id	sid	tid	token	lemma	pos
ejpam-5433	1	1	european	european	PROPN
ejpam-5433	1	2	journal	journal	PROPN
ejpam-5433	1	3	of	of	ADP
ejpam-5433	1	4	pure	pure	ADJ
ejpam-5433	1	5	and	and	CCONJ
ejpam-5433	1	6	applied	apply	VERB
ejpam-5433	1	7	mathematics	mathematic	NOUN
ejpam-5433	1	8	vol	vol	NOUN
ejpam-5433	1	9	.	.	PROPN
ejpam-5433	2	1	17	17	NUM
ejpam-5433	2	2	,	,	PUNCT
ejpam-5433	2	3	no	no	INTJ
ejpam-5433	2	4	.	.	NOUN
ejpam-5433	2	5	4	4	NUM
ejpam-5433	2	6	,	,	PUNCT
ejpam-5433	2	7	2024	2024	NUM
ejpam-5433	2	8	,	,	PUNCT
ejpam-5433	2	9	3061	3061	NUM
ejpam-5433	2	10	-	-	SYM
ejpam-5433	2	11	3078	3078	NUM
ejpam-5433	2	12	issn	issn	PROPN
ejpam-5433	2	13	1307	1307	NUM
ejpam-5433	2	14	-	-	SYM
ejpam-5433	2	15	5543	5543	NUM
ejpam-5433	2	16	–	–	PUNCT
ejpam-5433	3	1	ejpam.com	ejpam.com	X
ejpam-5433	3	2	published	publish	VERB
ejpam-5433	3	3	by	by	ADP
ejpam-5433	3	4	new	new	PROPN
ejpam-5433	3	5	york	york	PROPN
ejpam-5433	3	6	business	business	PROPN
ejpam-5433	3	7	global	global	ADJ
ejpam-5433	3	8	atomic	atomic	ADJ
ejpam-5433	3	9	solution	solution	NOUN
ejpam-5433	3	10	of	of	ADP
ejpam-5433	3	11	third	third	ADJ
ejpam-5433	3	12	order	order	NOUN
ejpam-5433	3	13	fractional	fractional	ADJ
ejpam-5433	3	14	abstract	abstract	ADJ
ejpam-5433	3	15	cauchy	cauchy	PROPN
ejpam-5433	3	16	problem	problem	NOUN
ejpam-5433	3	17	rami	rami	PROPN
ejpam-5433	3	18	alkhateeb1,∗	alkhateeb1,∗	PROPN
ejpam-5433	3	19	,	,	PUNCT
ejpam-5433	3	20	ghaith	ghaith	PROPN
ejpam-5433	3	21	awwad2	awwad2	PROPN
ejpam-5433	3	22	1	1	NUM
ejpam-5433	3	23	department	department	NOUN
ejpam-5433	3	24	of	of	ADP
ejpam-5433	3	25	basic	basic	ADJ
ejpam-5433	3	26	sciences	sciences	PROPN
ejpam-5433	3	27	,	,	PUNCT
ejpam-5433	3	28	al	al	PROPN
ejpam-5433	3	29	-	-	PUNCT
ejpam-5433	3	30	ahliyya	ahliyya	PROPN
ejpam-5433	3	31	amman	amman	PROPN
ejpam-5433	3	32	university	university	PROPN
ejpam-5433	3	33	,	,	PUNCT
ejpam-5433	3	34	amman	amman	PROPN
ejpam-5433	3	35	,	,	PUNCT
ejpam-5433	3	36	jordan	jordan	PROPN
ejpam-5433	3	37	2	2	NUM
ejpam-5433	3	38	department	department	NOUN
ejpam-5433	3	39	of	of	ADP
ejpam-5433	3	40	mathematics	mathematics	PROPN
ejpam-5433	3	41	,	,	PUNCT
ejpam-5433	3	42	university	university	PROPN
ejpam-5433	3	43	of	of	ADP
ejpam-5433	3	44	jordan	jordan	PROPN
ejpam-5433	3	45	,	,	PUNCT
ejpam-5433	3	46	amman	amman	PROPN
ejpam-5433	3	47	,	,	PUNCT
ejpam-5433	3	48	jordan	jordan	PROPN
ejpam-5433	3	49	abstract	abstract	PROPN
ejpam-5433	3	50	.	.	PUNCT
ejpam-5433	4	1	in	in	ADP
ejpam-5433	4	2	this	this	DET
ejpam-5433	4	3	paper	paper	NOUN
ejpam-5433	4	4	,	,	PUNCT
ejpam-5433	4	5	we	we	PRON
ejpam-5433	4	6	find	find	VERB
ejpam-5433	4	7	an	an	DET
ejpam-5433	4	8	atomic	atomic	ADJ
ejpam-5433	4	9	solution	solution	NOUN
ejpam-5433	4	10	of	of	ADP
ejpam-5433	4	11	the	the	DET
ejpam-5433	4	12	fractional	fractional	ADJ
ejpam-5433	4	13	abstract	abstract	ADJ
ejpam-5433	4	14	cauchy	cauchy	ADJ
ejpam-5433	4	15	problem	problem	NOUN
ejpam-5433	4	16	of	of	ADP
ejpam-5433	4	17	order	order	NOUN
ejpam-5433	4	18	three	three	NUM
ejpam-5433	4	19	.	.	PUNCT
ejpam-5433	5	1	the	the	DET
ejpam-5433	5	2	fractional	fractional	ADJ
ejpam-5433	5	3	derivative	derivative	NOUN
ejpam-5433	5	4	used	use	VERB
ejpam-5433	5	5	is	be	AUX
ejpam-5433	5	6	the	the	DET
ejpam-5433	5	7	conformable	conformable	ADJ
ejpam-5433	5	8	derivative	derivative	NOUN
ejpam-5433	5	9	.	.	PUNCT
ejpam-5433	6	1	the	the	DET
ejpam-5433	6	2	main	main	ADJ
ejpam-5433	6	3	idea	idea	NOUN
ejpam-5433	6	4	of	of	ADP
ejpam-5433	6	5	the	the	DET
ejpam-5433	6	6	proofs	proof	NOUN
ejpam-5433	6	7	are	be	AUX
ejpam-5433	6	8	based	base	VERB
ejpam-5433	6	9	on	on	ADP
ejpam-5433	6	10	theory	theory	NOUN
ejpam-5433	6	11	of	of	ADP
ejpam-5433	6	12	tensor	tensor	NOUN
ejpam-5433	6	13	product	product	NOUN
ejpam-5433	6	14	of	of	ADP
ejpam-5433	6	15	banach	banach	NOUN
ejpam-5433	6	16	space	space	NOUN
ejpam-5433	6	17	.	.	PUNCT
ejpam-5433	7	1	2020	2020	NUM
ejpam-5433	7	2	mathematics	mathematic	NOUN
ejpam-5433	7	3	subject	subject	NOUN
ejpam-5433	7	4	classifications	classification	NOUN
ejpam-5433	7	5	:	:	PUNCT
ejpam-5433	7	6	34a55	34a55	NUM
ejpam-5433	7	7	,	,	PUNCT
ejpam-5433	7	8	26a33	26a33	NUM
ejpam-5433	7	9	,	,	PUNCT
ejpam-5433	7	10	34g10	34g10	NUM
ejpam-5433	7	11	key	key	ADJ
ejpam-5433	7	12	words	word	NOUN
ejpam-5433	7	13	and	and	CCONJ
ejpam-5433	7	14	phrases	phrase	NOUN
ejpam-5433	7	15	:	:	PUNCT
ejpam-5433	7	16	fractional	fractional	ADJ
ejpam-5433	7	17	derivatives	derivative	NOUN
ejpam-5433	7	18	,	,	PUNCT
ejpam-5433	7	19	abstract	abstract	ADJ
ejpam-5433	7	20	cauchy	cauchy	PROPN
ejpam-5433	7	21	problem	problem	NOUN
ejpam-5433	7	22	,	,	PUNCT
ejpam-5433	7	23	atom	atom	NOUN
ejpam-5433	7	24	function	function	NOUN
ejpam-5433	7	25	,	,	PUNCT
ejpam-5433	7	26	conformable	conformable	ADJ
ejpam-5433	7	27	derivative	derivative	ADJ
ejpam-5433	7	28	,	,	PUNCT
ejpam-5433	7	29	tensor	tensor	NOUN
ejpam-5433	7	30	product	product	NOUN
ejpam-5433	7	31	of	of	ADP
ejpam-5433	7	32	banach	banach	NOUN
ejpam-5433	7	33	space	space	NOUN
ejpam-5433	7	34	1	1	NUM
ejpam-5433	7	35	.	.	PUNCT
ejpam-5433	8	1	introduction	introduction	NOUN
ejpam-5433	8	2	let	let	VERB
ejpam-5433	8	3	x	x	PRON
ejpam-5433	8	4	be	be	AUX
ejpam-5433	8	5	a	a	DET
ejpam-5433	8	6	banach	banach	NOUN
ejpam-5433	8	7	space	space	NOUN
ejpam-5433	9	1	and	and	CCONJ
ejpam-5433	9	2	i	i	PRON
ejpam-5433	9	3	=	=	PUNCT
ejpam-5433	10	1	[	[	X
ejpam-5433	10	2	0	0	NUM
ejpam-5433	10	3	,	,	PUNCT
ejpam-5433	10	4	1	1	NUM
ejpam-5433	10	5	]	]	PUNCT
ejpam-5433	10	6	.	.	PUNCT
ejpam-5433	11	1	let	let	AUX
ejpam-5433	11	2	c(i	c(i	NOUN
ejpam-5433	11	3	)	)	PUNCT
ejpam-5433	11	4	be	be	AUX
ejpam-5433	11	5	the	the	DET
ejpam-5433	11	6	banach	banach	NOUN
ejpam-5433	11	7	space	space	NOUN
ejpam-5433	11	8	of	of	ADP
ejpam-5433	11	9	all	all	DET
ejpam-5433	11	10	real	real	ADV
ejpam-5433	11	11	valued	value	VERB
ejpam-5433	11	12	continuous	continuous	ADJ
ejpam-5433	11	13	function	function	NOUN
ejpam-5433	11	14	on	on	ADP
ejpam-5433	11	15	i	i	PRON
ejpam-5433	11	16	under	under	ADP
ejpam-5433	11	17	the	the	DET
ejpam-5433	11	18	sup	sup	NOUN
ejpam-5433	11	19	-	-	PUNCT
ejpam-5433	11	20	norm	norm	NOUN
ejpam-5433	11	21	,	,	PUNCT
ejpam-5433	11	22	and	and	CCONJ
ejpam-5433	11	23	c(i	c(i	NOUN
ejpam-5433	11	24	,	,	PUNCT
ejpam-5433	11	25	x	x	PRON
ejpam-5433	11	26	)	)	PUNCT
ejpam-5433	11	27	be	be	AUX
ejpam-5433	11	28	the	the	DET
ejpam-5433	11	29	banach	banach	NOUN
ejpam-5433	11	30	space	space	NOUN
ejpam-5433	11	31	of	of	ADP
ejpam-5433	11	32	all	all	DET
ejpam-5433	11	33	continuous	continuous	ADJ
ejpam-5433	11	34	functions	function	NOUN
ejpam-5433	11	35	defined	define	VERB
ejpam-5433	11	36	on	on	ADP
ejpam-5433	11	37	i	i	PRON
ejpam-5433	11	38	with	with	ADP
ejpam-5433	11	39	values	value	NOUN
ejpam-5433	11	40	on	on	ADP
ejpam-5433	11	41	x.	x.	NOUN
ejpam-5433	11	42	in	in	ADP
ejpam-5433	11	43	recent	recent	ADJ
ejpam-5433	11	44	years	year	NOUN
ejpam-5433	11	45	,	,	PUNCT
ejpam-5433	11	46	many	many	ADJ
ejpam-5433	11	47	researchers	researcher	NOUN
ejpam-5433	11	48	were	be	AUX
ejpam-5433	11	49	devoted	devoted	ADJ
ejpam-5433	11	50	to	to	ADP
ejpam-5433	11	51	the	the	DET
ejpam-5433	11	52	problem	problem	NOUN
ejpam-5433	11	53	bu	bu	ADP
ejpam-5433	11	54	´	´	NOUN
ejpam-5433	11	55	=	=	PUNCT
ejpam-5433	11	56	au(t	au(t	PRON
ejpam-5433	11	57	)	)	PUNCT
ejpam-5433	12	1	+	+	NUM
ejpam-5433	12	2	f(t)z	f(t)z	PROPN
ejpam-5433	12	3	u(0	u(0	NOUN
ejpam-5433	12	4	)	)	PUNCT
ejpam-5433	12	5	=	=	SYM
ejpam-5433	13	1	x0	x0	PROPN
ejpam-5433	13	2	,	,	PUNCT
ejpam-5433	13	3	where	where	SCONJ
ejpam-5433	13	4	u	u	PROPN
ejpam-5433	13	5	∈	∈	PROPN
ejpam-5433	13	6	ć	ć	PROPN
ejpam-5433	13	7	(	(	PUNCT
ejpam-5433	13	8	i	i	NOUN
ejpam-5433	13	9	,	,	PUNCT
ejpam-5433	13	10	x	x	NOUN
ejpam-5433	13	11	)	)	PUNCT
ejpam-5433	13	12	and	and	CCONJ
ejpam-5433	13	13	a	a	DET
ejpam-5433	13	14	,	,	PUNCT
ejpam-5433	13	15	b	b	NOUN
ejpam-5433	13	16	are	be	AUX
ejpam-5433	13	17	densely	densely	ADV
ejpam-5433	13	18	defined	define	VERB
ejpam-5433	13	19	linear	linear	ADJ
ejpam-5433	13	20	operators	operator	NOUN
ejpam-5433	13	21	on	on	ADP
ejpam-5433	13	22	the	the	DET
ejpam-5433	13	23	codomain	codomain	ADJ
ejpam-5433	13	24	u.	u.	NOUN
ejpam-5433	14	1	this	this	PRON
ejpam-5433	14	2	is	be	AUX
ejpam-5433	14	3	called	call	VERB
ejpam-5433	14	4	the	the	DET
ejpam-5433	14	5	abstract	abstract	ADJ
ejpam-5433	14	6	cauchy	cauchy	ADJ
ejpam-5433	14	7	problem	problem	NOUN
ejpam-5433	14	8	which	which	PRON
ejpam-5433	14	9	is	be	AUX
ejpam-5433	14	10	:	:	PUNCT
ejpam-5433	14	11	if	if	SCONJ
ejpam-5433	14	12	f	f	PROPN
ejpam-5433	14	13	=	=	SYM
ejpam-5433	14	14	0	0	PROPN
ejpam-5433	14	15	or	or	CCONJ
ejpam-5433	14	16	z	z	NOUN
ejpam-5433	14	17	=	=	SYM
ejpam-5433	14	18	0	0	NUM
ejpam-5433	14	19	,	,	PUNCT
ejpam-5433	14	20	then	then	ADV
ejpam-5433	14	21	the	the	DET
ejpam-5433	14	22	equation	equation	NOUN
ejpam-5433	14	23	is	be	AUX
ejpam-5433	14	24	homogenous	homogenous	ADJ
ejpam-5433	14	25	,	,	PUNCT
ejpam-5433	14	26	otherwise	otherwise	ADV
ejpam-5433	14	27	it	it	PRON
ejpam-5433	14	28	is	be	AUX
ejpam-5433	14	29	called	call	VERB
ejpam-5433	14	30	non	non	ADJ
ejpam-5433	14	31	-	-	ADJ
ejpam-5433	14	32	homogenous	homogenous	ADJ
ejpam-5433	14	33	.	.	PUNCT
ejpam-5433	15	1	now	now	ADV
ejpam-5433	15	2	in	in	ADP
ejpam-5433	15	3	the	the	DET
ejpam-5433	15	4	non	non	ADJ
ejpam-5433	15	5	homogenous	homogenous	ADJ
ejpam-5433	15	6	problem	problem	NOUN
ejpam-5433	15	7	we	we	PRON
ejpam-5433	15	8	have	have	VERB
ejpam-5433	15	9	two	two	NUM
ejpam-5433	15	10	cases	case	NOUN
ejpam-5433	15	11	:	:	PUNCT
ejpam-5433	15	12	(	(	PUNCT
ejpam-5433	15	13	i	i	NOUN
ejpam-5433	15	14	)	)	PUNCT
ejpam-5433	15	15	the	the	DET
ejpam-5433	15	16	first	first	ADJ
ejpam-5433	15	17	case	case	NOUN
ejpam-5433	15	18	,	,	PUNCT
ejpam-5433	15	19	u	u	NOUN
ejpam-5433	15	20	is	be	AUX
ejpam-5433	15	21	unknown	unknown	ADJ
ejpam-5433	15	22	and	and	CCONJ
ejpam-5433	15	23	f	f	PROPN
ejpam-5433	15	24	is	be	AUX
ejpam-5433	15	25	given	give	VERB
ejpam-5433	15	26	.	.	PUNCT
ejpam-5433	16	1	in	in	ADP
ejpam-5433	16	2	this	this	DET
ejpam-5433	16	3	case	case	NOUN
ejpam-5433	16	4	the	the	DET
ejpam-5433	16	5	problem	problem	NOUN
ejpam-5433	16	6	is	be	AUX
ejpam-5433	16	7	called	call	VERB
ejpam-5433	16	8	a	a	DET
ejpam-5433	16	9	direct	direct	ADJ
ejpam-5433	16	10	problem	problem	NOUN
ejpam-5433	16	11	.	.	PUNCT
ejpam-5433	17	1	(	(	PUNCT
ejpam-5433	17	2	ii	ii	NOUN
ejpam-5433	17	3	)	)	PUNCT
ejpam-5433	17	4	the	the	DET
ejpam-5433	17	5	second	second	ADJ
ejpam-5433	17	6	case	case	NOUN
ejpam-5433	17	7	,	,	PUNCT
ejpam-5433	17	8	u	u	NOUN
ejpam-5433	17	9	and	and	CCONJ
ejpam-5433	17	10	f	f	PROPN
ejpam-5433	17	11	are	be	AUX
ejpam-5433	17	12	unknown	unknown	ADJ
ejpam-5433	17	13	.	.	PUNCT
ejpam-5433	18	1	in	in	ADP
ejpam-5433	18	2	this	this	DET
ejpam-5433	18	3	case	case	NOUN
ejpam-5433	18	4	the	the	DET
ejpam-5433	18	5	problem	problem	NOUN
ejpam-5433	18	6	is	be	AUX
ejpam-5433	18	7	called	call	VERB
ejpam-5433	18	8	an	an	DET
ejpam-5433	18	9	inverse	inverse	NOUN
ejpam-5433	18	10	problem	problem	NOUN
ejpam-5433	18	11	,	,	PUNCT
ejpam-5433	18	12	and	and	CCONJ
ejpam-5433	18	13	some	some	DET
ejpam-5433	18	14	other	other	ADJ
ejpam-5433	18	15	conditions	condition	NOUN
ejpam-5433	18	16	and	and	CCONJ
ejpam-5433	18	17	informations	information	NOUN
ejpam-5433	18	18	should	should	AUX
ejpam-5433	18	19	be	be	AUX
ejpam-5433	18	20	given	give	VERB
ejpam-5433	18	21	.	.	PUNCT
ejpam-5433	19	1	if	if	SCONJ
ejpam-5433	19	2	b	b	NOUN
ejpam-5433	19	3	is	be	AUX
ejpam-5433	19	4	not	not	PART
ejpam-5433	19	5	invertible	invertible	ADJ
ejpam-5433	19	6	,	,	PUNCT
ejpam-5433	19	7	then	then	ADV
ejpam-5433	19	8	the	the	DET
ejpam-5433	19	9	equation	equation	NOUN
ejpam-5433	19	10	is	be	AUX
ejpam-5433	19	11	called	call	VERB
ejpam-5433	19	12	non	non	ADJ
ejpam-5433	19	13	-	-	ADJ
ejpam-5433	19	14	degenerate	degenerate	ADJ
ejpam-5433	19	15	.	.	PUNCT
ejpam-5433	20	1	there	there	PRON
ejpam-5433	20	2	are	be	VERB
ejpam-5433	20	3	many	many	ADJ
ejpam-5433	20	4	different	different	ADJ
ejpam-5433	20	5	techniques	technique	NOUN
ejpam-5433	20	6	to	to	PART
ejpam-5433	20	7	solve	solve	VERB
ejpam-5433	20	8	abstract	abstract	ADJ
ejpam-5433	20	9	cauchy	cauchy	ADJ
ejpam-5433	20	10	problem	problem	NOUN
ejpam-5433	20	11	in	in	ADP
ejpam-5433	20	12	case	case	NOUN
ejpam-5433	20	13	(	(	PUNCT
ejpam-5433	20	14	i	i	NOUN
ejpam-5433	20	15	)	)	PUNCT
ejpam-5433	20	16	.	.	PUNCT
ejpam-5433	21	1	tensor	tensor	NOUN
ejpam-5433	21	2	product	product	NOUN
ejpam-5433	21	3	is	be	AUX
ejpam-5433	21	4	one	one	NUM
ejpam-5433	21	5	of	of	ADP
ejpam-5433	21	6	such	such	ADJ
ejpam-5433	21	7	techniques	technique	NOUN
ejpam-5433	21	8	.	.	PUNCT
ejpam-5433	22	1	∗corresponding	∗corresponde	VERB
ejpam-5433	22	2	author	author	NOUN
ejpam-5433	22	3	.	.	PUNCT
ejpam-5433	23	1	doi	doi	NOUN
ejpam-5433	23	2	:	:	PUNCT
ejpam-5433	23	3	https://doi.org/10.29020/nybg.ejpam.v17i4.5433	https://doi.org/10.29020/nybg.ejpam.v17i4.5433	PRON
ejpam-5433	23	4	email	email	NOUN
ejpam-5433	23	5	addresses	address	NOUN
ejpam-5433	23	6	:	:	PUNCT
ejpam-5433	23	7	r.alkhateeb@ammanu.edu.jo	r.alkhateeb@ammanu.edu.jo	ADJ
ejpam-5433	23	8	(	(	PUNCT
ejpam-5433	23	9	r.	r.	PROPN
ejpam-5433	23	10	alkhateeb	alkhateeb	PROPN
ejpam-5433	23	11	)	)	PUNCT
ejpam-5433	23	12	,	,	PUNCT
ejpam-5433	23	13	ghaithmawwad@gmail.com	ghaithmawwad@gmail.com	X
ejpam-5433	23	14	(	(	PUNCT
ejpam-5433	23	15	g.	g.	PROPN
ejpam-5433	23	16	awwad	awwad	PROPN
ejpam-5433	23	17	)	)	PUNCT
ejpam-5433	23	18	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5433	23	19	3061	3061	NUM
ejpam-5433	24	1	copyright	copyright	NOUN
ejpam-5433	24	2	:	:	PUNCT
ejpam-5433	24	3	©	©	PROPN
ejpam-5433	24	4	2024	2024	NUM
ejpam-5433	24	5	the	the	DET
ejpam-5433	24	6	author(s	author(s	NOUN
ejpam-5433	24	7	)	)	PUNCT
ejpam-5433	24	8	.	.	PUNCT
ejpam-5433	25	1	(	(	PUNCT
ejpam-5433	25	2	cc	cc	NOUN
ejpam-5433	25	3	by	by	ADP
ejpam-5433	25	4	-	-	PUNCT
ejpam-5433	25	5	nc	nc	PROPN
ejpam-5433	25	6	4.0	4.0	NUM
ejpam-5433	25	7	)	)	PUNCT
ejpam-5433	25	8	r.	r.	PROPN
ejpam-5433	25	9	alkhateeb	alkhateeb	PROPN
ejpam-5433	25	10	,	,	PUNCT
ejpam-5433	25	11	g.	g.	PROPN
ejpam-5433	25	12	awwad	awwad	PROPN
ejpam-5433	25	13	/	/	PUNCT
ejpam-5433	25	14	eur	eur	PROPN
ejpam-5433	25	15	.	.	PUNCT
ejpam-5433	26	1	j.	j.	PROPN
ejpam-5433	26	2	pure	pure	PROPN
ejpam-5433	26	3	appl	appl	PROPN
ejpam-5433	26	4	.	.	PROPN
ejpam-5433	26	5	math	math	PROPN
ejpam-5433	26	6	,	,	PUNCT
ejpam-5433	26	7	17	17	NUM
ejpam-5433	26	8	(	(	PUNCT
ejpam-5433	26	9	4	4	NUM
ejpam-5433	26	10	)	)	PUNCT
ejpam-5433	26	11	(	(	PUNCT
ejpam-5433	26	12	2024	2024	NUM
ejpam-5433	26	13	)	)	PUNCT
ejpam-5433	26	14	,	,	PUNCT
ejpam-5433	26	15	3061	3061	NUM
ejpam-5433	26	16	-	-	SYM
ejpam-5433	26	17	3078	3078	NUM
ejpam-5433	26	18	3062	3062	NUM
ejpam-5433	26	19	in	in	ADP
ejpam-5433	26	20	[	[	X
ejpam-5433	26	21	4	4	NUM
ejpam-5433	26	22	]	]	PUNCT
ejpam-5433	26	23	,	,	PUNCT
ejpam-5433	26	24	a	a	DET
ejpam-5433	26	25	new	new	ADJ
ejpam-5433	26	26	definition	definition	NOUN
ejpam-5433	26	27	called	call	VERB
ejpam-5433	26	28	α−conformable	α−conformable	ADJ
ejpam-5433	26	29	fractional	fractional	ADJ
ejpam-5433	26	30	derivative	derivative	NOUN
ejpam-5433	26	31	was	be	AUX
ejpam-5433	26	32	introduced	introduce	VERB
ejpam-5433	26	33	,	,	PUNCT
ejpam-5433	26	34	which	which	PRON
ejpam-5433	26	35	says	say	VERB
ejpam-5433	26	36	that	that	SCONJ
ejpam-5433	26	37	:	:	PUNCT
ejpam-5433	26	38	if	if	SCONJ
ejpam-5433	26	39	α	α	PROPN
ejpam-5433	26	40	∈	∈	PROPN
ejpam-5433	26	41	(	(	PUNCT
ejpam-5433	26	42	0	0	NUM
ejpam-5433	26	43	,	,	PUNCT
ejpam-5433	26	44	1	1	NUM
ejpam-5433	26	45	)	)	PUNCT
ejpam-5433	26	46	,	,	PUNCT
ejpam-5433	26	47	and	and	CCONJ
ejpam-5433	26	48	f	f	X
ejpam-5433	26	49	:	:	PUNCT
ejpam-5433	27	1	e	e	NOUN
ejpam-5433	27	2	⊆	⊆	NUM
ejpam-5433	27	3	(	(	PUNCT
ejpam-5433	27	4	0,∞	0,∞	NOUN
ejpam-5433	27	5	)	)	PUNCT
ejpam-5433	27	6	→	→	PUNCT
ejpam-5433	27	7	r.	r.	NOUN
ejpam-5433	27	8	for	for	ADP
ejpam-5433	27	9	x	x	PROPN
ejpam-5433	27	10	∈	∈	PROPN
ejpam-5433	27	11	e	e	NOUN
ejpam-5433	27	12	,	,	PUNCT
ejpam-5433	27	13	let	let	VERB
ejpam-5433	27	14	:	:	PUNCT
ejpam-5433	27	15	dαf(x	dαf(x	PROPN
ejpam-5433	27	16	)	)	PUNCT
ejpam-5433	27	17	=	=	PROPN
ejpam-5433	27	18	lim	lim	PROPN
ejpam-5433	27	19	ε→0	ε→0	NOUN
ejpam-5433	27	20	f(x+	f(x+	AUX
ejpam-5433	27	21	εx1−α)−	εx1−α)−	VERB
ejpam-5433	27	22	f(x	f(x	PROPN
ejpam-5433	27	23	)	)	PUNCT
ejpam-5433	27	24	ε	ε	PROPN
ejpam-5433	27	25	.	.	PUNCT
ejpam-5433	28	1	(	(	PUNCT
ejpam-5433	28	2	1	1	X
ejpam-5433	28	3	)	)	PUNCT
ejpam-5433	28	4	if	if	SCONJ
ejpam-5433	28	5	the	the	DET
ejpam-5433	28	6	limit	limit	NOUN
ejpam-5433	28	7	exists	exist	VERB
ejpam-5433	28	8	then	then	ADV
ejpam-5433	28	9	it	it	PRON
ejpam-5433	28	10	is	be	AUX
ejpam-5433	28	11	called	call	VERB
ejpam-5433	28	12	the	the	DET
ejpam-5433	28	13	α−conformable	α−conformable	ADJ
ejpam-5433	28	14	fractional	fractional	ADJ
ejpam-5433	28	15	derivative	derivative	NOUN
ejpam-5433	28	16	of	of	ADP
ejpam-5433	28	17	f	f	PROPN
ejpam-5433	28	18	at	at	ADP
ejpam-5433	28	19	x.	x.	NOUN
ejpam-5433	28	20	for	for	ADP
ejpam-5433	28	21	x	x	SYM
ejpam-5433	28	22	=	=	SYM
ejpam-5433	28	23	0	0	NUM
ejpam-5433	28	24	,	,	PUNCT
ejpam-5433	28	25	dαf(0	dαf(0	NOUN
ejpam-5433	28	26	)	)	PUNCT
ejpam-5433	29	1	=	=	SYM
ejpam-5433	29	2	lim	lim	PROPN
ejpam-5433	29	3	x→0	x→0	PROPN
ejpam-5433	29	4	dαf(0	dαf(0	PROPN
ejpam-5433	29	5	)	)	PUNCT
ejpam-5433	29	6	if	if	SCONJ
ejpam-5433	29	7	such	such	ADJ
ejpam-5433	29	8	limit	limit	NOUN
ejpam-5433	29	9	exists	exist	VERB
ejpam-5433	29	10	.	.	PUNCT
ejpam-5433	30	1	the	the	DET
ejpam-5433	30	2	new	new	ADJ
ejpam-5433	30	3	definition	definition	NOUN
ejpam-5433	30	4	satisfies	satisfy	VERB
ejpam-5433	30	5	:	:	PUNCT
ejpam-5433	30	6	(	(	PUNCT
ejpam-5433	30	7	i	i	NOUN
ejpam-5433	30	8	)	)	PUNCT
ejpam-5433	30	9	dα(af	dα(af	PROPN
ejpam-5433	30	10	+	+	CCONJ
ejpam-5433	30	11	bg	bg	PROPN
ejpam-5433	30	12	)	)	PUNCT
ejpam-5433	30	13	=	=	SYM
ejpam-5433	30	14	adα(f	adα(f	PROPN
ejpam-5433	30	15	)	)	PUNCT
ejpam-5433	31	1	+	+	CCONJ
ejpam-5433	31	2	bdα(g	bdα(g	PROPN
ejpam-5433	31	3	)	)	PUNCT
ejpam-5433	31	4	,	,	PUNCT
ejpam-5433	31	5	for	for	ADP
ejpam-5433	31	6	all	all	DET
ejpam-5433	31	7	a	a	PRON
ejpam-5433	31	8	,	,	PUNCT
ejpam-5433	31	9	b	b	PROPN
ejpam-5433	31	10	∈	∈	PROPN
ejpam-5433	31	11	r.	r.	PROPN
ejpam-5433	31	12	(	(	PUNCT
ejpam-5433	31	13	ii	ii	PROPN
ejpam-5433	31	14	)	)	PUNCT
ejpam-5433	31	15	dα(λ	dα(λ	PROPN
ejpam-5433	31	16	)	)	PUNCT
ejpam-5433	31	17	=	=	SYM
ejpam-5433	31	18	0	0	NUM
ejpam-5433	31	19	,	,	PUNCT
ejpam-5433	31	20	for	for	ADP
ejpam-5433	31	21	all	all	DET
ejpam-5433	31	22	constant	constant	ADJ
ejpam-5433	31	23	functions	function	NOUN
ejpam-5433	31	24	f(t	f(t	NOUN
ejpam-5433	31	25	)	)	PUNCT
ejpam-5433	32	1	=	=	SYM
ejpam-5433	32	2	λ	λ	X
ejpam-5433	32	3	.	.	NOUN
ejpam-5433	32	4	further	far	ADV
ejpam-5433	32	5	,	,	PUNCT
ejpam-5433	32	6	for	for	ADP
ejpam-5433	32	7	α	α	DET
ejpam-5433	32	8	∈	∈	PROPN
ejpam-5433	32	9	(	(	PUNCT
ejpam-5433	32	10	0	0	NUM
ejpam-5433	32	11	,	,	PUNCT
ejpam-5433	32	12	1	1	NUM
ejpam-5433	32	13	]	]	PUNCT
ejpam-5433	32	14	and	and	CCONJ
ejpam-5433	32	15	f	f	X
ejpam-5433	32	16	,	,	PUNCT
ejpam-5433	32	17	g	g	PROPN
ejpam-5433	32	18	be	be	AUX
ejpam-5433	32	19	α−differentiable	α−differentiable	ADJ
ejpam-5433	32	20	at	at	ADP
ejpam-5433	32	21	a	a	DET
ejpam-5433	32	22	point	point	NOUN
ejpam-5433	32	23	t	t	PROPN
ejpam-5433	32	24	,	,	PUNCT
ejpam-5433	32	25	with	with	ADP
ejpam-5433	32	26	g(t	g(t	PROPN
ejpam-5433	32	27	)	)	PUNCT
ejpam-5433	32	28	̸=	̸=	PROPN
ejpam-5433	32	29	0	0	NUM
ejpam-5433	32	30	.	.	PUNCT
ejpam-5433	33	1	then	then	ADV
ejpam-5433	33	2	(	(	PUNCT
ejpam-5433	33	3	iii	iii	NOUN
ejpam-5433	33	4	)	)	PUNCT
ejpam-5433	33	5	dα(fg	dα(fg	NOUN
ejpam-5433	33	6	)	)	PUNCT
ejpam-5433	33	7	=	=	PUNCT
ejpam-5433	33	8	fdα(g	fdα(g	PROPN
ejpam-5433	33	9	)	)	PUNCT
ejpam-5433	33	10	+	+	NUM
ejpam-5433	33	11	gdα(f	gdα(f	NOUN
ejpam-5433	33	12	)	)	PUNCT
ejpam-5433	33	13	.	.	PUNCT
ejpam-5433	34	1	(	(	PUNCT
ejpam-5433	34	2	iv	iv	X
ejpam-5433	34	3	)	)	PUNCT
ejpam-5433	34	4	dα	dα	PROPN
ejpam-5433	34	5	(	(	PUNCT
ejpam-5433	34	6	f	f	PROPN
ejpam-5433	34	7	g	g	PROPN
ejpam-5433	34	8	)	)	PUNCT
ejpam-5433	34	9	=	=	PUNCT
ejpam-5433	35	1	gdα(f)−fdα(g	gdα(f)−fdα(g	PROPN
ejpam-5433	35	2	)	)	PUNCT
ejpam-5433	35	3	g2	g2	PROPN
ejpam-5433	35	4	.	.	PUNCT
ejpam-5433	36	1	we	we	PRON
ejpam-5433	36	2	list	list	VERB
ejpam-5433	36	3	here	here	ADV
ejpam-5433	36	4	the	the	DET
ejpam-5433	36	5	fractional	fractional	ADJ
ejpam-5433	36	6	derivatives	derivative	NOUN
ejpam-5433	36	7	of	of	ADP
ejpam-5433	36	8	certain	certain	ADJ
ejpam-5433	36	9	functions	function	NOUN
ejpam-5433	36	10	,	,	PUNCT
ejpam-5433	36	11	(	(	PUNCT
ejpam-5433	36	12	v	v	NOUN
ejpam-5433	36	13	)	)	PUNCT
ejpam-5433	36	14	dα(tp	dα(tp	ADJ
ejpam-5433	36	15	)	)	PUNCT
ejpam-5433	36	16	=	=	SYM
ejpam-5433	36	17	ptp−α	ptp−α	PROPN
ejpam-5433	36	18	.	.	PUNCT
ejpam-5433	37	1	(	(	PUNCT
ejpam-5433	37	2	vi	vi	X
ejpam-5433	37	3	)	)	PUNCT
ejpam-5433	37	4	dα	dα	PROPN
ejpam-5433	37	5	α(sin	α(sin	PROPN
ejpam-5433	37	6	(	(	PUNCT
ejpam-5433	37	7	1	1	NUM
ejpam-5433	37	8	α	α	NOUN
ejpam-5433	37	9	t	t	NOUN
ejpam-5433	37	10	α	α	NOUN
ejpam-5433	37	11	)	)	PUNCT
ejpam-5433	37	12	)	)	PUNCT
ejpam-5433	38	1	=	=	PUNCT
ejpam-5433	38	2	cos	cos	X
ejpam-5433	38	3	(	(	PUNCT
ejpam-5433	38	4	1	1	NUM
ejpam-5433	38	5	α	α	NOUN
ejpam-5433	38	6	t	t	NOUN
ejpam-5433	38	7	α	α	NOUN
ejpam-5433	38	8	)	)	PUNCT
ejpam-5433	38	9	.	.	PUNCT
ejpam-5433	39	1	(	(	PUNCT
ejpam-5433	39	2	vii	vii	PROPN
ejpam-5433	39	3	)	)	PUNCT
ejpam-5433	39	4	dα	dα	PROPN
ejpam-5433	39	5	α(cos	α(co	NOUN
ejpam-5433	39	6	(	(	PUNCT
ejpam-5433	39	7	1	1	NUM
ejpam-5433	39	8	α	α	NOUN
ejpam-5433	39	9	t	t	NOUN
ejpam-5433	39	10	α	α	NOUN
ejpam-5433	39	11	)	)	PUNCT
ejpam-5433	39	12	)	)	PUNCT
ejpam-5433	40	1	=	=	SYM
ejpam-5433	41	1	−	−	PROPN
ejpam-5433	41	2	sin	sin	NOUN
ejpam-5433	41	3	(	(	PUNCT
ejpam-5433	41	4	1	1	NUM
ejpam-5433	41	5	α	α	NOUN
ejpam-5433	41	6	t	t	NOUN
ejpam-5433	41	7	α	α	NOUN
ejpam-5433	41	8	)	)	PUNCT
ejpam-5433	41	9	.	.	PUNCT
ejpam-5433	42	1	(	(	PUNCT
ejpam-5433	42	2	viii	viii	NOUN
ejpam-5433	42	3	)	)	PUNCT
ejpam-5433	42	4	dα(e	dα(e	VERB
ejpam-5433	42	5	1	1	NUM
ejpam-5433	42	6	α	α	NOUN
ejpam-5433	42	7	tα	tα	PROPN
ejpam-5433	42	8	)	)	PUNCT
ejpam-5433	42	9	=	=	PUNCT
ejpam-5433	43	1	e	e	X
ejpam-5433	43	2	1	1	NUM
ejpam-5433	43	3	α	α	NOUN
ejpam-5433	43	4	tα	tα	PROPN
ejpam-5433	43	5	.	.	PUNCT
ejpam-5433	44	1	on	on	ADP
ejpam-5433	44	2	letting	let	VERB
ejpam-5433	44	3	α	α	NOUN
ejpam-5433	44	4	=	=	NOUN
ejpam-5433	44	5	1	1	NUM
ejpam-5433	44	6	in	in	ADP
ejpam-5433	44	7	these	these	DET
ejpam-5433	44	8	derivatives	derivative	NOUN
ejpam-5433	44	9	,	,	PUNCT
ejpam-5433	44	10	we	we	PRON
ejpam-5433	44	11	get	get	VERB
ejpam-5433	44	12	the	the	DET
ejpam-5433	44	13	corresponding	corresponding	ADJ
ejpam-5433	44	14	ordinary	ordinary	ADJ
ejpam-5433	44	15	derivatives	derivative	NOUN
ejpam-5433	44	16	.	.	PUNCT
ejpam-5433	45	1	one	one	PRON
ejpam-5433	45	2	should	should	AUX
ejpam-5433	45	3	notice	notice	VERB
ejpam-5433	45	4	that	that	SCONJ
ejpam-5433	45	5	function	function	NOUN
ejpam-5433	45	6	could	could	AUX
ejpam-5433	45	7	be	be	AUX
ejpam-5433	45	8	α−conformable	α−conformable	ADJ
ejpam-5433	45	9	differentiable	differentiable	ADJ
ejpam-5433	45	10	at	at	ADP
ejpam-5433	45	11	a	a	DET
ejpam-5433	45	12	point	point	NOUN
ejpam-5433	45	13	but	but	CCONJ
ejpam-5433	45	14	not	not	PART
ejpam-5433	45	15	differentiable	differentiable	ADJ
ejpam-5433	45	16	,	,	PUNCT
ejpam-5433	45	17	for	for	ADP
ejpam-5433	45	18	example	example	NOUN
ejpam-5433	45	19	,	,	PUNCT
ejpam-5433	45	20	take	take	VERB
ejpam-5433	45	21	f(t	f(t	NOUN
ejpam-5433	45	22	)	)	PUNCT
ejpam-5433	46	1	=	=	SYM
ejpam-5433	46	2	2	2	NUM
ejpam-5433	46	3	√	√	NOUN
ejpam-5433	46	4	t.	t.	NOUN
ejpam-5433	47	1	then	then	ADV
ejpam-5433	47	2	d	d	PROPN
ejpam-5433	47	3	1	1	NUM
ejpam-5433	47	4	2	2	NUM
ejpam-5433	47	5	(	(	PUNCT
ejpam-5433	47	6	f)(t	f)(t	PROPN
ejpam-5433	47	7	)	)	PUNCT
ejpam-5433	47	8	=	=	SYM
ejpam-5433	47	9	1	1	X
ejpam-5433	47	10	.	.	PUNCT
ejpam-5433	48	1	hence	hence	ADV
ejpam-5433	48	2	d	d	NOUN
ejpam-5433	48	3	1	1	NUM
ejpam-5433	48	4	2	2	NUM
ejpam-5433	48	5	(	(	PUNCT
ejpam-5433	48	6	f)(0	f)(0	NUM
ejpam-5433	48	7	)	)	PUNCT
ejpam-5433	48	8	=	=	SYM
ejpam-5433	49	1	1	1	X
ejpam-5433	49	2	.	.	PUNCT
ejpam-5433	49	3	but	but	CCONJ
ejpam-5433	49	4	d1(f)(0	d1(f)(0	X
ejpam-5433	49	5	)	)	PUNCT
ejpam-5433	49	6	does	do	AUX
ejpam-5433	49	7	not	not	PART
ejpam-5433	49	8	exist	exist	VERB
ejpam-5433	49	9	.	.	PUNCT
ejpam-5433	50	1	this	this	PRON
ejpam-5433	50	2	is	be	AUX
ejpam-5433	50	3	not	not	PART
ejpam-5433	50	4	the	the	DET
ejpam-5433	50	5	case	case	NOUN
ejpam-5433	50	6	for	for	ADP
ejpam-5433	50	7	the	the	DET
ejpam-5433	50	8	known	know	VERB
ejpam-5433	50	9	classical	classical	ADJ
ejpam-5433	50	10	fractional	fractional	ADJ
ejpam-5433	50	11	derivatives	derivative	NOUN
ejpam-5433	50	12	.	.	PUNCT
ejpam-5433	51	1	for	for	ADP
ejpam-5433	51	2	more	more	ADJ
ejpam-5433	51	3	on	on	ADP
ejpam-5433	51	4	fractional	fractional	ADJ
ejpam-5433	51	5	calculus	calculus	NOUN
ejpam-5433	51	6	and	and	CCONJ
ejpam-5433	51	7	its	its	PRON
ejpam-5433	51	8	applications	application	NOUN
ejpam-5433	51	9	we	we	PRON
ejpam-5433	51	10	refer	refer	VERB
ejpam-5433	51	11	to	to	ADP
ejpam-5433	51	12	[	[	X
ejpam-5433	51	13	1	1	NUM
ejpam-5433	51	14	]	]	PUNCT
ejpam-5433	51	15	,	,	PUNCT
ejpam-5433	51	16	[	[	X
ejpam-5433	51	17	2	2	NUM
ejpam-5433	51	18	]	]	PUNCT
ejpam-5433	51	19	,	,	PUNCT
ejpam-5433	51	20	and	and	CCONJ
ejpam-5433	51	21	[	[	X
ejpam-5433	51	22	5	5	NUM
ejpam-5433	51	23	]	]	PUNCT
ejpam-5433	51	24	.	.	PUNCT
ejpam-5433	52	1	2	2	X
ejpam-5433	52	2	.	.	X
ejpam-5433	52	3	atomic	atomic	ADJ
ejpam-5433	52	4	solution	solution	NOUN
ejpam-5433	52	5	let	let	VERB
ejpam-5433	52	6	x	x	PRON
ejpam-5433	52	7	and	and	CCONJ
ejpam-5433	52	8	y	y	PROPN
ejpam-5433	52	9	be	be	AUX
ejpam-5433	52	10	two	two	NUM
ejpam-5433	52	11	banach	banach	NOUN
ejpam-5433	52	12	space	space	NOUN
ejpam-5433	52	13	and	and	CCONJ
ejpam-5433	52	14	x∗	x∗	PROPN
ejpam-5433	52	15	be	be	AUX
ejpam-5433	52	16	the	the	DET
ejpam-5433	52	17	dual	dual	ADJ
ejpam-5433	52	18	of	of	ADP
ejpam-5433	52	19	x.	x.	NOUN
ejpam-5433	52	20	assume	assume	VERB
ejpam-5433	52	21	x	x	X
ejpam-5433	52	22	∈	∈	PROPN
ejpam-5433	52	23	x	x	X
ejpam-5433	52	24	and	and	CCONJ
ejpam-5433	52	25	y	y	PROPN
ejpam-5433	52	26	∈	∈	PROPN
ejpam-5433	52	27	y	y	PROPN
ejpam-5433	52	28	.	.	PUNCT
ejpam-5433	53	1	define	define	VERB
ejpam-5433	53	2	the	the	DET
ejpam-5433	53	3	map	map	NOUN
ejpam-5433	53	4	x⊗	x⊗	VERB
ejpam-5433	53	5	y	y	PROPN
ejpam-5433	53	6	:	:	PUNCT
ejpam-5433	53	7	x∗	x∗	PROPN
ejpam-5433	53	8	−→	−→	PROPN
ejpam-5433	53	9	y	y	PROPN
ejpam-5433	53	10	,	,	PUNCT
ejpam-5433	53	11	by	by	ADP
ejpam-5433	53	12	x⊗	x⊗	PROPN
ejpam-5433	53	13	y(x∗	y(x∗	NUM
ejpam-5433	53	14	)	)	PUNCT
ejpam-5433	53	15	=	=	PUNCT
ejpam-5433	54	1	⟨x	⟨x	VERB
ejpam-5433	54	2	,	,	PUNCT
ejpam-5433	54	3	x∗⟩	x∗⟩	PROPN
ejpam-5433	54	4	y	y	PROPN
ejpam-5433	54	5	for	for	ADP
ejpam-5433	54	6	all	all	DET
ejpam-5433	54	7	x∗	x∗	PROPN
ejpam-5433	54	8	∈	∈	PROPN
ejpam-5433	54	9	x∗.	x∗.	PUNCT
ejpam-5433	55	1	it	it	PRON
ejpam-5433	55	2	is	be	AUX
ejpam-5433	55	3	well	well	ADV
ejpam-5433	55	4	known	know	VERB
ejpam-5433	55	5	that	that	PRON
ejpam-5433	55	6	x⊗	x⊗	VERB
ejpam-5433	55	7	y	y	PROPN
ejpam-5433	55	8	is	be	AUX
ejpam-5433	55	9	a	a	DET
ejpam-5433	55	10	bounded	bounded	ADJ
ejpam-5433	55	11	linear	linear	ADJ
ejpam-5433	55	12	operator	operator	NOUN
ejpam-5433	55	13	and	and	CCONJ
ejpam-5433	55	14	∥x⊗	∥x⊗	NOUN
ejpam-5433	55	15	y∥	y∥	NOUN
ejpam-5433	55	16	=	=	VERB
ejpam-5433	55	17	∥x∥	∥x∥	NOUN
ejpam-5433	55	18	∥y∥	∥y∥	NOUN
ejpam-5433	55	19	.	.	PUNCT
ejpam-5433	56	1	the	the	DET
ejpam-5433	56	2	operator	operator	NOUN
ejpam-5433	56	3	x	x	PROPN
ejpam-5433	57	1	⊗	⊗	PROPN
ejpam-5433	57	2	y	y	PROPN
ejpam-5433	57	3	is	be	AUX
ejpam-5433	57	4	called	call	VERB
ejpam-5433	57	5	an	an	DET
ejpam-5433	57	6	atom	atom	NOUN
ejpam-5433	57	7	.	.	PUNCT
ejpam-5433	58	1	the	the	DET
ejpam-5433	58	2	set	set	NOUN
ejpam-5433	58	3	x	x	PUNCT
ejpam-5433	58	4	⊗	⊗	PROPN
ejpam-5433	58	5	y	y	PROPN
ejpam-5433	58	6	=	=	PRON
ejpam-5433	58	7	span	span	NOUN
ejpam-5433	58	8	{	{	PUNCT
ejpam-5433	58	9	x⊗	x⊗	PROPN
ejpam-5433	58	10	y	y	PROPN
ejpam-5433	58	11	:	:	PUNCT
ejpam-5433	58	12	x	x	SYM
ejpam-5433	58	13	∈	∈	NOUN
ejpam-5433	58	14	x	x	X
ejpam-5433	58	15	and	and	CCONJ
ejpam-5433	58	16	y	y	PROPN
ejpam-5433	58	17	∈	∈	PROPN
ejpam-5433	58	18	y	y	PROPN
ejpam-5433	58	19	}	}	PUNCT
ejpam-5433	58	20	is	be	AUX
ejpam-5433	58	21	subspace	subspace	NOUN
ejpam-5433	58	22	of	of	ADP
ejpam-5433	58	23	l	l	NOUN
ejpam-5433	58	24	(	(	PUNCT
ejpam-5433	58	25	x∗	x∗	PROPN
ejpam-5433	58	26	,	,	PUNCT
ejpam-5433	58	27	y	y	PROPN
ejpam-5433	58	28	)	)	PUNCT
ejpam-5433	58	29	.	.	PUNCT
ejpam-5433	59	1	if	if	SCONJ
ejpam-5433	59	2	the	the	DET
ejpam-5433	59	3	sum	sum	NOUN
ejpam-5433	59	4	of	of	ADP
ejpam-5433	59	5	two	two	NUM
ejpam-5433	59	6	atoms	atom	NOUN
ejpam-5433	59	7	is	be	AUX
ejpam-5433	59	8	an	an	DET
ejpam-5433	59	9	atom	atom	NOUN
ejpam-5433	59	10	,	,	PUNCT
ejpam-5433	59	11	then	then	ADV
ejpam-5433	59	12	either	either	CCONJ
ejpam-5433	59	13	the	the	DET
ejpam-5433	59	14	first	first	ADJ
ejpam-5433	59	15	components	component	NOUN
ejpam-5433	59	16	are	be	AUX
ejpam-5433	59	17	dependent	dependent	ADJ
ejpam-5433	59	18	or	or	CCONJ
ejpam-5433	59	19	the	the	DET
ejpam-5433	59	20	second	second	ADJ
ejpam-5433	59	21	are	be	AUX
ejpam-5433	59	22	dependent	dependent	ADJ
ejpam-5433	59	23	.	.	PUNCT
ejpam-5433	60	1	r.	r.	PROPN
ejpam-5433	60	2	alkhateeb	alkhateeb	PROPN
ejpam-5433	60	3	,	,	PUNCT
ejpam-5433	60	4	g.	g.	PROPN
ejpam-5433	60	5	awwad	awwad	PROPN
ejpam-5433	60	6	/	/	PUNCT
ejpam-5433	60	7	eur	eur	PROPN
ejpam-5433	60	8	.	.	PUNCT
ejpam-5433	61	1	j.	j.	PROPN
ejpam-5433	61	2	pure	pure	PROPN
ejpam-5433	61	3	appl	appl	PROPN
ejpam-5433	61	4	.	.	PROPN
ejpam-5433	61	5	math	math	PROPN
ejpam-5433	61	6	,	,	PUNCT
ejpam-5433	61	7	17	17	NUM
ejpam-5433	61	8	(	(	PUNCT
ejpam-5433	61	9	4	4	NUM
ejpam-5433	61	10	)	)	PUNCT
ejpam-5433	61	11	(	(	PUNCT
ejpam-5433	61	12	2024	2024	NUM
ejpam-5433	61	13	)	)	PUNCT
ejpam-5433	61	14	,	,	PUNCT
ejpam-5433	61	15	3061	3061	NUM
ejpam-5433	61	16	-	-	SYM
ejpam-5433	61	17	3078	3078	NUM
ejpam-5433	61	18	3063	3063	NUM
ejpam-5433	61	19	an	an	DET
ejpam-5433	61	20	equation	equation	NOUN
ejpam-5433	61	21	of	of	ADP
ejpam-5433	61	22	the	the	DET
ejpam-5433	61	23	form	form	NOUN
ejpam-5433	61	24	d2αu(t	d2αu(t	PROPN
ejpam-5433	61	25	)	)	PUNCT
ejpam-5433	62	1	+	+	NOUN
ejpam-5433	62	2	adαu(t	adαu(t	X
ejpam-5433	62	3	)	)	PUNCT
ejpam-5433	62	4	+	+	NOUN
ejpam-5433	62	5	bu(t	bu(t	NUM
ejpam-5433	62	6	)	)	PUNCT
ejpam-5433	62	7	=	=	SYM
ejpam-5433	62	8	f(t	f(t	NOUN
ejpam-5433	62	9	)	)	PUNCT
ejpam-5433	62	10	(	(	PUNCT
ejpam-5433	62	11	2	2	X
ejpam-5433	62	12	)	)	PUNCT
ejpam-5433	62	13	is	be	AUX
ejpam-5433	62	14	called	call	VERB
ejpam-5433	62	15	the	the	DET
ejpam-5433	62	16	fractional	fractional	ADJ
ejpam-5433	62	17	abstract	abstract	ADJ
ejpam-5433	62	18	cauchy	cauchy	ADJ
ejpam-5433	62	19	problem	problem	NOUN
ejpam-5433	62	20	of	of	ADP
ejpam-5433	62	21	order	order	NOUN
ejpam-5433	62	22	two	two	NUM
ejpam-5433	62	23	,	,	PUNCT
ejpam-5433	62	24	where	where	SCONJ
ejpam-5433	62	25	v	v	NOUN
ejpam-5433	62	26	and	and	CCONJ
ejpam-5433	62	27	f	f	PROPN
ejpam-5433	62	28	are	be	AUX
ejpam-5433	62	29	nice	nice	ADJ
ejpam-5433	62	30	functions	function	NOUN
ejpam-5433	62	31	from	from	ADP
ejpam-5433	62	32	(	(	PUNCT
ejpam-5433	62	33	0,∞	0,∞	NOUN
ejpam-5433	62	34	)	)	PUNCT
ejpam-5433	62	35	to	to	ADP
ejpam-5433	62	36	the	the	DET
ejpam-5433	62	37	banach	banach	NOUN
ejpam-5433	62	38	space	space	NOUN
ejpam-5433	62	39	x	x	NOUN
ejpam-5433	62	40	,	,	PUNCT
ejpam-5433	62	41	aand	aand	PROPN
ejpam-5433	62	42	b	b	PROPN
ejpam-5433	62	43	are	be	AUX
ejpam-5433	62	44	closed	close	VERB
ejpam-5433	62	45	linear	linear	ADJ
ejpam-5433	62	46	operator	operator	NOUN
ejpam-5433	62	47	on	on	ADP
ejpam-5433	62	48	x.	x.	NOUN
ejpam-5433	62	49	a	a	DET
ejpam-5433	62	50	solution	solution	NOUN
ejpam-5433	62	51	of	of	ADP
ejpam-5433	62	52	this	this	DET
ejpam-5433	62	53	equation	equation	NOUN
ejpam-5433	62	54	of	of	ADP
ejpam-5433	62	55	the	the	DET
ejpam-5433	62	56	form	form	NOUN
ejpam-5433	62	57	v	v	ADP
ejpam-5433	62	58	=	=	SYM
ejpam-5433	62	59	u	u	NOUN
ejpam-5433	62	60	⊗	⊗	PROPN
ejpam-5433	62	61	x	x	PUNCT
ejpam-5433	62	62	.is	.i	VERB
ejpam-5433	62	63	called	call	VERB
ejpam-5433	62	64	an	an	DET
ejpam-5433	62	65	atomic	atomic	ADJ
ejpam-5433	62	66	solution	solution	NOUN
ejpam-5433	62	67	,	,	PUNCT
ejpam-5433	62	68	where	where	SCONJ
ejpam-5433	62	69	v(t	v(t	VERB
ejpam-5433	62	70	)	)	PUNCT
ejpam-5433	62	71	=	=	SYM
ejpam-5433	63	1	u(t)x.in	u(t)x.in	NOUN
ejpam-5433	63	2	this	this	DET
ejpam-5433	63	3	paper	paper	NOUN
ejpam-5433	63	4	,	,	PUNCT
ejpam-5433	63	5	we	we	PRON
ejpam-5433	63	6	are	be	AUX
ejpam-5433	63	7	interested	interested	ADJ
ejpam-5433	63	8	in	in	ADP
ejpam-5433	63	9	finding	find	VERB
ejpam-5433	63	10	an	an	DET
ejpam-5433	63	11	atomic	atomic	ADJ
ejpam-5433	63	12	solution	solution	NOUN
ejpam-5433	63	13	of	of	ADP
ejpam-5433	63	14	the	the	DET
ejpam-5433	63	15	third	third	ADJ
ejpam-5433	63	16	order	order	NOUN
ejpam-5433	63	17	vector	vector	NOUN
ejpam-5433	63	18	valued	value	VERB
ejpam-5433	63	19	fractional	fractional	ADJ
ejpam-5433	63	20	differential	differential	NOUN
ejpam-5433	63	21	equations	equation	NOUN
ejpam-5433	63	22	.	.	PUNCT
ejpam-5433	64	1	3	3	X
ejpam-5433	64	2	.	.	X
ejpam-5433	64	3	main	main	ADJ
ejpam-5433	64	4	results	result	NOUN
ejpam-5433	64	5	in	in	ADP
ejpam-5433	64	6	this	this	DET
ejpam-5433	64	7	section	section	NOUN
ejpam-5433	64	8	,	,	PUNCT
ejpam-5433	64	9	we	we	PRON
ejpam-5433	64	10	prove	prove	VERB
ejpam-5433	64	11	some	some	DET
ejpam-5433	64	12	nice	nice	ADJ
ejpam-5433	64	13	result	result	NOUN
ejpam-5433	64	14	containing	contain	VERB
ejpam-5433	64	15	certain	certain	ADJ
ejpam-5433	64	16	solution	solution	NOUN
ejpam-5433	64	17	of	of	ADP
ejpam-5433	64	18	atomic	atomic	ADJ
ejpam-5433	64	19	problem	problem	NOUN
ejpam-5433	64	20	.	.	PUNCT
ejpam-5433	65	1	consider	consider	VERB
ejpam-5433	65	2	the	the	DET
ejpam-5433	65	3	equation	equation	NOUN
ejpam-5433	65	4	v3α	v3α	PROPN
ejpam-5433	65	5	(	(	PUNCT
ejpam-5433	65	6	t	t	PROPN
ejpam-5433	65	7	)	)	PUNCT
ejpam-5433	65	8	+	+	NOUN
ejpam-5433	65	9	av2α	av2α	NOUN
ejpam-5433	65	10	(	(	PUNCT
ejpam-5433	65	11	t	t	NOUN
ejpam-5433	65	12	)	)	PUNCT
ejpam-5433	65	13	+	+	PROPN
ejpam-5433	65	14	bvα	bvα	X
ejpam-5433	65	15	(	(	PUNCT
ejpam-5433	65	16	t	t	NOUN
ejpam-5433	65	17	)	)	PUNCT
ejpam-5433	66	1	=	=	SYM
ejpam-5433	66	2	f	f	PROPN
ejpam-5433	66	3	(	(	PUNCT
ejpam-5433	66	4	t	t	PROPN
ejpam-5433	66	5	)	)	PUNCT
ejpam-5433	66	6	,	,	PUNCT
ejpam-5433	66	7	(	(	PUNCT
ejpam-5433	66	8	3	3	X
ejpam-5433	66	9	)	)	PUNCT
ejpam-5433	66	10	where	where	SCONJ
ejpam-5433	66	11	a	a	PRON
ejpam-5433	66	12	and	and	CCONJ
ejpam-5433	66	13	b	b	NOUN
ejpam-5433	66	14	are	be	AUX
ejpam-5433	66	15	closed	closed	ADJ
ejpam-5433	66	16	operators	operator	NOUN
ejpam-5433	66	17	,	,	PUNCT
ejpam-5433	66	18	f	f	PROPN
ejpam-5433	66	19	(	(	PUNCT
ejpam-5433	66	20	t	t	PROPN
ejpam-5433	66	21	)	)	PUNCT
ejpam-5433	66	22	is	be	AUX
ejpam-5433	66	23	given	give	VERB
ejpam-5433	66	24	and	and	CCONJ
ejpam-5433	66	25	u	u	NOUN
ejpam-5433	66	26	is	be	AUX
ejpam-5433	66	27	the	the	DET
ejpam-5433	66	28	unknown	unknown	ADJ
ejpam-5433	66	29	equation	equation	NOUN
ejpam-5433	66	30	(	(	PUNCT
ejpam-5433	66	31	3	3	X
ejpam-5433	66	32	)	)	PUNCT
ejpam-5433	66	33	was	be	AUX
ejpam-5433	66	34	discussed	discuss	VERB
ejpam-5433	66	35	in	in	ADP
ejpam-5433	66	36	[	[	X
ejpam-5433	66	37	5	5	NUM
ejpam-5433	66	38	]	]	PUNCT
ejpam-5433	66	39	for	for	ADP
ejpam-5433	66	40	the	the	DET
ejpam-5433	66	41	first	first	ADJ
ejpam-5433	66	42	order	order	NOUN
ejpam-5433	66	43	.	.	PUNCT
ejpam-5433	67	1	hence	hence	ADV
ejpam-5433	67	2	,	,	PUNCT
ejpam-5433	67	3	we	we	PRON
ejpam-5433	67	4	discuss	discuss	VERB
ejpam-5433	67	5	third	third	ADJ
ejpam-5433	67	6	order	order	NOUN
ejpam-5433	67	7	.	.	PUNCT
ejpam-5433	68	1	theorem	theorem	NOUN
ejpam-5433	68	2	1	1	NUM
ejpam-5433	68	3	.	.	PUNCT
ejpam-5433	69	1	the	the	DET
ejpam-5433	69	2	equation	equation	NOUN
ejpam-5433	69	3	v3α	v3α	PROPN
ejpam-5433	69	4	(	(	PUNCT
ejpam-5433	69	5	t	t	PROPN
ejpam-5433	69	6	)	)	PUNCT
ejpam-5433	69	7	+	+	NOUN
ejpam-5433	69	8	av2α	av2α	NOUN
ejpam-5433	69	9	(	(	PUNCT
ejpam-5433	69	10	t	t	NOUN
ejpam-5433	69	11	)	)	PUNCT
ejpam-5433	69	12	+	+	PROPN
ejpam-5433	69	13	bvα	bvα	X
ejpam-5433	69	14	(	(	PUNCT
ejpam-5433	69	15	t	t	NOUN
ejpam-5433	69	16	)	)	PUNCT
ejpam-5433	69	17	=	=	SYM
ejpam-5433	69	18	f	f	PROPN
ejpam-5433	69	19	(	(	PUNCT
ejpam-5433	69	20	t	t	PROPN
ejpam-5433	69	21	)	)	PUNCT
ejpam-5433	69	22	with	with	ADP
ejpam-5433	69	23	the	the	DET
ejpam-5433	69	24	initial	initial	ADJ
ejpam-5433	69	25	conditions	condition	NOUN
ejpam-5433	69	26	v(0	v(0	NOUN
ejpam-5433	69	27	)	)	PUNCT
ejpam-5433	69	28	=	=	SYM
ejpam-5433	69	29	2x0	2x0	NUM
ejpam-5433	69	30	,	,	PUNCT
ejpam-5433	69	31	v	v	NOUN
ejpam-5433	69	32	α(0	α(0	NOUN
ejpam-5433	69	33	)	)	PUNCT
ejpam-5433	69	34	=	=	SYM
ejpam-5433	69	35	x0	x0	PROPN
ejpam-5433	69	36	,	,	PUNCT
ejpam-5433	69	37	and	and	CCONJ
ejpam-5433	69	38	v2α(0	v2α(0	NUM
ejpam-5433	69	39	)	)	PUNCT
ejpam-5433	70	1	=	=	SYM
ejpam-5433	70	2	x0	x0	PROPN
ejpam-5433	70	3	has	have	VERB
ejpam-5433	70	4	an	an	DET
ejpam-5433	70	5	atomic	atomic	ADJ
ejpam-5433	70	6	solution	solution	NOUN
ejpam-5433	70	7	.where	.where	ADP
ejpam-5433	70	8	a	a	PROPN
ejpam-5433	70	9	and	and	CCONJ
ejpam-5433	70	10	b	b	NOUN
ejpam-5433	70	11	are	be	AUX
ejpam-5433	70	12	closed	close	VERB
ejpam-5433	70	13	operators	operator	NOUN
ejpam-5433	70	14	on	on	ADP
ejpam-5433	70	15	x	x	NOUN
ejpam-5433	70	16	,	,	PUNCT
ejpam-5433	70	17	and	and	CCONJ
ejpam-5433	70	18	f	f	PROPN
ejpam-5433	70	19	is	be	AUX
ejpam-5433	70	20	a	a	DET
ejpam-5433	70	21	given	give	VERB
ejpam-5433	70	22	atomic	atomic	ADJ
ejpam-5433	70	23	function	function	NOUN
ejpam-5433	70	24	,	,	PUNCT
ejpam-5433	70	25	f	f	X
ejpam-5433	70	26	:	:	PUNCT
ejpam-5433	71	1	[	[	X
ejpam-5433	71	2	0,∞	0,∞	X
ejpam-5433	71	3	]	]	PUNCT
ejpam-5433	71	4	→	→	PUNCT
ejpam-5433	71	5	x.	x.	NOUN
ejpam-5433	71	6	now	now	ADV
ejpam-5433	71	7	,	,	PUNCT
ejpam-5433	71	8	we	we	PRON
ejpam-5433	71	9	are	be	AUX
ejpam-5433	71	10	looking	look	VERB
ejpam-5433	71	11	for	for	ADP
ejpam-5433	71	12	atomic	atomic	ADJ
ejpam-5433	71	13	solution	solution	NOUN
ejpam-5433	71	14	of	of	ADP
ejpam-5433	71	15	(	(	PUNCT
ejpam-5433	71	16	3	3	NUM
ejpam-5433	71	17	)	)	PUNCT
ejpam-5433	71	18	.	.	PUNCT
ejpam-5433	72	1	so	so	ADV
ejpam-5433	72	2	put	put	VERB
ejpam-5433	72	3	v	v	NOUN
ejpam-5433	72	4	(	(	PUNCT
ejpam-5433	72	5	t	t	NOUN
ejpam-5433	72	6	)	)	PUNCT
ejpam-5433	72	7	=	=	SYM
ejpam-5433	72	8	u	u	NOUN
ejpam-5433	72	9	(	(	PUNCT
ejpam-5433	72	10	t)x	t)x	ADJ
ejpam-5433	72	11	,	,	PUNCT
ejpam-5433	72	12	u(t	u(t	NOUN
ejpam-5433	72	13	)	)	PUNCT
ejpam-5433	72	14	:	:	PUNCT
ejpam-5433	73	1	[	[	X
ejpam-5433	73	2	0,∞	0,∞	X
ejpam-5433	73	3	]	]	X
ejpam-5433	73	4	→	→	SYM
ejpam-5433	73	5	r	r	X
ejpam-5433	73	6	,	,	PUNCT
ejpam-5433	73	7	x	x	X
ejpam-5433	73	8	is	be	AUX
ejpam-5433	73	9	an	an	DET
ejpam-5433	73	10	element	element	NOUN
ejpam-5433	73	11	in	in	ADP
ejpam-5433	73	12	the	the	DET
ejpam-5433	73	13	banach	banach	NOUN
ejpam-5433	73	14	space	space	NOUN
ejpam-5433	73	15	x	x	NOUN
ejpam-5433	73	16	,	,	PUNCT
ejpam-5433	73	17	and	and	CCONJ
ejpam-5433	73	18	consider	consider	VERB
ejpam-5433	73	19	the	the	DET
ejpam-5433	73	20	case	case	NOUN
ejpam-5433	73	21	when	when	SCONJ
ejpam-5433	73	22	u(0	u(0	NOUN
ejpam-5433	73	23	)	)	PUNCT
ejpam-5433	73	24	=	=	SYM
ejpam-5433	73	25	1	1	NUM
ejpam-5433	73	26	,	,	PUNCT
ejpam-5433	73	27	then	then	ADV
ejpam-5433	73	28	the	the	DET
ejpam-5433	73	29	initial	initial	ADJ
ejpam-5433	73	30	conditions	condition	NOUN
ejpam-5433	73	31	given	give	VERB
ejpam-5433	73	32	in	in	ADP
ejpam-5433	73	33	theorem	theorem	NOUN
ejpam-5433	73	34	1	1	NUM
ejpam-5433	73	35	will	will	AUX
ejpam-5433	73	36	be	be	AUX
ejpam-5433	73	37	as	as	SCONJ
ejpam-5433	73	38	follows	follow	VERB
ejpam-5433	73	39	:(	:(	PUNCT
ejpam-5433	73	40	v(0	v(0	X
ejpam-5433	73	41	)	)	PUNCT
ejpam-5433	74	1	=	=	PUNCT
ejpam-5433	75	1	u(0)x	u(0)x	X
ejpam-5433	76	1	=	=	SYM
ejpam-5433	76	2	2x0	2x0	NUM
ejpam-5433	76	3	which	which	PRON
ejpam-5433	76	4	implies	imply	VERB
ejpam-5433	76	5	that	that	SCONJ
ejpam-5433	76	6	x	x	X
ejpam-5433	76	7	=	=	SYM
ejpam-5433	76	8	2x0	2x0	NUM
ejpam-5433	76	9	vα(0	vα(0	NOUN
ejpam-5433	76	10	)	)	PUNCT
ejpam-5433	76	11	=	=	SYM
ejpam-5433	76	12	x0	x0	PROPN
ejpam-5433	76	13	,	,	PUNCT
ejpam-5433	76	14	and	and	CCONJ
ejpam-5433	76	15	v2α(0	v2α(0	NUM
ejpam-5433	76	16	)	)	PUNCT
ejpam-5433	77	1	=	=	SYM
ejpam-5433	77	2	x0	x0	PROPN
ejpam-5433	77	3	.	.	PUNCT
ejpam-5433	77	4	)	)	PUNCT
ejpam-5433	78	1	(	(	PUNCT
ejpam-5433	78	2	4	4	X
ejpam-5433	78	3	)	)	PUNCT
ejpam-5433	78	4	further	far	ADV
ejpam-5433	78	5	assume	assume	VERB
ejpam-5433	78	6	f	f	PROPN
ejpam-5433	78	7	to	to	PART
ejpam-5433	78	8	be	be	AUX
ejpam-5433	78	9	an	an	DET
ejpam-5433	78	10	atom	atom	NOUN
ejpam-5433	78	11	:	:	PUNCT
ejpam-5433	78	12	f	f	X
ejpam-5433	79	1	=	=	PUNCT
ejpam-5433	79	2	h	h	PROPN
ejpam-5433	80	1	⊗	⊗	PROPN
ejpam-5433	80	2	z	z	PROPN
ejpam-5433	80	3	where	where	SCONJ
ejpam-5433	80	4	h	h	NOUN
ejpam-5433	81	1	:	:	PUNCT
ejpam-5433	81	2	[	[	X
ejpam-5433	81	3	0,∞	0,∞	X
ejpam-5433	81	4	]	]	X
ejpam-5433	81	5	→	→	SYM
ejpam-5433	81	6	r	r	NOUN
ejpam-5433	81	7	,	,	PUNCT
ejpam-5433	81	8	and	and	CCONJ
ejpam-5433	81	9	z	z	NOUN
ejpam-5433	81	10	∈	∈	PROPN
ejpam-5433	81	11	x.	x.	NOUN
ejpam-5433	82	1	so	so	ADV
ejpam-5433	82	2	,	,	PUNCT
ejpam-5433	82	3	(	(	PUNCT
ejpam-5433	82	4	3	3	X
ejpam-5433	82	5	)	)	PUNCT
ejpam-5433	82	6	becomes	become	VERB
ejpam-5433	82	7	:	:	PUNCT
ejpam-5433	82	8	u3α	u3α	ADJ
ejpam-5433	82	9	⊗	⊗	ADJ
ejpam-5433	82	10	x+	x+	ADJ
ejpam-5433	82	11	u2α	u2α	NOUN
ejpam-5433	82	12	⊗ax+	⊗ax+	ADV
ejpam-5433	82	13	uα	uα	NOUN
ejpam-5433	82	14	⊗bx	⊗bx	NOUN
ejpam-5433	82	15	=	=	SYM
ejpam-5433	82	16	f	f	X
ejpam-5433	82	17	(	(	PUNCT
ejpam-5433	82	18	t	t	PROPN
ejpam-5433	82	19	)	)	PUNCT
ejpam-5433	82	20	.	.	PUNCT
ejpam-5433	83	1	this	this	PRON
ejpam-5433	83	2	can	can	AUX
ejpam-5433	83	3	be	be	AUX
ejpam-5433	83	4	written	write	VERB
ejpam-5433	83	5	as	as	ADP
ejpam-5433	83	6	:	:	PUNCT
ejpam-5433	83	7	u3α	u3α	ADJ
ejpam-5433	83	8	⊗	⊗	ADJ
ejpam-5433	83	9	x+	x+	ADJ
ejpam-5433	83	10	u2α	u2α	NOUN
ejpam-5433	83	11	⊗ax+	⊗ax+	ADV
ejpam-5433	83	12	uα	uα	NOUN
ejpam-5433	83	13	⊗bx	⊗bx	NOUN
ejpam-5433	83	14	=	=	PUNCT
ejpam-5433	83	15	h⊗	h⊗	VERB
ejpam-5433	83	16	z.	z.	PROPN
ejpam-5433	83	17	(	(	PUNCT
ejpam-5433	83	18	5	5	X
ejpam-5433	83	19	)	)	PUNCT
ejpam-5433	83	20	there	there	PRON
ejpam-5433	83	21	are	be	VERB
ejpam-5433	83	22	four	four	NUM
ejpam-5433	83	23	cases	case	NOUN
ejpam-5433	83	24	that	that	PRON
ejpam-5433	83	25	must	must	AUX
ejpam-5433	83	26	be	be	AUX
ejpam-5433	83	27	discussed	discuss	VERB
ejpam-5433	83	28	when	when	SCONJ
ejpam-5433	83	29	solving	solve	VERB
ejpam-5433	83	30	the	the	DET
ejpam-5433	83	31	equation	equation	NOUN
ejpam-5433	83	32	(	(	PUNCT
ejpam-5433	83	33	5	5	NUM
ejpam-5433	83	34	)	)	PUNCT
ejpam-5433	83	35	as	as	SCONJ
ejpam-5433	83	36	follows	follow	VERB
ejpam-5433	83	37	:	:	PUNCT
ejpam-5433	83	38	case	case	NOUN
ejpam-5433	83	39	one	one	NUM
ejpam-5433	83	40	:	:	PUNCT
ejpam-5433	83	41	u3α	u3α	PROPN
ejpam-5433	84	1	⊗	⊗	ADJ
ejpam-5433	84	2	x+	x+	ADJ
ejpam-5433	84	3	u2α	u2α	NOUN
ejpam-5433	84	4	⊗ax	⊗ax	ADJ
ejpam-5433	84	5	is	be	AUX
ejpam-5433	84	6	an	an	DET
ejpam-5433	84	7	atom	atom	NOUN
ejpam-5433	84	8	.	.	PUNCT
ejpam-5433	85	1	in	in	ADP
ejpam-5433	85	2	this	this	DET
ejpam-5433	85	3	case	case	NOUN
ejpam-5433	85	4	we	we	PRON
ejpam-5433	85	5	have	have	VERB
ejpam-5433	85	6	two	two	NUM
ejpam-5433	85	7	situations	situation	NOUN
ejpam-5433	85	8	:	:	PUNCT
ejpam-5433	85	9	(	(	PUNCT
ejpam-5433	85	10	i	i	NOUN
ejpam-5433	85	11	)	)	PUNCT
ejpam-5433	85	12	u3α	u3α	PROPN
ejpam-5433	86	1	=	=	PUNCT
ejpam-5433	86	2	u2α	u2α	NOUN
ejpam-5433	86	3	.	.	PUNCT
ejpam-5433	87	1	(	(	PUNCT
ejpam-5433	87	2	ii	ii	NOUN
ejpam-5433	87	3	)	)	PUNCT
ejpam-5433	87	4	x	x	X
ejpam-5433	88	1	=	=	PUNCT
ejpam-5433	88	2	ax	ax	NOUN
ejpam-5433	88	3	.	.	PUNCT
ejpam-5433	88	4	r.	r.	PROPN
ejpam-5433	88	5	alkhateeb	alkhateeb	PROPN
ejpam-5433	88	6	,	,	PUNCT
ejpam-5433	88	7	g.	g.	PROPN
ejpam-5433	88	8	awwad	awwad	PROPN
ejpam-5433	88	9	/	/	PUNCT
ejpam-5433	88	10	eur	eur	PROPN
ejpam-5433	88	11	.	.	PUNCT
ejpam-5433	89	1	j.	j.	PROPN
ejpam-5433	89	2	pure	pure	PROPN
ejpam-5433	89	3	appl	appl	PROPN
ejpam-5433	89	4	.	.	PROPN
ejpam-5433	89	5	math	math	PROPN
ejpam-5433	89	6	,	,	PUNCT
ejpam-5433	89	7	17	17	NUM
ejpam-5433	89	8	(	(	PUNCT
ejpam-5433	89	9	4	4	NUM
ejpam-5433	89	10	)	)	PUNCT
ejpam-5433	89	11	(	(	PUNCT
ejpam-5433	89	12	2024	2024	NUM
ejpam-5433	89	13	)	)	PUNCT
ejpam-5433	89	14	,	,	PUNCT
ejpam-5433	89	15	3061	3061	NUM
ejpam-5433	89	16	-	-	SYM
ejpam-5433	89	17	3078	3078	NUM
ejpam-5433	89	18	3064	3064	NUM
ejpam-5433	89	19	let	let	VERB
ejpam-5433	89	20	us	we	PRON
ejpam-5433	89	21	take	take	VERB
ejpam-5433	89	22	situation	situation	NOUN
ejpam-5433	89	23	(	(	PUNCT
ejpam-5433	89	24	1).so	1).so	NUM
ejpam-5433	89	25	equation	equation	NOUN
ejpam-5433	89	26	(	(	PUNCT
ejpam-5433	89	27	5	5	X
ejpam-5433	89	28	)	)	PUNCT
ejpam-5433	89	29	becomes	become	VERB
ejpam-5433	89	30	:	:	PUNCT
ejpam-5433	89	31	u3α	u3α	PROPN
ejpam-5433	89	32	⊗	⊗	PROPN
ejpam-5433	89	33	(	(	PUNCT
ejpam-5433	89	34	x+ax	x+ax	PROPN
ejpam-5433	89	35	)	)	PUNCT
ejpam-5433	90	1	+	+	CCONJ
ejpam-5433	90	2	uα	uα	PROPN
ejpam-5433	90	3	⊗bx	⊗bx	NOUN
ejpam-5433	90	4	=	=	PUNCT
ejpam-5433	90	5	h⊗	h⊗	VERB
ejpam-5433	90	6	z	z	NOUN
ejpam-5433	90	7	,	,	PUNCT
ejpam-5433	90	8	(	(	PUNCT
ejpam-5433	90	9	6	6	NUM
ejpam-5433	90	10	)	)	PUNCT
ejpam-5433	90	11	where	where	SCONJ
ejpam-5433	90	12	h	h	NOUN
ejpam-5433	90	13	and	and	CCONJ
ejpam-5433	90	14	z	z	NOUN
ejpam-5433	90	15	are	be	AUX
ejpam-5433	90	16	given	give	VERB
ejpam-5433	90	17	.	.	PUNCT
ejpam-5433	91	1	so	so	ADV
ejpam-5433	91	2	we	we	PRON
ejpam-5433	91	3	have	have	VERB
ejpam-5433	91	4	two	two	NUM
ejpam-5433	91	5	cases	case	NOUN
ejpam-5433	91	6	:	:	PUNCT
ejpam-5433	91	7	(	(	PUNCT
ejpam-5433	91	8	a	a	X
ejpam-5433	91	9	)	)	PUNCT
ejpam-5433	91	10	u3α	u3α	PROPN
ejpam-5433	91	11	=	=	PUNCT
ejpam-5433	91	12	uα	uα	NOUN
ejpam-5433	91	13	=	=	PUNCT
ejpam-5433	91	14	h	h	NOUN
ejpam-5433	91	15	=	=	PUNCT
ejpam-5433	91	16	u2α	u2α	ADJ
ejpam-5433	91	17	.	.	PUNCT
ejpam-5433	92	1	(	(	PUNCT
ejpam-5433	92	2	b	b	X
ejpam-5433	92	3	)	)	PUNCT
ejpam-5433	92	4	x+ax	x+ax	PUNCT
ejpam-5433	93	1	=	=	SYM
ejpam-5433	93	2	bx	bx	PROPN
ejpam-5433	93	3	=	=	PUNCT
ejpam-5433	93	4	z.	z.	PROPN
ejpam-5433	94	1	in	in	ADP
ejpam-5433	94	2	case	case	NOUN
ejpam-5433	94	3	(	(	PUNCT
ejpam-5433	94	4	a	a	X
ejpam-5433	94	5	)	)	PUNCT
ejpam-5433	94	6	,	,	PUNCT
ejpam-5433	94	7	we	we	PRON
ejpam-5433	94	8	have	have	VERB
ejpam-5433	94	9	three	three	NUM
ejpam-5433	94	10	cases	case	NOUN
ejpam-5433	94	11	:	:	PUNCT
ejpam-5433	94	12	(	(	PUNCT
ejpam-5433	94	13	i	i	NOUN
ejpam-5433	94	14	)	)	PUNCT
ejpam-5433	94	15	u3α	u3α	ADV
ejpam-5433	94	16	−	−	NOUN
ejpam-5433	95	1	uα	uα	NOUN
ejpam-5433	95	2	=	=	NOUN
ejpam-5433	95	3	0	0	PROPN
ejpam-5433	95	4	.	.	PUNCT
ejpam-5433	96	1	this	this	DET
ejpam-5433	96	2	case	case	NOUN
ejpam-5433	96	3	can	can	AUX
ejpam-5433	96	4	be	be	AUX
ejpam-5433	96	5	solved	solve	VERB
ejpam-5433	96	6	as	as	ADP
ejpam-5433	96	7	in	in	ADP
ejpam-5433	96	8	[	[	X
ejpam-5433	96	9	3	3	NUM
ejpam-5433	96	10	]	]	X
ejpam-5433	96	11	:	:	PUNCT
ejpam-5433	96	12	r3	r3	PROPN
ejpam-5433	97	1	−	−	NOUN
ejpam-5433	98	1	r	r	NOUN
ejpam-5433	98	2	=	=	SYM
ejpam-5433	98	3	r(r	r(r	NOUN
ejpam-5433	98	4	−	−	PROPN
ejpam-5433	99	1	1)(r	1)(r	NUM
ejpam-5433	99	2	+	+	CCONJ
ejpam-5433	99	3	1	1	X
ejpam-5433	99	4	)	)	PUNCT
ejpam-5433	99	5	=	=	SYM
ejpam-5433	99	6	0	0	NUM
ejpam-5433	99	7	,	,	PUNCT
ejpam-5433	99	8	which	which	PRON
ejpam-5433	99	9	gives	give	VERB
ejpam-5433	99	10	r1	r1	PROPN
ejpam-5433	99	11	=	=	SYM
ejpam-5433	99	12	0	0	NUM
ejpam-5433	99	13	,	,	PUNCT
ejpam-5433	99	14	r2	r2	PROPN
ejpam-5433	99	15	=	=	SYM
ejpam-5433	99	16	1	1	NUM
ejpam-5433	99	17	,	,	PUNCT
ejpam-5433	99	18	and	and	CCONJ
ejpam-5433	99	19	r3	r3	PROPN
ejpam-5433	99	20	=	=	SYM
ejpam-5433	99	21	−1	−1	NOUN
ejpam-5433	99	22	.	.	PUNCT
ejpam-5433	100	1	consequently	consequently	ADV
ejpam-5433	100	2	,	,	PUNCT
ejpam-5433	100	3	u(t	u(t	NOUN
ejpam-5433	100	4	)	)	PUNCT
ejpam-5433	100	5	=	=	SYM
ejpam-5433	100	6	c1	c1	NOUN
ejpam-5433	100	7	+	+	CCONJ
ejpam-5433	100	8	c2e	c2e	PROPN
ejpam-5433	100	9	tα	tα	PROPN
ejpam-5433	100	10	α	α	NOUN
ejpam-5433	100	11	+	+	CCONJ
ejpam-5433	100	12	c3e	c3e	PROPN
ejpam-5433	100	13	−	−	PROPN
ejpam-5433	100	14	tα	tα	PROPN
ejpam-5433	100	15	α	α	PROPN
ejpam-5433	100	16	.	.	PUNCT
ejpam-5433	101	1	so	so	ADV
ejpam-5433	101	2	by	by	ADP
ejpam-5433	101	3	(	(	PUNCT
ejpam-5433	101	4	4	4	NUM
ejpam-5433	101	5	)	)	PUNCT
ejpam-5433	101	6	,	,	PUNCT
ejpam-5433	101	7	we	we	PRON
ejpam-5433	101	8	have	have	VERB
ejpam-5433	101	9	c1	c1	PROPN
ejpam-5433	101	10	+	+	CCONJ
ejpam-5433	101	11	c2	c2	PROPN
ejpam-5433	101	12	+	+	CCONJ
ejpam-5433	101	13	c3	c3	PROPN
ejpam-5433	101	14	=	=	SYM
ejpam-5433	101	15	2x0	2x0	PROPN
ejpam-5433	101	16	,	,	PUNCT
ejpam-5433	101	17	c2	c2	PROPN
ejpam-5433	101	18	−	−	PROPN
ejpam-5433	101	19	c3	c3	PROPN
ejpam-5433	101	20	=	=	PUNCT
ejpam-5433	101	21	x0	x0	PROPN
ejpam-5433	101	22	,	,	PUNCT
ejpam-5433	101	23	and	and	CCONJ
ejpam-5433	101	24	c2	c2	PROPN
ejpam-5433	101	25	+	+	CCONJ
ejpam-5433	101	26	c3	c3	PROPN
ejpam-5433	101	27	=	=	PUNCT
ejpam-5433	101	28	x0	x0	PROPN
ejpam-5433	101	29	,	,	PUNCT
ejpam-5433	101	30	which	which	PRON
ejpam-5433	101	31	implies	imply	VERB
ejpam-5433	101	32	that	that	DET
ejpam-5433	101	33	c1	c1	PROPN
ejpam-5433	101	34	=	=	PUNCT
ejpam-5433	101	35	x0	x0	PROPN
ejpam-5433	101	36	,	,	PUNCT
ejpam-5433	101	37	c2	c2	PROPN
ejpam-5433	101	38	=	=	PUNCT
ejpam-5433	101	39	x0	x0	PROPN
ejpam-5433	101	40	,	,	PUNCT
ejpam-5433	101	41	and	and	CCONJ
ejpam-5433	101	42	c3	c3	X
ejpam-5433	101	43	=	=	PROPN
ejpam-5433	101	44	0	0	X
ejpam-5433	101	45	.	.	PUNCT
ejpam-5433	102	1	hence	hence	ADV
ejpam-5433	102	2	,	,	PUNCT
ejpam-5433	102	3	we	we	PRON
ejpam-5433	102	4	have	have	VERB
ejpam-5433	102	5	u(t	u(t	NOUN
ejpam-5433	102	6	)	)	PUNCT
ejpam-5433	102	7	=	=	PUNCT
ejpam-5433	103	1	x0	x0	PROPN
ejpam-5433	104	1	+	+	CCONJ
ejpam-5433	104	2	x0e	x0e	PUNCT
ejpam-5433	104	3	tα	tα	PROPN
ejpam-5433	104	4	α	α	PROPN
ejpam-5433	104	5	.	.	PUNCT
ejpam-5433	105	1	(	(	PUNCT
ejpam-5433	105	2	7	7	NUM
ejpam-5433	105	3	)	)	PUNCT
ejpam-5433	105	4	(	(	PUNCT
ejpam-5433	105	5	ii	ii	NOUN
ejpam-5433	105	6	)	)	PUNCT
ejpam-5433	105	7	uα	uα	NOUN
ejpam-5433	105	8	=	=	PUNCT
ejpam-5433	105	9	h.	h.	PROPN
ejpam-5433	105	10	using	use	VERB
ejpam-5433	105	11	(	(	PUNCT
ejpam-5433	105	12	7	7	NUM
ejpam-5433	105	13	)	)	PUNCT
ejpam-5433	105	14	,	,	PUNCT
ejpam-5433	105	15	we	we	PRON
ejpam-5433	105	16	have	have	VERB
ejpam-5433	105	17	h	h	NOUN
ejpam-5433	105	18	=	=	PUNCT
ejpam-5433	105	19	x0e	x0e	PROPN
ejpam-5433	106	1	tα	tα	PROPN
ejpam-5433	106	2	α	α	PROPN
ejpam-5433	106	3	.	.	PUNCT
ejpam-5433	107	1	hence	hence	ADV
ejpam-5433	107	2	for	for	ADP
ejpam-5433	107	3	an	an	DET
ejpam-5433	107	4	atomic	atomic	ADJ
ejpam-5433	107	5	solution	solution	NOUN
ejpam-5433	107	6	to	to	PART
ejpam-5433	107	7	exist	exist	VERB
ejpam-5433	107	8	,	,	PUNCT
ejpam-5433	107	9	h	h	NOUN
ejpam-5433	107	10	must	must	AUX
ejpam-5433	107	11	=	=	VERB
ejpam-5433	107	12	x0e	x0e	PROPN
ejpam-5433	107	13	tα	tα	PROPN
ejpam-5433	107	14	α	α	INTJ
ejpam-5433	107	15	.	.	PUNCT
ejpam-5433	108	1	(	(	PUNCT
ejpam-5433	108	2	iii	iii	X
ejpam-5433	108	3	)	)	PUNCT
ejpam-5433	108	4	u3α	u3α	PROPN
ejpam-5433	108	5	=	=	PUNCT
ejpam-5433	108	6	h.	h.	NOUN
ejpam-5433	108	7	by	by	ADP
ejpam-5433	108	8	using	use	VERB
ejpam-5433	108	9	(	(	PUNCT
ejpam-5433	108	10	7	7	NUM
ejpam-5433	108	11	)	)	PUNCT
ejpam-5433	108	12	,	,	PUNCT
ejpam-5433	108	13	we	we	PRON
ejpam-5433	108	14	have	have	VERB
ejpam-5433	108	15	h	h	NOUN
ejpam-5433	108	16	=	=	PUNCT
ejpam-5433	108	17	x0e	x0e	PROPN
ejpam-5433	108	18	tα	tα	PROPN
ejpam-5433	108	19	α	α	PROPN
ejpam-5433	108	20	.	.	PUNCT
ejpam-5433	109	1	since	since	SCONJ
ejpam-5433	109	2	u3α	u3α	PROPN
ejpam-5433	109	3	=	=	SYM
ejpam-5433	109	4	uα	uα	NOUN
ejpam-5433	109	5	=	=	PUNCT
ejpam-5433	109	6	h	h	NOUN
ejpam-5433	109	7	=	=	PUNCT
ejpam-5433	109	8	u2α	u2α	PUNCT
ejpam-5433	109	9	=	=	PUNCT
ejpam-5433	109	10	x0e	x0e	PROPN
ejpam-5433	109	11	tα	tα	PROPN
ejpam-5433	109	12	α	α	PROPN
ejpam-5433	109	13	,	,	PUNCT
ejpam-5433	109	14	then	then	ADV
ejpam-5433	109	15	(	(	PUNCT
ejpam-5433	109	16	6	6	NUM
ejpam-5433	109	17	)	)	PUNCT
ejpam-5433	109	18	becomes	become	VERB
ejpam-5433	109	19	x+ax+bx	x+ax+bx	NOUN
ejpam-5433	109	20	=	=	SYM
ejpam-5433	109	21	z.	z.	PROPN
ejpam-5433	109	22	r.	r.	PROPN
ejpam-5433	109	23	alkhateeb	alkhateeb	PROPN
ejpam-5433	109	24	,	,	PUNCT
ejpam-5433	109	25	g.	g.	PROPN
ejpam-5433	109	26	awwad	awwad	PROPN
ejpam-5433	109	27	/	/	PUNCT
ejpam-5433	109	28	eur	eur	PROPN
ejpam-5433	109	29	.	.	PUNCT
ejpam-5433	110	1	j.	j.	PROPN
ejpam-5433	110	2	pure	pure	PROPN
ejpam-5433	110	3	appl	appl	PROPN
ejpam-5433	110	4	.	.	PROPN
ejpam-5433	110	5	math	math	PROPN
ejpam-5433	110	6	,	,	PUNCT
ejpam-5433	110	7	17	17	NUM
ejpam-5433	110	8	(	(	PUNCT
ejpam-5433	110	9	4	4	NUM
ejpam-5433	110	10	)	)	PUNCT
ejpam-5433	110	11	(	(	PUNCT
ejpam-5433	110	12	2024	2024	NUM
ejpam-5433	110	13	)	)	PUNCT
ejpam-5433	110	14	,	,	PUNCT
ejpam-5433	110	15	3061	3061	NUM
ejpam-5433	110	16	-	-	SYM
ejpam-5433	110	17	3078	3078	NUM
ejpam-5433	110	18	3065	3065	NUM
ejpam-5433	111	1	so	so	CCONJ
ejpam-5433	111	2	(	(	PUNCT
ejpam-5433	111	3	i	i	PRON
ejpam-5433	111	4	+	+	ADJ
ejpam-5433	111	5	a+	a+	X
ejpam-5433	111	6	b)x	b)x	X
ejpam-5433	112	1	=	=	SYM
ejpam-5433	112	2	z	z	X
ejpam-5433	112	3	,	,	PUNCT
ejpam-5433	112	4	this	this	PRON
ejpam-5433	112	5	means	mean	VERB
ejpam-5433	112	6	z	z	NOUN
ejpam-5433	112	7	will	will	AUX
ejpam-5433	112	8	be	be	AUX
ejpam-5433	112	9	in	in	ADP
ejpam-5433	112	10	the	the	DET
ejpam-5433	112	11	intersection	intersection	NOUN
ejpam-5433	112	12	of	of	ADP
ejpam-5433	112	13	the	the	DET
ejpam-5433	112	14	ranges	range	NOUN
ejpam-5433	112	15	(	(	PUNCT
ejpam-5433	112	16	i	i	PRON
ejpam-5433	112	17	+	+	NOUN
ejpam-5433	112	18	a+b	a+b	NUM
ejpam-5433	112	19	)	)	PUNCT
ejpam-5433	112	20	.	.	PUNCT
ejpam-5433	113	1	consequently	consequently	ADV
ejpam-5433	113	2	,	,	PUNCT
ejpam-5433	113	3	there	there	PRON
ejpam-5433	113	4	is	be	VERB
ejpam-5433	113	5	an	an	DET
ejpam-5433	113	6	atomic	atomic	ADJ
ejpam-5433	113	7	solution	solution	NOUN
ejpam-5433	113	8	in	in	ADP
ejpam-5433	113	9	this	this	DET
ejpam-5433	113	10	situation	situation	NOUN
ejpam-5433	113	11	.	.	PUNCT
ejpam-5433	114	1	in	in	ADP
ejpam-5433	114	2	case	case	NOUN
ejpam-5433	114	3	(	(	PUNCT
ejpam-5433	114	4	b	b	NOUN
ejpam-5433	114	5	)	)	PUNCT
ejpam-5433	114	6	,	,	PUNCT
ejpam-5433	114	7	equation	equation	NOUN
ejpam-5433	114	8	(	(	PUNCT
ejpam-5433	114	9	6	6	NUM
ejpam-5433	114	10	)	)	PUNCT
ejpam-5433	114	11	becomes	become	VERB
ejpam-5433	114	12	u3α	u3α	PROPN
ejpam-5433	114	13	⊗	⊗	PROPN
ejpam-5433	114	14	(	(	PUNCT
ejpam-5433	114	15	x+ax	x+ax	PROPN
ejpam-5433	114	16	)	)	PUNCT
ejpam-5433	115	1	+	+	CCONJ
ejpam-5433	115	2	uα	uα	PROPN
ejpam-5433	115	3	⊗bx	⊗bx	NOUN
ejpam-5433	115	4	=	=	PUNCT
ejpam-5433	115	5	h⊗	h⊗	VERB
ejpam-5433	115	6	z.	z.	PROPN
ejpam-5433	116	1	so	so	ADV
ejpam-5433	116	2	,	,	PUNCT
ejpam-5433	116	3	u3α	u3α	PROPN
ejpam-5433	116	4	+	+	CCONJ
ejpam-5433	116	5	uα	uα	X
ejpam-5433	116	6	=	=	SYM
ejpam-5433	116	7	h.	h.	PROPN
ejpam-5433	116	8	this	this	PRON
ejpam-5433	116	9	is	be	AUX
ejpam-5433	116	10	third	third	ADJ
ejpam-5433	116	11	order	order	NOUN
ejpam-5433	116	12	homogenous	homogenous	ADJ
ejpam-5433	116	13	linear	linear	ADJ
ejpam-5433	116	14	fractional	fractional	ADJ
ejpam-5433	116	15	differential	differential	NOUN
ejpam-5433	116	16	equation	equation	NOUN
ejpam-5433	116	17	.	.	PUNCT
ejpam-5433	117	1	to	to	PART
ejpam-5433	117	2	solve	solve	VERB
ejpam-5433	117	3	it	it	PRON
ejpam-5433	117	4	,	,	PUNCT
ejpam-5433	117	5	we	we	PRON
ejpam-5433	117	6	follow	follow	VERB
ejpam-5433	117	7	the	the	DET
ejpam-5433	117	8	variation	variation	NOUN
ejpam-5433	117	9	of	of	ADP
ejpam-5433	117	10	parameters	parameter	NOUN
ejpam-5433	117	11	method	method	VERB
ejpam-5433	117	12	.	.	PUNCT
ejpam-5433	118	1	the	the	DET
ejpam-5433	118	2	homogenous	homogenous	ADJ
ejpam-5433	118	3	part	part	NOUN
ejpam-5433	118	4	can	can	AUX
ejpam-5433	118	5	solved	solve	VERB
ejpam-5433	118	6	as	as	ADP
ejpam-5433	118	7	in	in	ADV
ejpam-5433	118	8	,	,	PUNCT
ejpam-5433	118	9	[	[	X
ejpam-5433	118	10	3	3	NUM
ejpam-5433	118	11	]	]	PUNCT
ejpam-5433	118	12	.	.	PUNCT
ejpam-5433	119	1	r3	r3	PROPN
ejpam-5433	119	2	+	+	CCONJ
ejpam-5433	119	3	r	r	NOUN
ejpam-5433	119	4	=	=	PUNCT
ejpam-5433	119	5	r(r2	r(r2	NOUN
ejpam-5433	119	6	+	+	NOUN
ejpam-5433	119	7	1	1	X
ejpam-5433	119	8	)	)	PUNCT
ejpam-5433	119	9	=	=	SYM
ejpam-5433	119	10	0	0	NUM
ejpam-5433	119	11	,	,	PUNCT
ejpam-5433	119	12	which	which	PRON
ejpam-5433	119	13	implies	imply	VERB
ejpam-5433	119	14	that	that	SCONJ
ejpam-5433	119	15	r1	r1	NOUN
ejpam-5433	119	16	=	=	SYM
ejpam-5433	119	17	0	0	NUM
ejpam-5433	119	18	,	,	PUNCT
ejpam-5433	119	19	r2	r2	PROPN
ejpam-5433	119	20	=	=	PUNCT
ejpam-5433	119	21	i	i	PROPN
ejpam-5433	119	22	,	,	PUNCT
ejpam-5433	119	23	and	and	CCONJ
ejpam-5433	119	24	r3	r3	PROPN
ejpam-5433	120	1	=	=	SYM
ejpam-5433	120	2	−i	−i	PROPN
ejpam-5433	120	3	.	.	PUNCT
ejpam-5433	121	1	hence	hence	ADV
ejpam-5433	121	2	uh(t	uh(t	X
ejpam-5433	121	3	)	)	PUNCT
ejpam-5433	122	1	=	=	SYM
ejpam-5433	122	2	c1	c1	PROPN
ejpam-5433	122	3	+	+	CCONJ
ejpam-5433	122	4	c2	c2	PROPN
ejpam-5433	122	5	cos	cos	PROPN
ejpam-5433	122	6	(	(	PUNCT
ejpam-5433	122	7	tα	tα	PROPN
ejpam-5433	122	8	α	α	PROPN
ejpam-5433	122	9	)	)	PUNCT
ejpam-5433	123	1	+	+	CCONJ
ejpam-5433	123	2	c3	c3	PROPN
ejpam-5433	123	3	sin	sin	NOUN
ejpam-5433	123	4	(	(	PUNCT
ejpam-5433	123	5	tα	tα	PROPN
ejpam-5433	123	6	α	α	PROPN
ejpam-5433	123	7	)	)	PUNCT
ejpam-5433	123	8	.	.	PUNCT
ejpam-5433	124	1	by	by	ADP
ejpam-5433	124	2	the	the	DET
ejpam-5433	124	3	assumption	assumption	NOUN
ejpam-5433	124	4	(	(	PUNCT
ejpam-5433	124	5	4	4	NUM
ejpam-5433	124	6	)	)	PUNCT
ejpam-5433	124	7	,	,	PUNCT
ejpam-5433	124	8	we	we	PRON
ejpam-5433	124	9	get	get	VERB
ejpam-5433	124	10	c1	c1	PROPN
ejpam-5433	124	11	=	=	PUNCT
ejpam-5433	124	12	3x0	3x0	NUM
ejpam-5433	124	13	,	,	PUNCT
ejpam-5433	124	14	c2	c2	PROPN
ejpam-5433	124	15	=	=	PUNCT
ejpam-5433	124	16	−x0	−x0	PROPN
ejpam-5433	124	17	,	,	PUNCT
ejpam-5433	124	18	and	and	CCONJ
ejpam-5433	124	19	c3	c3	PROPN
ejpam-5433	124	20	=	=	PUNCT
ejpam-5433	124	21	x0	x0	PROPN
ejpam-5433	124	22	.	.	PUNCT
ejpam-5433	125	1	hence	hence	ADV
ejpam-5433	125	2	uh(t	uh(t	X
ejpam-5433	125	3	)	)	PUNCT
ejpam-5433	125	4	=	=	PUNCT
ejpam-5433	126	1	3x0	3x0	NUM
ejpam-5433	126	2	−	−	NUM
ejpam-5433	126	3	x0	x0	PROPN
ejpam-5433	126	4	cos	cos	PROPN
ejpam-5433	126	5	(	(	PUNCT
ejpam-5433	126	6	tα	tα	PROPN
ejpam-5433	126	7	α	α	PROPN
ejpam-5433	126	8	)	)	PUNCT
ejpam-5433	127	1	+	+	CCONJ
ejpam-5433	127	2	x0	x0	PROPN
ejpam-5433	127	3	sin	sin	NOUN
ejpam-5433	127	4	(	(	PUNCT
ejpam-5433	127	5	tα	tα	PROPN
ejpam-5433	127	6	α	α	PROPN
ejpam-5433	127	7	)	)	PUNCT
ejpam-5433	127	8	.	.	PUNCT
ejpam-5433	128	1	for	for	ADP
ejpam-5433	128	2	the	the	DET
ejpam-5433	128	3	particular	particular	ADJ
ejpam-5433	128	4	part	part	NOUN
ejpam-5433	128	5	,	,	PUNCT
ejpam-5433	128	6	the	the	PRON
ejpam-5433	128	7	,	,	PUNCT
ejpam-5433	128	8	we	we	PRON
ejpam-5433	128	9	use	use	VERB
ejpam-5433	128	10	variation	variation	NOUN
ejpam-5433	128	11	of	of	ADP
ejpam-5433	128	12	parameters	parameter	NOUN
ejpam-5433	128	13	introduced	introduce	VERB
ejpam-5433	128	14	in	in	ADP
ejpam-5433	128	15	[	[	X
ejpam-5433	128	16	2	2	NUM
ejpam-5433	128	17	]	]	PUNCT
ejpam-5433	128	18	.	.	PUNCT
ejpam-5433	129	1	thus	thus	ADV
ejpam-5433	129	2	we	we	PRON
ejpam-5433	129	3	have	have	VERB
ejpam-5433	129	4	up(t	up(t	NOUN
ejpam-5433	129	5	)	)	PUNCT
ejpam-5433	129	6	=	=	SYM
ejpam-5433	130	1	3∑	3∑	NUM
ejpam-5433	130	2	m=1	m=1	PROPN
ejpam-5433	130	3	um	um	INTJ
ejpam-5433	130	4	t∫	t∫	PROPN
ejpam-5433	130	5	b	b	PROPN
ejpam-5433	130	6	hwα	hwα	PROPN
ejpam-5433	130	7	m(τ	m(τ	PROPN
ejpam-5433	130	8	)	)	PUNCT
ejpam-5433	130	9	wα(τ)τ1−α	wα(τ)τ1−α	PROPN
ejpam-5433	130	10	dτ	dτ	PROPN
ejpam-5433	130	11	.	.	PROPN
ejpam-5433	130	12	(	(	PUNCT
ejpam-5433	130	13	8)	8)	NUM
ejpam-5433	130	14	where	where	SCONJ
ejpam-5433	130	15	b	b	NOUN
ejpam-5433	130	16	is	be	AUX
ejpam-5433	130	17	an	an	DET
ejpam-5433	130	18	arbitrary	arbitrary	ADJ
ejpam-5433	130	19	positive	positive	ADJ
ejpam-5433	130	20	constant	constant	ADJ
ejpam-5433	130	21	,	,	PUNCT
ejpam-5433	130	22	and	and	CCONJ
ejpam-5433	130	23	wα[u1(t	wα[u1(t	PROPN
ejpam-5433	130	24	)	)	PUNCT
ejpam-5433	130	25	,	,	PUNCT
ejpam-5433	130	26	u2(t	u2(t	PROPN
ejpam-5433	130	27	)	)	PUNCT
ejpam-5433	130	28	,	,	PUNCT
ejpam-5433	130	29	u3(t	u3(t	PROPN
ejpam-5433	130	30	)	)	PUNCT
ejpam-5433	130	31	]	]	PUNCT
ejpam-5433	131	1	=	=	PUNCT
ejpam-5433	131	2	∣∣∣∣∣∣	∣∣∣∣∣∣	PROPN
ejpam-5433	131	3	u1(t	u1(t	PRON
ejpam-5433	131	4	)	)	PUNCT
ejpam-5433	131	5	u2(t	u2(t	NOUN
ejpam-5433	131	6	)	)	PUNCT
ejpam-5433	131	7	u3(t	u3(t	PROPN
ejpam-5433	131	8	)	)	PUNCT
ejpam-5433	131	9	uα1	uα1	PROPN
ejpam-5433	131	10	(	(	PUNCT
ejpam-5433	131	11	t	t	NOUN
ejpam-5433	131	12	)	)	PUNCT
ejpam-5433	131	13	uα2	uα2	NOUN
ejpam-5433	131	14	(	(	PUNCT
ejpam-5433	131	15	t	t	NOUN
ejpam-5433	131	16	)	)	PUNCT
ejpam-5433	131	17	uα3	uα3	X
ejpam-5433	131	18	(	(	PUNCT
ejpam-5433	131	19	t	t	NOUN
ejpam-5433	131	20	)	)	PUNCT
ejpam-5433	131	21	u2α1	u2α1	PROPN
ejpam-5433	131	22	(	(	PUNCT
ejpam-5433	131	23	t	t	NOUN
ejpam-5433	131	24	)	)	PUNCT
ejpam-5433	131	25	u2α2	u2α2	X
ejpam-5433	131	26	(	(	PUNCT
ejpam-5433	131	27	t	t	NOUN
ejpam-5433	131	28	)	)	PUNCT
ejpam-5433	131	29	u2α3	u2α3	PROPN
ejpam-5433	131	30	(	(	PUNCT
ejpam-5433	131	31	t	t	NOUN
ejpam-5433	131	32	)	)	PUNCT
ejpam-5433	131	33	∣∣∣∣∣∣	∣∣∣∣∣∣	NOUN
ejpam-5433	131	34	,	,	PUNCT
ejpam-5433	131	35	wα	wα	NOUN
ejpam-5433	131	36	1	1	NUM
ejpam-5433	131	37	=	=	SYM
ejpam-5433	131	38	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ejpam-5433	131	39	0	0	NUM
ejpam-5433	131	40	u2(t	u2(t	NOUN
ejpam-5433	131	41	)	)	PUNCT
ejpam-5433	131	42	u3(t	u3(t	PRON
ejpam-5433	131	43	)	)	PUNCT
ejpam-5433	131	44	0	0	NUM
ejpam-5433	132	1	uα2	uα2	NOUN
ejpam-5433	132	2	(	(	PUNCT
ejpam-5433	132	3	t	t	NOUN
ejpam-5433	132	4	)	)	PUNCT
ejpam-5433	132	5	uα3	uα3	X
ejpam-5433	132	6	(	(	PUNCT
ejpam-5433	132	7	t	t	PROPN
ejpam-5433	132	8	)	)	PUNCT
ejpam-5433	132	9	1	1	NUM
ejpam-5433	132	10	u2α2	u2α2	X
ejpam-5433	132	11	(	(	PUNCT
ejpam-5433	132	12	t	t	NOUN
ejpam-5433	132	13	)	)	PUNCT
ejpam-5433	132	14	u2α3	u2α3	PROPN
ejpam-5433	132	15	(	(	PUNCT
ejpam-5433	132	16	t	t	NOUN
ejpam-5433	132	17	)	)	PUNCT
ejpam-5433	132	18	∣∣∣∣∣∣	∣∣∣∣∣∣	NOUN
ejpam-5433	132	19	,	,	PUNCT
ejpam-5433	132	20	wα	wα	NOUN
ejpam-5433	132	21	2	2	NUM
ejpam-5433	132	22	=	=	SYM
ejpam-5433	132	23	∣∣∣∣∣∣	∣∣∣∣∣∣	PROPN
ejpam-5433	132	24	u1(t	u1(t	ADP
ejpam-5433	132	25	)	)	PUNCT
ejpam-5433	132	26	0	0	PUNCT
ejpam-5433	133	1	u3(t	u3(t	NUM
ejpam-5433	133	2	)	)	PUNCT
ejpam-5433	133	3	uα1	uα1	PROPN
ejpam-5433	133	4	(	(	PUNCT
ejpam-5433	133	5	t	t	PROPN
ejpam-5433	133	6	)	)	PUNCT
ejpam-5433	133	7	0	0	PUNCT
ejpam-5433	134	1	uα3	uα3	PROPN
ejpam-5433	134	2	(	(	PUNCT
ejpam-5433	134	3	t	t	NOUN
ejpam-5433	134	4	)	)	PUNCT
ejpam-5433	134	5	u2α1	u2α1	PROPN
ejpam-5433	134	6	(	(	PUNCT
ejpam-5433	134	7	t	t	NOUN
ejpam-5433	134	8	)	)	PUNCT
ejpam-5433	134	9	1	1	NUM
ejpam-5433	134	10	u2α3	u2α3	NOUN
ejpam-5433	134	11	(	(	PUNCT
ejpam-5433	134	12	t	t	NOUN
ejpam-5433	134	13	)	)	PUNCT
ejpam-5433	134	14	∣∣∣∣∣∣	∣∣∣∣∣∣	ADV
ejpam-5433	134	15	,	,	PUNCT
ejpam-5433	134	16	and	and	CCONJ
ejpam-5433	134	17	wα	wα	NOUN
ejpam-5433	134	18	3	3	NUM
ejpam-5433	134	19	=	=	SYM
ejpam-5433	134	20	∣∣∣∣∣∣	∣∣∣∣∣∣	PROPN
ejpam-5433	134	21	u1(t	u1(t	PRON
ejpam-5433	134	22	)	)	PUNCT
ejpam-5433	134	23	u2(t	u2(t	NOUN
ejpam-5433	134	24	)	)	PUNCT
ejpam-5433	134	25	0	0	NUM
ejpam-5433	135	1	uα1	uα1	PROPN
ejpam-5433	135	2	(	(	PUNCT
ejpam-5433	135	3	t	t	NOUN
ejpam-5433	135	4	)	)	PUNCT
ejpam-5433	135	5	uα2	uα2	NOUN
ejpam-5433	135	6	(	(	PUNCT
ejpam-5433	135	7	t	t	NOUN
ejpam-5433	135	8	)	)	PUNCT
ejpam-5433	135	9	0	0	PUNCT
ejpam-5433	136	1	u2α1	u2α1	PRON
ejpam-5433	136	2	(	(	PUNCT
ejpam-5433	136	3	t	t	NOUN
ejpam-5433	136	4	)	)	PUNCT
ejpam-5433	136	5	u2α2	u2α2	PROPN
ejpam-5433	136	6	(	(	PUNCT
ejpam-5433	136	7	t	t	NOUN
ejpam-5433	136	8	)	)	PUNCT
ejpam-5433	136	9	h	h	NOUN
ejpam-5433	136	10	∣∣∣∣∣∣	∣∣∣∣∣∣	PROPN
ejpam-5433	136	11	.	.	PUNCT
ejpam-5433	137	1	r.	r.	PROPN
ejpam-5433	137	2	alkhateeb	alkhateeb	PROPN
ejpam-5433	137	3	,	,	PUNCT
ejpam-5433	137	4	g.	g.	PROPN
ejpam-5433	137	5	awwad	awwad	PROPN
ejpam-5433	137	6	/	/	PUNCT
ejpam-5433	137	7	eur	eur	PROPN
ejpam-5433	137	8	.	.	PUNCT
ejpam-5433	138	1	j.	j.	PROPN
ejpam-5433	138	2	pure	pure	PROPN
ejpam-5433	138	3	appl	appl	PROPN
ejpam-5433	138	4	.	.	PROPN
ejpam-5433	138	5	math	math	PROPN
ejpam-5433	138	6	,	,	PUNCT
ejpam-5433	138	7	17	17	NUM
ejpam-5433	138	8	(	(	PUNCT
ejpam-5433	138	9	4	4	NUM
ejpam-5433	138	10	)	)	PUNCT
ejpam-5433	138	11	(	(	PUNCT
ejpam-5433	138	12	2024	2024	NUM
ejpam-5433	138	13	)	)	PUNCT
ejpam-5433	138	14	,	,	PUNCT
ejpam-5433	138	15	3061	3061	NUM
ejpam-5433	138	16	-	-	SYM
ejpam-5433	138	17	3078	3078	NUM
ejpam-5433	138	18	3066	3066	NUM
ejpam-5433	138	19	hence	hence	ADV
ejpam-5433	138	20	,	,	PUNCT
ejpam-5433	138	21	wα	wα	NOUN
ejpam-5433	138	22	=	=	SYM
ejpam-5433	138	23	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ejpam-5433	138	24	3x0	3x0	NUM
ejpam-5433	138	25	−x0	−x0	NOUN
ejpam-5433	138	26	cos	cos	PROPN
ejpam-5433	138	27	(	(	PUNCT
ejpam-5433	138	28	tα	tα	PROPN
ejpam-5433	138	29	α	α	PROPN
ejpam-5433	138	30	)	)	PUNCT
ejpam-5433	138	31	x0	x0	PROPN
ejpam-5433	138	32	sin	sin	NOUN
ejpam-5433	138	33	(	(	PUNCT
ejpam-5433	138	34	tα	tα	PROPN
ejpam-5433	138	35	α	α	PROPN
ejpam-5433	138	36	)	)	PUNCT
ejpam-5433	138	37	0	0	NUM
ejpam-5433	139	1	x0	x0	PROPN
ejpam-5433	139	2	sin	sin	NOUN
ejpam-5433	139	3	(	(	PUNCT
ejpam-5433	139	4	tα	tα	PROPN
ejpam-5433	139	5	α	α	PROPN
ejpam-5433	139	6	)	)	PUNCT
ejpam-5433	140	1	x0	x0	PROPN
ejpam-5433	140	2	cos	cos	PROPN
ejpam-5433	140	3	(	(	PUNCT
ejpam-5433	140	4	tα	tα	PROPN
ejpam-5433	140	5	α	α	PROPN
ejpam-5433	140	6	)	)	PUNCT
ejpam-5433	140	7	0	0	NUM
ejpam-5433	141	1	x0	x0	PROPN
ejpam-5433	141	2	cos	cos	PROPN
ejpam-5433	141	3	(	(	PUNCT
ejpam-5433	141	4	tα	tα	PROPN
ejpam-5433	141	5	α	α	PROPN
ejpam-5433	141	6	)	)	PUNCT
ejpam-5433	141	7	−x0	−x0	NOUN
ejpam-5433	141	8	sin	sin	NOUN
ejpam-5433	141	9	(	(	PUNCT
ejpam-5433	141	10	tα	tα	PROPN
ejpam-5433	141	11	α	α	NOUN
ejpam-5433	141	12	)	)	PUNCT
ejpam-5433	141	13	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ejpam-5433	141	14	=	=	SYM
ejpam-5433	141	15	−3x0	−3x0	PROPN
ejpam-5433	141	16	.	.	PUNCT
ejpam-5433	141	17	which	which	PRON
ejpam-5433	141	18	means	mean	VERB
ejpam-5433	141	19	that	that	SCONJ
ejpam-5433	141	20	:	:	PUNCT
ejpam-5433	141	21	wα	wα	NOUN
ejpam-5433	141	22	1	1	NUM
ejpam-5433	141	23	=	=	SYM
ejpam-5433	141	24	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ejpam-5433	141	25	0	0	NUM
ejpam-5433	141	26	−x0	−x0	NOUN
ejpam-5433	141	27	cos	cos	PROPN
ejpam-5433	141	28	(	(	PUNCT
ejpam-5433	141	29	tα	tα	PROPN
ejpam-5433	141	30	α	α	PROPN
ejpam-5433	141	31	)	)	PUNCT
ejpam-5433	141	32	x0	x0	PROPN
ejpam-5433	141	33	sin	sin	NOUN
ejpam-5433	141	34	(	(	PUNCT
ejpam-5433	141	35	tα	tα	PROPN
ejpam-5433	141	36	α	α	PROPN
ejpam-5433	141	37	)	)	PUNCT
ejpam-5433	141	38	0	0	NUM
ejpam-5433	142	1	x0	x0	PROPN
ejpam-5433	142	2	sin	sin	NOUN
ejpam-5433	142	3	(	(	PUNCT
ejpam-5433	142	4	tα	tα	PROPN
ejpam-5433	142	5	α	α	PROPN
ejpam-5433	142	6	)	)	PUNCT
ejpam-5433	143	1	x0	x0	PROPN
ejpam-5433	143	2	cos	cos	PROPN
ejpam-5433	143	3	(	(	PUNCT
ejpam-5433	143	4	tα	tα	PROPN
ejpam-5433	143	5	α	α	PROPN
ejpam-5433	143	6	)	)	PUNCT
ejpam-5433	143	7	1	1	NUM
ejpam-5433	143	8	x0	x0	PROPN
ejpam-5433	143	9	cos	cos	PROPN
ejpam-5433	143	10	(	(	PUNCT
ejpam-5433	143	11	tα	tα	PROPN
ejpam-5433	143	12	α	α	PROPN
ejpam-5433	143	13	)	)	PUNCT
ejpam-5433	143	14	−x0	−x0	NOUN
ejpam-5433	143	15	sin	sin	NOUN
ejpam-5433	143	16	(	(	PUNCT
ejpam-5433	143	17	tα	tα	PROPN
ejpam-5433	143	18	α	α	NOUN
ejpam-5433	143	19	)	)	PUNCT
ejpam-5433	143	20	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ejpam-5433	143	21	=	=	SYM
ejpam-5433	143	22	−x0	−x0	NOUN
ejpam-5433	143	23	,	,	PUNCT
ejpam-5433	143	24	wα	wα	NOUN
ejpam-5433	143	25	2	2	NUM
ejpam-5433	143	26	=	=	SYM
ejpam-5433	143	27	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ejpam-5433	143	28	3x0	3x0	NUM
ejpam-5433	143	29	0	0	NUM
ejpam-5433	143	30	x0	x0	PROPN
ejpam-5433	143	31	sin	sin	NOUN
ejpam-5433	143	32	(	(	PUNCT
ejpam-5433	143	33	tα	tα	PROPN
ejpam-5433	143	34	α	α	PROPN
ejpam-5433	143	35	)	)	PUNCT
ejpam-5433	143	36	0	0	NUM
ejpam-5433	143	37	0	0	NUM
ejpam-5433	144	1	x0	x0	PROPN
ejpam-5433	144	2	cos	cos	PROPN
ejpam-5433	144	3	(	(	PUNCT
ejpam-5433	144	4	tα	tα	PROPN
ejpam-5433	144	5	α	α	PROPN
ejpam-5433	144	6	)	)	PUNCT
ejpam-5433	144	7	0	0	NUM
ejpam-5433	144	8	1	1	NUM
ejpam-5433	144	9	−x0	−x0	NOUN
ejpam-5433	144	10	sin	sin	NOUN
ejpam-5433	144	11	(	(	PUNCT
ejpam-5433	144	12	tα	tα	PROPN
ejpam-5433	144	13	α	α	NOUN
ejpam-5433	144	14	)	)	PUNCT
ejpam-5433	144	15	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ejpam-5433	144	16	=	=	SYM
ejpam-5433	144	17	−3x0	−3x0	X
ejpam-5433	144	18	cos	cos	PROPN
ejpam-5433	144	19	(	(	PUNCT
ejpam-5433	144	20	tα	tα	PROPN
ejpam-5433	144	21	α	α	PROPN
ejpam-5433	144	22	)	)	PUNCT
ejpam-5433	144	23	,	,	PUNCT
ejpam-5433	144	24	and	and	CCONJ
ejpam-5433	144	25	wα	wα	NOUN
ejpam-5433	144	26	3	3	NUM
ejpam-5433	144	27	=	=	SYM
ejpam-5433	144	28	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ejpam-5433	144	29	3	3	NUM
ejpam-5433	144	30	−x0	−x0	NOUN
ejpam-5433	144	31	cos	cos	PROPN
ejpam-5433	144	32	(	(	PUNCT
ejpam-5433	144	33	tα	tα	PROPN
ejpam-5433	144	34	α	α	PROPN
ejpam-5433	144	35	)	)	PUNCT
ejpam-5433	144	36	0	0	NUM
ejpam-5433	144	37	0	0	NUM
ejpam-5433	144	38	x0	x0	PROPN
ejpam-5433	144	39	sin	sin	NOUN
ejpam-5433	144	40	(	(	PUNCT
ejpam-5433	144	41	tα	tα	PROPN
ejpam-5433	144	42	α	α	PROPN
ejpam-5433	144	43	)	)	PUNCT
ejpam-5433	144	44	0	0	NUM
ejpam-5433	144	45	0	0	NUM
ejpam-5433	145	1	x0	x0	PROPN
ejpam-5433	145	2	cos	cos	PROPN
ejpam-5433	145	3	(	(	PUNCT
ejpam-5433	145	4	tα	tα	PROPN
ejpam-5433	145	5	α	α	PROPN
ejpam-5433	145	6	)	)	PUNCT
ejpam-5433	145	7	1	1	NUM
ejpam-5433	145	8	∣∣∣∣∣∣	∣∣∣∣∣∣	VERB
ejpam-5433	145	9	=	=	SYM
ejpam-5433	145	10	3x0	3x0	NUM
ejpam-5433	145	11	sin	sin	NOUN
ejpam-5433	145	12	(	(	PUNCT
ejpam-5433	145	13	tα	tα	PROPN
ejpam-5433	145	14	α	α	PROPN
ejpam-5433	145	15	)	)	PUNCT
ejpam-5433	145	16	.	.	PUNCT
ejpam-5433	146	1	so	so	ADV
ejpam-5433	146	2	,	,	PUNCT
ejpam-5433	146	3	we	we	PRON
ejpam-5433	146	4	have	have	VERB
ejpam-5433	146	5	uα1	uα1	PROPN
ejpam-5433	146	6	(	(	PUNCT
ejpam-5433	146	7	t	t	NOUN
ejpam-5433	146	8	)	)	PUNCT
ejpam-5433	146	9	=	=	SYM
ejpam-5433	146	10	wα	wα	NOUN
ejpam-5433	146	11	1	1	NUM
ejpam-5433	146	12	wα	wα	NOUN
ejpam-5433	146	13	=	=	SYM
ejpam-5433	146	14	1	1	NUM
ejpam-5433	146	15	3	3	NUM
ejpam-5433	146	16	,	,	PUNCT
ejpam-5433	146	17	uα2	uα2	ADV
ejpam-5433	146	18	(	(	PUNCT
ejpam-5433	146	19	t	t	NOUN
ejpam-5433	146	20	)	)	PUNCT
ejpam-5433	147	1	=	=	SYM
ejpam-5433	147	2	wα	wα	NOUN
ejpam-5433	147	3	2	2	NUM
ejpam-5433	147	4	wα	wα	NOUN
ejpam-5433	147	5	=	=	SYM
ejpam-5433	147	6	−3x0	−3x0	X
ejpam-5433	147	7	cos	cos	PROPN
ejpam-5433	147	8	(	(	PUNCT
ejpam-5433	147	9	tα	tα	PROPN
ejpam-5433	147	10	α	α	PROPN
ejpam-5433	147	11	)	)	PUNCT
ejpam-5433	147	12	−3x0	−3x0	X
ejpam-5433	148	1	=	=	PUNCT
ejpam-5433	148	2	cos	cos	PROPN
ejpam-5433	148	3	(	(	PUNCT
ejpam-5433	148	4	tα	tα	PROPN
ejpam-5433	148	5	α	α	PROPN
ejpam-5433	148	6	)	)	PUNCT
ejpam-5433	148	7	,	,	PUNCT
ejpam-5433	148	8	and	and	CCONJ
ejpam-5433	148	9	uα3	uα3	ADJ
ejpam-5433	148	10	(	(	PUNCT
ejpam-5433	148	11	t	t	NOUN
ejpam-5433	148	12	)	)	PUNCT
ejpam-5433	148	13	=	=	SYM
ejpam-5433	148	14	wα	wα	NOUN
ejpam-5433	148	15	3	3	NUM
ejpam-5433	148	16	wα	wα	NOUN
ejpam-5433	148	17	=	=	SYM
ejpam-5433	148	18	3x0	3x0	NUM
ejpam-5433	148	19	sin	sin	NOUN
ejpam-5433	148	20	(	(	PUNCT
ejpam-5433	148	21	tα	tα	PROPN
ejpam-5433	148	22	α	α	PROPN
ejpam-5433	148	23	)	)	PUNCT
ejpam-5433	148	24	−3x0	−3x0	X
ejpam-5433	149	1	=	=	SYM
ejpam-5433	150	1	−	−	PROPN
ejpam-5433	150	2	sin	sin	NOUN
ejpam-5433	150	3	(	(	PUNCT
ejpam-5433	150	4	tα	tα	PROPN
ejpam-5433	150	5	α	α	PROPN
ejpam-5433	150	6	)	)	PUNCT
ejpam-5433	150	7	.	.	PUNCT
ejpam-5433	151	1	consequently	consequently	ADV
ejpam-5433	151	2	,	,	PUNCT
ejpam-5433	151	3	up(t	up(t	ADP
ejpam-5433	151	4	)	)	PUNCT
ejpam-5433	151	5	=	=	SYM
ejpam-5433	151	6	3x0	3x0	NUM
ejpam-5433	151	7	t∫	t∫	NUM
ejpam-5433	151	8	b	b	PROPN
ejpam-5433	151	9	h	h	NOUN
ejpam-5433	151	10	3	3	NUM
ejpam-5433	151	11	dτα	dτα	PROPN
ejpam-5433	151	12	τα−1	τα−1	PROPN
ejpam-5433	151	13	−x0	−x0	PROPN
ejpam-5433	151	14	cos	cos	PROPN
ejpam-5433	151	15	(	(	PUNCT
ejpam-5433	151	16	tα	tα	PROPN
ejpam-5433	151	17	α	α	PROPN
ejpam-5433	151	18	)	)	PUNCT
ejpam-5433	152	1	t∫	t∫	PROPN
ejpam-5433	152	2	b	b	PROPN
ejpam-5433	152	3	h	h	NOUN
ejpam-5433	152	4	cos	cos	PROPN
ejpam-5433	152	5	(	(	PUNCT
ejpam-5433	152	6	τα	τα	NOUN
ejpam-5433	152	7	α	α	PROPN
ejpam-5433	152	8	)	)	PUNCT
ejpam-5433	152	9	dτα	dτα	PROPN
ejpam-5433	152	10	τα−1	τα−1	PROPN
ejpam-5433	152	11	−x0	−x0	NOUN
ejpam-5433	152	12	sin	sin	NOUN
ejpam-5433	152	13	(	(	PUNCT
ejpam-5433	152	14	tα	tα	PROPN
ejpam-5433	152	15	α	α	PROPN
ejpam-5433	152	16	)	)	PUNCT
ejpam-5433	153	1	t∫	t∫	PROPN
ejpam-5433	153	2	b	b	NOUN
ejpam-5433	153	3	h	h	NOUN
ejpam-5433	153	4	sin	sin	NOUN
ejpam-5433	153	5	(	(	PUNCT
ejpam-5433	153	6	τα	τα	NOUN
ejpam-5433	153	7	α	α	PROPN
ejpam-5433	153	8	)	)	PUNCT
ejpam-5433	153	9	dτα	dτα	PROPN
ejpam-5433	153	10	τα−1	τα−1	PROPN
ejpam-5433	153	11	.	.	PUNCT
ejpam-5433	154	1	so	so	ADV
ejpam-5433	154	2	,	,	PUNCT
ejpam-5433	154	3	u(t	u(t	NOUN
ejpam-5433	154	4	)	)	PUNCT
ejpam-5433	154	5	=	=	PUNCT
ejpam-5433	154	6	uh(t	uh(t	X
ejpam-5433	154	7	)	)	PUNCT
ejpam-5433	154	8	+	+	CCONJ
ejpam-5433	154	9	up(t	up(t	NOUN
ejpam-5433	154	10	)	)	PUNCT
ejpam-5433	154	11	,	,	PUNCT
ejpam-5433	154	12	u(t	u(t	NOUN
ejpam-5433	154	13	)	)	PUNCT
ejpam-5433	154	14	=	=	PUNCT
ejpam-5433	155	1	3x0	3x0	NUM
ejpam-5433	155	2	−	−	NUM
ejpam-5433	156	1	x0	x0	PROPN
ejpam-5433	156	2	cos	cos	PROPN
ejpam-5433	156	3	(	(	PUNCT
ejpam-5433	156	4	tα	tα	PROPN
ejpam-5433	156	5	α	α	PROPN
ejpam-5433	156	6	)	)	PUNCT
ejpam-5433	157	1	+	+	CCONJ
ejpam-5433	157	2	x0	x0	PROPN
ejpam-5433	157	3	sin	sin	NOUN
ejpam-5433	157	4	(	(	PUNCT
ejpam-5433	157	5	tα	tα	PROPN
ejpam-5433	157	6	α	α	PROPN
ejpam-5433	157	7	)	)	PUNCT
ejpam-5433	158	1	+	+	CCONJ
ejpam-5433	158	2	3x0	3x0	NUM
ejpam-5433	158	3	t∫	t∫	NUM
ejpam-5433	158	4	b	b	PROPN
ejpam-5433	158	5	h	h	NOUN
ejpam-5433	158	6	dτα	dτα	PROPN
ejpam-5433	158	7	τα−1	τα−1	PROPN
ejpam-5433	158	8	−	−	PROPN
ejpam-5433	159	1	x0	x0	PROPN
ejpam-5433	159	2	cos	cos	PROPN
ejpam-5433	159	3	(	(	PUNCT
ejpam-5433	159	4	tα	tα	PROPN
ejpam-5433	159	5	α	α	PROPN
ejpam-5433	159	6	)	)	PUNCT
ejpam-5433	160	1	t∫	t∫	PROPN
ejpam-5433	160	2	b	b	PROPN
ejpam-5433	160	3	h	h	NOUN
ejpam-5433	160	4	cos	cos	PROPN
ejpam-5433	160	5	(	(	PUNCT
ejpam-5433	160	6	τα	τα	NOUN
ejpam-5433	160	7	α	α	PROPN
ejpam-5433	160	8	)	)	PUNCT
ejpam-5433	160	9	dτα	dτα	PROPN
ejpam-5433	160	10	τα−1	τα−1	PROPN
ejpam-5433	160	11	−x0	−x0	NOUN
ejpam-5433	160	12	sin	sin	NOUN
ejpam-5433	160	13	(	(	PUNCT
ejpam-5433	160	14	tα	tα	PROPN
ejpam-5433	160	15	α	α	PROPN
ejpam-5433	160	16	)	)	PUNCT
ejpam-5433	161	1	t∫	t∫	PROPN
ejpam-5433	161	2	b	b	NOUN
ejpam-5433	161	3	h	h	NOUN
ejpam-5433	161	4	sin	sin	NOUN
ejpam-5433	161	5	(	(	PUNCT
ejpam-5433	161	6	τα	τα	NOUN
ejpam-5433	161	7	α	α	PROPN
ejpam-5433	161	8	)	)	PUNCT
ejpam-5433	161	9	dτα	dτα	PROPN
ejpam-5433	161	10	τα−1	τα−1	PROPN
ejpam-5433	161	11	.	.	PUNCT
ejpam-5433	162	1	this	this	PRON
ejpam-5433	162	2	completes	complete	VERB
ejpam-5433	162	3	situation	situation	NOUN
ejpam-5433	162	4	(	(	PUNCT
ejpam-5433	162	5	1	1	NUM
ejpam-5433	162	6	)	)	PUNCT
ejpam-5433	162	7	.	.	PUNCT
ejpam-5433	163	1	r.	r.	PROPN
ejpam-5433	163	2	alkhateeb	alkhateeb	PROPN
ejpam-5433	163	3	,	,	PUNCT
ejpam-5433	163	4	g.	g.	PROPN
ejpam-5433	163	5	awwad	awwad	PROPN
ejpam-5433	163	6	/	/	PUNCT
ejpam-5433	163	7	eur	eur	PROPN
ejpam-5433	163	8	.	.	PUNCT
ejpam-5433	164	1	j.	j.	PROPN
ejpam-5433	164	2	pure	pure	PROPN
ejpam-5433	164	3	appl	appl	PROPN
ejpam-5433	164	4	.	.	PROPN
ejpam-5433	164	5	math	math	PROPN
ejpam-5433	164	6	,	,	PUNCT
ejpam-5433	164	7	17	17	NUM
ejpam-5433	164	8	(	(	PUNCT
ejpam-5433	164	9	4	4	NUM
ejpam-5433	164	10	)	)	PUNCT
ejpam-5433	164	11	(	(	PUNCT
ejpam-5433	164	12	2024	2024	NUM
ejpam-5433	164	13	)	)	PUNCT
ejpam-5433	164	14	,	,	PUNCT
ejpam-5433	164	15	3061	3061	NUM
ejpam-5433	164	16	-	-	SYM
ejpam-5433	164	17	3078	3078	NUM
ejpam-5433	164	18	3067	3067	NUM
ejpam-5433	164	19	considering	consider	VERB
ejpam-5433	164	20	situation	situation	NOUN
ejpam-5433	164	21	(	(	PUNCT
ejpam-5433	164	22	2	2	NUM
ejpam-5433	164	23	)	)	PUNCT
ejpam-5433	164	24	,	,	PUNCT
ejpam-5433	164	25	x	x	X
ejpam-5433	164	26	=	=	SYM
ejpam-5433	164	27	ax	ax	NOUN
ejpam-5433	164	28	,	,	PUNCT
ejpam-5433	164	29	equation	equation	NOUN
ejpam-5433	164	30	(	(	PUNCT
ejpam-5433	164	31	5	5	X
ejpam-5433	164	32	)	)	PUNCT
ejpam-5433	164	33	becomes	become	VERB
ejpam-5433	164	34	:(	:(	PUNCT
ejpam-5433	164	35	u3α	u3α	PROPN
ejpam-5433	164	36	+	+	CCONJ
ejpam-5433	164	37	u2α	u2α	ADJ
ejpam-5433	164	38	)	)	PUNCT
ejpam-5433	165	1	⊗	⊗	PROPN
ejpam-5433	165	2	x+	x+	NUM
ejpam-5433	165	3	uα	uα	PROPN
ejpam-5433	165	4	⊗bx	⊗bx	NOUN
ejpam-5433	165	5	=	=	PUNCT
ejpam-5433	165	6	h⊗	h⊗	VERB
ejpam-5433	165	7	z.	z.	PROPN
ejpam-5433	166	1	this	this	DET
ejpam-5433	166	2	situation	situation	NOUN
ejpam-5433	166	3	has	have	VERB
ejpam-5433	166	4	two	two	NUM
ejpam-5433	166	5	cases	case	NOUN
ejpam-5433	166	6	:	:	PUNCT
ejpam-5433	166	7	(	(	PUNCT
ejpam-5433	166	8	a	a	X
ejpam-5433	166	9	)	)	PUNCT
ejpam-5433	166	10	u3α	u3α	NOUN
ejpam-5433	167	1	+	+	CCONJ
ejpam-5433	167	2	u2α	u2α	NOUN
ejpam-5433	167	3	=	=	PUNCT
ejpam-5433	167	4	uα	uα	PROPN
ejpam-5433	167	5	=	=	PUNCT
ejpam-5433	167	6	h.	h.	PROPN
ejpam-5433	167	7	(	(	PUNCT
ejpam-5433	167	8	b	b	X
ejpam-5433	167	9	)	)	PUNCT
ejpam-5433	167	10	x	x	X
ejpam-5433	168	1	=	=	PUNCT
ejpam-5433	168	2	bx	bx	NOUN
ejpam-5433	168	3	=	=	PUNCT
ejpam-5433	168	4	z.	z.	PROPN
ejpam-5433	169	1	in	in	ADP
ejpam-5433	169	2	case	case	NOUN
ejpam-5433	169	3	(	(	PUNCT
ejpam-5433	169	4	a	a	NOUN
ejpam-5433	169	5	)	)	PUNCT
ejpam-5433	169	6	,	,	PUNCT
ejpam-5433	169	7	for	for	ADP
ejpam-5433	169	8	the	the	DET
ejpam-5433	169	9	existence	existence	NOUN
ejpam-5433	169	10	of	of	ADP
ejpam-5433	169	11	an	an	DET
ejpam-5433	169	12	atomic	atomic	ADJ
ejpam-5433	169	13	solution	solution	NOUN
ejpam-5433	169	14	,	,	PUNCT
ejpam-5433	169	15	we	we	PRON
ejpam-5433	169	16	have	have	VERB
ejpam-5433	169	17	three	three	NUM
ejpam-5433	169	18	situations	situation	NOUN
ejpam-5433	169	19	:	:	PUNCT
ejpam-5433	169	20	(	(	PUNCT
ejpam-5433	169	21	i	i	NOUN
ejpam-5433	169	22	)	)	PUNCT
ejpam-5433	169	23	u3α	u3α	PROPN
ejpam-5433	170	1	+	+	CCONJ
ejpam-5433	170	2	u2α	u2α	ADJ
ejpam-5433	170	3	−	−	NOUN
ejpam-5433	170	4	uα	uα	NOUN
ejpam-5433	170	5	=	=	NOUN
ejpam-5433	170	6	0	0	PROPN
ejpam-5433	170	7	.	.	PUNCT
ejpam-5433	171	1	this	this	PRON
ejpam-5433	171	2	can	can	AUX
ejpam-5433	171	3	be	be	AUX
ejpam-5433	171	4	solved	solve	VERB
ejpam-5433	171	5	as	as	ADP
ejpam-5433	171	6	in	in	ADP
ejpam-5433	171	7	[	[	X
ejpam-5433	171	8	3	3	NUM
ejpam-5433	171	9	]	]	PUNCT
ejpam-5433	171	10	,	,	PUNCT
ejpam-5433	171	11	r3	r3	PROPN
ejpam-5433	171	12	+	+	CCONJ
ejpam-5433	171	13	r2	r2	PROPN
ejpam-5433	171	14	−	−	NOUN
ejpam-5433	171	15	r	r	NOUN
ejpam-5433	171	16	=	=	PUNCT
ejpam-5433	171	17	r(r2	r(r2	NOUN
ejpam-5433	171	18	+	+	NOUN
ejpam-5433	171	19	r	r	NOUN
ejpam-5433	171	20	−	−	NOUN
ejpam-5433	171	21	1	1	NUM
ejpam-5433	171	22	)	)	PUNCT
ejpam-5433	171	23	=	=	SYM
ejpam-5433	172	1	0	0	X
ejpam-5433	172	2	.	.	NOUN
ejpam-5433	172	3	which	which	PRON
ejpam-5433	172	4	gives	give	VERB
ejpam-5433	172	5	r1	r1	PROPN
ejpam-5433	172	6	=	=	SYM
ejpam-5433	172	7	0	0	NUM
ejpam-5433	172	8	,	,	PUNCT
ejpam-5433	172	9	r2	r2	NOUN
ejpam-5433	172	10	=	=	SYM
ejpam-5433	172	11	−1	−1	NOUN
ejpam-5433	172	12	+	+	CCONJ
ejpam-5433	172	13	√	√	NUM
ejpam-5433	172	14	5	5	NUM
ejpam-5433	172	15	2	2	NUM
ejpam-5433	172	16	,	,	PUNCT
ejpam-5433	172	17	and	and	CCONJ
ejpam-5433	172	18	r3	r3	PROPN
ejpam-5433	172	19	=	=	SYM
ejpam-5433	173	1	−1−	−1−	NOUN
ejpam-5433	173	2	√	√	NUM
ejpam-5433	173	3	5	5	NUM
ejpam-5433	173	4	2	2	NUM
ejpam-5433	173	5	.	.	PUNCT
ejpam-5433	174	1	(	(	PUNCT
ejpam-5433	174	2	9	9	NUM
ejpam-5433	174	3	)	)	PUNCT
ejpam-5433	174	4	then	then	ADV
ejpam-5433	174	5	u(t	u(t	VERB
ejpam-5433	174	6	)	)	PUNCT
ejpam-5433	174	7	=	=	PROPN
ejpam-5433	174	8	c1	c1	NOUN
ejpam-5433	174	9	+	+	CCONJ
ejpam-5433	174	10	c2e	c2e	PROPN
ejpam-5433	174	11	r2	r2	PROPN
ejpam-5433	174	12	(	(	PUNCT
ejpam-5433	174	13	tα	tα	PROPN
ejpam-5433	174	14	α	α	PROPN
ejpam-5433	174	15	)	)	PUNCT
ejpam-5433	175	1	+	+	CCONJ
ejpam-5433	175	2	c3e	c3e	PROPN
ejpam-5433	175	3	r3	r3	PROPN
ejpam-5433	175	4	(	(	PUNCT
ejpam-5433	175	5	tα	tα	PROPN
ejpam-5433	175	6	α	α	PROPN
ejpam-5433	175	7	)	)	PUNCT
ejpam-5433	175	8	.	.	PUNCT
ejpam-5433	176	1	(	(	PUNCT
ejpam-5433	176	2	10	10	NUM
ejpam-5433	176	3	)	)	PUNCT
ejpam-5433	176	4	now	now	ADV
ejpam-5433	176	5	,	,	PUNCT
ejpam-5433	176	6	by	by	ADP
ejpam-5433	176	7	assumptions	assumption	NOUN
ejpam-5433	176	8	(	(	PUNCT
ejpam-5433	176	9	4	4	NUM
ejpam-5433	176	10	)	)	PUNCT
ejpam-5433	176	11	,	,	PUNCT
ejpam-5433	176	12	we	we	PRON
ejpam-5433	176	13	have	have	VERB
ejpam-5433	176	14	c1	c1	PROPN
ejpam-5433	176	15	+	+	CCONJ
ejpam-5433	176	16	c2	c2	PROPN
ejpam-5433	176	17	+	+	CCONJ
ejpam-5433	176	18	c3	c3	PROPN
ejpam-5433	176	19	=	=	PUNCT
ejpam-5433	176	20	2x0	2x0	NUM
ejpam-5433	176	21	,	,	PUNCT
ejpam-5433	176	22	r2c2	r2c2	X
ejpam-5433	176	23	+	+	NUM
ejpam-5433	176	24	r3c3	r3c3	NOUN
ejpam-5433	176	25	=	=	SYM
ejpam-5433	176	26	x0	x0	PROPN
ejpam-5433	176	27	,	,	PUNCT
ejpam-5433	176	28	and	and	CCONJ
ejpam-5433	176	29	r22c2	r22c2	PRON
ejpam-5433	177	1	+	+	CCONJ
ejpam-5433	177	2	r23c3	r23c3	NOUN
ejpam-5433	177	3	=	=	SYM
ejpam-5433	177	4	x0	x0	PROPN
ejpam-5433	177	5	.	.	PUNCT
ejpam-5433	178	1	so	so	ADV
ejpam-5433	178	2	,	,	PUNCT
ejpam-5433	178	3	c1	c1	PROPN
ejpam-5433	178	4	=	=	PROPN
ejpam-5433	178	5	2x0	2x0	NUM
ejpam-5433	178	6	−	−	PROPN
ejpam-5433	178	7	c2	c2	PROPN
ejpam-5433	178	8	−	−	PROPN
ejpam-5433	178	9	c3	c3	PROPN
ejpam-5433	178	10	,	,	PUNCT
ejpam-5433	178	11	c2	c2	PROPN
ejpam-5433	178	12	=	=	SYM
ejpam-5433	178	13	r3	r3	PROPN
ejpam-5433	178	14	−	−	NOUN
ejpam-5433	178	15	x0	x0	PROPN
ejpam-5433	178	16	r2r3	r2r3	PROPN
ejpam-5433	178	17	−	−	PROPN
ejpam-5433	178	18	r22	r22	NOUN
ejpam-5433	178	19	,	,	PUNCT
ejpam-5433	178	20	and	and	CCONJ
ejpam-5433	178	21	c3	c3	PROPN
ejpam-5433	178	22	=	=	PROPN
ejpam-5433	178	23	r2	r2	PROPN
ejpam-5433	179	1	−	−	PROPN
ejpam-5433	180	1	x0	x0	PROPN
ejpam-5433	181	1	r2r3	r2r3	PROPN
ejpam-5433	181	2	−	−	PROPN
ejpam-5433	181	3	r23	r23	NOUN
ejpam-5433	181	4	.	.	PUNCT
ejpam-5433	182	1	(	(	PUNCT
ejpam-5433	182	2	11	11	NUM
ejpam-5433	182	3	)	)	PUNCT
ejpam-5433	182	4	from	from	ADP
ejpam-5433	182	5	(	(	PUNCT
ejpam-5433	182	6	9	9	NUM
ejpam-5433	182	7	)	)	PUNCT
ejpam-5433	182	8	and	and	CCONJ
ejpam-5433	182	9	(	(	PUNCT
ejpam-5433	182	10	11	11	NUM
ejpam-5433	182	11	)	)	PUNCT
ejpam-5433	182	12	,	,	PUNCT
ejpam-5433	182	13	we	we	PRON
ejpam-5433	182	14	have	have	VERB
ejpam-5433	182	15	c1	c1	PROPN
ejpam-5433	182	16	=	=	SYM
ejpam-5433	182	17	0	0	PROPN
ejpam-5433	182	18	,	,	PUNCT
ejpam-5433	182	19	c2	c2	PROPN
ejpam-5433	182	20	=	=	PUNCT
ejpam-5433	182	21	3	3	NUM
ejpam-5433	182	22	+	+	CCONJ
ejpam-5433	182	23	√	√	NUM
ejpam-5433	182	24	5	5	NUM
ejpam-5433	182	25	5−	5−	NUM
ejpam-5433	182	26	√	√	NUM
ejpam-5433	182	27	5	5	NUM
ejpam-5433	182	28	x0	x0	PROPN
ejpam-5433	182	29	,	,	PUNCT
ejpam-5433	182	30	and	and	CCONJ
ejpam-5433	182	31	c3	c3	X
ejpam-5433	182	32	=	=	PUNCT
ejpam-5433	183	1	3−	3−	NUM
ejpam-5433	183	2	√	√	NUM
ejpam-5433	183	3	5√	5√	NOUN
ejpam-5433	183	4	5	5	NUM
ejpam-5433	183	5	+	+	SYM
ejpam-5433	183	6	5	5	NUM
ejpam-5433	183	7	x0	x0	NUM
ejpam-5433	183	8	.	.	PUNCT
ejpam-5433	184	1	so	so	ADV
ejpam-5433	184	2	,	,	PUNCT
ejpam-5433	184	3	the	the	DET
ejpam-5433	184	4	equation	equation	NOUN
ejpam-5433	184	5	(	(	PUNCT
ejpam-5433	184	6	10	10	NUM
ejpam-5433	184	7	)	)	PUNCT
ejpam-5433	184	8	will	will	AUX
ejpam-5433	184	9	be	be	AUX
ejpam-5433	184	10	u(t	u(t	NOUN
ejpam-5433	184	11	)	)	PUNCT
ejpam-5433	184	12	=	=	SYM
ejpam-5433	185	1	3	3	NUM
ejpam-5433	185	2	+	+	CCONJ
ejpam-5433	185	3	√	√	NUM
ejpam-5433	185	4	5	5	NUM
ejpam-5433	185	5	5−	5−	NUM
ejpam-5433	185	6	√	√	NUM
ejpam-5433	185	7	5	5	NUM
ejpam-5433	185	8	x0e	x0e	PUNCT
ejpam-5433	185	9	−1	−1	PROPN
ejpam-5433	186	1	+	+	NOUN
ejpam-5433	186	2	√	√	NUM
ejpam-5433	186	3	5	5	NUM
ejpam-5433	186	4	2	2	NUM
ejpam-5433	186	5	(	(	PUNCT
ejpam-5433	186	6	t	t	PROPN
ejpam-5433	186	7	α	α	PROPN
ejpam-5433	186	8	α	α	NOUN
ejpam-5433	186	9	)	)	PUNCT
ejpam-5433	187	1	+	+	CCONJ
ejpam-5433	188	1	3−	3−	NUM
ejpam-5433	188	2	√	√	NUM
ejpam-5433	188	3	5√	5√	NOUN
ejpam-5433	188	4	5	5	NUM
ejpam-5433	188	5	+	+	SYM
ejpam-5433	188	6	5	5	NUM
ejpam-5433	188	7	x0e	x0e	PUNCT
ejpam-5433	188	8	−1−	−1−	NOUN
ejpam-5433	188	9	√	√	ADV
ejpam-5433	188	10	5	5	NUM
ejpam-5433	188	11	2	2	NUM
ejpam-5433	188	12	(	(	PUNCT
ejpam-5433	188	13	t	t	PROPN
ejpam-5433	188	14	α	α	PROPN
ejpam-5433	188	15	α	α	PROPN
ejpam-5433	188	16	)	)	PUNCT
ejpam-5433	188	17	.	.	PUNCT
ejpam-5433	189	1	(	(	PUNCT
ejpam-5433	189	2	12	12	NUM
ejpam-5433	189	3	)	)	PUNCT
ejpam-5433	189	4	(	(	PUNCT
ejpam-5433	189	5	ii	ii	NOUN
ejpam-5433	189	6	)	)	PUNCT
ejpam-5433	189	7	uα	uα	PROPN
ejpam-5433	189	8	=	=	PUNCT
ejpam-5433	189	9	h.	h.	PROPN
ejpam-5433	189	10	for	for	ADP
ejpam-5433	189	11	an	an	DET
ejpam-5433	189	12	atomic	atomic	ADJ
ejpam-5433	189	13	solution	solution	NOUN
ejpam-5433	189	14	to	to	PART
ejpam-5433	189	15	exist	exist	VERB
ejpam-5433	189	16	h	h	NOUN
ejpam-5433	189	17	must	must	AUX
ejpam-5433	189	18	equal	equal	VERB
ejpam-5433	189	19	to	to	ADP
ejpam-5433	189	20	uα	uα	PROPN
ejpam-5433	189	21	.	.	PUNCT
ejpam-5433	190	1	hence	hence	ADV
ejpam-5433	190	2	,	,	PUNCT
ejpam-5433	190	3	from	from	ADP
ejpam-5433	190	4	(	(	PUNCT
ejpam-5433	190	5	12	12	NUM
ejpam-5433	190	6	)	)	PUNCT
ejpam-5433	190	7	,	,	PUNCT
ejpam-5433	190	8	we	we	PRON
ejpam-5433	190	9	have	have	VERB
ejpam-5433	190	10	h	h	NOUN
ejpam-5433	190	11	=	=	NOUN
ejpam-5433	190	12	1	1	NUM
ejpam-5433	190	13	+	+	CCONJ
ejpam-5433	190	14	√	√	NUM
ejpam-5433	190	15	5	5	NUM
ejpam-5433	190	16	5−	5−	NUM
ejpam-5433	190	17	√	√	NUM
ejpam-5433	190	18	5	5	NUM
ejpam-5433	190	19	x0e	x0e	PUNCT
ejpam-5433	191	1	−1	−1	PROPN
ejpam-5433	192	1	+	+	NOUN
ejpam-5433	192	2	√	√	NUM
ejpam-5433	192	3	5	5	NUM
ejpam-5433	192	4	2	2	NUM
ejpam-5433	192	5	(	(	PUNCT
ejpam-5433	192	6	t	t	PROPN
ejpam-5433	192	7	α	α	PROPN
ejpam-5433	192	8	α	α	NOUN
ejpam-5433	192	9	)	)	PUNCT
ejpam-5433	193	1	+	+	CCONJ
ejpam-5433	193	2	1−	1−	NUM
ejpam-5433	193	3	√	√	NUM
ejpam-5433	193	4	5	5	NUM
ejpam-5433	193	5	5	5	NUM
ejpam-5433	193	6	+	+	CCONJ
ejpam-5433	193	7	√	√	ADP
ejpam-5433	193	8	5	5	NUM
ejpam-5433	193	9	x0e	x0e	PUNCT
ejpam-5433	194	1	−1−	−1−	NOUN
ejpam-5433	194	2	√	√	ADV
ejpam-5433	194	3	5	5	NUM
ejpam-5433	194	4	2	2	NUM
ejpam-5433	194	5	(	(	PUNCT
ejpam-5433	194	6	t	t	PROPN
ejpam-5433	194	7	α	α	PROPN
ejpam-5433	194	8	α	α	PROPN
ejpam-5433	194	9	)	)	PUNCT
ejpam-5433	194	10	.	.	PUNCT
ejpam-5433	195	1	r.	r.	PROPN
ejpam-5433	195	2	alkhateeb	alkhateeb	PROPN
ejpam-5433	195	3	,	,	PUNCT
ejpam-5433	195	4	g.	g.	PROPN
ejpam-5433	195	5	awwad	awwad	PROPN
ejpam-5433	195	6	/	/	PUNCT
ejpam-5433	195	7	eur	eur	PROPN
ejpam-5433	195	8	.	.	PUNCT
ejpam-5433	196	1	j.	j.	PROPN
ejpam-5433	196	2	pure	pure	PROPN
ejpam-5433	196	3	appl	appl	PROPN
ejpam-5433	196	4	.	.	PROPN
ejpam-5433	196	5	math	math	PROPN
ejpam-5433	196	6	,	,	PUNCT
ejpam-5433	196	7	17	17	NUM
ejpam-5433	196	8	(	(	PUNCT
ejpam-5433	196	9	4	4	NUM
ejpam-5433	196	10	)	)	PUNCT
ejpam-5433	196	11	(	(	PUNCT
ejpam-5433	196	12	2024	2024	NUM
ejpam-5433	196	13	)	)	PUNCT
ejpam-5433	196	14	,	,	PUNCT
ejpam-5433	196	15	3061	3061	NUM
ejpam-5433	196	16	-	-	SYM
ejpam-5433	196	17	3078	3078	NUM
ejpam-5433	196	18	3068	3068	NUM
ejpam-5433	196	19	(	(	PUNCT
ejpam-5433	196	20	iii	iii	NOUN
ejpam-5433	196	21	)	)	PUNCT
ejpam-5433	196	22	u3α	u3α	NOUN
ejpam-5433	197	1	+	+	CCONJ
ejpam-5433	197	2	u2α	u2α	NOUN
ejpam-5433	197	3	=	=	SYM
ejpam-5433	197	4	h.	h.	PROPN
ejpam-5433	198	1	so	so	ADV
ejpam-5433	198	2	,	,	PUNCT
ejpam-5433	198	3	h	h	NOUN
ejpam-5433	198	4	=	=	PUNCT
ejpam-5433	199	1	c2(r	c2(r	ADJ
ejpam-5433	199	2	3	3	NUM
ejpam-5433	199	3	2	2	NUM
ejpam-5433	199	4	+	+	CCONJ
ejpam-5433	199	5	r22)e	r22)e	NOUN
ejpam-5433	199	6	r2	r2	NOUN
ejpam-5433	199	7	(	(	PUNCT
ejpam-5433	199	8	tα	tα	PROPN
ejpam-5433	199	9	α	α	PROPN
ejpam-5433	199	10	)	)	PUNCT
ejpam-5433	200	1	+	+	PUNCT
ejpam-5433	200	2	c3(r	c3(r	X
ejpam-5433	200	3	3	3	NUM
ejpam-5433	200	4	3	3	NUM
ejpam-5433	200	5	+	+	CCONJ
ejpam-5433	200	6	r23)e	r23)e	PROPN
ejpam-5433	200	7	r3	r3	PROPN
ejpam-5433	200	8	(	(	PUNCT
ejpam-5433	200	9	tα	tα	PROPN
ejpam-5433	200	10	α	α	NOUN
ejpam-5433	200	11	)	)	PUNCT
ejpam-5433	200	12	h	h	NOUN
ejpam-5433	200	13	=	=	NOUN
ejpam-5433	200	14	1	1	NUM
ejpam-5433	200	15	+	+	CCONJ
ejpam-5433	200	16	√	√	NUM
ejpam-5433	200	17	5	5	NUM
ejpam-5433	200	18	5−	5−	NUM
ejpam-5433	200	19	√	√	NUM
ejpam-5433	200	20	5	5	NUM
ejpam-5433	200	21	x0e	x0e	PUNCT
ejpam-5433	200	22	−1	−1	PROPN
ejpam-5433	200	23	+	+	NOUN
ejpam-5433	200	24	√	√	NUM
ejpam-5433	200	25	5	5	NUM
ejpam-5433	200	26	2	2	NUM
ejpam-5433	200	27	(	(	PUNCT
ejpam-5433	200	28	t	t	PROPN
ejpam-5433	200	29	α	α	PROPN
ejpam-5433	200	30	α	α	NOUN
ejpam-5433	200	31	)	)	PUNCT
ejpam-5433	201	1	+	+	CCONJ
ejpam-5433	201	2	1−	1−	NUM
ejpam-5433	201	3	√	√	NUM
ejpam-5433	201	4	5	5	NUM
ejpam-5433	201	5	5	5	NUM
ejpam-5433	201	6	+	+	CCONJ
ejpam-5433	201	7	√	√	ADP
ejpam-5433	201	8	5	5	NUM
ejpam-5433	201	9	x0e	x0e	PUNCT
ejpam-5433	202	1	−1−	−1−	NOUN
ejpam-5433	202	2	√	√	ADV
ejpam-5433	202	3	5	5	NUM
ejpam-5433	202	4	2	2	NUM
ejpam-5433	202	5	(	(	PUNCT
ejpam-5433	202	6	t	t	PROPN
ejpam-5433	202	7	α	α	PROPN
ejpam-5433	202	8	α	α	PROPN
ejpam-5433	202	9	)	)	PUNCT
ejpam-5433	202	10	.	.	PUNCT
ejpam-5433	203	1	(	(	PUNCT
ejpam-5433	203	2	13	13	NUM
ejpam-5433	203	3	)	)	PUNCT
ejpam-5433	203	4	hence	hence	ADV
ejpam-5433	203	5	,	,	PUNCT
ejpam-5433	203	6	the	the	DET
ejpam-5433	203	7	equations	equation	NOUN
ejpam-5433	203	8	(	(	PUNCT
ejpam-5433	203	9	12	12	NUM
ejpam-5433	203	10	)	)	PUNCT
ejpam-5433	203	11	and	and	CCONJ
ejpam-5433	203	12	(	(	PUNCT
ejpam-5433	203	13	13	13	NUM
ejpam-5433	203	14	)	)	PUNCT
ejpam-5433	203	15	are	be	AUX
ejpam-5433	203	16	equal	equal	ADJ
ejpam-5433	203	17	to	to	ADP
ejpam-5433	203	18	h.	h.	PROPN
ejpam-5433	204	1	so	so	ADV
ejpam-5433	204	2	,	,	PUNCT
ejpam-5433	204	3	there	there	PRON
ejpam-5433	204	4	is	be	VERB
ejpam-5433	204	5	an	an	DET
ejpam-5433	204	6	atomic	atomic	ADJ
ejpam-5433	204	7	solution	solution	NOUN
ejpam-5433	204	8	in	in	ADP
ejpam-5433	204	9	this	this	DET
ejpam-5433	204	10	case	case	NOUN
ejpam-5433	204	11	.	.	PUNCT
ejpam-5433	205	1	in	in	ADP
ejpam-5433	205	2	case	case	NOUN
ejpam-5433	205	3	(	(	PUNCT
ejpam-5433	205	4	b	b	NOUN
ejpam-5433	205	5	)	)	PUNCT
ejpam-5433	205	6	,	,	PUNCT
ejpam-5433	205	7	equation	equation	NOUN
ejpam-5433	205	8	(	(	PUNCT
ejpam-5433	205	9	5	5	X
ejpam-5433	205	10	)	)	PUNCT
ejpam-5433	205	11	becomes	become	VERB
ejpam-5433	205	12	(	(	PUNCT
ejpam-5433	205	13	u3α	u3α	ADJ
ejpam-5433	205	14	+	+	CCONJ
ejpam-5433	205	15	u2α	u2α	NOUN
ejpam-5433	205	16	)	)	PUNCT
ejpam-5433	206	1	⊗	⊗	PROPN
ejpam-5433	206	2	x+	x+	NUM
ejpam-5433	206	3	uα	uα	PROPN
ejpam-5433	206	4	⊗bx	⊗bx	NOUN
ejpam-5433	206	5	=	=	PUNCT
ejpam-5433	206	6	h⊗	h⊗	VERB
ejpam-5433	206	7	z.	z.	PROPN
ejpam-5433	207	1	so	so	ADV
ejpam-5433	207	2	,	,	PUNCT
ejpam-5433	207	3	u3α	u3α	PROPN
ejpam-5433	207	4	+	+	CCONJ
ejpam-5433	207	5	u2α	u2α	ADJ
ejpam-5433	207	6	+	+	CCONJ
ejpam-5433	207	7	uα	uα	PROPN
ejpam-5433	207	8	=	=	PUNCT
ejpam-5433	207	9	h.	h.	PROPN
ejpam-5433	207	10	(	(	PUNCT
ejpam-5433	207	11	14	14	NUM
ejpam-5433	207	12	)	)	PUNCT
ejpam-5433	207	13	this	this	PRON
ejpam-5433	207	14	is	be	AUX
ejpam-5433	207	15	third	third	ADJ
ejpam-5433	207	16	order	order	NOUN
ejpam-5433	207	17	homogenous	homogenous	ADJ
ejpam-5433	207	18	linear	linear	ADJ
ejpam-5433	207	19	fractional	fractional	ADJ
ejpam-5433	207	20	differential	differential	NOUN
ejpam-5433	207	21	equation	equation	NOUN
ejpam-5433	207	22	,	,	PUNCT
ejpam-5433	207	23	to	to	PART
ejpam-5433	207	24	solve	solve	VERB
ejpam-5433	207	25	it	it	PRON
ejpam-5433	207	26	we	we	PRON
ejpam-5433	207	27	follow	follow	VERB
ejpam-5433	207	28	the	the	DET
ejpam-5433	207	29	variation	variation	NOUN
ejpam-5433	207	30	of	of	ADP
ejpam-5433	207	31	parameters	parameter	NOUN
ejpam-5433	207	32	method	method	VERB
ejpam-5433	207	33	.	.	PUNCT
ejpam-5433	208	1	the	the	DET
ejpam-5433	208	2	homogenous	homogenous	ADJ
ejpam-5433	208	3	part	part	NOUN
ejpam-5433	208	4	can	can	AUX
ejpam-5433	208	5	solved	solve	VERB
ejpam-5433	208	6	as	as	ADP
ejpam-5433	208	7	in	in	ADP
ejpam-5433	208	8	[	[	X
ejpam-5433	208	9	3	3	NUM
ejpam-5433	208	10	]	]	PUNCT
ejpam-5433	208	11	.	.	PUNCT
ejpam-5433	209	1	r3	r3	PROPN
ejpam-5433	209	2	+	+	CCONJ
ejpam-5433	209	3	r2	r2	PROPN
ejpam-5433	209	4	+	+	CCONJ
ejpam-5433	209	5	r	r	NOUN
ejpam-5433	209	6	=	=	PUNCT
ejpam-5433	209	7	r(r2	r(r2	NOUN
ejpam-5433	209	8	+	+	NOUN
ejpam-5433	209	9	r	r	NOUN
ejpam-5433	209	10	+	+	NOUN
ejpam-5433	209	11	1	1	NUM
ejpam-5433	209	12	)	)	PUNCT
ejpam-5433	209	13	=	=	SYM
ejpam-5433	209	14	0	0	NUM
ejpam-5433	209	15	,	,	PUNCT
ejpam-5433	209	16	which	which	PRON
ejpam-5433	209	17	gives	give	VERB
ejpam-5433	209	18	r1	r1	PROPN
ejpam-5433	209	19	=	=	SYM
ejpam-5433	209	20	0	0	NUM
ejpam-5433	209	21	,	,	PUNCT
ejpam-5433	209	22	r2	r2	NOUN
ejpam-5433	209	23	=	=	PUNCT
ejpam-5433	209	24	−1+i	−1+i	NOUN
ejpam-5433	209	25	√	√	NOUN
ejpam-5433	209	26	3	3	NUM
ejpam-5433	209	27	2	2	NUM
ejpam-5433	209	28	,	,	PUNCT
ejpam-5433	209	29	and	and	CCONJ
ejpam-5433	209	30	r3	r3	PROPN
ejpam-5433	209	31	=	=	PRON
ejpam-5433	209	32	−1−i	−1−i	VERB
ejpam-5433	209	33	√	√	NUM
ejpam-5433	209	34	3	3	NUM
ejpam-5433	209	35	2	2	NUM
ejpam-5433	209	36	.	.	PUNCT
ejpam-5433	210	1	hence	hence	ADV
ejpam-5433	210	2	,	,	PUNCT
ejpam-5433	210	3	uh(t	uh(t	X
ejpam-5433	210	4	)	)	PUNCT
ejpam-5433	211	1	=	=	SYM
ejpam-5433	211	2	c1	c1	PROPN
ejpam-5433	211	3	+	+	CCONJ
ejpam-5433	211	4	e−	e−	PROPN
ejpam-5433	211	5	tα	tα	PROPN
ejpam-5433	211	6	2α	2α	PROPN
ejpam-5433	211	7	(	(	PUNCT
ejpam-5433	211	8	c2	c2	PROPN
ejpam-5433	211	9	cos	cos	PROPN
ejpam-5433	211	10	(	(	PUNCT
ejpam-5433	211	11	√	√	NUM
ejpam-5433	211	12	3tα	3tα	ADJ
ejpam-5433	211	13	2α	2α	NOUN
ejpam-5433	211	14	)	)	PUNCT
ejpam-5433	212	1	+	+	CCONJ
ejpam-5433	212	2	c3	c3	PROPN
ejpam-5433	212	3	sin	sin	NOUN
ejpam-5433	212	4	(	(	PUNCT
ejpam-5433	212	5	√	√	ADV
ejpam-5433	212	6	3tα	3tα	ADJ
ejpam-5433	212	7	2α	2α	NOUN
ejpam-5433	212	8	)	)	PUNCT
ejpam-5433	212	9	)	)	PUNCT
ejpam-5433	212	10	.	.	PUNCT
ejpam-5433	213	1	by	by	ADP
ejpam-5433	213	2	assumption	assumption	NOUN
ejpam-5433	213	3	(	(	PUNCT
ejpam-5433	213	4	4	4	NUM
ejpam-5433	213	5	)	)	PUNCT
ejpam-5433	213	6	,	,	PUNCT
ejpam-5433	213	7	we	we	PRON
ejpam-5433	213	8	have	have	VERB
ejpam-5433	213	9	c1	c1	NOUN
ejpam-5433	213	10	=	=	PUNCT
ejpam-5433	213	11	4x0	4x0	PROPN
ejpam-5433	213	12	,	,	PUNCT
ejpam-5433	213	13	c2	c2	PROPN
ejpam-5433	213	14	=	=	SYM
ejpam-5433	213	15	−2x0	−2x0	NUM
ejpam-5433	213	16	,	,	PUNCT
ejpam-5433	213	17	and	and	CCONJ
ejpam-5433	213	18	c3	c3	X
ejpam-5433	213	19	=	=	PROPN
ejpam-5433	213	20	0	0	X
ejpam-5433	213	21	.	.	PUNCT
ejpam-5433	214	1	so	so	ADV
ejpam-5433	214	2	,	,	PUNCT
ejpam-5433	214	3	uh(t	uh(t	X
ejpam-5433	214	4	)	)	PUNCT
ejpam-5433	214	5	=	=	SYM
ejpam-5433	215	1	4x0	4x0	NUM
ejpam-5433	216	1	−	−	NOUN
ejpam-5433	216	2	2x0e	2x0e	NOUN
ejpam-5433	217	1	−	−	PROPN
ejpam-5433	217	2	tα	tα	VERB
ejpam-5433	217	3	2α	2α	PROPN
ejpam-5433	217	4	cos	cos	X
ejpam-5433	217	5	(	(	PUNCT
ejpam-5433	217	6	√	√	NUM
ejpam-5433	217	7	3tα	3tα	ADJ
ejpam-5433	217	8	2α	2α	NOUN
ejpam-5433	217	9	)	)	PUNCT
ejpam-5433	217	10	.	.	PUNCT
ejpam-5433	218	1	since	since	SCONJ
ejpam-5433	218	2	c3	c3	PROPN
ejpam-5433	218	3	=	=	PROPN
ejpam-5433	218	4	0	0	PROPN
ejpam-5433	218	5	,	,	PUNCT
ejpam-5433	218	6	there	there	PRON
ejpam-5433	218	7	is	be	VERB
ejpam-5433	218	8	no	no	DET
ejpam-5433	218	9	particular	particular	ADJ
ejpam-5433	218	10	part	part	NOUN
ejpam-5433	218	11	,	,	PUNCT
ejpam-5433	218	12	and	and	CCONJ
ejpam-5433	218	13	for	for	ADP
ejpam-5433	218	14	an	an	DET
ejpam-5433	218	15	atomic	atomic	ADJ
ejpam-5433	218	16	solution	solution	NOUN
ejpam-5433	218	17	to	to	PART
ejpam-5433	218	18	exist	exist	VERB
ejpam-5433	218	19	,	,	PUNCT
ejpam-5433	218	20	h	h	NOUN
ejpam-5433	218	21	must	must	AUX
ejpam-5433	218	22	equal	equal	VERB
ejpam-5433	218	23	zero	zero	NUM
ejpam-5433	218	24	.	.	PUNCT
ejpam-5433	219	1	this	this	PRON
ejpam-5433	219	2	completes	complete	VERB
ejpam-5433	219	3	situation	situation	NOUN
ejpam-5433	219	4	(	(	PUNCT
ejpam-5433	219	5	2	2	NUM
ejpam-5433	219	6	)	)	PUNCT
ejpam-5433	219	7	,	,	PUNCT
ejpam-5433	219	8	and	and	CCONJ
ejpam-5433	219	9	hence	hence	ADV
ejpam-5433	219	10	,	,	PUNCT
ejpam-5433	219	11	case	case	NOUN
ejpam-5433	219	12	one	one	PRON
ejpam-5433	219	13	is	be	AUX
ejpam-5433	219	14	completed	complete	VERB
ejpam-5433	219	15	.	.	PUNCT
ejpam-5433	220	1	case	case	NOUN
ejpam-5433	220	2	two	two	NUM
ejpam-5433	220	3	:	:	PUNCT
ejpam-5433	220	4	(	(	PUNCT
ejpam-5433	220	5	u3α	u3α	INTJ
ejpam-5433	220	6	⊗	⊗	NOUN
ejpam-5433	220	7	x+	x+	PROPN
ejpam-5433	220	8	uα	uα	PROPN
ejpam-5433	220	9	⊗bx	⊗bx	X
ejpam-5433	220	10	)	)	PUNCT
ejpam-5433	220	11	is	be	AUX
ejpam-5433	220	12	an	an	DET
ejpam-5433	220	13	atom	atom	NOUN
ejpam-5433	220	14	.	.	PUNCT
ejpam-5433	221	1	in	in	ADP
ejpam-5433	221	2	this	this	DET
ejpam-5433	221	3	case	case	NOUN
ejpam-5433	221	4	we	we	PRON
ejpam-5433	221	5	have	have	VERB
ejpam-5433	221	6	two	two	NUM
ejpam-5433	221	7	situations	situation	NOUN
ejpam-5433	221	8	:	:	PUNCT
ejpam-5433	221	9	r.	r.	PROPN
ejpam-5433	221	10	alkhateeb	alkhateeb	PROPN
ejpam-5433	221	11	,	,	PUNCT
ejpam-5433	221	12	g.	g.	PROPN
ejpam-5433	221	13	awwad	awwad	PROPN
ejpam-5433	221	14	/	/	PUNCT
ejpam-5433	221	15	eur	eur	PROPN
ejpam-5433	221	16	.	.	PUNCT
ejpam-5433	222	1	j.	j.	PROPN
ejpam-5433	222	2	pure	pure	PROPN
ejpam-5433	222	3	appl	appl	PROPN
ejpam-5433	222	4	.	.	PROPN
ejpam-5433	222	5	math	math	PROPN
ejpam-5433	222	6	,	,	PUNCT
ejpam-5433	222	7	17	17	NUM
ejpam-5433	222	8	(	(	PUNCT
ejpam-5433	222	9	4	4	NUM
ejpam-5433	222	10	)	)	PUNCT
ejpam-5433	222	11	(	(	PUNCT
ejpam-5433	222	12	2024	2024	NUM
ejpam-5433	222	13	)	)	PUNCT
ejpam-5433	222	14	,	,	PUNCT
ejpam-5433	222	15	3061	3061	NUM
ejpam-5433	222	16	-	-	SYM
ejpam-5433	222	17	3078	3078	NUM
ejpam-5433	222	18	3069	3069	NUM
ejpam-5433	222	19	(	(	PUNCT
ejpam-5433	222	20	i	i	NOUN
ejpam-5433	222	21	)	)	PUNCT
ejpam-5433	223	1	u3α	u3α	PROPN
ejpam-5433	223	2	=	=	SYM
ejpam-5433	223	3	uα	uα	PROPN
ejpam-5433	223	4	.	.	PUNCT
ejpam-5433	224	1	(	(	PUNCT
ejpam-5433	224	2	ii	ii	NOUN
ejpam-5433	224	3	)	)	PUNCT
ejpam-5433	224	4	x	x	X
ejpam-5433	225	1	=	=	SYM
ejpam-5433	225	2	bx	bx	PROPN
ejpam-5433	225	3	.	.	PUNCT
ejpam-5433	226	1	considering	consider	VERB
ejpam-5433	226	2	situation	situation	NOUN
ejpam-5433	226	3	(	(	PUNCT
ejpam-5433	226	4	1	1	NUM
ejpam-5433	226	5	)	)	PUNCT
ejpam-5433	226	6	,	,	PUNCT
ejpam-5433	226	7	equation	equation	NOUN
ejpam-5433	226	8	(	(	PUNCT
ejpam-5433	226	9	5	5	X
ejpam-5433	226	10	)	)	PUNCT
ejpam-5433	226	11	becomes	become	VERB
ejpam-5433	226	12	:	:	PUNCT
ejpam-5433	226	13	u3α	u3α	PROPN
ejpam-5433	226	14	⊗	⊗	PROPN
ejpam-5433	226	15	(	(	PUNCT
ejpam-5433	226	16	x+bx	x+bx	X
ejpam-5433	226	17	)	)	PUNCT
ejpam-5433	227	1	+	+	CCONJ
ejpam-5433	227	2	u2α	u2α	ADJ
ejpam-5433	227	3	⊗ax	⊗ax	PUNCT
ejpam-5433	227	4	=	=	PUNCT
ejpam-5433	227	5	h⊗	h⊗	PROPN
ejpam-5433	227	6	z.	z.	PROPN
ejpam-5433	227	7	(	(	PUNCT
ejpam-5433	227	8	15	15	NUM
ejpam-5433	227	9	)	)	PUNCT
ejpam-5433	227	10	so	so	SCONJ
ejpam-5433	227	11	we	we	PRON
ejpam-5433	227	12	have	have	VERB
ejpam-5433	227	13	two	two	NUM
ejpam-5433	227	14	cases	case	NOUN
ejpam-5433	227	15	:	:	PUNCT
ejpam-5433	227	16	(	(	PUNCT
ejpam-5433	227	17	a	a	X
ejpam-5433	227	18	)	)	PUNCT
ejpam-5433	227	19	u3α(t	u3α(t	PROPN
ejpam-5433	227	20	)	)	PUNCT
ejpam-5433	227	21	=	=	SYM
ejpam-5433	227	22	u2α(t	u2α(t	NOUN
ejpam-5433	227	23	)	)	PUNCT
ejpam-5433	227	24	=	=	SYM
ejpam-5433	227	25	h	h	NOUN
ejpam-5433	227	26	=	=	PUNCT
ejpam-5433	227	27	uα	uα	PROPN
ejpam-5433	227	28	.	.	PUNCT
ejpam-5433	228	1	(	(	PUNCT
ejpam-5433	228	2	b	b	X
ejpam-5433	228	3	)	)	PUNCT
ejpam-5433	228	4	x+bx	x+bx	PUNCT
ejpam-5433	229	1	=	=	NOUN
ejpam-5433	229	2	ax	ax	NOUN
ejpam-5433	229	3	=	=	PUNCT
ejpam-5433	229	4	z.	z.	PROPN
ejpam-5433	229	5	in	in	ADP
ejpam-5433	229	6	case	case	NOUN
ejpam-5433	229	7	(	(	PUNCT
ejpam-5433	229	8	a	a	X
ejpam-5433	229	9	)	)	PUNCT
ejpam-5433	229	10	we	we	PRON
ejpam-5433	229	11	have	have	VERB
ejpam-5433	229	12	three	three	NUM
ejpam-5433	229	13	cases	case	NOUN
ejpam-5433	229	14	:	:	PUNCT
ejpam-5433	229	15	(	(	PUNCT
ejpam-5433	229	16	i	i	NOUN
ejpam-5433	229	17	)	)	PUNCT
ejpam-5433	229	18	u3α	u3α	ADV
ejpam-5433	229	19	−	−	NOUN
ejpam-5433	229	20	u2α	u2α	NOUN
ejpam-5433	229	21	=	=	PUNCT
ejpam-5433	229	22	0	0	X
ejpam-5433	229	23	.	.	PUNCT
ejpam-5433	230	1	this	this	DET
ejpam-5433	230	2	case	case	NOUN
ejpam-5433	230	3	can	can	AUX
ejpam-5433	230	4	be	be	AUX
ejpam-5433	230	5	solved	solve	VERB
ejpam-5433	230	6	as	as	ADP
ejpam-5433	230	7	in	in	ADP
ejpam-5433	230	8	[	[	X
ejpam-5433	230	9	3	3	NUM
ejpam-5433	230	10	]	]	SYM
ejpam-5433	230	11	:	:	PUNCT
ejpam-5433	230	12	r3	r3	PROPN
ejpam-5433	230	13	−	−	PROPN
ejpam-5433	230	14	r2	r2	NOUN
ejpam-5433	230	15	=	=	PUNCT
ejpam-5433	231	1	r2(r	r2(r	VERB
ejpam-5433	231	2	−	−	NOUN
ejpam-5433	231	3	1	1	NUM
ejpam-5433	231	4	)	)	PUNCT
ejpam-5433	231	5	=	=	SYM
ejpam-5433	232	1	0	0	NUM
ejpam-5433	232	2	,	,	PUNCT
ejpam-5433	232	3	which	which	PRON
ejpam-5433	232	4	gives	give	VERB
ejpam-5433	232	5	r1	r1	PROPN
ejpam-5433	232	6	=	=	SYM
ejpam-5433	232	7	0	0	NUM
ejpam-5433	232	8	,	,	PUNCT
ejpam-5433	232	9	r2	r2	PROPN
ejpam-5433	232	10	=	=	SYM
ejpam-5433	232	11	0	0	NUM
ejpam-5433	232	12	,	,	PUNCT
ejpam-5433	232	13	and	and	CCONJ
ejpam-5433	232	14	r3	r3	PROPN
ejpam-5433	232	15	=	=	SYM
ejpam-5433	232	16	1	1	X
ejpam-5433	232	17	.	.	PUNCT
ejpam-5433	233	1	consequently	consequently	ADV
ejpam-5433	233	2	,	,	PUNCT
ejpam-5433	233	3	u(t	u(t	PROPN
ejpam-5433	233	4	)	)	PUNCT
ejpam-5433	233	5	=	=	SYM
ejpam-5433	233	6	c1	c1	PROPN
ejpam-5433	233	7	+	+	CCONJ
ejpam-5433	233	8	c2	c2	PROPN
ejpam-5433	233	9	tα	tα	VERB
ejpam-5433	233	10	α	α	PROPN
ejpam-5433	234	1	+	+	CCONJ
ejpam-5433	234	2	c3e	c3e	PROPN
ejpam-5433	234	3	tα	tα	NUM
ejpam-5433	234	4	α	α	PROPN
ejpam-5433	234	5	.	.	PUNCT
ejpam-5433	235	1	hence	hence	ADV
ejpam-5433	235	2	,	,	PUNCT
ejpam-5433	235	3	by	by	ADP
ejpam-5433	235	4	the	the	DET
ejpam-5433	235	5	assumption	assumption	NOUN
ejpam-5433	235	6	(	(	PUNCT
ejpam-5433	235	7	4	4	NUM
ejpam-5433	235	8	)	)	PUNCT
ejpam-5433	235	9	,	,	PUNCT
ejpam-5433	235	10	we	we	PRON
ejpam-5433	235	11	have	have	VERB
ejpam-5433	235	12	c1	c1	PROPN
ejpam-5433	235	13	=	=	PROPN
ejpam-5433	235	14	x0	x0	PROPN
ejpam-5433	235	15	,	,	PUNCT
ejpam-5433	235	16	c2	c2	PROPN
ejpam-5433	235	17	=	=	SYM
ejpam-5433	235	18	0	0	PROPN
ejpam-5433	235	19	,	,	PUNCT
ejpam-5433	235	20	c3	c3	X
ejpam-5433	235	21	=	=	PUNCT
ejpam-5433	235	22	x0	x0	PROPN
ejpam-5433	235	23	.	.	PUNCT
ejpam-5433	236	1	hence	hence	ADV
ejpam-5433	236	2	,	,	PUNCT
ejpam-5433	236	3	u(t	u(t	PROPN
ejpam-5433	236	4	)	)	PUNCT
ejpam-5433	236	5	=	=	PUNCT
ejpam-5433	237	1	x0	x0	PROPN
ejpam-5433	238	1	+	+	CCONJ
ejpam-5433	238	2	x0e	x0e	PUNCT
ejpam-5433	238	3	tα	tα	PROPN
ejpam-5433	238	4	α	α	PROPN
ejpam-5433	238	5	.	.	PUNCT
ejpam-5433	239	1	(	(	PUNCT
ejpam-5433	239	2	16	16	NUM
ejpam-5433	239	3	)	)	PUNCT
ejpam-5433	239	4	(	(	PUNCT
ejpam-5433	239	5	ii	ii	NOUN
ejpam-5433	239	6	)	)	PUNCT
ejpam-5433	239	7	u2α	u2α	NOUN
ejpam-5433	239	8	=	=	PUNCT
ejpam-5433	239	9	h.	h.	PROPN
ejpam-5433	239	10	from	from	ADP
ejpam-5433	239	11	(	(	PUNCT
ejpam-5433	239	12	16	16	NUM
ejpam-5433	239	13	)	)	PUNCT
ejpam-5433	239	14	,	,	PUNCT
ejpam-5433	239	15	we	we	PRON
ejpam-5433	239	16	get	get	VERB
ejpam-5433	239	17	h	h	NOUN
ejpam-5433	240	1	=	=	PUNCT
ejpam-5433	240	2	x0e	x0e	PROPN
ejpam-5433	240	3	tα	tα	PROPN
ejpam-5433	240	4	α	α	INTJ
ejpam-5433	240	5	.	.	PUNCT
ejpam-5433	241	1	so	so	ADV
ejpam-5433	241	2	for	for	SCONJ
ejpam-5433	241	3	an	an	DET
ejpam-5433	241	4	atomic	atomic	ADJ
ejpam-5433	241	5	solution	solution	NOUN
ejpam-5433	241	6	to	to	PART
ejpam-5433	241	7	exist	exist	VERB
ejpam-5433	241	8	h	h	NOUN
ejpam-5433	241	9	must	must	AUX
ejpam-5433	241	10	=	=	VERB
ejpam-5433	241	11	x0e	x0e	PROPN
ejpam-5433	241	12	tα	tα	PROPN
ejpam-5433	241	13	α	α	INTJ
ejpam-5433	241	14	.	.	PUNCT
ejpam-5433	242	1	(	(	PUNCT
ejpam-5433	242	2	iii	iii	X
ejpam-5433	242	3	)	)	PUNCT
ejpam-5433	242	4	u3α	u3α	PROPN
ejpam-5433	242	5	=	=	PROPN
ejpam-5433	242	6	h.	h.	PROPN
ejpam-5433	242	7	r.	r.	PROPN
ejpam-5433	242	8	alkhateeb	alkhateeb	PROPN
ejpam-5433	242	9	,	,	PUNCT
ejpam-5433	242	10	g.	g.	PROPN
ejpam-5433	242	11	awwad	awwad	PROPN
ejpam-5433	242	12	/	/	PUNCT
ejpam-5433	242	13	eur	eur	PROPN
ejpam-5433	242	14	.	.	PUNCT
ejpam-5433	243	1	j.	j.	PROPN
ejpam-5433	243	2	pure	pure	PROPN
ejpam-5433	243	3	appl	appl	PROPN
ejpam-5433	243	4	.	.	PROPN
ejpam-5433	243	5	math	math	PROPN
ejpam-5433	243	6	,	,	PUNCT
ejpam-5433	243	7	17	17	NUM
ejpam-5433	243	8	(	(	PUNCT
ejpam-5433	243	9	4	4	NUM
ejpam-5433	243	10	)	)	PUNCT
ejpam-5433	243	11	(	(	PUNCT
ejpam-5433	243	12	2024	2024	NUM
ejpam-5433	243	13	)	)	PUNCT
ejpam-5433	243	14	,	,	PUNCT
ejpam-5433	243	15	3061	3061	NUM
ejpam-5433	243	16	-	-	SYM
ejpam-5433	243	17	3078	3078	NUM
ejpam-5433	243	18	3070	3070	NUM
ejpam-5433	243	19	from	from	ADP
ejpam-5433	243	20	(	(	PUNCT
ejpam-5433	243	21	16	16	NUM
ejpam-5433	243	22	)	)	PUNCT
ejpam-5433	243	23	,	,	PUNCT
ejpam-5433	243	24	we	we	PRON
ejpam-5433	243	25	get	get	VERB
ejpam-5433	243	26	h	h	NOUN
ejpam-5433	243	27	=	=	PUNCT
ejpam-5433	243	28	x0e	x0e	PROPN
ejpam-5433	244	1	tα	tα	PROPN
ejpam-5433	244	2	α	α	PROPN
ejpam-5433	244	3	.	.	PUNCT
ejpam-5433	245	1	since	since	SCONJ
ejpam-5433	245	2	u3α	u3α	NOUN
ejpam-5433	245	3	=	=	PUNCT
ejpam-5433	245	4	u2α	u2α	NOUN
ejpam-5433	245	5	=	=	PUNCT
ejpam-5433	245	6	uα	uα	NOUN
ejpam-5433	245	7	=	=	PUNCT
ejpam-5433	245	8	h	h	NOUN
ejpam-5433	246	1	=	=	PUNCT
ejpam-5433	246	2	x0e	x0e	PROPN
ejpam-5433	246	3	tα	tα	PROPN
ejpam-5433	246	4	α	α	PROPN
ejpam-5433	246	5	in	in	ADP
ejpam-5433	246	6	(	(	PUNCT
ejpam-5433	246	7	ii	ii	NOUN
ejpam-5433	246	8	)	)	PUNCT
ejpam-5433	246	9	and	and	CCONJ
ejpam-5433	246	10	(	(	PUNCT
ejpam-5433	246	11	iii	iii	NOUN
ejpam-5433	246	12	)	)	PUNCT
ejpam-5433	246	13	.	.	PUNCT
ejpam-5433	247	1	consequently	consequently	ADV
ejpam-5433	247	2	,	,	PUNCT
ejpam-5433	247	3	x+bx+ax	x+bx+ax	PROPN
ejpam-5433	247	4	=	=	PROPN
ejpam-5433	247	5	z.	z.	PROPN
ejpam-5433	248	1	so	so	ADV
ejpam-5433	248	2	(	(	PUNCT
ejpam-5433	248	3	i+b+a)x	i+b+a)x	X
ejpam-5433	248	4	=	=	SYM
ejpam-5433	248	5	z	z	NOUN
ejpam-5433	248	6	which	which	PRON
ejpam-5433	248	7	mean	mean	VERB
ejpam-5433	248	8	z	z	NOUN
ejpam-5433	248	9	will	will	AUX
ejpam-5433	248	10	be	be	AUX
ejpam-5433	248	11	in	in	ADP
ejpam-5433	248	12	the	the	DET
ejpam-5433	248	13	intersection	intersection	NOUN
ejpam-5433	248	14	of	of	ADP
ejpam-5433	248	15	the	the	DET
ejpam-5433	248	16	ranges	range	NOUN
ejpam-5433	248	17	of	of	ADP
ejpam-5433	248	18	(	(	PUNCT
ejpam-5433	248	19	i	i	PROPN
ejpam-5433	248	20	+	+	PROPN
ejpam-5433	248	21	b	b	X
ejpam-5433	248	22	+	+	NOUN
ejpam-5433	248	23	a	a	NOUN
ejpam-5433	248	24	)	)	PUNCT
ejpam-5433	248	25	.	.	PUNCT
ejpam-5433	249	1	hence	hence	ADV
ejpam-5433	249	2	,	,	PUNCT
ejpam-5433	249	3	there	there	PRON
ejpam-5433	249	4	is	be	VERB
ejpam-5433	249	5	an	an	DET
ejpam-5433	249	6	atomic	atomic	ADJ
ejpam-5433	249	7	solution	solution	NOUN
ejpam-5433	249	8	in	in	ADP
ejpam-5433	249	9	situation	situation	NOUN
ejpam-5433	249	10	(	(	PUNCT
ejpam-5433	249	11	1	1	NUM
ejpam-5433	249	12	)	)	PUNCT
ejpam-5433	249	13	.	.	PUNCT
ejpam-5433	250	1	now	now	ADV
ejpam-5433	250	2	,	,	PUNCT
ejpam-5433	250	3	in	in	ADP
ejpam-5433	250	4	case	case	NOUN
ejpam-5433	250	5	(	(	PUNCT
ejpam-5433	250	6	b	b	X
ejpam-5433	250	7	)	)	PUNCT
ejpam-5433	250	8	x	x	PUNCT
ejpam-5433	251	1	+	+	NUM
ejpam-5433	251	2	bx	bx	NOUN
ejpam-5433	251	3	=	=	NOUN
ejpam-5433	251	4	ax	ax	NOUN
ejpam-5433	251	5	=	=	PUNCT
ejpam-5433	251	6	z.	z.	PROPN
ejpam-5433	251	7	hence	hence	ADV
ejpam-5433	251	8	,	,	PUNCT
ejpam-5433	251	9	x	x	PUNCT
ejpam-5433	251	10	+	+	NUM
ejpam-5433	251	11	bx	bx	NOUN
ejpam-5433	251	12	=	=	NOUN
ejpam-5433	251	13	ax	ax	NOUN
ejpam-5433	251	14	,	,	PUNCT
ejpam-5433	251	15	x	x	PROPN
ejpam-5433	251	16	+	+	NUM
ejpam-5433	251	17	bx	bx	X
ejpam-5433	251	18	=	=	SYM
ejpam-5433	251	19	z	z	PROPN
ejpam-5433	251	20	,	,	PUNCT
ejpam-5433	251	21	and	and	CCONJ
ejpam-5433	251	22	ax	ax	NOUN
ejpam-5433	251	23	=	=	PUNCT
ejpam-5433	251	24	z.	z.	PROPN
ejpam-5433	252	1	so	so	ADV
ejpam-5433	252	2	,	,	PUNCT
ejpam-5433	252	3	equation	equation	NOUN
ejpam-5433	252	4	(	(	PUNCT
ejpam-5433	252	5	5	5	NUM
ejpam-5433	252	6	)	)	PUNCT
ejpam-5433	252	7	becomes	become	VERB
ejpam-5433	252	8	u3α	u3α	PROPN
ejpam-5433	252	9	⊗	⊗	PROPN
ejpam-5433	252	10	(	(	PUNCT
ejpam-5433	252	11	x+bx	x+bx	X
ejpam-5433	252	12	)	)	PUNCT
ejpam-5433	253	1	+	+	CCONJ
ejpam-5433	253	2	u2α	u2α	ADJ
ejpam-5433	253	3	⊗ax	⊗ax	PUNCT
ejpam-5433	253	4	=	=	PUNCT
ejpam-5433	253	5	h⊗	h⊗	PROPN
ejpam-5433	253	6	z.	z.	PROPN
ejpam-5433	253	7	(	(	PUNCT
ejpam-5433	253	8	17	17	NUM
ejpam-5433	253	9	)	)	PUNCT
ejpam-5433	253	10	substitute	substitute	NOUN
ejpam-5433	253	11	the	the	DET
ejpam-5433	253	12	equation	equation	NOUN
ejpam-5433	253	13	(	(	PUNCT
ejpam-5433	253	14	17	17	NUM
ejpam-5433	253	15	)	)	PUNCT
ejpam-5433	253	16	in	in	ADP
ejpam-5433	253	17	the	the	DET
ejpam-5433	253	18	equation	equation	NOUN
ejpam-5433	253	19	(	(	PUNCT
ejpam-5433	253	20	15	15	NUM
ejpam-5433	253	21	)	)	PUNCT
ejpam-5433	253	22	,	,	PUNCT
ejpam-5433	253	23	we	we	PRON
ejpam-5433	253	24	get	get	VERB
ejpam-5433	253	25	(	(	PUNCT
ejpam-5433	253	26	u3α	u3α	X
ejpam-5433	253	27	+	+	CCONJ
ejpam-5433	253	28	u2α	u2α	ADJ
ejpam-5433	253	29	)	)	PUNCT
ejpam-5433	253	30	⊗ax	⊗ax	PUNCT
ejpam-5433	254	1	=	=	NOUN
ejpam-5433	254	2	h⊗	h⊗	VERB
ejpam-5433	254	3	z.	z.	PROPN
ejpam-5433	254	4	hence	hence	PROPN
ejpam-5433	254	5	,	,	PUNCT
ejpam-5433	254	6	u3α	u3α	X
ejpam-5433	254	7	+	+	CCONJ
ejpam-5433	254	8	u2α	u2α	NOUN
ejpam-5433	254	9	=	=	SYM
ejpam-5433	254	10	h.	h.	NOUN
ejpam-5433	254	11	(	(	PUNCT
ejpam-5433	254	12	18	18	NUM
ejpam-5433	254	13	)	)	PUNCT
ejpam-5433	254	14	this	this	PRON
ejpam-5433	254	15	is	be	AUX
ejpam-5433	254	16	third	third	ADJ
ejpam-5433	254	17	order	order	NOUN
ejpam-5433	254	18	homogenous	homogenous	ADJ
ejpam-5433	254	19	linear	linear	ADJ
ejpam-5433	254	20	fractional	fractional	ADJ
ejpam-5433	254	21	differential	differential	NOUN
ejpam-5433	254	22	equation	equation	NOUN
ejpam-5433	254	23	,	,	PUNCT
ejpam-5433	254	24	to	to	PART
ejpam-5433	254	25	solve	solve	VERB
ejpam-5433	254	26	it	it	PRON
ejpam-5433	254	27	we	we	PRON
ejpam-5433	254	28	follow	follow	VERB
ejpam-5433	254	29	the	the	DET
ejpam-5433	254	30	variation	variation	NOUN
ejpam-5433	254	31	of	of	ADP
ejpam-5433	254	32	parameters	parameter	NOUN
ejpam-5433	254	33	method	method	VERB
ejpam-5433	254	34	.	.	PUNCT
ejpam-5433	255	1	the	the	DET
ejpam-5433	255	2	homogenous	homogenous	ADJ
ejpam-5433	255	3	part	part	NOUN
ejpam-5433	255	4	can	can	AUX
ejpam-5433	255	5	solved	solve	VERB
ejpam-5433	255	6	as	as	ADP
ejpam-5433	255	7	in	in	ADP
ejpam-5433	255	8	[	[	X
ejpam-5433	255	9	3	3	NUM
ejpam-5433	255	10	]	]	PUNCT
ejpam-5433	255	11	as	as	SCONJ
ejpam-5433	255	12	follows	follow	VERB
ejpam-5433	255	13	:	:	PUNCT
ejpam-5433	255	14	r3	r3	NOUN
ejpam-5433	255	15	+	+	CCONJ
ejpam-5433	255	16	r2	r2	PROPN
ejpam-5433	255	17	=	=	SYM
ejpam-5433	255	18	0	0	NUM
ejpam-5433	255	19	,	,	PUNCT
ejpam-5433	255	20	which	which	PRON
ejpam-5433	255	21	gives	give	VERB
ejpam-5433	255	22	r1	r1	PROPN
ejpam-5433	255	23	=	=	SYM
ejpam-5433	255	24	0	0	NUM
ejpam-5433	255	25	,	,	PUNCT
ejpam-5433	255	26	r2	r2	PROPN
ejpam-5433	255	27	=	=	SYM
ejpam-5433	255	28	0	0	NUM
ejpam-5433	255	29	,	,	PUNCT
ejpam-5433	255	30	and	and	CCONJ
ejpam-5433	255	31	r3	r3	PROPN
ejpam-5433	255	32	=	=	SYM
ejpam-5433	255	33	−1	−1	NOUN
ejpam-5433	255	34	.	.	PUNCT
ejpam-5433	256	1	hence	hence	ADV
ejpam-5433	256	2	,	,	PUNCT
ejpam-5433	256	3	uh(t	uh(t	ADV
ejpam-5433	256	4	)	)	PUNCT
ejpam-5433	257	1	=	=	SYM
ejpam-5433	257	2	c1	c1	PROPN
ejpam-5433	257	3	+	+	CCONJ
ejpam-5433	257	4	c2	c2	PROPN
ejpam-5433	257	5	tα	tα	VERB
ejpam-5433	257	6	α	α	PROPN
ejpam-5433	257	7	+	+	CCONJ
ejpam-5433	258	1	c3e	c3e	PROPN
ejpam-5433	259	1	−	−	PROPN
ejpam-5433	260	1	(	(	PUNCT
ejpam-5433	260	2	t	t	PROPN
ejpam-5433	260	3	α	α	PROPN
ejpam-5433	260	4	α	α	PROPN
ejpam-5433	260	5	)	)	PUNCT
ejpam-5433	260	6	.	.	PUNCT
ejpam-5433	261	1	(	(	PUNCT
ejpam-5433	261	2	19	19	NUM
ejpam-5433	261	3	)	)	PUNCT
ejpam-5433	261	4	so	so	ADV
ejpam-5433	261	5	by	by	ADP
ejpam-5433	261	6	the	the	DET
ejpam-5433	261	7	assumption	assumption	NOUN
ejpam-5433	261	8	(	(	PUNCT
ejpam-5433	261	9	4	4	NUM
ejpam-5433	261	10	)	)	PUNCT
ejpam-5433	261	11	,	,	PUNCT
ejpam-5433	261	12	we	we	PRON
ejpam-5433	261	13	have	have	VERB
ejpam-5433	261	14	c1	c1	PROPN
ejpam-5433	261	15	=	=	PUNCT
ejpam-5433	261	16	x0	x0	PROPN
ejpam-5433	261	17	,	,	PUNCT
ejpam-5433	261	18	c2	c2	PROPN
ejpam-5433	261	19	=	=	PUNCT
ejpam-5433	261	20	2x0	2x0	PROPN
ejpam-5433	261	21	,	,	PUNCT
ejpam-5433	261	22	c3	c3	X
ejpam-5433	261	23	=	=	PUNCT
ejpam-5433	261	24	x0	x0	PROPN
ejpam-5433	261	25	.	.	PUNCT
ejpam-5433	262	1	hence	hence	ADV
ejpam-5433	262	2	,	,	PUNCT
ejpam-5433	262	3	(	(	PUNCT
ejpam-5433	262	4	19	19	NUM
ejpam-5433	262	5	)	)	PUNCT
ejpam-5433	262	6	becomes	become	VERB
ejpam-5433	262	7	uh(t	uh(t	NOUN
ejpam-5433	262	8	)	)	PUNCT
ejpam-5433	262	9	=	=	PUNCT
ejpam-5433	263	1	x0	x0	PROPN
ejpam-5433	263	2	+	+	CCONJ
ejpam-5433	263	3	2x0	2x0	NUM
ejpam-5433	263	4	tα	tα	ADP
ejpam-5433	263	5	α	α	NOUN
ejpam-5433	264	1	+	+	NOUN
ejpam-5433	264	2	x0e	x0e	PUNCT
ejpam-5433	264	3	−	−	PROPN
ejpam-5433	264	4	(	(	PUNCT
ejpam-5433	264	5	t	t	PROPN
ejpam-5433	264	6	α	α	PROPN
ejpam-5433	264	7	α	α	PROPN
ejpam-5433	264	8	)	)	PUNCT
ejpam-5433	264	9	.	.	PUNCT
ejpam-5433	265	1	for	for	ADP
ejpam-5433	265	2	the	the	DET
ejpam-5433	265	3	particular	particular	ADJ
ejpam-5433	265	4	part	part	NOUN
ejpam-5433	265	5	we	we	PRON
ejpam-5433	265	6	use	use	VERB
ejpam-5433	265	7	variation	variation	NOUN
ejpam-5433	265	8	of	of	ADP
ejpam-5433	265	9	parameters	parameter	NOUN
ejpam-5433	265	10	introduced	introduce	VERB
ejpam-5433	265	11	in	in	ADP
ejpam-5433	265	12	[	[	X
ejpam-5433	265	13	2	2	NUM
ejpam-5433	265	14	]	]	PUNCT
ejpam-5433	265	15	.	.	PUNCT
ejpam-5433	266	1	thus	thus	ADV
ejpam-5433	266	2	,	,	PUNCT
ejpam-5433	266	3	by	by	ADP
ejpam-5433	266	4	using	use	VERB
ejpam-5433	266	5	(	(	PUNCT
ejpam-5433	266	6	8)	8)	NUM
ejpam-5433	266	7	,	,	PUNCT
ejpam-5433	266	8	the	the	DET
ejpam-5433	266	9	wronskian	wronskian	NOUN
ejpam-5433	266	10	will	will	AUX
ejpam-5433	266	11	given	give	VERB
ejpam-5433	266	12	by	by	ADP
ejpam-5433	266	13	:	:	PUNCT
ejpam-5433	266	14	r.	r.	PROPN
ejpam-5433	266	15	alkhateeb	alkhateeb	PROPN
ejpam-5433	266	16	,	,	PUNCT
ejpam-5433	266	17	g.	g.	PROPN
ejpam-5433	266	18	awwad	awwad	PROPN
ejpam-5433	266	19	/	/	PUNCT
ejpam-5433	266	20	eur	eur	PROPN
ejpam-5433	266	21	.	.	PUNCT
ejpam-5433	267	1	j.	j.	PROPN
ejpam-5433	267	2	pure	pure	PROPN
ejpam-5433	267	3	appl	appl	PROPN
ejpam-5433	267	4	.	.	PROPN
ejpam-5433	267	5	math	math	PROPN
ejpam-5433	267	6	,	,	PUNCT
ejpam-5433	267	7	17	17	NUM
ejpam-5433	267	8	(	(	PUNCT
ejpam-5433	267	9	4	4	NUM
ejpam-5433	267	10	)	)	PUNCT
ejpam-5433	267	11	(	(	PUNCT
ejpam-5433	267	12	2024	2024	NUM
ejpam-5433	267	13	)	)	PUNCT
ejpam-5433	267	14	,	,	PUNCT
ejpam-5433	267	15	3061	3061	NUM
ejpam-5433	267	16	-	-	SYM
ejpam-5433	267	17	3078	3078	NUM
ejpam-5433	267	18	3071	3071	NUM
ejpam-5433	267	19	wα	wα	NOUN
ejpam-5433	267	20	=	=	SYM
ejpam-5433	267	21	∣∣∣∣∣∣∣	∣∣∣∣∣∣∣	NOUN
ejpam-5433	267	22	x0	x0	PROPN
ejpam-5433	267	23	2x0	2x0	NUM
ejpam-5433	267	24	tα	tα	VERB
ejpam-5433	267	25	α	α	NOUN
ejpam-5433	267	26	x0e	x0e	PUNCT
ejpam-5433	268	1	−	−	PROPN
ejpam-5433	268	2	(	(	PUNCT
ejpam-5433	268	3	t	t	PROPN
ejpam-5433	268	4	α	α	PROPN
ejpam-5433	268	5	α	α	NOUN
ejpam-5433	268	6	)	)	PUNCT
ejpam-5433	268	7	0	0	NUM
ejpam-5433	269	1	2	2	NUM
ejpam-5433	269	2	−x0e	−x0e	NUM
ejpam-5433	269	3	−	−	PROPN
ejpam-5433	269	4	(	(	PUNCT
ejpam-5433	269	5	t	t	PROPN
ejpam-5433	269	6	α	α	PROPN
ejpam-5433	269	7	α	α	NOUN
ejpam-5433	269	8	)	)	PUNCT
ejpam-5433	269	9	0	0	NUM
ejpam-5433	269	10	0	0	NUM
ejpam-5433	270	1	x0e	x0e	PUNCT
ejpam-5433	271	1	−	−	PROPN
ejpam-5433	271	2	(	(	PUNCT
ejpam-5433	271	3	t	t	PROPN
ejpam-5433	271	4	α	α	PROPN
ejpam-5433	271	5	α	α	NOUN
ejpam-5433	271	6	)	)	PUNCT
ejpam-5433	271	7	∣∣∣∣∣∣∣	∣∣∣∣∣∣∣	PUNCT
ejpam-5433	271	8	=	=	PUNCT
ejpam-5433	272	1	2x0e	2x0e	NUM
ejpam-5433	273	1	−	−	PROPN
ejpam-5433	273	2	(	(	PUNCT
ejpam-5433	273	3	t	t	PROPN
ejpam-5433	273	4	α	α	PROPN
ejpam-5433	273	5	α	α	PROPN
ejpam-5433	273	6	)	)	PUNCT
ejpam-5433	273	7	.	.	PUNCT
ejpam-5433	274	1	so	so	ADV
ejpam-5433	274	2	,	,	PUNCT
ejpam-5433	274	3	we	we	PRON
ejpam-5433	274	4	have	have	VERB
ejpam-5433	274	5	wα	wα	NOUN
ejpam-5433	274	6	1	1	NUM
ejpam-5433	274	7	=	=	SYM
ejpam-5433	274	8	∣∣∣∣∣∣∣	∣∣∣∣∣∣∣	NOUN
ejpam-5433	274	9	0	0	NUM
ejpam-5433	274	10	2x0	2x0	NUM
ejpam-5433	274	11	tα	tα	VERB
ejpam-5433	274	12	α	α	NOUN
ejpam-5433	274	13	x0e	x0e	PUNCT
ejpam-5433	275	1	−	−	PROPN
ejpam-5433	275	2	(	(	PUNCT
ejpam-5433	275	3	t	t	PROPN
ejpam-5433	275	4	α	α	PROPN
ejpam-5433	275	5	α	α	NOUN
ejpam-5433	275	6	)	)	PUNCT
ejpam-5433	275	7	0	0	NUM
ejpam-5433	275	8	2x0	2x0	NUM
ejpam-5433	275	9	−x0e	−x0e	NUM
ejpam-5433	276	1	−	−	PROPN
ejpam-5433	276	2	(	(	PUNCT
ejpam-5433	276	3	t	t	PROPN
ejpam-5433	276	4	α	α	PROPN
ejpam-5433	276	5	α	α	NOUN
ejpam-5433	276	6	)	)	PUNCT
ejpam-5433	276	7	1	1	NUM
ejpam-5433	276	8	0	0	NUM
ejpam-5433	276	9	x0e	x0e	SYM
ejpam-5433	277	1	−	−	PROPN
ejpam-5433	277	2	(	(	PUNCT
ejpam-5433	277	3	t	t	PROPN
ejpam-5433	277	4	α	α	PROPN
ejpam-5433	277	5	α	α	NOUN
ejpam-5433	277	6	)	)	PUNCT
ejpam-5433	277	7	∣∣∣∣∣∣∣	∣∣∣∣∣∣∣	PUNCT
ejpam-5433	278	1	=	=	PUNCT
ejpam-5433	278	2	−2x0e	−2x0e	PROPN
ejpam-5433	278	3	−	−	PROPN
ejpam-5433	278	4	(	(	PUNCT
ejpam-5433	278	5	t	t	PROPN
ejpam-5433	278	6	α	α	PROPN
ejpam-5433	278	7	α	α	NOUN
ejpam-5433	278	8	)	)	PUNCT
ejpam-5433	278	9	(	(	PUNCT
ejpam-5433	278	10	tα	tα	PROPN
ejpam-5433	278	11	α	α	PROPN
ejpam-5433	278	12	+	+	NOUN
ejpam-5433	278	13	1	1	NUM
ejpam-5433	278	14	)	)	PUNCT
ejpam-5433	278	15	,	,	PUNCT
ejpam-5433	278	16	wα	wα	NOUN
ejpam-5433	278	17	2	2	NUM
ejpam-5433	278	18	=	=	SYM
ejpam-5433	278	19	∣∣∣∣∣∣∣	∣∣∣∣∣∣∣	NOUN
ejpam-5433	278	20	x0	x0	PROPN
ejpam-5433	278	21	0	0	PUNCT
ejpam-5433	279	1	x0e	x0e	PUNCT
ejpam-5433	280	1	−	−	PROPN
ejpam-5433	280	2	(	(	PUNCT
ejpam-5433	280	3	t	t	PROPN
ejpam-5433	280	4	α	α	PROPN
ejpam-5433	280	5	α	α	NOUN
ejpam-5433	280	6	)	)	PUNCT
ejpam-5433	280	7	0	0	NUM
ejpam-5433	280	8	0	0	NUM
ejpam-5433	281	1	−x0e	−x0e	NUM
ejpam-5433	282	1	−	−	PROPN
ejpam-5433	282	2	(	(	PUNCT
ejpam-5433	282	3	t	t	PROPN
ejpam-5433	282	4	α	α	PROPN
ejpam-5433	282	5	α	α	NOUN
ejpam-5433	282	6	)	)	PUNCT
ejpam-5433	282	7	0	0	NUM
ejpam-5433	283	1	1	1	NUM
ejpam-5433	283	2	x0e	x0e	SYM
ejpam-5433	284	1	−	−	PROPN
ejpam-5433	284	2	(	(	PUNCT
ejpam-5433	284	3	t	t	PROPN
ejpam-5433	284	4	α	α	PROPN
ejpam-5433	284	5	α	α	NOUN
ejpam-5433	284	6	)	)	PUNCT
ejpam-5433	284	7	∣∣∣∣∣∣∣	∣∣∣∣∣∣∣	PUNCT
ejpam-5433	285	1	=	=	PUNCT
ejpam-5433	286	1	x0e	x0e	PUNCT
ejpam-5433	287	1	−	−	PROPN
ejpam-5433	287	2	(	(	PUNCT
ejpam-5433	287	3	t	t	PROPN
ejpam-5433	287	4	α	α	PROPN
ejpam-5433	287	5	α	α	PROPN
ejpam-5433	287	6	)	)	PUNCT
ejpam-5433	287	7	,	,	PUNCT
ejpam-5433	287	8	and	and	CCONJ
ejpam-5433	287	9	wα	wα	NOUN
ejpam-5433	287	10	3	3	NUM
ejpam-5433	287	11	=	=	SYM
ejpam-5433	287	12	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ejpam-5433	287	13	x0	x0	PROPN
ejpam-5433	287	14	2x0	2x0	NUM
ejpam-5433	287	15	xtα	xtα	NOUN
ejpam-5433	287	16	α	α	NOUN
ejpam-5433	287	17	0	0	NUM
ejpam-5433	287	18	0	0	NUM
ejpam-5433	287	19	2x0	2x0	NUM
ejpam-5433	287	20	0	0	NUM
ejpam-5433	287	21	0	0	NUM
ejpam-5433	287	22	0	0	NUM
ejpam-5433	287	23	1	1	NUM
ejpam-5433	287	24	∣∣∣∣∣∣	∣∣∣∣∣∣	ADJ
ejpam-5433	287	25	=	=	ADJ
ejpam-5433	287	26	2	2	X
ejpam-5433	287	27	.	.	PUNCT
ejpam-5433	288	1	so	so	ADV
ejpam-5433	288	2	,	,	PUNCT
ejpam-5433	288	3	uα1	uα1	PROPN
ejpam-5433	288	4	(	(	PUNCT
ejpam-5433	288	5	t	t	NOUN
ejpam-5433	288	6	)	)	PUNCT
ejpam-5433	288	7	=	=	SYM
ejpam-5433	288	8	wα	wα	NOUN
ejpam-5433	288	9	1	1	NUM
ejpam-5433	288	10	wα	wα	NOUN
ejpam-5433	288	11	=	=	NOUN
ejpam-5433	288	12	−2x0e	−2x0e	PROPN
ejpam-5433	289	1	−	−	PROPN
ejpam-5433	289	2	(	(	PUNCT
ejpam-5433	289	3	t	t	PROPN
ejpam-5433	289	4	α	α	PROPN
ejpam-5433	289	5	α	α	NOUN
ejpam-5433	289	6	)	)	PUNCT
ejpam-5433	289	7	(	(	PUNCT
ejpam-5433	289	8	tα	tα	PROPN
ejpam-5433	289	9	α	α	PROPN
ejpam-5433	289	10	+	+	NOUN
ejpam-5433	289	11	1	1	NUM
ejpam-5433	289	12	)	)	PUNCT
ejpam-5433	289	13	2x0e	2x0e	NOUN
ejpam-5433	290	1	−	−	PROPN
ejpam-5433	290	2	(	(	PUNCT
ejpam-5433	290	3	t	t	PROPN
ejpam-5433	290	4	α	α	PROPN
ejpam-5433	290	5	α	α	NOUN
ejpam-5433	290	6	)	)	PUNCT
ejpam-5433	291	1	=	=	SYM
ejpam-5433	291	2	−	−	PROPN
ejpam-5433	292	1	(	(	PUNCT
ejpam-5433	292	2	tα	tα	PROPN
ejpam-5433	292	3	α	α	PROPN
ejpam-5433	292	4	+	+	NOUN
ejpam-5433	292	5	1	1	NUM
ejpam-5433	292	6	)	)	PUNCT
ejpam-5433	292	7	,	,	PUNCT
ejpam-5433	292	8	uα2	uα2	ADV
ejpam-5433	292	9	(	(	PUNCT
ejpam-5433	292	10	t	t	NOUN
ejpam-5433	292	11	)	)	PUNCT
ejpam-5433	292	12	=	=	SYM
ejpam-5433	292	13	wα	wα	NOUN
ejpam-5433	292	14	2	2	NUM
ejpam-5433	292	15	wα	wα	NOUN
ejpam-5433	292	16	=	=	SYM
ejpam-5433	292	17	e−	e−	PROPN
ejpam-5433	292	18	(	(	PUNCT
ejpam-5433	292	19	t	t	PROPN
ejpam-5433	292	20	α	α	PROPN
ejpam-5433	292	21	α	α	NOUN
ejpam-5433	292	22	)	)	PUNCT
ejpam-5433	293	1	2e−	2e−	PROPN
ejpam-5433	293	2	(	(	PUNCT
ejpam-5433	293	3	t	t	PROPN
ejpam-5433	293	4	α	α	PROPN
ejpam-5433	293	5	α	α	NOUN
ejpam-5433	293	6	)	)	PUNCT
ejpam-5433	293	7	=	=	SYM
ejpam-5433	293	8	1	1	NUM
ejpam-5433	293	9	2	2	NUM
ejpam-5433	293	10	,	,	PUNCT
ejpam-5433	293	11	and	and	CCONJ
ejpam-5433	293	12	uα3	uα3	ADJ
ejpam-5433	293	13	(	(	PUNCT
ejpam-5433	293	14	t	t	NOUN
ejpam-5433	293	15	)	)	PUNCT
ejpam-5433	293	16	=	=	SYM
ejpam-5433	293	17	wα	wα	NOUN
ejpam-5433	293	18	3	3	NUM
ejpam-5433	293	19	wα	wα	NOUN
ejpam-5433	293	20	=	=	SYM
ejpam-5433	293	21	2x0	2x0	NUM
ejpam-5433	293	22	2x0e	2x0e	NOUN
ejpam-5433	294	1	−	−	PROPN
ejpam-5433	294	2	(	(	PUNCT
ejpam-5433	294	3	t	t	PROPN
ejpam-5433	294	4	α	α	PROPN
ejpam-5433	294	5	α	α	NOUN
ejpam-5433	294	6	)	)	PUNCT
ejpam-5433	295	1	=	=	PUNCT
ejpam-5433	295	2	e	e	X
ejpam-5433	295	3	(	(	PUNCT
ejpam-5433	295	4	tα	tα	PROPN
ejpam-5433	295	5	α	α	PROPN
ejpam-5433	295	6	)	)	PUNCT
ejpam-5433	295	7	.	.	PUNCT
ejpam-5433	296	1	consequently	consequently	ADV
ejpam-5433	296	2	,	,	PUNCT
ejpam-5433	296	3	up	up	ADV
ejpam-5433	296	4	=	=	VERB
ejpam-5433	296	5	−x0	−x0	NOUN
ejpam-5433	296	6	t∫	t∫	PROPN
ejpam-5433	296	7	b	b	PROPN
ejpam-5433	296	8	h	h	NOUN
ejpam-5433	296	9	(	(	PUNCT
ejpam-5433	296	10	tα	tα	PROPN
ejpam-5433	296	11	α	α	NOUN
ejpam-5433	296	12	+	+	NOUN
ejpam-5433	296	13	1	1	X
ejpam-5433	296	14	)	)	PUNCT
ejpam-5433	296	15	dtα	dtα	NOUN
ejpam-5433	296	16	tα−1	tα−1	NOUN
ejpam-5433	296	17	+	+	CCONJ
ejpam-5433	296	18	2x0	2x0	NUM
ejpam-5433	296	19	tα	tα	ADP
ejpam-5433	296	20	α	α	PRON
ejpam-5433	296	21	t∫	t∫	PROPN
ejpam-5433	296	22	b	b	PROPN
ejpam-5433	296	23	h	h	NOUN
ejpam-5433	296	24	2	2	NUM
ejpam-5433	296	25	dtα	dtα	NOUN
ejpam-5433	296	26	tα−1	tα−1	NOUN
ejpam-5433	296	27	+	+	CCONJ
ejpam-5433	296	28	x0e	x0e	SYM
ejpam-5433	297	1	−	−	PROPN
ejpam-5433	297	2	(	(	PUNCT
ejpam-5433	297	3	t	t	PROPN
ejpam-5433	297	4	α	α	PROPN
ejpam-5433	297	5	α	α	NOUN
ejpam-5433	297	6	)	)	PUNCT
ejpam-5433	298	1	t∫	t∫	PROPN
ejpam-5433	298	2	b	b	NOUN
ejpam-5433	299	1	he	he	PRON
ejpam-5433	299	2	tα	tα	VERB
ejpam-5433	299	3	α	α	PRON
ejpam-5433	299	4	dtα	dtα	NOUN
ejpam-5433	299	5	tα−1	tα−1	NOUN
ejpam-5433	299	6	.	.	PUNCT
ejpam-5433	300	1	hence	hence	ADV
ejpam-5433	300	2	,	,	PUNCT
ejpam-5433	300	3	u(t	u(t	PROPN
ejpam-5433	300	4	)	)	PUNCT
ejpam-5433	300	5	=	=	PUNCT
ejpam-5433	301	1	uh	uh	INTJ
ejpam-5433	301	2	+	+	X
ejpam-5433	301	3	up	up	ADV
ejpam-5433	301	4	,	,	PUNCT
ejpam-5433	301	5	u(t	u(t	NOUN
ejpam-5433	301	6	)	)	PUNCT
ejpam-5433	301	7	=	=	PUNCT
ejpam-5433	302	1	x0	x0	PROPN
ejpam-5433	302	2	+	+	CCONJ
ejpam-5433	302	3	2x0	2x0	NUM
ejpam-5433	302	4	tα	tα	ADP
ejpam-5433	302	5	α	α	NOUN
ejpam-5433	303	1	+	+	NOUN
ejpam-5433	303	2	x0e	x0e	PUNCT
ejpam-5433	303	3	−	−	PROPN
ejpam-5433	303	4	(	(	PUNCT
ejpam-5433	303	5	t	t	PROPN
ejpam-5433	303	6	α	α	PROPN
ejpam-5433	303	7	α	α	NOUN
ejpam-5433	303	8	)	)	PUNCT
ejpam-5433	303	9	−	−	PROPN
ejpam-5433	304	1	t∫	t∫	PROPN
ejpam-5433	304	2	b	b	PROPN
ejpam-5433	304	3	h	h	NOUN
ejpam-5433	304	4	(	(	PUNCT
ejpam-5433	304	5	tα	tα	PROPN
ejpam-5433	304	6	α	α	NOUN
ejpam-5433	304	7	+	+	NOUN
ejpam-5433	304	8	1	1	X
ejpam-5433	304	9	)	)	PUNCT
ejpam-5433	304	10	dtα	dtα	NOUN
ejpam-5433	304	11	tα−1	tα−1	NOUN
ejpam-5433	304	12	+	+	CCONJ
ejpam-5433	304	13	tα	tα	PROPN
ejpam-5433	304	14	α	α	PRON
ejpam-5433	304	15	t∫	t∫	PROPN
ejpam-5433	304	16	b	b	PROPN
ejpam-5433	304	17	h	h	NOUN
ejpam-5433	304	18	dtα	dtα	NOUN
ejpam-5433	304	19	tα−1	tα−1	NOUN
ejpam-5433	304	20	+	+	CCONJ
ejpam-5433	305	1	e−	e−	PROPN
ejpam-5433	305	2	(	(	PUNCT
ejpam-5433	305	3	t	t	PROPN
ejpam-5433	305	4	α	α	PROPN
ejpam-5433	305	5	α	α	NOUN
ejpam-5433	305	6	)	)	PUNCT
ejpam-5433	306	1	t∫	t∫	PROPN
ejpam-5433	306	2	b	b	NOUN
ejpam-5433	307	1	he	he	PRON
ejpam-5433	307	2	tα	tα	VERB
ejpam-5433	307	3	α	α	PRON
ejpam-5433	307	4	dtα	dtα	NOUN
ejpam-5433	307	5	tα−1	tα−1	NOUN
ejpam-5433	307	6	.	.	PUNCT
ejpam-5433	308	1	r.	r.	PROPN
ejpam-5433	308	2	alkhateeb	alkhateeb	PROPN
ejpam-5433	308	3	,	,	PUNCT
ejpam-5433	308	4	g.	g.	PROPN
ejpam-5433	308	5	awwad	awwad	PROPN
ejpam-5433	308	6	/	/	PUNCT
ejpam-5433	308	7	eur	eur	PROPN
ejpam-5433	308	8	.	.	PUNCT
ejpam-5433	309	1	j.	j.	PROPN
ejpam-5433	309	2	pure	pure	PROPN
ejpam-5433	309	3	appl	appl	PROPN
ejpam-5433	309	4	.	.	PROPN
ejpam-5433	309	5	math	math	PROPN
ejpam-5433	309	6	,	,	PUNCT
ejpam-5433	309	7	17	17	NUM
ejpam-5433	309	8	(	(	PUNCT
ejpam-5433	309	9	4	4	NUM
ejpam-5433	309	10	)	)	PUNCT
ejpam-5433	309	11	(	(	PUNCT
ejpam-5433	309	12	2024	2024	NUM
ejpam-5433	309	13	)	)	PUNCT
ejpam-5433	309	14	,	,	PUNCT
ejpam-5433	309	15	3061	3061	NUM
ejpam-5433	309	16	-	-	SYM
ejpam-5433	309	17	3078	3078	NUM
ejpam-5433	309	18	3072	3072	NUM
ejpam-5433	309	19	now	now	ADV
ejpam-5433	309	20	,	,	PUNCT
ejpam-5433	309	21	we	we	PRON
ejpam-5433	309	22	will	will	AUX
ejpam-5433	309	23	take	take	VERB
ejpam-5433	309	24	situation	situation	NOUN
ejpam-5433	309	25	(	(	PUNCT
ejpam-5433	309	26	2	2	NUM
ejpam-5433	309	27	)	)	PUNCT
ejpam-5433	309	28	,	,	PUNCT
ejpam-5433	309	29	so	so	CCONJ
ejpam-5433	309	30	equation	equation	NOUN
ejpam-5433	309	31	(	(	PUNCT
ejpam-5433	309	32	5	5	X
ejpam-5433	309	33	)	)	PUNCT
ejpam-5433	309	34	becomes	become	VERB
ejpam-5433	309	35	:(	:(	PUNCT
ejpam-5433	309	36	u3α(t	u3α(t	PROPN
ejpam-5433	309	37	)	)	PUNCT
ejpam-5433	309	38	+	+	CCONJ
ejpam-5433	309	39	uα(t	uα(t	NOUN
ejpam-5433	309	40	)	)	PUNCT
ejpam-5433	309	41	)	)	PUNCT
ejpam-5433	310	1	⊗	⊗	ADV
ejpam-5433	310	2	x+	x+	X
ejpam-5433	310	3	u2α(t)⊗ax	u2α(t)⊗ax	X
ejpam-5433	310	4	=	=	AUX
ejpam-5433	310	5	h⊗	h⊗	VERB
ejpam-5433	310	6	z.	z.	PROPN
ejpam-5433	311	1	for	for	ADP
ejpam-5433	311	2	this	this	DET
ejpam-5433	311	3	case	case	NOUN
ejpam-5433	311	4	we	we	PRON
ejpam-5433	311	5	have	have	VERB
ejpam-5433	311	6	two	two	NUM
ejpam-5433	311	7	cases	case	NOUN
ejpam-5433	311	8	:	:	PUNCT
ejpam-5433	311	9	(	(	PUNCT
ejpam-5433	311	10	a	a	X
ejpam-5433	311	11	)	)	PUNCT
ejpam-5433	311	12	u3α	u3α	PROPN
ejpam-5433	312	1	+	+	CCONJ
ejpam-5433	312	2	uα	uα	NOUN
ejpam-5433	312	3	=	=	PUNCT
ejpam-5433	312	4	u2α	u2α	NOUN
ejpam-5433	312	5	=	=	PUNCT
ejpam-5433	312	6	h	h	NOUN
ejpam-5433	312	7	=	=	NOUN
ejpam-5433	312	8	uα	uα	PROPN
ejpam-5433	312	9	.	.	PUNCT
ejpam-5433	313	1	(	(	PUNCT
ejpam-5433	313	2	b	b	X
ejpam-5433	313	3	)	)	PUNCT
ejpam-5433	313	4	x	x	X
ejpam-5433	314	1	=	=	PUNCT
ejpam-5433	314	2	ax	ax	NOUN
ejpam-5433	314	3	=	=	PUNCT
ejpam-5433	314	4	z.	z.	PROPN
ejpam-5433	314	5	in	in	ADP
ejpam-5433	314	6	case	case	NOUN
ejpam-5433	314	7	(	(	PUNCT
ejpam-5433	314	8	a	a	NOUN
ejpam-5433	314	9	)	)	PUNCT
ejpam-5433	314	10	,	,	PUNCT
ejpam-5433	314	11	for	for	ADP
ejpam-5433	314	12	the	the	DET
ejpam-5433	314	13	existence	existence	NOUN
ejpam-5433	314	14	of	of	ADP
ejpam-5433	314	15	an	an	DET
ejpam-5433	314	16	atomic	atomic	ADJ
ejpam-5433	314	17	solution	solution	NOUN
ejpam-5433	314	18	,	,	PUNCT
ejpam-5433	314	19	we	we	PRON
ejpam-5433	314	20	have	have	VERB
ejpam-5433	314	21	five	five	NUM
ejpam-5433	314	22	situations	situation	NOUN
ejpam-5433	314	23	.	.	PUNCT
ejpam-5433	315	1	(	(	PUNCT
ejpam-5433	315	2	i	i	NOUN
ejpam-5433	315	3	)	)	PUNCT
ejpam-5433	315	4	u3α	u3α	ADV
ejpam-5433	315	5	−	−	NOUN
ejpam-5433	315	6	u2α	u2α	NOUN
ejpam-5433	315	7	+	+	CCONJ
ejpam-5433	315	8	uα	uα	X
ejpam-5433	315	9	=	=	NOUN
ejpam-5433	315	10	0	0	PROPN
ejpam-5433	315	11	.	.	PUNCT
ejpam-5433	316	1	so	so	ADV
ejpam-5433	316	2	we	we	PRON
ejpam-5433	316	3	have	have	VERB
ejpam-5433	316	4	from	from	ADP
ejpam-5433	316	5	[	[	X
ejpam-5433	316	6	3	3	NUM
ejpam-5433	316	7	]	]	X
ejpam-5433	316	8	r3	r3	PROPN
ejpam-5433	316	9	−	−	PROPN
ejpam-5433	316	10	r2	r2	NOUN
ejpam-5433	317	1	+	+	CCONJ
ejpam-5433	317	2	r	r	NOUN
ejpam-5433	317	3	=	=	PUNCT
ejpam-5433	317	4	r(r2	r(r2	NOUN
ejpam-5433	317	5	−	−	NOUN
ejpam-5433	317	6	r	r	NOUN
ejpam-5433	317	7	+	+	NOUN
ejpam-5433	317	8	1	1	NUM
ejpam-5433	317	9	)	)	PUNCT
ejpam-5433	317	10	=	=	SYM
ejpam-5433	317	11	0	0	NUM
ejpam-5433	317	12	,	,	PUNCT
ejpam-5433	317	13	which	which	PRON
ejpam-5433	317	14	gives	give	VERB
ejpam-5433	317	15	r1	r1	PROPN
ejpam-5433	317	16	=	=	SYM
ejpam-5433	317	17	0	0	NUM
ejpam-5433	317	18	,	,	PUNCT
ejpam-5433	317	19	r2	r2	PROPN
ejpam-5433	317	20	=	=	PUNCT
ejpam-5433	317	21	1+i	1+i	NUM
ejpam-5433	317	22	√	√	NUM
ejpam-5433	317	23	3	3	NUM
ejpam-5433	317	24	2	2	NUM
ejpam-5433	317	25	,	,	PUNCT
ejpam-5433	317	26	and	and	CCONJ
ejpam-5433	317	27	r3	r3	PROPN
ejpam-5433	317	28	=	=	SYM
ejpam-5433	318	1	1−i	1−i	NUM
ejpam-5433	318	2	√	√	NUM
ejpam-5433	318	3	3	3	NUM
ejpam-5433	318	4	2	2	NUM
ejpam-5433	318	5	.	.	PUNCT
ejpam-5433	319	1	then	then	ADV
ejpam-5433	319	2	,	,	PUNCT
ejpam-5433	319	3	u(t	u(t	PROPN
ejpam-5433	319	4	)	)	PUNCT
ejpam-5433	319	5	=	=	SYM
ejpam-5433	319	6	c1	c1	NOUN
ejpam-5433	319	7	+	+	CCONJ
ejpam-5433	319	8	e	e	PROPN
ejpam-5433	319	9	1	1	NUM
ejpam-5433	319	10	2	2	NUM
ejpam-5433	319	11	(	(	PUNCT
ejpam-5433	319	12	tα	tα	PROPN
ejpam-5433	319	13	α	α	PROPN
ejpam-5433	319	14	)	)	PUNCT
ejpam-5433	319	15	(	(	PUNCT
ejpam-5433	319	16	c2	c2	PROPN
ejpam-5433	319	17	cos	cos	PROPN
ejpam-5433	319	18	(	(	PUNCT
ejpam-5433	319	19	√	√	NUM
ejpam-5433	319	20	3tα	3tα	ADJ
ejpam-5433	319	21	2α	2α	NOUN
ejpam-5433	319	22	)	)	PUNCT
ejpam-5433	320	1	+	+	CCONJ
ejpam-5433	320	2	c3	c3	PROPN
ejpam-5433	320	3	sin	sin	NOUN
ejpam-5433	320	4	(	(	PUNCT
ejpam-5433	320	5	√	√	ADV
ejpam-5433	320	6	3tα	3tα	ADJ
ejpam-5433	320	7	2α	2α	NOUN
ejpam-5433	320	8	)	)	PUNCT
ejpam-5433	320	9	)	)	PUNCT
ejpam-5433	320	10	.	.	PUNCT
ejpam-5433	321	1	by	by	ADP
ejpam-5433	321	2	the	the	DET
ejpam-5433	321	3	assumption	assumption	NOUN
ejpam-5433	321	4	(	(	PUNCT
ejpam-5433	321	5	4	4	NUM
ejpam-5433	321	6	)	)	PUNCT
ejpam-5433	321	7	,	,	PUNCT
ejpam-5433	321	8	we	we	PRON
ejpam-5433	321	9	have	have	VERB
ejpam-5433	321	10	c1	c1	PROPN
ejpam-5433	321	11	=	=	SYM
ejpam-5433	321	12	2x0	2x0	PROPN
ejpam-5433	321	13	,	,	PUNCT
ejpam-5433	321	14	c2	c2	PROPN
ejpam-5433	321	15	=	=	SYM
ejpam-5433	321	16	0	0	NUM
ejpam-5433	321	17	,	,	PUNCT
ejpam-5433	321	18	and	and	CCONJ
ejpam-5433	321	19	c3	c3	X
ejpam-5433	321	20	=	=	SYM
ejpam-5433	321	21	2√	2√	PROPN
ejpam-5433	321	22	3	3	NUM
ejpam-5433	321	23	x0	x0	NOUN
ejpam-5433	321	24	.	.	PUNCT
ejpam-5433	322	1	hence	hence	ADV
ejpam-5433	322	2	,	,	PUNCT
ejpam-5433	322	3	u(t	u(t	PROPN
ejpam-5433	322	4	)	)	PUNCT
ejpam-5433	322	5	=	=	SYM
ejpam-5433	323	1	2x0	2x0	NUM
ejpam-5433	323	2	+	+	NUM
ejpam-5433	323	3	2√	2√	NUM
ejpam-5433	323	4	3	3	NUM
ejpam-5433	323	5	x0e	x0e	SYM
ejpam-5433	323	6	1	1	NUM
ejpam-5433	323	7	2	2	NUM
ejpam-5433	323	8	(	(	PUNCT
ejpam-5433	323	9	tα	tα	PROPN
ejpam-5433	323	10	α	α	NOUN
ejpam-5433	323	11	)	)	PUNCT
ejpam-5433	323	12	sin	sin	NOUN
ejpam-5433	323	13	(	(	PUNCT
ejpam-5433	323	14	√	√	ADV
ejpam-5433	323	15	3tα	3tα	ADJ
ejpam-5433	323	16	2α	2α	NOUN
ejpam-5433	323	17	)	)	PUNCT
ejpam-5433	323	18	.	.	PUNCT
ejpam-5433	324	1	(	(	PUNCT
ejpam-5433	324	2	20	20	NUM
ejpam-5433	324	3	)	)	PUNCT
ejpam-5433	324	4	(	(	PUNCT
ejpam-5433	324	5	ii	ii	NOUN
ejpam-5433	324	6	)	)	PUNCT
ejpam-5433	324	7	u3α	u3α	PROPN
ejpam-5433	325	1	+	+	CCONJ
ejpam-5433	325	2	uα	uα	PROPN
ejpam-5433	325	3	=	=	SYM
ejpam-5433	325	4	uα	uα	PROPN
ejpam-5433	325	5	.	.	PUNCT
ejpam-5433	326	1	u3α	u3α	PROPN
ejpam-5433	327	1	=	=	NOUN
ejpam-5433	327	2	0	0	NUM
ejpam-5433	327	3	,	,	PUNCT
ejpam-5433	327	4	from	from	ADP
ejpam-5433	327	5	[	[	X
ejpam-5433	327	6	3],we	3],we	NUM
ejpam-5433	327	7	have	have	VERB
ejpam-5433	327	8	r3	r3	NOUN
ejpam-5433	327	9	=	=	SYM
ejpam-5433	327	10	0	0	X
ejpam-5433	327	11	.	.	PUNCT
ejpam-5433	328	1	consequently	consequently	ADV
ejpam-5433	328	2	,	,	PUNCT
ejpam-5433	328	3	r1	r1	PROPN
ejpam-5433	328	4	=	=	PUNCT
ejpam-5433	328	5	r2	r2	PROPN
ejpam-5433	328	6	=	=	SYM
ejpam-5433	328	7	r3	r3	PROPN
ejpam-5433	328	8	=	=	SYM
ejpam-5433	328	9	0	0	PROPN
ejpam-5433	328	10	.	.	PUNCT
ejpam-5433	329	1	so	so	ADV
ejpam-5433	329	2	,	,	PUNCT
ejpam-5433	329	3	u(t	u(t	NOUN
ejpam-5433	329	4	)	)	PUNCT
ejpam-5433	329	5	=	=	SYM
ejpam-5433	329	6	c1	c1	PROPN
ejpam-5433	329	7	+	+	CCONJ
ejpam-5433	329	8	c2	c2	PROPN
ejpam-5433	329	9	(	(	PUNCT
ejpam-5433	329	10	tα	tα	PROPN
ejpam-5433	329	11	α	α	PROPN
ejpam-5433	329	12	)	)	PUNCT
ejpam-5433	330	1	+	+	CCONJ
ejpam-5433	330	2	c3	c3	PROPN
ejpam-5433	330	3	(	(	PUNCT
ejpam-5433	330	4	tα	tα	PROPN
ejpam-5433	330	5	α	α	PROPN
ejpam-5433	330	6	)	)	PUNCT
ejpam-5433	330	7	2	2	NUM
ejpam-5433	330	8	.	.	PUNCT
ejpam-5433	331	1	r.	r.	PROPN
ejpam-5433	331	2	alkhateeb	alkhateeb	PROPN
ejpam-5433	331	3	,	,	PUNCT
ejpam-5433	331	4	g.	g.	PROPN
ejpam-5433	331	5	awwad	awwad	PROPN
ejpam-5433	331	6	/	/	PUNCT
ejpam-5433	331	7	eur	eur	PROPN
ejpam-5433	331	8	.	.	PUNCT
ejpam-5433	332	1	j.	j.	PROPN
ejpam-5433	332	2	pure	pure	PROPN
ejpam-5433	332	3	appl	appl	PROPN
ejpam-5433	332	4	.	.	PROPN
ejpam-5433	332	5	math	math	PROPN
ejpam-5433	332	6	,	,	PUNCT
ejpam-5433	332	7	17	17	NUM
ejpam-5433	332	8	(	(	PUNCT
ejpam-5433	332	9	4	4	NUM
ejpam-5433	332	10	)	)	PUNCT
ejpam-5433	332	11	(	(	PUNCT
ejpam-5433	332	12	2024	2024	NUM
ejpam-5433	332	13	)	)	PUNCT
ejpam-5433	332	14	,	,	PUNCT
ejpam-5433	332	15	3061	3061	NUM
ejpam-5433	332	16	-	-	SYM
ejpam-5433	332	17	3078	3078	NUM
ejpam-5433	332	18	3073	3073	NUM
ejpam-5433	332	19	so	so	ADV
ejpam-5433	332	20	,	,	PUNCT
ejpam-5433	332	21	by	by	ADP
ejpam-5433	332	22	assumption	assumption	NOUN
ejpam-5433	332	23	(	(	PUNCT
ejpam-5433	332	24	10	10	NUM
ejpam-5433	332	25	)	)	PUNCT
ejpam-5433	333	1	,	,	PUNCT
ejpam-5433	333	2	we	we	PRON
ejpam-5433	333	3	have	have	VERB
ejpam-5433	333	4	c1	c1	PROPN
ejpam-5433	333	5	=	=	SYM
ejpam-5433	333	6	2x0	2x0	PROPN
ejpam-5433	333	7	,	,	PUNCT
ejpam-5433	333	8	c2	c2	PROPN
ejpam-5433	333	9	=	=	PUNCT
ejpam-5433	333	10	x0	x0	PROPN
ejpam-5433	333	11	,	,	PUNCT
ejpam-5433	333	12	c3	c3	X
ejpam-5433	333	13	=	=	PUNCT
ejpam-5433	333	14	x0	x0	PROPN
ejpam-5433	333	15	2	2	NUM
ejpam-5433	333	16	.	.	PUNCT
ejpam-5433	334	1	hence	hence	ADV
ejpam-5433	334	2	,	,	PUNCT
ejpam-5433	334	3	u(t	u(t	PROPN
ejpam-5433	334	4	)	)	PUNCT
ejpam-5433	334	5	=	=	SYM
ejpam-5433	335	1	2x0	2x0	NUM
ejpam-5433	336	1	+	+	CCONJ
ejpam-5433	336	2	x0	x0	PROPN
ejpam-5433	336	3	(	(	PUNCT
ejpam-5433	336	4	tα	tα	PROPN
ejpam-5433	336	5	α	α	PROPN
ejpam-5433	336	6	)	)	PUNCT
ejpam-5433	337	1	+	+	CCONJ
ejpam-5433	337	2	x0	x0	PROPN
ejpam-5433	337	3	2	2	NUM
ejpam-5433	337	4	(	(	PUNCT
ejpam-5433	337	5	tα	tα	PROPN
ejpam-5433	337	6	α	α	NOUN
ejpam-5433	337	7	)	)	PUNCT
ejpam-5433	337	8	2	2	NUM
ejpam-5433	337	9	.	.	PUNCT
ejpam-5433	337	10	(	(	PUNCT
ejpam-5433	337	11	iii	iii	NOUN
ejpam-5433	337	12	)	)	PUNCT
ejpam-5433	337	13	u2α	u2α	NOUN
ejpam-5433	337	14	=	=	X
ejpam-5433	337	15	h.	h.	PROPN
ejpam-5433	338	1	so	so	ADV
ejpam-5433	338	2	,	,	PUNCT
ejpam-5433	338	3	from	from	ADP
ejpam-5433	338	4	(	(	PUNCT
ejpam-5433	338	5	20	20	NUM
ejpam-5433	338	6	)	)	PUNCT
ejpam-5433	338	7	we	we	PRON
ejpam-5433	338	8	have	have	VERB
ejpam-5433	338	9	,	,	PUNCT
ejpam-5433	338	10	h	h	PROPN
ejpam-5433	339	1	=	=	PUNCT
ejpam-5433	339	2	x0e	x0e	NUM
ejpam-5433	339	3	1	1	NUM
ejpam-5433	339	4	2	2	NUM
ejpam-5433	339	5	(	(	PUNCT
ejpam-5433	339	6	tα	tα	PROPN
ejpam-5433	339	7	α	α	NOUN
ejpam-5433	339	8	)	)	PUNCT
ejpam-5433	339	9	(	(	PUNCT
ejpam-5433	339	10	cos	cos	X
ejpam-5433	339	11	(	(	PUNCT
ejpam-5433	339	12	√	√	NUM
ejpam-5433	339	13	3tα	3tα	ADJ
ejpam-5433	339	14	2α	2α	NOUN
ejpam-5433	339	15	)	)	PUNCT
ejpam-5433	340	1	−	−	PROPN
ejpam-5433	340	2	x0√	x0√	PROPN
ejpam-5433	340	3	3	3	NUM
ejpam-5433	340	4	sin	sin	NOUN
ejpam-5433	340	5	(	(	PUNCT
ejpam-5433	340	6	√	√	ADV
ejpam-5433	340	7	3tα	3tα	ADJ
ejpam-5433	340	8	2α	2α	NOUN
ejpam-5433	340	9	)	)	PUNCT
ejpam-5433	340	10	)	)	PUNCT
ejpam-5433	340	11	.	.	PUNCT
ejpam-5433	341	1	(	(	PUNCT
ejpam-5433	341	2	iv	iv	X
ejpam-5433	341	3	)	)	PUNCT
ejpam-5433	341	4	uα	uα	PROPN
ejpam-5433	341	5	=	=	PUNCT
ejpam-5433	341	6	h.	h.	PROPN
ejpam-5433	342	1	so	so	ADV
ejpam-5433	342	2	,	,	PUNCT
ejpam-5433	342	3	from	from	ADP
ejpam-5433	342	4	(	(	PUNCT
ejpam-5433	342	5	20	20	NUM
ejpam-5433	342	6	)	)	PUNCT
ejpam-5433	342	7	we	we	PRON
ejpam-5433	342	8	have	have	VERB
ejpam-5433	342	9	,	,	PUNCT
ejpam-5433	342	10	h	h	PROPN
ejpam-5433	343	1	=	=	PUNCT
ejpam-5433	343	2	x0e	x0e	NUM
ejpam-5433	343	3	1	1	NUM
ejpam-5433	343	4	2	2	NUM
ejpam-5433	343	5	(	(	PUNCT
ejpam-5433	343	6	tα	tα	PROPN
ejpam-5433	343	7	α	α	NOUN
ejpam-5433	343	8	)	)	PUNCT
ejpam-5433	343	9	(	(	PUNCT
ejpam-5433	343	10	cos	cos	X
ejpam-5433	343	11	(	(	PUNCT
ejpam-5433	343	12	√	√	NUM
ejpam-5433	343	13	3tα	3tα	ADJ
ejpam-5433	343	14	2α	2α	NOUN
ejpam-5433	343	15	)	)	PUNCT
ejpam-5433	344	1	+	+	CCONJ
ejpam-5433	344	2	x0√	x0√	PROPN
ejpam-5433	344	3	3	3	NUM
ejpam-5433	344	4	sin	sin	NOUN
ejpam-5433	344	5	(	(	PUNCT
ejpam-5433	344	6	√	√	ADV
ejpam-5433	344	7	3tα	3tα	ADJ
ejpam-5433	344	8	2α	2α	NOUN
ejpam-5433	344	9	)	)	PUNCT
ejpam-5433	344	10	)	)	PUNCT
ejpam-5433	344	11	.	.	PUNCT
ejpam-5433	345	1	(	(	PUNCT
ejpam-5433	345	2	v	v	NOUN
ejpam-5433	345	3	)	)	PUNCT
ejpam-5433	345	4	u3α	u3α	PROPN
ejpam-5433	346	1	+	+	CCONJ
ejpam-5433	346	2	uα	uα	PROPN
ejpam-5433	346	3	=	=	SYM
ejpam-5433	346	4	h.	h.	PROPN
ejpam-5433	347	1	so	so	ADV
ejpam-5433	347	2	,	,	PUNCT
ejpam-5433	347	3	from	from	ADP
ejpam-5433	347	4	(	(	PUNCT
ejpam-5433	347	5	20	20	NUM
ejpam-5433	347	6	)	)	PUNCT
ejpam-5433	347	7	,	,	PUNCT
ejpam-5433	347	8	we	we	PRON
ejpam-5433	347	9	have	have	VERB
ejpam-5433	347	10	h	h	NOUN
ejpam-5433	347	11	=	=	PUNCT
ejpam-5433	348	1	x0e	x0e	PUNCT
ejpam-5433	348	2	1	1	NUM
ejpam-5433	348	3	2	2	NUM
ejpam-5433	348	4	(	(	PUNCT
ejpam-5433	348	5	tα	tα	PROPN
ejpam-5433	348	6	α	α	PROPN
ejpam-5433	348	7	)	)	PUNCT
ejpam-5433	348	8	cos	cos	PROPN
ejpam-5433	348	9	(	(	PUNCT
ejpam-5433	348	10	√	√	NUM
ejpam-5433	348	11	3tα	3tα	ADJ
ejpam-5433	348	12	2α	2α	NOUN
ejpam-5433	348	13	)	)	PUNCT
ejpam-5433	348	14	.	.	PUNCT
ejpam-5433	349	1	since	since	SCONJ
ejpam-5433	349	2	we	we	PRON
ejpam-5433	349	3	do	do	AUX
ejpam-5433	349	4	n’t	not	PART
ejpam-5433	349	5	have	have	VERB
ejpam-5433	349	6	same	same	ADJ
ejpam-5433	349	7	solution	solution	NOUN
ejpam-5433	349	8	from	from	ADP
ejpam-5433	349	9	(	(	PUNCT
ejpam-5433	349	10	i	i	NOUN
ejpam-5433	349	11	)	)	PUNCT
ejpam-5433	349	12	,	,	PUNCT
ejpam-5433	349	13	(	(	PUNCT
ejpam-5433	349	14	ii	ii	NOUN
ejpam-5433	349	15	)	)	PUNCT
ejpam-5433	349	16	,	,	PUNCT
ejpam-5433	349	17	(	(	PUNCT
ejpam-5433	349	18	iii	iii	NOUN
ejpam-5433	349	19	)	)	PUNCT
ejpam-5433	349	20	,	,	PUNCT
ejpam-5433	349	21	(	(	PUNCT
ejpam-5433	349	22	iv	iv	X
ejpam-5433	349	23	)	)	PUNCT
ejpam-5433	349	24	,	,	PUNCT
ejpam-5433	349	25	and	and	CCONJ
ejpam-5433	349	26	(	(	PUNCT
ejpam-5433	349	27	v	v	NOUN
ejpam-5433	349	28	)	)	PUNCT
ejpam-5433	349	29	,	,	PUNCT
ejpam-5433	349	30	there	there	PRON
ejpam-5433	349	31	is	be	VERB
ejpam-5433	349	32	no	no	DET
ejpam-5433	349	33	an	an	DET
ejpam-5433	349	34	atomic	atomic	ADJ
ejpam-5433	349	35	solution	solution	NOUN
ejpam-5433	349	36	in	in	ADP
ejpam-5433	349	37	this	this	DET
ejpam-5433	349	38	case	case	NOUN
ejpam-5433	349	39	.	.	PUNCT
ejpam-5433	350	1	this	this	PRON
ejpam-5433	350	2	completes	complete	VERB
ejpam-5433	350	3	situation	situation	NOUN
ejpam-5433	350	4	(	(	PUNCT
ejpam-5433	350	5	2	2	NUM
ejpam-5433	350	6	)	)	PUNCT
ejpam-5433	350	7	,	,	PUNCT
ejpam-5433	350	8	and	and	CCONJ
ejpam-5433	350	9	hence	hence	ADV
ejpam-5433	350	10	,	,	PUNCT
ejpam-5433	350	11	case	case	NOUN
ejpam-5433	350	12	two	two	NUM
ejpam-5433	350	13	is	be	AUX
ejpam-5433	350	14	completed	complete	VERB
ejpam-5433	350	15	.	.	PUNCT
ejpam-5433	351	1	case	case	NOUN
ejpam-5433	351	2	three	three	NUM
ejpam-5433	351	3	:	:	PUNCT
ejpam-5433	351	4	(	(	PUNCT
ejpam-5433	351	5	u2α	u2α	NOUN
ejpam-5433	351	6	⊗ax+	⊗ax+	ADV
ejpam-5433	351	7	uα	uα	PROPN
ejpam-5433	351	8	⊗bx	⊗bx	X
ejpam-5433	351	9	)	)	PUNCT
ejpam-5433	351	10	is	be	AUX
ejpam-5433	351	11	an	an	DET
ejpam-5433	351	12	atom	atom	NOUN
ejpam-5433	351	13	.	.	PUNCT
ejpam-5433	352	1	this	this	PRON
ejpam-5433	352	2	has	have	VERB
ejpam-5433	352	3	two	two	NUM
ejpam-5433	352	4	situations	situation	NOUN
ejpam-5433	352	5	:	:	PUNCT
ejpam-5433	352	6	(	(	PUNCT
ejpam-5433	352	7	1	1	X
ejpam-5433	352	8	)	)	PUNCT
ejpam-5433	352	9	u2α	u2α	NOUN
ejpam-5433	352	10	=	=	PUNCT
ejpam-5433	352	11	uα	uα	PROPN
ejpam-5433	352	12	.	.	PUNCT
ejpam-5433	353	1	(	(	PUNCT
ejpam-5433	353	2	2	2	X
ejpam-5433	353	3	)	)	PUNCT
ejpam-5433	353	4	a	a	DET
ejpam-5433	353	5	x	x	X
ejpam-5433	353	6	=	=	SYM
ejpam-5433	353	7	bx	bx	PROPN
ejpam-5433	353	8	.	.	PUNCT
ejpam-5433	354	1	let	let	VERB
ejpam-5433	354	2	us	we	PRON
ejpam-5433	354	3	take	take	VERB
ejpam-5433	354	4	situation	situation	NOUN
ejpam-5433	354	5	(	(	PUNCT
ejpam-5433	354	6	1	1	NUM
ejpam-5433	354	7	)	)	PUNCT
ejpam-5433	354	8	,	,	PUNCT
ejpam-5433	354	9	so	so	CCONJ
ejpam-5433	354	10	equation	equation	NOUN
ejpam-5433	354	11	(	(	PUNCT
ejpam-5433	354	12	5	5	X
ejpam-5433	354	13	)	)	PUNCT
ejpam-5433	354	14	becomes	become	VERB
ejpam-5433	354	15	:	:	PUNCT
ejpam-5433	354	16	u3α	u3α	ADJ
ejpam-5433	354	17	⊗	⊗	ADJ
ejpam-5433	354	18	x+	x+	ADJ
ejpam-5433	354	19	u2α	u2α	PROPN
ejpam-5433	354	20	⊗	⊗	PROPN
ejpam-5433	354	21	(	(	PUNCT
ejpam-5433	354	22	ax+bx	ax+bx	X
ejpam-5433	354	23	)	)	PUNCT
ejpam-5433	354	24	=	=	SYM
ejpam-5433	354	25	h⊗	h⊗	VERB
ejpam-5433	354	26	z.	z.	PROPN
ejpam-5433	355	1	so	so	ADV
ejpam-5433	355	2	,	,	PUNCT
ejpam-5433	355	3	we	we	PRON
ejpam-5433	355	4	have	have	VERB
ejpam-5433	355	5	two	two	NUM
ejpam-5433	355	6	cases	case	NOUN
ejpam-5433	355	7	:	:	PUNCT
ejpam-5433	355	8	(	(	PUNCT
ejpam-5433	355	9	a	a	X
ejpam-5433	355	10	)	)	PUNCT
ejpam-5433	355	11	u3α(t	u3α(t	PROPN
ejpam-5433	355	12	)	)	PUNCT
ejpam-5433	355	13	=	=	SYM
ejpam-5433	355	14	u2α(t	u2α(t	NOUN
ejpam-5433	355	15	)	)	PUNCT
ejpam-5433	355	16	=	=	SYM
ejpam-5433	356	1	h	h	NOUN
ejpam-5433	356	2	=	=	SYM
ejpam-5433	356	3	uα	uα	PROPN
ejpam-5433	356	4	.	.	PUNCT
ejpam-5433	356	5	r.	r.	PROPN
ejpam-5433	356	6	alkhateeb	alkhateeb	PROPN
ejpam-5433	356	7	,	,	PUNCT
ejpam-5433	356	8	g.	g.	PROPN
ejpam-5433	356	9	awwad	awwad	PROPN
ejpam-5433	356	10	/	/	PUNCT
ejpam-5433	356	11	eur	eur	PROPN
ejpam-5433	356	12	.	.	PUNCT
ejpam-5433	357	1	j.	j.	PROPN
ejpam-5433	357	2	pure	pure	PROPN
ejpam-5433	357	3	appl	appl	PROPN
ejpam-5433	357	4	.	.	PROPN
ejpam-5433	357	5	math	math	PROPN
ejpam-5433	357	6	,	,	PUNCT
ejpam-5433	357	7	17	17	NUM
ejpam-5433	357	8	(	(	PUNCT
ejpam-5433	357	9	4	4	NUM
ejpam-5433	357	10	)	)	PUNCT
ejpam-5433	357	11	(	(	PUNCT
ejpam-5433	357	12	2024	2024	NUM
ejpam-5433	357	13	)	)	PUNCT
ejpam-5433	357	14	,	,	PUNCT
ejpam-5433	357	15	3061	3061	NUM
ejpam-5433	357	16	-	-	SYM
ejpam-5433	357	17	3078	3078	NUM
ejpam-5433	357	18	3074	3074	NUM
ejpam-5433	357	19	(	(	PUNCT
ejpam-5433	357	20	b	b	X
ejpam-5433	357	21	)	)	PUNCT
ejpam-5433	357	22	x	x	X
ejpam-5433	357	23	=	=	PUNCT
ejpam-5433	357	24	ax+bx	ax+bx	X
ejpam-5433	357	25	=	=	PUNCT
ejpam-5433	357	26	z.	z.	NOUN
ejpam-5433	358	1	in	in	ADP
ejpam-5433	358	2	case	case	NOUN
ejpam-5433	358	3	(	(	PUNCT
ejpam-5433	358	4	a	a	X
ejpam-5433	358	5	)	)	PUNCT
ejpam-5433	358	6	,	,	PUNCT
ejpam-5433	358	7	we	we	PRON
ejpam-5433	358	8	have	have	VERB
ejpam-5433	358	9	four	four	NUM
ejpam-5433	358	10	situations	situation	NOUN
ejpam-5433	358	11	:	:	PUNCT
ejpam-5433	358	12	(	(	PUNCT
ejpam-5433	358	13	i	i	NOUN
ejpam-5433	358	14	)	)	PUNCT
ejpam-5433	358	15	u3α	u3α	ADV
ejpam-5433	358	16	−	−	NOUN
ejpam-5433	358	17	u2α	u2α	NOUN
ejpam-5433	358	18	=	=	SYM
ejpam-5433	358	19	0	0	X
ejpam-5433	358	20	.	.	PUNCT
ejpam-5433	359	1	so	so	ADV
ejpam-5433	359	2	,	,	PUNCT
ejpam-5433	359	3	we	we	PRON
ejpam-5433	359	4	can	can	AUX
ejpam-5433	359	5	solve	solve	VERB
ejpam-5433	359	6	it	it	PRON
ejpam-5433	359	7	as	as	ADP
ejpam-5433	359	8	in	in	ADP
ejpam-5433	359	9	[	[	X
ejpam-5433	359	10	3	3	NUM
ejpam-5433	359	11	]	]	X
ejpam-5433	359	12	r3	r3	PROPN
ejpam-5433	359	13	−	−	PROPN
ejpam-5433	359	14	r2	r2	NOUN
ejpam-5433	359	15	=	=	PUNCT
ejpam-5433	360	1	r2(r	r2(r	VERB
ejpam-5433	360	2	−	−	NOUN
ejpam-5433	360	3	1	1	NUM
ejpam-5433	360	4	)	)	PUNCT
ejpam-5433	360	5	=	=	SYM
ejpam-5433	361	1	0	0	NUM
ejpam-5433	361	2	,	,	PUNCT
ejpam-5433	361	3	which	which	PRON
ejpam-5433	361	4	gives	give	VERB
ejpam-5433	361	5	r1	r1	PROPN
ejpam-5433	361	6	=	=	SYM
ejpam-5433	361	7	0	0	NUM
ejpam-5433	361	8	,	,	PUNCT
ejpam-5433	361	9	r2	r2	PROPN
ejpam-5433	361	10	=	=	SYM
ejpam-5433	361	11	0	0	NUM
ejpam-5433	361	12	,	,	PUNCT
ejpam-5433	361	13	and	and	CCONJ
ejpam-5433	361	14	r3	r3	PROPN
ejpam-5433	361	15	=	=	SYM
ejpam-5433	361	16	1	1	X
ejpam-5433	361	17	.	.	PUNCT
ejpam-5433	362	1	so	so	ADV
ejpam-5433	362	2	,	,	PUNCT
ejpam-5433	362	3	u(t	u(t	NOUN
ejpam-5433	362	4	)	)	PUNCT
ejpam-5433	362	5	=	=	SYM
ejpam-5433	362	6	c1	c1	PROPN
ejpam-5433	362	7	+	+	CCONJ
ejpam-5433	362	8	c2	c2	PROPN
ejpam-5433	362	9	tα	tα	VERB
ejpam-5433	362	10	α	α	PROPN
ejpam-5433	362	11	+	+	CCONJ
ejpam-5433	363	1	c3e	c3e	PROPN
ejpam-5433	364	1	(	(	PUNCT
ejpam-5433	364	2	t	t	PROPN
ejpam-5433	364	3	α	α	PROPN
ejpam-5433	364	4	α	α	PROPN
ejpam-5433	364	5	)	)	PUNCT
ejpam-5433	364	6	.	.	PUNCT
ejpam-5433	365	1	(	(	PUNCT
ejpam-5433	365	2	21	21	NUM
ejpam-5433	365	3	)	)	PUNCT
ejpam-5433	365	4	by	by	ADP
ejpam-5433	365	5	assumption	assumption	NOUN
ejpam-5433	365	6	(	(	PUNCT
ejpam-5433	365	7	4	4	NUM
ejpam-5433	365	8	)	)	PUNCT
ejpam-5433	365	9	,	,	PUNCT
ejpam-5433	365	10	we	we	PRON
ejpam-5433	365	11	have	have	VERB
ejpam-5433	365	12	c1	c1	PROPN
ejpam-5433	365	13	=	=	PUNCT
ejpam-5433	365	14	x0	x0	PROPN
ejpam-5433	365	15	,	,	PUNCT
ejpam-5433	365	16	c2	c2	PROPN
ejpam-5433	365	17	=	=	SYM
ejpam-5433	365	18	0	0	NUM
ejpam-5433	365	19	,	,	PUNCT
ejpam-5433	365	20	and	and	CCONJ
ejpam-5433	365	21	c3	c3	PROPN
ejpam-5433	365	22	=	=	PUNCT
ejpam-5433	365	23	x0	x0	PROPN
ejpam-5433	365	24	.	.	PUNCT
ejpam-5433	366	1	so	so	ADV
ejpam-5433	366	2	,	,	PUNCT
ejpam-5433	366	3	(	(	PUNCT
ejpam-5433	366	4	21	21	NUM
ejpam-5433	366	5	)	)	PUNCT
ejpam-5433	366	6	becomes	become	VERB
ejpam-5433	366	7	u(t	u(t	NOUN
ejpam-5433	366	8	)	)	PUNCT
ejpam-5433	367	1	=	=	PUNCT
ejpam-5433	368	1	x0	x0	PROPN
ejpam-5433	369	1	+	+	CCONJ
ejpam-5433	369	2	x0e	x0e	PUNCT
ejpam-5433	370	1	(	(	PUNCT
ejpam-5433	370	2	t	t	NOUN
ejpam-5433	370	3	α	α	PROPN
ejpam-5433	370	4	α	α	PROPN
ejpam-5433	370	5	)	)	PUNCT
ejpam-5433	370	6	.	.	PUNCT
ejpam-5433	371	1	(	(	PUNCT
ejpam-5433	371	2	22	22	NUM
ejpam-5433	371	3	)	)	PUNCT
ejpam-5433	371	4	(	(	PUNCT
ejpam-5433	371	5	ii	ii	NOUN
ejpam-5433	371	6	)	)	PUNCT
ejpam-5433	371	7	u2α	u2α	NOUN
ejpam-5433	371	8	=	=	X
ejpam-5433	371	9	h.	h.	NOUN
ejpam-5433	371	10	using	use	VERB
ejpam-5433	371	11	(	(	PUNCT
ejpam-5433	371	12	21	21	NUM
ejpam-5433	371	13	)	)	PUNCT
ejpam-5433	371	14	,	,	PUNCT
ejpam-5433	371	15	we	we	PRON
ejpam-5433	371	16	get	get	VERB
ejpam-5433	371	17	h	h	NOUN
ejpam-5433	371	18	=	=	PUNCT
ejpam-5433	372	1	x0e	x0e	PUNCT
ejpam-5433	372	2	(	(	PUNCT
ejpam-5433	372	3	t	t	NOUN
ejpam-5433	372	4	α	α	PROPN
ejpam-5433	372	5	α	α	PROPN
ejpam-5433	372	6	)	)	PUNCT
ejpam-5433	372	7	.	.	PUNCT
ejpam-5433	373	1	(	(	PUNCT
ejpam-5433	373	2	iii	iii	X
ejpam-5433	373	3	)	)	PUNCT
ejpam-5433	373	4	u3α	u3α	NOUN
ejpam-5433	373	5	=	=	SYM
ejpam-5433	373	6	uα	uα	PROPN
ejpam-5433	373	7	.	.	PUNCT
ejpam-5433	373	8	r3	r3	PROPN
ejpam-5433	373	9	=	=	SYM
ejpam-5433	373	10	r.	r.	PROPN
ejpam-5433	374	1	so	so	ADV
ejpam-5433	374	2	,	,	PUNCT
ejpam-5433	374	3	we	we	PRON
ejpam-5433	374	4	have	have	VERB
ejpam-5433	374	5	r1	r1	NOUN
ejpam-5433	374	6	=	=	SYM
ejpam-5433	374	7	0	0	NUM
ejpam-5433	374	8	,	,	PUNCT
ejpam-5433	374	9	r2	r2	PROPN
ejpam-5433	374	10	=	=	SYM
ejpam-5433	374	11	1	1	NUM
ejpam-5433	374	12	,	,	PUNCT
ejpam-5433	374	13	and	and	CCONJ
ejpam-5433	374	14	r3	r3	PROPN
ejpam-5433	374	15	=	=	SYM
ejpam-5433	374	16	−1	−1	NOUN
ejpam-5433	374	17	.	.	PUNCT
ejpam-5433	375	1	hence	hence	ADV
ejpam-5433	375	2	,	,	PUNCT
ejpam-5433	375	3	u(t	u(t	PROPN
ejpam-5433	375	4	)	)	PUNCT
ejpam-5433	375	5	=	=	SYM
ejpam-5433	375	6	c1	c1	NOUN
ejpam-5433	375	7	+	+	CCONJ
ejpam-5433	375	8	c2e	c2e	PROPN
ejpam-5433	376	1	(	(	PUNCT
ejpam-5433	376	2	t	t	NOUN
ejpam-5433	376	3	α	α	PROPN
ejpam-5433	376	4	α	α	NOUN
ejpam-5433	376	5	)	)	PUNCT
ejpam-5433	377	1	+	+	CCONJ
ejpam-5433	378	1	c3e	c3e	PROPN
ejpam-5433	378	2	−	−	NOUN
ejpam-5433	378	3	(	(	PUNCT
ejpam-5433	378	4	t	t	PROPN
ejpam-5433	378	5	α	α	PROPN
ejpam-5433	378	6	α	α	PROPN
ejpam-5433	378	7	)	)	PUNCT
ejpam-5433	378	8	.	.	PUNCT
ejpam-5433	379	1	by	by	ADP
ejpam-5433	379	2	assumption	assumption	NOUN
ejpam-5433	379	3	(	(	PUNCT
ejpam-5433	379	4	4	4	NUM
ejpam-5433	379	5	)	)	PUNCT
ejpam-5433	379	6	,	,	PUNCT
ejpam-5433	379	7	we	we	PRON
ejpam-5433	379	8	have	have	VERB
ejpam-5433	379	9	c1	c1	PROPN
ejpam-5433	379	10	=	=	PUNCT
ejpam-5433	379	11	x0.c2	x0.c2	X
ejpam-5433	380	1	=	=	PUNCT
ejpam-5433	380	2	x0	x0	PROPN
ejpam-5433	380	3	,	,	PUNCT
ejpam-5433	380	4	and	and	CCONJ
ejpam-5433	380	5	c3	c3	X
ejpam-5433	380	6	=	=	PROPN
ejpam-5433	380	7	0	0	X
ejpam-5433	380	8	.	.	PUNCT
ejpam-5433	381	1	consequently	consequently	ADV
ejpam-5433	381	2	,	,	PUNCT
ejpam-5433	381	3	u(t	u(t	NOUN
ejpam-5433	381	4	)	)	PUNCT
ejpam-5433	381	5	=	=	PUNCT
ejpam-5433	382	1	x0	x0	PROPN
ejpam-5433	383	1	+	+	CCONJ
ejpam-5433	383	2	x0e	x0e	PUNCT
ejpam-5433	384	1	(	(	PUNCT
ejpam-5433	384	2	t	t	NOUN
ejpam-5433	384	3	α	α	PROPN
ejpam-5433	384	4	α	α	PROPN
ejpam-5433	384	5	)	)	PUNCT
ejpam-5433	384	6	.	.	PUNCT
ejpam-5433	385	1	(	(	PUNCT
ejpam-5433	385	2	23	23	NUM
ejpam-5433	385	3	)	)	PUNCT
ejpam-5433	385	4	(	(	PUNCT
ejpam-5433	385	5	iv	iv	X
ejpam-5433	385	6	)	)	PUNCT
ejpam-5433	385	7	u3α	u3α	PROPN
ejpam-5433	385	8	=	=	PROPN
ejpam-5433	385	9	h.	h.	PROPN
ejpam-5433	385	10	r.	r.	PROPN
ejpam-5433	385	11	alkhateeb	alkhateeb	PROPN
ejpam-5433	385	12	,	,	PUNCT
ejpam-5433	385	13	g.	g.	PROPN
ejpam-5433	385	14	awwad	awwad	PROPN
ejpam-5433	385	15	/	/	PUNCT
ejpam-5433	385	16	eur	eur	PROPN
ejpam-5433	385	17	.	.	PUNCT
ejpam-5433	386	1	j.	j.	PROPN
ejpam-5433	386	2	pure	pure	PROPN
ejpam-5433	386	3	appl	appl	PROPN
ejpam-5433	386	4	.	.	PROPN
ejpam-5433	386	5	math	math	PROPN
ejpam-5433	386	6	,	,	PUNCT
ejpam-5433	386	7	17	17	NUM
ejpam-5433	386	8	(	(	PUNCT
ejpam-5433	386	9	4	4	NUM
ejpam-5433	386	10	)	)	PUNCT
ejpam-5433	386	11	(	(	PUNCT
ejpam-5433	386	12	2024	2024	NUM
ejpam-5433	386	13	)	)	PUNCT
ejpam-5433	386	14	,	,	PUNCT
ejpam-5433	386	15	3061	3061	NUM
ejpam-5433	386	16	-	-	SYM
ejpam-5433	386	17	3078	3078	NUM
ejpam-5433	386	18	3075	3075	NUM
ejpam-5433	386	19	using	use	VERB
ejpam-5433	386	20	(	(	PUNCT
ejpam-5433	386	21	21	21	NUM
ejpam-5433	386	22	)	)	PUNCT
ejpam-5433	386	23	,	,	PUNCT
ejpam-5433	386	24	we	we	PRON
ejpam-5433	386	25	get	get	VERB
ejpam-5433	386	26	h	h	NOUN
ejpam-5433	386	27	=	=	PUNCT
ejpam-5433	386	28	x0e	x0e	PUNCT
ejpam-5433	387	1	(	(	PUNCT
ejpam-5433	387	2	t	t	NOUN
ejpam-5433	387	3	α	α	PROPN
ejpam-5433	387	4	α	α	PROPN
ejpam-5433	387	5	)	)	PUNCT
ejpam-5433	387	6	.	.	PUNCT
ejpam-5433	388	1	since	since	SCONJ
ejpam-5433	388	2	u3α	u3α	NOUN
ejpam-5433	388	3	=	=	PUNCT
ejpam-5433	388	4	u2α	u2α	NOUN
ejpam-5433	388	5	=	=	PUNCT
ejpam-5433	388	6	h	h	NOUN
ejpam-5433	388	7	=	=	PUNCT
ejpam-5433	388	8	uα	uα	PROPN
ejpam-5433	388	9	=	=	PUNCT
ejpam-5433	388	10	x0e	x0e	PROPN
ejpam-5433	388	11	tα	tα	PROPN
ejpam-5433	388	12	α	α	PROPN
ejpam-5433	388	13	,	,	PUNCT
ejpam-5433	388	14	(	(	PUNCT
ejpam-5433	388	15	6	6	NUM
ejpam-5433	388	16	)	)	PUNCT
ejpam-5433	388	17	becomes	become	VERB
ejpam-5433	388	18	x	x	NOUN
ejpam-5433	388	19	=	=	PUNCT
ejpam-5433	388	20	ax+bx	ax+bx	VERB
ejpam-5433	388	21	=	=	PUNCT
ejpam-5433	388	22	z.	z.	PROPN
ejpam-5433	389	1	so	so	ADV
ejpam-5433	389	2	,	,	PUNCT
ejpam-5433	389	3	(	(	PUNCT
ejpam-5433	389	4	a+b)x	a+b)x	PROPN
ejpam-5433	389	5	=	=	SYM
ejpam-5433	389	6	z	z	NOUN
ejpam-5433	389	7	,	,	PUNCT
ejpam-5433	389	8	or	or	CCONJ
ejpam-5433	389	9	(	(	PUNCT
ejpam-5433	389	10	i)x	i)x	NOUN
ejpam-5433	389	11	=	=	PUNCT
ejpam-5433	389	12	z.	z.	NOUN
ejpam-5433	389	13	which	which	PRON
ejpam-5433	389	14	means	mean	VERB
ejpam-5433	389	15	that	that	SCONJ
ejpam-5433	389	16	z	z	NOUN
ejpam-5433	389	17	will	will	AUX
ejpam-5433	389	18	be	be	AUX
ejpam-5433	389	19	at	at	ADP
ejpam-5433	389	20	the	the	DET
ejpam-5433	389	21	range	range	NOUN
ejpam-5433	389	22	of	of	ADP
ejpam-5433	389	23	intersection	intersection	NOUN
ejpam-5433	389	24	of	of	ADP
ejpam-5433	389	25	(	(	PUNCT
ejpam-5433	389	26	a+b	a+b	NUM
ejpam-5433	389	27	)	)	PUNCT
ejpam-5433	389	28	and	and	CCONJ
ejpam-5433	389	29	i.	i.	PROPN
ejpam-5433	389	30	consequently	consequently	ADV
ejpam-5433	389	31	,	,	PUNCT
ejpam-5433	389	32	there	there	PRON
ejpam-5433	389	33	is	be	VERB
ejpam-5433	389	34	atomic	atomic	ADJ
ejpam-5433	389	35	solution	solution	NOUN
ejpam-5433	389	36	in	in	ADP
ejpam-5433	389	37	this	this	DET
ejpam-5433	389	38	case	case	NOUN
ejpam-5433	389	39	.	.	PUNCT
ejpam-5433	390	1	in	in	ADP
ejpam-5433	390	2	case	case	NOUN
ejpam-5433	390	3	(	(	PUNCT
ejpam-5433	390	4	b	b	NOUN
ejpam-5433	390	5	)	)	PUNCT
ejpam-5433	390	6	,	,	PUNCT
ejpam-5433	390	7	equation	equation	NOUN
ejpam-5433	390	8	(	(	PUNCT
ejpam-5433	390	9	5	5	NUM
ejpam-5433	390	10	)	)	PUNCT
ejpam-5433	390	11	becomes	become	VERB
ejpam-5433	390	12	u3α	u3α	PROPN
ejpam-5433	390	13	⊗	⊗	ADJ
ejpam-5433	390	14	x+	x+	ADJ
ejpam-5433	390	15	u2α	u2α	PROPN
ejpam-5433	390	16	⊗	⊗	PROPN
ejpam-5433	390	17	(	(	PUNCT
ejpam-5433	390	18	a+b)x	a+b)x	PROPN
ejpam-5433	390	19	=	=	SYM
ejpam-5433	390	20	h⊗	h⊗	PROPN
ejpam-5433	390	21	z.	z.	PROPN
ejpam-5433	391	1	so	so	ADV
ejpam-5433	391	2	,	,	PUNCT
ejpam-5433	391	3	u3α	u3α	PROPN
ejpam-5433	391	4	+	+	CCONJ
ejpam-5433	391	5	u2α	u2α	NOUN
ejpam-5433	391	6	=	=	X
ejpam-5433	392	1	h.	h.	NOUN
ejpam-5433	392	2	this	this	PRON
ejpam-5433	392	3	is	be	AUX
ejpam-5433	392	4	third	third	ADJ
ejpam-5433	392	5	order	order	NOUN
ejpam-5433	392	6	homogenous	homogenous	ADJ
ejpam-5433	392	7	linear	linear	ADJ
ejpam-5433	392	8	fractional	fractional	ADJ
ejpam-5433	392	9	differential	differential	NOUN
ejpam-5433	392	10	equation	equation	NOUN
ejpam-5433	392	11	,	,	PUNCT
ejpam-5433	392	12	to	to	PART
ejpam-5433	392	13	solve	solve	VERB
ejpam-5433	392	14	it	it	PRON
ejpam-5433	392	15	we	we	PRON
ejpam-5433	392	16	follow	follow	VERB
ejpam-5433	392	17	the	the	DET
ejpam-5433	392	18	variation	variation	NOUN
ejpam-5433	392	19	of	of	ADP
ejpam-5433	392	20	parameters	parameter	NOUN
ejpam-5433	392	21	method	method	VERB
ejpam-5433	392	22	.	.	PUNCT
ejpam-5433	393	1	the	the	DET
ejpam-5433	393	2	homogenous	homogenous	ADJ
ejpam-5433	393	3	and	and	CCONJ
ejpam-5433	393	4	particular	particular	ADJ
ejpam-5433	393	5	parts	part	NOUN
ejpam-5433	393	6	can	can	AUX
ejpam-5433	393	7	be	be	AUX
ejpam-5433	393	8	found	find	VERB
ejpam-5433	393	9	similarly	similarly	ADV
ejpam-5433	393	10	as	as	ADP
ejpam-5433	393	11	(	(	PUNCT
ejpam-5433	393	12	18	18	NUM
ejpam-5433	393	13	)	)	PUNCT
ejpam-5433	393	14	in	in	ADP
ejpam-5433	393	15	the	the	DET
ejpam-5433	393	16	case	case	NOUN
ejpam-5433	393	17	(	(	PUNCT
ejpam-5433	393	18	b	b	NOUN
ejpam-5433	393	19	)	)	PUNCT
ejpam-5433	393	20	in	in	ADP
ejpam-5433	393	21	situation	situation	NOUN
ejpam-5433	393	22	(	(	PUNCT
ejpam-5433	393	23	1	1	X
ejpam-5433	393	24	)	)	PUNCT
ejpam-5433	393	25	in	in	ADP
ejpam-5433	393	26	case	case	NOUN
ejpam-5433	393	27	two	two	NUM
ejpam-5433	393	28	,	,	PUNCT
ejpam-5433	393	29	and	and	CCONJ
ejpam-5433	393	30	u(t	u(t	NOUN
ejpam-5433	393	31	)	)	PUNCT
ejpam-5433	393	32	=	=	PUNCT
ejpam-5433	394	1	x0	x0	PROPN
ejpam-5433	394	2	+	+	CCONJ
ejpam-5433	394	3	2x0	2x0	NUM
ejpam-5433	394	4	tα	tα	ADP
ejpam-5433	394	5	α	α	NOUN
ejpam-5433	395	1	+	+	NOUN
ejpam-5433	395	2	x0e	x0e	PUNCT
ejpam-5433	395	3	−	−	PROPN
ejpam-5433	395	4	(	(	PUNCT
ejpam-5433	395	5	t	t	PROPN
ejpam-5433	395	6	α	α	PROPN
ejpam-5433	395	7	α	α	NOUN
ejpam-5433	395	8	)	)	PUNCT
ejpam-5433	395	9	−	−	PROPN
ejpam-5433	396	1	t∫	t∫	PROPN
ejpam-5433	396	2	b	b	PROPN
ejpam-5433	396	3	h	h	NOUN
ejpam-5433	396	4	(	(	PUNCT
ejpam-5433	396	5	tα	tα	PROPN
ejpam-5433	396	6	α	α	NOUN
ejpam-5433	396	7	+	+	NOUN
ejpam-5433	396	8	1	1	X
ejpam-5433	396	9	)	)	PUNCT
ejpam-5433	396	10	dtα	dtα	NOUN
ejpam-5433	396	11	tα−1	tα−1	NOUN
ejpam-5433	396	12	+	+	CCONJ
ejpam-5433	396	13	tα	tα	PROPN
ejpam-5433	396	14	α	α	PRON
ejpam-5433	396	15	t∫	t∫	PROPN
ejpam-5433	396	16	b	b	PROPN
ejpam-5433	396	17	h	h	NOUN
ejpam-5433	396	18	dtα	dtα	NOUN
ejpam-5433	396	19	tα−1	tα−1	NOUN
ejpam-5433	396	20	+	+	CCONJ
ejpam-5433	397	1	e−	e−	PROPN
ejpam-5433	397	2	(	(	PUNCT
ejpam-5433	397	3	t	t	PROPN
ejpam-5433	397	4	α	α	PROPN
ejpam-5433	397	5	α	α	NOUN
ejpam-5433	397	6	)	)	PUNCT
ejpam-5433	398	1	t∫	t∫	PROPN
ejpam-5433	398	2	b	b	NOUN
ejpam-5433	399	1	he	he	PRON
ejpam-5433	399	2	tα	tα	VERB
ejpam-5433	399	3	α	α	PRON
ejpam-5433	399	4	dtα	dtα	NOUN
ejpam-5433	399	5	tα−1	tα−1	NOUN
ejpam-5433	399	6	.	.	PUNCT
ejpam-5433	400	1	now	now	ADV
ejpam-5433	400	2	,	,	PUNCT
ejpam-5433	400	3	we	we	PRON
ejpam-5433	400	4	will	will	AUX
ejpam-5433	400	5	take	take	VERB
ejpam-5433	400	6	situation	situation	NOUN
ejpam-5433	400	7	(	(	PUNCT
ejpam-5433	400	8	2	2	NUM
ejpam-5433	400	9	)	)	PUNCT
ejpam-5433	400	10	,	,	PUNCT
ejpam-5433	400	11	so	so	CCONJ
ejpam-5433	400	12	equation	equation	NOUN
ejpam-5433	400	13	(	(	PUNCT
ejpam-5433	400	14	5	5	X
ejpam-5433	400	15	)	)	PUNCT
ejpam-5433	400	16	becomes	become	VERB
ejpam-5433	400	17	:	:	PUNCT
ejpam-5433	400	18	u3α	u3α	PROPN
ejpam-5433	401	1	⊗	⊗	NOUN
ejpam-5433	401	2	x+	x+	NUM
ejpam-5433	401	3	(	(	PUNCT
ejpam-5433	401	4	u2α	u2α	ADJ
ejpam-5433	401	5	+	+	CCONJ
ejpam-5433	401	6	uα)⊗ax	uα)⊗ax	ADJ
ejpam-5433	401	7	=	=	SYM
ejpam-5433	401	8	h⊗	h⊗	NOUN
ejpam-5433	401	9	z.	z.	PROPN
ejpam-5433	402	1	so	so	ADV
ejpam-5433	402	2	,	,	PUNCT
ejpam-5433	402	3	we	we	PRON
ejpam-5433	402	4	have	have	VERB
ejpam-5433	402	5	two	two	NUM
ejpam-5433	402	6	cases	case	NOUN
ejpam-5433	402	7	:	:	PUNCT
ejpam-5433	402	8	(	(	PUNCT
ejpam-5433	402	9	a	a	X
ejpam-5433	402	10	)	)	PUNCT
ejpam-5433	402	11	u3α(t	u3α(t	PROPN
ejpam-5433	402	12	)	)	PUNCT
ejpam-5433	402	13	=	=	SYM
ejpam-5433	402	14	u2α(t	u2α(t	PROPN
ejpam-5433	402	15	)	)	PUNCT
ejpam-5433	402	16	+	+	CCONJ
ejpam-5433	402	17	uα(t	uα(t	NOUN
ejpam-5433	402	18	)	)	PUNCT
ejpam-5433	403	1	=	=	SYM
ejpam-5433	403	2	h.	h.	NOUN
ejpam-5433	403	3	(	(	PUNCT
ejpam-5433	403	4	b	b	X
ejpam-5433	403	5	)	)	PUNCT
ejpam-5433	403	6	x	x	X
ejpam-5433	404	1	=	=	PUNCT
ejpam-5433	404	2	ax	ax	NOUN
ejpam-5433	404	3	=	=	PUNCT
ejpam-5433	404	4	z.	z.	PROPN
ejpam-5433	404	5	in	in	ADP
ejpam-5433	404	6	case	case	NOUN
ejpam-5433	404	7	(	(	PUNCT
ejpam-5433	404	8	a	a	NOUN
ejpam-5433	404	9	)	)	PUNCT
ejpam-5433	404	10	,	,	PUNCT
ejpam-5433	404	11	for	for	ADP
ejpam-5433	404	12	an	an	DET
ejpam-5433	404	13	atomic	atomic	ADJ
ejpam-5433	404	14	solution	solution	NOUN
ejpam-5433	404	15	to	to	PART
ejpam-5433	404	16	exist	exist	VERB
ejpam-5433	404	17	we	we	PRON
ejpam-5433	404	18	must	must	AUX
ejpam-5433	404	19	have	have	VERB
ejpam-5433	404	20	three	three	NUM
ejpam-5433	404	21	situations	situation	NOUN
ejpam-5433	404	22	(	(	PUNCT
ejpam-5433	404	23	i	i	NOUN
ejpam-5433	404	24	)	)	PUNCT
ejpam-5433	404	25	u3α(t)−	u3α(t)−	PROPN
ejpam-5433	404	26	u2α(t)−	u2α(t)−	PROPN
ejpam-5433	404	27	uα(t	uα(t	VERB
ejpam-5433	404	28	)	)	PUNCT
ejpam-5433	404	29	=	=	SYM
ejpam-5433	404	30	0	0	X
ejpam-5433	404	31	.	.	PUNCT
ejpam-5433	404	32	r.	r.	PROPN
ejpam-5433	404	33	alkhateeb	alkhateeb	PROPN
ejpam-5433	404	34	,	,	PUNCT
ejpam-5433	404	35	g.	g.	PROPN
ejpam-5433	404	36	awwad	awwad	PROPN
ejpam-5433	404	37	/	/	PUNCT
ejpam-5433	404	38	eur	eur	PROPN
ejpam-5433	404	39	.	.	PUNCT
ejpam-5433	405	1	j.	j.	PROPN
ejpam-5433	405	2	pure	pure	PROPN
ejpam-5433	405	3	appl	appl	PROPN
ejpam-5433	405	4	.	.	PROPN
ejpam-5433	405	5	math	math	PROPN
ejpam-5433	405	6	,	,	PUNCT
ejpam-5433	405	7	17	17	NUM
ejpam-5433	405	8	(	(	PUNCT
ejpam-5433	405	9	4	4	NUM
ejpam-5433	405	10	)	)	PUNCT
ejpam-5433	405	11	(	(	PUNCT
ejpam-5433	405	12	2024	2024	NUM
ejpam-5433	405	13	)	)	PUNCT
ejpam-5433	405	14	,	,	PUNCT
ejpam-5433	405	15	3061	3061	NUM
ejpam-5433	405	16	-	-	SYM
ejpam-5433	405	17	3078	3078	NUM
ejpam-5433	405	18	3076	3076	NUM
ejpam-5433	406	1	so	so	ADV
ejpam-5433	406	2	,	,	PUNCT
ejpam-5433	406	3	we	we	PRON
ejpam-5433	406	4	can	can	AUX
ejpam-5433	406	5	solve	solve	VERB
ejpam-5433	406	6	it	it	PRON
ejpam-5433	406	7	as	as	ADP
ejpam-5433	406	8	in	in	ADP
ejpam-5433	406	9	[	[	X
ejpam-5433	406	10	3	3	NUM
ejpam-5433	406	11	]	]	X
ejpam-5433	406	12	r3	r3	PROPN
ejpam-5433	406	13	−	−	PROPN
ejpam-5433	406	14	r2	r2	PROPN
ejpam-5433	406	15	−	−	NOUN
ejpam-5433	406	16	r	r	NOUN
ejpam-5433	406	17	=	=	PUNCT
ejpam-5433	406	18	r(r2	r(r2	NOUN
ejpam-5433	406	19	−	−	NOUN
ejpam-5433	406	20	r	r	NOUN
ejpam-5433	406	21	−	−	NOUN
ejpam-5433	406	22	1	1	NUM
ejpam-5433	406	23	)	)	PUNCT
ejpam-5433	406	24	=	=	SYM
ejpam-5433	406	25	0	0	NUM
ejpam-5433	406	26	,	,	PUNCT
ejpam-5433	406	27	which	which	PRON
ejpam-5433	406	28	gives	give	VERB
ejpam-5433	406	29	r1	r1	PROPN
ejpam-5433	406	30	=	=	SYM
ejpam-5433	406	31	0	0	NUM
ejpam-5433	406	32	,	,	PUNCT
ejpam-5433	406	33	r2	r2	NOUN
ejpam-5433	406	34	=	=	NOUN
ejpam-5433	406	35	1	1	NUM
ejpam-5433	406	36	+	+	NUM
ejpam-5433	406	37	√	√	NUM
ejpam-5433	406	38	5	5	NUM
ejpam-5433	406	39	2	2	NUM
ejpam-5433	406	40	,	,	PUNCT
ejpam-5433	406	41	and	and	CCONJ
ejpam-5433	406	42	r3	r3	PROPN
ejpam-5433	406	43	=	=	SYM
ejpam-5433	406	44	1−	1−	NUM
ejpam-5433	406	45	√	√	NUM
ejpam-5433	406	46	5	5	NUM
ejpam-5433	406	47	2	2	NUM
ejpam-5433	406	48	.	.	PUNCT
ejpam-5433	407	1	so	so	ADV
ejpam-5433	407	2	,	,	PUNCT
ejpam-5433	407	3	u(t	u(t	NOUN
ejpam-5433	407	4	)	)	PUNCT
ejpam-5433	407	5	=	=	SYM
ejpam-5433	407	6	c1	c1	NOUN
ejpam-5433	407	7	+	+	CCONJ
ejpam-5433	407	8	c2e	c2e	PROPN
ejpam-5433	407	9	r2	r2	PROPN
ejpam-5433	407	10	(	(	PUNCT
ejpam-5433	407	11	tα	tα	PROPN
ejpam-5433	407	12	α	α	PROPN
ejpam-5433	407	13	)	)	PUNCT
ejpam-5433	408	1	+	+	CCONJ
ejpam-5433	408	2	c3e	c3e	PROPN
ejpam-5433	408	3	r3	r3	PROPN
ejpam-5433	408	4	(	(	PUNCT
ejpam-5433	408	5	tα	tα	PROPN
ejpam-5433	408	6	α	α	PROPN
ejpam-5433	408	7	)	)	PUNCT
ejpam-5433	408	8	.	.	PUNCT
ejpam-5433	409	1	by	by	ADP
ejpam-5433	409	2	assumption	assumption	NOUN
ejpam-5433	409	3	(	(	PUNCT
ejpam-5433	409	4	4	4	NUM
ejpam-5433	409	5	)	)	PUNCT
ejpam-5433	409	6	,	,	PUNCT
ejpam-5433	409	7	we	we	PRON
ejpam-5433	409	8	have	have	VERB
ejpam-5433	409	9	c1	c1	PROPN
ejpam-5433	409	10	=	=	SYM
ejpam-5433	409	11	2x0	2x0	PROPN
ejpam-5433	409	12	,	,	PUNCT
ejpam-5433	409	13	c2	c2	PROPN
ejpam-5433	409	14	=	=	PUNCT
ejpam-5433	409	15	x0√	x0√	PROPN
ejpam-5433	409	16	5	5	NUM
ejpam-5433	409	17	,	,	PUNCT
ejpam-5433	409	18	and	and	CCONJ
ejpam-5433	409	19	c3	c3	X
ejpam-5433	409	20	=	=	SYM
ejpam-5433	409	21	−x0√	−x0√	PROPN
ejpam-5433	409	22	5	5	NUM
ejpam-5433	409	23	.	.	PUNCT
ejpam-5433	410	1	hence	hence	ADV
ejpam-5433	410	2	,	,	PUNCT
ejpam-5433	410	3	u(t	u(t	PROPN
ejpam-5433	410	4	)	)	PUNCT
ejpam-5433	410	5	=	=	SYM
ejpam-5433	411	1	2x0	2x0	NUM
ejpam-5433	412	1	+	+	CCONJ
ejpam-5433	412	2	x0√	x0√	PROPN
ejpam-5433	412	3	5	5	NUM
ejpam-5433	412	4	e	e	NOUN
ejpam-5433	412	5	−1	−1	NOUN
ejpam-5433	412	6	+	+	NOUN
ejpam-5433	412	7	√	√	NUM
ejpam-5433	412	8	5	5	NUM
ejpam-5433	412	9	2	2	NUM
ejpam-5433	412	10	(	(	PUNCT
ejpam-5433	412	11	t	t	PROPN
ejpam-5433	412	12	α	α	PROPN
ejpam-5433	412	13	α	α	NOUN
ejpam-5433	412	14	)	)	PUNCT
ejpam-5433	412	15	−	−	PROPN
ejpam-5433	413	1	x0√	x0√	PROPN
ejpam-5433	413	2	5	5	NUM
ejpam-5433	413	3	e	e	NOUN
ejpam-5433	413	4	−1−	−1−	NOUN
ejpam-5433	413	5	√	√	ADP
ejpam-5433	413	6	5	5	NUM
ejpam-5433	413	7	2	2	NUM
ejpam-5433	413	8	(	(	PUNCT
ejpam-5433	413	9	t	t	PROPN
ejpam-5433	413	10	α	α	PROPN
ejpam-5433	413	11	α	α	PROPN
ejpam-5433	413	12	)	)	PUNCT
ejpam-5433	413	13	.	.	PUNCT
ejpam-5433	414	1	(	(	PUNCT
ejpam-5433	414	2	24	24	NUM
ejpam-5433	414	3	)	)	PUNCT
ejpam-5433	414	4	(	(	PUNCT
ejpam-5433	414	5	ii	ii	NOUN
ejpam-5433	414	6	)	)	PUNCT
ejpam-5433	414	7	u2α(t	u2α(t	PROPN
ejpam-5433	414	8	)	)	PUNCT
ejpam-5433	414	9	+	+	CCONJ
ejpam-5433	414	10	uα(t	uα(t	NOUN
ejpam-5433	414	11	)	)	PUNCT
ejpam-5433	415	1	=	=	SYM
ejpam-5433	415	2	h.	h.	PROPN
ejpam-5433	416	1	so	so	ADV
ejpam-5433	416	2	from	from	ADP
ejpam-5433	416	3	(	(	PUNCT
ejpam-5433	416	4	24	24	NUM
ejpam-5433	416	5	)	)	PUNCT
ejpam-5433	416	6	,	,	PUNCT
ejpam-5433	416	7	we	we	PRON
ejpam-5433	416	8	have	have	VERB
ejpam-5433	416	9	h	h	NOUN
ejpam-5433	416	10	=	=	PUNCT
ejpam-5433	416	11	(	(	PUNCT
ejpam-5433	416	12	1	1	NUM
ejpam-5433	416	13	+	+	NUM
ejpam-5433	416	14	2√	2√	NUM
ejpam-5433	416	15	5	5	NUM
ejpam-5433	416	16	)	)	PUNCT
ejpam-5433	416	17	x0e	x0e	PUNCT
ejpam-5433	417	1	−1	−1	NOUN
ejpam-5433	417	2	+	+	CCONJ
ejpam-5433	417	3	√	√	NUM
ejpam-5433	417	4	5	5	NUM
ejpam-5433	417	5	2	2	NUM
ejpam-5433	417	6	(	(	PUNCT
ejpam-5433	417	7	t	t	PROPN
ejpam-5433	417	8	α	α	PROPN
ejpam-5433	417	9	α	α	NOUN
ejpam-5433	417	10	)	)	PUNCT
ejpam-5433	418	1	+	+	CCONJ
ejpam-5433	418	2	(	(	PUNCT
ejpam-5433	418	3	1−	1−	NUM
ejpam-5433	418	4	2√	2√	NUM
ejpam-5433	418	5	5	5	NUM
ejpam-5433	418	6	)	)	PUNCT
ejpam-5433	418	7	x0e	x0e	PUNCT
ejpam-5433	419	1	−1−	−1−	NOUN
ejpam-5433	419	2	√	√	ADV
ejpam-5433	419	3	5	5	NUM
ejpam-5433	419	4	2	2	NUM
ejpam-5433	419	5	(	(	PUNCT
ejpam-5433	419	6	t	t	PROPN
ejpam-5433	419	7	α	α	PROPN
ejpam-5433	419	8	α	α	PROPN
ejpam-5433	419	9	)	)	PUNCT
ejpam-5433	419	10	.	.	PUNCT
ejpam-5433	420	1	so	so	ADV
ejpam-5433	420	2	,	,	PUNCT
ejpam-5433	420	3	for	for	ADP
ejpam-5433	420	4	an	an	DET
ejpam-5433	420	5	atomic	atomic	ADJ
ejpam-5433	420	6	solution	solution	NOUN
ejpam-5433	420	7	to	to	PART
ejpam-5433	420	8	exist	exist	VERB
ejpam-5433	420	9	hmust	hmust	ADV
ejpam-5433	420	10	equal	equal	ADJ
ejpam-5433	420	11	(	(	PUNCT
ejpam-5433	420	12	1	1	NUM
ejpam-5433	420	13	+	+	NUM
ejpam-5433	420	14	2√	2√	NUM
ejpam-5433	420	15	5	5	NUM
ejpam-5433	420	16	)	)	PUNCT
ejpam-5433	420	17	x0e	x0e	PUNCT
ejpam-5433	421	1	−1	−1	NOUN
ejpam-5433	421	2	+	+	CCONJ
ejpam-5433	421	3	√	√	NUM
ejpam-5433	421	4	5	5	NUM
ejpam-5433	421	5	2	2	NUM
ejpam-5433	421	6	(	(	PUNCT
ejpam-5433	421	7	t	t	PROPN
ejpam-5433	421	8	α	α	PROPN
ejpam-5433	421	9	α	α	PROPN
ejpam-5433	421	10	)	)	PUNCT
ejpam-5433	422	1	+	+	CCONJ
ejpam-5433	422	2	(	(	PUNCT
ejpam-5433	422	3	1−	1−	NUM
ejpam-5433	422	4	2√	2√	NUM
ejpam-5433	422	5	5	5	NUM
ejpam-5433	422	6	)	)	PUNCT
ejpam-5433	422	7	x0e	x0e	PUNCT
ejpam-5433	423	1	−1−	−1−	NOUN
ejpam-5433	423	2	√	√	ADV
ejpam-5433	423	3	5	5	NUM
ejpam-5433	423	4	2	2	NUM
ejpam-5433	423	5	(	(	PUNCT
ejpam-5433	423	6	t	t	PROPN
ejpam-5433	423	7	α	α	PROPN
ejpam-5433	423	8	α	α	PROPN
ejpam-5433	423	9	)	)	PUNCT
ejpam-5433	423	10	.	.	PUNCT
ejpam-5433	424	1	(	(	PUNCT
ejpam-5433	424	2	iii	iii	X
ejpam-5433	424	3	)	)	PUNCT
ejpam-5433	424	4	u3α(t	u3α(t	PROPN
ejpam-5433	424	5	)	)	PUNCT
ejpam-5433	425	1	=	=	SYM
ejpam-5433	425	2	h.	h.	PROPN
ejpam-5433	426	1	so	so	ADV
ejpam-5433	426	2	from	from	ADP
ejpam-5433	426	3	(	(	PUNCT
ejpam-5433	426	4	24	24	NUM
ejpam-5433	426	5	)	)	PUNCT
ejpam-5433	426	6	,	,	PUNCT
ejpam-5433	426	7	we	we	PRON
ejpam-5433	426	8	have	have	VERB
ejpam-5433	426	9	h	h	NOUN
ejpam-5433	426	10	=	=	SYM
ejpam-5433	426	11	c2r	c2r	NOUN
ejpam-5433	426	12	3	3	NUM
ejpam-5433	426	13	2e	2e	NOUN
ejpam-5433	426	14	r2	r2	PROPN
ejpam-5433	426	15	t	t	PROPN
ejpam-5433	426	16	α	α	PROPN
ejpam-5433	426	17	α	α	NOUN
ejpam-5433	427	1	+	+	CCONJ
ejpam-5433	427	2	c3r	c3r	ADJ
ejpam-5433	427	3	3	3	NUM
ejpam-5433	427	4	3e	3e	PROPN
ejpam-5433	427	5	r3	r3	PROPN
ejpam-5433	427	6	t	t	PROPN
ejpam-5433	427	7	α	α	NOUN
ejpam-5433	427	8	α	α	PROPN
ejpam-5433	427	9	.	.	PUNCT
ejpam-5433	428	1	hence	hence	ADV
ejpam-5433	428	2	,	,	PUNCT
ejpam-5433	428	3	h	h	NOUN
ejpam-5433	428	4	=	=	PRON
ejpam-5433	428	5	(	(	PUNCT
ejpam-5433	428	6	2√	2√	NUM
ejpam-5433	428	7	5	5	NUM
ejpam-5433	428	8	+	+	CCONJ
ejpam-5433	428	9	1)x0e	1)x0e	NUM
ejpam-5433	428	10	1	1	NUM
ejpam-5433	428	11	+	+	NUM
ejpam-5433	428	12	√	√	NUM
ejpam-5433	428	13	5	5	NUM
ejpam-5433	428	14	2	2	NUM
ejpam-5433	428	15	tα	tα	PROPN
ejpam-5433	428	16	α	α	NOUN
ejpam-5433	428	17	+	+	X
ejpam-5433	428	18	(	(	PUNCT
ejpam-5433	428	19	1−	1−	NUM
ejpam-5433	428	20	2√	2√	NUM
ejpam-5433	428	21	5	5	NUM
ejpam-5433	428	22	)	)	PUNCT
ejpam-5433	428	23	x0e	x0e	PROPN
ejpam-5433	429	1	1−	1−	NUM
ejpam-5433	430	1	√	√	NUM
ejpam-5433	430	2	5	5	NUM
ejpam-5433	430	3	2	2	NUM
ejpam-5433	430	4	tα	tα	PROPN
ejpam-5433	430	5	α	α	NOUN
ejpam-5433	430	6	.	.	PUNCT
ejpam-5433	431	1	since	since	SCONJ
ejpam-5433	431	2	u2α(t	u2α(t	NOUN
ejpam-5433	431	3	)	)	PUNCT
ejpam-5433	431	4	+	+	CCONJ
ejpam-5433	431	5	uα(t	uα(t	NOUN
ejpam-5433	431	6	)	)	PUNCT
ejpam-5433	431	7	=	=	SYM
ejpam-5433	431	8	u3α(t	u3α(t	PROPN
ejpam-5433	431	9	)	)	PUNCT
ejpam-5433	432	1	=	=	SYM
ejpam-5433	432	2	h	h	NOUN
ejpam-5433	432	3	in	in	ADP
ejpam-5433	432	4	(	(	PUNCT
ejpam-5433	432	5	ii	ii	NOUN
ejpam-5433	432	6	)	)	PUNCT
ejpam-5433	432	7	and	and	CCONJ
ejpam-5433	432	8	(	(	PUNCT
ejpam-5433	432	9	iii	iii	NOUN
ejpam-5433	432	10	)	)	PUNCT
ejpam-5433	432	11	,	,	PUNCT
ejpam-5433	432	12	there	there	PRON
ejpam-5433	432	13	is	be	VERB
ejpam-5433	432	14	an	an	DET
ejpam-5433	432	15	atomic	atomic	ADJ
ejpam-5433	432	16	solution	solution	NOUN
ejpam-5433	432	17	.	.	PUNCT
ejpam-5433	433	1	this	this	PRON
ejpam-5433	433	2	completes	complete	VERB
ejpam-5433	433	3	situation	situation	NOUN
ejpam-5433	433	4	(	(	PUNCT
ejpam-5433	433	5	2	2	NUM
ejpam-5433	433	6	)	)	PUNCT
ejpam-5433	433	7	,	,	PUNCT
ejpam-5433	433	8	and	and	CCONJ
ejpam-5433	433	9	hence	hence	ADV
ejpam-5433	433	10	,	,	PUNCT
ejpam-5433	433	11	case	case	NOUN
ejpam-5433	433	12	three	three	NUM
ejpam-5433	433	13	is	be	AUX
ejpam-5433	433	14	completed	complete	VERB
ejpam-5433	433	15	.	.	PUNCT
ejpam-5433	434	1	case	case	NOUN
ejpam-5433	434	2	four	four	NUM
ejpam-5433	434	3	:	:	PUNCT
ejpam-5433	434	4	(	(	PUNCT
ejpam-5433	434	5	u3α	u3α	INTJ
ejpam-5433	434	6	⊗	⊗	ADJ
ejpam-5433	434	7	x+	x+	ADJ
ejpam-5433	434	8	u2α	u2α	NOUN
ejpam-5433	434	9	⊗ax+	⊗ax+	ADV
ejpam-5433	434	10	uα	uα	PROPN
ejpam-5433	434	11	⊗bx	⊗bx	X
ejpam-5433	434	12	)	)	PUNCT
ejpam-5433	434	13	is	be	AUX
ejpam-5433	434	14	an	an	DET
ejpam-5433	434	15	atom	atom	NOUN
ejpam-5433	434	16	.	.	PUNCT
ejpam-5433	435	1	this	this	PRON
ejpam-5433	435	2	has	have	VERB
ejpam-5433	435	3	two	two	NUM
ejpam-5433	435	4	situations	situation	NOUN
ejpam-5433	435	5	:	:	PUNCT
ejpam-5433	435	6	(	(	PUNCT
ejpam-5433	435	7	1	1	X
ejpam-5433	435	8	)	)	PUNCT
ejpam-5433	435	9	u3α	u3α	NOUN
ejpam-5433	435	10	=	=	NOUN
ejpam-5433	435	11	u2α	u2α	NOUN
ejpam-5433	435	12	=	=	PUNCT
ejpam-5433	435	13	uα	uα	PROPN
ejpam-5433	435	14	=	=	PUNCT
ejpam-5433	435	15	h.	h.	PROPN
ejpam-5433	435	16	(	(	PUNCT
ejpam-5433	435	17	2	2	NUM
ejpam-5433	435	18	)	)	PUNCT
ejpam-5433	435	19	x	x	X
ejpam-5433	436	1	=	=	PUNCT
ejpam-5433	436	2	ax	ax	NOUN
ejpam-5433	436	3	=	=	NOUN
ejpam-5433	436	4	bx	bx	NOUN
ejpam-5433	436	5	=	=	PUNCT
ejpam-5433	436	6	z.	z.	PROPN
ejpam-5433	436	7	considering	consider	VERB
ejpam-5433	436	8	situation	situation	NOUN
ejpam-5433	436	9	(	(	PUNCT
ejpam-5433	436	10	1	1	NUM
ejpam-5433	436	11	)	)	PUNCT
ejpam-5433	436	12	,	,	PUNCT
ejpam-5433	436	13	equation	equation	NOUN
ejpam-5433	436	14	(	(	PUNCT
ejpam-5433	436	15	5	5	X
ejpam-5433	436	16	)	)	PUNCT
ejpam-5433	436	17	becomes	become	VERB
ejpam-5433	436	18	:	:	PUNCT
ejpam-5433	436	19	u3α	u3α	PROPN
ejpam-5433	436	20	⊗	⊗	PROPN
ejpam-5433	436	21	(	(	PUNCT
ejpam-5433	436	22	x+ax+bx	x+ax+bx	PROPN
ejpam-5433	436	23	)	)	PUNCT
ejpam-5433	436	24	=	=	SYM
ejpam-5433	436	25	h⊗	h⊗	VERB
ejpam-5433	436	26	z.	z.	PROPN
ejpam-5433	437	1	so	so	ADV
ejpam-5433	437	2	,	,	PUNCT
ejpam-5433	437	3	we	we	PRON
ejpam-5433	437	4	have	have	VERB
ejpam-5433	437	5	seven	seven	NUM
ejpam-5433	437	6	cases	case	NOUN
ejpam-5433	437	7	:	:	PUNCT
ejpam-5433	437	8	r.	r.	PROPN
ejpam-5433	437	9	alkhateeb	alkhateeb	PROPN
ejpam-5433	437	10	,	,	PUNCT
ejpam-5433	437	11	g.	g.	PROPN
ejpam-5433	437	12	awwad	awwad	PROPN
ejpam-5433	437	13	/	/	PUNCT
ejpam-5433	437	14	eur	eur	PROPN
ejpam-5433	437	15	.	.	PUNCT
ejpam-5433	438	1	j.	j.	PROPN
ejpam-5433	438	2	pure	pure	PROPN
ejpam-5433	438	3	appl	appl	PROPN
ejpam-5433	438	4	.	.	PROPN
ejpam-5433	438	5	math	math	PROPN
ejpam-5433	438	6	,	,	PUNCT
ejpam-5433	438	7	17	17	NUM
ejpam-5433	438	8	(	(	PUNCT
ejpam-5433	438	9	4	4	NUM
ejpam-5433	438	10	)	)	PUNCT
ejpam-5433	438	11	(	(	PUNCT
ejpam-5433	438	12	2024	2024	NUM
ejpam-5433	438	13	)	)	PUNCT
ejpam-5433	438	14	,	,	PUNCT
ejpam-5433	438	15	3061	3061	NUM
ejpam-5433	438	16	-	-	SYM
ejpam-5433	438	17	3078	3078	NUM
ejpam-5433	438	18	3077	3077	NUM
ejpam-5433	438	19	(	(	PUNCT
ejpam-5433	438	20	a	a	NOUN
ejpam-5433	438	21	)	)	PUNCT
ejpam-5433	438	22	u3α	u3α	NOUN
ejpam-5433	438	23	=	=	PUNCT
ejpam-5433	438	24	u2α	u2α	ADJ
ejpam-5433	438	25	.	.	PUNCT
ejpam-5433	439	1	we	we	PRON
ejpam-5433	439	2	can	can	AUX
ejpam-5433	439	3	solve	solve	VERB
ejpam-5433	439	4	it	it	PRON
ejpam-5433	439	5	as	as	ADP
ejpam-5433	439	6	in	in	ADP
ejpam-5433	439	7	[	[	X
ejpam-5433	439	8	3	3	NUM
ejpam-5433	439	9	]	]	X
ejpam-5433	439	10	r3	r3	PROPN
ejpam-5433	439	11	−	−	PROPN
ejpam-5433	439	12	r2	r2	NOUN
ejpam-5433	439	13	=	=	PUNCT
ejpam-5433	440	1	r2(r	r2(r	VERB
ejpam-5433	440	2	−	−	NOUN
ejpam-5433	440	3	1	1	NUM
ejpam-5433	440	4	)	)	PUNCT
ejpam-5433	440	5	=	=	SYM
ejpam-5433	441	1	0	0	X
ejpam-5433	441	2	.	.	PUNCT
ejpam-5433	442	1	hence	hence	ADV
ejpam-5433	442	2	,	,	PUNCT
ejpam-5433	442	3	r1	r1	PROPN
ejpam-5433	442	4	=	=	SYM
ejpam-5433	442	5	0	0	NUM
ejpam-5433	442	6	,	,	PUNCT
ejpam-5433	442	7	r2	r2	PROPN
ejpam-5433	442	8	=	=	SYM
ejpam-5433	442	9	0	0	NUM
ejpam-5433	442	10	,	,	PUNCT
ejpam-5433	442	11	and	and	CCONJ
ejpam-5433	442	12	r3	r3	PROPN
ejpam-5433	442	13	=	=	SYM
ejpam-5433	442	14	1	1	X
ejpam-5433	442	15	.	.	PUNCT
ejpam-5433	442	16	consequently	consequently	ADV
ejpam-5433	442	17	,	,	PUNCT
ejpam-5433	442	18	u(t	u(t	PROPN
ejpam-5433	442	19	)	)	PUNCT
ejpam-5433	442	20	=	=	PROPN
ejpam-5433	442	21	c1	c1	PROPN
ejpam-5433	442	22	+	+	CCONJ
ejpam-5433	442	23	c2	c2	PROPN
ejpam-5433	442	24	(	(	PUNCT
ejpam-5433	442	25	tα	tα	PROPN
ejpam-5433	442	26	α	α	PROPN
ejpam-5433	442	27	)	)	PUNCT
ejpam-5433	443	1	+	+	CCONJ
ejpam-5433	443	2	c3e	c3e	PROPN
ejpam-5433	443	3	tα	tα	NUM
ejpam-5433	443	4	α	α	PROPN
ejpam-5433	443	5	.	.	PUNCT
ejpam-5433	444	1	by	by	ADP
ejpam-5433	444	2	assumption	assumption	NOUN
ejpam-5433	444	3	(	(	PUNCT
ejpam-5433	444	4	4	4	NUM
ejpam-5433	444	5	)	)	PUNCT
ejpam-5433	444	6	,	,	PUNCT
ejpam-5433	444	7	we	we	PRON
ejpam-5433	444	8	have	have	VERB
ejpam-5433	444	9	c1	c1	PROPN
ejpam-5433	444	10	=	=	PUNCT
ejpam-5433	444	11	x0	x0	PROPN
ejpam-5433	444	12	,	,	PUNCT
ejpam-5433	444	13	c2	c2	PROPN
ejpam-5433	444	14	=	=	SYM
ejpam-5433	444	15	0	0	NUM
ejpam-5433	444	16	,	,	PUNCT
ejpam-5433	444	17	and	and	CCONJ
ejpam-5433	444	18	c3	c3	PROPN
ejpam-5433	444	19	=	=	PUNCT
ejpam-5433	444	20	x0	x0	PROPN
ejpam-5433	444	21	.	.	PUNCT
ejpam-5433	445	1	hence	hence	ADV
ejpam-5433	445	2	,	,	PUNCT
ejpam-5433	445	3	u(t	u(t	PROPN
ejpam-5433	445	4	)	)	PUNCT
ejpam-5433	445	5	=	=	PUNCT
ejpam-5433	446	1	x0	x0	PROPN
ejpam-5433	447	1	+	+	CCONJ
ejpam-5433	447	2	x0e	x0e	PUNCT
ejpam-5433	447	3	tα	tα	PROPN
ejpam-5433	447	4	α	α	NOUN
ejpam-5433	447	5	.	.	PUNCT
ejpam-5433	448	1	(	(	PUNCT
ejpam-5433	448	2	b	b	X
ejpam-5433	448	3	)	)	PUNCT
ejpam-5433	448	4	u3α	u3α	NOUN
ejpam-5433	448	5	=	=	SYM
ejpam-5433	448	6	uα	uα	PROPN
ejpam-5433	448	7	.	.	PUNCT
ejpam-5433	449	1	we	we	PRON
ejpam-5433	449	2	can	can	AUX
ejpam-5433	449	3	solve	solve	VERB
ejpam-5433	449	4	it	it	PRON
ejpam-5433	449	5	as	as	ADP
ejpam-5433	449	6	in	in	ADP
ejpam-5433	449	7	[	[	X
ejpam-5433	449	8	3	3	NUM
ejpam-5433	449	9	]	]	X
ejpam-5433	449	10	r3	r3	NOUN
ejpam-5433	449	11	−	−	NOUN
ejpam-5433	449	12	r	r	NOUN
ejpam-5433	449	13	=	=	PUNCT
ejpam-5433	449	14	r(r2	r(r2	NOUN
ejpam-5433	449	15	−	−	NOUN
ejpam-5433	449	16	1	1	NUM
ejpam-5433	449	17	)	)	PUNCT
ejpam-5433	449	18	=	=	NOUN
ejpam-5433	450	1	r(r	r(r	NOUN
ejpam-5433	450	2	−	−	PROPN
ejpam-5433	451	1	1)(r	1)(r	NUM
ejpam-5433	451	2	+	+	CCONJ
ejpam-5433	451	3	1	1	X
ejpam-5433	451	4	)	)	PUNCT
ejpam-5433	451	5	=	=	SYM
ejpam-5433	452	1	0	0	X
ejpam-5433	452	2	.	.	PUNCT
ejpam-5433	453	1	hence	hence	ADV
ejpam-5433	453	2	,	,	PUNCT
ejpam-5433	453	3	r1	r1	PROPN
ejpam-5433	453	4	=	=	SYM
ejpam-5433	453	5	0	0	NUM
ejpam-5433	453	6	,	,	PUNCT
ejpam-5433	453	7	r2	r2	PROPN
ejpam-5433	453	8	=	=	SYM
ejpam-5433	453	9	1	1	NUM
ejpam-5433	453	10	,	,	PUNCT
ejpam-5433	453	11	and	and	CCONJ
ejpam-5433	453	12	r3	r3	PROPN
ejpam-5433	453	13	=	=	SYM
ejpam-5433	453	14	−1	−1	NOUN
ejpam-5433	453	15	.	.	PUNCT
ejpam-5433	454	1	consequently	consequently	ADV
ejpam-5433	454	2	,	,	PUNCT
ejpam-5433	454	3	u(t	u(t	NOUN
ejpam-5433	454	4	)	)	PUNCT
ejpam-5433	454	5	=	=	SYM
ejpam-5433	454	6	c1	c1	NOUN
ejpam-5433	454	7	+	+	CCONJ
ejpam-5433	454	8	c2e	c2e	PROPN
ejpam-5433	454	9	tα	tα	PROPN
ejpam-5433	454	10	α	α	NOUN
ejpam-5433	454	11	+	+	CCONJ
ejpam-5433	454	12	c3e	c3e	PROPN
ejpam-5433	454	13	−	−	PROPN
ejpam-5433	454	14	tα	tα	PROPN
ejpam-5433	454	15	α	α	PROPN
ejpam-5433	454	16	.	.	PUNCT
ejpam-5433	455	1	by	by	ADP
ejpam-5433	455	2	assumption	assumption	NOUN
ejpam-5433	455	3	(	(	PUNCT
ejpam-5433	455	4	4	4	NUM
ejpam-5433	455	5	)	)	PUNCT
ejpam-5433	455	6	,	,	PUNCT
ejpam-5433	455	7	we	we	PRON
ejpam-5433	455	8	have	have	VERB
ejpam-5433	455	9	c1	c1	PROPN
ejpam-5433	455	10	=	=	PUNCT
ejpam-5433	455	11	x0	x0	PROPN
ejpam-5433	455	12	,	,	PUNCT
ejpam-5433	455	13	c2	c2	PROPN
ejpam-5433	455	14	=	=	PUNCT
ejpam-5433	455	15	x0	x0	PROPN
ejpam-5433	455	16	,	,	PUNCT
ejpam-5433	455	17	and	and	CCONJ
ejpam-5433	455	18	c3	c3	X
ejpam-5433	455	19	=	=	PROPN
ejpam-5433	455	20	0	0	X
ejpam-5433	455	21	.	.	PUNCT
ejpam-5433	456	1	hence	hence	ADV
ejpam-5433	456	2	,	,	PUNCT
ejpam-5433	456	3	u(t	u(t	PROPN
ejpam-5433	456	4	)	)	PUNCT
ejpam-5433	456	5	=	=	PUNCT
ejpam-5433	457	1	x0	x0	PROPN
ejpam-5433	458	1	+	+	CCONJ
ejpam-5433	458	2	x0e	x0e	PUNCT
ejpam-5433	458	3	tα	tα	PROPN
ejpam-5433	458	4	α	α	PROPN
ejpam-5433	458	5	.	.	PUNCT
ejpam-5433	459	1	(	(	PUNCT
ejpam-5433	459	2	c	c	X
ejpam-5433	459	3	)	)	PUNCT
ejpam-5433	459	4	u2α	u2α	NOUN
ejpam-5433	459	5	=	=	PUNCT
ejpam-5433	459	6	uα	uα	PROPN
ejpam-5433	459	7	.	.	PUNCT
ejpam-5433	460	1	we	we	PRON
ejpam-5433	460	2	can	can	AUX
ejpam-5433	460	3	solve	solve	VERB
ejpam-5433	460	4	it	it	PRON
ejpam-5433	460	5	as	as	ADP
ejpam-5433	460	6	in	in	ADP
ejpam-5433	460	7	[	[	X
ejpam-5433	460	8	3	3	NUM
ejpam-5433	460	9	]	]	PUNCT
ejpam-5433	460	10	(	(	PUNCT
ejpam-5433	460	11	r2	r2	PROPN
ejpam-5433	460	12	−	−	PROPN
ejpam-5433	460	13	r	r	NOUN
ejpam-5433	460	14	)	)	PUNCT
ejpam-5433	460	15	=	=	NOUN
ejpam-5433	461	1	r(r	r(r	NOUN
ejpam-5433	461	2	−	−	PROPN
ejpam-5433	461	3	1	1	X
ejpam-5433	461	4	)	)	PUNCT
ejpam-5433	461	5	=	=	SYM
ejpam-5433	461	6	0	0	X
ejpam-5433	461	7	.	.	PUNCT
ejpam-5433	462	1	hence	hence	ADV
ejpam-5433	462	2	,	,	PUNCT
ejpam-5433	462	3	r1	r1	PROPN
ejpam-5433	462	4	=	=	SYM
ejpam-5433	462	5	0	0	NUM
ejpam-5433	462	6	and	and	CCONJ
ejpam-5433	462	7	r2	r2	PROPN
ejpam-5433	462	8	=	=	SYM
ejpam-5433	462	9	1	1	X
ejpam-5433	462	10	.	.	PUNCT
ejpam-5433	462	11	consequently	consequently	ADV
ejpam-5433	462	12	,	,	PUNCT
ejpam-5433	462	13	u(t	u(t	PROPN
ejpam-5433	462	14	)	)	PUNCT
ejpam-5433	462	15	=	=	SYM
ejpam-5433	462	16	c1	c1	NOUN
ejpam-5433	462	17	+	+	CCONJ
ejpam-5433	462	18	c2e	c2e	PROPN
ejpam-5433	462	19	tα	tα	PROPN
ejpam-5433	462	20	α	α	NOUN
ejpam-5433	462	21	by	by	ADP
ejpam-5433	462	22	assumption	assumption	NOUN
ejpam-5433	462	23	(	(	PUNCT
ejpam-5433	462	24	4	4	NUM
ejpam-5433	462	25	)	)	PUNCT
ejpam-5433	462	26	,	,	PUNCT
ejpam-5433	462	27	we	we	PRON
ejpam-5433	462	28	have	have	VERB
ejpam-5433	462	29	c1	c1	PROPN
ejpam-5433	462	30	=	=	PUNCT
ejpam-5433	462	31	x0	x0	PROPN
ejpam-5433	462	32	and	and	CCONJ
ejpam-5433	462	33	c2	c2	PROPN
ejpam-5433	462	34	=	=	PUNCT
ejpam-5433	462	35	x0	x0	PROPN
ejpam-5433	462	36	.	.	PUNCT
ejpam-5433	463	1	hence	hence	ADV
ejpam-5433	463	2	,	,	PUNCT
ejpam-5433	463	3	u(t	u(t	PROPN
ejpam-5433	463	4	)	)	PUNCT
ejpam-5433	463	5	=	=	PUNCT
ejpam-5433	464	1	x0	x0	PROPN
ejpam-5433	465	1	+	+	CCONJ
ejpam-5433	465	2	x0e	x0e	PUNCT
ejpam-5433	465	3	tα	tα	PROPN
ejpam-5433	465	4	α	α	PROPN
ejpam-5433	465	5	.	.	PUNCT
ejpam-5433	466	1	references	reference	NOUN
ejpam-5433	466	2	3078	3078	NUM
ejpam-5433	466	3	(	(	PUNCT
ejpam-5433	466	4	d	d	NOUN
ejpam-5433	466	5	)	)	PUNCT
ejpam-5433	466	6	u3α	u3α	PROPN
ejpam-5433	466	7	=	=	PROPN
ejpam-5433	466	8	h.	h.	PROPN
ejpam-5433	466	9	consequently	consequently	ADV
ejpam-5433	466	10	,	,	PUNCT
ejpam-5433	466	11	h	h	PROPN
ejpam-5433	467	1	=	=	PUNCT
ejpam-5433	467	2	x0e	x0e	PROPN
ejpam-5433	467	3	tα	tα	PROPN
ejpam-5433	467	4	α	α	INTJ
ejpam-5433	467	5	.	.	PUNCT
ejpam-5433	468	1	so	so	ADV
ejpam-5433	468	2	,	,	PUNCT
ejpam-5433	468	3	for	for	ADP
ejpam-5433	468	4	an	an	DET
ejpam-5433	468	5	atomic	atomic	ADJ
ejpam-5433	468	6	solution	solution	NOUN
ejpam-5433	468	7	to	to	PART
ejpam-5433	468	8	exist	exist	VERB
ejpam-5433	468	9	h	h	NOUN
ejpam-5433	468	10	must	must	AUX
ejpam-5433	468	11	equal	equal	VERB
ejpam-5433	468	12	x0e	x0e	PUNCT
ejpam-5433	468	13	tα	tα	PROPN
ejpam-5433	468	14	α	α	INTJ
ejpam-5433	468	15	.	.	PUNCT
ejpam-5433	469	1	(	(	PUNCT
ejpam-5433	469	2	e	e	NOUN
ejpam-5433	469	3	)	)	PUNCT
ejpam-5433	469	4	u2α	u2α	NOUN
ejpam-5433	469	5	=	=	PUNCT
ejpam-5433	469	6	h	h	NOUN
ejpam-5433	470	1	=	=	PUNCT
ejpam-5433	470	2	x0e	x0e	PROPN
ejpam-5433	470	3	tα	tα	PROPN
ejpam-5433	470	4	α	α	INTJ
ejpam-5433	470	5	.	.	PUNCT
ejpam-5433	471	1	(	(	PUNCT
ejpam-5433	471	2	f	f	X
ejpam-5433	471	3	)	)	PUNCT
ejpam-5433	471	4	uα	uα	NOUN
ejpam-5433	471	5	=	=	PUNCT
ejpam-5433	471	6	h	h	PROPN
ejpam-5433	472	1	=	=	PUNCT
ejpam-5433	472	2	x0e	x0e	PROPN
ejpam-5433	472	3	tα	tα	PROPN
ejpam-5433	472	4	α	α	PROPN
ejpam-5433	472	5	.	.	PUNCT
ejpam-5433	473	1	hence	hence	ADV
ejpam-5433	473	2	,	,	PUNCT
ejpam-5433	473	3	(	(	PUNCT
ejpam-5433	473	4	e	e	NOUN
ejpam-5433	473	5	)	)	PUNCT
ejpam-5433	473	6	and	and	CCONJ
ejpam-5433	473	7	(	(	PUNCT
ejpam-5433	473	8	f	f	X
ejpam-5433	473	9	)	)	PUNCT
ejpam-5433	473	10	give	give	VERB
ejpam-5433	473	11	the	the	DET
ejpam-5433	473	12	same	same	ADJ
ejpam-5433	473	13	result	result	NOUN
ejpam-5433	473	14	,	,	PUNCT
ejpam-5433	473	15	there	there	PRON
ejpam-5433	473	16	is	be	VERB
ejpam-5433	473	17	an	an	DET
ejpam-5433	473	18	atomic	atomic	ADJ
ejpam-5433	473	19	solution	solution	NOUN
ejpam-5433	473	20	in	in	ADP
ejpam-5433	473	21	this	this	DET
ejpam-5433	473	22	case	case	NOUN
ejpam-5433	473	23	and	and	CCONJ
ejpam-5433	473	24	h	h	NOUN
ejpam-5433	474	1	=	=	PUNCT
ejpam-5433	474	2	x0e	x0e	PROPN
ejpam-5433	474	3	tα	tα	PROPN
ejpam-5433	474	4	α	α	INTJ
ejpam-5433	474	5	.	.	PUNCT
ejpam-5433	475	1	in	in	ADP
ejpam-5433	475	2	situation	situation	NOUN
ejpam-5433	475	3	(	(	PUNCT
ejpam-5433	475	4	2	2	NUM
ejpam-5433	475	5	)	)	PUNCT
ejpam-5433	475	6	,	,	PUNCT
ejpam-5433	475	7	equation	equation	NOUN
ejpam-5433	475	8	(	(	PUNCT
ejpam-5433	475	9	5	5	NUM
ejpam-5433	475	10	)	)	PUNCT
ejpam-5433	475	11	will	will	AUX
ejpam-5433	475	12	be	be	AUX
ejpam-5433	475	13	e	e	NOUN
ejpam-5433	475	14	tα	tα	PROPN
ejpam-5433	475	15	α	α	PROPN
ejpam-5433	475	16	⊗	⊗	PROPN
ejpam-5433	475	17	x+	x+	PROPN
ejpam-5433	476	1	e	e	X
ejpam-5433	476	2	tα	tα	PROPN
ejpam-5433	476	3	α	α	PRON
ejpam-5433	476	4	⊗ax+	⊗ax+	ADJ
ejpam-5433	476	5	e	e	NOUN
ejpam-5433	476	6	tα	tα	PROPN
ejpam-5433	476	7	α	α	DET
ejpam-5433	476	8	bx	bx	NOUN
ejpam-5433	476	9	=	=	PUNCT
ejpam-5433	476	10	e	e	PROPN
ejpam-5433	476	11	tα	tα	PROPN
ejpam-5433	476	12	α	α	PROPN
ejpam-5433	476	13	⊗	⊗	PROPN
ejpam-5433	476	14	z.	z.	PROPN
ejpam-5433	477	1	so	so	ADV
ejpam-5433	477	2	,	,	PUNCT
ejpam-5433	477	3	(	(	PUNCT
ejpam-5433	477	4	i	i	NOUN
ejpam-5433	477	5	+	+	NOUN
ejpam-5433	477	6	a+b)x	a+b)x	X
ejpam-5433	477	7	=	=	PUNCT
ejpam-5433	477	8	z.	z.	PROPN
ejpam-5433	477	9	hence	hence	ADV
ejpam-5433	477	10	,	,	PUNCT
ejpam-5433	477	11	z	z	PROPN
ejpam-5433	477	12	is	be	AUX
ejpam-5433	477	13	the	the	DET
ejpam-5433	477	14	image	image	NOUN
ejpam-5433	477	15	of	of	ADP
ejpam-5433	477	16	x	x	SYM
ejpam-5433	477	17	under	under	ADP
ejpam-5433	477	18	(	(	PUNCT
ejpam-5433	477	19	i	i	PRON
ejpam-5433	477	20	+	+	NOUN
ejpam-5433	477	21	a+b	a+b	NUM
ejpam-5433	477	22	)	)	PUNCT
ejpam-5433	477	23	.	.	PUNCT
ejpam-5433	478	1	this	this	PRON
ejpam-5433	478	2	completes	complete	VERB
ejpam-5433	478	3	situation	situation	NOUN
ejpam-5433	478	4	(	(	PUNCT
ejpam-5433	478	5	2	2	NUM
ejpam-5433	478	6	)	)	PUNCT
ejpam-5433	478	7	,	,	PUNCT
ejpam-5433	478	8	and	and	CCONJ
ejpam-5433	478	9	hence	hence	ADV
ejpam-5433	478	10	,	,	PUNCT
ejpam-5433	478	11	case	case	NOUN
ejpam-5433	478	12	four	four	NUM
ejpam-5433	478	13	is	be	AUX
ejpam-5433	478	14	completed	complete	VERB
ejpam-5433	478	15	.	.	PUNCT
ejpam-5433	479	1	acknowledgements	acknowledgement	NOUN
ejpam-5433	479	2	the	the	DET
ejpam-5433	479	3	authors	author	NOUN
ejpam-5433	479	4	are	be	AUX
ejpam-5433	479	5	grateful	grateful	ADJ
ejpam-5433	479	6	to	to	ADP
ejpam-5433	479	7	the	the	DET
ejpam-5433	479	8	reviewers	reviewer	NOUN
ejpam-5433	479	9	for	for	ADP
ejpam-5433	479	10	their	their	PRON
ejpam-5433	479	11	careful	careful	ADJ
ejpam-5433	479	12	reading	reading	NOUN
ejpam-5433	479	13	and	and	CCONJ
ejpam-5433	479	14	valuable	valuable	ADJ
ejpam-5433	479	15	suggestions	suggestion	NOUN
ejpam-5433	479	16	.	.	PUNCT
ejpam-5433	480	1	references	reference	NOUN
ejpam-5433	480	2	[	[	X
ejpam-5433	480	3	1	1	NUM
ejpam-5433	480	4	]	]	PUNCT
ejpam-5433	480	5	t	t	NOUN
ejpam-5433	480	6	abdeljawad	abdeljawad	NOUN
ejpam-5433	480	7	.	.	PUNCT
ejpam-5433	481	1	on	on	ADP
ejpam-5433	481	2	conformable	conformable	ADJ
ejpam-5433	481	3	fractional	fractional	ADJ
ejpam-5433	481	4	calculus	calculus	NOUN
ejpam-5433	481	5	.	.	PUNCT
ejpam-5433	482	1	j.	j.	PROPN
ejpam-5433	482	2	comput	comput	PROPN
ejpam-5433	482	3	.	.	PUNCT
ejpam-5433	483	1	appl	appl	PROPN
ejpam-5433	483	2	.	.	PROPN
ejpam-5433	483	3	math	math	PROPN
ejpam-5433	483	4	.	.	PUNCT
ejpam-5433	483	5	,	,	PUNCT
ejpam-5433	483	6	279:57	279:57	NUM
ejpam-5433	483	7	–	–	PUNCT
ejpam-5433	483	8	66	66	NUM
ejpam-5433	483	9	,	,	PUNCT
ejpam-5433	483	10	2015	2015	NUM
ejpam-5433	483	11	.	.	PUNCT
ejpam-5433	484	1	[	[	X
ejpam-5433	484	2	2	2	NUM
ejpam-5433	484	3	]	]	PUNCT
ejpam-5433	484	4	m	m	VERB
ejpam-5433	484	5	alhorani	alhorani	ADJ
ejpam-5433	484	6	,	,	PUNCT
ejpam-5433	484	7	m	m	VERB
ejpam-5433	484	8	abuhammad	abuhammad	ADJ
ejpam-5433	484	9	,	,	PUNCT
ejpam-5433	484	10	and	and	CCONJ
ejpam-5433	484	11	r	r	PROPN
ejpam-5433	484	12	khalil	khalil	PROPN
ejpam-5433	484	13	.	.	PUNCT
ejpam-5433	485	1	variation	variation	NOUN
ejpam-5433	485	2	of	of	ADP
ejpam-5433	485	3	parameters	parameter	NOUN
ejpam-5433	485	4	for	for	ADP
ejpam-5433	485	5	local	local	ADJ
ejpam-5433	485	6	fractional	fractional	ADJ
ejpam-5433	485	7	nonhomogeneous	nonhomogeneous	ADJ
ejpam-5433	485	8	linear	linear	ADJ
ejpam-5433	485	9	-	-	PUNCT
ejpam-5433	485	10	differential	differential	NOUN
ejpam-5433	485	11	equation	equation	NOUN
ejpam-5433	485	12	.	.	PUNCT
ejpam-5433	486	1	j.	j.	PROPN
ejpam-5433	486	2	math	math	PROPN
ejpam-5433	486	3	.	.	PUNCT
ejpam-5433	487	1	computer	computer	PROPN
ejpam-5433	487	2	sci	sci	PROPN
ejpam-5433	487	3	.	.	PROPN
ejpam-5433	487	4	,	,	PUNCT
ejpam-5433	487	5	16:140–146	16:140–146	PROPN
ejpam-5433	487	6	,	,	PUNCT
ejpam-5433	487	7	2016	2016	NUM
ejpam-5433	487	8	.	.	PUNCT
ejpam-5433	488	1	[	[	X
ejpam-5433	488	2	3	3	NUM
ejpam-5433	488	3	]	]	X
ejpam-5433	488	4	m	m	VERB
ejpam-5433	488	5	alhorani	alhorani	ADJ
ejpam-5433	488	6	,	,	PUNCT
ejpam-5433	488	7	r	r	NOUN
ejpam-5433	488	8	khalil	khalil	PROPN
ejpam-5433	488	9	,	,	PUNCT
ejpam-5433	488	10	and	and	CCONJ
ejpam-5433	488	11	i	i	PRON
ejpam-5433	488	12	aldarawi	aldarawi	VERB
ejpam-5433	488	13	.	.	PUNCT
ejpam-5433	489	1	fractional	fractional	PROPN
ejpam-5433	489	2	cauchy	cauchy	PROPN
ejpam-5433	489	3	euler	euler	PROPN
ejpam-5433	489	4	differential	differential	PROPN
ejpam-5433	489	5	equation	equation	NOUN
ejpam-5433	489	6	.	.	PUNCT
ejpam-5433	490	1	j.	j.	PROPN
ejpam-5433	490	2	comput	comput	PROPN
ejpam-5433	490	3	.	.	PUNCT
ejpam-5433	491	1	anal	anal	PROPN
ejpam-5433	491	2	.	.	PUNCT
ejpam-5433	491	3	appl	appl	PROPN
ejpam-5433	491	4	.	.	PROPN
ejpam-5433	491	5	,	,	PUNCT
ejpam-5433	491	6	28:226–233	28:226–233	NUM
ejpam-5433	491	7	,	,	PUNCT
ejpam-5433	491	8	2020	2020	NUM
ejpam-5433	491	9	.	.	PUNCT
ejpam-5433	492	1	[	[	X
ejpam-5433	492	2	4	4	NUM
ejpam-5433	492	3	]	]	X
ejpam-5433	492	4	r	r	NOUN
ejpam-5433	492	5	khalil	khalil	PROPN
ejpam-5433	492	6	,	,	PUNCT
ejpam-5433	492	7	m	m	PROPN
ejpam-5433	492	8	alhorani	alhorani	ADJ
ejpam-5433	492	9	,	,	PUNCT
ejpam-5433	492	10	a	a	DET
ejpam-5433	492	11	yousef	yousef	PROPN
ejpam-5433	492	12	,	,	PUNCT
ejpam-5433	492	13	and	and	CCONJ
ejpam-5433	492	14	m	m	PROPN
ejpam-5433	492	15	sababheh	sababheh	ADJ
ejpam-5433	492	16	.	.	PUNCT
ejpam-5433	493	1	a	a	DET
ejpam-5433	493	2	new	new	ADJ
ejpam-5433	493	3	definition	definition	NOUN
ejpam-5433	493	4	of	of	ADP
ejpam-5433	493	5	fractional	fractional	ADJ
ejpam-5433	493	6	derivative	derivative	NOUN
ejpam-5433	493	7	.	.	PUNCT
ejpam-5433	494	1	j.	j.	PROPN
ejpam-5433	494	2	comput	comput	PROPN
ejpam-5433	494	3	.	.	PUNCT
ejpam-5433	495	1	appl	appl	PROPN
ejpam-5433	495	2	.	.	PROPN
ejpam-5433	495	3	math	math	PROPN
ejpam-5433	495	4	.	.	PUNCT
ejpam-5433	495	5	,	,	PUNCT
ejpam-5433	495	6	264:65–70	264:65–70	NUM
ejpam-5433	495	7	,	,	PUNCT
ejpam-5433	495	8	2014	2014	NUM
ejpam-5433	495	9	.	.	PUNCT
ejpam-5433	496	1	[	[	X
ejpam-5433	496	2	5	5	NUM
ejpam-5433	496	3	]	]	PUNCT
ejpam-5433	496	4	l	l	NOUN
ejpam-5433	496	5	rabhi	rabhi	NOUN
ejpam-5433	496	6	,	,	PUNCT
ejpam-5433	496	7	m	m	VERB
ejpam-5433	496	8	alhorani	alhorani	ADJ
ejpam-5433	496	9	,	,	PUNCT
ejpam-5433	496	10	and	and	CCONJ
ejpam-5433	496	11	r	r	PROPN
ejpam-5433	496	12	khalil	khalil	PROPN
ejpam-5433	496	13	.	.	PUNCT
ejpam-5433	497	1	inhomogeneous	inhomogeneous	ADJ
ejpam-5433	497	2	conformable	conformable	ADJ
ejpam-5433	497	3	abstract	abstract	ADJ
ejpam-5433	497	4	cauchy	cauchy	ADJ
ejpam-5433	497	5	problem	problem	NOUN
ejpam-5433	497	6	.	.	PUNCT
ejpam-5433	498	1	open	open	ADJ
ejpam-5433	498	2	mathematics	mathematic	NOUN
ejpam-5433	498	3	,	,	PUNCT
ejpam-5433	498	4	19:690–705	19:690–705	NUM
ejpam-5433	498	5	,	,	PUNCT
ejpam-5433	498	6	2021	2021	NUM
ejpam-5433	498	7	.	.	PUNCT