id	sid	tid	token	lemma	pos
ejpam-481	1	1	11_481_khalil.dvi	11_481_khalil.dvi	NUM
ejpam-481	1	2	european	european	PROPN
ejpam-481	1	3	journal	journal	PROPN
ejpam-481	1	4	of	of	ADP
ejpam-481	1	5	pure	pure	ADJ
ejpam-481	1	6	and	and	CCONJ
ejpam-481	1	7	applied	apply	VERB
ejpam-481	1	8	mathematics	mathematic	NOUN
ejpam-481	1	9	vol	vol	NOUN
ejpam-481	1	10	.	.	PUNCT
ejpam-481	2	1	3	3	NUM
ejpam-481	2	2	,	,	PUNCT
ejpam-481	2	3	no	no	INTJ
ejpam-481	2	4	.	.	NOUN
ejpam-481	2	5	4	4	NUM
ejpam-481	2	6	,	,	PUNCT
ejpam-481	2	7	2010	2010	NUM
ejpam-481	2	8	,	,	PUNCT
ejpam-481	2	9	725	725	NUM
ejpam-481	2	10	-	-	SYM
ejpam-481	2	11	729	729	NUM
ejpam-481	2	12	issn	issn	PROPN
ejpam-481	2	13	1307	1307	NUM
ejpam-481	2	14	-	-	SYM
ejpam-481	2	15	5543	5543	NUM
ejpam-481	2	16	–	–	PUNCT
ejpam-481	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-481	2	18	atomic	atomic	ADJ
ejpam-481	2	19	solution	solution	NOUN
ejpam-481	2	20	of	of	ADP
ejpam-481	2	21	certain	certain	ADJ
ejpam-481	2	22	inverse	inverse	NOUN
ejpam-481	2	23	problems	problem	NOUN
ejpam-481	2	24	roshdi	roshdi	PROPN
ejpam-481	2	25	rashid	rashid	PROPN
ejpam-481	2	26	khalil∗	khalil∗	PROPN
ejpam-481	2	27	,	,	PUNCT
ejpam-481	2	28	l.	l.	PROPN
ejpam-481	2	29	abdullah	abdullah	PROPN
ejpam-481	2	30	university	university	PROPN
ejpam-481	2	31	of	of	ADP
ejpam-481	2	32	jordan	jordan	PROPN
ejpam-481	2	33	,	,	PUNCT
ejpam-481	2	34	jordan	jordan	PROPN
ejpam-481	2	35	abstract	abstract	PROPN
ejpam-481	2	36	.	.	PUNCT
ejpam-481	3	1	in	in	ADP
ejpam-481	3	2	this	this	DET
ejpam-481	3	3	note	note	NOUN
ejpam-481	3	4	we	we	PRON
ejpam-481	3	5	find	find	VERB
ejpam-481	3	6	atomic	atomic	ADJ
ejpam-481	3	7	solution	solution	NOUN
ejpam-481	3	8	for	for	ADP
ejpam-481	3	9	certain	certain	ADJ
ejpam-481	3	10	degenerate	degenerate	ADJ
ejpam-481	3	11	and	and	CCONJ
ejpam-481	3	12	non	non	ADJ
ejpam-481	3	13	-	-	ADJ
ejpam-481	3	14	degenerate	degenerate	ADJ
ejpam-481	3	15	inverse	inverse	NOUN
ejpam-481	3	16	problems	problem	NOUN
ejpam-481	3	17	.	.	PUNCT
ejpam-481	4	1	the	the	DET
ejpam-481	4	2	main	main	ADJ
ejpam-481	4	3	idea	idea	NOUN
ejpam-481	4	4	of	of	ADP
ejpam-481	4	5	the	the	DET
ejpam-481	4	6	proofs	proof	NOUN
ejpam-481	4	7	are	be	AUX
ejpam-481	4	8	based	base	VERB
ejpam-481	4	9	on	on	ADP
ejpam-481	4	10	theory	theory	NOUN
ejpam-481	4	11	of	of	ADP
ejpam-481	4	12	tensor	tensor	NOUN
ejpam-481	4	13	product	product	NOUN
ejpam-481	4	14	of	of	ADP
ejpam-481	4	15	banach	banach	NOUN
ejpam-481	4	16	spaces	space	NOUN
ejpam-481	4	17	.	.	PUNCT
ejpam-481	5	1	2000	2000	NUM
ejpam-481	5	2	mathematics	mathematic	NOUN
ejpam-481	5	3	subject	subject	NOUN
ejpam-481	5	4	classifications	classification	NOUN
ejpam-481	5	5	:	:	PUNCT
ejpam-481	5	6	47d06	47d06	NUM
ejpam-481	5	7	key	key	ADJ
ejpam-481	5	8	words	word	NOUN
ejpam-481	5	9	and	and	CCONJ
ejpam-481	5	10	phrases	phrase	NOUN
ejpam-481	5	11	:	:	PUNCT
ejpam-481	5	12	tensor	tensor	NOUN
ejpam-481	5	13	product	product	NOUN
ejpam-481	5	14	,	,	PUNCT
ejpam-481	5	15	banach	banach	NOUN
ejpam-481	5	16	spaces	space	NOUN
ejpam-481	5	17	,	,	PUNCT
ejpam-481	5	18	non	non	ADJ
ejpam-481	5	19	-	-	ADJ
ejpam-481	5	20	degenerate	degenerate	ADJ
ejpam-481	5	21	cauchy	cauchy	ADJ
ejpam-481	5	22	problem	problem	NOUN
ejpam-481	5	23	1	1	NUM
ejpam-481	5	24	.	.	PUNCT
ejpam-481	6	1	introduction	introduction	NOUN
ejpam-481	6	2	let	let	VERB
ejpam-481	6	3	x	x	PRON
ejpam-481	6	4	be	be	AUX
ejpam-481	6	5	a	a	DET
ejpam-481	6	6	banach	banach	NOUN
ejpam-481	6	7	space	space	NOUN
ejpam-481	6	8	,	,	PUNCT
ejpam-481	6	9	and	and	CCONJ
ejpam-481	6	10	i	i	PRON
ejpam-481	6	11	=	=	PUNCT
ejpam-481	7	1	[	[	X
ejpam-481	7	2	0,1	0,1	NUM
ejpam-481	7	3	]	]	PUNCT
ejpam-481	7	4	.	.	PUNCT
ejpam-481	8	1	the	the	DET
ejpam-481	8	2	banach	banach	NOUN
ejpam-481	8	3	space	space	NOUN
ejpam-481	8	4	of	of	ADP
ejpam-481	8	5	continuous	continuous	ADJ
ejpam-481	8	6	functions	function	NOUN
ejpam-481	8	7	from	from	ADP
ejpam-481	8	8	i	i	PRON
ejpam-481	8	9	into	into	ADP
ejpam-481	8	10	x	x	PRON
ejpam-481	8	11	,	,	PUNCT
ejpam-481	8	12	is	be	AUX
ejpam-481	8	13	denoted	denote	VERB
ejpam-481	8	14	by	by	ADP
ejpam-481	8	15	c(i	c(i	NOUN
ejpam-481	8	16	,	,	PUNCT
ejpam-481	8	17	x	x	X
ejpam-481	8	18	)	)	PUNCT
ejpam-481	8	19	.	.	PUNCT
ejpam-481	9	1	it	it	PRON
ejpam-481	9	2	is	be	AUX
ejpam-481	9	3	well	well	ADV
ejpam-481	9	4	known	known	ADJ
ejpam-481	9	5	[	[	X
ejpam-481	9	6	4	4	NUM
ejpam-481	9	7	]	]	PUNCT
ejpam-481	9	8	,	,	PUNCT
ejpam-481	9	9	that	that	PRON
ejpam-481	9	10	c(i	c(i	VERB
ejpam-481	9	11	,	,	PUNCT
ejpam-481	9	12	x	x	X
ejpam-481	9	13	)	)	PUNCT
ejpam-481	9	14	is	be	AUX
ejpam-481	9	15	isometrically	isometrically	PROPN
ejpam-481	9	16	isomorphic	isomorphic	ADJ
ejpam-481	9	17	to	to	ADP
ejpam-481	9	18	the	the	DET
ejpam-481	9	19	injective	injective	ADJ
ejpam-481	9	20	tensor	tensor	NOUN
ejpam-481	9	21	product	product	NOUN
ejpam-481	9	22	of	of	ADP
ejpam-481	9	23	c(i	c(i	NOUN
ejpam-481	9	24	)	)	PUNCT
ejpam-481	9	25	with	with	ADP
ejpam-481	9	26	x	x	SYM
ejpam-481	9	27	,	,	PUNCT
ejpam-481	9	28	where	where	SCONJ
ejpam-481	9	29	c(i	c(i	NOUN
ejpam-481	9	30	)	)	PUNCT
ejpam-481	9	31	is	be	AUX
ejpam-481	9	32	the	the	DET
ejpam-481	9	33	space	space	NOUN
ejpam-481	9	34	of	of	ADP
ejpam-481	9	35	all	all	DET
ejpam-481	9	36	real	real	ADJ
ejpam-481	9	37	(	(	PUNCT
ejpam-481	9	38	or	or	CCONJ
ejpam-481	9	39	complex	complex	ADJ
ejpam-481	9	40	)	)	PUNCT
ejpam-481	9	41	valued	value	VERB
ejpam-481	9	42	continuous	continuous	ADJ
ejpam-481	9	43	functions	function	NOUN
ejpam-481	9	44	on	on	ADP
ejpam-481	9	45	i	i	PRON
ejpam-481	9	46	.	.	PUNCT
ejpam-481	10	1	one	one	NUM
ejpam-481	10	2	of	of	ADP
ejpam-481	10	3	the	the	DET
ejpam-481	10	4	classical	classical	ADJ
ejpam-481	10	5	differential	differential	ADJ
ejpam-481	10	6	equations	equation	NOUN
ejpam-481	10	7	in	in	ADP
ejpam-481	10	8	banach	banach	NOUN
ejpam-481	10	9	spaces	space	NOUN
ejpam-481	10	10	is	be	AUX
ejpam-481	10	11	the	the	DET
ejpam-481	10	12	so	so	ADV
ejpam-481	10	13	called	call	VERB
ejpam-481	10	14	abstract	abstract	ADJ
ejpam-481	10	15	cauchy	cauchy	PROPN
ejpam-481	10	16	problem	problem	NOUN
ejpam-481	10	17	.	.	PUNCT
ejpam-481	11	1	the	the	DET
ejpam-481	11	2	general	general	ADJ
ejpam-481	11	3	form	form	NOUN
ejpam-481	11	4	of	of	ADP
ejpam-481	11	5	such	such	DET
ejpam-481	11	6	a	a	DET
ejpam-481	11	7	problem	problem	NOUN
ejpam-481	11	8	,	,	PUNCT
ejpam-481	11	9	which	which	PRON
ejpam-481	11	10	we	we	PRON
ejpam-481	11	11	will	will	AUX
ejpam-481	11	12	denote	denote	VERB
ejpam-481	11	13	by	by	ADP
ejpam-481	11	14	(	(	PUNCT
ejpam-481	11	15	p1	p1	PROPN
ejpam-481	11	16	)	)	PUNCT
ejpam-481	11	17	is	be	AUX
ejpam-481	11	18	bu′(t	bu′(t	VERB
ejpam-481	11	19	)	)	PUNCT
ejpam-481	12	1	=	=	SYM
ejpam-481	12	2	au(t	au(t	PRON
ejpam-481	12	3	)	)	PUNCT
ejpam-481	13	1	+	+	NUM
ejpam-481	13	2	f	f	X
ejpam-481	13	3	(	(	PUNCT
ejpam-481	13	4	t)z	t)z	NOUN
ejpam-481	13	5	,	,	PUNCT
ejpam-481	13	6	u(0	u(0	NOUN
ejpam-481	13	7	)	)	PUNCT
ejpam-481	13	8	=	=	SYM
ejpam-481	13	9	y	y	PROPN
ejpam-481	13	10	,	,	PUNCT
ejpam-481	13	11	(	(	PUNCT
ejpam-481	13	12	1	1	X
ejpam-481	13	13	)	)	PUNCT
ejpam-481	13	14	where	where	SCONJ
ejpam-481	13	15	a	a	DET
ejpam-481	13	16	,	,	PUNCT
ejpam-481	13	17	b	b	NOUN
ejpam-481	13	18	are	be	AUX
ejpam-481	13	19	densely	densely	ADV
ejpam-481	13	20	defined	define	VERB
ejpam-481	13	21	linear	linear	ADJ
ejpam-481	13	22	operators	operator	NOUN
ejpam-481	13	23	on	on	ADP
ejpam-481	13	24	the	the	DET
ejpam-481	13	25	codomain	codomain	NOUN
ejpam-481	13	26	of	of	ADP
ejpam-481	13	27	the	the	DET
ejpam-481	13	28	function	function	NOUN
ejpam-481	13	29	u	u	NOUN
ejpam-481	13	30	,	,	PUNCT
ejpam-481	13	31	where	where	SCONJ
ejpam-481	13	32	u	u	NOUN
ejpam-481	13	33	is	be	AUX
ejpam-481	13	34	continuously	continuously	ADV
ejpam-481	13	35	differentiable	differentiable	ADJ
ejpam-481	13	36	on	on	ADP
ejpam-481	13	37	i	i	PRON
ejpam-481	13	38	=	=	PUNCT
ejpam-481	14	1	[	[	X
ejpam-481	14	2	0,1	0,1	NUM
ejpam-481	14	3	]	]	PUNCT
ejpam-481	14	4	or	or	CCONJ
ejpam-481	14	5	[	[	X
ejpam-481	14	6	0,∞	0,∞	NOUN
ejpam-481	14	7	)	)	PUNCT
ejpam-481	14	8	with	with	ADP
ejpam-481	14	9	values	value	NOUN
ejpam-481	14	10	in	in	ADP
ejpam-481	14	11	the	the	DET
ejpam-481	14	12	banach	banach	NOUN
ejpam-481	14	13	space	space	NOUN
ejpam-481	14	14	x	x	X
ejpam-481	14	15	.	.	PUNCT
ejpam-481	15	1	if	if	SCONJ
ejpam-481	15	2	b−1exists	b−1exist	NOUN
ejpam-481	15	3	,	,	PUNCT
ejpam-481	15	4	then	then	ADV
ejpam-481	15	5	the	the	DET
ejpam-481	15	6	equation	equation	NOUN
ejpam-481	15	7	is	be	AUX
ejpam-481	15	8	called	call	VERB
ejpam-481	15	9	degenerate	degenerate	ADJ
ejpam-481	15	10	,	,	PUNCT
ejpam-481	15	11	otherwise	otherwise	ADV
ejpam-481	15	12	,	,	PUNCT
ejpam-481	15	13	it	it	PRON
ejpam-481	15	14	is	be	AUX
ejpam-481	15	15	called	call	VERB
ejpam-481	15	16	non	non	ADJ
ejpam-481	15	17	-	-	ADJ
ejpam-481	15	18	degenerate	degenerate	ADJ
ejpam-481	15	19	.	.	PUNCT
ejpam-481	16	1	if	if	SCONJ
ejpam-481	16	2	f	f	PROPN
ejpam-481	16	3	=	=	SYM
ejpam-481	16	4	0	0	PROPN
ejpam-481	16	5	or	or	CCONJ
ejpam-481	16	6	z	z	NOUN
ejpam-481	16	7	=	=	SYM
ejpam-481	16	8	0	0	NUM
ejpam-481	16	9	,	,	PUNCT
ejpam-481	16	10	then	then	ADV
ejpam-481	16	11	the	the	DET
ejpam-481	16	12	equation	equation	NOUN
ejpam-481	16	13	is	be	AUX
ejpam-481	16	14	homogeneous	homogeneous	ADJ
ejpam-481	16	15	,	,	PUNCT
ejpam-481	16	16	otherwise	otherwise	ADV
ejpam-481	16	17	it	it	PRON
ejpam-481	16	18	is	be	AUX
ejpam-481	16	19	called	call	VERB
ejpam-481	16	20	nonhomogeneous	nonhomogeneous	ADJ
ejpam-481	16	21	.	.	PUNCT
ejpam-481	17	1	in	in	ADP
ejpam-481	17	2	such	such	ADJ
ejpam-481	17	3	equation	equation	NOUN
ejpam-481	17	4	,	,	PUNCT
ejpam-481	17	5	only	only	ADV
ejpam-481	17	6	u	u	NOUN
ejpam-481	17	7	is	be	AUX
ejpam-481	17	8	the	the	DET
ejpam-481	17	9	unknown	unknown	ADJ
ejpam-481	17	10	.	.	PUNCT
ejpam-481	18	1	however	however	ADV
ejpam-481	18	2	,	,	PUNCT
ejpam-481	18	3	if	if	SCONJ
ejpam-481	18	4	u	u	PROPN
ejpam-481	18	5	and	and	CCONJ
ejpam-481	18	6	f	f	PROPN
ejpam-481	18	7	are	be	AUX
ejpam-481	18	8	both	both	PRON
ejpam-481	18	9	unknowns	unknown	NOUN
ejpam-481	18	10	,	,	PUNCT
ejpam-481	18	11	but	but	CCONJ
ejpam-481	18	12	additional	additional	ADJ
ejpam-481	18	13	conditions	condition	NOUN
ejpam-481	18	14	are	be	AUX
ejpam-481	18	15	added	add	VERB
ejpam-481	18	16	to	to	PART
ejpam-481	18	17	be	be	AUX
ejpam-481	18	18	able	able	ADJ
ejpam-481	18	19	to	to	PART
ejpam-481	18	20	determine	determine	VERB
ejpam-481	18	21	u	u	NOUN
ejpam-481	18	22	and	and	CCONJ
ejpam-481	18	23	f	f	PROPN
ejpam-481	18	24	then	then	ADV
ejpam-481	18	25	problem	problem	NOUN
ejpam-481	18	26	p1	p1	PROPN
ejpam-481	18	27	is	be	AUX
ejpam-481	18	28	called	call	VERB
ejpam-481	18	29	an	an	DET
ejpam-481	18	30	inverse	inverse	NOUN
ejpam-481	18	31	problem	problem	NOUN
ejpam-481	18	32	.	.	PUNCT
ejpam-481	19	1	the	the	DET
ejpam-481	19	2	theory	theory	NOUN
ejpam-481	19	3	of	of	ADP
ejpam-481	19	4	inverse	inverse	NOUN
ejpam-481	19	5	problems	problem	NOUN
ejpam-481	19	6	for	for	ADP
ejpam-481	19	7	differential	differential	ADJ
ejpam-481	19	8	equations	equation	NOUN
ejpam-481	19	9	is	be	AUX
ejpam-481	19	10	being	be	AUX
ejpam-481	19	11	extensively	extensively	ADV
ejpam-481	19	12	developed	develop	VERB
ejpam-481	19	13	with	with	ADP
ejpam-481	19	14	the	the	DET
ejpam-481	19	15	frame	frame	NOUN
ejpam-481	19	16	work	work	NOUN
ejpam-481	19	17	of	of	ADP
ejpam-481	19	18	mathematical	mathematical	ADJ
ejpam-481	19	19	physics	physics	NOUN
ejpam-481	19	20	.	.	PUNCT
ejpam-481	20	1	to	to	PART
ejpam-481	20	2	determine	determine	VERB
ejpam-481	20	3	the	the	DET
ejpam-481	20	4	solution	solution	NOUN
ejpam-481	20	5	of	of	ADP
ejpam-481	20	6	an	an	DET
ejpam-481	20	7	inverse	inverse	NOUN
ejpam-481	20	8	problem	problem	NOUN
ejpam-481	20	9	additional	additional	ADJ
ejpam-481	20	10	conditions	condition	NOUN
ejpam-481	20	11	are	be	AUX
ejpam-481	20	12	needed	need	VERB
ejpam-481	20	13	.	.	PUNCT
ejpam-481	21	1	almost	almost	ADV
ejpam-481	21	2	all	all	DET
ejpam-481	21	3	researchers	researcher	NOUN
ejpam-481	21	4	,	,	PUNCT
ejpam-481	21	5	[	[	X
ejpam-481	21	6	1	1	NUM
ejpam-481	21	7	]	]	PUNCT
ejpam-481	21	8	,	,	PUNCT
ejpam-481	21	9	[	[	X
ejpam-481	21	10	2	2	NUM
ejpam-481	21	11	]	]	PUNCT
ejpam-481	21	12	,	,	PUNCT
ejpam-481	21	13	and	and	CCONJ
ejpam-481	21	14	[	[	X
ejpam-481	21	15	3	3	NUM
ejpam-481	21	16	]	]	PUNCT
ejpam-481	21	17	studied	study	VERB
ejpam-481	21	18	such	such	ADJ
ejpam-481	21	19	type	type	NOUN
ejpam-481	21	20	of	of	ADP
ejpam-481	21	21	problems	problem	NOUN
ejpam-481	21	22	using	use	VERB
ejpam-481	21	23	a	a	DET
ejpam-481	21	24	semigroup	semigroup	ADJ
ejpam-481	21	25	approach	approach	NOUN
ejpam-481	21	26	.	.	PUNCT
ejpam-481	22	1	for	for	ADP
ejpam-481	22	2	more	more	ADJ
ejpam-481	22	3	references	reference	NOUN
ejpam-481	22	4	and	and	CCONJ
ejpam-481	22	5	results	result	NOUN
ejpam-481	22	6	on	on	ADP
ejpam-481	22	7	inverse	inverse	NOUN
ejpam-481	22	8	∗corresponding	∗corresponde	VERB
ejpam-481	22	9	author	author	NOUN
ejpam-481	22	10	.	.	PUNCT
ejpam-481	23	1	email	email	NOUN
ejpam-481	23	2	address	address	NOUN
ejpam-481	23	3	:	:	PUNCT
ejpam-481	23	4	roshdi�ju.edu.jo	roshdi�ju.edu.jo	PROPN
ejpam-481	23	5	(	(	PUNCT
ejpam-481	23	6	r.	r.	PROPN
ejpam-481	23	7	khalil	khalil	PROPN
ejpam-481	23	8	)	)	PUNCT
ejpam-481	23	9	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-481	24	1	725	725	NUM
ejpam-481	24	2	c	c	NOUN
ejpam-481	24	3	©	©	NOUN
ejpam-481	24	4	2010	2010	NUM
ejpam-481	24	5	ejpam	ejpam	NOUN
ejpam-481	24	6	all	all	DET
ejpam-481	24	7	rights	right	NOUN
ejpam-481	24	8	reserved	reserve	VERB
ejpam-481	24	9	.	.	PUNCT
ejpam-481	25	1	r.	r.	PROPN
ejpam-481	25	2	khalil	khalil	PROPN
ejpam-481	25	3	,	,	PUNCT
ejpam-481	25	4	l.	l.	PROPN
ejpam-481	25	5	abdullah	abdullah	PROPN
ejpam-481	25	6	/	/	PUNCT
ejpam-481	25	7	eur	eur	PROPN
ejpam-481	25	8	.	.	PUNCT
ejpam-481	26	1	j.	j.	PROPN
ejpam-481	26	2	pure	pure	PROPN
ejpam-481	26	3	appl	appl	PROPN
ejpam-481	26	4	.	.	PROPN
ejpam-481	26	5	math	math	PROPN
ejpam-481	26	6	,	,	PUNCT
ejpam-481	26	7	3	3	NUM
ejpam-481	26	8	(	(	PUNCT
ejpam-481	26	9	2010	2010	NUM
ejpam-481	26	10	)	)	PUNCT
ejpam-481	26	11	,	,	PUNCT
ejpam-481	26	12	725	725	NUM
ejpam-481	26	13	-	-	SYM
ejpam-481	26	14	729	729	NUM
ejpam-481	26	15	726	726	NUM
ejpam-481	26	16	problems	problem	NOUN
ejpam-481	26	17	we	we	PRON
ejpam-481	26	18	refer	refer	VERB
ejpam-481	26	19	to	to	ADP
ejpam-481	26	20	[	[	X
ejpam-481	26	21	3	3	NUM
ejpam-481	26	22	]	]	PUNCT
ejpam-481	26	23	.	.	PUNCT
ejpam-481	27	1	in	in	ADP
ejpam-481	27	2	this	this	DET
ejpam-481	27	3	note	note	NOUN
ejpam-481	27	4	,	,	PUNCT
ejpam-481	27	5	we	we	PRON
ejpam-481	27	6	use	use	VERB
ejpam-481	27	7	a	a	DET
ejpam-481	27	8	new	new	ADJ
ejpam-481	27	9	method	method	NOUN
ejpam-481	27	10	that	that	PRON
ejpam-481	27	11	involves	involve	VERB
ejpam-481	27	12	tensor	tensor	NOUN
ejpam-481	27	13	product	product	NOUN
ejpam-481	27	14	techniques	technique	NOUN
ejpam-481	27	15	to	to	PART
ejpam-481	27	16	solve	solve	VERB
ejpam-481	27	17	inverse	inverse	NOUN
ejpam-481	27	18	problems	problem	NOUN
ejpam-481	27	19	for	for	ADP
ejpam-481	27	20	what	what	PRON
ejpam-481	27	21	we	we	PRON
ejpam-481	27	22	call	call	VERB
ejpam-481	27	23	atomic	atomic	ADJ
ejpam-481	27	24	functions	function	NOUN
ejpam-481	27	25	.	.	PUNCT
ejpam-481	28	1	we	we	PRON
ejpam-481	28	2	refer	refer	VERB
ejpam-481	28	3	to	to	ADP
ejpam-481	28	4	[	[	X
ejpam-481	28	5	4	4	X
ejpam-481	28	6	]	]	PUNCT
ejpam-481	28	7	for	for	ADP
ejpam-481	28	8	the	the	DET
ejpam-481	28	9	basic	basic	ADJ
ejpam-481	28	10	theory	theory	NOUN
ejpam-481	28	11	of	of	ADP
ejpam-481	28	12	tensor	tensor	NOUN
ejpam-481	28	13	products	product	NOUN
ejpam-481	28	14	of	of	ADP
ejpam-481	28	15	banach	banach	NOUN
ejpam-481	28	16	spaces	space	NOUN
ejpam-481	28	17	.	.	PUNCT
ejpam-481	29	1	2	2	X
ejpam-481	29	2	.	.	X
ejpam-481	29	3	degenerate	degenerate	ADJ
ejpam-481	29	4	inverse	inverse	NOUN
ejpam-481	29	5	problem	problem	NOUN
ejpam-481	29	6	consider	consider	VERB
ejpam-481	29	7	the	the	DET
ejpam-481	29	8	problem	problem	NOUN
ejpam-481	29	9	which	which	PRON
ejpam-481	29	10	we	we	PRON
ejpam-481	29	11	will	will	AUX
ejpam-481	29	12	denote	denote	VERB
ejpam-481	29	13	by	by	ADP
ejpam-481	29	14	p1	p1	NOUN
ejpam-481	29	15	:	:	PUNCT
ejpam-481	29	16	u′(t)x	u′(t)x	PROPN
ejpam-481	29	17	+	+	PROPN
ejpam-481	29	18	u(t)ax	u(t)ax	PROPN
ejpam-481	29	19	=	=	SYM
ejpam-481	29	20	f	f	PROPN
ejpam-481	29	21	(	(	PUNCT
ejpam-481	29	22	t)z	t)z	NOUN
ejpam-481	29	23	(	(	PUNCT
ejpam-481	29	24	2	2	NUM
ejpam-481	29	25	)	)	PUNCT
ejpam-481	29	26	with	with	ADP
ejpam-481	29	27	the	the	DET
ejpam-481	29	28	conditions	condition	NOUN
ejpam-481	29	29	(	(	PUNCT
ejpam-481	29	30	i	i	NOUN
ejpam-481	29	31	)	)	PUNCT
ejpam-481	29	32	there	there	PRON
ejpam-481	29	33	is	be	VERB
ejpam-481	29	34	x∗	x∗	PROPN
ejpam-481	29	35	∈	∈	PROPN
ejpam-481	29	36	x	x	X
ejpam-481	29	37	∗	∗	NOUN
ejpam-481	29	38	and	and	CCONJ
ejpam-481	29	39	g	g	PROPN
ejpam-481	29	40	∈	∈	PROPN
ejpam-481	29	41	c(i	c(i	NOUN
ejpam-481	29	42	,	,	PUNCT
ejpam-481	29	43	r	r	NOUN
ejpam-481	29	44	)	)	PUNCT
ejpam-481	29	45	such	such	ADJ
ejpam-481	29	46	that	that	SCONJ
ejpam-481	29	47	<	<	X
ejpam-481	29	48	u(t)x	u(t)x	PROPN
ejpam-481	29	49	,	,	PUNCT
ejpam-481	29	50	x∗	x∗	PROPN
ejpam-481	29	51	>	>	PUNCT
ejpam-481	29	52	=	=	SYM
ejpam-481	29	53	g(t	g(t	PROPN
ejpam-481	29	54	)	)	PUNCT
ejpam-481	29	55	(	(	PUNCT
ejpam-481	29	56	ii	ii	NOUN
ejpam-481	29	57	)	)	PUNCT
ejpam-481	29	58	ℓn(g(1)/g(0	ℓn(g(1)/g(0	NOUN
ejpam-481	29	59	)	)	PUNCT
ejpam-481	29	60	)	)	PUNCT
ejpam-481	30	1	∈	∈	PROPN
ejpam-481	30	2	ρ(a	ρ(a	PROPN
ejpam-481	30	3	)	)	PUNCT
ejpam-481	30	4	,	,	PUNCT
ejpam-481	30	5	the	the	DET
ejpam-481	30	6	resolvent	resolvent	ADJ
ejpam-481	30	7	set	set	NOUN
ejpam-481	30	8	of	of	ADP
ejpam-481	30	9	a.	a.	NOUN
ejpam-481	30	10	theorem	theorem	NOUN
ejpam-481	30	11	1	1	NUM
ejpam-481	30	12	.	.	PUNCT
ejpam-481	30	13	problem	problem	NOUN
ejpam-481	30	14	p1	p1	PROPN
ejpam-481	30	15	has	have	VERB
ejpam-481	30	16	a	a	DET
ejpam-481	30	17	unique	unique	ADJ
ejpam-481	30	18	solution	solution	NOUN
ejpam-481	30	19	.	.	PUNCT
ejpam-481	31	1	proof	proof	NOUN
ejpam-481	31	2	.	.	PUNCT
ejpam-481	32	1	using	use	VERB
ejpam-481	32	2	tensor	tensor	NOUN
ejpam-481	32	3	product	product	NOUN
ejpam-481	32	4	notation	notation	NOUN
ejpam-481	32	5	,	,	PUNCT
ejpam-481	32	6	equation	equation	NOUN
ejpam-481	32	7	(	(	PUNCT
ejpam-481	32	8	2	2	X
ejpam-481	32	9	)	)	PUNCT
ejpam-481	32	10	can	can	AUX
ejpam-481	32	11	be	be	AUX
ejpam-481	32	12	written	write	VERB
ejpam-481	32	13	in	in	ADP
ejpam-481	32	14	the	the	DET
ejpam-481	32	15	form	form	NOUN
ejpam-481	32	16	u′	u′	PROPN
ejpam-481	32	17	⊗	⊗	NOUN
ejpam-481	32	18	x	x	PUNCT
ejpam-481	33	1	+	+	NUM
ejpam-481	33	2	u⊗	u⊗	ADJ
ejpam-481	33	3	ax	ax	NOUN
ejpam-481	33	4	=	=	PUNCT
ejpam-481	33	5	f	f	X
ejpam-481	33	6	⊗	⊗	PROPN
ejpam-481	33	7	z	z	PROPN
ejpam-481	33	8	(	(	PUNCT
ejpam-481	33	9	3	3	NUM
ejpam-481	33	10	)	)	PUNCT
ejpam-481	33	11	since	since	SCONJ
ejpam-481	33	12	an	an	DET
ejpam-481	33	13	atom	atom	NOUN
ejpam-481	33	14	x	x	PUNCT
ejpam-481	33	15	⊗	⊗	PROPN
ejpam-481	33	16	y	y	PROPN
ejpam-481	33	17	has	have	VERB
ejpam-481	33	18	infinite	infinite	ADJ
ejpam-481	33	19	number	number	NOUN
ejpam-481	33	20	of	of	ADP
ejpam-481	33	21	representations	representation	NOUN
ejpam-481	33	22	:	:	PUNCT
ejpam-481	33	23	ax	ax	NOUN
ejpam-481	33	24	⊗	⊗	PROPN
ejpam-481	33	25	1	1	NUM
ejpam-481	33	26	a	a	DET
ejpam-481	33	27	y	y	NOUN
ejpam-481	33	28	,	,	PUNCT
ejpam-481	33	29	then	then	ADV
ejpam-481	33	30	without	without	ADP
ejpam-481	33	31	loss	loss	NOUN
ejpam-481	33	32	of	of	ADP
ejpam-481	33	33	generality	generality	NOUN
ejpam-481	33	34	we	we	PRON
ejpam-481	33	35	can	can	AUX
ejpam-481	33	36	assume	assume	VERB
ejpam-481	33	37	that	that	SCONJ
ejpam-481	33	38	u(0	u(0	NOUN
ejpam-481	33	39	)	)	PUNCT
ejpam-481	34	1	=	=	SYM
ejpam-481	34	2	f	f	PROPN
ejpam-481	34	3	(	(	PUNCT
ejpam-481	34	4	0	0	NUM
ejpam-481	34	5	)	)	PUNCT
ejpam-481	34	6	=	=	SYM
ejpam-481	34	7	1	1	X
ejpam-481	34	8	.	.	PUNCT
ejpam-481	34	9	further	far	ADV
ejpam-481	34	10	,	,	PUNCT
ejpam-481	34	11	[	[	X
ejpam-481	34	12	5	5	NUM
ejpam-481	34	13	]	]	PUNCT
ejpam-481	34	14	,	,	PUNCT
ejpam-481	34	15	since	since	SCONJ
ejpam-481	34	16	in	in	ADP
ejpam-481	34	17	equation	equation	NOUN
ejpam-481	34	18	(	(	PUNCT
ejpam-481	34	19	3	3	X
ejpam-481	34	20	)	)	PUNCT
ejpam-481	34	21	the	the	DET
ejpam-481	34	22	sum	sum	NOUN
ejpam-481	34	23	of	of	ADP
ejpam-481	34	24	two	two	NUM
ejpam-481	34	25	atoms	atom	NOUN
ejpam-481	34	26	is	be	AUX
ejpam-481	34	27	an	an	DET
ejpam-481	34	28	atom	atom	NOUN
ejpam-481	34	29	,	,	PUNCT
ejpam-481	34	30	then	then	ADV
ejpam-481	34	31	we	we	PRON
ejpam-481	34	32	have	have	VERB
ejpam-481	34	33	two	two	NUM
ejpam-481	34	34	cases	case	NOUN
ejpam-481	34	35	.	.	PUNCT
ejpam-481	35	1	(	(	PUNCT
ejpam-481	35	2	1	1	X
ejpam-481	35	3	)	)	PUNCT
ejpam-481	35	4	u′	u′	PROPN
ejpam-481	35	5	=	=	SYM
ejpam-481	35	6	λu	λu	PROPN
ejpam-481	35	7	,	,	PUNCT
ejpam-481	35	8	and	and	CCONJ
ejpam-481	35	9	(	(	PUNCT
ejpam-481	35	10	2	2	X
ejpam-481	35	11	)	)	PUNCT
ejpam-481	35	12	ax	ax	NOUN
ejpam-481	35	13	=	=	NOUN
ejpam-481	35	14	αx	αx	INTJ
ejpam-481	35	15	.	.	PUNCT
ejpam-481	36	1	now	now	ADV
ejpam-481	36	2	,	,	PUNCT
ejpam-481	36	3	assume	assume	VERB
ejpam-481	36	4	u′	u′	PROPN
ejpam-481	36	5	=	=	SYM
ejpam-481	36	6	λu	λu	PROPN
ejpam-481	36	7	.	.	PUNCT
ejpam-481	37	1	then	then	ADV
ejpam-481	37	2	u(t	u(t	VERB
ejpam-481	37	3	)	)	PUNCT
ejpam-481	38	1	=	=	X
ejpam-481	38	2	eλt	eλt	PROPN
ejpam-481	38	3	,	,	PUNCT
ejpam-481	38	4	noting	note	VERB
ejpam-481	38	5	that	that	SCONJ
ejpam-481	38	6	u(0	u(0	NOUN
ejpam-481	38	7	)	)	PUNCT
ejpam-481	38	8	=	=	SYM
ejpam-481	39	1	1	1	X
ejpam-481	39	2	.	.	X
ejpam-481	39	3	using	use	VERB
ejpam-481	39	4	condition	condition	NOUN
ejpam-481	39	5	(	(	PUNCT
ejpam-481	39	6	i	i	NOUN
ejpam-481	39	7	)	)	PUNCT
ejpam-481	39	8	in	in	ADP
ejpam-481	39	9	p1	p1	PROPN
ejpam-481	39	10	,	,	PUNCT
ejpam-481	39	11	we	we	PRON
ejpam-481	39	12	get	get	VERB
ejpam-481	39	13	<	<	X
ejpam-481	39	14	x	x	X
ejpam-481	39	15	,	,	PUNCT
ejpam-481	39	16	x∗	x∗	PROPN
ejpam-481	39	17	>	>	X
ejpam-481	39	18	=	=	PUNCT
ejpam-481	39	19	g(0	g(0	PROPN
ejpam-481	39	20	)	)	PUNCT
ejpam-481	39	21	.	.	PUNCT
ejpam-481	40	1	so	so	ADV
ejpam-481	40	2	eλt	eλt	PROPN
ejpam-481	40	3	g(0	g(0	PROPN
ejpam-481	40	4	)	)	PUNCT
ejpam-481	40	5	=	=	SYM
ejpam-481	40	6	g(t	g(t	PROPN
ejpam-481	40	7	)	)	PUNCT
ejpam-481	40	8	.	.	PUNCT
ejpam-481	41	1	this	this	PRON
ejpam-481	41	2	implies	imply	VERB
ejpam-481	41	3	that	that	SCONJ
ejpam-481	41	4	λ	λ	PROPN
ejpam-481	41	5	=	=	PRON
ejpam-481	41	6	ℓn	ℓn	PROPN
ejpam-481	41	7	(	(	PUNCT
ejpam-481	41	8	g(1	g(1	NOUN
ejpam-481	41	9	)	)	PUNCT
ejpam-481	41	10	g(0	g(0	PROPN
ejpam-481	41	11	)	)	PUNCT
ejpam-481	41	12	)	)	PUNCT
ejpam-481	41	13	,	,	PUNCT
ejpam-481	41	14	and	and	CCONJ
ejpam-481	41	15	u	u	NOUN
ejpam-481	41	16	is	be	AUX
ejpam-481	41	17	determined	determine	VERB
ejpam-481	41	18	.	.	PUNCT
ejpam-481	42	1	substitute	substitute	VERB
ejpam-481	42	2	such	such	ADJ
ejpam-481	42	3	values	value	NOUN
ejpam-481	42	4	in	in	ADP
ejpam-481	42	5	equation	equation	NOUN
ejpam-481	42	6	(	(	PUNCT
ejpam-481	42	7	2	2	NUM
ejpam-481	42	8	)	)	PUNCT
ejpam-481	42	9	and	and	CCONJ
ejpam-481	42	10	apply	apply	VERB
ejpam-481	42	11	x∗	x∗	PROPN
ejpam-481	42	12	to	to	ADP
ejpam-481	42	13	both	both	DET
ejpam-481	42	14	sides	side	NOUN
ejpam-481	42	15	of	of	ADP
ejpam-481	42	16	(	(	PUNCT
ejpam-481	42	17	4	4	X
ejpam-481	42	18	)	)	PUNCT
ejpam-481	42	19	we	we	PRON
ejpam-481	42	20	get	get	VERB
ejpam-481	42	21	λeλt	λeλt	PROPN
ejpam-481	42	22	<	<	X
ejpam-481	42	23	x	x	X
ejpam-481	42	24	,	,	PUNCT
ejpam-481	42	25	x∗	x∗	PROPN
ejpam-481	42	26	>	>	X
ejpam-481	43	1	+	+	NUM
ejpam-481	43	2	eλt	eλt	X
ejpam-481	43	3	<	<	X
ejpam-481	43	4	ax	ax	NOUN
ejpam-481	43	5	,	,	PUNCT
ejpam-481	43	6	x∗	x∗	PROPN
ejpam-481	43	7	>	>	PUNCT
ejpam-481	43	8	=	=	SYM
ejpam-481	43	9	f	f	X
ejpam-481	43	10	(	(	PUNCT
ejpam-481	43	11	t	t	PROPN
ejpam-481	43	12	)	)	PUNCT
ejpam-481	43	13	<	<	X
ejpam-481	44	1	z	z	PROPN
ejpam-481	44	2	,	,	PUNCT
ejpam-481	44	3	x∗	x∗	PROPN
ejpam-481	44	4	>	>	X
ejpam-481	44	5	.	.	PUNCT
ejpam-481	45	1	hence	hence	ADV
ejpam-481	45	2	g′(t	g′(t	VERB
ejpam-481	45	3	)	)	PUNCT
ejpam-481	46	1	+	+	CCONJ
ejpam-481	46	2	eλt	eλt	X
ejpam-481	46	3	<	<	X
ejpam-481	46	4	ax	ax	NOUN
ejpam-481	46	5	,	,	PUNCT
ejpam-481	46	6	x∗	x∗	PROPN
ejpam-481	46	7	>	>	PUNCT
ejpam-481	47	1	=	=	SYM
ejpam-481	47	2	f	f	X
ejpam-481	47	3	(	(	PUNCT
ejpam-481	47	4	t	t	PROPN
ejpam-481	47	5	)	)	PUNCT
ejpam-481	47	6	<	<	X
ejpam-481	47	7	z	z	X
ejpam-481	47	8	,	,	PUNCT
ejpam-481	47	9	x∗	x∗	PROPN
ejpam-481	47	10	>	>	X
ejpam-481	47	11	.	.	PUNCT
ejpam-481	48	1	(	(	PUNCT
ejpam-481	48	2	4	4	X
ejpam-481	48	3	)	)	PUNCT
ejpam-481	48	4	consequently	consequently	ADV
ejpam-481	48	5	,	,	PUNCT
ejpam-481	48	6	for	for	ADP
ejpam-481	48	7	t	t	NOUN
ejpam-481	48	8	=	=	SYM
ejpam-481	48	9	0	0	NUM
ejpam-481	48	10	we	we	PRON
ejpam-481	48	11	get	get	VERB
ejpam-481	48	12	<	<	X
ejpam-481	48	13	ax	ax	NOUN
ejpam-481	48	14	,	,	PUNCT
ejpam-481	48	15	x∗	x∗	X
ejpam-481	48	16	>	>	PUNCT
ejpam-481	49	1	=	=	PUNCT
ejpam-481	49	2	<	<	X
ejpam-481	49	3	z	z	PROPN
ejpam-481	49	4	,	,	PUNCT
ejpam-481	49	5	x∗	x∗	PROPN
ejpam-481	49	6	>	>	X
ejpam-481	49	7	−g′(0	−g′(0	PROPN
ejpam-481	49	8	)	)	PUNCT
ejpam-481	49	9	.	.	PUNCT
ejpam-481	50	1	but	but	CCONJ
ejpam-481	50	2	this	this	PRON
ejpam-481	50	3	together	together	ADV
ejpam-481	50	4	with	with	ADP
ejpam-481	50	5	(	(	PUNCT
ejpam-481	50	6	4	4	NUM
ejpam-481	50	7	)	)	PUNCT
ejpam-481	50	8	determines	determine	VERB
ejpam-481	50	9	f	f	X
ejpam-481	50	10	uniquely	uniquely	ADV
ejpam-481	50	11	.	.	PUNCT
ejpam-481	51	1	finally	finally	ADV
ejpam-481	51	2	we	we	PRON
ejpam-481	51	3	have	have	VERB
ejpam-481	51	4	to	to	PART
ejpam-481	51	5	determine	determine	VERB
ejpam-481	51	6	x	x	PUNCT
ejpam-481	51	7	.	.	PUNCT
ejpam-481	52	1	in	in	ADP
ejpam-481	52	2	(	(	PUNCT
ejpam-481	52	3	2	2	X
ejpam-481	52	4	)	)	PUNCT
ejpam-481	52	5	put	put	VERB
ejpam-481	52	6	t	t	NOUN
ejpam-481	52	7	=	=	SYM
ejpam-481	52	8	0	0	PROPN
ejpam-481	52	9	to	to	PART
ejpam-481	52	10	get	get	VERB
ejpam-481	52	11	λx	λx	NOUN
ejpam-481	52	12	+	+	NOUN
ejpam-481	52	13	ax	ax	NOUN
ejpam-481	52	14	=	=	SYM
ejpam-481	52	15	z	z	NOUN
ejpam-481	52	16	,	,	PUNCT
ejpam-481	52	17	and	and	CCONJ
ejpam-481	52	18	so	so	ADV
ejpam-481	52	19	(	(	PUNCT
ejpam-481	52	20	λ+	λ+	NUM
ejpam-481	52	21	a)x	a)x	PUNCT
ejpam-481	52	22	=	=	PUNCT
ejpam-481	52	23	z.	z.	PROPN
ejpam-481	52	24	however	however	ADV
ejpam-481	52	25	,	,	PUNCT
ejpam-481	52	26	the	the	DET
ejpam-481	52	27	value	value	NOUN
ejpam-481	52	28	of	of	ADP
ejpam-481	52	29	λ	λ	NOUN
ejpam-481	52	30	and	and	CCONJ
ejpam-481	52	31	condition	condition	NOUN
ejpam-481	52	32	(	(	PUNCT
ejpam-481	52	33	ii	ii	NOUN
ejpam-481	52	34	)	)	PUNCT
ejpam-481	52	35	in	in	ADP
ejpam-481	52	36	problem	problem	NOUN
ejpam-481	52	37	p1	p1	NOUN
ejpam-481	52	38	determines	determine	VERB
ejpam-481	52	39	x	x	X
ejpam-481	52	40	uniquely	uniquely	ADV
ejpam-481	52	41	.	.	PUNCT
ejpam-481	53	1	this	this	PRON
ejpam-481	53	2	ends	end	VERB
ejpam-481	53	3	the	the	DET
ejpam-481	53	4	proof	proof	NOUN
ejpam-481	53	5	for	for	ADP
ejpam-481	53	6	case	case	NOUN
ejpam-481	53	7	(	(	PUNCT
ejpam-481	53	8	1	1	X
ejpam-481	53	9	)	)	PUNCT
ejpam-481	53	10	r.	r.	PROPN
ejpam-481	53	11	khalil	khalil	PROPN
ejpam-481	53	12	,	,	PUNCT
ejpam-481	53	13	l.	l.	PROPN
ejpam-481	53	14	abdullah	abdullah	PROPN
ejpam-481	53	15	/	/	PUNCT
ejpam-481	53	16	eur	eur	PROPN
ejpam-481	53	17	.	.	PUNCT
ejpam-481	54	1	j.	j.	PROPN
ejpam-481	54	2	pure	pure	PROPN
ejpam-481	54	3	appl	appl	PROPN
ejpam-481	54	4	.	.	PROPN
ejpam-481	54	5	math	math	PROPN
ejpam-481	54	6	,	,	PUNCT
ejpam-481	54	7	3	3	NUM
ejpam-481	54	8	(	(	PUNCT
ejpam-481	54	9	2010	2010	NUM
ejpam-481	54	10	)	)	PUNCT
ejpam-481	54	11	,	,	PUNCT
ejpam-481	54	12	725	725	NUM
ejpam-481	54	13	-	-	SYM
ejpam-481	54	14	729	729	NUM
ejpam-481	54	15	727	727	NUM
ejpam-481	54	16	(	(	PUNCT
ejpam-481	54	17	2	2	NUM
ejpam-481	54	18	)	)	PUNCT
ejpam-481	54	19	ax	ax	NOUN
ejpam-481	54	20	=	=	NOUN
ejpam-481	54	21	ηx	ηx	NOUN
ejpam-481	54	22	.	.	PUNCT
ejpam-481	55	1	then	then	ADV
ejpam-481	55	2	from	from	ADP
ejpam-481	55	3	(	(	PUNCT
ejpam-481	55	4	2	2	X
ejpam-481	55	5	)	)	PUNCT
ejpam-481	55	6	we	we	PRON
ejpam-481	55	7	have	have	VERB
ejpam-481	55	8	u′	u′	PRON
ejpam-481	55	9	⊗	⊗	NOUN
ejpam-481	55	10	x	x	PUNCT
ejpam-481	56	1	+	+	ADV
ejpam-481	56	2	ηu⊗	ηu⊗	X
ejpam-481	56	3	x	x	X
ejpam-481	56	4	=	=	SYM
ejpam-481	56	5	f	f	PROPN
ejpam-481	56	6	⊗	⊗	PROPN
ejpam-481	56	7	z.	z.	PROPN
ejpam-481	56	8	(	(	PUNCT
ejpam-481	56	9	5	5	X
ejpam-481	56	10	)	)	PUNCT
ejpam-481	56	11	apply	apply	VERB
ejpam-481	56	12	x∗	x∗	PROPN
ejpam-481	56	13	to	to	ADP
ejpam-481	56	14	both	both	DET
ejpam-481	56	15	sides	side	NOUN
ejpam-481	56	16	of	of	ADP
ejpam-481	56	17	(	(	PUNCT
ejpam-481	56	18	5	5	NUM
ejpam-481	56	19	)	)	PUNCT
ejpam-481	56	20	to	to	PART
ejpam-481	56	21	get	get	VERB
ejpam-481	56	22	g′(t	g′(t	PROPN
ejpam-481	56	23	)	)	PUNCT
ejpam-481	56	24	+	+	NOUN
ejpam-481	56	25	ηg(t	ηg(t	NOUN
ejpam-481	56	26	)	)	PUNCT
ejpam-481	57	1	=	=	SYM
ejpam-481	57	2	f	f	PROPN
ejpam-481	57	3	(	(	PUNCT
ejpam-481	57	4	t	t	PROPN
ejpam-481	57	5	)	)	PUNCT
ejpam-481	57	6	<	<	X
ejpam-481	58	1	z	z	X
ejpam-481	58	2	,	,	PUNCT
ejpam-481	58	3	x∗	x∗	PROPN
ejpam-481	58	4	>	>	X
ejpam-481	58	5	.	.	PUNCT
ejpam-481	59	1	(	(	PUNCT
ejpam-481	59	2	6	6	X
ejpam-481	59	3	)	)	PUNCT
ejpam-481	59	4	use	use	NOUN
ejpam-481	59	5	condition	condition	NOUN
ejpam-481	59	6	(	(	PUNCT
ejpam-481	59	7	i	i	NOUN
ejpam-481	59	8	)	)	PUNCT
ejpam-481	59	9	in	in	ADP
ejpam-481	59	10	p1	p1	PROPN
ejpam-481	59	11	and	and	CCONJ
ejpam-481	59	12	put	put	VERB
ejpam-481	59	13	t	t	NOUN
ejpam-481	59	14	=	=	SYM
ejpam-481	59	15	0	0	PROPN
ejpam-481	59	16	to	to	PART
ejpam-481	59	17	get	get	VERB
ejpam-481	59	18	η	η	X
ejpam-481	59	19	=	=	PROPN
ejpam-481	59	20	<	<	X
ejpam-481	59	21	z	z	PROPN
ejpam-481	59	22	,	,	PUNCT
ejpam-481	59	23	x∗>−g	x∗>−g	PUNCT
ejpam-481	60	1	′(0	′(0	PROPN
ejpam-481	60	2	)	)	PUNCT
ejpam-481	60	3	g(0	g(0	NOUN
ejpam-481	60	4	)	)	PUNCT
ejpam-481	60	5	and	and	CCONJ
ejpam-481	60	6	so	so	ADV
ejpam-481	60	7	η	η	PROPN
ejpam-481	60	8	is	be	AUX
ejpam-481	60	9	determined	determine	VERB
ejpam-481	60	10	.	.	PUNCT
ejpam-481	61	1	in	in	ADP
ejpam-481	61	2	(	(	PUNCT
ejpam-481	61	3	6	6	NUM
ejpam-481	61	4	)	)	PUNCT
ejpam-481	61	5	,	,	PUNCT
ejpam-481	61	6	since	since	SCONJ
ejpam-481	61	7	η	η	PROPN
ejpam-481	61	8	and	and	CCONJ
ejpam-481	61	9	g(t	g(t	PROPN
ejpam-481	61	10	)	)	PUNCT
ejpam-481	61	11	are	be	AUX
ejpam-481	61	12	known	know	VERB
ejpam-481	61	13	,	,	PUNCT
ejpam-481	61	14	then	then	ADV
ejpam-481	61	15	f	f	PROPN
ejpam-481	61	16	(	(	PUNCT
ejpam-481	61	17	t	t	PROPN
ejpam-481	61	18	)	)	PUNCT
ejpam-481	61	19	is	be	AUX
ejpam-481	61	20	determined	determine	VERB
ejpam-481	61	21	uniquely	uniquely	ADV
ejpam-481	61	22	.	.	PUNCT
ejpam-481	62	1	so	so	ADV
ejpam-481	62	2	u	u	PRON
ejpam-481	62	3	and	and	CCONJ
ejpam-481	62	4	x	x	NOUN
ejpam-481	62	5	are	be	AUX
ejpam-481	62	6	what	what	PRON
ejpam-481	62	7	is	be	AUX
ejpam-481	62	8	left	leave	VERB
ejpam-481	62	9	to	to	PART
ejpam-481	62	10	be	be	AUX
ejpam-481	62	11	determined	determine	VERB
ejpam-481	62	12	.	.	PUNCT
ejpam-481	63	1	from	from	ADP
ejpam-481	63	2	(	(	PUNCT
ejpam-481	63	3	5	5	NUM
ejpam-481	63	4	)	)	PUNCT
ejpam-481	63	5	,	,	PUNCT
ejpam-481	63	6	we	we	PRON
ejpam-481	63	7	have	have	VERB
ejpam-481	63	8	(	(	PUNCT
ejpam-481	63	9	u′	u′	PROPN
ejpam-481	63	10	+	+	CCONJ
ejpam-481	63	11	ηu)⊗	ηu)⊗	NOUN
ejpam-481	63	12	x	x	SYM
ejpam-481	64	1	=	=	PUNCT
ejpam-481	64	2	f	f	PROPN
ejpam-481	64	3	⊗	⊗	PROPN
ejpam-481	64	4	z.	z.	PROPN
ejpam-481	65	1	so	so	ADV
ejpam-481	65	2	we	we	PRON
ejpam-481	65	3	have	have	VERB
ejpam-481	65	4	equality	equality	NOUN
ejpam-481	65	5	of	of	ADP
ejpam-481	65	6	two	two	NUM
ejpam-481	65	7	atoms	atom	NOUN
ejpam-481	65	8	.	.	PUNCT
ejpam-481	66	1	hence	hence	ADV
ejpam-481	66	2	from	from	ADP
ejpam-481	66	3	theory	theory	NOUN
ejpam-481	66	4	of	of	ADP
ejpam-481	66	5	tensor	tensor	NOUN
ejpam-481	66	6	product	product	NOUN
ejpam-481	66	7	we	we	PRON
ejpam-481	66	8	have	have	VERB
ejpam-481	66	9	u′	u′	PRON
ejpam-481	67	1	+	+	NOUN
ejpam-481	67	2	ηu	ηu	NOUN
ejpam-481	67	3	=	=	PUNCT
ejpam-481	67	4	γ	γ	X
ejpam-481	67	5	f	f	PROPN
ejpam-481	67	6	,	,	PUNCT
ejpam-481	67	7	and	and	CCONJ
ejpam-481	67	8	(	(	PUNCT
ejpam-481	67	9	7	7	X
ejpam-481	67	10	)	)	PUNCT
ejpam-481	67	11	x	x	X
ejpam-481	68	1	=	=	SYM
ejpam-481	68	2	1	1	NUM
ejpam-481	68	3	γ	γ	X
ejpam-481	68	4	z	z	PROPN
ejpam-481	68	5	(	(	PUNCT
ejpam-481	68	6	8)	8)	NUM
ejpam-481	68	7	the	the	DET
ejpam-481	68	8	first	first	ADJ
ejpam-481	68	9	equation	equation	NOUN
ejpam-481	68	10	is	be	AUX
ejpam-481	68	11	a	a	DET
ejpam-481	68	12	linear	linear	ADJ
ejpam-481	68	13	differential	differential	ADJ
ejpam-481	68	14	equation	equation	NOUN
ejpam-481	68	15	of	of	ADP
ejpam-481	68	16	order	order	NOUN
ejpam-481	68	17	one	one	NUM
ejpam-481	68	18	.	.	PUNCT
ejpam-481	69	1	so	so	ADV
ejpam-481	69	2	u(t	u(t	NOUN
ejpam-481	69	3	)	)	PUNCT
ejpam-481	69	4	=	=	SYM
ejpam-481	69	5	−ηt	−ηt	NOUN
ejpam-481	69	6	e	e	X
ejpam-481	69	7	[	[	PUNCT
ejpam-481	69	8	∫	∫	PROPN
ejpam-481	69	9	γ	γ	X
ejpam-481	69	10	f	f	PROPN
ejpam-481	69	11	(	(	PUNCT
ejpam-481	69	12	t	t	PROPN
ejpam-481	69	13	)	)	PUNCT
ejpam-481	69	14	ηt	ηt	ADP
ejpam-481	69	15	e	e	PROPN
ejpam-481	69	16	d	d	PROPN
ejpam-481	69	17	t	t	PROPN
ejpam-481	69	18	]	]	X
ejpam-481	69	19	+	+	CCONJ
ejpam-481	69	20	c	c	NOUN
ejpam-481	69	21	−ηt	−ηt	NOUN
ejpam-481	69	22	e	e	X
ejpam-481	69	23	.	.	PUNCT
ejpam-481	70	1	now	now	ADV
ejpam-481	70	2	,	,	PUNCT
ejpam-481	70	3	u	u	PRON
ejpam-481	70	4	will	will	AUX
ejpam-481	70	5	be	be	AUX
ejpam-481	70	6	determined	determine	VERB
ejpam-481	70	7	completely	completely	ADV
ejpam-481	70	8	if	if	SCONJ
ejpam-481	70	9	γ	γ	PROPN
ejpam-481	70	10	and	and	CCONJ
ejpam-481	70	11	c	c	PROPN
ejpam-481	70	12	are	be	AUX
ejpam-481	70	13	determined	determine	VERB
ejpam-481	70	14	.	.	PUNCT
ejpam-481	71	1	to	to	PART
ejpam-481	71	2	do	do	VERB
ejpam-481	71	3	that	that	SCONJ
ejpam-481	71	4	we	we	PRON
ejpam-481	71	5	take	take	VERB
ejpam-481	71	6	the	the	DET
ejpam-481	71	7	tensor	tensor	NOUN
ejpam-481	71	8	product	product	NOUN
ejpam-481	71	9	of	of	ADP
ejpam-481	71	10	x	x	PUNCT
ejpam-481	71	11	with	with	ADP
ejpam-481	71	12	both	both	DET
ejpam-481	71	13	sides	side	NOUN
ejpam-481	71	14	of	of	ADP
ejpam-481	71	15	u′	u′	PROPN
ejpam-481	71	16	+	+	CCONJ
ejpam-481	71	17	ηu	ηu	ADJ
ejpam-481	71	18	=	=	PUNCT
ejpam-481	71	19	γ	γ	X
ejpam-481	71	20	f	f	X
ejpam-481	71	21	to	to	PART
ejpam-481	71	22	get	get	VERB
ejpam-481	71	23	(	(	PUNCT
ejpam-481	71	24	u′	u′	PROPN
ejpam-481	71	25	+	+	CCONJ
ejpam-481	71	26	ηu)⊗	ηu)⊗	NOUN
ejpam-481	71	27	x	x	SYM
ejpam-481	71	28	=	=	SYM
ejpam-481	71	29	γ	γ	X
ejpam-481	71	30	f	f	PROPN
ejpam-481	71	31	⊗	⊗	PROPN
ejpam-481	71	32	x	x	INTJ
ejpam-481	71	33	.	.	PUNCT
ejpam-481	72	1	again	again	ADV
ejpam-481	72	2	,	,	PUNCT
ejpam-481	72	3	we	we	PRON
ejpam-481	72	4	use	use	VERB
ejpam-481	72	5	condition	condition	NOUN
ejpam-481	72	6	(	(	PUNCT
ejpam-481	72	7	i	i	NOUN
ejpam-481	72	8	)	)	PUNCT
ejpam-481	72	9	in	in	ADP
ejpam-481	72	10	p1	p1	PROPN
ejpam-481	72	11	to	to	PART
ejpam-481	72	12	conclude	conclude	VERB
ejpam-481	72	13	g′(t	g′(t	PROPN
ejpam-481	72	14	)	)	PUNCT
ejpam-481	72	15	+	+	NUM
ejpam-481	72	16	ηg(t	ηg(t	NOUN
ejpam-481	72	17	)	)	PUNCT
ejpam-481	72	18	=	=	SYM
ejpam-481	72	19	γ	γ	X
ejpam-481	72	20	f	f	PROPN
ejpam-481	72	21	(	(	PUNCT
ejpam-481	72	22	t	t	PROPN
ejpam-481	72	23	)	)	PUNCT
ejpam-481	72	24	<	<	X
ejpam-481	72	25	x	x	X
ejpam-481	72	26	,	,	PUNCT
ejpam-481	72	27	x∗	x∗	PROPN
ejpam-481	72	28	>	>	X
ejpam-481	72	29	.	.	PUNCT
ejpam-481	73	1	but	but	CCONJ
ejpam-481	73	2	<	<	X
ejpam-481	73	3	x	x	X
ejpam-481	73	4	,	,	PUNCT
ejpam-481	73	5	x∗	x∗	PROPN
ejpam-481	73	6	>	>	X
ejpam-481	73	7	=	=	SYM
ejpam-481	73	8	g(0	g(0	PROPN
ejpam-481	73	9	)	)	PUNCT
ejpam-481	73	10	.	.	PUNCT
ejpam-481	74	1	hence	hence	ADV
ejpam-481	74	2	γ=	γ=	PROPN
ejpam-481	74	3	g	g	PROPN
ejpam-481	74	4	′(0)+ηg(0	′(0)+ηg(0	NUM
ejpam-481	74	5	)	)	PUNCT
ejpam-481	74	6	f	f	PROPN
ejpam-481	74	7	(	(	PUNCT
ejpam-481	74	8	0	0	NUM
ejpam-481	74	9	)	)	PUNCT
ejpam-481	74	10	and	and	CCONJ
ejpam-481	74	11	γ	γ	NOUN
ejpam-481	74	12	is	be	AUX
ejpam-481	74	13	determined	determine	VERB
ejpam-481	74	14	uniquely	uniquely	ADV
ejpam-481	74	15	.	.	PUNCT
ejpam-481	75	1	hence	hence	ADV
ejpam-481	75	2	in	in	ADP
ejpam-481	75	3	equation	equation	NOUN
ejpam-481	75	4	(	(	PUNCT
ejpam-481	75	5	7	7	X
ejpam-481	75	6	)	)	PUNCT
ejpam-481	75	7	u	u	NOUN
ejpam-481	75	8	can	can	AUX
ejpam-481	75	9	be	be	AUX
ejpam-481	75	10	determined	determine	VERB
ejpam-481	75	11	uniquely	uniquely	ADV
ejpam-481	75	12	,	,	PUNCT
ejpam-481	75	13	noting	note	VERB
ejpam-481	75	14	that	that	SCONJ
ejpam-481	75	15	u(0	u(0	NOUN
ejpam-481	75	16	)	)	PUNCT
ejpam-481	75	17	=	=	SYM
ejpam-481	75	18	1	1	NUM
ejpam-481	75	19	which	which	PRON
ejpam-481	75	20	determines	determine	VERB
ejpam-481	75	21	c.	c.	NOUN
ejpam-481	75	22	as	as	ADP
ejpam-481	75	23	for	for	ADP
ejpam-481	75	24	x	x	PRON
ejpam-481	75	25	,	,	PUNCT
ejpam-481	75	26	from	from	ADP
ejpam-481	75	27	(	(	PUNCT
ejpam-481	75	28	5	5	X
ejpam-481	75	29	)	)	PUNCT
ejpam-481	75	30	we	we	PRON
ejpam-481	75	31	have	have	VERB
ejpam-481	75	32	u′(t)x	u′(t)x	PROPN
ejpam-481	75	33	+	+	PROPN
ejpam-481	75	34	ηu(t)x	ηu(t)x	PROPN
ejpam-481	75	35	=	=	SYM
ejpam-481	75	36	f	f	PROPN
ejpam-481	75	37	(	(	PUNCT
ejpam-481	75	38	t)z	t)z	NOUN
ejpam-481	75	39	.	.	PUNCT
ejpam-481	76	1	since	since	SCONJ
ejpam-481	76	2	this	this	PRON
ejpam-481	76	3	is	be	AUX
ejpam-481	76	4	true	true	ADJ
ejpam-481	76	5	for	for	ADP
ejpam-481	76	6	all	all	DET
ejpam-481	76	7	t	t	PROPN
ejpam-481	76	8	,	,	PUNCT
ejpam-481	76	9	we	we	PRON
ejpam-481	76	10	get	get	VERB
ejpam-481	76	11	x	x	X
ejpam-481	76	12	=	=	PUNCT
ejpam-481	76	13	z	z	PROPN
ejpam-481	76	14	u′(0)+η	u′(0)+η	PROPN
ejpam-481	76	15	.	.	PUNCT
ejpam-481	77	1	this	this	PRON
ejpam-481	77	2	ends	end	VERB
ejpam-481	77	3	the	the	DET
ejpam-481	77	4	proof	proof	NOUN
ejpam-481	77	5	of	of	ADP
ejpam-481	77	6	the	the	DET
ejpam-481	77	7	theorem	theorem	NOUN
ejpam-481	77	8	.	.	PROPN
ejpam-481	78	1	3	3	X
ejpam-481	78	2	.	.	X
ejpam-481	78	3	non	non	ADJ
ejpam-481	78	4	-	-	ADJ
ejpam-481	78	5	degenerate	degenerate	ADJ
ejpam-481	78	6	inverse	inverse	NOUN
ejpam-481	78	7	problem	problem	NOUN
ejpam-481	78	8	let	let	VERB
ejpam-481	78	9	a	a	PRON
ejpam-481	78	10	and	and	CCONJ
ejpam-481	78	11	b	b	NOUN
ejpam-481	78	12	be	be	AUX
ejpam-481	78	13	two	two	NUM
ejpam-481	78	14	closed	closed	ADJ
ejpam-481	78	15	linear	linear	ADJ
ejpam-481	78	16	operators	operator	NOUN
ejpam-481	78	17	on	on	ADP
ejpam-481	78	18	the	the	DET
ejpam-481	78	19	banach	banach	NOUN
ejpam-481	78	20	space	space	NOUN
ejpam-481	78	21	x	x	X
ejpam-481	78	22	.	.	PUNCT
ejpam-481	79	1	an	an	DET
ejpam-481	79	2	element	element	NOUN
ejpam-481	79	3	w	w	PROPN
ejpam-481	79	4	∈	∈	PROPN
ejpam-481	79	5	x	x	PUNCT
ejpam-481	79	6	is	be	AUX
ejpam-481	79	7	called	call	VERB
ejpam-481	79	8	uniquely	uniquely	ADV
ejpam-481	79	9	imaged	image	VERB
ejpam-481	79	10	by	by	ADP
ejpam-481	79	11	an	an	DET
ejpam-481	79	12	operator	operator	NOUN
ejpam-481	79	13	j	j	NOUN
ejpam-481	79	14	on	on	ADP
ejpam-481	79	15	x	x	SYM
ejpam-481	79	16	if	if	SCONJ
ejpam-481	79	17	there	there	PRON
ejpam-481	79	18	is	be	VERB
ejpam-481	79	19	a	a	DET
ejpam-481	79	20	unique	unique	ADJ
ejpam-481	79	21	y	y	NOUN
ejpam-481	79	22	∈	∈	PROPN
ejpam-481	79	23	x	x	PUNCT
ejpam-481	79	24	such	such	ADJ
ejpam-481	79	25	that	that	SCONJ
ejpam-481	79	26	j	j	PROPN
ejpam-481	79	27	y	y	PROPN
ejpam-481	79	28	=	=	PROPN
ejpam-481	79	29	w.	w.	PROPN
ejpam-481	79	30	note	note	VERB
ejpam-481	79	31	that	that	SCONJ
ejpam-481	79	32	for	for	ADP
ejpam-481	79	33	injective	injective	ADJ
ejpam-481	79	34	operators	operator	NOUN
ejpam-481	79	35	,	,	PUNCT
ejpam-481	79	36	every	every	DET
ejpam-481	79	37	element	element	NOUN
ejpam-481	79	38	in	in	ADP
ejpam-481	79	39	the	the	DET
ejpam-481	79	40	range	range	NOUN
ejpam-481	79	41	is	be	AUX
ejpam-481	79	42	uniquely	uniquely	ADV
ejpam-481	79	43	imaged	image	VERB
ejpam-481	79	44	.	.	PUNCT
ejpam-481	80	1	consider	consider	VERB
ejpam-481	80	2	the	the	DET
ejpam-481	80	3	problem	problem	NOUN
ejpam-481	80	4	u′(t)bx	u′(t)bx	PROPN
ejpam-481	81	1	+	+	NUM
ejpam-481	81	2	u(t)ax	u(t)ax	ADP
ejpam-481	81	3	=	=	SYM
ejpam-481	81	4	f	f	PROPN
ejpam-481	81	5	(	(	PUNCT
ejpam-481	81	6	t)z	t)z	NOUN
ejpam-481	81	7	(	(	PUNCT
ejpam-481	81	8	9	9	NUM
ejpam-481	81	9	)	)	PUNCT
ejpam-481	81	10	with	with	ADP
ejpam-481	81	11	the	the	DET
ejpam-481	81	12	conditions	condition	NOUN
ejpam-481	81	13	(	(	PUNCT
ejpam-481	81	14	i	i	NOUN
ejpam-481	81	15	)	)	PUNCT
ejpam-481	81	16	there	there	PRON
ejpam-481	81	17	is	be	VERB
ejpam-481	81	18	x∗	x∗	PROPN
ejpam-481	81	19	∈	∈	PROPN
ejpam-481	81	20	x	x	X
ejpam-481	81	21	∗	∗	NOUN
ejpam-481	81	22	and	and	CCONJ
ejpam-481	81	23	g	g	PROPN
ejpam-481	81	24	∈	∈	PROPN
ejpam-481	81	25	c(i	c(i	NOUN
ejpam-481	81	26	,	,	PUNCT
ejpam-481	81	27	r	r	NOUN
ejpam-481	81	28	)	)	PUNCT
ejpam-481	81	29	such	such	ADJ
ejpam-481	81	30	that	that	SCONJ
ejpam-481	81	31	<	<	X
ejpam-481	81	32	u(t)x	u(t)x	PROPN
ejpam-481	81	33	,	,	PUNCT
ejpam-481	81	34	x∗	x∗	PROPN
ejpam-481	81	35	>	>	PUNCT
ejpam-481	81	36	=	=	SYM
ejpam-481	81	37	g(t	g(t	PROPN
ejpam-481	81	38	)	)	PUNCT
ejpam-481	81	39	.	.	PUNCT
ejpam-481	82	1	(	(	PUNCT
ejpam-481	82	2	ii	ii	NOUN
ejpam-481	82	3	)	)	PUNCT
ejpam-481	82	4	z	z	NOUN
ejpam-481	82	5	is	be	AUX
ejpam-481	82	6	uniquely	uniquely	ADV
ejpam-481	82	7	imaged	image	VERB
ejpam-481	82	8	for	for	ADP
ejpam-481	82	9	the	the	DET
ejpam-481	82	10	operators	operator	NOUN
ejpam-481	82	11	a	a	PRON
ejpam-481	82	12	and	and	CCONJ
ejpam-481	82	13	ℓn	ℓn	ADV
ejpam-481	82	14	(	(	PUNCT
ejpam-481	82	15	g(1	g(1	NOUN
ejpam-481	82	16	)	)	PUNCT
ejpam-481	82	17	g(0	g(0	PROPN
ejpam-481	82	18	)	)	PUNCT
ejpam-481	82	19	)	)	PUNCT
ejpam-481	83	1	b+	b+	X
ejpam-481	83	2	a	a	PRON
ejpam-481	83	3	we	we	PRON
ejpam-481	83	4	call	call	VERB
ejpam-481	83	5	such	such	ADJ
ejpam-481	83	6	problem	problem	NOUN
ejpam-481	83	7	p2	p2	NOUN
ejpam-481	83	8	.	.	PUNCT
ejpam-481	84	1	r.	r.	PROPN
ejpam-481	84	2	khalil	khalil	PROPN
ejpam-481	84	3	,	,	PUNCT
ejpam-481	84	4	l.	l.	PROPN
ejpam-481	84	5	abdullah	abdullah	PROPN
ejpam-481	84	6	/	/	PUNCT
ejpam-481	84	7	eur	eur	PROPN
ejpam-481	84	8	.	.	PUNCT
ejpam-481	85	1	j.	j.	PROPN
ejpam-481	85	2	pure	pure	PROPN
ejpam-481	85	3	appl	appl	PROPN
ejpam-481	85	4	.	.	PROPN
ejpam-481	85	5	math	math	PROPN
ejpam-481	85	6	,	,	PUNCT
ejpam-481	85	7	3	3	NUM
ejpam-481	85	8	(	(	PUNCT
ejpam-481	85	9	2010	2010	NUM
ejpam-481	85	10	)	)	PUNCT
ejpam-481	85	11	,	,	PUNCT
ejpam-481	85	12	725	725	NUM
ejpam-481	85	13	-	-	SYM
ejpam-481	85	14	729	729	NUM
ejpam-481	85	15	728	728	NUM
ejpam-481	85	16	theorem	theorem	NOUN
ejpam-481	85	17	2	2	NUM
ejpam-481	85	18	.	.	NOUN
ejpam-481	85	19	problem	problem	NOUN
ejpam-481	85	20	p2	p2	PROPN
ejpam-481	85	21	has	have	VERB
ejpam-481	85	22	a	a	DET
ejpam-481	85	23	unique	unique	ADJ
ejpam-481	85	24	solution	solution	NOUN
ejpam-481	85	25	.	.	PUNCT
ejpam-481	86	1	proof	proof	NOUN
ejpam-481	86	2	.	.	PUNCT
ejpam-481	87	1	we	we	PRON
ejpam-481	87	2	solve	solve	VERB
ejpam-481	87	3	the	the	DET
ejpam-481	87	4	problem	problem	NOUN
ejpam-481	87	5	if	if	SCONJ
ejpam-481	87	6	we	we	PRON
ejpam-481	87	7	can	can	AUX
ejpam-481	87	8	determine	determine	VERB
ejpam-481	87	9	u	u	NOUN
ejpam-481	87	10	,	,	PUNCT
ejpam-481	87	11	x	x	PRON
ejpam-481	87	12	,	,	PUNCT
ejpam-481	87	13	and	and	CCONJ
ejpam-481	87	14	f	f	X
ejpam-481	87	15	uniquely	uniquely	ADV
ejpam-481	87	16	.	.	PUNCT
ejpam-481	88	1	as	as	ADP
ejpam-481	88	2	in	in	ADP
ejpam-481	88	3	theorem	theorem	NOUN
ejpam-481	88	4	1	1	NUM
ejpam-481	88	5	,	,	PUNCT
ejpam-481	88	6	we	we	PRON
ejpam-481	88	7	can	can	AUX
ejpam-481	88	8	assume	assume	VERB
ejpam-481	88	9	that	that	SCONJ
ejpam-481	88	10	u(0	u(0	NOUN
ejpam-481	88	11	)	)	PUNCT
ejpam-481	89	1	=	=	SYM
ejpam-481	89	2	f	f	PROPN
ejpam-481	89	3	(	(	PUNCT
ejpam-481	89	4	0	0	NUM
ejpam-481	89	5	)	)	PUNCT
ejpam-481	89	6	=	=	SYM
ejpam-481	90	1	1	1	X
ejpam-481	90	2	.	.	PUNCT
ejpam-481	91	1	so	so	ADV
ejpam-481	91	2	condition	condition	NOUN
ejpam-481	91	3	(	(	PUNCT
ejpam-481	91	4	i	i	NOUN
ejpam-481	91	5	)	)	PUNCT
ejpam-481	91	6	implies	imply	VERB
ejpam-481	91	7	that	that	SCONJ
ejpam-481	91	8	<	<	X
ejpam-481	91	9	x	x	X
ejpam-481	91	10	,	,	PUNCT
ejpam-481	91	11	x∗	x∗	PROPN
ejpam-481	91	12	>	>	X
ejpam-481	91	13	=	=	SYM
ejpam-481	91	14	g(0	g(0	PROPN
ejpam-481	91	15	)	)	PUNCT
ejpam-481	91	16	,	,	PUNCT
ejpam-481	91	17	and	and	CCONJ
ejpam-481	91	18	so	so	ADV
ejpam-481	91	19	from	from	ADP
ejpam-481	91	20	condition	condition	NOUN
ejpam-481	91	21	(	(	PUNCT
ejpam-481	91	22	i	i	NOUN
ejpam-481	91	23	)	)	PUNCT
ejpam-481	91	24	we	we	PRON
ejpam-481	91	25	get	get	VERB
ejpam-481	91	26	u(t	u(t	NOUN
ejpam-481	91	27	)	)	PUNCT
ejpam-481	91	28	=	=	SYM
ejpam-481	91	29	g(t	g(t	PROPN
ejpam-481	91	30	)	)	PUNCT
ejpam-481	91	31	g(0	g(0	PROPN
ejpam-481	91	32	)	)	PUNCT
ejpam-481	91	33	and	and	CCONJ
ejpam-481	91	34	u	u	NOUN
ejpam-481	91	35	is	be	AUX
ejpam-481	91	36	determined	determine	VERB
ejpam-481	91	37	uniquely	uniquely	ADV
ejpam-481	91	38	.	.	PUNCT
ejpam-481	92	1	now	now	ADV
ejpam-481	92	2	we	we	PRON
ejpam-481	92	3	write	write	VERB
ejpam-481	92	4	equation	equation	NOUN
ejpam-481	92	5	(	(	PUNCT
ejpam-481	92	6	9	9	NUM
ejpam-481	92	7	)	)	PUNCT
ejpam-481	92	8	in	in	ADP
ejpam-481	92	9	tensor	tensor	NOUN
ejpam-481	92	10	product	product	NOUN
ejpam-481	92	11	form	form	NOUN
ejpam-481	92	12	to	to	PART
ejpam-481	92	13	get	get	VERB
ejpam-481	92	14	u′	u′	PRON
ejpam-481	92	15	⊗	⊗	PROPN
ejpam-481	92	16	bx	bx	PROPN
ejpam-481	93	1	+	+	CCONJ
ejpam-481	93	2	u⊗	u⊗	ADJ
ejpam-481	93	3	ax	ax	NOUN
ejpam-481	93	4	=	=	PUNCT
ejpam-481	93	5	f	f	PROPN
ejpam-481	93	6	⊗	⊗	PROPN
ejpam-481	93	7	z.	z.	PROPN
ejpam-481	94	1	since	since	SCONJ
ejpam-481	94	2	we	we	PRON
ejpam-481	94	3	have	have	VERB
ejpam-481	94	4	the	the	DET
ejpam-481	94	5	sum	sum	NOUN
ejpam-481	94	6	of	of	ADP
ejpam-481	94	7	two	two	NUM
ejpam-481	94	8	atoms	atom	NOUN
ejpam-481	94	9	is	be	AUX
ejpam-481	94	10	an	an	DET
ejpam-481	94	11	atom	atom	NOUN
ejpam-481	94	12	,	,	PUNCT
ejpam-481	94	13	then	then	ADV
ejpam-481	94	14	we	we	PRON
ejpam-481	94	15	have	have	VERB
ejpam-481	94	16	two	two	NUM
ejpam-481	94	17	cases	case	NOUN
ejpam-481	94	18	(	(	PUNCT
ejpam-481	94	19	1	1	NUM
ejpam-481	94	20	)	)	PUNCT
ejpam-481	94	21	u′	u′	PROPN
ejpam-481	94	22	=	=	SYM
ejpam-481	94	23	λu	λu	PROPN
ejpam-481	94	24	and	and	CCONJ
ejpam-481	94	25	(	(	PUNCT
ejpam-481	94	26	2	2	X
ejpam-481	94	27	)	)	PUNCT
ejpam-481	94	28	bx	bx	NOUN
ejpam-481	95	1	=	=	NOUN
ejpam-481	96	1	γax	γax	PROPN
ejpam-481	96	2	.	.	PUNCT
ejpam-481	97	1	let	let	VERB
ejpam-481	97	2	us	we	PRON
ejpam-481	97	3	consider	consider	VERB
ejpam-481	97	4	case	case	NOUN
ejpam-481	97	5	(	(	PUNCT
ejpam-481	97	6	1	1	NUM
ejpam-481	97	7	)	)	PUNCT
ejpam-481	97	8	.	.	PUNCT
ejpam-481	98	1	since	since	SCONJ
ejpam-481	98	2	u(0	u(0	PROPN
ejpam-481	98	3	)	)	PUNCT
ejpam-481	98	4	=	=	SYM
ejpam-481	98	5	1	1	NUM
ejpam-481	98	6	,	,	PUNCT
ejpam-481	98	7	we	we	PRON
ejpam-481	98	8	get	get	VERB
ejpam-481	98	9	u(t	u(t	NOUN
ejpam-481	98	10	)	)	PUNCT
ejpam-481	99	1	=	=	X
ejpam-481	99	2	eλt	eλt	PROPN
ejpam-481	99	3	,	,	PUNCT
ejpam-481	99	4	where	where	SCONJ
ejpam-481	99	5	λ	λ	NOUN
ejpam-481	99	6	to	to	PART
ejpam-481	99	7	be	be	AUX
ejpam-481	99	8	determined	determine	VERB
ejpam-481	99	9	.	.	PUNCT
ejpam-481	100	1	further	far	ADV
ejpam-481	100	2	,	,	PUNCT
ejpam-481	100	3	condition	condition	NOUN
ejpam-481	100	4	(	(	PUNCT
ejpam-481	100	5	i	i	NOUN
ejpam-481	100	6	)	)	PUNCT
ejpam-481	100	7	gives	give	VERB
ejpam-481	100	8	u(t	u(t	NOUN
ejpam-481	100	9	)	)	PUNCT
ejpam-481	100	10	=	=	SYM
ejpam-481	100	11	g(t	g(t	PROPN
ejpam-481	100	12	)	)	PUNCT
ejpam-481	100	13	g(0	g(0	PROPN
ejpam-481	100	14	)	)	PUNCT
ejpam-481	100	15	.	.	PUNCT
ejpam-481	101	1	hence	hence	ADV
ejpam-481	101	2	λ=	λ=	VERB
ejpam-481	101	3	ln	ln	PROPN
ejpam-481	101	4	g(t	g(t	PROPN
ejpam-481	101	5	)	)	PUNCT
ejpam-481	101	6	g(0	g(0	PROPN
ejpam-481	101	7	)	)	PUNCT
ejpam-481	101	8	.	.	PUNCT
ejpam-481	102	1	so	so	ADV
ejpam-481	102	2	λ	λ	PROPN
ejpam-481	102	3	is	be	AUX
ejpam-481	102	4	determined	determine	VERB
ejpam-481	102	5	.	.	PUNCT
ejpam-481	103	1	equation	equation	NOUN
ejpam-481	103	2	(	(	PUNCT
ejpam-481	103	3	9	9	NUM
ejpam-481	103	4	)	)	PUNCT
ejpam-481	103	5	now	now	ADV
ejpam-481	103	6	reads	read	VERB
ejpam-481	103	7	λeλt	λeλt	PROPN
ejpam-481	103	8	bx	bx	PROPN
ejpam-481	103	9	+	+	CCONJ
ejpam-481	103	10	eλtax	eλtax	PROPN
ejpam-481	103	11	=	=	SYM
ejpam-481	103	12	f	f	X
ejpam-481	103	13	(	(	PUNCT
ejpam-481	103	14	t)z	t)z	NOUN
ejpam-481	103	15	.	.	PUNCT
ejpam-481	104	1	that	that	PRON
ejpam-481	104	2	is	be	AUX
ejpam-481	104	3	eλt	eλt	PROPN
ejpam-481	104	4	⊗	⊗	PROPN
ejpam-481	104	5	(	(	PUNCT
ejpam-481	104	6	λbx	λbx	X
ejpam-481	104	7	+	+	CCONJ
ejpam-481	104	8	ax	ax	NOUN
ejpam-481	104	9	)	)	PUNCT
ejpam-481	104	10	=	=	PUNCT
ejpam-481	105	1	f	f	PROPN
ejpam-481	105	2	⊗	⊗	PROPN
ejpam-481	105	3	z.	z.	PROPN
ejpam-481	106	1	so	so	ADV
ejpam-481	106	2	two	two	NUM
ejpam-481	106	3	atoms	atom	NOUN
ejpam-481	106	4	are	be	AUX
ejpam-481	106	5	equal	equal	ADJ
ejpam-481	106	6	.	.	PUNCT
ejpam-481	107	1	consequently	consequently	ADV
ejpam-481	107	2	,	,	PUNCT
ejpam-481	107	3	(	(	PUNCT
ejpam-481	107	4	a	a	X
ejpam-481	107	5	)	)	PUNCT
ejpam-481	107	6	eλt	eλt	PROPN
ejpam-481	108	1	=	=	PUNCT
ejpam-481	108	2	a	a	DET
ejpam-481	108	3	f	f	PROPN
ejpam-481	108	4	(	(	PUNCT
ejpam-481	108	5	t	t	PROPN
ejpam-481	108	6	)	)	PUNCT
ejpam-481	108	7	,	,	PUNCT
ejpam-481	108	8	and	and	CCONJ
ejpam-481	108	9	(	(	PUNCT
ejpam-481	108	10	b	b	X
ejpam-481	108	11	)	)	PUNCT
ejpam-481	108	12	(	(	PUNCT
ejpam-481	108	13	λbx	λbx	X
ejpam-481	108	14	+	+	NUM
ejpam-481	108	15	ax	ax	NOUN
ejpam-481	108	16	)	)	PUNCT
ejpam-481	108	17	=	=	SYM
ejpam-481	108	18	1	1	NUM
ejpam-481	108	19	a	a	DET
ejpam-481	108	20	z.	z.	NOUN
ejpam-481	108	21	from	from	ADP
ejpam-481	108	22	(	(	PUNCT
ejpam-481	108	23	a	a	X
ejpam-481	108	24	)	)	PUNCT
ejpam-481	108	25	we	we	PRON
ejpam-481	108	26	get	get	VERB
ejpam-481	108	27	1	1	NUM
ejpam-481	108	28	=	=	NOUN
ejpam-481	108	29	a	a	DET
ejpam-481	108	30	f	f	X
ejpam-481	108	31	(	(	PUNCT
ejpam-481	108	32	0	0	NUM
ejpam-481	108	33	)	)	PUNCT
ejpam-481	108	34	,	,	PUNCT
ejpam-481	108	35	and	and	CCONJ
ejpam-481	108	36	a	a	PRON
ejpam-481	108	37	is	be	AUX
ejpam-481	108	38	determined	determine	VERB
ejpam-481	108	39	,	,	PUNCT
ejpam-481	108	40	so	so	ADV
ejpam-481	108	41	f	f	PROPN
ejpam-481	108	42	is	be	AUX
ejpam-481	108	43	determined	determine	VERB
ejpam-481	108	44	.	.	PUNCT
ejpam-481	109	1	remains	remain	VERB
ejpam-481	109	2	to	to	PART
ejpam-481	109	3	determine	determine	VERB
ejpam-481	109	4	x	x	PUNCT
ejpam-481	109	5	.	.	PUNCT
ejpam-481	110	1	from	from	ADP
ejpam-481	110	2	(	(	PUNCT
ejpam-481	110	3	b	b	NOUN
ejpam-481	110	4	)	)	PUNCT
ejpam-481	110	5	,	,	PUNCT
ejpam-481	110	6	we	we	PRON
ejpam-481	110	7	have	have	VERB
ejpam-481	110	8	(	(	PUNCT
ejpam-481	110	9	λb	λb	X
ejpam-481	110	10	+	+	NOUN
ejpam-481	110	11	a)x	a)x	PUNCT
ejpam-481	111	1	=	=	PUNCT
ejpam-481	111	2	z.	z.	PROPN
ejpam-481	111	3	since	since	SCONJ
ejpam-481	111	4	we	we	PRON
ejpam-481	111	5	assumed	assume	VERB
ejpam-481	111	6	x	x	PUNCT
ejpam-481	111	7	to	to	PART
ejpam-481	111	8	be	be	AUX
ejpam-481	111	9	uniquely	uniquely	ADV
ejpam-481	111	10	imaged	image	VERB
ejpam-481	111	11	for	for	ADP
ejpam-481	111	12	λb+	λb+	PROPN
ejpam-481	111	13	a	a	PROPN
ejpam-481	111	14	,	,	PUNCT
ejpam-481	111	15	then	then	ADV
ejpam-481	111	16	x	x	PUNCT
ejpam-481	111	17	is	be	AUX
ejpam-481	111	18	uniquely	uniquely	ADV
ejpam-481	111	19	determined	determine	VERB
ejpam-481	111	20	.	.	PUNCT
ejpam-481	112	1	(	(	PUNCT
ejpam-481	112	2	2	2	X
ejpam-481	112	3	)	)	PUNCT
ejpam-481	112	4	now	now	ADV
ejpam-481	112	5	we	we	PRON
ejpam-481	112	6	consider	consider	VERB
ejpam-481	112	7	case	case	NOUN
ejpam-481	112	8	(	(	PUNCT
ejpam-481	112	9	2	2	NUM
ejpam-481	112	10	)	)	PUNCT
ejpam-481	112	11	.	.	PUNCT
ejpam-481	113	1	equation	equation	NOUN
ejpam-481	113	2	(	(	PUNCT
ejpam-481	113	3	9	9	NUM
ejpam-481	113	4	)	)	PUNCT
ejpam-481	113	5	now	now	ADV
ejpam-481	113	6	reads	read	VERB
ejpam-481	113	7	u′(t)γax	u′(t)γax	PROPN
ejpam-481	113	8	+	+	CCONJ
ejpam-481	113	9	u(t)ax	u(t)ax	PROPN
ejpam-481	113	10	=	=	SYM
ejpam-481	113	11	f	f	PROPN
ejpam-481	113	12	(	(	PUNCT
ejpam-481	113	13	t)z	t)z	NOUN
ejpam-481	113	14	.	.	PUNCT
ejpam-481	114	1	(	(	PUNCT
ejpam-481	114	2	10	10	NUM
ejpam-481	114	3	)	)	PUNCT
ejpam-481	114	4	since	since	SCONJ
ejpam-481	114	5	condition	condition	NOUN
ejpam-481	114	6	(	(	PUNCT
ejpam-481	114	7	i	i	NOUN
ejpam-481	114	8	)	)	PUNCT
ejpam-481	114	9	together	together	ADV
ejpam-481	114	10	with	with	ADP
ejpam-481	114	11	u(0	u(0	NOUN
ejpam-481	114	12	)	)	PUNCT
ejpam-481	114	13	=	=	SYM
ejpam-481	114	14	1	1	NUM
ejpam-481	114	15	gives	give	VERB
ejpam-481	114	16	u(t	u(t	NOUN
ejpam-481	114	17	)	)	PUNCT
ejpam-481	114	18	=	=	SYM
ejpam-481	114	19	g(t	g(t	PROPN
ejpam-481	114	20	)	)	PUNCT
ejpam-481	114	21	g(0	g(0	PROPN
ejpam-481	114	22	)	)	PUNCT
ejpam-481	114	23	,	,	PUNCT
ejpam-481	114	24	then	then	ADV
ejpam-481	114	25	in	in	ADP
ejpam-481	114	26	equation	equation	NOUN
ejpam-481	114	27	(	(	PUNCT
ejpam-481	114	28	10	10	NUM
ejpam-481	114	29	)	)	PUNCT
ejpam-481	114	30	only	only	ADV
ejpam-481	114	31	x	x	SYM
ejpam-481	114	32	,	,	PUNCT
ejpam-481	114	33	f	f	PROPN
ejpam-481	114	34	,	,	PUNCT
ejpam-481	114	35	and	and	CCONJ
ejpam-481	114	36	γ	γ	NOUN
ejpam-481	114	37	are	be	AUX
ejpam-481	114	38	to	to	PART
ejpam-481	114	39	be	be	AUX
ejpam-481	114	40	determined	determine	VERB
ejpam-481	114	41	.	.	PUNCT
ejpam-481	115	1	equation	equation	NOUN
ejpam-481	115	2	(	(	PUNCT
ejpam-481	115	3	10	10	NUM
ejpam-481	115	4	)	)	PUNCT
ejpam-481	115	5	can	can	AUX
ejpam-481	115	6	be	be	AUX
ejpam-481	115	7	written	write	VERB
ejpam-481	115	8	in	in	ADP
ejpam-481	115	9	the	the	DET
ejpam-481	115	10	form	form	NOUN
ejpam-481	115	11	(	(	PUNCT
ejpam-481	115	12	γu′	γu′	PROPN
ejpam-481	115	13	+	+	CCONJ
ejpam-481	115	14	u)⊗	u)⊗	NOUN
ejpam-481	115	15	ax	ax	NOUN
ejpam-481	115	16	=	=	PUNCT
ejpam-481	115	17	f	f	PROPN
ejpam-481	116	1	⊗	⊗	PROPN
ejpam-481	116	2	z	z	PROPN
ejpam-481	116	3	.	.	PUNCT
ejpam-481	117	1	since	since	SCONJ
ejpam-481	117	2	we	we	PRON
ejpam-481	117	3	have	have	VERB
ejpam-481	117	4	two	two	NUM
ejpam-481	117	5	equal	equal	ADJ
ejpam-481	117	6	atoms	atom	NOUN
ejpam-481	117	7	,	,	PUNCT
ejpam-481	117	8	then	then	ADV
ejpam-481	117	9	(	(	PUNCT
ejpam-481	117	10	c	c	X
ejpam-481	117	11	)	)	PUNCT
ejpam-481	117	12	γu′	γu′	PROPN
ejpam-481	118	1	+	+	CCONJ
ejpam-481	118	2	u	u	X
ejpam-481	118	3	=	=	PROPN
ejpam-481	118	4	η	η	PROPN
ejpam-481	118	5	f	f	PROPN
ejpam-481	118	6	and	and	CCONJ
ejpam-481	118	7	(	(	PUNCT
ejpam-481	118	8	d	d	NOUN
ejpam-481	118	9	)	)	PUNCT
ejpam-481	118	10	ax	ax	NOUN
ejpam-481	118	11	=	=	SYM
ejpam-481	118	12	1	1	NUM
ejpam-481	118	13	η	η	PROPN
ejpam-481	118	14	z.	z.	PROPN
ejpam-481	118	15	from	from	ADP
ejpam-481	118	16	(	(	PUNCT
ejpam-481	118	17	c	c	X
ejpam-481	118	18	)	)	PUNCT
ejpam-481	118	19	we	we	PRON
ejpam-481	118	20	get	get	VERB
ejpam-481	118	21	γu′(0)+	γu′(0)+	PUNCT
ejpam-481	118	22	1=	1=	X
ejpam-481	118	23	η	η	X
ejpam-481	118	24	.	.	PROPN
ejpam-481	119	1	(	(	PUNCT
ejpam-481	119	2	11	11	NUM
ejpam-481	119	3	)	)	PUNCT
ejpam-481	119	4	from	from	ADP
ejpam-481	119	5	(	(	PUNCT
ejpam-481	119	6	d	d	NOUN
ejpam-481	119	7	)	)	PUNCT
ejpam-481	119	8	and	and	CCONJ
ejpam-481	119	9	the	the	DET
ejpam-481	119	10	condition	condition	NOUN
ejpam-481	119	11	z	z	NOUN
ejpam-481	119	12	is	be	AUX
ejpam-481	119	13	uniquely	uniquely	ADV
ejpam-481	119	14	imaged	image	VERB
ejpam-481	119	15	under	under	ADP
ejpam-481	119	16	a	a	PRON
ejpam-481	119	17	we	we	PRON
ejpam-481	119	18	get	get	VERB
ejpam-481	119	19	x	x	X
ejpam-481	119	20	=	=	SYM
ejpam-481	119	21	1	1	NUM
ejpam-481	119	22	η	η	NOUN
ejpam-481	119	23	a−1z	a−1z	NOUN
ejpam-481	119	24	.	.	PUNCT
ejpam-481	119	25	substitute	substitute	NOUN
ejpam-481	119	26	this	this	PRON
ejpam-481	119	27	in	in	ADP
ejpam-481	119	28	(	(	PUNCT
ejpam-481	119	29	10	10	NUM
ejpam-481	119	30	)	)	PUNCT
ejpam-481	119	31	and	and	CCONJ
ejpam-481	119	32	apply	apply	VERB
ejpam-481	119	33	x∗	x∗	PROPN
ejpam-481	119	34	to	to	ADP
ejpam-481	119	35	both	both	DET
ejpam-481	119	36	sides	side	NOUN
ejpam-481	119	37	of	of	ADP
ejpam-481	119	38	the	the	DET
ejpam-481	119	39	resulting	result	VERB
ejpam-481	119	40	equation	equation	NOUN
ejpam-481	119	41	,	,	PUNCT
ejpam-481	119	42	together	together	ADV
ejpam-481	119	43	with	with	ADP
ejpam-481	119	44	<	<	X
ejpam-481	119	45	x	x	X
ejpam-481	119	46	,	,	PUNCT
ejpam-481	119	47	x∗	x∗	PROPN
ejpam-481	119	48	>	>	X
ejpam-481	119	49	=	=	SYM
ejpam-481	119	50	g(0	g(0	PROPN
ejpam-481	119	51	)	)	PUNCT
ejpam-481	119	52	implies	imply	VERB
ejpam-481	119	53	(	(	PUNCT
ejpam-481	119	54	γu′(0	γu′(0	NOUN
ejpam-481	119	55	)	)	PUNCT
ejpam-481	119	56	+	+	NUM
ejpam-481	119	57	1)g(0	1)g(0	NOUN
ejpam-481	119	58	)	)	PUNCT
ejpam-481	119	59	=	=	SYM
ejpam-481	119	60	1	1	NUM
ejpam-481	119	61	η	η	X
ejpam-481	119	62	<	<	X
ejpam-481	119	63	a−1z	a−1z	PROPN
ejpam-481	119	64	,	,	PUNCT
ejpam-481	119	65	x∗	x∗	PROPN
ejpam-481	119	66	>	>	X
ejpam-481	119	67	.	.	PUNCT
ejpam-481	120	1	(	(	PUNCT
ejpam-481	120	2	12	12	NUM
ejpam-481	120	3	)	)	PUNCT
ejpam-481	120	4	equations	equation	NOUN
ejpam-481	120	5	(	(	PUNCT
ejpam-481	120	6	11	11	NUM
ejpam-481	120	7	)	)	PUNCT
ejpam-481	120	8	and	and	CCONJ
ejpam-481	120	9	(	(	PUNCT
ejpam-481	120	10	12	12	NUM
ejpam-481	120	11	)	)	PUNCT
ejpam-481	120	12	determine	determine	VERB
ejpam-481	120	13	γ	γ	PROPN
ejpam-481	120	14	and	and	CCONJ
ejpam-481	120	15	η	η	PROPN
ejpam-481	120	16	uniquely	uniquely	ADV
ejpam-481	120	17	.	.	PUNCT
ejpam-481	121	1	hence	hence	ADV
ejpam-481	121	2	from	from	ADP
ejpam-481	121	3	x	x	SYM
ejpam-481	121	4	=	=	SYM
ejpam-481	121	5	1	1	NUM
ejpam-481	121	6	η	η	NOUN
ejpam-481	121	7	a−1z	a−1z	NOUN
ejpam-481	121	8	,	,	PUNCT
ejpam-481	121	9	x	x	PRON
ejpam-481	121	10	is	be	AUX
ejpam-481	121	11	determined	determine	VERB
ejpam-481	121	12	uniquely	uniquely	ADV
ejpam-481	121	13	,	,	PUNCT
ejpam-481	121	14	and	and	CCONJ
ejpam-481	121	15	finally	finally	ADV
ejpam-481	121	16	(	(	PUNCT
ejpam-481	121	17	5	5	X
ejpam-481	121	18	)	)	PUNCT
ejpam-481	121	19	determines	determine	VERB
ejpam-481	121	20	f	f	X
ejpam-481	121	21	uniquely	uniquely	ADV
ejpam-481	121	22	.	.	PUNCT
ejpam-481	122	1	references	reference	NOUN
ejpam-481	122	2	729	729	NUM
ejpam-481	122	3	this	this	PRON
ejpam-481	122	4	ends	end	VERB
ejpam-481	122	5	the	the	DET
ejpam-481	122	6	proof	proof	NOUN
ejpam-481	122	7	.	.	PUNCT
ejpam-481	123	1	as	as	SCONJ
ejpam-481	123	2	an	an	DET
ejpam-481	123	3	application	application	NOUN
ejpam-481	123	4	one	one	NOUN
ejpam-481	123	5	can	can	AUX
ejpam-481	123	6	consider	consider	VERB
ejpam-481	123	7	the	the	DET
ejpam-481	123	8	following	follow	VERB
ejpam-481	123	9	example	example	NOUN
ejpam-481	123	10	:	:	PUNCT
ejpam-481	123	11	let	let	VERB
ejpam-481	123	12	b	b	X
ejpam-481	123	13	=	=	SYM
ejpam-481	123	14	�	�	PROPN
ejpam-481	123	15	1	1	NUM
ejpam-481	123	16	1	1	NUM
ejpam-481	123	17	1	1	NUM
ejpam-481	123	18	1	1	NUM
ejpam-481	123	19	�	�	PROPN
ejpam-481	123	20	,	,	PUNCT
ejpam-481	123	21	a=	a=	PROPN
ejpam-481	123	22	�	�	NOUN
ejpam-481	123	23	1	1	NUM
ejpam-481	123	24	1	1	NUM
ejpam-481	123	25	0	0	NUM
ejpam-481	123	26	1	1	NUM
ejpam-481	123	27	�	�	PROPN
ejpam-481	123	28	,	,	PUNCT
ejpam-481	123	29	u=	u=	ADJ
ejpam-481	123	30	�	�	PROPN
ejpam-481	123	31	x(t	x(t	PROPN
ejpam-481	123	32	)	)	PUNCT
ejpam-481	123	33	y(t	y(t	NUM
ejpam-481	123	34	)	)	PUNCT
ejpam-481	123	35	�	�	PROPN
ejpam-481	123	36	,	,	PUNCT
ejpam-481	123	37	z	z	NOUN
ejpam-481	123	38	=	=	SYM
ejpam-481	123	39	�	�	PROPN
ejpam-481	123	40	1	1	NUM
ejpam-481	123	41	1	1	NUM
ejpam-481	123	42	�	�	PROPN
ejpam-481	123	43	,	,	PUNCT
ejpam-481	123	44	u(0	u(0	PROPN
ejpam-481	123	45	)	)	PUNCT
ejpam-481	123	46	=	=	SYM
ejpam-481	123	47	�	�	PROPN
ejpam-481	123	48	1	1	NUM
ejpam-481	123	49	1	1	NUM
ejpam-481	123	50	�	�	PROPN
ejpam-481	123	51	,	,	PUNCT
ejpam-481	123	52	x∗	x∗	PROPN
ejpam-481	123	53	=	=	SYM
ejpam-481	123	54	�	�	PROPN
ejpam-481	123	55	1	1	NUM
ejpam-481	123	56	1	1	NUM
ejpam-481	123	57	�	�	PROPN
ejpam-481	123	58	,	,	PUNCT
ejpam-481	123	59	and	and	CCONJ
ejpam-481	123	60	g(t	g(t	PROPN
ejpam-481	123	61	)	)	PUNCT
ejpam-481	123	62	=	=	SYM
ejpam-481	124	1	2	2	NUM
ejpam-481	124	2	+	+	NUM
ejpam-481	124	3	t2	t2	NOUN
ejpam-481	124	4	.	.	PUNCT
ejpam-481	125	1	then	then	ADV
ejpam-481	125	2	the	the	DET
ejpam-481	125	3	system	system	NOUN
ejpam-481	125	4	�	�	NOUN
ejpam-481	125	5	1	1	NUM
ejpam-481	125	6	1	1	NUM
ejpam-481	125	7	1	1	NUM
ejpam-481	125	8	1	1	NUM
ejpam-481	125	9	�	�	PROPN
ejpam-481	125	10	�	�	PROPN
ejpam-481	125	11	x	x	SYM
ejpam-481	125	12	′(t	′(t	PROPN
ejpam-481	125	13	)	)	PUNCT
ejpam-481	125	14	y	y	PROPN
ejpam-481	125	15	′(t	′(t	PROPN
ejpam-481	125	16	)	)	PUNCT
ejpam-481	125	17	�	�	PROPN
ejpam-481	125	18	+	+	CCONJ
ejpam-481	125	19	�	�	PROPN
ejpam-481	125	20	1	1	NUM
ejpam-481	125	21	1	1	NUM
ejpam-481	125	22	0	0	NUM
ejpam-481	125	23	1	1	NUM
ejpam-481	125	24	�	�	PROPN
ejpam-481	125	25	�	�	PROPN
ejpam-481	125	26	x(t	x(t	PROPN
ejpam-481	125	27	)	)	PUNCT
ejpam-481	125	28	y(t	y(t	NUM
ejpam-481	125	29	)	)	PUNCT
ejpam-481	125	30	�	�	PROPN
ejpam-481	125	31	=	=	SYM
ejpam-481	125	32	f	f	PROPN
ejpam-481	125	33	(	(	PUNCT
ejpam-481	125	34	t	t	PROPN
ejpam-481	125	35	)	)	PUNCT
ejpam-481	125	36	�	�	PROPN
ejpam-481	125	37	1	1	NUM
ejpam-481	125	38	1	1	NUM
ejpam-481	125	39	�	�	PROPN
ejpam-481	125	40	,	,	PUNCT
ejpam-481	125	41	with	with	ADP
ejpam-481	125	42	the	the	DET
ejpam-481	125	43	conditions	condition	NOUN
ejpam-481	125	44	:	:	PUNCT
ejpam-481	125	45	<	<	X
ejpam-481	125	46	x∗,u(t	x∗,u(t	PROPN
ejpam-481	125	47	)	)	PUNCT
ejpam-481	125	48	>	>	PUNCT
ejpam-481	126	1	=	=	PUNCT
ejpam-481	126	2	x+	x+	PUNCT
ejpam-481	126	3	y	y	NOUN
ejpam-481	126	4	=	=	SYM
ejpam-481	126	5	2	2	NUM
ejpam-481	126	6	+	+	NUM
ejpam-481	126	7	t2	t2	NOUN
ejpam-481	126	8	,	,	PUNCT
ejpam-481	126	9	and	and	CCONJ
ejpam-481	126	10	x(0	x(0	PROPN
ejpam-481	126	11	)	)	PUNCT
ejpam-481	126	12	=	=	SYM
ejpam-481	126	13	y(0	y(0	PROPN
ejpam-481	126	14	)	)	PUNCT
ejpam-481	126	15	=	=	SYM
ejpam-481	126	16	1	1	NUM
ejpam-481	126	17	has	have	VERB
ejpam-481	126	18	a	a	DET
ejpam-481	126	19	unique	unique	ADJ
ejpam-481	126	20	solution	solution	NOUN
ejpam-481	126	21	,	,	PUNCT
ejpam-481	126	22	noting	note	VERB
ejpam-481	126	23	that	that	SCONJ
ejpam-481	126	24	uniquely	uniquely	ADV
ejpam-481	126	25	imaged	imaged	ADJ
ejpam-481	126	26	condition	condition	NOUN
ejpam-481	126	27	is	be	AUX
ejpam-481	126	28	satisfied	satisfied	ADJ
ejpam-481	126	29	.	.	PUNCT
ejpam-481	127	1	references	reference	NOUN
ejpam-481	127	2	[	[	X
ejpam-481	127	3	1	1	NUM
ejpam-481	127	4	]	]	X
ejpam-481	127	5	y.	y.	PROPN
ejpam-481	127	6	eidelman	eidelman	PROPN
ejpam-481	127	7	.	.	PUNCT
ejpam-481	128	1	an	an	DET
ejpam-481	128	2	inverse	inverse	ADJ
ejpam-481	128	3	problem	problem	NOUN
ejpam-481	128	4	for	for	ADP
ejpam-481	128	5	a	a	DET
ejpam-481	128	6	second	second	ADJ
ejpam-481	128	7	-order	-order	NOUN
ejpam-481	128	8	differential	differential	ADJ
ejpam-481	128	9	equation	equation	NOUN
ejpam-481	128	10	in	in	ADP
ejpam-481	128	11	banach	banach	NOUN
ejpam-481	128	12	spaces	space	NOUN
ejpam-481	128	13	,	,	PUNCT
ejpam-481	128	14	abstract	abstract	ADJ
ejpam-481	128	15	and	and	CCONJ
ejpam-481	128	16	applied	apply	VERB
ejpam-481	128	17	analysis	analysis	NOUN
ejpam-481	128	18	,	,	PUNCT
ejpam-481	128	19	12	12	NUM
ejpam-481	128	20	.	.	PUNCT
ejpam-481	129	1	pps	pps	NOUN
ejpam-481	129	2	997	997	NUM
ejpam-481	129	3	-	-	PUNCT
ejpam-481	129	4	1005	1005	NUM
ejpam-481	129	5	.	.	PUNCT
ejpam-481	130	1	2004	2004	NUM
ejpam-481	130	2	.	.	PUNCT
ejpam-481	131	1	[	[	X
ejpam-481	131	2	2	2	NUM
ejpam-481	131	3	]	]	PUNCT
ejpam-481	131	4	a.	a.	NOUN
ejpam-481	131	5	lorenzi	lorenzi	PROPN
ejpam-481	131	6	.	.	PUNCT
ejpam-481	132	1	introduction	introduction	NOUN
ejpam-481	132	2	to	to	ADP
ejpam-481	132	3	identification	identification	NOUN
ejpam-481	132	4	problems	problem	NOUN
ejpam-481	132	5	via	via	ADP
ejpam-481	132	6	functional	functional	ADJ
ejpam-481	132	7	analysis	analysis	NOUN
ejpam-481	132	8	,	,	PUNCT
ejpam-481	132	9	vsp	vsp	NOUN
ejpam-481	132	10	,	,	PUNCT
ejpam-481	132	11	utrecht	utrecht	NOUN
ejpam-481	132	12	,	,	PUNCT
ejpam-481	132	13	2001	2001	NUM
ejpam-481	132	14	.	.	PUNCT
ejpam-481	133	1	[	[	X
ejpam-481	133	2	3	3	NUM
ejpam-481	133	3	]	]	PUNCT
ejpam-481	133	4	a.	a.	NOUN
ejpam-481	133	5	pirkpko	pirkpko	PROPN
ejpam-481	133	6	,	,	PUNCT
ejpam-481	133	7	d.g	d.g	PROPN
ejpam-481	133	8	,	,	PUNCT
ejpam-481	133	9	orlovsky	orlovsky	ADJ
ejpam-481	133	10	,	,	PUNCT
ejpam-481	133	11	and	and	CCONJ
ejpam-481	133	12	i.	i.	PROPN
ejpam-481	133	13	vasin	vasin	PROPN
ejpam-481	133	14	.	.	PUNCT
ejpam-481	134	1	methods	method	NOUN
ejpam-481	134	2	for	for	ADP
ejpam-481	134	3	solving	solve	VERB
ejpam-481	134	4	inverse	inverse	NOUN
ejpam-481	134	5	problems	problem	NOUN
ejpam-481	134	6	in	in	ADP
ejpam-481	134	7	mathematical	mathematical	ADJ
ejpam-481	134	8	physics	physics	NOUN
ejpam-481	134	9	,	,	PUNCT
ejpam-481	134	10	dekker	dekker	PROPN
ejpam-481	134	11	,	,	PUNCT
ejpam-481	134	12	new	new	PROPN
ejpam-481	134	13	york	york	PROPN
ejpam-481	134	14	,	,	PUNCT
ejpam-481	134	15	2000	2000	NUM
ejpam-481	134	16	.	.	PUNCT
ejpam-481	135	1	[	[	X
ejpam-481	135	2	4	4	X
ejpam-481	135	3	]	]	PUNCT
ejpam-481	135	4	w.	w.	PROPN
ejpam-481	135	5	a.	a.	PROPN
ejpam-481	135	6	light	light	PROPN
ejpam-481	135	7	,	,	PUNCT
ejpam-481	135	8	and	and	CCONJ
ejpam-481	135	9	e.w.cheney	e.w.cheney	NOUN
ejpam-481	135	10	.	.	PUNCT
ejpam-481	136	1	approximation	approximation	NOUN
ejpam-481	136	2	theory	theory	NOUN
ejpam-481	136	3	in	in	ADP
ejpam-481	136	4	tensor	tensor	NOUN
ejpam-481	136	5	product	product	NOUN
ejpam-481	136	6	spaces	space	VERB
ejpam-481	136	7	.	.	PUNCT
ejpam-481	137	1	lecture	lecture	NOUN
ejpam-481	137	2	notes	note	NOUN
ejpam-481	137	3	in	in	ADP
ejpam-481	137	4	math	math	NOUN
ejpam-481	137	5	.	.	PUNCT
ejpam-481	138	1	1169	1169	NUM
ejpam-481	138	2	.	.	PUNCT
ejpam-481	139	1	springer	springer	NOUN
ejpam-481	139	2	-	-	PUNCT
ejpam-481	139	3	verlag	verlag	PROPN
ejpam-481	139	4	,	,	PUNCT
ejpam-481	139	5	new	new	PROPN
ejpam-481	139	6	york	york	PROPN
ejpam-481	139	7	,	,	PUNCT
ejpam-481	139	8	1985	1985	NUM
ejpam-481	139	9	.	.	PUNCT
ejpam-481	140	1	[	[	X
ejpam-481	140	2	5	5	NUM
ejpam-481	140	3	]	]	PUNCT
ejpam-481	140	4	a.	a.	NOUN
ejpam-481	140	5	m.	m.	NOUN
ejpam-481	140	6	ziqan	ziqan	PROPN
ejpam-481	140	7	,	,	PUNCT
ejpam-481	140	8	m.	m.	PROPN
ejpam-481	140	9	al	al	PROPN
ejpam-481	140	10	horani	horani	PROPN
ejpam-481	140	11	,	,	PUNCT
ejpam-481	140	12	and	and	CCONJ
ejpam-481	140	13	r.	r.	PROPN
ejpam-481	140	14	khalil	khalil	PROPN
ejpam-481	140	15	.	.	PUNCT
ejpam-481	141	1	tensor	tensor	NOUN
ejpam-481	141	2	product	product	NOUN
ejpam-481	141	3	technique	technique	NOUN
ejpam-481	141	4	and	and	CCONJ
ejpam-481	141	5	the	the	DET
ejpam-481	141	6	degenerate	degenerate	ADJ
ejpam-481	141	7	homogeneous	homogeneous	ADJ
ejpam-481	141	8	abstract	abstract	ADJ
ejpam-481	141	9	cauchy	cauchy	PROPN
ejpam-481	141	10	problem	problem	NOUN
ejpam-481	141	11	,	,	PUNCT
ejpam-481	141	12	journal	journal	NOUN
ejpam-481	141	13	of	of	ADP
ejpam-481	141	14	applied	apply	VERB
ejpam-481	141	15	functional	functional	ADJ
ejpam-481	141	16	analysis	analysis	NOUN
ejpam-481	141	17	5	5	NUM
ejpam-481	141	18	.	.	PUNCT
ejpam-481	141	19	pps	pps	PROPN
ejpam-481	141	20	121	121	NUM
ejpam-481	141	21	-	-	SYM
ejpam-481	141	22	138	138	NUM
ejpam-481	141	23	.	.	PUNCT
ejpam-481	141	24	2010	2010	NUM
ejpam-481	141	25	.	.	PUNCT