id	sid	tid	token	lemma	pos
ejde-517	1	1	electronic	electronic	ADJ
ejde-517	1	2	journal	journal	NOUN
ejde-517	1	3	of	of	ADP
ejde-517	1	4	differential	differential	ADJ
ejde-517	1	5	equations	equation	NOUN
ejde-517	1	6	,	,	PUNCT
ejde-517	1	7	vol	vol	NOUN
ejde-517	1	8	.	.	PUNCT
ejde-517	1	9	2020	2020	NUM
ejde-517	1	10	(	(	PUNCT
ejde-517	1	11	2020	2020	NUM
ejde-517	1	12	)	)	PUNCT
ejde-517	1	13	,	,	PUNCT
ejde-517	1	14	no	no	INTJ
ejde-517	1	15	.	.	PROPN
ejde-517	1	16	93	93	NUM
ejde-517	1	17	,	,	PUNCT
ejde-517	1	18	pp	pp	ADJ
ejde-517	1	19	.	.	PUNCT
ejde-517	2	1	1–30	1–30	PROPN
ejde-517	2	2	.	.	PUNCT
ejde-517	3	1	issn	issn	PROPN
ejde-517	3	2	:	:	PUNCT
ejde-517	3	3	1072	1072	NUM
ejde-517	3	4	-	-	SYM
ejde-517	3	5	6691	6691	NUM
ejde-517	3	6	.	.	PUNCT
ejde-517	4	1	url	url	PROPN
ejde-517	4	2	:	:	PUNCT
ejde-517	4	3	http://ejde.math.txstate.edu	http://ejde.math.txstate.edu	PROPN
ejde-517	4	4	or	or	CCONJ
ejde-517	4	5	http://ejde.math.unt.edu	http://ejde.math.unt.edu	PROPN
ejde-517	4	6	existence	existence	NOUN
ejde-517	4	7	of	of	ADP
ejde-517	4	8	solution	solution	NOUN
ejde-517	4	9	for	for	ADP
ejde-517	4	10	a	a	DET
ejde-517	4	11	segmentation	segmentation	NOUN
ejde-517	4	12	approach	approach	NOUN
ejde-517	4	13	to	to	ADP
ejde-517	4	14	the	the	DET
ejde-517	4	15	impedance	impedance	NOUN
ejde-517	4	16	tomography	tomography	NOUN
ejde-517	4	17	problem	problem	NOUN
ejde-517	4	18	renier	renier	PROPN
ejde-517	4	19	mendoza	mendoza	PROPN
ejde-517	4	20	,	,	PUNCT
ejde-517	4	21	stephen	stephen	PROPN
ejde-517	4	22	keeling	keeling	PROPN
ejde-517	4	23	abstract	abstract	PROPN
ejde-517	4	24	.	.	PUNCT
ejde-517	5	1	in	in	ADP
ejde-517	5	2	electrical	electrical	ADJ
ejde-517	5	3	impedance	impedance	NOUN
ejde-517	5	4	tomography	tomography	NOUN
ejde-517	5	5	(	(	PUNCT
ejde-517	5	6	eit	eit	NOUN
ejde-517	5	7	)	)	PUNCT
ejde-517	5	8	,	,	PUNCT
ejde-517	5	9	image	image	NOUN
ejde-517	5	10	reconstruction	reconstruction	NOUN
ejde-517	5	11	of	of	ADP
ejde-517	5	12	the	the	DET
ejde-517	5	13	conductivity	conductivity	NOUN
ejde-517	5	14	distribution	distribution	NOUN
ejde-517	5	15	of	of	ADP
ejde-517	5	16	a	a	DET
ejde-517	5	17	body	body	NOUN
ejde-517	5	18	can	can	AUX
ejde-517	5	19	be	be	AUX
ejde-517	5	20	calculated	calculate	VERB
ejde-517	5	21	using	use	VERB
ejde-517	5	22	measured	measure	VERB
ejde-517	5	23	voltages	voltage	NOUN
ejde-517	5	24	at	at	ADP
ejde-517	5	25	the	the	DET
ejde-517	5	26	boundary	boundary	NOUN
ejde-517	5	27	.	.	PUNCT
ejde-517	6	1	this	this	PRON
ejde-517	6	2	is	be	AUX
ejde-517	6	3	done	do	VERB
ejde-517	6	4	by	by	ADP
ejde-517	6	5	solving	solve	VERB
ejde-517	6	6	an	an	DET
ejde-517	6	7	inverse	inverse	NOUN
ejde-517	6	8	problem	problem	NOUN
ejde-517	6	9	for	for	ADP
ejde-517	6	10	an	an	DET
ejde-517	6	11	elliptic	elliptic	ADJ
ejde-517	6	12	partial	partial	ADJ
ejde-517	6	13	differential	differential	NOUN
ejde-517	6	14	equation	equation	NOUN
ejde-517	6	15	(	(	PUNCT
ejde-517	6	16	pde	pde	NOUN
ejde-517	6	17	)	)	PUNCT
ejde-517	6	18	.	.	PUNCT
ejde-517	7	1	in	in	ADP
ejde-517	7	2	this	this	DET
ejde-517	7	3	work	work	NOUN
ejde-517	7	4	,	,	PUNCT
ejde-517	7	5	we	we	PRON
ejde-517	7	6	present	present	VERB
ejde-517	7	7	some	some	DET
ejde-517	7	8	sensitivity	sensitivity	NOUN
ejde-517	7	9	results	result	NOUN
ejde-517	7	10	arising	arise	VERB
ejde-517	7	11	from	from	ADP
ejde-517	7	12	the	the	DET
ejde-517	7	13	solution	solution	NOUN
ejde-517	7	14	of	of	ADP
ejde-517	7	15	the	the	DET
ejde-517	7	16	pde	pde	NOUN
ejde-517	7	17	.	.	PUNCT
ejde-517	8	1	we	we	PRON
ejde-517	8	2	use	use	VERB
ejde-517	8	3	these	these	PRON
ejde-517	8	4	to	to	PART
ejde-517	8	5	show	show	VERB
ejde-517	8	6	that	that	SCONJ
ejde-517	8	7	a	a	DET
ejde-517	8	8	segmentation	segmentation	NOUN
ejde-517	8	9	approach	approach	NOUN
ejde-517	8	10	to	to	ADP
ejde-517	8	11	the	the	DET
ejde-517	8	12	eit	eit	PROPN
ejde-517	8	13	inverse	inverse	NOUN
ejde-517	8	14	problem	problem	NOUN
ejde-517	8	15	has	have	VERB
ejde-517	8	16	a	a	DET
ejde-517	8	17	unique	unique	ADJ
ejde-517	8	18	solution	solution	NOUN
ejde-517	8	19	in	in	ADP
ejde-517	8	20	a	a	DET
ejde-517	8	21	suitable	suitable	ADJ
ejde-517	8	22	space	space	NOUN
ejde-517	8	23	using	use	VERB
ejde-517	8	24	a	a	DET
ejde-517	8	25	fixed	fix	VERB
ejde-517	8	26	point	point	NOUN
ejde-517	8	27	theorem	theorem	VERB
ejde-517	8	28	.	.	PROPN
ejde-517	8	29	1	1	X
ejde-517	8	30	.	.	X
ejde-517	8	31	introduction	introduction	NOUN
ejde-517	8	32	electrical	electrical	ADJ
ejde-517	8	33	impedance	impedance	NOUN
ejde-517	8	34	tomography	tomography	NOUN
ejde-517	8	35	(	(	PUNCT
ejde-517	8	36	eit	eit	PROPN
ejde-517	8	37	)	)	PUNCT
ejde-517	8	38	is	be	AUX
ejde-517	8	39	an	an	DET
ejde-517	8	40	imaging	imaging	NOUN
ejde-517	8	41	technique	technique	NOUN
ejde-517	8	42	proposed	propose	VERB
ejde-517	8	43	by	by	ADP
ejde-517	8	44	calderon	calderon	NOUN
ejde-517	9	1	[	[	X
ejde-517	9	2	6	6	NUM
ejde-517	9	3	]	]	PUNCT
ejde-517	9	4	in	in	ADP
ejde-517	9	5	recovering	recover	VERB
ejde-517	9	6	the	the	DET
ejde-517	9	7	spatial	spatial	ADJ
ejde-517	9	8	distribution	distribution	NOUN
ejde-517	9	9	of	of	ADP
ejde-517	9	10	the	the	DET
ejde-517	9	11	conductivities	conductivity	NOUN
ejde-517	9	12	in	in	ADP
ejde-517	9	13	the	the	DET
ejde-517	9	14	interior	interior	NOUN
ejde-517	9	15	of	of	ADP
ejde-517	9	16	a	a	DET
ejde-517	9	17	body	body	NOUN
ejde-517	9	18	ω	ω	NUM
ejde-517	9	19	based	base	VERB
ejde-517	9	20	on	on	ADP
ejde-517	9	21	the	the	DET
ejde-517	9	22	voltage	voltage	NOUN
ejde-517	9	23	and	and	CCONJ
ejde-517	9	24	current	current	ADJ
ejde-517	9	25	measurements	measurement	NOUN
ejde-517	9	26	from	from	ADP
ejde-517	9	27	electrodes	electrode	NOUN
ejde-517	9	28	placed	place	VERB
ejde-517	9	29	around	around	ADP
ejde-517	9	30	its	its	PRON
ejde-517	9	31	boundary	boundary	ADJ
ejde-517	9	32	∂ω	∂ω	PROPN
ejde-517	9	33	.	.	PUNCT
ejde-517	10	1	eit	eit	PROPN
ejde-517	10	2	is	be	AUX
ejde-517	10	3	a	a	DET
ejde-517	10	4	non	non	ADJ
ejde-517	10	5	-	-	ADJ
ejde-517	10	6	invasive	invasive	ADJ
ejde-517	10	7	imaging	imaging	NOUN
ejde-517	10	8	technique	technique	NOUN
ejde-517	10	9	with	with	ADP
ejde-517	10	10	a	a	DET
ejde-517	10	11	wide	wide	ADJ
ejde-517	10	12	range	range	NOUN
ejde-517	10	13	of	of	ADP
ejde-517	10	14	applications	application	NOUN
ejde-517	10	15	.	.	PUNCT
ejde-517	11	1	we	we	PRON
ejde-517	11	2	can	can	AUX
ejde-517	11	3	refer	refer	VERB
ejde-517	11	4	to	to	ADP
ejde-517	11	5	the	the	DET
ejde-517	11	6	following	follow	VERB
ejde-517	11	7	works	work	NOUN
ejde-517	11	8	[	[	X
ejde-517	11	9	12	12	NUM
ejde-517	11	10	,	,	PUNCT
ejde-517	11	11	13	13	NUM
ejde-517	11	12	,	,	PUNCT
ejde-517	11	13	22	22	NUM
ejde-517	11	14	,	,	PUNCT
ejde-517	11	15	23	23	NUM
ejde-517	11	16	,	,	PUNCT
ejde-517	11	17	24	24	NUM
ejde-517	11	18	,	,	PUNCT
ejde-517	11	19	29	29	NUM
ejde-517	11	20	,	,	PUNCT
ejde-517	11	21	30	30	NUM
ejde-517	11	22	,	,	PUNCT
ejde-517	11	23	38	38	NUM
ejde-517	11	24	]	]	PUNCT
ejde-517	11	25	.	.	PUNCT
ejde-517	12	1	the	the	DET
ejde-517	12	2	eit	eit	PROPN
ejde-517	12	3	consists	consist	VERB
ejde-517	12	4	of	of	ADP
ejde-517	12	5	two	two	NUM
ejde-517	12	6	sub	sub	NOUN
ejde-517	12	7	-	-	NOUN
ejde-517	12	8	problems	problem	NOUN
ejde-517	12	9	:	:	PUNCT
ejde-517	12	10	the	the	DET
ejde-517	12	11	forward	forward	ADJ
ejde-517	12	12	problem	problem	NOUN
ejde-517	12	13	and	and	CCONJ
ejde-517	12	14	the	the	DET
ejde-517	12	15	inverse	inverse	NOUN
ejde-517	12	16	problem	problem	NOUN
ejde-517	12	17	.	.	PUNCT
ejde-517	13	1	suppose	suppose	VERB
ejde-517	13	2	ω	ω	PROPN
ejde-517	13	3	⊆	⊆	NUM
ejde-517	13	4	rn	rn	PROPN
ejde-517	13	5	is	be	AUX
ejde-517	13	6	a	a	DET
ejde-517	13	7	bounded	bounded	ADJ
ejde-517	13	8	domain	domain	NOUN
ejde-517	13	9	with	with	ADP
ejde-517	13	10	a	a	DET
ejde-517	13	11	sufficiently	sufficiently	ADV
ejde-517	13	12	smooth	smooth	ADJ
ejde-517	13	13	boundary	boundary	NOUN
ejde-517	13	14	.	.	PUNCT
ejde-517	14	1	in	in	ADP
ejde-517	14	2	the	the	DET
ejde-517	14	3	forward	forward	ADJ
ejde-517	14	4	eit	eit	PROPN
ejde-517	14	5	problem	problem	NOUN
ejde-517	14	6	,	,	PUNCT
ejde-517	14	7	given	give	VERB
ejde-517	14	8	the	the	DET
ejde-517	14	9	boundary	boundary	ADJ
ejde-517	14	10	currents	current	NOUN
ejde-517	14	11	f	f	PROPN
ejde-517	14	12	∈	∈	PROPN
ejde-517	14	13	l2(∂ω	l2(∂ω	PUNCT
ejde-517	14	14	)	)	PUNCT
ejde-517	14	15	and	and	CCONJ
ejde-517	14	16	the	the	DET
ejde-517	14	17	conductivity	conductivity	NOUN
ejde-517	14	18	distribution	distribution	NOUN
ejde-517	14	19	σ	σ	X
ejde-517	14	20	∈	∈	PROPN
ejde-517	14	21	l∞(ω	l∞(ω	NOUN
ejde-517	14	22	)	)	PUNCT
ejde-517	14	23	satisfying	satisfy	VERB
ejde-517	14	24	σ(x	σ(x	PROPN
ejde-517	14	25	)	)	PUNCT
ejde-517	14	26	≥	≥	PROPN
ejde-517	14	27	σ	σ	X
ejde-517	14	28	>	>	X
ejde-517	14	29	0	0	NUM
ejde-517	14	30	,	,	PUNCT
ejde-517	14	31	for	for	ADP
ejde-517	14	32	all	all	DET
ejde-517	14	33	x	x	SYM
ejde-517	14	34	∈	∈	PROPN
ejde-517	14	35	ω	ω	PROPN
ejde-517	14	36	,	,	PUNCT
ejde-517	14	37	the	the	DET
ejde-517	14	38	electric	electric	ADJ
ejde-517	14	39	potential	potential	NOUN
ejde-517	14	40	φ	φ	PROPN
ejde-517	14	41	in	in	ADP
ejde-517	14	42	ω	ω	PROPN
ejde-517	14	43	and	and	CCONJ
ejde-517	14	44	the	the	DET
ejde-517	14	45	boundary	boundary	ADJ
ejde-517	14	46	voltage	voltage	NOUN
ejde-517	14	47	v	v	NOUN
ejde-517	14	48	=	=	SYM
ejde-517	14	49	φ	φ	X
ejde-517	14	50	∣∣	∣∣	X
ejde-517	14	51	∂ω	∂ω	PROPN
ejde-517	14	52	are	be	AUX
ejde-517	14	53	solved	solve	VERB
ejde-517	14	54	.	.	PUNCT
ejde-517	15	1	these	these	DET
ejde-517	15	2	electrical	electrical	ADJ
ejde-517	15	3	measurements	measurement	NOUN
ejde-517	15	4	satisfy	satisfy	VERB
ejde-517	15	5	a	a	DET
ejde-517	15	6	generalized	generalized	ADJ
ejde-517	15	7	laplace	laplace	NOUN
ejde-517	15	8	equation	equation	NOUN
ejde-517	15	9	:	:	PUNCT
ejde-517	15	10	∇	∇	X
ejde-517	15	11	·	·	PUNCT
ejde-517	15	12	(	(	PUNCT
ejde-517	15	13	σ∇φ	σ∇φ	NOUN
ejde-517	15	14	)	)	PUNCT
ejde-517	15	15	=	=	SYM
ejde-517	15	16	0	0	NUM
ejde-517	15	17	in	in	ADP
ejde-517	15	18	ω	ω	PROPN
ejde-517	15	19	,	,	PUNCT
ejde-517	15	20	σ	σ	X
ejde-517	15	21	∂φ∂n	∂φ∂n	NOUN
ejde-517	15	22	=	=	SYM
ejde-517	15	23	f	f	NOUN
ejde-517	15	24	on	on	ADP
ejde-517	15	25	∂ω	∂ω	PROPN
ejde-517	15	26	,	,	PUNCT
ejde-517	15	27	(	(	PUNCT
ejde-517	15	28	1.1	1.1	NUM
ejde-517	15	29	)	)	PUNCT
ejde-517	15	30	where	where	SCONJ
ejde-517	15	31	n	n	PRON
ejde-517	15	32	is	be	AUX
ejde-517	15	33	the	the	DET
ejde-517	15	34	outward	outward	ADJ
ejde-517	15	35	normal	normal	ADJ
ejde-517	15	36	direction	direction	NOUN
ejde-517	15	37	at	at	ADP
ejde-517	15	38	∂ω	∂ω	PROPN
ejde-517	15	39	.	.	PUNCT
ejde-517	16	1	the	the	DET
ejde-517	16	2	boundary	boundary	ADJ
ejde-517	16	3	currents	current	NOUN
ejde-517	16	4	are	be	AUX
ejde-517	16	5	chosen	choose	VERB
ejde-517	16	6	so	so	SCONJ
ejde-517	16	7	that	that	SCONJ
ejde-517	16	8	∫	∫	PROPN
ejde-517	16	9	∂ω	∂ω	ADJ
ejde-517	16	10	f	f	X
ejde-517	16	11	ds	ds	PROPN
ejde-517	16	12	=	=	NOUN
ejde-517	16	13	0	0	PROPN
ejde-517	16	14	.	.	PUNCT
ejde-517	17	1	this	this	DET
ejde-517	17	2	condition	condition	NOUN
ejde-517	17	3	is	be	AUX
ejde-517	17	4	imposed	impose	VERB
ejde-517	17	5	to	to	PART
ejde-517	17	6	satisfy	satisfy	VERB
ejde-517	17	7	the	the	DET
ejde-517	17	8	conservation	conservation	NOUN
ejde-517	17	9	of	of	ADP
ejde-517	17	10	charge	charge	NOUN
ejde-517	17	11	.	.	PUNCT
ejde-517	18	1	furthermore	furthermore	ADV
ejde-517	18	2	,	,	PUNCT
ejde-517	18	3	the	the	DET
ejde-517	18	4	electric	electric	ADJ
ejde-517	18	5	potential	potential	NOUN
ejde-517	18	6	φ	φ	PROPN
ejde-517	18	7	must	must	AUX
ejde-517	18	8	satisfy	satisfy	VERB
ejde-517	18	9	∫	∫	PROPN
ejde-517	19	1	∂ω	∂ω	ADJ
ejde-517	19	2	φds	φds	NOUN
ejde-517	19	3	=	=	NOUN
ejde-517	19	4	0	0	PROPN
ejde-517	19	5	.	.	PUNCT
ejde-517	20	1	this	this	PRON
ejde-517	20	2	amounts	amount	VERB
ejde-517	20	3	to	to	ADP
ejde-517	20	4	choosing	choose	VERB
ejde-517	20	5	the	the	DET
ejde-517	20	6	reference	reference	NOUN
ejde-517	20	7	voltage	voltage	NOUN
ejde-517	20	8	.	.	PUNCT
ejde-517	21	1	the	the	DET
ejde-517	21	2	equation	equation	NOUN
ejde-517	21	3	(	(	PUNCT
ejde-517	21	4	1.1	1.1	NUM
ejde-517	21	5	)	)	PUNCT
ejde-517	21	6	can	can	AUX
ejde-517	21	7	be	be	AUX
ejde-517	21	8	viewed	view	VERB
ejde-517	21	9	as	as	ADP
ejde-517	21	10	a	a	DET
ejde-517	21	11	generalized	generalized	ADJ
ejde-517	21	12	ohm	ohm	NOUN
ejde-517	21	13	’s	’s	PART
ejde-517	21	14	law	law	NOUN
ejde-517	21	15	and	and	CCONJ
ejde-517	21	16	is	be	AUX
ejde-517	21	17	a	a	DET
ejde-517	21	18	well	well	ADV
ejde-517	21	19	-	-	PUNCT
ejde-517	21	20	posed	pose	VERB
ejde-517	21	21	boundary	boundary	ADJ
ejde-517	21	22	value	value	NOUN
ejde-517	21	23	problem	problem	NOUN
ejde-517	21	24	with	with	ADP
ejde-517	21	25	a	a	DET
ejde-517	21	26	unique	unique	ADJ
ejde-517	21	27	solution	solution	NOUN
ejde-517	21	28	(	(	PUNCT
ejde-517	21	29	up	up	ADP
ejde-517	21	30	to	to	ADP
ejde-517	21	31	a	a	DET
ejde-517	21	32	constant	constant	ADJ
ejde-517	21	33	)	)	PUNCT
ejde-517	21	34	φ	φ	PROPN
ejde-517	21	35	∈	∈	PROPN
ejde-517	21	36	h1(ω	h1(ω	PROPN
ejde-517	21	37	)	)	PUNCT
ejde-517	21	38	.	.	PUNCT
ejde-517	22	1	the	the	DET
ejde-517	22	2	partial	partial	ADJ
ejde-517	22	3	differential	differential	NOUN
ejde-517	22	4	equation	equation	NOUN
ejde-517	22	5	(	(	PUNCT
ejde-517	22	6	pde	pde	NOUN
ejde-517	22	7	)	)	PUNCT
ejde-517	22	8	(	(	PUNCT
ejde-517	22	9	1.1	1.1	NUM
ejde-517	22	10	)	)	PUNCT
ejde-517	22	11	is	be	AUX
ejde-517	22	12	called	call	VERB
ejde-517	22	13	the	the	DET
ejde-517	22	14	continuum	continuum	ADJ
ejde-517	22	15	model	model	NOUN
ejde-517	22	16	of	of	ADP
ejde-517	22	17	eit	eit	PROPN
ejde-517	22	18	.	.	PUNCT
ejde-517	23	1	we	we	PRON
ejde-517	23	2	focus	focus	VERB
ejde-517	23	3	our	our	PRON
ejde-517	23	4	study	study	NOUN
ejde-517	23	5	on	on	ADP
ejde-517	23	6	this	this	DET
ejde-517	23	7	model	model	NOUN
ejde-517	23	8	.	.	PUNCT
ejde-517	24	1	other	other	ADJ
ejde-517	24	2	eit	eit	PROPN
ejde-517	24	3	models	model	NOUN
ejde-517	24	4	are	be	AUX
ejde-517	24	5	discussed	discuss	VERB
ejde-517	24	6	in	in	ADP
ejde-517	24	7	[	[	X
ejde-517	24	8	5	5	NUM
ejde-517	24	9	,	,	PUNCT
ejde-517	24	10	8	8	NUM
ejde-517	24	11	,	,	PUNCT
ejde-517	24	12	34	34	NUM
ejde-517	24	13	]	]	PUNCT
ejde-517	24	14	.	.	PUNCT
ejde-517	25	1	2010	2010	NUM
ejde-517	25	2	mathematics	mathematic	NOUN
ejde-517	25	3	subject	subject	NOUN
ejde-517	25	4	classification	classification	NOUN
ejde-517	25	5	.	.	PUNCT
ejde-517	26	1	35j20	35j20	NUM
ejde-517	26	2	,	,	PUNCT
ejde-517	26	3	47h10	47h10	NUM
ejde-517	26	4	,	,	PUNCT
ejde-517	26	5	35r30	35r30	NUM
ejde-517	26	6	.	.	PUNCT
ejde-517	27	1	key	key	ADJ
ejde-517	27	2	words	word	NOUN
ejde-517	27	3	and	and	CCONJ
ejde-517	27	4	phrases	phrase	NOUN
ejde-517	27	5	.	.	PUNCT
ejde-517	28	1	electrical	electrical	ADJ
ejde-517	28	2	impedance	impedance	NOUN
ejde-517	28	3	tomography	tomography	NOUN
ejde-517	28	4	problem	problem	NOUN
ejde-517	28	5	;	;	PUNCT
ejde-517	28	6	two	two	NUM
ejde-517	28	7	-	-	PUNCT
ejde-517	28	8	phase	phase	NOUN
ejde-517	28	9	segmentation	segmentation	NOUN
ejde-517	28	10	algorithm	algorithm	NOUN
ejde-517	28	11	;	;	PUNCT
ejde-517	28	12	fixed	fix	VERB
ejde-517	28	13	point	point	NOUN
ejde-517	28	14	theorem	theorem	VERB
ejde-517	28	15	.	.	PUNCT
ejde-517	29	1	c	c	X
ejde-517	29	2	©	©	PROPN
ejde-517	29	3	2020	2020	NUM
ejde-517	29	4	texas	texas	PROPN
ejde-517	29	5	state	state	PROPN
ejde-517	29	6	university	university	PROPN
ejde-517	29	7	.	.	PUNCT
ejde-517	29	8	submitted	submit	VERB
ejde-517	29	9	october	october	PROPN
ejde-517	29	10	23	23	NUM
ejde-517	29	11	,	,	PUNCT
ejde-517	29	12	2019	2019	NUM
ejde-517	29	13	.	.	PUNCT
ejde-517	30	1	published	publish	VERB
ejde-517	30	2	september	september	PROPN
ejde-517	30	3	16	16	NUM
ejde-517	30	4	,	,	PUNCT
ejde-517	30	5	2020	2020	NUM
ejde-517	30	6	.	.	PUNCT
ejde-517	31	1	1	1	NUM
ejde-517	31	2	2	2	NUM
ejde-517	31	3	r.	r.	PROPN
ejde-517	31	4	mendoza	mendoza	PROPN
ejde-517	31	5	,	,	PUNCT
ejde-517	31	6	s.	s.	PROPN
ejde-517	31	7	keeling	keeling	PROPN
ejde-517	31	8	ejde-2020/93	ejde-2020/93	PROPN
ejde-517	31	9	the	the	DET
ejde-517	31	10	inverse	inverse	NOUN
ejde-517	31	11	eit	eit	NOUN
ejde-517	31	12	problem	problem	NOUN
ejde-517	31	13	or	or	CCONJ
ejde-517	31	14	the	the	DET
ejde-517	31	15	conductivity	conductivity	NOUN
ejde-517	31	16	reconstruction	reconstruction	NOUN
ejde-517	31	17	problem	problem	NOUN
ejde-517	31	18	is	be	AUX
ejde-517	31	19	the	the	DET
ejde-517	31	20	recovery	recovery	NOUN
ejde-517	31	21	of	of	ADP
ejde-517	31	22	σ	σ	PROPN
ejde-517	31	23	inside	inside	ADP
ejde-517	31	24	ω	ω	PROPN
ejde-517	31	25	given	give	VERB
ejde-517	31	26	v	v	NOUN
ejde-517	31	27	and	and	CCONJ
ejde-517	31	28	f	f	PROPN
ejde-517	31	29	in	in	ADP
ejde-517	31	30	∂ω	∂ω	PROPN
ejde-517	31	31	.	.	PUNCT
ejde-517	32	1	denote	denote	VERB
ejde-517	32	2	l̃2(∂ω	l̃2(∂ω	NOUN
ejde-517	32	3	)	)	PUNCT
ejde-517	33	1	:	:	PUNCT
ejde-517	33	2	=	=	X
ejde-517	33	3	{	{	PUNCT
ejde-517	33	4	f	f	PROPN
ejde-517	33	5	∈	∈	PROPN
ejde-517	33	6	l2(∂ω	l2(∂ω	PROPN
ejde-517	33	7	)	)	PUNCT
ejde-517	33	8	:	:	PUNCT
ejde-517	34	1	∫	∫	PROPN
ejde-517	34	2	∂ω	∂ω	ADJ
ejde-517	34	3	f	f	X
ejde-517	34	4	ds	ds	PROPN
ejde-517	34	5	=	=	NOUN
ejde-517	34	6	0	0	NUM
ejde-517	34	7	}	}	PUNCT
ejde-517	34	8	and	and	CCONJ
ejde-517	34	9	define	define	VERB
ejde-517	34	10	λσ	λσ	PRON
ejde-517	34	11	:	:	PUNCT
ejde-517	34	12	l̃2(∂ω)→	l̃2(∂ω)→	X
ejde-517	34	13	l̃2(∂ω	l̃2(∂ω	NOUN
ejde-517	34	14	)	)	PUNCT
ejde-517	34	15	by	by	ADP
ejde-517	34	16	λσ(f	λσ(f	NUM
ejde-517	34	17	)	)	PUNCT
ejde-517	35	1	=	=	PUNCT
ejde-517	35	2	φ	φ	X
ejde-517	35	3	∣∣	∣∣	X
ejde-517	35	4	∂ω	∂ω	PROPN
ejde-517	35	5	,	,	PUNCT
ejde-517	35	6	(	(	PUNCT
ejde-517	35	7	1.2	1.2	NUM
ejde-517	35	8	)	)	PUNCT
ejde-517	35	9	where	where	SCONJ
ejde-517	35	10	φ	φ	PROPN
ejde-517	35	11	∈	∈	PROPN
ejde-517	35	12	h1(ω	h1(ω	PROPN
ejde-517	35	13	)	)	PUNCT
ejde-517	35	14	satisfies	satisfie	NOUN
ejde-517	35	15	(	(	PUNCT
ejde-517	35	16	1.1	1.1	NUM
ejde-517	35	17	)	)	PUNCT
ejde-517	35	18	and	and	CCONJ
ejde-517	35	19	∫	∫	PROPN
ejde-517	35	20	∂ω	∂ω	ADJ
ejde-517	35	21	φds	φds	NOUN
ejde-517	35	22	=	=	NOUN
ejde-517	35	23	0	0	NUM
ejde-517	35	24	.	.	PUNCT
ejde-517	36	1	the	the	DET
ejde-517	36	2	inverse	inverse	NOUN
ejde-517	36	3	eit	eit	PRON
ejde-517	36	4	problem	problem	NOUN
ejde-517	36	5	is	be	AUX
ejde-517	36	6	the	the	DET
ejde-517	36	7	recovery	recovery	NOUN
ejde-517	36	8	of	of	ADP
ejde-517	36	9	σ	σ	PROPN
ejde-517	36	10	given	give	VERB
ejde-517	36	11	λσ	λσ	PRON
ejde-517	36	12	.	.	PUNCT
ejde-517	37	1	although	although	SCONJ
ejde-517	37	2	the	the	DET
ejde-517	37	3	reconstruction	reconstruction	NOUN
ejde-517	37	4	problem	problem	NOUN
ejde-517	37	5	is	be	AUX
ejde-517	37	6	severely	severely	ADV
ejde-517	37	7	ill	ill	ADV
ejde-517	37	8	-	-	PUNCT
ejde-517	37	9	posed	pose	VERB
ejde-517	37	10	,	,	PUNCT
ejde-517	37	11	a	a	DET
ejde-517	37	12	unique	unique	ADJ
ejde-517	37	13	solution	solution	NOUN
ejde-517	37	14	exists	exist	VERB
ejde-517	37	15	.	.	PUNCT
ejde-517	38	1	physically	physically	ADV
ejde-517	38	2	,	,	PUNCT
ejde-517	38	3	this	this	PRON
ejde-517	38	4	makes	make	VERB
ejde-517	38	5	sense	sense	NOUN
ejde-517	38	6	but	but	CCONJ
ejde-517	38	7	to	to	PART
ejde-517	38	8	show	show	VERB
ejde-517	38	9	this	this	PRON
ejde-517	38	10	mathematically	mathematically	ADV
ejde-517	38	11	is	be	AUX
ejde-517	38	12	not	not	PART
ejde-517	38	13	trivial	trivial	ADJ
ejde-517	38	14	.	.	PUNCT
ejde-517	39	1	for	for	ADP
ejde-517	39	2	the	the	DET
ejde-517	39	3	discussion	discussion	NOUN
ejde-517	39	4	of	of	ADP
ejde-517	39	5	this	this	DET
ejde-517	39	6	result	result	NOUN
ejde-517	39	7	,	,	PUNCT
ejde-517	39	8	we	we	PRON
ejde-517	39	9	refer	refer	VERB
ejde-517	39	10	the	the	DET
ejde-517	39	11	readers	reader	NOUN
ejde-517	39	12	to	to	ADP
ejde-517	39	13	[	[	X
ejde-517	39	14	36	36	NUM
ejde-517	39	15	,	,	PUNCT
ejde-517	39	16	35	35	NUM
ejde-517	39	17	]	]	PUNCT
ejde-517	39	18	for	for	ADP
ejde-517	39	19	the	the	DET
ejde-517	39	20	case	case	NOUN
ejde-517	39	21	n	n	PRON
ejde-517	39	22	≥	≥	NOUN
ejde-517	39	23	3	3	NUM
ejde-517	39	24	and	and	CCONJ
ejde-517	39	25	to	to	ADP
ejde-517	39	26	[	[	X
ejde-517	39	27	2	2	NUM
ejde-517	39	28	,	,	PUNCT
ejde-517	39	29	5	5	NUM
ejde-517	39	30	,	,	PUNCT
ejde-517	39	31	25	25	NUM
ejde-517	39	32	]	]	PUNCT
ejde-517	39	33	for	for	ADP
ejde-517	39	34	the	the	DET
ejde-517	39	35	case	case	NOUN
ejde-517	39	36	n	n	NOUN
ejde-517	39	37	=	=	SYM
ejde-517	39	38	2	2	NUM
ejde-517	39	39	.	.	PUNCT
ejde-517	39	40	because	because	SCONJ
ejde-517	39	41	of	of	ADP
ejde-517	39	42	its	its	PRON
ejde-517	39	43	ill	ill	ADJ
ejde-517	39	44	-	-	PUNCT
ejde-517	39	45	posedness	posedness	NOUN
ejde-517	39	46	,	,	PUNCT
ejde-517	39	47	the	the	DET
ejde-517	39	48	inverse	inverse	NOUN
ejde-517	39	49	eit	eit	PRON
ejde-517	39	50	problem	problem	NOUN
ejde-517	39	51	is	be	AUX
ejde-517	39	52	an	an	DET
ejde-517	39	53	active	active	ADJ
ejde-517	39	54	research	research	NOUN
ejde-517	39	55	area	area	NOUN
ejde-517	39	56	.	.	PUNCT
ejde-517	40	1	hence	hence	ADV
ejde-517	40	2	,	,	PUNCT
ejde-517	40	3	several	several	ADJ
ejde-517	40	4	approaches	approach	NOUN
ejde-517	40	5	have	have	AUX
ejde-517	40	6	been	be	AUX
ejde-517	40	7	proposed	propose	VERB
ejde-517	40	8	to	to	PART
ejde-517	40	9	solve	solve	VERB
ejde-517	40	10	this	this	DET
ejde-517	40	11	problem	problem	NOUN
ejde-517	40	12	.	.	PUNCT
ejde-517	41	1	different	different	ADJ
ejde-517	41	2	techniques	technique	NOUN
ejde-517	41	3	are	be	AUX
ejde-517	41	4	discussed	discuss	VERB
ejde-517	41	5	in	in	ADP
ejde-517	41	6	[	[	X
ejde-517	41	7	5	5	NUM
ejde-517	41	8	,	,	PUNCT
ejde-517	41	9	8	8	NUM
ejde-517	41	10	,	,	PUNCT
ejde-517	41	11	20	20	NUM
ejde-517	41	12	,	,	PUNCT
ejde-517	41	13	28	28	NUM
ejde-517	41	14	,	,	PUNCT
ejde-517	41	15	37	37	NUM
ejde-517	41	16	]	]	PUNCT
ejde-517	41	17	.	.	PUNCT
ejde-517	42	1	in	in	ADP
ejde-517	42	2	this	this	DET
ejde-517	42	3	work	work	NOUN
ejde-517	42	4	,	,	PUNCT
ejde-517	42	5	we	we	PRON
ejde-517	42	6	focus	focus	VERB
ejde-517	42	7	on	on	ADP
ejde-517	42	8	a	a	DET
ejde-517	42	9	technique	technique	NOUN
ejde-517	42	10	proposed	propose	VERB
ejde-517	42	11	by	by	ADP
ejde-517	42	12	mendoza	mendoza	PROPN
ejde-517	42	13	and	and	CCONJ
ejde-517	42	14	keeling	keeling	PROPN
ejde-517	42	15	in	in	ADP
ejde-517	42	16	[	[	X
ejde-517	42	17	27	27	NUM
ejde-517	42	18	]	]	PUNCT
ejde-517	42	19	.	.	PUNCT
ejde-517	43	1	we	we	PRON
ejde-517	43	2	assume	assume	VERB
ejde-517	43	3	that	that	SCONJ
ejde-517	43	4	the	the	DET
ejde-517	43	5	conductivity	conductivity	NOUN
ejde-517	43	6	σ	σ	NOUN
ejde-517	43	7	is	be	AUX
ejde-517	43	8	piecewise	piecewise	NOUN
ejde-517	43	9	constant	constant	ADJ
ejde-517	43	10	.	.	PUNCT
ejde-517	44	1	this	this	DET
ejde-517	44	2	assumption	assumption	NOUN
ejde-517	44	3	is	be	AUX
ejde-517	44	4	based	base	VERB
ejde-517	44	5	on	on	ADP
ejde-517	44	6	the	the	DET
ejde-517	44	7	fact	fact	NOUN
ejde-517	44	8	that	that	SCONJ
ejde-517	44	9	the	the	DET
ejde-517	44	10	conductivities	conductivity	NOUN
ejde-517	44	11	of	of	ADP
ejde-517	44	12	healthy	healthy	ADJ
ejde-517	44	13	tissues	tissue	NOUN
ejde-517	44	14	show	show	VERB
ejde-517	44	15	great	great	ADJ
ejde-517	44	16	contrast	contrast	NOUN
ejde-517	44	17	[	[	X
ejde-517	44	18	3	3	NUM
ejde-517	44	19	,	,	PUNCT
ejde-517	44	20	17	17	NUM
ejde-517	44	21	]	]	PUNCT
ejde-517	44	22	.	.	PUNCT
ejde-517	45	1	by	by	ADP
ejde-517	45	2	assuming	assume	VERB
ejde-517	45	3	that	that	SCONJ
ejde-517	45	4	σ	σ	PROPN
ejde-517	45	5	is	be	AUX
ejde-517	45	6	piecewiseconstant	piecewiseconstant	ADJ
ejde-517	45	7	,	,	PUNCT
ejde-517	45	8	the	the	DET
ejde-517	45	9	inverse	inverse	NOUN
ejde-517	45	10	problem	problem	NOUN
ejde-517	45	11	is	be	AUX
ejde-517	45	12	treated	treat	VERB
ejde-517	45	13	as	as	ADP
ejde-517	45	14	a	a	DET
ejde-517	45	15	segmentation	segmentation	NOUN
ejde-517	45	16	problem	problem	NOUN
ejde-517	45	17	.	.	PUNCT
ejde-517	46	1	a	a	DET
ejde-517	46	2	segmentation	segmentation	NOUN
ejde-517	46	3	technique	technique	NOUN
ejde-517	46	4	called	call	VERB
ejde-517	46	5	“	"	PUNCT
ejde-517	46	6	multi	multi	ADJ
ejde-517	46	7	-	-	ADJ
ejde-517	46	8	phase	phase	ADJ
ejde-517	46	9	segmentation	segmentation	NOUN
ejde-517	46	10	”	"	PUNCT
ejde-517	46	11	,	,	PUNCT
ejde-517	46	12	proposed	propose	VERB
ejde-517	46	13	by	by	ADP
ejde-517	46	14	fürtinger	fürtinger	NOUN
ejde-517	46	15	in	in	ADP
ejde-517	46	16	[	[	X
ejde-517	46	17	15	15	NUM
ejde-517	46	18	]	]	PUNCT
ejde-517	46	19	,	,	PUNCT
ejde-517	46	20	is	be	AUX
ejde-517	46	21	explored	explore	VERB
ejde-517	46	22	in	in	ADP
ejde-517	46	23	[	[	X
ejde-517	46	24	27	27	NUM
ejde-517	46	25	]	]	PUNCT
ejde-517	46	26	.	.	PUNCT
ejde-517	47	1	moreover	moreover	ADV
ejde-517	47	2	,	,	PUNCT
ejde-517	47	3	it	it	PRON
ejde-517	47	4	is	be	AUX
ejde-517	47	5	assumed	assume	VERB
ejde-517	47	6	that	that	SCONJ
ejde-517	47	7	the	the	DET
ejde-517	47	8	desired	desire	VERB
ejde-517	47	9	conductivity	conductivity	NOUN
ejde-517	47	10	can	can	AUX
ejde-517	47	11	be	be	AUX
ejde-517	47	12	expressed	express	VERB
ejde-517	47	13	in	in	ADP
ejde-517	47	14	terms	term	NOUN
ejde-517	47	15	of	of	ADP
ejde-517	47	16	m	m	PROPN
ejde-517	47	17	phases	phase	NOUN
ejde-517	47	18	,	,	PUNCT
ejde-517	47	19	i.e.	i.e.	X
ejde-517	47	20	,	,	PUNCT
ejde-517	47	21	of	of	ADP
ejde-517	47	22	the	the	DET
ejde-517	47	23	form	form	NOUN
ejde-517	47	24	σ(x	σ(x	NOUN
ejde-517	47	25	)	)	PUNCT
ejde-517	47	26	=	=	PUNCT
ejde-517	48	1	m∑	m∑	CCONJ
ejde-517	48	2	m=1	m=1	PROPN
ejde-517	48	3	σm(x)χm(x	σm(x)χm(x	NOUN
ejde-517	48	4	)	)	PUNCT
ejde-517	48	5	,	,	PUNCT
ejde-517	48	6	(	(	PUNCT
ejde-517	48	7	1.3	1.3	NUM
ejde-517	48	8	)	)	PUNCT
ejde-517	48	9	where	where	SCONJ
ejde-517	48	10	for	for	ADP
ejde-517	48	11	the	the	DET
ejde-517	48	12	mth	mth	NOUN
ejde-517	48	13	phase	phase	NOUN
ejde-517	48	14	χm	χm	NOUN
ejde-517	48	15	is	be	AUX
ejde-517	48	16	the	the	DET
ejde-517	48	17	characteristic	characteristic	ADJ
ejde-517	48	18	function	function	NOUN
ejde-517	48	19	of	of	ADP
ejde-517	48	20	a	a	DET
ejde-517	48	21	subdomain	subdomain	NOUN
ejde-517	48	22	ωm	ωm	X
ejde-517	48	23	⊂	⊂	PROPN
ejde-517	48	24	ω	ω	PROPN
ejde-517	48	25	and	and	CCONJ
ejde-517	48	26	σm	σm	INTJ
ejde-517	48	27	is	be	AUX
ejde-517	48	28	globally	globally	ADV
ejde-517	48	29	smooth	smooth	ADJ
ejde-517	48	30	.	.	PUNCT
ejde-517	49	1	in	in	ADP
ejde-517	49	2	[	[	X
ejde-517	49	3	27	27	NUM
ejde-517	49	4	]	]	PUNCT
ejde-517	49	5	,	,	PUNCT
ejde-517	49	6	the	the	DET
ejde-517	49	7	number	number	NOUN
ejde-517	49	8	of	of	ADP
ejde-517	49	9	phases	phase	NOUN
ejde-517	49	10	is	be	AUX
ejde-517	49	11	fixed	fix	VERB
ejde-517	49	12	to	to	ADP
ejde-517	49	13	2	2	NUM
ejde-517	49	14	,	,	PUNCT
ejde-517	49	15	hence	hence	ADV
ejde-517	49	16	the	the	DET
ejde-517	49	17	method	method	NOUN
ejde-517	49	18	is	be	AUX
ejde-517	49	19	referred	refer	VERB
ejde-517	49	20	to	to	ADP
ejde-517	49	21	as	as	ADP
ejde-517	49	22	a	a	DET
ejde-517	49	23	two	two	NUM
ejde-517	49	24	-	-	PUNCT
ejde-517	49	25	phase	phase	NOUN
ejde-517	49	26	segmentation	segmentation	NOUN
ejde-517	49	27	approach	approach	NOUN
ejde-517	49	28	.	.	PUNCT
ejde-517	50	1	this	this	PRON
ejde-517	50	2	is	be	AUX
ejde-517	50	3	possible	possible	ADJ
ejde-517	50	4	if	if	SCONJ
ejde-517	50	5	the	the	DET
ejde-517	50	6	subdomain	subdomain	NOUN
ejde-517	50	7	ω1	ω1	PROPN
ejde-517	50	8	has	have	AUX
ejde-517	50	9	disjoint	disjoint	VERB
ejde-517	50	10	non	non	ADJ
ejde-517	50	11	-	-	ADJ
ejde-517	50	12	adjacent	adjacent	ADJ
ejde-517	50	13	components	component	NOUN
ejde-517	50	14	.	.	PUNCT
ejde-517	51	1	the	the	DET
ejde-517	51	2	subdomains	subdomain	NOUN
ejde-517	51	3	ω1	ω1	PROPN
ejde-517	51	4	and	and	CCONJ
ejde-517	51	5	ω2	ω2	ADJ
ejde-517	51	6	form	form	VERB
ejde-517	51	7	a	a	DET
ejde-517	51	8	disjoint	disjoint	ADJ
ejde-517	51	9	partition	partition	NOUN
ejde-517	51	10	of	of	ADP
ejde-517	51	11	ω	ω	PROPN
ejde-517	51	12	,	,	PUNCT
ejde-517	51	13	i.e.	i.e.	X
ejde-517	51	14	,	,	PUNCT
ejde-517	51	15	ω1	ω1	PROPN
ejde-517	51	16	∩ω2	∩ω2	PROPN
ejde-517	51	17	=	=	PUNCT
ejde-517	51	18	∅	∅	NOUN
ejde-517	51	19	and	and	CCONJ
ejde-517	51	20	ω	ω	NUM
ejde-517	51	21	=	=	PROPN
ejde-517	51	22	ω1	ω1	PROPN
ejde-517	51	23	∪ω2	∪ω2	NOUN
ejde-517	51	24	.	.	PUNCT
ejde-517	52	1	the	the	DET
ejde-517	52	2	conductivity	conductivity	NOUN
ejde-517	52	3	σ2	σ2	PROPN
ejde-517	52	4	in	in	ADP
ejde-517	52	5	ω2	ω2	ADJ
ejde-517	52	6	is	be	AUX
ejde-517	52	7	assumed	assume	VERB
ejde-517	52	8	to	to	PART
ejde-517	52	9	be	be	AUX
ejde-517	52	10	known	know	VERB
ejde-517	52	11	and	and	CCONJ
ejde-517	52	12	χ2	χ2	PROPN
ejde-517	52	13	=	=	PUNCT
ejde-517	52	14	1	1	NUM
ejde-517	52	15	−	−	PROPN
ejde-517	52	16	χ1	χ1	NOUN
ejde-517	52	17	.	.	PUNCT
ejde-517	53	1	therefore	therefore	ADV
ejde-517	53	2	,	,	PUNCT
ejde-517	53	3	the	the	DET
ejde-517	53	4	inverse	inverse	NOUN
ejde-517	53	5	eit	eit	DET
ejde-517	53	6	problem	problem	NOUN
ejde-517	53	7	becomes	become	VERB
ejde-517	53	8	a	a	DET
ejde-517	53	9	problem	problem	NOUN
ejde-517	53	10	of	of	ADP
ejde-517	53	11	identifying	identify	VERB
ejde-517	53	12	σ1	σ1	PROPN
ejde-517	53	13	and	and	CCONJ
ejde-517	53	14	χ1	χ1	NOUN
ejde-517	53	15	.	.	PUNCT
ejde-517	54	1	it	it	PRON
ejde-517	54	2	is	be	AUX
ejde-517	54	3	shown	show	VERB
ejde-517	54	4	in	in	ADP
ejde-517	54	5	[	[	X
ejde-517	54	6	27	27	NUM
ejde-517	54	7	]	]	PUNCT
ejde-517	54	8	that	that	SCONJ
ejde-517	54	9	σ1	σ1	PROPN
ejde-517	54	10	can	can	AUX
ejde-517	54	11	be	be	AUX
ejde-517	54	12	expressed	express	VERB
ejde-517	54	13	in	in	ADP
ejde-517	54	14	terms	term	NOUN
ejde-517	54	15	of	of	ADP
ejde-517	54	16	χ1	χ1	NOUN
ejde-517	54	17	.	.	PUNCT
ejde-517	55	1	given	give	VERB
ejde-517	55	2	an	an	DET
ejde-517	55	3	initial	initial	ADJ
ejde-517	55	4	guess	guess	NOUN
ejde-517	55	5	for	for	ADP
ejde-517	55	6	χ1	χ1	NOUN
ejde-517	55	7	,	,	PUNCT
ejde-517	55	8	an	an	DET
ejde-517	55	9	iterative	iterative	NOUN
ejde-517	55	10	algorithm	algorithm	NOUN
ejde-517	55	11	is	be	AUX
ejde-517	55	12	proposed	propose	VERB
ejde-517	55	13	.	.	PUNCT
ejde-517	56	1	the	the	DET
ejde-517	56	2	main	main	ADJ
ejde-517	56	3	goal	goal	NOUN
ejde-517	56	4	of	of	ADP
ejde-517	56	5	this	this	DET
ejde-517	56	6	paper	paper	NOUN
ejde-517	56	7	is	be	AUX
ejde-517	56	8	to	to	PART
ejde-517	56	9	show	show	VERB
ejde-517	56	10	that	that	SCONJ
ejde-517	56	11	this	this	DET
ejde-517	56	12	iterative	iterative	NOUN
ejde-517	56	13	process	process	NOUN
ejde-517	56	14	has	have	VERB
ejde-517	56	15	a	a	DET
ejde-517	56	16	unique	unique	ADJ
ejde-517	56	17	solution	solution	NOUN
ejde-517	56	18	given	give	VERB
ejde-517	56	19	an	an	DET
ejde-517	56	20	initial	initial	ADJ
ejde-517	56	21	guess	guess	NOUN
ejde-517	56	22	for	for	ADP
ejde-517	56	23	χ1	χ1	NOUN
ejde-517	56	24	.	.	PUNCT
ejde-517	57	1	in	in	ADP
ejde-517	57	2	the	the	DET
ejde-517	57	3	next	next	ADJ
ejde-517	57	4	section	section	NOUN
ejde-517	57	5	,	,	PUNCT
ejde-517	57	6	we	we	PRON
ejde-517	57	7	briefly	briefly	ADV
ejde-517	57	8	discuss	discuss	VERB
ejde-517	57	9	the	the	DET
ejde-517	57	10	two	two	NUM
ejde-517	57	11	-	-	PUNCT
ejde-517	57	12	phase	phase	NOUN
ejde-517	57	13	segmentation	segmentation	NOUN
ejde-517	57	14	algorithm	algorithm	NOUN
ejde-517	57	15	.	.	PUNCT
ejde-517	58	1	then	then	ADV
ejde-517	58	2	an	an	DET
ejde-517	58	3	analysis	analysis	NOUN
ejde-517	58	4	of	of	ADP
ejde-517	58	5	the	the	DET
ejde-517	58	6	algorithm	algorithm	NOUN
ejde-517	58	7	is	be	AUX
ejde-517	58	8	carried	carry	VERB
ejde-517	58	9	out	out	ADP
ejde-517	58	10	.	.	PUNCT
ejde-517	59	1	we	we	PRON
ejde-517	59	2	show	show	VERB
ejde-517	59	3	that	that	SCONJ
ejde-517	59	4	the	the	DET
ejde-517	59	5	algorithm	algorithm	NOUN
ejde-517	59	6	can	can	AUX
ejde-517	59	7	be	be	AUX
ejde-517	59	8	expressed	express	VERB
ejde-517	59	9	as	as	ADP
ejde-517	59	10	a	a	DET
ejde-517	59	11	fixed	fix	VERB
ejde-517	59	12	point	point	NOUN
ejde-517	59	13	iteration	iteration	NOUN
ejde-517	59	14	.	.	PUNCT
ejde-517	60	1	finally	finally	ADV
ejde-517	60	2	,	,	PUNCT
ejde-517	60	3	the	the	DET
ejde-517	60	4	existence	existence	NOUN
ejde-517	60	5	of	of	ADP
ejde-517	60	6	a	a	DET
ejde-517	60	7	fixed	fix	VERB
ejde-517	60	8	point	point	NOUN
ejde-517	60	9	in	in	ADP
ejde-517	60	10	a	a	DET
ejde-517	60	11	suitable	suitable	ADJ
ejde-517	60	12	space	space	NOUN
ejde-517	60	13	is	be	AUX
ejde-517	60	14	presented	present	VERB
ejde-517	60	15	.	.	PUNCT
ejde-517	61	1	2	2	X
ejde-517	61	2	.	.	X
ejde-517	61	3	two	two	NUM
ejde-517	61	4	-	-	PUNCT
ejde-517	61	5	phase	phase	NOUN
ejde-517	61	6	segmentation	segmentation	NOUN
ejde-517	61	7	algorithm	algorithm	NOUN
ejde-517	61	8	let	let	VERB
ejde-517	61	9	us	we	PRON
ejde-517	61	10	fix	fix	VERB
ejde-517	61	11	f	f	PROPN
ejde-517	61	12	∈	∈	PROPN
ejde-517	61	13	l̃2(∂ω	l̃2(∂ω	NOUN
ejde-517	61	14	)	)	PUNCT
ejde-517	61	15	and	and	CCONJ
ejde-517	61	16	define	define	VERB
ejde-517	61	17	the	the	DET
ejde-517	61	18	function	function	NOUN
ejde-517	61	19	f	f	NOUN
ejde-517	61	20	:	:	PUNCT
ejde-517	61	21	l2(ω)→	l2(ω)→	PROPN
ejde-517	61	22	l̃(∂ω	l̃(∂ω	PROPN
ejde-517	61	23	)	)	PUNCT
ejde-517	61	24	by	by	ADP
ejde-517	61	25	f	f	PROPN
ejde-517	61	26	(	(	PUNCT
ejde-517	61	27	σ	σ	PROPN
ejde-517	61	28	)	)	PUNCT
ejde-517	61	29	=	=	SYM
ejde-517	62	1	φ	φ	X
ejde-517	62	2	∣∣	∣∣	X
ejde-517	62	3	∂ω	∂ω	PROPN
ejde-517	62	4	,	,	PUNCT
ejde-517	62	5	(	(	PUNCT
ejde-517	62	6	2.1	2.1	NUM
ejde-517	62	7	)	)	PUNCT
ejde-517	62	8	where	where	SCONJ
ejde-517	62	9	φ	φ	PROPN
ejde-517	62	10	is	be	AUX
ejde-517	62	11	the	the	DET
ejde-517	62	12	solution	solution	NOUN
ejde-517	62	13	of	of	ADP
ejde-517	62	14	(	(	PUNCT
ejde-517	62	15	1.1	1.1	NUM
ejde-517	62	16	)	)	PUNCT
ejde-517	62	17	given	give	VERB
ejde-517	62	18	σ	σ	PROPN
ejde-517	62	19	and	and	CCONJ
ejde-517	62	20	f	f	PROPN
ejde-517	62	21	.	.	PUNCT
ejde-517	63	1	let	let	VERB
ejde-517	63	2	σ	σ	X
ejde-517	63	3	?	?	PROPN
ejde-517	63	4	be	be	AUX
ejde-517	63	5	the	the	DET
ejde-517	63	6	actual	actual	ADJ
ejde-517	63	7	conductivity	conductivity	NOUN
ejde-517	63	8	distribution	distribution	NOUN
ejde-517	63	9	in	in	ADP
ejde-517	63	10	ω	ω	PROPN
ejde-517	63	11	.	.	PUNCT
ejde-517	64	1	the	the	DET
ejde-517	64	2	inverse	inverse	NOUN
ejde-517	64	3	problem	problem	NOUN
ejde-517	64	4	is	be	AUX
ejde-517	64	5	to	to	PART
ejde-517	64	6	recover	recover	VERB
ejde-517	64	7	σ	σ	PROPN
ejde-517	64	8	?	?	PUNCT
ejde-517	64	9	from	from	ADP
ejde-517	64	10	λσ	λσ	ADV
ejde-517	64	11	?	?	PUNCT
ejde-517	64	12	.	.	PUNCT
ejde-517	65	1	suppose	suppose	VERB
ejde-517	65	2	f	f	X
ejde-517	65	3	∈	∈	PROPN
ejde-517	65	4	l̃2(∂ω	l̃2(∂ω	PROPN
ejde-517	65	5	)	)	PUNCT
ejde-517	65	6	and	and	CCONJ
ejde-517	65	7	let	let	VERB
ejde-517	65	8	v	v	NOUN
ejde-517	65	9	?	?	PUNCT
ejde-517	66	1	=	=	PUNCT
ejde-517	66	2	λσ?(f	λσ?(f	NOUN
ejde-517	66	3	)	)	PUNCT
ejde-517	66	4	=	=	SYM
ejde-517	66	5	f	f	PROPN
ejde-517	66	6	(	(	PUNCT
ejde-517	66	7	σ	σ	PROPN
ejde-517	66	8	?	?	PUNCT
ejde-517	66	9	)	)	PUNCT
ejde-517	66	10	be	be	VERB
ejde-517	66	11	the	the	DET
ejde-517	66	12	exact	exact	ADJ
ejde-517	66	13	boundary	boundary	ADJ
ejde-517	66	14	voltage	voltage	NOUN
ejde-517	66	15	.	.	PUNCT
ejde-517	67	1	moreover	moreover	ADV
ejde-517	67	2	,	,	PUNCT
ejde-517	67	3	ejde-2020/93	ejde-2020/93	PROPN
ejde-517	67	4	impedance	impedance	NOUN
ejde-517	67	5	tomography	tomography	NOUN
ejde-517	67	6	problem	problem	NOUN
ejde-517	67	7	3	3	NUM
ejde-517	67	8	let	let	VERB
ejde-517	67	9	ṽ	ṽ	PROPN
ejde-517	67	10	≈	≈	PROPN
ejde-517	67	11	v	v	PROPN
ejde-517	67	12	?	?	PUNCT
ejde-517	68	1	be	be	AUX
ejde-517	68	2	the	the	DET
ejde-517	68	3	measured	measure	VERB
ejde-517	68	4	boundary	boundary	ADJ
ejde-517	68	5	voltage	voltage	NOUN
ejde-517	68	6	.	.	PUNCT
ejde-517	69	1	let	let	VERB
ejde-517	69	2	σ̃1	σ̃1	PROPN
ejde-517	69	3	be	be	AUX
ejde-517	69	4	an	an	DET
ejde-517	69	5	estimate	estimate	NOUN
ejde-517	69	6	of	of	ADP
ejde-517	69	7	σ1	σ1	PROPN
ejde-517	69	8	.	.	PUNCT
ejde-517	70	1	to	to	PART
ejde-517	70	2	solve	solve	VERB
ejde-517	70	3	the	the	DET
ejde-517	70	4	eit	eit	PROPN
ejde-517	70	5	inverse	inverse	NOUN
ejde-517	70	6	problem	problem	NOUN
ejde-517	70	7	,	,	PUNCT
ejde-517	70	8	our	our	PRON
ejde-517	70	9	aim	aim	NOUN
ejde-517	70	10	is	be	AUX
ejde-517	70	11	to	to	PART
ejde-517	70	12	minimize	minimize	VERB
ejde-517	70	13	j̃(σ1	j̃(σ1	ADP
ejde-517	70	14	,	,	PUNCT
ejde-517	70	15	χ1	χ1	NOUN
ejde-517	70	16	)	)	PUNCT
ejde-517	70	17	=	=	SYM
ejde-517	71	1	∫	∫	PROPN
ejde-517	72	1	∂ω	∂ω	PROPN
ejde-517	72	2	|f	|f	PROPN
ejde-517	72	3	(	(	PUNCT
ejde-517	72	4	σ)−	σ)−	PROPN
ejde-517	72	5	ṽ	ṽ	PROPN
ejde-517	72	6	|2	|2	NUM
ejde-517	72	7	ds	ds	NOUN
ejde-517	72	8	+	+	CCONJ
ejde-517	72	9	∫	∫	PROPN
ejde-517	72	10	ω	ω	X
ejde-517	72	11	α|∇σ1|2(χ1	α|∇σ1|2(χ1	X
ejde-517	72	12	+	+	CCONJ
ejde-517	72	13	ε	ε	PROPN
ejde-517	72	14	)	)	PUNCT
ejde-517	72	15	+	+	NUM
ejde-517	72	16	λ(σ1	λ(σ1	NOUN
ejde-517	72	17	−	−	PROPN
ejde-517	72	18	σ̃1)2	σ̃1)2	PROPN
ejde-517	72	19	dv	dv	PROPN
ejde-517	72	20	(	(	PUNCT
ejde-517	72	21	2.2	2.2	NUM
ejde-517	72	22	)	)	PUNCT
ejde-517	72	23	with	with	ADP
ejde-517	72	24	σ	σ	PROPN
ejde-517	72	25	=	=	PUNCT
ejde-517	72	26	σ1χ1	σ1χ1	X
ejde-517	72	27	+	+	NUM
ejde-517	72	28	σ2(1	σ2(1	PROPN
ejde-517	72	29	−	−	PROPN
ejde-517	72	30	χ1	χ1	NOUN
ejde-517	72	31	)	)	PUNCT
ejde-517	72	32	and	and	CCONJ
ejde-517	72	33	σ2	σ2	PROPN
ejde-517	72	34	is	be	AUX
ejde-517	72	35	given	give	VERB
ejde-517	72	36	.	.	PUNCT
ejde-517	73	1	the	the	DET
ejde-517	73	2	first	first	ADJ
ejde-517	73	3	term	term	NOUN
ejde-517	73	4	of	of	ADP
ejde-517	73	5	the	the	DET
ejde-517	73	6	integral	integral	ADJ
ejde-517	73	7	is	be	AUX
ejde-517	73	8	the	the	DET
ejde-517	73	9	fidelity	fidelity	PROPN
ejde-517	73	10	term	term	NOUN
ejde-517	73	11	,	,	PUNCT
ejde-517	73	12	the	the	DET
ejde-517	73	13	second	second	ADJ
ejde-517	73	14	term	term	NOUN
ejde-517	73	15	provides	provide	VERB
ejde-517	73	16	smoothness	smoothness	ADJ
ejde-517	73	17	on	on	ADP
ejde-517	73	18	σ1	σ1	PROPN
ejde-517	73	19	on	on	ADP
ejde-517	73	20	ω1	ω1	PROPN
ejde-517	73	21	and	and	CCONJ
ejde-517	73	22	the	the	DET
ejde-517	73	23	third	third	ADJ
ejde-517	73	24	term	term	NOUN
ejde-517	73	25	comes	come	VERB
ejde-517	73	26	from	from	ADP
ejde-517	73	27	tikohonov	tikohonov	NOUN
ejde-517	73	28	regularization	regularization	NOUN
ejde-517	73	29	.	.	PUNCT
ejde-517	74	1	before	before	SCONJ
ejde-517	74	2	we	we	PRON
ejde-517	74	3	proceed	proceed	VERB
ejde-517	74	4	,	,	PUNCT
ejde-517	74	5	we	we	PRON
ejde-517	74	6	first	first	ADV
ejde-517	74	7	need	need	VERB
ejde-517	74	8	to	to	PART
ejde-517	74	9	define	define	VERB
ejde-517	74	10	the	the	DET
ejde-517	74	11	forward	forward	ADJ
ejde-517	74	12	solution	solution	NOUN
ejde-517	74	13	and	and	CCONJ
ejde-517	74	14	the	the	DET
ejde-517	74	15	adjoint	adjoint	NOUN
ejde-517	74	16	solution	solution	NOUN
ejde-517	74	17	of	of	ADP
ejde-517	74	18	the	the	DET
ejde-517	74	19	eit	eit	PROPN
ejde-517	74	20	problem	problem	NOUN
ejde-517	74	21	.	.	PUNCT
ejde-517	75	1	definition	definition	NOUN
ejde-517	75	2	2.1	2.1	NUM
ejde-517	75	3	.	.	PUNCT
ejde-517	76	1	the	the	DET
ejde-517	76	2	forward	forward	ADJ
ejde-517	76	3	solution	solution	NOUN
ejde-517	76	4	φ	φ	PROPN
ejde-517	76	5	is	be	AUX
ejde-517	76	6	the	the	DET
ejde-517	76	7	solution	solution	NOUN
ejde-517	76	8	of	of	ADP
ejde-517	76	9	(	(	PUNCT
ejde-517	76	10	1.1	1.1	NUM
ejde-517	76	11	)	)	PUNCT
ejde-517	76	12	given	give	VERB
ejde-517	76	13	f	f	PROPN
ejde-517	76	14	∈	∈	PROPN
ejde-517	76	15	l̃2(∂ω	l̃2(∂ω	NOUN
ejde-517	76	16	)	)	PUNCT
ejde-517	76	17	and	and	CCONJ
ejde-517	76	18	σ	σ	NUM
ejde-517	76	19	∈	∈	PROPN
ejde-517	76	20	l∞(ω	l∞(ω	NOUN
ejde-517	76	21	)	)	PUNCT
ejde-517	76	22	.	.	PUNCT
ejde-517	77	1	moreover	moreover	ADV
ejde-517	77	2	,	,	PUNCT
ejde-517	77	3	let	let	VERB
ejde-517	77	4	ṽ	ṽ	PROPN
ejde-517	77	5	be	be	AUX
ejde-517	77	6	the	the	DET
ejde-517	77	7	measured	measure	VERB
ejde-517	77	8	boundary	boundary	ADJ
ejde-517	77	9	voltage	voltage	NOUN
ejde-517	77	10	.	.	PUNCT
ejde-517	78	1	we	we	PRON
ejde-517	78	2	define	define	VERB
ejde-517	78	3	the	the	DET
ejde-517	78	4	adjoint	adjoint	NOUN
ejde-517	78	5	solution	solution	NOUN
ejde-517	78	6	φ∗	φ∗	NOUN
ejde-517	78	7	as	as	ADP
ejde-517	78	8	the	the	DET
ejde-517	78	9	solution	solution	NOUN
ejde-517	78	10	of	of	ADP
ejde-517	78	11	∇	∇	X
ejde-517	78	12	·	·	PUNCT
ejde-517	78	13	(	(	PUNCT
ejde-517	78	14	σ∇φ∗	σ∇φ∗	NOUN
ejde-517	78	15	)	)	PUNCT
ejde-517	78	16	=	=	SYM
ejde-517	78	17	0	0	NUM
ejde-517	79	1	in	in	ADP
ejde-517	79	2	ω	ω	PROPN
ejde-517	79	3	,	,	PUNCT
ejde-517	79	4	σ	σ	PROPN
ejde-517	79	5	∂φ∗	∂φ∗	NOUN
ejde-517	79	6	∂n	∂n	PROPN
ejde-517	79	7	=	=	SYM
ejde-517	79	8	f	f	PROPN
ejde-517	79	9	(	(	PUNCT
ejde-517	79	10	σ)−	σ)−	PROPN
ejde-517	79	11	ṽ	ṽ	PROPN
ejde-517	79	12	on	on	ADP
ejde-517	79	13	∂ω	∂ω	PROPN
ejde-517	79	14	.	.	PUNCT
ejde-517	80	1	(	(	PUNCT
ejde-517	80	2	2.3	2.3	NUM
ejde-517	80	3	)	)	PUNCT
ejde-517	80	4	both	both	DET
ejde-517	80	5	φ	φ	NOUN
ejde-517	80	6	and	and	CCONJ
ejde-517	80	7	φ∗	φ∗	NOUN
ejde-517	80	8	satisfy	satisfy	NOUN
ejde-517	80	9	∫	∫	PROPN
ejde-517	81	1	∂ω	∂ω	ADJ
ejde-517	81	2	φds	φds	NOUN
ejde-517	81	3	=	=	SYM
ejde-517	81	4	0	0	NUM
ejde-517	81	5	and	and	CCONJ
ejde-517	81	6	∫	∫	PROPN
ejde-517	81	7	∂ω	∂ω	ADJ
ejde-517	81	8	φ∗	φ∗	NOUN
ejde-517	81	9	ds	ds	NOUN
ejde-517	81	10	=	=	NOUN
ejde-517	81	11	0	0	X
ejde-517	81	12	.	.	PUNCT
ejde-517	82	1	using	use	VERB
ejde-517	82	2	(	(	PUNCT
ejde-517	82	3	1.1	1.1	NUM
ejde-517	82	4	)	)	PUNCT
ejde-517	82	5	,	,	PUNCT
ejde-517	82	6	(	(	PUNCT
ejde-517	82	7	2.3	2.3	NUM
ejde-517	82	8	)	)	PUNCT
ejde-517	82	9	,	,	PUNCT
ejde-517	82	10	and	and	CCONJ
ejde-517	82	11	(	(	PUNCT
ejde-517	82	12	1.3	1.3	NUM
ejde-517	82	13	)	)	PUNCT
ejde-517	82	14	,	,	PUNCT
ejde-517	82	15	the	the	DET
ejde-517	82	16	variational	variational	ADJ
ejde-517	82	17	formulations	formulation	NOUN
ejde-517	82	18	of	of	ADP
ejde-517	82	19	the	the	DET
ejde-517	82	20	forward	forward	ADJ
ejde-517	82	21	and	and	CCONJ
ejde-517	82	22	adjoint	adjoint	PROPN
ejde-517	82	23	problems	problem	NOUN
ejde-517	82	24	are∫	are∫	PROPN
ejde-517	83	1	ω	ω	PROPN
ejde-517	83	2	(	(	PUNCT
ejde-517	83	3	σ1χ1	σ1χ1	X
ejde-517	83	4	+	+	CCONJ
ejde-517	83	5	σ2(1−	σ2(1−	NOUN
ejde-517	83	6	χ1))∇φ	χ1))∇φ	NOUN
ejde-517	83	7	·	·	PUNCT
ejde-517	83	8	∇v	∇v	ADJ
ejde-517	83	9	dv	dv	PROPN
ejde-517	83	10	=	=	SYM
ejde-517	83	11	∫	∫	PROPN
ejde-517	83	12	∂ω	∂ω	PROPN
ejde-517	83	13	fv	fv	PROPN
ejde-517	83	14	ds	ds	PROPN
ejde-517	83	15	,	,	PUNCT
ejde-517	83	16	(	(	PUNCT
ejde-517	83	17	2.4)∫	2.4)∫	NUM
ejde-517	83	18	ω	ω	NUM
ejde-517	83	19	(	(	PUNCT
ejde-517	83	20	σ1χ1	σ1χ1	X
ejde-517	83	21	+	+	CCONJ
ejde-517	83	22	σ2(1−	σ2(1−	ADJ
ejde-517	83	23	χ1)∇φ∗	χ1)∇φ∗	NOUN
ejde-517	83	24	·	·	PUNCT
ejde-517	84	1	∇v	∇v	ADJ
ejde-517	84	2	dv	dv	PROPN
ejde-517	84	3	=	=	SYM
ejde-517	84	4	∫	∫	PROPN
ejde-517	85	1	∂ω	∂ω	PROPN
ejde-517	85	2	(	(	PUNCT
ejde-517	85	3	f	f	PROPN
ejde-517	85	4	(	(	PUNCT
ejde-517	85	5	σ1χ1	σ1χ1	X
ejde-517	85	6	+	+	X
ejde-517	85	7	σ2(1−	σ2(1−	VERB
ejde-517	85	8	χ1))−	χ1))−	PROPN
ejde-517	85	9	ṽ	ṽ	PROPN
ejde-517	85	10	)	)	PUNCT
ejde-517	85	11	v	v	NOUN
ejde-517	85	12	ds	ds	NOUN
ejde-517	85	13	,	,	PUNCT
ejde-517	85	14	(	(	PUNCT
ejde-517	85	15	2.5	2.5	NUM
ejde-517	85	16	)	)	PUNCT
ejde-517	85	17	for	for	ADP
ejde-517	85	18	all	all	PRON
ejde-517	85	19	v	v	ADP
ejde-517	85	20	∈	∈	PROPN
ejde-517	85	21	h1(ω	h1(ω	PROPN
ejde-517	85	22	)	)	PUNCT
ejde-517	85	23	.	.	PUNCT
ejde-517	86	1	formulations	formulation	NOUN
ejde-517	86	2	(	(	PUNCT
ejde-517	86	3	2.4	2.4	NUM
ejde-517	86	4	)	)	PUNCT
ejde-517	86	5	and	and	CCONJ
ejde-517	86	6	(	(	PUNCT
ejde-517	86	7	2.5	2.5	NUM
ejde-517	86	8	)	)	PUNCT
ejde-517	86	9	have	have	VERB
ejde-517	86	10	unique	unique	ADJ
ejde-517	86	11	solutions	solution	NOUN
ejde-517	86	12	[	[	X
ejde-517	86	13	27	27	NUM
ejde-517	86	14	]	]	PUNCT
ejde-517	86	15	in	in	ADP
ejde-517	86	16	h̃1(ω	h̃1(ω	PROPN
ejde-517	86	17	)	)	PUNCT
ejde-517	86	18	:	:	PUNCT
ejde-517	87	1	=	=	SYM
ejde-517	87	2	{	{	PUNCT
ejde-517	87	3	v	v	NOUN
ejde-517	87	4	∈	∈	NOUN
ejde-517	87	5	h1(ω)|	h1(ω)|	VERB
ejde-517	87	6	∫	∫	NOUN
ejde-517	88	1	∂ω	∂ω	ADJ
ejde-517	88	2	v	v	ADP
ejde-517	88	3	ds	ds	NOUN
ejde-517	88	4	=	=	NOUN
ejde-517	88	5	0	0	NUM
ejde-517	88	6	}	}	PUNCT
ejde-517	88	7	.	.	PUNCT
ejde-517	89	1	because	because	SCONJ
ejde-517	89	2	of	of	ADP
ejde-517	89	3	(	(	PUNCT
ejde-517	89	4	1.3	1.3	NUM
ejde-517	89	5	)	)	PUNCT
ejde-517	89	6	,	,	PUNCT
ejde-517	89	7	the	the	DET
ejde-517	89	8	forward	forward	ADJ
ejde-517	89	9	and	and	CCONJ
ejde-517	89	10	adjoint	adjoint	PROPN
ejde-517	89	11	solutions	solution	NOUN
ejde-517	89	12	φ	φ	PROPN
ejde-517	89	13	and	and	CCONJ
ejde-517	89	14	φ∗	φ∗	NOUN
ejde-517	89	15	are	be	AUX
ejde-517	89	16	dependent	dependent	ADJ
ejde-517	89	17	on	on	ADP
ejde-517	89	18	σ1	σ1	PROPN
ejde-517	89	19	and	and	CCONJ
ejde-517	89	20	χ1	χ1	NOUN
ejde-517	89	21	alone	alone	ADV
ejde-517	89	22	.	.	PUNCT
ejde-517	90	1	thus	thus	ADV
ejde-517	90	2	,	,	PUNCT
ejde-517	90	3	we	we	PRON
ejde-517	90	4	have	have	VERB
ejde-517	90	5	the	the	DET
ejde-517	90	6	following	follow	VERB
ejde-517	90	7	definition	definition	NOUN
ejde-517	90	8	.	.	PUNCT
ejde-517	91	1	definition	definition	NOUN
ejde-517	91	2	2.2	2.2	NUM
ejde-517	91	3	.	.	PUNCT
ejde-517	92	1	we	we	PRON
ejde-517	92	2	define	define	VERB
ejde-517	92	3	φ(σ1	φ(σ1	NOUN
ejde-517	92	4	,	,	PUNCT
ejde-517	92	5	χ1	χ1	NOUN
ejde-517	92	6	)	)	PUNCT
ejde-517	92	7	and	and	CCONJ
ejde-517	92	8	φ∗(σ1	φ∗(σ1	PROPN
ejde-517	92	9	,	,	PUNCT
ejde-517	92	10	χ1	χ1	NOUN
ejde-517	92	11	)	)	PUNCT
ejde-517	92	12	to	to	PART
ejde-517	92	13	be	be	AUX
ejde-517	92	14	the	the	DET
ejde-517	92	15	operators	operator	NOUN
ejde-517	92	16	that	that	PRON
ejde-517	92	17	map	map	VERB
ejde-517	92	18	any	any	PRON
ejde-517	92	19	given	give	VERB
ejde-517	92	20	σ1	σ1	PROPN
ejde-517	92	21	∈	∈	PROPN
ejde-517	92	22	l∞(ω	l∞(ω	X
ejde-517	92	23	)	)	PUNCT
ejde-517	92	24	and	and	CCONJ
ejde-517	92	25	characteristic	characteristic	ADJ
ejde-517	92	26	function	function	NOUN
ejde-517	92	27	χ1	χ1	NOUN
ejde-517	92	28	to	to	ADP
ejde-517	92	29	the	the	DET
ejde-517	92	30	respective	respective	ADJ
ejde-517	92	31	solutions	solution	NOUN
ejde-517	92	32	φ	φ	NOUN
ejde-517	92	33	and	and	CCONJ
ejde-517	92	34	φ∗	φ∗	NOUN
ejde-517	92	35	of	of	ADP
ejde-517	92	36	(	(	PUNCT
ejde-517	92	37	2.4	2.4	NUM
ejde-517	92	38	)	)	PUNCT
ejde-517	92	39	and	and	CCONJ
ejde-517	92	40	(	(	PUNCT
ejde-517	92	41	2.5	2.5	NUM
ejde-517	92	42	)	)	PUNCT
ejde-517	92	43	,	,	PUNCT
ejde-517	92	44	respectively	respectively	ADV
ejde-517	92	45	.	.	PUNCT
ejde-517	93	1	equivalently	equivalently	ADV
ejde-517	93	2	,	,	PUNCT
ejde-517	93	3	φ	φ	PROPN
ejde-517	93	4	:	:	PUNCT
ejde-517	93	5	(	(	PUNCT
ejde-517	93	6	σ1	σ1	PROPN
ejde-517	93	7	,	,	PUNCT
ejde-517	93	8	χ1	χ1	NOUN
ejde-517	93	9	)	)	PUNCT
ejde-517	93	10	→	→	SYM
ejde-517	93	11	φ	φ	PROPN
ejde-517	93	12	and	and	CCONJ
ejde-517	93	13	φ∗	φ∗	NOUN
ejde-517	93	14	:	:	PUNCT
ejde-517	93	15	(	(	PUNCT
ejde-517	93	16	σ1	σ1	PROPN
ejde-517	93	17	,	,	PUNCT
ejde-517	93	18	χ1)→	χ1)→	NOUN
ejde-517	93	19	φ∗.	φ∗.	VERB
ejde-517	93	20	the	the	DET
ejde-517	93	21	computation	computation	NOUN
ejde-517	93	22	of	of	ADP
ejde-517	93	23	the	the	DET
ejde-517	93	24	derivative	derivative	NOUN
ejde-517	93	25	of	of	ADP
ejde-517	93	26	j̃	j̃	PROPN
ejde-517	93	27	is	be	AUX
ejde-517	93	28	necessary	necessary	ADJ
ejde-517	93	29	to	to	PART
ejde-517	93	30	express	express	VERB
ejde-517	93	31	σ1	σ1	PROPN
ejde-517	93	32	in	in	ADP
ejde-517	93	33	terms	term	NOUN
ejde-517	93	34	of	of	ADP
ejde-517	93	35	χ1	χ1	NOUN
ejde-517	93	36	.	.	PUNCT
ejde-517	94	1	for	for	ADP
ejde-517	94	2	a	a	DET
ejde-517	94	3	fixed	fix	VERB
ejde-517	94	4	χ1	χ1	NOUN
ejde-517	94	5	,	,	PUNCT
ejde-517	94	6	the	the	DET
ejde-517	94	7	variational	variational	ADJ
ejde-517	94	8	derivative	derivative	NOUN
ejde-517	94	9	of	of	ADP
ejde-517	94	10	j̃	j̃	PROPN
ejde-517	94	11	in	in	ADP
ejde-517	94	12	(	(	PUNCT
ejde-517	94	13	2.2	2.2	NUM
ejde-517	94	14	)	)	PUNCT
ejde-517	94	15	with	with	ADP
ejde-517	94	16	respect	respect	NOUN
ejde-517	94	17	to	to	ADP
ejde-517	94	18	σ1	σ1	PROPN
ejde-517	94	19	∈	∈	PROPN
ejde-517	94	20	h1(ω	h1(ω	PROPN
ejde-517	94	21	)	)	PUNCT
ejde-517	94	22	in	in	ADP
ejde-517	94	23	the	the	DET
ejde-517	94	24	direction	direction	NOUN
ejde-517	94	25	of	of	ADP
ejde-517	94	26	δσ1	δσ1	NOUN
ejde-517	94	27	∈	∈	PROPN
ejde-517	94	28	h1(ω	h1(ω	PROPN
ejde-517	94	29	)	)	PUNCT
ejde-517	94	30	is	be	AUX
ejde-517	94	31	given	give	VERB
ejde-517	94	32	by	by	ADP
ejde-517	94	33	δj̃	δj̃	NUM
ejde-517	94	34	δσ1	δσ1	NOUN
ejde-517	94	35	(	(	PUNCT
ejde-517	94	36	σ1	σ1	PROPN
ejde-517	94	37	,	,	PUNCT
ejde-517	94	38	χ1	χ1	NOUN
ejde-517	94	39	;	;	PUNCT
ejde-517	94	40	δσ1	δσ1	NOUN
ejde-517	94	41	)	)	PUNCT
ejde-517	94	42	=	=	PUNCT
ejde-517	95	1	−	−	PROPN
ejde-517	95	2	∫	∫	PROPN
ejde-517	95	3	ω	ω	NUM
ejde-517	95	4	2χ1δσ1∇φ	2χ1δσ1∇φ	NUM
ejde-517	95	5	·	·	PUNCT
ejde-517	95	6	∇φ∗	∇φ∗	PROPN
ejde-517	96	1	dv	dv	PROPN
ejde-517	96	2	+	+	CCONJ
ejde-517	96	3	∫	∫	PROPN
ejde-517	96	4	ω	ω	NUM
ejde-517	96	5	2α(χ1	2α(χ1	NUM
ejde-517	96	6	+	+	NUM
ejde-517	96	7	ε)∇(δσ1	ε)∇(δσ1	NOUN
ejde-517	96	8	)	)	PUNCT
ejde-517	96	9	·	·	PUNCT
ejde-517	97	1	∇σ1	∇σ1	PROPN
ejde-517	97	2	dv	dv	PROPN
ejde-517	97	3	+	+	CCONJ
ejde-517	97	4	∫	∫	PROPN
ejde-517	97	5	ω	ω	NUM
ejde-517	97	6	2λ(σ1	2λ(σ1	NOUN
ejde-517	97	7	−	−	PROPN
ejde-517	97	8	σ̃1)δσ1	σ̃1)δσ1	PROPN
ejde-517	97	9	dv	dv	PROPN
ejde-517	97	10	.	.	PUNCT
ejde-517	98	1	if	if	SCONJ
ejde-517	98	2	we	we	PRON
ejde-517	98	3	equate	equate	VERB
ejde-517	98	4	the	the	DET
ejde-517	98	5	above	above	ADJ
ejde-517	98	6	expression	expression	NOUN
ejde-517	98	7	to	to	ADP
ejde-517	98	8	0	0	NUM
ejde-517	98	9	,	,	PUNCT
ejde-517	98	10	we	we	PRON
ejde-517	98	11	conclude	conclude	VERB
ejde-517	98	12	that	that	SCONJ
ejde-517	98	13	the	the	DET
ejde-517	98	14	following	follow	VERB
ejde-517	98	15	optimality	optimality	NOUN
ejde-517	98	16	condition	condition	NOUN
ejde-517	98	17	must	must	AUX
ejde-517	98	18	be	be	AUX
ejde-517	98	19	satisfied,∫	satisfied,∫	VERB
ejde-517	98	20	ω	ω	PROPN
ejde-517	99	1	[	[	X
ejde-517	99	2	α(χ1	α(χ1	NOUN
ejde-517	99	3	+	+	CCONJ
ejde-517	99	4	ε)∇σ1	ε)∇σ1	ADJ
ejde-517	99	5	·	·	PUNCT
ejde-517	99	6	∇v	∇v	ADV
ejde-517	99	7	+	+	NUM
ejde-517	99	8	λ(σ1	λ(σ1	NOUN
ejde-517	99	9	−	−	ADP
ejde-517	99	10	σ̃1)v	σ̃1)v	PROPN
ejde-517	99	11	]	]	X
ejde-517	99	12	dv	dv	PROPN
ejde-517	99	13	=	=	SYM
ejde-517	99	14	∫	∫	PROPN
ejde-517	99	15	ω	ω	PROPN
ejde-517	99	16	(	(	PUNCT
ejde-517	99	17	χ1∇φ	χ1∇φ	PROPN
ejde-517	99	18	·	·	PUNCT
ejde-517	99	19	∇φ∗)v	∇φ∗)v	CCONJ
ejde-517	99	20	dv	dv	PROPN
ejde-517	99	21	,	,	PUNCT
ejde-517	99	22	(	(	PUNCT
ejde-517	99	23	2.6	2.6	NUM
ejde-517	99	24	)	)	PUNCT
ejde-517	99	25	for	for	ADP
ejde-517	99	26	all	all	PRON
ejde-517	99	27	v	v	ADP
ejde-517	99	28	∈	∈	PROPN
ejde-517	99	29	h1(ω	h1(ω	PROPN
ejde-517	99	30	)	)	PUNCT
ejde-517	99	31	.	.	PUNCT
ejde-517	100	1	given	give	VERB
ejde-517	100	2	χ1	χ1	NOUN
ejde-517	100	3	and	and	CCONJ
ejde-517	100	4	an	an	DET
ejde-517	100	5	estimate	estimate	NOUN
ejde-517	100	6	σ̃1	σ̃1	PROPN
ejde-517	100	7	,	,	PUNCT
ejde-517	100	8	the	the	DET
ejde-517	100	9	quantity	quantity	NOUN
ejde-517	100	10	σ1	σ1	PROPN
ejde-517	100	11	is	be	AUX
ejde-517	100	12	calculated	calculate	VERB
ejde-517	100	13	via	via	ADP
ejde-517	100	14	(	(	PUNCT
ejde-517	100	15	2.6	2.6	NUM
ejde-517	100	16	)	)	PUNCT
ejde-517	100	17	.	.	PUNCT
ejde-517	101	1	we	we	PRON
ejde-517	101	2	formalize	formalize	VERB
ejde-517	101	3	this	this	PRON
ejde-517	101	4	in	in	ADP
ejde-517	101	5	the	the	DET
ejde-517	101	6	following	follow	VERB
ejde-517	101	7	definition	definition	NOUN
ejde-517	101	8	.	.	PUNCT
ejde-517	102	1	4	4	NUM
ejde-517	102	2	r.	r.	PROPN
ejde-517	102	3	mendoza	mendoza	PROPN
ejde-517	102	4	,	,	PUNCT
ejde-517	102	5	s.	s.	PROPN
ejde-517	102	6	keeling	keeling	PROPN
ejde-517	102	7	ejde-2020/93	ejde-2020/93	PROPN
ejde-517	102	8	definition	definition	NOUN
ejde-517	102	9	2.3	2.3	NUM
ejde-517	102	10	.	.	PUNCT
ejde-517	103	1	we	we	PRON
ejde-517	103	2	define	define	VERB
ejde-517	103	3	the	the	DET
ejde-517	103	4	operator	operator	NOUN
ejde-517	103	5	σ1	σ1	NOUN
ejde-517	103	6	:	:	PUNCT
ejde-517	103	7	χ1	χ1	NOUN
ejde-517	103	8	→	→	SYM
ejde-517	103	9	σ1	σ1	PROPN
ejde-517	103	10	that	that	PRON
ejde-517	103	11	maps	map	VERB
ejde-517	103	12	an	an	DET
ejde-517	103	13	element	element	NOUN
ejde-517	103	14	χ1	χ1	NOUN
ejde-517	103	15	∈	∈	NOUN
ejde-517	103	16	l∞(ω	l∞(ω	NOUN
ejde-517	103	17	)	)	PUNCT
ejde-517	103	18	to	to	ADP
ejde-517	103	19	an	an	DET
ejde-517	103	20	element	element	NOUN
ejde-517	103	21	σ1	σ1	PROPN
ejde-517	103	22	∈	∈	PROPN
ejde-517	103	23	h1(ω	h1(ω	PROPN
ejde-517	103	24	)	)	PUNCT
ejde-517	103	25	via	via	ADP
ejde-517	103	26	(	(	PUNCT
ejde-517	103	27	2.6	2.6	NUM
ejde-517	103	28	)	)	PUNCT
ejde-517	103	29	and	and	CCONJ
ejde-517	103	30	the	the	DET
ejde-517	103	31	the	the	DET
ejde-517	103	32	operator	operator	NOUN
ejde-517	103	33	σ	σ	NOUN
ejde-517	103	34	:	:	PUNCT
ejde-517	103	35	χ1	χ1	NOUN
ejde-517	103	36	→	→	SYM
ejde-517	103	37	σ	σ	PROPN
ejde-517	103	38	via	via	ADP
ejde-517	103	39	σ(χ1	σ(χ1	NOUN
ejde-517	103	40	)	)	PUNCT
ejde-517	103	41	=	=	SYM
ejde-517	103	42	σ1(χ1)χ1	σ1(χ1)χ1	PROPN
ejde-517	104	1	+	+	CCONJ
ejde-517	104	2	σ2(1−	σ2(1−	PROPN
ejde-517	104	3	χ1	χ1	NOUN
ejde-517	104	4	)	)	PUNCT
ejde-517	104	5	.	.	PUNCT
ejde-517	105	1	definitions	definition	NOUN
ejde-517	105	2	2.2	2.2	NUM
ejde-517	105	3	and	and	CCONJ
ejde-517	105	4	2.3	2.3	NUM
ejde-517	105	5	are	be	AUX
ejde-517	105	6	used	use	VERB
ejde-517	105	7	to	to	PART
ejde-517	105	8	replace	replace	VERB
ejde-517	105	9	σ̃1	σ̃1	PROPN
ejde-517	105	10	and	and	CCONJ
ejde-517	105	11	σ1	σ1	PROPN
ejde-517	105	12	in	in	ADP
ejde-517	105	13	(	(	PUNCT
ejde-517	105	14	2.6	2.6	NUM
ejde-517	105	15	)	)	PUNCT
ejde-517	105	16	with	with	ADP
ejde-517	105	17	σk1	σk1	NOUN
ejde-517	105	18	and	and	CCONJ
ejde-517	105	19	σk+1	σk+1	NUM
ejde-517	105	20	1	1	NUM
ejde-517	105	21	=	=	SYM
ejde-517	105	22	σ1(χ1	σ1(χ1	NOUN
ejde-517	105	23	)	)	PUNCT
ejde-517	105	24	,	,	PUNCT
ejde-517	105	25	respectively	respectively	ADV
ejde-517	105	26	.	.	PUNCT
ejde-517	106	1	hence,∫	hence,∫	PROPN
ejde-517	106	2	ω	ω	PROPN
ejde-517	106	3	α(χ1	α(χ1	ADJ
ejde-517	106	4	+	+	CCONJ
ejde-517	106	5	ε)∇σ1(χ1	ε)∇σ1(χ1	ADJ
ejde-517	106	6	)	)	PUNCT
ejde-517	106	7	·	·	PUNCT
ejde-517	107	1	∇v	∇v	ADJ
ejde-517	107	2	dv	dv	PROPN
ejde-517	107	3	+	+	CCONJ
ejde-517	107	4	∫	∫	PROPN
ejde-517	107	5	ω	ω	NUM
ejde-517	107	6	λ(σ1(χ1)−	λ(σ1(χ1)−	NOUN
ejde-517	107	7	σk1	σk1	PROPN
ejde-517	107	8	)	)	PUNCT
ejde-517	107	9	v	v	ADP
ejde-517	107	10	dv	dv	PROPN
ejde-517	107	11	=	=	SYM
ejde-517	107	12	∫	∫	PROPN
ejde-517	107	13	ω	ω	PROPN
ejde-517	107	14	χ1∇φ(σk1	χ1∇φ(σk1	PROPN
ejde-517	107	15	,	,	PUNCT
ejde-517	107	16	χ1	χ1	NOUN
ejde-517	107	17	)	)	PUNCT
ejde-517	107	18	·	·	PUNCT
ejde-517	107	19	∇φ∗(σk1	∇φ∗(σk1	NOUN
ejde-517	107	20	,	,	PUNCT
ejde-517	107	21	χ1)v	χ1)v	PROPN
ejde-517	107	22	dv	dv	PROPN
ejde-517	107	23	.	.	PROPN
ejde-517	107	24	(	(	PUNCT
ejde-517	107	25	2.7	2.7	NUM
ejde-517	107	26	)	)	PUNCT
ejde-517	107	27	furthermore	furthermore	ADV
ejde-517	107	28	,	,	PUNCT
ejde-517	107	29	the	the	DET
ejde-517	107	30	following	follow	VERB
ejde-517	107	31	operators	operator	NOUN
ejde-517	107	32	are	be	AUX
ejde-517	107	33	defined	define	VERB
ejde-517	107	34	for	for	ADP
ejde-517	107	35	the	the	DET
ejde-517	107	36	global	global	ADJ
ejde-517	107	37	conductivity	conductivity	NOUN
ejde-517	107	38	,	,	PUNCT
ejde-517	107	39	σk(χ1	σk(χ1	NUM
ejde-517	107	40	)	)	PUNCT
ejde-517	107	41	:	:	PUNCT
ejde-517	108	1	=	=	PUNCT
ejde-517	108	2	σk1χ1	σk1χ1	PROPN
ejde-517	108	3	+	+	NUM
ejde-517	108	4	σ2(1−	σ2(1−	NOUN
ejde-517	108	5	χ1	χ1	NOUN
ejde-517	108	6	)	)	PUNCT
ejde-517	108	7	,	,	PUNCT
ejde-517	108	8	(	(	PUNCT
ejde-517	108	9	2.8	2.8	NUM
ejde-517	108	10	)	)	PUNCT
ejde-517	108	11	σk+1(χ1	σk+1(χ1	NUM
ejde-517	108	12	)	)	PUNCT
ejde-517	108	13	:	:	PUNCT
ejde-517	108	14	=	=	PUNCT
ejde-517	108	15	σ1(χ1)χ1	σ1(χ1)χ1	PROPN
ejde-517	109	1	+	+	CCONJ
ejde-517	109	2	σ2(1−	σ2(1−	PROPN
ejde-517	109	3	χ1	χ1	NOUN
ejde-517	109	4	)	)	PUNCT
ejde-517	109	5	,	,	PUNCT
ejde-517	109	6	(	(	PUNCT
ejde-517	109	7	with	with	ADP
ejde-517	109	8	σ1(χ1	σ1(χ1	NUM
ejde-517	109	9	)	)	PUNCT
ejde-517	109	10	=	=	SYM
ejde-517	109	11	σk+1	σk+1	NOUN
ejde-517	109	12	1	1	NUM
ejde-517	109	13	)	)	PUNCT
ejde-517	109	14	.	.	PUNCT
ejde-517	110	1	(	(	PUNCT
ejde-517	110	2	2.9	2.9	NUM
ejde-517	110	3	)	)	PUNCT
ejde-517	110	4	under	under	ADP
ejde-517	110	5	some	some	DET
ejde-517	110	6	assumptions	assumption	NOUN
ejde-517	110	7	,	,	PUNCT
ejde-517	110	8	we	we	PRON
ejde-517	110	9	will	will	AUX
ejde-517	110	10	show	show	VERB
ejde-517	110	11	that	that	SCONJ
ejde-517	110	12	(	(	PUNCT
ejde-517	110	13	2.7	2.7	NUM
ejde-517	110	14	)	)	PUNCT
ejde-517	110	15	admits	admit	VERB
ejde-517	110	16	a	a	DET
ejde-517	110	17	unique	unique	ADJ
ejde-517	110	18	solution	solution	NOUN
ejde-517	110	19	(	(	PUNCT
ejde-517	110	20	see	see	VERB
ejde-517	110	21	lemma	lemma	PROPN
ejde-517	110	22	3.25	3.25	NUM
ejde-517	110	23	)	)	PUNCT
ejde-517	110	24	.	.	PUNCT
ejde-517	111	1	observe	observe	VERB
ejde-517	111	2	that	that	SCONJ
ejde-517	111	3	the	the	DET
ejde-517	111	4	functional	functional	ADJ
ejde-517	111	5	j̃(σ1	j̃(σ1	NOUN
ejde-517	111	6	,	,	PUNCT
ejde-517	111	7	χ1	χ1	NOUN
ejde-517	111	8	)	)	PUNCT
ejde-517	111	9	in	in	ADP
ejde-517	111	10	(	(	PUNCT
ejde-517	111	11	2.2	2.2	NUM
ejde-517	111	12	)	)	PUNCT
ejde-517	111	13	can	can	AUX
ejde-517	111	14	be	be	AUX
ejde-517	111	15	written	write	VERB
ejde-517	111	16	as	as	ADP
ejde-517	111	17	a	a	DET
ejde-517	111	18	functional	functional	ADJ
ejde-517	111	19	j̃(σ1(χ1	j̃(σ1(χ1	NOUN
ejde-517	111	20	)	)	PUNCT
ejde-517	111	21	,	,	PUNCT
ejde-517	111	22	χ1	χ1	NOUN
ejde-517	111	23	)	)	PUNCT
ejde-517	111	24	depending	depend	VERB
ejde-517	111	25	only	only	ADV
ejde-517	111	26	on	on	ADP
ejde-517	111	27	χ1	χ1	NOUN
ejde-517	111	28	.	.	PUNCT
ejde-517	112	1	to	to	PART
ejde-517	112	2	determine	determine	VERB
ejde-517	112	3	χ1	χ1	NOUN
ejde-517	112	4	,	,	PUNCT
ejde-517	112	5	we	we	PRON
ejde-517	112	6	add	add	VERB
ejde-517	112	7	a	a	DET
ejde-517	112	8	total	total	ADJ
ejde-517	112	9	variation	variation	NOUN
ejde-517	112	10	(	(	PUNCT
ejde-517	112	11	tv	tv	NOUN
ejde-517	112	12	)	)	PUNCT
ejde-517	112	13	regularization	regularization	NOUN
ejde-517	112	14	to	to	ADP
ejde-517	112	15	(	(	PUNCT
ejde-517	112	16	2.2	2.2	NUM
ejde-517	112	17	)	)	PUNCT
ejde-517	112	18	to	to	PART
ejde-517	112	19	penalize	penalize	VERB
ejde-517	112	20	oscillations	oscillation	NOUN
ejde-517	112	21	.	.	PUNCT
ejde-517	113	1	for	for	ADP
ejde-517	113	2	discussions	discussion	NOUN
ejde-517	113	3	of	of	ADP
ejde-517	113	4	tv	tv	NOUN
ejde-517	113	5	-	-	PUNCT
ejde-517	113	6	regularization	regularization	NOUN
ejde-517	113	7	,	,	PUNCT
ejde-517	113	8	one	one	PRON
ejde-517	113	9	can	can	AUX
ejde-517	113	10	refer	refer	VERB
ejde-517	113	11	to	to	ADP
ejde-517	113	12	[	[	X
ejde-517	113	13	31	31	NUM
ejde-517	113	14	,	,	PUNCT
ejde-517	113	15	32	32	NUM
ejde-517	113	16	,	,	PUNCT
ejde-517	113	17	10	10	NUM
ejde-517	113	18	,	,	PUNCT
ejde-517	113	19	21	21	NUM
ejde-517	113	20	]	]	PUNCT
ejde-517	113	21	.	.	PUNCT
ejde-517	114	1	given	give	VERB
ejde-517	114	2	a	a	DET
ejde-517	114	3	(	(	PUNCT
ejde-517	114	4	sufficiently	sufficiently	ADV
ejde-517	114	5	smooth	smooth	ADJ
ejde-517	114	6	)	)	PUNCT
ejde-517	114	7	function	function	NOUN
ejde-517	114	8	f	f	PROPN
ejde-517	114	9	,	,	PUNCT
ejde-517	114	10	its	its	PRON
ejde-517	114	11	total	total	ADJ
ejde-517	114	12	variation	variation	NOUN
ejde-517	114	13	is	be	AUX
ejde-517	114	14	given	give	VERB
ejde-517	114	15	by	by	ADP
ejde-517	114	16	tv	tv	NOUN
ejde-517	114	17	(	(	PUNCT
ejde-517	114	18	f	f	X
ejde-517	114	19	)	)	PUNCT
ejde-517	114	20	:	:	PUNCT
ejde-517	115	1	=	=	SYM
ejde-517	115	2	∫	∫	PROPN
ejde-517	115	3	ω	ω	PROPN
ejde-517	115	4	|∇f	|∇f	PROPN
ejde-517	116	1	|	|	ADV
ejde-517	117	1	dv	dv	PROPN
ejde-517	117	2	≈	≈	PROPN
ejde-517	117	3	∫	∫	PROPN
ejde-517	117	4	ω	ω	PROPN
ejde-517	117	5	√	√	PROPN
ejde-517	117	6	|∇f	|∇f	PROPN
ejde-517	117	7	|2	|2	X
ejde-517	118	1	+	+	NUM
ejde-517	118	2	β2	β2	PROPN
ejde-517	118	3	dv	dv	PROPN
ejde-517	118	4	,	,	PUNCT
ejde-517	118	5	for	for	ADP
ejde-517	118	6	some	some	PRON
ejde-517	118	7	0	0	NUM
ejde-517	118	8	<	<	X
ejde-517	118	9	β	β	X
ejde-517	118	10	�	�	PROPN
ejde-517	118	11	1	1	NUM
ejde-517	118	12	(	(	PUNCT
ejde-517	118	13	compare	compare	NOUN
ejde-517	118	14	,	,	PUNCT
ejde-517	118	15	e.g.	e.g.	ADV
ejde-517	118	16	,	,	PUNCT
ejde-517	118	17	[	[	X
ejde-517	118	18	7	7	NUM
ejde-517	118	19	,	,	PUNCT
ejde-517	118	20	11	11	NUM
ejde-517	118	21	]	]	NUM
ejde-517	118	22	)	)	PUNCT
ejde-517	118	23	.	.	PUNCT
ejde-517	119	1	to	to	PART
ejde-517	119	2	determine	determine	VERB
ejde-517	119	3	the	the	DET
ejde-517	119	4	optimal	optimal	ADJ
ejde-517	119	5	χ1	χ1	NOUN
ejde-517	119	6	,	,	PUNCT
ejde-517	119	7	our	our	PRON
ejde-517	119	8	aim	aim	NOUN
ejde-517	119	9	is	be	AUX
ejde-517	119	10	to	to	PART
ejde-517	119	11	minimize	minimize	VERB
ejde-517	119	12	the	the	DET
ejde-517	119	13	tv	tv	NOUN
ejde-517	119	14	-	-	PUNCT
ejde-517	119	15	regularized	regularize	VERB
ejde-517	119	16	functional	functional	ADJ
ejde-517	119	17	j(χ1	j(χ1	NOUN
ejde-517	119	18	)	)	PUNCT
ejde-517	120	1	=	=	SYM
ejde-517	120	2	∫	∫	PROPN
ejde-517	121	1	∂ω	∂ω	PROPN
ejde-517	121	2	|f	|f	PROPN
ejde-517	121	3	(	(	PUNCT
ejde-517	121	4	σ(χ1))−	σ(χ1))−	PROPN
ejde-517	121	5	ṽ	ṽ	PROPN
ejde-517	121	6	|2	|2	NUM
ejde-517	121	7	ds	ds	NOUN
ejde-517	121	8	+	+	CCONJ
ejde-517	121	9	∫	∫	PROPN
ejde-517	121	10	ω	ω	NUM
ejde-517	121	11	α|∇σ1(χ1)|2(χ1	α|∇σ1(χ1)|2(χ1	PUNCT
ejde-517	121	12	+	+	CCONJ
ejde-517	121	13	ε	ε	PROPN
ejde-517	121	14	)	)	PUNCT
ejde-517	122	1	+	+	NUM
ejde-517	122	2	∫	∫	PROPN
ejde-517	122	3	ω	ω	NUM
ejde-517	122	4	λ(σ1(χ1)−	λ(σ1(χ1)−	NOUN
ejde-517	122	5	σ̃1)2	σ̃1)2	PROPN
ejde-517	122	6	+	+	CCONJ
ejde-517	122	7	γ	γ	X
ejde-517	122	8	√	√	PROPN
ejde-517	122	9	|∇χ1|2	|∇χ1|2	PROPN
ejde-517	122	10	+	+	CCONJ
ejde-517	122	11	β2	β2	PROPN
ejde-517	122	12	dv	dv	PROPN
ejde-517	122	13	,	,	PUNCT
ejde-517	122	14	(	(	PUNCT
ejde-517	122	15	2.10	2.10	NUM
ejde-517	122	16	)	)	PUNCT
ejde-517	122	17	for	for	ADP
ejde-517	122	18	α	α	NOUN
ejde-517	122	19	,	,	PUNCT
ejde-517	122	20	λ	λ	PROPN
ejde-517	122	21	,	,	PUNCT
ejde-517	122	22	γ	γ	X
ejde-517	122	23	>	>	X
ejde-517	122	24	0	0	NUM
ejde-517	122	25	and	and	CCONJ
ejde-517	122	26	ε	ε	PROPN
ejde-517	122	27	,	,	PUNCT
ejde-517	122	28	β	β	X
ejde-517	122	29	∈	∈	PROPN
ejde-517	122	30	(	(	PUNCT
ejde-517	122	31	0	0	NUM
ejde-517	122	32	,	,	PUNCT
ejde-517	122	33	1	1	NUM
ejde-517	122	34	)	)	PUNCT
ejde-517	122	35	.	.	PUNCT
ejde-517	123	1	thus	thus	ADV
ejde-517	123	2	we	we	PRON
ejde-517	123	3	find	find	VERB
ejde-517	123	4	an	an	DET
ejde-517	123	5	update	update	NOUN
ejde-517	123	6	for	for	ADP
ejde-517	123	7	χ1	χ1	NOUN
ejde-517	123	8	that	that	PRON
ejde-517	123	9	reduces	reduce	VERB
ejde-517	123	10	the	the	DET
ejde-517	123	11	cost	cost	NOUN
ejde-517	123	12	j	j	PROPN
ejde-517	123	13	.	.	PUNCT
ejde-517	124	1	this	this	DET
ejde-517	124	2	update	update	NOUN
ejde-517	124	3	can	can	AUX
ejde-517	124	4	be	be	AUX
ejde-517	124	5	obtained	obtain	VERB
ejde-517	124	6	using	use	VERB
ejde-517	124	7	the	the	DET
ejde-517	124	8	method	method	NOUN
ejde-517	124	9	of	of	ADP
ejde-517	124	10	steepest	steep	ADJ
ejde-517	124	11	descent	descent	NOUN
ejde-517	125	1	[	[	X
ejde-517	125	2	33	33	NUM
ejde-517	125	3	]	]	PUNCT
ejde-517	125	4	,	,	PUNCT
ejde-517	125	5	which	which	PRON
ejde-517	125	6	is	be	AUX
ejde-517	125	7	given	give	VERB
ejde-517	125	8	in	in	ADP
ejde-517	125	9	weak	weak	ADJ
ejde-517	125	10	form	form	NOUN
ejde-517	125	11	for	for	ADP
ejde-517	125	12	j	j	PROPN
ejde-517	125	13	as	as	ADP
ejde-517	125	14	follows,∫	follows,∫	NOUN
ejde-517	125	15	ω	ω	X
ejde-517	125	16	χk+1	χk+1	ADP
ejde-517	125	17	1	1	NUM
ejde-517	125	18	v	v	NOUN
ejde-517	125	19	dv	dv	PROPN
ejde-517	125	20	=	=	SYM
ejde-517	125	21	∫	∫	PROPN
ejde-517	125	22	ω	ω	NUM
ejde-517	125	23	χk1v	χk1v	PROPN
ejde-517	125	24	dv	dv	PROPN
ejde-517	125	25	−	−	PROPN
ejde-517	125	26	ω	ω	PROPN
ejde-517	125	27	δj	δj	ADJ
ejde-517	125	28	δχ1	δχ1	PROPN
ejde-517	125	29	(	(	PUNCT
ejde-517	125	30	χk1	χk1	INTJ
ejde-517	125	31	;	;	PUNCT
ejde-517	125	32	v	v	NOUN
ejde-517	125	33	)	)	PUNCT
ejde-517	125	34	,	,	PUNCT
ejde-517	125	35	(	(	PUNCT
ejde-517	125	36	2.11	2.11	NUM
ejde-517	125	37	)	)	PUNCT
ejde-517	125	38	for	for	ADP
ejde-517	125	39	all	all	PRON
ejde-517	125	40	v	v	ADP
ejde-517	125	41	∈	∈	PROPN
ejde-517	125	42	h1(ω	h1(ω	PROPN
ejde-517	125	43	)	)	PUNCT
ejde-517	125	44	,	,	PUNCT
ejde-517	125	45	where	where	SCONJ
ejde-517	125	46	ω	ω	PROPN
ejde-517	125	47	∈	∈	PROPN
ejde-517	125	48	(	(	PUNCT
ejde-517	125	49	0	0	NUM
ejde-517	125	50	,	,	PUNCT
ejde-517	125	51	1	1	NUM
ejde-517	125	52	)	)	PUNCT
ejde-517	125	53	is	be	AUX
ejde-517	125	54	the	the	DET
ejde-517	125	55	step	step	NOUN
ejde-517	125	56	size	size	NOUN
ejde-517	125	57	and	and	CCONJ
ejde-517	125	58	k	k	PROPN
ejde-517	125	59	∈	∈	PROPN
ejde-517	125	60	n.	n.	PROPN
ejde-517	125	61	let	let	VERB
ejde-517	125	62	χk1	χk1	PROPN
ejde-517	125	63	,	,	PUNCT
ejde-517	125	64	δχ	δχ	ADP
ejde-517	125	65	k	k	PROPN
ejde-517	125	66	1	1	NUM
ejde-517	125	67	∈	∈	PROPN
ejde-517	125	68	l2(ω	l2(ω	NOUN
ejde-517	125	69	)	)	PUNCT
ejde-517	125	70	and	and	CCONJ
ejde-517	125	71	suppose	suppose	VERB
ejde-517	125	72	δς1	δς1	ADJ
ejde-517	125	73	δχk1	δχk1	PROPN
ejde-517	125	74	(	(	PUNCT
ejde-517	125	75	χk1	χk1	PROPN
ejde-517	125	76	;	;	PUNCT
ejde-517	125	77	δχk1	δχk1	PROPN
ejde-517	125	78	)	)	PUNCT
ejde-517	125	79	∈	∈	PROPN
ejde-517	125	80	h1(ω	h1(ω	PROPN
ejde-517	125	81	)	)	PUNCT
ejde-517	125	82	,	,	PUNCT
ejde-517	125	83	then	then	ADV
ejde-517	125	84	the	the	DET
ejde-517	125	85	variational	variational	ADJ
ejde-517	125	86	derivative	derivative	NOUN
ejde-517	125	87	of	of	ADP
ejde-517	125	88	j	j	PROPN
ejde-517	125	89	in	in	ADP
ejde-517	125	90	(	(	PUNCT
ejde-517	125	91	2.10	2.10	NUM
ejde-517	125	92	)	)	PUNCT
ejde-517	125	93	is	be	AUX
ejde-517	125	94	δj	δj	ADJ
ejde-517	125	95	δχk1	δχk1	NOUN
ejde-517	125	96	(	(	PUNCT
ejde-517	125	97	χk1	χk1	PROPN
ejde-517	125	98	;	;	PUNCT
ejde-517	125	99	δχ1	δχ1	X
ejde-517	125	100	)	)	PUNCT
ejde-517	126	1	=	=	SYM
ejde-517	126	2	∫	∫	PROPN
ejde-517	126	3	ω	ω	PROPN
ejde-517	126	4	−2(σ1(χk1)−	−2(σ1(χk1)−	PROPN
ejde-517	126	5	σ2)δχk1∇φ(σk1	σ2)δχk1∇φ(σk1	NOUN
ejde-517	126	6	,	,	PUNCT
ejde-517	126	7	χ	χ	PROPN
ejde-517	126	8	k	k	PROPN
ejde-517	126	9	1	1	X
ejde-517	126	10	)	)	PUNCT
ejde-517	126	11	·	·	PUNCT
ejde-517	126	12	∇φ∗(σk1	∇φ∗(σk1	NOUN
ejde-517	126	13	,	,	PUNCT
ejde-517	126	14	χ	χ	PROPN
ejde-517	126	15	k	k	PROPN
ejde-517	126	16	1	1	X
ejde-517	126	17	)	)	PUNCT
ejde-517	126	18	dv	dv	PROPN
ejde-517	126	19	+	+	CCONJ
ejde-517	126	20	∫	∫	PROPN
ejde-517	126	21	ω	ω	NUM
ejde-517	126	22	α|∇σ1(χk1)|2δχk1	α|∇σ1(χk1)|2δχk1	PROPN
ejde-517	126	23	dv	dv	PROPN
ejde-517	126	24	+	+	PROPN
ejde-517	126	25	γ	γ	PROPN
ejde-517	126	26	∫	∫	PROPN
ejde-517	126	27	ω	ω	PROPN
ejde-517	126	28	∇(δχk1	∇(δχk1	PROPN
ejde-517	126	29	)	)	PUNCT
ejde-517	126	30	·	·	PUNCT
ejde-517	127	1	∇χk1√	∇χk1√	VERB
ejde-517	127	2	|∇χk1	|∇χk1	PROPN
ejde-517	127	3	|2	|2	NUM
ejde-517	127	4	+	+	NUM
ejde-517	127	5	β2	β2	PROPN
ejde-517	127	6	dv	dv	PROPN
ejde-517	127	7	.	.	PROPN
ejde-517	128	1	(	(	PUNCT
ejde-517	128	2	2.12	2.12	NUM
ejde-517	128	3	)	)	PUNCT
ejde-517	128	4	ejde-2020/93	ejde-2020/93	NOUN
ejde-517	128	5	impedance	impedance	NOUN
ejde-517	128	6	tomography	tomography	NOUN
ejde-517	128	7	problem	problem	NOUN
ejde-517	128	8	5	5	NUM
ejde-517	128	9	remark	remark	NOUN
ejde-517	128	10	2.4	2.4	NUM
ejde-517	128	11	.	.	PUNCT
ejde-517	129	1	observe	observe	VERB
ejde-517	129	2	that	that	SCONJ
ejde-517	129	3	(	(	PUNCT
ejde-517	129	4	2.12	2.12	NUM
ejde-517	129	5	)	)	PUNCT
ejde-517	129	6	requires	require	VERB
ejde-517	129	7	the	the	DET
ejde-517	129	8	calculation	calculation	NOUN
ejde-517	129	9	of	of	ADP
ejde-517	129	10	∇χk1	∇χk1	NOUN
ejde-517	129	11	but	but	CCONJ
ejde-517	129	12	since	since	SCONJ
ejde-517	129	13	χk1	χk1	PROPN
ejde-517	129	14	is	be	AUX
ejde-517	129	15	binary	binary	ADJ
ejde-517	129	16	,	,	PUNCT
ejde-517	129	17	a	a	DET
ejde-517	129	18	smooth	smooth	ADJ
ejde-517	129	19	approximation	approximation	NOUN
ejde-517	129	20	of	of	ADP
ejde-517	129	21	χk1	χk1	PROPN
ejde-517	129	22	is	be	AUX
ejde-517	129	23	necessary	necessary	ADJ
ejde-517	129	24	.	.	PUNCT
ejde-517	130	1	this	this	PRON
ejde-517	130	2	will	will	AUX
ejde-517	130	3	be	be	AUX
ejde-517	130	4	discussed	discuss	VERB
ejde-517	130	5	later	later	ADV
ejde-517	130	6	.	.	PUNCT
ejde-517	131	1	the	the	DET
ejde-517	131	2	assumption	assumption	NOUN
ejde-517	131	3	that	that	SCONJ
ejde-517	131	4	δς1	δς1	ADJ
ejde-517	131	5	δχk1	δχk1	PROPN
ejde-517	131	6	(	(	PUNCT
ejde-517	131	7	χk1	χk1	PROPN
ejde-517	131	8	;	;	PUNCT
ejde-517	131	9	δχk1	δχk1	PROPN
ejde-517	131	10	)	)	PUNCT
ejde-517	131	11	∈	∈	PROPN
ejde-517	131	12	h1(ω	h1(ω	PROPN
ejde-517	131	13	)	)	PUNCT
ejde-517	131	14	can	can	AUX
ejde-517	131	15	be	be	AUX
ejde-517	131	16	shown	show	VERB
ejde-517	131	17	if	if	SCONJ
ejde-517	131	18	χk1	χk1	PRON
ejde-517	131	19	is	be	AUX
ejde-517	131	20	sufficiently	sufficiently	ADV
ejde-517	131	21	smooth	smooth	ADJ
ejde-517	131	22	(	(	PUNCT
ejde-517	131	23	see	see	INTJ
ejde-517	131	24	theorem	theorem	VERB
ejde-517	131	25	3.28	3.28	NUM
ejde-517	131	26	)	)	PUNCT
ejde-517	131	27	.	.	PUNCT
ejde-517	132	1	instead	instead	ADV
ejde-517	132	2	of	of	ADP
ejde-517	132	3	performing	perform	VERB
ejde-517	132	4	the	the	DET
ejde-517	132	5	iteration	iteration	NOUN
ejde-517	132	6	(	(	PUNCT
ejde-517	132	7	2.11	2.11	NUM
ejde-517	132	8	)	)	PUNCT
ejde-517	132	9	by	by	ADP
ejde-517	132	10	evaluating	evaluate	VERB
ejde-517	132	11	δj	δj	ADJ
ejde-517	132	12	/	/	SYM
ejde-517	132	13	δχ1(χk1	δχ1(χk1	NOUN
ejde-517	132	14	;	;	PUNCT
ejde-517	132	15	v	v	X
ejde-517	132	16	)	)	PUNCT
ejde-517	132	17	explicitly	explicitly	ADV
ejde-517	132	18	in	in	ADP
ejde-517	132	19	terms	term	NOUN
ejde-517	132	20	of	of	ADP
ejde-517	132	21	χk1	χk1	PROPN
ejde-517	132	22	,	,	PUNCT
ejde-517	132	23	the	the	DET
ejde-517	132	24	iteration	iteration	NOUN
ejde-517	132	25	may	may	AUX
ejde-517	132	26	be	be	AUX
ejde-517	132	27	performed	perform	VERB
ejde-517	132	28	semi	semi	ADV
ejde-517	132	29	-	-	ADJ
ejde-517	132	30	implicitly	implicitly	ADV
ejde-517	132	31	by	by	ADP
ejde-517	132	32	evaluating	evaluate	VERB
ejde-517	132	33	part	part	NOUN
ejde-517	132	34	of	of	ADP
ejde-517	132	35	the	the	DET
ejde-517	132	36	variational	variational	ADJ
ejde-517	132	37	derivative	derivative	NOUN
ejde-517	132	38	of	of	ADP
ejde-517	132	39	j	j	PROPN
ejde-517	132	40	in	in	ADP
ejde-517	132	41	(	(	PUNCT
ejde-517	132	42	2.12	2.12	NUM
ejde-517	132	43	)	)	PUNCT
ejde-517	132	44	at	at	ADP
ejde-517	132	45	χk+1	χk+1	SYM
ejde-517	132	46	1	1	NUM
ejde-517	132	47	as	as	ADP
ejde-517	132	48	follows:∫	follows:∫	PROPN
ejde-517	132	49	ω	ω	NOUN
ejde-517	132	50	[	[	PUNCT
ejde-517	132	51	vχk+1	vχk+1	X
ejde-517	132	52	1	1	NUM
ejde-517	132	53	+	+	CCONJ
ejde-517	132	54	ωγ	ωγ	ADP
ejde-517	132	55	∇v	∇v	ADJ
ejde-517	132	56	·	·	PUNCT
ejde-517	132	57	∇χk+1	∇χk+1	NOUN
ejde-517	132	58	1√	1√	PROPN
ejde-517	132	59	|∇χk1	|∇χk1	PROPN
ejde-517	132	60	|2	|2	NUM
ejde-517	133	1	+	+	CCONJ
ejde-517	133	2	β2	β2	NOUN
ejde-517	133	3	]	]	PUNCT
ejde-517	133	4	dv	dv	PROPN
ejde-517	133	5	=	=	SYM
ejde-517	133	6	∫	∫	PROPN
ejde-517	133	7	ω	ω	PROPN
ejde-517	133	8	vg(χk1	vg(χk1	NOUN
ejde-517	133	9	)	)	PUNCT
ejde-517	133	10	dv	dv	PROPN
ejde-517	133	11	,	,	PUNCT
ejde-517	133	12	(	(	PUNCT
ejde-517	133	13	2.13	2.13	NUM
ejde-517	133	14	)	)	PUNCT
ejde-517	133	15	for	for	ADP
ejde-517	133	16	all	all	PRON
ejde-517	133	17	v	v	ADP
ejde-517	133	18	∈	∈	PROPN
ejde-517	133	19	h1(ω	h1(ω	PROPN
ejde-517	133	20	)	)	PUNCT
ejde-517	133	21	,	,	PUNCT
ejde-517	133	22	where	where	SCONJ
ejde-517	133	23	g(χ1	g(χ1	NOUN
ejde-517	133	24	)	)	PUNCT
ejde-517	133	25	=	=	SYM
ejde-517	133	26	χ1−ωα|∇σ1(χ1)|2	χ1−ωα|∇σ1(χ1)|2	PROPN
ejde-517	133	27	+	+	CCONJ
ejde-517	133	28	2ω	2ω	NUM
ejde-517	133	29	[	[	PUNCT
ejde-517	133	30	(	(	PUNCT
ejde-517	133	31	σ1(χ1)−σ2)∇φ(σ̃1	σ1(χ1)−σ2)∇φ(σ̃1	PROPN
ejde-517	133	32	,	,	PUNCT
ejde-517	133	33	χ1	χ1	NOUN
ejde-517	133	34	)	)	PUNCT
ejde-517	133	35	·	·	SYM
ejde-517	133	36	∇φ∗(σ̃1	∇φ∗(σ̃1	PROPN
ejde-517	133	37	,	,	PUNCT
ejde-517	133	38	χ1	χ1	NOUN
ejde-517	133	39	)	)	PUNCT
ejde-517	133	40	]	]	PUNCT
ejde-517	133	41	.	.	PUNCT
ejde-517	134	1	(	(	PUNCT
ejde-517	134	2	2.14	2.14	NUM
ejde-517	134	3	)	)	PUNCT
ejde-517	134	4	we	we	PRON
ejde-517	134	5	show	show	VERB
ejde-517	134	6	later	later	ADV
ejde-517	134	7	that	that	SCONJ
ejde-517	134	8	(	(	PUNCT
ejde-517	134	9	2.13	2.13	NUM
ejde-517	134	10	)	)	PUNCT
ejde-517	134	11	admits	admit	VERB
ejde-517	134	12	a	a	DET
ejde-517	134	13	unique	unique	ADJ
ejde-517	134	14	solution	solution	NOUN
ejde-517	134	15	(	(	PUNCT
ejde-517	134	16	see	see	VERB
ejde-517	134	17	lemma	lemma	PROPN
ejde-517	134	18	4.3	4.3	NUM
ejde-517	134	19	)	)	PUNCT
ejde-517	134	20	.	.	PUNCT
ejde-517	135	1	as	as	SCONJ
ejde-517	135	2	mentioned	mention	VERB
ejde-517	135	3	in	in	ADP
ejde-517	135	4	remark	remark	NOUN
ejde-517	135	5	2.4	2.4	NUM
ejde-517	135	6	,	,	PUNCT
ejde-517	135	7	a	a	DET
ejde-517	135	8	smooth	smooth	ADJ
ejde-517	135	9	approximation	approximation	NOUN
ejde-517	135	10	of	of	ADP
ejde-517	135	11	χ1	χ1	NOUN
ejde-517	135	12	is	be	AUX
ejde-517	135	13	necessary	necessary	ADJ
ejde-517	135	14	.	.	PUNCT
ejde-517	136	1	to	to	PART
ejde-517	136	2	do	do	VERB
ejde-517	136	3	this	this	PRON
ejde-517	136	4	,	,	PUNCT
ejde-517	136	5	we	we	PRON
ejde-517	136	6	introduce	introduce	VERB
ejde-517	136	7	the	the	DET
ejde-517	136	8	kernel	kernel	NOUN
ejde-517	136	9	function	function	NOUN
ejde-517	136	10	ξδ(x	ξδ(x	PUNCT
ejde-517	136	11	)	)	PUNCT
ejde-517	136	12	=	=	SYM
ejde-517	137	1	1	1	NUM
ejde-517	137	2	4πδ	4πδ	NOUN
ejde-517	137	3	e	e	NOUN
ejde-517	137	4	−	−	NOUN
ejde-517	137	5	x2	x2	PROPN
ejde-517	137	6	4δ	4δ	NOUN
ejde-517	137	7	,	,	PUNCT
ejde-517	137	8	for	for	ADP
ejde-517	137	9	some	some	DET
ejde-517	137	10	δ	δ	PROPN
ejde-517	137	11	>	>	X
ejde-517	137	12	0	0	X
ejde-517	137	13	.	.	PUNCT
ejde-517	138	1	we	we	PRON
ejde-517	138	2	approximate	approximate	VERB
ejde-517	138	3	χk1	χk1	PROPN
ejde-517	138	4	using	use	VERB
ejde-517	138	5	the	the	DET
ejde-517	138	6	convolution	convolution	NOUN
ejde-517	138	7	of	of	ADP
ejde-517	138	8	χk1	χk1	PROPN
ejde-517	138	9	and	and	CCONJ
ejde-517	138	10	ξδ	ξδ	ADP
ejde-517	138	11	,	,	PUNCT
ejde-517	138	12	i.e.	i.e.	X
ejde-517	138	13	,	,	PUNCT
ejde-517	138	14	we	we	PRON
ejde-517	138	15	let	let	VERB
ejde-517	138	16	χ̃k1	χ̃k1	NOUN
ejde-517	138	17	:	:	PUNCT
ejde-517	138	18	=	=	PUNCT
ejde-517	138	19	χk1	χk1	NOUN
ejde-517	138	20	∗	∗	NOUN
ejde-517	138	21	ξδ	ξδ	ADP
ejde-517	138	22	=	=	ADJ
ejde-517	138	23	∫	∫	PROPN
ejde-517	138	24	r2	r2	PROPN
ejde-517	138	25	ξδ(x−	ξδ(x−	PROPN
ejde-517	138	26	y)χk1(y)dy	y)χk1(y)dy	NOUN
ejde-517	138	27	.	.	PUNCT
ejde-517	139	1	(	(	PUNCT
ejde-517	139	2	2.15	2.15	NUM
ejde-517	139	3	)	)	PUNCT
ejde-517	139	4	the	the	DET
ejde-517	139	5	following	following	ADJ
ejde-517	139	6	result	result	NOUN
ejde-517	139	7	gives	give	VERB
ejde-517	139	8	the	the	DET
ejde-517	139	9	regularity	regularity	NOUN
ejde-517	139	10	and	and	CCONJ
ejde-517	139	11	continuity	continuity	NOUN
ejde-517	139	12	of	of	ADP
ejde-517	139	13	the	the	DET
ejde-517	139	14	above	above	ADJ
ejde-517	139	15	mollification	mollification	NOUN
ejde-517	139	16	.	.	PUNCT
ejde-517	140	1	theorem	theorem	VERB
ejde-517	140	2	2.5	2.5	NUM
ejde-517	140	3	.	.	PUNCT
ejde-517	141	1	let	let	VERB
ejde-517	141	2	k	k	PROPN
ejde-517	141	3	∈	∈	PROPN
ejde-517	141	4	n	n	CCONJ
ejde-517	141	5	,	,	PUNCT
ejde-517	141	6	then	then	ADV
ejde-517	141	7	χ̃k1	χ̃k1	PROPN
ejde-517	141	8	is	be	AUX
ejde-517	141	9	a	a	DET
ejde-517	141	10	real	real	ADJ
ejde-517	141	11	analytic	analytic	ADJ
ejde-517	141	12	function	function	NOUN
ejde-517	141	13	on	on	ADP
ejde-517	141	14	ω	ω	NUM
ejde-517	141	15	and	and	CCONJ
ejde-517	141	16	χ̃k1	χ̃k1	NOUN
ejde-517	141	17	→	→	SYM
ejde-517	141	18	χk1	χk1	PROPN
ejde-517	141	19	almost	almost	ADV
ejde-517	141	20	everywhere	everywhere	ADV
ejde-517	141	21	as	as	ADP
ejde-517	141	22	δ	δ	PROPN
ejde-517	141	23	→	→	X
ejde-517	141	24	0	0	X
ejde-517	141	25	.	.	PUNCT
ejde-517	142	1	furthermore	furthermore	ADV
ejde-517	142	2	,	,	PUNCT
ejde-517	142	3	suppose	suppose	VERB
ejde-517	142	4	0	0	NUM
ejde-517	142	5	≤	≤	NUM
ejde-517	142	6	χk1	χk1	PROPN
ejde-517	142	7	≤	≤	ADV
ejde-517	142	8	1	1	NUM
ejde-517	142	9	,	,	PUNCT
ejde-517	142	10	for	for	ADP
ejde-517	142	11	all	all	DET
ejde-517	142	12	x	x	SYM
ejde-517	142	13	∈	∈	PROPN
ejde-517	142	14	ω	ω	X
ejde-517	142	15	.	.	PUNCT
ejde-517	143	1	then	then	ADV
ejde-517	143	2	0	0	NUM
ejde-517	143	3	≤	≤	NUM
ejde-517	143	4	χ̃k1	χ̃k1	NOUN
ejde-517	143	5	≤	≤	NUM
ejde-517	143	6	1	1	NUM
ejde-517	144	1	[	[	X
ejde-517	144	2	15	15	NUM
ejde-517	144	3	]	]	PUNCT
ejde-517	144	4	.	.	PUNCT
ejde-517	145	1	using	use	VERB
ejde-517	145	2	(	(	PUNCT
ejde-517	145	3	2.15	2.15	NUM
ejde-517	145	4	)	)	PUNCT
ejde-517	145	5	,	,	PUNCT
ejde-517	145	6	we	we	PRON
ejde-517	145	7	approximate	approximate	VERB
ejde-517	145	8	(	(	PUNCT
ejde-517	145	9	2.13	2.13	NUM
ejde-517	145	10	)	)	PUNCT
ejde-517	145	11	by∫	by∫	PROPN
ejde-517	145	12	ω	ω	NUM
ejde-517	145	13	ωγ	ωγ	ADP
ejde-517	145	14	∇χ̃k+1	∇χ̃k+1	ADJ
ejde-517	145	15	1	1	NUM
ejde-517	145	16	·	·	PUNCT
ejde-517	145	17	∇v√	∇v√	PROPN
ejde-517	145	18	|∇χ̃k1	|∇χ̃k1	NOUN
ejde-517	145	19	|2	|2	NUM
ejde-517	146	1	+	+	CCONJ
ejde-517	146	2	β2	β2	ADJ
ejde-517	146	3	+	+	CCONJ
ejde-517	146	4	χ̃k+1	χ̃k+1	ADJ
ejde-517	146	5	1	1	NUM
ejde-517	146	6	v	v	NOUN
ejde-517	146	7	dv	dv	PROPN
ejde-517	146	8	=	=	SYM
ejde-517	146	9	∫	∫	PROPN
ejde-517	146	10	ω	ω	PROPN
ejde-517	146	11	g(χ̃k1)v	g(χ̃k1)v	PROPN
ejde-517	146	12	dv	dv	PROPN
ejde-517	146	13	,	,	PUNCT
ejde-517	146	14	∀v	∀v	PROPN
ejde-517	146	15	∈	∈	PROPN
ejde-517	146	16	h1(ω	h1(ω	PROPN
ejde-517	146	17	)	)	PUNCT
ejde-517	146	18	.	.	PUNCT
ejde-517	147	1	(	(	PUNCT
ejde-517	147	2	2.16	2.16	NUM
ejde-517	147	3	)	)	PUNCT
ejde-517	147	4	definition	definition	NOUN
ejde-517	147	5	2.6	2.6	NUM
ejde-517	147	6	.	.	PUNCT
ejde-517	148	1	we	we	PRON
ejde-517	148	2	define	define	VERB
ejde-517	148	3	the	the	DET
ejde-517	148	4	operator	operator	NOUN
ejde-517	148	5	θ	θ	NOUN
ejde-517	148	6	:	:	PUNCT
ejde-517	148	7	l2(ω	l2(ω	NUM
ejde-517	148	8	)	)	PUNCT
ejde-517	148	9	→	→	SYM
ejde-517	148	10	l2(ω	l2(ω	NOUN
ejde-517	148	11	)	)	PUNCT
ejde-517	148	12	to	to	PART
ejde-517	148	13	be	be	AUX
ejde-517	148	14	the	the	DET
ejde-517	148	15	solution	solution	NOUN
ejde-517	148	16	χ̃k+1	χ̃k+1	VERB
ejde-517	148	17	1	1	NUM
ejde-517	148	18	∈	∈	NOUN
ejde-517	148	19	l2(ω	l2(ω	NOUN
ejde-517	148	20	)	)	PUNCT
ejde-517	148	21	of	of	ADP
ejde-517	148	22	(	(	PUNCT
ejde-517	148	23	2.16	2.16	NUM
ejde-517	148	24	)	)	PUNCT
ejde-517	148	25	for	for	ADP
ejde-517	148	26	a	a	DET
ejde-517	148	27	given	give	VERB
ejde-517	148	28	χ̃k1	χ̃k1	NOUN
ejde-517	148	29	∈	∈	PROPN
ejde-517	148	30	l2(ω	l2(ω	NOUN
ejde-517	148	31	)	)	PUNCT
ejde-517	148	32	.	.	PUNCT
ejde-517	149	1	because	because	SCONJ
ejde-517	149	2	the	the	DET
ejde-517	149	3	solution	solution	NOUN
ejde-517	149	4	of	of	ADP
ejde-517	149	5	(	(	PUNCT
ejde-517	149	6	2.16	2.16	NUM
ejde-517	149	7	)	)	PUNCT
ejde-517	149	8	is	be	AUX
ejde-517	149	9	not	not	PART
ejde-517	149	10	binary	binary	ADJ
ejde-517	149	11	,	,	PUNCT
ejde-517	149	12	the	the	DET
ejde-517	149	13	update	update	NOUN
ejde-517	149	14	for	for	ADP
ejde-517	149	15	χ	χ	NOUN
ejde-517	149	16	is	be	AUX
ejde-517	149	17	obtained	obtain	VERB
ejde-517	149	18	by	by	ADP
ejde-517	149	19	performing	perform	VERB
ejde-517	149	20	a	a	DET
ejde-517	149	21	thresholding	thresholde	VERB
ejde-517	149	22	step	step	NOUN
ejde-517	149	23	.	.	PUNCT
ejde-517	150	1	we	we	PRON
ejde-517	150	2	summarize	summarize	VERB
ejde-517	150	3	the	the	DET
ejde-517	150	4	two	two	NUM
ejde-517	150	5	-	-	PUNCT
ejde-517	150	6	phase	phase	NOUN
ejde-517	150	7	segmentation	segmentation	NOUN
ejde-517	150	8	method	method	NOUN
ejde-517	150	9	in	in	ADP
ejde-517	150	10	the	the	DET
ejde-517	150	11	algorithm	algorithm	NOUN
ejde-517	150	12	below	below	ADV
ejde-517	150	13	.	.	PUNCT
ejde-517	151	1	the	the	DET
ejde-517	151	2	analysis	analysis	NOUN
ejde-517	151	3	of	of	ADP
ejde-517	151	4	the	the	DET
ejde-517	151	5	numerical	numerical	ADJ
ejde-517	151	6	solution	solution	NOUN
ejde-517	151	7	of	of	ADP
ejde-517	151	8	the	the	DET
ejde-517	151	9	pdes	pde	NOUN
ejde-517	151	10	arising	arise	VERB
ejde-517	151	11	from	from	ADP
ejde-517	151	12	this	this	DET
ejde-517	151	13	algorithm	algorithm	NOUN
ejde-517	151	14	can	can	AUX
ejde-517	151	15	be	be	AUX
ejde-517	151	16	found	find	VERB
ejde-517	151	17	in	in	ADP
ejde-517	151	18	[	[	X
ejde-517	151	19	26	26	NUM
ejde-517	151	20	]	]	PUNCT
ejde-517	151	21	.	.	PUNCT
ejde-517	152	1	two	two	NUM
ejde-517	152	2	-	-	PUNCT
ejde-517	152	3	phase	phase	NOUN
ejde-517	152	4	segmentation	segmentation	NOUN
ejde-517	152	5	algorithm	algorithm	NOUN
ejde-517	152	6	.	.	PUNCT
ejde-517	153	1	(	(	PUNCT
ejde-517	153	2	1	1	X
ejde-517	153	3	)	)	PUNCT
ejde-517	153	4	given	give	VERB
ejde-517	153	5	f	f	PROPN
ejde-517	153	6	and	and	CCONJ
ejde-517	153	7	ṽ	ṽ	PROPN
ejde-517	153	8	.	.	PUNCT
ejde-517	154	1	choose	choose	VERB
ejde-517	154	2	parameters	parameter	NOUN
ejde-517	154	3	ε	ε	PROPN
ejde-517	154	4	,	,	PUNCT
ejde-517	154	5	δ	δ	PROPN
ejde-517	154	6	,	,	PUNCT
ejde-517	154	7	λ	λ	PROPN
ejde-517	154	8	,	,	PUNCT
ejde-517	154	9	γ	γ	PROPN
ejde-517	154	10	,	,	PUNCT
ejde-517	154	11	β	β	X
ejde-517	154	12	�	�	PROPN
ejde-517	154	13	1	1	NUM
ejde-517	154	14	,	,	PUNCT
ejde-517	154	15	α	α	PRON
ejde-517	154	16	�	�	PROPN
ejde-517	154	17	1	1	NUM
ejde-517	154	18	,	,	PUNCT
ejde-517	154	19	and	and	CCONJ
ejde-517	154	20	ζ	ζ	NOUN
ejde-517	154	21	,	,	PUNCT
ejde-517	154	22	ω	ω	PROPN
ejde-517	154	23	∈	∈	PROPN
ejde-517	154	24	(	(	PUNCT
ejde-517	154	25	0	0	NUM
ejde-517	154	26	,	,	PUNCT
ejde-517	154	27	1	1	NUM
ejde-517	154	28	)	)	PUNCT
ejde-517	154	29	.	.	PUNCT
ejde-517	155	1	select	select	VERB
ejde-517	155	2	the	the	DET
ejde-517	155	3	maximum	maximum	ADJ
ejde-517	155	4	number	number	NOUN
ejde-517	155	5	of	of	ADP
ejde-517	155	6	iterations	iteration	NOUN
ejde-517	155	7	k	k	PROPN
ejde-517	155	8	and	and	CCONJ
ejde-517	155	9	the	the	DET
ejde-517	155	10	tolerance	tolerance	NOUN
ejde-517	155	11	ρ	ρ	NOUN
ejde-517	155	12	.	.	PUNCT
ejde-517	156	1	set	set	VERB
ejde-517	156	2	k	k	PROPN
ejde-517	156	3	=	=	PUNCT
ejde-517	156	4	1	1	NUM
ejde-517	156	5	and	and	CCONJ
ejde-517	156	6	choose	choose	VERB
ejde-517	156	7	the	the	DET
ejde-517	156	8	initial	initial	ADJ
ejde-517	156	9	σk1	σk1	NOUN
ejde-517	156	10	.	.	PUNCT
ejde-517	157	1	select	select	VERB
ejde-517	157	2	an	an	DET
ejde-517	157	3	initial	initial	ADJ
ejde-517	157	4	guess	guess	NOUN
ejde-517	157	5	χk1	χk1	NOUN
ejde-517	157	6	.	.	PUNCT
ejde-517	158	1	the	the	DET
ejde-517	158	2	value	value	NOUN
ejde-517	158	3	of	of	ADP
ejde-517	158	4	σ2	σ2	PROPN
ejde-517	158	5	is	be	AUX
ejde-517	158	6	given	give	VERB
ejde-517	158	7	and	and	CCONJ
ejde-517	158	8	χk2	χk2	PROPN
ejde-517	158	9	=	=	SYM
ejde-517	158	10	1−	1−	NUM
ejde-517	158	11	χk1	χk1	NOUN
ejde-517	158	12	.	.	PUNCT
ejde-517	159	1	(	(	PUNCT
ejde-517	159	2	2	2	X
ejde-517	159	3	)	)	PUNCT
ejde-517	159	4	take	take	VERB
ejde-517	159	5	χ̃k1	χ̃k1	NOUN
ejde-517	159	6	=	=	NOUN
ejde-517	159	7	χk1	χk1	PROPN
ejde-517	159	8	∗	∗	NOUN
ejde-517	159	9	ξδ	ξδ	ADV
ejde-517	159	10	and	and	CCONJ
ejde-517	159	11	χ̃k+1	χ̃k+1	VERB
ejde-517	159	12	1	1	NUM
ejde-517	159	13	=	=	SYM
ejde-517	159	14	θ(χ̃k1	θ(χ̃k1	PROPN
ejde-517	159	15	)	)	PUNCT
ejde-517	159	16	.	.	PUNCT
ejde-517	160	1	then	then	ADV
ejde-517	160	2	,	,	PUNCT
ejde-517	160	3	χ1	χ1	NOUN
ejde-517	160	4	is	be	AUX
ejde-517	160	5	updated	update	VERB
ejde-517	160	6	by	by	ADP
ejde-517	160	7	χk+1	χk+1	X
ejde-517	160	8	1	1	NUM
ejde-517	160	9	(	(	PUNCT
ejde-517	160	10	x	x	NOUN
ejde-517	160	11	)	)	PUNCT
ejde-517	160	12	=	=	SYM
ejde-517	160	13	{	{	PUNCT
ejde-517	160	14	1	1	NUM
ejde-517	160	15	,	,	PUNCT
ejde-517	160	16	if	if	SCONJ
ejde-517	160	17	χ̃k+1	χ̃k+1	NOUN
ejde-517	160	18	1	1	NUM
ejde-517	160	19	(	(	PUNCT
ejde-517	160	20	x	x	NOUN
ejde-517	160	21	)	)	PUNCT
ejde-517	160	22	≥	≥	PROPN
ejde-517	160	23	ζ	ζ	NOUN
ejde-517	160	24	,	,	PUNCT
ejde-517	160	25	0	0	NUM
ejde-517	160	26	,	,	PUNCT
ejde-517	160	27	otherwise	otherwise	ADV
ejde-517	160	28	.	.	PUNCT
ejde-517	161	1	set	set	VERB
ejde-517	161	2	χk+1	χk+1	VERB
ejde-517	161	3	2	2	NUM
ejde-517	161	4	=	=	SYM
ejde-517	161	5	1−	1−	NUM
ejde-517	161	6	χk+1	χk+1	ADP
ejde-517	161	7	1	1	NUM
ejde-517	161	8	.	.	PUNCT
ejde-517	161	9	6	6	NUM
ejde-517	161	10	r.	r.	PROPN
ejde-517	161	11	mendoza	mendoza	PROPN
ejde-517	161	12	,	,	PUNCT
ejde-517	161	13	s.	s.	PROPN
ejde-517	161	14	keeling	keeling	PROPN
ejde-517	161	15	ejde-2020/93	ejde-2020/93	PROPN
ejde-517	161	16	(	(	PUNCT
ejde-517	161	17	3	3	X
ejde-517	161	18	)	)	PUNCT
ejde-517	161	19	if	if	SCONJ
ejde-517	161	20	k	k	PROPN
ejde-517	161	21	=	=	SYM
ejde-517	161	22	k	k	PROPN
ejde-517	161	23	or	or	CCONJ
ejde-517	161	24	‖χk+1	‖χk+1	X
ejde-517	161	25	1	1	NUM
ejde-517	161	26	−	−	PROPN
ejde-517	161	27	χk1‖l2(ω	χk1‖l2(ω	PROPN
ejde-517	161	28	)	)	PUNCT
ejde-517	162	1	<	<	X
ejde-517	162	2	ρ	ρ	PROPN
ejde-517	162	3	,	,	PUNCT
ejde-517	162	4	the	the	DET
ejde-517	162	5	algorithm	algorithm	NOUN
ejde-517	162	6	terminates	terminate	VERB
ejde-517	162	7	.	.	PUNCT
ejde-517	163	1	otherwise	otherwise	ADV
ejde-517	163	2	,	,	PUNCT
ejde-517	164	1	k	k	PROPN
ejde-517	164	2	←	←	PROPN
ejde-517	164	3	k	k	PROPN
ejde-517	164	4	+	+	CCONJ
ejde-517	164	5	1	1	NUM
ejde-517	164	6	and	and	CCONJ
ejde-517	164	7	go	go	VERB
ejde-517	164	8	back	back	ADV
ejde-517	164	9	to	to	PART
ejde-517	164	10	step	step	NOUN
ejde-517	164	11	2	2	NUM
ejde-517	164	12	.	.	NOUN
ejde-517	165	1	3	3	X
ejde-517	165	2	.	.	X
ejde-517	166	1	analysis	analysis	NOUN
ejde-517	166	2	of	of	ADP
ejde-517	166	3	the	the	DET
ejde-517	166	4	algorithm	algorithm	NOUN
ejde-517	166	5	in	in	ADP
ejde-517	166	6	this	this	DET
ejde-517	166	7	section	section	NOUN
ejde-517	166	8	,	,	PUNCT
ejde-517	166	9	we	we	PRON
ejde-517	166	10	analyze	analyze	VERB
ejde-517	166	11	the	the	DET
ejde-517	166	12	two	two	NUM
ejde-517	166	13	-	-	PUNCT
ejde-517	166	14	phase	phase	NOUN
ejde-517	166	15	segmentation	segmentation	NOUN
ejde-517	166	16	algorithm	algorithm	NOUN
ejde-517	166	17	.	.	PUNCT
ejde-517	167	1	we	we	PRON
ejde-517	167	2	start	start	VERB
ejde-517	167	3	with	with	ADP
ejde-517	167	4	results	result	NOUN
ejde-517	167	5	obtained	obtain	VERB
ejde-517	167	6	by	by	ADP
ejde-517	167	7	assuming	assume	VERB
ejde-517	167	8	that	that	SCONJ
ejde-517	167	9	σ	σ	PROPN
ejde-517	167	10	∈	∈	PROPN
ejde-517	167	11	l∞(ω	l∞(ω	NOUN
ejde-517	167	12	)	)	PUNCT
ejde-517	167	13	and	and	CCONJ
ejde-517	167	14	that	that	DET
ejde-517	167	15	χ1	χ1	NOUN
ejde-517	167	16	is	be	AUX
ejde-517	167	17	a	a	DET
ejde-517	167	18	characteristic	characteristic	ADJ
ejde-517	167	19	function	function	NOUN
ejde-517	167	20	.	.	PUNCT
ejde-517	168	1	because	because	SCONJ
ejde-517	168	2	the	the	DET
ejde-517	168	3	characteristic	characteristic	ADJ
ejde-517	168	4	function	function	NOUN
ejde-517	168	5	χ1	χ1	NOUN
ejde-517	168	6	is	be	AUX
ejde-517	168	7	binary	binary	ADJ
ejde-517	168	8	,	,	PUNCT
ejde-517	168	9	we	we	PRON
ejde-517	168	10	use	use	VERB
ejde-517	168	11	its	its	PRON
ejde-517	168	12	smooth	smooth	ADJ
ejde-517	168	13	approximation	approximation	NOUN
ejde-517	168	14	(	(	PUNCT
ejde-517	168	15	2.15	2.15	NUM
ejde-517	168	16	)	)	PUNCT
ejde-517	168	17	instead	instead	ADV
ejde-517	168	18	.	.	PUNCT
ejde-517	169	1	this	this	PRON
ejde-517	169	2	is	be	AUX
ejde-517	169	3	necessary	necessary	ADJ
ejde-517	169	4	because	because	SCONJ
ejde-517	169	5	some	some	PRON
ejde-517	169	6	of	of	ADP
ejde-517	169	7	the	the	DET
ejde-517	169	8	essential	essential	ADJ
ejde-517	169	9	results	result	NOUN
ejde-517	169	10	require	require	VERB
ejde-517	169	11	χ1	χ1	NOUN
ejde-517	169	12	to	to	PART
ejde-517	169	13	have	have	VERB
ejde-517	169	14	a	a	DET
ejde-517	169	15	higher	high	ADJ
ejde-517	169	16	regularity	regularity	NOUN
ejde-517	169	17	.	.	PUNCT
ejde-517	170	1	this	this	PRON
ejde-517	170	2	might	might	AUX
ejde-517	170	3	seem	seem	VERB
ejde-517	170	4	like	like	ADP
ejde-517	170	5	a	a	DET
ejde-517	170	6	deviation	deviation	NOUN
ejde-517	170	7	from	from	ADP
ejde-517	170	8	our	our	PRON
ejde-517	170	9	proposed	propose	VERB
ejde-517	170	10	method	method	NOUN
ejde-517	170	11	but	but	CCONJ
ejde-517	170	12	we	we	PRON
ejde-517	170	13	will	will	AUX
ejde-517	170	14	argue	argue	VERB
ejde-517	170	15	that	that	SCONJ
ejde-517	170	16	these	these	DET
ejde-517	170	17	modifications	modification	NOUN
ejde-517	170	18	can	can	AUX
ejde-517	170	19	be	be	AUX
ejde-517	170	20	justified	justify	VERB
ejde-517	170	21	.	.	PUNCT
ejde-517	171	1	we	we	PRON
ejde-517	171	2	will	will	AUX
ejde-517	171	3	then	then	ADV
ejde-517	171	4	introduce	introduce	VERB
ejde-517	171	5	a	a	DET
ejde-517	171	6	modification	modification	NOUN
ejde-517	171	7	of	of	ADP
ejde-517	171	8	the	the	DET
ejde-517	171	9	two	two	NUM
ejde-517	171	10	-	-	PUNCT
ejde-517	171	11	phase	phase	NOUN
ejde-517	171	12	segmentation	segmentation	NOUN
ejde-517	171	13	algorithm	algorithm	NOUN
ejde-517	171	14	to	to	PART
ejde-517	171	15	adapt	adapt	VERB
ejde-517	171	16	with	with	ADP
ejde-517	171	17	the	the	DET
ejde-517	171	18	mollification	mollification	NOUN
ejde-517	171	19	of	of	ADP
ejde-517	171	20	χ1	χ1	NOUN
ejde-517	171	21	.	.	PUNCT
ejde-517	172	1	in	in	ADP
ejde-517	172	2	the	the	DET
ejde-517	172	3	next	next	ADJ
ejde-517	172	4	section	section	NOUN
ejde-517	172	5	,	,	PUNCT
ejde-517	172	6	we	we	PRON
ejde-517	172	7	prove	prove	VERB
ejde-517	172	8	that	that	SCONJ
ejde-517	172	9	the	the	DET
ejde-517	172	10	modified	modify	VERB
ejde-517	172	11	version	version	NOUN
ejde-517	172	12	of	of	ADP
ejde-517	172	13	two	two	NUM
ejde-517	172	14	-	-	PUNCT
ejde-517	172	15	phase	phase	NOUN
ejde-517	172	16	segmentation	segmentation	NOUN
ejde-517	172	17	algorithm	algorithm	NOUN
ejde-517	172	18	has	have	VERB
ejde-517	172	19	a	a	DET
ejde-517	172	20	fixed	fix	VERB
ejde-517	172	21	point	point	NOUN
ejde-517	172	22	via	via	ADP
ejde-517	172	23	schauder	schauder	NOUN
ejde-517	172	24	’s	’s	PART
ejde-517	172	25	fixed	fix	VERB
ejde-517	172	26	point	point	NOUN
ejde-517	172	27	theorem	theorem	VERB
ejde-517	172	28	.	.	PROPN
ejde-517	172	29	3.1	3.1	NUM
ejde-517	172	30	.	.	PUNCT
ejde-517	173	1	preliminaries	preliminary	NOUN
ejde-517	173	2	.	.	PUNCT
ejde-517	174	1	we	we	PRON
ejde-517	174	2	already	already	ADV
ejde-517	174	3	emphasized	emphasize	VERB
ejde-517	174	4	that	that	SCONJ
ejde-517	174	5	φ	φ	PROPN
ejde-517	174	6	and	and	CCONJ
ejde-517	174	7	φ∗	φ∗	NOUN
ejde-517	174	8	are	be	AUX
ejde-517	174	9	solved	solve	VERB
ejde-517	174	10	using	use	VERB
ejde-517	174	11	σk	σk	NOUN
ejde-517	174	12	.	.	PUNCT
ejde-517	175	1	in	in	ADP
ejde-517	175	2	this	this	DET
ejde-517	175	3	section	section	NOUN
ejde-517	175	4	,	,	PUNCT
ejde-517	175	5	we	we	PRON
ejde-517	175	6	try	try	VERB
ejde-517	175	7	to	to	PART
ejde-517	175	8	understand	understand	VERB
ejde-517	175	9	how	how	SCONJ
ejde-517	175	10	a	a	DET
ejde-517	175	11	perturbation	perturbation	NOUN
ejde-517	175	12	on	on	ADP
ejde-517	175	13	σk	σk	ADV
ejde-517	175	14	affects	affect	VERB
ejde-517	175	15	φ	φ	PROPN
ejde-517	175	16	and	and	CCONJ
ejde-517	175	17	φ∗.	φ∗.	NOUN
ejde-517	175	18	recall	recall	VERB
ejde-517	175	19	that	that	SCONJ
ejde-517	175	20	σk	σk	PROPN
ejde-517	175	21	depends	depend	VERB
ejde-517	175	22	on	on	ADP
ejde-517	175	23	χ1	χ1	NOUN
ejde-517	175	24	.	.	PUNCT
ejde-517	176	1	therefore	therefore	ADV
ejde-517	176	2	,	,	PUNCT
ejde-517	176	3	φ	φ	PROPN
ejde-517	176	4	and	and	CCONJ
ejde-517	176	5	φ∗	φ∗	NOUN
ejde-517	176	6	depend	depend	VERB
ejde-517	176	7	on	on	ADP
ejde-517	176	8	χ1	χ1	NOUN
ejde-517	176	9	as	as	ADV
ejde-517	176	10	well	well	ADV
ejde-517	176	11	.	.	PUNCT
ejde-517	177	1	working	work	VERB
ejde-517	177	2	under	under	ADP
ejde-517	177	3	the	the	DET
ejde-517	177	4	assumption	assumption	NOUN
ejde-517	177	5	that	that	SCONJ
ejde-517	177	6	σ	σ	PROPN
ejde-517	177	7	∈	∈	PROPN
ejde-517	177	8	l∞(ω	l∞(ω	NOUN
ejde-517	177	9	)	)	PUNCT
ejde-517	177	10	and	and	CCONJ
ejde-517	177	11	χ1	χ1	NOUN
ejde-517	177	12	is	be	AUX
ejde-517	177	13	a	a	DET
ejde-517	177	14	characteristic	characteristic	ADJ
ejde-517	177	15	function	function	NOUN
ejde-517	177	16	,	,	PUNCT
ejde-517	177	17	we	we	PRON
ejde-517	177	18	show	show	VERB
ejde-517	177	19	that	that	SCONJ
ejde-517	177	20	φ	φ	PROPN
ejde-517	177	21	and	and	CCONJ
ejde-517	177	22	φ∗	φ∗	NOUN
ejde-517	177	23	depend	depend	VERB
ejde-517	177	24	continuously	continuously	ADV
ejde-517	177	25	on	on	ADP
ejde-517	177	26	σk	σk	ADV
ejde-517	177	27	and	and	CCONJ
ejde-517	177	28	on	on	ADP
ejde-517	177	29	χ1	χ1	NOUN
ejde-517	177	30	.	.	PUNCT
ejde-517	178	1	we	we	PRON
ejde-517	178	2	begin	begin	VERB
ejde-517	178	3	this	this	DET
ejde-517	178	4	section	section	NOUN
ejde-517	178	5	by	by	ADP
ejde-517	178	6	showing	show	VERB
ejde-517	178	7	that	that	SCONJ
ejde-517	178	8	the	the	DET
ejde-517	178	9	variational	variational	ADJ
ejde-517	178	10	forward	forward	ADJ
ejde-517	178	11	problem	problem	NOUN
ejde-517	178	12	and	and	CCONJ
ejde-517	178	13	the	the	DET
ejde-517	178	14	variational	variational	ADJ
ejde-517	178	15	adjoint	adjoint	PROPN
ejde-517	178	16	problem	problem	NOUN
ejde-517	178	17	both	both	PRON
ejde-517	178	18	have	have	VERB
ejde-517	178	19	unique	unique	ADJ
ejde-517	178	20	solutions	solution	NOUN
ejde-517	178	21	in	in	ADP
ejde-517	178	22	h1(ω	h1(ω	PROPN
ejde-517	178	23	)	)	PUNCT
ejde-517	178	24	under	under	ADP
ejde-517	178	25	stated	state	VERB
ejde-517	178	26	assumptions	assumption	NOUN
ejde-517	178	27	on	on	ADP
ejde-517	178	28	σ	σ	PROPN
ejde-517	178	29	.	.	PUNCT
ejde-517	179	1	in	in	ADP
ejde-517	179	2	the	the	DET
ejde-517	179	3	succeeding	succeed	VERB
ejde-517	179	4	sections	section	NOUN
ejde-517	179	5	,	,	PUNCT
ejde-517	179	6	we	we	PRON
ejde-517	179	7	study	study	VERB
ejde-517	179	8	the	the	DET
ejde-517	179	9	behavior	behavior	NOUN
ejde-517	179	10	of	of	ADP
ejde-517	179	11	φ	φ	PROPN
ejde-517	179	12	and	and	CCONJ
ejde-517	179	13	φ∗	φ∗	NOUN
ejde-517	179	14	when	when	SCONJ
ejde-517	179	15	we	we	PRON
ejde-517	179	16	require	require	VERB
ejde-517	179	17	additional	additional	ADJ
ejde-517	179	18	regularity	regularity	NOUN
ejde-517	179	19	of	of	ADP
ejde-517	179	20	σk	σk	PROPN
ejde-517	179	21	.	.	PUNCT
ejde-517	179	22	theorem	theorem	PROPN
ejde-517	179	23	3.1	3.1	NUM
ejde-517	179	24	.	.	PUNCT
ejde-517	180	1	let	let	VERB
ejde-517	180	2	σk	σk	PRON
ejde-517	180	3	∈	∈	PROPN
ejde-517	180	4	l∞(ω	l∞(ω	X
ejde-517	180	5	)	)	PUNCT
ejde-517	180	6	such	such	ADJ
ejde-517	180	7	that	that	SCONJ
ejde-517	180	8	0	0	NUM
ejde-517	180	9	<	<	X
ejde-517	180	10	σ	σ	PUNCT
ejde-517	180	11	≤	≤	NOUN
ejde-517	180	12	σk(x	σk(x	NOUN
ejde-517	180	13	)	)	PUNCT
ejde-517	180	14	for	for	ADP
ejde-517	180	15	all	all	DET
ejde-517	180	16	x	x	SYM
ejde-517	180	17	∈	∈	PROPN
ejde-517	180	18	ω	ω	NOUN
ejde-517	180	19	and	and	CCONJ
ejde-517	180	20	f	f	PROPN
ejde-517	180	21	∈	∈	PROPN
ejde-517	180	22	l̃2(∂ω	l̃2(∂ω	NOUN
ejde-517	180	23	)	)	PUNCT
ejde-517	180	24	.	.	PUNCT
ejde-517	181	1	then	then	ADV
ejde-517	181	2	(	(	PUNCT
ejde-517	181	3	the	the	DET
ejde-517	181	4	variational	variational	ADJ
ejde-517	181	5	forward	forward	ADV
ejde-517	181	6	eit	eit	PROPN
ejde-517	181	7	problem)∫	problem)∫	NOUN
ejde-517	181	8	ω	ω	NOUN
ejde-517	181	9	σk∇φ	σk∇φ	PROPN
ejde-517	181	10	·	·	PUNCT
ejde-517	182	1	∇v	∇v	ADJ
ejde-517	182	2	dv	dv	PROPN
ejde-517	182	3	=	=	SYM
ejde-517	182	4	∫	∫	PROPN
ejde-517	183	1	∂ω	∂ω	PROPN
ejde-517	184	1	σk	σk	ADP
ejde-517	184	2	∂φ	∂φ	PROPN
ejde-517	184	3	∂n	∂n	PROPN
ejde-517	184	4	v	v	NUM
ejde-517	184	5	ds	ds	PROPN
ejde-517	184	6	,	,	PUNCT
ejde-517	184	7	∀v	∀v	PROPN
ejde-517	184	8	∈	∈	PROPN
ejde-517	184	9	h1(ω	h1(ω	PROPN
ejde-517	184	10	)	)	PUNCT
ejde-517	184	11	(	(	PUNCT
ejde-517	184	12	3.1	3.1	NUM
ejde-517	184	13	)	)	PUNCT
ejde-517	184	14	has	have	VERB
ejde-517	184	15	a	a	DET
ejde-517	184	16	unique	unique	ADJ
ejde-517	184	17	solution	solution	NOUN
ejde-517	184	18	φ	φ	X
ejde-517	184	19	∈	∈	PROPN
ejde-517	184	20	h1(ω	h1(ω	PROPN
ejde-517	184	21	)	)	PUNCT
ejde-517	184	22	with	with	ADP
ejde-517	184	23	∫	∫	PROPN
ejde-517	184	24	∂ω	∂ω	ADJ
ejde-517	184	25	φds	φds	NOUN
ejde-517	184	26	=	=	NOUN
ejde-517	184	27	0	0	X
ejde-517	184	28	.	.	PUNCT
ejde-517	185	1	similarly	similarly	ADV
ejde-517	185	2	,	,	PUNCT
ejde-517	185	3	let	let	VERB
ejde-517	185	4	ṽ	ṽ	PROPN
ejde-517	185	5	∈	∈	PROPN
ejde-517	185	6	l̃2(∂ω	l̃2(∂ω	NOUN
ejde-517	185	7	)	)	PUNCT
ejde-517	185	8	be	be	VERB
ejde-517	185	9	the	the	DET
ejde-517	185	10	known	know	VERB
ejde-517	185	11	boundary	boundary	ADJ
ejde-517	185	12	voltage	voltage	NOUN
ejde-517	185	13	.	.	PUNCT
ejde-517	186	1	then	then	ADV
ejde-517	186	2	(	(	PUNCT
ejde-517	186	3	the	the	DET
ejde-517	186	4	variational	variational	ADJ
ejde-517	186	5	adjoint	adjoint	PROPN
ejde-517	186	6	problem)∫	problem)∫	NOUN
ejde-517	186	7	ω	ω	PROPN
ejde-517	186	8	σk∇φ∗	σk∇φ∗	PROPN
ejde-517	186	9	·	·	PUNCT
ejde-517	187	1	∇v	∇v	ADJ
ejde-517	187	2	dv	dv	PROPN
ejde-517	187	3	=	=	SYM
ejde-517	187	4	∫	∫	PROPN
ejde-517	188	1	∂ω	∂ω	PROPN
ejde-517	188	2	(	(	PUNCT
ejde-517	188	3	φ−	φ−	PROPN
ejde-517	188	4	ṽ	ṽ	PROPN
ejde-517	188	5	)	)	PUNCT
ejde-517	188	6	v	v	NOUN
ejde-517	188	7	ds	ds	ADJ
ejde-517	188	8	,	,	PUNCT
ejde-517	188	9	∀v	∀v	PROPN
ejde-517	188	10	∈	∈	PROPN
ejde-517	188	11	h1(ω	h1(ω	PROPN
ejde-517	188	12	)	)	PUNCT
ejde-517	188	13	(	(	PUNCT
ejde-517	188	14	3.2	3.2	NUM
ejde-517	188	15	)	)	PUNCT
ejde-517	188	16	has	have	VERB
ejde-517	188	17	a	a	DET
ejde-517	188	18	unique	unique	ADJ
ejde-517	188	19	solution	solution	NOUN
ejde-517	188	20	φ∗	φ∗	NOUN
ejde-517	188	21	∈	∈	PROPN
ejde-517	188	22	h1(ω	h1(ω	PROPN
ejde-517	188	23	)	)	PUNCT
ejde-517	188	24	with	with	ADP
ejde-517	188	25	∫	∫	PROPN
ejde-517	188	26	∂ω	∂ω	ADJ
ejde-517	188	27	φ∗	φ∗	NOUN
ejde-517	188	28	ds	ds	NOUN
ejde-517	188	29	=	=	NOUN
ejde-517	188	30	0	0	X
ejde-517	188	31	.	.	PUNCT
ejde-517	189	1	proof	proof	NOUN
ejde-517	189	2	.	.	PUNCT
ejde-517	190	1	we	we	PRON
ejde-517	190	2	define	define	VERB
ejde-517	190	3	i	i	PRON
ejde-517	190	4	:	:	PUNCT
ejde-517	190	5	=	=	SYM
ejde-517	190	6	{	{	PUNCT
ejde-517	190	7	u	u	NOUN
ejde-517	190	8	∈	∈	PROPN
ejde-517	190	9	h1(ω	h1(ω	PROPN
ejde-517	190	10	)	)	PUNCT
ejde-517	190	11	:	:	PUNCT
ejde-517	191	1	∫	∫	PROPN
ejde-517	191	2	∂ω	∂ω	ADJ
ejde-517	191	3	u	u	NOUN
ejde-517	191	4	ds	ds	NOUN
ejde-517	191	5	=	=	NOUN
ejde-517	191	6	0	0	NUM
ejde-517	191	7	}	}	PUNCT
ejde-517	191	8	,	,	PUNCT
ejde-517	191	9	a(u	a(u	PROPN
ejde-517	191	10	,	,	PUNCT
ejde-517	191	11	v	v	NOUN
ejde-517	191	12	)	)	PUNCT
ejde-517	191	13	:	:	PUNCT
ejde-517	192	1	=	=	SYM
ejde-517	192	2	∫	∫	PROPN
ejde-517	192	3	ω	ω	PROPN
ejde-517	192	4	σk∇u	σk∇u	PROPN
ejde-517	192	5	·	·	PROPN
ejde-517	192	6	∇v	∇v	PROPN
ejde-517	192	7	dv	dv	PROPN
ejde-517	192	8	,	,	PUNCT
ejde-517	192	9	and	and	CCONJ
ejde-517	192	10	b(v	b(v	NOUN
ejde-517	192	11	)	)	PUNCT
ejde-517	192	12	:	:	PUNCT
ejde-517	193	1	=	=	SYM
ejde-517	193	2	∫	∫	PROPN
ejde-517	194	1	∂ω	∂ω	ADJ
ejde-517	194	2	fv	fv	PROPN
ejde-517	194	3	ds	ds	PROPN
ejde-517	194	4	.	.	PROPN
ejde-517	195	1	clearly	clearly	ADV
ejde-517	195	2	,	,	PUNCT
ejde-517	195	3	a	a	PRON
ejde-517	195	4	is	be	AUX
ejde-517	195	5	bilinear	bilinear	NOUN
ejde-517	195	6	and	and	CCONJ
ejde-517	195	7	b	b	NOUN
ejde-517	195	8	is	be	AUX
ejde-517	195	9	linear	linear	ADJ
ejde-517	195	10	.	.	PUNCT
ejde-517	196	1	using	use	VERB
ejde-517	196	2	the	the	DET
ejde-517	196	3	cauchy	cauchy	NOUN
ejde-517	196	4	-	-	PUNCT
ejde-517	196	5	schwarz	schwarz	PROPN
ejde-517	196	6	identity	identity	NOUN
ejde-517	196	7	,	,	PUNCT
ejde-517	196	8	hölder	hölder	NOUN
ejde-517	196	9	’s	’s	PART
ejde-517	196	10	inequality	inequality	NOUN
ejde-517	196	11	,	,	PUNCT
ejde-517	196	12	and	and	CCONJ
ejde-517	196	13	the	the	DET
ejde-517	196	14	definition	definition	NOUN
ejde-517	196	15	of	of	ADP
ejde-517	196	16	the	the	DET
ejde-517	196	17	h1	h1	NOUN
ejde-517	196	18	norm	norm	NOUN
ejde-517	196	19	,	,	PUNCT
ejde-517	196	20	a	a	PRON
ejde-517	196	21	is	be	AUX
ejde-517	196	22	bounded	bound	VERB
ejde-517	196	23	,	,	PUNCT
ejde-517	196	24	i.e.	i.e.	X
ejde-517	196	25	,	,	PUNCT
ejde-517	196	26	|a(u	|a(u	PROPN
ejde-517	196	27	,	,	PUNCT
ejde-517	196	28	v)|	v)|	NOUN
ejde-517	196	29	≤	≤	NOUN
ejde-517	196	30	‖σk‖l∞(ω)‖u‖h1(ω)‖v‖h1(ω	‖σk‖l∞(ω)‖u‖h1(ω)‖v‖h1(ω	NUM
ejde-517	196	31	)	)	PUNCT
ejde-517	196	32	.	.	PUNCT
ejde-517	197	1	because	because	SCONJ
ejde-517	197	2	u	u	PROPN
ejde-517	197	3	∈	∈	PROPN
ejde-517	197	4	i	i	PRON
ejde-517	197	5	,	,	PUNCT
ejde-517	197	6	then	then	ADV
ejde-517	197	7	∫	∫	PROPN
ejde-517	197	8	∂ω	∂ω	ADJ
ejde-517	197	9	u	u	NOUN
ejde-517	197	10	ds	ds	ADJ
ejde-517	197	11	=	=	NOUN
ejde-517	197	12	0	0	NUM
ejde-517	197	13	.	.	PUNCT
ejde-517	197	14	therefore	therefore	ADV
ejde-517	197	15	,	,	PUNCT
ejde-517	197	16	using	use	VERB
ejde-517	197	17	the	the	DET
ejde-517	197	18	lower	low	ADJ
ejde-517	197	19	bound	bind	VERB
ejde-517	197	20	of	of	ADP
ejde-517	197	21	σ	σ	PROPN
ejde-517	197	22	,	,	PUNCT
ejde-517	197	23	and	and	CCONJ
ejde-517	197	24	the	the	DET
ejde-517	197	25	generalized	generalize	VERB
ejde-517	197	26	friedrich	friedrich	NOUN
ejde-517	197	27	’s	’s	PART
ejde-517	197	28	inequality	inequality	NOUN
ejde-517	197	29	[	[	X
ejde-517	197	30	4	4	NUM
ejde-517	197	31	]	]	PUNCT
ejde-517	197	32	,	,	PUNCT
ejde-517	197	33	we	we	PRON
ejde-517	197	34	obtain	obtain	VERB
ejde-517	197	35	|a(u	|a(u	PROPN
ejde-517	197	36	,	,	PUNCT
ejde-517	197	37	u)|	u)|	X
ejde-517	197	38	≥	≥	NOUN
ejde-517	197	39	σ‖∇u‖2l2(ω	σ‖∇u‖2l2(ω	ADV
ejde-517	197	40	)	)	PUNCT
ejde-517	198	1	=	=	SYM
ejde-517	198	2	σ	σ	PROPN
ejde-517	198	3	2	2	NUM
ejde-517	198	4	‖∇u‖2l2(ω	‖∇u‖2l2(ω	NUM
ejde-517	198	5	)	)	PUNCT
ejde-517	199	1	+	+	CCONJ
ejde-517	200	1	σ	σ	NUM
ejde-517	200	2	2	2	NUM
ejde-517	200	3	‖∇u‖2l2(ω	‖∇u‖2l2(ω	NUM
ejde-517	200	4	)	)	PUNCT
ejde-517	200	5	≥	≥	PROPN
ejde-517	200	6	σ	σ	PROPN
ejde-517	200	7	2	2	NUM
ejde-517	200	8	(	(	PUNCT
ejde-517	200	9	1	1	NUM
ejde-517	200	10	c	c	NOUN
ejde-517	200	11	‖u‖2l2(ω	‖u‖2l2(ω	NOUN
ejde-517	200	12	)	)	PUNCT
ejde-517	200	13	−	−	PROPN
ejde-517	200	14	(	(	PUNCT
ejde-517	200	15	∫	∫	PROPN
ejde-517	200	16	∂ω	∂ω	ADJ
ejde-517	200	17	u	u	NOUN
ejde-517	200	18	ds	ds	ADJ
ejde-517	200	19	)	)	PUNCT
ejde-517	200	20	2	2	NUM
ejde-517	200	21	)	)	PUNCT
ejde-517	200	22	+	+	CCONJ
ejde-517	200	23	σ	σ	NUM
ejde-517	200	24	2	2	NUM
ejde-517	200	25	‖∇u‖2l2(ω	‖∇u‖2l2(ω	ADV
ejde-517	200	26	)	)	PUNCT
ejde-517	200	27	ejde-2020/93	ejde-2020/93	PROPN
ejde-517	200	28	impedance	impedance	NOUN
ejde-517	200	29	tomography	tomography	NOUN
ejde-517	200	30	problem	problem	NOUN
ejde-517	200	31	7	7	NUM
ejde-517	200	32	=	=	SYM
ejde-517	200	33	σ	σ	PROPN
ejde-517	200	34	2c	2c	NOUN
ejde-517	200	35	‖u‖2l2(ω	‖u‖2l2(ω	NOUN
ejde-517	200	36	)	)	PUNCT
ejde-517	201	1	+	+	CCONJ
ejde-517	202	1	σ	σ	NUM
ejde-517	202	2	2	2	NUM
ejde-517	202	3	‖∇u‖2l2(ω	‖∇u‖2l2(ω	NOUN
ejde-517	202	4	)	)	PUNCT
ejde-517	202	5	≥	≥	PRON
ejde-517	202	6	σmin	σmin	VERB
ejde-517	202	7	{	{	PUNCT
ejde-517	202	8	1	1	NUM
ejde-517	202	9	c	c	NOUN
ejde-517	202	10	,	,	PUNCT
ejde-517	202	11	1	1	NUM
ejde-517	202	12	}	}	PUNCT
ejde-517	202	13	‖u‖2h1(ω	‖u‖2h1(ω	NOUN
ejde-517	202	14	)	)	PUNCT
ejde-517	202	15	,	,	PUNCT
ejde-517	202	16	for	for	ADP
ejde-517	202	17	some	some	DET
ejde-517	202	18	c	c	PROPN
ejde-517	202	19	>	>	X
ejde-517	202	20	0	0	X
ejde-517	202	21	.	.	PUNCT
ejde-517	203	1	finally	finally	ADV
ejde-517	203	2	,	,	PUNCT
ejde-517	203	3	by	by	ADP
ejde-517	203	4	the	the	DET
ejde-517	203	5	trace	trace	NOUN
ejde-517	203	6	theorem	theorem	ADJ
ejde-517	203	7	[	[	X
ejde-517	203	8	14	14	NUM
ejde-517	203	9	]	]	X
ejde-517	203	10	,	,	PUNCT
ejde-517	203	11	b	b	PROPN
ejde-517	203	12	is	be	AUX
ejde-517	203	13	bounded	bound	VERB
ejde-517	203	14	.	.	PUNCT
ejde-517	204	1	hence	hence	ADV
ejde-517	204	2	,	,	PUNCT
ejde-517	204	3	by	by	ADP
ejde-517	204	4	the	the	DET
ejde-517	204	5	lax	lax	PROPN
ejde-517	204	6	-	-	PUNCT
ejde-517	204	7	milgram	milgram	NOUN
ejde-517	204	8	theorem	theorem	PROPN
ejde-517	204	9	∃	∃	PROPN
ejde-517	204	10	!	!	PUNCT
ejde-517	204	11	φ	φ	PROPN
ejde-517	204	12	∈	∈	PROPN
ejde-517	204	13	h1(ω	h1(ω	PROPN
ejde-517	204	14	)	)	PUNCT
ejde-517	204	15	satisfying	satisfying	NOUN
ejde-517	204	16	(	(	PUNCT
ejde-517	204	17	3.1	3.1	NUM
ejde-517	204	18	)	)	PUNCT
ejde-517	204	19	.	.	PUNCT
ejde-517	205	1	similarly	similarly	ADV
ejde-517	205	2	,	,	PUNCT
ejde-517	205	3	there	there	PRON
ejde-517	205	4	exists	exist	VERB
ejde-517	205	5	a	a	DET
ejde-517	205	6	unique	unique	ADJ
ejde-517	205	7	φ∗	φ∗	NOUN
ejde-517	205	8	∈	∈	NOUN
ejde-517	205	9	i	i	PRON
ejde-517	205	10	satisfying	satisfy	VERB
ejde-517	205	11	(	(	PUNCT
ejde-517	205	12	3.2	3.2	NUM
ejde-517	205	13	)	)	PUNCT
ejde-517	205	14	.	.	PUNCT
ejde-517	206	1	�	�	PROPN
ejde-517	206	2	corollary	corollary	ADJ
ejde-517	206	3	3.2	3.2	NUM
ejde-517	206	4	.	.	PUNCT
ejde-517	207	1	let	let	VERB
ejde-517	207	2	φ	φ	NOUN
ejde-517	207	3	and	and	CCONJ
ejde-517	207	4	φ∗	φ∗	NOUN
ejde-517	207	5	satisfy	satisfy	NOUN
ejde-517	207	6	the	the	DET
ejde-517	207	7	variational	variational	ADJ
ejde-517	207	8	forward	forward	ADV
ejde-517	207	9	and	and	CCONJ
ejde-517	207	10	the	the	DET
ejde-517	207	11	variational	variational	ADJ
ejde-517	207	12	adjoint	adjoint	PROPN
ejde-517	207	13	problem	problem	NOUN
ejde-517	207	14	stated	state	VERB
ejde-517	207	15	in	in	ADP
ejde-517	207	16	the	the	DET
ejde-517	207	17	previous	previous	ADJ
ejde-517	207	18	theorem	theorem	NOUN
ejde-517	207	19	.	.	PUNCT
ejde-517	208	1	we	we	PRON
ejde-517	208	2	have	have	VERB
ejde-517	208	3	the	the	DET
ejde-517	208	4	following	follow	VERB
ejde-517	208	5	estimates	estimate	NOUN
ejde-517	208	6	:	:	PUNCT
ejde-517	208	7	‖φ‖h1(ω	‖φ‖h1(ω	X
ejde-517	208	8	)	)	PUNCT
ejde-517	208	9	≤	≤	NUM
ejde-517	208	10	c1‖f‖l̃2(∂ω	c1‖f‖l̃2(∂ω	PROPN
ejde-517	208	11	)	)	PUNCT
ejde-517	208	12	(	(	PUNCT
ejde-517	208	13	3.3	3.3	NUM
ejde-517	208	14	)	)	PUNCT
ejde-517	208	15	‖φ∗‖h1(ω	‖φ∗‖h1(ω	NOUN
ejde-517	208	16	)	)	PUNCT
ejde-517	208	17	≤	≤	NUM
ejde-517	208	18	c2‖(φ−	c2‖(φ−	PROPN
ejde-517	208	19	ṽ	ṽ	PROPN
ejde-517	208	20	)	)	PUNCT
ejde-517	208	21	‖l̃2(∂ω	‖l̃2(∂ω	PROPN
ejde-517	208	22	)	)	PUNCT
ejde-517	208	23	(	(	PUNCT
ejde-517	208	24	3.4	3.4	NUM
ejde-517	208	25	)	)	PUNCT
ejde-517	208	26	for	for	ADP
ejde-517	208	27	some	some	DET
ejde-517	208	28	c1	c1	NOUN
ejde-517	208	29	,	,	PUNCT
ejde-517	208	30	c2	c2	PROPN
ejde-517	208	31	>	>	X
ejde-517	208	32	0	0	X
ejde-517	208	33	.	.	PUNCT
ejde-517	209	1	note	note	VERB
ejde-517	209	2	that	that	SCONJ
ejde-517	209	3	using	use	VERB
ejde-517	209	4	the	the	DET
ejde-517	209	5	trace	trace	NOUN
ejde-517	209	6	theorem	theorem	NOUN
ejde-517	209	7	and	and	CCONJ
ejde-517	209	8	the	the	DET
ejde-517	209	9	triangle	triangle	NOUN
ejde-517	209	10	inequality	inequality	NOUN
ejde-517	209	11	,	,	PUNCT
ejde-517	209	12	φ∗	φ∗	NOUN
ejde-517	209	13	can	can	AUX
ejde-517	209	14	be	be	AUX
ejde-517	209	15	further	far	ADV
ejde-517	209	16	estimated	estimate	VERB
ejde-517	209	17	by	by	ADP
ejde-517	209	18	‖φ∗‖h1(ω	‖φ∗‖h1(ω	NOUN
ejde-517	209	19	)	)	PUNCT
ejde-517	209	20	≤	≤	NOUN
ejde-517	209	21	c3	c3	NOUN
ejde-517	209	22	(	(	PUNCT
ejde-517	209	23	‖f‖l̃2(∂ω	‖f‖l̃2(∂ω	NUM
ejde-517	209	24	)	)	PUNCT
ejde-517	210	1	+	+	NUM
ejde-517	210	2	‖ṽ	‖ṽ	PUNCT
ejde-517	210	3	‖l̃2(∂ω	‖l̃2(∂ω	X
ejde-517	210	4	)	)	PUNCT
ejde-517	210	5	)	)	PUNCT
ejde-517	211	1	(	(	PUNCT
ejde-517	211	2	3.5	3.5	NUM
ejde-517	211	3	)	)	PUNCT
ejde-517	211	4	for	for	ADP
ejde-517	211	5	some	some	DET
ejde-517	211	6	c3	c3	PROPN
ejde-517	211	7	>	>	X
ejde-517	211	8	0	0	X
ejde-517	211	9	.	.	PUNCT
ejde-517	212	1	throughout	throughout	ADP
ejde-517	212	2	this	this	DET
ejde-517	212	3	work	work	NOUN
ejde-517	212	4	,	,	PUNCT
ejde-517	212	5	we	we	PRON
ejde-517	212	6	use	use	VERB
ejde-517	212	7	the	the	DET
ejde-517	212	8	following	follow	VERB
ejde-517	212	9	notation	notation	NOUN
ejde-517	212	10	.	.	PUNCT
ejde-517	213	1	definition	definition	NOUN
ejde-517	213	2	3.3	3.3	NUM
ejde-517	213	3	.	.	PUNCT
ejde-517	214	1	we	we	PRON
ejde-517	214	2	let	let	VERB
ejde-517	214	3	δσk	δσk	NOUN
ejde-517	214	4	and	and	CCONJ
ejde-517	214	5	δχ1	δχ1	NOUN
ejde-517	214	6	denote	denote	NOUN
ejde-517	214	7	perturbations	perturbation	NOUN
ejde-517	214	8	of	of	ADP
ejde-517	214	9	σk	σk	PROPN
ejde-517	214	10	∈	∈	PROPN
ejde-517	214	11	l∞(ω	l∞(ω	NOUN
ejde-517	214	12	)	)	PUNCT
ejde-517	214	13	and	and	CCONJ
ejde-517	214	14	χ1	χ1	PROPN
ejde-517	214	15	∈	∈	PROPN
ejde-517	214	16	l∞(ω	l∞(ω	NOUN
ejde-517	214	17	)	)	PUNCT
ejde-517	214	18	,	,	PUNCT
ejde-517	214	19	respectively	respectively	ADV
ejde-517	214	20	.	.	PUNCT
ejde-517	215	1	in	in	ADP
ejde-517	215	2	definition	definition	NOUN
ejde-517	215	3	(	(	PUNCT
ejde-517	215	4	2.2	2.2	NUM
ejde-517	215	5	)	)	PUNCT
ejde-517	215	6	,	,	PUNCT
ejde-517	215	7	φ	φ	PROPN
ejde-517	215	8	and	and	CCONJ
ejde-517	215	9	φ∗	φ∗	NOUN
ejde-517	215	10	are	be	AUX
ejde-517	215	11	operators	operator	NOUN
ejde-517	215	12	that	that	PRON
ejde-517	215	13	map	map	NOUN
ejde-517	215	14	(	(	PUNCT
ejde-517	215	15	σk1	σk1	NOUN
ejde-517	215	16	,	,	PUNCT
ejde-517	215	17	χ1	χ1	PROPN
ejde-517	215	18	)	)	PUNCT
ejde-517	215	19	to	to	ADP
ejde-517	215	20	φ	φ	PROPN
ejde-517	215	21	and	and	CCONJ
ejde-517	215	22	φ∗	φ∗	NOUN
ejde-517	215	23	,	,	PUNCT
ejde-517	215	24	respectively	respectively	ADV
ejde-517	215	25	.	.	PUNCT
ejde-517	216	1	but	but	CCONJ
ejde-517	216	2	because	because	SCONJ
ejde-517	216	3	σk	σk	ADJ
ejde-517	216	4	=	=	SYM
ejde-517	216	5	σk1χ1	σk1χ1	PROPN
ejde-517	216	6	+	+	NUM
ejde-517	216	7	σ2(1	σ2(1	NOUN
ejde-517	216	8	−	−	PROPN
ejde-517	216	9	χ1	χ1	NOUN
ejde-517	216	10	)	)	PUNCT
ejde-517	216	11	,	,	PUNCT
ejde-517	216	12	we	we	PRON
ejde-517	216	13	can	can	AUX
ejde-517	216	14	make	make	VERB
ejde-517	216	15	the	the	DET
ejde-517	216	16	identifications	identification	NOUN
ejde-517	216	17	φ(σk	φ(σk	NOUN
ejde-517	216	18	)	)	PUNCT
ejde-517	217	1	=	=	SYM
ejde-517	217	2	φ(σk1	φ(σk1	PROPN
ejde-517	217	3	,	,	PUNCT
ejde-517	217	4	χ1	χ1	NOUN
ejde-517	217	5	)	)	PUNCT
ejde-517	217	6	,	,	PUNCT
ejde-517	217	7	φ∗(σk	φ∗(σk	NUM
ejde-517	217	8	)	)	PUNCT
ejde-517	217	9	=	=	SYM
ejde-517	217	10	φ∗(σk1	φ∗(σk1	NOUN
ejde-517	217	11	,	,	PUNCT
ejde-517	217	12	χ1	χ1	NOUN
ejde-517	217	13	)	)	PUNCT
ejde-517	217	14	.	.	PUNCT
ejde-517	218	1	hence	hence	ADV
ejde-517	218	2	,	,	PUNCT
ejde-517	218	3	φ	φ	PROPN
ejde-517	218	4	:	:	PUNCT
ejde-517	218	5	σk	σk	PROPN
ejde-517	218	6	→	→	NOUN
ejde-517	218	7	φ	φ	PROPN
ejde-517	218	8	and	and	CCONJ
ejde-517	218	9	φ∗	φ∗	NOUN
ejde-517	218	10	:	:	PUNCT
ejde-517	218	11	σk	σk	PROPN
ejde-517	218	12	→	→	NOUN
ejde-517	218	13	φ∗.	φ∗.	NOUN
ejde-517	218	14	remark	remark	VERB
ejde-517	218	15	3.4	3.4	NUM
ejde-517	218	16	.	.	PUNCT
ejde-517	219	1	given	give	VERB
ejde-517	219	2	a	a	DET
ejde-517	219	3	perturbation	perturbation	NOUN
ejde-517	219	4	δσk	δσk	NOUN
ejde-517	219	5	∈	∈	PROPN
ejde-517	219	6	l∞(ω	l∞(ω	NOUN
ejde-517	219	7	)	)	PUNCT
ejde-517	219	8	,	,	PUNCT
ejde-517	219	9	how	how	SCONJ
ejde-517	219	10	can	can	AUX
ejde-517	219	11	we	we	PRON
ejde-517	219	12	choose	choose	VERB
ejde-517	219	13	η	η	X
ejde-517	219	14	>	>	X
ejde-517	219	15	0	0	PUNCT
ejde-517	220	1	so	so	SCONJ
ejde-517	220	2	that	that	SCONJ
ejde-517	220	3	the	the	DET
ejde-517	220	4	forward	forward	NOUN
ejde-517	220	5	and	and	CCONJ
ejde-517	220	6	the	the	DET
ejde-517	220	7	adjoint	adjoint	NOUN
ejde-517	220	8	problems	problem	NOUN
ejde-517	220	9	have	have	VERB
ejde-517	220	10	unique	unique	ADJ
ejde-517	220	11	solutions	solution	NOUN
ejde-517	220	12	if	if	SCONJ
ejde-517	220	13	we	we	PRON
ejde-517	220	14	use	use	VERB
ejde-517	220	15	σk+ηδσk	σk+ηδσk	NOUN
ejde-517	220	16	?	?	PUNCT
ejde-517	221	1	we	we	PRON
ejde-517	221	2	know	know	VERB
ejde-517	221	3	that	that	SCONJ
ejde-517	221	4	the	the	DET
ejde-517	221	5	forward	forward	ADJ
ejde-517	221	6	and	and	CCONJ
ejde-517	221	7	adjoint	adjoint	NOUN
ejde-517	221	8	problems	problem	NOUN
ejde-517	221	9	have	have	VERB
ejde-517	221	10	unique	unique	ADJ
ejde-517	221	11	solutions	solution	NOUN
ejde-517	221	12	given	give	VERB
ejde-517	221	13	σk	σk	ADP
ejde-517	221	14	∈	∈	PROPN
ejde-517	221	15	l∞	l∞	NOUN
ejde-517	221	16	if	if	SCONJ
ejde-517	221	17	σk(x	σk(x	NOUN
ejde-517	221	18	)	)	PUNCT
ejde-517	221	19	≥	≥	PROPN
ejde-517	221	20	σ	σ	X
ejde-517	221	21	>	>	X
ejde-517	221	22	0	0	PUNCT
ejde-517	221	23	for	for	ADP
ejde-517	221	24	all	all	DET
ejde-517	221	25	x	x	SYM
ejde-517	221	26	∈	∈	PROPN
ejde-517	221	27	ω	ω	NOUN
ejde-517	221	28	.	.	PUNCT
ejde-517	221	29	to	to	PART
ejde-517	221	30	make	make	VERB
ejde-517	221	31	sure	sure	ADJ
ejde-517	221	32	that	that	SCONJ
ejde-517	221	33	φ(σk	φ(σk	NOUN
ejde-517	221	34	+	+	CCONJ
ejde-517	221	35	ηδσk	ηδσk	NOUN
ejde-517	221	36	)	)	PUNCT
ejde-517	221	37	is	be	AUX
ejde-517	221	38	unique	unique	ADJ
ejde-517	221	39	,	,	PUNCT
ejde-517	221	40	we	we	PRON
ejde-517	221	41	can	can	AUX
ejde-517	221	42	simply	simply	ADV
ejde-517	221	43	select	select	VERB
ejde-517	221	44	η	η	PROPN
ejde-517	221	45	sufficiently	sufficiently	ADV
ejde-517	221	46	small	small	ADJ
ejde-517	221	47	so	so	SCONJ
ejde-517	221	48	that	that	SCONJ
ejde-517	221	49	(	(	PUNCT
ejde-517	221	50	σk	σk	ADP
ejde-517	221	51	+	+	NUM
ejde-517	221	52	ηδσk)(x	ηδσk)(x	NOUN
ejde-517	221	53	)	)	PUNCT
ejde-517	221	54	≥	≥	NOUN
ejde-517	222	1	στ	στ	INTJ
ejde-517	222	2	>	>	X
ejde-517	222	3	0	0	PUNCT
ejde-517	223	1	for	for	ADP
ejde-517	223	2	all	all	DET
ejde-517	223	3	x	x	SYM
ejde-517	223	4	∈	∈	PROPN
ejde-517	223	5	ω	ω	PROPN
ejde-517	223	6	and	and	CCONJ
ejde-517	223	7	η	η	PROPN
ejde-517	223	8	∈	∈	PROPN
ejde-517	223	9	(	(	PUNCT
ejde-517	223	10	0	0	NUM
ejde-517	223	11	,	,	PUNCT
ejde-517	223	12	τ	τ	PROPN
ejde-517	223	13	)	)	PUNCT
ejde-517	223	14	for	for	ADP
ejde-517	223	15	some	some	PRON
ejde-517	223	16	τ	τ	PROPN
ejde-517	223	17	>	>	X
ejde-517	223	18	0	0	PROPN
ejde-517	223	19	.	.	PUNCT
ejde-517	224	1	this	this	PRON
ejde-517	224	2	is	be	AUX
ejde-517	224	3	possible	possible	ADJ
ejde-517	224	4	because	because	SCONJ
ejde-517	224	5	σk(x	σk(x	NOUN
ejde-517	224	6	)	)	PUNCT
ejde-517	224	7	≥	≥	PROPN
ejde-517	224	8	σ	σ	X
ejde-517	224	9	>	>	X
ejde-517	224	10	0	0	NUM
ejde-517	224	11	.	.	PUNCT
ejde-517	225	1	thus	thus	ADV
ejde-517	225	2	,	,	PUNCT
ejde-517	225	3	the	the	DET
ejde-517	225	4	coercivity	coercivity	NOUN
ejde-517	225	5	of	of	ADP
ejde-517	225	6	the	the	DET
ejde-517	225	7	bilinear	bilinear	NOUN
ejde-517	225	8	functional	functional	NOUN
ejde-517	225	9	in	in	ADP
ejde-517	225	10	the	the	DET
ejde-517	225	11	variational	variational	ADJ
ejde-517	225	12	formulations	formulation	NOUN
ejde-517	225	13	of	of	ADP
ejde-517	225	14	both	both	CCONJ
ejde-517	225	15	the	the	DET
ejde-517	225	16	forward	forward	NOUN
ejde-517	225	17	and	and	CCONJ
ejde-517	225	18	the	the	DET
ejde-517	225	19	adjoint	adjoint	NOUN
ejde-517	225	20	problems	problem	NOUN
ejde-517	225	21	is	be	AUX
ejde-517	225	22	guaranteed	guarantee	VERB
ejde-517	225	23	and	and	CCONJ
ejde-517	225	24	the	the	DET
ejde-517	225	25	solvability	solvability	NOUN
ejde-517	225	26	of	of	ADP
ejde-517	225	27	these	these	DET
ejde-517	225	28	problems	problem	NOUN
ejde-517	225	29	is	be	AUX
ejde-517	225	30	assured	assure	VERB
ejde-517	225	31	.	.	PUNCT
ejde-517	226	1	consequently	consequently	ADV
ejde-517	226	2	,	,	PUNCT
ejde-517	226	3	by	by	ADP
ejde-517	226	4	(	(	PUNCT
ejde-517	226	5	3.3	3.3	NUM
ejde-517	226	6	)	)	PUNCT
ejde-517	226	7	and	and	CCONJ
ejde-517	226	8	(	(	PUNCT
ejde-517	226	9	3.5	3.5	NUM
ejde-517	226	10	)	)	PUNCT
ejde-517	226	11	there	there	PRON
ejde-517	226	12	exist	exist	VERB
ejde-517	226	13	c1	c1	NOUN
ejde-517	226	14	,	,	PUNCT
ejde-517	226	15	c2	c2	PROPN
ejde-517	226	16	>	>	X
ejde-517	226	17	0	0	NUM
ejde-517	227	1	such	such	ADJ
ejde-517	227	2	that	that	SCONJ
ejde-517	227	3	‖φ(σk	‖φ(σk	PROPN
ejde-517	227	4	+	+	PROPN
ejde-517	227	5	ηδσk)‖h1(ω	ηδσk)‖h1(ω	NOUN
ejde-517	227	6	)	)	PUNCT
ejde-517	227	7	≤	≤	NUM
ejde-517	227	8	c1‖f‖l̃2(∂ω	c1‖f‖l̃2(∂ω	NOUN
ejde-517	227	9	)	)	PUNCT
ejde-517	227	10	,	,	PUNCT
ejde-517	227	11	(	(	PUNCT
ejde-517	227	12	3.6	3.6	NUM
ejde-517	227	13	)	)	PUNCT
ejde-517	227	14	‖φ∗(σk	‖φ∗(σk	PROPN
ejde-517	227	15	+	+	X
ejde-517	227	16	ηδσk)‖h1(ω	ηδσk)‖h1(ω	NOUN
ejde-517	227	17	)	)	PUNCT
ejde-517	227	18	≤	≤	NOUN
ejde-517	227	19	c2(‖f‖l̃2(∂ω	c2(‖f‖l̃2(∂ω	NOUN
ejde-517	227	20	)	)	PUNCT
ejde-517	228	1	+	+	NUM
ejde-517	228	2	‖ṽ	‖ṽ	PUNCT
ejde-517	228	3	‖l̃2(∂ω	‖l̃2(∂ω	X
ejde-517	228	4	)	)	PUNCT
ejde-517	228	5	)	)	PUNCT
ejde-517	228	6	,	,	PUNCT
ejde-517	228	7	(	(	PUNCT
ejde-517	228	8	3.7	3.7	NUM
ejde-517	228	9	)	)	PUNCT
ejde-517	228	10	for	for	ADP
ejde-517	228	11	any	any	DET
ejde-517	228	12	η	η	PROPN
ejde-517	228	13	∈	∈	PROPN
ejde-517	228	14	(	(	PUNCT
ejde-517	228	15	0	0	NUM
ejde-517	228	16	,	,	PUNCT
ejde-517	228	17	τ	τ	PROPN
ejde-517	228	18	)	)	PUNCT
ejde-517	228	19	.	.	PUNCT
ejde-517	229	1	the	the	DET
ejde-517	229	2	result	result	NOUN
ejde-517	229	3	below	below	ADP
ejde-517	229	4	shows	show	VERB
ejde-517	229	5	how	how	SCONJ
ejde-517	229	6	a	a	DET
ejde-517	229	7	perturbation	perturbation	NOUN
ejde-517	229	8	δσk	δσk	NOUN
ejde-517	229	9	affects	affect	VERB
ejde-517	229	10	φ	φ	PROPN
ejde-517	229	11	and	and	CCONJ
ejde-517	229	12	φ∗.	φ∗.	NOUN
ejde-517	229	13	theorem	theorem	VERB
ejde-517	229	14	3.5	3.5	NUM
ejde-517	229	15	.	.	PUNCT
ejde-517	230	1	let	let	VERB
ejde-517	230	2	σk	σk	VERB
ejde-517	230	3	,	,	PUNCT
ejde-517	230	4	δσk	δσk	NOUN
ejde-517	230	5	∈	∈	PROPN
ejde-517	230	6	l∞(ω	l∞(ω	NOUN
ejde-517	230	7	)	)	PUNCT
ejde-517	230	8	.	.	PUNCT
ejde-517	231	1	then	then	ADV
ejde-517	231	2	there	there	PRON
ejde-517	231	3	exist	exist	VERB
ejde-517	231	4	c1	c1	NOUN
ejde-517	231	5	,	,	PUNCT
ejde-517	231	6	c2	c2	PROPN
ejde-517	231	7	>	>	X
ejde-517	231	8	0	0	NUM
ejde-517	232	1	such	such	ADJ
ejde-517	232	2	that	that	SCONJ
ejde-517	232	3	‖φ(σk	‖φ(σk	PROPN
ejde-517	232	4	+	+	CCONJ
ejde-517	232	5	ηδσk)−	ηδσk)−	PROPN
ejde-517	232	6	φ(σk)‖h1(ω	φ(σk)‖h1(ω	X
ejde-517	232	7	)	)	PUNCT
ejde-517	232	8	≤	≤	NUM
ejde-517	232	9	c1η‖δσk‖l∞(ω	c1η‖δσk‖l∞(ω	PROPN
ejde-517	232	10	)	)	PUNCT
ejde-517	232	11	,	,	PUNCT
ejde-517	232	12	(	(	PUNCT
ejde-517	232	13	3.8	3.8	NUM
ejde-517	232	14	)	)	PUNCT
ejde-517	232	15	‖φ∗(σk	‖φ∗(σk	NUM
ejde-517	232	16	+	+	CCONJ
ejde-517	232	17	ηδσk)−	ηδσk)−	PROPN
ejde-517	232	18	φ∗(σk)‖h1(ω	φ∗(σk)‖h1(ω	NUM
ejde-517	232	19	)	)	PUNCT
ejde-517	232	20	≤	≤	NOUN
ejde-517	232	21	c2η‖δσk‖l∞(ω	c2η‖δσk‖l∞(ω	NOUN
ejde-517	232	22	)	)	PUNCT
ejde-517	232	23	,	,	PUNCT
ejde-517	232	24	(	(	PUNCT
ejde-517	232	25	3.9	3.9	NUM
ejde-517	232	26	)	)	PUNCT
ejde-517	232	27	for	for	ADP
ejde-517	232	28	any	any	DET
ejde-517	232	29	η	η	PROPN
ejde-517	232	30	∈	∈	PROPN
ejde-517	232	31	(	(	PUNCT
ejde-517	232	32	0	0	NUM
ejde-517	232	33	,	,	PUNCT
ejde-517	232	34	τ	τ	PROPN
ejde-517	232	35	)	)	PUNCT
ejde-517	232	36	,	,	PUNCT
ejde-517	232	37	where	where	SCONJ
ejde-517	232	38	τ	τ	PROPN
ejde-517	232	39	is	be	AUX
ejde-517	232	40	chosen	choose	VERB
ejde-517	232	41	according	accord	VERB
ejde-517	232	42	to	to	PART
ejde-517	232	43	remark	remark	NOUN
ejde-517	232	44	3.4	3.4	NUM
ejde-517	232	45	.	.	NOUN
ejde-517	232	46	8	8	NUM
ejde-517	232	47	r.	r.	PROPN
ejde-517	232	48	mendoza	mendoza	PROPN
ejde-517	232	49	,	,	PUNCT
ejde-517	232	50	s.	s.	PROPN
ejde-517	232	51	keeling	keeling	PROPN
ejde-517	232	52	ejde-2020/93	ejde-2020/93	PROPN
ejde-517	232	53	proof	proof	PROPN
ejde-517	232	54	.	.	PUNCT
ejde-517	233	1	from	from	ADP
ejde-517	233	2	(	(	PUNCT
ejde-517	233	3	3.1	3.1	NUM
ejde-517	233	4	)	)	PUNCT
ejde-517	233	5	,	,	PUNCT
ejde-517	233	6	we	we	PRON
ejde-517	233	7	have∫	have∫	VERB
ejde-517	233	8	ω	ω	NUM
ejde-517	233	9	σk∇φ(σk	σk∇φ(σk	PROPN
ejde-517	233	10	)	)	PUNCT
ejde-517	233	11	·	·	PUNCT
ejde-517	234	1	∇v	∇v	ADJ
ejde-517	234	2	dv	dv	PROPN
ejde-517	234	3	=	=	SYM
ejde-517	234	4	∫	∫	PROPN
ejde-517	234	5	ω	ω	PROPN
ejde-517	234	6	fv	fv	PROPN
ejde-517	234	7	dv	dv	PROPN
ejde-517	234	8	.	.	PROPN
ejde-517	235	1	(	(	PUNCT
ejde-517	235	2	3.10	3.10	NUM
ejde-517	235	3	)	)	PUNCT
ejde-517	235	4	similarly	similarly	ADV
ejde-517	235	5	,	,	PUNCT
ejde-517	235	6	for	for	ADP
ejde-517	235	7	σk	σk	ADV
ejde-517	235	8	+	+	PUNCT
ejde-517	235	9	ηδσk,∫	ηδσk,∫	ADV
ejde-517	235	10	ω	ω	NOUN
ejde-517	235	11	(	(	PUNCT
ejde-517	235	12	σk	σk	PROPN
ejde-517	235	13	+	+	X
ejde-517	235	14	ηδσk)∇(φ(σk	ηδσk)∇(φ(σk	NOUN
ejde-517	235	15	)	)	PUNCT
ejde-517	236	1	+	+	SYM
ejde-517	236	2	δφ	δφ	NOUN
ejde-517	236	3	)	)	PUNCT
ejde-517	236	4	·	·	PUNCT
ejde-517	237	1	∇v	∇v	ADJ
ejde-517	237	2	dv	dv	PROPN
ejde-517	237	3	=	=	SYM
ejde-517	237	4	∫	∫	PROPN
ejde-517	237	5	ω	ω	PROPN
ejde-517	237	6	fv	fv	PROPN
ejde-517	237	7	dv	dv	PROPN
ejde-517	237	8	,	,	PUNCT
ejde-517	237	9	(	(	PUNCT
ejde-517	237	10	3.11	3.11	NUM
ejde-517	237	11	)	)	PUNCT
ejde-517	237	12	where	where	SCONJ
ejde-517	237	13	we	we	PRON
ejde-517	237	14	denote	denote	VERB
ejde-517	237	15	δφ	δφ	ADV
ejde-517	237	16	:	:	PUNCT
ejde-517	237	17	=	=	SYM
ejde-517	237	18	φ(σk	φ(σk	NOUN
ejde-517	237	19	+	+	CCONJ
ejde-517	237	20	ηδσk)−	ηδσk)−	NUM
ejde-517	237	21	φ(σk	φ(σk	NOUN
ejde-517	237	22	)	)	PUNCT
ejde-517	237	23	.	.	PUNCT
ejde-517	238	1	subtracting	subtract	VERB
ejde-517	238	2	(	(	PUNCT
ejde-517	238	3	3.10	3.10	NUM
ejde-517	238	4	)	)	PUNCT
ejde-517	238	5	from	from	ADP
ejde-517	238	6	(	(	PUNCT
ejde-517	238	7	3.11	3.11	NUM
ejde-517	238	8	)	)	PUNCT
ejde-517	238	9	,	,	PUNCT
ejde-517	238	10	we	we	PRON
ejde-517	238	11	obtain	obtain	VERB
ejde-517	238	12	∫	∫	PROPN
ejde-517	238	13	ω	ω	PROPN
ejde-517	238	14	σk∇δφ	σk∇δφ	PROPN
ejde-517	238	15	·	·	PUNCT
ejde-517	239	1	∇v	∇v	ADJ
ejde-517	239	2	dv	dv	PROPN
ejde-517	239	3	=	=	PUNCT
ejde-517	240	1	−	−	PROPN
ejde-517	240	2	∫	∫	PROPN
ejde-517	240	3	ω	ω	PROPN
ejde-517	240	4	ηδσk∇φ(σk	ηδσk∇φ(σk	PROPN
ejde-517	240	5	+	+	CCONJ
ejde-517	240	6	ηδσk	ηδσk	NOUN
ejde-517	240	7	)	)	PUNCT
ejde-517	240	8	·	·	PUNCT
ejde-517	241	1	∇v	∇v	PROPN
ejde-517	241	2	dv	dv	PROPN
ejde-517	241	3	.	.	PUNCT
ejde-517	242	1	(	(	PUNCT
ejde-517	242	2	3.12	3.12	NUM
ejde-517	242	3	)	)	PUNCT
ejde-517	242	4	we	we	PRON
ejde-517	242	5	define	define	VERB
ejde-517	242	6	a(u	a(u	PROPN
ejde-517	242	7	,	,	PUNCT
ejde-517	242	8	v	v	NOUN
ejde-517	242	9	)	)	PUNCT
ejde-517	242	10	:	:	PUNCT
ejde-517	243	1	=	=	SYM
ejde-517	243	2	∫	∫	PROPN
ejde-517	244	1	ω	ω	PROPN
ejde-517	244	2	σk∇u·∇v	σk∇u·∇v	PROPN
ejde-517	244	3	dv	dv	PROPN
ejde-517	244	4	and	and	CCONJ
ejde-517	244	5	b1(v	b1(v	PROPN
ejde-517	244	6	)	)	PUNCT
ejde-517	244	7	:	:	PUNCT
ejde-517	244	8	=	=	PUNCT
ejde-517	245	1	−	−	PROPN
ejde-517	245	2	∫	∫	PROPN
ejde-517	245	3	ω	ω	PROPN
ejde-517	245	4	ηδσk∇φ(σk+ηδσk)·∇v	ηδσk∇φ(σk+ηδσk)·∇v	PROPN
ejde-517	245	5	dv	dv	PROPN
ejde-517	245	6	.	.	PUNCT
ejde-517	246	1	clearly	clearly	ADV
ejde-517	246	2	,	,	PUNCT
ejde-517	246	3	a	a	PRON
ejde-517	246	4	and	and	CCONJ
ejde-517	246	5	b1	b1	NOUN
ejde-517	246	6	are	be	AUX
ejde-517	246	7	bilinear	bilinear	ADJ
ejde-517	246	8	and	and	CCONJ
ejde-517	246	9	linear	linear	ADJ
ejde-517	246	10	,	,	PUNCT
ejde-517	246	11	respectively	respectively	ADV
ejde-517	246	12	.	.	PUNCT
ejde-517	247	1	recall	recall	PROPN
ejde-517	247	2	from	from	ADP
ejde-517	247	3	theorem	theorem	NOUN
ejde-517	247	4	(	(	PUNCT
ejde-517	247	5	3.1	3.1	NUM
ejde-517	247	6	)	)	PUNCT
ejde-517	247	7	that	that	SCONJ
ejde-517	247	8	for	for	ADP
ejde-517	247	9	any	any	DET
ejde-517	247	10	u	u	NOUN
ejde-517	247	11	,	,	PUNCT
ejde-517	247	12	v	v	NOUN
ejde-517	247	13	∈	∈	PROPN
ejde-517	247	14	i	i	PRON
ejde-517	247	15	,	,	PUNCT
ejde-517	247	16	a(u	a(u	PROPN
ejde-517	247	17	,	,	PUNCT
ejde-517	247	18	v	v	NOUN
ejde-517	247	19	)	)	PUNCT
ejde-517	247	20	is	be	AUX
ejde-517	247	21	coercive	coercive	ADJ
ejde-517	247	22	and	and	CCONJ
ejde-517	247	23	continuous	continuous	ADJ
ejde-517	247	24	.	.	PUNCT
ejde-517	248	1	by	by	ADP
ejde-517	248	2	the	the	DET
ejde-517	248	3	cauchy	cauchy	PROPN
ejde-517	248	4	-	-	PUNCT
ejde-517	248	5	schwarz	schwarz	PROPN
ejde-517	248	6	inequality	inequality	NOUN
ejde-517	248	7	and	and	CCONJ
ejde-517	248	8	(	(	PUNCT
ejde-517	248	9	3.6	3.6	NUM
ejde-517	248	10	)	)	PUNCT
ejde-517	248	11	,	,	PUNCT
ejde-517	248	12	b1	b1	PROPN
ejde-517	248	13	is	be	AUX
ejde-517	248	14	bounded	bound	VERB
ejde-517	248	15	.	.	PUNCT
ejde-517	249	1	thus	thus	ADV
ejde-517	249	2	,	,	PUNCT
ejde-517	249	3	if	if	SCONJ
ejde-517	249	4	we	we	PRON
ejde-517	249	5	take	take	VERB
ejde-517	249	6	u	u	NOUN
ejde-517	249	7	=	=	X
ejde-517	249	8	v	v	NOUN
ejde-517	249	9	=	=	SYM
ejde-517	249	10	δφ	δφ	NOUN
ejde-517	249	11	,	,	PUNCT
ejde-517	249	12	use	use	VERB
ejde-517	249	13	the	the	DET
ejde-517	249	14	previous	previous	ADJ
ejde-517	249	15	inequality	inequality	NOUN
ejde-517	249	16	,	,	PUNCT
ejde-517	249	17	and	and	CCONJ
ejde-517	249	18	the	the	DET
ejde-517	249	19	coercivity	coercivity	NOUN
ejde-517	249	20	of	of	ADP
ejde-517	249	21	a(u	a(u	PROPN
ejde-517	249	22	,	,	PUNCT
ejde-517	249	23	v	v	NOUN
ejde-517	249	24	)	)	PUNCT
ejde-517	249	25	we	we	PRON
ejde-517	249	26	obtain	obtain	VERB
ejde-517	249	27	‖δφ‖h1(ω	‖δφ‖h1(ω	NUM
ejde-517	249	28	)	)	PUNCT
ejde-517	249	29	≤	≤	NUM
ejde-517	249	30	1	1	NUM
ejde-517	249	31	c̄	c̄	PROPN
ejde-517	249	32	c̄1η‖f‖l̃2(∂ω)‖δσ	c̄1η‖f‖l̃2(∂ω)‖δσ	ADJ
ejde-517	249	33	k‖l∞(ω	k‖l∞(ω	NOUN
ejde-517	249	34	)	)	PUNCT
ejde-517	249	35	,	,	PUNCT
ejde-517	249	36	(	(	PUNCT
ejde-517	249	37	3.13	3.13	NUM
ejde-517	249	38	)	)	PUNCT
ejde-517	249	39	where	where	SCONJ
ejde-517	249	40	c̄	c̄	PROPN
ejde-517	249	41	>	>	SYM
ejde-517	249	42	0	0	NUM
ejde-517	249	43	is	be	AUX
ejde-517	249	44	the	the	DET
ejde-517	249	45	coercivity	coercivity	NOUN
ejde-517	249	46	constant	constant	ADJ
ejde-517	249	47	and	and	CCONJ
ejde-517	249	48	c̄1	c̄1	X
ejde-517	249	49	is	be	AUX
ejde-517	249	50	the	the	DET
ejde-517	249	51	constant	constant	ADJ
ejde-517	249	52	from	from	ADP
ejde-517	249	53	(	(	PUNCT
ejde-517	249	54	3.6	3.6	NUM
ejde-517	249	55	)	)	PUNCT
ejde-517	249	56	.	.	PUNCT
ejde-517	250	1	this	this	PRON
ejde-517	250	2	proves	prove	VERB
ejde-517	250	3	the	the	DET
ejde-517	250	4	first	first	ADJ
ejde-517	250	5	inequality	inequality	NOUN
ejde-517	250	6	.	.	PUNCT
ejde-517	251	1	using	use	VERB
ejde-517	251	2	similar	similar	ADJ
ejde-517	251	3	arguments	argument	NOUN
ejde-517	251	4	,	,	PUNCT
ejde-517	251	5	one	one	PRON
ejde-517	251	6	can	can	AUX
ejde-517	251	7	show	show	VERB
ejde-517	251	8	(	(	PUNCT
ejde-517	251	9	3.9	3.9	NUM
ejde-517	251	10	)	)	PUNCT
ejde-517	251	11	.	.	PUNCT
ejde-517	252	1	�	�	PROPN
ejde-517	252	2	definition	definition	NOUN
ejde-517	252	3	3.6	3.6	NUM
ejde-517	252	4	.	.	PUNCT
ejde-517	253	1	recall	recall	VERB
ejde-517	253	2	that	that	PRON
ejde-517	253	3	from	from	ADP
ejde-517	253	4	(	(	PUNCT
ejde-517	253	5	2.8	2.8	NUM
ejde-517	253	6	)	)	PUNCT
ejde-517	253	7	,	,	PUNCT
ejde-517	253	8	σk(χ1	σk(χ1	NUM
ejde-517	253	9	)	)	PUNCT
ejde-517	253	10	:	:	PUNCT
ejde-517	254	1	=	=	PUNCT
ejde-517	254	2	σk1χ1	σk1χ1	VERB
ejde-517	254	3	+	+	ADJ
ejde-517	254	4	σ2(1−χ1	σ2(1−χ1	NOUN
ejde-517	254	5	)	)	PUNCT
ejde-517	254	6	=	=	SYM
ejde-517	255	1	σk	σk	PROPN
ejde-517	255	2	.	.	PUNCT
ejde-517	256	1	therefore	therefore	ADV
ejde-517	256	2	,	,	PUNCT
ejde-517	256	3	φ	φ	PROPN
ejde-517	256	4	and	and	CCONJ
ejde-517	256	5	φ∗	φ∗	NOUN
ejde-517	256	6	depend	depend	VERB
ejde-517	256	7	on	on	ADP
ejde-517	256	8	χ1	χ1	NOUN
ejde-517	256	9	for	for	ADP
ejde-517	256	10	a	a	DET
ejde-517	256	11	fixed	fix	VERB
ejde-517	256	12	σk1	σk1	NOUN
ejde-517	256	13	.	.	PUNCT
ejde-517	257	1	hence	hence	ADV
ejde-517	257	2	,	,	PUNCT
ejde-517	257	3	for	for	ADP
ejde-517	257	4	brevity	brevity	NOUN
ejde-517	257	5	we	we	PRON
ejde-517	257	6	denote	denote	VERB
ejde-517	257	7	φ(χ1	φ(χ1	VERB
ejde-517	257	8	)	)	PUNCT
ejde-517	257	9	:	:	PUNCT
ejde-517	258	1	=	=	NOUN
ejde-517	258	2	φ(σk(χ1	φ(σk(χ1	ADJ
ejde-517	258	3	)	)	PUNCT
ejde-517	258	4	)	)	PUNCT
ejde-517	258	5	and	and	CCONJ
ejde-517	258	6	φ∗(χ1	φ∗(χ1	NOUN
ejde-517	258	7	)	)	PUNCT
ejde-517	258	8	:	:	PUNCT
ejde-517	258	9	=	=	PUNCT
ejde-517	258	10	φ∗(σk(χ1	φ∗(σk(χ1	VERB
ejde-517	258	11	)	)	PUNCT
ejde-517	258	12	)	)	PUNCT
ejde-517	258	13	.	.	PUNCT
ejde-517	259	1	(	(	PUNCT
ejde-517	259	2	3.14	3.14	NUM
ejde-517	259	3	)	)	PUNCT
ejde-517	259	4	from	from	ADP
ejde-517	259	5	here	here	ADV
ejde-517	259	6	onwards	onward	NOUN
ejde-517	259	7	,	,	PUNCT
ejde-517	259	8	it	it	PRON
ejde-517	259	9	is	be	AUX
ejde-517	259	10	assumed	assume	VERB
ejde-517	259	11	that	that	SCONJ
ejde-517	259	12	φ	φ	PROPN
ejde-517	259	13	and	and	CCONJ
ejde-517	259	14	φ∗	φ∗	NOUN
ejde-517	259	15	are	be	AUX
ejde-517	259	16	solved	solve	VERB
ejde-517	259	17	using	use	VERB
ejde-517	259	18	σk1χ1	σk1χ1	PROPN
ejde-517	259	19	+	+	ADJ
ejde-517	259	20	σ2(1−χ1	σ2(1−χ1	NOUN
ejde-517	259	21	)	)	PUNCT
ejde-517	259	22	.	.	PUNCT
ejde-517	260	1	we	we	PRON
ejde-517	260	2	now	now	ADV
ejde-517	260	3	show	show	VERB
ejde-517	260	4	that	that	SCONJ
ejde-517	260	5	φ	φ	PROPN
ejde-517	260	6	and	and	CCONJ
ejde-517	260	7	φ∗	φ∗	NOUN
ejde-517	260	8	depend	depend	VERB
ejde-517	260	9	continuously	continuously	ADV
ejde-517	260	10	on	on	ADP
ejde-517	260	11	χ1	χ1	NOUN
ejde-517	260	12	.	.	PUNCT
ejde-517	261	1	corollary	corollary	ADJ
ejde-517	261	2	3.7	3.7	NUM
ejde-517	261	3	.	.	PUNCT
ejde-517	262	1	let	let	VERB
ejde-517	262	2	χ1	χ1	NOUN
ejde-517	262	3	∈	∈	NOUN
ejde-517	262	4	l∞(ω	l∞(ω	NOUN
ejde-517	262	5	)	)	PUNCT
ejde-517	262	6	,	,	PUNCT
ejde-517	262	7	then	then	ADV
ejde-517	262	8	∃c̄1	∃c̄1	PROPN
ejde-517	262	9	,	,	PUNCT
ejde-517	262	10	c̄2	c̄2	X
ejde-517	262	11	>	>	X
ejde-517	262	12	0	0	NUM
ejde-517	263	1	such	such	ADJ
ejde-517	263	2	that	that	SCONJ
ejde-517	263	3	‖φ(χ1	‖φ(χ1	ADJ
ejde-517	263	4	+	+	PROPN
ejde-517	263	5	ηδχ1)−	ηδχ1)−	PROPN
ejde-517	263	6	φ(χ1)‖h1(ω	φ(χ1)‖h1(ω	NOUN
ejde-517	263	7	)	)	PUNCT
ejde-517	263	8	≤	≤	NUM
ejde-517	263	9	c̄1η‖δχ1‖l∞(ω	c̄1η‖δχ1‖l∞(ω	NOUN
ejde-517	263	10	)	)	PUNCT
ejde-517	263	11	,	,	PUNCT
ejde-517	263	12	(	(	PUNCT
ejde-517	263	13	3.15	3.15	NUM
ejde-517	263	14	)	)	PUNCT
ejde-517	263	15	‖φ∗(χ1	‖φ∗(χ1	NOUN
ejde-517	264	1	+	+	CCONJ
ejde-517	264	2	ηδχ1)−	ηδχ1)−	ADJ
ejde-517	264	3	φ∗(χ1)‖h1(ω	φ∗(χ1)‖h1(ω	NOUN
ejde-517	264	4	)	)	PUNCT
ejde-517	264	5	≤	≤	NUM
ejde-517	264	6	c̄2η‖δχ1‖l∞(ω	c̄2η‖δχ1‖l∞(ω	NOUN
ejde-517	264	7	)	)	PUNCT
ejde-517	264	8	,	,	PUNCT
ejde-517	264	9	(	(	PUNCT
ejde-517	264	10	3.16	3.16	NUM
ejde-517	264	11	)	)	PUNCT
ejde-517	264	12	for	for	ADP
ejde-517	264	13	any	any	DET
ejde-517	264	14	η	η	PROPN
ejde-517	264	15	∈	∈	PROPN
ejde-517	264	16	(	(	PUNCT
ejde-517	264	17	0	0	NUM
ejde-517	264	18	,	,	PUNCT
ejde-517	264	19	τ	τ	PROPN
ejde-517	264	20	)	)	PUNCT
ejde-517	264	21	,	,	PUNCT
ejde-517	264	22	where	where	SCONJ
ejde-517	264	23	τ	τ	PROPN
ejde-517	264	24	is	be	AUX
ejde-517	264	25	chosen	choose	VERB
ejde-517	264	26	according	accord	VERB
ejde-517	264	27	to	to	PART
ejde-517	264	28	remark	remark	NOUN
ejde-517	264	29	3.4	3.4	NUM
ejde-517	264	30	.	.	PUNCT
ejde-517	265	1	proof	proof	NOUN
ejde-517	265	2	.	.	PUNCT
ejde-517	266	1	we	we	PRON
ejde-517	266	2	use	use	VERB
ejde-517	266	3	the	the	DET
ejde-517	266	4	decomposition	decomposition	NOUN
ejde-517	266	5	σk(χ1	σk(χ1	PUNCT
ejde-517	266	6	)	)	PUNCT
ejde-517	266	7	=	=	PUNCT
ejde-517	267	1	σk1χ1	σk1χ1	PROPN
ejde-517	267	2	+	+	NUM
ejde-517	267	3	σ2(1−	σ2(1−	NOUN
ejde-517	267	4	χ1	χ1	NOUN
ejde-517	267	5	)	)	PUNCT
ejde-517	267	6	.	.	PUNCT
ejde-517	268	1	(	(	PUNCT
ejde-517	268	2	3.17	3.17	NUM
ejde-517	268	3	)	)	PUNCT
ejde-517	268	4	let	let	VERB
ejde-517	268	5	η	η	PROPN
ejde-517	268	6	∈	∈	PROPN
ejde-517	268	7	(	(	PUNCT
ejde-517	268	8	0	0	NUM
ejde-517	268	9	,	,	PUNCT
ejde-517	268	10	τ	τ	PROPN
ejde-517	268	11	)	)	PUNCT
ejde-517	268	12	.	.	PUNCT
ejde-517	269	1	if	if	SCONJ
ejde-517	269	2	we	we	PRON
ejde-517	269	3	use	use	VERB
ejde-517	269	4	χ1	χ1	NOUN
ejde-517	269	5	+	+	CCONJ
ejde-517	269	6	ηδχ1	ηδχ1	NOUN
ejde-517	269	7	instead	instead	ADV
ejde-517	269	8	of	of	ADP
ejde-517	269	9	χ1	χ1	NOUN
ejde-517	269	10	,	,	PUNCT
ejde-517	269	11	we	we	PRON
ejde-517	269	12	have	have	VERB
ejde-517	269	13	σk(χ1	σk(χ1	NOUN
ejde-517	269	14	)	)	PUNCT
ejde-517	270	1	+	+	NUM
ejde-517	270	2	δσk	δσk	NOUN
ejde-517	270	3	=	=	SYM
ejde-517	270	4	σk(χ1	σk(χ1	X
ejde-517	270	5	)	)	PUNCT
ejde-517	271	1	+	+	CCONJ
ejde-517	271	2	η(σk1	η(σk1	NOUN
ejde-517	271	3	−	−	NOUN
ejde-517	271	4	σ2)δχ1	σ2)δχ1	NOUN
ejde-517	271	5	,	,	PUNCT
ejde-517	271	6	(	(	PUNCT
ejde-517	271	7	3.18	3.18	NUM
ejde-517	271	8	)	)	PUNCT
ejde-517	271	9	where	where	SCONJ
ejde-517	271	10	δσk	δσk	NOUN
ejde-517	271	11	is	be	AUX
ejde-517	271	12	the	the	DET
ejde-517	271	13	associated	associated	ADJ
ejde-517	271	14	change	change	NOUN
ejde-517	271	15	in	in	ADP
ejde-517	271	16	σk	σk	ADV
ejde-517	271	17	given	give	VERB
ejde-517	271	18	a	a	DET
ejde-517	271	19	ηδχ1	ηδχ1	NOUN
ejde-517	271	20	perturbation	perturbation	NOUN
ejde-517	271	21	of	of	ADP
ejde-517	271	22	χ1	χ1	NOUN
ejde-517	271	23	.	.	PUNCT
ejde-517	272	1	subtracting	subtract	VERB
ejde-517	272	2	(	(	PUNCT
ejde-517	272	3	3.17	3.17	NUM
ejde-517	272	4	)	)	PUNCT
ejde-517	272	5	from	from	ADP
ejde-517	272	6	(	(	PUNCT
ejde-517	272	7	3.18	3.18	NUM
ejde-517	272	8	)	)	PUNCT
ejde-517	272	9	,	,	PUNCT
ejde-517	272	10	we	we	PRON
ejde-517	272	11	obtain	obtain	VERB
ejde-517	272	12	δσk	δσk	NOUN
ejde-517	272	13	=	=	SYM
ejde-517	272	14	η(σk1	η(σk1	NOUN
ejde-517	272	15	−	−	NOUN
ejde-517	272	16	σ2)δχ1	σ2)δχ1	NOUN
ejde-517	272	17	.	.	PUNCT
ejde-517	273	1	(	(	PUNCT
ejde-517	273	2	3.19	3.19	NUM
ejde-517	273	3	)	)	PUNCT
ejde-517	273	4	the	the	DET
ejde-517	273	5	inequalities	inequality	NOUN
ejde-517	273	6	we	we	PRON
ejde-517	273	7	need	need	VERB
ejde-517	273	8	to	to	PART
ejde-517	273	9	show	show	VERB
ejde-517	273	10	directly	directly	ADV
ejde-517	273	11	follow	follow	VERB
ejde-517	273	12	from	from	ADP
ejde-517	273	13	theorem	theorem	NOUN
ejde-517	273	14	(	(	PUNCT
ejde-517	273	15	3.5	3.5	NUM
ejde-517	273	16	)	)	PUNCT
ejde-517	273	17	and	and	CCONJ
ejde-517	273	18	‖δσk‖l∞(ω	‖δσk‖l∞(ω	NOUN
ejde-517	273	19	)	)	PUNCT
ejde-517	273	20	≤	≤	NOUN
ejde-517	273	21	η‖σk1	η‖σk1	ADP
ejde-517	273	22	−	−	PROPN
ejde-517	273	23	σ2‖l∞(ω)‖δχ1‖l∞(ω	σ2‖l∞(ω)‖δχ1‖l∞(ω	NUM
ejde-517	273	24	)	)	PUNCT
ejde-517	273	25	.	.	PUNCT
ejde-517	274	1	�	�	PROPN
ejde-517	274	2	ejde-2020/93	ejde-2020/93	PROPN
ejde-517	274	3	impedance	impedance	NOUN
ejde-517	274	4	tomography	tomography	NOUN
ejde-517	274	5	problem	problem	NOUN
ejde-517	274	6	9	9	NUM
ejde-517	274	7	3.2	3.2	NUM
ejde-517	274	8	.	.	PUNCT
ejde-517	275	1	smooth	smooth	ADJ
ejde-517	275	2	approximation	approximation	NOUN
ejde-517	275	3	of	of	ADP
ejde-517	275	4	χ1	χ1	NOUN
ejde-517	275	5	.	.	PUNCT
ejde-517	276	1	from	from	ADP
ejde-517	276	2	(	(	PUNCT
ejde-517	276	3	2.7	2.7	NUM
ejde-517	276	4	)	)	PUNCT
ejde-517	276	5	,	,	PUNCT
ejde-517	276	6	the	the	DET
ejde-517	276	7	quantity	quantity	NOUN
ejde-517	276	8	σk+1	σk+1	X
ejde-517	276	9	1	1	NUM
ejde-517	276	10	:	:	PUNCT
ejde-517	276	11	=	=	SYM
ejde-517	276	12	σ1(χ1	σ1(χ1	NOUN
ejde-517	276	13	)	)	PUNCT
ejde-517	276	14	can	can	AUX
ejde-517	276	15	be	be	AUX
ejde-517	276	16	obtained	obtain	VERB
ejde-517	276	17	via∫	via∫	PROPN
ejde-517	276	18	ω	ω	NOUN
ejde-517	276	19	α(χ1	α(χ1	ADJ
ejde-517	276	20	+	+	CCONJ
ejde-517	276	21	ε)∇σk+1	ε)∇σk+1	PROPN
ejde-517	276	22	1	1	NUM
ejde-517	276	23	·	·	PUNCT
ejde-517	276	24	∇v	∇v	ADJ
ejde-517	276	25	dv	dv	PROPN
ejde-517	276	26	+	+	CCONJ
ejde-517	276	27	∫	∫	PROPN
ejde-517	276	28	ω	ω	X
ejde-517	276	29	λ(σk+1	λ(σk+1	SYM
ejde-517	276	30	1	1	NUM
ejde-517	276	31	−	−	NOUN
ejde-517	276	32	σk1	σk1	NOUN
ejde-517	276	33	)	)	PUNCT
ejde-517	276	34	v	v	NOUN
ejde-517	276	35	dv	dv	PROPN
ejde-517	276	36	=	=	SYM
ejde-517	276	37	∫	∫	PROPN
ejde-517	276	38	ω	ω	PROPN
ejde-517	276	39	χ1∇φ(χ1	χ1∇φ(χ1	X
ejde-517	276	40	)	)	PUNCT
ejde-517	276	41	·	·	PUNCT
ejde-517	277	1	∇φ∗(χ1)v	∇φ∗(χ1)v	PROPN
ejde-517	277	2	dv	dv	PROPN
ejde-517	277	3	.	.	PROPN
ejde-517	278	1	(	(	PUNCT
ejde-517	278	2	3.20	3.20	NUM
ejde-517	278	3	)	)	PUNCT
ejde-517	278	4	this	this	DET
ejde-517	278	5	equation	equation	NOUN
ejde-517	278	6	can	can	AUX
ejde-517	278	7	be	be	AUX
ejde-517	278	8	interpreted	interpret	VERB
ejde-517	278	9	as	as	ADP
ejde-517	278	10	a(σk+1	a(σk+1	NOUN
ejde-517	278	11	1	1	NUM
ejde-517	278	12	,	,	PUNCT
ejde-517	278	13	v	v	NOUN
ejde-517	278	14	)	)	PUNCT
ejde-517	278	15	=	=	SYM
ejde-517	278	16	b(v	b(v	NOUN
ejde-517	278	17	)	)	PUNCT
ejde-517	278	18	,	,	PUNCT
ejde-517	278	19	∀v	∀v	PROPN
ejde-517	278	20	∈	∈	PROPN
ejde-517	278	21	h1(ω	h1(ω	PROPN
ejde-517	278	22	)	)	PUNCT
ejde-517	278	23	,	,	PUNCT
ejde-517	278	24	(	(	PUNCT
ejde-517	278	25	3.21	3.21	NUM
ejde-517	278	26	)	)	PUNCT
ejde-517	278	27	where	where	SCONJ
ejde-517	278	28	a(σk+1	a(σk+1	VERB
ejde-517	278	29	1	1	NUM
ejde-517	278	30	,	,	PUNCT
ejde-517	278	31	v	v	NOUN
ejde-517	278	32	)	)	PUNCT
ejde-517	278	33	:	:	PUNCT
ejde-517	279	1	=	=	SYM
ejde-517	279	2	∫	∫	PROPN
ejde-517	279	3	ω	ω	PROPN
ejde-517	279	4	α(χ1	α(χ1	NOUN
ejde-517	279	5	+	+	CCONJ
ejde-517	279	6	ε)∇σk+1	ε)∇σk+1	PROPN
ejde-517	279	7	1	1	NUM
ejde-517	279	8	·	·	PUNCT
ejde-517	279	9	∇v	∇v	ADJ
ejde-517	279	10	dv	dv	PROPN
ejde-517	280	1	+	+	CCONJ
ejde-517	280	2	∫	∫	PROPN
ejde-517	280	3	ω	ω	X
ejde-517	280	4	λσk+1	λσk+1	X
ejde-517	280	5	1	1	NUM
ejde-517	280	6	v	v	ADP
ejde-517	280	7	dv	dv	PROPN
ejde-517	280	8	,	,	PUNCT
ejde-517	280	9	b(v	b(v	NOUN
ejde-517	280	10	)	)	PUNCT
ejde-517	280	11	:	:	PUNCT
ejde-517	281	1	=	=	SYM
ejde-517	281	2	∫	∫	PROPN
ejde-517	282	1	ω	ω	NUM
ejde-517	282	2	λσk1v	λσk1v	PROPN
ejde-517	283	1	dv	dv	PROPN
ejde-517	283	2	+	+	PROPN
ejde-517	283	3	∫	∫	PROPN
ejde-517	283	4	ω	ω	NUM
ejde-517	283	5	χ1∇φ(χ1	χ1∇φ(χ1	X
ejde-517	283	6	)	)	PUNCT
ejde-517	283	7	·	·	PUNCT
ejde-517	284	1	∇φ∗(χ1)v	∇φ∗(χ1)v	PROPN
ejde-517	284	2	dv	dv	PROPN
ejde-517	284	3	.	.	PROPN
ejde-517	284	4	to	to	PART
ejde-517	284	5	guarantee	guarantee	VERB
ejde-517	284	6	solvability	solvability	NOUN
ejde-517	284	7	of	of	ADP
ejde-517	284	8	(	(	PUNCT
ejde-517	284	9	3.21	3.21	NUM
ejde-517	284	10	)	)	PUNCT
ejde-517	284	11	,	,	PUNCT
ejde-517	284	12	b(v	b(v	NOUN
ejde-517	284	13	)	)	PUNCT
ejde-517	284	14	must	must	AUX
ejde-517	284	15	be	be	AUX
ejde-517	284	16	bounded	bound	VERB
ejde-517	284	17	.	.	PUNCT
ejde-517	285	1	to	to	PART
ejde-517	285	2	show	show	VERB
ejde-517	285	3	this	this	PRON
ejde-517	285	4	,	,	PUNCT
ejde-517	285	5	it	it	PRON
ejde-517	285	6	is	be	AUX
ejde-517	285	7	necessary	necessary	ADJ
ejde-517	285	8	that	that	SCONJ
ejde-517	285	9	χ1∇φ(χ1	χ1∇φ(χ1	NOUN
ejde-517	285	10	)	)	PUNCT
ejde-517	285	11	·	·	PUNCT
ejde-517	285	12	∇φ∗(χ1	∇φ∗(χ1	X
ejde-517	285	13	)	)	PUNCT
ejde-517	285	14	be	be	AUX
ejde-517	285	15	in	in	ADP
ejde-517	285	16	l2(ω	l2(ω	NOUN
ejde-517	285	17	)	)	PUNCT
ejde-517	285	18	.	.	PUNCT
ejde-517	286	1	if	if	SCONJ
ejde-517	286	2	either	either	CCONJ
ejde-517	286	3	∇φ(χ1	∇φ(χ1	NOUN
ejde-517	286	4	)	)	PUNCT
ejde-517	286	5	or	or	CCONJ
ejde-517	286	6	∇φ∗(χ1	∇φ∗(χ1	NOUN
ejde-517	286	7	)	)	PUNCT
ejde-517	286	8	is	be	AUX
ejde-517	286	9	in	in	ADP
ejde-517	286	10	l∞(ω	l∞(ω	ADJ
ejde-517	286	11	)	)	PUNCT
ejde-517	286	12	,	,	PUNCT
ejde-517	286	13	then	then	ADV
ejde-517	286	14	∇φ(χ1	∇φ(χ1	X
ejde-517	286	15	)	)	PUNCT
ejde-517	286	16	·	·	PUNCT
ejde-517	286	17	∇φ∗(χ1	∇φ∗(χ1	X
ejde-517	286	18	)	)	PUNCT
ejde-517	286	19	∈	∈	PROPN
ejde-517	286	20	l2(ω	l2(ω	NOUN
ejde-517	286	21	)	)	PUNCT
ejde-517	286	22	.	.	PUNCT
ejde-517	287	1	in	in	ADP
ejde-517	287	2	[	[	X
ejde-517	287	3	9	9	NUM
ejde-517	287	4	]	]	PUNCT
ejde-517	287	5	,	,	PUNCT
ejde-517	287	6	it	it	PRON
ejde-517	287	7	was	be	AUX
ejde-517	287	8	shown	show	VERB
ejde-517	287	9	that	that	SCONJ
ejde-517	287	10	‖∇φ(χ1)‖l∞(ω′	‖∇φ(χ1)‖l∞(ω′	PUNCT
ejde-517	287	11	)	)	PUNCT
ejde-517	287	12	can	can	AUX
ejde-517	287	13	be	be	AUX
ejde-517	287	14	bounded	bound	VERB
ejde-517	287	15	by	by	ADP
ejde-517	287	16	‖∇φ(χ1)‖l2(ω	‖∇φ(χ1)‖l2(ω	ADV
ejde-517	287	17	)	)	PUNCT
ejde-517	287	18	for	for	ADP
ejde-517	287	19	some	some	DET
ejde-517	287	20	ω′	ω′	PROPN
ejde-517	287	21	compactly	compactly	ADV
ejde-517	287	22	embedded	embed	VERB
ejde-517	287	23	in	in	ADP
ejde-517	287	24	ω	ω	PROPN
ejde-517	287	25	.	.	PUNCT
ejde-517	288	1	this	this	PRON
ejde-517	288	2	was	be	AUX
ejde-517	288	3	proven	prove	VERB
ejde-517	288	4	under	under	ADP
ejde-517	288	5	the	the	DET
ejde-517	288	6	assumption	assumption	NOUN
ejde-517	288	7	that	that	SCONJ
ejde-517	288	8	σk	σk	PROPN
ejde-517	288	9	∈	∈	PROPN
ejde-517	288	10	c1(ω̄	c1(ω̄	NUM
ejde-517	288	11	)	)	PUNCT
ejde-517	288	12	.	.	PUNCT
ejde-517	289	1	recall	recall	VERB
ejde-517	289	2	that	that	PRON
ejde-517	289	3	σk	σk	NOUN
ejde-517	289	4	=	=	PUNCT
ejde-517	289	5	σk1χ1	σk1χ1	PROPN
ejde-517	289	6	+	+	ADJ
ejde-517	289	7	σ2(1−χ1	σ2(1−χ1	NOUN
ejde-517	289	8	)	)	PUNCT
ejde-517	289	9	.	.	PUNCT
ejde-517	290	1	clearly	clearly	ADV
ejde-517	290	2	,	,	PUNCT
ejde-517	290	3	σk	σk	PROPN
ejde-517	290	4	is	be	AUX
ejde-517	290	5	not	not	PART
ejde-517	290	6	necessarily	necessarily	ADV
ejde-517	290	7	in	in	ADP
ejde-517	290	8	c1(ω̄	c1(ω̄	NUM
ejde-517	290	9	)	)	PUNCT
ejde-517	290	10	because	because	SCONJ
ejde-517	290	11	χ1	χ1	NOUN
ejde-517	290	12	is	be	AUX
ejde-517	290	13	a	a	DET
ejde-517	290	14	characteristic	characteristic	ADJ
ejde-517	290	15	function	function	NOUN
ejde-517	290	16	.	.	PUNCT
ejde-517	291	1	we	we	PRON
ejde-517	291	2	have	have	AUX
ejde-517	291	3	introduced	introduce	VERB
ejde-517	291	4	a	a	DET
ejde-517	291	5	mollification	mollification	NOUN
ejde-517	291	6	χδ1	χδ1	NOUN
ejde-517	291	7	of	of	ADP
ejde-517	291	8	χ1	χ1	NOUN
ejde-517	291	9	in	in	ADP
ejde-517	291	10	(	(	PUNCT
ejde-517	291	11	2.15	2.15	NUM
ejde-517	291	12	)	)	PUNCT
ejde-517	291	13	to	to	PART
ejde-517	291	14	resolve	resolve	VERB
ejde-517	291	15	this	this	PRON
ejde-517	291	16	.	.	PUNCT
ejde-517	292	1	thus	thus	ADV
ejde-517	292	2	,	,	PUNCT
ejde-517	292	3	σk1	σk1	X
ejde-517	292	4	∈	∈	PROPN
ejde-517	292	5	c∞(ω̄	c∞(ω̄	PRON
ejde-517	292	6	)	)	PUNCT
ejde-517	292	7	.	.	PUNCT
ejde-517	293	1	moreover	moreover	ADV
ejde-517	293	2	,	,	PUNCT
ejde-517	293	3	σk	σk	X
ejde-517	293	4	is	be	AUX
ejde-517	293	5	not	not	PART
ejde-517	293	6	just	just	ADV
ejde-517	293	7	in	in	ADP
ejde-517	293	8	c1(ω̄	c1(ω̄	NOUN
ejde-517	293	9	)	)	PUNCT
ejde-517	293	10	but	but	CCONJ
ejde-517	293	11	in	in	ADP
ejde-517	293	12	c∞(ω̄	c∞(ω̄	PRON
ejde-517	293	13	)	)	PUNCT
ejde-517	293	14	as	as	ADV
ejde-517	293	15	well	well	ADV
ejde-517	293	16	.	.	PUNCT
ejde-517	294	1	this	this	PRON
ejde-517	294	2	might	might	AUX
ejde-517	294	3	seem	seem	VERB
ejde-517	294	4	like	like	ADP
ejde-517	294	5	a	a	DET
ejde-517	294	6	deviation	deviation	NOUN
ejde-517	294	7	from	from	ADP
ejde-517	294	8	our	our	PRON
ejde-517	294	9	proposed	propose	VERB
ejde-517	294	10	method	method	NOUN
ejde-517	294	11	but	but	CCONJ
ejde-517	294	12	technically	technically	ADV
ejde-517	294	13	,	,	PUNCT
ejde-517	294	14	we	we	PRON
ejde-517	294	15	can	can	AUX
ejde-517	294	16	choose	choose	VERB
ejde-517	294	17	δ	δ	PROPN
ejde-517	294	18	to	to	PART
ejde-517	294	19	be	be	AUX
ejde-517	294	20	extremely	extremely	ADV
ejde-517	294	21	close	close	ADJ
ejde-517	294	22	to	to	ADP
ejde-517	294	23	0	0	NUM
ejde-517	295	1	so	so	SCONJ
ejde-517	295	2	that	that	SCONJ
ejde-517	295	3	χδ1	χδ1	NOUN
ejde-517	295	4	is	be	AUX
ejde-517	295	5	a	a	DET
ejde-517	295	6	good	good	ADJ
ejde-517	295	7	approximation	approximation	NOUN
ejde-517	295	8	of	of	ADP
ejde-517	295	9	χ1	χ1	NOUN
ejde-517	295	10	.	.	PUNCT
ejde-517	296	1	we	we	PRON
ejde-517	296	2	show	show	VERB
ejde-517	296	3	that	that	SCONJ
ejde-517	296	4	the	the	DET
ejde-517	296	5	mollification	mollification	NOUN
ejde-517	296	6	affects	affect	VERB
ejde-517	296	7	the	the	DET
ejde-517	296	8	corresponding	correspond	VERB
ejde-517	296	9	φ	φ	NOUN
ejde-517	296	10	and	and	CCONJ
ejde-517	296	11	φ∗	φ∗	NOUN
ejde-517	296	12	to	to	ADP
ejde-517	296	13	a	a	DET
ejde-517	296	14	very	very	ADV
ejde-517	296	15	small	small	ADJ
ejde-517	296	16	extent	extent	NOUN
ejde-517	296	17	as	as	ADV
ejde-517	296	18	long	long	ADV
ejde-517	296	19	as	as	SCONJ
ejde-517	296	20	the	the	DET
ejde-517	296	21	distance	distance	NOUN
ejde-517	296	22	between	between	ADP
ejde-517	296	23	χδ1	χδ1	NOUN
ejde-517	296	24	and	and	CCONJ
ejde-517	296	25	χ1	χ1	NOUN
ejde-517	296	26	is	be	AUX
ejde-517	296	27	small	small	ADJ
ejde-517	296	28	enough	enough	ADV
ejde-517	296	29	.	.	PUNCT
ejde-517	297	1	but	but	CCONJ
ejde-517	297	2	first	first	ADV
ejde-517	297	3	,	,	PUNCT
ejde-517	297	4	we	we	PRON
ejde-517	297	5	need	need	VERB
ejde-517	297	6	the	the	DET
ejde-517	297	7	following	follow	VERB
ejde-517	297	8	results	result	NOUN
ejde-517	297	9	.	.	PUNCT
ejde-517	298	1	lemma	lemma	PROPN
ejde-517	298	2	3.8	3.8	NUM
ejde-517	298	3	.	.	PUNCT
ejde-517	299	1	let	let	VERB
ejde-517	299	2	1	1	NUM
ejde-517	299	3	≤	≤	NOUN
ejde-517	300	1	p	p	X
ejde-517	300	2	<	<	X
ejde-517	300	3	∞	∞	PROPN
ejde-517	301	1	and	and	CCONJ
ejde-517	301	2	take	take	VERB
ejde-517	301	3	1	1	NUM
ejde-517	301	4	≤	≤	NOUN
ejde-517	301	5	r	r	NOUN
ejde-517	301	6	≤	≤	NUM
ejde-517	301	7	∞	∞	NUM
ejde-517	301	8	such	such	ADJ
ejde-517	301	9	that	that	SCONJ
ejde-517	301	10	1	1	NUM
ejde-517	301	11	r	r	NOUN
ejde-517	301	12	+	+	NOUN
ejde-517	301	13	1	1	NUM
ejde-517	301	14	−	−	NOUN
ejde-517	301	15	1	1	NUM
ejde-517	301	16	p	p	NOUN
ejde-517	301	17	∈	∈	PROPN
ejde-517	302	1	[	[	X
ejde-517	302	2	0	0	NUM
ejde-517	302	3	,	,	PUNCT
ejde-517	302	4	1	1	NUM
ejde-517	302	5	]	]	PUNCT
ejde-517	302	6	.	.	PUNCT
ejde-517	303	1	define	define	VERB
ejde-517	303	2	the	the	DET
ejde-517	303	3	operator	operator	NOUN
ejde-517	303	4	from	from	ADP
ejde-517	303	5	lp(ω	lp(ω	PROPN
ejde-517	303	6	)	)	PUNCT
ejde-517	303	7	to	to	ADP
ejde-517	303	8	lr(ω	lr(ω	ADV
ejde-517	303	9	)	)	PUNCT
ejde-517	303	10	by	by	ADP
ejde-517	303	11	tδ(g	tδ(g	NUM
ejde-517	303	12	)	)	PUNCT
ejde-517	303	13	:	:	PUNCT
ejde-517	304	1	=	=	PUNCT
ejde-517	304	2	g	g	NOUN
ejde-517	304	3	∗	∗	NOUN
ejde-517	304	4	ξδ	ξδ	ADP
ejde-517	304	5	.	.	PUNCT
ejde-517	305	1	(	(	PUNCT
ejde-517	305	2	3.22	3.22	NUM
ejde-517	305	3	)	)	PUNCT
ejde-517	305	4	then	then	ADV
ejde-517	305	5	tδ	tδ	INTJ
ejde-517	305	6	is	be	AUX
ejde-517	305	7	continuous	continuous	ADJ
ejde-517	305	8	and	and	CCONJ
ejde-517	305	9	injective	injective	ADJ
ejde-517	305	10	[	[	X
ejde-517	305	11	15	15	NUM
ejde-517	305	12	]	]	PUNCT
ejde-517	305	13	.	.	PUNCT
ejde-517	306	1	lemma	lemma	PROPN
ejde-517	306	2	3.9	3.9	NUM
ejde-517	306	3	.	.	PUNCT
ejde-517	307	1	for	for	ADP
ejde-517	307	2	any	any	DET
ejde-517	307	3	g	g	NOUN
ejde-517	307	4	∈	∈	PROPN
ejde-517	307	5	lp(ω	lp(ω	PROPN
ejde-517	307	6	)	)	PUNCT
ejde-517	307	7	,	,	PUNCT
ejde-517	307	8	1	1	NUM
ejde-517	307	9	≤	≤	NOUN
ejde-517	307	10	p	p	X
ejde-517	307	11	<	<	X
ejde-517	307	12	∞	∞	PROPN
ejde-517	307	13	,	,	PUNCT
ejde-517	307	14	∂ν(g	∂ν(g	PROPN
ejde-517	307	15	∗	∗	NOUN
ejde-517	307	16	ξδ	ξδ	ADP
ejde-517	307	17	)	)	PUNCT
ejde-517	307	18	=	=	SYM
ejde-517	307	19	(	(	PUNCT
ejde-517	307	20	∂νg	∂νg	NOUN
ejde-517	307	21	)	)	PUNCT
ejde-517	307	22	∗	∗	NOUN
ejde-517	307	23	ξδ	ξδ	ADP
ejde-517	307	24	,	,	PUNCT
ejde-517	307	25	for	for	ADP
ejde-517	307	26	|ν|	|ν|	ADV
ejde-517	307	27	≤	≤	ADJ
ejde-517	307	28	1	1	NUM
ejde-517	307	29	.	.	PUNCT
ejde-517	308	1	moreover	moreover	ADV
ejde-517	308	2	,	,	PUNCT
ejde-517	308	3	∂ν(g	∂ν(g	PROPN
ejde-517	308	4	∗	∗	NOUN
ejde-517	308	5	ξδ)→	ξδ)→	NOUN
ejde-517	308	6	∂νg	∂νg	PROPN
ejde-517	308	7	almost	almost	ADV
ejde-517	308	8	everywhere	everywhere	ADV
ejde-517	308	9	as	as	ADP
ejde-517	308	10	δ	δ	PROPN
ejde-517	308	11	→	→	X
ejde-517	308	12	0	0	PROPN
ejde-517	308	13	.	.	PUNCT
ejde-517	309	1	the	the	DET
ejde-517	309	2	proof	proof	NOUN
ejde-517	309	3	of	of	ADP
ejde-517	309	4	the	the	DET
ejde-517	309	5	above	above	ADJ
ejde-517	309	6	lemma	lemma	PROPN
ejde-517	309	7	is	be	AUX
ejde-517	309	8	rather	rather	ADV
ejde-517	309	9	straightforward	straightforward	ADJ
ejde-517	309	10	and	and	CCONJ
ejde-517	309	11	is	be	AUX
ejde-517	309	12	omitted	omit	VERB
ejde-517	309	13	.	.	PUNCT
ejde-517	310	1	the	the	DET
ejde-517	310	2	second	second	ADJ
ejde-517	310	3	assertion	assertion	NOUN
ejde-517	310	4	follows	follow	VERB
ejde-517	310	5	from	from	ADP
ejde-517	310	6	lemma	lemma	PROPN
ejde-517	310	7	(	(	PUNCT
ejde-517	310	8	2.5	2.5	NUM
ejde-517	310	9	)	)	PUNCT
ejde-517	310	10	(	(	PUNCT
ejde-517	310	11	compare	compare	VERB
ejde-517	310	12	with	with	ADP
ejde-517	310	13	[	[	X
ejde-517	310	14	14	14	NUM
ejde-517	310	15	]	]	SYM
ejde-517	310	16	)	)	PUNCT
ejde-517	310	17	.	.	PUNCT
ejde-517	311	1	for	for	ADP
ejde-517	311	2	brevity	brevity	NOUN
ejde-517	311	3	,	,	PUNCT
ejde-517	311	4	from	from	ADP
ejde-517	311	5	here	here	ADV
ejde-517	311	6	onwards	onwards	ADV
ejde-517	311	7	we	we	PRON
ejde-517	311	8	let	let	VERB
ejde-517	311	9	χδ1	χδ1	NOUN
ejde-517	311	10	:	:	PUNCT
ejde-517	311	11	=	=	SYM
ejde-517	311	12	χ1	χ1	NOUN
ejde-517	311	13	∗	∗	NOUN
ejde-517	311	14	ξδ	ξδ	ADP
ejde-517	311	15	denote	denote	VERB
ejde-517	311	16	the	the	DET
ejde-517	311	17	mollification	mollification	NOUN
ejde-517	311	18	of	of	ADP
ejde-517	311	19	χ1	χ1	NOUN
ejde-517	311	20	.	.	PUNCT
ejde-517	312	1	we	we	PRON
ejde-517	312	2	now	now	ADV
ejde-517	312	3	show	show	VERB
ejde-517	312	4	how	how	SCONJ
ejde-517	312	5	the	the	DET
ejde-517	312	6	perturbation	perturbation	NOUN
ejde-517	312	7	of	of	ADP
ejde-517	312	8	χ1	χ1	NOUN
ejde-517	312	9	affects	affect	VERB
ejde-517	312	10	the	the	DET
ejde-517	312	11	solution	solution	NOUN
ejde-517	312	12	of	of	ADP
ejde-517	312	13	the	the	DET
ejde-517	312	14	forward	forward	ADJ
ejde-517	312	15	and	and	CCONJ
ejde-517	312	16	adjoint	adjoint	NOUN
ejde-517	312	17	problems	problem	NOUN
ejde-517	312	18	.	.	PUNCT
ejde-517	313	1	theorem	theorem	VERB
ejde-517	313	2	3.10	3.10	NUM
ejde-517	313	3	.	.	PUNCT
ejde-517	314	1	for	for	ADP
ejde-517	314	2	a	a	DET
ejde-517	314	3	fixed	fix	VERB
ejde-517	314	4	δ	δ	PROPN
ejde-517	314	5	,	,	PUNCT
ejde-517	314	6	the	the	DET
ejde-517	314	7	solution	solution	NOUN
ejde-517	314	8	of	of	ADP
ejde-517	314	9	the	the	DET
ejde-517	314	10	forward	forward	ADJ
ejde-517	314	11	problem	problem	NOUN
ejde-517	314	12	given	give	VERB
ejde-517	314	13	χ1	χ1	NOUN
ejde-517	314	14	∈	∈	NOUN
ejde-517	314	15	l∞(ω	l∞(ω	NOUN
ejde-517	314	16	)	)	PUNCT
ejde-517	314	17	and	and	CCONJ
ejde-517	314	18	the	the	DET
ejde-517	314	19	solution	solution	NOUN
ejde-517	314	20	of	of	ADP
ejde-517	314	21	the	the	DET
ejde-517	314	22	forward	forward	ADJ
ejde-517	314	23	problem	problem	NOUN
ejde-517	314	24	given	give	VERB
ejde-517	314	25	χδ1	χδ1	NUM
ejde-517	314	26	satisfy	satisfy	NOUN
ejde-517	314	27	‖φ(χδ1)−	‖φ(χδ1)−	VERB
ejde-517	314	28	φ(χ1)‖h1(ω	φ(χ1)‖h1(ω	PROPN
ejde-517	314	29	)	)	PUNCT
ejde-517	314	30	≤	≤	NUM
ejde-517	314	31	cδ1‖χδ1	cδ1‖χδ1	X
ejde-517	314	32	−	−	NOUN
ejde-517	314	33	χ1‖l∞(ω	χ1‖l∞(ω	PROPN
ejde-517	314	34	)	)	PUNCT
ejde-517	314	35	(	(	PUNCT
ejde-517	314	36	3.23	3.23	NUM
ejde-517	314	37	)	)	PUNCT
ejde-517	314	38	for	for	ADP
ejde-517	314	39	some	some	DET
ejde-517	314	40	c1	c1	PROPN
ejde-517	314	41	>	>	X
ejde-517	314	42	0	0	X
ejde-517	314	43	.	.	PUNCT
ejde-517	315	1	the	the	DET
ejde-517	315	2	same	same	ADJ
ejde-517	315	3	applies	apply	VERB
ejde-517	315	4	to	to	ADP
ejde-517	315	5	the	the	DET
ejde-517	315	6	adjoint	adjoint	PROPN
ejde-517	315	7	problem	problem	NOUN
ejde-517	315	8	‖φ∗(χδ1)−	‖φ∗(χδ1)−	PROPN
ejde-517	315	9	φ∗(χ1)‖h1(ω	φ∗(χ1)‖h1(ω	NOUN
ejde-517	315	10	)	)	PUNCT
ejde-517	315	11	≤	≤	NOUN
ejde-517	315	12	cδ2‖χδ1	cδ2‖χδ1	AUX
ejde-517	315	13	−	−	PROPN
ejde-517	315	14	χ1‖l∞(ω	χ1‖l∞(ω	PROPN
ejde-517	315	15	)	)	PUNCT
ejde-517	315	16	(	(	PUNCT
ejde-517	315	17	3.24	3.24	NUM
ejde-517	315	18	)	)	PUNCT
ejde-517	315	19	10	10	NUM
ejde-517	315	20	r.	r.	PROPN
ejde-517	315	21	mendoza	mendoza	PROPN
ejde-517	315	22	,	,	PUNCT
ejde-517	315	23	s.	s.	PROPN
ejde-517	315	24	keeling	keeling	PROPN
ejde-517	315	25	ejde-2020/93	ejde-2020/93	PROPN
ejde-517	315	26	for	for	ADP
ejde-517	315	27	some	some	DET
ejde-517	315	28	c2	c2	PROPN
ejde-517	315	29	>	>	X
ejde-517	315	30	0	0	PROPN
ejde-517	315	31	.	.	PUNCT
ejde-517	316	1	proof	proof	NOUN
ejde-517	316	2	.	.	PUNCT
ejde-517	317	1	we	we	PRON
ejde-517	317	2	proved	prove	VERB
ejde-517	317	3	in	in	ADP
ejde-517	317	4	(	(	PUNCT
ejde-517	317	5	3.15	3.15	NUM
ejde-517	317	6	)	)	PUNCT
ejde-517	317	7	that	that	SCONJ
ejde-517	317	8	φ	φ	PROPN
ejde-517	317	9	depends	depend	VERB
ejde-517	317	10	continuously	continuously	ADV
ejde-517	317	11	on	on	ADP
ejde-517	317	12	χ1	χ1	NOUN
ejde-517	317	13	.	.	PUNCT
ejde-517	318	1	note	note	VERB
ejde-517	318	2	that	that	SCONJ
ejde-517	318	3	we	we	PRON
ejde-517	318	4	proved	prove	VERB
ejde-517	318	5	this	this	PRON
ejde-517	318	6	given	give	VERB
ejde-517	318	7	the	the	DET
ejde-517	318	8	assumption	assumption	NOUN
ejde-517	318	9	that	that	SCONJ
ejde-517	318	10	χ1	χ1	NOUN
ejde-517	318	11	∈	∈	PROPN
ejde-517	318	12	l∞(ω	l∞(ω	NOUN
ejde-517	318	13	)	)	PUNCT
ejde-517	318	14	,	,	PUNCT
ejde-517	318	15	which	which	PRON
ejde-517	318	16	implies	imply	VERB
ejde-517	318	17	that	that	SCONJ
ejde-517	318	18	χ1	χ1	PROPN
ejde-517	318	19	∈	∈	PROPN
ejde-517	318	20	l2(ω	l2(ω	NOUN
ejde-517	318	21	)	)	PUNCT
ejde-517	318	22	as	as	ADV
ejde-517	318	23	well	well	ADV
ejde-517	318	24	.	.	PUNCT
ejde-517	319	1	by	by	ADP
ejde-517	319	2	lemma	lemma	PROPN
ejde-517	319	3	(	(	PUNCT
ejde-517	319	4	3.8	3.8	NUM
ejde-517	319	5	)	)	PUNCT
ejde-517	319	6	,	,	PUNCT
ejde-517	319	7	we	we	PRON
ejde-517	319	8	can	can	AUX
ejde-517	319	9	infer	infer	VERB
ejde-517	319	10	that	that	SCONJ
ejde-517	319	11	χδ1	χδ1	NOUN
ejde-517	319	12	∈	∈	NOUN
ejde-517	319	13	l∞(ω	l∞(ω	NOUN
ejde-517	319	14	)	)	PUNCT
ejde-517	319	15	by	by	ADP
ejde-517	319	16	choosing	choose	VERB
ejde-517	319	17	p	p	NOUN
ejde-517	319	18	=	=	PROPN
ejde-517	319	19	2	2	NUM
ejde-517	319	20	and	and	CCONJ
ejde-517	319	21	r	r	NOUN
ejde-517	319	22	=	=	SYM
ejde-517	319	23	∞.	∞.	PROPN
ejde-517	319	24	finally	finally	ADV
ejde-517	319	25	,	,	PUNCT
ejde-517	319	26	theorem	theorem	VERB
ejde-517	319	27	(	(	PUNCT
ejde-517	319	28	3.5	3.5	NUM
ejde-517	319	29	)	)	PUNCT
ejde-517	319	30	proves	prove	VERB
ejde-517	319	31	the	the	DET
ejde-517	319	32	rest	rest	NOUN
ejde-517	319	33	of	of	ADP
ejde-517	319	34	our	our	PRON
ejde-517	319	35	claim	claim	NOUN
ejde-517	319	36	.	.	PUNCT
ejde-517	320	1	�	�	PROPN
ejde-517	320	2	remark	remark	VERB
ejde-517	320	3	3.11	3.11	NUM
ejde-517	320	4	.	.	PUNCT
ejde-517	321	1	the	the	DET
ejde-517	321	2	superscript	superscript	PROPN
ejde-517	321	3	δ	δ	PROPN
ejde-517	321	4	in	in	ADP
ejde-517	321	5	cδ1	cδ1	PROPN
ejde-517	321	6	and	and	CCONJ
ejde-517	321	7	cδ2	cδ2	PROPN
ejde-517	321	8	from	from	ADP
ejde-517	321	9	(	(	PUNCT
ejde-517	321	10	3.23	3.23	NUM
ejde-517	321	11	)	)	PUNCT
ejde-517	321	12	and	and	CCONJ
ejde-517	321	13	(	(	PUNCT
ejde-517	321	14	3.24	3.24	NUM
ejde-517	321	15	)	)	PUNCT
ejde-517	321	16	are	be	AUX
ejde-517	321	17	used	use	VERB
ejde-517	321	18	to	to	PART
ejde-517	321	19	emphasize	emphasize	VERB
ejde-517	321	20	the	the	DET
ejde-517	321	21	dependence	dependence	NOUN
ejde-517	321	22	of	of	ADP
ejde-517	321	23	the	the	DET
ejde-517	321	24	inequality	inequality	NOUN
ejde-517	321	25	constants	constant	NOUN
ejde-517	321	26	on	on	ADP
ejde-517	321	27	the	the	DET
ejde-517	321	28	mollification	mollification	NOUN
ejde-517	321	29	parameter	parameter	PROPN
ejde-517	321	30	δ	δ	PROPN
ejde-517	321	31	.	.	PUNCT
ejde-517	322	1	from	from	ADP
ejde-517	322	2	here	here	ADV
ejde-517	322	3	onwards	onward	NOUN
ejde-517	322	4	,	,	PUNCT
ejde-517	322	5	we	we	PRON
ejde-517	322	6	use	use	VERB
ejde-517	322	7	the	the	DET
ejde-517	322	8	same	same	ADJ
ejde-517	322	9	notation	notation	NOUN
ejde-517	322	10	for	for	ADP
ejde-517	322	11	all	all	DET
ejde-517	322	12	constants	constant	NOUN
ejde-517	322	13	dependent	dependent	ADJ
ejde-517	322	14	on	on	ADP
ejde-517	322	15	δ	δ	PROPN
ejde-517	322	16	.	.	PUNCT
ejde-517	323	1	we	we	PRON
ejde-517	323	2	know	know	VERB
ejde-517	323	3	that	that	SCONJ
ejde-517	323	4	χδ1	χδ1	VERB
ejde-517	323	5	converges	converge	NOUN
ejde-517	323	6	to	to	ADP
ejde-517	323	7	χ1	χ1	NOUN
ejde-517	323	8	pointwise	pointwise	NOUN
ejde-517	323	9	[	[	X
ejde-517	323	10	15	15	NUM
ejde-517	323	11	]	]	PUNCT
ejde-517	323	12	.	.	PUNCT
ejde-517	324	1	although	although	SCONJ
ejde-517	324	2	it	it	PRON
ejde-517	324	3	does	do	AUX
ejde-517	324	4	not	not	PART
ejde-517	324	5	guarantee	guarantee	VERB
ejde-517	324	6	that	that	SCONJ
ejde-517	324	7	‖χδ1−χ1‖l∞(ω	‖χδ1−χ1‖l∞(ω	NOUN
ejde-517	324	8	)	)	PUNCT
ejde-517	324	9	converges	converge	VERB
ejde-517	324	10	to	to	ADP
ejde-517	324	11	0	0	NUM
ejde-517	324	12	,	,	PUNCT
ejde-517	324	13	this	this	PRON
ejde-517	324	14	can	can	AUX
ejde-517	324	15	still	still	ADV
ejde-517	324	16	be	be	AUX
ejde-517	324	17	a	a	DET
ejde-517	324	18	gauge	gauge	NOUN
ejde-517	324	19	to	to	PART
ejde-517	324	20	measure	measure	VERB
ejde-517	324	21	the	the	DET
ejde-517	324	22	distance	distance	NOUN
ejde-517	324	23	between	between	ADP
ejde-517	324	24	the	the	DET
ejde-517	324	25	solution	solution	NOUN
ejde-517	324	26	of	of	ADP
ejde-517	324	27	the	the	DET
ejde-517	324	28	forward	forward	ADJ
ejde-517	324	29	problem	problem	NOUN
ejde-517	324	30	using	use	VERB
ejde-517	324	31	χ1	χ1	NOUN
ejde-517	324	32	and	and	CCONJ
ejde-517	324	33	the	the	DET
ejde-517	324	34	solution	solution	NOUN
ejde-517	324	35	using	use	VERB
ejde-517	324	36	χδ1	χδ1	NOUN
ejde-517	324	37	.	.	PUNCT
ejde-517	324	38	to	to	PART
ejde-517	324	39	make	make	VERB
ejde-517	324	40	our	our	PRON
ejde-517	324	41	modifications	modification	NOUN
ejde-517	324	42	consistent	consistent	ADJ
ejde-517	324	43	,	,	PUNCT
ejde-517	324	44	we	we	PRON
ejde-517	324	45	find	find	VERB
ejde-517	324	46	a	a	DET
ejde-517	324	47	new	new	ADJ
ejde-517	324	48	thresholding	thresholde	VERB
ejde-517	324	49	approach	approach	NOUN
ejde-517	324	50	to	to	PART
ejde-517	324	51	adapt	adapt	VERB
ejde-517	324	52	with	with	ADP
ejde-517	324	53	the	the	DET
ejde-517	324	54	mollification	mollification	NOUN
ejde-517	324	55	of	of	ADP
ejde-517	324	56	χ1	χ1	NOUN
ejde-517	324	57	.	.	PUNCT
ejde-517	325	1	first	first	ADV
ejde-517	325	2	,	,	PUNCT
ejde-517	325	3	we	we	PRON
ejde-517	325	4	define	define	VERB
ejde-517	325	5	a	a	DET
ejde-517	325	6	space	space	NOUN
ejde-517	325	7	that	that	PRON
ejde-517	325	8	will	will	AUX
ejde-517	325	9	be	be	AUX
ejde-517	325	10	important	important	ADJ
ejde-517	325	11	in	in	ADP
ejde-517	325	12	our	our	PRON
ejde-517	325	13	succeeding	succeed	VERB
ejde-517	325	14	computations	computation	NOUN
ejde-517	325	15	.	.	PUNCT
ejde-517	326	1	let	let	AUX
ejde-517	326	2	b(ω	b(ω	ADV
ejde-517	326	3	)	)	PUNCT
ejde-517	326	4	be	be	AUX
ejde-517	326	5	the	the	DET
ejde-517	326	6	borel	borel	NOUN
ejde-517	326	7	σ−algebra	σ−algebra	PROPN
ejde-517	326	8	over	over	ADP
ejde-517	326	9	ω	ω	PROPN
ejde-517	326	10	and	and	CCONJ
ejde-517	326	11	let	let	VERB
ejde-517	326	12	µ	µ	X
ejde-517	326	13	(	(	PUNCT
ejde-517	326	14	·	·	PUNCT
ejde-517	326	15	)	)	PUNCT
ejde-517	326	16	denote	denote	VERB
ejde-517	326	17	the	the	DET
ejde-517	326	18	lebesgue	lebesgue	NOUN
ejde-517	326	19	measure	measure	NOUN
ejde-517	326	20	.	.	PUNCT
ejde-517	327	1	for	for	ADP
ejde-517	327	2	any	any	DET
ejde-517	327	3	a1	a1	NOUN
ejde-517	327	4	,	,	PUNCT
ejde-517	327	5	a2	a2	PROPN
ejde-517	327	6	∈	∈	PROPN
ejde-517	327	7	b(ω	b(ω	ADV
ejde-517	327	8	)	)	PUNCT
ejde-517	327	9	,	,	PUNCT
ejde-517	327	10	we	we	PRON
ejde-517	327	11	define	define	VERB
ejde-517	327	12	the	the	DET
ejde-517	327	13	symmetric	symmetric	ADJ
ejde-517	327	14	difference	difference	NOUN
ejde-517	327	15	of	of	ADP
ejde-517	327	16	a1	a1	NOUN
ejde-517	327	17	and	and	CCONJ
ejde-517	327	18	a2	a2	PROPN
ejde-517	327	19	to	to	PART
ejde-517	327	20	be	be	AUX
ejde-517	327	21	a1	a1	NOUN
ejde-517	327	22	4a2	4a2	NUM
ejde-517	327	23	:	:	PUNCT
ejde-517	327	24	=	=	SYM
ejde-517	327	25	(	(	PUNCT
ejde-517	327	26	a1\a2	a1\a2	ADJ
ejde-517	327	27	)	)	PUNCT
ejde-517	327	28	∪	∪	X
ejde-517	327	29	(	(	PUNCT
ejde-517	327	30	a2\a1	a2\a1	NUM
ejde-517	327	31	)	)	PUNCT
ejde-517	327	32	.	.	PUNCT
ejde-517	328	1	definition	definition	NOUN
ejde-517	328	2	3.12	3.12	NUM
ejde-517	328	3	.	.	PUNCT
ejde-517	329	1	let	let	VERB
ejde-517	329	2	the	the	DET
ejde-517	329	3	distance	distance	NOUN
ejde-517	329	4	d	d	X
ejde-517	329	5	:	:	PUNCT
ejde-517	329	6	b(ω	b(ω	X
ejde-517	329	7	)	)	PUNCT
ejde-517	329	8	×	×	NOUN
ejde-517	329	9	b(ω	b(ω	ADV
ejde-517	329	10	)	)	PUNCT
ejde-517	329	11	→	→	SYM
ejde-517	329	12	r	r	NOUN
ejde-517	329	13	∪	∪	X
ejde-517	329	14	{	{	PUNCT
ejde-517	329	15	∞	∞	NOUN
ejde-517	329	16	}	}	PUNCT
ejde-517	329	17	be	be	AUX
ejde-517	329	18	d(a1	d(a1	NOUN
ejde-517	329	19	,	,	PUNCT
ejde-517	329	20	a2	a2	PROPN
ejde-517	329	21	)	)	PUNCT
ejde-517	329	22	=	=	PRON
ejde-517	329	23	µ(a1	µ(a1	PROPN
ejde-517	329	24	4a2	4a2	NUM
ejde-517	329	25	)	)	PUNCT
ejde-517	329	26	.	.	PUNCT
ejde-517	330	1	we	we	PRON
ejde-517	330	2	now	now	ADV
ejde-517	330	3	define	define	VERB
ejde-517	330	4	m(ω	m(ω	NOUN
ejde-517	330	5	)	)	PUNCT
ejde-517	331	1	=	=	PUNCT
ejde-517	331	2	(	(	PUNCT
ejde-517	331	3	b(ω	b(ω	ADV
ejde-517	331	4	)	)	PUNCT
ejde-517	331	5	,	,	PUNCT
ejde-517	331	6	d)/ker(d	d)/ker(d	PROPN
ejde-517	331	7	)	)	PUNCT
ejde-517	331	8	.	.	PUNCT
ejde-517	332	1	the	the	DET
ejde-517	332	2	space	space	NOUN
ejde-517	332	3	m(ω	m(ω	PROPN
ejde-517	332	4	)	)	PUNCT
ejde-517	332	5	is	be	AUX
ejde-517	332	6	,	,	PUNCT
ejde-517	332	7	in	in	ADP
ejde-517	332	8	fact	fact	NOUN
ejde-517	332	9	,	,	PUNCT
ejde-517	332	10	a	a	DET
ejde-517	332	11	metric	metric	ADJ
ejde-517	332	12	space	space	NOUN
ejde-517	332	13	[	[	X
ejde-517	332	14	19	19	NUM
ejde-517	332	15	,	,	PUNCT
ejde-517	332	16	15	15	NUM
ejde-517	332	17	]	]	PUNCT
ejde-517	332	18	.	.	PUNCT
ejde-517	333	1	in	in	ADP
ejde-517	333	2	our	our	PRON
ejde-517	333	3	algorithm	algorithm	NOUN
ejde-517	333	4	,	,	PUNCT
ejde-517	333	5	we	we	PRON
ejde-517	333	6	did	do	VERB
ejde-517	333	7	a	a	DET
ejde-517	333	8	thresholding	thresholding	NOUN
ejde-517	333	9	on	on	ADP
ejde-517	333	10	θ	θ	PROPN
ejde-517	333	11	in	in	ADP
ejde-517	333	12	order	order	NOUN
ejde-517	333	13	to	to	PART
ejde-517	333	14	get	get	VERB
ejde-517	333	15	an	an	DET
ejde-517	333	16	update	update	NOUN
ejde-517	333	17	for	for	ADP
ejde-517	333	18	χ1	χ1	NOUN
ejde-517	333	19	.	.	PUNCT
ejde-517	334	1	in	in	ADP
ejde-517	334	2	the	the	DET
ejde-517	334	3	following	follow	VERB
ejde-517	334	4	definition	definition	NOUN
ejde-517	334	5	,	,	PUNCT
ejde-517	334	6	we	we	PRON
ejde-517	334	7	modify	modify	VERB
ejde-517	334	8	this	this	DET
ejde-517	334	9	thresholding	thresholding	NOUN
ejde-517	334	10	to	to	PART
ejde-517	334	11	make	make	VERB
ejde-517	334	12	it	it	PRON
ejde-517	334	13	coherent	coherent	ADJ
ejde-517	334	14	with	with	ADP
ejde-517	334	15	the	the	DET
ejde-517	334	16	mollification	mollification	NOUN
ejde-517	334	17	of	of	ADP
ejde-517	334	18	χ1	χ1	NOUN
ejde-517	334	19	.	.	PUNCT
ejde-517	335	1	definition	definition	NOUN
ejde-517	335	2	3.13	3.13	NUM
ejde-517	335	3	.	.	PUNCT
ejde-517	336	1	let	let	VERB
ejde-517	336	2	z	z	NOUN
ejde-517	336	3	∈	∈	PROPN
ejde-517	336	4	l2(ω)\h1(ω	l2(ω)\h1(ω	NOUN
ejde-517	336	5	)	)	PUNCT
ejde-517	336	6	.	.	PUNCT
ejde-517	337	1	we	we	PRON
ejde-517	337	2	define	define	VERB
ejde-517	337	3	h	h	NOUN
ejde-517	337	4	:	:	PUNCT
ejde-517	337	5	l2(ω)→m(ω	l2(ω)→m(ω	PROPN
ejde-517	337	6	)	)	PUNCT
ejde-517	337	7	by	by	ADP
ejde-517	337	8	h(g	h(g	NOUN
ejde-517	337	9	)	)	PUNCT
ejde-517	337	10	=	=	PRON
ejde-517	338	1	{	{	PUNCT
ejde-517	338	2	x	x	PUNCT
ejde-517	338	3	∈	∈	PROPN
ejde-517	338	4	ω	ω	NOUN
ejde-517	338	5	:	:	PUNCT
ejde-517	338	6	(	(	PUNCT
ejde-517	338	7	(	(	PUNCT
ejde-517	338	8	gδ	gδ	NOUN
ejde-517	338	9	−	−	PROPN
ejde-517	338	10	ζ	ζ	NOUN
ejde-517	338	11	+	+	NUM
ejde-517	338	12	δz	δz	X
ejde-517	338	13	)	)	PUNCT
ejde-517	338	14	∗	∗	NOUN
ejde-517	338	15	ξδ)(x	ξδ)(x	PROPN
ejde-517	338	16	)	)	PUNCT
ejde-517	338	17	≥	≥	NOUN
ejde-517	338	18	0	0	NUM
ejde-517	338	19	}	}	PUNCT
ejde-517	338	20	,	,	PUNCT
ejde-517	338	21	(	(	PUNCT
ejde-517	338	22	3.25	3.25	NUM
ejde-517	338	23	)	)	PUNCT
ejde-517	338	24	for	for	ADP
ejde-517	338	25	some	some	DET
ejde-517	338	26	ζ	ζ	NOUN
ejde-517	338	27	∈	∈	NOUN
ejde-517	338	28	(	(	PUNCT
ejde-517	338	29	0	0	NUM
ejde-517	338	30	,	,	PUNCT
ejde-517	338	31	1	1	NUM
ejde-517	338	32	)	)	PUNCT
ejde-517	338	33	and	and	CCONJ
ejde-517	338	34	gδ	gδ	VERB
ejde-517	338	35	=	=	SYM
ejde-517	338	36	g	g	PROPN
ejde-517	338	37	∗	∗	NOUN
ejde-517	338	38	ξδ	ξδ	ADP
ejde-517	338	39	.	.	PUNCT
ejde-517	339	1	moreover	moreover	ADV
ejde-517	339	2	,	,	PUNCT
ejde-517	339	3	define	define	VERB
ejde-517	339	4	m	m	NOUN
ejde-517	339	5	:	:	PUNCT
ejde-517	339	6	m(ω	m(ω	NOUN
ejde-517	339	7	)	)	PUNCT
ejde-517	339	8	→	→	SYM
ejde-517	340	1	l2(ω	l2(ω	CCONJ
ejde-517	340	2	)	)	PUNCT
ejde-517	340	3	as	as	SCONJ
ejde-517	340	4	the	the	DET
ejde-517	340	5	map	map	NOUN
ejde-517	340	6	that	that	PRON
ejde-517	340	7	assigns	assign	VERB
ejde-517	340	8	ω	ω	PROPN
ejde-517	340	9	∈m(ω	∈m(ω	PROPN
ejde-517	340	10	)	)	PUNCT
ejde-517	340	11	to	to	ADP
ejde-517	340	12	its	its	PRON
ejde-517	340	13	characteristic	characteristic	ADJ
ejde-517	340	14	function	function	NOUN
ejde-517	340	15	χω	χω	ADP
ejde-517	340	16	,	,	PUNCT
ejde-517	340	17	that	that	ADV
ejde-517	340	18	is	is	ADV
ejde-517	340	19	,	,	PUNCT
ejde-517	340	20	m(ω	m(ω	PROPN
ejde-517	340	21	)	)	PUNCT
ejde-517	341	1	=	=	SYM
ejde-517	341	2	χω	χω	INTJ
ejde-517	341	3	.	.	PUNCT
ejde-517	342	1	(	(	PUNCT
ejde-517	342	2	3.26	3.26	NUM
ejde-517	342	3	)	)	PUNCT
ejde-517	342	4	observe	observe	VERB
ejde-517	342	5	that	that	SCONJ
ejde-517	342	6	if	if	SCONJ
ejde-517	342	7	we	we	PRON
ejde-517	342	8	let	let	VERB
ejde-517	342	9	δ	δ	PROPN
ejde-517	342	10	→	→	X
ejde-517	342	11	0	0	NUM
ejde-517	342	12	,	,	PUNCT
ejde-517	342	13	then	then	ADV
ejde-517	342	14	(	(	PUNCT
ejde-517	342	15	gδ	gδ	NOUN
ejde-517	342	16	−	−	PROPN
ejde-517	342	17	ζ	ζ	NOUN
ejde-517	342	18	+	+	NUM
ejde-517	342	19	δz	δz	NOUN
ejde-517	342	20	)	)	PUNCT
ejde-517	342	21	∗	∗	NOUN
ejde-517	342	22	ξδ	ξδ	ADP
ejde-517	342	23	→	→	SYM
ejde-517	342	24	g	g	NOUN
ejde-517	342	25	−	−	PROPN
ejde-517	342	26	ζ	ζ	NOUN
ejde-517	342	27	.	.	PUNCT
ejde-517	343	1	(	(	PUNCT
ejde-517	343	2	3.27	3.27	NUM
ejde-517	343	3	)	)	PUNCT
ejde-517	343	4	see	see	VERB
ejde-517	343	5	[	[	X
ejde-517	343	6	15	15	NUM
ejde-517	343	7	]	]	PUNCT
ejde-517	343	8	.	.	PUNCT
ejde-517	344	1	this	this	PRON
ejde-517	344	2	means	mean	VERB
ejde-517	344	3	that	that	SCONJ
ejde-517	344	4	as	as	SCONJ
ejde-517	344	5	δ	δ	PROPN
ejde-517	344	6	→	→	SYM
ejde-517	344	7	0	0	NUM
ejde-517	344	8	,	,	PUNCT
ejde-517	344	9	h(g	h(g	NOUN
ejde-517	344	10	)	)	PUNCT
ejde-517	344	11	becomes	become	VERB
ejde-517	344	12	the	the	DET
ejde-517	344	13	set	set	NOUN
ejde-517	344	14	of	of	ADP
ejde-517	344	15	x	x	PROPN
ejde-517	344	16	∈	∈	PROPN
ejde-517	344	17	ω	ω	PROPN
ejde-517	344	18	for	for	ADP
ejde-517	344	19	which	which	PRON
ejde-517	344	20	g(x	g(x	NOUN
ejde-517	344	21	)	)	PUNCT
ejde-517	344	22	≥	≥	NOUN
ejde-517	344	23	ζ	ζ	NOUN
ejde-517	344	24	.	.	PUNCT
ejde-517	344	25	using	use	VERB
ejde-517	344	26	the	the	DET
ejde-517	344	27	above	above	ADV
ejde-517	344	28	-	-	PUNCT
ejde-517	344	29	mentioned	mention	VERB
ejde-517	344	30	functions	function	NOUN
ejde-517	344	31	tδ	tδ	ADP
ejde-517	344	32	,	,	PUNCT
ejde-517	344	33	h	h	NOUN
ejde-517	344	34	,	,	PUNCT
ejde-517	344	35	m	m	PROPN
ejde-517	344	36	,	,	PUNCT
ejde-517	344	37	and	and	CCONJ
ejde-517	344	38	θ	θ	PROPN
ejde-517	344	39	(	(	PUNCT
ejde-517	344	40	definition	definition	NOUN
ejde-517	344	41	2.6	2.6	NUM
ejde-517	344	42	)	)	PUNCT
ejde-517	344	43	,	,	PUNCT
ejde-517	344	44	we	we	PRON
ejde-517	344	45	can	can	AUX
ejde-517	344	46	modify	modify	VERB
ejde-517	344	47	the	the	DET
ejde-517	344	48	two	two	NUM
ejde-517	344	49	-	-	PUNCT
ejde-517	344	50	phase	phase	NOUN
ejde-517	344	51	segmentation	segmentation	NOUN
ejde-517	344	52	algorithm	algorithm	NOUN
ejde-517	344	53	into	into	ADP
ejde-517	344	54	χk+1	χk+1	SYM
ejde-517	344	55	1	1	NUM
ejde-517	344	56	=	=	SYM
ejde-517	344	57	(	(	PUNCT
ejde-517	344	58	tδ	tδ	PROPN
ejde-517	344	59	◦	◦	NOUN
ejde-517	344	60	m	m	NOUN
ejde-517	344	61	◦	◦	NOUN
ejde-517	344	62	h	h	NOUN
ejde-517	344	63	◦	◦	NOUN
ejde-517	344	64	θ	θ	NOUN
ejde-517	344	65	◦	◦	NOUN
ejde-517	344	66	tδ)(χk1	tδ)(χk1	NOUN
ejde-517	344	67	)	)	PUNCT
ejde-517	344	68	.	.	PUNCT
ejde-517	345	1	(	(	PUNCT
ejde-517	345	2	3.28	3.28	NUM
ejde-517	345	3	)	)	PUNCT
ejde-517	345	4	the	the	DET
ejde-517	345	5	main	main	ADJ
ejde-517	345	6	goal	goal	NOUN
ejde-517	345	7	of	of	ADP
ejde-517	345	8	this	this	DET
ejde-517	345	9	article	article	NOUN
ejde-517	345	10	is	be	AUX
ejde-517	345	11	to	to	PART
ejde-517	345	12	show	show	VERB
ejde-517	345	13	that	that	SCONJ
ejde-517	345	14	(	(	PUNCT
ejde-517	345	15	3.28	3.28	NUM
ejde-517	345	16	)	)	PUNCT
ejde-517	345	17	has	have	VERB
ejde-517	345	18	a	a	DET
ejde-517	345	19	fixed	fix	VERB
ejde-517	345	20	point	point	NOUN
ejde-517	345	21	.	.	PUNCT
ejde-517	346	1	remark	remark	PROPN
ejde-517	346	2	3.14	3.14	NUM
ejde-517	346	3	.	.	PUNCT
ejde-517	347	1	it	it	PRON
ejde-517	347	2	is	be	AUX
ejde-517	347	3	again	again	ADV
ejde-517	347	4	emphasized	emphasize	VERB
ejde-517	347	5	that	that	SCONJ
ejde-517	347	6	the	the	DET
ejde-517	347	7	introduction	introduction	NOUN
ejde-517	347	8	of	of	ADP
ejde-517	347	9	z	z	PROPN
ejde-517	347	10	∈	∈	PROPN
ejde-517	347	11	l2(ω)\h1(ω	l2(ω)\h1(ω	NOUN
ejde-517	347	12	)	)	PUNCT
ejde-517	347	13	in	in	ADP
ejde-517	347	14	(	(	PUNCT
ejde-517	347	15	3.25	3.25	NUM
ejde-517	347	16	)	)	PUNCT
ejde-517	347	17	and	and	CCONJ
ejde-517	347	18	the	the	DET
ejde-517	347	19	modification	modification	NOUN
ejde-517	347	20	of	of	ADP
ejde-517	347	21	algorithm	algorithm	NOUN
ejde-517	347	22	(	(	PUNCT
ejde-517	347	23	1	1	NUM
ejde-517	347	24	)	)	PUNCT
ejde-517	347	25	as	as	ADP
ejde-517	347	26	a	a	DET
ejde-517	347	27	result	result	NOUN
ejde-517	347	28	of	of	ADP
ejde-517	347	29	the	the	DET
ejde-517	347	30	mollification	mollification	NOUN
ejde-517	347	31	of	of	ADP
ejde-517	347	32	χ1	χ1	NOUN
ejde-517	347	33	are	be	AUX
ejde-517	347	34	purely	purely	ADV
ejde-517	347	35	technical	technical	ADJ
ejde-517	347	36	devices	device	NOUN
ejde-517	347	37	and	and	CCONJ
ejde-517	347	38	are	be	AUX
ejde-517	347	39	used	use	VERB
ejde-517	347	40	only	only	ADV
ejde-517	347	41	for	for	ADP
ejde-517	347	42	theoretical	theoretical	ADJ
ejde-517	347	43	purposes	purpose	NOUN
ejde-517	347	44	.	.	PUNCT
ejde-517	348	1	this	this	PRON
ejde-517	348	2	might	might	AUX
ejde-517	348	3	seem	seem	VERB
ejde-517	348	4	like	like	ADP
ejde-517	348	5	a	a	DET
ejde-517	348	6	deviation	deviation	NOUN
ejde-517	348	7	from	from	ADP
ejde-517	348	8	algorithm	algorithm	NOUN
ejde-517	348	9	(	(	PUNCT
ejde-517	348	10	1	1	NUM
ejde-517	348	11	)	)	PUNCT
ejde-517	348	12	but	but	CCONJ
ejde-517	348	13	as	as	SCONJ
ejde-517	348	14	shown	show	VERB
ejde-517	348	15	in	in	ADP
ejde-517	348	16	(	(	PUNCT
ejde-517	348	17	3.23	3.23	NUM
ejde-517	348	18	)	)	PUNCT
ejde-517	348	19	,	,	PUNCT
ejde-517	348	20	(	(	PUNCT
ejde-517	348	21	3.24	3.24	NUM
ejde-517	348	22	)	)	PUNCT
ejde-517	348	23	and	and	CCONJ
ejde-517	348	24	(	(	PUNCT
ejde-517	348	25	3.27	3.27	NUM
ejde-517	348	26	)	)	PUNCT
ejde-517	348	27	,	,	PUNCT
ejde-517	348	28	these	these	DET
ejde-517	348	29	changes	change	NOUN
ejde-517	348	30	are	be	AUX
ejde-517	348	31	justified	justify	VERB
ejde-517	348	32	.	.	PUNCT
ejde-517	349	1	ejde-2020/93	ejde-2020/93	PROPN
ejde-517	349	2	impedance	impedance	NOUN
ejde-517	349	3	tomography	tomography	NOUN
ejde-517	349	4	problem	problem	NOUN
ejde-517	349	5	11	11	NUM
ejde-517	349	6	3.3	3.3	NUM
ejde-517	349	7	.	.	PUNCT
ejde-517	350	1	gradient	gradient	NOUN
ejde-517	350	2	of	of	ADP
ejde-517	350	3	the	the	DET
ejde-517	350	4	functional	functional	ADJ
ejde-517	350	5	j	j	PROPN
ejde-517	350	6	.	.	PUNCT
ejde-517	351	1	this	this	DET
ejde-517	351	2	section	section	NOUN
ejde-517	351	3	is	be	AUX
ejde-517	351	4	devoted	devote	VERB
ejde-517	351	5	to	to	ADP
ejde-517	351	6	showing	show	VERB
ejde-517	351	7	the	the	DET
ejde-517	351	8	validity	validity	NOUN
ejde-517	351	9	of	of	ADP
ejde-517	351	10	the	the	DET
ejde-517	351	11	explicit	explicit	ADJ
ejde-517	351	12	formulation	formulation	NOUN
ejde-517	351	13	of	of	ADP
ejde-517	351	14	the	the	DET
ejde-517	351	15	gradient	gradient	NOUN
ejde-517	351	16	of	of	ADP
ejde-517	351	17	j	j	PROPN
ejde-517	351	18	in	in	ADP
ejde-517	351	19	(	(	PUNCT
ejde-517	351	20	2.10	2.10	NUM
ejde-517	351	21	)	)	PUNCT
ejde-517	351	22	.	.	PUNCT
ejde-517	352	1	as	as	SCONJ
ejde-517	352	2	shown	show	VERB
ejde-517	352	3	in	in	ADP
ejde-517	352	4	the	the	DET
ejde-517	352	5	computation	computation	NOUN
ejde-517	352	6	of	of	ADP
ejde-517	352	7	(	(	PUNCT
ejde-517	352	8	2.12	2.12	NUM
ejde-517	352	9	)	)	PUNCT
ejde-517	352	10	,	,	PUNCT
ejde-517	352	11	it	it	PRON
ejde-517	352	12	is	be	AUX
ejde-517	352	13	sufficient	sufficient	ADJ
ejde-517	352	14	to	to	PART
ejde-517	352	15	show	show	VERB
ejde-517	352	16	that	that	SCONJ
ejde-517	352	17	δς1	δς1	ADJ
ejde-517	352	18	δχ1	δχ1	X
ejde-517	352	19	(	(	PUNCT
ejde-517	352	20	χ1	χ1	NOUN
ejde-517	352	21	;	;	PUNCT
ejde-517	352	22	δχ1	δχ1	X
ejde-517	352	23	)	)	PUNCT
ejde-517	352	24	∈	∈	PROPN
ejde-517	352	25	h1(ω	h1(ω	PROPN
ejde-517	352	26	)	)	PUNCT
ejde-517	352	27	.	.	PUNCT
ejde-517	353	1	this	this	PRON
ejde-517	353	2	is	be	AUX
ejde-517	353	3	not	not	PART
ejde-517	353	4	necessarily	necessarily	ADV
ejde-517	353	5	true	true	ADJ
ejde-517	353	6	for	for	ADP
ejde-517	353	7	an	an	DET
ejde-517	353	8	arbitrary	arbitrary	ADJ
ejde-517	353	9	characteristic	characteristic	ADJ
ejde-517	353	10	function	function	NOUN
ejde-517	353	11	χ1	χ1	NOUN
ejde-517	353	12	.	.	PUNCT
ejde-517	354	1	hence	hence	ADV
ejde-517	354	2	,	,	PUNCT
ejde-517	354	3	we	we	PRON
ejde-517	354	4	use	use	VERB
ejde-517	354	5	χδ1	χδ1	NOUN
ejde-517	354	6	instead	instead	ADV
ejde-517	354	7	of	of	ADP
ejde-517	354	8	χ1	χ1	NOUN
ejde-517	354	9	so	so	SCONJ
ejde-517	354	10	that	that	SCONJ
ejde-517	354	11	we	we	PRON
ejde-517	354	12	are	be	AUX
ejde-517	354	13	dealing	deal	VERB
ejde-517	354	14	with	with	ADP
ejde-517	354	15	a	a	DET
ejde-517	354	16	smooth	smooth	ADJ
ejde-517	354	17	function	function	NOUN
ejde-517	354	18	rather	rather	ADV
ejde-517	354	19	than	than	ADP
ejde-517	354	20	a	a	DET
ejde-517	354	21	characteristic	characteristic	ADJ
ejde-517	354	22	function	function	NOUN
ejde-517	354	23	.	.	PUNCT
ejde-517	355	1	thus	thus	ADV
ejde-517	355	2	,	,	PUNCT
ejde-517	355	3	we	we	PRON
ejde-517	355	4	are	be	AUX
ejde-517	355	5	now	now	ADV
ejde-517	355	6	solving	solve	VERB
ejde-517	355	7	σk+1	σk+1	NOUN
ejde-517	355	8	1	1	NUM
ejde-517	355	9	using	use	VERB
ejde-517	355	10	the	the	DET
ejde-517	355	11	equation∫	equation∫	NOUN
ejde-517	355	12	ω	ω	X
ejde-517	355	13	α(χδ1	α(χδ1	X
ejde-517	355	14	+	+	CCONJ
ejde-517	355	15	ε)∇σk+1	ε)∇σk+1	PROPN
ejde-517	355	16	1	1	NUM
ejde-517	355	17	·	·	PUNCT
ejde-517	355	18	∇v	∇v	ADJ
ejde-517	355	19	dv	dv	PROPN
ejde-517	355	20	+	+	CCONJ
ejde-517	355	21	∫	∫	PROPN
ejde-517	355	22	ω	ω	X
ejde-517	356	1	λ(σk+1	λ(σk+1	SYM
ejde-517	356	2	1	1	NUM
ejde-517	356	3	−	−	NOUN
ejde-517	356	4	σk1	σk1	NOUN
ejde-517	356	5	)	)	PUNCT
ejde-517	356	6	v	v	NOUN
ejde-517	356	7	dv	dv	PROPN
ejde-517	356	8	=	=	SYM
ejde-517	356	9	∫	∫	PROPN
ejde-517	356	10	ω	ω	PROPN
ejde-517	356	11	χδ1∇φ	χδ1∇φ	PROPN
ejde-517	356	12	·	·	PUNCT
ejde-517	357	1	∇φ∗v	∇φ∗v	PROPN
ejde-517	357	2	dv	dv	PROPN
ejde-517	357	3	,	,	PUNCT
ejde-517	357	4	(	(	PUNCT
ejde-517	357	5	3.29	3.29	NUM
ejde-517	357	6	)	)	PUNCT
ejde-517	357	7	for	for	ADP
ejde-517	357	8	all	all	PRON
ejde-517	357	9	v	v	ADP
ejde-517	357	10	∈	∈	PROPN
ejde-517	357	11	h1(ω	h1(ω	PROPN
ejde-517	357	12	)	)	PUNCT
ejde-517	357	13	.	.	PUNCT
ejde-517	358	1	before	before	SCONJ
ejde-517	358	2	we	we	PRON
ejde-517	358	3	start	start	VERB
ejde-517	358	4	our	our	PRON
ejde-517	358	5	calculations	calculation	NOUN
ejde-517	358	6	,	,	PUNCT
ejde-517	358	7	we	we	PRON
ejde-517	358	8	first	first	ADV
ejde-517	358	9	make	make	VERB
ejde-517	358	10	few	few	ADJ
ejde-517	358	11	assumptions	assumption	NOUN
ejde-517	358	12	.	.	PUNCT
ejde-517	359	1	these	these	PRON
ejde-517	359	2	will	will	AUX
ejde-517	359	3	be	be	AUX
ejde-517	359	4	used	use	VERB
ejde-517	359	5	throughout	throughout	ADP
ejde-517	359	6	our	our	PRON
ejde-517	359	7	analysis	analysis	NOUN
ejde-517	359	8	.	.	PUNCT
ejde-517	360	1	let	let	VERB
ejde-517	360	2	α	α	PRON
ejde-517	360	3	,	,	PUNCT
ejde-517	360	4	σ	σ	PROPN
ejde-517	360	5	,	,	PUNCT
ejde-517	360	6	λ	λ	PROPN
ejde-517	360	7	,	,	PUNCT
ejde-517	360	8	δ	δ	PROPN
ejde-517	360	9	>	>	X
ejde-517	360	10	0	0	X
ejde-517	360	11	.	.	PUNCT
ejde-517	361	1	we	we	PRON
ejde-517	361	2	assume	assume	VERB
ejde-517	361	3	that	that	SCONJ
ejde-517	361	4	σk1	σk1	NOUN
ejde-517	361	5	∈	∈	PROPN
ejde-517	361	6	c∞(ω̄	c∞(ω̄	ADV
ejde-517	361	7	)	)	PUNCT
ejde-517	361	8	such	such	ADJ
ejde-517	361	9	that	that	SCONJ
ejde-517	361	10	σk(χδ1	σk(χδ1	PROPN
ejde-517	361	11	)	)	PUNCT
ejde-517	361	12	≥	≥	PROPN
ejde-517	361	13	σ	σ	X
ejde-517	361	14	>	>	X
ejde-517	361	15	0	0	X
ejde-517	361	16	.	.	PUNCT
ejde-517	362	1	we	we	PRON
ejde-517	362	2	also	also	ADV
ejde-517	362	3	assume	assume	VERB
ejde-517	362	4	that	that	SCONJ
ejde-517	362	5	∂ω	∂ω	PROPN
ejde-517	362	6	is	be	AUX
ejde-517	362	7	sufficiently	sufficiently	ADV
ejde-517	362	8	smooth	smooth	ADJ
ejde-517	362	9	.	.	PUNCT
ejde-517	363	1	(	(	PUNCT
ejde-517	363	2	3.30	3.30	NUM
ejde-517	363	3	)	)	PUNCT
ejde-517	363	4	the	the	DET
ejde-517	363	5	assumption	assumption	NOUN
ejde-517	363	6	that	that	PRON
ejde-517	363	7	σk1	σk1	PROPN
ejde-517	363	8	∈	∈	PROPN
ejde-517	363	9	c∞(ω̄	c∞(ω̄	ADV
ejde-517	363	10	)	)	PUNCT
ejde-517	363	11	might	might	AUX
ejde-517	363	12	seem	seem	VERB
ejde-517	363	13	like	like	ADP
ejde-517	363	14	a	a	DET
ejde-517	363	15	strong	strong	ADJ
ejde-517	363	16	assumption	assumption	NOUN
ejde-517	363	17	but	but	CCONJ
ejde-517	363	18	if	if	SCONJ
ejde-517	363	19	we	we	PRON
ejde-517	363	20	can	can	AUX
ejde-517	363	21	show	show	VERB
ejde-517	363	22	that	that	SCONJ
ejde-517	363	23	σk+1	σk+1	PROPN
ejde-517	363	24	1	1	NUM
ejde-517	363	25	∈	∈	NOUN
ejde-517	363	26	c∞(ω̄	c∞(ω̄	NOUN
ejde-517	363	27	)	)	PUNCT
ejde-517	363	28	as	as	ADV
ejde-517	363	29	well	well	ADV
ejde-517	363	30	,	,	PUNCT
ejde-517	363	31	then	then	ADV
ejde-517	363	32	this	this	DET
ejde-517	363	33	assumption	assumption	NOUN
ejde-517	363	34	makes	make	VERB
ejde-517	363	35	sense	sense	NOUN
ejde-517	363	36	.	.	PUNCT
ejde-517	364	1	moreover	moreover	ADV
ejde-517	364	2	,	,	PUNCT
ejde-517	364	3	the	the	DET
ejde-517	364	4	initial	initial	ADJ
ejde-517	364	5	guess	guess	NOUN
ejde-517	364	6	for	for	ADP
ejde-517	364	7	σ1	σ1	PROPN
ejde-517	364	8	in	in	ADP
ejde-517	364	9	our	our	PRON
ejde-517	364	10	algorithm	algorithm	NOUN
ejde-517	364	11	can	can	AUX
ejde-517	364	12	be	be	AUX
ejde-517	364	13	chosen	choose	VERB
ejde-517	364	14	to	to	PART
ejde-517	364	15	be	be	AUX
ejde-517	364	16	constant	constant	ADJ
ejde-517	364	17	throughout	throughout	ADP
ejde-517	364	18	ω	ω	PROPN
ejde-517	364	19	so	so	SCONJ
ejde-517	364	20	that	that	SCONJ
ejde-517	364	21	it	it	PRON
ejde-517	364	22	is	be	AUX
ejde-517	364	23	in	in	ADP
ejde-517	364	24	c∞(ω̄	c∞(ω̄	ADJ
ejde-517	364	25	)	)	PUNCT
ejde-517	364	26	.	.	PUNCT
ejde-517	365	1	we	we	PRON
ejde-517	365	2	now	now	ADV
ejde-517	365	3	investigate	investigate	VERB
ejde-517	365	4	what	what	PRON
ejde-517	365	5	happens	happen	VERB
ejde-517	365	6	to	to	ADP
ejde-517	365	7	φ	φ	PROPN
ejde-517	365	8	and	and	CCONJ
ejde-517	365	9	φ∗	φ∗	NOUN
ejde-517	365	10	if	if	SCONJ
ejde-517	365	11	we	we	PRON
ejde-517	365	12	use	use	VERB
ejde-517	365	13	the	the	DET
ejde-517	365	14	above	above	ADJ
ejde-517	365	15	assumption	assumption	NOUN
ejde-517	365	16	.	.	PUNCT
ejde-517	366	1	lemma	lemma	PROPN
ejde-517	366	2	3.15	3.15	NUM
ejde-517	366	3	.	.	PUNCT
ejde-517	367	1	under	under	ADP
ejde-517	367	2	assumption	assumption	NOUN
ejde-517	367	3	(	(	PUNCT
ejde-517	367	4	3.30	3.30	NUM
ejde-517	367	5	)	)	PUNCT
ejde-517	367	6	,	,	PUNCT
ejde-517	367	7	‖∇φ‖l∞(ω	‖∇φ‖l∞(ω	NOUN
ejde-517	367	8	)	)	PUNCT
ejde-517	367	9	≤	≤	NUM
ejde-517	367	10	cδ‖φ‖h1(ω	cδ‖φ‖h1(ω	NOUN
ejde-517	367	11	)	)	PUNCT
ejde-517	367	12	,	,	PUNCT
ejde-517	367	13	(	(	PUNCT
ejde-517	367	14	3.31	3.31	NUM
ejde-517	367	15	)	)	PUNCT
ejde-517	367	16	for	for	ADP
ejde-517	367	17	some	some	DET
ejde-517	367	18	cδ	cδ	NOUN
ejde-517	367	19	>	>	X
ejde-517	367	20	0	0	PUNCT
ejde-517	368	1	(	(	PUNCT
ejde-517	368	2	compare	compare	VERB
ejde-517	368	3	with	with	ADP
ejde-517	368	4	[	[	X
ejde-517	368	5	9	9	NUM
ejde-517	368	6	]	]	NUM
ejde-517	368	7	)	)	PUNCT
ejde-517	368	8	.	.	PUNCT
ejde-517	369	1	in	in	ADP
ejde-517	369	2	fact	fact	NOUN
ejde-517	369	3	,	,	PUNCT
ejde-517	369	4	φ	φ	PROPN
ejde-517	369	5	∈	∈	PROPN
ejde-517	369	6	c∞(ω̄	c∞(ω̄	PRON
ejde-517	369	7	)	)	PUNCT
ejde-517	369	8	.	.	PUNCT
ejde-517	370	1	proof	proof	NOUN
ejde-517	370	2	.	.	PUNCT
ejde-517	371	1	by	by	ADP
ejde-517	371	2	assumption	assumption	NOUN
ejde-517	371	3	(	(	PUNCT
ejde-517	371	4	3.30	3.30	NUM
ejde-517	371	5	)	)	PUNCT
ejde-517	371	6	and	and	CCONJ
ejde-517	371	7	lemma	lemma	PROPN
ejde-517	371	8	(	(	PUNCT
ejde-517	371	9	2.5	2.5	NUM
ejde-517	371	10	)	)	PUNCT
ejde-517	371	11	,	,	PUNCT
ejde-517	371	12	σk	σk	ADV
ejde-517	371	13	∈	∈	PROPN
ejde-517	371	14	c∞(ω̄	c∞(ω̄	NUM
ejde-517	371	15	)	)	PUNCT
ejde-517	371	16	.	.	PUNCT
ejde-517	372	1	let	let	VERB
ejde-517	372	2	l	l	NOUN
ejde-517	372	3	≥	≥	NUM
ejde-517	372	4	1	1	NUM
ejde-517	372	5	.	.	PUNCT
ejde-517	373	1	obviously	obviously	ADV
ejde-517	373	2	,	,	PUNCT
ejde-517	373	3	σk	σk	CCONJ
ejde-517	373	4	∈	∈	PROPN
ejde-517	373	5	cl(ω̄	cl(ω̄	PROPN
ejde-517	373	6	)	)	PUNCT
ejde-517	373	7	.	.	PUNCT
ejde-517	374	1	therefore	therefore	ADV
ejde-517	374	2	,	,	PUNCT
ejde-517	374	3	using	use	VERB
ejde-517	374	4	standard	standard	ADJ
ejde-517	374	5	regularity	regularity	NOUN
ejde-517	374	6	estimates	estimate	NOUN
ejde-517	374	7	(	(	PUNCT
ejde-517	374	8	see	see	VERB
ejde-517	374	9	,	,	PUNCT
ejde-517	374	10	e.g.	e.g.	ADV
ejde-517	374	11	,	,	PUNCT
ejde-517	374	12	[	[	X
ejde-517	374	13	16	16	NUM
ejde-517	374	14	]	]	PUNCT
ejde-517	374	15	)	)	PUNCT
ejde-517	374	16	,	,	PUNCT
ejde-517	374	17	we	we	PRON
ejde-517	374	18	obtain	obtain	VERB
ejde-517	374	19	‖φ‖hl+2(ω	‖φ‖hl+2(ω	NOUN
ejde-517	374	20	)	)	PUNCT
ejde-517	374	21	≤	≤	NOUN
ejde-517	374	22	c1‖φ‖h1(ω	c1‖φ‖h1(ω	NOUN
ejde-517	374	23	)	)	PUNCT
ejde-517	374	24	,	,	PUNCT
ejde-517	374	25	(	(	PUNCT
ejde-517	374	26	3.32	3.32	NUM
ejde-517	374	27	)	)	PUNCT
ejde-517	374	28	for	for	ADP
ejde-517	374	29	some	some	DET
ejde-517	374	30	c1	c1	PROPN
ejde-517	374	31	>	>	X
ejde-517	374	32	0	0	X
ejde-517	374	33	.	.	PUNCT
ejde-517	375	1	furthermore	furthermore	ADV
ejde-517	375	2	,	,	PUNCT
ejde-517	375	3	by	by	ADP
ejde-517	375	4	the	the	DET
ejde-517	375	5	sobolev	sobolev	NOUN
ejde-517	375	6	imbedding	imbedding	NOUN
ejde-517	375	7	theorem	theorem	NOUN
ejde-517	375	8	[	[	X
ejde-517	375	9	14	14	NUM
ejde-517	375	10	]	]	PUNCT
ejde-517	375	11	,	,	PUNCT
ejde-517	375	12	we	we	PRON
ejde-517	375	13	have	have	VERB
ejde-517	375	14	‖φ‖cl	‖φ‖cl	NOUN
ejde-517	375	15	,	,	PUNCT
ejde-517	375	16	γ(ω̄	γ(ω̄	NOUN
ejde-517	375	17	)	)	PUNCT
ejde-517	375	18	≤	≤	PUNCT
ejde-517	375	19	c2‖φ‖hl+2(ω	c2‖φ‖hl+2(ω	PROPN
ejde-517	375	20	)	)	PUNCT
ejde-517	375	21	.	.	PUNCT
ejde-517	376	1	(	(	PUNCT
ejde-517	376	2	3.33	3.33	NUM
ejde-517	376	3	)	)	PUNCT
ejde-517	376	4	by	by	ADP
ejde-517	376	5	the	the	DET
ejde-517	376	6	definition	definition	NOUN
ejde-517	376	7	of	of	ADP
ejde-517	376	8	‖	‖	PROPN
ejde-517	376	9	·	·	SYM
ejde-517	376	10	‖cl	‖cl	PROPN
ejde-517	376	11	,	,	PUNCT
ejde-517	376	12	γ(ω̄	γ(ω̄	NUM
ejde-517	376	13	)	)	PUNCT
ejde-517	376	14	,	,	PUNCT
ejde-517	376	15	the	the	DET
ejde-517	376	16	embedding	embed	VERB
ejde-517	376	17	c1,γ(ω̄	c1,γ(ω̄	NOUN
ejde-517	376	18	)	)	PUNCT
ejde-517	376	19	↪	↪	PROPN
ejde-517	376	20	→	→	SYM
ejde-517	376	21	c1(ω̄	c1(ω̄	NUM
ejde-517	376	22	)	)	PUNCT
ejde-517	376	23	(	(	PUNCT
ejde-517	376	24	3.34	3.34	NUM
ejde-517	376	25	)	)	PUNCT
ejde-517	376	26	is	be	AUX
ejde-517	376	27	continuous	continuous	ADJ
ejde-517	376	28	(	(	PUNCT
ejde-517	376	29	see	see	VERB
ejde-517	376	30	[	[	X
ejde-517	376	31	18	18	NUM
ejde-517	376	32	]	]	NUM
ejde-517	376	33	)	)	PUNCT
ejde-517	376	34	.	.	PUNCT
ejde-517	377	1	if	if	SCONJ
ejde-517	377	2	we	we	PRON
ejde-517	377	3	compare	compare	VERB
ejde-517	377	4	(	(	PUNCT
ejde-517	377	5	3.32	3.32	NUM
ejde-517	377	6	)	)	PUNCT
ejde-517	377	7	,	,	PUNCT
ejde-517	377	8	(	(	PUNCT
ejde-517	377	9	3.33	3.33	NUM
ejde-517	377	10	)	)	PUNCT
ejde-517	377	11	,	,	PUNCT
ejde-517	377	12	and	and	CCONJ
ejde-517	377	13	(	(	PUNCT
ejde-517	377	14	3.34	3.34	NUM
ejde-517	377	15	)	)	PUNCT
ejde-517	377	16	,	,	PUNCT
ejde-517	377	17	we	we	PRON
ejde-517	377	18	can	can	AUX
ejde-517	377	19	deduce	deduce	VERB
ejde-517	377	20	that	that	SCONJ
ejde-517	377	21	there	there	PRON
ejde-517	377	22	exists	exist	VERB
ejde-517	377	23	c	c	NOUN
ejde-517	377	24	>	>	X
ejde-517	377	25	0	0	NUM
ejde-517	377	26	such	such	ADJ
ejde-517	377	27	that	that	SCONJ
ejde-517	377	28	‖∇φ‖l∞(ω	‖∇φ‖l∞(ω	NOUN
ejde-517	377	29	)	)	PUNCT
ejde-517	377	30	≤	≤	NOUN
ejde-517	377	31	c‖∇φ‖h1(ω	c‖∇φ‖h1(ω	NOUN
ejde-517	377	32	)	)	PUNCT
ejde-517	377	33	,	,	PUNCT
ejde-517	377	34	(	(	PUNCT
ejde-517	377	35	3.35	3.35	NUM
ejde-517	377	36	)	)	PUNCT
ejde-517	377	37	which	which	PRON
ejde-517	377	38	completes	complete	VERB
ejde-517	377	39	the	the	DET
ejde-517	377	40	first	first	ADJ
ejde-517	377	41	part	part	NOUN
ejde-517	377	42	of	of	ADP
ejde-517	377	43	the	the	DET
ejde-517	377	44	proof	proof	NOUN
ejde-517	377	45	.	.	PUNCT
ejde-517	378	1	moreover	moreover	ADV
ejde-517	378	2	,	,	PUNCT
ejde-517	378	3	because	because	SCONJ
ejde-517	378	4	l	l	PROPN
ejde-517	378	5	≥	≥	NUM
ejde-517	378	6	1	1	NUM
ejde-517	378	7	,	,	PUNCT
ejde-517	378	8	it	it	PRON
ejde-517	378	9	follows	follow	VERB
ejde-517	378	10	that	that	SCONJ
ejde-517	378	11	φ(χδ1	φ(χδ1	NUM
ejde-517	378	12	)	)	PUNCT
ejde-517	378	13	∈	∈	NOUN
ejde-517	378	14	c∞(ω̄	c∞(ω̄	PROPN
ejde-517	378	15	)	)	PUNCT
ejde-517	378	16	.	.	PUNCT
ejde-517	379	1	�	�	PROPN
ejde-517	379	2	lemma	lemma	PROPN
ejde-517	379	3	3.16	3.16	NUM
ejde-517	379	4	.	.	PUNCT
ejde-517	380	1	under	under	ADP
ejde-517	380	2	assumption	assumption	NOUN
ejde-517	380	3	(	(	PUNCT
ejde-517	380	4	3.30	3.30	NUM
ejde-517	380	5	)	)	PUNCT
ejde-517	380	6	,	,	PUNCT
ejde-517	380	7	there	there	PRON
ejde-517	380	8	exists	exist	VERB
ejde-517	380	9	cδ	cδ	VERB
ejde-517	380	10	>	>	X
ejde-517	380	11	0	0	NUM
ejde-517	381	1	such	such	ADJ
ejde-517	381	2	that	that	DET
ejde-517	381	3	‖∇φ∗‖l∞(ω	‖∇φ∗‖l∞(ω	NOUN
ejde-517	381	4	)	)	PUNCT
ejde-517	381	5	≤	≤	NUM
ejde-517	381	6	cδ‖φ∗‖h1(ω	cδ‖φ∗‖h1(ω	PROPN
ejde-517	381	7	)	)	PUNCT
ejde-517	381	8	.	.	PUNCT
ejde-517	382	1	(	(	PUNCT
ejde-517	382	2	3.36	3.36	NUM
ejde-517	382	3	)	)	PUNCT
ejde-517	382	4	furthermore	furthermore	ADV
ejde-517	382	5	,	,	PUNCT
ejde-517	382	6	φ∗	φ∗	NOUN
ejde-517	382	7	∈	∈	NOUN
ejde-517	382	8	c∞(ω̄	c∞(ω̄	NOUN
ejde-517	382	9	)	)	PUNCT
ejde-517	382	10	.	.	PUNCT
ejde-517	383	1	12	12	NUM
ejde-517	383	2	r.	r.	PROPN
ejde-517	383	3	mendoza	mendoza	PROPN
ejde-517	383	4	,	,	PUNCT
ejde-517	383	5	s.	s.	PROPN
ejde-517	383	6	keeling	keeling	PROPN
ejde-517	383	7	ejde-2020/93	ejde-2020/93	PROPN
ejde-517	383	8	the	the	DET
ejde-517	383	9	proof	proof	NOUN
ejde-517	383	10	of	of	ADP
ejde-517	383	11	this	this	DET
ejde-517	383	12	theorem	theorem	NOUN
ejde-517	383	13	is	be	AUX
ejde-517	383	14	similar	similar	ADJ
ejde-517	383	15	to	to	ADP
ejde-517	383	16	that	that	PRON
ejde-517	383	17	of	of	ADP
ejde-517	383	18	the	the	DET
ejde-517	383	19	previous	previous	ADJ
ejde-517	383	20	theorem	theorem	NOUN
ejde-517	383	21	.	.	PUNCT
ejde-517	384	1	we	we	PRON
ejde-517	384	2	now	now	ADV
ejde-517	384	3	analyze	analyze	VERB
ejde-517	384	4	the	the	DET
ejde-517	384	5	dependence	dependence	NOUN
ejde-517	384	6	of	of	ADP
ejde-517	384	7	φ	φ	PROPN
ejde-517	384	8	and	and	CCONJ
ejde-517	384	9	φ∗	φ∗	NOUN
ejde-517	384	10	on	on	ADP
ejde-517	384	11	χδ1	χδ1	PROPN
ejde-517	384	12	.	.	PUNCT
ejde-517	385	1	from	from	ADP
ejde-517	385	2	here	here	ADV
ejde-517	385	3	onwards	onward	NOUN
ejde-517	385	4	,	,	PUNCT
ejde-517	385	5	we	we	PRON
ejde-517	385	6	denote	denote	VERB
ejde-517	385	7	δχδ1	δχδ1	NOUN
ejde-517	385	8	:	:	PUNCT
ejde-517	385	9	=	=	PUNCT
ejde-517	385	10	δχ1	δχ1	NOUN
ejde-517	385	11	∗	∗	NOUN
ejde-517	385	12	ξδ	ξδ	ADV
ejde-517	385	13	so	so	SCONJ
ejde-517	385	14	that	that	SCONJ
ejde-517	385	15	(	(	PUNCT
ejde-517	385	16	χ1	χ1	NOUN
ejde-517	385	17	+	+	CCONJ
ejde-517	385	18	ηδχ1	ηδχ1	PROPN
ejde-517	385	19	)	)	PUNCT
ejde-517	385	20	∗	∗	NOUN
ejde-517	385	21	ξδ	ξδ	ADP
ejde-517	385	22	=	=	PUNCT
ejde-517	385	23	χδ1	χδ1	X
ejde-517	385	24	+	+	CCONJ
ejde-517	385	25	ηδχδ1	ηδχδ1	ADJ
ejde-517	385	26	.	.	PUNCT
ejde-517	386	1	suppose	suppose	VERB
ejde-517	386	2	we	we	PRON
ejde-517	386	3	replace	replace	VERB
ejde-517	386	4	χδ1	χδ1	NOUN
ejde-517	386	5	with	with	ADP
ejde-517	386	6	χδ1	χδ1	NOUN
ejde-517	386	7	+	+	CCONJ
ejde-517	386	8	ηδχδ1	ηδχδ1	ADJ
ejde-517	386	9	.	.	X
ejde-517	386	10	again	again	ADV
ejde-517	386	11	by	by	ADP
ejde-517	386	12	remark	remark	NOUN
ejde-517	386	13	3.4	3.4	NUM
ejde-517	386	14	,	,	PUNCT
ejde-517	386	15	η	η	PROPN
ejde-517	386	16	should	should	AUX
ejde-517	386	17	be	be	AUX
ejde-517	386	18	taken	take	VERB
ejde-517	386	19	from	from	ADP
ejde-517	386	20	the	the	DET
ejde-517	386	21	set	set	NOUN
ejde-517	386	22	(	(	PUNCT
ejde-517	386	23	0	0	NUM
ejde-517	386	24	,	,	PUNCT
ejde-517	386	25	τ	τ	PROPN
ejde-517	386	26	)	)	PUNCT
ejde-517	386	27	where	where	SCONJ
ejde-517	386	28	τ	τ	PROPN
ejde-517	386	29	is	be	AUX
ejde-517	386	30	chosen	choose	VERB
ejde-517	386	31	so	so	SCONJ
ejde-517	386	32	that	that	SCONJ
ejde-517	386	33	σk	σk	PROPN
ejde-517	386	34	+	+	CCONJ
ejde-517	386	35	ηδσk	ηδσk	NOUN
ejde-517	386	36	≥	≥	NOUN
ejde-517	386	37	στ	στ	INTJ
ejde-517	386	38	>	>	X
ejde-517	387	1	0	0	X
ejde-517	387	2	.	.	PUNCT
ejde-517	388	1	therefore	therefore	ADV
ejde-517	388	2	,	,	PUNCT
ejde-517	388	3	from	from	ADP
ejde-517	388	4	(	(	PUNCT
ejde-517	388	5	3.6	3.6	NUM
ejde-517	388	6	)	)	PUNCT
ejde-517	388	7	,	,	PUNCT
ejde-517	388	8	(	(	PUNCT
ejde-517	388	9	3.7	3.7	NUM
ejde-517	388	10	)	)	PUNCT
ejde-517	388	11	,	,	PUNCT
ejde-517	388	12	(	(	PUNCT
ejde-517	388	13	3.14	3.14	NUM
ejde-517	388	14	)	)	PUNCT
ejde-517	388	15	,	,	PUNCT
ejde-517	388	16	(	(	PUNCT
ejde-517	388	17	3.31	3.31	NUM
ejde-517	388	18	)	)	PUNCT
ejde-517	388	19	,	,	PUNCT
ejde-517	388	20	and	and	CCONJ
ejde-517	388	21	(	(	PUNCT
ejde-517	388	22	3.36	3.36	NUM
ejde-517	388	23	)	)	PUNCT
ejde-517	388	24	,	,	PUNCT
ejde-517	388	25	the	the	DET
ejde-517	388	26	following	follow	VERB
ejde-517	388	27	estimates	estimate	NOUN
ejde-517	388	28	hold	hold	VERB
ejde-517	388	29	‖∇φ(χδ1	‖∇φ(χδ1	X
ejde-517	388	30	+	+	NOUN
ejde-517	388	31	ηδχδ1)‖l∞(ω	ηδχδ1)‖l∞(ω	NOUN
ejde-517	388	32	)	)	PUNCT
ejde-517	388	33	≤	≤	NOUN
ejde-517	388	34	c1‖f‖l̃2(∂ω	c1‖f‖l̃2(∂ω	NOUN
ejde-517	388	35	)	)	PUNCT
ejde-517	388	36	,	,	PUNCT
ejde-517	388	37	(	(	PUNCT
ejde-517	388	38	3.37	3.37	NUM
ejde-517	388	39	)	)	PUNCT
ejde-517	388	40	‖∇φ∗(χδ1	‖∇φ∗(χδ1	PROPN
ejde-517	388	41	+	+	CCONJ
ejde-517	388	42	ηδχδ1)‖l∞(ω	ηδχδ1)‖l∞(ω	NOUN
ejde-517	388	43	)	)	PUNCT
ejde-517	388	44	≤	≤	NOUN
ejde-517	388	45	c2	c2	PROPN
ejde-517	388	46	(	(	PUNCT
ejde-517	388	47	‖f‖l̃2(∂ω	‖f‖l̃2(∂ω	NUM
ejde-517	388	48	)	)	PUNCT
ejde-517	389	1	+	+	NUM
ejde-517	389	2	‖ṽ	‖ṽ	PUNCT
ejde-517	389	3	‖l̃2(∂ω	‖l̃2(∂ω	X
ejde-517	389	4	)	)	PUNCT
ejde-517	389	5	)	)	PUNCT
ejde-517	389	6	,	,	PUNCT
ejde-517	389	7	(	(	PUNCT
ejde-517	389	8	3.38	3.38	NUM
ejde-517	389	9	)	)	PUNCT
ejde-517	389	10	for	for	ADP
ejde-517	389	11	some	some	DET
ejde-517	389	12	c1	c1	NOUN
ejde-517	389	13	,	,	PUNCT
ejde-517	389	14	c2	c2	PROPN
ejde-517	389	15	>	>	X
ejde-517	389	16	0	0	PUNCT
ejde-517	389	17	and	and	CCONJ
ejde-517	389	18	for	for	ADP
ejde-517	389	19	all	all	DET
ejde-517	389	20	η	η	PROPN
ejde-517	389	21	∈	∈	PROPN
ejde-517	389	22	(	(	PUNCT
ejde-517	389	23	0	0	NUM
ejde-517	389	24	,	,	PUNCT
ejde-517	389	25	τ	τ	PROPN
ejde-517	389	26	)	)	PUNCT
ejde-517	389	27	.	.	PUNCT
ejde-517	390	1	in	in	ADP
ejde-517	390	2	corollary	corollary	ADJ
ejde-517	390	3	3.7	3.7	NUM
ejde-517	390	4	,	,	PUNCT
ejde-517	390	5	we	we	PRON
ejde-517	390	6	have	have	AUX
ejde-517	390	7	shown	show	VERB
ejde-517	390	8	that	that	SCONJ
ejde-517	390	9	φ	φ	PROPN
ejde-517	390	10	and	and	CCONJ
ejde-517	390	11	φ∗	φ∗	NOUN
ejde-517	390	12	depend	depend	VERB
ejde-517	390	13	continuously	continuously	ADV
ejde-517	390	14	on	on	ADP
ejde-517	390	15	χ1	χ1	NOUN
ejde-517	390	16	.	.	PUNCT
ejde-517	391	1	observe	observe	VERB
ejde-517	391	2	that	that	SCONJ
ejde-517	391	3	this	this	DET
ejde-517	391	4	theorem	theorem	NOUN
ejde-517	391	5	holds	hold	VERB
ejde-517	391	6	with	with	ADP
ejde-517	391	7	any	any	DET
ejde-517	391	8	χ1	χ1	NOUN
ejde-517	391	9	whose	whose	DET
ejde-517	391	10	value	value	NOUN
ejde-517	391	11	is	be	AUX
ejde-517	391	12	between	between	ADP
ejde-517	391	13	0	0	NUM
ejde-517	391	14	and	and	CCONJ
ejde-517	391	15	1	1	NUM
ejde-517	391	16	.	.	PUNCT
ejde-517	392	1	therefore	therefore	ADV
ejde-517	392	2	,	,	PUNCT
ejde-517	392	3	this	this	PRON
ejde-517	392	4	also	also	ADV
ejde-517	392	5	holds	hold	VERB
ejde-517	392	6	when	when	SCONJ
ejde-517	392	7	we	we	PRON
ejde-517	392	8	use	use	VERB
ejde-517	392	9	χδ1	χδ1	NOUN
ejde-517	392	10	instead	instead	ADV
ejde-517	392	11	because	because	SCONJ
ejde-517	392	12	0	0	NUM
ejde-517	392	13	≤	≤	NUM
ejde-517	392	14	χδ1	χδ1	VERB
ejde-517	392	15	≤	≤	NUM
ejde-517	392	16	1	1	NUM
ejde-517	392	17	as	as	SCONJ
ejde-517	392	18	proven	prove	VERB
ejde-517	392	19	in	in	ADP
ejde-517	392	20	lemma	lemma	PROPN
ejde-517	392	21	(	(	PUNCT
ejde-517	392	22	2.5	2.5	NUM
ejde-517	392	23	)	)	PUNCT
ejde-517	392	24	.	.	PUNCT
ejde-517	393	1	we	we	PRON
ejde-517	393	2	state	state	VERB
ejde-517	393	3	this	this	PRON
ejde-517	393	4	in	in	ADP
ejde-517	393	5	the	the	DET
ejde-517	393	6	following	follow	VERB
ejde-517	393	7	lemma	lemma	PROPN
ejde-517	393	8	.	.	PUNCT
ejde-517	394	1	lemma	lemma	PROPN
ejde-517	394	2	3.17	3.17	NUM
ejde-517	394	3	.	.	PUNCT
ejde-517	395	1	under	under	ADP
ejde-517	395	2	assumption	assumption	NOUN
ejde-517	395	3	(	(	PUNCT
ejde-517	395	4	3.30	3.30	NUM
ejde-517	395	5	)	)	PUNCT
ejde-517	395	6	,	,	PUNCT
ejde-517	395	7	there	there	PRON
ejde-517	395	8	exists	exist	VERB
ejde-517	395	9	cδ1	cδ1	PROPN
ejde-517	395	10	,	,	PUNCT
ejde-517	395	11	c	c	PROPN
ejde-517	395	12	δ	δ	PROPN
ejde-517	395	13	2	2	NUM
ejde-517	395	14	>	>	SYM
ejde-517	395	15	0	0	NUM
ejde-517	395	16	such	such	ADJ
ejde-517	395	17	that	that	SCONJ
ejde-517	395	18	‖φ(χδ1	‖φ(χδ1	NUM
ejde-517	395	19	+	+	CCONJ
ejde-517	395	20	ηδχδ1)−	ηδχδ1)−	PROPN
ejde-517	395	21	φ(χδ1)‖h1(ω	φ(χδ1)‖h1(ω	NUM
ejde-517	395	22	)	)	PUNCT
ejde-517	395	23	≤	≤	NOUN
ejde-517	395	24	cδ1η‖δχ1‖l2(ω	cδ1η‖δχ1‖l2(ω	ADV
ejde-517	395	25	)	)	PUNCT
ejde-517	395	26	,	,	PUNCT
ejde-517	395	27	(	(	PUNCT
ejde-517	395	28	3.39	3.39	NUM
ejde-517	395	29	)	)	PUNCT
ejde-517	395	30	‖φ∗(χδ1	‖φ∗(χδ1	PROPN
ejde-517	395	31	+	+	CCONJ
ejde-517	395	32	ηδχδ1)−	ηδχδ1)−	PROPN
ejde-517	395	33	φ∗(χδ1)‖h1(ω	φ∗(χδ1)‖h1(ω	NOUN
ejde-517	395	34	)	)	PUNCT
ejde-517	395	35	≤	≤	NUM
ejde-517	395	36	cδ2η‖δχ1‖l2(ω	cδ2η‖δχ1‖l2(ω	NOUN
ejde-517	395	37	)	)	PUNCT
ejde-517	395	38	,	,	PUNCT
ejde-517	395	39	(	(	PUNCT
ejde-517	395	40	3.40	3.40	NUM
ejde-517	395	41	)	)	PUNCT
ejde-517	395	42	for	for	ADP
ejde-517	395	43	any	any	DET
ejde-517	395	44	η	η	PROPN
ejde-517	395	45	∈	∈	PROPN
ejde-517	395	46	(	(	PUNCT
ejde-517	395	47	0	0	NUM
ejde-517	395	48	,	,	PUNCT
ejde-517	395	49	τ	τ	PROPN
ejde-517	395	50	)	)	PUNCT
ejde-517	395	51	,	,	PUNCT
ejde-517	395	52	where	where	SCONJ
ejde-517	395	53	τ	τ	PROPN
ejde-517	395	54	is	be	AUX
ejde-517	395	55	chosen	choose	VERB
ejde-517	395	56	according	accord	VERB
ejde-517	395	57	to	to	PART
ejde-517	395	58	remark	remark	NOUN
ejde-517	395	59	3.4	3.4	NUM
ejde-517	395	60	.	.	PUNCT
ejde-517	396	1	we	we	PRON
ejde-517	396	2	define	define	VERB
ejde-517	396	3	ψ(χδ1	ψ(χδ1	NOUN
ejde-517	396	4	)	)	PUNCT
ejde-517	396	5	:	:	PUNCT
ejde-517	396	6	=	=	PUNCT
ejde-517	396	7	∇φ(χδ1	∇φ(χδ1	NOUN
ejde-517	396	8	)	)	PUNCT
ejde-517	396	9	·	·	PUNCT
ejde-517	396	10	∇φ∗(χδ1	∇φ∗(χδ1	NOUN
ejde-517	396	11	)	)	PUNCT
ejde-517	396	12	.	.	PUNCT
ejde-517	397	1	(	(	PUNCT
ejde-517	397	2	3.41	3.41	NUM
ejde-517	397	3	)	)	PUNCT
ejde-517	397	4	observe	observe	VERB
ejde-517	397	5	that	that	SCONJ
ejde-517	397	6	the	the	DET
ejde-517	397	7	right	right	ADJ
ejde-517	397	8	-	-	PUNCT
ejde-517	397	9	hand	hand	NOUN
ejde-517	397	10	side	side	NOUN
ejde-517	397	11	of	of	ADP
ejde-517	397	12	(	(	PUNCT
ejde-517	397	13	3.29	3.29	NUM
ejde-517	397	14	)	)	PUNCT
ejde-517	397	15	includes	include	VERB
ejde-517	397	16	ψ(χδ1	ψ(χδ1	NOUN
ejde-517	397	17	)	)	PUNCT
ejde-517	397	18	.	.	PUNCT
ejde-517	398	1	in	in	ADP
ejde-517	398	2	the	the	DET
ejde-517	398	3	next	next	ADJ
ejde-517	398	4	lemma	lemma	PROPN
ejde-517	398	5	,	,	PUNCT
ejde-517	398	6	we	we	PRON
ejde-517	398	7	show	show	VERB
ejde-517	398	8	that	that	SCONJ
ejde-517	398	9	ψ	ψ	NOUN
ejde-517	398	10	depends	depend	VERB
ejde-517	398	11	continuously	continuously	ADV
ejde-517	398	12	on	on	ADP
ejde-517	398	13	χ1	χ1	NOUN
ejde-517	398	14	.	.	PUNCT
ejde-517	399	1	this	this	PRON
ejde-517	399	2	will	will	AUX
ejde-517	399	3	be	be	AUX
ejde-517	399	4	necessary	necessary	ADJ
ejde-517	399	5	when	when	SCONJ
ejde-517	399	6	we	we	PRON
ejde-517	399	7	analyze	analyze	VERB
ejde-517	399	8	the	the	DET
ejde-517	399	9	solution	solution	NOUN
ejde-517	399	10	of	of	ADP
ejde-517	399	11	(	(	PUNCT
ejde-517	399	12	3.29	3.29	NUM
ejde-517	399	13	)	)	PUNCT
ejde-517	399	14	.	.	PUNCT
ejde-517	400	1	note	note	VERB
ejde-517	400	2	that	that	SCONJ
ejde-517	400	3	∇φ∗(χδ1	∇φ∗(χδ1	NOUN
ejde-517	400	4	)	)	PUNCT
ejde-517	400	5	∈	∈	PROPN
ejde-517	400	6	l2(ω	l2(ω	NOUN
ejde-517	400	7	)	)	PUNCT
ejde-517	400	8	by	by	ADP
ejde-517	400	9	corollary	corollary	ADJ
ejde-517	400	10	3.2	3.2	NUM
ejde-517	400	11	and	and	CCONJ
ejde-517	400	12	∇φ(χδ1	∇φ(χδ1	NOUN
ejde-517	400	13	)	)	PUNCT
ejde-517	400	14	∈	∈	PROPN
ejde-517	400	15	l∞(ω	l∞(ω	NOUN
ejde-517	400	16	)	)	PUNCT
ejde-517	400	17	by	by	ADP
ejde-517	400	18	(	(	PUNCT
ejde-517	400	19	3.31	3.31	NUM
ejde-517	400	20	)	)	PUNCT
ejde-517	400	21	.	.	PUNCT
ejde-517	401	1	therefore	therefore	ADV
ejde-517	401	2	,	,	PUNCT
ejde-517	401	3	by	by	ADP
ejde-517	401	4	hölder	hölder	PROPN
ejde-517	401	5	’s	’s	PART
ejde-517	401	6	inequality	inequality	NOUN
ejde-517	401	7	,	,	PUNCT
ejde-517	401	8	ψ(χδ1	ψ(χδ1	NOUN
ejde-517	401	9	)	)	PUNCT
ejde-517	401	10	∈	∈	PROPN
ejde-517	401	11	l2(ω	l2(ω	PROPN
ejde-517	401	12	)	)	PUNCT
ejde-517	401	13	.	.	PUNCT
ejde-517	402	1	(	(	PUNCT
ejde-517	402	2	3.42	3.42	NUM
ejde-517	402	3	)	)	PUNCT
ejde-517	402	4	this	this	PRON
ejde-517	402	5	means	mean	VERB
ejde-517	402	6	that	that	SCONJ
ejde-517	402	7	ψ	ψ	NOUN
ejde-517	402	8	is	be	AUX
ejde-517	402	9	a	a	DET
ejde-517	402	10	map	map	NOUN
ejde-517	402	11	from	from	ADP
ejde-517	402	12	χ1	χ1	PROPN
ejde-517	402	13	∈	∈	PROPN
ejde-517	402	14	l2(ω	l2(ω	NOUN
ejde-517	402	15	)	)	PUNCT
ejde-517	402	16	to	to	ADP
ejde-517	402	17	∇φ(χδ1	∇φ(χδ1	NOUN
ejde-517	402	18	)	)	PUNCT
ejde-517	402	19	·	·	PUNCT
ejde-517	402	20	∇φ∗(χδ1	∇φ∗(χδ1	ADJ
ejde-517	402	21	)	)	PUNCT
ejde-517	402	22	∈	∈	PROPN
ejde-517	402	23	l2(ω	l2(ω	NOUN
ejde-517	402	24	)	)	PUNCT
ejde-517	402	25	.	.	PUNCT
ejde-517	403	1	in	in	ADP
ejde-517	403	2	the	the	DET
ejde-517	403	3	following	follow	VERB
ejde-517	403	4	lemma	lemma	PROPN
ejde-517	403	5	,	,	PUNCT
ejde-517	403	6	we	we	PRON
ejde-517	403	7	prove	prove	VERB
ejde-517	403	8	that	that	SCONJ
ejde-517	403	9	this	this	DET
ejde-517	403	10	mapping	mapping	NOUN
ejde-517	403	11	is	be	AUX
ejde-517	403	12	continuous	continuous	ADJ
ejde-517	403	13	.	.	PUNCT
ejde-517	404	1	lemma	lemma	PROPN
ejde-517	404	2	3.18	3.18	NUM
ejde-517	404	3	.	.	PUNCT
ejde-517	405	1	under	under	ADP
ejde-517	405	2	assumption	assumption	NOUN
ejde-517	405	3	(	(	PUNCT
ejde-517	405	4	3.30	3.30	NUM
ejde-517	405	5	)	)	PUNCT
ejde-517	405	6	,	,	PUNCT
ejde-517	405	7	there	there	PRON
ejde-517	405	8	exists	exist	VERB
ejde-517	405	9	cδ	cδ	NOUN
ejde-517	405	10	≥	≥	NOUN
ejde-517	405	11	0	0	NUM
ejde-517	405	12	such	such	ADJ
ejde-517	405	13	that	that	SCONJ
ejde-517	405	14	‖ψ(χδ1	‖ψ(χδ1	NUM
ejde-517	405	15	+	+	CCONJ
ejde-517	405	16	ηδχδ1)−	ηδχδ1)−	ADJ
ejde-517	405	17	ψ(χδ1)‖l2(ω	ψ(χδ1)‖l2(ω	NOUN
ejde-517	405	18	)	)	PUNCT
ejde-517	405	19	≤	≤	NOUN
ejde-517	405	20	cδη‖δχ1‖l2(ω	cδη‖δχ1‖l2(ω	ADV
ejde-517	405	21	)	)	PUNCT
ejde-517	405	22	,	,	PUNCT
ejde-517	405	23	(	(	PUNCT
ejde-517	405	24	3.43	3.43	NUM
ejde-517	405	25	)	)	PUNCT
ejde-517	405	26	for	for	ADP
ejde-517	405	27	any	any	DET
ejde-517	405	28	η	η	PROPN
ejde-517	405	29	∈	∈	PROPN
ejde-517	405	30	(	(	PUNCT
ejde-517	405	31	0	0	NUM
ejde-517	405	32	,	,	PUNCT
ejde-517	405	33	τ	τ	PROPN
ejde-517	405	34	)	)	PUNCT
ejde-517	405	35	,	,	PUNCT
ejde-517	405	36	where	where	SCONJ
ejde-517	405	37	τ	τ	PROPN
ejde-517	405	38	is	be	AUX
ejde-517	405	39	chosen	choose	VERB
ejde-517	405	40	according	accord	VERB
ejde-517	405	41	to	to	PART
ejde-517	405	42	remark	remark	NOUN
ejde-517	405	43	3.4	3.4	NUM
ejde-517	405	44	.	.	PUNCT
ejde-517	406	1	proof	proof	NOUN
ejde-517	406	2	.	.	PUNCT
ejde-517	407	1	adding	add	VERB
ejde-517	407	2	and	and	CCONJ
ejde-517	407	3	subtracting	subtract	VERB
ejde-517	407	4	∇φ(χδ1	∇φ(χδ1	PROPN
ejde-517	407	5	+	+	CCONJ
ejde-517	407	6	ηδχδ1	ηδχδ1	ADJ
ejde-517	407	7	)	)	PUNCT
ejde-517	407	8	·	·	PUNCT
ejde-517	407	9	∇φ∗(χδ1	∇φ∗(χδ1	NOUN
ejde-517	407	10	)	)	PUNCT
ejde-517	407	11	to	to	ADP
ejde-517	407	12	ψ(χδ1	ψ(χδ1	PROPN
ejde-517	407	13	+	+	CCONJ
ejde-517	407	14	ηδχδ1)−ψ(χδ1	ηδχδ1)−ψ(χδ1	NOUN
ejde-517	407	15	)	)	PUNCT
ejde-517	407	16	,	,	PUNCT
ejde-517	407	17	we	we	PRON
ejde-517	407	18	obtain	obtain	VERB
ejde-517	407	19	ψ(χδ1	ψ(χδ1	NOUN
ejde-517	407	20	+	+	CCONJ
ejde-517	407	21	ηδχδ1)−	ηδχδ1)−	PROPN
ejde-517	407	22	ψ(χδ1	ψ(χδ1	PROPN
ejde-517	407	23	)	)	PUNCT
ejde-517	407	24	=	=	NOUN
ejde-517	407	25	:	:	PUNCT
ejde-517	407	26	a1(χδ1	a1(χδ1	NUM
ejde-517	407	27	;	;	PUNCT
ejde-517	407	28	δχδ1	δχδ1	PROPN
ejde-517	407	29	)	)	PUNCT
ejde-517	408	1	+	+	ADV
ejde-517	408	2	a2(χδ1	a2(χδ1	X
ejde-517	408	3	;	;	PUNCT
ejde-517	408	4	δχδ1	δχδ1	PROPN
ejde-517	408	5	)	)	PUNCT
ejde-517	408	6	,	,	PUNCT
ejde-517	408	7	where	where	SCONJ
ejde-517	408	8	a1(χδ1	a1(χδ1	NUM
ejde-517	408	9	;	;	PUNCT
ejde-517	408	10	δχδ1	δχδ1	PROPN
ejde-517	408	11	)	)	PUNCT
ejde-517	408	12	=	=	SYM
ejde-517	409	1	∇φ(χδ1	∇φ(χδ1	NOUN
ejde-517	409	2	+	+	CCONJ
ejde-517	409	3	ηδχδ1	ηδχδ1	ADJ
ejde-517	409	4	)	)	PUNCT
ejde-517	409	5	·	·	PUNCT
ejde-517	409	6	∇φ∗(χδ1	∇φ∗(χδ1	VERB
ejde-517	409	7	+	+	CCONJ
ejde-517	409	8	ηδχδ1)−∇φ(χδ1	ηδχδ1)−∇φ(χδ1	PROPN
ejde-517	409	9	+	+	CCONJ
ejde-517	409	10	ηδχδ1	ηδχδ1	ADJ
ejde-517	409	11	)	)	PUNCT
ejde-517	409	12	·	·	PUNCT
ejde-517	409	13	∇φ∗(χδ1	∇φ∗(χδ1	NOUN
ejde-517	409	14	)	)	PUNCT
ejde-517	409	15	,	,	PUNCT
ejde-517	409	16	a2(χδ1	a2(χδ1	X
ejde-517	409	17	;	;	PUNCT
ejde-517	409	18	δχδ1	δχδ1	PROPN
ejde-517	409	19	)	)	PUNCT
ejde-517	410	1	=	=	SYM
ejde-517	410	2	∇φ(χδ1	∇φ(χδ1	NOUN
ejde-517	410	3	+	+	CCONJ
ejde-517	410	4	ηδχδ1	ηδχδ1	ADJ
ejde-517	410	5	)	)	PUNCT
ejde-517	410	6	·	·	PUNCT
ejde-517	410	7	∇φ∗(χδ1)−∇φ(χδ1	∇φ∗(χδ1)−∇φ(χδ1	NUM
ejde-517	410	8	)	)	PUNCT
ejde-517	410	9	·	·	PUNCT
ejde-517	410	10	∇φ∗(χδ1	∇φ∗(χδ1	NOUN
ejde-517	410	11	)	)	PUNCT
ejde-517	410	12	.	.	PUNCT
ejde-517	411	1	thus	thus	ADV
ejde-517	411	2	‖ψ(χδ1	‖ψ(χδ1	NUM
ejde-517	411	3	+	+	CCONJ
ejde-517	411	4	ηδχδ1)−	ηδχδ1)−	ADJ
ejde-517	411	5	ψ(χδ1)‖l2(ω	ψ(χδ1)‖l2(ω	NOUN
ejde-517	411	6	)	)	PUNCT
ejde-517	411	7	≤	≤	NOUN
ejde-517	411	8	‖a1(χ1	‖a1(χ1	NUM
ejde-517	411	9	;	;	PUNCT
ejde-517	411	10	δχ1)‖l2(ω	δχ1)‖l2(ω	NUM
ejde-517	411	11	)	)	PUNCT
ejde-517	411	12	+	+	CCONJ
ejde-517	411	13	‖a2(χ1	‖a2(χ1	NUM
ejde-517	411	14	;	;	PUNCT
ejde-517	411	15	δχ1)‖l2(ω	δχ1)‖l2(ω	NUM
ejde-517	411	16	)	)	PUNCT
ejde-517	411	17	.	.	PUNCT
ejde-517	412	1	(	(	PUNCT
ejde-517	412	2	3.44	3.44	NUM
ejde-517	412	3	)	)	PUNCT
ejde-517	412	4	ejde-2020/93	ejde-2020/93	PROPN
ejde-517	412	5	impedance	impedance	NOUN
ejde-517	412	6	tomography	tomography	NOUN
ejde-517	412	7	problem	problem	NOUN
ejde-517	412	8	13	13	NUM
ejde-517	412	9	we	we	PRON
ejde-517	412	10	can	can	AUX
ejde-517	412	11	estimate	estimate	VERB
ejde-517	412	12	a1(χδ1	a1(χδ1	NUM
ejde-517	412	13	;	;	PUNCT
ejde-517	412	14	δχδ1	δχδ1	PROPN
ejde-517	412	15	)	)	PUNCT
ejde-517	412	16	using	use	VERB
ejde-517	412	17	the	the	DET
ejde-517	412	18	hölder	hölder	NOUN
ejde-517	412	19	’s	’s	PART
ejde-517	412	20	inequality	inequality	NOUN
ejde-517	412	21	,	,	PUNCT
ejde-517	412	22	(	(	PUNCT
ejde-517	412	23	3.37	3.37	NUM
ejde-517	412	24	)	)	PUNCT
ejde-517	412	25	,	,	PUNCT
ejde-517	412	26	and	and	CCONJ
ejde-517	412	27	(	(	PUNCT
ejde-517	412	28	3.40	3.40	NUM
ejde-517	412	29	)	)	PUNCT
ejde-517	412	30	.	.	PUNCT
ejde-517	413	1	thus	thus	ADV
ejde-517	413	2	,	,	PUNCT
ejde-517	413	3	‖a1(χδ1	‖a1(χδ1	NOUN
ejde-517	413	4	;	;	PUNCT
ejde-517	413	5	δχδ1)‖l2(ω	δχδ1)‖l2(ω	PROPN
ejde-517	413	6	)	)	PUNCT
ejde-517	413	7	≤	≤	NOUN
ejde-517	413	8	c1η‖f‖l̃2(∂ω)‖δχ1‖l2(ω	c1η‖f‖l̃2(∂ω)‖δχ1‖l2(ω	NOUN
ejde-517	413	9	)	)	PUNCT
ejde-517	413	10	,	,	PUNCT
ejde-517	413	11	for	for	ADP
ejde-517	413	12	some	some	DET
ejde-517	413	13	c1	c1	PROPN
ejde-517	413	14	>	>	X
ejde-517	413	15	0	0	X
ejde-517	413	16	.	.	PUNCT
ejde-517	414	1	similarly	similarly	ADV
ejde-517	414	2	,	,	PUNCT
ejde-517	414	3	using	use	VERB
ejde-517	414	4	the	the	DET
ejde-517	414	5	hölder	hölder	NOUN
ejde-517	414	6	’s	’s	PART
ejde-517	414	7	inequality	inequality	NOUN
ejde-517	414	8	,	,	PUNCT
ejde-517	414	9	(	(	PUNCT
ejde-517	414	10	3.36	3.36	NUM
ejde-517	414	11	)	)	PUNCT
ejde-517	414	12	,	,	PUNCT
ejde-517	414	13	and	and	CCONJ
ejde-517	414	14	(	(	PUNCT
ejde-517	414	15	3.39	3.39	NUM
ejde-517	414	16	)	)	PUNCT
ejde-517	414	17	,	,	PUNCT
ejde-517	414	18	we	we	PRON
ejde-517	414	19	obtain	obtain	VERB
ejde-517	414	20	‖a2(χδ1	‖a2(χδ1	NOUN
ejde-517	414	21	;	;	PUNCT
ejde-517	414	22	δχδ1)‖l2(ω	δχδ1)‖l2(ω	PROPN
ejde-517	414	23	)	)	PUNCT
ejde-517	414	24	≤	≤	NOUN
ejde-517	414	25	c2η‖∇φ∗(χδ1)‖l∞(ω)‖δχ1‖l2(ω	c2η‖∇φ∗(χδ1)‖l∞(ω)‖δχ1‖l2(ω	NOUN
ejde-517	414	26	)	)	PUNCT
ejde-517	414	27	,	,	PUNCT
ejde-517	414	28	for	for	ADP
ejde-517	414	29	some	some	DET
ejde-517	414	30	c2	c2	PROPN
ejde-517	414	31	>	>	X
ejde-517	414	32	0	0	PROPN
ejde-517	414	33	.	.	PUNCT
ejde-517	415	1	the	the	DET
ejde-517	415	2	estimates	estimate	NOUN
ejde-517	415	3	for	for	ADP
ejde-517	415	4	a1(χδ1	a1(χδ1	NUM
ejde-517	415	5	;	;	PUNCT
ejde-517	415	6	δχδ1	δχδ1	PROPN
ejde-517	415	7	)	)	PUNCT
ejde-517	415	8	and	and	CCONJ
ejde-517	415	9	a2(χδ1	a2(χδ1	PROPN
ejde-517	415	10	;	;	PUNCT
ejde-517	415	11	δχδ1	δχδ1	PROPN
ejde-517	415	12	)	)	PUNCT
ejde-517	415	13	,	,	PUNCT
ejde-517	415	14	together	together	ADV
ejde-517	415	15	with	with	ADP
ejde-517	415	16	(	(	PUNCT
ejde-517	415	17	3.44	3.44	NUM
ejde-517	415	18	)	)	PUNCT
ejde-517	415	19	,	,	PUNCT
ejde-517	415	20	complete	complete	VERB
ejde-517	415	21	the	the	DET
ejde-517	415	22	proof	proof	NOUN
ejde-517	415	23	.	.	PUNCT
ejde-517	416	1	�	�	PROPN
ejde-517	416	2	recall	recall	VERB
ejde-517	416	3	that	that	SCONJ
ejde-517	416	4	the	the	DET
ejde-517	416	5	goal	goal	NOUN
ejde-517	416	6	of	of	ADP
ejde-517	416	7	this	this	DET
ejde-517	416	8	section	section	NOUN
ejde-517	416	9	is	be	AUX
ejde-517	416	10	to	to	PART
ejde-517	416	11	validate	validate	VERB
ejde-517	416	12	the	the	DET
ejde-517	416	13	explicit	explicit	ADJ
ejde-517	416	14	formulation	formulation	NOUN
ejde-517	416	15	of	of	ADP
ejde-517	416	16	the	the	DET
ejde-517	416	17	gradient	gradient	NOUN
ejde-517	416	18	of	of	ADP
ejde-517	416	19	j(χ1	j(χ1	NOUN
ejde-517	416	20	)	)	PUNCT
ejde-517	416	21	by	by	ADP
ejde-517	416	22	showing	show	VERB
ejde-517	416	23	that	that	SCONJ
ejde-517	416	24	δς1	δς1	ADJ
ejde-517	416	25	δχ1	δχ1	X
ejde-517	416	26	(	(	PUNCT
ejde-517	416	27	χδ1	χδ1	X
ejde-517	416	28	;	;	PUNCT
ejde-517	416	29	δχδ1	δχδ1	PROPN
ejde-517	416	30	)	)	PUNCT
ejde-517	416	31	∈	∈	PROPN
ejde-517	416	32	h1(ω	h1(ω	PROPN
ejde-517	416	33	)	)	PUNCT
ejde-517	416	34	.	.	PUNCT
ejde-517	417	1	to	to	PART
ejde-517	417	2	accomplish	accomplish	VERB
ejde-517	417	3	this	this	PRON
ejde-517	417	4	,	,	PUNCT
ejde-517	417	5	we	we	PRON
ejde-517	417	6	first	first	ADV
ejde-517	417	7	need	need	VERB
ejde-517	417	8	to	to	PART
ejde-517	417	9	show	show	VERB
ejde-517	417	10	that	that	SCONJ
ejde-517	417	11	the	the	DET
ejde-517	417	12	derivatives	derivative	NOUN
ejde-517	417	13	of	of	ADP
ejde-517	417	14	both	both	DET
ejde-517	417	15	φ	φ	NOUN
ejde-517	417	16	and	and	CCONJ
ejde-517	417	17	φ∗	φ∗	NOUN
ejde-517	417	18	with	with	ADP
ejde-517	417	19	respect	respect	NOUN
ejde-517	417	20	to	to	ADP
ejde-517	417	21	χ1	χ1	NOUN
ejde-517	417	22	converge	converge	NOUN
ejde-517	417	23	in	in	ADP
ejde-517	417	24	h1(ω	h1(ω	PROPN
ejde-517	417	25	)	)	PUNCT
ejde-517	417	26	.	.	PUNCT
ejde-517	418	1	we	we	PRON
ejde-517	418	2	start	start	VERB
ejde-517	418	3	by	by	ADP
ejde-517	418	4	looking	look	VERB
ejde-517	418	5	for	for	ADP
ejde-517	418	6	candidates	candidate	NOUN
ejde-517	418	7	for	for	ADP
ejde-517	418	8	the	the	DET
ejde-517	418	9	derivatives	derivative	NOUN
ejde-517	418	10	.	.	PUNCT
ejde-517	419	1	lemma	lemma	PROPN
ejde-517	419	2	3.19	3.19	NUM
ejde-517	419	3	.	.	PUNCT
ejde-517	420	1	under	under	ADP
ejde-517	420	2	assumption	assumption	NOUN
ejde-517	420	3	(	(	PUNCT
ejde-517	420	4	3.30	3.30	NUM
ejde-517	420	5	)	)	PUNCT
ejde-517	420	6	,	,	PUNCT
ejde-517	420	7	there	there	PRON
ejde-517	420	8	exists	exist	VERB
ejde-517	420	9	dφ(χ1	dφ(χ1	VERB
ejde-517	420	10	;	;	PUNCT
ejde-517	420	11	δχ1	δχ1	X
ejde-517	420	12	)	)	PUNCT
ejde-517	420	13	∈	∈	PROPN
ejde-517	420	14	h1(ω	h1(ω	PROPN
ejde-517	420	15	)	)	PUNCT
ejde-517	420	16	satisfying	satisfy	VERB
ejde-517	420	17	∫	∫	PROPN
ejde-517	420	18	ω	ω	NUM
ejde-517	420	19	σk∇dφ(χ1	σk∇dφ(χ1	NOUN
ejde-517	420	20	;	;	PUNCT
ejde-517	420	21	δχ1	δχ1	X
ejde-517	420	22	)	)	PUNCT
ejde-517	420	23	·	·	PUNCT
ejde-517	421	1	∇v	∇v	ADJ
ejde-517	421	2	dv	dv	PROPN
ejde-517	421	3	=	=	SYM
ejde-517	421	4	∫	∫	PROPN
ejde-517	421	5	ω	ω	PROPN
ejde-517	421	6	(	(	PUNCT
ejde-517	421	7	σk1	σk1	PROPN
ejde-517	421	8	−	−	PROPN
ejde-517	421	9	σ2)δχδ1∇φ(χδ1	σ2)δχδ1∇φ(χδ1	NUM
ejde-517	421	10	)	)	PUNCT
ejde-517	421	11	·	·	PUNCT
ejde-517	422	1	∇v	∇v	ADJ
ejde-517	422	2	dv	dv	PROPN
ejde-517	422	3	(	(	PUNCT
ejde-517	422	4	3.45	3.45	NUM
ejde-517	422	5	)	)	PUNCT
ejde-517	422	6	with	with	ADP
ejde-517	422	7	∫	∫	PROPN
ejde-517	422	8	∂ω	∂ω	ADJ
ejde-517	422	9	dφ(χ1	dφ(χ1	NOUN
ejde-517	422	10	;	;	PUNCT
ejde-517	422	11	δχ1	δχ1	X
ejde-517	422	12	)	)	PUNCT
ejde-517	422	13	ds	ds	NOUN
ejde-517	422	14	=	=	NOUN
ejde-517	422	15	0	0	NUM
ejde-517	422	16	,	,	PUNCT
ejde-517	422	17	for	for	ADP
ejde-517	422	18	all	all	PRON
ejde-517	422	19	v	v	ADP
ejde-517	422	20	∈	∈	PROPN
ejde-517	422	21	h1(ω	h1(ω	PROPN
ejde-517	422	22	)	)	PUNCT
ejde-517	422	23	,	,	PUNCT
ejde-517	422	24	such	such	ADJ
ejde-517	422	25	that	that	DET
ejde-517	422	26	∫	∫	PROPN
ejde-517	422	27	∂ω	∂ω	ADJ
ejde-517	422	28	v	v	ADP
ejde-517	422	29	ds	ds	ADJ
ejde-517	422	30	=	=	NOUN
ejde-517	422	31	0	0	X
ejde-517	422	32	.	.	PUNCT
ejde-517	422	33	proof	proof	NOUN
ejde-517	422	34	.	.	PUNCT
ejde-517	423	1	let	let	VERB
ejde-517	423	2	u	u	NOUN
ejde-517	423	3	,	,	PUNCT
ejde-517	423	4	v	v	ADP
ejde-517	423	5	∈	∈	PROPN
ejde-517	423	6	h1(ω	h1(ω	NOUN
ejde-517	423	7	)	)	PUNCT
ejde-517	423	8	such	such	ADJ
ejde-517	423	9	that	that	DET
ejde-517	423	10	∫	∫	PROPN
ejde-517	423	11	∂ω	∂ω	ADJ
ejde-517	423	12	u	u	NOUN
ejde-517	423	13	ds	ds	PROPN
ejde-517	423	14	=	=	SYM
ejde-517	423	15	∫	∫	PROPN
ejde-517	423	16	∂ω	∂ω	PROPN
ejde-517	423	17	v	v	ADP
ejde-517	423	18	ds	ds	NOUN
ejde-517	423	19	=	=	NOUN
ejde-517	423	20	0	0	X
ejde-517	423	21	.	.	PUNCT
ejde-517	424	1	we	we	PRON
ejde-517	424	2	define	define	VERB
ejde-517	424	3	a(u	a(u	PROPN
ejde-517	424	4	,	,	PUNCT
ejde-517	424	5	v	v	NOUN
ejde-517	424	6	)	)	PUNCT
ejde-517	424	7	:	:	PUNCT
ejde-517	425	1	=	=	SYM
ejde-517	425	2	∫	∫	PROPN
ejde-517	425	3	ω	ω	PROPN
ejde-517	425	4	σk∇u	σk∇u	PROPN
ejde-517	425	5	·	·	PUNCT
ejde-517	425	6	∇v	∇v	PROPN
ejde-517	425	7	dv	dv	PROPN
ejde-517	425	8	,	,	PUNCT
ejde-517	425	9	b(v	b(v	NOUN
ejde-517	425	10	)	)	PUNCT
ejde-517	425	11	:	:	PUNCT
ejde-517	426	1	=	=	SYM
ejde-517	426	2	∫	∫	PROPN
ejde-517	426	3	ω	ω	PROPN
ejde-517	426	4	(	(	PUNCT
ejde-517	426	5	σk1	σk1	PROPN
ejde-517	426	6	−	−	PROPN
ejde-517	426	7	σ2)δχδ1∇φ(χδ1	σ2)δχδ1∇φ(χδ1	NUM
ejde-517	426	8	)	)	PUNCT
ejde-517	426	9	·	·	PUNCT
ejde-517	427	1	∇v	∇v	PROPN
ejde-517	427	2	dv	dv	PROPN
ejde-517	427	3	.	.	PROPN
ejde-517	428	1	from	from	ADP
ejde-517	428	2	the	the	DET
ejde-517	428	3	proof	proof	NOUN
ejde-517	428	4	of	of	ADP
ejde-517	428	5	theorem	theorem	NOUN
ejde-517	428	6	(	(	PUNCT
ejde-517	428	7	3.1	3.1	NUM
ejde-517	428	8	)	)	PUNCT
ejde-517	428	9	,	,	PUNCT
ejde-517	428	10	a	a	PRON
ejde-517	428	11	is	be	AUX
ejde-517	428	12	bilinear	bilinear	ADJ
ejde-517	428	13	,	,	PUNCT
ejde-517	428	14	coercive	coercive	ADJ
ejde-517	428	15	and	and	CCONJ
ejde-517	428	16	bounded	bound	VERB
ejde-517	428	17	.	.	PUNCT
ejde-517	429	1	obviously	obviously	ADV
ejde-517	429	2	,	,	PUNCT
ejde-517	429	3	b	b	PROPN
ejde-517	429	4	is	be	AUX
ejde-517	429	5	linear	linear	ADJ
ejde-517	429	6	.	.	PUNCT
ejde-517	430	1	we	we	PRON
ejde-517	430	2	wish	wish	VERB
ejde-517	430	3	to	to	PART
ejde-517	430	4	employ	employ	VERB
ejde-517	430	5	the	the	DET
ejde-517	430	6	lax	lax	PROPN
ejde-517	430	7	-	-	PUNCT
ejde-517	430	8	milgram	milgram	NOUN
ejde-517	430	9	theorem	theorem	NOUN
ejde-517	430	10	so	so	SCONJ
ejde-517	430	11	it	it	PRON
ejde-517	430	12	is	be	AUX
ejde-517	430	13	sufficient	sufficient	ADJ
ejde-517	430	14	to	to	PART
ejde-517	430	15	show	show	VERB
ejde-517	430	16	that	that	SCONJ
ejde-517	430	17	b	b	PROPN
ejde-517	430	18	is	be	AUX
ejde-517	430	19	bounded	bound	VERB
ejde-517	430	20	.	.	PUNCT
ejde-517	431	1	indeed	indeed	ADV
ejde-517	431	2	,	,	PUNCT
ejde-517	431	3	using	use	VERB
ejde-517	431	4	the	the	DET
ejde-517	431	5	cauchy	cauchy	PROPN
ejde-517	431	6	-	-	PUNCT
ejde-517	431	7	schwarz	schwarz	PROPN
ejde-517	431	8	inequality	inequality	NOUN
ejde-517	431	9	and	and	CCONJ
ejde-517	431	10	the	the	DET
ejde-517	431	11	hölder	hölder	NOUN
ejde-517	431	12	’s	’s	PART
ejde-517	431	13	inequality	inequality	NOUN
ejde-517	431	14	we	we	PRON
ejde-517	431	15	obtain	obtain	VERB
ejde-517	431	16	|b(v)|	|b(v)|	NOUN
ejde-517	431	17	≤	≤	NUM
ejde-517	431	18	‖(σk1	‖(σk1	ADP
ejde-517	431	19	−	−	PROPN
ejde-517	431	20	σ2)δχδ1‖l∞(ω)‖∇φ(χδ1)‖l2(ω)‖v‖l2(ω	σ2)δχδ1‖l∞(ω)‖∇φ(χδ1)‖l2(ω)‖v‖l2(ω	NUM
ejde-517	431	21	)	)	PUNCT
ejde-517	431	22	.	.	PUNCT
ejde-517	432	1	the	the	DET
ejde-517	432	2	right	right	ADJ
ejde-517	432	3	-	-	PUNCT
ejde-517	432	4	hand	hand	NOUN
ejde-517	432	5	side	side	NOUN
ejde-517	432	6	of	of	ADP
ejde-517	432	7	the	the	DET
ejde-517	432	8	last	last	ADJ
ejde-517	432	9	inequality	inequality	NOUN
ejde-517	432	10	is	be	AUX
ejde-517	432	11	bounded	bound	VERB
ejde-517	432	12	because	because	SCONJ
ejde-517	432	13	of	of	ADP
ejde-517	432	14	corollary	corollary	ADJ
ejde-517	432	15	(	(	PUNCT
ejde-517	432	16	3.2	3.2	NUM
ejde-517	432	17	)	)	PUNCT
ejde-517	432	18	and	and	CCONJ
ejde-517	432	19	the	the	DET
ejde-517	432	20	fact	fact	NOUN
ejde-517	432	21	that	that	SCONJ
ejde-517	432	22	(	(	PUNCT
ejde-517	432	23	σk1	σk1	NOUN
ejde-517	432	24	−	−	NOUN
ejde-517	432	25	σ2)δχδ1	σ2)δχδ1	NOUN
ejde-517	432	26	∈	∈	NOUN
ejde-517	432	27	c∞(ω̄	c∞(ω̄	NOUN
ejde-517	432	28	)	)	PUNCT
ejde-517	432	29	.	.	PUNCT
ejde-517	433	1	�	�	PROPN
ejde-517	433	2	lemma	lemma	PROPN
ejde-517	433	3	3.20	3.20	NUM
ejde-517	433	4	.	.	PUNCT
ejde-517	434	1	under	under	ADP
ejde-517	434	2	assumption	assumption	NOUN
ejde-517	434	3	(	(	PUNCT
ejde-517	434	4	3.30	3.30	NUM
ejde-517	434	5	)	)	PUNCT
ejde-517	434	6	,	,	PUNCT
ejde-517	434	7	there	there	PRON
ejde-517	434	8	exists	exist	VERB
ejde-517	434	9	dφ∗(χ1	dφ∗(χ1	NOUN
ejde-517	434	10	;	;	PUNCT
ejde-517	434	11	δχ1	δχ1	X
ejde-517	434	12	)	)	PUNCT
ejde-517	434	13	∈	∈	PROPN
ejde-517	434	14	h1(ω	h1(ω	PROPN
ejde-517	434	15	)	)	PUNCT
ejde-517	434	16	satisfying	satisfy	VERB
ejde-517	434	17	∫	∫	PROPN
ejde-517	434	18	ω	ω	NUM
ejde-517	434	19	σk∇dφ∗(χ1	σk∇dφ∗(χ1	PROPN
ejde-517	434	20	;	;	PUNCT
ejde-517	434	21	δχ1	δχ1	NUM
ejde-517	434	22	)	)	PUNCT
ejde-517	434	23	·	·	PUNCT
ejde-517	435	1	∇v	∇v	ADJ
ejde-517	435	2	dv	dv	PROPN
ejde-517	435	3	=	=	SYM
ejde-517	435	4	∫	∫	PROPN
ejde-517	435	5	ω	ω	PROPN
ejde-517	435	6	(	(	PUNCT
ejde-517	435	7	σk1	σk1	NOUN
ejde-517	435	8	−	−	PROPN
ejde-517	435	9	σ2)δχδ1∇φ∗(χδ1	σ2)δχδ1∇φ∗(χδ1	NOUN
ejde-517	435	10	)	)	PUNCT
ejde-517	435	11	·	·	PUNCT
ejde-517	436	1	∇v	∇v	ADJ
ejde-517	436	2	dv	dv	PROPN
ejde-517	436	3	+	+	CCONJ
ejde-517	436	4	∫	∫	PROPN
ejde-517	436	5	∂ω	∂ω	ADJ
ejde-517	436	6	dφ(χ1	dφ(χ1	VERB
ejde-517	436	7	;	;	PUNCT
ejde-517	436	8	δχ1)v	δχ1)v	PROPN
ejde-517	436	9	dv	dv	PROPN
ejde-517	436	10	,	,	PUNCT
ejde-517	436	11	(	(	PUNCT
ejde-517	436	12	3.46	3.46	NUM
ejde-517	436	13	)	)	PUNCT
ejde-517	436	14	with	with	ADP
ejde-517	436	15	∫	∫	PROPN
ejde-517	436	16	∂ω	∂ω	PROPN
ejde-517	436	17	dφ∗(χ1	dφ∗(χ1	PROPN
ejde-517	436	18	;	;	PUNCT
ejde-517	436	19	δχ1	δχ1	X
ejde-517	436	20	)	)	PUNCT
ejde-517	436	21	ds	ds	NOUN
ejde-517	436	22	=	=	NOUN
ejde-517	436	23	0	0	NUM
ejde-517	436	24	,	,	PUNCT
ejde-517	436	25	for	for	ADP
ejde-517	436	26	all	all	PRON
ejde-517	436	27	v	v	ADP
ejde-517	436	28	∈	∈	PROPN
ejde-517	436	29	h1(ω	h1(ω	PROPN
ejde-517	436	30	)	)	PUNCT
ejde-517	436	31	,	,	PUNCT
ejde-517	436	32	such	such	ADJ
ejde-517	436	33	that	that	DET
ejde-517	436	34	∫	∫	PROPN
ejde-517	437	1	∂ω	∂ω	ADJ
ejde-517	437	2	v	v	ADP
ejde-517	437	3	ds	ds	NOUN
ejde-517	437	4	=	=	NOUN
ejde-517	437	5	0	0	NUM
ejde-517	437	6	.	.	PUNCT
ejde-517	438	1	the	the	DET
ejde-517	438	2	proof	proof	NOUN
ejde-517	438	3	of	of	ADP
ejde-517	438	4	this	this	DET
ejde-517	438	5	lemma	lemma	PROPN
ejde-517	438	6	is	be	AUX
ejde-517	438	7	similar	similar	ADJ
ejde-517	438	8	to	to	ADP
ejde-517	438	9	the	the	DET
ejde-517	438	10	proof	proof	NOUN
ejde-517	438	11	of	of	ADP
ejde-517	438	12	the	the	DET
ejde-517	438	13	previous	previous	ADJ
ejde-517	438	14	lemma	lemma	PROPN
ejde-517	438	15	;	;	PUNCT
ejde-517	438	16	we	we	PRON
ejde-517	438	17	omit	omit	VERB
ejde-517	438	18	it	it	PRON
ejde-517	438	19	.	.	PUNCT
ejde-517	439	1	now	now	ADV
ejde-517	439	2	we	we	PRON
ejde-517	439	3	prove	prove	VERB
ejde-517	439	4	that	that	SCONJ
ejde-517	439	5	dφ(χ1	dφ(χ1	VERB
ejde-517	439	6	;	;	PUNCT
ejde-517	439	7	δχ1	δχ1	NUM
ejde-517	439	8	)	)	PUNCT
ejde-517	439	9	and	and	CCONJ
ejde-517	439	10	dφ∗(χ1	dφ∗(χ1	NOUN
ejde-517	439	11	;	;	PUNCT
ejde-517	439	12	δχ1	δχ1	X
ejde-517	439	13	)	)	PUNCT
ejde-517	439	14	in	in	ADP
ejde-517	439	15	the	the	DET
ejde-517	439	16	last	last	ADJ
ejde-517	439	17	two	two	NUM
ejde-517	439	18	lemmas	lemma	NOUN
ejde-517	439	19	are	be	AUX
ejde-517	439	20	the	the	DET
ejde-517	439	21	derivatives	derivative	NOUN
ejde-517	439	22	of	of	ADP
ejde-517	439	23	φ	φ	PROPN
ejde-517	439	24	and	and	CCONJ
ejde-517	439	25	φ∗	φ∗	NOUN
ejde-517	439	26	at	at	ADP
ejde-517	439	27	χ1	χ1	NOUN
ejde-517	439	28	in	in	ADP
ejde-517	439	29	the	the	DET
ejde-517	439	30	direction	direction	NOUN
ejde-517	439	31	of	of	ADP
ejde-517	439	32	δχ1	δχ1	NOUN
ejde-517	439	33	,	,	PUNCT
ejde-517	439	34	respectively	respectively	ADV
ejde-517	439	35	.	.	PUNCT
ejde-517	440	1	we	we	PRON
ejde-517	440	2	state	state	VERB
ejde-517	440	3	and	and	CCONJ
ejde-517	440	4	prove	prove	VERB
ejde-517	440	5	this	this	PRON
ejde-517	440	6	in	in	ADP
ejde-517	440	7	the	the	DET
ejde-517	440	8	following	follow	VERB
ejde-517	440	9	lemma	lemma	PROPN
ejde-517	440	10	.	.	PUNCT
ejde-517	441	1	lemma	lemma	PROPN
ejde-517	441	2	3.21	3.21	NUM
ejde-517	441	3	.	.	PUNCT
ejde-517	442	1	under	under	ADP
ejde-517	442	2	assumption	assumption	NOUN
ejde-517	442	3	(	(	PUNCT
ejde-517	442	4	3.30	3.30	NUM
ejde-517	442	5	)	)	PUNCT
ejde-517	442	6	,	,	PUNCT
ejde-517	442	7	we	we	PRON
ejde-517	442	8	have	have	VERB
ejde-517	442	9	lim	lim	PROPN
ejde-517	442	10	η→0	η→0	PROPN
ejde-517	442	11	∥∥φ(χδ1	∥∥φ(χδ1	PROPN
ejde-517	443	1	+	+	CCONJ
ejde-517	443	2	ηδχδ1)−	ηδχδ1)−	PROPN
ejde-517	443	3	φ(χδ1	φ(χδ1	PROPN
ejde-517	443	4	)	)	PUNCT
ejde-517	443	5	η	η	PROPN
ejde-517	443	6	−dφ(χδ1	−dφ(χδ1	X
ejde-517	443	7	;	;	PUNCT
ejde-517	443	8	δχδ1	δχδ1	PROPN
ejde-517	443	9	)	)	PUNCT
ejde-517	443	10	∥∥	∥∥	X
ejde-517	443	11	h1(ω	h1(ω	X
ejde-517	443	12	)	)	PUNCT
ejde-517	443	13	=	=	SYM
ejde-517	443	14	0	0	NUM
ejde-517	443	15	,	,	PUNCT
ejde-517	443	16	(	(	PUNCT
ejde-517	443	17	3.47	3.47	NUM
ejde-517	443	18	)	)	PUNCT
ejde-517	443	19	14	14	NUM
ejde-517	443	20	r.	r.	PROPN
ejde-517	443	21	mendoza	mendoza	PROPN
ejde-517	443	22	,	,	PUNCT
ejde-517	443	23	s.	s.	PROPN
ejde-517	443	24	keeling	keeling	PROPN
ejde-517	443	25	ejde-2020/93	ejde-2020/93	PROPN
ejde-517	443	26	lim	lim	PROPN
ejde-517	443	27	η→0	η→0	X
ejde-517	443	28	∥∥φ∗(χδ1	∥∥φ∗(χδ1	X
ejde-517	444	1	+	+	CCONJ
ejde-517	444	2	ηδχδ1)−	ηδχδ1)−	PROPN
ejde-517	444	3	φ∗(χδ1	φ∗(χδ1	NOUN
ejde-517	444	4	)	)	PUNCT
ejde-517	444	5	η	η	PROPN
ejde-517	444	6	−dφ∗(χ	−dφ∗(χ	PROPN
ejde-517	444	7	δ	δ	PROPN
ejde-517	444	8	1	1	NUM
ejde-517	444	9	;	;	PUNCT
ejde-517	444	10	δχδ1	δχδ1	PROPN
ejde-517	444	11	)	)	PUNCT
ejde-517	444	12	∥∥	∥∥	X
ejde-517	444	13	h1(ω	h1(ω	X
ejde-517	444	14	)	)	PUNCT
ejde-517	444	15	=	=	NOUN
ejde-517	444	16	0	0	X
ejde-517	444	17	.	.	PUNCT
ejde-517	444	18	(	(	PUNCT
ejde-517	444	19	3.48	3.48	NUM
ejde-517	444	20	)	)	PUNCT
ejde-517	444	21	thus	thus	ADV
ejde-517	444	22	,	,	PUNCT
ejde-517	444	23	we	we	PRON
ejde-517	444	24	can	can	AUX
ejde-517	444	25	make	make	VERB
ejde-517	444	26	the	the	DET
ejde-517	444	27	identifications	identification	NOUN
ejde-517	444	28	δφ	δφ	ADP
ejde-517	444	29	δχ1	δχ1	NOUN
ejde-517	444	30	(	(	PUNCT
ejde-517	444	31	χδ1	χδ1	X
ejde-517	444	32	;	;	PUNCT
ejde-517	444	33	δχδ1	δχδ1	PROPN
ejde-517	444	34	)	)	PUNCT
ejde-517	444	35	=	=	PUNCT
ejde-517	444	36	dφ(χ1	dφ(χ1	NOUN
ejde-517	444	37	;	;	PUNCT
ejde-517	444	38	δχ1	δχ1	NUM
ejde-517	444	39	)	)	PUNCT
ejde-517	444	40	,	,	PUNCT
ejde-517	444	41	δφ∗	δφ∗	NOUN
ejde-517	444	42	δχ1	δχ1	NOUN
ejde-517	444	43	(	(	PUNCT
ejde-517	444	44	χδ1	χδ1	X
ejde-517	444	45	;	;	PUNCT
ejde-517	444	46	δχδ1	δχδ1	PROPN
ejde-517	444	47	)	)	PUNCT
ejde-517	444	48	=	=	SYM
ejde-517	444	49	dφ∗(χ1	dφ∗(χ1	NOUN
ejde-517	444	50	;	;	PUNCT
ejde-517	444	51	δχ1	δχ1	NUM
ejde-517	444	52	)	)	PUNCT
ejde-517	444	53	.	.	PUNCT
ejde-517	445	1	furthermore	furthermore	ADV
ejde-517	445	2	,	,	PUNCT
ejde-517	445	3	because	because	SCONJ
ejde-517	445	4	dφ(χ1	dφ(χ1	NOUN
ejde-517	445	5	;	;	PUNCT
ejde-517	445	6	δχ1	δχ1	NUM
ejde-517	445	7	)	)	PUNCT
ejde-517	445	8	,	,	PUNCT
ejde-517	445	9	dφ∗(χ1	dφ∗(χ1	PROPN
ejde-517	445	10	;	;	PUNCT
ejde-517	445	11	δχ1	δχ1	X
ejde-517	445	12	)	)	PUNCT
ejde-517	445	13	∈	∈	PROPN
ejde-517	445	14	h1(ω	h1(ω	PROPN
ejde-517	445	15	)	)	PUNCT
ejde-517	445	16	we	we	PRON
ejde-517	445	17	have	have	VERB
ejde-517	445	18	δφ	δφ	ADP
ejde-517	445	19	δχ1	δχ1	NOUN
ejde-517	445	20	(	(	PUNCT
ejde-517	445	21	χδ1	χδ1	X
ejde-517	445	22	;	;	PUNCT
ejde-517	445	23	δχδ1	δχδ1	PROPN
ejde-517	445	24	)	)	PUNCT
ejde-517	445	25	,	,	PUNCT
ejde-517	445	26	δφ∗	δφ∗	NOUN
ejde-517	445	27	δχ1	δχ1	NOUN
ejde-517	445	28	(	(	PUNCT
ejde-517	445	29	χδ1	χδ1	X
ejde-517	445	30	;	;	PUNCT
ejde-517	445	31	δχδ1	δχδ1	PROPN
ejde-517	445	32	)	)	PUNCT
ejde-517	445	33	∈	∈	PROPN
ejde-517	445	34	h1(ω	h1(ω	PROPN
ejde-517	445	35	)	)	PUNCT
ejde-517	445	36	,	,	PUNCT
ejde-517	445	37	with	with	ADP
ejde-517	445	38	∫	∫	PROPN
ejde-517	445	39	∂ω	∂ω	ADJ
ejde-517	445	40	δφ	δφ	ADP
ejde-517	445	41	δχ1	δχ1	NOUN
ejde-517	445	42	(	(	PUNCT
ejde-517	445	43	χδ1	χδ1	X
ejde-517	445	44	;	;	PUNCT
ejde-517	445	45	δχδ1	δχδ1	NOUN
ejde-517	445	46	)	)	PUNCT
ejde-517	445	47	ds	ds	PROPN
ejde-517	445	48	=	=	SYM
ejde-517	445	49	∫	∫	PROPN
ejde-517	445	50	∂ω	∂ω	ADJ
ejde-517	445	51	δφ∗	δφ∗	NOUN
ejde-517	445	52	δχ1	δχ1	NOUN
ejde-517	445	53	(	(	PUNCT
ejde-517	445	54	χδ1	χδ1	X
ejde-517	445	55	;	;	PUNCT
ejde-517	445	56	δχδ1	δχδ1	NOUN
ejde-517	445	57	)	)	PUNCT
ejde-517	446	1	ds	ds	PROPN
ejde-517	446	2	=	=	NOUN
ejde-517	446	3	0	0	X
ejde-517	446	4	.	.	PUNCT
ejde-517	446	5	proof	proof	NOUN
ejde-517	446	6	.	.	PUNCT
ejde-517	447	1	from	from	ADP
ejde-517	447	2	(	(	PUNCT
ejde-517	447	3	3.1	3.1	NUM
ejde-517	447	4	)	)	PUNCT
ejde-517	447	5	,	,	PUNCT
ejde-517	447	6	we	we	PRON
ejde-517	447	7	have	have	VERB
ejde-517	447	8	∫	∫	PROPN
ejde-517	447	9	ω	ω	PROPN
ejde-517	447	10	σk∇φ(χδ1	σk∇φ(χδ1	PROPN
ejde-517	447	11	)	)	PUNCT
ejde-517	447	12	·	·	PUNCT
ejde-517	448	1	∇v	∇v	ADJ
ejde-517	448	2	dv	dv	PROPN
ejde-517	448	3	=	=	SYM
ejde-517	448	4	∫	∫	PROPN
ejde-517	448	5	ω	ω	PROPN
ejde-517	448	6	fv	fv	PROPN
ejde-517	448	7	dv	dv	PROPN
ejde-517	448	8	,	,	PUNCT
ejde-517	448	9	where	where	SCONJ
ejde-517	448	10	σk	σk	ADV
ejde-517	448	11	=	=	SYM
ejde-517	448	12	σk(χδi	σk(χδi	PRON
ejde-517	448	13	)	)	PUNCT
ejde-517	448	14	.	.	PUNCT
ejde-517	449	1	then	then	ADV
ejde-517	449	2	we	we	PRON
ejde-517	449	3	obtain	obtain	VERB
ejde-517	449	4	∫	∫	PROPN
ejde-517	449	5	ω	ω	PROPN
ejde-517	449	6	σk∇φ(χδ1	σk∇φ(χδ1	PROPN
ejde-517	449	7	)	)	PUNCT
ejde-517	449	8	·	·	PUNCT
ejde-517	450	1	∇v	∇v	ADJ
ejde-517	450	2	dv	dv	PROPN
ejde-517	450	3	=	=	SYM
ejde-517	450	4	∫	∫	PROPN
ejde-517	450	5	ω	ω	PROPN
ejde-517	450	6	fv	fv	PROPN
ejde-517	450	7	dv	dv	PROPN
ejde-517	450	8	.	.	PROPN
ejde-517	451	1	(	(	PUNCT
ejde-517	451	2	3.49	3.49	NUM
ejde-517	451	3	)	)	PUNCT
ejde-517	451	4	similarly	similarly	ADV
ejde-517	451	5	,	,	PUNCT
ejde-517	451	6	for	for	ADP
ejde-517	451	7	χδ1	χδ1	NOUN
ejde-517	451	8	+	+	CCONJ
ejde-517	451	9	ηδχδ1,∫	ηδχδ1,∫	X
ejde-517	451	10	ω	ω	NOUN
ejde-517	451	11	[	[	X
ejde-517	451	12	σk	σk	ADJ
ejde-517	451	13	+	+	CCONJ
ejde-517	451	14	η(σk1	η(σk1	NOUN
ejde-517	451	15	−	−	NOUN
ejde-517	451	16	σ2)δχδ1]∇φ(χδ1	σ2)δχδ1]∇φ(χδ1	X
ejde-517	451	17	+	+	CCONJ
ejde-517	451	18	ηδχδ1	ηδχδ1	ADJ
ejde-517	451	19	)	)	PUNCT
ejde-517	451	20	·	·	PUNCT
ejde-517	452	1	∇v	∇v	ADJ
ejde-517	452	2	dv	dv	PROPN
ejde-517	452	3	=	=	SYM
ejde-517	452	4	∫	∫	PROPN
ejde-517	452	5	ω	ω	PROPN
ejde-517	452	6	fv	fv	PROPN
ejde-517	452	7	dv	dv	PROPN
ejde-517	452	8	.	.	PROPN
ejde-517	453	1	(	(	PUNCT
ejde-517	453	2	3.50	3.50	NUM
ejde-517	453	3	)	)	PUNCT
ejde-517	453	4	subtracting	subtracting	NOUN
ejde-517	453	5	(	(	PUNCT
ejde-517	453	6	3.49	3.49	NUM
ejde-517	453	7	)	)	PUNCT
ejde-517	453	8	from	from	ADP
ejde-517	453	9	(	(	PUNCT
ejde-517	453	10	3.50	3.50	NUM
ejde-517	453	11	)	)	PUNCT
ejde-517	453	12	,	,	PUNCT
ejde-517	453	13	we	we	PRON
ejde-517	453	14	obtain∫	obtain∫	VERB
ejde-517	453	15	ω	ω	X
ejde-517	453	16	σk∇(φ(χδ1	σk∇(φ(χδ1	X
ejde-517	453	17	+	+	CCONJ
ejde-517	453	18	ηδχδ1)−	ηδχδ1)−	PROPN
ejde-517	453	19	φ(χδ1	φ(χδ1	PROPN
ejde-517	453	20	)	)	PUNCT
ejde-517	453	21	)	)	PUNCT
ejde-517	453	22	·	·	PUNCT
ejde-517	454	1	∇v	∇v	ADJ
ejde-517	454	2	dv	dv	PROPN
ejde-517	454	3	=	=	SYM
ejde-517	454	4	∫	∫	PROPN
ejde-517	454	5	ω	ω	X
ejde-517	454	6	η(σk1	η(σk1	PROPN
ejde-517	454	7	−	−	PROPN
ejde-517	454	8	σ2)δχδ1∇φ(χδ1	σ2)δχδ1∇φ(χδ1	X
ejde-517	454	9	+	+	CCONJ
ejde-517	454	10	ηδχδ1	ηδχδ1	ADJ
ejde-517	454	11	)	)	PUNCT
ejde-517	454	12	·	·	PUNCT
ejde-517	455	1	∇v	∇v	PROPN
ejde-517	455	2	dv	dv	PROPN
ejde-517	455	3	.	.	PUNCT
ejde-517	455	4	(	(	PUNCT
ejde-517	455	5	3.51	3.51	NUM
ejde-517	455	6	)	)	PUNCT
ejde-517	455	7	dividing	dividing	NOUN
ejde-517	455	8	by	by	ADP
ejde-517	455	9	η	η	PROPN
ejde-517	455	10	,	,	PUNCT
ejde-517	455	11	we	we	PRON
ejde-517	455	12	have∫	have∫	VERB
ejde-517	455	13	ω	ω	NUM
ejde-517	455	14	σk∇	σk∇	NOUN
ejde-517	455	15	(	(	PUNCT
ejde-517	455	16	φ(χδ1	φ(χδ1	X
ejde-517	455	17	+	+	CCONJ
ejde-517	455	18	ηδχδ1)−	ηδχδ1)−	PROPN
ejde-517	455	19	φ(χδ1	φ(χδ1	PROPN
ejde-517	455	20	)	)	PUNCT
ejde-517	455	21	η	η	PROPN
ejde-517	455	22	)	)	PUNCT
ejde-517	455	23	·	·	PUNCT
ejde-517	456	1	∇v	∇v	ADJ
ejde-517	456	2	dv	dv	PROPN
ejde-517	456	3	=	=	SYM
ejde-517	456	4	∫	∫	PROPN
ejde-517	456	5	ω	ω	PROPN
ejde-517	456	6	(	(	PUNCT
ejde-517	456	7	σk1	σk1	PROPN
ejde-517	456	8	−	−	PROPN
ejde-517	456	9	σ2)δχδ1∇φ(χδ1	σ2)δχδ1∇φ(χδ1	X
ejde-517	456	10	+	+	CCONJ
ejde-517	456	11	ηδχδ1	ηδχδ1	ADJ
ejde-517	456	12	)	)	PUNCT
ejde-517	456	13	·	·	PUNCT
ejde-517	457	1	∇v	∇v	PROPN
ejde-517	457	2	dv	dv	PROPN
ejde-517	457	3	.	.	PUNCT
ejde-517	457	4	(	(	PUNCT
ejde-517	457	5	3.52	3.52	NUM
ejde-517	457	6	)	)	PUNCT
ejde-517	457	7	recall	recall	NOUN
ejde-517	457	8	from	from	ADP
ejde-517	457	9	(	(	PUNCT
ejde-517	457	10	3.45	3.45	NUM
ejde-517	457	11	)	)	PUNCT
ejde-517	457	12	that∫	that∫	NOUN
ejde-517	457	13	ω	ω	NUM
ejde-517	457	14	σk∇dφ(χδ1	σk∇dφ(χδ1	NOUN
ejde-517	457	15	;	;	PUNCT
ejde-517	457	16	δχδ1	δχδ1	PROPN
ejde-517	457	17	)	)	PUNCT
ejde-517	457	18	·	·	PUNCT
ejde-517	458	1	∇v	∇v	ADJ
ejde-517	458	2	dv	dv	PROPN
ejde-517	458	3	=	=	SYM
ejde-517	458	4	∫	∫	PROPN
ejde-517	458	5	ω	ω	PROPN
ejde-517	458	6	(	(	PUNCT
ejde-517	458	7	σk1	σk1	PROPN
ejde-517	458	8	−	−	PROPN
ejde-517	458	9	σ2)δχδ1∇φ(χδ1	σ2)δχδ1∇φ(χδ1	NUM
ejde-517	458	10	)	)	PUNCT
ejde-517	458	11	·	·	PUNCT
ejde-517	459	1	∇v	∇v	PROPN
ejde-517	459	2	dv	dv	PROPN
ejde-517	459	3	.	.	PUNCT
ejde-517	459	4	(	(	PUNCT
ejde-517	459	5	3.53	3.53	NUM
ejde-517	459	6	)	)	PUNCT
ejde-517	459	7	subtracting	subtract	VERB
ejde-517	459	8	(	(	PUNCT
ejde-517	459	9	3.52	3.52	NUM
ejde-517	459	10	)	)	PUNCT
ejde-517	459	11	and	and	CCONJ
ejde-517	459	12	(	(	PUNCT
ejde-517	459	13	3.53	3.53	NUM
ejde-517	459	14	)	)	PUNCT
ejde-517	459	15	,	,	PUNCT
ejde-517	459	16	we	we	PRON
ejde-517	459	17	obtain∫	obtain∫	VERB
ejde-517	459	18	ω	ω	NUM
ejde-517	459	19	σk∇	σk∇	NOUN
ejde-517	459	20	(	(	PUNCT
ejde-517	459	21	φ(χδ1	φ(χδ1	X
ejde-517	459	22	+	+	CCONJ
ejde-517	459	23	ηδχδ1)−	ηδχδ1)−	PROPN
ejde-517	459	24	φ(χδ1	φ(χδ1	PROPN
ejde-517	459	25	)	)	PUNCT
ejde-517	459	26	η	η	PROPN
ejde-517	459	27	−dφ(χδ1	−dφ(χδ1	X
ejde-517	459	28	;	;	PUNCT
ejde-517	459	29	δχδ1	δχδ1	PROPN
ejde-517	459	30	)	)	PUNCT
ejde-517	459	31	)	)	PUNCT
ejde-517	459	32	·	·	PUNCT
ejde-517	460	1	∇v	∇v	ADJ
ejde-517	460	2	dv	dv	PROPN
ejde-517	460	3	=	=	NOUN
ejde-517	460	4	:	:	PUNCT
ejde-517	460	5	a(v	a(v	NUM
ejde-517	460	6	)	)	PUNCT
ejde-517	460	7	(	(	PUNCT
ejde-517	460	8	3.54	3.54	NUM
ejde-517	460	9	)	)	PUNCT
ejde-517	460	10	where	where	SCONJ
ejde-517	460	11	a(v	a(v	NOUN
ejde-517	460	12	)	)	PUNCT
ejde-517	460	13	=	=	SYM
ejde-517	460	14	∫	∫	PROPN
ejde-517	460	15	ω	ω	PROPN
ejde-517	460	16	(	(	PUNCT
ejde-517	460	17	σk1	σk1	NOUN
ejde-517	460	18	−	−	PROPN
ejde-517	460	19	σ2)δχδ1∇[φ(χδ1	σ2)δχδ1∇[φ(χδ1	PROPN
ejde-517	460	20	+	+	CCONJ
ejde-517	460	21	ηδχδ1)−	ηδχδ1)−	PROPN
ejde-517	460	22	φ(χδ1	φ(χδ1	PROPN
ejde-517	460	23	)	)	PUNCT
ejde-517	460	24	]	]	PUNCT
ejde-517	460	25	·	·	PUNCT
ejde-517	461	1	∇v	∇v	ADJ
ejde-517	461	2	dv	dv	PROPN
ejde-517	461	3	,	,	PUNCT
ejde-517	461	4	which	which	PRON
ejde-517	461	5	can	can	AUX
ejde-517	461	6	be	be	AUX
ejde-517	461	7	estimated	estimate	VERB
ejde-517	461	8	using	use	VERB
ejde-517	461	9	the	the	DET
ejde-517	461	10	cauchy	cauchy	PROPN
ejde-517	461	11	-	-	PUNCT
ejde-517	461	12	schwarz	schwarz	PROPN
ejde-517	461	13	inequality	inequality	NOUN
ejde-517	461	14	and	and	CCONJ
ejde-517	461	15	(	(	PUNCT
ejde-517	461	16	3.15	3.15	NUM
ejde-517	461	17	):	):	PUNCT
ejde-517	461	18	|a(v)|	|a(v)|	ADP
ejde-517	461	19	≤	≤	NUM
ejde-517	461	20	c1η‖(σk1	c1η‖(σk1	NOUN
ejde-517	461	21	−	−	PROPN
ejde-517	461	22	σ2)δχδ1‖l∞(ω)‖δχ1‖l2(ω)‖v‖h1(ω	σ2)δχδ1‖l∞(ω)‖δχ1‖l2(ω)‖v‖h1(ω	NOUN
ejde-517	461	23	)	)	PUNCT
ejde-517	461	24	.	.	PUNCT
ejde-517	462	1	(	(	PUNCT
ejde-517	462	2	3.55	3.55	NUM
ejde-517	462	3	)	)	PUNCT
ejde-517	462	4	ejde-2020/93	ejde-2020/93	PROPN
ejde-517	462	5	impedance	impedance	NOUN
ejde-517	462	6	tomography	tomography	NOUN
ejde-517	462	7	problem	problem	NOUN
ejde-517	462	8	15	15	NUM
ejde-517	462	9	it	it	PRON
ejde-517	462	10	is	be	AUX
ejde-517	462	11	worth	worth	ADJ
ejde-517	462	12	noting	note	VERB
ejde-517	462	13	that	that	SCONJ
ejde-517	462	14	(	(	PUNCT
ejde-517	462	15	σk1	σk1	NOUN
ejde-517	462	16	−	−	NOUN
ejde-517	462	17	σ2)δχδ1	σ2)δχδ1	NUM
ejde-517	462	18	∈	∈	NOUN
ejde-517	462	19	l∞(ω	l∞(ω	NOUN
ejde-517	462	20	)	)	PUNCT
ejde-517	462	21	and	and	CCONJ
ejde-517	462	22	δχ1	δχ1	NOUN
ejde-517	462	23	∈	∈	PROPN
ejde-517	462	24	l2(ω	l2(ω	NOUN
ejde-517	462	25	)	)	PUNCT
ejde-517	462	26	so	so	SCONJ
ejde-517	462	27	that	that	SCONJ
ejde-517	462	28	the	the	DET
ejde-517	462	29	righthand	righthand	NOUN
ejde-517	462	30	side	side	NOUN
ejde-517	462	31	of	of	ADP
ejde-517	462	32	the	the	DET
ejde-517	462	33	above	above	ADJ
ejde-517	462	34	inequality	inequality	NOUN
ejde-517	462	35	is	be	AUX
ejde-517	462	36	bounded	bound	VERB
ejde-517	462	37	.	.	PUNCT
ejde-517	463	1	now	now	ADV
ejde-517	463	2	observe	observe	VERB
ejde-517	463	3	that	that	SCONJ
ejde-517	463	4	a(u	a(u	PROPN
ejde-517	463	5	,	,	PUNCT
ejde-517	463	6	v	v	NOUN
ejde-517	463	7	)	)	PUNCT
ejde-517	463	8	:	:	PUNCT
ejde-517	464	1	=	=	SYM
ejde-517	464	2	∫	∫	PROPN
ejde-517	464	3	ω	ω	NUM
ejde-517	464	4	σk∇u	σk∇u	PROPN
ejde-517	464	5	·	·	PUNCT
ejde-517	464	6	∇v	∇v	ADJ
ejde-517	464	7	dv	dv	PROPN
ejde-517	464	8	is	be	AUX
ejde-517	464	9	coercive	coercive	ADJ
ejde-517	464	10	as	as	SCONJ
ejde-517	464	11	demonstrated	demonstrate	VERB
ejde-517	464	12	in	in	ADP
ejde-517	464	13	the	the	DET
ejde-517	464	14	proof	proof	NOUN
ejde-517	464	15	of	of	ADP
ejde-517	464	16	theorem	theorem	NOUN
ejde-517	464	17	(	(	PUNCT
ejde-517	464	18	3.1	3.1	NUM
ejde-517	464	19	)	)	PUNCT
ejde-517	464	20	,	,	PUNCT
ejde-517	464	21	i.e.	i.e.	X
ejde-517	464	22	,	,	PUNCT
ejde-517	464	23	|a(u	|a(u	PROPN
ejde-517	464	24	,	,	PUNCT
ejde-517	464	25	u)|	u)|	X
ejde-517	464	26	≥	≥	NOUN
ejde-517	464	27	c̄‖u‖2h1(ω	c̄‖u‖2h1(ω	PROPN
ejde-517	464	28	)	)	PUNCT
ejde-517	464	29	,	,	PUNCT
ejde-517	464	30	(	(	PUNCT
ejde-517	464	31	3.56	3.56	NUM
ejde-517	464	32	)	)	PUNCT
ejde-517	464	33	for	for	ADP
ejde-517	464	34	some	some	DET
ejde-517	464	35	c̄	c̄	PROPN
ejde-517	464	36	>	>	SYM
ejde-517	464	37	0	0	NUM
ejde-517	464	38	,	,	PUNCT
ejde-517	464	39	for	for	ADP
ejde-517	464	40	any	any	DET
ejde-517	464	41	u	u	PROPN
ejde-517	464	42	∈	∈	PROPN
ejde-517	464	43	h1(ω	h1(ω	PROPN
ejde-517	464	44	)	)	PUNCT
ejde-517	464	45	such	such	ADJ
ejde-517	464	46	that	that	DET
ejde-517	464	47	∫	∫	PROPN
ejde-517	464	48	∂ω	∂ω	ADJ
ejde-517	464	49	u	u	NOUN
ejde-517	464	50	ds	ds	ADJ
ejde-517	464	51	=	=	NOUN
ejde-517	464	52	0	0	NUM
ejde-517	464	53	.	.	PUNCT
ejde-517	465	1	hence	hence	ADV
ejde-517	465	2	,	,	PUNCT
ejde-517	465	3	the	the	DET
ejde-517	465	4	left	left	ADJ
ejde-517	465	5	hand	hand	NOUN
ejde-517	465	6	side	side	NOUN
ejde-517	465	7	of	of	ADP
ejde-517	465	8	(	(	PUNCT
ejde-517	465	9	3.54	3.54	NUM
ejde-517	465	10	)	)	PUNCT
ejde-517	465	11	is	be	AUX
ejde-517	465	12	bounded	bound	VERB
ejde-517	465	13	from	from	ADP
ejde-517	465	14	above	above	ADV
ejde-517	465	15	if	if	SCONJ
ejde-517	465	16	we	we	PRON
ejde-517	465	17	set	set	VERB
ejde-517	465	18	u	u	NOUN
ejde-517	465	19	=	=	PUNCT
ejde-517	465	20	φ(χδ1	φ(χδ1	X
ejde-517	465	21	+	+	CCONJ
ejde-517	465	22	ηδχδ1)−	ηδχδ1)−	PROPN
ejde-517	465	23	φ(χδ1	φ(χδ1	PROPN
ejde-517	465	24	)	)	PUNCT
ejde-517	465	25	η	η	PROPN
ejde-517	465	26	−dφ(χδ1	−dφ(χδ1	X
ejde-517	465	27	;	;	PUNCT
ejde-517	465	28	δχδ1	δχδ1	PROPN
ejde-517	465	29	)	)	PUNCT
ejde-517	465	30	.	.	PUNCT
ejde-517	466	1	using	use	VERB
ejde-517	466	2	this	this	DET
ejde-517	466	3	fact	fact	NOUN
ejde-517	466	4	and	and	CCONJ
ejde-517	466	5	comparing	compare	VERB
ejde-517	466	6	(	(	PUNCT
ejde-517	466	7	3.54	3.54	NUM
ejde-517	466	8	)	)	PUNCT
ejde-517	466	9	and	and	CCONJ
ejde-517	466	10	(	(	PUNCT
ejde-517	466	11	3.55	3.55	NUM
ejde-517	466	12	)	)	PUNCT
ejde-517	466	13	,	,	PUNCT
ejde-517	466	14	we	we	PRON
ejde-517	466	15	obtain	obtain	VERB
ejde-517	466	16	the	the	DET
ejde-517	466	17	estimate	estimate	NOUN
ejde-517	466	18	c̄‖φ(χδ1	c̄‖φ(χδ1	NUM
ejde-517	466	19	+	+	CCONJ
ejde-517	466	20	ηδχδ1)−	ηδχδ1)−	PROPN
ejde-517	466	21	φ(χδ1	φ(χδ1	PROPN
ejde-517	466	22	)	)	PUNCT
ejde-517	466	23	η	η	PROPN
ejde-517	466	24	−dφ(χδ1	−dφ(χδ1	X
ejde-517	466	25	;	;	PUNCT
ejde-517	466	26	δχδ1)‖h1(ω	δχδ1)‖h1(ω	PROPN
ejde-517	466	27	)	)	PUNCT
ejde-517	466	28	≤	≤	NUM
ejde-517	466	29	c1η‖(σk1	c1η‖(σk1	NOUN
ejde-517	466	30	−	−	PROPN
ejde-517	466	31	σ2)δχδ1‖l∞(ω)‖δχ1‖l2(ω	σ2)δχδ1‖l∞(ω)‖δχ1‖l2(ω	NUM
ejde-517	466	32	)	)	PUNCT
ejde-517	466	33	.	.	PUNCT
ejde-517	467	1	therefore	therefore	ADV
ejde-517	467	2	,	,	PUNCT
ejde-517	467	3	taking	take	VERB
ejde-517	467	4	the	the	DET
ejde-517	467	5	limit	limit	NOUN
ejde-517	467	6	of	of	ADP
ejde-517	467	7	the	the	DET
ejde-517	467	8	last	last	ADJ
ejde-517	467	9	equality	equality	NOUN
ejde-517	467	10	as	as	ADP
ejde-517	467	11	η	η	PROPN
ejde-517	467	12	→	→	X
ejde-517	467	13	0	0	NUM
ejde-517	467	14	,	,	PUNCT
ejde-517	467	15	we	we	PRON
ejde-517	467	16	obtain	obtain	VERB
ejde-517	467	17	lim	lim	PROPN
ejde-517	467	18	η→0	η→0	X
ejde-517	467	19	‖φ(χδ1	‖φ(χδ1	NUM
ejde-517	467	20	+	+	CCONJ
ejde-517	467	21	ηδχδ1)−	ηδχδ1)−	PROPN
ejde-517	467	22	φ(χδ1	φ(χδ1	PROPN
ejde-517	467	23	)	)	PUNCT
ejde-517	467	24	η	η	PROPN
ejde-517	467	25	−dφ(χδ1	−dφ(χδ1	X
ejde-517	467	26	;	;	PUNCT
ejde-517	467	27	δχδ1)‖h1(ω	δχδ1)‖h1(ω	PROPN
ejde-517	467	28	)	)	PUNCT
ejde-517	467	29	=	=	PUNCT
ejde-517	468	1	0	0	X
ejde-517	468	2	.	.	PUNCT
ejde-517	469	1	(	(	PUNCT
ejde-517	469	2	3.57	3.57	NUM
ejde-517	469	3	)	)	PUNCT
ejde-517	469	4	the	the	DET
ejde-517	469	5	rest	rest	NOUN
ejde-517	469	6	of	of	ADP
ejde-517	469	7	the	the	DET
ejde-517	469	8	proof	proof	NOUN
ejde-517	469	9	is	be	AUX
ejde-517	469	10	similar	similar	ADJ
ejde-517	469	11	to	to	PART
ejde-517	469	12	show	show	VERB
ejde-517	469	13	the	the	DET
ejde-517	469	14	convergence	convergence	NOUN
ejde-517	469	15	of	of	ADP
ejde-517	469	16	the	the	DET
ejde-517	469	17	derivative	derivative	NOUN
ejde-517	469	18	of	of	ADP
ejde-517	469	19	φ∗	φ∗	NOUN
ejde-517	469	20	with	with	ADP
ejde-517	469	21	respect	respect	NOUN
ejde-517	469	22	to	to	ADP
ejde-517	469	23	χ1	χ1	NOUN
ejde-517	469	24	in	in	ADP
ejde-517	469	25	h1(ω	h1(ω	PROPN
ejde-517	469	26	)	)	PUNCT
ejde-517	469	27	.	.	PUNCT
ejde-517	470	1	the	the	DET
ejde-517	470	2	last	last	ADJ
ejde-517	470	3	statements	statement	NOUN
ejde-517	470	4	of	of	ADP
ejde-517	470	5	the	the	DET
ejde-517	470	6	lemma	lemma	PROPN
ejde-517	470	7	can	can	AUX
ejde-517	470	8	be	be	AUX
ejde-517	470	9	inferred	infer	VERB
ejde-517	470	10	directly	directly	ADV
ejde-517	470	11	from	from	ADP
ejde-517	470	12	the	the	DET
ejde-517	470	13	last	last	ADJ
ejde-517	470	14	two	two	NUM
ejde-517	470	15	lemmas	lemmas	ADJ
ejde-517	470	16	.	.	PUNCT
ejde-517	471	1	�	�	PROPN
ejde-517	471	2	now	now	ADV
ejde-517	471	3	that	that	SCONJ
ejde-517	471	4	we	we	PRON
ejde-517	471	5	have	have	AUX
ejde-517	471	6	shown	show	VERB
ejde-517	471	7	that	that	SCONJ
ejde-517	471	8	the	the	DET
ejde-517	471	9	derivatives	derivative	NOUN
ejde-517	471	10	of	of	ADP
ejde-517	471	11	both	both	DET
ejde-517	471	12	φ	φ	NOUN
ejde-517	471	13	and	and	CCONJ
ejde-517	471	14	φ∗	φ∗	NOUN
ejde-517	471	15	converge	converge	NOUN
ejde-517	471	16	in	in	ADP
ejde-517	471	17	h1(ω	h1(ω	PROPN
ejde-517	471	18	)	)	PUNCT
ejde-517	471	19	,	,	PUNCT
ejde-517	471	20	the	the	DET
ejde-517	471	21	next	next	ADJ
ejde-517	471	22	step	step	NOUN
ejde-517	471	23	is	be	AUX
ejde-517	471	24	to	to	PART
ejde-517	471	25	show	show	VERB
ejde-517	471	26	that	that	SCONJ
ejde-517	471	27	ψ	ψ	X
ejde-517	471	28	in	in	ADP
ejde-517	471	29	(	(	PUNCT
ejde-517	471	30	3.41	3.41	NUM
ejde-517	471	31	)	)	PUNCT
ejde-517	471	32	has	have	VERB
ejde-517	471	33	a	a	DET
ejde-517	471	34	derivative	derivative	NOUN
ejde-517	471	35	with	with	ADP
ejde-517	471	36	respect	respect	NOUN
ejde-517	471	37	to	to	ADP
ejde-517	471	38	χ1	χ1	NOUN
ejde-517	471	39	which	which	PRON
ejde-517	471	40	converges	converge	VERB
ejde-517	471	41	in	in	ADP
ejde-517	471	42	l2(ω	l2(ω	NOUN
ejde-517	471	43	)	)	PUNCT
ejde-517	471	44	.	.	PUNCT
ejde-517	472	1	we	we	PRON
ejde-517	472	2	first	first	ADV
ejde-517	472	3	prove	prove	VERB
ejde-517	472	4	the	the	DET
ejde-517	472	5	following	follow	VERB
ejde-517	472	6	lemma	lemma	PROPN
ejde-517	472	7	.	.	PUNCT
ejde-517	473	1	lemma	lemma	PROPN
ejde-517	473	2	3.22	3.22	NUM
ejde-517	473	3	.	.	PUNCT
ejde-517	474	1	under	under	ADP
ejde-517	474	2	assumption	assumption	NOUN
ejde-517	474	3	(	(	PUNCT
ejde-517	474	4	3.30	3.30	NUM
ejde-517	474	5	)	)	PUNCT
ejde-517	474	6	,	,	PUNCT
ejde-517	474	7	we	we	PRON
ejde-517	474	8	let	let	VERB
ejde-517	474	9	δφ	δφ	NOUN
ejde-517	474	10	:	:	PUNCT
ejde-517	474	11	=	=	SYM
ejde-517	474	12	φ(χδ1	φ(χδ1	X
ejde-517	474	13	+	+	CCONJ
ejde-517	474	14	ηδχδ1)−	ηδχδ1)−	PROPN
ejde-517	474	15	φ(χδ1	φ(χδ1	PROPN
ejde-517	474	16	)	)	PUNCT
ejde-517	474	17	.	.	PUNCT
ejde-517	475	1	(	(	PUNCT
ejde-517	475	2	3.58	3.58	NUM
ejde-517	475	3	)	)	PUNCT
ejde-517	475	4	then	then	ADV
ejde-517	475	5	there	there	PRON
ejde-517	475	6	exists	exist	VERB
ejde-517	475	7	cδ	cδ	VERB
ejde-517	475	8	>	>	X
ejde-517	475	9	0	0	NUM
ejde-517	476	1	such	such	ADJ
ejde-517	476	2	that	that	SCONJ
ejde-517	476	3	‖∇δφ‖l∞(ω	‖∇δφ‖l∞(ω	NOUN
ejde-517	476	4	)	)	PUNCT
ejde-517	476	5	≤	≤	NUM
ejde-517	476	6	cδ	cδ	NOUN
ejde-517	476	7	{	{	PUNCT
ejde-517	476	8	‖∇δφ‖l2(ω	‖∇δφ‖l2(ω	PRON
ejde-517	476	9	)	)	PUNCT
ejde-517	476	10	+	+	CCONJ
ejde-517	476	11	η‖∇	η‖∇	PROPN
ejde-517	476	12	·	·	PUNCT
ejde-517	476	13	(	(	PUNCT
ejde-517	476	14	(	(	PUNCT
ejde-517	476	15	σk1	σk1	NOUN
ejde-517	476	16	−	−	PROPN
ejde-517	476	17	σ2)δχδ1∇φ(χδ1	σ2)δχδ1∇φ(χδ1	X
ejde-517	476	18	+	+	X
ejde-517	476	19	ηδχδ1))‖h1(ω	ηδχδ1))‖h1(ω	NOUN
ejde-517	476	20	)	)	PUNCT
ejde-517	476	21	}	}	PUNCT
ejde-517	476	22	,	,	PUNCT
ejde-517	476	23	(	(	PUNCT
ejde-517	476	24	3.59	3.59	NUM
ejde-517	476	25	)	)	PUNCT
ejde-517	476	26	for	for	ADP
ejde-517	476	27	any	any	DET
ejde-517	476	28	η	η	PROPN
ejde-517	476	29	∈	∈	PROPN
ejde-517	476	30	(	(	PUNCT
ejde-517	476	31	0	0	NUM
ejde-517	476	32	,	,	PUNCT
ejde-517	476	33	τ	τ	PROPN
ejde-517	476	34	)	)	PUNCT
ejde-517	476	35	,	,	PUNCT
ejde-517	476	36	where	where	SCONJ
ejde-517	476	37	τ	τ	PROPN
ejde-517	476	38	is	be	AUX
ejde-517	476	39	chosen	choose	VERB
ejde-517	476	40	according	accord	VERB
ejde-517	476	41	to	to	PART
ejde-517	476	42	remark	remark	NOUN
ejde-517	476	43	3.4	3.4	NUM
ejde-517	476	44	.	.	PUNCT
ejde-517	477	1	proof	proof	NOUN
ejde-517	477	2	.	.	PUNCT
ejde-517	478	1	set	set	VERB
ejde-517	478	2	δσk	δσk	NOUN
ejde-517	478	3	=	=	SYM
ejde-517	478	4	σk(χδ1	σk(χδ1	X
ejde-517	479	1	+	+	CCONJ
ejde-517	480	1	ηδχδ1)−	ηδχδ1)−	PROPN
ejde-517	480	2	σk(χδ1	σk(χδ1	NOUN
ejde-517	480	3	)	)	PUNCT
ejde-517	480	4	.	.	PUNCT
ejde-517	481	1	(	(	PUNCT
ejde-517	481	2	3.60	3.60	NUM
ejde-517	481	3	)	)	PUNCT
ejde-517	481	4	then	then	ADV
ejde-517	481	5	δφ	δφ	NOUN
ejde-517	481	6	and	and	CCONJ
ejde-517	481	7	δσ	δσ	PROPN
ejde-517	481	8	satisfy	satisfy	VERB
ejde-517	481	9	∇	∇	X
ejde-517	481	10	·	·	PUNCT
ejde-517	481	11	(	(	PUNCT
ejde-517	481	12	σk(χδ1)∇(δφ	σk(χδ1)∇(δφ	NOUN
ejde-517	481	13	)	)	PUNCT
ejde-517	481	14	)	)	PUNCT
ejde-517	482	1	=	=	SYM
ejde-517	482	2	−∇	−∇	NOUN
ejde-517	482	3	·	·	PUNCT
ejde-517	482	4	(	(	PUNCT
ejde-517	482	5	δσk∇φ(χδ1	δσk∇φ(χδ1	X
ejde-517	482	6	+	+	X
ejde-517	482	7	ηδχδ1	ηδχδ1	ADJ
ejde-517	482	8	)	)	PUNCT
ejde-517	482	9	)	)	PUNCT
ejde-517	482	10	on	on	ADP
ejde-517	482	11	ω	ω	NUM
ejde-517	482	12	,	,	PUNCT
ejde-517	482	13	σ	σ	PROPN
ejde-517	482	14	∂(δφ	∂(δφ	NOUN
ejde-517	482	15	)	)	PUNCT
ejde-517	483	1	∂n	∂n	PROPN
ejde-517	483	2	=	=	NOUN
ejde-517	483	3	0	0	NUM
ejde-517	484	1	on	on	ADP
ejde-517	484	2	∂ω	∂ω	PROPN
ejde-517	484	3	.	.	PUNCT
ejde-517	485	1	by	by	ADP
ejde-517	485	2	assumption	assumption	NOUN
ejde-517	485	3	(	(	PUNCT
ejde-517	485	4	3.30	3.30	NUM
ejde-517	485	5	)	)	PUNCT
ejde-517	485	6	and	and	CCONJ
ejde-517	485	7	since	since	SCONJ
ejde-517	485	8	δχδ1	δχδ1	PROPN
ejde-517	485	9	is	be	AUX
ejde-517	485	10	a	a	DET
ejde-517	485	11	mollification	mollification	NOUN
ejde-517	485	12	of	of	ADP
ejde-517	485	13	δχ1	δχ1	NOUN
ejde-517	485	14	,	,	PUNCT
ejde-517	485	15	we	we	PRON
ejde-517	485	16	deduce	deduce	VERB
ejde-517	485	17	that	that	SCONJ
ejde-517	485	18	∇	∇	X
ejde-517	485	19	·	·	PUNCT
ejde-517	485	20	(	(	PUNCT
ejde-517	485	21	δσk∇φ(χδ1	δσk∇φ(χδ1	X
ejde-517	485	22	+	+	X
ejde-517	485	23	ηδχδ1	ηδχδ1	ADJ
ejde-517	485	24	)	)	PUNCT
ejde-517	485	25	)	)	PUNCT
ejde-517	486	1	∈	∈	PROPN
ejde-517	486	2	h1(ω	h1(ω	PROPN
ejde-517	486	3	)	)	PUNCT
ejde-517	486	4	.	.	PUNCT
ejde-517	487	1	because	because	SCONJ
ejde-517	487	2	χδ1	χδ1	X
ejde-517	487	3	,	,	PUNCT
ejde-517	487	4	σ	σ	PROPN
ejde-517	487	5	k	k	PROPN
ejde-517	487	6	1	1	NUM
ejde-517	487	7	∈	∈	NOUN
ejde-517	487	8	c∞(ω̄	c∞(ω̄	NOUN
ejde-517	487	9	)	)	PUNCT
ejde-517	487	10	,	,	PUNCT
ejde-517	487	11	then	then	ADV
ejde-517	487	12	σk(χδ1	σk(χδ1	X
ejde-517	487	13	)	)	PUNCT
ejde-517	487	14	∈	∈	NOUN
ejde-517	487	15	c∞(ω̄	c∞(ω̄	NOUN
ejde-517	487	16	)	)	PUNCT
ejde-517	487	17	.	.	PUNCT
ejde-517	488	1	thus	thus	ADV
ejde-517	488	2	,	,	PUNCT
ejde-517	488	3	σk(χδ1	σk(χδ1	PROPN
ejde-517	488	4	)	)	PUNCT
ejde-517	488	5	∈	∈	PROPN
ejde-517	488	6	c1(ω̄	c1(ω̄	NOUN
ejde-517	488	7	)	)	PUNCT
ejde-517	488	8	.	.	PUNCT
ejde-517	489	1	using	use	VERB
ejde-517	489	2	standard	standard	ADJ
ejde-517	489	3	regularity	regularity	NOUN
ejde-517	489	4	estimate	estimate	NOUN
ejde-517	489	5	(	(	PUNCT
ejde-517	489	6	see	see	VERB
ejde-517	489	7	,	,	PUNCT
ejde-517	489	8	e.g.	e.g.	ADV
ejde-517	489	9	,	,	PUNCT
ejde-517	489	10	[	[	X
ejde-517	489	11	16	16	NUM
ejde-517	489	12	]	]	SYM
ejde-517	489	13	)	)	PUNCT
ejde-517	489	14	,	,	PUNCT
ejde-517	489	15	‖δφ‖h3(ω	‖δφ‖h3(ω	NOUN
ejde-517	489	16	)	)	PUNCT
ejde-517	489	17	≤	≤	NUM
ejde-517	489	18	c1(‖δφ‖h1(ω	c1(‖δφ‖h1(ω	NOUN
ejde-517	489	19	)	)	PUNCT
ejde-517	489	20	+	+	CCONJ
ejde-517	490	1	‖∇	‖∇	NUM
ejde-517	490	2	·	·	PUNCT
ejde-517	490	3	(	(	PUNCT
ejde-517	490	4	δσk∇φ(χδ1	δσk∇φ(χδ1	X
ejde-517	490	5	+	+	X
ejde-517	490	6	ηδχδ1))‖h1(ω	ηδχδ1))‖h1(ω	NOUN
ejde-517	490	7	)	)	PUNCT
ejde-517	490	8	)	)	PUNCT
ejde-517	490	9	,	,	PUNCT
ejde-517	490	10	(	(	PUNCT
ejde-517	490	11	3.61	3.61	NUM
ejde-517	490	12	)	)	PUNCT
ejde-517	490	13	for	for	ADP
ejde-517	490	14	some	some	DET
ejde-517	490	15	c1	c1	PROPN
ejde-517	490	16	>	>	X
ejde-517	490	17	0	0	X
ejde-517	490	18	.	.	PUNCT
ejde-517	491	1	furthermore	furthermore	ADV
ejde-517	491	2	,	,	PUNCT
ejde-517	491	3	by	by	ADP
ejde-517	491	4	the	the	DET
ejde-517	491	5	sobolev	sobolev	NOUN
ejde-517	491	6	imbedding	imbedding	NOUN
ejde-517	491	7	theorem	theorem	NOUN
ejde-517	491	8	,	,	PUNCT
ejde-517	491	9	we	we	PRON
ejde-517	491	10	have	have	VERB
ejde-517	491	11	‖δφ‖c1,γ(ω̄	‖δφ‖c1,γ(ω̄	NOUN
ejde-517	491	12	)	)	PUNCT
ejde-517	491	13	≤	≤	NUM
ejde-517	491	14	c2‖δφ‖h3(ω	c2‖δφ‖h3(ω	NOUN
ejde-517	491	15	)	)	PUNCT
ejde-517	491	16	.	.	PUNCT
ejde-517	492	1	(	(	PUNCT
ejde-517	492	2	3.62	3.62	NUM
ejde-517	492	3	)	)	PUNCT
ejde-517	492	4	16	16	NUM
ejde-517	492	5	r.	r.	PROPN
ejde-517	492	6	mendoza	mendoza	PROPN
ejde-517	492	7	,	,	PUNCT
ejde-517	492	8	s.	s.	PROPN
ejde-517	492	9	keeling	keeling	PROPN
ejde-517	492	10	ejde-2020/93	ejde-2020/93	PROPN
ejde-517	492	11	by	by	ADP
ejde-517	492	12	the	the	DET
ejde-517	492	13	definition	definition	NOUN
ejde-517	492	14	of	of	ADP
ejde-517	492	15	‖	‖	PROPN
ejde-517	492	16	·	·	SYM
ejde-517	492	17	‖cl	‖cl	PROPN
ejde-517	492	18	,	,	PUNCT
ejde-517	492	19	γ(ω̄	γ(ω̄	NUM
ejde-517	492	20	)	)	PUNCT
ejde-517	492	21	,	,	PUNCT
ejde-517	492	22	the	the	DET
ejde-517	492	23	embedding	embed	VERB
ejde-517	492	24	c1,γ(ω̄	c1,γ(ω̄	NOUN
ejde-517	492	25	)	)	PUNCT
ejde-517	492	26	↪	↪	PROPN
ejde-517	492	27	→	→	SYM
ejde-517	492	28	c1(ω̄	c1(ω̄	NUM
ejde-517	492	29	)	)	PUNCT
ejde-517	492	30	(	(	PUNCT
ejde-517	492	31	3.63	3.63	NUM
ejde-517	492	32	)	)	PUNCT
ejde-517	492	33	is	be	AUX
ejde-517	492	34	continuous	continuous	ADJ
ejde-517	492	35	(	(	PUNCT
ejde-517	492	36	see	see	ADJ
ejde-517	492	37	,	,	PUNCT
ejde-517	492	38	e.g.	e.g.	ADV
ejde-517	492	39	,	,	PUNCT
ejde-517	492	40	[	[	X
ejde-517	492	41	18	18	NUM
ejde-517	492	42	]	]	PUNCT
ejde-517	492	43	)	)	PUNCT
ejde-517	492	44	.	.	PUNCT
ejde-517	493	1	if	if	SCONJ
ejde-517	493	2	we	we	PRON
ejde-517	493	3	compare	compare	VERB
ejde-517	493	4	(	(	PUNCT
ejde-517	493	5	3.61	3.61	NUM
ejde-517	493	6	)	)	PUNCT
ejde-517	493	7	,	,	PUNCT
ejde-517	493	8	(	(	PUNCT
ejde-517	493	9	3.62	3.62	NUM
ejde-517	493	10	)	)	PUNCT
ejde-517	493	11	,	,	PUNCT
ejde-517	493	12	and	and	CCONJ
ejde-517	493	13	(	(	PUNCT
ejde-517	493	14	3.63	3.63	NUM
ejde-517	493	15	)	)	PUNCT
ejde-517	493	16	,	,	PUNCT
ejde-517	493	17	we	we	PRON
ejde-517	493	18	can	can	AUX
ejde-517	493	19	deduce	deduce	VERB
ejde-517	493	20	that	that	DET
ejde-517	493	21	∃c̄	∃c̄	NOUN
ejde-517	493	22	>	>	X
ejde-517	493	23	0	0	NUM
ejde-517	494	1	such	such	ADJ
ejde-517	494	2	that	that	SCONJ
ejde-517	494	3	‖∇δφ‖l∞(ω	‖∇δφ‖l∞(ω	NOUN
ejde-517	494	4	)	)	PUNCT
ejde-517	494	5	≤	≤	NOUN
ejde-517	494	6	c2	c2	PROPN
ejde-517	494	7	(	(	PUNCT
ejde-517	494	8	‖δφ‖h1(ω	‖δφ‖h1(ω	ADJ
ejde-517	494	9	)	)	PUNCT
ejde-517	494	10	+	+	CCONJ
ejde-517	494	11	‖∇	‖∇	NUM
ejde-517	494	12	·	·	PUNCT
ejde-517	494	13	(	(	PUNCT
ejde-517	494	14	δσk∇φ(χδ1	δσk∇φ(χδ1	X
ejde-517	494	15	+	+	X
ejde-517	494	16	ηδχδ1))‖h1(ω	ηδχδ1))‖h1(ω	NOUN
ejde-517	494	17	)	)	PUNCT
ejde-517	494	18	)	)	PUNCT
ejde-517	494	19	.	.	PUNCT
ejde-517	495	1	(	(	PUNCT
ejde-517	495	2	3.64	3.64	X
ejde-517	495	3	)	)	PUNCT
ejde-517	495	4	observe	observe	VERB
ejde-517	495	5	that	that	DET
ejde-517	495	6	δσk	δσk	NOUN
ejde-517	495	7	=	=	PUNCT
ejde-517	495	8	η(σk1	η(σk1	NOUN
ejde-517	495	9	−	−	NUM
ejde-517	495	10	σ2)δχδ1	σ2)δχδ1	NOUN
ejde-517	495	11	.	.	PUNCT
ejde-517	496	1	therefore	therefore	ADV
ejde-517	496	2	,	,	PUNCT
ejde-517	496	3	‖∇	‖∇	X
ejde-517	496	4	·	·	PUNCT
ejde-517	496	5	(	(	PUNCT
ejde-517	496	6	δσk∇φ(χδ1	δσk∇φ(χδ1	X
ejde-517	496	7	+	+	X
ejde-517	496	8	ηδχδ1))‖h1(ω	ηδχδ1))‖h1(ω	NOUN
ejde-517	496	9	)	)	PUNCT
ejde-517	496	10	=	=	PUNCT
ejde-517	497	1	η‖∇	η‖∇	PUNCT
ejde-517	497	2	·	·	PUNCT
ejde-517	497	3	(	(	PUNCT
ejde-517	497	4	(	(	PUNCT
ejde-517	497	5	σk1	σk1	NOUN
ejde-517	497	6	−	−	PROPN
ejde-517	497	7	σ2)δχδ1∇φ(χδ1	σ2)δχδ1∇φ(χδ1	X
ejde-517	497	8	+	+	X
ejde-517	497	9	ηδχδ1))‖h1(ω	ηδχδ1))‖h1(ω	NOUN
ejde-517	497	10	)	)	PUNCT
ejde-517	497	11	.	.	PUNCT
ejde-517	498	1	(	(	PUNCT
ejde-517	498	2	3.65	3.65	NUM
ejde-517	498	3	)	)	PUNCT
ejde-517	498	4	recall	recall	NOUN
ejde-517	498	5	that	that	SCONJ
ejde-517	498	6	all	all	DET
ejde-517	498	7	solutions	solution	NOUN
ejde-517	498	8	of	of	ADP
ejde-517	498	9	the	the	DET
ejde-517	498	10	forward	forward	ADJ
ejde-517	498	11	problem	problem	NOUN
ejde-517	498	12	have	have	VERB
ejde-517	498	13	zero	zero	NUM
ejde-517	498	14	boundary	boundary	ADJ
ejde-517	498	15	integral	integral	ADJ
ejde-517	498	16	.	.	PUNCT
ejde-517	499	1	thus,∫	thus,∫	NOUN
ejde-517	500	1	∂ω	∂ω	ADJ
ejde-517	500	2	δφ	δφ	ADP
ejde-517	500	3	ds	ds	NOUN
ejde-517	500	4	=	=	PUNCT
ejde-517	500	5	∫	∫	PROPN
ejde-517	500	6	∂ω	∂ω	PROPN
ejde-517	500	7	φ(χδ1	φ(χδ1	X
ejde-517	500	8	+	+	CCONJ
ejde-517	500	9	ηδχδ1)−	ηδχδ1)−	PROPN
ejde-517	500	10	φ(χδ1	φ(χδ1	PROPN
ejde-517	500	11	)	)	PUNCT
ejde-517	500	12	ds	ds	NOUN
ejde-517	500	13	=	=	NOUN
ejde-517	500	14	0−	0−	NUM
ejde-517	500	15	0	0	NUM
ejde-517	501	1	=	=	SYM
ejde-517	501	2	0	0	X
ejde-517	501	3	.	.	PUNCT
ejde-517	502	1	using	use	VERB
ejde-517	502	2	this	this	PRON
ejde-517	502	3	and	and	CCONJ
ejde-517	502	4	the	the	DET
ejde-517	502	5	generalized	generalize	VERB
ejde-517	502	6	friedrich	friedrich	NOUN
ejde-517	502	7	’s	’s	PART
ejde-517	502	8	inequality	inequality	NOUN
ejde-517	502	9	,	,	PUNCT
ejde-517	502	10	we	we	PRON
ejde-517	502	11	obtain	obtain	VERB
ejde-517	502	12	‖∇δφ‖2l2(ω	‖∇δφ‖2l2(ω	ADV
ejde-517	502	13	)	)	PUNCT
ejde-517	502	14	=	=	SYM
ejde-517	502	15	1	1	NUM
ejde-517	502	16	2	2	NUM
ejde-517	502	17	‖∇δφ‖2l2(ω	‖∇δφ‖2l2(ω	NOUN
ejde-517	502	18	)	)	PUNCT
ejde-517	503	1	+	+	CCONJ
ejde-517	503	2	1	1	NUM
ejde-517	503	3	2	2	NUM
ejde-517	503	4	‖∇δφ‖2l2(ω	‖∇δφ‖2l2(ω	NOUN
ejde-517	503	5	)	)	PUNCT
ejde-517	503	6	≥	≥	NOUN
ejde-517	503	7	c3	c3	X
ejde-517	503	8	2	2	NUM
ejde-517	503	9	‖δφ‖2l2(ω	‖δφ‖2l2(ω	PROPN
ejde-517	503	10	)	)	PUNCT
ejde-517	503	11	−	−	NOUN
ejde-517	504	1	1	1	NUM
ejde-517	504	2	2	2	NUM
ejde-517	504	3	(	(	PUNCT
ejde-517	504	4	∫	∫	PROPN
ejde-517	504	5	∂ω	∂ω	ADJ
ejde-517	504	6	δφ	δφ	ADJ
ejde-517	504	7	ds	ds	NOUN
ejde-517	504	8	)	)	PUNCT
ejde-517	504	9	2	2	NUM
ejde-517	504	10	+	+	CCONJ
ejde-517	504	11	1	1	NUM
ejde-517	504	12	2	2	NUM
ejde-517	504	13	‖∇δφ‖2l2(ω	‖∇δφ‖2l2(ω	NOUN
ejde-517	504	14	)	)	PUNCT
ejde-517	505	1	=	=	SYM
ejde-517	505	2	c3	c3	X
ejde-517	505	3	2	2	NUM
ejde-517	505	4	‖δφ‖2l2(ω	‖δφ‖2l2(ω	NOUN
ejde-517	505	5	)	)	PUNCT
ejde-517	506	1	+	+	CCONJ
ejde-517	506	2	1	1	NUM
ejde-517	506	3	2	2	NUM
ejde-517	506	4	‖∇δφ‖2l2(ω	‖∇δφ‖2l2(ω	NOUN
ejde-517	506	5	)	)	PUNCT
ejde-517	506	6	≥	≥	NOUN
ejde-517	506	7	min	min	NOUN
ejde-517	506	8	{	{	PUNCT
ejde-517	506	9	c3	c3	PROPN
ejde-517	506	10	2	2	NUM
ejde-517	506	11	,	,	PUNCT
ejde-517	506	12	1	1	NUM
ejde-517	506	13	2	2	NUM
ejde-517	506	14	}	}	PUNCT
ejde-517	506	15	‖δφ‖2h1(ω	‖δφ‖2h1(ω	PROPN
ejde-517	506	16	)	)	PUNCT
ejde-517	506	17	(	(	PUNCT
ejde-517	506	18	3.66	3.66	NUM
ejde-517	506	19	)	)	PUNCT
ejde-517	506	20	for	for	ADP
ejde-517	506	21	some	some	DET
ejde-517	506	22	c3	c3	PROPN
ejde-517	506	23	>	>	X
ejde-517	506	24	0	0	X
ejde-517	506	25	.	.	PUNCT
ejde-517	507	1	using	use	VERB
ejde-517	507	2	(	(	PUNCT
ejde-517	507	3	3.66	3.66	NUM
ejde-517	507	4	)	)	PUNCT
ejde-517	507	5	and	and	CCONJ
ejde-517	507	6	(	(	PUNCT
ejde-517	507	7	3.65	3.65	NUM
ejde-517	507	8	)	)	PUNCT
ejde-517	507	9	,	,	PUNCT
ejde-517	507	10	(	(	PUNCT
ejde-517	507	11	3.64	3.64	NUM
ejde-517	507	12	)	)	PUNCT
ejde-517	507	13	becomes	become	VERB
ejde-517	507	14	‖∇δφ‖l∞(ω	‖∇δφ‖l∞(ω	NOUN
ejde-517	507	15	)	)	PUNCT
ejde-517	507	16	≤	≤	NOUN
ejde-517	507	17	c2	c2	PROPN
ejde-517	507	18	{	{	PUNCT
ejde-517	507	19	‖δφ‖h1(ω	‖δφ‖h1(ω	PROPN
ejde-517	507	20	)	)	PUNCT
ejde-517	507	21	+	+	CCONJ
ejde-517	508	1	‖∇	‖∇	NUM
ejde-517	508	2	·	·	PUNCT
ejde-517	508	3	(	(	PUNCT
ejde-517	508	4	δσk∇φ(χδ1	δσk∇φ(χδ1	X
ejde-517	508	5	+	+	X
ejde-517	508	6	ηδχδ1))‖h1(ω	ηδχδ1))‖h1(ω	NOUN
ejde-517	508	7	)	)	PUNCT
ejde-517	508	8	}	}	PUNCT
ejde-517	508	9	≤	≤	PROPN
ejde-517	508	10	c2	c2	PROPN
ejde-517	508	11	{	{	PUNCT
ejde-517	508	12	1√	1√	PROPN
ejde-517	508	13	min{c3	min{c3	NOUN
ejde-517	508	14	2	2	NUM
ejde-517	508	15	,	,	PUNCT
ejde-517	508	16	1	1	NUM
ejde-517	508	17	2	2	NUM
ejde-517	508	18	}	}	PUNCT
ejde-517	508	19	‖∇δφ‖l2(ω	‖∇δφ‖l2(ω	NUM
ejde-517	508	20	)	)	PUNCT
ejde-517	508	21	+	+	CCONJ
ejde-517	508	22	η‖∇	η‖∇	PROPN
ejde-517	508	23	·	·	PUNCT
ejde-517	508	24	(	(	PUNCT
ejde-517	508	25	(	(	PUNCT
ejde-517	508	26	σk1	σk1	NOUN
ejde-517	508	27	−	−	PROPN
ejde-517	508	28	σ2)δχδ1∇φ(χδ1	σ2)δχδ1∇φ(χδ1	X
ejde-517	508	29	+	+	CCONJ
ejde-517	508	30	ηδχδ1))‖h1(ω	ηδχδ1))‖h1(ω	SYM
ejde-517	508	31	)	)	PUNCT
ejde-517	508	32	}	}	PUNCT
ejde-517	508	33	≤	≤	NOUN
ejde-517	508	34	2c2	2c2	NUM
ejde-517	508	35	max	max	PROPN
ejde-517	508	36	{	{	PUNCT
ejde-517	508	37	1√	1√	PROPN
ejde-517	508	38	min{c3	min{c3	NOUN
ejde-517	508	39	2	2	NUM
ejde-517	508	40	,	,	PUNCT
ejde-517	508	41	1	1	NUM
ejde-517	508	42	2	2	NUM
ejde-517	508	43	}	}	PUNCT
ejde-517	508	44	,	,	PUNCT
ejde-517	508	45	1	1	X
ejde-517	508	46	}	}	PUNCT
ejde-517	508	47	{	{	PUNCT
ejde-517	508	48	‖∇δφ‖l2(ω	‖∇δφ‖l2(ω	ADV
ejde-517	508	49	)	)	PUNCT
ejde-517	508	50	+	+	CCONJ
ejde-517	508	51	η‖∇	η‖∇	PROPN
ejde-517	508	52	·	·	PUNCT
ejde-517	508	53	(	(	PUNCT
ejde-517	508	54	(	(	PUNCT
ejde-517	508	55	σk1	σk1	NOUN
ejde-517	508	56	−	−	PROPN
ejde-517	508	57	σ2)δχδ1∇φ(χδ1	σ2)δχδ1∇φ(χδ1	X
ejde-517	508	58	+	+	X
ejde-517	508	59	ηδχδ1))‖h1(ω	ηδχδ1))‖h1(ω	NOUN
ejde-517	508	60	)	)	PUNCT
ejde-517	508	61	}	}	PUNCT
ejde-517	508	62	.	.	PUNCT
ejde-517	509	1	because	because	SCONJ
ejde-517	509	2	of	of	ADP
ejde-517	509	3	(	(	PUNCT
ejde-517	509	4	3.58	3.58	NUM
ejde-517	509	5	)	)	PUNCT
ejde-517	509	6	and	and	CCONJ
ejde-517	509	7	(	(	PUNCT
ejde-517	509	8	3.60	3.60	NUM
ejde-517	509	9	)	)	PUNCT
ejde-517	509	10	,	,	PUNCT
ejde-517	509	11	our	our	PRON
ejde-517	509	12	claim	claim	NOUN
ejde-517	509	13	immediately	immediately	ADV
ejde-517	509	14	follows	follow	VERB
ejde-517	509	15	from	from	ADP
ejde-517	509	16	the	the	DET
ejde-517	509	17	above	above	ADJ
ejde-517	509	18	inequality	inequality	NOUN
ejde-517	509	19	.	.	PUNCT
ejde-517	510	1	�	�	PROPN
ejde-517	510	2	note	note	VERB
ejde-517	510	3	that	that	SCONJ
ejde-517	510	4	∇φ(χδ1	∇φ(χδ1	NOUN
ejde-517	510	5	)	)	PUNCT
ejde-517	510	6	∈	∈	PROPN
ejde-517	510	7	l∞(ω̄),∇φ∗(χδ1	l∞(ω̄),∇φ∗(χδ1	NUM
ejde-517	510	8	)	)	PUNCT
ejde-517	510	9	∈	∈	PROPN
ejde-517	510	10	l∞(ω	l∞(ω	NOUN
ejde-517	510	11	)	)	PUNCT
ejde-517	510	12	,	,	PUNCT
ejde-517	510	13	∇	∇	X
ejde-517	510	14	δφ	δφ	PROPN
ejde-517	510	15	δχδ1	δχδ1	PROPN
ejde-517	510	16	(	(	PUNCT
ejde-517	510	17	χδ1	χδ1	PROPN
ejde-517	510	18	;	;	PUNCT
ejde-517	510	19	δχδ1),∇δφ	δχδ1),∇δφ	PROPN
ejde-517	510	20	∗	∗	NOUN
ejde-517	510	21	δχδ1	δχδ1	PROPN
ejde-517	510	22	(	(	PUNCT
ejde-517	510	23	χδ1	χδ1	X
ejde-517	510	24	;	;	PUNCT
ejde-517	510	25	δχδ1	δχδ1	PROPN
ejde-517	510	26	)	)	PUNCT
ejde-517	510	27	∈	∈	PROPN
ejde-517	510	28	l2(ω	l2(ω	PROPN
ejde-517	510	29	)	)	PUNCT
ejde-517	510	30	.	.	PUNCT
ejde-517	511	1	therefore	therefore	ADV
ejde-517	511	2	,	,	PUNCT
ejde-517	511	3	∇φ(χδ1	∇φ(χδ1	NOUN
ejde-517	511	4	)	)	PUNCT
ejde-517	511	5	·	·	PUNCT
ejde-517	511	6	∇	∇	X
ejde-517	511	7	δφ∗	δφ∗	NOUN
ejde-517	511	8	δχ1	δχ1	NOUN
ejde-517	511	9	(	(	PUNCT
ejde-517	511	10	χδ1	χδ1	X
ejde-517	511	11	;	;	PUNCT
ejde-517	511	12	δχδ1	δχδ1	PROPN
ejde-517	511	13	)	)	PUNCT
ejde-517	512	1	+	+	NOUN
ejde-517	512	2	∇	∇	X
ejde-517	512	3	δφ	δφ	NOUN
ejde-517	512	4	δχ1	δχ1	NOUN
ejde-517	512	5	(	(	PUNCT
ejde-517	512	6	χδ1	χδ1	X
ejde-517	512	7	;	;	PUNCT
ejde-517	512	8	δχδ1	δχδ1	PROPN
ejde-517	512	9	)	)	PUNCT
ejde-517	512	10	·	·	PUNCT
ejde-517	512	11	∇φ∗(χδ1	∇φ∗(χδ1	VERB
ejde-517	512	12	)	)	PUNCT
ejde-517	512	13	∈	∈	PROPN
ejde-517	512	14	l2(ω	l2(ω	PROPN
ejde-517	512	15	)	)	PUNCT
ejde-517	512	16	.	.	PUNCT
ejde-517	513	1	we	we	PRON
ejde-517	513	2	show	show	VERB
ejde-517	513	3	in	in	ADP
ejde-517	513	4	the	the	DET
ejde-517	513	5	next	next	ADJ
ejde-517	513	6	lemma	lemma	PROPN
ejde-517	513	7	that	that	SCONJ
ejde-517	513	8	this	this	PRON
ejde-517	513	9	is	be	AUX
ejde-517	513	10	in	in	ADP
ejde-517	513	11	fact	fact	NOUN
ejde-517	513	12	the	the	DET
ejde-517	513	13	derivative	derivative	NOUN
ejde-517	513	14	of	of	ADP
ejde-517	513	15	ψ	ψ	PRON
ejde-517	513	16	defined	define	VERB
ejde-517	513	17	in	in	ADP
ejde-517	513	18	(	(	PUNCT
ejde-517	513	19	3.41	3.41	NUM
ejde-517	513	20	)	)	PUNCT
ejde-517	513	21	.	.	PUNCT
ejde-517	514	1	ejde-2020/93	ejde-2020/93	PROPN
ejde-517	514	2	impedance	impedance	NOUN
ejde-517	514	3	tomography	tomography	NOUN
ejde-517	514	4	problem	problem	NOUN
ejde-517	514	5	17	17	NUM
ejde-517	514	6	lemma	lemma	PROPN
ejde-517	514	7	3.23	3.23	NUM
ejde-517	514	8	.	.	PUNCT
ejde-517	515	1	under	under	ADP
ejde-517	515	2	assumption	assumption	NOUN
ejde-517	515	3	(	(	PUNCT
ejde-517	515	4	3.30	3.30	NUM
ejde-517	515	5	)	)	PUNCT
ejde-517	515	6	,	,	PUNCT
ejde-517	515	7	we	we	PRON
ejde-517	515	8	have	have	VERB
ejde-517	515	9	lim	lim	PROPN
ejde-517	515	10	η→0	η→0	X
ejde-517	515	11	‖ψ(χδ1	‖ψ(χδ1	NUM
ejde-517	515	12	+	+	CCONJ
ejde-517	515	13	ηδχδ1)−	ηδχδ1)−	PROPN
ejde-517	515	14	ψ(χδ1	ψ(χδ1	PROPN
ejde-517	515	15	)	)	PUNCT
ejde-517	515	16	η	η	PROPN
ejde-517	515	17	−	−	PROPN
ejde-517	515	18	δψ	δψ	NOUN
ejde-517	515	19	δχ1	δχ1	NOUN
ejde-517	515	20	(	(	PUNCT
ejde-517	515	21	χδ1	χδ1	X
ejde-517	515	22	;	;	PUNCT
ejde-517	515	23	δχδ1)‖l2(ω	δχδ1)‖l2(ω	PROPN
ejde-517	515	24	)	)	PUNCT
ejde-517	515	25	=	=	SYM
ejde-517	515	26	0	0	NUM
ejde-517	515	27	(	(	PUNCT
ejde-517	515	28	3.67	3.67	NUM
ejde-517	515	29	)	)	PUNCT
ejde-517	515	30	with	with	ADP
ejde-517	515	31	δψ	δψ	NOUN
ejde-517	515	32	δχ1	δχ1	PROPN
ejde-517	515	33	(	(	PUNCT
ejde-517	515	34	χδ1	χδ1	X
ejde-517	515	35	;	;	PUNCT
ejde-517	515	36	δχδ1	δχδ1	PROPN
ejde-517	515	37	)	)	PUNCT
ejde-517	515	38	:	:	PUNCT
ejde-517	516	1	=	=	PUNCT
ejde-517	516	2	∇φ(χδ1	∇φ(χδ1	NOUN
ejde-517	516	3	)	)	PUNCT
ejde-517	516	4	·	·	PUNCT
ejde-517	517	1	∇δφ	∇δφ	ADJ
ejde-517	517	2	∗	∗	NOUN
ejde-517	517	3	δχ1	δχ1	PROPN
ejde-517	517	4	(	(	PUNCT
ejde-517	517	5	χδ1	χδ1	X
ejde-517	517	6	;	;	PUNCT
ejde-517	517	7	δχδ1	δχδ1	PROPN
ejde-517	517	8	)	)	PUNCT
ejde-517	518	1	+	+	NOUN
ejde-517	518	2	∇	∇	X
ejde-517	518	3	δφ	δφ	NOUN
ejde-517	518	4	δχ1	δχ1	NOUN
ejde-517	518	5	(	(	PUNCT
ejde-517	518	6	χδ1	χδ1	X
ejde-517	518	7	;	;	PUNCT
ejde-517	518	8	δχδ1	δχδ1	PROPN
ejde-517	518	9	)	)	PUNCT
ejde-517	518	10	·	·	PUNCT
ejde-517	518	11	∇φ∗(χδ1	∇φ∗(χδ1	VERB
ejde-517	518	12	)	)	PUNCT
ejde-517	518	13	.	.	PUNCT
ejde-517	519	1	proof	proof	NOUN
ejde-517	519	2	.	.	PUNCT
ejde-517	520	1	for	for	ADP
ejde-517	520	2	any	any	DET
ejde-517	520	3	perturbation	perturbation	NOUN
ejde-517	520	4	δχ1	δχ1	NOUN
ejde-517	520	5	of	of	ADP
ejde-517	520	6	χ1	χ1	NOUN
ejde-517	520	7	,	,	PUNCT
ejde-517	520	8	we	we	PRON
ejde-517	520	9	have	have	VERB
ejde-517	520	10	ψ(χδ1	ψ(χδ1	NOUN
ejde-517	520	11	+	+	CCONJ
ejde-517	520	12	ηδχδ1)−	ηδχδ1)−	PROPN
ejde-517	520	13	ψ(χδ1	ψ(χδ1	PROPN
ejde-517	520	14	)	)	PUNCT
ejde-517	520	15	η	η	NOUN
ejde-517	520	16	=	=	PROPN
ejde-517	520	17	∇φ(χδ1	∇φ(χδ1	PROPN
ejde-517	520	18	+	+	CCONJ
ejde-517	520	19	ηδχδ1	ηδχδ1	ADJ
ejde-517	520	20	)	)	PUNCT
ejde-517	520	21	·	·	PUNCT
ejde-517	520	22	∇φ∗(χδ1	∇φ∗(χδ1	VERB
ejde-517	520	23	+	+	CCONJ
ejde-517	520	24	ηδχδ1	ηδχδ1	ADJ
ejde-517	520	25	)	)	PUNCT
ejde-517	520	26	η	η	PROPN
ejde-517	520	27	−	−	PROPN
ejde-517	520	28	∇φ(χδ1	∇φ(χδ1	NOUN
ejde-517	520	29	)	)	PUNCT
ejde-517	520	30	·	·	PUNCT
ejde-517	520	31	∇φ∗(χδ1	∇φ∗(χδ1	ADJ
ejde-517	520	32	)	)	PUNCT
ejde-517	520	33	η	η	PROPN
ejde-517	520	34	=	=	PUNCT
ejde-517	520	35	∇φ(χδ1	∇φ(χδ1	PROPN
ejde-517	520	36	+	+	CCONJ
ejde-517	520	37	ηδχδ1	ηδχδ1	ADJ
ejde-517	520	38	)	)	PUNCT
ejde-517	520	39	·	·	PUNCT
ejde-517	520	40	∇φ∗(χδ1	∇φ∗(χδ1	VERB
ejde-517	520	41	+	+	CCONJ
ejde-517	520	42	ηδχδ1)−∇φ∗(χδ1	ηδχδ1)−∇φ∗(χδ1	PROPN
ejde-517	520	43	)	)	PUNCT
ejde-517	520	44	η	η	PROPN
ejde-517	520	45	+	+	PROPN
ejde-517	520	46	∇φ(χδ1	∇φ(χδ1	PROPN
ejde-517	520	47	+	+	SYM
ejde-517	520	48	ηδχδ1)−∇φ(χδ1	ηδχδ1)−∇φ(χδ1	PROPN
ejde-517	520	49	)	)	PUNCT
ejde-517	520	50	η	η	PROPN
ejde-517	520	51	·	·	PUNCT
ejde-517	520	52	∇φ∗(χδ1	∇φ∗(χδ1	NOUN
ejde-517	520	53	)	)	PUNCT
ejde-517	520	54	.	.	PUNCT
ejde-517	521	1	(	(	PUNCT
ejde-517	521	2	3.68	3.68	NUM
ejde-517	521	3	)	)	PUNCT
ejde-517	521	4	to	to	PART
ejde-517	521	5	continue	continue	VERB
ejde-517	521	6	with	with	ADP
ejde-517	521	7	our	our	PRON
ejde-517	521	8	proof	proof	NOUN
ejde-517	521	9	,	,	PUNCT
ejde-517	521	10	we	we	PRON
ejde-517	521	11	first	first	ADV
ejde-517	521	12	perform	perform	VERB
ejde-517	521	13	some	some	DET
ejde-517	521	14	convenient	convenient	ADJ
ejde-517	521	15	calculations	calculation	NOUN
ejde-517	521	16	.	.	PUNCT
ejde-517	522	1	by	by	ADP
ejde-517	522	2	adding	add	VERB
ejde-517	522	3	and	and	CCONJ
ejde-517	522	4	subtracting	subtract	VERB
ejde-517	522	5	a	a	DET
ejde-517	522	6	term	term	NOUN
ejde-517	522	7	,	,	PUNCT
ejde-517	522	8	the	the	DET
ejde-517	522	9	following	follow	VERB
ejde-517	522	10	is	be	AUX
ejde-517	522	11	obtained	obtain	VERB
ejde-517	522	12	:	:	PUNCT
ejde-517	522	13	∇φ(χδ1	∇φ(χδ1	NOUN
ejde-517	522	14	+	+	CCONJ
ejde-517	522	15	ηδχδ1	ηδχδ1	ADJ
ejde-517	522	16	)	)	PUNCT
ejde-517	522	17	·	·	PUNCT
ejde-517	522	18	∇φ∗(χδ1	∇φ∗(χδ1	VERB
ejde-517	522	19	+	+	CCONJ
ejde-517	522	20	ηδχδ1)−∇φ∗(χδ1	ηδχδ1)−∇φ∗(χδ1	PROPN
ejde-517	522	21	)	)	PUNCT
ejde-517	522	22	η	η	NOUN
ejde-517	522	23	−∇φ(χδ1	−∇φ(χδ1	PROPN
ejde-517	522	24	)	)	PUNCT
ejde-517	522	25	·	·	PUNCT
ejde-517	522	26	∇δφ	∇δφ	ADJ
ejde-517	522	27	∗	∗	NOUN
ejde-517	522	28	δχδ1	δχδ1	PROPN
ejde-517	522	29	(	(	PUNCT
ejde-517	522	30	χδ1	χδ1	X
ejde-517	522	31	;	;	PUNCT
ejde-517	522	32	δχδ1	δχδ1	PROPN
ejde-517	522	33	)	)	PUNCT
ejde-517	522	34	:	:	PUNCT
ejde-517	523	1	=	=	PUNCT
ejde-517	523	2	a1	a1	PROPN
ejde-517	523	3	+	+	SYM
ejde-517	523	4	a2	a2	PROPN
ejde-517	523	5	,	,	PUNCT
ejde-517	523	6	(	(	PUNCT
ejde-517	523	7	3.69	3.69	NUM
ejde-517	523	8	)	)	PUNCT
ejde-517	523	9	where	where	SCONJ
ejde-517	523	10	a1	a1	NOUN
ejde-517	523	11	=	=	VERB
ejde-517	523	12	∇φ(χδ1	∇φ(χδ1	PROPN
ejde-517	523	13	+	+	CCONJ
ejde-517	523	14	ηδχδ1	ηδχδ1	ADJ
ejde-517	523	15	)	)	PUNCT
ejde-517	523	16	·	·	PUNCT
ejde-517	523	17	∇φ∗(χδ1	∇φ∗(χδ1	VERB
ejde-517	523	18	+	+	CCONJ
ejde-517	523	19	ηδχδ1)−∇φ∗(χδ1	ηδχδ1)−∇φ∗(χδ1	PROPN
ejde-517	523	20	)	)	PUNCT
ejde-517	523	21	η	η	NOUN
ejde-517	523	22	−∇φ(χδ1	−∇φ(χδ1	PROPN
ejde-517	523	23	+	+	CCONJ
ejde-517	523	24	ηδχδ1	ηδχδ1	ADJ
ejde-517	523	25	)	)	PUNCT
ejde-517	523	26	·	·	PUNCT
ejde-517	524	1	∇δφ	∇δφ	ADJ
ejde-517	524	2	∗	∗	NOUN
ejde-517	524	3	δχ1	δχ1	PROPN
ejde-517	524	4	(	(	PUNCT
ejde-517	524	5	χδ1	χδ1	X
ejde-517	524	6	;	;	PUNCT
ejde-517	524	7	δχδ1	δχδ1	PROPN
ejde-517	524	8	)	)	PUNCT
ejde-517	524	9	,	,	PUNCT
ejde-517	524	10	a2	a2	PROPN
ejde-517	524	11	=	=	PUNCT
ejde-517	524	12	∇φ(χδ1	∇φ(χδ1	PROPN
ejde-517	524	13	+	+	CCONJ
ejde-517	524	14	ηδχδ1	ηδχδ1	ADJ
ejde-517	524	15	)	)	PUNCT
ejde-517	524	16	·	·	PUNCT
ejde-517	524	17	δ∇φ∗	δ∇φ∗	ADJ
ejde-517	524	18	δχ1	δχ1	NOUN
ejde-517	524	19	(	(	PUNCT
ejde-517	524	20	χδ1	χδ1	X
ejde-517	524	21	;	;	PUNCT
ejde-517	524	22	δχδ1)−∇φ(χδ1	δχδ1)−∇φ(χδ1	X
ejde-517	524	23	)	)	PUNCT
ejde-517	524	24	·	·	PUNCT
ejde-517	524	25	∇δφ	∇δφ	ADJ
ejde-517	524	26	∗	∗	NOUN
ejde-517	524	27	δχ1	δχ1	PROPN
ejde-517	524	28	(	(	PUNCT
ejde-517	524	29	χδ1	χδ1	X
ejde-517	524	30	;	;	PUNCT
ejde-517	524	31	δχδ1	δχδ1	NOUN
ejde-517	524	32	)	)	PUNCT
ejde-517	524	33	.	.	PUNCT
ejde-517	525	1	using	use	VERB
ejde-517	525	2	the	the	DET
ejde-517	525	3	hölder	hölder	NOUN
ejde-517	525	4	’s	’s	PART
ejde-517	525	5	inequality	inequality	NOUN
ejde-517	525	6	and	and	CCONJ
ejde-517	525	7	(	(	PUNCT
ejde-517	525	8	3.37	3.37	NUM
ejde-517	525	9	)	)	PUNCT
ejde-517	525	10	,	,	PUNCT
ejde-517	525	11	we	we	PRON
ejde-517	525	12	obtain	obtain	VERB
ejde-517	525	13	‖a1‖l2(ω	‖a1‖l2(ω	NUM
ejde-517	525	14	)	)	PUNCT
ejde-517	525	15	≤	≤	NUM
ejde-517	525	16	c1‖f‖l̃2(∂ω)‖	c1‖f‖l̃2(∂ω)‖	NOUN
ejde-517	525	17	∇φ∗(χ1	∇φ∗(χ1	NOUN
ejde-517	525	18	+	+	CCONJ
ejde-517	525	19	ηδχ1)−∇φ∗(χ1	ηδχ1)−∇φ∗(χ1	PROPN
ejde-517	525	20	)	)	PUNCT
ejde-517	525	21	η	η	PROPN
ejde-517	525	22	−∇δφ	−∇δφ	PROPN
ejde-517	525	23	∗	∗	PROPN
ejde-517	525	24	δχ1	δχ1	PROPN
ejde-517	525	25	(	(	PUNCT
ejde-517	525	26	χδ1	χδ1	X
ejde-517	525	27	;	;	PUNCT
ejde-517	525	28	δχδ1)‖l2(ω	δχδ1)‖l2(ω	PROPN
ejde-517	525	29	)	)	PUNCT
ejde-517	525	30	,	,	PUNCT
ejde-517	525	31	for	for	ADP
ejde-517	525	32	some	some	DET
ejde-517	525	33	c1	c1	PROPN
ejde-517	525	34	>	>	X
ejde-517	525	35	0	0	X
ejde-517	525	36	.	.	PUNCT
ejde-517	526	1	recall	recall	PROPN
ejde-517	526	2	from	from	ADP
ejde-517	526	3	(	(	PUNCT
ejde-517	526	4	3.39	3.39	NUM
ejde-517	526	5	)	)	PUNCT
ejde-517	527	1	that	that	SCONJ
ejde-517	527	2	‖φ(χδ1	‖φ(χδ1	NUM
ejde-517	527	3	+	+	CCONJ
ejde-517	527	4	ηδχδ1)−	ηδχδ1)−	PROPN
ejde-517	527	5	φ(χδ1)‖h1(ω	φ(χδ1)‖h1(ω	NUM
ejde-517	527	6	)	)	PUNCT
ejde-517	527	7	≤	≤	NOUN
ejde-517	527	8	c2η‖δχ1‖l2(ω	c2η‖δχ1‖l2(ω	ADV
ejde-517	527	9	)	)	PUNCT
ejde-517	527	10	,	,	PUNCT
ejde-517	527	11	(	(	PUNCT
ejde-517	527	12	3.70	3.70	NUM
ejde-517	527	13	)	)	PUNCT
ejde-517	527	14	for	for	ADP
ejde-517	527	15	some	some	DET
ejde-517	527	16	c2	c2	PROPN
ejde-517	527	17	>	>	X
ejde-517	527	18	0	0	X
ejde-517	527	19	.	.	PUNCT
ejde-517	527	20	using	use	VERB
ejde-517	527	21	the	the	DET
ejde-517	527	22	cauchy	cauchy	NOUN
ejde-517	527	23	-	-	PUNCT
ejde-517	527	24	schwarz	schwarz	PROPN
ejde-517	527	25	inequality	inequality	NOUN
ejde-517	527	26	,	,	PUNCT
ejde-517	527	27	(	(	PUNCT
ejde-517	527	28	3.48	3.48	NUM
ejde-517	527	29	)	)	PUNCT
ejde-517	527	30	,	,	PUNCT
ejde-517	527	31	and	and	CCONJ
ejde-517	527	32	(	(	PUNCT
ejde-517	527	33	3.59	3.59	NUM
ejde-517	527	34	)	)	PUNCT
ejde-517	527	35	,	,	PUNCT
ejde-517	527	36	we	we	PRON
ejde-517	527	37	obtain	obtain	VERB
ejde-517	527	38	‖a2‖l2(ω	‖a2‖l2(ω	ADV
ejde-517	527	39	)	)	PUNCT
ejde-517	527	40	≤	≤	PROPN
ejde-517	527	41	c3η	c3η	ADP
ejde-517	527	42	{	{	PUNCT
ejde-517	527	43	c4‖δχ1‖l2(ω	c4‖δχ1‖l2(ω	ADV
ejde-517	527	44	)	)	PUNCT
ejde-517	528	1	+	+	CCONJ
ejde-517	529	1	‖∇	‖∇	NUM
ejde-517	529	2	·	·	PUNCT
ejde-517	529	3	(	(	PUNCT
ejde-517	529	4	[	[	X
ejde-517	529	5	σk1	σk1	NOUN
ejde-517	529	6	−	−	PROPN
ejde-517	529	7	σ2]δχδ1∇φ(χδ1	σ2]δχδ1∇φ(χδ1	X
ejde-517	529	8	+	+	X
ejde-517	529	9	ηδχδ1))‖h1(ω	ηδχδ1))‖h1(ω	NOUN
ejde-517	529	10	)	)	PUNCT
ejde-517	529	11	}	}	PUNCT
ejde-517	529	12	×	×	NOUN
ejde-517	529	13	‖∇δφ	‖∇δφ	PROPN
ejde-517	529	14	∗	∗	X
ejde-517	529	15	δχ1	δχ1	PROPN
ejde-517	529	16	(	(	PUNCT
ejde-517	529	17	χδ1	χδ1	X
ejde-517	529	18	;	;	PUNCT
ejde-517	529	19	δχδ1)‖h1(ω	δχδ1)‖h1(ω	PROPN
ejde-517	529	20	)	)	PUNCT
ejde-517	529	21	,	,	PUNCT
ejde-517	529	22	for	for	ADP
ejde-517	529	23	some	some	DET
ejde-517	529	24	c3	c3	NOUN
ejde-517	529	25	,	,	PUNCT
ejde-517	529	26	c4	c4	NOUN
ejde-517	529	27	>	>	X
ejde-517	529	28	0	0	X
ejde-517	529	29	.	.	PUNCT
ejde-517	529	30	define	define	NOUN
ejde-517	529	31	a3	a3	NOUN
ejde-517	529	32	:	:	PUNCT
ejde-517	529	33	=	=	PUNCT
ejde-517	529	34	∇φ(χ1	∇φ(χ1	X
ejde-517	529	35	+	+	CCONJ
ejde-517	529	36	ηδχ1)−∇φ(χ1	ηδχ1)−∇φ(χ1	ADJ
ejde-517	529	37	)	)	PUNCT
ejde-517	529	38	η	η	PROPN
ejde-517	529	39	·	·	PUNCT
ejde-517	529	40	∇φ∗(χ1)−∇	∇φ∗(χ1)−∇	VERB
ejde-517	529	41	δφ	δφ	ADP
ejde-517	529	42	δχ1	δχ1	X
ejde-517	529	43	(	(	PUNCT
ejde-517	529	44	χ1	χ1	NOUN
ejde-517	529	45	;	;	PUNCT
ejde-517	529	46	δχ1	δχ1	X
ejde-517	529	47	)	)	PUNCT
ejde-517	529	48	·	·	PUNCT
ejde-517	529	49	∇φ∗(χ1	∇φ∗(χ1	ADJ
ejde-517	529	50	)	)	PUNCT
ejde-517	529	51	.	.	PUNCT
ejde-517	530	1	(	(	PUNCT
ejde-517	530	2	3.71	3.71	NUM
ejde-517	530	3	)	)	PUNCT
ejde-517	530	4	18	18	NUM
ejde-517	530	5	r.	r.	PROPN
ejde-517	530	6	mendoza	mendoza	PROPN
ejde-517	530	7	,	,	PUNCT
ejde-517	530	8	s.	s.	PROPN
ejde-517	530	9	keeling	keeling	PROPN
ejde-517	530	10	ejde-2020/93	ejde-2020/93	PROPN
ejde-517	530	11	hence	hence	ADV
ejde-517	530	12	,	,	PUNCT
ejde-517	530	13	ψ(χδ1	ψ(χδ1	PROPN
ejde-517	530	14	+	+	CCONJ
ejde-517	530	15	ηδχδ1)−	ηδχδ1)−	PROPN
ejde-517	530	16	ψ(χδ1	ψ(χδ1	PROPN
ejde-517	530	17	)	)	PUNCT
ejde-517	530	18	η	η	NOUN
ejde-517	530	19	=	=	SYM
ejde-517	530	20	3∑	3∑	NUM
ejde-517	530	21	i=1	i=1	PRON
ejde-517	530	22	ai	ai	VERB
ejde-517	530	23	.	.	PUNCT
ejde-517	531	1	using	use	VERB
ejde-517	531	2	hölder	hölder	PROPN
ejde-517	531	3	’s	’s	PART
ejde-517	531	4	inequality	inequality	NOUN
ejde-517	531	5	and	and	CCONJ
ejde-517	531	6	(	(	PUNCT
ejde-517	531	7	3.36	3.36	NUM
ejde-517	531	8	)	)	PUNCT
ejde-517	531	9	,	,	PUNCT
ejde-517	531	10	‖a3‖l2(ω	‖a3‖l2(ω	NUM
ejde-517	531	11	)	)	PUNCT
ejde-517	531	12	≤	≤	NOUN
ejde-517	531	13	‖∇φ(χδ1	‖∇φ(χδ1	PUNCT
ejde-517	531	14	+	+	CCONJ
ejde-517	531	15	ηδχδ1)−∇φ(χδ1	ηδχδ1)−∇φ(χδ1	PROPN
ejde-517	531	16	)	)	PUNCT
ejde-517	531	17	η	η	NOUN
ejde-517	531	18	−∇	−∇	NOUN
ejde-517	531	19	δφ	δφ	ADJ
ejde-517	531	20	δχ1	δχ1	NOUN
ejde-517	531	21	(	(	PUNCT
ejde-517	531	22	χδ1	χδ1	X
ejde-517	531	23	;	;	PUNCT
ejde-517	531	24	δχδ1)‖l2(ω)‖∇φ∗(χδ1)‖l∞(ω	δχδ1)‖l2(ω)‖∇φ∗(χδ1)‖l∞(ω	NUM
ejde-517	531	25	)	)	PUNCT
ejde-517	531	26	.	.	PUNCT
ejde-517	532	1	comparing	compare	VERB
ejde-517	532	2	(	(	PUNCT
ejde-517	532	3	3.68	3.68	NUM
ejde-517	532	4	)	)	PUNCT
ejde-517	532	5	,	,	PUNCT
ejde-517	532	6	(	(	PUNCT
ejde-517	532	7	3.69	3.69	NUM
ejde-517	532	8	)	)	PUNCT
ejde-517	532	9	and	and	CCONJ
ejde-517	532	10	(	(	PUNCT
ejde-517	532	11	3.71	3.71	NUM
ejde-517	532	12	)	)	PUNCT
ejde-517	532	13	we	we	PRON
ejde-517	532	14	obtain	obtain	VERB
ejde-517	532	15	‖ψ(χδ1	‖ψ(χδ1	NUM
ejde-517	532	16	+	+	CCONJ
ejde-517	532	17	ηδχδ1)−	ηδχδ1)−	PROPN
ejde-517	532	18	ψ(χδ1	ψ(χδ1	PROPN
ejde-517	532	19	)	)	PUNCT
ejde-517	532	20	η	η	PROPN
ejde-517	532	21	−	−	PROPN
ejde-517	532	22	δψ	δψ	NOUN
ejde-517	532	23	δχ1	δχ1	NOUN
ejde-517	532	24	(	(	PUNCT
ejde-517	532	25	χδ1	χδ1	X
ejde-517	532	26	;	;	PUNCT
ejde-517	532	27	δχδ1)‖l2(ω	δχδ1)‖l2(ω	PROPN
ejde-517	532	28	)	)	PUNCT
ejde-517	532	29	≤	≤	NOUN
ejde-517	533	1	3∑	3∑	NUM
ejde-517	533	2	i=1	i=1	PRON
ejde-517	533	3	‖ai‖	‖ai‖	PROPN
ejde-517	533	4	,	,	PUNCT
ejde-517	533	5	using	use	VERB
ejde-517	533	6	the	the	DET
ejde-517	533	7	triangle	triangle	NOUN
ejde-517	533	8	inequality	inequality	NOUN
ejde-517	533	9	.	.	PUNCT
ejde-517	534	1	now	now	ADV
ejde-517	534	2	we	we	PRON
ejde-517	534	3	only	only	ADV
ejde-517	534	4	need	need	VERB
ejde-517	534	5	to	to	PART
ejde-517	534	6	show	show	VERB
ejde-517	534	7	that	that	SCONJ
ejde-517	534	8	all	all	DET
ejde-517	534	9	the	the	DET
ejde-517	534	10	terms	term	NOUN
ejde-517	534	11	on	on	ADP
ejde-517	534	12	the	the	DET
ejde-517	534	13	right	right	ADJ
ejde-517	534	14	-	-	PUNCT
ejde-517	534	15	hand	hand	NOUN
ejde-517	534	16	side	side	NOUN
ejde-517	534	17	of	of	ADP
ejde-517	534	18	this	this	DET
ejde-517	534	19	inequality	inequality	NOUN
ejde-517	534	20	converge	converge	VERB
ejde-517	534	21	to	to	ADP
ejde-517	534	22	0	0	NUM
ejde-517	534	23	as	as	SCONJ
ejde-517	534	24	η	η	PROPN
ejde-517	534	25	goes	go	VERB
ejde-517	534	26	to	to	ADP
ejde-517	534	27	0	0	NUM
ejde-517	534	28	.	.	PUNCT
ejde-517	535	1	from	from	ADP
ejde-517	535	2	the	the	DET
ejde-517	535	3	estimate	estimate	NOUN
ejde-517	535	4	of	of	ADP
ejde-517	535	5	the	the	DET
ejde-517	535	6	l2	l2	NOUN
ejde-517	535	7	-	-	PUNCT
ejde-517	535	8	norm	norm	NOUN
ejde-517	535	9	of	of	ADP
ejde-517	535	10	a2	a2	PROPN
ejde-517	535	11	above	above	ADV
ejde-517	535	12	,	,	PUNCT
ejde-517	535	13	we	we	PRON
ejde-517	535	14	can	can	AUX
ejde-517	535	15	see	see	VERB
ejde-517	535	16	that	that	PRON
ejde-517	535	17	‖a2‖l2(ω	‖a2‖l2(ω	ADV
ejde-517	535	18	)	)	PUNCT
ejde-517	535	19	→	→	SYM
ejde-517	536	1	0	0	X
ejde-517	536	2	.	.	X
ejde-517	537	1	from	from	ADP
ejde-517	537	2	(	(	PUNCT
ejde-517	537	3	3.47	3.47	NUM
ejde-517	537	4	)	)	PUNCT
ejde-517	537	5	and	and	CCONJ
ejde-517	537	6	(	(	PUNCT
ejde-517	537	7	3.48	3.48	NUM
ejde-517	537	8	)	)	PUNCT
ejde-517	537	9	,	,	PUNCT
ejde-517	537	10	we	we	PRON
ejde-517	537	11	can	can	AUX
ejde-517	537	12	deduce	deduce	VERB
ejde-517	537	13	that	that	DET
ejde-517	537	14	lim	lim	PROPN
ejde-517	537	15	η→0	η→0	X
ejde-517	537	16	‖∇φ(χδ1	‖∇φ(χδ1	PROPN
ejde-517	537	17	+	+	CCONJ
ejde-517	537	18	ηδχδ1)−∇φ(χδ1	ηδχδ1)−∇φ(χδ1	PROPN
ejde-517	537	19	)	)	PUNCT
ejde-517	537	20	η	η	NOUN
ejde-517	537	21	−∇	−∇	NOUN
ejde-517	537	22	δφ	δφ	PROPN
ejde-517	537	23	δχδ1	δχδ1	PROPN
ejde-517	537	24	(	(	PUNCT
ejde-517	537	25	χδ1	χδ1	X
ejde-517	537	26	;	;	PUNCT
ejde-517	537	27	δχδ1)‖l2(ω	δχδ1)‖l2(ω	PROPN
ejde-517	537	28	)	)	PUNCT
ejde-517	537	29	=	=	SYM
ejde-517	537	30	0	0	PROPN
ejde-517	537	31	,	,	PUNCT
ejde-517	537	32	lim	lim	NOUN
ejde-517	537	33	η→0	η→0	X
ejde-517	537	34	‖∇φ∗(χδ1	‖∇φ∗(χδ1	PROPN
ejde-517	537	35	+	+	CCONJ
ejde-517	537	36	ηδχδ1)−∇∗φ(χδ1	ηδχδ1)−∇∗φ(χδ1	PROPN
ejde-517	537	37	)	)	PUNCT
ejde-517	537	38	η	η	PROPN
ejde-517	537	39	−∇δφ	−∇δφ	PROPN
ejde-517	537	40	∗	∗	PROPN
ejde-517	537	41	δχδ1	δχδ1	PROPN
ejde-517	537	42	(	(	PUNCT
ejde-517	537	43	χδ1	χδ1	X
ejde-517	537	44	;	;	PUNCT
ejde-517	537	45	δχδ1)‖l2(ω	δχδ1)‖l2(ω	PROPN
ejde-517	537	46	)	)	PUNCT
ejde-517	537	47	=	=	SYM
ejde-517	538	1	0	0	X
ejde-517	538	2	.	.	PUNCT
ejde-517	539	1	these	these	PRON
ejde-517	539	2	imply	imply	VERB
ejde-517	539	3	that	that	SCONJ
ejde-517	539	4	‖a1‖l2(ω	‖a1‖l2(ω	NUM
ejde-517	539	5	)	)	PUNCT
ejde-517	539	6	,	,	PUNCT
ejde-517	539	7	‖a3‖l2(ω	‖a3‖l2(ω	NUM
ejde-517	539	8	)	)	PUNCT
ejde-517	539	9	→	→	SYM
ejde-517	539	10	0	0	X
ejde-517	539	11	.	.	X
ejde-517	540	1	�	�	PROPN
ejde-517	540	2	we	we	PRON
ejde-517	540	3	now	now	ADV
ejde-517	540	4	use	use	VERB
ejde-517	540	5	our	our	PRON
ejde-517	540	6	results	result	NOUN
ejde-517	540	7	on	on	ADP
ejde-517	540	8	φ	φ	PROPN
ejde-517	540	9	and	and	CCONJ
ejde-517	540	10	φ∗	φ∗	NOUN
ejde-517	540	11	to	to	PART
ejde-517	540	12	study	study	VERB
ejde-517	540	13	σ1	σ1	PROPN
ejde-517	540	14	.	.	PUNCT
ejde-517	541	1	we	we	PRON
ejde-517	541	2	first	first	ADV
ejde-517	541	3	show	show	VERB
ejde-517	541	4	that	that	SCONJ
ejde-517	541	5	under	under	ADP
ejde-517	541	6	assumption	assumption	NOUN
ejde-517	541	7	(	(	PUNCT
ejde-517	541	8	3.30	3.30	NUM
ejde-517	541	9	)	)	PUNCT
ejde-517	541	10	,	,	PUNCT
ejde-517	541	11	(	(	PUNCT
ejde-517	541	12	3.29	3.29	NUM
ejde-517	541	13	)	)	PUNCT
ejde-517	541	14	has	have	VERB
ejde-517	541	15	a	a	DET
ejde-517	541	16	unique	unique	ADJ
ejde-517	541	17	solution	solution	NOUN
ejde-517	541	18	σk+1	σk+1	ADP
ejde-517	541	19	1	1	NUM
ejde-517	541	20	.	.	PUNCT
ejde-517	542	1	we	we	PRON
ejde-517	542	2	then	then	ADV
ejde-517	542	3	proceed	proceed	VERB
ejde-517	542	4	with	with	ADP
ejde-517	542	5	finding	find	VERB
ejde-517	542	6	the	the	DET
ejde-517	542	7	regularity	regularity	NOUN
ejde-517	542	8	of	of	ADP
ejde-517	542	9	the	the	DET
ejde-517	542	10	said	say	VERB
ejde-517	542	11	solution	solution	NOUN
ejde-517	542	12	.	.	PUNCT
ejde-517	543	1	observe	observe	VERB
ejde-517	543	2	that	that	SCONJ
ejde-517	543	3	σk+1	σk+1	PROPN
ejde-517	543	4	1	1	NUM
ejde-517	543	5	depends	depend	VERB
ejde-517	543	6	on	on	ADP
ejde-517	543	7	φ	φ	PROPN
ejde-517	543	8	and	and	CCONJ
ejde-517	543	9	φ∗.	φ∗.	NOUN
ejde-517	543	10	hence	hence	ADV
ejde-517	543	11	,	,	PUNCT
ejde-517	543	12	we	we	PRON
ejde-517	543	13	can	can	AUX
ejde-517	543	14	investigate	investigate	VERB
ejde-517	543	15	how	how	SCONJ
ejde-517	543	16	the	the	DET
ejde-517	543	17	mollification	mollification	NOUN
ejde-517	543	18	of	of	ADP
ejde-517	543	19	χ1	χ1	NOUN
ejde-517	543	20	affects	affect	VERB
ejde-517	543	21	σk+1	σk+1	NUM
ejde-517	543	22	1	1	NUM
ejde-517	543	23	.	.	PUNCT
ejde-517	544	1	we	we	PRON
ejde-517	544	2	show	show	VERB
ejde-517	544	3	that	that	SCONJ
ejde-517	544	4	σk+1	σk+1	PROPN
ejde-517	544	5	1	1	NUM
ejde-517	544	6	continuously	continuously	ADV
ejde-517	544	7	depends	depend	VERB
ejde-517	544	8	on	on	ADP
ejde-517	544	9	χ1	χ1	NOUN
ejde-517	544	10	.	.	PUNCT
ejde-517	545	1	furthermore	furthermore	ADV
ejde-517	545	2	,	,	PUNCT
ejde-517	545	3	we	we	PRON
ejde-517	545	4	prove	prove	VERB
ejde-517	545	5	that	that	SCONJ
ejde-517	545	6	δς1	δς1	ADJ
ejde-517	545	7	δχ1	δχ1	X
ejde-517	545	8	(	(	PUNCT
ejde-517	545	9	χδ1	χδ1	X
ejde-517	545	10	;	;	PUNCT
ejde-517	545	11	δχδ1	δχδ1	PROPN
ejde-517	545	12	)	)	PUNCT
ejde-517	545	13	∈	∈	PROPN
ejde-517	545	14	h1(ω	h1(ω	PROPN
ejde-517	545	15	)	)	PUNCT
ejde-517	545	16	.	.	PUNCT
ejde-517	546	1	we	we	PRON
ejde-517	546	2	start	start	VERB
ejde-517	546	3	by	by	ADP
ejde-517	546	4	equipping	equip	VERB
ejde-517	546	5	h1(ω	h1(ω	PROPN
ejde-517	546	6	)	)	PUNCT
ejde-517	546	7	with	with	ADP
ejde-517	546	8	a	a	DET
ejde-517	546	9	suitable	suitable	ADJ
ejde-517	546	10	norm	norm	NOUN
ejde-517	546	11	.	.	PUNCT
ejde-517	547	1	proposition	proposition	NOUN
ejde-517	547	2	3.24	3.24	NUM
ejde-517	547	3	.	.	PUNCT
ejde-517	548	1	under	under	ADP
ejde-517	548	2	assumption	assumption	NOUN
ejde-517	548	3	(	(	PUNCT
ejde-517	548	4	3.30	3.30	NUM
ejde-517	548	5	)	)	PUNCT
ejde-517	548	6	we	we	PRON
ejde-517	548	7	define	define	VERB
ejde-517	548	8	|v|2h1(ω	|v|2h1(ω	NOUN
ejde-517	548	9	)	)	PUNCT
ejde-517	548	10	:	:	PUNCT
ejde-517	549	1	=	=	PUNCT
ejde-517	549	2	α	α	NUM
ejde-517	549	3	∫	∫	PROPN
ejde-517	549	4	ω	ω	PROPN
ejde-517	549	5	(	(	PUNCT
ejde-517	549	6	χ+	χ+	PROPN
ejde-517	549	7	ε)|∇v|2	ε)|∇v|2	PROPN
ejde-517	549	8	dv	dv	PROPN
ejde-517	549	9	+	+	PROPN
ejde-517	549	10	θλ	θλ	PROPN
ejde-517	549	11	∫	∫	PROPN
ejde-517	549	12	v2	v2	PROPN
ejde-517	549	13	dv	dv	PROPN
ejde-517	549	14	,	,	PUNCT
ejde-517	549	15	where	where	SCONJ
ejde-517	549	16	χ(x	χ(x	PROPN
ejde-517	549	17	)	)	PUNCT
ejde-517	549	18	∈	∈	PROPN
ejde-517	550	1	[	[	X
ejde-517	550	2	0	0	NUM
ejde-517	550	3	,	,	PUNCT
ejde-517	550	4	1	1	NUM
ejde-517	550	5	]	]	PUNCT
ejde-517	550	6	for	for	ADP
ejde-517	550	7	all	all	DET
ejde-517	550	8	x	x	SYM
ejde-517	550	9	∈	∈	PROPN
ejde-517	550	10	ω	ω	NUM
ejde-517	550	11	,	,	PUNCT
ejde-517	550	12	and	and	CCONJ
ejde-517	550	13	let	let	VERB
ejde-517	550	14	‖	‖	PROPN
ejde-517	550	15	·	·	PUNCT
ejde-517	550	16	‖h1(ω	‖h1(ω	PROPN
ejde-517	550	17	)	)	PUNCT
ejde-517	550	18	be	be	AUX
ejde-517	550	19	the	the	DET
ejde-517	550	20	standard	standard	ADJ
ejde-517	550	21	h1(ω	h1(ω	SYM
ejde-517	550	22	)	)	PUNCT
ejde-517	550	23	norm	norm	NOUN
ejde-517	550	24	.	.	PUNCT
ejde-517	551	1	then	then	ADV
ejde-517	551	2	|	|	ADV
ejde-517	551	3	·	·	PUNCT
ejde-517	551	4	|h1(ω	|h1(ω	NUM
ejde-517	551	5	)	)	PUNCT
ejde-517	551	6	and	and	CCONJ
ejde-517	551	7	‖	‖	PROPN
ejde-517	551	8	·	·	PUNCT
ejde-517	551	9	‖h1(ω	‖h1(ω	PROPN
ejde-517	551	10	)	)	PUNCT
ejde-517	551	11	are	be	AUX
ejde-517	551	12	equivalent	equivalent	ADJ
ejde-517	551	13	.	.	PUNCT
ejde-517	552	1	proof	proof	NOUN
ejde-517	552	2	.	.	PUNCT
ejde-517	553	1	observe	observe	VERB
ejde-517	553	2	that	that	SCONJ
ejde-517	553	3	min{αε	min{αε	NOUN
ejde-517	553	4	,	,	PUNCT
ejde-517	553	5	λ}‖v‖2h1(ω	λ}‖v‖2h1(ω	NOUN
ejde-517	553	6	)	)	PUNCT
ejde-517	553	7	≤	≤	NOUN
ejde-517	554	1	α	α	X
ejde-517	554	2	∫	∫	PROPN
ejde-517	554	3	ω	ω	PROPN
ejde-517	554	4	ε|∇v|2	ε|∇v|2	PROPN
ejde-517	555	1	dv	dv	PROPN
ejde-517	556	1	+	+	CCONJ
ejde-517	556	2	θ	θ	PROPN
ejde-517	556	3	∫	∫	PROPN
ejde-517	556	4	ω	ω	PROPN
ejde-517	556	5	|v|2	|v|2	PROPN
ejde-517	556	6	dv	dv	PROPN
ejde-517	556	7	≤	≤	PROPN
ejde-517	556	8	α	α	PROPN
ejde-517	556	9	∫	∫	PROPN
ejde-517	556	10	ω	ω	PROPN
ejde-517	556	11	(	(	PUNCT
ejde-517	556	12	χ+	χ+	PROPN
ejde-517	556	13	ε)|∇v|2	ε)|∇v|2	PROPN
ejde-517	556	14	dv	dv	PROPN
ejde-517	556	15	+	+	CCONJ
ejde-517	556	16	λ	λ	PROPN
ejde-517	556	17	∫	∫	PROPN
ejde-517	556	18	ω	ω	PROPN
ejde-517	556	19	|v|2	|v|2	PROPN
ejde-517	556	20	dv	dv	PROPN
ejde-517	556	21	=	=	PROPN
ejde-517	556	22	|v|2h1(ω	|v|2h1(ω	PROPN
ejde-517	556	23	)	)	PUNCT
ejde-517	556	24	.	.	PUNCT
ejde-517	557	1	on	on	ADP
ejde-517	557	2	the	the	DET
ejde-517	557	3	other	other	ADJ
ejde-517	557	4	hand	hand	NOUN
ejde-517	557	5	,	,	PUNCT
ejde-517	557	6	|v|2h1(ω	|v|2h1(ω	NOUN
ejde-517	557	7	)	)	PUNCT
ejde-517	557	8	=	=	PUNCT
ejde-517	558	1	α	α	NUM
ejde-517	558	2	∫	∫	PROPN
ejde-517	558	3	ω	ω	PROPN
ejde-517	558	4	(	(	PUNCT
ejde-517	558	5	χ+	χ+	PROPN
ejde-517	558	6	ε)|∇v|2	ε)|∇v|2	PROPN
ejde-517	558	7	dv	dv	PROPN
ejde-517	559	1	+	+	CCONJ
ejde-517	559	2	λ	λ	PROPN
ejde-517	559	3	∫	∫	PROPN
ejde-517	559	4	ω	ω	PROPN
ejde-517	559	5	|v|2	|v|2	PROPN
ejde-517	559	6	dv	dv	PROPN
ejde-517	559	7	≤	≤	PROPN
ejde-517	560	1	α	α	PROPN
ejde-517	560	2	∫	∫	PROPN
ejde-517	560	3	ω	ω	PROPN
ejde-517	560	4	(	(	PUNCT
ejde-517	560	5	1	1	NUM
ejde-517	560	6	+	+	NUM
ejde-517	560	7	ε)|∇v|2	ε)|∇v|2	PROPN
ejde-517	560	8	dv	dv	PROPN
ejde-517	560	9	+	+	CCONJ
ejde-517	560	10	λ	λ	PROPN
ejde-517	560	11	∫	∫	PROPN
ejde-517	560	12	ω	ω	PROPN
ejde-517	560	13	|v|2	|v|2	PROPN
ejde-517	560	14	dv	dv	PROPN
ejde-517	560	15	ejde-2020/93	ejde-2020/93	PROPN
ejde-517	560	16	impedance	impedance	PROPN
ejde-517	560	17	tomography	tomography	NOUN
ejde-517	560	18	problem	problem	NOUN
ejde-517	560	19	19	19	NUM
ejde-517	560	20	≤	≤	NUM
ejde-517	560	21	max	max	PROPN
ejde-517	560	22	{	{	PUNCT
ejde-517	560	23	α(1	α(1	PROPN
ejde-517	560	24	+	+	PROPN
ejde-517	560	25	ε	ε	PROPN
ejde-517	560	26	)	)	PUNCT
ejde-517	560	27	,	,	PUNCT
ejde-517	560	28	λ	λ	X
ejde-517	560	29	}	}	PUNCT
ejde-517	560	30	‖v‖2h1(ω	‖v‖2h1(ω	NOUN
ejde-517	560	31	)	)	PUNCT
ejde-517	560	32	.	.	PUNCT
ejde-517	561	1	�	�	PROPN
ejde-517	561	2	we	we	PRON
ejde-517	561	3	now	now	ADV
ejde-517	561	4	establish	establish	VERB
ejde-517	561	5	the	the	DET
ejde-517	561	6	regularity	regularity	NOUN
ejde-517	561	7	of	of	ADP
ejde-517	561	8	σk+1	σk+1	PROPN
ejde-517	561	9	1	1	NUM
ejde-517	561	10	.	.	PUNCT
ejde-517	562	1	lemma	lemma	PROPN
ejde-517	562	2	3.25	3.25	NUM
ejde-517	562	3	.	.	PUNCT
ejde-517	563	1	under	under	ADP
ejde-517	563	2	assumption	assumption	NOUN
ejde-517	563	3	(	(	PUNCT
ejde-517	563	4	3.30	3.30	NUM
ejde-517	563	5	)	)	PUNCT
ejde-517	563	6	,	,	PUNCT
ejde-517	563	7	the	the	DET
ejde-517	563	8	variational	variational	ADJ
ejde-517	563	9	formulation∫	formulation∫	NOUN
ejde-517	563	10	ω	ω	X
ejde-517	563	11	α(χδ1	α(χδ1	X
ejde-517	563	12	+	+	CCONJ
ejde-517	563	13	ε)∇σk+1	ε)∇σk+1	PROPN
ejde-517	563	14	1	1	NUM
ejde-517	563	15	·	·	PUNCT
ejde-517	563	16	∇v	∇v	ADJ
ejde-517	563	17	dv	dv	PROPN
ejde-517	564	1	+	+	CCONJ
ejde-517	564	2	∫	∫	PROPN
ejde-517	564	3	ω	ω	X
ejde-517	564	4	λ(σk+1	λ(σk+1	SYM
ejde-517	564	5	1	1	NUM
ejde-517	564	6	−	−	NOUN
ejde-517	564	7	σk1	σk1	NOUN
ejde-517	564	8	)	)	PUNCT
ejde-517	564	9	v	v	NOUN
ejde-517	564	10	dv	dv	PROPN
ejde-517	564	11	=	=	SYM
ejde-517	564	12	∫	∫	PROPN
ejde-517	564	13	ω	ω	PROPN
ejde-517	564	14	χδ1∇φ(χδ1	χδ1∇φ(χδ1	PROPN
ejde-517	564	15	)	)	PUNCT
ejde-517	564	16	·	·	PUNCT
ejde-517	564	17	∇φ∗(χδ1)v	∇φ∗(χδ1)v	PROPN
ejde-517	564	18	dv	dv	PROPN
ejde-517	564	19	(	(	PUNCT
ejde-517	564	20	3.72	3.72	NUM
ejde-517	564	21	)	)	PUNCT
ejde-517	564	22	for	for	ADP
ejde-517	564	23	all	all	DET
ejde-517	564	24	v	v	ADP
ejde-517	564	25	∈	∈	PROPN
ejde-517	564	26	h1(ω	h1(ω	PROPN
ejde-517	564	27	)	)	PUNCT
ejde-517	564	28	,	,	PUNCT
ejde-517	564	29	has	have	VERB
ejde-517	564	30	a	a	DET
ejde-517	564	31	unique	unique	ADJ
ejde-517	564	32	solution	solution	NOUN
ejde-517	564	33	σk+1	σk+1	NUM
ejde-517	564	34	1	1	NUM
ejde-517	564	35	∈	∈	PROPN
ejde-517	564	36	h1(ω	h1(ω	PROPN
ejde-517	564	37	)	)	PUNCT
ejde-517	564	38	.	.	PUNCT
ejde-517	565	1	furthermore	furthermore	ADV
ejde-517	565	2	,	,	PUNCT
ejde-517	565	3	‖σk+1	‖σk+1	NUM
ejde-517	565	4	1	1	NUM
ejde-517	565	5	‖h1(ω	‖h1(ω	PROPN
ejde-517	565	6	)	)	PUNCT
ejde-517	565	7	≤	≤	NUM
ejde-517	565	8	2	2	NUM
ejde-517	565	9	√	√	NUM
ejde-517	565	10	µ(ω	µ(ω	NOUN
ejde-517	565	11	)	)	PUNCT
ejde-517	565	12	max{cδ1	max{cδ1	PROPN
ejde-517	565	13	,	,	PUNCT
ejde-517	565	14	cδ2	cδ2	ADJ
ejde-517	565	15	}	}	PUNCT
ejde-517	565	16	min{αε	min{αε	NOUN
ejde-517	565	17	,	,	PUNCT
ejde-517	565	18	λ	λ	X
ejde-517	565	19	}	}	PUNCT
ejde-517	565	20	(	(	PUNCT
ejde-517	565	21	3.73	3.73	NUM
ejde-517	565	22	)	)	PUNCT
ejde-517	565	23	where	where	SCONJ
ejde-517	565	24	cδ1	cδ1	PROPN
ejde-517	565	25	=	=	SYM
ejde-517	565	26	‖∇φ(χδ1)‖l∞(ω)‖∇φ∗(χδ1)‖l∞(ω	‖∇φ(χδ1)‖l∞(ω)‖∇φ∗(χδ1)‖l∞(ω	PROPN
ejde-517	565	27	)	)	PUNCT
ejde-517	565	28	and	and	CCONJ
ejde-517	565	29	cδ2	cδ2	PROPN
ejde-517	565	30	=	=	PROPN
ejde-517	565	31	λ‖σk1‖l∞(ω	λ‖σk1‖l∞(ω	PROPN
ejde-517	565	32	)	)	PUNCT
ejde-517	565	33	.	.	PUNCT
ejde-517	566	1	proof	proof	NOUN
ejde-517	566	2	.	.	PUNCT
ejde-517	567	1	let	let	VERB
ejde-517	567	2	u	u	NOUN
ejde-517	567	3	,	,	PUNCT
ejde-517	567	4	v	v	ADP
ejde-517	567	5	∈	∈	PROPN
ejde-517	567	6	h1(ω	h1(ω	NOUN
ejde-517	567	7	)	)	PUNCT
ejde-517	567	8	and	and	CCONJ
ejde-517	567	9	define	define	VERB
ejde-517	567	10	a(u	a(u	NOUN
ejde-517	567	11	,	,	PUNCT
ejde-517	567	12	v	v	NOUN
ejde-517	567	13	)	)	PUNCT
ejde-517	567	14	=	=	SYM
ejde-517	568	1	∫	∫	PROPN
ejde-517	568	2	ω	ω	NUM
ejde-517	568	3	α(χδ1	α(χδ1	X
ejde-517	568	4	+	+	CCONJ
ejde-517	568	5	ε)∇u	ε)∇u	NOUN
ejde-517	568	6	·	·	PUNCT
ejde-517	568	7	∇v	∇v	ADJ
ejde-517	568	8	dv	dv	PROPN
ejde-517	569	1	+	+	CCONJ
ejde-517	569	2	∫	∫	PROPN
ejde-517	569	3	ω	ω	PROPN
ejde-517	569	4	λuv	λuv	VERB
ejde-517	569	5	dv	dv	PROPN
ejde-517	569	6	and	and	CCONJ
ejde-517	569	7	b(v	b(v	NOUN
ejde-517	569	8	)	)	PUNCT
ejde-517	570	1	=	=	SYM
ejde-517	570	2	∫	∫	PROPN
ejde-517	570	3	ω	ω	PROPN
ejde-517	570	4	(	(	PUNCT
ejde-517	570	5	χδ1)∇φ(χδ1	χδ1)∇φ(χδ1	PROPN
ejde-517	570	6	)	)	PUNCT
ejde-517	570	7	·	·	PUNCT
ejde-517	570	8	∇φ∗(χδ1)v	∇φ∗(χδ1)v	VERB
ejde-517	571	1	dv	dv	PROPN
ejde-517	571	2	+	+	PROPN
ejde-517	571	3	∫	∫	PROPN
ejde-517	571	4	ω	ω	NUM
ejde-517	572	1	λσk1v	λσk1v	PROPN
ejde-517	572	2	dv	dv	PROPN
ejde-517	572	3	.	.	PUNCT
ejde-517	573	1	it	it	PRON
ejde-517	573	2	is	be	AUX
ejde-517	573	3	obvious	obvious	ADJ
ejde-517	573	4	that	that	SCONJ
ejde-517	573	5	a	a	PRON
ejde-517	573	6	is	be	AUX
ejde-517	573	7	bilinear	bilinear	NOUN
ejde-517	573	8	and	and	CCONJ
ejde-517	573	9	b	b	NOUN
ejde-517	573	10	is	be	AUX
ejde-517	573	11	linear	linear	ADJ
ejde-517	573	12	.	.	PUNCT
ejde-517	574	1	using	use	VERB
ejde-517	574	2	the	the	DET
ejde-517	574	3	cauchy	cauchy	NOUN
ejde-517	574	4	-	-	PUNCT
ejde-517	574	5	schwarz	schwarz	PROPN
ejde-517	574	6	inequality	inequality	NOUN
ejde-517	574	7	,	,	PUNCT
ejde-517	574	8	one	one	PRON
ejde-517	574	9	can	can	AUX
ejde-517	574	10	prove	prove	VERB
ejde-517	574	11	that	that	SCONJ
ejde-517	574	12	a(u	a(u	PROPN
ejde-517	574	13	,	,	PUNCT
ejde-517	574	14	v	v	NOUN
ejde-517	574	15	)	)	PUNCT
ejde-517	574	16	is	be	AUX
ejde-517	574	17	continuous	continuous	ADJ
ejde-517	574	18	.	.	PUNCT
ejde-517	575	1	we	we	PRON
ejde-517	575	2	can	can	AUX
ejde-517	575	3	also	also	ADV
ejde-517	575	4	easily	easily	ADV
ejde-517	575	5	show	show	VERB
ejde-517	575	6	that	that	SCONJ
ejde-517	575	7	a(u	a(u	PROPN
ejde-517	575	8	,	,	PUNCT
ejde-517	575	9	v	v	NOUN
ejde-517	575	10	)	)	PUNCT
ejde-517	575	11	is	be	AUX
ejde-517	575	12	coercive	coercive	ADJ
ejde-517	575	13	using	use	VERB
ejde-517	575	14	the	the	DET
ejde-517	575	15	previous	previous	ADJ
ejde-517	575	16	proposition	proposition	NOUN
ejde-517	575	17	:	:	PUNCT
ejde-517	575	18	|a(u	|a(u	ADJ
ejde-517	575	19	,	,	PUNCT
ejde-517	575	20	u)|	u)|	NOUN
ejde-517	575	21	=	=	SYM
ejde-517	575	22	∫	∫	PROPN
ejde-517	575	23	ω	ω	PROPN
ejde-517	575	24	α(χδ1	α(χδ1	X
ejde-517	575	25	+	+	CCONJ
ejde-517	575	26	ε)|∇u|2v	ε)|∇u|2v	NOUN
ejde-517	575	27	+	+	CCONJ
ejde-517	575	28	∫	∫	PROPN
ejde-517	575	29	ω	ω	NUM
ejde-517	575	30	λu2	λu2	NOUN
ejde-517	575	31	dv	dv	PROPN
ejde-517	575	32	=	=	PROPN
ejde-517	575	33	|u|2h1(ω	|u|2h1(ω	NOUN
ejde-517	575	34	)	)	PUNCT
ejde-517	575	35	≥	≥	NOUN
ejde-517	575	36	min{αε	min{αε	NOUN
ejde-517	575	37	,	,	PUNCT
ejde-517	575	38	θ}‖u‖2h1(ω	θ}‖u‖2h1(ω	NOUN
ejde-517	575	39	)	)	PUNCT
ejde-517	575	40	.	.	PUNCT
ejde-517	576	1	furthermore	furthermore	ADV
ejde-517	576	2	,	,	PUNCT
ejde-517	576	3	the	the	DET
ejde-517	576	4	continuity	continuity	NOUN
ejde-517	576	5	of	of	ADP
ejde-517	576	6	b(v	b(v	NOUN
ejde-517	576	7	)	)	PUNCT
ejde-517	576	8	can	can	AUX
ejde-517	576	9	be	be	AUX
ejde-517	576	10	proven	prove	VERB
ejde-517	576	11	using	use	VERB
ejde-517	576	12	the	the	DET
ejde-517	576	13	cauchy	cauchy	NOUN
ejde-517	576	14	-	-	PUNCT
ejde-517	576	15	schwarz	schwarz	PROPN
ejde-517	576	16	inequality	inequality	NOUN
ejde-517	576	17	,	,	PUNCT
ejde-517	576	18	the	the	DET
ejde-517	576	19	bounds	bound	NOUN
ejde-517	576	20	in	in	ADP
ejde-517	576	21	(	(	PUNCT
ejde-517	576	22	3.31	3.31	NUM
ejde-517	576	23	)	)	PUNCT
ejde-517	576	24	,	,	PUNCT
ejde-517	576	25	and	and	CCONJ
ejde-517	576	26	(	(	PUNCT
ejde-517	576	27	3.36	3.36	NUM
ejde-517	576	28	)	)	PUNCT
ejde-517	576	29	.	.	PUNCT
ejde-517	577	1	hence	hence	ADV
ejde-517	577	2	,	,	PUNCT
ejde-517	577	3	by	by	ADP
ejde-517	577	4	lax	lax	PROPN
ejde-517	577	5	-	-	PUNCT
ejde-517	577	6	milgram	milgram	NOUN
ejde-517	577	7	theorem	theorem	NOUN
ejde-517	577	8	there	there	PRON
ejde-517	577	9	is	be	VERB
ejde-517	577	10	a	a	DET
ejde-517	577	11	unique	unique	ADJ
ejde-517	577	12	σk1	σk1	NOUN
ejde-517	577	13	∈	∈	PROPN
ejde-517	577	14	h1(ω	h1(ω	NOUN
ejde-517	577	15	)	)	PUNCT
ejde-517	577	16	satisfying	satisfying	NOUN
ejde-517	577	17	(	(	PUNCT
ejde-517	577	18	3.72	3.72	NUM
ejde-517	577	19	)	)	PUNCT
ejde-517	577	20	for	for	ADP
ejde-517	577	21	all	all	PRON
ejde-517	577	22	v	v	ADP
ejde-517	577	23	∈	∈	PROPN
ejde-517	577	24	h1(ω	h1(ω	PROPN
ejde-517	577	25	)	)	PUNCT
ejde-517	577	26	.	.	PUNCT
ejde-517	578	1	the	the	DET
ejde-517	578	2	h1(ω	h1(ω	PROPN
ejde-517	578	3	)	)	PUNCT
ejde-517	578	4	bound	bind	VERB
ejde-517	578	5	for	for	ADP
ejde-517	578	6	σk+1	σk+1	NUM
ejde-517	578	7	1	1	NUM
ejde-517	578	8	directly	directly	ADV
ejde-517	578	9	follows	follow	VERB
ejde-517	578	10	.	.	PUNCT
ejde-517	579	1	�	�	PROPN
ejde-517	579	2	remark	remark	VERB
ejde-517	579	3	3.26	3.26	NUM
ejde-517	579	4	.	.	PUNCT
ejde-517	580	1	given	give	VERB
ejde-517	580	2	any	any	DET
ejde-517	580	3	perturbation	perturbation	NOUN
ejde-517	580	4	δχδ1	δχδ1	NOUN
ejde-517	580	5	and	and	CCONJ
ejde-517	580	6	η	η	PROPN
ejde-517	580	7	>	>	X
ejde-517	580	8	0	0	PROPN
ejde-517	580	9	,	,	PUNCT
ejde-517	580	10	we	we	PRON
ejde-517	580	11	have	have	VERB
ejde-517	580	12	to	to	PART
ejde-517	580	13	make	make	VERB
ejde-517	580	14	sure	sure	ADJ
ejde-517	580	15	that	that	SCONJ
ejde-517	580	16	the	the	DET
ejde-517	580	17	quantity	quantity	NOUN
ejde-517	580	18	σ1(χδ1	σ1(χδ1	X
ejde-517	580	19	+	+	CCONJ
ejde-517	580	20	ηδχδ1	ηδχδ1	VERB
ejde-517	580	21	)	)	PUNCT
ejde-517	580	22	is	be	AUX
ejde-517	580	23	well	well	ADV
ejde-517	580	24	-	-	PUNCT
ejde-517	580	25	defined	define	VERB
ejde-517	580	26	.	.	PUNCT
ejde-517	581	1	as	as	SCONJ
ejde-517	581	2	shown	show	VERB
ejde-517	581	3	in	in	ADP
ejde-517	581	4	the	the	DET
ejde-517	581	5	proof	proof	NOUN
ejde-517	581	6	of	of	ADP
ejde-517	581	7	lemma	lemma	PROPN
ejde-517	581	8	(	(	PUNCT
ejde-517	581	9	3.25	3.25	NUM
ejde-517	581	10	)	)	PUNCT
ejde-517	581	11	,	,	PUNCT
ejde-517	581	12	replacing	replace	VERB
ejde-517	581	13	χδ1	χδ1	NOUN
ejde-517	581	14	with	with	ADP
ejde-517	581	15	χδ1	χδ1	NOUN
ejde-517	581	16	+	+	CCONJ
ejde-517	581	17	ηδχδ1	ηδχδ1	VERB
ejde-517	581	18	can	can	AUX
ejde-517	581	19	not	not	PART
ejde-517	581	20	be	be	AUX
ejde-517	581	21	done	do	VERB
ejde-517	581	22	with	with	ADP
ejde-517	581	23	just	just	ADV
ejde-517	581	24	any	any	DET
ejde-517	581	25	η	η	PROPN
ejde-517	581	26	.	.	PROPN
ejde-517	581	27	to	to	PART
ejde-517	581	28	make	make	VERB
ejde-517	581	29	sure	sure	ADJ
ejde-517	581	30	that	that	SCONJ
ejde-517	581	31	the	the	DET
ejde-517	581	32	bilinear	bilinear	NOUN
ejde-517	581	33	functional	functional	NOUN
ejde-517	581	34	a	a	PRON
ejde-517	581	35	is	be	AUX
ejde-517	581	36	coercive	coercive	ADJ
ejde-517	581	37	,	,	PUNCT
ejde-517	581	38	χδ1	χδ1	X
ejde-517	581	39	+	+	CCONJ
ejde-517	581	40	ηδχδ1	ηδχδ1	VERB
ejde-517	582	1	+	+	CCONJ
ejde-517	582	2	ε	ε	PROPN
ejde-517	582	3	must	must	AUX
ejde-517	582	4	be	be	AUX
ejde-517	582	5	positive	positive	ADJ
ejde-517	582	6	.	.	PUNCT
ejde-517	583	1	since	since	SCONJ
ejde-517	583	2	χδ1	χδ1	NOUN
ejde-517	583	3	+	+	CCONJ
ejde-517	583	4	ε	ε	PROPN
ejde-517	583	5	>	>	X
ejde-517	583	6	0	0	PROPN
ejde-517	583	7	,	,	PUNCT
ejde-517	583	8	we	we	PRON
ejde-517	583	9	can	can	AUX
ejde-517	583	10	choose	choose	VERB
ejde-517	583	11	η	η	PROPN
ejde-517	583	12	small	small	ADJ
ejde-517	583	13	enough	enough	ADV
ejde-517	583	14	so	so	SCONJ
ejde-517	583	15	that	that	PRON
ejde-517	583	16	χδ1	χδ1	NOUN
ejde-517	583	17	+	+	CCONJ
ejde-517	583	18	ηδχδ1	ηδχδ1	VERB
ejde-517	583	19	+	+	CCONJ
ejde-517	583	20	ε	ε	PROPN
ejde-517	583	21	>	>	X
ejde-517	583	22	0	0	NUM
ejde-517	583	23	is	be	AUX
ejde-517	583	24	satisfied	satisfied	ADJ
ejde-517	583	25	.	.	PUNCT
ejde-517	584	1	hence	hence	ADV
ejde-517	584	2	,	,	PUNCT
ejde-517	584	3	similar	similar	ADJ
ejde-517	584	4	to	to	PART
ejde-517	584	5	remark	remark	VERB
ejde-517	584	6	3.4	3.4	NUM
ejde-517	584	7	,	,	PUNCT
ejde-517	584	8	we	we	PRON
ejde-517	584	9	take	take	VERB
ejde-517	584	10	η	η	PROPN
ejde-517	584	11	from	from	ADP
ejde-517	584	12	the	the	DET
ejde-517	584	13	set	set	NOUN
ejde-517	584	14	(	(	PUNCT
ejde-517	584	15	0	0	NUM
ejde-517	584	16	,	,	PUNCT
ejde-517	584	17	τ̄	τ̄	INTJ
ejde-517	584	18	)	)	PUNCT
ejde-517	584	19	for	for	ADP
ejde-517	584	20	τ̄	τ̄	INTJ
ejde-517	584	21	sufficiently	sufficiently	ADV
ejde-517	584	22	small	small	ADJ
ejde-517	585	1	so	so	SCONJ
ejde-517	585	2	that	that	SCONJ
ejde-517	585	3	σ1(χδ1	σ1(χδ1	PRON
ejde-517	585	4	+	+	NOUN
ejde-517	585	5	ηδχδ1	ηδχδ1	ADJ
ejde-517	585	6	)	)	PUNCT
ejde-517	585	7	makes	make	VERB
ejde-517	585	8	sense	sense	NOUN
ejde-517	585	9	.	.	PUNCT
ejde-517	586	1	therefore	therefore	ADV
ejde-517	586	2	,	,	PUNCT
ejde-517	586	3	combining	combine	VERB
ejde-517	586	4	(	(	PUNCT
ejde-517	586	5	3.37	3.37	NUM
ejde-517	586	6	)	)	PUNCT
ejde-517	586	7	,	,	PUNCT
ejde-517	586	8	(	(	PUNCT
ejde-517	586	9	3.38	3.38	NUM
ejde-517	586	10	)	)	PUNCT
ejde-517	586	11	and	and	CCONJ
ejde-517	586	12	(	(	PUNCT
ejde-517	586	13	3.73	3.73	NUM
ejde-517	586	14	)	)	PUNCT
ejde-517	586	15	,	,	PUNCT
ejde-517	586	16	there	there	PRON
ejde-517	586	17	exists	exist	VERB
ejde-517	586	18	c	c	NOUN
ejde-517	586	19	>	>	X
ejde-517	586	20	0	0	NUM
ejde-517	586	21	such	such	ADJ
ejde-517	586	22	that	that	PRON
ejde-517	586	23	‖σ1(χδ1	‖σ1(χδ1	NOUN
ejde-517	586	24	+	+	CCONJ
ejde-517	586	25	ηδχδ1)‖h1(ω	ηδχδ1)‖h1(ω	X
ejde-517	586	26	)	)	PUNCT
ejde-517	586	27	<	<	X
ejde-517	586	28	∞	∞	PROPN
ejde-517	586	29	,	,	PUNCT
ejde-517	586	30	(	(	PUNCT
ejde-517	586	31	3.74	3.74	NUM
ejde-517	586	32	)	)	PUNCT
ejde-517	586	33	for	for	ADP
ejde-517	586	34	any	any	DET
ejde-517	586	35	η	η	PROPN
ejde-517	586	36	∈	∈	PROPN
ejde-517	586	37	(	(	PUNCT
ejde-517	586	38	0	0	NUM
ejde-517	586	39	,	,	PUNCT
ejde-517	586	40	τ̂	τ̂	NUM
ejde-517	586	41	)	)	PUNCT
ejde-517	586	42	,	,	PUNCT
ejde-517	586	43	where	where	SCONJ
ejde-517	586	44	τ̂	τ̂	PUNCT
ejde-517	586	45	=	=	SYM
ejde-517	586	46	min	min	X
ejde-517	586	47	{	{	PUNCT
ejde-517	586	48	τ	τ	PROPN
ejde-517	586	49	,	,	PUNCT
ejde-517	586	50	τ̄	τ̄	INTJ
ejde-517	586	51	}	}	PUNCT
ejde-517	586	52	.	.	PUNCT
ejde-517	587	1	because	because	SCONJ
ejde-517	587	2	χδ1	χδ1	NOUN
ejde-517	587	3	is	be	AUX
ejde-517	587	4	a	a	DET
ejde-517	587	5	mollification	mollification	NOUN
ejde-517	587	6	of	of	ADP
ejde-517	587	7	χ1	χ1	NOUN
ejde-517	587	8	,	,	PUNCT
ejde-517	587	9	it	it	PRON
ejde-517	587	10	is	be	AUX
ejde-517	587	11	real	real	ADJ
ejde-517	587	12	analytic	analytic	ADJ
ejde-517	587	13	.	.	PUNCT
ejde-517	588	1	then	then	ADV
ejde-517	588	2	χδ1	χδ1	VERB
ejde-517	588	3	+	+	CCONJ
ejde-517	588	4	ε	ε	PROPN
ejde-517	588	5	∈	∈	PROPN
ejde-517	588	6	c∞(ω̄	c∞(ω̄	PROPN
ejde-517	588	7	)	)	PUNCT
ejde-517	588	8	.	.	PUNCT
ejde-517	589	1	moreover	moreover	ADV
ejde-517	589	2	,	,	PUNCT
ejde-517	589	3	from	from	ADP
ejde-517	589	4	lemma	lemma	PROPN
ejde-517	589	5	(	(	PUNCT
ejde-517	589	6	3.15	3.15	NUM
ejde-517	589	7	)	)	PUNCT
ejde-517	589	8	,	,	PUNCT
ejde-517	589	9	∇φ(χδ1),∇φ∗(χδ1	∇φ(χδ1),∇φ∗(χδ1	PROPN
ejde-517	589	10	)	)	PUNCT
ejde-517	589	11	∈	∈	NOUN
ejde-517	589	12	c∞(ω̄	c∞(ω̄	PROPN
ejde-517	589	13	)	)	PUNCT
ejde-517	589	14	.	.	PUNCT
ejde-517	590	1	this	this	PRON
ejde-517	590	2	means	mean	VERB
ejde-517	590	3	that	that	SCONJ
ejde-517	590	4	χδ1∇φ(χδ1	χδ1∇φ(χδ1	X
ejde-517	590	5	)	)	PUNCT
ejde-517	590	6	·	·	PUNCT
ejde-517	590	7	∇φ∗(χδ1	∇φ∗(χδ1	NOUN
ejde-517	590	8	)	)	PUNCT
ejde-517	590	9	,	,	PUNCT
ejde-517	590	10	χδ1	χδ1	X
ejde-517	590	11	+	+	CCONJ
ejde-517	590	12	ε	ε	PROPN
ejde-517	590	13	,	,	PUNCT
ejde-517	590	14	λ	λ	NOUN
ejde-517	590	15	are	be	AUX
ejde-517	590	16	all	all	ADV
ejde-517	590	17	in	in	ADP
ejde-517	590	18	c∞(ω̄	c∞(ω̄	NUM
ejde-517	590	19	)	)	PUNCT
ejde-517	590	20	.	.	PUNCT
ejde-517	591	1	then	then	ADV
ejde-517	591	2	using	use	VERB
ejde-517	591	3	standard	standard	ADJ
ejde-517	591	4	regularity	regularity	NOUN
ejde-517	591	5	estimates	estimate	NOUN
ejde-517	591	6	[	[	X
ejde-517	591	7	16	16	NUM
ejde-517	591	8	]	]	PUNCT
ejde-517	591	9	on	on	ADP
ejde-517	591	10	−α∇	−α∇	PRON
ejde-517	591	11	·	·	PUNCT
ejde-517	592	1	[	[	X
ejde-517	592	2	(	(	PUNCT
ejde-517	592	3	χδ1	χδ1	X
ejde-517	592	4	+	+	X
ejde-517	592	5	ε)∇σk+1	ε)∇σk+1	NOUN
ejde-517	592	6	1	1	NUM
ejde-517	592	7	]	]	PUNCT
ejde-517	592	8	+	+	CCONJ
ejde-517	592	9	λ(σk+1	λ(σk+1	SYM
ejde-517	592	10	1	1	NUM
ejde-517	592	11	−	−	NOUN
ejde-517	592	12	σk1	σk1	NOUN
ejde-517	592	13	)	)	PUNCT
ejde-517	592	14	=	=	PUNCT
ejde-517	593	1	χδ1∇φ(χδ1	χδ1∇φ(χδ1	X
ejde-517	593	2	)	)	PUNCT
ejde-517	593	3	·	·	PUNCT
ejde-517	593	4	∇φ∗(χδ1	∇φ∗(χδ1	ADJ
ejde-517	593	5	)	)	PUNCT
ejde-517	593	6	on	on	ADP
ejde-517	593	7	ω	ω	NUM
ejde-517	593	8	,	,	PUNCT
ejde-517	593	9	∂σk+1	∂σk+1	VERB
ejde-517	593	10	1	1	NUM
ejde-517	593	11	∂n	∂n	PROPN
ejde-517	593	12	=	=	NOUN
ejde-517	593	13	0	0	NUM
ejde-517	594	1	on	on	ADP
ejde-517	594	2	∂ω	∂ω	PROPN
ejde-517	594	3	,	,	PUNCT
ejde-517	594	4	(	(	PUNCT
ejde-517	594	5	3.75	3.75	NUM
ejde-517	594	6	)	)	PUNCT
ejde-517	594	7	20	20	NUM
ejde-517	594	8	r.	r.	PROPN
ejde-517	594	9	mendoza	mendoza	PROPN
ejde-517	594	10	,	,	PUNCT
ejde-517	594	11	s.	s.	PROPN
ejde-517	594	12	keeling	keeling	PROPN
ejde-517	594	13	ejde-2020/93	ejde-2020/93	PROPN
ejde-517	594	14	gives	give	VERB
ejde-517	594	15	us	we	PRON
ejde-517	594	16	σk+1	σk+1	DET
ejde-517	594	17	1	1	NUM
ejde-517	594	18	∈	∈	NOUN
ejde-517	594	19	c∞(ω̄	c∞(ω̄	NOUN
ejde-517	594	20	)	)	PUNCT
ejde-517	594	21	.	.	PUNCT
ejde-517	595	1	consequently	consequently	ADV
ejde-517	595	2	,	,	PUNCT
ejde-517	595	3	‖∇σ1(χδ1)‖l∞(ω	‖∇σ1(χδ1)‖l∞(ω	PROPN
ejde-517	595	4	)	)	PUNCT
ejde-517	596	1	<	<	AUX
ejde-517	596	2	∞.	∞.	PROPN
ejde-517	596	3	furthermore	furthermore	ADV
ejde-517	596	4	,	,	PUNCT
ejde-517	596	5	‖∇σ1(χδ1	‖∇σ1(χδ1	X
ejde-517	596	6	+	+	NUM
ejde-517	596	7	ηδχδ1)‖l∞(ω	ηδχδ1)‖l∞(ω	NOUN
ejde-517	596	8	)	)	PUNCT
ejde-517	596	9	<	<	X
ejde-517	596	10	∞	∞	PROPN
ejde-517	596	11	,	,	PUNCT
ejde-517	596	12	(	(	PUNCT
ejde-517	596	13	3.76	3.76	NUM
ejde-517	596	14	)	)	PUNCT
ejde-517	596	15	for	for	ADP
ejde-517	596	16	any	any	DET
ejde-517	596	17	η	η	PROPN
ejde-517	596	18	∈	∈	PROPN
ejde-517	596	19	(	(	PUNCT
ejde-517	596	20	0	0	NUM
ejde-517	596	21	,	,	PUNCT
ejde-517	596	22	τ̂	τ̂	NUM
ejde-517	596	23	)	)	PUNCT
ejde-517	596	24	,	,	PUNCT
ejde-517	596	25	where	where	SCONJ
ejde-517	596	26	τ̂	τ̂	PUNCT
ejde-517	596	27	=	=	SYM
ejde-517	596	28	min	min	X
ejde-517	596	29	{	{	PUNCT
ejde-517	596	30	τ	τ	PROPN
ejde-517	596	31	,	,	PUNCT
ejde-517	596	32	τ̄	τ̄	PROPN
ejde-517	596	33	}	}	PUNCT
ejde-517	596	34	,	,	PUNCT
ejde-517	596	35	τ	τ	PROPN
ejde-517	596	36	and	and	CCONJ
ejde-517	596	37	τ̄	τ̄	INTJ
ejde-517	596	38	are	be	AUX
ejde-517	596	39	chosen	choose	VERB
ejde-517	596	40	according	accord	VERB
ejde-517	596	41	to	to	PART
ejde-517	596	42	remark	remark	NOUN
ejde-517	596	43	3.4	3.4	NUM
ejde-517	596	44	and	and	CCONJ
ejde-517	596	45	remark	remark	NOUN
ejde-517	596	46	3.26	3.26	NUM
ejde-517	596	47	,	,	PUNCT
ejde-517	596	48	respectively	respectively	ADV
ejde-517	596	49	.	.	PUNCT
ejde-517	597	1	before	before	SCONJ
ejde-517	597	2	we	we	PRON
ejde-517	597	3	can	can	AUX
ejde-517	597	4	show	show	VERB
ejde-517	597	5	that	that	SCONJ
ejde-517	597	6	δς1	δς1	ADJ
ejde-517	597	7	δχ1	δχ1	X
ejde-517	597	8	(	(	PUNCT
ejde-517	597	9	χδ1	χδ1	X
ejde-517	597	10	;	;	PUNCT
ejde-517	597	11	δχδ1	δχδ1	PROPN
ejde-517	597	12	)	)	PUNCT
ejde-517	597	13	∈	∈	PROPN
ejde-517	597	14	h1(ω	h1(ω	PROPN
ejde-517	597	15	)	)	PUNCT
ejde-517	597	16	,	,	PUNCT
ejde-517	597	17	we	we	PRON
ejde-517	597	18	first	first	ADV
ejde-517	597	19	need	need	VERB
ejde-517	597	20	to	to	PART
ejde-517	597	21	find	find	VERB
ejde-517	597	22	a	a	DET
ejde-517	597	23	candidate	candidate	NOUN
ejde-517	597	24	derivative	derivative	NOUN
ejde-517	597	25	.	.	PUNCT
ejde-517	598	1	lemma	lemma	PROPN
ejde-517	598	2	3.27	3.27	NUM
ejde-517	598	3	.	.	PUNCT
ejde-517	599	1	under	under	ADP
ejde-517	599	2	assumption	assumption	NOUN
ejde-517	599	3	(	(	PUNCT
ejde-517	599	4	3.30	3.30	NUM
ejde-517	599	5	)	)	PUNCT
ejde-517	599	6	,	,	PUNCT
ejde-517	599	7	there	there	PRON
ejde-517	599	8	exists	exist	VERB
ejde-517	599	9	dσ(χ1	dσ(χ1	VERB
ejde-517	599	10	;	;	PUNCT
ejde-517	599	11	δχ1	δχ1	X
ejde-517	599	12	)	)	PUNCT
ejde-517	599	13	∈	∈	PROPN
ejde-517	599	14	h1(ω	h1(ω	PROPN
ejde-517	599	15	)	)	PUNCT
ejde-517	599	16	such	such	ADJ
ejde-517	599	17	that∫	that∫	PROPN
ejde-517	599	18	ω	ω	PROPN
ejde-517	599	19	α(χδ1	α(χδ1	X
ejde-517	599	20	+	+	CCONJ
ejde-517	599	21	ε)∇dσ(χδ1	ε)∇dσ(χδ1	X
ejde-517	599	22	;	;	PUNCT
ejde-517	599	23	δχδ1	δχδ1	PROPN
ejde-517	599	24	)	)	PUNCT
ejde-517	599	25	·	·	PUNCT
ejde-517	600	1	∇v	∇v	ADJ
ejde-517	600	2	dv	dv	PROPN
ejde-517	600	3	+	+	CCONJ
ejde-517	600	4	∫	∫	PROPN
ejde-517	600	5	ω	ω	NUM
ejde-517	600	6	λdσ(χδ1	λdσ(χδ1	PROPN
ejde-517	600	7	;	;	PUNCT
ejde-517	600	8	δχδ1)v	δχδ1)v	PROPN
ejde-517	600	9	dv	dv	PROPN
ejde-517	600	10	=	=	SYM
ejde-517	600	11	∫	∫	PROPN
ejde-517	600	12	ω	ω	NUM
ejde-517	600	13	χδ1	χδ1	PROPN
ejde-517	600	14	δψ	δψ	NOUN
ejde-517	600	15	δχ1	δχ1	NOUN
ejde-517	600	16	(	(	PUNCT
ejde-517	600	17	χδ1	χδ1	X
ejde-517	600	18	;	;	PUNCT
ejde-517	600	19	δχδ1)v	δχδ1)v	PROPN
ejde-517	600	20	+	+	CCONJ
ejde-517	600	21	δχδ1∇φ(χδ1	δχδ1∇φ(χδ1	NOUN
ejde-517	600	22	)	)	PUNCT
ejde-517	600	23	·	·	PUNCT
ejde-517	600	24	∇φ∗(χδ1)v	∇φ∗(χδ1)v	NOUN
ejde-517	600	25	−	−	PROPN
ejde-517	600	26	αδχδ1∇(σ1(χδ1	αδχδ1∇(σ1(χδ1	PROPN
ejde-517	600	27	)	)	PUNCT
ejde-517	600	28	)	)	PUNCT
ejde-517	600	29	·	·	PUNCT
ejde-517	601	1	∇v	∇v	ADJ
ejde-517	601	2	dv	dv	PROPN
ejde-517	601	3	,	,	PUNCT
ejde-517	601	4	(	(	PUNCT
ejde-517	601	5	3.77	3.77	NUM
ejde-517	601	6	)	)	PUNCT
ejde-517	601	7	for	for	ADP
ejde-517	601	8	all	all	DET
ejde-517	601	9	v	v	ADP
ejde-517	601	10	∈	∈	PROPN
ejde-517	601	11	h1(ω	h1(ω	PROPN
ejde-517	601	12	)	)	PUNCT
ejde-517	601	13	.	.	PUNCT
ejde-517	602	1	the	the	DET
ejde-517	602	2	proof	proof	NOUN
ejde-517	602	3	of	of	ADP
ejde-517	602	4	the	the	DET
ejde-517	602	5	above	above	ADJ
ejde-517	602	6	lemma	lemma	PROPN
ejde-517	602	7	is	be	AUX
ejde-517	602	8	similar	similar	ADJ
ejde-517	602	9	to	to	ADP
ejde-517	602	10	that	that	PRON
ejde-517	602	11	of	of	ADP
ejde-517	602	12	lemma	lemma	PROPN
ejde-517	602	13	3.19	3.19	NUM
ejde-517	602	14	;	;	PUNCT
ejde-517	602	15	we	we	PRON
ejde-517	602	16	omit	omit	VERB
ejde-517	602	17	it	it	PRON
ejde-517	602	18	.	.	PUNCT
ejde-517	603	1	we	we	PRON
ejde-517	603	2	now	now	ADV
ejde-517	603	3	have	have	VERB
ejde-517	603	4	all	all	DET
ejde-517	603	5	the	the	DET
ejde-517	603	6	necessary	necessary	ADJ
ejde-517	603	7	tools	tool	NOUN
ejde-517	603	8	to	to	PART
ejde-517	603	9	show	show	VERB
ejde-517	603	10	that	that	SCONJ
ejde-517	603	11	δς1	δς1	ADJ
ejde-517	603	12	δχ1	δχ1	X
ejde-517	603	13	(	(	PUNCT
ejde-517	603	14	χδ1	χδ1	X
ejde-517	603	15	;	;	PUNCT
ejde-517	603	16	δχδ1	δχδ1	PROPN
ejde-517	603	17	)	)	PUNCT
ejde-517	603	18	∈	∈	PROPN
ejde-517	603	19	h1(ω	h1(ω	PROPN
ejde-517	603	20	)	)	PUNCT
ejde-517	603	21	.	.	PUNCT
ejde-517	604	1	we	we	PRON
ejde-517	604	2	prove	prove	VERB
ejde-517	604	3	that	that	SCONJ
ejde-517	604	4	this	this	PRON
ejde-517	604	5	is	be	AUX
ejde-517	604	6	exactly	exactly	ADV
ejde-517	604	7	dσ(χδ1	dσ(χδ1	NUM
ejde-517	604	8	;	;	PUNCT
ejde-517	604	9	δχδ1	δχδ1	PROPN
ejde-517	604	10	)	)	PUNCT
ejde-517	604	11	computed	compute	VERB
ejde-517	604	12	in	in	ADP
ejde-517	604	13	the	the	DET
ejde-517	604	14	previous	previous	ADJ
ejde-517	604	15	lemma	lemma	PROPN
ejde-517	604	16	.	.	PUNCT
ejde-517	604	17	theorem	theorem	VERB
ejde-517	604	18	3.28	3.28	NUM
ejde-517	604	19	.	.	PUNCT
ejde-517	605	1	under	under	ADP
ejde-517	605	2	assumption	assumption	NOUN
ejde-517	605	3	(	(	PUNCT
ejde-517	605	4	3.30	3.30	NUM
ejde-517	605	5	)	)	PUNCT
ejde-517	605	6	,	,	PUNCT
ejde-517	605	7	there	there	PRON
ejde-517	605	8	exists	exist	VERB
ejde-517	605	9	cδ	cδ	VERB
ejde-517	605	10	>	>	X
ejde-517	605	11	0	0	NUM
ejde-517	606	1	such	such	ADJ
ejde-517	606	2	that	that	PRON
ejde-517	606	3	‖σ1(χδ1	‖σ1(χδ1	VERB
ejde-517	606	4	+	+	CCONJ
ejde-517	606	5	ηδχδ1)−	ηδχδ1)−	PROPN
ejde-517	606	6	σ1(χδ1)‖h1(ω	σ1(χδ1)‖h1(ω	NOUN
ejde-517	606	7	)	)	PUNCT
ejde-517	606	8	≤	≤	NOUN
ejde-517	606	9	cδη‖δχ1‖l2(ω	cδη‖δχ1‖l2(ω	ADV
ejde-517	606	10	)	)	PUNCT
ejde-517	606	11	(	(	PUNCT
ejde-517	606	12	3.78	3.78	NUM
ejde-517	606	13	)	)	PUNCT
ejde-517	606	14	for	for	ADP
ejde-517	606	15	any	any	DET
ejde-517	606	16	η	η	PROPN
ejde-517	606	17	∈	∈	PROPN
ejde-517	606	18	(	(	PUNCT
ejde-517	606	19	0	0	NUM
ejde-517	606	20	,	,	PUNCT
ejde-517	606	21	τ̂	τ̂	NUM
ejde-517	606	22	)	)	PUNCT
ejde-517	606	23	,	,	PUNCT
ejde-517	606	24	where	where	SCONJ
ejde-517	606	25	τ̂	τ̂	PUNCT
ejde-517	606	26	=	=	SYM
ejde-517	606	27	min	min	X
ejde-517	606	28	{	{	PUNCT
ejde-517	606	29	τ	τ	PROPN
ejde-517	606	30	,	,	PUNCT
ejde-517	606	31	τ̄	τ̄	PROPN
ejde-517	606	32	}	}	PUNCT
ejde-517	606	33	,	,	PUNCT
ejde-517	606	34	τ	τ	PROPN
ejde-517	606	35	and	and	CCONJ
ejde-517	606	36	τ̄	τ̄	NOUN
ejde-517	606	37	are	be	AUX
ejde-517	606	38	both	both	ADV
ejde-517	606	39	chosen	choose	VERB
ejde-517	606	40	according	accord	VERB
ejde-517	606	41	to	to	PART
ejde-517	606	42	remark	remark	NOUN
ejde-517	606	43	3.4	3.4	NUM
ejde-517	606	44	and	and	CCONJ
ejde-517	606	45	remark	remark	NOUN
ejde-517	606	46	3.26	3.26	NUM
ejde-517	606	47	,	,	PUNCT
ejde-517	606	48	respectively	respectively	ADV
ejde-517	606	49	.	.	PUNCT
ejde-517	607	1	also	also	ADV
ejde-517	607	2	,	,	PUNCT
ejde-517	607	3	lim	lim	PROPN
ejde-517	607	4	η→0	η→0	X
ejde-517	607	5	‖σ1(χδ1	‖σ1(χδ1	PROPN
ejde-517	607	6	+	+	CCONJ
ejde-517	607	7	ηδχδ1)−	ηδχδ1)−	PROPN
ejde-517	607	8	σ1(χδ1	σ1(χδ1	PROPN
ejde-517	607	9	)	)	PUNCT
ejde-517	607	10	η	η	PROPN
ejde-517	607	11	−dσ(χδ1	−dσ(χδ1	PROPN
ejde-517	607	12	;	;	PUNCT
ejde-517	607	13	δχδ1)‖	δχδ1)‖	PROPN
ejde-517	607	14	=	=	PROPN
ejde-517	607	15	0	0	PROPN
ejde-517	607	16	.	.	PUNCT
ejde-517	608	1	(	(	PUNCT
ejde-517	608	2	3.79	3.79	NUM
ejde-517	608	3	)	)	PUNCT
ejde-517	608	4	furthermore	furthermore	ADV
ejde-517	608	5	,	,	PUNCT
ejde-517	608	6	we	we	PRON
ejde-517	608	7	make	make	VERB
ejde-517	608	8	the	the	DET
ejde-517	608	9	identification	identification	NOUN
ejde-517	608	10	δς1	δς1	NOUN
ejde-517	608	11	δχ1	δχ1	X
ejde-517	608	12	(	(	PUNCT
ejde-517	608	13	χδ1	χδ1	X
ejde-517	608	14	;	;	PUNCT
ejde-517	608	15	δχδ1	δχδ1	PROPN
ejde-517	608	16	)	)	PUNCT
ejde-517	608	17	=	=	PUNCT
ejde-517	609	1	dσ(χδ1	dσ(χδ1	NUM
ejde-517	609	2	;	;	PUNCT
ejde-517	609	3	δχδ1	δχδ1	PROPN
ejde-517	609	4	)	)	PUNCT
ejde-517	609	5	∈	∈	PROPN
ejde-517	609	6	h1(ω	h1(ω	PROPN
ejde-517	609	7	)	)	PUNCT
ejde-517	609	8	.	.	PUNCT
ejde-517	610	1	proof	proof	NOUN
ejde-517	610	2	.	.	PUNCT
ejde-517	611	1	let	let	VERB
ejde-517	611	2	v	v	NUM
ejde-517	611	3	∈	∈	PROPN
ejde-517	611	4	h1(ω	h1(ω	PROPN
ejde-517	611	5	)	)	PUNCT
ejde-517	611	6	and	and	CCONJ
ejde-517	611	7	η	η	PROPN
ejde-517	611	8	>	>	X
ejde-517	611	9	0	0	NUM
ejde-517	611	10	.	.	PUNCT
ejde-517	612	1	from	from	ADP
ejde-517	612	2	(	(	PUNCT
ejde-517	612	3	3.72	3.72	NUM
ejde-517	612	4	)	)	PUNCT
ejde-517	612	5	,	,	PUNCT
ejde-517	612	6	we	we	PRON
ejde-517	612	7	have∫	have∫	VERB
ejde-517	612	8	ω	ω	PRON
ejde-517	612	9	α(χδ1	α(χδ1	X
ejde-517	612	10	+	+	CCONJ
ejde-517	612	11	ε)∇σ1(χδ1	ε)∇σ1(χδ1	ADJ
ejde-517	612	12	)	)	PUNCT
ejde-517	612	13	·	·	PUNCT
ejde-517	613	1	∇v	∇v	ADV
ejde-517	614	1	+	+	CCONJ
ejde-517	614	2	λ(σ1(χδ1)−	λ(σ1(χδ1)−	PROPN
ejde-517	614	3	σk1	σk1	NOUN
ejde-517	614	4	)	)	PUNCT
ejde-517	614	5	v	v	ADP
ejde-517	614	6	dv	dv	PROPN
ejde-517	614	7	=	=	SYM
ejde-517	614	8	∫	∫	PROPN
ejde-517	614	9	ω	ω	PROPN
ejde-517	614	10	χδ1∇φ(χδ1	χδ1∇φ(χδ1	PROPN
ejde-517	614	11	)	)	PUNCT
ejde-517	614	12	·	·	PUNCT
ejde-517	614	13	∇φ∗(χδ1)v	∇φ∗(χδ1)v	PROPN
ejde-517	614	14	dv	dv	PROPN
ejde-517	614	15	.	.	PROPN
ejde-517	615	1	(	(	PUNCT
ejde-517	615	2	3.80	3.80	NUM
ejde-517	615	3	)	)	PUNCT
ejde-517	615	4	similarly	similarly	ADV
ejde-517	615	5	,	,	PUNCT
ejde-517	615	6	if	if	SCONJ
ejde-517	615	7	we	we	PRON
ejde-517	615	8	replace	replace	VERB
ejde-517	615	9	χδ1	χδ1	NOUN
ejde-517	615	10	in	in	ADP
ejde-517	615	11	(	(	PUNCT
ejde-517	615	12	3.72	3.72	NUM
ejde-517	615	13	)	)	PUNCT
ejde-517	615	14	with	with	ADP
ejde-517	615	15	χδ1	χδ1	NOUN
ejde-517	615	16	+	+	CCONJ
ejde-517	615	17	ηδχδ1	ηδχδ1	ADJ
ejde-517	615	18	,	,	PUNCT
ejde-517	615	19	we	we	PRON
ejde-517	615	20	have∫	have∫	VERB
ejde-517	615	21	ω	ω	PRON
ejde-517	615	22	α(χδ1	α(χδ1	X
ejde-517	615	23	+	+	CCONJ
ejde-517	615	24	ηδχδ1	ηδχδ1	VERB
ejde-517	615	25	+	+	CCONJ
ejde-517	615	26	ε)∇(σ1(χδ1	ε)∇(σ1(χδ1	X
ejde-517	615	27	+	+	CCONJ
ejde-517	615	28	ηδχδ1	ηδχδ1	ADJ
ejde-517	615	29	)	)	PUNCT
ejde-517	615	30	)	)	PUNCT
ejde-517	615	31	·	·	PUNCT
ejde-517	616	1	∇v	∇v	ADJ
ejde-517	616	2	dv	dv	PROPN
ejde-517	616	3	+	+	CCONJ
ejde-517	616	4	∫	∫	PROPN
ejde-517	616	5	ω	ω	NUM
ejde-517	616	6	λ(σ1(χδ1	λ(σ1(χδ1	X
ejde-517	617	1	+	+	CCONJ
ejde-517	617	2	ηδχδ1)−	ηδχδ1)−	PROPN
ejde-517	617	3	σk1	σk1	NOUN
ejde-517	617	4	)	)	PUNCT
ejde-517	617	5	v	v	ADP
ejde-517	617	6	dv	dv	PROPN
ejde-517	617	7	=	=	PROPN
ejde-517	617	8	:	:	PUNCT
ejde-517	617	9	a(v	a(v	NUM
ejde-517	617	10	)	)	PUNCT
ejde-517	617	11	,	,	PUNCT
ejde-517	617	12	(	(	PUNCT
ejde-517	617	13	3.81	3.81	NUM
ejde-517	617	14	)	)	PUNCT
ejde-517	617	15	where	where	SCONJ
ejde-517	617	16	a(v	a(v	NOUN
ejde-517	617	17	)	)	PUNCT
ejde-517	617	18	=	=	SYM
ejde-517	618	1	∫	∫	PROPN
ejde-517	618	2	ω	ω	PROPN
ejde-517	618	3	(	(	PUNCT
ejde-517	618	4	χδ1	χδ1	X
ejde-517	618	5	+	+	X
ejde-517	618	6	ηδχδ1)∇φ(χδ1	ηδχδ1)∇φ(χδ1	NOUN
ejde-517	618	7	+	+	CCONJ
ejde-517	618	8	ηδχδ1	ηδχδ1	VERB
ejde-517	618	9	)	)	PUNCT
ejde-517	618	10	·	·	PUNCT
ejde-517	618	11	∇φ∗(χδ1	∇φ∗(χδ1	VERB
ejde-517	618	12	+	+	X
ejde-517	618	13	δχδ1)v	δχδ1)v	PROPN
ejde-517	618	14	dv	dv	PROPN
ejde-517	618	15	.	.	PROPN
ejde-517	619	1	subtracting	subtract	VERB
ejde-517	619	2	(	(	PUNCT
ejde-517	619	3	3.80	3.80	NUM
ejde-517	619	4	)	)	PUNCT
ejde-517	619	5	from	from	ADP
ejde-517	619	6	(	(	PUNCT
ejde-517	619	7	3.81	3.81	NUM
ejde-517	619	8	)	)	PUNCT
ejde-517	619	9	,	,	PUNCT
ejde-517	619	10	we	we	PRON
ejde-517	619	11	obtain	obtain	VERB
ejde-517	619	12	a1(v	a1(v	NOUN
ejde-517	619	13	)	)	PUNCT
ejde-517	620	1	+	+	NOUN
ejde-517	620	2	a2(v	a2(v	X
ejde-517	620	3	)	)	PUNCT
ejde-517	620	4	=	=	SYM
ejde-517	620	5	b1(v	b1(v	NOUN
ejde-517	620	6	)	)	PUNCT
ejde-517	620	7	+	+	NOUN
ejde-517	620	8	b2(v	b2(v	X
ejde-517	620	9	)	)	PUNCT
ejde-517	620	10	+	+	NOUN
ejde-517	620	11	b3(v	b3(v	X
ejde-517	620	12	)	)	PUNCT
ejde-517	620	13	,	,	PUNCT
ejde-517	620	14	(	(	PUNCT
ejde-517	620	15	3.82	3.82	NUM
ejde-517	620	16	)	)	PUNCT
ejde-517	620	17	where	where	SCONJ
ejde-517	620	18	a1(v	a1(v	NOUN
ejde-517	620	19	)	)	PUNCT
ejde-517	620	20	:	:	PUNCT
ejde-517	620	21	=	=	SYM
ejde-517	620	22	∫	∫	PROPN
ejde-517	620	23	ω	ω	PROPN
ejde-517	620	24	α(χδ1	α(χδ1	X
ejde-517	620	25	+	+	CCONJ
ejde-517	620	26	ε)∇[σ1(χδ1	ε)∇[σ1(χδ1	PROPN
ejde-517	620	27	+	+	CCONJ
ejde-517	620	28	ηδχδ1)−	ηδχδ1)−	PROPN
ejde-517	620	29	σ1(χδ1	σ1(χδ1	NOUN
ejde-517	620	30	)	)	PUNCT
ejde-517	620	31	]	]	PUNCT
ejde-517	620	32	·	·	PUNCT
ejde-517	620	33	∇v	∇v	ADJ
ejde-517	620	34	dv	dv	PROPN
ejde-517	620	35	,	,	PUNCT
ejde-517	620	36	ejde-2020/93	ejde-2020/93	PROPN
ejde-517	620	37	impedance	impedance	NOUN
ejde-517	620	38	tomography	tomography	NOUN
ejde-517	620	39	problem	problem	NOUN
ejde-517	620	40	21	21	NUM
ejde-517	620	41	a2(v	a2(v	NOUN
ejde-517	620	42	)	)	PUNCT
ejde-517	620	43	:	:	PUNCT
ejde-517	621	1	=	=	SYM
ejde-517	621	2	∫	∫	PROPN
ejde-517	621	3	ω	ω	NUM
ejde-517	621	4	λ(σ1(χδ1	λ(σ1(χδ1	X
ejde-517	622	1	+	+	CCONJ
ejde-517	622	2	ηδχδ1)−	ηδχδ1)−	PROPN
ejde-517	622	3	σ1(χδ1))v	σ1(χδ1))v	X
ejde-517	623	1	dv	dv	PROPN
ejde-517	623	2	,	,	PUNCT
ejde-517	623	3	b1(v	b1(v	NOUN
ejde-517	623	4	)	)	PUNCT
ejde-517	623	5	:	:	PUNCT
ejde-517	623	6	=	=	SYM
ejde-517	623	7	∫	∫	PROPN
ejde-517	623	8	ω	ω	NUM
ejde-517	623	9	χδ1[∇φ(χδ1	χδ1[∇φ(χδ1	X
ejde-517	623	10	+	+	CCONJ
ejde-517	623	11	ηδχδ1	ηδχδ1	X
ejde-517	623	12	)	)	PUNCT
ejde-517	623	13	·	·	PUNCT
ejde-517	623	14	∇φ∗(χδ1	∇φ∗(χδ1	VERB
ejde-517	623	15	+	+	CCONJ
ejde-517	623	16	ηδχδ1)−∇φ(χδ1	ηδχδ1)−∇φ(χδ1	PROPN
ejde-517	623	17	)	)	PUNCT
ejde-517	623	18	·	·	PUNCT
ejde-517	623	19	∇φ∗(χδ1)]v	∇φ∗(χδ1)]v	PROPN
ejde-517	623	20	dv	dv	PROPN
ejde-517	623	21	,	,	PUNCT
ejde-517	623	22	b2(v	b2(v	PROPN
ejde-517	623	23	)	)	PUNCT
ejde-517	623	24	:	:	PUNCT
ejde-517	624	1	=	=	SYM
ejde-517	624	2	∫	∫	PROPN
ejde-517	625	1	ω	ω	NUM
ejde-517	625	2	ηδχδ1∇φ(χδ1	ηδχδ1∇φ(χδ1	PROPN
ejde-517	625	3	+	+	CCONJ
ejde-517	625	4	ηδχδ1	ηδχδ1	ADJ
ejde-517	625	5	)	)	PUNCT
ejde-517	625	6	·	·	PUNCT
ejde-517	625	7	∇φ∗(χδ1	∇φ∗(χδ1	VERB
ejde-517	625	8	+	+	CCONJ
ejde-517	625	9	ηδχδ1)v	ηδχδ1)v	PROPN
ejde-517	625	10	dv	dv	PROPN
ejde-517	625	11	,	,	PUNCT
ejde-517	625	12	b3(v	b3(v	PROPN
ejde-517	625	13	)	)	PUNCT
ejde-517	625	14	:	:	PUNCT
ejde-517	626	1	=	=	PUNCT
ejde-517	626	2	−	−	PROPN
ejde-517	627	1	∫	∫	PROPN
ejde-517	627	2	ω	ω	PROPN
ejde-517	627	3	αηδχδ1∇(σ1(χδ1	αηδχδ1∇(σ1(χδ1	PROPN
ejde-517	627	4	+	+	CCONJ
ejde-517	627	5	ηδχδ1	ηδχδ1	VERB
ejde-517	627	6	)	)	PUNCT
ejde-517	627	7	)	)	PUNCT
ejde-517	627	8	·	·	PUNCT
ejde-517	628	1	∇v	∇v	ADJ
ejde-517	628	2	dv	dv	PROPN
ejde-517	628	3	,	,	PUNCT
ejde-517	628	4	for	for	ADP
ejde-517	628	5	all	all	DET
ejde-517	628	6	v	v	ADP
ejde-517	628	7	∈	∈	PROPN
ejde-517	628	8	h1(ω	h1(ω	PROPN
ejde-517	628	9	)	)	PUNCT
ejde-517	628	10	.	.	PUNCT
ejde-517	629	1	we	we	PRON
ejde-517	629	2	define	define	VERB
ejde-517	629	3	a(σ1(χδ1	a(σ1(χδ1	NOUN
ejde-517	629	4	+	+	CCONJ
ejde-517	629	5	ηδχδ1	ηδχδ1	X
ejde-517	629	6	)	)	PUNCT
ejde-517	629	7	−	−	ADP
ejde-517	629	8	σ1(χδ1	σ1(χδ1	NOUN
ejde-517	629	9	)	)	PUNCT
ejde-517	629	10	,	,	PUNCT
ejde-517	629	11	v	v	NOUN
ejde-517	629	12	)	)	PUNCT
ejde-517	629	13	:	:	PUNCT
ejde-517	629	14	=	=	SYM
ejde-517	629	15	a1(v	a1(v	NOUN
ejde-517	629	16	)	)	PUNCT
ejde-517	630	1	+	+	NUM
ejde-517	630	2	a2(v	a2(v	X
ejde-517	630	3	)	)	PUNCT
ejde-517	630	4	and	and	CCONJ
ejde-517	630	5	b(v	b(v	NOUN
ejde-517	630	6	)	)	PUNCT
ejde-517	631	1	:	:	PUNCT
ejde-517	631	2	=	=	SYM
ejde-517	631	3	b1(v	b1(v	NOUN
ejde-517	631	4	)	)	PUNCT
ejde-517	631	5	+	+	NOUN
ejde-517	631	6	b2(v	b2(v	X
ejde-517	631	7	)	)	PUNCT
ejde-517	631	8	+	+	NOUN
ejde-517	631	9	b3(v	b3(v	X
ejde-517	631	10	)	)	PUNCT
ejde-517	631	11	,	,	PUNCT
ejde-517	631	12	for	for	ADP
ejde-517	631	13	all	all	PRON
ejde-517	631	14	v	v	ADP
ejde-517	631	15	∈	∈	PROPN
ejde-517	631	16	h1(ω	h1(ω	PROPN
ejde-517	631	17	)	)	PUNCT
ejde-517	631	18	.	.	PUNCT
ejde-517	632	1	in	in	ADP
ejde-517	632	2	lemma	lemma	PROPN
ejde-517	632	3	(	(	PUNCT
ejde-517	632	4	3.25	3.25	NUM
ejde-517	632	5	)	)	PUNCT
ejde-517	632	6	,	,	PUNCT
ejde-517	632	7	we	we	PRON
ejde-517	632	8	have	have	AUX
ejde-517	632	9	shown	show	VERB
ejde-517	632	10	already	already	ADV
ejde-517	632	11	that	that	SCONJ
ejde-517	632	12	a	a	PRON
ejde-517	632	13	is	be	AUX
ejde-517	632	14	bilinear	bilinear	ADJ
ejde-517	632	15	,	,	PUNCT
ejde-517	632	16	coercive	coercive	ADJ
ejde-517	632	17	,	,	PUNCT
ejde-517	632	18	and	and	CCONJ
ejde-517	632	19	continuous	continuous	ADJ
ejde-517	632	20	.	.	PUNCT
ejde-517	633	1	clearly	clearly	ADV
ejde-517	633	2	,	,	PUNCT
ejde-517	633	3	b	b	PROPN
ejde-517	633	4	is	be	AUX
ejde-517	633	5	linear	linear	ADJ
ejde-517	633	6	.	.	PUNCT
ejde-517	634	1	now	now	ADV
ejde-517	634	2	we	we	PRON
ejde-517	634	3	only	only	ADV
ejde-517	634	4	need	need	VERB
ejde-517	634	5	to	to	PART
ejde-517	634	6	show	show	VERB
ejde-517	634	7	that	that	SCONJ
ejde-517	634	8	b	b	NOUN
ejde-517	634	9	is	be	AUX
ejde-517	634	10	continuous	continuous	ADJ
ejde-517	634	11	.	.	PUNCT
ejde-517	635	1	so	so	ADV
ejde-517	635	2	we	we	PRON
ejde-517	635	3	need	need	VERB
ejde-517	635	4	to	to	PART
ejde-517	635	5	estimate	estimate	VERB
ejde-517	635	6	b1(v	b1(v	NOUN
ejde-517	635	7	)	)	PUNCT
ejde-517	635	8	,	,	PUNCT
ejde-517	635	9	b2(v	b2(v	PROPN
ejde-517	635	10	)	)	PUNCT
ejde-517	635	11	,	,	PUNCT
ejde-517	635	12	and	and	CCONJ
ejde-517	635	13	b3(v	b3(v	NOUN
ejde-517	635	14	)	)	PUNCT
ejde-517	635	15	.	.	PUNCT
ejde-517	636	1	for	for	ADP
ejde-517	636	2	all	all	DET
ejde-517	636	3	these	these	PRON
ejde-517	636	4	,	,	PUNCT
ejde-517	636	5	we	we	PRON
ejde-517	636	6	use	use	VERB
ejde-517	636	7	the	the	DET
ejde-517	636	8	cauchy	cauchy	NOUN
ejde-517	636	9	-	-	PUNCT
ejde-517	636	10	schwarz	schwarz	PROPN
ejde-517	636	11	inequality	inequality	NOUN
ejde-517	636	12	.	.	PUNCT
ejde-517	637	1	to	to	PART
ejde-517	637	2	show	show	VERB
ejde-517	637	3	continuity	continuity	NOUN
ejde-517	637	4	of	of	ADP
ejde-517	637	5	b1(v	b1(v	NOUN
ejde-517	637	6	)	)	PUNCT
ejde-517	637	7	,	,	PUNCT
ejde-517	637	8	we	we	PRON
ejde-517	637	9	also	also	ADV
ejde-517	637	10	use	use	VERB
ejde-517	637	11	(	(	PUNCT
ejde-517	637	12	3.43	3.43	NUM
ejde-517	637	13	)	)	PUNCT
ejde-517	637	14	.	.	PUNCT
ejde-517	638	1	for	for	ADP
ejde-517	638	2	b2(v	b2(v	NOUN
ejde-517	638	3	)	)	PUNCT
ejde-517	638	4	and	and	CCONJ
ejde-517	638	5	b3(v	b3(v	NOUN
ejde-517	638	6	)	)	PUNCT
ejde-517	638	7	,	,	PUNCT
ejde-517	638	8	one	one	PRON
ejde-517	638	9	uses	use	VERB
ejde-517	638	10	the	the	DET
ejde-517	638	11	cauchy	cauchy	PROPN
ejde-517	638	12	-	-	PUNCT
ejde-517	638	13	schwarz	schwarz	PROPN
ejde-517	638	14	inequality	inequality	NOUN
ejde-517	638	15	,	,	PUNCT
ejde-517	638	16	hölder	hölder	NOUN
ejde-517	638	17	’s	’s	PART
ejde-517	638	18	inequality	inequality	NOUN
ejde-517	638	19	,	,	PUNCT
ejde-517	638	20	and	and	CCONJ
ejde-517	638	21	young	young	ADJ
ejde-517	638	22	’s	’s	PART
ejde-517	638	23	inequality	inequality	NOUN
ejde-517	638	24	for	for	ADP
ejde-517	638	25	convolutions	convolution	NOUN
ejde-517	638	26	to	to	PART
ejde-517	638	27	show	show	VERB
ejde-517	638	28	continuity	continuity	NOUN
ejde-517	638	29	.	.	PUNCT
ejde-517	639	1	it	it	PRON
ejde-517	639	2	is	be	AUX
ejde-517	639	3	worth	worth	ADJ
ejde-517	639	4	noting	note	VERB
ejde-517	639	5	that	that	SCONJ
ejde-517	639	6	‖∇φ(χδ1	‖∇φ(χδ1	PUNCT
ejde-517	639	7	+	+	NUM
ejde-517	639	8	ηδχδ1)‖l∞(ω	ηδχδ1)‖l∞(ω	NOUN
ejde-517	639	9	)	)	PUNCT
ejde-517	639	10	,	,	PUNCT
ejde-517	639	11	‖∇φ∗(χδ1	‖∇φ∗(χδ1	PROPN
ejde-517	639	12	+	+	CCONJ
ejde-517	639	13	ηδχδ1)‖l∞(ω	ηδχδ1)‖l∞(ω	NOUN
ejde-517	639	14	)	)	PUNCT
ejde-517	639	15	,	,	PUNCT
ejde-517	639	16	and	and	CCONJ
ejde-517	639	17	the	the	DET
ejde-517	639	18	quantity	quantity	NOUN
ejde-517	639	19	‖σ1(χδ1	‖σ1(χδ1	VERB
ejde-517	639	20	+	+	NOUN
ejde-517	639	21	ηδχδ1)‖h1(ω	ηδχδ1)‖h1(ω	NOUN
ejde-517	639	22	)	)	PUNCT
ejde-517	639	23	are	be	AUX
ejde-517	639	24	independent	independent	ADJ
ejde-517	639	25	of	of	ADP
ejde-517	639	26	η	η	PROPN
ejde-517	639	27	as	as	SCONJ
ejde-517	639	28	shown	show	VERB
ejde-517	639	29	in	in	ADP
ejde-517	639	30	(	(	PUNCT
ejde-517	639	31	3.37	3.37	NUM
ejde-517	639	32	)	)	PUNCT
ejde-517	639	33	,	,	PUNCT
ejde-517	639	34	(	(	PUNCT
ejde-517	639	35	3.38	3.38	NUM
ejde-517	639	36	)	)	PUNCT
ejde-517	639	37	,	,	PUNCT
ejde-517	639	38	and	and	CCONJ
ejde-517	639	39	(	(	PUNCT
ejde-517	639	40	3.74	3.74	NUM
ejde-517	639	41	)	)	PUNCT
ejde-517	639	42	.	.	PUNCT
ejde-517	640	1	combining	combine	VERB
ejde-517	640	2	these	these	PRON
ejde-517	640	3	implies	imply	VERB
ejde-517	640	4	that	that	SCONJ
ejde-517	640	5	b(v	b(v	NOUN
ejde-517	640	6	)	)	PUNCT
ejde-517	640	7	is	be	AUX
ejde-517	640	8	bounded	bound	VERB
ejde-517	640	9	.	.	PUNCT
ejde-517	641	1	we	we	PRON
ejde-517	641	2	make	make	VERB
ejde-517	641	3	the	the	DET
ejde-517	641	4	substitution	substitution	NOUN
ejde-517	641	5	u	u	NOUN
ejde-517	641	6	=	=	PROPN
ejde-517	641	7	v	v	NOUN
ejde-517	641	8	=	=	PUNCT
ejde-517	641	9	σ1(χδ1	σ1(χδ1	PRON
ejde-517	641	10	+	+	NUM
ejde-517	641	11	ηδχδ1)−σ1(χδ1	ηδχδ1)−σ1(χδ1	NOUN
ejde-517	641	12	)	)	PUNCT
ejde-517	641	13	.	.	PUNCT
ejde-517	642	1	furthermore	furthermore	ADV
ejde-517	642	2	,	,	PUNCT
ejde-517	642	3	using	use	VERB
ejde-517	642	4	the	the	DET
ejde-517	642	5	coercivity	coercivity	NOUN
ejde-517	642	6	of	of	ADP
ejde-517	642	7	a	a	PRON
ejde-517	642	8	and	and	CCONJ
ejde-517	642	9	the	the	DET
ejde-517	642	10	boundedness	boundedness	NOUN
ejde-517	642	11	of	of	ADP
ejde-517	642	12	b	b	PROPN
ejde-517	642	13	,	,	PUNCT
ejde-517	642	14	we	we	PRON
ejde-517	642	15	conclude	conclude	VERB
ejde-517	642	16	that	that	SCONJ
ejde-517	642	17	‖σ1(χδ1	‖σ1(χδ1	VERB
ejde-517	642	18	+	+	CCONJ
ejde-517	642	19	ηδχδ1)−	ηδχδ1)−	PROPN
ejde-517	642	20	σ1(χδ1)‖h1(ω	σ1(χδ1)‖h1(ω	NOUN
ejde-517	642	21	)	)	PUNCT
ejde-517	642	22	≤	≤	NOUN
ejde-517	642	23	cη‖δχ1‖l2(ω	cη‖δχ1‖l2(ω	NOUN
ejde-517	642	24	)	)	PUNCT
ejde-517	642	25	.	.	PUNCT
ejde-517	643	1	(	(	PUNCT
ejde-517	643	2	3.83	3.83	NUM
ejde-517	643	3	)	)	PUNCT
ejde-517	643	4	hence	hence	ADV
ejde-517	643	5	,	,	PUNCT
ejde-517	643	6	the	the	DET
ejde-517	643	7	proof	proof	NOUN
ejde-517	643	8	of	of	ADP
ejde-517	643	9	our	our	PRON
ejde-517	643	10	first	first	ADJ
ejde-517	643	11	statement	statement	NOUN
ejde-517	643	12	is	be	AUX
ejde-517	643	13	complete	complete	ADJ
ejde-517	643	14	.	.	PUNCT
ejde-517	644	1	subtracting	subtract	VERB
ejde-517	644	2	(	(	PUNCT
ejde-517	644	3	3.77	3.77	NUM
ejde-517	644	4	)	)	PUNCT
ejde-517	644	5	from	from	ADP
ejde-517	644	6	(	(	PUNCT
ejde-517	644	7	3.82	3.82	NUM
ejde-517	644	8	)	)	PUNCT
ejde-517	644	9	,	,	PUNCT
ejde-517	644	10	we	we	PRON
ejde-517	644	11	obtain	obtain	VERB
ejde-517	644	12	d1(v	d1(v	X
ejde-517	644	13	)	)	PUNCT
ejde-517	644	14	+	+	NOUN
ejde-517	644	15	d2(v	d2(v	NOUN
ejde-517	644	16	)	)	PUNCT
ejde-517	644	17	=	=	SYM
ejde-517	644	18	e1(v	e1(v	X
ejde-517	644	19	)	)	PUNCT
ejde-517	644	20	+	+	NOUN
ejde-517	644	21	e2(v	e2(v	X
ejde-517	644	22	)	)	PUNCT
ejde-517	644	23	+	+	NUM
ejde-517	644	24	e3(v	e3(v	NOUN
ejde-517	644	25	)	)	PUNCT
ejde-517	644	26	,	,	PUNCT
ejde-517	644	27	(	(	PUNCT
ejde-517	644	28	3.84	3.84	NUM
ejde-517	644	29	)	)	PUNCT
ejde-517	644	30	where	where	SCONJ
ejde-517	644	31	d1(v	d1(v	X
ejde-517	644	32	)	)	PUNCT
ejde-517	644	33	=	=	SYM
ejde-517	645	1	∫	∫	PROPN
ejde-517	645	2	ω	ω	NUM
ejde-517	645	3	α(χδ1	α(χδ1	X
ejde-517	645	4	+	+	CCONJ
ejde-517	645	5	ε)∇	ε)∇	PROPN
ejde-517	645	6	[	[	X
ejde-517	645	7	σ1(χδ1	σ1(χδ1	PRON
ejde-517	645	8	+	+	CCONJ
ejde-517	645	9	ηδχδ1)−	ηδχδ1)−	PROPN
ejde-517	645	10	σ1(χδ1	σ1(χδ1	PROPN
ejde-517	645	11	)	)	PUNCT
ejde-517	645	12	η	η	PROPN
ejde-517	645	13	−dσ(χδ1	−dσ(χδ1	PROPN
ejde-517	645	14	;	;	PUNCT
ejde-517	645	15	δχδ1	δχδ1	PROPN
ejde-517	645	16	)	)	PUNCT
ejde-517	645	17	]	]	PUNCT
ejde-517	645	18	·	·	PUNCT
ejde-517	646	1	∇v	∇v	ADJ
ejde-517	646	2	dv	dv	PROPN
ejde-517	646	3	,	,	PUNCT
ejde-517	646	4	d2(v	d2(v	NOUN
ejde-517	646	5	)	)	PUNCT
ejde-517	646	6	=	=	SYM
ejde-517	646	7	∫	∫	PROPN
ejde-517	646	8	ω	ω	NUM
ejde-517	646	9	λ	λ	X
ejde-517	646	10	[	[	X
ejde-517	646	11	σ1(χδ1	σ1(χδ1	X
ejde-517	646	12	+	+	CCONJ
ejde-517	646	13	ηδχδ1)−	ηδχδ1)−	PROPN
ejde-517	646	14	σ1(χδ1	σ1(χδ1	PROPN
ejde-517	646	15	)	)	PUNCT
ejde-517	646	16	η	η	PROPN
ejde-517	646	17	−dσ(χδ1	−dσ(χδ1	PROPN
ejde-517	646	18	;	;	PUNCT
ejde-517	646	19	δχδ1	δχδ1	PROPN
ejde-517	646	20	)	)	PUNCT
ejde-517	646	21	]	]	PUNCT
ejde-517	647	1	v	v	X
ejde-517	647	2	dv	dv	PROPN
ejde-517	647	3	,	,	PUNCT
ejde-517	647	4	e1(v	e1(v	X
ejde-517	647	5	)	)	PUNCT
ejde-517	647	6	=	=	SYM
ejde-517	647	7	∫	∫	PROPN
ejde-517	647	8	ω	ω	NUM
ejde-517	647	9	χδ1	χδ1	X
ejde-517	647	10	[	[	X
ejde-517	647	11	ψ(χδ1	ψ(χδ1	X
ejde-517	647	12	+	+	CCONJ
ejde-517	647	13	ηδχδ1)−	ηδχδ1)−	PROPN
ejde-517	647	14	ψ(χδ1	ψ(χδ1	PROPN
ejde-517	647	15	)	)	PUNCT
ejde-517	647	16	η	η	PROPN
ejde-517	647	17	−	−	PROPN
ejde-517	647	18	δψ	δψ	PROPN
ejde-517	647	19	δχδ1	δχδ1	PROPN
ejde-517	647	20	(	(	PUNCT
ejde-517	647	21	χδ1	χδ1	X
ejde-517	647	22	;	;	PUNCT
ejde-517	647	23	δχδ1	δχδ1	PROPN
ejde-517	647	24	)	)	PUNCT
ejde-517	647	25	]	]	PUNCT
ejde-517	648	1	v	v	X
ejde-517	648	2	dv	dv	PROPN
ejde-517	648	3	,	,	PUNCT
ejde-517	648	4	e2(v	e2(v	NUM
ejde-517	648	5	)	)	PUNCT
ejde-517	648	6	=	=	SYM
ejde-517	648	7	∫	∫	PROPN
ejde-517	648	8	ω	ω	PROPN
ejde-517	648	9	δχδ1	δχδ1	PROPN
ejde-517	648	10	[	[	PUNCT
ejde-517	648	11	ψ(χδ1	ψ(χδ1	PROPN
ejde-517	648	12	+	+	CCONJ
ejde-517	648	13	ηδχδ1)−	ηδχδ1)−	PROPN
ejde-517	648	14	ψ(χδ1	ψ(χδ1	PROPN
ejde-517	648	15	)	)	PUNCT
ejde-517	648	16	]	]	PUNCT
ejde-517	648	17	v	v	X
ejde-517	648	18	dv	dv	PROPN
ejde-517	648	19	,	,	PUNCT
ejde-517	648	20	e3(v	e3(v	X
ejde-517	648	21	)	)	PUNCT
ejde-517	648	22	=	=	SYM
ejde-517	649	1	−	−	PROPN
ejde-517	649	2	∫	∫	PROPN
ejde-517	649	3	ω	ω	NUM
ejde-517	649	4	αδχδ1∇	αδχδ1∇	PROPN
ejde-517	649	5	[	[	PUNCT
ejde-517	649	6	σ1(χδ1	σ1(χδ1	X
ejde-517	649	7	+	+	CCONJ
ejde-517	649	8	ηδχδ1)−	ηδχδ1)−	PROPN
ejde-517	649	9	σ1(χδ1	σ1(χδ1	NOUN
ejde-517	649	10	)	)	PUNCT
ejde-517	649	11	]	]	PUNCT
ejde-517	649	12	·	·	PUNCT
ejde-517	650	1	∇v	∇v	ADJ
ejde-517	650	2	dv	dv	PROPN
ejde-517	650	3	,	,	PUNCT
ejde-517	650	4	and	and	CCONJ
ejde-517	650	5	ψ	ψ	NOUN
ejde-517	650	6	is	be	AUX
ejde-517	650	7	the	the	DET
ejde-517	650	8	function	function	NOUN
ejde-517	650	9	defined	define	VERB
ejde-517	650	10	in	in	ADP
ejde-517	650	11	(	(	PUNCT
ejde-517	650	12	3.41	3.41	NUM
ejde-517	650	13	)	)	PUNCT
ejde-517	650	14	.	.	PUNCT
ejde-517	651	1	using	use	VERB
ejde-517	651	2	the	the	DET
ejde-517	651	3	cauchy	cauchy	NOUN
ejde-517	651	4	-	-	PUNCT
ejde-517	651	5	schwarz	schwarz	PROPN
ejde-517	651	6	inequality	inequality	NOUN
ejde-517	651	7	,	,	PUNCT
ejde-517	651	8	hölder	hölder	PROPN
ejde-517	651	9	’s	’s	PART
ejde-517	651	10	inequality	inequality	NOUN
ejde-517	651	11	,	,	PUNCT
ejde-517	651	12	(	(	PUNCT
ejde-517	651	13	3.43	3.43	NUM
ejde-517	651	14	)	)	PUNCT
ejde-517	651	15	,	,	PUNCT
ejde-517	651	16	and	and	CCONJ
ejde-517	651	17	(	(	PUNCT
ejde-517	651	18	3.83	3.83	NUM
ejde-517	651	19	)	)	PUNCT
ejde-517	651	20	,	,	PUNCT
ejde-517	651	21	we	we	PRON
ejde-517	651	22	can	can	AUX
ejde-517	651	23	estimate	estimate	VERB
ejde-517	651	24	e1(v	e1(v	NOUN
ejde-517	651	25	)	)	PUNCT
ejde-517	651	26	,	,	PUNCT
ejde-517	651	27	e2(v	e2(v	X
ejde-517	651	28	)	)	PUNCT
ejde-517	651	29	,	,	PUNCT
ejde-517	651	30	and	and	CCONJ
ejde-517	651	31	e3(v	e3(v	NOUN
ejde-517	651	32	)	)	PUNCT
ejde-517	651	33	.	.	PUNCT
ejde-517	652	1	indeed	indeed	ADV
ejde-517	652	2	,	,	PUNCT
ejde-517	652	3	|e1(v)|	|e1(v)|	VERB
ejde-517	652	4	≤	≤	NUM
ejde-517	652	5	‖ψ(χδ1	‖ψ(χδ1	NUM
ejde-517	652	6	+	+	CCONJ
ejde-517	652	7	ηδχδ1)−	ηδχδ1)−	PROPN
ejde-517	652	8	ψ(χδ1	ψ(χδ1	PROPN
ejde-517	652	9	)	)	PUNCT
ejde-517	652	10	η	η	PROPN
ejde-517	652	11	−	−	PROPN
ejde-517	652	12	δψ	δψ	NOUN
ejde-517	652	13	δχ1	δχ1	NOUN
ejde-517	652	14	(	(	PUNCT
ejde-517	652	15	χδ1	χδ1	X
ejde-517	652	16	;	;	PUNCT
ejde-517	652	17	δχδ1)‖l2(ω)‖v‖l2(ω	δχδ1)‖l2(ω)‖v‖l2(ω	ADJ
ejde-517	652	18	)	)	PUNCT
ejde-517	652	19	.	.	PUNCT
ejde-517	653	1	similarly	similarly	ADV
ejde-517	653	2	,	,	PUNCT
ejde-517	653	3	|e2(v)|	|e2(v)|	PUNCT
ejde-517	653	4	≤	≤	X
ejde-517	653	5	c2η‖δχδ1‖l∞(ω)‖δχ1‖l2(ω)‖v‖h1(ω	c2η‖δχδ1‖l∞(ω)‖δχ1‖l2(ω)‖v‖h1(ω	NOUN
ejde-517	653	6	)	)	PUNCT
ejde-517	653	7	,	,	PUNCT
ejde-517	653	8	22	22	NUM
ejde-517	653	9	r.	r.	PROPN
ejde-517	653	10	mendoza	mendoza	PROPN
ejde-517	653	11	,	,	PUNCT
ejde-517	653	12	s.	s.	PROPN
ejde-517	653	13	keeling	keeling	PROPN
ejde-517	653	14	ejde-2020/93	ejde-2020/93	PROPN
ejde-517	653	15	for	for	ADP
ejde-517	653	16	some	some	DET
ejde-517	653	17	c2	c2	PROPN
ejde-517	653	18	>	>	X
ejde-517	653	19	0	0	PROPN
ejde-517	653	20	.	.	PUNCT
ejde-517	654	1	finally	finally	ADV
ejde-517	654	2	,	,	PUNCT
ejde-517	654	3	|e3(v)|	|e3(v)|	PUNCT
ejde-517	654	4	≤	≤	NUM
ejde-517	654	5	α‖δχδ1‖l∞(ω)‖∇[σ1(χδ1	α‖δχδ1‖l∞(ω)‖∇[σ1(χδ1	X
ejde-517	654	6	+	+	CCONJ
ejde-517	654	7	ηδχδ1)−	ηδχδ1)−	PROPN
ejde-517	654	8	σ1(χδ1)]‖l2(ω)‖∇v‖l2(ω	σ1(χδ1)]‖l2(ω)‖∇v‖l2(ω	ADV
ejde-517	654	9	)	)	PUNCT
ejde-517	654	10	≤	≤	NUM
ejde-517	654	11	cη‖δχδ1‖l∞(ω)‖δχ1‖l2(ω)‖v‖h1(ω	cη‖δχδ1‖l∞(ω)‖δχ1‖l2(ω)‖v‖h1(ω	NOUN
ejde-517	654	12	)	)	PUNCT
ejde-517	654	13	.	.	PUNCT
ejde-517	655	1	if	if	SCONJ
ejde-517	655	2	we	we	PRON
ejde-517	655	3	make	make	VERB
ejde-517	655	4	the	the	DET
ejde-517	655	5	substitution	substitution	NOUN
ejde-517	655	6	v	v	ADP
ejde-517	655	7	=	=	SYM
ejde-517	655	8	σ1(χδ1	σ1(χδ1	X
ejde-517	655	9	+	+	CCONJ
ejde-517	655	10	ηδχδ1)−	ηδχδ1)−	PROPN
ejde-517	655	11	σ1(χδ1	σ1(χδ1	PROPN
ejde-517	655	12	)	)	PUNCT
ejde-517	655	13	η	η	PROPN
ejde-517	655	14	−dσ(χδ1	−dσ(χδ1	PROPN
ejde-517	655	15	;	;	PUNCT
ejde-517	655	16	δχδ1	δχδ1	PROPN
ejde-517	655	17	)	)	PUNCT
ejde-517	655	18	,	,	PUNCT
ejde-517	655	19	then	then	ADV
ejde-517	655	20	by	by	ADP
ejde-517	655	21	proposition	proposition	NOUN
ejde-517	655	22	3.24	3.24	NUM
ejde-517	655	23	,	,	PUNCT
ejde-517	655	24	we	we	PRON
ejde-517	655	25	obtain	obtain	VERB
ejde-517	655	26	|d1(v	|d1(v	NUM
ejde-517	655	27	)	)	PUNCT
ejde-517	656	1	+	+	PUNCT
ejde-517	656	2	d2(v)|	d2(v)|	NOUN
ejde-517	656	3	=	=	SYM
ejde-517	656	4	∣∣σ1(χδ1	∣∣σ1(χδ1	PROPN
ejde-517	656	5	+	+	CCONJ
ejde-517	656	6	ηδχδ1)−	ηδχδ1)−	PROPN
ejde-517	656	7	σ1(χδ1	σ1(χδ1	PROPN
ejde-517	656	8	)	)	PUNCT
ejde-517	656	9	η	η	PROPN
ejde-517	656	10	−dσ(χδ1	−dσ(χδ1	PROPN
ejde-517	656	11	;	;	PUNCT
ejde-517	656	12	δχδ1	δχδ1	PROPN
ejde-517	656	13	)	)	PUNCT
ejde-517	656	14	∣∣2	∣∣2	PROPN
ejde-517	656	15	h1(ω	h1(ω	PROPN
ejde-517	656	16	)	)	PUNCT
ejde-517	656	17	≥	≥	NOUN
ejde-517	656	18	min{αε	min{αε	PROPN
ejde-517	656	19	,	,	PUNCT
ejde-517	656	20	λ}‖σ1(χδ1	λ}‖σ1(χδ1	PROPN
ejde-517	656	21	+	+	CCONJ
ejde-517	656	22	ηδχδ1)−	ηδχδ1)−	PROPN
ejde-517	656	23	σ1(χδ1	σ1(χδ1	PROPN
ejde-517	656	24	)	)	PUNCT
ejde-517	656	25	η	η	PROPN
ejde-517	656	26	−dσ(χδ1	−dσ(χδ1	PROPN
ejde-517	656	27	;	;	PUNCT
ejde-517	656	28	δχδ1)‖2h1(ω	δχδ1)‖2h1(ω	NUM
ejde-517	656	29	)	)	PUNCT
ejde-517	656	30	.	.	PUNCT
ejde-517	657	1	hence	hence	ADV
ejde-517	657	2	,	,	PUNCT
ejde-517	657	3	the	the	DET
ejde-517	657	4	above	above	ADJ
ejde-517	657	5	inequality	inequality	NOUN
ejde-517	657	6	and	and	CCONJ
ejde-517	657	7	(	(	PUNCT
ejde-517	657	8	3.84	3.84	NUM
ejde-517	657	9	)	)	PUNCT
ejde-517	657	10	imply	imply	VERB
ejde-517	657	11	min{αε	min{αε	PROPN
ejde-517	657	12	,	,	PUNCT
ejde-517	657	13	λ}‖σ1(χδ1	λ}‖σ1(χδ1	PROPN
ejde-517	657	14	+	+	CCONJ
ejde-517	657	15	ηδχδ1)−	ηδχδ1)−	PROPN
ejde-517	657	16	σ1(χδ1	σ1(χδ1	PROPN
ejde-517	657	17	)	)	PUNCT
ejde-517	657	18	η	η	PROPN
ejde-517	657	19	−dσ(χδ1	−dσ(χδ1	PROPN
ejde-517	657	20	;	;	PUNCT
ejde-517	657	21	δχδ1)‖h1(ω	δχδ1)‖h1(ω	PROPN
ejde-517	657	22	)	)	PUNCT
ejde-517	657	23	≤	≤	NOUN
ejde-517	658	1	|e1(v)|+	|e1(v)|+	PROPN
ejde-517	658	2	|e2(v)|+	|e2(v)|+	PROPN
ejde-517	658	3	|e3(v)|	|e3(v)|	NOUN
ejde-517	658	4	.	.	PUNCT
ejde-517	659	1	taking	take	VERB
ejde-517	659	2	the	the	DET
ejde-517	659	3	limit	limit	NOUN
ejde-517	659	4	as	as	ADP
ejde-517	659	5	η	η	PROPN
ejde-517	659	6	→	→	X
ejde-517	659	7	0	0	NUM
ejde-517	659	8	,	,	PUNCT
ejde-517	659	9	it	it	PRON
ejde-517	659	10	is	be	AUX
ejde-517	659	11	clear	clear	ADJ
ejde-517	659	12	that	that	SCONJ
ejde-517	659	13	|e2(v)|+	|e2(v)|+	PROPN
ejde-517	659	14	|e3(v)|	|e3(v)|	PUNCT
ejde-517	659	15	→	→	X
ejde-517	659	16	0	0	X
ejde-517	659	17	.	.	PUNCT
ejde-517	660	1	lastly	lastly	ADV
ejde-517	660	2	,	,	PUNCT
ejde-517	660	3	from	from	ADP
ejde-517	660	4	(	(	PUNCT
ejde-517	660	5	3.67	3.67	NUM
ejde-517	660	6	)	)	PUNCT
ejde-517	660	7	,	,	PUNCT
ejde-517	660	8	we	we	PRON
ejde-517	660	9	have	have	VERB
ejde-517	660	10	|e1(v)|	|e1(v)|	VERB
ejde-517	660	11	→	→	SYM
ejde-517	660	12	0	0	NUM
ejde-517	660	13	,	,	PUNCT
ejde-517	660	14	which	which	PRON
ejde-517	660	15	then	then	ADV
ejde-517	660	16	implies	imply	VERB
ejde-517	660	17	our	our	PRON
ejde-517	660	18	second	second	ADJ
ejde-517	660	19	statement	statement	NOUN
ejde-517	660	20	.	.	PUNCT
ejde-517	661	1	the	the	DET
ejde-517	661	2	last	last	ADJ
ejde-517	661	3	statement	statement	NOUN
ejde-517	661	4	follows	follow	VERB
ejde-517	661	5	immediately	immediately	ADV
ejde-517	661	6	from	from	ADP
ejde-517	661	7	the	the	DET
ejde-517	661	8	previous	previous	ADJ
ejde-517	661	9	lemma	lemma	PROPN
ejde-517	661	10	.	.	PUNCT
ejde-517	661	11	�	�	PROPN
ejde-517	661	12	now	now	ADV
ejde-517	661	13	that	that	SCONJ
ejde-517	661	14	we	we	PRON
ejde-517	661	15	have	have	AUX
ejde-517	661	16	established	establish	VERB
ejde-517	661	17	that	that	SCONJ
ejde-517	661	18	δς1	δς1	ADJ
ejde-517	661	19	δχ1	δχ1	X
ejde-517	661	20	(	(	PUNCT
ejde-517	661	21	χδ1	χδ1	X
ejde-517	661	22	;	;	PUNCT
ejde-517	661	23	δχδ1	δχδ1	PROPN
ejde-517	661	24	)	)	PUNCT
ejde-517	661	25	∈	∈	PROPN
ejde-517	661	26	h1(ω	h1(ω	PROPN
ejde-517	661	27	)	)	PUNCT
ejde-517	661	28	,	,	PUNCT
ejde-517	661	29	the	the	DET
ejde-517	661	30	gradient	gradient	NOUN
ejde-517	661	31	of	of	ADP
ejde-517	661	32	the	the	DET
ejde-517	661	33	functional	functional	ADJ
ejde-517	661	34	j	j	NOUN
ejde-517	661	35	shown	show	VERB
ejde-517	661	36	in	in	ADP
ejde-517	661	37	(	(	PUNCT
ejde-517	661	38	2.14	2.14	NUM
ejde-517	661	39	)	)	PUNCT
ejde-517	661	40	is	be	AUX
ejde-517	661	41	justified	justify	VERB
ejde-517	661	42	.	.	PUNCT
ejde-517	662	1	4	4	X
ejde-517	662	2	.	.	X
ejde-517	662	3	existence	existence	NOUN
ejde-517	662	4	of	of	ADP
ejde-517	662	5	a	a	DET
ejde-517	662	6	fixed	fix	VERB
ejde-517	662	7	point	point	NOUN
ejde-517	662	8	in	in	ADP
ejde-517	662	9	(	(	PUNCT
ejde-517	662	10	3.28	3.28	NUM
ejde-517	662	11	)	)	PUNCT
ejde-517	662	12	,	,	PUNCT
ejde-517	662	13	the	the	DET
ejde-517	662	14	update	update	NOUN
ejde-517	662	15	for	for	ADP
ejde-517	662	16	χ1	χ1	NOUN
ejde-517	662	17	was	be	AUX
ejde-517	662	18	introduced	introduce	VERB
ejde-517	662	19	.	.	PUNCT
ejde-517	663	1	in	in	ADP
ejde-517	663	2	this	this	DET
ejde-517	663	3	section	section	NOUN
ejde-517	663	4	,	,	PUNCT
ejde-517	663	5	we	we	PRON
ejde-517	663	6	show	show	VERB
ejde-517	663	7	that	that	SCONJ
ejde-517	663	8	this	this	DET
ejde-517	663	9	update	update	NOUN
ejde-517	663	10	has	have	VERB
ejde-517	663	11	a	a	DET
ejde-517	663	12	fixed	fix	VERB
ejde-517	663	13	point	point	NOUN
ejde-517	663	14	.	.	PUNCT
ejde-517	664	1	in	in	ADP
ejde-517	664	2	other	other	ADJ
ejde-517	664	3	words	word	NOUN
ejde-517	664	4	,	,	PUNCT
ejde-517	664	5	we	we	PRON
ejde-517	664	6	show	show	VERB
ejde-517	664	7	that	that	SCONJ
ejde-517	664	8	υ(χ1	υ(χ1	NOUN
ejde-517	664	9	)	)	PUNCT
ejde-517	664	10	:	:	PUNCT
ejde-517	665	1	=	=	SYM
ejde-517	665	2	(	(	PUNCT
ejde-517	665	3	tδ	tδ	INTJ
ejde-517	665	4	◦	◦	NOUN
ejde-517	665	5	m	m	NOUN
ejde-517	665	6	◦	◦	NOUN
ejde-517	665	7	h	h	NOUN
ejde-517	665	8	◦	◦	NOUN
ejde-517	665	9	θ	θ	NOUN
ejde-517	665	10	◦	◦	NOUN
ejde-517	665	11	g	g	NOUN
ejde-517	665	12	◦	◦	NOUN
ejde-517	665	13	tδ)(χ1	tδ)(χ1	NUM
ejde-517	665	14	)	)	PUNCT
ejde-517	665	15	(	(	PUNCT
ejde-517	665	16	4.1	4.1	NUM
ejde-517	665	17	)	)	PUNCT
ejde-517	665	18	has	have	VERB
ejde-517	665	19	a	a	DET
ejde-517	665	20	fixed	fix	VERB
ejde-517	665	21	point	point	NOUN
ejde-517	665	22	on	on	ADP
ejde-517	665	23	some	some	DET
ejde-517	665	24	suitable	suitable	ADJ
ejde-517	665	25	space	space	NOUN
ejde-517	665	26	.	.	PUNCT
ejde-517	666	1	we	we	PRON
ejde-517	666	2	use	use	VERB
ejde-517	666	3	the	the	DET
ejde-517	666	4	following	following	ADJ
ejde-517	666	5	fixed	fix	VERB
ejde-517	666	6	point	point	NOUN
ejde-517	666	7	theorem	theorem	VERB
ejde-517	666	8	to	to	PART
ejde-517	666	9	prove	prove	VERB
ejde-517	666	10	this	this	PRON
ejde-517	666	11	.	.	PUNCT
ejde-517	667	1	theorem	theorem	VERB
ejde-517	667	2	4.1	4.1	NUM
ejde-517	667	3	(	(	PUNCT
ejde-517	667	4	schauder	schauder	NOUN
ejde-517	667	5	fixed	fix	VERB
ejde-517	667	6	point	point	NOUN
ejde-517	667	7	)	)	PUNCT
ejde-517	667	8	.	.	PUNCT
ejde-517	668	1	let	let	VERB
ejde-517	668	2	k	k	PRON
ejde-517	668	3	be	be	AUX
ejde-517	668	4	a	a	DET
ejde-517	668	5	convex	convex	NOUN
ejde-517	668	6	subset	subset	NOUN
ejde-517	668	7	of	of	ADP
ejde-517	668	8	l2(ω	l2(ω	PROPN
ejde-517	668	9	)	)	PUNCT
ejde-517	668	10	and	and	CCONJ
ejde-517	668	11	suppose	suppose	VERB
ejde-517	668	12	υ	υ	X
ejde-517	668	13	:	:	PUNCT
ejde-517	668	14	k	k	PROPN
ejde-517	668	15	→	→	SYM
ejde-517	668	16	l2(ω	l2(ω	CCONJ
ejde-517	668	17	)	)	PUNCT
ejde-517	668	18	is	be	AUX
ejde-517	668	19	continuous	continuous	ADJ
ejde-517	668	20	.	.	PUNCT
ejde-517	669	1	suppose	suppose	VERB
ejde-517	669	2	υ(k	υ(k	PROPN
ejde-517	669	3	)	)	PUNCT
ejde-517	669	4	is	be	AUX
ejde-517	669	5	a	a	DET
ejde-517	669	6	compact	compact	ADJ
ejde-517	669	7	subset	subset	NOUN
ejde-517	669	8	of	of	ADP
ejde-517	669	9	k.	k.	PROPN
ejde-517	669	10	then	then	ADV
ejde-517	669	11	υ	υ	PROPN
ejde-517	669	12	has	have	VERB
ejde-517	669	13	a	a	DET
ejde-517	669	14	fixed	fix	VERB
ejde-517	669	15	point	point	NOUN
ejde-517	669	16	in	in	ADP
ejde-517	669	17	k	k	PROPN
ejde-517	669	18	(	(	PUNCT
ejde-517	669	19	see	see	VERB
ejde-517	669	20	[	[	X
ejde-517	669	21	15	15	NUM
ejde-517	669	22	]	]	NUM
ejde-517	669	23	)	)	PUNCT
ejde-517	669	24	.	.	PUNCT
ejde-517	670	1	thus	thus	ADV
ejde-517	670	2	,	,	PUNCT
ejde-517	670	3	it	it	PRON
ejde-517	670	4	is	be	AUX
ejde-517	670	5	necessary	necessary	ADJ
ejde-517	670	6	to	to	PART
ejde-517	670	7	show	show	VERB
ejde-517	670	8	that	that	SCONJ
ejde-517	670	9	υ	υ	NOUN
ejde-517	670	10	is	be	AUX
ejde-517	670	11	continuous	continuous	ADJ
ejde-517	670	12	on	on	ADP
ejde-517	670	13	a	a	DET
ejde-517	670	14	convex	convex	NOUN
ejde-517	670	15	subset	subset	NOUN
ejde-517	670	16	k	k	PROPN
ejde-517	670	17	of	of	ADP
ejde-517	670	18	l2(ω	l2(ω	PROPN
ejde-517	670	19	)	)	PUNCT
ejde-517	670	20	and	and	CCONJ
ejde-517	670	21	that	that	SCONJ
ejde-517	670	22	υ(k	υ(k	PROPN
ejde-517	670	23	)	)	PUNCT
ejde-517	670	24	is	be	AUX
ejde-517	670	25	compact	compact	ADJ
ejde-517	670	26	in	in	ADP
ejde-517	670	27	k.	k.	PROPN
ejde-517	670	28	the	the	DET
ejde-517	670	29	previous	previous	ADJ
ejde-517	670	30	section	section	NOUN
ejde-517	670	31	justified	justify	VERB
ejde-517	670	32	the	the	DET
ejde-517	670	33	calculated	calculated	ADJ
ejde-517	670	34	formulation	formulation	NOUN
ejde-517	670	35	of	of	ADP
ejde-517	670	36	the	the	DET
ejde-517	670	37	function	function	NOUN
ejde-517	670	38	g	g	PROPN
ejde-517	670	39	defined	define	VERB
ejde-517	670	40	in	in	ADP
ejde-517	670	41	(	(	PUNCT
ejde-517	670	42	2.14	2.14	NUM
ejde-517	670	43	)	)	PUNCT
ejde-517	670	44	.	.	PUNCT
ejde-517	671	1	we	we	PRON
ejde-517	671	2	now	now	ADV
ejde-517	671	3	show	show	VERB
ejde-517	671	4	that	that	SCONJ
ejde-517	671	5	g(χ1	g(χ1	NOUN
ejde-517	671	6	)	)	PUNCT
ejde-517	671	7	=	=	SYM
ejde-517	671	8	χ1	χ1	NOUN
ejde-517	671	9	−	−	PROPN
ejde-517	671	10	ω[−2(σ1(χ1)−	ω[−2(σ1(χ1)−	PROPN
ejde-517	671	11	σ2)ψ(χ1	σ2)ψ(χ1	PROPN
ejde-517	671	12	)	)	PUNCT
ejde-517	672	1	+	+	CCONJ
ejde-517	672	2	α|∇σ1(χ1)|2	α|∇σ1(χ1)|2	PROPN
ejde-517	672	3	]	]	X
ejde-517	672	4	(	(	PUNCT
ejde-517	672	5	4.2	4.2	NUM
ejde-517	672	6	)	)	PUNCT
ejde-517	672	7	is	be	AUX
ejde-517	672	8	continuous	continuous	ADJ
ejde-517	672	9	.	.	PUNCT
ejde-517	673	1	lemma	lemma	PROPN
ejde-517	673	2	4.2	4.2	NUM
ejde-517	673	3	.	.	PUNCT
ejde-517	674	1	under	under	ADP
ejde-517	674	2	assumption	assumption	NOUN
ejde-517	674	3	(	(	PUNCT
ejde-517	674	4	3.30	3.30	NUM
ejde-517	674	5	)	)	PUNCT
ejde-517	674	6	,	,	PUNCT
ejde-517	674	7	lim	lim	PROPN
ejde-517	674	8	η→0	η→0	X
ejde-517	674	9	‖g(χδ1	‖g(χδ1	PUNCT
ejde-517	674	10	+	+	CCONJ
ejde-517	674	11	ηδχδ1)−g(χδ1)‖l2(ω	ηδχδ1)−g(χδ1)‖l2(ω	ADJ
ejde-517	674	12	)	)	PUNCT
ejde-517	674	13	=	=	SYM
ejde-517	674	14	0	0	X
ejde-517	674	15	.	.	PUNCT
ejde-517	675	1	(	(	PUNCT
ejde-517	675	2	4.3	4.3	NUM
ejde-517	675	3	)	)	PUNCT
ejde-517	675	4	ejde-2020/93	ejde-2020/93	PROPN
ejde-517	675	5	impedance	impedance	NOUN
ejde-517	675	6	tomography	tomography	NOUN
ejde-517	675	7	problem	problem	NOUN
ejde-517	675	8	23	23	NUM
ejde-517	675	9	proof	proof	NOUN
ejde-517	675	10	.	.	PUNCT
ejde-517	676	1	denote	denote	VERB
ejde-517	676	2	a1(χδ1	a1(χδ1	NUM
ejde-517	676	3	)	)	PUNCT
ejde-517	676	4	:	:	PUNCT
ejde-517	677	1	=	=	SYM
ejde-517	677	2	2ω[σ1(χδ1	2ω[σ1(χδ1	NUM
ejde-517	677	3	+	+	CCONJ
ejde-517	677	4	ηδχδ1)−	ηδχδ1)−	PROPN
ejde-517	677	5	σ2]ψ(χδ1	σ2]ψ(χδ1	PROPN
ejde-517	677	6	)	)	PUNCT
ejde-517	677	7	,	,	PUNCT
ejde-517	677	8	a2(χδ1	a2(χδ1	X
ejde-517	677	9	)	)	PUNCT
ejde-517	677	10	:	:	PUNCT
ejde-517	677	11	=	=	PUNCT
ejde-517	677	12	−αω|∇σ1(χδ1)|2	−αω|∇σ1(χδ1)|2	PROPN
ejde-517	677	13	.	.	PUNCT
ejde-517	678	1	thus	thus	ADV
ejde-517	678	2	,	,	PUNCT
ejde-517	678	3	using	use	VERB
ejde-517	678	4	(	(	PUNCT
ejde-517	678	5	4.2	4.2	NUM
ejde-517	678	6	)	)	PUNCT
ejde-517	678	7	,	,	PUNCT
ejde-517	678	8	the	the	DET
ejde-517	678	9	triangle	triangle	NOUN
ejde-517	678	10	inequality	inequality	NOUN
ejde-517	678	11	,	,	PUNCT
ejde-517	678	12	and	and	CCONJ
ejde-517	678	13	young	young	ADJ
ejde-517	678	14	’s	’s	PART
ejde-517	678	15	inequality	inequality	NOUN
ejde-517	678	16	for	for	ADP
ejde-517	678	17	a	a	DET
ejde-517	678	18	convolution	convolution	NOUN
ejde-517	678	19	,	,	PUNCT
ejde-517	678	20	we	we	PRON
ejde-517	678	21	obtain	obtain	VERB
ejde-517	678	22	‖g(χδ1	‖g(χδ1	PUNCT
ejde-517	678	23	+	+	CCONJ
ejde-517	678	24	ηδχδ1)−g(χδ1)‖l2(ω	ηδχδ1)−g(χδ1)‖l2(ω	ADJ
ejde-517	678	25	)	)	PUNCT
ejde-517	678	26	≤	≤	NOUN
ejde-517	678	27	η‖ξδ‖l1(ω)‖δχ1‖l2(ω	η‖ξδ‖l1(ω)‖δχ1‖l2(ω	ADV
ejde-517	678	28	)	)	PUNCT
ejde-517	679	1	+	+	CCONJ
ejde-517	679	2	‖a1(χδ1	‖a1(χδ1	NOUN
ejde-517	679	3	+	+	CCONJ
ejde-517	679	4	ηδχδ1)−a1(χδ1)‖l2(ω	ηδχδ1)−a1(χδ1)‖l2(ω	NOUN
ejde-517	679	5	)	)	PUNCT
ejde-517	679	6	+	+	CCONJ
ejde-517	679	7	‖a2(χδ1	‖a2(χδ1	NOUN
ejde-517	679	8	+	+	X
ejde-517	679	9	ηδχδ1)−a2(χδ1)‖l2(ω	ηδχδ1)−a2(χδ1)‖l2(ω	ADV
ejde-517	679	10	)	)	PUNCT
ejde-517	679	11	.	.	PUNCT
ejde-517	680	1	(	(	PUNCT
ejde-517	680	2	4.4	4.4	NUM
ejde-517	680	3	)	)	PUNCT
ejde-517	680	4	adding	add	VERB
ejde-517	680	5	and	and	CCONJ
ejde-517	680	6	subtracting	subtract	VERB
ejde-517	680	7	2ω[σ1(χδ1	2ω[σ1(χδ1	NUM
ejde-517	680	8	+	+	NUM
ejde-517	680	9	ηδχδ1	ηδχδ1	ADJ
ejde-517	680	10	)	)	PUNCT
ejde-517	680	11	−	−	PROPN
ejde-517	680	12	σ2]ψ(χδ1	σ2]ψ(χδ1	NOUN
ejde-517	680	13	)	)	PUNCT
ejde-517	680	14	to	to	ADP
ejde-517	680	15	a1(χδ1	a1(χδ1	PRON
ejde-517	680	16	+	+	CCONJ
ejde-517	680	17	ηδχδ1	ηδχδ1	ADJ
ejde-517	680	18	)	)	PUNCT
ejde-517	680	19	−	−	NOUN
ejde-517	680	20	a1(χδ1	a1(χδ1	NUM
ejde-517	680	21	)	)	PUNCT
ejde-517	680	22	and	and	CCONJ
ejde-517	680	23	using	use	VERB
ejde-517	680	24	the	the	DET
ejde-517	680	25	triangle	triangle	NOUN
ejde-517	680	26	inequality	inequality	NOUN
ejde-517	680	27	,	,	PUNCT
ejde-517	680	28	we	we	PRON
ejde-517	680	29	obtain	obtain	VERB
ejde-517	680	30	‖a1(χδ1	‖a1(χδ1	NOUN
ejde-517	680	31	+	+	CCONJ
ejde-517	680	32	ηδχδ1)−a1(χδ1)‖l2(ω	ηδχδ1)−a1(χδ1)‖l2(ω	NOUN
ejde-517	680	33	)	)	PUNCT
ejde-517	680	34	≤	≤	NUM
ejde-517	680	35	‖b1(χ1	‖b1(χ1	VERB
ejde-517	680	36	;	;	PUNCT
ejde-517	680	37	δχ1)‖l2(ω	δχ1)‖l2(ω	NUM
ejde-517	680	38	)	)	PUNCT
ejde-517	680	39	+	+	CCONJ
ejde-517	680	40	‖b2(χ1	‖b2(χ1	NUM
ejde-517	680	41	;	;	PUNCT
ejde-517	680	42	δχ1)‖l2(ω	δχ1)‖l2(ω	NUM
ejde-517	680	43	)	)	PUNCT
ejde-517	680	44	,	,	PUNCT
ejde-517	680	45	where	where	SCONJ
ejde-517	680	46	b1(χδ1	b1(χδ1	NOUN
ejde-517	680	47	;	;	PUNCT
ejde-517	680	48	δχδ1	δχδ1	PROPN
ejde-517	680	49	)	)	PUNCT
ejde-517	680	50	=	=	PUNCT
ejde-517	681	1	−2ω[σ1(χδ1	−2ω[σ1(χδ1	PROPN
ejde-517	682	1	+	+	CCONJ
ejde-517	682	2	ηδχδ1)−	ηδχδ1)−	PROPN
ejde-517	682	3	σ2]ψ(χδ1	σ2]ψ(χδ1	PROPN
ejde-517	682	4	+	+	CCONJ
ejde-517	682	5	ηδχδ1	ηδχδ1	VERB
ejde-517	682	6	)	)	PUNCT
ejde-517	682	7	+	+	CCONJ
ejde-517	683	1	2ω[σ1(χδ1	2ω[σ1(χδ1	NUM
ejde-517	683	2	+	+	CCONJ
ejde-517	683	3	ηδχδ1)−	ηδχδ1)−	PROPN
ejde-517	683	4	σ2]ψ(χδ1	σ2]ψ(χδ1	PROPN
ejde-517	683	5	)	)	PUNCT
ejde-517	683	6	,	,	PUNCT
ejde-517	683	7	b2(χδ1	b2(χδ1	PROPN
ejde-517	683	8	;	;	PUNCT
ejde-517	683	9	δχδ1	δχδ1	PROPN
ejde-517	683	10	)	)	PUNCT
ejde-517	683	11	=	=	PUNCT
ejde-517	684	1	−2ω[σ1(χδ1	−2ω[σ1(χδ1	PROPN
ejde-517	684	2	+	+	CCONJ
ejde-517	684	3	ηδχδ1)−	ηδχδ1)−	PROPN
ejde-517	684	4	σ2]ψ(χδ1	σ2]ψ(χδ1	PROPN
ejde-517	684	5	)	)	PUNCT
ejde-517	685	1	+	+	CCONJ
ejde-517	685	2	2ω[σ1(χδ1)−	2ω[σ1(χδ1)−	NUM
ejde-517	685	3	σ2]ψ(χδ1	σ2]ψ(χδ1	NOUN
ejde-517	685	4	)	)	PUNCT
ejde-517	685	5	.	.	PUNCT
ejde-517	686	1	by	by	ADP
ejde-517	686	2	using	use	VERB
ejde-517	686	3	hölder	hölder	PROPN
ejde-517	686	4	’s	’s	PART
ejde-517	686	5	inequality	inequality	NOUN
ejde-517	686	6	,	,	PUNCT
ejde-517	686	7	(	(	PUNCT
ejde-517	686	8	3.76	3.76	NUM
ejde-517	686	9	)	)	PUNCT
ejde-517	686	10	,	,	PUNCT
ejde-517	686	11	(	(	PUNCT
ejde-517	686	12	3.43	3.43	NUM
ejde-517	686	13	)	)	PUNCT
ejde-517	686	14	,	,	PUNCT
ejde-517	686	15	(	(	PUNCT
ejde-517	686	16	3.31	3.31	NUM
ejde-517	686	17	)	)	PUNCT
ejde-517	686	18	,	,	PUNCT
ejde-517	686	19	(	(	PUNCT
ejde-517	686	20	3.36	3.36	NUM
ejde-517	686	21	)	)	PUNCT
ejde-517	686	22	,	,	PUNCT
ejde-517	686	23	and	and	CCONJ
ejde-517	686	24	(	(	PUNCT
ejde-517	686	25	3.78	3.78	NUM
ejde-517	686	26	)	)	PUNCT
ejde-517	686	27	,	,	PUNCT
ejde-517	686	28	we	we	PRON
ejde-517	686	29	can	can	AUX
ejde-517	686	30	estimate	estimate	VERB
ejde-517	686	31	b1(χδ1	b1(χδ1	NOUN
ejde-517	686	32	;	;	PUNCT
ejde-517	686	33	δχδ1	δχδ1	PROPN
ejde-517	686	34	)	)	PUNCT
ejde-517	686	35	and	and	CCONJ
ejde-517	686	36	b2(χδ1	b2(χδ1	PROPN
ejde-517	686	37	;	;	PUNCT
ejde-517	686	38	δχδ1	δχδ1	PROPN
ejde-517	686	39	)	)	PUNCT
ejde-517	686	40	as	as	SCONJ
ejde-517	686	41	follows	follow	VERB
ejde-517	686	42	:	:	PUNCT
ejde-517	687	1	‖b1(χδ1	‖b1(χδ1	ADV
ejde-517	687	2	;	;	PUNCT
ejde-517	687	3	δχδ1)‖l2(ω	δχδ1)‖l2(ω	PROPN
ejde-517	687	4	)	)	PUNCT
ejde-517	687	5	≤	≤	NOUN
ejde-517	687	6	2c1ωη‖[σ1(χδ1	2c1ωη‖[σ1(χδ1	NUM
ejde-517	687	7	+	+	CCONJ
ejde-517	687	8	ηδχδ1)−	ηδχδ1)−	PROPN
ejde-517	687	9	σ2]‖l∞(ω)‖δχ1‖l2(ω	σ2]‖l∞(ω)‖δχ1‖l2(ω	NUM
ejde-517	687	10	)	)	PUNCT
ejde-517	687	11	,	,	PUNCT
ejde-517	687	12	(	(	PUNCT
ejde-517	687	13	4.5	4.5	NUM
ejde-517	687	14	)	)	PUNCT
ejde-517	687	15	for	for	ADP
ejde-517	687	16	some	some	DET
ejde-517	687	17	c1	c1	PROPN
ejde-517	687	18	>	>	X
ejde-517	687	19	0	0	PUNCT
ejde-517	687	20	and	and	CCONJ
ejde-517	687	21	‖b2(χδ1	‖b2(χδ1	NOUN
ejde-517	687	22	;	;	PUNCT
ejde-517	687	23	δχδ1)‖l1(ω	δχδ1)‖l1(ω	PROPN
ejde-517	687	24	)	)	PUNCT
ejde-517	687	25	≤	≤	NUM
ejde-517	687	26	c2η‖δχ1‖l2(ω)‖∇φ(χδ1)‖l∞(ω)‖∇φ∗(χδ1)‖l2(ω	c2η‖δχ1‖l2(ω)‖∇φ(χδ1)‖l∞(ω)‖∇φ∗(χδ1)‖l2(ω	NOUN
ejde-517	687	27	)	)	PUNCT
ejde-517	687	28	,	,	PUNCT
ejde-517	687	29	(	(	PUNCT
ejde-517	687	30	4.6	4.6	NUM
ejde-517	687	31	)	)	PUNCT
ejde-517	687	32	for	for	ADP
ejde-517	687	33	some	some	DET
ejde-517	687	34	c2	c2	PROPN
ejde-517	687	35	>	>	X
ejde-517	687	36	0	0	X
ejde-517	687	37	.	.	PUNCT
ejde-517	688	1	also	also	ADV
ejde-517	688	2	,	,	PUNCT
ejde-517	688	3	a2(χδ1	a2(χδ1	X
ejde-517	688	4	+	+	PUNCT
ejde-517	688	5	ηδχδ1)−a2(χδ1	ηδχδ1)−a2(χδ1	VERB
ejde-517	688	6	)	)	PUNCT
ejde-517	688	7	can	can	AUX
ejde-517	688	8	be	be	AUX
ejde-517	688	9	estimated	estimate	VERB
ejde-517	688	10	using	use	VERB
ejde-517	688	11	(	(	PUNCT
ejde-517	688	12	3.76	3.76	NUM
ejde-517	688	13	)	)	PUNCT
ejde-517	688	14	and	and	CCONJ
ejde-517	688	15	(	(	PUNCT
ejde-517	688	16	3.78	3.78	NUM
ejde-517	688	17	):	):	PUNCT
ejde-517	688	18	‖a2(χδ1	‖a2(χδ1	NOUN
ejde-517	688	19	+	+	CCONJ
ejde-517	688	20	ηδχδ1)−a2(χδ1)‖l2(ω	ηδχδ1)−a2(χδ1)‖l2(ω	ADJ
ejde-517	688	21	)	)	PUNCT
ejde-517	688	22	≤	≤	NUM
ejde-517	688	23	αωc3η‖δχ1‖l2(ω	αωc3η‖δχ1‖l2(ω	ADV
ejde-517	688	24	)	)	PUNCT
ejde-517	688	25	{	{	PUNCT
ejde-517	688	26	‖σ1(χδ1ηδχ	‖σ1(χδ1ηδχ	NUM
ejde-517	688	27	δ	δ	PROPN
ejde-517	688	28	1)‖l∞(ω	1)‖l∞(ω	NUM
ejde-517	688	29	)	)	PUNCT
ejde-517	689	1	+	+	CCONJ
ejde-517	689	2	‖σ1(χδ1)‖l∞(ω	‖σ1(χδ1)‖l∞(ω	NOUN
ejde-517	689	3	)	)	PUNCT
ejde-517	689	4	}	}	PUNCT
ejde-517	689	5	,	,	PUNCT
ejde-517	689	6	(	(	PUNCT
ejde-517	689	7	4.7	4.7	NUM
ejde-517	689	8	)	)	PUNCT
ejde-517	689	9	for	for	ADP
ejde-517	689	10	some	some	DET
ejde-517	689	11	c3	c3	PROPN
ejde-517	689	12	>	>	X
ejde-517	689	13	0	0	X
ejde-517	689	14	.	.	PUNCT
ejde-517	690	1	comparing	compare	VERB
ejde-517	690	2	(	(	PUNCT
ejde-517	690	3	4.4	4.4	NUM
ejde-517	690	4	)	)	PUNCT
ejde-517	690	5	,	,	PUNCT
ejde-517	690	6	(	(	PUNCT
ejde-517	690	7	4.5	4.5	NUM
ejde-517	690	8	)	)	PUNCT
ejde-517	690	9	,	,	PUNCT
ejde-517	690	10	(	(	PUNCT
ejde-517	690	11	4.6	4.6	NUM
ejde-517	690	12	)	)	PUNCT
ejde-517	690	13	,	,	PUNCT
ejde-517	690	14	and	and	CCONJ
ejde-517	690	15	(	(	PUNCT
ejde-517	690	16	4.7	4.7	NUM
ejde-517	690	17	)	)	PUNCT
ejde-517	690	18	implies	imply	VERB
ejde-517	690	19	the	the	DET
ejde-517	690	20	existence	existence	NOUN
ejde-517	690	21	of	of	ADP
ejde-517	690	22	a	a	PRON
ejde-517	690	23	c	c	NOUN
ejde-517	690	24	>	>	X
ejde-517	690	25	0	0	NUM
ejde-517	690	26	such	such	ADJ
ejde-517	690	27	that	that	SCONJ
ejde-517	690	28	‖g(χδ1	‖g(χδ1	NUM
ejde-517	690	29	+	+	CCONJ
ejde-517	690	30	ηδχδ1)−g(χδ1)‖l2(ω	ηδχδ1)−g(χδ1)‖l2(ω	ADJ
ejde-517	690	31	)	)	PUNCT
ejde-517	690	32	≤	≤	NOUN
ejde-517	690	33	cη‖δχ1‖l2(ω	cη‖δχ1‖l2(ω	NOUN
ejde-517	690	34	)	)	PUNCT
ejde-517	690	35	,	,	PUNCT
ejde-517	690	36	for	for	ADP
ejde-517	690	37	any	any	DET
ejde-517	690	38	η	η	PROPN
ejde-517	690	39	∈	∈	PROPN
ejde-517	690	40	(	(	PUNCT
ejde-517	690	41	0	0	NUM
ejde-517	690	42	,	,	PUNCT
ejde-517	690	43	τ̂	τ̂	NUM
ejde-517	690	44	)	)	PUNCT
ejde-517	690	45	,	,	PUNCT
ejde-517	690	46	where	where	SCONJ
ejde-517	690	47	τ̂	τ̂	PUNCT
ejde-517	690	48	=	=	SYM
ejde-517	690	49	min	min	X
ejde-517	690	50	{	{	PUNCT
ejde-517	690	51	τ	τ	PROPN
ejde-517	690	52	,	,	PUNCT
ejde-517	690	53	τ̄	τ̄	PROPN
ejde-517	690	54	}	}	PUNCT
ejde-517	690	55	,	,	PUNCT
ejde-517	690	56	τ	τ	PROPN
ejde-517	690	57	and	and	CCONJ
ejde-517	690	58	τ̄	τ̄	NOUN
ejde-517	690	59	are	be	AUX
ejde-517	690	60	both	both	ADV
ejde-517	690	61	chosen	choose	VERB
ejde-517	690	62	according	accord	VERB
ejde-517	690	63	to	to	PART
ejde-517	690	64	remark	remark	NOUN
ejde-517	690	65	3.4	3.4	NUM
ejde-517	690	66	and	and	CCONJ
ejde-517	690	67	remark	remark	NOUN
ejde-517	690	68	3.26	3.26	NUM
ejde-517	690	69	,	,	PUNCT
ejde-517	690	70	respectively	respectively	ADV
ejde-517	690	71	.	.	PUNCT
ejde-517	691	1	taking	take	VERB
ejde-517	691	2	the	the	DET
ejde-517	691	3	limit	limit	NOUN
ejde-517	691	4	of	of	ADP
ejde-517	691	5	the	the	DET
ejde-517	691	6	above	above	ADJ
ejde-517	691	7	inequality	inequality	NOUN
ejde-517	691	8	as	as	ADP
ejde-517	691	9	η	η	PROPN
ejde-517	691	10	→	→	SYM
ejde-517	691	11	0	0	NUM
ejde-517	691	12	gives	give	VERB
ejde-517	691	13	us	we	PRON
ejde-517	691	14	our	our	PRON
ejde-517	691	15	desired	desire	VERB
ejde-517	691	16	result	result	NOUN
ejde-517	691	17	.	.	PUNCT
ejde-517	692	1	�	�	PROPN
ejde-517	692	2	now	now	ADV
ejde-517	692	3	that	that	SCONJ
ejde-517	692	4	we	we	PRON
ejde-517	692	5	have	have	AUX
ejde-517	692	6	shown	show	VERB
ejde-517	692	7	the	the	DET
ejde-517	692	8	continuity	continuity	NOUN
ejde-517	692	9	of	of	ADP
ejde-517	692	10	the	the	DET
ejde-517	692	11	function	function	NOUN
ejde-517	692	12	g	g	NOUN
ejde-517	692	13	,	,	PUNCT
ejde-517	692	14	we	we	PRON
ejde-517	692	15	prove	prove	VERB
ejde-517	692	16	the	the	DET
ejde-517	692	17	continuity	continuity	NOUN
ejde-517	692	18	of	of	ADP
ejde-517	692	19	the	the	DET
ejde-517	692	20	operator	operator	NOUN
ejde-517	692	21	θ	θ	PROPN
ejde-517	692	22	(	(	PUNCT
ejde-517	692	23	see	see	VERB
ejde-517	692	24	definition	definition	NOUN
ejde-517	692	25	2.6	2.6	NUM
ejde-517	692	26	)	)	PUNCT
ejde-517	692	27	.	.	PUNCT
ejde-517	693	1	before	before	ADP
ejde-517	693	2	proving	prove	VERB
ejde-517	693	3	continuity	continuity	NOUN
ejde-517	693	4	,	,	PUNCT
ejde-517	693	5	we	we	PRON
ejde-517	693	6	first	first	ADV
ejde-517	693	7	show	show	VERB
ejde-517	693	8	that	that	SCONJ
ejde-517	693	9	given	give	VERB
ejde-517	693	10	χδ1	χδ1	NUM
ejde-517	693	11	,	,	PUNCT
ejde-517	693	12	(	(	PUNCT
ejde-517	693	13	2.16	2.16	NUM
ejde-517	693	14	)	)	PUNCT
ejde-517	693	15	has	have	VERB
ejde-517	693	16	a	a	DET
ejde-517	693	17	solution	solution	NOUN
ejde-517	693	18	in	in	ADP
ejde-517	693	19	h1(ω	h1(ω	PROPN
ejde-517	693	20	)	)	PUNCT
ejde-517	693	21	.	.	PUNCT
ejde-517	694	1	note	note	VERB
ejde-517	694	2	that	that	SCONJ
ejde-517	694	3	because	because	SCONJ
ejde-517	694	4	χδ1	χδ1	NUM
ejde-517	694	5	∈	∈	PROPN
ejde-517	694	6	c∞(ω	c∞(ω	NOUN
ejde-517	694	7	)	)	PUNCT
ejde-517	694	8	,	,	PUNCT
ejde-517	694	9	∇χδ1	∇χδ1	PROPN
ejde-517	694	10	is	be	AUX
ejde-517	694	11	bounded	bound	VERB
ejde-517	694	12	in	in	ADP
ejde-517	694	13	ω	ω	PROPN
ejde-517	694	14	for	for	ADP
ejde-517	694	15	a	a	DET
ejde-517	694	16	fixed	fix	VERB
ejde-517	694	17	δ	δ	PROPN
ejde-517	694	18	.	.	PUNCT
ejde-517	695	1	hence,√	hence,√	ADJ
ejde-517	695	2	|∇χδ1|2	|∇χδ1|2	PUNCT
ejde-517	696	1	+	+	CCONJ
ejde-517	696	2	β2	β2	ADJ
ejde-517	696	3	≤	≤	NOUN
ejde-517	696	4	√	√	PUNCT
ejde-517	696	5	‖∇χδ1‖2l∞(ω	‖∇χδ1‖2l∞(ω	NOUN
ejde-517	696	6	)	)	PUNCT
ejde-517	697	1	+	+	NUM
ejde-517	697	2	β2	β2	NOUN
ejde-517	697	3	=	=	NOUN
ejde-517	697	4	:	:	PUNCT
ejde-517	697	5	k̄	k̄	X
ejde-517	697	6	<	<	X
ejde-517	697	7	∞.	∞.	PROPN
ejde-517	697	8	or	or	CCONJ
ejde-517	697	9	equivalently	equivalently	ADV
ejde-517	697	10	,	,	PUNCT
ejde-517	697	11	1√	1√	PROPN
ejde-517	697	12	|∇χδ1|2	|∇χδ1|2	ADJ
ejde-517	697	13	+	+	CCONJ
ejde-517	697	14	β2	β2	NOUN
ejde-517	697	15	≥	≥	NOUN
ejde-517	697	16	1	1	NUM
ejde-517	697	17	k̄	k̄	ADV
ejde-517	697	18	.	.	PUNCT
ejde-517	698	1	(	(	PUNCT
ejde-517	698	2	4.8	4.8	NUM
ejde-517	698	3	)	)	PUNCT
ejde-517	698	4	24	24	NUM
ejde-517	698	5	r.	r.	PROPN
ejde-517	698	6	mendoza	mendoza	PROPN
ejde-517	698	7	,	,	PUNCT
ejde-517	698	8	s.	s.	PROPN
ejde-517	698	9	keeling	keeling	PROPN
ejde-517	698	10	ejde-2020/93	ejde-2020/93	PROPN
ejde-517	698	11	obviously	obviously	ADV
ejde-517	698	12	,	,	PUNCT
ejde-517	698	13	for	for	ADP
ejde-517	698	14	any	any	DET
ejde-517	698	15	β	β	X
ejde-517	698	16	>	>	X
ejde-517	698	17	0	0	NUM
ejde-517	698	18	,	,	PUNCT
ejde-517	698	19	√	√	ADP
ejde-517	698	20	|∇χδ1|2	|∇χδ1|2	NUM
ejde-517	698	21	+	+	CCONJ
ejde-517	698	22	β2	β2	PROPN
ejde-517	698	23	≥	≥	PROPN
ejde-517	698	24	β	β	NOUN
ejde-517	698	25	,	,	PUNCT
ejde-517	698	26	which	which	PRON
ejde-517	698	27	can	can	AUX
ejde-517	698	28	be	be	AUX
ejde-517	698	29	expressed	express	VERB
ejde-517	698	30	as	as	ADP
ejde-517	698	31	1√	1√	PROPN
ejde-517	698	32	|∇χδ1|2	|∇χδ1|2	PROPN
ejde-517	698	33	+	+	CCONJ
ejde-517	698	34	β2	β2	NOUN
ejde-517	698	35	≤	≤	NOUN
ejde-517	698	36	1	1	NUM
ejde-517	698	37	β	β	NOUN
ejde-517	698	38	.	.	PUNCT
ejde-517	699	1	(	(	PUNCT
ejde-517	699	2	4.9	4.9	NUM
ejde-517	699	3	)	)	PUNCT
ejde-517	699	4	for	for	ADP
ejde-517	699	5	u	u	NOUN
ejde-517	699	6	,	,	PUNCT
ejde-517	699	7	v	v	ADP
ejde-517	699	8	∈	∈	PROPN
ejde-517	699	9	h1(ω	h1(ω	PROPN
ejde-517	699	10	)	)	PUNCT
ejde-517	699	11	,	,	PUNCT
ejde-517	699	12	we	we	PRON
ejde-517	699	13	define	define	VERB
ejde-517	699	14	a(u	a(u	PROPN
ejde-517	699	15	,	,	PUNCT
ejde-517	699	16	v	v	NOUN
ejde-517	699	17	)	)	PUNCT
ejde-517	699	18	=	=	SYM
ejde-517	700	1	∫	∫	PROPN
ejde-517	700	2	ω	ω	NUM
ejde-517	700	3	ωγ	ωγ	PROPN
ejde-517	700	4	∇u	∇u	PROPN
ejde-517	700	5	·	·	PUNCT
ejde-517	700	6	∇v√	∇v√	PROPN
ejde-517	700	7	|∇χδ1|2	|∇χδ1|2	PROPN
ejde-517	701	1	+	+	CCONJ
ejde-517	701	2	β2	β2	NOUN
ejde-517	701	3	+	+	CCONJ
ejde-517	701	4	uv	uv	PROPN
ejde-517	701	5	dv	dv	PROPN
ejde-517	701	6	,	,	PUNCT
ejde-517	701	7	(	(	PUNCT
ejde-517	701	8	4.10	4.10	NUM
ejde-517	701	9	)	)	PUNCT
ejde-517	701	10	b(v	b(v	NOUN
ejde-517	701	11	)	)	PUNCT
ejde-517	702	1	=	=	SYM
ejde-517	702	2	∫	∫	PROPN
ejde-517	702	3	ω	ω	PROPN
ejde-517	702	4	g(χδ1)v	g(χδ1)v	PROPN
ejde-517	702	5	dv	dv	PROPN
ejde-517	702	6	.	.	PROPN
ejde-517	702	7	clearly	clearly	ADV
ejde-517	702	8	,	,	PUNCT
ejde-517	702	9	a	a	PRON
ejde-517	702	10	and	and	CCONJ
ejde-517	702	11	b	b	NOUN
ejde-517	702	12	are	be	AUX
ejde-517	702	13	bilinear	bilinear	NOUN
ejde-517	702	14	and	and	CCONJ
ejde-517	702	15	linear	linear	ADJ
ejde-517	702	16	,	,	PUNCT
ejde-517	702	17	respectively	respectively	ADV
ejde-517	702	18	.	.	PUNCT
ejde-517	703	1	observe	observe	VERB
ejde-517	703	2	that	that	SCONJ
ejde-517	703	3	using	use	VERB
ejde-517	703	4	the	the	DET
ejde-517	703	5	cauchyschwarz	cauchyschwarz	PROPN
ejde-517	703	6	inequality	inequality	NOUN
ejde-517	703	7	and	and	CCONJ
ejde-517	703	8	(	(	PUNCT
ejde-517	703	9	4.9	4.9	NUM
ejde-517	703	10	)	)	PUNCT
ejde-517	703	11	,	,	PUNCT
ejde-517	703	12	we	we	PRON
ejde-517	703	13	obtain	obtain	VERB
ejde-517	703	14	|a(u	|a(u	PROPN
ejde-517	703	15	,	,	PUNCT
ejde-517	703	16	v)|	v)|	NOUN
ejde-517	703	17	≤	≤	ADJ
ejde-517	703	18	2	2	NUM
ejde-517	703	19	max{ωγ	max{ωγ	NOUN
ejde-517	703	20	β	β	X
ejde-517	703	21	,	,	PUNCT
ejde-517	703	22	1}‖u‖h1(ω)‖v‖h1(ω	1}‖u‖h1(ω)‖v‖h1(ω	NUM
ejde-517	703	23	)	)	PUNCT
ejde-517	703	24	,	,	PUNCT
ejde-517	703	25	for	for	ADP
ejde-517	703	26	all	all	PRON
ejde-517	703	27	v	v	ADP
ejde-517	703	28	∈	∈	PROPN
ejde-517	703	29	h1(ω	h1(ω	PROPN
ejde-517	703	30	)	)	PUNCT
ejde-517	703	31	,	,	PUNCT
ejde-517	703	32	which	which	PRON
ejde-517	703	33	makes	make	VERB
ejde-517	703	34	a	a	DET
ejde-517	703	35	continuous	continuous	ADJ
ejde-517	703	36	.	.	PUNCT
ejde-517	704	1	it	it	PRON
ejde-517	704	2	can	can	AUX
ejde-517	704	3	also	also	ADV
ejde-517	704	4	be	be	AUX
ejde-517	704	5	shown	show	VERB
ejde-517	704	6	using	use	VERB
ejde-517	704	7	the	the	DET
ejde-517	704	8	cauchy	cauchy	PROPN
ejde-517	704	9	-	-	PUNCT
ejde-517	704	10	schwarz	schwarz	PROPN
ejde-517	704	11	inequality	inequality	NOUN
ejde-517	704	12	that	that	SCONJ
ejde-517	704	13	b(v	b(v	NOUN
ejde-517	704	14	)	)	PUNCT
ejde-517	704	15	is	be	AUX
ejde-517	704	16	also	also	ADV
ejde-517	704	17	continuous	continuous	ADJ
ejde-517	704	18	.	.	PUNCT
ejde-517	705	1	using	use	VERB
ejde-517	705	2	(	(	PUNCT
ejde-517	705	3	4.9	4.9	NUM
ejde-517	705	4	)	)	PUNCT
ejde-517	705	5	,	,	PUNCT
ejde-517	705	6	a	a	PRON
ejde-517	705	7	can	can	AUX
ejde-517	705	8	be	be	AUX
ejde-517	705	9	proven	prove	VERB
ejde-517	705	10	to	to	PART
ejde-517	705	11	be	be	AUX
ejde-517	705	12	coercive	coercive	ADJ
ejde-517	705	13	.	.	PUNCT
ejde-517	706	1	therefore	therefore	ADV
ejde-517	706	2	,	,	PUNCT
ejde-517	706	3	using	use	VERB
ejde-517	706	4	the	the	DET
ejde-517	706	5	lax	lax	PROPN
ejde-517	706	6	-	-	PUNCT
ejde-517	706	7	milgram	milgram	NOUN
ejde-517	706	8	theorem	theorem	NOUN
ejde-517	706	9	,	,	PUNCT
ejde-517	706	10	there	there	PRON
ejde-517	706	11	exists	exist	VERB
ejde-517	706	12	a	a	DET
ejde-517	706	13	unique	unique	ADJ
ejde-517	706	14	θ	θ	NOUN
ejde-517	706	15	∈	∈	PROPN
ejde-517	706	16	h1(ω	h1(ω	PROPN
ejde-517	706	17	)	)	PUNCT
ejde-517	706	18	satisfying	satisfying	ADJ
ejde-517	706	19	a(θ	a(θ	PROPN
ejde-517	706	20	,	,	PUNCT
ejde-517	706	21	v	v	NOUN
ejde-517	706	22	)	)	PUNCT
ejde-517	706	23	=	=	SYM
ejde-517	706	24	b(v	b(v	NOUN
ejde-517	706	25	)	)	PUNCT
ejde-517	706	26	]	]	PUNCT
ejde-517	706	27	for	for	ADP
ejde-517	706	28	all	all	PRON
ejde-517	706	29	v	v	ADP
ejde-517	706	30	∈	∈	PROPN
ejde-517	706	31	h1(ω	h1(ω	PROPN
ejde-517	706	32	)	)	PUNCT
ejde-517	706	33	.	.	PUNCT
ejde-517	707	1	lemma	lemma	PROPN
ejde-517	707	2	4.3	4.3	NUM
ejde-517	707	3	.	.	PUNCT
ejde-517	708	1	under	under	ADP
ejde-517	708	2	assumption	assumption	NOUN
ejde-517	708	3	(	(	PUNCT
ejde-517	708	4	3.30	3.30	NUM
ejde-517	708	5	)	)	PUNCT
ejde-517	708	6	,	,	PUNCT
ejde-517	708	7	there	there	PRON
ejde-517	708	8	exists	exist	VERB
ejde-517	708	9	a	a	DET
ejde-517	708	10	unique	unique	ADJ
ejde-517	708	11	θ	θ	NOUN
ejde-517	708	12	∈	∈	PROPN
ejde-517	708	13	h1(ω	h1(ω	PROPN
ejde-517	708	14	)	)	PUNCT
ejde-517	708	15	satisfying∫	satisfying∫	NOUN
ejde-517	708	16	ω	ω	PROPN
ejde-517	708	17	ωγ	ωγ	ADP
ejde-517	708	18	∇θ	∇θ	PROPN
ejde-517	708	19	·	·	PUNCT
ejde-517	708	20	∇v√	∇v√	PROPN
ejde-517	708	21	|∇χδ1|2	|∇χδ1|2	PUNCT
ejde-517	709	1	+	+	CCONJ
ejde-517	709	2	β2	β2	NOUN
ejde-517	709	3	+	+	CCONJ
ejde-517	709	4	θv	θv	PROPN
ejde-517	709	5	dv	dv	PROPN
ejde-517	709	6	=	=	SYM
ejde-517	709	7	∫	∫	PROPN
ejde-517	709	8	ω	ω	PROPN
ejde-517	709	9	g(χδ1)v	g(χδ1)v	PROPN
ejde-517	709	10	dv	dv	PROPN
ejde-517	709	11	,	,	PUNCT
ejde-517	709	12	(	(	PUNCT
ejde-517	709	13	4.11	4.11	NUM
ejde-517	709	14	)	)	PUNCT
ejde-517	709	15	for	for	ADP
ejde-517	709	16	any	any	DET
ejde-517	709	17	v	v	NOUN
ejde-517	709	18	∈	∈	PROPN
ejde-517	709	19	h1(ω	h1(ω	PRON
ejde-517	709	20	)	)	PUNCT
ejde-517	709	21	provided	provide	VERB
ejde-517	709	22	that	that	SCONJ
ejde-517	709	23	∂v	∂v	PROPN
ejde-517	709	24	∂n	∂n	PROPN
ejde-517	710	1	=	=	PUNCT
ejde-517	710	2	0	0	NUM
ejde-517	710	3	on	on	ADP
ejde-517	710	4	∂ω	∂ω	PROPN
ejde-517	710	5	.	.	PUNCT
ejde-517	711	1	furthermore	furthermore	ADV
ejde-517	711	2	,	,	PUNCT
ejde-517	711	3	there	there	PRON
ejde-517	711	4	exists	exist	VERB
ejde-517	711	5	c	c	NOUN
ejde-517	711	6	>	>	X
ejde-517	711	7	0	0	NUM
ejde-517	711	8	such	such	ADJ
ejde-517	711	9	that	that	DET
ejde-517	711	10	‖θ‖h1(ω	‖θ‖h1(ω	NOUN
ejde-517	711	11	)	)	PUNCT
ejde-517	711	12	≤	≤	NUM
ejde-517	711	13	1	1	NUM
ejde-517	711	14	min{ωγ	min{ωγ	ADV
ejde-517	711	15	k̄	k̄	X
ejde-517	711	16	,	,	PUNCT
ejde-517	711	17	1	1	X
ejde-517	711	18	}	}	PUNCT
ejde-517	711	19	‖g(χδ1)‖l2(ω	‖g(χδ1)‖l2(ω	ADV
ejde-517	711	20	)	)	PUNCT
ejde-517	711	21	.	.	PUNCT
ejde-517	712	1	the	the	DET
ejde-517	712	2	above	above	ADJ
ejde-517	712	3	lemma	lemma	PROPN
ejde-517	712	4	tells	tell	VERB
ejde-517	712	5	us	we	PRON
ejde-517	712	6	that	that	SCONJ
ejde-517	712	7	given	give	VERB
ejde-517	712	8	χ1	χ1	NOUN
ejde-517	712	9	,	,	PUNCT
ejde-517	712	10	a	a	DET
ejde-517	712	11	mollification	mollification	NOUN
ejde-517	712	12	can	can	AUX
ejde-517	712	13	be	be	AUX
ejde-517	712	14	performed	perform	VERB
ejde-517	712	15	to	to	PART
ejde-517	712	16	obtain	obtain	VERB
ejde-517	712	17	a	a	DET
ejde-517	712	18	unique	unique	ADJ
ejde-517	712	19	solution	solution	NOUN
ejde-517	712	20	θ	θ	X
ejde-517	712	21	∈	∈	PROPN
ejde-517	712	22	h1(ω	h1(ω	PROPN
ejde-517	712	23	)	)	PUNCT
ejde-517	712	24	to	to	ADP
ejde-517	712	25	(	(	PUNCT
ejde-517	712	26	4.11	4.11	NUM
ejde-517	712	27	)	)	PUNCT
ejde-517	712	28	.	.	PUNCT
ejde-517	713	1	hence	hence	ADV
ejde-517	713	2	,	,	PUNCT
ejde-517	713	3	we	we	PRON
ejde-517	713	4	can	can	AUX
ejde-517	713	5	think	think	VERB
ejde-517	713	6	of	of	ADP
ejde-517	713	7	θ(χδ1	θ(χδ1	PROPN
ejde-517	713	8	)	)	PUNCT
ejde-517	713	9	as	as	ADP
ejde-517	713	10	a	a	DET
ejde-517	713	11	function	function	NOUN
ejde-517	713	12	that	that	PRON
ejde-517	713	13	maps	map	VERB
ejde-517	713	14	an	an	DET
ejde-517	713	15	element	element	NOUN
ejde-517	713	16	χ1	χ1	NOUN
ejde-517	713	17	∈	∈	PROPN
ejde-517	713	18	l2(ω	l2(ω	NOUN
ejde-517	713	19	)	)	PUNCT
ejde-517	713	20	to	to	ADP
ejde-517	713	21	an	an	DET
ejde-517	713	22	element	element	NOUN
ejde-517	713	23	θ	θ	PROPN
ejde-517	713	24	∈	∈	PROPN
ejde-517	713	25	h1(ω	h1(ω	PROPN
ejde-517	713	26	)	)	PUNCT
ejde-517	713	27	.	.	PUNCT
ejde-517	714	1	note	note	VERB
ejde-517	714	2	that	that	SCONJ
ejde-517	714	3	given	give	VERB
ejde-517	714	4	a	a	DET
ejde-517	714	5	perturbation	perturbation	NOUN
ejde-517	714	6	δχδ1	δχδ1	NOUN
ejde-517	714	7	of	of	ADP
ejde-517	714	8	χδ1	χδ1	PROPN
ejde-517	714	9	,	,	PUNCT
ejde-517	714	10	θ(χδ1	θ(χδ1	PROPN
ejde-517	714	11	+	+	CCONJ
ejde-517	714	12	ηδχδ1	ηδχδ1	X
ejde-517	714	13	)	)	PUNCT
ejde-517	714	14	is	be	AUX
ejde-517	714	15	well	well	ADV
ejde-517	714	16	-	-	PUNCT
ejde-517	714	17	defined	define	VERB
ejde-517	714	18	for	for	ADP
ejde-517	714	19	any	any	DET
ejde-517	714	20	0	0	PUNCT
ejde-517	714	21	<	<	X
ejde-517	714	22	η	η	X
ejde-517	714	23	<	<	X
ejde-517	714	24	∞	∞	PROPN
ejde-517	714	25	because	because	SCONJ
ejde-517	714	26	for	for	ADP
ejde-517	714	27	coercivity	coercivity	NOUN
ejde-517	714	28	we	we	PRON
ejde-517	714	29	just	just	ADV
ejde-517	714	30	need	need	VERB
ejde-517	714	31	√	√	NOUN
ejde-517	714	32	‖∇(χδ1	‖∇(χδ1	NOUN
ejde-517	715	1	+	+	CCONJ
ejde-517	715	2	ηδχδ1)‖2l∞(ω	ηδχδ1)‖2l∞(ω	NOUN
ejde-517	715	3	)	)	PUNCT
ejde-517	716	1	+	+	CCONJ
ejde-517	716	2	β2	β2	VERB
ejde-517	716	3	to	to	PART
ejde-517	716	4	be	be	AUX
ejde-517	716	5	finite	finite	VERB
ejde-517	716	6	.	.	PUNCT
ejde-517	717	1	since	since	SCONJ
ejde-517	717	2	χδ1	χδ1	NOUN
ejde-517	717	3	+	+	CCONJ
ejde-517	717	4	ηδχδ1	ηδχδ1	VERB
ejde-517	717	5	∈	∈	NOUN
ejde-517	717	6	c∞(ω̄	c∞(ω̄	NOUN
ejde-517	717	7	)	)	PUNCT
ejde-517	717	8	,	,	PUNCT
ejde-517	717	9	this	this	PRON
ejde-517	717	10	is	be	AUX
ejde-517	717	11	not	not	PART
ejde-517	717	12	a	a	DET
ejde-517	717	13	problem	problem	NOUN
ejde-517	717	14	.	.	PUNCT
ejde-517	718	1	from	from	ADP
ejde-517	718	2	the	the	DET
ejde-517	718	3	definition	definition	NOUN
ejde-517	718	4	of	of	ADP
ejde-517	718	5	g	g	PROPN
ejde-517	718	6	and	and	CCONJ
ejde-517	718	7	the	the	DET
ejde-517	718	8	inequalities	inequality	NOUN
ejde-517	718	9	(	(	PUNCT
ejde-517	718	10	3.37	3.37	NUM
ejde-517	718	11	)	)	PUNCT
ejde-517	718	12	,	,	PUNCT
ejde-517	718	13	(	(	PUNCT
ejde-517	718	14	3.38	3.38	NUM
ejde-517	718	15	)	)	PUNCT
ejde-517	718	16	,	,	PUNCT
ejde-517	718	17	and	and	CCONJ
ejde-517	718	18	(	(	PUNCT
ejde-517	718	19	3.76	3.76	NUM
ejde-517	718	20	)	)	PUNCT
ejde-517	718	21	,	,	PUNCT
ejde-517	718	22	we	we	PRON
ejde-517	718	23	can	can	AUX
ejde-517	718	24	infer	infer	VERB
ejde-517	718	25	that	that	SCONJ
ejde-517	718	26	‖θ(χδ1	‖θ(χδ1	NUM
ejde-517	719	1	+	+	X
ejde-517	719	2	ηδχδ1)‖h1(ω	ηδχδ1)‖h1(ω	NOUN
ejde-517	719	3	)	)	PUNCT
ejde-517	719	4	≤	≤	NOUN
ejde-517	719	5	c‖g(χδ1	c‖g(χδ1	NUM
ejde-517	719	6	+	+	CCONJ
ejde-517	719	7	ηδχδ1)‖l2(ω	ηδχδ1)‖l2(ω	ADJ
ejde-517	719	8	)	)	PUNCT
ejde-517	719	9	<	<	X
ejde-517	719	10	∞	∞	PROPN
ejde-517	719	11	,	,	PUNCT
ejde-517	719	12	(	(	PUNCT
ejde-517	719	13	4.12	4.12	NUM
ejde-517	719	14	)	)	PUNCT
ejde-517	719	15	for	for	ADP
ejde-517	719	16	some	some	DET
ejde-517	719	17	c	c	PROPN
ejde-517	719	18	>	>	X
ejde-517	719	19	0	0	X
ejde-517	719	20	.	.	PUNCT
ejde-517	720	1	we	we	PRON
ejde-517	720	2	now	now	ADV
ejde-517	720	3	prove	prove	VERB
ejde-517	720	4	that	that	SCONJ
ejde-517	720	5	this	this	DET
ejde-517	720	6	map	map	NOUN
ejde-517	720	7	is	be	AUX
ejde-517	720	8	continuous	continuous	ADJ
ejde-517	720	9	.	.	PUNCT
ejde-517	721	1	lemma	lemma	PROPN
ejde-517	721	2	4.4	4.4	NUM
ejde-517	721	3	.	.	PUNCT
ejde-517	722	1	under	under	ADP
ejde-517	722	2	assumption	assumption	NOUN
ejde-517	722	3	(	(	PUNCT
ejde-517	722	4	3.30	3.30	NUM
ejde-517	722	5	)	)	PUNCT
ejde-517	722	6	,	,	PUNCT
ejde-517	722	7	lim	lim	PROPN
ejde-517	722	8	η→0	η→0	X
ejde-517	722	9	‖θ(χδ1	‖θ(χδ1	X
ejde-517	722	10	+	+	X
ejde-517	722	11	ηδχδ1)−θ(χδ1)‖h1(ω	ηδχδ1)−θ(χδ1)‖h1(ω	PROPN
ejde-517	722	12	)	)	PUNCT
ejde-517	722	13	=	=	SYM
ejde-517	722	14	0	0	X
ejde-517	722	15	.	.	PUNCT
ejde-517	722	16	proof	proof	NOUN
ejde-517	722	17	.	.	PUNCT
ejde-517	723	1	by	by	ADP
ejde-517	723	2	the	the	DET
ejde-517	723	3	previous	previous	ADJ
ejde-517	723	4	lemma	lemma	PROPN
ejde-517	723	5	,	,	PUNCT
ejde-517	723	6	note	note	VERB
ejde-517	723	7	that	that	SCONJ
ejde-517	723	8	θ(χδ1	θ(χδ1	NOUN
ejde-517	723	9	)	)	PUNCT
ejde-517	723	10	satisfies∫	satisfies∫	PUNCT
ejde-517	723	11	ω	ω	NUM
ejde-517	723	12	ωγ	ωγ	ADP
ejde-517	723	13	∇θ(χδ1	∇θ(χδ1	PROPN
ejde-517	723	14	)	)	PUNCT
ejde-517	723	15	·	·	PUNCT
ejde-517	724	1	∇v√	∇v√	PROPN
ejde-517	724	2	|∇χδ1|2	|∇χδ1|2	PUNCT
ejde-517	725	1	+	+	CCONJ
ejde-517	725	2	β2	β2	PROPN
ejde-517	725	3	+	+	CCONJ
ejde-517	725	4	θ(χδ1)v	θ(χδ1)v	PROPN
ejde-517	725	5	dv	dv	PROPN
ejde-517	725	6	=	=	PROPN
ejde-517	725	7	∫	∫	PROPN
ejde-517	725	8	ω	ω	PROPN
ejde-517	725	9	g(χδ1)v	g(χδ1)v	PROPN
ejde-517	725	10	dv	dv	PROPN
ejde-517	725	11	.	.	PUNCT
ejde-517	726	1	(	(	PUNCT
ejde-517	726	2	4.13	4.13	NUM
ejde-517	726	3	)	)	PUNCT
ejde-517	726	4	ejde-2020/93	ejde-2020/93	PROPN
ejde-517	726	5	impedance	impedance	NOUN
ejde-517	726	6	tomography	tomography	NOUN
ejde-517	726	7	problem	problem	NOUN
ejde-517	726	8	25	25	NUM
ejde-517	726	9	similarly	similarly	ADV
ejde-517	726	10	,	,	PUNCT
ejde-517	726	11	θ(χδ1	θ(χδ1	PROPN
ejde-517	726	12	+	+	CCONJ
ejde-517	726	13	ηδχδ1	ηδχδ1	ADJ
ejde-517	726	14	)	)	PUNCT
ejde-517	726	15	satisfies∫	satisfies∫	X
ejde-517	726	16	ω	ω	NOUN
ejde-517	726	17	ωγ	ωγ	ADP
ejde-517	726	18	∇θ(χδ1	∇θ(χδ1	PROPN
ejde-517	726	19	+	+	CCONJ
ejde-517	726	20	ηδχδ1	ηδχδ1	VERB
ejde-517	726	21	)	)	PUNCT
ejde-517	726	22	·	·	PUNCT
ejde-517	727	1	∇v√	∇v√	PROPN
ejde-517	727	2	|∇(χδ1	|∇(χδ1	ADJ
ejde-517	727	3	+	+	CCONJ
ejde-517	727	4	ηδχδ1)|2	ηδχδ1)|2	NOUN
ejde-517	727	5	+	+	CCONJ
ejde-517	727	6	β2	β2	NOUN
ejde-517	727	7	+	+	CCONJ
ejde-517	727	8	θ(χδ1	θ(χδ1	PROPN
ejde-517	728	1	+	+	CCONJ
ejde-517	728	2	ηδχδ1)v	ηδχδ1)v	PROPN
ejde-517	728	3	dv	dv	PROPN
ejde-517	728	4	=	=	SYM
ejde-517	728	5	∫	∫	PROPN
ejde-517	728	6	ω	ω	PROPN
ejde-517	728	7	g(χδ1	g(χδ1	VERB
ejde-517	728	8	+	+	PROPN
ejde-517	728	9	ηδχδ1)v	ηδχδ1)v	PROPN
ejde-517	728	10	dv	dv	PROPN
ejde-517	728	11	.	.	PROPN
ejde-517	729	1	(	(	PUNCT
ejde-517	729	2	4.14	4.14	NUM
ejde-517	729	3	)	)	PUNCT
ejde-517	729	4	subtracting	subtract	VERB
ejde-517	729	5	(	(	PUNCT
ejde-517	729	6	4.13	4.13	NUM
ejde-517	729	7	)	)	PUNCT
ejde-517	729	8	from	from	ADP
ejde-517	729	9	(	(	PUNCT
ejde-517	729	10	4.14	4.14	NUM
ejde-517	729	11	)	)	PUNCT
ejde-517	729	12	,	,	PUNCT
ejde-517	729	13	we	we	PRON
ejde-517	729	14	obtain	obtain	VERB
ejde-517	729	15	a1(v	a1(v	NOUN
ejde-517	729	16	)	)	PUNCT
ejde-517	730	1	+	+	NOUN
ejde-517	730	2	a2(v	a2(v	X
ejde-517	730	3	)	)	PUNCT
ejde-517	730	4	=	=	SYM
ejde-517	730	5	b(v	b(v	NOUN
ejde-517	730	6	)	)	PUNCT
ejde-517	730	7	,	,	PUNCT
ejde-517	730	8	(	(	PUNCT
ejde-517	730	9	4.15	4.15	NUM
ejde-517	730	10	)	)	PUNCT
ejde-517	730	11	with	with	ADP
ejde-517	730	12	a1(v	a1(v	NOUN
ejde-517	730	13	)	)	PUNCT
ejde-517	730	14	:	:	PUNCT
ejde-517	731	1	=	=	SYM
ejde-517	731	2	∫	∫	PROPN
ejde-517	731	3	ω	ω	INTJ
ejde-517	731	4	ωγ	ωγ	X
ejde-517	731	5	[	[	PUNCT
ejde-517	731	6	∇θ(χδ1	∇θ(χδ1	X
ejde-517	731	7	+	+	CCONJ
ejde-517	731	8	ηδχδ1	ηδχδ1	VERB
ejde-517	731	9	)	)	PUNCT
ejde-517	731	10	·	·	PUNCT
ejde-517	731	11	∇v√	∇v√	VERB
ejde-517	731	12	|∇χδ1	|∇χδ1	PROPN
ejde-517	731	13	+	+	CCONJ
ejde-517	731	14	ηδχδ1|2	ηδχδ1|2	X
ejde-517	731	15	+	+	CCONJ
ejde-517	731	16	β2	β2	NOUN
ejde-517	731	17	−	−	PROPN
ejde-517	731	18	∇θ(χδ1	∇θ(χδ1	PROPN
ejde-517	731	19	)	)	PUNCT
ejde-517	731	20	·	·	PUNCT
ejde-517	732	1	∇v√	∇v√	PROPN
ejde-517	732	2	|∇χδ1|2	|∇χδ1|2	PUNCT
ejde-517	733	1	+	+	NUM
ejde-517	733	2	β2	β2	PROPN
ejde-517	733	3	]	]	PUNCT
ejde-517	733	4	dv	dv	PROPN
ejde-517	733	5	,	,	PUNCT
ejde-517	733	6	a2(v	a2(v	PROPN
ejde-517	733	7	)	)	PUNCT
ejde-517	733	8	:	:	PUNCT
ejde-517	734	1	=	=	SYM
ejde-517	734	2	∫	∫	PROPN
ejde-517	735	1	ω	ω	PROPN
ejde-517	736	1	[	[	X
ejde-517	736	2	θ(χδ1	θ(χδ1	X
ejde-517	736	3	+	+	X
ejde-517	736	4	ηδχδ1)−θ(χδ1)]v	ηδχδ1)−θ(χδ1)]v	VERB
ejde-517	736	5	dv	dv	PROPN
ejde-517	736	6	,	,	PUNCT
ejde-517	736	7	b(v	b(v	NOUN
ejde-517	736	8	)	)	PUNCT
ejde-517	736	9	:	:	PUNCT
ejde-517	737	1	=	=	SYM
ejde-517	737	2	∫	∫	PROPN
ejde-517	737	3	ω	ω	PROPN
ejde-517	738	1	[	[	X
ejde-517	738	2	g(χδ1	g(χδ1	ADP
ejde-517	738	3	+	+	CCONJ
ejde-517	738	4	ηδχδ1)−g(χδ1)]v	ηδχδ1)−g(χδ1)]v	ADJ
ejde-517	738	5	dv	dv	PROPN
ejde-517	738	6	.	.	PUNCT
ejde-517	739	1	we	we	PRON
ejde-517	739	2	subtract	subtract	VERB
ejde-517	739	3	and	and	CCONJ
ejde-517	739	4	add	add	VERB
ejde-517	739	5	the	the	DET
ejde-517	739	6	term∫	term∫	ADJ
ejde-517	739	7	ω	ω	NOUN
ejde-517	739	8	ωγ	ωγ	ADP
ejde-517	739	9	∇θ(χδ1	∇θ(χδ1	PROPN
ejde-517	739	10	+	+	CCONJ
ejde-517	739	11	ηδχδ1	ηδχδ1	VERB
ejde-517	739	12	)	)	PUNCT
ejde-517	739	13	·	·	PUNCT
ejde-517	740	1	∇v√	∇v√	NOUN
ejde-517	740	2	|∇χδ1|2	|∇χδ1|2	PUNCT
ejde-517	741	1	+	+	CCONJ
ejde-517	741	2	β2	β2	PROPN
ejde-517	741	3	dv	dv	PROPN
ejde-517	741	4	to	to	ADP
ejde-517	741	5	a1(v	a1(v	PROPN
ejde-517	741	6	)	)	PUNCT
ejde-517	741	7	to	to	PART
ejde-517	741	8	obtain	obtain	VERB
ejde-517	741	9	a1(v	a1(v	NOUN
ejde-517	741	10	)	)	PUNCT
ejde-517	741	11	=	=	SYM
ejde-517	741	12	a3(v	a3(v	NOUN
ejde-517	741	13	)	)	PUNCT
ejde-517	741	14	+	+	NOUN
ejde-517	741	15	a4(v	a4(v	PROPN
ejde-517	741	16	)	)	PUNCT
ejde-517	741	17	,	,	PUNCT
ejde-517	741	18	(	(	PUNCT
ejde-517	741	19	4.16	4.16	NUM
ejde-517	741	20	)	)	PUNCT
ejde-517	741	21	with	with	ADP
ejde-517	741	22	a4(v	a4(v	PROPN
ejde-517	741	23	)	)	PUNCT
ejde-517	741	24	:	:	PUNCT
ejde-517	742	1	=	=	SYM
ejde-517	742	2	∫	∫	PROPN
ejde-517	742	3	ω	ω	NUM
ejde-517	742	4	ωγd(η	ωγd(η	PROPN
ejde-517	742	5	)	)	PUNCT
ejde-517	742	6	∇θ(χδ1	∇θ(χδ1	NOUN
ejde-517	742	7	+	+	CCONJ
ejde-517	742	8	ηδχδ1	ηδχδ1	VERB
ejde-517	742	9	)	)	PUNCT
ejde-517	742	10	·	·	PUNCT
ejde-517	742	11	∇v√	∇v√	VERB
ejde-517	742	12	|∇(χδ1)|2	|∇(χδ1)|2	NOUN
ejde-517	742	13	+	+	CCONJ
ejde-517	742	14	β2	β2	NOUN
ejde-517	742	15	,	,	PUNCT
ejde-517	742	16	a3(v	a3(v	X
ejde-517	742	17	)	)	PUNCT
ejde-517	742	18	:	:	PUNCT
ejde-517	743	1	=	=	SYM
ejde-517	743	2	∫	∫	PROPN
ejde-517	743	3	ω	ω	NUM
ejde-517	743	4	ωγ	ωγ	PROPN
ejde-517	743	5	[	[	X
ejde-517	743	6	∇θ(χδ1	∇θ(χδ1	X
ejde-517	743	7	+	+	X
ejde-517	743	8	ηδχδ1)−∇θ(χδ1	ηδχδ1)−∇θ(χδ1	PROPN
ejde-517	743	9	)	)	PUNCT
ejde-517	743	10	]	]	PUNCT
ejde-517	743	11	·	·	PUNCT
ejde-517	743	12	∇v√	∇v√	PROPN
ejde-517	743	13	|∇χδ1|2	|∇χδ1|2	PUNCT
ejde-517	744	1	+	+	CCONJ
ejde-517	744	2	β2	β2	PROPN
ejde-517	744	3	dv	dv	PROPN
ejde-517	744	4	,	,	PUNCT
ejde-517	744	5	d(η	d(η	PROPN
ejde-517	744	6	)	)	PUNCT
ejde-517	744	7	:	:	PUNCT
ejde-517	744	8	=	=	SYM
ejde-517	744	9	1√	1√	PROPN
ejde-517	744	10	|∇(χδ1	|∇(χδ1	NOUN
ejde-517	744	11	+	+	CCONJ
ejde-517	744	12	ηδχδ1)|2	ηδχδ1)|2	NOUN
ejde-517	744	13	+	+	CCONJ
ejde-517	744	14	β2	β2	NOUN
ejde-517	744	15	−	−	PROPN
ejde-517	744	16	1√	1√	PROPN
ejde-517	744	17	|∇χδ1|2	|∇χδ1|2	PROPN
ejde-517	744	18	+	+	CCONJ
ejde-517	744	19	β2	β2	NOUN
ejde-517	744	20	.	.	PUNCT
ejde-517	745	1	from	from	ADP
ejde-517	745	2	(	(	PUNCT
ejde-517	745	3	4.15	4.15	NUM
ejde-517	745	4	)	)	PUNCT
ejde-517	745	5	and	and	CCONJ
ejde-517	745	6	(	(	PUNCT
ejde-517	745	7	4.16	4.16	NUM
ejde-517	745	8	)	)	PUNCT
ejde-517	745	9	,	,	PUNCT
ejde-517	745	10	we	we	PRON
ejde-517	745	11	have	have	VERB
ejde-517	745	12	a3(v	a3(v	X
ejde-517	745	13	)	)	PUNCT
ejde-517	746	1	+	+	X
ejde-517	746	2	a2(v	a2(v	X
ejde-517	746	3	)	)	PUNCT
ejde-517	746	4	=	=	SYM
ejde-517	746	5	b(v)−a4(v	b(v)−a4(v	PROPN
ejde-517	746	6	)	)	PUNCT
ejde-517	746	7	.	.	PUNCT
ejde-517	747	1	(	(	PUNCT
ejde-517	747	2	4.17	4.17	NUM
ejde-517	747	3	)	)	PUNCT
ejde-517	747	4	from	from	ADP
ejde-517	747	5	the	the	DET
ejde-517	747	6	definition	definition	NOUN
ejde-517	747	7	of	of	ADP
ejde-517	747	8	the	the	DET
ejde-517	747	9	bilinear	bilinear	NOUN
ejde-517	747	10	functional	functional	NOUN
ejde-517	747	11	a	a	DET
ejde-517	747	12	in	in	ADP
ejde-517	747	13	(	(	PUNCT
ejde-517	747	14	4.10	4.10	NUM
ejde-517	747	15	)	)	PUNCT
ejde-517	747	16	,	,	PUNCT
ejde-517	747	17	we	we	PRON
ejde-517	747	18	deduce	deduce	VERB
ejde-517	747	19	that	that	PRON
ejde-517	747	20	a3(v	a3(v	X
ejde-517	747	21	)	)	PUNCT
ejde-517	748	1	+	+	NOUN
ejde-517	748	2	a2(v	a2(v	X
ejde-517	748	3	)	)	PUNCT
ejde-517	748	4	=	=	SYM
ejde-517	748	5	a(θ(χδ1	a(θ(χδ1	NOUN
ejde-517	748	6	+	+	CCONJ
ejde-517	748	7	ηδχδ1)−θ(χδ1	ηδχδ1)−θ(χδ1	ADJ
ejde-517	748	8	)	)	PUNCT
ejde-517	748	9	,	,	PUNCT
ejde-517	748	10	v	v	NOUN
ejde-517	748	11	)	)	PUNCT
ejde-517	748	12	.	.	PUNCT
ejde-517	749	1	from	from	ADP
ejde-517	749	2	the	the	DET
ejde-517	749	3	coercivity	coercivity	NOUN
ejde-517	749	4	of	of	ADP
ejde-517	749	5	a	a	PRON
ejde-517	749	6	we	we	PRON
ejde-517	749	7	can	can	AUX
ejde-517	749	8	show	show	VERB
ejde-517	749	9	that	that	SCONJ
ejde-517	749	10	|(a3	|(a3	ADP
ejde-517	749	11	+	+	ADJ
ejde-517	749	12	a2)(θ(χδ1	a2)(θ(χδ1	VERB
ejde-517	749	13	+	+	CCONJ
ejde-517	749	14	ηδχδ1)−θ(χδ1))|	ηδχδ1)−θ(χδ1))|	PROPN
ejde-517	749	15	≥	≥	PROPN
ejde-517	749	16	min	min	PROPN
ejde-517	749	17	(	(	PUNCT
ejde-517	749	18	ωγ	ωγ	ADV
ejde-517	749	19	k̄	k̄	INTJ
ejde-517	749	20	,	,	PUNCT
ejde-517	749	21	1)‖θ(χδ1	1)‖θ(χδ1	PROPN
ejde-517	749	22	+	+	NUM
ejde-517	749	23	ηδχδ1)−θ(χδ1)‖2h1(ω	ηδχδ1)−θ(χδ1)‖2h1(ω	PROPN
ejde-517	749	24	)	)	PUNCT
ejde-517	749	25	.	.	PUNCT
ejde-517	750	1	(	(	PUNCT
ejde-517	750	2	4.18	4.18	NUM
ejde-517	750	3	)	)	PUNCT
ejde-517	750	4	on	on	ADP
ejde-517	750	5	the	the	DET
ejde-517	750	6	other	other	ADJ
ejde-517	750	7	hand	hand	NOUN
ejde-517	750	8	,	,	PUNCT
ejde-517	750	9	using	use	VERB
ejde-517	750	10	the	the	DET
ejde-517	750	11	cauchy	cauchy	NOUN
ejde-517	750	12	-	-	PUNCT
ejde-517	750	13	schwarz	schwarz	PROPN
ejde-517	750	14	inequality	inequality	NOUN
ejde-517	750	15	,	,	PUNCT
ejde-517	750	16	we	we	PRON
ejde-517	750	17	obtain	obtain	VERB
ejde-517	750	18	|b(v)|	|b(v)|	NOUN
ejde-517	750	19	≤	≤	ADV
ejde-517	750	20	‖g(χδ1	‖g(χδ1	NUM
ejde-517	750	21	+	+	CCONJ
ejde-517	750	22	ηδχδ1)−g(χδ1)‖l2(ω)‖v‖h1(ω	ηδχδ1)−g(χδ1)‖l2(ω)‖v‖h1(ω	NOUN
ejde-517	750	23	)	)	PUNCT
ejde-517	750	24	.	.	PUNCT
ejde-517	751	1	(	(	PUNCT
ejde-517	751	2	4.19	4.19	NUM
ejde-517	751	3	)	)	PUNCT
ejde-517	751	4	moreover	moreover	ADV
ejde-517	751	5	,	,	PUNCT
ejde-517	751	6	using	use	VERB
ejde-517	751	7	the	the	DET
ejde-517	751	8	cauchy	cauchy	NOUN
ejde-517	751	9	-	-	PUNCT
ejde-517	751	10	schwarz	schwarz	PROPN
ejde-517	751	11	inequality	inequality	NOUN
ejde-517	751	12	,	,	PUNCT
ejde-517	751	13	hölder	hölder	NOUN
ejde-517	751	14	’s	’s	PART
ejde-517	751	15	inequality	inequality	NOUN
ejde-517	751	16	,	,	PUNCT
ejde-517	751	17	and	and	CCONJ
ejde-517	751	18	(	(	PUNCT
ejde-517	751	19	4.9	4.9	NUM
ejde-517	751	20	)	)	PUNCT
ejde-517	751	21	,	,	PUNCT
ejde-517	751	22	we	we	PRON
ejde-517	751	23	have	have	VERB
ejde-517	751	24	|a4(v)|	|a4(v)|	NUM
ejde-517	751	25	≤	≤	PROPN
ejde-517	751	26	ωγ	ωγ	ADP
ejde-517	751	27	β	β	PROPN
ejde-517	751	28	‖d(η)‖l∞(ω)‖θ(χδ1	‖d(η)‖l∞(ω)‖θ(χδ1	NUM
ejde-517	751	29	+	+	X
ejde-517	751	30	ηδχδ1)‖h1(ω)‖v‖h1(ω	ηδχδ1)‖h1(ω)‖v‖h1(ω	NOUN
ejde-517	751	31	)	)	PUNCT
ejde-517	751	32	.	.	PUNCT
ejde-517	752	1	(	(	PUNCT
ejde-517	752	2	4.20	4.20	NUM
ejde-517	752	3	)	)	PUNCT
ejde-517	752	4	26	26	NUM
ejde-517	752	5	r.	r.	PROPN
ejde-517	752	6	mendoza	mendoza	PROPN
ejde-517	752	7	,	,	PUNCT
ejde-517	752	8	s.	s.	PROPN
ejde-517	752	9	keeling	keeling	PROPN
ejde-517	753	1	ejde-2020/93	ejde-2020/93	PROPN
ejde-517	753	2	comparing	compare	VERB
ejde-517	753	3	(	(	PUNCT
ejde-517	753	4	4.17	4.17	NUM
ejde-517	753	5	)	)	PUNCT
ejde-517	753	6	,	,	PUNCT
ejde-517	753	7	(	(	PUNCT
ejde-517	753	8	4.18	4.18	NUM
ejde-517	753	9	)	)	PUNCT
ejde-517	753	10	,	,	PUNCT
ejde-517	753	11	(	(	PUNCT
ejde-517	753	12	4.19	4.19	NUM
ejde-517	753	13	)	)	PUNCT
ejde-517	753	14	,	,	PUNCT
ejde-517	753	15	and	and	CCONJ
ejde-517	753	16	(	(	PUNCT
ejde-517	753	17	4.20	4.20	NUM
ejde-517	753	18	)	)	PUNCT
ejde-517	753	19	,	,	PUNCT
ejde-517	753	20	we	we	PRON
ejde-517	753	21	obtain	obtain	VERB
ejde-517	753	22	min{ωγ	min{ωγ	ADV
ejde-517	753	23	k̄	k̄	PROPN
ejde-517	753	24	,	,	PUNCT
ejde-517	753	25	1}‖θ(χδ1	1}‖θ(χδ1	NUM
ejde-517	753	26	+	+	CCONJ
ejde-517	753	27	ηδχδ1)−θ(χδ1)‖2h1(ω	ηδχδ1)−θ(χδ1)‖2h1(ω	NOUN
ejde-517	753	28	)	)	PUNCT
ejde-517	753	29	≤	≤	NOUN
ejde-517	753	30	‖g(χδ1	‖g(χδ1	NUM
ejde-517	754	1	+	+	CCONJ
ejde-517	754	2	ηδχδ1)−g(χδ1)‖l2(ω	ηδχδ1)−g(χδ1)‖l2(ω	ADJ
ejde-517	754	3	)	)	PUNCT
ejde-517	755	1	+	+	CCONJ
ejde-517	755	2	ωγ	ωγ	ADP
ejde-517	755	3	β	β	X
ejde-517	755	4	‖d(η)‖l∞(ω)‖θ(χδ1	‖d(η)‖l∞(ω)‖θ(χδ1	PROPN
ejde-517	755	5	+	+	X
ejde-517	755	6	ηδχδ1)‖h1(ω	ηδχδ1)‖h1(ω	NOUN
ejde-517	755	7	)	)	PUNCT
ejde-517	755	8	.	.	PUNCT
ejde-517	756	1	from	from	ADP
ejde-517	756	2	(	(	PUNCT
ejde-517	756	3	4.12	4.12	NUM
ejde-517	756	4	)	)	PUNCT
ejde-517	756	5	,	,	PUNCT
ejde-517	756	6	the	the	DET
ejde-517	756	7	right	right	ADJ
ejde-517	756	8	-	-	PUNCT
ejde-517	756	9	hand	hand	NOUN
ejde-517	756	10	side	side	NOUN
ejde-517	756	11	of	of	ADP
ejde-517	756	12	the	the	DET
ejde-517	756	13	above	above	ADJ
ejde-517	756	14	inequality	inequality	NOUN
ejde-517	756	15	is	be	AUX
ejde-517	756	16	bounded	bound	VERB
ejde-517	756	17	for	for	ADP
ejde-517	756	18	any	any	DET
ejde-517	756	19	η	η	PROPN
ejde-517	756	20	∈	∈	PROPN
ejde-517	756	21	(	(	PUNCT
ejde-517	756	22	0	0	NUM
ejde-517	756	23	,	,	PUNCT
ejde-517	756	24	τ̂	τ̂	NUM
ejde-517	756	25	)	)	PUNCT
ejde-517	756	26	,	,	PUNCT
ejde-517	756	27	where	where	SCONJ
ejde-517	756	28	τ̂	τ̂	PUNCT
ejde-517	756	29	=	=	SYM
ejde-517	756	30	min	min	X
ejde-517	756	31	{	{	PUNCT
ejde-517	756	32	τ	τ	PROPN
ejde-517	756	33	,	,	PUNCT
ejde-517	756	34	τ̄	τ̄	PROPN
ejde-517	756	35	}	}	PUNCT
ejde-517	756	36	,	,	PUNCT
ejde-517	756	37	τ	τ	PROPN
ejde-517	756	38	and	and	CCONJ
ejde-517	756	39	τ̄	τ̄	NOUN
ejde-517	756	40	are	be	AUX
ejde-517	756	41	both	both	ADV
ejde-517	756	42	chosen	choose	VERB
ejde-517	756	43	according	accord	VERB
ejde-517	756	44	to	to	PART
ejde-517	756	45	remark	remark	NOUN
ejde-517	756	46	3.4	3.4	NUM
ejde-517	756	47	and	and	CCONJ
ejde-517	756	48	remark	remark	NOUN
ejde-517	756	49	3.26	3.26	NUM
ejde-517	756	50	,	,	PUNCT
ejde-517	756	51	respectively	respectively	ADV
ejde-517	756	52	.	.	PUNCT
ejde-517	757	1	obviously	obviously	ADV
ejde-517	757	2	,	,	PUNCT
ejde-517	757	3	limη→0	limη→0	PROPN
ejde-517	757	4	‖d(η)‖l∞(ω	‖d(η)‖l∞(ω	PROPN
ejde-517	757	5	)	)	PUNCT
ejde-517	757	6	=	=	SYM
ejde-517	758	1	0	0	X
ejde-517	758	2	.	.	PUNCT
ejde-517	759	1	the	the	DET
ejde-517	759	2	above	above	ADJ
ejde-517	759	3	inequality	inequality	NOUN
ejde-517	759	4	,	,	PUNCT
ejde-517	759	5	together	together	ADV
ejde-517	759	6	with	with	ADP
ejde-517	759	7	(	(	PUNCT
ejde-517	759	8	4.3	4.3	NUM
ejde-517	759	9	)	)	PUNCT
ejde-517	759	10	,	,	PUNCT
ejde-517	759	11	establishes	establish	VERB
ejde-517	759	12	our	our	PRON
ejde-517	759	13	claim	claim	NOUN
ejde-517	759	14	.	.	PUNCT
ejde-517	760	1	�	�	PROPN
ejde-517	760	2	we	we	PRON
ejde-517	760	3	now	now	ADV
ejde-517	760	4	establish	establish	VERB
ejde-517	760	5	that	that	SCONJ
ejde-517	760	6	the	the	DET
ejde-517	760	7	function	function	NOUN
ejde-517	760	8	h	h	NOUN
ejde-517	760	9	defined	define	VERB
ejde-517	760	10	in	in	ADP
ejde-517	760	11	(	(	PUNCT
ejde-517	760	12	3.25	3.25	NUM
ejde-517	760	13	)	)	PUNCT
ejde-517	760	14	is	be	AUX
ejde-517	760	15	continuous	continuous	ADJ
ejde-517	760	16	.	.	PUNCT
ejde-517	761	1	the	the	DET
ejde-517	761	2	details	detail	NOUN
ejde-517	761	3	of	of	ADP
ejde-517	761	4	the	the	DET
ejde-517	761	5	proof	proof	NOUN
ejde-517	761	6	can	can	AUX
ejde-517	761	7	be	be	AUX
ejde-517	761	8	found	find	VERB
ejde-517	761	9	in	in	ADP
ejde-517	761	10	[	[	X
ejde-517	761	11	15	15	NUM
ejde-517	761	12	]	]	PUNCT
ejde-517	761	13	.	.	PUNCT
ejde-517	762	1	lemma	lemma	PROPN
ejde-517	762	2	4.5	4.5	NUM
ejde-517	762	3	.	.	PUNCT
ejde-517	763	1	let	let	VERB
ejde-517	763	2	z	z	NOUN
ejde-517	763	3	∈	∈	PROPN
ejde-517	763	4	l2(ω)\h1(ω	l2(ω)\h1(ω	NOUN
ejde-517	763	5	)	)	PUNCT
ejde-517	763	6	and	and	CCONJ
ejde-517	763	7	suppose	suppose	VERB
ejde-517	763	8	{	{	PUNCT
ejde-517	763	9	gn}∞n=1	gn}∞n=1	X
ejde-517	763	10	⊂	⊂	AUX
ejde-517	763	11	l2(ω	l2(ω	PROPN
ejde-517	763	12	)	)	PUNCT
ejde-517	763	13	converge	converge	VERB
ejde-517	763	14	to	to	ADP
ejde-517	763	15	g	g	NOUN
ejde-517	763	16	in	in	ADP
ejde-517	763	17	l2(ω	l2(ω	NOUN
ejde-517	763	18	)	)	PUNCT
ejde-517	763	19	.	.	PUNCT
ejde-517	764	1	then	then	ADV
ejde-517	764	2	lim	lim	PROPN
ejde-517	764	3	n→∞	n→∞	NUM
ejde-517	764	4	µ(h(g)4h(gn	µ(h(g)4h(gn	NOUN
ejde-517	764	5	)	)	PUNCT
ejde-517	764	6	)	)	PUNCT
ejde-517	764	7	=	=	SYM
ejde-517	764	8	0	0	NUM
ejde-517	764	9	,	,	PUNCT
ejde-517	764	10	(	(	PUNCT
ejde-517	764	11	4.21	4.21	NUM
ejde-517	764	12	)	)	PUNCT
ejde-517	764	13	where	where	SCONJ
ejde-517	764	14	h(g	h(g	VERB
ejde-517	764	15	)	)	PUNCT
ejde-517	764	16	=	=	PRON
ejde-517	764	17	{	{	PUNCT
ejde-517	764	18	x	x	PUNCT
ejde-517	764	19	∈	∈	PROPN
ejde-517	764	20	ω	ω	NOUN
ejde-517	764	21	:	:	PUNCT
ejde-517	764	22	(	(	PUNCT
ejde-517	764	23	(	(	PUNCT
ejde-517	764	24	gδ	gδ	NOUN
ejde-517	764	25	−	−	PROPN
ejde-517	764	26	ζ	ζ	NOUN
ejde-517	764	27	+	+	NUM
ejde-517	764	28	δz	δz	X
ejde-517	764	29	)	)	PUNCT
ejde-517	764	30	∗	∗	NOUN
ejde-517	764	31	ξδ)(x	ξδ)(x	PROPN
ejde-517	764	32	)	)	PUNCT
ejde-517	764	33	≥	≥	NOUN
ejde-517	764	34	0	0	NUM
ejde-517	764	35	}	}	PUNCT
ejde-517	764	36	,	,	PUNCT
ejde-517	764	37	for	for	ADP
ejde-517	764	38	some	some	DET
ejde-517	764	39	ζ	ζ	NOUN
ejde-517	764	40	∈	∈	NOUN
ejde-517	764	41	(	(	PUNCT
ejde-517	764	42	0	0	NUM
ejde-517	764	43	,	,	PUNCT
ejde-517	764	44	1	1	NUM
ejde-517	764	45	)	)	PUNCT
ejde-517	764	46	and	and	CCONJ
ejde-517	764	47	gδ	gδ	VERB
ejde-517	764	48	=	=	SYM
ejde-517	764	49	g	g	PROPN
ejde-517	764	50	∗	∗	NOUN
ejde-517	764	51	ξδ	ξδ	ADP
ejde-517	764	52	.	.	PUNCT
ejde-517	765	1	in	in	ADP
ejde-517	765	2	other	other	ADJ
ejde-517	765	3	words	word	NOUN
ejde-517	765	4	,	,	PUNCT
ejde-517	765	5	h	h	NOUN
ejde-517	765	6	is	be	AUX
ejde-517	765	7	continuous	continuous	ADJ
ejde-517	765	8	in	in	ADP
ejde-517	765	9	l2(ω	l2(ω	PROPN
ejde-517	765	10	)	)	PUNCT
ejde-517	765	11	(	(	PUNCT
ejde-517	765	12	see	see	VERB
ejde-517	765	13	[	[	X
ejde-517	765	14	15	15	NUM
ejde-517	765	15	]	]	NUM
ejde-517	765	16	)	)	PUNCT
ejde-517	765	17	.	.	PUNCT
ejde-517	766	1	in	in	ADP
ejde-517	766	2	our	our	PRON
ejde-517	766	3	next	next	ADJ
ejde-517	766	4	computations	computation	NOUN
ejde-517	766	5	,	,	PUNCT
ejde-517	766	6	we	we	PRON
ejde-517	766	7	prove	prove	VERB
ejde-517	766	8	the	the	DET
ejde-517	766	9	continuity	continuity	NOUN
ejde-517	766	10	of	of	ADP
ejde-517	766	11	the	the	DET
ejde-517	766	12	function	function	NOUN
ejde-517	766	13	m	m	AUX
ejde-517	766	14	defined	define	VERB
ejde-517	766	15	in	in	ADP
ejde-517	766	16	(	(	PUNCT
ejde-517	766	17	3.26	3.26	NUM
ejde-517	766	18	)	)	PUNCT
ejde-517	766	19	.	.	PUNCT
ejde-517	767	1	recall	recall	VERB
ejde-517	767	2	that	that	PRON
ejde-517	767	3	m	m	VERB
ejde-517	767	4	maps	map	VERB
ejde-517	767	5	elements	element	NOUN
ejde-517	767	6	ofm(ω	ofm(ω	PROPN
ejde-517	767	7	)	)	PUNCT
ejde-517	767	8	to	to	ADP
ejde-517	767	9	their	their	PRON
ejde-517	767	10	corresponding	corresponding	ADJ
ejde-517	767	11	characteristic	characteristic	ADJ
ejde-517	767	12	functions	function	NOUN
ejde-517	767	13	.	.	PUNCT
ejde-517	768	1	we	we	PRON
ejde-517	768	2	now	now	ADV
ejde-517	768	3	try	try	VERB
ejde-517	768	4	to	to	PART
ejde-517	768	5	find	find	VERB
ejde-517	768	6	a	a	DET
ejde-517	768	7	suitable	suitable	ADJ
ejde-517	768	8	space	space	NOUN
ejde-517	768	9	for	for	ADP
ejde-517	768	10	these	these	DET
ejde-517	768	11	characteristic	characteristic	ADJ
ejde-517	768	12	functions	function	NOUN
ejde-517	768	13	.	.	PUNCT
ejde-517	769	1	intuitively	intuitively	ADV
ejde-517	769	2	,	,	PUNCT
ejde-517	769	3	convergence	convergence	NOUN
ejde-517	769	4	of	of	ADP
ejde-517	769	5	these	these	DET
ejde-517	769	6	characteristic	characteristic	ADJ
ejde-517	769	7	functions	function	NOUN
ejde-517	769	8	is	be	AUX
ejde-517	769	9	dependent	dependent	ADJ
ejde-517	769	10	upon	upon	SCONJ
ejde-517	769	11	the	the	DET
ejde-517	769	12	convergence	convergence	NOUN
ejde-517	769	13	of	of	ADP
ejde-517	769	14	their	their	PRON
ejde-517	769	15	associated	associate	VERB
ejde-517	769	16	supports	support	NOUN
ejde-517	769	17	.	.	PUNCT
ejde-517	770	1	we	we	PRON
ejde-517	770	2	choose	choose	VERB
ejde-517	770	3	l2(ω	l2(ω	NOUN
ejde-517	770	4	)	)	PUNCT
ejde-517	770	5	to	to	PART
ejde-517	770	6	be	be	AUX
ejde-517	770	7	the	the	DET
ejde-517	770	8	space	space	NOUN
ejde-517	770	9	of	of	ADP
ejde-517	770	10	the	the	DET
ejde-517	770	11	characteristic	characteristic	ADJ
ejde-517	770	12	functions	function	NOUN
ejde-517	770	13	and	and	CCONJ
ejde-517	770	14	select	select	VERB
ejde-517	770	15	m(ω	m(ω	NOUN
ejde-517	770	16	)	)	PUNCT
ejde-517	770	17	to	to	PART
ejde-517	770	18	be	be	AUX
ejde-517	770	19	the	the	DET
ejde-517	770	20	space	space	NOUN
ejde-517	770	21	of	of	ADP
ejde-517	770	22	their	their	PRON
ejde-517	770	23	associated	associate	VERB
ejde-517	770	24	supports	support	NOUN
ejde-517	770	25	.	.	PUNCT
ejde-517	771	1	recall	recall	VERB
ejde-517	771	2	that	that	SCONJ
ejde-517	771	3	m(ω	m(ω	NOUN
ejde-517	771	4	)	)	PUNCT
ejde-517	771	5	is	be	AUX
ejde-517	771	6	a	a	DET
ejde-517	771	7	metric	metric	ADJ
ejde-517	771	8	space	space	NOUN
ejde-517	771	9	equipped	equip	VERB
ejde-517	771	10	with	with	ADP
ejde-517	771	11	the	the	DET
ejde-517	771	12	measure	measure	NOUN
ejde-517	771	13	of	of	ADP
ejde-517	771	14	the	the	DET
ejde-517	771	15	symmetric	symmetric	ADJ
ejde-517	771	16	difference	difference	NOUN
ejde-517	771	17	.	.	PUNCT
ejde-517	772	1	the	the	DET
ejde-517	772	2	following	follow	VERB
ejde-517	772	3	lemma	lemma	PROPN
ejde-517	772	4	proves	prove	VERB
ejde-517	772	5	how	how	SCONJ
ejde-517	772	6	these	these	DET
ejde-517	772	7	two	two	NUM
ejde-517	772	8	spaces	space	NOUN
ejde-517	772	9	are	be	AUX
ejde-517	772	10	related	relate	VERB
ejde-517	772	11	.	.	PUNCT
ejde-517	773	1	lemma	lemma	PROPN
ejde-517	773	2	4.6	4.6	NUM
ejde-517	773	3	.	.	PUNCT
ejde-517	774	1	let	let	VERB
ejde-517	774	2	χ̂	χ̂	PRON
ejde-517	774	3	and	and	CCONJ
ejde-517	774	4	χ	χ	PRON
ejde-517	774	5	be	be	AUX
ejde-517	774	6	characteristic	characteristic	ADJ
ejde-517	774	7	functions	function	NOUN
ejde-517	774	8	on	on	ADP
ejde-517	774	9	ω	ω	NUM
ejde-517	774	10	whose	whose	DET
ejde-517	774	11	supports	support	NOUN
ejde-517	774	12	are	be	AUX
ejde-517	774	13	given	give	VERB
ejde-517	774	14	by	by	ADP
ejde-517	774	15	ωχ̂	ωχ̂	NOUN
ejde-517	774	16	and	and	CCONJ
ejde-517	774	17	ωχ	ωχ	NOUN
ejde-517	774	18	,	,	PUNCT
ejde-517	774	19	respectively	respectively	ADV
ejde-517	774	20	.	.	PUNCT
ejde-517	775	1	then	then	ADV
ejde-517	775	2	µ(ωχ̂	µ(ωχ̂	ADP
ejde-517	775	3	4	4	NUM
ejde-517	775	4	ωχ	ωχ	NOUN
ejde-517	775	5	)	)	PUNCT
ejde-517	775	6	=	=	SYM
ejde-517	775	7	‖χ̂−	‖χ̂−	NOUN
ejde-517	775	8	χ‖2l2(ω	χ‖2l2(ω	ADV
ejde-517	775	9	)	)	PUNCT
ejde-517	775	10	.	.	PUNCT
ejde-517	776	1	proof	proof	NOUN
ejde-517	776	2	.	.	PUNCT
ejde-517	777	1	because	because	SCONJ
ejde-517	777	2	χ	χ	NOUN
ejde-517	777	3	and	and	CCONJ
ejde-517	777	4	χ̂	χ̂	PROPN
ejde-517	777	5	are	be	AUX
ejde-517	777	6	characteristic	characteristic	ADJ
ejde-517	777	7	functions	function	NOUN
ejde-517	777	8	,	,	PUNCT
ejde-517	777	9	we	we	PRON
ejde-517	777	10	have	have	VERB
ejde-517	777	11	ωχ̂\ωχ	ωχ̂\ωχ	PROPN
ejde-517	777	12	=	=	PUNCT
ejde-517	777	13	{	{	PUNCT
ejde-517	777	14	x	x	X
ejde-517	777	15	:	:	PUNCT
ejde-517	777	16	x	x	SYM
ejde-517	777	17	∈	∈	NOUN
ejde-517	777	18	ωχ̂	ωχ̂	NOUN
ejde-517	777	19	∧	∧	NOUN
ejde-517	777	20	x	x	INTJ
ejde-517	777	21	/∈	/∈	PUNCT
ejde-517	777	22	ωχ	ωχ	NOUN
ejde-517	777	23	}	}	PUNCT
ejde-517	777	24	=	=	SYM
ejde-517	777	25	{	{	PUNCT
ejde-517	777	26	x	x	NOUN
ejde-517	777	27	:	:	PUNCT
ejde-517	777	28	χ̂(x	χ̂(x	NOUN
ejde-517	777	29	)	)	PUNCT
ejde-517	777	30	=	=	SYM
ejde-517	777	31	1	1	NUM
ejde-517	777	32	∧	∧	PROPN
ejde-517	777	33	χ(x	χ(x	PROPN
ejde-517	777	34	)	)	PUNCT
ejde-517	777	35	=	=	PUNCT
ejde-517	778	1	0	0	NUM
ejde-517	778	2	}	}	PUNCT
ejde-517	778	3	.	.	PUNCT
ejde-517	779	1	similarly	similarly	ADV
ejde-517	779	2	,	,	PUNCT
ejde-517	779	3	ωχ\ωχ̂	ωχ\ωχ̂	X
ejde-517	779	4	=	=	PUNCT
ejde-517	779	5	{	{	PUNCT
ejde-517	779	6	x	x	X
ejde-517	779	7	:	:	PUNCT
ejde-517	779	8	χ(x	χ(x	PROPN
ejde-517	779	9	)	)	PUNCT
ejde-517	779	10	=	=	SYM
ejde-517	779	11	1	1	NUM
ejde-517	779	12	∧	∧	PROPN
ejde-517	779	13	χ̂(x	χ̂(x	NOUN
ejde-517	779	14	)	)	PUNCT
ejde-517	779	15	=	=	PUNCT
ejde-517	779	16	0	0	NUM
ejde-517	779	17	}	}	PUNCT
ejde-517	779	18	.	.	PUNCT
ejde-517	780	1	thus	thus	ADV
ejde-517	780	2	,	,	PUNCT
ejde-517	780	3	from	from	ADP
ejde-517	780	4	the	the	DET
ejde-517	780	5	definition	definition	NOUN
ejde-517	780	6	of	of	ADP
ejde-517	780	7	symmetric	symmetric	ADJ
ejde-517	780	8	difference	difference	NOUN
ejde-517	780	9	and	and	CCONJ
ejde-517	780	10	the	the	DET
ejde-517	780	11	fact	fact	NOUN
ejde-517	780	12	that	that	SCONJ
ejde-517	780	13	ωχ̂\ωχ	ωχ̂\ωχ	PROPN
ejde-517	780	14	and	and	CCONJ
ejde-517	780	15	ωχ\ωχ̂	ωχ\ωχ̂	NOUN
ejde-517	780	16	are	be	AUX
ejde-517	780	17	disjoint	disjoint	NOUN
ejde-517	780	18	sets	set	NOUN
ejde-517	780	19	,	,	PUNCT
ejde-517	780	20	we	we	PRON
ejde-517	780	21	obtain	obtain	VERB
ejde-517	780	22	µ(ωχ̂	µ(ωχ̂	ADP
ejde-517	780	23	4	4	NUM
ejde-517	780	24	ωχ	ωχ	NOUN
ejde-517	780	25	)	)	PUNCT
ejde-517	780	26	=	=	SYM
ejde-517	780	27	µ((ωχ̂\ωχ	µ((ωχ̂\ωχ	X
ejde-517	780	28	)	)	PUNCT
ejde-517	780	29	∪	∪	X
ejde-517	780	30	(	(	PUNCT
ejde-517	780	31	ωχ\ωχ̂	ωχ\ωχ̂	NUM
ejde-517	780	32	)	)	PUNCT
ejde-517	780	33	)	)	PUNCT
ejde-517	781	1	=	=	SYM
ejde-517	781	2	µ({x	µ({x	NOUN
ejde-517	781	3	:	:	PUNCT
ejde-517	781	4	χ̂(x	χ̂(x	NOUN
ejde-517	781	5	)	)	PUNCT
ejde-517	781	6	=	=	SYM
ejde-517	781	7	1	1	NUM
ejde-517	781	8	∧	∧	PROPN
ejde-517	781	9	χ(x	χ(x	PROPN
ejde-517	781	10	)	)	PUNCT
ejde-517	781	11	=	=	PUNCT
ejde-517	781	12	0	0	NUM
ejde-517	781	13	}	}	PUNCT
ejde-517	781	14	)	)	PUNCT
ejde-517	782	1	+	+	CCONJ
ejde-517	782	2	µ({x	µ({x	NOUN
ejde-517	782	3	:	:	PUNCT
ejde-517	782	4	χ(x	χ(x	PROPN
ejde-517	782	5	)	)	PUNCT
ejde-517	782	6	=	=	SYM
ejde-517	782	7	1	1	NUM
ejde-517	782	8	∧	∧	PROPN
ejde-517	782	9	χ̂(x	χ̂(x	NOUN
ejde-517	782	10	)	)	PUNCT
ejde-517	782	11	=	=	SYM
ejde-517	782	12	0	0	NUM
ejde-517	782	13	}	}	PUNCT
ejde-517	782	14	)	)	PUNCT
ejde-517	783	1	=	=	SYM
ejde-517	783	2	∫	∫	PROPN
ejde-517	784	1	ω	ω	PROPN
ejde-517	784	2	χ̂(1−	χ̂(1−	PROPN
ejde-517	784	3	χ	χ	PART
ejde-517	784	4	)	)	PUNCT
ejde-517	784	5	dv	dv	PROPN
ejde-517	784	6	+	+	CCONJ
ejde-517	784	7	∫	∫	PROPN
ejde-517	784	8	ω	ω	PROPN
ejde-517	784	9	χ(1−	χ(1−	PROPN
ejde-517	784	10	χ̂	χ̂	PROPN
ejde-517	784	11	)	)	PUNCT
ejde-517	785	1	dv	dv	PROPN
ejde-517	785	2	=	=	PUNCT
ejde-517	785	3	‖χ̂−	‖χ̂−	NOUN
ejde-517	785	4	χ‖2l2(ω	χ‖2l2(ω	ADV
ejde-517	785	5	)	)	PUNCT
ejde-517	785	6	.	.	PUNCT
ejde-517	786	1	�	�	PROPN
ejde-517	786	2	ejde-2020/93	ejde-2020/93	PROPN
ejde-517	786	3	impedance	impedance	NOUN
ejde-517	786	4	tomography	tomography	NOUN
ejde-517	786	5	problem	problem	NOUN
ejde-517	786	6	27	27	NUM
ejde-517	786	7	now	now	ADV
ejde-517	786	8	that	that	SCONJ
ejde-517	786	9	we	we	PRON
ejde-517	786	10	have	have	AUX
ejde-517	786	11	established	establish	VERB
ejde-517	786	12	a	a	DET
ejde-517	786	13	mode	mode	NOUN
ejde-517	786	14	of	of	ADP
ejde-517	786	15	convergence	convergence	NOUN
ejde-517	786	16	for	for	ADP
ejde-517	786	17	the	the	DET
ejde-517	786	18	characteristic	characteristic	ADJ
ejde-517	786	19	functions	function	NOUN
ejde-517	786	20	and	and	CCONJ
ejde-517	786	21	their	their	PRON
ejde-517	786	22	associated	associate	VERB
ejde-517	786	23	sets	set	NOUN
ejde-517	786	24	,	,	PUNCT
ejde-517	786	25	we	we	PRON
ejde-517	786	26	can	can	AUX
ejde-517	786	27	prove	prove	VERB
ejde-517	786	28	that	that	SCONJ
ejde-517	786	29	m	m	NOUN
ejde-517	786	30	is	be	AUX
ejde-517	786	31	continuous	continuous	ADJ
ejde-517	786	32	.	.	PUNCT
ejde-517	787	1	lemma	lemma	PROPN
ejde-517	787	2	4.7	4.7	NUM
ejde-517	787	3	.	.	PUNCT
ejde-517	787	4	suppose	suppose	VERB
ejde-517	787	5	{	{	PUNCT
ejde-517	787	6	ωn}∞n=1	ωn}∞n=1	NUM
ejde-517	787	7	⊂	⊂	X
ejde-517	787	8	m(ω	m(ω	NOUN
ejde-517	787	9	)	)	PUNCT
ejde-517	787	10	such	such	ADJ
ejde-517	787	11	that	that	SCONJ
ejde-517	787	12	ωn	ωn	ADP
ejde-517	787	13	→	→	SYM
ejde-517	787	14	ω	ω	PROPN
ejde-517	787	15	in	in	ADP
ejde-517	787	16	m(ω	m(ω	NOUN
ejde-517	787	17	)	)	PUNCT
ejde-517	787	18	,	,	PUNCT
ejde-517	787	19	that	that	ADV
ejde-517	787	20	is	is	ADV
ejde-517	787	21	,	,	PUNCT
ejde-517	787	22	limn→∞	limn→∞	PROPN
ejde-517	787	23	µ(ωn	µ(ωn	PROPN
ejde-517	787	24	4	4	NUM
ejde-517	787	25	ω	ω	NUM
ejde-517	787	26	)	)	PUNCT
ejde-517	787	27	=	=	SYM
ejde-517	788	1	0	0	X
ejde-517	788	2	.	.	PUNCT
ejde-517	789	1	then	then	ADV
ejde-517	789	2	lim	lim	PROPN
ejde-517	789	3	n→∞	n→∞	X
ejde-517	789	4	‖m(ωn)−m(ω)‖l2(ω	‖m(ωn)−m(ω)‖l2(ω	PROPN
ejde-517	789	5	)	)	PUNCT
ejde-517	789	6	=	=	SYM
ejde-517	789	7	0	0	NUM
ejde-517	789	8	,	,	PUNCT
ejde-517	789	9	where	where	SCONJ
ejde-517	789	10	m	m	VERB
ejde-517	789	11	:	:	PUNCT
ejde-517	789	12	m(ω	m(ω	NOUN
ejde-517	789	13	)	)	PUNCT
ejde-517	789	14	→	→	SYM
ejde-517	789	15	l2(ω	l2(ω	CCONJ
ejde-517	789	16	)	)	PUNCT
ejde-517	789	17	is	be	AUX
ejde-517	789	18	a	a	DET
ejde-517	789	19	function	function	NOUN
ejde-517	789	20	that	that	PRON
ejde-517	789	21	maps	map	VERB
ejde-517	789	22	ω	ω	NOUN
ejde-517	789	23	to	to	ADP
ejde-517	789	24	its	its	PRON
ejde-517	789	25	corresponding	corresponding	ADJ
ejde-517	789	26	characteristic	characteristic	ADJ
ejde-517	789	27	function	function	NOUN
ejde-517	789	28	,	,	PUNCT
ejde-517	789	29	that	that	ADV
ejde-517	789	30	is	is	ADV
ejde-517	789	31	,	,	PUNCT
ejde-517	789	32	m(ω	m(ω	PROPN
ejde-517	789	33	)	)	PUNCT
ejde-517	790	1	=	=	PUNCT
ejde-517	790	2	χω	χω	INTJ
ejde-517	790	3	.	.	PUNCT
ejde-517	791	1	in	in	ADP
ejde-517	791	2	other	other	ADJ
ejde-517	791	3	words	word	NOUN
ejde-517	791	4	,	,	PUNCT
ejde-517	791	5	m	m	VERB
ejde-517	791	6	is	be	AUX
ejde-517	791	7	continuous	continuous	ADJ
ejde-517	791	8	on	on	ADP
ejde-517	791	9	m(ω	m(ω	NOUN
ejde-517	791	10	)	)	PUNCT
ejde-517	791	11	.	.	PUNCT
ejde-517	792	1	proof	proof	NOUN
ejde-517	792	2	.	.	PUNCT
ejde-517	793	1	we	we	PRON
ejde-517	793	2	denote	denote	VERB
ejde-517	793	3	m(ωn	m(ωn	NOUN
ejde-517	793	4	)	)	PUNCT
ejde-517	794	1	=	=	NOUN
ejde-517	794	2	:	:	PUNCT
ejde-517	794	3	χn	χn	X
ejde-517	794	4	and	and	CCONJ
ejde-517	794	5	m(ω	m(ω	NOUN
ejde-517	794	6	)	)	PUNCT
ejde-517	795	1	:	:	PUNCT
ejde-517	795	2	=	=	PUNCT
ejde-517	795	3	χω	χω	INTJ
ejde-517	795	4	.	.	PUNCT
ejde-517	796	1	then	then	ADV
ejde-517	796	2	by	by	ADP
ejde-517	796	3	lemma	lemma	PROPN
ejde-517	796	4	(	(	PUNCT
ejde-517	796	5	4.6	4.6	NUM
ejde-517	796	6	)	)	PUNCT
ejde-517	796	7	,	,	PUNCT
ejde-517	796	8	lim	lim	PROPN
ejde-517	796	9	n→∞	n→∞	NUM
ejde-517	796	10	‖m(ωn)−m(ω)‖2l2(ω	‖m(ωn)−m(ω)‖2l2(ω	NOUN
ejde-517	796	11	)	)	PUNCT
ejde-517	797	1	=	=	VERB
ejde-517	797	2	lim	lim	PROPN
ejde-517	797	3	n→∞	n→∞	NUM
ejde-517	798	1	‖χn	‖χn	NUM
ejde-517	798	2	−	−	PROPN
ejde-517	798	3	χω‖2l2(ω	χω‖2l2(ω	NOUN
ejde-517	798	4	)	)	PUNCT
ejde-517	799	1	=	=	VERB
ejde-517	799	2	lim	lim	PROPN
ejde-517	799	3	n→∞	n→∞	NUM
ejde-517	799	4	µ(ωn	µ(ωn	PROPN
ejde-517	799	5	4	4	NUM
ejde-517	799	6	ω	ω	NUM
ejde-517	799	7	)	)	PUNCT
ejde-517	799	8	=	=	SYM
ejde-517	799	9	0	0	X
ejde-517	799	10	.	.	X
ejde-517	799	11	�	�	PROPN
ejde-517	799	12	we	we	PRON
ejde-517	799	13	have	have	AUX
ejde-517	799	14	shown	show	VERB
ejde-517	799	15	continuity	continuity	NOUN
ejde-517	799	16	of	of	ADP
ejde-517	799	17	g	g	PROPN
ejde-517	799	18	,	,	PUNCT
ejde-517	799	19	θ	θ	PROPN
ejde-517	799	20	,	,	PUNCT
ejde-517	799	21	h	h	NOUN
ejde-517	799	22	and	and	CCONJ
ejde-517	799	23	m	m	PROPN
ejde-517	799	24	.	.	PUNCT
ejde-517	800	1	finally	finally	ADV
ejde-517	800	2	,	,	PUNCT
ejde-517	800	3	we	we	PRON
ejde-517	800	4	can	can	AUX
ejde-517	800	5	prove	prove	VERB
ejde-517	800	6	that	that	SCONJ
ejde-517	800	7	υ	υ	PROPN
ejde-517	800	8	has	have	VERB
ejde-517	800	9	a	a	DET
ejde-517	800	10	fixed	fix	VERB
ejde-517	800	11	point	point	NOUN
ejde-517	800	12	.	.	PUNCT
ejde-517	801	1	theorem	theorem	NOUN
ejde-517	801	2	4.8	4.8	NUM
ejde-517	801	3	.	.	PUNCT
ejde-517	802	1	under	under	ADP
ejde-517	802	2	assumption	assumption	NOUN
ejde-517	802	3	(	(	PUNCT
ejde-517	802	4	3.30	3.30	NUM
ejde-517	802	5	)	)	PUNCT
ejde-517	802	6	we	we	PRON
ejde-517	802	7	let	let	VERB
ejde-517	802	8	z	z	X
ejde-517	802	9	∈	∈	PROPN
ejde-517	802	10	l2(ω)\h1(ω	l2(ω)\h1(ω	NOUN
ejde-517	802	11	)	)	PUNCT
ejde-517	802	12	.	.	PUNCT
ejde-517	803	1	then	then	ADV
ejde-517	803	2	the	the	DET
ejde-517	803	3	function	function	NOUN
ejde-517	803	4	υ	υ	PROPN
ejde-517	803	5	:	:	PUNCT
ejde-517	803	6	l2(ω)→	l2(ω)→	PROPN
ejde-517	803	7	l2(ω	l2(ω	PROPN
ejde-517	803	8	)	)	PUNCT
ejde-517	803	9	defined	define	VERB
ejde-517	803	10	by	by	ADP
ejde-517	803	11	υ(χ1	υ(χ1	NOUN
ejde-517	803	12	)	)	PUNCT
ejde-517	803	13	:	:	PUNCT
ejde-517	803	14	=	=	SYM
ejde-517	803	15	(	(	PUNCT
ejde-517	803	16	tδ	tδ	INTJ
ejde-517	803	17	◦	◦	NOUN
ejde-517	803	18	m	m	NOUN
ejde-517	803	19	◦	◦	NOUN
ejde-517	803	20	h	h	NOUN
ejde-517	803	21	◦	◦	NOUN
ejde-517	803	22	θ	θ	NOUN
ejde-517	803	23	◦	◦	NOUN
ejde-517	803	24	g	g	NOUN
ejde-517	803	25	◦	◦	NOUN
ejde-517	803	26	tδ)(χ1	tδ)(χ1	VERB
ejde-517	803	27	)	)	PUNCT
ejde-517	803	28	has	have	VERB
ejde-517	803	29	a	a	DET
ejde-517	803	30	fixed	fix	VERB
ejde-517	803	31	point	point	NOUN
ejde-517	803	32	in	in	ADP
ejde-517	803	33	the	the	DET
ejde-517	803	34	set	set	NOUN
ejde-517	803	35	k	k	NOUN
ejde-517	803	36	:	:	PUNCT
ejde-517	803	37	=	=	SYM
ejde-517	803	38	{	{	PUNCT
ejde-517	803	39	χ1	χ1	NOUN
ejde-517	803	40	∈	∈	PROPN
ejde-517	803	41	l2(ω	l2(ω	NOUN
ejde-517	803	42	)	)	PUNCT
ejde-517	803	43	:	:	PUNCT
ejde-517	803	44	0	0	NUM
ejde-517	803	45	≤	≤	NUM
ejde-517	803	46	χ1	χ1	NOUN
ejde-517	803	47	≤	≤	NUM
ejde-517	803	48	1	1	NUM
ejde-517	803	49	a.e	a.e	PROPN
ejde-517	803	50	.	.	PROPN
ejde-517	803	51	ω	ω	NUM
ejde-517	803	52	}	}	PUNCT
ejde-517	803	53	.	.	PUNCT
ejde-517	804	1	(	(	PUNCT
ejde-517	804	2	4.22	4.22	NUM
ejde-517	804	3	)	)	PUNCT
ejde-517	804	4	proof	proof	NOUN
ejde-517	804	5	.	.	PUNCT
ejde-517	805	1	we	we	PRON
ejde-517	805	2	employ	employ	VERB
ejde-517	805	3	the	the	DET
ejde-517	805	4	schauder	schauder	NOUN
ejde-517	805	5	fixed	fix	VERB
ejde-517	805	6	point	point	NOUN
ejde-517	805	7	theorem	theorem	VERB
ejde-517	805	8	.	.	PUNCT
ejde-517	806	1	we	we	PRON
ejde-517	806	2	first	first	ADV
ejde-517	806	3	need	need	VERB
ejde-517	806	4	to	to	PART
ejde-517	806	5	show	show	VERB
ejde-517	806	6	thatk	thatk	PROPN
ejde-517	806	7	is	be	AUX
ejde-517	806	8	a	a	DET
ejde-517	806	9	convex	convex	NOUN
ejde-517	806	10	set	set	VERB
ejde-517	806	11	in	in	ADP
ejde-517	806	12	l2(ω	l2(ω	PROPN
ejde-517	806	13	)	)	PUNCT
ejde-517	806	14	.	.	PUNCT
ejde-517	807	1	let	let	VERB
ejde-517	807	2	χ1	χ1	NOUN
ejde-517	807	3	,	,	PUNCT
ejde-517	807	4	χ̄1	χ̄1	NOUN
ejde-517	807	5	∈	∈	PROPN
ejde-517	807	6	k	k	PROPN
ejde-517	807	7	and	and	CCONJ
ejde-517	807	8	λ	λ	PROPN
ejde-517	807	9	∈	∈	PROPN
ejde-517	807	10	(	(	PUNCT
ejde-517	807	11	0	0	NUM
ejde-517	807	12	,	,	PUNCT
ejde-517	807	13	1	1	NUM
ejde-517	807	14	)	)	PUNCT
ejde-517	807	15	.	.	PUNCT
ejde-517	808	1	obviously	obviously	ADV
ejde-517	808	2	,	,	PUNCT
ejde-517	808	3	λχ1+(1−λ)χ̄1	λχ1+(1−λ)χ̄1	NOUN
ejde-517	808	4	∈	∈	PROPN
ejde-517	808	5	l2(ω	l2(ω	PROPN
ejde-517	808	6	)	)	PUNCT
ejde-517	808	7	.	.	PUNCT
ejde-517	809	1	we	we	PRON
ejde-517	809	2	only	only	ADV
ejde-517	809	3	need	need	VERB
ejde-517	809	4	to	to	PART
ejde-517	809	5	show	show	VERB
ejde-517	809	6	that	that	SCONJ
ejde-517	809	7	0	0	NUM
ejde-517	809	8	≤	≤	NOUN
ejde-517	809	9	λχ1	λχ1	X
ejde-517	809	10	+	+	CCONJ
ejde-517	809	11	(	(	PUNCT
ejde-517	809	12	1−	1−	NUM
ejde-517	809	13	λ)χ̄1	λ)χ̄1	ADJ
ejde-517	809	14	≤	≤	ADV
ejde-517	809	15	1	1	NUM
ejde-517	809	16	.	.	PUNCT
ejde-517	810	1	because	because	SCONJ
ejde-517	810	2	λ	λ	NOUN
ejde-517	810	3	,	,	PUNCT
ejde-517	810	4	1−	1−	NUM
ejde-517	810	5	λ	λ	X
ejde-517	810	6	>	>	X
ejde-517	810	7	0	0	PUNCT
ejde-517	810	8	then	then	ADV
ejde-517	810	9	λχ1	λχ1	X
ejde-517	810	10	+	+	CCONJ
ejde-517	810	11	(	(	PUNCT
ejde-517	810	12	1	1	NUM
ejde-517	810	13	−	−	NOUN
ejde-517	810	14	λ)χ̄1	λ)χ̄1	ADJ
ejde-517	810	15	≥	≥	NOUN
ejde-517	810	16	0	0	NUM
ejde-517	810	17	.	.	PUNCT
ejde-517	811	1	furthermore	furthermore	ADV
ejde-517	811	2	,	,	PUNCT
ejde-517	811	3	λχ1	λχ1	X
ejde-517	811	4	+	+	CCONJ
ejde-517	811	5	(	(	PUNCT
ejde-517	811	6	1	1	NUM
ejde-517	811	7	−	−	NOUN
ejde-517	812	1	λ)χ̄1	λ)χ̄1	ADJ
ejde-517	812	2	≤	≤	NOUN
ejde-517	812	3	λ	λ	X
ejde-517	812	4	+	+	NOUN
ejde-517	812	5	1	1	NUM
ejde-517	812	6	−	−	NOUN
ejde-517	812	7	λ	λ	X
ejde-517	812	8	=	=	NOUN
ejde-517	812	9	1	1	NUM
ejde-517	812	10	.	.	PUNCT
ejde-517	812	11	thus	thus	ADV
ejde-517	812	12	,	,	PUNCT
ejde-517	812	13	λχ1	λχ1	X
ejde-517	812	14	+	+	CCONJ
ejde-517	812	15	(	(	PUNCT
ejde-517	812	16	1−	1−	NUM
ejde-517	812	17	λ)χ̄1	λ)χ̄1	NOUN
ejde-517	812	18	∈	∈	PROPN
ejde-517	812	19	k	k	PROPN
ejde-517	812	20	and	and	CCONJ
ejde-517	812	21	k	k	PROPN
ejde-517	812	22	is	be	AUX
ejde-517	812	23	convex	convex	ADJ
ejde-517	812	24	in	in	ADP
ejde-517	812	25	l2(ω	l2(ω	PROPN
ejde-517	812	26	)	)	PUNCT
ejde-517	812	27	.	.	PUNCT
ejde-517	813	1	we	we	PRON
ejde-517	813	2	show	show	VERB
ejde-517	813	3	next	next	ADV
ejde-517	813	4	that	that	SCONJ
ejde-517	813	5	υ	υ	PROPN
ejde-517	813	6	is	be	AUX
ejde-517	813	7	continuous	continuous	ADJ
ejde-517	813	8	.	.	PUNCT
ejde-517	814	1	the	the	DET
ejde-517	814	2	functions	function	NOUN
ejde-517	814	3	g	g	NOUN
ejde-517	814	4	,	,	PUNCT
ejde-517	814	5	θ	θ	PROPN
ejde-517	814	6	,	,	PUNCT
ejde-517	814	7	h	h	NOUN
ejde-517	814	8	,	,	PUNCT
ejde-517	814	9	and	and	CCONJ
ejde-517	814	10	m	m	NOUN
ejde-517	814	11	are	be	AUX
ejde-517	814	12	continuous	continuous	ADJ
ejde-517	814	13	as	as	SCONJ
ejde-517	814	14	proven	prove	VERB
ejde-517	814	15	in	in	ADP
ejde-517	814	16	lemma	lemma	PROPN
ejde-517	814	17	4.2	4.2	NUM
ejde-517	814	18	,	,	PUNCT
ejde-517	814	19	lemma	lemma	PROPN
ejde-517	814	20	4.4	4.4	NUM
ejde-517	814	21	,	,	PUNCT
ejde-517	814	22	lemma	lemma	PROPN
ejde-517	814	23	4.5	4.5	NUM
ejde-517	814	24	,	,	PUNCT
ejde-517	814	25	and	and	CCONJ
ejde-517	814	26	lemma	lemma	PROPN
ejde-517	814	27	4.7	4.7	NUM
ejde-517	814	28	,	,	PUNCT
ejde-517	814	29	respectively	respectively	ADV
ejde-517	814	30	.	.	PUNCT
ejde-517	815	1	from	from	ADP
ejde-517	815	2	lemma	lemma	PROPN
ejde-517	815	3	3.8	3.8	NUM
ejde-517	815	4	,	,	PUNCT
ejde-517	815	5	tδ	tδ	PROPN
ejde-517	815	6	is	be	AUX
ejde-517	815	7	continuous	continuous	ADJ
ejde-517	815	8	as	as	ADV
ejde-517	815	9	well	well	ADV
ejde-517	815	10	by	by	ADP
ejde-517	815	11	choosing	choose	VERB
ejde-517	815	12	p	p	NOUN
ejde-517	815	13	=	=	PROPN
ejde-517	815	14	2	2	NUM
ejde-517	815	15	,	,	PUNCT
ejde-517	815	16	r	r	NOUN
ejde-517	815	17	=	=	SYM
ejde-517	815	18	2	2	NUM
ejde-517	815	19	,	,	PUNCT
ejde-517	815	20	and	and	CCONJ
ejde-517	815	21	q	q	NOUN
ejde-517	815	22	=	=	NOUN
ejde-517	815	23	1	1	X
ejde-517	815	24	.	.	PUNCT
ejde-517	816	1	because	because	SCONJ
ejde-517	816	2	composition	composition	NOUN
ejde-517	816	3	of	of	ADP
ejde-517	816	4	continuous	continuous	ADJ
ejde-517	816	5	functions	function	NOUN
ejde-517	816	6	is	be	AUX
ejde-517	816	7	continuous	continuous	ADJ
ejde-517	816	8	,	,	PUNCT
ejde-517	816	9	υ	υ	PROPN
ejde-517	816	10	is	be	AUX
ejde-517	816	11	continuous	continuous	ADJ
ejde-517	816	12	.	.	PUNCT
ejde-517	817	1	we	we	PRON
ejde-517	817	2	only	only	ADV
ejde-517	817	3	need	need	VERB
ejde-517	817	4	to	to	PART
ejde-517	817	5	show	show	VERB
ejde-517	817	6	that	that	SCONJ
ejde-517	817	7	υ(k	υ(k	PROPN
ejde-517	817	8	)	)	PUNCT
ejde-517	818	1	⊂	⊂	PROPN
ejde-517	818	2	k	k	PROPN
ejde-517	818	3	and	and	CCONJ
ejde-517	818	4	that	that	SCONJ
ejde-517	818	5	υ(k	υ(k	PROPN
ejde-517	818	6	)	)	PUNCT
ejde-517	818	7	is	be	AUX
ejde-517	818	8	compact	compact	ADJ
ejde-517	818	9	in	in	ADP
ejde-517	818	10	k.	k.	PROPN
ejde-517	818	11	recall	recall	VERB
ejde-517	818	12	that	that	PRON
ejde-517	818	13	(	(	PUNCT
ejde-517	819	1	m	m	NOUN
ejde-517	819	2	◦	◦	NOUN
ejde-517	819	3	h	h	NOUN
ejde-517	819	4	◦	◦	NOUN
ejde-517	819	5	θ	θ	PROPN
ejde-517	819	6	◦	◦	NOUN
ejde-517	819	7	g)(χδ1	g)(χδ1	NOUN
ejde-517	819	8	)	)	PUNCT
ejde-517	819	9	is	be	AUX
ejde-517	819	10	a	a	DET
ejde-517	819	11	characteristic	characteristic	ADJ
ejde-517	819	12	function	function	NOUN
ejde-517	819	13	.	.	PUNCT
ejde-517	820	1	thus	thus	ADV
ejde-517	820	2	,	,	PUNCT
ejde-517	820	3	0	0	NUM
ejde-517	820	4	≤	≤	NUM
ejde-517	820	5	(	(	PUNCT
ejde-517	820	6	m	m	NOUN
ejde-517	820	7	◦	◦	NOUN
ejde-517	820	8	h	h	NOUN
ejde-517	820	9	◦	◦	NOUN
ejde-517	820	10	θ	θ	PROPN
ejde-517	820	11	◦	◦	NOUN
ejde-517	820	12	g)(χδ1	g)(χδ1	NOUN
ejde-517	820	13	)	)	PUNCT
ejde-517	820	14	≤	≤	NUM
ejde-517	820	15	1	1	NUM
ejde-517	820	16	.	.	PUNCT
ejde-517	820	17	by	by	ADP
ejde-517	820	18	theorem	theorem	NOUN
ejde-517	820	19	2.5	2.5	NUM
ejde-517	820	20	,	,	PUNCT
ejde-517	820	21	0	0	NUM
ejde-517	820	22	≤	≤	NUM
ejde-517	820	23	(	(	PUNCT
ejde-517	820	24	tδ	tδ	ADP
ejde-517	820	25	◦	◦	NOUN
ejde-517	820	26	m	m	NOUN
ejde-517	820	27	◦	◦	NOUN
ejde-517	820	28	h	h	NOUN
ejde-517	820	29	◦	◦	NOUN
ejde-517	820	30	θ	θ	PROPN
ejde-517	820	31	◦	◦	NOUN
ejde-517	820	32	g)(χδ1	g)(χδ1	NOUN
ejde-517	820	33	)	)	PUNCT
ejde-517	820	34	≤	≤	NUM
ejde-517	820	35	1	1	NUM
ejde-517	820	36	,	,	PUNCT
ejde-517	820	37	and	and	CCONJ
ejde-517	820	38	so	so	ADV
ejde-517	820	39	υ(χ1	υ(χ1	ADJ
ejde-517	820	40	)	)	PUNCT
ejde-517	820	41	∈	∈	PROPN
ejde-517	820	42	k.	k.	PROPN
ejde-517	820	43	let	let	VERB
ejde-517	820	44	χ̄1	χ̄1	NOUN
ejde-517	820	45	be	be	AUX
ejde-517	820	46	an	an	DET
ejde-517	820	47	arbitrary	arbitrary	ADJ
ejde-517	820	48	element	element	NOUN
ejde-517	820	49	of	of	ADP
ejde-517	820	50	k.	k.	PROPN
ejde-517	820	51	let	let	VERB
ejde-517	820	52	us	we	PRON
ejde-517	820	53	denote	denote	VERB
ejde-517	820	54	ω	ω	NOUN
ejde-517	820	55	:	:	PUNCT
ejde-517	820	56	=	=	SYM
ejde-517	820	57	(	(	PUNCT
ejde-517	820	58	h	h	NOUN
ejde-517	820	59	◦	◦	NOUN
ejde-517	820	60	θ	θ	NOUN
ejde-517	820	61	◦	◦	NOUN
ejde-517	820	62	g)(χ̄δ1	g)(χ̄δ1	NOUN
ejde-517	820	63	)	)	PUNCT
ejde-517	820	64	,	,	PUNCT
ejde-517	820	65	χω	χω	ADP
ejde-517	820	66	:	:	PUNCT
ejde-517	820	67	=	=	SYM
ejde-517	820	68	m(ω	m(ω	NOUN
ejde-517	820	69	)	)	PUNCT
ejde-517	820	70	,	,	PUNCT
ejde-517	820	71	and	and	CCONJ
ejde-517	820	72	χωδ	χωδ	NOUN
ejde-517	820	73	:	:	PUNCT
ejde-517	820	74	=	=	SYM
ejde-517	820	75	tδ(χ	tδ(χ	X
ejde-517	820	76	ω	ω	NUM
ejde-517	820	77	)	)	PUNCT
ejde-517	820	78	.	.	PUNCT
ejde-517	821	1	by	by	ADP
ejde-517	821	2	lemma	lemma	PROPN
ejde-517	821	3	3.9	3.9	NUM
ejde-517	821	4	,	,	PUNCT
ejde-517	821	5	hölder	hölder	NOUN
ejde-517	821	6	’s	’s	PART
ejde-517	821	7	inequality	inequality	NOUN
ejde-517	821	8	,	,	PUNCT
ejde-517	821	9	and	and	CCONJ
ejde-517	821	10	the	the	DET
ejde-517	821	11	cauchy	cauchy	PROPN
ejde-517	821	12	-	-	PUNCT
ejde-517	821	13	schwarz	schwarz	PROPN
ejde-517	821	14	inequality	inequality	NOUN
ejde-517	821	15	,	,	PUNCT
ejde-517	821	16	we	we	PRON
ejde-517	821	17	obtain	obtain	VERB
ejde-517	821	18	|∇χωδ	|∇χωδ	PROPN
ejde-517	821	19	(	(	PUNCT
ejde-517	821	20	x)|	x)|	PROPN
ejde-517	821	21	=	=	SYM
ejde-517	822	1	|	|	CCONJ
ejde-517	822	2	∫	∫	PROPN
ejde-517	822	3	ω	ω	PROPN
ejde-517	822	4	∇ξδ(x−	∇ξδ(x−	PROPN
ejde-517	822	5	y)χω(y)dy|	y)χω(y)dy|	PROPN
ejde-517	822	6	≤	≤	PROPN
ejde-517	822	7	‖χω‖l∞(ω	‖χω‖l∞(ω	PROPN
ejde-517	822	8	)	)	PUNCT
ejde-517	822	9	∫	∫	PROPN
ejde-517	823	1	ω	ω	PROPN
ejde-517	823	2	|∇ξδ(x−	|∇ξδ(x−	PROPN
ejde-517	823	3	y)|dy	y)|dy	PROPN
ejde-517	823	4	≤	≤	PROPN
ejde-517	823	5	√	√	NUM
ejde-517	823	6	µ(ω)‖∇ξδ‖l2(ω	µ(ω)‖∇ξδ‖l2(ω	PRON
ejde-517	823	7	)	)	PUNCT
ejde-517	823	8	.	.	PUNCT
ejde-517	824	1	28	28	NUM
ejde-517	824	2	r.	r.	PROPN
ejde-517	824	3	mendoza	mendoza	PROPN
ejde-517	824	4	,	,	PUNCT
ejde-517	824	5	s.	s.	PROPN
ejde-517	824	6	keeling	keeling	PROPN
ejde-517	824	7	ejde-2020/93	ejde-2020/93	PROPN
ejde-517	824	8	hence	hence	ADV
ejde-517	824	9	,	,	PUNCT
ejde-517	824	10	‖∇χωδ	‖∇χωδ	PROPN
ejde-517	824	11	‖2l2(ω	‖2l2(ω	PUNCT
ejde-517	824	12	)	)	PUNCT
ejde-517	824	13	=	=	SYM
ejde-517	825	1	∫	∫	PROPN
ejde-517	825	2	ω	ω	NUM
ejde-517	826	1	|	|	ADV
ejde-517	826	2	∫	∫	PROPN
ejde-517	827	1	ω	ω	PROPN
ejde-517	827	2	∇ξδ(x−	∇ξδ(x−	PROPN
ejde-517	827	3	y)χω(y)dy|2dx	y)χω(y)dy|2dx	PROPN
ejde-517	827	4	≤	≤	NOUN
ejde-517	827	5	µ(ω)2‖∇ξδ‖2l2(ω	µ(ω)2‖∇ξδ‖2l2(ω	NOUN
ejde-517	827	6	)	)	PUNCT
ejde-517	827	7	.	.	PUNCT
ejde-517	828	1	from	from	ADP
ejde-517	828	2	lemma	lemma	PROPN
ejde-517	828	3	2.5	2.5	NUM
ejde-517	828	4	,	,	PUNCT
ejde-517	828	5	χωδ	χωδ	PROPN
ejde-517	828	6	is	be	AUX
ejde-517	828	7	real	real	ADV
ejde-517	828	8	analytic	analytic	ADJ
ejde-517	828	9	and	and	CCONJ
ejde-517	828	10	so	so	ADV
ejde-517	828	11	χωδ	χωδ	PROPN
ejde-517	828	12	∈	∈	PROPN
ejde-517	828	13	h1(ω	h1(ω	PROPN
ejde-517	828	14	)	)	PUNCT
ejde-517	828	15	.	.	PUNCT
ejde-517	829	1	for	for	ADP
ejde-517	829	2	a	a	DET
ejde-517	829	3	fixed	fix	VERB
ejde-517	829	4	δ	δ	PROPN
ejde-517	829	5	,	,	PUNCT
ejde-517	829	6	we	we	PRON
ejde-517	829	7	compute	compute	VERB
ejde-517	829	8	the	the	DET
ejde-517	829	9	h1(ω	h1(ω	NOUN
ejde-517	829	10	)	)	PUNCT
ejde-517	829	11	norm	norm	NOUN
ejde-517	829	12	of	of	ADP
ejde-517	829	13	χωδ	χωδ	PROPN
ejde-517	829	14	using	use	VERB
ejde-517	829	15	young	young	PROPN
ejde-517	829	16	’s	’s	PART
ejde-517	829	17	inequality	inequality	NOUN
ejde-517	829	18	for	for	ADP
ejde-517	829	19	convolutions	convolution	NOUN
ejde-517	829	20	and	and	CCONJ
ejde-517	829	21	the	the	DET
ejde-517	829	22	hölder	hölder	NOUN
ejde-517	829	23	’s	’s	PART
ejde-517	829	24	inequality	inequality	NOUN
ejde-517	829	25	:	:	PUNCT
ejde-517	829	26	‖υ(χ̄1)‖2h1(ω	‖υ(χ̄1)‖2h1(ω	PROPN
ejde-517	829	27	)	)	PUNCT
ejde-517	829	28	=	=	SYM
ejde-517	829	29	‖χωδ	‖χωδ	NOUN
ejde-517	829	30	‖2h1(ω	‖2h1(ω	NOUN
ejde-517	829	31	)	)	PUNCT
ejde-517	830	1	=	=	SYM
ejde-517	830	2	‖χωδ	‖χωδ	NOUN
ejde-517	830	3	‖2l2(ω	‖2l2(ω	ADV
ejde-517	830	4	)	)	PUNCT
ejde-517	831	1	+	+	CCONJ
ejde-517	831	2	‖∇χωδ	‖∇χωδ	NUM
ejde-517	831	3	‖2l2(ω	‖2l2(ω	NUM
ejde-517	831	4	)	)	PUNCT
ejde-517	831	5	≤	≤	NOUN
ejde-517	831	6	‖χω	‖χω	NUM
ejde-517	831	7	∗	∗	NOUN
ejde-517	831	8	ξδ‖2l2(ω	ξδ‖2l2(ω	ADV
ejde-517	831	9	)	)	PUNCT
ejde-517	832	1	+	+	CCONJ
ejde-517	832	2	µ(ω)2‖∇ξδ‖2l2(ω	µ(ω)2‖∇ξδ‖2l2(ω	ADJ
ejde-517	832	3	)	)	PUNCT
ejde-517	832	4	≤	≤	NUM
ejde-517	832	5	‖χω‖2l1(ω)‖ξδ‖	‖χω‖2l1(ω)‖ξδ‖	PUNCT
ejde-517	832	6	2	2	NUM
ejde-517	832	7	l2(ω	l2(ω	NOUN
ejde-517	832	8	)	)	PUNCT
ejde-517	832	9	+	+	CCONJ
ejde-517	832	10	µ(ω)2‖∇ξδ‖2l2(ω	µ(ω)2‖∇ξδ‖2l2(ω	ADJ
ejde-517	832	11	)	)	PUNCT
ejde-517	832	12	≤	≤	NOUN
ejde-517	832	13	‖χω‖2l∞(ω)µ(ω)2‖ξδ‖2l2(ω	‖χω‖2l∞(ω)µ(ω)2‖ξδ‖2l2(ω	ADV
ejde-517	832	14	)	)	PUNCT
ejde-517	832	15	+	+	CCONJ
ejde-517	832	16	µ(ω)2‖∇ξδ‖2l2(ω	µ(ω)2‖∇ξδ‖2l2(ω	ADJ
ejde-517	832	17	)	)	PUNCT
ejde-517	832	18	≤	≤	NUM
ejde-517	833	1	µ(ω)2	µ(ω)2	ADP
ejde-517	833	2	(	(	PUNCT
ejde-517	833	3	‖ξδ‖2l2(ω	‖ξδ‖2l2(ω	NOUN
ejde-517	833	4	)	)	PUNCT
ejde-517	833	5	+	+	CCONJ
ejde-517	833	6	‖∇ξδ‖2l2(ω	‖∇ξδ‖2l2(ω	NOUN
ejde-517	833	7	)	)	PUNCT
ejde-517	833	8	)	)	PUNCT
ejde-517	833	9	.	.	PUNCT
ejde-517	834	1	since	since	SCONJ
ejde-517	834	2	χ̄1	χ̄1	X
ejde-517	834	3	is	be	AUX
ejde-517	834	4	arbitrary	arbitrary	ADJ
ejde-517	834	5	,	,	PUNCT
ejde-517	834	6	any	any	DET
ejde-517	834	7	sequence	sequence	NOUN
ejde-517	834	8	{	{	PUNCT
ejde-517	834	9	υ(χn1	υ(χn1	PROPN
ejde-517	834	10	)	)	PUNCT
ejde-517	834	11	}	}	PUNCT
ejde-517	834	12	∞n=1	∞n=1	PROPN
ejde-517	834	13	is	be	AUX
ejde-517	834	14	bounded	bound	VERB
ejde-517	834	15	in	in	ADP
ejde-517	834	16	the	the	DET
ejde-517	834	17	h1(ω	h1(ω	NOUN
ejde-517	834	18	)	)	PUNCT
ejde-517	834	19	norm	norm	NOUN
ejde-517	834	20	for	for	ADP
ejde-517	834	21	a	a	DET
ejde-517	834	22	fixed	fixed	ADJ
ejde-517	834	23	δ	δ	PROPN
ejde-517	834	24	.	.	PUNCT
ejde-517	835	1	because	because	SCONJ
ejde-517	835	2	ω	ω	PROPN
ejde-517	835	3	is	be	AUX
ejde-517	835	4	bounded	bound	VERB
ejde-517	835	5	,	,	PUNCT
ejde-517	835	6	h1(ω	h1(ω	PROPN
ejde-517	835	7	)	)	PUNCT
ejde-517	835	8	is	be	AUX
ejde-517	835	9	compactly	compactly	ADV
ejde-517	835	10	embedded	embed	VERB
ejde-517	835	11	in	in	ADP
ejde-517	835	12	l2(ω	l2(ω	PROPN
ejde-517	835	13	)	)	PUNCT
ejde-517	835	14	and	and	CCONJ
ejde-517	835	15	{	{	PUNCT
ejde-517	835	16	υ(χn1	υ(χn1	PROPN
ejde-517	835	17	)	)	PUNCT
ejde-517	835	18	}	}	PUNCT
ejde-517	835	19	∞n=1	∞n=1	PROPN
ejde-517	835	20	has	have	VERB
ejde-517	835	21	a	a	DET
ejde-517	835	22	convergent	convergent	ADJ
ejde-517	835	23	subsequence	subsequence	NOUN
ejde-517	836	1	[	[	X
ejde-517	836	2	1	1	NUM
ejde-517	836	3	]	]	PUNCT
ejde-517	836	4	.	.	PUNCT
ejde-517	837	1	therefore	therefore	ADV
ejde-517	837	2	υ(k	υ(k	PROPN
ejde-517	837	3	)	)	PUNCT
ejde-517	837	4	is	be	AUX
ejde-517	837	5	compact	compact	ADJ
ejde-517	837	6	.	.	PUNCT
ejde-517	838	1	using	use	VERB
ejde-517	838	2	schauder	schauder	NOUN
ejde-517	838	3	fixed	fix	VERB
ejde-517	838	4	point	point	NOUN
ejde-517	838	5	theorem	theorem	VERB
ejde-517	838	6	,	,	PUNCT
ejde-517	838	7	υ1	υ1	PROPN
ejde-517	838	8	has	have	VERB
ejde-517	838	9	a	a	DET
ejde-517	838	10	fixed	fix	VERB
ejde-517	838	11	point	point	NOUN
ejde-517	838	12	on	on	ADP
ejde-517	838	13	k.	k.	PROPN
ejde-517	838	14	�	�	PROPN
ejde-517	838	15	the	the	DET
ejde-517	838	16	fixed	fix	VERB
ejde-517	838	17	point	point	NOUN
ejde-517	838	18	is	be	AUX
ejde-517	838	19	attained	attain	VERB
ejde-517	838	20	given	give	VERB
ejde-517	838	21	any	any	DET
ejde-517	838	22	arbitrary	arbitrary	ADJ
ejde-517	838	23	χ1	χ1	NOUN
ejde-517	838	24	∈	∈	PROPN
ejde-517	838	25	l2(ω	l2(ω	NOUN
ejde-517	838	26	)	)	PUNCT
ejde-517	838	27	such	such	ADJ
ejde-517	838	28	that	that	SCONJ
ejde-517	838	29	0	0	NUM
ejde-517	838	30	≤	≤	NOUN
ejde-517	838	31	χ1	χ1	NOUN
ejde-517	838	32	≤	≤	NUM
ejde-517	838	33	1	1	NUM
ejde-517	838	34	and	and	CCONJ
ejde-517	838	35	σ̄1	σ̄1	NUM
ejde-517	838	36	in	in	ADP
ejde-517	838	37	c∞(ω	c∞(ω	NOUN
ejde-517	838	38	)	)	PUNCT
ejde-517	838	39	,	,	PUNCT
ejde-517	838	40	which	which	PRON
ejde-517	838	41	can	can	AUX
ejde-517	838	42	be	be	AUX
ejde-517	838	43	chosen	choose	VERB
ejde-517	838	44	to	to	PART
ejde-517	838	45	be	be	AUX
ejde-517	838	46	a	a	DET
ejde-517	838	47	constant	constant	ADJ
ejde-517	838	48	.	.	PUNCT
ejde-517	839	1	the	the	DET
ejde-517	839	2	introduction	introduction	NOUN
ejde-517	839	3	of	of	ADP
ejde-517	839	4	a	a	DET
ejde-517	839	5	mollifier	mollifier	NOUN
ejde-517	839	6	was	be	AUX
ejde-517	839	7	used	use	VERB
ejde-517	839	8	to	to	PART
ejde-517	839	9	guarantee	guarantee	VERB
ejde-517	839	10	the	the	DET
ejde-517	839	11	existence	existence	NOUN
ejde-517	839	12	of	of	ADP
ejde-517	839	13	the	the	DET
ejde-517	839	14	fixed	fix	VERB
ejde-517	839	15	point	point	NOUN
ejde-517	839	16	.	.	PUNCT
ejde-517	840	1	note	note	VERB
ejde-517	840	2	that	that	SCONJ
ejde-517	840	3	a	a	DET
ejde-517	840	4	fixed	fix	VERB
ejde-517	840	5	point	point	NOUN
ejde-517	840	6	is	be	AUX
ejde-517	840	7	guaranteed	guarantee	VERB
ejde-517	840	8	for	for	ADP
ejde-517	840	9	any	any	DET
ejde-517	840	10	arbitrary	arbitrary	ADJ
ejde-517	840	11	δ	δ	NOUN
ejde-517	840	12	>	>	X
ejde-517	840	13	0	0	NUM
ejde-517	840	14	.	.	PROPN
ejde-517	841	1	5	5	NUM
ejde-517	841	2	.	.	X
ejde-517	841	3	conclusion	conclusion	NOUN
ejde-517	841	4	the	the	DET
ejde-517	841	5	eit	eit	PROPN
ejde-517	841	6	problem	problem	NOUN
ejde-517	841	7	is	be	AUX
ejde-517	841	8	the	the	DET
ejde-517	841	9	image	image	NOUN
ejde-517	841	10	reconstruction	reconstruction	NOUN
ejde-517	841	11	of	of	ADP
ejde-517	841	12	the	the	DET
ejde-517	841	13	conductivity	conductivity	NOUN
ejde-517	841	14	distribution	distribution	NOUN
ejde-517	841	15	of	of	ADP
ejde-517	841	16	a	a	DET
ejde-517	841	17	body	body	NOUN
ejde-517	841	18	ω	ω	NOUN
ejde-517	841	19	given	give	VERB
ejde-517	841	20	current	current	ADJ
ejde-517	841	21	and	and	CCONJ
ejde-517	841	22	electrical	electrical	ADJ
ejde-517	841	23	potential	potential	ADJ
ejde-517	841	24	data	datum	NOUN
ejde-517	841	25	on	on	ADP
ejde-517	841	26	the	the	DET
ejde-517	841	27	boundary	boundary	ADJ
ejde-517	841	28	∂ω	∂ω	PROPN
ejde-517	841	29	.	.	PUNCT
ejde-517	842	1	in	in	ADP
ejde-517	842	2	[	[	X
ejde-517	842	3	27	27	NUM
ejde-517	842	4	]	]	PUNCT
ejde-517	842	5	,	,	PUNCT
ejde-517	842	6	a	a	DET
ejde-517	842	7	two	two	NUM
ejde-517	842	8	-	-	PUNCT
ejde-517	842	9	phase	phase	NOUN
ejde-517	842	10	segmentation	segmentation	NOUN
ejde-517	842	11	algorithm	algorithm	NOUN
ejde-517	842	12	was	be	AUX
ejde-517	842	13	proposed	propose	VERB
ejde-517	842	14	in	in	ADP
ejde-517	842	15	reconstructing	reconstruct	VERB
ejde-517	842	16	conductivity	conductivity	NOUN
ejde-517	842	17	distribution	distribution	NOUN
ejde-517	842	18	in	in	ADP
ejde-517	842	19	eit	eit	PROPN
ejde-517	842	20	.	.	PUNCT
ejde-517	843	1	the	the	DET
ejde-517	843	2	algorithm	algorithm	NOUN
ejde-517	843	3	arised	arise	VERB
ejde-517	843	4	from	from	ADP
ejde-517	843	5	the	the	DET
ejde-517	843	6	minimization	minimization	NOUN
ejde-517	843	7	of	of	ADP
ejde-517	843	8	a	a	DET
ejde-517	843	9	functional	functional	ADJ
ejde-517	843	10	which	which	PRON
ejde-517	843	11	depends	depend	VERB
ejde-517	843	12	on	on	ADP
ejde-517	843	13	the	the	DET
ejde-517	843	14	conductivity	conductivity	NOUN
ejde-517	843	15	distribution	distribution	NOUN
ejde-517	843	16	σ	σ	NOUN
ejde-517	844	1	=	=	PUNCT
ejde-517	844	2	σ1χ1	σ1χ1	X
ejde-517	844	3	+	+	CCONJ
ejde-517	844	4	σ2(1−	σ2(1−	PROPN
ejde-517	844	5	χ1	χ1	NOUN
ejde-517	844	6	)	)	PUNCT
ejde-517	844	7	.	.	PUNCT
ejde-517	845	1	the	the	DET
ejde-517	845	2	value	value	NOUN
ejde-517	845	3	of	of	ADP
ejde-517	845	4	σ2	σ2	PROPN
ejde-517	845	5	is	be	AUX
ejde-517	845	6	fixed	fix	VERB
ejde-517	845	7	and	and	CCONJ
ejde-517	845	8	known	know	VERB
ejde-517	845	9	while	while	SCONJ
ejde-517	845	10	σ1	σ1	PROPN
ejde-517	845	11	is	be	AUX
ejde-517	845	12	expressed	express	VERB
ejde-517	845	13	in	in	ADP
ejde-517	845	14	terms	term	NOUN
ejde-517	845	15	of	of	ADP
ejde-517	845	16	χ1	χ1	NOUN
ejde-517	845	17	.	.	PUNCT
ejde-517	846	1	hence	hence	ADV
ejde-517	846	2	,	,	PUNCT
ejde-517	846	3	the	the	DET
ejde-517	846	4	functional	functional	ADJ
ejde-517	846	5	depends	depend	VERB
ejde-517	846	6	on	on	ADP
ejde-517	846	7	χ1	χ1	NOUN
ejde-517	846	8	alone	alone	ADV
ejde-517	846	9	.	.	PUNCT
ejde-517	847	1	an	an	DET
ejde-517	847	2	iterative	iterative	NOUN
ejde-517	847	3	algorithm	algorithm	NOUN
ejde-517	847	4	using	use	VERB
ejde-517	847	5	the	the	DET
ejde-517	847	6	method	method	NOUN
ejde-517	847	7	of	of	ADP
ejde-517	847	8	steepest	steep	ADJ
ejde-517	847	9	descent	descent	NOUN
ejde-517	847	10	is	be	AUX
ejde-517	847	11	then	then	ADV
ejde-517	847	12	explored	explore	VERB
ejde-517	847	13	.	.	PUNCT
ejde-517	848	1	moreover	moreover	ADV
ejde-517	848	2	,	,	PUNCT
ejde-517	848	3	the	the	DET
ejde-517	848	4	algorithm	algorithm	NOUN
ejde-517	848	5	is	be	AUX
ejde-517	848	6	summarized	summarize	VERB
ejde-517	848	7	using	use	VERB
ejde-517	848	8	a	a	DET
ejde-517	848	9	composition	composition	NOUN
ejde-517	848	10	of	of	ADP
ejde-517	848	11	several	several	ADJ
ejde-517	848	12	functions	function	NOUN
ejde-517	848	13	of	of	ADP
ejde-517	848	14	χ1	χ1	NOUN
ejde-517	848	15	.	.	PUNCT
ejde-517	849	1	by	by	ADP
ejde-517	849	2	introducing	introduce	VERB
ejde-517	849	3	a	a	DET
ejde-517	849	4	mollification	mollification	NOUN
ejde-517	849	5	on	on	ADP
ejde-517	849	6	χ1	χ1	NOUN
ejde-517	849	7	,	,	PUNCT
ejde-517	849	8	continuity	continuity	NOUN
ejde-517	849	9	of	of	ADP
ejde-517	849	10	these	these	DET
ejde-517	849	11	functions	function	NOUN
ejde-517	849	12	was	be	AUX
ejde-517	849	13	shown	show	VERB
ejde-517	849	14	.	.	PUNCT
ejde-517	850	1	finally	finally	ADV
ejde-517	850	2	,	,	PUNCT
ejde-517	850	3	the	the	DET
ejde-517	850	4	existence	existence	NOUN
ejde-517	850	5	of	of	ADP
ejde-517	850	6	a	a	DET
ejde-517	850	7	fixed	fix	VERB
ejde-517	850	8	point	point	NOUN
ejde-517	850	9	of	of	ADP
ejde-517	850	10	the	the	DET
ejde-517	850	11	proposed	propose	VERB
ejde-517	850	12	method	method	NOUN
ejde-517	850	13	was	be	AUX
ejde-517	850	14	proved	prove	VERB
ejde-517	850	15	using	use	VERB
ejde-517	850	16	the	the	DET
ejde-517	850	17	schauder	schauder	NOUN
ejde-517	850	18	fixed	fix	VERB
ejde-517	850	19	point	point	NOUN
ejde-517	850	20	theorem	theorem	VERB
ejde-517	850	21	.	.	PUNCT
ejde-517	850	22	acknowledgments	acknowledgment	NOUN
ejde-517	850	23	.	.	PUNCT
ejde-517	851	1	r.	r.	PROPN
ejde-517	851	2	mendoza	mendoza	PROPN
ejde-517	851	3	acknowledges	acknowledge	VERB
ejde-517	851	4	the	the	DET
ejde-517	851	5	office	office	NOUN
ejde-517	851	6	of	of	ADP
ejde-517	851	7	the	the	DET
ejde-517	851	8	chancellor	chancellor	NOUN
ejde-517	851	9	of	of	ADP
ejde-517	851	10	the	the	DET
ejde-517	851	11	university	university	NOUN
ejde-517	851	12	of	of	ADP
ejde-517	851	13	the	the	DET
ejde-517	851	14	philippines	philippine	NOUN
ejde-517	851	15	diliman	diliman	PROPN
ejde-517	851	16	,	,	PUNCT
ejde-517	851	17	through	through	ADP
ejde-517	851	18	the	the	DET
ejde-517	851	19	office	office	NOUN
ejde-517	851	20	of	of	ADP
ejde-517	851	21	the	the	DET
ejde-517	851	22	vice	vice	NOUN
ejde-517	851	23	chancellor	chancellor	NOUN
ejde-517	851	24	for	for	ADP
ejde-517	851	25	research	research	NOUN
ejde-517	851	26	and	and	CCONJ
ejde-517	851	27	development	development	NOUN
ejde-517	851	28	,	,	PUNCT
ejde-517	851	29	for	for	ADP
ejde-517	851	30	funding	fund	VERB
ejde-517	851	31	support	support	NOUN
ejde-517	851	32	through	through	ADP
ejde-517	851	33	the	the	DET
ejde-517	851	34	ph.d	ph.d	PROPN
ejde-517	851	35	.	.	PUNCT
ejde-517	851	36	incentive	incentive	PROPN
ejde-517	851	37	award	award	PROPN
ejde-517	851	38	.	.	PUNCT
ejde-517	852	1	references	reference	NOUN
ejde-517	852	2	[	[	X
ejde-517	852	3	1	1	NUM
ejde-517	852	4	]	]	PUNCT
ejde-517	852	5	r.	r.	PROPN
ejde-517	852	6	adams	adams	PROPN
ejde-517	852	7	,	,	PUNCT
ejde-517	852	8	j.	j.	PROPN
ejde-517	852	9	fournier	fournier	PROPN
ejde-517	852	10	;	;	PUNCT
ejde-517	852	11	sobolev	sobolev	NOUN
ejde-517	852	12	spaces	space	NOUN
ejde-517	852	13	(	(	PUNCT
ejde-517	852	14	second	second	ADJ
ejde-517	852	15	edition	edition	NOUN
ejde-517	852	16	)	)	PUNCT
ejde-517	852	17	,	,	PUNCT
ejde-517	852	18	elsevier	elsevier	NOUN
ejde-517	852	19	,	,	PUNCT
ejde-517	852	20	2003	2003	NUM
ejde-517	852	21	.	.	PUNCT
ejde-517	853	1	[	[	X
ejde-517	853	2	2	2	X
ejde-517	853	3	]	]	PUNCT
ejde-517	853	4	k.	k.	PROPN
ejde-517	853	5	astala	astala	PROPN
ejde-517	853	6	,	,	PUNCT
ejde-517	853	7	l.	l.	PROPN
ejde-517	853	8	päivärinta	päivärinta	PROPN
ejde-517	853	9	;	;	PUNCT
ejde-517	853	10	calderon	calderon	PROPN
ejde-517	853	11	’s	’s	PART
ejde-517	853	12	inverse	inverse	NOUN
ejde-517	853	13	conductivity	conductivity	NOUN
ejde-517	853	14	problem	problem	NOUN
ejde-517	853	15	in	in	ADP
ejde-517	853	16	the	the	DET
ejde-517	853	17	plane	plane	NOUN
ejde-517	853	18	,	,	PUNCT
ejde-517	853	19	annals	annal	NOUN
ejde-517	853	20	of	of	ADP
ejde-517	853	21	mathematics	mathematic	NOUN
ejde-517	853	22	,	,	PUNCT
ejde-517	853	23	163	163	NUM
ejde-517	853	24	(	(	PUNCT
ejde-517	853	25	2006	2006	NUM
ejde-517	853	26	)	)	PUNCT
ejde-517	853	27	,	,	PUNCT
ejde-517	853	28	265–299	265–299	NUM
ejde-517	853	29	.	.	PUNCT
ejde-517	854	1	[	[	X
ejde-517	854	2	3	3	X
ejde-517	854	3	]	]	X
ejde-517	854	4	d.	d.	PROPN
ejde-517	854	5	c.	c.	PROPN
ejde-517	854	6	barber	barber	PROPN
ejde-517	854	7	,	,	PUNCT
ejde-517	854	8	b.	b.	PROPN
ejde-517	854	9	h.	h.	PROPN
ejde-517	854	10	brown	brown	PROPN
ejde-517	854	11	;	;	PUNCT
ejde-517	854	12	progress	progress	NOUN
ejde-517	854	13	in	in	ADP
ejde-517	854	14	electrical	electrical	ADJ
ejde-517	854	15	impedance	impedance	NOUN
ejde-517	854	16	tomography	tomography	NOUN
ejde-517	854	17	,	,	PUNCT
ejde-517	854	18	siam	siam	ADJ
ejde-517	854	19	inverse	inverse	NOUN
ejde-517	854	20	problems	problem	NOUN
ejde-517	854	21	in	in	ADP
ejde-517	854	22	partial	partial	ADJ
ejde-517	854	23	differential	differential	NOUN
ejde-517	854	24	equations	equation	NOUN
ejde-517	854	25	,	,	PUNCT
ejde-517	854	26	(	(	PUNCT
ejde-517	854	27	1990	1990	NUM
ejde-517	854	28	)	)	PUNCT
ejde-517	854	29	,	,	PUNCT
ejde-517	854	30	151–164	151–164	NUM
ejde-517	854	31	.	.	PUNCT
ejde-517	855	1	ejde-2020/93	ejde-2020/93	PROPN
ejde-517	855	2	impedance	impedance	NOUN
ejde-517	855	3	tomography	tomography	NOUN
ejde-517	855	4	problem	problem	NOUN
ejde-517	855	5	29	29	NUM
ejde-517	856	1	[	[	SYM
ejde-517	856	2	4	4	NUM
ejde-517	856	3	]	]	PUNCT
ejde-517	856	4	p.	p.	NOUN
ejde-517	856	5	bochev	bochev	PROPN
ejde-517	856	6	,	,	PUNCT
ejde-517	856	7	r.	r.	PROPN
ejde-517	856	8	b.	b.	PROPN
ejde-517	856	9	lehoucq	lehoucq	PROPN
ejde-517	856	10	;	;	PUNCT
ejde-517	856	11	on	on	ADP
ejde-517	856	12	the	the	DET
ejde-517	856	13	finite	finite	ADJ
ejde-517	856	14	element	element	NOUN
ejde-517	856	15	solution	solution	NOUN
ejde-517	856	16	of	of	ADP
ejde-517	856	17	the	the	DET
ejde-517	856	18	pure	pure	ADJ
ejde-517	856	19	neumann	neumann	PROPN
ejde-517	856	20	problem	problem	NOUN
ejde-517	856	21	,	,	PUNCT
ejde-517	856	22	siam	siam	PROPN
ejde-517	856	23	review	review	NOUN
ejde-517	856	24	47	47	NUM
ejde-517	856	25	(	(	PUNCT
ejde-517	856	26	2005	2005	NUM
ejde-517	856	27	)	)	PUNCT
ejde-517	856	28	,	,	PUNCT
ejde-517	856	29	50–66	50–66	X
ejde-517	856	30	.	.	PUNCT
ejde-517	857	1	[	[	X
ejde-517	857	2	5	5	X
ejde-517	857	3	]	]	PUNCT
ejde-517	857	4	l.	l.	PROPN
ejde-517	857	5	borcea	borcea	PROPN
ejde-517	857	6	;	;	PUNCT
ejde-517	857	7	electrical	electrical	ADJ
ejde-517	857	8	impedance	impedance	NOUN
ejde-517	857	9	tomography	tomography	NOUN
ejde-517	857	10	,	,	PUNCT
ejde-517	857	11	iop	iop	PROPN
ejde-517	857	12	publishing	publish	VERB
ejde-517	857	13	inverse	inverse	NOUN
ejde-517	857	14	problems	problem	NOUN
ejde-517	857	15	,	,	PUNCT
ejde-517	857	16	18	18	NUM
ejde-517	857	17	(	(	PUNCT
ejde-517	857	18	2002	2002	NUM
ejde-517	857	19	)	)	PUNCT
ejde-517	857	20	,	,	PUNCT
ejde-517	857	21	r99	r99	PROPN
ejde-517	857	22	–	–	PUNCT
ejde-517	857	23	r136	r136	PROPN
ejde-517	857	24	.	.	PUNCT
ejde-517	858	1	[	[	X
ejde-517	858	2	6	6	NUM
ejde-517	858	3	]	]	PUNCT
ejde-517	858	4	a.	a.	NOUN
ejde-517	858	5	p.	p.	NOUN
ejde-517	858	6	calderon	calderon	NOUN
ejde-517	858	7	;	;	PUNCT
ejde-517	858	8	on	on	ADP
ejde-517	858	9	an	an	DET
ejde-517	858	10	inverse	inverse	NOUN
ejde-517	858	11	boundary	boundary	NOUN
ejde-517	858	12	value	value	NOUN
ejde-517	858	13	problem	problem	NOUN
ejde-517	858	14	,	,	PUNCT
ejde-517	858	15	seminar	seminar	NOUN
ejde-517	858	16	on	on	ADP
ejde-517	858	17	numerical	numerical	ADJ
ejde-517	858	18	analysis	analysis	NOUN
ejde-517	858	19	and	and	CCONJ
ejde-517	858	20	its	its	PRON
ejde-517	858	21	applications	application	NOUN
ejde-517	858	22	to	to	ADP
ejde-517	858	23	continuum	continuum	ADJ
ejde-517	858	24	physics	physics	PROPN
ejde-517	858	25	(	(	PUNCT
ejde-517	858	26	rio	rio	PROPN
ejde-517	858	27	de	de	PROPN
ejde-517	858	28	janeiro	janeiro	PROPN
ejde-517	858	29	)	)	PUNCT
ejde-517	858	30	,	,	PUNCT
ejde-517	858	31	(	(	PUNCT
ejde-517	858	32	1980	1980	NUM
ejde-517	858	33	)	)	PUNCT
ejde-517	858	34	,	,	PUNCT
ejde-517	858	35	65–73	65–73	NUM
ejde-517	858	36	.	.	PUNCT
ejde-517	859	1	[	[	X
ejde-517	859	2	7	7	X
ejde-517	859	3	]	]	PUNCT
ejde-517	859	4	t.	t.	PROPN
ejde-517	859	5	f.	f.	PROPN
ejde-517	859	6	chan	chan	PROPN
ejde-517	859	7	,	,	PUNCT
ejde-517	859	8	h.	h.	PROPN
ejde-517	859	9	m.	m.	PROPN
ejde-517	859	10	zhou	zhou	PROPN
ejde-517	859	11	,	,	PUNCT
ejde-517	859	12	r.	r.	PROPN
ejde-517	859	13	h.	h.	PROPN
ejde-517	859	14	chan	chan	PROPN
ejde-517	859	15	;	;	PUNCT
ejde-517	859	16	continuation	continuation	NOUN
ejde-517	859	17	method	method	NOUN
ejde-517	859	18	for	for	ADP
ejde-517	859	19	total	total	ADJ
ejde-517	859	20	variation	variation	NOUN
ejde-517	859	21	denoising	denoising	NOUN
ejde-517	859	22	problems	problem	NOUN
ejde-517	859	23	,	,	PUNCT
ejde-517	859	24	proceeding	proceed	VERB
ejde-517	859	25	of	of	ADP
ejde-517	859	26	spie	spie	ADJ
ejde-517	859	27	annual	annual	ADJ
ejde-517	859	28	meeting	meeting	NOUN
ejde-517	859	29	,	,	PUNCT
ejde-517	859	30	5	5	NUM
ejde-517	859	31	(	(	PUNCT
ejde-517	859	32	1995	1995	NUM
ejde-517	859	33	)	)	PUNCT
ejde-517	859	34	.	.	PUNCT
ejde-517	860	1	[	[	X
ejde-517	860	2	8	8	NUM
ejde-517	860	3	]	]	PUNCT
ejde-517	860	4	m.	m.	NOUN
ejde-517	860	5	cheney	cheney	PROPN
ejde-517	860	6	,	,	PUNCT
ejde-517	860	7	d.	d.	PROPN
ejde-517	860	8	isaacson	isaacson	PROPN
ejde-517	860	9	,	,	PUNCT
ejde-517	860	10	j.	j.	PROPN
ejde-517	860	11	newell	newell	PROPN
ejde-517	860	12	;	;	PUNCT
ejde-517	860	13	electrical	electrical	ADJ
ejde-517	860	14	impedance	impedance	NOUN
ejde-517	860	15	tomography	tomography	NOUN
ejde-517	860	16	,	,	PUNCT
ejde-517	860	17	siam	siam	PROPN
ejde-517	860	18	review	review	NOUN
ejde-517	860	19	42	42	NUM
ejde-517	860	20	(	(	PUNCT
ejde-517	860	21	1999	1999	NUM
ejde-517	860	22	)	)	PUNCT
ejde-517	860	23	,	,	PUNCT
ejde-517	860	24	no	no	INTJ
ejde-517	860	25	.	.	NOUN
ejde-517	860	26	1	1	NUM
ejde-517	860	27	,	,	PUNCT
ejde-517	860	28	85–101	85–101	NUM
ejde-517	860	29	.	.	PUNCT
ejde-517	861	1	[	[	X
ejde-517	861	2	9	9	NUM
ejde-517	861	3	]	]	X
ejde-517	861	4	d.	d.	PROPN
ejde-517	861	5	dobson	dobson	PROPN
ejde-517	861	6	;	;	PUNCT
ejde-517	861	7	convergence	convergence	NOUN
ejde-517	861	8	of	of	ADP
ejde-517	861	9	a	a	DET
ejde-517	861	10	reconstruction	reconstruction	NOUN
ejde-517	861	11	method	method	NOUN
ejde-517	861	12	for	for	ADP
ejde-517	861	13	the	the	DET
ejde-517	861	14	inverse	inverse	NOUN
ejde-517	861	15	conductivity	conductivity	NOUN
ejde-517	861	16	problem	problem	NOUN
ejde-517	861	17	,	,	PUNCT
ejde-517	861	18	siam	siam	ADJ
ejde-517	861	19	journal	journal	NOUN
ejde-517	861	20	of	of	ADP
ejde-517	861	21	applied	apply	VERB
ejde-517	861	22	mathematics	mathematic	NOUN
ejde-517	861	23	,	,	PUNCT
ejde-517	861	24	52	52	NUM
ejde-517	861	25	(	(	PUNCT
ejde-517	861	26	1992	1992	NUM
ejde-517	861	27	)	)	PUNCT
ejde-517	861	28	,	,	PUNCT
ejde-517	861	29	442–458	442–458	NUM
ejde-517	861	30	.	.	PUNCT
ejde-517	862	1	[	[	X
ejde-517	862	2	10	10	NUM
ejde-517	862	3	]	]	X
ejde-517	862	4	d.	d.	PROPN
ejde-517	862	5	dobson	dobson	PROPN
ejde-517	862	6	,	,	PUNCT
ejde-517	862	7	f.	f.	PROPN
ejde-517	862	8	santosa	santosa	PROPN
ejde-517	862	9	;	;	PUNCT
ejde-517	862	10	an	an	DET
ejde-517	862	11	image	image	NOUN
ejde-517	862	12	enhancement	enhancement	NOUN
ejde-517	862	13	technique	technique	NOUN
ejde-517	862	14	for	for	ADP
ejde-517	862	15	electrical	electrical	ADJ
ejde-517	862	16	impedance	impedance	NOUN
ejde-517	862	17	tomography	tomography	NOUN
ejde-517	862	18	,	,	PUNCT
ejde-517	862	19	iop	iop	PROPN
ejde-517	862	20	publishing	publish	VERB
ejde-517	862	21	inverse	inverse	NOUN
ejde-517	862	22	problems	problem	NOUN
ejde-517	862	23	10	10	NUM
ejde-517	862	24	(	(	PUNCT
ejde-517	862	25	1994	1994	NUM
ejde-517	862	26	)	)	PUNCT
ejde-517	862	27	,	,	PUNCT
ejde-517	862	28	no	no	INTJ
ejde-517	862	29	.	.	NOUN
ejde-517	862	30	2	2	NUM
ejde-517	862	31	,	,	PUNCT
ejde-517	862	32	317	317	NUM
ejde-517	862	33	.	.	PUNCT
ejde-517	863	1	[	[	X
ejde-517	863	2	11	11	NUM
ejde-517	863	3	]	]	X
ejde-517	863	4	d.	d.	PROPN
ejde-517	863	5	dobson	dobson	PROPN
ejde-517	863	6	,	,	PUNCT
ejde-517	863	7	c.	c.	PROPN
ejde-517	863	8	vogel	vogel	PROPN
ejde-517	863	9	;	;	PUNCT
ejde-517	863	10	continuation	continuation	NOUN
ejde-517	863	11	method	method	NOUN
ejde-517	863	12	for	for	ADP
ejde-517	863	13	total	total	ADJ
ejde-517	863	14	variation	variation	NOUN
ejde-517	863	15	denoising	denoising	NOUN
ejde-517	863	16	problems	problem	NOUN
ejde-517	863	17	,	,	PUNCT
ejde-517	863	18	siam	siam	ADJ
ejde-517	863	19	journal	journal	NOUN
ejde-517	863	20	on	on	ADP
ejde-517	863	21	numerical	numerical	ADJ
ejde-517	863	22	analysis	analysis	NOUN
ejde-517	863	23	,	,	PUNCT
ejde-517	863	24	34	34	NUM
ejde-517	863	25	(	(	PUNCT
ejde-517	863	26	1997	1997	NUM
ejde-517	863	27	)	)	PUNCT
ejde-517	863	28	,	,	PUNCT
ejde-517	863	29	no	no	INTJ
ejde-517	863	30	.	.	NOUN
ejde-517	863	31	5	5	NUM
ejde-517	863	32	,	,	PUNCT
ejde-517	863	33	1779–1791	1779–1791	NUM
ejde-517	863	34	.	.	PUNCT
ejde-517	864	1	[	[	X
ejde-517	864	2	12	12	NUM
ejde-517	864	3	]	]	PUNCT
ejde-517	864	4	p.	p.	NOUN
ejde-517	864	5	drabek	drabek	PROPN
ejde-517	864	6	,	,	PUNCT
ejde-517	864	7	j.	j.	PROPN
ejde-517	864	8	milota	milota	PROPN
ejde-517	864	9	;	;	PUNCT
ejde-517	864	10	methods	method	NOUN
ejde-517	864	11	of	of	ADP
ejde-517	864	12	nonlinear	nonlinear	ADJ
ejde-517	864	13	analysis	analysis	NOUN
ejde-517	864	14	,	,	PUNCT
ejde-517	864	15	birkhäuser	birkhäuser	NOUN
ejde-517	864	16	,	,	PUNCT
ejde-517	864	17	2007	2007	NUM
ejde-517	864	18	.	.	PUNCT
ejde-517	865	1	[	[	X
ejde-517	865	2	13	13	NUM
ejde-517	865	3	]	]	PUNCT
ejde-517	865	4	m.	m.	PROPN
ejde-517	865	5	r.	r.	PROPN
ejde-517	865	6	eggleston	eggleston	PROPN
ejde-517	865	7	,	,	PUNCT
ejde-517	865	8	r.	r.	PROPN
ejde-517	865	9	j.	j.	PROPN
ejde-517	865	10	schwabe	schwabe	PROPN
ejde-517	865	11	,	,	PUNCT
ejde-517	865	12	d.	d.	PROPN
ejde-517	865	13	isaacson	isaacson	PROPN
ejde-517	865	14	,	,	PUNCT
ejde-517	865	15	l.f	l.f	PROPN
ejde-517	865	16	.	.	PROPN
ejde-517	865	17	coffin	coffin	NOUN
ejde-517	865	18	;	;	PUNCT
ejde-517	865	19	the	the	DET
ejde-517	865	20	application	application	NOUN
ejde-517	865	21	of	of	ADP
ejde-517	865	22	electric	electric	PROPN
ejde-517	865	23	current	current	ADJ
ejde-517	865	24	computed	compute	VERB
ejde-517	865	25	tomography	tomography	NOUN
ejde-517	865	26	to	to	PART
ejde-517	865	27	defect	defect	VERB
ejde-517	865	28	imaging	imaging	NOUN
ejde-517	865	29	in	in	ADP
ejde-517	865	30	metals	metal	NOUN
ejde-517	865	31	,	,	PUNCT
ejde-517	865	32	review	review	NOUN
ejde-517	865	33	of	of	ADP
ejde-517	865	34	progress	progress	NOUN
ejde-517	865	35	in	in	ADP
ejde-517	865	36	quantitative	quantitative	ADJ
ejde-517	865	37	nondestructive	nondestructive	ADJ
ejde-517	865	38	evaluation	evaluation	NOUN
ejde-517	865	39	(	(	PUNCT
ejde-517	865	40	1990	1990	NUM
ejde-517	865	41	)	)	PUNCT
ejde-517	865	42	,	,	PUNCT
ejde-517	865	43	455–462	455–462	NUM
ejde-517	865	44	.	.	PUNCT
ejde-517	866	1	[	[	X
ejde-517	866	2	14	14	NUM
ejde-517	866	3	]	]	X
ejde-517	866	4	l.	l.	PROPN
ejde-517	866	5	evans	evans	PROPN
ejde-517	866	6	;	;	PUNCT
ejde-517	866	7	partial	partial	ADJ
ejde-517	866	8	differential	differential	NOUN
ejde-517	866	9	equations	equation	NOUN
ejde-517	866	10	,	,	PUNCT
ejde-517	866	11	american	american	PROPN
ejde-517	866	12	mathematical	mathematical	PROPN
ejde-517	866	13	society	society	NOUN
ejde-517	866	14	,	,	PUNCT
ejde-517	866	15	2010	2010	NUM
ejde-517	866	16	second	second	ADJ
ejde-517	866	17	edition	edition	NOUN
ejde-517	866	18	.	.	PUNCT
ejde-517	867	1	[	[	X
ejde-517	867	2	15	15	NUM
ejde-517	867	3	]	]	X
ejde-517	867	4	s.	s.	PROPN
ejde-517	867	5	fürtinger	fürtinger	PROPN
ejde-517	867	6	;	;	PUNCT
ejde-517	867	7	an	an	DET
ejde-517	867	8	approach	approach	NOUN
ejde-517	867	9	to	to	ADP
ejde-517	867	10	computing	compute	VERB
ejde-517	867	11	binary	binary	ADJ
ejde-517	867	12	edge	edge	NOUN
ejde-517	867	13	maps	map	NOUN
ejde-517	867	14	for	for	ADP
ejde-517	867	15	the	the	DET
ejde-517	867	16	purpose	purpose	NOUN
ejde-517	867	17	of	of	ADP
ejde-517	867	18	registering	register	VERB
ejde-517	867	19	intensity	intensity	NOUN
ejde-517	867	20	modulated	modulate	VERB
ejde-517	867	21	images	image	NOUN
ejde-517	867	22	,	,	PUNCT
ejde-517	867	23	ph.d	ph.d	PROPN
ejde-517	867	24	.	.	PUNCT
ejde-517	868	1	thesis	thesis	PROPN
ejde-517	868	2	,	,	PUNCT
ejde-517	868	3	karl	karl	PROPN
ejde-517	868	4	-	-	PUNCT
ejde-517	868	5	franzens	franzens	PROPN
ejde-517	868	6	university	university	PROPN
ejde-517	868	7	graz	graz	PROPN
ejde-517	868	8	,	,	PUNCT
ejde-517	868	9	2012	2012	NUM
ejde-517	868	10	.	.	PUNCT
ejde-517	869	1	[	[	X
ejde-517	869	2	16	16	NUM
ejde-517	869	3	]	]	X
ejde-517	869	4	d.	d.	PROPN
ejde-517	869	5	gilbarg	gilbarg	PROPN
ejde-517	869	6	,	,	PUNCT
ejde-517	869	7	n.	n.	PROPN
ejde-517	869	8	trudinger	trudinger	NOUN
ejde-517	869	9	;	;	PUNCT
ejde-517	869	10	elliptic	elliptic	ADJ
ejde-517	869	11	partial	partial	ADJ
ejde-517	869	12	differential	differential	ADJ
ejde-517	869	13	equations	equation	NOUN
ejde-517	869	14	of	of	ADP
ejde-517	869	15	second	second	ADJ
ejde-517	869	16	order	order	NOUN
ejde-517	869	17	,	,	PUNCT
ejde-517	869	18	springer	springer	NOUN
ejde-517	869	19	,	,	PUNCT
ejde-517	869	20	reprint	reprint	NOUN
ejde-517	869	21	of	of	ADP
ejde-517	869	22	the	the	DET
ejde-517	869	23	1998	1998	NUM
ejde-517	869	24	edition	edition	NOUN
ejde-517	869	25	.	.	PUNCT
ejde-517	870	1	[	[	X
ejde-517	870	2	17	17	NUM
ejde-517	870	3	]	]	X
ejde-517	870	4	g.	g.	PROPN
ejde-517	870	5	a.	a.	PROPN
ejde-517	870	6	gray	gray	PROPN
ejde-517	870	7	;	;	PUNCT
ejde-517	870	8	a	a	DET
ejde-517	870	9	variational	variational	ADJ
ejde-517	870	10	study	study	NOUN
ejde-517	870	11	of	of	ADP
ejde-517	870	12	the	the	DET
ejde-517	870	13	electrical	electrical	ADJ
ejde-517	870	14	impedance	impedance	NOUN
ejde-517	870	15	tomography	tomography	NOUN
ejde-517	870	16	problem	problem	NOUN
ejde-517	870	17	,	,	PUNCT
ejde-517	870	18	ph.d	ph.d	PROPN
ejde-517	870	19	.	.	PUNCT
ejde-517	871	1	thesis	thesis	PROPN
ejde-517	871	2	,	,	PUNCT
ejde-517	871	3	rice	rice	NOUN
ejde-517	871	4	university	university	NOUN
ejde-517	871	5	,	,	PUNCT
ejde-517	871	6	2002	2002	NUM
ejde-517	871	7	.	.	PUNCT
ejde-517	872	1	[	[	X
ejde-517	872	2	18	18	NUM
ejde-517	872	3	]	]	X
ejde-517	872	4	c.	c.	NOUN
ejde-517	872	5	großmann	großmann	PROPN
ejde-517	872	6	,	,	PUNCT
ejde-517	872	7	h	h	NOUN
ejde-517	872	8	-	-	PUNCT
ejde-517	872	9	g	g	NOUN
ejde-517	872	10	roos	roo	NOUN
ejde-517	872	11	,	,	PUNCT
ejde-517	872	12	m.	m.	NOUN
ejde-517	872	13	stynes	styne	NOUN
ejde-517	872	14	;	;	PUNCT
ejde-517	872	15	numerical	numerical	ADJ
ejde-517	872	16	treatment	treatment	NOUN
ejde-517	872	17	of	of	ADP
ejde-517	872	18	partial	partial	ADJ
ejde-517	872	19	differential	differential	ADJ
ejde-517	872	20	equations	equation	NOUN
ejde-517	872	21	(	(	PUNCT
ejde-517	872	22	universitext	universitext	PROPN
ejde-517	872	23	)	)	PUNCT
ejde-517	872	24	,	,	PUNCT
ejde-517	872	25	springer	springer	NOUN
ejde-517	872	26	,	,	PUNCT
ejde-517	872	27	2007	2007	NUM
ejde-517	872	28	.	.	PUNCT
ejde-517	873	1	[	[	X
ejde-517	873	2	19	19	NUM
ejde-517	873	3	]	]	PUNCT
ejde-517	873	4	p.	p.	NOUN
ejde-517	873	5	halmos	halmos	NOUN
ejde-517	873	6	;	;	PUNCT
ejde-517	873	7	measure	measure	NOUN
ejde-517	873	8	theory	theory	NOUN
ejde-517	873	9	,	,	PUNCT
ejde-517	873	10	springer	springer	NOUN
ejde-517	873	11	,	,	PUNCT
ejde-517	873	12	1974	1974	NUM
ejde-517	873	13	.	.	PUNCT
ejde-517	874	1	[	[	X
ejde-517	874	2	20	20	NUM
ejde-517	874	3	]	]	PUNCT
ejde-517	874	4	m.	m.	NOUN
ejde-517	874	5	hintermüller	hintermüller	PROPN
ejde-517	874	6	,	,	PUNCT
ejde-517	874	7	a.	a.	NOUN
ejde-517	874	8	laurain	laurain	NOUN
ejde-517	874	9	;	;	PUNCT
ejde-517	874	10	electrical	electrical	ADJ
ejde-517	874	11	impedance	impedance	NOUN
ejde-517	874	12	tomography	tomography	NOUN
ejde-517	874	13	:	:	PUNCT
ejde-517	874	14	from	from	ADP
ejde-517	874	15	topology	topology	NOUN
ejde-517	874	16	to	to	PART
ejde-517	874	17	shape	shape	VERB
ejde-517	874	18	,	,	PUNCT
ejde-517	874	19	control	control	NOUN
ejde-517	874	20	and	and	CCONJ
ejde-517	874	21	cybernetics	cybernetic	NOUN
ejde-517	874	22	37	37	NUM
ejde-517	874	23	(	(	PUNCT
ejde-517	874	24	2008	2008	NUM
ejde-517	874	25	)	)	PUNCT
ejde-517	874	26	,	,	PUNCT
ejde-517	874	27	no	no	INTJ
ejde-517	874	28	.	.	NOUN
ejde-517	874	29	4	4	X
ejde-517	874	30	.	.	PUNCT
ejde-517	875	1	[	[	X
ejde-517	875	2	21	21	NUM
ejde-517	875	3	]	]	X
ejde-517	875	4	david	david	PROPN
ejde-517	875	5	holder	holder	PROPN
ejde-517	875	6	(	(	PUNCT
ejde-517	875	7	ed	ed	NOUN
ejde-517	875	8	.	.	PUNCT
ejde-517	875	9	)	)	PUNCT
ejde-517	875	10	;	;	PUNCT
ejde-517	875	11	electrical	electrical	ADJ
ejde-517	875	12	impedance	impedance	NOUN
ejde-517	875	13	tomography	tomography	NOUN
ejde-517	875	14	:	:	PUNCT
ejde-517	875	15	methods	method	NOUN
ejde-517	875	16	,	,	PUNCT
ejde-517	875	17	history	history	NOUN
ejde-517	875	18	and	and	CCONJ
ejde-517	875	19	applications	application	NOUN
ejde-517	875	20	(	(	PUNCT
ejde-517	875	21	series	series	NOUN
ejde-517	875	22	in	in	ADP
ejde-517	875	23	medical	medical	ADJ
ejde-517	875	24	physics	physics	NOUN
ejde-517	875	25	and	and	CCONJ
ejde-517	875	26	biomedical	biomedical	ADJ
ejde-517	875	27	engineering	engineering	NOUN
ejde-517	875	28	)	)	PUNCT
ejde-517	875	29	,	,	PUNCT
ejde-517	875	30	iop	iop	NOUN
ejde-517	875	31	publishing	publishing	NOUN
ejde-517	875	32	,	,	PUNCT
ejde-517	875	33	2004	2004	NUM
ejde-517	875	34	.	.	PUNCT
ejde-517	876	1	[	[	X
ejde-517	876	2	22	22	NUM
ejde-517	876	3	]	]	X
ejde-517	876	4	d.	d.	PROPN
ejde-517	876	5	isaacson	isaacson	PROPN
ejde-517	876	6	,	,	PUNCT
ejde-517	876	7	j.	j.	PROPN
ejde-517	876	8	mueller	mueller	PROPN
ejde-517	876	9	,	,	PUNCT
ejde-517	876	10	s.	s.	PROPN
ejde-517	876	11	siltanen	siltanen	PROPN
ejde-517	876	12	;	;	PUNCT
ejde-517	876	13	biomedical	biomedical	ADJ
ejde-517	876	14	applications	application	NOUN
ejde-517	876	15	of	of	ADP
ejde-517	876	16	electrical	electrical	ADJ
ejde-517	876	17	impedance	impedance	NOUN
ejde-517	876	18	tomography	tomography	NOUN
ejde-517	876	19	,	,	PUNCT
ejde-517	876	20	iop	iop	PROPN
ejde-517	876	21	publishing	publish	VERB
ejde-517	876	22	physiological	physiological	ADJ
ejde-517	876	23	measurement	measurement	NOUN
ejde-517	876	24	24	24	NUM
ejde-517	876	25	(	(	PUNCT
ejde-517	876	26	2003	2003	NUM
ejde-517	876	27	)	)	PUNCT
ejde-517	876	28	,	,	PUNCT
ejde-517	876	29	no	no	INTJ
ejde-517	876	30	.	.	NOUN
ejde-517	876	31	2	2	X
ejde-517	876	32	.	.	PUNCT
ejde-517	877	1	[	[	X
ejde-517	877	2	23	23	NUM
ejde-517	877	3	]	]	X
ejde-517	877	4	d.	d.	PROPN
ejde-517	877	5	isaacson	isaacson	PROPN
ejde-517	877	6	,	,	PUNCT
ejde-517	877	7	j.	j.	PROPN
ejde-517	877	8	newell	newell	PROPN
ejde-517	877	9	,	,	PUNCT
ejde-517	877	10	j.	j.	PROPN
ejde-517	877	11	c.	c.	PROPN
ejde-517	877	12	goble	goble	PROPN
ejde-517	877	13	,	,	PUNCT
ejde-517	877	14	m.	m.	NOUN
ejde-517	877	15	cheney	cheney	PROPN
ejde-517	877	16	;	;	PUNCT
ejde-517	877	17	thoracic	thoracic	NOUN
ejde-517	877	18	impedance	impedance	NOUN
ejde-517	877	19	images	image	NOUN
ejde-517	877	20	during	during	ADP
ejde-517	877	21	ventilation	ventilation	NOUN
ejde-517	877	22	,	,	PUNCT
ejde-517	877	23	proceedings	proceeding	NOUN
ejde-517	877	24	of	of	ADP
ejde-517	877	25	the	the	DET
ejde-517	877	26	twelfth	twelfth	ADJ
ejde-517	877	27	annual	annual	ADJ
ejde-517	877	28	international	international	ADJ
ejde-517	877	29	conference	conference	NOUN
ejde-517	877	30	of	of	ADP
ejde-517	877	31	the	the	DET
ejde-517	877	32	ieee	ieee	NOUN
ejde-517	877	33	(	(	PUNCT
ejde-517	877	34	1	1	NUM
ejde-517	877	35	-	-	SYM
ejde-517	877	36	4	4	NUM
ejde-517	877	37	nov	nov	NOUN
ejde-517	877	38	,	,	PUNCT
ejde-517	877	39	1990	1990	NUM
ejde-517	877	40	)	)	PUNCT
ejde-517	877	41	,	,	PUNCT
ejde-517	877	42	106–107	106–107	NUM
ejde-517	877	43	.	.	PUNCT
ejde-517	878	1	[	[	X
ejde-517	878	2	24	24	NUM
ejde-517	878	3	]	]	PUNCT
ejde-517	878	4	j.	j.	PROPN
ejde-517	878	5	jordana	jordana	PROPN
ejde-517	878	6	,	,	PUNCT
ejde-517	878	7	m.	m.	NOUN
ejde-517	878	8	gasulla	gasulla	PROPN
ejde-517	878	9	,	,	PUNCT
ejde-517	878	10	r.	r.	PROPN
ejde-517	878	11	pallas	pallas	PROPN
ejde-517	878	12	-	-	PUNCT
ejde-517	878	13	areny	areny	PROPN
ejde-517	878	14	;	;	PUNCT
ejde-517	878	15	electrical	electrical	ADJ
ejde-517	878	16	resistance	resistance	NOUN
ejde-517	878	17	tomography	tomography	NOUN
ejde-517	878	18	to	to	PART
ejde-517	878	19	detect	detect	VERB
ejde-517	878	20	leaks	leak	NOUN
ejde-517	878	21	from	from	ADP
ejde-517	878	22	buried	bury	VERB
ejde-517	878	23	pipes	pipe	NOUN
ejde-517	878	24	,	,	PUNCT
ejde-517	878	25	iop	iop	PROPN
ejde-517	878	26	publishing	publishing	NOUN
ejde-517	878	27	measurement	measurement	NOUN
ejde-517	878	28	science	science	NOUN
ejde-517	878	29	and	and	CCONJ
ejde-517	878	30	technology	technology	NOUN
ejde-517	878	31	12	12	NUM
ejde-517	878	32	(	(	PUNCT
ejde-517	878	33	2001	2001	NUM
ejde-517	878	34	)	)	PUNCT
ejde-517	878	35	,	,	PUNCT
ejde-517	878	36	no	no	INTJ
ejde-517	878	37	.	.	NOUN
ejde-517	878	38	8	8	NUM
ejde-517	878	39	.	.	PUNCT
ejde-517	879	1	[	[	X
ejde-517	879	2	25	25	NUM
ejde-517	879	3	]	]	X
ejde-517	879	4	h.	h.	PROPN
ejde-517	879	5	kang	kang	PROPN
ejde-517	879	6	;	;	PUNCT
ejde-517	879	7	a	a	DET
ejde-517	879	8	uniqueness	uniqueness	NOUN
ejde-517	879	9	theorem	theorem	VERB
ejde-517	879	10	for	for	ADP
ejde-517	879	11	an	an	DET
ejde-517	879	12	inverse	inverse	NOUN
ejde-517	879	13	boundary	boundary	NOUN
ejde-517	879	14	value	value	NOUN
ejde-517	879	15	problem	problem	NOUN
ejde-517	879	16	in	in	ADP
ejde-517	879	17	two	two	NUM
ejde-517	879	18	dimensions	dimension	NOUN
ejde-517	879	19	,	,	PUNCT
ejde-517	879	20	journal	journal	NOUN
ejde-517	879	21	of	of	ADP
ejde-517	879	22	mathematical	mathematical	ADJ
ejde-517	879	23	analysis	analysis	NOUN
ejde-517	879	24	and	and	CCONJ
ejde-517	879	25	applications	application	NOUN
ejde-517	879	26	,	,	PUNCT
ejde-517	879	27	270	270	NUM
ejde-517	879	28	(	(	PUNCT
ejde-517	879	29	2002	2002	NUM
ejde-517	879	30	)	)	PUNCT
ejde-517	879	31	,	,	PUNCT
ejde-517	879	32	no	no	INTJ
ejde-517	879	33	.	.	NOUN
ejde-517	879	34	1	1	NUM
ejde-517	879	35	,	,	PUNCT
ejde-517	879	36	291–302	291–302	NUM
ejde-517	879	37	.	.	PUNCT
ejde-517	880	1	[	[	X
ejde-517	880	2	26	26	NUM
ejde-517	880	3	]	]	X
ejde-517	880	4	r.	r.	PROPN
ejde-517	880	5	mendoza	mendoza	PROPN
ejde-517	880	6	,	,	PUNCT
ejde-517	880	7	s.	s.	PROPN
ejde-517	880	8	keeling	keeling	PROPN
ejde-517	880	9	;	;	PUNCT
ejde-517	880	10	fem	fem	NOUN
ejde-517	880	11	convergence	convergence	NOUN
ejde-517	880	12	of	of	ADP
ejde-517	880	13	a	a	DET
ejde-517	880	14	segmentation	segmentation	NOUN
ejde-517	880	15	approach	approach	NOUN
ejde-517	880	16	to	to	ADP
ejde-517	880	17	the	the	DET
ejde-517	880	18	electrical	electrical	ADJ
ejde-517	880	19	impedance	impedance	NOUN
ejde-517	880	20	tomography	tomography	NOUN
ejde-517	880	21	problem	problem	NOUN
ejde-517	880	22	,	,	PUNCT
ejde-517	880	23	aip	aip	PROPN
ejde-517	880	24	conference	conference	NOUN
ejde-517	880	25	proceedings	proceeding	NOUN
ejde-517	880	26	1707	1707	NUM
ejde-517	880	27	(	(	PUNCT
ejde-517	880	28	2016	2016	NUM
ejde-517	880	29	)	)	PUNCT
ejde-517	880	30	,	,	PUNCT
ejde-517	880	31	no	no	INTJ
ejde-517	880	32	.	.	NOUN
ejde-517	880	33	1	1	NUM
ejde-517	880	34	,	,	PUNCT
ejde-517	880	35	050009	050009	NUM
ejde-517	880	36	.	.	PUNCT
ejde-517	881	1	[	[	X
ejde-517	881	2	27	27	NUM
ejde-517	881	3	]	]	X
ejde-517	881	4	r.	r.	PROPN
ejde-517	881	5	mendoza	mendoza	PROPN
ejde-517	881	6	,	,	PUNCT
ejde-517	881	7	s.	s.	PROPN
ejde-517	881	8	keeling	keeling	PROPN
ejde-517	881	9	;	;	PUNCT
ejde-517	881	10	a	a	DET
ejde-517	881	11	two	two	NUM
ejde-517	881	12	-	-	PUNCT
ejde-517	881	13	phase	phase	NOUN
ejde-517	881	14	segmentation	segmentation	NOUN
ejde-517	881	15	approach	approach	NOUN
ejde-517	881	16	to	to	ADP
ejde-517	881	17	the	the	DET
ejde-517	881	18	impedance	impedance	NOUN
ejde-517	881	19	tomography	tomography	NOUN
ejde-517	881	20	problem	problem	NOUN
ejde-517	881	21	,	,	PUNCT
ejde-517	881	22	inverse	inverse	NOUN
ejde-517	881	23	problems	problem	NOUN
ejde-517	881	24	,	,	PUNCT
ejde-517	881	25	33	33	NUM
ejde-517	881	26	(	(	PUNCT
ejde-517	881	27	2017	2017	NUM
ejde-517	881	28	)	)	PUNCT
ejde-517	881	29	,	,	PUNCT
ejde-517	881	30	no	no	INTJ
ejde-517	881	31	.	.	NOUN
ejde-517	881	32	1	1	NUM
ejde-517	881	33	,	,	PUNCT
ejde-517	881	34	015001	015001	NUM
ejde-517	881	35	.	.	PUNCT
ejde-517	882	1	[	[	X
ejde-517	882	2	28	28	NUM
ejde-517	882	3	]	]	X
ejde-517	882	4	r.	r.	PROPN
ejde-517	882	5	mendoza	mendoza	PROPN
ejde-517	882	6	,	,	PUNCT
ejde-517	882	7	j.	j.	PROPN
ejde-517	882	8	e.	e.	PROPN
ejde-517	882	9	lope	lope	PROPN
ejde-517	882	10	;	;	PUNCT
ejde-517	882	11	reconstructing	reconstruct	VERB
ejde-517	882	12	images	image	NOUN
ejde-517	882	13	in	in	ADP
ejde-517	882	14	electrical	electrical	ADJ
ejde-517	882	15	impedance	impedance	NOUN
ejde-517	882	16	tomography	tomography	NOUN
ejde-517	882	17	problem	problem	NOUN
ejde-517	882	18	using	use	VERB
ejde-517	882	19	hybrid	hybrid	ADJ
ejde-517	882	20	genetic	genetic	ADJ
ejde-517	882	21	algorithms	algorithm	NOUN
ejde-517	882	22	,	,	PUNCT
ejde-517	882	23	science	science	NOUN
ejde-517	882	24	diliman	diliman	PROPN
ejde-517	882	25	,	,	PUNCT
ejde-517	882	26	242	242	NUM
ejde-517	882	27	(	(	PUNCT
ejde-517	882	28	2012	2012	NUM
ejde-517	882	29	)	)	PUNCT
ejde-517	882	30	,	,	PUNCT
ejde-517	882	31	no	no	INTJ
ejde-517	882	32	.	.	NOUN
ejde-517	882	33	2	2	NUM
ejde-517	882	34	,	,	PUNCT
ejde-517	882	35	50–66	50–66	NUM
ejde-517	882	36	.	.	PUNCT
ejde-517	883	1	[	[	X
ejde-517	883	2	29	29	NUM
ejde-517	883	3	]	]	X
ejde-517	883	4	r.	r.	PROPN
ejde-517	883	5	parker	parker	PROPN
ejde-517	883	6	;	;	PUNCT
ejde-517	883	7	the	the	DET
ejde-517	883	8	inverse	inverse	NOUN
ejde-517	883	9	problem	problem	NOUN
ejde-517	883	10	of	of	ADP
ejde-517	883	11	resistivity	resistivity	NOUN
ejde-517	883	12	sounding	sounding	NOUN
ejde-517	883	13	,	,	PUNCT
ejde-517	883	14	geophysics	geophysic	NOUN
ejde-517	883	15	,	,	PUNCT
ejde-517	883	16	49	49	NUM
ejde-517	883	17	(	(	PUNCT
ejde-517	883	18	1984	1984	NUM
ejde-517	883	19	)	)	PUNCT
ejde-517	883	20	,	,	PUNCT
ejde-517	883	21	2143–2158	2143–2158	NUM
ejde-517	883	22	.	.	PUNCT
ejde-517	884	1	[	[	X
ejde-517	884	2	30	30	NUM
ejde-517	884	3	]	]	PUNCT
ejde-517	884	4	a.	a.	NOUN
ejde-517	884	5	ramirez	ramirez	PROPN
ejde-517	884	6	,	,	PUNCT
ejde-517	884	7	w.	w.	PROPN
ejde-517	884	8	daily	daily	PROPN
ejde-517	884	9	,	,	PUNCT
ejde-517	884	10	d.	d.	PROPN
ejde-517	884	11	labrecque	labrecque	PROPN
ejde-517	884	12	,	,	PUNCT
ejde-517	884	13	e.	e.	PROPN
ejde-517	884	14	owen	owen	PROPN
ejde-517	884	15	,	,	PUNCT
ejde-517	884	16	d.	d.	PROPN
ejde-517	884	17	chestnut	chestnut	PROPN
ejde-517	884	18	;	;	PUNCT
ejde-517	884	19	monitoring	monitor	VERB
ejde-517	884	20	an	an	DET
ejde-517	884	21	underground	underground	ADJ
ejde-517	884	22	steam	steam	NOUN
ejde-517	884	23	injection	injection	NOUN
ejde-517	884	24	process	process	NOUN
ejde-517	884	25	using	use	VERB
ejde-517	884	26	electrical	electrical	ADJ
ejde-517	884	27	resistance	resistance	NOUN
ejde-517	884	28	tomography	tomography	NOUN
ejde-517	884	29	,	,	PUNCT
ejde-517	884	30	water	water	NOUN
ejde-517	884	31	resources	resource	NOUN
ejde-517	884	32	research	research	VERB
ejde-517	884	33	29	29	NUM
ejde-517	884	34	(	(	PUNCT
ejde-517	884	35	1993	1993	NUM
ejde-517	884	36	)	)	PUNCT
ejde-517	884	37	,	,	PUNCT
ejde-517	884	38	no	no	INTJ
ejde-517	884	39	.	.	NOUN
ejde-517	884	40	1	1	NUM
ejde-517	884	41	,	,	PUNCT
ejde-517	884	42	73–87	73–87	NUM
ejde-517	884	43	.	.	PUNCT
ejde-517	885	1	[	[	X
ejde-517	885	2	31	31	NUM
ejde-517	885	3	]	]	PUNCT
ejde-517	885	4	l.	l.	PROPN
ejde-517	885	5	i.	i.	PROPN
ejde-517	885	6	rudin	rudin	PROPN
ejde-517	885	7	;	;	PUNCT
ejde-517	885	8	images	image	NOUN
ejde-517	885	9	,	,	PUNCT
ejde-517	885	10	numerical	numerical	ADJ
ejde-517	885	11	analysis	analysis	NOUN
ejde-517	885	12	of	of	ADP
ejde-517	885	13	singularities	singularity	NOUN
ejde-517	885	14	and	and	CCONJ
ejde-517	885	15	shock	shock	NOUN
ejde-517	885	16	filters	filter	NOUN
ejde-517	885	17	,	,	PUNCT
ejde-517	885	18	ph.d	ph.d	PROPN
ejde-517	885	19	.	.	PUNCT
ejde-517	886	1	thesis	thesis	PROPN
ejde-517	886	2	,	,	PUNCT
ejde-517	886	3	california	california	PROPN
ejde-517	886	4	institute	institute	PROPN
ejde-517	886	5	of	of	ADP
ejde-517	886	6	technology	technology	PROPN
ejde-517	886	7	,	,	PUNCT
ejde-517	886	8	1987	1987	NUM
ejde-517	886	9	.	.	PUNCT
ejde-517	887	1	[	[	X
ejde-517	887	2	32	32	NUM
ejde-517	887	3	]	]	PUNCT
ejde-517	887	4	l.	l.	PROPN
ejde-517	887	5	i.	i.	PROPN
ejde-517	887	6	rudin	rudin	PROPN
ejde-517	887	7	,	,	PUNCT
ejde-517	887	8	s.	s.	PROPN
ejde-517	887	9	osher	osher	PROPN
ejde-517	887	10	,	,	PUNCT
ejde-517	887	11	e.	e.	PROPN
ejde-517	887	12	fatemi	fatemi	PROPN
ejde-517	887	13	;	;	PUNCT
ejde-517	887	14	nonlinear	nonlinear	ADJ
ejde-517	887	15	total	total	ADJ
ejde-517	887	16	variation	variation	NOUN
ejde-517	887	17	bases	basis	NOUN
ejde-517	887	18	noise	noise	VERB
ejde-517	887	19	removal	removal	NOUN
ejde-517	887	20	algorithms	algorithm	NOUN
ejde-517	887	21	,	,	PUNCT
ejde-517	887	22	physica	physica	NOUN
ejde-517	887	23	d	d	PROPN
ejde-517	887	24	60	60	NUM
ejde-517	887	25	(	(	PUNCT
ejde-517	887	26	1992	1992	NUM
ejde-517	887	27	)	)	PUNCT
ejde-517	887	28	,	,	PUNCT
ejde-517	887	29	259–268	259–268	NUM
ejde-517	887	30	.	.	PUNCT
ejde-517	888	1	30	30	NUM
ejde-517	888	2	r.	r.	PROPN
ejde-517	888	3	mendoza	mendoza	PROPN
ejde-517	888	4	,	,	PUNCT
ejde-517	888	5	s.	s.	PROPN
ejde-517	888	6	keeling	keeling	PROPN
ejde-517	888	7	ejde-2020/93	ejde-2020/93	PROPN
ejde-517	889	1	[	[	X
ejde-517	889	2	33	33	NUM
ejde-517	889	3	]	]	PUNCT
ejde-517	889	4	j.	j.	PROPN
ejde-517	889	5	snyman	snyman	PROPN
ejde-517	889	6	;	;	PUNCT
ejde-517	889	7	practical	practical	ADJ
ejde-517	889	8	mathematical	mathematical	ADJ
ejde-517	889	9	optimization	optimization	NOUN
ejde-517	889	10	:	:	PUNCT
ejde-517	889	11	an	an	DET
ejde-517	889	12	introduction	introduction	NOUN
ejde-517	889	13	to	to	ADP
ejde-517	889	14	basic	basic	ADJ
ejde-517	889	15	optimization	optimization	NOUN
ejde-517	889	16	theory	theory	NOUN
ejde-517	889	17	and	and	CCONJ
ejde-517	889	18	classical	classical	ADJ
ejde-517	889	19	and	and	CCONJ
ejde-517	889	20	new	new	ADJ
ejde-517	889	21	gradient	gradient	NOUN
ejde-517	889	22	-	-	PUNCT
ejde-517	889	23	based	base	VERB
ejde-517	889	24	algorithms	algorithm	NOUN
ejde-517	889	25	,	,	PUNCT
ejde-517	889	26	springer	springer	NOUN
ejde-517	889	27	,	,	PUNCT
ejde-517	889	28	2005	2005	NUM
ejde-517	889	29	.	.	PUNCT
ejde-517	890	1	[	[	X
ejde-517	890	2	34	34	NUM
ejde-517	890	3	]	]	X
ejde-517	890	4	e.	e.	PROPN
ejde-517	890	5	somersalo	somersalo	PROPN
ejde-517	890	6	,	,	PUNCT
ejde-517	890	7	m.	m.	PROPN
ejde-517	890	8	cheney	cheney	PROPN
ejde-517	890	9	,	,	PUNCT
ejde-517	890	10	d.	d.	PROPN
ejde-517	890	11	isaacson	isaacson	PROPN
ejde-517	890	12	;	;	PUNCT
ejde-517	890	13	existence	existence	NOUN
ejde-517	890	14	and	and	CCONJ
ejde-517	890	15	uniqueness	uniqueness	NOUN
ejde-517	890	16	for	for	ADP
ejde-517	890	17	electrode	electrode	NOUN
ejde-517	890	18	models	model	NOUN
ejde-517	890	19	for	for	ADP
ejde-517	890	20	electric	electric	ADJ
ejde-517	890	21	current	current	ADJ
ejde-517	890	22	computed	compute	VERB
ejde-517	890	23	tomography	tomography	NOUN
ejde-517	890	24	,	,	PUNCT
ejde-517	890	25	siam	siam	ADJ
ejde-517	890	26	journal	journal	NOUN
ejde-517	890	27	on	on	ADP
ejde-517	890	28	applied	apply	VERB
ejde-517	890	29	mathematics	mathematic	NOUN
ejde-517	890	30	,	,	PUNCT
ejde-517	890	31	52	52	NUM
ejde-517	890	32	(	(	PUNCT
ejde-517	890	33	1992	1992	NUM
ejde-517	890	34	)	)	PUNCT
ejde-517	890	35	,	,	PUNCT
ejde-517	890	36	no	no	INTJ
ejde-517	890	37	.	.	NOUN
ejde-517	890	38	4	4	NUM
ejde-517	890	39	,	,	PUNCT
ejde-517	890	40	1023–1040	1023–1040	NUM
ejde-517	890	41	.	.	PUNCT
ejde-517	891	1	[	[	X
ejde-517	891	2	35	35	NUM
ejde-517	891	3	]	]	X
ejde-517	891	4	j.	j.	PROPN
ejde-517	891	5	sylvester	sylvester	PROPN
ejde-517	891	6	,	,	PUNCT
ejde-517	891	7	g.	g.	PROPN
ejde-517	891	8	uhlmann	uhlmann	PROPN
ejde-517	891	9	;	;	PUNCT
ejde-517	891	10	a	a	DET
ejde-517	891	11	global	global	ADJ
ejde-517	891	12	uniqueness	uniqueness	NOUN
ejde-517	891	13	theorem	theorem	VERB
ejde-517	891	14	for	for	ADP
ejde-517	891	15	an	an	DET
ejde-517	891	16	inverse	inverse	NOUN
ejde-517	891	17	boundary	boundary	NOUN
ejde-517	891	18	value	value	NOUN
ejde-517	891	19	problem	problem	NOUN
ejde-517	891	20	,	,	PUNCT
ejde-517	891	21	annals	annal	NOUN
ejde-517	891	22	of	of	ADP
ejde-517	891	23	mathematics	mathematic	NOUN
ejde-517	891	24	125	125	NUM
ejde-517	891	25	(	(	PUNCT
ejde-517	891	26	1987	1987	NUM
ejde-517	891	27	)	)	PUNCT
ejde-517	891	28	,	,	PUNCT
ejde-517	891	29	no	no	INTJ
ejde-517	891	30	.	.	NOUN
ejde-517	891	31	1	1	NUM
ejde-517	891	32	,	,	PUNCT
ejde-517	891	33	153–169	153–169	NUM
ejde-517	891	34	.	.	PUNCT
ejde-517	892	1	[	[	X
ejde-517	892	2	36	36	NUM
ejde-517	892	3	]	]	X
ejde-517	892	4	g.	g.	PROPN
ejde-517	892	5	uhlmann	uhlmann	PROPN
ejde-517	892	6	;	;	PUNCT
ejde-517	892	7	electrical	electrical	ADJ
ejde-517	892	8	impedance	impedance	NOUN
ejde-517	892	9	tomography	tomography	NOUN
ejde-517	892	10	and	and	CCONJ
ejde-517	892	11	calderon	calderon	NOUN
ejde-517	892	12	’s	’s	PART
ejde-517	892	13	problem	problem	NOUN
ejde-517	892	14	,	,	PUNCT
ejde-517	892	15	iop	iop	PROPN
ejde-517	892	16	,	,	PUNCT
ejde-517	892	17	25	25	NUM
ejde-517	892	18	(	(	PUNCT
ejde-517	892	19	2009	2009	NUM
ejde-517	892	20	)	)	PUNCT
ejde-517	892	21	.	.	PUNCT
ejde-517	893	1	[	[	X
ejde-517	893	2	37	37	NUM
ejde-517	893	3	]	]	PUNCT
ejde-517	893	4	a.	a.	PROPN
ejde-517	893	5	c.	c.	PROPN
ejde-517	893	6	velasco	velasco	PROPN
ejde-517	893	7	,	,	PUNCT
ejde-517	893	8	m.	m.	NOUN
ejde-517	893	9	darbas	darbas	PROPN
ejde-517	893	10	,	,	PUNCT
ejde-517	893	11	r.	r.	PROPN
ejde-517	893	12	mendoza	mendoza	PROPN
ejde-517	893	13	,	,	PUNCT
ejde-517	893	14	m.	m.	NOUN
ejde-517	893	15	bacon	bacon	NOUN
ejde-517	893	16	,	,	PUNCT
ejde-517	893	17	j.	j.	PROPN
ejde-517	893	18	c.	c.	PROPN
ejde-517	893	19	de	de	PROPN
ejde-517	893	20	leon	leon	PROPN
ejde-517	893	21	;	;	PUNCT
ejde-517	893	22	comparative	comparative	ADJ
ejde-517	893	23	study	study	NOUN
ejde-517	893	24	of	of	ADP
ejde-517	893	25	heuristic	heuristic	ADJ
ejde-517	893	26	algorithms	algorithm	NOUN
ejde-517	893	27	for	for	ADP
ejde-517	893	28	electrical	electrical	ADJ
ejde-517	893	29	impedance	impedance	NOUN
ejde-517	893	30	tomography	tomography	NOUN
ejde-517	893	31	,	,	PUNCT
ejde-517	893	32	philippine	philippine	ADJ
ejde-517	893	33	journal	journal	NOUN
ejde-517	893	34	of	of	ADP
ejde-517	893	35	science	science	PROPN
ejde-517	893	36	149	149	NUM
ejde-517	893	37	(	(	PUNCT
ejde-517	893	38	2020	2020	NUM
ejde-517	893	39	)	)	PUNCT
ejde-517	893	40	,	,	PUNCT
ejde-517	893	41	no	no	INTJ
ejde-517	893	42	.	.	PUNCT
ejde-517	894	1	3a	3a	NUM
ejde-517	894	2	,	,	PUNCT
ejde-517	894	3	747–761	747–761	NUM
ejde-517	894	4	.	.	PUNCT
ejde-517	895	1	[	[	X
ejde-517	895	2	38	38	NUM
ejde-517	895	3	]	]	X
ejde-517	895	4	y.	y.	PROPN
ejde-517	895	5	zuo	zuo	PROPN
ejde-517	895	6	,	,	PUNCT
ejde-517	895	7	z.	z.	PROPN
ejde-517	895	8	guo	guo	PROPN
ejde-517	895	9	;	;	PUNCT
ejde-517	895	10	a	a	DET
ejde-517	895	11	review	review	NOUN
ejde-517	895	12	of	of	ADP
ejde-517	895	13	electrical	electrical	ADJ
ejde-517	895	14	impedance	impedance	NOUN
ejde-517	895	15	techniques	technique	NOUN
ejde-517	895	16	for	for	ADP
ejde-517	895	17	breast	breast	NOUN
ejde-517	895	18	cancer	cancer	NOUN
ejde-517	895	19	detection	detection	NOUN
ejde-517	895	20	,	,	PUNCT
ejde-517	895	21	elsevier	elsevier	PROPN
ejde-517	895	22	medical	medical	PROPN
ejde-517	895	23	engineering	engineering	PROPN
ejde-517	895	24	&	&	CCONJ
ejde-517	895	25	physics	physics	PROPN
ejde-517	895	26	,	,	PUNCT
ejde-517	895	27	25	25	NUM
ejde-517	895	28	(	(	PUNCT
ejde-517	895	29	2003	2003	NUM
ejde-517	895	30	)	)	PUNCT
ejde-517	895	31	,	,	PUNCT
ejde-517	895	32	no	no	INTJ
ejde-517	895	33	.	.	NOUN
ejde-517	895	34	2	2	NUM
ejde-517	895	35	,	,	PUNCT
ejde-517	895	36	79–90	79–90	NUM
ejde-517	895	37	.	.	PUNCT
ejde-517	896	1	renier	reni	ADJ
ejde-517	896	2	mendoza	mendoza	PROPN
ejde-517	896	3	institute	institute	PROPN
ejde-517	896	4	of	of	ADP
ejde-517	896	5	mathematics	mathematics	PROPN
ejde-517	896	6	,	,	PUNCT
ejde-517	896	7	university	university	NOUN
ejde-517	896	8	of	of	ADP
ejde-517	896	9	the	the	DET
ejde-517	896	10	philippines	philippine	NOUN
ejde-517	896	11	,	,	PUNCT
ejde-517	896	12	diliman	diliman	PROPN
ejde-517	896	13	,	,	PUNCT
ejde-517	896	14	quezon	quezon	PROPN
ejde-517	896	15	city	city	PROPN
ejde-517	896	16	,	,	PUNCT
ejde-517	896	17	philippines	philippine	NOUN
ejde-517	896	18	email	email	NOUN
ejde-517	896	19	address	address	NOUN
ejde-517	896	20	:	:	PUNCT
ejde-517	896	21	rmendoza@math.upd.edu.ph	rmendoza@math.upd.edu.ph	PROPN
ejde-517	896	22	stephen	stephen	PROPN
ejde-517	896	23	keeling	keeling	PROPN
ejde-517	896	24	institute	institute	PROPN
ejde-517	896	25	for	for	ADP
ejde-517	896	26	mathematics	mathematic	NOUN
ejde-517	896	27	and	and	CCONJ
ejde-517	896	28	scientific	scientific	ADJ
ejde-517	896	29	computing	computing	NOUN
ejde-517	896	30	,	,	PUNCT
ejde-517	896	31	karl	karl	PROPN
ejde-517	896	32	-	-	PUNCT
ejde-517	896	33	franzens	franzens	PROPN
ejde-517	896	34	university	university	PROPN
ejde-517	896	35	of	of	ADP
ejde-517	896	36	graz	graz	PROPN
ejde-517	896	37	,	,	PUNCT
ejde-517	896	38	austria	austria	PROPN
ejde-517	896	39	email	email	NOUN
ejde-517	896	40	address	address	NOUN
ejde-517	896	41	:	:	PUNCT
ejde-517	896	42	stephen.keeling@uni-graz.at	stephen.keeling@uni-graz.at	PROPN
ejde-517	896	43	1	1	NUM
ejde-517	896	44	.	.	PUNCT
ejde-517	897	1	introduction	introduction	NOUN
ejde-517	897	2	2	2	NUM
ejde-517	897	3	.	.	X
ejde-517	897	4	two	two	NUM
ejde-517	897	5	-	-	PUNCT
ejde-517	897	6	phase	phase	NOUN
ejde-517	897	7	segmentation	segmentation	NOUN
ejde-517	897	8	algorithm	algorithm	NOUN
ejde-517	897	9	two	two	NUM
ejde-517	897	10	-	-	PUNCT
ejde-517	897	11	phase	phase	NOUN
ejde-517	897	12	segmentation	segmentation	NOUN
ejde-517	897	13	algorithm	algorithm	NOUN
ejde-517	897	14	3	3	NUM
ejde-517	897	15	.	.	PUNCT
ejde-517	897	16	analysis	analysis	NOUN
ejde-517	897	17	of	of	ADP
ejde-517	897	18	the	the	DET
ejde-517	897	19	algorithm	algorithm	NOUN
ejde-517	897	20	3.1	3.1	NUM
ejde-517	897	21	.	.	PUNCT
ejde-517	897	22	preliminaries	preliminary	NOUN
ejde-517	897	23	3.2	3.2	NUM
ejde-517	897	24	.	.	PUNCT
ejde-517	898	1	smooth	smooth	ADJ
ejde-517	898	2	approximation	approximation	NOUN
ejde-517	898	3	of	of	ADP
ejde-517	898	4	1	1	NUM
ejde-517	898	5	3.3	3.3	NUM
ejde-517	898	6	.	.	PUNCT
ejde-517	899	1	gradient	gradient	NOUN
ejde-517	899	2	of	of	ADP
ejde-517	899	3	the	the	DET
ejde-517	899	4	functional	functional	ADJ
ejde-517	899	5	j	j	PROPN
ejde-517	899	6	4	4	X
ejde-517	899	7	.	.	PUNCT
ejde-517	899	8	existence	existence	NOUN
ejde-517	899	9	of	of	ADP
ejde-517	899	10	a	a	DET
ejde-517	899	11	fixed	fix	VERB
ejde-517	899	12	point	point	NOUN
ejde-517	899	13	5	5	NUM
ejde-517	899	14	.	.	PUNCT
ejde-517	900	1	conclusion	conclusion	NOUN
ejde-517	900	2	acknowledgments	acknowledgment	NOUN
ejde-517	900	3	references	reference	NOUN