id	sid	tid	token	lemma	pos
ejpam-3950	1	1	european	european	PROPN
ejpam-3950	1	2	journal	journal	PROPN
ejpam-3950	1	3	of	of	ADP
ejpam-3950	1	4	pure	pure	ADJ
ejpam-3950	1	5	and	and	CCONJ
ejpam-3950	1	6	applied	apply	VERB
ejpam-3950	1	7	mathematics	mathematic	NOUN
ejpam-3950	1	8	vol	vol	NOUN
ejpam-3950	1	9	.	.	PUNCT
ejpam-3950	2	1	14	14	NUM
ejpam-3950	2	2	,	,	PUNCT
ejpam-3950	2	3	no	no	INTJ
ejpam-3950	2	4	.	.	NOUN
ejpam-3950	2	5	2	2	NUM
ejpam-3950	2	6	,	,	PUNCT
ejpam-3950	2	7	2021	2021	NUM
ejpam-3950	2	8	,	,	PUNCT
ejpam-3950	2	9	493	493	NUM
ejpam-3950	2	10	-	-	SYM
ejpam-3950	2	11	505	505	NUM
ejpam-3950	2	12	issn	issn	PROPN
ejpam-3950	2	13	1307	1307	NUM
ejpam-3950	2	14	-	-	SYM
ejpam-3950	2	15	5543	5543	NUM
ejpam-3950	2	16	–	–	PUNCT
ejpam-3950	2	17	ejpam.com	ejpam.com	X
ejpam-3950	2	18	published	publish	VERB
ejpam-3950	2	19	by	by	ADP
ejpam-3950	2	20	new	new	PROPN
ejpam-3950	2	21	york	york	PROPN
ejpam-3950	2	22	business	business	PROPN
ejpam-3950	2	23	global	global	PROPN
ejpam-3950	2	24	finite	finite	PROPN
ejpam-3950	2	25	rank	rank	NOUN
ejpam-3950	2	26	solution	solution	NOUN
ejpam-3950	2	27	for	for	ADP
ejpam-3950	2	28	conformable	conformable	ADJ
ejpam-3950	2	29	degenerate	degenerate	ADJ
ejpam-3950	2	30	first	first	ADJ
ejpam-3950	2	31	-	-	PUNCT
ejpam-3950	2	32	order	order	NOUN
ejpam-3950	2	33	abstract	abstract	ADJ
ejpam-3950	2	34	cauchy	cauchy	ADJ
ejpam-3950	2	35	problem	problem	NOUN
ejpam-3950	2	36	in	in	ADP
ejpam-3950	2	37	hilbert	hilbert	NOUN
ejpam-3950	2	38	spaces	space	NOUN
ejpam-3950	2	39	fahkreddin	fahkreddin	VERB
ejpam-3950	2	40	seddiki1	seddiki1	PROPN
ejpam-3950	2	41	,	,	PUNCT
ejpam-3950	2	42	mohammed	mohammed	PROPN
ejpam-3950	2	43	al	al	PROPN
ejpam-3950	2	44	horani1	horani1	PROPN
ejpam-3950	2	45	,	,	PUNCT
ejpam-3950	2	46	roshdi	roshdi	ADJ
ejpam-3950	2	47	khalil1,∗	khalil1,∗	NOUN
ejpam-3950	2	48	1	1	NUM
ejpam-3950	2	49	department	department	NOUN
ejpam-3950	2	50	of	of	ADP
ejpam-3950	2	51	mathematics	mathematic	NOUN
ejpam-3950	2	52	,	,	PUNCT
ejpam-3950	2	53	school	school	NOUN
ejpam-3950	2	54	of	of	ADP
ejpam-3950	2	55	science	science	NOUN
ejpam-3950	2	56	,	,	PUNCT
ejpam-3950	2	57	the	the	DET
ejpam-3950	2	58	university	university	PROPN
ejpam-3950	2	59	of	of	ADP
ejpam-3950	2	60	jordan	jordan	PROPN
ejpam-3950	2	61	,	,	PUNCT
ejpam-3950	2	62	amman	amman	PROPN
ejpam-3950	2	63	,	,	PUNCT
ejpam-3950	2	64	jordan	jordan	PROPN
ejpam-3950	2	65	abstract	abstract	PROPN
ejpam-3950	2	66	.	.	PUNCT
ejpam-3950	3	1	in	in	ADP
ejpam-3950	3	2	this	this	DET
ejpam-3950	3	3	paper	paper	NOUN
ejpam-3950	3	4	,	,	PUNCT
ejpam-3950	3	5	we	we	PRON
ejpam-3950	3	6	find	find	VERB
ejpam-3950	3	7	a	a	DET
ejpam-3950	3	8	solution	solution	NOUN
ejpam-3950	3	9	of	of	ADP
ejpam-3950	3	10	finite	finite	ADJ
ejpam-3950	3	11	rank	rank	NOUN
ejpam-3950	3	12	form	form	NOUN
ejpam-3950	3	13	of	of	ADP
ejpam-3950	3	14	fractional	fractional	ADJ
ejpam-3950	3	15	abstract	abstract	ADJ
ejpam-3950	3	16	cauchy	cauchy	PROPN
ejpam-3950	3	17	problem	problem	NOUN
ejpam-3950	3	18	.	.	PUNCT
ejpam-3950	4	1	the	the	DET
ejpam-3950	4	2	fractional	fractional	ADJ
ejpam-3950	4	3	derivative	derivative	NOUN
ejpam-3950	4	4	used	use	VERB
ejpam-3950	4	5	is	be	AUX
ejpam-3950	4	6	the	the	DET
ejpam-3950	4	7	conformable	conformable	ADJ
ejpam-3950	4	8	derivative	derivative	NOUN
ejpam-3950	4	9	.	.	PUNCT
ejpam-3950	5	1	the	the	DET
ejpam-3950	5	2	main	main	ADJ
ejpam-3950	5	3	idea	idea	NOUN
ejpam-3950	5	4	of	of	ADP
ejpam-3950	5	5	the	the	DET
ejpam-3950	5	6	proofs	proof	NOUN
ejpam-3950	5	7	are	be	AUX
ejpam-3950	5	8	based	base	VERB
ejpam-3950	5	9	on	on	ADP
ejpam-3950	5	10	theory	theory	NOUN
ejpam-3950	5	11	of	of	ADP
ejpam-3950	5	12	tensor	tensor	NOUN
ejpam-3950	5	13	product	product	NOUN
ejpam-3950	5	14	of	of	ADP
ejpam-3950	5	15	banach	banach	NOUN
ejpam-3950	5	16	spaces	space	NOUN
ejpam-3950	5	17	.	.	PUNCT
ejpam-3950	6	1	2020	2020	NUM
ejpam-3950	6	2	mathematics	mathematic	NOUN
ejpam-3950	6	3	subject	subject	NOUN
ejpam-3950	6	4	classifications	classification	NOUN
ejpam-3950	6	5	:	:	PUNCT
ejpam-3950	6	6	26a33	26a33	NUM
ejpam-3950	6	7	,	,	PUNCT
ejpam-3950	6	8	34a55	34a55	NUM
ejpam-3950	6	9	key	key	ADJ
ejpam-3950	6	10	words	word	NOUN
ejpam-3950	6	11	and	and	CCONJ
ejpam-3950	6	12	phrases	phrase	NOUN
ejpam-3950	6	13	:	:	PUNCT
ejpam-3950	6	14	tensor	tensor	NOUN
ejpam-3950	6	15	product	product	NOUN
ejpam-3950	6	16	of	of	ADP
ejpam-3950	6	17	banach	banach	NOUN
ejpam-3950	6	18	spaces	space	NOUN
ejpam-3950	6	19	,	,	PUNCT
ejpam-3950	6	20	finite	finite	PROPN
ejpam-3950	6	21	rank	rank	NOUN
ejpam-3950	6	22	function	function	NOUN
ejpam-3950	6	23	,	,	PUNCT
ejpam-3950	6	24	conformable	conformable	ADJ
ejpam-3950	6	25	derivative	derivative	ADJ
ejpam-3950	6	26	,	,	PUNCT
ejpam-3950	6	27	abstract	abstract	ADJ
ejpam-3950	6	28	cauchy	cauchy	PROPN
ejpam-3950	6	29	problem	problem	NOUN
ejpam-3950	6	30	.	.	PUNCT
ejpam-3950	7	1	1	1	X
ejpam-3950	7	2	.	.	X
ejpam-3950	7	3	introduction	introduction	NOUN
ejpam-3950	7	4	let	let	VERB
ejpam-3950	7	5	x	x	PRON
ejpam-3950	7	6	be	be	AUX
ejpam-3950	7	7	a	a	DET
ejpam-3950	7	8	banach	banach	NOUN
ejpam-3950	7	9	space	space	NOUN
ejpam-3950	8	1	and	and	CCONJ
ejpam-3950	8	2	i	i	PRON
ejpam-3950	8	3	=	=	PUNCT
ejpam-3950	9	1	[	[	X
ejpam-3950	9	2	0	0	NUM
ejpam-3950	9	3	,	,	PUNCT
ejpam-3950	9	4	1	1	NUM
ejpam-3950	9	5	]	]	PUNCT
ejpam-3950	9	6	.	.	PUNCT
ejpam-3950	10	1	let	let	AUX
ejpam-3950	10	2	c(i	c(i	NOUN
ejpam-3950	10	3	)	)	PUNCT
ejpam-3950	10	4	be	be	AUX
ejpam-3950	10	5	the	the	DET
ejpam-3950	10	6	banach	banach	NOUN
ejpam-3950	10	7	space	space	NOUN
ejpam-3950	10	8	of	of	ADP
ejpam-3950	10	9	all	all	DET
ejpam-3950	10	10	real	real	ADV
ejpam-3950	10	11	valued	value	VERB
ejpam-3950	10	12	continuous	continuous	ADJ
ejpam-3950	10	13	functions	function	NOUN
ejpam-3950	10	14	defined	define	VERB
ejpam-3950	10	15	on	on	ADP
ejpam-3950	10	16	i	i	PRON
ejpam-3950	10	17	under	under	ADP
ejpam-3950	10	18	the	the	DET
ejpam-3950	10	19	sup	sup	NOUN
ejpam-3950	10	20	-	-	PUNCT
ejpam-3950	10	21	norm	norm	NOUN
ejpam-3950	10	22	.	.	PUNCT
ejpam-3950	11	1	let	let	VERB
ejpam-3950	11	2	c(i	c(i	NOUN
ejpam-3950	11	3	,	,	PUNCT
ejpam-3950	11	4	x	x	PRON
ejpam-3950	11	5	)	)	PUNCT
ejpam-3950	11	6	be	be	AUX
ejpam-3950	11	7	the	the	DET
ejpam-3950	11	8	banach	banach	NOUN
ejpam-3950	11	9	space	space	NOUN
ejpam-3950	11	10	of	of	ADP
ejpam-3950	11	11	all	all	DET
ejpam-3950	11	12	continuous	continuous	ADJ
ejpam-3950	11	13	function	function	NOUN
ejpam-3950	11	14	defined	define	VERB
ejpam-3950	11	15	on	on	ADP
ejpam-3950	11	16	i	i	PRON
ejpam-3950	11	17	with	with	ADP
ejpam-3950	11	18	values	value	NOUN
ejpam-3950	11	19	in	in	ADP
ejpam-3950	11	20	x.	x.	NOUN
ejpam-3950	11	21	a	a	DET
ejpam-3950	11	22	classical	classical	ADJ
ejpam-3950	11	23	and	and	CCONJ
ejpam-3950	11	24	important	important	ADJ
ejpam-3950	11	25	differential	differential	ADJ
ejpam-3950	11	26	equation	equation	NOUN
ejpam-3950	11	27	is	be	AUX
ejpam-3950	11	28	the	the	DET
ejpam-3950	11	29	so	so	ADV
ejpam-3950	11	30	called	call	VERB
ejpam-3950	11	31	abstract	abstract	ADJ
ejpam-3950	11	32	cauchy	cauchy	PROPN
ejpam-3950	11	33	problem	problem	NOUN
ejpam-3950	11	34	.	.	PUNCT
ejpam-3950	12	1	one	one	NUM
ejpam-3950	12	2	form	form	NOUN
ejpam-3950	12	3	such	such	ADJ
ejpam-3950	12	4	equation	equation	NOUN
ejpam-3950	12	5	is	be	AUX
ejpam-3950	12	6	bu	bu	ADP
ejpam-3950	12	7	′	′	NUM
ejpam-3950	12	8	=	=	NOUN
ejpam-3950	12	9	au(t	au(t	NUM
ejpam-3950	12	10	)	)	PUNCT
ejpam-3950	13	1	+	+	NUM
ejpam-3950	13	2	f(t)z	f(t)z	PROPN
ejpam-3950	13	3	u(0	u(0	PROPN
ejpam-3950	13	4	)	)	PUNCT
ejpam-3950	13	5	=	=	PUNCT
ejpam-3950	14	1	x0	x0	PROPN
ejpam-3950	14	2	here	here	ADV
ejpam-3950	14	3	u	u	PROPN
ejpam-3950	14	4	∈	∈	PROPN
ejpam-3950	14	5	c1(i	c1(i	PROPN
ejpam-3950	14	6	,	,	PUNCT
ejpam-3950	14	7	x	x	NOUN
ejpam-3950	14	8	)	)	PUNCT
ejpam-3950	14	9	and	and	CCONJ
ejpam-3950	14	10	a	a	DET
ejpam-3950	14	11	,	,	PUNCT
ejpam-3950	14	12	b	b	NOUN
ejpam-3950	14	13	are	be	AUX
ejpam-3950	14	14	densely	densely	ADV
ejpam-3950	14	15	defined	define	VERB
ejpam-3950	14	16	linear	linear	ADJ
ejpam-3950	14	17	operators	operator	NOUN
ejpam-3950	14	18	on	on	ADP
ejpam-3950	14	19	the	the	DET
ejpam-3950	14	20	codomain	codomain	NOUN
ejpam-3950	14	21	of	of	ADP
ejpam-3950	14	22	u.	u.	NOUN
ejpam-3950	14	23	if	if	SCONJ
ejpam-3950	14	24	f	f	PROPN
ejpam-3950	14	25	=	=	SYM
ejpam-3950	14	26	0	0	PROPN
ejpam-3950	14	27	or	or	CCONJ
ejpam-3950	14	28	z	z	NOUN
ejpam-3950	14	29	=	=	SYM
ejpam-3950	14	30	0	0	NUM
ejpam-3950	14	31	,	,	PUNCT
ejpam-3950	14	32	then	then	ADV
ejpam-3950	14	33	the	the	DET
ejpam-3950	14	34	equation	equation	NOUN
ejpam-3950	14	35	is	be	AUX
ejpam-3950	14	36	homogeneous	homogeneous	ADJ
ejpam-3950	14	37	otherwise	otherwise	ADV
ejpam-3950	14	38	it	it	PRON
ejpam-3950	14	39	is	be	AUX
ejpam-3950	14	40	called	call	VERB
ejpam-3950	14	41	non	non	ADJ
ejpam-3950	14	42	-	-	ADJ
ejpam-3950	14	43	homogeneous	homogeneous	ADJ
ejpam-3950	14	44	.	.	PUNCT
ejpam-3950	15	1	now	now	ADV
ejpam-3950	15	2	in	in	ADP
ejpam-3950	15	3	the	the	DET
ejpam-3950	15	4	non	non	ADJ
ejpam-3950	15	5	-	-	ADJ
ejpam-3950	15	6	homogeneous	homogeneous	ADJ
ejpam-3950	15	7	problem	problem	NOUN
ejpam-3950	15	8	we	we	PRON
ejpam-3950	15	9	have	have	VERB
ejpam-3950	15	10	two	two	NUM
ejpam-3950	15	11	cases	case	NOUN
ejpam-3950	15	12	.	.	PUNCT
ejpam-3950	16	1	the	the	DET
ejpam-3950	16	2	first	first	ADJ
ejpam-3950	16	3	type	type	NOUN
ejpam-3950	16	4	if	if	SCONJ
ejpam-3950	16	5	u	u	NOUN
ejpam-3950	16	6	is	be	AUX
ejpam-3950	16	7	unknown	unknown	ADJ
ejpam-3950	16	8	and	and	CCONJ
ejpam-3950	16	9	f	f	PROPN
ejpam-3950	16	10	is	be	AUX
ejpam-3950	16	11	given	give	VERB
ejpam-3950	16	12	and	and	CCONJ
ejpam-3950	16	13	this	this	PRON
ejpam-3950	16	14	is	be	AUX
ejpam-3950	16	15	called	call	VERB
ejpam-3950	16	16	the	the	DET
ejpam-3950	16	17	direct	direct	ADJ
ejpam-3950	16	18	problem	problem	NOUN
ejpam-3950	16	19	,	,	PUNCT
ejpam-3950	16	20	the	the	DET
ejpam-3950	16	21	second	second	ADJ
ejpam-3950	16	22	type	type	NOUN
ejpam-3950	16	23	u	u	NOUN
ejpam-3950	16	24	and	and	CCONJ
ejpam-3950	16	25	f	f	PROPN
ejpam-3950	16	26	are	be	AUX
ejpam-3950	16	27	unknown	unknown	ADJ
ejpam-3950	16	28	and	and	CCONJ
ejpam-3950	16	29	it	it	PRON
ejpam-3950	16	30	is	be	AUX
ejpam-3950	16	31	called	call	VERB
ejpam-3950	16	32	the	the	DET
ejpam-3950	16	33	inverse	inverse	NOUN
ejpam-3950	16	34	problem	problem	NOUN
ejpam-3950	16	35	.	.	PUNCT
ejpam-3950	17	1	if	if	SCONJ
ejpam-3950	17	2	b	b	NOUN
ejpam-3950	17	3	is	be	AUX
ejpam-3950	17	4	not	not	PART
ejpam-3950	17	5	invertible	invertible	ADJ
ejpam-3950	17	6	,	,	PUNCT
ejpam-3950	17	7	then	then	ADV
ejpam-3950	17	8	the	the	DET
ejpam-3950	17	9	equation	equation	NOUN
ejpam-3950	17	10	is	be	AUX
ejpam-3950	17	11	called	call	VERB
ejpam-3950	17	12	degenerate	degenerate	ADJ
ejpam-3950	17	13	otherwise	otherwise	ADV
ejpam-3950	17	14	it	it	PRON
ejpam-3950	17	15	is	be	AUX
ejpam-3950	17	16	called	call	VERB
ejpam-3950	17	17	nondegenerate	nondegenerate	ADJ
ejpam-3950	17	18	.	.	PUNCT
ejpam-3950	18	1	in	in	ADP
ejpam-3950	18	2	this	this	DET
ejpam-3950	18	3	paper	paper	NOUN
ejpam-3950	18	4	we	we	PRON
ejpam-3950	18	5	will	will	AUX
ejpam-3950	18	6	look	look	VERB
ejpam-3950	18	7	for	for	ADP
ejpam-3950	18	8	certain	certain	ADJ
ejpam-3950	18	9	solutions	solution	NOUN
ejpam-3950	18	10	called	call	VERB
ejpam-3950	18	11	finite	finite	PROPN
ejpam-3950	18	12	rank	rank	NOUN
ejpam-3950	18	13	solutions	solution	NOUN
ejpam-3950	18	14	for	for	ADP
ejpam-3950	18	15	the	the	DET
ejpam-3950	18	16	fractional	fractional	ADJ
ejpam-3950	18	17	∗corresponding	∗corresponde	VERB
ejpam-3950	18	18	author	author	NOUN
ejpam-3950	18	19	.	.	PUNCT
ejpam-3950	19	1	doi	doi	NOUN
ejpam-3950	19	2	:	:	PUNCT
ejpam-3950	19	3	https://doi.org/10.29020/nybg.ejpam.v14i2.3950	https://doi.org/10.29020/nybg.ejpam.v14i2.3950	PROPN
ejpam-3950	19	4	email	email	NOUN
ejpam-3950	19	5	addresses	address	VERB
ejpam-3950	19	6	:	:	PUNCT
ejpam-3950	19	7	fakhrseddik@gmail.com	fakhrseddik@gmail.com	X
ejpam-3950	19	8	(	(	PUNCT
ejpam-3950	19	9	f.	f.	PROPN
ejpam-3950	19	10	seddiki	seddiki	PROPN
ejpam-3950	19	11	)	)	PUNCT
ejpam-3950	19	12	,	,	PUNCT
ejpam-3950	20	1	horani@ju.edu.jo	horani@ju.edu.jo	NOUN
ejpam-3950	20	2	(	(	PUNCT
ejpam-3950	20	3	m.	m.	NOUN
ejpam-3950	20	4	al	al	PROPN
ejpam-3950	20	5	horani	horani	PROPN
ejpam-3950	20	6	)	)	PUNCT
ejpam-3950	20	7	,	,	PUNCT
ejpam-3950	20	8	roshdi@ju.edu.jo	roshdi@ju.edu.jo	PROPN
ejpam-3950	20	9	(	(	PUNCT
ejpam-3950	20	10	r.	r.	PROPN
ejpam-3950	20	11	khalil	khalil	PROPN
ejpam-3950	20	12	)	)	PUNCT
ejpam-3950	20	13	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3950	21	1	493	493	NUM
ejpam-3950	21	2	c	c	X
ejpam-3950	21	3	©	©	PROPN
ejpam-3950	21	4	2021	2021	NUM
ejpam-3950	21	5	ejpam	ejpam	VERB
ejpam-3950	21	6	all	all	DET
ejpam-3950	21	7	rights	right	NOUN
ejpam-3950	21	8	reserved	reserve	VERB
ejpam-3950	21	9	.	.	PUNCT
ejpam-3950	22	1	f.	f.	PROPN
ejpam-3950	22	2	seddiki	seddiki	PROPN
ejpam-3950	22	3	,	,	PUNCT
ejpam-3950	22	4	m.	m.	NOUN
ejpam-3950	22	5	al	al	PROPN
ejpam-3950	22	6	horani	horani	PROPN
ejpam-3950	22	7	,	,	PUNCT
ejpam-3950	22	8	r.	r.	PROPN
ejpam-3950	22	9	khalil	khalil	PROPN
ejpam-3950	22	10	/	/	SYM
ejpam-3950	22	11	eur	eur	PROPN
ejpam-3950	22	12	.	.	PUNCT
ejpam-3950	23	1	j.	j.	PROPN
ejpam-3950	23	2	pure	pure	PROPN
ejpam-3950	23	3	appl	appl	PROPN
ejpam-3950	23	4	.	.	PROPN
ejpam-3950	23	5	math	math	PROPN
ejpam-3950	23	6	,	,	PUNCT
ejpam-3950	23	7	14	14	NUM
ejpam-3950	23	8	(	(	PUNCT
ejpam-3950	23	9	2	2	NUM
ejpam-3950	23	10	)	)	PUNCT
ejpam-3950	23	11	(	(	PUNCT
ejpam-3950	23	12	2021	2021	NUM
ejpam-3950	23	13	)	)	PUNCT
ejpam-3950	23	14	,	,	PUNCT
ejpam-3950	23	15	493	493	NUM
ejpam-3950	23	16	-	-	SYM
ejpam-3950	23	17	505	505	NUM
ejpam-3950	23	18	494	494	NUM
ejpam-3950	23	19	abstract	abstract	ADJ
ejpam-3950	23	20	cauchy	cauchy	ADJ
ejpam-3950	23	21	problem	problem	NOUN
ejpam-3950	23	22	,	,	PUNCT
ejpam-3950	23	23	using	use	VERB
ejpam-3950	23	24	the	the	DET
ejpam-3950	23	25	tensor	tensor	NOUN
ejpam-3950	23	26	product	product	NOUN
ejpam-3950	23	27	technique	technique	NOUN
ejpam-3950	23	28	.	.	PUNCT
ejpam-3950	24	1	first	first	ADV
ejpam-3950	24	2	let	let	VERB
ejpam-3950	24	3	us	we	PRON
ejpam-3950	24	4	present	present	VERB
ejpam-3950	24	5	some	some	DET
ejpam-3950	24	6	basic	basic	ADJ
ejpam-3950	24	7	facts	fact	NOUN
ejpam-3950	24	8	on	on	ADP
ejpam-3950	24	9	conformable	conformable	ADJ
ejpam-3950	24	10	fractional	fractional	ADJ
ejpam-3950	24	11	derivative	derivative	NOUN
ejpam-3950	24	12	.	.	PUNCT
ejpam-3950	25	1	for	for	ADP
ejpam-3950	25	2	f	f	PROPN
ejpam-3950	25	3	:	:	PUNCT
ejpam-3950	26	1	[	[	X
ejpam-3950	26	2	0;∞)→	0;∞)→	NUM
ejpam-3950	26	3	r	r	NOUN
ejpam-3950	26	4	and	and	CCONJ
ejpam-3950	26	5	0	0	NUM
ejpam-3950	26	6	<	<	X
ejpam-3950	26	7	α	α	PROPN
ejpam-3950	26	8	≤	≤	NUM
ejpam-3950	26	9	1	1	NUM
ejpam-3950	26	10	,	,	PUNCT
ejpam-3950	26	11	the	the	DET
ejpam-3950	26	12	conformable	conformable	ADJ
ejpam-3950	26	13	fractional	fractional	ADJ
ejpam-3950	26	14	derivative	derivative	NOUN
ejpam-3950	26	15	of	of	ADP
ejpam-3950	26	16	f	f	PROPN
ejpam-3950	26	17	of	of	ADP
ejpam-3950	26	18	order	order	NOUN
ejpam-3950	26	19	α	α	NOUN
ejpam-3950	26	20	is	be	AUX
ejpam-3950	26	21	defined	define	VERB
ejpam-3950	26	22	by	by	ADP
ejpam-3950	26	23	tα(f)(t	tα(f)(t	ADJ
ejpam-3950	26	24	)	)	PUNCT
ejpam-3950	27	1	=	=	SYM
ejpam-3950	27	2	lim	lim	PROPN
ejpam-3950	27	3	ε→0	ε→0	VERB
ejpam-3950	27	4	f(t+	f(t+	ADJ
ejpam-3950	27	5	εt1−α)−	εt1−α)−	NOUN
ejpam-3950	27	6	f(t	f(t	NOUN
ejpam-3950	27	7	)	)	PUNCT
ejpam-3950	27	8	ε	ε	PROPN
ejpam-3950	27	9	for	for	ADP
ejpam-3950	27	10	all	all	DET
ejpam-3950	27	11	t	t	PROPN
ejpam-3950	27	12	>	>	X
ejpam-3950	27	13	0	0	NUM
ejpam-3950	27	14	,	,	PUNCT
ejpam-3950	27	15	if	if	SCONJ
ejpam-3950	27	16	f	f	PROPN
ejpam-3950	27	17	is	be	AUX
ejpam-3950	27	18	α	α	PRON
ejpam-3950	27	19	differentiable	differentiable	ADJ
ejpam-3950	27	20	on	on	ADP
ejpam-3950	27	21	(	(	PUNCT
ejpam-3950	27	22	0	0	NUM
ejpam-3950	27	23	,	,	PUNCT
ejpam-3950	27	24	b	b	NOUN
ejpam-3950	27	25	)	)	PUNCT
ejpam-3950	28	1	where	where	SCONJ
ejpam-3950	28	2	b	b	X
ejpam-3950	28	3	>	>	X
ejpam-3950	28	4	0	0	NUM
ejpam-3950	28	5	and	and	CCONJ
ejpam-3950	28	6	limt→0	limt→0	PROPN
ejpam-3950	28	7	+	+	CCONJ
ejpam-3950	28	8	f	f	PROPN
ejpam-3950	28	9	(	(	PUNCT
ejpam-3950	28	10	α)(t	α)(t	ADJ
ejpam-3950	28	11	)	)	PUNCT
ejpam-3950	28	12	exists	exist	VERB
ejpam-3950	28	13	,	,	PUNCT
ejpam-3950	28	14	then	then	ADV
ejpam-3950	28	15	define	define	VERB
ejpam-3950	28	16	f	f	PROPN
ejpam-3950	28	17	(	(	PUNCT
ejpam-3950	28	18	α)(0	α)(0	NUM
ejpam-3950	28	19	)	)	PUNCT
ejpam-3950	29	1	=	=	SYM
ejpam-3950	29	2	limt→0	limt→0	PROPN
ejpam-3950	29	3	+	+	X
ejpam-3950	29	4	f	f	X
ejpam-3950	29	5	(	(	PUNCT
ejpam-3950	29	6	α)(t	α)(t	PROPN
ejpam-3950	29	7	)	)	PUNCT
ejpam-3950	29	8	.	.	PUNCT
ejpam-3950	30	1	we	we	PRON
ejpam-3950	30	2	denote	denote	VERB
ejpam-3950	30	3	f	f	PROPN
ejpam-3950	30	4	(	(	PUNCT
ejpam-3950	30	5	α)(t	α)(t	PROPN
ejpam-3950	30	6	)	)	PUNCT
ejpam-3950	30	7	for	for	ADP
ejpam-3950	30	8	tα(f)(t	tα(f)(t	NUM
ejpam-3950	30	9	)	)	PUNCT
ejpam-3950	30	10	and	and	CCONJ
ejpam-3950	30	11	we	we	PRON
ejpam-3950	30	12	say	say	VERB
ejpam-3950	30	13	f	f	PROPN
ejpam-3950	30	14	is	be	AUX
ejpam-3950	30	15	α	α	PRON
ejpam-3950	30	16	differentiable	differentiable	ADJ
ejpam-3950	30	17	if	if	SCONJ
ejpam-3950	30	18	the	the	DET
ejpam-3950	30	19	conformable	conformable	ADJ
ejpam-3950	30	20	fractional	fractional	ADJ
ejpam-3950	30	21	derivative	derivative	NOUN
ejpam-3950	30	22	of	of	ADP
ejpam-3950	30	23	f	f	PROPN
ejpam-3950	30	24	of	of	ADP
ejpam-3950	30	25	order	order	NOUN
ejpam-3950	30	26	α	α	NOUN
ejpam-3950	30	27	exists	exist	VERB
ejpam-3950	30	28	.	.	PUNCT
ejpam-3950	31	1	for	for	ADP
ejpam-3950	31	2	0	0	NUM
ejpam-3950	31	3	<	<	X
ejpam-3950	31	4	α	α	PROPN
ejpam-3950	31	5	≤	≤	NUM
ejpam-3950	31	6	1	1	NUM
ejpam-3950	31	7	and	and	CCONJ
ejpam-3950	31	8	f	f	NOUN
ejpam-3950	31	9	,	,	PUNCT
ejpam-3950	31	10	g	g	PROPN
ejpam-3950	31	11	be	be	VERB
ejpam-3950	31	12	α	α	NOUN
ejpam-3950	31	13	differentiable	differentiable	ADJ
ejpam-3950	31	14	at	at	ADP
ejpam-3950	31	15	a	a	DET
ejpam-3950	31	16	point	point	NOUN
ejpam-3950	31	17	t	t	X
ejpam-3950	31	18	>	>	X
ejpam-3950	31	19	0	0	NUM
ejpam-3950	31	20	,	,	PUNCT
ejpam-3950	31	21	we	we	PRON
ejpam-3950	31	22	have	have	VERB
ejpam-3950	31	23	the	the	DET
ejpam-3950	31	24	following	follow	VERB
ejpam-3950	31	25	properties	property	NOUN
ejpam-3950	31	26	:	:	PUNCT
ejpam-3950	31	27	(	(	PUNCT
ejpam-3950	31	28	1	1	X
ejpam-3950	31	29	)	)	PUNCT
ejpam-3950	31	30	tα(af	tα(af	PROPN
ejpam-3950	31	31	+	+	CCONJ
ejpam-3950	31	32	bg	bg	NOUN
ejpam-3950	31	33	)	)	PUNCT
ejpam-3950	31	34	=	=	SYM
ejpam-3950	31	35	atα(f	atα(f	PROPN
ejpam-3950	31	36	)	)	PUNCT
ejpam-3950	32	1	+	+	SYM
ejpam-3950	32	2	btα(g	btα(g	PROPN
ejpam-3950	32	3	)	)	PUNCT
ejpam-3950	32	4	,	,	PUNCT
ejpam-3950	32	5	for	for	ADP
ejpam-3950	32	6	all	all	DET
ejpam-3950	32	7	a	a	DET
ejpam-3950	32	8	,	,	PUNCT
ejpam-3950	32	9	b	b	PROPN
ejpam-3950	32	10	∈	∈	PROPN
ejpam-3950	32	11	r.	r.	NOUN
ejpam-3950	32	12	(	(	PUNCT
ejpam-3950	32	13	2	2	NUM
ejpam-3950	32	14	)	)	PUNCT
ejpam-3950	32	15	tα(tp	tα(tp	NUM
ejpam-3950	32	16	)	)	PUNCT
ejpam-3950	33	1	=	=	SYM
ejpam-3950	33	2	ptp−α	ptp−α	PROPN
ejpam-3950	33	3	,	,	PUNCT
ejpam-3950	33	4	for	for	ADP
ejpam-3950	33	5	all	all	DET
ejpam-3950	33	6	p	p	PROPN
ejpam-3950	33	7	∈	∈	PROPN
ejpam-3950	33	8	r.	r.	NOUN
ejpam-3950	33	9	(	(	PUNCT
ejpam-3950	33	10	3	3	NUM
ejpam-3950	33	11	)	)	PUNCT
ejpam-3950	33	12	tα(fg	tα(fg	NOUN
ejpam-3950	33	13	)	)	PUNCT
ejpam-3950	33	14	=	=	SYM
ejpam-3950	33	15	ftα(g	ftα(g	PROPN
ejpam-3950	33	16	)	)	PUNCT
ejpam-3950	33	17	+	+	NUM
ejpam-3950	33	18	gtα(f	gtα(f	NOUN
ejpam-3950	33	19	)	)	PUNCT
ejpam-3950	33	20	.	.	PUNCT
ejpam-3950	34	1	(	(	PUNCT
ejpam-3950	34	2	4	4	X
ejpam-3950	34	3	)	)	PUNCT
ejpam-3950	34	4	tα(fg	tα(fg	NOUN
ejpam-3950	34	5	)	)	PUNCT
ejpam-3950	35	1	=	=	PUNCT
ejpam-3950	35	2	gtα(f)−ftα(g	gtα(f)−ftα(g	X
ejpam-3950	35	3	)	)	PUNCT
ejpam-3950	35	4	g2	g2	PROPN
ejpam-3950	35	5	.	.	PUNCT
ejpam-3950	36	1	(	(	PUNCT
ejpam-3950	36	2	5	5	NUM
ejpam-3950	36	3	)	)	PUNCT
ejpam-3950	36	4	tα(λ	tα(λ	NUM
ejpam-3950	36	5	)	)	PUNCT
ejpam-3950	37	1	=	=	PUNCT
ejpam-3950	37	2	0	0	NUM
ejpam-3950	37	3	,	,	PUNCT
ejpam-3950	37	4	for	for	ADP
ejpam-3950	37	5	all	all	DET
ejpam-3950	37	6	λ	λ	NOUN
ejpam-3950	37	7	is	be	AUX
ejpam-3950	37	8	constant	constant	ADJ
ejpam-3950	37	9	function	function	NOUN
ejpam-3950	37	10	.	.	PUNCT
ejpam-3950	38	1	(	(	PUNCT
ejpam-3950	38	2	6	6	NUM
ejpam-3950	38	3	)	)	PUNCT
ejpam-3950	38	4	if	if	SCONJ
ejpam-3950	38	5	f	f	PROPN
ejpam-3950	38	6	is	be	AUX
ejpam-3950	38	7	differentiable	differentiable	ADJ
ejpam-3950	38	8	,	,	PUNCT
ejpam-3950	38	9	then	then	ADV
ejpam-3950	38	10	tα(f)(t	tα(f)(t	ADJ
ejpam-3950	38	11	)	)	PUNCT
ejpam-3950	39	1	=	=	SYM
ejpam-3950	39	2	t1−α	t1−α	ADJ
ejpam-3950	39	3	dfdt	dfdt	NOUN
ejpam-3950	39	4	(	(	PUNCT
ejpam-3950	39	5	t	t	PROPN
ejpam-3950	39	6	)	)	PUNCT
ejpam-3950	39	7	.	.	PUNCT
ejpam-3950	40	1	the	the	DET
ejpam-3950	40	2	α	α	PROPN
ejpam-3950	40	3	fractional	fractional	ADJ
ejpam-3950	40	4	integral	integral	ADJ
ejpam-3950	40	5	of	of	ADP
ejpam-3950	40	6	a	a	DET
ejpam-3950	40	7	function	function	NOUN
ejpam-3950	40	8	f	f	X
ejpam-3950	40	9	starting	start	VERB
ejpam-3950	40	10	from	from	ADP
ejpam-3950	40	11	a	a	DET
ejpam-3950	40	12	≥	≥	NOUN
ejpam-3950	40	13	0	0	NUM
ejpam-3950	40	14	is	be	AUX
ejpam-3950	40	15	:	:	PUNCT
ejpam-3950	40	16	iaα(f(t	iaα(f(t	NOUN
ejpam-3950	40	17	)	)	PUNCT
ejpam-3950	40	18	)	)	PUNCT
ejpam-3950	41	1	=	=	SYM
ejpam-3950	41	2	ia1	ia1	NOUN
ejpam-3950	41	3	(	(	PUNCT
ejpam-3950	41	4	tα−1f(t	tα−1f(t	ADV
ejpam-3950	41	5	)	)	PUNCT
ejpam-3950	41	6	)	)	PUNCT
ejpam-3950	42	1	=	=	SYM
ejpam-3950	42	2	∫	∫	PROPN
ejpam-3950	42	3	t	t	PROPN
ejpam-3950	42	4	a	a	DET
ejpam-3950	42	5	f(s	f(	NOUN
ejpam-3950	42	6	)	)	PUNCT
ejpam-3950	43	1	s1−α	s1−α	PROPN
ejpam-3950	43	2	ds	ds	NOUN
ejpam-3950	43	3	for	for	ADP
ejpam-3950	43	4	more	more	ADV
ejpam-3950	43	5	on	on	ADP
ejpam-3950	43	6	conformable	conformable	ADJ
ejpam-3950	43	7	fractional	fractional	ADJ
ejpam-3950	43	8	derivative	derivative	NOUN
ejpam-3950	43	9	we	we	PRON
ejpam-3950	43	10	refer	refer	VERB
ejpam-3950	43	11	to	to	ADP
ejpam-3950	43	12	[	[	X
ejpam-3950	43	13	1	1	NUM
ejpam-3950	43	14	]	]	PUNCT
ejpam-3950	43	15	,	,	PUNCT
ejpam-3950	43	16	[	[	X
ejpam-3950	43	17	6]-[18	6]-[18	NUM
ejpam-3950	43	18	]	]	PUNCT
ejpam-3950	43	19	,	,	PUNCT
ejpam-3950	43	20	[	[	X
ejpam-3950	43	21	20	20	NUM
ejpam-3950	43	22	]	]	PUNCT
ejpam-3950	43	23	and	and	CCONJ
ejpam-3950	43	24	[	[	X
ejpam-3950	43	25	21	21	NUM
ejpam-3950	43	26	]	]	PUNCT
ejpam-3950	43	27	.	.	PUNCT
ejpam-3950	44	1	2	2	X
ejpam-3950	44	2	.	.	X
ejpam-3950	44	3	basic	basic	ADJ
ejpam-3950	44	4	facts	fact	NOUN
ejpam-3950	44	5	of	of	ADP
ejpam-3950	44	6	the	the	DET
ejpam-3950	44	7	tensor	tensor	NOUN
ejpam-3950	44	8	product	product	NOUN
ejpam-3950	44	9	of	of	ADP
ejpam-3950	44	10	banach	banach	NOUN
ejpam-3950	44	11	space	space	NOUN
ejpam-3950	44	12	let	let	VERB
ejpam-3950	44	13	x	x	PRON
ejpam-3950	44	14	and	and	CCONJ
ejpam-3950	44	15	y	y	PROPN
ejpam-3950	44	16	be	be	VERB
ejpam-3950	44	17	banach	banach	ADV
ejpam-3950	44	18	spaces	space	NOUN
ejpam-3950	44	19	,	,	PUNCT
ejpam-3950	44	20	x∗	x∗	PROPN
ejpam-3950	44	21	denotes	denote	VERB
ejpam-3950	44	22	the	the	DET
ejpam-3950	44	23	dual	dual	ADJ
ejpam-3950	44	24	of	of	ADP
ejpam-3950	44	25	x.	x.	NOUN
ejpam-3950	44	26	for	for	ADP
ejpam-3950	44	27	x	x	SYM
ejpam-3950	44	28	∈	∈	PROPN
ejpam-3950	44	29	x	x	X
ejpam-3950	44	30	and	and	CCONJ
ejpam-3950	44	31	y	y	PROPN
ejpam-3950	44	32	∈	∈	PROPN
ejpam-3950	45	1	y	y	PROPN
ejpam-3950	45	2	define	define	VERB
ejpam-3950	45	3	the	the	DET
ejpam-3950	45	4	map	map	NOUN
ejpam-3950	45	5	x⊗	x⊗	VERB
ejpam-3950	45	6	y	y	PROPN
ejpam-3950	45	7	:	:	PUNCT
ejpam-3950	45	8	x∗	x∗	PROPN
ejpam-3950	45	9	→	→	SYM
ejpam-3950	45	10	y	y	PROPN
ejpam-3950	45	11	as	as	ADP
ejpam-3950	45	12	:	:	PUNCT
ejpam-3950	45	13	x⊗	x⊗	PROPN
ejpam-3950	45	14	y(x∗	y(x∗	PROPN
ejpam-3950	45	15	)	)	PUNCT
ejpam-3950	46	1	=	=	PUNCT
ejpam-3950	46	2	〈	〈	PROPN
ejpam-3950	46	3	x	x	X
ejpam-3950	46	4	,	,	PUNCT
ejpam-3950	46	5	x∗〉y	x∗〉y	PROPN
ejpam-3950	46	6	,	,	PUNCT
ejpam-3950	46	7	for	for	ADP
ejpam-3950	46	8	all	all	DET
ejpam-3950	46	9	x∗	x∗	PROPN
ejpam-3950	46	10	∈	∈	PROPN
ejpam-3950	46	11	x∗.	x∗.	X
ejpam-3950	47	1	cleaarly	cleaarly	ADV
ejpam-3950	47	2	,	,	PUNCT
ejpam-3950	47	3	x⊗	x⊗	PROPN
ejpam-3950	47	4	y	y	PROPN
ejpam-3950	47	5	is	be	AUX
ejpam-3950	47	6	a	a	DET
ejpam-3950	47	7	bounded	bounded	ADJ
ejpam-3950	47	8	linear	linear	ADJ
ejpam-3950	47	9	operator	operator	NOUN
ejpam-3950	47	10	and	and	CCONJ
ejpam-3950	47	11	‖	‖	PROPN
ejpam-3950	47	12	x⊗	x⊗	PROPN
ejpam-3950	48	1	y	y	PROPN
ejpam-3950	48	2	‖=‖	‖=‖	PROPN
ejpam-3950	48	3	x	x	PUNCT
ejpam-3950	48	4	‖‖	‖‖	VERB
ejpam-3950	48	5	y	y	PROPN
ejpam-3950	48	6	‖[2	‖[2	NOUN
ejpam-3950	48	7	]	]	PUNCT
ejpam-3950	48	8	.	.	PUNCT
ejpam-3950	49	1	such	such	DET
ejpam-3950	49	2	an	an	DET
ejpam-3950	49	3	operator	operator	NOUN
ejpam-3950	49	4	x⊗	x⊗	AUX
ejpam-3950	49	5	y	y	PROPN
ejpam-3950	49	6	is	be	AUX
ejpam-3950	49	7	called	call	VERB
ejpam-3950	49	8	an	an	DET
ejpam-3950	49	9	atom	atom	NOUN
ejpam-3950	49	10	.	.	PUNCT
ejpam-3950	50	1	the	the	DET
ejpam-3950	50	2	set	set	NOUN
ejpam-3950	50	3	x	x	PUNCT
ejpam-3950	50	4	⊗	⊗	PROPN
ejpam-3950	50	5	y	y	PROPN
ejpam-3950	50	6	=	=	PUNCT
ejpam-3950	50	7	span{x⊗	span{x⊗	ADP
ejpam-3950	50	8	y	y	NOUN
ejpam-3950	50	9	:	:	PUNCT
ejpam-3950	50	10	x	x	PUNCT
ejpam-3950	50	11	∈	∈	NOUN
ejpam-3950	50	12	x	x	X
ejpam-3950	50	13	and	and	CCONJ
ejpam-3950	50	14	y	y	PROPN
ejpam-3950	50	15	∈	∈	PROPN
ejpam-3950	50	16	y	y	PROPN
ejpam-3950	50	17	}	}	PUNCT
ejpam-3950	50	18	is	be	AUX
ejpam-3950	50	19	a	a	DET
ejpam-3950	50	20	subspace	subspace	NOUN
ejpam-3950	50	21	of	of	ADP
ejpam-3950	50	22	l(x∗	l(x∗	NOUN
ejpam-3950	50	23	,	,	PUNCT
ejpam-3950	50	24	y	y	PROPN
ejpam-3950	50	25	)	)	PUNCT
ejpam-3950	50	26	.	.	PUNCT
ejpam-3950	51	1	the	the	DET
ejpam-3950	51	2	following	follow	VERB
ejpam-3950	51	3	lemma	lemma	PROPN
ejpam-3950	51	4	,	,	PUNCT
ejpam-3950	51	5	[	[	X
ejpam-3950	51	6	5	5	NUM
ejpam-3950	51	7	]	]	PUNCT
ejpam-3950	51	8	,	,	PUNCT
ejpam-3950	51	9	is	be	AUX
ejpam-3950	51	10	needed	need	VERB
ejpam-3950	51	11	in	in	ADP
ejpam-3950	51	12	our	our	PRON
ejpam-3950	51	13	paper	paper	NOUN
ejpam-3950	51	14	.	.	PUNCT
ejpam-3950	52	1	lemma	lemma	PROPN
ejpam-3950	52	2	1	1	X
ejpam-3950	52	3	.	.	PUNCT
ejpam-3950	53	1	let	let	VERB
ejpam-3950	53	2	x1	x1	PROPN
ejpam-3950	53	3	⊗	⊗	PROPN
ejpam-3950	53	4	y1	y1	PROPN
ejpam-3950	54	1	and	and	CCONJ
ejpam-3950	55	1	x2	x2	PROPN
ejpam-3950	55	2	⊗	⊗	PROPN
ejpam-3950	55	3	y2	y2	INTJ
ejpam-3950	55	4	be	be	VERB
ejpam-3950	55	5	two	two	NUM
ejpam-3950	55	6	nonzero	nonzero	NOUN
ejpam-3950	55	7	atoms	atom	NOUN
ejpam-3950	55	8	in	in	ADP
ejpam-3950	55	9	x	x	PROPN
ejpam-3950	55	10	⊗	⊗	PROPN
ejpam-3950	55	11	y	y	PROPN
ejpam-3950	55	12	such	such	ADJ
ejpam-3950	55	13	that	that	SCONJ
ejpam-3950	55	14	x1	x1	PROPN
ejpam-3950	55	15	⊗	⊗	PROPN
ejpam-3950	55	16	y1	y1	PROPN
ejpam-3950	56	1	+	+	CCONJ
ejpam-3950	56	2	x2	x2	PROPN
ejpam-3950	57	1	⊗	⊗	ADJ
ejpam-3950	57	2	y2	y2	PROPN
ejpam-3950	57	3	=	=	SYM
ejpam-3950	58	1	x3	x3	PROPN
ejpam-3950	58	2	⊗	⊗	PROPN
ejpam-3950	58	3	y3	y3	PROPN
ejpam-3950	58	4	.	.	PUNCT
ejpam-3950	59	1	then	then	ADV
ejpam-3950	59	2	either	either	CCONJ
ejpam-3950	59	3	x1	x1	PROPN
ejpam-3950	59	4	,	,	PUNCT
ejpam-3950	59	5	x2	x2	PROPN
ejpam-3950	59	6	or	or	CCONJ
ejpam-3950	59	7	y1	y1	NOUN
ejpam-3950	59	8	,	,	PUNCT
ejpam-3950	59	9	y2	y2	PROPN
ejpam-3950	59	10	are	be	AUX
ejpam-3950	59	11	linearly	linearly	ADV
ejpam-3950	59	12	dependent	dependent	ADJ
ejpam-3950	59	13	.	.	PUNCT
ejpam-3950	60	1	we	we	PRON
ejpam-3950	60	2	can	can	AUX
ejpam-3950	60	3	define	define	VERB
ejpam-3950	60	4	many	many	ADJ
ejpam-3950	60	5	norms	norm	NOUN
ejpam-3950	60	6	on	on	ADP
ejpam-3950	60	7	x	x	PROPN
ejpam-3950	60	8	⊗	⊗	PROPN
ejpam-3950	60	9	y	y	PROPN
ejpam-3950	60	10	.	.	PUNCT
ejpam-3950	61	1	the	the	DET
ejpam-3950	61	2	most	most	ADV
ejpam-3950	61	3	important	important	ADJ
ejpam-3950	61	4	one	one	NOUN
ejpam-3950	61	5	is	be	AUX
ejpam-3950	61	6	:	:	PUNCT
ejpam-3950	61	7	the	the	DET
ejpam-3950	61	8	injective	injective	ADJ
ejpam-3950	61	9	norm	norm	NOUN
ejpam-3950	61	10	for	for	ADP
ejpam-3950	61	11	t	t	NOUN
ejpam-3950	61	12	=	=	PUNCT
ejpam-3950	62	1	∑n	∑n	PROPN
ejpam-3950	62	2	i=1	i=1	X
ejpam-3950	62	3	xi	xi	PROPN
ejpam-3950	62	4	⊗	⊗	PROPN
ejpam-3950	62	5	yi	yi	PROPN
ejpam-3950	63	1	∈	∈	PROPN
ejpam-3950	63	2	x	x	X
ejpam-3950	63	3	⊗	⊗	PROPN
ejpam-3950	63	4	y	y	PROPN
ejpam-3950	63	5	define	define	VERB
ejpam-3950	63	6	‖	‖	PROPN
ejpam-3950	63	7	t	t	PROPN
ejpam-3950	63	8	‖∨=	‖∨=	X
ejpam-3950	63	9	sup{|	sup{|	PROPN
ejpam-3950	63	10	n∑	n∑	PROPN
ejpam-3950	63	11	i=1	i=1	PROPN
ejpam-3950	64	1	〈	〈	PROPN
ejpam-3950	64	2	xi	xi	PROPN
ejpam-3950	64	3	,	,	PUNCT
ejpam-3950	64	4	x∗〉〈yi	x∗〉〈yi	PROPN
ejpam-3950	64	5	,	,	PUNCT
ejpam-3950	64	6	y∗	y∗	PROPN
ejpam-3950	64	7	〉	〉	NUM
ejpam-3950	64	8	|	|	NOUN
ejpam-3950	64	9	:	:	PUNCT
ejpam-3950	64	10	x∗	x∗	PROPN
ejpam-3950	64	11	∈	∈	PROPN
ejpam-3950	64	12	b1(x	b1(x	NOUN
ejpam-3950	64	13	∗	∗	NOUN
ejpam-3950	64	14	)	)	PUNCT
ejpam-3950	64	15	and	and	CCONJ
ejpam-3950	64	16	y∗	y∗	PROPN
ejpam-3950	64	17	∈	∈	PROPN
ejpam-3950	64	18	b1(y	b1(y	NUM
ejpam-3950	64	19	∗	∗	NOUN
ejpam-3950	64	20	)	)	PUNCT
ejpam-3950	64	21	}	}	PUNCT
ejpam-3950	64	22	.	.	PUNCT
ejpam-3950	65	1	f.	f.	PROPN
ejpam-3950	65	2	seddiki	seddiki	PROPN
ejpam-3950	65	3	,	,	PUNCT
ejpam-3950	65	4	m.	m.	NOUN
ejpam-3950	65	5	al	al	PROPN
ejpam-3950	65	6	horani	horani	PROPN
ejpam-3950	65	7	,	,	PUNCT
ejpam-3950	65	8	r.	r.	PROPN
ejpam-3950	65	9	khalil	khalil	PROPN
ejpam-3950	65	10	/	/	SYM
ejpam-3950	65	11	eur	eur	PROPN
ejpam-3950	65	12	.	.	PUNCT
ejpam-3950	66	1	j.	j.	PROPN
ejpam-3950	66	2	pure	pure	PROPN
ejpam-3950	66	3	appl	appl	PROPN
ejpam-3950	66	4	.	.	PROPN
ejpam-3950	66	5	math	math	PROPN
ejpam-3950	66	6	,	,	PUNCT
ejpam-3950	66	7	14	14	NUM
ejpam-3950	66	8	(	(	PUNCT
ejpam-3950	66	9	2	2	NUM
ejpam-3950	66	10	)	)	PUNCT
ejpam-3950	66	11	(	(	PUNCT
ejpam-3950	66	12	2021	2021	NUM
ejpam-3950	66	13	)	)	PUNCT
ejpam-3950	66	14	,	,	PUNCT
ejpam-3950	66	15	493	493	NUM
ejpam-3950	66	16	-	-	SYM
ejpam-3950	66	17	505	505	NUM
ejpam-3950	66	18	495	495	NUM
ejpam-3950	66	19	so	so	ADV
ejpam-3950	66	20	,	,	PUNCT
ejpam-3950	66	21	‖	‖	PROPN
ejpam-3950	66	22	.	.	PUNCT
ejpam-3950	67	1	‖∨	‖∨	PRON
ejpam-3950	67	2	is	be	AUX
ejpam-3950	67	3	just	just	ADV
ejpam-3950	67	4	the	the	DET
ejpam-3950	67	5	operator	operator	NOUN
ejpam-3950	67	6	norm	norm	NOUN
ejpam-3950	67	7	on	on	ADP
ejpam-3950	67	8	l(x∗	l(x∗	PROPN
ejpam-3950	67	9	,	,	PUNCT
ejpam-3950	67	10	y	y	PROPN
ejpam-3950	67	11	)	)	PUNCT
ejpam-3950	67	12	.	.	PUNCT
ejpam-3950	68	1	this	this	PRON
ejpam-3950	68	2	called	call	VERB
ejpam-3950	68	3	the	the	DET
ejpam-3950	68	4	injective	injective	ADJ
ejpam-3950	68	5	norm	norm	NOUN
ejpam-3950	68	6	of	of	ADP
ejpam-3950	68	7	t	t	PROPN
ejpam-3950	68	8	.	.	PUNCT
ejpam-3950	69	1	the	the	DET
ejpam-3950	69	2	space	space	NOUN
ejpam-3950	69	3	(	(	PUNCT
ejpam-3950	69	4	x	x	PROPN
ejpam-3950	69	5	⊗	⊗	PROPN
ejpam-3950	69	6	y	y	PROPN
ejpam-3950	69	7	,	,	PUNCT
ejpam-3950	69	8	‖	‖	PROPN
ejpam-3950	69	9	.	.	PUNCT
ejpam-3950	69	10	‖∨	‖∨	NOUN
ejpam-3950	69	11	)	)	PUNCT
ejpam-3950	69	12	need	need	AUX
ejpam-3950	69	13	not	not	PART
ejpam-3950	69	14	be	be	AUX
ejpam-3950	69	15	complete	complete	ADJ
ejpam-3950	69	16	.	.	PUNCT
ejpam-3950	70	1	let	let	VERB
ejpam-3950	70	2	x	x	SYM
ejpam-3950	70	3	∨	∨	NUM
ejpam-3950	70	4	⊗y	⊗y	NOUN
ejpam-3950	70	5	denote	denote	VERB
ejpam-3950	70	6	the	the	DET
ejpam-3950	70	7	completion	completion	NOUN
ejpam-3950	70	8	of	of	ADP
ejpam-3950	70	9	(	(	PUNCT
ejpam-3950	70	10	x⊗y	x⊗y	PROPN
ejpam-3950	70	11	,	,	PUNCT
ejpam-3950	70	12	‖	‖	PROPN
ejpam-3950	70	13	.	.	PUNCT
ejpam-3950	71	1	‖∨	‖∨	PUNCT
ejpam-3950	71	2	)	)	PUNCT
ejpam-3950	71	3	and	and	CCONJ
ejpam-3950	71	4	it	it	PRON
ejpam-3950	71	5	is	be	AUX
ejpam-3950	71	6	called	call	VERB
ejpam-3950	71	7	the	the	DET
ejpam-3950	71	8	completed	complete	VERB
ejpam-3950	71	9	injective	injective	ADJ
ejpam-3950	71	10	tensor	tensor	NOUN
ejpam-3950	71	11	product	product	NOUN
ejpam-3950	71	12	of	of	ADP
ejpam-3950	71	13	x	x	PUNCT
ejpam-3950	71	14	with	with	ADP
ejpam-3950	71	15	y	y	PROPN
ejpam-3950	71	16	.	.	PUNCT
ejpam-3950	72	1	a	a	DET
ejpam-3950	72	2	nice	nice	ADJ
ejpam-3950	72	3	result	result	NOUN
ejpam-3950	72	4	that	that	PRON
ejpam-3950	72	5	is	be	AUX
ejpam-3950	72	6	used	use	VERB
ejpam-3950	72	7	in	in	ADP
ejpam-3950	72	8	theory	theory	NOUN
ejpam-3950	72	9	of	of	ADP
ejpam-3950	72	10	differential	differential	ADJ
ejpam-3950	72	11	equations	equation	NOUN
ejpam-3950	72	12	is	be	AUX
ejpam-3950	72	13	:	:	PUNCT
ejpam-3950	72	14	theorem	theorem	ADJ
ejpam-3950	72	15	1	1	NUM
ejpam-3950	72	16	.	.	X
ejpam-3950	73	1	for	for	ADP
ejpam-3950	73	2	any	any	DET
ejpam-3950	73	3	compact	compact	ADJ
ejpam-3950	73	4	housdorff	housdorff	NOUN
ejpam-3950	73	5	space	space	NOUN
ejpam-3950	73	6	k	k	PROPN
ejpam-3950	73	7	,	,	PUNCT
ejpam-3950	73	8	and	and	CCONJ
ejpam-3950	73	9	any	any	DET
ejpam-3950	73	10	banach	banach	NOUN
ejpam-3950	73	11	space	space	NOUN
ejpam-3950	73	12	x	x	X
ejpam-3950	73	13	,	,	PUNCT
ejpam-3950	73	14	c(k	c(k	PROPN
ejpam-3950	73	15	,	,	PUNCT
ejpam-3950	73	16	x	x	X
ejpam-3950	73	17	)	)	PUNCT
ejpam-3950	73	18	is	be	AUX
ejpam-3950	73	19	isometrically	isometrically	PROPN
ejpam-3950	73	20	isomorphic	isomorphic	ADJ
ejpam-3950	73	21	to	to	ADP
ejpam-3950	73	22	c(k	c(k	PROPN
ejpam-3950	73	23	)	)	PUNCT
ejpam-3950	73	24	∨	∨	NUM
ejpam-3950	73	25	⊗x	⊗x	NOUN
ejpam-3950	73	26	.	.	PUNCT
ejpam-3950	74	1	in	in	ADP
ejpam-3950	74	2	particular	particular	ADJ
ejpam-3950	74	3	,	,	PUNCT
ejpam-3950	74	4	for	for	ADP
ejpam-3950	74	5	any	any	DET
ejpam-3950	74	6	two	two	NUM
ejpam-3950	74	7	compact	compact	ADJ
ejpam-3950	74	8	metric	metric	ADJ
ejpam-3950	74	9	spaces	space	NOUN
ejpam-3950	74	10	i	i	PRON
ejpam-3950	74	11	and	and	CCONJ
ejpam-3950	74	12	j	j	PROPN
ejpam-3950	74	13	,	,	PUNCT
ejpam-3950	74	14	one	one	PRON
ejpam-3950	74	15	has	have	AUX
ejpam-3950	74	16	c(i×j	c(i×j	VERB
ejpam-3950	74	17	)	)	PUNCT
ejpam-3950	75	1	=	=	SYM
ejpam-3950	75	2	c(i	c(i	PROPN
ejpam-3950	75	3	)	)	PUNCT
ejpam-3950	75	4	∨	∨	NUM
ejpam-3950	75	5	⊗c(j	⊗c(j	NOUN
ejpam-3950	75	6	)	)	PUNCT
ejpam-3950	75	7	.	.	PUNCT
ejpam-3950	76	1	3	3	X
ejpam-3950	76	2	.	.	X
ejpam-3950	76	3	main	main	ADJ
ejpam-3950	76	4	results	result	NOUN
ejpam-3950	76	5	3.1	3.1	NUM
ejpam-3950	76	6	.	.	PUNCT
ejpam-3950	77	1	direct	direct	ADJ
ejpam-3950	77	2	problem	problem	NOUN
ejpam-3950	77	3	let	let	VERB
ejpam-3950	77	4	u	u	PRON
ejpam-3950	77	5	be	be	AUX
ejpam-3950	77	6	an	an	DET
ejpam-3950	77	7	α	α	NOUN
ejpam-3950	77	8	-	-	NOUN
ejpam-3950	77	9	differentiable	differentiable	ADJ
ejpam-3950	77	10	on	on	ADP
ejpam-3950	77	11	i	i	PRON
ejpam-3950	77	12	=	=	PUNCT
ejpam-3950	78	1	[	[	X
ejpam-3950	78	2	0	0	NUM
ejpam-3950	78	3	,	,	PUNCT
ejpam-3950	78	4	1	1	NUM
ejpam-3950	78	5	]	]	PUNCT
ejpam-3950	78	6	with	with	ADP
ejpam-3950	78	7	values	value	NOUN
ejpam-3950	78	8	in	in	ADP
ejpam-3950	78	9	the	the	DET
ejpam-3950	78	10	hilbert	hilbert	NOUN
ejpam-3950	78	11	space	space	NOUN
ejpam-3950	78	12	x	x	PUNCT
ejpam-3950	78	13	=	=	PUNCT
ejpam-3950	78	14	`	`	PUNCT
ejpam-3950	78	15	2	2	NUM
ejpam-3950	78	16	,	,	PUNCT
ejpam-3950	78	17	where	where	SCONJ
ejpam-3950	78	18	`	`	PUNCT
ejpam-3950	78	19	2	2	X
ejpam-3950	78	20	=	=	SYM
ejpam-3950	78	21	{	{	PUNCT
ejpam-3950	78	22	(	(	PUNCT
ejpam-3950	78	23	xn	xn	PROPN
ejpam-3950	78	24	)	)	PUNCT
ejpam-3950	78	25	:	:	PUNCT
ejpam-3950	78	26	∑∞	∑∞	NOUN
ejpam-3950	78	27	n=1	n=1	PUNCT
ejpam-3950	78	28	|	|	ADV
ejpam-3950	78	29	xn	xn	PROPN
ejpam-3950	78	30	|2	|2	PUNCT
ejpam-3950	78	31	<	<	X
ejpam-3950	78	32	∞	∞	NUM
ejpam-3950	78	33	}	}	PUNCT
ejpam-3950	78	34	.	.	PUNCT
ejpam-3950	79	1	the	the	DET
ejpam-3950	79	2	natural	natural	ADJ
ejpam-3950	79	3	basis	basis	NOUN
ejpam-3950	79	4	of	of	ADP
ejpam-3950	79	5	`	`	PUNCT
ejpam-3950	79	6	2	2	NUM
ejpam-3950	79	7	is	be	AUX
ejpam-3950	79	8	denotes	denote	NOUN
ejpam-3950	79	9	by	by	ADP
ejpam-3950	79	10	{	{	PUNCT
ejpam-3950	79	11	δ1	δ1	NOUN
ejpam-3950	79	12	,	,	PUNCT
ejpam-3950	79	13	δ2	δ2	VERB
ejpam-3950	79	14	,	,	PUNCT
ejpam-3950	79	15	...	...	PUNCT
ejpam-3950	79	16	}	}	PUNCT
ejpam-3950	79	17	.	.	PUNCT
ejpam-3950	80	1	in	in	ADP
ejpam-3950	80	2	`	`	PUNCT
ejpam-3950	80	3	2	2	NUM
ejpam-3950	80	4	we	we	PRON
ejpam-3950	80	5	write	write	VERB
ejpam-3950	80	6	[	[	X
ejpam-3950	80	7	x1	x1	PROPN
ejpam-3950	80	8	,	,	PUNCT
ejpam-3950	80	9	x2	x2	PROPN
ejpam-3950	80	10	,	,	PUNCT
ejpam-3950	80	11	...	...	PUNCT
ejpam-3950	80	12	,	,	PUNCT
ejpam-3950	80	13	xn	xn	PROPN
ejpam-3950	80	14	]	]	X
ejpam-3950	80	15	to	to	PART
ejpam-3950	80	16	denote	denote	VERB
ejpam-3950	80	17	the	the	DET
ejpam-3950	80	18	span	span	NOUN
ejpam-3950	80	19	of	of	ADP
ejpam-3950	80	20	{	{	PUNCT
ejpam-3950	80	21	x1	x1	PROPN
ejpam-3950	80	22	,	,	PUNCT
ejpam-3950	80	23	x2	x2	PROPN
ejpam-3950	80	24	,	,	PUNCT
ejpam-3950	80	25	...	...	PUNCT
ejpam-3950	80	26	,	,	PUNCT
ejpam-3950	80	27	xn	xn	PROPN
ejpam-3950	80	28	}	}	PUNCT
ejpam-3950	80	29	.	.	PUNCT
ejpam-3950	81	1	let	let	VERB
ejpam-3950	81	2	a	a	DET
ejpam-3950	81	3	:	:	PUNCT
ejpam-3950	81	4	dom(a	dom(a	PROPN
ejpam-3950	81	5	)	)	PUNCT
ejpam-3950	81	6	⊆	⊆	NUM
ejpam-3950	81	7	`	`	PUNCT
ejpam-3950	81	8	2	2	NUM
ejpam-3950	81	9	→	→	SYM
ejpam-3950	81	10	`	`	PUNCT
ejpam-3950	81	11	2	2	NUM
ejpam-3950	81	12	,	,	PUNCT
ejpam-3950	81	13	b	b	NOUN
ejpam-3950	81	14	:	:	PUNCT
ejpam-3950	81	15	dom(b	dom(b	PROPN
ejpam-3950	81	16	)	)	PUNCT
ejpam-3950	81	17	⊆	⊆	NUM
ejpam-3950	81	18	`	`	PUNCT
ejpam-3950	81	19	2	2	NUM
ejpam-3950	81	20	→	→	SYM
ejpam-3950	81	21	`	`	PUNCT
ejpam-3950	81	22	2	2	NUM
ejpam-3950	81	23	be	be	AUX
ejpam-3950	81	24	two	two	NUM
ejpam-3950	81	25	densely	densely	ADV
ejpam-3950	81	26	defined	define	VERB
ejpam-3950	81	27	linear	linear	NOUN
ejpam-3950	81	28	operators	operator	NOUN
ejpam-3950	81	29	on	on	ADP
ejpam-3950	81	30	`	`	PUNCT
ejpam-3950	81	31	2	2	NUM
ejpam-3950	81	32	,	,	PUNCT
ejpam-3950	81	33	where	where	SCONJ
ejpam-3950	81	34	domains	domain	NOUN
ejpam-3950	81	35	of	of	ADP
ejpam-3950	81	36	a	a	PRON
ejpam-3950	81	37	and	and	CCONJ
ejpam-3950	81	38	b	b	NOUN
ejpam-3950	81	39	contain	contain	VERB
ejpam-3950	81	40	the	the	DET
ejpam-3950	81	41	elements	element	NOUN
ejpam-3950	81	42	of	of	ADP
ejpam-3950	81	43	the	the	DET
ejpam-3950	81	44	natural	natural	ADJ
ejpam-3950	81	45	basis	basis	NOUN
ejpam-3950	81	46	of	of	ADP
ejpam-3950	81	47	`	`	PUNCT
ejpam-3950	81	48	2	2	X
ejpam-3950	81	49	.	.	PUNCT
ejpam-3950	82	1	the	the	DET
ejpam-3950	82	2	homogeneous	homogeneous	ADJ
ejpam-3950	82	3	degenerate	degenerate	ADJ
ejpam-3950	82	4	fractional	fractional	ADJ
ejpam-3950	82	5	abstract	abstract	ADJ
ejpam-3950	82	6	cauchy	cauchy	ADJ
ejpam-3950	82	7	problem	problem	NOUN
ejpam-3950	82	8	is	be	AUX
ejpam-3950	82	9	{	{	PUNCT
ejpam-3950	82	10	bu(α)(t	bu(α)(t	NOUN
ejpam-3950	82	11	)	)	PUNCT
ejpam-3950	82	12	=	=	SYM
ejpam-3950	82	13	au(t	au(t	X
ejpam-3950	82	14	)	)	PUNCT
ejpam-3950	82	15	u(0	u(0	NOUN
ejpam-3950	82	16	)	)	PUNCT
ejpam-3950	82	17	=	=	SYM
ejpam-3950	83	1	x0	x0	PROPN
ejpam-3950	83	2	(	(	PUNCT
ejpam-3950	83	3	1	1	X
ejpam-3950	83	4	)	)	PUNCT
ejpam-3950	83	5	the	the	DET
ejpam-3950	83	6	nonhomogeneous	nonhomogeneous	ADJ
ejpam-3950	83	7	degenerate	degenerate	ADJ
ejpam-3950	83	8	fractional	fractional	ADJ
ejpam-3950	83	9	abstract	abstract	ADJ
ejpam-3950	83	10	cauchy	cauchy	ADJ
ejpam-3950	83	11	problem	problem	NOUN
ejpam-3950	83	12	is	be	AUX
ejpam-3950	83	13	{	{	PUNCT
ejpam-3950	83	14	bu(α)(t	bu(α)(t	NOUN
ejpam-3950	83	15	)	)	PUNCT
ejpam-3950	83	16	=	=	NOUN
ejpam-3950	83	17	au(t	au(t	NUM
ejpam-3950	83	18	)	)	PUNCT
ejpam-3950	84	1	+	+	NUM
ejpam-3950	84	2	f(t)z	f(t)z	PROPN
ejpam-3950	84	3	u(0	u(0	PROPN
ejpam-3950	84	4	)	)	PUNCT
ejpam-3950	84	5	=	=	SYM
ejpam-3950	85	1	x0	x0	PROPN
ejpam-3950	85	2	(	(	PUNCT
ejpam-3950	85	3	2	2	NUM
ejpam-3950	85	4	)	)	PUNCT
ejpam-3950	85	5	where	where	SCONJ
ejpam-3950	85	6	u(t	u(t	NOUN
ejpam-3950	85	7	)	)	PUNCT
ejpam-3950	85	8	∈	∈	PROPN
ejpam-3950	85	9	dom(a	dom(a	PROPN
ejpam-3950	85	10	)	)	PUNCT
ejpam-3950	85	11	∩dom(b	∩dom(b	NOUN
ejpam-3950	85	12	)	)	PUNCT
ejpam-3950	85	13	,	,	PUNCT
ejpam-3950	85	14	u(α)(t	u(α)(t	X
ejpam-3950	85	15	)	)	PUNCT
ejpam-3950	85	16	∈	∈	PROPN
ejpam-3950	85	17	dom(b	dom(b	PROPN
ejpam-3950	85	18	)	)	PUNCT
ejpam-3950	85	19	,	,	PUNCT
ejpam-3950	85	20	f	f	PROPN
ejpam-3950	85	21	∈	∈	PROPN
ejpam-3950	85	22	c(i	c(i	PROPN
ejpam-3950	85	23	)	)	PUNCT
ejpam-3950	85	24	and	and	CCONJ
ejpam-3950	85	25	z	z	NOUN
ejpam-3950	85	26	∈	∈	PROPN
ejpam-3950	85	27	`	`	PUNCT
ejpam-3950	85	28	2	2	NUM
ejpam-3950	85	29	.	.	PUNCT
ejpam-3950	86	1	in	in	ADP
ejpam-3950	86	2	this	this	DET
ejpam-3950	86	3	section	section	NOUN
ejpam-3950	86	4	we	we	PRON
ejpam-3950	86	5	look	look	VERB
ejpam-3950	86	6	for	for	ADP
ejpam-3950	86	7	a	a	DET
ejpam-3950	86	8	solution	solution	NOUN
ejpam-3950	86	9	to	to	ADP
ejpam-3950	86	10	problems	problem	NOUN
ejpam-3950	86	11	(	(	PUNCT
ejpam-3950	86	12	1	1	NUM
ejpam-3950	86	13	)	)	PUNCT
ejpam-3950	86	14	and	and	CCONJ
ejpam-3950	86	15	(	(	PUNCT
ejpam-3950	86	16	2	2	X
ejpam-3950	86	17	)	)	PUNCT
ejpam-3950	86	18	among	among	ADP
ejpam-3950	86	19	finite	finite	ADJ
ejpam-3950	86	20	rank	rank	NOUN
ejpam-3950	86	21	function	function	NOUN
ejpam-3950	86	22	of	of	ADP
ejpam-3950	86	23	the	the	DET
ejpam-3950	86	24	form	form	NOUN
ejpam-3950	86	25	u(t	u(t	NOUN
ejpam-3950	86	26	)	)	PUNCT
ejpam-3950	86	27	=	=	SYM
ejpam-3950	87	1	∑n	∑n	PROPN
ejpam-3950	87	2	i=1	i=1	PRON
ejpam-3950	87	3	ui(t)δi	ui(t)δi	ADJ
ejpam-3950	87	4	,	,	PUNCT
ejpam-3950	87	5	where	where	SCONJ
ejpam-3950	87	6	u	u	PROPN
ejpam-3950	87	7	(	(	PUNCT
ejpam-3950	87	8	α	α	NOUN
ejpam-3950	87	9	)	)	PUNCT
ejpam-3950	87	10	i	i	PRON
ejpam-3950	87	11	∈	∈	PROPN
ejpam-3950	87	12	c(i	c(i	PROPN
ejpam-3950	87	13	)	)	PUNCT
ejpam-3950	87	14	,	,	PUNCT
ejpam-3950	87	15	i	i	PRON
ejpam-3950	87	16	=	=	NOUN
ejpam-3950	87	17	1	1	NUM
ejpam-3950	87	18	,	,	PUNCT
ejpam-3950	87	19	2	2	NUM
ejpam-3950	87	20	,	,	PUNCT
ejpam-3950	87	21	...	...	PUNCT
ejpam-3950	87	22	n.	n.	PROPN
ejpam-3950	87	23	theorem	theorem	VERB
ejpam-3950	87	24	2	2	NUM
ejpam-3950	87	25	.	.	PUNCT
ejpam-3950	88	1	in	in	ADP
ejpam-3950	88	2	problem	problem	NOUN
ejpam-3950	88	3	(	(	PUNCT
ejpam-3950	88	4	p1	p1	PROPN
ejpam-3950	88	5	)	)	PUNCT
ejpam-3950	88	6	,	,	PUNCT
ejpam-3950	88	7	let	let	VERB
ejpam-3950	88	8	u(t	u(t	NOUN
ejpam-3950	88	9	)	)	PUNCT
ejpam-3950	88	10	=	=	SYM
ejpam-3950	89	1	∑n	∑n	PROPN
ejpam-3950	89	2	i=1	i=1	PRON
ejpam-3950	89	3	ui(t)δi	ui(t)δi	ADJ
ejpam-3950	89	4	,	,	PUNCT
ejpam-3950	89	5	where	where	SCONJ
ejpam-3950	89	6	u	u	PROPN
ejpam-3950	89	7	(	(	PUNCT
ejpam-3950	89	8	α	α	NOUN
ejpam-3950	89	9	)	)	PUNCT
ejpam-3950	89	10	i	i	PRON
ejpam-3950	89	11	∈	∈	PROPN
ejpam-3950	89	12	c(i	c(i	PROPN
ejpam-3950	89	13	)	)	PUNCT
ejpam-3950	89	14	,	,	PUNCT
ejpam-3950	89	15	i	i	PRON
ejpam-3950	89	16	=	=	NOUN
ejpam-3950	89	17	1	1	NUM
ejpam-3950	89	18	,	,	PUNCT
ejpam-3950	89	19	2	2	NUM
ejpam-3950	89	20	,	,	PUNCT
ejpam-3950	89	21	...	...	PUNCT
ejpam-3950	89	22	n	n	CCONJ
ejpam-3950	89	23	and	and	CCONJ
ejpam-3950	89	24	assume	assume	VERB
ejpam-3950	89	25	b	b	X
ejpam-3950	89	26	=	=	SYM
ejpam-3950	89	27	i	i	PROPN
ejpam-3950	89	28	,	,	PUNCT
ejpam-3950	89	29	then	then	ADV
ejpam-3950	89	30	the	the	DET
ejpam-3950	89	31	problem	problem	NOUN
ejpam-3950	89	32	(	(	PUNCT
ejpam-3950	89	33	1	1	X
ejpam-3950	89	34	)	)	PUNCT
ejpam-3950	89	35	has	have	VERB
ejpam-3950	89	36	a	a	DET
ejpam-3950	89	37	unique	unique	ADJ
ejpam-3950	89	38	solution	solution	NOUN
ejpam-3950	89	39	.	.	PUNCT
ejpam-3950	90	1	proof	proof	NOUN
ejpam-3950	90	2	.	.	PUNCT
ejpam-3950	91	1	we	we	PRON
ejpam-3950	91	2	have	have	VERB
ejpam-3950	91	3	,	,	PUNCT
ejpam-3950	91	4	u(t	u(t	NOUN
ejpam-3950	91	5	)	)	PUNCT
ejpam-3950	91	6	=	=	SYM
ejpam-3950	92	1	∑n	∑n	PROPN
ejpam-3950	92	2	i=1	i=1	PRON
ejpam-3950	92	3	ui(t)δi	ui(t)δi	ADJ
ejpam-3950	92	4	,	,	PUNCT
ejpam-3950	92	5	then	then	ADV
ejpam-3950	92	6	u(α)(t	u(α)(t	NOUN
ejpam-3950	92	7	)	)	PUNCT
ejpam-3950	92	8	=	=	SYM
ejpam-3950	93	1	∑n	∑n	PROPN
ejpam-3950	93	2	i=1	i=1	PROPN
ejpam-3950	93	3	u	u	PROPN
ejpam-3950	93	4	(	(	PUNCT
ejpam-3950	93	5	α	α	NOUN
ejpam-3950	93	6	)	)	PUNCT
ejpam-3950	93	7	i	i	PRON
ejpam-3950	93	8	(	(	PUNCT
ejpam-3950	93	9	t)δi	t)δi	PROPN
ejpam-3950	93	10	,	,	PUNCT
ejpam-3950	93	11	thus	thus	ADV
ejpam-3950	93	12	n∑	n∑	PROPN
ejpam-3950	93	13	i=1	i=1	PROPN
ejpam-3950	93	14	u	u	PROPN
ejpam-3950	93	15	(	(	PUNCT
ejpam-3950	93	16	α	α	NOUN
ejpam-3950	93	17	)	)	PUNCT
ejpam-3950	93	18	i	i	PRON
ejpam-3950	93	19	(	(	PUNCT
ejpam-3950	93	20	t)δi	t)δi	PROPN
ejpam-3950	93	21	=	=	SYM
ejpam-3950	93	22	n∑	n∑	PROPN
ejpam-3950	93	23	i=1	i=1	PROPN
ejpam-3950	93	24	ui(t)aδi	ui(t)aδi	PROPN
ejpam-3950	93	25	.	.	PUNCT
ejpam-3950	94	1	(	(	PUNCT
ejpam-3950	94	2	3	3	X
ejpam-3950	94	3	)	)	PUNCT
ejpam-3950	94	4	so	so	ADV
ejpam-3950	94	5	,	,	PUNCT
ejpam-3950	94	6	au(t	au(t	NUM
ejpam-3950	94	7	)	)	PUNCT
ejpam-3950	94	8	∈	∈	PROPN
ejpam-3950	95	1	[	[	X
ejpam-3950	95	2	δ1	δ1	NOUN
ejpam-3950	95	3	,	,	PUNCT
ejpam-3950	95	4	δ2	δ2	VERB
ejpam-3950	95	5	,	,	PUNCT
ejpam-3950	95	6	...	...	PUNCT
ejpam-3950	95	7	,	,	PUNCT
ejpam-3950	95	8	δn	δn	X
ejpam-3950	95	9	]	]	PUNCT
ejpam-3950	95	10	,	,	PUNCT
ejpam-3950	95	11	since	since	SCONJ
ejpam-3950	95	12	u(α)(t	u(α)(t	NOUN
ejpam-3950	95	13	)	)	PUNCT
ejpam-3950	95	14	is	be	AUX
ejpam-3950	95	15	linear	linear	ADJ
ejpam-3950	95	16	combination	combination	NOUN
ejpam-3950	95	17	of	of	ADP
ejpam-3950	95	18	δ1	δ1	NOUN
ejpam-3950	95	19	,	,	PUNCT
ejpam-3950	95	20	δ2	δ2	PROPN
ejpam-3950	95	21	,	,	PUNCT
ejpam-3950	95	22	...	...	PUNCT
ejpam-3950	95	23	,	,	PUNCT
ejpam-3950	95	24	δn	δn	X
ejpam-3950	95	25	.	.	PUNCT
ejpam-3950	96	1	hence	hence	ADV
ejpam-3950	96	2	[	[	X
ejpam-3950	96	3	δ1	δ1	NOUN
ejpam-3950	96	4	,	,	PUNCT
ejpam-3950	96	5	δ2	δ2	VERB
ejpam-3950	96	6	,	,	PUNCT
ejpam-3950	96	7	...	...	PUNCT
ejpam-3950	96	8	,	,	PUNCT
ejpam-3950	96	9	δn	δn	X
ejpam-3950	96	10	]	]	PUNCT
ejpam-3950	96	11	is	be	AUX
ejpam-3950	96	12	invariant	invariant	ADJ
ejpam-3950	96	13	subspace	subspace	NOUN
ejpam-3950	96	14	of	of	ADP
ejpam-3950	96	15	a.	a.	PROPN
ejpam-3950	96	16	f.	f.	PROPN
ejpam-3950	96	17	seddiki	seddiki	PROPN
ejpam-3950	96	18	,	,	PUNCT
ejpam-3950	96	19	m.	m.	NOUN
ejpam-3950	96	20	al	al	PROPN
ejpam-3950	96	21	horani	horani	PROPN
ejpam-3950	96	22	,	,	PUNCT
ejpam-3950	96	23	r.	r.	PROPN
ejpam-3950	96	24	khalil	khalil	PROPN
ejpam-3950	96	25	/	/	SYM
ejpam-3950	96	26	eur	eur	PROPN
ejpam-3950	96	27	.	.	PUNCT
ejpam-3950	97	1	j.	j.	PROPN
ejpam-3950	97	2	pure	pure	PROPN
ejpam-3950	97	3	appl	appl	PROPN
ejpam-3950	97	4	.	.	PROPN
ejpam-3950	97	5	math	math	PROPN
ejpam-3950	97	6	,	,	PUNCT
ejpam-3950	97	7	14	14	NUM
ejpam-3950	97	8	(	(	PUNCT
ejpam-3950	97	9	2	2	NUM
ejpam-3950	97	10	)	)	PUNCT
ejpam-3950	97	11	(	(	PUNCT
ejpam-3950	97	12	2021	2021	NUM
ejpam-3950	97	13	)	)	PUNCT
ejpam-3950	97	14	,	,	PUNCT
ejpam-3950	97	15	493	493	NUM
ejpam-3950	97	16	-	-	SYM
ejpam-3950	97	17	505	505	NUM
ejpam-3950	97	18	496	496	NUM
ejpam-3950	97	19	let	let	VERB
ejpam-3950	97	20	â	â	PUNCT
ejpam-3950	97	21	=	=	PUNCT
ejpam-3950	97	22	a	a	DET
ejpam-3950	97	23	|[δ1,δ2,	|[δ1,δ2,	NUM
ejpam-3950	97	24	...	...	PUNCT
ejpam-3950	97	25	,δn	,δn	PUNCT
ejpam-3950	97	26	]	]	PUNCT
ejpam-3950	97	27	be	be	AUX
ejpam-3950	97	28	the	the	DET
ejpam-3950	97	29	restriction	restriction	NOUN
ejpam-3950	97	30	of	of	ADP
ejpam-3950	97	31	a	a	DET
ejpam-3950	97	32	on	on	ADP
ejpam-3950	97	33	[	[	X
ejpam-3950	97	34	δ1	δ1	NOUN
ejpam-3950	97	35	,	,	PUNCT
ejpam-3950	97	36	δ2	δ2	VERB
ejpam-3950	97	37	,	,	PUNCT
ejpam-3950	97	38	...	...	PUNCT
ejpam-3950	97	39	,	,	PUNCT
ejpam-3950	98	1	δn	δn	ADP
ejpam-3950	98	2	]	]	PUNCT
ejpam-3950	98	3	and	and	CCONJ
ejpam-3950	98	4	so	so	ADV
ejpam-3950	98	5	â	â	PRON
ejpam-3950	98	6	has	have	VERB
ejpam-3950	98	7	a	a	DET
ejpam-3950	98	8	matrix	matrix	NOUN
ejpam-3950	98	9	representation	representation	NOUN
ejpam-3950	98	10	which	which	PRON
ejpam-3950	98	11	is	be	AUX
ejpam-3950	98	12	â	â	ADP
ejpam-3950	98	13	=	=	PUNCT
ejpam-3950	99	1	[	[	X
ejpam-3950	99	2	aij	aij	X
ejpam-3950	99	3	]	]	X
ejpam-3950	99	4	,	,	PUNCT
ejpam-3950	99	5	such	such	ADJ
ejpam-3950	99	6	that	that	SCONJ
ejpam-3950	99	7	aij	aij	PROPN
ejpam-3950	99	8	=	=	SYM
ejpam-3950	99	9	〈	〈	PROPN
ejpam-3950	99	10	aδj	aδj	NOUN
ejpam-3950	99	11	,	,	PUNCT
ejpam-3950	99	12	δi	δi	PROPN
ejpam-3950	99	13	〉	〉	NOUN
ejpam-3950	99	14	.	.	PUNCT
ejpam-3950	100	1	taking	take	VERB
ejpam-3950	100	2	the	the	DET
ejpam-3950	100	3	inner	inner	ADJ
ejpam-3950	100	4	product	product	NOUN
ejpam-3950	100	5	of	of	ADP
ejpam-3950	100	6	δj	δj	NOUN
ejpam-3950	100	7	with	with	ADP
ejpam-3950	100	8	both	both	DET
ejpam-3950	100	9	sides	side	NOUN
ejpam-3950	100	10	of	of	ADP
ejpam-3950	100	11	equation	equation	NOUN
ejpam-3950	100	12	(	(	PUNCT
ejpam-3950	100	13	3	3	NUM
ejpam-3950	100	14	)	)	PUNCT
ejpam-3950	100	15	,	,	PUNCT
ejpam-3950	100	16	we	we	PRON
ejpam-3950	100	17	get	get	VERB
ejpam-3950	101	1	n∑	n∑	PROPN
ejpam-3950	101	2	i=1	i=1	PROPN
ejpam-3950	101	3	u	u	PROPN
ejpam-3950	101	4	(	(	PUNCT
ejpam-3950	101	5	α	α	NOUN
ejpam-3950	101	6	)	)	PUNCT
ejpam-3950	101	7	i	i	PRON
ejpam-3950	101	8	(	(	PUNCT
ejpam-3950	101	9	t)〈δi	t)〈δi	NUM
ejpam-3950	101	10	,	,	PUNCT
ejpam-3950	101	11	δj	δj	PROPN
ejpam-3950	101	12	〉	〉	NUM
ejpam-3950	101	13	=	=	SYM
ejpam-3950	101	14	n∑	n∑	PROPN
ejpam-3950	101	15	i=1	i=1	PROPN
ejpam-3950	101	16	ui(t)〈aδi	ui(t)〈aδi	PROPN
ejpam-3950	101	17	,	,	PUNCT
ejpam-3950	101	18	δj	δj	PROPN
ejpam-3950	101	19	〉	〉	PROPN
ejpam-3950	101	20	.	.	PUNCT
ejpam-3950	102	1	since	since	SCONJ
ejpam-3950	102	2	{	{	PUNCT
ejpam-3950	102	3	δi}ni=1	δi}ni=1	PROPN
ejpam-3950	102	4	is	be	AUX
ejpam-3950	102	5	orthonormal	orthonormal	ADJ
ejpam-3950	102	6	,	,	PUNCT
ejpam-3950	102	7	we	we	PRON
ejpam-3950	102	8	obtain	obtain	VERB
ejpam-3950	102	9	u	u	NOUN
ejpam-3950	102	10	(	(	PUNCT
ejpam-3950	102	11	α	α	NOUN
ejpam-3950	102	12	)	)	PUNCT
ejpam-3950	102	13	j	j	PROPN
ejpam-3950	102	14	(	(	PUNCT
ejpam-3950	102	15	t	t	PROPN
ejpam-3950	102	16	)	)	PUNCT
ejpam-3950	102	17	=	=	SYM
ejpam-3950	103	1	n∑	n∑	PROPN
ejpam-3950	103	2	i=1	i=1	PROPN
ejpam-3950	103	3	ui(t)〈aδi	ui(t)〈aδi	PROPN
ejpam-3950	103	4	,	,	PUNCT
ejpam-3950	103	5	δj	δj	PROPN
ejpam-3950	103	6	〉	〉	PROPN
ejpam-3950	103	7	.	.	PUNCT
ejpam-3950	104	1	(	(	PUNCT
ejpam-3950	104	2	4	4	X
ejpam-3950	104	3	)	)	PUNCT
ejpam-3950	104	4	which	which	PRON
ejpam-3950	104	5	is	be	AUX
ejpam-3950	104	6	a	a	DET
ejpam-3950	104	7	homogeneous	homogeneous	ADJ
ejpam-3950	104	8	linear	linear	NOUN
ejpam-3950	104	9	system	system	NOUN
ejpam-3950	104	10	of	of	ADP
ejpam-3950	104	11	differential	differential	ADJ
ejpam-3950	104	12	equations	equation	NOUN
ejpam-3950	104	13	u	u	PROPN
ejpam-3950	104	14	(	(	PUNCT
ejpam-3950	104	15	α)(t	α)(t	PROPN
ejpam-3950	104	16	)	)	PUNCT
ejpam-3950	104	17	=	=	SYM
ejpam-3950	104	18	âu(t	âu(t	PROPN
ejpam-3950	104	19	)	)	PUNCT
ejpam-3950	104	20	,	,	PUNCT
ejpam-3950	104	21	where	where	SCONJ
ejpam-3950	104	22	u(t	u(t	NOUN
ejpam-3950	104	23	)	)	PUNCT
ejpam-3950	104	24	=	=	SYM
ejpam-3950	104	25	(	(	PUNCT
ejpam-3950	104	26	u1(t	u1(t	PROPN
ejpam-3950	104	27	)	)	PUNCT
ejpam-3950	104	28	,	,	PUNCT
ejpam-3950	104	29	u2(t	u2(t	NOUN
ejpam-3950	104	30	)	)	PUNCT
ejpam-3950	104	31	,	,	PUNCT
ejpam-3950	104	32	...	...	PUNCT
ejpam-3950	104	33	,	,	PUNCT
ejpam-3950	104	34	un(t))t	un(t))t	PROPN
ejpam-3950	104	35	.	.	PUNCT
ejpam-3950	105	1	this	this	PRON
ejpam-3950	105	2	is	be	AUX
ejpam-3950	105	3	system	system	NOUN
ejpam-3950	105	4	has	have	VERB
ejpam-3950	105	5	a	a	DET
ejpam-3950	105	6	unique	unique	ADJ
ejpam-3950	105	7	solution	solution	NOUN
ejpam-3950	105	8	of	of	ADP
ejpam-3950	105	9	the	the	DET
ejpam-3950	105	10	form	form	NOUN
ejpam-3950	105	11	u(t	u(t	NOUN
ejpam-3950	105	12	)	)	PUNCT
ejpam-3950	105	13	=	=	SYM
ejpam-3950	106	1	φ(t)c	φ(t)c	PROPN
ejpam-3950	106	2	.	.	PUNCT
ejpam-3950	107	1	here	here	ADV
ejpam-3950	107	2	φ(t	φ(t	PROPN
ejpam-3950	107	3	)	)	PUNCT
ejpam-3950	107	4	is	be	AUX
ejpam-3950	107	5	the	the	DET
ejpam-3950	107	6	fundamental	fundamental	ADJ
ejpam-3950	107	7	matrix	matrix	NOUN
ejpam-3950	107	8	,	,	PUNCT
ejpam-3950	107	9	which	which	PRON
ejpam-3950	107	10	is	be	AUX
ejpam-3950	107	11	invertible	invertible	ADJ
ejpam-3950	107	12	.	.	PUNCT
ejpam-3950	108	1	by	by	ADP
ejpam-3950	108	2	the	the	DET
ejpam-3950	108	3	initial	initial	ADJ
ejpam-3950	108	4	condition	condition	NOUN
ejpam-3950	108	5	,	,	PUNCT
ejpam-3950	108	6	we	we	PRON
ejpam-3950	108	7	have	have	VERB
ejpam-3950	108	8	ci	ci	NOUN
ejpam-3950	108	9	=	=	SYM
ejpam-3950	108	10	〈	〈	PROPN
ejpam-3950	108	11	φ−1(0)x0	φ−1(0)x0	PROPN
ejpam-3950	108	12	,	,	PUNCT
ejpam-3950	108	13	δi	δi	ADP
ejpam-3950	108	14	〉	〉	PROPN
ejpam-3950	108	15	,	,	PUNCT
ejpam-3950	108	16	i	i	PRON
ejpam-3950	108	17	=	=	NOUN
ejpam-3950	108	18	1	1	NUM
ejpam-3950	108	19	,	,	PUNCT
ejpam-3950	108	20	...	...	PUNCT
ejpam-3950	108	21	,	,	PUNCT
ejpam-3950	108	22	n.	n.	PROPN
ejpam-3950	108	23	consequently	consequently	ADV
ejpam-3950	108	24	,	,	PUNCT
ejpam-3950	108	25	the	the	DET
ejpam-3950	108	26	problem	problem	NOUN
ejpam-3950	108	27	(	(	PUNCT
ejpam-3950	108	28	1	1	X
ejpam-3950	108	29	)	)	PUNCT
ejpam-3950	108	30	has	have	VERB
ejpam-3950	108	31	a	a	DET
ejpam-3950	108	32	unique	unique	ADJ
ejpam-3950	108	33	solution	solution	NOUN
ejpam-3950	108	34	.	.	PUNCT
ejpam-3950	109	1	theorem	theorem	NOUN
ejpam-3950	109	2	3	3	NUM
ejpam-3950	109	3	.	.	PUNCT
ejpam-3950	110	1	in	in	ADP
ejpam-3950	110	2	problem	problem	NOUN
ejpam-3950	110	3	(	(	PUNCT
ejpam-3950	110	4	2	2	NUM
ejpam-3950	110	5	)	)	PUNCT
ejpam-3950	110	6	,	,	PUNCT
ejpam-3950	110	7	let	let	VERB
ejpam-3950	110	8	u(t	u(t	NOUN
ejpam-3950	110	9	)	)	PUNCT
ejpam-3950	110	10	=	=	SYM
ejpam-3950	111	1	∑n	∑n	PROPN
ejpam-3950	111	2	i=1	i=1	PRON
ejpam-3950	111	3	ui(t)δi	ui(t)δi	ADJ
ejpam-3950	111	4	,	,	PUNCT
ejpam-3950	111	5	where	where	SCONJ
ejpam-3950	111	6	u	u	PROPN
ejpam-3950	111	7	(	(	PUNCT
ejpam-3950	111	8	α	α	NOUN
ejpam-3950	111	9	)	)	PUNCT
ejpam-3950	111	10	i	i	PRON
ejpam-3950	111	11	∈	∈	PROPN
ejpam-3950	111	12	c(i	c(i	PROPN
ejpam-3950	111	13	)	)	PUNCT
ejpam-3950	111	14	,	,	PUNCT
ejpam-3950	111	15	i	i	PRON
ejpam-3950	111	16	=	=	NOUN
ejpam-3950	111	17	1	1	NUM
ejpam-3950	111	18	,	,	PUNCT
ejpam-3950	111	19	2	2	NUM
ejpam-3950	111	20	,	,	PUNCT
ejpam-3950	111	21	...	...	PUNCT
ejpam-3950	111	22	n	n	CCONJ
ejpam-3950	111	23	and	and	CCONJ
ejpam-3950	111	24	assume	assume	VERB
ejpam-3950	111	25	b	b	X
ejpam-3950	111	26	=	=	SYM
ejpam-3950	111	27	i	i	PRON
ejpam-3950	111	28	and	and	CCONJ
ejpam-3950	111	29	z	z	NOUN
ejpam-3950	111	30	∈	∈	PROPN
ejpam-3950	112	1	[	[	X
ejpam-3950	112	2	δ1	δ1	NOUN
ejpam-3950	112	3	,	,	PUNCT
ejpam-3950	112	4	...	...	PUNCT
ejpam-3950	112	5	,	,	PUNCT
ejpam-3950	112	6	δn	δn	X
ejpam-3950	112	7	]	]	PUNCT
ejpam-3950	112	8	,	,	PUNCT
ejpam-3950	112	9	then	then	ADV
ejpam-3950	112	10	the	the	DET
ejpam-3950	112	11	problem	problem	NOUN
ejpam-3950	112	12	(	(	PUNCT
ejpam-3950	112	13	2	2	X
ejpam-3950	112	14	)	)	PUNCT
ejpam-3950	112	15	has	have	VERB
ejpam-3950	112	16	a	a	DET
ejpam-3950	112	17	unique	unique	ADJ
ejpam-3950	112	18	solution	solution	NOUN
ejpam-3950	112	19	.	.	PUNCT
ejpam-3950	113	1	proof	proof	NOUN
ejpam-3950	113	2	.	.	PUNCT
ejpam-3950	114	1	we	we	PRON
ejpam-3950	114	2	have	have	VERB
ejpam-3950	114	3	,	,	PUNCT
ejpam-3950	114	4	u(t	u(t	NOUN
ejpam-3950	114	5	)	)	PUNCT
ejpam-3950	114	6	=	=	SYM
ejpam-3950	115	1	∑n	∑n	PROPN
ejpam-3950	115	2	i=1	i=1	PRON
ejpam-3950	115	3	ui(t)δi	ui(t)δi	ADJ
ejpam-3950	115	4	,	,	PUNCT
ejpam-3950	115	5	then	then	ADV
ejpam-3950	115	6	u(α)(t	u(α)(t	NOUN
ejpam-3950	115	7	)	)	PUNCT
ejpam-3950	115	8	=	=	SYM
ejpam-3950	116	1	∑n	∑n	PROPN
ejpam-3950	116	2	i=1	i=1	PROPN
ejpam-3950	116	3	u	u	PROPN
ejpam-3950	116	4	(	(	PUNCT
ejpam-3950	116	5	α	α	NOUN
ejpam-3950	116	6	)	)	PUNCT
ejpam-3950	116	7	i	i	PRON
ejpam-3950	116	8	(	(	PUNCT
ejpam-3950	116	9	t)δi	t)δi	PROPN
ejpam-3950	116	10	,	,	PUNCT
ejpam-3950	116	11	thus	thus	ADV
ejpam-3950	116	12	n∑	n∑	PROPN
ejpam-3950	116	13	i=1	i=1	PROPN
ejpam-3950	116	14	u	u	PROPN
ejpam-3950	116	15	(	(	PUNCT
ejpam-3950	116	16	α	α	NOUN
ejpam-3950	116	17	)	)	PUNCT
ejpam-3950	116	18	i	i	PRON
ejpam-3950	116	19	(	(	PUNCT
ejpam-3950	116	20	t)δi	t)δi	PROPN
ejpam-3950	116	21	=	=	SYM
ejpam-3950	116	22	n∑	n∑	PROPN
ejpam-3950	116	23	i=1	i=1	PROPN
ejpam-3950	116	24	ui(t)aδi	ui(t)aδi	PROPN
ejpam-3950	116	25	+	+	NUM
ejpam-3950	116	26	f(t)z	f(t)z	NOUN
ejpam-3950	116	27	.	.	PUNCT
ejpam-3950	117	1	(	(	PUNCT
ejpam-3950	117	2	5	5	X
ejpam-3950	117	3	)	)	PUNCT
ejpam-3950	117	4	let	let	VERB
ejpam-3950	117	5	â	â	X
ejpam-3950	117	6	=	=	PUNCT
ejpam-3950	117	7	a	a	DET
ejpam-3950	117	8	|[δ1,δ2,	|[δ1,δ2,	NUM
ejpam-3950	117	9	...	...	PUNCT
ejpam-3950	117	10	,δn	,δn	PUNCT
ejpam-3950	117	11	]	]	PUNCT
ejpam-3950	117	12	the	the	DET
ejpam-3950	117	13	restriction	restriction	NOUN
ejpam-3950	117	14	of	of	ADP
ejpam-3950	117	15	a	a	DET
ejpam-3950	117	16	on	on	ADP
ejpam-3950	117	17	[	[	X
ejpam-3950	117	18	δ1	δ1	NOUN
ejpam-3950	117	19	,	,	PUNCT
ejpam-3950	117	20	δ2	δ2	VERB
ejpam-3950	117	21	,	,	PUNCT
ejpam-3950	117	22	...	...	PUNCT
ejpam-3950	117	23	,	,	PUNCT
ejpam-3950	117	24	δn	δn	ADP
ejpam-3950	117	25	]	]	PUNCT
ejpam-3950	117	26	and	and	CCONJ
ejpam-3950	117	27	so	so	ADV
ejpam-3950	117	28	â	â	PRON
ejpam-3950	117	29	has	have	VERB
ejpam-3950	117	30	a	a	DET
ejpam-3950	117	31	matrix	matrix	NOUN
ejpam-3950	117	32	representation	representation	NOUN
ejpam-3950	117	33	which	which	PRON
ejpam-3950	117	34	is	be	AUX
ejpam-3950	117	35	â	â	ADP
ejpam-3950	117	36	=	=	PUNCT
ejpam-3950	118	1	[	[	X
ejpam-3950	118	2	aij	aij	X
ejpam-3950	118	3	]	]	X
ejpam-3950	118	4	,	,	PUNCT
ejpam-3950	118	5	such	such	ADJ
ejpam-3950	118	6	that	that	SCONJ
ejpam-3950	118	7	aij	aij	PROPN
ejpam-3950	118	8	=	=	SYM
ejpam-3950	118	9	〈	〈	PROPN
ejpam-3950	118	10	aδj	aδj	NOUN
ejpam-3950	118	11	,	,	PUNCT
ejpam-3950	118	12	δi	δi	PROPN
ejpam-3950	118	13	〉	〉	NOUN
ejpam-3950	118	14	.	.	PUNCT
ejpam-3950	119	1	taking	take	VERB
ejpam-3950	119	2	the	the	DET
ejpam-3950	119	3	inner	inner	ADJ
ejpam-3950	119	4	product	product	NOUN
ejpam-3950	119	5	of	of	ADP
ejpam-3950	119	6	δj	δj	NOUN
ejpam-3950	119	7	with	with	ADP
ejpam-3950	119	8	both	both	DET
ejpam-3950	119	9	sides	side	NOUN
ejpam-3950	119	10	of	of	ADP
ejpam-3950	119	11	equation	equation	NOUN
ejpam-3950	119	12	(	(	PUNCT
ejpam-3950	119	13	5	5	NUM
ejpam-3950	119	14	)	)	PUNCT
ejpam-3950	119	15	,	,	PUNCT
ejpam-3950	119	16	we	we	PRON
ejpam-3950	119	17	get	get	VERB
ejpam-3950	120	1	n∑	n∑	PROPN
ejpam-3950	120	2	i=1	i=1	PROPN
ejpam-3950	120	3	u	u	PROPN
ejpam-3950	120	4	(	(	PUNCT
ejpam-3950	120	5	α	α	NOUN
ejpam-3950	120	6	)	)	PUNCT
ejpam-3950	120	7	i	i	PRON
ejpam-3950	120	8	(	(	PUNCT
ejpam-3950	120	9	t)〈δi	t)〈δi	NUM
ejpam-3950	120	10	,	,	PUNCT
ejpam-3950	120	11	δj	δj	PROPN
ejpam-3950	120	12	〉	〉	NUM
ejpam-3950	120	13	=	=	SYM
ejpam-3950	120	14	n∑	n∑	PROPN
ejpam-3950	120	15	i=1	i=1	PROPN
ejpam-3950	120	16	ui(t)〈aδi	ui(t)〈aδi	PROPN
ejpam-3950	120	17	,	,	PUNCT
ejpam-3950	120	18	δj〉+	δj〉+	PROPN
ejpam-3950	120	19	f(t)〈z	f(t)〈z	PROPN
ejpam-3950	120	20	,	,	PUNCT
ejpam-3950	120	21	δj	δj	PROPN
ejpam-3950	120	22	〉	〉	PROPN
ejpam-3950	120	23	.	.	PUNCT
ejpam-3950	121	1	since	since	SCONJ
ejpam-3950	121	2	{	{	PUNCT
ejpam-3950	121	3	δi}ni=1	δi}ni=1	PROPN
ejpam-3950	121	4	is	be	AUX
ejpam-3950	121	5	orthonormal	orthonormal	ADJ
ejpam-3950	121	6	,	,	PUNCT
ejpam-3950	121	7	we	we	PRON
ejpam-3950	121	8	obtain	obtain	VERB
ejpam-3950	121	9	u	u	NOUN
ejpam-3950	121	10	(	(	PUNCT
ejpam-3950	121	11	α	α	NOUN
ejpam-3950	121	12	)	)	PUNCT
ejpam-3950	121	13	j	j	PROPN
ejpam-3950	121	14	(	(	PUNCT
ejpam-3950	121	15	t	t	PROPN
ejpam-3950	121	16	)	)	PUNCT
ejpam-3950	121	17	=	=	SYM
ejpam-3950	122	1	n∑	n∑	PROPN
ejpam-3950	122	2	i=1	i=1	PROPN
ejpam-3950	122	3	ui(t)〈aδi	ui(t)〈aδi	PROPN
ejpam-3950	122	4	,	,	PUNCT
ejpam-3950	122	5	δj〉+	δj〉+	PROPN
ejpam-3950	122	6	f(t)〈z	f(t)〈z	PROPN
ejpam-3950	122	7	,	,	PUNCT
ejpam-3950	122	8	δj	δj	PROPN
ejpam-3950	122	9	〉	〉	PROPN
ejpam-3950	122	10	.	.	PUNCT
ejpam-3950	123	1	(	(	PUNCT
ejpam-3950	123	2	6	6	NUM
ejpam-3950	123	3	)	)	PUNCT
ejpam-3950	123	4	f.	f.	PROPN
ejpam-3950	123	5	seddiki	seddiki	PROPN
ejpam-3950	123	6	,	,	PUNCT
ejpam-3950	123	7	m.	m.	NOUN
ejpam-3950	123	8	al	al	PROPN
ejpam-3950	123	9	horani	horani	PROPN
ejpam-3950	123	10	,	,	PUNCT
ejpam-3950	123	11	r.	r.	PROPN
ejpam-3950	123	12	khalil	khalil	PROPN
ejpam-3950	123	13	/	/	SYM
ejpam-3950	123	14	eur	eur	PROPN
ejpam-3950	123	15	.	.	PUNCT
ejpam-3950	124	1	j.	j.	PROPN
ejpam-3950	124	2	pure	pure	PROPN
ejpam-3950	124	3	appl	appl	PROPN
ejpam-3950	124	4	.	.	PROPN
ejpam-3950	124	5	math	math	PROPN
ejpam-3950	124	6	,	,	PUNCT
ejpam-3950	124	7	14	14	NUM
ejpam-3950	124	8	(	(	PUNCT
ejpam-3950	124	9	2	2	NUM
ejpam-3950	124	10	)	)	PUNCT
ejpam-3950	124	11	(	(	PUNCT
ejpam-3950	124	12	2021	2021	NUM
ejpam-3950	124	13	)	)	PUNCT
ejpam-3950	124	14	,	,	PUNCT
ejpam-3950	124	15	493	493	NUM
ejpam-3950	124	16	-	-	SYM
ejpam-3950	124	17	505	505	NUM
ejpam-3950	124	18	497	497	NUM
ejpam-3950	124	19	we	we	PRON
ejpam-3950	124	20	set	set	VERB
ejpam-3950	124	21	,	,	PUNCT
ejpam-3950	124	22	u(t	u(t	PROPN
ejpam-3950	124	23	)	)	PUNCT
ejpam-3950	124	24	=	=	PUNCT
ejpam-3950	124	25	(	(	PUNCT
ejpam-3950	124	26	u1(t	u1(t	PROPN
ejpam-3950	124	27	)	)	PUNCT
ejpam-3950	124	28	,	,	PUNCT
ejpam-3950	124	29	...	...	PUNCT
ejpam-3950	124	30	,	,	PUNCT
ejpam-3950	124	31	un(t))t	un(t))t	PROPN
ejpam-3950	124	32	and	and	CCONJ
ejpam-3950	124	33	f	f	PROPN
ejpam-3950	124	34	(	(	PUNCT
ejpam-3950	124	35	t	t	PROPN
ejpam-3950	124	36	)	)	PUNCT
ejpam-3950	124	37	=	=	SYM
ejpam-3950	124	38	f(t)(〈z	f(t)(〈z	PROPN
ejpam-3950	124	39	,	,	PUNCT
ejpam-3950	124	40	δ1	δ1	NOUN
ejpam-3950	124	41	〉	〉	PROPN
ejpam-3950	124	42	,	,	PUNCT
ejpam-3950	124	43	...	...	PUNCT
ejpam-3950	124	44	,	,	PUNCT
ejpam-3950	124	45	〈	〈	PROPN
ejpam-3950	124	46	z	z	PROPN
ejpam-3950	124	47	,	,	PUNCT
ejpam-3950	124	48	δn〉)t	δn〉)t	PROPN
ejpam-3950	124	49	,	,	PUNCT
ejpam-3950	124	50	so	so	CCONJ
ejpam-3950	124	51	equation	equation	NOUN
ejpam-3950	124	52	(	(	PUNCT
ejpam-3950	124	53	6	6	NUM
ejpam-3950	124	54	)	)	PUNCT
ejpam-3950	124	55	can	can	AUX
ejpam-3950	124	56	be	be	AUX
ejpam-3950	124	57	written	write	VERB
ejpam-3950	124	58	in	in	ADP
ejpam-3950	124	59	the	the	DET
ejpam-3950	124	60	form	form	NOUN
ejpam-3950	124	61	u	u	NOUN
ejpam-3950	124	62	(	(	PUNCT
ejpam-3950	124	63	α)(t	α)(t	PROPN
ejpam-3950	124	64	)	)	PUNCT
ejpam-3950	124	65	=	=	SYM
ejpam-3950	124	66	âu(t	âu(t	PROPN
ejpam-3950	124	67	)	)	PUNCT
ejpam-3950	125	1	+	+	CCONJ
ejpam-3950	125	2	f	f	X
ejpam-3950	125	3	(	(	PUNCT
ejpam-3950	125	4	t	t	PROPN
ejpam-3950	125	5	)	)	PUNCT
ejpam-3950	125	6	.	.	PUNCT
ejpam-3950	126	1	this	this	DET
ejpam-3950	126	2	system	system	NOUN
ejpam-3950	126	3	has	have	VERB
ejpam-3950	126	4	a	a	DET
ejpam-3950	126	5	unique	unique	ADJ
ejpam-3950	126	6	solution	solution	NOUN
ejpam-3950	126	7	of	of	ADP
ejpam-3950	126	8	the	the	DET
ejpam-3950	126	9	form	form	NOUN
ejpam-3950	126	10	u(t	u(t	NOUN
ejpam-3950	126	11	)	)	PUNCT
ejpam-3950	126	12	=	=	SYM
ejpam-3950	126	13	φ(t)c+	φ(t)c+	SYM
ejpam-3950	126	14	φ(t	φ(t	PROPN
ejpam-3950	126	15	)	)	PUNCT
ejpam-3950	126	16	∫	∫	PROPN
ejpam-3950	126	17	t	t	PROPN
ejpam-3950	126	18	0	0	NUM
ejpam-3950	127	1	φ−1(s)f	φ−1(s)f	PROPN
ejpam-3950	127	2	(	(	PUNCT
ejpam-3950	127	3	s	s	NOUN
ejpam-3950	127	4	)	)	PUNCT
ejpam-3950	127	5	s1−α	s1−α	PROPN
ejpam-3950	127	6	ds	ds	NOUN
ejpam-3950	127	7	.	.	PROPN
ejpam-3950	127	8	where	where	SCONJ
ejpam-3950	127	9	φ(t	φ(t	PROPN
ejpam-3950	127	10	)	)	PUNCT
ejpam-3950	127	11	is	be	AUX
ejpam-3950	127	12	the	the	DET
ejpam-3950	127	13	fundamental	fundamental	ADJ
ejpam-3950	127	14	matrix	matrix	NOUN
ejpam-3950	127	15	.	.	PUNCT
ejpam-3950	128	1	this	this	PRON
ejpam-3950	128	2	is	be	AUX
ejpam-3950	128	3	an	an	DET
ejpam-3950	128	4	invertible	invertible	ADJ
ejpam-3950	128	5	matrix	matrix	NOUN
ejpam-3950	128	6	.	.	PUNCT
ejpam-3950	129	1	now	now	ADV
ejpam-3950	129	2	we	we	PRON
ejpam-3950	129	3	use	use	VERB
ejpam-3950	129	4	the	the	DET
ejpam-3950	129	5	initial	initial	ADJ
ejpam-3950	129	6	condition	condition	NOUN
ejpam-3950	129	7	to	to	PART
ejpam-3950	129	8	find	find	VERB
ejpam-3950	129	9	the	the	DET
ejpam-3950	129	10	constant	constant	ADJ
ejpam-3950	129	11	c.	c.	NOUN
ejpam-3950	129	12	consequently	consequently	ADV
ejpam-3950	129	13	,	,	PUNCT
ejpam-3950	129	14	the	the	DET
ejpam-3950	129	15	problem	problem	NOUN
ejpam-3950	129	16	(	(	PUNCT
ejpam-3950	129	17	2	2	X
ejpam-3950	129	18	)	)	PUNCT
ejpam-3950	129	19	has	have	VERB
ejpam-3950	129	20	a	a	DET
ejpam-3950	129	21	unique	unique	ADJ
ejpam-3950	129	22	solution	solution	NOUN
ejpam-3950	129	23	.	.	PUNCT
ejpam-3950	130	1	now	now	ADV
ejpam-3950	130	2	,	,	PUNCT
ejpam-3950	130	3	let	let	VERB
ejpam-3950	130	4	b	b	NOUN
ejpam-3950	130	5	6=	6=	NUM
ejpam-3950	130	6	i	i	PRON
ejpam-3950	130	7	and	and	CCONJ
ejpam-3950	130	8	u(t	u(t	NOUN
ejpam-3950	130	9	)	)	PUNCT
ejpam-3950	130	10	is	be	AUX
ejpam-3950	130	11	finite	finite	ADJ
ejpam-3950	130	12	rank	rank	NOUN
ejpam-3950	130	13	function	function	NOUN
ejpam-3950	130	14	.	.	PUNCT
ejpam-3950	131	1	in	in	ADP
ejpam-3950	131	2	addition	addition	NOUN
ejpam-3950	131	3	assume	assume	VERB
ejpam-3950	131	4	that	that	SCONJ
ejpam-3950	131	5	[	[	X
ejpam-3950	131	6	δ1	δ1	NOUN
ejpam-3950	131	7	,	,	PUNCT
ejpam-3950	131	8	δ2	δ2	VERB
ejpam-3950	131	9	,	,	PUNCT
ejpam-3950	131	10	...	...	PUNCT
ejpam-3950	131	11	,	,	PUNCT
ejpam-3950	131	12	δn	δn	X
ejpam-3950	131	13	]	]	PUNCT
ejpam-3950	131	14	is	be	AUX
ejpam-3950	131	15	invariant	invariant	ADJ
ejpam-3950	131	16	under	under	ADP
ejpam-3950	131	17	both	both	CCONJ
ejpam-3950	131	18	a	a	PRON
ejpam-3950	131	19	and	and	CCONJ
ejpam-3950	131	20	b	b	NOUN
ejpam-3950	131	21	and	and	CCONJ
ejpam-3950	131	22	let	let	VERB
ejpam-3950	131	23	an	an	PRON
ejpam-3950	131	24	,	,	PUNCT
ejpam-3950	131	25	bn	bn	ADJ
ejpam-3950	131	26	be	be	AUX
ejpam-3950	131	27	the	the	DET
ejpam-3950	131	28	restriction	restriction	NOUN
ejpam-3950	131	29	of	of	ADP
ejpam-3950	131	30	a	a	PRON
ejpam-3950	131	31	and	and	CCONJ
ejpam-3950	131	32	b	b	NOUN
ejpam-3950	131	33	to	to	PART
ejpam-3950	131	34	[	[	X
ejpam-3950	131	35	δ1	δ1	NOUN
ejpam-3950	131	36	,	,	PUNCT
ejpam-3950	131	37	δ2	δ2	VERB
ejpam-3950	131	38	,	,	PUNCT
ejpam-3950	131	39	...	...	PUNCT
ejpam-3950	131	40	,	,	PUNCT
ejpam-3950	131	41	δn	δn	X
ejpam-3950	131	42	]	]	PUNCT
ejpam-3950	131	43	.	.	PUNCT
ejpam-3950	132	1	theorem	theorem	ADJ
ejpam-3950	132	2	4	4	NUM
ejpam-3950	132	3	.	.	PUNCT
ejpam-3950	133	1	in	in	ADP
ejpam-3950	133	2	problem	problem	NOUN
ejpam-3950	133	3	(	(	PUNCT
ejpam-3950	133	4	1	1	NUM
ejpam-3950	133	5	)	)	PUNCT
ejpam-3950	133	6	,	,	PUNCT
ejpam-3950	133	7	let	let	VERB
ejpam-3950	133	8	bn	bn	PART
ejpam-3950	133	9	be	be	AUX
ejpam-3950	133	10	orthogonally	orthogonally	ADV
ejpam-3950	133	11	diagonalizable	diagonalizable	ADJ
ejpam-3950	133	12	linear	linear	ADJ
ejpam-3950	133	13	operator	operator	NOUN
ejpam-3950	133	14	such	such	ADJ
ejpam-3950	133	15	that	that	SCONJ
ejpam-3950	133	16	an	an	DET
ejpam-3950	133	17	|ker(bn	|ker(bn	NOUN
ejpam-3950	133	18	)	)	PUNCT
ejpam-3950	133	19	is	be	AUX
ejpam-3950	133	20	invertible	invertible	ADJ
ejpam-3950	133	21	.	.	PUNCT
ejpam-3950	134	1	then	then	ADV
ejpam-3950	134	2	problem	problem	NOUN
ejpam-3950	134	3	(	(	PUNCT
ejpam-3950	134	4	1	1	X
ejpam-3950	134	5	)	)	PUNCT
ejpam-3950	134	6	has	have	VERB
ejpam-3950	134	7	a	a	DET
ejpam-3950	134	8	unique	unique	ADJ
ejpam-3950	134	9	solution	solution	NOUN
ejpam-3950	134	10	.	.	PUNCT
ejpam-3950	135	1	proof	proof	NOUN
ejpam-3950	135	2	.	.	PUNCT
ejpam-3950	136	1	let	let	VERB
ejpam-3950	136	2	{	{	PUNCT
ejpam-3950	136	3	θ1	θ1	PROPN
ejpam-3950	136	4	,	,	PUNCT
ejpam-3950	136	5	θ2	θ2	PROPN
ejpam-3950	136	6	,	,	PUNCT
ejpam-3950	136	7	...	...	PUNCT
ejpam-3950	136	8	,	,	PUNCT
ejpam-3950	136	9	θn	θn	VERB
ejpam-3950	136	10	}	}	PUNCT
ejpam-3950	136	11	be	be	AUX
ejpam-3950	136	12	an	an	DET
ejpam-3950	136	13	orthonormal	orthonormal	ADJ
ejpam-3950	136	14	basis	basis	NOUN
ejpam-3950	136	15	such	such	ADJ
ejpam-3950	136	16	that	that	SCONJ
ejpam-3950	136	17	the	the	DET
ejpam-3950	136	18	matrix	matrix	NOUN
ejpam-3950	136	19	representation	representation	NOUN
ejpam-3950	136	20	of	of	ADP
ejpam-3950	136	21	bn	bn	NOUN
ejpam-3950	136	22	with	with	ADP
ejpam-3950	136	23	respect	respect	NOUN
ejpam-3950	136	24	this	this	DET
ejpam-3950	136	25	basis	basis	NOUN
ejpam-3950	136	26	is	be	AUX
ejpam-3950	136	27	d̃	d̃	PROPN
ejpam-3950	136	28	=	=	SYM
ejpam-3950	136	29	diag(λ1	diag(λ1	PROPN
ejpam-3950	136	30	,	,	PUNCT
ejpam-3950	136	31	...	...	PUNCT
ejpam-3950	136	32	,	,	PUNCT
ejpam-3950	136	33	λn	λn	NOUN
ejpam-3950	136	34	)	)	PUNCT
ejpam-3950	136	35	,	,	PUNCT
ejpam-3950	136	36	when	when	SCONJ
ejpam-3950	136	37	λ1	λ1	ADJ
ejpam-3950	136	38	,	,	PUNCT
ejpam-3950	136	39	...	...	PUNCT
ejpam-3950	136	40	,	,	PUNCT
ejpam-3950	136	41	λn	λn	X
ejpam-3950	136	42	the	the	DET
ejpam-3950	136	43	corresponding	corresponding	ADJ
ejpam-3950	136	44	eigenvalues	eigenvalue	NOUN
ejpam-3950	136	45	of	of	ADP
ejpam-3950	136	46	bn	bn	NOUN
ejpam-3950	136	47	.	.	PUNCT
ejpam-3950	137	1	now	now	ADV
ejpam-3950	137	2	,	,	PUNCT
ejpam-3950	137	3	if	if	SCONJ
ejpam-3950	137	4	λi	λi	ADP
ejpam-3950	137	5	6=	6=	ADP
ejpam-3950	137	6	0	0	NUM
ejpam-3950	137	7	for	for	ADP
ejpam-3950	137	8	all	all	DET
ejpam-3950	137	9	i	i	PRON
ejpam-3950	137	10	=	=	NOUN
ejpam-3950	137	11	1	1	NUM
ejpam-3950	137	12	,	,	PUNCT
ejpam-3950	137	13	2	2	NUM
ejpam-3950	137	14	,	,	PUNCT
ejpam-3950	137	15	...	...	PUNCT
ejpam-3950	137	16	n	n	CCONJ
ejpam-3950	137	17	,	,	PUNCT
ejpam-3950	137	18	then	then	ADV
ejpam-3950	137	19	problem	problem	NOUN
ejpam-3950	137	20	(	(	PUNCT
ejpam-3950	137	21	1	1	X
ejpam-3950	137	22	)	)	PUNCT
ejpam-3950	137	23	becomes	become	VERB
ejpam-3950	137	24	u(α)(t	u(α)(t	NOUN
ejpam-3950	137	25	)	)	PUNCT
ejpam-3950	137	26	=	=	SYM
ejpam-3950	137	27	b−1n	b−1n	NOUN
ejpam-3950	137	28	anu(t	anu(t	PROPN
ejpam-3950	137	29	)	)	PUNCT
ejpam-3950	137	30	and	and	CCONJ
ejpam-3950	137	31	hence	hence	ADV
ejpam-3950	137	32	has	have	VERB
ejpam-3950	137	33	a	a	DET
ejpam-3950	137	34	unique	unique	ADJ
ejpam-3950	137	35	solution	solution	NOUN
ejpam-3950	137	36	by	by	ADP
ejpam-3950	137	37	theorem	theorem	NOUN
ejpam-3950	137	38	3.1	3.1	NUM
ejpam-3950	137	39	.	.	PUNCT
ejpam-3950	138	1	suppose	suppose	VERB
ejpam-3950	138	2	λi	λi	ADP
ejpam-3950	138	3	6=	6=	X
ejpam-3950	138	4	0	0	NUM
ejpam-3950	138	5	for	for	ADP
ejpam-3950	138	6	i	i	PRON
ejpam-3950	138	7	=	=	NOUN
ejpam-3950	138	8	1	1	NUM
ejpam-3950	138	9	,	,	PUNCT
ejpam-3950	138	10	2	2	NUM
ejpam-3950	138	11	,	,	PUNCT
ejpam-3950	138	12	...	...	PUNCT
ejpam-3950	139	1	r	r	NOUN
ejpam-3950	139	2	,	,	PUNCT
ejpam-3950	139	3	and	and	CCONJ
ejpam-3950	139	4	λi	λi	X
ejpam-3950	139	5	=	=	NOUN
ejpam-3950	139	6	0	0	PROPN
ejpam-3950	139	7	for	for	ADP
ejpam-3950	139	8	i	i	PRON
ejpam-3950	139	9	=	=	SYM
ejpam-3950	139	10	r+1	r+1	PROPN
ejpam-3950	139	11	,	,	PUNCT
ejpam-3950	139	12	r+2	r+2	PRON
ejpam-3950	139	13	,	,	PUNCT
ejpam-3950	139	14	...	...	PUNCT
ejpam-3950	139	15	n.	n.	PROPN
ejpam-3950	139	16	let	let	VERB
ejpam-3950	139	17	u(t	u(t	NOUN
ejpam-3950	139	18	)	)	PUNCT
ejpam-3950	139	19	=	=	SYM
ejpam-3950	140	1	∑n	∑n	PROPN
ejpam-3950	140	2	i=1	i=1	PROPN
ejpam-3950	140	3	vi(t)θi	vi(t)θi	PROPN
ejpam-3950	140	4	:	:	PUNCT
ejpam-3950	140	5	then	then	ADV
ejpam-3950	141	1	n∑	n∑	PROPN
ejpam-3950	141	2	i=1	i=1	PROPN
ejpam-3950	142	1	v	v	PROPN
ejpam-3950	142	2	(	(	PUNCT
ejpam-3950	142	3	α	α	NOUN
ejpam-3950	142	4	)	)	PUNCT
ejpam-3950	142	5	i	i	PRON
ejpam-3950	142	6	(	(	PUNCT
ejpam-3950	142	7	t)bnθi	t)bnθi	X
ejpam-3950	143	1	=	=	SYM
ejpam-3950	143	2	n∑	n∑	PROPN
ejpam-3950	143	3	i=1	i=1	PROPN
ejpam-3950	143	4	vi(t)anθi	vi(t)anθi	NOUN
ejpam-3950	143	5	.	.	PUNCT
ejpam-3950	144	1	(	(	PUNCT
ejpam-3950	144	2	7	7	X
ejpam-3950	144	3	)	)	PUNCT
ejpam-3950	144	4	taking	take	VERB
ejpam-3950	144	5	the	the	DET
ejpam-3950	144	6	inner	inner	ADJ
ejpam-3950	144	7	product	product	NOUN
ejpam-3950	144	8	of	of	ADP
ejpam-3950	144	9	θj	θj	NOUN
ejpam-3950	144	10	with	with	ADP
ejpam-3950	144	11	both	both	DET
ejpam-3950	144	12	sides	side	NOUN
ejpam-3950	144	13	of	of	ADP
ejpam-3950	144	14	(	(	PUNCT
ejpam-3950	144	15	7	7	NUM
ejpam-3950	144	16	)	)	PUNCT
ejpam-3950	144	17	,	,	PUNCT
ejpam-3950	144	18	we	we	PRON
ejpam-3950	144	19	obtain	obtain	VERB
ejpam-3950	145	1	n∑	n∑	PROPN
ejpam-3950	145	2	i=1	i=1	PROPN
ejpam-3950	145	3	v	v	PROPN
ejpam-3950	145	4	(	(	PUNCT
ejpam-3950	145	5	α	α	NOUN
ejpam-3950	145	6	)	)	PUNCT
ejpam-3950	146	1	i	i	PRON
ejpam-3950	146	2	(	(	PUNCT
ejpam-3950	146	3	t)〈bnθi	t)〈bnθi	PROPN
ejpam-3950	146	4	,	,	PUNCT
ejpam-3950	146	5	θj	θj	NOUN
ejpam-3950	146	6	〉	〉	NOUN
ejpam-3950	146	7	=	=	SYM
ejpam-3950	146	8	n∑	n∑	PROPN
ejpam-3950	146	9	i=1	i=1	PROPN
ejpam-3950	146	10	vi(t)〈anθi	vi(t)〈anθi	NOUN
ejpam-3950	146	11	,	,	PUNCT
ejpam-3950	146	12	θj	θj	PRON
ejpam-3950	146	13	〉	〉	NOUN
ejpam-3950	146	14	.	.	PUNCT
ejpam-3950	147	1	so	so	ADV
ejpam-3950	147	2	,	,	PUNCT
ejpam-3950	147	3	we	we	PRON
ejpam-3950	147	4	get	get	VERB
ejpam-3950	147	5	the	the	DET
ejpam-3950	147	6	following	follow	VERB
ejpam-3950	147	7	system	system	NOUN
ejpam-3950	147	8	[	[	PUNCT
ejpam-3950	147	9	d	d	NOUN
ejpam-3950	147	10	0	0	NUM
ejpam-3950	147	11	0	0	NUM
ejpam-3950	147	12	0	0	NUM
ejpam-3950	147	13	]	]	PUNCT
ejpam-3950	147	14			VERB
ejpam-3950	147	15	v	v	NOUN
ejpam-3950	147	16	(	(	PUNCT
ejpam-3950	147	17	α	α	NOUN
ejpam-3950	147	18	)	)	PUNCT
ejpam-3950	147	19	1	1	NUM
ejpam-3950	147	20	(	(	PUNCT
ejpam-3950	147	21	t	t	PROPN
ejpam-3950	147	22	)	)	PUNCT
ejpam-3950	147	23	.	.	PUNCT
ejpam-3950	147	24	.	.	PUNCT
ejpam-3950	148	1	.	.	PUNCT
ejpam-3950	149	1	v	v	X
ejpam-3950	149	2	(	(	PUNCT
ejpam-3950	149	3	α	α	NOUN
ejpam-3950	149	4	)	)	PUNCT
ejpam-3950	149	5	n	n	PROPN
ejpam-3950	149	6	(	(	PUNCT
ejpam-3950	149	7	t	t	NOUN
ejpam-3950	149	8	)	)	PUNCT
ejpam-3950	149	9			NOUN
ejpam-3950	149	10	=	=	PUNCT
ejpam-3950	149	11	[	[	PUNCT
ejpam-3950	149	12	a1	a1	NOUN
ejpam-3950	149	13	a2	a2	PROPN
ejpam-3950	149	14	a3	a3	NOUN
ejpam-3950	149	15	ã	ã	PROPN
ejpam-3950	149	16	]	]	PUNCT
ejpam-3950	149	17			NOUN
ejpam-3950	149	18	v1(t	v1(t	PRON
ejpam-3950	149	19	)	)	PUNCT
ejpam-3950	149	20	.	.	PUNCT
ejpam-3950	149	21	.	.	PUNCT
ejpam-3950	149	22	.	.	PUNCT
ejpam-3950	150	1	vn(t	vn(t	NUM
ejpam-3950	150	2	)	)	PUNCT
ejpam-3950	150	3			NOUN
ejpam-3950	150	4	.	.	PUNCT
ejpam-3950	151	1	(	(	PUNCT
ejpam-3950	151	2	8)	8)	NUM
ejpam-3950	151	3	where	where	SCONJ
ejpam-3950	151	4	d	d	NOUN
ejpam-3950	151	5	=	=	SYM
ejpam-3950	151	6	diag(λ1	diag(λ1	NOUN
ejpam-3950	151	7	,	,	PUNCT
ejpam-3950	151	8	.	.	PUNCT
ejpam-3950	151	9	,	,	PUNCT
ejpam-3950	151	10	.	.	PUNCT
ejpam-3950	151	11	,	,	PUNCT
ejpam-3950	151	12	.	.	PUNCT
ejpam-3950	151	13	,	,	PUNCT
ejpam-3950	151	14	λr	λr	X
ejpam-3950	151	15	)	)	PUNCT
ejpam-3950	151	16	and	and	CCONJ
ejpam-3950	151	17	ã	ã	PROPN
ejpam-3950	151	18	=	=	PROPN
ejpam-3950	151	19	an	an	DET
ejpam-3950	151	20	|ker(bn)=	|ker(bn)=	PROPN
ejpam-3950	151	21	[	[	X
ejpam-3950	151	22	〈	〈	PROPN
ejpam-3950	151	23	anθj	anθj	NOUN
ejpam-3950	151	24	,	,	PUNCT
ejpam-3950	151	25	θi〉]i	θi〉]i	PROPN
ejpam-3950	151	26	,	,	PUNCT
ejpam-3950	151	27	j	j	NOUN
ejpam-3950	151	28	=	=	NOUN
ejpam-3950	151	29	r+1,	r+1,	NOUN
ejpam-3950	151	30	...	...	PUNCT
ejpam-3950	151	31	,n	,n	NOUN
ejpam-3950	151	32	.	.	PUNCT
ejpam-3950	152	1	multiplying	multiply	VERB
ejpam-3950	152	2	(	(	PUNCT
ejpam-3950	152	3	8)	8)	NUM
ejpam-3950	152	4	by	by	ADP
ejpam-3950	152	5	[	[	PUNCT
ejpam-3950	152	6	i	i	NOUN
ejpam-3950	152	7	0	0	NUM
ejpam-3950	152	8	0	0	NUM
ejpam-3950	152	9	ã−1	ã−1	PROPN
ejpam-3950	152	10	]	]	PUNCT
ejpam-3950	152	11	,	,	PUNCT
ejpam-3950	152	12	we	we	PRON
ejpam-3950	152	13	obtain	obtain	VERB
ejpam-3950	152	14	[	[	PUNCT
ejpam-3950	152	15	d	d	NOUN
ejpam-3950	152	16	0	0	NUM
ejpam-3950	152	17	0	0	NUM
ejpam-3950	152	18	0	0	NUM
ejpam-3950	152	19	]	]	PUNCT
ejpam-3950	152	20			VERB
ejpam-3950	152	21	v	v	NOUN
ejpam-3950	152	22	(	(	PUNCT
ejpam-3950	152	23	α	α	NOUN
ejpam-3950	152	24	)	)	PUNCT
ejpam-3950	152	25	1	1	NUM
ejpam-3950	152	26	(	(	PUNCT
ejpam-3950	152	27	t	t	PROPN
ejpam-3950	152	28	)	)	PUNCT
ejpam-3950	152	29	.	.	PUNCT
ejpam-3950	152	30	.	.	PUNCT
ejpam-3950	152	31	.	.	PUNCT
ejpam-3950	153	1	v	v	X
ejpam-3950	153	2	(	(	PUNCT
ejpam-3950	153	3	α	α	NOUN
ejpam-3950	153	4	)	)	PUNCT
ejpam-3950	153	5	n	n	PROPN
ejpam-3950	153	6	(	(	PUNCT
ejpam-3950	153	7	t	t	NOUN
ejpam-3950	153	8	)	)	PUNCT
ejpam-3950	153	9			NOUN
ejpam-3950	153	10	=	=	PUNCT
ejpam-3950	153	11	[	[	PUNCT
ejpam-3950	153	12	a1	a1	NOUN
ejpam-3950	153	13	a2	a2	PROPN
ejpam-3950	153	14	ã−1a3	ã−1a3	NUM
ejpam-3950	153	15	in−r	in−r	NOUN
ejpam-3950	153	16	]	]	PUNCT
ejpam-3950	153	17			NOUN
ejpam-3950	153	18	v1(t	v1(t	PRON
ejpam-3950	153	19	)	)	PUNCT
ejpam-3950	153	20	.	.	PUNCT
ejpam-3950	153	21	.	.	PUNCT
ejpam-3950	153	22	.	.	PUNCT
ejpam-3950	154	1	vn(t	vn(t	X
ejpam-3950	154	2	)	)	PUNCT
ejpam-3950	154	3			NOUN
ejpam-3950	154	4	.	.	PUNCT
ejpam-3950	155	1	f.	f.	PROPN
ejpam-3950	155	2	seddiki	seddiki	PROPN
ejpam-3950	155	3	,	,	PUNCT
ejpam-3950	155	4	m.	m.	NOUN
ejpam-3950	155	5	al	al	PROPN
ejpam-3950	155	6	horani	horani	PROPN
ejpam-3950	155	7	,	,	PUNCT
ejpam-3950	155	8	r.	r.	PROPN
ejpam-3950	155	9	khalil	khalil	PROPN
ejpam-3950	155	10	/	/	SYM
ejpam-3950	155	11	eur	eur	PROPN
ejpam-3950	155	12	.	.	PUNCT
ejpam-3950	156	1	j.	j.	PROPN
ejpam-3950	156	2	pure	pure	PROPN
ejpam-3950	156	3	appl	appl	PROPN
ejpam-3950	156	4	.	.	PROPN
ejpam-3950	156	5	math	math	PROPN
ejpam-3950	156	6	,	,	PUNCT
ejpam-3950	156	7	14	14	NUM
ejpam-3950	156	8	(	(	PUNCT
ejpam-3950	156	9	2	2	NUM
ejpam-3950	156	10	)	)	PUNCT
ejpam-3950	156	11	(	(	PUNCT
ejpam-3950	156	12	2021	2021	NUM
ejpam-3950	156	13	)	)	PUNCT
ejpam-3950	156	14	,	,	PUNCT
ejpam-3950	156	15	493	493	NUM
ejpam-3950	156	16	-	-	SYM
ejpam-3950	156	17	505	505	NUM
ejpam-3950	156	18	498	498	NUM
ejpam-3950	156	19	thus	thus	ADV
ejpam-3950	156	20	,	,	PUNCT
ejpam-3950	156	21	we	we	PRON
ejpam-3950	156	22	get	get	VERB
ejpam-3950	156	23	d	d	PROPN
ejpam-3950	156	24			NOUN
ejpam-3950	156	25	v	v	NOUN
ejpam-3950	156	26	(	(	PUNCT
ejpam-3950	156	27	α	α	NOUN
ejpam-3950	156	28	)	)	PUNCT
ejpam-3950	156	29	1	1	NUM
ejpam-3950	156	30	(	(	PUNCT
ejpam-3950	156	31	t	t	PROPN
ejpam-3950	156	32	)	)	PUNCT
ejpam-3950	156	33	.	.	PUNCT
ejpam-3950	156	34	.	.	PUNCT
ejpam-3950	157	1	.	.	PUNCT
ejpam-3950	158	1	v	v	X
ejpam-3950	158	2	(	(	PUNCT
ejpam-3950	158	3	α	α	NOUN
ejpam-3950	158	4	)	)	PUNCT
ejpam-3950	158	5	r	r	NOUN
ejpam-3950	158	6	(	(	PUNCT
ejpam-3950	158	7	t	t	NOUN
ejpam-3950	158	8	)	)	PUNCT
ejpam-3950	158	9			NOUN
ejpam-3950	158	10	=	=	SYM
ejpam-3950	158	11	a1	a1	NOUN
ejpam-3950	158	12			NOUN
ejpam-3950	158	13	v1(t	v1(t	PRON
ejpam-3950	158	14	)	)	PUNCT
ejpam-3950	158	15	.	.	PUNCT
ejpam-3950	158	16	.	.	PUNCT
ejpam-3950	158	17	.	.	PUNCT
ejpam-3950	159	1	vr(t	vr(t	X
ejpam-3950	159	2	)	)	PUNCT
ejpam-3950	159	3	+a2	+a2	NOUN
ejpam-3950	159	4			NOUN
ejpam-3950	159	5	vr+1(t	vr+1(t	PROPN
ejpam-3950	159	6	)	)	PUNCT
ejpam-3950	159	7	.	.	PUNCT
ejpam-3950	159	8	.	.	PUNCT
ejpam-3950	160	1	.	.	PUNCT
ejpam-3950	161	1	vn(t	vn(t	X
ejpam-3950	161	2	)	)	PUNCT
ejpam-3950	161	3			NOUN
ejpam-3950	161	4	,	,	PUNCT
ejpam-3950	161	5	(	(	PUNCT
ejpam-3950	161	6	9	9	NUM
ejpam-3950	161	7	)	)	PUNCT
ejpam-3950	161	8	and	and	CCONJ
ejpam-3950	161	9	ã−1a3	ã−1a3	NUM
ejpam-3950	161	10			NOUN
ejpam-3950	161	11	v1(t	v1(t	PRON
ejpam-3950	161	12	)	)	PUNCT
ejpam-3950	161	13	.	.	PUNCT
ejpam-3950	161	14	.	.	PUNCT
ejpam-3950	162	1	.	.	PUNCT
ejpam-3950	163	1	vr(t	vr(t	X
ejpam-3950	163	2	)	)	PUNCT
ejpam-3950	163	3	+	+	VERB
ejpam-3950	163	4	in−r	in−r	ADJ
ejpam-3950	163	5			NOUN
ejpam-3950	163	6	vr+1(t	vr+1(t	PROPN
ejpam-3950	163	7	)	)	PUNCT
ejpam-3950	163	8	.	.	PUNCT
ejpam-3950	163	9	.	.	PUNCT
ejpam-3950	163	10	.	.	PUNCT
ejpam-3950	164	1	vn(t	vn(t	X
ejpam-3950	164	2	)	)	PUNCT
ejpam-3950	164	3			NOUN
ejpam-3950	164	4	=	=	NOUN
ejpam-3950	165	1	0	0	X
ejpam-3950	165	2	.	.	PUNCT
ejpam-3950	166	1	(	(	PUNCT
ejpam-3950	166	2	10	10	NUM
ejpam-3950	166	3	)	)	PUNCT
ejpam-3950	166	4	from	from	ADP
ejpam-3950	166	5	equation	equation	NOUN
ejpam-3950	166	6	(	(	PUNCT
ejpam-3950	166	7	10	10	NUM
ejpam-3950	166	8	)	)	PUNCT
ejpam-3950	166	9	,	,	PUNCT
ejpam-3950	166	10	we	we	PRON
ejpam-3950	166	11	have	have	VERB
ejpam-3950	166	12			ADJ
ejpam-3950	166	13	vr+1(t	vr+1(t	NOUN
ejpam-3950	166	14	)	)	PUNCT
ejpam-3950	166	15	.	.	PUNCT
ejpam-3950	166	16	.	.	PUNCT
ejpam-3950	167	1	.	.	PUNCT
ejpam-3950	168	1	vn(t	vn(t	NUM
ejpam-3950	168	2	)	)	PUNCT
ejpam-3950	169	1			NOUN
ejpam-3950	169	2	=	=	SYM
ejpam-3950	169	3	−ã−1a3	−ã−1a3	X
ejpam-3950	169	4			NOUN
ejpam-3950	169	5	v1(t	v1(t	PRON
ejpam-3950	169	6	)	)	PUNCT
ejpam-3950	169	7	.	.	PUNCT
ejpam-3950	169	8	.	.	PUNCT
ejpam-3950	170	1	.	.	PUNCT
ejpam-3950	171	1	vr(t	vr(t	X
ejpam-3950	171	2	)	)	PUNCT
ejpam-3950	171	3			NOUN
ejpam-3950	171	4	.	.	PUNCT
ejpam-3950	172	1	(	(	PUNCT
ejpam-3950	172	2	11	11	NUM
ejpam-3950	172	3	)	)	PUNCT
ejpam-3950	172	4	substitute	substitute	NOUN
ejpam-3950	172	5	(	(	PUNCT
ejpam-3950	172	6	11	11	NUM
ejpam-3950	172	7	)	)	PUNCT
ejpam-3950	172	8	in	in	ADP
ejpam-3950	172	9	equation	equation	NOUN
ejpam-3950	172	10	(	(	PUNCT
ejpam-3950	172	11	9	9	NUM
ejpam-3950	172	12	)	)	PUNCT
ejpam-3950	172	13	,	,	PUNCT
ejpam-3950	172	14	to	to	ADP
ejpam-3950	172	15	get	get	PROPN
ejpam-3950	172	16	v	v	PROPN
ejpam-3950	172	17	(	(	PUNCT
ejpam-3950	172	18	α	α	NOUN
ejpam-3950	172	19	)	)	PUNCT
ejpam-3950	172	20	1	1	NUM
ejpam-3950	172	21	(	(	PUNCT
ejpam-3950	172	22	t	t	PROPN
ejpam-3950	172	23	)	)	PUNCT
ejpam-3950	172	24	.	.	PUNCT
ejpam-3950	172	25	.	.	PUNCT
ejpam-3950	173	1	.	.	PUNCT
ejpam-3950	174	1	v	v	X
ejpam-3950	174	2	(	(	PUNCT
ejpam-3950	174	3	α	α	NOUN
ejpam-3950	174	4	)	)	PUNCT
ejpam-3950	174	5	r	r	NOUN
ejpam-3950	174	6	(	(	PUNCT
ejpam-3950	174	7	t	t	NOUN
ejpam-3950	174	8	)	)	PUNCT
ejpam-3950	174	9			NOUN
ejpam-3950	174	10	=	=	SYM
ejpam-3950	174	11	d−1(a1	d−1(a1	X
ejpam-3950	174	12	−a2ã	−a2ã	VERB
ejpam-3950	174	13	−1a3	−1a3	NUM
ejpam-3950	174	14	)	)	PUNCT
ejpam-3950	174	15			NOUN
ejpam-3950	174	16	v1(t	v1(t	PRON
ejpam-3950	174	17	)	)	PUNCT
ejpam-3950	174	18	.	.	PUNCT
ejpam-3950	174	19	.	.	PUNCT
ejpam-3950	174	20	.	.	PUNCT
ejpam-3950	175	1	vr(t	vr(t	X
ejpam-3950	175	2	)	)	PUNCT
ejpam-3950	175	3			NOUN
ejpam-3950	175	4	.	.	PUNCT
ejpam-3950	176	1	we	we	PRON
ejpam-3950	176	2	put	put	VERB
ejpam-3950	176	3	,	,	PUNCT
ejpam-3950	176	4	u1(t	u1(t	ADV
ejpam-3950	176	5	)	)	PUNCT
ejpam-3950	176	6	=	=	SYM
ejpam-3950	176	7			NOUN
ejpam-3950	176	8	v1(t	v1(t	PRON
ejpam-3950	176	9	)	)	PUNCT
ejpam-3950	176	10	.	.	PUNCT
ejpam-3950	176	11	.	.	PUNCT
ejpam-3950	177	1	.	.	PUNCT
ejpam-3950	178	1	vr(t	vr(t	X
ejpam-3950	178	2	)	)	PUNCT
ejpam-3950	178	3			NOUN
ejpam-3950	178	4	,	,	PUNCT
ejpam-3950	178	5	u2(t	u2(t	NOUN
ejpam-3950	178	6	)	)	PUNCT
ejpam-3950	178	7	=	=	SYM
ejpam-3950	178	8			NOUN
ejpam-3950	178	9	vr+1(t	vr+1(t	PROPN
ejpam-3950	178	10	)	)	PUNCT
ejpam-3950	178	11	.	.	PUNCT
ejpam-3950	178	12	.	.	PUNCT
ejpam-3950	179	1	.	.	PUNCT
ejpam-3950	180	1	vn(t	vn(t	X
ejpam-3950	180	2	)	)	PUNCT
ejpam-3950	180	3			NOUN
ejpam-3950	180	4	and	and	CCONJ
ejpam-3950	180	5	m	m	PROPN
ejpam-3950	180	6	=	=	NOUN
ejpam-3950	180	7	d−1(a1	d−1(a1	VERB
ejpam-3950	180	8	−a2ã	−a2ã	PROPN
ejpam-3950	180	9	−1a3	−1a3	NUM
ejpam-3950	180	10	)	)	PUNCT
ejpam-3950	180	11	.	.	PUNCT
ejpam-3950	181	1	we	we	PRON
ejpam-3950	181	2	get	get	VERB
ejpam-3950	181	3	the	the	DET
ejpam-3950	181	4	system	system	NOUN
ejpam-3950	181	5	,	,	PUNCT
ejpam-3950	181	6	u	u	NOUN
ejpam-3950	181	7	(	(	PUNCT
ejpam-3950	181	8	α	α	NOUN
ejpam-3950	181	9	)	)	PUNCT
ejpam-3950	181	10	1	1	NUM
ejpam-3950	181	11	(	(	PUNCT
ejpam-3950	181	12	t	t	NOUN
ejpam-3950	181	13	)	)	PUNCT
ejpam-3950	181	14	=	=	SYM
ejpam-3950	181	15	mu1(t	mu1(t	PROPN
ejpam-3950	181	16	)	)	PUNCT
ejpam-3950	181	17	,	,	PUNCT
ejpam-3950	181	18	which	which	PRON
ejpam-3950	181	19	has	have	VERB
ejpam-3950	181	20	a	a	DET
ejpam-3950	181	21	unique	unique	ADJ
ejpam-3950	181	22	solution	solution	NOUN
ejpam-3950	181	23	u1(t	u1(t	ADP
ejpam-3950	181	24	)	)	PUNCT
ejpam-3950	181	25	=	=	SYM
ejpam-3950	181	26	φ(t)c	φ(t)c	PROPN
ejpam-3950	181	27	,	,	PUNCT
ejpam-3950	181	28	where	where	SCONJ
ejpam-3950	181	29	φ(t	φ(t	NOUN
ejpam-3950	181	30	)	)	PUNCT
ejpam-3950	181	31	is	be	AUX
ejpam-3950	181	32	the	the	DET
ejpam-3950	181	33	fundamental	fundamental	ADJ
ejpam-3950	181	34	matrix	matrix	NOUN
ejpam-3950	181	35	.	.	PUNCT
ejpam-3950	182	1	so	so	ADV
ejpam-3950	182	2	we	we	PRON
ejpam-3950	182	3	have	have	VERB
ejpam-3950	182	4	u2(t	u2(t	PRON
ejpam-3950	182	5	)	)	PUNCT
ejpam-3950	182	6	=	=	PUNCT
ejpam-3950	182	7	−ã−1a3u1(t	−ã−1a3u1(t	PROPN
ejpam-3950	182	8	)	)	PUNCT
ejpam-3950	182	9	.	.	PUNCT
ejpam-3950	183	1	therefore	therefore	ADV
ejpam-3950	183	2	u(t	u(t	NOUN
ejpam-3950	183	3	)	)	PUNCT
ejpam-3950	183	4	=	=	PUNCT
ejpam-3950	184	1	[	[	PUNCT
ejpam-3950	184	2	u1(t	u1(t	NOUN
ejpam-3950	184	3	)	)	PUNCT
ejpam-3950	184	4	u2(t	u2(t	NOUN
ejpam-3950	184	5	)	)	PUNCT
ejpam-3950	184	6	]	]	PUNCT
ejpam-3950	184	7	t	t	PROPN
ejpam-3950	184	8			NOUN
ejpam-3950	184	9	θ1	θ1	NOUN
ejpam-3950	184	10	.	.	PUNCT
ejpam-3950	184	11	.	.	PUNCT
ejpam-3950	184	12	.	.	PUNCT
ejpam-3950	185	1	θn	θn	INTJ
ejpam-3950	185	2			NOUN
ejpam-3950	185	3	.	.	PUNCT
ejpam-3950	186	1	we	we	PRON
ejpam-3950	186	2	conclude	conclude	VERB
ejpam-3950	186	3	the	the	DET
ejpam-3950	186	4	problem	problem	NOUN
ejpam-3950	186	5	(	(	PUNCT
ejpam-3950	186	6	1	1	X
ejpam-3950	186	7	)	)	PUNCT
ejpam-3950	186	8	has	have	VERB
ejpam-3950	186	9	a	a	DET
ejpam-3950	186	10	unique	unique	ADJ
ejpam-3950	186	11	solution	solution	NOUN
ejpam-3950	186	12	.	.	PUNCT
ejpam-3950	187	1	f.	f.	PROPN
ejpam-3950	187	2	seddiki	seddiki	PROPN
ejpam-3950	187	3	,	,	PUNCT
ejpam-3950	187	4	m.	m.	NOUN
ejpam-3950	187	5	al	al	PROPN
ejpam-3950	187	6	horani	horani	PROPN
ejpam-3950	187	7	,	,	PUNCT
ejpam-3950	187	8	r.	r.	PROPN
ejpam-3950	187	9	khalil	khalil	PROPN
ejpam-3950	187	10	/	/	SYM
ejpam-3950	187	11	eur	eur	PROPN
ejpam-3950	187	12	.	.	PUNCT
ejpam-3950	188	1	j.	j.	PROPN
ejpam-3950	188	2	pure	pure	PROPN
ejpam-3950	188	3	appl	appl	PROPN
ejpam-3950	188	4	.	.	PROPN
ejpam-3950	188	5	math	math	PROPN
ejpam-3950	188	6	,	,	PUNCT
ejpam-3950	188	7	14	14	NUM
ejpam-3950	188	8	(	(	PUNCT
ejpam-3950	188	9	2	2	NUM
ejpam-3950	188	10	)	)	PUNCT
ejpam-3950	188	11	(	(	PUNCT
ejpam-3950	188	12	2021	2021	NUM
ejpam-3950	188	13	)	)	PUNCT
ejpam-3950	188	14	,	,	PUNCT
ejpam-3950	188	15	493	493	NUM
ejpam-3950	188	16	-	-	SYM
ejpam-3950	188	17	505	505	NUM
ejpam-3950	188	18	499	499	NUM
ejpam-3950	188	19	theorem	theorem	NOUN
ejpam-3950	188	20	5	5	NUM
ejpam-3950	188	21	.	.	PUNCT
ejpam-3950	189	1	in	in	ADP
ejpam-3950	189	2	problem	problem	NOUN
ejpam-3950	189	3	(	(	PUNCT
ejpam-3950	189	4	2	2	NUM
ejpam-3950	189	5	)	)	PUNCT
ejpam-3950	189	6	,	,	PUNCT
ejpam-3950	189	7	let	let	VERB
ejpam-3950	189	8	bn	bn	PART
ejpam-3950	189	9	be	be	AUX
ejpam-3950	189	10	orthogonally	orthogonally	ADV
ejpam-3950	189	11	diagonalizable	diagonalizable	ADJ
ejpam-3950	189	12	linear	linear	ADJ
ejpam-3950	189	13	operator	operator	NOUN
ejpam-3950	189	14	such	such	ADJ
ejpam-3950	189	15	that	that	SCONJ
ejpam-3950	189	16	an	an	DET
ejpam-3950	189	17	|ker(bn	|ker(bn	NOUN
ejpam-3950	189	18	)	)	PUNCT
ejpam-3950	189	19	is	be	AUX
ejpam-3950	189	20	invertible	invertible	ADJ
ejpam-3950	189	21	.	.	PUNCT
ejpam-3950	190	1	then	then	ADV
ejpam-3950	190	2	problem	problem	NOUN
ejpam-3950	190	3	(	(	PUNCT
ejpam-3950	190	4	2	2	X
ejpam-3950	190	5	)	)	PUNCT
ejpam-3950	190	6	has	have	VERB
ejpam-3950	190	7	a	a	DET
ejpam-3950	190	8	unique	unique	ADJ
ejpam-3950	190	9	solution	solution	NOUN
ejpam-3950	190	10	.	.	PUNCT
ejpam-3950	191	1	proof	proof	NOUN
ejpam-3950	191	2	.	.	PUNCT
ejpam-3950	192	1	let	let	VERB
ejpam-3950	192	2	{	{	PUNCT
ejpam-3950	192	3	θ1	θ1	PROPN
ejpam-3950	192	4	,	,	PUNCT
ejpam-3950	192	5	θ2	θ2	PROPN
ejpam-3950	192	6	,	,	PUNCT
ejpam-3950	192	7	...	...	PUNCT
ejpam-3950	192	8	,	,	PUNCT
ejpam-3950	192	9	θn	θn	VERB
ejpam-3950	192	10	}	}	PUNCT
ejpam-3950	192	11	be	be	AUX
ejpam-3950	192	12	an	an	DET
ejpam-3950	192	13	orthonormal	orthonormal	ADJ
ejpam-3950	192	14	basis	basis	NOUN
ejpam-3950	192	15	such	such	ADJ
ejpam-3950	192	16	that	that	SCONJ
ejpam-3950	192	17	the	the	DET
ejpam-3950	192	18	matrix	matrix	NOUN
ejpam-3950	192	19	representation	representation	NOUN
ejpam-3950	192	20	of	of	ADP
ejpam-3950	192	21	bn	bn	NOUN
ejpam-3950	192	22	with	with	ADP
ejpam-3950	192	23	respect	respect	NOUN
ejpam-3950	192	24	this	this	DET
ejpam-3950	192	25	basis	basis	NOUN
ejpam-3950	192	26	is	be	AUX
ejpam-3950	192	27	d̃	d̃	PROPN
ejpam-3950	192	28	=	=	SYM
ejpam-3950	192	29	diag(λ1	diag(λ1	PROPN
ejpam-3950	192	30	,	,	PUNCT
ejpam-3950	192	31	...	...	PUNCT
ejpam-3950	192	32	,	,	PUNCT
ejpam-3950	192	33	λn	λn	NOUN
ejpam-3950	192	34	)	)	PUNCT
ejpam-3950	192	35	,	,	PUNCT
ejpam-3950	192	36	when	when	SCONJ
ejpam-3950	192	37	λ1	λ1	ADJ
ejpam-3950	192	38	,	,	PUNCT
ejpam-3950	192	39	...	...	PUNCT
ejpam-3950	192	40	,	,	PUNCT
ejpam-3950	192	41	λn	λn	X
ejpam-3950	192	42	the	the	DET
ejpam-3950	192	43	corresponding	corresponding	ADJ
ejpam-3950	192	44	eigenvalues	eigenvalue	NOUN
ejpam-3950	192	45	of	of	ADP
ejpam-3950	192	46	bn	bn	NOUN
ejpam-3950	192	47	.	.	PUNCT
ejpam-3950	193	1	now	now	ADV
ejpam-3950	193	2	,	,	PUNCT
ejpam-3950	193	3	if	if	SCONJ
ejpam-3950	193	4	λi	λi	ADP
ejpam-3950	193	5	6=	6=	PROPN
ejpam-3950	193	6	0	0	NUM
ejpam-3950	193	7	,	,	PUNCT
ejpam-3950	193	8	for	for	ADP
ejpam-3950	193	9	all	all	DET
ejpam-3950	193	10	i	i	PRON
ejpam-3950	193	11	=	=	NOUN
ejpam-3950	193	12	1	1	NUM
ejpam-3950	193	13	,	,	PUNCT
ejpam-3950	193	14	2	2	NUM
ejpam-3950	193	15	,	,	PUNCT
ejpam-3950	193	16	...	...	PUNCT
ejpam-3950	193	17	n	n	CCONJ
ejpam-3950	193	18	,	,	PUNCT
ejpam-3950	193	19	then	then	ADV
ejpam-3950	193	20	the	the	DET
ejpam-3950	193	21	problem	problem	NOUN
ejpam-3950	193	22	(	(	PUNCT
ejpam-3950	193	23	2	2	X
ejpam-3950	193	24	)	)	PUNCT
ejpam-3950	193	25	becomes	become	VERB
ejpam-3950	193	26	u(α)(t	u(α)(t	NOUN
ejpam-3950	193	27	)	)	PUNCT
ejpam-3950	193	28	=	=	SYM
ejpam-3950	193	29	b−1n	b−1n	NOUN
ejpam-3950	193	30	anu(t	anu(t	PROPN
ejpam-3950	193	31	)	)	PUNCT
ejpam-3950	194	1	+	+	NUM
ejpam-3950	194	2	f(t)b−1n	f(t)b−1n	X
ejpam-3950	194	3	z.	z.	PROPN
ejpam-3950	194	4	hence	hence	ADV
ejpam-3950	194	5	has	have	VERB
ejpam-3950	194	6	a	a	DET
ejpam-3950	194	7	unique	unique	ADJ
ejpam-3950	194	8	solution	solution	NOUN
ejpam-3950	194	9	by	by	ADP
ejpam-3950	194	10	theorem	theorem	NOUN
ejpam-3950	194	11	3.2	3.2	NUM
ejpam-3950	194	12	.	.	PUNCT
ejpam-3950	195	1	suppose	suppose	VERB
ejpam-3950	195	2	λi	λi	ADP
ejpam-3950	195	3	6=	6=	NUM
ejpam-3950	195	4	0	0	NUM
ejpam-3950	195	5	,	,	PUNCT
ejpam-3950	195	6	for	for	ADP
ejpam-3950	195	7	i	i	PROPN
ejpam-3950	195	8	=	=	SYM
ejpam-3950	195	9	1	1	NUM
ejpam-3950	195	10	,	,	PUNCT
ejpam-3950	195	11	2	2	NUM
ejpam-3950	195	12	,	,	PUNCT
ejpam-3950	195	13	...	...	PUNCT
ejpam-3950	196	1	r	r	NOUN
ejpam-3950	196	2	,	,	PUNCT
ejpam-3950	196	3	and	and	CCONJ
ejpam-3950	196	4	λi	λi	X
ejpam-3950	196	5	=	=	NOUN
ejpam-3950	196	6	0	0	NUM
ejpam-3950	196	7	,	,	PUNCT
ejpam-3950	196	8	for	for	ADP
ejpam-3950	196	9	i	i	PRON
ejpam-3950	196	10	=	=	SYM
ejpam-3950	196	11	r+1	r+1	PROPN
ejpam-3950	196	12	,	,	PUNCT
ejpam-3950	196	13	r+2	r+2	PRON
ejpam-3950	196	14	,	,	PUNCT
ejpam-3950	196	15	...	...	PUNCT
ejpam-3950	196	16	n.	n.	PROPN
ejpam-3950	196	17	let	let	VERB
ejpam-3950	196	18	u(t	u(t	NOUN
ejpam-3950	196	19	)	)	PUNCT
ejpam-3950	196	20	=	=	SYM
ejpam-3950	197	1	∑n	∑n	PROPN
ejpam-3950	197	2	i=1	i=1	PROPN
ejpam-3950	197	3	vi(t)θi	vi(t)θi	PROPN
ejpam-3950	197	4	:	:	PUNCT
ejpam-3950	197	5	then	then	ADV
ejpam-3950	198	1	n∑	n∑	PROPN
ejpam-3950	198	2	i=1	i=1	PROPN
ejpam-3950	199	1	v	v	PROPN
ejpam-3950	199	2	(	(	PUNCT
ejpam-3950	199	3	α	α	NOUN
ejpam-3950	199	4	)	)	PUNCT
ejpam-3950	199	5	i	i	PRON
ejpam-3950	199	6	(	(	PUNCT
ejpam-3950	199	7	t)bnθi	t)bnθi	X
ejpam-3950	200	1	=	=	SYM
ejpam-3950	200	2	n∑	n∑	NOUN
ejpam-3950	200	3	i=1	i=1	PROPN
ejpam-3950	200	4	vi(t)anθi	vi(t)anθi	NOUN
ejpam-3950	200	5	+	+	X
ejpam-3950	200	6	f(t)z	f(t)z	NOUN
ejpam-3950	200	7	.	.	PUNCT
ejpam-3950	201	1	(	(	PUNCT
ejpam-3950	201	2	12	12	X
ejpam-3950	201	3	)	)	PUNCT
ejpam-3950	201	4	taking	take	VERB
ejpam-3950	201	5	the	the	DET
ejpam-3950	201	6	inner	inner	ADJ
ejpam-3950	201	7	product	product	NOUN
ejpam-3950	201	8	of	of	ADP
ejpam-3950	201	9	θj	θj	NOUN
ejpam-3950	201	10	with	with	ADP
ejpam-3950	201	11	both	both	DET
ejpam-3950	201	12	sides	side	NOUN
ejpam-3950	201	13	of	of	ADP
ejpam-3950	201	14	equation	equation	NOUN
ejpam-3950	201	15	(	(	PUNCT
ejpam-3950	201	16	12	12	NUM
ejpam-3950	201	17	)	)	PUNCT
ejpam-3950	201	18	,	,	PUNCT
ejpam-3950	201	19	we	we	PRON
ejpam-3950	201	20	obtain	obtain	VERB
ejpam-3950	202	1	n∑	n∑	PROPN
ejpam-3950	202	2	i=1	i=1	PROPN
ejpam-3950	202	3	v	v	PROPN
ejpam-3950	202	4	(	(	PUNCT
ejpam-3950	202	5	α	α	NOUN
ejpam-3950	202	6	)	)	PUNCT
ejpam-3950	203	1	i	i	PRON
ejpam-3950	203	2	(	(	PUNCT
ejpam-3950	203	3	t)〈bnθi	t)〈bnθi	PROPN
ejpam-3950	203	4	,	,	PUNCT
ejpam-3950	203	5	θj	θj	NOUN
ejpam-3950	203	6	〉	〉	NOUN
ejpam-3950	203	7	=	=	SYM
ejpam-3950	203	8	n∑	n∑	PROPN
ejpam-3950	203	9	i=1	i=1	PROPN
ejpam-3950	203	10	vi(t)〈anθi	vi(t)〈anθi	NOUN
ejpam-3950	203	11	,	,	PUNCT
ejpam-3950	203	12	θj〉+	θj〉+	PROPN
ejpam-3950	203	13	f(t)〈z	f(t)〈z	PROPN
ejpam-3950	203	14	,	,	PUNCT
ejpam-3950	203	15	θj	θj	PRON
ejpam-3950	203	16	〉	〉	NOUN
ejpam-3950	203	17	.	.	PUNCT
ejpam-3950	204	1	so	so	ADV
ejpam-3950	204	2	,	,	PUNCT
ejpam-3950	204	3	we	we	PRON
ejpam-3950	204	4	get	get	VERB
ejpam-3950	204	5	the	the	DET
ejpam-3950	204	6	following	follow	VERB
ejpam-3950	204	7	system	system	NOUN
ejpam-3950	204	8	[	[	PUNCT
ejpam-3950	204	9	d	d	NOUN
ejpam-3950	204	10	0	0	NUM
ejpam-3950	204	11	0	0	NUM
ejpam-3950	204	12	0	0	NUM
ejpam-3950	204	13	]	]	PUNCT
ejpam-3950	204	14			VERB
ejpam-3950	204	15	v	v	NOUN
ejpam-3950	204	16	(	(	PUNCT
ejpam-3950	204	17	α	α	NOUN
ejpam-3950	204	18	)	)	PUNCT
ejpam-3950	204	19	1	1	NUM
ejpam-3950	204	20	(	(	PUNCT
ejpam-3950	204	21	t	t	PROPN
ejpam-3950	204	22	)	)	PUNCT
ejpam-3950	204	23	.	.	PUNCT
ejpam-3950	204	24	.	.	PUNCT
ejpam-3950	205	1	.	.	PUNCT
ejpam-3950	206	1	v	v	X
ejpam-3950	206	2	(	(	PUNCT
ejpam-3950	206	3	α	α	NOUN
ejpam-3950	206	4	)	)	PUNCT
ejpam-3950	206	5	n	n	PROPN
ejpam-3950	206	6	(	(	PUNCT
ejpam-3950	206	7	t	t	NOUN
ejpam-3950	206	8	)	)	PUNCT
ejpam-3950	206	9			NOUN
ejpam-3950	206	10	=	=	PUNCT
ejpam-3950	206	11	[	[	PUNCT
ejpam-3950	206	12	a1	a1	NOUN
ejpam-3950	206	13	a2	a2	PROPN
ejpam-3950	206	14	a3	a3	NOUN
ejpam-3950	206	15	ã	ã	PROPN
ejpam-3950	206	16	]	]	PUNCT
ejpam-3950	206	17			NOUN
ejpam-3950	206	18	v1(t	v1(t	PRON
ejpam-3950	206	19	)	)	PUNCT
ejpam-3950	206	20	.	.	PUNCT
ejpam-3950	206	21	.	.	PUNCT
ejpam-3950	206	22	.	.	PUNCT
ejpam-3950	207	1	vn(t	vn(t	X
ejpam-3950	208	1	)	)	PUNCT
ejpam-3950	208	2	+	+	VERB
ejpam-3950	208	3	f(t	f(t	NOUN
ejpam-3950	208	4	)	)	PUNCT
ejpam-3950	208	5			NOUN
ejpam-3950	209	1	〈	〈	PROPN
ejpam-3950	209	2	z	z	PROPN
ejpam-3950	209	3	,	,	PUNCT
ejpam-3950	209	4	θ1	θ1	PROPN
ejpam-3950	209	5	〉	〉	PROPN
ejpam-3950	209	6	.	.	PUNCT
ejpam-3950	209	7	.	.	PUNCT
ejpam-3950	209	8	.	.	PUNCT
ejpam-3950	210	1	〈	〈	PROPN
ejpam-3950	210	2	z	z	PROPN
ejpam-3950	210	3	,	,	PUNCT
ejpam-3950	210	4	θn	θn	PROPN
ejpam-3950	210	5	〉	〉	PROPN
ejpam-3950	210	6			NOUN
ejpam-3950	210	7	.	.	PUNCT
ejpam-3950	211	1	(	(	PUNCT
ejpam-3950	211	2	13	13	NUM
ejpam-3950	211	3	)	)	PUNCT
ejpam-3950	211	4	where	where	SCONJ
ejpam-3950	211	5	d	d	NOUN
ejpam-3950	211	6	=	=	SYM
ejpam-3950	211	7	diag(λ1	diag(λ1	NOUN
ejpam-3950	211	8	,	,	PUNCT
ejpam-3950	211	9	.	.	PUNCT
ejpam-3950	211	10	,	,	PUNCT
ejpam-3950	211	11	.	.	PUNCT
ejpam-3950	211	12	,	,	PUNCT
ejpam-3950	211	13	.	.	PUNCT
ejpam-3950	211	14	,	,	PUNCT
ejpam-3950	211	15	λr	λr	X
ejpam-3950	211	16	)	)	PUNCT
ejpam-3950	211	17	and	and	CCONJ
ejpam-3950	211	18	ã	ã	PROPN
ejpam-3950	211	19	=	=	PROPN
ejpam-3950	211	20	an	an	DET
ejpam-3950	211	21	|ker(bn)=	|ker(bn)=	PROPN
ejpam-3950	211	22	[	[	X
ejpam-3950	211	23	〈	〈	PROPN
ejpam-3950	211	24	anθj	anθj	NOUN
ejpam-3950	211	25	,	,	PUNCT
ejpam-3950	211	26	θi〉]i	θi〉]i	PROPN
ejpam-3950	211	27	,	,	PUNCT
ejpam-3950	211	28	j	j	NOUN
ejpam-3950	211	29	=	=	NOUN
ejpam-3950	211	30	r+1,	r+1,	NOUN
ejpam-3950	211	31	...	...	PUNCT
ejpam-3950	211	32	,n	,n	NOUN
ejpam-3950	211	33	.	.	PUNCT
ejpam-3950	212	1	multiplying	multiplying	NOUN
ejpam-3950	212	2	(	(	PUNCT
ejpam-3950	212	3	13	13	NUM
ejpam-3950	212	4	)	)	PUNCT
ejpam-3950	212	5	by	by	ADP
ejpam-3950	212	6	[	[	PUNCT
ejpam-3950	212	7	i	i	NOUN
ejpam-3950	212	8	0	0	NUM
ejpam-3950	212	9	0	0	NUM
ejpam-3950	212	10	ã−1	ã−1	PROPN
ejpam-3950	212	11	]	]	PUNCT
ejpam-3950	212	12	,	,	PUNCT
ejpam-3950	212	13	we	we	PRON
ejpam-3950	212	14	obtain	obtain	VERB
ejpam-3950	212	15	[	[	PUNCT
ejpam-3950	212	16	d	d	NOUN
ejpam-3950	212	17	0	0	NUM
ejpam-3950	212	18	0	0	NUM
ejpam-3950	212	19	0	0	NUM
ejpam-3950	212	20	]	]	PUNCT
ejpam-3950	212	21			VERB
ejpam-3950	212	22	v	v	NOUN
ejpam-3950	212	23	(	(	PUNCT
ejpam-3950	212	24	α	α	NOUN
ejpam-3950	212	25	)	)	PUNCT
ejpam-3950	212	26	1	1	NUM
ejpam-3950	212	27	(	(	PUNCT
ejpam-3950	212	28	t	t	PROPN
ejpam-3950	212	29	)	)	PUNCT
ejpam-3950	212	30	.	.	PUNCT
ejpam-3950	212	31	.	.	PUNCT
ejpam-3950	212	32	.	.	PUNCT
ejpam-3950	213	1	v	v	X
ejpam-3950	213	2	(	(	PUNCT
ejpam-3950	213	3	α	α	NOUN
ejpam-3950	213	4	)	)	PUNCT
ejpam-3950	213	5	n	n	PROPN
ejpam-3950	213	6	(	(	PUNCT
ejpam-3950	213	7	t	t	NOUN
ejpam-3950	213	8	)	)	PUNCT
ejpam-3950	213	9			NOUN
ejpam-3950	213	10	=	=	PUNCT
ejpam-3950	213	11	[	[	PUNCT
ejpam-3950	213	12	a1	a1	NOUN
ejpam-3950	213	13	a2	a2	PROPN
ejpam-3950	213	14	ã−1a3	ã−1a3	NUM
ejpam-3950	213	15	in−r	in−r	NOUN
ejpam-3950	213	16	]	]	PUNCT
ejpam-3950	213	17			NOUN
ejpam-3950	213	18	v1(t	v1(t	PRON
ejpam-3950	213	19	)	)	PUNCT
ejpam-3950	213	20	.	.	PUNCT
ejpam-3950	213	21	.	.	PUNCT
ejpam-3950	213	22	.	.	PUNCT
ejpam-3950	214	1	vn(t	vn(t	X
ejpam-3950	215	1	)	)	PUNCT
ejpam-3950	215	2	+	+	VERB
ejpam-3950	215	3	f(t	f(t	NOUN
ejpam-3950	215	4	)	)	PUNCT
ejpam-3950	216	1	[	[	PUNCT
ejpam-3950	216	2	i	i	NOUN
ejpam-3950	216	3	0	0	NUM
ejpam-3950	216	4	0	0	X
ejpam-3950	216	5	ã−1	ã−1	PROPN
ejpam-3950	216	6	]	]	PUNCT
ejpam-3950	216	7			NOUN
ejpam-3950	217	1	〈	〈	PROPN
ejpam-3950	217	2	z	z	PROPN
ejpam-3950	217	3	,	,	PUNCT
ejpam-3950	217	4	θ1	θ1	PROPN
ejpam-3950	217	5	〉	〉	PROPN
ejpam-3950	217	6	.	.	PUNCT
ejpam-3950	217	7	.	.	PUNCT
ejpam-3950	217	8	.	.	PUNCT
ejpam-3950	218	1	〈	〈	PROPN
ejpam-3950	218	2	z	z	PROPN
ejpam-3950	218	3	,	,	PUNCT
ejpam-3950	218	4	θn	θn	PROPN
ejpam-3950	218	5	〉	〉	PROPN
ejpam-3950	218	6			NOUN
ejpam-3950	218	7	.	.	PUNCT
ejpam-3950	219	1	thus	thus	ADV
ejpam-3950	219	2	,	,	PUNCT
ejpam-3950	219	3	we	we	PRON
ejpam-3950	219	4	get	get	VERB
ejpam-3950	219	5	d	d	PROPN
ejpam-3950	219	6			NOUN
ejpam-3950	219	7	v	v	NOUN
ejpam-3950	219	8	(	(	PUNCT
ejpam-3950	219	9	α	α	NOUN
ejpam-3950	219	10	)	)	PUNCT
ejpam-3950	219	11	1	1	NUM
ejpam-3950	219	12	(	(	PUNCT
ejpam-3950	219	13	t	t	PROPN
ejpam-3950	219	14	)	)	PUNCT
ejpam-3950	219	15	.	.	PUNCT
ejpam-3950	219	16	.	.	PUNCT
ejpam-3950	220	1	.	.	PUNCT
ejpam-3950	221	1	v	v	X
ejpam-3950	221	2	(	(	PUNCT
ejpam-3950	221	3	α	α	NOUN
ejpam-3950	221	4	)	)	PUNCT
ejpam-3950	221	5	r	r	NOUN
ejpam-3950	221	6	(	(	PUNCT
ejpam-3950	221	7	t	t	NOUN
ejpam-3950	221	8	)	)	PUNCT
ejpam-3950	221	9			NOUN
ejpam-3950	221	10	=	=	SYM
ejpam-3950	221	11	a1	a1	NOUN
ejpam-3950	221	12			NOUN
ejpam-3950	221	13	v1(t	v1(t	PRON
ejpam-3950	221	14	)	)	PUNCT
ejpam-3950	221	15	.	.	PUNCT
ejpam-3950	221	16	.	.	PUNCT
ejpam-3950	221	17	.	.	PUNCT
ejpam-3950	222	1	vr(t	vr(t	X
ejpam-3950	222	2	)	)	PUNCT
ejpam-3950	222	3	+a2	+a2	NOUN
ejpam-3950	222	4			NOUN
ejpam-3950	222	5	vr+1(t	vr+1(t	PROPN
ejpam-3950	222	6	)	)	PUNCT
ejpam-3950	222	7	.	.	PUNCT
ejpam-3950	222	8	.	.	PUNCT
ejpam-3950	223	1	.	.	PUNCT
ejpam-3950	224	1	vn(t	vn(t	X
ejpam-3950	225	1	)	)	PUNCT
ejpam-3950	225	2	+	+	VERB
ejpam-3950	225	3	f(t	f(t	NOUN
ejpam-3950	225	4	)	)	PUNCT
ejpam-3950	225	5			NOUN
ejpam-3950	226	1	〈	〈	PROPN
ejpam-3950	226	2	z	z	PROPN
ejpam-3950	226	3	,	,	PUNCT
ejpam-3950	226	4	θ1	θ1	PROPN
ejpam-3950	226	5	〉	〉	PROPN
ejpam-3950	226	6	.	.	PUNCT
ejpam-3950	226	7	.	.	PUNCT
ejpam-3950	226	8	.	.	PUNCT
ejpam-3950	227	1	〈	〈	PROPN
ejpam-3950	227	2	z	z	PROPN
ejpam-3950	227	3	,	,	PUNCT
ejpam-3950	227	4	θr	θr	DET
ejpam-3950	227	5	〉	〉	NOUN
ejpam-3950	227	6			NOUN
ejpam-3950	227	7	,	,	PUNCT
ejpam-3950	227	8	(	(	PUNCT
ejpam-3950	227	9	14	14	NUM
ejpam-3950	227	10	)	)	PUNCT
ejpam-3950	227	11	f.	f.	PROPN
ejpam-3950	227	12	seddiki	seddiki	PROPN
ejpam-3950	227	13	,	,	PUNCT
ejpam-3950	227	14	m.	m.	NOUN
ejpam-3950	227	15	al	al	PROPN
ejpam-3950	227	16	horani	horani	PROPN
ejpam-3950	227	17	,	,	PUNCT
ejpam-3950	227	18	r.	r.	PROPN
ejpam-3950	227	19	khalil	khalil	PROPN
ejpam-3950	227	20	/	/	SYM
ejpam-3950	227	21	eur	eur	PROPN
ejpam-3950	227	22	.	.	PUNCT
ejpam-3950	228	1	j.	j.	PROPN
ejpam-3950	228	2	pure	pure	PROPN
ejpam-3950	228	3	appl	appl	PROPN
ejpam-3950	228	4	.	.	PROPN
ejpam-3950	228	5	math	math	PROPN
ejpam-3950	228	6	,	,	PUNCT
ejpam-3950	228	7	14	14	NUM
ejpam-3950	228	8	(	(	PUNCT
ejpam-3950	228	9	2	2	NUM
ejpam-3950	228	10	)	)	PUNCT
ejpam-3950	228	11	(	(	PUNCT
ejpam-3950	228	12	2021	2021	NUM
ejpam-3950	228	13	)	)	PUNCT
ejpam-3950	228	14	,	,	PUNCT
ejpam-3950	228	15	493	493	NUM
ejpam-3950	228	16	-	-	SYM
ejpam-3950	228	17	505	505	NUM
ejpam-3950	228	18	500	500	NUM
ejpam-3950	228	19	and	and	CCONJ
ejpam-3950	228	20	ã−1a3	ã−1a3	NUM
ejpam-3950	228	21			NOUN
ejpam-3950	228	22	v1(t	v1(t	PRON
ejpam-3950	228	23	)	)	PUNCT
ejpam-3950	228	24	.	.	PUNCT
ejpam-3950	228	25	.	.	PUNCT
ejpam-3950	229	1	.	.	PUNCT
ejpam-3950	230	1	vr(t	vr(t	X
ejpam-3950	230	2	)	)	PUNCT
ejpam-3950	230	3	+	+	VERB
ejpam-3950	230	4	in−r	in−r	ADJ
ejpam-3950	230	5			NOUN
ejpam-3950	230	6	vr+1(t	vr+1(t	PROPN
ejpam-3950	230	7	)	)	PUNCT
ejpam-3950	230	8	.	.	PUNCT
ejpam-3950	230	9	.	.	PUNCT
ejpam-3950	230	10	.	.	PUNCT
ejpam-3950	231	1	vn(t	vn(t	PUNCT
ejpam-3950	232	1	)	)	PUNCT
ejpam-3950	232	2	+	+	VERB
ejpam-3950	232	3	f(t)ã−1	f(t)ã−1	ADV
ejpam-3950	232	4			NOUN
ejpam-3950	232	5	〈	〈	PROPN
ejpam-3950	232	6	z	z	PROPN
ejpam-3950	232	7	,	,	PUNCT
ejpam-3950	232	8	θr+1	θr+1	PROPN
ejpam-3950	232	9	〉	〉	NOUN
ejpam-3950	232	10	.	.	PUNCT
ejpam-3950	232	11	.	.	PUNCT
ejpam-3950	232	12	.	.	PUNCT
ejpam-3950	233	1	〈	〈	PROPN
ejpam-3950	233	2	z	z	PROPN
ejpam-3950	233	3	,	,	PUNCT
ejpam-3950	233	4	θn	θn	PROPN
ejpam-3950	233	5	〉	〉	NOUN
ejpam-3950	233	6			NOUN
ejpam-3950	233	7	=	=	NOUN
ejpam-3950	233	8	0	0	X
ejpam-3950	233	9	.	.	PUNCT
ejpam-3950	234	1	(	(	PUNCT
ejpam-3950	234	2	15	15	NUM
ejpam-3950	234	3	)	)	PUNCT
ejpam-3950	234	4	from	from	ADP
ejpam-3950	234	5	equation	equation	NOUN
ejpam-3950	234	6	(	(	PUNCT
ejpam-3950	234	7	15	15	NUM
ejpam-3950	234	8	)	)	PUNCT
ejpam-3950	234	9	,	,	PUNCT
ejpam-3950	235	1	we	we	PRON
ejpam-3950	235	2	have	have	PROPN
ejpam-3950	235	3	vr+1(t	vr+1(t	PROPN
ejpam-3950	235	4	)	)	PUNCT
ejpam-3950	235	5	.	.	PUNCT
ejpam-3950	235	6	.	.	PUNCT
ejpam-3950	235	7	.	.	PUNCT
ejpam-3950	236	1	vn(t	vn(t	NUM
ejpam-3950	236	2	)	)	PUNCT
ejpam-3950	237	1			NOUN
ejpam-3950	237	2	=	=	SYM
ejpam-3950	237	3	−ã−1a3	−ã−1a3	X
ejpam-3950	237	4			NOUN
ejpam-3950	237	5	v1(t	v1(t	PRON
ejpam-3950	237	6	)	)	PUNCT
ejpam-3950	237	7	.	.	PUNCT
ejpam-3950	237	8	.	.	PUNCT
ejpam-3950	238	1	.	.	PUNCT
ejpam-3950	239	1	vr(t	vr(t	X
ejpam-3950	239	2	)	)	PUNCT
ejpam-3950	239	3	−	−	PROPN
ejpam-3950	239	4	f(t)ã−1	f(t)ã−1	PUNCT
ejpam-3950	239	5			NOUN
ejpam-3950	239	6	〈	〈	PROPN
ejpam-3950	239	7	z	z	PROPN
ejpam-3950	239	8	,	,	PUNCT
ejpam-3950	239	9	θr+1	θr+1	PROPN
ejpam-3950	239	10	〉	〉	NOUN
ejpam-3950	239	11	.	.	PUNCT
ejpam-3950	239	12	.	.	PUNCT
ejpam-3950	239	13	.	.	PUNCT
ejpam-3950	240	1	〈	〈	PROPN
ejpam-3950	240	2	z	z	PROPN
ejpam-3950	240	3	,	,	PUNCT
ejpam-3950	240	4	θn	θn	PROPN
ejpam-3950	240	5	〉	〉	PROPN
ejpam-3950	240	6			NOUN
ejpam-3950	240	7	.	.	PUNCT
ejpam-3950	241	1	(	(	PUNCT
ejpam-3950	241	2	16	16	NUM
ejpam-3950	241	3	)	)	PUNCT
ejpam-3950	241	4	substitute	substitute	NOUN
ejpam-3950	241	5	(	(	PUNCT
ejpam-3950	241	6	16	16	NUM
ejpam-3950	241	7	)	)	PUNCT
ejpam-3950	241	8	in	in	ADP
ejpam-3950	241	9	equation	equation	NOUN
ejpam-3950	241	10	(	(	PUNCT
ejpam-3950	241	11	14	14	NUM
ejpam-3950	241	12	)	)	PUNCT
ejpam-3950	241	13	,	,	PUNCT
ejpam-3950	241	14	we	we	PRON
ejpam-3950	241	15	get	get	NOUN
ejpam-3950	241	16	v	v	X
ejpam-3950	241	17	(	(	PUNCT
ejpam-3950	241	18	α	α	NOUN
ejpam-3950	241	19	)	)	PUNCT
ejpam-3950	241	20	1	1	NUM
ejpam-3950	241	21	(	(	PUNCT
ejpam-3950	241	22	t	t	PROPN
ejpam-3950	241	23	)	)	PUNCT
ejpam-3950	241	24	.	.	PUNCT
ejpam-3950	241	25	.	.	PUNCT
ejpam-3950	242	1	.	.	PUNCT
ejpam-3950	243	1	v	v	X
ejpam-3950	243	2	(	(	PUNCT
ejpam-3950	243	3	α	α	NOUN
ejpam-3950	243	4	)	)	PUNCT
ejpam-3950	243	5	r	r	NOUN
ejpam-3950	243	6	(	(	PUNCT
ejpam-3950	243	7	t	t	NOUN
ejpam-3950	243	8	)	)	PUNCT
ejpam-3950	243	9			NOUN
ejpam-3950	243	10	=	=	SYM
ejpam-3950	243	11	d−1(a1	d−1(a1	X
ejpam-3950	243	12	−a2ã	−a2ã	VERB
ejpam-3950	243	13	−1a3	−1a3	NUM
ejpam-3950	243	14	)	)	PUNCT
ejpam-3950	243	15			NOUN
ejpam-3950	243	16	v1(t	v1(t	PRON
ejpam-3950	243	17	)	)	PUNCT
ejpam-3950	243	18	.	.	PUNCT
ejpam-3950	243	19	.	.	PUNCT
ejpam-3950	244	1	.	.	PUNCT
ejpam-3950	245	1	vr(t	vr(t	X
ejpam-3950	245	2	)	)	PUNCT
ejpam-3950	245	3	+	+	VERB
ejpam-3950	245	4	f(t)d−1	f(t)d−1	PROPN
ejpam-3950	245	5	(	(	PUNCT
ejpam-3950	245	6			NOUN
ejpam-3950	245	7	〈	〈	PROPN
ejpam-3950	245	8	z	z	PROPN
ejpam-3950	245	9	,	,	PUNCT
ejpam-3950	245	10	θ1	θ1	PROPN
ejpam-3950	245	11	〉	〉	PROPN
ejpam-3950	245	12	.	.	PUNCT
ejpam-3950	245	13	.	.	PUNCT
ejpam-3950	245	14	.	.	PUNCT
ejpam-3950	246	1	〈	〈	PROPN
ejpam-3950	246	2	z	z	PROPN
ejpam-3950	246	3	,	,	PUNCT
ejpam-3950	246	4	θr	θr	DET
ejpam-3950	246	5	〉	〉	NOUN
ejpam-3950	246	6	−a2ã	−a2ã	NOUN
ejpam-3950	246	7	−1	−1	NOUN
ejpam-3950	246	8			NOUN
ejpam-3950	247	1	〈	〈	PROPN
ejpam-3950	247	2	z	z	PROPN
ejpam-3950	247	3	,	,	PUNCT
ejpam-3950	247	4	θr+1	θr+1	PROPN
ejpam-3950	247	5	〉	〉	NOUN
ejpam-3950	247	6	.	.	PUNCT
ejpam-3950	247	7	.	.	PUNCT
ejpam-3950	247	8	.	.	PUNCT
ejpam-3950	248	1	〈	〈	PROPN
ejpam-3950	248	2	z	z	PROPN
ejpam-3950	248	3	,	,	PUNCT
ejpam-3950	248	4	θn	θn	PROPN
ejpam-3950	248	5	〉	〉	PROPN
ejpam-3950	248	6			NUM
ejpam-3950	248	7	)	)	PUNCT
ejpam-3950	248	8	.	.	PUNCT
ejpam-3950	249	1	we	we	PRON
ejpam-3950	249	2	put	put	VERB
ejpam-3950	249	3	,	,	PUNCT
ejpam-3950	249	4	u1(t	u1(t	ADV
ejpam-3950	249	5	)	)	PUNCT
ejpam-3950	249	6	=	=	SYM
ejpam-3950	249	7			NOUN
ejpam-3950	249	8	v1(t	v1(t	PRON
ejpam-3950	249	9	)	)	PUNCT
ejpam-3950	249	10	.	.	PUNCT
ejpam-3950	249	11	.	.	PUNCT
ejpam-3950	249	12	.	.	PUNCT
ejpam-3950	250	1	vr(t	vr(t	X
ejpam-3950	250	2	)	)	PUNCT
ejpam-3950	250	3			NOUN
ejpam-3950	250	4	,	,	PUNCT
ejpam-3950	250	5	u2(t	u2(t	NOUN
ejpam-3950	250	6	)	)	PUNCT
ejpam-3950	250	7	=	=	SYM
ejpam-3950	250	8			NOUN
ejpam-3950	250	9	vr+1(t	vr+1(t	PROPN
ejpam-3950	250	10	)	)	PUNCT
ejpam-3950	250	11	.	.	PUNCT
ejpam-3950	250	12	.	.	PUNCT
ejpam-3950	251	1	.	.	PUNCT
ejpam-3950	252	1	vn(t	vn(t	X
ejpam-3950	252	2	)	)	PUNCT
ejpam-3950	252	3			NOUN
ejpam-3950	252	4	,	,	PUNCT
ejpam-3950	252	5	m	m	VERB
ejpam-3950	252	6	=	=	SYM
ejpam-3950	252	7	d−1(a1	d−1(a1	VERB
ejpam-3950	252	8	−	−	PROPN
ejpam-3950	252	9	a2ã	a2ã	ADV
ejpam-3950	252	10	−1a3	−1a3	NUM
ejpam-3950	252	11	)	)	PUNCT
ejpam-3950	252	12	and	and	CCONJ
ejpam-3950	252	13	f	f	PROPN
ejpam-3950	252	14	(	(	PUNCT
ejpam-3950	252	15	t	t	PROPN
ejpam-3950	252	16	)	)	PUNCT
ejpam-3950	252	17	=	=	PUNCT
ejpam-3950	253	1	f(t)d−1	f(t)d−1	PROPN
ejpam-3950	253	2	(	(	PUNCT
ejpam-3950	253	3			NOUN
ejpam-3950	253	4	〈	〈	PROPN
ejpam-3950	253	5	z	z	PROPN
ejpam-3950	253	6	,	,	PUNCT
ejpam-3950	253	7	θ1	θ1	PROPN
ejpam-3950	253	8	〉	〉	PROPN
ejpam-3950	253	9	.	.	PUNCT
ejpam-3950	253	10	.	.	PUNCT
ejpam-3950	253	11	.	.	PUNCT
ejpam-3950	254	1	〈	〈	PROPN
ejpam-3950	254	2	z	z	PROPN
ejpam-3950	254	3	,	,	PUNCT
ejpam-3950	254	4	θr	θr	DET
ejpam-3950	254	5	〉	〉	NOUN
ejpam-3950	254	6	−a2ã	−a2ã	NOUN
ejpam-3950	254	7	−1	−1	NOUN
ejpam-3950	254	8			NOUN
ejpam-3950	255	1	〈	〈	PROPN
ejpam-3950	255	2	z	z	PROPN
ejpam-3950	255	3	,	,	PUNCT
ejpam-3950	255	4	θr+1	θr+1	PROPN
ejpam-3950	255	5	〉	〉	NOUN
ejpam-3950	255	6	.	.	PUNCT
ejpam-3950	255	7	.	.	PUNCT
ejpam-3950	255	8	.	.	PUNCT
ejpam-3950	256	1	〈	〈	PROPN
ejpam-3950	256	2	z	z	PROPN
ejpam-3950	256	3	,	,	PUNCT
ejpam-3950	256	4	θn	θn	PROPN
ejpam-3950	256	5	〉	〉	PROPN
ejpam-3950	256	6			NUM
ejpam-3950	256	7	)	)	PUNCT
ejpam-3950	256	8	.	.	PUNCT
ejpam-3950	257	1	then	then	ADV
ejpam-3950	257	2	we	we	PRON
ejpam-3950	257	3	obtain	obtain	VERB
ejpam-3950	257	4	the	the	DET
ejpam-3950	257	5	system	system	NOUN
ejpam-3950	257	6	u	u	NOUN
ejpam-3950	257	7	(	(	PUNCT
ejpam-3950	257	8	α	α	NOUN
ejpam-3950	257	9	)	)	PUNCT
ejpam-3950	257	10	1	1	NUM
ejpam-3950	257	11	(	(	PUNCT
ejpam-3950	257	12	t	t	NOUN
ejpam-3950	257	13	)	)	PUNCT
ejpam-3950	257	14	=	=	SYM
ejpam-3950	257	15	mu1(t	mu1(t	PROPN
ejpam-3950	257	16	)	)	PUNCT
ejpam-3950	258	1	+	+	NUM
ejpam-3950	258	2	f	f	X
ejpam-3950	258	3	(	(	PUNCT
ejpam-3950	258	4	t	t	PROPN
ejpam-3950	258	5	)	)	PUNCT
ejpam-3950	258	6	.	.	PUNCT
ejpam-3950	259	1	which	which	PRON
ejpam-3950	259	2	is	be	AUX
ejpam-3950	259	3	has	have	VERB
ejpam-3950	259	4	a	a	DET
ejpam-3950	259	5	unique	unique	ADJ
ejpam-3950	259	6	solution	solution	NOUN
ejpam-3950	259	7	u1(t	u1(t	ADP
ejpam-3950	259	8	)	)	PUNCT
ejpam-3950	259	9	=	=	SYM
ejpam-3950	259	10	φ(t)c+	φ(t)c+	SYM
ejpam-3950	259	11	φ(t	φ(t	PROPN
ejpam-3950	259	12	)	)	PUNCT
ejpam-3950	259	13	∫	∫	PROPN
ejpam-3950	259	14	t	t	PROPN
ejpam-3950	259	15	0	0	NUM
ejpam-3950	259	16	φ−1(s)f	φ−1(s)f	PROPN
ejpam-3950	259	17	(	(	PUNCT
ejpam-3950	259	18	s	s	X
ejpam-3950	259	19	)	)	PUNCT
ejpam-3950	259	20	s1−α	s1−α	PROPN
ejpam-3950	259	21	ds	ds	NOUN
ejpam-3950	259	22	,	,	PUNCT
ejpam-3950	259	23	where	where	SCONJ
ejpam-3950	259	24	φ(t	φ(t	NOUN
ejpam-3950	259	25	)	)	PUNCT
ejpam-3950	259	26	is	be	AUX
ejpam-3950	259	27	the	the	DET
ejpam-3950	259	28	fundamental	fundamental	ADJ
ejpam-3950	259	29	matrix	matrix	NOUN
ejpam-3950	259	30	and	and	CCONJ
ejpam-3950	259	31	we	we	PRON
ejpam-3950	259	32	have	have	VERB
ejpam-3950	259	33	u2(t	u2(t	PRON
ejpam-3950	259	34	)	)	PUNCT
ejpam-3950	260	1	=	=	SYM
ejpam-3950	260	2	−ã−1a3u1(t)−	−ã−1a3u1(t)−	PROPN
ejpam-3950	260	3	f(t)ã−1	f(t)ã−1	ADV
ejpam-3950	260	4			NOUN
ejpam-3950	261	1	〈	〈	PROPN
ejpam-3950	261	2	z	z	PROPN
ejpam-3950	261	3	,	,	PUNCT
ejpam-3950	261	4	θr+1	θr+1	PROPN
ejpam-3950	261	5	〉	〉	NOUN
ejpam-3950	261	6	.	.	PUNCT
ejpam-3950	261	7	.	.	PUNCT
ejpam-3950	261	8	.	.	PUNCT
ejpam-3950	262	1	〈	〈	PROPN
ejpam-3950	262	2	z	z	PROPN
ejpam-3950	262	3	,	,	PUNCT
ejpam-3950	262	4	θn	θn	PROPN
ejpam-3950	262	5	〉	〉	PROPN
ejpam-3950	262	6			NOUN
ejpam-3950	262	7	.	.	PUNCT
ejpam-3950	263	1	f.	f.	PROPN
ejpam-3950	263	2	seddiki	seddiki	PROPN
ejpam-3950	263	3	,	,	PUNCT
ejpam-3950	263	4	m.	m.	NOUN
ejpam-3950	263	5	al	al	PROPN
ejpam-3950	263	6	horani	horani	PROPN
ejpam-3950	263	7	,	,	PUNCT
ejpam-3950	263	8	r.	r.	PROPN
ejpam-3950	263	9	khalil	khalil	PROPN
ejpam-3950	263	10	/	/	SYM
ejpam-3950	263	11	eur	eur	PROPN
ejpam-3950	263	12	.	.	PUNCT
ejpam-3950	264	1	j.	j.	PROPN
ejpam-3950	264	2	pure	pure	PROPN
ejpam-3950	264	3	appl	appl	PROPN
ejpam-3950	264	4	.	.	PROPN
ejpam-3950	264	5	math	math	PROPN
ejpam-3950	264	6	,	,	PUNCT
ejpam-3950	264	7	14	14	NUM
ejpam-3950	264	8	(	(	PUNCT
ejpam-3950	264	9	2	2	NUM
ejpam-3950	264	10	)	)	PUNCT
ejpam-3950	264	11	(	(	PUNCT
ejpam-3950	264	12	2021	2021	NUM
ejpam-3950	264	13	)	)	PUNCT
ejpam-3950	264	14	,	,	PUNCT
ejpam-3950	264	15	493	493	NUM
ejpam-3950	264	16	-	-	SYM
ejpam-3950	264	17	505	505	NUM
ejpam-3950	264	18	501	501	NUM
ejpam-3950	264	19	hence	hence	ADV
ejpam-3950	264	20	,	,	PUNCT
ejpam-3950	264	21	u(t	u(t	PROPN
ejpam-3950	264	22	)	)	PUNCT
ejpam-3950	264	23	=	=	PUNCT
ejpam-3950	265	1	[	[	PUNCT
ejpam-3950	265	2	u1(t	u1(t	NOUN
ejpam-3950	265	3	)	)	PUNCT
ejpam-3950	265	4	u2(t	u2(t	NOUN
ejpam-3950	265	5	)	)	PUNCT
ejpam-3950	265	6	]	]	PUNCT
ejpam-3950	265	7	t	t	PROPN
ejpam-3950	265	8			NOUN
ejpam-3950	265	9	θ1	θ1	NOUN
ejpam-3950	265	10	.	.	PUNCT
ejpam-3950	265	11	.	.	PUNCT
ejpam-3950	265	12	.	.	PUNCT
ejpam-3950	266	1	θn	θn	INTJ
ejpam-3950	266	2			NOUN
ejpam-3950	266	3	.	.	PUNCT
ejpam-3950	267	1	therefore	therefore	ADV
ejpam-3950	267	2	,	,	PUNCT
ejpam-3950	267	3	the	the	DET
ejpam-3950	267	4	problem	problem	NOUN
ejpam-3950	267	5	(	(	PUNCT
ejpam-3950	267	6	2	2	X
ejpam-3950	267	7	)	)	PUNCT
ejpam-3950	267	8	has	have	VERB
ejpam-3950	267	9	a	a	DET
ejpam-3950	267	10	unique	unique	ADJ
ejpam-3950	267	11	solution	solution	NOUN
ejpam-3950	267	12	.	.	PUNCT
ejpam-3950	268	1	3.2	3.2	NUM
ejpam-3950	268	2	.	.	PUNCT
ejpam-3950	268	3	inverse	inverse	NOUN
ejpam-3950	268	4	problem	problem	NOUN
ejpam-3950	268	5	case	case	NOUN
ejpam-3950	268	6	let	let	VERB
ejpam-3950	268	7	x	x	PUNCT
ejpam-3950	268	8	=	=	PRON
ejpam-3950	268	9	`	`	PUNCT
ejpam-3950	268	10	2	2	NUM
ejpam-3950	268	11	be	be	AUX
ejpam-3950	268	12	the	the	DET
ejpam-3950	268	13	hilbert	hilbert	NOUN
ejpam-3950	268	14	space	space	NOUN
ejpam-3950	268	15	.	.	PUNCT
ejpam-3950	269	1	let	let	VERB
ejpam-3950	269	2	a	a	DET
ejpam-3950	269	3	:	:	PUNCT
ejpam-3950	269	4	dom(a	dom(a	PROPN
ejpam-3950	269	5	)	)	PUNCT
ejpam-3950	269	6	⊆	⊆	NUM
ejpam-3950	269	7	`	`	PUNCT
ejpam-3950	269	8	2	2	NUM
ejpam-3950	269	9	→	→	SYM
ejpam-3950	269	10	`	`	PUNCT
ejpam-3950	269	11	2	2	NUM
ejpam-3950	269	12	,	,	PUNCT
ejpam-3950	269	13	b	b	NOUN
ejpam-3950	269	14	:	:	PUNCT
ejpam-3950	269	15	dom(b	dom(b	PROPN
ejpam-3950	269	16	)	)	PUNCT
ejpam-3950	269	17	⊆	⊆	NUM
ejpam-3950	269	18	`	`	PUNCT
ejpam-3950	269	19	2	2	NUM
ejpam-3950	269	20	→	→	SYM
ejpam-3950	269	21	`	`	PUNCT
ejpam-3950	269	22	2	2	NUM
ejpam-3950	269	23	be	be	AUX
ejpam-3950	269	24	two	two	NUM
ejpam-3950	269	25	densely	densely	ADV
ejpam-3950	269	26	defined	define	VERB
ejpam-3950	269	27	linear	linear	NOUN
ejpam-3950	269	28	operators	operator	NOUN
ejpam-3950	269	29	on	on	ADP
ejpam-3950	269	30	`	`	PUNCT
ejpam-3950	269	31	2	2	NUM
ejpam-3950	269	32	,	,	PUNCT
ejpam-3950	269	33	where	where	SCONJ
ejpam-3950	269	34	domains	domain	NOUN
ejpam-3950	269	35	of	of	ADP
ejpam-3950	269	36	a	a	PRON
ejpam-3950	269	37	and	and	CCONJ
ejpam-3950	269	38	b	b	NOUN
ejpam-3950	269	39	contain	contain	VERB
ejpam-3950	269	40	the	the	DET
ejpam-3950	269	41	elements	element	NOUN
ejpam-3950	269	42	of	of	ADP
ejpam-3950	269	43	the	the	DET
ejpam-3950	269	44	natural	natural	ADJ
ejpam-3950	269	45	basis	basis	NOUN
ejpam-3950	269	46	of	of	ADP
ejpam-3950	269	47	`	`	PUNCT
ejpam-3950	269	48	2	2	X
ejpam-3950	269	49	.	.	X
ejpam-3950	269	50	consider	consider	VERB
ejpam-3950	269	51	the	the	DET
ejpam-3950	269	52	two	two	NUM
ejpam-3950	269	53	inverse	inverse	NOUN
ejpam-3950	269	54	problems	problem	NOUN
ejpam-3950	269	55	(	(	PUNCT
ejpam-3950	269	56	p3	p3	PROPN
ejpam-3950	269	57	)	)	PUNCT
ejpam-3950	269	58	and	and	CCONJ
ejpam-3950	269	59	(	(	PUNCT
ejpam-3950	269	60	p4	p4	ADJ
ejpam-3950	269	61	)	)	PUNCT
ejpam-3950	269	62	respectively	respectively	ADV
ejpam-3950	269	63	{	{	PUNCT
ejpam-3950	269	64	u(α)(t	u(α)(t	NOUN
ejpam-3950	269	65	)	)	PUNCT
ejpam-3950	269	66	=	=	NOUN
ejpam-3950	269	67	au(t	au(t	PRON
ejpam-3950	269	68	)	)	PUNCT
ejpam-3950	270	1	+	+	CCONJ
ejpam-3950	270	2	f(t	f(t	NOUN
ejpam-3950	270	3	)	)	PUNCT
ejpam-3950	270	4	u(0	u(0	NOUN
ejpam-3950	270	5	)	)	PUNCT
ejpam-3950	270	6	=	=	SYM
ejpam-3950	271	1	x0	x0	PROPN
ejpam-3950	271	2	{	{	PUNCT
ejpam-3950	271	3	bu(α)(t	bu(α)(t	PROPN
ejpam-3950	271	4	)	)	PUNCT
ejpam-3950	271	5	=	=	NOUN
ejpam-3950	271	6	au(t	au(t	PRON
ejpam-3950	271	7	)	)	PUNCT
ejpam-3950	272	1	+	+	CCONJ
ejpam-3950	272	2	f(t	f(t	NOUN
ejpam-3950	272	3	)	)	PUNCT
ejpam-3950	272	4	u(0	u(0	NOUN
ejpam-3950	272	5	)	)	PUNCT
ejpam-3950	272	6	=	=	SYM
ejpam-3950	273	1	x0	x0	PROPN
ejpam-3950	273	2	where	where	SCONJ
ejpam-3950	273	3	u(α	u(α	NOUN
ejpam-3950	273	4	)	)	PUNCT
ejpam-3950	273	5	∈	∈	PROPN
ejpam-3950	273	6	c(i	c(i	NOUN
ejpam-3950	273	7	,	,	PUNCT
ejpam-3950	273	8	x	x	NOUN
ejpam-3950	273	9	)	)	PUNCT
ejpam-3950	273	10	,	,	PUNCT
ejpam-3950	273	11	f	f	PROPN
ejpam-3950	273	12	∈	∈	PROPN
ejpam-3950	273	13	c(i	c(i	PROPN
ejpam-3950	273	14	,	,	PUNCT
ejpam-3950	273	15	x	x	NOUN
ejpam-3950	273	16	)	)	PUNCT
ejpam-3950	273	17	.	.	PUNCT
ejpam-3950	274	1	in	in	ADP
ejpam-3950	274	2	this	this	DET
ejpam-3950	274	3	section	section	NOUN
ejpam-3950	274	4	we	we	PRON
ejpam-3950	274	5	look	look	VERB
ejpam-3950	274	6	for	for	ADP
ejpam-3950	274	7	a	a	DET
ejpam-3950	274	8	solution	solution	NOUN
ejpam-3950	274	9	to	to	ADP
ejpam-3950	274	10	problems	problem	NOUN
ejpam-3950	274	11	(	(	PUNCT
ejpam-3950	274	12	p3	p3	PROPN
ejpam-3950	274	13	)	)	PUNCT
ejpam-3950	274	14	and	and	CCONJ
ejpam-3950	274	15	(	(	PUNCT
ejpam-3950	274	16	p4	p4	ADJ
ejpam-3950	274	17	)	)	PUNCT
ejpam-3950	274	18	among	among	ADP
ejpam-3950	274	19	finite	finite	PROPN
ejpam-3950	274	20	rank	rank	NOUN
ejpam-3950	274	21	functions	function	NOUN
ejpam-3950	274	22	of	of	ADP
ejpam-3950	274	23	the	the	DET
ejpam-3950	274	24	form	form	NOUN
ejpam-3950	274	25	u(t	u(t	NOUN
ejpam-3950	274	26	)	)	PUNCT
ejpam-3950	274	27	=	=	SYM
ejpam-3950	275	1	∑n	∑n	PROPN
ejpam-3950	275	2	i=1	i=1	PRON
ejpam-3950	275	3	ui(t)δi	ui(t)δi	ADJ
ejpam-3950	275	4	,	,	PUNCT
ejpam-3950	275	5	and	and	CCONJ
ejpam-3950	275	6	f(t	f(t	NOUN
ejpam-3950	275	7	)	)	PUNCT
ejpam-3950	276	1	=	=	SYM
ejpam-3950	277	1	∑n	∑n	PROPN
ejpam-3950	277	2	i=1	i=1	PROPN
ejpam-3950	277	3	fi(t)δi	fi(t)δi	PROPN
ejpam-3950	277	4	,	,	PUNCT
ejpam-3950	277	5	where	where	SCONJ
ejpam-3950	277	6	,	,	PUNCT
ejpam-3950	277	7	u	u	PROPN
ejpam-3950	277	8	(	(	PUNCT
ejpam-3950	277	9	α	α	NOUN
ejpam-3950	277	10	)	)	PUNCT
ejpam-3950	277	11	i	i	PRON
ejpam-3950	277	12	∈	∈	PROPN
ejpam-3950	277	13	c(i	c(i	PROPN
ejpam-3950	277	14	)	)	PUNCT
ejpam-3950	277	15	and	and	CCONJ
ejpam-3950	277	16	fi	fi	NOUN
ejpam-3950	277	17	∈	∈	NOUN
ejpam-3950	277	18	c(i	c(i	PROPN
ejpam-3950	277	19	)	)	PUNCT
ejpam-3950	277	20	,	,	PUNCT
ejpam-3950	277	21	for	for	ADP
ejpam-3950	277	22	i	i	PROPN
ejpam-3950	277	23	=	=	SYM
ejpam-3950	277	24	1	1	NUM
ejpam-3950	277	25	,	,	PUNCT
ejpam-3950	277	26	2	2	NUM
ejpam-3950	277	27	,	,	PUNCT
ejpam-3950	277	28	...	...	PUNCT
ejpam-3950	278	1	n.	n.	NOUN
ejpam-3950	278	2	here	here	ADV
ejpam-3950	278	3	we	we	PRON
ejpam-3950	278	4	use	use	VERB
ejpam-3950	278	5	a	a	DET
ejpam-3950	278	6	condition	condition	NOUN
ejpam-3950	278	7	similar	similar	ADJ
ejpam-3950	278	8	to	to	ADP
ejpam-3950	278	9	that	that	PRON
ejpam-3950	278	10	used	use	VERB
ejpam-3950	278	11	in	in	ADP
ejpam-3950	278	12	[	[	X
ejpam-3950	278	13	22	22	NUM
ejpam-3950	278	14	]	]	PUNCT
ejpam-3950	278	15	.	.	PUNCT
ejpam-3950	279	1	theorem	theorem	ADJ
ejpam-3950	279	2	6	6	NUM
ejpam-3950	279	3	.	.	PUNCT
ejpam-3950	280	1	in	in	ADP
ejpam-3950	280	2	problem	problem	NOUN
ejpam-3950	280	3	(	(	PUNCT
ejpam-3950	280	4	p3	p3	PROPN
ejpam-3950	280	5	)	)	PUNCT
ejpam-3950	280	6	,	,	PUNCT
ejpam-3950	280	7	let	let	VERB
ejpam-3950	280	8	u(t	u(t	NOUN
ejpam-3950	280	9	)	)	PUNCT
ejpam-3950	280	10	=	=	SYM
ejpam-3950	281	1	∑n	∑n	PROPN
ejpam-3950	281	2	i=1	i=1	PRON
ejpam-3950	281	3	ui(t)δi	ui(t)δi	ADJ
ejpam-3950	281	4	,	,	PUNCT
ejpam-3950	281	5	and	and	CCONJ
ejpam-3950	281	6	f(t	f(t	NOUN
ejpam-3950	281	7	)	)	PUNCT
ejpam-3950	282	1	=	=	SYM
ejpam-3950	283	1	∑n	∑n	PROPN
ejpam-3950	283	2	i=1	i=1	NOUN
ejpam-3950	283	3	fi(t)δi	fi(t)δi	PROPN
ejpam-3950	284	1	where	where	SCONJ
ejpam-3950	284	2	,	,	PUNCT
ejpam-3950	284	3	u	u	PROPN
ejpam-3950	284	4	(	(	PUNCT
ejpam-3950	284	5	α	α	NOUN
ejpam-3950	284	6	)	)	PUNCT
ejpam-3950	284	7	i	i	PRON
ejpam-3950	284	8	∈	∈	PROPN
ejpam-3950	284	9	c(i	c(i	PROPN
ejpam-3950	284	10	)	)	PUNCT
ejpam-3950	284	11	and	and	CCONJ
ejpam-3950	284	12	fi	fi	NOUN
ejpam-3950	284	13	∈	∈	NOUN
ejpam-3950	284	14	c(i	c(i	PROPN
ejpam-3950	284	15	)	)	PUNCT
ejpam-3950	284	16	,	,	PUNCT
ejpam-3950	284	17	for	for	ADP
ejpam-3950	284	18	i	i	PROPN
ejpam-3950	284	19	=	=	SYM
ejpam-3950	284	20	1	1	NUM
ejpam-3950	284	21	,	,	PUNCT
ejpam-3950	284	22	2	2	NUM
ejpam-3950	284	23	,	,	PUNCT
ejpam-3950	284	24	...	...	PUNCT
ejpam-3950	284	25	n.	n.	PROPN
ejpam-3950	284	26	assume	assume	VERB
ejpam-3950	284	27	the	the	DET
ejpam-3950	284	28	following	follow	VERB
ejpam-3950	284	29	two	two	NUM
ejpam-3950	284	30	condition	condition	NOUN
ejpam-3950	284	31	are	be	AUX
ejpam-3950	284	32	satisfied	satisfied	ADJ
ejpam-3950	284	33	:	:	PUNCT
ejpam-3950	284	34	1)there	1)there	NUM
ejpam-3950	284	35	exist	exist	VERB
ejpam-3950	284	36	,	,	PUNCT
ejpam-3950	284	37	x	x	SYM
ejpam-3950	284	38	∈	∈	NOUN
ejpam-3950	284	39	`	`	PUNCT
ejpam-3950	284	40	2	2	NUM
ejpam-3950	284	41	such	such	ADJ
ejpam-3950	284	42	that	that	SCONJ
ejpam-3950	284	43	〈	〈	PROPN
ejpam-3950	284	44	ui(t)δi	ui(t)δi	ADJ
ejpam-3950	284	45	,	,	PUNCT
ejpam-3950	284	46	x	x	NOUN
ejpam-3950	284	47	〉	〉	NOUN
ejpam-3950	284	48	=	=	SYM
ejpam-3950	284	49	gi(t	gi(t	X
ejpam-3950	284	50	)	)	PUNCT
ejpam-3950	284	51	where	where	SCONJ
ejpam-3950	284	52	g	g	PROPN
ejpam-3950	284	53	(	(	PUNCT
ejpam-3950	284	54	α	α	NOUN
ejpam-3950	284	55	)	)	PUNCT
ejpam-3950	284	56	i	i	PRON
ejpam-3950	284	57	∈	∈	PROPN
ejpam-3950	284	58	c(i	c(i	PROPN
ejpam-3950	284	59	)	)	PUNCT
ejpam-3950	284	60	and	and	CCONJ
ejpam-3950	284	61	〈	〈	PROPN
ejpam-3950	284	62	δi	δi	PRON
ejpam-3950	284	63	,	,	PUNCT
ejpam-3950	284	64	x	x	PROPN
ejpam-3950	284	65	〉	〉	NOUN
ejpam-3950	284	66	6=	6=	NUM
ejpam-3950	284	67	0	0	NUM
ejpam-3950	284	68	.	.	NOUN
ejpam-3950	284	69	2	2	NUM
ejpam-3950	284	70	)	)	PUNCT
ejpam-3950	284	71	a	a	PRON
ejpam-3950	284	72	is	be	AUX
ejpam-3950	284	73	diagonal	diagonal	ADJ
ejpam-3950	284	74	with	with	ADP
ejpam-3950	284	75	respect	respect	NOUN
ejpam-3950	284	76	to	to	ADP
ejpam-3950	284	77	the	the	DET
ejpam-3950	284	78	basis	basis	NOUN
ejpam-3950	284	79	{	{	PUNCT
ejpam-3950	284	80	δi}ni=1	δi}ni=1	PROPN
ejpam-3950	284	81	.	.	PUNCT
ejpam-3950	285	1	that	that	PRON
ejpam-3950	285	2	is	be	AUX
ejpam-3950	285	3	,	,	PUNCT
ejpam-3950	285	4	aδi	aδi	NOUN
ejpam-3950	285	5	=	=	PUNCT
ejpam-3950	285	6	λiδi	λiδi	ADJ
ejpam-3950	285	7	for	for	ADP
ejpam-3950	285	8	all	all	DET
ejpam-3950	285	9	i	i	PRON
ejpam-3950	285	10	=	=	NOUN
ejpam-3950	285	11	1	1	NUM
ejpam-3950	285	12	,	,	PUNCT
ejpam-3950	285	13	...	...	PUNCT
ejpam-3950	285	14	,	,	PUNCT
ejpam-3950	285	15	n.	n.	PROPN
ejpam-3950	285	16	then	then	ADV
ejpam-3950	285	17	the	the	DET
ejpam-3950	285	18	problem	problem	NOUN
ejpam-3950	285	19	(	(	PUNCT
ejpam-3950	285	20	p3	p3	PROPN
ejpam-3950	285	21	)	)	PUNCT
ejpam-3950	285	22	has	have	VERB
ejpam-3950	285	23	a	a	DET
ejpam-3950	285	24	unique	unique	ADJ
ejpam-3950	285	25	solution	solution	NOUN
ejpam-3950	285	26	.	.	PUNCT
ejpam-3950	286	1	proof	proof	NOUN
ejpam-3950	286	2	.	.	PUNCT
ejpam-3950	287	1	substitute	substitute	PROPN
ejpam-3950	287	2	u(t	u(t	PROPN
ejpam-3950	287	3	)	)	PUNCT
ejpam-3950	288	1	=	=	SYM
ejpam-3950	289	1	∑n	∑n	PROPN
ejpam-3950	289	2	i=1	i=1	PRON
ejpam-3950	289	3	ui(t)δi	ui(t)δi	ADJ
ejpam-3950	289	4	,	,	PUNCT
ejpam-3950	289	5	and	and	CCONJ
ejpam-3950	289	6	f(t	f(t	NOUN
ejpam-3950	289	7	)	)	PUNCT
ejpam-3950	290	1	=	=	SYM
ejpam-3950	291	1	∑n	∑n	PROPN
ejpam-3950	291	2	i=1	i=1	PROPN
ejpam-3950	291	3	fi(t)δi	fi(t)δi	PROPN
ejpam-3950	291	4	,	,	PUNCT
ejpam-3950	291	5	in	in	ADP
ejpam-3950	291	6	(	(	PUNCT
ejpam-3950	291	7	p3	p3	PROPN
ejpam-3950	291	8	)	)	PUNCT
ejpam-3950	291	9	,	,	PUNCT
ejpam-3950	291	10	we	we	PRON
ejpam-3950	291	11	get	get	VERB
ejpam-3950	291	12	n∑	n∑	PROPN
ejpam-3950	291	13	i=1	i=1	PROPN
ejpam-3950	291	14	u	u	PROPN
ejpam-3950	291	15	(	(	PUNCT
ejpam-3950	291	16	α	α	NOUN
ejpam-3950	291	17	)	)	PUNCT
ejpam-3950	291	18	i	i	PRON
ejpam-3950	291	19	(	(	PUNCT
ejpam-3950	291	20	t)δi	t)δi	PROPN
ejpam-3950	291	21	=	=	SYM
ejpam-3950	292	1	n∑	n∑	PROPN
ejpam-3950	292	2	i=1	i=1	PROPN
ejpam-3950	293	1	ui(t)aδi	ui(t)aδi	PROPN
ejpam-3950	294	1	+	+	CCONJ
ejpam-3950	294	2	n∑	n∑	ADJ
ejpam-3950	294	3	i=1	i=1	PROPN
ejpam-3950	294	4	fi(t)δi	fi(t)δi	PROPN
ejpam-3950	294	5	.	.	PUNCT
ejpam-3950	295	1	since	since	SCONJ
ejpam-3950	295	2	a	a	PRON
ejpam-3950	295	3	is	be	AUX
ejpam-3950	295	4	diagonal	diagonal	ADJ
ejpam-3950	295	5	with	with	ADP
ejpam-3950	295	6	respect	respect	NOUN
ejpam-3950	295	7	to	to	ADP
ejpam-3950	295	8	{	{	PUNCT
ejpam-3950	295	9	δi}ni=1	δi}ni=1	PROPN
ejpam-3950	295	10	,	,	PUNCT
ejpam-3950	295	11	we	we	PRON
ejpam-3950	295	12	have	have	VERB
ejpam-3950	295	13	n∑	n∑	PROPN
ejpam-3950	295	14	i=1	i=1	PROPN
ejpam-3950	295	15	u	u	PROPN
ejpam-3950	295	16	(	(	PUNCT
ejpam-3950	295	17	α	α	NOUN
ejpam-3950	295	18	)	)	PUNCT
ejpam-3950	295	19	i	i	PRON
ejpam-3950	295	20	(	(	PUNCT
ejpam-3950	295	21	t)δi	t)δi	PROPN
ejpam-3950	296	1	=	=	SYM
ejpam-3950	296	2	n∑	n∑	PROPN
ejpam-3950	296	3	i=1	i=1	PRON
ejpam-3950	297	1	λiui(t)δi	λiui(t)δi	X
ejpam-3950	298	1	+	+	NUM
ejpam-3950	298	2	n∑	n∑	ADJ
ejpam-3950	298	3	i=1	i=1	X
ejpam-3950	298	4	fi(t)δi	fi(t)δi	PROPN
ejpam-3950	298	5	.	.	PUNCT
ejpam-3950	299	1	(	(	PUNCT
ejpam-3950	299	2	17	17	NUM
ejpam-3950	299	3	)	)	PUNCT
ejpam-3950	299	4	taking	take	VERB
ejpam-3950	299	5	the	the	DET
ejpam-3950	299	6	inner	inner	ADJ
ejpam-3950	299	7	product	product	NOUN
ejpam-3950	299	8	of	of	ADP
ejpam-3950	299	9	δj	δj	NOUN
ejpam-3950	299	10	with	with	ADP
ejpam-3950	299	11	both	both	DET
ejpam-3950	299	12	sides	side	NOUN
ejpam-3950	299	13	of	of	ADP
ejpam-3950	299	14	equation	equation	NOUN
ejpam-3950	299	15	(	(	PUNCT
ejpam-3950	299	16	17	17	NUM
ejpam-3950	299	17	)	)	PUNCT
ejpam-3950	299	18	,	,	PUNCT
ejpam-3950	299	19	we	we	PRON
ejpam-3950	299	20	obtain	obtain	VERB
ejpam-3950	299	21	u	u	NOUN
ejpam-3950	299	22	(	(	PUNCT
ejpam-3950	299	23	α	α	NOUN
ejpam-3950	299	24	)	)	PUNCT
ejpam-3950	299	25	j	j	PROPN
ejpam-3950	299	26	(	(	PUNCT
ejpam-3950	299	27	t	t	PROPN
ejpam-3950	299	28	)	)	PUNCT
ejpam-3950	300	1	=	=	SYM
ejpam-3950	300	2	λjuj(t	λjuj(t	PROPN
ejpam-3950	300	3	)	)	PUNCT
ejpam-3950	300	4	+	+	NUM
ejpam-3950	300	5	fj(t	fj(t	NUM
ejpam-3950	300	6	)	)	PUNCT
ejpam-3950	300	7	.	.	PUNCT
ejpam-3950	301	1	(	(	PUNCT
ejpam-3950	301	2	18	18	NUM
ejpam-3950	301	3	)	)	PUNCT
ejpam-3950	301	4	f.	f.	PROPN
ejpam-3950	301	5	seddiki	seddiki	PROPN
ejpam-3950	301	6	,	,	PUNCT
ejpam-3950	301	7	m.	m.	NOUN
ejpam-3950	301	8	al	al	PROPN
ejpam-3950	301	9	horani	horani	PROPN
ejpam-3950	301	10	,	,	PUNCT
ejpam-3950	301	11	r.	r.	PROPN
ejpam-3950	301	12	khalil	khalil	PROPN
ejpam-3950	301	13	/	/	SYM
ejpam-3950	301	14	eur	eur	PROPN
ejpam-3950	301	15	.	.	PUNCT
ejpam-3950	302	1	j.	j.	PROPN
ejpam-3950	302	2	pure	pure	PROPN
ejpam-3950	302	3	appl	appl	PROPN
ejpam-3950	302	4	.	.	PROPN
ejpam-3950	302	5	math	math	PROPN
ejpam-3950	302	6	,	,	PUNCT
ejpam-3950	302	7	14	14	NUM
ejpam-3950	302	8	(	(	PUNCT
ejpam-3950	302	9	2	2	NUM
ejpam-3950	302	10	)	)	PUNCT
ejpam-3950	302	11	(	(	PUNCT
ejpam-3950	302	12	2021	2021	NUM
ejpam-3950	302	13	)	)	PUNCT
ejpam-3950	302	14	,	,	PUNCT
ejpam-3950	302	15	493	493	NUM
ejpam-3950	302	16	-	-	SYM
ejpam-3950	302	17	505	505	NUM
ejpam-3950	302	18	502	502	NUM
ejpam-3950	302	19	multiplying	multiply	VERB
ejpam-3950	302	20	equation	equation	NOUN
ejpam-3950	302	21	(	(	PUNCT
ejpam-3950	302	22	18	18	NUM
ejpam-3950	302	23	)	)	PUNCT
ejpam-3950	302	24	by	by	ADP
ejpam-3950	302	25	δj	δj	ADJ
ejpam-3950	302	26	and	and	CCONJ
ejpam-3950	302	27	use	use	VERB
ejpam-3950	302	28	condition	condition	NOUN
ejpam-3950	302	29	(	(	PUNCT
ejpam-3950	302	30	1	1	NUM
ejpam-3950	302	31	)	)	PUNCT
ejpam-3950	302	32	,	,	PUNCT
ejpam-3950	302	33	we	we	PRON
ejpam-3950	302	34	obtain	obtain	VERB
ejpam-3950	302	35	g	g	PROPN
ejpam-3950	302	36	(	(	PUNCT
ejpam-3950	302	37	α	α	NOUN
ejpam-3950	302	38	)	)	PUNCT
ejpam-3950	302	39	j	j	PROPN
ejpam-3950	302	40	(	(	PUNCT
ejpam-3950	302	41	t	t	PROPN
ejpam-3950	302	42	)	)	PUNCT
ejpam-3950	303	1	=	=	SYM
ejpam-3950	303	2	λjgj(t	λjgj(t	PROPN
ejpam-3950	303	3	)	)	PUNCT
ejpam-3950	303	4	+	+	CCONJ
ejpam-3950	304	1	〈	〈	PROPN
ejpam-3950	304	2	fj(t)δj	fj(t)δj	NOUN
ejpam-3950	304	3	,	,	PUNCT
ejpam-3950	304	4	x	x	NOUN
ejpam-3950	304	5	〉	〉	NOUN
ejpam-3950	304	6	.	.	PUNCT
ejpam-3950	305	1	thus	thus	ADV
ejpam-3950	305	2	,	,	PUNCT
ejpam-3950	305	3	we	we	PRON
ejpam-3950	305	4	have	have	AUX
ejpam-3950	305	5	fj(t	fj(t	VERB
ejpam-3950	305	6	)	)	PUNCT
ejpam-3950	306	1	=	=	SYM
ejpam-3950	306	2	g	g	PROPN
ejpam-3950	306	3	(	(	PUNCT
ejpam-3950	306	4	α	α	NOUN
ejpam-3950	306	5	)	)	PUNCT
ejpam-3950	306	6	j	j	PROPN
ejpam-3950	306	7	(	(	PUNCT
ejpam-3950	306	8	t)−	t)−	PROPN
ejpam-3950	306	9	λjgj(t	λjgj(t	PROPN
ejpam-3950	306	10	)	)	PUNCT
ejpam-3950	306	11	〈	〈	NOUN
ejpam-3950	306	12	δj	δj	NOUN
ejpam-3950	306	13	,	,	PUNCT
ejpam-3950	306	14	x	x	X
ejpam-3950	306	15	〉	〉	NOUN
ejpam-3950	306	16	.	.	PUNCT
ejpam-3950	307	1	hence	hence	ADV
ejpam-3950	307	2	,	,	PUNCT
ejpam-3950	307	3	fj(t	fj(t	PROPN
ejpam-3950	307	4	)	)	PUNCT
ejpam-3950	307	5	is	be	AUX
ejpam-3950	307	6	determined	determine	VERB
ejpam-3950	307	7	uniquely	uniquely	ADV
ejpam-3950	307	8	for	for	ADP
ejpam-3950	307	9	j	j	PROPN
ejpam-3950	307	10	=	=	SYM
ejpam-3950	307	11	1	1	NUM
ejpam-3950	307	12	,	,	PUNCT
ejpam-3950	307	13	...	...	PUNCT
ejpam-3950	308	1	n	n	CCONJ
ejpam-3950	308	2	and	and	CCONJ
ejpam-3950	308	3	thus	thus	ADV
ejpam-3950	308	4	f(t	f(t	NOUN
ejpam-3950	308	5	)	)	PUNCT
ejpam-3950	308	6	is	be	AUX
ejpam-3950	308	7	determined	determine	VERB
ejpam-3950	308	8	uniquely	uniquely	ADV
ejpam-3950	308	9	.	.	PUNCT
ejpam-3950	309	1	now	now	ADV
ejpam-3950	309	2	to	to	PART
ejpam-3950	309	3	find	find	VERB
ejpam-3950	309	4	u(t	u(t	NOUN
ejpam-3950	309	5	)	)	PUNCT
ejpam-3950	309	6	.	.	PUNCT
ejpam-3950	310	1	since	since	SCONJ
ejpam-3950	310	2	f(t	f(t	PROPN
ejpam-3950	310	3	)	)	PUNCT
ejpam-3950	310	4	is	be	AUX
ejpam-3950	310	5	determined	determine	VERB
ejpam-3950	310	6	,	,	PUNCT
ejpam-3950	310	7	then	then	ADV
ejpam-3950	310	8	we	we	PRON
ejpam-3950	310	9	have	have	VERB
ejpam-3950	310	10	uj(t	uj(t	PUNCT
ejpam-3950	310	11	)	)	PUNCT
ejpam-3950	311	1	=	=	PUNCT
ejpam-3950	312	1	uj(0)eλj	uj(0)eλj	NUM
ejpam-3950	312	2	tα	tα	VERB
ejpam-3950	312	3	α	α	NOUN
ejpam-3950	313	1	+	+	CCONJ
ejpam-3950	313	2	eλj	eλj	PROPN
ejpam-3950	313	3	tα	tα	NUM
ejpam-3950	313	4	α	α	NUM
ejpam-3950	313	5	∫	∫	PROPN
ejpam-3950	314	1	t	t	PROPN
ejpam-3950	314	2	0	0	NUM
ejpam-3950	315	1	e−λj	e−λj	PRON
ejpam-3950	315	2	sα	sα	PROPN
ejpam-3950	315	3	α	α	PROPN
ejpam-3950	315	4	fj(s	fj(s	PUNCT
ejpam-3950	315	5	)	)	PUNCT
ejpam-3950	316	1	s1−α	s1−α	PROPN
ejpam-3950	316	2	ds	ds	NOUN
ejpam-3950	316	3	.	.	PUNCT
ejpam-3950	316	4	consequently	consequently	ADV
ejpam-3950	316	5	,	,	PUNCT
ejpam-3950	316	6	the	the	DET
ejpam-3950	316	7	problem	problem	NOUN
ejpam-3950	316	8	(	(	PUNCT
ejpam-3950	316	9	p3	p3	PROPN
ejpam-3950	316	10	)	)	PUNCT
ejpam-3950	316	11	has	have	VERB
ejpam-3950	316	12	a	a	DET
ejpam-3950	316	13	unique	unique	ADJ
ejpam-3950	316	14	solution	solution	NOUN
ejpam-3950	316	15	.	.	PUNCT
ejpam-3950	317	1	now	now	ADV
ejpam-3950	317	2	,	,	PUNCT
ejpam-3950	317	3	to	to	PART
ejpam-3950	317	4	solve	solve	VERB
ejpam-3950	317	5	problem	problem	NOUN
ejpam-3950	317	6	(	(	PUNCT
ejpam-3950	317	7	p4	p4	ADJ
ejpam-3950	317	8	)	)	PUNCT
ejpam-3950	317	9	we	we	PRON
ejpam-3950	317	10	need	need	VERB
ejpam-3950	317	11	to	to	PART
ejpam-3950	317	12	assume	assume	VERB
ejpam-3950	317	13	the	the	DET
ejpam-3950	317	14	following	follow	VERB
ejpam-3950	317	15	satisfy	satisfy	NOUN
ejpam-3950	317	16	:	:	PUNCT
ejpam-3950	317	17	assumption	assumption	NOUN
ejpam-3950	317	18	1	1	NUM
ejpam-3950	317	19	.	.	PUNCT
ejpam-3950	317	20	bn	bn	NOUN
ejpam-3950	318	1	=	=	SYM
ejpam-3950	318	2	b	b	PROPN
ejpam-3950	318	3	|[δ1,	|[δ1,	NOUN
ejpam-3950	318	4	...	...	PUNCT
ejpam-3950	318	5	,δn	,δn	PUNCT
ejpam-3950	318	6	]	]	PUNCT
ejpam-3950	318	7	is	be	AUX
ejpam-3950	318	8	orthogonally	orthogonally	ADV
ejpam-3950	318	9	diagonalizable	diagonalizable	ADJ
ejpam-3950	318	10	linear	linear	ADJ
ejpam-3950	318	11	operator	operator	NOUN
ejpam-3950	318	12	with	with	ADP
ejpam-3950	318	13	respect	respect	NOUN
ejpam-3950	318	14	to	to	ADP
ejpam-3950	318	15	the	the	DET
ejpam-3950	318	16	orthonormal	orthonormal	ADJ
ejpam-3950	318	17	basis	basis	NOUN
ejpam-3950	318	18	{	{	PUNCT
ejpam-3950	318	19	θ1	θ1	NOUN
ejpam-3950	318	20	,	,	PUNCT
ejpam-3950	318	21	...	...	PUNCT
ejpam-3950	318	22	,	,	PUNCT
ejpam-3950	318	23	θn	θn	ADP
ejpam-3950	318	24	}	}	PUNCT
ejpam-3950	318	25	and	and	CCONJ
ejpam-3950	318	26	corresponding	corresponding	ADJ
ejpam-3950	318	27	eigenvalues	eigenvalue	NOUN
ejpam-3950	318	28	λ1	λ1	ADJ
ejpam-3950	318	29	,	,	PUNCT
ejpam-3950	318	30	...	...	PUNCT
ejpam-3950	318	31	,	,	PUNCT
ejpam-3950	318	32	λn	λn	ADP
ejpam-3950	318	33	such	such	ADJ
ejpam-3950	318	34	that	that	SCONJ
ejpam-3950	318	35	an	an	DET
ejpam-3950	318	36	|ker(bn	|ker(bn	NOUN
ejpam-3950	318	37	)	)	PUNCT
ejpam-3950	318	38	is	be	AUX
ejpam-3950	318	39	invertible	invertible	ADJ
ejpam-3950	318	40	,	,	PUNCT
ejpam-3950	319	1	where	where	SCONJ
ejpam-3950	319	2	an	an	DET
ejpam-3950	319	3	=	=	X
ejpam-3950	319	4	a	a	DET
ejpam-3950	319	5	|[δ1,	|[δ1,	NOUN
ejpam-3950	319	6	...	...	PUNCT
ejpam-3950	319	7	,δn	,δn	PUNCT
ejpam-3950	319	8	]	]	X
ejpam-3950	319	9	.	.	PUNCT
ejpam-3950	320	1	assumption	assumption	NOUN
ejpam-3950	320	2	2	2	NUM
ejpam-3950	320	3	.	.	PUNCT
ejpam-3950	321	1	an	an	PRON
ejpam-3950	321	2	is	be	AUX
ejpam-3950	321	3	diagonal	diagonal	ADJ
ejpam-3950	321	4	with	with	ADP
ejpam-3950	321	5	respect	respect	NOUN
ejpam-3950	321	6	to	to	ADP
ejpam-3950	321	7	{	{	PUNCT
ejpam-3950	321	8	θ1	θ1	NOUN
ejpam-3950	321	9	,	,	PUNCT
ejpam-3950	321	10	...	...	PUNCT
ejpam-3950	321	11	,	,	PUNCT
ejpam-3950	321	12	θn	θn	ADP
ejpam-3950	321	13	}	}	PUNCT
ejpam-3950	321	14	ie	ie	ADJ
ejpam-3950	321	15	anθj	anθj	NOUN
ejpam-3950	321	16	=	=	PRON
ejpam-3950	321	17	µjθj	µjθj	VERB
ejpam-3950	321	18	for	for	ADP
ejpam-3950	321	19	j	j	PROPN
ejpam-3950	321	20	=	=	SYM
ejpam-3950	321	21	1	1	NUM
ejpam-3950	321	22	,	,	PUNCT
ejpam-3950	321	23	...	...	PUNCT
ejpam-3950	321	24	,	,	PUNCT
ejpam-3950	321	25	n.	n.	PROPN
ejpam-3950	321	26	now	now	ADV
ejpam-3950	321	27	,	,	PUNCT
ejpam-3950	321	28	let	let	VERB
ejpam-3950	321	29	u(t	u(t	NOUN
ejpam-3950	321	30	)	)	PUNCT
ejpam-3950	321	31	=	=	SYM
ejpam-3950	322	1	∑n	∑n	PROPN
ejpam-3950	322	2	i=1	i=1	PROPN
ejpam-3950	322	3	ui(t)θi	ui(t)θi	ADJ
ejpam-3950	322	4	assumption	assumption	NOUN
ejpam-3950	322	5	3	3	X
ejpam-3950	322	6	.	.	X
ejpam-3950	322	7	there	there	PRON
ejpam-3950	322	8	exist	exist	VERB
ejpam-3950	322	9	,	,	PUNCT
ejpam-3950	322	10	x	x	PUNCT
ejpam-3950	322	11	∈	∈	NOUN
ejpam-3950	322	12	`	`	PUNCT
ejpam-3950	322	13	2	2	NUM
ejpam-3950	322	14	such	such	ADJ
ejpam-3950	322	15	that	that	SCONJ
ejpam-3950	322	16	〈	〈	PROPN
ejpam-3950	322	17	ui(t)θi	ui(t)θi	PROPN
ejpam-3950	322	18	,	,	PUNCT
ejpam-3950	322	19	x	x	NOUN
ejpam-3950	322	20	〉	〉	NOUN
ejpam-3950	322	21	=	=	SYM
ejpam-3950	322	22	gi(t	gi(t	X
ejpam-3950	322	23	)	)	PUNCT
ejpam-3950	322	24	where	where	SCONJ
ejpam-3950	322	25	g	g	PROPN
ejpam-3950	322	26	(	(	PUNCT
ejpam-3950	322	27	α	α	NOUN
ejpam-3950	322	28	)	)	PUNCT
ejpam-3950	322	29	i	i	PRON
ejpam-3950	322	30	∈	∈	PROPN
ejpam-3950	322	31	c(i	c(i	PROPN
ejpam-3950	322	32	)	)	PUNCT
ejpam-3950	322	33	.	.	PUNCT
ejpam-3950	323	1	assumption	assumption	NOUN
ejpam-3950	323	2	4	4	NUM
ejpam-3950	323	3	.	.	PUNCT
ejpam-3950	324	1	m	m	VERB
ejpam-3950	324	2	=	=	PUNCT
ejpam-3950	325	1	[	[	X
ejpam-3950	325	2	〈	〈	PROPN
ejpam-3950	325	3	δi	δi	ADP
ejpam-3950	325	4	,	,	PUNCT
ejpam-3950	325	5	θj〉〈θj	θj〉〈θj	NOUN
ejpam-3950	325	6	,	,	PUNCT
ejpam-3950	325	7	x〉]i	x〉]i	PROPN
ejpam-3950	325	8	,	,	PUNCT
ejpam-3950	325	9	j=1,	j=1,	NOUN
ejpam-3950	325	10	...	...	PUNCT
ejpam-3950	325	11	,nis	,nis	PUNCT
ejpam-3950	325	12	invertible	invertible	ADJ
ejpam-3950	325	13	.	.	PUNCT
ejpam-3950	326	1	theorem	theorem	VERB
ejpam-3950	326	2	7	7	NUM
ejpam-3950	326	3	.	.	PUNCT
ejpam-3950	327	1	under	under	ADP
ejpam-3950	327	2	assumptions	assumption	NOUN
ejpam-3950	327	3	1,2	1,2	NUM
ejpam-3950	327	4	,	,	PUNCT
ejpam-3950	327	5	3	3	NUM
ejpam-3950	327	6	and	and	CCONJ
ejpam-3950	327	7	4	4	NUM
ejpam-3950	327	8	,	,	PUNCT
ejpam-3950	327	9	problem	problem	NOUN
ejpam-3950	327	10	(	(	PUNCT
ejpam-3950	327	11	p4	p4	ADJ
ejpam-3950	327	12	)	)	PUNCT
ejpam-3950	327	13	has	have	VERB
ejpam-3950	327	14	a	a	DET
ejpam-3950	327	15	unique	unique	ADJ
ejpam-3950	327	16	solution	solution	NOUN
ejpam-3950	327	17	.	.	PUNCT
ejpam-3950	328	1	proof	proof	NOUN
ejpam-3950	328	2	.	.	PUNCT
ejpam-3950	329	1	since	since	SCONJ
ejpam-3950	329	2	u(t	u(t	NOUN
ejpam-3950	329	3	)	)	PUNCT
ejpam-3950	329	4	=	=	SYM
ejpam-3950	330	1	∑n	∑n	PROPN
ejpam-3950	330	2	i=1	i=1	PROPN
ejpam-3950	330	3	ui(t)θi	ui(t)θi	PROPN
ejpam-3950	330	4	,	,	PUNCT
ejpam-3950	330	5	then	then	ADV
ejpam-3950	330	6	we	we	PRON
ejpam-3950	330	7	substitute	substitute	VERB
ejpam-3950	330	8	in	in	ADP
ejpam-3950	330	9	problem	problem	NOUN
ejpam-3950	330	10	(	(	PUNCT
ejpam-3950	330	11	p4	p4	ADJ
ejpam-3950	330	12	)	)	PUNCT
ejpam-3950	330	13	,	,	PUNCT
ejpam-3950	330	14	we	we	PRON
ejpam-3950	330	15	have	have	VERB
ejpam-3950	330	16	n∑	n∑	PROPN
ejpam-3950	330	17	i=1	i=1	PROPN
ejpam-3950	330	18	u	u	PROPN
ejpam-3950	330	19	(	(	PUNCT
ejpam-3950	330	20	α	α	NOUN
ejpam-3950	330	21	)	)	PUNCT
ejpam-3950	330	22	i	i	PRON
ejpam-3950	330	23	(	(	PUNCT
ejpam-3950	330	24	t)bnθi	t)bnθi	X
ejpam-3950	331	1	=	=	SYM
ejpam-3950	331	2	n∑	n∑	PROPN
ejpam-3950	331	3	i=1	i=1	X
ejpam-3950	331	4	ui(t)anθi	ui(t)anθi	VERB
ejpam-3950	332	1	+	+	X
ejpam-3950	332	2	n∑	n∑	ADJ
ejpam-3950	332	3	i=1	i=1	X
ejpam-3950	332	4	fi(t)δi	fi(t)δi	PROPN
ejpam-3950	332	5	.	.	PUNCT
ejpam-3950	333	1	this	this	PRON
ejpam-3950	333	2	implies	imply	VERB
ejpam-3950	333	3	n∑	n∑	PROPN
ejpam-3950	333	4	i=1	i=1	PROPN
ejpam-3950	333	5	u	u	PROPN
ejpam-3950	333	6	(	(	PUNCT
ejpam-3950	333	7	α	α	NOUN
ejpam-3950	333	8	)	)	PUNCT
ejpam-3950	333	9	i	i	PRON
ejpam-3950	333	10	(	(	PUNCT
ejpam-3950	333	11	t)λiθi	t)λiθi	NOUN
ejpam-3950	333	12	=	=	SYM
ejpam-3950	333	13	n∑	n∑	NOUN
ejpam-3950	333	14	i=1	i=1	PROPN
ejpam-3950	333	15	ui(t)µiθi	ui(t)µiθi	VERB
ejpam-3950	334	1	+	+	CCONJ
ejpam-3950	334	2	n∑	n∑	ADJ
ejpam-3950	334	3	i=1	i=1	X
ejpam-3950	334	4	fi(t)δi	fi(t)δi	PROPN
ejpam-3950	334	5	.	.	PUNCT
ejpam-3950	335	1	(	(	PUNCT
ejpam-3950	335	2	19	19	NUM
ejpam-3950	335	3	)	)	PUNCT
ejpam-3950	335	4	taking	take	VERB
ejpam-3950	335	5	the	the	DET
ejpam-3950	335	6	inner	inner	ADJ
ejpam-3950	335	7	product	product	NOUN
ejpam-3950	335	8	of	of	ADP
ejpam-3950	335	9	θj	θj	NOUN
ejpam-3950	335	10	with	with	ADP
ejpam-3950	335	11	both	both	DET
ejpam-3950	335	12	sides	side	NOUN
ejpam-3950	335	13	of	of	ADP
ejpam-3950	335	14	equation	equation	NOUN
ejpam-3950	335	15	(	(	PUNCT
ejpam-3950	335	16	19	19	NUM
ejpam-3950	335	17	)	)	PUNCT
ejpam-3950	335	18	,	,	PUNCT
ejpam-3950	335	19	we	we	PRON
ejpam-3950	335	20	obtain	obtain	VERB
ejpam-3950	335	21	λju	λju	NOUN
ejpam-3950	335	22	(	(	PUNCT
ejpam-3950	335	23	α	α	NOUN
ejpam-3950	335	24	)	)	PUNCT
ejpam-3950	335	25	j	j	PROPN
ejpam-3950	335	26	(	(	PUNCT
ejpam-3950	335	27	t	t	PROPN
ejpam-3950	335	28	)	)	PUNCT
ejpam-3950	335	29	=	=	SYM
ejpam-3950	335	30	µjuj(t	µjuj(t	PROPN
ejpam-3950	335	31	)	)	PUNCT
ejpam-3950	336	1	+	+	NUM
ejpam-3950	336	2	n∑	n∑	PROPN
ejpam-3950	336	3	i=1	i=1	PROPN
ejpam-3950	336	4	fi(t)〈δi	fi(t)〈δi	PROPN
ejpam-3950	336	5	,	,	PUNCT
ejpam-3950	336	6	θj	θj	PROPN
ejpam-3950	336	7	〉	〉	NOUN
ejpam-3950	336	8	.	.	PUNCT
ejpam-3950	337	1	(	(	PUNCT
ejpam-3950	337	2	20	20	NUM
ejpam-3950	337	3	)	)	PUNCT
ejpam-3950	337	4	multiplying	multiply	VERB
ejpam-3950	337	5	equation	equation	NOUN
ejpam-3950	337	6	(	(	PUNCT
ejpam-3950	337	7	20	20	NUM
ejpam-3950	337	8	)	)	PUNCT
ejpam-3950	337	9	by	by	ADP
ejpam-3950	337	10	θj	θj	ADV
ejpam-3950	337	11	and	and	CCONJ
ejpam-3950	337	12	using	use	VERB
ejpam-3950	337	13	assumption	assumption	NOUN
ejpam-3950	337	14	3	3	NUM
ejpam-3950	337	15	,	,	PUNCT
ejpam-3950	337	16	we	we	PRON
ejpam-3950	337	17	obtain	obtain	VERB
ejpam-3950	337	18	λjg	λjg	PRON
ejpam-3950	337	19	(	(	PUNCT
ejpam-3950	337	20	α	α	NOUN
ejpam-3950	337	21	)	)	PUNCT
ejpam-3950	337	22	j	j	PROPN
ejpam-3950	337	23	(	(	PUNCT
ejpam-3950	337	24	t	t	PROPN
ejpam-3950	337	25	)	)	PUNCT
ejpam-3950	337	26	=	=	SYM
ejpam-3950	337	27	µjgj(t	µjgj(t	PROPN
ejpam-3950	337	28	)	)	PUNCT
ejpam-3950	338	1	+	+	CCONJ
ejpam-3950	338	2	n∑	n∑	PROPN
ejpam-3950	338	3	i=1	i=1	PROPN
ejpam-3950	338	4	fi(t)〈(δi	fi(t)〈(δi	PROPN
ejpam-3950	338	5	,	,	PUNCT
ejpam-3950	338	6	θj〉〈θj	θj〉〈θj	NOUN
ejpam-3950	338	7	,	,	PUNCT
ejpam-3950	338	8	x	x	NOUN
ejpam-3950	338	9	〉	〉	NOUN
ejpam-3950	338	10	.	.	PUNCT
ejpam-3950	339	1	references	reference	NOUN
ejpam-3950	339	2	503	503	NUM
ejpam-3950	339	3	hence	hence	ADV
ejpam-3950	339	4	,	,	PUNCT
ejpam-3950	339	5	we	we	PRON
ejpam-3950	339	6	get	get	VERB
ejpam-3950	339	7	the	the	DET
ejpam-3950	339	8	following	follow	VERB
ejpam-3950	339	9	system:	system:	ADJ
ejpam-3950	339	10	λ1	λ1	PROPN
ejpam-3950	339	11	g	g	PROPN
ejpam-3950	339	12	(	(	PUNCT
ejpam-3950	339	13	α	α	NOUN
ejpam-3950	339	14	)	)	PUNCT
ejpam-3950	339	15	1	1	NUM
ejpam-3950	339	16	(	(	PUNCT
ejpam-3950	339	17	t)−	t)−	PROPN
ejpam-3950	339	18	µ1g1(t	µ1g1(t	PROPN
ejpam-3950	339	19	)	)	PUNCT
ejpam-3950	339	20	.	.	PUNCT
ejpam-3950	339	21	.	.	PUNCT
ejpam-3950	339	22	.	.	PUNCT
ejpam-3950	340	1	λng	λng	NOUN
ejpam-3950	340	2	(	(	PUNCT
ejpam-3950	340	3	α	α	NOUN
ejpam-3950	340	4	)	)	PUNCT
ejpam-3950	340	5	n	n	PROPN
ejpam-3950	340	6	(	(	PUNCT
ejpam-3950	340	7	t)−	t)−	PROPN
ejpam-3950	340	8	µngn(t	µngn(t	PROPN
ejpam-3950	340	9	)	)	PUNCT
ejpam-3950	340	10			PROPN
ejpam-3950	340	11	=	=	SYM
ejpam-3950	340	12	mt	mt	PROPN
ejpam-3950	340	13			NOUN
ejpam-3950	340	14	f1(t	f1(t	NUM
ejpam-3950	340	15	)	)	PUNCT
ejpam-3950	340	16	.	.	PUNCT
ejpam-3950	340	17	.	.	PUNCT
ejpam-3950	340	18	.	.	PUNCT
ejpam-3950	341	1	fn(t	fn(t	PUNCT
ejpam-3950	342	1	)	)	PUNCT
ejpam-3950	342	2			NOUN
ejpam-3950	342	3	.	.	PUNCT
ejpam-3950	343	1	where	where	SCONJ
ejpam-3950	343	2	,	,	PUNCT
ejpam-3950	343	3	m	m	VERB
ejpam-3950	343	4	=	=	PUNCT
ejpam-3950	344	1	[	[	X
ejpam-3950	344	2	〈	〈	PROPN
ejpam-3950	344	3	δi	δi	ADP
ejpam-3950	344	4	,	,	PUNCT
ejpam-3950	344	5	θj〉〈θj	θj〉〈θj	NOUN
ejpam-3950	344	6	,	,	PUNCT
ejpam-3950	344	7	x〉]i	x〉]i	PROPN
ejpam-3950	344	8	,	,	PUNCT
ejpam-3950	344	9	j=1,	j=1,	NOUN
ejpam-3950	344	10	...	...	PUNCT
ejpam-3950	344	11	,n	,n	PUNCT
ejpam-3950	344	12	.	.	PUNCT
ejpam-3950	345	1	by	by	ADP
ejpam-3950	345	2	assumption	assumption	NOUN
ejpam-3950	345	3	4	4	NUM
ejpam-3950	345	4	m	m	NOUN
ejpam-3950	345	5	is	be	AUX
ejpam-3950	345	6	invertible	invertible	ADJ
ejpam-3950	345	7	,	,	PUNCT
ejpam-3950	345	8	then	then	ADV
ejpam-3950	345	9	mt	mt	PROPN
ejpam-3950	345	10	is	be	AUX
ejpam-3950	345	11	also	also	ADV
ejpam-3950	345	12	invertible	invertible	ADJ
ejpam-3950	345	13	and	and	CCONJ
ejpam-3950	345	14	(	(	PUNCT
ejpam-3950	345	15	mt	mt	PROPN
ejpam-3950	345	16	)	)	PUNCT
ejpam-3950	345	17	−1	−1	NOUN
ejpam-3950	346	1	=	=	SYM
ejpam-3950	346	2	(	(	PUNCT
ejpam-3950	346	3	m−1)t	m−1)t	PROPN
ejpam-3950	346	4	,	,	PUNCT
ejpam-3950	346	5	thus	thus	PROPN
ejpam-3950	346	6	f1(t	f1(t	PROPN
ejpam-3950	346	7	)	)	PUNCT
ejpam-3950	346	8	.	.	PUNCT
ejpam-3950	346	9	.	.	PUNCT
ejpam-3950	346	10	.	.	PUNCT
ejpam-3950	347	1	fn(t	fn(t	PUNCT
ejpam-3950	347	2	)	)	PUNCT
ejpam-3950	348	1			NOUN
ejpam-3950	349	1	=	=	SYM
ejpam-3950	349	2	(	(	PUNCT
ejpam-3950	349	3	m−1)t	m−1)t	PROPN
ejpam-3950	349	4			VERB
ejpam-3950	350	1	λ1	λ1	PROPN
ejpam-3950	350	2	g	g	PROPN
ejpam-3950	350	3	(	(	PUNCT
ejpam-3950	350	4	α	α	NOUN
ejpam-3950	350	5	)	)	PUNCT
ejpam-3950	350	6	1	1	NUM
ejpam-3950	350	7	(	(	PUNCT
ejpam-3950	350	8	t)−	t)−	PROPN
ejpam-3950	350	9	µ1g1(t	µ1g1(t	PROPN
ejpam-3950	350	10	)	)	PUNCT
ejpam-3950	350	11	.	.	PUNCT
ejpam-3950	350	12	.	.	PUNCT
ejpam-3950	350	13	.	.	PUNCT
ejpam-3950	351	1	λng	λng	NOUN
ejpam-3950	351	2	(	(	PUNCT
ejpam-3950	351	3	α	α	NOUN
ejpam-3950	351	4	)	)	PUNCT
ejpam-3950	351	5	n	n	PROPN
ejpam-3950	351	6	(	(	PUNCT
ejpam-3950	351	7	t)−	t)−	PROPN
ejpam-3950	351	8	µngn(t	µngn(t	PROPN
ejpam-3950	351	9	)	)	PUNCT
ejpam-3950	351	10			NOUN
ejpam-3950	351	11	.	.	PUNCT
ejpam-3950	352	1	therefore	therefore	ADV
ejpam-3950	352	2	f	f	PROPN
ejpam-3950	352	3	is	be	AUX
ejpam-3950	352	4	determined	determine	VERB
ejpam-3950	352	5	uniquely	uniquely	ADV
ejpam-3950	352	6	.	.	PUNCT
ejpam-3950	353	1	now	now	ADV
ejpam-3950	353	2	to	to	PART
ejpam-3950	353	3	find	find	VERB
ejpam-3950	353	4	u(t	u(t	NOUN
ejpam-3950	353	5	)	)	PUNCT
ejpam-3950	353	6	,	,	PUNCT
ejpam-3950	353	7	we	we	PRON
ejpam-3950	353	8	have	have	VERB
ejpam-3950	353	9	•	•	NOUN
ejpam-3950	353	10	if	if	SCONJ
ejpam-3950	353	11	λj	λj	PROPN
ejpam-3950	353	12	=	=	SYM
ejpam-3950	353	13	0	0	PROPN
ejpam-3950	353	14	,	,	PUNCT
ejpam-3950	353	15	then	then	ADV
ejpam-3950	353	16	uj(t	uj(t	PUNCT
ejpam-3950	353	17	)	)	PUNCT
ejpam-3950	354	1	=	=	SYM
ejpam-3950	354	2	∑n	∑n	PROPN
ejpam-3950	354	3	i=1	i=1	PROPN
ejpam-3950	354	4	fi(t)〈δi	fi(t)〈δi	PROPN
ejpam-3950	354	5	,	,	PUNCT
ejpam-3950	354	6	θj	θj	NOUN
ejpam-3950	354	7	〉	〉	NOUN
ejpam-3950	354	8	−µj	−µj	NOUN
ejpam-3950	354	9	.	.	PUNCT
ejpam-3950	355	1	•	•	INTJ
ejpam-3950	355	2	if	if	SCONJ
ejpam-3950	355	3	λj	λj	PROPN
ejpam-3950	355	4	6=	6=	PROPN
ejpam-3950	355	5	0	0	NUM
ejpam-3950	355	6	,	,	PUNCT
ejpam-3950	355	7	then	then	ADV
ejpam-3950	355	8	uj(t	uj(t	PUNCT
ejpam-3950	355	9	)	)	PUNCT
ejpam-3950	356	1	=	=	SYM
ejpam-3950	356	2	uj(0)e	uj(0)e	PROPN
ejpam-3950	356	3	µjt	µjt	NOUN
ejpam-3950	356	4	α	α	PROPN
ejpam-3950	356	5	λjα	λjα	PROPN
ejpam-3950	357	1	+	+	X
ejpam-3950	357	2	n∑	n∑	ADJ
ejpam-3950	357	3	i=1	i=1	PROPN
ejpam-3950	358	1	e	e	PROPN
ejpam-3950	358	2	µjt	µjt	PROPN
ejpam-3950	358	3	α	α	PROPN
ejpam-3950	358	4	λjα	λjα	PROPN
ejpam-3950	359	1	〈	〈	PROPN
ejpam-3950	359	2	δi	δi	NOUN
ejpam-3950	359	3	,	,	PUNCT
ejpam-3950	359	4	θj	θj	PRON
ejpam-3950	359	5	〉	〉	PROPN
ejpam-3950	359	6	∫	∫	PROPN
ejpam-3950	359	7	t	t	PROPN
ejpam-3950	359	8	0	0	NUM
ejpam-3950	360	1	fi(s)e	fi(s)e	NOUN
ejpam-3950	360	2	−µjs	−µjs	NUM
ejpam-3950	361	1	α	α	NOUN
ejpam-3950	361	2	λjα	λjα	VERB
ejpam-3950	361	3	s1−α	s1−α	PROPN
ejpam-3950	361	4	ds	ds	NOUN
ejpam-3950	361	5	.	.	PUNCT
ejpam-3950	362	1	consequently	consequently	ADV
ejpam-3950	362	2	,	,	PUNCT
ejpam-3950	362	3	the	the	DET
ejpam-3950	362	4	problem	problem	NOUN
ejpam-3950	362	5	(	(	PUNCT
ejpam-3950	362	6	p4	p4	ADJ
ejpam-3950	362	7	)	)	PUNCT
ejpam-3950	362	8	has	have	VERB
ejpam-3950	362	9	a	a	DET
ejpam-3950	362	10	unique	unique	ADJ
ejpam-3950	362	11	solution	solution	NOUN
ejpam-3950	362	12	.	.	PUNCT
ejpam-3950	363	1	references	reference	NOUN
ejpam-3950	363	2	[	[	X
ejpam-3950	363	3	1	1	NUM
ejpam-3950	363	4	]	]	PUNCT
ejpam-3950	363	5	r.	r.	PROPN
ejpam-3950	363	6	khalil	khalil	PROPN
ejpam-3950	363	7	,	,	PUNCT
ejpam-3950	363	8	m.	m.	PROPN
ejpam-3950	363	9	al	al	PROPN
ejpam-3950	363	10	horani	horani	PROPN
ejpam-3950	363	11	,	,	PUNCT
ejpam-3950	363	12	a.	a.	PROPN
ejpam-3950	363	13	yousef	yousef	PROPN
ejpam-3950	363	14	.	.	PUNCT
ejpam-3950	364	1	and	and	CCONJ
ejpam-3950	364	2	m.	m.	NOUN
ejpam-3950	364	3	sababheh	sababheh	PROPN
ejpam-3950	364	4	,	,	PUNCT
ejpam-3950	364	5	a	a	DET
ejpam-3950	364	6	new	new	ADJ
ejpam-3950	364	7	definition	definition	NOUN
ejpam-3950	364	8	of	of	ADP
ejpam-3950	364	9	fractional	fractional	ADJ
ejpam-3950	364	10	derivative	derivative	NOUN
ejpam-3950	364	11	,	,	PUNCT
ejpam-3950	364	12	j.	j.	PROPN
ejpam-3950	364	13	comput	comput	PROPN
ejpam-3950	364	14	.	.	PUNCT
ejpam-3950	365	1	appl	appl	PROPN
ejpam-3950	365	2	.	.	PROPN
ejpam-3950	365	3	math	math	PROPN
ejpam-3950	365	4	.	.	PUNCT
ejpam-3950	365	5	,	,	PUNCT
ejpam-3950	365	6	264:65	264:65	PROPN
ejpam-3950	365	7	-	-	SYM
ejpam-3950	365	8	70	70	NUM
ejpam-3950	365	9	,	,	PUNCT
ejpam-3950	365	10	(	(	PUNCT
ejpam-3950	365	11	2014	2014	NUM
ejpam-3950	365	12	)	)	PUNCT
ejpam-3950	365	13	.	.	PUNCT
ejpam-3950	366	1	[	[	X
ejpam-3950	366	2	2	2	X
ejpam-3950	366	3	]	]	PUNCT
ejpam-3950	366	4	w.	w.	PROPN
ejpam-3950	366	5	a.	a.	PROPN
ejpam-3950	366	6	light	light	PROPN
ejpam-3950	366	7	,	,	PUNCT
ejpam-3950	366	8	e.	e.	PROPN
ejpam-3950	366	9	w.	w.	PROPN
ejpam-3950	366	10	cheney	cheney	PROPN
ejpam-3950	366	11	,	,	PUNCT
ejpam-3950	366	12	approximation	approximation	NOUN
ejpam-3950	366	13	theory	theory	NOUN
ejpam-3950	366	14	in	in	ADP
ejpam-3950	366	15	tensor	tensor	NOUN
ejpam-3950	366	16	product	product	NOUN
ejpam-3950	366	17	spaces	space	VERB
ejpam-3950	366	18	.	.	PUNCT
ejpam-3950	367	1	lecture	lecture	NOUN
ejpam-3950	367	2	notes	note	NOUN
ejpam-3950	367	3	in	in	ADP
ejpam-3950	367	4	math	math	NOUN
ejpam-3950	367	5	.	.	PUNCT
ejpam-3950	368	1	1169	1169	NUM
ejpam-3950	368	2	.	.	PUNCT
ejpam-3950	369	1	springer	springer	NOUN
ejpam-3950	369	2	-	-	PUNCT
ejpam-3950	369	3	verlag	verlag	PROPN
ejpam-3950	369	4	,	,	PUNCT
ejpam-3950	369	5	new	new	PROPN
ejpam-3950	369	6	york	york	PROPN
ejpam-3950	369	7	,	,	PUNCT
ejpam-3950	369	8	1985	1985	NUM
ejpam-3950	369	9	.	.	PUNCT
ejpam-3950	370	1	[	[	X
ejpam-3950	370	2	3	3	NUM
ejpam-3950	370	3	]	]	PUNCT
ejpam-3950	370	4	a.	a.	NOUN
ejpam-3950	370	5	m.	m.	NOUN
ejpam-3950	370	6	ziqan	ziqan	PROPN
ejpam-3950	370	7	,	,	PUNCT
ejpam-3950	370	8	m.	m.	PROPN
ejpam-3950	370	9	h.	h.	PROPN
ejpam-3950	370	10	al	al	PROPN
ejpam-3950	370	11	horani	horani	PROPN
ejpam-3950	370	12	,	,	PUNCT
ejpam-3950	370	13	and	and	CCONJ
ejpam-3950	370	14	r.	r.	PROPN
ejpam-3950	370	15	khalil	khalil	PROPN
ejpam-3950	370	16	,	,	PUNCT
ejpam-3950	370	17	tensor	tensor	NOUN
ejpam-3950	370	18	product	product	NOUN
ejpam-3950	370	19	technique	technique	NOUN
ejpam-3950	370	20	and	and	CCONJ
ejpam-3950	370	21	the	the	DET
ejpam-3950	370	22	degenerate	degenerate	ADJ
ejpam-3950	370	23	homogeneous	homogeneous	ADJ
ejpam-3950	370	24	abstract	abstract	ADJ
ejpam-3950	370	25	cauchy	cauchy	PROPN
ejpam-3950	370	26	problem	problem	NOUN
ejpam-3950	370	27	,	,	PUNCT
ejpam-3950	370	28	j.	j.	PROPN
ejpam-3950	370	29	appl	appl	PROPN
ejpam-3950	370	30	.	.	PROPN
ejpam-3950	371	1	funct	funct	PROPN
ejpam-3950	371	2	.	.	PUNCT
ejpam-3950	372	1	anal	anal	PROPN
ejpam-3950	372	2	.	.	PROPN
ejpam-3950	372	3	,	,	PUNCT
ejpam-3950	372	4	5	5	NUM
ejpam-3950	372	5	(	(	PUNCT
ejpam-3950	372	6	1):121138	1):121138	NUM
ejpam-3950	372	7	,	,	PUNCT
ejpam-3950	372	8	(	(	PUNCT
ejpam-3950	372	9	2010	2010	NUM
ejpam-3950	372	10	)	)	PUNCT
ejpam-3950	372	11	.	.	PUNCT
ejpam-3950	373	1	[	[	X
ejpam-3950	373	2	4	4	NUM
ejpam-3950	373	3	]	]	PUNCT
ejpam-3950	373	4	a.	a.	NOUN
ejpam-3950	373	5	m.	m.	NOUN
ejpam-3950	373	6	ziqan	ziqan	PROPN
ejpam-3950	373	7	,	,	PUNCT
ejpam-3950	373	8	m.	m.	PROPN
ejpam-3950	373	9	h.	h.	PROPN
ejpam-3950	373	10	al	al	PROPN
ejpam-3950	373	11	horani	horani	PROPN
ejpam-3950	373	12	,	,	PUNCT
ejpam-3950	373	13	and	and	CCONJ
ejpam-3950	373	14	r.	r.	PROPN
ejpam-3950	373	15	khalil	khalil	PROPN
ejpam-3950	373	16	,	,	PUNCT
ejpam-3950	373	17	tensor	tensor	NOUN
ejpam-3950	373	18	product	product	NOUN
ejpam-3950	373	19	technique	technique	NOUN
ejpam-3950	373	20	and	and	CCONJ
ejpam-3950	373	21	the	the	DET
ejpam-3950	373	22	degenerate	degenerate	ADJ
ejpam-3950	373	23	nonhomogeneous	nonhomogeneous	ADJ
ejpam-3950	373	24	abstract	abstract	ADJ
ejpam-3950	373	25	cauchy	cauchy	PROPN
ejpam-3950	373	26	problem	problem	NOUN
ejpam-3950	373	27	,	,	PUNCT
ejpam-3950	373	28	j.	j.	PROPN
ejpam-3950	373	29	appl	appl	PROPN
ejpam-3950	373	30	.	.	PROPN
ejpam-3950	374	1	funct	funct	PROPN
ejpam-3950	374	2	.	.	PUNCT
ejpam-3950	375	1	anal	anal	PROPN
ejpam-3950	375	2	.	.	PROPN
ejpam-3950	375	3	,	,	PUNCT
ejpam-3950	375	4	23	23	NUM
ejpam-3950	375	5	(	(	PUNCT
ejpam-3950	375	6	1):137	1):137	NUM
ejpam-3950	375	7	-	-	SYM
ejpam-3950	375	8	158	158	NUM
ejpam-3950	375	9	,	,	PUNCT
ejpam-3950	375	10	(	(	PUNCT
ejpam-3950	375	11	2010	2010	NUM
ejpam-3950	375	12	)	)	PUNCT
ejpam-3950	375	13	.	.	PUNCT
ejpam-3950	376	1	[	[	X
ejpam-3950	376	2	5	5	X
ejpam-3950	376	3	]	]	PUNCT
ejpam-3950	376	4	r.	r.	PROPN
ejpam-3950	376	5	khalil	khalil	PROPN
ejpam-3950	376	6	,	,	PUNCT
ejpam-3950	376	7	isometries	isometry	NOUN
ejpam-3950	376	8	on	on	ADP
ejpam-3950	376	9	lp	lp	PROPN
ejpam-3950	376	10	⊗	⊗	PROPN
ejpam-3950	376	11	lp	lp	PROPN
ejpam-3950	376	12	,	,	PUNCT
ejpam-3950	376	13	tamkang	tamkang	PROPN
ejpam-3950	376	14	j.	j.	PROPN
ejpam-3950	376	15	math	math	PROPN
ejpam-3950	376	16	.	.	PUNCT
ejpam-3950	377	1	16(2):77	16(2):77	PROPN
ejpam-3950	377	2	-	-	PUNCT
ejpam-3950	377	3	85	85	NUM
ejpam-3950	377	4	,	,	PUNCT
ejpam-3950	377	5	(	(	PUNCT
ejpam-3950	377	6	1985	1985	NUM
ejpam-3950	377	7	)	)	PUNCT
ejpam-3950	377	8	.	.	PUNCT
ejpam-3950	378	1	references	reference	NOUN
ejpam-3950	378	2	504	504	NUM
ejpam-3950	378	3	[	[	SYM
ejpam-3950	378	4	6	6	NUM
ejpam-3950	378	5	]	]	PUNCT
ejpam-3950	378	6	t.	t.	NOUN
ejpam-3950	378	7	abdeljawad	abdeljawad	NOUN
ejpam-3950	378	8	,	,	PUNCT
ejpam-3950	378	9	conformable	conformable	ADJ
ejpam-3950	378	10	fractional	fractional	ADJ
ejpam-3950	378	11	calculus	calculus	NOUN
ejpam-3950	378	12	,	,	PUNCT
ejpam-3950	378	13	j.	j.	PROPN
ejpam-3950	378	14	comput	comput	PROPN
ejpam-3950	378	15	.	.	PUNCT
ejpam-3950	379	1	appl	appl	PROPN
ejpam-3950	379	2	.	.	PUNCT
ejpam-3950	379	3	math	math	NOUN
ejpam-3950	379	4	.	.	PUNCT
ejpam-3950	380	1	279:57	279:57	NUM
ejpam-3950	380	2	-	-	SYM
ejpam-3950	380	3	66	66	NUM
ejpam-3950	380	4	,	,	PUNCT
ejpam-3950	380	5	(	(	PUNCT
ejpam-3950	380	6	2015	2015	NUM
ejpam-3950	380	7	)	)	PUNCT
ejpam-3950	380	8	.	.	PUNCT
ejpam-3950	381	1	[	[	X
ejpam-3950	381	2	7	7	X
ejpam-3950	381	3	]	]	PUNCT
ejpam-3950	381	4	m.	m.	NOUN
ejpam-3950	381	5	abu	abu	PROPN
ejpam-3950	381	6	hammad	hammad	PROPN
ejpam-3950	381	7	,	,	PUNCT
ejpam-3950	381	8	r.	r.	PROPN
ejpam-3950	381	9	khalil	khalil	PROPN
ejpam-3950	381	10	,	,	PUNCT
ejpam-3950	381	11	systems	system	NOUN
ejpam-3950	381	12	of	of	ADP
ejpam-3950	381	13	linear	linear	ADJ
ejpam-3950	381	14	fractional	fractional	ADJ
ejpam-3950	381	15	differential	differential	NOUN
ejpam-3950	381	16	equations	equation	NOUN
ejpam-3950	381	17	,	,	PUNCT
ejpam-3950	381	18	asian	asian	ADJ
ejpam-3950	381	19	j.	j.	PROPN
ejpam-3950	381	20	math.comput	math.comput	PROPN
ejpam-3950	381	21	.	.	PUNCT
ejpam-3950	382	1	res	re	NOUN
ejpam-3950	382	2	.	.	PROPN
ejpam-3950	382	3	,	,	PUNCT
ejpam-3950	382	4	12(2):120	12(2):120	PROPN
ejpam-3950	382	5	-	-	SYM
ejpam-3950	382	6	126	126	NUM
ejpam-3950	382	7	,	,	PUNCT
ejpam-3950	382	8	(	(	PUNCT
ejpam-3950	382	9	2016	2016	NUM
ejpam-3950	382	10	)	)	PUNCT
ejpam-3950	382	11	.	.	PUNCT
ejpam-3950	383	1	[	[	X
ejpam-3950	383	2	8	8	X
ejpam-3950	383	3	]	]	X
ejpam-3950	383	4	b.	b.	NOUN
ejpam-3950	383	5	thaller	thaller	NOUN
ejpam-3950	383	6	,	,	PUNCT
ejpam-3950	383	7	s.thaller	s.thaller	NOUN
ejpam-3950	383	8	,	,	PUNCT
ejpam-3950	383	9	factorization	factorization	NOUN
ejpam-3950	383	10	of	of	ADP
ejpam-3950	383	11	degenerate	degenerate	ADJ
ejpam-3950	383	12	cauchy	cauchy	PROPN
ejpam-3950	383	13	problem	problem	NOUN
ejpam-3950	383	14	,	,	PUNCT
ejpam-3950	383	15	the	the	DET
ejpam-3950	383	16	linear	linear	ADJ
ejpam-3950	383	17	case	case	NOUN
ejpam-3950	383	18	,	,	PUNCT
ejpam-3950	383	19	j.oper	j.oper	NOUN
ejpam-3950	383	20	.	.	PUNCT
ejpam-3950	383	21	theory	theory	NOUN
ejpam-3950	383	22	36:121	36:121	NUM
ejpam-3950	383	23	-	-	SYM
ejpam-3950	383	24	146	146	NUM
ejpam-3950	383	25	,	,	PUNCT
ejpam-3950	383	26	(	(	PUNCT
ejpam-3950	383	27	1996	1996	NUM
ejpam-3950	383	28	)	)	PUNCT
ejpam-3950	383	29	.	.	PUNCT
ejpam-3950	384	1	[	[	X
ejpam-3950	384	2	9	9	NUM
ejpam-3950	384	3	]	]	PUNCT
ejpam-3950	384	4	a.	a.	NOUN
ejpam-3950	384	5	atangana	atangana	PROPN
ejpam-3950	384	6	,	,	PUNCT
ejpam-3950	384	7	d.	d.	PROPN
ejpam-3950	384	8	baleanu	baleanu	PROPN
ejpam-3950	384	9	,	,	PUNCT
ejpam-3950	384	10	a.	a.	NOUN
ejpam-3950	384	11	alsaedi	alsaedi	PROPN
ejpam-3950	384	12	,	,	PUNCT
ejpam-3950	384	13	new	new	ADJ
ejpam-3950	384	14	properties	property	NOUN
ejpam-3950	384	15	of	of	ADP
ejpam-3950	384	16	conformable	conformable	ADJ
ejpam-3950	384	17	derivative	derivative	ADJ
ejpam-3950	384	18	,	,	PUNCT
ejpam-3950	384	19	open	open	ADJ
ejpam-3950	384	20	mathematics	mathematic	NOUN
ejpam-3950	384	21	13(2015	13(2015	NUM
ejpam-3950	384	22	)	)	PUNCT
ejpam-3950	384	23	.	.	PUNCT
ejpam-3950	385	1	[	[	X
ejpam-3950	385	2	10	10	NUM
ejpam-3950	385	3	]	]	X
ejpam-3950	385	4	m.	m.	NOUN
ejpam-3950	385	5	alhorani	alhorani	PROPN
ejpam-3950	385	6	,	,	PUNCT
ejpam-3950	385	7	r.	r.	PROPN
ejpam-3950	385	8	khalil	khalil	PROPN
ejpam-3950	385	9	,	,	PUNCT
ejpam-3950	385	10	total	total	ADJ
ejpam-3950	385	11	fractional	fractional	ADJ
ejpam-3950	385	12	differentials	differential	NOUN
ejpam-3950	385	13	with	with	ADP
ejpam-3950	385	14	applications	application	NOUN
ejpam-3950	385	15	to	to	PART
ejpam-3950	385	16	exact	exact	VERB
ejpam-3950	385	17	fractional	fractional	ADJ
ejpam-3950	385	18	differential	differential	ADJ
ejpam-3950	385	19	equations	equation	NOUN
ejpam-3950	385	20	,	,	PUNCT
ejpam-3950	385	21	international	international	ADJ
ejpam-3950	385	22	journal	journal	NOUN
ejpam-3950	385	23	of	of	ADP
ejpam-3950	385	24	computer	computer	NOUN
ejpam-3950	385	25	mathematics	mathematic	NOUN
ejpam-3950	385	26	,	,	PUNCT
ejpam-3950	385	27	95:1444	95:1444	NOUN
ejpam-3950	385	28	-	-	SYM
ejpam-3950	385	29	1452	1452	NUM
ejpam-3950	385	30	,	,	PUNCT
ejpam-3950	385	31	(	(	PUNCT
ejpam-3950	385	32	2018	2018	NUM
ejpam-3950	385	33	)	)	PUNCT
ejpam-3950	385	34	.	.	PUNCT
ejpam-3950	386	1	[	[	X
ejpam-3950	386	2	11	11	NUM
ejpam-3950	386	3	]	]	PUNCT
ejpam-3950	386	4	r.	r.	PROPN
ejpam-3950	386	5	khalil	khalil	PROPN
ejpam-3950	386	6	,	,	PUNCT
ejpam-3950	386	7	m.	m.	PROPN
ejpam-3950	386	8	al	al	PROPN
ejpam-3950	386	9	horani	horani	PROPN
ejpam-3950	386	10	,	,	PUNCT
ejpam-3950	386	11	d.	d.	PROPN
ejpam-3950	386	12	anderson	anderson	PROPN
ejpam-3950	386	13	,	,	PUNCT
ejpam-3950	386	14	undetermined	undetermined	ADJ
ejpam-3950	386	15	coeficients	coeficient	NOUN
ejpam-3950	386	16	for	for	ADP
ejpam-3950	386	17	local	local	ADJ
ejpam-3950	386	18	fractional	fractional	ADJ
ejpam-3950	386	19	differential	differential	ADJ
ejpam-3950	386	20	equations	equation	NOUN
ejpam-3950	386	21	j.	j.	PROPN
ejpam-3950	386	22	math	math	PROPN
ejpam-3950	386	23	.	.	PUNCT
ejpam-3950	387	1	comput	comput	NOUN
ejpam-3950	387	2	.	.	PUNCT
ejpam-3950	388	1	sci	sci	PROPN
ejpam-3950	388	2	16:140	16:140	NUM
ejpam-3950	388	3	-	-	SYM
ejpam-3950	388	4	146	146	NUM
ejpam-3950	388	5	,	,	PUNCT
ejpam-3950	388	6	(	(	PUNCT
ejpam-3950	388	7	2016	2016	NUM
ejpam-3950	388	8	)	)	PUNCT
ejpam-3950	388	9	.	.	PUNCT
ejpam-3950	389	1	[	[	X
ejpam-3950	389	2	12	12	NUM
ejpam-3950	389	3	]	]	X
ejpam-3950	389	4	d.	d.	PROPN
ejpam-3950	389	5	r.	r.	PROPN
ejpam-3950	389	6	anderson	anderson	PROPN
ejpam-3950	389	7	,	,	PUNCT
ejpam-3950	389	8	e.	e.	PROPN
ejpam-3950	389	9	camud	camud	PROPN
ejpam-3950	389	10	,	,	PUNCT
ejpam-3950	389	11	and	and	CCONJ
ejpam-3950	389	12	d.	d.	PROPN
ejpam-3950	389	13	j.	j.	PROPN
ejpam-3950	389	14	ulness	ulness	PROPN
ejpam-3950	389	15	,	,	PUNCT
ejpam-3950	389	16	on	on	ADP
ejpam-3950	389	17	the	the	DET
ejpam-3950	389	18	nature	nature	NOUN
ejpam-3950	389	19	of	of	ADP
ejpam-3950	389	20	the	the	DET
ejpam-3950	389	21	conformable	conformable	ADJ
ejpam-3950	389	22	derivative	derivative	NOUN
ejpam-3950	389	23	and	and	CCONJ
ejpam-3950	389	24	its	its	PRON
ejpam-3950	389	25	applications	application	NOUN
ejpam-3950	389	26	to	to	ADP
ejpam-3950	389	27	physics	physics	PROPN
ejpam-3950	389	28	,	,	PUNCT
ejpam-3950	389	29	journal	journal	NOUN
ejpam-3950	389	30	of	of	ADP
ejpam-3950	389	31	fractional	fractional	ADJ
ejpam-3950	389	32	calculus	calculus	NOUN
ejpam-3950	389	33	and	and	CCONJ
ejpam-3950	389	34	applications	application	NOUN
ejpam-3950	389	35	,	,	PUNCT
ejpam-3950	389	36	14:92	14:92	NUM
ejpam-3950	389	37	-	-	SYM
ejpam-3950	389	38	135	135	NUM
ejpam-3950	389	39	,	,	PUNCT
ejpam-3950	389	40	(	(	PUNCT
ejpam-3950	389	41	2019	2019	NUM
ejpam-3950	389	42	)	)	PUNCT
ejpam-3950	389	43	.	.	PUNCT
ejpam-3950	390	1	[	[	X
ejpam-3950	390	2	13	13	NUM
ejpam-3950	390	3	]	]	PUNCT
ejpam-3950	390	4	m.	m.	NOUN
ejpam-3950	390	5	mhailan	mhailan	PROPN
ejpam-3950	390	6	,	,	PUNCT
ejpam-3950	390	7	m.	m.	NOUN
ejpam-3950	390	8	abuhammad	abuhammad	PROPN
ejpam-3950	390	9	,	,	PUNCT
ejpam-3950	390	10	m.	m.	NOUN
ejpam-3950	390	11	alhorani	alhorani	PROPN
ejpam-3950	390	12	,	,	PUNCT
ejpam-3950	390	13	r.	r.	PROPN
ejpam-3950	390	14	khalil	khalil	PROPN
ejpam-3950	390	15	,	,	PUNCT
ejpam-3950	390	16	fractional	fractional	ADJ
ejpam-3950	390	17	vector	vector	NOUN
ejpam-3950	390	18	analysis	analysis	NOUN
ejpam-3950	390	19	,	,	PUNCT
ejpam-3950	390	20	journal	journal	NOUN
ejpam-3950	390	21	of	of	ADP
ejpam-3950	390	22	mathematical	mathematical	ADJ
ejpam-3950	390	23	and	and	CCONJ
ejpam-3950	390	24	computational	computational	ADJ
ejpam-3950	390	25	science,10:2320	science,10:2320	PROPN
ejpam-3950	390	26	-	-	PUNCT
ejpam-3950	390	27	2326	2326	NUM
ejpam-3950	390	28	,	,	PUNCT
ejpam-3950	390	29	(	(	PUNCT
ejpam-3950	390	30	2020	2020	NUM
ejpam-3950	390	31	)	)	PUNCT
ejpam-3950	390	32	.	.	PUNCT
ejpam-3950	391	1	[	[	X
ejpam-3950	391	2	14	14	NUM
ejpam-3950	391	3	]	]	PUNCT
ejpam-3950	391	4	a.	a.	NOUN
ejpam-3950	391	5	kilbas	kilbas	PROPN
ejpam-3950	391	6	,	,	PUNCT
ejpam-3950	391	7	h.	h.	PROPN
ejpam-3950	391	8	srivastava	srivastava	PROPN
ejpam-3950	391	9	,	,	PUNCT
ejpam-3950	391	10	j.	j.	PROPN
ejpam-3950	391	11	trujillo	trujillo	PROPN
ejpam-3950	391	12	,	,	PUNCT
ejpam-3950	391	13	theory	theory	NOUN
ejpam-3950	391	14	and	and	CCONJ
ejpam-3950	391	15	applications	application	NOUN
ejpam-3950	391	16	of	of	ADP
ejpam-3950	391	17	fractional	fractional	ADJ
ejpam-3950	391	18	differential	differential	ADJ
ejpam-3950	391	19	equations	equation	NOUN
ejpam-3950	391	20	,	,	PUNCT
ejpam-3950	391	21	in	in	ADP
ejpam-3950	391	22	:	:	PUNCT
ejpam-3950	391	23	math	math	NOUN
ejpam-3950	391	24	.	.	PUNCT
ejpam-3950	392	1	studies	study	NOUN
ejpam-3950	392	2	.	.	PUNCT
ejpam-3950	392	3	,	,	PUNCT
ejpam-3950	392	4	north	north	NOUN
ejpam-3950	392	5	-	-	PUNCT
ejpam-3950	392	6	holland	holland	PROPN
ejpam-3950	392	7	,	,	PUNCT
ejpam-3950	392	8	new	new	PROPN
ejpam-3950	392	9	york	york	PROPN
ejpam-3950	392	10	,	,	PUNCT
ejpam-3950	392	11	2006	2006	NUM
ejpam-3950	392	12	.	.	PUNCT
ejpam-3950	393	1	[	[	X
ejpam-3950	393	2	15	15	NUM
ejpam-3950	393	3	]	]	X
ejpam-3950	393	4	m.	m.	NOUN
ejpam-3950	393	5	abu	abu	PROPN
ejpam-3950	393	6	hammad	hammad	PROPN
ejpam-3950	393	7	,	,	PUNCT
ejpam-3950	393	8	r.	r.	PROPN
ejpam-3950	393	9	khalil	khalil	PROPN
ejpam-3950	393	10	,	,	PUNCT
ejpam-3950	393	11	conformable	conformable	ADJ
ejpam-3950	393	12	fractional	fractional	ADJ
ejpam-3950	393	13	heat	heat	NOUN
ejpam-3950	393	14	differential	differential	NOUN
ejpam-3950	393	15	equation	equation	NOUN
ejpam-3950	393	16	,	,	PUNCT
ejpam-3950	393	17	international	international	ADJ
ejpam-3950	393	18	journal	journal	NOUN
ejpam-3950	393	19	of	of	ADP
ejpam-3950	393	20	pure	pure	ADJ
ejpam-3950	393	21	and	and	CCONJ
ejpam-3950	393	22	applied	apply	VERB
ejpam-3950	393	23	mathematics	mathematic	NOUN
ejpam-3950	393	24	94(2):215221	94(2):215221	NUM
ejpam-3950	393	25	,	,	PUNCT
ejpam-3950	393	26	(	(	PUNCT
ejpam-3950	393	27	2014	2014	NUM
ejpam-3950	393	28	)	)	PUNCT
ejpam-3950	393	29	.	.	PUNCT
ejpam-3950	394	1	[	[	X
ejpam-3950	394	2	16	16	NUM
ejpam-3950	394	3	]	]	PUNCT
ejpam-3950	394	4	m.	m.	NOUN
ejpam-3950	394	5	abu	abu	PROPN
ejpam-3950	394	6	hammad	hammad	PROPN
ejpam-3950	394	7	,	,	PUNCT
ejpam-3950	394	8	r.	r.	PROPN
ejpam-3950	394	9	khalil	khalil	PROPN
ejpam-3950	394	10	.	.	PUNCT
ejpam-3950	394	11	,	,	PUNCT
ejpam-3950	394	12	fractional	fractional	ADJ
ejpam-3950	394	13	fourier	fourier	NOUN
ejpam-3950	394	14	series	series	NOUN
ejpam-3950	394	15	with	with	ADP
ejpam-3950	394	16	applications	application	NOUN
ejpam-3950	394	17	,	,	PUNCT
ejpam-3950	394	18	american	american	ADJ
ejpam-3950	394	19	journal	journal	PROPN
ejpam-3950	394	20	of	of	ADP
ejpam-3950	394	21	computational	computational	ADJ
ejpam-3950	394	22	and	and	CCONJ
ejpam-3950	394	23	applied	apply	VERB
ejpam-3950	394	24	mathematics	mathematic	NOUN
ejpam-3950	394	25	4(6):187	4(6):187	NUM
ejpam-3950	394	26	-	-	SYM
ejpam-3950	394	27	191	191	NUM
ejpam-3950	394	28	,	,	PUNCT
ejpam-3950	394	29	(	(	PUNCT
ejpam-3950	394	30	2014	2014	NUM
ejpam-3950	394	31	)	)	PUNCT
ejpam-3950	394	32	.	.	PUNCT
ejpam-3950	395	1	[	[	X
ejpam-3950	395	2	17	17	NUM
ejpam-3950	395	3	]	]	X
ejpam-3950	395	4	w.	w.	PROPN
ejpam-3950	395	5	s	s	PROPN
ejpam-3950	395	6	chung	chung	PROPN
ejpam-3950	395	7	,	,	PUNCT
ejpam-3950	395	8	fractional	fractional	PROPN
ejpam-3950	395	9	newton	newton	PROPN
ejpam-3950	395	10	mechanics	mechanic	NOUN
ejpam-3950	395	11	with	with	ADP
ejpam-3950	395	12	conformable	conformable	ADJ
ejpam-3950	395	13	fractional	fractional	ADJ
ejpam-3950	395	14	derivative	derivative	ADJ
ejpam-3950	395	15	,	,	PUNCT
ejpam-3950	395	16	journal	journal	NOUN
ejpam-3950	395	17	of	of	ADP
ejpam-3950	395	18	computational	computational	ADJ
ejpam-3950	395	19	and	and	CCONJ
ejpam-3950	395	20	applied	applied	ADJ
ejpam-3950	395	21	mathematics	mathematic	NOUN
ejpam-3950	395	22	,	,	PUNCT
ejpam-3950	395	23	290:150	290:150	NOUN
ejpam-3950	395	24	-	-	SYM
ejpam-3950	395	25	158	158	NUM
ejpam-3950	395	26	,	,	PUNCT
ejpam-3950	395	27	(	(	PUNCT
ejpam-3950	395	28	2015	2015	NUM
ejpam-3950	395	29	)	)	PUNCT
ejpam-3950	395	30	.	.	PUNCT
ejpam-3950	396	1	[	[	X
ejpam-3950	396	2	18	18	NUM
ejpam-3950	396	3	]	]	PUNCT
ejpam-3950	396	4	m.	m.	NOUN
ejpam-3950	396	5	alhorani	alhorani	PROPN
ejpam-3950	396	6	,	,	PUNCT
ejpam-3950	396	7	m.	m.	NOUN
ejpam-3950	396	8	abuhammad	abuhammad	PROPN
ejpam-3950	396	9	,	,	PUNCT
ejpam-3950	396	10	r.	r.	PROPN
ejpam-3950	396	11	khalil	khalil	PROPN
ejpam-3950	396	12	,	,	PUNCT
ejpam-3950	396	13	variation	variation	NOUN
ejpam-3950	396	14	of	of	ADP
ejpam-3950	396	15	parameters	parameter	NOUN
ejpam-3950	396	16	for	for	ADP
ejpam-3950	396	17	local	local	ADJ
ejpam-3950	396	18	fractional	fractional	ADJ
ejpam-3950	396	19	nonhomogenous	nonhomogenous	ADJ
ejpam-3950	396	20	linear	linear	ADJ
ejpam-3950	396	21	-	-	PUNCT
ejpam-3950	396	22	differential	differential	NOUN
ejpam-3950	396	23	equations	equation	NOUN
ejpam-3950	396	24	j.	j.	PROPN
ejpam-3950	396	25	math	math	PROPN
ejpam-3950	396	26	.	.	PUNCT
ejpam-3950	397	1	computer	computer	NOUN
ejpam-3950	397	2	sci	sci	PROPN
ejpam-3950	397	3	16:140	16:140	NUM
ejpam-3950	397	4	-	-	SYM
ejpam-3950	397	5	146	146	NUM
ejpam-3950	397	6	,	,	PUNCT
ejpam-3950	397	7	(	(	PUNCT
ejpam-3950	397	8	2016	2016	NUM
ejpam-3950	397	9	)	)	PUNCT
ejpam-3950	397	10	.	.	PUNCT
ejpam-3950	398	1	[	[	X
ejpam-3950	398	2	19	19	NUM
ejpam-3950	398	3	]	]	X
ejpam-3950	398	4	w.	w.	PROPN
ejpam-3950	398	5	deeb	deeb	PROPN
ejpam-3950	398	6	,	,	PUNCT
ejpam-3950	398	7	r.	r.	PROPN
ejpam-3950	398	8	khalil	khalil	PROPN
ejpam-3950	398	9	,	,	PUNCT
ejpam-3950	398	10	best	good	ADJ
ejpam-3950	398	11	approximation	approximation	NOUN
ejpam-3950	398	12	in	in	ADP
ejpam-3950	398	13	l(x;y	l(x;y	PROPN
ejpam-3950	398	14	)	)	PUNCT
ejpam-3950	398	15	,	,	PUNCT
ejpam-3950	398	16	mathematical	mathematical	ADJ
ejpam-3950	398	17	proceedings	proceeding	NOUN
ejpam-3950	398	18	of	of	ADP
ejpam-3950	398	19	the	the	DET
ejpam-3950	398	20	cambridge	cambridge	PROPN
ejpam-3950	398	21	philosophical	philosophical	ADJ
ejpam-3950	398	22	society	society	NOUN
ejpam-3950	398	23	104:527	104:527	PROPN
ejpam-3950	398	24	-	-	SYM
ejpam-3950	398	25	531	531	NUM
ejpam-3950	398	26	,	,	PUNCT
ejpam-3950	398	27	(	(	PUNCT
ejpam-3950	398	28	1988	1988	NUM
ejpam-3950	398	29	)	)	PUNCT
ejpam-3950	398	30	.	.	PUNCT
ejpam-3950	399	1	[	[	X
ejpam-3950	399	2	20	20	NUM
ejpam-3950	399	3	]	]	PUNCT
ejpam-3950	399	4	m.	m.	NOUN
ejpam-3950	399	5	al	al	PROPN
ejpam-3950	399	6	-	-	PUNCT
ejpam-3950	399	7	horani	horani	PROPN
ejpam-3950	399	8	,	,	PUNCT
ejpam-3950	399	9	r.	r.	PROPN
ejpam-3950	399	10	khalil	khalil	PROPN
ejpam-3950	399	11	and	and	CCONJ
ejpam-3950	399	12	aldarawi	aldarawi	VERB
ejpam-3950	399	13	,	,	PUNCT
ejpam-3950	399	14	fractional	fractional	PROPN
ejpam-3950	399	15	cauchy	cauchy	PROPN
ejpam-3950	399	16	euler	euler	PROPN
ejpam-3950	399	17	differential	differential	PROPN
ejpam-3950	399	18	equation	equation	NOUN
ejpam-3950	399	19	,	,	PUNCT
ejpam-3950	399	20	j.	j.	PROPN
ejpam-3950	399	21	computational	computational	ADJ
ejpam-3950	399	22	analysis	analysis	NOUN
ejpam-3950	399	23	and	and	CCONJ
ejpam-3950	399	24	applications	application	NOUN
ejpam-3950	399	25	28(2):226	28(2):226	NOUN
ejpam-3950	399	26	-	-	SYM
ejpam-3950	399	27	233	233	NUM
ejpam-3950	399	28	,	,	PUNCT
ejpam-3950	399	29	(	(	PUNCT
ejpam-3950	399	30	2019	2019	NUM
ejpam-3950	399	31	)	)	PUNCT
ejpam-3950	399	32	.	.	PUNCT
ejpam-3950	400	1	references	reference	NOUN
ejpam-3950	400	2	505	505	NUM
ejpam-3950	400	3	[	[	X
ejpam-3950	400	4	21	21	NUM
ejpam-3950	400	5	]	]	X
ejpam-3950	400	6	r.	r.	PROPN
ejpam-3950	400	7	khalil	khalil	PROPN
ejpam-3950	400	8	,	,	PUNCT
ejpam-3950	400	9	m.	m.	PROPN
ejpam-3950	400	10	al	al	PROPN
ejpam-3950	400	11	horani	horani	PROPN
ejpam-3950	400	12	,	,	PUNCT
ejpam-3950	400	13	m.	m.	NOUN
ejpam-3950	400	14	a.	a.	PROPN
ejpam-3950	400	15	hammad	hammad	PROPN
ejpam-3950	400	16	,	,	PUNCT
ejpam-3950	400	17	geometric	geometric	ADJ
ejpam-3950	400	18	meaning	meaning	NOUN
ejpam-3950	400	19	of	of	ADP
ejpam-3950	400	20	conformable	conformable	ADJ
ejpam-3950	400	21	derivative	derivative	NOUN
ejpam-3950	400	22	via	via	ADP
ejpam-3950	400	23	fractional	fractional	ADJ
ejpam-3950	400	24	cords	cord	NOUN
ejpam-3950	400	25	,	,	PUNCT
ejpam-3950	400	26	j.	j.	PROPN
ejpam-3950	400	27	math	math	PROPN
ejpam-3950	400	28	.	.	PUNCT
ejpam-3950	401	1	computer	computer	PROPN
ejpam-3950	401	2	sci	sci	PROPN
ejpam-3950	401	3	.	.	PROPN
ejpam-3950	401	4	,	,	PUNCT
ejpam-3950	401	5	19:241	19:241	PROPN
ejpam-3950	401	6	-	-	SYM
ejpam-3950	401	7	245	245	NUM
ejpam-3950	401	8	,	,	PUNCT
ejpam-3950	401	9	(	(	PUNCT
ejpam-3950	401	10	2019	2019	NUM
ejpam-3950	401	11	)	)	PUNCT
ejpam-3950	401	12	.	.	PUNCT
ejpam-3950	402	1	[	[	X
ejpam-3950	402	2	22	22	NUM
ejpam-3950	402	3	]	]	PUNCT
ejpam-3950	402	4	m.	m.	NOUN
ejpam-3950	402	5	al	al	PROPN
ejpam-3950	402	6	horani	horani	PROPN
ejpam-3950	402	7	,	,	PUNCT
ejpam-3950	402	8	m.	m.	NOUN
ejpam-3950	402	9	fabrizio	fabrizio	PROPN
ejpam-3950	402	10	,	,	PUNCT
ejpam-3950	402	11	a.	a.	NOUN
ejpam-3950	402	12	favini	favini	PROPN
ejpam-3950	402	13	,	,	PUNCT
ejpam-3950	402	14	and	and	CCONJ
ejpam-3950	402	15	h.	h.	PROPN
ejpam-3950	402	16	tanabe	tanabe	PROPN
ejpam-3950	402	17	,	,	PUNCT
ejpam-3950	402	18	fractional	fractional	ADJ
ejpam-3950	402	19	cauchy	cauchy	NOUN
ejpam-3950	402	20	problems	problem	NOUN
ejpam-3950	402	21	for	for	ADP
ejpam-3950	402	22	infnite	infnite	ADJ
ejpam-3950	402	23	interval	interval	NOUN
ejpam-3950	402	24	case	case	NOUN
ejpam-3950	402	25	,	,	PUNCT
ejpam-3950	402	26	discrete	discrete	VERB
ejpam-3950	402	27	continuous	continuous	ADJ
ejpam-3950	402	28	dynamical	dynamical	ADJ
ejpam-3950	402	29	systems	system	NOUN
ejpam-3950	402	30	-	-	PUNCT
ejpam-3950	402	31	s	s	NOUN
ejpam-3950	402	32	,	,	PUNCT
ejpam-3950	402	33	3(12):3285	3(12):3285	NUM
ejpam-3950	402	34	,	,	PUNCT
ejpam-3950	402	35	(	(	PUNCT
ejpam-3950	402	36	2020	2020	NUM
ejpam-3950	402	37	)	)	PUNCT
ejpam-3950	402	38	.	.	PUNCT
ejpam-3950	403	1	[	[	X
ejpam-3950	403	2	23	23	NUM
ejpam-3950	403	3	]	]	X
ejpam-3950	403	4	o.	o.	NOUN
ejpam-3950	403	5	a.	a.	NOUN
ejpam-3950	403	6	arqub	arqub	PROPN
ejpam-3950	403	7	,	,	PUNCT
ejpam-3950	403	8	m.	m.	NOUN
ejpam-3950	403	9	al	al	PROPN
ejpam-3950	403	10	-	-	PUNCT
ejpam-3950	403	11	smadi	smadi	NOUN
ejpam-3950	403	12	,	,	PUNCT
ejpam-3950	403	13	fuzzy	fuzzy	ADJ
ejpam-3950	403	14	conformable	conformable	ADJ
ejpam-3950	403	15	fractional	fractional	ADJ
ejpam-3950	403	16	differential	differential	ADJ
ejpam-3950	403	17	equations	equation	NOUN
ejpam-3950	403	18	:	:	PUNCT
ejpam-3950	403	19	novel	novel	NOUN
ejpam-3950	403	20	extended	extend	VERB
ejpam-3950	403	21	approach	approach	NOUN
ejpam-3950	403	22	and	and	CCONJ
ejpam-3950	403	23	new	new	ADJ
ejpam-3950	403	24	numerical	numerical	ADJ
ejpam-3950	403	25	solutions	solution	NOUN
ejpam-3950	403	26	,	,	PUNCT
ejpam-3950	403	27	soft	soft	ADJ
ejpam-3950	403	28	computing	computing	NOUN
ejpam-3950	403	29	.	.	PUNCT
ejpam-3950	403	30	,	,	PUNCT
ejpam-3950	403	31	1	1	NUM
ejpam-3950	403	32	-	-	SYM
ejpam-3950	403	33	22	22	NUM
ejpam-3950	403	34	,	,	PUNCT
ejpam-3950	403	35	(	(	PUNCT
ejpam-3950	403	36	2020	2020	NUM
ejpam-3950	403	37	)	)	PUNCT
ejpam-3950	403	38	.	.	PUNCT
ejpam-3950	404	1	[	[	X
ejpam-3950	404	2	24	24	NUM
ejpam-3950	404	3	]	]	PUNCT
ejpam-3950	404	4	m.	m.	NOUN
ejpam-3950	404	5	al	al	PROPN
ejpam-3950	404	6	-	-	PUNCT
ejpam-3950	404	7	smadi	smadi	NOUN
ejpam-3950	404	8	,	,	PUNCT
ejpam-3950	404	9	o.	o.	NOUN
ejpam-3950	404	10	a.	a.	NOUN
ejpam-3950	404	11	arqub	arqub	PROPN
ejpam-3950	404	12	,	,	PUNCT
ejpam-3950	404	13	s.	s.	PROPN
ejpam-3950	404	14	hadid	hadid	PROPN
ejpam-3950	404	15	,	,	PUNCT
ejpam-3950	404	16	an	an	DET
ejpam-3950	404	17	attractive	attractive	ADJ
ejpam-3950	404	18	analytical	analytical	ADJ
ejpam-3950	404	19	technique	technique	NOUN
ejpam-3950	404	20	for	for	ADP
ejpam-3950	404	21	coupled	couple	VERB
ejpam-3950	404	22	system	system	NOUN
ejpam-3950	404	23	of	of	ADP
ejpam-3950	404	24	fractional	fractional	ADJ
ejpam-3950	404	25	partial	partial	ADJ
ejpam-3950	404	26	differential	differential	ADJ
ejpam-3950	404	27	equations	equation	NOUN
ejpam-3950	404	28	in	in	ADP
ejpam-3950	404	29	shallow	shallow	ADJ
ejpam-3950	404	30	water	water	NOUN
ejpam-3950	404	31	waves	wave	NOUN
ejpam-3950	404	32	with	with	ADP
ejpam-3950	404	33	conformable	conformable	ADJ
ejpam-3950	404	34	derivative	derivative	NOUN
ejpam-3950	404	35	.	.	PUNCT
ejpam-3950	405	1	communications	communication	NOUN
ejpam-3950	405	2	in	in	ADP
ejpam-3950	405	3	theoretical	theoretical	ADJ
ejpam-3950	405	4	physics	physic	NOUN
ejpam-3950	405	5	,	,	PUNCT
ejpam-3950	405	6	72(8):085001	72(8):085001	NUM
ejpam-3950	405	7	,	,	PUNCT
ejpam-3950	405	8	(	(	PUNCT
ejpam-3950	405	9	2020	2020	NUM
ejpam-3950	405	10	)	)	PUNCT
ejpam-3950	405	11	.	.	PUNCT
ejpam-3950	406	1	[	[	X
ejpam-3950	406	2	25	25	NUM
ejpam-3950	406	3	]	]	X
ejpam-3950	406	4	o.	o.	PROPN
ejpam-3950	406	5	abu	abu	PROPN
ejpam-3950	406	6	arqub	arqub	PROPN
ejpam-3950	406	7	,	,	PUNCT
ejpam-3950	406	8	solutions	solution	NOUN
ejpam-3950	406	9	of	of	ADP
ejpam-3950	406	10	timefractional	timefractional	ADJ
ejpam-3950	406	11	tricomi	tricomi	NOUN
ejpam-3950	406	12	and	and	CCONJ
ejpam-3950	406	13	keldysh	keldysh	ADJ
ejpam-3950	406	14	equations	equation	NOUN
ejpam-3950	406	15	of	of	ADP
ejpam-3950	406	16	dirichlet	dirichlet	PROPN
ejpam-3950	406	17	functions	function	NOUN
ejpam-3950	406	18	types	type	NOUN
ejpam-3950	406	19	in	in	ADP
ejpam-3950	406	20	hilbert	hilbert	NOUN
ejpam-3950	406	21	space	space	NOUN
ejpam-3950	406	22	.	.	PUNCT
ejpam-3950	407	1	numerical	numerical	ADJ
ejpam-3950	407	2	methods	method	NOUN
ejpam-3950	407	3	for	for	ADP
ejpam-3950	407	4	partial	partial	ADJ
ejpam-3950	407	5	differential	differential	NOUN
ejpam-3950	407	6	equations	equation	NOUN
ejpam-3950	407	7	,	,	PUNCT
ejpam-3950	407	8	34(5):1759	34(5):1759	NUM
ejpam-3950	407	9	-	-	SYM
ejpam-3950	407	10	1780	1780	NUM
ejpam-3950	407	11	,	,	PUNCT
ejpam-3950	407	12	(	(	PUNCT
ejpam-3950	407	13	2018	2018	NUM
ejpam-3950	407	14	)	)	PUNCT
ejpam-3950	407	15	.	.	PUNCT