	233	9	1	1	NUM
ejpam-4226	233	10	)	)	PUNCT
ejpam-4226	233	11	(	(	PUNCT
ejpam-4226	233	12	2022	2022	NUM
ejpam-4226	233	13	)	)	PUNCT
ejpam-4226	233	14	,	,	PUNCT
ejpam-4226	233	15	106	106	NUM
ejpam-4226	233	16	-	-	SYM
ejpam-4226	233	17	125	125	NUM
ejpam-4226	233	18	116	116	NUM
ejpam-4226	233	19	+	+	NOUN
ejpam-4226	233	20	sin	sin	NOUN
ejpam-4226	233	21	1	1	NUM
ejpam-4226	233	22	α	α	NOUN
ejpam-4226	233	23	tα	tα	PROPN
ejpam-4226	233	24	∫	∫	PROPN
ejpam-4226	233	25	t	t	PROPN
ejpam-4226	233	26	a	a	DET
ejpam-4226	233	27	f(s	f(	NOUN
ejpam-4226	233	28	)	)	PUNCT
ejpam-4226	233	29	(	(	PUNCT
ejpam-4226	233	30	cos	cos	PROPN
ejpam-4226	233	31	s−	s−	PROPN
ejpam-4226	233	32	sin	sin	VERB
ejpam-4226	233	33	s	s	NOUN
ejpam-4226	233	34	)	)	PUNCT
ejpam-4226	233	35	2s1−α	2s1−α	NUM
ejpam-4226	233	36	ds	ds	ADJ
ejpam-4226	233	37	=	=	PUNCT
ejpam-4226	233	38	exp	exp	NOUN
ejpam-4226	233	39	(	(	PUNCT
ejpam-4226	233	40	−	−	PROPN
ejpam-4226	233	41	1	1	NUM
ejpam-4226	233	42	α	α	NOUN
ejpam-4226	233	43	tα	tα	PROPN
ejpam-4226	233	44	)	)	PUNCT
ejpam-4226	233	45	iaα	iaα	PROPN
ejpam-4226	233	46	(	(	PUNCT
ejpam-4226	233	47	f(t	f(t	PROPN
ejpam-4226	233	48	)	)	PUNCT
ejpam-4226	233	49	2	2	NUM
ejpam-4226	233	50	exp	exp	NOUN
ejpam-4226	233	51	(	(	PUNCT
ejpam-4226	233	52	−	−	PROPN
ejpam-4226	233	53	1	1	NUM
ejpam-4226	233	54	α	α	NOUN
ejpam-4226	233	55	t	t	NOUN
ejpam-4226	233	56	α	α	NOUN
ejpam-4226	233	57	)	)	PUNCT
ejpam-4226	233	58	)	)	PUNCT
ejpam-4226	233	59	−	−	PROPN
ejpam-4226	234	1	cos	cos	PROPN
ejpam-4226	234	2	1	1	NUM
ejpam-4226	234	3	α	α	NOUN
ejpam-4226	234	4	tαiaα	tαiaα	NOUN
ejpam-4226	234	5	(	(	PUNCT
ejpam-4226	234	6	f(t	f(t	PROPN
ejpam-4226	234	7	)	)	PUNCT
ejpam-4226	234	8	(	(	PUNCT
ejpam-4226	234	9	cos	cos	X
ejpam-4226	234	10	t+	t+	PROPN
ejpam-4226	234	11	sin	sin	NOUN
ejpam-4226	234	12	t	t	PROPN
ejpam-4226	234	13	)	)	PUNCT
ejpam-4226	234	14	2	2	NUM
ejpam-4226	234	15	)	)	PUNCT
ejpam-4226	235	1	+	+	VERB
ejpam-4226	235	2	sin	sin	NOUN
ejpam-4226	235	3	1	1	NUM
ejpam-4226	235	4	α	α	NOUN
ejpam-4226	235	5	tαiaα	tαiaα	NOUN
ejpam-4226	235	6	(	(	PUNCT
ejpam-4226	235	7	f(t	f(t	PROPN
ejpam-4226	235	8	)	)	PUNCT
ejpam-4226	235	9	(	(	PUNCT
ejpam-4226	235	10	cos	cos	PROPN
ejpam-4226	235	11	s−	s−	PROPN
ejpam-4226	235	12	sin	sin	VERB
ejpam-4226	235	13	t	t	PROPN
ejpam-4226	235	14	)	)	PUNCT
ejpam-4226	235	15	2	2	NUM
ejpam-4226	235	16	)	)	PUNCT
ejpam-4226	235	17	hence	hence	ADV
ejpam-4226	235	18	v(t	v(t	NOUN
ejpam-4226	235	19	)	)	PUNCT
ejpam-4226	235	20	=	=	PUNCT
ejpam-4226	235	21	vh(t	vh(t	X
ejpam-4226	235	22	)	)	PUNCT
ejpam-4226	235	23	+	+	CCONJ
ejpam-4226	235	24	vp(t	vp(t	X
ejpam-4226	235	25	)	)	PUNCT
ejpam-4226	235	26	=	=	SYM
ejpam-4226	235	27	c1	c1	PROPN
ejpam-4226	235	28	exp	exp	NOUN
ejpam-4226	235	29	(	(	PUNCT
ejpam-4226	235	30	−	−	PROPN
ejpam-4226	235	31	1	1	NUM
ejpam-4226	235	32	α	α	NOUN
ejpam-4226	235	33	tα	tα	PROPN
ejpam-4226	235	34	)	)	PUNCT
ejpam-4226	236	1	+	+	CCONJ
ejpam-4226	236	2	c2	c2	PROPN
ejpam-4226	236	3	cos	cos	PROPN
ejpam-4226	236	4	1	1	NUM
ejpam-4226	236	5	α	α	NOUN
ejpam-4226	236	6	tα	tα	PROPN
ejpam-4226	236	7	+	+	CCONJ
ejpam-4226	236	8	c3	c3	PROPN
ejpam-4226	236	9	sin	sin	NOUN
ejpam-4226	236	10	1	1	NUM
ejpam-4226	236	11	α	α	NOUN
ejpam-4226	236	12	tα	tα	VERB
ejpam-4226	236	13	+	+	NOUN
ejpam-4226	236	14	exp	exp	NOUN
ejpam-4226	236	15	(	(	PUNCT
ejpam-4226	236	16	−	−	PROPN
ejpam-4226	236	17	1	1	NUM
ejpam-4226	236	18	α	α	NOUN
ejpam-4226	236	19	tα	tα	PROPN
ejpam-4226	236	20	)	)	PUNCT
ejpam-4226	236	21	iaα	iaα	PROPN
ejpam-4226	236	22	(	(	PUNCT
ejpam-4226	236	23	f(t	f(t	PROPN
ejpam-4226	236	24	)	)	PUNCT
ejpam-4226	236	25	2	2	NUM
ejpam-4226	236	26	exp	exp	NOUN
ejpam-4226	236	27	(	(	PUNCT
ejpam-4226	236	28	−	−	PROPN
ejpam-4226	236	29	1	1	NUM
ejpam-4226	236	30	α	α	NOUN
ejpam-4226	236	31	t	t	NOUN
ejpam-4226	236	32	α	α	NOUN
ejpam-4226	236	33	)	)	PUNCT
ejpam-4226	236	34	)	)	PUNCT
ejpam-4226	237	1	−	−	PROPN
ejpam-4226	237	2	cos	cos	PROPN
ejpam-4226	237	3	1	1	NUM
ejpam-4226	237	4	α	α	NOUN
ejpam-4226	237	5	tαiaα	tαiaα	NOUN
ejpam-4226	237	6	(	(	PUNCT
ejpam-4226	237	7	f(t	f(t	PROPN
ejpam-4226	237	8	)	)	PUNCT
ejpam-4226	237	9	(	(	PUNCT
ejpam-4226	237	10	cos	cos	X
ejpam-4226	237	11	t+	t+	PROPN
ejpam-4226	237	12	sin	sin	NOUN
ejpam-4226	237	13	t	t	PROPN
ejpam-4226	237	14	)	)	PUNCT
ejpam-4226	237	15	2	2	NUM
ejpam-4226	237	16	)	)	PUNCT
ejpam-4226	238	1	+	+	VERB
ejpam-4226	238	2	sin	sin	NOUN
ejpam-4226	238	3	1	1	NUM
ejpam-4226	238	4	α	α	NOUN
ejpam-4226	238	5	tαiaα	tαiaα	NOUN
ejpam-4226	238	6	(	(	PUNCT
ejpam-4226	238	7	f(t	f(t	PROPN
ejpam-4226	238	8	)	)	PUNCT
ejpam-4226	238	9	(	(	PUNCT
ejpam-4226	238	10	cos	cos	ADP
ejpam-4226	238	11	t−	t−	PROPN
ejpam-4226	238	12	sin	sin	NOUN
ejpam-4226	238	13	t	t	PROPN
ejpam-4226	238	14	)	)	PUNCT
ejpam-4226	238	15	2	2	NUM
ejpam-4226	238	16	)	)	PUNCT
ejpam-4226	238	17	v(α)(t	v(α)(t	NUM
ejpam-4226	238	18	)	)	PUNCT
ejpam-4226	238	19	=	=	SYM
ejpam-4226	238	20	−c1	−c1	NOUN
ejpam-4226	238	21	exp	exp	NOUN
ejpam-4226	238	22	(	(	PUNCT
ejpam-4226	238	23	−	−	PROPN
ejpam-4226	238	24	1	1	NUM
ejpam-4226	238	25	α	α	NOUN
ejpam-4226	238	26	tα	tα	PROPN
ejpam-4226	238	27	)	)	PUNCT
ejpam-4226	238	28	−	−	PROPN
ejpam-4226	238	29	c2	c2	PROPN
ejpam-4226	238	30	sin	sin	VERB
ejpam-4226	238	31	1	1	NUM
ejpam-4226	238	32	α	α	NOUN
ejpam-4226	238	33	tα	tα	PROPN
ejpam-4226	238	34	+	+	CCONJ
ejpam-4226	238	35	c3	c3	X
ejpam-4226	238	36	cos	cos	PROPN
ejpam-4226	238	37	1	1	NUM
ejpam-4226	238	38	α	α	NOUN
ejpam-4226	238	39	tα	tα	VERB
ejpam-4226	238	40	+	+	NOUN
ejpam-4226	238	41	exp	exp	NOUN
ejpam-4226	238	42	(	(	PUNCT
ejpam-4226	238	43	−	−	PROPN
ejpam-4226	238	44	1	1	NUM
ejpam-4226	238	45	α	α	NOUN
ejpam-4226	238	46	tα	tα	PROPN
ejpam-4226	238	47	)	)	PUNCT
ejpam-4226	238	48	[	[	PUNCT
ejpam-4226	238	49	−iaα	−iaα	PROPN
ejpam-4226	238	50	(	(	PUNCT
ejpam-4226	238	51	f(t	f(t	PROPN
ejpam-4226	238	52	)	)	PUNCT
ejpam-4226	238	53	2	2	NUM
ejpam-4226	238	54	exp	exp	NOUN
ejpam-4226	238	55	(	(	PUNCT
ejpam-4226	238	56	−	−	PROPN
ejpam-4226	238	57	1	1	NUM
ejpam-4226	238	58	α	α	NOUN
ejpam-4226	238	59	t	t	NOUN
ejpam-4226	238	60	α	α	NOUN
ejpam-4226	238	61	)	)	PUNCT
ejpam-4226	238	62	)	)	PUNCT
ejpam-4226	239	1	+	+	CCONJ
ejpam-4226	239	2	f(t	f(t	NOUN
ejpam-4226	239	3	)	)	PUNCT
ejpam-4226	239	4	2	2	NUM
ejpam-4226	239	5	exp	exp	NOUN
ejpam-4226	239	6	(	(	PUNCT
ejpam-4226	239	7	−	−	PROPN
ejpam-4226	239	8	1	1	NUM
ejpam-4226	239	9	α	α	NOUN
ejpam-4226	239	10	t	t	NOUN
ejpam-4226	239	11	α	α	NOUN
ejpam-4226	239	12	)	)	PUNCT
ejpam-4226	239	13	]	]	PUNCT
ejpam-4226	240	1	+	+	PUNCT
ejpam-4226	240	2	sin	sin	NOUN
ejpam-4226	240	3	1	1	NUM
ejpam-4226	240	4	α	α	NOUN
ejpam-4226	240	5	tα	tα	PROPN
ejpam-4226	240	6	[	[	PUNCT
ejpam-4226	240	7	iaα	iaα	NOUN
ejpam-4226	240	8	(	(	PUNCT
ejpam-4226	240	9	f(t	f(t	PROPN
ejpam-4226	240	10	)	)	PUNCT
ejpam-4226	240	11	(	(	PUNCT
ejpam-4226	240	12	cos	cos	X
ejpam-4226	240	13	t+	t+	PROPN
ejpam-4226	240	14	sin	sin	NOUN
ejpam-4226	240	15	t	t	PROPN
ejpam-4226	240	16	)	)	PUNCT
ejpam-4226	240	17	2	2	NUM
ejpam-4226	240	18	)	)	PUNCT
ejpam-4226	240	19	+	+	CCONJ
ejpam-4226	240	20	f(t	f(t	NOUN
ejpam-4226	240	21	)	)	PUNCT
ejpam-4226	240	22	(	(	PUNCT
ejpam-4226	240	23	cos	cos	ADP
ejpam-4226	240	24	t−	t−	PROPN
ejpam-4226	240	25	sin	sin	NOUN
ejpam-4226	240	26	t	t	PROPN
ejpam-4226	240	27	)	)	PUNCT
ejpam-4226	240	28	2	2	NUM
ejpam-4226	240	29	]	]	PUNCT
ejpam-4226	240	30	+	+	ADJ
ejpam-4226	240	31	cos	cos	ADJ
ejpam-4226	240	32	1	1	NUM
ejpam-4226	240	33	α	α	NOUN
ejpam-4226	240	34	tα	tα	PROPN
ejpam-4226	240	35	[	[	PUNCT
ejpam-4226	240	36	iaα	iaα	NOUN
ejpam-4226	240	37	(	(	PUNCT
ejpam-4226	240	38	f(t	f(t	PROPN
ejpam-4226	240	39	)	)	PUNCT
ejpam-4226	240	40	(	(	PUNCT
ejpam-4226	240	41	cos	cos	ADP
ejpam-4226	240	42	t−	t−	PROPN
ejpam-4226	240	43	sin	sin	NOUN
ejpam-4226	240	44	t	t	PROPN
ejpam-4226	240	45	)	)	PUNCT
ejpam-4226	240	46	2	2	NUM
ejpam-4226	240	47	)	)	PUNCT
ejpam-4226	240	48	−	−	PRON
ejpam-4226	240	49	f(t	f(t	NOUN
ejpam-4226	240	50	)	)	PUNCT
ejpam-4226	240	51	(	(	PUNCT
ejpam-4226	240	52	cos	cos	X
ejpam-4226	240	53	t+	t+	PROPN
ejpam-4226	240	54	sin	sin	NOUN
ejpam-4226	240	55	t	t	PROPN
ejpam-4226	240	56	)	)	PUNCT
ejpam-4226	240	57	2	2	NUM
ejpam-4226	240	58	]	]	PUNCT
ejpam-4226	240	59	v(2α)(t	v(2α)(t	X
ejpam-4226	240	60	)	)	PUNCT
ejpam-4226	240	61	=	=	SYM
ejpam-4226	240	62	c1	c1	PROPN
ejpam-4226	240	63	exp	exp	NOUN
ejpam-4226	240	64	(	(	PUNCT
ejpam-4226	240	65	−	−	PROPN
ejpam-4226	240	66	1	1	NUM
ejpam-4226	240	67	α	α	NOUN
ejpam-4226	240	68	tα	tα	PROPN
ejpam-4226	240	69	)	)	PUNCT
ejpam-4226	240	70	−	−	PROPN
ejpam-4226	240	71	c2	c2	PROPN
ejpam-4226	240	72	cos	cos	PROPN
ejpam-4226	240	73	1	1	NUM
ejpam-4226	240	74	α	α	NOUN
ejpam-4226	240	75	tα	tα	PROPN
ejpam-4226	240	76	−	−	PROPN
ejpam-4226	240	77	c3	c3	PROPN
ejpam-4226	240	78	sin	sin	NOUN
ejpam-4226	240	79	1	1	NUM
ejpam-4226	240	80	α	α	NOUN
ejpam-4226	240	81	tα	tα	VERB
ejpam-4226	240	82	+	+	NOUN
ejpam-4226	240	83	exp	exp	NOUN
ejpam-4226	240	84	(	(	PUNCT
ejpam-4226	240	85	−	−	PROPN
ejpam-4226	240	86	1	1	NUM
ejpam-4226	240	87	α	α	NOUN
ejpam-4226	240	88	tα	tα	NOUN
ejpam-4226	240	89	)	)	PUNCT
ejpam-4226	240	90			NOUN
ejpam-4226	240	91	iaα	iaα	NOUN
ejpam-4226	240	92	(	(	PUNCT
ejpam-4226	240	93	f(t	f(t	PROPN
ejpam-4226	240	94	)	)	PUNCT
ejpam-4226	240	95	2	2	NUM
ejpam-4226	240	96	exp(−	exp(−	PROPN
ejpam-4226	240	97	1	1	NUM
ejpam-4226	240	98	α	α	NOUN
ejpam-4226	240	99	tα	tα	PROPN
ejpam-4226	240	100	)	)	PUNCT
ejpam-4226	240	101	)	)	PUNCT
ejpam-4226	241	1	+	+	CCONJ
ejpam-4226	241	2	f	f	X
ejpam-4226	241	3	(	(	PUNCT
ejpam-4226	241	4	α)(t	α)(t	PROPN
ejpam-4226	241	5	)	)	PUNCT
ejpam-4226	241	6	exp(−	exp(−	ADJ
ejpam-4226	241	7	1	1	NUM
ejpam-4226	241	8	α	α	NOUN
ejpam-4226	241	9	tα)+f(t	tα)+f(t	NOUN
ejpam-4226	241	10	)	)	PUNCT
ejpam-4226	241	11	exp(−	exp(−	PROPN
ejpam-4226	241	12	1	1	NUM
ejpam-4226	241	13	α	α	NOUN
ejpam-4226	241	14	tα	tα	PROPN
ejpam-4226	241	15	)	)	PUNCT
ejpam-4226	241	16	2	2	NUM
ejpam-4226	241	17	exp(−	exp(−	PROPN
ejpam-4226	241	18	2	2	NUM
ejpam-4226	241	19	α	α	NOUN
ejpam-4226	241	20	tα	tα	PROPN
ejpam-4226	241	21	)	)	PUNCT
ejpam-4226	241	22			NUM
ejpam-4226	241	23	−	−	NOUN
ejpam-4226	241	24	f(t	f(t	NOUN
ejpam-4226	241	25	)	)	PUNCT
ejpam-4226	242	1	+	+	CCONJ
ejpam-4226	242	2	cos	cos	ADP
ejpam-4226	242	3	1	1	NUM
ejpam-4226	242	4	α	α	NOUN
ejpam-4226	242	5	tα	tα	PROPN
ejpam-4226	242	6			PROPN
ejpam-4226	242	7	iaα	iaα	NOUN
ejpam-4226	242	8	(	(	PUNCT
ejpam-4226	242	9	f(t)(cos	f(t)(cos	PROPN
ejpam-4226	242	10	t+sin	t+sin	X
ejpam-4226	242	11	t	t	PROPN
ejpam-4226	242	12	)	)	PUNCT
ejpam-4226	242	13	2	2	NUM
ejpam-4226	242	14	)	)	PUNCT
ejpam-4226	243	1	+	+	ADJ
ejpam-4226	243	2	f(t)(cos	f(t)(cos	PROPN
ejpam-4226	243	3	t−sin	t−sin	NOUN
ejpam-4226	243	4	t	t	PROPN
ejpam-4226	243	5	)	)	PUNCT
ejpam-4226	243	6	2	2	NUM
ejpam-4226	243	7	−	−	PROPN
ejpam-4226	243	8	f	f	X
ejpam-4226	243	9	(	(	PUNCT
ejpam-4226	243	10	α)(t)(cos	α)(t)(cos	PROPN
ejpam-4226	243	11	t+sin	t+sin	NOUN
ejpam-4226	243	12	t	t	NOUN
ejpam-4226	243	13	)	)	PUNCT
ejpam-4226	243	14	2	2	NUM
ejpam-4226	243	15			NOUN
ejpam-4226	243	16	f.	f.	PROPN
ejpam-4226	243	17	bekraoui	bekraoui	PROPN
ejpam-4226	243	18	,	,	PUNCT
ejpam-4226	243	19	m.	m.	PROPN
ejpam-4226	243	20	al	al	PROPN
ejpam-4226	243	21	horani	horani	PROPN
ejpam-4226	243	22	,	,	PUNCT
ejpam-4226	243	23	r.	r.	PROPN
ejpam-4226	243	24	khalil	khalil	PROPN
ejpam-4226	243	25	/	/	SYM
ejpam-4226	243	26	eur	eur	PROPN
ejpam-4226	243	27	.	.	PUNCT
ejpam-4226	244	1	j.	j.	PROPN
ejpam-4226	244	2	pure	pure	PROPN
ejpam-4226	244	3	appl	appl	PROPN
ejpam-4226	244	4	.	.	PROPN
ejpam-4226	244	5	math	math	PROPN
ejpam-4226	244	6	,	,	PUNCT
ejpam-4226	244	7	15	15	NUM
ejpam-4226	244	8	(	(	PUNCT
ejpam-4226	244	9	1	1	NUM
ejpam-4226	244	10	)	)	PUNCT
ejpam-4226	244	11	(	(	PUNCT
ejpam-4226	244	12	2022	2022	NUM
ejpam-4226	244	13	)	)	PUNCT
ejpam-4226	244	14	,	,	PUNCT
ejpam-4226	244	15	106	106	NUM
ejpam-4226	244	16	-	-	SYM
ejpam-4226	244	17	125	125	NUM
ejpam-4226	244	18	117	117	NUM
ejpam-4226	244	19	−	−	NOUN
ejpam-4226	244	20	sin	sin	NOUN
ejpam-4226	244	21	1	1	NUM
ejpam-4226	244	22	α	α	NOUN
ejpam-4226	244	23	tα	tα	PROPN
ejpam-4226	244	24			PROPN
ejpam-4226	244	25	iaα	iaα	NOUN
ejpam-4226	244	26	(	(	PUNCT
ejpam-4226	244	27	f(t)(cos	f(t)(cos	AUX
ejpam-4226	244	28	t−sin	t−sin	VERB
ejpam-4226	244	29	t	t	PROPN
ejpam-4226	244	30	)	)	PUNCT
ejpam-4226	244	31	2	2	NUM
ejpam-4226	244	32	)	)	PUNCT
ejpam-4226	244	33	−f(t)(cos	−f(t)(co	NOUN
ejpam-4226	244	34	t+sin	t+sin	INTJ
ejpam-4226	245	1	t	t	NOUN
ejpam-4226	245	2	)	)	PUNCT
ejpam-4226	245	3	2	2	NUM
ejpam-4226	246	1	−	−	PROPN
ejpam-4226	246	2	f	f	X
ejpam-4226	246	3	(	(	PUNCT
ejpam-4226	246	4	α)(t)(cos	α)(t)(co	NOUN
ejpam-4226	246	5	t−sin	t−sin	VERB
ejpam-4226	246	6	t	t	NOUN
ejpam-4226	246	7	)	)	PUNCT
ejpam-4226	246	8	2	2	NUM
ejpam-4226	246	9			NOUN
ejpam-4226	246	10	using	use	VERB
ejpam-4226	246	11	conditions	condition	NOUN
ejpam-4226	246	12	in	in	ADP
ejpam-4226	246	13	(	(	PUNCT
ejpam-4226	246	14	∗∗	∗∗	X
ejpam-4226	246	15	)	)	PUNCT
ejpam-4226	246	16	we	we	PRON
ejpam-4226	246	17	get	get	VERB
ejpam-4226	246	18	c1	c1	PROPN
ejpam-4226	246	19	+	+	CCONJ
ejpam-4226	246	20	c2	c2	PROPN
ejpam-4226	246	21	=	=	SYM
ejpam-4226	246	22	1	1	NUM
ejpam-4226	246	23	c3	c3	PROPN
ejpam-4226	246	24	−	−	PROPN
ejpam-4226	246	25	c1	c1	PROPN
ejpam-4226	246	26	=	=	PROPN
ejpam-4226	246	27	1	1	NUM
ejpam-4226	246	28	c1	c1	PROPN
ejpam-4226	246	29	−	−	PROPN
ejpam-4226	246	30	c2	c2	PROPN
ejpam-4226	247	1	+	+	CCONJ
ejpam-4226	247	2	iaα	iaα	PROPN
ejpam-4226	247	3	(	(	PUNCT
ejpam-4226	247	4	f(0	f(0	NOUN
ejpam-4226	247	5	)	)	PUNCT
ejpam-4226	247	6	)	)	PUNCT
ejpam-4226	248	1	=	=	SYM
ejpam-4226	248	2	1	1	NUM
ejpam-4226	248	3	⇔	⇔	PROPN
ejpam-4226	248	4			PROPN
ejpam-4226	248	5	c1	c1	NOUN
ejpam-4226	248	6	=	=	SYM
ejpam-4226	248	7	1−	1−	NUM
ejpam-4226	248	8	1	1	NUM
ejpam-4226	248	9	2i	2i	NOUN
ejpam-4226	248	10	a	a	DET
ejpam-4226	248	11	α	α	PROPN
ejpam-4226	248	12	(	(	PUNCT
ejpam-4226	248	13	f(0	f(0	NOUN
ejpam-4226	248	14	)	)	PUNCT
ejpam-4226	248	15	)	)	PUNCT
ejpam-4226	248	16	c2	c2	PROPN
ejpam-4226	248	17	=	=	SYM
ejpam-4226	248	18	1	1	NUM
ejpam-4226	248	19	2i	2i	NUM
ejpam-4226	248	20	a	a	DET
ejpam-4226	248	21	α	α	PROPN
ejpam-4226	248	22	(	(	PUNCT
ejpam-4226	248	23	f(0	f(0	NOUN
ejpam-4226	248	24	)	)	PUNCT
ejpam-4226	248	25	)	)	PUNCT
ejpam-4226	249	1	c3	c3	NOUN
ejpam-4226	249	2	=	=	PUNCT
ejpam-4226	249	3	2−	2−	NUM
ejpam-4226	249	4	1	1	NUM
ejpam-4226	249	5	2i	2i	NOUN
ejpam-4226	249	6	a	a	DET
ejpam-4226	249	7	α	α	PROPN
ejpam-4226	249	8	(	(	PUNCT
ejpam-4226	249	9	f(0	f(0	NOUN
ejpam-4226	249	10	)	)	PUNCT
ejpam-4226	249	11	)	)	PUNCT
ejpam-4226	249	12	hence	hence	ADV
ejpam-4226	249	13	v(t	v(t	X
ejpam-4226	249	14	)	)	PUNCT
ejpam-4226	249	15	=	=	PUNCT
ejpam-4226	250	1	(	(	PUNCT
ejpam-4226	250	2	1−	1−	NUM
ejpam-4226	250	3	1	1	NUM
ejpam-4226	250	4	2	2	NUM
ejpam-4226	250	5	iaα	iaα	NOUN
ejpam-4226	250	6	(	(	PUNCT
ejpam-4226	250	7	f(0	f(0	NOUN
ejpam-4226	250	8	)	)	PUNCT
ejpam-4226	250	9	)	)	PUNCT
ejpam-4226	250	10	)	)	PUNCT
ejpam-4226	250	11	exp	exp	NOUN
ejpam-4226	250	12	(	(	PUNCT
ejpam-4226	250	13	−	−	PROPN
ejpam-4226	250	14	1	1	NUM
ejpam-4226	250	15	α	α	NOUN
ejpam-4226	250	16	tα	tα	PROPN
ejpam-4226	250	17	)	)	PUNCT
ejpam-4226	251	1	+	+	CCONJ
ejpam-4226	251	2	1	1	NUM
ejpam-4226	251	3	2	2	NUM
ejpam-4226	251	4	iaα	iaα	NOUN
ejpam-4226	251	5	(	(	PUNCT
ejpam-4226	251	6	f(0	f(0	NOUN
ejpam-4226	251	7	)	)	PUNCT
ejpam-4226	251	8	)	)	PUNCT
ejpam-4226	252	1	cos	cos	ADP
ejpam-4226	252	2	1	1	NUM
ejpam-4226	252	3	α	α	NOUN
ejpam-4226	252	4	tα	tα	PROPN
ejpam-4226	252	5	+	+	CCONJ
ejpam-4226	252	6	(	(	PUNCT
ejpam-4226	252	7	2−	2−	NUM
ejpam-4226	252	8	1	1	NUM
ejpam-4226	252	9	2	2	NUM
ejpam-4226	252	10	iaα	iaα	NOUN
ejpam-4226	252	11	(	(	PUNCT
ejpam-4226	252	12	f(0	f(0	NOUN
ejpam-4226	252	13	)	)	PUNCT
ejpam-4226	252	14	)	)	PUNCT
ejpam-4226	252	15	)	)	PUNCT
ejpam-4226	252	16	sin	sin	NOUN
ejpam-4226	252	17	1	1	NUM
ejpam-4226	252	18	α	α	NOUN
ejpam-4226	252	19	tα	tα	PROPN
ejpam-4226	252	20	+	+	CCONJ
ejpam-4226	252	21	exp	exp	NOUN
ejpam-4226	252	22	(	(	PUNCT
ejpam-4226	252	23	−	−	PROPN
ejpam-4226	252	24	1	1	NUM
ejpam-4226	252	25	α	α	NOUN
ejpam-4226	252	26	tα	tα	PROPN
ejpam-4226	252	27	)	)	PUNCT
ejpam-4226	253	1	iaα	iaα	PROPN
ejpam-4226	253	2	(	(	PUNCT
ejpam-4226	253	3	f(t	f(t	PROPN
ejpam-4226	253	4	)	)	PUNCT
ejpam-4226	253	5	2	2	NUM
ejpam-4226	253	6	exp	exp	NOUN
ejpam-4226	253	7	(	(	PUNCT
ejpam-4226	253	8	−	−	PROPN
ejpam-4226	253	9	1	1	NUM
ejpam-4226	253	10	α	α	NOUN
ejpam-4226	253	11	t	t	NOUN
ejpam-4226	253	12	α	α	NOUN
ejpam-4226	253	13	)	)	PUNCT
ejpam-4226	253	14	)	)	PUNCT
ejpam-4226	254	1	−	−	PROPN
ejpam-4226	254	2	cos	cos	PROPN
ejpam-4226	254	3	1	1	NUM
ejpam-4226	254	4	α	α	NOUN
ejpam-4226	254	5	tαiaα	tαiaα	NOUN
ejpam-4226	254	6	(	(	PUNCT
ejpam-4226	254	7	f(t	f(t	PROPN
ejpam-4226	254	8	)	)	PUNCT
ejpam-4226	254	9	(	(	PUNCT
ejpam-4226	254	10	cos	cos	X
ejpam-4226	254	11	t+	t+	PROPN
ejpam-4226	254	12	sin	sin	NOUN
ejpam-4226	254	13	t	t	PROPN
ejpam-4226	254	14	)	)	PUNCT
ejpam-4226	254	15	2	2	NUM
ejpam-4226	254	16	)	)	PUNCT
ejpam-4226	255	1	+	+	VERB
ejpam-4226	255	2	sin	sin	NOUN
ejpam-4226	255	3	1	1	NUM
ejpam-4226	255	4	α	α	NOUN
ejpam-4226	255	5	tαiaα	tαiaα	NOUN
ejpam-4226	255	6	(	(	PUNCT
ejpam-4226	255	7	f(t	f(t	PROPN
ejpam-4226	255	8	)	)	PUNCT
ejpam-4226	255	9	(	(	PUNCT
ejpam-4226	255	10	cos	cos	ADP
ejpam-4226	255	11	t−	t−	PROPN
ejpam-4226	255	12	sin	sin	NOUN
ejpam-4226	255	13	t	t	PROPN
ejpam-4226	255	14	)	)	PUNCT
ejpam-4226	255	15	2	2	NUM
ejpam-4226	255	16	)	)	PUNCT
ejpam-4226	255	17	and	and	CCONJ
ejpam-4226	255	18	the	the	DET
ejpam-4226	255	19	atomic	atomic	ADJ
ejpam-4226	255	20	solution	solution	NOUN
ejpam-4226	255	21	that	that	PRON
ejpam-4226	255	22	satisfies	satisfy	VERB
ejpam-4226	255	23	the	the	DET
ejpam-4226	255	24	conditions	condition	NOUN
ejpam-4226	255	25	is	be	AUX
ejpam-4226	255	26	u(t	u(t	NOUN
ejpam-4226	255	27	)	)	PUNCT
ejpam-4226	256	1	=	=	PUNCT
ejpam-4226	256	2	v(t)⊗	v(t)⊗	VERB
ejpam-4226	256	3	z.	z.	PROPN
ejpam-4226	256	4	now	now	ADV
ejpam-4226	256	5	,	,	PUNCT
ejpam-4226	256	6	if	if	SCONJ
ejpam-4226	256	7	v(3α	v(3α	NOUN
ejpam-4226	256	8	)	)	PUNCT
ejpam-4226	256	9	+	+	NOUN
ejpam-4226	256	10	v(2α	v(2α	X
ejpam-4226	256	11	)	)	PUNCT
ejpam-4226	256	12	=	=	SYM
ejpam-4226	257	1	v(α	v(α	PROPN
ejpam-4226	257	2	)	)	PUNCT
ejpam-4226	257	3	+	+	X
ejpam-4226	257	4	v	v	NOUN
ejpam-4226	257	5	=	=	SYM
ejpam-4226	257	6	f	f	NOUN
ejpam-4226	257	7	,	,	PUNCT
ejpam-4226	257	8	then	then	ADV
ejpam-4226	257	9	(	(	PUNCT
ejpam-4226	257	10	i	i	PRON
ejpam-4226	257	11	+	+	PROPN
ejpam-4226	257	12	b)x	b)x	NOUN
ejpam-4226	257	13	=	=	X
ejpam-4226	258	1	z	z	NOUN
ejpam-4226	258	2	we	we	PRON
ejpam-4226	258	3	want	want	VERB
ejpam-4226	258	4	to	to	PART
ejpam-4226	258	5	solve	solve	VERB
ejpam-4226	258	6	v(3α	v(3α	NOUN
ejpam-4226	258	7	)	)	PUNCT
ejpam-4226	259	1	+	+	NOUN
ejpam-4226	259	2	v(2α	v(2α	X
ejpam-4226	259	3	)	)	PUNCT
ejpam-4226	259	4	=	=	SYM
ejpam-4226	259	5	f	f	PROPN
ejpam-4226	259	6	and	and	CCONJ
ejpam-4226	259	7	v(α	v(α	PROPN
ejpam-4226	259	8	)	)	PUNCT
ejpam-4226	260	1	+	+	X
ejpam-4226	260	2	v	v	NOUN
ejpam-4226	260	3	=	=	SYM
ejpam-4226	260	4	f	f	PROPN
ejpam-4226	260	5	for	for	ADP
ejpam-4226	260	6	v(3α	v(3α	NOUN
ejpam-4226	260	7	)	)	PUNCT
ejpam-4226	261	1	+	+	NUM
ejpam-4226	261	2	v(2α	v(2α	NOUN
ejpam-4226	261	3	)	)	PUNCT
ejpam-4226	261	4	=	=	SYM
ejpam-4226	262	1	f	f	NOUN
ejpam-4226	262	2	using	use	VERB
ejpam-4226	262	3	[	[	X
ejpam-4226	262	4	12	12	NUM
ejpam-4226	262	5	]	]	PUNCT
ejpam-4226	262	6	,	,	PUNCT
ejpam-4226	262	7	we	we	PRON
ejpam-4226	262	8	get	get	VERB
ejpam-4226	262	9	the	the	DET
ejpam-4226	262	10	general	general	ADJ
ejpam-4226	262	11	solution	solution	NOUN
ejpam-4226	262	12	vg	vg	ADP
ejpam-4226	262	13	=	=	SYM
ejpam-4226	262	14	vh	vh	PROPN
ejpam-4226	262	15	+	+	CCONJ
ejpam-4226	262	16	vp	vp	PROPN
ejpam-4226	262	17	,	,	PUNCT
ejpam-4226	262	18	the	the	DET
ejpam-4226	262	19	sum	sum	NOUN
ejpam-4226	262	20	of	of	ADP
ejpam-4226	262	21	the	the	DET
ejpam-4226	262	22	homogenous	homogenous	ADJ
ejpam-4226	262	23	solution	solution	NOUN
ejpam-4226	262	24	and	and	CCONJ
ejpam-4226	262	25	the	the	DET
ejpam-4226	262	26	particular	particular	ADJ
ejpam-4226	262	27	solution	solution	NOUN
ejpam-4226	262	28	.	.	PUNCT
ejpam-4226	263	1	for	for	ADP
ejpam-4226	263	2	homogenous	homogenous	ADJ
ejpam-4226	263	3	solution	solution	NOUN
ejpam-4226	263	4	vh	vh	PROPN
ejpam-4226	263	5	,	,	PUNCT
ejpam-4226	263	6	the	the	DET
ejpam-4226	263	7	associated	associated	ADJ
ejpam-4226	263	8	characteristic	characteristic	ADJ
ejpam-4226	263	9	equation	equation	NOUN
ejpam-4226	263	10	is	be	AUX
ejpam-4226	263	11	r2	r2	PROPN
ejpam-4226	263	12	(	(	PUNCT
ejpam-4226	263	13	r	r	NOUN
ejpam-4226	263	14	+	+	NOUN
ejpam-4226	263	15	1	1	NUM
ejpam-4226	263	16	)	)	PUNCT
ejpam-4226	263	17	=	=	SYM
ejpam-4226	263	18	0	0	NUM
ejpam-4226	263	19	,	,	PUNCT
ejpam-4226	263	20	which	which	PRON
ejpam-4226	263	21	has	have	VERB
ejpam-4226	263	22	the	the	DET
ejpam-4226	263	23	roots	root	NOUN
ejpam-4226	263	24	0	0	NUM
ejpam-4226	263	25	,	,	PUNCT
ejpam-4226	263	26	0	0	NUM
ejpam-4226	263	27	and	and	CCONJ
ejpam-4226	263	28	−1	−1	NOUN
ejpam-4226	263	29	.	.	PUNCT
ejpam-4226	263	30	vh(t	vh(t	PUNCT
ejpam-4226	263	31	)	)	PUNCT
ejpam-4226	264	1	=	=	SYM
ejpam-4226	264	2	c1	c1	PROPN
ejpam-4226	264	3	+	+	CCONJ
ejpam-4226	264	4	c2	c2	PROPN
ejpam-4226	264	5	tα	tα	VERB
ejpam-4226	264	6	α	α	PROPN
ejpam-4226	265	1	+	+	CCONJ
ejpam-4226	266	1	c3e	c3e	PROPN
ejpam-4226	266	2	−tα	−tα	X
ejpam-4226	266	3	α	α	NOUN
ejpam-4226	266	4	for	for	ADP
ejpam-4226	266	5	the	the	DET
ejpam-4226	266	6	particular	particular	ADJ
ejpam-4226	266	7	solution	solution	NOUN
ejpam-4226	266	8	,	,	PUNCT
ejpam-4226	266	9	we	we	PRON
ejpam-4226	266	10	use	use	VERB
ejpam-4226	266	11	variation	variation	NOUN
ejpam-4226	266	12	of	of	ADP
ejpam-4226	266	13	parameters	parameter	NOUN
ejpam-4226	266	14	introduced	introduce	VERB
ejpam-4226	266	15	in	in	ADP
ejpam-4226	266	16	[	[	X
ejpam-4226	266	17	12	12	NUM
ejpam-4226	266	18	]	]	PUNCT
ejpam-4226	266	19	.	.	PUNCT
ejpam-4226	267	1	let	let	VERB
ejpam-4226	267	2	u1	u1	NOUN
ejpam-4226	267	3	=	=	SYM
ejpam-4226	267	4	1	1	NUM
ejpam-4226	267	5	,	,	PUNCT
ejpam-4226	267	6	u2	u2	NOUN
ejpam-4226	267	7	=	=	NOUN
ejpam-4226	267	8	1	1	NUM
ejpam-4226	267	9	α	α	NOUN
ejpam-4226	267	10	t	t	NOUN
ejpam-4226	267	11	α	α	NOUN
ejpam-4226	267	12	and	and	CCONJ
ejpam-4226	267	13	u3	u3	NOUN
ejpam-4226	267	14	=	=	SYM
ejpam-4226	267	15	e	e	PROPN
ejpam-4226	267	16	−tα	−tα	X
ejpam-4226	267	17	α	α	NOUN
ejpam-4226	267	18	vp(t	vp(t	PUNCT
ejpam-4226	267	19	)	)	PUNCT
ejpam-4226	267	20	=	=	SYM
ejpam-4226	267	21	3∑	3∑	NUM
ejpam-4226	267	22	m=1	m=1	X
ejpam-4226	267	23	um(t	um(t	NUM
ejpam-4226	267	24	)	)	PUNCT
ejpam-4226	268	1	∫	∫	PROPN
ejpam-4226	268	2	t	t	PROPN
ejpam-4226	268	3	a	a	DET
ejpam-4226	268	4	f(s)wα	f(s)wα	PROPN
ejpam-4226	268	5	m(s	m(s	PROPN
ejpam-4226	268	6	)	)	PUNCT
ejpam-4226	268	7	wα(s)s1−α	wα(s)s1−α	PROPN
ejpam-4226	269	1	ds	ds	PROPN
ejpam-4226	269	2	f.	f.	PROPN
ejpam-4226	269	3	bekraoui	bekraoui	PROPN
ejpam-4226	269	4	,	,	PUNCT
ejpam-4226	269	5	m.	m.	PROPN
ejpam-4226	269	6	al	al	PROPN
ejpam-4226	269	7	horani	horani	PROPN
ejpam-4226	269	8	,	,	PUNCT
ejpam-4226	269	9	r.	r.	PROPN
ejpam-4226	269	10	khalil	khalil	PROPN
ejpam-4226	269	11	/	/	SYM
ejpam-4226	269	12	eur	eur	PROPN
ejpam-4226	269	13	.	.	PUNCT
ejpam-4226	270	1	j.	j.	PROPN
ejpam-4226	270	2	pure	pure	PROPN
ejpam-4226	270	3	appl	appl	PROPN
ejpam-4226	270	4	.	.	PROPN
ejpam-4226	270	5	math	math	PROPN
ejpam-4226	270	6	,	,	PUNCT
ejpam-4226	270	7	15	15	NUM
ejpam-4226	270	8	(	(	PUNCT
ejpam-4226	270	9	1	1	NUM
ejpam-4226	270	10	)	)	PUNCT
ejpam-4226	270	11	(	(	PUNCT
ejpam-4226	270	12	2022	2022	NUM
ejpam-4226	270	13	)	)	PUNCT
ejpam-4226	270	14	,	,	PUNCT
ejpam-4226	270	15	106	106	NUM
ejpam-4226	270	16	-	-	SYM
ejpam-4226	270	17	125	125	NUM
ejpam-4226	270	18	118	118	NUM
ejpam-4226	270	19	=	=	SYM
ejpam-4226	270	20	∫	∫	PROPN
ejpam-4226	270	21	t	t	PROPN
ejpam-4226	270	22	a	a	DET
ejpam-4226	270	23	f(s)wα	f(s)wα	PROPN
ejpam-4226	270	24	1	1	NUM
ejpam-4226	270	25	(	(	PUNCT
ejpam-4226	270	26	s	s	NOUN
ejpam-4226	270	27	)	)	PUNCT
ejpam-4226	270	28	wα(s)s1−α	wα(s)s1−α	PROPN
ejpam-4226	270	29	ds+	ds+	NOUN
ejpam-4226	270	30	1	1	NUM
ejpam-4226	270	31	α	α	NOUN
ejpam-4226	271	1	tα	tα	PROPN
ejpam-4226	271	2	∫	∫	PROPN
ejpam-4226	271	3	t	t	PROPN
ejpam-4226	271	4	a	a	DET
ejpam-4226	271	5	f(s)wα	f(s)wα	PROPN
ejpam-4226	271	6	2	2	NUM
ejpam-4226	271	7	(	(	PUNCT
ejpam-4226	271	8	s	s	NOUN
ejpam-4226	271	9	)	)	PUNCT
ejpam-4226	271	10	wα(s)s1−α	wα(s)s1−α	PROPN
ejpam-4226	271	11	ds+	ds+	PROPN
ejpam-4226	271	12	e	e	NOUN
ejpam-4226	271	13	−tα	−tα	X
ejpam-4226	271	14	α	α	X
ejpam-4226	271	15	∫	∫	PROPN
ejpam-4226	271	16	t	t	PROPN
ejpam-4226	271	17	a	a	DET
ejpam-4226	271	18	f(s)wα	f(s)wα	PROPN
ejpam-4226	271	19	3	3	NUM
ejpam-4226	271	20	(	(	PUNCT
ejpam-4226	271	21	s	s	NOUN
ejpam-4226	271	22	)	)	PUNCT
ejpam-4226	271	23	wα(s)s1−α	wα(s)s1−α	PROPN
ejpam-4226	272	1	ds	ds	NOUN
ejpam-4226	272	2	=	=	SYM
ejpam-4226	272	3	−	−	PROPN
ejpam-4226	272	4	∫	∫	PROPN
ejpam-4226	272	5	t	t	PROPN
ejpam-4226	272	6	a	a	DET
ejpam-4226	272	7	f(s	f(	NOUN
ejpam-4226	272	8	)	)	PUNCT
ejpam-4226	272	9	(	(	PUNCT
ejpam-4226	272	10	sα	sα	ADV
ejpam-4226	272	11	α	α	NOUN
ejpam-4226	272	12	+	+	NOUN
ejpam-4226	272	13	1	1	NUM
ejpam-4226	272	14	)	)	PUNCT
ejpam-4226	272	15	s1−α	s1−α	PROPN
ejpam-4226	272	16	ds+	ds+	NOUN
ejpam-4226	273	1	tα	tα	PROPN
ejpam-4226	273	2	α	α	PROPN
ejpam-4226	273	3	∫	∫	PROPN
ejpam-4226	273	4	t	t	PROPN
ejpam-4226	273	5	a	a	DET
ejpam-4226	273	6	f(s	f(	NOUN
ejpam-4226	273	7	)	)	PUNCT
ejpam-4226	274	1	s1−α	s1−α	PROPN
ejpam-4226	274	2	ds+	ds+	NOUN
ejpam-4226	274	3	e	e	NOUN
ejpam-4226	274	4	−tα	−tα	X
ejpam-4226	274	5	α	α	X
ejpam-4226	274	6	∫	∫	PROPN
ejpam-4226	274	7	t	t	PROPN
ejpam-4226	274	8	a	a	DET
ejpam-4226	274	9	f(s	f(	NOUN
ejpam-4226	274	10	)	)	PUNCT
ejpam-4226	274	11	e	e	X
ejpam-4226	274	12	−sα	−sα	X
ejpam-4226	274	13	α	α	PRON
ejpam-4226	274	14	s1−α	s1−α	ADJ
ejpam-4226	274	15	ds	ds	NOUN
ejpam-4226	274	16	=	=	PUNCT
ejpam-4226	274	17	−iaα	−iaα	NOUN
ejpam-4226	274	18	(	(	PUNCT
ejpam-4226	274	19	f(t	f(t	PROPN
ejpam-4226	274	20	)	)	PUNCT
ejpam-4226	274	21	(	(	PUNCT
ejpam-4226	274	22	tα	tα	PROPN
ejpam-4226	274	23	α	α	PROPN
ejpam-4226	274	24	+	+	NOUN
ejpam-4226	274	25	1	1	NUM
ejpam-4226	274	26	)	)	PUNCT
ejpam-4226	274	27	)	)	PUNCT
ejpam-4226	275	1	+	+	CCONJ
ejpam-4226	275	2	tα	tα	VERB
ejpam-4226	275	3	α	α	DET
ejpam-4226	275	4	iaα	iaα	NOUN
ejpam-4226	275	5	(	(	PUNCT
ejpam-4226	275	6	f(t	f(t	PROPN
ejpam-4226	275	7	)	)	PUNCT
ejpam-4226	275	8	)	)	PUNCT
ejpam-4226	276	1	+	+	CCONJ
ejpam-4226	276	2	e	e	X
ejpam-4226	276	3	−tα	−tα	X
ejpam-4226	276	4	α	α	PRON
ejpam-4226	276	5	iaα	iaα	NOUN
ejpam-4226	276	6	(	(	PUNCT
ejpam-4226	276	7	f(t	f(t	PROPN
ejpam-4226	276	8	)	)	PUNCT
ejpam-4226	276	9	e	e	NOUN
ejpam-4226	276	10	−tα	−tα	X
ejpam-4226	276	11	α	α	NOUN
ejpam-4226	276	12	)	)	PUNCT
ejpam-4226	276	13	hence	hence	ADV
ejpam-4226	276	14	v(t	v(t	NOUN
ejpam-4226	276	15	)	)	PUNCT
ejpam-4226	276	16	=	=	PUNCT
ejpam-4226	276	17	vh(t	vh(t	X
ejpam-4226	276	18	)	)	PUNCT
ejpam-4226	277	1	+	+	CCONJ
ejpam-4226	277	2	vp(t	vp(t	X
ejpam-4226	277	3	)	)	PUNCT
ejpam-4226	277	4	=	=	SYM
ejpam-4226	277	5	c1	c1	PROPN
ejpam-4226	277	6	+	+	CCONJ
ejpam-4226	277	7	c2	c2	PROPN
ejpam-4226	277	8	tα	tα	VERB
ejpam-4226	277	9	α	α	PROPN
ejpam-4226	278	1	+	+	CCONJ
ejpam-4226	279	1	c3e	c3e	PROPN
ejpam-4226	279	2	−tα	−tα	X
ejpam-4226	279	3	α	α	X
ejpam-4226	279	4	−	−	NOUN
ejpam-4226	279	5	iaα	iaα	NOUN
ejpam-4226	279	6	(	(	PUNCT
ejpam-4226	279	7	f(t	f(t	PROPN
ejpam-4226	279	8	)	)	PUNCT
ejpam-4226	279	9	(	(	PUNCT
ejpam-4226	279	10	tα	tα	PROPN
ejpam-4226	279	11	α	α	PROPN
ejpam-4226	279	12	+	+	NOUN
ejpam-4226	279	13	1	1	NUM
ejpam-4226	279	14	)	)	PUNCT
ejpam-4226	279	15	)	)	PUNCT
ejpam-4226	280	1	+	+	CCONJ
ejpam-4226	280	2	tα	tα	VERB
ejpam-4226	280	3	α	α	DET
ejpam-4226	280	4	iaα	iaα	NOUN
ejpam-4226	280	5	(	(	PUNCT
ejpam-4226	280	6	f(t	f(t	PROPN
ejpam-4226	280	7	)	)	PUNCT
ejpam-4226	280	8	)	)	PUNCT
ejpam-4226	281	1	+	+	CCONJ
ejpam-4226	281	2	e	e	X
ejpam-4226	281	3	−tα	−tα	X
ejpam-4226	281	4	α	α	PRON
ejpam-4226	281	5	iaα	iaα	NOUN
ejpam-4226	281	6	(	(	PUNCT
ejpam-4226	281	7	f(t	f(t	PROPN
ejpam-4226	281	8	)	)	PUNCT
ejpam-4226	281	9	e	e	NOUN
ejpam-4226	281	10	−tα	−tα	X
ejpam-4226	281	11	α	α	NOUN
ejpam-4226	281	12	)	)	PUNCT
ejpam-4226	281	13	for	for	ADP
ejpam-4226	281	14	v(α	v(α	NOUN
ejpam-4226	281	15	)	)	PUNCT
ejpam-4226	281	16	+	+	X
ejpam-4226	281	17	v	v	NOUN
ejpam-4226	281	18	=	=	SYM
ejpam-4226	281	19	f	f	NOUN
ejpam-4226	281	20	by	by	ADP
ejpam-4226	281	21	result	result	NOUN
ejpam-4226	281	22	in	in	ADP
ejpam-4226	281	23	[	[	X
ejpam-4226	281	24	12	12	NUM
ejpam-4226	281	25	]	]	PUNCT
ejpam-4226	281	26	the	the	DET
ejpam-4226	281	27	solution	solution	NOUN
ejpam-4226	281	28	of	of	ADP
ejpam-4226	281	29	equation	equation	NOUN
ejpam-4226	281	30	(	(	PUNCT
ejpam-4226	281	31	7	7	X
ejpam-4226	281	32	)	)	PUNCT
ejpam-4226	281	33	is	be	AUX
ejpam-4226	281	34	given	give	VERB
ejpam-4226	281	35	by	by	ADP
ejpam-4226	281	36	v(t	v(t	NOUN
ejpam-4226	281	37	)	)	PUNCT
ejpam-4226	281	38	=	=	PUNCT
ejpam-4226	282	1	e−	e−	NUM
ejpam-4226	282	2	∫	∫	PROPN
ejpam-4226	282	3	t	t	PROPN
ejpam-4226	282	4	0	0	NUM
ejpam-4226	283	1	xα−1dx	xα−1dx	NUM
ejpam-4226	284	1	+	+	CCONJ
ejpam-4226	284	2	∫	∫	PROPN
ejpam-4226	284	3	t	t	PROPN
ejpam-4226	284	4	0	0	NUM
ejpam-4226	285	1	(	(	PUNCT
ejpam-4226	285	2	e−	e−	PROPN
ejpam-4226	285	3	∫	∫	PROPN
ejpam-4226	285	4	t	t	PROPN
ejpam-4226	285	5	s	s	PART
ejpam-4226	285	6	xα−1dxf(s)sα−1	xα−1dxf(s)sα−1	PUNCT
ejpam-4226	285	7	)	)	PUNCT
ejpam-4226	285	8	ds	ds	NOUN
ejpam-4226	285	9	=	=	SYM
ejpam-4226	285	10	e−	e−	X
ejpam-4226	285	11	1	1	NUM
ejpam-4226	285	12	α	α	NOUN
ejpam-4226	285	13	tα	tα	PROPN
ejpam-4226	286	1	+	+	CCONJ
ejpam-4226	286	2	∫	∫	PROPN
ejpam-4226	286	3	t	t	PROPN
ejpam-4226	286	4	0	0	NUM
ejpam-4226	287	1	(	(	PUNCT
ejpam-4226	287	2	e−	e−	PROPN
ejpam-4226	287	3	1	1	NUM
ejpam-4226	287	4	α	α	PROPN
ejpam-4226	287	5	(	(	PUNCT
ejpam-4226	287	6	tα−sα)f(s)sα−1	tα−sα)f(s)sα−1	NOUN
ejpam-4226	287	7	)	)	PUNCT
ejpam-4226	287	8	ds	ds	NOUN
ejpam-4226	288	1	but	but	CCONJ
ejpam-4226	288	2	the	the	DET
ejpam-4226	288	3	two	two	NUM
ejpam-4226	288	4	solution	solution	NOUN
ejpam-4226	288	5	must	must	AUX
ejpam-4226	288	6	be	be	AUX
ejpam-4226	288	7	equal	equal	ADJ
ejpam-4226	288	8	,	,	PUNCT
ejpam-4226	288	9	then	then	ADV
ejpam-4226	288	10	c3	c3	PROPN
ejpam-4226	288	11	+	+	CCONJ
ejpam-4226	288	12	iaα	iaα	ADJ
ejpam-4226	288	13	(	(	PUNCT
ejpam-4226	288	14	f(t	f(t	PROPN
ejpam-4226	288	15	)	)	PUNCT
ejpam-4226	288	16	e	e	NOUN
ejpam-4226	288	17	−tα	−tα	X
ejpam-4226	288	18	α	α	NOUN
ejpam-4226	288	19	)	)	PUNCT
ejpam-4226	289	1	=	=	SYM
ejpam-4226	289	2	1	1	NUM
ejpam-4226	289	3	and	and	CCONJ
ejpam-4226	289	4	∫	∫	PROPN
ejpam-4226	289	5	t	t	PROPN
ejpam-4226	289	6	0	0	NUM
ejpam-4226	290	1	(	(	PUNCT
ejpam-4226	290	2	e−	e−	PROPN
ejpam-4226	290	3	1	1	NUM
ejpam-4226	290	4	α	α	PROPN
ejpam-4226	290	5	(	(	PUNCT
ejpam-4226	290	6	tα−sα)f(s)sα−1	tα−sα)f(s)sα−1	NOUN
ejpam-4226	290	7	)	)	PUNCT
ejpam-4226	290	8	ds	ds	PROPN
ejpam-4226	290	9	=	=	PROPN
ejpam-4226	290	10	c1	c1	PROPN
ejpam-4226	290	11	+	+	CCONJ
ejpam-4226	291	1	(	(	PUNCT
ejpam-4226	292	1	c2	c2	PROPN
ejpam-4226	292	2	+	+	CCONJ
ejpam-4226	292	3	iaα	iaα	PROPN
ejpam-4226	292	4	(	(	PUNCT
ejpam-4226	292	5	f(t	f(t	PROPN
ejpam-4226	292	6	)	)	PUNCT
ejpam-4226	292	7	)	)	PUNCT
ejpam-4226	292	8	)	)	PUNCT
ejpam-4226	293	1	tα	tα	VERB
ejpam-4226	293	2	α	α	PRON
ejpam-4226	293	3	−	−	NOUN
ejpam-4226	294	1	iaα	iaα	NOUN
ejpam-4226	294	2	(	(	PUNCT
ejpam-4226	294	3	f(t	f(t	PROPN
ejpam-4226	294	4	)	)	PUNCT
ejpam-4226	294	5	(	(	PUNCT
ejpam-4226	294	6	tα	tα	PROPN
ejpam-4226	294	7	α	α	PROPN
ejpam-4226	294	8	+	+	NOUN
ejpam-4226	294	9	1	1	NUM
ejpam-4226	294	10	)	)	PUNCT
ejpam-4226	294	11	)	)	PUNCT
ejpam-4226	295	1	then	then	ADV
ejpam-4226	295	2	v(t	v(t	X
ejpam-4226	295	3	)	)	PUNCT
ejpam-4226	295	4	=	=	PUNCT
ejpam-4226	296	1	e−	e−	X
ejpam-4226	296	2	1	1	NUM
ejpam-4226	296	3	α	α	NOUN
ejpam-4226	296	4	tα	tα	PROPN
ejpam-4226	297	1	+	+	CCONJ
ejpam-4226	297	2	∫	∫	PROPN
ejpam-4226	297	3	t	t	PROPN
ejpam-4226	297	4	0	0	NUM
ejpam-4226	298	1	(	(	PUNCT
ejpam-4226	298	2	e−	e−	PROPN
ejpam-4226	298	3	1	1	NUM
ejpam-4226	298	4	α	α	PROPN
ejpam-4226	298	5	(	(	PUNCT
ejpam-4226	298	6	tα−sα)f(s)sα−1	tα−sα)f(s)sα−1	NOUN
ejpam-4226	298	7	)	)	PUNCT
ejpam-4226	298	8	ds	ds	PROPN
ejpam-4226	298	9	c.	c.	NOUN
ejpam-4226	298	10	the	the	DET
ejpam-4226	298	11	third	third	ADJ
ejpam-4226	298	12	case	case	NOUN
ejpam-4226	298	13	.	.	PUNCT
ejpam-4226	299	1	x	x	X
ejpam-4226	299	2	=	=	PRON
ejpam-4226	300	1	ax	ax	NOUN
ejpam-4226	300	2	and	and	CCONJ
ejpam-4226	300	3	bx	bx	NOUN
ejpam-4226	300	4	=	=	SYM
ejpam-4226	300	5	cx	cx	PROPN
ejpam-4226	300	6	(	(	PUNCT
ejpam-4226	300	7	a	a	NOUN
ejpam-4226	300	8	)	)	PUNCT
ejpam-4226	300	9	in	in	ADP
ejpam-4226	300	10	this	this	DET
ejpam-4226	300	11	case	case	NOUN
ejpam-4226	300	12	[	[	PUNCT
ejpam-4226	300	13	v(3α)(t	v(3α)(t	NOUN
ejpam-4226	300	14	)	)	PUNCT
ejpam-4226	300	15	+	+	CCONJ
ejpam-4226	300	16	v(2α)(t	v(2α)(t	NUM
ejpam-4226	300	17	)	)	PUNCT
ejpam-4226	300	18	]	]	PUNCT
ejpam-4226	301	1	⊗	⊗	ADJ
ejpam-4226	301	2	x+	x+	X
ejpam-4226	301	3	[	[	PUNCT
ejpam-4226	301	4	v(α)(t	v(α)(t	NUM
ejpam-4226	301	5	)	)	PUNCT
ejpam-4226	301	6	+	+	CCONJ
ejpam-4226	301	7	v(t	v(t	VERB
ejpam-4226	301	8	)	)	PUNCT
ejpam-4226	301	9	]	]	PUNCT
ejpam-4226	301	10	⊗bx	⊗bx	NOUN
ejpam-4226	301	11	=	=	SYM
ejpam-4226	301	12	f(t)⊗	f(t)⊗	NOUN
ejpam-4226	301	13	z	z	NOUN
ejpam-4226	301	14	if	if	SCONJ
ejpam-4226	301	15	x	x	X
ejpam-4226	301	16	=	=	PUNCT
ejpam-4226	301	17	bx	bx	X
ejpam-4226	301	18	=	=	PUNCT
ejpam-4226	301	19	z	z	PROPN
ejpam-4226	301	20	,	,	PUNCT
ejpam-4226	301	21	(	(	PUNCT
ejpam-4226	301	22	9	9	NUM
ejpam-4226	301	23	)	)	PUNCT
ejpam-4226	301	24	then	then	ADV
ejpam-4226	301	25	v(3α)(t	v(3α)(t	VERB
ejpam-4226	301	26	)	)	PUNCT
ejpam-4226	301	27	+	+	CCONJ
ejpam-4226	301	28	v(2α)(t	v(2α)(t	X
ejpam-4226	301	29	)	)	PUNCT
ejpam-4226	301	30	+	+	PUNCT
ejpam-4226	301	31	v(α)(t	v(α)(t	NUM
ejpam-4226	301	32	)	)	PUNCT
ejpam-4226	301	33	+	+	CCONJ
ejpam-4226	301	34	v(t	v(t	NUM
ejpam-4226	301	35	)	)	PUNCT
ejpam-4226	301	36	=	=	SYM
ejpam-4226	301	37	f(t	f(t	NOUN
ejpam-4226	301	38	)	)	PUNCT
ejpam-4226	301	39	.	.	PUNCT
ejpam-4226	302	1	f.	f.	PROPN
ejpam-4226	302	2	bekraoui	bekraoui	PROPN
ejpam-4226	302	3	,	,	PUNCT
ejpam-4226	302	4	m.	m.	PROPN
ejpam-4226	302	5	al	al	PROPN
ejpam-4226	302	6	horani	horani	PROPN
ejpam-4226	302	7	,	,	PUNCT
ejpam-4226	302	8	r.	r.	PROPN
ejpam-4226	302	9	khalil	khalil	PROPN
ejpam-4226	302	10	/	/	SYM
ejpam-4226	302	11	eur	eur	PROPN
ejpam-4226	302	12	.	.	PUNCT
ejpam-4226	303	1	j.	j.	PROPN
ejpam-4226	303	2	pure	pure	PROPN
ejpam-4226	303	3	appl	appl	PROPN
ejpam-4226	303	4	.	.	PROPN
ejpam-4226	303	5	math	math	PROPN
ejpam-4226	303	6	,	,	PUNCT
ejpam-4226	303	7	15	15	NUM
ejpam-4226	303	8	(	(	PUNCT
ejpam-4226	303	9	1	1	NUM
ejpam-4226	303	10	)	)	PUNCT
ejpam-4226	303	11	(	(	PUNCT
ejpam-4226	303	12	2022	2022	NUM
ejpam-4226	303	13	)	)	PUNCT
ejpam-4226	303	14	,	,	PUNCT
ejpam-4226	303	15	106	106	NUM
ejpam-4226	303	16	-	-	SYM
ejpam-4226	303	17	125	125	NUM
ejpam-4226	303	18	119	119	NUM
ejpam-4226	303	19	and	and	CCONJ
ejpam-4226	303	20	this	this	PRON
ejpam-4226	303	21	can	can	AUX
ejpam-4226	303	22	be	be	AUX
ejpam-4226	303	23	solved	solve	VERB
ejpam-4226	303	24	as	as	ADP
ejpam-4226	303	25	before	before	ADP
ejpam-4226	303	26	in	in	ADP
ejpam-4226	303	27	case1	case1	PROPN
ejpam-4226	303	28	.	.	PUNCT
ejpam-4226	304	1	v(3α)(t	v(3α)(t	NOUN
ejpam-4226	304	2	)	)	PUNCT
ejpam-4226	305	1	+	+	CCONJ
ejpam-4226	305	2	v(2α)(t	v(2α)(t	X
ejpam-4226	305	3	)	)	PUNCT
ejpam-4226	305	4	=	=	SYM
ejpam-4226	305	5	v(α)(t	v(α)(t	NUM
ejpam-4226	305	6	)	)	PUNCT
ejpam-4226	306	1	+	+	CCONJ
ejpam-4226	306	2	v(t	v(t	NUM
ejpam-4226	306	3	)	)	PUNCT
ejpam-4226	306	4	=	=	SYM
ejpam-4226	306	5	f(t	f(t	NOUN
ejpam-4226	306	6	)	)	PUNCT
ejpam-4226	306	7	.	.	PUNCT
ejpam-4226	307	1	(	(	PUNCT
ejpam-4226	307	2	b	b	X
ejpam-4226	307	3	)	)	PUNCT
ejpam-4226	307	4	now	now	ADV
ejpam-4226	307	5	v(3α)(t	v(3α)(t	VERB
ejpam-4226	307	6	)	)	PUNCT
ejpam-4226	308	1	+	+	CCONJ
ejpam-4226	308	2	v(2α)(t	v(2α)(t	X
ejpam-4226	308	3	)	)	PUNCT
ejpam-4226	308	4	=	=	SYM
ejpam-4226	308	5	v(α)(t	v(α)(t	NUM
ejpam-4226	308	6	)	)	PUNCT
ejpam-4226	309	1	+	+	CCONJ
ejpam-4226	309	2	v(t	v(t	NOUN
ejpam-4226	309	3	)	)	PUNCT
ejpam-4226	309	4	,	,	PUNCT
ejpam-4226	309	5	the	the	DET
ejpam-4226	309	6	associated	associated	ADJ
ejpam-4226	309	7	characteristic	characteristic	ADJ
ejpam-4226	309	8	equation	equation	NOUN
ejpam-4226	309	9	is	be	AUX
ejpam-4226	309	10	r3	r3	PROPN
ejpam-4226	309	11	+	+	CCONJ
ejpam-4226	309	12	r2	r2	PROPN
ejpam-4226	310	1	−	−	PROPN
ejpam-4226	310	2	r	r	NOUN
ejpam-4226	310	3	−	−	NOUN
ejpam-4226	310	4	1	1	NUM
ejpam-4226	310	5	=	=	SYM
ejpam-4226	310	6	0	0	NUM
ejpam-4226	310	7	which	which	PRON
ejpam-4226	310	8	has	have	VERB
ejpam-4226	310	9	the	the	DET
ejpam-4226	310	10	roots	root	NOUN
ejpam-4226	310	11	−1,−1	−1,−1	NOUN
ejpam-4226	310	12	and	and	CCONJ
ejpam-4226	310	13	1	1	NUM
ejpam-4226	310	14	.	.	PUNCT
ejpam-4226	311	1	then	then	ADV
ejpam-4226	311	2	v(t	v(t	NOUN
ejpam-4226	311	3	)	)	PUNCT
ejpam-4226	311	4	=	=	SYM
ejpam-4226	311	5	c1e	c1e	NOUN
ejpam-4226	311	6	1	1	NUM
ejpam-4226	311	7	α	α	NOUN
ejpam-4226	311	8	tα	tα	PROPN
ejpam-4226	312	1	+	+	CCONJ
ejpam-4226	312	2	c2	c2	PROPN
ejpam-4226	312	3	1	1	NUM
ejpam-4226	312	4	α	α	NOUN
ejpam-4226	312	5	tαe−	tαe−	PROPN
ejpam-4226	312	6	1	1	NUM
ejpam-4226	312	7	α	α	NOUN
ejpam-4226	312	8	tα	tα	NOUN
ejpam-4226	313	1	+	+	CCONJ
ejpam-4226	313	2	c3e	c3e	PROPN
ejpam-4226	313	3	−	−	NOUN
ejpam-4226	313	4	1	1	NUM
ejpam-4226	313	5	α	α	NOUN
ejpam-4226	313	6	tα	tα	PROPN
ejpam-4226	313	7	.	.	PUNCT
ejpam-4226	314	1	v(0	v(0	X
ejpam-4226	314	2	)	)	PUNCT
ejpam-4226	314	3	=	=	SYM
ejpam-4226	314	4	v(α)(0	v(α)(0	NOUN
ejpam-4226	314	5	)	)	PUNCT
ejpam-4226	315	1	=	=	SYM
ejpam-4226	315	2	v(2α)(0	v(2α)(0	NOUN
ejpam-4226	315	3	)	)	PUNCT
ejpam-4226	315	4	=	=	SYM
ejpam-4226	316	1	1	1	NUM
ejpam-4226	316	2	gives	gives	NUM
ejpam-4226	316	3	c1	c1	NOUN
ejpam-4226	316	4	+	+	CCONJ
ejpam-4226	316	5	c3	c3	X
ejpam-4226	316	6	=	=	SYM
ejpam-4226	316	7	1	1	NUM
ejpam-4226	316	8	c1	c1	NOUN
ejpam-4226	316	9	+	+	CCONJ
ejpam-4226	316	10	c2	c2	PROPN
ejpam-4226	316	11	−	−	PROPN
ejpam-4226	316	12	c3	c3	PROPN
ejpam-4226	316	13	=	=	SYM
ejpam-4226	316	14	1	1	NUM
ejpam-4226	316	15	c1	c1	NOUN
ejpam-4226	316	16	−	−	PROPN
ejpam-4226	316	17	2c2	2c2	NUM
ejpam-4226	317	1	+	+	CCONJ
ejpam-4226	317	2	c3	c3	X
ejpam-4226	317	3	=	=	SYM
ejpam-4226	317	4	1	1	NUM
ejpam-4226	317	5	⇔	⇔	PROPN
ejpam-4226	317	6			PROPN
ejpam-4226	317	7	c1	c1	NOUN
ejpam-4226	317	8	=	=	NOUN
ejpam-4226	317	9	1	1	NUM
ejpam-4226	317	10	c2	c2	PROPN
ejpam-4226	317	11	=	=	SYM
ejpam-4226	317	12	0	0	NUM
ejpam-4226	318	1	c3	c3	NOUN
ejpam-4226	318	2	=	=	SYM
ejpam-4226	318	3	0	0	PUNCT
ejpam-4226	318	4	hence	hence	ADV
ejpam-4226	318	5	v(t	v(t	NUM
ejpam-4226	318	6	)	)	PUNCT
ejpam-4226	318	7	=	=	PUNCT
ejpam-4226	319	1	e	e	X
ejpam-4226	319	2	1	1	NUM
ejpam-4226	319	3	α	α	NOUN
ejpam-4226	319	4	tα	tα	PROPN
ejpam-4226	319	5	.	.	PUNCT
ejpam-4226	320	1	this	this	DET
ejpam-4226	320	2	forces	force	NOUN
ejpam-4226	320	3	f(t	f(t	NOUN
ejpam-4226	320	4	)	)	PUNCT
ejpam-4226	321	1	=	=	SYM
ejpam-4226	321	2	2e	2e	NOUN
ejpam-4226	321	3	1	1	NUM
ejpam-4226	321	4	α	α	NOUN
ejpam-4226	321	5	tα	tα	PROPN
ejpam-4226	321	6	,	,	PUNCT
ejpam-4226	321	7	if	if	SCONJ
ejpam-4226	321	8	not	not	PART
ejpam-4226	321	9	then	then	ADV
ejpam-4226	321	10	there	there	PRON
ejpam-4226	321	11	is	be	VERB
ejpam-4226	321	12	no	no	DET
ejpam-4226	321	13	atomic	atomic	ADJ
ejpam-4226	321	14	solution	solution	NOUN
ejpam-4226	321	15	.	.	PUNCT
ejpam-4226	322	1	now	now	ADV
ejpam-4226	322	2	in	in	ADP
ejpam-4226	322	3	case	case	NOUN
ejpam-4226	322	4	of	of	ADP
ejpam-4226	322	5	(	(	PUNCT
ejpam-4226	322	6	9	9	NUM
ejpam-4226	322	7	)	)	PUNCT
ejpam-4226	322	8	and	and	CCONJ
ejpam-4226	322	9	from	from	ADP
ejpam-4226	322	10	(	(	PUNCT
ejpam-4226	322	11	a	a	X
ejpam-4226	322	12	)	)	PUNCT
ejpam-4226	322	13	we	we	PRON
ejpam-4226	322	14	get	get	VERB
ejpam-4226	322	15	x	x	PUNCT
ejpam-4226	322	16	=	=	PUNCT
ejpam-4226	322	17	ax	ax	NOUN
ejpam-4226	322	18	=	=	PUNCT
ejpam-4226	322	19	bx	bx	NOUN
ejpam-4226	322	20	=	=	SYM
ejpam-4226	322	21	cx	cx	PROPN
ejpam-4226	322	22	,	,	PUNCT
ejpam-4226	322	23	so	so	ADV
ejpam-4226	322	24	x	x	PUNCT
ejpam-4226	322	25	is	be	AUX
ejpam-4226	322	26	an	an	DET
ejpam-4226	322	27	eigenvector	eigenvector	NOUN
ejpam-4226	322	28	for	for	ADP
ejpam-4226	322	29	a	a	DET
ejpam-4226	322	30	,	,	PUNCT
ejpam-4226	322	31	b	b	NOUN
ejpam-4226	322	32	,	,	PUNCT
ejpam-4226	322	33	c	c	NOUN
ejpam-4226	322	34	and	and	CCONJ
ejpam-4226	322	35	x	x	X
ejpam-4226	322	36	=	=	PUNCT
ejpam-4226	322	37	z.	z.	PROPN
ejpam-4226	323	1	in	in	ADP
ejpam-4226	323	2	case	case	NOUN
ejpam-4226	323	3	(	(	PUNCT
ejpam-4226	323	4	b	b	NOUN
ejpam-4226	323	5	)	)	PUNCT
ejpam-4226	323	6	,	,	PUNCT
ejpam-4226	323	7	we	we	PRON
ejpam-4226	323	8	get	get	VERB
ejpam-4226	323	9	2e	2e	NUM
ejpam-4226	323	10	1	1	NUM
ejpam-4226	323	11	α	α	NOUN
ejpam-4226	323	12	tα	tα	NOUN
ejpam-4226	324	1	+	+	X
ejpam-4226	324	2	2e	2e	NUM
ejpam-4226	324	3	1	1	NUM
ejpam-4226	324	4	α	α	NOUN
ejpam-4226	324	5	tα	tα	NOUN
ejpam-4226	324	6	=	=	SYM
ejpam-4226	324	7	2e	2e	PROPN
ejpam-4226	324	8	1	1	NUM
ejpam-4226	324	9	α	α	NOUN
ejpam-4226	324	10	tαz	tαz	NOUN
ejpam-4226	325	1	so	so	ADV
ejpam-4226	325	2	x+bx	x+bx	PROPN
ejpam-4226	325	3	=	=	PUNCT
ejpam-4226	325	4	z.	z.	PROPN
ejpam-4226	326	1	hence	hence	ADV
ejpam-4226	326	2	(	(	PUNCT
ejpam-4226	326	3	i	i	PRON
ejpam-4226	326	4	+	+	PROPN
ejpam-4226	326	5	b)x	b)x	X
ejpam-4226	326	6	=	=	PUNCT
ejpam-4226	326	7	z.	z.	PROPN
ejpam-4226	326	8	d.	d.	PROPN
ejpam-4226	326	9	the	the	DET
ejpam-4226	326	10	forth	forth	ADJ
ejpam-4226	326	11	case	case	PROPN
ejpam-4226	326	12	(	(	PUNCT
ejpam-4226	326	13	i	i	NOUN
ejpam-4226	326	14	)	)	PUNCT
ejpam-4226	326	15	v(3α)(t)⊗	v(3α)(t)⊗	VERB
ejpam-4226	326	16	x+	x+	PROPN
ejpam-4226	326	17	v(t)⊗	v(t)⊗	NOUN
ejpam-4226	326	18	cx	cx	NOUN
ejpam-4226	326	19	=	=	PUNCT
ejpam-4226	326	20	v1(t)⊗	v1(t)⊗	ADJ
ejpam-4226	326	21	y1	y1	NOUN
ejpam-4226	326	22	and	and	CCONJ
ejpam-4226	326	23	(	(	PUNCT
ejpam-4226	326	24	ii	ii	NOUN
ejpam-4226	326	25	)	)	PUNCT
ejpam-4226	326	26	v(2α)(t)⊗	v(2α)(t)⊗	VERB
ejpam-4226	326	27	ax+	ax+	ADJ
ejpam-4226	326	28	v(α)(t)⊗bx	v(α)(t)⊗bx	X
ejpam-4226	326	29	=	=	SYM
ejpam-4226	326	30	v2(t)⊗	v2(t)⊗	NUM
ejpam-4226	326	31	y2	y2	INTJ
ejpam-4226	326	32	which	which	PRON
ejpam-4226	326	33	gives	give	VERB
ejpam-4226	326	34	situation	situation	NOUN
ejpam-4226	326	35	(	(	PUNCT
ejpam-4226	326	36	1	1	NUM
ejpam-4226	326	37	)	)	PUNCT
ejpam-4226	326	38			VERB
ejpam-4226	326	39	v(3α	v(3α	NOUN
ejpam-4226	326	40	)	)	PUNCT
ejpam-4226	326	41	=	=	SYM
ejpam-4226	326	42	v	v	NOUN
ejpam-4226	326	43	=	=	SYM
ejpam-4226	326	44	v1(t	v1(t	NOUN
ejpam-4226	326	45	)	)	PUNCT
ejpam-4226	326	46	and	and	CCONJ
ejpam-4226	326	47	v(2α	v(2α	NOUN
ejpam-4226	326	48	)	)	PUNCT
ejpam-4226	326	49	=	=	SYM
ejpam-4226	326	50	v(α	v(α	PROPN
ejpam-4226	326	51	)	)	PUNCT
ejpam-4226	326	52	=	=	SYM
ejpam-4226	326	53	v2(t	v2(t	NOUN
ejpam-4226	326	54	)	)	PUNCT
ejpam-4226	326	55	for	for	ADP
ejpam-4226	326	56	v(3α	v(3α	NOUN
ejpam-4226	326	57	)	)	PUNCT
ejpam-4226	326	58	=	=	SYM
ejpam-4226	326	59	v	v	NOUN
ejpam-4226	326	60	=	=	SYM
ejpam-4226	326	61	v1(t	v1(t	NUM
ejpam-4226	326	62	)	)	PUNCT
ejpam-4226	326	63	,	,	PUNCT
ejpam-4226	326	64	the	the	DET
ejpam-4226	326	65	associated	associated	ADJ
ejpam-4226	326	66	characteristic	characteristic	ADJ
ejpam-4226	326	67	equation	equation	NOUN
ejpam-4226	326	68	is	be	AUX
ejpam-4226	326	69	r3	r3	NOUN
ejpam-4226	326	70	−	−	NOUN
ejpam-4226	326	71	1	1	NUM
ejpam-4226	326	72	=	=	SYM
ejpam-4226	326	73	0	0	PROPN
ejpam-4226	326	74	.	.	NOUN
ejpam-4226	326	75	which	which	PRON
ejpam-4226	326	76	has	have	VERB
ejpam-4226	326	77	the	the	DET
ejpam-4226	326	78	roots	root	NOUN
ejpam-4226	326	79	1	1	NUM
ejpam-4226	326	80	,	,	PUNCT
ejpam-4226	326	81	−1±	−1±	NOUN
ejpam-4226	326	82	√	√	NOUN
ejpam-4226	326	83	3i	3i	NOUN
ejpam-4226	326	84	2	2	NUM
ejpam-4226	326	85	.	.	PUNCT
ejpam-4226	327	1	hence	hence	ADV
ejpam-4226	327	2	using	use	VERB
ejpam-4226	327	3	[	[	X
ejpam-4226	327	4	12	12	NUM
ejpam-4226	327	5	]	]	PUNCT
ejpam-4226	327	6	,	,	PUNCT
ejpam-4226	327	7	we	we	PRON
ejpam-4226	327	8	get	get	VERB
ejpam-4226	327	9	v(t	v(t	NOUN
ejpam-4226	327	10	)	)	PUNCT
ejpam-4226	327	11	=	=	SYM
ejpam-4226	327	12	c1	c1	PROPN
ejpam-4226	327	13	exp	exp	NOUN
ejpam-4226	327	14	1	1	NUM
ejpam-4226	327	15	α	α	NOUN
ejpam-4226	327	16	tα	tα	PROPN
ejpam-4226	327	17	+	+	CCONJ
ejpam-4226	327	18	exp	exp	NOUN
ejpam-4226	327	19	(	(	PUNCT
ejpam-4226	327	20	−	−	PROPN
ejpam-4226	327	21	1	1	NUM
ejpam-4226	327	22	2α	2α	NOUN
ejpam-4226	327	23	tα	tα	PROPN
ejpam-4226	327	24	)	)	PUNCT
ejpam-4226	327	25	(	(	PUNCT
ejpam-4226	327	26	c2	c2	PROPN
ejpam-4226	327	27	cos	cos	PROPN
ejpam-4226	327	28	√	√	PROPN
ejpam-4226	327	29	3	3	NUM
ejpam-4226	327	30	2α	2α	NOUN
ejpam-4226	327	31	tα	tα	PROPN
ejpam-4226	327	32	+	+	CCONJ
ejpam-4226	327	33	c3	c3	PROPN
ejpam-4226	327	34	sin	sin	NOUN
ejpam-4226	327	35	√	√	NUM
ejpam-4226	327	36	3	3	NUM
ejpam-4226	327	37	2α	2α	NOUN
ejpam-4226	327	38	tα	tα	PROPN
ejpam-4226	327	39	)	)	PUNCT
ejpam-4226	327	40	.	.	PUNCT
ejpam-4226	328	1	f.	f.	PROPN
ejpam-4226	328	2	bekraoui	bekraoui	PROPN
ejpam-4226	328	3	,	,	PUNCT
ejpam-4226	328	4	m.	m.	PROPN
ejpam-4226	328	5	al	al	PROPN
ejpam-4226	328	6	horani	horani	PROPN
ejpam-4226	328	7	,	,	PUNCT
ejpam-4226	328	8	r.	r.	PROPN
ejpam-4226	328	9	khalil	khalil	PROPN
ejpam-4226	328	10	/	/	SYM
ejpam-4226	328	11	eur	eur	PROPN
ejpam-4226	328	12	.	.	PUNCT
ejpam-4226	329	1	j.	j.	PROPN
ejpam-4226	329	2	pure	pure	PROPN
ejpam-4226	329	3	appl	appl	PROPN
ejpam-4226	329	4	.	.	PROPN
ejpam-4226	329	5	math	math	PROPN
ejpam-4226	329	6	,	,	PUNCT
ejpam-4226	329	7	15	15	NUM
ejpam-4226	329	8	(	(	PUNCT
ejpam-4226	329	9	1	1	NUM
ejpam-4226	329	10	)	)	PUNCT
ejpam-4226	329	11	(	(	PUNCT
ejpam-4226	329	12	2022	2022	NUM
ejpam-4226	329	13	)	)	PUNCT
ejpam-4226	329	14	,	,	PUNCT
ejpam-4226	329	15	106	106	NUM
ejpam-4226	329	16	-	-	SYM
ejpam-4226	329	17	125	125	NUM
ejpam-4226	329	18	120	120	NUM
ejpam-4226	329	19	using	use	VERB
ejpam-4226	329	20	conditions	condition	NOUN
ejpam-4226	329	21	(	(	PUNCT
ejpam-4226	329	22	∗∗	∗∗	NOUN
ejpam-4226	329	23	)	)	PUNCT
ejpam-4226	329	24	to	to	PART
ejpam-4226	329	25	get	get	VERB
ejpam-4226	329	26	v(t	v(t	VERB
ejpam-4226	329	27	)	)	PUNCT
ejpam-4226	329	28	=	=	SYM
ejpam-4226	329	29	exp	exp	NOUN
ejpam-4226	329	30	1	1	NUM
ejpam-4226	329	31	α	α	NOUN
ejpam-4226	329	32	tα	tα	PROPN
ejpam-4226	329	33	.	.	PUNCT
ejpam-4226	330	1	now	now	ADV
ejpam-4226	330	2	for	for	ADP
ejpam-4226	330	3	v(2α	v(2α	NOUN
ejpam-4226	330	4	)	)	PUNCT
ejpam-4226	330	5	=	=	SYM
ejpam-4226	330	6	v(α	v(α	PROPN
ejpam-4226	330	7	)	)	PUNCT
ejpam-4226	330	8	,	,	PUNCT
ejpam-4226	330	9	the	the	DET
ejpam-4226	330	10	associated	associated	ADJ
ejpam-4226	330	11	characteristic	characteristic	ADJ
ejpam-4226	330	12	equation	equation	NOUN
ejpam-4226	330	13	is	be	AUX
ejpam-4226	330	14	r2	r2	NOUN
ejpam-4226	330	15	−	−	NOUN
ejpam-4226	330	16	r	r	NOUN
ejpam-4226	330	17	=	=	NOUN
ejpam-4226	330	18	0	0	NUM
ejpam-4226	330	19	.	.	PUNCT
ejpam-4226	331	1	hence	hence	ADV
ejpam-4226	331	2	using	use	VERB
ejpam-4226	331	3	[	[	X
ejpam-4226	331	4	12	12	NUM
ejpam-4226	331	5	]	]	PUNCT
ejpam-4226	331	6	,	,	PUNCT
ejpam-4226	331	7	we	we	PRON
ejpam-4226	331	8	get	get	VERB
ejpam-4226	331	9	v(t	v(t	NOUN
ejpam-4226	331	10	)	)	PUNCT
ejpam-4226	332	1	=	=	SYM
ejpam-4226	332	2	c1	c1	PROPN
ejpam-4226	332	3	+	+	CCONJ
ejpam-4226	332	4	c2	c2	PROPN
ejpam-4226	332	5	exp	exp	VERB
ejpam-4226	332	6	1	1	NUM
ejpam-4226	332	7	α	α	NOUN
ejpam-4226	332	8	tα	tα	PROPN
ejpam-4226	332	9	.	.	PUNCT
ejpam-4226	333	1	by	by	ADP
ejpam-4226	333	2	the	the	DET
ejpam-4226	333	3	conditions	condition	NOUN
ejpam-4226	333	4	(	(	PUNCT
ejpam-4226	333	5	∗∗	∗∗	X
ejpam-4226	333	6	)	)	PUNCT
ejpam-4226	333	7	we	we	PRON
ejpam-4226	333	8	get	get	VERB
ejpam-4226	333	9	v(t	v(t	NOUN
ejpam-4226	333	10	)	)	PUNCT
ejpam-4226	333	11	=	=	SYM
ejpam-4226	333	12	exp	exp	NOUN
ejpam-4226	333	13	1	1	NUM
ejpam-4226	333	14	α	α	NOUN
ejpam-4226	333	15	tα	tα	PROPN
ejpam-4226	333	16	.	.	PUNCT
ejpam-4226	334	1	substitute	substitute	PROPN
ejpam-4226	334	2	in	in	ADP
ejpam-4226	334	3	the	the	DET
ejpam-4226	334	4	main	main	ADJ
ejpam-4226	334	5	equation	equation	NOUN
ejpam-4226	334	6	exp	exp	NOUN
ejpam-4226	334	7	1	1	NUM
ejpam-4226	334	8	α	α	NOUN
ejpam-4226	334	9	tα	tα	VERB
ejpam-4226	334	10	⊗	⊗	PROPN
ejpam-4226	335	1	[	[	X
ejpam-4226	335	2	x+	x+	ADJ
ejpam-4226	335	3	ax+bx+	ax+bx+	PROPN
ejpam-4226	335	4	cx	cx	X
ejpam-4226	335	5	]	]	X
ejpam-4226	335	6	=	=	SYM
ejpam-4226	335	7	f(t)⊗	f(t)⊗	PROPN
ejpam-4226	335	8	z	z	NOUN
ejpam-4226	335	9	.	.	PUNCT
ejpam-4226	336	1	so	so	ADV
ejpam-4226	336	2	,	,	PUNCT
ejpam-4226	336	3	f	f	PROPN
ejpam-4226	336	4	must	must	AUX
ejpam-4226	336	5	be	be	AUX
ejpam-4226	336	6	equal	equal	ADJ
ejpam-4226	336	7	to	to	ADP
ejpam-4226	336	8	exp	exp	NOUN
ejpam-4226	336	9	1	1	NUM
ejpam-4226	336	10	α	α	NOUN
ejpam-4226	336	11	t	t	NOUN
ejpam-4226	336	12	α	α	NOUN
ejpam-4226	336	13	for	for	ADP
ejpam-4226	336	14	the	the	DET
ejpam-4226	336	15	atomic	atomic	ADJ
ejpam-4226	336	16	solution	solution	NOUN
ejpam-4226	336	17	to	to	PART
ejpam-4226	336	18	exist	exist	VERB
ejpam-4226	336	19	and	and	CCONJ
ejpam-4226	336	20	the	the	DET
ejpam-4226	336	21	image	image	NOUN
ejpam-4226	336	22	of	of	ADP
ejpam-4226	336	23	x	x	PUNCT
ejpam-4226	336	24	under	under	ADP
ejpam-4226	336	25	[	[	X
ejpam-4226	336	26	i	i	PRON
ejpam-4226	336	27	+	+	X
ejpam-4226	336	28	a+b	a+b	NUM
ejpam-4226	337	1	+	+	CCONJ
ejpam-4226	338	1	c]x	c]x	NOUN
ejpam-4226	338	2	=	=	SYM
ejpam-4226	338	3	z.	z.	PROPN
ejpam-4226	338	4	situation	situation	NOUN
ejpam-4226	338	5	(	(	PUNCT
ejpam-4226	338	6	2	2	NUM
ejpam-4226	338	7	)	)	PUNCT
ejpam-4226	338	8			VERB
ejpam-4226	338	9	v(3α	v(3α	NOUN
ejpam-4226	338	10	)	)	PUNCT
ejpam-4226	338	11	=	=	SYM
ejpam-4226	338	12	v	v	NOUN
ejpam-4226	338	13	=	=	SYM
ejpam-4226	338	14	v1(t	v1(t	NOUN
ejpam-4226	338	15	)	)	PUNCT
ejpam-4226	338	16	and	and	CCONJ
ejpam-4226	338	17	ax	ax	NOUN
ejpam-4226	338	18	=	=	PUNCT
ejpam-4226	338	19	bx	bx	NOUN
ejpam-4226	338	20	=	=	PUNCT
ejpam-4226	338	21	y2	y2	PROPN
ejpam-4226	338	22	now	now	ADV
ejpam-4226	338	23	for	for	ADP
ejpam-4226	338	24	v(3α	v(3α	NOUN
ejpam-4226	338	25	)	)	PUNCT
ejpam-4226	338	26	=	=	SYM
ejpam-4226	338	27	v	v	NOUN
ejpam-4226	338	28	,	,	PUNCT
ejpam-4226	338	29	we	we	PRON
ejpam-4226	338	30	previously	previously	ADV
ejpam-4226	338	31	found	find	VERB
ejpam-4226	338	32	v(t	v(t	NOUN
ejpam-4226	338	33	)	)	PUNCT
ejpam-4226	338	34	=	=	SYM
ejpam-4226	338	35	exp	exp	NOUN
ejpam-4226	338	36	1	1	NUM
ejpam-4226	338	37	α	α	NOUN
ejpam-4226	338	38	tα	tα	PROPN
ejpam-4226	338	39	.	.	PUNCT
ejpam-4226	339	1	substitute	substitute	PROPN
ejpam-4226	339	2	in	in	ADP
ejpam-4226	339	3	the	the	DET
ejpam-4226	339	4	main	main	ADJ
ejpam-4226	339	5	equation	equation	NOUN
ejpam-4226	339	6	we	we	PRON
ejpam-4226	339	7	get	get	VERB
ejpam-4226	339	8	exp	exp	NOUN
ejpam-4226	339	9	1	1	NUM
ejpam-4226	339	10	α	α	NOUN
ejpam-4226	339	11	tα	tα	VERB
ejpam-4226	340	1	⊗	⊗	PROPN
ejpam-4226	340	2	x+	x+	INTJ
ejpam-4226	340	3	exp	exp	NOUN
ejpam-4226	340	4	1	1	NUM
ejpam-4226	340	5	α	α	NOUN
ejpam-4226	340	6	tα	tα	PROPN
ejpam-4226	340	7	⊗	⊗	PROPN
ejpam-4226	340	8	ax+	ax+	PROPN
ejpam-4226	340	9	exp	exp	NOUN
ejpam-4226	340	10	1	1	NUM
ejpam-4226	340	11	α	α	NOUN
ejpam-4226	340	12	tα	tα	VERB
ejpam-4226	340	13	⊗bx+	⊗bx+	PROPN
ejpam-4226	340	14	exp	exp	NOUN
ejpam-4226	340	15	1	1	NUM
ejpam-4226	340	16	α	α	NOUN
ejpam-4226	340	17	tα	tα	VERB
ejpam-4226	340	18	⊗	⊗	PROPN
ejpam-4226	340	19	cx	cx	PROPN
ejpam-4226	341	1	=	=	PUNCT
ejpam-4226	341	2	f(t)⊗	f(t)⊗	PROPN
ejpam-4226	341	3	z	z	NOUN
ejpam-4226	341	4	but	but	CCONJ
ejpam-4226	341	5	ax	ax	NOUN
ejpam-4226	341	6	=	=	PUNCT
ejpam-4226	341	7	bx	bx	PROPN
ejpam-4226	341	8	,	,	PUNCT
ejpam-4226	341	9	so	so	ADV
ejpam-4226	341	10	exp	exp	NOUN
ejpam-4226	341	11	1	1	NUM
ejpam-4226	341	12	α	α	NOUN
ejpam-4226	341	13	tα	tα	PROPN
ejpam-4226	341	14	⊗	⊗	PROPN
ejpam-4226	341	15	(	(	PUNCT
ejpam-4226	341	16	x+	x+	PROPN
ejpam-4226	341	17	2ax+	2ax+	NUM
ejpam-4226	341	18	cx	cx	NOUN
ejpam-4226	341	19	)	)	PUNCT
ejpam-4226	341	20	=	=	SYM
ejpam-4226	341	21	f(t)⊗	f(t)⊗	PROPN
ejpam-4226	341	22	z	z	NOUN
ejpam-4226	341	23	.	.	PUNCT
ejpam-4226	342	1	then	then	ADV
ejpam-4226	342	2	for	for	SCONJ
ejpam-4226	342	3	the	the	DET
ejpam-4226	342	4	atomic	atomic	ADJ
ejpam-4226	342	5	solution	solution	NOUN
ejpam-4226	342	6	to	to	PART
ejpam-4226	342	7	exist	exist	VERB
ejpam-4226	342	8	,	,	PUNCT
ejpam-4226	342	9	f	f	PROPN
ejpam-4226	342	10	must	must	AUX
ejpam-4226	342	11	be	be	AUX
ejpam-4226	342	12	equal	equal	ADJ
ejpam-4226	342	13	to	to	ADP
ejpam-4226	342	14	exp	exp	NOUN
ejpam-4226	342	15	1	1	NUM
ejpam-4226	342	16	α	α	NOUN
ejpam-4226	342	17	t	t	NOUN
ejpam-4226	342	18	α	α	NOUN
ejpam-4226	342	19	,	,	PUNCT
ejpam-4226	342	20	and	and	CCONJ
ejpam-4226	342	21	[	[	X
ejpam-4226	342	22	i	i	X
ejpam-4226	342	23	+	+	NOUN
ejpam-4226	342	24	2a+	2a+	NUM
ejpam-4226	342	25	c]x	c]x	NOUN
ejpam-4226	342	26	=	=	SYM
ejpam-4226	342	27	z.	z.	PROPN
ejpam-4226	342	28	situation	situation	NOUN
ejpam-4226	342	29	(	(	PUNCT
ejpam-4226	342	30	3	3	NUM
ejpam-4226	342	31	)	)	PUNCT
ejpam-4226	342	32			PUNCT
ejpam-4226	342	33	x	x	PUNCT
ejpam-4226	342	34	=	=	PUNCT
ejpam-4226	342	35	cx	cx	PROPN
ejpam-4226	342	36	=	=	PUNCT
ejpam-4226	342	37	y1	y1	PROPN
ejpam-4226	342	38	and	and	CCONJ
ejpam-4226	342	39	v(2α	v(2α	NOUN
ejpam-4226	342	40	)	)	PUNCT
ejpam-4226	343	1	=	=	SYM
ejpam-4226	343	2	v(α	v(α	PROPN
ejpam-4226	343	3	)	)	PUNCT
ejpam-4226	343	4	=	=	SYM
ejpam-4226	343	5	v2	v2	PROPN
ejpam-4226	343	6	f.	f.	PROPN
ejpam-4226	343	7	bekraoui	bekraoui	PROPN
ejpam-4226	343	8	,	,	PUNCT
ejpam-4226	343	9	m.	m.	PROPN
ejpam-4226	343	10	al	al	PROPN
ejpam-4226	343	11	horani	horani	PROPN
ejpam-4226	343	12	,	,	PUNCT
ejpam-4226	343	13	r.	r.	PROPN
ejpam-4226	343	14	khalil	khalil	PROPN
ejpam-4226	343	15	/	/	SYM
ejpam-4226	343	16	eur	eur	PROPN
ejpam-4226	343	17	.	.	PUNCT
ejpam-4226	344	1	j.	j.	PROPN
ejpam-4226	344	2	pure	pure	PROPN
ejpam-4226	344	3	appl	appl	PROPN
ejpam-4226	344	4	.	.	PROPN
ejpam-4226	344	5	math	math	PROPN
ejpam-4226	344	6	,	,	PUNCT
ejpam-4226	344	7	15	15	NUM
ejpam-4226	344	8	(	(	PUNCT
ejpam-4226	344	9	1	1	NUM
ejpam-4226	344	10	)	)	PUNCT
ejpam-4226	344	11	(	(	PUNCT
ejpam-4226	344	12	2022	2022	NUM
ejpam-4226	344	13	)	)	PUNCT
ejpam-4226	344	14	,	,	PUNCT
ejpam-4226	344	15	106	106	NUM
ejpam-4226	344	16	-	-	SYM
ejpam-4226	344	17	125	125	NUM
ejpam-4226	344	18	121	121	NUM
ejpam-4226	344	19	now	now	ADV
ejpam-4226	344	20	for	for	ADP
ejpam-4226	344	21	v(2α	v(2α	NOUN
ejpam-4226	344	22	)	)	PUNCT
ejpam-4226	344	23	=	=	SYM
ejpam-4226	344	24	v(α	v(α	PROPN
ejpam-4226	344	25	)	)	PUNCT
ejpam-4226	345	1	,	,	PUNCT
ejpam-4226	345	2	we	we	PRON
ejpam-4226	345	3	already	already	ADV
ejpam-4226	345	4	have	have	VERB
ejpam-4226	345	5	v(t	v(t	NOUN
ejpam-4226	345	6	)	)	PUNCT
ejpam-4226	345	7	=	=	SYM
ejpam-4226	345	8	exp	exp	NOUN
ejpam-4226	345	9	1	1	NUM
ejpam-4226	345	10	α	α	NOUN
ejpam-4226	345	11	tα	tα	PROPN
ejpam-4226	345	12	.	.	PUNCT
ejpam-4226	346	1	substitute	substitute	PROPN
ejpam-4226	346	2	in	in	ADP
ejpam-4226	346	3	the	the	DET
ejpam-4226	346	4	main	main	ADJ
ejpam-4226	346	5	equation	equation	NOUN
ejpam-4226	346	6	we	we	PRON
ejpam-4226	346	7	get	get	VERB
ejpam-4226	346	8	exp	exp	NOUN
ejpam-4226	346	9	1	1	NUM
ejpam-4226	346	10	α	α	NOUN
ejpam-4226	346	11	tα	tα	VERB
ejpam-4226	347	1	⊗	⊗	PROPN
ejpam-4226	347	2	x+	x+	INTJ
ejpam-4226	347	3	exp	exp	NOUN
ejpam-4226	347	4	1	1	NUM
ejpam-4226	347	5	α	α	NOUN
ejpam-4226	347	6	tα	tα	VERB
ejpam-4226	347	7	⊗ax+	⊗ax+	ADJ
ejpam-4226	347	8	exp	exp	NOUN
ejpam-4226	347	9	1	1	NUM
ejpam-4226	347	10	α	α	NOUN
ejpam-4226	347	11	tα	tα	VERB
ejpam-4226	347	12	⊗bx+	⊗bx+	PROPN
ejpam-4226	347	13	exp	exp	NOUN
ejpam-4226	347	14	1	1	NUM
ejpam-4226	347	15	α	α	NOUN
ejpam-4226	347	16	tα	tα	VERB
ejpam-4226	347	17	⊗	⊗	PROPN
ejpam-4226	347	18	cx	cx	PROPN
ejpam-4226	348	1	=	=	PUNCT
ejpam-4226	349	1	f(t)⊗	f(t)⊗	PROPN
ejpam-4226	350	1	z	z	NOUN
ejpam-4226	350	2	since	since	SCONJ
ejpam-4226	350	3	x	x	PROPN
ejpam-4226	350	4	=	=	SYM
ejpam-4226	350	5	cx	cx	PROPN
ejpam-4226	350	6	,	,	PUNCT
ejpam-4226	350	7	then	then	ADV
ejpam-4226	350	8	exp	exp	NOUN
ejpam-4226	350	9	1	1	NUM
ejpam-4226	350	10	α	α	NOUN
ejpam-4226	350	11	tα	tα	PROPN
ejpam-4226	350	12	⊗	⊗	PROPN
ejpam-4226	350	13	(	(	PUNCT
ejpam-4226	350	14	2x+ax+bx	2x+ax+bx	NUM
ejpam-4226	350	15	)	)	PUNCT
ejpam-4226	350	16	=	=	SYM
ejpam-4226	350	17	f(t)⊗	f(t)⊗	PROPN
ejpam-4226	350	18	z	z	NOUN
ejpam-4226	350	19	.	.	PUNCT
ejpam-4226	351	1	then	then	ADV
ejpam-4226	351	2	for	for	SCONJ
ejpam-4226	351	3	the	the	DET
ejpam-4226	351	4	atomic	atomic	ADJ
ejpam-4226	351	5	solution	solution	NOUN
ejpam-4226	351	6	to	to	PART
ejpam-4226	351	7	exist	exist	VERB
ejpam-4226	351	8	,	,	PUNCT
ejpam-4226	351	9	f	f	PROPN
ejpam-4226	351	10	must	must	AUX
ejpam-4226	351	11	be	be	AUX
ejpam-4226	351	12	equal	equal	ADJ
ejpam-4226	351	13	to	to	ADP
ejpam-4226	351	14	exp	exp	NOUN
ejpam-4226	351	15	1	1	NUM
ejpam-4226	351	16	α	α	NOUN
ejpam-4226	351	17	t	t	NOUN
ejpam-4226	351	18	α	α	NOUN
ejpam-4226	351	19	,	,	PUNCT
ejpam-4226	351	20	and	and	CCONJ
ejpam-4226	351	21	[	[	X
ejpam-4226	351	22	2i	2i	NUM
ejpam-4226	351	23	+	+	NOUN
ejpam-4226	351	24	a+b]x	a+b]x	PROPN
ejpam-4226	351	25	=	=	ADJ
ejpam-4226	351	26	z.	z.	PROPN
ejpam-4226	351	27	situation	situation	NOUN
ejpam-4226	351	28	(	(	PUNCT
ejpam-4226	351	29	4	4	NUM
ejpam-4226	351	30	)	)	PUNCT
ejpam-4226	351	31			PUNCT
ejpam-4226	351	32	x	x	PUNCT
ejpam-4226	352	1	=	=	PUNCT
ejpam-4226	352	2	cx	cx	PROPN
ejpam-4226	352	3	=	=	PUNCT
ejpam-4226	352	4	y1	y1	NOUN
ejpam-4226	352	5	and	and	CCONJ
ejpam-4226	352	6	ax	ax	NOUN
ejpam-4226	352	7	=	=	PUNCT
ejpam-4226	352	8	bx	bx	NOUN
ejpam-4226	353	1	=	=	PUNCT
ejpam-4226	353	2	y2	y2	PROPN
ejpam-4226	354	1	so	so	SCONJ
ejpam-4226	354	2	[	[	PUNCT
ejpam-4226	354	3	v(3α	v(3α	NOUN
ejpam-4226	354	4	)	)	PUNCT
ejpam-4226	354	5	+	+	X
ejpam-4226	355	1	v	v	ADP
ejpam-4226	355	2	]	]	PUNCT
ejpam-4226	355	3	⊗	⊗	NUM
ejpam-4226	355	4	x+	x+	PUNCT
ejpam-4226	355	5	[	[	PUNCT
ejpam-4226	355	6	v(2α	v(2α	X
ejpam-4226	355	7	)	)	PUNCT
ejpam-4226	355	8	+	+	CCONJ
ejpam-4226	355	9	v(α	v(α	NOUN
ejpam-4226	355	10	)	)	PUNCT
ejpam-4226	355	11	]	]	PUNCT
ejpam-4226	355	12	⊗ax	⊗ax	PUNCT
ejpam-4226	356	1	=	=	PUNCT
ejpam-4226	356	2	f	f	PROPN
ejpam-4226	356	3	⊗	⊗	PROPN
ejpam-4226	356	4	z.	z.	PROPN
ejpam-4226	356	5	then	then	ADV
ejpam-4226	356	6	we	we	PRON
ejpam-4226	356	7	have	have	VERB
ejpam-4226	356	8	two	two	NUM
ejpam-4226	356	9	cases	case	NOUN
ejpam-4226	356	10	v(3α	v(3α	NOUN
ejpam-4226	356	11	)	)	PUNCT
ejpam-4226	357	1	+	+	CCONJ
ejpam-4226	357	2	v	v	NOUN
ejpam-4226	357	3	=	=	SYM
ejpam-4226	357	4	v(2α	v(2α	NOUN
ejpam-4226	357	5	)	)	PUNCT
ejpam-4226	358	1	+	+	CCONJ
ejpam-4226	358	2	v(α	v(α	NOUN
ejpam-4226	358	3	)	)	PUNCT
ejpam-4226	358	4	=	=	SYM
ejpam-4226	358	5	f	f	PROPN
ejpam-4226	358	6	or	or	CCONJ
ejpam-4226	358	7	x	x	X
ejpam-4226	358	8	=	=	NOUN
ejpam-4226	358	9	ax	ax	NOUN
ejpam-4226	359	1	=	=	PUNCT
ejpam-4226	359	2	z	z	NOUN
ejpam-4226	359	3	if	if	SCONJ
ejpam-4226	359	4	x	x	X
ejpam-4226	359	5	=	=	SYM
ejpam-4226	359	6	ax	ax	NOUN
ejpam-4226	359	7	,	,	PUNCT
ejpam-4226	359	8	then	then	ADV
ejpam-4226	359	9	[	[	PUNCT
ejpam-4226	359	10	v(3α	v(3α	NOUN
ejpam-4226	359	11	)	)	PUNCT
ejpam-4226	359	12	+	+	NUM
ejpam-4226	359	13	v(2α	v(2α	NOUN
ejpam-4226	359	14	)	)	PUNCT
ejpam-4226	359	15	+	+	CCONJ
ejpam-4226	359	16	v(α	v(α	NOUN
ejpam-4226	359	17	)	)	PUNCT
ejpam-4226	360	1	+	+	X
ejpam-4226	360	2	v	v	ADP
ejpam-4226	360	3	]	]	PUNCT
ejpam-4226	360	4	⊗	⊗	PROPN
ejpam-4226	360	5	x	x	X
ejpam-4226	361	1	=	=	PUNCT
ejpam-4226	361	2	f	f	PROPN
ejpam-4226	361	3	⊗	⊗	PROPN
ejpam-4226	361	4	z	z	PROPN
ejpam-4226	361	5	.	.	PUNCT
ejpam-4226	362	1	then	then	ADV
ejpam-4226	362	2	v(3α	v(3α	NOUN
ejpam-4226	362	3	)	)	PUNCT
ejpam-4226	362	4	+	+	NOUN
ejpam-4226	362	5	v(2α	v(2α	NOUN
ejpam-4226	362	6	)	)	PUNCT
ejpam-4226	363	1	+	+	CCONJ
ejpam-4226	364	1	v(α	v(α	NOUN
ejpam-4226	364	2	)	)	PUNCT
ejpam-4226	364	3	+	+	X
ejpam-4226	364	4	v	v	NOUN
ejpam-4226	364	5	=	=	SYM
ejpam-4226	364	6	f	f	X
ejpam-4226	364	7	which	which	PRON
ejpam-4226	364	8	already	already	ADV
ejpam-4226	364	9	solved	solve	VERB
ejpam-4226	364	10	in	in	ADP
ejpam-4226	364	11	case	case	NOUN
ejpam-4226	364	12	2	2	NUM
ejpam-4226	364	13	.	.	PUNCT
ejpam-4226	365	1	if	if	SCONJ
ejpam-4226	365	2	v(3α	v(3α	NOUN
ejpam-4226	365	3	)	)	PUNCT
ejpam-4226	366	1	+	+	CCONJ
ejpam-4226	366	2	v	v	NOUN
ejpam-4226	366	3	=	=	SYM
ejpam-4226	366	4	v(2α	v(2α	NOUN
ejpam-4226	366	5	)	)	PUNCT
ejpam-4226	366	6	+	+	CCONJ
ejpam-4226	366	7	v(α	v(α	NOUN
ejpam-4226	366	8	)	)	PUNCT
ejpam-4226	366	9	=	=	SYM
ejpam-4226	366	10	f	f	PROPN
ejpam-4226	366	11	,	,	PUNCT
ejpam-4226	366	12	then	then	ADV
ejpam-4226	366	13	(	(	PUNCT
ejpam-4226	366	14	i	i	PRON
ejpam-4226	366	15	+	+	X
ejpam-4226	366	16	a)x	a)x	PUNCT
ejpam-4226	367	1	=	=	VERB
ejpam-4226	367	2	z.	z.	PROPN
ejpam-4226	367	3	now	now	ADV
ejpam-4226	367	4	for	for	ADP
ejpam-4226	367	5	v(3α	v(3α	NOUN
ejpam-4226	367	6	)	)	PUNCT
ejpam-4226	367	7	+	+	CCONJ
ejpam-4226	367	8	v	v	X
ejpam-4226	367	9	=	=	SYM
ejpam-4226	367	10	f	f	NOUN
ejpam-4226	367	11	,	,	PUNCT
ejpam-4226	367	12	the	the	DET
ejpam-4226	367	13	general	general	ADJ
ejpam-4226	367	14	solution	solution	NOUN
ejpam-4226	367	15	is	be	AUX
ejpam-4226	367	16	given	give	VERB
ejpam-4226	367	17	by	by	ADP
ejpam-4226	367	18	vg	vg	NOUN
ejpam-4226	367	19	=	=	SYM
ejpam-4226	367	20	vh	vh	PROPN
ejpam-4226	367	21	+	+	CCONJ
ejpam-4226	367	22	vp	vp	PROPN
ejpam-4226	367	23	,	,	PUNCT
ejpam-4226	367	24	the	the	DET
ejpam-4226	367	25	sum	sum	NOUN
ejpam-4226	367	26	of	of	ADP
ejpam-4226	367	27	the	the	DET
ejpam-4226	367	28	homogenous	homogenous	ADJ
ejpam-4226	367	29	solution	solution	NOUN
ejpam-4226	367	30	and	and	CCONJ
ejpam-4226	367	31	the	the	DET
ejpam-4226	367	32	particular	particular	ADJ
ejpam-4226	367	33	solution	solution	NOUN
ejpam-4226	367	34	.	.	PUNCT
ejpam-4226	368	1	for	for	ADP
ejpam-4226	368	2	the	the	DET
ejpam-4226	368	3	homogenous	homogenous	ADJ
ejpam-4226	368	4	solution	solution	NOUN
ejpam-4226	368	5	vh	vh	PROPN
ejpam-4226	368	6	,	,	PUNCT
ejpam-4226	368	7	the	the	DET
ejpam-4226	368	8	associated	associated	ADJ
ejpam-4226	368	9	characteristic	characteristic	ADJ
ejpam-4226	368	10	equation	equation	NOUN
ejpam-4226	368	11	is	be	AUX
ejpam-4226	368	12	r3	r3	PROPN
ejpam-4226	368	13	+	+	CCONJ
ejpam-4226	368	14	1	1	NUM
ejpam-4226	368	15	=	=	SYM
ejpam-4226	368	16	0	0	NUM
ejpam-4226	368	17	,	,	PUNCT
ejpam-4226	368	18	which	which	PRON
ejpam-4226	368	19	has	have	VERB
ejpam-4226	368	20	the	the	DET
ejpam-4226	368	21	roots	root	NOUN
ejpam-4226	368	22	−1	−1	NOUN
ejpam-4226	368	23	,	,	PUNCT
ejpam-4226	368	24	1±	1±	NUM
ejpam-4226	368	25	√	√	NOUN
ejpam-4226	368	26	3i	3i	NUM
ejpam-4226	368	27	2	2	NUM
ejpam-4226	368	28	.	.	PUNCT
ejpam-4226	369	1	then	then	ADV
ejpam-4226	369	2	vh(t	vh(t	PUNCT
ejpam-4226	369	3	)	)	PUNCT
ejpam-4226	370	1	=	=	SYM
ejpam-4226	370	2	c1	c1	PROPN
ejpam-4226	370	3	exp	exp	NOUN
ejpam-4226	370	4	(	(	PUNCT
ejpam-4226	370	5	−	−	PROPN
ejpam-4226	370	6	1	1	NUM
ejpam-4226	370	7	α	α	NOUN
ejpam-4226	370	8	tα	tα	PROPN
ejpam-4226	370	9	)	)	PUNCT
ejpam-4226	371	1	+	+	CCONJ
ejpam-4226	371	2	exp	exp	NOUN
ejpam-4226	371	3	(	(	PUNCT
ejpam-4226	371	4	1	1	NUM
ejpam-4226	371	5	2α	2α	NOUN
ejpam-4226	371	6	tα	tα	PROPN
ejpam-4226	371	7	)	)	PUNCT
ejpam-4226	371	8	(	(	PUNCT
ejpam-4226	371	9	c2	c2	PROPN
ejpam-4226	371	10	cos	cos	PROPN
ejpam-4226	371	11	√	√	PROPN
ejpam-4226	371	12	3	3	NUM
ejpam-4226	371	13	2α	2α	NOUN
ejpam-4226	371	14	tα	tα	PROPN
ejpam-4226	371	15	+	+	CCONJ
ejpam-4226	371	16	c3	c3	PROPN
ejpam-4226	371	17	sin	sin	NOUN
ejpam-4226	371	18	√	√	NUM
ejpam-4226	371	19	3	3	NUM
ejpam-4226	371	20	2α	2α	NOUN
ejpam-4226	371	21	tα	tα	PROPN
ejpam-4226	371	22	)	)	PUNCT
ejpam-4226	371	23	.	.	PUNCT
ejpam-4226	372	1	for	for	ADP
ejpam-4226	372	2	the	the	DET
ejpam-4226	372	3	particular	particular	ADJ
ejpam-4226	372	4	solution	solution	NOUN
ejpam-4226	372	5	,	,	PUNCT
ejpam-4226	372	6	we	we	PRON
ejpam-4226	372	7	use	use	VERB
ejpam-4226	372	8	variation	variation	NOUN
ejpam-4226	372	9	of	of	ADP
ejpam-4226	372	10	parameters	parameter	NOUN
ejpam-4226	372	11	.	.	PUNCT
ejpam-4226	373	1	let	let	VERB
ejpam-4226	373	2	u1	u1	NOUN
ejpam-4226	373	3	=	=	PUNCT
ejpam-4226	373	4	exp	exp	NOUN
ejpam-4226	373	5	(	(	PUNCT
ejpam-4226	373	6	−	−	PROPN
ejpam-4226	373	7	1	1	NUM
ejpam-4226	373	8	α	α	NOUN
ejpam-4226	373	9	tα	tα	PROPN
ejpam-4226	373	10	)	)	PUNCT
ejpam-4226	373	11	,	,	PUNCT
ejpam-4226	373	12	u2	u2	NOUN
ejpam-4226	373	13	=	=	PUNCT
ejpam-4226	373	14	exp	exp	NOUN
ejpam-4226	373	15	(	(	PUNCT
ejpam-4226	373	16	1	1	NUM
ejpam-4226	373	17	2α	2α	NOUN
ejpam-4226	373	18	tα	tα	PROPN
ejpam-4226	373	19	)	)	PUNCT
ejpam-4226	374	1	cos	cos	ADP
ejpam-4226	374	2	√	√	ADV
ejpam-4226	374	3	3	3	NUM
ejpam-4226	374	4	2α	2α	NOUN
ejpam-4226	374	5	tα	tα	PROPN
ejpam-4226	374	6	and	and	CCONJ
ejpam-4226	374	7	u3	u3	NOUN
ejpam-4226	374	8	=	=	PUNCT
ejpam-4226	374	9	exp	exp	NOUN
ejpam-4226	374	10	(	(	PUNCT
ejpam-4226	374	11	1	1	NUM
ejpam-4226	374	12	2α	2α	NOUN
ejpam-4226	374	13	tα	tα	PROPN
ejpam-4226	374	14	)	)	PUNCT
ejpam-4226	374	15	sin	sin	NOUN
ejpam-4226	374	16	√	√	NUM
ejpam-4226	374	17	3	3	NUM
ejpam-4226	374	18	2α	2α	NOUN
ejpam-4226	374	19	tα	tα	PROPN
ejpam-4226	374	20	.	.	PUNCT
ejpam-4226	374	21	vp(t	vp(t	PUNCT
ejpam-4226	374	22	)	)	PUNCT
ejpam-4226	375	1	=	=	SYM
ejpam-4226	375	2	3∑	3∑	NUM
ejpam-4226	375	3	m=1	m=1	X
ejpam-4226	375	4	um(t	um(t	NUM
ejpam-4226	375	5	)	)	PUNCT
ejpam-4226	376	1	∫	∫	PROPN
ejpam-4226	376	2	t	t	PROPN
ejpam-4226	376	3	a	a	DET
ejpam-4226	376	4	f(s)wα	f(s)wα	PROPN
ejpam-4226	376	5	m(s	m(s	PROPN
ejpam-4226	376	6	)	)	PUNCT
ejpam-4226	376	7	wα(s)s1−α	wα(s)s1−α	PROPN
ejpam-4226	377	1	ds	ds	PROPN
ejpam-4226	377	2	f.	f.	PROPN
ejpam-4226	377	3	bekraoui	bekraoui	PROPN
ejpam-4226	377	4	,	,	PUNCT
ejpam-4226	377	5	m.	m.	PROPN
ejpam-4226	377	6	al	al	PROPN
ejpam-4226	377	7	horani	horani	PROPN
ejpam-4226	377	8	,	,	PUNCT
ejpam-4226	377	9	r.	r.	PROPN
ejpam-4226	377	10	khalil	khalil	PROPN
ejpam-4226	377	11	/	/	SYM
ejpam-4226	377	12	eur	eur	PROPN
ejpam-4226	377	13	.	.	PUNCT
ejpam-4226	378	1	j.	j.	PROPN
ejpam-4226	378	2	pure	pure	PROPN
ejpam-4226	378	3	appl	appl	PROPN
ejpam-4226	378	4	.	.	PROPN
ejpam-4226	378	5	math	math	PROPN
ejpam-4226	378	6	,	,	PUNCT
ejpam-4226	378	7	15	15	NUM
ejpam-4226	378	8	(	(	PUNCT
ejpam-4226	378	9	1	1	NUM
ejpam-4226	378	10	)	)	PUNCT
ejpam-4226	378	11	(	(	PUNCT
ejpam-4226	378	12	2022	2022	NUM
ejpam-4226	378	13	)	)	PUNCT
ejpam-4226	378	14	,	,	PUNCT
ejpam-4226	378	15	106	106	NUM
ejpam-4226	378	16	-	-	SYM
ejpam-4226	378	17	125	125	NUM
ejpam-4226	378	18	122	122	NUM
ejpam-4226	378	19	=	=	SYM
ejpam-4226	378	20	exp	exp	NOUN
ejpam-4226	378	21	(	(	PUNCT
ejpam-4226	378	22	−	−	PROPN
ejpam-4226	378	23	1	1	NUM
ejpam-4226	378	24	α	α	NOUN
ejpam-4226	378	25	tα	tα	PROPN
ejpam-4226	378	26	)	)	PUNCT
ejpam-4226	379	1	∫	∫	PROPN
ejpam-4226	379	2	t	t	PROPN
ejpam-4226	379	3	a	a	DET
ejpam-4226	379	4	f(s)wα	f(s)wα	PROPN
ejpam-4226	379	5	1	1	NUM
ejpam-4226	379	6	(	(	PUNCT
ejpam-4226	379	7	s	s	NOUN
ejpam-4226	379	8	)	)	PUNCT
ejpam-4226	379	9	wα(s)s1−α	wα(s)s1−α	PROPN
ejpam-4226	380	1	ds	ds	PROPN
ejpam-4226	380	2	+	+	NOUN
ejpam-4226	380	3	exp	exp	NOUN
ejpam-4226	380	4	(	(	PUNCT
ejpam-4226	380	5	1	1	NUM
ejpam-4226	380	6	2α	2α	NOUN
ejpam-4226	380	7	tα	tα	PROPN
ejpam-4226	380	8	)	)	PUNCT
ejpam-4226	380	9	cos	cos	PROPN
ejpam-4226	380	10	(	(	PUNCT
ejpam-4226	380	11	√	√	NUM
ejpam-4226	380	12	3	3	NUM
ejpam-4226	380	13	2α	2α	PROPN
ejpam-4226	380	14	tα	tα	PROPN
ejpam-4226	380	15	)	)	PUNCT
ejpam-4226	380	16	∫	∫	PROPN
ejpam-4226	380	17	t	t	PROPN
ejpam-4226	380	18	a	a	DET
ejpam-4226	380	19	f(s)wα	f(s)wα	PROPN
ejpam-4226	380	20	2	2	NUM
ejpam-4226	380	21	(	(	PUNCT
ejpam-4226	380	22	s	s	NOUN
ejpam-4226	380	23	)	)	PUNCT
ejpam-4226	380	24	wα(s)s1−α	wα(s)s1−α	PROPN
ejpam-4226	380	25	ds	ds	PROPN
ejpam-4226	380	26	+	+	NOUN
ejpam-4226	380	27	exp	exp	NOUN
ejpam-4226	380	28	(	(	PUNCT
ejpam-4226	380	29	1	1	NUM
ejpam-4226	380	30	2α	2α	NOUN
ejpam-4226	380	31	tα	tα	PROPN
ejpam-4226	380	32	)	)	PUNCT
ejpam-4226	380	33	sin	sin	NOUN
ejpam-4226	380	34	(	(	PUNCT
ejpam-4226	380	35	√	√	NUM
ejpam-4226	380	36	3	3	NUM
ejpam-4226	380	37	2α	2α	NOUN
ejpam-4226	380	38	tα	tα	PROPN
ejpam-4226	380	39	)	)	PUNCT
ejpam-4226	380	40	∫	∫	PROPN
ejpam-4226	380	41	t	t	PROPN
ejpam-4226	380	42	a	a	DET
ejpam-4226	380	43	f(s)wα	f(s)wα	PROPN
ejpam-4226	380	44	3	3	NUM
ejpam-4226	380	45	(	(	PUNCT
ejpam-4226	380	46	s	s	NOUN
ejpam-4226	380	47	)	)	PUNCT
ejpam-4226	380	48	wα(s)s1−α	wα(s)s1−α	PROPN
ejpam-4226	380	49	ds	ds	PROPN
ejpam-4226	380	50	=	=	PUNCT
ejpam-4226	380	51	exp	exp	NOUN
ejpam-4226	380	52	(	(	PUNCT
ejpam-4226	380	53	−	−	PROPN
ejpam-4226	380	54	1	1	NUM
ejpam-4226	380	55	α	α	NOUN
ejpam-4226	380	56	tα	tα	PROPN
ejpam-4226	380	57	)	)	PUNCT
ejpam-4226	380	58	∫	∫	PROPN
ejpam-4226	380	59	t	t	PROPN
ejpam-4226	380	60	a	a	DET
ejpam-4226	380	61	f(s	f(	NOUN
ejpam-4226	380	62	)	)	PUNCT
ejpam-4226	380	63	3s1−α	3s1−α	PROPN
ejpam-4226	380	64	ds	ds	ADJ
ejpam-4226	380	65	−	−	NOUN
ejpam-4226	380	66	exp	exp	NOUN
ejpam-4226	380	67	(	(	PUNCT
ejpam-4226	380	68	1	1	NUM
ejpam-4226	380	69	2α	2α	NOUN
ejpam-4226	380	70	tα	tα	PROPN
ejpam-4226	380	71	)	)	PUNCT
ejpam-4226	380	72	cos	cos	PROPN
ejpam-4226	380	73	(	(	PUNCT
ejpam-4226	380	74	√	√	NUM
ejpam-4226	380	75	3	3	NUM
ejpam-4226	380	76	2α	2α	PROPN
ejpam-4226	380	77	tα	tα	PROPN
ejpam-4226	380	78	)	)	PUNCT
ejpam-4226	381	1	×	×	PROPN
ejpam-4226	381	2	∫	∫	PROPN
ejpam-4226	381	3	t	t	PROPN
ejpam-4226	381	4	a	a	DET
ejpam-4226	381	5	f(s	f(	NOUN
ejpam-4226	381	6	)	)	PUNCT
ejpam-4226	381	7	exp	exp	NOUN
ejpam-4226	381	8	(	(	PUNCT
ejpam-4226	381	9	−	−	PROPN
ejpam-4226	381	10	1	1	NUM
ejpam-4226	381	11	2α	2α	NOUN
ejpam-4226	381	12	sα	sα	ADV
ejpam-4226	381	13	)	)	PUNCT
ejpam-4226	382	1	[	[	PUNCT
ejpam-4226	382	2	cos	cos	X
ejpam-4226	382	3	(	(	PUNCT
ejpam-4226	382	4	√	√	NUM
ejpam-4226	382	5	3	3	NUM
ejpam-4226	382	6	2α	2α	NOUN
ejpam-4226	382	7	sα	sα	ADV
ejpam-4226	382	8	)	)	PUNCT
ejpam-4226	382	9	+	+	CCONJ
ejpam-4226	382	10	sin	sin	NOUN
ejpam-4226	382	11	(	(	PUNCT
ejpam-4226	382	12	√	√	NUM
ejpam-4226	382	13	3	3	NUM
ejpam-4226	382	14	2α	2α	NOUN
ejpam-4226	382	15	sα	sα	ADV
ejpam-4226	382	16	)	)	PUNCT
ejpam-4226	382	17	]	]	PUNCT
ejpam-4226	382	18	3	3	NUM
ejpam-4226	382	19	√	√	NUM
ejpam-4226	382	20	3s1−α	3s1−α	NUM
ejpam-4226	382	21	ds	ds	ADJ
ejpam-4226	382	22	+	+	NOUN
ejpam-4226	382	23	exp	exp	NOUN
ejpam-4226	382	24	(	(	PUNCT
ejpam-4226	382	25	1	1	NUM
ejpam-4226	382	26	2α	2α	NOUN
ejpam-4226	382	27	tα	tα	PROPN
ejpam-4226	382	28	)	)	PUNCT
ejpam-4226	382	29	sin	sin	NOUN
ejpam-4226	382	30	(	(	PUNCT
ejpam-4226	382	31	√	√	NUM
ejpam-4226	382	32	3	3	NUM
ejpam-4226	382	33	2α	2α	NOUN
ejpam-4226	382	34	tα	tα	PROPN
ejpam-4226	382	35	)	)	PUNCT
ejpam-4226	382	36	×	×	PROPN
ejpam-4226	382	37	∫	∫	PROPN
ejpam-4226	382	38	t	t	PROPN
ejpam-4226	382	39	a	a	DET
ejpam-4226	382	40	f(s	f(	NOUN
ejpam-4226	382	41	)	)	PUNCT
ejpam-4226	382	42	exp	exp	NOUN
ejpam-4226	382	43	(	(	PUNCT
ejpam-4226	382	44	−	−	PROPN
ejpam-4226	382	45	1	1	NUM
ejpam-4226	382	46	2α	2α	NOUN
ejpam-4226	382	47	sα	sα	ADV
ejpam-4226	382	48	)	)	PUNCT
ejpam-4226	382	49	[	[	PUNCT
ejpam-4226	382	50	cos	cos	X
ejpam-4226	382	51	(	(	PUNCT
ejpam-4226	382	52	√	√	NUM
ejpam-4226	382	53	3	3	NUM
ejpam-4226	382	54	2α	2α	NOUN
ejpam-4226	382	55	sα	sα	ADV
ejpam-4226	382	56	)	)	PUNCT
ejpam-4226	382	57	−	−	ADP
ejpam-4226	382	58	√	√	NUM
ejpam-4226	382	59	3	3	NUM
ejpam-4226	382	60	sin	sin	NOUN
ejpam-4226	382	61	(	(	PUNCT
ejpam-4226	382	62	√	√	NUM
ejpam-4226	382	63	3	3	NUM
ejpam-4226	382	64	2α	2α	NOUN
ejpam-4226	382	65	sα	sα	ADV
ejpam-4226	382	66	)	)	PUNCT
ejpam-4226	382	67	]	]	PUNCT
ejpam-4226	382	68	3	3	NUM
ejpam-4226	382	69	√	√	NUM
ejpam-4226	382	70	3s1−α	3s1−α	NUM
ejpam-4226	382	71	ds	ds	ADJ
ejpam-4226	382	72	=	=	PUNCT
ejpam-4226	382	73	exp	exp	NOUN
ejpam-4226	382	74	(	(	PUNCT
ejpam-4226	382	75	−	−	PROPN
ejpam-4226	382	76	1	1	NUM
ejpam-4226	382	77	α	α	NOUN
ejpam-4226	382	78	tα	tα	PROPN
ejpam-4226	382	79	)	)	PUNCT
ejpam-4226	382	80	iaα	iaα	NOUN
ejpam-4226	382	81	(	(	PUNCT
ejpam-4226	382	82	1	1	NUM
ejpam-4226	382	83	3	3	NUM
ejpam-4226	382	84	f(t	f(t	NOUN
ejpam-4226	382	85	)	)	PUNCT
ejpam-4226	382	86	)	)	PUNCT
ejpam-4226	383	1	−	−	PROPN
ejpam-4226	383	2	exp	exp	NOUN
ejpam-4226	383	3	(	(	PUNCT
ejpam-4226	383	4	1	1	NUM
ejpam-4226	383	5	2α	2α	NOUN
ejpam-4226	383	6	tα	tα	PROPN
ejpam-4226	383	7	)	)	PUNCT
ejpam-4226	383	8	cos	cos	PROPN
ejpam-4226	383	9	(	(	PUNCT
ejpam-4226	383	10	√	√	NUM
ejpam-4226	383	11	3	3	NUM
ejpam-4226	383	12	2α	2α	PROPN
ejpam-4226	383	13	tα	tα	PROPN
ejpam-4226	383	14	)	)	PUNCT
ejpam-4226	383	15	×	×	NOUN
ejpam-4226	383	16	iaα	iaα	NOUN
ejpam-4226	383	17	(	(	PUNCT
ejpam-4226	383	18	1	1	NUM
ejpam-4226	383	19	3	3	NUM
ejpam-4226	383	20	f(t	f(t	NOUN
ejpam-4226	383	21	)	)	PUNCT
ejpam-4226	383	22	exp	exp	NOUN
ejpam-4226	383	23	(	(	PUNCT
ejpam-4226	383	24	−	−	PROPN
ejpam-4226	383	25	1	1	NUM
ejpam-4226	383	26	2α	2α	NOUN
ejpam-4226	383	27	tα	tα	PROPN
ejpam-4226	383	28	)	)	PUNCT
ejpam-4226	383	29	[	[	PUNCT
ejpam-4226	383	30	cos	cos	X
ejpam-4226	383	31	(	(	PUNCT
ejpam-4226	383	32	√	√	NUM
ejpam-4226	383	33	3	3	NUM
ejpam-4226	383	34	2α	2α	NOUN
ejpam-4226	383	35	tα	tα	PROPN
ejpam-4226	383	36	)	)	PUNCT
ejpam-4226	383	37	+	+	CCONJ
ejpam-4226	383	38	sin	sin	NOUN
ejpam-4226	383	39	(	(	PUNCT
ejpam-4226	383	40	√	√	NUM
ejpam-4226	383	41	3	3	NUM
ejpam-4226	383	42	2α	2α	NOUN
ejpam-4226	383	43	tα	tα	PROPN
ejpam-4226	383	44	)	)	PUNCT
ejpam-4226	383	45	]	]	PUNCT
ejpam-4226	383	46	)	)	PUNCT
ejpam-4226	384	1	+	+	NOUN
ejpam-4226	384	2	exp	exp	NOUN
ejpam-4226	384	3	(	(	PUNCT
ejpam-4226	384	4	1	1	NUM
ejpam-4226	384	5	2α	2α	NOUN
ejpam-4226	384	6	tα	tα	PROPN
ejpam-4226	384	7	)	)	PUNCT
ejpam-4226	384	8	sin	sin	NOUN
ejpam-4226	384	9	(	(	PUNCT
ejpam-4226	384	10	√	√	NUM
ejpam-4226	384	11	3	3	NUM
ejpam-4226	384	12	2α	2α	NOUN
ejpam-4226	384	13	tα	tα	PROPN
ejpam-4226	384	14	)	)	PUNCT
ejpam-4226	384	15	iaα	iaα	NOUN
ejpam-4226	384	16	(	(	PUNCT
ejpam-4226	384	17	1	1	NUM
ejpam-4226	384	18	3	3	NUM
ejpam-4226	384	19	f(t	f(t	NOUN
ejpam-4226	384	20	)	)	PUNCT
ejpam-4226	384	21	exp	exp	NOUN
ejpam-4226	384	22	(	(	PUNCT
ejpam-4226	384	23	−	−	PROPN
ejpam-4226	384	24	1	1	NUM
ejpam-4226	384	25	2α	2α	NOUN
ejpam-4226	384	26	tα	tα	PROPN
ejpam-4226	384	27	)	)	PUNCT
ejpam-4226	384	28	×	×	PROPN
ejpam-4226	384	29	[	[	PUNCT
ejpam-4226	384	30	cos	cos	NOUN
ejpam-4226	384	31	(	(	PUNCT
ejpam-4226	384	32	√	√	NUM
ejpam-4226	384	33	3	3	NUM
ejpam-4226	384	34	2α	2α	NOUN
ejpam-4226	384	35	tα	tα	PROPN
ejpam-4226	384	36	)	)	PUNCT
ejpam-4226	384	37	−	−	ADP
ejpam-4226	385	1	√	√	NUM
ejpam-4226	385	2	3	3	NUM
ejpam-4226	385	3	sin	sin	NOUN
ejpam-4226	385	4	(	(	PUNCT
ejpam-4226	385	5	√	√	NUM
ejpam-4226	385	6	3	3	NUM
ejpam-4226	385	7	2α	2α	NOUN
ejpam-4226	385	8	tα	tα	PROPN
ejpam-4226	385	9	)	)	PUNCT
ejpam-4226	385	10	]	]	PUNCT
ejpam-4226	385	11	)	)	PUNCT
ejpam-4226	385	12	hence	hence	ADV
ejpam-4226	385	13	v(t	v(t	NOUN
ejpam-4226	385	14	)	)	PUNCT
ejpam-4226	385	15	=	=	SYM
ejpam-4226	385	16	vh	vh	PROPN
ejpam-4226	385	17	+	+	CCONJ
ejpam-4226	385	18	vp	vp	PROPN
ejpam-4226	385	19	=	=	SYM
ejpam-4226	385	20	c1	c1	PROPN
ejpam-4226	385	21	exp	exp	NOUN
ejpam-4226	385	22	(	(	PUNCT
ejpam-4226	385	23	−	−	PROPN
ejpam-4226	385	24	1	1	NUM
ejpam-4226	385	25	α	α	NOUN
ejpam-4226	385	26	tα	tα	PROPN
ejpam-4226	385	27	)	)	PUNCT
ejpam-4226	386	1	+	+	CCONJ
ejpam-4226	386	2	exp	exp	NOUN
ejpam-4226	386	3	(	(	PUNCT
ejpam-4226	386	4	1	1	NUM
ejpam-4226	386	5	2α	2α	NOUN
ejpam-4226	386	6	tα	tα	PROPN
ejpam-4226	386	7	)	)	PUNCT
ejpam-4226	386	8	(	(	PUNCT
ejpam-4226	386	9	c2	c2	PROPN
ejpam-4226	386	10	cos	cos	PROPN
ejpam-4226	386	11	√	√	PROPN
ejpam-4226	386	12	3	3	NUM
ejpam-4226	386	13	2α	2α	NOUN
ejpam-4226	386	14	tα	tα	PROPN
ejpam-4226	386	15	+	+	CCONJ
ejpam-4226	386	16	c3	c3	PROPN
ejpam-4226	386	17	sin	sin	NOUN
ejpam-4226	386	18	√	√	NUM
ejpam-4226	386	19	3	3	NUM
ejpam-4226	386	20	2α	2α	NOUN
ejpam-4226	386	21	tα	tα	PROPN
ejpam-4226	386	22	)	)	PUNCT
ejpam-4226	387	1	+	+	NOUN
ejpam-4226	387	2	exp	exp	NOUN
ejpam-4226	387	3	(	(	PUNCT
ejpam-4226	387	4	−	−	PROPN
ejpam-4226	387	5	1	1	NUM
ejpam-4226	387	6	α	α	NOUN
ejpam-4226	387	7	tα	tα	PROPN
ejpam-4226	387	8	)	)	PUNCT
ejpam-4226	387	9	iaα	iaα	NOUN
ejpam-4226	387	10	(	(	PUNCT
ejpam-4226	387	11	1	1	NUM
ejpam-4226	387	12	3	3	NUM
ejpam-4226	387	13	f(t	f(t	NOUN
ejpam-4226	387	14	)	)	PUNCT
ejpam-4226	387	15	)	)	PUNCT
ejpam-4226	388	1	−	−	PROPN
ejpam-4226	388	2	exp	exp	NOUN
ejpam-4226	388	3	(	(	PUNCT
ejpam-4226	388	4	1	1	NUM
ejpam-4226	388	5	2α	2α	NOUN
ejpam-4226	388	6	tα	tα	PROPN
ejpam-4226	388	7	)	)	PUNCT
ejpam-4226	388	8	cos	cos	PROPN
ejpam-4226	388	9	(	(	PUNCT
ejpam-4226	388	10	√	√	NUM
ejpam-4226	388	11	3	3	NUM
ejpam-4226	388	12	2α	2α	PROPN
ejpam-4226	388	13	tα	tα	PROPN
ejpam-4226	388	14	)	)	PUNCT
ejpam-4226	388	15	×	×	PROPN
ejpam-4226	388	16	f.	f.	PROPN
ejpam-4226	388	17	bekraoui	bekraoui	PROPN
ejpam-4226	388	18	,	,	PUNCT
ejpam-4226	388	19	m.	m.	PROPN
ejpam-4226	388	20	al	al	PROPN
ejpam-4226	388	21	horani	horani	PROPN
ejpam-4226	388	22	,	,	PUNCT
ejpam-4226	388	23	r.	r.	PROPN
ejpam-4226	388	24	khalil	khalil	PROPN
ejpam-4226	388	25	/	/	SYM
ejpam-4226	388	26	eur	eur	PROPN
ejpam-4226	388	27	.	.	PUNCT
ejpam-4226	389	1	j.	j.	PROPN
ejpam-4226	389	2	pure	pure	PROPN
ejpam-4226	389	3	appl	appl	PROPN
ejpam-4226	389	4	.	.	PROPN
ejpam-4226	389	5	math	math	PROPN
ejpam-4226	389	6	,	,	PUNCT
ejpam-4226	389	7	15	15	NUM
ejpam-4226	389	8	(	(	PUNCT
ejpam-4226	389	9	1	1	NUM
ejpam-4226	389	10	)	)	PUNCT
ejpam-4226	389	11	(	(	PUNCT
ejpam-4226	389	12	2022	2022	NUM
ejpam-4226	389	13	)	)	PUNCT
ejpam-4226	389	14	,	,	PUNCT
ejpam-4226	389	15	106	106	NUM
ejpam-4226	389	16	-	-	SYM
ejpam-4226	389	17	125	125	NUM
ejpam-4226	389	18	123	123	NUM
ejpam-4226	389	19	iaα	iaα	NOUN
ejpam-4226	389	20	(	(	PUNCT
ejpam-4226	389	21	1	1	NUM
ejpam-4226	389	22	3	3	NUM
ejpam-4226	389	23	f(t	f(t	NOUN
ejpam-4226	389	24	)	)	PUNCT
ejpam-4226	389	25	exp	exp	NOUN
ejpam-4226	389	26	(	(	PUNCT
ejpam-4226	389	27	−	−	PROPN
ejpam-4226	389	28	1	1	NUM
ejpam-4226	389	29	2α	2α	NOUN
ejpam-4226	389	30	tα	tα	PROPN
ejpam-4226	389	31	)	)	PUNCT
ejpam-4226	389	32	[	[	PUNCT
ejpam-4226	389	33	cos	cos	X
ejpam-4226	389	34	(	(	PUNCT
ejpam-4226	389	35	√	√	NUM
ejpam-4226	389	36	3	3	NUM
ejpam-4226	389	37	2α	2α	NOUN
ejpam-4226	389	38	tα	tα	PROPN
ejpam-4226	389	39	)	)	PUNCT
ejpam-4226	390	1	+	+	CCONJ
ejpam-4226	390	2	sin	sin	NOUN
ejpam-4226	390	3	(	(	PUNCT
ejpam-4226	390	4	√	√	NUM
ejpam-4226	390	5	3	3	NUM
ejpam-4226	390	6	2α	2α	NOUN
ejpam-4226	390	7	tα	tα	PROPN
ejpam-4226	390	8	)	)	PUNCT
ejpam-4226	390	9	]	]	PUNCT
ejpam-4226	390	10	)	)	PUNCT
ejpam-4226	391	1	+	+	NOUN
ejpam-4226	391	2	exp	exp	NOUN
ejpam-4226	391	3	(	(	PUNCT
ejpam-4226	391	4	1	1	NUM
ejpam-4226	391	5	2α	2α	NOUN
ejpam-4226	391	6	tα	tα	PROPN
ejpam-4226	391	7	)	)	PUNCT
ejpam-4226	391	8	sin	sin	NOUN
ejpam-4226	391	9	(	(	PUNCT
ejpam-4226	391	10	√	√	NUM
ejpam-4226	391	11	3	3	NUM
ejpam-4226	391	12	2α	2α	NOUN
ejpam-4226	391	13	tα	tα	PROPN
ejpam-4226	391	14	)	)	PUNCT
ejpam-4226	391	15	×	×	NOUN
ejpam-4226	391	16	iaα	iaα	NOUN
ejpam-4226	391	17	(	(	PUNCT
ejpam-4226	391	18	1	1	NUM
ejpam-4226	391	19	3	3	NUM
ejpam-4226	391	20	f(t	f(t	NOUN
ejpam-4226	391	21	)	)	PUNCT
ejpam-4226	391	22	exp	exp	NOUN
ejpam-4226	391	23	(	(	PUNCT
ejpam-4226	391	24	−	−	PROPN
ejpam-4226	391	25	1	1	NUM
ejpam-4226	391	26	2α	2α	NOUN
ejpam-4226	391	27	tα	tα	PROPN
ejpam-4226	391	28	)	)	PUNCT
ejpam-4226	391	29	[	[	PUNCT
ejpam-4226	391	30	cos	cos	X
ejpam-4226	391	31	(	(	PUNCT
ejpam-4226	391	32	√	√	NUM
ejpam-4226	391	33	3	3	NUM
ejpam-4226	391	34	2α	2α	NOUN
ejpam-4226	391	35	tα	tα	PROPN
ejpam-4226	391	36	)	)	PUNCT
ejpam-4226	391	37	−	−	ADP
ejpam-4226	391	38	√	√	NUM
ejpam-4226	391	39	3	3	NUM
ejpam-4226	391	40	sin	sin	NOUN
ejpam-4226	391	41	(	(	PUNCT
ejpam-4226	391	42	√	√	NUM
ejpam-4226	391	43	3	3	NUM
ejpam-4226	391	44	2α	2α	NOUN
ejpam-4226	391	45	tα	tα	PROPN
ejpam-4226	391	46	)	)	PUNCT
ejpam-4226	391	47	]	]	PUNCT
ejpam-4226	391	48	)	)	PUNCT
ejpam-4226	391	49	.	.	PUNCT
ejpam-4226	392	1	for	for	ADP
ejpam-4226	392	2	v(2α)+	v(2α)+	X
ejpam-4226	392	3	v(α	v(α	PROPN
ejpam-4226	392	4	)	)	PUNCT
ejpam-4226	392	5	=	=	SYM
ejpam-4226	392	6	f	f	X
ejpam-4226	392	7	,	,	PUNCT
ejpam-4226	392	8	the	the	DET
ejpam-4226	392	9	associated	associated	ADJ
ejpam-4226	392	10	characteristic	characteristic	ADJ
ejpam-4226	392	11	equation	equation	NOUN
ejpam-4226	392	12	is	be	AUX
ejpam-4226	392	13	r2	r2	NOUN
ejpam-4226	392	14	+	+	CCONJ
ejpam-4226	392	15	r	r	NOUN
ejpam-4226	392	16	=	=	SYM
ejpam-4226	392	17	0	0	NUM
ejpam-4226	392	18	,	,	PUNCT
ejpam-4226	392	19	which	which	PRON
ejpam-4226	392	20	has	have	VERB
ejpam-4226	392	21	the	the	DET
ejpam-4226	392	22	roots	root	NOUN
ejpam-4226	392	23	0	0	PUNCT
ejpam-4226	392	24	and	and	CCONJ
ejpam-4226	392	25	−1	−1	NOUN
ejpam-4226	392	26	.	.	PUNCT
ejpam-4226	393	1	then	then	ADV
ejpam-4226	393	2	vh(t	vh(t	PUNCT
ejpam-4226	393	3	)	)	PUNCT
ejpam-4226	394	1	=	=	VERB
ejpam-4226	394	2	c4	c4	NOUN
ejpam-4226	394	3	+	+	CCONJ
ejpam-4226	394	4	c5	c5	PROPN
ejpam-4226	394	5	exp	exp	NOUN
ejpam-4226	394	6	(	(	PUNCT
ejpam-4226	394	7	−	−	PROPN
ejpam-4226	394	8	1	1	NUM
ejpam-4226	394	9	α	α	NOUN
ejpam-4226	394	10	tα	tα	PROPN
ejpam-4226	394	11	)	)	PUNCT
ejpam-4226	394	12	.	.	PUNCT
ejpam-4226	395	1	for	for	ADP
ejpam-4226	395	2	the	the	DET
ejpam-4226	395	3	particular	particular	ADJ
ejpam-4226	395	4	solution	solution	NOUN
ejpam-4226	395	5	,	,	PUNCT
ejpam-4226	395	6	we	we	PRON
ejpam-4226	395	7	use	use	VERB
ejpam-4226	395	8	variation	variation	NOUN
ejpam-4226	395	9	of	of	ADP
ejpam-4226	395	10	parameters	parameter	NOUN
ejpam-4226	395	11	.	.	PUNCT
ejpam-4226	396	1	let	let	VERB
ejpam-4226	396	2	u1	u1	NOUN
ejpam-4226	396	3	=	=	SYM
ejpam-4226	396	4	1	1	NUM
ejpam-4226	396	5	,	,	PUNCT
ejpam-4226	396	6	u2	u2	NOUN
ejpam-4226	396	7	=	=	PUNCT
ejpam-4226	396	8	exp	exp	NOUN
ejpam-4226	396	9	(	(	PUNCT
ejpam-4226	396	10	−	−	PROPN
ejpam-4226	396	11	1	1	NUM
ejpam-4226	396	12	α	α	NOUN
ejpam-4226	396	13	t	t	NOUN
ejpam-4226	396	14	α	α	NOUN
ejpam-4226	396	15	)	)	PUNCT
ejpam-4226	396	16	so	so	ADV
ejpam-4226	396	17	vp(t	vp(t	PUNCT
ejpam-4226	396	18	)	)	PUNCT
ejpam-4226	397	1	=	=	SYM
ejpam-4226	398	1	∫	∫	PROPN
ejpam-4226	398	2	t	t	PROPN
ejpam-4226	398	3	a	a	DET
ejpam-4226	398	4	f(s)wα	f(s)wα	PROPN
ejpam-4226	398	5	1	1	NUM
ejpam-4226	398	6	(	(	PUNCT
ejpam-4226	398	7	s	s	NOUN
ejpam-4226	398	8	)	)	PUNCT
ejpam-4226	398	9	wα(s)s1−α	wα(s)s1−α	PROPN
ejpam-4226	398	10	ds+	ds+	PROPN
ejpam-4226	398	11	exp	exp	NOUN
ejpam-4226	398	12	(	(	PUNCT
ejpam-4226	398	13	−	−	PROPN
ejpam-4226	398	14	1	1	NUM
ejpam-4226	398	15	α	α	NOUN
ejpam-4226	398	16	tα	tα	PROPN
ejpam-4226	398	17	)	)	PUNCT
ejpam-4226	398	18	∫	∫	PROPN
ejpam-4226	398	19	t	t	PROPN
ejpam-4226	398	20	a	a	DET
ejpam-4226	398	21	f(s)wα	f(s)wα	PROPN
ejpam-4226	398	22	2	2	NUM
ejpam-4226	398	23	(	(	PUNCT
ejpam-4226	398	24	s	s	NOUN
ejpam-4226	398	25	)	)	PUNCT
ejpam-4226	398	26	wα(s)s1−α	wα(s)s1−α	PROPN
ejpam-4226	399	1	ds	ds	PROPN
ejpam-4226	399	2	=	=	SYM
ejpam-4226	399	3	∫	∫	PROPN
ejpam-4226	399	4	t	t	PROPN
ejpam-4226	399	5	a	a	DET
ejpam-4226	399	6	f(s	f(	NOUN
ejpam-4226	399	7	)	)	PUNCT
ejpam-4226	399	8	s1−α	s1−α	PROPN
ejpam-4226	399	9	ds−	ds−	PROPN
ejpam-4226	399	10	exp	exp	NOUN
ejpam-4226	399	11	(	(	PUNCT
ejpam-4226	399	12	−	−	PROPN
ejpam-4226	399	13	1	1	NUM
ejpam-4226	399	14	α	α	NOUN
ejpam-4226	399	15	tα	tα	PROPN
ejpam-4226	399	16	)	)	PUNCT
ejpam-4226	399	17	∫	∫	PROPN
ejpam-4226	399	18	t	t	PROPN
ejpam-4226	399	19	a	a	DET
ejpam-4226	399	20	f(s	f(	NOUN
ejpam-4226	399	21	)	)	PUNCT
ejpam-4226	399	22	exp	exp	NOUN
ejpam-4226	399	23	(	(	PUNCT
ejpam-4226	399	24	1	1	NUM
ejpam-4226	399	25	α	α	NOUN
ejpam-4226	399	26	sα	sα	ADJ
ejpam-4226	399	27	)	)	PUNCT
ejpam-4226	399	28	(	(	PUNCT
ejpam-4226	399	29	s)s1−α	s)s1−α	ADJ
ejpam-4226	399	30	ds	ds	NOUN
ejpam-4226	399	31	=	=	NOUN
ejpam-4226	399	32	iaα	iaα	NOUN
ejpam-4226	399	33	(	(	PUNCT
ejpam-4226	399	34	f(t))−	f(t))−	ADJ
ejpam-4226	399	35	exp	exp	NOUN
ejpam-4226	399	36	(	(	PUNCT
ejpam-4226	399	37	−	−	PROPN
ejpam-4226	399	38	1	1	NUM
ejpam-4226	399	39	α	α	NOUN
ejpam-4226	399	40	tα	tα	PROPN
ejpam-4226	399	41	)	)	PUNCT
ejpam-4226	399	42	iaα	iaα	PROPN
ejpam-4226	399	43	(	(	PUNCT
ejpam-4226	399	44	f(t	f(t	PROPN
ejpam-4226	399	45	)	)	PUNCT
ejpam-4226	399	46	exp	exp	NOUN
ejpam-4226	399	47	(	(	PUNCT
ejpam-4226	399	48	1	1	NUM
ejpam-4226	399	49	α	α	NOUN
ejpam-4226	399	50	tα	tα	PROPN
ejpam-4226	399	51	)	)	PUNCT
ejpam-4226	399	52	)	)	PUNCT
ejpam-4226	399	53	hence	hence	ADV
ejpam-4226	399	54	v(t	v(t	X
ejpam-4226	399	55	)	)	PUNCT
ejpam-4226	399	56	=	=	SYM
ejpam-4226	399	57	vh	vh	PROPN
ejpam-4226	399	58	+	+	CCONJ
ejpam-4226	399	59	vp	vp	PROPN
ejpam-4226	399	60	=	=	SYM
ejpam-4226	399	61	c4	c4	PROPN
ejpam-4226	399	62	+	+	CCONJ
ejpam-4226	399	63	c5	c5	PROPN
ejpam-4226	399	64	exp	exp	NOUN
ejpam-4226	399	65	(	(	PUNCT
ejpam-4226	399	66	−	−	PROPN
ejpam-4226	399	67	1	1	NUM
ejpam-4226	399	68	α	α	NOUN
ejpam-4226	399	69	tα	tα	PROPN
ejpam-4226	399	70	)	)	PUNCT
ejpam-4226	400	1	+	+	CCONJ
ejpam-4226	400	2	iaα	iaα	ADJ
ejpam-4226	400	3	(	(	PUNCT
ejpam-4226	400	4	f(t))−	f(t))−	ADJ
ejpam-4226	400	5	exp	exp	NOUN
ejpam-4226	400	6	(	(	PUNCT
ejpam-4226	400	7	−	−	PROPN
ejpam-4226	400	8	1	1	NUM
ejpam-4226	400	9	α	α	NOUN
ejpam-4226	400	10	tα	tα	PROPN
ejpam-4226	400	11	)	)	PUNCT
ejpam-4226	400	12	iaα	iaα	PROPN
ejpam-4226	400	13	(	(	PUNCT
ejpam-4226	400	14	f(t	f(t	PROPN
ejpam-4226	400	15	)	)	PUNCT
ejpam-4226	400	16	exp	exp	NOUN
ejpam-4226	400	17	(	(	PUNCT
ejpam-4226	400	18	1	1	NUM
ejpam-4226	400	19	α	α	NOUN
ejpam-4226	400	20	tα	tα	PROPN
ejpam-4226	400	21	)	)	PUNCT
ejpam-4226	400	22	)	)	PUNCT
ejpam-4226	400	23	by	by	ADP
ejpam-4226	400	24	the	the	DET
ejpam-4226	400	25	condition	condition	NOUN
ejpam-4226	400	26	(	(	PUNCT
ejpam-4226	400	27	∗∗	∗∗	NOUN
ejpam-4226	400	28	)	)	PUNCT
ejpam-4226	400	29	we	we	PRON
ejpam-4226	400	30	get	get	VERB
ejpam-4226	400	31	{	{	PUNCT
ejpam-4226	400	32	c4	c4	NOUN
ejpam-4226	400	33	=	=	SYM
ejpam-4226	400	34	2−	2−	NUM
ejpam-4226	400	35	iaα	iaα	ADJ
ejpam-4226	400	36	(	(	PUNCT
ejpam-4226	400	37	f(0	f(0	NOUN
ejpam-4226	400	38	)	)	PUNCT
ejpam-4226	400	39	)	)	PUNCT
ejpam-4226	401	1	c5	c5	PROPN
ejpam-4226	401	2	=	=	PUNCT
ejpam-4226	401	3	−1	−1	NOUN
ejpam-4226	402	1	+	+	CCONJ
ejpam-4226	402	2	iaα	iaα	ADJ
ejpam-4226	402	3	(	(	PUNCT
ejpam-4226	402	4	f(0	f(0	NOUN
ejpam-4226	402	5	)	)	PUNCT
ejpam-4226	402	6	)	)	PUNCT
ejpam-4226	402	7	.	.	PUNCT
ejpam-4226	403	1	but	but	CCONJ
ejpam-4226	403	2	the	the	DET
ejpam-4226	403	3	two	two	NUM
ejpam-4226	403	4	solutions	solution	NOUN
ejpam-4226	403	5	must	must	AUX
ejpam-4226	403	6	be	be	AUX
ejpam-4226	403	7	equal	equal	ADJ
ejpam-4226	403	8	,	,	PUNCT
ejpam-4226	403	9	then	then	ADV
ejpam-4226	403	10	{	{	PUNCT
ejpam-4226	403	11	c1	c1	PROPN
ejpam-4226	403	12	=	=	PROPN
ejpam-4226	403	13	c5	c5	PROPN
ejpam-4226	403	14	c2	c2	PROPN
ejpam-4226	403	15	=	=	PROPN
ejpam-4226	403	16	c3	c3	PROPN
ejpam-4226	403	17	=	=	NOUN
ejpam-4226	403	18	0	0	PROPN
ejpam-4226	403	19	.	.	PUNCT
ejpam-4226	404	1	hence	hence	ADV
ejpam-4226	404	2	v(t	v(t	NOUN
ejpam-4226	404	3	)	)	PUNCT
ejpam-4226	404	4	=	=	PUNCT
ejpam-4226	404	5	(	(	PUNCT
ejpam-4226	404	6	−1	−1	NOUN
ejpam-4226	404	7	+	+	CCONJ
ejpam-4226	404	8	iaα	iaα	ADJ
ejpam-4226	404	9	(	(	PUNCT
ejpam-4226	404	10	f(0	f(0	NOUN
ejpam-4226	404	11	)	)	PUNCT
ejpam-4226	404	12	)	)	PUNCT
ejpam-4226	404	13	)	)	PUNCT
ejpam-4226	404	14	exp	exp	NOUN
ejpam-4226	404	15	(	(	PUNCT
ejpam-4226	404	16	−	−	PROPN
ejpam-4226	404	17	1	1	NUM
ejpam-4226	404	18	α	α	NOUN
ejpam-4226	404	19	tα	tα	PROPN
ejpam-4226	404	20	)	)	PUNCT
ejpam-4226	405	1	+	+	CCONJ
ejpam-4226	405	2	iaα	iaα	ADJ
ejpam-4226	405	3	(	(	PUNCT
ejpam-4226	405	4	f(t	f(t	PROPN
ejpam-4226	405	5	)	)	PUNCT
ejpam-4226	405	6	)	)	PUNCT
ejpam-4226	406	1	−	−	PROPN
ejpam-4226	406	2	exp	exp	NOUN
ejpam-4226	406	3	(	(	PUNCT
ejpam-4226	406	4	−	−	PROPN
ejpam-4226	406	5	1	1	NUM
ejpam-4226	406	6	α	α	NOUN
ejpam-4226	406	7	tα	tα	PROPN
ejpam-4226	406	8	)	)	PUNCT
ejpam-4226	406	9	iaα	iaα	PROPN
ejpam-4226	406	10	(	(	PUNCT
ejpam-4226	406	11	f(t	f(t	PROPN
ejpam-4226	406	12	)	)	PUNCT
ejpam-4226	406	13	exp	exp	NOUN
ejpam-4226	406	14	(	(	PUNCT
ejpam-4226	406	15	1	1	NUM
ejpam-4226	406	16	α	α	NOUN
ejpam-4226	406	17	tα	tα	PROPN
ejpam-4226	406	18	)	)	PUNCT
ejpam-4226	406	19	)	)	PUNCT
ejpam-4226	407	1	+	+	CCONJ
ejpam-4226	407	2	2−	2−	NUM
ejpam-4226	407	3	iaα	iaα	ADJ
ejpam-4226	407	4	(	(	PUNCT
ejpam-4226	407	5	f(0	f(0	NOUN
ejpam-4226	407	6	)	)	PUNCT
ejpam-4226	407	7	)	)	PUNCT
ejpam-4226	407	8	references	reference	VERB
ejpam-4226	407	9	124	124	NUM
ejpam-4226	407	10	references	reference	NOUN
ejpam-4226	407	11	[	[	X
ejpam-4226	407	12	1	1	NUM
ejpam-4226	407	13	]	]	PUNCT
ejpam-4226	407	14	m.	m.	NOUN
ejpam-4226	407	15	al	al	PROPN
ejpam-4226	407	16	horani	horani	PROPN
ejpam-4226	407	17	,	,	PUNCT
ejpam-4226	407	18	m.	m.	NOUN
ejpam-4226	407	19	fabrizio	fabrizio	PROPN
ejpam-4226	407	20	,	,	PUNCT
ejpam-4226	407	21	a.	a.	NOUN
ejpam-4226	407	22	favini	favini	PROPN
ejpam-4226	407	23	,	,	PUNCT
ejpam-4226	407	24	and	and	CCONJ
ejpam-4226	407	25	h.	h.	PROPN
ejpam-4226	407	26	tanabe	tanabe	PROPN
ejpam-4226	407	27	,	,	PUNCT
ejpam-4226	407	28	fractional	fractional	ADJ
ejpam-4226	407	29	cauchy	cauchy	NOUN
ejpam-4226	407	30	problems	problem	NOUN
ejpam-4226	407	31	for	for	ADP
ejpam-4226	407	32	infnite	infnite	ADJ
ejpam-4226	407	33	interval	interval	NOUN
ejpam-4226	407	34	case	case	NOUN
ejpam-4226	407	35	,	,	PUNCT
ejpam-4226	407	36	discrete	discrete	VERB
ejpam-4226	407	37	continuous	continuous	ADJ
ejpam-4226	407	38	dynamical	dynamical	ADJ
ejpam-4226	407	39	systems	system	NOUN
ejpam-4226	407	40	-	-	PUNCT
ejpam-4226	407	41	s	s	PROPN
ejpam-4226	407	42	,	,	PUNCT
ejpam-4226	407	43	13	13	NUM
ejpam-4226	407	44	(	(	PUNCT
ejpam-4226	407	45	12	12	NUM
ejpam-4226	407	46	)	)	PUNCT
ejpam-4226	407	47	,	,	PUNCT
ejpam-4226	407	48	(	(	PUNCT
ejpam-4226	407	49	2020	2020	NUM
ejpam-4226	407	50	)	)	PUNCT
ejpam-4226	407	51	3285	3285	NUM
ejpam-4226	407	52	-	-	SYM
ejpam-4226	407	53	3304	3304	NUM
ejpam-4226	407	54	.	.	PUNCT
ejpam-4226	408	1	[	[	X
ejpam-4226	408	2	2	2	NUM
ejpam-4226	408	3	]	]	PUNCT
ejpam-4226	408	4	b.	b.	NOUN
ejpam-4226	408	5	thaller	thaller	NOUN
ejpam-4226	408	6	and	and	CCONJ
ejpam-4226	408	7	s.	s.	PROPN
ejpam-4226	408	8	thaller	thaller	NOUN
ejpam-4226	408	9	,	,	PUNCT
ejpam-4226	408	10	factorization	factorization	NOUN
ejpam-4226	408	11	of	of	ADP
ejpam-4226	408	12	degenerate	degenerate	ADJ
ejpam-4226	408	13	cauchy	cauchy	ADJ
ejpam-4226	408	14	problem	problem	NOUN
ejpam-4226	408	15	:	:	PUNCT
ejpam-4226	408	16	the	the	DET
ejpam-4226	408	17	linear	linear	ADJ
ejpam-4226	408	18	case	case	NOUN
ejpam-4226	408	19	,	,	PUNCT
ejpam-4226	408	20	j.oper	j.oper	NOUN
ejpam-4226	408	21	.	.	PUNCT
ejpam-4226	409	1	theory	theory	NOUN
ejpam-4226	409	2	36	36	NUM
ejpam-4226	409	3	(	(	PUNCT
ejpam-4226	409	4	1996	1996	NUM
ejpam-4226	409	5	)	)	PUNCT
ejpam-4226	409	6	,	,	PUNCT
ejpam-4226	409	7	121	121	NUM
ejpam-4226	409	8	-	-	SYM
ejpam-4226	409	9	146	146	NUM
ejpam-4226	409	10	.	.	PUNCT
ejpam-4226	410	1	[	[	X
ejpam-4226	410	2	3	3	NUM
ejpam-4226	410	3	]	]	PUNCT
ejpam-4226	410	4	a.	a.	NOUN
ejpam-4226	410	5	ziqan	ziqan	PROPN
ejpam-4226	410	6	,	,	PUNCT
ejpam-4226	410	7	m.	m.	PROPN
ejpam-4226	410	8	al	al	PROPN
ejpam-4226	410	9	horani	horani	PROPN
ejpam-4226	410	10	and	and	CCONJ
ejpam-4226	410	11	r.	r.	PROPN
ejpam-4226	410	12	khalil	khalil	PROPN
ejpam-4226	410	13	,	,	PUNCT
ejpam-4226	410	14	tensor	tensor	NOUN
ejpam-4226	410	15	product	product	NOUN
ejpam-4226	410	16	technique	technique	NOUN
ejpam-4226	410	17	and	and	CCONJ
ejpam-4226	410	18	the	the	DET
ejpam-4226	410	19	degenerate	degenerate	ADJ
ejpam-4226	410	20	homogeneous	homogeneous	ADJ
ejpam-4226	410	21	abstract	abstract	ADJ
ejpam-4226	410	22	cauchy	cauchy	PROPN
ejpam-4226	410	23	problem	problem	NOUN
ejpam-4226	410	24	,	,	PUNCT
ejpam-4226	410	25	j.	j.	PROPN
ejpam-4226	410	26	appl	appl	PROPN
ejpam-4226	410	27	.	.	PROPN
ejpam-4226	411	1	funct	funct	PROPN
ejpam-4226	411	2	.	.	PUNCT
ejpam-4226	412	1	anal	anal	PROPN
ejpam-4226	412	2	.	.	PROPN
ejpam-4226	412	3	,	,	PUNCT
ejpam-4226	412	4	5	5	NUM
ejpam-4226	412	5	(	(	PUNCT
ejpam-4226	412	6	1	1	NUM
ejpam-4226	412	7	)	)	PUNCT
ejpam-4226	412	8	(	(	PUNCT
ejpam-4226	412	9	2010	2010	NUM
ejpam-4226	412	10	)	)	PUNCT
ejpam-4226	412	11	,	,	PUNCT
ejpam-4226	412	12	121	121	NUM
ejpam-4226	412	13	-	-	SYM
ejpam-4226	412	14	138	138	NUM
ejpam-4226	412	15	.	.	PUNCT
ejpam-4226	413	1	[	[	X
ejpam-4226	413	2	4	4	NUM
ejpam-4226	413	3	]	]	PUNCT
ejpam-4226	413	4	a.	a.	NOUN
ejpam-4226	413	5	ziqan	ziqan	PROPN
ejpam-4226	413	6	,	,	PUNCT
ejpam-4226	413	7	m.	m.	PROPN
ejpam-4226	413	8	al	al	PROPN
ejpam-4226	413	9	horani	horani	PROPN
ejpam-4226	413	10	and	and	CCONJ
ejpam-4226	413	11	r.	r.	PROPN
ejpam-4226	413	12	khalil	khalil	PROPN
ejpam-4226	413	13	,	,	PUNCT
ejpam-4226	413	14	tensor	tensor	NOUN
ejpam-4226	413	15	product	product	NOUN
ejpam-4226	413	16	technique	technique	NOUN
ejpam-4226	413	17	and	and	CCONJ
ejpam-4226	413	18	the	the	DET
ejpam-4226	413	19	degenerate	degenerate	ADJ
ejpam-4226	413	20	nonhomogeneous	nonhomogeneous	ADJ
ejpam-4226	413	21	abstract	abstract	ADJ
ejpam-4226	413	22	cauchy	cauchy	PROPN
ejpam-4226	413	23	problem	problem	NOUN
ejpam-4226	413	24	,	,	PUNCT
ejpam-4226	413	25	international	international	ADJ
ejpam-4226	413	26	journal	journal	NOUN
ejpam-4226	413	27	of	of	ADP
ejpam-4226	413	28	applied	apply	VERB
ejpam-4226	413	29	mathematics	mathematic	NOUN
ejpam-4226	413	30	,	,	PUNCT
ejpam-4226	413	31	23	23	NUM
ejpam-4226	413	32	(	(	PUNCT
ejpam-4226	413	33	1	1	NUM
ejpam-4226	413	34	)	)	PUNCT
ejpam-4226	413	35	(	(	PUNCT
ejpam-4226	413	36	2010	2010	NUM
ejpam-4226	413	37	)	)	PUNCT
ejpam-4226	413	38	,	,	PUNCT
ejpam-4226	413	39	137	137	NUM
ejpam-4226	413	40	-	-	SYM
ejpam-4226	413	41	158	158	NUM
ejpam-4226	413	42	.	.	PUNCT
ejpam-4226	414	1	[	[	X
ejpam-4226	414	2	5	5	NUM
ejpam-4226	414	3	]	]	PUNCT
ejpam-4226	414	4	r.	r.	PROPN
ejpam-4226	414	5	khalil	khalil	PROPN
ejpam-4226	414	6	,	,	PUNCT
ejpam-4226	414	7	m.	m.	PROPN
ejpam-4226	414	8	al	al	PROPN
ejpam-4226	414	9	horani	horani	PROPN
ejpam-4226	414	10	,	,	PUNCT
ejpam-4226	414	11	a.	a.	PROPN
ejpam-4226	414	12	yousef	yousef	PROPN
ejpam-4226	414	13	.	.	PUNCT
ejpam-4226	415	1	and	and	CCONJ
ejpam-4226	415	2	m.	m.	NOUN
ejpam-4226	415	3	sababheh	sababheh	PROPN
ejpam-4226	415	4	,	,	PUNCT
ejpam-4226	415	5	a	a	DET
ejpam-4226	415	6	new	new	ADJ
ejpam-4226	415	7	definition	definition	NOUN
ejpam-4226	415	8	of	of	ADP
ejpam-4226	415	9	fractional	fractional	ADJ
ejpam-4226	415	10	derivative	derivative	NOUN
ejpam-4226	415	11	,	,	PUNCT
ejpam-4226	415	12	j.	j.	PROPN
ejpam-4226	415	13	comput	comput	PROPN
ejpam-4226	415	14	.	.	PUNCT
ejpam-4226	416	1	appl	appl	PROPN
ejpam-4226	416	2	.	.	PROPN
ejpam-4226	416	3	math	math	PROPN
ejpam-4226	416	4	.	.	PUNCT
ejpam-4226	417	1	,	,	PUNCT
ejpam-4226	417	2	264	264	NUM
ejpam-4226	417	3	(	(	PUNCT
ejpam-4226	417	4	2014	2014	NUM
ejpam-4226	417	5	)	)	PUNCT
ejpam-4226	417	6	,	,	PUNCT
ejpam-4226	417	7	65	65	NUM
ejpam-4226	417	8	-	-	SYM
ejpam-4226	417	9	70	70	NUM
ejpam-4226	417	10	.	.	PUNCT
ejpam-4226	418	1	[	[	X
ejpam-4226	418	2	6	6	NUM
ejpam-4226	418	3	]	]	PUNCT
ejpam-4226	418	4	t.	t.	NOUN
ejpam-4226	418	5	abdeljawad	abdeljawad	NOUN
ejpam-4226	418	6	,	,	PUNCT
ejpam-4226	418	7	on	on	ADP
ejpam-4226	418	8	conformable	conformable	ADJ
ejpam-4226	418	9	fractional	fractional	ADJ
ejpam-4226	418	10	calculus	calculus	NOUN
ejpam-4226	418	11	,	,	PUNCT
ejpam-4226	418	12	journal	journal	NOUN
ejpam-4226	418	13	of	of	ADP
ejpam-4226	418	14	computational	computational	ADJ
ejpam-4226	418	15	and	and	CCONJ
ejpam-4226	418	16	applied	applied	ADJ
ejpam-4226	418	17	mathematics	mathematic	NOUN
ejpam-4226	418	18	,	,	PUNCT
ejpam-4226	418	19	259(2015	259(2015	NUM
ejpam-4226	418	20	)	)	PUNCT
ejpam-4226	418	21	,	,	PUNCT
ejpam-4226	418	22	57	57	NUM
ejpam-4226	418	23	-	-	SYM
ejpam-4226	418	24	66	66	NUM
ejpam-4226	418	25	.	.	PUNCT
ejpam-4226	419	1	[	[	X
ejpam-4226	419	2	7	7	X
ejpam-4226	419	3	]	]	PUNCT
ejpam-4226	419	4	m.	m.	NOUN
ejpam-4226	419	5	al	al	PROPN
ejpam-4226	419	6	horani	horani	PROPN
ejpam-4226	419	7	and	and	CCONJ
ejpam-4226	419	8	r.	r.	PROPN
ejpam-4226	419	9	khalil	khalil	PROPN
ejpam-4226	419	10	,	,	PUNCT
ejpam-4226	419	11	total	total	ADJ
ejpam-4226	419	12	fractional	fractional	ADJ
ejpam-4226	419	13	differentials	differential	NOUN
ejpam-4226	419	14	with	with	ADP
ejpam-4226	419	15	applications	application	NOUN
ejpam-4226	419	16	to	to	PART
ejpam-4226	419	17	exact	exact	VERB
ejpam-4226	419	18	fractional	fractional	ADJ
ejpam-4226	419	19	differential	differential	ADJ
ejpam-4226	419	20	equations	equation	NOUN
ejpam-4226	419	21	,	,	PUNCT
ejpam-4226	419	22	int	int	NOUN
ejpam-4226	419	23	.	.	PUNCT
ejpam-4226	420	1	j.	j.	PROPN
ejpam-4226	420	2	comput	comput	PROPN
ejpam-4226	420	3	.	.	PUNCT
ejpam-4226	421	1	math	math	NOUN
ejpam-4226	421	2	.	.	PUNCT
ejpam-4226	421	3	,	,	PUNCT
ejpam-4226	421	4	95(2018	95(2018	NUM
ejpam-4226	421	5	)	)	PUNCT
ejpam-4226	421	6	,	,	PUNCT
ejpam-4226	421	7	1444	1444	NUM
ejpam-4226	421	8	-	-	SYM
ejpam-4226	421	9	1452	1452	NUM
ejpam-4226	421	10	.	.	PUNCT
ejpam-4226	422	1	[	[	X
ejpam-4226	422	2	8	8	NUM
ejpam-4226	422	3	]	]	X
ejpam-4226	422	4	i.	i.	PROPN
ejpam-4226	422	5	benkemache	benkemache	PROPN
ejpam-4226	422	6	,	,	PUNCT
ejpam-4226	422	7	m.	m.	NOUN
ejpam-4226	422	8	al	al	PROPN
ejpam-4226	422	9	horani	horani	PROPN
ejpam-4226	422	10	and	and	CCONJ
ejpam-4226	422	11	r.	r.	PROPN
ejpam-4226	422	12	khalil	khalil	PROPN
ejpam-4226	422	13	,	,	PUNCT
ejpam-4226	422	14	tensor	tensor	NOUN
ejpam-4226	422	15	product	product	NOUN
ejpam-4226	422	16	and	and	CCONJ
ejpam-4226	422	17	certain	certain	ADJ
ejpam-4226	422	18	solutions	solution	NOUN
ejpam-4226	422	19	of	of	ADP
ejpam-4226	422	20	fractional	fractional	ADJ
ejpam-4226	422	21	wave	wave	NOUN
ejpam-4226	422	22	type	type	NOUN
ejpam-4226	422	23	equation	equation	NOUN
ejpam-4226	422	24	,	,	PUNCT
ejpam-4226	422	25	european	european	PROPN
ejpam-4226	422	26	journal	journal	PROPN
ejpam-4226	422	27	of	of	ADP
ejpam-4226	422	28	pure	pure	ADJ
ejpam-4226	422	29	and	and	CCONJ
ejpam-4226	422	30	applied	applied	ADJ
ejpam-4226	422	31	mathematics	mathematic	NOUN
ejpam-4226	422	32	14	14	NUM
ejpam-4226	422	33	(	(	PUNCT
ejpam-4226	422	34	3	3	NUM
ejpam-4226	422	35	)	)	PUNCT
ejpam-4226	422	36	,	,	PUNCT
ejpam-4226	422	37	(	(	PUNCT
ejpam-4226	422	38	2021	2021	NUM
ejpam-4226	422	39	)	)	PUNCT
ejpam-4226	422	40	,	,	PUNCT
ejpam-4226	422	41	942	942	NUM
ejpam-4226	422	42	-	-	SYM
ejpam-4226	422	43	948	948	NUM
ejpam-4226	422	44	,	,	PUNCT
ejpam-4226	422	45	[	[	X
ejpam-4226	422	46	9	9	NUM
ejpam-4226	422	47	]	]	X
ejpam-4226	422	48	f.	f.	PROPN
ejpam-4226	422	49	seddiki	seddiki	PROPN
ejpam-4226	422	50	,	,	PUNCT
ejpam-4226	422	51	m.	m.	NOUN
ejpam-4226	422	52	al	al	PROPN
ejpam-4226	422	53	horani	horani	PROPN
ejpam-4226	422	54	and	and	CCONJ
ejpam-4226	422	55	r.	r.	PROPN
ejpam-4226	422	56	khalil	khalil	PROPN
ejpam-4226	422	57	,	,	PUNCT
ejpam-4226	422	58	finite	finite	PROPN
ejpam-4226	422	59	rank	rank	NOUN
ejpam-4226	422	60	solution	solution	NOUN
ejpam-4226	422	61	for	for	ADP
ejpam-4226	422	62	conformable	conformable	ADJ
ejpam-4226	422	63	degenerate	degenerate	ADJ
ejpam-4226	422	64	first	first	ADJ
ejpam-4226	422	65	-	-	PUNCT
ejpam-4226	422	66	order	order	NOUN
ejpam-4226	422	67	abstract	abstract	ADJ
ejpam-4226	422	68	cauchy	cauchy	ADJ
ejpam-4226	422	69	problem	problem	NOUN
ejpam-4226	422	70	in	in	ADP
ejpam-4226	422	71	hilbert	hilbert	PROPN
ejpam-4226	422	72	spaces	space	NOUN
ejpam-4226	422	73	,	,	PUNCT
ejpam-4226	422	74	european	european	PROPN
ejpam-4226	422	75	journal	journal	PROPN
ejpam-4226	422	76	of	of	ADP
ejpam-4226	422	77	pure	pure	ADJ
ejpam-4226	422	78	and	and	CCONJ
ejpam-4226	422	79	applied	applied	ADJ
ejpam-4226	422	80	mathematics	mathematic	NOUN
ejpam-4226	422	81	14	14	NUM
ejpam-4226	422	82	(	(	PUNCT
ejpam-4226	422	83	2	2	NUM
ejpam-4226	422	84	)	)	PUNCT
ejpam-4226	422	85	,	,	PUNCT
ejpam-4226	422	86	(	(	PUNCT
ejpam-4226	422	87	2021),493	2021),493	PROPN
ejpam-4226	422	88	-	-	NUM
ejpam-4226	422	89	505	505	NUM
ejpam-4226	422	90	,	,	PUNCT
ejpam-4226	422	91	[	[	X
ejpam-4226	422	92	10	10	NUM
ejpam-4226	422	93	]	]	PUNCT
ejpam-4226	422	94	m.	m.	NOUN
ejpam-4226	422	95	abu	abu	PROPN
ejpam-4226	422	96	hammad	hammad	PROPN
ejpam-4226	422	97	and	and	CCONJ
ejpam-4226	422	98	r.	r.	PROPN
ejpam-4226	422	99	khalil	khalil	PROPN
ejpam-4226	422	100	,	,	PUNCT
ejpam-4226	422	101	conformable	conformable	ADJ
ejpam-4226	422	102	fractional	fractional	ADJ
ejpam-4226	422	103	heat	heat	NOUN
ejpam-4226	422	104	differential	differential	NOUN
ejpam-4226	422	105	equation	equation	NOUN
ejpam-4226	422	106	,	,	PUNCT
ejpam-4226	422	107	inter	inter	PROPN
ejpam-4226	422	108	national	national	ADJ
ejpam-4226	422	109	journal	journal	NOUN
ejpam-4226	422	110	of	of	ADP
ejpam-4226	422	111	pure	pure	ADJ
ejpam-4226	422	112	and	and	CCONJ
ejpam-4226	422	113	applied	applied	ADJ
ejpam-4226	422	114	mathematics	mathematic	NOUN
ejpam-4226	422	115	94	94	NUM
ejpam-4226	422	116	(	(	PUNCT
ejpam-4226	422	117	2	2	NUM
ejpam-4226	422	118	)	)	PUNCT
ejpam-4226	422	119	,	,	PUNCT
ejpam-4226	422	120	215221	215221	NUM
ejpam-4226	422	121	.	.	PUNCT
ejpam-4226	423	1	[	[	X
ejpam-4226	423	2	11	11	NUM
ejpam-4226	423	3	]	]	PUNCT
ejpam-4226	423	4	m.	m.	NOUN
ejpam-4226	423	5	abu	abu	PROPN
ejpam-4226	423	6	hammad	hammad	PROPN
ejpam-4226	423	7	and	and	CCONJ
ejpam-4226	423	8	r.	r.	PROPN
ejpam-4226	423	9	khalil	khalil	PROPN
ejpam-4226	423	10	,	,	PUNCT
ejpam-4226	423	11	fractional	fractional	ADJ
ejpam-4226	423	12	fourier	fourier	NOUN
ejpam-4226	423	13	series	series	NOUN
ejpam-4226	423	14	with	with	ADP
ejpam-4226	423	15	applications	application	NOUN
ejpam-4226	423	16	,	,	PUNCT
ejpam-4226	423	17	american	american	ADJ
ejpam-4226	423	18	journal	journal	PROPN
ejpam-4226	423	19	of	of	ADP
ejpam-4226	423	20	computational	computational	ADJ
ejpam-4226	423	21	and	and	CCONJ
ejpam-4226	423	22	applied	apply	VERB
ejpam-4226	423	23	mathematics	mathematic	NOUN
ejpam-4226	423	24	,	,	PUNCT
ejpam-4226	423	25	4(6	4(6	NUM
ejpam-4226	423	26	)	)	PUNCT
ejpam-4226	423	27	,	,	PUNCT
ejpam-4226	423	28	(	(	PUNCT
ejpam-4226	423	29	2014	2014	NUM
ejpam-4226	423	30	)	)	PUNCT
ejpam-4226	423	31	187	187	NUM
ejpam-4226	423	32	-	-	SYM
ejpam-4226	423	33	191	191	NUM
ejpam-4226	423	34	.	.	PUNCT
ejpam-4226	424	1	[	[	X
ejpam-4226	424	2	12	12	NUM
ejpam-4226	424	3	]	]	PUNCT
ejpam-4226	424	4	m.	m.	NOUN
ejpam-4226	424	5	al	al	PROPN
ejpam-4226	424	6	horani	horani	PROPN
ejpam-4226	424	7	,	,	PUNCT
ejpam-4226	424	8	m.	m.	PROPN
ejpam-4226	424	9	abu	abu	PROPN
ejpam-4226	424	10	hammad	hammad	PROPN
ejpam-4226	424	11	and	and	CCONJ
ejpam-4226	424	12	r.	r.	PROPN
ejpam-4226	424	13	khalil	khalil	PROPN
ejpam-4226	424	14	,	,	PUNCT
ejpam-4226	424	15	variation	variation	NOUN
ejpam-4226	424	16	of	of	ADP
ejpam-4226	424	17	parameters	parameter	NOUN
ejpam-4226	424	18	for	for	ADP
ejpam-4226	424	19	local	local	ADJ
ejpam-4226	424	20	fractional	fractional	ADJ
ejpam-4226	424	21	nonhomogeneous	nonhomogeneous	ADJ
ejpam-4226	424	22	linear	linear	ADJ
ejpam-4226	424	23	-	-	PUNCT
ejpam-4226	424	24	differential	differential	NOUN
ejpam-4226	424	25	equations	equation	NOUN
ejpam-4226	424	26	j.	j.	PROPN
ejpam-4226	424	27	math	math	PROPN
ejpam-4226	424	28	.	.	PUNCT
ejpam-4226	425	1	computer	computer	NOUN
ejpam-4226	425	2	sci	sci	PROPN
ejpam-4226	425	3	16	16	NUM
ejpam-4226	425	4	,	,	PUNCT
ejpam-4226	425	5	(	(	PUNCT
ejpam-4226	425	6	2016	2016	NUM
ejpam-4226	425	7	)	)	PUNCT
ejpam-4226	425	8	,	,	PUNCT
ejpam-4226	425	9	140	140	NUM
ejpam-4226	425	10	-	-	SYM
ejpam-4226	425	11	146	146	NUM
ejpam-4226	425	12	[	[	X
ejpam-4226	425	13	13	13	NUM
ejpam-4226	425	14	]	]	PUNCT
ejpam-4226	425	15	m.	m.	NOUN
ejpam-4226	425	16	al	al	PROPN
ejpam-4226	425	17	horani	horani	PROPN
ejpam-4226	425	18	,	,	PUNCT
ejpam-4226	425	19	r.	r.	PROPN
ejpam-4226	425	20	khalil	khalil	PROPN
ejpam-4226	425	21	and	and	CCONJ
ejpam-4226	425	22	i.	i.	PROPN
ejpam-4226	425	23	aldarawi	aldarawi	PROPN
ejpam-4226	425	24	,	,	PUNCT
ejpam-4226	425	25	fractional	fractional	PROPN
ejpam-4226	425	26	cauchy	cauchy	PROPN
ejpam-4226	425	27	euler	euler	PROPN
ejpam-4226	425	28	differential	differential	PROPN
ejpam-4226	425	29	equation	equation	NOUN
ejpam-4226	425	30	,	,	PUNCT
ejpam-4226	425	31	j.	j.	PROPN
ejpam-4226	425	32	comp	comp	PROPN
ejpam-4226	425	33	.	.	PUNCT
ejpam-4226	426	1	anal	anal	PROPN
ejpam-4226	426	2	.	.	PUNCT
ejpam-4226	427	1	app	app	PROPN
ejpam-4226	427	2	,	,	PUNCT
ejpam-4226	427	3	28	28	NUM
ejpam-4226	427	4	(	(	PUNCT
ejpam-4226	427	5	2)(2019	2)(2019	NUM
ejpam-4226	427	6	)	)	PUNCT
ejpam-4226	427	7	,	,	PUNCT
ejpam-4226	427	8	226	226	NUM
ejpam-4226	427	9	-	-	SYM
ejpam-4226	427	10	233	233	NUM
ejpam-4226	427	11	.	.	PUNCT
ejpam-4226	428	1	references	reference	NOUN
ejpam-4226	428	2	125	125	NUM
ejpam-4226	428	3	[	[	X
ejpam-4226	428	4	14	14	NUM
ejpam-4226	428	5	]	]	X
ejpam-4226	428	6	d.	d.	PROPN
ejpam-4226	428	7	r.	r.	PROPN
ejpam-4226	428	8	anderson	anderson	PROPN
ejpam-4226	428	9	,	,	PUNCT
ejpam-4226	428	10	e.	e.	PROPN
ejpam-4226	428	11	camud	camud	PROPN
ejpam-4226	428	12	,	,	PUNCT
ejpam-4226	428	13	and	and	CCONJ
ejpam-4226	428	14	d.	d.	PROPN
ejpam-4226	428	15	j.	j.	PROPN
ejpam-4226	428	16	ulness	ulness	PROPN
ejpam-4226	428	17	,	,	PUNCT
ejpam-4226	428	18	on	on	ADP
ejpam-4226	428	19	the	the	DET
ejpam-4226	428	20	nature	nature	NOUN
ejpam-4226	428	21	of	of	ADP
ejpam-4226	428	22	the	the	DET
ejpam-4226	428	23	conformable	conformable	ADJ
ejpam-4226	428	24	derivative	derivative	NOUN
ejpam-4226	428	25	and	and	CCONJ
ejpam-4226	428	26	its	its	PRON
ejpam-4226	428	27	applications	application	NOUN
ejpam-4226	428	28	to	to	ADP
ejpam-4226	428	29	physics	physics	PROPN
ejpam-4226	428	30	,	,	PUNCT
ejpam-4226	428	31	journal	journal	NOUN
ejpam-4226	428	32	of	of	ADP
ejpam-4226	428	33	fractional	fractional	ADJ
ejpam-4226	428	34	calculus	calculus	NOUN
ejpam-4226	428	35	and	and	CCONJ
ejpam-4226	428	36	applications	application	NOUN
ejpam-4226	428	37	,	,	PUNCT
ejpam-4226	428	38	14(2019	14(2019	NUM
ejpam-4226	428	39	)	)	PUNCT
ejpam-4226	428	40	,	,	PUNCT
ejpam-4226	428	41	92	92	NUM
ejpam-4226	428	42	-	-	SYM
ejpam-4226	428	43	135	135	NUM
ejpam-4226	428	44	.	.	PUNCT
ejpam-4226	429	1	[	[	X
ejpam-4226	429	2	15	15	NUM
ejpam-4226	429	3	]	]	PUNCT
ejpam-4226	429	4	a.	a.	NOUN
ejpam-4226	429	5	atangana	atangana	PROPN
ejpam-4226	429	6	,	,	PUNCT
ejpam-4226	429	7	d.	d.	PROPN
ejpam-4226	429	8	baleanu	baleanu	PROPN
ejpam-4226	429	9	and	and	CCONJ
ejpam-4226	429	10	a.	a.	NOUN
ejpam-4226	429	11	alsaedi	alsaedi	PROPN
ejpam-4226	429	12	,	,	PUNCT
ejpam-4226	429	13	new	new	ADJ
ejpam-4226	429	14	properties	property	NOUN
ejpam-4226	429	15	of	of	ADP
ejpam-4226	429	16	conformable	conformable	ADJ
ejpam-4226	429	17	derivative	derivative	ADJ
ejpam-4226	429	18	,	,	PUNCT
ejpam-4226	429	19	open	open	ADJ
ejpam-4226	429	20	mathematics	mathematic	NOUN
ejpam-4226	429	21	13(2015)doi	13(2015)doi	NUM
ejpam-4226	429	22	:	:	PUNCT
ejpam-4226	429	23	10.1515	10.1515	NUM
ejpam-4226	429	24	/	/	SYM
ejpam-4226	429	25	math-2015	math-2015	NOUN
ejpam-4226	429	26	-	-	PUNCT
ejpam-4226	429	27	0081	0081	NUM
ejpam-4226	429	28	.	.	PUNCT
ejpam-4226	430	1	[	[	X
ejpam-4226	430	2	16	16	NUM
ejpam-4226	430	3	]	]	X
ejpam-4226	430	4	w.s	w.s	PROPN
ejpam-4226	430	5	.	.	PROPN
ejpam-4226	430	6	chung	chung	PROPN
ejpam-4226	430	7	,	,	PUNCT
ejpam-4226	430	8	fractional	fractional	PROPN
ejpam-4226	430	9	newton	newton	PROPN
ejpam-4226	430	10	mechanics	mechanic	NOUN
ejpam-4226	430	11	with	with	ADP
ejpam-4226	430	12	conformable	conformable	ADJ
ejpam-4226	430	13	fractional	fractional	ADJ
ejpam-4226	430	14	derivative	derivative	ADJ
ejpam-4226	430	15	,	,	PUNCT
ejpam-4226	430	16	journal	journal	NOUN
ejpam-4226	430	17	of	of	ADP
ejpam-4226	430	18	computational	computational	ADJ
ejpam-4226	430	19	and	and	CCONJ
ejpam-4226	430	20	applied	applied	ADJ
ejpam-4226	430	21	mathematics	mathematic	NOUN
ejpam-4226	430	22	,	,	PUNCT
ejpam-4226	430	23	2015	2015	NUM
ejpam-4226	430	24	.	.	PUNCT
ejpam-4226	431	1	[	[	X
ejpam-4226	431	2	17	17	NUM
ejpam-4226	431	3	]	]	X
ejpam-4226	431	4	r.	r.	PROPN
ejpam-4226	431	5	khalil	khalil	PROPN
ejpam-4226	431	6	,	,	PUNCT
ejpam-4226	431	7	m.	m.	PROPN
ejpam-4226	431	8	al	al	PROPN
ejpam-4226	431	9	horani	horani	PROPN
ejpam-4226	431	10	and	and	CCONJ
ejpam-4226	431	11	d.	d.	PROPN
ejpam-4226	431	12	anderson	anderson	PROPN
ejpam-4226	431	13	.	.	PUNCT
ejpam-4226	432	1	undetermined	undetermined	ADJ
ejpam-4226	432	2	coeficients	coeficient	NOUN
ejpam-4226	432	3	for	for	ADP
ejpam-4226	432	4	local	local	ADJ
ejpam-4226	432	5	fractional	fractional	ADJ
ejpam-4226	432	6	differential	differential	ADJ
ejpam-4226	432	7	equations	equation	NOUN
ejpam-4226	432	8	j.	j.	PROPN
ejpam-4226	432	9	math	math	PROPN
ejpam-4226	432	10	.	.	PUNCT
ejpam-4226	433	1	comput	comput	NOUN
ejpam-4226	433	2	.	.	PUNCT
ejpam-4226	434	1	sci	sci	PROPN
ejpam-4226	434	2	16	16	NUM
ejpam-4226	434	3	(	(	PUNCT
ejpam-4226	434	4	2016),140	2016),140	NUM
ejpam-4226	434	5	-	-	SYM
ejpam-4226	434	6	146	146	NUM
ejpam-4226	434	7	.	.	PUNCT
ejpam-4226	435	1	[	[	X
ejpam-4226	435	2	18	18	NUM
ejpam-4226	435	3	]	]	X
ejpam-4226	435	4	r.	r.	PROPN
ejpam-4226	435	5	khalil	khalil	PROPN
ejpam-4226	435	6	,	,	PUNCT
ejpam-4226	435	7	m.	m.	PROPN
ejpam-4226	435	8	al	al	PROPN
ejpam-4226	435	9	horani	horani	PROPN
ejpam-4226	435	10	and	and	CCONJ
ejpam-4226	435	11	m.	m.	PROPN
ejpam-4226	435	12	abu	abu	PROPN
ejpam-4226	435	13	hammad	hammad	PROPN
ejpam-4226	435	14	,	,	PUNCT
ejpam-4226	435	15	geometric	geometric	ADJ
ejpam-4226	435	16	meaning	meaning	NOUN
ejpam-4226	435	17	of	of	ADP
ejpam-4226	435	18	conformable	conformable	ADJ
ejpam-4226	435	19	derivative	derivative	NOUN
ejpam-4226	435	20	via	via	ADP
ejpam-4226	435	21	fractional	fractional	ADJ
ejpam-4226	435	22	cords	cord	NOUN
ejpam-4226	435	23	,	,	PUNCT
ejpam-4226	435	24	j.	j.	PROPN
ejpam-4226	435	25	math	math	PROPN
ejpam-4226	435	26	.	.	PUNCT
ejpam-4226	436	1	computer	computer	NOUN
ejpam-4226	436	2	sci	sci	PROPN
ejpam-4226	436	3	.	.	PROPN
ejpam-4226	436	4	,	,	PUNCT
ejpam-4226	436	5	19	19	NUM
ejpam-4226	436	6	(	(	PUNCT
ejpam-4226	436	7	2019	2019	NUM
ejpam-4226	436	8	)	)	PUNCT
ejpam-4226	436	9	,	,	PUNCT
ejpam-4226	436	10	241	241	PROPN
ejpam-4226	436	11	-	-	SYM
ejpam-4226	436	12	245	245	NUM
ejpam-4226	436	13	.	.	PUNCT
ejpam-4226	437	1	[	[	X
ejpam-4226	437	2	19	19	NUM
ejpam-4226	437	3	]	]	PUNCT
ejpam-4226	437	4	m.	m.	NOUN
ejpam-4226	437	5	mhailan	mhailan	NOUN
ejpam-4226	437	6	,	,	PUNCT
ejpam-4226	437	7	m.	m.	NOUN
ejpam-4226	437	8	abu	abu	PROPN
ejpam-4226	437	9	hammad	hammad	PROPN
ejpam-4226	437	10	,	,	PUNCT
ejpam-4226	437	11	m.	m.	NOUN
ejpam-4226	437	12	al	al	PROPN
ejpam-4226	437	13	horani	horani	PROPN
ejpam-4226	437	14	and	and	CCONJ
ejpam-4226	437	15	r.	r.	PROPN
ejpam-4226	437	16	khalil	khalil	PROPN
ejpam-4226	437	17	,	,	PUNCT
ejpam-4226	437	18	fractional	fractional	ADJ
ejpam-4226	437	19	vector	vector	NOUN
ejpam-4226	437	20	analysis	analysis	NOUN
ejpam-4226	437	21	,	,	PUNCT
ejpam-4226	437	22	journal	journal	NOUN
ejpam-4226	437	23	of	of	ADP
ejpam-4226	437	24	mathematical	mathematical	ADJ
ejpam-4226	437	25	and	and	CCONJ
ejpam-4226	437	26	computational	computational	ADJ
ejpam-4226	437	27	science,10(2020	science,10(2020	NOUN
ejpam-4226	437	28	)	)	PUNCT
ejpam-4226	437	29	,	,	PUNCT
ejpam-4226	437	30	23202326	23202326	NUM
ejpam-4226	437	31	.	.	PUNCT
ejpam-4226	438	1	[	[	X
ejpam-4226	438	2	20	20	NUM
ejpam-4226	438	3	]	]	PUNCT
ejpam-4226	438	4	w.	w.	PROPN
ejpam-4226	438	5	deeb	deeb	PROPN
ejpam-4226	438	6	and	and	CCONJ
ejpam-4226	438	7	r.	r.	PROPN
ejpam-4226	438	8	khalil	khalil	PROPN
ejpam-4226	438	9	,	,	PUNCT
ejpam-4226	438	10	best	good	ADJ
ejpam-4226	438	11	approximation	approximation	NOUN
ejpam-4226	438	12	in	in	ADP
ejpam-4226	438	13	l(x	l(x	PROPN
ejpam-4226	438	14	;	;	PUNCT
ejpam-4226	438	15	y	y	PROPN
ejpam-4226	438	16	)	)	PUNCT
ejpam-4226	438	17	,	,	PUNCT
ejpam-4226	438	18	mathematical	mathematical	ADJ
ejpam-4226	438	19	proceedings	proceeding	NOUN
ejpam-4226	438	20	of	of	ADP
ejpam-4226	438	21	the	the	DET
ejpam-4226	438	22	cambridge	cambridge	PROPN
ejpam-4226	438	23	philosophical	philosophical	PROPN
ejpam-4226	438	24	society	society	NOUN
ejpam-4226	438	25	104	104	NUM
ejpam-4226	438	26	(	(	PUNCT
ejpam-4226	438	27	1988	1988	NUM
ejpam-4226	438	28	)	)	PUNCT
ejpam-4226	438	29	,	,	PUNCT
ejpam-4226	438	30	527	527	NUM
ejpam-4226	438	31	-	-	SYM
ejpam-4226	438	32	531	531	NUM
ejpam-4226	438	33	.	.	PUNCT
ejpam-4226	439	1	[	[	X
ejpam-4226	439	2	21	21	NUM
ejpam-4226	439	3	]	]	X
ejpam-4226	439	4	w.	w.	PROPN
ejpam-4226	439	5	a.	a.	PROPN
ejpam-4226	439	6	light	light	PROPN
ejpam-4226	439	7	,	,	PUNCT
ejpam-4226	439	8	and	and	CCONJ
ejpam-4226	439	9	e.w.cheney	e.w.cheney	NOUN
ejpam-4226	439	10	,	,	PUNCT
ejpam-4226	439	11	approximation	approximation	NOUN
ejpam-4226	439	12	theory	theory	NOUN
ejpam-4226	439	13	in	in	ADP
ejpam-4226	439	14	tensor	tensor	NOUN
ejpam-4226	439	15	product	product	NOUN
ejpam-4226	439	16	spaces	space	NOUN
ejpam-4226	439	17	,	,	PUNCT
ejpam-4226	439	18	lecture	lecture	NOUN
ejpam-4226	439	19	notes	note	NOUN
ejpam-4226	439	20	in	in	ADP
ejpam-4226	439	21	math	math	NOUN
ejpam-4226	439	22	.	.	PUNCT
ejpam-4226	440	1	1169	1169	NUM
ejpam-4226	440	2	.	.	PUNCT
ejpam-4226	441	1	springer	springer	NOUN
ejpam-4226	441	2	-	-	PUNCT
ejpam-4226	441	3	verlag	verlag	PROPN
ejpam-4226	441	4	,	,	PUNCT
ejpam-4226	441	5	new	new	PROPN
ejpam-4226	441	6	york	york	PROPN
ejpam-4226	441	7	,	,	PUNCT
ejpam-4226	441	8	1985	1985	NUM
ejpam-4226	441	9	.	.	PUNCT
ejpam-4226	442	1	[	[	X
ejpam-4226	442	2	22	22	NUM
ejpam-4226	442	3	]	]	PUNCT
ejpam-4226	442	4	r.	r.	PROPN
ejpam-4226	442	5	khalil	khalil	PROPN
ejpam-4226	442	6	,	,	PUNCT
ejpam-4226	442	7	isometries	isometry	NOUN
ejpam-4226	442	8	on	on	ADP
ejpam-4226	442	9	lp⊗	lp⊗	PROPN
ejpam-4226	442	10	lp	lp	NOUN
ejpam-4226	442	11	,	,	PUNCT
ejpam-4226	442	12	tamkang	tamkang	PROPN
ejpam-4226	442	13	j.	j.	PROPN
ejpam-4226	442	14	math	math	PROPN
ejpam-4226	442	15	.	.	PUNCT
ejpam-4226	443	1	16	16	NUM
ejpam-4226	443	2	(	(	PUNCT
ejpam-4226	443	3	2)(1985	2)(1985	NUM
ejpam-4226	443	4	)	)	PUNCT
ejpam-4226	443	5	,	,	PUNCT
ejpam-4226	443	6	77	77	NUM
ejpam-4226	443	7	-	-	SYM
ejpam-4226	443	8	85	85	NUM
ejpam-4226	443	9	.	.	PUNCT