id	sid	tid	token	lemma	pos
ejpam-6238	1	1	european	european	PROPN
ejpam-6238	1	2	journal	journal	PROPN
ejpam-6238	1	3	of	of	ADP
ejpam-6238	1	4	pure	pure	ADJ
ejpam-6238	1	5	and	and	CCONJ
ejpam-6238	1	6	applied	applied	ADJ
ejpam-6238	1	7	mathematics	mathematic	NOUN
ejpam-6238	1	8	2025	2025	NUM
ejpam-6238	1	9	,	,	PUNCT
ejpam-6238	1	10	vol	vol	NOUN
ejpam-6238	1	11	.	.	PROPN
ejpam-6238	1	12	18	18	NUM
ejpam-6238	1	13	,	,	PUNCT
ejpam-6238	1	14	issue	issue	NOUN
ejpam-6238	1	15	3	3	NUM
ejpam-6238	1	16	,	,	PUNCT
ejpam-6238	1	17	article	article	NOUN
ejpam-6238	1	18	number	number	NOUN
ejpam-6238	1	19	6238	6238	NUM
ejpam-6238	1	20	issn	issn	PROPN
ejpam-6238	1	21	1307	1307	NUM
ejpam-6238	1	22	-	-	SYM
ejpam-6238	1	23	5543	5543	NUM
ejpam-6238	1	24	–	–	PUNCT
ejpam-6238	1	25	ejpam.com	ejpam.com	X
ejpam-6238	1	26	published	publish	VERB
ejpam-6238	1	27	by	by	ADP
ejpam-6238	1	28	new	new	PROPN
ejpam-6238	1	29	york	york	PROPN
ejpam-6238	1	30	business	business	PROPN
ejpam-6238	1	31	global	global	PROPN
ejpam-6238	1	32	finite	finite	PROPN
ejpam-6238	1	33	rank	rank	NOUN
ejpam-6238	1	34	solution	solution	NOUN
ejpam-6238	1	35	for	for	ADP
ejpam-6238	1	36	conformable	conformable	ADJ
ejpam-6238	1	37	second	second	ADJ
ejpam-6238	1	38	-	-	PUNCT
ejpam-6238	1	39	order	order	NOUN
ejpam-6238	1	40	abstract	abstract	ADJ
ejpam-6238	1	41	cauchy	cauchy	ADJ
ejpam-6238	1	42	problem	problem	NOUN
ejpam-6238	1	43	in	in	ADP
ejpam-6238	1	44	hilbert	hilbert	PROPN
ejpam-6238	1	45	space	space	PROPN
ejpam-6238	1	46	huda	huda	PROPN
ejpam-6238	1	47	odetallah1,∗	odetallah1,∗	PROPN
ejpam-6238	1	48	,	,	PUNCT
ejpam-6238	1	49	mayada	mayada	NOUN
ejpam-6238	1	50	abualhomos1	abualhomos1	PROPN
ejpam-6238	1	51	,	,	PUNCT
ejpam-6238	1	52	tala	tala	PROPN
ejpam-6238	1	53	sasa1	sasa1	NOUN
ejpam-6238	1	54	,	,	PUNCT
ejpam-6238	1	55	lubaba	lubaba	PROPN
ejpam-6238	1	56	shaikh1	shaikh1	NOUN
ejpam-6238	1	57	,	,	PUNCT
ejpam-6238	1	58	omniya	omniya	PROPN
ejpam-6238	1	59	miri2	miri2	NOUN
ejpam-6238	1	60	1	1	NUM
ejpam-6238	1	61	department	department	NOUN
ejpam-6238	1	62	of	of	ADP
ejpam-6238	1	63	mathematics	mathematic	NOUN
ejpam-6238	1	64	,	,	PUNCT
ejpam-6238	1	65	applied	apply	VERB
ejpam-6238	1	66	science	science	NOUN
ejpam-6238	1	67	private	private	ADJ
ejpam-6238	1	68	university	university	NOUN
ejpam-6238	1	69	,	,	PUNCT
ejpam-6238	1	70	amman	amman	PROPN
ejpam-6238	1	71	11931	11931	NUM
ejpam-6238	1	72	,	,	PUNCT
ejpam-6238	1	73	jordan	jordan	PROPN
ejpam-6238	1	74	2	2	NUM
ejpam-6238	1	75	department	department	NOUN
ejpam-6238	1	76	of	of	ADP
ejpam-6238	1	77	basic	basic	ADJ
ejpam-6238	1	78	science	science	NOUN
ejpam-6238	1	79	,	,	PUNCT
ejpam-6238	1	80	deanship	deanship	NOUN
ejpam-6238	1	81	of	of	ADP
ejpam-6238	1	82	preparatory	preparatory	ADJ
ejpam-6238	1	83	year	year	NOUN
ejpam-6238	1	84	and	and	CCONJ
ejpam-6238	1	85	supporting	support	VERB
ejpam-6238	1	86	studies	study	NOUN
ejpam-6238	1	87	,	,	PUNCT
ejpam-6238	1	88	imam	imam	PROPN
ejpam-6238	1	89	abdulrahman	abdulrahman	PROPN
ejpam-6238	1	90	bin	bin	PROPN
ejpam-6238	1	91	faisal	faisal	PROPN
ejpam-6238	1	92	university	university	PROPN
ejpam-6238	1	93	,	,	PUNCT
ejpam-6238	1	94	p.o	p.o	PROPN
ejpam-6238	1	95	.	.	PROPN
ejpam-6238	1	96	box	box	PROPN
ejpam-6238	1	97	1982	1982	NUM
ejpam-6238	1	98	,	,	PUNCT
ejpam-6238	1	99	dammam	dammam	PROPN
ejpam-6238	1	100	34212	34212	NUM
ejpam-6238	1	101	,	,	PUNCT
ejpam-6238	1	102	saudi	saudi	PROPN
ejpam-6238	1	103	arabia	arabia	PROPN
ejpam-6238	1	104	abstract	abstract	NOUN
ejpam-6238	1	105	.	.	PUNCT
ejpam-6238	2	1	this	this	DET
ejpam-6238	2	2	paper	paper	NOUN
ejpam-6238	2	3	presents	present	VERB
ejpam-6238	2	4	a	a	DET
ejpam-6238	2	5	comprehensive	comprehensive	ADJ
ejpam-6238	2	6	analytical	analytical	ADJ
ejpam-6238	2	7	framework	framework	NOUN
ejpam-6238	2	8	for	for	ADP
ejpam-6238	2	9	constructing	construct	VERB
ejpam-6238	2	10	finiterank	finiterank	NOUN
ejpam-6238	2	11	solution	solution	NOUN
ejpam-6238	2	12	to	to	ADP
ejpam-6238	2	13	second	second	ADJ
ejpam-6238	2	14	-	-	PUNCT
ejpam-6238	2	15	order	order	NOUN
ejpam-6238	2	16	conformable	conformable	ADJ
ejpam-6238	2	17	fractional	fractional	ADJ
ejpam-6238	2	18	abstract	abstract	ADJ
ejpam-6238	2	19	cauchy	cauchy	PROPN
ejpam-6238	2	20	problem	problem	NOUN
ejpam-6238	2	21	.	.	PUNCT
ejpam-6238	3	1	we	we	PRON
ejpam-6238	3	2	examine	examine	VERB
ejpam-6238	3	3	the	the	DET
ejpam-6238	3	4	mathematical	mathematical	ADJ
ejpam-6238	3	5	structure	structure	NOUN
ejpam-6238	3	6	:	:	PUNCT
ejpam-6238	3	7	eu(2α)(t	eu(2α)(t	X
ejpam-6238	3	8	)	)	PUNCT
ejpam-6238	4	1	+	+	NOUN
ejpam-6238	4	2	au(α)(t	au(α)(t	NUM
ejpam-6238	4	3	)	)	PUNCT
ejpam-6238	4	4	+	+	ADJ
ejpam-6238	4	5	bu(t	bu(t	NOUN
ejpam-6238	4	6	)	)	PUNCT
ejpam-6238	4	7	=	=	SYM
ejpam-6238	4	8	f(t	f(t	NOUN
ejpam-6238	4	9	)	)	PUNCT
ejpam-6238	4	10	subject	subject	NOUN
ejpam-6238	4	11	to	to	ADP
ejpam-6238	4	12	prescribed	prescribed	ADJ
ejpam-6238	4	13	initial	initial	ADJ
ejpam-6238	4	14	conditions	condition	NOUN
ejpam-6238	4	15	u(0	u(0	NOUN
ejpam-6238	4	16	)	)	PUNCT
ejpam-6238	4	17	=	=	PUNCT
ejpam-6238	4	18	u0	u0	ADJ
ejpam-6238	4	19	and	and	CCONJ
ejpam-6238	4	20	u(α)(0	u(α)(0	NUM
ejpam-6238	4	21	)	)	PUNCT
ejpam-6238	5	1	=	=	SYM
ejpam-6238	5	2	u	u	NOUN
ejpam-6238	5	3	(	(	PUNCT
ejpam-6238	5	4	α	α	NOUN
ejpam-6238	5	5	)	)	PUNCT
ejpam-6238	5	6	0	0	NUM
ejpam-6238	5	7	,	,	PUNCT
ejpam-6238	5	8	where	where	SCONJ
ejpam-6238	5	9	a	a	DET
ejpam-6238	5	10	,	,	PUNCT
ejpam-6238	5	11	b	b	NOUN
ejpam-6238	5	12	,	,	PUNCT
ejpam-6238	5	13	and	and	CCONJ
ejpam-6238	5	14	e	e	PROPN
ejpam-6238	5	15	represent	represent	VERB
ejpam-6238	5	16	closed	close	VERB
ejpam-6238	5	17	linear	linear	PROPN
ejpam-6238	5	18	operators	operator	NOUN
ejpam-6238	5	19	acting	act	VERB
ejpam-6238	5	20	on	on	ADP
ejpam-6238	5	21	a	a	DET
ejpam-6238	5	22	banach	banach	NOUN
ejpam-6238	5	23	space	space	NOUN
ejpam-6238	5	24	x	x	NOUN
ejpam-6238	5	25	,	,	PUNCT
ejpam-6238	5	26	f	f	X
ejpam-6238	5	27	:	:	PUNCT
ejpam-6238	6	1	[	[	X
ejpam-6238	6	2	0,∞	0,∞	NOUN
ejpam-6238	6	3	)	)	PUNCT
ejpam-6238	6	4	→	→	PUNCT
ejpam-6238	6	5	x	x	X
ejpam-6238	6	6	is	be	AUX
ejpam-6238	6	7	continuous	continuous	ADJ
ejpam-6238	6	8	,	,	PUNCT
ejpam-6238	6	9	and	and	CCONJ
ejpam-6238	6	10	u	u	NOUN
ejpam-6238	6	11	is	be	AUX
ejpam-6238	6	12	continuously	continuously	ADV
ejpam-6238	6	13	differentiable	differentiable	ADJ
ejpam-6238	6	14	on	on	ADP
ejpam-6238	6	15	[	[	X
ejpam-6238	6	16	0,∞	0,∞	NOUN
ejpam-6238	6	17	)	)	PUNCT
ejpam-6238	6	18	.	.	PUNCT
ejpam-6238	7	1	our	our	PRON
ejpam-6238	7	2	analytical	analytical	ADJ
ejpam-6238	7	3	methodology	methodology	NOUN
ejpam-6238	7	4	exploits	exploit	VERB
ejpam-6238	7	5	tensor	tensor	NOUN
ejpam-6238	7	6	product	product	NOUN
ejpam-6238	7	7	decomposition	decomposition	NOUN
ejpam-6238	7	8	techniques	technique	NOUN
ejpam-6238	7	9	to	to	PART
ejpam-6238	7	10	transform	transform	VERB
ejpam-6238	7	11	the	the	DET
ejpam-6238	7	12	problem	problem	NOUN
ejpam-6238	7	13	into	into	ADP
ejpam-6238	7	14	finite	finite	ADJ
ejpam-6238	7	15	-	-	ADJ
ejpam-6238	7	16	dimensional	dimensional	ADJ
ejpam-6238	7	17	systems	system	NOUN
ejpam-6238	7	18	.	.	PUNCT
ejpam-6238	8	1	this	this	DET
ejpam-6238	8	2	work	work	NOUN
ejpam-6238	8	3	proves	prove	VERB
ejpam-6238	8	4	solution	solution	NOUN
ejpam-6238	8	5	existence	existence	NOUN
ejpam-6238	8	6	and	and	CCONJ
ejpam-6238	8	7	uniqueness	uniqueness	NOUN
ejpam-6238	8	8	under	under	ADP
ejpam-6238	8	9	specific	specific	ADJ
ejpam-6238	8	10	conditions	condition	NOUN
ejpam-6238	8	11	,	,	PUNCT
ejpam-6238	8	12	and	and	CCONJ
ejpam-6238	8	13	provides	provide	VERB
ejpam-6238	8	14	computational	computational	ADJ
ejpam-6238	8	15	methods	method	NOUN
ejpam-6238	8	16	for	for	ADP
ejpam-6238	8	17	many	many	ADJ
ejpam-6238	8	18	types	type	NOUN
ejpam-6238	8	19	of	of	ADP
ejpam-6238	8	20	this	this	DET
ejpam-6238	8	21	problem	problem	NOUN
ejpam-6238	8	22	.	.	PUNCT
ejpam-6238	9	1	2020	2020	NUM
ejpam-6238	9	2	mathematics	mathematic	NOUN
ejpam-6238	9	3	subject	subject	NOUN
ejpam-6238	9	4	classifications	classification	NOUN
ejpam-6238	9	5	:	:	PUNCT
ejpam-6238	9	6	34g10	34g10	NUM
ejpam-6238	9	7	,	,	PUNCT
ejpam-6238	9	8	26a33	26a33	NUM
ejpam-6238	9	9	,	,	PUNCT
ejpam-6238	9	10	34a08	34a08	NUM
ejpam-6238	9	11	,	,	PUNCT
ejpam-6238	9	12	46m05	46m05	NUM
ejpam-6238	9	13	key	key	ADJ
ejpam-6238	9	14	words	word	NOUN
ejpam-6238	9	15	and	and	CCONJ
ejpam-6238	9	16	phrases	phrase	NOUN
ejpam-6238	9	17	:	:	PUNCT
ejpam-6238	9	18	abstract	abstract	ADJ
ejpam-6238	9	19	cauchy	cauchy	PROPN
ejpam-6238	9	20	problem	problem	NOUN
ejpam-6238	9	21	,	,	PUNCT
ejpam-6238	9	22	conformable	conformable	ADJ
ejpam-6238	9	23	fractional	fractional	ADJ
ejpam-6238	9	24	derivative	derivative	ADJ
ejpam-6238	9	25	,	,	PUNCT
ejpam-6238	9	26	tensor	tensor	NOUN
ejpam-6238	9	27	product	product	NOUN
ejpam-6238	9	28	of	of	ADP
ejpam-6238	9	29	banach	banach	NOUN
ejpam-6238	9	30	spaces	space	NOUN
ejpam-6238	9	31	,	,	PUNCT
ejpam-6238	9	32	finite	finite	ADJ
ejpam-6238	9	33	-	-	ADJ
ejpam-6238	9	34	rank	rank	ADJ
ejpam-6238	9	35	function	function	NOUN
ejpam-6238	9	36	1	1	NUM
ejpam-6238	9	37	.	.	PUNCT
ejpam-6238	9	38	introduction	introduction	NOUN
ejpam-6238	9	39	for	for	ADP
ejpam-6238	9	40	a	a	DET
ejpam-6238	9	41	banach	banach	NOUN
ejpam-6238	9	42	space	space	NOUN
ejpam-6238	9	43	x	x	PUNCT
ejpam-6238	10	1	and	and	CCONJ
ejpam-6238	10	2	i	i	PRON
ejpam-6238	10	3	=	=	PUNCT
ejpam-6238	11	1	[	[	X
ejpam-6238	11	2	0	0	NUM
ejpam-6238	11	3	,	,	PUNCT
ejpam-6238	11	4	1	1	NUM
ejpam-6238	11	5	]	]	PUNCT
ejpam-6238	11	6	or	or	CCONJ
ejpam-6238	11	7	[	[	X
ejpam-6238	11	8	0,∞	0,∞	NOUN
ejpam-6238	11	9	)	)	PUNCT
ejpam-6238	11	10	,	,	PUNCT
ejpam-6238	11	11	c(i	c(i	PROPN
ejpam-6238	11	12	)	)	PUNCT
ejpam-6238	11	13	is	be	AUX
ejpam-6238	11	14	the	the	DET
ejpam-6238	11	15	banach	banach	NOUN
ejpam-6238	11	16	space	space	NOUN
ejpam-6238	11	17	of	of	ADP
ejpam-6238	11	18	all	all	DET
ejpam-6238	11	19	real	real	ADV
ejpam-6238	11	20	-	-	PUNCT
ejpam-6238	11	21	valued	value	VERB
ejpam-6238	11	22	continuous	continuous	ADJ
ejpam-6238	11	23	functions	function	NOUN
ejpam-6238	11	24	defined	define	VERB
ejpam-6238	11	25	on	on	ADP
ejpam-6238	11	26	i	i	PRON
ejpam-6238	11	27	with	with	ADP
ejpam-6238	11	28	the	the	DET
ejpam-6238	11	29	supremum	supremum	ADJ
ejpam-6238	11	30	norm	norm	NOUN
ejpam-6238	11	31	,	,	PUNCT
ejpam-6238	11	32	c(i	c(i	NOUN
ejpam-6238	11	33	,	,	PUNCT
ejpam-6238	11	34	x	x	X
ejpam-6238	11	35	)	)	PUNCT
ejpam-6238	11	36	is	be	AUX
ejpam-6238	11	37	the	the	DET
ejpam-6238	11	38	space	space	NOUN
ejpam-6238	11	39	of	of	ADP
ejpam-6238	11	40	all	all	DET
ejpam-6238	11	41	continuous	continuous	ADJ
ejpam-6238	11	42	functions	function	NOUN
ejpam-6238	11	43	defined	define	VERB
ejpam-6238	11	44	on	on	ADP
ejpam-6238	11	45	i	i	PRON
ejpam-6238	11	46	taking	take	VERB
ejpam-6238	11	47	values	value	NOUN
ejpam-6238	11	48	in	in	ADP
ejpam-6238	11	49	x	x	NOUN
ejpam-6238	11	50	,	,	PUNCT
ejpam-6238	11	51	and	and	CCONJ
ejpam-6238	11	52	c(2α	c(2α	NOUN
ejpam-6238	11	53	)	)	PUNCT
ejpam-6238	11	54	(	(	PUNCT
ejpam-6238	11	55	i	i	PRON
ejpam-6238	11	56	,	,	PUNCT
ejpam-6238	11	57	x	x	X
ejpam-6238	11	58	)	)	PUNCT
ejpam-6238	11	59	is	be	AUX
ejpam-6238	11	60	the	the	DET
ejpam-6238	11	61	space	space	NOUN
ejpam-6238	11	62	of	of	ADP
ejpam-6238	11	63	functions	function	NOUN
ejpam-6238	11	64	on	on	ADP
ejpam-6238	11	65	i	i	PRON
ejpam-6238	11	66	taking	take	VERB
ejpam-6238	11	67	values	value	NOUN
ejpam-6238	11	68	in	in	ADP
ejpam-6238	11	69	x	x	PUNCT
ejpam-6238	11	70	with	with	ADP
ejpam-6238	11	71	continuous	continuous	ADJ
ejpam-6238	11	72	conformable	conformable	ADJ
ejpam-6238	11	73	derivatives	derivative	NOUN
ejpam-6238	11	74	up	up	ADP
ejpam-6238	11	75	to	to	PART
ejpam-6238	11	76	order	order	VERB
ejpam-6238	11	77	2α	2α	NOUN
ejpam-6238	11	78	.	.	PUNCT
ejpam-6238	12	1	the	the	DET
ejpam-6238	12	2	abstract	abstract	ADJ
ejpam-6238	12	3	cauchy	cauchy	ADJ
ejpam-6238	12	4	problem	problem	NOUN
ejpam-6238	12	5	represents	represent	VERB
ejpam-6238	12	6	one	one	NUM
ejpam-6238	12	7	of	of	ADP
ejpam-6238	12	8	the	the	DET
ejpam-6238	12	9	most	most	ADV
ejpam-6238	12	10	fundamental	fundamental	ADJ
ejpam-6238	12	11	classes	class	NOUN
ejpam-6238	12	12	of	of	ADP
ejpam-6238	12	13	differential	differential	ADJ
ejpam-6238	12	14	equations	equation	NOUN
ejpam-6238	12	15	in	in	ADP
ejpam-6238	12	16	applied	applied	ADJ
ejpam-6238	12	17	mathematics	mathematic	NOUN
ejpam-6238	12	18	,	,	PUNCT
ejpam-6238	12	19	with	with	ADP
ejpam-6238	12	20	applications	application	NOUN
ejpam-6238	12	21	spanning	span	VERB
ejpam-6238	12	22	from	from	ADP
ejpam-6238	12	23	heat	heat	NOUN
ejpam-6238	12	24	conduction	conduction	NOUN
ejpam-6238	12	25	and	and	CCONJ
ejpam-6238	12	26	wave	wave	NOUN
ejpam-6238	12	27	propagation	propagation	NOUN
ejpam-6238	12	28	to	to	ADP
ejpam-6238	12	29	population	population	NOUN
ejpam-6238	12	30	dynamics	dynamic	NOUN
ejpam-6238	12	31	and	and	CCONJ
ejpam-6238	12	32	financial	financial	ADJ
ejpam-6238	12	33	modeling	modeling	NOUN
ejpam-6238	12	34	.	.	PUNCT
ejpam-6238	13	1	the	the	DET
ejpam-6238	13	2	∗corresponding	∗corresponde	VERB
ejpam-6238	13	3	author	author	NOUN
ejpam-6238	13	4	.	.	PUNCT
ejpam-6238	14	1	doi	doi	NOUN
ejpam-6238	14	2	:	:	PUNCT
ejpam-6238	14	3	https://doi.org/10.29020/nybg.ejpam.v18i3.6238	https://doi.org/10.29020/nybg.ejpam.v18i3.6238	ADP
ejpam-6238	14	4	email	email	NOUN
ejpam-6238	14	5	addresses	address	NOUN
ejpam-6238	14	6	:	:	PUNCT
ejpam-6238	14	7	h	h	NOUN
ejpam-6238	14	8	odetallah@asu.edu.jo	odetallah@asu.edu.jo	ADJ
ejpam-6238	14	9	(	(	PUNCT
ejpam-6238	14	10	h.	h.	PROPN
ejpam-6238	14	11	odetallah	odetallah	PROPN
ejpam-6238	14	12	)	)	PUNCT
ejpam-6238	14	13	,	,	PUNCT
ejpam-6238	14	14	abuhomos@asu.edu.jo	abuhomos@asu.edu.jo	PROPN
ejpam-6238	14	15	(	(	PUNCT
ejpam-6238	14	16	m.	m.	NOUN
ejpam-6238	14	17	abualhomos	abualhomos	PROPN
ejpam-6238	14	18	)	)	PUNCT
ejpam-6238	14	19	,	,	PUNCT
ejpam-6238	14	20	t	t	PROPN
ejpam-6238	14	21	sasa@asu.edu.jo	sasa@asu.edu.jo	NOUN
ejpam-6238	14	22	(	(	PUNCT
ejpam-6238	14	23	t.	t.	PROPN
ejpam-6238	14	24	sasa	sasa	PROPN
ejpam-6238	14	25	)	)	PUNCT
ejpam-6238	14	26	,	,	PUNCT
ejpam-6238	14	27	l	l	PROPN
ejpam-6238	14	28	shaikh@asu.edu.jo	shaikh@asu.edu.jo	NOUN
ejpam-6238	14	29	(	(	PUNCT
ejpam-6238	14	30	l.	l.	PROPN
ejpam-6238	14	31	shaikh	shaikh	PROPN
ejpam-6238	14	32	)	)	PUNCT
ejpam-6238	14	33	,	,	PUNCT
ejpam-6238	14	34	ormiri@iau.edu.sa	ormiri@iau.edu.sa	PROPN
ejpam-6238	14	35	(	(	PUNCT
ejpam-6238	14	36	o.	o.	PROPN
ejpam-6238	14	37	miri	miri	PROPN
ejpam-6238	14	38	)	)	PUNCT
ejpam-6238	14	39	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-6238	15	1	1	1	NUM
ejpam-6238	15	2	copyright	copyright	NOUN
ejpam-6238	15	3	:	:	PUNCT
ejpam-6238	15	4	©	©	PROPN
ejpam-6238	15	5	2025	2025	NUM
ejpam-6238	15	6	the	the	DET
ejpam-6238	15	7	author(s	author(s	NOUN
ejpam-6238	15	8	)	)	PUNCT
ejpam-6238	15	9	.	.	PUNCT
ejpam-6238	16	1	(	(	PUNCT
ejpam-6238	16	2	cc	cc	NOUN
ejpam-6238	16	3	by	by	ADP
ejpam-6238	16	4	-	-	PUNCT
ejpam-6238	16	5	nc	nc	PROPN
ejpam-6238	16	6	4.0	4.0	NUM
ejpam-6238	16	7	)	)	PUNCT
ejpam-6238	16	8	h.	h.	NOUN
ejpam-6238	17	1	odetallah	odetallah	PROPN
ejpam-6238	17	2	et	et	PROPN
ejpam-6238	17	3	al	al	PROPN
ejpam-6238	17	4	.	.	PUNCT
ejpam-6238	17	5	/	/	SYM
ejpam-6238	17	6	eur	eur	PROPN
ejpam-6238	17	7	.	.	PUNCT
ejpam-6238	18	1	j.	j.	PROPN
ejpam-6238	18	2	pure	pure	PROPN
ejpam-6238	18	3	appl	appl	PROPN
ejpam-6238	18	4	.	.	PROPN
ejpam-6238	18	5	math	math	PROPN
ejpam-6238	18	6	,	,	PUNCT
ejpam-6238	18	7	18	18	NUM
ejpam-6238	18	8	(	(	PUNCT
ejpam-6238	18	9	3	3	NUM
ejpam-6238	18	10	)	)	PUNCT
ejpam-6238	18	11	(	(	PUNCT
ejpam-6238	18	12	2025	2025	NUM
ejpam-6238	18	13	)	)	PUNCT
ejpam-6238	18	14	,	,	PUNCT
ejpam-6238	18	15	6238	6238	NUM
ejpam-6238	18	16	2	2	NUM
ejpam-6238	18	17	of	of	ADP
ejpam-6238	18	18	11	11	NUM
ejpam-6238	18	19	general	general	ADJ
ejpam-6238	18	20	form	form	NOUN
ejpam-6238	18	21	of	of	ADP
ejpam-6238	18	22	the	the	DET
ejpam-6238	18	23	second	second	ADJ
ejpam-6238	18	24	-	-	PUNCT
ejpam-6238	18	25	order	order	NOUN
ejpam-6238	18	26	conformable	conformable	ADJ
ejpam-6238	18	27	fractional	fractional	ADJ
ejpam-6238	18	28	abstract	abstract	ADJ
ejpam-6238	18	29	cauchy	cauchy	ADJ
ejpam-6238	18	30	problem	problem	NOUN
ejpam-6238	18	31	under	under	ADP
ejpam-6238	18	32	investigation	investigation	NOUN
ejpam-6238	18	33	is	be	AUX
ejpam-6238	18	34	:	:	PUNCT
ejpam-6238	18	35	eu(2α)(t	eu(2α)(t	X
ejpam-6238	18	36	)	)	PUNCT
ejpam-6238	18	37	+	+	NOUN
ejpam-6238	18	38	au(α)(t	au(α)(t	NUM
ejpam-6238	18	39	)	)	PUNCT
ejpam-6238	19	1	+	+	ADJ
ejpam-6238	19	2	bu(t	bu(t	NOUN
ejpam-6238	19	3	)	)	PUNCT
ejpam-6238	19	4	=	=	SYM
ejpam-6238	19	5	f(t)z	f(t)z	NOUN
ejpam-6238	19	6	(	(	PUNCT
ejpam-6238	19	7	1	1	X
ejpam-6238	19	8	)	)	PUNCT
ejpam-6238	19	9	u(0	u(0	NOUN
ejpam-6238	19	10	)	)	PUNCT
ejpam-6238	19	11	=	=	PUNCT
ejpam-6238	19	12	u0	u0	PROPN
ejpam-6238	19	13	u(α)(0	u(α)(0	PROPN
ejpam-6238	19	14	)	)	PUNCT
ejpam-6238	19	15	=	=	SYM
ejpam-6238	19	16	u	u	NOUN
ejpam-6238	19	17	(	(	PUNCT
ejpam-6238	19	18	α	α	NOUN
ejpam-6238	19	19	)	)	PUNCT
ejpam-6238	19	20	0	0	NUM
ejpam-6238	19	21	where	where	SCONJ
ejpam-6238	19	22	a	a	DET
ejpam-6238	19	23	,	,	PUNCT
ejpam-6238	19	24	b	b	NOUN
ejpam-6238	19	25	and	and	CCONJ
ejpam-6238	19	26	e	e	NOUN
ejpam-6238	19	27	are	be	AUX
ejpam-6238	19	28	closed	close	VERB
ejpam-6238	19	29	linear	linear	ADJ
ejpam-6238	19	30	operators	operator	NOUN
ejpam-6238	19	31	on	on	ADP
ejpam-6238	19	32	a	a	DET
ejpam-6238	19	33	banach	banach	NOUN
ejpam-6238	19	34	space	space	NOUN
ejpam-6238	19	35	x	x	NOUN
ejpam-6238	19	36	,	,	PUNCT
ejpam-6238	19	37	u	u	PROPN
ejpam-6238	19	38	∈	∈	PROPN
ejpam-6238	19	39	c(2α)(i	c(2α)(i	PROPN
ejpam-6238	19	40	,	,	PUNCT
ejpam-6238	19	41	x	x	X
ejpam-6238	19	42	)	)	PUNCT
ejpam-6238	19	43	is	be	AUX
ejpam-6238	19	44	the	the	DET
ejpam-6238	19	45	unknown	unknown	ADJ
ejpam-6238	19	46	function	function	NOUN
ejpam-6238	19	47	,	,	PUNCT
ejpam-6238	19	48	f	f	PROPN
ejpam-6238	19	49	∈	∈	PROPN
ejpam-6238	19	50	c(i	c(i	PROPN
ejpam-6238	19	51	)	)	PUNCT
ejpam-6238	19	52	and	and	CCONJ
ejpam-6238	19	53	z	z	PROPN
ejpam-6238	19	54	,	,	PUNCT
ejpam-6238	19	55	u0	u0	ADJ
ejpam-6238	19	56	,	,	PUNCT
ejpam-6238	19	57	u	u	PROPN
ejpam-6238	19	58	(	(	PUNCT
ejpam-6238	19	59	α	α	NOUN
ejpam-6238	19	60	)	)	PUNCT
ejpam-6238	19	61	0	0	NUM
ejpam-6238	20	1	∈	∈	PROPN
ejpam-6238	20	2	x.	x.	NOUN
ejpam-6238	21	1	if	if	SCONJ
ejpam-6238	21	2	f	f	PROPN
ejpam-6238	21	3	=	=	SYM
ejpam-6238	21	4	0	0	PROPN
ejpam-6238	21	5	or	or	CCONJ
ejpam-6238	21	6	z	z	NOUN
ejpam-6238	21	7	=	=	SYM
ejpam-6238	21	8	0	0	NUM
ejpam-6238	21	9	,	,	PUNCT
ejpam-6238	21	10	then	then	ADV
ejpam-6238	21	11	the	the	DET
ejpam-6238	21	12	equation	equation	NOUN
ejpam-6238	21	13	is	be	AUX
ejpam-6238	21	14	homogeneous	homogeneous	ADJ
ejpam-6238	21	15	otherwise	otherwise	ADV
ejpam-6238	21	16	it	it	PRON
ejpam-6238	21	17	is	be	AUX
ejpam-6238	21	18	called	call	VERB
ejpam-6238	21	19	nonhomogeneous	nonhomogeneous	ADJ
ejpam-6238	21	20	.	.	PUNCT
ejpam-6238	22	1	if	if	SCONJ
ejpam-6238	22	2	f	f	PROPN
ejpam-6238	22	3	̸=	̸=	PROPN
ejpam-6238	22	4	0	0	NUM
ejpam-6238	22	5	and	and	CCONJ
ejpam-6238	22	6	z	z	PROPN
ejpam-6238	22	7	̸=	̸=	PROPN
ejpam-6238	22	8	0	0	NUM
ejpam-6238	22	9	,	,	PUNCT
ejpam-6238	22	10	then	then	ADV
ejpam-6238	22	11	we	we	PRON
ejpam-6238	22	12	have	have	VERB
ejpam-6238	22	13	two	two	NUM
ejpam-6238	22	14	cases	case	NOUN
ejpam-6238	22	15	.	.	PUNCT
ejpam-6238	23	1	if	if	SCONJ
ejpam-6238	23	2	f	f	PROPN
ejpam-6238	23	3	is	be	AUX
ejpam-6238	23	4	given	give	VERB
ejpam-6238	23	5	,	,	PUNCT
ejpam-6238	23	6	then	then	ADV
ejpam-6238	23	7	the	the	DET
ejpam-6238	23	8	problem	problem	NOUN
ejpam-6238	23	9	is	be	AUX
ejpam-6238	23	10	called	call	VERB
ejpam-6238	23	11	a	a	DET
ejpam-6238	23	12	direct	direct	ADJ
ejpam-6238	23	13	problem	problem	NOUN
ejpam-6238	23	14	,	,	PUNCT
ejpam-6238	23	15	otherwise	otherwise	ADV
ejpam-6238	23	16	the	the	DET
ejpam-6238	23	17	problem	problem	NOUN
ejpam-6238	23	18	is	be	AUX
ejpam-6238	23	19	called	call	VERB
ejpam-6238	23	20	an	an	DET
ejpam-6238	23	21	inverse	inverse	NOUN
ejpam-6238	23	22	problem	problem	NOUN
ejpam-6238	23	23	.	.	PUNCT
ejpam-6238	24	1	in	in	ADP
ejpam-6238	24	2	this	this	DET
ejpam-6238	24	3	paper	paper	NOUN
ejpam-6238	24	4	,	,	PUNCT
ejpam-6238	24	5	we	we	PRON
ejpam-6238	24	6	find	find	VERB
ejpam-6238	24	7	a	a	DET
ejpam-6238	24	8	finite	finite	ADJ
ejpam-6238	24	9	-	-	ADJ
ejpam-6238	24	10	rank	rank	ADJ
ejpam-6238	24	11	solution	solution	NOUN
ejpam-6238	24	12	of	of	ADP
ejpam-6238	24	13	the	the	DET
ejpam-6238	24	14	second	second	ADJ
ejpam-6238	24	15	-	-	PUNCT
ejpam-6238	24	16	order	order	NOUN
ejpam-6238	24	17	fractional	fractional	ADJ
ejpam-6238	24	18	type	type	NOUN
ejpam-6238	24	19	of	of	ADP
ejpam-6238	24	20	the	the	DET
ejpam-6238	24	21	abstract	abstract	ADJ
ejpam-6238	24	22	cauchy	cauchy	ADJ
ejpam-6238	24	23	problem	problem	NOUN
ejpam-6238	24	24	with	with	ADP
ejpam-6238	24	25	some	some	DET
ejpam-6238	24	26	conditions	condition	NOUN
ejpam-6238	24	27	on	on	ADP
ejpam-6238	24	28	a	a	DET
ejpam-6238	24	29	,	,	PUNCT
ejpam-6238	24	30	b	b	PROPN
ejpam-6238	24	31	and	and	CCONJ
ejpam-6238	24	32	e.	e.	PROPN
ejpam-6238	24	33	among	among	ADP
ejpam-6238	24	34	various	various	ADJ
ejpam-6238	24	35	fractional	fractional	ADJ
ejpam-6238	24	36	derivative	derivative	ADJ
ejpam-6238	24	37	definitions	definition	NOUN
ejpam-6238	24	38	available	available	ADJ
ejpam-6238	24	39	in	in	ADP
ejpam-6238	24	40	the	the	DET
ejpam-6238	24	41	literature	literature	NOUN
ejpam-6238	25	1	[	[	X
ejpam-6238	25	2	12,15	12,15	NUM
ejpam-6238	25	3	]	]	X
ejpam-6238	25	4	,	,	PUNCT
ejpam-6238	25	5	this	this	DET
ejpam-6238	25	6	paper	paper	NOUN
ejpam-6238	25	7	employs	employ	VERB
ejpam-6238	25	8	the	the	DET
ejpam-6238	25	9	conformable	conformable	ADJ
ejpam-6238	25	10	fractional	fractional	ADJ
ejpam-6238	25	11	derivative	derivative	NOUN
ejpam-6238	25	12	introduced	introduce	VERB
ejpam-6238	25	13	by	by	ADP
ejpam-6238	25	14	khalil	khalil	PROPN
ejpam-6238	25	15	et	et	PROPN
ejpam-6238	25	16	al	al	PROPN
ejpam-6238	25	17	.	.	PUNCT
ejpam-6238	26	1	[	[	X
ejpam-6238	26	2	10	10	NUM
ejpam-6238	26	3	]	]	PUNCT
ejpam-6238	26	4	due	due	ADP
ejpam-6238	26	5	to	to	ADP
ejpam-6238	26	6	its	its	PRON
ejpam-6238	26	7	advantageous	advantageous	ADJ
ejpam-6238	26	8	properties	property	NOUN
ejpam-6238	26	9	.	.	PUNCT
ejpam-6238	27	1	definition	definition	NOUN
ejpam-6238	27	2	1	1	NUM
ejpam-6238	27	3	.	.	PUNCT
ejpam-6238	28	1	let	let	VERB
ejpam-6238	28	2	f	f	NOUN
ejpam-6238	28	3	:	:	PUNCT
ejpam-6238	29	1	[	[	X
ejpam-6238	29	2	0,∞	0,∞	NUM
ejpam-6238	29	3	)	)	PUNCT
ejpam-6238	29	4	→	→	PUNCT
ejpam-6238	29	5	r	r	NOUN
ejpam-6238	29	6	be	be	AUX
ejpam-6238	29	7	a	a	DET
ejpam-6238	29	8	function	function	NOUN
ejpam-6238	29	9	.	.	PUNCT
ejpam-6238	30	1	the	the	DET
ejpam-6238	30	2	conformable	conformable	ADJ
ejpam-6238	30	3	fractional	fractional	ADJ
ejpam-6238	30	4	derivative	derivative	NOUN
ejpam-6238	30	5	of	of	ADP
ejpam-6238	30	6	f	f	PROPN
ejpam-6238	30	7	of	of	ADP
ejpam-6238	30	8	order	order	NOUN
ejpam-6238	30	9	α	α	NOUN
ejpam-6238	30	10	,	,	PUNCT
ejpam-6238	30	11	where	where	SCONJ
ejpam-6238	30	12	0	0	X
ejpam-6238	30	13	<	<	X
ejpam-6238	30	14	α	α	PROPN
ejpam-6238	30	15	≤	≤	ADJ
ejpam-6238	30	16	1	1	NUM
ejpam-6238	30	17	is	be	AUX
ejpam-6238	30	18	defined	define	VERB
ejpam-6238	30	19	by	by	ADP
ejpam-6238	30	20	:	:	PUNCT
ejpam-6238	30	21	f	f	PROPN
ejpam-6238	30	22	(	(	PUNCT
ejpam-6238	30	23	α)(t	α)(t	PROPN
ejpam-6238	30	24	)	)	PUNCT
ejpam-6238	30	25	=	=	SYM
ejpam-6238	31	1	lim	lim	PROPN
ejpam-6238	31	2	ϵ→0	ϵ→0	X
ejpam-6238	31	3	f(t+	f(t+	PROPN
ejpam-6238	31	4	ϵt1−α)−	ϵt1−α)−	NOUN
ejpam-6238	31	5	f(t	f(t	NOUN
ejpam-6238	31	6	)	)	PUNCT
ejpam-6238	31	7	ϵ	ϵ	X
ejpam-6238	31	8	for	for	ADP
ejpam-6238	31	9	all	all	DET
ejpam-6238	31	10	t	t	PROPN
ejpam-6238	31	11	>	>	X
ejpam-6238	31	12	0	0	X
ejpam-6238	31	13	.	.	PUNCT
ejpam-6238	32	1	if	if	SCONJ
ejpam-6238	32	2	f	f	PROPN
ejpam-6238	32	3	is	be	AUX
ejpam-6238	32	4	α−differentiable	α−differentiable	ADJ
ejpam-6238	32	5	on	on	ADP
ejpam-6238	32	6	(	(	PUNCT
ejpam-6238	32	7	0	0	NUM
ejpam-6238	32	8	,	,	PUNCT
ejpam-6238	32	9	c	c	NOUN
ejpam-6238	32	10	)	)	PUNCT
ejpam-6238	32	11	and	and	CCONJ
ejpam-6238	32	12	limt→0	limt→0	PROPN
ejpam-6238	32	13	+	+	CCONJ
ejpam-6238	32	14	f	f	X
ejpam-6238	32	15	(	(	PUNCT
ejpam-6238	32	16	α)(t	α)(t	ADJ
ejpam-6238	32	17	)	)	PUNCT
ejpam-6238	32	18	exists	exist	VERB
ejpam-6238	32	19	,	,	PUNCT
ejpam-6238	32	20	then	then	ADV
ejpam-6238	32	21	we	we	PRON
ejpam-6238	32	22	define	define	VERB
ejpam-6238	32	23	f	f	X
ejpam-6238	32	24	(	(	PUNCT
ejpam-6238	32	25	α)(0	α)(0	NUM
ejpam-6238	32	26	)	)	PUNCT
ejpam-6238	32	27	=	=	SYM
ejpam-6238	32	28	limt→0	limt→0	PROPN
ejpam-6238	32	29	+	+	X
ejpam-6238	32	30	f	f	X
ejpam-6238	32	31	(	(	PUNCT
ejpam-6238	32	32	α)(t	α)(t	PROPN
ejpam-6238	32	33	)	)	PUNCT
ejpam-6238	32	34	.	.	PUNCT
ejpam-6238	33	1	the	the	DET
ejpam-6238	33	2	power	power	NOUN
ejpam-6238	33	3	of	of	ADP
ejpam-6238	33	4	this	this	DET
ejpam-6238	33	5	definition	definition	NOUN
ejpam-6238	33	6	is	be	AUX
ejpam-6238	33	7	that	that	SCONJ
ejpam-6238	33	8	it	it	PRON
ejpam-6238	33	9	satisfies	satisfy	VERB
ejpam-6238	33	10	the	the	DET
ejpam-6238	33	11	most	most	ADJ
ejpam-6238	33	12	of	of	ADP
ejpam-6238	33	13	the	the	DET
ejpam-6238	33	14	properties	property	NOUN
ejpam-6238	33	15	of	of	ADP
ejpam-6238	33	16	the	the	DET
ejpam-6238	33	17	usual	usual	ADJ
ejpam-6238	33	18	derivatives	derivative	NOUN
ejpam-6238	33	19	such	such	ADJ
ejpam-6238	33	20	as	as	ADP
ejpam-6238	33	21	product	product	NOUN
ejpam-6238	33	22	rule	rule	NOUN
ejpam-6238	33	23	,	,	PUNCT
ejpam-6238	33	24	quotient	quotient	NOUN
ejpam-6238	33	25	rule	rule	NOUN
ejpam-6238	33	26	and	and	CCONJ
ejpam-6238	33	27	chain	chain	NOUN
ejpam-6238	33	28	rule	rule	NOUN
ejpam-6238	33	29	,	,	PUNCT
ejpam-6238	33	30	etc	etc	X
ejpam-6238	33	31	.	.	X
ejpam-6238	33	32	to	to	PART
ejpam-6238	33	33	read	read	VERB
ejpam-6238	33	34	more	more	ADJ
ejpam-6238	33	35	about	about	ADP
ejpam-6238	33	36	the	the	DET
ejpam-6238	33	37	conformable	conformable	ADJ
ejpam-6238	33	38	fractional	fractional	ADJ
ejpam-6238	33	39	derivatives	derivative	NOUN
ejpam-6238	33	40	see	see	VERB
ejpam-6238	33	41	[	[	X
ejpam-6238	33	42	1,2,9	1,2,9	NUM
ejpam-6238	33	43	]	]	X
ejpam-6238	33	44	.	.	PUNCT
ejpam-6238	34	1	first	first	ADV
ejpam-6238	34	2	of	of	ADP
ejpam-6238	34	3	all	all	PRON
ejpam-6238	34	4	,	,	PUNCT
ejpam-6238	34	5	let	let	VERB
ejpam-6238	34	6	us	we	PRON
ejpam-6238	34	7	define	define	VERB
ejpam-6238	34	8	what	what	PRON
ejpam-6238	34	9	the	the	DET
ejpam-6238	34	10	tensor	tensor	NOUN
ejpam-6238	34	11	product	product	NOUN
ejpam-6238	34	12	and	and	CCONJ
ejpam-6238	34	13	the	the	DET
ejpam-6238	34	14	finite	finite	ADJ
ejpam-6238	34	15	-	-	ADJ
ejpam-6238	34	16	rank	rank	ADJ
ejpam-6238	34	17	function	function	NOUN
ejpam-6238	34	18	are	be	AUX
ejpam-6238	34	19	.	.	PUNCT
ejpam-6238	35	1	definition	definition	NOUN
ejpam-6238	35	2	2	2	NUM
ejpam-6238	35	3	.	.	PUNCT
ejpam-6238	36	1	let	let	VERB
ejpam-6238	36	2	x	x	PRON
ejpam-6238	36	3	and	and	CCONJ
ejpam-6238	36	4	y	y	PROPN
ejpam-6238	36	5	be	be	VERB
ejpam-6238	36	6	banach	banach	ADV
ejpam-6238	36	7	spaces	space	NOUN
ejpam-6238	36	8	,	,	PUNCT
ejpam-6238	36	9	and	and	CCONJ
ejpam-6238	36	10	t	t	PROPN
ejpam-6238	36	11	∈	∈	PROPN
ejpam-6238	36	12	x∗	x∗	PROPN
ejpam-6238	36	13	(	(	PUNCT
ejpam-6238	36	14	the	the	DET
ejpam-6238	36	15	dual	dual	ADJ
ejpam-6238	36	16	of	of	ADP
ejpam-6238	36	17	x	x	NOUN
ejpam-6238	36	18	)	)	PUNCT
ejpam-6238	36	19	.	.	PUNCT
ejpam-6238	37	1	for	for	SCONJ
ejpam-6238	37	2	x	x	SYM
ejpam-6238	37	3	∈	∈	PROPN
ejpam-6238	37	4	x	x	X
ejpam-6238	37	5	and	and	CCONJ
ejpam-6238	37	6	y	y	PROPN
ejpam-6238	37	7	∈	∈	PROPN
ejpam-6238	37	8	y	y	PROPN
ejpam-6238	37	9	,	,	PUNCT
ejpam-6238	37	10	the	the	DET
ejpam-6238	37	11	tensor	tensor	NOUN
ejpam-6238	37	12	product	product	NOUN
ejpam-6238	37	13	of	of	ADP
ejpam-6238	37	14	x	x	PROPN
ejpam-6238	37	15	and	and	CCONJ
ejpam-6238	37	16	y	y	PROPN
ejpam-6238	37	17	is	be	AUX
ejpam-6238	37	18	the	the	DET
ejpam-6238	37	19	map	map	NOUN
ejpam-6238	37	20	x⊗y	x⊗y	PUNCT
ejpam-6238	37	21	:	:	PUNCT
ejpam-6238	37	22	x∗	x∗	PROPN
ejpam-6238	37	23	→	→	SYM
ejpam-6238	37	24	y	y	PROPN
ejpam-6238	37	25	as	as	ADP
ejpam-6238	37	26	x⊗y(t	x⊗y(t	PROPN
ejpam-6238	37	27	)	)	PUNCT
ejpam-6238	38	1	=	=	SYM
ejpam-6238	38	2	t	t	PROPN
ejpam-6238	38	3	(	(	PUNCT
ejpam-6238	38	4	x)y	x)y	X
ejpam-6238	38	5	for	for	ADP
ejpam-6238	38	6	all	all	DET
ejpam-6238	38	7	t	t	NOUN
ejpam-6238	38	8	∈	∈	PROPN
ejpam-6238	38	9	x∗.	x∗.	PUNCT
ejpam-6238	39	1	the	the	DET
ejpam-6238	39	2	operator	operator	NOUN
ejpam-6238	39	3	x	x	PROPN
ejpam-6238	40	1	⊗	⊗	PROPN
ejpam-6238	40	2	y	y	PROPN
ejpam-6238	40	3	is	be	AUX
ejpam-6238	40	4	bounded	bound	VERB
ejpam-6238	40	5	and	and	CCONJ
ejpam-6238	40	6	linear	linear	VERB
ejpam-6238	40	7	with	with	ADP
ejpam-6238	40	8	∥x⊗	∥x⊗	NOUN
ejpam-6238	40	9	y∥	y∥	NOUN
ejpam-6238	40	10	=	=	VERB
ejpam-6238	40	11	∥x∥	∥x∥	NOUN
ejpam-6238	40	12	∥y∥	∥y∥	NOUN
ejpam-6238	40	13	(	(	PUNCT
ejpam-6238	40	14	see	see	VERB
ejpam-6238	40	15	[	[	X
ejpam-6238	40	16	13	13	NUM
ejpam-6238	40	17	]	]	NUM
ejpam-6238	40	18	)	)	PUNCT
ejpam-6238	40	19	.	.	PUNCT
ejpam-6238	41	1	such	such	ADJ
ejpam-6238	41	2	operators	operator	NOUN
ejpam-6238	41	3	are	be	AUX
ejpam-6238	41	4	called	call	VERB
ejpam-6238	41	5	atoms	atom	NOUN
ejpam-6238	41	6	,	,	PUNCT
ejpam-6238	41	7	and	and	CCONJ
ejpam-6238	41	8	every	every	DET
ejpam-6238	41	9	atom	atom	NOUN
ejpam-6238	41	10	has	have	AUX
ejpam-6238	41	11	rank	rank	NOUN
ejpam-6238	41	12	1	1	NUM
ejpam-6238	41	13	.	.	PUNCT
ejpam-6238	42	1	the	the	DET
ejpam-6238	42	2	span	span	NOUN
ejpam-6238	42	3	of	of	ADP
ejpam-6238	42	4	all	all	DET
ejpam-6238	42	5	atoms	atom	NOUN
ejpam-6238	42	6	forms	form	VERB
ejpam-6238	42	7	a	a	DET
ejpam-6238	42	8	subspace	subspace	NOUN
ejpam-6238	42	9	of	of	ADP
ejpam-6238	42	10	l(x∗	l(x∗	NOUN
ejpam-6238	42	11	,	,	PUNCT
ejpam-6238	42	12	y	y	PROPN
ejpam-6238	42	13	)	)	PUNCT
ejpam-6238	42	14	,	,	PUNCT
ejpam-6238	42	15	denoted	denote	VERB
ejpam-6238	42	16	by	by	ADP
ejpam-6238	42	17	x	x	PROPN
ejpam-6238	42	18	⊗	⊗	PROPN
ejpam-6238	42	19	y.	y.	PROPN
ejpam-6238	42	20	a	a	DET
ejpam-6238	42	21	finite	finite	ADJ
ejpam-6238	42	22	sum	sum	NOUN
ejpam-6238	42	23	of	of	ADP
ejpam-6238	42	24	atoms	atom	NOUN
ejpam-6238	42	25	:	:	PUNCT
ejpam-6238	42	26	n	n	NUM
ejpam-6238	42	27	i=1xi	i=1xi	PROPN
ejpam-6238	42	28	⊗	⊗	PROPN
ejpam-6238	42	29	yi	yi	PROPN
ejpam-6238	42	30	constitutes	constitute	VERB
ejpam-6238	42	31	a	a	DET
ejpam-6238	42	32	finite	finite	ADJ
ejpam-6238	42	33	-	-	ADJ
ejpam-6238	42	34	rank	rank	ADJ
ejpam-6238	42	35	function	function	NOUN
ejpam-6238	42	36	,	,	PUNCT
ejpam-6238	42	37	which	which	PRON
ejpam-6238	42	38	forms	form	VERB
ejpam-6238	42	39	the	the	DET
ejpam-6238	42	40	basis	basis	NOUN
ejpam-6238	42	41	of	of	ADP
ejpam-6238	42	42	our	our	PRON
ejpam-6238	42	43	solution	solution	NOUN
ejpam-6238	42	44	approach	approach	NOUN
ejpam-6238	42	45	.	.	PUNCT
ejpam-6238	43	1	there	there	PRON
ejpam-6238	43	2	are	be	VERB
ejpam-6238	43	3	many	many	ADJ
ejpam-6238	43	4	norms	norm	NOUN
ejpam-6238	43	5	on	on	ADP
ejpam-6238	43	6	x	x	PROPN
ejpam-6238	43	7	⊗	⊗	PROPN
ejpam-6238	43	8	y	y	PROPN
ejpam-6238	43	9	,	,	PUNCT
ejpam-6238	43	10	but	but	CCONJ
ejpam-6238	43	11	the	the	DET
ejpam-6238	43	12	most	most	ADV
ejpam-6238	43	13	important	important	ADJ
ejpam-6238	43	14	one	one	NOUN
ejpam-6238	43	15	is	be	AUX
ejpam-6238	43	16	that	that	PRON
ejpam-6238	43	17	called	call	VERB
ejpam-6238	43	18	the	the	DET
ejpam-6238	43	19	injective	injective	ADJ
ejpam-6238	43	20	norm	norm	NOUN
ejpam-6238	43	21	.	.	PUNCT
ejpam-6238	44	1	furthermore	furthermore	ADV
ejpam-6238	44	2	,	,	PUNCT
ejpam-6238	44	3	for	for	ADP
ejpam-6238	44	4	any	any	DET
ejpam-6238	44	5	t	t	NOUN
ejpam-6238	44	6	=	=	SYM
ejpam-6238	44	7	n	n	CCONJ
ejpam-6238	44	8	i=1	i=1	NOUN
ejpam-6238	44	9	xi	xi	PROPN
ejpam-6238	44	10	⊗	⊗	PROPN
ejpam-6238	44	11	yi	yi	PROPN
ejpam-6238	44	12	∈	∈	PROPN
ejpam-6238	44	13	x	x	PUNCT
ejpam-6238	44	14	⊗	⊗	PROPN
ejpam-6238	44	15	y	y	PROPN
ejpam-6238	44	16	,	,	PUNCT
ejpam-6238	44	17	the	the	DET
ejpam-6238	44	18	injective	injective	ADJ
ejpam-6238	44	19	norm	norm	NOUN
ejpam-6238	44	20	is	be	AUX
ejpam-6238	44	21	defined	define	VERB
ejpam-6238	44	22	as	as	ADP
ejpam-6238	44	23	∥t∥∨	∥t∥∨	NOUN
ejpam-6238	44	24	=	=	SYM
ejpam-6238	44	25	sup	sup	NOUN
ejpam-6238	44	26	{	{	PUNCT
ejpam-6238	44	27	ni=1x	ni=1x	NOUN
ejpam-6238	44	28	∗(xi).y	∗(xi).y	PROPN
ejpam-6238	44	29	∗(yi	∗(yi	NOUN
ejpam-6238	44	30	)	)	PUNCT
ejpam-6238	44	31	:	:	PUNCT
ejpam-6238	45	1	x	x	X
ejpam-6238	45	2	∗	∗	NOUN
ejpam-6238	45	3	∈	∈	NOUN
ejpam-6238	45	4	x∗	x∗	NOUN
ejpam-6238	45	5	,	,	PUNCT
ejpam-6238	45	6	y∗	y∗	PROPN
ejpam-6238	45	7	∈	∈	PROPN
ejpam-6238	45	8	y	y	PROPN
ejpam-6238	45	9	∗	∗	NOUN
ejpam-6238	45	10	,	,	PUNCT
ejpam-6238	45	11	∥x∗∥	∥x∗∥	NOUN
ejpam-6238	45	12	=	=	SYM
ejpam-6238	45	13	∥y∗∥	∥y∗∥	NOUN
ejpam-6238	45	14	=	=	SYM
ejpam-6238	45	15	1	1	NUM
ejpam-6238	45	16	}	}	PUNCT
ejpam-6238	45	17	h.	h.	NOUN
ejpam-6238	45	18	odetallah	odetallah	INTJ
ejpam-6238	45	19	et	et	PROPN
ejpam-6238	45	20	al	al	PROPN
ejpam-6238	45	21	.	.	PUNCT
ejpam-6238	45	22	/	/	SYM
ejpam-6238	45	23	eur	eur	PROPN
ejpam-6238	45	24	.	.	PUNCT
ejpam-6238	46	1	j.	j.	PROPN
ejpam-6238	46	2	pure	pure	PROPN
ejpam-6238	46	3	appl	appl	PROPN
ejpam-6238	46	4	.	.	PROPN
ejpam-6238	46	5	math	math	PROPN
ejpam-6238	46	6	,	,	PUNCT
ejpam-6238	46	7	18	18	NUM
ejpam-6238	46	8	(	(	PUNCT
ejpam-6238	46	9	3	3	NUM
ejpam-6238	46	10	)	)	PUNCT
ejpam-6238	46	11	(	(	PUNCT
ejpam-6238	46	12	2025	2025	NUM
ejpam-6238	46	13	)	)	PUNCT
ejpam-6238	46	14	,	,	PUNCT
ejpam-6238	46	15	6238	6238	NUM
ejpam-6238	46	16	3	3	NUM
ejpam-6238	46	17	of	of	ADP
ejpam-6238	46	18	11	11	NUM
ejpam-6238	46	19	it	it	PRON
ejpam-6238	46	20	should	should	AUX
ejpam-6238	46	21	be	be	AUX
ejpam-6238	46	22	noted	note	VERB
ejpam-6238	46	23	that	that	SCONJ
ejpam-6238	46	24	the	the	DET
ejpam-6238	46	25	space	space	NOUN
ejpam-6238	46	26	(	(	PUNCT
ejpam-6238	46	27	x	x	PROPN
ejpam-6238	46	28	⊗	⊗	PROPN
ejpam-6238	46	29	y	y	PROPN
ejpam-6238	46	30	,	,	PUNCT
ejpam-6238	46	31	∥.∥∨	∥.∥∨	PROPN
ejpam-6238	46	32	)	)	PUNCT
ejpam-6238	46	33	does	do	AUX
ejpam-6238	46	34	not	not	PART
ejpam-6238	46	35	necessarily	necessarily	ADV
ejpam-6238	46	36	exhibit	exhibit	VERB
ejpam-6238	46	37	completeness	completeness	NOUN
ejpam-6238	46	38	.	.	PUNCT
ejpam-6238	47	1	we	we	PRON
ejpam-6238	47	2	denote	denote	VERB
ejpam-6238	47	3	by	by	ADP
ejpam-6238	47	4	x	x	PROPN
ejpam-6238	47	5	∨	∨	PROPN
ejpam-6238	47	6	⊗	⊗	PROPN
ejpam-6238	47	7	y	y	PROPN
ejpam-6238	47	8	the	the	DET
ejpam-6238	47	9	completion	completion	NOUN
ejpam-6238	47	10	of	of	ADP
ejpam-6238	47	11	(	(	PUNCT
ejpam-6238	47	12	x	x	PROPN
ejpam-6238	47	13	⊗	⊗	PROPN
ejpam-6238	47	14	y	y	PROPN
ejpam-6238	47	15	,	,	PUNCT
ejpam-6238	47	16	∥.∥∨	∥.∥∨	PROPN
ejpam-6238	47	17	)	)	PUNCT
ejpam-6238	47	18	,	,	PUNCT
ejpam-6238	47	19	which	which	PRON
ejpam-6238	47	20	is	be	AUX
ejpam-6238	47	21	referred	refer	VERB
ejpam-6238	47	22	to	to	ADP
ejpam-6238	47	23	as	as	ADP
ejpam-6238	47	24	the	the	DET
ejpam-6238	47	25	completed	complete	VERB
ejpam-6238	47	26	injective	injective	ADJ
ejpam-6238	47	27	tensor	tensor	NOUN
ejpam-6238	47	28	product	product	NOUN
ejpam-6238	47	29	of	of	ADP
ejpam-6238	47	30	x	x	PUNCT
ejpam-6238	47	31	with	with	ADP
ejpam-6238	47	32	y.	y.	PROPN
ejpam-6238	47	33	a	a	DET
ejpam-6238	47	34	fundamental	fundamental	ADJ
ejpam-6238	47	35	result	result	NOUN
ejpam-6238	47	36	with	with	ADP
ejpam-6238	47	37	significant	significant	ADJ
ejpam-6238	47	38	applications	application	NOUN
ejpam-6238	47	39	in	in	ADP
ejpam-6238	47	40	differential	differential	ADJ
ejpam-6238	47	41	equation	equation	NOUN
ejpam-6238	47	42	theory	theory	NOUN
ejpam-6238	47	43	can	can	AUX
ejpam-6238	47	44	be	be	AUX
ejpam-6238	47	45	formulated	formulate	VERB
ejpam-6238	47	46	as	as	SCONJ
ejpam-6238	47	47	follows	follow	VERB
ejpam-6238	47	48	:	:	PUNCT
ejpam-6238	47	49	theorem	theorem	NOUN
ejpam-6238	47	50	1	1	NUM
ejpam-6238	47	51	.	.	PUNCT
ejpam-6238	48	1	[	[	X
ejpam-6238	48	2	16	16	NUM
ejpam-6238	48	3	]	]	PUNCT
ejpam-6238	48	4	for	for	ADP
ejpam-6238	48	5	any	any	DET
ejpam-6238	48	6	compact	compact	ADJ
ejpam-6238	48	7	hausdorff	hausdorff	NOUN
ejpam-6238	48	8	space	space	NOUN
ejpam-6238	48	9	k	k	PROPN
ejpam-6238	48	10	and	and	CCONJ
ejpam-6238	48	11	any	any	DET
ejpam-6238	48	12	banach	banach	NOUN
ejpam-6238	48	13	space	space	NOUN
ejpam-6238	48	14	x	x	NOUN
ejpam-6238	48	15	,	,	PUNCT
ejpam-6238	48	16	the	the	DET
ejpam-6238	48	17	space	space	NOUN
ejpam-6238	48	18	c	c	NOUN
ejpam-6238	48	19	(	(	PUNCT
ejpam-6238	48	20	k	k	X
ejpam-6238	48	21	,	,	PUNCT
ejpam-6238	48	22	x	x	X
ejpam-6238	48	23	)	)	PUNCT
ejpam-6238	48	24	is	be	AUX
ejpam-6238	48	25	isometrically	isometrically	PROPN
ejpam-6238	48	26	isomorphic	isomorphic	ADJ
ejpam-6238	48	27	to	to	ADP
ejpam-6238	48	28	c	c	PROPN
ejpam-6238	48	29	(	(	PUNCT
ejpam-6238	48	30	k	k	NOUN
ejpam-6238	48	31	)	)	PUNCT
ejpam-6238	48	32	∨	∨	NUM
ejpam-6238	48	33	⊗x∗.	⊗x∗.	PROPN
ejpam-6238	48	34	this	this	DET
ejpam-6238	48	35	theorem	theorem	ADJ
ejpam-6238	48	36	yields	yield	NOUN
ejpam-6238	48	37	the	the	DET
ejpam-6238	48	38	important	important	ADJ
ejpam-6238	48	39	corollary	corollary	NOUN
ejpam-6238	48	40	that	that	SCONJ
ejpam-6238	48	41	for	for	ADP
ejpam-6238	48	42	any	any	DET
ejpam-6238	48	43	two	two	NUM
ejpam-6238	48	44	compact	compact	ADJ
ejpam-6238	48	45	metric	metric	ADJ
ejpam-6238	48	46	spaces	space	NOUN
ejpam-6238	48	47	i	i	PRON
ejpam-6238	48	48	and	and	CCONJ
ejpam-6238	48	49	j	j	PROPN
ejpam-6238	48	50	,	,	PUNCT
ejpam-6238	48	51	we	we	PRON
ejpam-6238	48	52	have	have	VERB
ejpam-6238	48	53	c	c	NOUN
ejpam-6238	48	54	(	(	PUNCT
ejpam-6238	48	55	i	i	PRON
ejpam-6238	48	56	×	×	PROPN
ejpam-6238	48	57	j	j	NOUN
ejpam-6238	48	58	)	)	PUNCT
ejpam-6238	48	59	∼=	∼=	PROPN
ejpam-6238	48	60	c	c	NOUN
ejpam-6238	48	61	(	(	PUNCT
ejpam-6238	48	62	i	i	NOUN
ejpam-6238	48	63	)	)	PUNCT
ejpam-6238	48	64	∨	∨	PROPN
ejpam-6238	48	65	⊗	⊗	PROPN
ejpam-6238	48	66	c	c	PROPN
ejpam-6238	48	67	(	(	PUNCT
ejpam-6238	48	68	j	j	PROPN
ejpam-6238	48	69	)	)	PUNCT
ejpam-6238	48	70	.	.	PUNCT
ejpam-6238	49	1	for	for	ADP
ejpam-6238	49	2	more	more	ADJ
ejpam-6238	49	3	on	on	ADP
ejpam-6238	49	4	tensor	tensor	NOUN
ejpam-6238	49	5	product	product	NOUN
ejpam-6238	49	6	we	we	PRON
ejpam-6238	49	7	refer	refer	VERB
ejpam-6238	49	8	to	to	ADP
ejpam-6238	49	9	[	[	X
ejpam-6238	49	10	6,7,13,16	6,7,13,16	NUM
ejpam-6238	49	11	]	]	SYM
ejpam-6238	49	12	.	.	PUNCT
ejpam-6238	50	1	2	2	X
ejpam-6238	50	2	.	.	X
ejpam-6238	50	3	direct	direct	ADJ
ejpam-6238	50	4	problem	problem	NOUN
ejpam-6238	50	5	let	let	VERB
ejpam-6238	50	6	u	u	PRON
ejpam-6238	50	7	be	be	AUX
ejpam-6238	50	8	an	an	DET
ejpam-6238	50	9	2α−differentiable	2α−differentiable	NOUN
ejpam-6238	50	10	on	on	ADP
ejpam-6238	50	11	i	i	PRON
ejpam-6238	50	12	=	=	PUNCT
ejpam-6238	51	1	[	[	X
ejpam-6238	51	2	0	0	NUM
ejpam-6238	51	3	,	,	PUNCT
ejpam-6238	51	4	1	1	NUM
ejpam-6238	51	5	]	]	PUNCT
ejpam-6238	51	6	into	into	ADP
ejpam-6238	51	7	the	the	DET
ejpam-6238	51	8	hilbert	hilbert	NOUN
ejpam-6238	51	9	space	space	NOUN
ejpam-6238	51	10	x	x	PUNCT
ejpam-6238	51	11	=	=	SYM
ejpam-6238	51	12	ℓ2	ℓ2	NOUN
ejpam-6238	51	13	,	,	PUNCT
ejpam-6238	51	14	where	where	SCONJ
ejpam-6238	51	15	ℓ2	ℓ2	NOUN
ejpam-6238	51	16	=	=	SYM
ejpam-6238	51	17	{	{	PUNCT
ejpam-6238	51	18	(	(	PUNCT
ejpam-6238	51	19	xn	xn	PROPN
ejpam-6238	51	20	)	)	PUNCT
ejpam-6238	51	21	:	:	PUNCT
ejpam-6238	51	22	∞n=1	∞n=1	PROPN
ejpam-6238	51	23	|xn|2	|xn|2	ADP
ejpam-6238	51	24	<	<	X
ejpam-6238	51	25	∞	∞	NUM
ejpam-6238	51	26	}	}	PUNCT
ejpam-6238	51	27	.	.	PUNCT
ejpam-6238	52	1	the	the	DET
ejpam-6238	52	2	standard	standard	ADJ
ejpam-6238	52	3	basis	basis	NOUN
ejpam-6238	52	4	of	of	ADP
ejpam-6238	52	5	ℓ2	ℓ2	NOUN
ejpam-6238	52	6	is	be	AUX
ejpam-6238	52	7	denoted	denote	VERB
ejpam-6238	52	8	by	by	ADP
ejpam-6238	52	9	{	{	PUNCT
ejpam-6238	52	10	δ1	δ1	NOUN
ejpam-6238	52	11	,	,	PUNCT
ejpam-6238	52	12	δ2	δ2	VERB
ejpam-6238	52	13	,	,	PUNCT
ejpam-6238	52	14	...	...	PUNCT
ejpam-6238	52	15	}	}	PUNCT
ejpam-6238	52	16	.	.	PUNCT
ejpam-6238	53	1	let	let	VERB
ejpam-6238	53	2	a	a	DET
ejpam-6238	53	3	,	,	PUNCT
ejpam-6238	53	4	b	b	NOUN
ejpam-6238	53	5	be	be	AUX
ejpam-6238	53	6	two	two	NUM
ejpam-6238	53	7	closed	closed	ADJ
ejpam-6238	53	8	operators	operator	NOUN
ejpam-6238	53	9	on	on	ADP
ejpam-6238	53	10	ℓ2	ℓ2	NOUN
ejpam-6238	53	11	such	such	ADJ
ejpam-6238	53	12	that	that	SCONJ
ejpam-6238	53	13	domains	domain	NOUN
ejpam-6238	53	14	of	of	ADP
ejpam-6238	53	15	a	a	PRON
ejpam-6238	53	16	and	and	CCONJ
ejpam-6238	53	17	b	b	NOUN
ejpam-6238	53	18	contain	contain	VERB
ejpam-6238	53	19	the	the	DET
ejpam-6238	53	20	elements	element	NOUN
ejpam-6238	53	21	of	of	ADP
ejpam-6238	53	22	the	the	DET
ejpam-6238	53	23	standard	standard	ADJ
ejpam-6238	53	24	basis	basis	NOUN
ejpam-6238	53	25	of	of	ADP
ejpam-6238	53	26	ℓ2	ℓ2	NOUN
ejpam-6238	53	27	.	.	PUNCT
ejpam-6238	54	1	in	in	ADP
ejpam-6238	54	2	this	this	DET
ejpam-6238	54	3	section	section	NOUN
ejpam-6238	54	4	we	we	PRON
ejpam-6238	54	5	look	look	VERB
ejpam-6238	54	6	for	for	ADP
ejpam-6238	54	7	a	a	DET
ejpam-6238	54	8	solution	solution	NOUN
ejpam-6238	54	9	to	to	ADP
ejpam-6238	54	10	the	the	DET
ejpam-6238	54	11	direct	direct	ADJ
ejpam-6238	54	12	problem	problem	NOUN
ejpam-6238	54	13	(	(	PUNCT
ejpam-6238	54	14	1	1	NUM
ejpam-6238	54	15	)	)	PUNCT
ejpam-6238	54	16	among	among	ADP
ejpam-6238	54	17	finite	finite	ADJ
ejpam-6238	54	18	-	-	ADJ
ejpam-6238	54	19	rank	rank	ADJ
ejpam-6238	54	20	functions	function	NOUN
ejpam-6238	54	21	of	of	ADP
ejpam-6238	54	22	the	the	DET
ejpam-6238	54	23	form	form	NOUN
ejpam-6238	54	24	u(t	u(t	NOUN
ejpam-6238	54	25	)	)	PUNCT
ejpam-6238	55	1	=	=	SYM
ejpam-6238	55	2	n	n	SYM
ejpam-6238	55	3	i=1	i=1	NOUN
ejpam-6238	55	4	ui(t)δi	ui(t)δi	ADJ
ejpam-6238	55	5	,	,	PUNCT
ejpam-6238	55	6	where	where	SCONJ
ejpam-6238	55	7	u	u	PROPN
ejpam-6238	55	8	(	(	PUNCT
ejpam-6238	55	9	2α	2α	PROPN
ejpam-6238	55	10	)	)	PUNCT
ejpam-6238	55	11	i	i	PRON
ejpam-6238	55	12	(	(	PUNCT
ejpam-6238	55	13	t	t	PROPN
ejpam-6238	55	14	)	)	PUNCT
ejpam-6238	55	15	∈	∈	PROPN
ejpam-6238	55	16	c(i	c(i	PROPN
ejpam-6238	55	17	)	)	PUNCT
ejpam-6238	55	18	,	,	PUNCT
ejpam-6238	55	19	i	i	PRON
ejpam-6238	55	20	=	=	NOUN
ejpam-6238	55	21	1	1	NUM
ejpam-6238	55	22	,	,	PUNCT
ejpam-6238	55	23	2	2	NUM
ejpam-6238	55	24	,	,	PUNCT
ejpam-6238	55	25	...	...	PUNCT
ejpam-6238	55	26	,	,	PUNCT
ejpam-6238	55	27	n.	n.	NOUN
ejpam-6238	55	28	before	before	ADP
ejpam-6238	55	29	analyzing	analyze	VERB
ejpam-6238	55	30	the	the	DET
ejpam-6238	55	31	main	main	ADJ
ejpam-6238	55	32	problem	problem	NOUN
ejpam-6238	55	33	,	,	PUNCT
ejpam-6238	55	34	we	we	PRON
ejpam-6238	55	35	establish	establish	VERB
ejpam-6238	55	36	the	the	DET
ejpam-6238	55	37	theoretical	theoretical	ADJ
ejpam-6238	55	38	foundation	foundation	NOUN
ejpam-6238	55	39	using	use	VERB
ejpam-6238	55	40	fundamental	fundamental	ADJ
ejpam-6238	55	41	matrices	matrix	NOUN
ejpam-6238	55	42	.	.	PUNCT
ejpam-6238	56	1	definition	definition	NOUN
ejpam-6238	56	2	3	3	NUM
ejpam-6238	56	3	.	.	PUNCT
ejpam-6238	57	1	the	the	DET
ejpam-6238	57	2	conformable	conformable	ADJ
ejpam-6238	57	3	fractional	fractional	ADJ
ejpam-6238	57	4	fundamental	fundamental	ADJ
ejpam-6238	57	5	matrix	matrix	NOUN
ejpam-6238	57	6	ϕα	ϕα	ADV
ejpam-6238	57	7	(	(	PUNCT
ejpam-6238	57	8	t	t	NOUN
ejpam-6238	57	9	)	)	PUNCT
ejpam-6238	57	10	is	be	AUX
ejpam-6238	57	11	the	the	DET
ejpam-6238	57	12	unique	unique	ADJ
ejpam-6238	57	13	n×	n×	NOUN
ejpam-6238	57	14	n	n	NOUN
ejpam-6238	57	15	matrix	matrix	NOUN
ejpam-6238	57	16	-	-	PUNCT
ejpam-6238	57	17	valued	value	VERB
ejpam-6238	57	18	function	function	NOUN
ejpam-6238	57	19	that	that	PRON
ejpam-6238	57	20	satisfies	satisfy	VERB
ejpam-6238	57	21	the	the	DET
ejpam-6238	57	22	fractional	fractional	ADJ
ejpam-6238	57	23	differential	differential	NOUN
ejpam-6238	57	24	equation	equation	NOUN
ejpam-6238	57	25	ϕ	ϕ	X
ejpam-6238	57	26	(	(	PUNCT
ejpam-6238	57	27	α	α	NOUN
ejpam-6238	57	28	)	)	PUNCT
ejpam-6238	57	29	α	α	PROPN
ejpam-6238	57	30	(	(	PUNCT
ejpam-6238	57	31	t	t	NOUN
ejpam-6238	57	32	)	)	PUNCT
ejpam-6238	58	1	=	=	SYM
ejpam-6238	58	2	aϕα	aϕα	PROPN
ejpam-6238	58	3	(	(	PUNCT
ejpam-6238	58	4	t	t	PROPN
ejpam-6238	58	5	)	)	PUNCT
ejpam-6238	58	6	,	,	PUNCT
ejpam-6238	58	7	t	t	X
ejpam-6238	58	8	>	>	X
ejpam-6238	58	9	0	0	PUNCT
ejpam-6238	59	1	and	and	CCONJ
ejpam-6238	59	2	α	α	PRON
ejpam-6238	59	3	∈	∈	PROPN
ejpam-6238	59	4	(	(	PUNCT
ejpam-6238	59	5	0	0	NUM
ejpam-6238	59	6	,	,	PUNCT
ejpam-6238	59	7	1	1	NUM
ejpam-6238	59	8	]	]	PUNCT
ejpam-6238	59	9	with	with	ADP
ejpam-6238	59	10	initial	initial	ADJ
ejpam-6238	59	11	condition	condition	NOUN
ejpam-6238	59	12	ϕα	ϕα	ADV
ejpam-6238	59	13	(	(	PUNCT
ejpam-6238	59	14	0	0	NUM
ejpam-6238	59	15	)	)	PUNCT
ejpam-6238	59	16	=	=	SYM
ejpam-6238	60	1	i	i	PROPN
ejpam-6238	60	2	,	,	PUNCT
ejpam-6238	60	3	where	where	SCONJ
ejpam-6238	60	4	i	i	PRON
ejpam-6238	60	5	is	be	AUX
ejpam-6238	60	6	the	the	PRON
ejpam-6238	60	7	n	n	NUM
ejpam-6238	60	8	×	×	NOUN
ejpam-6238	60	9	n	n	CCONJ
ejpam-6238	60	10	identity	identity	NOUN
ejpam-6238	60	11	matrix	matrix	NOUN
ejpam-6238	60	12	.	.	PUNCT
ejpam-6238	61	1	for	for	ADP
ejpam-6238	61	2	the	the	DET
ejpam-6238	61	3	conformable	conformable	ADJ
ejpam-6238	61	4	fractional	fractional	ADJ
ejpam-6238	61	5	derivative	derivative	NOUN
ejpam-6238	61	6	,	,	PUNCT
ejpam-6238	61	7	the	the	DET
ejpam-6238	61	8	fundamental	fundamental	ADJ
ejpam-6238	61	9	matrix	matrix	NOUN
ejpam-6238	61	10	can	can	AUX
ejpam-6238	61	11	be	be	AUX
ejpam-6238	61	12	expressed	express	VERB
ejpam-6238	61	13	as	as	ADP
ejpam-6238	61	14	:	:	PUNCT
ejpam-6238	61	15	ϕα	ϕα	INTJ
ejpam-6238	61	16	(	(	PUNCT
ejpam-6238	61	17	t	t	NOUN
ejpam-6238	61	18	)	)	PUNCT
ejpam-6238	61	19	=	=	NOUN
ejpam-6238	61	20	exp	exp	NOUN
ejpam-6238	61	21	(	(	PUNCT
ejpam-6238	61	22	atα	atα	NOUN
ejpam-6238	61	23	α	α	X
ejpam-6238	61	24	)	)	PUNCT
ejpam-6238	61	25	the	the	DET
ejpam-6238	61	26	essential	essential	ADJ
ejpam-6238	61	27	properties	property	NOUN
ejpam-6238	61	28	of	of	ADP
ejpam-6238	61	29	the	the	DET
ejpam-6238	61	30	fundamental	fundamental	ADJ
ejpam-6238	61	31	matrix	matrix	NOUN
ejpam-6238	61	32	are	be	AUX
ejpam-6238	61	33	:	:	PUNCT
ejpam-6238	61	34	1ϕα	1ϕα	ADJ
ejpam-6238	61	35	(	(	PUNCT
ejpam-6238	61	36	t	t	NOUN
ejpam-6238	61	37	)	)	PUNCT
ejpam-6238	61	38	is	be	AUX
ejpam-6238	61	39	continuously	continuously	ADV
ejpam-6238	61	40	differentiable	differentiable	ADJ
ejpam-6238	61	41	in	in	ADP
ejpam-6238	61	42	the	the	DET
ejpam-6238	61	43	conformable	conformable	ADJ
ejpam-6238	61	44	sense	sense	NOUN
ejpam-6238	61	45	for	for	ADP
ejpam-6238	61	46	t	t	PROPN
ejpam-6238	61	47	>	>	X
ejpam-6238	61	48	0	0	PROPN
ejpam-6238	61	49	.	.	PUNCT
ejpam-6238	62	1	2ϕα	2ϕα	NOUN
ejpam-6238	62	2	(	(	PUNCT
ejpam-6238	62	3	t	t	PROPN
ejpam-6238	62	4	)	)	PUNCT
ejpam-6238	62	5	is	be	AUX
ejpam-6238	62	6	continuous	continuous	ADJ
ejpam-6238	62	7	at	at	ADP
ejpam-6238	62	8	t	t	NOUN
ejpam-6238	62	9	=	=	SYM
ejpam-6238	62	10	0	0	NUM
ejpam-6238	62	11	.	.	PUNCT
ejpam-6238	63	1	3ϕα	3ϕα	NOUN
ejpam-6238	63	2	(	(	PUNCT
ejpam-6238	63	3	t	t	NOUN
ejpam-6238	63	4	)	)	PUNCT
ejpam-6238	63	5	is	be	AUX
ejpam-6238	63	6	invertible	invertible	ADJ
ejpam-6238	63	7	for	for	ADP
ejpam-6238	63	8	all	all	DET
ejpam-6238	63	9	t	t	PROPN
ejpam-6238	63	10	≥	≥	NOUN
ejpam-6238	63	11	0	0	NUM
ejpam-6238	63	12	.	.	PUNCT
ejpam-6238	64	1	4the	4the	NUM
ejpam-6238	64	2	inverse	inverse	NOUN
ejpam-6238	64	3	satisfies	satisfie	NOUN
ejpam-6238	64	4	ϕ−1	ϕ−1	ADP
ejpam-6238	64	5	α	α	PROPN
ejpam-6238	64	6	(	(	PUNCT
ejpam-6238	64	7	t	t	PROPN
ejpam-6238	64	8	)	)	PUNCT
ejpam-6238	64	9	=	=	NOUN
ejpam-6238	64	10	ϕα	ϕα	ADV
ejpam-6238	64	11	(	(	PUNCT
ejpam-6238	64	12	−t	−t	NOUN
ejpam-6238	64	13	)	)	PUNCT
ejpam-6238	64	14	.	.	PUNCT
ejpam-6238	65	1	5d	5d	PROPN
ejpam-6238	65	2	dtϕα	dtϕα	PROPN
ejpam-6238	65	3	(	(	PUNCT
ejpam-6238	65	4	t	t	PROPN
ejpam-6238	65	5	)	)	PUNCT
ejpam-6238	65	6	=	=	SYM
ejpam-6238	65	7	1	1	NUM
ejpam-6238	65	8	t1−αaϕα	t1−αaϕα	NOUN
ejpam-6238	65	9	(	(	PUNCT
ejpam-6238	65	10	t	t	PROPN
ejpam-6238	65	11	)	)	PUNCT
ejpam-6238	65	12	.	.	PUNCT
ejpam-6238	66	1	to	to	PART
ejpam-6238	66	2	read	read	VERB
ejpam-6238	66	3	more	more	ADJ
ejpam-6238	66	4	about	about	ADP
ejpam-6238	66	5	ϕα	ϕα	ADV
ejpam-6238	66	6	(	(	PUNCT
ejpam-6238	66	7	t	t	NOUN
ejpam-6238	66	8	)	)	PUNCT
ejpam-6238	66	9	see	see	VERB
ejpam-6238	66	10	[	[	X
ejpam-6238	66	11	10	10	NUM
ejpam-6238	66	12	]	]	PUNCT
ejpam-6238	66	13	.	.	PUNCT
ejpam-6238	67	1	we	we	PRON
ejpam-6238	67	2	now	now	ADV
ejpam-6238	67	3	present	present	VERB
ejpam-6238	67	4	the	the	DET
ejpam-6238	67	5	main	main	ADJ
ejpam-6238	67	6	theorem	theorem	NOUN
ejpam-6238	67	7	.	.	PUNCT
ejpam-6238	68	1	h.	h.	PROPN
ejpam-6238	68	2	odetallah	odetallah	PROPN
ejpam-6238	68	3	et	et	PROPN
ejpam-6238	68	4	al	al	PROPN
ejpam-6238	68	5	.	.	PUNCT
ejpam-6238	68	6	/	/	SYM
ejpam-6238	68	7	eur	eur	PROPN
ejpam-6238	68	8	.	.	PUNCT
ejpam-6238	69	1	j.	j.	PROPN
ejpam-6238	69	2	pure	pure	PROPN
ejpam-6238	69	3	appl	appl	PROPN
ejpam-6238	69	4	.	.	PROPN
ejpam-6238	69	5	math	math	PROPN
ejpam-6238	69	6	,	,	PUNCT
ejpam-6238	69	7	18	18	NUM
ejpam-6238	69	8	(	(	PUNCT
ejpam-6238	69	9	3	3	NUM
ejpam-6238	69	10	)	)	PUNCT
ejpam-6238	69	11	(	(	PUNCT
ejpam-6238	69	12	2025	2025	NUM
ejpam-6238	69	13	)	)	PUNCT
ejpam-6238	69	14	,	,	PUNCT
ejpam-6238	69	15	6238	6238	NUM
ejpam-6238	69	16	4	4	NUM
ejpam-6238	69	17	of	of	ADP
ejpam-6238	69	18	11	11	NUM
ejpam-6238	69	19	theorem	theorem	NOUN
ejpam-6238	69	20	2	2	NUM
ejpam-6238	69	21	.	.	PUNCT
ejpam-6238	70	1	in	in	ADP
ejpam-6238	70	2	problem	problem	NOUN
ejpam-6238	70	3	(	(	PUNCT
ejpam-6238	70	4	1	1	NUM
ejpam-6238	70	5	)	)	PUNCT
ejpam-6238	70	6	,	,	PUNCT
ejpam-6238	70	7	let	let	VERB
ejpam-6238	70	8	e	e	NOUN
ejpam-6238	70	9	=	=	PRON
ejpam-6238	70	10	i	i	PRON
ejpam-6238	70	11	(	(	PUNCT
ejpam-6238	70	12	the	the	DET
ejpam-6238	70	13	identity	identity	NOUN
ejpam-6238	70	14	operator	operator	NOUN
ejpam-6238	70	15	)	)	PUNCT
ejpam-6238	70	16	and	and	CCONJ
ejpam-6238	70	17	u(t	u(t	NOUN
ejpam-6238	70	18	)	)	PUNCT
ejpam-6238	70	19	=	=	SYM
ejpam-6238	70	20	n	n	SYM
ejpam-6238	70	21	i=1	i=1	NOUN
ejpam-6238	70	22	ui(t)δi	ui(t)δi	ADJ
ejpam-6238	70	23	,	,	PUNCT
ejpam-6238	70	24	where	where	SCONJ
ejpam-6238	70	25	u	u	PROPN
ejpam-6238	70	26	(	(	PUNCT
ejpam-6238	70	27	2α	2α	PROPN
ejpam-6238	70	28	)	)	PUNCT
ejpam-6238	70	29	i	i	PRON
ejpam-6238	70	30	(	(	PUNCT
ejpam-6238	70	31	t	t	PROPN
ejpam-6238	70	32	)	)	PUNCT
ejpam-6238	70	33	∈	∈	PROPN
ejpam-6238	70	34	c(i	c(i	PROPN
ejpam-6238	70	35	)	)	PUNCT
ejpam-6238	70	36	,	,	PUNCT
ejpam-6238	70	37	i	i	PRON
ejpam-6238	70	38	=	=	NOUN
ejpam-6238	70	39	1	1	NUM
ejpam-6238	70	40	,	,	PUNCT
ejpam-6238	70	41	2	2	NUM
ejpam-6238	70	42	,	,	PUNCT
ejpam-6238	70	43	...	...	PUNCT
ejpam-6238	70	44	,	,	PUNCT
ejpam-6238	70	45	n.	n.	PROPN
ejpam-6238	70	46	then	then	ADV
ejpam-6238	70	47	,	,	PUNCT
ejpam-6238	70	48	the	the	DET
ejpam-6238	70	49	problem	problem	NOUN
ejpam-6238	70	50	has	have	VERB
ejpam-6238	70	51	a	a	DET
ejpam-6238	70	52	unique	unique	ADJ
ejpam-6238	70	53	solution	solution	NOUN
ejpam-6238	70	54	.	.	PUNCT
ejpam-6238	71	1	proof	proof	NOUN
ejpam-6238	71	2	.	.	PUNCT
ejpam-6238	72	1	since	since	SCONJ
ejpam-6238	72	2	u(t	u(t	NOUN
ejpam-6238	72	3	)	)	PUNCT
ejpam-6238	72	4	=	=	SYM
ejpam-6238	72	5	n	n	NUM
ejpam-6238	72	6	i=1	i=1	NOUN
ejpam-6238	72	7	ui(t)δi	ui(t)δi	ADJ
ejpam-6238	72	8	,	,	PUNCT
ejpam-6238	72	9	the	the	DET
ejpam-6238	72	10	derivatives	derivative	NOUN
ejpam-6238	72	11	are	be	AUX
ejpam-6238	72	12	u	u	NOUN
ejpam-6238	72	13	(	(	PUNCT
ejpam-6238	72	14	α)(t	α)(t	PROPN
ejpam-6238	72	15	)	)	PUNCT
ejpam-6238	73	1	=	=	NOUN
ejpam-6238	73	2	n	n	NUM
ejpam-6238	73	3	i=1	i=1	PROPN
ejpam-6238	73	4	u	u	PROPN
ejpam-6238	73	5	(	(	PUNCT
ejpam-6238	73	6	α	α	NOUN
ejpam-6238	73	7	)	)	PUNCT
ejpam-6238	73	8	i	i	PRON
ejpam-6238	73	9	(	(	PUNCT
ejpam-6238	73	10	t)δi	t)δi	PROPN
ejpam-6238	73	11	,	,	PUNCT
ejpam-6238	73	12	u	u	NOUN
ejpam-6238	73	13	(	(	PUNCT
ejpam-6238	73	14	2α)(t	2α)(t	NUM
ejpam-6238	73	15	)	)	PUNCT
ejpam-6238	73	16	=	=	NOUN
ejpam-6238	73	17	n	n	NUM
ejpam-6238	73	18	i=1	i=1	PROPN
ejpam-6238	73	19	u	u	PROPN
ejpam-6238	73	20	(	(	PUNCT
ejpam-6238	73	21	2α	2α	NOUN
ejpam-6238	73	22	)	)	PUNCT
ejpam-6238	74	1	i	i	PRON
ejpam-6238	74	2	(	(	PUNCT
ejpam-6238	74	3	t)δi	t)δi	PROPN
ejpam-6238	74	4	.	.	PUNCT
ejpam-6238	75	1	substituting	substitute	VERB
ejpam-6238	75	2	into	into	ADP
ejpam-6238	75	3	problem	problem	NOUN
ejpam-6238	75	4	(	(	PUNCT
ejpam-6238	75	5	1	1	NUM
ejpam-6238	75	6	):	):	PUNCT
ejpam-6238	75	7	n	n	PRON
ejpam-6238	75	8	i=1u	i=1u	ADJ
ejpam-6238	75	9	(	(	PUNCT
ejpam-6238	75	10	2α	2α	NOUN
ejpam-6238	75	11	)	)	PUNCT
ejpam-6238	75	12	i	i	PRON
ejpam-6238	75	13	(	(	PUNCT
ejpam-6238	75	14	t)δi	t)δi	PROPN
ejpam-6238	75	15	+	+	NUM
ejpam-6238	75	16	n	n	CCONJ
ejpam-6238	75	17	i=1	i=1	PROPN
ejpam-6238	75	18	u	u	PROPN
ejpam-6238	75	19	(	(	PUNCT
ejpam-6238	75	20	α	α	NOUN
ejpam-6238	75	21	)	)	PUNCT
ejpam-6238	75	22	i	i	PRON
ejpam-6238	75	23	(	(	PUNCT
ejpam-6238	75	24	t)a(δi	t)a(δi	NUM
ejpam-6238	75	25	)	)	PUNCT
ejpam-6238	75	26	+	+	CCONJ
ejpam-6238	75	27	n	n	CCONJ
ejpam-6238	75	28	i=1	i=1	PROPN
ejpam-6238	75	29	ui(t)b(δi	ui(t)b(δi	NUM
ejpam-6238	75	30	)	)	PUNCT
ejpam-6238	75	31	=	=	SYM
ejpam-6238	75	32	f(t)z	f(t)z	NOUN
ejpam-6238	75	33	(	(	PUNCT
ejpam-6238	75	34	2	2	X
ejpam-6238	75	35	)	)	PUNCT
ejpam-6238	75	36	taking	take	VERB
ejpam-6238	75	37	the	the	DET
ejpam-6238	75	38	inner	inner	ADJ
ejpam-6238	75	39	product	product	NOUN
ejpam-6238	75	40	with	with	ADP
ejpam-6238	75	41	δj	δj	PROPN
ejpam-6238	75	42	(	(	PUNCT
ejpam-6238	75	43	2	2	NUM
ejpam-6238	75	44	):	):	PUNCT
ejpam-6238	75	45	n	n	PRON
ejpam-6238	75	46	i=1u	i=1u	ADJ
ejpam-6238	75	47	(	(	PUNCT
ejpam-6238	75	48	2α	2α	NOUN
ejpam-6238	75	49	)	)	PUNCT
ejpam-6238	75	50	i	i	PRON
ejpam-6238	75	51	(	(	PUNCT
ejpam-6238	75	52	t	t	PROPN
ejpam-6238	75	53	)	)	PUNCT
ejpam-6238	75	54	⟨δi	⟨δi	PROPN
ejpam-6238	75	55	,	,	PUNCT
ejpam-6238	75	56	δj⟩+n	δj⟩+n	PROPN
ejpam-6238	75	57	i=1	i=1	PROPN
ejpam-6238	75	58	u	u	PROPN
ejpam-6238	75	59	(	(	PUNCT
ejpam-6238	75	60	α	α	NOUN
ejpam-6238	75	61	)	)	PUNCT
ejpam-6238	75	62	i	i	PRON
ejpam-6238	75	63	(	(	PUNCT
ejpam-6238	75	64	t	t	NOUN
ejpam-6238	75	65	)	)	PUNCT
ejpam-6238	75	66	⟨a(δi	⟨a(δi	NUM
ejpam-6238	75	67	)	)	PUNCT
ejpam-6238	75	68	,	,	PUNCT
ejpam-6238	75	69	δj⟩+n	δj⟩+n	PROPN
ejpam-6238	75	70	i=1	i=1	PROPN
ejpam-6238	75	71	ui(t	ui(t	NOUN
ejpam-6238	75	72	)	)	PUNCT
ejpam-6238	75	73	⟨b(δi	⟨b(δi	NOUN
ejpam-6238	75	74	)	)	PUNCT
ejpam-6238	75	75	,	,	PUNCT
ejpam-6238	75	76	δj⟩	δj⟩	NOUN
ejpam-6238	75	77	=	=	SYM
ejpam-6238	75	78	f(t	f(t	PROPN
ejpam-6238	75	79	)	)	PUNCT
ejpam-6238	75	80	⟨z	⟨z	PROPN
ejpam-6238	75	81	,	,	PUNCT
ejpam-6238	75	82	δj⟩	δj⟩	X
ejpam-6238	75	83	(	(	PUNCT
ejpam-6238	75	84	3	3	NUM
ejpam-6238	75	85	)	)	PUNCT
ejpam-6238	75	86	using	use	VERB
ejpam-6238	75	87	orthonormality	orthonormality	NOUN
ejpam-6238	75	88	of	of	ADP
ejpam-6238	75	89	the	the	DET
ejpam-6238	75	90	standard	standard	ADJ
ejpam-6238	75	91	basis	basis	NOUN
ejpam-6238	75	92	:	:	PUNCT
ejpam-6238	75	93	u	u	NOUN
ejpam-6238	75	94	(	(	PUNCT
ejpam-6238	75	95	2α	2α	PROPN
ejpam-6238	75	96	)	)	PUNCT
ejpam-6238	75	97	j	j	PROPN
ejpam-6238	75	98	(	(	PUNCT
ejpam-6238	75	99	t	t	PROPN
ejpam-6238	75	100	)	)	PUNCT
ejpam-6238	75	101	+	+	PROPN
ejpam-6238	75	102	n	n	NUM
ejpam-6238	75	103	i=1	i=1	PROPN
ejpam-6238	75	104	u	u	PROPN
ejpam-6238	75	105	(	(	PUNCT
ejpam-6238	75	106	α	α	NOUN
ejpam-6238	75	107	)	)	PUNCT
ejpam-6238	75	108	i	i	PRON
ejpam-6238	75	109	(	(	PUNCT
ejpam-6238	75	110	t	t	NOUN
ejpam-6238	75	111	)	)	PUNCT
ejpam-6238	75	112	⟨a(δi	⟨a(δi	NUM
ejpam-6238	75	113	)	)	PUNCT
ejpam-6238	75	114	,	,	PUNCT
ejpam-6238	75	115	δj⟩+n	δj⟩+n	PROPN
ejpam-6238	75	116	i=1	i=1	PROPN
ejpam-6238	75	117	ui(t	ui(t	NOUN
ejpam-6238	75	118	)	)	PUNCT
ejpam-6238	75	119	⟨b(δi	⟨b(δi	NOUN
ejpam-6238	75	120	)	)	PUNCT
ejpam-6238	75	121	,	,	PUNCT
ejpam-6238	75	122	δj⟩	δj⟩	NOUN
ejpam-6238	75	123	=	=	SYM
ejpam-6238	75	124	f(t	f(t	PROPN
ejpam-6238	75	125	)	)	PUNCT
ejpam-6238	75	126	⟨z	⟨z	PROPN
ejpam-6238	75	127	,	,	PUNCT
ejpam-6238	75	128	δj⟩	δj⟩	X
ejpam-6238	75	129	(	(	PUNCT
ejpam-6238	75	130	4	4	X
ejpam-6238	75	131	)	)	PUNCT
ejpam-6238	75	132	this	this	PRON
ejpam-6238	75	133	yields	yield	VERB
ejpam-6238	75	134	a	a	DET
ejpam-6238	75	135	system	system	NOUN
ejpam-6238	75	136	of	of	ADP
ejpam-6238	75	137	second	second	ADJ
ejpam-6238	75	138	-	-	PUNCT
ejpam-6238	75	139	order	order	NOUN
ejpam-6238	75	140	conformable	conformable	ADJ
ejpam-6238	75	141	fractional	fractional	ADJ
ejpam-6238	75	142	differential	differential	ADJ
ejpam-6238	75	143	equations	equation	NOUN
ejpam-6238	75	144	.	.	PUNCT
ejpam-6238	76	1	converting	convert	VERB
ejpam-6238	76	2	to	to	ADP
ejpam-6238	76	3	first	first	ADJ
ejpam-6238	76	4	-	-	PUNCT
ejpam-6238	76	5	order	order	NOUN
ejpam-6238	76	6	form	form	NOUN
ejpam-6238	76	7	by	by	ADP
ejpam-6238	76	8	introducing	introduce	VERB
ejpam-6238	76	9	new	new	ADJ
ejpam-6238	76	10	variables	variable	NOUN
ejpam-6238	76	11	:	:	PUNCT
ejpam-6238	76	12	vi	vi	ADJ
ejpam-6238	76	13	=	=	SYM
ejpam-6238	76	14	ui	ui	PROPN
ejpam-6238	76	15	,	,	PUNCT
ejpam-6238	76	16	vn+i	vn+i	PROPN
ejpam-6238	76	17	=	=	SYM
ejpam-6238	76	18	u	u	NOUN
ejpam-6238	76	19	(	(	PUNCT
ejpam-6238	76	20	α	α	NOUN
ejpam-6238	76	21	)	)	PUNCT
ejpam-6238	76	22	i	i	PRON
ejpam-6238	76	23	,	,	PUNCT
ejpam-6238	76	24	i	i	PRON
ejpam-6238	76	25	=	=	NOUN
ejpam-6238	76	26	1	1	NUM
ejpam-6238	76	27	,	,	PUNCT
ejpam-6238	76	28	2	2	NUM
ejpam-6238	76	29	,	,	PUNCT
ejpam-6238	76	30	...	...	PUNCT
ejpam-6238	76	31	,	,	PUNCT
ejpam-6238	77	1	n	n	CCONJ
ejpam-6238	77	2	then	then	ADV
ejpam-6238	77	3	the	the	DET
ejpam-6238	77	4	system	system	NOUN
ejpam-6238	77	5	can	can	AUX
ejpam-6238	77	6	be	be	AUX
ejpam-6238	77	7	written	write	VERB
ejpam-6238	77	8	as	as	ADP
ejpam-6238	77	9	:	:	PUNCT
ejpam-6238	77	10	v	v	X
ejpam-6238	77	11	(	(	PUNCT
ejpam-6238	77	12	α	α	NOUN
ejpam-6238	77	13	)	)	PUNCT
ejpam-6238	77	14	i	i	PROPN
ejpam-6238	77	15	=	=	SYM
ejpam-6238	77	16	vn+i	vn+i	PROPN
ejpam-6238	77	17	,	,	PUNCT
ejpam-6238	77	18	i	i	NOUN
ejpam-6238	77	19	=	=	NOUN
ejpam-6238	77	20	1	1	NUM
ejpam-6238	77	21	,	,	PUNCT
ejpam-6238	77	22	2	2	NUM
ejpam-6238	77	23	,	,	PUNCT
ejpam-6238	77	24	...	...	PUNCT
ejpam-6238	77	25	,	,	PUNCT
ejpam-6238	77	26	n	n	PROPN
ejpam-6238	77	27	v	v	NOUN
ejpam-6238	77	28	(	(	PUNCT
ejpam-6238	77	29	α	α	NOUN
ejpam-6238	77	30	)	)	PUNCT
ejpam-6238	77	31	n+j(t	n+j(t	NUM
ejpam-6238	77	32	)	)	PUNCT
ejpam-6238	77	33	=	=	PUNCT
ejpam-6238	78	1	−	−	PROPN
ejpam-6238	78	2	n∑	n∑	NOUN
ejpam-6238	78	3	i=1	i=1	PROPN
ejpam-6238	78	4	vn+i(t	vn+i(t	PROPN
ejpam-6238	78	5	)	)	PUNCT
ejpam-6238	78	6	⟨a(δi	⟨a(δi	NUM
ejpam-6238	78	7	)	)	PUNCT
ejpam-6238	78	8	,	,	PUNCT
ejpam-6238	78	9	δj⟩	δj⟩	PROPN
ejpam-6238	78	10	−	−	PROPN
ejpam-6238	78	11	n∑	n∑	NOUN
ejpam-6238	78	12	i=1	i=1	PROPN
ejpam-6238	78	13	vi(t	vi(t	ADV
ejpam-6238	78	14	)	)	PUNCT
ejpam-6238	78	15	⟨b(δi	⟨b(δi	NOUN
ejpam-6238	78	16	)	)	PUNCT
ejpam-6238	78	17	,	,	PUNCT
ejpam-6238	78	18	δj⟩+	δj⟩+	PROPN
ejpam-6238	78	19	f(t	f(t	PROPN
ejpam-6238	78	20	)	)	PUNCT
ejpam-6238	78	21	⟨z	⟨z	PROPN
ejpam-6238	78	22	,	,	PUNCT
ejpam-6238	78	23	δj⟩	δj⟩	X
ejpam-6238	78	24	(	(	PUNCT
ejpam-6238	78	25	5	5	NUM
ejpam-6238	78	26	)	)	PUNCT
ejpam-6238	78	27	in	in	ADP
ejpam-6238	78	28	matrix	matrix	NOUN
ejpam-6238	78	29	form	form	NOUN
ejpam-6238	78	30	:	:	PUNCT
ejpam-6238	78	31	v	v	NOUN
ejpam-6238	78	32	(	(	PUNCT
ejpam-6238	78	33	α)(t	α)(t	NUM
ejpam-6238	78	34	)	)	PUNCT
ejpam-6238	78	35	=	=	SYM
ejpam-6238	79	1	ģv	ģv	PROPN
ejpam-6238	79	2	(	(	PUNCT
ejpam-6238	79	3	t	t	PROPN
ejpam-6238	79	4	)	)	PUNCT
ejpam-6238	79	5	+	+	CCONJ
ejpam-6238	79	6	f(t	f(t	NOUN
ejpam-6238	79	7	)	)	PUNCT
ejpam-6238	79	8	(	(	PUNCT
ejpam-6238	79	9	6	6	NUM
ejpam-6238	79	10	)	)	PUNCT
ejpam-6238	79	11	where	where	SCONJ
ejpam-6238	79	12	:	:	PUNCT
ejpam-6238	79	13	v	v	NOUN
ejpam-6238	79	14	=	=	SYM
ejpam-6238	79	15			NOUN
ejpam-6238	79	16	v1	v1	PROPN
ejpam-6238	79	17	v2	v2	PROPN
ejpam-6238	79	18	...	...	PUNCT
ejpam-6238	80	1	vn	vn	PROPN
ejpam-6238	80	2	vn+1	vn+1	PROPN
ejpam-6238	80	3	vn+2	vn+2	NUM
ejpam-6238	80	4	...	...	PUNCT
ejpam-6238	80	5	v2n	v2n	NOUN
ejpam-6238	80	6			NOUN
ejpam-6238	80	7	=	=	SYM
ejpam-6238	80	8			NOUN
ejpam-6238	80	9	u1	u1	NOUN
ejpam-6238	80	10	u2	u2	PROPN
ejpam-6238	80	11	...	...	PUNCT
ejpam-6238	80	12	un	un	PROPN
ejpam-6238	80	13	u	u	PROPN
ejpam-6238	80	14	(	(	PUNCT
ejpam-6238	80	15	α	α	NOUN
ejpam-6238	80	16	)	)	PUNCT
ejpam-6238	80	17	1	1	NUM
ejpam-6238	80	18	u	u	NOUN
ejpam-6238	80	19	(	(	PUNCT
ejpam-6238	80	20	α	α	NOUN
ejpam-6238	80	21	)	)	PUNCT
ejpam-6238	80	22	2	2	NUM
ejpam-6238	80	23	...	...	PUNCT
ejpam-6238	80	24	u	u	NOUN
ejpam-6238	80	25	(	(	PUNCT
ejpam-6238	80	26	α	α	NOUN
ejpam-6238	80	27	)	)	PUNCT
ejpam-6238	80	28	n	n	PRON
ejpam-6238	80	29			NOUN
ejpam-6238	80	30	,	,	PUNCT
ejpam-6238	80	31	ģ=	ģ=	NOUN
ejpam-6238	80	32	(	(	PUNCT
ejpam-6238	80	33	0	0	NUM
ejpam-6238	80	34	−b	−b	VERB
ejpam-6238	80	35	i	i	PRON
ejpam-6238	80	36	−a	−a	VERB
ejpam-6238	80	37	)	)	PUNCT
ejpam-6238	80	38	,	,	PUNCT
ejpam-6238	80	39	f(t	f(t	PROPN
ejpam-6238	80	40	)	)	PUNCT
ejpam-6238	80	41	=	=	SYM
ejpam-6238	80	42			ADJ
ejpam-6238	80	43	0	0	NUM
ejpam-6238	80	44	...	...	SYM
ejpam-6238	80	45	0	0	NUM
ejpam-6238	80	46	f(t	f(t	NOUN
ejpam-6238	80	47	)	)	PUNCT
ejpam-6238	80	48	⟨z	⟨z	PROPN
ejpam-6238	80	49	,	,	PUNCT
ejpam-6238	80	50	δ1⟩	δ1⟩	INTJ
ejpam-6238	80	51	...	...	PUNCT
ejpam-6238	80	52	f(t	f(t	PROPN
ejpam-6238	80	53	)	)	PUNCT
ejpam-6238	80	54	⟨z	⟨z	PROPN
ejpam-6238	80	55	,	,	PUNCT
ejpam-6238	80	56	δn⟩	δn⟩	X
ejpam-6238	80	57			PROPN
ejpam-6238	80	58	here	here	ADV
ejpam-6238	80	59	,	,	PUNCT
ejpam-6238	80	60	0	0	NUM
ejpam-6238	80	61	is	be	AUX
ejpam-6238	80	62	a	a	DET
ejpam-6238	80	63	zero	zero	NUM
ejpam-6238	80	64	matrix	matrix	NOUN
ejpam-6238	80	65	,	,	PUNCT
ejpam-6238	80	66	i	i	PRON
ejpam-6238	80	67	is	be	AUX
ejpam-6238	80	68	the	the	DET
ejpam-6238	80	69	identity	identity	NOUN
ejpam-6238	80	70	matrix	matrix	NOUN
ejpam-6238	80	71	,	,	PUNCT
ejpam-6238	80	72	a	a	PRON
ejpam-6238	80	73	and	and	CCONJ
ejpam-6238	80	74	b	b	NOUN
ejpam-6238	80	75	are	be	AUX
ejpam-6238	80	76	n	n	PRON
ejpam-6238	80	77	×	×	NOUN
ejpam-6238	80	78	n	n	CCONJ
ejpam-6238	80	79	coefficient	coefficient	NOUN
ejpam-6238	80	80	matrices	matrix	NOUN
ejpam-6238	80	81	:	:	PUNCT
ejpam-6238	81	1	h.	h.	PROPN
ejpam-6238	81	2	odetallah	odetallah	PROPN
ejpam-6238	81	3	et	et	PROPN
ejpam-6238	81	4	al	al	PROPN
ejpam-6238	81	5	.	.	PUNCT
ejpam-6238	81	6	/	/	SYM
ejpam-6238	81	7	eur	eur	PROPN
ejpam-6238	81	8	.	.	PUNCT
ejpam-6238	82	1	j.	j.	PROPN
ejpam-6238	82	2	pure	pure	PROPN
ejpam-6238	82	3	appl	appl	PROPN
ejpam-6238	82	4	.	.	PROPN
ejpam-6238	82	5	math	math	PROPN
ejpam-6238	82	6	,	,	PUNCT
ejpam-6238	82	7	18	18	NUM
ejpam-6238	82	8	(	(	PUNCT
ejpam-6238	82	9	3	3	NUM
ejpam-6238	82	10	)	)	PUNCT
ejpam-6238	82	11	(	(	PUNCT
ejpam-6238	82	12	2025	2025	NUM
ejpam-6238	82	13	)	)	PUNCT
ejpam-6238	82	14	,	,	PUNCT
ejpam-6238	82	15	6238	6238	NUM
ejpam-6238	82	16	5	5	NUM
ejpam-6238	82	17	of	of	ADP
ejpam-6238	82	18	11	11	NUM
ejpam-6238	82	19	a	a	PRON
ejpam-6238	82	20	=	=	SYM
ejpam-6238	82	21	(	(	PUNCT
ejpam-6238	82	22	aij)n×n	aij)n×n	NOUN
ejpam-6238	82	23	,	,	PUNCT
ejpam-6238	82	24	b	b	PROPN
ejpam-6238	82	25	=(	=(	NOUN
ejpam-6238	82	26	bij)n×n	bij)n×n	PROPN
ejpam-6238	82	27	where	where	SCONJ
ejpam-6238	82	28	aij	aij	PROPN
ejpam-6238	82	29	=	=	SYM
ejpam-6238	82	30	⟨a(δi	⟨a(δi	X
ejpam-6238	82	31	)	)	PUNCT
ejpam-6238	82	32	,	,	PUNCT
ejpam-6238	82	33	δj⟩	δj⟩	PROPN
ejpam-6238	82	34	,	,	PUNCT
ejpam-6238	82	35	bij	bij	NOUN
ejpam-6238	82	36	=	=	PUNCT
ejpam-6238	82	37	⟨b(δi	⟨b(δi	NOUN
ejpam-6238	82	38	)	)	PUNCT
ejpam-6238	82	39	,	,	PUNCT
ejpam-6238	82	40	δj⟩	δj⟩	PROPN
ejpam-6238	82	41	for	for	ADP
ejpam-6238	82	42	all	all	DET
ejpam-6238	82	43	i	i	PROPN
ejpam-6238	82	44	,	,	PUNCT
ejpam-6238	82	45	j	j	PROPN
ejpam-6238	82	46	=	=	SYM
ejpam-6238	82	47	1	1	NUM
ejpam-6238	82	48	,	,	PUNCT
ejpam-6238	82	49	2	2	NUM
ejpam-6238	82	50	,	,	PUNCT
ejpam-6238	82	51	...	...	PUNCT
ejpam-6238	82	52	,	,	PUNCT
ejpam-6238	82	53	n.	n.	NOUN
ejpam-6238	82	54	this	this	DET
ejpam-6238	82	55	system	system	NOUN
ejpam-6238	82	56	has	have	VERB
ejpam-6238	82	57	a	a	DET
ejpam-6238	82	58	unique	unique	ADJ
ejpam-6238	82	59	solution	solution	NOUN
ejpam-6238	82	60	of	of	ADP
ejpam-6238	82	61	the	the	DET
ejpam-6238	82	62	form	form	NOUN
ejpam-6238	82	63	:	:	PUNCT
ejpam-6238	82	64	v	v	X
ejpam-6238	82	65	(	(	PUNCT
ejpam-6238	82	66	t	t	NOUN
ejpam-6238	82	67	)	)	PUNCT
ejpam-6238	82	68	=	=	NOUN
ejpam-6238	83	1	ϕα	ϕα	ADV
ejpam-6238	83	2	(	(	PUNCT
ejpam-6238	83	3	t)v	t)v	X
ejpam-6238	83	4	(	(	PUNCT
ejpam-6238	83	5	0	0	NUM
ejpam-6238	83	6	)	)	PUNCT
ejpam-6238	84	1	+	+	CCONJ
ejpam-6238	84	2	ϕα	ϕα	ADJ
ejpam-6238	84	3	(	(	PUNCT
ejpam-6238	84	4	t	t	PROPN
ejpam-6238	84	5	)	)	PUNCT
ejpam-6238	84	6	∫	∫	PROPN
ejpam-6238	85	1	t	t	PROPN
ejpam-6238	85	2	0	0	NUM
ejpam-6238	86	1	ϕ−1	ϕ−1	PROPN
ejpam-6238	86	2	α	α	PROPN
ejpam-6238	86	3	(	(	PUNCT
ejpam-6238	86	4	s)f	s)f	X
ejpam-6238	86	5	(	(	PUNCT
ejpam-6238	86	6	s	s	X
ejpam-6238	86	7	)	)	PUNCT
ejpam-6238	86	8	s1−α	s1−α	ADJ
ejpam-6238	86	9	ds	ds	ADJ
ejpam-6238	86	10	(	(	PUNCT
ejpam-6238	86	11	7	7	NUM
ejpam-6238	86	12	)	)	PUNCT
ejpam-6238	86	13	where	where	SCONJ
ejpam-6238	86	14	ϕα	ϕα	ADV
ejpam-6238	86	15	(	(	PUNCT
ejpam-6238	86	16	t	t	NOUN
ejpam-6238	86	17	)	)	PUNCT
ejpam-6238	86	18	is	be	AUX
ejpam-6238	86	19	the	the	DET
ejpam-6238	86	20	n	n	NUM
ejpam-6238	86	21	×	×	NOUN
ejpam-6238	86	22	n	n	CCONJ
ejpam-6238	86	23	conformable	conformable	ADJ
ejpam-6238	86	24	fundamental	fundamental	ADJ
ejpam-6238	86	25	matrix	matrix	NOUN
ejpam-6238	86	26	,	,	PUNCT
ejpam-6238	86	27	and	and	CCONJ
ejpam-6238	86	28	v	v	NOUN
ejpam-6238	86	29	(	(	PUNCT
ejpam-6238	86	30	0	0	NUM
ejpam-6238	86	31	)	)	PUNCT
ejpam-6238	86	32	is	be	AUX
ejpam-6238	86	33	the	the	DET
ejpam-6238	86	34	initial	initial	ADJ
ejpam-6238	86	35	condition	condition	NOUN
ejpam-6238	86	36	vector	vector	NOUN
ejpam-6238	86	37	containing	contain	VERB
ejpam-6238	86	38	the	the	DET
ejpam-6238	86	39	initial	initial	ADJ
ejpam-6238	86	40	value	value	NOUN
ejpam-6238	86	41	of	of	ADP
ejpam-6238	86	42	u0	u0	ADJ
ejpam-6238	86	43	and	and	CCONJ
ejpam-6238	86	44	u	u	NOUN
ejpam-6238	86	45	(	(	PUNCT
ejpam-6238	86	46	α	α	NOUN
ejpam-6238	86	47	)	)	PUNCT
ejpam-6238	86	48	0	0	NUM
ejpam-6238	86	49	.	.	PUNCT
ejpam-6238	87	1	now	now	ADV
ejpam-6238	87	2	,	,	PUNCT
ejpam-6238	87	3	the	the	DET
ejpam-6238	87	4	following	follow	VERB
ejpam-6238	87	5	theorem	theorem	NOUN
ejpam-6238	87	6	takes	take	VERB
ejpam-6238	87	7	a	a	DET
ejpam-6238	87	8	special	special	ADJ
ejpam-6238	87	9	case	case	NOUN
ejpam-6238	87	10	on	on	ADP
ejpam-6238	87	11	the	the	DET
ejpam-6238	87	12	operators	operator	NOUN
ejpam-6238	87	13	a	a	DET
ejpam-6238	87	14	and	and	CCONJ
ejpam-6238	87	15	b.	b.	PROPN
ejpam-6238	87	16	theorem	theorem	NOUN
ejpam-6238	87	17	3	3	X
ejpam-6238	87	18	.	.	X
ejpam-6238	87	19	consider	consider	VERB
ejpam-6238	87	20	problem	problem	NOUN
ejpam-6238	87	21	(	(	PUNCT
ejpam-6238	87	22	1	1	NUM
ejpam-6238	87	23	)	)	PUNCT
ejpam-6238	87	24	with	with	ADP
ejpam-6238	87	25	e	e	NOUN
ejpam-6238	87	26	=	=	PUNCT
ejpam-6238	87	27	i	i	PROPN
ejpam-6238	87	28	and	and	CCONJ
ejpam-6238	87	29	u(t	u(t	NOUN
ejpam-6238	87	30	)	)	PUNCT
ejpam-6238	88	1	=	=	SYM
ejpam-6238	88	2	n	n	SYM
ejpam-6238	88	3	i=1	i=1	NOUN
ejpam-6238	88	4	ui(t)δi	ui(t)δi	ADJ
ejpam-6238	88	5	,	,	PUNCT
ejpam-6238	88	6	where	where	SCONJ
ejpam-6238	88	7	u	u	PROPN
ejpam-6238	88	8	(	(	PUNCT
ejpam-6238	88	9	2α	2α	PROPN
ejpam-6238	88	10	)	)	PUNCT
ejpam-6238	88	11	i	i	PRON
ejpam-6238	88	12	(	(	PUNCT
ejpam-6238	88	13	t	t	PROPN
ejpam-6238	88	14	)	)	PUNCT
ejpam-6238	88	15	∈	∈	PROPN
ejpam-6238	88	16	c(i	c(i	PROPN
ejpam-6238	88	17	)	)	PUNCT
ejpam-6238	88	18	,	,	PUNCT
ejpam-6238	88	19	i	i	PRON
ejpam-6238	88	20	=	=	NOUN
ejpam-6238	88	21	1	1	NUM
ejpam-6238	88	22	,	,	PUNCT
ejpam-6238	88	23	2	2	NUM
ejpam-6238	88	24	,	,	PUNCT
ejpam-6238	88	25	...	...	PUNCT
ejpam-6238	88	26	,	,	PUNCT
ejpam-6238	88	27	n.	n.	NOUN
ejpam-6238	88	28	if	if	SCONJ
ejpam-6238	88	29	a(δi	a(δi	NUM
ejpam-6238	88	30	)	)	PUNCT
ejpam-6238	88	31	=	=	SYM
ejpam-6238	89	1	λiδi	λiδi	NOUN
ejpam-6238	89	2	and	and	CCONJ
ejpam-6238	89	3	b(δi	b(δi	ADJ
ejpam-6238	89	4	)	)	PUNCT
ejpam-6238	90	1	=	=	SYM
ejpam-6238	90	2	βiδi	βiδi	ADV
ejpam-6238	90	3	,	,	PUNCT
ejpam-6238	90	4	then	then	ADV
ejpam-6238	90	5	the	the	DET
ejpam-6238	90	6	problem	problem	NOUN
ejpam-6238	90	7	has	have	VERB
ejpam-6238	90	8	a	a	DET
ejpam-6238	90	9	unique	unique	ADJ
ejpam-6238	90	10	solution	solution	NOUN
ejpam-6238	90	11	.	.	PUNCT
ejpam-6238	91	1	proof	proof	NOUN
ejpam-6238	91	2	.	.	PUNCT
ejpam-6238	92	1	we	we	PRON
ejpam-6238	92	2	have	have	VERB
ejpam-6238	92	3	u(t	u(t	NOUN
ejpam-6238	92	4	)	)	PUNCT
ejpam-6238	93	1	=	=	SYM
ejpam-6238	93	2	n	n	SYM
ejpam-6238	93	3	i=1	i=1	NOUN
ejpam-6238	93	4	ui(t)δi	ui(t)δi	ADJ
ejpam-6238	93	5	,	,	PUNCT
ejpam-6238	93	6	then	then	ADV
ejpam-6238	93	7	u(α)(t	u(α)(t	NOUN
ejpam-6238	93	8	)	)	PUNCT
ejpam-6238	93	9	=	=	NOUN
ejpam-6238	93	10	n	n	NUM
ejpam-6238	93	11	i=1	i=1	PROPN
ejpam-6238	93	12	u	u	PROPN
ejpam-6238	93	13	(	(	PUNCT
ejpam-6238	93	14	α	α	NOUN
ejpam-6238	93	15	)	)	PUNCT
ejpam-6238	93	16	i	i	PRON
ejpam-6238	93	17	(	(	PUNCT
ejpam-6238	93	18	t)δi	t)δi	PROPN
ejpam-6238	93	19	,	,	PUNCT
ejpam-6238	93	20	and	and	CCONJ
ejpam-6238	93	21	u(2α)(t	u(2α)(t	NOUN
ejpam-6238	93	22	)	)	PUNCT
ejpam-6238	94	1	=	=	SYM
ejpam-6238	94	2	n	n	NUM
ejpam-6238	94	3	i=1	i=1	PROPN
ejpam-6238	94	4	u	u	PROPN
ejpam-6238	94	5	(	(	PUNCT
ejpam-6238	94	6	2α	2α	NOUN
ejpam-6238	94	7	)	)	PUNCT
ejpam-6238	95	1	i	i	PRON
ejpam-6238	95	2	(	(	PUNCT
ejpam-6238	95	3	t)δi	t)δi	PROPN
ejpam-6238	95	4	.	.	PUNCT
ejpam-6238	96	1	thus	thus	ADV
ejpam-6238	96	2	n	n	DET
ejpam-6238	96	3	i=1u	i=1u	ADJ
ejpam-6238	96	4	(	(	PUNCT
ejpam-6238	96	5	2α	2α	NOUN
ejpam-6238	96	6	)	)	PUNCT
ejpam-6238	96	7	i	i	PRON
ejpam-6238	96	8	(	(	PUNCT
ejpam-6238	96	9	t)δi	t)δi	PROPN
ejpam-6238	96	10	+	+	NUM
ejpam-6238	96	11	n	n	CCONJ
ejpam-6238	96	12	i=1	i=1	PROPN
ejpam-6238	96	13	u	u	PROPN
ejpam-6238	96	14	(	(	PUNCT
ejpam-6238	96	15	α	α	NOUN
ejpam-6238	96	16	)	)	PUNCT
ejpam-6238	96	17	i	i	PRON
ejpam-6238	96	18	(	(	PUNCT
ejpam-6238	96	19	t)a(δi	t)a(δi	NUM
ejpam-6238	96	20	)	)	PUNCT
ejpam-6238	97	1	+	+	CCONJ
ejpam-6238	97	2	n	n	CCONJ
ejpam-6238	97	3	i=1	i=1	PROPN
ejpam-6238	97	4	ui(t)b(δi	ui(t)b(δi	NUM
ejpam-6238	97	5	)	)	PUNCT
ejpam-6238	97	6	=	=	SYM
ejpam-6238	97	7	f(t)z	f(t)z	NOUN
ejpam-6238	97	8	(	(	PUNCT
ejpam-6238	97	9	8)	8)	NUM
ejpam-6238	97	10	if	if	SCONJ
ejpam-6238	97	11	we	we	PRON
ejpam-6238	97	12	take	take	VERB
ejpam-6238	97	13	the	the	DET
ejpam-6238	97	14	inner	inner	ADJ
ejpam-6238	97	15	product	product	NOUN
ejpam-6238	97	16	of	of	ADP
ejpam-6238	97	17	δj	δj	NOUN
ejpam-6238	97	18	with	with	ADP
ejpam-6238	97	19	both	both	DET
ejpam-6238	97	20	sides	side	NOUN
ejpam-6238	97	21	of	of	ADP
ejpam-6238	97	22	equation	equation	NOUN
ejpam-6238	97	23	(	(	PUNCT
ejpam-6238	97	24	8)	8)	NUM
ejpam-6238	97	25	,	,	PUNCT
ejpam-6238	97	26	then	then	ADV
ejpam-6238	97	27	the	the	DET
ejpam-6238	97	28	equation	equation	NOUN
ejpam-6238	97	29	becomes	become	VERB
ejpam-6238	97	30	n	n	DET
ejpam-6238	97	31	i=1u	i=1u	ADJ
ejpam-6238	97	32	(	(	PUNCT
ejpam-6238	97	33	2α	2α	NOUN
ejpam-6238	97	34	)	)	PUNCT
ejpam-6238	98	1	i	i	PRON
ejpam-6238	98	2	(	(	PUNCT
ejpam-6238	98	3	t	t	PROPN
ejpam-6238	98	4	)	)	PUNCT
ejpam-6238	98	5	⟨δi	⟨δi	PROPN
ejpam-6238	98	6	,	,	PUNCT
ejpam-6238	98	7	δj⟩+n	δj⟩+n	PROPN
ejpam-6238	98	8	i=1	i=1	PROPN
ejpam-6238	98	9	u	u	PROPN
ejpam-6238	98	10	(	(	PUNCT
ejpam-6238	98	11	α	α	NOUN
ejpam-6238	98	12	)	)	PUNCT
ejpam-6238	98	13	i	i	PRON
ejpam-6238	98	14	(	(	PUNCT
ejpam-6238	98	15	t	t	NOUN
ejpam-6238	98	16	)	)	PUNCT
ejpam-6238	98	17	⟨a(δi	⟨a(δi	NUM
ejpam-6238	98	18	)	)	PUNCT
ejpam-6238	98	19	,	,	PUNCT
ejpam-6238	98	20	δj⟩+n	δj⟩+n	PROPN
ejpam-6238	98	21	i=1	i=1	PROPN
ejpam-6238	98	22	ui(t	ui(t	NOUN
ejpam-6238	98	23	)	)	PUNCT
ejpam-6238	98	24	⟨b(δi	⟨b(δi	NOUN
ejpam-6238	98	25	)	)	PUNCT
ejpam-6238	98	26	,	,	PUNCT
ejpam-6238	98	27	δj⟩	δj⟩	NOUN
ejpam-6238	98	28	=	=	SYM
ejpam-6238	98	29	f(t	f(t	PROPN
ejpam-6238	98	30	)	)	PUNCT
ejpam-6238	98	31	⟨z	⟨z	PROPN
ejpam-6238	98	32	,	,	PUNCT
ejpam-6238	98	33	δj⟩	δj⟩	X
ejpam-6238	98	34	(	(	PUNCT
ejpam-6238	98	35	9	9	NUM
ejpam-6238	98	36	)	)	PUNCT
ejpam-6238	98	37	but	but	CCONJ
ejpam-6238	98	38	since	since	SCONJ
ejpam-6238	98	39	the	the	DET
ejpam-6238	98	40	standard	standard	ADJ
ejpam-6238	98	41	basis	basis	NOUN
ejpam-6238	98	42	is	be	AUX
ejpam-6238	98	43	orthonormal	orthonormal	ADJ
ejpam-6238	98	44	and	and	CCONJ
ejpam-6238	98	45	a(δi	a(δi	NUM
ejpam-6238	98	46	)	)	PUNCT
ejpam-6238	98	47	=	=	VERB
ejpam-6238	98	48	λiδi	λiδi	ADJ
ejpam-6238	98	49	,	,	PUNCT
ejpam-6238	98	50	b(δi	b(δi	NUM
ejpam-6238	98	51	)	)	PUNCT
ejpam-6238	98	52	=	=	SYM
ejpam-6238	99	1	βiδi	βiδi	ADV
ejpam-6238	99	2	,	,	PUNCT
ejpam-6238	99	3	then	then	ADV
ejpam-6238	99	4	u	u	X
ejpam-6238	99	5	(	(	PUNCT
ejpam-6238	99	6	2α	2α	PROPN
ejpam-6238	99	7	)	)	PUNCT
ejpam-6238	99	8	j	j	PROPN
ejpam-6238	99	9	(	(	PUNCT
ejpam-6238	99	10	t	t	PROPN
ejpam-6238	99	11	)	)	PUNCT
ejpam-6238	99	12	+	+	CCONJ
ejpam-6238	99	13	λju	λju	NOUN
ejpam-6238	99	14	(	(	PUNCT
ejpam-6238	99	15	α	α	NOUN
ejpam-6238	99	16	)	)	PUNCT
ejpam-6238	99	17	j	j	PROPN
ejpam-6238	99	18	(	(	PUNCT
ejpam-6238	99	19	t	t	PROPN
ejpam-6238	99	20	)	)	PUNCT
ejpam-6238	99	21	+	+	CCONJ
ejpam-6238	99	22	βjuj(t	βjuj(t	ADJ
ejpam-6238	99	23	)	)	PUNCT
ejpam-6238	99	24	=	=	SYM
ejpam-6238	99	25	f(t	f(t	NOUN
ejpam-6238	99	26	)	)	PUNCT
ejpam-6238	99	27	⟨z	⟨z	PROPN
ejpam-6238	99	28	,	,	PUNCT
ejpam-6238	99	29	δj⟩	δj⟩	PROPN
ejpam-6238	99	30	(	(	PUNCT
ejpam-6238	99	31	10	10	NUM
ejpam-6238	99	32	)	)	PUNCT
ejpam-6238	99	33	each	each	DET
ejpam-6238	99	34	equation	equation	NOUN
ejpam-6238	99	35	represents	represent	VERB
ejpam-6238	99	36	a	a	DET
ejpam-6238	99	37	second	second	ADJ
ejpam-6238	99	38	-	-	PUNCT
ejpam-6238	99	39	order	order	NOUN
ejpam-6238	99	40	linear	linear	ADJ
ejpam-6238	99	41	conformable	conformable	ADJ
ejpam-6238	99	42	fractional	fractional	ADJ
ejpam-6238	99	43	differential	differential	ADJ
ejpam-6238	99	44	equation	equation	NOUN
ejpam-6238	99	45	with	with	ADP
ejpam-6238	99	46	constant	constant	ADJ
ejpam-6238	99	47	coefficients	coefficient	NOUN
ejpam-6238	99	48	.	.	PUNCT
ejpam-6238	100	1	given	give	VERB
ejpam-6238	100	2	appropriate	appropriate	ADJ
ejpam-6238	100	3	initial	initial	ADJ
ejpam-6238	100	4	conditions	condition	NOUN
ejpam-6238	100	5	uj	uj	X
ejpam-6238	100	6	(	(	PUNCT
ejpam-6238	100	7	0	0	NUM
ejpam-6238	100	8	)	)	PUNCT
ejpam-6238	100	9	and	and	CCONJ
ejpam-6238	100	10	u	u	PROPN
ejpam-6238	100	11	(	(	PUNCT
ejpam-6238	100	12	α	α	NOUN
ejpam-6238	100	13	)	)	PUNCT
ejpam-6238	100	14	j	j	PROPN
ejpam-6238	100	15	(	(	PUNCT
ejpam-6238	100	16	0	0	NUM
ejpam-6238	100	17	)	)	PUNCT
ejpam-6238	100	18	for	for	ADP
ejpam-6238	100	19	all	all	DET
ejpam-6238	100	20	j	j	NOUN
ejpam-6238	100	21	=	=	SYM
ejpam-6238	100	22	1	1	NUM
ejpam-6238	100	23	,	,	PUNCT
ejpam-6238	100	24	2	2	NUM
ejpam-6238	100	25	,	,	PUNCT
ejpam-6238	100	26	...	...	PUNCT
ejpam-6238	100	27	,	,	PUNCT
ejpam-6238	100	28	n	n	CCONJ
ejpam-6238	100	29	,	,	PUNCT
ejpam-6238	100	30	each	each	DET
ejpam-6238	100	31	equation	equation	NOUN
ejpam-6238	100	32	admits	admit	VERB
ejpam-6238	100	33	a	a	DET
ejpam-6238	100	34	unique	unique	ADJ
ejpam-6238	100	35	solution	solution	NOUN
ejpam-6238	100	36	.	.	PUNCT
ejpam-6238	101	1	now	now	ADV
ejpam-6238	101	2	,	,	PUNCT
ejpam-6238	101	3	in	in	ADP
ejpam-6238	101	4	the	the	DET
ejpam-6238	101	5	following	follow	VERB
ejpam-6238	101	6	theorem	theorem	NOUN
ejpam-6238	101	7	we	we	PRON
ejpam-6238	101	8	take	take	VERB
ejpam-6238	101	9	the	the	DET
ejpam-6238	101	10	case	case	NOUN
ejpam-6238	101	11	where	where	SCONJ
ejpam-6238	101	12	e	e	AUX
ejpam-6238	101	13	̸=	̸=	PROPN
ejpam-6238	101	14	i.	i.	NOUN
ejpam-6238	101	15	theorem	theorem	VERB
ejpam-6238	101	16	4	4	NUM
ejpam-6238	101	17	.	.	PUNCT
ejpam-6238	101	18	consider	consider	VERB
ejpam-6238	101	19	problem	problem	NOUN
ejpam-6238	101	20	(	(	PUNCT
ejpam-6238	101	21	1	1	NUM
ejpam-6238	101	22	)	)	PUNCT
ejpam-6238	101	23	where	where	SCONJ
ejpam-6238	101	24	en	en	X
ejpam-6238	101	25	is	be	AUX
ejpam-6238	101	26	orthogonally	orthogonally	ADV
ejpam-6238	101	27	diagonalizable	diagonalizable	ADJ
ejpam-6238	101	28	with	with	ADP
ejpam-6238	101	29	an|ker(en	an|ker(en	NOUN
ejpam-6238	101	30	)	)	PUNCT
ejpam-6238	101	31	invertible	invertible	ADJ
ejpam-6238	101	32	.	.	PUNCT
ejpam-6238	102	1	if	if	SCONJ
ejpam-6238	102	2	u(t	u(t	NOUN
ejpam-6238	102	3	)	)	PUNCT
ejpam-6238	102	4	=	=	SYM
ejpam-6238	102	5	n	n	NOUN
ejpam-6238	102	6	i=1	i=1	X
ejpam-6238	102	7	ui(t)δi	ui(t)δi	ADJ
ejpam-6238	102	8	with	with	ADP
ejpam-6238	102	9	u	u	PROPN
ejpam-6238	102	10	(	(	PUNCT
ejpam-6238	102	11	2α	2α	NOUN
ejpam-6238	102	12	)	)	PUNCT
ejpam-6238	102	13	i	i	PRON
ejpam-6238	102	14	(	(	PUNCT
ejpam-6238	102	15	t	t	PROPN
ejpam-6238	102	16	)	)	PUNCT
ejpam-6238	102	17	∈	∈	PROPN
ejpam-6238	102	18	c(i	c(i	PROPN
ejpam-6238	102	19	)	)	PUNCT
ejpam-6238	102	20	for	for	ADP
ejpam-6238	102	21	i	i	PROPN
ejpam-6238	102	22	=	=	SYM
ejpam-6238	102	23	1	1	NUM
ejpam-6238	102	24	,	,	PUNCT
ejpam-6238	102	25	2	2	NUM
ejpam-6238	102	26	,	,	PUNCT
ejpam-6238	102	27	...	...	PUNCT
ejpam-6238	102	28	,	,	PUNCT
ejpam-6238	102	29	n	n	CCONJ
ejpam-6238	102	30	,	,	PUNCT
ejpam-6238	102	31	then	then	ADV
ejpam-6238	102	32	problem	problem	NOUN
ejpam-6238	102	33	(	(	PUNCT
ejpam-6238	102	34	1	1	X
ejpam-6238	102	35	)	)	PUNCT
ejpam-6238	102	36	has	have	VERB
ejpam-6238	102	37	a	a	DET
ejpam-6238	102	38	unique	unique	ADJ
ejpam-6238	102	39	solution	solution	NOUN
ejpam-6238	102	40	.	.	PUNCT
ejpam-6238	103	1	proof	proof	NOUN
ejpam-6238	103	2	.	.	PUNCT
ejpam-6238	104	1	let	let	VERB
ejpam-6238	104	2	{	{	PUNCT
ejpam-6238	104	3	θ1	θ1	PROPN
ejpam-6238	104	4	,	,	PUNCT
ejpam-6238	104	5	θ2	θ2	PROPN
ejpam-6238	104	6	,	,	PUNCT
ejpam-6238	104	7	...	...	PUNCT
ejpam-6238	104	8	,	,	PUNCT
ejpam-6238	104	9	θn	θn	VERB
ejpam-6238	104	10	}	}	PUNCT
ejpam-6238	104	11	be	be	AUX
ejpam-6238	104	12	an	an	DET
ejpam-6238	104	13	orthonormal	orthonormal	ADJ
ejpam-6238	104	14	basis	basis	NOUN
ejpam-6238	104	15	such	such	ADJ
ejpam-6238	104	16	that	that	SCONJ
ejpam-6238	104	17	the	the	DET
ejpam-6238	104	18	matrix	matrix	NOUN
ejpam-6238	104	19	representation	representation	NOUN
ejpam-6238	104	20	of	of	ADP
ejpam-6238	104	21	en	en	X
ejpam-6238	104	22	with	with	ADP
ejpam-6238	104	23	respect	respect	NOUN
ejpam-6238	104	24	to	to	ADP
ejpam-6238	104	25	this	this	DET
ejpam-6238	104	26	basis	basis	NOUN
ejpam-6238	104	27	is	be	AUX
ejpam-6238	104	28	d	d	NOUN
ejpam-6238	104	29	=	=	SYM
ejpam-6238	104	30	diag	diag	X
ejpam-6238	104	31	(	(	PUNCT
ejpam-6238	104	32	λ1	λ1	ADJ
ejpam-6238	104	33	,	,	PUNCT
ejpam-6238	104	34	λ2	λ2	NOUN
ejpam-6238	104	35	,	,	PUNCT
ejpam-6238	104	36	...	...	PUNCT
ejpam-6238	104	37	,	,	PUNCT
ejpam-6238	104	38	λn	λn	NOUN
ejpam-6238	104	39	)	)	PUNCT
ejpam-6238	104	40	with	with	ADP
ejpam-6238	104	41	λ1	λ1	ADJ
ejpam-6238	104	42	,	,	PUNCT
ejpam-6238	104	43	λ2	λ2	NOUN
ejpam-6238	104	44	,	,	PUNCT
ejpam-6238	104	45	...	...	PUNCT
ejpam-6238	104	46	,	,	PUNCT
ejpam-6238	104	47	λn	λn	ADP
ejpam-6238	104	48	corresponding	correspond	VERB
ejpam-6238	104	49	eigenvalues	eigenvalue	NOUN
ejpam-6238	104	50	.	.	PUNCT
ejpam-6238	105	1	now	now	ADV
ejpam-6238	105	2	,	,	PUNCT
ejpam-6238	105	3	if	if	SCONJ
ejpam-6238	105	4	λi	λi	ADP
ejpam-6238	105	5	̸=	̸=	PROPN
ejpam-6238	105	6	0	0	NUM
ejpam-6238	105	7	,	,	PUNCT
ejpam-6238	105	8	for	for	ADP
ejpam-6238	105	9	all	all	DET
ejpam-6238	105	10	i	i	PRON
ejpam-6238	105	11	=	=	NOUN
ejpam-6238	105	12	1	1	NUM
ejpam-6238	105	13	,	,	PUNCT
ejpam-6238	105	14	2	2	NUM
ejpam-6238	105	15	,	,	PUNCT
ejpam-6238	105	16	...	...	PUNCT
ejpam-6238	105	17	,	,	PUNCT
ejpam-6238	105	18	n	n	CCONJ
ejpam-6238	105	19	,	,	PUNCT
ejpam-6238	105	20	then	then	ADV
ejpam-6238	105	21	problem	problem	NOUN
ejpam-6238	105	22	(	(	PUNCT
ejpam-6238	105	23	1	1	X
ejpam-6238	105	24	)	)	PUNCT
ejpam-6238	105	25	reduces	reduce	VERB
ejpam-6238	105	26	to	to	PART
ejpam-6238	105	27	:	:	PUNCT
ejpam-6238	105	28	u(2α)(t	u(2α)(t	X
ejpam-6238	105	29	)	)	PUNCT
ejpam-6238	106	1	+	+	CCONJ
ejpam-6238	106	2	e−1	e−1	PROPN
ejpam-6238	106	3	n	n	PRON
ejpam-6238	106	4	anu	anu	NOUN
ejpam-6238	106	5	(	(	PUNCT
ejpam-6238	106	6	α)(t	α)(t	PROPN
ejpam-6238	106	7	)	)	PUNCT
ejpam-6238	106	8	+	+	CCONJ
ejpam-6238	106	9	e−1	e−1	PROPN
ejpam-6238	106	10	n	n	NUM
ejpam-6238	106	11	bnu(t	bnu(t	NUM
ejpam-6238	106	12	)	)	PUNCT
ejpam-6238	106	13	=	=	SYM
ejpam-6238	107	1	e−1	e−1	PROPN
ejpam-6238	107	2	n	n	PRON
ejpam-6238	107	3	f(t	f(t	PROPN
ejpam-6238	107	4	)	)	PUNCT
ejpam-6238	107	5	h.	h.	PROPN
ejpam-6238	108	1	odetallah	odetallah	PROPN
ejpam-6238	108	2	et	et	PROPN
ejpam-6238	108	3	al	al	PROPN
ejpam-6238	108	4	.	.	PUNCT
ejpam-6238	108	5	/	/	SYM
ejpam-6238	108	6	eur	eur	PROPN
ejpam-6238	108	7	.	.	PUNCT
ejpam-6238	109	1	j.	j.	PROPN
ejpam-6238	109	2	pure	pure	PROPN
ejpam-6238	109	3	appl	appl	PROPN
ejpam-6238	109	4	.	.	PROPN
ejpam-6238	109	5	math	math	PROPN
ejpam-6238	109	6	,	,	PUNCT
ejpam-6238	109	7	18	18	NUM
ejpam-6238	109	8	(	(	PUNCT
ejpam-6238	109	9	3	3	NUM
ejpam-6238	109	10	)	)	PUNCT
ejpam-6238	109	11	(	(	PUNCT
ejpam-6238	109	12	2025	2025	NUM
ejpam-6238	109	13	)	)	PUNCT
ejpam-6238	109	14	,	,	PUNCT
ejpam-6238	109	15	6238	6238	NUM
ejpam-6238	109	16	6	6	NUM
ejpam-6238	109	17	of	of	ADP
ejpam-6238	109	18	11	11	NUM
ejpam-6238	109	19	this	this	PRON
ejpam-6238	109	20	has	have	VERB
ejpam-6238	109	21	a	a	DET
ejpam-6238	109	22	unique	unique	ADJ
ejpam-6238	109	23	solution	solution	NOUN
ejpam-6238	109	24	by	by	ADP
ejpam-6238	109	25	theorem	theorem	NOUN
ejpam-6238	109	26	3	3	X
ejpam-6238	109	27	.	.	PUNCT
ejpam-6238	109	28	suppose	suppose	VERB
ejpam-6238	109	29	λi	λi	ADP
ejpam-6238	109	30	̸=	̸=	PROPN
ejpam-6238	109	31	0	0	NUM
ejpam-6238	109	32	,	,	PUNCT
ejpam-6238	109	33	for	for	ADP
ejpam-6238	109	34	i	i	PROPN
ejpam-6238	109	35	=	=	SYM
ejpam-6238	109	36	1	1	NUM
ejpam-6238	109	37	,	,	PUNCT
ejpam-6238	109	38	2	2	NUM
ejpam-6238	109	39	,	,	PUNCT
ejpam-6238	109	40	...	...	PUNCT
ejpam-6238	109	41	,	,	PUNCT
ejpam-6238	109	42	r	r	NOUN
ejpam-6238	109	43	,	,	PUNCT
ejpam-6238	109	44	and	and	CCONJ
ejpam-6238	109	45	λi	λi	X
ejpam-6238	109	46	=	=	NOUN
ejpam-6238	109	47	0	0	NUM
ejpam-6238	109	48	,	,	PUNCT
ejpam-6238	109	49	for	for	ADP
ejpam-6238	109	50	i	i	PRON
ejpam-6238	109	51	=	=	NOUN
ejpam-6238	110	1	r	r	NOUN
ejpam-6238	110	2	+	+	NUM
ejpam-6238	110	3	1	1	NUM
ejpam-6238	110	4	,	,	PUNCT
ejpam-6238	110	5	r	r	NOUN
ejpam-6238	110	6	+	+	PROPN
ejpam-6238	110	7	2	2	NUM
ejpam-6238	110	8	,	,	PUNCT
ejpam-6238	110	9	...	...	PUNCT
ejpam-6238	110	10	,	,	PUNCT
ejpam-6238	110	11	n.	n.	PROPN
ejpam-6238	110	12	let	let	VERB
ejpam-6238	110	13	u	u	PROPN
ejpam-6238	110	14	(	(	PUNCT
ejpam-6238	110	15	t	t	PROPN
ejpam-6238	110	16	)	)	PUNCT
ejpam-6238	110	17	=	=	SYM
ejpam-6238	111	1	∑n	∑n	PROPN
ejpam-6238	111	2	i=1	i=1	PROPN
ejpam-6238	111	3	vi	vi	PROPN
ejpam-6238	111	4	(	(	PUNCT
ejpam-6238	111	5	t	t	PROPN
ejpam-6238	111	6	)	)	PUNCT
ejpam-6238	111	7	θi	θi	PROPN
ejpam-6238	111	8	.	.	PUNCT
ejpam-6238	112	1	the	the	DET
ejpam-6238	112	2	system	system	NOUN
ejpam-6238	112	3	becomes	become	VERB
ejpam-6238	112	4	:	:	PUNCT
ejpam-6238	113	1	n∑	n∑	PROPN
ejpam-6238	113	2	i=1	i=1	PROPN
ejpam-6238	113	3	v	v	PROPN
ejpam-6238	113	4	(	(	PUNCT
ejpam-6238	113	5	2α	2α	NOUN
ejpam-6238	113	6	)	)	PUNCT
ejpam-6238	113	7	i	i	PRON
ejpam-6238	113	8	(	(	PUNCT
ejpam-6238	113	9	t)en	t)en	PROPN
ejpam-6238	113	10	(	(	PUNCT
ejpam-6238	113	11	θi	θi	NOUN
ejpam-6238	113	12	)	)	PUNCT
ejpam-6238	114	1	+	+	NUM
ejpam-6238	115	1	n∑	n∑	PROPN
ejpam-6238	115	2	i=1	i=1	PROPN
ejpam-6238	115	3	v	v	PROPN
ejpam-6238	115	4	(	(	PUNCT
ejpam-6238	115	5	α	α	NOUN
ejpam-6238	115	6	)	)	PUNCT
ejpam-6238	115	7	i	i	PRON
ejpam-6238	115	8	(	(	PUNCT
ejpam-6238	115	9	t)an	t)an	PROPN
ejpam-6238	115	10	(	(	PUNCT
ejpam-6238	115	11	θi	θi	NOUN
ejpam-6238	115	12	)	)	PUNCT
ejpam-6238	116	1	+	+	NUM
ejpam-6238	116	2	n∑	n∑	PROPN
ejpam-6238	116	3	i=1	i=1	PROPN
ejpam-6238	116	4	vi	vi	PROPN
ejpam-6238	117	1	(	(	PUNCT
ejpam-6238	117	2	t)bn	t)bn	PROPN
ejpam-6238	117	3	(	(	PUNCT
ejpam-6238	117	4	θi	θi	NUM
ejpam-6238	117	5	)	)	PUNCT
ejpam-6238	117	6	=	=	SYM
ejpam-6238	117	7	f	f	PROPN
ejpam-6238	117	8	(	(	PUNCT
ejpam-6238	117	9	t	t	PROPN
ejpam-6238	117	10	)	)	PUNCT
ejpam-6238	117	11	z	z	NOUN
ejpam-6238	117	12	(	(	PUNCT
ejpam-6238	117	13	11	11	NUM
ejpam-6238	117	14	)	)	PUNCT
ejpam-6238	117	15	taking	take	VERB
ejpam-6238	117	16	the	the	DET
ejpam-6238	117	17	inner	inner	ADJ
ejpam-6238	117	18	product	product	NOUN
ejpam-6238	117	19	of	of	ADP
ejpam-6238	117	20	θj	θj	NOUN
ejpam-6238	117	21	with	with	ADP
ejpam-6238	117	22	both	both	DET
ejpam-6238	117	23	sides	side	NOUN
ejpam-6238	117	24	of	of	ADP
ejpam-6238	117	25	equation	equation	NOUN
ejpam-6238	117	26	(	(	PUNCT
ejpam-6238	117	27	11	11	NUM
ejpam-6238	117	28	)	)	PUNCT
ejpam-6238	117	29	,	,	PUNCT
ejpam-6238	117	30	we	we	PRON
ejpam-6238	117	31	obtain	obtain	VERB
ejpam-6238	117	32	n∑	n∑	PROPN
ejpam-6238	117	33	i=1	i=1	PROPN
ejpam-6238	117	34	v	v	PROPN
ejpam-6238	117	35	(	(	PUNCT
ejpam-6238	117	36	2α	2α	NOUN
ejpam-6238	117	37	)	)	PUNCT
ejpam-6238	118	1	i	i	PRON
ejpam-6238	118	2	(	(	PUNCT
ejpam-6238	118	3	t	t	PROPN
ejpam-6238	118	4	)	)	PUNCT
ejpam-6238	118	5	⟨en	⟨en	NUM
ejpam-6238	118	6	(	(	PUNCT
ejpam-6238	118	7	θi	θi	NOUN
ejpam-6238	118	8	)	)	PUNCT
ejpam-6238	118	9	,	,	PUNCT
ejpam-6238	118	10	θj⟩+	θj⟩+	PROPN
ejpam-6238	118	11	n∑	n∑	PROPN
ejpam-6238	118	12	i=1	i=1	PROPN
ejpam-6238	118	13	v	v	PROPN
ejpam-6238	118	14	(	(	PUNCT
ejpam-6238	118	15	α	α	NOUN
ejpam-6238	118	16	)	)	PUNCT
ejpam-6238	118	17	i	i	PRON
ejpam-6238	118	18	(	(	PUNCT
ejpam-6238	118	19	t	t	PROPN
ejpam-6238	118	20	)	)	PUNCT
ejpam-6238	118	21	⟨an	⟨an	PROPN
ejpam-6238	118	22	(	(	PUNCT
ejpam-6238	118	23	θi	θi	NOUN
ejpam-6238	118	24	)	)	PUNCT
ejpam-6238	118	25	,	,	PUNCT
ejpam-6238	118	26	θj⟩+	θj⟩+	PROPN
ejpam-6238	118	27	n∑	n∑	PROPN
ejpam-6238	118	28	i=1	i=1	PROPN
ejpam-6238	118	29	vi	vi	PROPN
ejpam-6238	118	30	(	(	PUNCT
ejpam-6238	118	31	t	t	PROPN
ejpam-6238	118	32	)	)	PUNCT
ejpam-6238	118	33	⟨bn	⟨bn	PROPN
ejpam-6238	118	34	(	(	PUNCT
ejpam-6238	118	35	θi	θi	NOUN
ejpam-6238	118	36	)	)	PUNCT
ejpam-6238	118	37	,	,	PUNCT
ejpam-6238	118	38	θj⟩	θj⟩	PROPN
ejpam-6238	118	39	=	=	SYM
ejpam-6238	118	40	f	f	PROPN
ejpam-6238	118	41	(	(	PUNCT
ejpam-6238	118	42	t	t	PROPN
ejpam-6238	118	43	)	)	PUNCT
ejpam-6238	118	44	⟨z	⟨z	PROPN
ejpam-6238	118	45	,	,	PUNCT
ejpam-6238	118	46	θj⟩	θj⟩	PROPN
ejpam-6238	118	47	(	(	PUNCT
ejpam-6238	118	48	12	12	NUM
ejpam-6238	118	49	)	)	PUNCT
ejpam-6238	118	50	since	since	SCONJ
ejpam-6238	118	51	θi	θi	NUM
ejpam-6238	118	52	is	be	AUX
ejpam-6238	118	53	an	an	DET
ejpam-6238	118	54	eigenvector	eigenvector	NOUN
ejpam-6238	118	55	of	of	ADP
ejpam-6238	118	56	en	en	X
ejpam-6238	118	57	with	with	ADP
ejpam-6238	118	58	corresponding	correspond	VERB
ejpam-6238	118	59	eigenvalue	eigenvalue	PROPN
ejpam-6238	118	60	λi	λi	NOUN
ejpam-6238	118	61	for	for	ADP
ejpam-6238	118	62	every	every	DET
ejpam-6238	118	63	i	i	PRON
ejpam-6238	118	64	and	and	CCONJ
ejpam-6238	118	65	{	{	PUNCT
ejpam-6238	118	66	θ1	θ1	PROPN
ejpam-6238	118	67	,	,	PUNCT
ejpam-6238	118	68	θ2	θ2	PROPN
ejpam-6238	118	69	,	,	PUNCT
ejpam-6238	118	70	...	...	PUNCT
ejpam-6238	118	71	,	,	PUNCT
ejpam-6238	118	72	θn	θn	VERB
ejpam-6238	118	73	}	}	PUNCT
ejpam-6238	118	74	is	be	AUX
ejpam-6238	118	75	an	an	DET
ejpam-6238	118	76	orthonormal	orthonormal	ADJ
ejpam-6238	118	77	basis	basis	NOUN
ejpam-6238	118	78	,	,	PUNCT
ejpam-6238	118	79	we	we	PRON
ejpam-6238	118	80	get	get	VERB
ejpam-6238	118	81	λjv	λjv	ADJ
ejpam-6238	118	82	(	(	PUNCT
ejpam-6238	118	83	2α	2α	NOUN
ejpam-6238	118	84	)	)	PUNCT
ejpam-6238	118	85	j	j	PROPN
ejpam-6238	118	86	(	(	PUNCT
ejpam-6238	118	87	t	t	PROPN
ejpam-6238	118	88	)	)	PUNCT
ejpam-6238	119	1	+	+	NUM
ejpam-6238	120	1	n∑	n∑	PROPN
ejpam-6238	120	2	i=1	i=1	PROPN
ejpam-6238	120	3	v	v	PROPN
ejpam-6238	120	4	(	(	PUNCT
ejpam-6238	120	5	α	α	NOUN
ejpam-6238	120	6	)	)	PUNCT
ejpam-6238	120	7	i	i	PRON
ejpam-6238	120	8	(	(	PUNCT
ejpam-6238	120	9	t	t	PROPN
ejpam-6238	120	10	)	)	PUNCT
ejpam-6238	120	11	⟨an	⟨an	PROPN
ejpam-6238	120	12	(	(	PUNCT
ejpam-6238	120	13	θi	θi	NOUN
ejpam-6238	120	14	)	)	PUNCT
ejpam-6238	120	15	,	,	PUNCT
ejpam-6238	120	16	θj⟩+	θj⟩+	PROPN
ejpam-6238	120	17	n∑	n∑	PROPN
ejpam-6238	120	18	i=1	i=1	PROPN
ejpam-6238	120	19	vi	vi	PROPN
ejpam-6238	120	20	(	(	PUNCT
ejpam-6238	120	21	t	t	PROPN
ejpam-6238	120	22	)	)	PUNCT
ejpam-6238	120	23	⟨bn	⟨bn	PROPN
ejpam-6238	120	24	(	(	PUNCT
ejpam-6238	120	25	θi	θi	NOUN
ejpam-6238	120	26	)	)	PUNCT
ejpam-6238	120	27	,	,	PUNCT
ejpam-6238	120	28	θj⟩	θj⟩	PROPN
ejpam-6238	120	29	=	=	SYM
ejpam-6238	120	30	f	f	PROPN
ejpam-6238	120	31	(	(	PUNCT
ejpam-6238	120	32	t	t	PROPN
ejpam-6238	120	33	)	)	PUNCT
ejpam-6238	120	34	⟨z	⟨z	PROPN
ejpam-6238	120	35	,	,	PUNCT
ejpam-6238	120	36	θj⟩	θj⟩	PROPN
ejpam-6238	120	37	(	(	PUNCT
ejpam-6238	120	38	13	13	NUM
ejpam-6238	120	39	)	)	PUNCT
ejpam-6238	120	40	introducing	introduce	VERB
ejpam-6238	120	41	new	new	ADJ
ejpam-6238	120	42	variables	variable	NOUN
ejpam-6238	120	43	to	to	PART
ejpam-6238	120	44	represents	represent	VERB
ejpam-6238	120	45	the	the	DET
ejpam-6238	120	46	first	first	ADJ
ejpam-6238	120	47	derivatives	derivative	NOUN
ejpam-6238	120	48	of	of	ADP
ejpam-6238	120	49	vi	vi	NOUN
ejpam-6238	120	50	:	:	PUNCT
ejpam-6238	120	51	wi	wi	PROPN
ejpam-6238	120	52	=	=	SYM
ejpam-6238	120	53	vi	vi	PROPN
ejpam-6238	120	54	,	,	PUNCT
ejpam-6238	120	55	wn+i	wn+i	NOUN
ejpam-6238	120	56	=	=	SYM
ejpam-6238	120	57	v	v	PROPN
ejpam-6238	120	58	(	(	PUNCT
ejpam-6238	120	59	α	α	NOUN
ejpam-6238	120	60	)	)	PUNCT
ejpam-6238	120	61	i	i	PRON
ejpam-6238	120	62	,	,	PUNCT
ejpam-6238	120	63	i	i	PRON
ejpam-6238	120	64	=	=	NOUN
ejpam-6238	120	65	1	1	NUM
ejpam-6238	120	66	,	,	PUNCT
ejpam-6238	120	67	2	2	NUM
ejpam-6238	120	68	,	,	PUNCT
ejpam-6238	120	69	...	...	PUNCT
ejpam-6238	120	70	,	,	PUNCT
ejpam-6238	120	71	n	n	X
ejpam-6238	120	72	w	w	PROPN
ejpam-6238	120	73	(	(	PUNCT
ejpam-6238	120	74	α	α	NOUN
ejpam-6238	120	75	)	)	PUNCT
ejpam-6238	120	76	i	i	NOUN
ejpam-6238	120	77	=	=	SYM
ejpam-6238	120	78	wn+i	wn+i	PROPN
ejpam-6238	120	79	,	,	PUNCT
ejpam-6238	120	80	i	i	PRON
ejpam-6238	120	81	=	=	NOUN
ejpam-6238	120	82	1	1	NUM
ejpam-6238	120	83	,	,	PUNCT
ejpam-6238	120	84	2	2	NUM
ejpam-6238	120	85	,	,	PUNCT
ejpam-6238	120	86	...	...	PUNCT
ejpam-6238	120	87	,	,	PUNCT
ejpam-6238	120	88	n	n	CCONJ
ejpam-6238	120	89	then	then	ADV
ejpam-6238	120	90	the	the	DET
ejpam-6238	120	91	system	system	NOUN
ejpam-6238	120	92	can	can	AUX
ejpam-6238	120	93	be	be	AUX
ejpam-6238	120	94	written	write	VERB
ejpam-6238	120	95	as	as	ADP
ejpam-6238	120	96	:	:	PUNCT
ejpam-6238	120	97	λjw	λjw	NOUN
ejpam-6238	120	98	(	(	PUNCT
ejpam-6238	120	99	α	α	NOUN
ejpam-6238	120	100	)	)	PUNCT
ejpam-6238	120	101	n+j(t	n+j(t	NUM
ejpam-6238	120	102	)	)	PUNCT
ejpam-6238	120	103	=	=	PUNCT
ejpam-6238	121	1	−	−	PROPN
ejpam-6238	121	2	n∑	n∑	PROPN
ejpam-6238	121	3	i=1	i=1	PROPN
ejpam-6238	121	4	wn+i(t	wn+i(t	PROPN
ejpam-6238	121	5	)	)	PUNCT
ejpam-6238	121	6	⟨an(θi	⟨an(θi	NUM
ejpam-6238	121	7	)	)	PUNCT
ejpam-6238	121	8	,	,	PUNCT
ejpam-6238	121	9	θj⟩	θj⟩	PROPN
ejpam-6238	121	10	−	−	PROPN
ejpam-6238	121	11	n∑	n∑	PROPN
ejpam-6238	121	12	i=1	i=1	PROPN
ejpam-6238	121	13	wi(t	wi(t	PROPN
ejpam-6238	121	14	)	)	PUNCT
ejpam-6238	121	15	⟨bn(θi	⟨bn(θi	NUM
ejpam-6238	121	16	)	)	PUNCT
ejpam-6238	121	17	,	,	PUNCT
ejpam-6238	121	18	θj⟩+	θj⟩+	PROPN
ejpam-6238	121	19	f(t	f(t	PROPN
ejpam-6238	121	20	)	)	PUNCT
ejpam-6238	121	21	⟨z	⟨z	PROPN
ejpam-6238	121	22	,	,	PUNCT
ejpam-6238	121	23	θj⟩	θj⟩	PROPN
ejpam-6238	121	24	(	(	PUNCT
ejpam-6238	121	25	14	14	NUM
ejpam-6238	121	26	)	)	PUNCT
ejpam-6238	122	1	so	so	ADV
ejpam-6238	122	2	,	,	PUNCT
ejpam-6238	122	3	we	we	PRON
ejpam-6238	122	4	get	get	VERB
ejpam-6238	122	5	the	the	DET
ejpam-6238	122	6	following	follow	VERB
ejpam-6238	122	7	system	system	NOUN
ejpam-6238	122	8	(	(	PUNCT
ejpam-6238	122	9	in	in	ADP
ejpam-6238	122	10	0	0	NUM
ejpam-6238	122	11	0	0	X
ejpam-6238	122	12	d̃	d̃	PROPN
ejpam-6238	122	13	)	)	PUNCT
ejpam-6238	122	14	w(α)(t	w(α)(t	PROPN
ejpam-6238	122	15	)	)	PUNCT
ejpam-6238	122	16	=	=	SYM
ejpam-6238	123	1	(	(	PUNCT
ejpam-6238	123	2	0	0	NUM
ejpam-6238	123	3	−b	−b	VERB
ejpam-6238	123	4	in	in	ADP
ejpam-6238	123	5	−a	−a	NOUN
ejpam-6238	123	6	)	)	PUNCT
ejpam-6238	123	7	w	w	PROPN
ejpam-6238	123	8	(	(	PUNCT
ejpam-6238	123	9	t	t	PROPN
ejpam-6238	123	10	)	)	PUNCT
ejpam-6238	124	1	+	+	CCONJ
ejpam-6238	124	2	f(t	f(t	NOUN
ejpam-6238	124	3	)	)	PUNCT
ejpam-6238	124	4	(	(	PUNCT
ejpam-6238	124	5	15	15	NUM
ejpam-6238	124	6	)	)	PUNCT
ejpam-6238	124	7	where	where	SCONJ
ejpam-6238	124	8	w(t	w(t	X
ejpam-6238	124	9	)	)	PUNCT
ejpam-6238	125	1	=	=	PRON
ejpam-6238	125	2			VERB
ejpam-6238	125	3	w1	w1	NOUN
ejpam-6238	125	4	w2	w2	PROPN
ejpam-6238	125	5	...	...	PUNCT
ejpam-6238	126	1	wn	wn	PROPN
ejpam-6238	126	2	wn+1	wn+1	VERB
ejpam-6238	126	3	wn+2	wn+2	PRON
ejpam-6238	126	4	...	...	PUNCT
ejpam-6238	126	5	w2n	w2n	DET
ejpam-6238	126	6			NOUN
ejpam-6238	126	7	,	,	PUNCT
ejpam-6238	126	8	d̃	d̃	PROPN
ejpam-6238	126	9	=	=	PUNCT
ejpam-6238	126	10	(	(	PUNCT
ejpam-6238	126	11	d	d	NOUN
ejpam-6238	126	12	0	0	NUM
ejpam-6238	126	13	0	0	NUM
ejpam-6238	126	14	0	0	NUM
ejpam-6238	126	15	)	)	PUNCT
ejpam-6238	126	16	,	,	PUNCT
ejpam-6238	126	17	a	a	PRON
ejpam-6238	126	18	=	=	X
ejpam-6238	126	19	(	(	PUNCT
ejpam-6238	126	20	g1	g1	PROPN
ejpam-6238	126	21	g3	g3	PROPN
ejpam-6238	126	22	g2	g2	PROPN
ejpam-6238	126	23	ĝ	ĝ	PROPN
ejpam-6238	126	24	)	)	PUNCT
ejpam-6238	126	25	,	,	PUNCT
ejpam-6238	126	26	b	b	X
ejpam-6238	126	27	=	=	PRON
ejpam-6238	126	28	(	(	PUNCT
ejpam-6238	126	29	h1	h1	PROPN
ejpam-6238	126	30	h3	h3	VERB
ejpam-6238	126	31	h2	h2	NOUN
ejpam-6238	126	32	h4	h4	PROPN
ejpam-6238	126	33	)	)	PUNCT
ejpam-6238	126	34	where	where	SCONJ
ejpam-6238	126	35	ĝ	ĝ	X
ejpam-6238	126	36	=	=	SYM
ejpam-6238	126	37	an|ker(en	an|ker(en	PROPN
ejpam-6238	126	38	)	)	PUNCT
ejpam-6238	126	39	=	=	PUNCT
ejpam-6238	127	1	[	[	X
ejpam-6238	127	2	⟨an(θj	⟨an(θj	NOUN
ejpam-6238	127	3	)	)	PUNCT
ejpam-6238	127	4	,	,	PUNCT
ejpam-6238	127	5	θi⟩]i	θi⟩]i	NUM
ejpam-6238	127	6	,	,	PUNCT
ejpam-6238	127	7	j	j	NOUN
ejpam-6238	127	8	=	=	NOUN
ejpam-6238	127	9	r+1,	r+1,	NOUN
ejpam-6238	127	10	...	...	PUNCT
ejpam-6238	127	11	,n	,n	PUNCT
ejpam-6238	127	12	.	.	PUNCT
ejpam-6238	128	1	h.	h.	PROPN
ejpam-6238	128	2	odetallah	odetallah	PROPN
ejpam-6238	128	3	et	et	PROPN
ejpam-6238	128	4	al	al	PROPN
ejpam-6238	128	5	.	.	PUNCT
ejpam-6238	128	6	/	/	SYM
ejpam-6238	128	7	eur	eur	PROPN
ejpam-6238	128	8	.	.	PUNCT
ejpam-6238	129	1	j.	j.	PROPN
ejpam-6238	129	2	pure	pure	PROPN
ejpam-6238	129	3	appl	appl	PROPN
ejpam-6238	129	4	.	.	PROPN
ejpam-6238	129	5	math	math	PROPN
ejpam-6238	129	6	,	,	PUNCT
ejpam-6238	129	7	18	18	NUM
ejpam-6238	129	8	(	(	PUNCT
ejpam-6238	129	9	3	3	NUM
ejpam-6238	129	10	)	)	PUNCT
ejpam-6238	129	11	(	(	PUNCT
ejpam-6238	129	12	2025	2025	NUM
ejpam-6238	129	13	)	)	PUNCT
ejpam-6238	129	14	,	,	PUNCT
ejpam-6238	129	15	6238	6238	NUM
ejpam-6238	129	16	7	7	NUM
ejpam-6238	129	17	of	of	ADP
ejpam-6238	129	18	11	11	NUM
ejpam-6238	129	19	now	now	ADV
ejpam-6238	129	20	,	,	PUNCT
ejpam-6238	129	21	multiplying	multiply	VERB
ejpam-6238	129	22	(	(	PUNCT
ejpam-6238	129	23	15	15	NUM
ejpam-6238	129	24	)	)	PUNCT
ejpam-6238	129	25	by	by	ADP
ejpam-6238	129	26	(	(	PUNCT
ejpam-6238	129	27	in	in	ADP
ejpam-6238	129	28	0	0	NUM
ejpam-6238	129	29	0	0	NUM
ejpam-6238	129	30	k	k	X
ejpam-6238	129	31	)	)	PUNCT
ejpam-6238	129	32	2n×2n	2n×2n	NOUN
ejpam-6238	130	1	where	where	SCONJ
ejpam-6238	130	2	k	k	PROPN
ejpam-6238	130	3	=	=	PRON
ejpam-6238	131	1	(	(	PUNCT
ejpam-6238	131	2	d−1	d−1	PROPN
ejpam-6238	131	3	0	0	NUM
ejpam-6238	131	4	0	0	NUM
ejpam-6238	131	5	ĝ−1	ĝ−1	NOUN
ejpam-6238	131	6	)	)	PUNCT
ejpam-6238	131	7	,	,	PUNCT
ejpam-6238	131	8	we	we	PRON
ejpam-6238	131	9	get	get	VERB
ejpam-6238	131	10	(	(	PUNCT
ejpam-6238	131	11	in	in	ADP
ejpam-6238	131	12	0	0	NUM
ejpam-6238	131	13	0	0	NUM
ejpam-6238	131	14	kd̃	kd̃	PROPN
ejpam-6238	131	15	)	)	PUNCT
ejpam-6238	131	16	w(α)(t	w(α)(t	PROPN
ejpam-6238	131	17	)	)	PUNCT
ejpam-6238	131	18	=	=	SYM
ejpam-6238	131	19	(	(	PUNCT
ejpam-6238	131	20	0	0	NUM
ejpam-6238	131	21	−kb	−kb	PROPN
ejpam-6238	131	22	in	in	ADP
ejpam-6238	131	23	−ka	−ka	NOUN
ejpam-6238	131	24	)	)	PUNCT
ejpam-6238	131	25	w(t	w(t	PROPN
ejpam-6238	131	26	)	)	PUNCT
ejpam-6238	132	1	+	+	CCONJ
ejpam-6238	132	2	(	(	PUNCT
ejpam-6238	132	3	in	in	ADP
ejpam-6238	132	4	0	0	NUM
ejpam-6238	132	5	0	0	NUM
ejpam-6238	132	6	k	k	X
ejpam-6238	132	7	)	)	PUNCT
ejpam-6238	132	8	f(t	f(t	PROPN
ejpam-6238	132	9	)	)	PUNCT
ejpam-6238	132	10	(	(	PUNCT
ejpam-6238	132	11	16	16	NUM
ejpam-6238	132	12	)	)	PUNCT
ejpam-6238	132	13	wherekd̃	wherekd̃	PROPN
ejpam-6238	132	14	=	=	PRON
ejpam-6238	132	15	(	(	PUNCT
ejpam-6238	132	16	ir	ir	PROPN
ejpam-6238	132	17	0	0	NUM
ejpam-6238	132	18	0	0	NUM
ejpam-6238	132	19	0	0	NUM
ejpam-6238	132	20	)	)	PUNCT
ejpam-6238	132	21	,	,	PUNCT
ejpam-6238	132	22	ka	ka	PROPN
ejpam-6238	132	23	=	=	PUNCT
ejpam-6238	132	24	(	(	PUNCT
ejpam-6238	132	25	d−1g1	d−1g1	ADJ
ejpam-6238	132	26	ĝ−1g3	ĝ−1g3	PROPN
ejpam-6238	132	27	d−1g2	d−1g2	PROPN
ejpam-6238	132	28	in−r	in−r	NOUN
ejpam-6238	132	29	)	)	PUNCT
ejpam-6238	132	30	andkb	andkb	X
ejpam-6238	132	31	=	=	PUNCT
ejpam-6238	132	32	(	(	PUNCT
ejpam-6238	132	33	d−1h1	d−1h1	NOUN
ejpam-6238	132	34	ĝ−1h3	ĝ−1h3	NOUN
ejpam-6238	132	35	d−1h2	d−1h2	NOUN
ejpam-6238	132	36	â−1h4	â−1h4	PROPN
ejpam-6238	132	37	)	)	PUNCT
ejpam-6238	132	38	let	let	VERB
ejpam-6238	132	39	u1	u1	NOUN
ejpam-6238	132	40	=	=	SYM
ejpam-6238	132	41			PROPN
ejpam-6238	132	42	w1	w1	NOUN
ejpam-6238	132	43	w2	w2	NOUN
ejpam-6238	132	44	...	...	PUNCT
ejpam-6238	132	45	wr	wr	AUX
ejpam-6238	132	46			NOUN
ejpam-6238	132	47	,	,	PUNCT
ejpam-6238	132	48	u2	u2	NOUN
ejpam-6238	132	49	=	=	PUNCT
ejpam-6238	132	50			NOUN
ejpam-6238	132	51	wr+1	wr+1	X
ejpam-6238	132	52	wr+2	wr+2	AUX
ejpam-6238	132	53	...	...	PUNCT
ejpam-6238	133	1	wn	wn	PROPN
ejpam-6238	133	2			PROPN
ejpam-6238	133	3	,	,	PUNCT
ejpam-6238	133	4	u3	u3	NOUN
ejpam-6238	133	5	=	=	SYM
ejpam-6238	133	6			PROPN
ejpam-6238	133	7	wn+1	wn+1	VERB
ejpam-6238	133	8	wn+2	wn+2	NOUN
ejpam-6238	133	9	...	...	PUNCT
ejpam-6238	134	1	wn+r	wn+r	NOUN
ejpam-6238	134	2			NOUN
ejpam-6238	134	3	,	,	PUNCT
ejpam-6238	134	4	u4	u4	PROPN
ejpam-6238	134	5	=	=	PUNCT
ejpam-6238	134	6			PROPN
ejpam-6238	134	7	wn+r+1	wn+r+1	NOUN
ejpam-6238	134	8	wn+r+2	wn+r+2	PROPN
ejpam-6238	134	9	...	...	PUNCT
ejpam-6238	135	1	w2n	w2n	PRON
ejpam-6238	135	2			NOUN
ejpam-6238	135	3	,	,	PUNCT
ejpam-6238	135	4	f1(t	f1(t	NUM
ejpam-6238	135	5	)	)	PUNCT
ejpam-6238	135	6	=	=	SYM
ejpam-6238	135	7	f	f	PROPN
ejpam-6238	135	8	(	(	PUNCT
ejpam-6238	135	9	t	t	PROPN
ejpam-6238	135	10	)	)	PUNCT
ejpam-6238	135	11			NOUN
ejpam-6238	135	12	⟨z	⟨z	PROPN
ejpam-6238	135	13	,	,	PUNCT
ejpam-6238	135	14	θ1⟩	θ1⟩	PRON
ejpam-6238	135	15	⟨z	⟨z	PROPN
ejpam-6238	135	16	,	,	PUNCT
ejpam-6238	135	17	θ2⟩	θ2⟩	X
ejpam-6238	135	18	...	...	PUNCT
ejpam-6238	135	19	⟨z	⟨z	PROPN
ejpam-6238	135	20	,	,	PUNCT
ejpam-6238	135	21	θr⟩	θr⟩	PRON
ejpam-6238	135	22			PROPN
ejpam-6238	135	23	and	and	CCONJ
ejpam-6238	135	24	f2	f2	PROPN
ejpam-6238	135	25	(	(	PUNCT
ejpam-6238	135	26	t	t	NOUN
ejpam-6238	135	27	)	)	PUNCT
ejpam-6238	135	28	=	=	SYM
ejpam-6238	136	1	f	f	PROPN
ejpam-6238	136	2	(	(	PUNCT
ejpam-6238	136	3	t	t	PROPN
ejpam-6238	136	4	)	)	PUNCT
ejpam-6238	136	5			NOUN
ejpam-6238	136	6	⟨z	⟨z	PROPN
ejpam-6238	136	7	,	,	PUNCT
ejpam-6238	136	8	θr+1⟩	θr+1⟩	PROPN
ejpam-6238	136	9	⟨z	⟨z	PROPN
ejpam-6238	136	10	,	,	PUNCT
ejpam-6238	136	11	θr+2⟩	θr+2⟩	X
ejpam-6238	136	12	...	...	PUNCT
ejpam-6238	136	13	⟨z	⟨z	X
ejpam-6238	136	14	,	,	PUNCT
ejpam-6238	136	15	θn⟩	θn⟩	NOUN
ejpam-6238	136	16			NOUN
ejpam-6238	136	17	.	.	PUNCT
ejpam-6238	137	1	then	then	ADV
ejpam-6238	137	2	,	,	PUNCT
ejpam-6238	137	3	we	we	PRON
ejpam-6238	137	4	have	have	VERB
ejpam-6238	137	5	u	u	NOUN
ejpam-6238	137	6	(	(	PUNCT
ejpam-6238	137	7	α	α	NOUN
ejpam-6238	137	8	)	)	PUNCT
ejpam-6238	137	9	1	1	NUM
ejpam-6238	137	10	(	(	PUNCT
ejpam-6238	137	11	t	t	NOUN
ejpam-6238	137	12	)	)	PUNCT
ejpam-6238	137	13	=	=	NOUN
ejpam-6238	137	14	u3	u3	NOUN
ejpam-6238	137	15	(	(	PUNCT
ejpam-6238	137	16	t	t	PROPN
ejpam-6238	137	17	)	)	PUNCT
ejpam-6238	137	18	(	(	PUNCT
ejpam-6238	137	19	17	17	NUM
ejpam-6238	137	20	)	)	PUNCT
ejpam-6238	137	21	u	u	NOUN
ejpam-6238	137	22	(	(	PUNCT
ejpam-6238	137	23	α	α	NOUN
ejpam-6238	137	24	)	)	PUNCT
ejpam-6238	137	25	2	2	NUM
ejpam-6238	137	26	(	(	PUNCT
ejpam-6238	137	27	t	t	NOUN
ejpam-6238	137	28	)	)	PUNCT
ejpam-6238	138	1	=	=	SYM
ejpam-6238	138	2	u4	u4	PROPN
ejpam-6238	138	3	(	(	PUNCT
ejpam-6238	138	4	t	t	PROPN
ejpam-6238	138	5	)	)	PUNCT
ejpam-6238	138	6	(	(	PUNCT
ejpam-6238	138	7	18	18	NUM
ejpam-6238	138	8	)	)	PUNCT
ejpam-6238	138	9	u	u	NOUN
ejpam-6238	138	10	(	(	PUNCT
ejpam-6238	138	11	α	α	NOUN
ejpam-6238	138	12	)	)	PUNCT
ejpam-6238	138	13	3	3	NUM
ejpam-6238	138	14	(	(	PUNCT
ejpam-6238	138	15	t	t	NOUN
ejpam-6238	138	16	)	)	PUNCT
ejpam-6238	138	17	=	=	SYM
ejpam-6238	139	1	−d−1h1u1(t)−d−1h2u2(t)−d−1g1u3(t)−d−1g2u4(t	−d−1h1u1(t)−d−1h2u2(t)−d−1g1u3(t)−d−1g2u4(t	PROPN
ejpam-6238	139	2	)	)	PUNCT
ejpam-6238	139	3	+	+	SYM
ejpam-6238	139	4	d−1f1(t	d−1f1(t	PROPN
ejpam-6238	139	5	)	)	PUNCT
ejpam-6238	139	6	(	(	PUNCT
ejpam-6238	139	7	19	19	NUM
ejpam-6238	139	8	)	)	PUNCT
ejpam-6238	139	9	and	and	CCONJ
ejpam-6238	139	10	0	0	NUM
ejpam-6238	139	11	=	=	SYM
ejpam-6238	139	12	−ĝ−1h3u1(t)−	−ĝ−1h3u1(t)−	PROPN
ejpam-6238	139	13	ĝ−1h4u2(t)−	ĝ−1h4u2(t)−	PROPN
ejpam-6238	139	14	ĝ−1g3u3(t)−	ĝ−1g3u3(t)−	PROPN
ejpam-6238	139	15	u4(t	u4(t	PROPN
ejpam-6238	139	16	)	)	PUNCT
ejpam-6238	139	17	+	+	CCONJ
ejpam-6238	139	18	ĝ−1f2(t	ĝ−1f2(t	NOUN
ejpam-6238	139	19	)	)	PUNCT
ejpam-6238	139	20	(	(	PUNCT
ejpam-6238	139	21	20	20	NUM
ejpam-6238	139	22	)	)	PUNCT
ejpam-6238	139	23	from	from	ADP
ejpam-6238	139	24	the	the	DET
ejpam-6238	139	25	last	last	ADJ
ejpam-6238	139	26	equation	equation	NOUN
ejpam-6238	139	27	,	,	PUNCT
ejpam-6238	139	28	we	we	PRON
ejpam-6238	139	29	get	get	VERB
ejpam-6238	139	30	u4(t	u4(t	ADJ
ejpam-6238	139	31	)	)	PUNCT
ejpam-6238	139	32	=	=	SYM
ejpam-6238	139	33	−ĝ−1h3u1(t)−	−ĝ−1h3u1(t)−	PROPN
ejpam-6238	139	34	ĝ−1h4u2(t)−	ĝ−1h4u2(t)−	PROPN
ejpam-6238	139	35	ĝ−1g3u3(t	ĝ−1g3u3(t	PROPN
ejpam-6238	139	36	)	)	PUNCT
ejpam-6238	139	37	+	+	CCONJ
ejpam-6238	139	38	ĝ−1f2(t	ĝ−1f2(t	NOUN
ejpam-6238	139	39	)	)	PUNCT
ejpam-6238	139	40	(	(	PUNCT
ejpam-6238	139	41	21	21	NUM
ejpam-6238	139	42	)	)	PUNCT
ejpam-6238	139	43	substituting	substitute	VERB
ejpam-6238	139	44	(	(	PUNCT
ejpam-6238	139	45	21	21	NUM
ejpam-6238	139	46	)	)	PUNCT
ejpam-6238	139	47	in	in	ADP
ejpam-6238	139	48	(	(	PUNCT
ejpam-6238	139	49	18	18	NUM
ejpam-6238	139	50	)	)	PUNCT
ejpam-6238	139	51	and	and	CCONJ
ejpam-6238	139	52	(	(	PUNCT
ejpam-6238	139	53	19	19	NUM
ejpam-6238	139	54	)	)	PUNCT
ejpam-6238	139	55	,	,	PUNCT
ejpam-6238	139	56	we	we	PRON
ejpam-6238	139	57	get	get	VERB
ejpam-6238	139	58	u	u	NOUN
ejpam-6238	139	59	(	(	PUNCT
ejpam-6238	139	60	α	α	NOUN
ejpam-6238	139	61	)	)	PUNCT
ejpam-6238	139	62	2	2	NUM
ejpam-6238	139	63	(	(	PUNCT
ejpam-6238	139	64	t	t	NOUN
ejpam-6238	139	65	)	)	PUNCT
ejpam-6238	139	66	=	=	SYM
ejpam-6238	140	1	−ĝ−1h3u1(t)−	−ĝ−1h3u1(t)−	PROPN
ejpam-6238	140	2	ĝ−1h4u2(t)−	ĝ−1h4u2(t)−	PROPN
ejpam-6238	140	3	ĝ−1g3u3(t	ĝ−1g3u3(t	PROPN
ejpam-6238	140	4	)	)	PUNCT
ejpam-6238	141	1	+	+	CCONJ
ejpam-6238	141	2	ĝ−1f2(t	ĝ−1f2(t	NOUN
ejpam-6238	141	3	)	)	PUNCT
ejpam-6238	142	1	(	(	PUNCT
ejpam-6238	142	2	22	22	X
ejpam-6238	142	3	)	)	PUNCT
ejpam-6238	142	4	u	u	NOUN
ejpam-6238	142	5	(	(	PUNCT
ejpam-6238	142	6	α	α	NOUN
ejpam-6238	142	7	)	)	PUNCT
ejpam-6238	142	8	3	3	NUM
ejpam-6238	142	9	(	(	PUNCT
ejpam-6238	142	10	t	t	NOUN
ejpam-6238	142	11	)	)	PUNCT
ejpam-6238	142	12	=	=	SYM
ejpam-6238	143	1	d−1	d−1	PROPN
ejpam-6238	143	2	(	(	PUNCT
ejpam-6238	143	3	g2ĝ	g2ĝ	ADJ
ejpam-6238	143	4	−1h3	−1h3	NUM
ejpam-6238	143	5	−h1	−h1	PROPN
ejpam-6238	143	6	)	)	PUNCT
ejpam-6238	143	7	u1(t	u1(t	ADP
ejpam-6238	143	8	)	)	PUNCT
ejpam-6238	144	1	+	+	ADP
ejpam-6238	144	2	d−1	d−1	PROPN
ejpam-6238	144	3	(	(	PUNCT
ejpam-6238	144	4	g2ĝ	g2ĝ	NOUN
ejpam-6238	144	5	−1h4	−1h4	PUNCT
ejpam-6238	144	6	−h2	−h2	NOUN
ejpam-6238	144	7	)	)	PUNCT
ejpam-6238	144	8	u2(t	u2(t	PROPN
ejpam-6238	144	9	)	)	PUNCT
ejpam-6238	144	10	+	+	ADP
ejpam-6238	144	11	d−1	d−1	PROPN
ejpam-6238	144	12	(	(	PUNCT
ejpam-6238	144	13	g2ĝ	g2ĝ	PROPN
ejpam-6238	144	14	−1g3	−1g3	NUM
ejpam-6238	144	15	−g1	−g1	VERB
ejpam-6238	144	16	)	)	PUNCT
ejpam-6238	144	17	u3(t)(23	u3(t)(23	NOUN
ejpam-6238	144	18	)	)	PUNCT
ejpam-6238	145	1	+	+	PUNCT
ejpam-6238	145	2	d−1f1(t)−d−1g2ĝ	d−1f1(t)−d−1g2ĝ	NOUN
ejpam-6238	145	3	−1f2	−1f2	NUM
ejpam-6238	145	4	(	(	PUNCT
ejpam-6238	145	5	t	t	NOUN
ejpam-6238	145	6	)	)	PUNCT
ejpam-6238	145	7	if	if	SCONJ
ejpam-6238	145	8	we	we	PRON
ejpam-6238	145	9	define	define	VERB
ejpam-6238	145	10	a	a	DET
ejpam-6238	145	11	combined	combined	ADJ
ejpam-6238	145	12	state	state	NOUN
ejpam-6238	145	13	vector	vector	NOUN
ejpam-6238	145	14	u	u	PROPN
ejpam-6238	145	15	(	(	PUNCT
ejpam-6238	145	16	t	t	PROPN
ejpam-6238	145	17	)	)	PUNCT
ejpam-6238	146	1	=	=	SYM
ejpam-6238	146	2			PROPN
ejpam-6238	146	3	u1	u1	NOUN
ejpam-6238	146	4	(	(	PUNCT
ejpam-6238	146	5	t	t	PROPN
ejpam-6238	146	6	)	)	PUNCT
ejpam-6238	146	7	u2	u2	PROPN
ejpam-6238	146	8	(	(	PUNCT
ejpam-6238	146	9	t	t	PROPN
ejpam-6238	146	10	)	)	PUNCT
ejpam-6238	146	11	u3	u3	NOUN
ejpam-6238	146	12	(	(	PUNCT
ejpam-6238	146	13	t	t	PROPN
ejpam-6238	146	14	)	)	PUNCT
ejpam-6238	146	15			PROPN
ejpam-6238	146	16	that	that	PRON
ejpam-6238	146	17	includes	include	VERB
ejpam-6238	146	18	all	all	DET
ejpam-6238	146	19	variables	variable	NOUN
ejpam-6238	146	20	except	except	SCONJ
ejpam-6238	146	21	u4	u4	PROPN
ejpam-6238	146	22	(	(	PUNCT
ejpam-6238	146	23	which	which	PRON
ejpam-6238	146	24	has	have	AUX
ejpam-6238	146	25	been	be	AUX
ejpam-6238	146	26	eliminated	eliminate	VERB
ejpam-6238	146	27	)	)	PUNCT
ejpam-6238	146	28	,	,	PUNCT
ejpam-6238	146	29	then	then	ADV
ejpam-6238	146	30	the	the	DET
ejpam-6238	146	31	merged	merge	VERB
ejpam-6238	146	32	system	system	NOUN
ejpam-6238	146	33	can	can	AUX
ejpam-6238	146	34	be	be	AUX
ejpam-6238	146	35	written	write	VERB
ejpam-6238	146	36	as	as	ADP
ejpam-6238	146	37	:	:	PUNCT
ejpam-6238	146	38	u	u	NOUN
ejpam-6238	146	39	(	(	PUNCT
ejpam-6238	146	40	α	α	NOUN
ejpam-6238	146	41	)	)	PUNCT
ejpam-6238	146	42	(	(	PUNCT
ejpam-6238	146	43	t	t	NOUN
ejpam-6238	146	44	)	)	PUNCT
ejpam-6238	146	45	=	=	NOUN
ejpam-6238	146	46	mu	mu	PROPN
ejpam-6238	146	47	(	(	PUNCT
ejpam-6238	146	48	t	t	PROPN
ejpam-6238	146	49	)	)	PUNCT
ejpam-6238	147	1	+	+	PROPN
ejpam-6238	147	2	g	g	PROPN
ejpam-6238	147	3	(	(	PUNCT
ejpam-6238	147	4	t	t	PROPN
ejpam-6238	147	5	)	)	PUNCT
ejpam-6238	147	6	(	(	PUNCT
ejpam-6238	147	7	24	24	NUM
ejpam-6238	147	8	)	)	PUNCT
ejpam-6238	147	9	h.	h.	NOUN
ejpam-6238	148	1	odetallah	odetallah	PROPN
ejpam-6238	148	2	et	et	PROPN
ejpam-6238	148	3	al	al	PROPN
ejpam-6238	148	4	.	.	PUNCT
ejpam-6238	148	5	/	/	SYM
ejpam-6238	148	6	eur	eur	PROPN
ejpam-6238	148	7	.	.	PUNCT
ejpam-6238	149	1	j.	j.	PROPN
ejpam-6238	149	2	pure	pure	PROPN
ejpam-6238	149	3	appl	appl	PROPN
ejpam-6238	149	4	.	.	PROPN
ejpam-6238	149	5	math	math	PROPN
ejpam-6238	149	6	,	,	PUNCT
ejpam-6238	149	7	18	18	NUM
ejpam-6238	149	8	(	(	PUNCT
ejpam-6238	149	9	3	3	NUM
ejpam-6238	149	10	)	)	PUNCT
ejpam-6238	149	11	(	(	PUNCT
ejpam-6238	149	12	2025	2025	NUM
ejpam-6238	149	13	)	)	PUNCT
ejpam-6238	149	14	,	,	PUNCT
ejpam-6238	149	15	6238	6238	NUM
ejpam-6238	149	16	8	8	NUM
ejpam-6238	149	17	of	of	ADP
ejpam-6238	149	18	11	11	NUM
ejpam-6238	149	19	wherem	wherem	ADJ
ejpam-6238	149	20	=	=	NOUN
ejpam-6238	149	21			X
ejpam-6238	149	22	0	0	NUM
ejpam-6238	150	1	−ĝ−1h3	−ĝ−1h3	NUM
ejpam-6238	151	1	d−1	d−1	PROPN
ejpam-6238	151	2	(	(	PUNCT
ejpam-6238	151	3	g2ĝ	g2ĝ	PROPN
ejpam-6238	151	4	−1h3	−1h3	NUM
ejpam-6238	151	5	−h1	−h1	PROPN
ejpam-6238	151	6	)	)	PUNCT
ejpam-6238	151	7	0	0	PUNCT
ejpam-6238	152	1	−ĝ−1h4	−ĝ−1h4	PROPN
ejpam-6238	152	2	d−1	d−1	PROPN
ejpam-6238	152	3	(	(	PUNCT
ejpam-6238	152	4	g2ĝ	g2ĝ	NOUN
ejpam-6238	152	5	−1h4	−1h4	NUM
ejpam-6238	152	6	−h2	−h2	NOUN
ejpam-6238	152	7	)	)	PUNCT
ejpam-6238	152	8	ir	ir	PROPN
ejpam-6238	152	9	−ĝ−1g3	−ĝ−1g3	PUNCT
ejpam-6238	152	10	d−1	d−1	PROPN
ejpam-6238	152	11	(	(	PUNCT
ejpam-6238	152	12	g2ĝ	g2ĝ	PROPN
ejpam-6238	152	13	−1g3	−1g3	NUM
ejpam-6238	152	14	−g1	−g1	VERB
ejpam-6238	152	15	)	)	PUNCT
ejpam-6238	152	16			PROPN
ejpam-6238	152	17	and	and	CCONJ
ejpam-6238	152	18	g	g	PROPN
ejpam-6238	152	19	(	(	PUNCT
ejpam-6238	152	20	t	t	PROPN
ejpam-6238	152	21	)	)	PUNCT
ejpam-6238	152	22	=	=	SYM
ejpam-6238	153	1			PROPN
ejpam-6238	153	2	0	0	NUM
ejpam-6238	153	3	0	0	NUM
ejpam-6238	153	4	d−1	d−1	PROPN
ejpam-6238	153	5	f1	f1	PROPN
ejpam-6238	153	6	(	(	PUNCT
ejpam-6238	153	7	t	t	PROPN
ejpam-6238	153	8	)	)	PUNCT
ejpam-6238	153	9	+	+	CCONJ
ejpam-6238	153	10			PROPN
ejpam-6238	153	11	0	0	NUM
ejpam-6238	153	12	ĝ−1	ĝ−1	PROPN
ejpam-6238	153	13	−d−1g2ĝ	−d−1g2ĝ	NUM
ejpam-6238	153	14	−1	−1	NOUN
ejpam-6238	153	15	f2	f2	PRON
ejpam-6238	153	16	(	(	PUNCT
ejpam-6238	153	17	t	t	PROPN
ejpam-6238	153	18	)	)	PUNCT
ejpam-6238	153	19	.	.	PUNCT
ejpam-6238	154	1	thus	thus	ADV
ejpam-6238	154	2	,	,	PUNCT
ejpam-6238	154	3	the	the	DET
ejpam-6238	154	4	system	system	NOUN
ejpam-6238	154	5	(	(	PUNCT
ejpam-6238	154	6	24	24	NUM
ejpam-6238	154	7	)	)	PUNCT
ejpam-6238	154	8	has	have	VERB
ejpam-6238	154	9	a	a	DET
ejpam-6238	154	10	unique	unique	ADJ
ejpam-6238	154	11	solution	solution	NOUN
ejpam-6238	154	12	and	and	CCONJ
ejpam-6238	154	13	then	then	ADV
ejpam-6238	154	14	the	the	DET
ejpam-6238	154	15	problem	problem	NOUN
ejpam-6238	154	16	(	(	PUNCT
ejpam-6238	154	17	1	1	X
ejpam-6238	154	18	)	)	PUNCT
ejpam-6238	154	19	has	have	VERB
ejpam-6238	154	20	a	a	DET
ejpam-6238	154	21	unique	unique	ADJ
ejpam-6238	154	22	solution	solution	NOUN
ejpam-6238	154	23	as	as	SCONJ
ejpam-6238	154	24	required	require	VERB
ejpam-6238	154	25	.	.	PUNCT
ejpam-6238	155	1	3	3	X
ejpam-6238	155	2	.	.	NOUN
ejpam-6238	155	3	inverse	inverse	ADJ
ejpam-6238	155	4	problem	problem	NOUN
ejpam-6238	155	5	case	case	NOUN
ejpam-6238	155	6	in	in	ADP
ejpam-6238	155	7	this	this	DET
ejpam-6238	155	8	section	section	NOUN
ejpam-6238	155	9	,	,	PUNCT
ejpam-6238	155	10	we	we	PRON
ejpam-6238	155	11	consider	consider	VERB
ejpam-6238	155	12	the	the	DET
ejpam-6238	155	13	inverse	inverse	NOUN
ejpam-6238	155	14	problem	problem	NOUN
ejpam-6238	155	15	where	where	SCONJ
ejpam-6238	155	16	both	both	DET
ejpam-6238	155	17	solution	solution	NOUN
ejpam-6238	155	18	u	u	X
ejpam-6238	155	19	(	(	PUNCT
ejpam-6238	155	20	t	t	PROPN
ejpam-6238	155	21	)	)	PUNCT
ejpam-6238	155	22	and	and	CCONJ
ejpam-6238	155	23	function	function	NOUN
ejpam-6238	155	24	f	f	PROPN
ejpam-6238	155	25	(	(	PUNCT
ejpam-6238	155	26	t	t	PROPN
ejpam-6238	155	27	)	)	PUNCT
ejpam-6238	155	28	have	have	VERB
ejpam-6238	155	29	finite	finite	VERB
ejpam-6238	155	30	-	-	ADJ
ejpam-6238	155	31	rank	rank	ADJ
ejpam-6238	155	32	representations	representation	NOUN
ejpam-6238	155	33	:	:	PUNCT
ejpam-6238	155	34	u	u	NOUN
ejpam-6238	155	35	(	(	PUNCT
ejpam-6238	155	36	t	t	PROPN
ejpam-6238	155	37	)	)	PUNCT
ejpam-6238	155	38	=	=	SYM
ejpam-6238	156	1	∑n	∑n	PROPN
ejpam-6238	156	2	i=1	i=1	PROPN
ejpam-6238	156	3	ui	ui	PROPN
ejpam-6238	156	4	(	(	PUNCT
ejpam-6238	156	5	t	t	NOUN
ejpam-6238	156	6	)	)	PUNCT
ejpam-6238	156	7	δi	δi	PROPN
ejpam-6238	156	8	,	,	PUNCT
ejpam-6238	156	9	f	f	PROPN
ejpam-6238	156	10	(	(	PUNCT
ejpam-6238	156	11	t	t	PROPN
ejpam-6238	156	12	)	)	PUNCT
ejpam-6238	156	13	=	=	SYM
ejpam-6238	157	1	∑n	∑n	PROPN
ejpam-6238	157	2	i=1	i=1	PROPN
ejpam-6238	157	3	fi	fi	NOUN
ejpam-6238	157	4	(	(	PUNCT
ejpam-6238	157	5	t	t	NOUN
ejpam-6238	157	6	)	)	PUNCT
ejpam-6238	157	7	δi	δi	ADV
ejpam-6238	157	8	,	,	PUNCT
ejpam-6238	157	9	with	with	ADP
ejpam-6238	157	10	u	u	NOUN
ejpam-6238	157	11	(	(	PUNCT
ejpam-6238	157	12	2α	2α	NOUN
ejpam-6238	157	13	)	)	PUNCT
ejpam-6238	157	14	i	i	PRON
ejpam-6238	157	15	,	,	PUNCT
ejpam-6238	157	16	fi	fi	NOUN
ejpam-6238	157	17	∈	∈	PROPN
ejpam-6238	157	18	c	c	X
ejpam-6238	157	19	(	(	PUNCT
ejpam-6238	157	20	i	i	NOUN
ejpam-6238	157	21	)	)	PUNCT
ejpam-6238	157	22	for	for	ADP
ejpam-6238	157	23	i	i	PROPN
ejpam-6238	157	24	=	=	SYM
ejpam-6238	157	25	1	1	NUM
ejpam-6238	157	26	,	,	PUNCT
ejpam-6238	157	27	2	2	NUM
ejpam-6238	157	28	,	,	PUNCT
ejpam-6238	157	29	...	...	PUNCT
ejpam-6238	157	30	,	,	PUNCT
ejpam-6238	157	31	n.	n.	PROPN
ejpam-6238	157	32	theorem	theorem	VERB
ejpam-6238	157	33	5	5	NUM
ejpam-6238	157	34	.	.	X
ejpam-6238	157	35	consider	consider	VERB
ejpam-6238	157	36	problem	problem	NOUN
ejpam-6238	157	37	(	(	PUNCT
ejpam-6238	157	38	1	1	NUM
ejpam-6238	157	39	)	)	PUNCT
ejpam-6238	157	40	with	with	ADP
ejpam-6238	157	41	u	u	PROPN
ejpam-6238	157	42	(	(	PUNCT
ejpam-6238	157	43	t	t	PROPN
ejpam-6238	157	44	)	)	PUNCT
ejpam-6238	157	45	=	=	SYM
ejpam-6238	158	1	∑n	∑n	PROPN
ejpam-6238	158	2	i=1	i=1	PROPN
ejpam-6238	158	3	ui	ui	PROPN
ejpam-6238	158	4	(	(	PUNCT
ejpam-6238	158	5	t	t	NOUN
ejpam-6238	158	6	)	)	PUNCT
ejpam-6238	158	7	δi	δi	PROPN
ejpam-6238	158	8	and	and	CCONJ
ejpam-6238	158	9	f	f	PROPN
ejpam-6238	158	10	(	(	PUNCT
ejpam-6238	158	11	t	t	PROPN
ejpam-6238	158	12	)	)	PUNCT
ejpam-6238	158	13	=	=	SYM
ejpam-6238	159	1	∑n	∑n	PROPN
ejpam-6238	159	2	i=1	i=1	PROPN
ejpam-6238	159	3	fi	fi	NOUN
ejpam-6238	159	4	(	(	PUNCT
ejpam-6238	159	5	t	t	NOUN
ejpam-6238	159	6	)	)	PUNCT
ejpam-6238	159	7	δi	δi	PROPN
ejpam-6238	159	8	,	,	PUNCT
ejpam-6238	159	9	where	where	SCONJ
ejpam-6238	159	10	u	u	PROPN
ejpam-6238	159	11	(	(	PUNCT
ejpam-6238	159	12	2α	2α	NOUN
ejpam-6238	159	13	)	)	PUNCT
ejpam-6238	159	14	i	i	PRON
ejpam-6238	159	15	,	,	PUNCT
ejpam-6238	159	16	fi	fi	NOUN
ejpam-6238	159	17	∈	∈	PROPN
ejpam-6238	159	18	c	c	X
ejpam-6238	159	19	(	(	PUNCT
ejpam-6238	159	20	i	i	NOUN
ejpam-6238	159	21	)	)	PUNCT
ejpam-6238	159	22	for	for	ADP
ejpam-6238	159	23	i	i	PROPN
ejpam-6238	159	24	=	=	SYM
ejpam-6238	159	25	1	1	NUM
ejpam-6238	159	26	,	,	PUNCT
ejpam-6238	159	27	2	2	NUM
ejpam-6238	159	28	,	,	PUNCT
ejpam-6238	159	29	...	...	PUNCT
ejpam-6238	159	30	,	,	PUNCT
ejpam-6238	159	31	n.	n.	NOUN
ejpam-6238	159	32	if	if	SCONJ
ejpam-6238	159	33	the	the	DET
ejpam-6238	159	34	following	follow	VERB
ejpam-6238	159	35	conditions	condition	NOUN
ejpam-6238	159	36	hold	hold	VERB
ejpam-6238	159	37	:	:	PUNCT
ejpam-6238	159	38	1	1	X
ejpam-6238	159	39	)	)	PUNCT
ejpam-6238	159	40	there	there	PRON
ejpam-6238	159	41	exists	exist	VERB
ejpam-6238	159	42	x	x	X
ejpam-6238	159	43	∈	∈	NOUN
ejpam-6238	159	44	ℓ2	ℓ2	NOUN
ejpam-6238	159	45	such	such	ADJ
ejpam-6238	159	46	that	that	SCONJ
ejpam-6238	159	47	⟨ui	⟨ui	PROPN
ejpam-6238	159	48	(	(	PUNCT
ejpam-6238	159	49	t	t	NOUN
ejpam-6238	159	50	)	)	PUNCT
ejpam-6238	159	51	δi	δi	PROPN
ejpam-6238	159	52	,	,	PUNCT
ejpam-6238	159	53	x⟩	x⟩	PUNCT
ejpam-6238	160	1	=	=	PRON
ejpam-6238	160	2	hi	hi	INTJ
ejpam-6238	160	3	(	(	PUNCT
ejpam-6238	160	4	t	t	PROPN
ejpam-6238	160	5	)	)	PUNCT
ejpam-6238	161	1	where	where	SCONJ
ejpam-6238	161	2	h	h	NOUN
ejpam-6238	161	3	(	(	PUNCT
ejpam-6238	161	4	2α	2α	PROPN
ejpam-6238	161	5	)	)	PUNCT
ejpam-6238	162	1	i	i	PRON
ejpam-6238	162	2	∈	∈	PROPN
ejpam-6238	163	1	c	c	X
ejpam-6238	163	2	(	(	PUNCT
ejpam-6238	163	3	i	i	NOUN
ejpam-6238	163	4	)	)	PUNCT
ejpam-6238	163	5	and	and	CCONJ
ejpam-6238	163	6	⟨δi	⟨δi	NUM
ejpam-6238	163	7	,	,	PUNCT
ejpam-6238	163	8	x⟩	x⟩	PUNCT
ejpam-6238	164	1	=	=	X
ejpam-6238	164	2	̸	̸	ADV
ejpam-6238	164	3	0	0	NUM
ejpam-6238	164	4	2	2	NUM
ejpam-6238	164	5	)	)	PUNCT
ejpam-6238	164	6	aδi	aδi	NOUN
ejpam-6238	164	7	=	=	SYM
ejpam-6238	164	8	λiδi	λiδi	NOUN
ejpam-6238	164	9	and	and	CCONJ
ejpam-6238	164	10	bδi	bδi	PROPN
ejpam-6238	164	11	=	=	PUNCT
ejpam-6238	164	12	βiδi	βiδi	ADV
ejpam-6238	164	13	for	for	ADP
ejpam-6238	164	14	all	all	DET
ejpam-6238	164	15	i	i	PRON
ejpam-6238	164	16	=	=	NOUN
ejpam-6238	164	17	1	1	NUM
ejpam-6238	164	18	,	,	PUNCT
ejpam-6238	164	19	2	2	NUM
ejpam-6238	164	20	,	,	PUNCT
ejpam-6238	164	21	...	...	PUNCT
ejpam-6238	164	22	,	,	PUNCT
ejpam-6238	164	23	n.	n.	PROPN
ejpam-6238	164	24	then	then	ADV
ejpam-6238	164	25	the	the	DET
ejpam-6238	164	26	problem	problem	NOUN
ejpam-6238	164	27	has	have	VERB
ejpam-6238	164	28	a	a	DET
ejpam-6238	164	29	unique	unique	ADJ
ejpam-6238	164	30	solution	solution	NOUN
ejpam-6238	164	31	.	.	PUNCT
ejpam-6238	165	1	proof	proof	NOUN
ejpam-6238	165	2	.	.	PUNCT
ejpam-6238	166	1	under	under	ADP
ejpam-6238	166	2	the	the	DET
ejpam-6238	166	3	given	give	VERB
ejpam-6238	166	4	representations	representation	NOUN
ejpam-6238	166	5	,	,	PUNCT
ejpam-6238	166	6	problem	problem	NOUN
ejpam-6238	166	7	(	(	PUNCT
ejpam-6238	166	8	1	1	X
ejpam-6238	166	9	)	)	PUNCT
ejpam-6238	166	10	becomes	become	VERB
ejpam-6238	166	11	n∑	n∑	PROPN
ejpam-6238	166	12	i=1	i=1	PROPN
ejpam-6238	166	13	u	u	PROPN
ejpam-6238	166	14	(	(	PUNCT
ejpam-6238	166	15	2α	2α	NOUN
ejpam-6238	166	16	)	)	PUNCT
ejpam-6238	167	1	i	i	PRON
ejpam-6238	167	2	(	(	PUNCT
ejpam-6238	167	3	t	t	NOUN
ejpam-6238	167	4	)	)	PUNCT
ejpam-6238	167	5	δi	δi	PROPN
ejpam-6238	168	1	+	+	CCONJ
ejpam-6238	168	2	n∑	n∑	ADJ
ejpam-6238	168	3	i=1	i=1	PROPN
ejpam-6238	168	4	u	u	PROPN
ejpam-6238	168	5	(	(	PUNCT
ejpam-6238	168	6	α	α	NOUN
ejpam-6238	168	7	)	)	PUNCT
ejpam-6238	168	8	i	i	PRON
ejpam-6238	168	9	(	(	PUNCT
ejpam-6238	168	10	t)aδi	t)aδi	PROPN
ejpam-6238	168	11	+	+	NUM
ejpam-6238	168	12	n∑	n∑	PROPN
ejpam-6238	168	13	i=1	i=1	PROPN
ejpam-6238	168	14	ui	ui	PROPN
ejpam-6238	168	15	(	(	PUNCT
ejpam-6238	168	16	t)bδi	t)bδi	PROPN
ejpam-6238	168	17	=	=	SYM
ejpam-6238	168	18	n∑	n∑	NOUN
ejpam-6238	168	19	i=1	i=1	PROPN
ejpam-6238	168	20	fi	fi	NOUN
ejpam-6238	168	21	(	(	PUNCT
ejpam-6238	168	22	t	t	NOUN
ejpam-6238	168	23	)	)	PUNCT
ejpam-6238	168	24	δi	δi	PROPN
ejpam-6238	168	25	(	(	PUNCT
ejpam-6238	168	26	25	25	NUM
ejpam-6238	168	27	)	)	PUNCT
ejpam-6238	168	28	but	but	CCONJ
ejpam-6238	168	29	aδi	aδi	NOUN
ejpam-6238	168	30	=	=	SYM
ejpam-6238	168	31	λiδi	λiδi	NOUN
ejpam-6238	168	32	and	and	CCONJ
ejpam-6238	168	33	bδi	bδi	PROPN
ejpam-6238	168	34	=	=	PUNCT
ejpam-6238	168	35	βiδi	βiδi	ADV
ejpam-6238	168	36	for	for	ADP
ejpam-6238	168	37	all	all	PRON
ejpam-6238	168	38	i	i	PRON
ejpam-6238	168	39	=	=	NOUN
ejpam-6238	168	40	1	1	NUM
ejpam-6238	168	41	,	,	PUNCT
ejpam-6238	168	42	2	2	NUM
ejpam-6238	168	43	,	,	PUNCT
ejpam-6238	168	44	...	...	PUNCT
ejpam-6238	168	45	,	,	PUNCT
ejpam-6238	168	46	n	n	CCONJ
ejpam-6238	168	47	by	by	ADP
ejpam-6238	168	48	condition	condition	NOUN
ejpam-6238	168	49	2	2	NUM
ejpam-6238	168	50	,	,	PUNCT
ejpam-6238	168	51	so	so	SCONJ
ejpam-6238	168	52	we	we	PRON
ejpam-6238	168	53	get	get	VERB
ejpam-6238	168	54	n∑	n∑	PROPN
ejpam-6238	168	55	i=1	i=1	PROPN
ejpam-6238	168	56	u	u	PROPN
ejpam-6238	168	57	(	(	PUNCT
ejpam-6238	168	58	2α	2α	NOUN
ejpam-6238	168	59	)	)	PUNCT
ejpam-6238	169	1	i	i	PRON
ejpam-6238	169	2	(	(	PUNCT
ejpam-6238	169	3	t	t	NOUN
ejpam-6238	169	4	)	)	PUNCT
ejpam-6238	169	5	δi	δi	PROPN
ejpam-6238	170	1	+	+	CCONJ
ejpam-6238	170	2	n∑	n∑	ADJ
ejpam-6238	170	3	i=1	i=1	PROPN
ejpam-6238	170	4	λiu	λiu	PROPN
ejpam-6238	170	5	(	(	PUNCT
ejpam-6238	170	6	α	α	NOUN
ejpam-6238	170	7	)	)	PUNCT
ejpam-6238	170	8	i	i	PRON
ejpam-6238	170	9	(	(	PUNCT
ejpam-6238	170	10	t	t	NOUN
ejpam-6238	170	11	)	)	PUNCT
ejpam-6238	171	1	δi	δi	PROPN
ejpam-6238	172	1	+	+	CCONJ
ejpam-6238	172	2	n∑	n∑	PROPN
ejpam-6238	172	3	i=1	i=1	PROPN
ejpam-6238	172	4	βiui	βiui	PROPN
ejpam-6238	172	5	(	(	PUNCT
ejpam-6238	172	6	t	t	NOUN
ejpam-6238	172	7	)	)	PUNCT
ejpam-6238	172	8	δi	δi	PROPN
ejpam-6238	173	1	=	=	SYM
ejpam-6238	173	2	n∑	n∑	PROPN
ejpam-6238	173	3	i=1	i=1	PROPN
ejpam-6238	173	4	fi	fi	NOUN
ejpam-6238	173	5	(	(	PUNCT
ejpam-6238	173	6	t	t	NOUN
ejpam-6238	173	7	)	)	PUNCT
ejpam-6238	173	8	δi	δi	PROPN
ejpam-6238	173	9	(	(	PUNCT
ejpam-6238	173	10	26	26	NUM
ejpam-6238	173	11	)	)	PUNCT
ejpam-6238	173	12	taking	take	VERB
ejpam-6238	173	13	inner	inner	ADJ
ejpam-6238	173	14	products	product	NOUN
ejpam-6238	173	15	with	with	ADP
ejpam-6238	173	16	δj	δj	NOUN
ejpam-6238	173	17	:	:	PUNCT
ejpam-6238	173	18	n∑	n∑	PROPN
ejpam-6238	173	19	i=1	i=1	PROPN
ejpam-6238	173	20	u	u	PROPN
ejpam-6238	173	21	(	(	PUNCT
ejpam-6238	173	22	2α	2α	NOUN
ejpam-6238	173	23	)	)	PUNCT
ejpam-6238	173	24	i	i	PRON
ejpam-6238	173	25	(	(	PUNCT
ejpam-6238	173	26	t	t	PROPN
ejpam-6238	173	27	)	)	PUNCT
ejpam-6238	173	28	⟨δi	⟨δi	PROPN
ejpam-6238	173	29	,	,	PUNCT
ejpam-6238	173	30	δj⟩+	δj⟩+	PROPN
ejpam-6238	173	31	n∑	n∑	PROPN
ejpam-6238	173	32	i=1	i=1	PROPN
ejpam-6238	173	33	λiu	λiu	PROPN
ejpam-6238	173	34	(	(	PUNCT
ejpam-6238	173	35	α	α	NOUN
ejpam-6238	173	36	)	)	PUNCT
ejpam-6238	173	37	i	i	PRON
ejpam-6238	173	38	(	(	PUNCT
ejpam-6238	173	39	t	t	PROPN
ejpam-6238	173	40	)	)	PUNCT
ejpam-6238	173	41	⟨δi	⟨δi	PROPN
ejpam-6238	173	42	,	,	PUNCT
ejpam-6238	173	43	δj⟩+	δj⟩+	PROPN
ejpam-6238	173	44	n∑	n∑	PROPN
ejpam-6238	173	45	i=1	i=1	PROPN
ejpam-6238	173	46	βiui	βiui	PROPN
ejpam-6238	173	47	(	(	PUNCT
ejpam-6238	173	48	t	t	PROPN
ejpam-6238	173	49	)	)	PUNCT
ejpam-6238	173	50	⟨δi	⟨δi	PROPN
ejpam-6238	173	51	,	,	PUNCT
ejpam-6238	173	52	δj⟩	δj⟩	PROPN
ejpam-6238	173	53	=	=	SYM
ejpam-6238	174	1	n∑	n∑	PROPN
ejpam-6238	174	2	i=1	i=1	PROPN
ejpam-6238	174	3	fi	fi	NOUN
ejpam-6238	174	4	(	(	PUNCT
ejpam-6238	174	5	t	t	PROPN
ejpam-6238	174	6	)	)	PUNCT
ejpam-6238	174	7	⟨δi	⟨δi	PROPN
ejpam-6238	174	8	,	,	PUNCT
ejpam-6238	174	9	δj⟩	δj⟩	PROPN
ejpam-6238	174	10	(	(	PUNCT
ejpam-6238	174	11	27	27	NUM
ejpam-6238	174	12	)	)	PUNCT
ejpam-6238	174	13	moreover	moreover	ADV
ejpam-6238	174	14	,	,	PUNCT
ejpam-6238	174	15	the	the	DET
ejpam-6238	174	16	basis	basis	NOUN
ejpam-6238	174	17	{	{	PUNCT
ejpam-6238	174	18	δi}ni=1	δi}ni=1	PROPN
ejpam-6238	174	19	is	be	AUX
ejpam-6238	174	20	orthonormal	orthonormal	ADJ
ejpam-6238	174	21	so	so	ADV
ejpam-6238	174	22	then	then	ADV
ejpam-6238	174	23	the	the	DET
ejpam-6238	174	24	equation	equation	NOUN
ejpam-6238	174	25	(	(	PUNCT
ejpam-6238	174	26	27	27	NUM
ejpam-6238	174	27	)	)	PUNCT
ejpam-6238	174	28	becomes	become	VERB
ejpam-6238	174	29	u	u	NOUN
ejpam-6238	174	30	(	(	PUNCT
ejpam-6238	174	31	2α	2α	PROPN
ejpam-6238	174	32	)	)	PUNCT
ejpam-6238	174	33	j	j	PROPN
ejpam-6238	174	34	(	(	PUNCT
ejpam-6238	174	35	t	t	PROPN
ejpam-6238	174	36	)	)	PUNCT
ejpam-6238	175	1	+	+	CCONJ
ejpam-6238	175	2	λju	λju	NOUN
ejpam-6238	175	3	(	(	PUNCT
ejpam-6238	175	4	α	α	NOUN
ejpam-6238	175	5	)	)	PUNCT
ejpam-6238	175	6	j	j	PROPN
ejpam-6238	175	7	(	(	PUNCT
ejpam-6238	175	8	t	t	PROPN
ejpam-6238	175	9	)	)	PUNCT
ejpam-6238	176	1	+	+	CCONJ
ejpam-6238	176	2	βjuj	βjuj	ADJ
ejpam-6238	176	3	(	(	PUNCT
ejpam-6238	176	4	t	t	NOUN
ejpam-6238	176	5	)	)	PUNCT
ejpam-6238	176	6	=	=	SYM
ejpam-6238	177	1	fj	fj	PROPN
ejpam-6238	177	2	(	(	PUNCT
ejpam-6238	177	3	t	t	PROPN
ejpam-6238	177	4	)	)	PUNCT
ejpam-6238	177	5	(	(	PUNCT
ejpam-6238	177	6	28	28	NUM
ejpam-6238	177	7	)	)	PUNCT
ejpam-6238	177	8	multiplying	multiplying	NOUN
ejpam-6238	177	9	(	(	PUNCT
ejpam-6238	177	10	28	28	NUM
ejpam-6238	177	11	)	)	PUNCT
ejpam-6238	177	12	by	by	ADP
ejpam-6238	177	13	δj	δj	ADV
ejpam-6238	177	14	and	and	CCONJ
ejpam-6238	177	15	taking	take	VERB
ejpam-6238	177	16	inner	inner	ADJ
ejpam-6238	177	17	product	product	NOUN
ejpam-6238	177	18	x	x	X
ejpam-6238	177	19	:	:	PUNCT
ejpam-6238	177	20	g	g	NOUN
ejpam-6238	177	21	(	(	PUNCT
ejpam-6238	177	22	2α	2α	PROPN
ejpam-6238	177	23	)	)	PUNCT
ejpam-6238	177	24	j	j	PROPN
ejpam-6238	177	25	(	(	PUNCT
ejpam-6238	177	26	t	t	PROPN
ejpam-6238	177	27	)	)	PUNCT
ejpam-6238	177	28	+	+	NUM
ejpam-6238	177	29	λjg	λjg	PRON
ejpam-6238	177	30	(	(	PUNCT
ejpam-6238	177	31	α	α	NOUN
ejpam-6238	177	32	)	)	PUNCT
ejpam-6238	177	33	j	j	PROPN
ejpam-6238	177	34	(	(	PUNCT
ejpam-6238	177	35	t	t	PROPN
ejpam-6238	177	36	)	)	PUNCT
ejpam-6238	178	1	+	+	CCONJ
ejpam-6238	178	2	βjgj	βjgj	NOUN
ejpam-6238	178	3	(	(	PUNCT
ejpam-6238	178	4	t	t	NOUN
ejpam-6238	178	5	)	)	PUNCT
ejpam-6238	178	6	=	=	SYM
ejpam-6238	178	7	fj	fj	PROPN
ejpam-6238	178	8	(	(	PUNCT
ejpam-6238	178	9	t	t	PROPN
ejpam-6238	178	10	)	)	PUNCT
ejpam-6238	178	11	⟨δj	⟨δj	NUM
ejpam-6238	178	12	,	,	PUNCT
ejpam-6238	178	13	x⟩	x⟩	PUNCT
ejpam-6238	178	14	(	(	PUNCT
ejpam-6238	178	15	29	29	NUM
ejpam-6238	178	16	)	)	PUNCT
ejpam-6238	178	17	h.	h.	NOUN
ejpam-6238	179	1	odetallah	odetallah	INTJ
ejpam-6238	179	2	et	et	PROPN
ejpam-6238	179	3	al	al	PROPN
ejpam-6238	179	4	.	.	PUNCT
ejpam-6238	179	5	/	/	SYM
ejpam-6238	179	6	eur	eur	PROPN
ejpam-6238	179	7	.	.	PUNCT
ejpam-6238	180	1	j.	j.	PROPN
ejpam-6238	180	2	pure	pure	PROPN
ejpam-6238	180	3	appl	appl	PROPN
ejpam-6238	180	4	.	.	PROPN
ejpam-6238	180	5	math	math	PROPN
ejpam-6238	180	6	,	,	PUNCT
ejpam-6238	180	7	18	18	NUM
ejpam-6238	180	8	(	(	PUNCT
ejpam-6238	180	9	3	3	NUM
ejpam-6238	180	10	)	)	PUNCT
ejpam-6238	180	11	(	(	PUNCT
ejpam-6238	180	12	2025	2025	NUM
ejpam-6238	180	13	)	)	PUNCT
ejpam-6238	180	14	,	,	PUNCT
ejpam-6238	180	15	6238	6238	NUM
ejpam-6238	180	16	9	9	NUM
ejpam-6238	180	17	of	of	ADP
ejpam-6238	180	18	11	11	NUM
ejpam-6238	180	19	therefore	therefore	ADV
ejpam-6238	180	20	,	,	PUNCT
ejpam-6238	180	21	fj	fj	PROPN
ejpam-6238	180	22	(	(	PUNCT
ejpam-6238	180	23	t	t	PROPN
ejpam-6238	180	24	)	)	PUNCT
ejpam-6238	180	25	is	be	AUX
ejpam-6238	180	26	uniquely	uniquely	ADV
ejpam-6238	180	27	determined	determine	VERB
ejpam-6238	180	28	by	by	ADP
ejpam-6238	180	29	fj	fj	PROPN
ejpam-6238	180	30	(	(	PUNCT
ejpam-6238	180	31	t	t	PROPN
ejpam-6238	180	32	)	)	PUNCT
ejpam-6238	181	1	=	=	SYM
ejpam-6238	181	2	g	g	PROPN
ejpam-6238	181	3	(	(	PUNCT
ejpam-6238	181	4	2α	2α	PROPN
ejpam-6238	181	5	)	)	PUNCT
ejpam-6238	181	6	j	j	PROPN
ejpam-6238	181	7	(	(	PUNCT
ejpam-6238	181	8	t	t	PROPN
ejpam-6238	181	9	)	)	PUNCT
ejpam-6238	181	10	+	+	NUM
ejpam-6238	181	11	λjg	λjg	PRON
ejpam-6238	181	12	(	(	PUNCT
ejpam-6238	181	13	α	α	NOUN
ejpam-6238	181	14	)	)	PUNCT
ejpam-6238	181	15	j	j	PROPN
ejpam-6238	181	16	(	(	PUNCT
ejpam-6238	181	17	t	t	PROPN
ejpam-6238	181	18	)	)	PUNCT
ejpam-6238	182	1	+	+	CCONJ
ejpam-6238	182	2	βjgj	βjgj	NOUN
ejpam-6238	182	3	(	(	PUNCT
ejpam-6238	182	4	t	t	PROPN
ejpam-6238	182	5	)	)	PUNCT
ejpam-6238	182	6	⟨δj	⟨δj	NUM
ejpam-6238	182	7	,	,	PUNCT
ejpam-6238	182	8	x⟩	x⟩	PUNCT
ejpam-6238	182	9	(	(	PUNCT
ejpam-6238	182	10	30	30	NUM
ejpam-6238	182	11	)	)	PUNCT
ejpam-6238	182	12	since	since	SCONJ
ejpam-6238	182	13	⟨δj	⟨δj	PROPN
ejpam-6238	182	14	,	,	PUNCT
ejpam-6238	182	15	x⟩	x⟩	PUNCT
ejpam-6238	183	1	̸=	̸=	PROPN
ejpam-6238	183	2	0	0	NUM
ejpam-6238	183	3	by	by	ADP
ejpam-6238	183	4	assumption	assumption	NOUN
ejpam-6238	183	5	.	.	PUNCT
ejpam-6238	184	1	hence	hence	ADV
ejpam-6238	184	2	,	,	PUNCT
ejpam-6238	184	3	f	f	PROPN
ejpam-6238	184	4	(	(	PUNCT
ejpam-6238	184	5	t	t	PROPN
ejpam-6238	184	6	)	)	PUNCT
ejpam-6238	184	7	has	have	AUX
ejpam-6238	184	8	been	be	AUX
ejpam-6238	184	9	completely	completely	ADV
ejpam-6238	184	10	determined	determine	VERB
ejpam-6238	184	11	.	.	PUNCT
ejpam-6238	185	1	each	each	DET
ejpam-6238	185	2	differential	differential	ADJ
ejpam-6238	185	3	equation	equation	NOUN
ejpam-6238	185	4	admits	admit	VERB
ejpam-6238	185	5	a	a	DET
ejpam-6238	185	6	unique	unique	ADJ
ejpam-6238	185	7	solution	solution	NOUN
ejpam-6238	185	8	given	give	VERB
ejpam-6238	185	9	initial	initial	ADJ
ejpam-6238	185	10	conditions	condition	NOUN
ejpam-6238	185	11	uj	uj	X
ejpam-6238	185	12	(	(	PUNCT
ejpam-6238	185	13	0	0	NUM
ejpam-6238	185	14	)	)	PUNCT
ejpam-6238	185	15	and	and	CCONJ
ejpam-6238	185	16	u	u	PROPN
ejpam-6238	185	17	(	(	PUNCT
ejpam-6238	185	18	α	α	NOUN
ejpam-6238	185	19	)	)	PUNCT
ejpam-6238	185	20	j	j	PROPN
ejpam-6238	185	21	(	(	PUNCT
ejpam-6238	185	22	0	0	NUM
ejpam-6238	185	23	)	)	PUNCT
ejpam-6238	185	24	.	.	PUNCT
ejpam-6238	186	1	4	4	X
ejpam-6238	186	2	.	.	X
ejpam-6238	186	3	physical	physical	ADJ
ejpam-6238	186	4	applications	application	NOUN
ejpam-6238	186	5	and	and	CCONJ
ejpam-6238	186	6	engineering	engineering	NOUN
ejpam-6238	186	7	relevance	relevance	NOUN
ejpam-6238	186	8	1viscoelastic	1viscoelastic	NUM
ejpam-6238	186	9	material	material	NOUN
ejpam-6238	186	10	modeling	modeling	NOUN
ejpam-6238	186	11	:	:	PUNCT
ejpam-6238	186	12	in	in	ADP
ejpam-6238	186	13	viscoelastic	viscoelastic	ADJ
ejpam-6238	186	14	material	material	NOUN
ejpam-6238	186	15	analysis	analysis	NOUN
ejpam-6238	186	16	,	,	PUNCT
ejpam-6238	186	17	stress	stress	NOUN
ejpam-6238	186	18	-	-	PUNCT
ejpam-6238	186	19	stain	stain	NOUN
ejpam-6238	186	20	relationships	relationship	NOUN
ejpam-6238	186	21	naturally	naturally	ADV
ejpam-6238	186	22	incorporate	incorporate	VERB
ejpam-6238	186	23	memory	memory	NOUN
ejpam-6238	186	24	effects	effect	NOUN
ejpam-6238	186	25	through	through	ADP
ejpam-6238	186	26	fractional	fractional	ADJ
ejpam-6238	186	27	derivative	derivative	ADJ
ejpam-6238	186	28	formulations	formulation	NOUN
ejpam-6238	186	29	:	:	PUNCT
ejpam-6238	187	1	e	e	X
ejpam-6238	187	2	∂2αu	∂2αu	VERB
ejpam-6238	187	3	∂t2α	∂t2α	PROPN
ejpam-6238	188	1	+	+	CCONJ
ejpam-6238	188	2	a	a	DET
ejpam-6238	188	3	∂αu	∂αu	PROPN
ejpam-6238	188	4	∂tα	∂tα	PROPN
ejpam-6238	188	5	+	+	PROPN
ejpam-6238	188	6	bu	bu	PROPN
ejpam-6238	188	7	=	=	ADJ
ejpam-6238	188	8	f	f	PROPN
ejpam-6238	188	9	(	(	PUNCT
ejpam-6238	188	10	t	t	PROPN
ejpam-6238	188	11	)	)	PUNCT
ejpam-6238	188	12	where	where	SCONJ
ejpam-6238	188	13	u	u	PRON
ejpam-6238	188	14	represents	represent	VERB
ejpam-6238	188	15	displacement	displacement	ADJ
ejpam-6238	188	16	field	field	NOUN
ejpam-6238	188	17	distribution	distribution	NOUN
ejpam-6238	188	18	,	,	PUNCT
ejpam-6238	188	19	e	e	PROPN
ejpam-6238	188	20	captures	capture	VERB
ejpam-6238	188	21	internal	internal	ADJ
ejpam-6238	188	22	effects	effect	NOUN
ejpam-6238	188	23	(	(	PUNCT
ejpam-6238	188	24	potentially	potentially	ADV
ejpam-6238	188	25	degenerate	degenerate	ADJ
ejpam-6238	188	26	in	in	ADP
ejpam-6238	188	27	quasi	quasi	ADJ
ejpam-6238	188	28	-	-	ADJ
ejpam-6238	188	29	static	static	ADJ
ejpam-6238	188	30	scenarios	scenario	NOUN
ejpam-6238	188	31	)	)	PUNCT
ejpam-6238	188	32	,	,	PUNCT
ejpam-6238	188	33	a	a	DET
ejpam-6238	188	34	models	model	NOUN
ejpam-6238	188	35	viscous	viscous	ADJ
ejpam-6238	188	36	damping	damp	VERB
ejpam-6238	188	37	mechanisms	mechanism	NOUN
ejpam-6238	188	38	,	,	PUNCT
ejpam-6238	188	39	and	and	CCONJ
ejpam-6238	188	40	b	b	NOUN
ejpam-6238	188	41	represents	represent	VERB
ejpam-6238	188	42	elastic	elastic	ADJ
ejpam-6238	188	43	restoring	restore	VERB
ejpam-6238	188	44	forces	force	NOUN
ejpam-6238	188	45	.	.	PUNCT
ejpam-6238	189	1	2anomalous	2anomalous	NUM
ejpam-6238	189	2	diffusion	diffusion	NOUN
ejpam-6238	189	3	phenomena	phenomenon	NOUN
ejpam-6238	189	4	:	:	PUNCT
ejpam-6238	189	5	in	in	ADP
ejpam-6238	189	6	systems	system	NOUN
ejpam-6238	189	7	exhibiting	exhibit	VERB
ejpam-6238	189	8	anomalous	anomalous	ADJ
ejpam-6238	189	9	diffusion	diffusion	NOUN
ejpam-6238	189	10	characteristics	characteristic	NOUN
ejpam-6238	189	11	,	,	PUNCT
ejpam-6238	189	12	finite	finite	ADJ
ejpam-6238	189	13	-	-	ADJ
ejpam-6238	189	14	rank	rank	ADJ
ejpam-6238	189	15	approaches	approach	NOUN
ejpam-6238	189	16	naturally	naturally	ADV
ejpam-6238	189	17	capture	capture	VERB
ejpam-6238	189	18	dominant	dominant	ADJ
ejpam-6238	189	19	transport	transport	NOUN
ejpam-6238	189	20	modes	mode	NOUN
ejpam-6238	189	21	:	:	PUNCT
ejpam-6238	189	22	e	e	X
ejpam-6238	189	23	∂2αc	∂2αc	X
ejpam-6238	189	24	∂t2α	∂t2α	PROPN
ejpam-6238	189	25	−d	−d	PROPN
ejpam-6238	189	26	∂αc	∂αc	PROPN
ejpam-6238	189	27	∂tα	∂tα	PROPN
ejpam-6238	189	28	+	+	PROPN
ejpam-6238	189	29	rc	rc	PROPN
ejpam-6238	189	30	=	=	SYM
ejpam-6238	189	31	s	s	X
ejpam-6238	189	32	(	(	PUNCT
ejpam-6238	189	33	x	x	PROPN
ejpam-6238	189	34	,	,	PUNCT
ejpam-6238	189	35	t	t	PROPN
ejpam-6238	189	36	)	)	PUNCT
ejpam-6238	189	37	where	where	SCONJ
ejpam-6238	189	38	c	c	PROPN
ejpam-6238	189	39	denotes	denote	VERB
ejpam-6238	189	40	concentration	concentration	NOUN
ejpam-6238	189	41	distribution	distribution	NOUN
ejpam-6238	189	42	,	,	PUNCT
ejpam-6238	189	43	d	d	PRON
ejpam-6238	189	44	represents	represent	VERB
ejpam-6238	189	45	diffusion	diffusion	NOUN
ejpam-6238	189	46	operator	operator	NOUN
ejpam-6238	189	47	,	,	PUNCT
ejpam-6238	189	48	and	and	CCONJ
ejpam-6238	189	49	r	r	NOUN
ejpam-6238	189	50	models	model	NOUN
ejpam-6238	189	51	reaction	reaction	NOUN
ejpam-6238	189	52	mechanisms	mechanism	NOUN
ejpam-6238	189	53	.	.	PUNCT
ejpam-6238	190	1	5	5	X
ejpam-6238	190	2	.	.	X
ejpam-6238	190	3	conclusion	conclusion	NOUN
ejpam-6238	190	4	this	this	DET
ejpam-6238	190	5	study	study	NOUN
ejpam-6238	190	6	presents	present	VERB
ejpam-6238	190	7	a	a	DET
ejpam-6238	190	8	comprehensive	comprehensive	ADJ
ejpam-6238	190	9	framework	framework	NOUN
ejpam-6238	190	10	for	for	ADP
ejpam-6238	190	11	analyzing	analyze	VERB
ejpam-6238	190	12	conformable	conformable	ADJ
ejpam-6238	190	13	fractional	fractional	ADJ
ejpam-6238	190	14	abstract	abstract	ADJ
ejpam-6238	190	15	cauchy	cauchy	NOUN
ejpam-6238	190	16	problems	problem	NOUN
ejpam-6238	190	17	through	through	ADP
ejpam-6238	190	18	finite	finite	ADJ
ejpam-6238	190	19	-	-	ADJ
ejpam-6238	190	20	rank	rank	ADJ
ejpam-6238	190	21	solution	solution	NOUN
ejpam-6238	190	22	techniques	technique	NOUN
ejpam-6238	190	23	.	.	PUNCT
ejpam-6238	191	1	the	the	DET
ejpam-6238	191	2	main	main	ADJ
ejpam-6238	191	3	contributions	contribution	NOUN
ejpam-6238	191	4	include	include	VERB
ejpam-6238	191	5	:	:	PUNCT
ejpam-6238	191	6	1theoretical	1theoretical	ADJ
ejpam-6238	191	7	achievements	achievement	NOUN
ejpam-6238	191	8	existence	existence	NOUN
ejpam-6238	191	9	and	and	CCONJ
ejpam-6238	191	10	uniqueness	uniqueness	NOUN
ejpam-6238	191	11	theorems	theorem	NOUN
ejpam-6238	191	12	:	:	PUNCT
ejpam-6238	191	13	established	establish	VERB
ejpam-6238	191	14	under	under	ADP
ejpam-6238	191	15	various	various	ADJ
ejpam-6238	191	16	operator	operator	NOUN
ejpam-6238	191	17	conditions	condition	NOUN
ejpam-6238	191	18	including	include	VERB
ejpam-6238	191	19	degenerate	degenerate	ADJ
ejpam-6238	191	20	cases	case	NOUN
ejpam-6238	191	21	.	.	PUNCT
ejpam-6238	192	1	solution	solution	NOUN
ejpam-6238	192	2	methodology	methodology	NOUN
ejpam-6238	192	3	:	:	PUNCT
ejpam-6238	192	4	developed	develop	VERB
ejpam-6238	192	5	systematic	systematic	ADJ
ejpam-6238	192	6	approach	approach	NOUN
ejpam-6238	192	7	using	use	VERB
ejpam-6238	192	8	tensor	tensor	NOUN
ejpam-6238	192	9	product	product	NOUN
ejpam-6238	192	10	decomposition	decomposition	NOUN
ejpam-6238	192	11	.	.	PUNCT
ejpam-6238	193	1	computational	computational	ADJ
ejpam-6238	193	2	framework	framework	NOUN
ejpam-6238	193	3	:	:	PUNCT
ejpam-6238	193	4	provided	provide	VERB
ejpam-6238	193	5	constructive	constructive	ADJ
ejpam-6238	193	6	algorithms	algorithm	NOUN
ejpam-6238	193	7	for	for	ADP
ejpam-6238	193	8	solution	solution	NOUN
ejpam-6238	193	9	computation	computation	NOUN
ejpam-6238	193	10	.	.	PUNCT
ejpam-6238	194	1	2practical	2practical	NUM
ejpam-6238	194	2	impact	impact	VERB
ejpam-6238	194	3	the	the	DET
ejpam-6238	194	4	finite	finite	ADJ
ejpam-6238	194	5	-	-	ADJ
ejpam-6238	194	6	rank	rank	ADJ
ejpam-6238	194	7	approach	approach	NOUN
ejpam-6238	194	8	offers	offer	VERB
ejpam-6238	194	9	significant	significant	ADJ
ejpam-6238	194	10	computational	computational	ADJ
ejpam-6238	194	11	advantages	advantage	NOUN
ejpam-6238	194	12	by	by	ADP
ejpam-6238	194	13	reducing	reduce	VERB
ejpam-6238	194	14	infinite	infinite	ADJ
ejpam-6238	194	15	-	-	PUNCT
ejpam-6238	194	16	dimensional	dimensional	ADJ
ejpam-6238	194	17	problems	problem	NOUN
ejpam-6238	194	18	to	to	ADP
ejpam-6238	194	19	finite	finite	VERB
ejpam-6238	194	20	-	-	ADJ
ejpam-6238	194	21	dimensional	dimensional	ADJ
ejpam-6238	194	22	systems	system	NOUN
ejpam-6238	194	23	.	.	PUNCT
ejpam-6238	195	1	applications	application	NOUN
ejpam-6238	195	2	in	in	ADP
ejpam-6238	195	3	viscoelastic	viscoelastic	ADJ
ejpam-6238	195	4	materials	material	NOUN
ejpam-6238	195	5	and	and	CCONJ
ejpam-6238	195	6	anomalous	anomalous	ADJ
ejpam-6238	195	7	diffusion	diffusion	NOUN
ejpam-6238	195	8	demonstrate	demonstrate	VERB
ejpam-6238	195	9	practical	practical	ADJ
ejpam-6238	195	10	relevance	relevance	NOUN
ejpam-6238	195	11	.	.	PUNCT
ejpam-6238	196	1	h.	h.	PROPN
ejpam-6238	196	2	odetallah	odetallah	PROPN
ejpam-6238	196	3	et	et	PROPN
ejpam-6238	196	4	al	al	PROPN
ejpam-6238	196	5	.	.	PUNCT
ejpam-6238	196	6	/	/	SYM
ejpam-6238	196	7	eur	eur	PROPN
ejpam-6238	196	8	.	.	PUNCT
ejpam-6238	197	1	j.	j.	PROPN
ejpam-6238	197	2	pure	pure	PROPN
ejpam-6238	197	3	appl	appl	PROPN
ejpam-6238	197	4	.	.	PROPN
ejpam-6238	197	5	math	math	PROPN
ejpam-6238	197	6	,	,	PUNCT
ejpam-6238	197	7	18	18	NUM
ejpam-6238	197	8	(	(	PUNCT
ejpam-6238	197	9	3	3	NUM
ejpam-6238	197	10	)	)	PUNCT
ejpam-6238	197	11	(	(	PUNCT
ejpam-6238	197	12	2025	2025	NUM
ejpam-6238	197	13	)	)	PUNCT
ejpam-6238	197	14	,	,	PUNCT
ejpam-6238	197	15	6238	6238	NUM
ejpam-6238	197	16	10	10	NUM
ejpam-6238	197	17	of	of	ADP
ejpam-6238	197	18	11	11	NUM
ejpam-6238	197	19	3novel	3novel	NUM
ejpam-6238	197	20	contributions	contribution	NOUN
ejpam-6238	197	21	extension	extension	NOUN
ejpam-6238	197	22	of	of	ADP
ejpam-6238	197	23	tensor	tensor	NOUN
ejpam-6238	197	24	product	product	NOUN
ejpam-6238	197	25	techniques	technique	NOUN
ejpam-6238	197	26	to	to	PART
ejpam-6238	197	27	conformable	conformable	VERB
ejpam-6238	197	28	fractional	fractional	ADJ
ejpam-6238	197	29	derivatives	derivative	NOUN
ejpam-6238	197	30	.	.	PUNCT
ejpam-6238	198	1	treatment	treatment	NOUN
ejpam-6238	198	2	of	of	ADP
ejpam-6238	198	3	degenerate	degenerate	ADJ
ejpam-6238	198	4	operators	operator	NOUN
ejpam-6238	198	5	through	through	ADP
ejpam-6238	198	6	spectral	spectral	ADJ
ejpam-6238	198	7	decomposition	decomposition	NOUN
ejpam-6238	198	8	.	.	PUNCT
ejpam-6238	199	1	unified	unified	ADJ
ejpam-6238	199	2	approach	approach	NOUN
ejpam-6238	199	3	handling	handle	VERB
ejpam-6238	199	4	both	both	CCONJ
ejpam-6238	199	5	direct	direct	ADJ
ejpam-6238	199	6	and	and	CCONJ
ejpam-6238	199	7	inverse	inverse	NOUN
ejpam-6238	199	8	problems	problem	NOUN
ejpam-6238	199	9	.	.	PUNCT
ejpam-6238	200	1	4future	4future	NUM
ejpam-6238	200	2	research	research	NOUN
ejpam-6238	200	3	directions	direction	NOUN
ejpam-6238	200	4	higher	high	ADJ
ejpam-6238	200	5	-	-	PUNCT
ejpam-6238	200	6	order	order	NOUN
ejpam-6238	200	7	problems	problem	NOUN
ejpam-6238	200	8	:	:	PUNCT
ejpam-6238	200	9	extension	extension	NOUN
ejpam-6238	200	10	to	to	PART
ejpam-6238	200	11	conformable	conformable	VERB
ejpam-6238	200	12	fractional	fractional	ADJ
ejpam-6238	200	13	problems	problem	NOUN
ejpam-6238	200	14	of	of	ADP
ejpam-6238	200	15	order	order	NOUN
ejpam-6238	200	16	greater	great	ADJ
ejpam-6238	200	17	than	than	ADP
ejpam-6238	200	18	2	2	NUM
ejpam-6238	200	19	.	.	PUNCT
ejpam-6238	201	1	the	the	DET
ejpam-6238	201	2	framework	framework	NOUN
ejpam-6238	201	3	established	establish	VERB
ejpam-6238	201	4	here	here	ADV
ejpam-6238	201	5	provides	provide	VERB
ejpam-6238	201	6	a	a	DET
ejpam-6238	201	7	solid	solid	ADJ
ejpam-6238	201	8	foundation	foundation	NOUN
ejpam-6238	201	9	for	for	ADP
ejpam-6238	201	10	further	further	ADJ
ejpam-6238	201	11	research	research	NOUN
ejpam-6238	201	12	in	in	ADP
ejpam-6238	201	13	fractional	fractional	ADJ
ejpam-6238	201	14	differential	differential	ADJ
ejpam-6238	201	15	equations	equation	NOUN
ejpam-6238	201	16	and	and	CCONJ
ejpam-6238	201	17	their	their	PRON
ejpam-6238	201	18	applications	application	NOUN
ejpam-6238	201	19	to	to	ADP
ejpam-6238	201	20	real	real	ADJ
ejpam-6238	201	21	-	-	PUNCT
ejpam-6238	201	22	world	world	NOUN
ejpam-6238	201	23	phenomena	phenomenon	NOUN
ejpam-6238	201	24	exhibiting	exhibit	VERB
ejpam-6238	201	25	memory	memory	NOUN
ejpam-6238	201	26	effects	effect	NOUN
ejpam-6238	201	27	and	and	CCONJ
ejpam-6238	201	28	anomalous	anomalous	ADJ
ejpam-6238	201	29	behavior	behavior	NOUN
ejpam-6238	201	30	.	.	PUNCT
ejpam-6238	202	1	references	reference	NOUN
ejpam-6238	202	2	[	[	X
ejpam-6238	202	3	1	1	NUM
ejpam-6238	202	4	]	]	PUNCT
ejpam-6238	202	5	t.	t.	NOUN
ejpam-6238	202	6	abdeljawad	abdeljawad	NOUN
ejpam-6238	202	7	,	,	PUNCT
ejpam-6238	202	8	“	"	PUNCT
ejpam-6238	202	9	conformable	conformable	ADJ
ejpam-6238	202	10	fractional	fractional	ADJ
ejpam-6238	202	11	calculus	calculus	NOUN
ejpam-6238	202	12	,	,	PUNCT
ejpam-6238	202	13	”	"	PUNCT
ejpam-6238	202	14	journal	journal	NOUN
ejpam-6238	202	15	of	of	ADP
ejpam-6238	202	16	computational	computational	ADJ
ejpam-6238	202	17	and	and	CCONJ
ejpam-6238	202	18	applied	applied	ADJ
ejpam-6238	202	19	mathematics	mathematic	NOUN
ejpam-6238	202	20	,	,	PUNCT
ejpam-6238	202	21	vol	vol	NOUN
ejpam-6238	202	22	.	.	PROPN
ejpam-6238	202	23	279	279	NUM
ejpam-6238	202	24	,	,	PUNCT
ejpam-6238	202	25	pp	pp	ADJ
ejpam-6238	202	26	.	.	PUNCT
ejpam-6238	203	1	57–66	57–66	NUM
ejpam-6238	203	2	,	,	PUNCT
ejpam-6238	203	3	2015	2015	NUM
ejpam-6238	203	4	.	.	PUNCT
ejpam-6238	204	1	[	[	X
ejpam-6238	204	2	2	2	NUM
ejpam-6238	204	3	]	]	PUNCT
ejpam-6238	204	4	m.	m.	NOUN
ejpam-6238	204	5	abu	abu	PROPN
ejpam-6238	204	6	hammad	hammad	PROPN
ejpam-6238	204	7	and	and	CCONJ
ejpam-6238	204	8	r.	r.	PROPN
ejpam-6238	204	9	khalil	khalil	PROPN
ejpam-6238	204	10	,	,	PUNCT
ejpam-6238	204	11	“	"	PUNCT
ejpam-6238	204	12	systems	system	NOUN
ejpam-6238	204	13	of	of	ADP
ejpam-6238	204	14	linear	linear	ADJ
ejpam-6238	204	15	fractional	fractional	ADJ
ejpam-6238	204	16	differential	differential	NOUN
ejpam-6238	204	17	equations	equation	NOUN
ejpam-6238	204	18	,	,	PUNCT
ejpam-6238	204	19	”	"	PUNCT
ejpam-6238	204	20	asian	asian	ADJ
ejpam-6238	204	21	journal	journal	NOUN
ejpam-6238	204	22	of	of	ADP
ejpam-6238	204	23	mathematics	mathematics	PROPN
ejpam-6238	204	24	and	and	CCONJ
ejpam-6238	204	25	computer	computer	NOUN
ejpam-6238	204	26	research	research	NOUN
ejpam-6238	204	27	,	,	PUNCT
ejpam-6238	204	28	vol	vol	NOUN
ejpam-6238	204	29	.	.	PROPN
ejpam-6238	204	30	12	12	NUM
ejpam-6238	204	31	,	,	PUNCT
ejpam-6238	204	32	no	no	INTJ
ejpam-6238	204	33	.	.	NOUN
ejpam-6238	204	34	2	2	NUM
ejpam-6238	204	35	,	,	PUNCT
ejpam-6238	204	36	pp	pp	ADJ
ejpam-6238	204	37	.	.	PUNCT
ejpam-6238	205	1	120–126	120–126	NUM
ejpam-6238	205	2	,	,	PUNCT
ejpam-6238	205	3	2016	2016	NUM
ejpam-6238	205	4	.	.	PUNCT
ejpam-6238	206	1	[	[	X
ejpam-6238	206	2	3	3	X
ejpam-6238	206	3	]	]	PUNCT
ejpam-6238	206	4	m.	m.	NOUN
ejpam-6238	206	5	al	al	PROPN
ejpam-6238	206	6	horani	horani	PROPN
ejpam-6238	206	7	,	,	PUNCT
ejpam-6238	206	8	m.	m.	NOUN
ejpam-6238	206	9	fabrizio	fabrizio	PROPN
ejpam-6238	206	10	,	,	PUNCT
ejpam-6238	206	11	a.	a.	NOUN
ejpam-6238	206	12	favini	favini	PROPN
ejpam-6238	206	13	,	,	PUNCT
ejpam-6238	206	14	and	and	CCONJ
ejpam-6238	206	15	h.	h.	PROPN
ejpam-6238	206	16	tanabe	tanabe	PROPN
ejpam-6238	206	17	,	,	PUNCT
ejpam-6238	206	18	“	"	PUNCT
ejpam-6238	206	19	fractional	fractional	ADJ
ejpam-6238	206	20	cauchy	cauchy	NOUN
ejpam-6238	206	21	problems	problem	NOUN
ejpam-6238	206	22	for	for	ADP
ejpam-6238	206	23	infinite	infinite	ADJ
ejpam-6238	206	24	interval	interval	NOUN
ejpam-6238	206	25	case	case	NOUN
ejpam-6238	206	26	,	,	PUNCT
ejpam-6238	206	27	”	"	PUNCT
ejpam-6238	206	28	discrete	discrete	ADJ
ejpam-6238	206	29	and	and	CCONJ
ejpam-6238	206	30	continuous	continuous	ADJ
ejpam-6238	206	31	dynamical	dynamical	ADJ
ejpam-6238	206	32	systems	system	NOUN
ejpam-6238	206	33	s	s	NOUN
ejpam-6238	206	34	,	,	PUNCT
ejpam-6238	206	35	vol	vol	NOUN
ejpam-6238	206	36	.	.	PROPN
ejpam-6238	207	1	3	3	NUM
ejpam-6238	207	2	,	,	PUNCT
ejpam-6238	207	3	no	no	INTJ
ejpam-6238	207	4	.	.	NOUN
ejpam-6238	207	5	12	12	NUM
ejpam-6238	207	6	,	,	PUNCT
ejpam-6238	207	7	pp	pp	ADJ
ejpam-6238	207	8	.	.	PUNCT
ejpam-6238	208	1	32–85	32–85	NUM
ejpam-6238	208	2	,	,	PUNCT
ejpam-6238	208	3	2020	2020	NUM
ejpam-6238	208	4	.	.	PUNCT
ejpam-6238	209	1	[	[	X
ejpam-6238	209	2	4	4	X
ejpam-6238	209	3	]	]	PUNCT
ejpam-6238	209	4	w.	w.	PROPN
ejpam-6238	209	5	deeb	deeb	PROPN
ejpam-6238	209	6	and	and	CCONJ
ejpam-6238	209	7	r.	r.	PROPN
ejpam-6238	209	8	khalil	khalil	PROPN
ejpam-6238	209	9	,	,	PUNCT
ejpam-6238	209	10	“	"	PUNCT
ejpam-6238	209	11	best	good	ADJ
ejpam-6238	209	12	approximation	approximation	NOUN
ejpam-6238	209	13	in	in	ADP
ejpam-6238	209	14	l(x	l(x	PROPN
ejpam-6238	209	15	,	,	PUNCT
ejpam-6238	209	16	y	y	PROPN
ejpam-6238	209	17	)	)	PUNCT
ejpam-6238	209	18	,	,	PUNCT
ejpam-6238	209	19	”	"	PUNCT
ejpam-6238	209	20	mathematical	mathematical	ADJ
ejpam-6238	209	21	proceedings	proceeding	NOUN
ejpam-6238	209	22	of	of	ADP
ejpam-6238	209	23	the	the	DET
ejpam-6238	209	24	cambridge	cambridge	PROPN
ejpam-6238	209	25	philosophical	philosophical	ADJ
ejpam-6238	209	26	society	society	NOUN
ejpam-6238	209	27	,	,	PUNCT
ejpam-6238	209	28	vol	vol	NOUN
ejpam-6238	209	29	.	.	PROPN
ejpam-6238	209	30	104	104	NUM
ejpam-6238	209	31	,	,	PUNCT
ejpam-6238	209	32	pp	pp	ADJ
ejpam-6238	209	33	.	.	PUNCT
ejpam-6238	210	1	527–531	527–531	NUM
ejpam-6238	210	2	,	,	PUNCT
ejpam-6238	210	3	1988	1988	NUM
ejpam-6238	210	4	.	.	PUNCT
ejpam-6238	211	1	[	[	X
ejpam-6238	211	2	5	5	NUM
ejpam-6238	211	3	]	]	PUNCT
ejpam-6238	211	4	a.	a.	NOUN
ejpam-6238	211	5	favini	favini	NOUN
ejpam-6238	211	6	and	and	CCONJ
ejpam-6238	211	7	a.	a.	NOUN
ejpam-6238	211	8	yagi	yagi	NOUN
ejpam-6238	211	9	,	,	PUNCT
ejpam-6238	211	10	degenerate	degenerate	ADJ
ejpam-6238	211	11	differential	differential	ADJ
ejpam-6238	211	12	equations	equation	NOUN
ejpam-6238	211	13	in	in	ADP
ejpam-6238	211	14	banach	banach	NOUN
ejpam-6238	211	15	spaces	space	NOUN
ejpam-6238	211	16	,	,	PUNCT
ejpam-6238	211	17	new	new	PROPN
ejpam-6238	211	18	york	york	PROPN
ejpam-6238	211	19	:	:	PUNCT
ejpam-6238	211	20	dekker	dekker	NOUN
ejpam-6238	211	21	,	,	PUNCT
ejpam-6238	211	22	1999	1999	NUM
ejpam-6238	211	23	.	.	PUNCT
ejpam-6238	212	1	[	[	X
ejpam-6238	212	2	6	6	NUM
ejpam-6238	212	3	]	]	PUNCT
ejpam-6238	212	4	r.	r.	PROPN
ejpam-6238	212	5	khalil	khalil	PROPN
ejpam-6238	212	6	,	,	PUNCT
ejpam-6238	212	7	“	"	PUNCT
ejpam-6238	212	8	isometries	isometry	NOUN
ejpam-6238	212	9	on	on	ADP
ejpam-6238	212	10	lp	lp	PROPN
ejpam-6238	212	11	⊗	⊗	PROPN
ejpam-6238	212	12	lp	lp	NOUN
ejpam-6238	212	13	,	,	PUNCT
ejpam-6238	212	14	”	"	PUNCT
ejpam-6238	212	15	tamkang	tamkang	PROPN
ejpam-6238	212	16	journal	journal	PROPN
ejpam-6238	212	17	of	of	ADP
ejpam-6238	212	18	mathematics	mathematics	PROPN
ejpam-6238	212	19	,	,	PUNCT
ejpam-6238	212	20	vol	vol	NOUN
ejpam-6238	212	21	.	.	PROPN
ejpam-6238	213	1	16	16	NUM
ejpam-6238	213	2	,	,	PUNCT
ejpam-6238	213	3	no	no	INTJ
ejpam-6238	213	4	.	.	NOUN
ejpam-6238	213	5	2	2	NUM
ejpam-6238	213	6	,	,	PUNCT
ejpam-6238	213	7	pp	pp	ADJ
ejpam-6238	213	8	.	.	PUNCT
ejpam-6238	214	1	77–85	77–85	NUM
ejpam-6238	214	2	,	,	PUNCT
ejpam-6238	214	3	1985	1985	NUM
ejpam-6238	214	4	.	.	PUNCT
ejpam-6238	215	1	[	[	X
ejpam-6238	215	2	7	7	X
ejpam-6238	215	3	]	]	X
ejpam-6238	215	4	r.	r.	PROPN
ejpam-6238	215	5	khalil	khalil	PROPN
ejpam-6238	215	6	,	,	PUNCT
ejpam-6238	215	7	“	"	PUNCT
ejpam-6238	215	8	best	good	ADJ
ejpam-6238	215	9	approximation	approximation	NOUN
ejpam-6238	215	10	in	in	ADP
ejpam-6238	215	11	tensor	tensor	NOUN
ejpam-6238	215	12	products	product	NOUN
ejpam-6238	215	13	,	,	PUNCT
ejpam-6238	215	14	”	"	PUNCT
ejpam-6238	215	15	numerical	numerical	ADJ
ejpam-6238	215	16	functional	functional	ADJ
ejpam-6238	215	17	analysis	analysis	NOUN
ejpam-6238	215	18	and	and	CCONJ
ejpam-6238	215	19	optimization	optimization	NOUN
ejpam-6238	215	20	,	,	PUNCT
ejpam-6238	215	21	vol	vol	NOUN
ejpam-6238	215	22	.	.	PROPN
ejpam-6238	215	23	8	8	NUM
ejpam-6238	215	24	,	,	PUNCT
ejpam-6238	215	25	pp	pp	ADJ
ejpam-6238	215	26	.	.	PUNCT
ejpam-6238	216	1	347–356	347–356	NUM
ejpam-6238	216	2	,	,	PUNCT
ejpam-6238	216	3	1986	1986	NUM
ejpam-6238	216	4	.	.	PUNCT
ejpam-6238	217	1	[	[	X
ejpam-6238	217	2	8	8	NUM
ejpam-6238	217	3	]	]	X
ejpam-6238	217	4	r.	r.	PROPN
ejpam-6238	217	5	khalil	khalil	PROPN
ejpam-6238	217	6	and	and	CCONJ
ejpam-6238	217	7	l.	l.	PROPN
ejpam-6238	217	8	abdullah	abdullah	PROPN
ejpam-6238	217	9	,	,	PUNCT
ejpam-6238	217	10	“	"	PUNCT
ejpam-6238	217	11	atomic	atomic	ADJ
ejpam-6238	217	12	solution	solution	NOUN
ejpam-6238	217	13	of	of	ADP
ejpam-6238	217	14	certain	certain	ADJ
ejpam-6238	217	15	inverse	inverse	NOUN
ejpam-6238	217	16	problems	problem	NOUN
ejpam-6238	217	17	,	,	PUNCT
ejpam-6238	217	18	”	"	PUNCT
ejpam-6238	217	19	european	european	ADJ
ejpam-6238	217	20	journal	journal	PROPN
ejpam-6238	217	21	of	of	ADP
ejpam-6238	217	22	pure	pure	ADJ
ejpam-6238	217	23	and	and	CCONJ
ejpam-6238	217	24	applied	applied	ADJ
ejpam-6238	217	25	mathematics	mathematic	NOUN
ejpam-6238	217	26	,	,	PUNCT
ejpam-6238	217	27	vol	vol	NOUN
ejpam-6238	217	28	.	.	PROPN
ejpam-6238	218	1	3	3	NUM
ejpam-6238	218	2	,	,	PUNCT
ejpam-6238	218	3	no	no	INTJ
ejpam-6238	218	4	.	.	NOUN
ejpam-6238	218	5	4	4	NUM
ejpam-6238	218	6	,	,	PUNCT
ejpam-6238	218	7	pp	pp	ADJ
ejpam-6238	218	8	.	.	PUNCT
ejpam-6238	219	1	725–729	725–729	NUM
ejpam-6238	219	2	,	,	PUNCT
ejpam-6238	219	3	2010	2010	NUM
ejpam-6238	219	4	.	.	PUNCT
ejpam-6238	220	1	[	[	X
ejpam-6238	220	2	9	9	NUM
ejpam-6238	220	3	]	]	PUNCT
ejpam-6238	220	4	r.	r.	PROPN
ejpam-6238	220	5	khalil	khalil	PROPN
ejpam-6238	220	6	,	,	PUNCT
ejpam-6238	220	7	m.	m.	PROPN
ejpam-6238	220	8	al	al	PROPN
ejpam-6238	220	9	horani	horani	PROPN
ejpam-6238	220	10	,	,	PUNCT
ejpam-6238	220	11	and	and	CCONJ
ejpam-6238	220	12	m.	m.	PROPN
ejpam-6238	220	13	abu	abu	PROPN
ejpam-6238	220	14	hammad	hammad	PROPN
ejpam-6238	220	15	,	,	PUNCT
ejpam-6238	220	16	“	"	PUNCT
ejpam-6238	220	17	geometric	geometric	ADJ
ejpam-6238	220	18	meaning	meaning	NOUN
ejpam-6238	220	19	of	of	ADP
ejpam-6238	220	20	conformable	conformable	ADJ
ejpam-6238	220	21	derivative	derivative	NOUN
ejpam-6238	220	22	via	via	ADP
ejpam-6238	220	23	fractional	fractional	ADJ
ejpam-6238	220	24	cords	cord	NOUN
ejpam-6238	220	25	,	,	PUNCT
ejpam-6238	220	26	”	"	PUNCT
ejpam-6238	220	27	journal	journal	NOUN
ejpam-6238	220	28	of	of	ADP
ejpam-6238	220	29	mathematics	mathematic	NOUN
ejpam-6238	220	30	and	and	CCONJ
ejpam-6238	220	31	computer	computer	NOUN
ejpam-6238	220	32	science	science	NOUN
ejpam-6238	220	33	,	,	PUNCT
ejpam-6238	220	34	vol	vol	NOUN
ejpam-6238	220	35	.	.	PROPN
ejpam-6238	220	36	19	19	NUM
ejpam-6238	220	37	,	,	PUNCT
ejpam-6238	220	38	pp	pp	ADJ
ejpam-6238	220	39	.	.	PUNCT
ejpam-6238	221	1	241–245	241–245	NUM
ejpam-6238	221	2	,	,	PUNCT
ejpam-6238	221	3	2019	2019	NUM
ejpam-6238	221	4	.	.	PUNCT
ejpam-6238	222	1	[	[	X
ejpam-6238	222	2	10	10	NUM
ejpam-6238	222	3	]	]	X
ejpam-6238	222	4	r.	r.	PROPN
ejpam-6238	222	5	khalil	khalil	PROPN
ejpam-6238	222	6	,	,	PUNCT
ejpam-6238	222	7	m.	m.	PROPN
ejpam-6238	222	8	al	al	PROPN
ejpam-6238	222	9	horani	horani	PROPN
ejpam-6238	222	10	,	,	PUNCT
ejpam-6238	222	11	a.	a.	NOUN
ejpam-6238	222	12	yousef	yousef	PROPN
ejpam-6238	222	13	,	,	PUNCT
ejpam-6238	222	14	and	and	CCONJ
ejpam-6238	222	15	m.	m.	NOUN
ejpam-6238	222	16	sababheh	sababheh	NOUN
ejpam-6238	222	17	,	,	PUNCT
ejpam-6238	222	18	“	"	PUNCT
ejpam-6238	222	19	a	a	DET
ejpam-6238	222	20	new	new	ADJ
ejpam-6238	222	21	definition	definition	NOUN
ejpam-6238	222	22	of	of	ADP
ejpam-6238	222	23	fractional	fractional	ADJ
ejpam-6238	222	24	derivative	derivative	ADJ
ejpam-6238	222	25	,	,	PUNCT
ejpam-6238	222	26	”	"	PUNCT
ejpam-6238	222	27	journal	journal	NOUN
ejpam-6238	222	28	of	of	ADP
ejpam-6238	222	29	computational	computational	ADJ
ejpam-6238	222	30	and	and	CCONJ
ejpam-6238	222	31	applied	applied	ADJ
ejpam-6238	222	32	mathematics	mathematic	NOUN
ejpam-6238	222	33	,	,	PUNCT
ejpam-6238	222	34	vol	vol	NOUN
ejpam-6238	222	35	.	.	PROPN
ejpam-6238	222	36	264	264	NUM
ejpam-6238	222	37	,	,	PUNCT
ejpam-6238	222	38	pp	pp	ADJ
ejpam-6238	222	39	.	.	PUNCT
ejpam-6238	223	1	65–70	65–70	NUM
ejpam-6238	223	2	,	,	PUNCT
ejpam-6238	223	3	2014	2014	NUM
ejpam-6238	223	4	.	.	PUNCT
ejpam-6238	224	1	[	[	X
ejpam-6238	224	2	11	11	NUM
ejpam-6238	224	3	]	]	PUNCT
ejpam-6238	224	4	r.	r.	PROPN
ejpam-6238	224	5	khalil	khalil	PROPN
ejpam-6238	224	6	,	,	PUNCT
ejpam-6238	224	7	s.	s.	PROPN
ejpam-6238	224	8	alsharif	alsharif	PROPN
ejpam-6238	224	9	,	,	PUNCT
ejpam-6238	224	10	and	and	CCONJ
ejpam-6238	224	11	s.	s.	PROPN
ejpam-6238	224	12	khamis	khamis	PROPN
ejpam-6238	224	13	,	,	PUNCT
ejpam-6238	224	14	“	"	PUNCT
ejpam-6238	224	15	second	second	ADJ
ejpam-6238	224	16	-	-	PUNCT
ejpam-6238	224	17	order	order	NOUN
ejpam-6238	224	18	abstract	abstract	ADJ
ejpam-6238	224	19	cauchy	cauchy	ADJ
ejpam-6238	224	20	problem	problem	NOUN
ejpam-6238	224	21	of	of	ADP
ejpam-6238	224	22	conformable	conformable	ADJ
ejpam-6238	224	23	fractional	fractional	ADJ
ejpam-6238	224	24	type	type	NOUN
ejpam-6238	224	25	,	,	PUNCT
ejpam-6238	224	26	”	"	PUNCT
ejpam-6238	224	27	international	international	ADJ
ejpam-6238	224	28	journal	journal	NOUN
ejpam-6238	224	29	of	of	ADP
ejpam-6238	224	30	nonlinear	nonlinear	ADJ
ejpam-6238	224	31	analysis	analysis	NOUN
ejpam-6238	224	32	and	and	CCONJ
ejpam-6238	224	33	applications	application	NOUN
ejpam-6238	224	34	,	,	PUNCT
ejpam-6238	224	35	vol	vol	NOUN
ejpam-6238	224	36	.	.	PROPN
ejpam-6238	224	37	13	13	NUM
ejpam-6238	224	38	,	,	PUNCT
ejpam-6238	224	39	no	no	INTJ
ejpam-6238	224	40	.	.	NOUN
ejpam-6238	224	41	2	2	NUM
ejpam-6238	224	42	,	,	PUNCT
ejpam-6238	224	43	pp	pp	ADJ
ejpam-6238	224	44	.	.	PUNCT
ejpam-6238	224	45	1143–1150	1143–1150	NUM
ejpam-6238	224	46	,	,	PUNCT
ejpam-6238	224	47	2022	2022	NUM
ejpam-6238	224	48	.	.	PUNCT
ejpam-6238	225	1	[	[	X
ejpam-6238	225	2	12	12	NUM
ejpam-6238	225	3	]	]	PUNCT
ejpam-6238	225	4	a.	a.	NOUN
ejpam-6238	225	5	kilbas	kilbas	PROPN
ejpam-6238	225	6	,	,	PUNCT
ejpam-6238	225	7	h.	h.	PROPN
ejpam-6238	225	8	srivastava	srivastava	PROPN
ejpam-6238	225	9	,	,	PUNCT
ejpam-6238	225	10	and	and	CCONJ
ejpam-6238	225	11	j.	j.	PROPN
ejpam-6238	225	12	trujillo	trujillo	PROPN
ejpam-6238	225	13	,	,	PUNCT
ejpam-6238	225	14	theory	theory	NOUN
ejpam-6238	225	15	and	and	CCONJ
ejpam-6238	225	16	applications	application	NOUN
ejpam-6238	225	17	of	of	ADP
ejpam-6238	225	18	fractional	fractional	ADJ
ejpam-6238	225	19	differential	differential	ADJ
ejpam-6238	225	20	equations	equation	NOUN
ejpam-6238	225	21	,	,	PUNCT
ejpam-6238	225	22	new	new	PROPN
ejpam-6238	225	23	york	york	PROPN
ejpam-6238	225	24	:	:	PUNCT
ejpam-6238	225	25	north	north	PROPN
ejpam-6238	225	26	-	-	PUNCT
ejpam-6238	225	27	holland	holland	PROPN
ejpam-6238	225	28	,	,	PUNCT
ejpam-6238	225	29	2006	2006	NUM
ejpam-6238	225	30	.	.	PUNCT
ejpam-6238	226	1	h.	h.	PROPN
ejpam-6238	226	2	odetallah	odetallah	PROPN
ejpam-6238	226	3	et	et	PROPN
ejpam-6238	226	4	al	al	PROPN
ejpam-6238	226	5	.	.	PUNCT
ejpam-6238	226	6	/	/	SYM
ejpam-6238	226	7	eur	eur	PROPN
ejpam-6238	226	8	.	.	PUNCT
ejpam-6238	227	1	j.	j.	PROPN
ejpam-6238	227	2	pure	pure	PROPN
ejpam-6238	227	3	appl	appl	PROPN
ejpam-6238	227	4	.	.	PROPN
ejpam-6238	227	5	math	math	PROPN
ejpam-6238	227	6	,	,	PUNCT
ejpam-6238	227	7	18	18	NUM
ejpam-6238	227	8	(	(	PUNCT
ejpam-6238	227	9	3	3	NUM
ejpam-6238	227	10	)	)	PUNCT
ejpam-6238	227	11	(	(	PUNCT
ejpam-6238	227	12	2025	2025	NUM
ejpam-6238	227	13	)	)	PUNCT
ejpam-6238	227	14	,	,	PUNCT
ejpam-6238	227	15	6238	6238	NUM
ejpam-6238	227	16	11	11	NUM
ejpam-6238	227	17	of	of	ADP
ejpam-6238	227	18	11	11	NUM
ejpam-6238	227	19	[	[	SYM
ejpam-6238	227	20	13	13	NUM
ejpam-6238	227	21	]	]	PUNCT
ejpam-6238	227	22	w.	w.	PROPN
ejpam-6238	227	23	a.	a.	NOUN
ejpam-6238	227	24	light	light	PROPN
ejpam-6238	227	25	and	and	CCONJ
ejpam-6238	227	26	e.	e.	PROPN
ejpam-6238	227	27	w.	w.	PROPN
ejpam-6238	227	28	cheney	cheney	PROPN
ejpam-6238	227	29	,	,	PUNCT
ejpam-6238	227	30	approximation	approximation	NOUN
ejpam-6238	227	31	theory	theory	NOUN
ejpam-6238	227	32	in	in	ADP
ejpam-6238	227	33	tensor	tensor	NOUN
ejpam-6238	227	34	product	product	NOUN
ejpam-6238	227	35	spaces	space	NOUN
ejpam-6238	227	36	,	,	PUNCT
ejpam-6238	227	37	lecture	lecture	NOUN
ejpam-6238	227	38	notes	note	NOUN
ejpam-6238	227	39	in	in	ADP
ejpam-6238	227	40	mathematics	mathematic	NOUN
ejpam-6238	227	41	,	,	PUNCT
ejpam-6238	227	42	vol	vol	NOUN
ejpam-6238	227	43	.	.	PROPN
ejpam-6238	227	44	1169	1169	NUM
ejpam-6238	227	45	,	,	PUNCT
ejpam-6238	227	46	new	new	PROPN
ejpam-6238	227	47	york	york	PROPN
ejpam-6238	227	48	:	:	PUNCT
ejpam-6238	227	49	springer	springer	NOUN
ejpam-6238	227	50	-	-	PUNCT
ejpam-6238	227	51	verlag	verlag	PROPN
ejpam-6238	227	52	,	,	PUNCT
ejpam-6238	227	53	1985	1985	NUM
ejpam-6238	227	54	.	.	PUNCT
ejpam-6238	228	1	[	[	X
ejpam-6238	228	2	14	14	NUM
ejpam-6238	228	3	]	]	X
ejpam-6238	228	4	h.	h.	PROPN
ejpam-6238	228	5	odetallah	odetallah	PROPN
ejpam-6238	228	6	and	and	CCONJ
ejpam-6238	228	7	r.	r.	PROPN
ejpam-6238	228	8	khalil	khalil	PROPN
ejpam-6238	228	9	,	,	PUNCT
ejpam-6238	228	10	“	"	PUNCT
ejpam-6238	228	11	two	two	NUM
ejpam-6238	228	12	rank	rank	NOUN
ejpam-6238	228	13	solution	solution	NOUN
ejpam-6238	228	14	of	of	ADP
ejpam-6238	228	15	the	the	DET
ejpam-6238	228	16	abstract	abstract	ADJ
ejpam-6238	228	17	cauchy	cauchy	PROPN
ejpam-6238	228	18	problem	problem	NOUN
ejpam-6238	228	19	,	,	PUNCT
ejpam-6238	228	20	”	"	PUNCT
ejpam-6238	228	21	journal	journal	NOUN
ejpam-6238	228	22	of	of	ADP
ejpam-6238	228	23	semigroup	semigroup	PROPN
ejpam-6238	228	24	theory	theory	NOUN
ejpam-6238	228	25	and	and	CCONJ
ejpam-6238	228	26	applications	application	NOUN
ejpam-6238	228	27	,	,	PUNCT
ejpam-6238	228	28	2014	2014	NUM
ejpam-6238	228	29	,	,	PUNCT
ejpam-6238	228	30	article	article	NOUN
ejpam-6238	228	31	i	i	PROPN
ejpam-6238	228	32	d	d	PROPN
ejpam-6238	228	33	8	8	NUM
ejpam-6238	228	34	.	.	PUNCT
ejpam-6238	229	1	[	[	X
ejpam-6238	229	2	15	15	NUM
ejpam-6238	229	3	]	]	X
ejpam-6238	229	4	i.	i.	NOUN
ejpam-6238	229	5	podlubny	podlubny	PROPN
ejpam-6238	229	6	,	,	PUNCT
ejpam-6238	229	7	fractional	fractional	ADJ
ejpam-6238	229	8	differential	differential	NOUN
ejpam-6238	229	9	equations	equation	NOUN
ejpam-6238	229	10	,	,	PUNCT
ejpam-6238	229	11	san	san	PROPN
ejpam-6238	229	12	diego	diego	PROPN
ejpam-6238	229	13	:	:	PUNCT
ejpam-6238	229	14	academic	academic	ADJ
ejpam-6238	229	15	press	press	NOUN
ejpam-6238	229	16	,	,	PUNCT
ejpam-6238	229	17	1999	1999	NUM
ejpam-6238	229	18	.	.	PUNCT
ejpam-6238	230	1	[	[	X
ejpam-6238	230	2	16	16	NUM
ejpam-6238	230	3	]	]	X
ejpam-6238	230	4	r.	r.	PROPN
ejpam-6238	230	5	ryan	ryan	PROPN
ejpam-6238	230	6	,	,	PUNCT
ejpam-6238	230	7	introduction	introduction	NOUN
ejpam-6238	230	8	to	to	ADP
ejpam-6238	230	9	tensor	tensor	NOUN
ejpam-6238	230	10	products	product	NOUN
ejpam-6238	230	11	of	of	ADP
ejpam-6238	230	12	banach	banach	NOUN
ejpam-6238	230	13	spaces	space	NOUN
ejpam-6238	230	14	,	,	PUNCT
ejpam-6238	230	15	2nd	2nd	ADJ
ejpam-6238	230	16	ed	ed	NOUN
ejpam-6238	230	17	.	.	PROPN
ejpam-6238	230	18	,	,	PUNCT
ejpam-6238	230	19	new	new	PROPN
ejpam-6238	230	20	york	york	PROPN
ejpam-6238	230	21	:	:	PUNCT
ejpam-6238	230	22	springer	springer	NOUN
ejpam-6238	230	23	,	,	PUNCT
ejpam-6238	230	24	2002	2002	NUM
ejpam-6238	230	25	.	.	PUNCT
ejpam-6238	231	1	[	[	X
ejpam-6238	231	2	17	17	NUM
ejpam-6238	231	3	]	]	X
ejpam-6238	231	4	f.	f.	PROPN
ejpam-6238	231	5	seddiki	seddiki	PROPN
ejpam-6238	231	6	,	,	PUNCT
ejpam-6238	231	7	m.	m.	NOUN
ejpam-6238	231	8	al	al	PROPN
ejpam-6238	231	9	horani	horani	PROPN
ejpam-6238	231	10	,	,	PUNCT
ejpam-6238	231	11	and	and	CCONJ
ejpam-6238	231	12	r.	r.	PROPN
ejpam-6238	231	13	khalil	khalil	PROPN
ejpam-6238	231	14	,	,	PUNCT
ejpam-6238	231	15	“	"	PUNCT
ejpam-6238	231	16	finite	finite	VERB
ejpam-6238	231	17	rank	rank	NOUN
ejpam-6238	231	18	solution	solution	NOUN
ejpam-6238	231	19	for	for	ADP
ejpam-6238	231	20	conformable	conformable	ADJ
ejpam-6238	231	21	degenerate	degenerate	ADJ
ejpam-6238	231	22	first	first	ADJ
ejpam-6238	231	23	order	order	NOUN
ejpam-6238	231	24	abstract	abstract	ADJ
ejpam-6238	231	25	cauchy	cauchy	ADJ
ejpam-6238	231	26	problem	problem	NOUN
ejpam-6238	231	27	in	in	ADP
ejpam-6238	231	28	hilbert	hilbert	NOUN
ejpam-6238	231	29	space	space	NOUN
ejpam-6238	231	30	,	,	PUNCT
ejpam-6238	231	31	”	"	PUNCT
ejpam-6238	231	32	european	european	PROPN
ejpam-6238	231	33	journal	journal	PROPN
ejpam-6238	231	34	of	of	ADP
ejpam-6238	231	35	pure	pure	ADJ
ejpam-6238	231	36	and	and	CCONJ
ejpam-6238	231	37	applied	applied	ADJ
ejpam-6238	231	38	mathematics	mathematic	NOUN
ejpam-6238	231	39	,	,	PUNCT
ejpam-6238	231	40	vol	vol	NOUN
ejpam-6238	231	41	.	.	PROPN
ejpam-6238	231	42	14	14	NUM
ejpam-6238	231	43	,	,	PUNCT
ejpam-6238	231	44	no	no	INTJ
ejpam-6238	231	45	.	.	NOUN
ejpam-6238	231	46	2	2	NUM
ejpam-6238	231	47	,	,	PUNCT
ejpam-6238	231	48	pp	pp	ADJ
ejpam-6238	231	49	.	.	PUNCT
ejpam-6238	232	1	493–505	493–505	NUM
ejpam-6238	232	2	,	,	PUNCT
ejpam-6238	232	3	2021	2021	NUM
ejpam-6238	232	4	.	.	PUNCT
ejpam-6238	233	1	[	[	X
ejpam-6238	233	2	18	18	NUM
ejpam-6238	233	3	]	]	X
ejpam-6238	233	4	f.	f.	PROPN
ejpam-6238	233	5	seddiki	seddiki	PROPN
ejpam-6238	233	6	,	,	PUNCT
ejpam-6238	233	7	m.	m.	NOUN
ejpam-6238	233	8	al	al	PROPN
ejpam-6238	233	9	horani	horani	PROPN
ejpam-6238	233	10	,	,	PUNCT
ejpam-6238	233	11	and	and	CCONJ
ejpam-6238	233	12	r.	r.	PROPN
ejpam-6238	233	13	khalil	khalil	PROPN
ejpam-6238	233	14	,	,	PUNCT
ejpam-6238	233	15	“	"	PUNCT
ejpam-6238	233	16	tensor	tensor	NOUN
ejpam-6238	233	17	product	product	NOUN
ejpam-6238	233	18	and	and	CCONJ
ejpam-6238	233	19	inverse	inverse	NOUN
ejpam-6238	233	20	fractional	fractional	ADJ
ejpam-6238	233	21	abstract	abstract	ADJ
ejpam-6238	233	22	cauchy	cauchy	PROPN
ejpam-6238	233	23	problem	problem	NOUN
ejpam-6238	233	24	,	,	PUNCT
ejpam-6238	233	25	”	"	PUNCT
ejpam-6238	233	26	rendiconti	rendiconti	ADJ
ejpam-6238	233	27	del	del	PROPN
ejpam-6238	233	28	circolo	circolo	PROPN
ejpam-6238	233	29	matematico	matematico	NOUN
ejpam-6238	233	30	di	di	PROPN
ejpam-6238	233	31	palermo	palermo	PROPN
ejpam-6238	233	32	series	series	PROPN
ejpam-6238	233	33	2	2	NUM
ejpam-6238	233	34	,	,	PUNCT
ejpam-6238	233	35	vol	vol	NOUN
ejpam-6238	233	36	.	.	PROPN
ejpam-6238	233	37	72	72	NUM
ejpam-6238	233	38	,	,	PUNCT
ejpam-6238	233	39	pp	pp	ADJ
ejpam-6238	233	40	.	.	PUNCT
ejpam-6238	234	1	2321–2332	2321–2332	NUM
ejpam-6238	234	2	,	,	PUNCT
ejpam-6238	234	3	2023	2023	NUM
ejpam-6238	234	4	.	.	PUNCT
ejpam-6238	235	1	[	[	X
ejpam-6238	235	2	19	19	NUM
ejpam-6238	235	3	]	]	X
ejpam-6238	235	4	f.	f.	PROPN
ejpam-6238	235	5	seddiki	seddiki	PROPN
ejpam-6238	235	6	,	,	PUNCT
ejpam-6238	235	7	m.	m.	NOUN
ejpam-6238	235	8	al	al	PROPN
ejpam-6238	235	9	horani	horani	PROPN
ejpam-6238	235	10	,	,	PUNCT
ejpam-6238	235	11	and	and	CCONJ
ejpam-6238	235	12	r.	r.	PROPN
ejpam-6238	235	13	khalil	khalil	PROPN
ejpam-6238	235	14	,	,	PUNCT
ejpam-6238	235	15	“	"	PUNCT
ejpam-6238	235	16	infinite	infinite	ADJ
ejpam-6238	235	17	rank	rank	NOUN
ejpam-6238	235	18	solution	solution	NOUN
ejpam-6238	235	19	for	for	ADP
ejpam-6238	235	20	conformable	conformable	ADJ
ejpam-6238	235	21	degenerate	degenerate	ADJ
ejpam-6238	235	22	abstract	abstract	ADJ
ejpam-6238	235	23	cauchy	cauchy	ADJ
ejpam-6238	235	24	problem	problem	NOUN
ejpam-6238	235	25	in	in	ADP
ejpam-6238	235	26	hilbert	hilbert	PROPN
ejpam-6238	235	27	spaces	space	NOUN
ejpam-6238	235	28	,	,	PUNCT
ejpam-6238	235	29	”	"	PUNCT
ejpam-6238	235	30	journal	journal	NOUN
ejpam-6238	235	31	of	of	ADP
ejpam-6238	235	32	mathematics	mathematic	NOUN
ejpam-6238	235	33	and	and	CCONJ
ejpam-6238	235	34	computer	computer	NOUN
ejpam-6238	235	35	science	science	NOUN
ejpam-6238	235	36	,	,	PUNCT
ejpam-6238	235	37	vol	vol	NOUN
ejpam-6238	235	38	.	.	PROPN
ejpam-6238	235	39	31	31	NUM
ejpam-6238	235	40	,	,	PUNCT
ejpam-6238	235	41	pp	pp	ADJ
ejpam-6238	235	42	.	.	PUNCT
ejpam-6238	236	1	150–161	150–161	NUM
ejpam-6238	236	2	,	,	PUNCT
ejpam-6238	236	3	2023	2023	NUM
ejpam-6238	236	4	.	.	PUNCT
ejpam-6238	237	1	[	[	X
ejpam-6238	237	2	20	20	NUM
ejpam-6238	237	3	]	]	PUNCT
ejpam-6238	237	4	b.	b.	NOUN
ejpam-6238	237	5	thaller	thaller	NOUN
ejpam-6238	237	6	and	and	CCONJ
ejpam-6238	237	7	s.	s.	PROPN
ejpam-6238	237	8	thaller	thaller	NOUN
ejpam-6238	237	9	,	,	PUNCT
ejpam-6238	237	10	“	"	PUNCT
ejpam-6238	237	11	factorization	factorization	NOUN
ejpam-6238	237	12	of	of	ADP
ejpam-6238	237	13	degenerate	degenerate	ADJ
ejpam-6238	237	14	cauchy	cauchy	PROPN
ejpam-6238	237	15	problem	problem	NOUN
ejpam-6238	237	16	,	,	PUNCT
ejpam-6238	237	17	the	the	DET
ejpam-6238	237	18	linear	linear	ADJ
ejpam-6238	237	19	case	case	NOUN
ejpam-6238	237	20	,	,	PUNCT
ejpam-6238	237	21	”	"	PUNCT
ejpam-6238	237	22	journal	journal	NOUN
ejpam-6238	237	23	of	of	ADP
ejpam-6238	237	24	operator	operator	NOUN
ejpam-6238	237	25	theory	theory	NOUN
ejpam-6238	237	26	,	,	PUNCT
ejpam-6238	237	27	vol	vol	NOUN
ejpam-6238	237	28	.	.	PROPN
ejpam-6238	237	29	36	36	NUM
ejpam-6238	237	30	,	,	PUNCT
ejpam-6238	237	31	pp	pp	ADJ
ejpam-6238	237	32	.	.	PUNCT
ejpam-6238	238	1	121–146	121–146	NUM
ejpam-6238	238	2	,	,	PUNCT
ejpam-6238	238	3	1996	1996	NUM
ejpam-6238	238	4	.	.	PUNCT
ejpam-6238	239	1	[	[	X
ejpam-6238	239	2	21	21	NUM
ejpam-6238	239	3	]	]	PUNCT
ejpam-6238	239	4	a.	a.	NOUN
ejpam-6238	239	5	ziqan	ziqan	PROPN
ejpam-6238	239	6	,	,	PUNCT
ejpam-6238	239	7	m.	m.	PROPN
ejpam-6238	239	8	al	al	PROPN
ejpam-6238	239	9	horani	horani	PROPN
ejpam-6238	239	10	,	,	PUNCT
ejpam-6238	239	11	and	and	CCONJ
ejpam-6238	239	12	r.	r.	PROPN
ejpam-6238	239	13	khalil	khalil	PROPN
ejpam-6238	239	14	,	,	PUNCT
ejpam-6238	239	15	“	"	PUNCT
ejpam-6238	239	16	tensor	tensor	NOUN
ejpam-6238	239	17	product	product	NOUN
ejpam-6238	239	18	technique	technique	NOUN
ejpam-6238	239	19	and	and	CCONJ
ejpam-6238	239	20	the	the	DET
ejpam-6238	239	21	degenerate	degenerate	ADJ
ejpam-6238	239	22	homogeneous	homogeneous	ADJ
ejpam-6238	239	23	abstract	abstract	ADJ
ejpam-6238	239	24	cauchy	cauchy	PROPN
ejpam-6238	239	25	problem	problem	NOUN
ejpam-6238	239	26	,	,	PUNCT
ejpam-6238	239	27	”	"	PUNCT
ejpam-6238	239	28	journal	journal	NOUN
ejpam-6238	239	29	of	of	ADP
ejpam-6238	239	30	applied	apply	VERB
ejpam-6238	239	31	functional	functional	ADJ
ejpam-6238	239	32	analysis	analysis	NOUN
ejpam-6238	239	33	,	,	PUNCT
ejpam-6238	239	34	vol	vol	NOUN
ejpam-6238	239	35	.	.	PROPN
ejpam-6238	239	36	5	5	NUM
ejpam-6238	239	37	,	,	PUNCT
ejpam-6238	239	38	no	no	INTJ
ejpam-6238	239	39	.	.	NOUN
ejpam-6238	239	40	1	1	NUM
ejpam-6238	239	41	,	,	PUNCT
ejpam-6238	239	42	pp	pp	ADJ
ejpam-6238	239	43	.	.	PUNCT
ejpam-6238	240	1	121–138	121–138	NUM
ejpam-6238	240	2	,	,	PUNCT
ejpam-6238	240	3	2010	2010	NUM
ejpam-6238	240	4	.	.	PUNCT
ejpam-6238	241	1	[	[	X
ejpam-6238	241	2	22	22	NUM
ejpam-6238	241	3	]	]	PUNCT
ejpam-6238	241	4	a.	a.	NOUN
ejpam-6238	241	5	ziqan	ziqan	PROPN
ejpam-6238	241	6	,	,	PUNCT
ejpam-6238	241	7	m.	m.	PROPN
ejpam-6238	241	8	al	al	PROPN
ejpam-6238	241	9	horani	horani	PROPN
ejpam-6238	241	10	,	,	PUNCT
ejpam-6238	241	11	and	and	CCONJ
ejpam-6238	241	12	r.	r.	PROPN
ejpam-6238	241	13	khalil	khalil	PROPN
ejpam-6238	241	14	,	,	PUNCT
ejpam-6238	241	15	“	"	PUNCT
ejpam-6238	241	16	tensor	tensor	NOUN
ejpam-6238	241	17	product	product	NOUN
ejpam-6238	241	18	technique	technique	NOUN
ejpam-6238	241	19	and	and	CCONJ
ejpam-6238	241	20	the	the	DET
ejpam-6238	241	21	degenerate	degenerate	ADJ
ejpam-6238	241	22	nonhomogeneous	nonhomogeneous	ADJ
ejpam-6238	241	23	abstract	abstract	ADJ
ejpam-6238	241	24	cauchy	cauchy	PROPN
ejpam-6238	241	25	problem	problem	NOUN
ejpam-6238	241	26	,	,	PUNCT
ejpam-6238	241	27	”	"	PUNCT
ejpam-6238	241	28	journal	journal	NOUN
ejpam-6238	241	29	of	of	ADP
ejpam-6238	241	30	applied	apply	VERB
ejpam-6238	241	31	functional	functional	ADJ
ejpam-6238	241	32	analysis	analysis	NOUN
ejpam-6238	241	33	,	,	PUNCT
ejpam-6238	241	34	vol	vol	NOUN
ejpam-6238	241	35	.	.	PROPN
ejpam-6238	241	36	23	23	NUM
ejpam-6238	241	37	,	,	PUNCT
ejpam-6238	241	38	no	no	INTJ
ejpam-6238	241	39	.	.	NOUN
ejpam-6238	241	40	1	1	NUM
ejpam-6238	241	41	,	,	PUNCT
ejpam-6238	241	42	pp	pp	ADJ
ejpam-6238	241	43	.	.	PUNCT
ejpam-6238	242	1	137–158	137–158	NUM
ejpam-6238	242	2	,	,	PUNCT
ejpam-6238	242	3	2010	2010	NUM
ejpam-6238	242	4	.	.	PUNCT