id	sid	tid	token	lemma	pos
ejde-355	1	1	electronic	electronic	ADJ
ejde-355	1	2	journal	journal	NOUN
ejde-355	1	3	of	of	ADP
ejde-355	1	4	differential	differential	ADJ
ejde-355	1	5	equations	equation	NOUN
ejde-355	1	6	,	,	PUNCT
ejde-355	1	7	vol	vol	NOUN
ejde-355	1	8	.	.	PUNCT
ejde-355	1	9	2023	2023	NUM
ejde-355	1	10	(	(	PUNCT
ejde-355	1	11	2023	2023	NUM
ejde-355	1	12	)	)	PUNCT
ejde-355	1	13	,	,	PUNCT
ejde-355	1	14	no	no	INTJ
ejde-355	1	15	.	.	NOUN
ejde-355	1	16	57	57	NUM
ejde-355	1	17	,	,	PUNCT
ejde-355	1	18	pp	pp	ADJ
ejde-355	1	19	.	.	PUNCT
ejde-355	2	1	1–21	1–21	PROPN
ejde-355	2	2	.	.	PUNCT
ejde-355	3	1	issn	issn	PROPN
ejde-355	3	2	:	:	PUNCT
ejde-355	3	3	1072	1072	NUM
ejde-355	3	4	-	-	SYM
ejde-355	3	5	6691	6691	NUM
ejde-355	3	6	.	.	PUNCT
ejde-355	4	1	url	url	PROPN
ejde-355	4	2	:	:	PUNCT
ejde-355	4	3	https://ejde.math.txstate.edu	https://ejde.math.txstate.edu	PROPN
ejde-355	4	4	,	,	PUNCT
ejde-355	4	5	https://ejde.math.unt.edu	https://ejde.math.unt.edu	PROPN
ejde-355	4	6	doi	doi	PROPN
ejde-355	4	7	:	:	PUNCT
ejde-355	4	8	10.58997	10.58997	NUM
ejde-355	4	9	/	/	SYM
ejde-355	4	10	ejde.2023.57	ejde.2023.57	NOUN
ejde-355	4	11	asymptotic	asymptotic	ADJ
ejde-355	4	12	analysis	analysis	NOUN
ejde-355	4	13	of	of	ADP
ejde-355	4	14	perturbed	perturb	VERB
ejde-355	4	15	robin	robin	PROPN
ejde-355	4	16	problems	problem	NOUN
ejde-355	4	17	in	in	ADP
ejde-355	4	18	a	a	DET
ejde-355	4	19	planar	planar	ADJ
ejde-355	4	20	domain	domain	NOUN
ejde-355	4	21	paolo	paolo	NOUN
ejde-355	4	22	musolino	musolino	PROPN
ejde-355	4	23	,	,	PUNCT
ejde-355	4	24	martin	martin	PROPN
ejde-355	4	25	dutko	dutko	PROPN
ejde-355	4	26	,	,	PUNCT
ejde-355	4	27	gennady	gennady	PROPN
ejde-355	4	28	mishuris	mishuris	PROPN
ejde-355	4	29	abstract	abstract	ADJ
ejde-355	4	30	.	.	PUNCT
ejde-355	5	1	we	we	PRON
ejde-355	5	2	consider	consider	VERB
ejde-355	5	3	a	a	DET
ejde-355	5	4	perforated	perforated	ADJ
ejde-355	5	5	domain	domain	NOUN
ejde-355	5	6	ω(ε	ω(ε	PROPN
ejde-355	5	7	)	)	PUNCT
ejde-355	5	8	of	of	ADP
ejde-355	5	9	r2	r2	PROPN
ejde-355	5	10	with	with	ADP
ejde-355	5	11	a	a	DET
ejde-355	5	12	small	small	ADJ
ejde-355	5	13	hole	hole	NOUN
ejde-355	5	14	of	of	ADP
ejde-355	5	15	size	size	NOUN
ejde-355	5	16	ε	ε	PROPN
ejde-355	5	17	and	and	CCONJ
ejde-355	5	18	we	we	PRON
ejde-355	5	19	study	study	VERB
ejde-355	5	20	the	the	DET
ejde-355	5	21	behavior	behavior	NOUN
ejde-355	5	22	of	of	ADP
ejde-355	5	23	the	the	DET
ejde-355	5	24	solution	solution	NOUN
ejde-355	5	25	of	of	ADP
ejde-355	5	26	a	a	DET
ejde-355	5	27	mixed	mixed	ADJ
ejde-355	5	28	neumann	neumann	PROPN
ejde-355	5	29	-	-	PUNCT
ejde-355	5	30	robin	robin	PROPN
ejde-355	5	31	problem	problem	NOUN
ejde-355	5	32	in	in	ADP
ejde-355	5	33	ω(ε	ω(ε	PROPN
ejde-355	5	34	)	)	PUNCT
ejde-355	5	35	as	as	SCONJ
ejde-355	5	36	the	the	DET
ejde-355	5	37	size	size	NOUN
ejde-355	5	38	ε	ε	PROPN
ejde-355	5	39	of	of	ADP
ejde-355	5	40	the	the	DET
ejde-355	5	41	small	small	ADJ
ejde-355	5	42	hole	hole	NOUN
ejde-355	5	43	tends	tend	VERB
ejde-355	5	44	to	to	ADP
ejde-355	5	45	0	0	NUM
ejde-355	5	46	.	.	PUNCT
ejde-355	6	1	in	in	ADP
ejde-355	6	2	addition	addition	NOUN
ejde-355	6	3	to	to	ADP
ejde-355	6	4	the	the	DET
ejde-355	6	5	geometric	geometric	ADJ
ejde-355	6	6	degeneracy	degeneracy	NOUN
ejde-355	6	7	of	of	ADP
ejde-355	6	8	the	the	DET
ejde-355	6	9	problem	problem	NOUN
ejde-355	6	10	,	,	PUNCT
ejde-355	6	11	the	the	DET
ejde-355	6	12	nonlinear	nonlinear	NOUN
ejde-355	6	13	ε	ε	PROPN
ejde-355	6	14	-	-	PUNCT
ejde-355	6	15	dependent	dependent	ADJ
ejde-355	6	16	robin	robin	PROPN
ejde-355	6	17	condition	condition	NOUN
ejde-355	6	18	may	may	AUX
ejde-355	6	19	degenerate	degenerate	VERB
ejde-355	6	20	into	into	ADP
ejde-355	6	21	a	a	DET
ejde-355	6	22	neumann	neumann	PROPN
ejde-355	6	23	condition	condition	NOUN
ejde-355	6	24	for	for	ADP
ejde-355	6	25	ε	ε	PROPN
ejde-355	6	26	=	=	SYM
ejde-355	6	27	0	0	PROPN
ejde-355	6	28	and	and	CCONJ
ejde-355	6	29	the	the	DET
ejde-355	6	30	robin	robin	PROPN
ejde-355	6	31	datum	datum	NOUN
ejde-355	6	32	may	may	AUX
ejde-355	6	33	diverge	diverge	VERB
ejde-355	6	34	to	to	PART
ejde-355	6	35	infinity	infinity	VERB
ejde-355	6	36	.	.	PUNCT
ejde-355	7	1	our	our	PRON
ejde-355	7	2	goal	goal	NOUN
ejde-355	7	3	is	be	AUX
ejde-355	7	4	to	to	PART
ejde-355	7	5	analyze	analyze	VERB
ejde-355	7	6	the	the	DET
ejde-355	7	7	asymptotic	asymptotic	ADJ
ejde-355	7	8	behavior	behavior	NOUN
ejde-355	7	9	of	of	ADP
ejde-355	7	10	the	the	DET
ejde-355	7	11	solutions	solution	NOUN
ejde-355	7	12	to	to	ADP
ejde-355	7	13	the	the	DET
ejde-355	7	14	problem	problem	NOUN
ejde-355	7	15	as	as	SCONJ
ejde-355	7	16	ε	ε	PROPN
ejde-355	7	17	tends	tend	VERB
ejde-355	7	18	to	to	ADP
ejde-355	7	19	0	0	NUM
ejde-355	7	20	and	and	CCONJ
ejde-355	7	21	to	to	PART
ejde-355	7	22	understand	understand	VERB
ejde-355	7	23	how	how	SCONJ
ejde-355	7	24	the	the	DET
ejde-355	7	25	boundary	boundary	ADJ
ejde-355	7	26	condition	condition	NOUN
ejde-355	7	27	affects	affect	VERB
ejde-355	7	28	the	the	DET
ejde-355	7	29	behavior	behavior	NOUN
ejde-355	7	30	of	of	ADP
ejde-355	7	31	the	the	DET
ejde-355	7	32	solutions	solution	NOUN
ejde-355	7	33	when	when	SCONJ
ejde-355	7	34	ε	ε	PROPN
ejde-355	7	35	is	be	AUX
ejde-355	7	36	close	close	ADJ
ejde-355	7	37	to	to	ADP
ejde-355	7	38	0	0	NUM
ejde-355	7	39	.	.	PUNCT
ejde-355	8	1	the	the	DET
ejde-355	8	2	present	present	ADJ
ejde-355	8	3	paper	paper	NOUN
ejde-355	8	4	extends	extend	VERB
ejde-355	8	5	to	to	ADP
ejde-355	8	6	the	the	DET
ejde-355	8	7	planar	planar	ADJ
ejde-355	8	8	case	case	NOUN
ejde-355	8	9	the	the	DET
ejde-355	8	10	results	result	NOUN
ejde-355	8	11	of	of	ADP
ejde-355	8	12	[	[	X
ejde-355	8	13	36	36	NUM
ejde-355	8	14	]	]	PUNCT
ejde-355	8	15	dealing	deal	VERB
ejde-355	8	16	with	with	ADP
ejde-355	8	17	the	the	DET
ejde-355	8	18	case	case	NOUN
ejde-355	8	19	of	of	ADP
ejde-355	8	20	dimension	dimension	NOUN
ejde-355	8	21	n	n	PRON
ejde-355	8	22	≥	≥	NOUN
ejde-355	8	23	3	3	NUM
ejde-355	8	24	.	.	NOUN
ejde-355	8	25	1	1	NUM
ejde-355	8	26	.	.	X
ejde-355	8	27	introduction	introduction	NOUN
ejde-355	8	28	in	in	ADP
ejde-355	8	29	this	this	DET
ejde-355	8	30	article	article	NOUN
ejde-355	8	31	we	we	PRON
ejde-355	8	32	continue	continue	VERB
ejde-355	8	33	the	the	DET
ejde-355	8	34	analysis	analysis	NOUN
ejde-355	8	35	of	of	ADP
ejde-355	8	36	[	[	X
ejde-355	8	37	36	36	NUM
ejde-355	8	38	]	]	PUNCT
ejde-355	8	39	,	,	PUNCT
ejde-355	8	40	where	where	SCONJ
ejde-355	8	41	we	we	PRON
ejde-355	8	42	have	have	AUX
ejde-355	8	43	studied	study	VERB
ejde-355	8	44	the	the	DET
ejde-355	8	45	asymptotic	asymptotic	ADJ
ejde-355	8	46	behavior	behavior	NOUN
ejde-355	8	47	of	of	ADP
ejde-355	8	48	the	the	DET
ejde-355	8	49	solutions	solution	NOUN
ejde-355	8	50	of	of	ADP
ejde-355	8	51	a	a	DET
ejde-355	8	52	boundary	boundary	ADJ
ejde-355	8	53	value	value	NOUN
ejde-355	8	54	problem	problem	NOUN
ejde-355	8	55	for	for	ADP
ejde-355	8	56	the	the	DET
ejde-355	8	57	laplace	laplace	NOUN
ejde-355	8	58	equation	equation	NOUN
ejde-355	8	59	in	in	ADP
ejde-355	8	60	a	a	DET
ejde-355	8	61	perforated	perforated	ADJ
ejde-355	8	62	domain	domain	NOUN
ejde-355	8	63	in	in	ADP
ejde-355	8	64	rn	rn	PROPN
ejde-355	8	65	,	,	PUNCT
ejde-355	8	66	n	n	PRON
ejde-355	8	67	≥	≥	NOUN
ejde-355	8	68	3	3	NUM
ejde-355	8	69	,	,	PUNCT
ejde-355	8	70	with	with	ADP
ejde-355	8	71	a	a	DET
ejde-355	8	72	nonlinear	nonlinear	ADJ
ejde-355	8	73	robin	robin	PROPN
ejde-355	8	74	boundary	boundary	ADJ
ejde-355	8	75	condition	condition	NOUN
ejde-355	8	76	degenerating	degenerate	VERB
ejde-355	8	77	into	into	ADP
ejde-355	8	78	a	a	DET
ejde-355	8	79	neumann	neumann	PROPN
ejde-355	8	80	condition	condition	NOUN
ejde-355	8	81	on	on	ADP
ejde-355	8	82	the	the	DET
ejde-355	8	83	boundary	boundary	NOUN
ejde-355	8	84	of	of	ADP
ejde-355	8	85	the	the	DET
ejde-355	8	86	small	small	ADJ
ejde-355	8	87	hole	hole	NOUN
ejde-355	8	88	.	.	PUNCT
ejde-355	9	1	the	the	DET
ejde-355	9	2	problem	problem	NOUN
ejde-355	9	3	considered	consider	VERB
ejde-355	9	4	in	in	ADP
ejde-355	9	5	[	[	X
ejde-355	9	6	36	36	NUM
ejde-355	9	7	]	]	PUNCT
ejde-355	9	8	was	be	AUX
ejde-355	9	9	degenerating	degenerate	VERB
ejde-355	9	10	under	under	ADP
ejde-355	9	11	three	three	NUM
ejde-355	9	12	aspects	aspect	NOUN
ejde-355	9	13	:	:	PUNCT
ejde-355	9	14	in	in	ADP
ejde-355	9	15	the	the	DET
ejde-355	9	16	limit	limit	NOUN
ejde-355	9	17	case	case	NOUN
ejde-355	9	18	the	the	DET
ejde-355	9	19	robin	robin	PROPN
ejde-355	9	20	boundary	boundary	ADJ
ejde-355	9	21	condition	condition	NOUN
ejde-355	9	22	may	may	AUX
ejde-355	9	23	degenerate	degenerate	VERB
ejde-355	9	24	into	into	ADP
ejde-355	9	25	a	a	DET
ejde-355	9	26	neumann	neumann	PROPN
ejde-355	9	27	boundary	boundary	ADJ
ejde-355	9	28	condition	condition	NOUN
ejde-355	9	29	,	,	PUNCT
ejde-355	9	30	the	the	DET
ejde-355	9	31	robin	robin	PROPN
ejde-355	9	32	datum	datum	NOUN
ejde-355	9	33	may	may	AUX
ejde-355	9	34	tend	tend	VERB
ejde-355	9	35	to	to	PART
ejde-355	9	36	infinity	infinity	VERB
ejde-355	9	37	,	,	PUNCT
ejde-355	9	38	and	and	CCONJ
ejde-355	9	39	,	,	PUNCT
ejde-355	9	40	finally	finally	ADV
ejde-355	9	41	,	,	PUNCT
ejde-355	9	42	the	the	DET
ejde-355	9	43	size	size	NOUN
ejde-355	9	44	ε	ε	PROPN
ejde-355	9	45	of	of	ADP
ejde-355	9	46	the	the	DET
ejde-355	9	47	small	small	ADJ
ejde-355	9	48	hole	hole	NOUN
ejde-355	9	49	where	where	SCONJ
ejde-355	9	50	we	we	PRON
ejde-355	9	51	consider	consider	VERB
ejde-355	9	52	the	the	DET
ejde-355	9	53	robin	robin	PROPN
ejde-355	9	54	condition	condition	NOUN
ejde-355	9	55	tends	tend	VERB
ejde-355	9	56	to	to	ADP
ejde-355	9	57	0	0	NUM
ejde-355	9	58	.	.	PUNCT
ejde-355	10	1	the	the	DET
ejde-355	10	2	analysis	analysis	NOUN
ejde-355	10	3	of	of	ADP
ejde-355	10	4	[	[	X
ejde-355	10	5	36	36	NUM
ejde-355	10	6	]	]	PUNCT
ejde-355	10	7	was	be	AUX
ejde-355	10	8	confined	confine	VERB
ejde-355	10	9	to	to	ADP
ejde-355	10	10	the	the	DET
ejde-355	10	11	case	case	NOUN
ejde-355	10	12	of	of	ADP
ejde-355	10	13	dimension	dimension	NOUN
ejde-355	10	14	n	n	CCONJ
ejde-355	10	15	≥	≥	NOUN
ejde-355	10	16	3	3	NUM
ejde-355	10	17	,	,	PUNCT
ejde-355	10	18	since	since	SCONJ
ejde-355	10	19	the	the	DET
ejde-355	10	20	two	two	NUM
ejde-355	10	21	-	-	PUNCT
ejde-355	10	22	dimensional	dimensional	ADJ
ejde-355	10	23	case	case	NOUN
ejde-355	10	24	requires	require	VERB
ejde-355	10	25	a	a	DET
ejde-355	10	26	different	different	ADJ
ejde-355	10	27	treatment	treatment	NOUN
ejde-355	10	28	.	.	PUNCT
ejde-355	11	1	indeed	indeed	ADV
ejde-355	11	2	the	the	DET
ejde-355	11	3	technique	technique	NOUN
ejde-355	11	4	of	of	ADP
ejde-355	11	5	[	[	X
ejde-355	11	6	36	36	NUM
ejde-355	11	7	]	]	PUNCT
ejde-355	11	8	is	be	AUX
ejde-355	11	9	based	base	VERB
ejde-355	11	10	on	on	ADP
ejde-355	11	11	potential	potential	ADJ
ejde-355	11	12	theory	theory	NOUN
ejde-355	11	13	,	,	PUNCT
ejde-355	11	14	and	and	CCONJ
ejde-355	11	15	as	as	SCONJ
ejde-355	11	16	it	it	PRON
ejde-355	11	17	happens	happen	VERB
ejde-355	11	18	often	often	ADV
ejde-355	11	19	with	with	ADP
ejde-355	11	20	such	such	ADJ
ejde-355	11	21	method	method	NOUN
ejde-355	11	22	,	,	PUNCT
ejde-355	11	23	the	the	DET
ejde-355	11	24	case	case	NOUN
ejde-355	11	25	of	of	ADP
ejde-355	11	26	dimension	dimension	NOUN
ejde-355	11	27	n	n	NOUN
ejde-355	11	28	=	=	SYM
ejde-355	11	29	2	2	NUM
ejde-355	11	30	and	and	CCONJ
ejde-355	11	31	the	the	DET
ejde-355	11	32	one	one	NUM
ejde-355	11	33	of	of	ADP
ejde-355	11	34	dimension	dimension	NOUN
ejde-355	11	35	n	n	PRON
ejde-355	11	36	≥	≥	NUM
ejde-355	11	37	3	3	NUM
ejde-355	11	38	need	need	VERB
ejde-355	11	39	to	to	PART
ejde-355	11	40	be	be	AUX
ejde-355	11	41	treated	treat	VERB
ejde-355	11	42	separately	separately	ADV
ejde-355	11	43	because	because	SCONJ
ejde-355	11	44	of	of	ADP
ejde-355	11	45	the	the	DET
ejde-355	11	46	different	different	ADJ
ejde-355	11	47	aspect	aspect	NOUN
ejde-355	11	48	of	of	ADP
ejde-355	11	49	the	the	DET
ejde-355	11	50	fundamental	fundamental	ADJ
ejde-355	11	51	solution	solution	NOUN
ejde-355	11	52	of	of	ADP
ejde-355	11	53	the	the	DET
ejde-355	11	54	laplacian	laplacian	PROPN
ejde-355	11	55	.	.	PUNCT
ejde-355	12	1	boundary	boundary	ADJ
ejde-355	12	2	value	value	NOUN
ejde-355	12	3	problems	problem	NOUN
ejde-355	12	4	with	with	ADP
ejde-355	12	5	degenerating	degenerate	VERB
ejde-355	12	6	or	or	CCONJ
ejde-355	12	7	perturbed	perturb	VERB
ejde-355	12	8	boundary	boundary	ADJ
ejde-355	12	9	conditions	condition	NOUN
ejde-355	12	10	have	have	AUX
ejde-355	12	11	been	be	AUX
ejde-355	12	12	analyzed	analyze	VERB
ejde-355	12	13	by	by	ADP
ejde-355	12	14	many	many	ADJ
ejde-355	12	15	authors	author	NOUN
ejde-355	12	16	.	.	PUNCT
ejde-355	13	1	here	here	ADV
ejde-355	13	2	we	we	PRON
ejde-355	13	3	mention	mention	VERB
ejde-355	13	4	,	,	PUNCT
ejde-355	13	5	for	for	ADP
ejde-355	13	6	example	example	NOUN
ejde-355	13	7	,	,	PUNCT
ejde-355	13	8	wendland	wendland	PROPN
ejde-355	13	9	,	,	PUNCT
ejde-355	13	10	stephan	stephan	PROPN
ejde-355	13	11	,	,	PUNCT
ejde-355	13	12	and	and	CCONJ
ejde-355	13	13	hsiao	hsiao	PROPN
ejde-355	14	1	[	[	X
ejde-355	14	2	43	43	NUM
ejde-355	14	3	]	]	PUNCT
ejde-355	14	4	,	,	PUNCT
ejde-355	14	5	kirsch	kirsch	PROPN
ejde-355	15	1	[	[	X
ejde-355	15	2	18	18	NUM
ejde-355	15	3	]	]	PUNCT
ejde-355	15	4	,	,	PUNCT
ejde-355	15	5	costabel	costabel	NOUN
ejde-355	15	6	and	and	CCONJ
ejde-355	15	7	dauge	dauge	NOUN
ejde-355	16	1	[	[	X
ejde-355	16	2	4	4	NUM
ejde-355	16	3	]	]	PUNCT
ejde-355	16	4	,	,	PUNCT
ejde-355	16	5	ammari	ammari	NOUN
ejde-355	16	6	and	and	CCONJ
ejde-355	16	7	nédélec	nédélec	VERB
ejde-355	17	1	[	[	X
ejde-355	17	2	2	2	NUM
ejde-355	17	3	]	]	PUNCT
ejde-355	17	4	,	,	PUNCT
ejde-355	17	5	schmidt	schmidt	NOUN
ejde-355	17	6	and	and	CCONJ
ejde-355	17	7	hiptmair	hiptmair	NOUN
ejde-355	17	8	[	[	X
ejde-355	17	9	40	40	NUM
ejde-355	17	10	]	]	PUNCT
ejde-355	17	11	,	,	PUNCT
ejde-355	17	12	and	and	CCONJ
ejde-355	17	13	[	[	X
ejde-355	17	14	35	35	NUM
ejde-355	17	15	,	,	PUNCT
ejde-355	17	16	36	36	NUM
ejde-355	17	17	]	]	PUNCT
ejde-355	17	18	.	.	PUNCT
ejde-355	18	1	as	as	SCONJ
ejde-355	18	2	already	already	ADV
ejde-355	18	3	mentioned	mention	VERB
ejde-355	18	4	,	,	PUNCT
ejde-355	18	5	another	another	DET
ejde-355	18	6	feature	feature	NOUN
ejde-355	18	7	of	of	ADP
ejde-355	18	8	the	the	DET
ejde-355	18	9	problem	problem	NOUN
ejde-355	18	10	considered	consider	VERB
ejde-355	18	11	in	in	ADP
ejde-355	18	12	the	the	DET
ejde-355	18	13	present	present	ADJ
ejde-355	18	14	paper	paper	NOUN
ejde-355	18	15	and	and	CCONJ
ejde-355	18	16	in	in	ADP
ejde-355	18	17	[	[	X
ejde-355	18	18	36	36	NUM
ejde-355	18	19	]	]	PUNCT
ejde-355	18	20	is	be	AUX
ejde-355	18	21	the	the	DET
ejde-355	18	22	fact	fact	NOUN
ejde-355	18	23	that	that	SCONJ
ejde-355	18	24	the	the	DET
ejde-355	18	25	degenerating	degenerate	VERB
ejde-355	18	26	boundary	boundary	ADJ
ejde-355	18	27	condition	condition	NOUN
ejde-355	18	28	is	be	AUX
ejde-355	18	29	posed	pose	VERB
ejde-355	18	30	on	on	ADP
ejde-355	18	31	2020	2020	NUM
ejde-355	18	32	mathematics	mathematic	NOUN
ejde-355	18	33	subject	subject	ADJ
ejde-355	18	34	classification	classification	NOUN
ejde-355	18	35	.	.	PUNCT
ejde-355	19	1	35j25	35j25	NUM
ejde-355	19	2	,	,	PUNCT
ejde-355	19	3	31b10	31b10	NUM
ejde-355	19	4	,	,	PUNCT
ejde-355	19	5	35b25	35b25	NUM
ejde-355	19	6	,	,	PUNCT
ejde-355	19	7	35c20	35c20	NUM
ejde-355	19	8	,	,	PUNCT
ejde-355	19	9	47h30	47h30	NUM
ejde-355	19	10	.	.	PUNCT
ejde-355	20	1	key	key	ADJ
ejde-355	20	2	words	word	NOUN
ejde-355	20	3	and	and	CCONJ
ejde-355	20	4	phrases	phrase	NOUN
ejde-355	20	5	.	.	PUNCT
ejde-355	21	1	singularly	singularly	ADV
ejde-355	21	2	perturbed	perturb	VERB
ejde-355	21	3	boundary	boundary	ADJ
ejde-355	21	4	value	value	NOUN
ejde-355	21	5	problem	problem	NOUN
ejde-355	21	6	;	;	PUNCT
ejde-355	21	7	laplace	laplace	NOUN
ejde-355	21	8	equation	equation	NOUN
ejde-355	21	9	;	;	PUNCT
ejde-355	21	10	nonlinear	nonlinear	PROPN
ejde-355	21	11	robin	robin	PROPN
ejde-355	21	12	condition	condition	NOUN
ejde-355	21	13	;	;	PUNCT
ejde-355	21	14	perforated	perforate	VERB
ejde-355	21	15	planar	planar	ADJ
ejde-355	21	16	domain	domain	NOUN
ejde-355	21	17	;	;	PUNCT
ejde-355	21	18	integral	integral	ADJ
ejde-355	21	19	equation	equation	NOUN
ejde-355	21	20	.	.	PUNCT
ejde-355	22	1	©	©	ADP
ejde-355	22	2	2023	2023	NUM
ejde-355	22	3	.	.	PUNCT
ejde-355	23	1	this	this	DET
ejde-355	23	2	work	work	NOUN
ejde-355	23	3	is	be	AUX
ejde-355	23	4	licensed	license	VERB
ejde-355	23	5	under	under	ADP
ejde-355	23	6	a	a	DET
ejde-355	23	7	cc	cc	NOUN
ejde-355	23	8	by	by	ADP
ejde-355	23	9	4.0	4.0	NUM
ejde-355	23	10	license	license	NOUN
ejde-355	23	11	.	.	PUNCT
ejde-355	24	1	submitted	submit	VERB
ejde-355	24	2	february	february	PROPN
ejde-355	24	3	15	15	NUM
ejde-355	24	4	,	,	PUNCT
ejde-355	24	5	2023	2023	NUM
ejde-355	24	6	.	.	PUNCT
ejde-355	25	1	published	publish	VERB
ejde-355	25	2	september	september	PROPN
ejde-355	25	3	11	11	NUM
ejde-355	25	4	,	,	PUNCT
ejde-355	25	5	2023	2023	NUM
ejde-355	25	6	.	.	PUNCT
ejde-355	25	7	1	1	NUM
ejde-355	25	8	2	2	NUM
ejde-355	25	9	p.	p.	NOUN
ejde-355	25	10	musolino	musolino	NOUN
ejde-355	25	11	,	,	PUNCT
ejde-355	25	12	m.	m.	NOUN
ejde-355	25	13	dutko	dutko	PROPN
ejde-355	25	14	,	,	PUNCT
ejde-355	25	15	g.	g.	PROPN
ejde-355	25	16	mishuris	mishuris	PROPN
ejde-355	25	17	ejde-2023/57	ejde-2023/57	NOUN
ejde-355	25	18	the	the	DET
ejde-355	25	19	boundary	boundary	NOUN
ejde-355	25	20	of	of	ADP
ejde-355	25	21	a	a	DET
ejde-355	25	22	small	small	ADJ
ejde-355	25	23	hole	hole	NOUN
ejde-355	25	24	.	.	PUNCT
ejde-355	26	1	boundary	boundary	ADJ
ejde-355	26	2	value	value	NOUN
ejde-355	26	3	problems	problem	NOUN
ejde-355	26	4	in	in	ADP
ejde-355	26	5	domain	domain	NOUN
ejde-355	26	6	with	with	ADP
ejde-355	26	7	small	small	ADJ
ejde-355	26	8	holes	hole	NOUN
ejde-355	26	9	have	have	AUX
ejde-355	26	10	been	be	AUX
ejde-355	26	11	studied	study	VERB
ejde-355	26	12	by	by	ADP
ejde-355	26	13	many	many	ADJ
ejde-355	26	14	authors	author	NOUN
ejde-355	26	15	.	.	PUNCT
ejde-355	27	1	asymptotic	asymptotic	ADJ
ejde-355	27	2	analysis	analysis	NOUN
ejde-355	27	3	techniques	technique	NOUN
ejde-355	27	4	have	have	AUX
ejde-355	27	5	been	be	AUX
ejde-355	27	6	used	use	VERB
ejde-355	27	7	for	for	ADP
ejde-355	27	8	example	example	NOUN
ejde-355	27	9	in	in	ADP
ejde-355	27	10	the	the	DET
ejde-355	27	11	works	work	NOUN
ejde-355	27	12	of	of	ADP
ejde-355	27	13	ammari	ammari	PROPN
ejde-355	27	14	and	and	CCONJ
ejde-355	27	15	kang	kang	PROPN
ejde-355	28	1	[	[	X
ejde-355	28	2	1	1	NUM
ejde-355	28	3	]	]	PUNCT
ejde-355	28	4	,	,	PUNCT
ejde-355	28	5	il’in	il’in	PROPN
ejde-355	29	1	[	[	X
ejde-355	29	2	17	17	NUM
ejde-355	29	3	]	]	PUNCT
ejde-355	29	4	,	,	PUNCT
ejde-355	29	5	maz’ya	maz’ya	NOUN
ejde-355	29	6	,	,	PUNCT
ejde-355	29	7	movchan	movchan	ADV
ejde-355	29	8	,	,	PUNCT
ejde-355	29	9	and	and	CCONJ
ejde-355	29	10	nieves	nieve	NOUN
ejde-355	30	1	[	[	X
ejde-355	30	2	24	24	NUM
ejde-355	30	3	,	,	PUNCT
ejde-355	30	4	25	25	NUM
ejde-355	30	5	,	,	PUNCT
ejde-355	30	6	26	26	NUM
ejde-355	30	7	,	,	PUNCT
ejde-355	30	8	27	27	NUM
ejde-355	30	9	,	,	PUNCT
ejde-355	30	10	28	28	NUM
ejde-355	30	11	]	]	PUNCT
ejde-355	30	12	,	,	PUNCT
ejde-355	30	13	maz’ya	maz’ya	NOUN
ejde-355	30	14	,	,	PUNCT
ejde-355	30	15	nazarov	nazarov	NOUN
ejde-355	30	16	,	,	PUNCT
ejde-355	30	17	and	and	CCONJ
ejde-355	30	18	plamenevskij	plamenevskij	NOUN
ejde-355	30	19	[	[	X
ejde-355	30	20	29	29	NUM
ejde-355	30	21	,	,	PUNCT
ejde-355	30	22	30	30	NUM
ejde-355	30	23	]	]	PUNCT
ejde-355	30	24	,	,	PUNCT
ejde-355	30	25	nieves	nieve	VERB
ejde-355	31	1	[	[	X
ejde-355	31	2	38	38	NUM
ejde-355	31	3	]	]	PUNCT
ejde-355	31	4	,	,	PUNCT
ejde-355	31	5	nieves	nieve	NOUN
ejde-355	31	6	and	and	CCONJ
ejde-355	31	7	movchan	movchan	ADV
ejde-355	32	1	[	[	X
ejde-355	32	2	37	37	NUM
ejde-355	32	3	]	]	PUNCT
ejde-355	32	4	,	,	PUNCT
ejde-355	32	5	novotny	novotny	PROPN
ejde-355	32	6	and	and	CCONJ
ejde-355	32	7	soko	soko	PROPN
ejde-355	32	8	lowski	lowski	PROPN
ejde-355	33	1	[	[	X
ejde-355	33	2	39	39	NUM
ejde-355	33	3	]	]	PUNCT
ejde-355	33	4	.	.	PUNCT
ejde-355	34	1	we	we	PRON
ejde-355	34	2	also	also	ADV
ejde-355	34	3	note	note	VERB
ejde-355	34	4	that	that	SCONJ
ejde-355	34	5	in	in	ADP
ejde-355	34	6	grossi	grossi	PROPN
ejde-355	34	7	and	and	CCONJ
ejde-355	34	8	luo	luo	PROPN
ejde-355	35	1	[	[	X
ejde-355	35	2	15	15	NUM
ejde-355	35	3	]	]	SYM
ejde-355	35	4	boundary	boundary	ADJ
ejde-355	35	5	value	value	NOUN
ejde-355	35	6	problems	problem	NOUN
ejde-355	35	7	in	in	ADP
ejde-355	35	8	domains	domain	NOUN
ejde-355	35	9	with	with	ADP
ejde-355	35	10	small	small	ADJ
ejde-355	35	11	holes	hole	NOUN
ejde-355	35	12	have	have	AUX
ejde-355	35	13	been	be	AUX
ejde-355	35	14	studied	study	VERB
ejde-355	35	15	with	with	ADP
ejde-355	35	16	the	the	DET
ejde-355	35	17	goal	goal	NOUN
ejde-355	35	18	of	of	ADP
ejde-355	35	19	analyzing	analyze	VERB
ejde-355	35	20	critical	critical	ADJ
ejde-355	35	21	points	point	NOUN
ejde-355	35	22	of	of	ADP
ejde-355	35	23	solutions	solution	NOUN
ejde-355	35	24	.	.	PUNCT
ejde-355	36	1	the	the	DET
ejde-355	36	2	method	method	NOUN
ejde-355	36	3	of	of	ADP
ejde-355	36	4	the	the	DET
ejde-355	36	5	present	present	ADJ
ejde-355	36	6	paper	paper	NOUN
ejde-355	36	7	is	be	AUX
ejde-355	36	8	instead	instead	ADV
ejde-355	36	9	,	,	PUNCT
ejde-355	36	10	as	as	ADP
ejde-355	36	11	in	in	ADP
ejde-355	36	12	[	[	X
ejde-355	36	13	36	36	NUM
ejde-355	36	14	]	]	PUNCT
ejde-355	36	15	,	,	PUNCT
ejde-355	36	16	the	the	DET
ejde-355	36	17	functional	functional	ADJ
ejde-355	36	18	analytic	analytic	ADJ
ejde-355	36	19	approach	approach	NOUN
ejde-355	36	20	proposed	propose	VERB
ejde-355	36	21	by	by	ADP
ejde-355	36	22	lanza	lanza	PROPN
ejde-355	36	23	de	de	X
ejde-355	36	24	cristoforis	cristoforis	PROPN
ejde-355	36	25	in	in	ADP
ejde-355	36	26	[	[	X
ejde-355	36	27	19	19	NUM
ejde-355	36	28	]	]	PUNCT
ejde-355	36	29	for	for	ADP
ejde-355	36	30	the	the	DET
ejde-355	36	31	analysis	analysis	NOUN
ejde-355	36	32	of	of	ADP
ejde-355	36	33	singular	singular	ADJ
ejde-355	36	34	perturbation	perturbation	NOUN
ejde-355	36	35	problems	problem	NOUN
ejde-355	36	36	in	in	ADP
ejde-355	36	37	perforated	perforate	VERB
ejde-355	36	38	domains	domain	NOUN
ejde-355	36	39	.	.	PUNCT
ejde-355	37	1	the	the	DET
ejde-355	37	2	purpose	purpose	NOUN
ejde-355	37	3	of	of	ADP
ejde-355	37	4	the	the	DET
ejde-355	37	5	method	method	NOUN
ejde-355	37	6	is	be	AUX
ejde-355	37	7	to	to	PART
ejde-355	37	8	represent	represent	VERB
ejde-355	37	9	the	the	DET
ejde-355	37	10	solution	solution	NOUN
ejde-355	37	11	of	of	ADP
ejde-355	37	12	a	a	DET
ejde-355	37	13	pertubed	pertube	VERB
ejde-355	37	14	problem	problem	NOUN
ejde-355	37	15	in	in	ADP
ejde-355	37	16	terms	term	NOUN
ejde-355	37	17	of	of	ADP
ejde-355	37	18	real	real	ADJ
ejde-355	37	19	analytic	analytic	ADJ
ejde-355	37	20	maps	map	NOUN
ejde-355	37	21	and	and	CCONJ
ejde-355	37	22	known	know	VERB
ejde-355	37	23	functions	function	NOUN
ejde-355	37	24	of	of	ADP
ejde-355	37	25	the	the	DET
ejde-355	37	26	perturbation	perturbation	NOUN
ejde-355	37	27	parameters	parameter	NOUN
ejde-355	37	28	.	.	PUNCT
ejde-355	38	1	in	in	ADP
ejde-355	38	2	particular	particular	ADJ
ejde-355	38	3	,	,	PUNCT
ejde-355	38	4	we	we	PRON
ejde-355	38	5	observe	observe	VERB
ejde-355	38	6	that	that	SCONJ
ejde-355	38	7	such	such	ADJ
ejde-355	38	8	method	method	NOUN
ejde-355	38	9	has	have	AUX
ejde-355	38	10	been	be	AUX
ejde-355	38	11	successfully	successfully	ADV
ejde-355	38	12	used	use	VERB
ejde-355	38	13	for	for	ADP
ejde-355	38	14	example	example	NOUN
ejde-355	38	15	in	in	ADP
ejde-355	38	16	dalla	dalla	PROPN
ejde-355	38	17	riva	riva	PROPN
ejde-355	38	18	and	and	CCONJ
ejde-355	38	19	lanza	lanza	NOUN
ejde-355	38	20	de	de	PROPN
ejde-355	38	21	cristoforis	cristoforis	PROPN
ejde-355	39	1	[	[	X
ejde-355	39	2	5	5	NUM
ejde-355	39	3	,	,	PUNCT
ejde-355	39	4	6	6	NUM
ejde-355	39	5	,	,	PUNCT
ejde-355	39	6	7	7	NUM
ejde-355	39	7	,	,	PUNCT
ejde-355	39	8	8	8	NUM
ejde-355	39	9	]	]	PUNCT
ejde-355	39	10	and	and	CCONJ
ejde-355	39	11	lanza	lanza	PROPN
ejde-355	39	12	de	de	PROPN
ejde-355	39	13	cristoforis	cristoforis	PROPN
ejde-355	39	14	[	[	X
ejde-355	39	15	20	20	NUM
ejde-355	39	16	]	]	PUNCT
ejde-355	39	17	,	,	PUNCT
ejde-355	39	18	for	for	ADP
ejde-355	39	19	the	the	DET
ejde-355	39	20	analysis	analysis	NOUN
ejde-355	39	21	of	of	ADP
ejde-355	39	22	nonlinear	nonlinear	ADJ
ejde-355	39	23	boundary	boundary	ADJ
ejde-355	39	24	value	value	NOUN
ejde-355	39	25	problems	problem	NOUN
ejde-355	39	26	.	.	PUNCT
ejde-355	40	1	in	in	ADP
ejde-355	40	2	scientific	scientific	ADJ
ejde-355	40	3	and	and	CCONJ
ejde-355	40	4	engineering	engineering	NOUN
ejde-355	40	5	practice	practice	NOUN
ejde-355	40	6	,	,	PUNCT
ejde-355	40	7	robin	robin	PROPN
ejde-355	40	8	boundary	boundary	PROPN
ejde-355	40	9	condition	condition	NOUN
ejde-355	40	10	has	have	VERB
ejde-355	40	11	an	an	DET
ejde-355	40	12	important	important	ADJ
ejde-355	40	13	role	role	NOUN
ejde-355	40	14	in	in	ADP
ejde-355	40	15	many	many	ADJ
ejde-355	40	16	applications	application	NOUN
ejde-355	40	17	.	.	PUNCT
ejde-355	41	1	perhaps	perhaps	ADV
ejde-355	41	2	the	the	DET
ejde-355	41	3	most	most	ADV
ejde-355	41	4	common	common	ADJ
ejde-355	41	5	use	use	NOUN
ejde-355	41	6	are	be	AUX
ejde-355	41	7	the	the	DET
ejde-355	41	8	transport	transport	NOUN
ejde-355	41	9	pdes	pde	NOUN
ejde-355	41	10	utilized	utilize	VERB
ejde-355	41	11	in	in	ADP
ejde-355	41	12	the	the	DET
ejde-355	41	13	systems	system	NOUN
ejde-355	41	14	such	such	ADJ
ejde-355	41	15	as	as	ADP
ejde-355	41	16	convective	convective	ADJ
ejde-355	41	17	-	-	PUNCT
ejde-355	41	18	dispersive	dispersive	ADJ
ejde-355	41	19	solute	solute	NOUN
ejde-355	41	20	transport	transport	NOUN
ejde-355	41	21	(	(	PUNCT
ejde-355	41	22	van	van	NOUN
ejde-355	41	23	genuchten	genuchten	NOUN
ejde-355	41	24	and	and	CCONJ
ejde-355	41	25	alves	alve	VERB
ejde-355	42	1	[	[	X
ejde-355	42	2	42	42	NUM
ejde-355	42	3	]	]	SYM
ejde-355	42	4	)	)	PUNCT
ejde-355	42	5	,	,	PUNCT
ejde-355	42	6	heat	heat	NOUN
ejde-355	42	7	transfer	transfer	NOUN
ejde-355	42	8	(	(	PUNCT
ejde-355	42	9	e.g.	e.g.	ADV
ejde-355	42	10	temperature	temperature	NOUN
ejde-355	42	11	dependent	dependent	ADJ
ejde-355	42	12	boundary	boundary	ADJ
ejde-355	42	13	conditions	condition	NOUN
ejde-355	42	14	in	in	ADP
ejde-355	42	15	forming	form	VERB
ejde-355	42	16	of	of	ADP
ejde-355	42	17	the	the	DET
ejde-355	42	18	glass	glass	NOUN
ejde-355	42	19	containers	container	NOUN
ejde-355	42	20	ass	ass	NOUN
ejde-355	42	21	seen	see	VERB
ejde-355	42	22	at	at	ADP
ejde-355	42	23	[	[	X
ejde-355	42	24	12	12	NUM
ejde-355	42	25	]	]	NUM
ejde-355	42	26	)	)	PUNCT
ejde-355	42	27	,	,	PUNCT
ejde-355	42	28	and	and	CCONJ
ejde-355	42	29	convectivediffusive	convectivediffusive	ADJ
ejde-355	42	30	mass	mass	NOUN
ejde-355	42	31	transfer	transfer	NOUN
ejde-355	42	32	of	of	ADP
ejde-355	42	33	different	different	ADJ
ejde-355	42	34	species	specie	NOUN
ejde-355	42	35	.	.	PUNCT
ejde-355	43	1	here	here	ADV
ejde-355	43	2	,	,	PUNCT
ejde-355	43	3	the	the	DET
ejde-355	43	4	ability	ability	NOUN
ejde-355	43	5	to	to	PART
ejde-355	43	6	define	define	VERB
ejde-355	43	7	arbitrary	arbitrary	ADJ
ejde-355	43	8	size	size	NOUN
ejde-355	43	9	of	of	ADP
ejde-355	43	10	the	the	DET
ejde-355	43	11	internal	internal	ADJ
ejde-355	43	12	perturbation	perturbation	NOUN
ejde-355	43	13	with	with	ADP
ejde-355	43	14	robin	robin	PROPN
ejde-355	43	15	boundary	boundary	PROPN
ejde-355	43	16	condition	condition	NOUN
ejde-355	43	17	is	be	AUX
ejde-355	43	18	important	important	ADJ
ejde-355	43	19	when	when	SCONJ
ejde-355	43	20	assessing	assess	VERB
ejde-355	43	21	processes	process	NOUN
ejde-355	43	22	at	at	ADP
ejde-355	43	23	different	different	ADJ
ejde-355	43	24	scales	scale	NOUN
ejde-355	43	25	–	–	PUNCT
ejde-355	43	26	for	for	ADP
ejde-355	43	27	example	example	NOUN
ejde-355	43	28	when	when	SCONJ
ejde-355	43	29	analyzing	analyze	VERB
ejde-355	43	30	sand	sand	NOUN
ejde-355	43	31	fines	fine	NOUN
ejde-355	43	32	migration	migration	NOUN
ejde-355	43	33	from	from	ADP
ejde-355	43	34	or	or	CCONJ
ejde-355	43	35	into	into	ADP
ejde-355	43	36	the	the	DET
ejde-355	43	37	well	well	NOUN
ejde-355	43	38	during	during	ADP
ejde-355	43	39	oil	oil	NOUN
ejde-355	43	40	or	or	CCONJ
ejde-355	43	41	gas	gas	NOUN
ejde-355	43	42	production	production	NOUN
ejde-355	43	43	the	the	DET
ejde-355	43	44	size	size	NOUN
ejde-355	43	45	of	of	ADP
ejde-355	43	46	the	the	DET
ejde-355	43	47	perturbation	perturbation	NOUN
ejde-355	43	48	δ	δ	PROPN
ejde-355	43	49	(	(	PUNCT
ejde-355	43	50	wellbore	wellbore	NOUN
ejde-355	43	51	diameter	diameter	NOUN
ejde-355	43	52	)	)	PUNCT
ejde-355	43	53	will	will	AUX
ejde-355	43	54	be	be	AUX
ejde-355	43	55	finite	finite	ADJ
ejde-355	43	56	at	at	ADP
ejde-355	43	57	the	the	DET
ejde-355	43	58	wellbore	wellbore	NOUN
ejde-355	43	59	scale	scale	NOUN
ejde-355	43	60	assessment	assessment	NOUN
ejde-355	43	61	but	but	CCONJ
ejde-355	43	62	δ	δ	PROPN
ejde-355	43	63	→	→	SYM
ejde-355	43	64	0	0	NUM
ejde-355	43	65	for	for	ADP
ejde-355	43	66	field	field	NOUN
ejde-355	43	67	scale	scale	NOUN
ejde-355	43	68	analysis	analysis	NOUN
ejde-355	43	69	(	(	PUNCT
ejde-355	43	70	see	see	VERB
ejde-355	43	71	e.g.	e.g.	ADV
ejde-355	43	72	[	[	X
ejde-355	43	73	13	13	NUM
ejde-355	43	74	]	]	PUNCT
ejde-355	43	75	for	for	ADP
ejde-355	43	76	various	various	ADJ
ejde-355	43	77	oil	oil	NOUN
ejde-355	43	78	and	and	CCONJ
ejde-355	43	79	gas	gas	NOUN
ejde-355	43	80	applications	application	NOUN
ejde-355	43	81	)	)	PUNCT
ejde-355	43	82	.	.	PUNCT
ejde-355	44	1	in	in	ADP
ejde-355	44	2	[	[	X
ejde-355	44	3	35	35	NUM
ejde-355	44	4	,	,	PUNCT
ejde-355	44	5	36	36	NUM
ejde-355	44	6	]	]	PUNCT
ejde-355	44	7	and	and	CCONJ
ejde-355	44	8	in	in	ADP
ejde-355	44	9	the	the	DET
ejde-355	44	10	present	present	ADJ
ejde-355	44	11	paper	paper	NOUN
ejde-355	44	12	,	,	PUNCT
ejde-355	44	13	we	we	PRON
ejde-355	44	14	have	have	AUX
ejde-355	44	15	considered	consider	VERB
ejde-355	44	16	a	a	DET
ejde-355	44	17	robin	robin	PROPN
ejde-355	44	18	problem	problem	NOUN
ejde-355	44	19	as	as	ADP
ejde-355	44	20	simplified	simplified	ADJ
ejde-355	44	21	model	model	NOUN
ejde-355	44	22	for	for	ADP
ejde-355	44	23	the	the	DET
ejde-355	44	24	transmission	transmission	NOUN
ejde-355	44	25	problem	problem	NOUN
ejde-355	44	26	for	for	ADP
ejde-355	44	27	a	a	DET
ejde-355	44	28	composite	composite	ADJ
ejde-355	44	29	domain	domain	NOUN
ejde-355	44	30	with	with	ADP
ejde-355	44	31	imperfect	imperfect	ADJ
ejde-355	44	32	conditions	condition	NOUN
ejde-355	44	33	along	along	ADP
ejde-355	44	34	the	the	DET
ejde-355	44	35	joint	joint	ADJ
ejde-355	44	36	boundary	boundary	NOUN
ejde-355	44	37	.	.	PUNCT
ejde-355	45	1	such	such	ADJ
ejde-355	45	2	nonlinear	nonlinear	ADJ
ejde-355	45	3	transmission	transmission	NOUN
ejde-355	45	4	conditions	condition	NOUN
ejde-355	45	5	frequently	frequently	ADV
ejde-355	45	6	appear	appear	VERB
ejde-355	45	7	in	in	ADP
ejde-355	45	8	practical	practical	ADJ
ejde-355	45	9	applications	application	NOUN
ejde-355	45	10	for	for	ADP
ejde-355	45	11	various	various	ADJ
ejde-355	45	12	nonlinear	nonlinear	ADJ
ejde-355	45	13	multiphysics	multiphysic	NOUN
ejde-355	45	14	problems	problem	NOUN
ejde-355	45	15	(	(	PUNCT
ejde-355	45	16	e.g.	e.g.	ADV
ejde-355	45	17	,	,	PUNCT
ejde-355	45	18	[	[	X
ejde-355	45	19	32	32	NUM
ejde-355	45	20	,	,	PUNCT
ejde-355	45	21	33	33	NUM
ejde-355	45	22	,	,	PUNCT
ejde-355	45	23	34	34	NUM
ejde-355	45	24	]	]	PUNCT
ejde-355	45	25	)	)	PUNCT
ejde-355	45	26	.	.	PUNCT
ejde-355	46	1	we	we	PRON
ejde-355	46	2	begin	begin	VERB
ejde-355	46	3	by	by	ADP
ejde-355	46	4	introducing	introduce	VERB
ejde-355	46	5	the	the	DET
ejde-355	46	6	geometry	geometry	NOUN
ejde-355	46	7	of	of	ADP
ejde-355	46	8	our	our	PRON
ejde-355	46	9	problem	problem	NOUN
ejde-355	46	10	.	.	PUNCT
ejde-355	47	1	therefore	therefore	ADV
ejde-355	47	2	,	,	PUNCT
ejde-355	47	3	we	we	PRON
ejde-355	47	4	fix	fix	VERB
ejde-355	47	5	a	a	DET
ejde-355	47	6	regularity	regularity	NOUN
ejde-355	47	7	parameter	parameter	NOUN
ejde-355	47	8	α	α	PROPN
ejde-355	47	9	∈]0	∈]0	ADJ
ejde-355	47	10	,	,	PUNCT
ejde-355	47	11	1	1	NUM
ejde-355	47	12	[	[	PUNCT
ejde-355	47	13	and	and	CCONJ
ejde-355	47	14	we	we	PRON
ejde-355	47	15	take	take	VERB
ejde-355	47	16	two	two	NUM
ejde-355	47	17	subsets	subset	NOUN
ejde-355	47	18	,	,	PUNCT
ejde-355	47	19	one	one	NUM
ejde-355	47	20	representing	represent	VERB
ejde-355	47	21	the	the	DET
ejde-355	47	22	unperturbed	unperturbed	ADJ
ejde-355	47	23	domain	domain	NOUN
ejde-355	47	24	ωo	ωo	ADP
ejde-355	47	25	and	and	CCONJ
ejde-355	47	26	another	another	PRON
ejde-355	47	27	representing	represent	VERB
ejde-355	47	28	the	the	DET
ejde-355	47	29	shape	shape	NOUN
ejde-355	47	30	of	of	ADP
ejde-355	47	31	the	the	DET
ejde-355	47	32	hole	hole	NOUN
ejde-355	47	33	ωi	ωi	PROPN
ejde-355	47	34	.	.	PUNCT
ejde-355	48	1	the	the	DET
ejde-355	48	2	sets	set	NOUN
ejde-355	48	3	ωo	ωo	ADP
ejde-355	48	4	and	and	CCONJ
ejde-355	48	5	ωi	ωi	PUNCT
ejde-355	48	6	satisfy	satisfy	VERB
ejde-355	48	7	the	the	DET
ejde-355	48	8	assumption	assumption	NOUN
ejde-355	48	9	ωi	ωi	NOUN
ejde-355	48	10	and	and	CCONJ
ejde-355	48	11	ωo	ωo	PROPN
ejde-355	48	12	are	be	AUX
ejde-355	48	13	bounded	bound	VERB
ejde-355	48	14	open	open	ADJ
ejde-355	48	15	connected	connected	ADJ
ejde-355	48	16	subsets	subset	NOUN
ejde-355	48	17	of	of	ADP
ejde-355	48	18	r2	r2	PROPN
ejde-355	48	19	of	of	ADP
ejde-355	48	20	class	class	NOUN
ejde-355	48	21	c1,α	c1,α	PROPN
ejde-355	48	22	such	such	ADJ
ejde-355	48	23	that	that	SCONJ
ejde-355	48	24	0	0	NUM
ejde-355	48	25	∈	∈	NOUN
ejde-355	48	26	ωo	ωo	ADP
ejde-355	48	27	∩	∩	NOUN
ejde-355	48	28	ωi	ωi	X
ejde-355	48	29	and	and	CCONJ
ejde-355	48	30	that	that	DET
ejde-355	48	31	r2	r2	PROPN
ejde-355	48	32	\	\	PROPN
ejde-355	48	33	ωi	ωi	PROPN
ejde-355	48	34	and	and	CCONJ
ejde-355	48	35	r2	r2	PROPN
ejde-355	48	36	\ωo	\ωo	PROPN
ejde-355	48	37	are	be	AUX
ejde-355	48	38	connected	connect	VERB
ejde-355	48	39	.	.	PUNCT
ejde-355	49	1	we	we	PRON
ejde-355	49	2	refer	refer	VERB
ejde-355	49	3	to	to	ADP
ejde-355	49	4	gilbarg	gilbarg	NOUN
ejde-355	49	5	and	and	CCONJ
ejde-355	49	6	trudinger	trudinger	NOUN
ejde-355	49	7	[	[	X
ejde-355	49	8	14	14	NUM
ejde-355	49	9	]	]	PUNCT
ejde-355	49	10	for	for	ADP
ejde-355	49	11	the	the	DET
ejde-355	49	12	definition	definition	NOUN
ejde-355	49	13	of	of	ADP
ejde-355	49	14	sets	set	NOUN
ejde-355	49	15	and	and	CCONJ
ejde-355	49	16	functions	function	NOUN
ejde-355	49	17	of	of	ADP
ejde-355	49	18	the	the	DET
ejde-355	49	19	schauder	schauder	NOUN
ejde-355	49	20	class	class	PROPN
ejde-355	49	21	ck	ck	PROPN
ejde-355	49	22	,	,	PUNCT
ejde-355	49	23	α	α	PROPN
ejde-355	49	24	(	(	PUNCT
ejde-355	49	25	k	k	PROPN
ejde-355	49	26	∈	∈	PROPN
ejde-355	49	27	n	n	CCONJ
ejde-355	49	28	)	)	PUNCT
ejde-355	49	29	.	.	PUNCT
ejde-355	50	1	we	we	PRON
ejde-355	50	2	set	set	VERB
ejde-355	50	3	ε0	ε0	PROPN
ejde-355	50	4	≡	≡	PROPN
ejde-355	50	5	sup{θ	sup{θ	PROPN
ejde-355	50	6	∈	∈	PROPN
ejde-355	50	7	]	]	PUNCT
ejde-355	50	8	0,+∞	0,+∞	NUM
ejde-355	50	9	[	[	PUNCT
ejde-355	50	10	:	:	PUNCT
ejde-355	50	11	εωi	εωi	NOUN
ejde-355	50	12	⊆	⊆	NUM
ejde-355	50	13	ωo	ωo	ADP
ejde-355	50	14	,	,	PUNCT
ejde-355	50	15	∀ε	∀ε	NOUN
ejde-355	50	16	∈	∈	PROPN
ejde-355	50	17	]	]	PUNCT
ejde-355	50	18	−θ	−θ	ADJ
ejde-355	50	19	,	,	PUNCT
ejde-355	50	20	θ	θ	PROPN
ejde-355	50	21	[	[	X
ejde-355	50	22	}	}	PUNCT
ejde-355	50	23	.	.	PUNCT
ejde-355	51	1	if	if	SCONJ
ejde-355	51	2	ε	ε	PROPN
ejde-355	51	3	∈]0	∈]0	X
ejde-355	51	4	,	,	PUNCT
ejde-355	51	5	ε0	ε0	PROPN
ejde-355	51	6	[	[	NOUN
ejde-355	51	7	,	,	PUNCT
ejde-355	51	8	then	then	ADV
ejde-355	51	9	the	the	DET
ejde-355	51	10	set	set	NOUN
ejde-355	51	11	εωi	εωi	NOUN
ejde-355	51	12	is	be	AUX
ejde-355	51	13	contained	contain	VERB
ejde-355	51	14	in	in	ADP
ejde-355	51	15	ωo	ωo	NOUN
ejde-355	51	16	.	.	PUNCT
ejde-355	52	1	we	we	PRON
ejde-355	52	2	think	think	VERB
ejde-355	52	3	of	of	ADP
ejde-355	52	4	εωi	εωi	NOUN
ejde-355	52	5	as	as	ADP
ejde-355	52	6	a	a	DET
ejde-355	52	7	hole	hole	NOUN
ejde-355	52	8	and	and	CCONJ
ejde-355	52	9	we	we	PRON
ejde-355	52	10	remove	remove	VERB
ejde-355	52	11	it	it	PRON
ejde-355	52	12	from	from	ADP
ejde-355	52	13	the	the	DET
ejde-355	52	14	unperturbed	unperturbed	ADJ
ejde-355	52	15	domain	domain	NOUN
ejde-355	52	16	.	.	PUNCT
ejde-355	53	1	hence	hence	ADV
ejde-355	53	2	,	,	PUNCT
ejde-355	53	3	we	we	PRON
ejde-355	53	4	introduce	introduce	VERB
ejde-355	53	5	the	the	DET
ejde-355	53	6	perforated	perforated	ADJ
ejde-355	53	7	domain	domain	NOUN
ejde-355	53	8	ω(ε	ω(ε	PROPN
ejde-355	53	9	)	)	PUNCT
ejde-355	53	10	by	by	ADP
ejde-355	53	11	setting	set	VERB
ejde-355	53	12	ω(ε	ω(ε	NOUN
ejde-355	53	13	)	)	PUNCT
ejde-355	53	14	≡	≡	PROPN
ejde-355	53	15	ωo	ωo	ADP
ejde-355	53	16	\	\	PROPN
ejde-355	53	17	εωi	εωi	X
ejde-355	53	18	∀ε	∀ε	PROPN
ejde-355	53	19	∈	∈	PROPN
ejde-355	53	20	]	]	X
ejde-355	53	21	0	0	NUM
ejde-355	53	22	,	,	PUNCT
ejde-355	53	23	ε0	ε0	PROPN
ejde-355	53	24	[	[	PUNCT
ejde-355	53	25	.	.	PUNCT
ejde-355	54	1	as	as	SCONJ
ejde-355	54	2	the	the	DET
ejde-355	54	3	parameter	parameter	NOUN
ejde-355	54	4	ε	ε	PROPN
ejde-355	54	5	tends	tend	VERB
ejde-355	54	6	to	to	ADP
ejde-355	54	7	0	0	NUM
ejde-355	54	8	,	,	PUNCT
ejde-355	54	9	the	the	DET
ejde-355	54	10	perforated	perforate	VERB
ejde-355	54	11	set	set	VERB
ejde-355	54	12	ω(ε	ω(ε	PROPN
ejde-355	54	13	)	)	PUNCT
ejde-355	54	14	degenerates	degenerate	NOUN
ejde-355	54	15	to	to	ADP
ejde-355	54	16	the	the	DET
ejde-355	54	17	punctured	punctured	ADJ
ejde-355	54	18	domain	domain	NOUN
ejde-355	54	19	ωo	ωo	ADP
ejde-355	54	20	\	\	PROPN
ejde-355	54	21	{	{	PUNCT
ejde-355	54	22	0	0	NUM
ejde-355	54	23	}	}	PUNCT
ejde-355	54	24	.	.	PUNCT
ejde-355	55	1	ejde-2023/57	ejde-2023/57	NOUN
ejde-355	55	2	asymptotic	asymptotic	ADJ
ejde-355	55	3	analysis	analysis	NOUN
ejde-355	55	4	of	of	ADP
ejde-355	55	5	perturbed	perturb	VERB
ejde-355	55	6	robin	robin	PROPN
ejde-355	55	7	problems	problem	VERB
ejde-355	55	8	3	3	NUM
ejde-355	55	9	as	as	SCONJ
ejde-355	55	10	we	we	PRON
ejde-355	55	11	have	have	AUX
ejde-355	55	12	done	do	VERB
ejde-355	55	13	in	in	ADP
ejde-355	55	14	[	[	X
ejde-355	55	15	36	36	NUM
ejde-355	55	16	]	]	PUNCT
ejde-355	55	17	,	,	PUNCT
ejde-355	55	18	for	for	ADP
ejde-355	55	19	each	each	DET
ejde-355	55	20	ε	ε	PROPN
ejde-355	55	21	∈]0	∈]0	X
ejde-355	55	22	,	,	PUNCT
ejde-355	55	23	ε0	ε0	PROPN
ejde-355	55	24	[	[	PUNCT
ejde-355	55	25	we	we	PRON
ejde-355	55	26	study	study	VERB
ejde-355	55	27	a	a	DET
ejde-355	55	28	nonlinear	nonlinear	ADJ
ejde-355	55	29	boundary	boundary	ADJ
ejde-355	55	30	value	value	NOUN
ejde-355	55	31	problem	problem	NOUN
ejde-355	55	32	for	for	ADP
ejde-355	55	33	the	the	DET
ejde-355	55	34	laplace	laplace	NOUN
ejde-355	55	35	operator	operator	NOUN
ejde-355	55	36	:	:	PUNCT
ejde-355	55	37	we	we	PRON
ejde-355	55	38	consider	consider	VERB
ejde-355	55	39	a	a	DET
ejde-355	55	40	neumann	neumann	PROPN
ejde-355	55	41	condition	condition	NOUN
ejde-355	55	42	on	on	ADP
ejde-355	55	43	∂ωo	∂ωo	NOUN
ejde-355	55	44	and	and	CCONJ
ejde-355	55	45	a	a	DET
ejde-355	55	46	nonlinear	nonlinear	ADJ
ejde-355	55	47	robin	robin	PROPN
ejde-355	55	48	condition	condition	NOUN
ejde-355	55	49	on	on	ADP
ejde-355	55	50	ε∂ωi	ε∂ωi	ADV
ejde-355	55	51	.	.	PUNCT
ejde-355	56	1	in	in	ADP
ejde-355	56	2	order	order	NOUN
ejde-355	56	3	to	to	PART
ejde-355	56	4	define	define	VERB
ejde-355	56	5	the	the	DET
ejde-355	56	6	boundary	boundary	ADJ
ejde-355	56	7	value	value	NOUN
ejde-355	56	8	problem	problem	NOUN
ejde-355	56	9	in	in	ADP
ejde-355	56	10	the	the	DET
ejde-355	56	11	set	set	NOUN
ejde-355	56	12	ω(ε	ω(ε	PROPN
ejde-355	56	13	)	)	PUNCT
ejde-355	56	14	,	,	PUNCT
ejde-355	56	15	we	we	PRON
ejde-355	56	16	fix	fix	VERB
ejde-355	56	17	two	two	NUM
ejde-355	56	18	functions	function	NOUN
ejde-355	56	19	go	go	VERB
ejde-355	56	20	∈	∈	PROPN
ejde-355	56	21	c0,α(∂ωo	c0,α(∂ωo	NOUN
ejde-355	56	22	)	)	PUNCT
ejde-355	56	23	,	,	PUNCT
ejde-355	56	24	gi	gi	NOUN
ejde-355	56	25	∈	∈	PROPN
ejde-355	56	26	c0,α(∂ωi	c0,α(∂ωi	ADV
ejde-355	56	27	)	)	PUNCT
ejde-355	56	28	.	.	PUNCT
ejde-355	57	1	next	next	ADV
ejde-355	57	2	we	we	PRON
ejde-355	57	3	take	take	VERB
ejde-355	57	4	a	a	DET
ejde-355	57	5	family	family	NOUN
ejde-355	57	6	{	{	PUNCT
ejde-355	57	7	fε}ε∈]0,ε0	fε}ε∈]0,ε0	PROPN
ejde-355	57	8	[	[	PUNCT
ejde-355	57	9	of	of	ADP
ejde-355	57	10	functions	function	NOUN
ejde-355	57	11	from	from	ADP
ejde-355	57	12	r	r	NOUN
ejde-355	57	13	to	to	ADP
ejde-355	57	14	r	r	NOUN
ejde-355	57	15	,	,	PUNCT
ejde-355	57	16	and	and	CCONJ
ejde-355	57	17	two	two	NUM
ejde-355	57	18	functions	function	NOUN
ejde-355	57	19	δ	δ	PROPN
ejde-355	57	20	(	(	PUNCT
ejde-355	57	21	·	·	PUNCT
ejde-355	57	22	)	)	PUNCT
ejde-355	57	23	and	and	CCONJ
ejde-355	57	24	ρ	ρ	PROPN
ejde-355	57	25	(	(	PUNCT
ejde-355	57	26	·	·	PUNCT
ejde-355	57	27	)	)	PUNCT
ejde-355	57	28	from	from	ADP
ejde-355	57	29	]	]	SYM
ejde-355	57	30	0	0	NUM
ejde-355	57	31	,	,	PUNCT
ejde-355	57	32	ε0	ε0	PROPN
ejde-355	57	33	[	[	PUNCT
ejde-355	57	34	to	to	ADP
ejde-355	57	35	]	]	PUNCT
ejde-355	57	36	0,+∞	0,+∞	PROPN
ejde-355	58	1	[	[	X
ejde-355	58	2	.	.	PUNCT
ejde-355	59	1	now	now	ADV
ejde-355	59	2	for	for	ADP
ejde-355	59	3	each	each	DET
ejde-355	59	4	ε	ε	PROPN
ejde-355	59	5	∈]0	∈]0	X
ejde-355	59	6	,	,	PUNCT
ejde-355	59	7	ε0	ε0	PROPN
ejde-355	59	8	[	[	PUNCT
ejde-355	59	9	we	we	PRON
ejde-355	59	10	consider	consider	VERB
ejde-355	59	11	the	the	DET
ejde-355	59	12	following	follow	VERB
ejde-355	59	13	boundary	boundary	ADJ
ejde-355	59	14	value	value	NOUN
ejde-355	59	15	problem	problem	NOUN
ejde-355	59	16	:	:	PUNCT
ejde-355	59	17	∆u(x	∆u(x	ADV
ejde-355	59	18	)	)	PUNCT
ejde-355	59	19	=	=	SYM
ejde-355	59	20	0	0	PUNCT
ejde-355	60	1	∀x	∀x	X
ejde-355	60	2	∈	∈	PROPN
ejde-355	60	3	ω(ε	ω(ε	PROPN
ejde-355	60	4	)	)	PUNCT
ejde-355	60	5	,	,	PUNCT
ejde-355	60	6	∂	∂	NUM
ejde-355	60	7	∂νωo	∂νωo	NUM
ejde-355	60	8	u(x	u(x	NOUN
ejde-355	60	9	)	)	PUNCT
ejde-355	60	10	=	=	SYM
ejde-355	60	11	go(x	go(x	X
ejde-355	60	12	)	)	PUNCT
ejde-355	60	13	∀x	∀x	VERB
ejde-355	60	14	∈	∈	PROPN
ejde-355	60	15	∂ωo	∂ωo	NOUN
ejde-355	60	16	,	,	PUNCT
ejde-355	60	17	∂	∂	NOUN
ejde-355	60	18	∂νεωi	∂νεωi	VERB
ejde-355	60	19	u(x	u(x	NOUN
ejde-355	60	20	)	)	PUNCT
ejde-355	60	21	=	=	PUNCT
ejde-355	60	22	δ(ε)fε(u(x	δ(ε)fε(u(x	PROPN
ejde-355	60	23	)	)	PUNCT
ejde-355	60	24	)	)	PUNCT
ejde-355	61	1	+	+	CCONJ
ejde-355	61	2	gi(x	gi(x	PROPN
ejde-355	61	3	/	/	SYM
ejde-355	61	4	ε	ε	PROPN
ejde-355	61	5	)	)	PUNCT
ejde-355	61	6	ρ(ε	ρ(ε	PROPN
ejde-355	61	7	)	)	PUNCT
ejde-355	62	1	∀x	∀x	VERB
ejde-355	62	2	∈	∈	PROPN
ejde-355	63	1	ε∂ωi	ε∂ωi	ADV
ejde-355	63	2	,	,	PUNCT
ejde-355	63	3	(	(	PUNCT
ejde-355	63	4	1.1	1.1	NUM
ejde-355	63	5	)	)	PUNCT
ejde-355	63	6	where	where	SCONJ
ejde-355	63	7	νωo	νωo	NOUN
ejde-355	63	8	and	and	CCONJ
ejde-355	63	9	νεωi	νεωi	PROPN
ejde-355	63	10	denote	denote	VERB
ejde-355	63	11	the	the	DET
ejde-355	63	12	outward	outward	ADJ
ejde-355	63	13	unit	unit	NOUN
ejde-355	63	14	normal	normal	ADJ
ejde-355	63	15	to	to	ADP
ejde-355	63	16	∂ωo	∂ωo	NOUN
ejde-355	63	17	and	and	CCONJ
ejde-355	63	18	to	to	ADP
ejde-355	63	19	∂(εωi	∂(εωi	PROPN
ejde-355	63	20	)	)	PUNCT
ejde-355	63	21	,	,	PUNCT
ejde-355	63	22	respectively	respectively	ADV
ejde-355	63	23	.	.	PUNCT
ejde-355	64	1	as	as	ADP
ejde-355	64	2	in	in	ADP
ejde-355	64	3	in	in	ADP
ejde-355	64	4	[	[	X
ejde-355	64	5	36	36	NUM
ejde-355	64	6	]	]	PUNCT
ejde-355	64	7	,	,	PUNCT
ejde-355	64	8	our	our	PRON
ejde-355	64	9	aim	aim	NOUN
ejde-355	64	10	is	be	AUX
ejde-355	64	11	to	to	PART
ejde-355	64	12	analyze	analyze	VERB
ejde-355	64	13	the	the	DET
ejde-355	64	14	behavior	behavior	NOUN
ejde-355	64	15	of	of	ADP
ejde-355	64	16	the	the	DET
ejde-355	64	17	solutions	solution	NOUN
ejde-355	64	18	to	to	ADP
ejde-355	64	19	problem	problem	NOUN
ejde-355	64	20	(	(	PUNCT
ejde-355	64	21	1.1	1.1	NUM
ejde-355	64	22	)	)	PUNCT
ejde-355	64	23	as	as	ADP
ejde-355	64	24	ε→	ε→	X
ejde-355	64	25	0	0	NUM
ejde-355	64	26	and	and	CCONJ
ejde-355	64	27	to	to	PART
ejde-355	64	28	understand	understand	VERB
ejde-355	64	29	how	how	SCONJ
ejde-355	64	30	the	the	DET
ejde-355	64	31	size	size	NOUN
ejde-355	64	32	of	of	ADP
ejde-355	64	33	the	the	DET
ejde-355	64	34	hole	hole	NOUN
ejde-355	64	35	and	and	CCONJ
ejde-355	64	36	the	the	DET
ejde-355	64	37	functions	function	NOUN
ejde-355	64	38	δ	δ	PROPN
ejde-355	64	39	and	and	CCONJ
ejde-355	64	40	ρ	ρ	PROPN
ejde-355	64	41	that	that	PRON
ejde-355	64	42	intervene	intervene	VERB
ejde-355	64	43	in	in	ADP
ejde-355	64	44	the	the	DET
ejde-355	64	45	nonlinear	nonlinear	ADJ
ejde-355	64	46	robin	robin	PROPN
ejde-355	64	47	condition	condition	NOUN
ejde-355	64	48	affect	affect	VERB
ejde-355	64	49	the	the	DET
ejde-355	64	50	asymptotic	asymptotic	ADJ
ejde-355	64	51	behavior	behavior	NOUN
ejde-355	64	52	of	of	ADP
ejde-355	64	53	solutions	solution	NOUN
ejde-355	64	54	to	to	ADP
ejde-355	64	55	problem	problem	NOUN
ejde-355	64	56	(	(	PUNCT
ejde-355	64	57	1.1	1.1	NUM
ejde-355	64	58	)	)	PUNCT
ejde-355	64	59	.	.	PUNCT
ejde-355	65	1	we	we	PRON
ejde-355	65	2	will	will	AUX
ejde-355	65	3	adapt	adapt	VERB
ejde-355	65	4	the	the	DET
ejde-355	65	5	techniques	technique	NOUN
ejde-355	65	6	of	of	ADP
ejde-355	65	7	[	[	X
ejde-355	65	8	36	36	NUM
ejde-355	65	9	]	]	PUNCT
ejde-355	65	10	for	for	ADP
ejde-355	65	11	the	the	DET
ejde-355	65	12	case	case	NOUN
ejde-355	65	13	of	of	ADP
ejde-355	65	14	dimension	dimension	NOUN
ejde-355	65	15	n	n	PRON
ejde-355	65	16	≥	≥	NUM
ejde-355	65	17	3	3	NUM
ejde-355	65	18	to	to	ADP
ejde-355	65	19	the	the	DET
ejde-355	65	20	planar	planar	ADJ
ejde-355	65	21	perforated	perforate	VERB
ejde-355	65	22	domain	domain	NOUN
ejde-355	65	23	of	of	ADP
ejde-355	65	24	the	the	DET
ejde-355	65	25	present	present	ADJ
ejde-355	65	26	paper	paper	NOUN
ejde-355	65	27	.	.	PUNCT
ejde-355	66	1	the	the	DET
ejde-355	66	2	article	article	NOUN
ejde-355	66	3	is	be	AUX
ejde-355	66	4	organized	organize	VERB
ejde-355	66	5	as	as	SCONJ
ejde-355	66	6	follows	follow	VERB
ejde-355	66	7	.	.	PUNCT
ejde-355	67	1	in	in	ADP
ejde-355	67	2	section	section	NOUN
ejde-355	67	3	2	2	NUM
ejde-355	67	4	we	we	PRON
ejde-355	67	5	analyze	analyze	VERB
ejde-355	67	6	a	a	DET
ejde-355	67	7	toy	toy	NOUN
ejde-355	67	8	problem	problem	NOUN
ejde-355	67	9	in	in	ADP
ejde-355	67	10	an	an	DET
ejde-355	67	11	annular	annular	ADJ
ejde-355	67	12	domain	domain	NOUN
ejde-355	67	13	.	.	PUNCT
ejde-355	68	1	in	in	ADP
ejde-355	68	2	section	section	NOUN
ejde-355	68	3	3	3	NUM
ejde-355	68	4	we	we	PRON
ejde-355	68	5	transform	transform	VERB
ejde-355	68	6	problem	problem	NOUN
ejde-355	68	7	(	(	PUNCT
ejde-355	68	8	1.1	1.1	NUM
ejde-355	68	9	)	)	PUNCT
ejde-355	68	10	into	into	ADP
ejde-355	68	11	an	an	DET
ejde-355	68	12	equivalent	equivalent	ADJ
ejde-355	68	13	system	system	NOUN
ejde-355	68	14	of	of	ADP
ejde-355	68	15	integral	integral	ADJ
ejde-355	68	16	equations	equation	NOUN
ejde-355	68	17	.	.	PUNCT
ejde-355	69	1	in	in	ADP
ejde-355	69	2	section	section	NOUN
ejde-355	69	3	4	4	NUM
ejde-355	69	4	,	,	PUNCT
ejde-355	69	5	we	we	PRON
ejde-355	69	6	analyze	analyze	VERB
ejde-355	69	7	such	such	ADJ
ejde-355	69	8	system	system	NOUN
ejde-355	69	9	and	and	CCONJ
ejde-355	69	10	we	we	PRON
ejde-355	69	11	prove	prove	VERB
ejde-355	69	12	our	our	PRON
ejde-355	69	13	main	main	ADJ
ejde-355	69	14	results	result	NOUN
ejde-355	69	15	on	on	ADP
ejde-355	69	16	the	the	DET
ejde-355	69	17	asymptotic	asymptotic	ADJ
ejde-355	69	18	behavior	behavior	NOUN
ejde-355	69	19	of	of	ADP
ejde-355	69	20	a	a	DET
ejde-355	69	21	family	family	NOUN
ejde-355	69	22	of	of	ADP
ejde-355	69	23	solutions	solution	NOUN
ejde-355	69	24	and	and	CCONJ
ejde-355	69	25	of	of	ADP
ejde-355	69	26	the	the	DET
ejde-355	69	27	corresponding	corresponding	ADJ
ejde-355	69	28	energy	energy	NOUN
ejde-355	69	29	integrals	integral	NOUN
ejde-355	69	30	.	.	PUNCT
ejde-355	70	1	finally	finally	ADV
ejde-355	70	2	,	,	PUNCT
ejde-355	70	3	section	section	NOUN
ejde-355	70	4	5	5	NUM
ejde-355	70	5	contains	contain	VERB
ejde-355	70	6	some	some	DET
ejde-355	70	7	remarks	remark	NOUN
ejde-355	70	8	on	on	ADP
ejde-355	70	9	the	the	DET
ejde-355	70	10	linear	linear	ADJ
ejde-355	70	11	case	case	NOUN
ejde-355	70	12	and	and	CCONJ
ejde-355	70	13	section	section	NOUN
ejde-355	70	14	6	6	NUM
ejde-355	70	15	some	some	DET
ejde-355	70	16	conclusions	conclusion	NOUN
ejde-355	70	17	.	.	PUNCT
ejde-355	71	1	2	2	X
ejde-355	71	2	.	.	X
ejde-355	71	3	a	a	DET
ejde-355	71	4	toy	toy	NOUN
ejde-355	71	5	problem	problem	NOUN
ejde-355	71	6	as	as	SCONJ
ejde-355	71	7	we	we	PRON
ejde-355	71	8	have	have	AUX
ejde-355	71	9	done	do	VERB
ejde-355	71	10	in	in	ADP
ejde-355	71	11	[	[	X
ejde-355	71	12	35	35	NUM
ejde-355	71	13	,	,	PUNCT
ejde-355	71	14	36	36	NUM
ejde-355	71	15	]	]	PUNCT
ejde-355	71	16	,	,	PUNCT
ejde-355	71	17	we	we	PRON
ejde-355	71	18	consider	consider	VERB
ejde-355	71	19	problem	problem	NOUN
ejde-355	71	20	(	(	PUNCT
ejde-355	71	21	1.1	1.1	NUM
ejde-355	71	22	)	)	PUNCT
ejde-355	71	23	in	in	ADP
ejde-355	71	24	the	the	DET
ejde-355	71	25	annular	annular	ADJ
ejde-355	71	26	domain	domain	NOUN
ejde-355	71	27	ω(ε	ω(ε	PROPN
ejde-355	71	28	)	)	PUNCT
ejde-355	71	29	≡	≡	PROPN
ejde-355	71	30	b2(0	b2(0	NOUN
ejde-355	71	31	,	,	PUNCT
ejde-355	71	32	1	1	NUM
ejde-355	71	33	)	)	PUNCT
ejde-355	71	34	\	\	PROPN
ejde-355	71	35	b2(0	b2(0	PROPN
ejde-355	71	36	,	,	PUNCT
ejde-355	71	37	ε	ε	PROPN
ejde-355	71	38	)	)	PUNCT
ejde-355	71	39	,	,	PUNCT
ejde-355	71	40	where	where	SCONJ
ejde-355	71	41	,	,	PUNCT
ejde-355	71	42	for	for	ADP
ejde-355	71	43	r	r	NOUN
ejde-355	71	44	>	>	X
ejde-355	71	45	0	0	NUM
ejde-355	71	46	,	,	PUNCT
ejde-355	71	47	the	the	DET
ejde-355	71	48	symbol	symbol	NOUN
ejde-355	71	49	b2(0	b2(0	NOUN
ejde-355	71	50	,	,	PUNCT
ejde-355	71	51	r	r	NOUN
ejde-355	71	52	)	)	PUNCT
ejde-355	71	53	denotes	denote	VERB
ejde-355	71	54	the	the	DET
ejde-355	71	55	open	open	ADJ
ejde-355	71	56	ball	ball	NOUN
ejde-355	71	57	in	in	ADP
ejde-355	71	58	r2	r2	PROPN
ejde-355	71	59	of	of	ADP
ejde-355	71	60	center	center	NOUN
ejde-355	71	61	0	0	PUNCT
ejde-355	72	1	and	and	CCONJ
ejde-355	72	2	radius	radius	PROPN
ejde-355	72	3	r.	r.	PROPN
ejde-355	72	4	in	in	ADP
ejde-355	72	5	other	other	ADJ
ejde-355	72	6	words	word	NOUN
ejde-355	72	7	,	,	PUNCT
ejde-355	72	8	we	we	PRON
ejde-355	72	9	take	take	VERB
ejde-355	72	10	ωo	ωo	PRON
ejde-355	72	11	≡	≡	PROPN
ejde-355	72	12	b2(0	b2(0	NOUN
ejde-355	72	13	,	,	PUNCT
ejde-355	72	14	1	1	NUM
ejde-355	72	15	)	)	PUNCT
ejde-355	72	16	and	and	CCONJ
ejde-355	72	17	ωi	ωi	PROPN
ejde-355	72	18	≡	≡	PROPN
ejde-355	72	19	b2(0	b2(0	PROPN
ejde-355	72	20	,	,	PUNCT
ejde-355	72	21	1	1	NUM
ejde-355	72	22	)	)	PUNCT
ejde-355	72	23	.	.	PUNCT
ejde-355	73	1	we	we	PRON
ejde-355	73	2	set	set	VERB
ejde-355	73	3	ε0	ε0	NOUN
ejde-355	73	4	=	=	SYM
ejde-355	73	5	1	1	NUM
ejde-355	73	6	,	,	PUNCT
ejde-355	73	7	fε(τ	fε(τ	NUM
ejde-355	73	8	)	)	PUNCT
ejde-355	73	9	=	=	SYM
ejde-355	73	10	τ	τ	PROPN
ejde-355	73	11	for	for	ADP
ejde-355	73	12	all	all	DET
ejde-355	73	13	τ	τ	X
ejde-355	73	14	∈	∈	NOUN
ejde-355	73	15	r	r	NOUN
ejde-355	73	16	and	and	CCONJ
ejde-355	73	17	for	for	ADP
ejde-355	73	18	all	all	DET
ejde-355	73	19	ε	ε	PROPN
ejde-355	73	20	∈]0	∈]0	X
ejde-355	73	21	,	,	PUNCT
ejde-355	73	22	ε0	ε0	PROPN
ejde-355	73	23	[	[	NOUN
ejde-355	73	24	,	,	PUNCT
ejde-355	73	25	go	go	VERB
ejde-355	73	26	=	=	SYM
ejde-355	73	27	a	a	NOUN
ejde-355	73	28	,	,	PUNCT
ejde-355	73	29	and	and	CCONJ
ejde-355	73	30	gi	gi	NOUN
ejde-355	73	31	=	=	SYM
ejde-355	73	32	b	b	PROPN
ejde-355	73	33	,	,	PUNCT
ejde-355	73	34	where	where	SCONJ
ejde-355	73	35	a	a	DET
ejde-355	73	36	,	,	PUNCT
ejde-355	73	37	b	b	PROPN
ejde-355	73	38	∈	∈	PROPN
ejde-355	73	39	r.	r.	PROPN
ejde-355	73	40	in	in	ADP
ejde-355	73	41	addition	addition	NOUN
ejde-355	73	42	,	,	PUNCT
ejde-355	73	43	we	we	PRON
ejde-355	73	44	take	take	VERB
ejde-355	73	45	two	two	NUM
ejde-355	73	46	functions	function	NOUN
ejde-355	73	47	δ	δ	PROPN
ejde-355	73	48	,	,	PUNCT
ejde-355	73	49	ρ	ρ	PROPN
ejde-355	73	50	:	:	PUNCT
ejde-355	73	51	]	]	X
ejde-355	73	52	0	0	NUM
ejde-355	73	53	,	,	PUNCT
ejde-355	73	54	1[7→]0,+∞	1[7→]0,+∞	NUM
ejde-355	73	55	[	[	PUNCT
ejde-355	73	56	and	and	CCONJ
ejde-355	73	57	for	for	ADP
ejde-355	73	58	each	each	DET
ejde-355	73	59	ε	ε	PROPN
ejde-355	73	60	∈]0	∈]0	X
ejde-355	73	61	,	,	PUNCT
ejde-355	73	62	1	1	NUM
ejde-355	73	63	[	[	PUNCT
ejde-355	73	64	we	we	PRON
ejde-355	73	65	consider	consider	VERB
ejde-355	73	66	the	the	DET
ejde-355	73	67	problem	problem	NOUN
ejde-355	73	68	∆u(x	∆u(x	VERB
ejde-355	73	69	)	)	PUNCT
ejde-355	73	70	=	=	SYM
ejde-355	73	71	0	0	PUNCT
ejde-355	73	72	∀x	∀x	X
ejde-355	73	73	∈	∈	PROPN
ejde-355	73	74	b2(0	b2(0	NOUN
ejde-355	73	75	,	,	PUNCT
ejde-355	73	76	1	1	NUM
ejde-355	73	77	)	)	PUNCT
ejde-355	73	78	\	\	PROPN
ejde-355	73	79	b2(0	b2(0	PROPN
ejde-355	73	80	,	,	PUNCT
ejde-355	73	81	ε	ε	PROPN
ejde-355	73	82	)	)	PUNCT
ejde-355	73	83	,	,	PUNCT
ejde-355	73	84	∂	∂	NUM
ejde-355	73	85	∂νb2(0,1	∂νb2(0,1	NOUN
ejde-355	73	86	)	)	PUNCT
ejde-355	73	87	u(x	u(x	PROPN
ejde-355	73	88	)	)	PUNCT
ejde-355	73	89	=	=	PUNCT
ejde-355	73	90	a	a	DET
ejde-355	73	91	∀x	∀x	NUM
ejde-355	73	92	∈	∈	PROPN
ejde-355	73	93	∂b2(0	∂b2(0	NOUN
ejde-355	73	94	,	,	PUNCT
ejde-355	73	95	1	1	NUM
ejde-355	73	96	)	)	PUNCT
ejde-355	73	97	,	,	PUNCT
ejde-355	73	98	∂	∂	NUM
ejde-355	73	99	∂νb2(0,ε	∂νb2(0,ε	NOUN
ejde-355	73	100	)	)	PUNCT
ejde-355	73	101	u(x	u(x	PROPN
ejde-355	73	102	)	)	PUNCT
ejde-355	73	103	=	=	SYM
ejde-355	73	104	δ(ε)u(x	δ(ε)u(x	NOUN
ejde-355	73	105	)	)	PUNCT
ejde-355	74	1	+	+	NUM
ejde-355	74	2	b	b	X
ejde-355	74	3	ρ(ε	ρ(ε	PROPN
ejde-355	74	4	)	)	PUNCT
ejde-355	75	1	∀x	∀x	X
ejde-355	75	2	∈	∈	PROPN
ejde-355	75	3	∂b2(0	∂b2(0	NOUN
ejde-355	75	4	,	,	PUNCT
ejde-355	75	5	ε	ε	PROPN
ejde-355	75	6	)	)	PUNCT
ejde-355	75	7	.	.	PUNCT
ejde-355	76	1	(	(	PUNCT
ejde-355	76	2	2.1	2.1	NUM
ejde-355	76	3	)	)	PUNCT
ejde-355	76	4	it	it	PRON
ejde-355	76	5	is	be	AUX
ejde-355	76	6	well	well	ADV
ejde-355	76	7	known	know	VERB
ejde-355	76	8	that	that	SCONJ
ejde-355	76	9	for	for	ADP
ejde-355	76	10	each	each	DET
ejde-355	76	11	ε	ε	PROPN
ejde-355	76	12	∈]0	∈]0	X
ejde-355	76	13	,	,	PUNCT
ejde-355	76	14	1	1	NUM
ejde-355	76	15	[	[	PUNCT
ejde-355	76	16	problem	problem	NOUN
ejde-355	76	17	(	(	PUNCT
ejde-355	76	18	2.1	2.1	NUM
ejde-355	76	19	)	)	PUNCT
ejde-355	76	20	has	have	VERB
ejde-355	76	21	a	a	DET
ejde-355	76	22	unique	unique	ADJ
ejde-355	76	23	solution	solution	NOUN
ejde-355	76	24	in	in	ADP
ejde-355	76	25	c1,α(ω(ε	c1,α(ω(ε	NOUN
ejde-355	76	26	)	)	PUNCT
ejde-355	76	27	)	)	PUNCT
ejde-355	76	28	.	.	PUNCT
ejde-355	77	1	we	we	PRON
ejde-355	77	2	denote	denote	VERB
ejde-355	77	3	such	such	DET
ejde-355	77	4	a	a	DET
ejde-355	77	5	solution	solution	NOUN
ejde-355	77	6	by	by	ADP
ejde-355	77	7	uε	uε	PROPN
ejde-355	77	8	.	.	PROPN
ejde-355	77	9	4	4	NUM
ejde-355	77	10	p.	p.	NOUN
ejde-355	77	11	musolino	musolino	NOUN
ejde-355	77	12	,	,	PUNCT
ejde-355	77	13	m.	m.	NOUN
ejde-355	77	14	dutko	dutko	PROPN
ejde-355	77	15	,	,	PUNCT
ejde-355	77	16	g.	g.	PROPN
ejde-355	77	17	mishuris	mishuris	PROPN
ejde-355	77	18	ejde-2023/57	ejde-2023/57	NOUN
ejde-355	77	19	on	on	ADP
ejde-355	77	20	the	the	DET
ejde-355	77	21	other	other	ADJ
ejde-355	77	22	hand	hand	NOUN
ejde-355	77	23	,	,	PUNCT
ejde-355	77	24	in	in	ADP
ejde-355	77	25	the	the	DET
ejde-355	77	26	unperturbed	unperturbed	ADJ
ejde-355	77	27	domain	domain	NOUN
ejde-355	77	28	b2(0	b2(0	NOUN
ejde-355	77	29	,	,	PUNCT
ejde-355	77	30	1	1	NUM
ejde-355	77	31	)	)	PUNCT
ejde-355	77	32	the	the	DET
ejde-355	77	33	neumann	neumann	PROPN
ejde-355	77	34	problem	problem	NOUN
ejde-355	77	35	∆u(x	∆u(x	VERB
ejde-355	77	36	)	)	PUNCT
ejde-355	77	37	=	=	SYM
ejde-355	77	38	0	0	PUNCT
ejde-355	77	39	∀x	∀x	X
ejde-355	77	40	∈	∈	PROPN
ejde-355	77	41	b2(0	b2(0	NOUN
ejde-355	77	42	,	,	PUNCT
ejde-355	77	43	1	1	NUM
ejde-355	77	44	)	)	PUNCT
ejde-355	77	45	,	,	PUNCT
ejde-355	77	46	∂	∂	NUM
ejde-355	77	47	∂νb2(0,1	∂νb2(0,1	NOUN
ejde-355	77	48	)	)	PUNCT
ejde-355	77	49	u(x	u(x	PROPN
ejde-355	77	50	)	)	PUNCT
ejde-355	77	51	=	=	PUNCT
ejde-355	77	52	a	a	DET
ejde-355	77	53	∀x	∀x	NUM
ejde-355	77	54	∈	∈	PROPN
ejde-355	77	55	∂b2(0	∂b2(0	NOUN
ejde-355	77	56	,	,	PUNCT
ejde-355	77	57	1	1	NUM
ejde-355	77	58	)	)	PUNCT
ejde-355	77	59	(	(	PUNCT
ejde-355	77	60	2.2	2.2	NUM
ejde-355	77	61	)	)	PUNCT
ejde-355	77	62	is	be	AUX
ejde-355	77	63	subject	subject	ADJ
ejde-355	77	64	to	to	ADP
ejde-355	77	65	compatibility	compatibility	NOUN
ejde-355	77	66	conditions	condition	NOUN
ejde-355	77	67	on	on	ADP
ejde-355	77	68	the	the	DET
ejde-355	77	69	neumann	neumann	PROPN
ejde-355	77	70	datum	datum	PROPN
ejde-355	77	71	on	on	ADP
ejde-355	77	72	∂b2(0	∂b2(0	PROPN
ejde-355	77	73	,	,	PUNCT
ejde-355	77	74	1	1	NUM
ejde-355	77	75	)	)	PUNCT
ejde-355	77	76	.	.	PUNCT
ejde-355	78	1	in	in	ADP
ejde-355	78	2	particular	particular	ADJ
ejde-355	78	3	,	,	PUNCT
ejde-355	78	4	in	in	ADP
ejde-355	78	5	this	this	DET
ejde-355	78	6	specific	specific	ADJ
ejde-355	78	7	case	case	NOUN
ejde-355	78	8	of	of	ADP
ejde-355	78	9	constant	constant	ADJ
ejde-355	78	10	neumann	neumann	PROPN
ejde-355	78	11	datum	datum	PROPN
ejde-355	78	12	,	,	PUNCT
ejde-355	78	13	problem	problem	NOUN
ejde-355	78	14	(	(	PUNCT
ejde-355	78	15	2.2	2.2	NUM
ejde-355	78	16	)	)	PUNCT
ejde-355	78	17	has	have	VERB
ejde-355	78	18	a	a	DET
ejde-355	78	19	solution	solution	NOUN
ejde-355	78	20	if	if	SCONJ
ejde-355	78	21	and	and	CCONJ
ejde-355	78	22	only	only	ADV
ejde-355	78	23	if	if	SCONJ
ejde-355	78	24	a	a	PRON
ejde-355	78	25	=	=	NOUN
ejde-355	78	26	0	0	NUM
ejde-355	78	27	.	.	PUNCT
ejde-355	79	1	(	(	PUNCT
ejde-355	79	2	2.3	2.3	NUM
ejde-355	79	3	)	)	PUNCT
ejde-355	79	4	for	for	ADP
ejde-355	79	5	a	a	DET
ejde-355	79	6	=	=	SYM
ejde-355	79	7	0	0	NUM
ejde-355	79	8	,	,	PUNCT
ejde-355	79	9	the	the	DET
ejde-355	79	10	neumann	neumann	PROPN
ejde-355	79	11	problem	problem	NOUN
ejde-355	79	12	(	(	PUNCT
ejde-355	79	13	2.2	2.2	NUM
ejde-355	79	14	)	)	PUNCT
ejde-355	79	15	has	have	VERB
ejde-355	79	16	the	the	DET
ejde-355	79	17	one	one	NUM
ejde-355	79	18	-	-	PUNCT
ejde-355	79	19	dimensional	dimensional	ADJ
ejde-355	79	20	space	space	NOUN
ejde-355	79	21	of	of	ADP
ejde-355	79	22	constant	constant	ADJ
ejde-355	79	23	functions	function	NOUN
ejde-355	79	24	in	in	ADP
ejde-355	79	25	b2(0	b2(0	NOUN
ejde-355	79	26	,	,	PUNCT
ejde-355	79	27	1	1	NUM
ejde-355	79	28	)	)	PUNCT
ejde-355	79	29	as	as	ADP
ejde-355	79	30	the	the	DET
ejde-355	79	31	space	space	NOUN
ejde-355	79	32	of	of	ADP
ejde-355	79	33	solutions	solution	NOUN
ejde-355	79	34	,	,	PUNCT
ejde-355	79	35	whereas	whereas	SCONJ
ejde-355	79	36	if	if	SCONJ
ejde-355	79	37	instead	instead	ADV
ejde-355	79	38	we	we	PRON
ejde-355	79	39	have	have	VERB
ejde-355	79	40	that	that	PRON
ejde-355	79	41	a	a	DET
ejde-355	79	42	6=	6=	NUM
ejde-355	79	43	0	0	NUM
ejde-355	79	44	,	,	PUNCT
ejde-355	79	45	then	then	ADV
ejde-355	79	46	problem	problem	NOUN
ejde-355	79	47	(	(	PUNCT
ejde-355	79	48	2.2	2.2	NUM
ejde-355	79	49	)	)	PUNCT
ejde-355	79	50	does	do	AUX
ejde-355	79	51	not	not	PART
ejde-355	79	52	have	have	VERB
ejde-355	79	53	any	any	DET
ejde-355	79	54	solution	solution	NOUN
ejde-355	79	55	.	.	PUNCT
ejde-355	80	1	as	as	ADP
ejde-355	80	2	a	a	DET
ejde-355	80	3	consequence	consequence	NOUN
ejde-355	80	4	,	,	PUNCT
ejde-355	80	5	if	if	SCONJ
ejde-355	80	6	the	the	DET
ejde-355	80	7	compatibility	compatibility	NOUN
ejde-355	80	8	condition	condition	NOUN
ejde-355	80	9	(	(	PUNCT
ejde-355	80	10	2.3	2.3	NUM
ejde-355	80	11	)	)	PUNCT
ejde-355	80	12	does	do	AUX
ejde-355	80	13	not	not	PART
ejde-355	80	14	hold	hold	VERB
ejde-355	80	15	,	,	PUNCT
ejde-355	80	16	the	the	DET
ejde-355	80	17	unique	unique	ADJ
ejde-355	80	18	solution	solution	NOUN
ejde-355	80	19	uε	uε	NOUN
ejde-355	80	20	of	of	ADP
ejde-355	80	21	problem	problem	NOUN
ejde-355	80	22	(	(	PUNCT
ejde-355	80	23	2.1	2.1	NUM
ejde-355	80	24	)	)	PUNCT
ejde-355	80	25	clearly	clearly	ADV
ejde-355	80	26	can	can	AUX
ejde-355	80	27	not	not	PART
ejde-355	80	28	converge	converge	VERB
ejde-355	80	29	to	to	ADP
ejde-355	80	30	a	a	DET
ejde-355	80	31	solution	solution	NOUN
ejde-355	80	32	of	of	ADP
ejde-355	80	33	(	(	PUNCT
ejde-355	80	34	2.2	2.2	NUM
ejde-355	80	35	)	)	PUNCT
ejde-355	80	36	as	as	ADP
ejde-355	80	37	ε→	ε→	NUM
ejde-355	80	38	0	0	NUM
ejde-355	81	1	(	(	PUNCT
ejde-355	81	2	since	since	SCONJ
ejde-355	81	3	problem	problem	NOUN
ejde-355	81	4	(	(	PUNCT
ejde-355	81	5	2.2	2.2	NUM
ejde-355	81	6	)	)	PUNCT
ejde-355	81	7	has	have	VERB
ejde-355	81	8	no	no	DET
ejde-355	81	9	solutions	solution	NOUN
ejde-355	81	10	)	)	PUNCT
ejde-355	81	11	.	.	PUNCT
ejde-355	82	1	also	also	ADV
ejde-355	82	2	,	,	PUNCT
ejde-355	82	3	as	as	SCONJ
ejde-355	82	4	we	we	PRON
ejde-355	82	5	shall	shall	AUX
ejde-355	82	6	see	see	VERB
ejde-355	82	7	,	,	PUNCT
ejde-355	82	8	the	the	DET
ejde-355	82	9	solutions	solution	NOUN
ejde-355	82	10	may	may	AUX
ejde-355	82	11	diverge	diverge	VERB
ejde-355	82	12	as	as	ADP
ejde-355	82	13	ε→	ε→	NUM
ejde-355	82	14	0	0	PUNCT
ejde-355	83	1	even	even	ADV
ejde-355	83	2	if	if	SCONJ
ejde-355	83	3	a	a	DET
ejde-355	83	4	=	=	NOUN
ejde-355	83	5	0	0	NUM
ejde-355	83	6	,	,	PUNCT
ejde-355	83	7	because	because	SCONJ
ejde-355	83	8	of	of	ADP
ejde-355	83	9	the	the	DET
ejde-355	83	10	terms	term	NOUN
ejde-355	83	11	δ(ε	δ(ε	NOUN
ejde-355	83	12	)	)	PUNCT
ejde-355	83	13	and	and	CCONJ
ejde-355	83	14	ρ(ε	ρ(ε	NUM
ejde-355	83	15	)	)	PUNCT
ejde-355	83	16	.	.	PUNCT
ejde-355	84	1	here	here	ADV
ejde-355	84	2	we	we	PRON
ejde-355	84	3	wish	wish	VERB
ejde-355	84	4	to	to	PART
ejde-355	84	5	investigate	investigate	VERB
ejde-355	84	6	how	how	SCONJ
ejde-355	84	7	the	the	DET
ejde-355	84	8	robin	robin	PROPN
ejde-355	84	9	condition	condition	NOUN
ejde-355	84	10	on	on	ADP
ejde-355	84	11	the	the	DET
ejde-355	84	12	region	region	NOUN
ejde-355	84	13	ε∂ωi	ε∂ωi	ADV
ejde-355	84	14	influences	influence	VERB
ejde-355	84	15	the	the	DET
ejde-355	84	16	asymptotic	asymptotic	ADJ
ejde-355	84	17	behavior	behavior	NOUN
ejde-355	84	18	of	of	ADP
ejde-355	84	19	the	the	DET
ejde-355	84	20	solution	solution	NOUN
ejde-355	84	21	as	as	ADP
ejde-355	84	22	ε→	ε→	X
ejde-355	84	23	0	0	NUM
ejde-355	84	24	.	.	PUNCT
ejde-355	85	1	now	now	ADV
ejde-355	85	2	,	,	PUNCT
ejde-355	85	3	our	our	PRON
ejde-355	85	4	goal	goal	NOUN
ejde-355	85	5	is	be	AUX
ejde-355	85	6	to	to	PART
ejde-355	85	7	explicitly	explicitly	ADV
ejde-355	85	8	construct	construct	VERB
ejde-355	85	9	the	the	DET
ejde-355	85	10	solution	solution	NOUN
ejde-355	85	11	uε	uε	ADP
ejde-355	85	12	of	of	ADP
ejde-355	85	13	our	our	PRON
ejde-355	85	14	toy	toy	NOUN
ejde-355	85	15	problem	problem	NOUN
ejde-355	85	16	(	(	PUNCT
ejde-355	85	17	2.1	2.1	NUM
ejde-355	85	18	)	)	PUNCT
ejde-355	85	19	and	and	CCONJ
ejde-355	85	20	then	then	ADV
ejde-355	85	21	analyze	analyze	VERB
ejde-355	85	22	the	the	DET
ejde-355	85	23	behavior	behavior	NOUN
ejde-355	85	24	of	of	ADP
ejde-355	85	25	uε	uε	PROPN
ejde-355	85	26	as	as	ADP
ejde-355	85	27	ε→	ε→	NUM
ejde-355	85	28	0	0	NUM
ejde-355	85	29	.	.	PUNCT
ejde-355	86	1	we	we	PRON
ejde-355	86	2	search	search	VERB
ejde-355	86	3	for	for	ADP
ejde-355	86	4	the	the	DET
ejde-355	86	5	solution	solution	NOUN
ejde-355	86	6	uε	uε	INTJ
ejde-355	86	7	in	in	ADP
ejde-355	86	8	the	the	DET
ejde-355	86	9	form	form	NOUN
ejde-355	86	10	uε(x	uε(x	SYM
ejde-355	86	11	)	)	PUNCT
ejde-355	86	12	≡	≡	PROPN
ejde-355	86	13	aε	aε	PROPN
ejde-355	86	14	log	log	VERB
ejde-355	86	15	|x|+bε	|x|+bε	X
ejde-355	86	16	∀x	∀x	X
ejde-355	86	17	∈	∈	PROPN
ejde-355	86	18	ω(ε	ω(ε	PROPN
ejde-355	86	19	)	)	PUNCT
ejde-355	86	20	,	,	PUNCT
ejde-355	86	21	and	and	CCONJ
ejde-355	86	22	we	we	PRON
ejde-355	86	23	need	need	VERB
ejde-355	86	24	to	to	PART
ejde-355	86	25	determine	determine	VERB
ejde-355	86	26	the	the	DET
ejde-355	86	27	constants	constant	NOUN
ejde-355	86	28	aε	aε	VERB
ejde-355	86	29	and	and	CCONJ
ejde-355	86	30	bε	bε	VERB
ejde-355	86	31	so	so	SCONJ
ejde-355	86	32	that	that	SCONJ
ejde-355	86	33	the	the	DET
ejde-355	86	34	boundary	boundary	ADJ
ejde-355	86	35	conditions	condition	NOUN
ejde-355	86	36	of	of	ADP
ejde-355	86	37	problem	problem	NOUN
ejde-355	86	38	(	(	PUNCT
ejde-355	86	39	2.1	2.1	NUM
ejde-355	86	40	)	)	PUNCT
ejde-355	86	41	hold	hold	NOUN
ejde-355	86	42	.	.	PUNCT
ejde-355	87	1	since	since	SCONJ
ejde-355	87	2	∇uε(x	∇uε(x	NOUN
ejde-355	87	3	)	)	PUNCT
ejde-355	87	4	=	=	SYM
ejde-355	87	5	aε	aε	NOUN
ejde-355	87	6	x	x	PUNCT
ejde-355	87	7	|x|2	|x|2	PROPN
ejde-355	87	8	,	,	PUNCT
ejde-355	87	9	to	to	PART
ejde-355	87	10	satisfy	satisfy	VERB
ejde-355	87	11	the	the	DET
ejde-355	87	12	neumann	neumann	PROPN
ejde-355	87	13	condition	condition	NOUN
ejde-355	87	14	on	on	ADP
ejde-355	87	15	∂b2(0	∂b2(0	PROPN
ejde-355	87	16	,	,	PUNCT
ejde-355	87	17	1	1	NUM
ejde-355	87	18	)	)	PUNCT
ejde-355	87	19	,	,	PUNCT
ejde-355	87	20	we	we	PRON
ejde-355	87	21	must	must	AUX
ejde-355	87	22	have	have	VERB
ejde-355	87	23	aε	aε	NOUN
ejde-355	87	24	=	=	VERB
ejde-355	87	25	a	a	X
ejde-355	87	26	.	.	PUNCT
ejde-355	88	1	on	on	ADP
ejde-355	88	2	the	the	DET
ejde-355	88	3	other	other	ADJ
ejde-355	88	4	hand	hand	NOUN
ejde-355	88	5	,	,	PUNCT
ejde-355	88	6	to	to	PART
ejde-355	88	7	satisfy	satisfy	VERB
ejde-355	88	8	the	the	DET
ejde-355	88	9	robin	robin	PROPN
ejde-355	88	10	condition	condition	NOUN
ejde-355	88	11	on	on	ADP
ejde-355	88	12	∂b2(0	∂b2(0	PROPN
ejde-355	88	13	,	,	PUNCT
ejde-355	88	14	ε	ε	PROPN
ejde-355	88	15	)	)	PUNCT
ejde-355	88	16	,	,	PUNCT
ejde-355	88	17	we	we	PRON
ejde-355	88	18	need	need	VERB
ejde-355	88	19	to	to	PART
ejde-355	88	20	determine	determine	VERB
ejde-355	88	21	bε	bε	NOUN
ejde-355	88	22	so	so	SCONJ
ejde-355	88	23	that	that	SCONJ
ejde-355	88	24	x	x	X
ejde-355	89	1	|x|	|x|	PROPN
ejde-355	89	2	·	·	PUNCT
ejde-355	89	3	a	a	DET
ejde-355	89	4	x	x	X
ejde-355	89	5	|x|2	|x|2	NOUN
ejde-355	89	6	=	=	PUNCT
ejde-355	89	7	δ(ε)(a	δ(ε)(a	ADJ
ejde-355	89	8	log	log	VERB
ejde-355	89	9	|x|+bε	|x|+bε	NOUN
ejde-355	89	10	)	)	PUNCT
ejde-355	89	11	+	+	NUM
ejde-355	89	12	b	b	X
ejde-355	89	13	ρ(ε	ρ(ε	PROPN
ejde-355	89	14	)	)	PUNCT
ejde-355	89	15	∀x	∀x	X
ejde-355	89	16	∈	∈	PROPN
ejde-355	89	17	∂b2(0	∂b2(0	NOUN
ejde-355	89	18	,	,	PUNCT
ejde-355	89	19	ε	ε	PROPN
ejde-355	89	20	)	)	PUNCT
ejde-355	89	21	,	,	PUNCT
ejde-355	89	22	(	(	PUNCT
ejde-355	89	23	2.4	2.4	NUM
ejde-355	89	24	)	)	PUNCT
ejde-355	89	25	i.e.	i.e.	X
ejde-355	89	26	,	,	PUNCT
ejde-355	89	27	a	a	DET
ejde-355	89	28	ε	ε	NOUN
ejde-355	89	29	=	=	PUNCT
ejde-355	89	30	δ(ε)(a	δ(ε)(a	NUM
ejde-355	89	31	log	log	NOUN
ejde-355	89	32	ε+bε	ε+bε	NUM
ejde-355	89	33	)	)	PUNCT
ejde-355	90	1	+	+	NUM
ejde-355	90	2	b	b	X
ejde-355	90	3	ρ(ε	ρ(ε	PROPN
ejde-355	90	4	)	)	PUNCT
ejde-355	91	1	∀x	∀x	X
ejde-355	91	2	∈	∈	PROPN
ejde-355	91	3	∂b2(0	∂b2(0	NOUN
ejde-355	91	4	,	,	PUNCT
ejde-355	91	5	ε	ε	PROPN
ejde-355	91	6	)	)	PUNCT
ejde-355	91	7	.	.	PUNCT
ejde-355	92	1	therefore	therefore	ADV
ejde-355	92	2	,	,	PUNCT
ejde-355	92	3	bε	bε	NOUN
ejde-355	92	4	=	=	SYM
ejde-355	92	5	1	1	NUM
ejde-355	92	6	δ(ε	δ(ε	NOUN
ejde-355	92	7	)	)	PUNCT
ejde-355	92	8	(	(	PUNCT
ejde-355	92	9	a	a	DET
ejde-355	92	10	ε	ε	PROPN
ejde-355	92	11	−	−	PROPN
ejde-355	92	12	b	b	PROPN
ejde-355	92	13	ρ(ε	ρ(ε	PROPN
ejde-355	92	14	)	)	PUNCT
ejde-355	92	15	)	)	PUNCT
ejde-355	92	16	−	−	ADP
ejde-355	92	17	a	a	DET
ejde-355	92	18	log	log	NOUN
ejde-355	92	19	ε	ε	PROPN
ejde-355	92	20	,	,	PUNCT
ejde-355	92	21	and	and	CCONJ
ejde-355	92	22	,	,	PUNCT
ejde-355	92	23	as	as	ADP
ejde-355	92	24	a	a	DET
ejde-355	92	25	consequence	consequence	NOUN
ejde-355	92	26	,	,	PUNCT
ejde-355	92	27	also	also	ADV
ejde-355	92	28	uε(x	uε(x	PRON
ejde-355	92	29	)	)	PUNCT
ejde-355	92	30	≡	≡	PROPN
ejde-355	92	31	a	a	DET
ejde-355	92	32	log	log	NOUN
ejde-355	92	33	|x|+	|x|+	NOUN
ejde-355	92	34	1	1	NUM
ejde-355	92	35	δ(ε	δ(ε	NOUN
ejde-355	92	36	)	)	PUNCT
ejde-355	92	37	(	(	PUNCT
ejde-355	92	38	a	a	DET
ejde-355	92	39	ε	ε	PROPN
ejde-355	92	40	−	−	PROPN
ejde-355	92	41	b	b	PROPN
ejde-355	92	42	ρ(ε	ρ(ε	PROPN
ejde-355	92	43	)	)	PUNCT
ejde-355	92	44	)	)	PUNCT
ejde-355	93	1	−	−	ADP
ejde-355	93	2	a	a	DET
ejde-355	93	3	log	log	NOUN
ejde-355	93	4	ε	ε	PROPN
ejde-355	93	5	∀x	∀x	X
ejde-355	93	6	∈	∈	PROPN
ejde-355	93	7	ω(ε	ω(ε	PROPN
ejde-355	93	8	)	)	PUNCT
ejde-355	93	9	.	.	PUNCT
ejde-355	94	1	(	(	PUNCT
ejde-355	94	2	2.5	2.5	NUM
ejde-355	94	3	)	)	PUNCT
ejde-355	94	4	we	we	PRON
ejde-355	94	5	can	can	AUX
ejde-355	94	6	rewrite	rewrite	VERB
ejde-355	94	7	(	(	PUNCT
ejde-355	94	8	2.5	2.5	NUM
ejde-355	94	9	)	)	PUNCT
ejde-355	94	10	as	as	ADP
ejde-355	94	11	uε(x	uε(x	NOUN
ejde-355	94	12	)	)	PUNCT
ejde-355	94	13	≡	≡	PROPN
ejde-355	94	14	a	a	DET
ejde-355	94	15	log	log	NOUN
ejde-355	94	16	|x|+	|x|+	NOUN
ejde-355	94	17	1	1	NUM
ejde-355	94	18	εδ(ε	εδ(ε	NOUN
ejde-355	94	19	)	)	PUNCT
ejde-355	94	20	(	(	PUNCT
ejde-355	94	21	a−	a−	PROPN
ejde-355	94	22	b	b	PROPN
ejde-355	94	23	ε	ε	PROPN
ejde-355	94	24	ρ(ε	ρ(ε	PROPN
ejde-355	94	25	)	)	PUNCT
ejde-355	94	26	−	−	PROPN
ejde-355	94	27	aεδ(ε	aεδ(ε	PROPN
ejde-355	94	28	)	)	PUNCT
ejde-355	94	29	log	log	NOUN
ejde-355	94	30	ε	ε	PROPN
ejde-355	94	31	)	)	PUNCT
ejde-355	95	1	∀x	∀x	VERB
ejde-355	95	2	∈	∈	PROPN
ejde-355	95	3	ω(ε	ω(ε	PROPN
ejde-355	95	4	)	)	PUNCT
ejde-355	95	5	.	.	PUNCT
ejde-355	96	1	ejde-2023/57	ejde-2023/57	NOUN
ejde-355	96	2	asymptotic	asymptotic	ADJ
ejde-355	96	3	analysis	analysis	NOUN
ejde-355	96	4	of	of	ADP
ejde-355	96	5	perturbed	perturb	VERB
ejde-355	96	6	robin	robin	PROPN
ejde-355	96	7	problems	problem	VERB
ejde-355	96	8	5	5	NUM
ejde-355	96	9	this	this	PRON
ejde-355	96	10	,	,	PUNCT
ejde-355	96	11	for	for	ADP
ejde-355	96	12	example	example	NOUN
ejde-355	96	13	,	,	PUNCT
ejde-355	96	14	implies	imply	VERB
ejde-355	96	15	that	that	SCONJ
ejde-355	96	16	if	if	SCONJ
ejde-355	96	17	l0	l0	PROPN
ejde-355	96	18	≡	≡	PROPN
ejde-355	96	19	lim	lim	PROPN
ejde-355	96	20	ε→0	ε→0	NOUN
ejde-355	96	21	εδ(ε	εδ(ε	ADV
ejde-355	96	22	)	)	PUNCT
ejde-355	96	23	log	log	VERB
ejde-355	96	24	ε	ε	PROPN
ejde-355	96	25	∈	∈	PROPN
ejde-355	96	26	r	r	NOUN
ejde-355	96	27	,	,	PUNCT
ejde-355	96	28	r0	r0	PROPN
ejde-355	96	29	≡	≡	PROPN
ejde-355	96	30	lim	lim	PROPN
ejde-355	96	31	ε→0	ε→0	X
ejde-355	96	32	ε	ε	PROPN
ejde-355	96	33	ρ(ε	ρ(ε	PROPN
ejde-355	96	34	)	)	PUNCT
ejde-355	96	35	∈	∈	PROPN
ejde-355	96	36	r	r	NOUN
ejde-355	96	37	,	,	PUNCT
ejde-355	96	38	and	and	CCONJ
ejde-355	96	39	a−	a−	PROPN
ejde-355	96	40	br0	br0	VERB
ejde-355	96	41	−	−	PROPN
ejde-355	96	42	al0	al0	NOUN
ejde-355	96	43	6=	6=	ADP
ejde-355	96	44	0	0	NUM
ejde-355	96	45	,	,	PUNCT
ejde-355	96	46	then	then	ADV
ejde-355	96	47	the	the	DET
ejde-355	96	48	value	value	NOUN
ejde-355	96	49	of	of	ADP
ejde-355	96	50	the	the	DET
ejde-355	96	51	solution	solution	NOUN
ejde-355	96	52	uε(x	uε(x	PRON
ejde-355	96	53	)	)	PUNCT
ejde-355	96	54	is	be	AUX
ejde-355	96	55	asymptotic	asymptotic	ADJ
ejde-355	96	56	to	to	ADP
ejde-355	96	57	(	(	PUNCT
ejde-355	96	58	a	a	DET
ejde-355	96	59	−	−	NOUN
ejde-355	96	60	br0	br0	NOUN
ejde-355	96	61	−	−	ADV
ejde-355	96	62	al0)/(εδ(ε	al0)/(εδ(ε	NOUN
ejde-355	96	63	)	)	PUNCT
ejde-355	96	64	)	)	PUNCT
ejde-355	96	65	as	as	SCONJ
ejde-355	96	66	ε	ε	PROPN
ejde-355	96	67	tends	tend	VERB
ejde-355	96	68	to	to	ADP
ejde-355	96	69	0	0	NUM
ejde-355	96	70	for	for	ADP
ejde-355	96	71	all	all	DET
ejde-355	96	72	fixed	fix	VERB
ejde-355	96	73	x	x	X
ejde-355	96	74	∈	∈	PROPN
ejde-355	96	75	ω	ω	X
ejde-355	96	76	\	\	X
ejde-355	96	77	{	{	PUNCT
ejde-355	96	78	0	0	NUM
ejde-355	96	79	}	}	PUNCT
ejde-355	96	80	.	.	PUNCT
ejde-355	97	1	this	this	PRON
ejde-355	97	2	means	mean	VERB
ejde-355	97	3	that	that	SCONJ
ejde-355	97	4	,	,	PUNCT
ejde-355	97	5	under	under	ADP
ejde-355	97	6	suitable	suitable	ADJ
ejde-355	97	7	assumptions	assumption	NOUN
ejde-355	97	8	on	on	ADP
ejde-355	97	9	the	the	DET
ejde-355	97	10	behavior	behavior	NOUN
ejde-355	97	11	of	of	ADP
ejde-355	97	12	δ(ε	δ(ε	PROPN
ejde-355	97	13	)	)	PUNCT
ejde-355	97	14	and	and	CCONJ
ejde-355	97	15	ρ(ε	ρ(ε	NUM
ejde-355	97	16	)	)	PUNCT
ejde-355	97	17	as	as	ADP
ejde-355	97	18	ε	ε	PROPN
ejde-355	97	19	→	→	SYM
ejde-355	97	20	0	0	PROPN
ejde-355	97	21	,	,	PUNCT
ejde-355	97	22	the	the	DET
ejde-355	97	23	value	value	NOUN
ejde-355	97	24	of	of	ADP
ejde-355	97	25	the	the	DET
ejde-355	97	26	solution	solution	NOUN
ejde-355	97	27	uε(x	uε(x	PRON
ejde-355	97	28	)	)	PUNCT
ejde-355	97	29	at	at	ADP
ejde-355	97	30	a	a	DET
ejde-355	97	31	fixed	fixed	ADJ
ejde-355	97	32	point	point	NOUN
ejde-355	97	33	x	x	X
ejde-355	97	34	∈	∈	PROPN
ejde-355	97	35	ω	ω	X
ejde-355	97	36	\	\	X
ejde-355	97	37	{	{	PUNCT
ejde-355	97	38	0	0	NUM
ejde-355	97	39	}	}	PUNCT
ejde-355	97	40	behaves	behave	VERB
ejde-355	97	41	like	like	ADP
ejde-355	97	42	(	(	PUNCT
ejde-355	97	43	a−	a−	PROPN
ejde-355	97	44	br0	br0	VERB
ejde-355	97	45	−	−	NOUN
ejde-355	97	46	al0)/(εδ(ε	al0)/(εδ(ε	NOUN
ejde-355	97	47	)	)	PUNCT
ejde-355	97	48	)	)	PUNCT
ejde-355	97	49	.	.	PUNCT
ejde-355	98	1	if	if	SCONJ
ejde-355	98	2	instead	instead	ADV
ejde-355	98	3	for	for	SCONJ
ejde-355	98	4	each	each	DET
ejde-355	98	5	ε	ε	PROPN
ejde-355	98	6	positive	positive	ADJ
ejde-355	98	7	and	and	CCONJ
ejde-355	98	8	small	small	ADJ
ejde-355	98	9	enough	enough	ADV
ejde-355	98	10	,	,	PUNCT
ejde-355	98	11	we	we	PRON
ejde-355	98	12	take	take	VERB
ejde-355	98	13	x̃ε	x̃ε	PROPN
ejde-355	98	14	such	such	ADJ
ejde-355	98	15	that	that	SCONJ
ejde-355	98	16	|x̃ε|	|x̃ε|	NOUN
ejde-355	98	17	=	=	SYM
ejde-355	98	18	ε	ε	PROPN
ejde-355	98	19	,	,	PUNCT
ejde-355	98	20	then	then	ADV
ejde-355	98	21	uε(x̃ε	uε(x̃ε	ADP
ejde-355	98	22	)	)	PUNCT
ejde-355	98	23	=	=	PUNCT
ejde-355	99	1	a	a	DET
ejde-355	99	2	log	log	NOUN
ejde-355	99	3	ε+	ε+	NOUN
ejde-355	99	4	1	1	NUM
ejde-355	99	5	εδ(ε	εδ(ε	NOUN
ejde-355	99	6	)	)	PUNCT
ejde-355	99	7	(	(	PUNCT
ejde-355	99	8	a−	a−	PROPN
ejde-355	99	9	b	b	PROPN
ejde-355	99	10	ε	ε	PROPN
ejde-355	99	11	ρ(ε	ρ(ε	PROPN
ejde-355	99	12	)	)	PUNCT
ejde-355	99	13	−	−	PROPN
ejde-355	99	14	aεδ(ε	aεδ(ε	PROPN
ejde-355	99	15	)	)	PUNCT
ejde-355	99	16	log	log	NOUN
ejde-355	99	17	ε	ε	PROPN
ejde-355	99	18	)	)	PUNCT
ejde-355	99	19	=	=	SYM
ejde-355	99	20	1	1	NUM
ejde-355	99	21	εδ(ε	εδ(ε	NOUN
ejde-355	99	22	)	)	PUNCT
ejde-355	99	23	(	(	PUNCT
ejde-355	99	24	aεδ(ε	aεδ(ε	PROPN
ejde-355	99	25	)	)	PUNCT
ejde-355	99	26	log	log	NOUN
ejde-355	99	27	ε+	ε+	X
ejde-355	99	28	a−	a−	PROPN
ejde-355	99	29	b	b	PROPN
ejde-355	99	30	ε	ε	PROPN
ejde-355	99	31	ρ(ε	ρ(ε	PROPN
ejde-355	99	32	)	)	PUNCT
ejde-355	99	33	−	−	PROPN
ejde-355	99	34	aεδ(ε	aεδ(ε	PROPN
ejde-355	99	35	)	)	PUNCT
ejde-355	99	36	log	log	NOUN
ejde-355	99	37	ε	ε	PROPN
ejde-355	99	38	)	)	PUNCT
ejde-355	99	39	=	=	SYM
ejde-355	99	40	1	1	NUM
ejde-355	99	41	εδ(ε	εδ(ε	NOUN
ejde-355	99	42	)	)	PUNCT
ejde-355	99	43	(	(	PUNCT
ejde-355	99	44	a−	a−	PROPN
ejde-355	99	45	b	b	PROPN
ejde-355	99	46	ε	ε	PROPN
ejde-355	99	47	ρ(ε	ρ(ε	PROPN
ejde-355	99	48	)	)	PUNCT
ejde-355	99	49	)	)	PUNCT
ejde-355	99	50	.	.	PUNCT
ejde-355	100	1	in	in	ADP
ejde-355	100	2	particular	particular	ADJ
ejde-355	100	3	,	,	PUNCT
ejde-355	100	4	if	if	SCONJ
ejde-355	100	5	a−	a−	PROPN
ejde-355	100	6	br0	br0	VERB
ejde-355	100	7	6=	6=	ADP
ejde-355	100	8	0	0	NUM
ejde-355	100	9	,	,	PUNCT
ejde-355	100	10	then	then	ADV
ejde-355	100	11	the	the	DET
ejde-355	100	12	value	value	NOUN
ejde-355	100	13	uε(x̃ε	uε(x̃ε	NOUN
ejde-355	100	14	)	)	PUNCT
ejde-355	100	15	of	of	ADP
ejde-355	100	16	the	the	DET
ejde-355	100	17	solution	solution	NOUN
ejde-355	100	18	at	at	ADP
ejde-355	100	19	x̃ε	x̃ε	PROPN
ejde-355	100	20	is	be	AUX
ejde-355	100	21	asymptotic	asymptotic	ADJ
ejde-355	100	22	to	to	ADP
ejde-355	100	23	(	(	PUNCT
ejde-355	100	24	a	a	DET
ejde-355	100	25	−	−	NOUN
ejde-355	100	26	br0)/(εδ(ε	br0)/(εδ(ε	NOUN
ejde-355	100	27	)	)	PUNCT
ejde-355	100	28	)	)	PUNCT
ejde-355	100	29	as	as	ADP
ejde-355	100	30	ε→	ε→	X
ejde-355	100	31	0	0	NUM
ejde-355	100	32	.	.	PUNCT
ejde-355	101	1	we	we	PRON
ejde-355	101	2	now	now	ADV
ejde-355	101	3	consider	consider	VERB
ejde-355	101	4	the	the	DET
ejde-355	101	5	energy	energy	NOUN
ejde-355	101	6	integral	integral	ADJ
ejde-355	101	7	of	of	ADP
ejde-355	101	8	uε	uε	PROPN
ejde-355	101	9	.	.	PUNCT
ejde-355	102	1	a	a	DET
ejde-355	102	2	direct	direct	ADJ
ejde-355	102	3	computation	computation	NOUN
ejde-355	102	4	shows	show	VERB
ejde-355	102	5	that∫	that∫	NOUN
ejde-355	102	6	ω(ε	ω(ε	PROPN
ejde-355	102	7	)	)	PUNCT
ejde-355	102	8	|∇uε(x)|2	|∇uε(x)|2	PROPN
ejde-355	102	9	dx	dx	PROPN
ejde-355	102	10	=	=	SYM
ejde-355	102	11	∫	∫	PROPN
ejde-355	102	12	ω(ε	ω(ε	PROPN
ejde-355	102	13	)	)	PUNCT
ejde-355	103	1	|∇	|∇	PROPN
ejde-355	103	2	(	(	PUNCT
ejde-355	103	3	a	a	DET
ejde-355	103	4	log	log	NOUN
ejde-355	103	5	|x|	|x|	PROPN
ejde-355	103	6	)	)	PUNCT
ejde-355	103	7	|2	|2	NUM
ejde-355	104	1	dx	dx	PROPN
ejde-355	105	1	=	=	SYM
ejde-355	105	2	∫	∫	PROPN
ejde-355	105	3	ω(ε	ω(ε	PROPN
ejde-355	105	4	)	)	PUNCT
ejde-355	105	5	a2	a2	PROPN
ejde-355	105	6	1	1	NUM
ejde-355	105	7	|x|2	|x|2	NOUN
ejde-355	105	8	dx	dx	PROPN
ejde-355	105	9	=	=	PUNCT
ejde-355	106	1	a22π	a22π	ADP
ejde-355	106	2	∫	∫	PROPN
ejde-355	106	3	1	1	NUM
ejde-355	106	4	ε	ε	PROPN
ejde-355	106	5	1	1	NUM
ejde-355	106	6	r	r	NOUN
ejde-355	106	7	dr	dr	PROPN
ejde-355	106	8	=	=	PUNCT
ejde-355	106	9	a22π	a22π	ADP
ejde-355	106	10	(	(	PUNCT
ejde-355	106	11	−	−	PUNCT
ejde-355	106	12	log	log	NOUN
ejde-355	106	13	ε	ε	PROPN
ejde-355	106	14	)	)	PUNCT
ejde-355	106	15	.	.	PUNCT
ejde-355	107	1	we	we	PRON
ejde-355	107	2	note	note	VERB
ejde-355	107	3	that	that	SCONJ
ejde-355	107	4	equation	equation	NOUN
ejde-355	107	5	(	(	PUNCT
ejde-355	107	6	2.5	2.5	NUM
ejde-355	107	7	)	)	PUNCT
ejde-355	107	8	provides	provide	VERB
ejde-355	107	9	a	a	DET
ejde-355	107	10	solution	solution	NOUN
ejde-355	107	11	of	of	ADP
ejde-355	107	12	the	the	DET
ejde-355	107	13	linear	linear	ADJ
ejde-355	107	14	toy	toy	NOUN
ejde-355	107	15	problem	problem	NOUN
ejde-355	107	16	(	(	PUNCT
ejde-355	107	17	2.1	2.1	NUM
ejde-355	107	18	)	)	PUNCT
ejde-355	107	19	also	also	ADV
ejde-355	107	20	if	if	SCONJ
ejde-355	107	21	δ(ε	δ(ε	NOUN
ejde-355	107	22	)	)	PUNCT
ejde-355	107	23	<	<	X
ejde-355	107	24	0	0	X
ejde-355	107	25	.	.	PUNCT
ejde-355	108	1	in	in	ADP
ejde-355	108	2	case	case	NOUN
ejde-355	108	3	δ(ε	δ(ε	NOUN
ejde-355	108	4	)	)	PUNCT
ejde-355	108	5	<	<	X
ejde-355	108	6	0	0	NUM
ejde-355	108	7	,	,	PUNCT
ejde-355	108	8	uniqueness	uniqueness	NOUN
ejde-355	108	9	for	for	ADP
ejde-355	108	10	the	the	DET
ejde-355	108	11	solution	solution	NOUN
ejde-355	108	12	of	of	ADP
ejde-355	108	13	problem	problem	NOUN
ejde-355	108	14	(	(	PUNCT
ejde-355	108	15	2.1	2.1	NUM
ejde-355	108	16	)	)	PUNCT
ejde-355	108	17	may	may	AUX
ejde-355	108	18	fail	fail	VERB
ejde-355	108	19	since	since	SCONJ
ejde-355	108	20	indeed	indeed	ADV
ejde-355	108	21	σ	σ	PROPN
ejde-355	108	22	=	=	SYM
ejde-355	108	23	−δ(ε	−δ(ε	NOUN
ejde-355	108	24	)	)	PUNCT
ejde-355	108	25	could	could	AUX
ejde-355	108	26	be	be	AUX
ejde-355	108	27	a	a	DET
ejde-355	108	28	mixed	mixed	ADJ
ejde-355	108	29	steklov	steklov	NOUN
ejde-355	108	30	-	-	PUNCT
ejde-355	108	31	neumann	neumann	PROPN
ejde-355	108	32	eigenvalue	eigenvalue	PROPN
ejde-355	108	33	of	of	ADP
ejde-355	108	34	problem	problem	NOUN
ejde-355	109	1	∆u	∆u	PROPN
ejde-355	109	2	=	=	SYM
ejde-355	109	3	0	0	NUM
ejde-355	109	4	in	in	ADP
ejde-355	109	5	ω(ε	ω(ε	PROPN
ejde-355	109	6	)	)	PUNCT
ejde-355	109	7	,	,	PUNCT
ejde-355	109	8	∂	∂	NUM
ejde-355	109	9	∂νω(ε	∂νω(ε	PROPN
ejde-355	109	10	)	)	PUNCT
ejde-355	109	11	u	u	NOUN
ejde-355	109	12	=	=	NOUN
ejde-355	109	13	0	0	NUM
ejde-355	109	14	on	on	ADP
ejde-355	109	15	∂b2(0	∂b2(0	NOUN
ejde-355	109	16	,	,	PUNCT
ejde-355	109	17	1	1	NUM
ejde-355	109	18	)	)	PUNCT
ejde-355	109	19	,	,	PUNCT
ejde-355	110	1	∂	∂	NUM
ejde-355	110	2	∂νω(ε	∂νω(ε	PROPN
ejde-355	110	3	)	)	PUNCT
ejde-355	110	4	u	u	NOUN
ejde-355	110	5	=	=	PUNCT
ejde-355	110	6	σu	σu	PROPN
ejde-355	110	7	on	on	ADP
ejde-355	110	8	∂b2(0	∂b2(0	PROPN
ejde-355	110	9	,	,	PUNCT
ejde-355	110	10	ε	ε	PROPN
ejde-355	110	11	)	)	PUNCT
ejde-355	110	12	.	.	PUNCT
ejde-355	111	1	a	a	DET
ejde-355	111	2	detailed	detailed	ADJ
ejde-355	111	3	discussion	discussion	NOUN
ejde-355	111	4	on	on	ADP
ejde-355	111	5	how	how	SCONJ
ejde-355	111	6	to	to	PART
ejde-355	111	7	extends	extend	VERB
ejde-355	111	8	the	the	DET
ejde-355	111	9	results	result	NOUN
ejde-355	111	10	also	also	ADV
ejde-355	111	11	to	to	ADP
ejde-355	111	12	the	the	DET
ejde-355	111	13	case	case	NOUN
ejde-355	111	14	δ(ε	δ(ε	NOUN
ejde-355	111	15	)	)	PUNCT
ejde-355	111	16	<	<	X
ejde-355	111	17	0	0	PUNCT
ejde-355	111	18	and	and	CCONJ
ejde-355	111	19	the	the	DET
ejde-355	111	20	analysis	analysis	NOUN
ejde-355	111	21	of	of	ADP
ejde-355	111	22	the	the	DET
ejde-355	111	23	behavior	behavior	NOUN
ejde-355	111	24	of	of	ADP
ejde-355	111	25	steklov	steklov	PROPN
ejde-355	111	26	-	-	PUNCT
ejde-355	111	27	neumann	neumann	PROPN
ejde-355	111	28	eigenvalues	eigenvalue	NOUN
ejde-355	111	29	may	may	AUX
ejde-355	111	30	be	be	AUX
ejde-355	111	31	the	the	DET
ejde-355	111	32	subject	subject	NOUN
ejde-355	111	33	of	of	ADP
ejde-355	111	34	future	future	ADJ
ejde-355	111	35	investigations	investigation	NOUN
ejde-355	111	36	.	.	PUNCT
ejde-355	112	1	it	it	PRON
ejde-355	112	2	is	be	AUX
ejde-355	112	3	also	also	ADV
ejde-355	112	4	interesting	interesting	ADJ
ejde-355	112	5	to	to	PART
ejde-355	112	6	look	look	VERB
ejde-355	112	7	at	at	ADP
ejde-355	112	8	a	a	DET
ejde-355	112	9	nonlinear	nonlinear	ADJ
ejde-355	112	10	toy	toy	NOUN
ejde-355	112	11	problem	problem	NOUN
ejde-355	112	12	with	with	ADP
ejde-355	112	13	arbitrary	arbitrary	ADJ
ejde-355	112	14	functions	function	NOUN
ejde-355	112	15	fε	fε	X
ejde-355	112	16	(	(	PUNCT
ejde-355	112	17	·	·	PUNCT
ejde-355	112	18	)	)	PUNCT
ejde-355	112	19	.	.	PUNCT
ejde-355	113	1	then	then	ADV
ejde-355	113	2	repeating	repeat	VERB
ejde-355	113	3	the	the	DET
ejde-355	113	4	same	same	ADJ
ejde-355	113	5	line	line	NOUN
ejde-355	113	6	of	of	ADP
ejde-355	113	7	reasoning	reasoning	NOUN
ejde-355	113	8	,	,	PUNCT
ejde-355	113	9	the	the	DET
ejde-355	113	10	only	only	ADJ
ejde-355	113	11	difference	difference	NOUN
ejde-355	113	12	appears	appear	VERB
ejde-355	113	13	in	in	ADP
ejde-355	113	14	the	the	DET
ejde-355	113	15	6	6	NUM
ejde-355	113	16	p.	p.	NOUN
ejde-355	113	17	musolino	musolino	NOUN
ejde-355	113	18	,	,	PUNCT
ejde-355	113	19	m.	m.	NOUN
ejde-355	113	20	dutko	dutko	PROPN
ejde-355	113	21	,	,	PUNCT
ejde-355	113	22	g.	g.	PROPN
ejde-355	113	23	mishuris	mishuris	PROPN
ejde-355	113	24	ejde-2023/57	ejde-2023/57	NOUN
ejde-355	113	25	equation	equation	NOUN
ejde-355	113	26	(	(	PUNCT
ejde-355	113	27	2.4	2.4	NUM
ejde-355	113	28	)	)	PUNCT
ejde-355	113	29	,	,	PUNCT
ejde-355	113	30	that	that	PRON
ejde-355	113	31	will	will	AUX
ejde-355	113	32	take	take	VERB
ejde-355	113	33	the	the	DET
ejde-355	113	34	form	form	NOUN
ejde-355	113	35	x	x	X
ejde-355	113	36	|x|	|x|	PROPN
ejde-355	113	37	·	·	PUNCT
ejde-355	113	38	a	a	DET
ejde-355	113	39	x	x	X
ejde-355	113	40	|x|2	|x|2	NOUN
ejde-355	113	41	=	=	PUNCT
ejde-355	113	42	δ(ε)fε(a	δ(ε)fε(a	VERB
ejde-355	113	43	log	log	VERB
ejde-355	113	44	|x|+bε	|x|+bε	NOUN
ejde-355	113	45	)	)	PUNCT
ejde-355	113	46	+	+	NUM
ejde-355	113	47	b	b	X
ejde-355	113	48	ρ(ε	ρ(ε	PROPN
ejde-355	113	49	)	)	PUNCT
ejde-355	113	50	∀x	∀x	X
ejde-355	113	51	∈	∈	PROPN
ejde-355	113	52	∂b2(0	∂b2(0	NOUN
ejde-355	113	53	,	,	PUNCT
ejde-355	113	54	ε	ε	PROPN
ejde-355	113	55	)	)	PUNCT
ejde-355	113	56	.	.	PUNCT
ejde-355	114	1	(	(	PUNCT
ejde-355	114	2	2.6	2.6	NUM
ejde-355	114	3	)	)	PUNCT
ejde-355	114	4	if	if	SCONJ
ejde-355	114	5	we	we	PRON
ejde-355	114	6	additionally	additionally	ADV
ejde-355	114	7	assume	assume	VERB
ejde-355	114	8	that	that	SCONJ
ejde-355	114	9	the	the	DET
ejde-355	114	10	functions	function	NOUN
ejde-355	114	11	fε	fε	VERB
ejde-355	114	12	:	:	PUNCT
ejde-355	114	13	r→	r→	PROPN
ejde-355	114	14	r	r	NOUN
ejde-355	114	15	are	be	AUX
ejde-355	114	16	invertible	invertible	ADJ
ejde-355	114	17	then	then	ADV
ejde-355	114	18	by	by	ADP
ejde-355	114	19	(	(	PUNCT
ejde-355	114	20	2.6	2.6	NUM
ejde-355	114	21	)	)	PUNCT
ejde-355	114	22	for	for	ADP
ejde-355	114	23	each	each	DET
ejde-355	114	24	ε	ε	PROPN
ejde-355	114	25	∈]0	∈]0	X
ejde-355	114	26	,	,	PUNCT
ejde-355	114	27	1	1	NUM
ejde-355	114	28	[	[	PUNCT
ejde-355	114	29	the	the	DET
ejde-355	114	30	constant	constant	ADJ
ejde-355	114	31	bε	bε	NOUN
ejde-355	114	32	can	can	AUX
ejde-355	114	33	be	be	AUX
ejde-355	114	34	uniquely	uniquely	ADV
ejde-355	114	35	found	find	VERB
ejde-355	114	36	,	,	PUNCT
ejde-355	114	37	bε	bε	NOUN
ejde-355	114	38	=	=	SYM
ejde-355	114	39	f−1	f−1	PROPN
ejde-355	114	40	ε	ε	PROPN
ejde-355	114	41	(	(	PUNCT
ejde-355	114	42	aρ(ε)−	aρ(ε)−	VERB
ejde-355	114	43	εb	εb	ADP
ejde-355	114	44	ερ(ε)δ(ε	ερ(ε)δ(ε	NOUN
ejde-355	114	45	)	)	PUNCT
ejde-355	114	46	)	)	PUNCT
ejde-355	115	1	−	−	ADP
ejde-355	115	2	a	a	DET
ejde-355	115	3	log	log	NOUN
ejde-355	115	4	ε	ε	PROPN
ejde-355	115	5	,	,	PUNCT
ejde-355	115	6	and	and	CCONJ
ejde-355	115	7	the	the	DET
ejde-355	115	8	analysis	analysis	NOUN
ejde-355	115	9	can	can	AUX
ejde-355	115	10	be	be	AUX
ejde-355	115	11	performed	perform	VERB
ejde-355	115	12	in	in	ADP
ejde-355	115	13	a	a	DET
ejde-355	115	14	similar	similar	ADJ
ejde-355	115	15	way	way	NOUN
ejde-355	115	16	as	as	SCONJ
ejde-355	115	17	we	we	PRON
ejde-355	115	18	have	have	AUX
ejde-355	115	19	previously	previously	ADV
ejde-355	115	20	done	do	VERB
ejde-355	115	21	.	.	PUNCT
ejde-355	116	1	however	however	ADV
ejde-355	116	2	,	,	PUNCT
ejde-355	116	3	if	if	SCONJ
ejde-355	116	4	the	the	DET
ejde-355	116	5	functions	function	NOUN
ejde-355	116	6	fε	fε	NOUN
ejde-355	116	7	are	be	AUX
ejde-355	116	8	not	not	PART
ejde-355	116	9	bijections	bijection	NOUN
ejde-355	116	10	,	,	PUNCT
ejde-355	116	11	then	then	ADV
ejde-355	116	12	the	the	DET
ejde-355	116	13	analysis	analysis	NOUN
ejde-355	116	14	of	of	ADP
ejde-355	116	15	the	the	DET
ejde-355	116	16	existence	existence	NOUN
ejde-355	116	17	(	(	PUNCT
ejde-355	116	18	and	and	CCONJ
ejde-355	116	19	possibly	possibly	ADV
ejde-355	116	20	uniqueness	uniqueness	VERB
ejde-355	116	21	)	)	PUNCT
ejde-355	116	22	of	of	ADP
ejde-355	116	23	the	the	DET
ejde-355	116	24	solution	solution	NOUN
ejde-355	116	25	becomes	become	VERB
ejde-355	116	26	more	more	ADV
ejde-355	116	27	complex	complex	ADJ
ejde-355	116	28	.	.	PUNCT
ejde-355	117	1	for	for	ADP
ejde-355	117	2	example	example	NOUN
ejde-355	117	3	,	,	PUNCT
ejde-355	117	4	a	a	DET
ejde-355	117	5	solutions	solution	NOUN
ejde-355	117	6	can	can	AUX
ejde-355	117	7	be	be	AUX
ejde-355	117	8	derived	derive	VERB
ejde-355	117	9	under	under	ADP
ejde-355	117	10	specific	specific	ADJ
ejde-355	117	11	conditions	condition	NOUN
ejde-355	117	12	on	on	ADP
ejde-355	117	13	the	the	DET
ejde-355	117	14	parameters	parameter	NOUN
ejde-355	117	15	if	if	SCONJ
ejde-355	117	16	suitable	suitable	ADJ
ejde-355	117	17	rescaling	rescaling	NOUN
ejde-355	117	18	of	of	ADP
ejde-355	117	19	the	the	DET
ejde-355	117	20	functions	function	NOUN
ejde-355	117	21	fε	fε	NOUN
ejde-355	117	22	are	be	AUX
ejde-355	117	23	locally	locally	ADV
ejde-355	117	24	invertible	invertible	ADJ
ejde-355	117	25	.	.	PUNCT
ejde-355	118	1	this	this	PRON
ejde-355	118	2	shows	show	VERB
ejde-355	118	3	how	how	SCONJ
ejde-355	118	4	rich	rich	ADJ
ejde-355	118	5	the	the	DET
ejde-355	118	6	problem	problem	NOUN
ejde-355	118	7	is	be	AUX
ejde-355	118	8	even	even	ADV
ejde-355	118	9	in	in	ADP
ejde-355	118	10	the	the	DET
ejde-355	118	11	simple	simple	ADJ
ejde-355	118	12	situation	situation	NOUN
ejde-355	118	13	of	of	ADP
ejde-355	118	14	a	a	DET
ejde-355	118	15	circular	circular	ADJ
ejde-355	118	16	annular	annular	ADJ
ejde-355	118	17	domain	domain	NOUN
ejde-355	118	18	.	.	PUNCT
ejde-355	119	1	on	on	ADP
ejde-355	119	2	the	the	DET
ejde-355	119	3	other	other	ADJ
ejde-355	119	4	hand	hand	NOUN
ejde-355	119	5	,	,	PUNCT
ejde-355	119	6	many	many	ADJ
ejde-355	119	7	of	of	ADP
ejde-355	119	8	the	the	DET
ejde-355	119	9	features	feature	NOUN
ejde-355	119	10	mentioned	mention	VERB
ejde-355	119	11	here	here	ADV
ejde-355	119	12	are	be	AUX
ejde-355	119	13	preserved	preserve	VERB
ejde-355	119	14	for	for	ADP
ejde-355	119	15	the	the	DET
ejde-355	119	16	general	general	ADJ
ejde-355	119	17	2d	2d	NUM
ejde-355	119	18	case	case	NOUN
ejde-355	119	19	.	.	PUNCT
ejde-355	120	1	below	below	ADV
ejde-355	120	2	,	,	PUNCT
ejde-355	120	3	we	we	PRON
ejde-355	120	4	provide	provide	VERB
ejde-355	120	5	an	an	DET
ejde-355	120	6	accurate	accurate	ADJ
ejde-355	120	7	analysis	analysis	NOUN
ejde-355	120	8	of	of	ADP
ejde-355	120	9	the	the	DET
ejde-355	120	10	general	general	ADJ
ejde-355	120	11	problem	problem	NOUN
ejde-355	120	12	formulated	formulate	VERB
ejde-355	120	13	above	above	ADV
ejde-355	120	14	,	,	PUNCT
ejde-355	120	15	making	make	VERB
ejde-355	120	16	,	,	PUNCT
ejde-355	120	17	where	where	SCONJ
ejde-355	120	18	appropriate	appropriate	ADJ
ejde-355	120	19	,	,	PUNCT
ejde-355	120	20	a	a	DET
ejde-355	120	21	reference	reference	NOUN
ejde-355	120	22	to	to	ADP
ejde-355	120	23	the	the	DET
ejde-355	120	24	similar	similar	ADJ
ejde-355	120	25	feature	feature	NOUN
ejde-355	120	26	highlighted	highlight	VERB
ejde-355	120	27	here	here	ADV
ejde-355	120	28	for	for	ADP
ejde-355	120	29	the	the	DET
ejde-355	120	30	toy	toy	NOUN
ejde-355	120	31	problem	problem	NOUN
ejde-355	120	32	.	.	PUNCT
ejde-355	121	1	3	3	X
ejde-355	121	2	.	.	X
ejde-355	121	3	integral	integral	ADJ
ejde-355	121	4	equation	equation	NOUN
ejde-355	121	5	formulation	formulation	NOUN
ejde-355	121	6	of	of	ADP
ejde-355	121	7	the	the	DET
ejde-355	121	8	boundary	boundary	ADJ
ejde-355	121	9	value	value	NOUN
ejde-355	121	10	problem	problem	NOUN
ejde-355	121	11	as	as	ADP
ejde-355	121	12	in	in	ADP
ejde-355	121	13	[	[	NOUN
ejde-355	121	14	35	35	NUM
ejde-355	121	15	,	,	PUNCT
ejde-355	121	16	36	36	NUM
ejde-355	121	17	]	]	PUNCT
ejde-355	121	18	,	,	PUNCT
ejde-355	121	19	we	we	PRON
ejde-355	121	20	use	use	VERB
ejde-355	121	21	the	the	DET
ejde-355	121	22	functional	functional	ADJ
ejde-355	121	23	analytic	analytic	ADJ
ejde-355	121	24	approach	approach	NOUN
ejde-355	121	25	,	,	PUNCT
ejde-355	121	26	introduced	introduce	VERB
ejde-355	121	27	by	by	ADP
ejde-355	121	28	lanza	lanza	X
ejde-355	121	29	de	de	X
ejde-355	121	30	cristoforis	cristoforis	PROPN
ejde-355	121	31	in	in	ADP
ejde-355	121	32	[	[	X
ejde-355	121	33	19	19	NUM
ejde-355	121	34	]	]	PUNCT
ejde-355	121	35	,	,	PUNCT
ejde-355	121	36	to	to	PART
ejde-355	121	37	analyze	analyze	VERB
ejde-355	121	38	problem	problem	NOUN
ejde-355	121	39	(	(	PUNCT
ejde-355	121	40	1.1	1.1	NUM
ejde-355	121	41	)	)	PUNCT
ejde-355	121	42	when	when	SCONJ
ejde-355	121	43	the	the	DET
ejde-355	121	44	parameter	parameter	NOUN
ejde-355	121	45	ε	ε	PROPN
ejde-355	121	46	is	be	AUX
ejde-355	121	47	close	close	ADJ
ejde-355	121	48	to	to	ADP
ejde-355	121	49	0	0	NUM
ejde-355	121	50	.	.	PUNCT
ejde-355	122	1	we	we	PRON
ejde-355	122	2	refer	refer	VERB
ejde-355	122	3	to	to	ADP
ejde-355	122	4	[	[	X
ejde-355	122	5	9	9	NUM
ejde-355	122	6	]	]	PUNCT
ejde-355	122	7	for	for	ADP
ejde-355	122	8	a	a	DET
ejde-355	122	9	detailed	detailed	ADJ
ejde-355	122	10	presentation	presentation	NOUN
ejde-355	122	11	of	of	ADP
ejde-355	122	12	the	the	DET
ejde-355	122	13	method	method	NOUN
ejde-355	122	14	.	.	PUNCT
ejde-355	123	1	in	in	ADP
ejde-355	123	2	order	order	NOUN
ejde-355	123	3	to	to	PART
ejde-355	123	4	apply	apply	VERB
ejde-355	123	5	such	such	ADJ
ejde-355	123	6	approach	approach	NOUN
ejde-355	123	7	,	,	PUNCT
ejde-355	123	8	we	we	PRON
ejde-355	123	9	need	need	VERB
ejde-355	123	10	to	to	PART
ejde-355	123	11	define	define	VERB
ejde-355	123	12	classical	classical	ADJ
ejde-355	123	13	objects	object	NOUN
ejde-355	123	14	of	of	ADP
ejde-355	123	15	potential	potential	ADJ
ejde-355	123	16	theory	theory	NOUN
ejde-355	123	17	.	.	PUNCT
ejde-355	124	1	we	we	PRON
ejde-355	124	2	first	first	ADV
ejde-355	124	3	denote	denote	VERB
ejde-355	124	4	by	by	ADP
ejde-355	124	5	s2	s2	VERB
ejde-355	124	6	the	the	DET
ejde-355	124	7	fundamental	fundamental	ADJ
ejde-355	124	8	solution	solution	NOUN
ejde-355	124	9	of	of	ADP
ejde-355	124	10	the	the	DET
ejde-355	124	11	laplace	laplace	NOUN
ejde-355	124	12	operator	operator	NOUN
ejde-355	124	13	,	,	PUNCT
ejde-355	124	14	i.e.	i.e.	X
ejde-355	124	15	the	the	DET
ejde-355	124	16	function	function	NOUN
ejde-355	124	17	from	from	ADP
ejde-355	124	18	r2	r2	PROPN
ejde-355	124	19	\	\	PROPN
ejde-355	124	20	{	{	PUNCT
ejde-355	124	21	0	0	NUM
ejde-355	124	22	}	}	PUNCT
ejde-355	124	23	to	to	ADP
ejde-355	124	24	r	r	NOUN
ejde-355	124	25	defined	define	VERB
ejde-355	124	26	by	by	ADP
ejde-355	124	27	s2(x	s2(x	PROPN
ejde-355	124	28	)	)	PUNCT
ejde-355	124	29	≡	≡	PROPN
ejde-355	124	30	1	1	NUM
ejde-355	124	31	2π	2π	NOUN
ejde-355	124	32	log	log	VERB
ejde-355	124	33	|x|	|x|	PROPN
ejde-355	124	34	∀x	∀x	PUNCT
ejde-355	124	35	∈	∈	PROPN
ejde-355	124	36	r2	r2	NOUN
ejde-355	124	37	\	\	PROPN
ejde-355	124	38	{	{	PUNCT
ejde-355	124	39	0	0	NUM
ejde-355	124	40	}	}	PUNCT
ejde-355	124	41	.	.	PUNCT
ejde-355	125	1	by	by	ADP
ejde-355	125	2	means	mean	NOUN
ejde-355	125	3	of	of	ADP
ejde-355	125	4	s2	s2	NOUN
ejde-355	125	5	,	,	PUNCT
ejde-355	125	6	we	we	PRON
ejde-355	125	7	construct	construct	VERB
ejde-355	125	8	the	the	DET
ejde-355	125	9	single	single	ADJ
ejde-355	125	10	layer	layer	NOUN
ejde-355	125	11	potentials	potential	VERB
ejde-355	125	12	,	,	PUNCT
ejde-355	125	13	that	that	SCONJ
ejde-355	125	14	we	we	PRON
ejde-355	125	15	use	use	VERB
ejde-355	125	16	to	to	PART
ejde-355	125	17	represent	represent	VERB
ejde-355	125	18	the	the	DET
ejde-355	125	19	solutions	solution	NOUN
ejde-355	125	20	of	of	ADP
ejde-355	125	21	problem	problem	NOUN
ejde-355	125	22	(	(	PUNCT
ejde-355	125	23	1.1	1.1	NUM
ejde-355	125	24	)	)	PUNCT
ejde-355	125	25	.	.	PUNCT
ejde-355	126	1	so	so	ADV
ejde-355	126	2	let	let	VERB
ejde-355	126	3	ω	ω	PRON
ejde-355	126	4	be	be	AUX
ejde-355	126	5	a	a	DET
ejde-355	126	6	bounded	bounded	ADJ
ejde-355	126	7	open	open	ADJ
ejde-355	126	8	connected	connected	ADJ
ejde-355	126	9	subset	subset	NOUN
ejde-355	126	10	of	of	ADP
ejde-355	126	11	r2	r2	PROPN
ejde-355	126	12	of	of	ADP
ejde-355	126	13	class	class	PROPN
ejde-355	126	14	c1,α	c1,α	PROPN
ejde-355	126	15	.	.	PUNCT
ejde-355	127	1	we	we	PRON
ejde-355	127	2	introduce	introduce	VERB
ejde-355	127	3	the	the	DET
ejde-355	127	4	single	single	ADJ
ejde-355	127	5	layer	layer	NOUN
ejde-355	127	6	potential	potential	NOUN
ejde-355	127	7	by	by	ADP
ejde-355	127	8	v[∂ω	v[∂ω	PROPN
ejde-355	127	9	,	,	PUNCT
ejde-355	127	10	µ](x	µ](x	ADJ
ejde-355	127	11	)	)	PUNCT
ejde-355	127	12	≡	≡	PROPN
ejde-355	127	13	∫	∫	PROPN
ejde-355	128	1	∂ω	∂ω	PROPN
ejde-355	128	2	s2(x−	s2(x−	PROPN
ejde-355	128	3	y)µ(y	y)µ(y	NOUN
ejde-355	128	4	)	)	PUNCT
ejde-355	128	5	dσy	dσy	PROPN
ejde-355	128	6	∀x	∀x	PUNCT
ejde-355	128	7	∈	∈	PROPN
ejde-355	128	8	r2	r2	NOUN
ejde-355	128	9	,	,	PUNCT
ejde-355	128	10	for	for	ADP
ejde-355	128	11	all	all	DET
ejde-355	128	12	µ	µ	PRON
ejde-355	128	13	∈	∈	NOUN
ejde-355	128	14	c0(∂ω	c0(∂ω	PROPN
ejde-355	128	15	)	)	PUNCT
ejde-355	128	16	.	.	PUNCT
ejde-355	129	1	if	if	SCONJ
ejde-355	129	2	µ	µ	PRON
ejde-355	129	3	∈	∈	NOUN
ejde-355	129	4	c0(∂ω	c0(∂ω	PROPN
ejde-355	129	5	)	)	PUNCT
ejde-355	129	6	,	,	PUNCT
ejde-355	129	7	then	then	ADV
ejde-355	129	8	v[∂ω	v[∂ω	PROPN
ejde-355	129	9	,	,	PUNCT
ejde-355	129	10	µ	µ	X
ejde-355	129	11	]	]	PUNCT
ejde-355	129	12	is	be	AUX
ejde-355	129	13	continuous	continuous	ADJ
ejde-355	129	14	in	in	ADP
ejde-355	129	15	r2	r2	PROPN
ejde-355	129	16	.	.	PUNCT
ejde-355	130	1	moreover	moreover	ADV
ejde-355	130	2	,	,	PUNCT
ejde-355	130	3	if	if	SCONJ
ejde-355	130	4	µ	µ	PRON
ejde-355	130	5	∈	∈	PROPN
ejde-355	130	6	c0,α(∂ω	c0,α(∂ω	NOUN
ejde-355	130	7	)	)	PUNCT
ejde-355	130	8	,	,	PUNCT
ejde-355	130	9	then	then	ADV
ejde-355	130	10	the	the	DET
ejde-355	130	11	function	function	NOUN
ejde-355	130	12	v+[∂ω	v+[∂ω	NOUN
ejde-355	130	13	,	,	PUNCT
ejde-355	130	14	µ	µ	NOUN
ejde-355	130	15	]	]	X
ejde-355	130	16	≡	≡	PROPN
ejde-355	130	17	v[∂ω	v[∂ω	PROPN
ejde-355	130	18	,	,	PUNCT
ejde-355	130	19	µ]|ω	µ]|ω	PROPN
ejde-355	130	20	belongs	belong	VERB
ejde-355	130	21	to	to	ADP
ejde-355	130	22	c1,α(ω	c1,α(ω	NOUN
ejde-355	130	23	)	)	PUNCT
ejde-355	130	24	,	,	PUNCT
ejde-355	130	25	and	and	CCONJ
ejde-355	130	26	the	the	DET
ejde-355	130	27	function	function	NOUN
ejde-355	130	28	v−[∂ω	v−[∂ω	PROPN
ejde-355	130	29	,	,	PUNCT
ejde-355	130	30	µ	µ	X
ejde-355	130	31	]	]	X
ejde-355	130	32	≡	≡	PROPN
ejde-355	130	33	v[∂ω	v[∂ω	PROPN
ejde-355	130	34	,	,	PUNCT
ejde-355	130	35	µ]|r2\ω	µ]|r2\ω	PROPN
ejde-355	130	36	belongs	belong	VERB
ejde-355	130	37	to	to	ADP
ejde-355	130	38	c1,α	c1,α	PROPN
ejde-355	130	39	loc	loc	PROPN
ejde-355	130	40	(	(	PUNCT
ejde-355	130	41	r2	r2	PROPN
ejde-355	130	42	\	\	PROPN
ejde-355	130	43	ω	ω	PROPN
ejde-355	130	44	)	)	PUNCT
ejde-355	130	45	.	.	PUNCT
ejde-355	131	1	the	the	DET
ejde-355	131	2	normal	normal	ADJ
ejde-355	131	3	derivative	derivative	NOUN
ejde-355	131	4	of	of	ADP
ejde-355	131	5	the	the	DET
ejde-355	131	6	single	single	ADJ
ejde-355	131	7	layer	layer	NOUN
ejde-355	131	8	potential	potential	NOUN
ejde-355	131	9	on	on	ADP
ejde-355	131	10	∂ω	∂ω	PROPN
ejde-355	131	11	,	,	PUNCT
ejde-355	131	12	instead	instead	ADV
ejde-355	131	13	,	,	PUNCT
ejde-355	131	14	presents	present	VERB
ejde-355	131	15	a	a	DET
ejde-355	131	16	jump	jump	NOUN
ejde-355	131	17	.	.	PUNCT
ejde-355	132	1	to	to	PART
ejde-355	132	2	describe	describe	VERB
ejde-355	132	3	such	such	ADJ
ejde-355	132	4	jump	jump	NOUN
ejde-355	132	5	,	,	PUNCT
ejde-355	132	6	we	we	PRON
ejde-355	132	7	set	set	VERB
ejde-355	132	8	w	w	ADP
ejde-355	132	9	∗[∂ω	∗[∂ω	PROPN
ejde-355	132	10	,	,	PUNCT
ejde-355	132	11	µ](x	µ](x	ADJ
ejde-355	132	12	)	)	PUNCT
ejde-355	132	13	≡	≡	PROPN
ejde-355	132	14	∫	∫	PROPN
ejde-355	133	1	∂ω	∂ω	PROPN
ejde-355	133	2	νω(x	νω(x	PUNCT
ejde-355	133	3	)	)	PUNCT
ejde-355	133	4	·	·	PUNCT
ejde-355	134	1	∇s2(x−	∇s2(x−	ADP
ejde-355	134	2	y)µ(y	y)µ(y	NOUN
ejde-355	134	3	)	)	PUNCT
ejde-355	134	4	dσy	dσy	PROPN
ejde-355	134	5	∀x	∀x	PUNCT
ejde-355	134	6	∈	∈	PROPN
ejde-355	134	7	∂ω	∂ω	PROPN
ejde-355	134	8	,	,	PUNCT
ejde-355	134	9	where	where	SCONJ
ejde-355	134	10	νω	νω	PRON
ejde-355	134	11	denotes	denote	VERB
ejde-355	134	12	the	the	DET
ejde-355	134	13	outward	outward	ADJ
ejde-355	134	14	unit	unit	NOUN
ejde-355	134	15	normal	normal	ADJ
ejde-355	134	16	to	to	ADP
ejde-355	134	17	∂ω	∂ω	PROPN
ejde-355	134	18	.	.	PUNCT
ejde-355	135	1	if	if	SCONJ
ejde-355	135	2	µ	µ	PRON
ejde-355	135	3	∈	∈	PROPN
ejde-355	135	4	c0,α(∂ω	c0,α(∂ω	NOUN
ejde-355	135	5	)	)	PUNCT
ejde-355	135	6	,	,	PUNCT
ejde-355	135	7	the	the	DET
ejde-355	135	8	function	function	NOUN
ejde-355	135	9	w	w	ADP
ejde-355	135	10	∗[∂ω	∗[∂ω	PROPN
ejde-355	135	11	,	,	PUNCT
ejde-355	135	12	µ	µ	X
ejde-355	135	13	]	]	PUNCT
ejde-355	135	14	belongs	belong	VERB
ejde-355	135	15	to	to	ADP
ejde-355	135	16	c0,α(∂ω	c0,α(∂ω	PROPN
ejde-355	135	17	)	)	PUNCT
ejde-355	135	18	and	and	CCONJ
ejde-355	135	19	we	we	PRON
ejde-355	135	20	have	have	VERB
ejde-355	135	21	∂	∂	NUM
ejde-355	135	22	∂νω	∂νω	PROPN
ejde-355	135	23	v±[∂ω	v±[∂ω	NOUN
ejde-355	135	24	,	,	PUNCT
ejde-355	135	25	µ	µ	X
ejde-355	135	26	]	]	X
ejde-355	135	27	=	=	SYM
ejde-355	135	28	∓1	∓1	NOUN
ejde-355	135	29	2	2	NUM
ejde-355	135	30	µ+w	µ+w	NUM
ejde-355	135	31	∗[∂ω	∗[∂ω	PROPN
ejde-355	135	32	,	,	PUNCT
ejde-355	135	33	µ	µ	X
ejde-355	135	34	]	]	X
ejde-355	135	35	on	on	ADP
ejde-355	135	36	∂ω	∂ω	PROPN
ejde-355	135	37	.	.	PUNCT
ejde-355	136	1	ejde-2023/57	ejde-2023/57	NOUN
ejde-355	136	2	asymptotic	asymptotic	ADJ
ejde-355	136	3	analysis	analysis	NOUN
ejde-355	136	4	of	of	ADP
ejde-355	136	5	perturbed	perturb	VERB
ejde-355	136	6	robin	robin	PROPN
ejde-355	136	7	problems	problem	VERB
ejde-355	136	8	7	7	NUM
ejde-355	136	9	we	we	PRON
ejde-355	136	10	will	will	AUX
ejde-355	136	11	use	use	VERB
ejde-355	136	12	density	density	NOUN
ejde-355	136	13	functions	function	NOUN
ejde-355	136	14	with	with	ADP
ejde-355	136	15	zero	zero	NUM
ejde-355	136	16	integral	integral	ADJ
ejde-355	136	17	mean	mean	NOUN
ejde-355	136	18	and	and	CCONJ
ejde-355	136	19	thus	thus	ADV
ejde-355	136	20	we	we	PRON
ejde-355	136	21	find	find	VERB
ejde-355	136	22	it	it	PRON
ejde-355	136	23	convenient	convenient	ADJ
ejde-355	136	24	to	to	PART
ejde-355	136	25	set	set	VERB
ejde-355	136	26	c0,α(∂ωo)0	c0,α(∂ωo)0	DET
ejde-355	136	27	≡	≡	PROPN
ejde-355	136	28	{	{	PUNCT
ejde-355	136	29	f	f	PROPN
ejde-355	136	30	∈	∈	PROPN
ejde-355	136	31	c0,α(∂ωo	c0,α(∂ωo	PROPN
ejde-355	136	32	)	)	PUNCT
ejde-355	136	33	:	:	PUNCT
ejde-355	137	1	∫	∫	PROPN
ejde-355	137	2	∂ωo	∂ωo	NOUN
ejde-355	137	3	f	f	PROPN
ejde-355	137	4	dσ	dσ	PROPN
ejde-355	137	5	=	=	PROPN
ejde-355	137	6	0	0	NUM
ejde-355	137	7	}	}	PUNCT
ejde-355	137	8	.	.	PUNCT
ejde-355	138	1	by	by	ADP
ejde-355	138	2	arguing	argue	VERB
ejde-355	138	3	as	as	ADP
ejde-355	138	4	in	in	ADP
ejde-355	138	5	[	[	X
ejde-355	138	6	36	36	NUM
ejde-355	138	7	,	,	PUNCT
ejde-355	138	8	§	§	NOUN
ejde-355	138	9	3	3	NUM
ejde-355	138	10	]	]	PUNCT
ejde-355	138	11	,	,	PUNCT
ejde-355	138	12	we	we	PRON
ejde-355	138	13	are	be	AUX
ejde-355	138	14	ready	ready	ADJ
ejde-355	138	15	to	to	PART
ejde-355	138	16	establish	establish	VERB
ejde-355	138	17	in	in	ADP
ejde-355	138	18	proposition	proposition	NOUN
ejde-355	138	19	3.1	3.1	NUM
ejde-355	138	20	a	a	DET
ejde-355	138	21	correspondence	correspondence	NOUN
ejde-355	138	22	between	between	ADP
ejde-355	138	23	the	the	DET
ejde-355	138	24	solutions	solution	NOUN
ejde-355	138	25	of	of	ADP
ejde-355	138	26	problem	problem	NOUN
ejde-355	138	27	(	(	PUNCT
ejde-355	138	28	1.1	1.1	NUM
ejde-355	138	29	)	)	PUNCT
ejde-355	138	30	and	and	CCONJ
ejde-355	138	31	those	those	PRON
ejde-355	138	32	of	of	ADP
ejde-355	138	33	a	a	DET
ejde-355	138	34	(	(	PUNCT
ejde-355	138	35	nonlinear	nonlinear	ADJ
ejde-355	138	36	)	)	PUNCT
ejde-355	138	37	system	system	NOUN
ejde-355	138	38	of	of	ADP
ejde-355	138	39	integral	integral	ADJ
ejde-355	138	40	equations	equation	NOUN
ejde-355	138	41	.	.	PUNCT
ejde-355	139	1	proposition	proposition	NOUN
ejde-355	139	2	3.1	3.1	NUM
ejde-355	139	3	.	.	PUNCT
ejde-355	140	1	let	let	VERB
ejde-355	140	2	ε	ε	PROPN
ejde-355	140	3	∈]0	∈]0	X
ejde-355	140	4	,	,	PUNCT
ejde-355	140	5	ε0	ε0	PROPN
ejde-355	140	6	[	[	X
ejde-355	140	7	.	.	PUNCT
ejde-355	141	1	then	then	ADV
ejde-355	141	2	the	the	DET
ejde-355	141	3	map	map	NOUN
ejde-355	141	4	from	from	ADP
ejde-355	141	5	the	the	DET
ejde-355	141	6	set	set	NOUN
ejde-355	141	7	of	of	ADP
ejde-355	141	8	triples	triple	NOUN
ejde-355	141	9	(	(	PUNCT
ejde-355	141	10	µo	µo	NOUN
ejde-355	141	11	,	,	PUNCT
ejde-355	141	12	µi	µi	PROPN
ejde-355	141	13	,	,	PUNCT
ejde-355	141	14	ξ	ξ	X
ejde-355	141	15	)	)	PUNCT
ejde-355	141	16	∈	∈	PROPN
ejde-355	141	17	c0,α(∂ωo)0	c0,α(∂ωo)0	NUM
ejde-355	141	18	×	×	NOUN
ejde-355	141	19	c0,α(∂ωi)×	c0,α(∂ωi)×	PROPN
ejde-355	141	20	r	r	NOUN
ejde-355	141	21	such	such	ADJ
ejde-355	141	22	that	that	DET
ejde-355	141	23	−	−	PROPN
ejde-355	141	24	1	1	NUM
ejde-355	141	25	2	2	NUM
ejde-355	141	26	µo(x	µo(x	PUNCT
ejde-355	141	27	)	)	PUNCT
ejde-355	142	1	+	+	CCONJ
ejde-355	142	2	∫	∫	PROPN
ejde-355	142	3	∂ωo	∂ωo	NOUN
ejde-355	142	4	νωo(x	νωo(x	PROPN
ejde-355	142	5	)	)	PUNCT
ejde-355	142	6	·	·	PUNCT
ejde-355	142	7	∇s2(x−	∇s2(x−	ADP
ejde-355	142	8	y)µo(y	y)µo(y	NUM
ejde-355	142	9	)	)	PUNCT
ejde-355	142	10	dσy	dσy	PROPN
ejde-355	142	11	+	+	CCONJ
ejde-355	142	12	∫	∫	PROPN
ejde-355	142	13	∂ωi	∂ωi	PROPN
ejde-355	142	14	νωo(x	νωo(x	PROPN
ejde-355	142	15	)	)	PUNCT
ejde-355	142	16	·	·	PUNCT
ejde-355	142	17	∇s2(x−	∇s2(x−	X
ejde-355	142	18	εs)µi(s	εs)µi(s	NOUN
ejde-355	142	19	)	)	PUNCT
ejde-355	142	20	dσs	dσs	NOUN
ejde-355	142	21	=	=	PUNCT
ejde-355	142	22	go(x	go(x	X
ejde-355	142	23	)	)	PUNCT
ejde-355	143	1	∀x	∀x	VERB
ejde-355	143	2	∈	∈	PROPN
ejde-355	143	3	∂ωo	∂ωo	NOUN
ejde-355	143	4	,	,	PUNCT
ejde-355	143	5	(	(	PUNCT
ejde-355	143	6	3.1	3.1	NUM
ejde-355	143	7	)	)	PUNCT
ejde-355	143	8	1	1	NUM
ejde-355	143	9	2	2	NUM
ejde-355	143	10	µi(t	µi(t	NUM
ejde-355	143	11	)	)	PUNCT
ejde-355	143	12	+	+	CCONJ
ejde-355	143	13	ε	ε	PROPN
ejde-355	143	14	∫	∫	PROPN
ejde-355	143	15	∂ωo	∂ωo	NOUN
ejde-355	143	16	νωi(t	νωi(t	PROPN
ejde-355	143	17	)	)	PUNCT
ejde-355	143	18	·	·	PUNCT
ejde-355	143	19	∇s2(εt−	∇s2(εt−	NOUN
ejde-355	143	20	y)µo(y	y)µo(y	PRON
ejde-355	143	21	)	)	PUNCT
ejde-355	143	22	dσy	dσy	PROPN
ejde-355	144	1	+	+	CCONJ
ejde-355	144	2	∫	∫	PROPN
ejde-355	144	3	∂ωi	∂ωi	PROPN
ejde-355	144	4	νωi(t	νωi(t	PROPN
ejde-355	144	5	)	)	PUNCT
ejde-355	144	6	·	·	PUNCT
ejde-355	145	1	∇s2(t−	∇s2(t−	PRON
ejde-355	145	2	s)µi(s	s)µi(s	NOUN
ejde-355	145	3	)	)	PUNCT
ejde-355	145	4	dσs	dσs	NOUN
ejde-355	145	5	=	=	SYM
ejde-355	145	6	εδ(ε)fε	εδ(ε)fε	PROPN
ejde-355	145	7	(	(	PUNCT
ejde-355	145	8	∫	∫	PROPN
ejde-355	145	9	∂ωo	∂ωo	NOUN
ejde-355	145	10	s2(εt−	s2(εt−	VERB
ejde-355	145	11	y)µo(y	y)µo(y	NUM
ejde-355	145	12	)	)	PUNCT
ejde-355	145	13	dσy	dσy	PROPN
ejde-355	146	1	+	+	CCONJ
ejde-355	146	2	∫	∫	PROPN
ejde-355	146	3	∂ωi	∂ωi	PROPN
ejde-355	146	4	s2(t−	s2(t−	PROPN
ejde-355	146	5	s)µi(s	s)µi(s	NOUN
ejde-355	146	6	)	)	PUNCT
ejde-355	146	7	dσs	dσs	NOUN
ejde-355	146	8	+	+	CCONJ
ejde-355	146	9	log	log	NOUN
ejde-355	146	10	ε	ε	PROPN
ejde-355	146	11	2π	2π	PROPN
ejde-355	146	12	∫	∫	INTJ
ejde-355	147	1	∂ωi	∂ωi	PROPN
ejde-355	147	2	µi	µi	PROPN
ejde-355	147	3	dσ	dσ	PROPN
ejde-355	147	4	+	+	PROPN
ejde-355	147	5	ξ	ξ	X
ejde-355	147	6	δ(ε)ε	δ(ε)ε	PROPN
ejde-355	147	7	)	)	PUNCT
ejde-355	148	1	+	+	CCONJ
ejde-355	148	2	gi(t	gi(t	NOUN
ejde-355	148	3	)	)	PUNCT
ejde-355	148	4	ε	ε	PROPN
ejde-355	148	5	ρ(ε	ρ(ε	NUM
ejde-355	148	6	)	)	PUNCT
ejde-355	148	7	∀t	∀t	PROPN
ejde-355	148	8	∈	∈	PROPN
ejde-355	148	9	∂ωi	∂ωi	NOUN
ejde-355	148	10	,	,	PUNCT
ejde-355	148	11	(	(	PUNCT
ejde-355	148	12	3.2	3.2	NUM
ejde-355	148	13	)	)	PUNCT
ejde-355	148	14	to	to	ADP
ejde-355	148	15	the	the	DET
ejde-355	148	16	set	set	NOUN
ejde-355	148	17	of	of	ADP
ejde-355	148	18	those	those	DET
ejde-355	148	19	functions	function	NOUN
ejde-355	148	20	u	u	NOUN
ejde-355	148	21	∈	∈	PROPN
ejde-355	148	22	c1,α(ω(ε	c1,α(ω(ε	PRON
ejde-355	148	23	)	)	PUNCT
ejde-355	148	24	)	)	PUNCT
ejde-355	148	25	which	which	PRON
ejde-355	148	26	solve	solve	VERB
ejde-355	148	27	problem	problem	NOUN
ejde-355	148	28	(	(	PUNCT
ejde-355	148	29	1.1	1.1	NUM
ejde-355	148	30	)	)	PUNCT
ejde-355	148	31	,	,	PUNCT
ejde-355	148	32	which	which	PRON
ejde-355	148	33	takes	take	VERB
ejde-355	148	34	a	a	DET
ejde-355	148	35	triple	triple	ADJ
ejde-355	148	36	(	(	PUNCT
ejde-355	148	37	µo	µo	NOUN
ejde-355	148	38	,	,	PUNCT
ejde-355	148	39	µi	µi	PROPN
ejde-355	148	40	,	,	PUNCT
ejde-355	148	41	ξ	ξ	PROPN
ejde-355	148	42	)	)	PUNCT
ejde-355	148	43	to	to	ADP
ejde-355	148	44	the	the	DET
ejde-355	148	45	function∫	function∫	NOUN
ejde-355	148	46	∂ωo	∂ωo	NOUN
ejde-355	148	47	s2(x−	s2(x−	NUM
ejde-355	148	48	y)µo(y	y)µo(y	PRON
ejde-355	148	49	)	)	PUNCT
ejde-355	148	50	dσy	dσy	PROPN
ejde-355	148	51	+	+	CCONJ
ejde-355	148	52	∫	∫	PROPN
ejde-355	148	53	∂ωi	∂ωi	PROPN
ejde-355	148	54	s2(x−	s2(x−	PROPN
ejde-355	148	55	εs)µi(s	εs)µi(s	PROPN
ejde-355	148	56	)	)	PUNCT
ejde-355	148	57	dσs	dσs	NOUN
ejde-355	148	58	+	+	CCONJ
ejde-355	148	59	ξ	ξ	DET
ejde-355	148	60	δ(ε)ε	δ(ε)ε	PROPN
ejde-355	148	61	∀x	∀x	X
ejde-355	148	62	∈	∈	PROPN
ejde-355	148	63	ω(ε	ω(ε	PROPN
ejde-355	148	64	)	)	PUNCT
ejde-355	148	65	is	be	AUX
ejde-355	148	66	a	a	DET
ejde-355	148	67	bijection	bijection	NOUN
ejde-355	148	68	.	.	PUNCT
ejde-355	149	1	by	by	ADP
ejde-355	149	2	proposition	proposition	NOUN
ejde-355	149	3	3.1	3.1	NUM
ejde-355	149	4	we	we	PRON
ejde-355	149	5	can	can	AUX
ejde-355	149	6	study	study	VERB
ejde-355	149	7	the	the	DET
ejde-355	149	8	behavior	behavior	NOUN
ejde-355	149	9	of	of	ADP
ejde-355	149	10	the	the	DET
ejde-355	149	11	solutions	solution	NOUN
ejde-355	149	12	of	of	ADP
ejde-355	149	13	boundary	boundary	ADJ
ejde-355	149	14	value	value	NOUN
ejde-355	149	15	problem	problem	NOUN
ejde-355	149	16	(	(	PUNCT
ejde-355	149	17	1.1	1.1	NUM
ejde-355	149	18	)	)	PUNCT
ejde-355	149	19	by	by	ADP
ejde-355	149	20	analyzing	analyze	VERB
ejde-355	149	21	those	those	PRON
ejde-355	149	22	of	of	ADP
ejde-355	149	23	the	the	DET
ejde-355	149	24	system	system	NOUN
ejde-355	149	25	of	of	ADP
ejde-355	149	26	integral	integral	ADJ
ejde-355	149	27	equations	equation	NOUN
ejde-355	149	28	(	(	PUNCT
ejde-355	149	29	3.1)-(3.2	3.1)-(3.2	NUM
ejde-355	149	30	)	)	PUNCT
ejde-355	149	31	as	as	ADP
ejde-355	149	32	ε	ε	PROPN
ejde-355	149	33	→	→	SYM
ejde-355	149	34	0	0	NUM
ejde-355	149	35	.	.	PUNCT
ejde-355	150	1	as	as	SCONJ
ejde-355	150	2	we	we	PRON
ejde-355	150	3	have	have	AUX
ejde-355	150	4	done	do	VERB
ejde-355	150	5	in	in	ADP
ejde-355	150	6	[	[	X
ejde-355	150	7	36	36	NUM
ejde-355	150	8	]	]	PUNCT
ejde-355	150	9	,	,	PUNCT
ejde-355	150	10	we	we	PRON
ejde-355	150	11	make	make	VERB
ejde-355	150	12	some	some	DET
ejde-355	150	13	structural	structural	ADJ
ejde-355	150	14	assumptions	assumption	NOUN
ejde-355	150	15	on	on	ADP
ejde-355	150	16	the	the	DET
ejde-355	150	17	nonlinearity	nonlinearity	NOUN
ejde-355	150	18	and	and	CCONJ
ejde-355	150	19	we	we	PRON
ejde-355	150	20	assume	assume	VERB
ejde-355	150	21	that	that	SCONJ
ejde-355	150	22	there	there	PRON
ejde-355	150	23	exist	exist	VERB
ejde-355	150	24	ε1	ε1	VERB
ejde-355	150	25	∈]0	∈]0	ADJ
ejde-355	150	26	,	,	PUNCT
ejde-355	150	27	ε0	ε0	PROPN
ejde-355	150	28	[	[	X
ejde-355	150	29	,	,	PUNCT
ejde-355	150	30	m	m	PROPN
ejde-355	150	31	∈	∈	PROPN
ejde-355	150	32	n	n	CCONJ
ejde-355	150	33	,	,	PUNCT
ejde-355	150	34	a	a	DET
ejde-355	150	35	real	real	ADJ
ejde-355	150	36	analytic	analytic	ADJ
ejde-355	150	37	function	function	NOUN
ejde-355	150	38	f̃	f̃	PROPN
ejde-355	150	39	from	from	ADP
ejde-355	150	40	rm+1	rm+1	PRON
ejde-355	150	41	to	to	ADP
ejde-355	150	42	r	r	NOUN
ejde-355	150	43	,	,	PUNCT
ejde-355	150	44	and	and	CCONJ
ejde-355	150	45	a	a	DET
ejde-355	150	46	function	function	NOUN
ejde-355	150	47	η	η	PROPN
ejde-355	150	48	(	(	PUNCT
ejde-355	150	49	·	·	PUNCT
ejde-355	150	50	)	)	PUNCT
ejde-355	150	51	from	from	ADP
ejde-355	150	52	]	]	SYM
ejde-355	150	53	0	0	NUM
ejde-355	150	54	,	,	PUNCT
ejde-355	150	55	ε1	ε1	PROPN
ejde-355	150	56	[	[	PUNCT
ejde-355	150	57	to	to	ADP
ejde-355	150	58	rm	rm	NOUN
ejde-355	150	59	such	such	ADJ
ejde-355	150	60	that	that	DET
ejde-355	150	61	η0	η0	PROPN
ejde-355	150	62	≡	≡	PROPN
ejde-355	150	63	lim	lim	PROPN
ejde-355	150	64	ε→0	ε→0	NOUN
ejde-355	150	65	η(ε	η(ε	NOUN
ejde-355	150	66	)	)	PUNCT
ejde-355	150	67	∈	∈	PROPN
ejde-355	150	68	rm	rm	NOUN
ejde-355	150	69	and	and	CCONJ
ejde-355	150	70	that	that	SCONJ
ejde-355	150	71	εδ(ε)fε	εδ(ε)fε	NOUN
ejde-355	150	72	(	(	PUNCT
ejde-355	150	73	1	1	NUM
ejde-355	150	74	εδ(ε	εδ(ε	NOUN
ejde-355	150	75	)	)	PUNCT
ejde-355	150	76	τ	τ	PROPN
ejde-355	150	77	)	)	PUNCT
ejde-355	150	78	=	=	SYM
ejde-355	150	79	f̃	f̃	PROPN
ejde-355	150	80	(	(	PUNCT
ejde-355	150	81	τ	τ	PROPN
ejde-355	150	82	,	,	PUNCT
ejde-355	150	83	η(ε	η(ε	NOUN
ejde-355	150	84	)	)	PUNCT
ejde-355	150	85	)	)	PUNCT
ejde-355	150	86	for	for	ADP
ejde-355	150	87	all	all	PRON
ejde-355	150	88	(	(	PUNCT
ejde-355	150	89	τ	τ	PROPN
ejde-355	150	90	,	,	PUNCT
ejde-355	150	91	ε	ε	PROPN
ejde-355	150	92	)	)	PUNCT
ejde-355	150	93	∈	∈	PROPN
ejde-355	150	94	r×]0	r×]0	PROPN
ejde-355	150	95	,	,	PUNCT
ejde-355	150	96	ε1	ε1	PROPN
ejde-355	150	97	[	[	X
ejde-355	150	98	.	.	PUNCT
ejde-355	151	1	(	(	PUNCT
ejde-355	151	2	3.3	3.3	NUM
ejde-355	151	3	)	)	PUNCT
ejde-355	151	4	4	4	NUM
ejde-355	151	5	.	.	PUNCT
ejde-355	151	6	analytic	analytic	ADJ
ejde-355	151	7	representation	representation	NOUN
ejde-355	151	8	formulas	formula	NOUN
ejde-355	151	9	for	for	ADP
ejde-355	151	10	the	the	DET
ejde-355	151	11	solution	solution	NOUN
ejde-355	151	12	of	of	ADP
ejde-355	151	13	the	the	DET
ejde-355	151	14	boundary	boundary	ADJ
ejde-355	151	15	value	value	NOUN
ejde-355	151	16	problem	problem	NOUN
ejde-355	151	17	under	under	ADP
ejde-355	151	18	the	the	DET
ejde-355	151	19	additional	additional	ADJ
ejde-355	151	20	assumption	assumption	NOUN
ejde-355	151	21	(	(	PUNCT
ejde-355	151	22	3.3	3.3	NUM
ejde-355	151	23	)	)	PUNCT
ejde-355	151	24	,	,	PUNCT
ejde-355	151	25	we	we	PRON
ejde-355	151	26	can	can	AUX
ejde-355	151	27	rewrite	rewrite	VERB
ejde-355	151	28	the	the	DET
ejde-355	151	29	set	set	NOUN
ejde-355	151	30	of	of	ADP
ejde-355	151	31	equations	equation	NOUN
ejde-355	151	32	(	(	PUNCT
ejde-355	151	33	3.1)(3.2	3.1)(3.2	NUM
ejde-355	151	34	)	)	PUNCT
ejde-355	151	35	as	as	ADP
ejde-355	151	36	−	−	PROPN
ejde-355	151	37	1	1	NUM
ejde-355	151	38	2	2	NUM
ejde-355	151	39	µo(x	µo(x	PUNCT
ejde-355	151	40	)	)	PUNCT
ejde-355	152	1	+	+	CCONJ
ejde-355	152	2	∫	∫	PROPN
ejde-355	152	3	∂ωo	∂ωo	NOUN
ejde-355	152	4	νωo(x	νωo(x	PROPN
ejde-355	152	5	)	)	PUNCT
ejde-355	152	6	·	·	PUNCT
ejde-355	152	7	∇s2(x−	∇s2(x−	ADP
ejde-355	152	8	y)µo(y	y)µo(y	NUM
ejde-355	152	9	)	)	PUNCT
ejde-355	152	10	dσy	dσy	PROPN
ejde-355	152	11	+	+	CCONJ
ejde-355	152	12	∫	∫	PROPN
ejde-355	152	13	∂ωi	∂ωi	PROPN
ejde-355	152	14	νωo(x	νωo(x	PROPN
ejde-355	152	15	)	)	PUNCT
ejde-355	152	16	·	·	PUNCT
ejde-355	152	17	∇s2(x−	∇s2(x−	X
ejde-355	152	18	εs)µi(s	εs)µi(s	NOUN
ejde-355	152	19	)	)	PUNCT
ejde-355	152	20	dσs	dσs	NOUN
ejde-355	152	21	=	=	PUNCT
ejde-355	152	22	go(x	go(x	X
ejde-355	152	23	)	)	PUNCT
ejde-355	153	1	∀x	∀x	VERB
ejde-355	153	2	∈	∈	PROPN
ejde-355	153	3	∂ωo	∂ωo	NOUN
ejde-355	153	4	,	,	PUNCT
ejde-355	153	5	(	(	PUNCT
ejde-355	153	6	4.1	4.1	NUM
ejde-355	153	7	)	)	PUNCT
ejde-355	153	8	8	8	NUM
ejde-355	153	9	p.	p.	NOUN
ejde-355	153	10	musolino	musolino	NOUN
ejde-355	153	11	,	,	PUNCT
ejde-355	153	12	m.	m.	NOUN
ejde-355	153	13	dutko	dutko	PROPN
ejde-355	153	14	,	,	PUNCT
ejde-355	153	15	g.	g.	PROPN
ejde-355	153	16	mishuris	mishuris	PROPN
ejde-355	153	17	ejde-2023/57	ejde-2023/57	NOUN
ejde-355	153	18	1	1	NUM
ejde-355	153	19	2	2	NUM
ejde-355	153	20	µi(t	µi(t	NUM
ejde-355	153	21	)	)	PUNCT
ejde-355	153	22	+	+	CCONJ
ejde-355	153	23	ε	ε	PROPN
ejde-355	153	24	∫	∫	PROPN
ejde-355	153	25	∂ωo	∂ωo	NOUN
ejde-355	153	26	νωi(t	νωi(t	PROPN
ejde-355	153	27	)	)	PUNCT
ejde-355	153	28	·	·	PUNCT
ejde-355	153	29	∇s2(εt−	∇s2(εt−	NOUN
ejde-355	153	30	y)µo(y	y)µo(y	PRON
ejde-355	153	31	)	)	PUNCT
ejde-355	153	32	dσy	dσy	PROPN
ejde-355	154	1	+	+	CCONJ
ejde-355	154	2	∫	∫	PROPN
ejde-355	154	3	∂ωi	∂ωi	PROPN
ejde-355	154	4	νωi(t	νωi(t	PROPN
ejde-355	154	5	)	)	PUNCT
ejde-355	154	6	·	·	PUNCT
ejde-355	155	1	∇s2(t−	∇s2(t−	PRON
ejde-355	155	2	s)µi(s	s)µi(s	NOUN
ejde-355	155	3	)	)	PUNCT
ejde-355	155	4	dσs	dσs	NOUN
ejde-355	155	5	=	=	SYM
ejde-355	155	6	f̃	f̃	PROPN
ejde-355	155	7	(	(	PUNCT
ejde-355	155	8	εδ(ε	εδ(ε	NOUN
ejde-355	155	9	)	)	PUNCT
ejde-355	155	10	∫	∫	PROPN
ejde-355	156	1	∂ωo	∂ωo	NOUN
ejde-355	156	2	s2(εt−	s2(εt−	VERB
ejde-355	156	3	y)µo(y	y)µo(y	NUM
ejde-355	156	4	)	)	PUNCT
ejde-355	156	5	dσy	dσy	NOUN
ejde-355	156	6	+	+	SYM
ejde-355	156	7	εδ(ε	εδ(ε	NOUN
ejde-355	156	8	)	)	PUNCT
ejde-355	156	9	∫	∫	PROPN
ejde-355	157	1	∂ωi	∂ωi	PROPN
ejde-355	157	2	s2(t−	s2(t−	PROPN
ejde-355	157	3	s)µi(s	s)µi(s	NOUN
ejde-355	157	4	)	)	PUNCT
ejde-355	157	5	dσs	dσs	NOUN
ejde-355	157	6	+	+	SYM
ejde-355	157	7	εδ(ε	εδ(ε	NOUN
ejde-355	157	8	)	)	PUNCT
ejde-355	157	9	log	log	AUX
ejde-355	157	10	ε	ε	PROPN
ejde-355	157	11	2π	2π	PROPN
ejde-355	157	12	∫	∫	INTJ
ejde-355	157	13	∂ωi	∂ωi	PROPN
ejde-355	157	14	µi	µi	PROPN
ejde-355	157	15	dσ	dσ	PROPN
ejde-355	157	16	+	+	PROPN
ejde-355	157	17	ξ	ξ	PROPN
ejde-355	157	18	,	,	PUNCT
ejde-355	157	19	η(ε	η(ε	NOUN
ejde-355	157	20	)	)	PUNCT
ejde-355	157	21	)	)	PUNCT
ejde-355	158	1	+	+	CCONJ
ejde-355	158	2	gi(t	gi(t	NOUN
ejde-355	158	3	)	)	PUNCT
ejde-355	158	4	ε	ε	PROPN
ejde-355	158	5	ρ(ε	ρ(ε	NUM
ejde-355	158	6	)	)	PUNCT
ejde-355	158	7	∀t	∀t	PROPN
ejde-355	158	8	∈	∈	PROPN
ejde-355	158	9	∂ωi	∂ωi	NOUN
ejde-355	158	10	,	,	PUNCT
ejde-355	158	11	(	(	PUNCT
ejde-355	158	12	4.2	4.2	NUM
ejde-355	158	13	)	)	PUNCT
ejde-355	158	14	for	for	ADP
ejde-355	158	15	all	all	DET
ejde-355	158	16	ε	ε	PROPN
ejde-355	158	17	∈]0	∈]0	X
ejde-355	158	18	,	,	PUNCT
ejde-355	158	19	ε1	ε1	PROPN
ejde-355	158	20	[	[	X
ejde-355	158	21	.	.	PUNCT
ejde-355	159	1	in	in	ADP
ejde-355	159	2	order	order	NOUN
ejde-355	159	3	to	to	PART
ejde-355	159	4	pass	pass	VERB
ejde-355	159	5	to	to	ADP
ejde-355	159	6	the	the	DET
ejde-355	159	7	limit	limit	NOUN
ejde-355	159	8	as	as	ADP
ejde-355	159	9	ε	ε	PROPN
ejde-355	159	10	→	→	SYM
ejde-355	159	11	0	0	NUM
ejde-355	159	12	in	in	ADP
ejde-355	159	13	equations	equation	NOUN
ejde-355	159	14	(	(	PUNCT
ejde-355	159	15	4.1)-(4.2	4.1)-(4.2	NUM
ejde-355	159	16	)	)	PUNCT
ejde-355	159	17	,	,	PUNCT
ejde-355	159	18	we	we	PRON
ejde-355	159	19	need	need	VERB
ejde-355	159	20	to	to	PART
ejde-355	159	21	know	know	VERB
ejde-355	159	22	the	the	DET
ejde-355	159	23	asymptotic	asymptotic	ADJ
ejde-355	159	24	behavior	behavior	NOUN
ejde-355	159	25	for	for	ADP
ejde-355	159	26	ε	ε	PROPN
ejde-355	159	27	close	close	ADJ
ejde-355	159	28	to	to	ADP
ejde-355	159	29	0	0	NUM
ejde-355	159	30	of	of	ADP
ejde-355	159	31	the	the	DET
ejde-355	159	32	quantities	quantity	NOUN
ejde-355	159	33	εδ(ε	εδ(ε	NOUN
ejde-355	159	34	)	)	PUNCT
ejde-355	159	35	,	,	PUNCT
ejde-355	159	36	εδ(ε	εδ(ε	VERB
ejde-355	159	37	)	)	PUNCT
ejde-355	159	38	log	log	PROPN
ejde-355	159	39	ε	ε	PROPN
ejde-355	159	40	,	,	PUNCT
ejde-355	159	41	and	and	CCONJ
ejde-355	159	42	ε	ε	PROPN
ejde-355	159	43	ρ(ε	ρ(ε	PROPN
ejde-355	159	44	)	)	PUNCT
ejde-355	159	45	which	which	PRON
ejde-355	159	46	appear	appear	VERB
ejde-355	159	47	in	in	ADP
ejde-355	159	48	(	(	PUNCT
ejde-355	159	49	4.2	4.2	NUM
ejde-355	159	50	)	)	PUNCT
ejde-355	159	51	.	.	PUNCT
ejde-355	160	1	as	as	ADP
ejde-355	160	2	a	a	DET
ejde-355	160	3	consequence	consequence	NOUN
ejde-355	160	4	,	,	PUNCT
ejde-355	160	5	we	we	PRON
ejde-355	160	6	now	now	ADV
ejde-355	160	7	assume	assume	VERB
ejde-355	160	8	that	that	SCONJ
ejde-355	160	9	l0	l0	PROPN
ejde-355	160	10	≡	≡	PROPN
ejde-355	160	11	lim	lim	PROPN
ejde-355	160	12	ε→0	ε→0	NOUN
ejde-355	160	13	εδ(ε	εδ(ε	ADV
ejde-355	160	14	)	)	PUNCT
ejde-355	160	15	log	log	VERB
ejde-355	160	16	ε	ε	PROPN
ejde-355	160	17	∈	∈	PROPN
ejde-355	160	18	r	r	NOUN
ejde-355	160	19	,	,	PUNCT
ejde-355	160	20	r0	r0	PROPN
ejde-355	160	21	≡	≡	PROPN
ejde-355	160	22	lim	lim	PROPN
ejde-355	160	23	ε→0	ε→0	X
ejde-355	160	24	ε	ε	PROPN
ejde-355	160	25	ρ(ε	ρ(ε	PROPN
ejde-355	160	26	)	)	PUNCT
ejde-355	160	27	∈	∈	PROPN
ejde-355	160	28	r	r	NOUN
ejde-355	160	29	.	.	PUNCT
ejde-355	161	1	(	(	PUNCT
ejde-355	161	2	4.3	4.3	NUM
ejde-355	161	3	)	)	PUNCT
ejde-355	161	4	condition	condition	NOUN
ejde-355	161	5	(	(	PUNCT
ejde-355	161	6	4.3	4.3	NUM
ejde-355	161	7	)	)	PUNCT
ejde-355	161	8	implies	imply	VERB
ejde-355	161	9	also	also	ADV
ejde-355	161	10	limε→0	limε→0	NOUN
ejde-355	161	11	εδ(ε	εδ(ε	NOUN
ejde-355	161	12	)	)	PUNCT
ejde-355	161	13	=	=	SYM
ejde-355	162	1	0	0	X
ejde-355	162	2	.	.	PUNCT
ejde-355	163	1	in	in	ADP
ejde-355	163	2	(	(	PUNCT
ejde-355	163	3	4.1)-(4.2	4.1)-(4.2	NUM
ejde-355	163	4	)	)	PUNCT
ejde-355	163	5	,	,	PUNCT
ejde-355	163	6	we	we	PRON
ejde-355	163	7	replace	replace	VERB
ejde-355	163	8	the	the	DET
ejde-355	163	9	quantities	quantity	NOUN
ejde-355	163	10	εδ(ε	εδ(ε	PUNCT
ejde-355	163	11	)	)	PUNCT
ejde-355	163	12	,	,	PUNCT
ejde-355	163	13	εδ(ε	εδ(ε	NOUN
ejde-355	163	14	)	)	PUNCT
ejde-355	163	15	log	log	PROPN
ejde-355	163	16	ε	ε	PROPN
ejde-355	163	17	,	,	PUNCT
ejde-355	163	18	η(ε	η(ε	PROPN
ejde-355	163	19	)	)	PUNCT
ejde-355	163	20	,	,	PUNCT
ejde-355	163	21	ε	ε	PROPN
ejde-355	163	22	ρ(ε	ρ(ε	NUM
ejde-355	163	23	)	)	PUNCT
ejde-355	163	24	,	,	PUNCT
ejde-355	163	25	by	by	ADP
ejde-355	163	26	the	the	DET
ejde-355	163	27	auxiliary	auxiliary	ADJ
ejde-355	163	28	variables	variable	NOUN
ejde-355	163	29	γ1	γ1	PROPN
ejde-355	163	30	,	,	PUNCT
ejde-355	163	31	γ2	γ2	PROPN
ejde-355	163	32	,	,	PUNCT
ejde-355	163	33	γ3	γ3	NOUN
ejde-355	163	34	,	,	PUNCT
ejde-355	163	35	and	and	CCONJ
ejde-355	163	36	γ4,respectively	γ4,respectively	ADV
ejde-355	163	37	,	,	PUNCT
ejde-355	163	38	and	and	CCONJ
ejde-355	163	39	we	we	PRON
ejde-355	163	40	introduce	introduce	VERB
ejde-355	163	41	the	the	DET
ejde-355	163	42	operator	operator	NOUN
ejde-355	163	43	λ	λ	PROPN
ejde-355	163	44	≡	≡	PROPN
ejde-355	163	45	(	(	PUNCT
ejde-355	163	46	λo	λo	PROPN
ejde-355	163	47	,	,	PUNCT
ejde-355	163	48	λi	λi	NOUN
ejde-355	163	49	)	)	PUNCT
ejde-355	163	50	from	from	ADP
ejde-355	163	51	]	]	PUNCT
ejde-355	163	52	−	−	PROPN
ejde-355	163	53	ε1	ε1	PROPN
ejde-355	163	54	,	,	PUNCT
ejde-355	163	55	ε1[×rm+3	ε1[×rm+3	PROPN
ejde-355	163	56	×	×	VERB
ejde-355	163	57	c0,α(∂ωo)0	c0,α(∂ωo)0	NUM
ejde-355	163	58	×	×	PROPN
ejde-355	163	59	c0,α(∂ωi	c0,α(∂ωi	ADJ
ejde-355	163	60	)	)	PUNCT
ejde-355	163	61	×	×	NOUN
ejde-355	163	62	r	r	NOUN
ejde-355	163	63	to	to	ADP
ejde-355	163	64	c0,α(∂ωo)×	c0,α(∂ωo)×	NOUN
ejde-355	163	65	c0,α(∂ωi	c0,α(∂ωi	ADV
ejde-355	163	66	)	)	PUNCT
ejde-355	163	67	by	by	ADP
ejde-355	163	68	setting	set	VERB
ejde-355	163	69	λo[ε	λo[ε	PROPN
ejde-355	163	70	,	,	PUNCT
ejde-355	163	71	γ1	γ1	NOUN
ejde-355	163	72	,	,	PUNCT
ejde-355	163	73	γ2	γ2	PROPN
ejde-355	163	74	,	,	PUNCT
ejde-355	163	75	γ3	γ3	NOUN
ejde-355	163	76	,	,	PUNCT
ejde-355	163	77	γ4	γ4	PROPN
ejde-355	163	78	,	,	PUNCT
ejde-355	163	79	µ	µ	NOUN
ejde-355	163	80	o	o	NOUN
ejde-355	163	81	,	,	PUNCT
ejde-355	163	82	µi	µi	PROPN
ejde-355	163	83	,	,	PUNCT
ejde-355	163	84	ξ](x	ξ](x	ADJ
ejde-355	163	85	)	)	PUNCT
ejde-355	163	86	≡	≡	PROPN
ejde-355	163	87	−1	−1	NOUN
ejde-355	163	88	2	2	NUM
ejde-355	163	89	µo(x	µo(x	PUNCT
ejde-355	163	90	)	)	PUNCT
ejde-355	164	1	+	+	CCONJ
ejde-355	164	2	∫	∫	PROPN
ejde-355	164	3	∂ωo	∂ωo	NOUN
ejde-355	164	4	νωo(x	νωo(x	PROPN
ejde-355	164	5	)	)	PUNCT
ejde-355	164	6	·	·	PUNCT
ejde-355	164	7	∇s2(x−	∇s2(x−	ADP
ejde-355	164	8	y)µo(y	y)µo(y	NUM
ejde-355	164	9	)	)	PUNCT
ejde-355	164	10	dσy	dσy	PROPN
ejde-355	164	11	+	+	CCONJ
ejde-355	164	12	∫	∫	PROPN
ejde-355	164	13	∂ωi	∂ωi	PROPN
ejde-355	164	14	νωo(x	νωo(x	PROPN
ejde-355	164	15	)	)	PUNCT
ejde-355	164	16	·	·	PUNCT
ejde-355	164	17	∇s2(x−	∇s2(x−	X
ejde-355	164	18	εs)µi(s	εs)µi(s	NOUN
ejde-355	164	19	)	)	PUNCT
ejde-355	164	20	dσs	dσs	NOUN
ejde-355	164	21	−	−	PROPN
ejde-355	164	22	go(x	go(x	PUNCT
ejde-355	164	23	)	)	PUNCT
ejde-355	165	1	∀x	∀x	VERB
ejde-355	165	2	∈	∈	PROPN
ejde-355	165	3	∂ωo	∂ωo	NOUN
ejde-355	165	4	,	,	PUNCT
ejde-355	165	5	(	(	PUNCT
ejde-355	165	6	4.4	4.4	NUM
ejde-355	165	7	)	)	PUNCT
ejde-355	165	8	λi[ε	λi[ε	PROPN
ejde-355	165	9	,	,	PUNCT
ejde-355	165	10	γ1	γ1	NOUN
ejde-355	165	11	,	,	PUNCT
ejde-355	165	12	γ2	γ2	PROPN
ejde-355	165	13	,	,	PUNCT
ejde-355	165	14	γ3	γ3	NOUN
ejde-355	165	15	,	,	PUNCT
ejde-355	165	16	γ4	γ4	PROPN
ejde-355	165	17	,	,	PUNCT
ejde-355	165	18	µ	µ	NOUN
ejde-355	165	19	o	o	NOUN
ejde-355	165	20	,	,	PUNCT
ejde-355	165	21	µi	µi	PROPN
ejde-355	165	22	,	,	PUNCT
ejde-355	165	23	ξ](t	ξ](t	ADJ
ejde-355	165	24	)	)	PUNCT
ejde-355	165	25	≡	≡	PROPN
ejde-355	165	26	1	1	NUM
ejde-355	165	27	2	2	NUM
ejde-355	165	28	µi(t	µi(t	NUM
ejde-355	165	29	)	)	PUNCT
ejde-355	165	30	+	+	CCONJ
ejde-355	165	31	ε	ε	PROPN
ejde-355	165	32	∫	∫	PROPN
ejde-355	165	33	∂ωo	∂ωo	NOUN
ejde-355	165	34	νωi(t	νωi(t	PROPN
ejde-355	165	35	)	)	PUNCT
ejde-355	165	36	·	·	PUNCT
ejde-355	165	37	∇s2(εt−	∇s2(εt−	NOUN
ejde-355	165	38	y)µo(y	y)µo(y	PRON
ejde-355	165	39	)	)	PUNCT
ejde-355	165	40	dσy	dσy	PROPN
ejde-355	166	1	+	+	CCONJ
ejde-355	166	2	∫	∫	PROPN
ejde-355	166	3	∂ωi	∂ωi	PROPN
ejde-355	166	4	νωi(t	νωi(t	PROPN
ejde-355	166	5	)	)	PUNCT
ejde-355	166	6	·	·	PUNCT
ejde-355	167	1	∇s2(t−	∇s2(t−	PRON
ejde-355	167	2	s)µi(s	s)µi(s	NOUN
ejde-355	167	3	)	)	PUNCT
ejde-355	167	4	dσs	dσs	NOUN
ejde-355	167	5	−	−	PROPN
ejde-355	167	6	f̃	f̃	PROPN
ejde-355	167	7	(	(	PUNCT
ejde-355	167	8	γ1	γ1	PROPN
ejde-355	167	9	∫	∫	PROPN
ejde-355	168	1	∂ωo	∂ωo	PROPN
ejde-355	168	2	s2(εt−	s2(εt−	VERB
ejde-355	168	3	y)µo(y	y)µo(y	NUM
ejde-355	168	4	)	)	PUNCT
ejde-355	168	5	dσy	dσy	PROPN
ejde-355	168	6	+	+	CCONJ
ejde-355	168	7	γ1	γ1	PROPN
ejde-355	168	8	∫	∫	PROPN
ejde-355	168	9	∂ωi	∂ωi	PROPN
ejde-355	168	10	s2(t−	s2(t−	PROPN
ejde-355	168	11	s)µi(s	s)µi(s	NOUN
ejde-355	168	12	)	)	PUNCT
ejde-355	168	13	dσs	dσs	NOUN
ejde-355	168	14	+	+	CCONJ
ejde-355	168	15	γ2	γ2	ADJ
ejde-355	168	16	2π	2π	NOUN
ejde-355	168	17	∫	∫	NOUN
ejde-355	169	1	∂ωi	∂ωi	PROPN
ejde-355	169	2	µi	µi	PROPN
ejde-355	169	3	dσ	dσ	PROPN
ejde-355	169	4	+	+	PROPN
ejde-355	169	5	ξ	ξ	PROPN
ejde-355	169	6	,	,	PUNCT
ejde-355	169	7	γ3	γ3	NOUN
ejde-355	169	8	)	)	PUNCT
ejde-355	170	1	−	−	PROPN
ejde-355	171	1	gi(t)γ4	gi(t)γ4	ADP
ejde-355	171	2	∀t	∀t	PROPN
ejde-355	171	3	∈	∈	PROPN
ejde-355	171	4	∂ωi	∂ωi	NOUN
ejde-355	171	5	,	,	PUNCT
ejde-355	171	6	(	(	PUNCT
ejde-355	171	7	4.5	4.5	NUM
ejde-355	171	8	)	)	PUNCT
ejde-355	171	9	for	for	ADP
ejde-355	171	10	all	all	DET
ejde-355	171	11	(	(	PUNCT
ejde-355	171	12	ε	ε	PROPN
ejde-355	171	13	,	,	PUNCT
ejde-355	171	14	γ1	γ1	NOUN
ejde-355	171	15	,	,	PUNCT
ejde-355	171	16	γ2	γ2	PROPN
ejde-355	171	17	,	,	PUNCT
ejde-355	171	18	γ3	γ3	NOUN
ejde-355	171	19	,	,	PUNCT
ejde-355	171	20	γ4	γ4	PROPN
ejde-355	171	21	,	,	PUNCT
ejde-355	171	22	µ	µ	NOUN
ejde-355	171	23	o	o	NOUN
ejde-355	171	24	,	,	PUNCT
ejde-355	171	25	µi	µi	PROPN
ejde-355	171	26	,	,	PUNCT
ejde-355	171	27	ξ	ξ	NOUN
ejde-355	171	28	)	)	PUNCT
ejde-355	171	29	∈	∈	PROPN
ejde-355	171	30	]	]	PUNCT
ejde-355	171	31	−	−	PROPN
ejde-355	171	32	ε1	ε1	PROPN
ejde-355	171	33	,	,	PUNCT
ejde-355	171	34	ε1[×rm+3	ε1[×rm+3	PROPN
ejde-355	171	35	×	×	VERB
ejde-355	171	36	c0,α(∂ωo)0	c0,α(∂ωo)0	NUM
ejde-355	171	37	×	×	PROPN
ejde-355	171	38	c0,α(∂ωi	c0,α(∂ωi	ADJ
ejde-355	171	39	)	)	PUNCT
ejde-355	171	40	×	×	PROPN
ejde-355	171	41	r.	r.	NOUN
ejde-355	171	42	by	by	ADP
ejde-355	171	43	definitions	definition	NOUN
ejde-355	171	44	(	(	PUNCT
ejde-355	171	45	4.4)-(4.5	4.4)-(4.5	NUM
ejde-355	171	46	)	)	PUNCT
ejde-355	171	47	,	,	PUNCT
ejde-355	171	48	for	for	ADP
ejde-355	171	49	ε	ε	PROPN
ejde-355	171	50	∈]0	∈]0	X
ejde-355	171	51	,	,	PUNCT
ejde-355	171	52	ε1	ε1	PROPN
ejde-355	171	53	[	[	PUNCT
ejde-355	171	54	the	the	DET
ejde-355	171	55	system	system	NOUN
ejde-355	171	56	of	of	ADP
ejde-355	171	57	equations	equation	NOUN
ejde-355	171	58	λo[ε	λo[ε	PROPN
ejde-355	171	59	,	,	PUNCT
ejde-355	171	60	εδ(ε	εδ(ε	NOUN
ejde-355	171	61	)	)	PUNCT
ejde-355	171	62	,	,	PUNCT
ejde-355	171	63	εδ(ε	εδ(ε	VERB
ejde-355	171	64	)	)	PUNCT
ejde-355	171	65	log	log	PROPN
ejde-355	171	66	ε	ε	PROPN
ejde-355	171	67	,	,	PUNCT
ejde-355	171	68	η(ε	η(ε	NOUN
ejde-355	171	69	)	)	PUNCT
ejde-355	171	70	,	,	PUNCT
ejde-355	171	71	ε	ε	PROPN
ejde-355	171	72	ρ(ε	ρ(ε	NUM
ejde-355	171	73	)	)	PUNCT
ejde-355	171	74	,	,	PUNCT
ejde-355	171	75	µo	µo	PROPN
ejde-355	171	76	,	,	PUNCT
ejde-355	171	77	µi	µi	PROPN
ejde-355	171	78	,	,	PUNCT
ejde-355	171	79	ξ](x	ξ](x	NOUN
ejde-355	171	80	)	)	PUNCT
ejde-355	171	81	=	=	SYM
ejde-355	171	82	0	0	PUNCT
ejde-355	171	83	∀x	∀x	X
ejde-355	171	84	∈	∈	PROPN
ejde-355	171	85	∂ωo	∂ωo	NOUN
ejde-355	171	86	,	,	PUNCT
ejde-355	171	87	(	(	PUNCT
ejde-355	171	88	4.6	4.6	X
ejde-355	171	89	)	)	PUNCT
ejde-355	171	90	λi[ε	λi[ε	PROPN
ejde-355	171	91	,	,	PUNCT
ejde-355	171	92	εδ(ε	εδ(ε	NOUN
ejde-355	171	93	)	)	PUNCT
ejde-355	171	94	,	,	PUNCT
ejde-355	171	95	εδ(ε	εδ(ε	VERB
ejde-355	171	96	)	)	PUNCT
ejde-355	171	97	log	log	PROPN
ejde-355	171	98	ε	ε	PROPN
ejde-355	171	99	,	,	PUNCT
ejde-355	171	100	η(ε	η(ε	NOUN
ejde-355	171	101	)	)	PUNCT
ejde-355	171	102	,	,	PUNCT
ejde-355	171	103	ε	ε	PROPN
ejde-355	171	104	ρ(ε	ρ(ε	NUM
ejde-355	171	105	)	)	PUNCT
ejde-355	171	106	,	,	PUNCT
ejde-355	171	107	µo	µo	PROPN
ejde-355	171	108	,	,	PUNCT
ejde-355	171	109	µi	µi	PROPN
ejde-355	171	110	,	,	PUNCT
ejde-355	171	111	ξ](t	ξ](t	NOUN
ejde-355	171	112	)	)	PUNCT
ejde-355	171	113	=	=	SYM
ejde-355	171	114	0	0	NUM
ejde-355	171	115	∀t	∀t	PROPN
ejde-355	171	116	∈	∈	PROPN
ejde-355	171	117	∂ωi	∂ωi	NOUN
ejde-355	171	118	(	(	PUNCT
ejde-355	171	119	4.7	4.7	NUM
ejde-355	171	120	)	)	PUNCT
ejde-355	171	121	ejde-2023/57	ejde-2023/57	NOUN
ejde-355	171	122	asymptotic	asymptotic	ADJ
ejde-355	171	123	analysis	analysis	NOUN
ejde-355	171	124	of	of	ADP
ejde-355	171	125	perturbed	perturb	VERB
ejde-355	171	126	robin	robin	PROPN
ejde-355	171	127	problems	problem	NOUN
ejde-355	171	128	9	9	NUM
ejde-355	171	129	is	be	AUX
ejde-355	171	130	equivalent	equivalent	ADJ
ejde-355	171	131	to	to	ADP
ejde-355	171	132	the	the	DET
ejde-355	171	133	system	system	NOUN
ejde-355	171	134	of	of	ADP
ejde-355	171	135	integral	integral	ADJ
ejde-355	171	136	equations	equation	NOUN
ejde-355	171	137	(	(	PUNCT
ejde-355	171	138	4.1)-(4.2	4.1)-(4.2	NUM
ejde-355	171	139	)	)	PUNCT
ejde-355	171	140	.	.	PUNCT
ejde-355	172	1	letting	let	VERB
ejde-355	172	2	ε	ε	PROPN
ejde-355	172	3	→	→	SYM
ejde-355	172	4	0	0	NUM
ejde-355	172	5	in	in	ADP
ejde-355	172	6	(	(	PUNCT
ejde-355	172	7	4.6)-(4.7	4.6)-(4.7	NUM
ejde-355	172	8	)	)	PUNCT
ejde-355	172	9	,	,	PUNCT
ejde-355	172	10	we	we	PRON
ejde-355	172	11	obtain	obtain	VERB
ejde-355	172	12	the	the	DET
ejde-355	172	13	equations	equation	NOUN
ejde-355	172	14	−	−	ADP
ejde-355	172	15	1	1	NUM
ejde-355	172	16	2	2	NUM
ejde-355	172	17	µo(x	µo(x	PUNCT
ejde-355	172	18	)	)	PUNCT
ejde-355	173	1	+	+	CCONJ
ejde-355	173	2	∫	∫	PROPN
ejde-355	173	3	∂ωo	∂ωo	NOUN
ejde-355	173	4	νωo(x	νωo(x	PROPN
ejde-355	173	5	)	)	PUNCT
ejde-355	173	6	·	·	PUNCT
ejde-355	174	1	∇s2(x−	∇s2(x−	ADP
ejde-355	174	2	y)µo(y	y)µo(y	NUM
ejde-355	174	3	)	)	PUNCT
ejde-355	174	4	dσy	dσy	PROPN
ejde-355	174	5	+	+	CCONJ
ejde-355	174	6	νωo(x	νωo(x	PROPN
ejde-355	174	7	)	)	PUNCT
ejde-355	174	8	·	·	PUNCT
ejde-355	174	9	∇s2(x	∇s2(x	NUM
ejde-355	174	10	)	)	PUNCT
ejde-355	174	11	∫	∫	PROPN
ejde-355	175	1	∂ωi	∂ωi	NOUN
ejde-355	175	2	µi(s	µi(s	NUM
ejde-355	175	3	)	)	PUNCT
ejde-355	175	4	dσs	dσs	NOUN
ejde-355	175	5	=	=	PUNCT
ejde-355	175	6	go(x	go(x	X
ejde-355	175	7	)	)	PUNCT
ejde-355	175	8	∀x	∀x	VERB
ejde-355	175	9	∈	∈	PROPN
ejde-355	175	10	∂ωo	∂ωo	NOUN
ejde-355	175	11	,	,	PUNCT
ejde-355	175	12	(	(	PUNCT
ejde-355	175	13	4.8	4.8	NUM
ejde-355	175	14	)	)	PUNCT
ejde-355	175	15	1	1	NUM
ejde-355	175	16	2	2	NUM
ejde-355	175	17	µi(t	µi(t	NUM
ejde-355	175	18	)	)	PUNCT
ejde-355	175	19	+	+	CCONJ
ejde-355	175	20	∫	∫	X
ejde-355	175	21	∂ωi	∂ωi	PROPN
ejde-355	175	22	νωi(t	νωi(t	PROPN
ejde-355	175	23	)	)	PUNCT
ejde-355	175	24	·	·	PUNCT
ejde-355	176	1	∇s2(t−	∇s2(t−	PRON
ejde-355	176	2	s)µi(s	s)µi(s	NOUN
ejde-355	176	3	)	)	PUNCT
ejde-355	176	4	dσs	dσs	NOUN
ejde-355	176	5	=	=	SYM
ejde-355	176	6	f̃	f̃	PROPN
ejde-355	176	7	(	(	PUNCT
ejde-355	176	8	l0	l0	PROPN
ejde-355	176	9	2π	2π	PROPN
ejde-355	176	10	∫	∫	INTJ
ejde-355	176	11	∂ωi	∂ωi	PROPN
ejde-355	176	12	µi	µi	PROPN
ejde-355	176	13	dσ	dσ	PROPN
ejde-355	176	14	+	+	PROPN
ejde-355	176	15	ξ	ξ	PROPN
ejde-355	176	16	,	,	PUNCT
ejde-355	176	17	η0	η0	ADJ
ejde-355	176	18	)	)	PUNCT
ejde-355	176	19	+	+	CCONJ
ejde-355	176	20	gi(t)r0	gi(t)r0	NOUN
ejde-355	176	21	∀t	∀t	PROPN
ejde-355	176	22	∈	∈	PROPN
ejde-355	176	23	∂ωi	∂ωi	NOUN
ejde-355	176	24	.	.	PUNCT
ejde-355	177	1	(	(	PUNCT
ejde-355	177	2	4.9	4.9	NUM
ejde-355	177	3	)	)	PUNCT
ejde-355	177	4	for	for	ADP
ejde-355	177	5	ε	ε	PROPN
ejde-355	177	6	∈]0	∈]0	X
ejde-355	177	7	,	,	PUNCT
ejde-355	177	8	ε1	ε1	PROPN
ejde-355	177	9	[	[	PUNCT
ejde-355	177	10	small	small	ADJ
ejde-355	177	11	enough	enough	ADV
ejde-355	177	12	,	,	PUNCT
ejde-355	177	13	we	we	PRON
ejde-355	177	14	would	would	AUX
ejde-355	177	15	like	like	VERB
ejde-355	177	16	to	to	PART
ejde-355	177	17	prove	prove	VERB
ejde-355	177	18	the	the	DET
ejde-355	177	19	existence	existence	NOUN
ejde-355	177	20	of	of	ADP
ejde-355	177	21	solutions	solution	NOUN
ejde-355	177	22	(	(	PUNCT
ejde-355	177	23	µo	µo	NOUN
ejde-355	177	24	,	,	PUNCT
ejde-355	177	25	µi	µi	PROPN
ejde-355	177	26	,	,	PUNCT
ejde-355	177	27	ξ	ξ	PROPN
ejde-355	177	28	)	)	PUNCT
ejde-355	177	29	to	to	ADP
ejde-355	177	30	(	(	PUNCT
ejde-355	177	31	4.6)-(4.7	4.6)-(4.7	NUM
ejde-355	177	32	)	)	PUNCT
ejde-355	177	33	around	around	ADP
ejde-355	177	34	a	a	DET
ejde-355	177	35	solution	solution	NOUN
ejde-355	177	36	of	of	ADP
ejde-355	177	37	the	the	DET
ejde-355	177	38	limiting	limit	VERB
ejde-355	177	39	system	system	NOUN
ejde-355	177	40	(	(	PUNCT
ejde-355	177	41	4.8)-(4.9	4.8)-(4.9	NOUN
ejde-355	177	42	)	)	PUNCT
ejde-355	177	43	.	.	PUNCT
ejde-355	178	1	therefore	therefore	ADV
ejde-355	178	2	,	,	PUNCT
ejde-355	178	3	we	we	PRON
ejde-355	178	4	further	far	ADV
ejde-355	178	5	assume	assume	VERB
ejde-355	178	6	that	that	SCONJ
ejde-355	178	7	system	system	NOUN
ejde-355	178	8	(	(	PUNCT
ejde-355	178	9	4.8)-(4.9	4.8)-(4.9	NOUN
ejde-355	178	10	)	)	PUNCT
ejde-355	178	11	in	in	ADP
ejde-355	178	12	the	the	DET
ejde-355	178	13	unknown	unknown	ADJ
ejde-355	178	14	(	(	PUNCT
ejde-355	178	15	µo	µo	PROPN
ejde-355	178	16	,	,	PUNCT
ejde-355	178	17	µi	µi	PROPN
ejde-355	178	18	,	,	PUNCT
ejde-355	178	19	ξ	ξ	PROPN
ejde-355	178	20	)	)	PUNCT
ejde-355	178	21	admits	admit	VERB
ejde-355	178	22	a	a	DET
ejde-355	178	23	solution	solution	NOUN
ejde-355	178	24	(	(	PUNCT
ejde-355	178	25	µ̃o	µ̃o	NOUN
ejde-355	178	26	,	,	PUNCT
ejde-355	178	27	µ̃i	µ̃i	NOUN
ejde-355	178	28	,	,	PUNCT
ejde-355	178	29	ξ̃	ξ̃	PROPN
ejde-355	178	30	)	)	PUNCT
ejde-355	178	31	in	in	ADP
ejde-355	178	32	c0,α(∂ωo)0	c0,α(∂ωo)0	NUM
ejde-355	178	33	×	×	NOUN
ejde-355	178	34	c0,α(∂ωi)×	c0,α(∂ωi)×	PROPN
ejde-355	178	35	r.	r.	PROPN
ejde-355	178	36	(	(	PUNCT
ejde-355	178	37	4.10	4.10	NUM
ejde-355	178	38	)	)	PUNCT
ejde-355	178	39	we	we	PRON
ejde-355	178	40	now	now	ADV
ejde-355	178	41	note	note	VERB
ejde-355	178	42	that	that	SCONJ
ejde-355	178	43	if	if	SCONJ
ejde-355	178	44	(	(	PUNCT
ejde-355	178	45	µ̃o	µ̃o	NOUN
ejde-355	178	46	,	,	PUNCT
ejde-355	178	47	µ̃i	µ̃i	NOUN
ejde-355	178	48	,	,	PUNCT
ejde-355	178	49	ξ̃	ξ̃	PROPN
ejde-355	178	50	)	)	PUNCT
ejde-355	178	51	is	be	AUX
ejde-355	178	52	a	a	DET
ejde-355	178	53	solution	solution	NOUN
ejde-355	178	54	of	of	ADP
ejde-355	178	55	the	the	DET
ejde-355	178	56	system	system	NOUN
ejde-355	178	57	(	(	PUNCT
ejde-355	178	58	4.8)-(4.9	4.8)-(4.9	NOUN
ejde-355	178	59	)	)	PUNCT
ejde-355	178	60	,	,	PUNCT
ejde-355	178	61	by	by	ADP
ejde-355	178	62	integrating	integrate	VERB
ejde-355	178	63	(	(	PUNCT
ejde-355	178	64	4.8	4.8	NUM
ejde-355	178	65	)	)	PUNCT
ejde-355	178	66	on	on	ADP
ejde-355	178	67	∂ωo	∂ωo	NOUN
ejde-355	178	68	and	and	CCONJ
ejde-355	178	69	by	by	ADP
ejde-355	178	70	the	the	DET
ejde-355	178	71	equalities∫	equalities∫	NOUN
ejde-355	178	72	∂ωo	∂ωo	PROPN
ejde-355	178	73	∫	∫	PROPN
ejde-355	178	74	∂ωo	∂ωo	PROPN
ejde-355	178	75	νωo(x	νωo(x	PROPN
ejde-355	178	76	)	)	PUNCT
ejde-355	178	77	·	·	PUNCT
ejde-355	178	78	∇s2(x−	∇s2(x−	ADV
ejde-355	178	79	y)µ̃o(y	y)µ̃o(y	X
ejde-355	178	80	)	)	PUNCT
ejde-355	178	81	dσy	dσy	PROPN
ejde-355	178	82	dσx	dσx	NOUN
ejde-355	178	83	=	=	SYM
ejde-355	178	84	1	1	NUM
ejde-355	178	85	2	2	NUM
ejde-355	178	86	∫	∫	NOUN
ejde-355	178	87	∂ωo	∂ωo	NOUN
ejde-355	178	88	µ̃o(y	µ̃o(y	NOUN
ejde-355	178	89	)	)	PUNCT
ejde-355	178	90	dσy	dσy	PROPN
ejde-355	178	91	(	(	PUNCT
ejde-355	178	92	cf	cf	NOUN
ejde-355	178	93	.	.	PUNCT
ejde-355	179	1	[	[	X
ejde-355	179	2	9	9	NUM
ejde-355	179	3	,	,	PUNCT
ejde-355	179	4	lemma	lemma	PROPN
ejde-355	179	5	6.11	6.11	NUM
ejde-355	179	6	]	]	PUNCT
ejde-355	179	7	)	)	PUNCT
ejde-355	179	8	and	and	CCONJ
ejde-355	179	9	∫	∫	PROPN
ejde-355	179	10	∂ωo	∂ωo	PROPN
ejde-355	179	11	νωo(x	νωo(x	PROPN
ejde-355	179	12	)	)	PUNCT
ejde-355	179	13	·	·	PUNCT
ejde-355	179	14	∇s2(x	∇s2(x	NUM
ejde-355	179	15	)	)	PUNCT
ejde-355	179	16	dσx	dσx	NOUN
ejde-355	179	17	=	=	SYM
ejde-355	179	18	1	1	NUM
ejde-355	179	19	(	(	PUNCT
ejde-355	179	20	cf	cf	NOUN
ejde-355	179	21	.	.	PUNCT
ejde-355	180	1	[	[	X
ejde-355	180	2	9	9	NUM
ejde-355	180	3	,	,	PUNCT
ejde-355	180	4	corollary	corollary	ADJ
ejde-355	180	5	4.6	4.6	NUM
ejde-355	180	6	]	]	PUNCT
ejde-355	180	7	)	)	PUNCT
ejde-355	180	8	,	,	PUNCT
ejde-355	180	9	we	we	PRON
ejde-355	180	10	must	must	AUX
ejde-355	180	11	have∫	have∫	VERB
ejde-355	180	12	∂ωi	∂ωi	PROPN
ejde-355	180	13	µ̃i(s	µ̃i(s	NOUN
ejde-355	180	14	)	)	PUNCT
ejde-355	180	15	dσs	dσs	NOUN
ejde-355	180	16	=	=	SYM
ejde-355	180	17	∫	∫	PROPN
ejde-355	180	18	∂ωo	∂ωo	NOUN
ejde-355	180	19	go(x	go(x	NUM
ejde-355	180	20	)	)	PUNCT
ejde-355	180	21	dσx	dσx	NOUN
ejde-355	180	22	.	.	PUNCT
ejde-355	181	1	this	this	PRON
ejde-355	181	2	implies	imply	VERB
ejde-355	181	3	that	that	SCONJ
ejde-355	181	4	the	the	DET
ejde-355	181	5	triple	triple	ADJ
ejde-355	181	6	(	(	PUNCT
ejde-355	181	7	µ̃o	µ̃o	NOUN
ejde-355	181	8	,	,	PUNCT
ejde-355	181	9	µ̃i	µ̃i	NOUN
ejde-355	181	10	,	,	PUNCT
ejde-355	181	11	ξ̃	ξ̃	PROPN
ejde-355	181	12	)	)	PUNCT
ejde-355	181	13	in	in	ADP
ejde-355	181	14	c0,α(∂ωo)0	c0,α(∂ωo)0	NUM
ejde-355	181	15	×	×	NOUN
ejde-355	181	16	c0,α(∂ωi)×	c0,α(∂ωi)×	PROPN
ejde-355	181	17	r	r	NOUN
ejde-355	181	18	is	be	AUX
ejde-355	181	19	a	a	DET
ejde-355	181	20	solution	solution	NOUN
ejde-355	181	21	of	of	ADP
ejde-355	181	22	system	system	NOUN
ejde-355	181	23	(	(	PUNCT
ejde-355	181	24	4.11)–(4.13	4.11)–(4.13	NOUN
ejde-355	181	25	)	)	PUNCT
ejde-355	181	26	below	below	ADP
ejde-355	181	27	−	−	PROPN
ejde-355	181	28	1	1	NUM
ejde-355	181	29	2	2	NUM
ejde-355	181	30	µo(x	µo(x	PUNCT
ejde-355	181	31	)	)	PUNCT
ejde-355	181	32	+	+	CCONJ
ejde-355	181	33	∫	∫	PROPN
ejde-355	181	34	∂ωo	∂ωo	NOUN
ejde-355	181	35	νωo(x	νωo(x	PROPN
ejde-355	181	36	)	)	PUNCT
ejde-355	181	37	·	·	PUNCT
ejde-355	181	38	∇s2(x−	∇s2(x−	ADP
ejde-355	181	39	y)µo(y	y)µo(y	NUM
ejde-355	181	40	)	)	PUNCT
ejde-355	181	41	dσy	dσy	PROPN
ejde-355	181	42	=	=	SYM
ejde-355	181	43	go(x)−	go(x)−	PROPN
ejde-355	181	44	νωo(x	νωo(x	PROPN
ejde-355	181	45	)	)	PUNCT
ejde-355	181	46	·	·	PUNCT
ejde-355	181	47	∇s2(x	∇s2(x	NUM
ejde-355	181	48	)	)	PUNCT
ejde-355	181	49	∫	∫	PROPN
ejde-355	181	50	∂ωo	∂ωo	NOUN
ejde-355	181	51	go(y	go(y	NOUN
ejde-355	181	52	)	)	PUNCT
ejde-355	181	53	dσy	dσy	PROPN
ejde-355	181	54	∀x	∀x	PUNCT
ejde-355	181	55	∈	∈	PROPN
ejde-355	181	56	∂ωo	∂ωo	NOUN
ejde-355	181	57	,	,	PUNCT
ejde-355	181	58	(	(	PUNCT
ejde-355	181	59	4.11	4.11	NUM
ejde-355	181	60	)	)	PUNCT
ejde-355	181	61	1	1	NUM
ejde-355	181	62	2	2	NUM
ejde-355	181	63	µi(t	µi(t	NUM
ejde-355	181	64	)	)	PUNCT
ejde-355	181	65	+	+	CCONJ
ejde-355	181	66	∫	∫	X
ejde-355	181	67	∂ωi	∂ωi	PROPN
ejde-355	181	68	νωi(t	νωi(t	PROPN
ejde-355	181	69	)	)	PUNCT
ejde-355	181	70	·	·	PUNCT
ejde-355	182	1	∇s2(t−	∇s2(t−	PRON
ejde-355	182	2	s)µi(s	s)µi(s	NOUN
ejde-355	182	3	)	)	PUNCT
ejde-355	182	4	dσs	dσs	NOUN
ejde-355	182	5	=	=	SYM
ejde-355	182	6	f̃	f̃	PROPN
ejde-355	182	7	(	(	PUNCT
ejde-355	182	8	l0	l0	PROPN
ejde-355	182	9	2π	2π	PROPN
ejde-355	182	10	∫	∫	PROPN
ejde-355	183	1	∂ωo	∂ωo	NOUN
ejde-355	183	2	go	go	VERB
ejde-355	183	3	dσ	dσ	PROPN
ejde-355	183	4	+	+	CCONJ
ejde-355	183	5	ξ	ξ	PROPN
ejde-355	183	6	,	,	PUNCT
ejde-355	183	7	η0	η0	ADJ
ejde-355	183	8	)	)	PUNCT
ejde-355	184	1	+	+	CCONJ
ejde-355	184	2	gi(t)r0	gi(t)r0	NOUN
ejde-355	184	3	∀t	∀t	PROPN
ejde-355	184	4	∈	∈	NOUN
ejde-355	184	5	∂ωi	∂ωi	NOUN
ejde-355	184	6	,	,	PUNCT
ejde-355	184	7	(	(	PUNCT
ejde-355	184	8	4.12	4.12	NUM
ejde-355	184	9	)	)	PUNCT
ejde-355	184	10	∫	∫	PROPN
ejde-355	184	11	∂ωi	∂ωi	NOUN
ejde-355	184	12	µi(s	µi(s	NUM
ejde-355	184	13	)	)	PUNCT
ejde-355	184	14	dσs	dσs	NOUN
ejde-355	184	15	=	=	SYM
ejde-355	184	16	∫	∫	PROPN
ejde-355	184	17	∂ωo	∂ωo	NOUN
ejde-355	184	18	go(x	go(x	NUM
ejde-355	184	19	)	)	PUNCT
ejde-355	184	20	dσx	dσx	NOUN
ejde-355	184	21	.	.	PUNCT
ejde-355	185	1	(	(	PUNCT
ejde-355	185	2	4.13	4.13	NUM
ejde-355	185	3	)	)	PUNCT
ejde-355	185	4	by	by	ADP
ejde-355	185	5	[	[	X
ejde-355	185	6	9	9	NUM
ejde-355	185	7	,	,	PUNCT
ejde-355	185	8	theorem	theorem	VERB
ejde-355	185	9	6.25	6.25	NUM
ejde-355	185	10	]	]	PUNCT
ejde-355	185	11	,	,	PUNCT
ejde-355	185	12	we	we	PRON
ejde-355	185	13	deduce	deduce	VERB
ejde-355	185	14	that	that	SCONJ
ejde-355	185	15	there	there	PRON
ejde-355	185	16	exists	exist	VERB
ejde-355	185	17	a	a	DET
ejde-355	185	18	unique	unique	ADJ
ejde-355	185	19	solution	solution	NOUN
ejde-355	185	20	µ̃o	µ̃o	NOUN
ejde-355	185	21	in	in	ADP
ejde-355	185	22	c0,α(∂ωo)0	c0,α(∂ωo)0	PROPN
ejde-355	185	23	of	of	ADP
ejde-355	185	24	(	(	PUNCT
ejde-355	185	25	4.11	4.11	NUM
ejde-355	185	26	)	)	PUNCT
ejde-355	185	27	.	.	PUNCT
ejde-355	186	1	in	in	ADP
ejde-355	186	2	other	other	ADJ
ejde-355	186	3	words	word	NOUN
ejde-355	186	4	,	,	PUNCT
ejde-355	186	5	if	if	SCONJ
ejde-355	186	6	there	there	PRON
ejde-355	186	7	exists	exist	VERB
ejde-355	186	8	a	a	DET
ejde-355	186	9	solution	solution	NOUN
ejde-355	186	10	(	(	PUNCT
ejde-355	186	11	µ̃o	µ̃o	NOUN
ejde-355	186	12	,	,	PUNCT
ejde-355	186	13	µ̃i	µ̃i	NOUN
ejde-355	186	14	,	,	PUNCT
ejde-355	186	15	ξ̃	ξ̃	PROPN
ejde-355	186	16	)	)	PUNCT
ejde-355	186	17	of	of	ADP
ejde-355	186	18	the	the	DET
ejde-355	186	19	system	system	NOUN
ejde-355	186	20	(	(	PUNCT
ejde-355	186	21	4.8)-(4.9	4.8)-(4.9	NOUN
ejde-355	186	22	)	)	PUNCT
ejde-355	186	23	,	,	PUNCT
ejde-355	186	24	then	then	ADV
ejde-355	186	25	µ̃o	µ̃o	PROPN
ejde-355	186	26	is	be	AUX
ejde-355	186	27	determined	determine	VERB
ejde-355	186	28	as	as	ADP
ejde-355	186	29	the	the	DET
ejde-355	186	30	unique	unique	ADJ
ejde-355	186	31	solution	solution	NOUN
ejde-355	186	32	in	in	ADP
ejde-355	186	33	c0,α(∂ωo)0	c0,α(∂ωo)0	PROPN
ejde-355	186	34	of	of	ADP
ejde-355	186	35	(	(	PUNCT
ejde-355	186	36	4.11	4.11	NUM
ejde-355	186	37	)	)	PUNCT
ejde-355	186	38	.	.	PUNCT
ejde-355	187	1	10	10	NUM
ejde-355	187	2	p.	p.	NOUN
ejde-355	187	3	musolino	musolino	NOUN
ejde-355	187	4	,	,	PUNCT
ejde-355	187	5	m.	m.	NOUN
ejde-355	187	6	dutko	dutko	PROPN
ejde-355	187	7	,	,	PUNCT
ejde-355	187	8	g.	g.	PROPN
ejde-355	187	9	mishuris	mishuris	PROPN
ejde-355	187	10	ejde-2023/57	ejde-2023/57	NOUN
ejde-355	187	11	to	to	PART
ejde-355	187	12	have	have	VERB
ejde-355	187	13	a	a	DET
ejde-355	187	14	pair	pair	NOUN
ejde-355	187	15	(	(	PUNCT
ejde-355	187	16	µ̃i	µ̃i	NOUN
ejde-355	187	17	,	,	PUNCT
ejde-355	187	18	ξ̃	ξ̃	PROPN
ejde-355	187	19	)	)	PUNCT
ejde-355	187	20	in	in	ADP
ejde-355	187	21	c0,α(∂ωi)×	c0,α(∂ωi)×	PROPN
ejde-355	187	22	r	r	NOUN
ejde-355	187	23	solving	solving	NOUN
ejde-355	187	24	(	(	PUNCT
ejde-355	187	25	4.12)-(4.13	4.12)-(4.13	NUM
ejde-355	187	26	)	)	PUNCT
ejde-355	187	27	,	,	PUNCT
ejde-355	187	28	we	we	PRON
ejde-355	187	29	observe	observe	VERB
ejde-355	187	30	that	that	SCONJ
ejde-355	187	31	if	if	SCONJ
ejde-355	187	32	there	there	PRON
ejde-355	187	33	exists	exist	VERB
ejde-355	187	34	ξ̃	ξ̃	PROPN
ejde-355	187	35	∈	∈	NOUN
ejde-355	187	36	r	r	NOUN
ejde-355	187	37	such	such	ADJ
ejde-355	187	38	that∫	that∫	NOUN
ejde-355	187	39	∂ωo	∂ωo	NOUN
ejde-355	187	40	go(x	go(x	NUM
ejde-355	187	41	)	)	PUNCT
ejde-355	187	42	dσx	dσx	NOUN
ejde-355	187	43	=	=	PUNCT
ejde-355	187	44	|∂ωi|1f̃	|∂ωi|1f̃	PROPN
ejde-355	188	1	(	(	PUNCT
ejde-355	188	2	l0	l0	NOUN
ejde-355	188	3	2π	2π	PROPN
ejde-355	188	4	∫	∫	PROPN
ejde-355	188	5	∂ωo	∂ωo	NOUN
ejde-355	188	6	go	go	VERB
ejde-355	188	7	dσ	dσ	PROPN
ejde-355	188	8	+	+	CCONJ
ejde-355	188	9	ξ̃	ξ̃	PROPN
ejde-355	188	10	,	,	PUNCT
ejde-355	188	11	η0	η0	NOUN
ejde-355	188	12	)	)	PUNCT
ejde-355	189	1	+	+	CCONJ
ejde-355	189	2	∫	∫	PROPN
ejde-355	189	3	∂ωi	∂ωi	NOUN
ejde-355	189	4	gi(t	gi(t	NOUN
ejde-355	189	5	)	)	PUNCT
ejde-355	189	6	dσtr0	dσtr0	NOUN
ejde-355	190	1	(	(	PUNCT
ejde-355	190	2	4.14	4.14	NUM
ejde-355	190	3	)	)	PUNCT
ejde-355	190	4	then	then	ADV
ejde-355	190	5	[	[	X
ejde-355	190	6	9	9	NUM
ejde-355	190	7	,	,	PUNCT
ejde-355	190	8	corollary	corollary	NOUN
ejde-355	190	9	6.15	6.15	NUM
ejde-355	190	10	]	]	PUNCT
ejde-355	190	11	implies	imply	VERB
ejde-355	190	12	the	the	DET
ejde-355	190	13	existence	existence	NOUN
ejde-355	190	14	of	of	ADP
ejde-355	190	15	a	a	DET
ejde-355	190	16	unique	unique	ADJ
ejde-355	190	17	solution	solution	NOUN
ejde-355	190	18	µ̃i	µ̃i	NOUN
ejde-355	190	19	in	in	ADP
ejde-355	190	20	c0,α(∂ωi	c0,α(∂ωi	NOUN
ejde-355	190	21	)	)	PUNCT
ejde-355	190	22	of	of	ADP
ejde-355	190	23	1	1	NUM
ejde-355	190	24	2	2	NUM
ejde-355	190	25	µi(t	µi(t	NUM
ejde-355	190	26	)	)	PUNCT
ejde-355	191	1	+	+	CCONJ
ejde-355	191	2	∫	∫	X
ejde-355	191	3	∂ωi	∂ωi	PROPN
ejde-355	191	4	νωi(t	νωi(t	PROPN
ejde-355	191	5	)	)	PUNCT
ejde-355	191	6	·	·	PUNCT
ejde-355	192	1	∇s2(t−	∇s2(t−	PRON
ejde-355	192	2	s)µi(s	s)µi(s	NOUN
ejde-355	192	3	)	)	PUNCT
ejde-355	192	4	dσs	dσs	NOUN
ejde-355	192	5	=	=	SYM
ejde-355	192	6	f̃	f̃	PROPN
ejde-355	192	7	(	(	PUNCT
ejde-355	192	8	l0	l0	PROPN
ejde-355	192	9	2π	2π	PROPN
ejde-355	192	10	∫	∫	PROPN
ejde-355	193	1	∂ωo	∂ωo	NOUN
ejde-355	193	2	go	go	VERB
ejde-355	193	3	dσ	dσ	PROPN
ejde-355	193	4	+	+	CCONJ
ejde-355	193	5	ξ̃	ξ̃	PROPN
ejde-355	193	6	,	,	PUNCT
ejde-355	193	7	η0	η0	NOUN
ejde-355	193	8	)	)	PUNCT
ejde-355	194	1	+	+	CCONJ
ejde-355	194	2	gi(t)r0	gi(t)r0	NOUN
ejde-355	194	3	∀t	∀t	PROPN
ejde-355	194	4	∈	∈	NOUN
ejde-355	194	5	∂ωi	∂ωi	NOUN
ejde-355	194	6	,	,	PUNCT
ejde-355	194	7	and	and	CCONJ
ejde-355	194	8	such	such	ADJ
ejde-355	194	9	solution	solution	NOUN
ejde-355	194	10	satisfies	satisfie	NOUN
ejde-355	194	11	also∫	also∫	VERB
ejde-355	194	12	∂ωi	∂ωi	NOUN
ejde-355	194	13	µ̃i(s	µ̃i(s	NOUN
ejde-355	194	14	)	)	PUNCT
ejde-355	194	15	dσs	dσs	NOUN
ejde-355	194	16	=	=	SYM
ejde-355	194	17	∫	∫	PROPN
ejde-355	194	18	∂ωo	∂ωo	NOUN
ejde-355	194	19	go(x	go(x	NUM
ejde-355	194	20	)	)	PUNCT
ejde-355	194	21	dσx	dσx	NOUN
ejde-355	194	22	.	.	PUNCT
ejde-355	195	1	in	in	ADP
ejde-355	195	2	other	other	ADJ
ejde-355	195	3	words	word	NOUN
ejde-355	195	4	this	this	PRON
ejde-355	195	5	means	mean	VERB
ejde-355	195	6	that	that	SCONJ
ejde-355	195	7	if	if	SCONJ
ejde-355	195	8	there	there	PRON
ejde-355	195	9	exists	exist	VERB
ejde-355	195	10	ξ̃	ξ̃	PROPN
ejde-355	195	11	∈	∈	NOUN
ejde-355	195	12	r	r	NOUN
ejde-355	195	13	such	such	DET
ejde-355	195	14	that	that	DET
ejde-355	195	15	equation	equation	NOUN
ejde-355	195	16	(	(	PUNCT
ejde-355	195	17	4.14	4.14	NUM
ejde-355	195	18	)	)	PUNCT
ejde-355	195	19	holds	hold	VERB
ejde-355	195	20	,	,	PUNCT
ejde-355	195	21	then	then	ADV
ejde-355	195	22	there	there	PRON
ejde-355	195	23	exists	exist	VERB
ejde-355	195	24	a	a	DET
ejde-355	195	25	unique	unique	ADJ
ejde-355	195	26	pair	pair	NOUN
ejde-355	195	27	(	(	PUNCT
ejde-355	195	28	µ̃o	µ̃o	NOUN
ejde-355	195	29	,	,	PUNCT
ejde-355	195	30	µ̃i	µ̃i	NUM
ejde-355	195	31	)	)	PUNCT
ejde-355	195	32	in	in	ADP
ejde-355	195	33	c0,α(∂ωo)0	c0,α(∂ωo)0	NUM
ejde-355	195	34	×	×	NOUN
ejde-355	195	35	c0,α(∂ωi	c0,α(∂ωi	ADV
ejde-355	195	36	)	)	PUNCT
ejde-355	195	37	such	such	ADJ
ejde-355	195	38	that	that	SCONJ
ejde-355	195	39	the	the	DET
ejde-355	195	40	triple	triple	ADJ
ejde-355	195	41	(	(	PUNCT
ejde-355	195	42	µ̃o	µ̃o	NOUN
ejde-355	195	43	,	,	PUNCT
ejde-355	195	44	µ̃i	µ̃i	NOUN
ejde-355	195	45	,	,	PUNCT
ejde-355	195	46	ξ̃	ξ̃	PROPN
ejde-355	195	47	)	)	PUNCT
ejde-355	195	48	in	in	ADP
ejde-355	195	49	c0,α(∂ωo)0	c0,α(∂ωo)0	NUM
ejde-355	195	50	×	×	NOUN
ejde-355	195	51	c0,α(∂ωi)×	c0,α(∂ωi)×	PROPN
ejde-355	195	52	r	r	NOUN
ejde-355	195	53	solves	solve	NOUN
ejde-355	195	54	system	system	NOUN
ejde-355	195	55	(	(	PUNCT
ejde-355	195	56	4.8)-(4.9	4.8)-(4.9	NOUN
ejde-355	195	57	)	)	PUNCT
ejde-355	195	58	.	.	PUNCT
ejde-355	196	1	furthermore	furthermore	ADV
ejde-355	196	2	,	,	PUNCT
ejde-355	196	3	we	we	PRON
ejde-355	196	4	note	note	VERB
ejde-355	196	5	that	that	SCONJ
ejde-355	196	6	equality	equality	NOUN
ejde-355	196	7	(	(	PUNCT
ejde-355	196	8	4.14	4.14	NUM
ejde-355	196	9	)	)	PUNCT
ejde-355	196	10	can	can	AUX
ejde-355	196	11	be	be	AUX
ejde-355	196	12	rewritten	rewrite	VERB
ejde-355	196	13	as	as	ADP
ejde-355	196	14	f̃	f̃	PROPN
ejde-355	196	15	(	(	PUNCT
ejde-355	196	16	l0	l0	PROPN
ejde-355	196	17	2π	2π	PROPN
ejde-355	196	18	∫	∫	PROPN
ejde-355	196	19	∂ωo	∂ωo	NOUN
ejde-355	196	20	go	go	VERB
ejde-355	196	21	dσ	dσ	PROPN
ejde-355	196	22	+	+	CCONJ
ejde-355	196	23	ξ̃	ξ̃	PROPN
ejde-355	196	24	,	,	PUNCT
ejde-355	196	25	η0	η0	NOUN
ejde-355	196	26	)	)	PUNCT
ejde-355	196	27	=	=	SYM
ejde-355	196	28	1	1	NUM
ejde-355	196	29	|∂ωi|1	|∂ωi|1	NOUN
ejde-355	196	30	(	(	PUNCT
ejde-355	196	31	r0	r0	NOUN
ejde-355	196	32	∫	∫	PROPN
ejde-355	196	33	∂ωi	∂ωi	PROPN
ejde-355	196	34	gi	gi	PROPN
ejde-355	196	35	dσ	dσ	PROPN
ejde-355	196	36	−	−	PROPN
ejde-355	196	37	∫	∫	PROPN
ejde-355	196	38	∂ωo	∂ωo	NOUN
ejde-355	196	39	go	go	VERB
ejde-355	196	40	dσ	dσ	PROPN
ejde-355	196	41	)	)	PUNCT
ejde-355	196	42	.	.	PUNCT
ejde-355	197	1	(	(	PUNCT
ejde-355	197	2	4.15	4.15	NUM
ejde-355	197	3	)	)	PUNCT
ejde-355	197	4	thus	thus	ADV
ejde-355	197	5	,	,	PUNCT
ejde-355	197	6	in	in	ADP
ejde-355	197	7	particular	particular	ADJ
ejde-355	197	8	,	,	PUNCT
ejde-355	197	9	if	if	SCONJ
ejde-355	197	10	f̃	f̃	PROPN
ejde-355	197	11	(	(	PUNCT
ejde-355	197	12	·	·	PUNCT
ejde-355	197	13	,	,	PUNCT
ejde-355	197	14	η0	η0	NOUN
ejde-355	197	15	)	)	PUNCT
ejde-355	197	16	is	be	AUX
ejde-355	197	17	not	not	PART
ejde-355	197	18	globally	globally	ADV
ejde-355	197	19	invertible	invertible	ADJ
ejde-355	197	20	,	,	PUNCT
ejde-355	197	21	there	there	PRON
ejde-355	197	22	can	can	AUX
ejde-355	197	23	be	be	AUX
ejde-355	197	24	multiple	multiple	ADJ
ejde-355	197	25	ξ̃	ξ̃	PROPN
ejde-355	197	26	∈	∈	NOUN
ejde-355	197	27	r	r	NOUN
ejde-355	197	28	such	such	ADJ
ejde-355	197	29	that	that	SCONJ
ejde-355	197	30	(	(	PUNCT
ejde-355	197	31	4.15	4.15	NUM
ejde-355	197	32	)	)	PUNCT
ejde-355	197	33	holds	hold	VERB
ejde-355	197	34	.	.	PUNCT
ejde-355	198	1	in	in	ADP
ejde-355	198	2	the	the	DET
ejde-355	198	3	following	follow	VERB
ejde-355	198	4	proposition	proposition	NOUN
ejde-355	198	5	,	,	PUNCT
ejde-355	198	6	we	we	PRON
ejde-355	198	7	study	study	VERB
ejde-355	198	8	the	the	DET
ejde-355	198	9	solvability	solvability	NOUN
ejde-355	198	10	of	of	ADP
ejde-355	198	11	the	the	DET
ejde-355	198	12	system	system	NOUN
ejde-355	198	13	of	of	ADP
ejde-355	198	14	integral	integral	ADJ
ejde-355	198	15	equations	equation	NOUN
ejde-355	198	16	(	(	PUNCT
ejde-355	198	17	4.1)-(4.2	4.1)-(4.2	NOUN
ejde-355	198	18	)	)	PUNCT
ejde-355	198	19	,	,	PUNCT
ejde-355	198	20	by	by	ADP
ejde-355	198	21	applying	apply	VERB
ejde-355	198	22	the	the	DET
ejde-355	198	23	implicit	implicit	ADJ
ejde-355	198	24	function	function	NOUN
ejde-355	198	25	theorem	theorem	VERB
ejde-355	198	26	to	to	PART
ejde-355	198	27	λ	λ	SYM
ejde-355	198	28	,	,	PUNCT
ejde-355	198	29	under	under	ADP
ejde-355	198	30	suitable	suitable	ADJ
ejde-355	198	31	assumptions	assumption	NOUN
ejde-355	198	32	on	on	ADP
ejde-355	198	33	the	the	DET
ejde-355	198	34	partial	partial	ADJ
ejde-355	198	35	derivative	derivative	NOUN
ejde-355	198	36	∂τ	∂τ	PROPN
ejde-355	198	37	f̃	f̃	PROPN
ejde-355	198	38	(	(	PUNCT
ejde-355	198	39	l0	l0	PROPN
ejde-355	198	40	2π	2π	PROPN
ejde-355	198	41	∫	∫	PROPN
ejde-355	198	42	∂ωo	∂ωo	NOUN
ejde-355	198	43	g	g	NOUN
ejde-355	198	44	o	o	NOUN
ejde-355	198	45	dσ	dσ	PROPN
ejde-355	198	46	+	+	CCONJ
ejde-355	198	47	ξ̃	ξ̃	PROPN
ejde-355	198	48	,	,	PUNCT
ejde-355	198	49	η0	η0	NOUN
ejde-355	198	50	)	)	PUNCT
ejde-355	198	51	.	.	PUNCT
ejde-355	199	1	the	the	DET
ejde-355	199	2	symbol	symbol	NOUN
ejde-355	199	3	∂τ	∂τ	PROPN
ejde-355	199	4	f̃	f̃	PROPN
ejde-355	199	5	(	(	PUNCT
ejde-355	199	6	τ	τ	PROPN
ejde-355	199	7	,	,	PUNCT
ejde-355	199	8	η	η	NOUN
ejde-355	199	9	)	)	PUNCT
ejde-355	199	10	denotes	denote	VERB
ejde-355	199	11	the	the	DET
ejde-355	199	12	partial	partial	ADJ
ejde-355	199	13	derivative	derivative	NOUN
ejde-355	199	14	of	of	ADP
ejde-355	199	15	f̃	f̃	PROPN
ejde-355	199	16	with	with	ADP
ejde-355	199	17	respect	respect	NOUN
ejde-355	199	18	to	to	ADP
ejde-355	199	19	the	the	DET
ejde-355	199	20	first	first	ADJ
ejde-355	199	21	variable	variable	NOUN
ejde-355	199	22	.	.	PUNCT
ejde-355	200	1	proposition	proposition	NOUN
ejde-355	200	2	4.1	4.1	NUM
ejde-355	200	3	.	.	PUNCT
ejde-355	201	1	let	let	VERB
ejde-355	201	2	assumptions	assumption	NOUN
ejde-355	201	3	(	(	PUNCT
ejde-355	201	4	3.3	3.3	NUM
ejde-355	201	5	)	)	PUNCT
ejde-355	201	6	and	and	CCONJ
ejde-355	201	7	(	(	PUNCT
ejde-355	201	8	4.3	4.3	NUM
ejde-355	201	9	)	)	PUNCT
ejde-355	201	10	hold	hold	NOUN
ejde-355	201	11	.	.	PUNCT
ejde-355	202	1	let	let	VERB
ejde-355	202	2	(	(	PUNCT
ejde-355	202	3	µ̃o	µ̃o	NOUN
ejde-355	202	4	,	,	PUNCT
ejde-355	202	5	µ̃i	µ̃i	NOUN
ejde-355	202	6	,	,	PUNCT
ejde-355	202	7	ξ̃	ξ̃	PROPN
ejde-355	202	8	)	)	PUNCT
ejde-355	202	9	be	be	VERB
ejde-355	202	10	as	as	ADP
ejde-355	202	11	in	in	ADP
ejde-355	202	12	assumption	assumption	NOUN
ejde-355	202	13	(	(	PUNCT
ejde-355	202	14	4.10	4.10	NUM
ejde-355	202	15	)	)	PUNCT
ejde-355	202	16	.	.	PUNCT
ejde-355	203	1	assume	assume	VERB
ejde-355	203	2	that	that	SCONJ
ejde-355	203	3	∂τ	∂τ	PROPN
ejde-355	203	4	f̃	f̃	PROPN
ejde-355	203	5	(	(	PUNCT
ejde-355	203	6	l0	l0	PROPN
ejde-355	203	7	2π	2π	PROPN
ejde-355	203	8	∫	∫	PROPN
ejde-355	203	9	∂ωo	∂ωo	NOUN
ejde-355	203	10	go	go	VERB
ejde-355	203	11	dσ	dσ	PROPN
ejde-355	203	12	+	+	CCONJ
ejde-355	203	13	ξ̃	ξ̃	PROPN
ejde-355	203	14	,	,	PUNCT
ejde-355	203	15	η0	η0	NOUN
ejde-355	203	16	)	)	PUNCT
ejde-355	203	17	6=	6=	ADP
ejde-355	203	18	0	0	NUM
ejde-355	203	19	.	.	PUNCT
ejde-355	204	1	then	then	ADV
ejde-355	204	2	there	there	PRON
ejde-355	204	3	exist	exist	VERB
ejde-355	204	4	ε2	ε2	ADJ
ejde-355	204	5	∈]0	∈]0	ADV
ejde-355	204	6	,	,	PUNCT
ejde-355	204	7	ε1	ε1	PROPN
ejde-355	204	8	[	[	X
ejde-355	204	9	,	,	PUNCT
ejde-355	204	10	an	an	DET
ejde-355	204	11	open	open	ADJ
ejde-355	204	12	neighborhood	neighborhood	NOUN
ejde-355	204	13	u	u	NOUN
ejde-355	204	14	of	of	ADP
ejde-355	204	15	(	(	PUNCT
ejde-355	204	16	0	0	NUM
ejde-355	204	17	,	,	PUNCT
ejde-355	204	18	l0	l0	PROPN
ejde-355	204	19	,	,	PUNCT
ejde-355	204	20	η0	η0	NOUN
ejde-355	204	21	,	,	PUNCT
ejde-355	204	22	r0	r0	NOUN
ejde-355	204	23	)	)	PUNCT
ejde-355	204	24	in	in	ADP
ejde-355	204	25	rm+3	rm+3	PROPN
ejde-355	204	26	,	,	PUNCT
ejde-355	204	27	an	an	DET
ejde-355	204	28	open	open	ADJ
ejde-355	204	29	neighborhood	neighborhood	NOUN
ejde-355	204	30	v	v	X
ejde-355	204	31	of	of	ADP
ejde-355	204	32	(	(	PUNCT
ejde-355	204	33	µ̃o	µ̃o	NOUN
ejde-355	204	34	,	,	PUNCT
ejde-355	204	35	µ̃i	µ̃i	NOUN
ejde-355	204	36	,	,	PUNCT
ejde-355	204	37	ξ̃	ξ̃	PROPN
ejde-355	204	38	)	)	PUNCT
ejde-355	204	39	in	in	ADP
ejde-355	204	40	c0,α(∂ωo)0×c0,α(∂ωi)×r	c0,α(∂ωo)0×c0,α(∂ωi)×r	NOUN
ejde-355	204	41	,	,	PUNCT
ejde-355	204	42	and	and	CCONJ
ejde-355	204	43	a	a	DET
ejde-355	204	44	real	real	ADJ
ejde-355	204	45	analytic	analytic	ADJ
ejde-355	204	46	map	map	NOUN
ejde-355	204	47	(	(	PUNCT
ejde-355	204	48	mo	mo	PROPN
ejde-355	204	49	,	,	PUNCT
ejde-355	204	50	m	m	VERB
ejde-355	204	51	i	i	PRON
ejde-355	204	52	,	,	PUNCT
ejde-355	204	53	ξ	ξ	PROPN
ejde-355	204	54	)	)	PUNCT
ejde-355	204	55	from	from	ADP
ejde-355	204	56	]	]	PUNCT
ejde-355	204	57	−	−	PROPN
ejde-355	204	58	ε2	ε2	ADJ
ejde-355	204	59	,	,	PUNCT
ejde-355	204	60	ε2[×u	ε2[×u	ADJ
ejde-355	204	61	to	to	ADP
ejde-355	204	62	v	v	ADP
ejde-355	204	63	such	such	ADJ
ejde-355	204	64	that	that	PRON
ejde-355	204	65	(	(	PUNCT
ejde-355	204	66	εδ(ε	εδ(ε	NOUN
ejde-355	204	67	)	)	PUNCT
ejde-355	204	68	,	,	PUNCT
ejde-355	204	69	εδ(ε	εδ(ε	VERB
ejde-355	204	70	)	)	PUNCT
ejde-355	204	71	log	log	PROPN
ejde-355	204	72	ε	ε	PROPN
ejde-355	204	73	,	,	PUNCT
ejde-355	204	74	η(ε	η(ε	NOUN
ejde-355	204	75	)	)	PUNCT
ejde-355	204	76	,	,	PUNCT
ejde-355	204	77	ε	ε	PROPN
ejde-355	204	78	ρ(ε	ρ(ε	NUM
ejde-355	204	79	)	)	PUNCT
ejde-355	204	80	)	)	PUNCT
ejde-355	205	1	∈	∈	PROPN
ejde-355	205	2	u	u	NOUN
ejde-355	205	3	∀ε	∀ε	PROPN
ejde-355	205	4	∈]0	∈]0	X
ejde-355	205	5	,	,	PUNCT
ejde-355	205	6	ε2	ε2	PROPN
ejde-355	205	7	[	[	PUNCT
ejde-355	205	8	,	,	PUNCT
ejde-355	205	9	and	and	CCONJ
ejde-355	205	10	such	such	ADJ
ejde-355	205	11	that	that	SCONJ
ejde-355	205	12	the	the	DET
ejde-355	205	13	set	set	NOUN
ejde-355	205	14	of	of	ADP
ejde-355	205	15	zeros	zero	NOUN
ejde-355	205	16	of	of	ADP
ejde-355	205	17	λ	λ	PROPN
ejde-355	205	18	in	in	ADP
ejde-355	205	19	]	]	PUNCT
ejde-355	205	20	−	−	PROPN
ejde-355	205	21	ε2	ε2	ADJ
ejde-355	205	22	,	,	PUNCT
ejde-355	205	23	ε2[×u	ε2[×u	ADJ
ejde-355	205	24	×	×	NOUN
ejde-355	205	25	v	v	ADP
ejde-355	205	26	coincides	coincide	VERB
ejde-355	205	27	with	with	ADP
ejde-355	205	28	the	the	DET
ejde-355	205	29	graph	graph	NOUN
ejde-355	205	30	of	of	ADP
ejde-355	205	31	(	(	PUNCT
ejde-355	205	32	mo	mo	PROPN
ejde-355	205	33	,	,	PUNCT
ejde-355	205	34	m	m	VERB
ejde-355	205	35	i	i	PRON
ejde-355	205	36	,	,	PUNCT
ejde-355	205	37	ξ	ξ	PROPN
ejde-355	205	38	)	)	PUNCT
ejde-355	205	39	.	.	PUNCT
ejde-355	206	1	in	in	ADP
ejde-355	206	2	particular	particular	ADJ
ejde-355	206	3	,	,	PUNCT
ejde-355	206	4	(	(	PUNCT
ejde-355	206	5	mo[0	mo[0	PROPN
ejde-355	206	6	,	,	PUNCT
ejde-355	206	7	0	0	NUM
ejde-355	206	8	,	,	PUNCT
ejde-355	206	9	l0	l0	PROPN
ejde-355	206	10	,	,	PUNCT
ejde-355	206	11	η0	η0	NOUN
ejde-355	206	12	,	,	PUNCT
ejde-355	206	13	r0],m	r0],m	PROPN
ejde-355	206	14	i[0	i[0	PROPN
ejde-355	206	15	,	,	PUNCT
ejde-355	206	16	0	0	NUM
ejde-355	206	17	,	,	PUNCT
ejde-355	206	18	l0	l0	PROPN
ejde-355	206	19	,	,	PUNCT
ejde-355	206	20	η0	η0	NOUN
ejde-355	206	21	,	,	PUNCT
ejde-355	206	22	r0],ξ[0	r0],ξ[0	PROPN
ejde-355	206	23	,	,	PUNCT
ejde-355	206	24	0	0	NUM
ejde-355	206	25	,	,	PUNCT
ejde-355	206	26	l0	l0	PROPN
ejde-355	206	27	,	,	PUNCT
ejde-355	206	28	η0	η0	NOUN
ejde-355	206	29	,	,	PUNCT
ejde-355	206	30	r0	r0	NOUN
ejde-355	206	31	]	]	PUNCT
ejde-355	206	32	)	)	PUNCT
ejde-355	207	1	=	=	SYM
ejde-355	207	2	(	(	PUNCT
ejde-355	207	3	µ̃o	µ̃o	NOUN
ejde-355	207	4	,	,	PUNCT
ejde-355	207	5	µ̃i	µ̃i	NOUN
ejde-355	207	6	,	,	PUNCT
ejde-355	207	7	ξ̃	ξ̃	PROPN
ejde-355	207	8	)	)	PUNCT
ejde-355	207	9	.	.	PUNCT
ejde-355	208	1	proof	proof	NOUN
ejde-355	208	2	.	.	PUNCT
ejde-355	209	1	standard	standard	ADJ
ejde-355	209	2	results	result	NOUN
ejde-355	209	3	of	of	ADP
ejde-355	209	4	classical	classical	ADJ
ejde-355	209	5	potential	potential	ADJ
ejde-355	209	6	theory	theory	NOUN
ejde-355	209	7	(	(	PUNCT
ejde-355	209	8	see	see	VERB
ejde-355	209	9	,	,	PUNCT
ejde-355	209	10	e.g.	e.g.	ADV
ejde-355	209	11	,	,	PUNCT
ejde-355	209	12	[	[	X
ejde-355	209	13	9	9	NUM
ejde-355	209	14	]	]	PUNCT
ejde-355	209	15	,	,	PUNCT
ejde-355	209	16	miranda	miranda	PROPN
ejde-355	210	1	[	[	X
ejde-355	210	2	31	31	NUM
ejde-355	210	3	]	]	PUNCT
ejde-355	210	4	,	,	PUNCT
ejde-355	210	5	lanza	lanza	X
ejde-355	210	6	de	de	PROPN
ejde-355	210	7	cristoforis	cristoforis	PROPN
ejde-355	210	8	and	and	CCONJ
ejde-355	210	9	rossi	rossi	ADJ
ejde-355	211	1	[	[	X
ejde-355	211	2	22	22	NUM
ejde-355	211	3	]	]	SYM
ejde-355	211	4	)	)	PUNCT
ejde-355	211	5	,	,	PUNCT
ejde-355	211	6	real	real	ADJ
ejde-355	211	7	analyticity	analyticity	NOUN
ejde-355	211	8	results	result	NOUN
ejde-355	211	9	for	for	ADP
ejde-355	211	10	integral	integral	ADJ
ejde-355	211	11	operators	operator	NOUN
ejde-355	211	12	with	with	ADP
ejde-355	211	13	real	real	ADJ
ejde-355	211	14	analytic	analytic	ADJ
ejde-355	211	15	kernel	kernel	NOUN
ejde-355	211	16	[	[	X
ejde-355	211	17	21	21	NUM
ejde-355	211	18	]	]	PUNCT
ejde-355	211	19	,	,	PUNCT
ejde-355	211	20	assumption	assumption	NOUN
ejde-355	211	21	(	(	PUNCT
ejde-355	211	22	3.3	3.3	NUM
ejde-355	211	23	)	)	PUNCT
ejde-355	211	24	and	and	CCONJ
ejde-355	211	25	real	real	ADJ
ejde-355	211	26	analyticity	analyticity	NOUN
ejde-355	211	27	results	result	NOUN
ejde-355	211	28	for	for	ADP
ejde-355	211	29	the	the	DET
ejde-355	211	30	composition	composition	NOUN
ejde-355	211	31	operator	operator	NOUN
ejde-355	211	32	(	(	PUNCT
ejde-355	211	33	[	[	X
ejde-355	211	34	3	3	NUM
ejde-355	211	35	,	,	PUNCT
ejde-355	211	36	p.	p.	NOUN
ejde-355	211	37	10	10	NUM
ejde-355	211	38	]	]	PUNCT
ejde-355	211	39	,	,	PUNCT
ejde-355	211	40	[	[	X
ejde-355	211	41	16	16	NUM
ejde-355	211	42	]	]	PUNCT
ejde-355	211	43	,	,	PUNCT
ejde-355	211	44	and	and	CCONJ
ejde-355	211	45	valent	valent	NOUN
ejde-355	211	46	[	[	X
ejde-355	211	47	41	41	NUM
ejde-355	211	48	,	,	PUNCT
ejde-355	211	49	thm	thm	PROPN
ejde-355	211	50	.	.	PUNCT
ejde-355	212	1	5.2	5.2	NUM
ejde-355	212	2	]	]	PUNCT
ejde-355	212	3	)	)	PUNCT
ejde-355	212	4	imply	imply	VERB
ejde-355	212	5	that	that	SCONJ
ejde-355	212	6	λ	λ	PROPN
ejde-355	212	7	is	be	AUX
ejde-355	212	8	a	a	DET
ejde-355	212	9	real	real	ADJ
ejde-355	212	10	analytic	analytic	ADJ
ejde-355	212	11	operator	operator	NOUN
ejde-355	212	12	from	from	ADP
ejde-355	212	13	]	]	PUNCT
ejde-355	212	14	−	−	PROPN
ejde-355	212	15	ε1	ε1	PROPN
ejde-355	212	16	,	,	PUNCT
ejde-355	212	17	ε1[×rm+3	ε1[×rm+3	PROPN
ejde-355	212	18	×	×	VERB
ejde-355	212	19	c0,α(∂ωo)0	c0,α(∂ωo)0	NUM
ejde-355	212	20	×	×	PROPN
ejde-355	212	21	c0,α(∂ωi	c0,α(∂ωi	ADJ
ejde-355	212	22	)	)	PUNCT
ejde-355	212	23	×	×	NOUN
ejde-355	212	24	r	r	NOUN
ejde-355	212	25	to	to	ADP
ejde-355	212	26	ejde-2023/57	ejde-2023/57	NOUN
ejde-355	212	27	asymptotic	asymptotic	ADJ
ejde-355	212	28	analysis	analysis	NOUN
ejde-355	212	29	of	of	ADP
ejde-355	212	30	perturbed	perturb	VERB
ejde-355	212	31	robin	robin	PROPN
ejde-355	212	32	problems	problem	VERB
ejde-355	212	33	11	11	NUM
ejde-355	212	34	c0,α(∂ωo	c0,α(∂ωo	NOUN
ejde-355	212	35	)	)	PUNCT
ejde-355	212	36	×	×	NOUN
ejde-355	212	37	c0,α(∂ωi	c0,α(∂ωi	ADV
ejde-355	212	38	)	)	PUNCT
ejde-355	212	39	.	.	PUNCT
ejde-355	213	1	we	we	PRON
ejde-355	213	2	verify	verify	VERB
ejde-355	213	3	that	that	SCONJ
ejde-355	213	4	by	by	ADP
ejde-355	213	5	standard	standard	ADJ
ejde-355	213	6	calculus	calculus	NOUN
ejde-355	213	7	in	in	ADP
ejde-355	213	8	banach	banach	NOUN
ejde-355	213	9	space	space	NOUN
ejde-355	213	10	the	the	DET
ejde-355	213	11	partial	partial	ADJ
ejde-355	213	12	differential	differential	NOUN
ejde-355	213	13	∂(µo,µi	∂(µo,µi	PROPN
ejde-355	213	14	,	,	PUNCT
ejde-355	213	15	ξ)λ[0	ξ)λ[0	PROPN
ejde-355	213	16	,	,	PUNCT
ejde-355	213	17	0	0	NUM
ejde-355	213	18	,	,	PUNCT
ejde-355	213	19	l0	l0	PROPN
ejde-355	213	20	,	,	PUNCT
ejde-355	213	21	η0	η0	NOUN
ejde-355	213	22	,	,	PUNCT
ejde-355	213	23	r0	r0	NOUN
ejde-355	213	24	,	,	PUNCT
ejde-355	213	25	µ̃	µ̃	PROPN
ejde-355	213	26	o	o	PROPN
ejde-355	213	27	,	,	PUNCT
ejde-355	213	28	µ̃i	µ̃i	NUM
ejde-355	213	29	,	,	PUNCT
ejde-355	213	30	ξ̃	ξ̃	PROPN
ejde-355	213	31	]	]	PUNCT
ejde-355	213	32	of	of	ADP
ejde-355	213	33	λ	λ	PROPN
ejde-355	213	34	at	at	ADP
ejde-355	213	35	(	(	PUNCT
ejde-355	213	36	0	0	NUM
ejde-355	213	37	,	,	PUNCT
ejde-355	213	38	0	0	NUM
ejde-355	213	39	,	,	PUNCT
ejde-355	213	40	l0	l0	PROPN
ejde-355	213	41	,	,	PUNCT
ejde-355	213	42	η0	η0	NOUN
ejde-355	213	43	,	,	PUNCT
ejde-355	213	44	r0	r0	NOUN
ejde-355	213	45	,	,	PUNCT
ejde-355	213	46	µ̃	µ̃	PROPN
ejde-355	213	47	o	o	PROPN
ejde-355	213	48	,	,	PUNCT
ejde-355	213	49	µ̃i	µ̃i	NUM
ejde-355	213	50	,	,	PUNCT
ejde-355	213	51	ξ̃	ξ̃	PROPN
ejde-355	213	52	)	)	PUNCT
ejde-355	213	53	with	with	ADP
ejde-355	213	54	respect	respect	NOUN
ejde-355	213	55	to	to	ADP
ejde-355	213	56	the	the	DET
ejde-355	213	57	variable	variable	NOUN
ejde-355	213	58	(	(	PUNCT
ejde-355	213	59	µo	µo	PROPN
ejde-355	213	60	,	,	PUNCT
ejde-355	213	61	µi	µi	PROPN
ejde-355	213	62	,	,	PUNCT
ejde-355	213	63	ξ	ξ	X
ejde-355	213	64	)	)	PUNCT
ejde-355	213	65	is	be	AUX
ejde-355	213	66	delivered	deliver	VERB
ejde-355	213	67	by	by	ADP
ejde-355	213	68	∂(µo,µi	∂(µo,µi	PROPN
ejde-355	213	69	,	,	PUNCT
ejde-355	213	70	ξ)λ	ξ)λ	PUNCT
ejde-355	213	71	o[0	o[0	PROPN
ejde-355	213	72	,	,	PUNCT
ejde-355	213	73	0	0	NUM
ejde-355	213	74	,	,	PUNCT
ejde-355	213	75	l0	l0	PROPN
ejde-355	213	76	,	,	PUNCT
ejde-355	213	77	η0	η0	NOUN
ejde-355	213	78	,	,	PUNCT
ejde-355	213	79	r0	r0	NOUN
ejde-355	213	80	,	,	PUNCT
ejde-355	213	81	µ̃	µ̃	PROPN
ejde-355	213	82	o	o	PROPN
ejde-355	213	83	,	,	PUNCT
ejde-355	213	84	µ̃i	µ̃i	PROPN
ejde-355	213	85	,	,	PUNCT
ejde-355	213	86	ξ̃](µo	ξ̃](µo	PROPN
ejde-355	213	87	,	,	PUNCT
ejde-355	213	88	µi	µi	PROPN
ejde-355	213	89	,	,	PUNCT
ejde-355	213	90	ξ)(x	ξ)(x	PROPN
ejde-355	213	91	)	)	PUNCT
ejde-355	213	92	≡	≡	PROPN
ejde-355	213	93	−1	−1	NOUN
ejde-355	213	94	2	2	NUM
ejde-355	213	95	µo(x	µo(x	PUNCT
ejde-355	213	96	)	)	PUNCT
ejde-355	214	1	+	+	CCONJ
ejde-355	214	2	∫	∫	PROPN
ejde-355	214	3	∂ωo	∂ωo	NOUN
ejde-355	214	4	νωo(x	νωo(x	PROPN
ejde-355	214	5	)	)	PUNCT
ejde-355	214	6	·	·	PUNCT
ejde-355	215	1	∇s2(x−	∇s2(x−	ADP
ejde-355	215	2	y)µo(y	y)µo(y	NUM
ejde-355	215	3	)	)	PUNCT
ejde-355	215	4	dσy	dσy	PROPN
ejde-355	215	5	+	+	CCONJ
ejde-355	215	6	νωo(x	νωo(x	PROPN
ejde-355	215	7	)	)	PUNCT
ejde-355	215	8	·	·	PUNCT
ejde-355	215	9	∇s2(x	∇s2(x	NUM
ejde-355	215	10	)	)	PUNCT
ejde-355	215	11	∫	∫	PROPN
ejde-355	216	1	∂ωi	∂ωi	NOUN
ejde-355	216	2	µi(s	µi(s	NUM
ejde-355	216	3	)	)	PUNCT
ejde-355	216	4	dσs	dσs	PROPN
ejde-355	216	5	∀x	∀x	NUM
ejde-355	216	6	∈	∈	PROPN
ejde-355	216	7	∂ωo	∂ωo	NOUN
ejde-355	216	8	,	,	PUNCT
ejde-355	216	9	∂(µo,µi	∂(µo,µi	PROPN
ejde-355	216	10	,	,	PUNCT
ejde-355	216	11	ξ)λ	ξ)λ	NOUN
ejde-355	216	12	i[0	i[0	PROPN
ejde-355	216	13	,	,	PUNCT
ejde-355	216	14	0	0	NUM
ejde-355	216	15	,	,	PUNCT
ejde-355	216	16	l0	l0	PROPN
ejde-355	216	17	,	,	PUNCT
ejde-355	216	18	η0	η0	NOUN
ejde-355	216	19	,	,	PUNCT
ejde-355	216	20	r0	r0	NOUN
ejde-355	216	21	,	,	PUNCT
ejde-355	216	22	µ̃	µ̃	PROPN
ejde-355	216	23	o	o	PROPN
ejde-355	216	24	,	,	PUNCT
ejde-355	216	25	µ̃i	µ̃i	PROPN
ejde-355	216	26	,	,	PUNCT
ejde-355	216	27	ξ̃](µo	ξ̃](µo	PROPN
ejde-355	216	28	,	,	PUNCT
ejde-355	216	29	µi	µi	PROPN
ejde-355	216	30	,	,	PUNCT
ejde-355	216	31	ξ)(t	ξ)(t	PROPN
ejde-355	216	32	)	)	PUNCT
ejde-355	216	33	≡	≡	PROPN
ejde-355	216	34	1	1	NUM
ejde-355	216	35	2	2	NUM
ejde-355	216	36	µi(t	µi(t	NUM
ejde-355	216	37	)	)	PUNCT
ejde-355	216	38	+	+	CCONJ
ejde-355	216	39	∫	∫	X
ejde-355	216	40	∂ωi	∂ωi	PROPN
ejde-355	216	41	νωi(t	νωi(t	PROPN
ejde-355	216	42	)	)	PUNCT
ejde-355	216	43	·	·	PUNCT
ejde-355	217	1	∇s2(t−	∇s2(t−	PRON
ejde-355	217	2	s)µi(s	s)µi(s	NOUN
ejde-355	217	3	)	)	PUNCT
ejde-355	217	4	dσs	dσs	NOUN
ejde-355	217	5	−	−	PROPN
ejde-355	217	6	∂τ	∂τ	PROPN
ejde-355	217	7	f̃	f̃	PROPN
ejde-355	217	8	(	(	PUNCT
ejde-355	217	9	l0	l0	PROPN
ejde-355	217	10	2π	2π	PROPN
ejde-355	217	11	∫	∫	PROPN
ejde-355	218	1	∂ωo	∂ωo	NOUN
ejde-355	218	2	go	go	VERB
ejde-355	218	3	dσ	dσ	PROPN
ejde-355	218	4	+	+	CCONJ
ejde-355	218	5	ξ̃	ξ̃	PROPN
ejde-355	218	6	,	,	PUNCT
ejde-355	218	7	η0	η0	NOUN
ejde-355	218	8	)	)	PUNCT
ejde-355	218	9	(	(	PUNCT
ejde-355	218	10	l0	l0	NOUN
ejde-355	218	11	2π	2π	PROPN
ejde-355	218	12	∫	∫	INTJ
ejde-355	219	1	∂ωi	∂ωi	PROPN
ejde-355	219	2	µi	µi	PROPN
ejde-355	219	3	dσ	dσ	PROPN
ejde-355	219	4	+	+	PROPN
ejde-355	219	5	ξ	ξ	X
ejde-355	219	6	)	)	PUNCT
ejde-355	219	7	∀t	∀t	PROPN
ejde-355	219	8	∈	∈	PROPN
ejde-355	219	9	∂ωi	∂ωi	NOUN
ejde-355	219	10	,	,	PUNCT
ejde-355	219	11	for	for	ADP
ejde-355	219	12	all	all	PRON
ejde-355	219	13	(	(	PUNCT
ejde-355	219	14	µo	µo	PROPN
ejde-355	219	15	,	,	PUNCT
ejde-355	219	16	µi	µi	PROPN
ejde-355	219	17	,	,	PUNCT
ejde-355	219	18	ξ	ξ	X
ejde-355	219	19	)	)	PUNCT
ejde-355	219	20	∈	∈	PROPN
ejde-355	219	21	c0,α(∂ωo)0	c0,α(∂ωo)0	NUM
ejde-355	219	22	×	×	NOUN
ejde-355	219	23	c0,α(∂ωi	c0,α(∂ωi	ADJ
ejde-355	219	24	)	)	PUNCT
ejde-355	219	25	×	×	PROPN
ejde-355	219	26	r.	r.	NOUN
ejde-355	220	1	the	the	DET
ejde-355	220	2	next	next	ADJ
ejde-355	220	3	step	step	NOUN
ejde-355	220	4	is	be	AUX
ejde-355	220	5	to	to	PART
ejde-355	220	6	prove	prove	VERB
ejde-355	220	7	that	that	SCONJ
ejde-355	220	8	the	the	DET
ejde-355	220	9	partial	partial	ADJ
ejde-355	220	10	differential	differential	NOUN
ejde-355	220	11	∂(µo,µi	∂(µo,µi	PROPN
ejde-355	220	12	,	,	PUNCT
ejde-355	220	13	ξ)λ[0	ξ)λ[0	PROPN
ejde-355	220	14	,	,	PUNCT
ejde-355	220	15	0	0	NUM
ejde-355	220	16	,	,	PUNCT
ejde-355	220	17	l0	l0	PROPN
ejde-355	220	18	,	,	PUNCT
ejde-355	220	19	η0	η0	NOUN
ejde-355	220	20	,	,	PUNCT
ejde-355	220	21	r0	r0	NOUN
ejde-355	220	22	,	,	PUNCT
ejde-355	220	23	µ̃	µ̃	PROPN
ejde-355	220	24	o	o	PROPN
ejde-355	220	25	,	,	PUNCT
ejde-355	220	26	µ̃i	µ̃i	NUM
ejde-355	220	27	,	,	PUNCT
ejde-355	220	28	ξ̃	ξ̃	PROPN
ejde-355	220	29	]	]	PUNCT
ejde-355	220	30	is	be	AUX
ejde-355	220	31	a	a	DET
ejde-355	220	32	homeomorphism	homeomorphism	NOUN
ejde-355	220	33	from	from	ADP
ejde-355	220	34	c0,α(∂ωo)0	c0,α(∂ωo)0	NUM
ejde-355	220	35	×	×	NOUN
ejde-355	220	36	c0,α(∂ωi	c0,α(∂ωi	ADJ
ejde-355	220	37	)	)	PUNCT
ejde-355	220	38	×	×	NOUN
ejde-355	220	39	r	r	NOUN
ejde-355	220	40	onto	onto	ADP
ejde-355	220	41	c0,α(∂ωo	c0,α(∂ωo	NOUN
ejde-355	220	42	)	)	PUNCT
ejde-355	220	43	×	×	NOUN
ejde-355	220	44	c0,α(∂ωi	c0,α(∂ωi	ADV
ejde-355	220	45	)	)	PUNCT
ejde-355	220	46	.	.	PUNCT
ejde-355	221	1	we	we	PRON
ejde-355	221	2	observe	observe	VERB
ejde-355	221	3	that	that	SCONJ
ejde-355	221	4	the	the	DET
ejde-355	221	5	partial	partial	ADJ
ejde-355	221	6	differential	differential	NOUN
ejde-355	221	7	∂(µo,µi	∂(µo,µi	PROPN
ejde-355	221	8	,	,	PUNCT
ejde-355	221	9	ξ)λ[0	ξ)λ[0	PROPN
ejde-355	221	10	,	,	PUNCT
ejde-355	221	11	0	0	NUM
ejde-355	221	12	,	,	PUNCT
ejde-355	221	13	l0	l0	PROPN
ejde-355	221	14	,	,	PUNCT
ejde-355	221	15	η0	η0	NOUN
ejde-355	221	16	,	,	PUNCT
ejde-355	221	17	r0	r0	NOUN
ejde-355	221	18	,	,	PUNCT
ejde-355	221	19	µ̃	µ̃	PROPN
ejde-355	221	20	o	o	PROPN
ejde-355	221	21	,	,	PUNCT
ejde-355	221	22	µ̃i	µ̃i	NUM
ejde-355	221	23	,	,	PUNCT
ejde-355	221	24	ξ̃	ξ̃	PROPN
ejde-355	221	25	]	]	PUNCT
ejde-355	221	26	is	be	AUX
ejde-355	221	27	a	a	DET
ejde-355	221	28	fredholm	fredholm	NOUN
ejde-355	221	29	operator	operator	NOUN
ejde-355	221	30	of	of	ADP
ejde-355	221	31	index	index	NOUN
ejde-355	221	32	0	0	NUM
ejde-355	221	33	:	:	PUNCT
ejde-355	221	34	indeed	indeed	ADV
ejde-355	221	35	it	it	PRON
ejde-355	221	36	is	be	AUX
ejde-355	221	37	the	the	DET
ejde-355	221	38	sum	sum	NOUN
ejde-355	221	39	of	of	ADP
ejde-355	221	40	an	an	DET
ejde-355	221	41	invertible	invertible	ADJ
ejde-355	221	42	operator	operator	NOUN
ejde-355	221	43	and	and	CCONJ
ejde-355	221	44	a	a	DET
ejde-355	221	45	compact	compact	ADJ
ejde-355	221	46	operator	operator	NOUN
ejde-355	221	47	.	.	PUNCT
ejde-355	222	1	as	as	SCONJ
ejde-355	222	2	a	a	DET
ejde-355	222	3	consequence	consequence	NOUN
ejde-355	222	4	,	,	PUNCT
ejde-355	222	5	to	to	PART
ejde-355	222	6	prove	prove	VERB
ejde-355	222	7	that	that	SCONJ
ejde-355	222	8	the	the	DET
ejde-355	222	9	operator	operator	NOUN
ejde-355	222	10	∂(µo,µi	∂(µo,µi	PROPN
ejde-355	222	11	,	,	PUNCT
ejde-355	222	12	ξ)λ[0	ξ)λ[0	PROPN
ejde-355	222	13	,	,	PUNCT
ejde-355	222	14	0	0	NUM
ejde-355	222	15	,	,	PUNCT
ejde-355	222	16	l0	l0	PROPN
ejde-355	222	17	,	,	PUNCT
ejde-355	222	18	η0	η0	NOUN
ejde-355	222	19	,	,	PUNCT
ejde-355	222	20	r0	r0	NOUN
ejde-355	222	21	,	,	PUNCT
ejde-355	222	22	µ̃	µ̃	PROPN
ejde-355	222	23	o	o	PROPN
ejde-355	222	24	,	,	PUNCT
ejde-355	222	25	µ̃i	µ̃i	NUM
ejde-355	222	26	,	,	PUNCT
ejde-355	222	27	ξ̃	ξ̃	PROPN
ejde-355	222	28	]	]	PUNCT
ejde-355	222	29	is	be	AUX
ejde-355	222	30	a	a	DET
ejde-355	222	31	homeomorphism	homeomorphism	NOUN
ejde-355	222	32	,	,	PUNCT
ejde-355	222	33	it	it	PRON
ejde-355	222	34	is	be	AUX
ejde-355	222	35	enough	enough	ADJ
ejde-355	222	36	to	to	PART
ejde-355	222	37	show	show	VERB
ejde-355	222	38	that	that	SCONJ
ejde-355	222	39	it	it	PRON
ejde-355	222	40	is	be	AUX
ejde-355	222	41	injective	injective	ADJ
ejde-355	222	42	.	.	PUNCT
ejde-355	223	1	therefore	therefore	ADV
ejde-355	223	2	,	,	PUNCT
ejde-355	223	3	let	let	VERB
ejde-355	223	4	us	we	PRON
ejde-355	223	5	assume	assume	VERB
ejde-355	223	6	that	that	SCONJ
ejde-355	223	7	∂(µo,µi	∂(µo,µi	PROPN
ejde-355	223	8	,	,	PUNCT
ejde-355	223	9	ξ)λ[0	ξ)λ[0	PROPN
ejde-355	223	10	,	,	PUNCT
ejde-355	223	11	0	0	NUM
ejde-355	223	12	,	,	PUNCT
ejde-355	223	13	l0	l0	PROPN
ejde-355	223	14	,	,	PUNCT
ejde-355	223	15	η0	η0	NOUN
ejde-355	223	16	,	,	PUNCT
ejde-355	223	17	r0	r0	NOUN
ejde-355	223	18	,	,	PUNCT
ejde-355	223	19	µ̃	µ̃	PROPN
ejde-355	223	20	o	o	PROPN
ejde-355	223	21	,	,	PUNCT
ejde-355	223	22	µ̃i	µ̃i	PROPN
ejde-355	223	23	,	,	PUNCT
ejde-355	223	24	ξ̃](µo	ξ̃](µo	PROPN
ejde-355	223	25	,	,	PUNCT
ejde-355	223	26	µi	µi	PROPN
ejde-355	223	27	,	,	PUNCT
ejde-355	223	28	ξ	ξ	PROPN
ejde-355	223	29	)	)	PUNCT
ejde-355	223	30	=	=	SYM
ejde-355	223	31	0	0	X
ejde-355	223	32	.	.	PUNCT
ejde-355	224	1	we	we	PRON
ejde-355	224	2	integrate	integrate	VERB
ejde-355	224	3	the	the	DET
ejde-355	224	4	equality	equality	NOUN
ejde-355	224	5	∂(µo,µi	∂(µo,µi	PROPN
ejde-355	224	6	,	,	PUNCT
ejde-355	224	7	ξ)λ	ξ)λ	PUNCT
ejde-355	224	8	o[0	o[0	PROPN
ejde-355	224	9	,	,	PUNCT
ejde-355	224	10	0	0	NUM
ejde-355	224	11	,	,	PUNCT
ejde-355	224	12	l0	l0	PROPN
ejde-355	224	13	,	,	PUNCT
ejde-355	224	14	η0	η0	NOUN
ejde-355	224	15	,	,	PUNCT
ejde-355	224	16	r0	r0	NOUN
ejde-355	224	17	,	,	PUNCT
ejde-355	224	18	µ̃	µ̃	PROPN
ejde-355	224	19	o	o	PROPN
ejde-355	224	20	,	,	PUNCT
ejde-355	224	21	µ̃i	µ̃i	PROPN
ejde-355	224	22	,	,	PUNCT
ejde-355	224	23	ξ̃](µo	ξ̃](µo	PROPN
ejde-355	224	24	,	,	PUNCT
ejde-355	224	25	µi	µi	PROPN
ejde-355	224	26	,	,	PUNCT
ejde-355	224	27	ξ)(x	ξ)(x	PROPN
ejde-355	224	28	)	)	PUNCT
ejde-355	225	1	=	=	SYM
ejde-355	225	2	0	0	NUM
ejde-355	226	1	∀x	∀x	X
ejde-355	226	2	∈	∈	PROPN
ejde-355	226	3	∂ωo	∂ωo	NOUN
ejde-355	226	4	,	,	PUNCT
ejde-355	226	5	that	that	SCONJ
ejde-355	226	6	together	together	ADV
ejde-355	226	7	with	with	ADP
ejde-355	226	8	the	the	DET
ejde-355	226	9	equalities∫	equalities∫	NOUN
ejde-355	226	10	∂ωo	∂ωo	PROPN
ejde-355	226	11	∫	∫	PROPN
ejde-355	226	12	∂ωo	∂ωo	PROPN
ejde-355	226	13	νωo(x	νωo(x	PROPN
ejde-355	226	14	)	)	PUNCT
ejde-355	226	15	·	·	PUNCT
ejde-355	226	16	∇s2(x−	∇s2(x−	ADP
ejde-355	226	17	y)µo(y	y)µo(y	NUM
ejde-355	226	18	)	)	PUNCT
ejde-355	226	19	dσy	dσy	NOUN
ejde-355	226	20	dσx	dσx	NOUN
ejde-355	226	21	=	=	SYM
ejde-355	226	22	1	1	NUM
ejde-355	226	23	2	2	NUM
ejde-355	226	24	∫	∫	NOUN
ejde-355	226	25	∂ωo	∂ωo	NOUN
ejde-355	226	26	µo(y	µo(y	NOUN
ejde-355	226	27	)	)	PUNCT
ejde-355	226	28	dσy	dσy	NOUN
ejde-355	226	29	(	(	PUNCT
ejde-355	226	30	cf	cf	NOUN
ejde-355	226	31	.	.	PUNCT
ejde-355	227	1	[	[	X
ejde-355	227	2	9	9	NUM
ejde-355	227	3	,	,	PUNCT
ejde-355	227	4	lemma	lemma	PROPN
ejde-355	227	5	6.11	6.11	NUM
ejde-355	227	6	]	]	PUNCT
ejde-355	227	7	)	)	PUNCT
ejde-355	227	8	and	and	CCONJ
ejde-355	227	9	∫	∫	PROPN
ejde-355	227	10	∂ωo	∂ωo	PROPN
ejde-355	227	11	νωo(x	νωo(x	PROPN
ejde-355	227	12	)	)	PUNCT
ejde-355	227	13	·	·	PUNCT
ejde-355	227	14	∇s2(x	∇s2(x	NUM
ejde-355	227	15	)	)	PUNCT
ejde-355	227	16	dσx	dσx	NOUN
ejde-355	227	17	=	=	SYM
ejde-355	227	18	1	1	NUM
ejde-355	227	19	(	(	PUNCT
ejde-355	227	20	cf	cf	NOUN
ejde-355	227	21	.	.	PUNCT
ejde-355	228	1	[	[	X
ejde-355	228	2	9	9	NUM
ejde-355	228	3	,	,	PUNCT
ejde-355	228	4	corollary	corollary	ADJ
ejde-355	228	5	4.6	4.6	NUM
ejde-355	228	6	]	]	PUNCT
ejde-355	228	7	)	)	PUNCT
ejde-355	228	8	,	,	PUNCT
ejde-355	228	9	implies	imply	VERB
ejde-355	228	10	∫	∫	PROPN
ejde-355	228	11	∂ωi	∂ωi	PROPN
ejde-355	228	12	µi(s	µi(s	NUM
ejde-355	228	13	)	)	PUNCT
ejde-355	228	14	dσs	dσs	NOUN
ejde-355	228	15	=	=	NOUN
ejde-355	228	16	0	0	PROPN
ejde-355	228	17	.	.	PUNCT
ejde-355	229	1	(	(	PUNCT
ejde-355	229	2	4.16	4.16	NUM
ejde-355	229	3	)	)	PUNCT
ejde-355	229	4	accordingly	accordingly	ADV
ejde-355	229	5	,	,	PUNCT
ejde-355	229	6	−1	−1	NOUN
ejde-355	229	7	2	2	NUM
ejde-355	229	8	µo(x	µo(x	PUNCT
ejde-355	229	9	)	)	PUNCT
ejde-355	230	1	+	+	CCONJ
ejde-355	230	2	∫	∫	PROPN
ejde-355	230	3	∂ωo	∂ωo	NOUN
ejde-355	230	4	νωo(x	νωo(x	PROPN
ejde-355	230	5	)	)	PUNCT
ejde-355	230	6	·	·	PUNCT
ejde-355	230	7	∇s2(x−	∇s2(x−	ADP
ejde-355	230	8	y)µo(y	y)µo(y	NUM
ejde-355	230	9	)	)	PUNCT
ejde-355	230	10	dσy	dσy	NOUN
ejde-355	230	11	=	=	SYM
ejde-355	230	12	0	0	PUNCT
ejde-355	230	13	∀x	∀x	NUM
ejde-355	230	14	∈	∈	PROPN
ejde-355	230	15	∂ωo	∂ωo	NOUN
ejde-355	230	16	.	.	PUNCT
ejde-355	231	1	since	since	SCONJ
ejde-355	231	2	∫	∫	PROPN
ejde-355	231	3	∂ωo	∂ωo	PROPN
ejde-355	231	4	µ	µ	X
ejde-355	231	5	o	o	X
ejde-355	231	6	dσ	dσ	NOUN
ejde-355	231	7	=	=	PROPN
ejde-355	231	8	0	0	PROPN
ejde-355	231	9	,	,	PUNCT
ejde-355	231	10	by	by	ADP
ejde-355	231	11	[	[	PUNCT
ejde-355	231	12	9	9	NUM
ejde-355	231	13	,	,	PUNCT
ejde-355	231	14	theorem	theorem	VERB
ejde-355	231	15	6.25	6.25	NUM
ejde-355	231	16	]	]	PUNCT
ejde-355	231	17	we	we	PRON
ejde-355	231	18	have	have	VERB
ejde-355	231	19	µo	µo	NOUN
ejde-355	231	20	=	=	NOUN
ejde-355	231	21	0	0	PROPN
ejde-355	231	22	.	.	PUNCT
ejde-355	232	1	then	then	ADV
ejde-355	232	2	we	we	PRON
ejde-355	232	3	note	note	VERB
ejde-355	232	4	that	that	SCONJ
ejde-355	232	5	by	by	ADP
ejde-355	232	6	(	(	PUNCT
ejde-355	232	7	4.16	4.16	NUM
ejde-355	232	8	)	)	PUNCT
ejde-355	232	9	equality	equality	NOUN
ejde-355	232	10	∂(µo,µi	∂(µo,µi	PROPN
ejde-355	232	11	,	,	PUNCT
ejde-355	232	12	ξ)λ	ξ)λ	NOUN
ejde-355	232	13	i[0	i[0	PROPN
ejde-355	232	14	,	,	PUNCT
ejde-355	232	15	0	0	NUM
ejde-355	232	16	,	,	PUNCT
ejde-355	232	17	l0	l0	PROPN
ejde-355	232	18	,	,	PUNCT
ejde-355	232	19	η0	η0	NOUN
ejde-355	232	20	,	,	PUNCT
ejde-355	232	21	r0	r0	NOUN
ejde-355	232	22	,	,	PUNCT
ejde-355	232	23	µ̃	µ̃	PROPN
ejde-355	232	24	o	o	PROPN
ejde-355	232	25	,	,	PUNCT
ejde-355	232	26	µ̃i	µ̃i	PROPN
ejde-355	232	27	,	,	PUNCT
ejde-355	232	28	ξ̃](µo	ξ̃](µo	PROPN
ejde-355	232	29	,	,	PUNCT
ejde-355	232	30	µi	µi	PROPN
ejde-355	232	31	,	,	PUNCT
ejde-355	232	32	ξ)(t	ξ)(t	PROPN
ejde-355	232	33	)	)	PUNCT
ejde-355	232	34	=	=	SYM
ejde-355	232	35	0	0	NUM
ejde-355	232	36	∀t	∀t	PROPN
ejde-355	232	37	∈	∈	PROPN
ejde-355	232	38	∂ωi	∂ωi	NOUN
ejde-355	232	39	reads	read	VERB
ejde-355	232	40	as	as	ADP
ejde-355	232	41	1	1	NUM
ejde-355	232	42	2	2	NUM
ejde-355	232	43	µi(t	µi(t	NUM
ejde-355	232	44	)	)	PUNCT
ejde-355	233	1	+	+	CCONJ
ejde-355	233	2	∫	∫	X
ejde-355	233	3	∂ωi	∂ωi	PROPN
ejde-355	233	4	νωi(t	νωi(t	PROPN
ejde-355	233	5	)	)	PUNCT
ejde-355	233	6	·	·	PUNCT
ejde-355	234	1	∇s2(t−	∇s2(t−	PRON
ejde-355	234	2	s)µi(s	s)µi(s	NOUN
ejde-355	234	3	)	)	PUNCT
ejde-355	234	4	dσs	dσs	NOUN
ejde-355	234	5	−	−	PROPN
ejde-355	234	6	∂τ	∂τ	PROPN
ejde-355	234	7	f̃	f̃	PROPN
ejde-355	234	8	(	(	PUNCT
ejde-355	234	9	l0	l0	PROPN
ejde-355	234	10	2π	2π	PROPN
ejde-355	234	11	∫	∫	PROPN
ejde-355	235	1	∂ωo	∂ωo	NOUN
ejde-355	235	2	go	go	VERB
ejde-355	235	3	dσ	dσ	PROPN
ejde-355	235	4	+	+	CCONJ
ejde-355	235	5	ξ̃	ξ̃	PROPN
ejde-355	235	6	,	,	PUNCT
ejde-355	235	7	η0	η0	NOUN
ejde-355	235	8	)	)	PUNCT
ejde-355	235	9	(	(	PUNCT
ejde-355	235	10	4.17	4.17	NUM
ejde-355	235	11	)	)	PUNCT
ejde-355	235	12	12	12	NUM
ejde-355	235	13	p.	p.	NOUN
ejde-355	235	14	musolino	musolino	NOUN
ejde-355	235	15	,	,	PUNCT
ejde-355	235	16	m.	m.	NOUN
ejde-355	235	17	dutko	dutko	PROPN
ejde-355	235	18	,	,	PUNCT
ejde-355	235	19	g.	g.	PROPN
ejde-355	235	20	mishuris	mishuris	PROPN
ejde-355	235	21	ejde-2023/57	ejde-2023/57	NOUN
ejde-355	235	22	for	for	ADP
ejde-355	235	23	all	all	PRON
ejde-355	235	24	t	t	NOUN
ejde-355	235	25	∈	∈	PROPN
ejde-355	235	26	∂ωi	∂ωi	PROPN
ejde-355	235	27	.	.	PUNCT
ejde-355	236	1	by	by	ADP
ejde-355	236	2	equality	equality	NOUN
ejde-355	236	3	(	(	PUNCT
ejde-355	236	4	4.16	4.16	NUM
ejde-355	236	5	)	)	PUNCT
ejde-355	236	6	,	,	PUNCT
ejde-355	236	7	by∫	by∫	PROPN
ejde-355	236	8	∂ωi	∂ωi	PROPN
ejde-355	236	9	∫	∫	PROPN
ejde-355	236	10	∂ωi	∂ωi	PROPN
ejde-355	236	11	νωi(t	νωi(t	PROPN
ejde-355	236	12	)	)	PUNCT
ejde-355	236	13	·	·	PUNCT
ejde-355	237	1	∇s2(t−	∇s2(t−	PRON
ejde-355	237	2	s)µi(s	s)µi(s	NOUN
ejde-355	237	3	)	)	PUNCT
ejde-355	237	4	dσs	dσs	NOUN
ejde-355	237	5	dσt	dσt	NOUN
ejde-355	237	6	=	=	NOUN
ejde-355	237	7	1	1	NUM
ejde-355	237	8	2	2	NUM
ejde-355	237	9	∫	∫	NOUN
ejde-355	237	10	∂ωi	∂ωi	NOUN
ejde-355	237	11	µi(s	µi(s	NUM
ejde-355	237	12	)	)	PUNCT
ejde-355	237	13	dσs	dσs	NOUN
ejde-355	237	14	(	(	PUNCT
ejde-355	237	15	cf	cf	NOUN
ejde-355	237	16	.	.	PUNCT
ejde-355	238	1	[	[	X
ejde-355	238	2	9	9	NUM
ejde-355	238	3	,	,	PUNCT
ejde-355	238	4	lemma	lemma	PROPN
ejde-355	238	5	6.11	6.11	NUM
ejde-355	238	6	]	]	PUNCT
ejde-355	238	7	)	)	PUNCT
ejde-355	238	8	,	,	PUNCT
ejde-355	238	9	and	and	CCONJ
ejde-355	238	10	by	by	ADP
ejde-355	238	11	integrating	integrate	VERB
ejde-355	238	12	(	(	PUNCT
ejde-355	238	13	4.17	4.17	NUM
ejde-355	238	14	)	)	PUNCT
ejde-355	238	15	on	on	ADP
ejde-355	238	16	∂ωi	∂ωi	NOUN
ejde-355	238	17	,	,	PUNCT
ejde-355	238	18	we	we	PRON
ejde-355	238	19	deduce	deduce	VERB
ejde-355	238	20	that	that	PRON
ejde-355	238	21	ξ	ξ	X
ejde-355	238	22	=	=	SYM
ejde-355	238	23	0	0	PROPN
ejde-355	238	24	.	.	PUNCT
ejde-355	239	1	then	then	ADV
ejde-355	239	2	[	[	X
ejde-355	239	3	9	9	NUM
ejde-355	239	4	,	,	PUNCT
ejde-355	239	5	corollary	corollary	NOUN
ejde-355	239	6	6.15	6.15	NUM
ejde-355	239	7	]	]	PUNCT
ejde-355	239	8	implies	imply	VERB
ejde-355	239	9	that	that	SCONJ
ejde-355	239	10	µi	µi	PROPN
ejde-355	239	11	=	=	SYM
ejde-355	239	12	0	0	NUM
ejde-355	239	13	.	.	PUNCT
ejde-355	240	1	hence	hence	ADV
ejde-355	240	2	,	,	PUNCT
ejde-355	240	3	we	we	PRON
ejde-355	240	4	have	have	AUX
ejde-355	240	5	shown	show	VERB
ejde-355	240	6	that	that	SCONJ
ejde-355	240	7	the	the	DET
ejde-355	240	8	operator	operator	NOUN
ejde-355	240	9	∂(µo,µi	∂(µo,µi	PROPN
ejde-355	240	10	,	,	PUNCT
ejde-355	240	11	ξ)λ[0	ξ)λ[0	PROPN
ejde-355	240	12	,	,	PUNCT
ejde-355	240	13	0	0	NUM
ejde-355	240	14	,	,	PUNCT
ejde-355	240	15	l0	l0	PROPN
ejde-355	240	16	,	,	PUNCT
ejde-355	240	17	η0	η0	NOUN
ejde-355	240	18	,	,	PUNCT
ejde-355	240	19	r0	r0	NOUN
ejde-355	240	20	,	,	PUNCT
ejde-355	240	21	µ̃	µ̃	PROPN
ejde-355	240	22	o	o	PROPN
ejde-355	240	23	,	,	PUNCT
ejde-355	240	24	µ̃i	µ̃i	NUM
ejde-355	240	25	,	,	PUNCT
ejde-355	240	26	ξ̃	ξ̃	PROPN
ejde-355	240	27	]	]	PUNCT
ejde-355	240	28	is	be	AUX
ejde-355	240	29	injective	injective	ADJ
ejde-355	240	30	,	,	PUNCT
ejde-355	240	31	and	and	CCONJ
ejde-355	240	32	as	as	ADP
ejde-355	240	33	a	a	DET
ejde-355	240	34	consequence	consequence	NOUN
ejde-355	240	35	,	,	PUNCT
ejde-355	240	36	being	be	AUX
ejde-355	240	37	a	a	DET
ejde-355	240	38	fredholm	fredholm	NOUN
ejde-355	240	39	operator	operator	NOUN
ejde-355	240	40	of	of	ADP
ejde-355	240	41	index	index	NOUN
ejde-355	240	42	0	0	NUM
ejde-355	240	43	,	,	PUNCT
ejde-355	240	44	also	also	ADV
ejde-355	240	45	a	a	DET
ejde-355	240	46	homeomorphism	homeomorphism	NOUN
ejde-355	240	47	.	.	PUNCT
ejde-355	241	1	therefore	therefore	ADV
ejde-355	241	2	,	,	PUNCT
ejde-355	241	3	we	we	PRON
ejde-355	241	4	can	can	AUX
ejde-355	241	5	apply	apply	VERB
ejde-355	241	6	the	the	DET
ejde-355	241	7	implicit	implicit	ADJ
ejde-355	241	8	function	function	NOUN
ejde-355	241	9	theorem	theorem	VERB
ejde-355	241	10	for	for	ADP
ejde-355	241	11	real	real	ADJ
ejde-355	241	12	analytic	analytic	ADJ
ejde-355	241	13	maps	map	NOUN
ejde-355	241	14	in	in	ADP
ejde-355	241	15	banach	banach	NOUN
ejde-355	241	16	spaces	space	NOUN
ejde-355	241	17	(	(	PUNCT
ejde-355	241	18	cf	cf	NOUN
ejde-355	241	19	.	.	PUNCT
ejde-355	242	1	deimling	deimle	VERB
ejde-355	243	1	[	[	X
ejde-355	243	2	11	11	NUM
ejde-355	243	3	,	,	PUNCT
ejde-355	243	4	thm	thm	PROPN
ejde-355	243	5	.	.	PUNCT
ejde-355	244	1	15.3	15.3	NUM
ejde-355	244	2	]	]	PUNCT
ejde-355	244	3	)	)	PUNCT
ejde-355	245	1	and	and	CCONJ
ejde-355	245	2	deduce	deduce	VERB
ejde-355	245	3	that	that	SCONJ
ejde-355	245	4	there	there	PRON
ejde-355	245	5	exist	exist	VERB
ejde-355	245	6	ε2	ε2	ADJ
ejde-355	245	7	∈]0	∈]0	ADV
ejde-355	245	8	,	,	PUNCT
ejde-355	245	9	ε1	ε1	PROPN
ejde-355	245	10	[	[	X
ejde-355	245	11	,	,	PUNCT
ejde-355	245	12	an	an	DET
ejde-355	245	13	open	open	ADJ
ejde-355	245	14	neighborhood	neighborhood	NOUN
ejde-355	245	15	u	u	NOUN
ejde-355	245	16	of	of	ADP
ejde-355	245	17	(	(	PUNCT
ejde-355	245	18	0	0	NUM
ejde-355	245	19	,	,	PUNCT
ejde-355	245	20	l0	l0	PROPN
ejde-355	245	21	,	,	PUNCT
ejde-355	245	22	η0	η0	NOUN
ejde-355	245	23	,	,	PUNCT
ejde-355	245	24	r0	r0	NOUN
ejde-355	245	25	)	)	PUNCT
ejde-355	245	26	in	in	ADP
ejde-355	245	27	rm+3	rm+3	PROPN
ejde-355	245	28	,	,	PUNCT
ejde-355	245	29	an	an	DET
ejde-355	245	30	open	open	ADJ
ejde-355	245	31	neighborhood	neighborhood	NOUN
ejde-355	245	32	v	v	X
ejde-355	245	33	of	of	ADP
ejde-355	245	34	(	(	PUNCT
ejde-355	245	35	µ̃o	µ̃o	NOUN
ejde-355	245	36	,	,	PUNCT
ejde-355	245	37	µ̃i	µ̃i	NOUN
ejde-355	245	38	,	,	PUNCT
ejde-355	245	39	ξ̃	ξ̃	PROPN
ejde-355	245	40	)	)	PUNCT
ejde-355	245	41	in	in	ADP
ejde-355	245	42	c0,α(∂ωo)0	c0,α(∂ωo)0	NUM
ejde-355	245	43	×	×	NOUN
ejde-355	245	44	c0,α(∂ωi	c0,α(∂ωi	ADJ
ejde-355	245	45	)	)	PUNCT
ejde-355	245	46	×	×	NOUN
ejde-355	245	47	r	r	NOUN
ejde-355	245	48	,	,	PUNCT
ejde-355	245	49	and	and	CCONJ
ejde-355	245	50	a	a	DET
ejde-355	245	51	real	real	ADJ
ejde-355	245	52	analytic	analytic	ADJ
ejde-355	245	53	map	map	NOUN
ejde-355	245	54	(	(	PUNCT
ejde-355	245	55	mo	mo	PROPN
ejde-355	245	56	,	,	PUNCT
ejde-355	245	57	m	m	VERB
ejde-355	245	58	i	i	PRON
ejde-355	245	59	,	,	PUNCT
ejde-355	245	60	ξ	ξ	PROPN
ejde-355	245	61	)	)	PUNCT
ejde-355	245	62	from	from	ADP
ejde-355	245	63	]	]	PUNCT
ejde-355	245	64	−	−	PROPN
ejde-355	245	65	ε2	ε2	PROPN
ejde-355	245	66	,	,	PUNCT
ejde-355	245	67	ε2[×u	ε2[×u	ADJ
ejde-355	245	68	to	to	ADP
ejde-355	245	69	v	v	NOUN
ejde-355	245	70	such	such	ADJ
ejde-355	245	71	that	that	PRON
ejde-355	245	72	(	(	PUNCT
ejde-355	245	73	εδ(ε	εδ(ε	NOUN
ejde-355	245	74	)	)	PUNCT
ejde-355	245	75	,	,	PUNCT
ejde-355	245	76	εδ(ε	εδ(ε	VERB
ejde-355	245	77	)	)	PUNCT
ejde-355	245	78	log	log	PROPN
ejde-355	245	79	ε	ε	PROPN
ejde-355	245	80	,	,	PUNCT
ejde-355	245	81	η(ε	η(ε	NOUN
ejde-355	245	82	)	)	PUNCT
ejde-355	245	83	,	,	PUNCT
ejde-355	245	84	ε	ε	PROPN
ejde-355	245	85	ρ(ε	ρ(ε	NUM
ejde-355	245	86	)	)	PUNCT
ejde-355	245	87	)	)	PUNCT
ejde-355	246	1	∈	∈	PROPN
ejde-355	246	2	u	u	NOUN
ejde-355	246	3	∀ε	∀ε	PROPN
ejde-355	246	4	∈]0	∈]0	X
ejde-355	246	5	,	,	PUNCT
ejde-355	246	6	ε2	ε2	PROPN
ejde-355	246	7	[	[	PUNCT
ejde-355	246	8	,	,	PUNCT
ejde-355	246	9	and	and	CCONJ
ejde-355	246	10	such	such	ADJ
ejde-355	246	11	that	that	SCONJ
ejde-355	246	12	the	the	DET
ejde-355	246	13	set	set	NOUN
ejde-355	246	14	of	of	ADP
ejde-355	246	15	zeros	zero	NOUN
ejde-355	246	16	of	of	ADP
ejde-355	246	17	λ	λ	PROPN
ejde-355	246	18	in	in	ADP
ejde-355	246	19	]	]	PUNCT
ejde-355	246	20	−	−	PROPN
ejde-355	246	21	ε2	ε2	ADJ
ejde-355	246	22	,	,	PUNCT
ejde-355	246	23	ε2[×u	ε2[×u	ADJ
ejde-355	246	24	×	×	NOUN
ejde-355	246	25	v	v	ADP
ejde-355	246	26	coincides	coincide	VERB
ejde-355	246	27	with	with	ADP
ejde-355	246	28	the	the	DET
ejde-355	246	29	graph	graph	NOUN
ejde-355	246	30	of	of	ADP
ejde-355	246	31	(	(	PUNCT
ejde-355	246	32	mo	mo	PROPN
ejde-355	246	33	,	,	PUNCT
ejde-355	246	34	m	m	VERB
ejde-355	246	35	i	i	PRON
ejde-355	246	36	,	,	PUNCT
ejde-355	246	37	ξ	ξ	PROPN
ejde-355	246	38	)	)	PUNCT
ejde-355	246	39	.	.	PUNCT
ejde-355	247	1	in	in	ADP
ejde-355	247	2	particular	particular	ADJ
ejde-355	247	3	,	,	PUNCT
ejde-355	247	4	(	(	PUNCT
ejde-355	247	5	mo[0	mo[0	PROPN
ejde-355	247	6	,	,	PUNCT
ejde-355	247	7	0	0	NUM
ejde-355	247	8	,	,	PUNCT
ejde-355	247	9	l0	l0	PROPN
ejde-355	247	10	,	,	PUNCT
ejde-355	247	11	η0	η0	NOUN
ejde-355	247	12	,	,	PUNCT
ejde-355	247	13	r0],m	r0],m	PROPN
ejde-355	247	14	i[0	i[0	PROPN
ejde-355	247	15	,	,	PUNCT
ejde-355	247	16	0	0	NUM
ejde-355	247	17	,	,	PUNCT
ejde-355	247	18	l0	l0	PROPN
ejde-355	247	19	,	,	PUNCT
ejde-355	247	20	η0	η0	NOUN
ejde-355	247	21	,	,	PUNCT
ejde-355	247	22	r0],ξ[0	r0],ξ[0	PROPN
ejde-355	247	23	,	,	PUNCT
ejde-355	247	24	0	0	NUM
ejde-355	247	25	,	,	PUNCT
ejde-355	247	26	l0	l0	PROPN
ejde-355	247	27	,	,	PUNCT
ejde-355	247	28	η0	η0	NOUN
ejde-355	247	29	,	,	PUNCT
ejde-355	247	30	r0	r0	NOUN
ejde-355	247	31	]	]	PUNCT
ejde-355	247	32	)	)	PUNCT
ejde-355	248	1	=	=	SYM
ejde-355	248	2	(	(	PUNCT
ejde-355	248	3	µ̃o	µ̃o	NOUN
ejde-355	248	4	,	,	PUNCT
ejde-355	248	5	µ̃i	µ̃i	NOUN
ejde-355	248	6	,	,	PUNCT
ejde-355	248	7	ξ̃	ξ̃	PROPN
ejde-355	248	8	)	)	PUNCT
ejde-355	248	9	,	,	PUNCT
ejde-355	248	10	and	and	CCONJ
ejde-355	248	11	thus	thus	ADV
ejde-355	248	12	the	the	DET
ejde-355	248	13	proof	proof	NOUN
ejde-355	248	14	is	be	AUX
ejde-355	248	15	complete	complete	ADJ
ejde-355	248	16	.	.	PUNCT
ejde-355	249	1	�	�	PROPN
ejde-355	249	2	by	by	ADP
ejde-355	249	3	proposition	proposition	NOUN
ejde-355	249	4	4.1	4.1	NUM
ejde-355	249	5	we	we	PRON
ejde-355	249	6	know	know	VERB
ejde-355	249	7	that	that	SCONJ
ejde-355	249	8	there	there	PRON
ejde-355	249	9	exists	exist	VERB
ejde-355	249	10	a	a	DET
ejde-355	249	11	family	family	NOUN
ejde-355	249	12	of	of	ADP
ejde-355	249	13	solutions	solution	NOUN
ejde-355	249	14	to	to	ADP
ejde-355	249	15	the	the	DET
ejde-355	249	16	system	system	NOUN
ejde-355	249	17	of	of	ADP
ejde-355	249	18	integral	integral	ADJ
ejde-355	249	19	equations	equation	NOUN
ejde-355	249	20	(	(	PUNCT
ejde-355	249	21	4.1)-(4.2	4.1)-(4.2	NUM
ejde-355	249	22	)	)	PUNCT
ejde-355	249	23	.	.	PUNCT
ejde-355	250	1	then	then	ADV
ejde-355	250	2	we	we	PRON
ejde-355	250	3	can	can	AUX
ejde-355	250	4	exploit	exploit	VERB
ejde-355	250	5	the	the	DET
ejde-355	250	6	representation	representation	NOUN
ejde-355	250	7	formula	formula	NOUN
ejde-355	250	8	of	of	ADP
ejde-355	250	9	proposition	proposition	NOUN
ejde-355	250	10	3.1	3.1	NUM
ejde-355	250	11	and	and	CCONJ
ejde-355	250	12	introduce	introduce	VERB
ejde-355	250	13	a	a	DET
ejde-355	250	14	family	family	NOUN
ejde-355	250	15	of	of	ADP
ejde-355	250	16	solutions	solution	NOUN
ejde-355	250	17	to	to	ADP
ejde-355	250	18	(	(	PUNCT
ejde-355	250	19	1.1	1.1	NUM
ejde-355	250	20	)	)	PUNCT
ejde-355	250	21	.	.	PUNCT
ejde-355	251	1	we	we	PRON
ejde-355	251	2	do	do	VERB
ejde-355	251	3	so	so	ADV
ejde-355	251	4	in	in	ADP
ejde-355	251	5	the	the	DET
ejde-355	251	6	following	follow	VERB
ejde-355	251	7	definition	definition	NOUN
ejde-355	251	8	4.2	4.2	NUM
ejde-355	251	9	.	.	PUNCT
ejde-355	252	1	definition	definition	NOUN
ejde-355	252	2	4.2	4.2	NUM
ejde-355	252	3	.	.	PUNCT
ejde-355	253	1	let	let	VERB
ejde-355	253	2	the	the	DET
ejde-355	253	3	assumptions	assumption	NOUN
ejde-355	253	4	of	of	ADP
ejde-355	253	5	proposition	proposition	NOUN
ejde-355	253	6	4.1	4.1	NUM
ejde-355	253	7	hold	hold	NOUN
ejde-355	253	8	.	.	PUNCT
ejde-355	254	1	then	then	ADV
ejde-355	254	2	we	we	PRON
ejde-355	254	3	set	set	VERB
ejde-355	254	4	u(ε	u(ε	PROPN
ejde-355	254	5	,	,	PUNCT
ejde-355	254	6	x	x	X
ejde-355	254	7	)	)	PUNCT
ejde-355	254	8	=	=	SYM
ejde-355	254	9	∫	∫	PROPN
ejde-355	254	10	∂ωo	∂ωo	NOUN
ejde-355	254	11	s2(x−	s2(x−	PROPN
ejde-355	254	12	y)mo[ε	y)mo[ε	NUM
ejde-355	254	13	,	,	PUNCT
ejde-355	254	14	εδ(ε	εδ(ε	NOUN
ejde-355	254	15	)	)	PUNCT
ejde-355	254	16	,	,	PUNCT
ejde-355	254	17	εδ(ε	εδ(ε	VERB
ejde-355	254	18	)	)	PUNCT
ejde-355	254	19	log	log	PROPN
ejde-355	254	20	ε	ε	PROPN
ejde-355	254	21	,	,	PUNCT
ejde-355	254	22	η(ε	η(ε	NOUN
ejde-355	254	23	)	)	PUNCT
ejde-355	254	24	,	,	PUNCT
ejde-355	254	25	ε	ε	PROPN
ejde-355	254	26	ρ(ε	ρ(ε	NUM
ejde-355	254	27	)	)	PUNCT
ejde-355	254	28	]	]	PUNCT
ejde-355	254	29	(	(	PUNCT
ejde-355	254	30	y	y	X
ejde-355	254	31	)	)	PUNCT
ejde-355	254	32	dσy	dσy	PROPN
ejde-355	255	1	+	+	CCONJ
ejde-355	255	2	∫	∫	PROPN
ejde-355	255	3	∂ωi	∂ωi	PROPN
ejde-355	255	4	s2(x−	s2(x−	NOUN
ejde-355	255	5	εs)m	εs)m	PROPN
ejde-355	255	6	i[ε	i[ε	NOUN
ejde-355	255	7	,	,	PUNCT
ejde-355	255	8	εδ(ε	εδ(ε	NOUN
ejde-355	255	9	)	)	PUNCT
ejde-355	255	10	,	,	PUNCT
ejde-355	255	11	εδ(ε	εδ(ε	VERB
ejde-355	255	12	)	)	PUNCT
ejde-355	255	13	log	log	PROPN
ejde-355	255	14	ε	ε	PROPN
ejde-355	255	15	,	,	PUNCT
ejde-355	255	16	η(ε	η(ε	NOUN
ejde-355	255	17	)	)	PUNCT
ejde-355	255	18	,	,	PUNCT
ejde-355	255	19	ε	ε	PROPN
ejde-355	255	20	ρ(ε	ρ(ε	NUM
ejde-355	255	21	)	)	PUNCT
ejde-355	255	22	]	]	PUNCT
ejde-355	255	23	(	(	PUNCT
ejde-355	255	24	s	s	X
ejde-355	255	25	)	)	PUNCT
ejde-355	255	26	dσs	dσs	NOUN
ejde-355	255	27	+	+	CCONJ
ejde-355	255	28	ξ[ε	ξ[ε	NOUN
ejde-355	255	29	,	,	PUNCT
ejde-355	255	30	εδ(ε	εδ(ε	NOUN
ejde-355	255	31	)	)	PUNCT
ejde-355	255	32	,	,	PUNCT
ejde-355	255	33	εδ(ε	εδ(ε	VERB
ejde-355	255	34	)	)	PUNCT
ejde-355	255	35	log	log	PROPN
ejde-355	255	36	ε	ε	PROPN
ejde-355	255	37	,	,	PUNCT
ejde-355	255	38	η(ε	η(ε	NOUN
ejde-355	255	39	)	)	PUNCT
ejde-355	255	40	,	,	PUNCT
ejde-355	255	41	ε	ε	PROPN
ejde-355	255	42	ρ(ε	ρ(ε	NUM
ejde-355	255	43	)	)	PUNCT
ejde-355	255	44	]	]	PUNCT
ejde-355	256	1	δ(ε)ε	δ(ε)ε	PROPN
ejde-355	256	2	for	for	ADP
ejde-355	256	3	all	all	DET
ejde-355	256	4	x	x	SYM
ejde-355	256	5	∈	∈	PROPN
ejde-355	256	6	ω(ε	ω(ε	PROPN
ejde-355	256	7	)	)	PUNCT
ejde-355	256	8	and	and	CCONJ
ejde-355	256	9	all	all	DET
ejde-355	256	10	ε	ε	PROPN
ejde-355	256	11	∈]0	∈]0	X
ejde-355	256	12	,	,	PUNCT
ejde-355	256	13	ε2	ε2	PROPN
ejde-355	256	14	[	[	X
ejde-355	256	15	.	.	PUNCT
ejde-355	257	1	we	we	PRON
ejde-355	257	2	are	be	AUX
ejde-355	257	3	ready	ready	ADJ
ejde-355	257	4	to	to	PART
ejde-355	257	5	exploit	exploit	VERB
ejde-355	257	6	the	the	DET
ejde-355	257	7	representation	representation	NOUN
ejde-355	257	8	formula	formula	NOUN
ejde-355	257	9	of	of	ADP
ejde-355	257	10	proposition	proposition	NOUN
ejde-355	257	11	3.1	3.1	NUM
ejde-355	257	12	and	and	CCONJ
ejde-355	257	13	the	the	DET
ejde-355	257	14	analyticity	analyticity	NOUN
ejde-355	257	15	result	result	NOUN
ejde-355	257	16	of	of	ADP
ejde-355	257	17	proposition	proposition	NOUN
ejde-355	257	18	4.1	4.1	NUM
ejde-355	257	19	concerning	concern	VERB
ejde-355	257	20	the	the	DET
ejde-355	257	21	solutions	solution	NOUN
ejde-355	257	22	of	of	ADP
ejde-355	257	23	the	the	DET
ejde-355	257	24	system	system	NOUN
ejde-355	257	25	of	of	ADP
ejde-355	257	26	integral	integral	ADJ
ejde-355	257	27	equations	equation	NOUN
ejde-355	257	28	(	(	PUNCT
ejde-355	257	29	4.1)-(4.2	4.1)-(4.2	NUM
ejde-355	257	30	)	)	PUNCT
ejde-355	257	31	in	in	ADP
ejde-355	257	32	order	order	NOUN
ejde-355	257	33	to	to	PART
ejde-355	257	34	prove	prove	VERB
ejde-355	257	35	formulas	formula	NOUN
ejde-355	257	36	for	for	ADP
ejde-355	257	37	suitable	suitable	ADJ
ejde-355	257	38	restrictions	restriction	NOUN
ejde-355	257	39	of	of	ADP
ejde-355	257	40	the	the	DET
ejde-355	257	41	solutions	solution	NOUN
ejde-355	257	42	u(ε	u(ε	PROPN
ejde-355	257	43	,	,	PUNCT
ejde-355	257	44	·	·	PUNCT
ejde-355	257	45	)	)	PUNCT
ejde-355	257	46	and	and	CCONJ
ejde-355	257	47	for	for	SCONJ
ejde-355	257	48	the	the	DET
ejde-355	257	49	corresponding	corresponding	ADJ
ejde-355	257	50	energy	energy	NOUN
ejde-355	257	51	integral	integral	ADJ
ejde-355	257	52	in	in	ADP
ejde-355	257	53	terms	term	NOUN
ejde-355	257	54	of	of	ADP
ejde-355	257	55	real	real	ADJ
ejde-355	257	56	analytic	analytic	ADJ
ejde-355	257	57	maps	map	NOUN
ejde-355	257	58	.	.	PUNCT
ejde-355	258	1	we	we	PRON
ejde-355	258	2	start	start	VERB
ejde-355	258	3	by	by	ADP
ejde-355	258	4	considering	consider	VERB
ejde-355	258	5	the	the	DET
ejde-355	258	6	restriction	restriction	NOUN
ejde-355	258	7	of	of	ADP
ejde-355	258	8	the	the	DET
ejde-355	258	9	solution	solution	NOUN
ejde-355	258	10	u(ε	u(ε	PROPN
ejde-355	258	11	,	,	PUNCT
ejde-355	258	12	·	·	PUNCT
ejde-355	258	13	)	)	PUNCT
ejde-355	258	14	to	to	ADP
ejde-355	258	15	a	a	DET
ejde-355	258	16	set	set	NOUN
ejde-355	258	17	which	which	PRON
ejde-355	258	18	is	be	AUX
ejde-355	258	19	“	"	PUNCT
ejde-355	258	20	far	far	ADJ
ejde-355	258	21	”	"	PUNCT
ejde-355	258	22	from	from	ADP
ejde-355	258	23	the	the	DET
ejde-355	258	24	point	point	NOUN
ejde-355	258	25	where	where	SCONJ
ejde-355	258	26	the	the	DET
ejde-355	258	27	hole	hole	NOUN
ejde-355	258	28	degenerates	degenerate	NOUN
ejde-355	258	29	.	.	PUNCT
ejde-355	259	1	theorem	theorem	VERB
ejde-355	259	2	4.3	4.3	NUM
ejde-355	259	3	.	.	PUNCT
ejde-355	260	1	let	let	VERB
ejde-355	260	2	the	the	DET
ejde-355	260	3	assumptions	assumption	NOUN
ejde-355	260	4	of	of	ADP
ejde-355	260	5	proposition	proposition	NOUN
ejde-355	260	6	4.1	4.1	NUM
ejde-355	260	7	hold	hold	NOUN
ejde-355	260	8	.	.	PUNCT
ejde-355	261	1	let	let	VERB
ejde-355	261	2	ωm	ωm	PUNCT
ejde-355	261	3	be	be	AUX
ejde-355	261	4	a	a	DET
ejde-355	261	5	bounded	bounded	ADJ
ejde-355	261	6	open	open	ADJ
ejde-355	261	7	subset	subset	NOUN
ejde-355	261	8	of	of	ADP
ejde-355	261	9	ωo	ωo	ADP
ejde-355	261	10	such	such	ADJ
ejde-355	261	11	that	that	DET
ejde-355	261	12	0	0	NUM
ejde-355	261	13	6∈	6∈	NOUN
ejde-355	261	14	ωm	ωm	VERB
ejde-355	261	15	.	.	PUNCT
ejde-355	262	1	then	then	ADV
ejde-355	262	2	there	there	PRON
ejde-355	262	3	exist	exist	VERB
ejde-355	262	4	εm	εm	NOUN
ejde-355	262	5	∈]0	∈]0	ADJ
ejde-355	262	6	,	,	PUNCT
ejde-355	262	7	ε2	ε2	PROPN
ejde-355	262	8	[	[	PUNCT
ejde-355	262	9	and	and	CCONJ
ejde-355	262	10	a	a	DET
ejde-355	262	11	real	real	ADJ
ejde-355	262	12	analytic	analytic	ADJ
ejde-355	262	13	map	map	NOUN
ejde-355	262	14	um	um	INTJ
ejde-355	262	15	from	from	ADP
ejde-355	262	16	]	]	PUNCT
ejde-355	262	17	−	−	PROPN
ejde-355	262	18	εm	εm	NOUN
ejde-355	262	19	,	,	PUNCT
ejde-355	262	20	εm	εm	NOUN
ejde-355	262	21	[	[	X
ejde-355	262	22	×u	×u	X
ejde-355	262	23	to	to	PART
ejde-355	262	24	c1,α(ωm	c1,α(ωm	VERB
ejde-355	262	25	)	)	PUNCT
ejde-355	262	26	such	such	ADJ
ejde-355	262	27	that	that	SCONJ
ejde-355	262	28	ωm	ωm	NUM
ejde-355	262	29	⊆	⊆	NUM
ejde-355	262	30	ω(ε	ω(ε	PROPN
ejde-355	262	31	)	)	PUNCT
ejde-355	262	32	∀ε	∀ε	X
ejde-355	262	33	∈]0	∈]0	X
ejde-355	262	34	,	,	PUNCT
ejde-355	262	35	εm	εm	PROPN
ejde-355	262	36	[	[	PUNCT
ejde-355	262	37	,	,	PUNCT
ejde-355	262	38	ejde-2023/57	ejde-2023/57	NOUN
ejde-355	262	39	asymptotic	asymptotic	ADJ
ejde-355	262	40	analysis	analysis	NOUN
ejde-355	262	41	of	of	ADP
ejde-355	262	42	perturbed	perturb	VERB
ejde-355	262	43	robin	robin	PROPN
ejde-355	262	44	problems	problem	VERB
ejde-355	262	45	13	13	NUM
ejde-355	262	46	and	and	CCONJ
ejde-355	262	47	that	that	SCONJ
ejde-355	262	48	u(ε	u(ε	PROPN
ejde-355	262	49	,	,	PUNCT
ejde-355	262	50	x	x	NOUN
ejde-355	262	51	)	)	PUNCT
ejde-355	262	52	=	=	PUNCT
ejde-355	262	53	um	um	INTJ
ejde-355	262	54	[	[	X
ejde-355	262	55	ε	ε	PROPN
ejde-355	262	56	,	,	PUNCT
ejde-355	262	57	εδ(ε	εδ(ε	NOUN
ejde-355	262	58	)	)	PUNCT
ejde-355	262	59	,	,	PUNCT
ejde-355	262	60	εδ(ε	εδ(ε	VERB
ejde-355	262	61	)	)	PUNCT
ejde-355	262	62	log	log	PROPN
ejde-355	262	63	ε	ε	PROPN
ejde-355	262	64	,	,	PUNCT
ejde-355	262	65	η(ε	η(ε	NOUN
ejde-355	262	66	)	)	PUNCT
ejde-355	262	67	,	,	PUNCT
ejde-355	262	68	ε	ε	PROPN
ejde-355	262	69	ρ(ε	ρ(ε	NUM
ejde-355	262	70	)	)	PUNCT
ejde-355	262	71	]	]	PUNCT
ejde-355	262	72	(	(	PUNCT
ejde-355	262	73	x	x	X
ejde-355	262	74	)	)	PUNCT
ejde-355	263	1	+	+	X
ejde-355	263	2	ξ[ε	ξ[ε	NUM
ejde-355	263	3	,	,	PUNCT
ejde-355	263	4	εδ(ε	εδ(ε	NOUN
ejde-355	263	5	)	)	PUNCT
ejde-355	263	6	,	,	PUNCT
ejde-355	263	7	εδ(ε	εδ(ε	VERB
ejde-355	263	8	)	)	PUNCT
ejde-355	263	9	log	log	PROPN
ejde-355	263	10	ε	ε	PROPN
ejde-355	263	11	,	,	PUNCT
ejde-355	263	12	η(ε	η(ε	NOUN
ejde-355	263	13	)	)	PUNCT
ejde-355	263	14	,	,	PUNCT
ejde-355	263	15	ε	ε	PROPN
ejde-355	263	16	ρ(ε	ρ(ε	NUM
ejde-355	263	17	)	)	PUNCT
ejde-355	263	18	]	]	PUNCT
ejde-355	264	1	δ(ε)ε	δ(ε)ε	PROPN
ejde-355	264	2	(	(	PUNCT
ejde-355	264	3	4.18	4.18	NUM
ejde-355	264	4	)	)	PUNCT
ejde-355	264	5	for	for	ADP
ejde-355	264	6	all	all	DET
ejde-355	264	7	x	x	SYM
ejde-355	264	8	∈	∈	NOUN
ejde-355	264	9	ωm	ωm	X
ejde-355	264	10	and	and	CCONJ
ejde-355	264	11	al	al	PROPN
ejde-355	264	12	ε	ε	PROPN
ejde-355	264	13	∈]0	∈]0	AUX
ejde-355	264	14	,	,	PUNCT
ejde-355	264	15	εm	εm	PROPN
ejde-355	265	1	[	[	X
ejde-355	265	2	.	.	PUNCT
ejde-355	266	1	moreover	moreover	ADV
ejde-355	266	2	,	,	PUNCT
ejde-355	266	3	if	if	SCONJ
ejde-355	266	4	we	we	PRON
ejde-355	266	5	set	set	VERB
ejde-355	266	6	ũm	ũm	PROPN
ejde-355	266	7	(	(	PUNCT
ejde-355	266	8	x	x	X
ejde-355	266	9	)	)	PUNCT
ejde-355	266	10	≡	≡	PROPN
ejde-355	266	11	∫	∫	PROPN
ejde-355	266	12	∂ωo	∂ωo	NOUN
ejde-355	266	13	s2(x−	s2(x−	X
ejde-355	266	14	y)µ̃o(y	y)µ̃o(y	PROPN
ejde-355	266	15	)	)	PUNCT
ejde-355	267	1	dσy	dσy	PROPN
ejde-355	267	2	∀x	∀x	PUNCT
ejde-355	267	3	∈	∈	NOUN
ejde-355	267	4	ωo	ωo	ADP
ejde-355	267	5	,	,	PUNCT
ejde-355	267	6	we	we	PRON
ejde-355	267	7	have	have	VERB
ejde-355	267	8	that	that	PRON
ejde-355	267	9	um	um	INTJ
ejde-355	267	10	[	[	X
ejde-355	267	11	0	0	NUM
ejde-355	267	12	,	,	PUNCT
ejde-355	267	13	0	0	NUM
ejde-355	267	14	,	,	PUNCT
ejde-355	267	15	l0	l0	PROPN
ejde-355	267	16	,	,	PUNCT
ejde-355	267	17	η0	η0	NOUN
ejde-355	267	18	,	,	PUNCT
ejde-355	267	19	r0	r0	NOUN
ejde-355	267	20	]	]	PUNCT
ejde-355	267	21	=	=	SYM
ejde-355	268	1	ũm	ũm	X
ejde-355	268	2	|ωm	|ωm	X
ejde-355	269	1	+	+	CCONJ
ejde-355	269	2	s2|ωm	s2|ωm	PROPN
ejde-355	269	3	∫	∫	PROPN
ejde-355	269	4	∂ωo	∂ωo	NOUN
ejde-355	269	5	g	g	PROPN
ejde-355	269	6	o	o	PROPN
ejde-355	269	7	dσ	dσ	VERB
ejde-355	269	8	,	,	PUNCT
ejde-355	269	9	and	and	CCONJ
ejde-355	269	10	ũm	ũm	PROPN
ejde-355	269	11	is	be	AUX
ejde-355	269	12	a	a	DET
ejde-355	269	13	solution	solution	NOUN
ejde-355	269	14	of	of	ADP
ejde-355	269	15	the	the	DET
ejde-355	269	16	neumann	neumann	PROPN
ejde-355	269	17	problem	problem	NOUN
ejde-355	269	18	∆u(x	∆u(x	VERB
ejde-355	269	19	)	)	PUNCT
ejde-355	269	20	=	=	SYM
ejde-355	269	21	0	0	PUNCT
ejde-355	270	1	∀x	∀x	NUM
ejde-355	270	2	∈	∈	PROPN
ejde-355	270	3	ωo	ωo	ADP
ejde-355	270	4	,	,	PUNCT
ejde-355	270	5	∂	∂	NUM
ejde-355	270	6	∂νωo	∂νωo	NUM
ejde-355	270	7	u(x	u(x	NOUN
ejde-355	270	8	)	)	PUNCT
ejde-355	270	9	=	=	SYM
ejde-355	270	10	go(x)−	go(x)−	PROPN
ejde-355	270	11	∂	∂	X
ejde-355	270	12	∂νωo	∂νωo	NUM
ejde-355	270	13	s2(x	s2(x	NOUN
ejde-355	270	14	)	)	PUNCT
ejde-355	270	15	∫	∫	PROPN
ejde-355	270	16	∂ωo	∂ωo	NOUN
ejde-355	270	17	go	go	VERB
ejde-355	270	18	dσ	dσ	VERB
ejde-355	270	19	∀x	∀x	PUNCT
ejde-355	270	20	∈	∈	PROPN
ejde-355	270	21	∂ωo	∂ωo	NOUN
ejde-355	270	22	.	.	PUNCT
ejde-355	271	1	(	(	PUNCT
ejde-355	271	2	4.19	4.19	NUM
ejde-355	271	3	)	)	PUNCT
ejde-355	271	4	proof	proof	NOUN
ejde-355	271	5	.	.	PUNCT
ejde-355	272	1	we	we	PRON
ejde-355	272	2	can	can	AUX
ejde-355	272	3	take	take	VERB
ejde-355	272	4	εm	εm	NOUN
ejde-355	272	5	∈]0	∈]0	ADJ
ejde-355	272	6	,	,	PUNCT
ejde-355	272	7	ε2	ε2	ADJ
ejde-355	272	8	[	[	PUNCT
ejde-355	272	9	small	small	ADJ
ejde-355	272	10	enough	enough	ADV
ejde-355	273	1	so	so	SCONJ
ejde-355	273	2	that	that	SCONJ
ejde-355	273	3	ωm	ωm	ADP
ejde-355	273	4	∩	∩	ADJ
ejde-355	273	5	εωi	εωi	NOUN
ejde-355	273	6	=	=	NOUN
ejde-355	273	7	∅	∅	NOUN
ejde-355	273	8	∀ε	∀ε	NOUN
ejde-355	273	9	∈]−	∈]−	PROPN
ejde-355	273	10	εm	εm	PROPN
ejde-355	273	11	,	,	PUNCT
ejde-355	273	12	εm	εm	PROPN
ejde-355	273	13	[	[	PUNCT
ejde-355	273	14	.	.	PUNCT
ejde-355	274	1	recalling	recall	VERB
ejde-355	274	2	definition	definition	NOUN
ejde-355	274	3	4.2	4.2	NUM
ejde-355	274	4	,	,	PUNCT
ejde-355	274	5	we	we	PRON
ejde-355	274	6	set	set	VERB
ejde-355	274	7	um	um	INTJ
ejde-355	274	8	[	[	X
ejde-355	274	9	ε	ε	PROPN
ejde-355	274	10	,	,	PUNCT
ejde-355	274	11	γ1	γ1	NOUN
ejde-355	274	12	,	,	PUNCT
ejde-355	274	13	γ2	γ2	PROPN
ejde-355	274	14	,	,	PUNCT
ejde-355	274	15	γ3	γ3	NOUN
ejde-355	274	16	,	,	PUNCT
ejde-355	274	17	γ4](x	γ4](x	PROPN
ejde-355	274	18	)	)	PUNCT
ejde-355	274	19	≡	≡	PROPN
ejde-355	274	20	∫	∫	PROPN
ejde-355	274	21	∂ωo	∂ωo	PROPN
ejde-355	274	22	s2(x−	s2(x−	PROPN
ejde-355	274	23	y)mo[ε	y)mo[ε	NUM
ejde-355	274	24	,	,	PUNCT
ejde-355	274	25	γ1	γ1	NOUN
ejde-355	274	26	,	,	PUNCT
ejde-355	274	27	γ2	γ2	PROPN
ejde-355	274	28	,	,	PUNCT
ejde-355	274	29	γ3	γ3	NOUN
ejde-355	274	30	,	,	PUNCT
ejde-355	274	31	γ4](y	γ4](y	PROPN
ejde-355	274	32	)	)	PUNCT
ejde-355	275	1	dσy	dσy	NOUN
ejde-355	276	1	+	+	NUM
ejde-355	276	2	∫	∫	PROPN
ejde-355	276	3	∂ωi	∂ωi	PROPN
ejde-355	276	4	s2(x−	s2(x−	NOUN
ejde-355	276	5	εs)m	εs)m	PROPN
ejde-355	276	6	i[ε	i[ε	NOUN
ejde-355	276	7	,	,	PUNCT
ejde-355	276	8	γ1	γ1	NOUN
ejde-355	276	9	,	,	PUNCT
ejde-355	276	10	γ2	γ2	PROPN
ejde-355	276	11	,	,	PUNCT
ejde-355	276	12	γ3	γ3	NOUN
ejde-355	276	13	,	,	PUNCT
ejde-355	276	14	γ4](s	γ4](s	PROPN
ejde-355	276	15	)	)	PUNCT
ejde-355	276	16	dσs	dσs	PROPN
ejde-355	276	17	∀x	∀x	X
ejde-355	276	18	∈	∈	PROPN
ejde-355	276	19	ωm	ωm	PART
ejde-355	276	20	,	,	PUNCT
ejde-355	276	21	for	for	ADP
ejde-355	276	22	all	all	DET
ejde-355	276	23	(	(	PUNCT
ejde-355	276	24	ε	ε	PROPN
ejde-355	276	25	,	,	PUNCT
ejde-355	276	26	γ1	γ1	NOUN
ejde-355	276	27	,	,	PUNCT
ejde-355	276	28	γ2	γ2	PROPN
ejde-355	276	29	,	,	PUNCT
ejde-355	276	30	γ3	γ3	NOUN
ejde-355	276	31	,	,	PUNCT
ejde-355	276	32	γ4	γ4	PROPN
ejde-355	276	33	)	)	PUNCT
ejde-355	276	34	∈]−	∈]−	PROPN
ejde-355	276	35	εm	εm	NOUN
ejde-355	276	36	,	,	PUNCT
ejde-355	276	37	εm	εm	NOUN
ejde-355	276	38	[	[	X
ejde-355	276	39	×u	×u	X
ejde-355	276	40	.	.	PUNCT
ejde-355	277	1	then	then	ADV
ejde-355	277	2	proposition	proposition	VERB
ejde-355	277	3	4.1	4.1	NUM
ejde-355	277	4	and	and	CCONJ
ejde-355	277	5	real	real	ADJ
ejde-355	277	6	analyticity	analyticity	NOUN
ejde-355	277	7	results	result	NOUN
ejde-355	277	8	for	for	ADP
ejde-355	277	9	integral	integral	ADJ
ejde-355	277	10	operators	operator	NOUN
ejde-355	277	11	with	with	ADP
ejde-355	277	12	real	real	ADJ
ejde-355	277	13	analytic	analytic	ADJ
ejde-355	277	14	kernel	kernel	NOUN
ejde-355	277	15	(	(	PUNCT
ejde-355	277	16	cf	cf	NOUN
ejde-355	277	17	.	.	PUNCT
ejde-355	278	1	[	[	X
ejde-355	278	2	21	21	NUM
ejde-355	278	3	]	]	PUNCT
ejde-355	278	4	)	)	PUNCT
ejde-355	278	5	imply	imply	VERB
ejde-355	278	6	that	that	SCONJ
ejde-355	278	7	um	um	INTJ
ejde-355	278	8	is	be	AUX
ejde-355	278	9	a	a	DET
ejde-355	278	10	real	real	ADJ
ejde-355	278	11	analytic	analytic	ADJ
ejde-355	278	12	map	map	NOUN
ejde-355	278	13	from	from	ADP
ejde-355	278	14	]	]	PUNCT
ejde-355	278	15	−	−	PROPN
ejde-355	278	16	εm	εm	NOUN
ejde-355	278	17	,	,	PUNCT
ejde-355	278	18	εm	εm	NOUN
ejde-355	279	1	[	[	X
ejde-355	279	2	×u	×u	X
ejde-355	279	3	to	to	PART
ejde-355	279	4	c1,α(ωm	c1,α(ωm	VERB
ejde-355	279	5	)	)	PUNCT
ejde-355	279	6	and	and	CCONJ
ejde-355	279	7	that	that	DET
ejde-355	279	8	equality	equality	NOUN
ejde-355	279	9	(	(	PUNCT
ejde-355	279	10	4.18	4.18	NUM
ejde-355	279	11	)	)	PUNCT
ejde-355	279	12	holds	hold	VERB
ejde-355	279	13	.	.	PUNCT
ejde-355	280	1	by	by	ADP
ejde-355	280	2	proposition	proposition	NOUN
ejde-355	280	3	4.1	4.1	NUM
ejde-355	280	4	,	,	PUNCT
ejde-355	280	5	we	we	PRON
ejde-355	280	6	also	also	ADV
ejde-355	280	7	have	have	VERB
ejde-355	280	8	um	um	INTJ
ejde-355	280	9	[	[	X
ejde-355	280	10	0	0	NUM
ejde-355	280	11	,	,	PUNCT
ejde-355	280	12	0	0	NUM
ejde-355	280	13	,	,	PUNCT
ejde-355	280	14	l0	l0	PROPN
ejde-355	280	15	,	,	PUNCT
ejde-355	280	16	η0	η0	NOUN
ejde-355	280	17	,	,	PUNCT
ejde-355	280	18	r0	r0	NOUN
ejde-355	280	19	]	]	PUNCT
ejde-355	280	20	=	=	SYM
ejde-355	281	1	ũm	ũm	X
ejde-355	281	2	|ωm	|ωm	X
ejde-355	282	1	+	+	CCONJ
ejde-355	282	2	s2|ωm	s2|ωm	PROPN
ejde-355	282	3	∫	∫	PROPN
ejde-355	282	4	∂ωo	∂ωo	NOUN
ejde-355	282	5	g	g	PROPN
ejde-355	282	6	o	o	PROPN
ejde-355	282	7	dσ	dσ	VERB
ejde-355	282	8	,	,	PUNCT
ejde-355	282	9	moreover	moreover	ADV
ejde-355	282	10	,	,	PUNCT
ejde-355	282	11	standard	standard	ADJ
ejde-355	282	12	properties	property	NOUN
ejde-355	282	13	of	of	ADP
ejde-355	282	14	the	the	DET
ejde-355	282	15	single	single	ADJ
ejde-355	282	16	layer	layer	NOUN
ejde-355	282	17	potential	potential	NOUN
ejde-355	282	18	(	(	PUNCT
ejde-355	282	19	cf	cf	NOUN
ejde-355	282	20	.	.	PUNCT
ejde-355	283	1	[	[	X
ejde-355	283	2	9	9	NUM
ejde-355	283	3	,	,	PUNCT
ejde-355	283	4	§	§	NOUN
ejde-355	283	5	4.4	4.4	NUM
ejde-355	283	6	]	]	PUNCT
ejde-355	283	7	)	)	PUNCT
ejde-355	283	8	imply	imply	VERB
ejde-355	283	9	that	that	SCONJ
ejde-355	283	10	ũm	ũm	PROPN
ejde-355	283	11	is	be	AUX
ejde-355	283	12	a	a	DET
ejde-355	283	13	solution	solution	NOUN
ejde-355	283	14	of	of	ADP
ejde-355	283	15	the	the	DET
ejde-355	283	16	neumann	neumann	PROPN
ejde-355	283	17	problem	problem	NOUN
ejde-355	283	18	(	(	PUNCT
ejde-355	283	19	4.19	4.19	NUM
ejde-355	283	20	)	)	PUNCT
ejde-355	283	21	.	.	PUNCT
ejde-355	284	1	�	�	PROPN
ejde-355	284	2	then	then	ADV
ejde-355	284	3	we	we	PRON
ejde-355	284	4	consider	consider	VERB
ejde-355	284	5	the	the	DET
ejde-355	284	6	behavior	behavior	NOUN
ejde-355	284	7	of	of	ADP
ejde-355	284	8	the	the	DET
ejde-355	284	9	rescaled	rescaled	ADJ
ejde-355	284	10	solution	solution	NOUN
ejde-355	284	11	u(ε	u(ε	PROPN
ejde-355	284	12	,	,	PUNCT
ejde-355	284	13	εt	εt	PROPN
ejde-355	284	14	)	)	PUNCT
ejde-355	284	15	.	.	PUNCT
ejde-355	285	1	theorem	theorem	VERB
ejde-355	285	2	4.4	4.4	NUM
ejde-355	285	3	.	.	PUNCT
ejde-355	286	1	let	let	VERB
ejde-355	286	2	the	the	DET
ejde-355	286	3	assumptions	assumption	NOUN
ejde-355	286	4	of	of	ADP
ejde-355	286	5	proposition	proposition	NOUN
ejde-355	286	6	4.1	4.1	NUM
ejde-355	286	7	hold	hold	NOUN
ejde-355	286	8	.	.	PUNCT
ejde-355	287	1	let	let	VERB
ejde-355	287	2	zm	zm	PROPN
ejde-355	287	3	be	be	AUX
ejde-355	287	4	the	the	DET
ejde-355	287	5	real	real	ADJ
ejde-355	287	6	analytic	analytic	ADJ
ejde-355	287	7	map	map	NOUN
ejde-355	287	8	from	from	ADP
ejde-355	287	9	]	]	PUNCT
ejde-355	287	10	−	−	PROPN
ejde-355	287	11	ε2	ε2	ADJ
ejde-355	287	12	,	,	PUNCT
ejde-355	288	1	ε2[×u	ε2[×u	ADJ
ejde-355	288	2	to	to	ADP
ejde-355	288	3	r	r	NOUN
ejde-355	288	4	defined	define	VERB
ejde-355	288	5	by	by	ADP
ejde-355	288	6	zm[ε	zm[ε	PROPN
ejde-355	288	7	,	,	PUNCT
ejde-355	288	8	γ1	γ1	PROPN
ejde-355	288	9	,	,	PUNCT
ejde-355	288	10	γ2	γ2	PROPN
ejde-355	288	11	,	,	PUNCT
ejde-355	288	12	γ3	γ3	NOUN
ejde-355	288	13	,	,	PUNCT
ejde-355	288	14	γ4	γ4	PROPN
ejde-355	288	15	]	]	PUNCT
ejde-355	288	16	≡	≡	PROPN
ejde-355	288	17	∫	∫	PROPN
ejde-355	288	18	∂ωi	∂ωi	PROPN
ejde-355	288	19	m	m	NOUN
ejde-355	288	20	i[ε	i[ε	NOUN
ejde-355	288	21	,	,	PUNCT
ejde-355	288	22	γ1	γ1	NOUN
ejde-355	288	23	,	,	PUNCT
ejde-355	288	24	γ2	γ2	PROPN
ejde-355	288	25	,	,	PUNCT
ejde-355	288	26	γ3	γ3	NOUN
ejde-355	288	27	,	,	PUNCT
ejde-355	288	28	γ4](s	γ4](s	PROPN
ejde-355	288	29	)	)	PUNCT
ejde-355	288	30	dσs	dσs	NOUN
ejde-355	288	31	,	,	PUNCT
ejde-355	288	32	for	for	ADP
ejde-355	288	33	all	all	DET
ejde-355	288	34	(	(	PUNCT
ejde-355	288	35	ε	ε	PROPN
ejde-355	288	36	,	,	PUNCT
ejde-355	288	37	γ1	γ1	NOUN
ejde-355	288	38	,	,	PUNCT
ejde-355	288	39	γ2	γ2	PROPN
ejde-355	288	40	,	,	PUNCT
ejde-355	288	41	γ3	γ3	NOUN
ejde-355	288	42	,	,	PUNCT
ejde-355	288	43	γ4	γ4	PROPN
ejde-355	288	44	)	)	PUNCT
ejde-355	288	45	∈]−	∈]−	PROPN
ejde-355	288	46	ε2	ε2	ADJ
ejde-355	288	47	,	,	PUNCT
ejde-355	288	48	ε2[×u	ε2[×u	PROPN
ejde-355	288	49	.	.	PUNCT
ejde-355	289	1	let	let	AUX
ejde-355	289	2	ωm	ωm	PUNCT
ejde-355	289	3	be	be	AUX
ejde-355	289	4	a	a	DET
ejde-355	289	5	bounded	bounded	ADJ
ejde-355	289	6	open	open	ADJ
ejde-355	289	7	subset	subset	NOUN
ejde-355	289	8	of	of	ADP
ejde-355	289	9	r2	r2	PROPN
ejde-355	289	10	\ωi	\ωi	PROPN
ejde-355	289	11	.	.	PUNCT
ejde-355	290	1	then	then	ADV
ejde-355	290	2	there	there	PRON
ejde-355	290	3	exist	exist	VERB
ejde-355	290	4	εm	εm	NOUN
ejde-355	290	5	∈]0	∈]0	ADJ
ejde-355	290	6	,	,	PUNCT
ejde-355	290	7	ε2	ε2	PROPN
ejde-355	290	8	[	[	PUNCT
ejde-355	290	9	and	and	CCONJ
ejde-355	290	10	a	a	DET
ejde-355	290	11	real	real	ADJ
ejde-355	290	12	analytic	analytic	ADJ
ejde-355	290	13	map	map	NOUN
ejde-355	290	14	um	um	INTJ
ejde-355	290	15	from	from	ADP
ejde-355	290	16	]	]	PUNCT
ejde-355	290	17	−	−	PROPN
ejde-355	290	18	εm	εm	PROPN
ejde-355	290	19	,	,	PUNCT
ejde-355	290	20	εm[×u	εm[×u	NOUN
ejde-355	290	21	to	to	PART
ejde-355	290	22	c1,α(ωm	c1,α(ωm	VERB
ejde-355	290	23	)	)	PUNCT
ejde-355	290	24	such	such	ADJ
ejde-355	290	25	that	that	DET
ejde-355	290	26	εωm	εωm	NOUN
ejde-355	290	27	⊆	⊆	NUM
ejde-355	290	28	ω(ε	ω(ε	PROPN
ejde-355	290	29	)	)	PUNCT
ejde-355	290	30	∀ε	∀ε	X
ejde-355	290	31	∈]0	∈]0	X
ejde-355	290	32	,	,	PUNCT
ejde-355	290	33	εm	εm	PROPN
ejde-355	290	34	[	[	PUNCT
ejde-355	290	35	,	,	PUNCT
ejde-355	290	36	and	and	CCONJ
ejde-355	290	37	that	that	SCONJ
ejde-355	290	38	u(ε	u(ε	PROPN
ejde-355	290	39	,	,	PUNCT
ejde-355	290	40	εt	εt	PROPN
ejde-355	290	41	)	)	PUNCT
ejde-355	290	42	=	=	SYM
ejde-355	290	43	um[ε	um[ε	PROPN
ejde-355	290	44	,	,	PUNCT
ejde-355	290	45	εδ(ε	εδ(ε	NOUN
ejde-355	290	46	)	)	PUNCT
ejde-355	290	47	,	,	PUNCT
ejde-355	290	48	εδ(ε	εδ(ε	VERB
ejde-355	290	49	)	)	PUNCT
ejde-355	290	50	log	log	PROPN
ejde-355	290	51	ε	ε	PROPN
ejde-355	290	52	,	,	PUNCT
ejde-355	290	53	η(ε	η(ε	NOUN
ejde-355	290	54	)	)	PUNCT
ejde-355	290	55	,	,	PUNCT
ejde-355	290	56	ε	ε	PROPN
ejde-355	290	57	ρ(ε	ρ(ε	NUM
ejde-355	290	58	)	)	PUNCT
ejde-355	290	59	]	]	PUNCT
ejde-355	290	60	(	(	PUNCT
ejde-355	290	61	t	t	NOUN
ejde-355	290	62	)	)	PUNCT
ejde-355	290	63	+	+	CCONJ
ejde-355	290	64	log	log	NOUN
ejde-355	290	65	ε	ε	PROPN
ejde-355	290	66	2π	2π	PROPN
ejde-355	290	67	zm[ε	zm[ε	PROPN
ejde-355	290	68	,	,	PUNCT
ejde-355	290	69	εδ(ε	εδ(ε	NOUN
ejde-355	290	70	)	)	PUNCT
ejde-355	290	71	,	,	PUNCT
ejde-355	290	72	εδ(ε	εδ(ε	VERB
ejde-355	290	73	)	)	PUNCT
ejde-355	290	74	log	log	PROPN
ejde-355	290	75	ε	ε	PROPN
ejde-355	290	76	,	,	PUNCT
ejde-355	290	77	η(ε	η(ε	NOUN
ejde-355	290	78	)	)	PUNCT
ejde-355	290	79	,	,	PUNCT
ejde-355	290	80	ε	ε	PROPN
ejde-355	290	81	ρ(ε	ρ(ε	NUM
ejde-355	290	82	)	)	PUNCT
ejde-355	290	83	]	]	PUNCT
ejde-355	291	1	+	+	CCONJ
ejde-355	291	2	ξ[ε	ξ[ε	NUM
ejde-355	291	3	,	,	PUNCT
ejde-355	291	4	εδ(ε	εδ(ε	NOUN
ejde-355	291	5	)	)	PUNCT
ejde-355	291	6	,	,	PUNCT
ejde-355	291	7	εδ(ε	εδ(ε	VERB
ejde-355	291	8	)	)	PUNCT
ejde-355	291	9	log	log	PROPN
ejde-355	291	10	ε	ε	PROPN
ejde-355	291	11	,	,	PUNCT
ejde-355	291	12	η(ε	η(ε	NOUN
ejde-355	291	13	)	)	PUNCT
ejde-355	291	14	,	,	PUNCT
ejde-355	291	15	ε	ε	PROPN
ejde-355	291	16	ρ(ε	ρ(ε	NUM
ejde-355	291	17	)	)	PUNCT
ejde-355	291	18	]	]	PUNCT
ejde-355	292	1	δ(ε)ε	δ(ε)ε	PROPN
ejde-355	292	2	∀t	∀t	PROPN
ejde-355	292	3	∈	∈	PROPN
ejde-355	292	4	ωm	ωm	NUM
ejde-355	292	5	,	,	PUNCT
ejde-355	292	6	14	14	NUM
ejde-355	292	7	p.	p.	NOUN
ejde-355	292	8	musolino	musolino	PROPN
ejde-355	292	9	,	,	PUNCT
ejde-355	292	10	m.	m.	NOUN
ejde-355	292	11	dutko	dutko	PROPN
ejde-355	292	12	,	,	PUNCT
ejde-355	292	13	g.	g.	PROPN
ejde-355	292	14	mishuris	mishuris	PROPN
ejde-355	292	15	ejde-2023/57	ejde-2023/57	NOUN
ejde-355	292	16	for	for	ADP
ejde-355	292	17	all	all	DET
ejde-355	292	18	ε	ε	PROPN
ejde-355	292	19	∈]0	∈]0	X
ejde-355	292	20	,	,	PUNCT
ejde-355	292	21	εm	εm	PROPN
ejde-355	292	22	[	[	X
ejde-355	292	23	.	.	PUNCT
ejde-355	293	1	moreover	moreover	ADV
ejde-355	293	2	,	,	PUNCT
ejde-355	293	3	if	if	SCONJ
ejde-355	293	4	we	we	PRON
ejde-355	293	5	set	set	VERB
ejde-355	293	6	ũm(t	ũm(t	NOUN
ejde-355	293	7	)	)	PUNCT
ejde-355	294	1	≡	≡	PROPN
ejde-355	294	2	∫	∫	PROPN
ejde-355	295	1	∂ωi	∂ωi	PROPN
ejde-355	295	2	s2(t−	s2(t−	PROPN
ejde-355	295	3	s)µ̃i(s	s)µ̃i(s	PROPN
ejde-355	295	4	)	)	PUNCT
ejde-355	295	5	dσs	dσs	NOUN
ejde-355	295	6	+	+	CCONJ
ejde-355	295	7	∫	∫	PROPN
ejde-355	295	8	∂ωo	∂ωo	PROPN
ejde-355	295	9	s2(y)µ̃o(y	s2(y)µ̃o(y	PROPN
ejde-355	295	10	)	)	PUNCT
ejde-355	295	11	dσy	dσy	PROPN
ejde-355	295	12	∀t	∀t	PROPN
ejde-355	295	13	∈	∈	PROPN
ejde-355	295	14	r2	r2	PROPN
ejde-355	295	15	\	\	PROPN
ejde-355	295	16	ωi	ωi	PUNCT
ejde-355	295	17	,	,	PUNCT
ejde-355	295	18	we	we	PRON
ejde-355	295	19	have	have	VERB
ejde-355	295	20	that	that	DET
ejde-355	295	21	um[0	um[0	NOUN
ejde-355	295	22	,	,	PUNCT
ejde-355	295	23	0	0	NUM
ejde-355	295	24	,	,	PUNCT
ejde-355	295	25	l0	l0	PROPN
ejde-355	295	26	,	,	PUNCT
ejde-355	295	27	η0	η0	NOUN
ejde-355	295	28	,	,	PUNCT
ejde-355	295	29	r0	r0	NOUN
ejde-355	295	30	]	]	PUNCT
ejde-355	295	31	=	=	SYM
ejde-355	295	32	ũm|ωm	ũm|ωm	NOUN
ejde-355	295	33	,	,	PUNCT
ejde-355	295	34	and	and	CCONJ
ejde-355	295	35	ũm	ũm	PROPN
ejde-355	295	36	is	be	AUX
ejde-355	295	37	a	a	DET
ejde-355	295	38	solution	solution	NOUN
ejde-355	295	39	of	of	ADP
ejde-355	295	40	the	the	DET
ejde-355	295	41	neumann	neumann	PROPN
ejde-355	295	42	problem	problem	PROPN
ejde-355	295	43	∆u(t	∆u(t	PROPN
ejde-355	295	44	)	)	PUNCT
ejde-355	295	45	=	=	PUNCT
ejde-355	295	46	0	0	NUM
ejde-355	295	47	∀t	∀t	PROPN
ejde-355	295	48	∈	∈	PROPN
ejde-355	295	49	r2	r2	PROPN
ejde-355	295	50	\	\	PROPN
ejde-355	295	51	ωi	ωi	PROPN
ejde-355	295	52	,	,	PUNCT
ejde-355	295	53	∂	∂	NUM
ejde-355	295	54	∂νωi	∂νωi	NUM
ejde-355	295	55	u(t	u(t	NOUN
ejde-355	295	56	)	)	PUNCT
ejde-355	296	1	=	=	SYM
ejde-355	296	2	f̃	f̃	PROPN
ejde-355	296	3	(	(	PUNCT
ejde-355	296	4	l0	l0	PROPN
ejde-355	296	5	2π	2π	PROPN
ejde-355	296	6	∫	∫	PROPN
ejde-355	296	7	∂ωo	∂ωo	NOUN
ejde-355	296	8	go	go	VERB
ejde-355	296	9	dσ	dσ	PROPN
ejde-355	296	10	+	+	CCONJ
ejde-355	296	11	ξ̃	ξ̃	PROPN
ejde-355	296	12	,	,	PUNCT
ejde-355	296	13	η0	η0	NOUN
ejde-355	296	14	)	)	PUNCT
ejde-355	297	1	+	+	CCONJ
ejde-355	297	2	gi(t)r0	gi(t)r0	NOUN
ejde-355	297	3	∀t	∀t	PROPN
ejde-355	297	4	∈	∈	NOUN
ejde-355	297	5	∂ωi	∂ωi	NOUN
ejde-355	297	6	,	,	PUNCT
ejde-355	297	7	(	(	PUNCT
ejde-355	297	8	4.20	4.20	NUM
ejde-355	297	9	)	)	PUNCT
ejde-355	297	10	and	and	CCONJ
ejde-355	297	11	zm[0	zm[0	NUM
ejde-355	297	12	,	,	PUNCT
ejde-355	297	13	0	0	NUM
ejde-355	297	14	,	,	PUNCT
ejde-355	297	15	l0	l0	PROPN
ejde-355	297	16	,	,	PUNCT
ejde-355	297	17	η0	η0	NOUN
ejde-355	297	18	,	,	PUNCT
ejde-355	297	19	r0	r0	NOUN
ejde-355	297	20	]	]	PUNCT
ejde-355	297	21	=	=	SYM
ejde-355	298	1	∫	∫	PROPN
ejde-355	298	2	∂ωo	∂ωo	NOUN
ejde-355	298	3	go	go	VERB
ejde-355	298	4	dσ	dσ	PROPN
ejde-355	298	5	.	.	PUNCT
ejde-355	299	1	proof	proof	NOUN
ejde-355	299	2	.	.	PUNCT
ejde-355	300	1	we	we	PRON
ejde-355	300	2	take	take	VERB
ejde-355	300	3	εm	εm	NOUN
ejde-355	300	4	∈]0	∈]0	ADJ
ejde-355	300	5	,	,	PUNCT
ejde-355	300	6	ε2	ε2	ADJ
ejde-355	300	7	[	[	PUNCT
ejde-355	300	8	small	small	ADJ
ejde-355	300	9	enough	enough	ADV
ejde-355	300	10	and	and	CCONJ
ejde-355	300	11	we	we	PRON
ejde-355	300	12	can	can	AUX
ejde-355	300	13	assume	assume	VERB
ejde-355	300	14	that	that	DET
ejde-355	300	15	εωm	εωm	NOUN
ejde-355	300	16	⊆	⊆	SYM
ejde-355	300	17	ωo	ωo	ADP
ejde-355	300	18	∀ε	∀ε	PROPN
ejde-355	300	19	∈]−	∈]−	PROPN
ejde-355	300	20	εm	εm	PROPN
ejde-355	300	21	,	,	PUNCT
ejde-355	300	22	εm	εm	PROPN
ejde-355	300	23	[	[	PUNCT
ejde-355	300	24	.	.	PUNCT
ejde-355	301	1	if	if	SCONJ
ejde-355	301	2	ε	ε	PROPN
ejde-355	301	3	∈]0	∈]0	AUX
ejde-355	301	4	,	,	PUNCT
ejde-355	301	5	εm	εm	PROPN
ejde-355	301	6	[	[	PUNCT
ejde-355	301	7	then	then	ADV
ejde-355	301	8	u(ε	u(ε	PROPN
ejde-355	301	9	,	,	PUNCT
ejde-355	301	10	εt	εt	PROPN
ejde-355	301	11	)	)	PUNCT
ejde-355	301	12	=	=	SYM
ejde-355	301	13	∫	∫	PROPN
ejde-355	301	14	∂ωo	∂ωo	NOUN
ejde-355	301	15	s2(εt−	s2(εt−	PROPN
ejde-355	301	16	y)mo[ε	y)mo[ε	PROPN
ejde-355	301	17	,	,	PUNCT
ejde-355	301	18	εδ(ε	εδ(ε	NOUN
ejde-355	301	19	)	)	PUNCT
ejde-355	301	20	,	,	PUNCT
ejde-355	301	21	εδ(ε	εδ(ε	VERB
ejde-355	301	22	)	)	PUNCT
ejde-355	301	23	log	log	PROPN
ejde-355	301	24	ε	ε	PROPN
ejde-355	301	25	,	,	PUNCT
ejde-355	301	26	η(ε	η(ε	NOUN
ejde-355	301	27	)	)	PUNCT
ejde-355	301	28	,	,	PUNCT
ejde-355	301	29	ε	ε	PROPN
ejde-355	301	30	ρ(ε	ρ(ε	NUM
ejde-355	301	31	)	)	PUNCT
ejde-355	301	32	]	]	PUNCT
ejde-355	301	33	(	(	PUNCT
ejde-355	301	34	y	y	X
ejde-355	301	35	)	)	PUNCT
ejde-355	301	36	dσy	dσy	PROPN
ejde-355	302	1	+	+	CCONJ
ejde-355	302	2	∫	∫	PROPN
ejde-355	302	3	∂ωi	∂ωi	PROPN
ejde-355	302	4	s2(εt−	s2(εt−	PROPN
ejde-355	302	5	εs)m	εs)m	NUM
ejde-355	302	6	i[ε	i[ε	NOUN
ejde-355	302	7	,	,	PUNCT
ejde-355	302	8	εδ(ε	εδ(ε	NOUN
ejde-355	302	9	)	)	PUNCT
ejde-355	302	10	,	,	PUNCT
ejde-355	302	11	εδ(ε	εδ(ε	VERB
ejde-355	302	12	)	)	PUNCT
ejde-355	302	13	log	log	PROPN
ejde-355	302	14	ε	ε	PROPN
ejde-355	302	15	,	,	PUNCT
ejde-355	302	16	η(ε	η(ε	NOUN
ejde-355	302	17	)	)	PUNCT
ejde-355	302	18	,	,	PUNCT
ejde-355	302	19	ε	ε	PROPN
ejde-355	302	20	ρ(ε	ρ(ε	NUM
ejde-355	302	21	)	)	PUNCT
ejde-355	302	22	]	]	PUNCT
ejde-355	302	23	(	(	PUNCT
ejde-355	302	24	s	s	X
ejde-355	302	25	)	)	PUNCT
ejde-355	302	26	dσs	dσs	NOUN
ejde-355	302	27	+	+	CCONJ
ejde-355	302	28	ξ[ε	ξ[ε	NOUN
ejde-355	302	29	,	,	PUNCT
ejde-355	302	30	εδ(ε	εδ(ε	NOUN
ejde-355	302	31	)	)	PUNCT
ejde-355	302	32	,	,	PUNCT
ejde-355	302	33	εδ(ε	εδ(ε	VERB
ejde-355	302	34	)	)	PUNCT
ejde-355	302	35	log	log	PROPN
ejde-355	302	36	ε	ε	PROPN
ejde-355	302	37	,	,	PUNCT
ejde-355	302	38	η(ε	η(ε	NOUN
ejde-355	302	39	)	)	PUNCT
ejde-355	302	40	,	,	PUNCT
ejde-355	302	41	ε	ε	PROPN
ejde-355	302	42	ρ(ε	ρ(ε	NUM
ejde-355	302	43	)	)	PUNCT
ejde-355	302	44	]	]	PUNCT
ejde-355	303	1	δ(ε)ε	δ(ε)ε	PROPN
ejde-355	303	2	=	=	SYM
ejde-355	303	3	∫	∫	PROPN
ejde-355	303	4	∂ωo	∂ωo	PROPN
ejde-355	303	5	s2(εt−	s2(εt−	PROPN
ejde-355	303	6	y)mo[ε	y)mo[ε	PROPN
ejde-355	303	7	,	,	PUNCT
ejde-355	303	8	εδ(ε	εδ(ε	NOUN
ejde-355	303	9	)	)	PUNCT
ejde-355	303	10	,	,	PUNCT
ejde-355	303	11	εδ(ε	εδ(ε	VERB
ejde-355	303	12	)	)	PUNCT
ejde-355	303	13	log	log	PROPN
ejde-355	303	14	ε	ε	PROPN
ejde-355	303	15	,	,	PUNCT
ejde-355	303	16	η(ε	η(ε	NOUN
ejde-355	303	17	)	)	PUNCT
ejde-355	303	18	,	,	PUNCT
ejde-355	303	19	ε	ε	PROPN
ejde-355	303	20	ρ(ε	ρ(ε	NUM
ejde-355	303	21	)	)	PUNCT
ejde-355	303	22	]	]	PUNCT
ejde-355	303	23	(	(	PUNCT
ejde-355	303	24	y	y	X
ejde-355	303	25	)	)	PUNCT
ejde-355	303	26	dσy	dσy	PROPN
ejde-355	304	1	+	+	CCONJ
ejde-355	304	2	∫	∫	PROPN
ejde-355	304	3	∂ωi	∂ωi	PROPN
ejde-355	304	4	s2(t−	s2(t−	NOUN
ejde-355	304	5	s)m	s)m	ADJ
ejde-355	304	6	i[ε	i[ε	NOUN
ejde-355	304	7	,	,	PUNCT
ejde-355	304	8	εδ(ε	εδ(ε	NOUN
ejde-355	304	9	)	)	PUNCT
ejde-355	304	10	,	,	PUNCT
ejde-355	304	11	εδ(ε	εδ(ε	VERB
ejde-355	304	12	)	)	PUNCT
ejde-355	304	13	log	log	PROPN
ejde-355	304	14	ε	ε	PROPN
ejde-355	304	15	,	,	PUNCT
ejde-355	304	16	η(ε	η(ε	NOUN
ejde-355	304	17	)	)	PUNCT
ejde-355	304	18	,	,	PUNCT
ejde-355	304	19	ε	ε	PROPN
ejde-355	304	20	ρ(ε	ρ(ε	NUM
ejde-355	304	21	)	)	PUNCT
ejde-355	304	22	]	]	PUNCT
ejde-355	304	23	(	(	PUNCT
ejde-355	304	24	s	s	X
ejde-355	304	25	)	)	PUNCT
ejde-355	304	26	dσs	dσs	NOUN
ejde-355	304	27	+	+	CCONJ
ejde-355	304	28	log	log	NOUN
ejde-355	304	29	ε	ε	PROPN
ejde-355	304	30	2π	2π	PROPN
ejde-355	304	31	∫	∫	INTJ
ejde-355	305	1	∂ωi	∂ωi	PROPN
ejde-355	305	2	m	m	NOUN
ejde-355	305	3	i[ε	i[ε	NOUN
ejde-355	305	4	,	,	PUNCT
ejde-355	305	5	εδ(ε	εδ(ε	NOUN
ejde-355	305	6	)	)	PUNCT
ejde-355	305	7	,	,	PUNCT
ejde-355	305	8	εδ(ε	εδ(ε	VERB
ejde-355	305	9	)	)	PUNCT
ejde-355	305	10	log	log	PROPN
ejde-355	305	11	ε	ε	PROPN
ejde-355	305	12	,	,	PUNCT
ejde-355	305	13	η(ε	η(ε	NOUN
ejde-355	305	14	)	)	PUNCT
ejde-355	305	15	,	,	PUNCT
ejde-355	305	16	ε	ε	PROPN
ejde-355	305	17	ρ(ε	ρ(ε	NUM
ejde-355	305	18	)	)	PUNCT
ejde-355	305	19	]	]	PUNCT
ejde-355	305	20	(	(	PUNCT
ejde-355	305	21	s	s	X
ejde-355	305	22	)	)	PUNCT
ejde-355	305	23	dσs	dσs	NOUN
ejde-355	305	24	+	+	CCONJ
ejde-355	305	25	ξ[ε	ξ[ε	NOUN
ejde-355	305	26	,	,	PUNCT
ejde-355	305	27	εδ(ε	εδ(ε	NOUN
ejde-355	305	28	)	)	PUNCT
ejde-355	305	29	,	,	PUNCT
ejde-355	305	30	εδ(ε	εδ(ε	VERB
ejde-355	305	31	)	)	PUNCT
ejde-355	305	32	log	log	PROPN
ejde-355	305	33	ε	ε	PROPN
ejde-355	305	34	,	,	PUNCT
ejde-355	305	35	η(ε	η(ε	NOUN
ejde-355	305	36	)	)	PUNCT
ejde-355	305	37	,	,	PUNCT
ejde-355	305	38	ε	ε	PROPN
ejde-355	305	39	ρ(ε	ρ(ε	NUM
ejde-355	305	40	)	)	PUNCT
ejde-355	305	41	]	]	PUNCT
ejde-355	306	1	δ(ε)ε	δ(ε)ε	PROPN
ejde-355	306	2	∀t	∀t	PROPN
ejde-355	306	3	∈	∈	PRON
ejde-355	306	4	ωm	ωm	X
ejde-355	306	5	(	(	PUNCT
ejde-355	306	6	cf	cf	NOUN
ejde-355	306	7	.	.	PUNCT
ejde-355	307	1	definition	definition	NOUN
ejde-355	307	2	4.2	4.2	NUM
ejde-355	307	3	)	)	PUNCT
ejde-355	307	4	.	.	PUNCT
ejde-355	308	1	hence	hence	ADV
ejde-355	308	2	,	,	PUNCT
ejde-355	308	3	we	we	PRON
ejde-355	308	4	set	set	VERB
ejde-355	308	5	um[ε	um[ε	PROPN
ejde-355	308	6	,	,	PUNCT
ejde-355	308	7	γ1	γ1	NOUN
ejde-355	308	8	,	,	PUNCT
ejde-355	308	9	γ2	γ2	PROPN
ejde-355	308	10	,	,	PUNCT
ejde-355	308	11	γ3	γ3	NOUN
ejde-355	308	12	,	,	PUNCT
ejde-355	308	13	γ4](t	γ4](t	ADV
ejde-355	308	14	)	)	PUNCT
ejde-355	308	15	≡	≡	PROPN
ejde-355	308	16	∫	∫	PROPN
ejde-355	308	17	∂ωo	∂ωo	PROPN
ejde-355	308	18	s2(εt−	s2(εt−	VERB
ejde-355	308	19	y)mo[ε	y)mo[ε	PROPN
ejde-355	308	20	,	,	PUNCT
ejde-355	308	21	γ1	γ1	NOUN
ejde-355	308	22	,	,	PUNCT
ejde-355	308	23	γ2	γ2	PROPN
ejde-355	308	24	,	,	PUNCT
ejde-355	308	25	γ3	γ3	NOUN
ejde-355	308	26	,	,	PUNCT
ejde-355	308	27	γ4](y	γ4](y	PROPN
ejde-355	308	28	)	)	PUNCT
ejde-355	308	29	dσy	dσy	NOUN
ejde-355	309	1	+	+	CCONJ
ejde-355	309	2	∫	∫	PROPN
ejde-355	309	3	∂ωi	∂ωi	PROPN
ejde-355	309	4	s2(t−	s2(t−	NOUN
ejde-355	309	5	s)m	s)m	ADJ
ejde-355	309	6	i[ε	i[ε	NOUN
ejde-355	309	7	,	,	PUNCT
ejde-355	309	8	γ1	γ1	NOUN
ejde-355	309	9	,	,	PUNCT
ejde-355	309	10	γ2	γ2	PROPN
ejde-355	309	11	,	,	PUNCT
ejde-355	309	12	γ3	γ3	NOUN
ejde-355	309	13	,	,	PUNCT
ejde-355	309	14	γ4](s	γ4](s	PROPN
ejde-355	309	15	)	)	PUNCT
ejde-355	309	16	dσs	dσs	NOUN
ejde-355	309	17	∀t	∀t	PROPN
ejde-355	309	18	∈	∈	NOUN
ejde-355	309	19	ωm	ωm	NUM
ejde-355	309	20	,	,	PUNCT
ejde-355	309	21	for	for	ADP
ejde-355	309	22	all	all	DET
ejde-355	309	23	(	(	PUNCT
ejde-355	309	24	ε	ε	PROPN
ejde-355	309	25	,	,	PUNCT
ejde-355	309	26	γ1	γ1	NOUN
ejde-355	309	27	,	,	PUNCT
ejde-355	309	28	γ2	γ2	PROPN
ejde-355	309	29	,	,	PUNCT
ejde-355	309	30	γ3	γ3	NOUN
ejde-355	309	31	,	,	PUNCT
ejde-355	309	32	γ4	γ4	NOUN
ejde-355	309	33	)	)	PUNCT
ejde-355	309	34	∈	∈	PROPN
ejde-355	309	35	]	]	PUNCT
ejde-355	309	36	−	−	PROPN
ejde-355	309	37	εm	εm	PROPN
ejde-355	309	38	,	,	PUNCT
ejde-355	309	39	εm[×u	εm[×u	NOUN
ejde-355	309	40	.	.	PUNCT
ejde-355	310	1	by	by	ADP
ejde-355	310	2	arguing	argue	VERB
ejde-355	310	3	as	as	ADP
ejde-355	310	4	in	in	ADP
ejde-355	310	5	the	the	DET
ejde-355	310	6	proof	proof	NOUN
ejde-355	310	7	of	of	ADP
ejde-355	310	8	theorem	theorem	NOUN
ejde-355	310	9	4.3	4.3	NUM
ejde-355	310	10	,	,	PUNCT
ejde-355	310	11	we	we	PRON
ejde-355	310	12	verify	verify	VERB
ejde-355	310	13	that	that	SCONJ
ejde-355	310	14	um	um	INTJ
ejde-355	310	15	and	and	CCONJ
ejde-355	310	16	the	the	DET
ejde-355	310	17	map	map	NOUN
ejde-355	310	18	zm	zm	PROPN
ejde-355	310	19	of	of	ADP
ejde-355	310	20	the	the	DET
ejde-355	310	21	statement	statement	NOUN
ejde-355	310	22	are	be	AUX
ejde-355	310	23	real	real	ADV
ejde-355	310	24	analytic	analytic	ADJ
ejde-355	310	25	from	from	ADP
ejde-355	310	26	]	]	PUNCT
ejde-355	310	27	−	−	PROPN
ejde-355	310	28	εm	εm	PROPN
ejde-355	310	29	,	,	PUNCT
ejde-355	310	30	εm[×u	εm[×u	NOUN
ejde-355	310	31	to	to	PART
ejde-355	310	32	c1,α(ωm	c1,α(ωm	VERB
ejde-355	310	33	)	)	PUNCT
ejde-355	310	34	and	and	CCONJ
ejde-355	310	35	to	to	ADP
ejde-355	310	36	r	r	NOUN
ejde-355	310	37	,	,	PUNCT
ejde-355	310	38	respectively	respectively	ADV
ejde-355	310	39	,	,	PUNCT
ejde-355	310	40	and	and	CCONJ
ejde-355	310	41	that	that	DET
ejde-355	310	42	equality	equality	NOUN
ejde-355	310	43	(	(	PUNCT
ejde-355	310	44	4.18	4.18	NUM
ejde-355	310	45	)	)	PUNCT
ejde-355	310	46	holds	hold	VERB
ejde-355	310	47	.	.	PUNCT
ejde-355	311	1	by	by	ADP
ejde-355	311	2	proposition	proposition	NOUN
ejde-355	311	3	4.1	4.1	NUM
ejde-355	311	4	,	,	PUNCT
ejde-355	311	5	we	we	PRON
ejde-355	311	6	also	also	ADV
ejde-355	311	7	deduce	deduce	VERB
ejde-355	311	8	that	that	SCONJ
ejde-355	311	9	zm[0	zm[0	NUM
ejde-355	311	10	,	,	PUNCT
ejde-355	311	11	0	0	NUM
ejde-355	311	12	,	,	PUNCT
ejde-355	311	13	l0	l0	PROPN
ejde-355	311	14	,	,	PUNCT
ejde-355	311	15	η0	η0	NOUN
ejde-355	311	16	,	,	PUNCT
ejde-355	311	17	r0	r0	NOUN
ejde-355	311	18	]	]	PUNCT
ejde-355	311	19	=	=	PUNCT
ejde-355	311	20	∫	∫	PROPN
ejde-355	311	21	∂ωo	∂ωo	NOUN
ejde-355	311	22	g	g	PROPN
ejde-355	311	23	o	o	NOUN
ejde-355	311	24	dσ	dσ	ADP
ejde-355	311	25	,	,	PUNCT
ejde-355	311	26	that	that	SCONJ
ejde-355	311	27	um[0	um[0	NOUN
ejde-355	311	28	,	,	PUNCT
ejde-355	311	29	0	0	NUM
ejde-355	311	30	,	,	PUNCT
ejde-355	311	31	l0	l0	PROPN
ejde-355	311	32	,	,	PUNCT
ejde-355	311	33	η0	η0	NOUN
ejde-355	311	34	,	,	PUNCT
ejde-355	311	35	r0	r0	NOUN
ejde-355	311	36	]	]	PUNCT
ejde-355	311	37	=	=	SYM
ejde-355	311	38	ũm|ωm	ũm|ωm	NOUN
ejde-355	311	39	.	.	PUNCT
ejde-355	312	1	also	also	ADV
ejde-355	312	2	by	by	ADP
ejde-355	312	3	standard	standard	ADJ
ejde-355	312	4	properties	property	NOUN
ejde-355	312	5	of	of	ADP
ejde-355	312	6	the	the	DET
ejde-355	312	7	single	single	ADJ
ejde-355	312	8	layer	layer	NOUN
ejde-355	312	9	potential	potential	NOUN
ejde-355	312	10	(	(	PUNCT
ejde-355	312	11	cf	cf	NOUN
ejde-355	312	12	.	.	PUNCT
ejde-355	313	1	[	[	X
ejde-355	313	2	9	9	NUM
ejde-355	313	3	,	,	PUNCT
ejde-355	313	4	§	§	NOUN
ejde-355	313	5	4.4	4.4	NUM
ejde-355	313	6	]	]	PUNCT
ejde-355	313	7	)	)	PUNCT
ejde-355	313	8	,	,	PUNCT
ejde-355	313	9	we	we	PRON
ejde-355	313	10	deduce	deduce	VERB
ejde-355	313	11	that	that	SCONJ
ejde-355	313	12	ũm	ũm	PROPN
ejde-355	313	13	is	be	AUX
ejde-355	313	14	a	a	DET
ejde-355	313	15	solution	solution	NOUN
ejde-355	313	16	of	of	ADP
ejde-355	313	17	the	the	DET
ejde-355	313	18	neumann	neumann	PROPN
ejde-355	313	19	problem	problem	NOUN
ejde-355	313	20	(	(	PUNCT
ejde-355	313	21	4.20	4.20	NUM
ejde-355	313	22	)	)	PUNCT
ejde-355	313	23	.	.	PUNCT
ejde-355	314	1	�	�	PROPN
ejde-355	314	2	remark	remark	VERB
ejde-355	314	3	4.5	4.5	NUM
ejde-355	314	4	.	.	PUNCT
ejde-355	315	1	we	we	PRON
ejde-355	315	2	note	note	VERB
ejde-355	315	3	that	that	SCONJ
ejde-355	315	4	if	if	SCONJ
ejde-355	315	5	∫	∫	PROPN
ejde-355	315	6	∂ωi	∂ωi	NOUN
ejde-355	315	7	µ̃	µ̃	PROPN
ejde-355	315	8	i	i	PRON
ejde-355	315	9	dσ	dσ	VERB
ejde-355	315	10	6=	6=	PRON
ejde-355	315	11	0	0	NUM
ejde-355	315	12	(	(	PUNCT
ejde-355	315	13	i.e.	i.e.	X
ejde-355	315	14	,	,	PUNCT
ejde-355	315	15	if	if	SCONJ
ejde-355	315	16	∫	∫	PROPN
ejde-355	315	17	∂ωo	∂ωo	NOUN
ejde-355	315	18	g	g	ADP
ejde-355	315	19	o	o	NOUN
ejde-355	315	20	dσ	dσ	ADP
ejde-355	315	21	6=	6=	PROPN
ejde-355	315	22	0	0	NUM
ejde-355	315	23	)	)	PUNCT
ejde-355	315	24	,	,	PUNCT
ejde-355	315	25	then	then	ADV
ejde-355	315	26	the	the	DET
ejde-355	315	27	function	function	NOUN
ejde-355	315	28	ũm	ũm	X
ejde-355	315	29	of	of	ADP
ejde-355	315	30	theorem	theorem	ADJ
ejde-355	315	31	4.4	4.4	NUM
ejde-355	315	32	is	be	AUX
ejde-355	315	33	not	not	PART
ejde-355	315	34	harmonic	harmonic	ADJ
ejde-355	315	35	at	at	ADP
ejde-355	315	36	infinity	infinity	NOUN
ejde-355	315	37	(	(	PUNCT
ejde-355	315	38	cf	cf	NOUN
ejde-355	315	39	.	.	PUNCT
ejde-355	316	1	[	[	X
ejde-355	316	2	9	9	NUM
ejde-355	316	3	,	,	PUNCT
ejde-355	316	4	definition	definition	NOUN
ejde-355	316	5	3.21	3.21	NUM
ejde-355	316	6	and	and	CCONJ
ejde-355	316	7	theorem	theorem	VERB
ejde-355	316	8	4.23	4.23	NUM
ejde-355	316	9	]	]	PUNCT
ejde-355	316	10	)	)	PUNCT
ejde-355	316	11	.	.	PUNCT
ejde-355	317	1	ejde-2023/57	ejde-2023/57	NOUN
ejde-355	317	2	asymptotic	asymptotic	ADJ
ejde-355	317	3	analysis	analysis	NOUN
ejde-355	317	4	of	of	ADP
ejde-355	317	5	perturbed	perturb	VERB
ejde-355	317	6	robin	robin	PROPN
ejde-355	317	7	problems	problem	VERB
ejde-355	317	8	15	15	NUM
ejde-355	317	9	finally	finally	ADV
ejde-355	317	10	,	,	PUNCT
ejde-355	317	11	we	we	PRON
ejde-355	317	12	study	study	VERB
ejde-355	317	13	the	the	DET
ejde-355	317	14	behavior	behavior	NOUN
ejde-355	317	15	of	of	ADP
ejde-355	317	16	the	the	DET
ejde-355	317	17	energy	energy	NOUN
ejde-355	317	18	integral	integral	ADJ
ejde-355	317	19	∫	∫	PROPN
ejde-355	317	20	ω(ε	ω(ε	PROPN
ejde-355	317	21	)	)	PUNCT
ejde-355	317	22	|∇u(ε	|∇u(ε	X
ejde-355	317	23	,	,	PUNCT
ejde-355	317	24	x)|2	x)|2	PROPN
ejde-355	317	25	dx	dx	PROPN
ejde-355	317	26	as	as	SCONJ
ejde-355	317	27	the	the	DET
ejde-355	317	28	parameter	parameter	NOUN
ejde-355	317	29	ε	ε	PROPN
ejde-355	317	30	approaches	approach	VERB
ejde-355	317	31	0	0	NUM
ejde-355	317	32	.	.	PUNCT
ejde-355	318	1	theorem	theorem	VERB
ejde-355	318	2	4.6	4.6	NUM
ejde-355	318	3	.	.	PUNCT
ejde-355	319	1	let	let	VERB
ejde-355	319	2	the	the	DET
ejde-355	319	3	assumptions	assumption	NOUN
ejde-355	319	4	of	of	ADP
ejde-355	319	5	proposition	proposition	NOUN
ejde-355	319	6	4.1	4.1	NUM
ejde-355	319	7	hold	hold	NOUN
ejde-355	319	8	.	.	PUNCT
ejde-355	320	1	let	let	VERB
ejde-355	320	2	ũm	ũm	NOUN
ejde-355	320	3	and	and	CCONJ
ejde-355	320	4	ũm	ũm	NOUN
ejde-355	320	5	be	be	VERB
ejde-355	320	6	as	as	ADP
ejde-355	320	7	in	in	ADP
ejde-355	320	8	theorem	theorem	ADJ
ejde-355	320	9	4.3	4.3	NUM
ejde-355	320	10	and	and	CCONJ
ejde-355	320	11	theorem	theorem	VERB
ejde-355	320	12	4.4	4.4	NUM
ejde-355	320	13	,	,	PUNCT
ejde-355	320	14	respectively	respectively	ADV
ejde-355	320	15	.	.	PUNCT
ejde-355	321	1	then	then	ADV
ejde-355	321	2	there	there	PRON
ejde-355	321	3	exist	exist	VERB
ejde-355	321	4	εe	εe	ADP
ejde-355	321	5	∈]0	∈]0	ADJ
ejde-355	321	6	,	,	PUNCT
ejde-355	321	7	ε2	ε2	PROPN
ejde-355	321	8	[	[	PUNCT
ejde-355	321	9	and	and	CCONJ
ejde-355	321	10	two	two	NUM
ejde-355	321	11	real	real	ADJ
ejde-355	321	12	analytic	analytic	ADJ
ejde-355	321	13	maps	map	NOUN
ejde-355	321	14	e1	e1	PROPN
ejde-355	321	15	and	and	CCONJ
ejde-355	321	16	e2	e2	PROPN
ejde-355	321	17	from	from	ADP
ejde-355	321	18	]	]	PUNCT
ejde-355	321	19	−	−	NOUN
ejde-355	321	20	εe	εe	NOUN
ejde-355	321	21	,	,	PUNCT
ejde-355	321	22	εe[×u	εe[×u	NOUN
ejde-355	321	23	to	to	PART
ejde-355	321	24	r	r	VERB
ejde-355	321	25	such	such	ADJ
ejde-355	321	26	that∫	that∫	NOUN
ejde-355	321	27	ω(ε	ω(ε	PROPN
ejde-355	321	28	)	)	PUNCT
ejde-355	321	29	|∇u(ε	|∇u(ε	X
ejde-355	321	30	,	,	PUNCT
ejde-355	321	31	x)|2	x)|2	PROPN
ejde-355	321	32	dx	dx	PROPN
ejde-355	321	33	=	=	SYM
ejde-355	321	34	e1[ε	e1[ε	PROPN
ejde-355	321	35	,	,	PUNCT
ejde-355	321	36	εδ(ε	εδ(ε	NOUN
ejde-355	321	37	)	)	PUNCT
ejde-355	321	38	,	,	PUNCT
ejde-355	321	39	εδ(ε	εδ(ε	VERB
ejde-355	321	40	)	)	PUNCT
ejde-355	321	41	log	log	PROPN
ejde-355	321	42	ε	ε	PROPN
ejde-355	321	43	,	,	PUNCT
ejde-355	321	44	η(ε	η(ε	NOUN
ejde-355	321	45	)	)	PUNCT
ejde-355	321	46	,	,	PUNCT
ejde-355	321	47	ε	ε	PROPN
ejde-355	321	48	ρ(ε	ρ(ε	NUM
ejde-355	321	49	)	)	PUNCT
ejde-355	321	50	]	]	PUNCT
ejde-355	322	1	+	+	CCONJ
ejde-355	322	2	(	(	PUNCT
ejde-355	322	3	log	log	VERB
ejde-355	322	4	ε)e2[ε	ε)e2[ε	NOUN
ejde-355	322	5	,	,	PUNCT
ejde-355	322	6	εδ(ε	εδ(ε	NOUN
ejde-355	322	7	)	)	PUNCT
ejde-355	322	8	,	,	PUNCT
ejde-355	322	9	εδ(ε	εδ(ε	VERB
ejde-355	322	10	)	)	PUNCT
ejde-355	322	11	log	log	PROPN
ejde-355	322	12	ε	ε	PROPN
ejde-355	322	13	,	,	PUNCT
ejde-355	322	14	η(ε	η(ε	NOUN
ejde-355	322	15	)	)	PUNCT
ejde-355	322	16	,	,	PUNCT
ejde-355	322	17	ε	ε	PROPN
ejde-355	322	18	ρ(ε	ρ(ε	NUM
ejde-355	322	19	)	)	PUNCT
ejde-355	322	20	]	]	PUNCT
ejde-355	322	21	,	,	PUNCT
ejde-355	322	22	(	(	PUNCT
ejde-355	322	23	4.21	4.21	NUM
ejde-355	322	24	)	)	PUNCT
ejde-355	322	25	for	for	ADP
ejde-355	322	26	all	all	DET
ejde-355	322	27	ε	ε	PROPN
ejde-355	322	28	∈]0	∈]0	AUX
ejde-355	322	29	,	,	PUNCT
ejde-355	322	30	εe	εe	ADP
ejde-355	322	31	[	[	X
ejde-355	322	32	.	.	PUNCT
ejde-355	323	1	moreover	moreover	ADV
ejde-355	323	2	,	,	PUNCT
ejde-355	323	3	e1[0	e1[0	PROPN
ejde-355	323	4	,	,	PUNCT
ejde-355	323	5	0	0	NUM
ejde-355	323	6	,	,	PUNCT
ejde-355	323	7	l0	l0	PROPN
ejde-355	323	8	,	,	PUNCT
ejde-355	323	9	η0	η0	NOUN
ejde-355	323	10	,	,	PUNCT
ejde-355	323	11	r0	r0	NOUN
ejde-355	323	12	]	]	PUNCT
ejde-355	323	13	=	=	SYM
ejde-355	323	14	∫	∫	PROPN
ejde-355	323	15	∂ωo	∂ωo	NOUN
ejde-355	323	16	(	(	PUNCT
ejde-355	323	17	ũm	ũm	X
ejde-355	323	18	(	(	PUNCT
ejde-355	323	19	x	x	X
ejde-355	323	20	)	)	PUNCT
ejde-355	323	21	+	+	NUM
ejde-355	323	22	s2(x	s2(x	X
ejde-355	323	23	)	)	PUNCT
ejde-355	323	24	∫	∫	PROPN
ejde-355	324	1	∂ωo	∂ωo	NOUN
ejde-355	324	2	go	go	VERB
ejde-355	324	3	dσ	dσ	PROPN
ejde-355	324	4	)	)	PUNCT
ejde-355	324	5	νωo(x	νωo(x	PROPN
ejde-355	324	6	)	)	PUNCT
ejde-355	324	7	·	·	PUNCT
ejde-355	324	8	∇	∇	X
ejde-355	324	9	(	(	PUNCT
ejde-355	324	10	ũm	ũm	X
ejde-355	324	11	(	(	PUNCT
ejde-355	324	12	x	x	X
ejde-355	324	13	)	)	PUNCT
ejde-355	324	14	+	+	NUM
ejde-355	324	15	s2(x	s2(x	X
ejde-355	324	16	)	)	PUNCT
ejde-355	324	17	∫	∫	PROPN
ejde-355	325	1	∂ωo	∂ωo	NOUN
ejde-355	325	2	go	go	VERB
ejde-355	325	3	dσ	dσ	PROPN
ejde-355	325	4	)	)	PUNCT
ejde-355	325	5	dσx	dσx	NOUN
ejde-355	325	6	−	−	PROPN
ejde-355	325	7	∫	∫	NOUN
ejde-355	325	8	∂ωi	∂ωi	PROPN
ejde-355	325	9	ũm(t)νωi(t	ũm(t)νωi(t	NOUN
ejde-355	325	10	)	)	PUNCT
ejde-355	325	11	·	·	PUNCT
ejde-355	326	1	∇ũm(t	∇ũm(t	NOUN
ejde-355	326	2	)	)	PUNCT
ejde-355	326	3	dσt	dσt	NOUN
ejde-355	326	4	(	(	PUNCT
ejde-355	326	5	4.22	4.22	NUM
ejde-355	326	6	)	)	PUNCT
ejde-355	326	7	and	and	CCONJ
ejde-355	326	8	e2[0	e2[0	PROPN
ejde-355	326	9	,	,	PUNCT
ejde-355	326	10	0	0	NUM
ejde-355	326	11	,	,	PUNCT
ejde-355	326	12	l0	l0	PROPN
ejde-355	326	13	,	,	PUNCT
ejde-355	326	14	η0	η0	NOUN
ejde-355	326	15	,	,	PUNCT
ejde-355	326	16	r0	r0	NOUN
ejde-355	326	17	]	]	PUNCT
ejde-355	326	18	=	=	PUNCT
ejde-355	327	1	−	−	PROPN
ejde-355	327	2	1	1	NUM
ejde-355	327	3	2π	2π	NOUN
ejde-355	327	4	(	(	PUNCT
ejde-355	327	5	∫	∫	PROPN
ejde-355	327	6	∂ωo	∂ωo	NOUN
ejde-355	327	7	go	go	VERB
ejde-355	327	8	dσ	dσ	PROPN
ejde-355	327	9	)	)	PUNCT
ejde-355	327	10	2	2	NUM
ejde-355	327	11	.	.	PUNCT
ejde-355	328	1	(	(	PUNCT
ejde-355	328	2	4.23	4.23	NUM
ejde-355	328	3	)	)	PUNCT
ejde-355	328	4	proof	proof	NOUN
ejde-355	328	5	.	.	PUNCT
ejde-355	329	1	we	we	PRON
ejde-355	329	2	set	set	VERB
ejde-355	329	3	cε	cε	PUNCT
ejde-355	329	4	≡	≡	PROPN
ejde-355	329	5	log	log	PROPN
ejde-355	329	6	ε	ε	PROPN
ejde-355	329	7	2π	2π	PROPN
ejde-355	329	8	zm	zm	PROPN
ejde-355	329	9	[	[	PUNCT
ejde-355	329	10	ε	ε	PROPN
ejde-355	329	11	,	,	PUNCT
ejde-355	329	12	εδ(ε	εδ(ε	NOUN
ejde-355	329	13	)	)	PUNCT
ejde-355	329	14	,	,	PUNCT
ejde-355	329	15	εδ(ε	εδ(ε	VERB
ejde-355	329	16	)	)	PUNCT
ejde-355	329	17	log	log	PROPN
ejde-355	329	18	ε	ε	PROPN
ejde-355	329	19	,	,	PUNCT
ejde-355	329	20	η(ε	η(ε	NOUN
ejde-355	329	21	)	)	PUNCT
ejde-355	329	22	,	,	PUNCT
ejde-355	329	23	ε	ε	PROPN
ejde-355	329	24	ρ(ε	ρ(ε	NUM
ejde-355	329	25	)	)	PUNCT
ejde-355	329	26	]	]	PUNCT
ejde-355	330	1	+	+	CCONJ
ejde-355	330	2	ξ[ε	ξ[ε	NUM
ejde-355	330	3	,	,	PUNCT
ejde-355	330	4	εδ(ε	εδ(ε	NOUN
ejde-355	330	5	)	)	PUNCT
ejde-355	330	6	,	,	PUNCT
ejde-355	330	7	εδ(ε	εδ(ε	VERB
ejde-355	330	8	)	)	PUNCT
ejde-355	330	9	log	log	PROPN
ejde-355	330	10	ε	ε	PROPN
ejde-355	330	11	,	,	PUNCT
ejde-355	330	12	η(ε	η(ε	NOUN
ejde-355	330	13	)	)	PUNCT
ejde-355	330	14	,	,	PUNCT
ejde-355	330	15	ε	ε	PROPN
ejde-355	330	16	ρ(ε	ρ(ε	NUM
ejde-355	330	17	)	)	PUNCT
ejde-355	330	18	]	]	PUNCT
ejde-355	331	1	δ(ε)ε	δ(ε)ε	PROPN
ejde-355	331	2	∀ε	∀ε	PUNCT
ejde-355	331	3	∈]0	∈]0	X
ejde-355	331	4	,	,	PUNCT
ejde-355	331	5	ε2	ε2	PROPN
ejde-355	331	6	[	[	PUNCT
ejde-355	331	7	.	.	PUNCT
ejde-355	332	1	the	the	DET
ejde-355	332	2	divergence	divergence	NOUN
ejde-355	332	3	theorem	theorem	NOUN
ejde-355	332	4	implies	imply	VERB
ejde-355	332	5	that∫	that∫	PROPN
ejde-355	332	6	ω(ε	ω(ε	PROPN
ejde-355	332	7	)	)	PUNCT
ejde-355	333	1	|∇u(ε	|∇u(ε	X
ejde-355	333	2	,	,	PUNCT
ejde-355	333	3	x)|2	x)|2	PROPN
ejde-355	333	4	dx	dx	PROPN
ejde-355	333	5	=	=	SYM
ejde-355	333	6	∫	∫	PROPN
ejde-355	333	7	ω(ε	ω(ε	PROPN
ejde-355	333	8	)	)	PUNCT
ejde-355	334	1	|∇	|∇	PROPN
ejde-355	334	2	(	(	PUNCT
ejde-355	334	3	u(ε	u(ε	PROPN
ejde-355	334	4	,	,	PUNCT
ejde-355	334	5	x)−	x)−	PROPN
ejde-355	334	6	cε	cε	NUM
ejde-355	334	7	)	)	PUNCT
ejde-355	334	8	|2	|2	NUM
ejde-355	334	9	dx	dx	PROPN
ejde-355	335	1	=	=	SYM
ejde-355	335	2	∫	∫	PROPN
ejde-355	335	3	∂ωo	∂ωo	NOUN
ejde-355	335	4	(	(	PUNCT
ejde-355	335	5	u(ε	u(ε	PROPN
ejde-355	335	6	,	,	PUNCT
ejde-355	335	7	x)−	x)−	PROPN
ejde-355	335	8	cε	cε	NUM
ejde-355	335	9	)	)	PUNCT
ejde-355	335	10	∂	∂	X
ejde-355	335	11	∂νωo	∂νωo	NUM
ejde-355	335	12	(	(	PUNCT
ejde-355	335	13	u(ε	u(ε	PROPN
ejde-355	335	14	,	,	PUNCT
ejde-355	335	15	x)−	x)−	PROPN
ejde-355	335	16	cε	cε	PART
ejde-355	335	17	)	)	PUNCT
ejde-355	335	18	dσx	dσx	NOUN
ejde-355	335	19	−	−	PROPN
ejde-355	335	20	∫	∫	PROPN
ejde-355	335	21	∂εωi	∂εωi	PUNCT
ejde-355	335	22	(	(	PUNCT
ejde-355	335	23	u(ε	u(ε	PROPN
ejde-355	335	24	,	,	PUNCT
ejde-355	335	25	x)−	x)−	PROPN
ejde-355	335	26	cε	cε	NUM
ejde-355	335	27	)	)	PUNCT
ejde-355	335	28	∂	∂	NOUN
ejde-355	335	29	∂νεωi	∂νεωi	VERB
ejde-355	335	30	(	(	PUNCT
ejde-355	335	31	u(ε	u(ε	PROPN
ejde-355	335	32	,	,	PUNCT
ejde-355	335	33	x)−	x)−	PROPN
ejde-355	335	34	cε	cε	PART
ejde-355	335	35	)	)	PUNCT
ejde-355	335	36	dσx	dσx	NOUN
ejde-355	335	37	=	=	SYM
ejde-355	335	38	∫	∫	PROPN
ejde-355	335	39	∂ωo	∂ωo	NOUN
ejde-355	335	40	(	(	PUNCT
ejde-355	335	41	u(ε	u(ε	PROPN
ejde-355	335	42	,	,	PUNCT
ejde-355	335	43	x)−	x)−	PROPN
ejde-355	335	44	cε	cε	NUM
ejde-355	335	45	)	)	PUNCT
ejde-355	335	46	∂	∂	X
ejde-355	335	47	∂νωo	∂νωo	NUM
ejde-355	335	48	(	(	PUNCT
ejde-355	335	49	u(ε	u(ε	PROPN
ejde-355	335	50	,	,	PUNCT
ejde-355	335	51	x)−	x)−	PROPN
ejde-355	335	52	cε	cε	PART
ejde-355	335	53	)	)	PUNCT
ejde-355	335	54	dσx	dσx	NOUN
ejde-355	335	55	−	−	PROPN
ejde-355	335	56	∫	∫	PROPN
ejde-355	335	57	∂ωi	∂ωi	PROPN
ejde-355	335	58	(	(	PUNCT
ejde-355	335	59	u(ε	u(ε	PROPN
ejde-355	335	60	,	,	PUNCT
ejde-355	335	61	εt)−	εt)−	PROPN
ejde-355	335	62	cε	cε	PART
ejde-355	335	63	)	)	PUNCT
ejde-355	335	64	νωi(t	νωi(t	PROPN
ejde-355	335	65	)	)	PUNCT
ejde-355	335	66	·	·	PUNCT
ejde-355	336	1	∇t	∇t	NOUN
ejde-355	336	2	(	(	PUNCT
ejde-355	336	3	u(ε	u(ε	PROPN
ejde-355	336	4	,	,	PUNCT
ejde-355	336	5	εt)−	εt)−	PROPN
ejde-355	336	6	cε	cε	PART
ejde-355	336	7	)	)	PUNCT
ejde-355	336	8	dσt	dσt	NOUN
ejde-355	336	9	,	,	PUNCT
ejde-355	336	10	for	for	ADP
ejde-355	336	11	all	all	DET
ejde-355	336	12	ε	ε	PROPN
ejde-355	336	13	∈]0	∈]0	X
ejde-355	336	14	,	,	PUNCT
ejde-355	336	15	ε2	ε2	PROPN
ejde-355	336	16	[	[	X
ejde-355	336	17	.	.	PUNCT
ejde-355	337	1	then	then	ADV
ejde-355	337	2	we	we	PRON
ejde-355	337	3	take	take	VERB
ejde-355	337	4	um	um	INTJ
ejde-355	337	5	and	and	CCONJ
ejde-355	337	6	εm	εm	NOUN
ejde-355	337	7	as	as	ADP
ejde-355	337	8	in	in	ADP
ejde-355	337	9	theorem	theorem	NOUN
ejde-355	337	10	4.3	4.3	NUM
ejde-355	337	11	,	,	PUNCT
ejde-355	337	12	with	with	ADP
ejde-355	337	13	ωm	ωm	PROPN
ejde-355	337	14	≡	≡	PROPN
ejde-355	337	15	ωo	ωo	ADP
ejde-355	337	16	\	\	PROPN
ejde-355	337	17	b2(0	b2(0	PROPN
ejde-355	337	18	,	,	PUNCT
ejde-355	337	19	rm	rm	PROPN
ejde-355	337	20	)	)	PUNCT
ejde-355	337	21	,	,	PUNCT
ejde-355	337	22	16	16	NUM
ejde-355	337	23	p.	p.	NOUN
ejde-355	337	24	musolino	musolino	PROPN
ejde-355	337	25	,	,	PUNCT
ejde-355	337	26	m.	m.	NOUN
ejde-355	337	27	dutko	dutko	PROPN
ejde-355	337	28	,	,	PUNCT
ejde-355	337	29	g.	g.	PROPN
ejde-355	337	30	mishuris	mishuris	PROPN
ejde-355	337	31	ejde-2023/57	ejde-2023/57	NOUN
ejde-355	337	32	for	for	ADP
ejde-355	337	33	some	some	DET
ejde-355	337	34	rm	rm	NOUN
ejde-355	337	35	>	>	X
ejde-355	337	36	0	0	NUM
ejde-355	337	37	such	such	ADJ
ejde-355	337	38	that	that	DET
ejde-355	337	39	b2(0	b2(0	NOUN
ejde-355	337	40	,	,	PUNCT
ejde-355	337	41	rm	rm	PROPN
ejde-355	337	42	)	)	PUNCT
ejde-355	337	43	⊆	⊆	NUM
ejde-355	337	44	ωo	ωo	NOUN
ejde-355	337	45	.	.	PUNCT
ejde-355	338	1	we	we	PRON
ejde-355	338	2	verify	verify	VERB
ejde-355	338	3	that	that	SCONJ
ejde-355	338	4	if	if	SCONJ
ejde-355	338	5	ε	ε	PROPN
ejde-355	338	6	∈]0	∈]0	AUX
ejde-355	338	7	,	,	PUNCT
ejde-355	338	8	εm	εm	PROPN
ejde-355	338	9	[	[	X
ejde-355	338	10	,	,	PUNCT
ejde-355	338	11	then∫	then∫	NOUN
ejde-355	338	12	∂ωo	∂ωo	NOUN
ejde-355	338	13	(	(	PUNCT
ejde-355	338	14	u(ε	u(ε	PROPN
ejde-355	338	15	,	,	PUNCT
ejde-355	338	16	x)−	x)−	PROPN
ejde-355	338	17	cε	cε	NUM
ejde-355	338	18	)	)	PUNCT
ejde-355	338	19	∂	∂	X
ejde-355	338	20	∂νωo	∂νωo	NUM
ejde-355	338	21	(	(	PUNCT
ejde-355	338	22	u(ε	u(ε	PROPN
ejde-355	338	23	,	,	PUNCT
ejde-355	338	24	x)−	x)−	PROPN
ejde-355	338	25	cε	cε	PART
ejde-355	338	26	)	)	PUNCT
ejde-355	338	27	dσx	dσx	NOUN
ejde-355	338	28	=	=	SYM
ejde-355	338	29	∫	∫	PROPN
ejde-355	338	30	∂ωo	∂ωo	NOUN
ejde-355	338	31	um	um	INTJ
ejde-355	338	32	[	[	X
ejde-355	338	33	ε	ε	PROPN
ejde-355	338	34	,	,	PUNCT
ejde-355	338	35	εδ(ε	εδ(ε	NOUN
ejde-355	338	36	)	)	PUNCT
ejde-355	338	37	,	,	PUNCT
ejde-355	338	38	εδ(ε	εδ(ε	VERB
ejde-355	338	39	)	)	PUNCT
ejde-355	338	40	log	log	PROPN
ejde-355	338	41	ε	ε	PROPN
ejde-355	338	42	,	,	PUNCT
ejde-355	338	43	η(ε	η(ε	NOUN
ejde-355	338	44	)	)	PUNCT
ejde-355	338	45	,	,	PUNCT
ejde-355	338	46	ε	ε	PROPN
ejde-355	338	47	ρ(ε	ρ(ε	NUM
ejde-355	338	48	)	)	PUNCT
ejde-355	338	49	]	]	PUNCT
ejde-355	338	50	(	(	PUNCT
ejde-355	338	51	x	x	X
ejde-355	338	52	)	)	PUNCT
ejde-355	338	53	×	×	PROPN
ejde-355	338	54	νωo(x	νωo(x	PROPN
ejde-355	338	55	)	)	PUNCT
ejde-355	338	56	·	·	PUNCT
ejde-355	338	57	∇um	∇um	NOUN
ejde-355	338	58	[	[	X
ejde-355	338	59	ε	ε	PROPN
ejde-355	338	60	,	,	PUNCT
ejde-355	338	61	εδ(ε	εδ(ε	NOUN
ejde-355	338	62	)	)	PUNCT
ejde-355	338	63	,	,	PUNCT
ejde-355	338	64	εδ(ε	εδ(ε	VERB
ejde-355	338	65	)	)	PUNCT
ejde-355	338	66	log	log	PROPN
ejde-355	338	67	ε	ε	PROPN
ejde-355	338	68	,	,	PUNCT
ejde-355	338	69	η(ε	η(ε	NOUN
ejde-355	338	70	)	)	PUNCT
ejde-355	338	71	,	,	PUNCT
ejde-355	338	72	ε	ε	PROPN
ejde-355	338	73	ρ(ε	ρ(ε	NUM
ejde-355	338	74	)	)	PUNCT
ejde-355	338	75	]	]	PUNCT
ejde-355	338	76	(	(	PUNCT
ejde-355	338	77	x	x	X
ejde-355	338	78	)	)	PUNCT
ejde-355	338	79	dσx	dσx	NOUN
ejde-355	338	80	−	−	PROPN
ejde-355	338	81	log	log	NOUN
ejde-355	338	82	ε	ε	PROPN
ejde-355	338	83	2π	2π	PROPN
ejde-355	338	84	zm[ε	zm[ε	PROPN
ejde-355	338	85	,	,	PUNCT
ejde-355	338	86	εδ(ε	εδ(ε	NOUN
ejde-355	338	87	)	)	PUNCT
ejde-355	338	88	,	,	PUNCT
ejde-355	338	89	εδ(ε	εδ(ε	VERB
ejde-355	338	90	)	)	PUNCT
ejde-355	338	91	log	log	PROPN
ejde-355	338	92	ε	ε	PROPN
ejde-355	338	93	,	,	PUNCT
ejde-355	338	94	η(ε	η(ε	NOUN
ejde-355	338	95	)	)	PUNCT
ejde-355	338	96	,	,	PUNCT
ejde-355	338	97	ε	ε	PROPN
ejde-355	338	98	ρ(ε	ρ(ε	NUM
ejde-355	338	99	)	)	PUNCT
ejde-355	338	100	]	]	PUNCT
ejde-355	339	1	×	×	NOUN
ejde-355	339	2	∫	∫	PROPN
ejde-355	339	3	∂ωo	∂ωo	PROPN
ejde-355	339	4	νωo(x	νωo(x	PROPN
ejde-355	339	5	)	)	PUNCT
ejde-355	340	1	·	·	PUNCT
ejde-355	340	2	∇um	∇um	NOUN
ejde-355	340	3	[	[	X
ejde-355	340	4	ε	ε	PROPN
ejde-355	340	5	,	,	PUNCT
ejde-355	340	6	εδ(ε	εδ(ε	NOUN
ejde-355	340	7	)	)	PUNCT
ejde-355	340	8	,	,	PUNCT
ejde-355	340	9	εδ(ε	εδ(ε	VERB
ejde-355	340	10	)	)	PUNCT
ejde-355	340	11	log	log	PROPN
ejde-355	340	12	ε	ε	PROPN
ejde-355	340	13	,	,	PUNCT
ejde-355	340	14	η(ε	η(ε	NOUN
ejde-355	340	15	)	)	PUNCT
ejde-355	340	16	,	,	PUNCT
ejde-355	340	17	ε	ε	PROPN
ejde-355	340	18	ρ(ε	ρ(ε	NUM
ejde-355	340	19	)	)	PUNCT
ejde-355	340	20	]	]	PUNCT
ejde-355	340	21	(	(	PUNCT
ejde-355	340	22	x	x	X
ejde-355	340	23	)	)	PUNCT
ejde-355	340	24	dσx	dσx	NOUN
ejde-355	340	25	.	.	PUNCT
ejde-355	341	1	similarly	similarly	ADV
ejde-355	341	2	,	,	PUNCT
ejde-355	341	3	if	if	SCONJ
ejde-355	341	4	um	um	INTJ
ejde-355	341	5	and	and	CCONJ
ejde-355	341	6	εm	εm	NOUN
ejde-355	341	7	are	be	AUX
ejde-355	341	8	as	as	ADP
ejde-355	341	9	in	in	ADP
ejde-355	341	10	theorem	theorem	NOUN
ejde-355	341	11	4.4	4.4	NUM
ejde-355	341	12	,	,	PUNCT
ejde-355	341	13	with	with	ADP
ejde-355	341	14	ωm	ωm	PROPN
ejde-355	341	15	≡	≡	PROPN
ejde-355	341	16	b2(0	b2(0	PROPN
ejde-355	341	17	,	,	PUNCT
ejde-355	341	18	rm	rm	PROPN
ejde-355	341	19	)	)	PUNCT
ejde-355	341	20	\	\	PROPN
ejde-355	341	21	ωi	ωi	PUNCT
ejde-355	341	22	,	,	PUNCT
ejde-355	341	23	for	for	ADP
ejde-355	341	24	some	some	DET
ejde-355	341	25	rm	rm	NOUN
ejde-355	341	26	>	>	X
ejde-355	341	27	0	0	NUM
ejde-355	342	1	such	such	ADJ
ejde-355	342	2	that	that	DET
ejde-355	342	3	b2(0	b2(0	NOUN
ejde-355	342	4	,	,	PUNCT
ejde-355	342	5	rm	rm	PROPN
ejde-355	342	6	)	)	PUNCT
ejde-355	342	7	⊇	⊇	PROPN
ejde-355	342	8	ωi	ωi	PROPN
ejde-355	342	9	,	,	PUNCT
ejde-355	342	10	then	then	ADV
ejde-355	342	11	if	if	SCONJ
ejde-355	342	12	ε	ε	PROPN
ejde-355	342	13	∈]0	∈]0	AUX
ejde-355	342	14	,	,	PUNCT
ejde-355	342	15	εm[,∫	εm[,∫	NOUN
ejde-355	342	16	∂ωi	∂ωi	NOUN
ejde-355	342	17	(	(	PUNCT
ejde-355	342	18	u(ε	u(ε	PROPN
ejde-355	342	19	,	,	PUNCT
ejde-355	342	20	εt)−	εt)−	PROPN
ejde-355	342	21	cε	cε	PART
ejde-355	342	22	)	)	PUNCT
ejde-355	342	23	νωi(t	νωi(t	PROPN
ejde-355	342	24	)	)	PUNCT
ejde-355	342	25	·	·	PUNCT
ejde-355	342	26	∇t	∇t	NOUN
ejde-355	342	27	(	(	PUNCT
ejde-355	342	28	u(ε	u(ε	PROPN
ejde-355	342	29	,	,	PUNCT
ejde-355	342	30	εt)−	εt)−	PROPN
ejde-355	342	31	cε	cε	PART
ejde-355	342	32	)	)	PUNCT
ejde-355	342	33	dσt	dσt	PROPN
ejde-355	342	34	=	=	SYM
ejde-355	342	35	∫	∫	PROPN
ejde-355	342	36	∂ωi	∂ωi	PROPN
ejde-355	342	37	um[ε	um[ε	PROPN
ejde-355	342	38	,	,	PUNCT
ejde-355	342	39	εδ(ε	εδ(ε	NOUN
ejde-355	342	40	)	)	PUNCT
ejde-355	342	41	,	,	PUNCT
ejde-355	342	42	εδ(ε	εδ(ε	VERB
ejde-355	342	43	)	)	PUNCT
ejde-355	342	44	log	log	PROPN
ejde-355	342	45	ε	ε	PROPN
ejde-355	342	46	,	,	PUNCT
ejde-355	342	47	η(ε	η(ε	NOUN
ejde-355	342	48	)	)	PUNCT
ejde-355	342	49	,	,	PUNCT
ejde-355	342	50	ε	ε	PROPN
ejde-355	342	51	ρ(ε	ρ(ε	NUM
ejde-355	342	52	)	)	PUNCT
ejde-355	342	53	]	]	PUNCT
ejde-355	342	54	(	(	PUNCT
ejde-355	342	55	t	t	PROPN
ejde-355	342	56	)	)	PUNCT
ejde-355	342	57	×	×	NOUN
ejde-355	342	58	νωi(t	νωi(t	PROPN
ejde-355	342	59	)	)	PUNCT
ejde-355	342	60	·	·	PUNCT
ejde-355	342	61	∇um[ε	∇um[ε	NOUN
ejde-355	342	62	,	,	PUNCT
ejde-355	342	63	εδ(ε	εδ(ε	NOUN
ejde-355	342	64	)	)	PUNCT
ejde-355	342	65	,	,	PUNCT
ejde-355	342	66	εδ(ε	εδ(ε	VERB
ejde-355	342	67	)	)	PUNCT
ejde-355	342	68	log	log	PROPN
ejde-355	342	69	ε	ε	PROPN
ejde-355	342	70	,	,	PUNCT
ejde-355	342	71	η(ε	η(ε	NOUN
ejde-355	342	72	)	)	PUNCT
ejde-355	342	73	,	,	PUNCT
ejde-355	342	74	ε	ε	PROPN
ejde-355	342	75	ρ(ε	ρ(ε	NUM
ejde-355	342	76	)	)	PUNCT
ejde-355	342	77	]	]	PUNCT
ejde-355	342	78	(	(	PUNCT
ejde-355	342	79	t	t	NOUN
ejde-355	342	80	)	)	PUNCT
ejde-355	342	81	dσt	dσt	NOUN
ejde-355	342	82	.	.	PUNCT
ejde-355	343	1	therefore	therefore	ADV
ejde-355	343	2	,	,	PUNCT
ejde-355	343	3	we	we	PRON
ejde-355	343	4	set	set	VERB
ejde-355	343	5	εe	εe	ADP
ejde-355	343	6	≡	≡	PROPN
ejde-355	343	7	min{εm	min{εm	PROPN
ejde-355	343	8	,	,	PUNCT
ejde-355	343	9	εm	εm	PROPN
ejde-355	343	10	}	}	PUNCT
ejde-355	343	11	and	and	CCONJ
ejde-355	343	12	e1[ε	e1[ε	ADJ
ejde-355	343	13	,	,	PUNCT
ejde-355	343	14	γ1	γ1	NOUN
ejde-355	343	15	,	,	PUNCT
ejde-355	343	16	γ2	γ2	PROPN
ejde-355	343	17	,	,	PUNCT
ejde-355	343	18	γ3	γ3	NOUN
ejde-355	343	19	,	,	PUNCT
ejde-355	343	20	γ4	γ4	PROPN
ejde-355	343	21	]	]	PUNCT
ejde-355	344	1	≡	≡	PROPN
ejde-355	344	2	∫	∫	PROPN
ejde-355	344	3	∂ωo	∂ωo	PROPN
ejde-355	344	4	um	um	INTJ
ejde-355	344	5	[	[	X
ejde-355	344	6	ε	ε	PROPN
ejde-355	344	7	,	,	PUNCT
ejde-355	344	8	γ1	γ1	NOUN
ejde-355	344	9	,	,	PUNCT
ejde-355	344	10	γ2	γ2	PROPN
ejde-355	344	11	,	,	PUNCT
ejde-355	344	12	γ3	γ3	NOUN
ejde-355	344	13	,	,	PUNCT
ejde-355	344	14	γ4](x)νωo(x	γ4](x)νωo(x	NOUN
ejde-355	344	15	)	)	PUNCT
ejde-355	344	16	·	·	PUNCT
ejde-355	345	1	∇um	∇um	NOUN
ejde-355	345	2	[	[	X
ejde-355	345	3	ε	ε	PROPN
ejde-355	345	4	,	,	PUNCT
ejde-355	345	5	γ1	γ1	PROPN
ejde-355	345	6	,	,	PUNCT
ejde-355	345	7	γ2	γ2	PROPN
ejde-355	345	8	,	,	PUNCT
ejde-355	345	9	γ3	γ3	NOUN
ejde-355	345	10	,	,	PUNCT
ejde-355	345	11	γ4](x	γ4](x	NOUN
ejde-355	345	12	)	)	PUNCT
ejde-355	345	13	dσx	dσx	NOUN
ejde-355	345	14	−	−	PROPN
ejde-355	345	15	∫	∫	NOUN
ejde-355	345	16	∂ωi	∂ωi	PROPN
ejde-355	345	17	um[ε	um[ε	PROPN
ejde-355	345	18	,	,	PUNCT
ejde-355	345	19	γ1	γ1	NOUN
ejde-355	345	20	,	,	PUNCT
ejde-355	345	21	γ2	γ2	PROPN
ejde-355	345	22	,	,	PUNCT
ejde-355	345	23	γ3	γ3	NOUN
ejde-355	345	24	,	,	PUNCT
ejde-355	345	25	γ4](t)νωi(t	γ4](t)νωi(t	PROPN
ejde-355	345	26	)	)	PUNCT
ejde-355	345	27	·	·	PUNCT
ejde-355	345	28	∇um[ε	∇um[ε	NOUN
ejde-355	345	29	,	,	PUNCT
ejde-355	345	30	γ1	γ1	PROPN
ejde-355	345	31	,	,	PUNCT
ejde-355	345	32	γ2	γ2	PROPN
ejde-355	345	33	,	,	PUNCT
ejde-355	345	34	γ3	γ3	NOUN
ejde-355	345	35	,	,	PUNCT
ejde-355	345	36	γ4](t	γ4](t	PROPN
ejde-355	345	37	)	)	PUNCT
ejde-355	345	38	dσt	dσt	NOUN
ejde-355	345	39	and	and	CCONJ
ejde-355	345	40	e2[ε	e2[ε	NOUN
ejde-355	345	41	,	,	PUNCT
ejde-355	345	42	γ1	γ1	NOUN
ejde-355	345	43	,	,	PUNCT
ejde-355	345	44	γ2	γ2	PROPN
ejde-355	345	45	,	,	PUNCT
ejde-355	345	46	γ3	γ3	NOUN
ejde-355	345	47	,	,	PUNCT
ejde-355	345	48	γ4	γ4	PROPN
ejde-355	345	49	]	]	PUNCT
ejde-355	345	50	≡	≡	PROPN
ejde-355	345	51	−	−	PROPN
ejde-355	346	1	1	1	NUM
ejde-355	346	2	2π	2π	PROPN
ejde-355	346	3	zm[ε	zm[ε	PROPN
ejde-355	346	4	,	,	PUNCT
ejde-355	346	5	γ1	γ1	NOUN
ejde-355	346	6	,	,	PUNCT
ejde-355	346	7	γ2	γ2	PROPN
ejde-355	346	8	,	,	PUNCT
ejde-355	346	9	γ3	γ3	NOUN
ejde-355	346	10	,	,	PUNCT
ejde-355	346	11	γ4	γ4	PROPN
ejde-355	346	12	]	]	PUNCT
ejde-355	346	13	∫	∫	PROPN
ejde-355	346	14	∂ωo	∂ωo	PROPN
ejde-355	346	15	νωo(x	νωo(x	PROPN
ejde-355	346	16	)	)	PUNCT
ejde-355	346	17	·	·	PUNCT
ejde-355	346	18	∇um	∇um	NOUN
ejde-355	346	19	[	[	X
ejde-355	346	20	ε	ε	PROPN
ejde-355	346	21	,	,	PUNCT
ejde-355	346	22	γ1	γ1	PROPN
ejde-355	346	23	,	,	PUNCT
ejde-355	346	24	γ2	γ2	PROPN
ejde-355	346	25	,	,	PUNCT
ejde-355	346	26	γ3	γ3	NOUN
ejde-355	346	27	,	,	PUNCT
ejde-355	346	28	γ4](x	γ4](x	NOUN
ejde-355	346	29	)	)	PUNCT
ejde-355	346	30	dσx	dσx	NOUN
ejde-355	346	31	for	for	ADP
ejde-355	346	32	all	all	DET
ejde-355	346	33	(	(	PUNCT
ejde-355	346	34	ε	ε	PROPN
ejde-355	346	35	,	,	PUNCT
ejde-355	346	36	γ1	γ1	NOUN
ejde-355	346	37	,	,	PUNCT
ejde-355	346	38	γ2	γ2	PROPN
ejde-355	346	39	,	,	PUNCT
ejde-355	346	40	γ3	γ3	NOUN
ejde-355	346	41	,	,	PUNCT
ejde-355	346	42	γ4	γ4	PROPN
ejde-355	346	43	)	)	PUNCT
ejde-355	346	44	∈]−	∈]−	PROPN
ejde-355	346	45	εe	εe	NOUN
ejde-355	346	46	,	,	PUNCT
ejde-355	346	47	εe[×u	εe[×u	NOUN
ejde-355	346	48	.	.	PUNCT
ejde-355	347	1	we	we	PRON
ejde-355	347	2	verify	verify	VERB
ejde-355	347	3	that	that	SCONJ
ejde-355	347	4	the	the	DET
ejde-355	347	5	maps	map	NOUN
ejde-355	347	6	e1	e1	PROPN
ejde-355	347	7	and	and	CCONJ
ejde-355	347	8	e2	e2	PROPN
ejde-355	347	9	are	be	AUX
ejde-355	347	10	real	real	ADV
ejde-355	347	11	analytic	analytic	ADJ
ejde-355	347	12	from	from	ADP
ejde-355	347	13	]	]	PUNCT
ejde-355	347	14	−	−	NOUN
ejde-355	347	15	εe	εe	NOUN
ejde-355	347	16	,	,	PUNCT
ejde-355	347	17	εe[×u	εe[×u	NOUN
ejde-355	347	18	to	to	ADP
ejde-355	347	19	r	r	NOUN
ejde-355	347	20	and	and	CCONJ
ejde-355	347	21	that	that	DET
ejde-355	347	22	equality	equality	NOUN
ejde-355	347	23	(	(	PUNCT
ejde-355	347	24	4.21	4.21	NUM
ejde-355	347	25	)	)	PUNCT
ejde-355	347	26	holds	hold	VERB
ejde-355	347	27	.	.	PUNCT
ejde-355	348	1	moreover	moreover	ADV
ejde-355	348	2	,	,	PUNCT
ejde-355	348	3	we	we	PRON
ejde-355	348	4	also	also	ADV
ejde-355	348	5	have	have	VERB
ejde-355	348	6	e1[0	e1[0	NOUN
ejde-355	348	7	,	,	PUNCT
ejde-355	348	8	0	0	NUM
ejde-355	348	9	,	,	PUNCT
ejde-355	348	10	l0	l0	PROPN
ejde-355	348	11	,	,	PUNCT
ejde-355	348	12	η0	η0	NOUN
ejde-355	348	13	,	,	PUNCT
ejde-355	348	14	r0	r0	NOUN
ejde-355	348	15	]	]	PUNCT
ejde-355	348	16	=	=	SYM
ejde-355	348	17	∫	∫	PROPN
ejde-355	348	18	∂ωo	∂ωo	NOUN
ejde-355	348	19	(	(	PUNCT
ejde-355	348	20	ũm	ũm	X
ejde-355	348	21	(	(	PUNCT
ejde-355	348	22	x	x	X
ejde-355	348	23	)	)	PUNCT
ejde-355	348	24	+	+	NUM
ejde-355	348	25	s2(x	s2(x	X
ejde-355	348	26	)	)	PUNCT
ejde-355	348	27	∫	∫	PROPN
ejde-355	349	1	∂ωo	∂ωo	NOUN
ejde-355	349	2	go	go	VERB
ejde-355	349	3	dσ	dσ	PROPN
ejde-355	349	4	)	)	PUNCT
ejde-355	349	5	νωo(x	νωo(x	PROPN
ejde-355	349	6	)	)	PUNCT
ejde-355	349	7	·	·	PUNCT
ejde-355	349	8	∇	∇	X
ejde-355	349	9	(	(	PUNCT
ejde-355	349	10	ũm	ũm	X
ejde-355	349	11	(	(	PUNCT
ejde-355	349	12	x	x	X
ejde-355	349	13	)	)	PUNCT
ejde-355	349	14	+	+	NUM
ejde-355	349	15	s2(x	s2(x	X
ejde-355	349	16	)	)	PUNCT
ejde-355	349	17	∫	∫	PROPN
ejde-355	350	1	∂ωo	∂ωo	NOUN
ejde-355	350	2	go	go	VERB
ejde-355	350	3	dσ	dσ	PROPN
ejde-355	350	4	)	)	PUNCT
ejde-355	350	5	dσx	dσx	NOUN
ejde-355	350	6	−	−	PROPN
ejde-355	350	7	∫	∫	NOUN
ejde-355	350	8	∂ωi	∂ωi	PROPN
ejde-355	350	9	ũm(t)νωi(t	ũm(t)νωi(t	NOUN
ejde-355	350	10	)	)	PUNCT
ejde-355	350	11	·	·	PUNCT
ejde-355	351	1	∇ũm(t	∇ũm(t	NOUN
ejde-355	351	2	)	)	PUNCT
ejde-355	351	3	dσt	dσt	NOUN
ejde-355	351	4	and	and	CCONJ
ejde-355	351	5	e2[0	e2[0	PROPN
ejde-355	351	6	,	,	PUNCT
ejde-355	351	7	0	0	NUM
ejde-355	351	8	,	,	PUNCT
ejde-355	351	9	l0	l0	PROPN
ejde-355	351	10	,	,	PUNCT
ejde-355	351	11	η0	η0	NOUN
ejde-355	351	12	,	,	PUNCT
ejde-355	351	13	r0	r0	NOUN
ejde-355	351	14	]	]	PUNCT
ejde-355	351	15	ejde-2023/57	ejde-2023/57	NOUN
ejde-355	351	16	asymptotic	asymptotic	ADJ
ejde-355	351	17	analysis	analysis	NOUN
ejde-355	351	18	of	of	ADP
ejde-355	351	19	perturbed	perturb	VERB
ejde-355	351	20	robin	robin	PROPN
ejde-355	351	21	problems	problem	VERB
ejde-355	351	22	17	17	NUM
ejde-355	351	23	=	=	SYM
ejde-355	351	24	−	−	PROPN
ejde-355	351	25	1	1	NUM
ejde-355	351	26	2π	2π	NUM
ejde-355	351	27	∫	∫	PROPN
ejde-355	351	28	∂ωo	∂ωo	NOUN
ejde-355	351	29	go	go	VERB
ejde-355	351	30	dσ	dσ	PROPN
ejde-355	351	31	∫	∫	PROPN
ejde-355	351	32	∂ωo	∂ωo	PROPN
ejde-355	351	33	νωo(x	νωo(x	PROPN
ejde-355	351	34	)	)	PUNCT
ejde-355	351	35	·	·	PUNCT
ejde-355	351	36	∇	∇	X
ejde-355	351	37	(	(	PUNCT
ejde-355	351	38	ũm	ũm	X
ejde-355	351	39	(	(	PUNCT
ejde-355	351	40	x	x	X
ejde-355	351	41	)	)	PUNCT
ejde-355	352	1	+	+	NUM
ejde-355	352	2	s2(x	s2(x	X
ejde-355	352	3	)	)	PUNCT
ejde-355	352	4	∫	∫	PROPN
ejde-355	352	5	∂ωo	∂ωo	NOUN
ejde-355	352	6	go	go	VERB
ejde-355	352	7	dσ	dσ	PROPN
ejde-355	352	8	)	)	PUNCT
ejde-355	352	9	dσx	dσx	NOUN
ejde-355	352	10	=	=	PUNCT
ejde-355	353	1	−	−	PROPN
ejde-355	353	2	1	1	NUM
ejde-355	353	3	2π	2π	NOUN
ejde-355	353	4	(	(	PUNCT
ejde-355	353	5	∫	∫	PROPN
ejde-355	353	6	∂ωo	∂ωo	NOUN
ejde-355	353	7	go	go	VERB
ejde-355	353	8	dσ	dσ	PROPN
ejde-355	353	9	)	)	PUNCT
ejde-355	353	10	2	2	NUM
ejde-355	353	11	,	,	PUNCT
ejde-355	353	12	and	and	CCONJ
ejde-355	353	13	accordingly	accordingly	ADV
ejde-355	353	14	equalities	equalitie	VERB
ejde-355	353	15	(	(	PUNCT
ejde-355	353	16	4.22	4.22	NUM
ejde-355	353	17	)	)	PUNCT
ejde-355	353	18	and	and	CCONJ
ejde-355	353	19	(	(	PUNCT
ejde-355	353	20	4.23	4.23	NUM
ejde-355	353	21	)	)	PUNCT
ejde-355	353	22	hold	hold	VERB
ejde-355	353	23	.	.	PUNCT
ejde-355	354	1	�	�	PROPN
ejde-355	354	2	5	5	NUM
ejde-355	354	3	.	.	PUNCT
ejde-355	355	1	remarks	remark	NOUN
ejde-355	355	2	on	on	ADP
ejde-355	355	3	the	the	DET
ejde-355	355	4	linear	linear	ADJ
ejde-355	355	5	case	case	NOUN
ejde-355	355	6	in	in	ADP
ejde-355	355	7	this	this	DET
ejde-355	355	8	section	section	NOUN
ejde-355	355	9	,	,	PUNCT
ejde-355	355	10	we	we	PRON
ejde-355	355	11	make	make	VERB
ejde-355	355	12	further	further	ADJ
ejde-355	355	13	considerations	consideration	NOUN
ejde-355	355	14	on	on	ADP
ejde-355	355	15	the	the	DET
ejde-355	355	16	asymptotic	asymptotic	ADJ
ejde-355	355	17	behavior	behavior	NOUN
ejde-355	355	18	of	of	ADP
ejde-355	355	19	the	the	DET
ejde-355	355	20	solution	solution	NOUN
ejde-355	355	21	in	in	ADP
ejde-355	355	22	the	the	DET
ejde-355	355	23	linear	linear	ADJ
ejde-355	355	24	case	case	NOUN
ejde-355	355	25	as	as	SCONJ
ejde-355	355	26	the	the	DET
ejde-355	355	27	parameter	parameter	NOUN
ejde-355	355	28	ε	ε	PROPN
ejde-355	355	29	tends	tend	VERB
ejde-355	355	30	to	to	ADP
ejde-355	355	31	0	0	NUM
ejde-355	355	32	.	.	PUNCT
ejde-355	356	1	clearly	clearly	ADV
ejde-355	356	2	,	,	PUNCT
ejde-355	356	3	we	we	PRON
ejde-355	356	4	can	can	AUX
ejde-355	356	5	apply	apply	VERB
ejde-355	356	6	the	the	DET
ejde-355	356	7	results	result	NOUN
ejde-355	356	8	of	of	ADP
ejde-355	356	9	section	section	NOUN
ejde-355	356	10	3	3	NUM
ejde-355	356	11	to	to	ADP
ejde-355	356	12	the	the	DET
ejde-355	356	13	linear	linear	ADJ
ejde-355	356	14	case	case	NOUN
ejde-355	356	15	.	.	PUNCT
ejde-355	357	1	in	in	ADP
ejde-355	357	2	particular	particular	ADJ
ejde-355	357	3	,	,	PUNCT
ejde-355	357	4	if	if	SCONJ
ejde-355	357	5	we	we	PRON
ejde-355	357	6	have	have	AUX
ejde-355	357	7	fε(τ	fε(τ	VERB
ejde-355	357	8	)	)	PUNCT
ejde-355	357	9	=	=	SYM
ejde-355	358	1	τ	τ	X
ejde-355	358	2	∀(τ	∀(τ	X
ejde-355	358	3	,	,	PUNCT
ejde-355	358	4	ε	ε	PROPN
ejde-355	358	5	)	)	PUNCT
ejde-355	358	6	∈	∈	PROPN
ejde-355	358	7	r×]0	r×]0	PROPN
ejde-355	358	8	,	,	PUNCT
ejde-355	358	9	ε0	ε0	PROPN
ejde-355	358	10	[	[	PUNCT
ejde-355	358	11	,	,	PUNCT
ejde-355	358	12	problem	problem	NOUN
ejde-355	358	13	(	(	PUNCT
ejde-355	358	14	1.1	1.1	NUM
ejde-355	358	15	)	)	PUNCT
ejde-355	358	16	reduces	reduce	VERB
ejde-355	358	17	to	to	ADP
ejde-355	358	18	the	the	DET
ejde-355	358	19	linear	linear	ADJ
ejde-355	358	20	problem	problem	NOUN
ejde-355	358	21	∆u(x	∆u(x	VERB
ejde-355	358	22	)	)	PUNCT
ejde-355	358	23	=	=	SYM
ejde-355	358	24	0	0	PUNCT
ejde-355	359	1	∀x	∀x	X
ejde-355	359	2	∈	∈	PROPN
ejde-355	359	3	ω(ε	ω(ε	PROPN
ejde-355	359	4	)	)	PUNCT
ejde-355	359	5	,	,	PUNCT
ejde-355	359	6	∂	∂	NUM
ejde-355	359	7	∂νωo	∂νωo	NUM
ejde-355	359	8	u(x	u(x	NOUN
ejde-355	359	9	)	)	PUNCT
ejde-355	359	10	=	=	SYM
ejde-355	359	11	go(x	go(x	X
ejde-355	359	12	)	)	PUNCT
ejde-355	359	13	∀x	∀x	VERB
ejde-355	359	14	∈	∈	PROPN
ejde-355	359	15	∂ωo	∂ωo	NOUN
ejde-355	359	16	,	,	PUNCT
ejde-355	359	17	∂	∂	NOUN
ejde-355	359	18	∂νεωi	∂νεωi	VERB
ejde-355	359	19	u(x	u(x	NOUN
ejde-355	359	20	)	)	PUNCT
ejde-355	359	21	=	=	SYM
ejde-355	359	22	δ(ε)u(x	δ(ε)u(x	NOUN
ejde-355	359	23	)	)	PUNCT
ejde-355	359	24	+	+	CCONJ
ejde-355	359	25	gi(x	gi(x	PROPN
ejde-355	359	26	/	/	SYM
ejde-355	359	27	ε	ε	PROPN
ejde-355	359	28	)	)	PUNCT
ejde-355	359	29	ρ(ε	ρ(ε	PROPN
ejde-355	359	30	)	)	PUNCT
ejde-355	360	1	∀x	∀x	VERB
ejde-355	360	2	∈	∈	PROPN
ejde-355	360	3	ε∂ωi	ε∂ωi	ADV
ejde-355	360	4	.	.	PUNCT
ejde-355	361	1	(	(	PUNCT
ejde-355	361	2	5.1	5.1	NUM
ejde-355	361	3	)	)	PUNCT
ejde-355	361	4	we	we	PRON
ejde-355	361	5	also	also	ADV
ejde-355	361	6	know	know	VERB
ejde-355	361	7	that	that	SCONJ
ejde-355	361	8	for	for	ADP
ejde-355	361	9	each	each	DET
ejde-355	361	10	ε	ε	PROPN
ejde-355	361	11	∈]0	∈]0	X
ejde-355	361	12	,	,	PUNCT
ejde-355	361	13	ε0	ε0	PROPN
ejde-355	361	14	[	[	NOUN
ejde-355	361	15	,	,	PUNCT
ejde-355	361	16	problem	problem	NOUN
ejde-355	361	17	(	(	PUNCT
ejde-355	361	18	5.1	5.1	NUM
ejde-355	361	19	)	)	PUNCT
ejde-355	361	20	has	have	VERB
ejde-355	361	21	a	a	DET
ejde-355	361	22	unique	unique	ADJ
ejde-355	361	23	solution	solution	NOUN
ejde-355	361	24	in	in	ADP
ejde-355	361	25	c1,α(ω(ε	c1,α(ω(ε	NOUN
ejde-355	361	26	)	)	PUNCT
ejde-355	361	27	)	)	PUNCT
ejde-355	361	28	,	,	PUNCT
ejde-355	361	29	which	which	PRON
ejde-355	361	30	we	we	PRON
ejde-355	361	31	denote	denote	VERB
ejde-355	361	32	by	by	ADP
ejde-355	361	33	u[ε	u[ε	NOUN
ejde-355	361	34	]	]	PUNCT
ejde-355	361	35	.	.	PUNCT
ejde-355	362	1	clearly	clearly	ADV
ejde-355	362	2	,	,	PUNCT
ejde-355	362	3	εδ(ε)fε	εδ(ε)fε	PROPN
ejde-355	362	4	(	(	PUNCT
ejde-355	362	5	1	1	NUM
ejde-355	362	6	εδ(ε	εδ(ε	NOUN
ejde-355	362	7	)	)	PUNCT
ejde-355	362	8	τ	τ	PROPN
ejde-355	362	9	)	)	PUNCT
ejde-355	362	10	=	=	PUNCT
ejde-355	362	11	τ	τ	X
ejde-355	362	12	∀(τ	∀(τ	X
ejde-355	362	13	,	,	PUNCT
ejde-355	362	14	ε	ε	PROPN
ejde-355	362	15	)	)	PUNCT
ejde-355	362	16	∈	∈	PROPN
ejde-355	362	17	r×]0	r×]0	PROPN
ejde-355	362	18	,	,	PUNCT
ejde-355	362	19	ε0	ε0	PROPN
ejde-355	362	20	[	[	PUNCT
ejde-355	362	21	,	,	PUNCT
ejde-355	362	22	and	and	CCONJ
ejde-355	362	23	thus	thus	ADV
ejde-355	362	24	we	we	PRON
ejde-355	362	25	can	can	AUX
ejde-355	362	26	take	take	VERB
ejde-355	362	27	for	for	ADP
ejde-355	362	28	example	example	NOUN
ejde-355	362	29	η(ε	η(ε	NOUN
ejde-355	362	30	)	)	PUNCT
ejde-355	362	31	=	=	SYM
ejde-355	362	32	0	0	NUM
ejde-355	362	33	∀ε	∀ε	NOUN
ejde-355	362	34	∈]0	∈]0	X
ejde-355	362	35	,	,	PUNCT
ejde-355	362	36	ε0	ε0	PROPN
ejde-355	362	37	[	[	PUNCT
ejde-355	362	38	,	,	PUNCT
ejde-355	362	39	f̃	f̃	PROPN
ejde-355	362	40	(	(	PUNCT
ejde-355	362	41	τ	τ	PROPN
ejde-355	362	42	,	,	PUNCT
ejde-355	362	43	η	η	PROPN
ejde-355	362	44	)	)	PUNCT
ejde-355	362	45	=	=	SYM
ejde-355	363	1	τ	τ	X
ejde-355	363	2	∀(τ	∀(τ	NUM
ejde-355	363	3	,	,	PUNCT
ejde-355	363	4	η	η	NOUN
ejde-355	363	5	)	)	PUNCT
ejde-355	363	6	∈	∈	PROPN
ejde-355	363	7	r2	r2	NOUN
ejde-355	363	8	.	.	PUNCT
ejde-355	364	1	in	in	ADP
ejde-355	364	2	particular	particular	ADJ
ejde-355	364	3	,	,	PUNCT
ejde-355	364	4	η0	η0	NOUN
ejde-355	364	5	=	=	SYM
ejde-355	364	6	0	0	NUM
ejde-355	364	7	,	,	PUNCT
ejde-355	364	8	∂τ	∂τ	PROPN
ejde-355	364	9	f̃	f̃	PROPN
ejde-355	364	10	(	(	PUNCT
ejde-355	364	11	τ	τ	PROPN
ejde-355	364	12	,	,	PUNCT
ejde-355	364	13	η	η	PROPN
ejde-355	364	14	)	)	PUNCT
ejde-355	364	15	=	=	SYM
ejde-355	364	16	1	1	NUM
ejde-355	364	17	∀(τ	∀(τ	NUM
ejde-355	364	18	,	,	PUNCT
ejde-355	364	19	η	η	NOUN
ejde-355	364	20	)	)	PUNCT
ejde-355	364	21	∈	∈	PROPN
ejde-355	364	22	r2	r2	NOUN
ejde-355	364	23	.	.	PUNCT
ejde-355	365	1	all	all	DET
ejde-355	365	2	the	the	DET
ejde-355	365	3	assumptions	assumption	NOUN
ejde-355	365	4	in	in	ADP
ejde-355	365	5	sections	section	NOUN
ejde-355	365	6	3	3	NUM
ejde-355	365	7	and	and	CCONJ
ejde-355	365	8	4	4	NUM
ejde-355	365	9	are	be	AUX
ejde-355	365	10	satisfied	satisfied	ADJ
ejde-355	365	11	.	.	PUNCT
ejde-355	366	1	in	in	ADP
ejde-355	366	2	particular	particular	ADJ
ejde-355	366	3	,	,	PUNCT
ejde-355	366	4	the	the	DET
ejde-355	366	5	solutions	solution	NOUN
ejde-355	366	6	of	of	ADP
ejde-355	366	7	the	the	DET
ejde-355	366	8	corresponding	corresponding	ADJ
ejde-355	366	9	limiting	limit	VERB
ejde-355	366	10	system	system	NOUN
ejde-355	366	11	exist	exist	VERB
ejde-355	366	12	and	and	CCONJ
ejde-355	366	13	are	be	AUX
ejde-355	366	14	unique	unique	ADJ
ejde-355	366	15	(	(	PUNCT
ejde-355	366	16	see	see	VERB
ejde-355	366	17	assumption	assumption	NOUN
ejde-355	366	18	(	(	PUNCT
ejde-355	366	19	4.10	4.10	NUM
ejde-355	366	20	)	)	PUNCT
ejde-355	366	21	)	)	PUNCT
ejde-355	366	22	.	.	PUNCT
ejde-355	367	1	in	in	ADP
ejde-355	367	2	the	the	DET
ejde-355	367	3	linear	linear	ADJ
ejde-355	367	4	case	case	NOUN
ejde-355	367	5	,	,	PUNCT
ejde-355	367	6	equations	equation	NOUN
ejde-355	367	7	(	(	PUNCT
ejde-355	367	8	4.8)-(4.9	4.8)-(4.9	NOUN
ejde-355	367	9	)	)	PUNCT
ejde-355	367	10	become	become	VERB
ejde-355	367	11	−	−	PROPN
ejde-355	367	12	1	1	NUM
ejde-355	367	13	2	2	NUM
ejde-355	367	14	µo(x	µo(x	PUNCT
ejde-355	367	15	)	)	PUNCT
ejde-355	368	1	+	+	CCONJ
ejde-355	368	2	∫	∫	PROPN
ejde-355	368	3	∂ωo	∂ωo	NOUN
ejde-355	368	4	νωo(x	νωo(x	PROPN
ejde-355	368	5	)	)	PUNCT
ejde-355	368	6	·	·	PUNCT
ejde-355	369	1	∇s2(x−	∇s2(x−	ADP
ejde-355	369	2	y)µo(y	y)µo(y	NUM
ejde-355	369	3	)	)	PUNCT
ejde-355	369	4	dσy	dσy	PROPN
ejde-355	369	5	+	+	CCONJ
ejde-355	369	6	νωo(x	νωo(x	PROPN
ejde-355	369	7	)	)	PUNCT
ejde-355	369	8	·	·	PUNCT
ejde-355	369	9	∇s2(x	∇s2(x	NUM
ejde-355	369	10	)	)	PUNCT
ejde-355	369	11	∫	∫	PROPN
ejde-355	370	1	∂ωi	∂ωi	NOUN
ejde-355	370	2	µi(s	µi(s	NUM
ejde-355	370	3	)	)	PUNCT
ejde-355	370	4	dσs	dσs	NOUN
ejde-355	370	5	=	=	PUNCT
ejde-355	370	6	go(x	go(x	X
ejde-355	370	7	)	)	PUNCT
ejde-355	370	8	∀x	∀x	VERB
ejde-355	370	9	∈	∈	PROPN
ejde-355	370	10	∂ωo	∂ωo	NOUN
ejde-355	370	11	,	,	PUNCT
ejde-355	370	12	(	(	PUNCT
ejde-355	370	13	5.2	5.2	NUM
ejde-355	370	14	)	)	PUNCT
ejde-355	370	15	1	1	NUM
ejde-355	370	16	2	2	NUM
ejde-355	370	17	µi(t	µi(t	NUM
ejde-355	370	18	)	)	PUNCT
ejde-355	370	19	+	+	CCONJ
ejde-355	370	20	∫	∫	X
ejde-355	370	21	∂ωi	∂ωi	PROPN
ejde-355	370	22	νωi(t	νωi(t	PROPN
ejde-355	370	23	)	)	PUNCT
ejde-355	370	24	·	·	PUNCT
ejde-355	371	1	∇s2(t−	∇s2(t−	PRON
ejde-355	371	2	s)µi(s	s)µi(s	NOUN
ejde-355	371	3	)	)	PUNCT
ejde-355	371	4	dσs	dσs	NOUN
ejde-355	371	5	=	=	SYM
ejde-355	371	6	l0	l0	PROPN
ejde-355	371	7	2π	2π	NOUN
ejde-355	371	8	∫	∫	INTJ
ejde-355	371	9	∂ωi	∂ωi	PROPN
ejde-355	371	10	µi	µi	PROPN
ejde-355	371	11	dσ	dσ	PROPN
ejde-355	371	12	+	+	PROPN
ejde-355	371	13	ξ	ξ	PROPN
ejde-355	372	1	+	+	PUNCT
ejde-355	372	2	gi(t)r0	gi(t)r0	NOUN
ejde-355	372	3	∀t	∀t	PROPN
ejde-355	372	4	∈	∈	PROPN
ejde-355	372	5	∂ωi	∂ωi	NOUN
ejde-355	372	6	.	.	PUNCT
ejde-355	373	1	(	(	PUNCT
ejde-355	373	2	5.3	5.3	NUM
ejde-355	373	3	)	)	PUNCT
ejde-355	373	4	18	18	NUM
ejde-355	373	5	p.	p.	NOUN
ejde-355	373	6	musolino	musolino	NOUN
ejde-355	373	7	,	,	PUNCT
ejde-355	373	8	m.	m.	NOUN
ejde-355	373	9	dutko	dutko	PROPN
ejde-355	373	10	,	,	PUNCT
ejde-355	373	11	g.	g.	PROPN
ejde-355	373	12	mishuris	mishuris	PROPN
ejde-355	373	13	ejde-2023/57	ejde-2023/57	NOUN
ejde-355	373	14	by	by	ADP
ejde-355	373	15	arguing	argue	VERB
ejde-355	373	16	as	as	ADP
ejde-355	373	17	in	in	ADP
ejde-355	373	18	the	the	DET
ejde-355	373	19	proof	proof	NOUN
ejde-355	373	20	of	of	ADP
ejde-355	373	21	proposition	proposition	NOUN
ejde-355	373	22	4.1	4.1	NUM
ejde-355	373	23	,	,	PUNCT
ejde-355	373	24	one	one	PRON
ejde-355	373	25	can	can	AUX
ejde-355	373	26	prove	prove	VERB
ejde-355	373	27	that	that	SCONJ
ejde-355	373	28	the	the	DET
ejde-355	373	29	system	system	NOUN
ejde-355	373	30	(	(	PUNCT
ejde-355	373	31	5.2)(5.3	5.2)(5.3	NUM
ejde-355	373	32	)	)	PUNCT
ejde-355	373	33	in	in	ADP
ejde-355	373	34	the	the	DET
ejde-355	373	35	unknown	unknown	ADJ
ejde-355	373	36	(	(	PUNCT
ejde-355	373	37	µo	µo	PROPN
ejde-355	373	38	,	,	PUNCT
ejde-355	373	39	µi	µi	PROPN
ejde-355	373	40	,	,	PUNCT
ejde-355	373	41	ξ	ξ	PROPN
ejde-355	373	42	)	)	PUNCT
ejde-355	373	43	admits	admit	VERB
ejde-355	373	44	a	a	DET
ejde-355	373	45	unique	unique	ADJ
ejde-355	373	46	solution	solution	NOUN
ejde-355	373	47	(	(	PUNCT
ejde-355	373	48	µ̃o	µ̃o	NOUN
ejde-355	373	49	,	,	PUNCT
ejde-355	373	50	µ̃i	µ̃i	NOUN
ejde-355	373	51	,	,	PUNCT
ejde-355	373	52	ξ̃	ξ̃	PROPN
ejde-355	373	53	)	)	PUNCT
ejde-355	373	54	in	in	ADP
ejde-355	373	55	c0,α(∂ωo)0×	c0,α(∂ωo)0×	PROPN
ejde-355	373	56	c0,α(∂ωi)×	c0,α(∂ωi)×	PROPN
ejde-355	373	57	r.	r.	PROPN
ejde-355	373	58	in	in	ADP
ejde-355	373	59	particular	particular	ADJ
ejde-355	373	60	,	,	PUNCT
ejde-355	373	61	by	by	ADP
ejde-355	373	62	integrating	integrate	VERB
ejde-355	373	63	(	(	PUNCT
ejde-355	373	64	5.2	5.2	NUM
ejde-355	373	65	)	)	PUNCT
ejde-355	373	66	,	,	PUNCT
ejde-355	373	67	we	we	PRON
ejde-355	373	68	recall	recall	VERB
ejde-355	373	69	that	that	SCONJ
ejde-355	373	70	we	we	PRON
ejde-355	373	71	obtain∫	obtain∫	VERB
ejde-355	373	72	∂ωi	∂ωi	PROPN
ejde-355	373	73	µ̃i(s	µ̃i(s	NOUN
ejde-355	373	74	)	)	PUNCT
ejde-355	374	1	dσs	dσs	NOUN
ejde-355	374	2	=	=	SYM
ejde-355	374	3	∫	∫	PROPN
ejde-355	374	4	∂ωo	∂ωo	NOUN
ejde-355	374	5	go(x	go(x	NUM
ejde-355	374	6	)	)	PUNCT
ejde-355	374	7	dσx	dσx	NOUN
ejde-355	374	8	.	.	PUNCT
ejde-355	375	1	by	by	ADP
ejde-355	375	2	integrating	integrate	VERB
ejde-355	375	3	(	(	PUNCT
ejde-355	375	4	5.3	5.3	NUM
ejde-355	375	5	)	)	PUNCT
ejde-355	375	6	,	,	PUNCT
ejde-355	375	7	we	we	PRON
ejde-355	375	8	deduce	deduce	VERB
ejde-355	375	9	that∫	that∫	NOUN
ejde-355	375	10	∂ωo	∂ωo	NOUN
ejde-355	375	11	go(x	go(x	NUM
ejde-355	375	12	)	)	PUNCT
ejde-355	375	13	dσx	dσx	NOUN
ejde-355	375	14	=	=	SYM
ejde-355	375	15	|∂ωi|1	|∂ωi|1	NUM
ejde-355	375	16	l0	l0	NOUN
ejde-355	375	17	2π	2π	NUM
ejde-355	375	18	∫	∫	NOUN
ejde-355	375	19	∂ωo	∂ωo	NOUN
ejde-355	375	20	go(x	go(x	NUM
ejde-355	375	21	)	)	PUNCT
ejde-355	375	22	dσx	dσx	NOUN
ejde-355	375	23	+	+	X
ejde-355	375	24	|∂ωi|1ξ̃	|∂ωi|1ξ̃	PUNCT
ejde-355	375	25	+	+	CCONJ
ejde-355	375	26	r0	r0	NOUN
ejde-355	375	27	∫	∫	NOUN
ejde-355	375	28	∂ωi	∂ωi	PROPN
ejde-355	375	29	gi(t	gi(t	NOUN
ejde-355	375	30	)	)	PUNCT
ejde-355	375	31	dσt	dσt	NOUN
ejde-355	375	32	,	,	PUNCT
ejde-355	375	33	which	which	PRON
ejde-355	375	34	implies	imply	VERB
ejde-355	375	35	ξ̃	ξ̃	PROPN
ejde-355	375	36	=	=	SYM
ejde-355	375	37	1	1	NUM
ejde-355	375	38	|∂ωi|1	|∂ωi|1	NOUN
ejde-355	375	39	(	(	PUNCT
ejde-355	375	40	(	(	PUNCT
ejde-355	375	41	1−	1−	NUM
ejde-355	375	42	|∂ωi|1	|∂ωi|1	NUM
ejde-355	375	43	l0	l0	NOUN
ejde-355	375	44	2π	2π	NOUN
ejde-355	375	45	)	)	PUNCT
ejde-355	375	46	∫	∫	PROPN
ejde-355	375	47	∂ωo	∂ωo	NOUN
ejde-355	375	48	go(x	go(x	NUM
ejde-355	375	49	)	)	PUNCT
ejde-355	375	50	dσx	dσx	NOUN
ejde-355	375	51	−	−	PROPN
ejde-355	375	52	r0	r0	NOUN
ejde-355	375	53	∫	∫	PROPN
ejde-355	375	54	∂ωi	∂ωi	PROPN
ejde-355	375	55	gi(t	gi(t	NOUN
ejde-355	375	56	)	)	PUNCT
ejde-355	375	57	dσt	dσt	NOUN
ejde-355	375	58	)	)	PUNCT
ejde-355	375	59	.	.	PUNCT
ejde-355	376	1	we	we	PRON
ejde-355	376	2	note	note	VERB
ejde-355	376	3	that	that	SCONJ
ejde-355	376	4	in	in	ADP
ejde-355	376	5	case	case	NOUN
ejde-355	376	6	ωo	ωo	ADP
ejde-355	376	7	=	=	SYM
ejde-355	376	8	ωi	ωi	PROPN
ejde-355	376	9	=	=	PROPN
ejde-355	376	10	b2(0	b2(0	PROPN
ejde-355	376	11	,	,	PUNCT
ejde-355	376	12	1	1	NUM
ejde-355	376	13	)	)	PUNCT
ejde-355	376	14	and	and	CCONJ
ejde-355	376	15	go(x	go(x	NUM
ejde-355	376	16	)	)	PUNCT
ejde-355	376	17	=	=	SYM
ejde-355	376	18	a	a	DET
ejde-355	376	19	∀x	∀x	NUM
ejde-355	376	20	∈	∈	PROPN
ejde-355	376	21	∂b2(0	∂b2(0	NOUN
ejde-355	376	22	,	,	PUNCT
ejde-355	376	23	1	1	NUM
ejde-355	376	24	)	)	PUNCT
ejde-355	376	25	,	,	PUNCT
ejde-355	376	26	gi(t	gi(t	X
ejde-355	376	27	)	)	PUNCT
ejde-355	376	28	=	=	SYM
ejde-355	377	1	b	b	X
ejde-355	377	2	∀t	∀t	PROPN
ejde-355	377	3	∈	∈	NOUN
ejde-355	377	4	∂b2(0	∂b2(0	NOUN
ejde-355	377	5	,	,	PUNCT
ejde-355	377	6	1	1	NUM
ejde-355	377	7	)	)	PUNCT
ejde-355	377	8	,	,	PUNCT
ejde-355	377	9	we	we	PRON
ejde-355	377	10	obtain	obtain	VERB
ejde-355	377	11	ξ̃	ξ̃	PROPN
ejde-355	377	12	=	=	SYM
ejde-355	377	13	(	(	PUNCT
ejde-355	377	14	(	(	PUNCT
ejde-355	377	15	1−	1−	NUM
ejde-355	377	16	2π	2π	NUM
ejde-355	377	17	l0	l0	NOUN
ejde-355	377	18	2π	2π	NOUN
ejde-355	377	19	)	)	PUNCT
ejde-355	377	20	a−	a−	PROPN
ejde-355	377	21	br0	br0	VERB
ejde-355	377	22	)	)	PUNCT
ejde-355	378	1	=	=	SYM
ejde-355	378	2	(	(	PUNCT
ejde-355	378	3	a−	a−	PROPN
ejde-355	378	4	al0	al0	NOUN
ejde-355	378	5	−	−	PROPN
ejde-355	378	6	br0	br0	VERB
ejde-355	378	7	)	)	PUNCT
ejde-355	378	8	.	.	PUNCT
ejde-355	379	1	therefore	therefore	ADV
ejde-355	379	2	,	,	PUNCT
ejde-355	379	3	we	we	PRON
ejde-355	379	4	recover	recover	VERB
ejde-355	379	5	also	also	ADV
ejde-355	379	6	the	the	DET
ejde-355	379	7	results	result	NOUN
ejde-355	379	8	of	of	ADP
ejde-355	379	9	section	section	NOUN
ejde-355	379	10	2	2	NUM
ejde-355	379	11	.	.	NOUN
ejde-355	379	12	6	6	NUM
ejde-355	379	13	.	.	PUNCT
ejde-355	379	14	conclusions	conclusion	NOUN
ejde-355	379	15	in	in	ADP
ejde-355	379	16	this	this	DET
ejde-355	379	17	article	article	NOUN
ejde-355	379	18	,	,	PUNCT
ejde-355	379	19	we	we	PRON
ejde-355	379	20	have	have	AUX
ejde-355	379	21	considered	consider	VERB
ejde-355	379	22	a	a	DET
ejde-355	379	23	perforated	perforated	ADJ
ejde-355	379	24	domain	domain	NOUN
ejde-355	379	25	ω(ε	ω(ε	PROPN
ejde-355	379	26	)	)	PUNCT
ejde-355	379	27	of	of	ADP
ejde-355	379	28	r2	r2	PROPN
ejde-355	379	29	with	with	ADP
ejde-355	379	30	a	a	DET
ejde-355	379	31	small	small	ADJ
ejde-355	379	32	hole	hole	NOUN
ejde-355	379	33	of	of	ADP
ejde-355	379	34	size	size	NOUN
ejde-355	379	35	ε	ε	PROPN
ejde-355	379	36	and	and	CCONJ
ejde-355	379	37	we	we	PRON
ejde-355	379	38	have	have	AUX
ejde-355	379	39	studied	study	VERB
ejde-355	379	40	the	the	DET
ejde-355	379	41	behavior	behavior	NOUN
ejde-355	379	42	of	of	ADP
ejde-355	379	43	the	the	DET
ejde-355	379	44	solution	solution	NOUN
ejde-355	379	45	to	to	ADP
ejde-355	379	46	a	a	DET
ejde-355	379	47	degenearing	degeneare	VERB
ejde-355	379	48	mixed	mix	VERB
ejde-355	379	49	neumann	neumann	PROPN
ejde-355	379	50	-	-	PUNCT
ejde-355	379	51	robin	robin	PROPN
ejde-355	379	52	problem	problem	NOUN
ejde-355	379	53	in	in	ADP
ejde-355	379	54	ω(ε	ω(ε	PROPN
ejde-355	379	55	)	)	PUNCT
ejde-355	379	56	as	as	SCONJ
ejde-355	379	57	the	the	DET
ejde-355	379	58	size	size	NOUN
ejde-355	379	59	ε	ε	PROPN
ejde-355	379	60	of	of	ADP
ejde-355	379	61	the	the	DET
ejde-355	379	62	small	small	ADJ
ejde-355	379	63	hole	hole	NOUN
ejde-355	379	64	tends	tend	VERB
ejde-355	379	65	to	to	ADP
ejde-355	379	66	0	0	NUM
ejde-355	379	67	.	.	PUNCT
ejde-355	380	1	in	in	ADP
ejde-355	380	2	addition	addition	NOUN
ejde-355	380	3	to	to	ADP
ejde-355	380	4	the	the	DET
ejde-355	380	5	geometric	geometric	ADJ
ejde-355	380	6	degeneracy	degeneracy	NOUN
ejde-355	380	7	of	of	ADP
ejde-355	380	8	the	the	DET
ejde-355	380	9	problem	problem	NOUN
ejde-355	380	10	,	,	PUNCT
ejde-355	380	11	the	the	DET
ejde-355	380	12	nonlinear	nonlinear	NOUN
ejde-355	380	13	ε	ε	PROPN
ejde-355	380	14	-	-	PUNCT
ejde-355	380	15	dependent	dependent	ADJ
ejde-355	380	16	robin	robin	PROPN
ejde-355	380	17	condition	condition	NOUN
ejde-355	380	18	may	may	AUX
ejde-355	380	19	degenerate	degenerate	VERB
ejde-355	380	20	into	into	ADP
ejde-355	380	21	a	a	DET
ejde-355	380	22	neumann	neumann	PROPN
ejde-355	380	23	condition	condition	NOUN
ejde-355	380	24	for	for	ADP
ejde-355	380	25	ε	ε	PROPN
ejde-355	380	26	=	=	SYM
ejde-355	380	27	0	0	PROPN
ejde-355	380	28	and	and	CCONJ
ejde-355	380	29	the	the	DET
ejde-355	380	30	robin	robin	PROPN
ejde-355	380	31	datum	datum	NOUN
ejde-355	380	32	may	may	AUX
ejde-355	380	33	diverge	diverge	VERB
ejde-355	380	34	to	to	PART
ejde-355	380	35	infinity	infinity	VERB
ejde-355	380	36	.	.	PUNCT
ejde-355	381	1	our	our	PRON
ejde-355	381	2	goal	goal	NOUN
ejde-355	381	3	was	be	AUX
ejde-355	381	4	to	to	PART
ejde-355	381	5	prove	prove	VERB
ejde-355	381	6	the	the	DET
ejde-355	381	7	existence	existence	NOUN
ejde-355	381	8	of	of	ADP
ejde-355	381	9	solutions	solution	NOUN
ejde-355	381	10	for	for	ADP
ejde-355	381	11	ε	ε	PROPN
ejde-355	381	12	small	small	ADJ
ejde-355	381	13	and	and	CCONJ
ejde-355	381	14	positive	positive	ADJ
ejde-355	381	15	and	and	CCONJ
ejde-355	381	16	to	to	PART
ejde-355	381	17	study	study	VERB
ejde-355	381	18	the	the	DET
ejde-355	381	19	corresponding	corresponding	ADJ
ejde-355	381	20	asymptotic	asymptotic	ADJ
ejde-355	381	21	behavior	behavior	NOUN
ejde-355	381	22	as	as	ADP
ejde-355	381	23	ε→	ε→	X
ejde-355	381	24	0	0	NUM
ejde-355	381	25	.	.	PUNCT
ejde-355	382	1	instead	instead	ADV
ejde-355	382	2	of	of	ADP
ejde-355	382	3	the	the	DET
ejde-355	382	4	more	more	ADV
ejde-355	382	5	common	common	ADJ
ejde-355	382	6	methods	method	NOUN
ejde-355	382	7	of	of	ADP
ejde-355	382	8	asymptotic	asymptotic	ADJ
ejde-355	382	9	analysis	analysis	NOUN
ejde-355	382	10	dealing	deal	VERB
ejde-355	382	11	with	with	ADP
ejde-355	382	12	asymptotic	asymptotic	ADJ
ejde-355	382	13	expansions	expansion	NOUN
ejde-355	382	14	,	,	PUNCT
ejde-355	382	15	here	here	ADV
ejde-355	382	16	we	we	PRON
ejde-355	382	17	have	have	AUX
ejde-355	382	18	employed	employ	VERB
ejde-355	382	19	the	the	DET
ejde-355	382	20	functional	functional	ADJ
ejde-355	382	21	analytic	analytic	ADJ
ejde-355	382	22	approach	approach	NOUN
ejde-355	382	23	proposed	propose	VERB
ejde-355	382	24	by	by	ADP
ejde-355	382	25	lanza	lanza	PROPN
ejde-355	382	26	de	de	PROPN
ejde-355	382	27	cristoforis	cristoforis	PROPN
ejde-355	382	28	.	.	PUNCT
ejde-355	383	1	such	such	ADJ
ejde-355	383	2	method	method	NOUN
ejde-355	383	3	has	have	VERB
ejde-355	383	4	the	the	DET
ejde-355	383	5	advantages	advantage	NOUN
ejde-355	383	6	to	to	PART
ejde-355	383	7	be	be	AUX
ejde-355	383	8	applicable	applicable	ADJ
ejde-355	383	9	to	to	ADP
ejde-355	383	10	nonlinear	nonlinear	ADJ
ejde-355	383	11	boundary	boundary	ADJ
ejde-355	383	12	conditions	condition	NOUN
ejde-355	383	13	as	as	ADP
ejde-355	383	14	in	in	ADP
ejde-355	383	15	the	the	DET
ejde-355	383	16	present	present	ADJ
ejde-355	383	17	paper	paper	NOUN
ejde-355	383	18	and	and	CCONJ
ejde-355	383	19	to	to	PART
ejde-355	383	20	provide	provide	VERB
ejde-355	383	21	rigorous	rigorous	ADJ
ejde-355	383	22	justifications	justification	NOUN
ejde-355	383	23	to	to	ADP
ejde-355	383	24	power	power	NOUN
ejde-355	383	25	series	series	NOUN
ejde-355	383	26	expansions	expansion	NOUN
ejde-355	383	27	.	.	PUNCT
ejde-355	384	1	moreover	moreover	ADV
ejde-355	384	2	,	,	PUNCT
ejde-355	384	3	such	such	ADJ
ejde-355	384	4	approach	approach	NOUN
ejde-355	384	5	is	be	AUX
ejde-355	384	6	quite	quite	ADV
ejde-355	384	7	versatile	versatile	ADJ
ejde-355	384	8	:	:	PUNCT
ejde-355	384	9	it	it	PRON
ejde-355	384	10	has	have	AUX
ejde-355	384	11	been	be	AUX
ejde-355	384	12	applied	apply	VERB
ejde-355	384	13	to	to	ADP
ejde-355	384	14	elliptic	elliptic	ADJ
ejde-355	384	15	systems	system	NOUN
ejde-355	384	16	of	of	ADP
ejde-355	384	17	partial	partial	ADJ
ejde-355	384	18	differential	differential	ADJ
ejde-355	384	19	equations	equation	NOUN
ejde-355	384	20	(	(	PUNCT
ejde-355	384	21	see	see	VERB
ejde-355	384	22	dalla	dalla	PROPN
ejde-355	384	23	riva	riva	PROPN
ejde-355	384	24	and	and	CCONJ
ejde-355	384	25	lanza	lanza	NOUN
ejde-355	384	26	de	de	PROPN
ejde-355	384	27	cristoforis	cristoforis	PROPN
ejde-355	385	1	[	[	X
ejde-355	385	2	5	5	NUM
ejde-355	385	3	,	,	PUNCT
ejde-355	385	4	6	6	NUM
ejde-355	385	5	]	]	PUNCT
ejde-355	385	6	)	)	PUNCT
ejde-355	385	7	and	and	CCONJ
ejde-355	385	8	currently	currently	ADV
ejde-355	385	9	some	some	DET
ejde-355	385	10	preliminary	preliminary	ADJ
ejde-355	385	11	results	result	NOUN
ejde-355	385	12	have	have	AUX
ejde-355	385	13	been	be	AUX
ejde-355	385	14	obtained	obtain	VERB
ejde-355	385	15	also	also	ADV
ejde-355	385	16	in	in	ADP
ejde-355	385	17	order	order	NOUN
ejde-355	385	18	to	to	PART
ejde-355	385	19	consider	consider	VERB
ejde-355	385	20	parabolic	parabolic	ADJ
ejde-355	385	21	equations	equation	NOUN
ejde-355	385	22	(	(	PUNCT
ejde-355	385	23	see	see	VERB
ejde-355	385	24	dalla	dalla	PROPN
ejde-355	385	25	riva	riva	NOUN
ejde-355	385	26	and	and	CCONJ
ejde-355	385	27	luzzini	luzzini	NOUN
ejde-355	385	28	[	[	X
ejde-355	385	29	10	10	NUM
ejde-355	385	30	]	]	PUNCT
ejde-355	385	31	and	and	CCONJ
ejde-355	385	32	luzzini	luzzini	ADJ
ejde-355	386	1	[	[	X
ejde-355	386	2	23	23	NUM
ejde-355	386	3	]	]	SYM
ejde-355	386	4	)	)	PUNCT
ejde-355	386	5	.	.	PUNCT
ejde-355	387	1	acknowledgements	acknowledgement	NOUN
ejde-355	387	2	.	.	PUNCT
ejde-355	388	1	the	the	DET
ejde-355	388	2	authors	author	NOUN
ejde-355	388	3	acknowledge	acknowledge	VERB
ejde-355	388	4	the	the	DET
ejde-355	388	5	support	support	NOUN
ejde-355	388	6	from	from	ADP
ejde-355	388	7	eu	eu	PROPN
ejde-355	388	8	through	through	ADP
ejde-355	388	9	the	the	DET
ejde-355	388	10	h2020	h2020	NOUN
ejde-355	388	11	-	-	PUNCT
ejde-355	388	12	msca	msca	NOUN
ejde-355	388	13	-	-	PUNCT
ejde-355	388	14	rise-2020	rise-2020	ADJ
ejde-355	388	15	project	project	NOUN
ejde-355	388	16	effectfact	effectfact	NOUN
ejde-355	388	17	,	,	PUNCT
ejde-355	388	18	grant	grant	NOUN
ejde-355	388	19	agreement	agreement	NOUN
ejde-355	388	20	i	i	PROPN
ejde-355	388	21	d	d	PROPN
ejde-355	388	22	:	:	PUNCT
ejde-355	388	23	101008140	101008140	NUM
ejde-355	388	24	.	.	PUNCT
ejde-355	389	1	the	the	DET
ejde-355	389	2	authors	author	NOUN
ejde-355	389	3	thank	thank	VERB
ejde-355	389	4	dr	dr	PROPN
ejde-355	389	5	.	.	PROPN
ejde-355	389	6	luigi	luigi	PROPN
ejde-355	389	7	provenzano	provenzano	PROPN
ejde-355	389	8	for	for	ADP
ejde-355	389	9	valuable	valuable	ADJ
ejde-355	389	10	discussions	discussion	NOUN
ejde-355	389	11	on	on	ADP
ejde-355	389	12	steklov	steklov	NOUN
ejde-355	389	13	eigenvalues	eigenvalue	NOUN
ejde-355	389	14	in	in	ADP
ejde-355	389	15	relation	relation	NOUN
ejde-355	389	16	to	to	ADP
ejde-355	389	17	the	the	DET
ejde-355	389	18	toy	toy	NOUN
ejde-355	389	19	problem	problem	NOUN
ejde-355	389	20	of	of	ADP
ejde-355	389	21	section	section	NOUN
ejde-355	389	22	2	2	NUM
ejde-355	389	23	.	.	PUNCT
ejde-355	390	1	p.	p.	NOUN
ejde-355	390	2	musolino	musolino	PROPN
ejde-355	390	3	also	also	ADV
ejde-355	390	4	acknowledges	acknowledge	VERB
ejde-355	390	5	the	the	DET
ejde-355	390	6	support	support	NOUN
ejde-355	390	7	of	of	ADP
ejde-355	390	8	the	the	DET
ejde-355	390	9	spin	spin	NOUN
ejde-355	390	10	project	project	NOUN
ejde-355	390	11	“	"	PUNCT
ejde-355	390	12	domain	domain	NOUN
ejde-355	390	13	perturbation	perturbation	NOUN
ejde-355	390	14	problems	problem	NOUN
ejde-355	390	15	and	and	CCONJ
ejde-355	390	16	interactions	interaction	NOUN
ejde-355	390	17	of	of	ADP
ejde-355	390	18	scales	scale	NOUN
ejde-355	390	19	domino	domino	NOUN
ejde-355	390	20	”	"	PUNCT
ejde-355	390	21	of	of	ADP
ejde-355	390	22	the	the	DET
ejde-355	390	23	ca	ca	NOUN
ejde-355	390	24	’	'	PUNCT
ejde-355	390	25	foscari	foscari	PROPN
ejde-355	390	26	university	university	PROPN
ejde-355	390	27	of	of	ADP
ejde-355	390	28	venice	venice	PROPN
ejde-355	390	29	.	.	PUNCT
ejde-355	391	1	part	part	NOUN
ejde-355	391	2	of	of	ADP
ejde-355	391	3	the	the	DET
ejde-355	391	4	work	work	NOUN
ejde-355	391	5	was	be	AUX
ejde-355	391	6	done	do	VERB
ejde-355	391	7	while	while	SCONJ
ejde-355	391	8	p.	p.	PROPN
ejde-355	391	9	musolino	musolino	PROPN
ejde-355	391	10	was	be	AUX
ejde-355	391	11	visiting	visit	VERB
ejde-355	391	12	m.	m.	NOUN
ejde-355	391	13	dutko	dutko	NOUN
ejde-355	391	14	at	at	ADP
ejde-355	391	15	rockfield	rockfield	ADJ
ejde-355	391	16	software	software	NOUN
ejde-355	391	17	limited	limit	VERB
ejde-355	391	18	.	.	PUNCT
ejde-355	392	1	p.	p.	NOUN
ejde-355	392	2	musolino	musolino	PROPN
ejde-355	392	3	wishes	wish	VERB
ejde-355	392	4	to	to	PART
ejde-355	392	5	thank	thank	VERB
ejde-355	392	6	m.	m.	NOUN
ejde-355	392	7	dutko	dutko	PROPN
ejde-355	392	8	and	and	CCONJ
ejde-355	392	9	rockfield	rockfield	ADJ
ejde-355	392	10	software	software	NOUN
ejde-355	392	11	limited	limit	VERB
ejde-355	392	12	for	for	ADP
ejde-355	392	13	the	the	DET
ejde-355	392	14	kind	kind	ADJ
ejde-355	392	15	hospitality	hospitality	NOUN
ejde-355	392	16	.	.	PUNCT
ejde-355	393	1	p.	p.	NOUN
ejde-355	393	2	musolino	musolino	PROPN
ejde-355	393	3	is	be	AUX
ejde-355	393	4	a	a	DET
ejde-355	393	5	member	member	NOUN
ejde-355	393	6	of	of	ADP
ejde-355	393	7	the	the	DET
ejde-355	393	8	gruppo	gruppo	PROPN
ejde-355	393	9	nazionale	nazionale	NOUN
ejde-355	393	10	per	per	ADP
ejde-355	393	11	l’analisi	l’analisi	PROPN
ejde-355	393	12	matematica	matematica	PROPN
ejde-355	393	13	,	,	PUNCT
ejde-355	393	14	la	la	X
ejde-355	393	15	probabilità	probabilità	PROPN
ejde-355	393	16	e	e	X
ejde-355	393	17	le	le	X
ejde-355	393	18	loro	loro	X
ejde-355	393	19	applicazioni	applicazioni	PROPN
ejde-355	393	20	(	(	PUNCT
ejde-355	393	21	gnampa	gnampa	NOUN
ejde-355	393	22	)	)	PUNCT
ejde-355	393	23	of	of	ADP
ejde-355	393	24	the	the	DET
ejde-355	393	25	istituto	istituto	X
ejde-355	393	26	nazionale	nazionale	PROPN
ejde-355	393	27	di	di	PROPN
ejde-355	393	28	ejde-2023/57	ejde-2023/57	NOUN
ejde-355	393	29	asymptotic	asymptotic	ADJ
ejde-355	393	30	analysis	analysis	NOUN
ejde-355	393	31	of	of	ADP
ejde-355	393	32	perturbed	perturb	VERB
ejde-355	393	33	robin	robin	PROPN
ejde-355	393	34	problems	problem	VERB
ejde-355	393	35	19	19	NUM
ejde-355	393	36	alta	alta	PROPN
ejde-355	393	37	matematica	matematica	PROPN
ejde-355	393	38	(	(	PUNCT
ejde-355	393	39	indam	indam	NOUN
ejde-355	393	40	)	)	PUNCT
ejde-355	393	41	.	.	PUNCT
ejde-355	394	1	g.	g.	PROPN
ejde-355	394	2	mishuris	mishuris	PROPN
ejde-355	394	3	acknowledges	acknowledge	VERB
ejde-355	394	4	also	also	ADV
ejde-355	394	5	ser	ser	NOUN
ejde-355	394	6	cymru	cymru	PROPN
ejde-355	394	7	future	future	ADJ
ejde-355	394	8	generation	generation	NOUN
ejde-355	394	9	industrial	industrial	ADJ
ejde-355	394	10	fellowship	fellowship	NOUN
ejde-355	394	11	number	number	NOUN
ejde-355	394	12	au224	au224	ADV
ejde-355	394	13	–	–	PUNCT
ejde-355	394	14	80761	80761	NUM
ejde-355	394	15	.	.	PUNCT
ejde-355	395	1	m.	m.	NOUN
ejde-355	395	2	dutko	dutko	PROPN
ejde-355	395	3	also	also	ADV
ejde-355	395	4	acknowledges	acknowledge	VERB
ejde-355	395	5	the	the	DET
ejde-355	395	6	royal	royal	PROPN
ejde-355	395	7	academy	academy	NOUN
ejde-355	395	8	of	of	ADP
ejde-355	395	9	engineering	engineering	NOUN
ejde-355	395	10	for	for	ADP
ejde-355	395	11	the	the	DET
ejde-355	395	12	industrial	industrial	ADJ
ejde-355	395	13	fellowship	fellowship	NOUN
ejde-355	395	14	.	.	PUNCT
ejde-355	396	1	references	reference	NOUN
ejde-355	396	2	[	[	X
ejde-355	396	3	1	1	NUM
ejde-355	396	4	]	]	PUNCT
ejde-355	396	5	h.	h.	PROPN
ejde-355	396	6	ammari	ammari	PROPN
ejde-355	396	7	,	,	PUNCT
ejde-355	396	8	h.	h.	PROPN
ejde-355	396	9	kang	kang	PROPN
ejde-355	396	10	;	;	PUNCT
ejde-355	396	11	polarization	polarization	NOUN
ejde-355	396	12	and	and	CCONJ
ejde-355	396	13	moment	moment	NOUN
ejde-355	396	14	tensors	tensor	NOUN
ejde-355	396	15	,	,	PUNCT
ejde-355	396	16	volume	volume	NOUN
ejde-355	396	17	162	162	NUM
ejde-355	396	18	of	of	ADP
ejde-355	396	19	applied	apply	VERB
ejde-355	396	20	mathematical	mathematical	ADJ
ejde-355	396	21	sciences	science	NOUN
ejde-355	396	22	,	,	PUNCT
ejde-355	396	23	springer	springer	NOUN
ejde-355	396	24	,	,	PUNCT
ejde-355	396	25	new	new	PROPN
ejde-355	396	26	york	york	PROPN
ejde-355	396	27	,	,	PUNCT
ejde-355	396	28	2007	2007	NUM
ejde-355	397	1	[	[	X
ejde-355	397	2	2	2	X
ejde-355	397	3	]	]	X
ejde-355	397	4	h.	h.	PROPN
ejde-355	397	5	ammari	ammari	PROPN
ejde-355	397	6	,	,	PUNCT
ejde-355	397	7	j.-c	j.-c	PROPN
ejde-355	397	8	.	.	PUNCT
ejde-355	397	9	nédélec	nédélec	PROPN
ejde-355	397	10	;	;	PUNCT
ejde-355	397	11	generalized	generalize	VERB
ejde-355	397	12	impedance	impedance	NOUN
ejde-355	397	13	boundary	boundary	ADJ
ejde-355	397	14	conditions	condition	NOUN
ejde-355	397	15	for	for	ADP
ejde-355	397	16	the	the	DET
ejde-355	397	17	maxwell	maxwell	PROPN
ejde-355	397	18	equations	equation	NOUN
ejde-355	397	19	as	as	ADP
ejde-355	397	20	singular	singular	ADJ
ejde-355	397	21	perturbations	perturbation	NOUN
ejde-355	397	22	problems	problem	NOUN
ejde-355	397	23	,	,	PUNCT
ejde-355	397	24	comm	comm	NOUN
ejde-355	397	25	.	.	PUNCT
ejde-355	398	1	partial	partial	ADJ
ejde-355	398	2	differential	differential	NOUN
ejde-355	398	3	equations	equation	NOUN
ejde-355	398	4	,	,	PUNCT
ejde-355	398	5	24	24	NUM
ejde-355	398	6	(	(	PUNCT
ejde-355	398	7	5	5	NUM
ejde-355	398	8	-	-	SYM
ejde-355	398	9	6	6	NUM
ejde-355	398	10	)	)	PUNCT
ejde-355	398	11	(	(	PUNCT
ejde-355	398	12	1999	1999	NUM
ejde-355	398	13	)	)	PUNCT
ejde-355	398	14	,	,	PUNCT
ejde-355	398	15	821–849	821–849	NUM
ejde-355	398	16	.	.	PUNCT
ejde-355	399	1	[	[	X
ejde-355	399	2	3	3	X
ejde-355	399	3	]	]	PUNCT
ejde-355	399	4	r.	r.	PROPN
ejde-355	399	5	böhme	böhme	PROPN
ejde-355	399	6	,	,	PUNCT
ejde-355	399	7	f.	f.	PROPN
ejde-355	399	8	tomi	tomi	PROPN
ejde-355	399	9	;	;	PUNCT
ejde-355	399	10	zur	zur	NOUN
ejde-355	399	11	struktur	struktur	X
ejde-355	399	12	der	der	NOUN
ejde-355	399	13	lösungsmenge	lösungsmenge	VERB
ejde-355	399	14	des	des	PROPN
ejde-355	399	15	plateauproblems	plateauproblem	NOUN
ejde-355	399	16	,	,	PUNCT
ejde-355	399	17	math	math	NOUN
ejde-355	399	18	.	.	PUNCT
ejde-355	400	1	z.	z.	PROPN
ejde-355	400	2	,	,	PUNCT
ejde-355	400	3	133	133	NUM
ejde-355	400	4	(	(	PUNCT
ejde-355	400	5	1973	1973	NUM
ejde-355	400	6	)	)	PUNCT
ejde-355	400	7	,	,	PUNCT
ejde-355	400	8	1–29	1–29	PROPN
ejde-355	400	9	.	.	PUNCT
ejde-355	401	1	[	[	X
ejde-355	401	2	4	4	X
ejde-355	401	3	]	]	PUNCT
ejde-355	401	4	m.	m.	NOUN
ejde-355	401	5	costabel	costabel	NOUN
ejde-355	401	6	,	,	PUNCT
ejde-355	401	7	m.	m.	NOUN
ejde-355	401	8	dauge	dauge	PROPN
ejde-355	401	9	;	;	PUNCT
ejde-355	401	10	a	a	DET
ejde-355	401	11	singularly	singularly	ADV
ejde-355	401	12	perturbed	perturb	VERB
ejde-355	401	13	mixed	mixed	ADJ
ejde-355	401	14	boundary	boundary	ADJ
ejde-355	401	15	value	value	NOUN
ejde-355	401	16	problem	problem	NOUN
ejde-355	401	17	,	,	PUNCT
ejde-355	401	18	comm	comm	NOUN
ejde-355	401	19	.	.	PUNCT
ejde-355	402	1	partial	partial	ADJ
ejde-355	402	2	differential	differential	NOUN
ejde-355	402	3	equations	equation	NOUN
ejde-355	402	4	,	,	PUNCT
ejde-355	402	5	21(11	21(11	NUM
ejde-355	402	6	-	-	SYM
ejde-355	402	7	12	12	NUM
ejde-355	402	8	)	)	PUNCT
ejde-355	402	9	(	(	PUNCT
ejde-355	402	10	1996	1996	NUM
ejde-355	402	11	)	)	PUNCT
ejde-355	402	12	,	,	PUNCT
ejde-355	402	13	1919–1949	1919–1949	NUM
ejde-355	402	14	.	.	PUNCT
ejde-355	403	1	[	[	X
ejde-355	403	2	5	5	NUM
ejde-355	403	3	]	]	PUNCT
ejde-355	403	4	m.	m.	NOUN
ejde-355	403	5	dalla	dalla	PROPN
ejde-355	403	6	riva	riva	PROPN
ejde-355	403	7	,	,	PUNCT
ejde-355	403	8	m.	m.	NOUN
ejde-355	403	9	lanza	lanza	PROPN
ejde-355	403	10	de	de	PROPN
ejde-355	403	11	cristoforis	cristoforis	PROPN
ejde-355	403	12	;	;	PUNCT
ejde-355	403	13	microscopically	microscopically	ADV
ejde-355	403	14	weakly	weakly	ADV
ejde-355	403	15	singularly	singularly	ADV
ejde-355	403	16	perturbed	perturb	VERB
ejde-355	403	17	loads	load	NOUN
ejde-355	403	18	for	for	ADP
ejde-355	403	19	a	a	DET
ejde-355	403	20	nonlinear	nonlinear	ADJ
ejde-355	403	21	traction	traction	NOUN
ejde-355	403	22	boundary	boundary	ADJ
ejde-355	403	23	value	value	NOUN
ejde-355	403	24	problem	problem	NOUN
ejde-355	403	25	:	:	PUNCT
ejde-355	403	26	a	a	DET
ejde-355	403	27	functional	functional	ADJ
ejde-355	403	28	analytic	analytic	ADJ
ejde-355	403	29	approach	approach	NOUN
ejde-355	403	30	,	,	PUNCT
ejde-355	403	31	complex	complex	ADJ
ejde-355	403	32	var	var	NOUN
ejde-355	403	33	.	.	PUNCT
ejde-355	404	1	elliptic	elliptic	PROPN
ejde-355	404	2	equ	equ	PROPN
ejde-355	404	3	.	.	PROPN
ejde-355	404	4	,	,	PUNCT
ejde-355	404	5	55(8	55(8	NUM
ejde-355	404	6	-	-	SYM
ejde-355	404	7	10	10	NUM
ejde-355	404	8	)	)	PUNCT
ejde-355	404	9	(	(	PUNCT
ejde-355	404	10	2010	2010	NUM
ejde-355	404	11	)	)	PUNCT
ejde-355	404	12	,	,	PUNCT
ejde-355	404	13	771–794	771–794	NUM
ejde-355	404	14	.	.	PUNCT
ejde-355	405	1	[	[	X
ejde-355	405	2	6	6	NUM
ejde-355	405	3	]	]	PUNCT
ejde-355	405	4	m.	m.	NOUN
ejde-355	405	5	dalla	dalla	PROPN
ejde-355	405	6	riva	riva	PROPN
ejde-355	405	7	,	,	PUNCT
ejde-355	405	8	m.	m.	NOUN
ejde-355	405	9	lanza	lanza	PROPN
ejde-355	405	10	de	de	PROPN
ejde-355	405	11	cristoforis	cristoforis	PROPN
ejde-355	405	12	;	;	PUNCT
ejde-355	405	13	a	a	DET
ejde-355	405	14	singularly	singularly	ADV
ejde-355	405	15	perturbed	perturb	VERB
ejde-355	405	16	nonlinear	nonlinear	ADJ
ejde-355	405	17	traction	traction	NOUN
ejde-355	405	18	boundary	boundary	ADJ
ejde-355	405	19	value	value	NOUN
ejde-355	405	20	problem	problem	NOUN
ejde-355	405	21	for	for	ADP
ejde-355	405	22	linearized	linearized	ADJ
ejde-355	405	23	elastostatics	elastostatic	NOUN
ejde-355	405	24	.	.	PUNCT
ejde-355	406	1	a	a	DET
ejde-355	406	2	functional	functional	ADJ
ejde-355	406	3	analytic	analytic	ADJ
ejde-355	406	4	approach	approach	NOUN
ejde-355	406	5	,	,	PUNCT
ejde-355	406	6	analysis	analysis	NOUN
ejde-355	406	7	(	(	PUNCT
ejde-355	406	8	munich	munich	PROPN
ejde-355	406	9	)	)	PUNCT
ejde-355	406	10	,	,	PUNCT
ejde-355	406	11	30(1	30(1	NUM
ejde-355	406	12	)	)	PUNCT
ejde-355	406	13	(	(	PUNCT
ejde-355	406	14	2010	2010	NUM
ejde-355	406	15	)	)	PUNCT
ejde-355	406	16	,	,	PUNCT
ejde-355	406	17	1	1	NUM
ejde-355	406	18	,	,	PUNCT
ejde-355	406	19	67–92	67–92	NUM
ejde-355	406	20	.	.	PUNCT
ejde-355	407	1	[	[	X
ejde-355	407	2	7	7	X
ejde-355	407	3	]	]	X
ejde-355	407	4	m.	m.	NOUN
ejde-355	407	5	dalla	dalla	PROPN
ejde-355	407	6	riva	riva	PROPN
ejde-355	407	7	,	,	PUNCT
ejde-355	407	8	m.	m.	NOUN
ejde-355	407	9	lanza	lanza	PROPN
ejde-355	407	10	de	de	PROPN
ejde-355	407	11	cristoforis	cristoforis	PROPN
ejde-355	407	12	;	;	PUNCT
ejde-355	407	13	hypersingularly	hypersingularly	ADV
ejde-355	407	14	perturbed	perturb	VERB
ejde-355	407	15	loads	load	NOUN
ejde-355	407	16	for	for	ADP
ejde-355	407	17	a	a	DET
ejde-355	407	18	nonlinear	nonlinear	ADJ
ejde-355	407	19	traction	traction	NOUN
ejde-355	407	20	boundary	boundary	ADJ
ejde-355	407	21	value	value	NOUN
ejde-355	407	22	problem	problem	NOUN
ejde-355	407	23	.	.	PUNCT
ejde-355	408	1	a	a	DET
ejde-355	408	2	functional	functional	ADJ
ejde-355	408	3	analytic	analytic	ADJ
ejde-355	408	4	approach	approach	NOUN
ejde-355	408	5	,	,	PUNCT
ejde-355	408	6	eurasian	eurasian	ADJ
ejde-355	408	7	math	math	NOUN
ejde-355	408	8	.	.	PUNCT
ejde-355	409	1	j.	j.	PROPN
ejde-355	409	2	,	,	PUNCT
ejde-355	409	3	1(2	1(2	NUM
ejde-355	409	4	)	)	PUNCT
ejde-355	409	5	(	(	PUNCT
ejde-355	409	6	2010	2010	NUM
ejde-355	409	7	)	)	PUNCT
ejde-355	409	8	,	,	PUNCT
ejde-355	409	9	31–58	31–58	NUM
ejde-355	409	10	.	.	PUNCT
ejde-355	410	1	[	[	X
ejde-355	410	2	8	8	NUM
ejde-355	410	3	]	]	PUNCT
ejde-355	410	4	m.	m.	NOUN
ejde-355	410	5	dalla	dalla	PROPN
ejde-355	410	6	riva	riva	PROPN
ejde-355	410	7	,	,	PUNCT
ejde-355	410	8	m.	m.	NOUN
ejde-355	410	9	lanza	lanza	PROPN
ejde-355	410	10	de	de	PROPN
ejde-355	410	11	cristoforis	cristoforis	PROPN
ejde-355	410	12	;	;	PUNCT
ejde-355	410	13	weakly	weakly	ADJ
ejde-355	410	14	singular	singular	NOUN
ejde-355	410	15	and	and	CCONJ
ejde-355	410	16	microscopically	microscopically	ADV
ejde-355	410	17	hypersingular	hypersingular	ADJ
ejde-355	410	18	load	load	NOUN
ejde-355	410	19	perturbation	perturbation	NOUN
ejde-355	410	20	for	for	ADP
ejde-355	410	21	a	a	DET
ejde-355	410	22	nonlinear	nonlinear	ADJ
ejde-355	410	23	traction	traction	NOUN
ejde-355	410	24	boundary	boundary	ADJ
ejde-355	410	25	value	value	NOUN
ejde-355	410	26	problem	problem	NOUN
ejde-355	410	27	:	:	PUNCT
ejde-355	410	28	a	a	DET
ejde-355	410	29	functional	functional	ADJ
ejde-355	410	30	analytic	analytic	ADJ
ejde-355	410	31	approach	approach	NOUN
ejde-355	410	32	,	,	PUNCT
ejde-355	410	33	complex	complex	ADJ
ejde-355	410	34	anal	anal	NOUN
ejde-355	410	35	.	.	PUNCT
ejde-355	411	1	oper	oper	PROPN
ejde-355	411	2	.	.	PUNCT
ejde-355	411	3	theory	theory	NOUN
ejde-355	411	4	.	.	PUNCT
ejde-355	411	5	,	,	PUNCT
ejde-355	411	6	5(3	5(3	NUM
ejde-355	411	7	)	)	PUNCT
ejde-355	411	8	(	(	PUNCT
ejde-355	411	9	2011	2011	NUM
ejde-355	411	10	)	)	PUNCT
ejde-355	411	11	,	,	PUNCT
ejde-355	411	12	811–833	811–833	NUM
ejde-355	411	13	.	.	PUNCT
ejde-355	412	1	[	[	X
ejde-355	412	2	9	9	NUM
ejde-355	412	3	]	]	PUNCT
ejde-355	412	4	m.	m.	NOUN
ejde-355	412	5	dalla	dalla	PROPN
ejde-355	412	6	riva	riva	PROPN
ejde-355	412	7	,	,	PUNCT
ejde-355	412	8	m.	m.	NOUN
ejde-355	412	9	lanza	lanza	PROPN
ejde-355	412	10	de	de	PROPN
ejde-355	412	11	cristoforis	cristoforis	PROPN
ejde-355	412	12	,	,	PUNCT
ejde-355	412	13	p.	p.	NOUN
ejde-355	412	14	musolino	musolino	PROPN
ejde-355	412	15	;	;	PUNCT
ejde-355	412	16	singularly	singularly	ADV
ejde-355	412	17	perturbed	perturb	VERB
ejde-355	412	18	boundary	boundary	ADJ
ejde-355	412	19	value	value	NOUN
ejde-355	412	20	problems	problem	NOUN
ejde-355	412	21	.	.	PUNCT
ejde-355	413	1	a	a	DET
ejde-355	413	2	functional	functional	ADJ
ejde-355	413	3	analytic	analytic	ADJ
ejde-355	413	4	approach	approach	NOUN
ejde-355	413	5	.	.	PUNCT
ejde-355	414	1	springer	springer	NOUN
ejde-355	414	2	,	,	PUNCT
ejde-355	414	3	cham	cham	NOUN
ejde-355	414	4	,	,	PUNCT
ejde-355	414	5	2021	2021	NUM
ejde-355	414	6	.	.	PUNCT
ejde-355	415	1	[	[	X
ejde-355	415	2	10	10	NUM
ejde-355	415	3	]	]	PUNCT
ejde-355	415	4	m.	m.	NOUN
ejde-355	415	5	dalla	dalla	PROPN
ejde-355	415	6	riva	riva	PROPN
ejde-355	415	7	,	,	PUNCT
ejde-355	415	8	p.	p.	NOUN
ejde-355	415	9	luzzini	luzzini	PROPN
ejde-355	415	10	;	;	PUNCT
ejde-355	415	11	dependence	dependence	NOUN
ejde-355	415	12	of	of	ADP
ejde-355	415	13	the	the	DET
ejde-355	415	14	layer	layer	NOUN
ejde-355	415	15	heat	heat	NOUN
ejde-355	415	16	potentials	potential	VERB
ejde-355	415	17	upon	upon	SCONJ
ejde-355	415	18	support	support	NOUN
ejde-355	415	19	perturbations	perturbation	NOUN
ejde-355	415	20	,	,	PUNCT
ejde-355	415	21	differential	differential	ADJ
ejde-355	415	22	integral	integral	ADJ
ejde-355	415	23	equations	equation	NOUN
ejde-355	415	24	36(11	36(11	NUM
ejde-355	415	25	-	-	SYM
ejde-355	415	26	12	12	NUM
ejde-355	415	27	)	)	PUNCT
ejde-355	415	28	(	(	PUNCT
ejde-355	415	29	2023	2023	NUM
ejde-355	415	30	)	)	PUNCT
ejde-355	415	31	,	,	PUNCT
ejde-355	415	32	971–1003	971–1003	NUM
ejde-355	415	33	.	.	PUNCT
ejde-355	416	1	[	[	X
ejde-355	416	2	11	11	NUM
ejde-355	416	3	]	]	PUNCT
ejde-355	416	4	k.	k.	PROPN
ejde-355	416	5	deimling	deimling	PROPN
ejde-355	416	6	;	;	PUNCT
ejde-355	416	7	nonlinear	nonlinear	ADJ
ejde-355	416	8	functional	functional	ADJ
ejde-355	416	9	analysis	analysis	NOUN
ejde-355	416	10	.	.	PUNCT
ejde-355	417	1	springer	springer	NOUN
ejde-355	417	2	-	-	PUNCT
ejde-355	417	3	verlag	verlag	PROPN
ejde-355	417	4	,	,	PUNCT
ejde-355	417	5	berlin	berlin	PROPN
ejde-355	417	6	,	,	PUNCT
ejde-355	417	7	1985	1985	NUM
ejde-355	417	8	.	.	PUNCT
ejde-355	418	1	[	[	X
ejde-355	418	2	12	12	NUM
ejde-355	418	3	]	]	PUNCT
ejde-355	418	4	elfen	elfen	PROPN
ejde-355	418	5	glass	glass	PROPN
ejde-355	418	6	design	design	PROPN
ejde-355	418	7	,	,	PUNCT
ejde-355	418	8	https://www.elfen-glassdesign.com/	https://www.elfen-glassdesign.com/	NOUN
ejde-355	418	9	accessed	access	VERB
ejde-355	418	10	on	on	ADP
ejde-355	418	11	december	december	PROPN
ejde-355	418	12	7	7	NUM
ejde-355	418	13	,	,	PUNCT
ejde-355	418	14	2022	2022	NUM
ejde-355	418	15	.	.	PUNCT
ejde-355	419	1	[	[	X
ejde-355	419	2	13	13	NUM
ejde-355	419	3	]	]	PUNCT
ejde-355	419	4	elfen	elfen	PROPN
ejde-355	419	5	welbore	welbore	PROPN
ejde-355	419	6	https://www.rockfieldglobal.com/software/elfen-wellbore/	https://www.rockfieldglobal.com/software/elfen-wellbore/	VERB
ejde-355	419	7	accessed	access	VERB
ejde-355	419	8	on	on	ADP
ejde-355	419	9	december	december	PROPN
ejde-355	419	10	7	7	NUM
ejde-355	419	11	,	,	PUNCT
ejde-355	419	12	2022	2022	NUM
ejde-355	419	13	.	.	PUNCT
ejde-355	420	1	[	[	X
ejde-355	420	2	14	14	NUM
ejde-355	420	3	]	]	X
ejde-355	420	4	d.	d.	PROPN
ejde-355	420	5	gilbarg	gilbarg	PROPN
ejde-355	420	6	,	,	PUNCT
ejde-355	420	7	ns	ns	PROPN
ejde-355	420	8	.	.	PROPN
ejde-355	420	9	trudinger	trudinger	NOUN
ejde-355	420	10	;	;	PUNCT
ejde-355	420	11	elliptic	elliptic	ADJ
ejde-355	420	12	partial	partial	ADJ
ejde-355	420	13	differential	differential	ADJ
ejde-355	420	14	equations	equation	NOUN
ejde-355	420	15	of	of	ADP
ejde-355	420	16	second	second	ADJ
ejde-355	420	17	order	order	NOUN
ejde-355	420	18	grundlehren	grundlehren	PROPN
ejde-355	420	19	der	der	PROPN
ejde-355	420	20	mathematischen	mathematischen	PROPN
ejde-355	420	21	wissenschaften	wissenschaften	PROPN
ejde-355	420	22	[	[	X
ejde-355	420	23	fundamental	fundamental	ADJ
ejde-355	420	24	principles	principle	NOUN
ejde-355	420	25	of	of	ADP
ejde-355	420	26	mathematical	mathematical	ADJ
ejde-355	420	27	sciences	science	NOUN
ejde-355	420	28	]	]	PUNCT
ejde-355	420	29	,	,	PUNCT
ejde-355	420	30	vol	vol	NOUN
ejde-355	420	31	.	.	PROPN
ejde-355	421	1	224	224	NUM
ejde-355	421	2	,	,	PUNCT
ejde-355	421	3	springer	springer	NOUN
ejde-355	421	4	-	-	PUNCT
ejde-355	421	5	verlag	verlag	PROPN
ejde-355	421	6	,	,	PUNCT
ejde-355	421	7	berlin	berlin	PROPN
ejde-355	421	8	;	;	PUNCT
ejde-355	421	9	second	second	ADJ
ejde-355	421	10	ed	ed	NOUN
ejde-355	421	11	,	,	PUNCT
ejde-355	421	12	1983	1983	NUM
ejde-355	422	1	[	[	X
ejde-355	422	2	15	15	NUM
ejde-355	422	3	]	]	X
ejde-355	422	4	m.	m.	NOUN
ejde-355	422	5	grossi	grossi	PROPN
ejde-355	422	6	,	,	PUNCT
ejde-355	422	7	p.	p.	PROPN
ejde-355	422	8	luo	luo	PROPN
ejde-355	422	9	;	;	PUNCT
ejde-355	422	10	critical	critical	ADJ
ejde-355	422	11	points	point	NOUN
ejde-355	422	12	of	of	ADP
ejde-355	422	13	positive	positive	ADJ
ejde-355	422	14	solutions	solution	NOUN
ejde-355	422	15	of	of	ADP
ejde-355	422	16	nonlinear	nonlinear	ADJ
ejde-355	422	17	elliptic	elliptic	ADJ
ejde-355	422	18	equations	equation	NOUN
ejde-355	422	19	:	:	PUNCT
ejde-355	422	20	multiplicity	multiplicity	NOUN
ejde-355	422	21	,	,	PUNCT
ejde-355	422	22	location	location	NOUN
ejde-355	422	23	,	,	PUNCT
ejde-355	422	24	and	and	CCONJ
ejde-355	422	25	non	non	ADJ
ejde-355	422	26	-	-	NOUN
ejde-355	422	27	degeneracy	degeneracy	NOUN
ejde-355	422	28	,	,	PUNCT
ejde-355	422	29	indiana	indiana	PROPN
ejde-355	422	30	univ	univ	PROPN
ejde-355	422	31	.	.	PUNCT
ejde-355	422	32	math	math	PROPN
ejde-355	422	33	.	.	PUNCT
ejde-355	423	1	j.	j.	PROPN
ejde-355	423	2	72	72	NUM
ejde-355	423	3	(	(	PUNCT
ejde-355	423	4	2023	2023	NUM
ejde-355	423	5	)	)	PUNCT
ejde-355	423	6	,	,	PUNCT
ejde-355	423	7	821	821	NUM
ejde-355	423	8	-	-	SYM
ejde-355	423	9	871	871	NUM
ejde-355	423	10	.	.	PUNCT
ejde-355	424	1	[	[	X
ejde-355	424	2	16	16	NUM
ejde-355	424	3	]	]	X
ejde-355	424	4	d.	d.	PROPN
ejde-355	424	5	henry	henry	PROPN
ejde-355	424	6	;	;	PUNCT
ejde-355	424	7	topics	topic	NOUN
ejde-355	424	8	in	in	ADP
ejde-355	424	9	nonlinear	nonlinear	ADJ
ejde-355	424	10	analysis	analysis	NOUN
ejde-355	424	11	.	.	PUNCT
ejde-355	425	1	trabalho	trabalho	PROPN
ejde-355	425	2	de	de	PROPN
ejde-355	425	3	matemática	matemática	PROPN
ejde-355	425	4	,	,	PUNCT
ejde-355	425	5	1982	1982	NUM
ejde-355	425	6	.	.	PUNCT
ejde-355	426	1	[	[	X
ejde-355	426	2	17	17	NUM
ejde-355	426	3	]	]	PUNCT
ejde-355	426	4	a.	a.	NOUN
ejde-355	426	5	m.	m.	NOUN
ejde-355	426	6	il’in	il’in	PROPN
ejde-355	426	7	;	;	PUNCT
ejde-355	426	8	matching	match	VERB
ejde-355	426	9	of	of	ADP
ejde-355	426	10	asymptotic	asymptotic	ADJ
ejde-355	426	11	expansions	expansion	NOUN
ejde-355	426	12	of	of	ADP
ejde-355	426	13	solutions	solution	NOUN
ejde-355	426	14	of	of	ADP
ejde-355	426	15	boundary	boundary	ADJ
ejde-355	426	16	value	value	NOUN
ejde-355	426	17	problems	problem	NOUN
ejde-355	426	18	,	,	PUNCT
ejde-355	426	19	translations	translation	NOUN
ejde-355	426	20	of	of	ADP
ejde-355	426	21	mathematical	mathematical	ADJ
ejde-355	426	22	monographs	monograph	NOUN
ejde-355	426	23	102	102	NUM
ejde-355	426	24	,	,	PUNCT
ejde-355	426	25	american	american	PROPN
ejde-355	426	26	mathematical	mathematical	ADJ
ejde-355	426	27	society	society	NOUN
ejde-355	426	28	,	,	PUNCT
ejde-355	426	29	providence	providence	NOUN
ejde-355	426	30	,	,	PUNCT
ejde-355	426	31	1992	1992	NUM
ejde-355	426	32	.	.	PUNCT
ejde-355	427	1	[	[	X
ejde-355	427	2	18	18	NUM
ejde-355	427	3	]	]	PUNCT
ejde-355	427	4	a.	a.	NOUN
ejde-355	427	5	kirsch	kirsch	PROPN
ejde-355	427	6	;	;	PUNCT
ejde-355	427	7	the	the	DET
ejde-355	427	8	robin	robin	PROPN
ejde-355	427	9	problem	problem	NOUN
ejde-355	427	10	for	for	ADP
ejde-355	427	11	the	the	DET
ejde-355	427	12	helmholtz	helmholtz	NOUN
ejde-355	427	13	equation	equation	NOUN
ejde-355	427	14	as	as	ADP
ejde-355	427	15	a	a	DET
ejde-355	427	16	singular	singular	ADJ
ejde-355	427	17	perturbation	perturbation	NOUN
ejde-355	427	18	problem	problem	NOUN
ejde-355	427	19	,	,	PUNCT
ejde-355	427	20	numer	numer	PROPN
ejde-355	427	21	.	.	PUNCT
ejde-355	427	22	funct	funct	PROPN
ejde-355	427	23	.	.	PUNCT
ejde-355	428	1	anal	anal	PROPN
ejde-355	428	2	.	.	PUNCT
ejde-355	429	1	optim	optim	PROPN
ejde-355	429	2	.	.	PROPN
ejde-355	429	3	,	,	PUNCT
ejde-355	429	4	8(1	8(1	PROPN
ejde-355	429	5	-	-	SYM
ejde-355	429	6	2	2	NUM
ejde-355	429	7	)	)	PUNCT
ejde-355	429	8	(	(	PUNCT
ejde-355	429	9	1985	1985	NUM
ejde-355	429	10	)	)	PUNCT
ejde-355	429	11	,	,	PUNCT
ejde-355	429	12	1–20	1–20	NOUN
ejde-355	429	13	.	.	PUNCT
ejde-355	430	1	[	[	X
ejde-355	430	2	19	19	NUM
ejde-355	430	3	]	]	PUNCT
ejde-355	430	4	m.	m.	NOUN
ejde-355	430	5	lanza	lanza	PROPN
ejde-355	430	6	de	de	PROPN
ejde-355	430	7	cristoforis	cristoforis	PROPN
ejde-355	430	8	;	;	PUNCT
ejde-355	430	9	asymptotic	asymptotic	ADJ
ejde-355	430	10	behaviour	behaviour	NOUN
ejde-355	430	11	of	of	ADP
ejde-355	430	12	the	the	DET
ejde-355	430	13	conformal	conformal	ADJ
ejde-355	430	14	representation	representation	NOUN
ejde-355	430	15	of	of	ADP
ejde-355	430	16	a	a	DET
ejde-355	430	17	jordan	jordan	PROPN
ejde-355	430	18	domain	domain	NOUN
ejde-355	430	19	with	with	ADP
ejde-355	430	20	a	a	DET
ejde-355	430	21	small	small	ADJ
ejde-355	430	22	hole	hole	NOUN
ejde-355	430	23	in	in	ADP
ejde-355	430	24	schauder	schauder	NOUN
ejde-355	430	25	spaces	space	NOUN
ejde-355	430	26	,	,	PUNCT
ejde-355	430	27	comput	comput	NOUN
ejde-355	430	28	.	.	PUNCT
ejde-355	431	1	methods	method	NOUN
ejde-355	431	2	funct	funct	VERB
ejde-355	431	3	.	.	PUNCT
ejde-355	432	1	theory	theory	NOUN
ejde-355	432	2	,	,	PUNCT
ejde-355	432	3	2(1	2(1	NUM
ejde-355	432	4	)	)	PUNCT
ejde-355	432	5	(	(	PUNCT
ejde-355	432	6	2002	2002	NUM
ejde-355	432	7	)	)	PUNCT
ejde-355	432	8	,	,	PUNCT
ejde-355	432	9	1–27	1–27	NOUN
ejde-355	432	10	.	.	PUNCT
ejde-355	433	1	[	[	X
ejde-355	433	2	20	20	NUM
ejde-355	433	3	]	]	PUNCT
ejde-355	433	4	m.	m.	NOUN
ejde-355	433	5	lanza	lanza	PROPN
ejde-355	433	6	de	de	PROPN
ejde-355	433	7	cristoforis	cristoforis	PROPN
ejde-355	433	8	;	;	PUNCT
ejde-355	433	9	asymptotic	asymptotic	ADJ
ejde-355	433	10	behavior	behavior	NOUN
ejde-355	433	11	of	of	ADP
ejde-355	433	12	the	the	DET
ejde-355	433	13	solutions	solution	NOUN
ejde-355	433	14	of	of	ADP
ejde-355	433	15	a	a	DET
ejde-355	433	16	nonlinear	nonlinear	ADJ
ejde-355	433	17	robin	robin	PROPN
ejde-355	433	18	problem	problem	NOUN
ejde-355	433	19	for	for	ADP
ejde-355	433	20	the	the	DET
ejde-355	433	21	laplace	laplace	NOUN
ejde-355	433	22	operator	operator	NOUN
ejde-355	433	23	in	in	ADP
ejde-355	433	24	a	a	DET
ejde-355	433	25	domain	domain	NOUN
ejde-355	433	26	with	with	ADP
ejde-355	433	27	a	a	DET
ejde-355	433	28	small	small	ADJ
ejde-355	433	29	hole	hole	NOUN
ejde-355	433	30	:	:	PUNCT
ejde-355	433	31	a	a	DET
ejde-355	433	32	functional	functional	ADJ
ejde-355	433	33	analytic	analytic	ADJ
ejde-355	433	34	approach	approach	NOUN
ejde-355	433	35	,	,	PUNCT
ejde-355	433	36	complex	complex	ADJ
ejde-355	433	37	var	var	NOUN
ejde-355	433	38	.	.	PUNCT
ejde-355	434	1	elliptic	elliptic	PROPN
ejde-355	434	2	equ	equ	PROPN
ejde-355	434	3	.	.	PROPN
ejde-355	434	4	,	,	PUNCT
ejde-355	434	5	52(10	52(10	NUM
ejde-355	434	6	-	-	SYM
ejde-355	434	7	11	11	NUM
ejde-355	434	8	)	)	PUNCT
ejde-355	434	9	(	(	PUNCT
ejde-355	434	10	2007	2007	NUM
ejde-355	434	11	)	)	PUNCT
ejde-355	434	12	,	,	PUNCT
ejde-355	434	13	945–977	945–977	NUM
ejde-355	434	14	.	.	PUNCT
ejde-355	435	1	[	[	X
ejde-355	435	2	21	21	NUM
ejde-355	435	3	]	]	PUNCT
ejde-355	435	4	m.	m.	NOUN
ejde-355	435	5	lanza	lanza	PROPN
ejde-355	435	6	de	de	PROPN
ejde-355	435	7	cristoforis	cristoforis	PROPN
ejde-355	435	8	,	,	PUNCT
ejde-355	435	9	p.	p.	NOUN
ejde-355	435	10	musolino	musolino	PROPN
ejde-355	435	11	;	;	PUNCT
ejde-355	435	12	a	a	DET
ejde-355	435	13	real	real	ADJ
ejde-355	435	14	analyticity	analyticity	NOUN
ejde-355	435	15	result	result	NOUN
ejde-355	435	16	for	for	ADP
ejde-355	435	17	a	a	DET
ejde-355	435	18	nonlinear	nonlinear	ADJ
ejde-355	435	19	integral	integral	ADJ
ejde-355	435	20	operator	operator	NOUN
ejde-355	435	21	,	,	PUNCT
ejde-355	435	22	j.	j.	PROPN
ejde-355	435	23	integral	integral	PROPN
ejde-355	435	24	equations	equation	NOUN
ejde-355	435	25	appl	appl	PROPN
ejde-355	435	26	.	.	PROPN
ejde-355	435	27	,	,	PUNCT
ejde-355	435	28	25(1	25(1	NUM
ejde-355	435	29	)	)	PUNCT
ejde-355	435	30	(	(	PUNCT
ejde-355	435	31	2013	2013	NUM
ejde-355	435	32	)	)	PUNCT
ejde-355	435	33	,	,	PUNCT
ejde-355	435	34	21–46	21–46	NUM
ejde-355	435	35	.	.	PUNCT
ejde-355	436	1	[	[	X
ejde-355	436	2	22	22	NUM
ejde-355	436	3	]	]	PUNCT
ejde-355	436	4	m.	m.	NOUN
ejde-355	436	5	lanza	lanza	PROPN
ejde-355	436	6	de	de	PROPN
ejde-355	436	7	cristoforis	cristoforis	PROPN
ejde-355	436	8	,	,	PUNCT
ejde-355	436	9	l.	l.	PROPN
ejde-355	436	10	rossi	rossi	PROPN
ejde-355	436	11	;	;	PUNCT
ejde-355	436	12	real	real	ADJ
ejde-355	436	13	analytic	analytic	ADJ
ejde-355	436	14	dependence	dependence	NOUN
ejde-355	436	15	of	of	ADP
ejde-355	436	16	simple	simple	ADJ
ejde-355	436	17	and	and	CCONJ
ejde-355	436	18	double	double	ADJ
ejde-355	436	19	layer	layer	NOUN
ejde-355	436	20	potentials	potential	VERB
ejde-355	436	21	upon	upon	SCONJ
ejde-355	436	22	perturbation	perturbation	NOUN
ejde-355	436	23	of	of	ADP
ejde-355	436	24	the	the	DET
ejde-355	436	25	support	support	NOUN
ejde-355	436	26	and	and	CCONJ
ejde-355	436	27	of	of	ADP
ejde-355	436	28	the	the	DET
ejde-355	436	29	density	density	NOUN
ejde-355	436	30	,	,	PUNCT
ejde-355	436	31	j.	j.	PROPN
ejde-355	436	32	integral	integral	PROPN
ejde-355	436	33	equations	equation	NOUN
ejde-355	436	34	appl	appl	PROPN
ejde-355	436	35	.	.	PROPN
ejde-355	437	1	16(2	16(2	NUM
ejde-355	437	2	)	)	PUNCT
ejde-355	437	3	(	(	PUNCT
ejde-355	437	4	2004	2004	NUM
ejde-355	437	5	)	)	PUNCT
ejde-355	437	6	,	,	PUNCT
ejde-355	438	1	137–174	137–174	NUM
ejde-355	438	2	.	.	PUNCT
ejde-355	439	1	20	20	NUM
ejde-355	439	2	p.	p.	NOUN
ejde-355	439	3	musolino	musolino	NOUN
ejde-355	439	4	,	,	PUNCT
ejde-355	439	5	m.	m.	NOUN
ejde-355	439	6	dutko	dutko	PROPN
ejde-355	439	7	,	,	PUNCT
ejde-355	439	8	g.	g.	PROPN
ejde-355	439	9	mishuris	mishuris	PROPN
ejde-355	439	10	ejde-2023/57	ejde-2023/57	NOUN
ejde-355	440	1	[	[	X
ejde-355	440	2	23	23	NUM
ejde-355	440	3	]	]	X
ejde-355	440	4	p.	p.	NOUN
ejde-355	440	5	luzzini	luzzini	PROPN
ejde-355	440	6	;	;	PUNCT
ejde-355	440	7	a	a	DET
ejde-355	440	8	mapping	mapping	NOUN
ejde-355	440	9	property	property	NOUN
ejde-355	440	10	of	of	ADP
ejde-355	440	11	the	the	DET
ejde-355	440	12	heat	heat	NOUN
ejde-355	440	13	volume	volume	NOUN
ejde-355	440	14	potential	potential	NOUN
ejde-355	440	15	,	,	PUNCT
ejde-355	440	16	boll	boll	NOUN
ejde-355	440	17	.	.	PUNCT
ejde-355	441	1	unione	unione	PROPN
ejde-355	441	2	mat	mat	PROPN
ejde-355	441	3	.	.	PUNCT
ejde-355	441	4	ital	ital	PROPN
ejde-355	441	5	.	.	PROPN
ejde-355	441	6	,	,	PUNCT
ejde-355	441	7	to	to	PART
ejde-355	441	8	appear	appear	VERB
ejde-355	441	9	.	.	PUNCT
ejde-355	442	1	[	[	X
ejde-355	442	2	24	24	NUM
ejde-355	442	3	]	]	PUNCT
ejde-355	442	4	v.	v.	PROPN
ejde-355	442	5	g.	g.	PROPN
ejde-355	442	6	maz’ya	maz’ya	PROPN
ejde-355	442	7	,	,	PUNCT
ejde-355	442	8	a.	a.	PROPN
ejde-355	442	9	b.	b.	PROPN
ejde-355	442	10	movchan	movchan	ADV
ejde-355	442	11	,	,	PUNCT
ejde-355	442	12	m.	m.	PROPN
ejde-355	442	13	j.	j.	PROPN
ejde-355	442	14	nieves	nieves	PROPN
ejde-355	442	15	;	;	PUNCT
ejde-355	442	16	green	green	PROPN
ejde-355	442	17	’s	’s	PART
ejde-355	442	18	kernels	kernel	NOUN
ejde-355	442	19	and	and	CCONJ
ejde-355	442	20	meso	meso	NOUN
ejde-355	442	21	-	-	PUNCT
ejde-355	442	22	scale	scale	NOUN
ejde-355	442	23	approximations	approximation	NOUN
ejde-355	442	24	in	in	ADP
ejde-355	442	25	perforated	perforate	VERB
ejde-355	442	26	domains	domain	NOUN
ejde-355	442	27	,	,	PUNCT
ejde-355	442	28	lecture	lecture	NOUN
ejde-355	442	29	notes	note	NOUN
ejde-355	442	30	in	in	ADP
ejde-355	442	31	mathematics	mathematic	NOUN
ejde-355	442	32	,	,	PUNCT
ejde-355	442	33	vol	vol	NOUN
ejde-355	442	34	.	.	PROPN
ejde-355	442	35	2077	2077	NUM
ejde-355	442	36	.	.	PUNCT
ejde-355	443	1	springer	springer	NOUN
ejde-355	443	2	,	,	PUNCT
ejde-355	443	3	heidelberg	heidelberg	PROPN
ejde-355	443	4	,	,	PUNCT
ejde-355	443	5	2013	2013	NUM
ejde-355	443	6	.	.	PUNCT
ejde-355	444	1	[	[	X
ejde-355	444	2	25	25	NUM
ejde-355	444	3	]	]	X
ejde-355	444	4	v.g	v.g	PROPN
ejde-355	444	5	.	.	PROPN
ejde-355	444	6	maz’ya	maz’ya	PROPN
ejde-355	444	7	,	,	PUNCT
ejde-355	444	8	a.	a.	PROPN
ejde-355	444	9	b.	b.	PROPN
ejde-355	445	1	movchan	movchan	ADV
ejde-355	445	2	,	,	PUNCT
ejde-355	445	3	m.	m.	PROPN
ejde-355	445	4	j.	j.	PROPN
ejde-355	445	5	nieves	nieves	PROPN
ejde-355	445	6	;	;	PUNCT
ejde-355	445	7	mesoscale	mesoscale	ADJ
ejde-355	445	8	approximations	approximation	NOUN
ejde-355	445	9	for	for	ADP
ejde-355	445	10	solutions	solution	NOUN
ejde-355	445	11	of	of	ADP
ejde-355	445	12	the	the	DET
ejde-355	445	13	dirichlet	dirichlet	PROPN
ejde-355	445	14	problem	problem	NOUN
ejde-355	445	15	in	in	ADP
ejde-355	445	16	a	a	DET
ejde-355	445	17	perforated	perforate	VERB
ejde-355	445	18	elastic	elastic	ADJ
ejde-355	445	19	body	body	NOUN
ejde-355	445	20	,	,	PUNCT
ejde-355	445	21	j.	j.	PROPN
ejde-355	445	22	math	math	PROPN
ejde-355	445	23	.	.	PUNCT
ejde-355	446	1	sci	sci	PROPN
ejde-355	446	2	.	.	PUNCT
ejde-355	446	3	(	(	PUNCT
ejde-355	446	4	n.y	n.y	PROPN
ejde-355	446	5	.	.	PROPN
ejde-355	446	6	)	)	PUNCT
ejde-355	446	7	202(2	202(2	NUM
ejde-355	446	8	)	)	PUNCT
ejde-355	446	9	(	(	PUNCT
ejde-355	446	10	2014	2014	NUM
ejde-355	446	11	)	)	PUNCT
ejde-355	446	12	,	,	PUNCT
ejde-355	446	13	problems	problem	NOUN
ejde-355	446	14	in	in	ADP
ejde-355	446	15	mathematical	mathematical	ADJ
ejde-355	446	16	analysis	analysis	NOUN
ejde-355	446	17	.	.	PUNCT
ejde-355	447	1	no	no	INTJ
ejde-355	447	2	.	.	NOUN
ejde-355	448	1	76	76	NUM
ejde-355	449	1	(	(	PUNCT
ejde-355	449	2	russian	russian	NOUN
ejde-355	449	3	):	):	PUNCT
ejde-355	449	4	215–244	215–244	NUM
ejde-355	449	5	.	.	PUNCT
ejde-355	450	1	[	[	X
ejde-355	450	2	26	26	NUM
ejde-355	450	3	]	]	PUNCT
ejde-355	450	4	v.	v.	PROPN
ejde-355	450	5	g.	g.	PROPN
ejde-355	450	6	maz’ya	maz’ya	PROPN
ejde-355	450	7	,	,	PUNCT
ejde-355	450	8	a.	a.	PROPN
ejde-355	450	9	b.	b.	PROPN
ejde-355	450	10	movchan	movchan	ADV
ejde-355	450	11	,	,	PUNCT
ejde-355	450	12	m.	m.	PROPN
ejde-355	450	13	j.	j.	PROPN
ejde-355	450	14	nieves	nieves	PROPN
ejde-355	450	15	;	;	PUNCT
ejde-355	450	16	mesoscale	mesoscale	ADJ
ejde-355	450	17	models	model	NOUN
ejde-355	450	18	and	and	CCONJ
ejde-355	450	19	approximate	approximate	ADJ
ejde-355	450	20	solutions	solution	NOUN
ejde-355	450	21	for	for	ADP
ejde-355	450	22	solids	solid	NOUN
ejde-355	450	23	containing	contain	VERB
ejde-355	450	24	clouds	cloud	NOUN
ejde-355	450	25	of	of	ADP
ejde-355	450	26	voids	voids	NOUN
ejde-355	450	27	,	,	PUNCT
ejde-355	450	28	multiscale	multiscale	NOUN
ejde-355	450	29	model	model	NOUN
ejde-355	450	30	.	.	PUNCT
ejde-355	451	1	simul	simul	PROPN
ejde-355	451	2	.	.	PUNCT
ejde-355	451	3	14(1	14(1	NUM
ejde-355	451	4	)	)	PUNCT
ejde-355	451	5	(	(	PUNCT
ejde-355	451	6	2016	2016	NUM
ejde-355	451	7	)	)	PUNCT
ejde-355	451	8	,	,	PUNCT
ejde-355	451	9	138–172	138–172	NUM
ejde-355	451	10	.	.	PUNCT
ejde-355	452	1	[	[	X
ejde-355	452	2	27	27	NUM
ejde-355	452	3	]	]	X
ejde-355	452	4	v.	v.	PROPN
ejde-355	452	5	g.	g.	PROPN
ejde-355	452	6	maz’ya	maz’ya	PROPN
ejde-355	452	7	,	,	PUNCT
ejde-355	452	8	a.	a.	PROPN
ejde-355	452	9	b.	b.	PROPN
ejde-355	453	1	movchan	movchan	ADV
ejde-355	453	2	,	,	PUNCT
ejde-355	453	3	m.	m.	PROPN
ejde-355	453	4	j.	j.	PROPN
ejde-355	453	5	nieves	nieves	PROPN
ejde-355	453	6	;	;	PUNCT
ejde-355	453	7	eigenvalue	eigenvalue	NOUN
ejde-355	453	8	problem	problem	NOUN
ejde-355	453	9	in	in	ADP
ejde-355	453	10	a	a	DET
ejde-355	453	11	solid	solid	NOUN
ejde-355	453	12	with	with	ADP
ejde-355	453	13	many	many	ADJ
ejde-355	453	14	inclusions	inclusion	NOUN
ejde-355	453	15	:	:	PUNCT
ejde-355	453	16	asymptotic	asymptotic	ADJ
ejde-355	453	17	analysis	analysis	NOUN
ejde-355	453	18	,	,	PUNCT
ejde-355	453	19	multiscale	multiscale	NOUN
ejde-355	453	20	model	model	NOUN
ejde-355	453	21	.	.	PUNCT
ejde-355	454	1	simul	simul	PROPN
ejde-355	454	2	.	.	PUNCT
ejde-355	455	1	15(2	15(2	NUM
ejde-355	455	2	)	)	PUNCT
ejde-355	455	3	(	(	PUNCT
ejde-355	455	4	2017	2017	NUM
ejde-355	455	5	)	)	PUNCT
ejde-355	455	6	,	,	PUNCT
ejde-355	455	7	1003–1047	1003–1047	NUM
ejde-355	455	8	.	.	PUNCT
ejde-355	456	1	[	[	X
ejde-355	456	2	28	28	NUM
ejde-355	456	3	]	]	X
ejde-355	456	4	v.	v.	PROPN
ejde-355	456	5	g.	g.	PROPN
ejde-355	456	6	maz’ya	maz’ya	PROPN
ejde-355	456	7	,	,	PUNCT
ejde-355	456	8	a.	a.	PROPN
ejde-355	456	9	b.	b.	PROPN
ejde-355	456	10	movchan	movchan	ADV
ejde-355	456	11	,	,	PUNCT
ejde-355	456	12	m.	m.	PROPN
ejde-355	456	13	j.	j.	PROPN
ejde-355	456	14	nieves	nieves	PROPN
ejde-355	456	15	;	;	PUNCT
ejde-355	456	16	on	on	ADP
ejde-355	456	17	mesoscale	mesoscale	ADJ
ejde-355	456	18	approximations	approximation	NOUN
ejde-355	456	19	for	for	ADP
ejde-355	456	20	vibrations	vibration	NOUN
ejde-355	456	21	of	of	ADP
ejde-355	456	22	membranes	membrane	NOUN
ejde-355	456	23	with	with	ADP
ejde-355	456	24	lower	lower	ADV
ejde-355	456	25	-	-	PUNCT
ejde-355	456	26	dimensional	dimensional	ADJ
ejde-355	456	27	clusters	cluster	NOUN
ejde-355	456	28	of	of	ADP
ejde-355	456	29	inertial	inertial	ADJ
ejde-355	456	30	inclusions	inclusion	NOUN
ejde-355	456	31	,	,	PUNCT
ejde-355	456	32	algebra	algebra	NOUN
ejde-355	456	33	i	i	PRON
ejde-355	456	34	analiz	analiz	NOUN
ejde-355	456	35	,	,	PUNCT
ejde-355	456	36	32(3	32(3	NUM
ejde-355	456	37	):	):	PUNCT
ejde-355	456	38	219–237	219–237	NUM
ejde-355	456	39	(	(	PUNCT
ejde-355	456	40	2020	2020	NUM
ejde-355	456	41	)	)	PUNCT
ejde-355	456	42	;	;	PUNCT
ejde-355	456	43	reprinted	reprint	VERB
ejde-355	456	44	in	in	ADP
ejde-355	456	45	st	st	PROPN
ejde-355	456	46	.	.	PROPN
ejde-355	456	47	petersburg	petersburg	PROPN
ejde-355	456	48	math	math	PROPN
ejde-355	456	49	.	.	PUNCT
ejde-355	457	1	j.	j.	PROPN
ejde-355	457	2	32(3	32(3	PROPN
ejde-355	457	3	)	)	PUNCT
ejde-355	457	4	(	(	PUNCT
ejde-355	457	5	2021	2021	NUM
ejde-355	457	6	)	)	PUNCT
ejde-355	457	7	,	,	PUNCT
ejde-355	458	1	551–564	551–564	NUM
ejde-355	458	2	[	[	X
ejde-355	458	3	29	29	NUM
ejde-355	458	4	]	]	X
ejde-355	458	5	v.	v.	ADP
ejde-355	458	6	maz’ya	maz’ya	PROPN
ejde-355	458	7	,	,	PUNCT
ejde-355	458	8	s.	s.	PROPN
ejde-355	458	9	nazarov	nazarov	PROPN
ejde-355	458	10	,	,	PUNCT
ejde-355	458	11	b.	b.	PROPN
ejde-355	458	12	plamenevskij	plamenevskij	PROPN
ejde-355	458	13	;	;	PUNCT
ejde-355	458	14	asymptotic	asymptotic	ADJ
ejde-355	458	15	theory	theory	NOUN
ejde-355	458	16	of	of	ADP
ejde-355	458	17	elliptic	elliptic	ADJ
ejde-355	458	18	boundary	boundary	ADJ
ejde-355	458	19	value	value	NOUN
ejde-355	458	20	problems	problem	NOUN
ejde-355	458	21	in	in	ADP
ejde-355	458	22	singularly	singularly	ADV
ejde-355	458	23	perturbed	perturb	VERB
ejde-355	458	24	domains	domain	NOUN
ejde-355	458	25	.	.	PUNCT
ejde-355	459	1	vol	vol	NOUN
ejde-355	459	2	.	.	PUNCT
ejde-355	460	1	i	i	PRON
ejde-355	460	2	operator	operator	NOUN
ejde-355	460	3	theory	theory	NOUN
ejde-355	460	4	:	:	PUNCT
ejde-355	460	5	advances	advance	NOUN
ejde-355	460	6	and	and	CCONJ
ejde-355	460	7	applications	application	NOUN
ejde-355	460	8	,	,	PUNCT
ejde-355	460	9	vol	vol	NOUN
ejde-355	460	10	.	.	NOUN
ejde-355	460	11	111	111	NUM
ejde-355	460	12	,	,	PUNCT
ejde-355	460	13	birkhäuser	birkhäuser	NOUN
ejde-355	460	14	verlag	verlag	PROPN
ejde-355	460	15	,	,	PUNCT
ejde-355	460	16	basel	basel	PROPN
ejde-355	460	17	,	,	PUNCT
ejde-355	460	18	2000	2000	NUM
ejde-355	460	19	.	.	PUNCT
ejde-355	461	1	translated	translate	VERB
ejde-355	461	2	from	from	ADP
ejde-355	461	3	the	the	DET
ejde-355	461	4	german	german	NOUN
ejde-355	461	5	by	by	ADP
ejde-355	461	6	georg	georg	PROPN
ejde-355	461	7	heinig	heinig	PROPN
ejde-355	461	8	and	and	CCONJ
ejde-355	461	9	christian	christian	ADJ
ejde-355	461	10	posthoff	posthoff	NOUN
ejde-355	461	11	.	.	PUNCT
ejde-355	462	1	[	[	X
ejde-355	462	2	30	30	NUM
ejde-355	462	3	]	]	X
ejde-355	462	4	v.	v.	ADP
ejde-355	462	5	maz’ya	maz’ya	PROPN
ejde-355	462	6	,	,	PUNCT
ejde-355	462	7	s.	s.	PROPN
ejde-355	462	8	nazarov	nazarov	PROPN
ejde-355	462	9	,	,	PUNCT
ejde-355	462	10	b.	b.	PROPN
ejde-355	462	11	plamenevskij	plamenevskij	PROPN
ejde-355	462	12	;	;	PUNCT
ejde-355	462	13	asymptotic	asymptotic	ADJ
ejde-355	462	14	theory	theory	NOUN
ejde-355	462	15	of	of	ADP
ejde-355	462	16	elliptic	elliptic	ADJ
ejde-355	462	17	boundary	boundary	ADJ
ejde-355	462	18	value	value	NOUN
ejde-355	462	19	problems	problem	NOUN
ejde-355	462	20	in	in	ADP
ejde-355	462	21	singularly	singularly	ADV
ejde-355	462	22	perturbed	perturb	VERB
ejde-355	462	23	domains	domain	NOUN
ejde-355	462	24	.	.	PUNCT
ejde-355	462	25	vol	vol	NOUN
ejde-355	462	26	.	.	PUNCT
ejde-355	462	27	ii	ii	PROPN
ejde-355	462	28	operator	operator	NOUN
ejde-355	462	29	theory	theory	NOUN
ejde-355	462	30	:	:	PUNCT
ejde-355	462	31	advances	advance	NOUN
ejde-355	462	32	and	and	CCONJ
ejde-355	462	33	applications	application	NOUN
ejde-355	462	34	,	,	PUNCT
ejde-355	462	35	vol	vol	NOUN
ejde-355	462	36	.	.	PROPN
ejde-355	462	37	112	112	NUM
ejde-355	462	38	,	,	PUNCT
ejde-355	462	39	birkhäuser	birkhäuser	NOUN
ejde-355	462	40	verlag	verlag	PROPN
ejde-355	462	41	,	,	PUNCT
ejde-355	462	42	basel	basel	PROPN
ejde-355	462	43	,	,	PUNCT
ejde-355	462	44	2000	2000	NUM
ejde-355	462	45	.	.	PUNCT
ejde-355	463	1	translated	translate	VERB
ejde-355	463	2	from	from	ADP
ejde-355	463	3	the	the	DET
ejde-355	463	4	german	german	NOUN
ejde-355	463	5	by	by	ADP
ejde-355	463	6	plamenevskij	plamenevskij	NOUN
ejde-355	463	7	.	.	PUNCT
ejde-355	464	1	[	[	X
ejde-355	464	2	31	31	NUM
ejde-355	464	3	]	]	X
ejde-355	464	4	c.	c.	PROPN
ejde-355	464	5	miranda	miranda	PROPN
ejde-355	464	6	;	;	PUNCT
ejde-355	464	7	sulle	sulle	PROPN
ejde-355	464	8	proprietà	proprietà	PROPN
ejde-355	464	9	di	di	PROPN
ejde-355	464	10	regolarità	regolarità	PROPN
ejde-355	464	11	di	di	PROPN
ejde-355	464	12	certe	certe	PROPN
ejde-355	464	13	trasformazioni	trasformazioni	PROPN
ejde-355	464	14	integrali	integrali	PROPN
ejde-355	464	15	,	,	PUNCT
ejde-355	464	16	atti	atti	PROPN
ejde-355	464	17	accad	accad	PROPN
ejde-355	464	18	.	.	PUNCT
ejde-355	465	1	naz	naz	PROPN
ejde-355	465	2	.	.	PUNCT
ejde-355	466	1	lincei	lincei	NOUN
ejde-355	466	2	mem	mem	PROPN
ejde-355	466	3	.	.	PUNCT
ejde-355	467	1	cl	cl	NOUN
ejde-355	467	2	.	.	PUNCT
ejde-355	468	1	sci	sci	PROPN
ejde-355	468	2	.	.	PROPN
ejde-355	468	3	fis	fis	PROPN
ejde-355	468	4	.	.	PUNCT
ejde-355	468	5	mat	mat	PROPN
ejde-355	468	6	.	.	PUNCT
ejde-355	468	7	natur	natur	PROPN
ejde-355	468	8	.	.	PUNCT
ejde-355	469	1	sez	sez	PROPN
ejde-355	469	2	.	.	PUNCT
ejde-355	470	1	i	i	PRON
ejde-355	470	2	,	,	PUNCT
ejde-355	470	3	(	(	PUNCT
ejde-355	470	4	8)	8)	NUM
ejde-355	470	5	7	7	NUM
ejde-355	470	6	(	(	PUNCT
ejde-355	470	7	1965	1965	NUM
ejde-355	470	8	)	)	PUNCT
ejde-355	470	9	,	,	PUNCT
ejde-355	470	10	303–336	303–336	NUM
ejde-355	470	11	.	.	PUNCT
ejde-355	471	1	[	[	X
ejde-355	471	2	32	32	NUM
ejde-355	471	3	]	]	X
ejde-355	471	4	g.	g.	PROPN
ejde-355	471	5	mishuris	mishuris	PROPN
ejde-355	471	6	;	;	PUNCT
ejde-355	471	7	imperfect	imperfect	ADJ
ejde-355	471	8	transmission	transmission	NOUN
ejde-355	471	9	conditions	condition	NOUN
ejde-355	471	10	for	for	ADP
ejde-355	471	11	a	a	DET
ejde-355	471	12	thin	thin	ADJ
ejde-355	471	13	weakly	weakly	ADJ
ejde-355	471	14	compressible	compressible	ADJ
ejde-355	471	15	interface	interface	NOUN
ejde-355	471	16	.	.	PUNCT
ejde-355	472	1	2d	2d	NOUN
ejde-355	472	2	problems	problem	NOUN
ejde-355	472	3	,	,	PUNCT
ejde-355	472	4	arch	arch	NOUN
ejde-355	472	5	.	.	PUNCT
ejde-355	473	1	mech	mech	PROPN
ejde-355	473	2	.	.	PUNCT
ejde-355	474	1	(	(	PUNCT
ejde-355	474	2	arch	arch	NOUN
ejde-355	474	3	.	.	PUNCT
ejde-355	475	1	mech	mech	PROPN
ejde-355	475	2	.	.	PUNCT
ejde-355	476	1	stos	stos	PROPN
ejde-355	476	2	.	.	PUNCT
ejde-355	476	3	)	)	PUNCT
ejde-355	476	4	,	,	PUNCT
ejde-355	476	5	56(2	56(2	X
ejde-355	476	6	)	)	PUNCT
ejde-355	476	7	(	(	PUNCT
ejde-355	476	8	2004	2004	NUM
ejde-355	476	9	)	)	PUNCT
ejde-355	476	10	,	,	PUNCT
ejde-355	476	11	103–115	103–115	NUM
ejde-355	476	12	.	.	PUNCT
ejde-355	477	1	[	[	X
ejde-355	477	2	33	33	NUM
ejde-355	477	3	]	]	PUNCT
ejde-355	477	4	g.	g.	PROPN
ejde-355	477	5	mishuris	mishuris	PROPN
ejde-355	477	6	,	,	PUNCT
ejde-355	477	7	w.	w.	PROPN
ejde-355	477	8	miszuris	miszuris	PROPN
ejde-355	477	9	,	,	PUNCT
ejde-355	477	10	a.	a.	PROPN
ejde-355	477	11	öchsner	öchsner	PROPN
ejde-355	477	12	;	;	PUNCT
ejde-355	477	13	evaluation	evaluation	NOUN
ejde-355	477	14	of	of	ADP
ejde-355	477	15	transmission	transmission	NOUN
ejde-355	477	16	conditions	condition	NOUN
ejde-355	477	17	for	for	ADP
ejde-355	477	18	thin	thin	ADJ
ejde-355	477	19	reactive	reactive	ADJ
ejde-355	477	20	heat	heat	NOUN
ejde-355	477	21	-	-	PUNCT
ejde-355	477	22	conducting	conduct	VERB
ejde-355	477	23	interphases	interphase	NOUN
ejde-355	477	24	,	,	PUNCT
ejde-355	477	25	in	in	ADP
ejde-355	477	26	defect	defect	NOUN
ejde-355	477	27	and	and	CCONJ
ejde-355	477	28	diffusion	diffusion	NOUN
ejde-355	477	29	forum	forum	PROPN
ejde-355	477	30	,	,	PUNCT
ejde-355	477	31	vol	vol	NOUN
ejde-355	477	32	.	.	PUNCT
ejde-355	477	33	273	273	NUM
ejde-355	477	34	:	:	PUNCT
ejde-355	477	35	394–399	394–399	NUM
ejde-355	477	36	,	,	PUNCT
ejde-355	477	37	trans	trans	PROPN
ejde-355	477	38	tech	tech	NOUN
ejde-355	477	39	publications	publication	NOUN
ejde-355	477	40	,	,	PUNCT
ejde-355	477	41	2008	2008	NUM
ejde-355	477	42	.	.	PUNCT
ejde-355	478	1	[	[	X
ejde-355	478	2	34	34	NUM
ejde-355	478	3	]	]	X
ejde-355	478	4	g.	g.	PROPN
ejde-355	478	5	mishuris	mishuris	PROPN
ejde-355	478	6	,	,	PUNCT
ejde-355	478	7	w.	w.	PROPN
ejde-355	478	8	miszuris	miszuris	PROPN
ejde-355	478	9	,	,	PUNCT
ejde-355	478	10	a.	a.	PROPN
ejde-355	478	11	öchsner	öchsner	PROPN
ejde-355	478	12	;	;	PUNCT
ejde-355	478	13	transmission	transmission	NOUN
ejde-355	478	14	conditions	condition	NOUN
ejde-355	478	15	for	for	ADP
ejde-355	478	16	thin	thin	ADJ
ejde-355	478	17	reactive	reactive	ADJ
ejde-355	478	18	heatconducting	heatconducting	NOUN
ejde-355	478	19	interphases	interphase	NOUN
ejde-355	478	20	:	:	PUNCT
ejde-355	478	21	general	general	ADJ
ejde-355	478	22	case	case	NOUN
ejde-355	478	23	,	,	PUNCT
ejde-355	478	24	defect	defect	NOUN
ejde-355	478	25	and	and	CCONJ
ejde-355	478	26	diffusion	diffusion	NOUN
ejde-355	478	27	forum	forum	PROPN
ejde-355	478	28	,	,	PUNCT
ejde-355	478	29	vol	vol	NOUN
ejde-355	478	30	.	.	PROPN
ejde-355	478	31	283	283	NUM
ejde-355	478	32	:	:	SYM
ejde-355	478	33	521–526,t	521–526,t	NUM
ejde-355	478	34	rans	ran	VERB
ejde-355	478	35	tech	tech	NOUN
ejde-355	478	36	publications	publication	NOUN
ejde-355	478	37	,	,	PUNCT
ejde-355	478	38	2009	2009	NUM
ejde-355	478	39	[	[	X
ejde-355	478	40	35	35	NUM
ejde-355	478	41	]	]	PUNCT
ejde-355	478	42	p.	p.	NOUN
ejde-355	478	43	musolino	musolino	PROPN
ejde-355	478	44	,	,	PUNCT
ejde-355	478	45	g.	g.	PROPN
ejde-355	478	46	mishuris	mishuris	PROPN
ejde-355	478	47	;	;	PUNCT
ejde-355	478	48	a	a	DET
ejde-355	478	49	nonlinear	nonlinear	ADJ
ejde-355	478	50	problem	problem	NOUN
ejde-355	478	51	for	for	ADP
ejde-355	478	52	the	the	DET
ejde-355	478	53	laplace	laplace	NOUN
ejde-355	478	54	equation	equation	NOUN
ejde-355	478	55	with	with	ADP
ejde-355	478	56	a	a	DET
ejde-355	478	57	degenerating	degenerate	VERB
ejde-355	478	58	robin	robin	PROPN
ejde-355	478	59	condition	condition	NOUN
ejde-355	478	60	,	,	PUNCT
ejde-355	478	61	math	math	NOUN
ejde-355	478	62	.	.	PUNCT
ejde-355	479	1	methods	method	NOUN
ejde-355	479	2	appl	appl	PROPN
ejde-355	479	3	.	.	PUNCT
ejde-355	480	1	sci	sci	PROPN
ejde-355	480	2	.	.	PROPN
ejde-355	480	3	,	,	PUNCT
ejde-355	480	4	41(13	41(13	PROPN
ejde-355	480	5	)	)	PUNCT
ejde-355	480	6	(	(	PUNCT
ejde-355	480	7	2018	2018	NUM
ejde-355	480	8	)	)	PUNCT
ejde-355	480	9	,	,	PUNCT
ejde-355	480	10	5211–5229	5211–5229	NUM
ejde-355	480	11	.	.	PUNCT
ejde-355	481	1	[	[	X
ejde-355	481	2	36	36	NUM
ejde-355	481	3	]	]	X
ejde-355	481	4	p.	p.	NOUN
ejde-355	481	5	musolino	musolino	PROPN
ejde-355	481	6	,	,	PUNCT
ejde-355	481	7	g.	g.	PROPN
ejde-355	481	8	mishuris	mishuris	PROPN
ejde-355	481	9	;	;	PUNCT
ejde-355	481	10	interaction	interaction	NOUN
ejde-355	481	11	of	of	ADP
ejde-355	481	12	scales	scale	NOUN
ejde-355	481	13	for	for	ADP
ejde-355	481	14	a	a	DET
ejde-355	481	15	singularly	singularly	ADV
ejde-355	481	16	perturbed	perturb	VERB
ejde-355	481	17	degenerating	degenerate	VERB
ejde-355	481	18	nonlinear	nonlinear	NOUN
ejde-355	481	19	robin	robin	PROPN
ejde-355	481	20	problem	problem	NOUN
ejde-355	481	21	,	,	PUNCT
ejde-355	481	22	philos	philos	PROPN
ejde-355	481	23	.	.	PUNCT
ejde-355	482	1	trans	trans	PROPN
ejde-355	482	2	.	.	PUNCT
ejde-355	483	1	roy	roy	PROPN
ejde-355	483	2	.	.	PROPN
ejde-355	483	3	soc	soc	PROPN
ejde-355	483	4	.	.	PUNCT
ejde-355	484	1	a	a	DET
ejde-355	484	2	,	,	PUNCT
ejde-355	484	3	380(2236	380(2236	NUM
ejde-355	484	4	)	)	PUNCT
ejde-355	484	5	(	(	PUNCT
ejde-355	484	6	2022	2022	NUM
ejde-355	484	7	)	)	PUNCT
ejde-355	484	8	,	,	PUNCT
ejde-355	484	9	20220159	20220159	NUM
ejde-355	484	10	.	.	PUNCT
ejde-355	485	1	[	[	X
ejde-355	485	2	37	37	NUM
ejde-355	485	3	]	]	PUNCT
ejde-355	485	4	m.	m.	NOUN
ejde-355	485	5	j.	j.	PROPN
ejde-355	485	6	nieves	nieves	PROPN
ejde-355	485	7	,	,	PUNCT
ejde-355	485	8	a.	a.	PROPN
ejde-355	485	9	b.	b.	PROPN
ejde-355	485	10	movchan	movchan	ADV
ejde-355	485	11	;	;	PUNCT
ejde-355	485	12	asymptotic	asymptotic	ADJ
ejde-355	485	13	analysis	analysis	NOUN
ejde-355	485	14	of	of	ADP
ejde-355	485	15	in	in	ADP
ejde-355	485	16	-	-	PUNCT
ejde-355	485	17	plane	plane	NOUN
ejde-355	485	18	dynamic	dynamic	ADJ
ejde-355	485	19	problems	problem	NOUN
ejde-355	485	20	for	for	ADP
ejde-355	485	21	elastic	elastic	ADJ
ejde-355	485	22	media	medium	NOUN
ejde-355	485	23	with	with	ADP
ejde-355	485	24	rigid	rigid	ADJ
ejde-355	485	25	clusters	cluster	NOUN
ejde-355	485	26	of	of	ADP
ejde-355	485	27	small	small	ADJ
ejde-355	485	28	inclusions	inclusion	NOUN
ejde-355	485	29	,	,	PUNCT
ejde-355	485	30	philos	philos	PROPN
ejde-355	485	31	.	.	PUNCT
ejde-355	486	1	trans	trans	PROPN
ejde-355	486	2	.	.	PUNCT
ejde-355	487	1	roy	roy	PROPN
ejde-355	487	2	.	.	PROPN
ejde-355	487	3	soc	soc	PROPN
ejde-355	487	4	.	.	PUNCT
ejde-355	488	1	a	a	DET
ejde-355	488	2	,	,	PUNCT
ejde-355	488	3	380(2237	380(2237	NUM
ejde-355	488	4	)	)	PUNCT
ejde-355	488	5	(	(	PUNCT
ejde-355	488	6	2022	2022	NUM
ejde-355	488	7	)	)	PUNCT
ejde-355	488	8	,	,	PUNCT
ejde-355	488	9	20210392	20210392	NUM
ejde-355	488	10	[	[	X
ejde-355	488	11	38	38	NUM
ejde-355	488	12	]	]	PUNCT
ejde-355	488	13	m.	m.	NOUN
ejde-355	488	14	j.	j.	PROPN
ejde-355	488	15	nieves	nieves	PROPN
ejde-355	488	16	;	;	PUNCT
ejde-355	489	1	asymptotic	asymptotic	ADJ
ejde-355	489	2	analysis	analysis	NOUN
ejde-355	489	3	of	of	ADP
ejde-355	489	4	solutions	solution	NOUN
ejde-355	489	5	to	to	ADP
ejde-355	489	6	transmission	transmission	NOUN
ejde-355	489	7	problems	problem	NOUN
ejde-355	489	8	in	in	ADP
ejde-355	489	9	solids	solid	NOUN
ejde-355	489	10	with	with	ADP
ejde-355	489	11	many	many	ADJ
ejde-355	489	12	inclusions	inclusion	NOUN
ejde-355	489	13	,	,	PUNCT
ejde-355	489	14	siam	siam	PROPN
ejde-355	489	15	j.	j.	PROPN
ejde-355	489	16	appl	appl	PROPN
ejde-355	489	17	.	.	PROPN
ejde-355	489	18	math	math	PROPN
ejde-355	489	19	.	.	PUNCT
ejde-355	489	20	,	,	PUNCT
ejde-355	489	21	77(4	77(4	X
ejde-355	489	22	)	)	PUNCT
ejde-355	489	23	(	(	PUNCT
ejde-355	489	24	2017	2017	NUM
ejde-355	489	25	)	)	PUNCT
ejde-355	489	26	,	,	PUNCT
ejde-355	489	27	1417–1443	1417–1443	NUM
ejde-355	489	28	.	.	PUNCT
ejde-355	490	1	[	[	X
ejde-355	490	2	39	39	NUM
ejde-355	490	3	]	]	PUNCT
ejde-355	490	4	a.	a.	NOUN
ejde-355	490	5	a.	a.	PROPN
ejde-355	490	6	novotny	novotny	PROPN
ejde-355	490	7	,	,	PUNCT
ejde-355	490	8	j.	j.	PROPN
ejde-355	490	9	soko	soko	PROPN
ejde-355	490	10	lowski	lowski	PROPN
ejde-355	490	11	;	;	PUNCT
ejde-355	490	12	topological	topological	ADJ
ejde-355	490	13	derivatives	derivative	NOUN
ejde-355	490	14	in	in	ADP
ejde-355	490	15	shape	shape	NOUN
ejde-355	490	16	optimization	optimization	NOUN
ejde-355	490	17	,	,	PUNCT
ejde-355	490	18	interaction	interaction	NOUN
ejde-355	490	19	of	of	ADP
ejde-355	490	20	mechanics	mechanic	NOUN
ejde-355	490	21	and	and	CCONJ
ejde-355	490	22	mathematics	mathematic	NOUN
ejde-355	490	23	,	,	PUNCT
ejde-355	490	24	springer	springer	NOUN
ejde-355	490	25	,	,	PUNCT
ejde-355	490	26	heidelberg	heidelberg	PROPN
ejde-355	490	27	,	,	PUNCT
ejde-355	490	28	2013	2013	NUM
ejde-355	491	1	[	[	X
ejde-355	491	2	40	40	NUM
ejde-355	491	3	]	]	PUNCT
ejde-355	491	4	k.	k.	PROPN
ejde-355	491	5	schmidt	schmidt	PROPN
ejde-355	491	6	,	,	PUNCT
ejde-355	491	7	r.	r.	PROPN
ejde-355	491	8	hiptmair	hiptmair	PROPN
ejde-355	491	9	;	;	PUNCT
ejde-355	491	10	asymptotic	asymptotic	ADJ
ejde-355	491	11	expansion	expansion	NOUN
ejde-355	491	12	techniques	technique	NOUN
ejde-355	491	13	for	for	ADP
ejde-355	491	14	singularly	singularly	ADV
ejde-355	491	15	perturbed	perturb	VERB
ejde-355	491	16	boundary	boundary	ADJ
ejde-355	491	17	integral	integral	ADJ
ejde-355	491	18	equations	equation	NOUN
ejde-355	491	19	,	,	PUNCT
ejde-355	491	20	numer	numer	PROPN
ejde-355	491	21	.	.	PROPN
ejde-355	491	22	math	math	PROPN
ejde-355	491	23	.	.	PUNCT
ejde-355	491	24	,	,	PUNCT
ejde-355	491	25	137(2	137(2	NUM
ejde-355	491	26	)	)	PUNCT
ejde-355	491	27	(	(	PUNCT
ejde-355	491	28	2017	2017	NUM
ejde-355	491	29	)	)	PUNCT
ejde-355	491	30	,	,	PUNCT
ejde-355	491	31	397–415	397–415	NUM
ejde-355	491	32	.	.	PUNCT
ejde-355	492	1	[	[	X
ejde-355	492	2	41	41	NUM
ejde-355	492	3	]	]	PUNCT
ejde-355	492	4	t.	t.	NOUN
ejde-355	492	5	valent	valent	NOUN
ejde-355	492	6	;	;	PUNCT
ejde-355	492	7	boundary	boundary	ADJ
ejde-355	492	8	value	value	NOUN
ejde-355	492	9	problems	problem	NOUN
ejde-355	492	10	of	of	ADP
ejde-355	492	11	finite	finite	PROPN
ejde-355	492	12	elasticity	elasticity	NOUN
ejde-355	492	13	springer	springer	NOUN
ejde-355	492	14	tracts	tract	NOUN
ejde-355	492	15	in	in	ADP
ejde-355	492	16	natural	natural	ADJ
ejde-355	492	17	philosophy	philosophy	NOUN
ejde-355	492	18	,	,	PUNCT
ejde-355	492	19	vol	vol	NOUN
ejde-355	492	20	.	.	PROPN
ejde-355	492	21	31	31	NUM
ejde-355	492	22	.	.	PUNCT
ejde-355	492	23	springer	springer	NOUN
ejde-355	492	24	-	-	PUNCT
ejde-355	492	25	verlag	verlag	PROPN
ejde-355	492	26	,	,	PUNCT
ejde-355	492	27	new	new	PROPN
ejde-355	492	28	york	york	PROPN
ejde-355	492	29	,	,	PUNCT
ejde-355	492	30	1999	1999	NUM
ejde-355	492	31	.	.	PUNCT
ejde-355	493	1	local	local	ADJ
ejde-355	493	2	theorems	theorem	NOUN
ejde-355	493	3	on	on	ADP
ejde-355	493	4	existence	existence	NOUN
ejde-355	493	5	,	,	PUNCT
ejde-355	493	6	uniqueness	uniqueness	NOUN
ejde-355	493	7	,	,	PUNCT
ejde-355	493	8	and	and	CCONJ
ejde-355	493	9	analytic	analytic	ADJ
ejde-355	493	10	dependence	dependence	NOUN
ejde-355	493	11	on	on	ADP
ejde-355	493	12	data	datum	NOUN
ejde-355	493	13	.	.	PUNCT
ejde-355	494	1	[	[	X
ejde-355	494	2	42	42	NUM
ejde-355	494	3	]	]	PUNCT
ejde-355	494	4	m.	m.	NOUN
ejde-355	494	5	th	th	PROPN
ejde-355	494	6	.	.	PUNCT
ejde-355	495	1	van	van	PROPN
ejde-355	495	2	genuchten	genuchten	NOUN
ejde-355	495	3	,	,	PUNCT
ejde-355	495	4	w.	w.	PROPN
ejde-355	495	5	j.	j.	PROPN
ejde-355	495	6	alves	alves	PROPN
ejde-355	495	7	;	;	PUNCT
ejde-355	495	8	analytical	analytical	ADJ
ejde-355	495	9	solutions	solution	NOUN
ejde-355	495	10	of	of	ADP
ejde-355	495	11	the	the	DET
ejde-355	495	12	one	one	NUM
ejde-355	495	13	-dimensional	-dimensional	ADJ
ejde-355	495	14	convective	convective	ADJ
ejde-355	495	15	-	-	PUNCT
ejde-355	495	16	dispersive	dispersive	ADJ
ejde-355	495	17	solute	solute	NOUN
ejde-355	495	18	transport	transport	NOUN
ejde-355	495	19	equation	equation	NOUN
ejde-355	495	20	,	,	PUNCT
ejde-355	495	21	technical	technical	ADJ
ejde-355	495	22	bulletin	bulletin	NOUN
ejde-355	495	23	united	united	PROPN
ejde-355	495	24	states	states	PROPN
ejde-355	495	25	department	department	PROPN
ejde-355	495	26	of	of	ADP
ejde-355	495	27	agriculture	agriculture	PROPN
ejde-355	495	28	,	,	PUNCT
ejde-355	495	29	1661	1661	NUM
ejde-355	495	30	(	(	PUNCT
ejde-355	495	31	1982	1982	NUM
ejde-355	495	32	)	)	PUNCT
ejde-355	495	33	.	.	PUNCT
ejde-355	496	1	[	[	X
ejde-355	496	2	43	43	NUM
ejde-355	496	3	]	]	X
ejde-355	496	4	w.	w.	PROPN
ejde-355	496	5	l.	l.	PROPN
ejde-355	496	6	wendland	wendland	PROPN
ejde-355	496	7	,	,	PUNCT
ejde-355	496	8	e.	e.	PROPN
ejde-355	496	9	stephan	stephan	PROPN
ejde-355	496	10	,	,	PUNCT
ejde-355	496	11	g.	g.	PROPN
ejde-355	496	12	c.	c.	PROPN
ejde-355	496	13	hsiao	hsiao	PROPN
ejde-355	496	14	;	;	PUNCT
ejde-355	496	15	on	on	ADP
ejde-355	496	16	the	the	DET
ejde-355	496	17	integral	integral	ADJ
ejde-355	496	18	equation	equation	NOUN
ejde-355	496	19	method	method	NOUN
ejde-355	496	20	for	for	ADP
ejde-355	496	21	the	the	DET
ejde-355	496	22	plane	plane	NOUN
ejde-355	496	23	mixed	mix	VERB
ejde-355	496	24	boundary	boundary	ADJ
ejde-355	496	25	value	value	NOUN
ejde-355	496	26	problem	problem	NOUN
ejde-355	496	27	of	of	ADP
ejde-355	496	28	the	the	DET
ejde-355	496	29	laplacian	laplacian	PROPN
ejde-355	496	30	,	,	PUNCT
ejde-355	496	31	math	math	NOUN
ejde-355	496	32	.	.	PUNCT
ejde-355	497	1	methods	method	NOUN
ejde-355	497	2	appl	appl	PROPN
ejde-355	497	3	.	.	PUNCT
ejde-355	498	1	sci	sci	PROPN
ejde-355	498	2	.	.	PROPN
ejde-355	498	3	,	,	PUNCT
ejde-355	498	4	1(3	1(3	NUM
ejde-355	498	5	)	)	PUNCT
ejde-355	498	6	(	(	PUNCT
ejde-355	498	7	1979	1979	NUM
ejde-355	498	8	)	)	PUNCT
ejde-355	498	9	,	,	PUNCT
ejde-355	498	10	265–321	265–321	NUM
ejde-355	498	11	.	.	PUNCT
ejde-355	499	1	paolo	paolo	PROPN
ejde-355	499	2	musolino	musolino	PROPN
ejde-355	499	3	dipartimento	dipartimento	PROPN
ejde-355	499	4	di	di	PROPN
ejde-355	499	5	scienze	scienze	PROPN
ejde-355	499	6	molecolari	molecolari	PROPN
ejde-355	499	7	e	e	PROPN
ejde-355	499	8	nanosistemi	nanosistemi	NOUN
ejde-355	499	9	,	,	PUNCT
ejde-355	499	10	università	università	PROPN
ejde-355	499	11	ca	ca	NOUN
ejde-355	499	12	’	'	PUNCT
ejde-355	499	13	foscari	foscari	PROPN
ejde-355	499	14	venezia	venezia	PROPN
ejde-355	499	15	,	,	PUNCT
ejde-355	499	16	via	via	ADP
ejde-355	499	17	torino	torino	NOUN
ejde-355	499	18	155	155	NUM
ejde-355	499	19	,	,	PUNCT
ejde-355	499	20	30172	30172	NUM
ejde-355	499	21	venezia	venezia	PROPN
ejde-355	499	22	mestre	mestre	PROPN
ejde-355	499	23	,	,	PUNCT
ejde-355	499	24	italy	italy	PROPN
ejde-355	499	25	email	email	NOUN
ejde-355	499	26	address	address	NOUN
ejde-355	499	27	:	:	PUNCT
ejde-355	499	28	paolo.musolino@unive.it	paolo.musolino@unive.it	NOUN
ejde-355	499	29	ejde-2023/57	ejde-2023/57	NOUN
ejde-355	499	30	asymptotic	asymptotic	ADJ
ejde-355	499	31	analysis	analysis	NOUN
ejde-355	499	32	of	of	ADP
ejde-355	499	33	perturbed	perturb	VERB
ejde-355	499	34	robin	robin	PROPN
ejde-355	499	35	problems	problem	VERB
ejde-355	499	36	21	21	NUM
ejde-355	499	37	martin	martin	PROPN
ejde-355	499	38	dutko	dutko	PROPN
ejde-355	499	39	rockfield	rockfield	PROPN
ejde-355	499	40	software	software	PROPN
ejde-355	499	41	limited	limit	VERB
ejde-355	499	42	,	,	PUNCT
ejde-355	499	43	king	king	NOUN
ejde-355	499	44	’s	’s	PART
ejde-355	499	45	road	road	NOUN
ejde-355	499	46	,	,	PUNCT
ejde-355	499	47	ethos	ethos	ADJ
ejde-355	499	48	building	building	NOUN
ejde-355	499	49	,	,	PUNCT
ejde-355	499	50	swansea	swansea	NOUN
ejde-355	499	51	,	,	PUNCT
ejde-355	499	52	sa1	sa1	PROPN
ejde-355	499	53	8ph	8ph	PROPN
ejde-355	499	54	,	,	PUNCT
ejde-355	499	55	wales	wales	PROPN
ejde-355	499	56	uk	uk	PROPN
ejde-355	499	57	email	email	NOUN
ejde-355	499	58	address	address	NOUN
ejde-355	499	59	:	:	PUNCT
ejde-355	499	60	martin.dutko@rockfieldglobal.com	martin.dutko@rockfieldglobal.com	X
ejde-355	499	61	gennady	gennady	PROPN
ejde-355	499	62	mishuris	mishuris	PROPN
ejde-355	499	63	department	department	PROPN
ejde-355	499	64	of	of	ADP
ejde-355	499	65	mathematics	mathematics	PROPN
ejde-355	499	66	,	,	PUNCT
ejde-355	499	67	aberystwyth	aberystwyth	PROPN
ejde-355	499	68	university	university	PROPN
ejde-355	499	69	,	,	PUNCT
ejde-355	499	70	ceredigion	ceredigion	NOUN
ejde-355	499	71	,	,	PUNCT
ejde-355	499	72	aberystwyth	aberystwyth	PROPN
ejde-355	499	73	,	,	PUNCT
ejde-355	499	74	sy23	sy23	PROPN
ejde-355	499	75	3bz	3bz	ADJ
ejde-355	499	76	wales	wale	NOUN
ejde-355	499	77	,	,	PUNCT
ejde-355	499	78	uk	uk	PROPN
ejde-355	499	79	email	email	NOUN
ejde-355	499	80	address	address	NOUN
ejde-355	499	81	:	:	PUNCT
ejde-355	499	82	ggm@aber.ac.uk	ggm@aber.ac.uk	ADJ
ejde-355	499	83	1	1	NUM
ejde-355	499	84	.	.	PUNCT
ejde-355	500	1	introduction	introduction	NOUN
ejde-355	500	2	2	2	NUM
ejde-355	500	3	.	.	PUNCT
ejde-355	501	1	a	a	DET
ejde-355	501	2	toy	toy	NOUN
ejde-355	501	3	problem	problem	NOUN
ejde-355	501	4	3	3	X
ejde-355	501	5	.	.	PUNCT
ejde-355	501	6	integral	integral	ADJ
ejde-355	501	7	equation	equation	NOUN
ejde-355	501	8	formulation	formulation	NOUN
ejde-355	501	9	of	of	ADP
ejde-355	501	10	the	the	DET
ejde-355	501	11	boundary	boundary	ADJ
ejde-355	501	12	value	value	NOUN
ejde-355	501	13	problem	problem	NOUN
ejde-355	501	14	4	4	NUM
ejde-355	501	15	.	.	PUNCT
ejde-355	501	16	analytic	analytic	ADJ
ejde-355	501	17	representation	representation	NOUN
ejde-355	501	18	formulas	formula	NOUN
ejde-355	501	19	for	for	ADP
ejde-355	501	20	the	the	DET
ejde-355	501	21	solution	solution	NOUN
ejde-355	501	22	of	of	ADP
ejde-355	501	23	the	the	DET
ejde-355	501	24	boundary	boundary	ADJ
ejde-355	501	25	value	value	NOUN
ejde-355	501	26	problem	problem	NOUN
ejde-355	501	27	5	5	NUM
ejde-355	501	28	.	.	PUNCT
ejde-355	502	1	remarks	remark	NOUN
ejde-355	502	2	on	on	ADP
ejde-355	502	3	the	the	DET
ejde-355	502	4	linear	linear	ADJ
ejde-355	502	5	case	case	NOUN
ejde-355	502	6	6	6	NUM
ejde-355	502	7	.	.	PUNCT
ejde-355	503	1	conclusions	conclusion	NOUN
ejde-355	503	2	acknowledgements	acknowledgement	NOUN
ejde-355	503	3	references	reference	NOUN