id	sid	tid	token	lemma	pos
ma-105	1	1	2023	2023	NUM
ma-105	1	2	ada	ada	PROPN
ma-105	1	3	academica	academica	PROPN
ma-105	1	4	https://adac.eeeur	https://adac.eeeur	PROPN
ma-105	1	5	.	.	PUNCT
ma-105	2	1	j.	j.	PROPN
ma-105	2	2	math	math	PROPN
ma-105	2	3	.	.	PUNCT
ma-105	3	1	anal	anal	ADJ
ma-105	3	2	.	.	PUNCT
ma-105	4	1	3	3	NUM
ma-105	4	2	(	(	PUNCT
ma-105	4	3	2023	2023	NUM
ma-105	4	4	)	)	PUNCT
ma-105	5	1	1doi	1doi	NUM
ma-105	5	2	:	:	PUNCT
ma-105	5	3	10.28924	10.28924	NUM
ma-105	5	4	/	/	SYM
ma-105	5	5	ada	ada	PROPN
ma-105	5	6	/	/	SYM
ma-105	5	7	ma.3.1	ma.3.1	PROPN
ma-105	5	8	global	global	ADJ
ma-105	5	9	analysis	analysis	NOUN
ma-105	5	10	of	of	ADP
ma-105	5	11	a	a	DET
ma-105	5	12	spatiotemporal	spatiotemporal	ADJ
ma-105	5	13	cellular	cellular	ADJ
ma-105	5	14	model	model	NOUN
ma-105	5	15	for	for	ADP
ma-105	5	16	the	the	DET
ma-105	5	17	transmission	transmission	NOUN
ma-105	5	18	of	of	ADP
ma-105	5	19	hepatitis	hepatitis	PROPN
ma-105	5	20	c	c	PROPN
ma-105	5	21	virus	virus	NOUN
ma-105	5	22	with	with	ADP
ma-105	5	23	hattaf	hattaf	NOUN
ma-105	5	24	-	-	PUNCT
ma-105	5	25	yousfi	yousfi	ADJ
ma-105	5	26	functional	functional	ADJ
ma-105	5	27	response	response	NOUN
ma-105	5	28	alexis	alexis	PROPN
ma-105	5	29	nangue1,∗	nangue1,∗	PROPN
ma-105	5	30	,	,	PUNCT
ma-105	5	31	bruno	bruno	PROPN
ma-105	5	32	nde	nde	PROPN
ma-105	5	33	tchiffo2	tchiffo2	PROPN
ma-105	6	1	1university	1university	NUM
ma-105	6	2	of	of	ADP
ma-105	6	3	maroua	maroua	ADJ
ma-105	6	4	,	,	PUNCT
ma-105	6	5	higher	high	ADJ
ma-105	6	6	teachers	teacher	NOUN
ma-105	6	7	’	’	PART
ma-105	6	8	training	training	NOUN
ma-105	6	9	college	college	NOUN
ma-105	6	10	,	,	PUNCT
ma-105	6	11	department	department	NOUN
ma-105	6	12	of	of	ADP
ma-105	6	13	mathematics	mathematic	NOUN
ma-105	6	14	,	,	PUNCT
ma-105	6	15	p.o.box	p.o.box	PROPN
ma-105	6	16	55	55	NUM
ma-105	6	17	maroua	maroua	NOUN
ma-105	6	18	,	,	PUNCT
ma-105	6	19	cameroon	cameroon	NOUN
ma-105	6	20	alexnanga02@gmail.com	alexnanga02@gmail.com	PROPN
ma-105	7	1	2university	2university	NUM
ma-105	7	2	of	of	ADP
ma-105	7	3	maroua	maroua	ADJ
ma-105	7	4	,	,	PUNCT
ma-105	7	5	faculty	faculty	NOUN
ma-105	7	6	of	of	ADP
ma-105	7	7	science	science	NOUN
ma-105	7	8	,	,	PUNCT
ma-105	7	9	department	department	NOUN
ma-105	7	10	of	of	ADP
ma-105	7	11	mathematics	mathematics	PROPN
ma-105	7	12	and	and	CCONJ
ma-105	7	13	computer	computer	NOUN
ma-105	7	14	science	science	NOUN
ma-105	7	15	,	,	PUNCT
ma-105	7	16	p.o	p.o	PROPN
ma-105	7	17	.	.	PROPN
ma-105	7	18	box	box	PROPN
ma-105	7	19	814	814	NUM
ma-105	7	20	maroua	maroua	ADJ
ma-105	7	21	,	,	PUNCT
ma-105	7	22	cameroon	cameroon	NOUN
ma-105	7	23	ndebruno2@gmail.com	ndebruno2@gmail.com	X
ma-105	8	1	∗correspondence	∗correspondence	NOUN
ma-105	8	2	:	:	PUNCT
ma-105	8	3	alexnanga02@gmail.com	alexnanga02@gmail.com	PROPN
ma-105	8	4	abstract	abstract	NOUN
ma-105	8	5	.	.	PUNCT
ma-105	9	1	this	this	DET
ma-105	9	2	paper	paper	NOUN
ma-105	9	3	carries	carry	VERB
ma-105	9	4	out	out	ADP
ma-105	9	5	a	a	DET
ma-105	9	6	mathematical	mathematical	ADJ
ma-105	9	7	analysis	analysis	NOUN
ma-105	9	8	of	of	ADP
ma-105	9	9	the	the	DET
ma-105	9	10	global	global	ADJ
ma-105	9	11	dynamics	dynamic	NOUN
ma-105	9	12	of	of	ADP
ma-105	9	13	a	a	DET
ma-105	9	14	partial	partial	ADJ
ma-105	9	15	differen	differen	ADJ
ma-105	9	16	-	-	ADJ
ma-105	9	17	tial	tial	ADJ
ma-105	9	18	equation	equation	NOUN
ma-105	9	19	viral	viral	ADJ
ma-105	9	20	infection	infection	NOUN
ma-105	9	21	cellular	cellular	ADJ
ma-105	9	22	model	model	NOUN
ma-105	9	23	.	.	PUNCT
ma-105	10	1	we	we	PRON
ma-105	10	2	study	study	VERB
ma-105	10	3	the	the	DET
ma-105	10	4	dynamics	dynamic	NOUN
ma-105	10	5	of	of	ADP
ma-105	10	6	a	a	DET
ma-105	10	7	hepatitis	hepatitis	NOUN
ma-105	10	8	c	c	PROPN
ma-105	10	9	virus	virus	NOUN
ma-105	10	10	(	(	PUNCT
ma-105	10	11	hcv	hcv	PROPN
ma-105	10	12	)	)	PUNCT
ma-105	10	13	model	model	NOUN
ma-105	10	14	,	,	PUNCT
ma-105	10	15	under	under	ADP
ma-105	10	16	therapy	therapy	NOUN
ma-105	10	17	,	,	PUNCT
ma-105	10	18	that	that	PRON
ma-105	10	19	considers	consider	VERB
ma-105	10	20	both	both	DET
ma-105	10	21	absorption	absorption	NOUN
ma-105	10	22	phenomenon	phenomenon	NOUN
ma-105	10	23	and	and	CCONJ
ma-105	10	24	diffusion	diffusion	NOUN
ma-105	10	25	of	of	ADP
ma-105	10	26	virions	virion	NOUN
ma-105	10	27	,	,	PUNCT
ma-105	10	28	infected	infected	ADJ
ma-105	10	29	and	and	CCONJ
ma-105	10	30	un	un	ADJ
ma-105	10	31	-	-	ADJ
ma-105	10	32	infected	infected	ADJ
ma-105	10	33	hepatocytes	hepatocyte	NOUN
ma-105	10	34	in	in	ADP
ma-105	10	35	the	the	DET
ma-105	10	36	liver	liver	NOUN
ma-105	10	37	.	.	PUNCT
ma-105	11	1	firstly	firstly	ADV
ma-105	11	2	,	,	PUNCT
ma-105	11	3	we	we	PRON
ma-105	11	4	prove	prove	VERB
ma-105	11	5	the	the	DET
ma-105	11	6	boundedness	boundedness	NOUN
ma-105	11	7	of	of	ADP
ma-105	11	8	the	the	DET
ma-105	11	9	potential	potential	ADJ
ma-105	11	10	solutions	solution	NOUN
ma-105	11	11	,	,	PUNCT
ma-105	11	12	globalexistence	globalexistence	NOUN
ma-105	11	13	,	,	PUNCT
ma-105	11	14	uniqueness	uniqueness	NOUN
ma-105	11	15	,	,	PUNCT
ma-105	11	16	and	and	CCONJ
ma-105	11	17	positivity	positivity	NOUN
ma-105	11	18	of	of	ADP
ma-105	11	19	the	the	DET
ma-105	11	20	obtained	obtain	VERB
ma-105	11	21	initial	initial	ADJ
ma-105	11	22	value	value	NOUN
ma-105	11	23	and	and	CCONJ
ma-105	11	24	boundary	boundary	ADJ
ma-105	11	25	problem	problem	NOUN
ma-105	11	26	solution.then	solution.then	PROPN
ma-105	11	27	,	,	PUNCT
ma-105	11	28	the	the	DET
ma-105	11	29	dynamical	dynamical	ADJ
ma-105	11	30	behaviour	behaviour	NOUN
ma-105	11	31	of	of	ADP
ma-105	11	32	the	the	DET
ma-105	11	33	model	model	NOUN
ma-105	11	34	is	be	AUX
ma-105	11	35	entirely	entirely	ADV
ma-105	11	36	determined	determine	VERB
ma-105	11	37	by	by	ADP
ma-105	11	38	a	a	DET
ma-105	11	39	threshold	threshold	NOUN
ma-105	11	40	parameter	parameter	NOUN
ma-105	11	41	calledthe	calledthe	DET
ma-105	11	42	basic	basic	ADJ
ma-105	11	43	reproduction	reproduction	NOUN
ma-105	11	44	number	number	NOUN
ma-105	11	45	denoted	denote	VERB
ma-105	11	46	r0	r0	NOUN
ma-105	11	47	.	.	PUNCT
ma-105	12	1	we	we	PRON
ma-105	12	2	show	show	VERB
ma-105	12	3	that	that	SCONJ
ma-105	12	4	the	the	DET
ma-105	12	5	uninfected	uninfected	ADJ
ma-105	12	6	spatially	spatially	ADJ
ma-105	12	7	homogeneousequilibrium	homogeneousequilibrium	NOUN
ma-105	12	8	of	of	ADP
ma-105	12	9	the	the	DET
ma-105	12	10	model	model	NOUN
ma-105	12	11	is	be	AUX
ma-105	12	12	globally	globally	ADV
ma-105	12	13	asymptotically	asymptotically	ADV
ma-105	12	14	stable	stable	ADJ
ma-105	12	15	if	if	SCONJ
ma-105	12	16	r0	r0	NOUN
ma-105	12	17	≤	≤	NOUN
ma-105	12	18	1	1	NUM
ma-105	12	19	by	by	ADP
ma-105	12	20	using	use	VERB
ma-105	12	21	the	the	DET
ma-105	12	22	direct	direct	ADJ
ma-105	12	23	lyapunovmethod	lyapunovmethod	NOUN
ma-105	12	24	.	.	PUNCT
ma-105	13	1	the	the	DET
ma-105	13	2	latter	latter	ADJ
ma-105	13	3	means	mean	VERB
ma-105	13	4	that	that	SCONJ
ma-105	13	5	the	the	DET
ma-105	13	6	hcv	hcv	ADJ
ma-105	13	7	infection	infection	NOUN
ma-105	13	8	is	be	AUX
ma-105	13	9	cleared	clear	VERB
ma-105	13	10	,	,	PUNCT
ma-105	13	11	and	and	CCONJ
ma-105	13	12	the	the	DET
ma-105	13	13	disease	disease	NOUN
ma-105	13	14	dies	die	VERB
ma-105	13	15	out	out	ADP
ma-105	13	16	.	.	PUNCT
ma-105	14	1	also	also	ADV
ma-105	14	2	,	,	PUNCT
ma-105	14	3	the	the	DET
ma-105	14	4	globalasymptotical	globalasymptotical	ADJ
ma-105	14	5	properties	property	NOUN
ma-105	14	6	stability	stability	NOUN
ma-105	14	7	of	of	ADP
ma-105	14	8	the	the	DET
ma-105	14	9	infected	infect	VERB
ma-105	14	10	spatially	spatially	ADV
ma-105	14	11	homogeneous	homogeneous	ADJ
ma-105	14	12	equilibrium	equilibrium	NOUN
ma-105	14	13	of	of	ADP
ma-105	14	14	the	the	DET
ma-105	14	15	model	model	NOUN
ma-105	14	16	arestudied	arestudie	VERB
ma-105	14	17	via	via	ADP
ma-105	14	18	a	a	DET
ma-105	14	19	skilful	skilful	ADJ
ma-105	14	20	construction	construction	NOUN
ma-105	14	21	of	of	ADP
ma-105	14	22	a	a	DET
ma-105	14	23	suitable	suitable	ADJ
ma-105	14	24	lyapunov	lyapunov	ADJ
ma-105	14	25	functional	functional	NOUN
ma-105	14	26	.	.	PUNCT
ma-105	15	1	it	it	PRON
ma-105	15	2	means	mean	VERB
ma-105	15	3	that	that	SCONJ
ma-105	15	4	the	the	DET
ma-105	15	5	hcv	hcv	NOUN
ma-105	15	6	infectionpersists	infectionpersist	NOUN
ma-105	15	7	in	in	ADP
ma-105	15	8	the	the	DET
ma-105	15	9	host	host	NOUN
ma-105	15	10	,	,	PUNCT
ma-105	15	11	and	and	CCONJ
ma-105	15	12	the	the	DET
ma-105	15	13	infection	infection	NOUN
ma-105	15	14	becomes	become	VERB
ma-105	15	15	chronic	chronic	ADJ
ma-105	15	16	.	.	PUNCT
ma-105	16	1	finally	finally	ADV
ma-105	16	2	,	,	PUNCT
ma-105	16	3	numerical	numerical	ADJ
ma-105	16	4	simulations	simulation	NOUN
ma-105	16	5	are	be	AUX
ma-105	16	6	performedto	performedto	ADJ
ma-105	16	7	support	support	NOUN
ma-105	16	8	the	the	DET
ma-105	16	9	obtained	obtain	VERB
ma-105	16	10	theoretical	theoretical	ADJ
ma-105	16	11	results	result	NOUN
ma-105	16	12	.	.	PUNCT
ma-105	17	1	1	1	X
ma-105	17	2	.	.	X
ma-105	17	3	introduction	introduction	NOUN
ma-105	17	4	the	the	DET
ma-105	17	5	dynamics	dynamic	NOUN
ma-105	17	6	of	of	ADP
ma-105	17	7	viruses	virus	NOUN
ma-105	17	8	,	,	PUNCT
ma-105	17	9	in	in	ADP
ma-105	17	10	particular	particular	ADJ
ma-105	17	11	the	the	DET
ma-105	17	12	dynamics	dynamic	NOUN
ma-105	17	13	of	of	ADP
ma-105	17	14	the	the	DET
ma-105	17	15	hepatitis	hepatitis	PROPN
ma-105	17	16	c	c	PROPN
ma-105	17	17	virus	virus	PROPN
ma-105	17	18	,	,	PUNCT
ma-105	17	19	remains	remain	VERB
ma-105	17	20	a	a	DET
ma-105	17	21	veryactive	veryactive	ADJ
ma-105	17	22	field	field	NOUN
ma-105	17	23	of	of	ADP
ma-105	17	24	research	research	NOUN
ma-105	17	25	in	in	ADP
ma-105	17	26	the	the	DET
ma-105	17	27	world	world	NOUN
ma-105	17	28	of	of	ADP
ma-105	17	29	sciences	science	NOUN
ma-105	17	30	.	.	PUNCT
ma-105	18	1	moreover	moreover	ADV
ma-105	18	2	,	,	PUNCT
ma-105	18	3	the	the	DET
ma-105	18	4	2020	2020	NUM
ma-105	18	5	nobel	nobel	PROPN
ma-105	18	6	prize	prize	PROPN
ma-105	18	7	in	in	ADP
ma-105	18	8	medicinewas	medicinewas	PROPN
ma-105	18	9	awarded	award	VERB
ma-105	18	10	to	to	ADP
ma-105	18	11	three	three	NUM
ma-105	18	12	researchers	researcher	NOUN
ma-105	18	13	,	,	PUNCT
ma-105	18	14	namely	namely	ADV
ma-105	18	15	the	the	DET
ma-105	18	16	british	british	ADJ
ma-105	18	17	michael	michael	PROPN
ma-105	18	18	hougton	hougton	PROPN
ma-105	18	19	and	and	CCONJ
ma-105	18	20	the	the	DET
ma-105	18	21	americans	americans	PROPN
ma-105	18	22	harveyalter	harveyalter	PROPN
ma-105	18	23	and	and	CCONJ
ma-105	18	24	charles	charles	PROPN
ma-105	18	25	rice	rice	PROPN
ma-105	18	26	.	.	PUNCT
ma-105	19	1	they	they	PRON
ma-105	19	2	were	be	AUX
ma-105	19	3	awarded	award	VERB
ma-105	19	4	this	this	DET
ma-105	19	5	nobel	nobel	PROPN
ma-105	19	6	prize	prize	PROPN
ma-105	19	7	for	for	ADP
ma-105	19	8	their	their	PRON
ma-105	19	9	very	very	ADV
ma-105	19	10	advanced	advanced	ADJ
ma-105	19	11	research	research	NOUN
ma-105	19	12	workon	workon	NOUN
ma-105	19	13	the	the	DET
ma-105	19	14	hepatitis	hepatitis	PROPN
ma-105	19	15	c	c	PROPN
ma-105	19	16	virus	virus	NOUN
ma-105	19	17	.	.	PUNCT
ma-105	20	1	according	accord	VERB
ma-105	20	2	to	to	ADP
ma-105	20	3	world	world	PROPN
ma-105	20	4	health	health	NOUN
ma-105	20	5	organization(who	organization(who	PROPN
ma-105	20	6	)	)	PUNCT
ma-105	21	1	[	[	X
ma-105	21	2	41	41	NUM
ma-105	21	3	]	]	PUNCT
ma-105	21	4	,	,	PUNCT
ma-105	21	5	71	71	NUM
ma-105	21	6	million	million	NUM
ma-105	21	7	personswere	personswere	NOUN
ma-105	21	8	living	live	VERB
ma-105	21	9	with	with	ADP
ma-105	21	10	chronic	chronic	ADJ
ma-105	21	11	hepatitis	hepatitis	PROPN
ma-105	21	12	c	c	PROPN
ma-105	21	13	virus	virus	NOUN
ma-105	21	14	(	(	PUNCT
ma-105	21	15	hcv	hcv	NOUN
ma-105	21	16	)	)	PUNCT
ma-105	21	17	infection	infection	NOUN
ma-105	21	18	worldwide	worldwide	ADV
ma-105	21	19	and	and	CCONJ
ma-105	21	20	399	399	NUM
ma-105	21	21	000	000	NUM
ma-105	21	22	persons	person	NOUN
ma-105	21	23	had	have	AUX
ma-105	21	24	received	receive	VERB
ma-105	21	25	:	:	PUNCT
ma-105	21	26	29	29	NUM
ma-105	21	27	apr	apr	NOUN
ma-105	21	28	2022	2022	NUM
ma-105	21	29	.	.	PUNCT
ma-105	22	1	key	key	ADJ
ma-105	22	2	words	word	NOUN
ma-105	22	3	and	and	CCONJ
ma-105	22	4	phrases	phrase	NOUN
ma-105	22	5	.	.	PUNCT
ma-105	23	1	reaction	reaction	NOUN
ma-105	23	2	-	-	PUNCT
ma-105	23	3	diffusion	diffusion	NOUN
ma-105	23	4	model	model	NOUN
ma-105	23	5	;	;	PUNCT
ma-105	23	6	hcv	hcv	X
ma-105	23	7	infection	infection	NOUN
ma-105	23	8	;	;	PUNCT
ma-105	23	9	hattaf	hattaf	NOUN
ma-105	23	10	-	-	PUNCT
ma-105	23	11	yousfi	yousfi	ADJ
ma-105	23	12	functional	functional	ADJ
ma-105	23	13	response	response	NOUN
ma-105	23	14	;	;	PUNCT
ma-105	23	15	semigroup	semigroup	PROPN
ma-105	23	16	;	;	PUNCT
ma-105	23	17	globalstability	globalstability	NOUN
ma-105	23	18	;	;	PUNCT
ma-105	23	19	variational	variational	ADJ
ma-105	23	20	method	method	NOUN
ma-105	23	21	;	;	PUNCT
ma-105	23	22	cure	cure	NOUN
ma-105	23	23	rate	rate	NOUN
ma-105	23	24	.	.	PUNCT
ma-105	24	1	1	1	NUM
ma-105	24	2	https://adac.ee	https://adac.ee	PROPN
ma-105	24	3	https://doi.org/10.28924/ada/ma.3.1	https://doi.org/10.28924/ada/ma.3.1	PROPN
ma-105	24	4	eur	eur	PROPN
ma-105	24	5	.	.	PUNCT
ma-105	25	1	j.	j.	PROPN
ma-105	25	2	math	math	PROPN
ma-105	25	3	.	.	PUNCT
ma-105	26	1	anal	anal	PROPN
ma-105	26	2	.	.	PUNCT
ma-105	27	1	10.28924	10.28924	NUM
ma-105	27	2	/	/	SYM
ma-105	27	3	ada	ada	PROPN
ma-105	27	4	/	/	SYM
ma-105	27	5	ma.3.1	ma.3.1	PROPN
ma-105	27	6	2died	2died	NUM
ma-105	27	7	from	from	ADP
ma-105	27	8	cirrhosis	cirrhosis	NOUN
ma-105	27	9	or	or	CCONJ
ma-105	27	10	hepatocellular	hepatocellular	ADJ
ma-105	27	11	carcinoma	carcinoma	NOUN
ma-105	27	12	following	follow	VERB
ma-105	27	13	a	a	DET
ma-105	27	14	survey	survey	NOUN
ma-105	27	15	done	do	VERB
ma-105	27	16	in	in	ADP
ma-105	27	17	2015	2015	NUM
ma-105	27	18	.	.	PUNCT
ma-105	28	1	aside	aside	ADV
ma-105	28	2	from	from	ADP
ma-105	28	3	theburden	theburden	PROPN
ma-105	28	4	of	of	ADP
ma-105	28	5	hcv	hcv	PROPN
ma-105	28	6	infection	infection	NOUN
ma-105	28	7	secondary	secondary	ADJ
ma-105	28	8	to	to	ADP
ma-105	28	9	liver	liver	NOUN
ma-105	28	10	-	-	PUNCT
ma-105	28	11	related	relate	VERB
ma-105	28	12	sequelae	sequelae	NOUN
ma-105	28	13	,	,	PUNCT
ma-105	28	14	hcv	hcv	PROPN
ma-105	28	15	causes	cause	VERB
ma-105	28	16	an	an	DET
ma-105	28	17	additional	additional	ADJ
ma-105	28	18	burdenthrough	burdenthrough	NOUN
ma-105	28	19	comorbidities	comorbiditie	NOUN
ma-105	28	20	among	among	ADP
ma-105	28	21	persons	person	NOUN
ma-105	28	22	with	with	ADP
ma-105	28	23	hcv	hcv	NOUN
ma-105	28	24	infection	infection	NOUN
ma-105	28	25	,	,	PUNCT
ma-105	28	26	including	include	VERB
ma-105	28	27	depression	depression	NOUN
ma-105	28	28	,	,	PUNCT
ma-105	28	29	diabetes	diabetes	NOUN
ma-105	28	30	mellitusand	mellitusand	NOUN
ma-105	28	31	chronic	chronic	ADJ
ma-105	28	32	renal	renal	ADJ
ma-105	28	33	disease	disease	NOUN
ma-105	28	34	.	.	PUNCT
ma-105	29	1	in	in	ADP
ma-105	29	2	may	may	PROPN
ma-105	29	3	2016	2016	NUM
ma-105	29	4	,	,	PUNCT
ma-105	29	5	the	the	DET
ma-105	29	6	world	world	PROPN
ma-105	29	7	health	health	PROPN
ma-105	29	8	assembly	assembly	NOUN
ma-105	29	9	endorsed	endorse	VERB
ma-105	29	10	the	the	DET
ma-105	29	11	global	global	ADJ
ma-105	29	12	healthsector	healthsector	NOUN
ma-105	29	13	strategy	strategy	NOUN
ma-105	29	14	for	for	ADP
ma-105	29	15	2016	2016	NUM
ma-105	29	16	-	-	SYM
ma-105	29	17	2021	2021	NUM
ma-105	29	18	on	on	ADP
ma-105	29	19	viral	viral	ADJ
ma-105	29	20	hepatitis	hepatitis	NOUN
ma-105	29	21	(	(	PUNCT
ma-105	29	22	hbv	hbv	NOUN
ma-105	29	23	and	and	CCONJ
ma-105	29	24	hcv	hcv	PROPN
ma-105	29	25	infection	infection	NOUN
ma-105	29	26	)	)	PUNCT
ma-105	29	27	,	,	PUNCT
ma-105	29	28	which	which	PRON
ma-105	29	29	proposes	propose	VERB
ma-105	29	30	toeliminate	toeliminate	VERB
ma-105	29	31	viral	viral	ADJ
ma-105	29	32	hepatitis	hepatitis	NOUN
ma-105	29	33	as	as	ADP
ma-105	29	34	a	a	DET
ma-105	29	35	public	public	ADJ
ma-105	29	36	health	health	NOUN
ma-105	29	37	threat	threat	NOUN
ma-105	29	38	by	by	ADP
ma-105	29	39	2030	2030	NUM
ma-105	29	40	.	.	PUNCT
ma-105	30	1	elimination	elimination	NOUN
ma-105	30	2	is	be	AUX
ma-105	30	3	defined	define	VERB
ma-105	30	4	as	as	ADP
ma-105	30	5	a	a	DET
ma-105	30	6	90%reduction	90%reduction	NOUN
ma-105	30	7	in	in	ADP
ma-105	30	8	new	new	ADJ
ma-105	30	9	chronic	chronic	ADJ
ma-105	30	10	infections	infection	NOUN
ma-105	30	11	and	and	CCONJ
ma-105	30	12	a	a	DET
ma-105	30	13	65	65	NUM
ma-105	30	14	%	%	NOUN
ma-105	30	15	reduction	reduction	NOUN
ma-105	30	16	in	in	ADP
ma-105	30	17	mortality	mortality	NOUN
ma-105	30	18	compared	compare	VERB
ma-105	30	19	with	with	ADP
ma-105	30	20	the	the	DET
ma-105	30	21	2015baseline	2015baseline	NUM
ma-105	30	22	.	.	PUNCT
ma-105	31	1	mathematicians	mathematician	NOUN
ma-105	31	2	can	can	AUX
ma-105	31	3	not	not	PART
ma-105	31	4	stay	stay	VERB
ma-105	31	5	aside	aside	ADV
ma-105	31	6	from	from	ADP
ma-105	31	7	this	this	DET
ma-105	31	8	disastrous	disastrous	ADJ
ma-105	31	9	situation	situation	NOUN
ma-105	31	10	decried	decry	VERB
ma-105	31	11	by	by	ADP
ma-105	31	12	who	who	PRON
ma-105	31	13	.	.	PUNCT
ma-105	32	1	inview	inview	NOUN
ma-105	32	2	of	of	ADP
ma-105	32	3	the	the	DET
ma-105	32	4	vital	vital	ADJ
ma-105	32	5	importance	importance	NOUN
ma-105	32	6	of	of	ADP
ma-105	32	7	the	the	DET
ma-105	32	8	liver	liver	NOUN
ma-105	32	9	and	and	CCONJ
ma-105	32	10	the	the	DET
ma-105	32	11	aforementioned	aforementione	VERB
ma-105	32	12	facts	fact	NOUN
ma-105	32	13	,	,	PUNCT
ma-105	32	14	any	any	DET
ma-105	32	15	contribution	contribution	NOUN
ma-105	32	16	to	to	ADP
ma-105	32	17	a	a	DET
ma-105	32	18	betterunderstanding	betterunderstanding	NOUN
ma-105	32	19	of	of	ADP
ma-105	32	20	hcv	hcv	NOUN
ma-105	32	21	infection	infection	NOUN
ma-105	32	22	process	process	NOUN
ma-105	32	23	and	and	CCONJ
ma-105	32	24	strategy	strategy	NOUN
ma-105	32	25	to	to	PART
ma-105	32	26	eradicate	eradicate	VERB
ma-105	32	27	this	this	DET
ma-105	32	28	infection	infection	NOUN
ma-105	32	29	is	be	AUX
ma-105	32	30	of	of	ADP
ma-105	32	31	great	great	ADJ
ma-105	32	32	interest.mathematical	interest.mathematical	ADJ
ma-105	32	33	models	model	NOUN
ma-105	32	34	have	have	AUX
ma-105	32	35	been	be	AUX
ma-105	32	36	developed	develop	VERB
ma-105	32	37	to	to	PART
ma-105	32	38	help	help	VERB
ma-105	32	39	understand	understand	VERB
ma-105	32	40	and	and	CCONJ
ma-105	32	41	control	control	VERB
ma-105	32	42	the	the	DET
ma-105	32	43	dynamics	dynamic	NOUN
ma-105	32	44	of	of	ADP
ma-105	32	45	hcvwithin	hcvwithin	ADJ
ma-105	32	46	an	an	DET
ma-105	32	47	infected	infected	ADJ
ma-105	32	48	host	host	NOUN
ma-105	32	49	such	such	ADJ
ma-105	32	50	as	as	ADP
ma-105	32	51	in	in	ADP
ma-105	32	52	[	[	X
ma-105	32	53	6	6	NUM
ma-105	32	54	,	,	PUNCT
ma-105	32	55	7	7	NUM
ma-105	32	56	,	,	PUNCT
ma-105	32	57	14	14	NUM
ma-105	32	58	,	,	PUNCT
ma-105	32	59	35	35	NUM
ma-105	32	60	]	]	PUNCT
ma-105	32	61	.	.	PUNCT
ma-105	33	1	the	the	DET
ma-105	33	2	dynamics	dynamic	NOUN
ma-105	33	3	of	of	ADP
ma-105	33	4	viral	viral	ADJ
ma-105	33	5	infections	infection	NOUN
ma-105	33	6	such	such	ADJ
ma-105	33	7	as	as	ADP
ma-105	33	8	theebola	theebola	PROPN
ma-105	33	9	virus	virus	PROPN
ma-105	33	10	disease(evd	disease(evd	PROPN
ma-105	33	11	)	)	PUNCT
ma-105	33	12	,	,	PUNCT
ma-105	33	13	the	the	DET
ma-105	33	14	human	human	ADJ
ma-105	33	15	immunodeficiency	immunodeficiency	NOUN
ma-105	33	16	virus	virus	NOUN
ma-105	33	17	(	(	PUNCT
ma-105	33	18	hiv	hiv	NOUN
ma-105	33	19	)	)	PUNCT
ma-105	33	20	infection	infection	NOUN
ma-105	33	21	,	,	PUNCT
ma-105	33	22	the	the	DET
ma-105	33	23	hepatitis	hepatitis	PROPN
ma-105	33	24	b	b	PROPN
ma-105	33	25	virus(hbv	virus(hbv	PROPN
ma-105	33	26	)	)	PUNCT
ma-105	33	27	infection	infection	NOUN
ma-105	33	28	,	,	PUNCT
ma-105	33	29	the	the	DET
ma-105	33	30	hepatitis	hepatitis	PROPN
ma-105	33	31	c	c	PROPN
ma-105	33	32	virus	virus	NOUN
ma-105	33	33	(	(	PUNCT
ma-105	33	34	hcv	hcv	NOUN
ma-105	33	35	)	)	PUNCT
ma-105	33	36	infection	infection	NOUN
ma-105	33	37	and	and	CCONJ
ma-105	33	38	,	,	PUNCT
ma-105	33	39	new	new	ADJ
ma-105	33	40	corona	corona	NOUN
ma-105	33	41	virus	virus	NOUN
ma-105	33	42	infection	infection	NOUN
ma-105	33	43	have	have	AUX
ma-105	33	44	beenmodeled	beenmodele	VERB
ma-105	33	45	mathematically	mathematically	ADV
ma-105	33	46	in	in	ADP
ma-105	33	47	a	a	DET
ma-105	33	48	host	host	NOUN
ma-105	33	49	.	.	PUNCT
ma-105	34	1	one	one	NUM
ma-105	34	2	of	of	ADP
ma-105	34	3	the	the	DET
ma-105	34	4	earliest	early	ADJ
ma-105	34	5	temporal	temporal	ADJ
ma-105	34	6	models	model	NOUN
ma-105	34	7	was	be	AUX
ma-105	34	8	the	the	DET
ma-105	34	9	within	within	ADP
ma-105	34	10	-	-	PUNCT
ma-105	34	11	host	host	NOUN
ma-105	34	12	basicviral	basicviral	ADJ
ma-105	34	13	infection	infection	NOUN
ma-105	34	14	model	model	NOUN
ma-105	34	15	proposed	propose	VERB
ma-105	34	16	in	in	ADP
ma-105	34	17	[	[	X
ma-105	34	18	31	31	NUM
ma-105	34	19	]	]	PUNCT
ma-105	34	20	to	to	PART
ma-105	34	21	study	study	VERB
ma-105	34	22	hiv	hiv	PROPN
ma-105	34	23	infection	infection	NOUN
ma-105	34	24	,	,	PUNCT
ma-105	34	25	and	and	CCONJ
ma-105	34	26	later	later	ADV
ma-105	34	27	adopted	adopt	VERB
ma-105	34	28	to	to	PART
ma-105	34	29	hbv	hbv	NOUN
ma-105	34	30	[	[	X
ma-105	34	31	8	8	NUM
ma-105	34	32	,	,	PUNCT
ma-105	34	33	32].particularly	32].particularly	PROPN
ma-105	34	34	,	,	PUNCT
ma-105	34	35	numerous	numerous	ADJ
ma-105	34	36	mathematical	mathematical	ADJ
ma-105	34	37	models	model	NOUN
ma-105	34	38	describing	describe	VERB
ma-105	34	39	the	the	DET
ma-105	34	40	temporal	temporal	ADJ
ma-105	34	41	dynamics	dynamic	NOUN
ma-105	34	42	of	of	ADP
ma-105	34	43	hcv	hcv	PROPN
ma-105	34	44	have	have	AUX
ma-105	34	45	beeninitially	beeninitially	ADV
ma-105	34	46	proposed	propose	VERB
ma-105	34	47	by	by	ADP
ma-105	34	48	neumann	neumann	PROPN
ma-105	34	49	and	and	CCONJ
ma-105	34	50	al	al	PROPN
ma-105	35	1	[	[	X
ma-105	35	2	30	30	NUM
ma-105	35	3	]	]	PUNCT
ma-105	35	4	using	use	VERB
ma-105	35	5	the	the	DET
ma-105	35	6	classical	classical	ADJ
ma-105	35	7	viral	viral	ADJ
ma-105	35	8	infection	infection	NOUN
ma-105	35	9	cellular	cellular	ADJ
ma-105	35	10	model	model	NOUN
ma-105	35	11	,	,	PUNCT
ma-105	35	12	andlater	andlater	ADJ
ma-105	35	13	have	have	AUX
ma-105	35	14	been	be	AUX
ma-105	35	15	extended	extend	VERB
ma-105	35	16	in	in	ADP
ma-105	35	17	[	[	X
ma-105	35	18	6	6	NUM
ma-105	35	19	,	,	PUNCT
ma-105	35	20	10	10	NUM
ma-105	35	21	,	,	PUNCT
ma-105	35	22	14	14	NUM
ma-105	35	23	,	,	PUNCT
ma-105	35	24	35	35	NUM
ma-105	35	25	]	]	PUNCT
ma-105	35	26	.	.	PUNCT
ma-105	36	1	motivated	motivate	VERB
ma-105	36	2	by	by	ADP
ma-105	36	3	what	what	PRON
ma-105	36	4	has	have	AUX
ma-105	36	5	been	be	AUX
ma-105	36	6	done	do	VERB
ma-105	36	7	in	in	ADP
ma-105	36	8	[	[	X
ma-105	36	9	8	8	NUM
ma-105	36	10	,	,	PUNCT
ma-105	36	11	30	30	NUM
ma-105	36	12	,	,	PUNCT
ma-105	36	13	32	32	NUM
ma-105	36	14	]	]	PUNCT
ma-105	36	15	,	,	PUNCT
ma-105	36	16	chongand	chongand	PROPN
ma-105	36	17	al	al	PROPN
ma-105	36	18	.	.	PUNCT
ma-105	37	1	[	[	X
ma-105	37	2	7	7	NUM
ma-105	37	3	]	]	PUNCT
ma-105	37	4	formulated	formulate	VERB
ma-105	37	5	the	the	DET
ma-105	37	6	basic	basic	ADJ
ma-105	37	7	hcv	hcv	PROPN
ma-105	37	8	temporal	temporal	ADJ
ma-105	37	9	intra	intra	ADJ
ma-105	37	10	-	-	ADJ
ma-105	37	11	host	host	ADJ
ma-105	37	12	model	model	NOUN
ma-105	37	13	with	with	ADP
ma-105	37	14	therapy	therapy	NOUN
ma-105	37	15	as	as	ADP
ma-105	37	16	a	a	DET
ma-105	37	17	system	system	NOUN
ma-105	37	18	of	of	ADP
ma-105	37	19	threedifferential	threedifferential	ADJ
ma-105	37	20	equations	equation	NOUN
ma-105	37	21	:	:	PUNCT
ma-105	37	22			X
ma-105	37	23	dh(t	dh(t	NUM
ma-105	37	24	)	)	PUNCT
ma-105	37	25	dt	dt	X
ma-105	38	1	=	=	SYM
ma-105	38	2	λ−	λ−	PROPN
ma-105	38	3	dh(t)−	dh(t)−	PROPN
ma-105	38	4	(	(	PUNCT
ma-105	38	5	1−	1−	NUM
ma-105	38	6	η)βh(t)v	η)βh(t)v	PROPN
ma-105	38	7	(	(	PUNCT
ma-105	38	8	t	t	PROPN
ma-105	38	9	)	)	PUNCT
ma-105	38	10	,	,	PUNCT
ma-105	38	11	di(t	di(t	NOUN
ma-105	38	12	)	)	PUNCT
ma-105	38	13	dt	dt	NOUN
ma-105	38	14	=	=	PUNCT
ma-105	38	15	(	(	PUNCT
ma-105	38	16	1−	1−	NUM
ma-105	38	17	η)βh(t)v	η)βh(t)v	INTJ
ma-105	38	18	(	(	PUNCT
ma-105	38	19	t)−	t)−	PROPN
ma-105	38	20	αi(t	αi(t	NOUN
ma-105	38	21	)	)	PUNCT
ma-105	38	22	,	,	PUNCT
ma-105	38	23	(	(	PUNCT
ma-105	38	24	1.1	1.1	NUM
ma-105	38	25	)	)	PUNCT
ma-105	38	26	dv	dv	PROPN
ma-105	38	27	(	(	PUNCT
ma-105	38	28	t	t	PROPN
ma-105	38	29	)	)	PUNCT
ma-105	38	30	dt	dt	NOUN
ma-105	38	31	=	=	PUNCT
ma-105	38	32	(	(	PUNCT
ma-105	38	33	1−	1−	NUM
ma-105	38	34	ε)ki(t)−	ε)ki(t)−	PROPN
ma-105	38	35	µv	µv	PROPN
ma-105	38	36	(	(	PUNCT
ma-105	38	37	t	t	PROPN
ma-105	38	38	)	)	PUNCT
ma-105	38	39	,	,	PUNCT
ma-105	38	40	where	where	SCONJ
ma-105	38	41	the	the	DET
ma-105	38	42	equations	equation	NOUN
ma-105	38	43	relate	relate	VERB
ma-105	38	44	the	the	DET
ma-105	38	45	dynamics	dynamic	NOUN
ma-105	38	46	relationship	relationship	NOUN
ma-105	38	47	between	between	ADP
ma-105	38	48	,	,	PUNCT
ma-105	38	49	h	h	NOUN
ma-105	38	50	as	as	ADP
ma-105	38	51	the	the	DET
ma-105	38	52	uninfected	uninfected	ADJ
ma-105	38	53	target	target	NOUN
ma-105	38	54	cells(hepatocytes	cells(hepatocyte	NOUN
ma-105	38	55	)	)	PUNCT
ma-105	38	56	,	,	PUNCT
ma-105	38	57	i	i	PRON
ma-105	38	58	as	as	ADP
ma-105	38	59	the	the	DET
ma-105	38	60	infected	infected	ADJ
ma-105	38	61	cells	cell	NOUN
ma-105	38	62	and	and	CCONJ
ma-105	38	63	v	v	NOUN
ma-105	38	64	as	as	ADP
ma-105	38	65	the	the	DET
ma-105	38	66	viral	viral	ADJ
ma-105	38	67	load	load	NOUN
ma-105	38	68	(	(	PUNCT
ma-105	38	69	amount	amount	NOUN
ma-105	38	70	of	of	ADP
ma-105	38	71	viruses	virus	NOUN
ma-105	38	72	present	present	ADJ
ma-105	38	73	in	in	ADP
ma-105	38	74	theliver	theliver	NOUN
ma-105	38	75	)	)	PUNCT
ma-105	38	76	.	.	PUNCT
ma-105	39	1	in	in	ADP
ma-105	39	2	the	the	DET
ma-105	39	3	system	system	NOUN
ma-105	39	4	(	(	PUNCT
ma-105	39	5	1.1	1.1	NUM
ma-105	39	6	)	)	PUNCT
ma-105	39	7	the	the	DET
ma-105	39	8	key	key	ADJ
ma-105	39	9	assumption	assumption	NOUN
ma-105	39	10	is	be	AUX
ma-105	39	11	that	that	SCONJ
ma-105	39	12	hepatocytes	hepatocyte	NOUN
ma-105	39	13	and	and	CCONJ
ma-105	39	14	viruses	virus	NOUN
ma-105	39	15	are	be	AUX
ma-105	39	16	well	well	ADV
ma-105	39	17	mixed	mixed	ADJ
ma-105	39	18	,	,	PUNCT
ma-105	39	19	andneglects	andneglect	VERB
ma-105	39	20	the	the	DET
ma-105	39	21	mobility	mobility	NOUN
ma-105	39	22	of	of	ADP
ma-105	39	23	hepatocytes	hepatocytes	PROPN
ma-105	39	24	c	c	NOUN
ma-105	39	25	viruses	virus	NOUN
ma-105	39	26	,	,	PUNCT
ma-105	39	27	the	the	DET
ma-105	39	28	infected	infected	ADJ
ma-105	39	29	and	and	CCONJ
ma-105	39	30	uninfected	uninfected	ADJ
ma-105	39	31	target	target	NOUN
ma-105	39	32	cells	cell	NOUN
ma-105	39	33	.	.	PUNCT
ma-105	40	1	to	to	ADP
ma-105	40	2	studythe	studythe	PRON
ma-105	40	3	influences	influence	NOUN
ma-105	40	4	of	of	ADP
ma-105	40	5	spatial	spatial	ADJ
ma-105	40	6	structures	structure	NOUN
ma-105	40	7	of	of	ADP
ma-105	40	8	virus	virus	NOUN
ma-105	40	9	dynamics	dynamic	NOUN
ma-105	40	10	,	,	PUNCT
ma-105	40	11	wang	wang	PROPN
ma-105	40	12	and	and	CCONJ
ma-105	40	13	wang	wang	PROPN
ma-105	40	14	in	in	ADP
ma-105	40	15	[	[	X
ma-105	40	16	39	39	NUM
ma-105	40	17	]	]	PUNCT
ma-105	40	18	assuming	assume	VERB
ma-105	40	19	that	that	SCONJ
ma-105	40	20	themotion	themotion	NOUN
ma-105	40	21	of	of	ADP
ma-105	40	22	virus	virus	NOUN
ma-105	40	23	follows	follow	VERB
ma-105	40	24	fickian	fickian	ADJ
ma-105	40	25	diffusion	diffusion	NOUN
ma-105	40	26	,	,	PUNCT
ma-105	40	27	that	that	PRON
ma-105	40	28	is	be	AUX
ma-105	40	29	to	to	PART
ma-105	40	30	say	say	VERB
ma-105	40	31	,	,	PUNCT
ma-105	40	32	the	the	DET
ma-105	40	33	population	population	NOUN
ma-105	40	34	flux	flux	NOUN
ma-105	40	35	of	of	ADP
ma-105	40	36	virus	virus	NOUN
ma-105	40	37	is	be	AUX
ma-105	40	38	proportionalto	proportionalto	NOUN
ma-105	40	39	the	the	DET
ma-105	40	40	concentration	concentration	NOUN
ma-105	40	41	gradient	gradient	NOUN
ma-105	40	42	and	and	CCONJ
ma-105	40	43	the	the	DET
ma-105	40	44	proportionality	proportionality	NOUN
ma-105	40	45	constant	constant	ADJ
ma-105	40	46	is	be	AUX
ma-105	40	47	taken	take	VERB
ma-105	40	48	to	to	PART
ma-105	40	49	be	be	AUX
ma-105	40	50	negative	negative	ADJ
ma-105	40	51	[	[	X
ma-105	40	52	13	13	NUM
ma-105	40	53	]	]	PUNCT
ma-105	40	54	.	.	PUNCT
ma-105	41	1	more	more	ADJ
ma-105	41	2	-	-	PUNCT
ma-105	41	3	over	over	ADV
ma-105	41	4	,	,	PUNCT
ma-105	41	5	in	in	ADP
ma-105	41	6	model	model	NOUN
ma-105	41	7	(	(	PUNCT
ma-105	41	8	1.1	1.1	NUM
ma-105	41	9	)	)	PUNCT
ma-105	41	10	,	,	PUNCT
ma-105	41	11	the	the	DET
ma-105	41	12	rate	rate	NOUN
ma-105	41	13	of	of	ADP
ma-105	41	14	infection	infection	NOUN
ma-105	41	15	is	be	AUX
ma-105	41	16	assumed	assume	VERB
ma-105	41	17	to	to	PART
ma-105	41	18	be	be	AUX
ma-105	41	19	bilinear	bilinear	ADJ
ma-105	41	20	in	in	ADP
ma-105	41	21	the	the	DET
ma-105	41	22	virus	virus	NOUN
ma-105	41	23	v	v	NOUN
ma-105	41	24	and	and	CCONJ
ma-105	41	25	uninfectedhepatocytes	uninfectedhepatocyte	VERB
ma-105	41	26	t.	t.	NOUN
ma-105	41	27	it	it	PRON
ma-105	41	28	is	be	AUX
ma-105	41	29	shown	show	VERB
ma-105	41	30	in	in	ADP
ma-105	41	31	[	[	X
ma-105	41	32	29	29	NUM
ma-105	41	33	]	]	PUNCT
ma-105	41	34	that	that	SCONJ
ma-105	41	35	this	this	DET
ma-105	41	36	bilinear	bilinear	ADJ
ma-105	41	37	rate	rate	NOUN
ma-105	41	38	of	of	ADP
ma-105	41	39	infection	infection	NOUN
ma-105	41	40	could	could	AUX
ma-105	41	41	be	be	AUX
ma-105	41	42	unrealistic	unrealistic	ADJ
ma-105	41	43	.	.	PUNCT
ma-105	42	1	however	however	ADV
ma-105	42	2	,	,	PUNCT
ma-105	42	3	the	the	DET
ma-105	42	4	actual	actual	ADJ
ma-105	42	5	incidence	incidence	NOUN
ma-105	42	6	rate	rate	NOUN
ma-105	42	7	is	be	AUX
ma-105	42	8	probably	probably	ADV
ma-105	42	9	not	not	PART
ma-105	42	10	linear	linear	ADJ
ma-105	42	11	over	over	ADP
ma-105	42	12	the	the	DET
ma-105	42	13	entire	entire	ADJ
ma-105	42	14	range	range	NOUN
ma-105	42	15	of	of	ADP
ma-105	42	16	t	t	PROPN
ma-105	42	17	and	and	CCONJ
ma-105	42	18	v.	v.	CCONJ
ma-105	42	19	thus	thus	ADV
ma-105	42	20	is	be	AUX
ma-105	42	21	reason	reason	NOUN
ma-105	42	22	-	-	PUNCT
ma-105	42	23	able	able	ADJ
ma-105	42	24	to	to	PART
ma-105	42	25	assume	assume	VERB
ma-105	42	26	that	that	SCONJ
ma-105	42	27	the	the	DET
ma-105	42	28	infection	infection	NOUN
ma-105	42	29	rate	rate	NOUN
ma-105	42	30	is	be	AUX
ma-105	42	31	given	give	VERB
ma-105	42	32	by	by	ADP
ma-105	42	33	a	a	DET
ma-105	42	34	more	more	ADV
ma-105	42	35	general	general	ADJ
ma-105	42	36	one	one	NOUN
ma-105	42	37	,	,	PUNCT
ma-105	42	38	known	know	VERB
ma-105	42	39	as	as	ADP
ma-105	42	40	the	the	DET
ma-105	42	41	hattaf	hattaf	NOUN
ma-105	42	42	-	-	PUNCT
ma-105	42	43	yousfi	yousfi	NOUN
ma-105	42	44	https://doi.org/10.28924/ada/ma.3.1	https://doi.org/10.28924/ada/ma.3.1	PROPN
ma-105	42	45	eur	eur	PROPN
ma-105	42	46	.	.	PUNCT
ma-105	43	1	j.	j.	PROPN
ma-105	43	2	math	math	PROPN
ma-105	43	3	.	.	PUNCT
ma-105	44	1	anal	anal	PROPN
ma-105	44	2	.	.	PUNCT
ma-105	45	1	10.28924	10.28924	NUM
ma-105	45	2	/	/	SYM
ma-105	45	3	ada	ada	PROPN
ma-105	45	4	/	/	SYM
ma-105	45	5	ma.3.1	ma.3.1	PROPN
ma-105	45	6	3	3	NUM
ma-105	45	7	functional	functional	ADJ
ma-105	45	8	response	response	NOUN
ma-105	45	9	[	[	X
ma-105	45	10	18	18	NUM
ma-105	45	11	]	]	PUNCT
ma-105	45	12	of	of	ADP
ma-105	45	13	the	the	DET
ma-105	45	14	form	form	NOUN
ma-105	45	15	βhv	βhv	NOUN
ma-105	45	16	α0+α1h+α2v	α0+α1h+α2v	ADP
ma-105	45	17	+	+	NOUN
ma-105	45	18	α3hv	α3hv	NOUN
ma-105	45	19	where	where	SCONJ
ma-105	45	20	α0	α0	ADJ
ma-105	45	21	>	>	X
ma-105	45	22	0	0	NUM
ma-105	45	23	,	,	PUNCT
ma-105	45	24	α1	α1	X
ma-105	45	25	≥	≥	NUM
ma-105	45	26	0	0	NUM
ma-105	45	27	,	,	PUNCT
ma-105	45	28	α2	α2	PROPN
ma-105	45	29	≥	≥	NOUN
ma-105	45	30	0	0	NUM
ma-105	45	31	,	,	PUNCT
ma-105	45	32	α3	α3	PROPN
ma-105	45	33	≥	≥	NOUN
ma-105	45	34	0are	0are	PROPN
ma-105	45	35	constants	constant	NOUN
ma-105	45	36	.	.	PUNCT
ma-105	46	1	the	the	DET
ma-105	46	2	function	function	NOUN
ma-105	46	3	βh	βh	ADP
ma-105	46	4	α0+α1h+α2v	α0+α1h+α2v	NUM
ma-105	46	5	+	+	NOUN
ma-105	46	6	α3hv	α3hv	NOUN
ma-105	46	7	satisfies	satisfy	VERB
ma-105	46	8	the	the	DET
ma-105	46	9	hypotheses	hypothesis	NOUN
ma-105	46	10	(	(	PUNCT
ma-105	46	11	h1	h1	PROPN
ma-105	46	12	)	)	PUNCT
ma-105	46	13	,	,	PUNCT
ma-105	46	14	(	(	PUNCT
ma-105	46	15	h2	h2	NOUN
ma-105	46	16	)	)	PUNCT
ma-105	46	17	and	and	CCONJ
ma-105	46	18	(	(	PUNCT
ma-105	46	19	h3	h3	NOUN
ma-105	46	20	)	)	PUNCT
ma-105	46	21	ofgeneral	ofgeneral	ADJ
ma-105	46	22	incidence	incidence	NOUN
ma-105	46	23	rate	rate	NOUN
ma-105	46	24	presented	present	VERB
ma-105	46	25	in	in	ADP
ma-105	46	26	[	[	X
ma-105	46	27	16,19–21	16,19–21	NUM
ma-105	46	28	]	]	PUNCT
ma-105	46	29	.	.	PUNCT
ma-105	47	1	the	the	DET
ma-105	47	2	hattaf	hattaf	NOUN
ma-105	47	3	-	-	PUNCT
ma-105	47	4	yousfi	yousfi	ADJ
ma-105	47	5	type	type	NOUN
ma-105	47	6	of	of	ADP
ma-105	47	7	functional	functional	ADJ
ma-105	47	8	response	response	NOUN
ma-105	47	9	wasintroduced	wasintroduce	VERB
ma-105	47	10	by	by	ADP
ma-105	47	11	hattaf	hattaf	NOUN
ma-105	47	12	and	and	CCONJ
ma-105	47	13	al	al	PROPN
ma-105	47	14	.	.	PUNCT
ma-105	48	1	[	[	X
ma-105	48	2	18	18	NUM
ma-105	48	3	]	]	PUNCT
ma-105	48	4	.	.	PUNCT
ma-105	49	1	this	this	DET
ma-105	49	2	functional	functional	ADJ
ma-105	49	3	response	response	NOUN
ma-105	49	4	generalizes	generalize	VERB
ma-105	49	5	many	many	ADJ
ma-105	49	6	functional	functional	ADJ
ma-105	49	7	responsesand	responsesand	NOUN
ma-105	49	8	it	it	PRON
ma-105	49	9	was	be	AUX
ma-105	49	10	used	use	VERB
ma-105	49	11	in	in	ADP
ma-105	49	12	[	[	X
ma-105	49	13	34	34	NUM
ma-105	49	14	]	]	PUNCT
ma-105	49	15	to	to	PART
ma-105	49	16	describe	describe	VERB
ma-105	49	17	the	the	DET
ma-105	49	18	dynamics	dynamic	NOUN
ma-105	49	19	of	of	ADP
ma-105	49	20	labour	labour	NOUN
ma-105	49	21	market	market	NOUN
ma-105	49	22	.	.	PUNCT
ma-105	50	1	thus	thus	ADV
ma-105	50	2	,	,	PUNCT
ma-105	50	3	when	when	SCONJ
ma-105	50	4	α0	α0	ADJ
ma-105	50	5	=	=	SYM
ma-105	50	6	1	1	NUM
ma-105	50	7	,	,	PUNCT
ma-105	50	8	the	the	DET
ma-105	50	9	hattaf	hattaf	NOUN
ma-105	50	10	-	-	PUNCT
ma-105	50	11	yousfi	yousfi	ADJ
ma-105	50	12	functional	functional	ADJ
ma-105	50	13	response	response	NOUN
ma-105	50	14	is	be	AUX
ma-105	50	15	reduced	reduce	VERB
ma-105	50	16	to	to	ADP
ma-105	50	17	the	the	DET
ma-105	50	18	specific	specific	ADJ
ma-105	50	19	functional	functional	ADJ
ma-105	50	20	response	response	NOUN
ma-105	50	21	used	use	VERB
ma-105	50	22	by	by	ADP
ma-105	50	23	hattaf	hattaf	NOUN
ma-105	50	24	and	and	CCONJ
ma-105	50	25	alin	alin	PROPN
ma-105	50	26	[	[	X
ma-105	50	27	17	17	NUM
ma-105	50	28	]	]	PUNCT
ma-105	50	29	.	.	PUNCT
ma-105	51	1	furthermore	furthermore	ADV
ma-105	51	2	,	,	PUNCT
ma-105	51	3	if	if	SCONJ
ma-105	51	4	α3	α3	ADJ
ma-105	51	5	=	=	SYM
ma-105	51	6	α1α2	α1α2	PUNCT
ma-105	51	7	and	and	CCONJ
ma-105	51	8	α0	α0	ADJ
ma-105	51	9	=	=	SYM
ma-105	51	10	1	1	NUM
ma-105	51	11	,	,	PUNCT
ma-105	51	12	the	the	DET
ma-105	51	13	hattaf	hattaf	NOUN
ma-105	51	14	-	-	PUNCT
ma-105	51	15	yousfi	yousfi	ADJ
ma-105	51	16	functional	functional	ADJ
ma-105	51	17	response	response	NOUN
ma-105	51	18	is	be	AUX
ma-105	51	19	reducedto	reducedto	PROPN
ma-105	51	20	crowley	crowley	PROPN
ma-105	51	21	-	-	PUNCT
ma-105	51	22	martin	martin	PROPN
ma-105	51	23	functional	functional	ADJ
ma-105	51	24	response	response	NOUN
ma-105	51	25	[	[	X
ma-105	51	26	9	9	NUM
ma-105	51	27	]	]	PUNCT
ma-105	51	28	and	and	CCONJ
ma-105	51	29	was	be	AUX
ma-105	51	30	used	use	VERB
ma-105	51	31	in	in	ADP
ma-105	51	32	[	[	X
ma-105	51	33	43	43	NUM
ma-105	51	34	]	]	PUNCT
ma-105	51	35	.	.	PUNCT
ma-105	52	1	when	when	SCONJ
ma-105	52	2	α3	α3	PROPN
ma-105	52	3	=	=	SYM
ma-105	52	4	0	0	NUM
ma-105	52	5	et	et	NOUN
ma-105	52	6	α0	α0	ADJ
ma-105	52	7	=	=	SYM
ma-105	52	8	1	1	NUM
ma-105	52	9	thehattaf	thehattaf	NOUN
ma-105	52	10	-	-	PUNCT
ma-105	52	11	yousfi	yousfi	NOUN
ma-105	52	12	functional	functional	ADJ
ma-105	52	13	response	response	NOUN
ma-105	52	14	is	be	AUX
ma-105	52	15	simplified	simplify	VERB
ma-105	52	16	to	to	ADP
ma-105	52	17	beddington	beddington	PROPN
ma-105	52	18	-	-	PUNCT
ma-105	52	19	deangelis	deangelis	PROPN
ma-105	52	20	functional	functional	ADJ
ma-105	52	21	response	response	NOUN
ma-105	52	22	[	[	X
ma-105	52	23	5,11],and	5,11],and	NUM
ma-105	52	24	was	be	AUX
ma-105	52	25	used	use	VERB
ma-105	52	26	in	in	ADP
ma-105	52	27	[	[	X
ma-105	52	28	25	25	NUM
ma-105	52	29	,	,	PUNCT
ma-105	52	30	26	26	NUM
ma-105	52	31	,	,	PUNCT
ma-105	52	32	38	38	NUM
ma-105	52	33	,	,	PUNCT
ma-105	52	34	42	42	NUM
ma-105	52	35	]	]	PUNCT
ma-105	52	36	.	.	PUNCT
ma-105	53	1	when	when	SCONJ
ma-105	53	2	α1	α1	PROPN
ma-105	53	3	>	>	X
ma-105	53	4	0	0	NUM
ma-105	53	5	,	,	PUNCT
ma-105	53	6	α2	α2	NOUN
ma-105	53	7	=	=	SYM
ma-105	53	8	α3	α3	NOUN
ma-105	53	9	=	=	SYM
ma-105	53	10	0	0	NUM
ma-105	53	11	and	and	CCONJ
ma-105	53	12	α0	α0	ADJ
ma-105	53	13	=	=	SYM
ma-105	53	14	1	1	NUM
ma-105	53	15	,	,	PUNCT
ma-105	53	16	the	the	DET
ma-105	53	17	hattaf	hattaf	NOUN
ma-105	53	18	-	-	PUNCT
ma-105	53	19	yousfifunctional	yousfifunctional	ADJ
ma-105	53	20	response	response	NOUN
ma-105	53	21	is	be	AUX
ma-105	53	22	reduced	reduce	VERB
ma-105	53	23	to	to	ADP
ma-105	53	24	holling	holle	VERB
ma-105	53	25	type	type	NOUN
ma-105	53	26	ii	ii	NOUN
ma-105	53	27	functional	functional	ADJ
ma-105	53	28	response	response	NOUN
ma-105	53	29	[	[	X
ma-105	53	30	28	28	NUM
ma-105	53	31	]	]	PUNCT
ma-105	53	32	.	.	PUNCT
ma-105	54	1	and	and	CCONJ
ma-105	54	2	when	when	SCONJ
ma-105	54	3	α1	α1	PROPN
ma-105	54	4	=	=	SYM
ma-105	54	5	α3	α3	NOUN
ma-105	54	6	=	=	SYM
ma-105	54	7	0	0	NUM
ma-105	54	8	,	,	PUNCT
ma-105	54	9	α2	α2	ADV
ma-105	54	10	>	>	X
ma-105	54	11	0	0	PUNCT
ma-105	55	1	and	and	CCONJ
ma-105	55	2	α0	α0	ADJ
ma-105	55	3	=	=	SYM
ma-105	55	4	1	1	NUM
ma-105	55	5	it	it	PRON
ma-105	55	6	expresses	express	VERB
ma-105	55	7	a	a	DET
ma-105	55	8	saturation	saturation	NOUN
ma-105	55	9	response	response	NOUN
ma-105	55	10	[	[	X
ma-105	55	11	36	36	NUM
ma-105	55	12	]	]	PUNCT
ma-105	55	13	.	.	PUNCT
ma-105	56	1	moreover	moreover	ADV
ma-105	56	2	,	,	PUNCT
ma-105	56	3	when	when	SCONJ
ma-105	56	4	α1	α1	PROPN
ma-105	56	5	=	=	SYM
ma-105	56	6	α2	α2	ADJ
ma-105	56	7	=	=	SYM
ma-105	56	8	α3	α3	NOUN
ma-105	56	9	=	=	SYM
ma-105	56	10	0,and	0,and	NUM
ma-105	56	11	α0	α0	ADJ
ma-105	56	12	=	=	SYM
ma-105	56	13	1	1	NUM
ma-105	56	14	the	the	DET
ma-105	56	15	hattaf	hattaf	NOUN
ma-105	56	16	-	-	PUNCT
ma-105	56	17	yousfi	yousfi	ADJ
ma-105	56	18	functional	functional	ADJ
ma-105	56	19	response	response	NOUN
ma-105	56	20	is	be	AUX
ma-105	56	21	reduced	reduce	VERB
ma-105	56	22	to	to	ADP
ma-105	56	23	the	the	DET
ma-105	56	24	mass	mass	ADJ
ma-105	56	25	action	action	NOUN
ma-105	56	26	principle(or	principle(or	NOUN
ma-105	56	27	hollingtype	hollingtype	NOUN
ma-105	56	28	i	i	PRON
ma-105	56	29	functional	functional	ADJ
ma-105	56	30	response	response	NOUN
ma-105	56	31	)	)	PUNCT
ma-105	56	32	.	.	PUNCT
ma-105	57	1	also	also	ADV
ma-105	57	2	ordinary	ordinary	ADJ
ma-105	57	3	differential	differential	ADJ
ma-105	57	4	system	system	NOUN
ma-105	57	5	(	(	PUNCT
ma-105	57	6	1.1	1.1	NUM
ma-105	57	7	)	)	PUNCT
ma-105	57	8	do	do	AUX
ma-105	57	9	n’t	not	PART
ma-105	57	10	take	take	VERB
ma-105	57	11	into	into	ADP
ma-105	57	12	consideration	consideration	NOUN
ma-105	57	13	thecure	thecure	NOUN
ma-105	57	14	of	of	ADP
ma-105	57	15	infected	infected	ADJ
ma-105	57	16	hepatocytes	hepatocyte	NOUN
ma-105	57	17	.	.	PUNCT
ma-105	58	1	in	in	ADP
ma-105	58	2	this	this	DET
ma-105	58	3	work	work	NOUN
ma-105	58	4	,	,	PUNCT
ma-105	58	5	motivated	motivate	VERB
ma-105	58	6	by	by	ADP
ma-105	58	7	the	the	DET
ma-105	58	8	breaches	breach	NOUN
ma-105	58	9	observed	observe	VERB
ma-105	58	10	in	in	ADP
ma-105	58	11	the	the	DET
ma-105	58	12	analysis	analysis	NOUN
ma-105	58	13	andthe	andthe	ADJ
ma-105	58	14	formulation	formulation	NOUN
ma-105	58	15	of	of	ADP
ma-105	58	16	system	system	NOUN
ma-105	58	17	(	(	PUNCT
ma-105	58	18	1.1	1.1	NUM
ma-105	58	19	)	)	PUNCT
ma-105	58	20	,	,	PUNCT
ma-105	58	21	we	we	PRON
ma-105	58	22	construct	construct	VERB
ma-105	58	23	and	and	CCONJ
ma-105	58	24	analyze	analyze	VERB
ma-105	58	25	a	a	DET
ma-105	58	26	partial	partial	ADJ
ma-105	58	27	differential	differential	NOUN
ma-105	58	28	equation	equation	NOUN
ma-105	58	29	(	(	PUNCT
ma-105	58	30	pde)-cellular	pde)-cellular	ADJ
ma-105	58	31	model	model	NOUN
ma-105	58	32	system	system	NOUN
ma-105	58	33	for	for	ADP
ma-105	58	34	hcv	hcv	NOUN
ma-105	58	35	infection	infection	NOUN
ma-105	58	36	,	,	PUNCT
ma-105	58	37	which	which	PRON
ma-105	58	38	derives	derive	VERB
ma-105	58	39	from	from	ADP
ma-105	58	40	system	system	NOUN
ma-105	58	41	(	(	PUNCT
ma-105	58	42	1.1	1.1	NUM
ma-105	58	43	)	)	PUNCT
ma-105	58	44	by	by	ADP
ma-105	58	45	incorporating	incorporate	VERB
ma-105	58	46	the	the	DET
ma-105	58	47	space	space	NOUN
ma-105	58	48	,	,	PUNCT
ma-105	58	49	hattaf	hattaf	NOUN
ma-105	58	50	-	-	PUNCT
ma-105	58	51	yousfi	yousfi	ADJ
ma-105	58	52	incidence	incidence	NOUN
ma-105	58	53	rate	rate	NOUN
ma-105	58	54	,	,	PUNCT
ma-105	58	55	absorption	absorption	NOUN
ma-105	58	56	effect	effect	NOUN
ma-105	58	57	and	and	CCONJ
ma-105	58	58	spontaneous	spontaneous	ADJ
ma-105	58	59	cure	cure	NOUN
ma-105	58	60	.	.	PUNCT
ma-105	59	1	it	it	PRON
ma-105	59	2	is	be	AUX
ma-105	59	3	worth	worth	ADJ
ma-105	59	4	mentioning	mention	VERB
ma-105	59	5	thatin	thatin	PRON
ma-105	60	1	[	[	X
ma-105	60	2	7	7	X
ma-105	60	3	]	]	PUNCT
ma-105	60	4	the	the	DET
ma-105	60	5	authors	author	NOUN
ma-105	60	6	used	use	VERB
ma-105	60	7	mass	mass	ADJ
ma-105	60	8	-	-	PUNCT
ma-105	60	9	action	action	NOUN
ma-105	60	10	kinetics	kinetic	NOUN
ma-105	60	11	for	for	ADP
ma-105	60	12	viral	viral	ADJ
ma-105	60	13	infection	infection	NOUN
ma-105	60	14	,	,	PUNCT
ma-105	60	15	neglected	neglect	VERB
ma-105	60	16	the	the	DET
ma-105	60	17	cure	cure	NOUN
ma-105	60	18	rate	rate	NOUN
ma-105	60	19	,	,	PUNCT
ma-105	60	20	ignored	ignore	VERB
ma-105	60	21	theabsorption	theabsorption	NOUN
ma-105	60	22	effect	effect	NOUN
ma-105	60	23	and	and	CCONJ
ma-105	60	24	the	the	DET
ma-105	60	25	diffusion	diffusion	NOUN
ma-105	60	26	of	of	ADP
ma-105	60	27	free	free	ADJ
ma-105	60	28	virions	virion	NOUN
ma-105	60	29	,	,	PUNCT
ma-105	60	30	susceptible	susceptible	ADJ
ma-105	60	31	cells	cell	NOUN
ma-105	60	32	and	and	CCONJ
ma-105	60	33	infected	infected	ADJ
ma-105	60	34	cells	cell	NOUN
ma-105	60	35	.	.	PUNCT
ma-105	61	1	thus	thus	ADV
ma-105	61	2	theobtained	theobtaine	VERB
ma-105	61	3	model	model	NOUN
ma-105	61	4	is	be	AUX
ma-105	61	5	an	an	DET
ma-105	61	6	extension	extension	NOUN
ma-105	61	7	of	of	ADP
ma-105	61	8	the	the	DET
ma-105	61	9	one	one	NOUN
ma-105	61	10	in	in	ADP
ma-105	61	11	the	the	DET
ma-105	61	12	first	first	ADJ
ma-105	61	13	part	part	NOUN
ma-105	61	14	of	of	ADP
ma-105	61	15	the	the	DET
ma-105	61	16	work	work	NOUN
ma-105	61	17	done	do	VERB
ma-105	61	18	by	by	ADP
ma-105	61	19	chong	chong	PROPN
ma-105	61	20	et	et	PROPN
ma-105	61	21	al	al	PROPN
ma-105	61	22	.	.	PUNCT
ma-105	62	1	[	[	X
ma-105	62	2	7].the	7].the	DET
ma-105	62	3	work	work	NOUN
ma-105	62	4	is	be	AUX
ma-105	62	5	organized	organize	VERB
ma-105	62	6	as	as	SCONJ
ma-105	62	7	follows	follow	VERB
ma-105	62	8	.	.	PUNCT
ma-105	63	1	in	in	ADP
ma-105	63	2	section	section	NOUN
ma-105	63	3	2	2	NUM
ma-105	63	4	,	,	PUNCT
ma-105	63	5	we	we	PRON
ma-105	63	6	model	model	VERB
ma-105	63	7	the	the	DET
ma-105	63	8	phenomenon	phenomenon	NOUN
ma-105	63	9	described	describe	VERB
ma-105	63	10	througha	througha	PROPN
ma-105	63	11	reaction	reaction	NOUN
ma-105	63	12	-	-	PUNCT
ma-105	63	13	diffusion	diffusion	NOUN
ma-105	63	14	equations	equation	NOUN
ma-105	63	15	which	which	PRON
ma-105	63	16	leads	lead	VERB
ma-105	63	17	to	to	ADP
ma-105	63	18	a	a	DET
ma-105	63	19	initial	initial	ADJ
ma-105	63	20	value	value	NOUN
ma-105	63	21	and	and	CCONJ
ma-105	63	22	boundary	boundary	ADJ
ma-105	63	23	problem	problem	NOUN
ma-105	63	24	.	.	PUNCT
ma-105	64	1	section	section	NOUN
ma-105	64	2	3is	3is	PROPN
ma-105	64	3	devoted	devote	VERB
ma-105	64	4	to	to	ADP
ma-105	64	5	the	the	DET
ma-105	64	6	study	study	NOUN
ma-105	64	7	of	of	ADP
ma-105	64	8	the	the	DET
ma-105	64	9	existence	existence	NOUN
ma-105	64	10	and	and	CCONJ
ma-105	64	11	uniqueness	uniqueness	NOUN
ma-105	64	12	of	of	ADP
ma-105	64	13	the	the	DET
ma-105	64	14	global	global	ADJ
ma-105	64	15	solution	solution	NOUN
ma-105	64	16	of	of	ADP
ma-105	64	17	our	our	PRON
ma-105	64	18	initial	initial	ADJ
ma-105	64	19	andboundary	andboundary	ADJ
ma-105	64	20	value	value	NOUN
ma-105	64	21	problem	problem	NOUN
ma-105	64	22	,	,	PUNCT
ma-105	64	23	and	and	CCONJ
ma-105	64	24	of	of	ADP
ma-105	64	25	the	the	DET
ma-105	64	26	properties	property	NOUN
ma-105	64	27	of	of	ADP
ma-105	64	28	this	this	DET
ma-105	64	29	solution	solution	NOUN
ma-105	64	30	,	,	PUNCT
ma-105	64	31	namely	namely	ADV
ma-105	64	32	positivity	positivity	NOUN
ma-105	64	33	and	and	CCONJ
ma-105	64	34	bounded	bound	VERB
ma-105	64	35	-	-	PUNCT
ma-105	64	36	ness	ness	NOUN
ma-105	64	37	.	.	PUNCT
ma-105	65	1	section	section	NOUN
ma-105	65	2	4	4	NUM
ma-105	65	3	deals	deal	NOUN
ma-105	65	4	with	with	ADP
ma-105	65	5	the	the	DET
ma-105	65	6	stability	stability	NOUN
ma-105	65	7	and	and	CCONJ
ma-105	65	8	the	the	DET
ma-105	65	9	analysis	analysis	NOUN
ma-105	65	10	of	of	ADP
ma-105	65	11	spatially	spatially	ADV
ma-105	65	12	homogeneous	homogeneous	ADJ
ma-105	65	13	equilibria	equilibrium	NOUN
ma-105	65	14	andnumerical	andnumerical	ADJ
ma-105	65	15	simulations	simulation	NOUN
ma-105	65	16	in	in	ADP
ma-105	65	17	section	section	NOUN
ma-105	65	18	5	5	NUM
ma-105	65	19	.	.	PUNCT
ma-105	66	1	we	we	PRON
ma-105	66	2	conclude	conclude	VERB
ma-105	66	3	our	our	PRON
ma-105	66	4	work	work	NOUN
ma-105	66	5	and	and	CCONJ
ma-105	66	6	provide	provide	VERB
ma-105	66	7	a	a	DET
ma-105	66	8	discussion	discussion	NOUN
ma-105	66	9	in	in	ADP
ma-105	66	10	section	section	NOUN
ma-105	66	11	6	6	NUM
ma-105	66	12	.	.	NOUN
ma-105	66	13	2	2	NUM
ma-105	66	14	.	.	X
ma-105	66	15	formulation	formulation	NOUN
ma-105	66	16	of	of	ADP
ma-105	66	17	the	the	DET
ma-105	66	18	pde	pde	NOUN
ma-105	66	19	-	-	PUNCT
ma-105	66	20	cellular	cellular	ADJ
ma-105	66	21	model	model	NOUN
ma-105	66	22	let	let	VERB
ma-105	66	23	ω	ω	PROPN
ma-105	66	24	⊂	⊂	PROPN
ma-105	66	25	r3	r3	PROPN
ma-105	66	26	be	be	AUX
ma-105	66	27	a	a	DET
ma-105	66	28	bounded	bounded	ADJ
ma-105	66	29	connected	connected	ADJ
ma-105	66	30	domain	domain	NOUN
ma-105	66	31	representing	represent	VERB
ma-105	66	32	the	the	DET
ma-105	66	33	liver	liver	NOUN
ma-105	66	34	.	.	PUNCT
ma-105	67	1	let	let	VERB
ma-105	67	2	t	t	PROPN
ma-105	67	3	≥	≥	PRON
ma-105	67	4	0	0	NUM
ma-105	67	5	be	be	AUX
ma-105	67	6	a	a	DET
ma-105	67	7	given	give	VERB
ma-105	67	8	timeand	timeand	NOUN
ma-105	67	9	x	x	AUX
ma-105	67	10	=	=	SYM
ma-105	67	11	(	(	PUNCT
ma-105	67	12	x1	x1	PROPN
ma-105	67	13	,	,	PUNCT
ma-105	67	14	x2	x2	PROPN
ma-105	67	15	,	,	PUNCT
ma-105	67	16	x3	x3	ADJ
ma-105	67	17	)	)	PUNCT
ma-105	67	18	∈	∈	PROPN
ma-105	67	19	ω	ω	PROPN
ma-105	67	20	.	.	PROPN
ma-105	67	21	denote	denote	VERB
ma-105	67	22	respectively	respectively	ADV
ma-105	67	23	by	by	ADP
ma-105	67	24	h(x	h(x	PROPN
ma-105	67	25	,	,	PUNCT
ma-105	67	26	t	t	PROPN
ma-105	67	27	)	)	PUNCT
ma-105	67	28	,	,	PUNCT
ma-105	67	29	i(x	i(x	PROPN
ma-105	67	30	,	,	PUNCT
ma-105	67	31	t	t	PROPN
ma-105	67	32	)	)	PUNCT
ma-105	67	33	and	and	CCONJ
ma-105	67	34	v	v	NOUN
ma-105	67	35	(	(	PUNCT
ma-105	67	36	x	x	NOUN
ma-105	67	37	,	,	PUNCT
ma-105	67	38	t	t	PROPN
ma-105	67	39	)	)	PUNCT
ma-105	67	40	the	the	DET
ma-105	67	41	concentrations	concentration	NOUN
ma-105	67	42	ofhealthy	ofhealthy	ADJ
ma-105	67	43	hepatocytes	hepatocyte	NOUN
ma-105	67	44	,	,	PUNCT
ma-105	67	45	hcv	hcv	X
ma-105	67	46	infected	infect	VERB
ma-105	67	47	hepatocytes	hepatocyte	NOUN
ma-105	67	48	,	,	PUNCT
ma-105	67	49	and	and	CCONJ
ma-105	67	50	free	free	ADJ
ma-105	67	51	hcv	hcv	NOUN
ma-105	67	52	virions	virion	NOUN
ma-105	67	53	at	at	ADP
ma-105	67	54	time	time	NOUN
ma-105	67	55	t	t	NOUN
ma-105	67	56	and	and	CCONJ
ma-105	67	57	location	location	NOUN
ma-105	67	58	x	x	X
ma-105	67	59	.	.	PUNCT
ma-105	68	1	thedynamics	thedynamic	NOUN
ma-105	68	2	of	of	ADP
ma-105	68	3	hcv	hcv	PROPN
ma-105	68	4	infection	infection	NOUN
ma-105	68	5	intra	intra	ADJ
ma-105	68	6	-	-	ADJ
ma-105	68	7	host	host	NOUN
ma-105	68	8	is	be	AUX
ma-105	68	9	the	the	DET
ma-105	68	10	result	result	NOUN
ma-105	68	11	of	of	ADP
ma-105	68	12	the	the	DET
ma-105	68	13	dynamics	dynamic	NOUN
ma-105	68	14	of	of	ADP
ma-105	68	15	each	each	DET
ma-105	68	16	compartment	compartment	NOUN
ma-105	68	17	h	h	NOUN
ma-105	68	18	,	,	PUNCT
ma-105	68	19	i	i	PRON
ma-105	68	20	,	,	PUNCT
ma-105	68	21	andv	andv	PROPN
ma-105	68	22	,	,	PUNCT
ma-105	68	23	and	and	CCONJ
ma-105	68	24	the	the	DET
ma-105	68	25	various	various	ADJ
ma-105	68	26	interactions	interaction	NOUN
ma-105	68	27	between	between	ADP
ma-105	68	28	them	they	PRON
ma-105	68	29	.	.	PUNCT
ma-105	69	1	we	we	PRON
ma-105	69	2	now	now	ADV
ma-105	69	3	describe	describe	VERB
ma-105	69	4	the	the	DET
ma-105	69	5	evolution	evolution	NOUN
ma-105	69	6	of	of	ADP
ma-105	69	7	each	each	DET
ma-105	69	8	compartment	compartment	NOUN
ma-105	69	9	.	.	PUNCT
ma-105	70	1	2.1	2.1	NUM
ma-105	70	2	.	.	PUNCT
ma-105	70	3	fluctuation	fluctuation	NOUN
ma-105	70	4	of	of	ADP
ma-105	70	5	healthy	healthy	ADJ
ma-105	70	6	hepatocytes	hepatocyte	NOUN
ma-105	70	7	.	.	PUNCT
ma-105	71	1	let	let	VERB
ma-105	71	2	ν	ν	NOUN
ma-105	71	3	be	be	AUX
ma-105	71	4	an	an	DET
ma-105	71	5	elementary	elementary	ADJ
ma-105	71	6	volume	volume	NOUN
ma-105	71	7	in	in	ADP
ma-105	71	8	ω	ω	PROPN
ma-105	71	9	.	.	PUNCT
ma-105	72	1	the	the	DET
ma-105	72	2	variation	variation	NOUN
ma-105	72	3	ofthe	ofthe	NOUN
ma-105	72	4	quantity	quantity	NOUN
ma-105	72	5	of	of	ADP
ma-105	72	6	healthy	healthy	ADJ
ma-105	72	7	hepatocytes	hepatocyte	NOUN
ma-105	72	8	in	in	ADP
ma-105	72	9	ν	ν	NOUN
ma-105	72	10	is	be	AUX
ma-105	72	11	described	describe	VERB
ma-105	72	12	under	under	ADP
ma-105	72	13	the	the	DET
ma-105	72	14	following	follow	VERB
ma-105	72	15	assumptions	assumption	NOUN
ma-105	72	16	.	.	PUNCT
ma-105	73	1	healthy	healthy	ADJ
ma-105	73	2	https://doi.org/10.28924/ada/ma.3.1	https://doi.org/10.28924/ada/ma.3.1	PROPN
ma-105	73	3	eur	eur	PROPN
ma-105	73	4	.	.	PUNCT
ma-105	74	1	j.	j.	PROPN
ma-105	74	2	math	math	PROPN
ma-105	74	3	.	.	PUNCT
ma-105	75	1	anal	anal	PROPN
ma-105	75	2	.	.	PUNCT
ma-105	76	1	10.28924	10.28924	NUM
ma-105	76	2	/	/	SYM
ma-105	76	3	ada	ada	PROPN
ma-105	76	4	/	/	SYM
ma-105	76	5	ma.3.1	ma.3.1	PROPN
ma-105	76	6	4hepatocytes	4hepatocyte	NOUN
ma-105	76	7	are	be	AUX
ma-105	76	8	produced	produce	VERB
ma-105	76	9	at	at	ADP
ma-105	76	10	constant	constant	ADJ
ma-105	76	11	rate	rate	NOUN
ma-105	76	12	λ	λ	PROPN
ma-105	76	13	from	from	ADP
ma-105	76	14	the	the	DET
ma-105	76	15	bone	bone	NOUN
ma-105	76	16	narrow	narrow	NOUN
ma-105	76	17	and	and	CCONJ
ma-105	76	18	die	die	VERB
ma-105	76	19	at	at	ADP
ma-105	76	20	rate	rate	NOUN
ma-105	76	21	dh	dh	PROPN
ma-105	76	22	.	.	PUNCT
ma-105	77	1	virions	virion	NOUN
ma-105	77	2	infectthe	infectthe	DET
ma-105	77	3	healthy	healthy	ADJ
ma-105	77	4	hepatocytes	hepatocyte	NOUN
ma-105	77	5	at	at	ADP
ma-105	77	6	the	the	DET
ma-105	77	7	rate	rate	NOUN
ma-105	77	8	βhv	βhv	NOUN
ma-105	77	9	α0+α1h+α2v	α0+α1h+α2v	ADP
ma-105	77	10	+	+	NOUN
ma-105	77	11	α3hv	α3hv	NOUN
ma-105	77	12	,	,	PUNCT
ma-105	77	13	where	where	SCONJ
ma-105	77	14	β	β	PROPN
ma-105	77	15	is	be	AUX
ma-105	77	16	the	the	DET
ma-105	77	17	rate	rate	NOUN
ma-105	77	18	of	of	ADP
ma-105	77	19	transmission	transmission	NOUN
ma-105	77	20	of	of	ADP
ma-105	77	21	theinfection	theinfection	NOUN
ma-105	77	22	and	and	CCONJ
ma-105	77	23	αj	αj	NOUN
ma-105	77	24	,	,	PUNCT
ma-105	77	25	j	j	PROPN
ma-105	77	26	=	=	SYM
ma-105	77	27	0	0	NUM
ma-105	77	28	,	,	PUNCT
ma-105	77	29	1	1	NUM
ma-105	77	30	,	,	PUNCT
ma-105	77	31	2	2	NUM
ma-105	77	32	,	,	PUNCT
ma-105	77	33	3	3	NUM
ma-105	77	34	are	be	AUX
ma-105	77	35	positive	positive	ADJ
ma-105	77	36	constants	constant	NOUN
ma-105	77	37	.	.	PUNCT
ma-105	78	1	this	this	DET
ma-105	78	2	generalized	generalized	ADJ
ma-105	78	3	incidence	incidence	NOUN
ma-105	78	4	function	function	VERB
ma-105	78	5	replacesthe	replacesthe	DET
ma-105	78	6	mass	mass	ADJ
ma-105	78	7	-	-	PUNCT
ma-105	78	8	action	action	NOUN
ma-105	78	9	function	function	NOUN
ma-105	78	10	which	which	PRON
ma-105	78	11	has	have	AUX
ma-105	78	12	been	be	AUX
ma-105	78	13	shown	show	VERB
ma-105	78	14	to	to	PART
ma-105	78	15	cause	cause	VERB
ma-105	78	16	unrealistic	unrealistic	ADJ
ma-105	78	17	conditions	condition	NOUN
ma-105	78	18	for	for	ADP
ma-105	78	19	successful	successful	ADJ
ma-105	78	20	chronichcv	chronichcv	NOUN
ma-105	78	21	infection	infection	NOUN
ma-105	78	22	.	.	PUNCT
ma-105	79	1	ρi	ρi	NOUN
ma-105	79	2	is	be	AUX
ma-105	79	3	the	the	DET
ma-105	79	4	cure	cure	NOUN
ma-105	79	5	rate	rate	NOUN
ma-105	79	6	of	of	ADP
ma-105	79	7	infected	infected	ADJ
ma-105	79	8	hepatocytes	hepatocyte	NOUN
ma-105	79	9	either	either	CCONJ
ma-105	79	10	by	by	ADP
ma-105	79	11	noncytolytic	noncytolytic	ADJ
ma-105	79	12	mechanism	mechanism	NOUN
ma-105	79	13	orimmunity	orimmunity	NOUN
ma-105	79	14	or	or	CCONJ
ma-105	79	15	treatment	treatment	NOUN
ma-105	79	16	.	.	PUNCT
ma-105	80	1	in	in	ADP
ma-105	80	2	addition	addition	NOUN
ma-105	80	3	,	,	PUNCT
ma-105	80	4	the	the	DET
ma-105	80	5	therapeutic	therapeutic	ADJ
ma-105	80	6	effect	effect	NOUN
ma-105	80	7	of	of	ADP
ma-105	80	8	treatment	treatment	NOUN
ma-105	80	9	in	in	ADP
ma-105	80	10	this	this	DET
ma-105	80	11	model	model	NOUN
ma-105	80	12	involved	involve	VERB
ma-105	80	13	thereduction	thereduction	NOUN
ma-105	80	14	of	of	ADP
ma-105	80	15	new	new	ADJ
ma-105	80	16	infections	infection	NOUN
ma-105	80	17	,	,	PUNCT
ma-105	80	18	which	which	PRON
ma-105	80	19	is	be	AUX
ma-105	80	20	described	describe	VERB
ma-105	80	21	in	in	ADP
ma-105	80	22	a	a	DET
ma-105	80	23	fraction	fraction	NOUN
ma-105	80	24	as	as	ADP
ma-105	80	25	(	(	PUNCT
ma-105	80	26	1	1	NUM
ma-105	80	27	−	−	PROPN
ma-105	80	28	η	η	PROPN
ma-105	80	29	)	)	PUNCT
ma-105	80	30	.	.	PUNCT
ma-105	81	1	the	the	DET
ma-105	81	2	spatial	spatial	ADJ
ma-105	81	3	motion	motion	NOUN
ma-105	81	4	ofhealthy	ofhealthy	ADJ
ma-105	81	5	hepatocytes	hepatocytes	PROPN
ma-105	81	6	follows	follow	VERB
ma-105	81	7	the	the	DET
ma-105	81	8	fickian	fickian	ADJ
ma-105	81	9	diffusion	diffusion	NOUN
ma-105	81	10	law	law	NOUN
ma-105	81	11	.	.	PUNCT
ma-105	82	1	thus	thus	ADV
ma-105	82	2	,	,	PUNCT
ma-105	82	3	the	the	DET
ma-105	82	4	variation	variation	NOUN
ma-105	82	5	of	of	ADP
ma-105	82	6	healthy	healthy	ADJ
ma-105	82	7	hepatocytesis	hepatocytesis	NOUN
ma-105	82	8	expressed	express	VERB
ma-105	82	9	by	by	ADP
ma-105	82	10	the	the	DET
ma-105	82	11	following	follow	VERB
ma-105	82	12	equation	equation	NOUN
ma-105	82	13	:	:	PUNCT
ma-105	82	14	∂h	∂h	PROPN
ma-105	82	15	∂t	∂t	PROPN
ma-105	82	16	=	=	SYM
ma-105	82	17	d1∆h(x	d1∆h(x	PROPN
ma-105	82	18	,	,	PUNCT
ma-105	82	19	t	t	PROPN
ma-105	82	20	)	)	PUNCT
ma-105	82	21	+	+	CCONJ
ma-105	82	22	λ−	λ−	PROPN
ma-105	82	23	dh(x	dh(x	NUM
ma-105	82	24	,	,	PUNCT
ma-105	82	25	t)−	t)−	PROPN
ma-105	82	26	(	(	PUNCT
ma-105	82	27	1−	1−	NUM
ma-105	82	28	η)βh(x	η)βh(x	PROPN
ma-105	82	29	,	,	PUNCT
ma-105	82	30	t)v	t)v	PUNCT
ma-105	82	31	(	(	PUNCT
ma-105	82	32	x	x	X
ma-105	82	33	,	,	PUNCT
ma-105	82	34	t	t	PROPN
ma-105	82	35	)	)	PUNCT
ma-105	82	36	α0	α0	PROPN
ma-105	82	37	+	+	SYM
ma-105	82	38	α1h(x	α1h(x	PROPN
ma-105	82	39	,	,	PUNCT
ma-105	82	40	t	t	PROPN
ma-105	82	41	)	)	PUNCT
ma-105	83	1	+	+	CCONJ
ma-105	83	2	α2v	α2v	NUM
ma-105	83	3	(	(	PUNCT
ma-105	83	4	x	x	X
ma-105	83	5	,	,	PUNCT
ma-105	83	6	t	t	PROPN
ma-105	83	7	)	)	PUNCT
ma-105	83	8	+	+	CCONJ
ma-105	83	9	α3h(x	α3h(x	PROPN
ma-105	83	10	,	,	PUNCT
ma-105	83	11	t)v	t)v	PUNCT
ma-105	83	12	(	(	PUNCT
ma-105	83	13	x	x	X
ma-105	83	14	,	,	PUNCT
ma-105	83	15	t	t	PROPN
ma-105	83	16	)	)	PUNCT
ma-105	83	17	+	+	CCONJ
ma-105	83	18	ρi(x	ρi(x	NUM
ma-105	83	19	,	,	PUNCT
ma-105	83	20	t	t	PROPN
ma-105	83	21	)	)	PUNCT
ma-105	83	22	,	,	PUNCT
ma-105	83	23	where	where	SCONJ
ma-105	83	24	d1	d1	PROPN
ma-105	83	25	represents	represent	VERB
ma-105	83	26	the	the	DET
ma-105	83	27	healthy	healthy	ADJ
ma-105	83	28	hepatocytes	hepatocyte	NOUN
ma-105	83	29	diffusion	diffusion	NOUN
ma-105	83	30	coefficient	coefficient	NOUN
ma-105	83	31	and	and	CCONJ
ma-105	83	32	∆	∆	PROPN
ma-105	83	33	=	=	SYM
ma-105	83	34	∂2	∂2	ADJ
ma-105	83	35	∂x2	∂x2	NOUN
ma-105	83	36	1	1	NUM
ma-105	83	37	+	+	NUM
ma-105	83	38	∂2	∂2	NUM
ma-105	83	39	∂x2	∂x2	NOUN
ma-105	83	40	2	2	NUM
ma-105	83	41	+	+	SYM
ma-105	83	42	∂2	∂2	NUM
ma-105	83	43	∂x2	∂x2	NOUN
ma-105	83	44	3is	3is	NOUN
ma-105	83	45	the	the	DET
ma-105	83	46	usual	usual	ADJ
ma-105	83	47	laplacian	laplacian	ADJ
ma-105	83	48	operator	operator	NOUN
ma-105	83	49	in	in	ADP
ma-105	83	50	three	three	NUM
ma-105	83	51	-	-	PUNCT
ma-105	83	52	dimensional	dimensional	ADJ
ma-105	83	53	space	space	NOUN
ma-105	83	54	.	.	PUNCT
ma-105	84	1	2.2	2.2	NUM
ma-105	84	2	.	.	PUNCT
ma-105	84	3	fluctuation	fluctuation	NOUN
ma-105	84	4	of	of	ADP
ma-105	84	5	hcv	hcv	PROPN
ma-105	84	6	infected	infected	ADJ
ma-105	84	7	cells	cell	NOUN
ma-105	84	8	.	.	PUNCT
ma-105	85	1	the	the	DET
ma-105	85	2	hcv	hcv	PROPN
ma-105	85	3	infected	infect	VERB
ma-105	85	4	cells	cell	NOUN
ma-105	85	5	die	die	VERB
ma-105	85	6	at	at	ADP
ma-105	85	7	rate	rate	NOUN
ma-105	85	8	α	α	NOUN
ma-105	85	9	per	per	ADP
ma-105	85	10	day	day	NOUN
ma-105	85	11	so	so	SCONJ
ma-105	85	12	that	that	SCONJ
ma-105	85	13	1	1	NUM
ma-105	85	14	αis	αis	INTJ
ma-105	85	15	the	the	DET
ma-105	85	16	life	life	NOUN
ma-105	85	17	-	-	PUNCT
ma-105	85	18	expectancy	expectancy	NOUN
ma-105	85	19	of	of	ADP
ma-105	85	20	hcv	hcv	PROPN
ma-105	85	21	infected	infect	VERB
ma-105	85	22	hepatocytes	hepatocyte	NOUN
ma-105	85	23	.	.	PUNCT
ma-105	86	1	healthy	healthy	ADJ
ma-105	86	2	hepatocytes	hepatocyte	NOUN
ma-105	86	3	become	become	VERB
ma-105	86	4	infected	infected	ADJ
ma-105	86	5	at	at	ADP
ma-105	86	6	therate	therate	NOUN
ma-105	86	7	βhv	βhv	NOUN
ma-105	86	8	α0+α1h+α2v	α0+α1h+α2v	ADP
ma-105	86	9	+	+	NOUN
ma-105	86	10	α3hv	α3hv	NOUN
ma-105	86	11	.	.	PUNCT
ma-105	87	1	the	the	DET
ma-105	87	2	spatial	spatial	ADJ
ma-105	87	3	motion	motion	NOUN
ma-105	87	4	of	of	ADP
ma-105	87	5	hcv	hcv	PROPN
ma-105	87	6	infected	infected	ADJ
ma-105	87	7	cells	cell	NOUN
ma-105	87	8	follows	follow	VERB
ma-105	87	9	the	the	DET
ma-105	87	10	fickian	fickian	ADJ
ma-105	87	11	diffusion	diffusion	NOUN
ma-105	87	12	law.thus	law.thus	PROPN
ma-105	87	13	,	,	PUNCT
ma-105	87	14	the	the	DET
ma-105	87	15	variation	variation	NOUN
ma-105	87	16	of	of	ADP
ma-105	87	17	infected	infected	ADJ
ma-105	87	18	hepatocytes	hepatocyte	NOUN
ma-105	87	19	is	be	AUX
ma-105	87	20	expressed	express	VERB
ma-105	87	21	by	by	ADP
ma-105	87	22	the	the	DET
ma-105	87	23	following	follow	VERB
ma-105	87	24	equation	equation	NOUN
ma-105	87	25	∂i	∂i	PROPN
ma-105	87	26	∂t	∂t	PROPN
ma-105	87	27	=	=	PUNCT
ma-105	87	28	d2∆i(x	d2∆i(x	PROPN
ma-105	87	29	,	,	PUNCT
ma-105	87	30	t	t	PROPN
ma-105	87	31	)	)	PUNCT
ma-105	88	1	+	+	CCONJ
ma-105	88	2	(	(	PUNCT
ma-105	88	3	1−	1−	NUM
ma-105	88	4	η)βh(x	η)βh(x	PROPN
ma-105	88	5	,	,	PUNCT
ma-105	88	6	t)v	t)v	PUNCT
ma-105	88	7	(	(	PUNCT
ma-105	88	8	x	x	X
ma-105	88	9	,	,	PUNCT
ma-105	88	10	t	t	PROPN
ma-105	88	11	)	)	PUNCT
ma-105	88	12	α0	α0	PROPN
ma-105	88	13	+	+	SYM
ma-105	88	14	α1h(x	α1h(x	PROPN
ma-105	88	15	,	,	PUNCT
ma-105	88	16	t	t	PROPN
ma-105	88	17	)	)	PUNCT
ma-105	89	1	+	+	CCONJ
ma-105	89	2	α2v	α2v	NUM
ma-105	89	3	(	(	PUNCT
ma-105	89	4	x	x	X
ma-105	89	5	,	,	PUNCT
ma-105	89	6	t	t	PROPN
ma-105	89	7	)	)	PUNCT
ma-105	89	8	+	+	CCONJ
ma-105	89	9	α3h(x	α3h(x	PROPN
ma-105	89	10	,	,	PUNCT
ma-105	89	11	t)v	t)v	PUNCT
ma-105	89	12	(	(	PUNCT
ma-105	89	13	x	x	X
ma-105	89	14	,	,	PUNCT
ma-105	89	15	t	t	PROPN
ma-105	89	16	)	)	PUNCT
ma-105	89	17	−	−	PROPN
ma-105	89	18	(	(	PUNCT
ma-105	89	19	α+	α+	NOUN
ma-105	89	20	ρ)i(x	ρ)i(x	NOUN
ma-105	89	21	,	,	PUNCT
ma-105	89	22	t	t	PROPN
ma-105	89	23	)	)	PUNCT
ma-105	89	24	,	,	PUNCT
ma-105	89	25	where	where	SCONJ
ma-105	89	26	d2	d2	PROPN
ma-105	89	27	represents	represent	VERB
ma-105	89	28	the	the	DET
ma-105	89	29	hcv	hcv	PROPN
ma-105	89	30	infected	infect	VERB
ma-105	89	31	cells	cell	NOUN
ma-105	89	32	diffusion	diffusion	NOUN
ma-105	89	33	coefficient	coefficient	NOUN
ma-105	89	34	.	.	PUNCT
ma-105	90	1	2.3	2.3	NUM
ma-105	90	2	.	.	PUNCT
ma-105	90	3	fluctuation	fluctuation	NOUN
ma-105	90	4	of	of	ADP
ma-105	90	5	free	free	ADJ
ma-105	90	6	hcv	hcv	NOUN
ma-105	90	7	virions	virion	NOUN
ma-105	90	8	.	.	PUNCT
ma-105	91	1	the	the	DET
ma-105	91	2	infected	infect	VERB
ma-105	91	3	hepatocytes	hepatocyte	NOUN
ma-105	91	4	produce	produce	VERB
ma-105	91	5	virus	virus	NOUN
ma-105	91	6	at	at	ADP
ma-105	91	7	rate	rate	NOUN
ma-105	91	8	ki	ki	PROPN
ma-105	91	9	,	,	PUNCT
ma-105	91	10	and	and	CCONJ
ma-105	91	11	virusis	virusis	NOUN
ma-105	91	12	cleared	clear	VERB
ma-105	91	13	at	at	ADP
ma-105	91	14	the	the	DET
ma-105	91	15	rate	rate	NOUN
ma-105	91	16	µv	µv	NOUN
ma-105	91	17	.	.	PUNCT
ma-105	92	1	also	also	ADV
ma-105	92	2	,	,	PUNCT
ma-105	92	3	the	the	DET
ma-105	92	4	population	population	NOUN
ma-105	92	5	of	of	ADP
ma-105	92	6	virions	virion	NOUN
ma-105	92	7	decreases	decrease	VERB
ma-105	92	8	due	due	ADP
ma-105	92	9	to	to	ADP
ma-105	92	10	the	the	DET
ma-105	92	11	infection	infection	NOUN
ma-105	92	12	at	at	ADP
ma-105	92	13	the	the	DET
ma-105	92	14	rate	rate	NOUN
ma-105	92	15	u(1−η)βhv	u(1−η)βhv	PROPN
ma-105	92	16	α0+α1h+α2v	α0+α1h+α2v	DET
ma-105	92	17	+	+	NOUN
ma-105	92	18	α3hv	α3hv	NOUN
ma-105	92	19	due	due	ADP
ma-105	92	20	to	to	ADP
ma-105	92	21	absorption	absorption	NOUN
ma-105	92	22	effect	effect	NOUN
ma-105	92	23	,	,	PUNCT
ma-105	92	24	where	where	SCONJ
ma-105	92	25	u	u	PROPN
ma-105	92	26	∈	∈	PROPN
ma-105	92	27	{	{	PUNCT
ma-105	92	28	0	0	NUM
ma-105	92	29	,	,	PUNCT
ma-105	92	30	1	1	NUM
ma-105	92	31	}	}	PUNCT
ma-105	92	32	.	.	PUNCT
ma-105	93	1	the	the	DET
ma-105	93	2	spatial	spatial	ADJ
ma-105	93	3	motion	motion	NOUN
ma-105	93	4	of	of	ADP
ma-105	93	5	virions	virion	NOUN
ma-105	93	6	followsthe	followsthe	PROPN
ma-105	93	7	fickian	fickian	ADJ
ma-105	93	8	diffusion	diffusion	NOUN
ma-105	93	9	law	law	NOUN
ma-105	93	10	.	.	PUNCT
ma-105	94	1	in	in	ADP
ma-105	94	2	addition	addition	NOUN
ma-105	94	3	,	,	PUNCT
ma-105	94	4	the	the	DET
ma-105	94	5	therapeutic	therapeutic	ADJ
ma-105	94	6	effect	effect	NOUN
ma-105	94	7	of	of	ADP
ma-105	94	8	treatment	treatment	NOUN
ma-105	94	9	in	in	ADP
ma-105	94	10	this	this	DET
ma-105	94	11	model	model	NOUN
ma-105	94	12	involvedblocking	involvedblocke	VERB
ma-105	94	13	virions	virion	NOUN
ma-105	94	14	production	production	NOUN
ma-105	94	15	(	(	PUNCT
ma-105	94	16	referred	refer	VERB
ma-105	94	17	to	to	ADP
ma-105	94	18	as	as	ADP
ma-105	94	19	drug	drug	NOUN
ma-105	94	20	effectiveness	effectiveness	NOUN
ma-105	94	21	)	)	PUNCT
ma-105	94	22	which	which	PRON
ma-105	94	23	,	,	PUNCT
ma-105	94	24	is	be	AUX
ma-105	94	25	described	describe	VERB
ma-105	94	26	in	in	ADP
ma-105	94	27	fraction	fraction	NOUN
ma-105	94	28	(	(	PUNCT
ma-105	94	29	1−ε).thus	1−ε).thus	NUM
ma-105	94	30	,	,	PUNCT
ma-105	94	31	the	the	DET
ma-105	94	32	variation	variation	NOUN
ma-105	94	33	of	of	ADP
ma-105	94	34	free	free	ADJ
ma-105	94	35	virions	virion	NOUN
ma-105	94	36	is	be	AUX
ma-105	94	37	expressed	express	VERB
ma-105	94	38	by	by	ADP
ma-105	94	39	the	the	DET
ma-105	94	40	following	follow	VERB
ma-105	94	41	equation	equation	NOUN
ma-105	94	42	:	:	PUNCT
ma-105	95	1	∂v	∂v	PROPN
ma-105	95	2	∂t	∂t	PROPN
ma-105	95	3	=	=	PUNCT
ma-105	95	4	d3∆v	d3∆v	NOUN
ma-105	95	5	(	(	PUNCT
ma-105	95	6	x	x	NOUN
ma-105	95	7	,	,	PUNCT
ma-105	95	8	t)+(1−ε)ki(x	t)+(1−ε)ki(x	PROPN
ma-105	95	9	,	,	PUNCT
ma-105	95	10	t)−µv	t)−µv	PUNCT
ma-105	95	11	(	(	PUNCT
ma-105	95	12	x	x	X
ma-105	95	13	,	,	PUNCT
ma-105	95	14	t)−u	t)−u	X
ma-105	95	15	(	(	PUNCT
ma-105	95	16	1−	1−	NUM
ma-105	95	17	η)βh(x	η)βh(x	PROPN
ma-105	95	18	,	,	PUNCT
ma-105	95	19	t)v	t)v	PUNCT
ma-105	95	20	(	(	PUNCT
ma-105	95	21	x	x	X
ma-105	95	22	,	,	PUNCT
ma-105	95	23	t	t	PROPN
ma-105	95	24	)	)	PUNCT
ma-105	95	25	α0	α0	PROPN
ma-105	95	26	+	+	SYM
ma-105	95	27	α1h(x	α1h(x	PROPN
ma-105	95	28	,	,	PUNCT
ma-105	95	29	t	t	PROPN
ma-105	95	30	)	)	PUNCT
ma-105	95	31	+	+	CCONJ
ma-105	95	32	α2v	α2v	NUM
ma-105	95	33	(	(	PUNCT
ma-105	95	34	x	x	X
ma-105	95	35	,	,	PUNCT
ma-105	95	36	t	t	PROPN
ma-105	95	37	)	)	PUNCT
ma-105	95	38	+	+	CCONJ
ma-105	95	39	α3h(x	α3h(x	PROPN
ma-105	95	40	,	,	PUNCT
ma-105	95	41	t)v	t)v	PUNCT
ma-105	95	42	(	(	PUNCT
ma-105	95	43	x	x	X
ma-105	95	44	,	,	PUNCT
ma-105	95	45	t	t	PROPN
ma-105	95	46	)	)	PUNCT
ma-105	95	47	,	,	PUNCT
ma-105	95	48	where	where	SCONJ
ma-105	95	49	d3	d3	PROPN
ma-105	95	50	represents	represent	VERB
ma-105	95	51	the	the	DET
ma-105	95	52	free	free	ADJ
ma-105	95	53	hcv	hcv	X
ma-105	95	54	virions	virion	NOUN
ma-105	95	55	diffusion	diffusion	NOUN
ma-105	95	56	coefficient	coefficient	NOUN
ma-105	95	57	.	.	PUNCT
ma-105	96	1	2.4	2.4	NUM
ma-105	96	2	.	.	PUNCT
ma-105	97	1	the	the	DET
ma-105	97	2	initial	initial	ADJ
ma-105	97	3	boundary	boundary	ADJ
ma-105	97	4	value	value	NOUN
ma-105	97	5	problem	problem	NOUN
ma-105	97	6	associated	associate	VERB
ma-105	97	7	to	to	ADP
ma-105	97	8	pde	pde	NOUN
ma-105	97	9	-	-	PUNCT
ma-105	97	10	cellular	cellular	ADJ
ma-105	97	11	model	model	NOUN
ma-105	97	12	.	.	PUNCT
ma-105	98	1	in	in	ADP
ma-105	98	2	this	this	DET
ma-105	98	3	section	section	NOUN
ma-105	98	4	,	,	PUNCT
ma-105	98	5	we	we	PRON
ma-105	98	6	usethe	usethe	VERB
ma-105	98	7	previous	previous	ADJ
ma-105	98	8	equations	equation	NOUN
ma-105	98	9	describing	describe	VERB
ma-105	98	10	variables	variable	NOUN
ma-105	98	11	variations	variation	NOUN
ma-105	98	12	to	to	PART
ma-105	98	13	set	set	VERB
ma-105	98	14	up	up	ADP
ma-105	98	15	a	a	DET
ma-105	98	16	complete	complete	ADJ
ma-105	98	17	pde	pde	NOUN
ma-105	98	18	system	system	NOUN
ma-105	98	19	modellingbiological	modellingbiological	ADJ
ma-105	98	20	dynamics	dynamic	NOUN
ma-105	98	21	for	for	ADP
ma-105	98	22	hcv	hcv	NOUN
ma-105	98	23	infection	infection	NOUN
ma-105	98	24	.	.	PUNCT
ma-105	99	1	let	let	VERB
ma-105	99	2	t	t	PROPN
ma-105	99	3	>	>	X
ma-105	99	4	0	0	PUNCT
ma-105	99	5	be	be	AUX
ma-105	99	6	a	a	DET
ma-105	99	7	fixed	fix	VERB
ma-105	99	8	time	time	NOUN
ma-105	99	9	and	and	CCONJ
ma-105	99	10	define	define	VERB
ma-105	99	11	ωt	ωt	ADP
ma-105	99	12	=	=	PUNCT
ma-105	99	13	ω×	ω×	X
ma-105	99	14	(	(	PUNCT
ma-105	99	15	0	0	NUM
ma-105	99	16	,	,	PUNCT
ma-105	99	17	t	t	NOUN
ma-105	99	18	)	)	PUNCT
ma-105	99	19	.	.	PUNCT
ma-105	100	1	https://doi.org/10.28924/ada/ma.3.1	https://doi.org/10.28924/ada/ma.3.1	PROPN
ma-105	100	2	eur	eur	PROPN
ma-105	100	3	.	.	PUNCT
ma-105	101	1	j.	j.	PROPN
ma-105	101	2	math	math	PROPN
ma-105	101	3	.	.	PUNCT
ma-105	102	1	anal	anal	PROPN
ma-105	102	2	.	.	PUNCT
ma-105	103	1	10.28924	10.28924	NUM
ma-105	103	2	/	/	SYM
ma-105	103	3	ada	ada	PROPN
ma-105	103	4	/	/	SYM
ma-105	103	5	ma.3.1	ma.3.1	PROPN
ma-105	103	6	5therefore	5therefore	NUM
ma-105	103	7	,	,	PUNCT
ma-105	103	8	in	in	ADP
ma-105	103	9	ωt	ωt	ADP
ma-105	103	10	the	the	DET
ma-105	103	11	full	full	ADJ
ma-105	103	12	system	system	NOUN
ma-105	103	13	of	of	ADP
ma-105	103	14	pde	pde	NOUN
ma-105	103	15	governing	govern	VERB
ma-105	103	16	the	the	DET
ma-105	103	17	hcv	hcv	ADJ
ma-105	103	18	infection	infection	NOUN
ma-105	103	19	becomes	become	VERB
ma-105	103	20	:	:	PUNCT
ma-105	103	21			PROPN
ma-105	104	1	∂h	∂h	PROPN
ma-105	104	2	∂t	∂t	PROPN
ma-105	104	3	=	=	PUNCT
ma-105	104	4	d1∆h(x	d1∆h(x	PROPN
ma-105	104	5	,	,	PUNCT
ma-105	104	6	t	t	PROPN
ma-105	104	7	)	)	PUNCT
ma-105	105	1	+	+	CCONJ
ma-105	106	1	λ−	λ−	PROPN
ma-105	106	2	dh	dh	NOUN
ma-105	106	3	−	−	PROPN
ma-105	106	4	(	(	PUNCT
ma-105	106	5	1−	1−	NUM
ma-105	106	6	η)βhv	η)βhv	PROPN
ma-105	106	7	α0	α0	PROPN
ma-105	106	8	+	+	CCONJ
ma-105	106	9	α1h	α1h	PROPN
ma-105	106	10	+	+	SYM
ma-105	106	11	α2v	α2v	NUM
ma-105	106	12	+	+	CCONJ
ma-105	106	13	α3hv	α3hv	NOUN
ma-105	107	1	+	+	NUM
ma-105	107	2	ρi	ρi	NOUN
ma-105	107	3	,	,	PUNCT
ma-105	107	4	∂i	∂i	PROPN
ma-105	107	5	∂t	∂t	PROPN
ma-105	107	6	=	=	PUNCT
ma-105	107	7	d2∆i(x	d2∆i(x	PROPN
ma-105	107	8	,	,	PUNCT
ma-105	107	9	t	t	PROPN
ma-105	107	10	)	)	PUNCT
ma-105	107	11	+	+	CCONJ
ma-105	107	12	(	(	PUNCT
ma-105	107	13	1−	1−	NUM
ma-105	107	14	η)βhv	η)βhv	PROPN
ma-105	107	15	α0	α0	PROPN
ma-105	107	16	+	+	CCONJ
ma-105	107	17	α1h	α1h	PROPN
ma-105	107	18	+	+	SYM
ma-105	107	19	α2v	α2v	NUM
ma-105	107	20	+	+	CCONJ
ma-105	107	21	α3hv	α3hv	NUM
ma-105	107	22	−	−	NOUN
ma-105	107	23	(	(	PUNCT
ma-105	107	24	α+	α+	X
ma-105	107	25	ρ)i	ρ)i	NOUN
ma-105	107	26	,	,	PUNCT
ma-105	107	27	(	(	PUNCT
ma-105	108	1	2.1	2.1	NUM
ma-105	108	2	)	)	PUNCT
ma-105	108	3	∂v	∂v	PROPN
ma-105	108	4	∂t	∂t	PROPN
ma-105	109	1	=	=	PUNCT
ma-105	109	2	d3∆v	d3∆v	NOUN
ma-105	109	3	+	+	X
ma-105	109	4	(	(	PUNCT
ma-105	109	5	1−	1−	NUM
ma-105	109	6	ε)ki	ε)ki	PROPN
ma-105	109	7	−	−	PROPN
ma-105	110	1	µv	µv	NOUN
ma-105	110	2	−	−	PROPN
ma-105	110	3	u(1−	u(1−	ADJ
ma-105	110	4	η)βhv	η)βhv	PROPN
ma-105	110	5	α0	α0	PROPN
ma-105	110	6	+	+	CCONJ
ma-105	110	7	α1h	α1h	PROPN
ma-105	111	1	+	+	SYM
ma-105	111	2	α2v	α2v	NOUN
ma-105	111	3	+	+	CCONJ
ma-105	111	4	α3hv	α3hv	NOUN
ma-105	111	5	.	.	PUNCT
ma-105	112	1	we	we	PRON
ma-105	112	2	use	use	VERB
ma-105	112	3	the	the	DET
ma-105	112	4	neumann	neumann	PROPN
ma-105	112	5	homogeneous	homogeneous	ADJ
ma-105	112	6	boundary	boundary	ADJ
ma-105	112	7	conditions	condition	NOUN
ma-105	112	8	:	:	PUNCT
ma-105	113	1	∂h	∂h	PROPN
ma-105	113	2	∂η	∂η	X
ma-105	113	3	=	=	PUNCT
ma-105	113	4	∂i	∂i	PROPN
ma-105	113	5	∂η	∂η	PROPN
ma-105	113	6	=	=	SYM
ma-105	113	7	∂v	∂v	PROPN
ma-105	113	8	∂η	∂η	PROPN
ma-105	114	1	=	=	NOUN
ma-105	114	2	0	0	NUM
ma-105	114	3	on	on	ADP
ma-105	114	4	∂ω×	∂ω×	PROPN
ma-105	115	1	[	[	X
ma-105	115	2	0	0	NUM
ma-105	115	3	,	,	PUNCT
ma-105	115	4	t	t	X
ma-105	115	5	]	]	PUNCT
ma-105	115	6	,	,	PUNCT
ma-105	115	7	(	(	PUNCT
ma-105	115	8	2.2	2.2	NUM
ma-105	115	9	)	)	PUNCT
ma-105	115	10	where	where	SCONJ
ma-105	115	11	∂	∂	ADJ
ma-105	115	12	∂η	∂η	PROPN
ma-105	115	13	denotes	denote	VERB
ma-105	115	14	the	the	DET
ma-105	115	15	outward	outward	ADJ
ma-105	115	16	normal	normal	ADJ
ma-105	115	17	derivative	derivative	NOUN
ma-105	115	18	on	on	ADP
ma-105	115	19	∂ω	∂ω	PROPN
ma-105	115	20	.	.	PUNCT
ma-105	116	1	the	the	DET
ma-105	116	2	initial	initial	ADJ
ma-105	116	3	conditions	condition	NOUN
ma-105	116	4	are	be	AUX
ma-105	116	5	the	the	DET
ma-105	116	6	following	follow	VERB
ma-105	116	7	:	:	PUNCT
ma-105	116	8	h(x	h(x	PROPN
ma-105	116	9	,	,	PUNCT
ma-105	116	10	0	0	NUM
ma-105	116	11	)	)	PUNCT
ma-105	116	12	=	=	SYM
ma-105	116	13	h0	h0	PROPN
ma-105	116	14	,	,	PUNCT
ma-105	116	15	i(x	i(x	PROPN
ma-105	116	16	,	,	PUNCT
ma-105	116	17	0	0	NUM
ma-105	116	18	)	)	PUNCT
ma-105	116	19	=	=	SYM
ma-105	116	20	i0	i0	PROPN
ma-105	116	21	,	,	PUNCT
ma-105	116	22	v	v	NOUN
ma-105	116	23	(	(	PUNCT
ma-105	116	24	x	x	NOUN
ma-105	116	25	,	,	PUNCT
ma-105	116	26	0	0	NUM
ma-105	116	27	)	)	PUNCT
ma-105	116	28	=	=	SYM
ma-105	116	29	v0	v0	NOUN
ma-105	116	30	,	,	PUNCT
ma-105	116	31	x	x	X
ma-105	116	32	∈	∈	PROPN
ma-105	116	33	ω	ω	PROPN
ma-105	116	34	.	.	PUNCT
ma-105	117	1	(	(	PUNCT
ma-105	117	2	2.3	2.3	NUM
ma-105	117	3	)	)	PUNCT
ma-105	117	4	the	the	DET
ma-105	117	5	boundary	boundary	ADJ
ma-105	117	6	conditions	condition	NOUN
ma-105	117	7	in	in	ADP
ma-105	117	8	(	(	PUNCT
ma-105	117	9	2.2	2.2	NUM
ma-105	117	10	)	)	PUNCT
ma-105	117	11	imply	imply	VERB
ma-105	117	12	that	that	SCONJ
ma-105	117	13	the	the	DET
ma-105	117	14	healthy	healthy	ADJ
ma-105	117	15	hepatocytes	hepatocyte	NOUN
ma-105	117	16	,	,	PUNCT
ma-105	117	17	the	the	DET
ma-105	117	18	hcv	hcv	PROPN
ma-105	117	19	infected	infect	VERB
ma-105	117	20	cells	cell	NOUN
ma-105	117	21	and	and	CCONJ
ma-105	117	22	freehcv	freehcv	VERB
ma-105	117	23	virions	virion	NOUN
ma-105	117	24	do	do	AUX
ma-105	117	25	not	not	PART
ma-105	117	26	move	move	VERB
ma-105	117	27	across	across	ADP
ma-105	117	28	the	the	DET
ma-105	117	29	boundary	boundary	ADJ
ma-105	117	30	∂ω	∂ω	PROPN
ma-105	117	31	.	.	PUNCT
ma-105	118	1	for	for	ADP
ma-105	118	2	an	an	DET
ma-105	118	3	epidemiological	epidemiological	ADJ
ma-105	118	4	significance	significance	NOUN
ma-105	118	5	,	,	PUNCT
ma-105	118	6	we	we	PRON
ma-105	118	7	assumethat	assumethat	VERB
ma-105	118	8	the	the	DET
ma-105	118	9	initial	initial	ADJ
ma-105	118	10	conditions	condition	NOUN
ma-105	118	11	are	be	AUX
ma-105	118	12	positive	positive	ADJ
ma-105	118	13	and	and	CCONJ
ma-105	118	14	hölder	hölder	X
ma-105	118	15	continuous	continuous	ADJ
ma-105	118	16	,	,	PUNCT
ma-105	118	17	and	and	CCONJ
ma-105	118	18	satisfy	satisfy	VERB
ma-105	118	19	∂h0	∂h0	ADV
ma-105	119	1	∂η	∂η	PROPN
ma-105	119	2	=	=	PUNCT
ma-105	119	3	∂i0	∂i0	PROPN
ma-105	119	4	∂η	∂η	X
ma-105	120	1	=	=	PRON
ma-105	120	2	∂v0	∂v0	NOUN
ma-105	120	3	∂η	∂η	X
ma-105	120	4	=	=	NOUN
ma-105	120	5	0	0	NUM
ma-105	120	6	on	on	ADP
ma-105	120	7	∂ω	∂ω	PROPN
ma-105	120	8	.	.	PUNCT
ma-105	121	1	we	we	PRON
ma-105	121	2	then	then	ADV
ma-105	121	3	obtain	obtain	VERB
ma-105	121	4	the	the	DET
ma-105	121	5	following	following	ADJ
ma-105	121	6	initial	initial	ADJ
ma-105	121	7	boundary	boundary	ADJ
ma-105	121	8	value	value	NOUN
ma-105	121	9	problem	problem	NOUN
ma-105	121	10	,	,	PUNCT
ma-105	121	11	denoted	denote	VERB
ma-105	121	12	ibvp	ibvp	NOUN
ma-105	121	13	associated	associate	VERB
ma-105	121	14	to	to	ADP
ma-105	121	15	theprevious	theprevious	ADJ
ma-105	121	16	pde	pde	NOUN
ma-105	121	17	-	-	PUNCT
ma-105	121	18	cellular	cellular	ADJ
ma-105	121	19	model:	model:	PROPN
ma-105	121	20	∂h	∂h	PROPN
ma-105	121	21	∂t	∂t	PROPN
ma-105	121	22	=	=	SYM
ma-105	121	23	d1∆h	d1∆h	PROPN
ma-105	122	1	+	+	CCONJ
ma-105	122	2	λ−	λ−	PROPN
ma-105	122	3	dh	dh	NOUN
ma-105	122	4	−	−	PROPN
ma-105	122	5	(	(	PUNCT
ma-105	122	6	1−	1−	NUM
ma-105	122	7	η)βhv	η)βhv	PROPN
ma-105	122	8	α0	α0	PROPN
ma-105	122	9	+	+	CCONJ
ma-105	123	1	α1h	α1h	PROPN
ma-105	123	2	+	+	SYM
ma-105	123	3	α2v	α2v	NUM
ma-105	123	4	+	+	CCONJ
ma-105	123	5	α3hv	α3hv	NOUN
ma-105	124	1	+	+	CCONJ
ma-105	124	2	ρi	ρi	NOUN
ma-105	124	3	in	in	ADP
ma-105	124	4	ωt	ωt	PROPN
ma-105	124	5	,	,	PUNCT
ma-105	124	6	∂i	∂i	PROPN
ma-105	124	7	∂t	∂t	PROPN
ma-105	124	8	=	=	PUNCT
ma-105	124	9	d2∆i	d2∆i	VERB
ma-105	125	1	+	+	CCONJ
ma-105	125	2	(	(	PUNCT
ma-105	125	3	1−	1−	NUM
ma-105	125	4	η)βhv	η)βhv	PROPN
ma-105	125	5	α0	α0	PROPN
ma-105	125	6	+	+	CCONJ
ma-105	125	7	α1h	α1h	PROPN
ma-105	125	8	+	+	SYM
ma-105	125	9	α2v	α2v	NUM
ma-105	125	10	+	+	CCONJ
ma-105	125	11	α3hv	α3hv	NUM
ma-105	125	12	−	−	NOUN
ma-105	125	13	(	(	PUNCT
ma-105	125	14	α+	α+	X
ma-105	125	15	ρ)i	ρ)i	NOUN
ma-105	125	16	in	in	ADP
ma-105	125	17	ωt	ωt	PROPN
ma-105	125	18	,	,	PUNCT
ma-105	126	1	∂v	∂v	PROPN
ma-105	126	2	∂t	∂t	PROPN
ma-105	127	1	=	=	PUNCT
ma-105	127	2	d3∆v	d3∆v	NOUN
ma-105	127	3	+	+	X
ma-105	127	4	(	(	PUNCT
ma-105	127	5	1−	1−	NUM
ma-105	127	6	ε)ki	ε)ki	PROPN
ma-105	127	7	−	−	PROPN
ma-105	128	1	µv	µv	NOUN
ma-105	128	2	−	−	PROPN
ma-105	128	3	u(1−	u(1−	ADJ
ma-105	128	4	η)βhv	η)βhv	PROPN
ma-105	128	5	α0	α0	PROPN
ma-105	128	6	+	+	CCONJ
ma-105	128	7	α1h	α1h	PROPN
ma-105	128	8	+	+	SYM
ma-105	128	9	α2v	α2v	NOUN
ma-105	128	10	+	+	CCONJ
ma-105	128	11	α3hv	α3hv	NOUN
ma-105	128	12	in	in	ADP
ma-105	128	13	ωt	ωt	PROPN
ma-105	128	14	,	,	PUNCT
ma-105	128	15	(	(	PUNCT
ma-105	128	16	2.4	2.4	NUM
ma-105	128	17	)	)	PUNCT
ma-105	128	18	∂h	∂h	PROPN
ma-105	128	19	∂η	∂η	PROPN
ma-105	129	1	=	=	PUNCT
ma-105	129	2	∂i	∂i	PROPN
ma-105	129	3	∂η	∂η	PROPN
ma-105	129	4	=	=	SYM
ma-105	129	5	∂v	∂v	PROPN
ma-105	129	6	∂η	∂η	PROPN
ma-105	130	1	=	=	NOUN
ma-105	130	2	0	0	NUM
ma-105	130	3	on	on	ADP
ma-105	130	4	∂ω×	∂ω×	PROPN
ma-105	131	1	[	[	X
ma-105	131	2	0	0	NUM
ma-105	131	3	,	,	PUNCT
ma-105	131	4	t	t	X
ma-105	131	5	]	]	PUNCT
ma-105	131	6	,	,	PUNCT
ma-105	131	7	h(x	h(x	PROPN
ma-105	131	8	,	,	PUNCT
ma-105	131	9	0	0	NUM
ma-105	131	10	)	)	PUNCT
ma-105	131	11	=	=	SYM
ma-105	131	12	h0	h0	PROPN
ma-105	131	13	,	,	PUNCT
ma-105	131	14	i(x	i(x	PROPN
ma-105	131	15	,	,	PUNCT
ma-105	131	16	0	0	NUM
ma-105	131	17	)	)	PUNCT
ma-105	131	18	=	=	SYM
ma-105	131	19	i0	i0	PROPN
ma-105	131	20	,	,	PUNCT
ma-105	131	21	v	v	NOUN
ma-105	131	22	(	(	PUNCT
ma-105	131	23	x	x	NOUN
ma-105	131	24	,	,	PUNCT
ma-105	131	25	0	0	NUM
ma-105	131	26	)	)	PUNCT
ma-105	131	27	=	=	SYM
ma-105	131	28	v0	v0	NOUN
ma-105	131	29	,	,	PUNCT
ma-105	131	30	x	x	X
ma-105	131	31	∈	∈	PROPN
ma-105	131	32	ω	ω	PROPN
ma-105	131	33	,	,	PUNCT
ma-105	131	34	on	on	ADP
ma-105	131	35	which	which	PRON
ma-105	131	36	our	our	PRON
ma-105	131	37	study	study	NOUN
ma-105	131	38	will	will	AUX
ma-105	131	39	focus	focus	VERB
ma-105	131	40	on	on	ADP
ma-105	131	41	.	.	PUNCT
ma-105	132	1	3	3	X
ma-105	132	2	.	.	X
ma-105	132	3	qualitative	qualitative	ADJ
ma-105	132	4	and	and	CCONJ
ma-105	132	5	quantitative	quantitative	ADJ
ma-105	132	6	analysis	analysis	NOUN
ma-105	132	7	and	and	CCONJ
ma-105	132	8	some	some	DET
ma-105	132	9	properties	property	NOUN
ma-105	132	10	of	of	ADP
ma-105	132	11	the	the	DET
ma-105	132	12	solutions	solution	NOUN
ma-105	132	13	for	for	ADP
ma-105	132	14	ibvp	ibvp	NOUN
ma-105	132	15	(	(	PUNCT
ma-105	132	16	2.4	2.4	NUM
ma-105	132	17	)	)	PUNCT
ma-105	132	18	in	in	ADP
ma-105	132	19	this	this	DET
ma-105	132	20	section	section	NOUN
ma-105	132	21	,	,	PUNCT
ma-105	132	22	we	we	PRON
ma-105	132	23	provide	provide	VERB
ma-105	132	24	a	a	DET
ma-105	132	25	thorough	thorough	ADJ
ma-105	132	26	study	study	NOUN
ma-105	132	27	of	of	ADP
ma-105	132	28	the	the	DET
ma-105	132	29	dynamics	dynamic	NOUN
ma-105	132	30	of	of	ADP
ma-105	132	31	ibvp	ibvp	NOUN
ma-105	132	32	(	(	PUNCT
ma-105	132	33	2.4	2.4	NUM
ma-105	132	34	)	)	PUNCT
ma-105	132	35	which	which	PRON
ma-105	132	36	yields	yield	VERB
ma-105	132	37	variousoutcomes	variousoutcome	NOUN
ma-105	132	38	.	.	PUNCT
ma-105	133	1	precisely	precisely	ADV
ma-105	133	2	,	,	PUNCT
ma-105	133	3	we	we	PRON
ma-105	133	4	prove	prove	VERB
ma-105	133	5	existence	existence	NOUN
ma-105	133	6	,	,	PUNCT
ma-105	133	7	uniqueness	uniqueness	NOUN
ma-105	133	8	,	,	PUNCT
ma-105	133	9	positivity	positivity	NOUN
ma-105	133	10	and	and	CCONJ
ma-105	133	11	boundedness	boundedness	NOUN
ma-105	133	12	of	of	ADP
ma-105	133	13	solutions	solution	NOUN
ma-105	133	14	foribvp	foribvp	NOUN
ma-105	133	15	(	(	PUNCT
ma-105	133	16	2.4	2.4	NUM
ma-105	133	17	)	)	PUNCT
ma-105	133	18	.	.	PUNCT
ma-105	134	1	this	this	PRON
ma-105	134	2	is	be	AUX
ma-105	134	3	done	do	VERB
ma-105	134	4	by	by	ADP
ma-105	134	5	combining	combine	VERB
ma-105	134	6	variational	variational	ADJ
ma-105	134	7	method	method	NOUN
ma-105	134	8	and	and	CCONJ
ma-105	134	9	semigroups	semigroup	VERB
ma-105	134	10	techniques	technique	NOUN
ma-105	134	11	to	to	ADP
ma-105	134	12	someuseful	someuseful	ADJ
ma-105	134	13	functional	functional	ADJ
ma-105	134	14	analysis	analysis	NOUN
ma-105	134	15	arguments	argument	NOUN
ma-105	134	16	.	.	PUNCT
ma-105	135	1	3.1	3.1	NUM
ma-105	135	2	.	.	PUNCT
ma-105	135	3	local	local	ADJ
ma-105	135	4	existence	existence	NOUN
ma-105	135	5	and	and	CCONJ
ma-105	135	6	uniqueness	uniqueness	NOUN
ma-105	135	7	of	of	ADP
ma-105	135	8	solutions	solution	NOUN
ma-105	135	9	for	for	ADP
ma-105	135	10	the	the	DET
ma-105	135	11	ibvp	ibvp	NOUN
ma-105	135	12	(	(	PUNCT
ma-105	135	13	2.4	2.4	NUM
ma-105	135	14	)	)	PUNCT
ma-105	135	15	.	.	PUNCT
ma-105	136	1	set	set	VERB
ma-105	136	2	f	f	PROPN
ma-105	136	3	(	(	PUNCT
ma-105	136	4	h	h	NOUN
ma-105	136	5	,	,	PUNCT
ma-105	136	6	i	i	PRON
ma-105	136	7	,	,	PUNCT
ma-105	136	8	v	v	NOUN
ma-105	136	9	)	)	PUNCT
ma-105	136	10	=	=	SYM
ma-105	136	11	(	(	PUNCT
ma-105	136	12	f1(h	f1(h	PROPN
ma-105	136	13	,	,	PUNCT
ma-105	136	14	i	i	PRON
ma-105	136	15	,	,	PUNCT
ma-105	136	16	v	v	NOUN
ma-105	136	17	)	)	PUNCT
ma-105	136	18	,	,	PUNCT
ma-105	136	19	f2(h	f2(h	PROPN
ma-105	136	20	,	,	PUNCT
ma-105	136	21	i	i	PRON
ma-105	136	22	,	,	PUNCT
ma-105	136	23	v	v	NOUN
ma-105	136	24	)	)	PUNCT
ma-105	136	25	,	,	PUNCT
ma-105	136	26	f3(h	f3(h	PROPN
ma-105	136	27	,	,	PUNCT
ma-105	136	28	i	i	PRON
ma-105	136	29	,	,	PUNCT
ma-105	136	30	v	v	NOUN
ma-105	136	31	)	)	PUNCT
ma-105	136	32	)	)	PUNCT
ma-105	137	1	t	t	PROPN
ma-105	137	2	(	(	PUNCT
ma-105	137	3	3.1	3.1	NUM
ma-105	137	4	)	)	PUNCT
ma-105	137	5	where	where	SCONJ
ma-105	137	6	f1(h	f1(h	PROPN
ma-105	137	7	,	,	PUNCT
ma-105	137	8	i	i	PRON
ma-105	137	9	,	,	PUNCT
ma-105	137	10	v	v	NOUN
ma-105	137	11	)	)	PUNCT
ma-105	137	12	=	=	SYM
ma-105	138	1	λ−	λ−	PROPN
ma-105	138	2	dh	dh	NOUN
ma-105	138	3	−	−	PROPN
ma-105	138	4	(	(	PUNCT
ma-105	138	5	1−	1−	NUM
ma-105	138	6	η)βhv	η)βhv	PROPN
ma-105	138	7	α0	α0	PROPN
ma-105	138	8	+	+	CCONJ
ma-105	139	1	α1h	α1h	PROPN
ma-105	139	2	+	+	SYM
ma-105	139	3	α2v	α2v	NUM
ma-105	139	4	+	+	CCONJ
ma-105	139	5	α3hv	α3hv	NOUN
ma-105	140	1	+	+	NUM
ma-105	140	2	ρi	ρi	PROPN
ma-105	140	3	,	,	PUNCT
ma-105	140	4	https://doi.org/10.28924/ada/ma.3.1	https://doi.org/10.28924/ada/ma.3.1	PROPN
ma-105	140	5	eur	eur	PROPN
ma-105	140	6	.	.	PUNCT
ma-105	141	1	j.	j.	PROPN
ma-105	141	2	math	math	PROPN
ma-105	141	3	.	.	PUNCT
ma-105	142	1	anal	anal	PROPN
ma-105	142	2	.	.	PUNCT
ma-105	143	1	10.28924	10.28924	NUM
ma-105	143	2	/	/	SYM
ma-105	143	3	ada	ada	PROPN
ma-105	143	4	/	/	SYM
ma-105	143	5	ma.3.1	ma.3.1	PROPN
ma-105	143	6	6	6	NUM
ma-105	143	7	f2(h	f2(h	PROPN
ma-105	143	8	,	,	PUNCT
ma-105	143	9	i	i	PRON
ma-105	143	10	,	,	PUNCT
ma-105	143	11	v	v	NOUN
ma-105	143	12	)	)	PUNCT
ma-105	143	13	=	=	SYM
ma-105	143	14	(	(	PUNCT
ma-105	143	15	1−	1−	NUM
ma-105	143	16	η)βhv	η)βhv	PROPN
ma-105	143	17	α0	α0	PROPN
ma-105	143	18	+	+	CCONJ
ma-105	143	19	α1h	α1h	PROPN
ma-105	143	20	+	+	SYM
ma-105	143	21	α2v	α2v	NUM
ma-105	143	22	+	+	CCONJ
ma-105	143	23	α3hv	α3hv	NUM
ma-105	143	24	−	−	NOUN
ma-105	143	25	(	(	PUNCT
ma-105	143	26	α+	α+	X
ma-105	143	27	ρ)i	ρ)i	NOUN
ma-105	143	28	,	,	PUNCT
ma-105	143	29	and	and	CCONJ
ma-105	143	30	f3(h	f3(h	PROPN
ma-105	143	31	,	,	PUNCT
ma-105	143	32	i	i	PRON
ma-105	143	33	,	,	PUNCT
ma-105	143	34	v	v	NOUN
ma-105	143	35	)	)	PUNCT
ma-105	143	36	=	=	SYM
ma-105	143	37	(	(	PUNCT
ma-105	143	38	1−	1−	NUM
ma-105	143	39	ε)ki	ε)ki	PROPN
ma-105	143	40	−	−	PROPN
ma-105	144	1	µv	µv	NOUN
ma-105	144	2	−	−	PROPN
ma-105	144	3	u	u	NOUN
ma-105	144	4	(	(	PUNCT
ma-105	144	5	1−	1−	NUM
ma-105	144	6	η)βhv	η)βhv	PROPN
ma-105	144	7	α0	α0	PROPN
ma-105	144	8	+	+	CCONJ
ma-105	144	9	α1h	α1h	PROPN
ma-105	144	10	+	+	SYM
ma-105	144	11	α2v	α2v	NOUN
ma-105	144	12	+	+	CCONJ
ma-105	144	13	α3hv	α3hv	NUM
ma-105	144	14	.we	.we	PUNCT
ma-105	144	15	have	have	VERB
ma-105	144	16	the	the	DET
ma-105	144	17	following	following	ADJ
ma-105	144	18	result	result	NOUN
ma-105	144	19	which	which	PRON
ma-105	144	20	guarantees	guarantee	VERB
ma-105	144	21	that	that	SCONJ
ma-105	144	22	the	the	DET
ma-105	144	23	right	right	ADJ
ma-105	144	24	-	-	PUNCT
ma-105	144	25	hand	hand	NOUN
ma-105	144	26	side	side	NOUN
ma-105	144	27	,	,	PUNCT
ma-105	144	28	without	without	ADP
ma-105	144	29	diffusion	diffusion	NOUN
ma-105	144	30	,	,	PUNCT
ma-105	144	31	of	of	ADP
ma-105	144	32	thepde	thepde	ADJ
ma-105	144	33	-	-	PUNCT
ma-105	144	34	model	model	NOUN
ma-105	144	35	system	system	NOUN
ma-105	144	36	(	(	PUNCT
ma-105	144	37	2.4	2.4	NUM
ma-105	144	38	)	)	PUNCT
ma-105	144	39	is	be	AUX
ma-105	144	40	lipschitz	lipschitz	ADJ
ma-105	144	41	.	.	PUNCT
ma-105	145	1	proposition	proposition	NOUN
ma-105	145	2	3.1	3.1	NUM
ma-105	145	3	.	.	PUNCT
ma-105	146	1	let	let	VERB
ma-105	146	2	t	t	PROPN
ma-105	146	3	∈	∈	PROPN
ma-105	146	4	r∗+	r∗+	PROPN
ma-105	146	5	and	and	CCONJ
ma-105	146	6	(	(	PUNCT
ma-105	146	7	h	h	NOUN
ma-105	146	8	,	,	PUNCT
ma-105	146	9	i	i	PRON
ma-105	146	10	,	,	PUNCT
ma-105	146	11	v	v	NOUN
ma-105	146	12	)	)	PUNCT
ma-105	146	13	∈	∈	PROPN
ma-105	146	14	(	(	PUNCT
ma-105	146	15	c0	c0	NOUN
ma-105	146	16	b(ω	b(ω	PROPN
ma-105	146	17	×	×	NOUN
ma-105	147	1	[	[	X
ma-105	147	2	0	0	NUM
ma-105	147	3	,	,	PUNCT
ma-105	147	4	t	t	X
ma-105	147	5	]	]	PUNCT
ma-105	147	6	)	)	PUNCT
ma-105	147	7	)	)	PUNCT
ma-105	147	8	3	3	NUM
ma-105	147	9	,	,	PUNCT
ma-105	147	10	where	where	SCONJ
ma-105	147	11	c0	c0	PROPN
ma-105	147	12	b(ω	b(ω	PROPN
ma-105	147	13	×	×	PROPN
ma-105	147	14	[	[	X
ma-105	147	15	0	0	NUM
ma-105	147	16	,	,	PUNCT
ma-105	147	17	t	t	X
ma-105	147	18	]	]	PUNCT
ma-105	147	19	)	)	PUNCT
ma-105	147	20	is	be	AUX
ma-105	147	21	the	the	DET
ma-105	147	22	space	space	NOUN
ma-105	147	23	of	of	ADP
ma-105	147	24	bounded	bounded	ADJ
ma-105	147	25	and	and	CCONJ
ma-105	147	26	continuous	continuous	ADJ
ma-105	147	27	functions	function	NOUN
ma-105	147	28	on	on	ADP
ma-105	147	29	ω	ω	NUM
ma-105	147	30	×	×	NOUN
ma-105	148	1	[	[	X
ma-105	148	2	0	0	NUM
ma-105	148	3	,	,	PUNCT
ma-105	148	4	t	t	X
ma-105	148	5	]	]	PUNCT
ma-105	148	6	.	.	PUNCT
ma-105	149	1	we	we	PRON
ma-105	149	2	suppose	suppose	VERB
ma-105	149	3	that	that	SCONJ
ma-105	149	4	f	f	PROPN
ma-105	149	5	in	in	ADP
ma-105	149	6	(	(	PUNCT
ma-105	149	7	3.1	3.1	NUM
ma-105	149	8	)	)	PUNCT
ma-105	149	9	is	be	AUX
ma-105	149	10	defined	define	VERB
ma-105	149	11	on	on	ADP
ma-105	149	12	l2(ω×	l2(ω×	PROPN
ma-105	149	13	(	(	PUNCT
ma-105	149	14	0	0	NUM
ma-105	149	15	,	,	PUNCT
ma-105	149	16	t	t	NOUN
ma-105	149	17	)	)	PUNCT
ma-105	149	18	)	)	PUNCT
ma-105	149	19	.	.	PUNCT
ma-105	150	1	then	then	ADV
ma-105	150	2	f1	f1	PROPN
ma-105	150	3	,	,	PUNCT
ma-105	150	4	f2	f2	PROPN
ma-105	150	5	and	and	CCONJ
ma-105	150	6	f3	f3	PROPN
ma-105	150	7	are	be	AUX
ma-105	150	8	uniformly	uniformly	ADV
ma-105	150	9	lipschitz	lipschitz	VERB
ma-105	150	10	continuous	continuous	ADJ
ma-105	150	11	on	on	ADP
ma-105	150	12	l2(ω×	l2(ω×	PROPN
ma-105	150	13	(	(	PUNCT
ma-105	150	14	0	0	NUM
ma-105	150	15	,	,	PUNCT
ma-105	150	16	t	t	NOUN
ma-105	150	17	)	)	PUNCT
ma-105	150	18	)	)	PUNCT
ma-105	150	19	with	with	ADP
ma-105	150	20	respect	respect	NOUN
ma-105	150	21	to	to	ADP
ma-105	150	22	h	h	NOUN
ma-105	150	23	,	,	PUNCT
ma-105	150	24	i	i	PRON
ma-105	150	25	and	and	CCONJ
ma-105	150	26	v.	v.	ADP
ma-105	150	27	proof	proof	NOUN
ma-105	150	28	.	.	PUNCT
ma-105	151	1	let	let	VERB
ma-105	151	2	t	t	PROPN
ma-105	151	3	∈	∈	PROPN
ma-105	151	4	r∗+	r∗+	PROPN
ma-105	151	5	and	and	CCONJ
ma-105	151	6	(	(	PUNCT
ma-105	151	7	h1	h1	PROPN
ma-105	151	8	,	,	PUNCT
ma-105	151	9	i1	i1	PROPN
ma-105	151	10	,	,	PUNCT
ma-105	151	11	v1	v1	PROPN
ma-105	151	12	)	)	PUNCT
ma-105	151	13	,	,	PUNCT
ma-105	151	14	(	(	PUNCT
ma-105	151	15	h2	h2	PROPN
ma-105	151	16	,	,	PUNCT
ma-105	151	17	i2	i2	PROPN
ma-105	151	18	,	,	PUNCT
ma-105	151	19	v2	v2	PROPN
ma-105	151	20	)	)	PUNCT
ma-105	151	21	∈	∈	PROPN
ma-105	151	22	(	(	PUNCT
ma-105	151	23	c0	c0	NOUN
ma-105	151	24	b(ω×	b(ω×	PROPN
ma-105	152	1	[	[	X
ma-105	152	2	0	0	NUM
ma-105	152	3	,	,	PUNCT
ma-105	152	4	t	t	X
ma-105	152	5	]	]	PUNCT
ma-105	152	6	)	)	PUNCT
ma-105	152	7	)	)	PUNCT
ma-105	153	1	3	3	X
ma-105	153	2	.	.	X
ma-105	153	3	first	first	ADV
ma-105	153	4	,	,	PUNCT
ma-105	153	5	by	by	ADP
ma-105	153	6	direct	direct	ADJ
ma-105	153	7	computation	computation	NOUN
ma-105	153	8	,	,	PUNCT
ma-105	153	9	we	we	PRON
ma-105	153	10	have	have	VERB
ma-105	153	11	:	:	PUNCT
ma-105	153	12	‖f1(h1	‖f1(h1	PROPN
ma-105	153	13	,	,	PUNCT
ma-105	153	14	i1	i1	PROPN
ma-105	153	15	,	,	PUNCT
ma-105	153	16	v1)−	v1)−	PROPN
ma-105	153	17	f1(h2	f1(h2	PROPN
ma-105	153	18	,	,	PUNCT
ma-105	153	19	i2	i2	PROPN
ma-105	153	20	,	,	PUNCT
ma-105	153	21	v2)‖2	v2)‖2	ADJ
ma-105	153	22	≤	≤	NUM
ma-105	153	23	k1	k1	NOUN
ma-105	153	24	1‖h1	1‖h1	NUM
ma-105	154	1	−h2‖2	−h2‖2	PROPN
ma-105	154	2	+	+	PROPN
ma-105	154	3	k1	k1	NOUN
ma-105	154	4	2‖i1	2‖i1	NUM
ma-105	154	5	−	−	PROPN
ma-105	155	1	i2‖2	i2‖2	X
ma-105	156	1	+	+	NUM
ma-105	156	2	k1	k1	NOUN
ma-105	156	3	3‖v1	3‖v1	NUM
ma-105	156	4	−	−	NOUN
ma-105	156	5	v2‖2	v2‖2	NUM
ma-105	156	6	,	,	PUNCT
ma-105	156	7	(	(	PUNCT
ma-105	156	8	3.2	3.2	NUM
ma-105	156	9	)	)	PUNCT
ma-105	156	10	with	with	ADP
ma-105	156	11	k1	k1	NOUN
ma-105	156	12	1	1	NUM
ma-105	156	13	=	=	SYM
ma-105	156	14	d	d	NOUN
ma-105	156	15	+	+	CCONJ
ma-105	156	16	(	(	PUNCT
ma-105	156	17	1−	1−	NUM
ma-105	156	18	η)β	η)β	PUNCT
ma-105	156	19	(	(	PUNCT
ma-105	156	20	1	1	NUM
ma-105	156	21	α2	α2	ADJ
ma-105	156	22	+	+	CCONJ
ma-105	156	23	vm	vm	PROPN
ma-105	157	1	α0	α0	PROPN
ma-105	157	2	)	)	PUNCT
ma-105	158	1	,	,	PUNCT
ma-105	158	2	k1	k1	NOUN
ma-105	158	3	2	2	NUM
ma-105	158	4	=	=	SYM
ma-105	158	5	ρ	ρ	PROPN
ma-105	158	6	,	,	PUNCT
ma-105	158	7	k1	k1	NOUN
ma-105	158	8	3	3	NUM
ma-105	158	9	=	=	SYM
ma-105	158	10	(	(	PUNCT
ma-105	158	11	1−	1−	NUM
ma-105	158	12	η)β	η)β	PUNCT
ma-105	158	13	(	(	PUNCT
ma-105	158	14	1	1	NUM
ma-105	158	15	α1	α1	NOUN
ma-105	158	16	+	+	CCONJ
ma-105	158	17	hm	hm	INTJ
ma-105	158	18	α0	α0	ADJ
ma-105	158	19	)	)	PUNCT
ma-105	158	20	,	,	PUNCT
ma-105	158	21	(	(	PUNCT
ma-105	158	22	3.3)with	3.3)with	NUM
ma-105	158	23	hm	hm	INTJ
ma-105	158	24	and	and	CCONJ
ma-105	158	25	vm	vm	PROPN
ma-105	158	26	given	give	VERB
ma-105	158	27	below.then	below.then	PROPN
ma-105	158	28	‖f2(h1	‖f2(h1	NOUN
ma-105	158	29	,	,	PUNCT
ma-105	158	30	i1	i1	PROPN
ma-105	158	31	,	,	PUNCT
ma-105	158	32	v1)−	v1)−	PROPN
ma-105	158	33	f2(h2	f2(h2	NOUN
ma-105	158	34	,	,	PUNCT
ma-105	158	35	i2	i2	PROPN
ma-105	158	36	,	,	PUNCT
ma-105	158	37	v2)‖2	v2)‖2	ADJ
ma-105	158	38	≤	≤	NUM
ma-105	158	39	k2	k2	NOUN
ma-105	158	40	1‖h1	1‖h1	ADJ
ma-105	159	1	−h2‖2	−h2‖2	PROPN
ma-105	159	2	+	+	PROPN
ma-105	159	3	k2	k2	ADJ
ma-105	159	4	2‖i1	2‖i1	NUM
ma-105	159	5	−	−	PROPN
ma-105	159	6	i2‖2	i2‖2	PROPN
ma-105	160	1	+	+	SYM
ma-105	160	2	k2	k2	ADJ
ma-105	160	3	3‖v1	3‖v1	PROPN
ma-105	160	4	−	−	PROPN
ma-105	160	5	v2‖2	v2‖2	NUM
ma-105	160	6	,	,	PUNCT
ma-105	160	7	(	(	PUNCT
ma-105	160	8	3.4	3.4	NUM
ma-105	160	9	)	)	PUNCT
ma-105	160	10	with	with	ADP
ma-105	160	11	k2	k2	PROPN
ma-105	160	12	1	1	NUM
ma-105	160	13	=	=	SYM
ma-105	160	14	(	(	PUNCT
ma-105	160	15	1−	1−	NUM
ma-105	160	16	η)β	η)β	PUNCT
ma-105	160	17	(	(	PUNCT
ma-105	160	18	1	1	NUM
ma-105	160	19	α2	α2	ADJ
ma-105	160	20	+	+	CCONJ
ma-105	160	21	vm	vm	PROPN
ma-105	160	22	α0	α0	PROPN
ma-105	160	23	)	)	PUNCT
ma-105	160	24	,	,	PUNCT
ma-105	160	25	k2	k2	NOUN
ma-105	160	26	2	2	NUM
ma-105	160	27	=	=	SYM
ma-105	160	28	(	(	PUNCT
ma-105	160	29	α+	α+	NOUN
ma-105	160	30	ρ	ρ	NOUN
ma-105	160	31	)	)	PUNCT
ma-105	160	32	and	and	CCONJ
ma-105	160	33	k2	k2	ADJ
ma-105	160	34	3	3	NUM
ma-105	160	35	=	=	SYM
ma-105	160	36	(	(	PUNCT
ma-105	160	37	1−	1−	NUM
ma-105	160	38	η)β	η)β	PUNCT
ma-105	160	39	(	(	PUNCT
ma-105	160	40	1	1	NUM
ma-105	160	41	α1	α1	NOUN
ma-105	160	42	+	+	CCONJ
ma-105	160	43	hm	hm	INTJ
ma-105	160	44	α0	α0	ADJ
ma-105	160	45	)	)	PUNCT
ma-105	160	46	.	.	PUNCT
ma-105	161	1	(	(	PUNCT
ma-105	161	2	3.5	3.5	NUM
ma-105	161	3	)	)	PUNCT
ma-105	161	4	finally	finally	ADV
ma-105	161	5	‖f3(h1	‖f3(h1	PROPN
ma-105	161	6	,	,	PUNCT
ma-105	161	7	i1	i1	PROPN
ma-105	161	8	,	,	PUNCT
ma-105	161	9	v1)−	v1)−	PROPN
ma-105	161	10	f3(h2	f3(h2	NOUN
ma-105	161	11	,	,	PUNCT
ma-105	161	12	i2	i2	PROPN
ma-105	161	13	,	,	PUNCT
ma-105	161	14	v2)‖2	v2)‖2	ADJ
ma-105	161	15	≤	≤	NOUN
ma-105	161	16	k3	k3	VERB
ma-105	161	17	1‖h1	1‖h1	ADJ
ma-105	162	1	−h2‖2	−h2‖2	PROPN
ma-105	162	2	+	+	ADP
ma-105	162	3	k3	k3	VERB
ma-105	162	4	2‖i1	2‖i1	NUM
ma-105	162	5	−	−	PROPN
ma-105	162	6	i2‖2	i2‖2	X
ma-105	163	1	+	+	CCONJ
ma-105	163	2	k3	k3	ADJ
ma-105	163	3	3‖v1	3‖v1	PROPN
ma-105	163	4	−	−	PROPN
ma-105	163	5	v2‖2	v2‖2	NUM
ma-105	163	6	,	,	PUNCT
ma-105	163	7	(	(	PUNCT
ma-105	163	8	3.6	3.6	NUM
ma-105	163	9	)	)	PUNCT
ma-105	163	10	with	with	ADP
ma-105	163	11	k3	k3	ADJ
ma-105	163	12	1	1	NUM
ma-105	163	13	=	=	SYM
ma-105	163	14	u(1−	u(1−	NOUN
ma-105	163	15	η)β	η)β	PUNCT
ma-105	163	16	(	(	PUNCT
ma-105	163	17	1	1	NUM
ma-105	163	18	α2	α2	ADJ
ma-105	163	19	+	+	CCONJ
ma-105	163	20	vm	vm	PROPN
ma-105	163	21	α0	α0	PROPN
ma-105	163	22	)	)	PUNCT
ma-105	163	23	,	,	PUNCT
ma-105	163	24	k3	k3	VERB
ma-105	163	25	2	2	NUM
ma-105	163	26	=	=	SYM
ma-105	163	27	k(1−	k(1−	PROPN
ma-105	163	28	ε	ε	PROPN
ma-105	163	29	)	)	PUNCT
ma-105	163	30	,	,	PUNCT
ma-105	163	31	and	and	CCONJ
ma-105	163	32	k3	k3	VERB
ma-105	163	33	3	3	NUM
ma-105	163	34	=	=	SYM
ma-105	163	35	µ+	µ+	X
ma-105	163	36	u(1−	u(1−	PROPN
ma-105	163	37	η)β	η)β	PUNCT
ma-105	163	38	(	(	PUNCT
ma-105	163	39	1	1	NUM
ma-105	163	40	α1	α1	NOUN
ma-105	163	41	+	+	CCONJ
ma-105	163	42	hm	hm	INTJ
ma-105	163	43	α0	α0	ADJ
ma-105	163	44	)	)	PUNCT
ma-105	163	45	.	.	PUNCT
ma-105	164	1	(	(	PUNCT
ma-105	164	2	3.7	3.7	NUM
ma-105	164	3	)	)	PUNCT
ma-105	164	4	this	this	PRON
ma-105	164	5	completes	complete	VERB
ma-105	164	6	the	the	DET
ma-105	164	7	proof	proof	NOUN
ma-105	164	8	of	of	ADP
ma-105	164	9	proposition	proposition	NOUN
ma-105	164	10	3.1	3.1	NUM
ma-105	164	11	.	.	PUNCT
ma-105	164	12	�	�	PROPN
ma-105	164	13	now	now	ADV
ma-105	164	14	,	,	PUNCT
ma-105	164	15	consider	consider	VERB
ma-105	164	16	the	the	DET
ma-105	164	17	following	follow	VERB
ma-105	164	18	ibvp	ibvp	PROPN
ma-105	164	19	∂th	∂th	PROPN
ma-105	164	20	−d1∆h	−d1∆h	NOUN
ma-105	164	21	=	=	SYM
ma-105	164	22	f	f	X
ma-105	164	23	(	(	PUNCT
ma-105	164	24	t	t	PROPN
ma-105	164	25	,	,	PUNCT
ma-105	164	26	h	h	NOUN
ma-105	164	27	,	,	PUNCT
ma-105	164	28	i	i	PRON
ma-105	164	29	,	,	PUNCT
ma-105	164	30	v	v	NOUN
ma-105	164	31	)	)	PUNCT
ma-105	164	32	in	in	ADP
ma-105	164	33	ω×	ω×	PROPN
ma-105	164	34	(	(	PUNCT
ma-105	164	35	0	0	NUM
ma-105	164	36	,	,	PUNCT
ma-105	164	37	t	t	NOUN
ma-105	164	38	)	)	PUNCT
ma-105	165	1	∂t	∂t	PROPN
ma-105	166	1	i	i	PRON
ma-105	166	2	−d2∆i	−d2∆i	NOUN
ma-105	166	3	=	=	SYM
ma-105	167	1	g(t	g(t	PROPN
ma-105	167	2	,	,	PUNCT
ma-105	167	3	h	h	NOUN
ma-105	167	4	,	,	PUNCT
ma-105	167	5	i	i	PRON
ma-105	167	6	,	,	PUNCT
ma-105	167	7	v	v	NOUN
ma-105	167	8	)	)	PUNCT
ma-105	167	9	in	in	ADP
ma-105	167	10	ω×	ω×	PROPN
ma-105	167	11	(	(	PUNCT
ma-105	167	12	0	0	NUM
ma-105	167	13	,	,	PUNCT
ma-105	167	14	t	t	NOUN
ma-105	167	15	)	)	PUNCT
ma-105	167	16	∂tv	∂tv	PROPN
ma-105	167	17	−d3∆v	−d3∆v	NOUN
ma-105	167	18	=	=	PUNCT
ma-105	167	19	h(t	h(t	PROPN
ma-105	167	20	,	,	PUNCT
ma-105	167	21	h	h	NOUN
ma-105	167	22	,	,	PUNCT
ma-105	167	23	i	i	PRON
ma-105	167	24	,	,	PUNCT
ma-105	167	25	v	v	NOUN
ma-105	167	26	)	)	PUNCT
ma-105	167	27	in	in	ADP
ma-105	167	28	ω×	ω×	PROPN
ma-105	167	29	(	(	PUNCT
ma-105	167	30	0	0	NUM
ma-105	167	31	,	,	PUNCT
ma-105	167	32	t	t	NOUN
ma-105	167	33	)	)	PUNCT
ma-105	168	1	∂h	∂h	PROPN
ma-105	168	2	∂η	∂η	PROPN
ma-105	169	1	=	=	NOUN
ma-105	169	2	0	0	NUM
ma-105	169	3	;	;	PUNCT
ma-105	170	1	∂i	∂i	PROPN
ma-105	170	2	∂η	∂η	PROPN
ma-105	170	3	=	=	NOUN
ma-105	170	4	0	0	NUM
ma-105	170	5	;	;	PUNCT
ma-105	171	1	∂v	∂v	PROPN
ma-105	171	2	∂η	∂η	PROPN
ma-105	172	1	=	=	NOUN
ma-105	172	2	0	0	NUM
ma-105	173	1	on	on	ADP
ma-105	173	2	∂ω×	∂ω×	PROPN
ma-105	174	1	[	[	X
ma-105	174	2	0	0	NUM
ma-105	174	3	,	,	PUNCT
ma-105	174	4	t	t	NOUN
ma-105	174	5	]	]	PUNCT
ma-105	174	6	h	h	PROPN
ma-105	174	7	=	=	PUNCT
ma-105	174	8	h0	h0	PROPN
ma-105	174	9	,	,	PUNCT
ma-105	174	10	i	i	PROPN
ma-105	174	11	=	=	SYM
ma-105	174	12	i0	i0	PROPN
ma-105	174	13	,	,	PUNCT
ma-105	174	14	v	v	NOUN
ma-105	174	15	=	=	SYM
ma-105	174	16	v0	v0	NOUN
ma-105	174	17	on	on	ADP
ma-105	174	18	ω×	ω×	PROPN
ma-105	174	19	{	{	PUNCT
ma-105	174	20	t	t	NOUN
ma-105	174	21	=	=	SYM
ma-105	174	22	0	0	NUM
ma-105	174	23	}	}	PUNCT
ma-105	174	24	.	.	PUNCT
ma-105	175	1	(	(	PUNCT
ma-105	175	2	3.8	3.8	NUM
ma-105	175	3	)	)	PUNCT
ma-105	175	4	in	in	ADP
ma-105	175	5	what	what	PRON
ma-105	175	6	follows	follow	VERB
ma-105	175	7	,	,	PUNCT
ma-105	175	8	we	we	PRON
ma-105	175	9	will	will	AUX
ma-105	175	10	need	need	VERB
ma-105	175	11	the	the	DET
ma-105	175	12	following	follow	VERB
ma-105	175	13	definition	definition	NOUN
ma-105	175	14	and	and	CCONJ
ma-105	175	15	results	result	NOUN
ma-105	175	16	.	.	PUNCT
ma-105	176	1	https://doi.org/10.28924/ada/ma.3.1	https://doi.org/10.28924/ada/ma.3.1	PROPN
ma-105	176	2	eur	eur	PROPN
ma-105	176	3	.	.	PUNCT
ma-105	177	1	j.	j.	PROPN
ma-105	177	2	math	math	PROPN
ma-105	177	3	.	.	PUNCT
ma-105	178	1	anal	anal	PROPN
ma-105	178	2	.	.	PUNCT
ma-105	179	1	10.28924	10.28924	NUM
ma-105	179	2	/	/	SYM
ma-105	179	3	ada	ada	PROPN
ma-105	179	4	/	/	SYM
ma-105	179	5	ma.3.1	ma.3.1	PROPN
ma-105	179	6	7	7	NUM
ma-105	179	7	definition	definition	NOUN
ma-105	179	8	3.1	3.1	NUM
ma-105	179	9	.	.	PUNCT
ma-105	180	1	(	(	PUNCT
ma-105	180	2	sectorial	sectorial	ADJ
ma-105	180	3	operator	operator	NOUN
ma-105	180	4	,	,	PUNCT
ma-105	180	5	[	[	X
ma-105	180	6	22	22	NUM
ma-105	180	7	]	]	PUNCT
ma-105	180	8	)	)	PUNCT
ma-105	180	9	let	let	VERB
ma-105	180	10	a	a	PRON
ma-105	180	11	be	be	AUX
ma-105	180	12	a	a	DET
ma-105	180	13	linear	linear	ADJ
ma-105	180	14	operator	operator	NOUN
ma-105	180	15	in	in	ADP
ma-105	180	16	a	a	DET
ma-105	180	17	banach	banach	NOUN
ma-105	180	18	space	space	NOUN
ma-105	180	19	x	x	X
ma-105	180	20	andsuppose	andsuppose	ADV
ma-105	180	21	a	a	PRON
ma-105	180	22	is	be	AUX
ma-105	180	23	closed	closed	ADJ
ma-105	180	24	and	and	CCONJ
ma-105	180	25	densely	densely	ADV
ma-105	180	26	defined	define	VERB
ma-105	180	27	.	.	PUNCT
ma-105	181	1	if	if	SCONJ
ma-105	181	2	there	there	PRON
ma-105	181	3	exist	exist	VERB
ma-105	181	4	real	real	ADJ
ma-105	181	5	numbers	number	NOUN
ma-105	181	6	a	a	DET
ma-105	181	7	,	,	PUNCT
ma-105	181	8	ω	ω	PROPN
ma-105	181	9	∈	∈	PROPN
ma-105	181	10	(	(	PUNCT
ma-105	181	11	0	0	NUM
ma-105	181	12	,	,	PUNCT
ma-105	181	13	π	π	PROPN
ma-105	181	14	)	)	PUNCT
ma-105	181	15	,	,	PUNCT
ma-105	181	16	m	m	VERB
ma-105	181	17	≥	≥	NUM
ma-105	181	18	1	1	NUM
ma-105	181	19	suchthat	suchthat	VERB
ma-105	181	20	ρ(a	ρ(a	PROPN
ma-105	181	21	)	)	PUNCT
ma-105	182	1	⊃	⊃	PROPN
ma-105	182	2	σ	σ	X
ma-105	182	3	=	=	SYM
ma-105	182	4	{	{	PUNCT
ma-105	182	5	λ0	λ0	NOUN
ma-105	182	6	∈	∈	NOUN
ma-105	182	7	c	c	NOUN
ma-105	182	8	:	:	PUNCT
ma-105	182	9	ω	ω	NUM
ma-105	182	10	≤	≤	PUNCT
ma-105	182	11	arg(λ0	arg(λ0	PROPN
ma-105	182	12	−	−	PROPN
ma-105	182	13	a	a	X
ma-105	182	14	)	)	PUNCT
ma-105	182	15	≤	≤	PROPN
ma-105	182	16	π	π	PROPN
ma-105	182	17	,	,	PUNCT
ma-105	182	18	λ0	λ0	NOUN
ma-105	182	19	6=	6=	PRON
ma-105	182	20	0	0	NUM
ma-105	182	21	}	}	PUNCT
ma-105	182	22	(	(	PUNCT
ma-105	182	23	3.9)and	3.9)and	NUM
ma-105	182	24	‖rλ0	‖rλ0	PROPN
ma-105	182	25	(	(	PUNCT
ma-105	182	26	a)‖	a)‖	ADJ
ma-105	182	27	≤	≤	PUNCT
ma-105	182	28	m	m	VERB
ma-105	182	29	|λ0	|λ0	NOUN
ma-105	182	30	−	−	PROPN
ma-105	182	31	a|	a|	PROPN
ma-105	182	32	for	for	ADP
ma-105	182	33	all	all	DET
ma-105	182	34	λ0	λ0	NOUN
ma-105	182	35	∈	∈	PROPN
ma-105	182	36	σ	σ	NOUN
ma-105	182	37	,	,	PUNCT
ma-105	182	38	(	(	PUNCT
ma-105	182	39	3.10)then	3.10)then	NUM
ma-105	182	40	we	we	PRON
ma-105	182	41	say	say	VERB
ma-105	182	42	that	that	SCONJ
ma-105	182	43	a	a	PRON
ma-105	182	44	is	be	AUX
ma-105	182	45	sectorial	sectorial	ADJ
ma-105	182	46	.	.	PUNCT
ma-105	183	1	remark	remark	NOUN
ma-105	183	2	3.1	3.1	NUM
ma-105	183	3	.	.	PUNCT
ma-105	184	1	the	the	DET
ma-105	184	2	neumann	neumann	PROPN
ma-105	184	3	realization	realization	NOUN
ma-105	184	4	of	of	ADP
ma-105	184	5	the	the	DET
ma-105	184	6	laplacian	laplacian	ADJ
ma-105	184	7	a	a	PRON
ma-105	184	8	=	=	SYM
ma-105	184	9	−∆	−∆	NOUN
ma-105	184	10	,	,	PUNCT
ma-105	184	11	with	with	ADP
ma-105	184	12	domain	domain	NOUN
ma-105	184	13	d(a	d(a	PROPN
ma-105	184	14	)	)	PUNCT
ma-105	184	15	=	=	PRON
ma-105	184	16	{	{	PUNCT
ma-105	184	17	ω	ω	NUM
ma-105	184	18	∈	∈	PROPN
ma-105	184	19	h2(ω	h2(ω	NOUN
ma-105	184	20	)	)	PUNCT
ma-105	184	21	:	:	PUNCT
ma-105	185	1	∂ω	∂ω	PROPN
ma-105	185	2	∂η	∂η	PROPN
ma-105	185	3	=	=	SYM
ma-105	185	4	0	0	NUM
ma-105	185	5	}	}	PUNCT
ma-105	185	6	is	be	AUX
ma-105	185	7	a	a	DET
ma-105	185	8	sectorial	sectorial	ADJ
ma-105	185	9	operator	operator	NOUN
ma-105	185	10	in	in	ADP
ma-105	185	11	l2(ω	l2(ω	PROPN
ma-105	185	12	)	)	PUNCT
ma-105	185	13	.	.	PUNCT
ma-105	186	1	but	but	CCONJ
ma-105	186	2	since	since	SCONJ
ma-105	186	3	c∞0	c∞0	PROPN
ma-105	186	4	(	(	PUNCT
ma-105	186	5	ω	ω	NUM
ma-105	186	6	)	)	PUNCT
ma-105	186	7	⊂	⊂	PROPN
ma-105	186	8	d(a	d(a	PROPN
ma-105	186	9	)	)	PUNCT
ma-105	186	10	,	,	PUNCT
ma-105	186	11	it	it	PRON
ma-105	186	12	is	be	AUX
ma-105	186	13	densely	densely	ADV
ma-105	186	14	defined	define	VERB
ma-105	186	15	in	in	ADP
ma-105	186	16	l2(ω	l2(ω	NOUN
ma-105	186	17	)	)	PUNCT
ma-105	186	18	.	.	PUNCT
ma-105	187	1	for	for	ADP
ma-105	187	2	β	β	X
ma-105	187	3	≥	≥	X
ma-105	187	4	0	0	NUM
ma-105	187	5	large	large	ADJ
ma-105	187	6	enough	enough	ADV
ma-105	187	7	,	,	PUNCT
ma-105	187	8	we	we	PRON
ma-105	187	9	define	define	VERB
ma-105	187	10	the	the	DET
ma-105	187	11	fractional	fractional	ADJ
ma-105	187	12	powers	power	NOUN
ma-105	187	13	of	of	ADP
ma-105	187	14	the	the	DET
ma-105	187	15	helmholtz	helmholtz	NOUN
ma-105	187	16	operator	operator	NOUN
ma-105	187	17	,	,	PUNCT
ma-105	187	18	h	h	NOUN
ma-105	187	19	�	�	X
ma-105	187	20	=	=	PUNCT
ma-105	187	21	−∆	−∆	NOUN
ma-105	187	22	+	+	CCONJ
ma-105	187	23	βi	βi	PRON
ma-105	187	24	,	,	PUNCT
ma-105	187	25	with	with	ADP
ma-105	187	26	domain	domain	NOUN
ma-105	187	27	d(h	d(h	PROPN
ma-105	187	28	�	�	PROPN
ma-105	187	29	)	)	PUNCT
ma-105	187	30	equipped	equip	VERB
ma-105	187	31	with	with	ADP
ma-105	187	32	graph	graph	NOUN
ma-105	187	33	norm	norm	NOUN
ma-105	187	34	‖	‖	PROPN
ma-105	187	35	.	.	PUNCT
ma-105	188	1	‖d(h	‖d(h	SYM
ma-105	188	2	�	�	PROPN
ma-105	188	3	)	)	PUNCT
ma-105	188	4	=	=	PUNCT
ma-105	189	1	‖	‖	PROPN
ma-105	189	2	.	.	PUNCT
ma-105	190	1	‖2	‖2	NOUN
ma-105	190	2	+	+	CCONJ
ma-105	190	3	‖h	‖h	NOUN
ma-105	190	4	�	�	NOUN
ma-105	190	5	.‖2	.‖2	PROPN
ma-105	190	6	.	.	PUNCT
ma-105	191	1	we	we	PRON
ma-105	191	2	have	have	VERB
ma-105	191	3	the	the	DET
ma-105	191	4	following	follow	VERB
ma-105	191	5	general	general	ADJ
ma-105	191	6	results	result	NOUN
ma-105	191	7	.	.	PUNCT
ma-105	192	1	lemma	lemma	PROPN
ma-105	192	2	3.2	3.2	NUM
ma-105	192	3	.	.	PUNCT
ma-105	193	1	[	[	X
ma-105	193	2	1	1	X
ma-105	193	3	]	]	PUNCT
ma-105	193	4	let	let	VERB
ma-105	193	5	1	1	NUM
ma-105	193	6	≤	≤	NOUN
ma-105	194	1	p	p	NOUN
ma-105	194	2	<	<	X
ma-105	194	3	∞.	∞.	PROPN
ma-105	194	4	then	then	ADV
ma-105	194	5	d(h	d(h	PROPN
ma-105	194	6	�	�	PROPN
ma-105	194	7	)	)	PUNCT
ma-105	194	8	⊂	⊂	PROPN
ma-105	194	9	c∞0	c∞0	PROPN
ma-105	194	10	(	(	PUNCT
ma-105	194	11	ω	ω	NOUN
ma-105	194	12	)	)	PUNCT
ma-105	194	13	with	with	ADP
ma-105	194	14	continuous	continuous	ADJ
ma-105	194	15	injection	injection	NOUN
ma-105	194	16	for	for	ADP
ma-105	194	17	β	β	X
ma-105	194	18	>	>	X
ma-105	194	19	n	n	PRON
ma-105	194	20	2p	2p	NUM
ma-105	194	21	.	.	PUNCT
ma-105	195	1	lemma	lemma	PROPN
ma-105	195	2	3.3	3.3	NUM
ma-105	195	3	.	.	PUNCT
ma-105	196	1	[	[	X
ma-105	196	2	22	22	NUM
ma-105	196	3	]	]	PUNCT
ma-105	196	4	d(hβ	d(hβ	NUM
ma-105	196	5	)	)	PUNCT
ma-105	196	6	⊂	⊂	PROPN
ma-105	196	7	c0	c0	PROPN
ma-105	196	8	b(ω	b(ω	ADV
ma-105	196	9	)	)	PUNCT
ma-105	196	10	with	with	ADP
ma-105	196	11	continuous	continuous	ADJ
ma-105	196	12	injection	injection	NOUN
ma-105	196	13	for	for	ADP
ma-105	196	14	β	β	X
ma-105	196	15	>	>	X
ma-105	196	16	n	n	PROPN
ma-105	196	17	4	4	NUM
ma-105	196	18	.	.	PUNCT
ma-105	196	19	theorem	theorem	VERB
ma-105	196	20	3.4	3.4	NUM
ma-105	196	21	.	.	PUNCT
ma-105	197	1	[	[	X
ma-105	197	2	22	22	NUM
ma-105	197	3	]	]	X
ma-105	197	4	if	if	SCONJ
ma-105	197	5	a	a	PRON
ma-105	197	6	is	be	AUX
ma-105	197	7	sectorial	sectorial	ADJ
ma-105	197	8	,	,	PUNCT
ma-105	197	9	then	then	ADV
ma-105	197	10	−a	−a	VERB
ma-105	197	11	is	be	AUX
ma-105	197	12	the	the	DET
ma-105	197	13	infinitesimal	infinitesimal	ADJ
ma-105	197	14	generator	generator	NOUN
ma-105	197	15	of	of	ADP
ma-105	197	16	an	an	DET
ma-105	197	17	analytic	analytic	ADJ
ma-105	197	18	semigroup	semigroup	NOUN
ma-105	197	19	,	,	PUNCT
ma-105	197	20	g(t	g(t	PROPN
ma-105	197	21	)	)	PUNCT
ma-105	197	22	.	.	PUNCT
ma-105	198	1	if	if	SCONJ
ma-105	198	2	rλ0	rλ0	VERB
ma-105	198	3	>	>	PUNCT
ma-105	198	4	a	a	PRON
ma-105	198	5	,	,	PUNCT
ma-105	198	6	a	a	DET
ma-105	198	7	∈	∈	NOUN
ma-105	198	8	r	r	NOUN
ma-105	198	9	whenever	whenever	SCONJ
ma-105	198	10	λ0	λ0	NOUN
ma-105	198	11	∈	∈	PROPN
ma-105	198	12	σ	σ	NOUN
ma-105	198	13	,	,	PUNCT
ma-105	198	14	then	then	ADV
ma-105	198	15	for	for	ADP
ma-105	198	16	any	any	DET
ma-105	198	17	t	t	PROPN
ma-105	198	18	>	>	X
ma-105	198	19	0	0	NUM
ma-105	198	20	,	,	PUNCT
ma-105	198	21	‖g(t)‖	‖g(t)‖	PUNCT
ma-105	198	22	≤	≤	ADJ
ma-105	198	23	ce−at	ce−at	NOUN
ma-105	198	24	,	,	PUNCT
ma-105	198	25	‖ag(t)‖	‖ag(t)‖	PROPN
ma-105	199	1	≤	≤	PROPN
ma-105	199	2	c	c	NOUN
ma-105	199	3	t	t	PROPN
ma-105	199	4	e−at	e−at	PROPN
ma-105	199	5	and	and	CCONJ
ma-105	199	6	d	d	NOUN
ma-105	199	7	dt	dt	X
ma-105	199	8	g(t	g(t	PROPN
ma-105	199	9	)	)	PUNCT
ma-105	199	10	=	=	SYM
ma-105	199	11	−ag(t	−ag(t	NOUN
ma-105	199	12	)	)	PUNCT
ma-105	199	13	,	,	PUNCT
ma-105	199	14	t	t	X
ma-105	199	15	>	>	X
ma-105	199	16	0	0	X
ma-105	199	17	.	.	PUNCT
ma-105	200	1	corollary	corollary	ADJ
ma-105	200	2	3.5	3.5	NUM
ma-105	200	3	.	.	PUNCT
ma-105	201	1	let	let	VERB
ma-105	201	2	g	g	NOUN
ma-105	201	3	be	be	AUX
ma-105	201	4	the	the	DET
ma-105	201	5	analytic	analytic	ADJ
ma-105	201	6	semigroup	semigroup	NOUN
ma-105	201	7	generated	generate	VERB
ma-105	201	8	by	by	ADP
ma-105	201	9	−a	−a	ADV
ma-105	201	10	.	.	PUNCT
ma-105	202	1	the	the	DET
ma-105	202	2	following	follow	VERB
ma-105	202	3	properties	property	NOUN
ma-105	202	4	hold	hold	VERB
ma-105	202	5	for	for	ADP
ma-105	202	6	the	the	DET
ma-105	202	7	semigroup	semigroup	PROPN
ma-105	202	8	g	g	PROPN
ma-105	202	9	and	and	CCONJ
ma-105	202	10	the	the	DET
ma-105	202	11	fractional	fractional	ADJ
ma-105	202	12	powers	power	NOUN
ma-105	202	13	of	of	ADP
ma-105	202	14	the	the	DET
ma-105	202	15	helmholtz	helmholtz	NOUN
ma-105	202	16	operator	operator	NOUN
ma-105	202	17	hβ	hβ	PROPN
ma-105	202	18	:1	:1	PUNCT
ma-105	202	19	)	)	PUNCT
ma-105	202	20	g(t	g(t	PROPN
ma-105	202	21	)	)	PUNCT
ma-105	202	22	:	:	PUNCT
ma-105	203	1	l2(ω)→	l2(ω)→	PROPN
ma-105	203	2	d(h	d(h	PROPN
ma-105	203	3	�	�	PROPN
ma-105	203	4	)	)	PUNCT
ma-105	203	5	for	for	ADP
ma-105	203	6	all	all	DET
ma-105	203	7	t	t	PROPN
ma-105	203	8	>	>	X
ma-105	203	9	0,2	0,2	NUM
ma-105	203	10	)	)	PUNCT
ma-105	203	11	‖g(t)ω‖h	‖g(t)ω‖h	PUNCT
ma-105	203	12	�	�	NOUN
ma-105	203	13	≤	≤	ADJ
ma-105	203	14	cβ,2t−β‖ω‖2	cβ,2t−β‖ω‖2	PROPN
ma-105	203	15	for	for	ADP
ma-105	203	16	all	all	DET
ma-105	203	17	t	t	PROPN
ma-105	203	18	>	>	X
ma-105	203	19	0	0	PROPN
ma-105	203	20	,	,	PUNCT
ma-105	203	21	ω	ω	NUM
ma-105	203	22	∈	∈	PROPN
ma-105	203	23	l2,3	l2,3	NOUN
ma-105	203	24	)	)	PUNCT
ma-105	203	25	g(t)h	g(t)h	PROPN
ma-105	203	26	�	�	PROPN
ma-105	203	27	ω	ω	NOUN
ma-105	203	28	=	=	SYM
ma-105	203	29	h	h	PROPN
ma-105	203	30	�	�	PROPN
ma-105	203	31	g(t)ω	g(t)ω	PROPN
ma-105	203	32	for	for	ADP
ma-105	203	33	all	all	DET
ma-105	203	34	t	t	PROPN
ma-105	203	35	>	>	X
ma-105	203	36	0	0	PROPN
ma-105	203	37	,	,	PUNCT
ma-105	203	38	ω	ω	PROPN
ma-105	203	39	∈	∈	PROPN
ma-105	203	40	d(h	d(h	PROPN
ma-105	203	41	�	�	PROPN
ma-105	203	42	)	)	PUNCT
ma-105	203	43	.	.	PUNCT
ma-105	204	1	remark	remark	PROPN
ma-105	204	2	3.2	3.2	NUM
ma-105	204	3	.	.	PUNCT
ma-105	205	1	the	the	DET
ma-105	205	2	following	follow	VERB
ma-105	205	3	basic	basic	ADJ
ma-105	205	4	hypotheses	hypothesis	NOUN
ma-105	205	5	are	be	AUX
ma-105	205	6	assumed	assume	VERB
ma-105	205	7	to	to	PART
ma-105	205	8	hold	hold	VERB
ma-105	205	9	:	:	PUNCT
ma-105	205	10	(	(	PUNCT
ma-105	205	11	h1	h1	PROPN
ma-105	205	12	):	):	PUNCT
ma-105	205	13	d1	d1	PROPN
ma-105	205	14	>	>	X
ma-105	205	15	0	0	NUM
ma-105	205	16	,	,	PUNCT
ma-105	205	17	d2	d2	VERB
ma-105	205	18	>	>	X
ma-105	205	19	0	0	PUNCT
ma-105	206	1	and	and	CCONJ
ma-105	206	2	d3	d3	PROPN
ma-105	206	3	>	>	X
ma-105	206	4	0	0	NUM
ma-105	206	5	,	,	PUNCT
ma-105	206	6	(	(	PUNCT
ma-105	206	7	h2	h2	NOUN
ma-105	206	8	):	):	PUNCT
ma-105	206	9	h0	h0	NOUN
ma-105	206	10	≥	≥	NOUN
ma-105	206	11	0	0	NUM
ma-105	206	12	,	,	PUNCT
ma-105	206	13	i0	i0	PROPN
ma-105	206	14	≥	≥	NUM
ma-105	206	15	0	0	NUM
ma-105	206	16	and	and	CCONJ
ma-105	206	17	v0	v0	PROPN
ma-105	206	18	≥	≥	NOUN
ma-105	206	19	0	0	NUM
ma-105	206	20	are	be	AUX
ma-105	206	21	continuous	continuous	ADJ
ma-105	206	22	on	on	ADP
ma-105	206	23	ω	ω	PROPN
ma-105	206	24	,	,	PUNCT
ma-105	206	25	h0	h0	PROPN
ma-105	206	26	,	,	PUNCT
ma-105	206	27	i0	i0	PROPN
ma-105	206	28	,	,	PUNCT
ma-105	206	29	v0	v0	PROPN
ma-105	206	30	∈	∈	PROPN
ma-105	206	31	c0	c0	PROPN
ma-105	206	32	b(ω	b(ω	ADV
ma-105	206	33	)	)	PUNCT
ma-105	206	34	,	,	PUNCT
ma-105	206	35	(	(	PUNCT
ma-105	206	36	h3	h3	NOUN
ma-105	206	37	):	):	PUNCT
ma-105	206	38	f	f	PROPN
ma-105	206	39	,	,	PUNCT
ma-105	206	40	g	g	PROPN
ma-105	206	41	and	and	CCONJ
ma-105	206	42	h	h	NOUN
ma-105	206	43	are	be	AUX
ma-105	206	44	continuously	continuously	ADV
ma-105	206	45	differentiable	differentiable	ADJ
ma-105	206	46	functions	function	NOUN
ma-105	206	47	fromr4	fromr4	NOUN
ma-105	207	1	+	+	CCONJ
ma-105	207	2	intor	intor	NOUN
ma-105	207	3	with	with	ADP
ma-105	207	4	f	f	PROPN
ma-105	207	5	(	(	PUNCT
ma-105	207	6	t	t	PROPN
ma-105	207	7	,	,	PUNCT
ma-105	207	8	0	0	NUM
ma-105	207	9	,	,	PUNCT
ma-105	207	10	s	s	X
ma-105	207	11	,	,	PUNCT
ma-105	207	12	z	z	NOUN
ma-105	207	13	)	)	PUNCT
ma-105	207	14	≥	≥	NOUN
ma-105	207	15	0	0	NUM
ma-105	207	16	,	,	PUNCT
ma-105	207	17	g(t	g(t	PROPN
ma-105	207	18	,	,	PUNCT
ma-105	207	19	r	r	NOUN
ma-105	207	20	,	,	PUNCT
ma-105	207	21	0	0	NUM
ma-105	207	22	,	,	PUNCT
ma-105	207	23	z	z	NOUN
ma-105	207	24	)	)	PUNCT
ma-105	207	25	≥	≥	NOUN
ma-105	207	26	0	0	NUM
ma-105	207	27	and	and	CCONJ
ma-105	207	28	h(t	h(t	PROPN
ma-105	207	29	,	,	PUNCT
ma-105	207	30	r	r	NOUN
ma-105	207	31	,	,	PUNCT
ma-105	207	32	s	s	PROPN
ma-105	207	33	,	,	PUNCT
ma-105	207	34	0	0	NUM
ma-105	207	35	)	)	PUNCT
ma-105	207	36	≥	≥	NOUN
ma-105	207	37	0	0	NUM
ma-105	207	38	for	for	ADP
ma-105	207	39	all	all	DET
ma-105	207	40	t	t	NOUN
ma-105	207	41	,	,	PUNCT
ma-105	207	42	r	r	NOUN
ma-105	207	43	,	,	PUNCT
ma-105	207	44	s	s	PART
ma-105	207	45	,	,	PUNCT
ma-105	207	46	z	z	NOUN
ma-105	207	47	≥	≥	NOUN
ma-105	207	48	0	0	NUM
ma-105	207	49	.	.	PUNCT
ma-105	208	1	https://doi.org/10.28924/ada/ma.3.1	https://doi.org/10.28924/ada/ma.3.1	PROPN
ma-105	208	2	eur	eur	PROPN
ma-105	208	3	.	.	PUNCT
ma-105	209	1	j.	j.	PROPN
ma-105	209	2	math	math	PROPN
ma-105	209	3	.	.	PUNCT
ma-105	210	1	anal	anal	PROPN
ma-105	210	2	.	.	PUNCT
ma-105	211	1	10.28924	10.28924	NUM
ma-105	211	2	/	/	SYM
ma-105	211	3	ada	ada	PROPN
ma-105	211	4	/	/	SYM
ma-105	211	5	ma.3.1	ma.3.1	PROPN
ma-105	211	6	8for	8for	ADP
ma-105	211	7	x	x	SYM
ma-105	211	8	∈	∈	PROPN
ma-105	211	9	ω	ω	PROPN
ma-105	211	10	,	,	PUNCT
ma-105	211	11	t	t	PROPN
ma-105	211	12	≥	≥	NUM
ma-105	211	13	0	0	NUM
ma-105	211	14	,	,	PUNCT
ma-105	211	15	h	h	NOUN
ma-105	211	16	,	,	PUNCT
ma-105	211	17	i	i	PRON
ma-105	211	18	,	,	PUNCT
ma-105	211	19	v	v	PROPN
ma-105	211	20	∈	∈	PROPN
ma-105	211	21	(	(	PUNCT
ma-105	211	22	c0	c0	PROPN
ma-105	211	23	b(ω))3	b(ω))3	PROPN
ma-105	211	24	,	,	PUNCT
ma-105	211	25	define	define	VERB
ma-105	211	26	f	f	PROPN
ma-105	211	27	,	,	PUNCT
ma-105	211	28	g	g	PROPN
ma-105	211	29	and	and	CCONJ
ma-105	211	30	q	q	NOUN
ma-105	211	31	on	on	ADP
ma-105	211	32	r+	r+	X
ma-105	211	33	×	×	PROPN
ma-105	211	34	(	(	PUNCT
ma-105	211	35	c0	c0	NOUN
ma-105	211	36	b(ω))3	b(ω))3	VERB
ma-105	211	37	by	by	ADP
ma-105	211	38	:	:	PUNCT
ma-105	212	1	[	[	X
ma-105	212	2	f(t	f(t	NOUN
ma-105	212	3	,	,	PUNCT
ma-105	212	4	h	h	NOUN
ma-105	212	5	,	,	PUNCT
ma-105	212	6	i	i	PRON
ma-105	212	7	,	,	PUNCT
ma-105	212	8	v	v	NOUN
ma-105	212	9	)	)	PUNCT
ma-105	212	10	]	]	PUNCT
ma-105	212	11	(	(	PUNCT
ma-105	212	12	x	x	X
ma-105	212	13	)	)	PUNCT
ma-105	212	14	=	=	SYM
ma-105	212	15	f	f	PROPN
ma-105	212	16	(	(	PUNCT
ma-105	212	17	t	t	PROPN
ma-105	212	18	,	,	PUNCT
ma-105	212	19	h(x	h(x	PROPN
ma-105	212	20	)	)	PUNCT
ma-105	212	21	,	,	PUNCT
ma-105	212	22	i(x	i(x	PROPN
ma-105	212	23	)	)	PUNCT
ma-105	212	24	,	,	PUNCT
ma-105	212	25	v	v	X
ma-105	212	26	(	(	PUNCT
ma-105	212	27	x	x	NOUN
ma-105	212	28	)	)	PUNCT
ma-105	212	29	)	)	PUNCT
ma-105	212	30	,	,	PUNCT
ma-105	212	31	[	[	X
ma-105	212	32	g(t	g(t	PROPN
ma-105	212	33	,	,	PUNCT
ma-105	212	34	h	h	NOUN
ma-105	212	35	,	,	PUNCT
ma-105	212	36	i	i	PRON
ma-105	212	37	,	,	PUNCT
ma-105	212	38	v	v	NOUN
ma-105	212	39	)	)	PUNCT
ma-105	212	40	]	]	PUNCT
ma-105	212	41	(	(	PUNCT
ma-105	212	42	x	x	X
ma-105	212	43	)	)	PUNCT
ma-105	212	44	=	=	SYM
ma-105	212	45	g(t	g(t	PROPN
ma-105	212	46	,	,	PUNCT
ma-105	212	47	h(x	h(x	PROPN
ma-105	212	48	)	)	PUNCT
ma-105	212	49	,	,	PUNCT
ma-105	212	50	i(x	i(x	PROPN
ma-105	212	51	)	)	PUNCT
ma-105	212	52	,	,	PUNCT
ma-105	212	53	v	v	X
ma-105	212	54	(	(	PUNCT
ma-105	212	55	x	x	NOUN
ma-105	212	56	)	)	PUNCT
ma-105	212	57	)	)	PUNCT
ma-105	212	58	,	,	PUNCT
ma-105	212	59	[	[	X
ma-105	212	60	q(t	q(t	ADJ
ma-105	212	61	,	,	PUNCT
ma-105	212	62	h	h	NOUN
ma-105	212	63	,	,	PUNCT
ma-105	212	64	i	i	PRON
ma-105	212	65	,	,	PUNCT
ma-105	212	66	v	v	NOUN
ma-105	212	67	)	)	PUNCT
ma-105	212	68	]	]	PUNCT
ma-105	212	69	(	(	PUNCT
ma-105	212	70	x	x	X
ma-105	212	71	)	)	PUNCT
ma-105	212	72	=	=	SYM
ma-105	212	73	h(t	h(t	PROPN
ma-105	212	74	,	,	PUNCT
ma-105	212	75	h(x	h(x	PROPN
ma-105	212	76	)	)	PUNCT
ma-105	212	77	,	,	PUNCT
ma-105	212	78	i(x	i(x	PROPN
ma-105	212	79	)	)	PUNCT
ma-105	212	80	,	,	PUNCT
ma-105	212	81	v	v	NOUN
ma-105	212	82	(	(	PUNCT
ma-105	212	83	x)).in	x)).in	ADV
ma-105	212	84	addition	addition	NOUN
ma-105	212	85	,	,	PUNCT
ma-105	212	86	we	we	PRON
ma-105	212	87	let	let	VERB
ma-105	212	88	g1	g1	NOUN
ma-105	212	89	,	,	PUNCT
ma-105	212	90	g2	g2	PROPN
ma-105	212	91	and	and	CCONJ
ma-105	212	92	g3	g3	PROPN
ma-105	212	93	be	be	AUX
ma-105	212	94	the	the	DET
ma-105	212	95	analytical	analytical	ADJ
ma-105	212	96	semigroup	semigroup	NOUN
ma-105	212	97	generated	generate	VERB
ma-105	212	98	by	by	ADP
ma-105	212	99	a1	a1	NOUN
ma-105	212	100	=	=	SYM
ma-105	212	101	d1	d1	PROPN
ma-105	212	102	×	×	NOUN
ma-105	212	103	∆	∆	X
ma-105	212	104	,	,	PUNCT
ma-105	212	105	a2	a2	PROPN
ma-105	212	106	=	=	SYM
ma-105	212	107	d2	d2	PROPN
ma-105	212	108	×	×	PROPN
ma-105	212	109	∆	∆	PROPN
ma-105	212	110	and	and	CCONJ
ma-105	212	111	a3	a3	NOUN
ma-105	212	112	=	=	PRON
ma-105	212	113	d3	d3	VERB
ma-105	212	114	×	×	NOUN
ma-105	212	115	∆	∆	PROPN
ma-105	212	116	respectively	respectively	ADV
ma-105	212	117	.	.	PUNCT
ma-105	213	1	in	in	ADP
ma-105	213	2	the	the	DET
ma-105	213	3	sequel	sequel	NOUN
ma-105	213	4	,	,	PUNCT
ma-105	213	5	we	we	PRON
ma-105	213	6	will	will	AUX
ma-105	213	7	need	need	VERB
ma-105	213	8	the	the	DET
ma-105	213	9	following	follow	VERB
ma-105	213	10	results	result	NOUN
ma-105	213	11	.	.	PUNCT
ma-105	214	1	lemma	lemma	PROPN
ma-105	214	2	3.6	3.6	NUM
ma-105	214	3	.	.	PUNCT
ma-105	215	1	[	[	X
ma-105	215	2	22	22	NUM
ma-105	215	3	]	]	PUNCT
ma-105	215	4	if	if	SCONJ
ma-105	215	5	h	h	NOUN
ma-105	215	6	,	,	PUNCT
ma-105	215	7	i	i	PRON
ma-105	215	8	and	and	CCONJ
ma-105	215	9	v	v	NOUN
ma-105	215	10	are	be	AUX
ma-105	215	11	continuous	continuous	ADJ
ma-105	215	12	from	from	ADP
ma-105	215	13	[	[	X
ma-105	215	14	0	0	NUM
ma-105	215	15	,	,	PUNCT
ma-105	215	16	t	t	NOUN
ma-105	215	17	]	]	PUNCT
ma-105	215	18	to	to	ADP
ma-105	215	19	l2(ω	l2(ω	PROPN
ma-105	215	20	)	)	PUNCT
ma-105	215	21	,	,	PUNCT
ma-105	215	22	then	then	ADV
ma-105	215	23	the	the	DET
ma-105	215	24	integrals	integral	NOUN
ma-105	215	25	:	:	PUNCT
ma-105	215	26	i1(t	i1(t	X
ma-105	215	27	)	)	PUNCT
ma-105	215	28	=	=	SYM
ma-105	216	1	∫	∫	PROPN
ma-105	216	2	t	t	NOUN
ma-105	216	3	0	0	NUM
ma-105	217	1	g1(t	g1(t	ADP
ma-105	217	2	−	−	PROPN
ma-105	217	3	τ)f(τ	τ)f(τ	NOUN
ma-105	217	4	,	,	PUNCT
ma-105	217	5	h(τ	h(τ	PROPN
ma-105	217	6	)	)	PUNCT
ma-105	217	7	,	,	PUNCT
ma-105	217	8	i(τ	i(τ	PROPN
ma-105	217	9	)	)	PUNCT
ma-105	217	10	,	,	PUNCT
ma-105	217	11	v	v	X
ma-105	217	12	(	(	PUNCT
ma-105	217	13	τ))dτ	τ))dτ	PROPN
ma-105	217	14	,	,	PUNCT
ma-105	217	15	i2(t	i2(t	PROPN
ma-105	217	16	)	)	PUNCT
ma-105	217	17	=	=	SYM
ma-105	218	1	∫	∫	PROPN
ma-105	218	2	t	t	NOUN
ma-105	218	3	0	0	NUM
ma-105	219	1	g2(t	g2(t	NOUN
ma-105	220	1	−	−	NOUN
ma-105	220	2	τ)g(τ	τ)g(τ	ADJ
ma-105	220	3	,	,	PUNCT
ma-105	220	4	h(τ	h(τ	PROPN
ma-105	220	5	)	)	PUNCT
ma-105	220	6	,	,	PUNCT
ma-105	220	7	i(τ	i(τ	PROPN
ma-105	220	8	)	)	PUNCT
ma-105	220	9	,	,	PUNCT
ma-105	220	10	v	v	X
ma-105	220	11	(	(	PUNCT
ma-105	220	12	τ))dτ	τ))dτ	PROPN
ma-105	220	13	,	,	PUNCT
ma-105	220	14	i3(t	i3(t	PROPN
ma-105	220	15	)	)	PUNCT
ma-105	220	16	=	=	SYM
ma-105	221	1	∫	∫	PROPN
ma-105	221	2	t	t	NOUN
ma-105	221	3	0	0	NUM
ma-105	222	1	g3(t	g3(t	NUM
ma-105	222	2	−	−	NOUN
ma-105	222	3	τ)q(τ	τ)q(τ	ADJ
ma-105	222	4	,	,	PUNCT
ma-105	222	5	h(τ	h(τ	PROPN
ma-105	222	6	)	)	PUNCT
ma-105	222	7	,	,	PUNCT
ma-105	222	8	i(τ	i(τ	PROPN
ma-105	222	9	)	)	PUNCT
ma-105	222	10	,	,	PUNCT
ma-105	222	11	v	v	X
ma-105	222	12	(	(	PUNCT
ma-105	222	13	τ))dτ	τ))dτ	NOUN
ma-105	222	14	,	,	PUNCT
ma-105	222	15	exist	exist	VERB
ma-105	222	16	and	and	CCONJ
ma-105	222	17	i1(t	i1(t	PROPN
ma-105	222	18	)	)	PUNCT
ma-105	222	19	,	,	PUNCT
ma-105	222	20	i2(t	i2(t	PROPN
ma-105	222	21	)	)	PUNCT
ma-105	222	22	and	and	CCONJ
ma-105	222	23	i3(t	i3(t	PROPN
ma-105	222	24	)	)	PUNCT
ma-105	222	25	are	be	AUX
ma-105	222	26	continues	continue	VERB
ma-105	222	27	on	on	ADP
ma-105	222	28	[	[	X
ma-105	222	29	0	0	NUM
ma-105	222	30	,	,	PUNCT
ma-105	222	31	t	t	X
ma-105	222	32	[	[	PUNCT
ma-105	222	33	with	with	ADP
ma-105	222	34	i1(t	i1(t	PROPN
ma-105	222	35	)	)	PUNCT
ma-105	222	36	∈	∈	PROPN
ma-105	222	37	d(a1	d(a1	NOUN
ma-105	222	38	)	)	PUNCT
ma-105	222	39	,	,	PUNCT
ma-105	222	40	i2(t	i2(t	PROPN
ma-105	222	41	)	)	PUNCT
ma-105	222	42	∈	∈	PROPN
ma-105	222	43	d(a2	d(a2	NOUN
ma-105	222	44	)	)	PUNCT
ma-105	222	45	,	,	PUNCT
ma-105	222	46	i3(t	i3(t	PROPN
ma-105	222	47	)	)	PUNCT
ma-105	222	48	∈	∈	PROPN
ma-105	222	49	d(a3	d(a3	NOUN
ma-105	222	50	)	)	PUNCT
ma-105	222	51	and	and	CCONJ
ma-105	222	52	i1(t)→	i1(t)→	PROPN
ma-105	222	53	0	0	NUM
ma-105	223	1	+	+	CCONJ
ma-105	223	2	in	in	ADP
ma-105	223	3	l2	l2	NOUN
ma-105	223	4	as	as	ADP
ma-105	223	5	t	t	PROPN
ma-105	223	6	→	→	SYM
ma-105	223	7	0	0	NUM
ma-105	223	8	+	+	ADJ
ma-105	223	9	,	,	PUNCT
ma-105	223	10	i2(t)→	i2(t)→	PROPN
ma-105	223	11	0	0	PUNCT
ma-105	223	12	+	+	NOUN
ma-105	223	13	in	in	ADP
ma-105	223	14	l2	l2	NOUN
ma-105	223	15	as	as	ADP
ma-105	223	16	t	t	PROPN
ma-105	223	17	→	→	SYM
ma-105	223	18	0	0	NUM
ma-105	223	19	+	+	NUM
ma-105	223	20	and	and	CCONJ
ma-105	223	21	i3(t)→	i3(t)→	PROPN
ma-105	223	22	0	0	NUM
ma-105	224	1	+	+	CCONJ
ma-105	224	2	in	in	ADP
ma-105	224	3	l2	l2	NOUN
ma-105	224	4	as	as	ADP
ma-105	224	5	t	t	PROPN
ma-105	224	6	→	→	SYM
ma-105	224	7	0	0	NUM
ma-105	224	8	+	+	NOUN
ma-105	224	9	.	.	PUNCT
ma-105	224	10	lemma	lemma	PROPN
ma-105	224	11	3.7	3.7	NUM
ma-105	224	12	.	.	PUNCT
ma-105	225	1	if	if	SCONJ
ma-105	225	2	the	the	DET
ma-105	225	3	ibvp	ibvp	NOUN
ma-105	225	4	(	(	PUNCT
ma-105	225	5	3.8	3.8	NUM
ma-105	225	6	)	)	PUNCT
ma-105	225	7	has	have	VERB
ma-105	225	8	a	a	DET
ma-105	225	9	classical	classical	ADJ
ma-105	225	10	solution	solution	NOUN
ma-105	225	11	,	,	PUNCT
ma-105	225	12	then	then	ADV
ma-105	225	13	h	h	NOUN
ma-105	225	14	,	,	PUNCT
ma-105	225	15	i	i	PRON
ma-105	225	16	and	and	CCONJ
ma-105	225	17	v	v	AUX
ma-105	225	18	satisfy	satisfy	VERB
ma-105	225	19	the	the	DET
ma-105	225	20	following	follow	VERB
ma-105	225	21	equalities	equality	NOUN
ma-105	225	22	:	:	PUNCT
ma-105	225	23	h(t	h(t	X
ma-105	225	24	)	)	PUNCT
ma-105	225	25	=	=	PRON
ma-105	225	26	g1(t)h0	g1(t)h0	X
ma-105	225	27	+	+	CCONJ
ma-105	225	28	∫	∫	PROPN
ma-105	225	29	t	t	NOUN
ma-105	225	30	0	0	PUNCT
ma-105	226	1	g1(t	g1(t	ADP
ma-105	226	2	−	−	PROPN
ma-105	226	3	τ)f(τ	τ)f(τ	NOUN
ma-105	226	4	,	,	PUNCT
ma-105	226	5	h(τ	h(τ	PROPN
ma-105	226	6	)	)	PUNCT
ma-105	226	7	,	,	PUNCT
ma-105	226	8	i(τ	i(τ	PROPN
ma-105	226	9	)	)	PUNCT
ma-105	226	10	,	,	PUNCT
ma-105	226	11	v	v	X
ma-105	226	12	(	(	PUNCT
ma-105	226	13	τ))dτ	τ))dτ	PROPN
ma-105	226	14	,	,	PUNCT
ma-105	226	15	(	(	PUNCT
ma-105	226	16	3.11	3.11	NUM
ma-105	226	17	)	)	PUNCT
ma-105	226	18	i(t	i(t	NOUN
ma-105	226	19	)	)	PUNCT
ma-105	226	20	=	=	SYM
ma-105	226	21	g2(t)i0	g2(t)i0	NOUN
ma-105	227	1	+	+	CCONJ
ma-105	228	1	∫	∫	PROPN
ma-105	228	2	t	t	NOUN
ma-105	228	3	0	0	NUM
ma-105	229	1	g2(t	g2(t	NOUN
ma-105	230	1	−	−	NOUN
ma-105	230	2	τ)g(τ	τ)g(τ	ADJ
ma-105	230	3	,	,	PUNCT
ma-105	230	4	h(τ	h(τ	PROPN
ma-105	230	5	)	)	PUNCT
ma-105	230	6	,	,	PUNCT
ma-105	230	7	i(τ	i(τ	PROPN
ma-105	230	8	)	)	PUNCT
ma-105	230	9	,	,	PUNCT
ma-105	230	10	v	v	X
ma-105	230	11	(	(	PUNCT
ma-105	230	12	τ))dτ	τ))dτ	PROPN
ma-105	230	13	,	,	PUNCT
ma-105	230	14	(	(	PUNCT
ma-105	230	15	3.12	3.12	NUM
ma-105	230	16	)	)	PUNCT
ma-105	230	17	v	v	NOUN
ma-105	230	18	(	(	PUNCT
ma-105	230	19	t	t	NOUN
ma-105	230	20	)	)	PUNCT
ma-105	230	21	=	=	SYM
ma-105	231	1	g3(t)v0	g3(t)v0	NOUN
ma-105	231	2	+	+	CCONJ
ma-105	231	3	∫	∫	PROPN
ma-105	231	4	t	t	PROPN
ma-105	231	5	0	0	NUM
ma-105	232	1	g3(t	g3(t	NUM
ma-105	232	2	−	−	NOUN
ma-105	232	3	τ)q(τ	τ)q(τ	ADJ
ma-105	232	4	,	,	PUNCT
ma-105	232	5	h(τ	h(τ	PROPN
ma-105	232	6	)	)	PUNCT
ma-105	232	7	,	,	PUNCT
ma-105	232	8	i(τ	i(τ	PROPN
ma-105	232	9	)	)	PUNCT
ma-105	232	10	,	,	PUNCT
ma-105	232	11	v	v	X
ma-105	232	12	(	(	PUNCT
ma-105	232	13	τ))dτ	τ))dτ	PROPN
ma-105	232	14	.	.	PUNCT
ma-105	233	1	(	(	PUNCT
ma-105	233	2	3.13	3.13	NUM
ma-105	233	3	)	)	PUNCT
ma-105	233	4	proof	proof	NOUN
ma-105	233	5	.	.	PUNCT
ma-105	234	1	consider	consider	VERB
ma-105	234	2	the	the	DET
ma-105	234	3	l2−valued	l2−value	VERB
ma-105	234	4	functions	function	NOUN
ma-105	234	5	θj(τ	θj(τ	PUNCT
ma-105	234	6	)	)	PUNCT
ma-105	234	7	=	=	SYM
ma-105	234	8	gj(t	gj(t	PROPN
ma-105	234	9	−	−	PROPN
ma-105	234	10	τ)ωj(τ	τ)ωj(τ	PROPN
ma-105	234	11	)	)	PUNCT
ma-105	234	12	,	,	PUNCT
ma-105	234	13	j	j	PROPN
ma-105	234	14	=	=	SYM
ma-105	234	15	1	1	NUM
ma-105	234	16	,	,	PUNCT
ma-105	234	17	2	2	NUM
ma-105	234	18	,	,	PUNCT
ma-105	234	19	3	3	NUM
ma-105	234	20	with	with	ADP
ma-105	234	21	ω1	ω1	PROPN
ma-105	234	22	=	=	SYM
ma-105	234	23	h	h	PROPN
ma-105	234	24	,	,	PUNCT
ma-105	234	25	ω2	ω2	NOUN
ma-105	234	26	=	=	PUNCT
ma-105	234	27	iand	iand	NOUN
ma-105	234	28	ω3	ω3	NOUN
ma-105	234	29	=	=	SYM
ma-105	234	30	v	v	X
ma-105	234	31	.	.	PUNCT
ma-105	235	1	then	then	ADV
ma-105	235	2	θj	θj	ADV
ma-105	235	3	is	be	AUX
ma-105	235	4	differentiable	differentiable	ADJ
ma-105	235	5	since	since	SCONJ
ma-105	235	6	gj	gj	PROPN
ma-105	235	7	is	be	AUX
ma-105	235	8	analytic	analytic	ADJ
ma-105	235	9	and	and	CCONJ
ma-105	235	10	ωj	ωj	ADV
ma-105	235	11	is	be	AUX
ma-105	235	12	differentiable	differentiable	ADJ
ma-105	235	13	.	.	PUNCT
ma-105	236	1	then	then	ADV
ma-105	236	2	bytheorem	bytheorem	VERB
ma-105	236	3	3.4	3.4	NUM
ma-105	236	4	,	,	PUNCT
ma-105	236	5	we	we	PRON
ma-105	236	6	have	have	VERB
ma-105	236	7	dθ1	dθ1	NOUN
ma-105	236	8	dτ	dτ	NOUN
ma-105	236	9	=	=	PROPN
ma-105	236	10	d	d	X
ma-105	236	11	dτ	dτ	PROPN
ma-105	236	12	[	[	PUNCT
ma-105	236	13	g1(t	g1(t	ADP
ma-105	236	14	−	−	PROPN
ma-105	236	15	τ	τ	PROPN
ma-105	236	16	)	)	PUNCT
ma-105	236	17	]	]	PUNCT
ma-105	237	1	h(τ	h(τ	PROPN
ma-105	237	2	)	)	PUNCT
ma-105	238	1	+	+	CCONJ
ma-105	238	2	g1(t	g1(t	ADP
ma-105	238	3	−	−	NOUN
ma-105	238	4	τ)h	τ)h	NOUN
ma-105	239	1	′	′	NUM
ma-105	239	2	(	(	PUNCT
ma-105	239	3	τ	τ	NOUN
ma-105	239	4	)	)	PUNCT
ma-105	239	5	,	,	PUNCT
ma-105	239	6	=	=	PUNCT
ma-105	239	7	−d1	−d1	NOUN
ma-105	239	8	×	×	NOUN
ma-105	239	9	∆	∆	PROPN
ma-105	239	10	(	(	PUNCT
ma-105	239	11	g1(t	g1(t	ADP
ma-105	239	12	−	−	PROPN
ma-105	239	13	τ	τ	NOUN
ma-105	239	14	)	)	PUNCT
ma-105	239	15	)	)	PUNCT
ma-105	240	1	h(τ	h(τ	PROPN
ma-105	240	2	)	)	PUNCT
ma-105	241	1	+	+	CCONJ
ma-105	241	2	g1(t	g1(t	ADP
ma-105	241	3	−	−	PROPN
ma-105	241	4	τ	τ	NOUN
ma-105	241	5	)	)	PUNCT
ma-105	241	6	[	[	PUNCT
ma-105	241	7	d1	d1	NOUN
ma-105	241	8	×	×	NOUN
ma-105	241	9	∆h(τ	∆h(τ	PROPN
ma-105	241	10	)	)	PUNCT
ma-105	241	11	+	+	CCONJ
ma-105	242	1	f(τ	f(τ	PROPN
ma-105	242	2	,	,	PUNCT
ma-105	242	3	h(τ	h(τ	PROPN
ma-105	242	4	)	)	PUNCT
ma-105	242	5	,	,	PUNCT
ma-105	242	6	i(τ	i(τ	PROPN
ma-105	242	7	)	)	PUNCT
ma-105	242	8	,	,	PUNCT
ma-105	242	9	v	v	X
ma-105	242	10	(	(	PUNCT
ma-105	242	11	τ	τ	PROPN
ma-105	242	12	)	)	PUNCT
ma-105	242	13	)	)	PUNCT
ma-105	242	14	]	]	PUNCT
ma-105	242	15	,	,	PUNCT
ma-105	242	16	=	=	PUNCT
ma-105	242	17	−d1	−d1	NOUN
ma-105	242	18	×	×	NOUN
ma-105	242	19	∆	∆	PROPN
ma-105	242	20	(	(	PUNCT
ma-105	242	21	g1(t	g1(t	ADP
ma-105	242	22	−	−	PROPN
ma-105	242	23	τ	τ	NOUN
ma-105	242	24	)	)	PUNCT
ma-105	242	25	)	)	PUNCT
ma-105	243	1	h(τ	h(τ	PROPN
ma-105	243	2	)	)	PUNCT
ma-105	244	1	+	+	ADP
ma-105	244	2	d1	d1	ADJ
ma-105	244	3	×	×	NOUN
ma-105	244	4	g1(t	g1(t	ADP
ma-105	244	5	−	−	NOUN
ma-105	244	6	τ)×	τ)×	X
ma-105	244	7	∆h(τ	∆h(τ	PROPN
ma-105	244	8	)	)	PUNCT
ma-105	244	9	+	+	CCONJ
ma-105	244	10	g1(t	g1(t	ADP
ma-105	244	11	−	−	NOUN
ma-105	244	12	τ)f(τ	τ)f(τ	NOUN
ma-105	244	13	,	,	PUNCT
ma-105	244	14	h(τ	h(τ	PROPN
ma-105	244	15	)	)	PUNCT
ma-105	244	16	,	,	PUNCT
ma-105	244	17	i(τ	i(τ	PROPN
ma-105	244	18	)	)	PUNCT
ma-105	244	19	,	,	PUNCT
ma-105	244	20	v	v	X
ma-105	244	21	(	(	PUNCT
ma-105	244	22	τ	τ	PROPN
ma-105	244	23	)	)	PUNCT
ma-105	244	24	)	)	PUNCT
ma-105	244	25	,	,	PUNCT
ma-105	244	26	according	accord	VERB
ma-105	244	27	to	to	ADP
ma-105	244	28	corollary	corollary	ADJ
ma-105	244	29	3.5	3.5	NUM
ma-105	244	30	with	with	ADP
ma-105	244	31	β	β	X
ma-105	244	32	=	=	SYM
ma-105	244	33	0	0	NUM
ma-105	244	34	,	,	PUNCT
ma-105	244	35	we	we	PRON
ma-105	244	36	have	have	VERB
ma-105	244	37	d1	d1	PROPN
ma-105	244	38	×	×	NOUN
ma-105	244	39	g1(t	g1(t	NOUN
ma-105	244	40	−	−	NOUN
ma-105	244	41	τ)∆h(τ	τ)∆h(τ	NOUN
ma-105	244	42	)	)	PUNCT
ma-105	245	1	=	=	SYM
ma-105	245	2	d1	d1	ADJ
ma-105	245	3	×	×	NOUN
ma-105	245	4	∆g1(t	∆g1(t	ADJ
ma-105	245	5	−	−	PROPN
ma-105	245	6	τ)h(τ	τ)h(τ	NOUN
ma-105	245	7	)	)	PUNCT
ma-105	245	8	.	.	PUNCT
ma-105	246	1	therefore	therefore	ADV
ma-105	246	2	dθ1	dθ1	PROPN
ma-105	246	3	dτ	dτ	PROPN
ma-105	246	4	=	=	PROPN
ma-105	246	5	−d1	−d1	NOUN
ma-105	246	6	×	×	NOUN
ma-105	246	7	∆g1(t	∆g1(t	ADJ
ma-105	246	8	−	−	NOUN
ma-105	246	9	τ)h(τ	τ)h(τ	PUNCT
ma-105	246	10	)	)	PUNCT
ma-105	247	1	+	+	ADP
ma-105	247	2	d1	d1	PROPN
ma-105	247	3	×	×	NOUN
ma-105	247	4	∆g1(t	∆g1(t	ADJ
ma-105	247	5	−	−	PROPN
ma-105	247	6	τ)h(τ	τ)h(τ	PUNCT
ma-105	247	7	)	)	PUNCT
ma-105	248	1	+	+	CCONJ
ma-105	248	2	g1(t	g1(t	ADP
ma-105	248	3	−	−	NOUN
ma-105	248	4	τ)f(τ	τ)f(τ	NOUN
ma-105	248	5	,	,	PUNCT
ma-105	248	6	h(τ	h(τ	PROPN
ma-105	248	7	)	)	PUNCT
ma-105	248	8	,	,	PUNCT
ma-105	248	9	i(τ	i(τ	PROPN
ma-105	248	10	)	)	PUNCT
ma-105	248	11	,	,	PUNCT
ma-105	248	12	v	v	X
ma-105	248	13	(	(	PUNCT
ma-105	248	14	τ	τ	PROPN
ma-105	248	15	)	)	PUNCT
ma-105	248	16	)	)	PUNCT
ma-105	248	17	,	,	PUNCT
ma-105	248	18	=	=	PUNCT
ma-105	248	19	g1(t	g1(t	ADP
ma-105	248	20	−	−	NOUN
ma-105	248	21	τ)f(τ	τ)f(τ	NOUN
ma-105	248	22	,	,	PUNCT
ma-105	248	23	h(τ	h(τ	PROPN
ma-105	248	24	)	)	PUNCT
ma-105	248	25	,	,	PUNCT
ma-105	248	26	i(τ	i(τ	PROPN
ma-105	248	27	)	)	PUNCT
ma-105	248	28	,	,	PUNCT
ma-105	248	29	v	v	X
ma-105	248	30	(	(	PUNCT
ma-105	248	31	τ	τ	PROPN
ma-105	248	32	)	)	PUNCT
ma-105	248	33	)	)	PUNCT
ma-105	248	34	.	.	PUNCT
ma-105	249	1	(	(	PUNCT
ma-105	249	2	3.14	3.14	NUM
ma-105	249	3	)	)	PUNCT
ma-105	249	4	https://doi.org/10.28924/ada/ma.3.1	https://doi.org/10.28924/ada/ma.3.1	PROPN
ma-105	249	5	eur	eur	PROPN
ma-105	249	6	.	.	PUNCT
ma-105	250	1	j.	j.	PROPN
ma-105	250	2	math	math	PROPN
ma-105	250	3	.	.	PUNCT
ma-105	251	1	anal	anal	PROPN
ma-105	251	2	.	.	PUNCT
ma-105	252	1	10.28924	10.28924	NUM
ma-105	252	2	/	/	SYM
ma-105	252	3	ada	ada	PROPN
ma-105	252	4	/	/	SYM
ma-105	252	5	ma.3.1	ma.3.1	PROPN
ma-105	252	6	9	9	NUM
ma-105	252	7	in	in	ADP
ma-105	252	8	the	the	DET
ma-105	252	9	similar	similar	ADJ
ma-105	252	10	way	way	NOUN
ma-105	252	11	,	,	PUNCT
ma-105	252	12	we	we	PRON
ma-105	252	13	also	also	ADV
ma-105	252	14	have	have	VERB
ma-105	252	15	:	:	PUNCT
ma-105	252	16	dθ2	dθ2	NOUN
ma-105	252	17	dτ	dτ	NOUN
ma-105	252	18	=	=	SYM
ma-105	252	19	d	d	X
ma-105	252	20	dτ	dτ	PROPN
ma-105	252	21	[	[	PUNCT
ma-105	252	22	g2(t	g2(t	NOUN
ma-105	252	23	−	−	PROPN
ma-105	252	24	τ	τ	PROPN
ma-105	252	25	)	)	PUNCT
ma-105	252	26	]	]	PUNCT
ma-105	253	1	i(τ	i(τ	PROPN
ma-105	253	2	)	)	PUNCT
ma-105	254	1	+	+	CCONJ
ma-105	255	1	g2(t	g2(t	PROPN
ma-105	255	2	−	−	NOUN
ma-105	255	3	τ)i	τ)i	PUNCT
ma-105	256	1	′	′	NUM
ma-105	256	2	(	(	PUNCT
ma-105	256	3	τ	τ	PROPN
ma-105	256	4	)	)	PUNCT
ma-105	256	5	,	,	PUNCT
ma-105	256	6	=	=	PUNCT
ma-105	257	1	−d2	−d2	NUM
ma-105	257	2	×	×	NOUN
ma-105	257	3	∆	∆	PROPN
ma-105	257	4	(	(	PUNCT
ma-105	257	5	g2(t	g2(t	X
ma-105	257	6	−	−	X
ma-105	257	7	τ	τ	PROPN
ma-105	257	8	)	)	PUNCT
ma-105	257	9	)	)	PUNCT
ma-105	257	10	i(τ	i(τ	PROPN
ma-105	257	11	)	)	PUNCT
ma-105	258	1	+	+	NUM
ma-105	258	2	d2	d2	PROPN
ma-105	258	3	×	×	NOUN
ma-105	258	4	g2(t	g2(t	PROPN
ma-105	258	5	−	−	X
ma-105	258	6	τ)×	τ)×	X
ma-105	258	7	∆i(τ	∆i(τ	NOUN
ma-105	258	8	)	)	PUNCT
ma-105	258	9	+	+	CCONJ
ma-105	259	1	g2(t	g2(t	NOUN
ma-105	260	1	−	−	NOUN
ma-105	260	2	τ)g(τ	τ)g(τ	ADJ
ma-105	260	3	,	,	PUNCT
ma-105	260	4	h(τ	h(τ	PROPN
ma-105	260	5	)	)	PUNCT
ma-105	260	6	,	,	PUNCT
ma-105	260	7	i(τ	i(τ	PROPN
ma-105	260	8	)	)	PUNCT
ma-105	260	9	,	,	PUNCT
ma-105	260	10	v	v	X
ma-105	260	11	(	(	PUNCT
ma-105	260	12	τ	τ	PROPN
ma-105	260	13	)	)	PUNCT
ma-105	260	14	)	)	PUNCT
ma-105	260	15	,	,	PUNCT
ma-105	261	1	=	=	PUNCT
ma-105	261	2	g2(t	g2(t	NOUN
ma-105	262	1	−	−	NOUN
ma-105	262	2	τ)g(τ	τ)g(τ	ADJ
ma-105	262	3	,	,	PUNCT
ma-105	262	4	h(τ	h(τ	PROPN
ma-105	262	5	)	)	PUNCT
ma-105	262	6	,	,	PUNCT
ma-105	262	7	i(τ	i(τ	PROPN
ma-105	262	8	)	)	PUNCT
ma-105	262	9	,	,	PUNCT
ma-105	262	10	v	v	X
ma-105	262	11	(	(	PUNCT
ma-105	262	12	τ	τ	PROPN
ma-105	262	13	)	)	PUNCT
ma-105	262	14	)	)	PUNCT
ma-105	262	15	.	.	PUNCT
ma-105	263	1	(	(	PUNCT
ma-105	263	2	3.15	3.15	NUM
ma-105	263	3	)	)	PUNCT
ma-105	263	4	dθ3	dθ3	NOUN
ma-105	263	5	dτ	dτ	NOUN
ma-105	263	6	=	=	SYM
ma-105	263	7	d	d	X
ma-105	263	8	dτ	dτ	PROPN
ma-105	263	9	[	[	PUNCT
ma-105	263	10	g3(t	g3(t	PROPN
ma-105	263	11	−	−	PROPN
ma-105	263	12	τ	τ	PROPN
ma-105	263	13	)	)	PUNCT
ma-105	263	14	]	]	PUNCT
ma-105	264	1	v	v	X
ma-105	264	2	(	(	PUNCT
ma-105	264	3	τ	τ	X
ma-105	264	4	)	)	PUNCT
ma-105	264	5	+	+	CCONJ
ma-105	264	6	g3(t	g3(t	NUM
ma-105	264	7	−	−	NOUN
ma-105	264	8	τ)v	τ)v	PUNCT
ma-105	265	1	′	′	NUM
ma-105	265	2	(	(	PUNCT
ma-105	265	3	τ	τ	PROPN
ma-105	265	4	)	)	PUNCT
ma-105	265	5	,	,	PUNCT
ma-105	265	6	=	=	SYM
ma-105	265	7	−d	−d	PROPN
ma-105	265	8	×	×	PROPN
ma-105	265	9	∆g3(t	∆g3(t	PROPN
ma-105	265	10	−	−	PROPN
ma-105	265	11	τ)v	τ)v	PUNCT
ma-105	265	12	(	(	PUNCT
ma-105	265	13	τ	τ	X
ma-105	265	14	)	)	PUNCT
ma-105	266	1	+	+	PROPN
ma-105	266	2	d	d	PROPN
ma-105	266	3	×	×	NOUN
ma-105	266	4	g3(t	g3(t	NUM
ma-105	266	5	−	−	NOUN
ma-105	266	6	τ)∆v	τ)∆v	PUNCT
ma-105	266	7	(	(	PUNCT
ma-105	266	8	τ	τ	X
ma-105	266	9	)	)	PUNCT
ma-105	266	10	+	+	CCONJ
ma-105	267	1	g3(t	g3(t	NUM
ma-105	267	2	−	−	NOUN
ma-105	267	3	τ)q(τ	τ)q(τ	ADJ
ma-105	267	4	,	,	PUNCT
ma-105	267	5	h(τ	h(τ	PROPN
ma-105	267	6	)	)	PUNCT
ma-105	267	7	,	,	PUNCT
ma-105	267	8	i(τ	i(τ	PROPN
ma-105	267	9	)	)	PUNCT
ma-105	267	10	,	,	PUNCT
ma-105	267	11	v	v	X
ma-105	267	12	(	(	PUNCT
ma-105	267	13	τ	τ	PROPN
ma-105	267	14	)	)	PUNCT
ma-105	267	15	)	)	PUNCT
ma-105	267	16	,	,	PUNCT
ma-105	268	1	=	=	PUNCT
ma-105	268	2	g3(t	g3(t	PROPN
ma-105	268	3	−	−	NOUN
ma-105	268	4	τ)q(τ	τ)q(τ	ADJ
ma-105	268	5	,	,	PUNCT
ma-105	268	6	h(τ	h(τ	PROPN
ma-105	268	7	)	)	PUNCT
ma-105	268	8	,	,	PUNCT
ma-105	268	9	i(τ	i(τ	PROPN
ma-105	268	10	)	)	PUNCT
ma-105	268	11	,	,	PUNCT
ma-105	268	12	v	v	X
ma-105	268	13	(	(	PUNCT
ma-105	268	14	τ	τ	PROPN
ma-105	268	15	)	)	PUNCT
ma-105	268	16	)	)	PUNCT
ma-105	268	17	.	.	PUNCT
ma-105	269	1	(	(	PUNCT
ma-105	269	2	3.16	3.16	NUM
ma-105	269	3	)	)	PUNCT
ma-105	269	4	integrating	integrate	VERB
ma-105	269	5	equations	equation	NOUN
ma-105	269	6	(	(	PUNCT
ma-105	269	7	3.14	3.14	NUM
ma-105	269	8	)	)	PUNCT
ma-105	269	9	,	,	PUNCT
ma-105	269	10	(	(	PUNCT
ma-105	269	11	3.15	3.15	NUM
ma-105	269	12	)	)	PUNCT
ma-105	269	13	and	and	CCONJ
ma-105	269	14	(	(	PUNCT
ma-105	269	15	3.16	3.16	NUM
ma-105	269	16	)	)	PUNCT
ma-105	269	17	with	with	ADP
ma-105	269	18	respect	respect	NOUN
ma-105	269	19	to	to	ADP
ma-105	269	20	time	time	NOUN
ma-105	269	21	,	,	PUNCT
ma-105	269	22	we	we	PRON
ma-105	269	23	obtain	obtain	VERB
ma-105	269	24	equations	equation	NOUN
ma-105	269	25	(	(	PUNCT
ma-105	269	26	3.11),(3.12	3.11),(3.12	NUM
ma-105	269	27	)	)	PUNCT
ma-105	269	28	and	and	CCONJ
ma-105	269	29	(	(	PUNCT
ma-105	269	30	3.13	3.13	NUM
ma-105	269	31	)	)	PUNCT
ma-105	269	32	respectively	respectively	ADV
ma-105	269	33	.	.	PUNCT
ma-105	270	1	�	�	PROPN
ma-105	270	2	remark	remark	VERB
ma-105	270	3	3.3	3.3	NUM
ma-105	270	4	.	.	PUNCT
ma-105	271	1	since	since	SCONJ
ma-105	271	2	in	in	ADP
ma-105	271	3	this	this	DET
ma-105	271	4	work	work	NOUN
ma-105	271	5	,	,	PUNCT
ma-105	271	6	n	n	NOUN
ma-105	271	7	=	=	SYM
ma-105	271	8	3	3	NUM
ma-105	271	9	,	,	PUNCT
ma-105	271	10	we	we	PRON
ma-105	271	11	take	take	VERB
ma-105	271	12	p	p	NOUN
ma-105	271	13	=	=	NOUN
ma-105	271	14	2	2	NUM
ma-105	271	15	so	so	SCONJ
ma-105	271	16	that	that	SCONJ
ma-105	271	17	β	β	NOUN
ma-105	271	18	>	>	X
ma-105	271	19	3	3	NUM
ma-105	271	20	4	4	NUM
ma-105	271	21	and	and	CCONJ
ma-105	271	22	therefore	therefore	ADV
ma-105	271	23	the	the	DET
ma-105	271	24	domain	domain	NOUN
ma-105	271	25	d(h	d(h	PROPN
ma-105	271	26	�	�	PROPN
ma-105	271	27	)	)	PUNCT
ma-105	271	28	is	be	AUX
ma-105	271	29	continuously	continuously	ADV
ma-105	271	30	embedded	embed	VERB
ma-105	271	31	in	in	ADP
ma-105	271	32	c∞0	c∞0	PROPN
ma-105	271	33	(	(	PUNCT
ma-105	271	34	ω	ω	PROPN
ma-105	271	35	)	)	PUNCT
ma-105	271	36	by	by	ADP
ma-105	271	37	lemma	lemma	PROPN
ma-105	271	38	3.2	3.2	NUM
ma-105	271	39	.	.	PUNCT
ma-105	272	1	now	now	ADV
ma-105	272	2	,	,	PUNCT
ma-105	272	3	let	let	VERB
ma-105	272	4	h	h	NOUN
ma-105	272	5	,	,	PUNCT
ma-105	272	6	i	i	PRON
ma-105	272	7	and	and	CCONJ
ma-105	272	8	v	v	NOUN
ma-105	272	9	be	be	AUX
ma-105	272	10	continuousfunctions	continuousfunction	NOUN
ma-105	272	11	from	from	ADP
ma-105	272	12	[	[	X
ma-105	272	13	0	0	NUM
ma-105	272	14	,	,	PUNCT
ma-105	272	15	t	t	NOUN
ma-105	272	16	]	]	PUNCT
ma-105	272	17	to	to	ADP
ma-105	272	18	d(h	d(h	PROPN
ma-105	272	19	�	�	PROPN
ma-105	272	20	)	)	PUNCT
ma-105	272	21	↪	↪	PROPN
ma-105	272	22	→	→	SYM
ma-105	272	23	c0	c0	NOUN
ma-105	272	24	b(ω	b(ω	ADV
ma-105	272	25	)	)	PUNCT
ma-105	273	1	satisfying	satisfying	NOUN
ma-105	273	2	(	(	PUNCT
ma-105	273	3	3.11	3.11	NUM
ma-105	273	4	)	)	PUNCT
ma-105	273	5	,	,	PUNCT
ma-105	273	6	(	(	PUNCT
ma-105	273	7	3.12	3.12	NUM
ma-105	273	8	)	)	PUNCT
ma-105	273	9	and	and	CCONJ
ma-105	273	10	(	(	PUNCT
ma-105	273	11	3.13	3.13	NUM
ma-105	273	12	)	)	PUNCT
ma-105	273	13	respectively	respectively	ADV
ma-105	273	14	.	.	PUNCT
ma-105	274	1	we	we	PRON
ma-105	274	2	canthen	canthen	VERB
ma-105	274	3	claim	claim	VERB
ma-105	274	4	that	that	SCONJ
ma-105	274	5	h	h	NOUN
ma-105	274	6	,	,	PUNCT
ma-105	274	7	i	i	PRON
ma-105	274	8	and	and	CCONJ
ma-105	274	9	v	v	NOUN
ma-105	274	10	verify	verify	NOUN
ma-105	274	11	system	system	NOUN
ma-105	274	12	(	(	PUNCT
ma-105	274	13	3.8	3.8	NUM
ma-105	274	14	)	)	PUNCT
ma-105	274	15	.	.	PUNCT
ma-105	275	1	the	the	DET
ma-105	275	2	continuity	continuity	NOUN
ma-105	275	3	of	of	ADP
ma-105	275	4	h	h	NOUN
ma-105	275	5	,	,	PUNCT
ma-105	275	6	i	i	PRON
ma-105	275	7	and	and	CCONJ
ma-105	275	8	v	v	NOUN
ma-105	275	9	implies	imply	VERB
ma-105	275	10	continuity	continuity	NOUN
ma-105	275	11	of	of	ADP
ma-105	275	12	t	t	PROPN
ma-105	275	13	7→	7→	NUM
ma-105	275	14	f(t	f(t	NOUN
ma-105	275	15	,	,	PUNCT
ma-105	275	16	h(t	h(t	PROPN
ma-105	275	17	)	)	PUNCT
ma-105	275	18	,	,	PUNCT
ma-105	275	19	i(t	i(t	PROPN
ma-105	275	20	)	)	PUNCT
ma-105	275	21	,	,	PUNCT
ma-105	275	22	v	v	X
ma-105	275	23	(	(	PUNCT
ma-105	275	24	t	t	PROPN
ma-105	275	25	)	)	PUNCT
ma-105	275	26	)	)	PUNCT
ma-105	275	27	,	,	PUNCT
ma-105	275	28	t	t	PROPN
ma-105	275	29	7→	7→	NUM
ma-105	275	30	g(t	g(t	PROPN
ma-105	275	31	,	,	PUNCT
ma-105	275	32	h(t	h(t	PROPN
ma-105	275	33	)	)	PUNCT
ma-105	275	34	,	,	PUNCT
ma-105	275	35	i(t	i(t	PROPN
ma-105	275	36	)	)	PUNCT
ma-105	275	37	,	,	PUNCT
ma-105	275	38	v	v	X
ma-105	275	39	(	(	PUNCT
ma-105	275	40	t	t	PROPN
ma-105	275	41	)	)	PUNCT
ma-105	275	42	)	)	PUNCT
ma-105	275	43	and	and	CCONJ
ma-105	275	44	t	t	X
ma-105	275	45	7→	7→	NUM
ma-105	275	46	q(t	q(t	PROPN
ma-105	275	47	,	,	PUNCT
ma-105	275	48	h(t	h(t	PROPN
ma-105	275	49	)	)	PUNCT
ma-105	275	50	,	,	PUNCT
ma-105	275	51	i(t	i(t	PROPN
ma-105	275	52	)	)	PUNCT
ma-105	275	53	,	,	PUNCT
ma-105	275	54	v	v	X
ma-105	275	55	(	(	PUNCT
ma-105	275	56	t)).one	t)).one	NOUN
ma-105	275	57	can	can	AUX
ma-105	275	58	then	then	ADV
ma-105	275	59	conclude	conclude	VERB
ma-105	275	60	that	that	SCONJ
ma-105	275	61	,	,	PUNCT
ma-105	275	62	the	the	DET
ma-105	275	63	linear	linear	ADJ
ma-105	275	64	cauchy	cauchy	PROPN
ma-105	275	65	problem	problem	PROPN
ma-105	275	66	∂ty1	∂ty1	NOUN
ma-105	275	67	−d1∆y1	−d1∆y1	NOUN
ma-105	275	68	=	=	PUNCT
ma-105	275	69	f(t	f(t	NOUN
ma-105	275	70	,	,	PUNCT
ma-105	275	71	h(t	h(t	PROPN
ma-105	275	72	)	)	PUNCT
ma-105	275	73	,	,	PUNCT
ma-105	275	74	i(t	i(t	PROPN
ma-105	275	75	)	)	PUNCT
ma-105	275	76	,	,	PUNCT
ma-105	275	77	v	v	X
ma-105	275	78	(	(	PUNCT
ma-105	275	79	t	t	PROPN
ma-105	275	80	)	)	PUNCT
ma-105	275	81	)	)	PUNCT
ma-105	275	82	,	,	PUNCT
ma-105	275	83	∂ty2	∂ty2	X
ma-105	275	84	−d2∆y2	−d2∆y2	NOUN
ma-105	275	85	=	=	SYM
ma-105	275	86	g(t	g(t	PROPN
ma-105	275	87	,	,	PUNCT
ma-105	275	88	h(t	h(t	PROPN
ma-105	275	89	)	)	PUNCT
ma-105	275	90	,	,	PUNCT
ma-105	275	91	i(t	i(t	PROPN
ma-105	275	92	)	)	PUNCT
ma-105	275	93	,	,	PUNCT
ma-105	275	94	v	v	X
ma-105	275	95	(	(	PUNCT
ma-105	275	96	t	t	PROPN
ma-105	275	97	)	)	PUNCT
ma-105	275	98	)	)	PUNCT
ma-105	275	99	,	,	PUNCT
ma-105	275	100	∂ty3	∂ty3	PROPN
ma-105	275	101	−d∆y3	−d∆y3	NOUN
ma-105	275	102	=	=	SYM
ma-105	275	103	q(t	q(t	PROPN
ma-105	275	104	,	,	PUNCT
ma-105	275	105	h(t	h(t	PROPN
ma-105	275	106	)	)	PUNCT
ma-105	275	107	,	,	PUNCT
ma-105	275	108	i(t	i(t	PROPN
ma-105	275	109	)	)	PUNCT
ma-105	275	110	,	,	PUNCT
ma-105	275	111	v	v	X
ma-105	275	112	(	(	PUNCT
ma-105	275	113	t	t	PROPN
ma-105	275	114	)	)	PUNCT
ma-105	275	115	)	)	PUNCT
ma-105	275	116	,	,	PUNCT
ma-105	275	117	y1(0	y1(0	PROPN
ma-105	275	118	)	)	PUNCT
ma-105	275	119	=	=	SYM
ma-105	275	120	h0	h0	PROPN
ma-105	275	121	,	,	PUNCT
ma-105	275	122	y2(0	y2(0	PROPN
ma-105	275	123	)	)	PUNCT
ma-105	275	124	=	=	SYM
ma-105	275	125	i0	i0	PROPN
ma-105	275	126	,	,	PUNCT
ma-105	275	127	y3(0	y3(0	PROPN
ma-105	275	128	)	)	PUNCT
ma-105	275	129	=	=	SYM
ma-105	275	130	v0	v0	NOUN
ma-105	275	131	,	,	PUNCT
ma-105	275	132	has	have	VERB
ma-105	275	133	a	a	DET
ma-105	275	134	unique	unique	ADJ
ma-105	275	135	solution	solution	NOUN
ma-105	275	136	,	,	PUNCT
ma-105	275	137	with	with	ADP
ma-105	275	138	y1	y1	NOUN
ma-105	275	139	,	,	PUNCT
ma-105	275	140	y2	y2	PROPN
ma-105	275	141	and	and	CCONJ
ma-105	275	142	y3	y3	NOUN
ma-105	275	143	given	give	VERB
ma-105	275	144	by	by	ADP
ma-105	275	145	(	(	PUNCT
ma-105	275	146	3.11	3.11	NUM
ma-105	275	147	)	)	PUNCT
ma-105	275	148	,	,	PUNCT
ma-105	275	149	(	(	PUNCT
ma-105	275	150	3.12	3.12	NUM
ma-105	275	151	)	)	PUNCT
ma-105	275	152	and	and	CCONJ
ma-105	275	153	(	(	PUNCT
ma-105	275	154	3.13	3.13	NUM
ma-105	275	155	)	)	PUNCT
ma-105	275	156	respectively	respectively	ADV
ma-105	275	157	.	.	PUNCT
ma-105	276	1	following	follow	VERB
ma-105	276	2	[	[	X
ma-105	276	3	2	2	NUM
ma-105	276	4	]	]	PUNCT
ma-105	276	5	,	,	PUNCT
ma-105	276	6	[	[	X
ma-105	276	7	4	4	NUM
ma-105	276	8	]	]	PUNCT
ma-105	276	9	,	,	PUNCT
ma-105	276	10	[	[	X
ma-105	276	11	3	3	NUM
ma-105	276	12	]	]	PUNCT
ma-105	276	13	,	,	PUNCT
ma-105	276	14	[	[	X
ma-105	276	15	22	22	NUM
ma-105	276	16	]	]	PUNCT
ma-105	276	17	,	,	PUNCT
ma-105	276	18	[	[	X
ma-105	276	19	24	24	NUM
ma-105	276	20	]	]	PUNCT
ma-105	276	21	,	,	PUNCT
ma-105	276	22	we	we	PRON
ma-105	276	23	have	have	VERB
ma-105	276	24	the	the	DET
ma-105	276	25	following	follow	VERB
ma-105	276	26	main	main	ADJ
ma-105	276	27	result	result	NOUN
ma-105	276	28	for	for	ADP
ma-105	276	29	the	the	DET
ma-105	276	30	local	local	ADJ
ma-105	276	31	existence	existence	NOUN
ma-105	276	32	of	of	ADP
ma-105	276	33	(	(	PUNCT
ma-105	276	34	2.4),based	2.4),base	VERB
ma-105	276	35	on	on	ADP
ma-105	276	36	l2	l2	NOUN
ma-105	276	37	-	-	PUNCT
ma-105	276	38	theory	theory	NOUN
ma-105	276	39	.	.	PUNCT
ma-105	277	1	proposition	proposition	NOUN
ma-105	277	2	3.8	3.8	NUM
ma-105	277	3	.	.	PUNCT
ma-105	278	1	if	if	SCONJ
ma-105	278	2	hypotheses	hypothesis	NOUN
ma-105	278	3	(	(	PUNCT
ma-105	278	4	h1	h1	PROPN
ma-105	278	5	)	)	PUNCT
ma-105	278	6	,	,	PUNCT
ma-105	278	7	(	(	PUNCT
ma-105	278	8	h2	h2	NOUN
ma-105	278	9	)	)	PUNCT
ma-105	278	10	and	and	CCONJ
ma-105	278	11	(	(	PUNCT
ma-105	278	12	h3	h3	NOUN
ma-105	278	13	)	)	PUNCT
ma-105	278	14	are	be	AUX
ma-105	278	15	satisfied	satisfied	ADJ
ma-105	278	16	,	,	PUNCT
ma-105	278	17	then	then	ADV
ma-105	278	18	the	the	DET
ma-105	278	19	initial	initial	ADJ
ma-105	278	20	value	value	NOUN
ma-105	278	21	and	and	CCONJ
ma-105	278	22	boundary	boundary	ADJ
ma-105	278	23	problem	problem	NOUN
ma-105	278	24	(	(	PUNCT
ma-105	278	25	3.8	3.8	NUM
ma-105	278	26	)	)	PUNCT
ma-105	278	27	admits	admit	VERB
ma-105	278	28	a	a	DET
ma-105	278	29	unique	unique	ADJ
ma-105	278	30	solution	solution	NOUN
ma-105	278	31	(	(	PUNCT
ma-105	278	32	h	h	NOUN
ma-105	278	33	,	,	PUNCT
ma-105	278	34	i	i	PRON
ma-105	278	35	,	,	PUNCT
ma-105	278	36	v	v	NOUN
ma-105	278	37	)	)	PUNCT
ma-105	278	38	∈	∈	PROPN
ma-105	278	39	(	(	PUNCT
ma-105	278	40	c0	c0	PROPN
ma-105	278	41	b(]0	b(]0	PROPN
ma-105	278	42	,	,	PUNCT
ma-105	278	43	t	t	X
ma-105	278	44	]	]	PUNCT
ma-105	278	45	,	,	PUNCT
ma-105	278	46	d(hβ)))3	d(hβ)))3	PROPN
ma-105	278	47	,	,	PUNCT
ma-105	278	48	with	with	ADP
ma-105	278	49	h(0	h(0	PROPN
ma-105	278	50	)	)	PUNCT
ma-105	278	51	=	=	SYM
ma-105	278	52	h0	h0	NOUN
ma-105	278	53	∈	∈	PROPN
ma-105	278	54	c0	c0	PROPN
ma-105	278	55	b(ω	b(ω	ADV
ma-105	278	56	)	)	PUNCT
ma-105	278	57	,	,	PUNCT
ma-105	278	58	i(0	i(0	PROPN
ma-105	278	59	)	)	PUNCT
ma-105	279	1	=	=	PUNCT
ma-105	279	2	i0	i0	PROPN
ma-105	279	3	∈	∈	PROPN
ma-105	279	4	c0	c0	PROPN
ma-105	279	5	b(ω	b(ω	ADV
ma-105	279	6	)	)	PUNCT
ma-105	279	7	and	and	CCONJ
ma-105	279	8	v	v	X
ma-105	279	9	(	(	PUNCT
ma-105	279	10	0	0	NUM
ma-105	279	11	)	)	PUNCT
ma-105	279	12	=	=	SYM
ma-105	279	13	v0	v0	NOUN
ma-105	279	14	∈	∈	PROPN
ma-105	279	15	c0	c0	PROPN
ma-105	279	16	b(ω	b(ω	ADV
ma-105	279	17	)	)	PUNCT
ma-105	279	18	.	.	PUNCT
ma-105	280	1	the	the	DET
ma-105	280	2	proof	proof	NOUN
ma-105	280	3	of	of	ADP
ma-105	280	4	this	this	DET
ma-105	280	5	proposition	proposition	NOUN
ma-105	280	6	is	be	AUX
ma-105	280	7	given	give	VERB
ma-105	280	8	in	in	ADP
ma-105	280	9	"	"	PUNCT
ma-105	280	10	appendix	appendix	VERB
ma-105	280	11	a	a	PRON
ma-105	280	12	"	"	PUNCT
ma-105	280	13	.	.	PUNCT
ma-105	281	1	3.2	3.2	NUM
ma-105	281	2	.	.	PUNCT
ma-105	282	1	boundedness	boundedness	NOUN
ma-105	282	2	of	of	ADP
ma-105	282	3	the	the	DET
ma-105	282	4	solutions	solution	NOUN
ma-105	282	5	for	for	ADP
ma-105	282	6	ibvp	ibvp	NOUN
ma-105	282	7	(	(	PUNCT
ma-105	282	8	2.4	2.4	NUM
ma-105	282	9	)	)	PUNCT
ma-105	282	10	.	.	PUNCT
ma-105	283	1	proposition	proposition	NOUN
ma-105	283	2	3.9	3.9	NUM
ma-105	283	3	.	.	PUNCT
ma-105	284	1	let	let	VERB
ma-105	284	2	(	(	PUNCT
ma-105	284	3	h	h	NOUN
ma-105	284	4	,	,	PUNCT
ma-105	284	5	i	i	PRON
ma-105	284	6	,	,	PUNCT
ma-105	284	7	v	v	NOUN
ma-105	284	8	)	)	PUNCT
ma-105	284	9	∈	∈	PROPN
ma-105	284	10	(	(	PUNCT
ma-105	284	11	c0	c0	NOUN
ma-105	284	12	(	(	PUNCT
ma-105	284	13	ω×	ω×	X
ma-105	284	14	[	[	X
ma-105	284	15	0	0	NUM
ma-105	284	16	,	,	PUNCT
ma-105	284	17	t	t	NOUN
ma-105	284	18	)	)	PUNCT
ma-105	284	19	)	)	PUNCT
ma-105	285	1	∩	∩	PROPN
ma-105	285	2	c2,1	c2,1	PROPN
ma-105	285	3	b	b	PROPN
ma-105	285	4	(	(	PUNCT
ma-105	285	5	ω×	ω×	X
ma-105	285	6	[	[	X
ma-105	285	7	0	0	NUM
ma-105	285	8	,	,	PUNCT
ma-105	285	9	t	t	NOUN
ma-105	285	10	)	)	PUNCT
ma-105	285	11	)	)	PUNCT
ma-105	285	12	)	)	PUNCT
ma-105	285	13	3	3	NUM
ma-105	285	14	be	be	AUX
ma-105	285	15	the	the	DET
ma-105	285	16	solution	solution	NOUN
ma-105	285	17	of	of	ADP
ma-105	285	18	(	(	PUNCT
ma-105	285	19	2.4	2.4	NUM
ma-105	285	20	)	)	PUNCT
ma-105	285	21	with	with	ADP
ma-105	285	22	bounded	bounded	ADJ
ma-105	285	23	initial	initial	ADJ
ma-105	285	24	conditions	condition	NOUN
ma-105	285	25	i.e.	i.e.	X
ma-105	285	26	0	0	PUNCT
ma-105	285	27	<	<	X
ma-105	285	28	h0(x	h0(x	X
ma-105	285	29	)	)	PUNCT
ma-105	285	30	<	<	X
ma-105	285	31	hm	hm	INTJ
ma-105	285	32	,	,	PUNCT
ma-105	285	33	0	0	PUNCT
ma-105	285	34	<	<	X
ma-105	285	35	i0(x	i0(x	NOUN
ma-105	285	36	)	)	PUNCT
ma-105	285	37	<	<	X
ma-105	285	38	hm	hm	INTJ
ma-105	285	39	,	,	PUNCT
ma-105	285	40	https://doi.org/10.28924/ada/ma.3.1	https://doi.org/10.28924/ada/ma.3.1	PROPN
ma-105	285	41	eur	eur	PROPN
ma-105	285	42	.	.	PUNCT
ma-105	286	1	j.	j.	PROPN
ma-105	286	2	math	math	PROPN
ma-105	286	3	.	.	PUNCT
ma-105	287	1	anal	anal	PROPN
ma-105	287	2	.	.	PUNCT
ma-105	288	1	10.28924	10.28924	NUM
ma-105	288	2	/	/	SYM
ma-105	288	3	ada	ada	PROPN
ma-105	288	4	/	/	SYM
ma-105	288	5	ma.3.1	ma.3.1	PROPN
ma-105	289	1	10	10	NUM
ma-105	289	2	0	0	NUM
ma-105	289	3	<	<	X
ma-105	289	4	v0(x	v0(x	PROPN
ma-105	289	5	)	)	PUNCT
ma-105	289	6	<	<	X
ma-105	289	7	vm	vm	PROPN
ma-105	289	8	for	for	ADP
ma-105	289	9	all	all	DET
ma-105	289	10	x	x	SYM
ma-105	289	11	∈	∈	PROPN
ma-105	289	12	ω	ω	NOUN
ma-105	289	13	,	,	PUNCT
ma-105	289	14	and	and	CCONJ
ma-105	289	15	satisfying	satisfy	VERB
ma-105	289	16	the	the	DET
ma-105	289	17	boundary	boundary	ADJ
ma-105	289	18	condition	condition	NOUN
ma-105	289	19	∂h0	∂h0	ADP
ma-105	289	20	∂η	∂η	PROPN
ma-105	289	21	=	=	SYM
ma-105	289	22	0	0	NUM
ma-105	289	23	,	,	PUNCT
ma-105	289	24	∂i0∂η	∂i0∂η	PROPN
ma-105	289	25	=	=	SYM
ma-105	289	26	0	0	NUM
ma-105	289	27	,	,	PUNCT
ma-105	289	28	∂v0	∂v0	VERB
ma-105	289	29	∂η	∂η	PROPN
ma-105	289	30	=	=	NOUN
ma-105	289	31	0	0	NUM
ma-105	289	32	on	on	ADP
ma-105	289	33	∂ω	∂ω	PROPN
ma-105	289	34	.	.	PUNCT
ma-105	290	1	then	then	ADV
ma-105	290	2	,	,	PUNCT
ma-105	290	3	∀(x	∀(x	PRON
ma-105	290	4	,	,	PUNCT
ma-105	290	5	t	t	PROPN
ma-105	290	6	)	)	PUNCT
ma-105	290	7	∈	∈	NOUN
ma-105	290	8	ω×	ω×	PUNCT
ma-105	291	1	[	[	X
ma-105	291	2	0	0	NUM
ma-105	291	3	,	,	PUNCT
ma-105	291	4	t	t	X
ma-105	291	5	]	]	PUNCT
ma-105	291	6	,	,	PUNCT
ma-105	291	7	h(x	h(x	PROPN
ma-105	291	8	,	,	PUNCT
ma-105	291	9	t	t	PROPN
ma-105	291	10	)	)	PUNCT
ma-105	291	11	≤	≤	NUM
ma-105	291	12	hm	hm	INTJ
ma-105	291	13	,	,	PUNCT
ma-105	291	14	i(x	i(x	PROPN
ma-105	291	15	,	,	PUNCT
ma-105	291	16	t	t	PROPN
ma-105	291	17	)	)	PUNCT
ma-105	291	18	≤	≤	PUNCT
ma-105	292	1	hm	hm	INTJ
ma-105	292	2	and	and	CCONJ
ma-105	292	3	v	v	INTJ
ma-105	292	4	(	(	PUNCT
ma-105	292	5	x	x	NOUN
ma-105	292	6	,	,	PUNCT
ma-105	292	7	t	t	PROPN
ma-105	292	8	)	)	PUNCT
ma-105	292	9	≤	≤	PROPN
ma-105	292	10	vm	vm	PROPN
ma-105	292	11	with	with	ADP
ma-105	292	12	hm	hm	INTJ
ma-105	292	13	=	=	SYM
ma-105	292	14	max	max	PROPN
ma-105	292	15	{	{	PUNCT
ma-105	292	16	λ	λ	X
ma-105	292	17	δ2	δ2	VERB
ma-105	292	18	,	,	PUNCT
ma-105	292	19	max	max	PROPN
ma-105	292	20	x∈ω̄	x∈ω̄	PROPN
ma-105	292	21	{	{	PUNCT
ma-105	292	22	h(x	h(x	PROPN
ma-105	292	23	,	,	PUNCT
ma-105	292	24	0	0	NUM
ma-105	292	25	)	)	PUNCT
ma-105	293	1	+	+	CCONJ
ma-105	293	2	i(x	i(x	PROPN
ma-105	293	3	,	,	PUNCT
ma-105	293	4	0	0	NUM
ma-105	293	5	)	)	PUNCT
ma-105	293	6	}	}	PUNCT
ma-105	293	7	}	}	PUNCT
ma-105	293	8	and	and	CCONJ
ma-105	293	9	vm	vm	PROPN
ma-105	293	10	=	=	SYM
ma-105	293	11	max	max	PROPN
ma-105	293	12	{	{	PUNCT
ma-105	293	13	(	(	PUNCT
ma-105	293	14	1−	1−	NUM
ma-105	293	15	ε)khm	ε)khm	PROPN
ma-105	293	16	µ	µ	X
ma-105	293	17	,	,	PUNCT
ma-105	293	18	max	max	PROPN
ma-105	293	19	x∈ω	x∈ω	PROPN
ma-105	293	20	v0(x	v0(x	PROPN
ma-105	293	21	)	)	PUNCT
ma-105	293	22	}	}	PUNCT
ma-105	293	23	.	.	PUNCT
ma-105	294	1	proof	proof	NOUN
ma-105	294	2	.	.	PUNCT
ma-105	295	1	consider	consider	VERB
ma-105	295	2	the	the	DET
ma-105	295	3	function	function	NOUN
ma-105	295	4	s	s	AUX
ma-105	295	5	defined	define	VERB
ma-105	295	6	for	for	ADP
ma-105	295	7	all	all	DET
ma-105	295	8	(	(	PUNCT
ma-105	295	9	x	x	NOUN
ma-105	295	10	,	,	PUNCT
ma-105	295	11	t	t	PROPN
ma-105	295	12	)	)	PUNCT
ma-105	295	13	∈	∈	NOUN
ma-105	295	14	ω×	ω×	PUNCT
ma-105	296	1	[	[	X
ma-105	296	2	0	0	NUM
ma-105	296	3	,	,	PUNCT
ma-105	296	4	t	t	X
ma-105	296	5	]	]	PUNCT
ma-105	296	6	by	by	ADP
ma-105	296	7	s(x	s(x	PROPN
ma-105	296	8	,	,	PUNCT
ma-105	296	9	t	t	PROPN
ma-105	296	10	)	)	PUNCT
ma-105	296	11	=	=	SYM
ma-105	296	12	h(x	h(x	PROPN
ma-105	296	13	,	,	PUNCT
ma-105	296	14	t	t	PROPN
ma-105	296	15	)	)	PUNCT
ma-105	297	1	+	+	CCONJ
ma-105	297	2	i(x	i(x	PROPN
ma-105	297	3	,	,	PUNCT
ma-105	297	4	t	t	PROPN
ma-105	297	5	)	)	PUNCT
ma-105	297	6	.	.	PUNCT
ma-105	298	1	adding	add	VERB
ma-105	298	2	the	the	DET
ma-105	298	3	first	first	ADJ
ma-105	298	4	two	two	NUM
ma-105	298	5	equations	equation	NOUN
ma-105	298	6	in	in	ADP
ma-105	298	7	(	(	PUNCT
ma-105	298	8	2.4	2.4	NUM
ma-105	298	9	)	)	PUNCT
ma-105	298	10	,	,	PUNCT
ma-105	298	11	yields	yield	NOUN
ma-105	298	12	∂s(x	∂s(x	PROPN
ma-105	298	13	,	,	PUNCT
ma-105	298	14	t	t	PROPN
ma-105	298	15	)	)	PUNCT
ma-105	298	16	∂t	∂t	PROPN
ma-105	298	17	−d1∆h(x	−d1∆h(x	PROPN
ma-105	298	18	,	,	PUNCT
ma-105	298	19	t)−d2∆i(x	t)−d2∆i(x	NUM
ma-105	298	20	,	,	PUNCT
ma-105	298	21	t	t	PROPN
ma-105	298	22	)	)	PUNCT
ma-105	298	23	=	=	SYM
ma-105	299	1	λ−	λ−	PROPN
ma-105	299	2	dh(x	dh(x	NUM
ma-105	299	3	,	,	PUNCT
ma-105	299	4	t)−	t)−	PROPN
ma-105	299	5	αi(x	αi(x	NUM
ma-105	299	6	,	,	PUNCT
ma-105	299	7	t	t	PROPN
ma-105	299	8	)	)	PUNCT
ma-105	299	9	.	.	PUNCT
ma-105	300	1	it	it	PRON
ma-105	300	2	follows	follow	VERB
ma-105	300	3	that	that	SCONJ
ma-105	301	1	∂s(x	∂s(x	PROPN
ma-105	301	2	,	,	PUNCT
ma-105	301	3	t	t	PROPN
ma-105	301	4	)	)	PUNCT
ma-105	301	5	∂t	∂t	PROPN
ma-105	301	6	−max{d1	−max{d1	NOUN
ma-105	301	7	,	,	PUNCT
ma-105	301	8	d2}∆	d2}∆	PROPN
ma-105	301	9	(	(	PUNCT
ma-105	301	10	h(x	h(x	PROPN
ma-105	301	11	,	,	PUNCT
ma-105	301	12	t	t	PROPN
ma-105	301	13	)	)	PUNCT
ma-105	301	14	+	+	CCONJ
ma-105	301	15	i(x	i(x	PROPN
ma-105	301	16	,	,	PUNCT
ma-105	301	17	t	t	PROPN
ma-105	301	18	)	)	PUNCT
ma-105	301	19	)	)	PUNCT
ma-105	302	1	≤	≤	NUM
ma-105	302	2	λ−min{d	λ−min{d	NOUN
ma-105	302	3	,	,	PUNCT
ma-105	302	4	α	α	NOUN
ma-105	302	5	}	}	PUNCT
ma-105	302	6	(	(	PUNCT
ma-105	302	7	h(x	h(x	PROPN
ma-105	302	8	,	,	PUNCT
ma-105	302	9	t	t	PROPN
ma-105	302	10	)	)	PUNCT
ma-105	302	11	+	+	CCONJ
ma-105	302	12	i(x	i(x	PROPN
ma-105	302	13	,	,	PUNCT
ma-105	302	14	t	t	PROPN
ma-105	302	15	)	)	PUNCT
ma-105	302	16	)	)	PUNCT
ma-105	302	17	,	,	PUNCT
ma-105	302	18	we	we	PRON
ma-105	302	19	have	have	VERB
ma-105	302	20			NUM
ma-105	302	21	∂s(x	∂s(x	PROPN
ma-105	302	22	,	,	PUNCT
ma-105	302	23	t	t	PROPN
ma-105	302	24	)	)	PUNCT
ma-105	303	1	∂t	∂t	PROPN
ma-105	303	2	−	−	PROPN
ma-105	303	3	δ1∆s(x	δ1∆s(x	PROPN
ma-105	303	4	,	,	PUNCT
ma-105	303	5	t	t	PROPN
ma-105	303	6	)	)	PUNCT
ma-105	303	7	≤	≤	NOUN
ma-105	303	8	λ−	λ−	PROPN
ma-105	303	9	δ2s(x	δ2s(x	PROPN
ma-105	303	10	,	,	PUNCT
ma-105	303	11	t	t	PROPN
ma-105	303	12	)	)	PUNCT
ma-105	303	13	,	,	PUNCT
ma-105	303	14	x	x	PUNCT
ma-105	303	15	∈	∈	PROPN
ma-105	303	16	ω	ω	PROPN
ma-105	303	17	,	,	PUNCT
ma-105	303	18	t	t	PROPN
ma-105	303	19	∈	∈	PROPN
ma-105	304	1	[	[	X
ma-105	304	2	0	0	NUM
ma-105	304	3	,	,	PUNCT
ma-105	304	4	t	t	NOUN
ma-105	304	5	]	]	PUNCT
ma-105	304	6	∂s(x	∂s(x	PROPN
ma-105	304	7	,	,	PUNCT
ma-105	304	8	t	t	PROPN
ma-105	304	9	)	)	PUNCT
ma-105	304	10	∂η	∂η	PROPN
ma-105	304	11	=	=	SYM
ma-105	304	12	0	0	PROPN
ma-105	304	13	,	,	PUNCT
ma-105	304	14	x	x	SYM
ma-105	304	15	∈	∈	PROPN
ma-105	304	16	∂ω	∂ω	PROPN
ma-105	304	17	,	,	PUNCT
ma-105	304	18	t	t	PROPN
ma-105	304	19	∈	∈	PROPN
ma-105	305	1	[	[	X
ma-105	305	2	0	0	NUM
ma-105	305	3	,	,	PUNCT
ma-105	305	4	t	t	NOUN
ma-105	305	5	]	]	PUNCT
ma-105	305	6	s(x	s(x	PROPN
ma-105	305	7	,	,	PUNCT
ma-105	305	8	0	0	NUM
ma-105	305	9	)	)	PUNCT
ma-105	305	10	=	=	SYM
ma-105	305	11	max	max	PROPN
ma-105	305	12	x∈ω	x∈ω	PROPN
ma-105	305	13	s0(x	s0(x	PROPN
ma-105	305	14	)	)	PUNCT
ma-105	305	15	,	,	PUNCT
ma-105	305	16	(	(	PUNCT
ma-105	305	17	3.17	3.17	NUM
ma-105	305	18	)	)	PUNCT
ma-105	305	19	where	where	SCONJ
ma-105	305	20	s0(x	s0(x	VERB
ma-105	305	21	)	)	PUNCT
ma-105	305	22	=	=	SYM
ma-105	305	23	{	{	PUNCT
ma-105	305	24	h(x	h(x	PROPN
ma-105	305	25	,	,	PUNCT
ma-105	305	26	0	0	NUM
ma-105	305	27	)	)	PUNCT
ma-105	306	1	+	+	CCONJ
ma-105	306	2	i(x	i(x	PROPN
ma-105	306	3	,	,	PUNCT
ma-105	306	4	0	0	NUM
ma-105	306	5	)	)	PUNCT
ma-105	306	6	}	}	PUNCT
ma-105	306	7	,	,	PUNCT
ma-105	306	8	δ1	δ1	NOUN
ma-105	306	9	=	=	SYM
ma-105	306	10	max{d1	max{d1	X
ma-105	306	11	,	,	PUNCT
ma-105	306	12	d2	d2	PROPN
ma-105	306	13	}	}	PUNCT
ma-105	306	14	et	et	NOUN
ma-105	306	15	δ2	δ2	VERB
ma-105	306	16	=	=	SYM
ma-105	306	17	min{d	min{d	NOUN
ma-105	306	18	,	,	PUNCT
ma-105	306	19	α	α	NOUN
ma-105	306	20	}	}	PUNCT
ma-105	306	21	.	.	PUNCT
ma-105	307	1	by	by	ADP
ma-105	307	2	using	use	VERB
ma-105	307	3	the	the	DET
ma-105	307	4	standardparabolic	standardparabolic	ADJ
ma-105	307	5	comparison	comparison	NOUN
ma-105	307	6	of	of	ADP
ma-105	307	7	the	the	DET
ma-105	307	8	scalar	scalar	ADJ
ma-105	307	9	parabolic	parabolic	ADJ
ma-105	307	10	equations	equation	NOUN
ma-105	307	11	[	[	X
ma-105	307	12	33	33	NUM
ma-105	307	13	]	]	PUNCT
ma-105	307	14	,	,	PUNCT
ma-105	307	15	one	one	PRON
ma-105	307	16	has	have	VERB
ma-105	307	17	s(x	s(x	PROPN
ma-105	307	18	,	,	PUNCT
ma-105	307	19	t	t	PROPN
ma-105	307	20	)	)	PUNCT
ma-105	307	21	≤	≤	NUM
ma-105	307	22	s̄(t	s̄(t	PROPN
ma-105	307	23	)	)	PUNCT
ma-105	307	24	,	,	PUNCT
ma-105	307	25	where	where	SCONJ
ma-105	307	26	s̄(t	s̄(t	ADJ
ma-105	307	27	)	)	PUNCT
ma-105	307	28	=	=	PUNCT
ma-105	308	1	λ	λ	X
ma-105	308	2	δ2	δ2	VERB
ma-105	308	3	(	(	PUNCT
ma-105	308	4	1−	1−	NUM
ma-105	308	5	e−δ2	e−δ2	NOUN
ma-105	308	6	t	t	PROPN
ma-105	308	7	)	)	PUNCT
ma-105	309	1	+	+	CCONJ
ma-105	309	2	max	max	PROPN
ma-105	309	3	x∈ω̄	x∈ω̄	PROPN
ma-105	309	4	s0(x)e−δ2	s0(x)e−δ2	PROPN
ma-105	309	5	t	t	PROPN
ma-105	309	6	is	be	AUX
ma-105	309	7	the	the	DET
ma-105	309	8	solution	solution	NOUN
ma-105	309	9	of	of	ADP
ma-105	309	10	the	the	DET
ma-105	309	11	problem	problem	PROPN
ma-105	309	12	ds̄(t	ds̄(t	PROPN
ma-105	309	13	)	)	PUNCT
ma-105	309	14	dt	dt	NOUN
ma-105	310	1	=	=	SYM
ma-105	310	2	λ−	λ−	PROPN
ma-105	310	3	δ2s̄(t	δ2s̄(t	ADJ
ma-105	310	4	)	)	PUNCT
ma-105	310	5	,	,	PUNCT
ma-105	310	6	s̄(0	s̄(0	NUM
ma-105	310	7	)	)	PUNCT
ma-105	310	8	=	=	SYM
ma-105	311	1	max	max	PROPN
ma-105	311	2	x∈ω̄	x∈ω̄	PROPN
ma-105	311	3	s0(x	s0(x	PROPN
ma-105	311	4	)	)	PUNCT
ma-105	311	5	,	,	PUNCT
ma-105	311	6	(	(	PUNCT
ma-105	311	7	3.18	3.18	NUM
ma-105	311	8	)	)	PUNCT
ma-105	311	9	which	which	PRON
ma-105	311	10	dominates	dominate	VERB
ma-105	311	11	system	system	NOUN
ma-105	311	12	(	(	PUNCT
ma-105	311	13	3.17	3.17	NUM
ma-105	311	14	)	)	PUNCT
ma-105	311	15	.	.	PUNCT
ma-105	312	1	the	the	DET
ma-105	312	2	general	general	ADJ
ma-105	312	3	solution	solution	NOUN
ma-105	312	4	of	of	ADP
ma-105	312	5	(	(	PUNCT
ma-105	312	6	3.18	3.18	NUM
ma-105	312	7	)	)	PUNCT
ma-105	312	8	is	be	AUX
ma-105	312	9	on	on	ADP
ma-105	312	10	the	the	DET
ma-105	312	11	form	form	NOUN
ma-105	312	12	s̄(t	s̄(t	PROPN
ma-105	312	13	)	)	PUNCT
ma-105	312	14	=	=	PUNCT
ma-105	312	15	k(t)e−δ2	k(t)e−δ2	PROPN
ma-105	312	16	t	t	NOUN
ma-105	312	17	.	.	PUNCT
ma-105	313	1	bylagrange	bylagrange	PROPN
ma-105	313	2	’s	’s	PART
ma-105	313	3	method	method	NOUN
ma-105	313	4	,	,	PUNCT
ma-105	313	5	we	we	PRON
ma-105	313	6	have	have	VERB
ma-105	313	7	k(t	k(t	PUNCT
ma-105	313	8	)	)	PUNCT
ma-105	314	1	=	=	PUNCT
ma-105	315	1	λ	λ	PROPN
ma-105	315	2	δ2	δ2	VERB
ma-105	315	3	eδ2	eδ2	PROPN
ma-105	315	4	t	t	PROPN
ma-105	315	5	+	+	CCONJ
ma-105	315	6	c	c	PROPN
ma-105	315	7	,	,	PUNCT
ma-105	315	8	c	c	PROPN
ma-105	315	9	∈	∈	PROPN
ma-105	315	10	r.	r.	PROPN
ma-105	315	11	hence	hence	ADV
ma-105	315	12	s̄(t	s̄(t	PROPN
ma-105	315	13	)	)	PUNCT
ma-105	315	14	=	=	PUNCT
ma-105	316	1	(	(	PUNCT
ma-105	316	2	λ	λ	X
ma-105	316	3	δ2	δ2	VERB
ma-105	316	4	eδ2	eδ2	PROPN
ma-105	316	5	t	t	PROPN
ma-105	316	6	+	+	NUM
ma-105	316	7	c	c	NOUN
ma-105	316	8	)	)	PUNCT
ma-105	316	9	e−δ2	e−δ2	ADP
ma-105	316	10	t	t	PROPN
ma-105	316	11	.	.	PUNCT
ma-105	317	1	initial	initial	ADJ
ma-105	317	2	condition	condition	NOUN
ma-105	317	3	yields	yield	VERB
ma-105	317	4	c	c	NOUN
ma-105	317	5	=	=	SYM
ma-105	317	6	max	max	PROPN
ma-105	317	7	x∈ω	x∈ω	NOUN
ma-105	317	8	s0(x)−	s0(x)−	PROPN
ma-105	317	9	λ	λ	PROPN
ma-105	317	10	δ2	δ2	VERB
ma-105	317	11	.therefore	.therefore	ADP
ma-105	317	12	s̄(t	s̄(t	PROPN
ma-105	317	13	)	)	PUNCT
ma-105	317	14	=	=	PUNCT
ma-105	318	1	λ	λ	X
ma-105	318	2	δ2	δ2	VERB
ma-105	318	3	(	(	PUNCT
ma-105	318	4	1−	1−	NUM
ma-105	318	5	e−δ2	e−δ2	NOUN
ma-105	318	6	t	t	PROPN
ma-105	318	7	)	)	PUNCT
ma-105	319	1	+	+	CCONJ
ma-105	319	2	max	max	PROPN
ma-105	319	3	x∈ω̄	x∈ω̄	PROPN
ma-105	319	4	s0(x)e−δ2	s0(x)e−δ2	PROPN
ma-105	319	5	t	t	PROPN
ma-105	319	6	.	.	PUNCT
ma-105	320	1	https://doi.org/10.28924/ada/ma.3.1	https://doi.org/10.28924/ada/ma.3.1	PROPN
ma-105	320	2	eur	eur	PROPN
ma-105	320	3	.	.	PUNCT
ma-105	321	1	j.	j.	PROPN
ma-105	321	2	math	math	PROPN
ma-105	321	3	.	.	PUNCT
ma-105	322	1	anal	anal	PROPN
ma-105	322	2	.	.	PUNCT
ma-105	323	1	10.28924	10.28924	NUM
ma-105	323	2	/	/	SYM
ma-105	323	3	ada	ada	PROPN
ma-105	323	4	/	/	SYM
ma-105	323	5	ma.3.1	ma.3.1	PROPN
ma-105	323	6	11then	11then	ADV
ma-105	323	7	,	,	PUNCT
ma-105	323	8	it	it	PRON
ma-105	323	9	follows	follow	VERB
ma-105	323	10	that	that	SCONJ
ma-105	323	11	:	:	PUNCT
ma-105	323	12	s(x	s(x	PROPN
ma-105	323	13	,	,	PUNCT
ma-105	323	14	t	t	PROPN
ma-105	323	15	)	)	PUNCT
ma-105	323	16	≤	≤	NUM
ma-105	323	17	s̄(t	s̄(t	ADJ
ma-105	323	18	)	)	PUNCT
ma-105	323	19	≤	≤	NUM
ma-105	324	1	λ	λ	PROPN
ma-105	324	2	δ2	δ2	VERB
ma-105	324	3	(	(	PUNCT
ma-105	324	4	1−	1−	NUM
ma-105	324	5	e−δ2	e−δ2	NOUN
ma-105	324	6	t	t	PROPN
ma-105	324	7	)	)	PUNCT
ma-105	325	1	+	+	CCONJ
ma-105	325	2	max	max	PROPN
ma-105	325	3	x∈ω̄	x∈ω̄	PROPN
ma-105	325	4	s0(x)e−δ2	s0(x)e−δ2	PROPN
ma-105	325	5	t	t	PROPN
ma-105	325	6	≤	≤	NUM
ma-105	325	7	max	max	PROPN
ma-105	325	8	{	{	PUNCT
ma-105	325	9	λ	λ	X
ma-105	325	10	δ2	δ2	VERB
ma-105	325	11	,	,	PUNCT
ma-105	325	12	max	max	PROPN
ma-105	325	13	x∈ω̄	x∈ω̄	PROPN
ma-105	325	14	s0(x	s0(x	PROPN
ma-105	325	15	)	)	PUNCT
ma-105	325	16	}	}	PUNCT
ma-105	325	17	(	(	PUNCT
ma-105	325	18	1−	1−	NUM
ma-105	325	19	e−δ2	e−δ2	NOUN
ma-105	325	20	t	t	PROPN
ma-105	325	21	)	)	PUNCT
ma-105	326	1	+	+	CCONJ
ma-105	326	2	max	max	PROPN
ma-105	326	3	{	{	PUNCT
ma-105	327	1	λ	λ	X
ma-105	327	2	δ2	δ2	VERB
ma-105	327	3	,	,	PUNCT
ma-105	327	4	max	max	PROPN
ma-105	327	5	x∈ω̄	x∈ω̄	PROPN
ma-105	327	6	s0(x	s0(x	PROPN
ma-105	327	7	)	)	PUNCT
ma-105	327	8	}	}	PUNCT
ma-105	327	9	e−δ2	e−δ2	ADP
ma-105	327	10	t	t	PROPN
ma-105	327	11	≤	≤	PROPN
ma-105	327	12	max	max	PROPN
ma-105	327	13	{	{	PUNCT
ma-105	327	14	λ	λ	X
ma-105	327	15	δ2	δ2	VERB
ma-105	327	16	,	,	PUNCT
ma-105	327	17	max	max	PROPN
ma-105	327	18	x∈ω̄	x∈ω̄	PROPN
ma-105	327	19	s0(x	s0(x	PROPN
ma-105	327	20	)	)	PUNCT
ma-105	327	21	}	}	PUNCT
ma-105	327	22	.	.	PUNCT
ma-105	328	1	thus	thus	ADV
ma-105	328	2	,	,	PUNCT
ma-105	328	3	s(x	s(x	PROPN
ma-105	328	4	,	,	PUNCT
ma-105	328	5	t	t	PROPN
ma-105	328	6	)	)	PUNCT
ma-105	328	7	≤	≤	NUM
ma-105	328	8	max	max	PROPN
ma-105	328	9	{	{	PUNCT
ma-105	329	1	λ	λ	X
ma-105	329	2	δ2	δ2	VERB
ma-105	329	3	,	,	PUNCT
ma-105	329	4	max	max	PROPN
ma-105	329	5	x∈ω̄	x∈ω̄	PROPN
ma-105	329	6	{	{	PUNCT
ma-105	329	7	h(x	h(x	PROPN
ma-105	329	8	,	,	PUNCT
ma-105	329	9	0	0	NUM
ma-105	329	10	)	)	PUNCT
ma-105	329	11	+	+	CCONJ
ma-105	329	12	i(x	i(x	PROPN
ma-105	329	13	,	,	PUNCT
ma-105	329	14	0	0	NUM
ma-105	329	15	)	)	PUNCT
ma-105	329	16	}	}	PUNCT
ma-105	329	17	}	}	PUNCT
ma-105	329	18	.	.	PUNCT
ma-105	330	1	therefore	therefore	ADV
ma-105	330	2	s(x	s(x	PROPN
ma-105	330	3	,	,	PUNCT
ma-105	330	4	t	t	PROPN
ma-105	330	5	)	)	PUNCT
ma-105	330	6	≤	≤	PUNCT
ma-105	331	1	hm	hm	INTJ
ma-105	331	2	=	=	SYM
ma-105	331	3	max	max	PROPN
ma-105	331	4	{	{	PUNCT
ma-105	331	5	λ	λ	X
ma-105	331	6	δ2	δ2	VERB
ma-105	331	7	,	,	PUNCT
ma-105	331	8	max	max	PROPN
ma-105	331	9	x∈ω̄	x∈ω̄	PROPN
ma-105	331	10	{	{	PUNCT
ma-105	331	11	h(x	h(x	PROPN
ma-105	331	12	,	,	PUNCT
ma-105	331	13	0	0	NUM
ma-105	331	14	)	)	PUNCT
ma-105	332	1	+	+	CCONJ
ma-105	332	2	i(x	i(x	PROPN
ma-105	332	3	,	,	PUNCT
ma-105	332	4	0	0	NUM
ma-105	332	5	)	)	PUNCT
ma-105	332	6	}	}	PUNCT
ma-105	332	7	}	}	PUNCT
ma-105	332	8	,	,	PUNCT
ma-105	332	9	∀(x	∀(x	X
ma-105	332	10	,	,	PUNCT
ma-105	332	11	t	t	PROPN
ma-105	332	12	)	)	PUNCT
ma-105	332	13	∈	∈	NOUN
ma-105	332	14	ω×	ω×	PUNCT
ma-105	333	1	[	[	X
ma-105	333	2	0	0	NUM
ma-105	333	3	,	,	PUNCT
ma-105	333	4	tmax	tmax	NUM
ma-105	333	5	)	)	PUNCT
ma-105	333	6	,	,	PUNCT
ma-105	333	7	where	where	SCONJ
ma-105	333	8	tmax	tmax	ADV
ma-105	333	9	is	be	AUX
ma-105	333	10	the	the	DET
ma-105	333	11	maximal	maximal	ADJ
ma-105	333	12	time	time	NOUN
ma-105	333	13	of	of	ADP
ma-105	333	14	existence	existence	NOUN
ma-105	333	15	of	of	ADP
ma-105	333	16	the	the	DET
ma-105	333	17	solution	solution	NOUN
ma-105	333	18	of	of	ADP
ma-105	333	19	system	system	NOUN
ma-105	333	20	(	(	PUNCT
ma-105	333	21	2.4	2.4	NUM
ma-105	333	22	)	)	PUNCT
ma-105	333	23	,	,	PUNCT
ma-105	333	24	this	this	PRON
ma-105	333	25	implies	imply	VERB
ma-105	333	26	that	that	SCONJ
ma-105	333	27	s	s	VERB
ma-105	333	28	isbounded.hence	isbounded.hence	ADJ
ma-105	333	29	h	h	NOUN
ma-105	334	1	and	and	CCONJ
ma-105	334	2	i	i	PRON
ma-105	334	3	are	be	AUX
ma-105	334	4	bounded	bound	VERB
ma-105	334	5	since	since	SCONJ
ma-105	334	6	s	s	PROPN
ma-105	334	7	is	be	AUX
ma-105	334	8	bounded	bound	VERB
ma-105	334	9	.	.	PUNCT
ma-105	335	1	this	this	PRON
ma-105	335	2	prove	prove	VERB
ma-105	335	3	that	that	SCONJ
ma-105	335	4	h	h	NOUN
ma-105	335	5	and	and	CCONJ
ma-105	335	6	i	i	PRON
ma-105	335	7	are	be	AUX
ma-105	335	8	bounded.now	bounded.now	VERB
ma-105	335	9	,	,	PUNCT
ma-105	335	10	to	to	PART
ma-105	335	11	show	show	VERB
ma-105	335	12	that	that	SCONJ
ma-105	335	13	v	v	NOUN
ma-105	335	14	is	be	AUX
ma-105	335	15	bounded	bound	VERB
ma-105	335	16	,	,	PUNCT
ma-105	335	17	from	from	ADP
ma-105	335	18	the	the	DET
ma-105	335	19	third	third	ADJ
ma-105	335	20	equation	equation	NOUN
ma-105	335	21	of	of	ADP
ma-105	335	22	ibvp	ibvp	NOUN
ma-105	335	23	(	(	PUNCT
ma-105	335	24	2.4	2.4	NUM
ma-105	335	25	)	)	PUNCT
ma-105	335	26	,	,	PUNCT
ma-105	335	27	we	we	PRON
ma-105	335	28	have	have	VERB
ma-105	335	29	∂v	∂v	PROPN
ma-105	335	30	(	(	PUNCT
ma-105	335	31	x	x	X
ma-105	335	32	,	,	PUNCT
ma-105	335	33	t	t	PROPN
ma-105	335	34	)	)	PUNCT
ma-105	335	35	∂t	∂t	PROPN
ma-105	335	36	−d3∆v	−d3∆v	PROPN
ma-105	335	37	(	(	PUNCT
ma-105	335	38	x	x	X
ma-105	335	39	,	,	PUNCT
ma-105	335	40	t	t	PROPN
ma-105	335	41	)	)	PUNCT
ma-105	335	42	≤	≤	NOUN
ma-105	335	43	(	(	PUNCT
ma-105	335	44	1−	1−	NUM
ma-105	335	45	ε)ki(x	ε)ki(x	ADJ
ma-105	335	46	,	,	PUNCT
ma-105	335	47	t)−	t)−	PROPN
ma-105	335	48	µv	µv	NOUN
ma-105	335	49	(	(	PUNCT
ma-105	335	50	x	x	X
ma-105	335	51	,	,	PUNCT
ma-105	335	52	t	t	PROPN
ma-105	335	53	)	)	PUNCT
ma-105	335	54	,	,	PUNCT
ma-105	335	55	x	x	PUNCT
ma-105	335	56	∈	∈	PROPN
ma-105	335	57	ω	ω	PROPN
ma-105	335	58	,	,	PUNCT
ma-105	335	59	t	t	PROPN
ma-105	335	60	∈	∈	PROPN
ma-105	336	1	[	[	X
ma-105	336	2	0	0	NUM
ma-105	336	3	,	,	PUNCT
ma-105	336	4	t	t	X
ma-105	336	5	]	]	X
ma-105	336	6	∂v	∂v	PROPN
ma-105	336	7	(	(	PUNCT
ma-105	336	8	x	x	X
ma-105	336	9	,	,	PUNCT
ma-105	336	10	t	t	PROPN
ma-105	336	11	)	)	PUNCT
ma-105	336	12	∂η	∂η	PROPN
ma-105	337	1	=	=	SYM
ma-105	337	2	0	0	PROPN
ma-105	337	3	,	,	PUNCT
ma-105	337	4	x	x	SYM
ma-105	337	5	∈	∈	PROPN
ma-105	337	6	∂ω	∂ω	PROPN
ma-105	337	7	,	,	PUNCT
ma-105	337	8	t	t	PROPN
ma-105	337	9	∈	∈	PROPN
ma-105	338	1	[	[	X
ma-105	338	2	0	0	NUM
ma-105	338	3	,	,	PUNCT
ma-105	338	4	t	t	PROPN
ma-105	338	5	]	]	X
ma-105	338	6	v	v	PROPN
ma-105	338	7	(	(	PUNCT
ma-105	338	8	x	x	NOUN
ma-105	338	9	,	,	PUNCT
ma-105	338	10	0	0	NUM
ma-105	338	11	)	)	PUNCT
ma-105	338	12	=	=	SYM
ma-105	338	13	max	max	PROPN
ma-105	338	14	x∈ω	x∈ω	PROPN
ma-105	338	15	v0(x	v0(x	PROPN
ma-105	338	16	)	)	PUNCT
ma-105	338	17	.	.	PUNCT
ma-105	339	1	it	it	PRON
ma-105	339	2	follows	follow	VERB
ma-105	339	3	from	from	ADP
ma-105	339	4	the	the	DET
ma-105	339	5	previous	previous	ADJ
ma-105	339	6	system	system	NOUN
ma-105	339	7	,	,	PUNCT
ma-105	340	1	inequality	inequality	PROPN
ma-105	340	2	∂v	∂v	PROPN
ma-105	340	3	(	(	PUNCT
ma-105	340	4	x	x	X
ma-105	340	5	,	,	PUNCT
ma-105	340	6	t	t	PROPN
ma-105	340	7	)	)	PUNCT
ma-105	340	8	∂t	∂t	PROPN
ma-105	340	9	−d∆v	−d∆v	PROPN
ma-105	340	10	(	(	PUNCT
ma-105	340	11	x	x	X
ma-105	340	12	,	,	PUNCT
ma-105	340	13	t	t	PROPN
ma-105	340	14	)	)	PUNCT
ma-105	340	15	≤	≤	NOUN
ma-105	340	16	(	(	PUNCT
ma-105	340	17	1−	1−	NUM
ma-105	340	18	ε)khm	ε)khm	PROPN
ma-105	340	19	−	−	PROPN
ma-105	340	20	µv	µv	NOUN
ma-105	340	21	(	(	PUNCT
ma-105	340	22	x	x	NOUN
ma-105	340	23	,	,	PUNCT
ma-105	340	24	t	t	PROPN
ma-105	340	25	)	)	PUNCT
ma-105	340	26	∂v	∂v	PROPN
ma-105	340	27	(	(	PUNCT
ma-105	340	28	x	x	X
ma-105	340	29	,	,	PUNCT
ma-105	340	30	t	t	PROPN
ma-105	340	31	)	)	PUNCT
ma-105	340	32	∂η	∂η	PROPN
ma-105	340	33	=	=	NOUN
ma-105	340	34	0	0	NUM
ma-105	340	35	v	v	NOUN
ma-105	340	36	(	(	PUNCT
ma-105	340	37	x	x	NOUN
ma-105	340	38	,	,	PUNCT
ma-105	340	39	0	0	NUM
ma-105	340	40	)	)	PUNCT
ma-105	340	41	=	=	SYM
ma-105	340	42	max	max	PROPN
ma-105	340	43	x∈ω̄	x∈ω̄	PROPN
ma-105	340	44	v0(x	v0(x	PROPN
ma-105	340	45	)	)	PUNCT
ma-105	340	46	,	,	PUNCT
ma-105	340	47	(	(	PUNCT
ma-105	340	48	3.19	3.19	NUM
ma-105	340	49	)	)	PUNCT
ma-105	340	50	by	by	ADP
ma-105	340	51	using	use	VERB
ma-105	340	52	the	the	DET
ma-105	340	53	standard	standard	ADJ
ma-105	340	54	parabolic	parabolic	ADJ
ma-105	340	55	comparison	comparison	NOUN
ma-105	340	56	of	of	ADP
ma-105	340	57	the	the	DET
ma-105	340	58	scalar	scalar	ADJ
ma-105	340	59	parabolic	parabolic	ADJ
ma-105	340	60	equations	equation	NOUN
ma-105	340	61	[	[	X
ma-105	340	62	33	33	NUM
ma-105	340	63	]	]	PUNCT
ma-105	340	64	,	,	PUNCT
ma-105	340	65	one	one	PRON
ma-105	340	66	has	have	VERB
ma-105	340	67	v	v	NUM
ma-105	340	68	(	(	PUNCT
ma-105	340	69	x	x	NOUN
ma-105	340	70	,	,	PUNCT
ma-105	340	71	t	t	PROPN
ma-105	340	72	)	)	PUNCT
ma-105	340	73	≤	≤	NOUN
ma-105	340	74	v	v	X
ma-105	340	75	(	(	PUNCT
ma-105	340	76	t	t	PROPN
ma-105	340	77	)	)	PUNCT
ma-105	340	78	,	,	PUNCT
ma-105	340	79	where	where	SCONJ
ma-105	340	80	v	v	X
ma-105	340	81	(	(	PUNCT
ma-105	340	82	t	t	PROPN
ma-105	340	83	)	)	PUNCT
ma-105	340	84	=	=	PUNCT
ma-105	340	85	(	(	PUNCT
ma-105	340	86	1−ε)khm	1−ε)khm	NUM
ma-105	340	87	µ	µ	X
ma-105	340	88	(	(	PUNCT
ma-105	340	89	1−	1−	NUM
ma-105	340	90	e−µt	e−µt	PROPN
ma-105	340	91	)	)	PUNCT
ma-105	341	1	+	+	CCONJ
ma-105	341	2	maxx∈ω̄	maxx∈ω̄	ADJ
ma-105	341	3	v0(x)e−µt	v0(x)e−µt	NOUN
ma-105	341	4	is	be	AUX
ma-105	341	5	the	the	DET
ma-105	341	6	solution	solution	NOUN
ma-105	341	7	of	of	ADP
ma-105	341	8	the	the	DET
ma-105	341	9	problem	problem	PROPN
ma-105	341	10	dv	dv	PROPN
ma-105	341	11	(	(	PUNCT
ma-105	341	12	t	t	PROPN
ma-105	341	13	)	)	PUNCT
ma-105	341	14	dt	dt	NOUN
ma-105	342	1	=	=	PUNCT
ma-105	342	2	(	(	PUNCT
ma-105	342	3	1−	1−	NUM
ma-105	342	4	ε)khm	ε)khm	PROPN
ma-105	342	5	−	−	PROPN
ma-105	342	6	µv	µv	PROPN
ma-105	342	7	(	(	PUNCT
ma-105	342	8	t	t	PROPN
ma-105	342	9	)	)	PUNCT
ma-105	342	10	,	,	PUNCT
ma-105	342	11	v	v	X
ma-105	342	12	(	(	PUNCT
ma-105	342	13	0	0	NUM
ma-105	342	14	)	)	PUNCT
ma-105	342	15	=	=	SYM
ma-105	342	16	max	max	PROPN
ma-105	342	17	x∈ω	x∈ω	PROPN
ma-105	342	18	v0(x	v0(x	PROPN
ma-105	342	19	)	)	PUNCT
ma-105	342	20	,	,	PUNCT
ma-105	342	21	(	(	PUNCT
ma-105	342	22	3.20	3.20	NUM
ma-105	342	23	)	)	PUNCT
ma-105	342	24	https://doi.org/10.28924/ada/ma.3.1	https://doi.org/10.28924/ada/ma.3.1	PROPN
ma-105	342	25	eur	eur	PROPN
ma-105	342	26	.	.	PUNCT
ma-105	343	1	j.	j.	PROPN
ma-105	343	2	math	math	PROPN
ma-105	343	3	.	.	PUNCT
ma-105	344	1	anal	anal	PROPN
ma-105	344	2	.	.	PUNCT
ma-105	345	1	10.28924	10.28924	NUM
ma-105	345	2	/	/	SYM
ma-105	345	3	ada	ada	PROPN
ma-105	345	4	/	/	SYM
ma-105	345	5	ma.3.1	ma.3.1	PROPN
ma-105	345	6	12which	12which	NUM
ma-105	345	7	dominates	dominate	VERB
ma-105	345	8	system	system	NOUN
ma-105	345	9	(	(	PUNCT
ma-105	345	10	3.19	3.19	NUM
ma-105	345	11	)	)	PUNCT
ma-105	345	12	.	.	PUNCT
ma-105	346	1	indeed	indeed	ADV
ma-105	346	2	,	,	PUNCT
ma-105	346	3	the	the	DET
ma-105	346	4	general	general	ADJ
ma-105	346	5	solution	solution	NOUN
ma-105	346	6	of	of	ADP
ma-105	346	7	(	(	PUNCT
ma-105	346	8	3.20	3.20	NUM
ma-105	346	9	)	)	PUNCT
ma-105	346	10	is	be	AUX
ma-105	346	11	on	on	ADP
ma-105	346	12	the	the	DET
ma-105	346	13	form	form	NOUN
ma-105	346	14	v	v	NOUN
ma-105	346	15	(	(	PUNCT
ma-105	346	16	t	t	NOUN
ma-105	346	17	)	)	PUNCT
ma-105	346	18	=	=	SYM
ma-105	346	19	c(t)e−µt	c(t)e−µt	NOUN
ma-105	346	20	.	.	PUNCT
ma-105	347	1	by	by	ADP
ma-105	347	2	the	the	DET
ma-105	347	3	lagrange	lagrange	PROPN
ma-105	347	4	’s	’s	PART
ma-105	347	5	method	method	NOUN
ma-105	347	6	,	,	PUNCT
ma-105	347	7	we	we	PRON
ma-105	347	8	have	have	VERB
ma-105	347	9	c(t	c(t	NUM
ma-105	347	10	)	)	PUNCT
ma-105	347	11	=	=	PUNCT
ma-105	347	12	(	(	PUNCT
ma-105	347	13	1−ε)khm	1−ε)khm	NUM
ma-105	347	14	µ	µ	X
ma-105	347	15	(	(	PUNCT
ma-105	347	16	eµt	eµt	ADV
ma-105	347	17	−	−	PROPN
ma-105	347	18	1	1	NUM
ma-105	347	19	)	)	PUNCT
ma-105	348	1	+	+	CCONJ
ma-105	348	2	c0	c0	PROPN
ma-105	348	3	,	,	PUNCT
ma-105	348	4	c0	c0	PROPN
ma-105	348	5	∈	∈	PROPN
ma-105	348	6	r.thus	r.thu	NOUN
ma-105	348	7	,	,	PUNCT
ma-105	348	8	v	v	X
ma-105	348	9	(	(	PUNCT
ma-105	348	10	t	t	NOUN
ma-105	348	11	)	)	PUNCT
ma-105	349	1	=	=	PUNCT
ma-105	350	1	[	[	X
ma-105	350	2	(	(	PUNCT
ma-105	350	3	1−	1−	NUM
ma-105	350	4	ε)khm	ε)khm	PROPN
ma-105	350	5	µ	µ	X
ma-105	350	6	(	(	PUNCT
ma-105	350	7	eµt	eµt	ADV
ma-105	350	8	−	−	PROPN
ma-105	350	9	1	1	NUM
ma-105	350	10	)	)	PUNCT
ma-105	350	11	+	+	CCONJ
ma-105	350	12	c0	c0	PROPN
ma-105	350	13	]	]	PUNCT
ma-105	350	14	e−µt	e−µt	PROPN
ma-105	350	15	.	.	PUNCT
ma-105	351	1	initial	initial	ADJ
ma-105	351	2	condition	condition	NOUN
ma-105	351	3	yields	yield	VERB
ma-105	351	4	max	max	PROPN
ma-105	351	5	x∈ω̄	x∈ω̄	PROPN
ma-105	351	6	v0(x	v0(x	PROPN
ma-105	351	7	)	)	PUNCT
ma-105	351	8	=	=	NOUN
ma-105	351	9	v	v	NOUN
ma-105	351	10	(	(	PUNCT
ma-105	351	11	0	0	NUM
ma-105	351	12	)	)	PUNCT
ma-105	351	13	=	=	SYM
ma-105	351	14	c0	c0	NOUN
ma-105	351	15	.	.	PUNCT
ma-105	352	1	it	it	PRON
ma-105	352	2	follows	follow	VERB
ma-105	352	3	from	from	ADP
ma-105	352	4	that	that	DET
ma-105	352	5	v	v	NOUN
ma-105	352	6	(	(	PUNCT
ma-105	352	7	t	t	NOUN
ma-105	352	8	)	)	PUNCT
ma-105	352	9	=	=	PUNCT
ma-105	352	10	(	(	PUNCT
ma-105	352	11	1−	1−	NUM
ma-105	352	12	ε)khm	ε)khm	PROPN
ma-105	352	13	µ	µ	X
ma-105	352	14	(	(	PUNCT
ma-105	352	15	1−	1−	NUM
ma-105	352	16	e−µt	e−µt	PROPN
ma-105	352	17	)	)	PUNCT
ma-105	353	1	+	+	CCONJ
ma-105	353	2	max	max	PROPN
ma-105	353	3	x∈ω̄	x∈ω̄	PROPN
ma-105	353	4	v0(x)e−µt	v0(x)e−µt	PROPN
ma-105	353	5	.	.	PUNCT
ma-105	354	1	therefore	therefore	ADV
ma-105	354	2	v	v	X
ma-105	354	3	(	(	PUNCT
ma-105	354	4	x	x	NOUN
ma-105	354	5	,	,	PUNCT
ma-105	354	6	t	t	PROPN
ma-105	354	7	)	)	PUNCT
ma-105	354	8	≤	≤	NOUN
ma-105	354	9	v	v	ADP
ma-105	354	10	(	(	PUNCT
ma-105	354	11	t	t	NOUN
ma-105	354	12	)	)	PUNCT
ma-105	354	13	≤	≤	NUM
ma-105	355	1	max	max	PROPN
ma-105	356	1	{	{	PUNCT
ma-105	357	1	(	(	PUNCT
ma-105	357	2	1−	1−	NUM
ma-105	357	3	ε)khm	ε)khm	PROPN
ma-105	357	4	µ	µ	X
ma-105	357	5	,	,	PUNCT
ma-105	357	6	max	max	PROPN
ma-105	357	7	x∈ω̄	x∈ω̄	PROPN
ma-105	357	8	v0(x	v0(x	PROPN
ma-105	357	9	)	)	PUNCT
ma-105	357	10	}	}	PUNCT
ma-105	357	11	(	(	PUNCT
ma-105	357	12	1−	1−	NUM
ma-105	357	13	e−µt	e−µt	PROPN
ma-105	357	14	)	)	PUNCT
ma-105	358	1	+	+	CCONJ
ma-105	358	2	max	max	PROPN
ma-105	358	3	{	{	PUNCT
ma-105	358	4	(	(	PUNCT
ma-105	358	5	1−	1−	NUM
ma-105	358	6	ε)khm	ε)khm	PROPN
ma-105	358	7	µ	µ	X
ma-105	358	8	,	,	PUNCT
ma-105	358	9	max	max	PROPN
ma-105	358	10	x∈ω̄	x∈ω̄	PROPN
ma-105	358	11	v0(x	v0(x	PROPN
ma-105	358	12	)	)	PUNCT
ma-105	358	13	}	}	PUNCT
ma-105	358	14	e−µt	e−µt	PROPN
ma-105	358	15	≤	≤	NUM
ma-105	358	16	max	max	PROPN
ma-105	358	17	{	{	PUNCT
ma-105	358	18	(	(	PUNCT
ma-105	358	19	1−	1−	NUM
ma-105	358	20	ε)khm	ε)khm	PROPN
ma-105	358	21	µ	µ	X
ma-105	358	22	,	,	PUNCT
ma-105	358	23	max	max	PROPN
ma-105	358	24	x∈ω̄	x∈ω̄	PROPN
ma-105	358	25	v0(x	v0(x	PROPN
ma-105	358	26	)	)	PUNCT
ma-105	358	27	}	}	PUNCT
ma-105	358	28	.	.	PUNCT
ma-105	359	1	since	since	SCONJ
ma-105	359	2	v	v	NUM
ma-105	359	3	(	(	PUNCT
ma-105	359	4	x	x	NOUN
ma-105	359	5	,	,	PUNCT
ma-105	359	6	t	t	PROPN
ma-105	359	7	)	)	PUNCT
ma-105	359	8	≤	≤	NOUN
ma-105	359	9	v	v	ADP
ma-105	359	10	(	(	PUNCT
ma-105	359	11	t	t	NOUN
ma-105	359	12	)	)	PUNCT
ma-105	359	13	≤	≤	NUM
ma-105	359	14	max	max	PROPN
ma-105	359	15	{	{	PUNCT
ma-105	359	16	(	(	PUNCT
ma-105	359	17	1−	1−	NUM
ma-105	359	18	ε)khm	ε)khm	PROPN
ma-105	359	19	µ	µ	X
ma-105	359	20	,	,	PUNCT
ma-105	359	21	max	max	PROPN
ma-105	359	22	x∈ω	x∈ω	PROPN
ma-105	359	23	v0(x	v0(x	PROPN
ma-105	359	24	)	)	PUNCT
ma-105	359	25	}	}	PUNCT
ma-105	359	26	,	,	PUNCT
ma-105	359	27	∀(x	∀(x	X
ma-105	359	28	,	,	PUNCT
ma-105	359	29	t	t	PROPN
ma-105	359	30	)	)	PUNCT
ma-105	359	31	∈	∈	NOUN
ma-105	359	32	ω×	ω×	PUNCT
ma-105	360	1	[	[	X
ma-105	360	2	0	0	NUM
ma-105	360	3	,	,	PUNCT
ma-105	360	4	tmax	tmax	NUM
ma-105	360	5	)	)	PUNCT
ma-105	360	6	;	;	PUNCT
ma-105	360	7	where	where	SCONJ
ma-105	360	8	tmax	tmax	ADV
ma-105	360	9	is	be	AUX
ma-105	360	10	the	the	DET
ma-105	360	11	maximal	maximal	ADJ
ma-105	360	12	time	time	NOUN
ma-105	360	13	of	of	ADP
ma-105	360	14	existence	existence	NOUN
ma-105	360	15	of	of	ADP
ma-105	360	16	the	the	DET
ma-105	360	17	solution	solution	NOUN
ma-105	360	18	of	of	ADP
ma-105	360	19	system	system	NOUN
ma-105	360	20	(	(	PUNCT
ma-105	360	21	2.4	2.4	NUM
ma-105	360	22	)	)	PUNCT
ma-105	360	23	,	,	PUNCT
ma-105	360	24	this	this	PRON
ma-105	360	25	implies	imply	VERB
ma-105	360	26	that	that	SCONJ
ma-105	360	27	v	v	ADP
ma-105	360	28	isbounded.thus	isbounded.thus	PRON
ma-105	360	29	h(x	h(x	PROPN
ma-105	360	30	,	,	PUNCT
ma-105	360	31	t	t	PROPN
ma-105	360	32	)	)	PUNCT
ma-105	360	33	,	,	PUNCT
ma-105	360	34	i(x	i(x	PROPN
ma-105	360	35	,	,	PUNCT
ma-105	360	36	t	t	PROPN
ma-105	360	37	)	)	PUNCT
ma-105	360	38	and	and	CCONJ
ma-105	360	39	v	v	NOUN
ma-105	360	40	(	(	PUNCT
ma-105	360	41	x	x	NOUN
ma-105	360	42	,	,	PUNCT
ma-105	360	43	t	t	PROPN
ma-105	360	44	)	)	PUNCT
ma-105	360	45	are	be	AUX
ma-105	360	46	bounded	bound	VERB
ma-105	360	47	on	on	ADP
ma-105	360	48	ω	ω	NUM
ma-105	360	49	×	×	NOUN
ma-105	361	1	[	[	X
ma-105	361	2	0	0	NUM
ma-105	361	3	,	,	PUNCT
ma-105	361	4	tmax	tmax	NUM
ma-105	361	5	)	)	PUNCT
ma-105	361	6	.	.	PUNCT
ma-105	362	1	therefore	therefore	ADV
ma-105	362	2	,	,	PUNCT
ma-105	362	3	it	it	PRON
ma-105	362	4	follows	follow	VERB
ma-105	362	5	from	from	ADP
ma-105	362	6	thestandard	thestandard	NOUN
ma-105	362	7	theory	theory	NOUN
ma-105	362	8	of	of	ADP
ma-105	362	9	semi	semi	ADJ
ma-105	362	10	-	-	ADJ
ma-105	362	11	linear	linear	ADJ
ma-105	362	12	parabolic	parabolic	NOUN
ma-105	362	13	system	system	NOUN
ma-105	362	14	in	in	ADP
ma-105	362	15	[	[	X
ma-105	362	16	23	23	NUM
ma-105	362	17	]	]	PUNCT
ma-105	362	18	that	that	PRON
ma-105	362	19	tmax	tmax	NOUN
ma-105	363	1	=	=	X
ma-105	364	1	+	+	NUM
ma-105	364	2	∞.	∞.	PROPN
ma-105	364	3	this	this	PRON
ma-105	364	4	completes	complete	VERB
ma-105	364	5	the	the	DET
ma-105	364	6	proofof	proofof	ADJ
ma-105	364	7	proposition	proposition	NOUN
ma-105	364	8	3.9	3.9	NUM
ma-105	364	9	.	.	PUNCT
ma-105	364	10	�	�	PROPN
ma-105	364	11	3.3	3.3	NUM
ma-105	364	12	.	.	PUNCT
ma-105	365	1	global	global	ADJ
ma-105	365	2	existence	existence	NOUN
ma-105	365	3	,	,	PUNCT
ma-105	365	4	uniqueness	uniqueness	NOUN
ma-105	365	5	and	and	CCONJ
ma-105	365	6	positivity	positivity	NOUN
ma-105	365	7	for	for	ADP
ma-105	365	8	the	the	DET
ma-105	365	9	ibvp	ibvp	NOUN
ma-105	365	10	(	(	PUNCT
ma-105	365	11	2.4	2.4	NUM
ma-105	365	12	)	)	PUNCT
ma-105	365	13	.	.	PUNCT
ma-105	366	1	we	we	PRON
ma-105	366	2	recast	recast	VERB
ma-105	366	3	the	the	DET
ma-105	366	4	ibvp	ibvp	NOUN
ma-105	366	5	(	(	PUNCT
ma-105	366	6	2.4	2.4	NUM
ma-105	366	7	)	)	PUNCT
ma-105	366	8	asfollows	asfollow	VERB
ma-105	366	9	:	:	PUNCT
ma-105	366	10			PROPN
ma-105	366	11	∂w	∂w	PROPN
ma-105	367	1	∂t	∂t	PROPN
ma-105	367	2	−d∆w	−d∆w	X
ma-105	368	1	+	+	CCONJ
ma-105	368	2	q(w)w	q(w)w	PROPN
ma-105	368	3	=	=	SYM
ma-105	368	4	f	f	PROPN
ma-105	368	5	(	(	PUNCT
ma-105	368	6	w	w	NOUN
ma-105	368	7	)	)	PUNCT
ma-105	368	8	in	in	ADP
ma-105	368	9	ω×	ω×	PROPN
ma-105	368	10	[	[	X
ma-105	368	11	0	0	NUM
ma-105	368	12	,	,	PUNCT
ma-105	368	13	t	t	NOUN
ma-105	368	14	)	)	PUNCT
ma-105	368	15	,	,	PUNCT
ma-105	368	16	∂w1	∂w1	PROPN
ma-105	368	17	∂η	∂η	PROPN
ma-105	368	18	=	=	SYM
ma-105	368	19	0	0	PROPN
ma-105	368	20	,	,	PUNCT
ma-105	368	21	∂w2	∂w2	PROPN
ma-105	368	22	∂η	∂η	PROPN
ma-105	368	23	=	=	NOUN
ma-105	368	24	0	0	PROPN
ma-105	368	25	,	,	PUNCT
ma-105	368	26	∂w3	∂w3	PROPN
ma-105	368	27	∂η	∂η	PROPN
ma-105	368	28	=	=	NOUN
ma-105	368	29	0	0	NUM
ma-105	368	30	on	on	ADP
ma-105	368	31	∂ω×	∂ω×	PROPN
ma-105	369	1	[	[	X
ma-105	369	2	0	0	NUM
ma-105	369	3	,	,	PUNCT
ma-105	369	4	t	t	NOUN
ma-105	369	5	)	)	PUNCT
ma-105	369	6	,	,	PUNCT
ma-105	369	7	(	(	PUNCT
ma-105	369	8	3.21	3.21	NUM
ma-105	369	9	)	)	PUNCT
ma-105	369	10	w(x	w(x	NOUN
ma-105	369	11	,	,	PUNCT
ma-105	369	12	0	0	NUM
ma-105	369	13	)	)	PUNCT
ma-105	369	14	=	=	SYM
ma-105	369	15	w0(x	w0(x	NOUN
ma-105	369	16	)	)	PUNCT
ma-105	369	17	in	in	ADP
ma-105	369	18	ω	ω	PROPN
ma-105	369	19	,	,	PUNCT
ma-105	369	20	https://doi.org/10.28924/ada/ma.3.1	https://doi.org/10.28924/ada/ma.3.1	PROPN
ma-105	369	21	eur	eur	PROPN
ma-105	369	22	.	.	PUNCT
ma-105	370	1	j.	j.	PROPN
ma-105	370	2	math	math	PROPN
ma-105	370	3	.	.	PUNCT
ma-105	371	1	anal	anal	PROPN
ma-105	371	2	.	.	PUNCT
ma-105	372	1	10.28924	10.28924	NUM
ma-105	372	2	/	/	SYM
ma-105	372	3	ada	ada	PROPN
ma-105	372	4	/	/	SYM
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ma-105	373	3	=	=	PUNCT
ma-105	373	4	(	(	PUNCT
ma-105	373	5	w1	w1	NOUN
ma-105	373	6	,	,	PUNCT
ma-105	373	7	w2	w2	NOUN
ma-105	373	8	,	,	PUNCT
ma-105	373	9	w3)t	w3)t	NOUN
ma-105	373	10	=	=	SYM
ma-105	373	11	(	(	PUNCT
ma-105	373	12	h	h	NOUN
ma-105	373	13	,	,	PUNCT
ma-105	373	14	i	i	PRON
ma-105	373	15	,	,	PUNCT
ma-105	373	16	v	v	NOUN
ma-105	373	17	)	)	PUNCT
ma-105	373	18	t	t	NOUN
ma-105	373	19	,	,	PUNCT
ma-105	373	20	d	d	X
ma-105	373	21	=	=	PUNCT
ma-105	373	22	diag(d1	diag(d1	NOUN
ma-105	373	23	,	,	PUNCT
ma-105	373	24	d2	d2	PROPN
ma-105	373	25	,	,	PUNCT
ma-105	373	26	d3	d3	PROPN
ma-105	373	27	)	)	PUNCT
ma-105	373	28	,	,	PUNCT
ma-105	373	29	q(w	q(w	NOUN
ma-105	373	30	)	)	PUNCT
ma-105	374	1	=	=	SYM
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ma-105	374	3	(	(	PUNCT
ma-105	374	4	q1(w	q1(w	NOUN
ma-105	374	5	)	)	PUNCT
ma-105	374	6	,	,	PUNCT
ma-105	374	7	q2(w	q2(w	PROPN
ma-105	374	8	)	)	PUNCT
ma-105	374	9	,	,	PUNCT
ma-105	374	10	q3(w	q3(w	NOUN
ma-105	374	11	)	)	PUNCT
ma-105	374	12	)	)	PUNCT
ma-105	374	13	,	,	PUNCT
ma-105	374	14	f	f	PROPN
ma-105	374	15	(	(	PUNCT
ma-105	374	16	w	w	NOUN
ma-105	374	17	)	)	PUNCT
ma-105	374	18	=	=	SYM
ma-105	374	19	(	(	PUNCT
ma-105	374	20	f1(w	f1(w	NOUN
ma-105	374	21	)	)	PUNCT
ma-105	374	22	,	,	PUNCT
ma-105	374	23	f2(w	f2(w	NUM
ma-105	374	24	)	)	PUNCT
ma-105	374	25	,	,	PUNCT
ma-105	374	26	f3(w	f3(w	PROPN
ma-105	374	27	)	)	PUNCT
ma-105	374	28	)	)	PUNCT
ma-105	374	29	t	t	NOUN
ma-105	374	30	,	,	PUNCT
ma-105	374	31	with	with	ADP
ma-105	374	32	q1(w	q1(w	NOUN
ma-105	374	33	)	)	PUNCT
ma-105	374	34	=	=	SYM
ma-105	375	1	d	d	PROPN
ma-105	375	2	+	+	CCONJ
ma-105	375	3	(	(	PUNCT
ma-105	375	4	1−	1−	NUM
ma-105	375	5	η)βw3	η)βw3	VERB
ma-105	375	6	α0	α0	ADJ
ma-105	375	7	+	+	CCONJ
ma-105	375	8	α1w1	α1w1	NUM
ma-105	375	9	+	+	CCONJ
ma-105	375	10	α2w3	α2w3	NOUN
ma-105	375	11	+	+	NOUN
ma-105	375	12	α3w1w3	α3w1w3	PROPN
ma-105	375	13	,	,	PUNCT
ma-105	375	14	q2(w	q2(w	PROPN
ma-105	375	15	)	)	PUNCT
ma-105	375	16	=	=	SYM
ma-105	375	17	(	(	PUNCT
ma-105	375	18	α+	α+	NOUN
ma-105	375	19	ρ	ρ	NOUN
ma-105	375	20	)	)	PUNCT
ma-105	375	21	,	,	PUNCT
ma-105	375	22	q3(w	q3(w	ADP
ma-105	375	23	)	)	PUNCT
ma-105	375	24	=	=	NOUN
ma-105	375	25	µ+	µ+	PUNCT
ma-105	375	26	u(1−	u(1−	ADJ
ma-105	375	27	η)βw1	η)βw1	NOUN
ma-105	375	28	α0	α0	ADJ
ma-105	375	29	+	+	CCONJ
ma-105	375	30	α1w1	α1w1	NUM
ma-105	375	31	+	+	CCONJ
ma-105	375	32	α2w3	α2w3	NOUN
ma-105	375	33	+	+	CCONJ
ma-105	375	34	α3w1w3	α3w1w3	PROPN
ma-105	375	35	,	,	PUNCT
ma-105	375	36	f1(w	f1(w	NOUN
ma-105	375	37	)	)	PUNCT
ma-105	375	38	=	=	NOUN
ma-105	375	39	λ+	λ+	PUNCT
ma-105	375	40	ρw2	ρw2	NOUN
ma-105	375	41	,	,	PUNCT
ma-105	375	42	f2(w	f2(w	NUM
ma-105	375	43	)	)	PUNCT
ma-105	375	44	=	=	NOUN
ma-105	375	45	(	(	PUNCT
ma-105	375	46	1−	1−	NUM
ma-105	375	47	η)βw1w3	η)βw1w3	NOUN
ma-105	375	48	α0	α0	ADJ
ma-105	375	49	+	+	CCONJ
ma-105	375	50	α1w1	α1w1	NUM
ma-105	375	51	+	+	CCONJ
ma-105	375	52	α2w3	α2w3	NOUN
ma-105	375	53	+	+	CCONJ
ma-105	375	54	α3w1w3	α3w1w3	PROPN
ma-105	375	55	,	,	PUNCT
ma-105	375	56	f3(w	f3(w	PROPN
ma-105	375	57	)	)	PUNCT
ma-105	375	58	=	=	PUNCT
ma-105	375	59	(	(	PUNCT
ma-105	375	60	1−	1−	NUM
ma-105	375	61	ε)kw2	ε)kw2	NOUN
ma-105	375	62	.	.	PUNCT
ma-105	376	1	note	note	VERB
ma-105	376	2	that	that	SCONJ
ma-105	376	3	d1	d1	PROPN
ma-105	376	4	,	,	PUNCT
ma-105	376	5	d2	d2	PROPN
ma-105	376	6	,	,	PUNCT
ma-105	376	7	d3	d3	PROPN
ma-105	376	8	>	>	X
ma-105	376	9	0	0	X
ma-105	376	10	.	.	PUNCT
ma-105	377	1	denote	denote	VERB
ma-105	377	2	h	h	NOUN
ma-105	377	3	=	=	SYM
ma-105	377	4	l2(ω	l2(ω	NOUN
ma-105	377	5	)	)	PUNCT
ma-105	377	6	and	and	CCONJ
ma-105	377	7	e	e	X
ma-105	377	8	=	=	PUNCT
ma-105	377	9	h1(ω	h1(ω	PROPN
ma-105	377	10	)	)	PUNCT
ma-105	377	11	and	and	CCONJ
ma-105	377	12	define	define	VERB
ma-105	377	13	as	as	ADP
ma-105	377	14	in	in	ADP
ma-105	377	15	[	[	X
ma-105	377	16	12	12	NUM
ma-105	377	17	]	]	PUNCT
ma-105	377	18	the	the	DET
ma-105	377	19	hilbertspace	hilbertspace	NOUN
ma-105	377	20	w	w	PROPN
ma-105	377	21	(	(	PUNCT
ma-105	377	22	0	0	NUM
ma-105	377	23	,	,	PUNCT
ma-105	377	24	t	t	PROPN
ma-105	377	25	,	,	PUNCT
ma-105	377	26	e	e	NOUN
ma-105	377	27	,	,	PUNCT
ma-105	377	28	e′	e′	ADJ
ma-105	377	29	)	)	PUNCT
ma-105	378	1	=	=	PRON
ma-105	378	2	{	{	PUNCT
ma-105	378	3	u	u	NOUN
ma-105	378	4	∈	∈	NOUN
ma-105	378	5	l2	l2	NOUN
ma-105	378	6	(	(	PUNCT
ma-105	378	7	(	(	PUNCT
ma-105	378	8	0	0	NUM
ma-105	378	9	,	,	PUNCT
ma-105	378	10	t	t	NOUN
ma-105	378	11	)	)	PUNCT
ma-105	378	12	,	,	PUNCT
ma-105	378	13	e	e	X
ma-105	378	14	)	)	PUNCT
ma-105	378	15	:	:	PUNCT
ma-105	378	16	∂u	∂u	PROPN
ma-105	378	17	∂t	∂t	PROPN
ma-105	378	18	∈	∈	PROPN
ma-105	378	19	l2	l2	NOUN
ma-105	378	20	(	(	PUNCT
ma-105	378	21	(	(	PUNCT
ma-105	378	22	0	0	NUM
ma-105	378	23	,	,	PUNCT
ma-105	378	24	t	t	PROPN
ma-105	378	25	)	)	PUNCT
ma-105	378	26	,	,	PUNCT
ma-105	378	27	e′	e′	NOUN
ma-105	378	28	)	)	PUNCT
ma-105	378	29	}	}	PUNCT
ma-105	378	30	,	,	PUNCT
ma-105	378	31	endowed	endow	VERB
ma-105	378	32	with	with	ADP
ma-105	378	33	the	the	DET
ma-105	378	34	norm	norm	NOUN
ma-105	378	35	‖u‖2	‖u‖2	PROPN
ma-105	378	36	w	w	PROPN
ma-105	378	37	=	=	PROPN
ma-105	378	38	‖u‖2	‖u‖2	PROPN
ma-105	378	39	l2((0,t	l2((0,t	PROPN
ma-105	378	40	)	)	PUNCT
ma-105	378	41	,	,	PUNCT
ma-105	378	42	e	e	X
ma-105	378	43	)	)	PUNCT
ma-105	378	44	+	+	NUM
ma-105	378	45	∥∥∥∂u	∥∥∥∂u	ADJ
ma-105	378	46	∂t	∂t	PROPN
ma-105	378	47	∥∥∥2	∥∥∥2	NOUN
ma-105	378	48	l2((0,t	l2((0,t	PROPN
ma-105	378	49	)	)	PUNCT
ma-105	378	50	,	,	PUNCT
ma-105	378	51	e′)and	e′)and	PRON
ma-105	378	52	the	the	DET
ma-105	378	53	following	follow	VERB
ma-105	378	54	hypothesis	hypothesis	NOUN
ma-105	378	55	for	for	ADP
ma-105	378	56	initial	initial	ADJ
ma-105	378	57	conditions	condition	NOUN
ma-105	378	58	:	:	PUNCT
ma-105	378	59	w01	w01	PROPN
ma-105	378	60	∈	∈	PROPN
ma-105	378	61	l∞(ω	l∞(ω	NOUN
ma-105	378	62	)	)	PUNCT
ma-105	378	63	,	,	PUNCT
ma-105	378	64	w02	w02	NOUN
ma-105	378	65	,	,	PUNCT
ma-105	378	66	w03	w03	NOUN
ma-105	378	67	∈	∈	PROPN
ma-105	378	68	h	h	NOUN
ma-105	378	69	and	and	CCONJ
ma-105	378	70	w0i	w0i	PROPN
ma-105	378	71	≥	≥	NUM
ma-105	378	72	0	0	NUM
ma-105	378	73	for	for	ADP
ma-105	378	74	i	i	PRON
ma-105	378	75	∈	∈	PROPN
ma-105	378	76	{	{	PUNCT
ma-105	378	77	1	1	NUM
ma-105	378	78	,	,	PUNCT
ma-105	378	79	2	2	NUM
ma-105	378	80	,	,	PUNCT
ma-105	378	81	3	3	NUM
ma-105	378	82	}	}	PUNCT
ma-105	378	83	.	.	PUNCT
ma-105	379	1	(	(	PUNCT
ma-105	379	2	3.22	3.22	NUM
ma-105	379	3	)	)	PUNCT
ma-105	379	4	here	here	ADV
ma-105	379	5	,	,	PUNCT
ma-105	379	6	we	we	PRON
ma-105	379	7	apply	apply	VERB
ma-105	379	8	theorem	theorem	ADJ
ma-105	379	9	2.7	2.7	NUM
ma-105	379	10	of	of	ADP
ma-105	379	11	[	[	X
ma-105	379	12	12	12	NUM
ma-105	379	13	]	]	PUNCT
ma-105	379	14	.	.	PUNCT
ma-105	380	1	so	so	ADV
ma-105	380	2	,	,	PUNCT
ma-105	380	3	one	one	NUM
ma-105	380	4	approaches	approach	VERB
ma-105	380	5	the	the	DET
ma-105	380	6	solution	solution	NOUN
ma-105	380	7	by	by	ADP
ma-105	380	8	a	a	DET
ma-105	380	9	sequence	sequence	NOUN
ma-105	380	10	of	of	ADP
ma-105	380	11	solutions	solution	NOUN
ma-105	380	12	oflinear	oflinear	NOUN
ma-105	380	13	equations	equation	NOUN
ma-105	380	14	.	.	PUNCT
ma-105	381	1	for	for	ADP
ma-105	381	2	n	n	NOUN
ma-105	381	3	=	=	SYM
ma-105	381	4	0	0	NUM
ma-105	381	5	,	,	PUNCT
ma-105	381	6	w0	w0	PROPN
ma-105	381	7	denotes	denote	VERB
ma-105	381	8	the	the	DET
ma-105	381	9	solution	solution	NOUN
ma-105	381	10	of	of	PROPN
ma-105	381	11	∂w0	∂w0	VERB
ma-105	381	12	∂t	∂t	PROPN
ma-105	381	13	−d∆w0	−d∆w0	PROPN
ma-105	381	14	=	=	SYM
ma-105	381	15	0	0	NUM
ma-105	381	16	in	in	ADP
ma-105	381	17	ω×	ω×	PROPN
ma-105	381	18	(	(	PUNCT
ma-105	381	19	0	0	NUM
ma-105	381	20	,	,	PUNCT
ma-105	381	21	t	t	NOUN
ma-105	381	22	)	)	PUNCT
ma-105	381	23	,	,	PUNCT
ma-105	381	24	w0(0	w0(0	PROPN
ma-105	381	25	)	)	PUNCT
ma-105	381	26	=	=	PROPN
ma-105	381	27	w0	w0	PROPN
ma-105	381	28	in	in	ADP
ma-105	381	29	ω	ω	PROPN
ma-105	381	30	,	,	PUNCT
ma-105	381	31	∂w0	∂w0	NOUN
ma-105	381	32	i	i	PRON
ma-105	381	33	∂η	∂η	PROPN
ma-105	381	34	=	=	NOUN
ma-105	381	35	0	0	X
ma-105	381	36	.	.	PUNCT
ma-105	382	1	on	on	ADP
ma-105	382	2	∂ω	∂ω	PROPN
ma-105	382	3	(	(	PUNCT
ma-105	382	4	3.23	3.23	NUM
ma-105	382	5	)	)	PUNCT
ma-105	382	6	this	this	DET
ma-105	382	7	equation	equation	NOUN
ma-105	382	8	admits	admit	VERB
ma-105	382	9	a	a	DET
ma-105	382	10	strong	strong	ADJ
ma-105	382	11	solution	solution	NOUN
ma-105	382	12	and	and	CCONJ
ma-105	382	13	w0	w0	PROPN
ma-105	382	14	≥	≥	NOUN
ma-105	382	15	0.by	0.by	NUM
ma-105	382	16	induction	induction	NOUN
ma-105	382	17	,	,	PUNCT
ma-105	382	18	wn	wn	PROPN
ma-105	382	19	=	=	PRON
ma-105	382	20	(	(	PUNCT
ma-105	382	21	(	(	PUNCT
ma-105	382	22	wn1	wn1	X
ma-105	382	23	,	,	PUNCT
ma-105	382	24	w	w	NOUN
ma-105	382	25	n	n	PRON
ma-105	382	26	1	1	NUM
ma-105	382	27	,	,	PUNCT
ma-105	382	28	w	w	NOUN
ma-105	382	29	n	n	ADJ
ma-105	382	30	1	1	NUM
ma-105	382	31	)	)	PUNCT
ma-105	382	32	)	)	PUNCT
ma-105	383	1	denotes	denote	VERB
ma-105	383	2	the	the	DET
ma-105	383	3	solution	solution	NOUN
ma-105	383	4	of	of	PROPN
ma-105	383	5	∂wn	∂wn	PROPN
ma-105	383	6	∂t	∂t	PROPN
ma-105	384	1	−d∆wn	−d∆wn	PROPN
ma-105	385	1	+	+	NUM
ma-105	385	2	q(wn−1)wn	q(wn−1)wn	NOUN
ma-105	385	3	=	=	SYM
ma-105	385	4	f	f	X
ma-105	385	5	(	(	PUNCT
ma-105	385	6	wn−1	wn−1	PROPN
ma-105	385	7	)	)	PUNCT
ma-105	385	8	in	in	ADP
ma-105	385	9	ω×	ω×	PROPN
ma-105	385	10	(	(	PUNCT
ma-105	385	11	0	0	NUM
ma-105	385	12	,	,	PUNCT
ma-105	385	13	t	t	NOUN
ma-105	385	14	)	)	PUNCT
ma-105	385	15	,	,	PUNCT
ma-105	385	16	wn(0	wn(0	PROPN
ma-105	385	17	)	)	PUNCT
ma-105	385	18	=	=	NOUN
ma-105	385	19	w0	w0	PROPN
ma-105	385	20	in	in	ADP
ma-105	385	21	ω	ω	PROPN
ma-105	385	22	,	,	PUNCT
ma-105	385	23	∂wn	∂wn	PROPN
ma-105	385	24	∂η	∂η	PROPN
ma-105	385	25	=	=	NOUN
ma-105	385	26	0	0	PROPN
ma-105	385	27	.	.	PUNCT
ma-105	386	1	on	on	ADP
ma-105	386	2	∂ω	∂ω	PROPN
ma-105	386	3	.	.	PUNCT
ma-105	387	1	(	(	PUNCT
ma-105	387	2	3.24	3.24	NUM
ma-105	387	3	)	)	PUNCT
ma-105	387	4	since	since	SCONJ
ma-105	387	5	(	(	PUNCT
ma-105	387	6	3.24	3.24	NUM
ma-105	387	7	)	)	PUNCT
ma-105	387	8	is	be	AUX
ma-105	387	9	a	a	DET
ma-105	387	10	linear	linear	ADJ
ma-105	387	11	equation	equation	NOUN
ma-105	387	12	,	,	PUNCT
ma-105	387	13	qi(wn−1	qi(wn−1	PROPN
ma-105	387	14	)	)	PUNCT
ma-105	387	15	and	and	CCONJ
ma-105	387	16	fi(wn−1	fi(wn−1	NOUN
ma-105	387	17	)	)	PUNCT
ma-105	387	18	can	can	AUX
ma-105	387	19	replace	replace	VERB
ma-105	387	20	a0	a0	NOUN
ma-105	387	21	and	and	CCONJ
ma-105	387	22	f	f	PROPN
ma-105	387	23	(	(	PUNCT
ma-105	387	24	t	t	PROPN
ma-105	387	25	)	)	PUNCT
ma-105	387	26	of	of	ADP
ma-105	387	27	corollary	corollary	ADJ
ma-105	387	28	2.10	2.10	NUM
ma-105	387	29	in	in	ADP
ma-105	387	30	[	[	X
ma-105	387	31	12	12	NUM
ma-105	387	32	]	]	PUNCT
ma-105	387	33	.	.	PUNCT
ma-105	388	1	suppose	suppose	VERB
ma-105	388	2	that	that	SCONJ
ma-105	388	3	there	there	PRON
ma-105	388	4	exists	exist	VERB
ma-105	388	5	a	a	DET
ma-105	388	6	unique	unique	ADJ
ma-105	388	7	nonnegative	nonnegative	ADJ
ma-105	388	8	solution	solution	NOUN
ma-105	388	9	wn−1	wn−1	PROPN
ma-105	388	10	i	i	PRON
ma-105	388	11	.	.	PUNCT
ma-105	389	1	assuming	assume	VERB
ma-105	389	2	by	by	ADP
ma-105	389	3	induction	induction	NOUN
ma-105	389	4	that	that	PRON
ma-105	389	5	w	w	PROPN
ma-105	389	6	ji	ji	PROPN
ma-105	389	7	≥	≥	NOUN
ma-105	389	8	0	0	NUM
ma-105	389	9	for	for	ADP
ma-105	389	10	0	0	NUM
ma-105	389	11	≤	≤	NUM
ma-105	389	12	j	j	PROPN
ma-105	389	13	≤	≤	PROPN
ma-105	389	14	n	n	CCONJ
ma-105	389	15	−	−	PROPN
ma-105	389	16	1	1	NUM
ma-105	389	17	and	and	CCONJ
ma-105	389	18	that	that	SCONJ
ma-105	389	19	by	by	ADP
ma-105	389	20	proposition	proposition	NOUN
ma-105	389	21	3.9	3.9	NUM
ma-105	389	22	w	w	NOUN
ma-105	389	23	ji	ji	PROPN
ma-105	389	24	is	be	AUX
ma-105	389	25	bounded	bound	VERB
ma-105	389	26	for	for	ADP
ma-105	389	27	0	0	NUM
ma-105	389	28	≤	≤	NUM
ma-105	389	29	j	j	PROPN
ma-105	389	30	≤	≤	PROPN
ma-105	389	31	n	n	CCONJ
ma-105	389	32	−	−	PROPN
ma-105	389	33	1	1	NUM
ma-105	389	34	,	,	PUNCT
ma-105	389	35	one	one	PRON
ma-105	389	36	has	have	VERB
ma-105	389	37	0	0	NUM
ma-105	389	38	≤	≤	NUM
ma-105	389	39	u(1−	u(1−	PROPN
ma-105	389	40	η)βwn−1	η)βwn−1	PROPN
ma-105	389	41	1	1	NUM
ma-105	389	42	α0	α0	ADJ
ma-105	389	43	+	+	CCONJ
ma-105	389	44	α1w	α1w	PROPN
ma-105	389	45	n−1	n−1	PROPN
ma-105	389	46	1	1	NUM
ma-105	389	47	+	+	CCONJ
ma-105	389	48	α2w	α2w	PUNCT
ma-105	389	49	n−1	n−1	PROPN
ma-105	389	50	3	3	NUM
ma-105	389	51	+	+	CCONJ
ma-105	389	52	α3w	α3w	VERB
ma-105	389	53	n−1	n−1	PROPN
ma-105	389	54	1	1	NUM
ma-105	389	55	wn−1	wn−1	PROPN
ma-105	389	56	3	3	NUM
ma-105	389	57	≤	≤	NOUN
ma-105	389	58	u(1−	u(1−	NOUN
ma-105	389	59	η)β	η)β	PUNCT
ma-105	389	60	(	(	PUNCT
ma-105	389	61	3.25	3.25	NUM
ma-105	389	62	)	)	PUNCT
ma-105	389	63	https://doi.org/10.28924/ada/ma.3.1	https://doi.org/10.28924/ada/ma.3.1	PROPN
ma-105	389	64	eur	eur	PROPN
ma-105	389	65	.	.	PUNCT
ma-105	390	1	j.	j.	PROPN
ma-105	390	2	math	math	PROPN
ma-105	390	3	.	.	PUNCT
ma-105	391	1	anal	anal	PROPN
ma-105	391	2	.	.	PUNCT
ma-105	392	1	10.28924	10.28924	NUM
ma-105	392	2	/	/	SYM
ma-105	392	3	ada	ada	PROPN
ma-105	392	4	/	/	SYM
ma-105	392	5	ma.3.1	ma.3.1	PROPN
ma-105	392	6	14which	14which	PRON
ma-105	392	7	implies	imply	VERB
ma-105	392	8	that	that	SCONJ
ma-105	392	9	µ	µ	NUM
ma-105	392	10	≤	≤	NUM
ma-105	392	11	q3(wn−1	q3(wn−1	NOUN
ma-105	392	12	)	)	PUNCT
ma-105	392	13	≤	≤	NOUN
ma-105	392	14	µ+	µ+	PUNCT
ma-105	392	15	u(1−	u(1−	NOUN
ma-105	392	16	η)β	η)β	NOUN
ma-105	392	17	.	.	PUNCT
ma-105	393	1	(	(	PUNCT
ma-105	393	2	3.26	3.26	NUM
ma-105	393	3	)	)	PUNCT
ma-105	393	4	since	since	SCONJ
ma-105	393	5	w	w	PROPN
ma-105	393	6	ji	ji	PROPN
ma-105	393	7	are	be	AUX
ma-105	393	8	bounded	bound	VERB
ma-105	393	9	,	,	PUNCT
ma-105	393	10	we	we	PRON
ma-105	393	11	have	have	VERB
ma-105	393	12	d	d	NOUN
ma-105	393	13	≤	≤	X
ma-105	393	14	q1(wn−1	q1(wn−1	NUM
ma-105	393	15	)	)	PUNCT
ma-105	393	16	≤	≤	PUNCT
ma-105	394	1	d	d	NOUN
ma-105	394	2	+	+	CCONJ
ma-105	394	3	(	(	PUNCT
ma-105	394	4	1−	1−	NUM
ma-105	394	5	η)β	η)β	NOUN
ma-105	394	6	.	.	PUNCT
ma-105	395	1	in	in	ADP
ma-105	395	2	addition	addition	NOUN
ma-105	395	3	,	,	PUNCT
ma-105	395	4	q2	q2	NOUN
ma-105	395	5	is	be	AUX
ma-105	395	6	a	a	DET
ma-105	395	7	constant.it	constant.it	NOUN
ma-105	395	8	then	then	ADV
ma-105	395	9	follows	follow	VERB
ma-105	395	10	that	that	PRON
ma-105	395	11	q1(wn−1	q1(wn−1	NUM
ma-105	395	12	)	)	PUNCT
ma-105	395	13	,	,	PUNCT
ma-105	395	14	q2(wn−1	q2(wn−1	X
ma-105	395	15	)	)	PUNCT
ma-105	395	16	,	,	PUNCT
ma-105	395	17	q3(wn−1	q3(wn−1	X
ma-105	395	18	)	)	PUNCT
ma-105	395	19	∈	∈	PROPN
ma-105	395	20	l∞(ω×	l∞(ω×	X
ma-105	395	21	(	(	PUNCT
ma-105	395	22	0	0	NUM
ma-105	395	23	,	,	PUNCT
ma-105	395	24	t	t	NOUN
ma-105	395	25	)	)	PUNCT
ma-105	395	26	)	)	PUNCT
ma-105	395	27	.	.	PUNCT
ma-105	396	1	we	we	PRON
ma-105	396	2	also	also	ADV
ma-105	396	3	have	have	VERB
ma-105	396	4	f	f	X
ma-105	396	5	(	(	PUNCT
ma-105	396	6	wn−1	wn−1	PROPN
ma-105	396	7	)	)	PUNCT
ma-105	396	8	≥	≥	NOUN
ma-105	396	9	0and	0and	PROPN
ma-105	396	10	f	f	PROPN
ma-105	396	11	(	(	PUNCT
ma-105	396	12	wn−1	wn−1	PROPN
ma-105	396	13	)	)	PUNCT
ma-105	396	14	∈	∈	PROPN
ma-105	396	15	l2((0	l2((0	PROPN
ma-105	396	16	,	,	PUNCT
ma-105	396	17	t	t	PROPN
ma-105	396	18	)	)	PUNCT
ma-105	396	19	,	,	PUNCT
ma-105	396	20	e′	e′	NOUN
ma-105	396	21	)	)	PUNCT
ma-105	396	22	.	.	PUNCT
ma-105	397	1	then	then	ADV
ma-105	397	2	,	,	PUNCT
ma-105	397	3	by	by	ADP
ma-105	397	4	corollary	corollary	ADJ
ma-105	397	5	2.10	2.10	NUM
ma-105	397	6	of	of	ADP
ma-105	397	7	[	[	X
ma-105	397	8	12	12	NUM
ma-105	397	9	]	]	PUNCT
ma-105	397	10	,	,	PUNCT
ma-105	397	11	there	there	PRON
ma-105	397	12	exists	exist	VERB
ma-105	397	13	a	a	DET
ma-105	397	14	unique	unique	ADJ
ma-105	397	15	solution	solution	NOUN
ma-105	397	16	wn	wn	PROPN
ma-105	397	17	∈	∈	PROPN
ma-105	397	18	w	w	PROPN
ma-105	397	19	(	(	PUNCT
ma-105	397	20	0	0	NUM
ma-105	397	21	,	,	PUNCT
ma-105	397	22	t	t	PROPN
ma-105	397	23	,	,	PUNCT
ma-105	397	24	e	e	NOUN
ma-105	397	25	,	,	PUNCT
ma-105	397	26	e′	e′	ADJ
ma-105	397	27	)	)	PUNCT
ma-105	397	28	with	with	ADP
ma-105	397	29	wn	wn	PROPN
ma-105	397	30	≥	≥	PROPN
ma-105	397	31	0	0	NUM
ma-105	397	32	.	.	PUNCT
ma-105	398	1	since	since	SCONJ
ma-105	398	2	f1(w	f1(w	VERB
ma-105	398	3	)	)	PUNCT
ma-105	398	4	=	=	SYM
ma-105	398	5	λ	λ	PROPN
ma-105	398	6	+	+	NUM
ma-105	398	7	ρw2	ρw2	PROPN
ma-105	398	8	,	,	PUNCT
ma-105	398	9	f2(w	f2(w	NUM
ma-105	398	10	)	)	PUNCT
ma-105	398	11	=	=	SYM
ma-105	398	12	(	(	PUNCT
ma-105	398	13	1−η)βw1w3	1−η)βw1w3	NUM
ma-105	398	14	α0+α1w1+α2w3+α3w1w3	α0+α1w1+α2w3+α3w1w3	NOUN
ma-105	398	15	≤	≤	NOUN
ma-105	398	16	(	(	PUNCT
ma-105	398	17	1−	1−	NUM
ma-105	398	18	η)βw3	η)βw3	NOUN
ma-105	398	19	and	and	CCONJ
ma-105	398	20	f3(w	f3(w	NUM
ma-105	398	21	)	)	PUNCT
ma-105	398	22	=	=	NOUN
ma-105	398	23	(	(	PUNCT
ma-105	398	24	1−	1−	NUM
ma-105	398	25	ε)kw2	ε)kw2	NOUN
ma-105	398	26	,	,	PUNCT
ma-105	398	27	then	then	ADV
ma-105	398	28	f1(wn−1	f1(wn−1	NUM
ma-105	398	29	)	)	PUNCT
ma-105	398	30	=	=	NOUN
ma-105	398	31	λ+	λ+	PUNCT
ma-105	398	32	ρwn−1	ρwn−1	PROPN
ma-105	398	33	2	2	NUM
ma-105	398	34	,	,	PUNCT
ma-105	398	35	f2(wn−1	f2(wn−1	ADJ
ma-105	398	36	)	)	PUNCT
ma-105	398	37	≤	≤	NOUN
ma-105	398	38	(	(	PUNCT
ma-105	398	39	1−	1−	NUM
ma-105	398	40	η)βwn−1	η)βwn−1	PROPN
ma-105	398	41	3	3	NUM
ma-105	398	42	and	and	CCONJ
ma-105	398	43	f3(wn−1	f3(wn−1	PUNCT
ma-105	398	44	)	)	PUNCT
ma-105	398	45	=	=	NOUN
ma-105	398	46	(	(	PUNCT
ma-105	398	47	1	1	NUM
ma-105	398	48	−	−	NOUN
ma-105	398	49	ε)kwn−1	ε)kwn−1	SYM
ma-105	398	50	2	2	NUM
ma-105	398	51	remain	remain	VERB
ma-105	398	52	bounded	bounded	ADJ
ma-105	398	53	in	in	ADP
ma-105	398	54	l2(]0	l2(]0	PROPN
ma-105	398	55	,	,	PUNCT
ma-105	398	56	t	t	X
ma-105	399	1	[	[	X
ma-105	399	2	,	,	PUNCT
ma-105	399	3	e	e	NOUN
ma-105	399	4	)	)	PUNCT
ma-105	399	5	.	.	PUNCT
ma-105	400	1	we	we	PRON
ma-105	400	2	deduce	deduce	VERB
ma-105	400	3	that	that	DET
ma-105	400	4	wn2	wn2	PROPN
ma-105	400	5	and	and	CCONJ
ma-105	400	6	wn3	wn3	PROPN
ma-105	400	7	remainbounded	remainbounde	VERB
ma-105	400	8	in	in	ADP
ma-105	400	9	c0([0	c0([0	PROPN
ma-105	400	10	,	,	PUNCT
ma-105	400	11	t	t	X
ma-105	400	12	]	]	PUNCT
ma-105	400	13	,	,	PUNCT
ma-105	400	14	h	h	NOUN
ma-105	400	15	)	)	PUNCT
ma-105	400	16	and	and	CCONJ
ma-105	400	17	l2((0	l2((0	PROPN
ma-105	400	18	,	,	PUNCT
ma-105	400	19	t	t	PROPN
ma-105	400	20	)	)	PUNCT
ma-105	400	21	,	,	PUNCT
ma-105	400	22	e).now	e).now	ADV
ma-105	400	23	,	,	PUNCT
ma-105	400	24	we	we	PRON
ma-105	400	25	deduce	deduce	VERB
ma-105	400	26	that	that	SCONJ
ma-105	400	27	the	the	DET
ma-105	400	28	sequence	sequence	NOUN
ma-105	400	29	(	(	PUNCT
ma-105	400	30	wni	wni	PROPN
ma-105	400	31	)	)	PUNCT
ma-105	400	32	n≥0	n≥0	PROPN
ma-105	400	33	(	(	PUNCT
ma-105	400	34	one	one	PRON
ma-105	400	35	can	can	AUX
ma-105	400	36	extract	extract	VERB
ma-105	400	37	a	a	DET
ma-105	400	38	subsequence	subsequence	NOUN
ma-105	400	39	(	(	PUNCT
ma-105	400	40	wmi	wmi	NOUN
ma-105	400	41	)	)	PUNCT
ma-105	400	42	m≥0	m≥0	PROPN
ma-105	400	43	)	)	PUNCT
ma-105	400	44	convergesweakly	convergesweakly	ADV
ma-105	400	45	to	to	ADP
ma-105	400	46	wi	wi	PROPN
ma-105	400	47	in	in	ADP
ma-105	400	48	l2((0	l2((0	PROPN
ma-105	400	49	,	,	PUNCT
ma-105	400	50	t	t	PROPN
ma-105	400	51	)	)	PUNCT
ma-105	400	52	,	,	PUNCT
ma-105	400	53	e	e	NOUN
ma-105	400	54	)	)	PUNCT
ma-105	400	55	and	and	CCONJ
ma-105	400	56	weakly	weakly	ADJ
ma-105	400	57	star	star	NOUN
ma-105	400	58	in	in	ADP
ma-105	400	59	l∞((0	l∞((0	PROPN
ma-105	400	60	,	,	PUNCT
ma-105	400	61	t	t	PROPN
ma-105	400	62	)	)	PUNCT
ma-105	400	63	,	,	PUNCT
ma-105	400	64	h	h	NOUN
ma-105	400	65	)	)	PUNCT
ma-105	400	66	to	to	ADP
ma-105	400	67	wi	wi	PROPN
ma-105	400	68	.	.	PUNCT
ma-105	401	1	applying	apply	VERB
ma-105	401	2	proposition	proposition	NOUN
ma-105	401	3	2.11	2.11	NUM
ma-105	401	4	in	in	ADP
ma-105	401	5	[	[	X
ma-105	401	6	12	12	NUM
ma-105	401	7	]	]	PUNCT
ma-105	401	8	,	,	PUNCT
ma-105	401	9	it	it	PRON
ma-105	401	10	holds	hold	VERB
ma-105	401	11	that	that	SCONJ
ma-105	401	12	for	for	ADP
ma-105	401	13	all	all	DET
ma-105	401	14	n	n	CCONJ
ma-105	401	15	,	,	PUNCT
ma-105	401	16	wni	wni	PROPN
ma-105	401	17	(	(	PUNCT
ma-105	401	18	t	t	PROPN
ma-105	401	19	)	)	PUNCT
ma-105	401	20	=	=	NOUN
ma-105	401	21	gi(t)w0i	gi(t)w0i	VERB
ma-105	402	1	+	+	CCONJ
ma-105	402	2	∫	∫	PROPN
ma-105	402	3	t	t	PROPN
ma-105	402	4	0	0	NUM
ma-105	402	5	gi(t	gi(t	PROPN
ma-105	402	6	−	−	PROPN
ma-105	402	7	s)gni	s)gni	NOUN
ma-105	402	8	(	(	PUNCT
ma-105	402	9	s)ds	s)ds	PROPN
ma-105	402	10	,	,	PUNCT
ma-105	402	11	(	(	PUNCT
ma-105	402	12	3.27	3.27	NUM
ma-105	402	13	)	)	PUNCT
ma-105	403	1	where	where	SCONJ
ma-105	403	2	gi(t	gi(t	NOUN
ma-105	403	3	)	)	PUNCT
ma-105	403	4	is	be	AUX
ma-105	403	5	the	the	DET
ma-105	403	6	semigroup	semigroup	NOUN
ma-105	403	7	generated	generate	VERB
ma-105	403	8	by	by	ADP
ma-105	403	9	the	the	DET
ma-105	403	10	unbounded	unbounded	ADJ
ma-105	403	11	operator	operator	NOUN
ma-105	403	12	ai	ai	PROPN
ma-105	403	13	=	=	NOUN
ma-105	403	14	−diah	−diah	PROPN
ma-105	403	15	,	,	PUNCT
ma-105	403	16	and	and	CCONJ
ma-105	403	17	gni	gni	NOUN
ma-105	403	18	(	(	PUNCT
ma-105	403	19	s	s	NOUN
ma-105	403	20	)	)	PUNCT
ma-105	404	1	=	=	SYM
ma-105	404	2	−qi(wn−1(s))wni	−qi(wn−1(s))wni	NOUN
ma-105	404	3	(	(	PUNCT
ma-105	404	4	s	s	NOUN
ma-105	404	5	)	)	PUNCT
ma-105	404	6	+	+	CCONJ
ma-105	404	7	fi(w	fi(w	PUNCT
ma-105	404	8	n−1(s	n−1(s	NUM
ma-105	404	9	)	)	PUNCT
ma-105	404	10	)	)	PUNCT
ma-105	404	11	.	.	PUNCT
ma-105	405	1	(	(	PUNCT
ma-105	405	2	3.28	3.28	NUM
ma-105	405	3	)	)	PUNCT
ma-105	405	4	then	then	ADV
ma-105	405	5	,	,	PUNCT
ma-105	405	6	gni	gni	PROPN
ma-105	405	7	∈	∈	PROPN
ma-105	405	8	l2((0	l2((0	PROPN
ma-105	405	9	,	,	PUNCT
ma-105	405	10	t	t	PROPN
ma-105	405	11	)	)	PUNCT
ma-105	405	12	,	,	PUNCT
ma-105	405	13	e	e	NOUN
ma-105	405	14	)	)	PUNCT
ma-105	405	15	.	.	PUNCT
ma-105	406	1	since	since	SCONJ
ma-105	406	2	the	the	DET
ma-105	406	3	sequence	sequence	NOUN
ma-105	406	4	(	(	PUNCT
ma-105	406	5	wni	wni	PROPN
ma-105	406	6	)	)	PUNCT
ma-105	406	7	n≥0	n≥0	PROPN
ma-105	406	8	is	be	AUX
ma-105	406	9	bounded	bound	VERB
ma-105	406	10	in	in	ADP
ma-105	406	11	c0([0	c0([0	PROPN
ma-105	406	12	,	,	PUNCT
ma-105	406	13	t	t	X
ma-105	406	14	]	]	PUNCT
ma-105	406	15	,	,	PUNCT
ma-105	406	16	h	h	NOUN
ma-105	406	17	)	)	PUNCT
ma-105	406	18	,	,	PUNCT
ma-105	406	19	the	the	DET
ma-105	406	20	se	se	NOUN
ma-105	406	21	-	-	NOUN
ma-105	406	22	quence	quence	NOUN
ma-105	406	23	(	(	PUNCT
ma-105	406	24	gni	gni	NOUN
ma-105	406	25	)	)	PUNCT
ma-105	406	26	n≥0	n≥0	PROPN
ma-105	406	27	is	be	AUX
ma-105	406	28	bounded	bound	VERB
ma-105	406	29	in	in	ADP
ma-105	406	30	c0([0	c0([0	PROPN
ma-105	406	31	,	,	PUNCT
ma-105	406	32	t	t	X
ma-105	406	33	]	]	PUNCT
ma-105	406	34	,	,	PUNCT
ma-105	406	35	h	h	NOUN
ma-105	406	36	)	)	PUNCT
ma-105	406	37	.	.	PUNCT
ma-105	407	1	now	now	ADV
ma-105	407	2	,	,	PUNCT
ma-105	407	3	consider	consider	VERB
ma-105	407	4	the	the	DET
ma-105	407	5	operator	operator	NOUN
ma-105	407	6	gi	gi	VERB
ma-105	407	7	from	from	ADP
ma-105	407	8	c0((0	c0((0	PROPN
ma-105	407	9	,	,	PUNCT
ma-105	407	10	t	t	PROPN
ma-105	407	11	)	)	PUNCT
ma-105	407	12	,	,	PUNCT
ma-105	407	13	h)into	h)into	PROPN
ma-105	407	14	c0((0	c0((0	PROPN
ma-105	407	15	,	,	PUNCT
ma-105	407	16	t	t	PROPN
ma-105	407	17	)	)	PUNCT
ma-105	407	18	,	,	PUNCT
ma-105	407	19	h	h	NOUN
ma-105	407	20	)	)	PUNCT
ma-105	407	21	defined	define	VERB
ma-105	407	22	by	by	ADP
ma-105	407	23	gi(f	gi(f	NOUN
ma-105	407	24	)	)	PUNCT
ma-105	407	25	=	=	SYM
ma-105	408	1	∫	∫	PROPN
ma-105	408	2	t	t	PROPN
ma-105	408	3	0	0	NUM
ma-105	408	4	gi(t	gi(t	PROPN
ma-105	408	5	−	−	NOUN
ma-105	408	6	s)f	s)f	NOUN
ma-105	408	7	(	(	PUNCT
ma-105	408	8	s)ds	s)ds	PROPN
ma-105	408	9	.	.	PUNCT
ma-105	409	1	(	(	PUNCT
ma-105	409	2	3.29	3.29	NUM
ma-105	409	3	)	)	PUNCT
ma-105	409	4	let	let	VERB
ma-105	409	5	us	we	PRON
ma-105	409	6	prove	prove	VERB
ma-105	409	7	that	that	SCONJ
ma-105	409	8	gi	gi	PROPN
ma-105	409	9	is	be	AUX
ma-105	409	10	a	a	DET
ma-105	409	11	compact	compact	ADJ
ma-105	409	12	operator	operator	NOUN
ma-105	409	13	.	.	PUNCT
ma-105	410	1	considering	consider	VERB
ma-105	410	2	the	the	DET
ma-105	410	3	triple	triple	ADJ
ma-105	410	4	(	(	PUNCT
ma-105	410	5	l2(ω	l2(ω	NOUN
ma-105	410	6	)	)	PUNCT
ma-105	410	7	,	,	PUNCT
ma-105	410	8	h1(ω	h1(ω	PROPN
ma-105	410	9	)	)	PUNCT
ma-105	410	10	,	,	PUNCT
ma-105	410	11	a	a	X
ma-105	410	12	)	)	PUNCT
ma-105	410	13	with	with	ADP
ma-105	410	14	a(w	a(w	PROPN
ma-105	410	15	,	,	PUNCT
ma-105	410	16	v	v	NOUN
ma-105	410	17	)	)	PUNCT
ma-105	410	18	=	=	SYM
ma-105	411	1	3∑	3∑	NUM
ma-105	411	2	j=1	j=1	NOUN
ma-105	411	3	∫	∫	PROPN
ma-105	411	4	ω	ω	PROPN
ma-105	411	5	∂w	∂w	PROPN
ma-105	411	6	∂xj	∂xj	PROPN
ma-105	411	7	∂v	∂v	PROPN
ma-105	411	8	∂xj	∂xj	PROPN
ma-105	411	9	dx	dx	PROPN
ma-105	411	10	,	,	PUNCT
ma-105	411	11	(	(	PUNCT
ma-105	411	12	3.30	3.30	NUM
ma-105	411	13	)	)	PUNCT
ma-105	411	14	where	where	SCONJ
ma-105	411	15	ω	ω	PROPN
ma-105	411	16	is	be	AUX
ma-105	411	17	regular	regular	ADJ
ma-105	411	18	and	and	CCONJ
ma-105	411	19	bounded	bound	VERB
ma-105	411	20	.	.	PUNCT
ma-105	412	1	as	as	ADP
ma-105	412	2	in	in	ADP
ma-105	412	3	[	[	X
ma-105	412	4	12	12	NUM
ma-105	412	5	]	]	PUNCT
ma-105	412	6	,	,	PUNCT
ma-105	412	7	the	the	DET
ma-105	412	8	unbounded	unbounded	ADJ
ma-105	412	9	variational	variational	ADJ
ma-105	412	10	operator	operator	NOUN
ma-105	412	11	ah	ah	INTJ
ma-105	412	12	associated	associate	VERB
ma-105	412	13	to	to	ADP
ma-105	412	14	a	a	PRON
ma-105	412	15	is	be	AUX
ma-105	412	16	a	a	DET
ma-105	412	17	positive	positive	ADJ
ma-105	412	18	symmetric	symmetric	ADJ
ma-105	412	19	operator	operator	NOUN
ma-105	412	20	with	with	ADP
ma-105	412	21	compact	compact	ADJ
ma-105	412	22	resolvent	resolvent	ADJ
ma-105	412	23	rλ(ah	rλ(ah	NOUN
ma-105	412	24	)	)	PUNCT
ma-105	412	25	.	.	PUNCT
ma-105	413	1	it	it	PRON
ma-105	413	2	admits	admit	VERB
ma-105	413	3	a	a	DET
ma-105	413	4	sequence	sequence	NOUN
ma-105	413	5	(	(	PUNCT
ma-105	413	6	λk)k	λk)k	PROPN
ma-105	413	7	ofpositive	ofpositive	ADJ
ma-105	413	8	eigenvalues	eigenvalue	VERB
ma-105	413	9	with	with	ADP
ma-105	413	10	lim	lim	PROPN
ma-105	413	11	k→+∞	k→+∞	PROPN
ma-105	413	12	λk	λk	NOUN
ma-105	414	1	=	=	PUNCT
ma-105	415	1	+	+	NOUN
ma-105	415	2	∞	∞	PROPN
ma-105	415	3	and	and	CCONJ
ma-105	415	4	a	a	DET
ma-105	415	5	hilbert	hilbert	NOUN
ma-105	415	6	basis	basis	NOUN
ma-105	415	7	(	(	PUNCT
ma-105	415	8	ek)k	ek)k	PROPN
ma-105	415	9	ofh	ofh	NUM
ma-105	415	10	consisting	consisting	NOUN
ma-105	415	11	of	of	ADP
ma-105	415	12	eigenvectorsof	eigenvectorsof	NOUN
ma-105	415	13	ah	ah	INTJ
ma-105	415	14	.	.	PUNCT
ma-105	416	1	if	if	SCONJ
ma-105	416	2	(	(	PUNCT
ma-105	416	3	g(t))t>0	g(t))t>0	PROPN
ma-105	416	4	is	be	AUX
ma-105	416	5	the	the	DET
ma-105	416	6	semigroup	semigroup	NOUN
ma-105	416	7	generated	generate	VERB
ma-105	416	8	by	by	ADP
ma-105	416	9	−ah	−ah	NOUN
ma-105	416	10	,	,	PUNCT
ma-105	416	11	then	then	ADV
ma-105	416	12	for	for	ADP
ma-105	416	13	all	all	DET
ma-105	416	14	w0	w0	PROPN
ma-105	416	15	∈	∈	PROPN
ma-105	416	16	h	h	NOUN
ma-105	416	17	,	,	PUNCT
ma-105	416	18	g(t)w0	g(t)w0	NOUN
ma-105	416	19	=	=	PUNCT
ma-105	417	1	+	+	ADP
ma-105	417	2	∞∑	∞∑	ADJ
ma-105	417	3	k=0	k=0	ADJ
ma-105	417	4	e−tλk	e−tλk	NOUN
ma-105	417	5	(	(	PUNCT
ma-105	417	6	w0	w0	PROPN
ma-105	417	7	,	,	PUNCT
ma-105	417	8	ek)ek	ek)ek	X
ma-105	417	9	.	.	PUNCT
ma-105	418	1	(	(	PUNCT
ma-105	418	2	3.31	3.31	NUM
ma-105	418	3	)	)	PUNCT
ma-105	418	4	this	this	PRON
ma-105	418	5	proves	prove	VERB
ma-105	418	6	that	that	SCONJ
ma-105	418	7	the	the	DET
ma-105	418	8	operator	operator	NOUN
ma-105	418	9	is	be	AUX
ma-105	418	10	compact	compact	ADJ
ma-105	418	11	for	for	ADP
ma-105	418	12	all	all	DET
ma-105	418	13	t	t	NOUN
ma-105	418	14	>	>	X
ma-105	418	15	0	0	PUNCT
ma-105	418	16	since	since	SCONJ
ma-105	418	17	lim	lim	PROPN
ma-105	418	18	k→+∞	k→+∞	PROPN
ma-105	418	19	e−tλk	e−tλk	NOUN
ma-105	418	20	=	=	NOUN
ma-105	419	1	0	0	X
ma-105	419	2	.	.	X
ma-105	420	1	https://doi.org/10.28924/ada/ma.3.1	https://doi.org/10.28924/ada/ma.3.1	PROPN
ma-105	420	2	eur	eur	PROPN
ma-105	420	3	.	.	PUNCT
ma-105	421	1	j.	j.	PROPN
ma-105	421	2	math	math	PROPN
ma-105	421	3	.	.	PUNCT
ma-105	422	1	anal	anal	PROPN
ma-105	422	2	.	.	PUNCT
ma-105	423	1	10.28924	10.28924	NUM
ma-105	423	2	/	/	SYM
ma-105	423	3	ada	ada	PROPN
ma-105	423	4	/	/	SYM
ma-105	423	5	ma.3.1	ma.3.1	PROPN
ma-105	423	6	15we	15we	NOUN
ma-105	423	7	have	have	VERB
ma-105	423	8	the	the	DET
ma-105	423	9	same	same	ADJ
ma-105	423	10	formula	formula	NOUN
ma-105	423	11	for	for	ADP
ma-105	423	12	gi(t	gi(t	NOUN
ma-105	423	13	)	)	PUNCT
ma-105	423	14	,	,	PUNCT
ma-105	423	15	and	and	CCONJ
ma-105	423	16	it	it	PRON
ma-105	423	17	suffices	suffice	VERB
ma-105	423	18	to	to	PART
ma-105	423	19	replace	replace	VERB
ma-105	423	20	λk	λk	ADP
ma-105	423	21	by	by	ADP
ma-105	423	22	diλk	diλk	ADV
ma-105	423	23	.	.	PUNCT
ma-105	424	1	setting	set	VERB
ma-105	424	2	gn(t)w	gn(t)w	PROPN
ma-105	424	3	=	=	SYM
ma-105	424	4	n∑	n∑	DET
ma-105	424	5	k=0	k=0	PROPN
ma-105	424	6	e−tλk	e−tλk	NOUN
ma-105	424	7	(	(	PUNCT
ma-105	424	8	w	w	PROPN
ma-105	424	9	,	,	PUNCT
ma-105	424	10	ek)ek	ek)ek	NOUN
ma-105	424	11	,	,	PUNCT
ma-105	424	12	(	(	PUNCT
ma-105	424	13	3.32	3.32	NUM
ma-105	424	14	)	)	PUNCT
ma-105	424	15	one	one	NOUN
ma-105	424	16	sees	see	VERB
ma-105	424	17	that	that	PRON
ma-105	424	18	gn(t	gn(t	PUNCT
ma-105	424	19	)	)	PUNCT
ma-105	424	20	is	be	AUX
ma-105	424	21	an	an	DET
ma-105	424	22	operator	operator	NOUN
ma-105	424	23	with	with	ADP
ma-105	424	24	finite	finite	PROPN
ma-105	424	25	rank	rank	NOUN
ma-105	424	26	which	which	PRON
ma-105	424	27	converges	converge	VERB
ma-105	424	28	to	to	ADP
ma-105	424	29	g(t	g(t	PROPN
ma-105	424	30	)	)	PUNCT
ma-105	424	31	.	.	PUNCT
ma-105	425	1	the	the	DET
ma-105	425	2	following	follow	VERB
ma-105	425	3	theoremis	theoremis	NOUN
ma-105	425	4	relevant	relevant	ADJ
ma-105	425	5	in	in	ADP
ma-105	425	6	the	the	DET
ma-105	425	7	sequel	sequel	NOUN
ma-105	425	8	.	.	PUNCT
ma-105	426	1	theorem	theorem	VERB
ma-105	426	2	3.10	3.10	NUM
ma-105	426	3	.	.	PUNCT
ma-105	427	1	[	[	X
ma-105	427	2	12	12	NUM
ma-105	427	3	]	]	PUNCT
ma-105	427	4	let	let	VERB
ma-105	427	5	t	t	PROPN
ma-105	427	6	7→	7→	NUM
ma-105	427	7	g(t	g(t	PROPN
ma-105	427	8	)	)	PUNCT
ma-105	427	9	be	be	VERB
ma-105	427	10	an	an	DET
ma-105	427	11	application	application	NOUN
ma-105	427	12	from	from	ADP
ma-105	427	13	[	[	X
ma-105	427	14	0,+∞	0,+∞	NUM
ma-105	427	15	)	)	PUNCT
ma-105	427	16	into	into	ADP
ma-105	427	17	l(h	l(h	PROPN
ma-105	427	18	)	)	PUNCT
ma-105	427	19	.	.	PUNCT
ma-105	428	1	one	one	NUM
ma-105	428	2	assumes	assume	VERB
ma-105	428	3	that	that	SCONJ
ma-105	428	4	there	there	PRON
ma-105	428	5	exists	exist	VERB
ma-105	428	6	a	a	DET
ma-105	428	7	sequence	sequence	NOUN
ma-105	428	8	of	of	ADP
ma-105	428	9	operators	operator	NOUN
ma-105	428	10	(	(	PUNCT
ma-105	428	11	gn(t))n≥0	gn(t))n≥0	PROPN
ma-105	428	12	on	on	ADP
ma-105	428	13	h	h	NOUN
ma-105	428	14	verifying	verify	VERB
ma-105	428	15	the	the	DET
ma-105	428	16	following	following	NOUN
ma-105	428	17	properties:1	properties:1	VERB
ma-105	428	18	)	)	PUNCT
ma-105	428	19	for	for	ADP
ma-105	428	20	all	all	DET
ma-105	428	21	n	n	PRON
ma-105	428	22	and	and	CCONJ
ma-105	428	23	all	all	DET
ma-105	428	24	t	t	NOUN
ma-105	428	25	>	>	X
ma-105	428	26	0	0	NUM
ma-105	428	27	,	,	PUNCT
ma-105	428	28	gn(t	gn(t	NUM
ma-105	428	29	)	)	PUNCT
ma-105	428	30	has	have	VERB
ma-105	428	31	finite	finite	VERB
ma-105	428	32	rank	rank	PROPN
ma-105	428	33	independent	independent	NOUN
ma-105	428	34	of	of	ADP
ma-105	428	35	t	t	PROPN
ma-105	428	36	,	,	PUNCT
ma-105	428	37	2	2	NUM
ma-105	428	38	)	)	PUNCT
ma-105	428	39	t	t	NOUN
ma-105	428	40	7→	7→	NUM
ma-105	428	41	gn(t	gn(t	PUNCT
ma-105	428	42	)	)	PUNCT
ma-105	428	43	is	be	AUX
ma-105	428	44	continuous	continuous	ADJ
ma-105	428	45	from	from	ADP
ma-105	428	46	[	[	NOUN
ma-105	428	47	0,+∞	0,+∞	NUM
ma-105	428	48	)	)	PUNCT
ma-105	428	49	into	into	ADP
ma-105	428	50	l(h	l(h	PROPN
ma-105	428	51	)	)	PUNCT
ma-105	428	52	for	for	ADP
ma-105	428	53	all	all	DET
ma-105	428	54	n	n	PROPN
ma-105	428	55	,	,	PUNCT
ma-105	428	56	3	3	X
ma-105	428	57	)	)	PUNCT
ma-105	428	58	for	for	ADP
ma-105	428	59	n	n	PRON
ma-105	428	60	→	→	SYM
ma-105	428	61	+	+	PROPN
ma-105	428	62	∞	∞	PROPN
ma-105	428	63	,	,	PUNCT
ma-105	428	64	gn(t	gn(t	NUM
ma-105	428	65	)	)	PUNCT
ma-105	428	66	converges	converge	NOUN
ma-105	428	67	to	to	ADP
ma-105	428	68	g(t	g(t	PROPN
ma-105	428	69	)	)	PUNCT
ma-105	428	70	in	in	ADP
ma-105	428	71	l1(]0	l1(]0	ADJ
ma-105	428	72	,	,	PUNCT
ma-105	428	73	t	t	X
ma-105	429	1	[	[	X
ma-105	429	2	,	,	PUNCT
ma-105	429	3	l(h	l(h	PROPN
ma-105	429	4	)	)	PUNCT
ma-105	429	5	)	)	PUNCT
ma-105	430	1	for	for	ADP
ma-105	430	2	all	all	DET
ma-105	430	3	t	t	PROPN
ma-105	430	4	>	>	X
ma-105	430	5	0	0	X
ma-105	430	6	.	.	PUNCT
ma-105	431	1	then	then	ADV
ma-105	431	2	the	the	DET
ma-105	431	3	operator	operator	NOUN
ma-105	431	4	g	g	NOUN
ma-105	431	5	is	be	AUX
ma-105	431	6	compact	compact	ADJ
ma-105	431	7	from	from	ADP
ma-105	431	8	c0([0	c0([0	PROPN
ma-105	431	9	,	,	PUNCT
ma-105	431	10	t	t	X
ma-105	431	11	]	]	PUNCT
ma-105	431	12	,	,	PUNCT
ma-105	431	13	h	h	NOUN
ma-105	431	14	)	)	PUNCT
ma-105	431	15	to	to	ADP
ma-105	431	16	c0([0	c0([0	PROPN
ma-105	431	17	,	,	PUNCT
ma-105	431	18	t	t	X
ma-105	431	19	]	]	PUNCT
ma-105	431	20	,	,	PUNCT
ma-105	431	21	h	h	NOUN
ma-105	431	22	)	)	PUNCT
ma-105	431	23	for	for	ADP
ma-105	431	24	all	all	DET
ma-105	431	25	t	t	PROPN
ma-105	431	26	>	>	X
ma-105	431	27	0	0	X
ma-105	431	28	.	.	PUNCT
ma-105	432	1	we	we	PRON
ma-105	432	2	are	be	AUX
ma-105	432	3	now	now	ADV
ma-105	432	4	in	in	ADP
ma-105	432	5	the	the	DET
ma-105	432	6	position	position	NOUN
ma-105	432	7	to	to	PART
ma-105	432	8	prove	prove	VERB
ma-105	432	9	the	the	DET
ma-105	432	10	global	global	ADJ
ma-105	432	11	existence	existence	NOUN
ma-105	432	12	,	,	PUNCT
ma-105	432	13	uniqueness	uniqueness	NOUN
ma-105	432	14	and	and	CCONJ
ma-105	432	15	positivity	positivity	NOUN
ma-105	432	16	of	of	ADP
ma-105	432	17	the	the	DET
ma-105	432	18	solutionto	solutionto	NOUN
ma-105	432	19	the	the	DET
ma-105	432	20	ibvp	ibvp	NOUN
ma-105	432	21	(	(	PUNCT
ma-105	432	22	2.4	2.4	NUM
ma-105	432	23	)	)	PUNCT
ma-105	432	24	.	.	PUNCT
ma-105	433	1	theorem	theorem	VERB
ma-105	433	2	3.11	3.11	NUM
ma-105	433	3	.	.	PUNCT
ma-105	434	1	if	if	SCONJ
ma-105	434	2	the	the	DET
ma-105	434	3	initial	initial	ADJ
ma-105	434	4	condition	condition	NOUN
ma-105	434	5	satisfies	satisfie	NOUN
ma-105	434	6	(	(	PUNCT
ma-105	434	7	3.22	3.22	NUM
ma-105	434	8	)	)	PUNCT
ma-105	434	9	,	,	PUNCT
ma-105	434	10	then	then	ADV
ma-105	434	11	the	the	DET
ma-105	434	12	ibvp	ibvp	NOUN
ma-105	434	13	(	(	PUNCT
ma-105	434	14	3.21	3.21	NUM
ma-105	434	15	)	)	PUNCT
ma-105	434	16	admits	admit	VERB
ma-105	434	17	a	a	DET
ma-105	434	18	unique	unique	ADJ
ma-105	434	19	nonnegative	nonnegative	ADJ
ma-105	434	20	solution	solution	NOUN
ma-105	434	21	w	w	PROPN
ma-105	434	22	∈	∈	PROPN
ma-105	434	23	(	(	PUNCT
ma-105	434	24	w	w	NOUN
ma-105	434	25	(	(	PUNCT
ma-105	434	26	0	0	NUM
ma-105	434	27	,	,	PUNCT
ma-105	434	28	t	t	PROPN
ma-105	434	29	,	,	PUNCT
ma-105	434	30	e	e	NOUN
ma-105	434	31	,	,	PUNCT
ma-105	434	32	e′))3	e′))3	PROPN
ma-105	434	33	.	.	PUNCT
ma-105	435	1	the	the	DET
ma-105	435	2	proof	proof	NOUN
ma-105	435	3	of	of	ADP
ma-105	435	4	theorem	theorem	ADJ
ma-105	435	5	3.11	3.11	NUM
ma-105	435	6	is	be	AUX
ma-105	435	7	contained	contain	VERB
ma-105	435	8	in	in	ADP
ma-105	435	9	"	"	PUNCT
ma-105	435	10	appendix	appendix	VERB
ma-105	435	11	b	b	NOUN
ma-105	435	12	"	"	PUNCT
ma-105	435	13	.	.	PUNCT
ma-105	436	1	remark	remark	VERB
ma-105	436	2	3.4	3.4	NUM
ma-105	436	3	.	.	PUNCT
ma-105	437	1	it	it	PRON
ma-105	437	2	is	be	AUX
ma-105	437	3	worth	worth	ADJ
ma-105	437	4	noting	note	VERB
ma-105	437	5	that	that	SCONJ
ma-105	437	6	positivity	positivity	NOUN
ma-105	437	7	of	of	ADP
ma-105	437	8	the	the	DET
ma-105	437	9	solution	solution	NOUN
ma-105	437	10	may	may	AUX
ma-105	437	11	be	be	AUX
ma-105	437	12	proved	prove	VERB
ma-105	437	13	by	by	ADP
ma-105	437	14	applying	apply	VERB
ma-105	437	15	the	the	DET
ma-105	437	16	maximumprinciple	maximumprinciple	NOUN
ma-105	437	17	.	.	PUNCT
ma-105	438	1	moreover	moreover	ADV
ma-105	438	2	,	,	PUNCT
ma-105	438	3	from	from	ADP
ma-105	438	4	the	the	DET
ma-105	438	5	above	above	ADJ
ma-105	438	6	results	result	NOUN
ma-105	438	7	and	and	CCONJ
ma-105	438	8	the	the	DET
ma-105	438	9	boundedness	boundedness	NOUN
ma-105	438	10	of	of	ADP
ma-105	438	11	the	the	DET
ma-105	438	12	solution	solution	NOUN
ma-105	438	13	,	,	PUNCT
ma-105	438	14	one	one	PRON
ma-105	438	15	has	have	VERB
ma-105	438	16	observedthat	observedthat	ADP
ma-105	438	17	the	the	DET
ma-105	438	18	solution	solution	NOUN
ma-105	438	19	of	of	ADP
ma-105	438	20	ibvp	ibvp	NOUN
ma-105	438	21	(	(	PUNCT
ma-105	438	22	2.4	2.4	NUM
ma-105	438	23	)	)	PUNCT
ma-105	438	24	enters	enter	VERB
ma-105	438	25	the	the	DET
ma-105	438	26	region	region	NOUN
ma-105	438	27	:	:	PUNCT
ma-105	439	1	σ	σ	X
ma-105	439	2	=	=	SYM
ma-105	439	3	{	{	PUNCT
ma-105	439	4	(	(	PUNCT
ma-105	439	5	h	h	NOUN
ma-105	439	6	,	,	PUNCT
ma-105	439	7	i	i	PRON
ma-105	439	8	,	,	PUNCT
ma-105	439	9	v	v	NOUN
ma-105	439	10	)	)	PUNCT
ma-105	439	11	∈	∈	PROPN
ma-105	439	12	ω3	ω3	NOUN
ma-105	439	13	×r3	×r3	PROPN
ma-105	440	1	+	+	PUNCT
ma-105	440	2	:	:	SYM
ma-105	440	3	0	0	NUM
ma-105	440	4	<	<	X
ma-105	440	5	h(x	h(x	PROPN
ma-105	440	6	,	,	PUNCT
ma-105	440	7	t	t	PROPN
ma-105	440	8	)	)	PUNCT
ma-105	440	9	≤	≤	NUM
ma-105	441	1	hm	hm	INTJ
ma-105	441	2	,	,	PUNCT
ma-105	441	3	0	0	PUNCT
ma-105	441	4	<	<	X
ma-105	441	5	i(x	i(x	PROPN
ma-105	441	6	,	,	PUNCT
ma-105	441	7	t	t	PROPN
ma-105	441	8	)	)	PUNCT
ma-105	441	9	≤	≤	NUM
ma-105	442	1	hm	hm	INTJ
ma-105	442	2	,	,	PUNCT
ma-105	442	3	0	0	PUNCT
ma-105	442	4	<	<	X
ma-105	442	5	v	v	X
ma-105	442	6	(	(	PUNCT
ma-105	442	7	x	x	PROPN
ma-105	442	8	,	,	PUNCT
ma-105	442	9	t	t	PROPN
ma-105	442	10	)	)	PUNCT
ma-105	442	11	≤	≤	PROPN
ma-105	442	12	vm	vm	PROPN
ma-105	442	13	}	}	PUNCT
ma-105	442	14	,	,	PUNCT
ma-105	442	15	where	where	SCONJ
ma-105	442	16	hm	hm	INTJ
ma-105	442	17	=	=	SYM
ma-105	442	18	max	max	PROPN
ma-105	442	19	{	{	PUNCT
ma-105	443	1	λ	λ	X
ma-105	443	2	δ2	δ2	VERB
ma-105	443	3	,	,	PUNCT
ma-105	443	4	max	max	PROPN
ma-105	443	5	x∈ω	x∈ω	PROPN
ma-105	443	6	{	{	PUNCT
ma-105	443	7	h(x	h(x	PROPN
ma-105	443	8	,	,	PUNCT
ma-105	443	9	0	0	NUM
ma-105	443	10	)	)	PUNCT
ma-105	444	1	+	+	CCONJ
ma-105	444	2	i(x	i(x	PROPN
ma-105	444	3	,	,	PUNCT
ma-105	444	4	0	0	NUM
ma-105	444	5	)	)	PUNCT
ma-105	444	6	}	}	PUNCT
ma-105	444	7	}	}	PUNCT
ma-105	444	8	et	et	NOUN
ma-105	444	9	vm	vm	PROPN
ma-105	444	10	=	=	PROPN
ma-105	444	11	max	max	PROPN
ma-105	444	12	{	{	PUNCT
ma-105	444	13	(	(	PUNCT
ma-105	444	14	1−	1−	NUM
ma-105	444	15	ε)khm	ε)khm	PROPN
ma-105	444	16	µ	µ	X
ma-105	444	17	,	,	PUNCT
ma-105	444	18	max	max	PROPN
ma-105	444	19	x∈ω	x∈ω	PROPN
ma-105	444	20	v	v	PROPN
ma-105	444	21	(	(	PUNCT
ma-105	444	22	x	x	NOUN
ma-105	444	23	,	,	PUNCT
ma-105	444	24	0	0	NUM
ma-105	444	25	)	)	PUNCT
ma-105	444	26	}	}	PUNCT
ma-105	444	27	.	.	PUNCT
ma-105	445	1	hence	hence	ADV
ma-105	445	2	the	the	DET
ma-105	445	3	region	region	NOUN
ma-105	445	4	σ	σ	PROPN
ma-105	445	5	,	,	PUNCT
ma-105	445	6	of	of	ADP
ma-105	445	7	biological	biological	ADJ
ma-105	445	8	interest	interest	NOUN
ma-105	445	9	,	,	PUNCT
ma-105	445	10	is	be	AUX
ma-105	445	11	positively	positively	ADV
ma-105	445	12	-	-	PUNCT
ma-105	445	13	invariant	invariant	ADJ
ma-105	445	14	under	under	ADP
ma-105	445	15	the	the	DET
ma-105	445	16	flow	flow	NOUN
ma-105	445	17	induced	induce	VERB
ma-105	445	18	by	by	ADP
ma-105	445	19	ibvp(2.4	ibvp(2.4	NOUN
ma-105	445	20	)	)	PUNCT
ma-105	445	21	.	.	PUNCT
ma-105	446	1	4	4	X
ma-105	446	2	.	.	X
ma-105	446	3	stability	stability	NOUN
ma-105	446	4	analysis	analysis	NOUN
ma-105	446	5	of	of	ADP
ma-105	446	6	the	the	DET
ma-105	446	7	spatially	spatially	ADV
ma-105	446	8	homogeneous	homogeneous	ADJ
ma-105	446	9	equilibria	equilibrium	NOUN
ma-105	446	10	4.1	4.1	NUM
ma-105	446	11	.	.	PUNCT
ma-105	447	1	hcv	hcv	NOUN
ma-105	447	2	-	-	PUNCT
ma-105	447	3	spatial	spatial	ADJ
ma-105	447	4	homogeneous	homogeneous	ADJ
ma-105	447	5	uninfected	uninfected	ADJ
ma-105	447	6	equilibrium	equilibrium	NOUN
ma-105	447	7	e0	e0	PROPN
ma-105	447	8	.	.	PUNCT
ma-105	448	1	the	the	DET
ma-105	448	2	spatial	spatial	ADJ
ma-105	448	3	homogeneous	homogeneous	ADJ
ma-105	448	4	uninfectedequilibrium	uninfectedequilibrium	NOUN
ma-105	448	5	of	of	ADP
ma-105	448	6	the	the	DET
ma-105	448	7	pde	pde	NOUN
ma-105	448	8	-	-	PUNCT
ma-105	448	9	model	model	NOUN
ma-105	448	10	system	system	NOUN
ma-105	448	11	(	(	PUNCT
ma-105	448	12	2.4	2.4	NUM
ma-105	448	13	)	)	PUNCT
ma-105	448	14	arises	arise	VERB
ma-105	448	15	when	when	SCONJ
ma-105	448	16	there	there	PRON
ma-105	448	17	is	be	VERB
ma-105	448	18	no	no	DET
ma-105	448	19	virus	virus	NOUN
ma-105	448	20	within	within	ADP
ma-105	448	21	a	a	DET
ma-105	448	22	host	host	NOUN
ma-105	448	23	i.e.	i.e.	X
ma-105	448	24	,	,	PUNCT
ma-105	448	25	v=0.easy	v=0.easy	ADJ
ma-105	448	26	calculations	calculation	NOUN
ma-105	448	27	shows	show	VERB
ma-105	448	28	that	that	SCONJ
ma-105	448	29	the	the	DET
ma-105	448	30	hcv	hcv	PROPN
ma-105	448	31	-	-	PUNCT
ma-105	448	32	spatial	spatial	ADJ
ma-105	448	33	homogeneous	homogeneous	ADJ
ma-105	448	34	uninfected	uninfected	ADJ
ma-105	448	35	equilibrium	equilibrium	NOUN
ma-105	448	36	for	for	ADP
ma-105	448	37	pde	pde	NOUN
ma-105	448	38	-	-	PUNCT
ma-105	448	39	modelsystem	modelsystem	NOUN
ma-105	448	40	(	(	PUNCT
ma-105	448	41	2.4	2.4	NUM
ma-105	448	42	)	)	PUNCT
ma-105	448	43	is	be	AUX
ma-105	448	44	given	give	VERB
ma-105	448	45	by	by	ADP
ma-105	448	46	e0	e0	PROPN
ma-105	448	47	=	=	SYM
ma-105	448	48	(	(	PUNCT
ma-105	448	49	λ	λ	PROPN
ma-105	448	50	,	,	PUNCT
ma-105	448	51	0	0	NUM
ma-105	448	52	,	,	PUNCT
ma-105	448	53	0	0	NUM
ma-105	448	54	)	)	PUNCT
ma-105	448	55	https://doi.org/10.28924/ada/ma.3.1	https://doi.org/10.28924/ada/ma.3.1	PROPN
ma-105	448	56	eur	eur	PROPN
ma-105	448	57	.	.	PUNCT
ma-105	449	1	j.	j.	PROPN
ma-105	449	2	math	math	PROPN
ma-105	449	3	.	.	PUNCT
ma-105	450	1	anal	anal	PROPN
ma-105	450	2	.	.	PUNCT
ma-105	451	1	10.28924	10.28924	NUM
ma-105	451	2	/	/	SYM
ma-105	451	3	ada	ada	PROPN
ma-105	451	4	/	/	SYM
ma-105	451	5	ma.3.1	ma.3.1	PROPN
ma-105	451	6	16where	16where	NUM
ma-105	452	1	λ	λ	X
ma-105	452	2	=	=	SYM
ma-105	453	1	λ	λ	X
ma-105	453	2	d	d	PROPN
ma-105	453	3	.	.	PUNCT
ma-105	454	1	4.2	4.2	NUM
ma-105	454	2	.	.	PUNCT
ma-105	454	3	basic	basic	ADJ
ma-105	454	4	reproduction	reproduction	NOUN
ma-105	454	5	number	number	NOUN
ma-105	454	6	r0	r0	NOUN
ma-105	454	7	.	.	PUNCT
ma-105	455	1	in	in	ADP
ma-105	455	2	order	order	NOUN
ma-105	455	3	to	to	PART
ma-105	455	4	define	define	VERB
ma-105	455	5	the	the	DET
ma-105	455	6	basic	basic	ADJ
ma-105	455	7	reproduction	reproduction	NOUN
ma-105	455	8	number	number	NOUN
ma-105	455	9	r0	r0	NOUN
ma-105	455	10	forsystem	forsystem	NOUN
ma-105	455	11	(	(	PUNCT
ma-105	455	12	2.4	2.4	NUM
ma-105	455	13	)	)	PUNCT
ma-105	455	14	,	,	PUNCT
ma-105	455	15	we	we	PRON
ma-105	455	16	first	first	ADV
ma-105	455	17	observe	observe	VERB
ma-105	455	18	that	that	DET
ma-105	455	19	system	system	NOUN
ma-105	455	20	(	(	PUNCT
ma-105	455	21	2.4	2.4	NUM
ma-105	455	22	)	)	PUNCT
ma-105	455	23	has	have	VERB
ma-105	455	24	a	a	DET
ma-105	455	25	spatially	spatially	ADV
ma-105	455	26	homogeneous	homogeneous	ADJ
ma-105	455	27	uninfected	uninfected	ADJ
ma-105	455	28	equilibrium	equilibrium	NOUN
ma-105	455	29	e0	e0	PROPN
ma-105	455	30	.	.	PUNCT
ma-105	456	1	it	it	PRON
ma-105	456	2	should	should	AUX
ma-105	456	3	be	be	AUX
ma-105	456	4	noted	note	VERB
ma-105	456	5	that	that	SCONJ
ma-105	456	6	one	one	NUM
ma-105	456	7	of	of	ADP
ma-105	456	8	the	the	DET
ma-105	456	9	main	main	ADJ
ma-105	456	10	tools	tool	NOUN
ma-105	456	11	in	in	ADP
ma-105	456	12	epidemic	epidemic	NOUN
ma-105	456	13	models	model	NOUN
ma-105	456	14	is	be	AUX
ma-105	456	15	the	the	DET
ma-105	456	16	basic	basic	ADJ
ma-105	456	17	reproductionnumber	reproductionnumber	NOUN
ma-105	456	18	r0	r0	NOUN
ma-105	456	19	which	which	PRON
ma-105	456	20	is	be	AUX
ma-105	456	21	an	an	DET
ma-105	456	22	important	important	ADJ
ma-105	456	23	threshold	threshold	NOUN
ma-105	456	24	parameter	parameter	NOUN
ma-105	456	25	to	to	PART
ma-105	456	26	discuss	discuss	VERB
ma-105	456	27	the	the	DET
ma-105	456	28	dynamic	dynamic	ADJ
ma-105	456	29	behaviour	behaviour	NOUN
ma-105	456	30	of	of	ADP
ma-105	456	31	theepidemic	theepidemic	ADJ
ma-105	456	32	model	model	NOUN
ma-105	456	33	.	.	PUNCT
ma-105	457	1	it	it	PRON
ma-105	457	2	quantifies	quantify	VERB
ma-105	457	3	the	the	DET
ma-105	457	4	infection	infection	NOUN
ma-105	457	5	risk	risk	NOUN
ma-105	457	6	.	.	PUNCT
ma-105	458	1	it	it	PRON
ma-105	458	2	measures	measure	VERB
ma-105	458	3	the	the	DET
ma-105	458	4	expected	expect	VERB
ma-105	458	5	average	average	ADJ
ma-105	458	6	number	number	NOUN
ma-105	458	7	ofnew	ofnew	ADJ
ma-105	458	8	infected	infect	VERB
ma-105	458	9	hepatocytes	hepatocyte	NOUN
ma-105	458	10	generated	generate	VERB
ma-105	458	11	by	by	ADP
ma-105	458	12	a	a	DET
ma-105	458	13	single	single	ADJ
ma-105	458	14	virion	virion	NOUN
ma-105	458	15	in	in	ADP
ma-105	458	16	a	a	DET
ma-105	458	17	completely	completely	ADV
ma-105	458	18	healthy	healthy	ADJ
ma-105	458	19	hepatocyte	hepatocyte	NOUN
ma-105	458	20	.	.	PUNCT
ma-105	459	1	itshould	itshould	AUX
ma-105	459	2	be	be	AUX
ma-105	459	3	also	also	ADV
ma-105	459	4	noted	note	VERB
ma-105	459	5	that	that	SCONJ
ma-105	459	6	,	,	PUNCT
ma-105	459	7	while	while	SCONJ
ma-105	459	8	a	a	DET
ma-105	459	9	huge	huge	ADJ
ma-105	459	10	number	number	NOUN
ma-105	459	11	of	of	ADP
ma-105	459	12	works	work	NOUN
ma-105	459	13	deals	deal	NOUN
ma-105	459	14	with	with	ADP
ma-105	459	15	the	the	DET
ma-105	459	16	threshold	threshold	NOUN
ma-105	459	17	dynamics	dynamic	NOUN
ma-105	459	18	forode	forode	ADJ
ma-105	459	19	-	-	PUNCT
ma-105	459	20	models	model	NOUN
ma-105	459	21	,	,	PUNCT
ma-105	459	22	very	very	ADV
ma-105	459	23	few	few	ADJ
ma-105	459	24	studies	study	NOUN
ma-105	459	25	are	be	AUX
ma-105	459	26	devoted	devote	VERB
ma-105	459	27	to	to	ADP
ma-105	459	28	pde	pde	NOUN
ma-105	459	29	-	-	PUNCT
ma-105	459	30	models	model	NOUN
ma-105	459	31	.	.	PUNCT
ma-105	460	1	this	this	PRON
ma-105	460	2	is	be	AUX
ma-105	460	3	eventually	eventually	ADV
ma-105	460	4	due	due	ADJ
ma-105	460	5	to	to	ADP
ma-105	460	6	the	the	DET
ma-105	460	7	factthat	factthat	NOUN
ma-105	460	8	the	the	DET
ma-105	460	9	concept	concept	NOUN
ma-105	460	10	of	of	ADP
ma-105	460	11	basic	basic	ADJ
ma-105	460	12	reproduction	reproduction	NOUN
ma-105	460	13	number	number	NOUN
ma-105	460	14	has	have	AUX
ma-105	460	15	just	just	ADV
ma-105	460	16	recently	recently	ADV
ma-105	460	17	been	be	AUX
ma-105	460	18	extended	extend	VERB
ma-105	460	19	to	to	ADP
ma-105	460	20	pde	pde	NOUN
ma-105	460	21	-	-	PUNCT
ma-105	460	22	modelssuch	modelssuch	NOUN
ma-105	460	23	as	as	ADP
ma-105	460	24	reaction	reaction	NOUN
ma-105	460	25	-	-	PUNCT
ma-105	460	26	diffusion	diffusion	NOUN
ma-105	460	27	and	and	CCONJ
ma-105	460	28	reaction	reaction	NOUN
ma-105	460	29	-	-	PUNCT
ma-105	460	30	convection	convection	NOUN
ma-105	460	31	-	-	PUNCT
ma-105	460	32	diffusion	diffusion	NOUN
ma-105	460	33	epidemic	epidemic	NOUN
ma-105	460	34	models	model	NOUN
ma-105	460	35	with	with	ADP
ma-105	460	36	mixed	mixed	ADJ
ma-105	460	37	boundaryconditions	boundarycondition	NOUN
ma-105	460	38	[	[	X
ma-105	460	39	37,40	37,40	VERB
ma-105	460	40	]	]	X
ma-105	460	41	.	.	PUNCT
ma-105	461	1	the	the	DET
ma-105	461	2	definition	definition	NOUN
ma-105	461	3	of	of	ADP
ma-105	461	4	r0	r0	NOUN
ma-105	461	5	in	in	ADP
ma-105	461	6	this	this	DET
ma-105	461	7	work	work	NOUN
ma-105	461	8	follows	follow	VERB
ma-105	461	9	the	the	DET
ma-105	461	10	approach	approach	NOUN
ma-105	461	11	developed	develop	VERB
ma-105	461	12	in	in	ADP
ma-105	461	13	[	[	X
ma-105	461	14	40	40	NUM
ma-105	461	15	]	]	PUNCT
ma-105	461	16	.	.	PUNCT
ma-105	462	1	in	in	ADP
ma-105	462	2	order	order	NOUN
ma-105	462	3	to	to	PART
ma-105	462	4	find	find	VERB
ma-105	462	5	the	the	DET
ma-105	462	6	basic	basic	ADJ
ma-105	462	7	reproduction	reproduction	NOUN
ma-105	462	8	number	number	NOUN
ma-105	462	9	r0	r0	NOUN
ma-105	462	10	for	for	ADP
ma-105	462	11	the	the	DET
ma-105	462	12	system	system	NOUN
ma-105	462	13	(	(	PUNCT
ma-105	462	14	2.4	2.4	NUM
ma-105	462	15	)	)	PUNCT
ma-105	462	16	,	,	PUNCT
ma-105	462	17	we	we	PRON
ma-105	462	18	obtain	obtain	VERB
ma-105	462	19	the	the	DET
ma-105	462	20	followinglinear	followinglinear	ADJ
ma-105	462	21	system	system	NOUN
ma-105	462	22	at	at	ADP
ma-105	462	23	e0	e0	PROPN
ma-105	462	24	for	for	ADP
ma-105	462	25	the	the	DET
ma-105	462	26	infected	infected	ADJ
ma-105	462	27	classes	class	NOUN
ma-105	462	28	:	:	PUNCT
ma-105	462	29			PROPN
ma-105	462	30	∂i	∂i	PROPN
ma-105	463	1	∂t	∂t	PROPN
ma-105	463	2	=	=	PUNCT
ma-105	463	3	d2∆i	d2∆i	VERB
ma-105	463	4	−	−	PROPN
ma-105	463	5	(	(	PUNCT
ma-105	463	6	α+	α+	PROPN
ma-105	463	7	ρ)i	ρ)i	NOUN
ma-105	464	1	+	+	CCONJ
ma-105	464	2	(	(	PUNCT
ma-105	464	3	1−	1−	NUM
ma-105	464	4	η)βλ	η)βλ	PROPN
ma-105	464	5	α0	α0	ADJ
ma-105	464	6	+	+	CCONJ
ma-105	464	7	α1λ	α1λ	PRON
ma-105	464	8	v	v	NOUN
ma-105	464	9	in	in	ADP
ma-105	464	10	ωt	ωt	PROPN
ma-105	464	11	,	,	PUNCT
ma-105	464	12	∂v	∂v	PROPN
ma-105	464	13	∂t	∂t	PROPN
ma-105	465	1	=	=	PUNCT
ma-105	465	2	d3∆v	d3∆v	NOUN
ma-105	465	3	+	+	X
ma-105	465	4	(	(	PUNCT
ma-105	465	5	1−	1−	NUM
ma-105	465	6	ε)ki	ε)ki	PROPN
ma-105	465	7	−	−	PROPN
ma-105	465	8	µv	µv	NOUN
ma-105	465	9	−	−	PROPN
ma-105	465	10	u(1−	u(1−	ADJ
ma-105	465	11	η)βλ	η)βλ	PROPN
ma-105	465	12	α0	α0	PROPN
ma-105	465	13	+	+	CCONJ
ma-105	465	14	α1λ	α1λ	PRON
ma-105	465	15	v	v	NOUN
ma-105	465	16	in	in	ADP
ma-105	465	17	ωt	ωt	PROPN
ma-105	465	18	,	,	PUNCT
ma-105	465	19	(	(	PUNCT
ma-105	465	20	4.1	4.1	NUM
ma-105	465	21	)	)	PUNCT
ma-105	465	22	∂i	∂i	PROPN
ma-105	465	23	∂η	∂η	PROPN
ma-105	466	1	=	=	SYM
ma-105	466	2	∂v	∂v	PROPN
ma-105	466	3	∂η	∂η	PROPN
ma-105	467	1	=	=	NOUN
ma-105	467	2	0	0	NUM
ma-105	467	3	on	on	ADP
ma-105	467	4	∂ω×	∂ω×	PROPN
ma-105	468	1	[	[	X
ma-105	468	2	0	0	NUM
ma-105	468	3	,	,	PUNCT
ma-105	468	4	t	t	X
ma-105	468	5	]	]	PUNCT
ma-105	468	6	.	.	PUNCT
ma-105	469	1	substituting	substitute	VERB
ma-105	469	2	i(x	i(x	PROPN
ma-105	469	3	,	,	PUNCT
ma-105	469	4	t	t	PROPN
ma-105	469	5	)	)	PUNCT
ma-105	469	6	=	=	PUNCT
ma-105	469	7	eλtψ2(x	eλtψ2(x	NOUN
ma-105	469	8	)	)	PUNCT
ma-105	469	9	and	and	CCONJ
ma-105	469	10	v	v	X
ma-105	469	11	(	(	PUNCT
ma-105	469	12	x	x	NOUN
ma-105	469	13	,	,	PUNCT
ma-105	469	14	t	t	PROPN
ma-105	469	15	)	)	PUNCT
ma-105	469	16	=	=	SYM
ma-105	469	17	eλtψ3(x	eλtψ3(x	PROPN
ma-105	469	18	)	)	PUNCT
ma-105	469	19	in	in	ADP
ma-105	469	20	(	(	PUNCT
ma-105	469	21	4.1	4.1	NUM
ma-105	469	22	)	)	PUNCT
ma-105	469	23	,	,	PUNCT
ma-105	469	24	we	we	PRON
ma-105	469	25	obtain	obtain	VERB
ma-105	469	26	the	the	DET
ma-105	469	27	following	follow	VERB
ma-105	469	28	cooper	cooper	NOUN
ma-105	469	29	-	-	PUNCT
ma-105	469	30	ative	ative	PROPN
ma-105	469	31	eigenvalue	eigenvalue	PROPN
ma-105	469	32	problem	problem	NOUN
ma-105	469	33	:	:	PUNCT
ma-105	469	34			NUM
ma-105	469	35	λψ2(x	λψ2(x	PROPN
ma-105	469	36	)	)	PUNCT
ma-105	470	1	=	=	SYM
ma-105	470	2	d2∆ψ2(x)−	d2∆ψ2(x)−	PROPN
ma-105	470	3	(	(	PUNCT
ma-105	470	4	α+	α+	X
ma-105	470	5	ρ)ψ2(x	ρ)ψ2(x	NOUN
ma-105	470	6	)	)	PUNCT
ma-105	470	7	+	+	CCONJ
ma-105	470	8	(	(	PUNCT
ma-105	470	9	1−	1−	NUM
ma-105	470	10	η)βλ	η)βλ	PROPN
ma-105	470	11	α0	α0	ADJ
ma-105	470	12	+	+	CCONJ
ma-105	470	13	α1λ	α1λ	DET
ma-105	470	14	ψ3(x	ψ3(x	NOUN
ma-105	470	15	)	)	PUNCT
ma-105	470	16	in	in	ADP
ma-105	470	17	ω	ω	PROPN
ma-105	470	18	,	,	PUNCT
ma-105	470	19	λψ3(x	λψ3(x	PROPN
ma-105	470	20	)	)	PUNCT
ma-105	470	21	=	=	SYM
ma-105	470	22	d3∆ψ3(x	d3∆ψ3(x	PROPN
ma-105	470	23	)	)	PUNCT
ma-105	471	1	+	+	CCONJ
ma-105	472	1	(	(	PUNCT
ma-105	472	2	1−	1−	NUM
ma-105	472	3	ε)kψ2(x)−	ε)kψ2(x)−	PROPN
ma-105	472	4	µψ3(x)−	µψ3(x)−	PROPN
ma-105	472	5	u(1−	u(1−	PROPN
ma-105	472	6	η)βλ	η)βλ	PROPN
ma-105	472	7	α0	α0	PROPN
ma-105	472	8	+	+	CCONJ
ma-105	472	9	α1λ	α1λ	DET
ma-105	472	10	ψ3(x	ψ3(x	NOUN
ma-105	472	11	)	)	PUNCT
ma-105	472	12	in	in	ADP
ma-105	472	13	ω	ω	NUM
ma-105	472	14	,	,	PUNCT
ma-105	472	15	(	(	PUNCT
ma-105	472	16	4.2	4.2	NUM
ma-105	472	17	)	)	PUNCT
ma-105	472	18	∂ψ2(x	∂ψ2(x	NOUN
ma-105	472	19	)	)	PUNCT
ma-105	472	20	∂η	∂η	PROPN
ma-105	472	21	=	=	SYM
ma-105	472	22	∂ψ3(x	∂ψ3(x	PROPN
ma-105	472	23	)	)	PUNCT
ma-105	472	24	∂η	∂η	PROPN
ma-105	473	1	=	=	NOUN
ma-105	473	2	0	0	NUM
ma-105	473	3	on	on	ADP
ma-105	473	4	∂ω	∂ω	PROPN
ma-105	473	5	.	.	PUNCT
ma-105	474	1	https://doi.org/10.28924/ada/ma.3.1	https://doi.org/10.28924/ada/ma.3.1	PROPN
ma-105	474	2	eur	eur	PROPN
ma-105	474	3	.	.	PUNCT
ma-105	475	1	j.	j.	PROPN
ma-105	475	2	math	math	PROPN
ma-105	475	3	.	.	PUNCT
ma-105	476	1	anal	anal	PROPN
ma-105	476	2	.	.	PUNCT
ma-105	477	1	10.28924	10.28924	NUM
ma-105	477	2	/	/	SYM
ma-105	477	3	ada	ada	PROPN
ma-105	477	4	/	/	SYM
ma-105	477	5	ma.3.1	ma.3.1	PROPN
ma-105	477	6	17as	17as	ADJ
ma-105	477	7	in	in	ADP
ma-105	477	8	[	[	X
ma-105	477	9	40	40	NUM
ma-105	477	10	]	]	PUNCT
ma-105	477	11	,	,	PUNCT
ma-105	477	12	let	let	VERB
ma-105	477	13	t	t	PROPN
ma-105	477	14	:	:	PUNCT
ma-105	477	15	c(ω̄,r2)→	c(ω̄,r2)→	NUM
ma-105	477	16	c(ω̄,r2	c(ω̄,r2	CCONJ
ma-105	477	17	)	)	PUNCT
ma-105	477	18	be	be	VERB
ma-105	477	19	the	the	DET
ma-105	477	20	solution	solution	NOUN
ma-105	477	21	semigroup	semigroup	NOUN
ma-105	477	22	of	of	ADP
ma-105	477	23	the	the	DET
ma-105	477	24	following	follow	VERB
ma-105	477	25	reaction	reaction	NOUN
ma-105	477	26	-	-	PUNCT
ma-105	477	27	diffusionsystem	diffusionsystem	NOUN
ma-105	477	28	:	:	PUNCT
ma-105	478	1			PROPN
ma-105	478	2	∂i	∂i	PROPN
ma-105	478	3	∂t	∂t	PROPN
ma-105	478	4	=	=	PUNCT
ma-105	478	5	d2∆i	d2∆i	VERB
ma-105	478	6	−	−	PROPN
ma-105	478	7	(	(	PUNCT
ma-105	478	8	α+	α+	X
ma-105	478	9	ρ)i	ρ)i	NOUN
ma-105	478	10	in	in	ADP
ma-105	478	11	ωt	ωt	PROPN
ma-105	478	12	,	,	PUNCT
ma-105	478	13	∂v	∂v	PROPN
ma-105	478	14	∂t	∂t	PROPN
ma-105	479	1	=	=	PUNCT
ma-105	479	2	d3∆v	d3∆v	NOUN
ma-105	479	3	+	+	X
ma-105	479	4	(	(	PUNCT
ma-105	479	5	1−	1−	NUM
ma-105	479	6	ε)ki	ε)ki	PROPN
ma-105	479	7	−	−	PROPN
ma-105	479	8	µv	µv	NOUN
ma-105	479	9	−	−	PROPN
ma-105	479	10	u(1−	u(1−	ADJ
ma-105	479	11	η)βλ	η)βλ	PROPN
ma-105	479	12	α0	α0	PROPN
ma-105	479	13	+	+	CCONJ
ma-105	479	14	α1λ	α1λ	PRON
ma-105	479	15	v	v	NOUN
ma-105	479	16	in	in	ADP
ma-105	479	17	ωt	ωt	PROPN
ma-105	479	18	,	,	PUNCT
ma-105	479	19	(	(	PUNCT
ma-105	479	20	4.3	4.3	NUM
ma-105	479	21	)	)	PUNCT
ma-105	479	22	i(x	i(x	PROPN
ma-105	479	23	,	,	PUNCT
ma-105	479	24	0	0	NUM
ma-105	479	25	)	)	PUNCT
ma-105	479	26	=	=	SYM
ma-105	479	27	ψ2(x	ψ2(x	PROPN
ma-105	479	28	)	)	PUNCT
ma-105	479	29	,	,	PUNCT
ma-105	479	30	v	v	NOUN
ma-105	479	31	(	(	PUNCT
ma-105	479	32	x	x	NOUN
ma-105	479	33	,	,	PUNCT
ma-105	479	34	0	0	NUM
ma-105	479	35	)	)	PUNCT
ma-105	479	36	=	=	SYM
ma-105	479	37	ψ3(x	ψ3(x	PROPN
ma-105	479	38	)	)	PUNCT
ma-105	479	39	,	,	PUNCT
ma-105	479	40	in	in	ADP
ma-105	479	41	ωt	ωt	ADP
ma-105	479	42	∂i	∂i	PROPN
ma-105	479	43	∂η	∂η	PROPN
ma-105	479	44	=	=	SYM
ma-105	479	45	∂v	∂v	PROPN
ma-105	479	46	∂η	∂η	PROPN
ma-105	480	1	=	=	NOUN
ma-105	480	2	0	0	NUM
ma-105	480	3	on	on	ADP
ma-105	480	4	∂ω	∂ω	PROPN
ma-105	480	5	.	.	PUNCT
ma-105	481	1	thus	thus	ADV
ma-105	481	2	,	,	PUNCT
ma-105	481	3	with	with	ADP
ma-105	481	4	initial	initial	ADJ
ma-105	481	5	infection	infection	NOUN
ma-105	481	6	ψ(x	ψ(x	NOUN
ma-105	481	7	)	)	PUNCT
ma-105	481	8	=	=	PUNCT
ma-105	481	9	(	(	PUNCT
ma-105	481	10	ψ2	ψ2	NOUN
ma-105	481	11	,	,	PUNCT
ma-105	481	12	ψ3	ψ3	NOUN
ma-105	481	13	)	)	PUNCT
ma-105	481	14	the	the	DET
ma-105	481	15	distribution	distribution	NOUN
ma-105	481	16	of	of	ADP
ma-105	481	17	those	those	DET
ma-105	481	18	infections	infection	NOUN
ma-105	481	19	members	member	NOUN
ma-105	481	20	becomes	become	VERB
ma-105	481	21	t	t	NOUN
ma-105	481	22	(	(	PUNCT
ma-105	481	23	t)ψ(x	t)ψ(x	NOUN
ma-105	481	24	)	)	PUNCT
ma-105	481	25	as	as	SCONJ
ma-105	481	26	time	time	NOUN
ma-105	481	27	evolves	evolve	VERB
ma-105	481	28	.	.	PUNCT
ma-105	482	1	therefore	therefore	ADV
ma-105	482	2	,	,	PUNCT
ma-105	482	3	the	the	DET
ma-105	482	4	distribution	distribution	NOUN
ma-105	482	5	of	of	ADP
ma-105	482	6	total	total	ADJ
ma-105	482	7	new	new	ADJ
ma-105	482	8	infections	infection	NOUN
ma-105	482	9	is∫	is∫	PROPN
ma-105	482	10	∞	∞	PROPN
ma-105	482	11	0	0	PUNCT
ma-105	482	12	f	f	PROPN
ma-105	482	13	(	(	PUNCT
ma-105	482	14	x)t	x)t	X
ma-105	482	15	(	(	PUNCT
ma-105	482	16	t)ψ(x)dt	t)ψ(x)dt	NOUN
ma-105	482	17	,	,	PUNCT
ma-105	482	18	then	then	ADV
ma-105	482	19	,	,	PUNCT
ma-105	482	20	we	we	PRON
ma-105	482	21	define	define	VERB
ma-105	482	22	l(φ)(x	l(φ)(x	PROPN
ma-105	482	23	)	)	PUNCT
ma-105	482	24	:	:	PUNCT
ma-105	483	1	=	=	SYM
ma-105	483	2	∫	∫	PROPN
ma-105	484	1	∞	∞	NUM
ma-105	484	2	0	0	NUM
ma-105	484	3	f	f	PROPN
ma-105	484	4	(	(	PUNCT
ma-105	484	5	x)t	x)t	X
ma-105	484	6	(	(	PUNCT
ma-105	484	7	t)ψ(x)dt	t)ψ(x)dt	NOUN
ma-105	484	8	=	=	SYM
ma-105	484	9	f	f	PROPN
ma-105	484	10	(	(	PUNCT
ma-105	484	11	x	x	X
ma-105	484	12	)	)	PUNCT
ma-105	484	13	∫	∫	PROPN
ma-105	484	14	∞	∞	PROPN
ma-105	484	15	0	0	PROPN
ma-105	484	16	t	t	PROPN
ma-105	484	17	(	(	PUNCT
ma-105	484	18	t)ψ(x)dt	t)ψ(x)dt	NOUN
ma-105	484	19	.	.	PUNCT
ma-105	485	1	l	l	NOUN
ma-105	485	2	is	be	AUX
ma-105	485	3	a	a	DET
ma-105	485	4	positive	positive	ADJ
ma-105	485	5	and	and	CCONJ
ma-105	485	6	continuous	continuous	ADJ
ma-105	485	7	operator	operator	NOUN
ma-105	485	8	which	which	PRON
ma-105	485	9	maps	map	VERB
ma-105	485	10	the	the	DET
ma-105	485	11	initial	initial	ADJ
ma-105	485	12	infection	infection	NOUN
ma-105	485	13	distribution	distribution	NOUN
ma-105	485	14	to	to	ADP
ma-105	485	15	the	the	DET
ma-105	485	16	distri	distri	NOUN
ma-105	485	17	-	-	NOUN
ma-105	485	18	bution	bution	NOUN
ma-105	485	19	of	of	ADP
ma-105	485	20	the	the	DET
ma-105	485	21	total	total	ADJ
ma-105	485	22	infective	infective	ADJ
ma-105	485	23	members	member	NOUN
ma-105	485	24	produced	produce	VERB
ma-105	485	25	during	during	ADP
ma-105	485	26	the	the	DET
ma-105	485	27	infection	infection	NOUN
ma-105	485	28	period	period	NOUN
ma-105	485	29	.	.	PUNCT
ma-105	486	1	applying	apply	VERB
ma-105	486	2	the	the	DET
ma-105	486	3	idea	idea	NOUN
ma-105	486	4	ofnext	ofnext	ADJ
ma-105	486	5	generation	generation	NOUN
ma-105	486	6	operators	operator	NOUN
ma-105	486	7	[	[	X
ma-105	486	8	40	40	NUM
ma-105	486	9	]	]	PUNCT
ma-105	486	10	,	,	PUNCT
ma-105	486	11	we	we	PRON
ma-105	486	12	define	define	VERB
ma-105	486	13	the	the	DET
ma-105	486	14	spectral	spectral	ADJ
ma-105	486	15	radius	radius	NOUN
ma-105	486	16	of	of	ADP
ma-105	486	17	l	l	NOUN
ma-105	486	18	as	as	ADP
ma-105	486	19	the	the	DET
ma-105	486	20	basic	basic	ADJ
ma-105	486	21	reproduction	reproduction	NOUN
ma-105	486	22	number	number	NOUN
ma-105	486	23	r0	r0	NOUN
ma-105	486	24	:	:	PUNCT
ma-105	486	25	=	=	SYM
ma-105	486	26	ρ(l	ρ(l	PROPN
ma-105	486	27	)	)	PUNCT
ma-105	486	28	.	.	PUNCT
ma-105	487	1	the	the	DET
ma-105	487	2	matrices	matrix	NOUN
ma-105	487	3	f	f	PROPN
ma-105	487	4	and	and	CCONJ
ma-105	487	5	v	v	PRON
ma-105	487	6	defined	define	VERB
ma-105	487	7	as	as	ADP
ma-105	487	8	f	f	PROPN
ma-105	487	9	(	(	PUNCT
ma-105	487	10	x	x	NOUN
ma-105	487	11	)	)	PUNCT
ma-105	487	12	=	=	SYM
ma-105	487	13			ADJ
ma-105	487	14	0	0	PUNCT
ma-105	488	1	(	(	PUNCT
ma-105	488	2	1−η)βλ	1−η)βλ	NUM
ma-105	488	3	α0+α1λ	α0+α1λ	NUM
ma-105	488	4	0	0	NUM
ma-105	488	5	0	0	NUM
ma-105	489	1			NOUN
ma-105	489	2	,	,	PUNCT
ma-105	489	3	v	v	NOUN
ma-105	489	4	(	(	PUNCT
ma-105	489	5	x	x	NOUN
ma-105	489	6	)	)	PUNCT
ma-105	489	7	=	=	SYM
ma-105	489	8			PROPN
ma-105	489	9	α+	α+	PUNCT
ma-105	489	10	ρ	ρ	NOUN
ma-105	489	11	0	0	NUM
ma-105	489	12	−(1−	−(1−	NOUN
ma-105	489	13	ε)k	ε)k	NOUN
ma-105	489	14	[	[	PUNCT
ma-105	489	15	µ+	µ+	X
ma-105	489	16	u	u	NOUN
ma-105	489	17	(	(	PUNCT
ma-105	489	18	1−η)βλ	1−η)βλ	NUM
ma-105	489	19	α0+α1λ	α0+α1λ	NUM
ma-105	489	20	]	]	PUNCT
ma-105	489	21			NOUN
ma-105	489	22	.	.	PUNCT
ma-105	490	1	then	then	ADV
ma-105	490	2	fv	fv	VERB
ma-105	490	3	−1	−1	NOUN
ma-105	491	1	=	=	PROPN
ma-105	492	1	α0	α0	ADJ
ma-105	492	2	+	+	CCONJ
ma-105	492	3	α1λ	α1λ	PRON
ma-105	492	4	(	(	PUNCT
ma-105	492	5	α+	α+	X
ma-105	492	6	ρ	ρ	NOUN
ma-105	492	7	)	)	PUNCT
ma-105	493	1	[	[	X
ma-105	493	2	µ(α0	µ(α0	ADV
ma-105	493	3	+	+	CCONJ
ma-105	493	4	α1λ	α1λ	NUM
ma-105	493	5	)	)	PUNCT
ma-105	493	6	+	+	CCONJ
ma-105	493	7	u(1−	u(1−	PROPN
ma-105	493	8	η)βλ	η)βλ	PROPN
ma-105	493	9	]	]	X
ma-105	493	10			NOUN
ma-105	493	11	(	(	PUNCT
ma-105	493	12	1−η)(1−ε)kβλ	1−η)(1−ε)kβλ	NUM
ma-105	493	13	α0+α1λ	α0+α1λ	NUM
ma-105	493	14	(	(	PUNCT
ma-105	493	15	α+ρ)(1−η)βλ	α+ρ)(1−η)βλ	X
ma-105	493	16	α0+α1λ	α0+α1λ	NOUN
ma-105	493	17	0	0	NUM
ma-105	493	18	0	0	NUM
ma-105	493	19			PRON
ma-105	493	20	.	.	PUNCT
ma-105	494	1	by	by	ADP
ma-105	494	2	[	[	X
ma-105	494	3	40	40	NUM
ma-105	494	4	]	]	PUNCT
ma-105	494	5	(	(	PUNCT
ma-105	494	6	theorem	theorem	VERB
ma-105	494	7	3.4	3.4	NUM
ma-105	494	8	)	)	PUNCT
ma-105	494	9	,	,	PUNCT
ma-105	494	10	one	one	PRON
ma-105	494	11	has	have	VERB
ma-105	494	12	r0	r0	NOUN
ma-105	494	13	=	=	SYM
ma-105	494	14	(	(	PUNCT
ma-105	494	15	1−	1−	NUM
ma-105	494	16	η)(1−	η)(1−	NUM
ma-105	494	17	ε)kβλ	ε)kβλ	PROPN
ma-105	494	18	(	(	PUNCT
ma-105	494	19	α+	α+	NOUN
ma-105	494	20	ρ	ρ	NOUN
ma-105	494	21	)	)	PUNCT
ma-105	495	1	[	[	X
ma-105	495	2	µ(α0	µ(α0	ADV
ma-105	495	3	+	+	CCONJ
ma-105	495	4	α1λ	α1λ	NUM
ma-105	495	5	)	)	PUNCT
ma-105	495	6	+	+	CCONJ
ma-105	495	7	u(1−	u(1−	PROPN
ma-105	495	8	η)βλ	η)βλ	PROPN
ma-105	495	9	]	]	PUNCT
ma-105	495	10	.	.	PUNCT
ma-105	496	1	(	(	PUNCT
ma-105	496	2	4.4	4.4	NUM
ma-105	496	3	)	)	PUNCT
ma-105	496	4	https://doi.org/10.28924/ada/ma.3.1	https://doi.org/10.28924/ada/ma.3.1	PROPN
ma-105	496	5	eur	eur	PROPN
ma-105	496	6	.	.	PUNCT
ma-105	497	1	j.	j.	PROPN
ma-105	497	2	math	math	PROPN
ma-105	497	3	.	.	PUNCT
ma-105	498	1	anal	anal	PROPN
ma-105	498	2	.	.	PUNCT
ma-105	499	1	10.28924	10.28924	NUM
ma-105	499	2	/	/	SYM
ma-105	499	3	ada	ada	PROPN
ma-105	499	4	/	/	SYM
ma-105	499	5	ma.3.1	ma.3.1	PROPN
ma-105	499	6	184.3	184.3	NUM
ma-105	499	7	.	.	PUNCT
ma-105	500	1	existence	existence	NOUN
ma-105	500	2	and	and	CCONJ
ma-105	500	3	uniqueness	uniqueness	NOUN
ma-105	500	4	of	of	ADP
ma-105	500	5	hcv	hcv	NOUN
ma-105	500	6	-	-	PUNCT
ma-105	500	7	spatial	spatial	ADJ
ma-105	500	8	homogeneous	homogeneous	ADJ
ma-105	500	9	infected	infected	ADJ
ma-105	500	10	equilibrium	equilibrium	NOUN
ma-105	500	11	e∗.	e∗.	NOUN
ma-105	500	12	in	in	ADP
ma-105	500	13	thissection	thissection	NOUN
ma-105	501	1	,	,	PUNCT
ma-105	501	2	we	we	PRON
ma-105	501	3	address	address	VERB
ma-105	501	4	the	the	DET
ma-105	501	5	existence	existence	NOUN
ma-105	501	6	and	and	CCONJ
ma-105	501	7	uniqueness	uniqueness	NOUN
ma-105	501	8	of	of	ADP
ma-105	501	9	infected	infect	VERB
ma-105	501	10	spatial	spatial	ADJ
ma-105	501	11	homogeneous	homogeneous	ADJ
ma-105	501	12	equilibrium(2.4	equilibrium(2.4	NOUN
ma-105	501	13	)	)	PUNCT
ma-105	501	14	.	.	PUNCT
ma-105	502	1	the	the	DET
ma-105	502	2	latter	latter	ADJ
ma-105	502	3	denoted	denote	VERB
ma-105	502	4	as	as	ADP
ma-105	502	5	e∗	e∗	NOUN
ma-105	502	6	=	=	SYM
ma-105	502	7	(	(	PUNCT
ma-105	502	8	h∗	h∗	PROPN
ma-105	502	9	,	,	PUNCT
ma-105	502	10	i∗	i∗	PROPN
ma-105	502	11	,	,	PUNCT
ma-105	502	12	v	v	NOUN
ma-105	502	13	∗	∗	NOUN
ma-105	502	14	)	)	PUNCT
ma-105	502	15	with	with	ADP
ma-105	502	16	h∗	h∗	PROPN
ma-105	502	17	6=	6=	PROPN
ma-105	502	18	0	0	NUM
ma-105	502	19	,	,	PUNCT
ma-105	502	20	i∗	i∗	NOUN
ma-105	502	21	6=	6=	ADP
ma-105	502	22	0	0	NUM
ma-105	502	23	et	et	NOUN
ma-105	502	24	v	v	ADP
ma-105	502	25	∗	∗	NOUN
ma-105	502	26	6=	6=	ADP
ma-105	502	27	0	0	NUM
ma-105	502	28	satisfying	satisfy	VERB
ma-105	502	29	thefollowing	thefollowe	VERB
ma-105	502	30	algebraic	algebraic	ADJ
ma-105	502	31	system	system	NOUN
ma-105	502	32	:	:	PUNCT
ma-105	502	33			PROPN
ma-105	502	34	λ−	λ−	PROPN
ma-105	502	35	dh∗	dh∗	NOUN
ma-105	502	36	−	−	PROPN
ma-105	502	37	(	(	PUNCT
ma-105	502	38	1−	1−	NUM
ma-105	502	39	η)l(h∗	η)l(h∗	NUM
ma-105	502	40	,	,	PUNCT
ma-105	502	41	i∗	i∗	NOUN
ma-105	502	42	,	,	PUNCT
ma-105	502	43	v	v	NOUN
ma-105	502	44	∗)v	∗)v	PROPN
ma-105	502	45	∗	∗	NOUN
ma-105	502	46	+	+	NOUN
ma-105	502	47	ρi∗	ρi∗	ADJ
ma-105	502	48	=	=	SYM
ma-105	502	49	0	0	NUM
ma-105	502	50	,	,	PUNCT
ma-105	502	51	(	(	PUNCT
ma-105	502	52	1−	1−	NUM
ma-105	502	53	η)l(h∗	η)l(h∗	NUM
ma-105	502	54	,	,	PUNCT
ma-105	502	55	i∗	i∗	NOUN
ma-105	502	56	,	,	PUNCT
ma-105	502	57	v	v	NOUN
ma-105	502	58	∗)v	∗)v	PROPN
ma-105	502	59	∗	∗	NOUN
ma-105	502	60	−	−	PROPN
ma-105	502	61	(	(	PUNCT
ma-105	502	62	α+	α+	NOUN
ma-105	502	63	ρ)i∗	ρ)i∗	NOUN
ma-105	502	64	=	=	SYM
ma-105	502	65	0	0	NUM
ma-105	502	66	,	,	PUNCT
ma-105	502	67	(	(	PUNCT
ma-105	502	68	1−	1−	NUM
ma-105	502	69	ε)ki∗	ε)ki∗	NOUN
ma-105	502	70	−	−	PROPN
ma-105	503	1	µv	µv	PROPN
ma-105	503	2	∗	∗	VERB
ma-105	503	3	−	−	PROPN
ma-105	504	1	u(1−	u(1−	PROPN
ma-105	504	2	η)l(h∗	η)l(h∗	PROPN
ma-105	504	3	,	,	PUNCT
ma-105	504	4	i∗	i∗	NOUN
ma-105	504	5	,	,	PUNCT
ma-105	504	6	v	v	NOUN
ma-105	504	7	∗)v	∗)v	PROPN
ma-105	504	8	∗	∗	NOUN
ma-105	504	9	=	=	SYM
ma-105	504	10	0	0	NUM
ma-105	504	11	,	,	PUNCT
ma-105	504	12	(	(	PUNCT
ma-105	504	13	4.5	4.5	NUM
ma-105	504	14	)	)	PUNCT
ma-105	504	15	where	where	SCONJ
ma-105	504	16	l(h	l(h	PROPN
ma-105	504	17	,	,	PUNCT
ma-105	504	18	i	i	PRON
ma-105	504	19	,	,	PUNCT
ma-105	504	20	v	v	NOUN
ma-105	504	21	)	)	PUNCT
ma-105	504	22	=	=	SYM
ma-105	505	1	βh	βh	ADP
ma-105	505	2	α0	α0	ADJ
ma-105	505	3	+	+	CCONJ
ma-105	505	4	α1h	α1h	PROPN
ma-105	505	5	+	+	SYM
ma-105	505	6	α2v	α2v	NOUN
ma-105	505	7	+	+	CCONJ
ma-105	505	8	α3hv	α3hv	NOUN
ma-105	505	9	.adding	.adde	VERB
ma-105	505	10	the	the	DET
ma-105	505	11	first	first	ADJ
ma-105	505	12	and	and	CCONJ
ma-105	505	13	second	second	ADJ
ma-105	505	14	equation	equation	NOUN
ma-105	505	15	of	of	ADP
ma-105	505	16	(	(	PUNCT
ma-105	505	17	4.5	4.5	NUM
ma-105	505	18	)	)	PUNCT
ma-105	505	19	,	,	PUNCT
ma-105	505	20	we	we	PRON
ma-105	505	21	have	have	VERB
ma-105	505	22	λ−	λ−	PROPN
ma-105	505	23	dh∗	dh∗	PROPN
ma-105	505	24	−	−	PROPN
ma-105	505	25	αi∗	αi∗	NOUN
ma-105	506	1	=	=	SYM
ma-105	506	2	0	0	NUM
ma-105	506	3	which	which	PRON
ma-105	506	4	yields	yield	VERB
ma-105	506	5	i∗	i∗	NOUN
ma-105	506	6	=	=	SYM
ma-105	506	7	λ−	λ−	PROPN
ma-105	506	8	dh∗	dh∗	NOUN
ma-105	506	9	α	α	X
ma-105	506	10	.	.	PUNCT
ma-105	507	1	(	(	PUNCT
ma-105	507	2	4.6)as	4.6)as	NUM
ma-105	507	3	far	far	ADV
ma-105	507	4	as	as	ADP
ma-105	507	5	,	,	PUNCT
ma-105	507	6	using	use	VERB
ma-105	507	7	the	the	DET
ma-105	507	8	second	second	ADJ
ma-105	507	9	and	and	CCONJ
ma-105	507	10	third	third	ADJ
ma-105	507	11	equation	equation	NOUN
ma-105	507	12	of	of	ADP
ma-105	507	13	(	(	PUNCT
ma-105	507	14	4.5	4.5	NUM
ma-105	507	15	)	)	PUNCT
ma-105	507	16	,	,	PUNCT
ma-105	507	17	one	one	PRON
ma-105	507	18	has	have	VERB
ma-105	507	19	−u(α+	−u(α+	DET
ma-105	507	20	ρ)i∗	ρ)i∗	PROPN
ma-105	507	21	+	+	CCONJ
ma-105	507	22	(	(	PUNCT
ma-105	507	23	1−	1−	NUM
ma-105	507	24	ε)ki∗	ε)ki∗	NOUN
ma-105	507	25	−	−	PROPN
ma-105	508	1	µv	µv	NOUN
ma-105	508	2	∗	∗	VERB
ma-105	508	3	=	=	SYM
ma-105	508	4	0	0	NUM
ma-105	508	5	,	,	PUNCT
ma-105	508	6	i.e.	i.e.	X
ma-105	508	7	,	,	PUNCT
ma-105	508	8	v	v	NOUN
ma-105	508	9	∗	∗	NOUN
ma-105	508	10	=	=	SYM
ma-105	508	11	(	(	PUNCT
ma-105	508	12	1−	1−	NUM
ma-105	508	13	ε)k	ε)k	NOUN
ma-105	508	14	−	−	PUNCT
ma-105	508	15	u(α+	u(α+	PROPN
ma-105	508	16	ρ	ρ	PROPN
ma-105	508	17	)	)	PUNCT
ma-105	508	18	µ	µ	PRON
ma-105	508	19	i∗	i∗	NOUN
ma-105	508	20	,	,	PUNCT
ma-105	508	21	hence	hence	ADV
ma-105	508	22	v	v	ADP
ma-105	508	23	∗	∗	NOUN
ma-105	508	24	=	=	SYM
ma-105	508	25	(	(	PUNCT
ma-105	508	26	1−	1−	NUM
ma-105	508	27	ε)k	ε)k	NOUN
ma-105	508	28	−	−	PUNCT
ma-105	508	29	u(α+	u(α+	PROPN
ma-105	508	30	ρ	ρ	PROPN
ma-105	508	31	)	)	PUNCT
ma-105	508	32	µ	µ	PROPN
ma-105	508	33	λ−	λ−	PROPN
ma-105	508	34	dh∗	dh∗	NOUN
ma-105	508	35	α	α	X
ma-105	508	36	(	(	PUNCT
ma-105	508	37	4.7	4.7	NUM
ma-105	508	38	)	)	PUNCT
ma-105	508	39	according	accord	VERB
ma-105	508	40	to	to	ADP
ma-105	508	41	(	(	PUNCT
ma-105	508	42	4.6	4.6	NUM
ma-105	508	43	)	)	PUNCT
ma-105	508	44	.	.	PUNCT
ma-105	509	1	the	the	DET
ma-105	509	2	substitution	substitution	NOUN
ma-105	509	3	of	of	ADP
ma-105	509	4	(	(	PUNCT
ma-105	509	5	4.7	4.7	NUM
ma-105	509	6	)	)	PUNCT
ma-105	509	7	in	in	ADP
ma-105	509	8	(	(	PUNCT
ma-105	509	9	4.5	4.5	NUM
ma-105	509	10	)	)	PUNCT
ma-105	509	11	yields	yield	NOUN
ma-105	509	12	:	:	PUNCT
ma-105	509	13	(	(	PUNCT
ma-105	509	14	1−	1−	NUM
ma-105	509	15	η)l	η)l	X
ma-105	509	16	(	(	PUNCT
ma-105	509	17	h∗	h∗	PROPN
ma-105	509	18	,	,	PUNCT
ma-105	509	19	λ−	λ−	PROPN
ma-105	509	20	dh∗	dh∗	PROPN
ma-105	509	21	α	α	PROPN
ma-105	509	22	,	,	PUNCT
ma-105	509	23	(	(	PUNCT
ma-105	509	24	1−	1−	NUM
ma-105	509	25	ε)k	ε)k	ADJ
ma-105	509	26	−	−	PUNCT
ma-105	509	27	u(α+	u(α+	PROPN
ma-105	509	28	ρ	ρ	PROPN
ma-105	509	29	)	)	PUNCT
ma-105	509	30	µ	µ	PROPN
ma-105	509	31	λ−	λ−	PROPN
ma-105	509	32	dh∗	dh∗	NOUN
ma-105	509	33	α	α	PROPN
ma-105	509	34	)	)	PUNCT
ma-105	509	35	(	(	PUNCT
ma-105	509	36	1−	1−	NUM
ma-105	509	37	ε)k	ε)k	NOUN
ma-105	509	38	−	−	PUNCT
ma-105	509	39	u(α+	u(α+	PROPN
ma-105	509	40	ρ	ρ	PROPN
ma-105	509	41	)	)	PUNCT
ma-105	509	42	µ	µ	PRON
ma-105	509	43	i∗	i∗	NOUN
ma-105	509	44	−	−	PROPN
ma-105	509	45	(	(	PUNCT
ma-105	509	46	α+	α+	NOUN
ma-105	509	47	ρ)i∗	ρ)i∗	NOUN
ma-105	509	48	=	=	SYM
ma-105	509	49	0	0	NUM
ma-105	509	50	.	.	PUNCT
ma-105	510	1	thus	thus	ADV
ma-105	510	2	,	,	PUNCT
ma-105	510	3	we	we	PRON
ma-105	510	4	have	have	VERB
ma-105	510	5	(	(	PUNCT
ma-105	510	6	1−	1−	NUM
ma-105	510	7	η	η	NOUN
ma-105	510	8	)	)	PUNCT
ma-105	510	9	(	(	PUNCT
ma-105	510	10	(	(	PUNCT
ma-105	510	11	1−	1−	NUM
ma-105	510	12	ε)k	ε)k	NOUN
ma-105	510	13	−	−	PUNCT
ma-105	510	14	u(α+	u(α+	PROPN
ma-105	510	15	ρ	ρ	PROPN
ma-105	510	16	)	)	PUNCT
ma-105	510	17	)	)	PUNCT
ma-105	511	1	l	l	NOUN
ma-105	511	2	(	(	PUNCT
ma-105	511	3	h∗	h∗	PROPN
ma-105	511	4	,	,	PUNCT
ma-105	511	5	λ−	λ−	PROPN
ma-105	511	6	dh∗	dh∗	PROPN
ma-105	511	7	α	α	PROPN
ma-105	511	8	,	,	PUNCT
ma-105	511	9	(	(	PUNCT
ma-105	511	10	1−	1−	NUM
ma-105	511	11	ε)k	ε)k	ADJ
ma-105	511	12	−	−	PUNCT
ma-105	511	13	u(α+	u(α+	PROPN
ma-105	511	14	ρ	ρ	PROPN
ma-105	511	15	)	)	PUNCT
ma-105	511	16	µ	µ	PROPN
ma-105	511	17	λ−	λ−	PROPN
ma-105	511	18	dh∗	dh∗	NOUN
ma-105	511	19	α	α	NOUN
ma-105	511	20	)	)	PUNCT
ma-105	511	21	=	=	PUNCT
ma-105	512	1	(	(	PUNCT
ma-105	512	2	α+	α+	NOUN
ma-105	512	3	ρ)µ	ρ)µ	NOUN
ma-105	512	4	since	since	SCONJ
ma-105	512	5	i∗	i∗	NOUN
ma-105	512	6	6=	6=	ADP
ma-105	512	7	0	0	NUM
ma-105	512	8	.	.	PUNCT
ma-105	513	1	furthermore	furthermore	ADV
ma-105	513	2	,	,	PUNCT
ma-105	513	3	i∗	i∗	NOUN
ma-105	513	4	≥	≥	NOUN
ma-105	513	5	0	0	NUM
ma-105	513	6	,	,	PUNCT
ma-105	513	7	gives	give	VERB
ma-105	513	8	λ−dh∗	λ−dh∗	PRON
ma-105	513	9	α	α	PRON
ma-105	513	10	≥	≥	NOUN
ma-105	513	11	0	0	NUM
ma-105	513	12	.	.	PUNCT
ma-105	514	1	thus	thus	ADV
ma-105	514	2	h∗	h∗	PROPN
ma-105	514	3	≤	≤	PROPN
ma-105	514	4	λ	λ	PROPN
ma-105	514	5	d	d	PROPN
ma-105	514	6	.	.	PUNCT
ma-105	515	1	hence	hence	ADV
ma-105	515	2	there	there	PRON
ma-105	515	3	is	be	VERB
ma-105	515	4	not	not	PART
ma-105	515	5	a	a	DET
ma-105	515	6	biologicalequilibrium	biologicalequilibrium	NOUN
ma-105	515	7	when	when	SCONJ
ma-105	515	8	h∗	h∗	PROPN
ma-105	515	9	>	>	X
ma-105	515	10	λ	λ	PROPN
ma-105	516	1	d	d	NOUN
ma-105	516	2	.let	.let	PUNCT
ma-105	516	3	us	we	PRON
ma-105	516	4	consider	consider	VERB
ma-105	516	5	the	the	DET
ma-105	516	6	function	function	NOUN
ma-105	516	7	ψ	ψ	PRON
ma-105	516	8	defined	define	VERB
ma-105	516	9	on	on	ADP
ma-105	516	10	[	[	X
ma-105	516	11	0	0	NUM
ma-105	516	12	,	,	PUNCT
ma-105	516	13	λd	λd	NOUN
ma-105	516	14	]	]	PUNCT
ma-105	516	15	by	by	ADP
ma-105	516	16	:	:	PUNCT
ma-105	516	17	ψ(x	ψ(x	NUM
ma-105	516	18	)	)	PUNCT
ma-105	516	19	=	=	PUNCT
ma-105	517	1	(	(	PUNCT
ma-105	517	2	1−	1−	NUM
ma-105	517	3	η)γl	η)γl	PROPN
ma-105	517	4	(	(	PUNCT
ma-105	517	5	x	x	X
ma-105	517	6	,	,	PUNCT
ma-105	517	7	λ−	λ−	PROPN
ma-105	517	8	dx	dx	PROPN
ma-105	517	9	α	α	PROPN
ma-105	517	10	,	,	PUNCT
ma-105	517	11	γ(λ−	γ(λ−	PROPN
ma-105	517	12	dx	dx	PROPN
ma-105	517	13	)	)	PUNCT
ma-105	517	14	µα	µα	ADP
ma-105	517	15	)	)	PUNCT
ma-105	517	16	−	−	PROPN
ma-105	517	17	(	(	PUNCT
ma-105	517	18	α+	α+	X
ma-105	517	19	ρ)µ	ρ)µ	NOUN
ma-105	517	20	,	,	PUNCT
ma-105	517	21	where	where	SCONJ
ma-105	517	22	γ	γ	X
ma-105	517	23	=	=	SYM
ma-105	517	24	(	(	PUNCT
ma-105	517	25	1−	1−	NUM
ma-105	517	26	ε)k	ε)k	NOUN
ma-105	517	27	−	−	PUNCT
ma-105	517	28	u(α+	u(α+	PROPN
ma-105	517	29	ρ	ρ	PROPN
ma-105	517	30	)	)	PUNCT
ma-105	517	31	.	.	PUNCT
ma-105	518	1	https://doi.org/10.28924/ada/ma.3.1	https://doi.org/10.28924/ada/ma.3.1	PROPN
ma-105	518	2	eur	eur	PROPN
ma-105	518	3	.	.	PUNCT
ma-105	519	1	j.	j.	PROPN
ma-105	519	2	math	math	PROPN
ma-105	519	3	.	.	PUNCT
ma-105	520	1	anal	anal	PROPN
ma-105	520	2	.	.	PUNCT
ma-105	521	1	10.28924	10.28924	NUM
ma-105	521	2	/	/	SYM
ma-105	521	3	ada	ada	PROPN
ma-105	521	4	/	/	SYM
ma-105	521	5	ma.3.1	ma.3.1	PROPN
ma-105	521	6	19we	19we	NOUN
ma-105	521	7	have	have	VERB
ma-105	521	8	ψ(0	ψ(0	NOUN
ma-105	521	9	)	)	PUNCT
ma-105	521	10	=	=	PUNCT
ma-105	522	1	−(α+	−(α+	INTJ
ma-105	522	2	ρ)µ	ρ)µ	ADJ
ma-105	522	3	<	<	X
ma-105	522	4	0	0	NUM
ma-105	522	5	and	and	CCONJ
ma-105	522	6	ψ	ψ	X
ma-105	522	7	(	(	PUNCT
ma-105	522	8	λ	λ	X
ma-105	522	9	d	d	NOUN
ma-105	522	10	)	)	PUNCT
ma-105	522	11	=	=	SYM
ma-105	522	12	(	(	PUNCT
ma-105	522	13	1−	1−	NUM
ma-105	522	14	η)γl	η)γl	PROPN
ma-105	522	15	(	(	PUNCT
ma-105	522	16	λ	λ	X
ma-105	522	17	d	d	PROPN
ma-105	522	18	,	,	PUNCT
ma-105	522	19	0	0	NUM
ma-105	522	20	,	,	PUNCT
ma-105	522	21	0	0	NUM
ma-105	522	22	)	)	PUNCT
ma-105	522	23	−	−	PROPN
ma-105	522	24	(	(	PUNCT
ma-105	522	25	α+	α+	X
ma-105	522	26	ρ)µ	ρ)µ	ADJ
ma-105	522	27	,	,	PUNCT
ma-105	522	28	=	=	SYM
ma-105	522	29	(	(	PUNCT
ma-105	522	30	1−	1−	NUM
ma-105	522	31	η	η	NOUN
ma-105	522	32	)	)	PUNCT
ma-105	523	1	[	[	X
ma-105	523	2	(	(	PUNCT
ma-105	523	3	1−	1−	NUM
ma-105	523	4	ε)k	ε)k	ADJ
ma-105	523	5	−	−	PUNCT
ma-105	523	6	u(α+	u(α+	PROPN
ma-105	523	7	ρ	ρ	PROPN
ma-105	523	8	)	)	PUNCT
ma-105	523	9	]	]	PUNCT
ma-105	524	1	βλ	βλ	PROPN
ma-105	524	2	α0	α0	VERB
ma-105	524	3	+	+	CCONJ
ma-105	524	4	α1λ	α1λ	PRON
ma-105	524	5	−	−	PROPN
ma-105	524	6	(	(	PUNCT
ma-105	524	7	α+	α+	X
ma-105	524	8	ρ)µ	ρ)µ	ADJ
ma-105	524	9	,	,	PUNCT
ma-105	524	10	=	=	SYM
ma-105	524	11	(	(	PUNCT
ma-105	524	12	1−	1−	NUM
ma-105	524	13	η)(1−	η)(1−	NUM
ma-105	524	14	ε)kβλ	ε)kβλ	PROPN
ma-105	524	15	α0	α0	VERB
ma-105	524	16	+	+	CCONJ
ma-105	524	17	α1λ	α1λ	PRON
ma-105	524	18	−	−	NOUN
ma-105	524	19	u(1−	u(1−	ADJ
ma-105	524	20	η)(α+	η)(α+	NOUN
ma-105	524	21	ρ)βλ	ρ)βλ	PROPN
ma-105	524	22	α0	α0	ADJ
ma-105	524	23	+	+	CCONJ
ma-105	524	24	α1λ	α1λ	PRON
ma-105	524	25	−	−	PROPN
ma-105	524	26	(	(	PUNCT
ma-105	524	27	α+	α+	X
ma-105	524	28	ρ)µ	ρ)µ	ADJ
ma-105	524	29	,	,	PUNCT
ma-105	524	30	=	=	SYM
ma-105	524	31	1	1	NUM
ma-105	524	32	α0	α0	ADJ
ma-105	524	33	+	+	PUNCT
ma-105	524	34	α1λ	α1λ	NUM
ma-105	524	35	[	[	X
ma-105	524	36	(	(	PUNCT
ma-105	524	37	1−	1−	NUM
ma-105	524	38	η)(1−	η)(1−	PROPN
ma-105	524	39	ε)kβλ−	ε)kβλ−	X
ma-105	524	40	µ(α+	µ(α+	X
ma-105	524	41	ρ)(α0	ρ)(α0	PROPN
ma-105	524	42	+	+	CCONJ
ma-105	524	43	α1λ)−	α1λ)−	PROPN
ma-105	524	44	u(1−	u(1−	PROPN
ma-105	524	45	η)(α+	η)(α+	PROPN
ma-105	524	46	ρ)βλ	ρ)βλ	PROPN
ma-105	524	47	]	]	PUNCT
ma-105	524	48	,	,	PUNCT
ma-105	524	49	=	=	SYM
ma-105	524	50	1	1	NUM
ma-105	524	51	α0	α0	ADJ
ma-105	524	52	+	+	PUNCT
ma-105	524	53	α1λ	α1λ	PRON
ma-105	524	54	[	[	PUNCT
ma-105	524	55	(	(	PUNCT
ma-105	524	56	1−	1−	NUM
ma-105	524	57	η)(1−	η)(1−	PROPN
ma-105	524	58	ε)kβλ−	ε)kβλ−	PROPN
ma-105	524	59	(	(	PUNCT
ma-105	524	60	α+	α+	X
ma-105	524	61	ρ	ρ	NOUN
ma-105	524	62	)	)	PUNCT
ma-105	525	1	[	[	X
ma-105	525	2	µ(α0	µ(α0	ADV
ma-105	525	3	+	+	CCONJ
ma-105	525	4	α1λ	α1λ	NUM
ma-105	525	5	)	)	PUNCT
ma-105	525	6	+	+	CCONJ
ma-105	525	7	u(1−	u(1−	PROPN
ma-105	525	8	η)βλ	η)βλ	PROPN
ma-105	525	9	]	]	X
ma-105	525	10	]	]	PUNCT
ma-105	525	11	,	,	PUNCT
ma-105	525	12	=	=	SYM
ma-105	525	13	(	(	PUNCT
ma-105	525	14	α+	α+	NOUN
ma-105	525	15	ρ	ρ	NOUN
ma-105	525	16	)	)	PUNCT
ma-105	526	1	[	[	X
ma-105	526	2	µ(α0	µ(α0	ADV
ma-105	526	3	+	+	CCONJ
ma-105	526	4	α1λ	α1λ	NUM
ma-105	526	5	)	)	PUNCT
ma-105	526	6	+	+	CCONJ
ma-105	526	7	u(1−	u(1−	PROPN
ma-105	526	8	η)βλ	η)βλ	PROPN
ma-105	526	9	]	]	X
ma-105	526	10	α0	α0	PROPN
ma-105	526	11	+	+	PUNCT
ma-105	526	12	α1λ	α1λ	PRON
ma-105	526	13	(	(	PUNCT
ma-105	526	14	r0	r0	NOUN
ma-105	526	15	−	−	PROPN
ma-105	526	16	1	1	NUM
ma-105	526	17	)	)	PUNCT
ma-105	526	18	,	,	PUNCT
ma-105	526	19	it	it	PRON
ma-105	526	20	follows	follow	VERB
ma-105	526	21	that	that	SCONJ
ma-105	526	22	ψ	ψ	X
ma-105	526	23	(	(	PUNCT
ma-105	526	24	λ	λ	X
ma-105	526	25	d	d	NOUN
ma-105	526	26	)	)	PUNCT
ma-105	526	27	=	=	SYM
ma-105	526	28	(	(	PUNCT
ma-105	526	29	α+	α+	NOUN
ma-105	526	30	ρ	ρ	NOUN
ma-105	526	31	)	)	PUNCT
ma-105	527	1	[	[	X
ma-105	527	2	µ(α0	µ(α0	ADV
ma-105	527	3	+	+	CCONJ
ma-105	527	4	α1λ	α1λ	NUM
ma-105	527	5	)	)	PUNCT
ma-105	527	6	+	+	CCONJ
ma-105	527	7	u(1−	u(1−	PROPN
ma-105	527	8	η)βλ	η)βλ	PROPN
ma-105	527	9	]	]	X
ma-105	527	10	α0	α0	PROPN
ma-105	527	11	+	+	PUNCT
ma-105	527	12	α1λ	α1λ	PRON
ma-105	527	13	(	(	PUNCT
ma-105	527	14	r0	r0	NOUN
ma-105	527	15	−	−	PROPN
ma-105	527	16	1	1	NUM
ma-105	527	17	)	)	PUNCT
ma-105	527	18	>	>	X
ma-105	527	19	0	0	PUNCT
ma-105	528	1	if	if	SCONJ
ma-105	528	2	and	and	CCONJ
ma-105	528	3	only	only	ADV
ma-105	528	4	if	if	SCONJ
ma-105	528	5	r0	r0	NOUN
ma-105	528	6	>	>	X
ma-105	528	7	1	1	X
ma-105	528	8	.	.	PUNCT
ma-105	529	1	moreover	moreover	ADV
ma-105	529	2	,	,	PUNCT
ma-105	529	3	letting	let	VERB
ma-105	529	4	y	y	PROPN
ma-105	529	5	=	=	PUNCT
ma-105	530	1	λ−	λ−	PROPN
ma-105	530	2	d.x	d.x	PROPN
ma-105	530	3	α	α	PROPN
ma-105	530	4	and	and	CCONJ
ma-105	530	5	z	z	NOUN
ma-105	530	6	=	=	SYM
ma-105	530	7	γ(λ−	γ(λ−	PROPN
ma-105	530	8	d.x	d.x	PROPN
ma-105	530	9	)	)	PUNCT
ma-105	530	10	µα	µα	ADP
ma-105	530	11	,	,	PUNCT
ma-105	530	12	we	we	PRON
ma-105	530	13	have	have	VERB
ma-105	530	14	ψ	ψ	X
ma-105	530	15	′	′	NUM
ma-105	530	16	(	(	PUNCT
ma-105	530	17	x	x	X
ma-105	530	18	)	)	PUNCT
ma-105	530	19	=	=	SYM
ma-105	530	20	(	(	PUNCT
ma-105	530	21	1−	1−	NUM
ma-105	530	22	η)γ	η)γ	PUNCT
ma-105	530	23	.	.	PUNCT
ma-105	531	1	d	d	X
ma-105	531	2	dx	dx	PROPN
ma-105	532	1	[	[	PUNCT
ma-105	532	2	l	l	X
ma-105	532	3	(	(	PUNCT
ma-105	532	4	x	x	X
ma-105	532	5	,	,	PUNCT
ma-105	532	6	λ−	λ−	PROPN
ma-105	532	7	dx	dx	PROPN
ma-105	532	8	α	α	PROPN
ma-105	532	9	,	,	PUNCT
ma-105	532	10	γ(λ−	γ(λ−	PROPN
ma-105	532	11	dx	dx	PROPN
ma-105	532	12	)	)	PUNCT
ma-105	532	13	µα	µα	ADP
ma-105	532	14	)	)	PUNCT
ma-105	532	15	−	−	PROPN
ma-105	532	16	(	(	PUNCT
ma-105	532	17	α+	α+	X
ma-105	532	18	ρ)µ	ρ)µ	NOUN
ma-105	532	19	]	]	PUNCT
ma-105	532	20	,	,	PUNCT
ma-105	532	21	=	=	SYM
ma-105	532	22	(	(	PUNCT
ma-105	532	23	1−	1−	NUM
ma-105	532	24	η)γ	η)γ	NUM
ma-105	532	25	(	(	PUNCT
ma-105	532	26	∂l	∂l	PROPN
ma-105	532	27	∂x	∂x	PROPN
ma-105	532	28	−	−	PROPN
ma-105	533	1	d	d	NOUN
ma-105	533	2	α	α	PRON
ma-105	533	3	∂l	∂l	NOUN
ma-105	533	4	∂y	∂y	NUM
ma-105	534	1	−	−	NOUN
ma-105	534	2	γd	γd	ADP
ma-105	534	3	µα	µα	ADP
ma-105	534	4	∂l	∂l	PROPN
ma-105	534	5	∂z	∂z	PROPN
ma-105	534	6	)	)	PUNCT
ma-105	534	7	,	,	PUNCT
ma-105	534	8	=	=	SYM
ma-105	534	9	(	(	PUNCT
ma-105	534	10	1−	1−	NUM
ma-105	534	11	η)γ	η)γ	NUM
ma-105	534	12	(	(	PUNCT
ma-105	534	13	∂l	∂l	PROPN
ma-105	534	14	∂x	∂x	PROPN
ma-105	534	15	−	−	PROPN
ma-105	535	1	d	d	NOUN
ma-105	535	2	α	α	NOUN
ma-105	535	3	∂l	∂l	NOUN
ma-105	535	4	∂x	∂x	NOUN
ma-105	535	5	∂x	∂x	PROPN
ma-105	535	6	∂y	∂y	NOUN
ma-105	535	7	−	−	NOUN
ma-105	535	8	γd	γd	ADP
ma-105	535	9	µα	µα	ADP
ma-105	535	10	∂l	∂l	PROPN
ma-105	535	11	∂x	∂x	PROPN
ma-105	535	12	∂x	∂x	PROPN
ma-105	535	13	∂z	∂z	PROPN
ma-105	535	14	)	)	PUNCT
ma-105	535	15	,	,	PUNCT
ma-105	535	16	=	=	SYM
ma-105	535	17	(	(	PUNCT
ma-105	535	18	1−	1−	NUM
ma-105	535	19	η)γ	η)γ	NUM
ma-105	535	20	(	(	PUNCT
ma-105	535	21	∂l	∂l	PROPN
ma-105	535	22	∂x	∂x	PROPN
ma-105	535	23	−	−	PROPN
ma-105	536	1	d	d	NOUN
ma-105	536	2	α	α	NOUN
ma-105	536	3	∂l	∂l	PROPN
ma-105	536	4	∂x	∂x	PROPN
ma-105	536	5	(	(	PUNCT
ma-105	536	6	−	−	PROPN
ma-105	536	7	α	α	PROPN
ma-105	536	8	d	d	NOUN
ma-105	536	9	)	)	PUNCT
ma-105	536	10	−	−	NOUN
ma-105	536	11	γd	γd	ADP
ma-105	536	12	µα	µα	ADP
ma-105	536	13	∂l	∂l	PROPN
ma-105	536	14	∂x	∂x	PROPN
ma-105	536	15	(	(	PUNCT
ma-105	536	16	−	−	PROPN
ma-105	536	17	µα	µα	ADP
ma-105	536	18	γd	γd	NOUN
ma-105	536	19	)	)	PUNCT
ma-105	536	20	)	)	PUNCT
ma-105	536	21	,	,	PUNCT
ma-105	537	1	=	=	SYM
ma-105	537	2	3(1−	3(1−	NUM
ma-105	537	3	η)γ	η)γ	PUNCT
ma-105	537	4	∂l	∂l	PROPN
ma-105	537	5	∂x	∂x	PROPN
ma-105	537	6	,	,	PUNCT
ma-105	537	7	=	=	SYM
ma-105	537	8	3(1−	3(1−	NUM
ma-105	537	9	η)γ	η)γ	PROPN
ma-105	537	10	βα0	βα0	PROPN
ma-105	538	1	+	+	CCONJ
ma-105	538	2	βα2v	βα2v	SYM
ma-105	538	3	(	(	PUNCT
ma-105	538	4	α0	α0	ADJ
ma-105	538	5	+	+	CCONJ
ma-105	538	6	(	(	PUNCT
ma-105	538	7	α1	α1	NOUN
ma-105	538	8	+	+	NUM
ma-105	538	9	α3v	α3v	NOUN
ma-105	538	10	)	)	PUNCT
ma-105	538	11	x	x	SYM
ma-105	539	1	+	+	NUM
ma-105	539	2	α2v	α2v	NOUN
ma-105	539	3	)	)	PUNCT
ma-105	539	4	2	2	NUM
ma-105	539	5	>	>	X
ma-105	539	6	0	0	PUNCT
ma-105	539	7	if	if	SCONJ
ma-105	539	8	γ	γ	X
ma-105	539	9	>	>	X
ma-105	539	10	0	0	NUM
ma-105	539	11	.	.	PUNCT
ma-105	540	1	therefore	therefore	ADV
ma-105	540	2	,	,	PUNCT
ma-105	540	3	if	if	SCONJ
ma-105	540	4	r0	r0	NOUN
ma-105	540	5	>	>	X
ma-105	540	6	1	1	NUM
ma-105	540	7	there	there	PRON
ma-105	540	8	exists	exist	VERB
ma-105	540	9	a	a	DET
ma-105	540	10	unique	unique	ADJ
ma-105	540	11	spatially	spatially	ADV
ma-105	540	12	homogeneous	homogeneous	ADJ
ma-105	540	13	infected	infected	ADJ
ma-105	540	14	equilibrium	equilibrium	NOUN
ma-105	540	15	e∗	e∗	NOUN
ma-105	540	16	=	=	SYM
ma-105	540	17	(	(	PUNCT
ma-105	540	18	h∗	h∗	PROPN
ma-105	540	19	,	,	PUNCT
ma-105	540	20	i∗	i∗	PROPN
ma-105	540	21	,	,	PUNCT
ma-105	540	22	v	v	NOUN
ma-105	540	23	∗	∗	NOUN
ma-105	540	24	)	)	PUNCT
ma-105	540	25	with	with	ADP
ma-105	540	26	h∗	h∗	PROPN
ma-105	540	27	∈	∈	PROPN
ma-105	540	28	(	(	PUNCT
ma-105	540	29	0	0	NUM
ma-105	540	30	,	,	PUNCT
ma-105	540	31	λd	λd	NOUN
ma-105	540	32	)	)	PUNCT
ma-105	540	33	,	,	PUNCT
ma-105	540	34	i∗	i∗	NOUN
ma-105	540	35	>	>	X
ma-105	540	36	0	0	PUNCT
ma-105	540	37	and	and	CCONJ
ma-105	540	38	v	v	ADP
ma-105	540	39	∗	∗	NOUN
ma-105	540	40	>	>	X
ma-105	541	1	0.the	0.the	DET
ma-105	541	2	previous	previous	ADJ
ma-105	541	3	investigations	investigation	NOUN
ma-105	541	4	can	can	AUX
ma-105	541	5	be	be	AUX
ma-105	541	6	summarized	summarize	VERB
ma-105	541	7	in	in	ADP
ma-105	541	8	the	the	DET
ma-105	541	9	following	follow	VERB
ma-105	541	10	theorem	theorem	NOUN
ma-105	541	11	:	:	PUNCT
ma-105	541	12	theorem	theorem	VERB
ma-105	541	13	4.1	4.1	NUM
ma-105	541	14	.	.	NOUN
ma-105	541	15	1	1	NUM
ma-105	541	16	)	)	PUNCT
ma-105	541	17	if	if	SCONJ
ma-105	541	18	r0	r0	VERB
ma-105	541	19	≤	≤	NOUN
ma-105	541	20	1	1	NUM
ma-105	541	21	,	,	PUNCT
ma-105	541	22	then	then	ADV
ma-105	541	23	the	the	DET
ma-105	541	24	pde	pde	NOUN
ma-105	541	25	-	-	PUNCT
ma-105	541	26	system	system	NOUN
ma-105	541	27	(	(	PUNCT
ma-105	541	28	2.4	2.4	NUM
ma-105	541	29	)	)	PUNCT
ma-105	541	30	admits	admit	VERB
ma-105	541	31	a	a	DET
ma-105	541	32	unique	unique	ADJ
ma-105	541	33	spatially	spatially	ADV
ma-105	541	34	homogeneous	homogeneous	ADJ
ma-105	541	35	uninfected	uninfected	ADJ
ma-105	541	36	equilibrium	equilibrium	NOUN
ma-105	541	37	e0	e0	PROPN
ma-105	541	38	=	=	PUNCT
ma-105	541	39	(	(	PUNCT
ma-105	541	40	λ	λ	X
ma-105	541	41	d	d	PROPN
ma-105	541	42	,	,	PUNCT
ma-105	541	43	0	0	NUM
ma-105	541	44	,	,	PUNCT
ma-105	541	45	0	0	NUM
ma-105	541	46	)	)	PUNCT
ma-105	541	47	.	.	PUNCT
ma-105	542	1	2	2	X
ma-105	542	2	)	)	PUNCT
ma-105	542	3	if	if	SCONJ
ma-105	542	4	r0	r0	NOUN
ma-105	542	5	>	>	X
ma-105	542	6	1	1	NUM
ma-105	542	7	and	and	CCONJ
ma-105	542	8	γ	γ	X
ma-105	542	9	>	>	X
ma-105	542	10	0	0	NUM
ma-105	542	11	,	,	PUNCT
ma-105	542	12	then	then	ADV
ma-105	542	13	the	the	DET
ma-105	542	14	pde	pde	NOUN
ma-105	542	15	system	system	NOUN
ma-105	542	16	(	(	PUNCT
ma-105	542	17	2.4	2.4	NUM
ma-105	542	18	)	)	PUNCT
ma-105	542	19	admits	admit	VERB
ma-105	542	20	a	a	DET
ma-105	542	21	unique	unique	ADJ
ma-105	542	22	spatially	spatially	ADV
ma-105	542	23	homogeneous	homogeneous	ADJ
ma-105	542	24	infected	infected	ADJ
ma-105	542	25	equilibrium	equilibrium	NOUN
ma-105	542	26	e∗	e∗	NOUN
ma-105	542	27	=	=	SYM
ma-105	542	28	(	(	PUNCT
ma-105	542	29	h∗	h∗	PROPN
ma-105	542	30	,	,	PUNCT
ma-105	542	31	i∗	i∗	PROPN
ma-105	542	32	,	,	PUNCT
ma-105	542	33	v	v	NOUN
ma-105	542	34	∗	∗	NOUN
ma-105	542	35	)	)	PUNCT
ma-105	542	36	with	with	ADP
ma-105	542	37	h∗	h∗	PROPN
ma-105	542	38	∈	∈	PROPN
ma-105	542	39	(	(	PUNCT
ma-105	542	40	0	0	NUM
ma-105	542	41	,	,	PUNCT
ma-105	542	42	λd	λd	NOUN
ma-105	542	43	)	)	PUNCT
ma-105	542	44	,	,	PUNCT
ma-105	542	45	i∗	i∗	NOUN
ma-105	542	46	>	>	X
ma-105	542	47	0	0	PUNCT
ma-105	542	48	and	and	CCONJ
ma-105	542	49	v	v	ADP
ma-105	542	50	∗	∗	NOUN
ma-105	542	51	>	>	X
ma-105	542	52	0	0	NUM
ma-105	542	53	.	.	PUNCT
ma-105	543	1	https://doi.org/10.28924/ada/ma.3.1	https://doi.org/10.28924/ada/ma.3.1	PROPN
ma-105	543	2	eur	eur	PROPN
ma-105	543	3	.	.	PUNCT
ma-105	544	1	j.	j.	PROPN
ma-105	544	2	math	math	PROPN
ma-105	544	3	.	.	PUNCT
ma-105	545	1	anal	anal	PROPN
ma-105	545	2	.	.	PUNCT
ma-105	546	1	10.28924	10.28924	NUM
ma-105	546	2	/	/	SYM
ma-105	546	3	ada	ada	PROPN
ma-105	546	4	/	/	SYM
ma-105	546	5	ma.3.1	ma.3.1	PROPN
ma-105	546	6	20	20	NUM
ma-105	546	7	remark	remark	NOUN
ma-105	546	8	4.1	4.1	NUM
ma-105	546	9	.	.	PUNCT
ma-105	547	1	due	due	ADP
ma-105	547	2	to	to	ADP
ma-105	547	3	the	the	DET
ma-105	547	4	spatial	spatial	ADJ
ma-105	547	5	dependence	dependence	NOUN
ma-105	547	6	of	of	ADP
ma-105	547	7	the	the	DET
ma-105	547	8	state	state	NOUN
ma-105	547	9	variables	variable	NOUN
ma-105	547	10	,	,	PUNCT
ma-105	547	11	spatially	spatially	ADV
ma-105	547	12	-	-	PUNCT
ma-105	547	13	inhomogeneous	inhomogeneous	ADJ
ma-105	547	14	steadystates	steadystate	NOUN
ma-105	547	15	can	can	AUX
ma-105	547	16	exist.indeed	exist.indeed	VERB
ma-105	547	17	,	,	PUNCT
ma-105	547	18	any	any	DET
ma-105	547	19	spatially	spatially	ADV
ma-105	547	20	-	-	PUNCT
ma-105	547	21	inhomogeneous	inhomogeneous	ADJ
ma-105	547	22	equilibrium	equilibrium	NOUN
ma-105	547	23	point	point	NOUN
ma-105	547	24	e	e	X
ma-105	548	1	=	=	PUNCT
ma-105	548	2	(	(	PUNCT
ma-105	548	3	h	h	NOUN
ma-105	548	4	,	,	PUNCT
ma-105	548	5	i	i	PRON
ma-105	548	6	,	,	PUNCT
ma-105	548	7	v	v	NOUN
ma-105	548	8	)	)	PUNCT
ma-105	548	9	of	of	ADP
ma-105	548	10	the	the	DET
ma-105	548	11	model	model	NOUN
ma-105	548	12	(	(	PUNCT
ma-105	548	13	2.4	2.4	NUM
ma-105	548	14	)	)	PUNCT
ma-105	548	15	subjectto	subjectto	VERB
ma-105	548	16	the	the	DET
ma-105	548	17	homogeneous	homogeneous	ADJ
ma-105	548	18	neumann	neumann	PROPN
ma-105	548	19	boundary	boundary	PROPN
ma-105	548	20	condition	condition	NOUN
ma-105	548	21	must	must	AUX
ma-105	548	22	solve	solve	VERB
ma-105	548	23	the	the	DET
ma-105	548	24	following	follow	VERB
ma-105	548	25	system.	system.	PROPN
ma-105	548	26	d1∆h	d1∆h	PROPN
ma-105	549	1	+	+	CCONJ
ma-105	549	2	λ−	λ−	PROPN
ma-105	549	3	dh	dh	NOUN
ma-105	549	4	−	−	PROPN
ma-105	549	5	(	(	PUNCT
ma-105	549	6	1−	1−	NUM
ma-105	549	7	η)βhv	η)βhv	PROPN
ma-105	549	8	α0	α0	PROPN
ma-105	549	9	+	+	CCONJ
ma-105	550	1	α1h	α1h	PROPN
ma-105	550	2	+	+	SYM
ma-105	550	3	α2v	α2v	NUM
ma-105	550	4	+	+	CCONJ
ma-105	550	5	α3hv	α3hv	NOUN
ma-105	551	1	+	+	CCONJ
ma-105	551	2	ρi	ρi	NOUN
ma-105	551	3	=	=	SYM
ma-105	551	4	0	0	NUM
ma-105	551	5	,	,	PUNCT
ma-105	551	6	d2∆i	d2∆i	VERB
ma-105	551	7	+	+	CCONJ
ma-105	551	8	(	(	PUNCT
ma-105	551	9	1−	1−	NUM
ma-105	551	10	η)βhv	η)βhv	PROPN
ma-105	551	11	α0	α0	PROPN
ma-105	551	12	+	+	CCONJ
ma-105	551	13	α1h	α1h	PROPN
ma-105	551	14	+	+	SYM
ma-105	551	15	α2v	α2v	NUM
ma-105	551	16	+	+	CCONJ
ma-105	551	17	α3hv	α3hv	NUM
ma-105	551	18	−	−	NOUN
ma-105	551	19	(	(	PUNCT
ma-105	551	20	α+	α+	NOUN
ma-105	551	21	ρ)i	ρ)i	NOUN
ma-105	552	1	=	=	SYM
ma-105	552	2	0	0	NUM
ma-105	552	3	,	,	PUNCT
ma-105	552	4	d3∆v	d3∆v	X
ma-105	552	5	+	+	X
ma-105	552	6	(	(	PUNCT
ma-105	552	7	1−	1−	NUM
ma-105	552	8	ε)ki	ε)ki	PROPN
ma-105	552	9	−	−	PROPN
ma-105	552	10	µv	µv	NOUN
ma-105	552	11	−	−	PROPN
ma-105	552	12	u(1−	u(1−	ADJ
ma-105	552	13	η)βhv	η)βhv	PROPN
ma-105	552	14	α0	α0	PROPN
ma-105	552	15	+	+	CCONJ
ma-105	553	1	α1h	α1h	PROPN
ma-105	553	2	+	+	SYM
ma-105	553	3	α2v	α2v	NUM
ma-105	553	4	+	+	CCONJ
ma-105	553	5	α3hv	α3hv	NOUN
ma-105	553	6	=	=	SYM
ma-105	553	7	0	0	NUM
ma-105	553	8	,	,	PUNCT
ma-105	553	9	(	(	PUNCT
ma-105	553	10	4.8	4.8	NUM
ma-105	553	11	)	)	PUNCT
ma-105	554	1	∂h	∂h	PROPN
ma-105	554	2	∂η	∂η	PROPN
ma-105	555	1	=	=	PUNCT
ma-105	555	2	∂i	∂i	PROPN
ma-105	555	3	∂η	∂η	PROPN
ma-105	555	4	=	=	SYM
ma-105	555	5	∂v	∂v	PROPN
ma-105	555	6	∂η	∂η	PROPN
ma-105	555	7	=	=	NOUN
ma-105	555	8	0	0	PROPN
ma-105	555	9	.	.	PUNCT
ma-105	555	10	investigation	investigation	NOUN
ma-105	555	11	of	of	ADP
ma-105	555	12	the	the	DET
ma-105	555	13	local	local	ADJ
ma-105	555	14	stability	stability	NOUN
ma-105	555	15	of	of	ADP
ma-105	555	16	such	such	ADJ
ma-105	555	17	spatially	spatially	ADV
ma-105	555	18	-	-	PUNCT
ma-105	555	19	inhomogeneous	inhomogeneous	ADJ
ma-105	555	20	equilibria	equilibrium	NOUN
ma-105	555	21	will	will	AUX
ma-105	555	22	be	be	AUX
ma-105	555	23	the	the	DET
ma-105	555	24	concernof	concernof	NOUN
ma-105	555	25	a	a	DET
ma-105	555	26	forthcoming	forthcoming	ADJ
ma-105	555	27	paper	paper	NOUN
ma-105	555	28	via	via	ADP
ma-105	555	29	an	an	DET
ma-105	555	30	in	in	ADP
ma-105	555	31	-	-	PUNCT
ma-105	555	32	depth	depth	NOUN
ma-105	555	33	analysis	analysis	NOUN
ma-105	555	34	of	of	ADP
ma-105	555	35	the	the	DET
ma-105	555	36	above	above	ADJ
ma-105	555	37	system	system	NOUN
ma-105	555	38	.	.	PUNCT
ma-105	556	1	4.4	4.4	NUM
ma-105	556	2	.	.	PUNCT
ma-105	557	1	local	local	ADJ
ma-105	557	2	stability	stability	NOUN
ma-105	557	3	of	of	ADP
ma-105	557	4	hcv	hcv	NOUN
ma-105	557	5	-	-	PUNCT
ma-105	557	6	uninfected	uninfected	ADJ
ma-105	557	7	equilibrium	equilibrium	NOUN
ma-105	557	8	.	.	PUNCT
ma-105	558	1	the	the	DET
ma-105	558	2	objective	objective	NOUN
ma-105	558	3	of	of	ADP
ma-105	558	4	this	this	DET
ma-105	558	5	section	section	NOUN
ma-105	558	6	is	be	AUX
ma-105	558	7	to	to	PART
ma-105	558	8	discuss	discuss	VERB
ma-105	558	9	thelocal	thelocal	ADJ
ma-105	558	10	stability	stability	NOUN
ma-105	558	11	of	of	ADP
ma-105	558	12	the	the	DET
ma-105	558	13	spatially	spatially	ADV
ma-105	558	14	homogeneous	homogeneous	ADJ
ma-105	558	15	uninfected	uninfected	ADJ
ma-105	558	16	equilibrium	equilibrium	NOUN
ma-105	558	17	for	for	ADP
ma-105	558	18	the	the	DET
ma-105	558	19	pde	pde	NOUN
ma-105	558	20	system	system	NOUN
ma-105	558	21	(	(	PUNCT
ma-105	558	22	2.4	2.4	NUM
ma-105	558	23	)	)	PUNCT
ma-105	558	24	.	.	PUNCT
ma-105	559	1	weaddress	weaddress	PROPN
ma-105	559	2	local	local	ADJ
ma-105	559	3	stability	stability	NOUN
ma-105	559	4	by	by	ADP
ma-105	559	5	analysing	analyse	VERB
ma-105	559	6	the	the	DET
ma-105	559	7	characteristic	characteristic	ADJ
ma-105	559	8	equation	equation	NOUN
ma-105	559	9	.	.	PUNCT
ma-105	560	1	theorem	theorem	VERB
ma-105	560	2	4.2	4.2	NUM
ma-105	560	3	.	.	PUNCT
ma-105	561	1	the	the	DET
ma-105	561	2	spatially	spatially	ADV
ma-105	561	3	homogeneous	homogeneous	ADJ
ma-105	561	4	uninfected	uninfected	ADJ
ma-105	561	5	equilibrium	equilibrium	NOUN
ma-105	561	6	e0	e0	PROPN
ma-105	561	7	of	of	ADP
ma-105	561	8	pde	pde	NOUN
ma-105	561	9	-	-	PUNCT
ma-105	561	10	model	model	NOUN
ma-105	561	11	system	system	NOUN
ma-105	561	12	(	(	PUNCT
ma-105	561	13	2.4	2.4	NUM
ma-105	561	14	)	)	PUNCT
ma-105	561	15	is	be	AUX
ma-105	561	16	locally	locally	ADV
ma-105	561	17	asymptotically	asymptotically	ADV
ma-105	561	18	stable	stable	ADJ
ma-105	561	19	if	if	SCONJ
ma-105	561	20	r0	r0	NOUN
ma-105	561	21	≤	≤	NOUN
ma-105	561	22	1	1	NUM
ma-105	562	1	and	and	CCONJ
ma-105	562	2	it	it	PRON
ma-105	562	3	is	be	AUX
ma-105	562	4	unstable	unstable	ADJ
ma-105	562	5	if	if	SCONJ
ma-105	562	6	r0	r0	NOUN
ma-105	562	7	>	>	X
ma-105	562	8	1	1	X
ma-105	562	9	.	.	PUNCT
ma-105	562	10	proof	proof	NOUN
ma-105	562	11	.	.	PUNCT
ma-105	563	1	let	let	VERB
ma-105	563	2	{	{	PUNCT
ma-105	563	3	µl	µl	AUX
ma-105	563	4	,	,	PUNCT
ma-105	563	5	ϕl	ϕl	AUX
ma-105	563	6	}	}	PUNCT
ma-105	563	7	be	be	AUX
ma-105	563	8	an	an	DET
ma-105	563	9	eigenpair	eigenpair	NOUN
ma-105	563	10	of	of	ADP
ma-105	563	11	the	the	DET
ma-105	563	12	laplace	laplace	NOUN
ma-105	563	13	operator	operator	NOUN
ma-105	563	14	−∆	−∆	NOUN
ma-105	563	15	on	on	ADP
ma-105	563	16	ω	ω	PROPN
ma-105	563	17	with	with	ADP
ma-105	563	18	the	the	DET
ma-105	563	19	homogeneous	homogeneous	PROPN
ma-105	563	20	neu	neu	PROPN
ma-105	563	21	-	-	PUNCT
ma-105	563	22	mann	mann	PROPN
ma-105	563	23	boundary	boundary	ADJ
ma-105	563	24	condition	condition	NOUN
ma-105	563	25	where	where	SCONJ
ma-105	563	26	0	0	NUM
ma-105	563	27	=	=	SYM
ma-105	563	28	µ1	µ1	PROPN
ma-105	563	29	<	<	X
ma-105	563	30	µ2	µ2	PROPN
ma-105	563	31	<	<	X
ma-105	563	32	µ3	µ3	PROPN
ma-105	563	33	<	<	X
ma-105	563	34	·	·	PUNCT
ma-105	563	35	·	·	PUNCT
ma-105	563	36	·	·	PUNCT
ma-105	563	37	.	.	PUNCT
ma-105	564	1	let	let	VERB
ma-105	564	2	eµl	eµl	NOUN
ma-105	564	3	be	be	AUX
ma-105	564	4	the	the	DET
ma-105	564	5	eigenspace	eigenspace	NOUN
ma-105	564	6	correspondingto	correspondingto	NOUN
ma-105	564	7	µl	µl	ADP
ma-105	564	8	in	in	ADP
ma-105	564	9	c1(ω	c1(ω	NOUN
ma-105	564	10	)	)	PUNCT
ma-105	564	11	and	and	CCONJ
ma-105	564	12	{	{	PUNCT
ma-105	564	13	ϕl	ϕl	INTJ
ma-105	564	14	j	j	PROPN
ma-105	564	15	,	,	PUNCT
ma-105	564	16	j	j	PROPN
ma-105	564	17	=	=	SYM
ma-105	564	18	1	1	NUM
ma-105	564	19	,	,	PUNCT
ma-105	564	20	2	2	NUM
ma-105	564	21	,	,	PUNCT
ma-105	564	22	·	·	PUNCT
ma-105	564	23	·	·	PUNCT
ma-105	564	24	·	·	PUNCT
ma-105	564	25	,	,	PUNCT
ma-105	564	26	dimeµl	dimeµl	PROPN
ma-105	564	27	}	}	PUNCT
ma-105	564	28	be	be	AUX
ma-105	564	29	an	an	DET
ma-105	564	30	orthogonal	orthogonal	ADJ
ma-105	564	31	basis	basis	NOUN
ma-105	564	32	of	of	ADP
ma-105	564	33	eµl	eµl	NOUN
ma-105	564	34	.	.	PUNCT
ma-105	565	1	let	let	VERB
ma-105	565	2	x	x	PUNCT
ma-105	565	3	=	=	PUNCT
ma-105	565	4	(	(	PUNCT
ma-105	565	5	c1(ω))3and	c1(ω))3and	NUM
ma-105	565	6	xl	xl	PROPN
ma-105	565	7	j	j	PROPN
ma-105	566	1	=	=	PRON
ma-105	566	2	{	{	PUNCT
ma-105	566	3	ϕl	ϕl	PROPN
ma-105	566	4	jc	jc	PROPN
ma-105	566	5	,	,	PUNCT
ma-105	566	6	/	/	SYM
ma-105	566	7	c	c	NOUN
ma-105	566	8	∈	∈	PROPN
ma-105	566	9	r3}.consider	r3}.consider	NOUN
ma-105	566	10	the	the	DET
ma-105	566	11	following	follow	VERB
ma-105	566	12	direct	direct	ADJ
ma-105	566	13	sum	sum	NOUN
ma-105	566	14	x	x	PUNCT
ma-105	566	15	=	=	PUNCT
ma-105	566	16	∞⊕	∞⊕	PROPN
ma-105	567	1	l=1	l=1	X
ma-105	567	2	xl	xl	INTJ
ma-105	567	3	with	with	ADP
ma-105	567	4	xl	xl	PROPN
ma-105	567	5	=	=	PUNCT
ma-105	568	1	dimeµl⊕	dimeµl⊕	NOUN
ma-105	568	2	j=1	j=1	PROPN
ma-105	568	3	xl	xl	PROPN
ma-105	568	4	j	j	PROPN
ma-105	568	5	,	,	PUNCT
ma-105	568	6	where	where	SCONJ
ma-105	568	7	xl	xl	PROPN
ma-105	568	8	j	j	PROPN
ma-105	568	9	is	be	AUX
ma-105	568	10	the	the	DET
ma-105	568	11	eigenspace	eigenspace	NOUN
ma-105	568	12	corresponding	correspond	VERB
ma-105	568	13	to	to	AUX
ma-105	568	14	µl	µl	VERB
ma-105	568	15	.	.	PUNCT
ma-105	569	1	linearizing	linearize	VERB
ma-105	569	2	(	(	PUNCT
ma-105	569	3	2.4	2.4	NUM
ma-105	569	4	)	)	PUNCT
ma-105	569	5	at	at	ADP
ma-105	569	6	the	the	DET
ma-105	569	7	spatially	spatially	ADV
ma-105	569	8	homogeneousuninfected	homogeneousuninfecte	VERB
ma-105	569	9	equilibrium	equilibrium	NOUN
ma-105	569	10	e0	e0	PROPN
ma-105	569	11	we	we	PRON
ma-105	569	12	obtain	obtain	VERB
ma-105	569	13	the	the	DET
ma-105	569	14	following	follow	VERB
ma-105	569	15	linearized	linearize	VERB
ma-105	569	16	system	system	NOUN
ma-105	569	17	:	:	PUNCT
ma-105	569	18			PROPN
ma-105	570	1	∂w1	∂w1	PROPN
ma-105	570	2	∂t	∂t	PROPN
ma-105	571	1	=	=	PUNCT
ma-105	572	1	d1∆w1	d1∆w1	PROPN
ma-105	572	2	−	−	PROPN
ma-105	572	3	dw1	dw1	NOUN
ma-105	573	1	+	+	CCONJ
ma-105	574	1	ρw2	ρw2	NOUN
ma-105	574	2	−	−	PROPN
ma-105	574	3	(	(	PUNCT
ma-105	574	4	1−	1−	NUM
ma-105	574	5	η)βλ	η)βλ	PROPN
ma-105	575	1	α0	α0	ADJ
ma-105	575	2	+	+	CCONJ
ma-105	575	3	α1λ	α1λ	NUM
ma-105	575	4	w3	w3	NOUN
ma-105	575	5	,	,	PUNCT
ma-105	576	1	∂w2	∂w2	PROPN
ma-105	576	2	∂t	∂t	PROPN
ma-105	576	3	=	=	PUNCT
ma-105	576	4	d2∆w2	d2∆w2	PROPN
ma-105	576	5	−	−	PROPN
ma-105	576	6	(	(	PUNCT
ma-105	576	7	α+	α+	PROPN
ma-105	576	8	ρ)w2	ρ)w2	PROPN
ma-105	576	9	+	+	CCONJ
ma-105	576	10	(	(	PUNCT
ma-105	576	11	1−	1−	NUM
ma-105	576	12	η)βλ	η)βλ	PROPN
ma-105	576	13	α0	α0	ADJ
ma-105	576	14	+	+	CCONJ
ma-105	576	15	α1λ	α1λ	NUM
ma-105	576	16	w3	w3	NOUN
ma-105	576	17	,	,	PUNCT
ma-105	576	18	(	(	PUNCT
ma-105	576	19	4.9	4.9	NUM
ma-105	576	20	)	)	PUNCT
ma-105	577	1	∂w3	∂w3	PROPN
ma-105	577	2	∂t	∂t	PROPN
ma-105	577	3	=	=	SYM
ma-105	577	4	d3∆w3	d3∆w3	PROPN
ma-105	577	5	+	+	CCONJ
ma-105	577	6	(	(	PUNCT
ma-105	577	7	1−	1−	NUM
ma-105	577	8	ε)kw2	ε)kw2	NOUN
ma-105	577	9	−	−	PROPN
ma-105	577	10	[	[	PUNCT
ma-105	577	11	µ+	µ+	PROPN
ma-105	577	12	u	u	NOUN
ma-105	577	13	(	(	PUNCT
ma-105	577	14	1−	1−	NUM
ma-105	577	15	η)βλ	η)βλ	PROPN
ma-105	578	1	α0	α0	ADJ
ma-105	578	2	+	+	CCONJ
ma-105	578	3	α1λ	α1λ	DET
ma-105	578	4	]	]	PUNCT
ma-105	578	5	w3	w3	PROPN
ma-105	578	6	,	,	PUNCT
ma-105	578	7	https://doi.org/10.28924/ada/ma.3.1	https://doi.org/10.28924/ada/ma.3.1	PROPN
ma-105	578	8	eur	eur	PROPN
ma-105	578	9	.	.	PUNCT
ma-105	579	1	j.	j.	PROPN
ma-105	579	2	math	math	PROPN
ma-105	579	3	.	.	PUNCT
ma-105	580	1	anal	anal	PROPN
ma-105	580	2	.	.	PUNCT
ma-105	581	1	10.28924	10.28924	NUM
ma-105	581	2	/	/	SYM
ma-105	581	3	ada	ada	PROPN
ma-105	581	4	/	/	SYM
ma-105	581	5	ma.3.1	ma.3.1	PROPN
ma-105	581	6	21where	21where	X
ma-105	582	1	w	w	NOUN
ma-105	582	2	=	=	SYM
ma-105	582	3	(	(	PUNCT
ma-105	582	4	w1	w1	NOUN
ma-105	582	5	,	,	PUNCT
ma-105	582	6	w2	w2	NOUN
ma-105	582	7	,	,	PUNCT
ma-105	582	8	w3)t	w3)t	NOUN
ma-105	582	9	=	=	SYM
ma-105	582	10	(	(	PUNCT
ma-105	582	11	h	h	NOUN
ma-105	582	12	,	,	PUNCT
ma-105	582	13	i	i	PRON
ma-105	582	14	,	,	PUNCT
ma-105	582	15	v	v	NOUN
ma-105	582	16	)	)	PUNCT
ma-105	582	17	t	t	NOUN
ma-105	582	18	.from	.from	ADP
ma-105	582	19	the	the	DET
ma-105	582	20	previous	previous	ADJ
ma-105	582	21	system	system	NOUN
ma-105	582	22	(	(	PUNCT
ma-105	582	23	4.9	4.9	NUM
ma-105	582	24	)	)	PUNCT
ma-105	582	25	,	,	PUNCT
ma-105	582	26	we	we	PRON
ma-105	582	27	obtain	obtain	VERB
ma-105	582	28	wt	wt	NOUN
ma-105	582	29	=	=	PUNCT
ma-105	582	30	lw	lw	NOUN
ma-105	582	31	=	=	PUNCT
ma-105	582	32	d∆w	d∆w	PROPN
ma-105	583	1	+	+	PUNCT
ma-105	583	2	k(e0)w	k(e0)w	PROPN
ma-105	583	3	where	where	SCONJ
ma-105	583	4	k(e0)w	k(e0)w	PROPN
ma-105	583	5	=	=	PRON
ma-105	583	6			PROPN
ma-105	584	1	−dw1	−dw1	NOUN
ma-105	585	1	+	+	PUNCT
ma-105	585	2	ρw2	ρw2	NOUN
ma-105	585	3	−	−	PROPN
ma-105	586	1	(	(	PUNCT
ma-105	586	2	1−η)βλ	1−η)βλ	NUM
ma-105	586	3	α0+α1λ	α0+α1λ	NUM
ma-105	586	4	w3	w3	NOUN
ma-105	586	5	−(α+	−(α+	PRON
ma-105	586	6	ρ)w2	ρ)w2	PROPN
ma-105	586	7	+	+	CCONJ
ma-105	586	8	(	(	PUNCT
ma-105	586	9	1−η)βλ	1−η)βλ	NUM
ma-105	586	10	α0+α1λ	α0+α1λ	NUM
ma-105	586	11	w3	w3	PROPN
ma-105	586	12	(	(	PUNCT
ma-105	586	13	1−	1−	NUM
ma-105	586	14	ε)kw2	ε)kw2	NOUN
ma-105	586	15	−	−	PROPN
ma-105	586	16	(	(	PUNCT
ma-105	586	17	µ+	µ+	X
ma-105	586	18	u	u	NOUN
ma-105	586	19	(	(	PUNCT
ma-105	586	20	1−η)βλ	1−η)βλ	NUM
ma-105	586	21	α0+α1λ	α0+α1λ	NUM
ma-105	586	22	)	)	PUNCT
ma-105	586	23	w3	w3	PROPN
ma-105	586	24			NOUN
ma-105	586	25	.	.	PUNCT
ma-105	587	1	(	(	PUNCT
ma-105	587	2	4.10	4.10	NUM
ma-105	587	3	)	)	PUNCT
ma-105	587	4	for	for	ADP
ma-105	587	5	each	each	DET
ma-105	587	6	l	l	NOUN
ma-105	587	7	≥	≥	NUM
ma-105	587	8	1	1	NUM
ma-105	587	9	,	,	PUNCT
ma-105	587	10	xl	xl	PROPN
ma-105	587	11	is	be	AUX
ma-105	587	12	invariant	invariant	ADJ
ma-105	587	13	under	under	ADP
ma-105	587	14	the	the	DET
ma-105	587	15	operator	operator	NOUN
ma-105	587	16	l	l	NOUN
ma-105	587	17	,	,	PUNCT
ma-105	587	18	and	and	CCONJ
ma-105	587	19	λ̃	λ̃	PROPN
ma-105	587	20	is	be	AUX
ma-105	587	21	an	an	DET
ma-105	587	22	eigenvalue	eigenvalue	NOUN
ma-105	587	23	of	of	ADP
ma-105	587	24	l	l	NOUN
ma-105	587	25	if	if	SCONJ
ma-105	588	1	and	and	CCONJ
ma-105	588	2	only	only	ADV
ma-105	588	3	if	if	SCONJ
ma-105	588	4	it	it	PRON
ma-105	588	5	isan	isan	ADJ
ma-105	588	6	eigenvalue	eigenvalue	PROPN
ma-105	588	7	of	of	ADP
ma-105	588	8	the	the	DET
ma-105	588	9	matrix	matrix	NOUN
ma-105	588	10	−µld	−µld	VERB
ma-105	588	11	+	+	X
ma-105	588	12	k(e0	k(e0	NOUN
ma-105	588	13	)	)	PUNCT
ma-105	588	14	for	for	ADP
ma-105	588	15	some	some	DET
ma-105	588	16	l	l	NOUN
ma-105	588	17	≥	≥	NOUN
ma-105	588	18	1	1	NUM
ma-105	588	19	,	,	PUNCT
ma-105	588	20	in	in	ADP
ma-105	588	21	which	which	DET
ma-105	588	22	case	case	NOUN
ma-105	588	23	,	,	PUNCT
ma-105	588	24	there	there	PRON
ma-105	588	25	is	be	VERB
ma-105	588	26	an	an	DET
ma-105	588	27	eigenvectorin	eigenvectorin	NOUN
ma-105	588	28	xl	xl	PROPN
ma-105	588	29	.	.	PUNCT
ma-105	589	1	so	so	ADV
ma-105	589	2	,	,	PUNCT
ma-105	589	3	one	one	PRON
ma-105	589	4	has	have	VERB
ma-105	589	5	det	det	NOUN
ma-105	589	6	(	(	PUNCT
ma-105	589	7	−µld	−µld	VERB
ma-105	589	8	+	+	PROPN
ma-105	589	9	k(e0)−	k(e0)−	X
ma-105	589	10	λ̃id	λ̃id	PROPN
ma-105	589	11	)	)	PUNCT
ma-105	589	12	=	=	SYM
ma-105	590	1	∣∣∣∣∣∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣∣∣∣∣∣	ADJ
ma-105	590	2	−	−	PROPN
ma-105	591	1	(	(	PUNCT
ma-105	591	2	µld1	µld1	VERB
ma-105	591	3	+	+	CCONJ
ma-105	591	4	d	d	X
ma-105	591	5	+	+	CCONJ
ma-105	591	6	λ̃	λ̃	PROPN
ma-105	591	7	)	)	PUNCT
ma-105	591	8	ρ	ρ	PROPN
ma-105	591	9	−	−	PROPN
ma-105	591	10	(	(	PUNCT
ma-105	591	11	1−η)βλ	1−η)βλ	NUM
ma-105	591	12	α0+α1λ	α0+α1λ	NUM
ma-105	591	13	0	0	NUM
ma-105	592	1	−	−	PRON
ma-105	592	2	(	(	PUNCT
ma-105	592	3	µld2	µld2	PROPN
ma-105	592	4	+	+	CCONJ
ma-105	592	5	(	(	PUNCT
ma-105	592	6	α+	α+	X
ma-105	592	7	ρ	ρ	NOUN
ma-105	592	8	)	)	PUNCT
ma-105	593	1	+	+	CCONJ
ma-105	593	2	λ̃	λ̃	PROPN
ma-105	593	3	)	)	PUNCT
ma-105	593	4	(	(	PUNCT
ma-105	593	5	1−η)βλ	1−η)βλ	NUM
ma-105	593	6	α0+α1λ	α0+α1λ	NUM
ma-105	593	7	0	0	NUM
ma-105	593	8	(	(	PUNCT
ma-105	593	9	1−	1−	NUM
ma-105	593	10	ε)k	ε)k	ADJ
ma-105	593	11	−	−	PROPN
ma-105	593	12	(	(	PUNCT
ma-105	593	13	µld3	µld3	NOUN
ma-105	593	14	+	+	CCONJ
ma-105	593	15	µ+	µ+	PROPN
ma-105	593	16	u	u	X
ma-105	593	17	(	(	PUNCT
ma-105	593	18	1−η)βλ	1−η)βλ	NUM
ma-105	593	19	α0+α1λ	α0+α1λ	NUM
ma-105	593	20	)	)	PUNCT
ma-105	593	21	−	−	PROPN
ma-105	594	1	λ̃	λ̃	PROPN
ma-105	594	2	∣∣∣∣∣∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣∣∣∣∣∣	PROPN
ma-105	594	3	the	the	DET
ma-105	594	4	characteristic	characteristic	ADJ
ma-105	594	5	equation	equation	NOUN
ma-105	594	6	of	of	ADP
ma-105	594	7	−µld	−µld	X
ma-105	594	8	+	+	ADJ
ma-105	594	9	k(e0	k(e0	NOUN
ma-105	594	10	)	)	PUNCT
ma-105	594	11	is	be	AUX
ma-105	594	12	−	−	PROPN
ma-105	594	13	(	(	PUNCT
ma-105	594	14	µld1	µld1	VERB
ma-105	595	1	+	+	CCONJ
ma-105	595	2	d	d	PROPN
ma-105	595	3	+	+	CCONJ
ma-105	595	4	λ̃	λ̃	PROPN
ma-105	595	5	)	)	PUNCT
ma-105	596	1	[	[	X
ma-105	596	2	[	[	PUNCT
ma-105	596	3	µld2	µld2	NOUN
ma-105	596	4	+	+	CCONJ
ma-105	596	5	(	(	PUNCT
ma-105	596	6	α+	α+	X
ma-105	596	7	ρ	ρ	NOUN
ma-105	596	8	)	)	PUNCT
ma-105	596	9	+	+	CCONJ
ma-105	596	10	λ̃	λ̃	PROPN
ma-105	596	11	]	]	PUNCT
ma-105	597	1	[	[	X
ma-105	597	2	(	(	PUNCT
ma-105	597	3	µld3	µld3	NOUN
ma-105	597	4	+	+	CCONJ
ma-105	597	5	µ+	µ+	PROPN
ma-105	597	6	u	u	NOUN
ma-105	597	7	(	(	PUNCT
ma-105	597	8	1−	1−	NUM
ma-105	597	9	η)βλ	η)βλ	PROPN
ma-105	597	10	α0	α0	ADJ
ma-105	597	11	+	+	CCONJ
ma-105	597	12	α1λ	α1λ	NUM
ma-105	597	13	)	)	PUNCT
ma-105	598	1	+	+	CCONJ
ma-105	598	2	λ̃	λ̃	PROPN
ma-105	598	3	]	]	PUNCT
ma-105	598	4	−	−	PROPN
ma-105	598	5	(	(	PUNCT
ma-105	598	6	1−	1−	NUM
ma-105	598	7	ε)(1−	ε)(1−	NOUN
ma-105	598	8	η)kβλ	η)kβλ	PROPN
ma-105	598	9	α0	α0	PROPN
ma-105	598	10	+	+	CCONJ
ma-105	598	11	α1λ	α1λ	NUM
ma-105	598	12	]	]	PUNCT
ma-105	598	13	=	=	SYM
ma-105	598	14	0	0	NUM
ma-105	598	15	,	,	PUNCT
ma-105	598	16	(	(	PUNCT
ma-105	598	17	4.11	4.11	NUM
ma-105	598	18	)	)	PUNCT
ma-105	598	19	from	from	ADP
ma-105	598	20	(	(	PUNCT
ma-105	598	21	4.11	4.11	NUM
ma-105	598	22	)	)	PUNCT
ma-105	598	23	,	,	PUNCT
ma-105	598	24	we	we	PRON
ma-105	598	25	get	get	VERB
ma-105	598	26	λ̃0	λ̃0	PROPN
ma-105	598	27	=	=	PUNCT
ma-105	599	1	−µld1	−µld1	ADP
ma-105	599	2	−	−	PROPN
ma-105	600	1	d	d	X
ma-105	600	2	<	<	X
ma-105	600	3	0	0	NUM
ma-105	600	4	,	,	PUNCT
ma-105	600	5	and	and	CCONJ
ma-105	600	6	another	another	DET
ma-105	600	7	characteristic	characteristic	ADJ
ma-105	600	8	eigenvalues	eigenvalue	NOUN
ma-105	600	9	are	be	AUX
ma-105	600	10	the	the	DET
ma-105	600	11	roots	root	NOUN
ma-105	600	12	of	of	ADP
ma-105	600	13	the	the	DET
ma-105	600	14	following	follow	VERB
ma-105	600	15	equation	equation	NOUN
ma-105	600	16	:	:	PUNCT
ma-105	601	1	λ̃2	λ̃2	PROPN
ma-105	601	2	+	+	NUM
ma-105	601	3	bλ̃+	bλ̃+	X
ma-105	601	4	(	(	PUNCT
ma-105	601	5	µld2	µld2	PROPN
ma-105	601	6	+	+	CCONJ
ma-105	601	7	α+	α+	PUNCT
ma-105	601	8	ρ	ρ	NOUN
ma-105	601	9	)	)	PUNCT
ma-105	601	10	(	(	PUNCT
ma-105	601	11	µld3	µld3	NOUN
ma-105	601	12	+	+	CCONJ
ma-105	601	13	µ+	µ+	PROPN
ma-105	601	14	u	u	NOUN
ma-105	601	15	(	(	PUNCT
ma-105	601	16	1−	1−	NUM
ma-105	601	17	η)βλ	η)βλ	PROPN
ma-105	602	1	α0	α0	ADJ
ma-105	602	2	+	+	CCONJ
ma-105	602	3	α1λ	α1λ	NUM
ma-105	602	4	)	)	PUNCT
ma-105	603	1	−	−	PROPN
ma-105	604	1	(	(	PUNCT
ma-105	604	2	1−	1−	NUM
ma-105	604	3	ε)(1−	ε)(1−	NOUN
ma-105	604	4	η)kβλ	η)kβλ	PROPN
ma-105	604	5	α0	α0	PROPN
ma-105	604	6	+	+	CCONJ
ma-105	604	7	α1λ	α1λ	NUM
ma-105	604	8	=	=	SYM
ma-105	604	9	0	0	NUM
ma-105	604	10	,	,	PUNCT
ma-105	604	11	(	(	PUNCT
ma-105	604	12	4.12	4.12	NUM
ma-105	604	13	)	)	PUNCT
ma-105	604	14	where	where	SCONJ
ma-105	604	15	b	b	X
ma-105	604	16	=	=	SYM
ma-105	605	1	[	[	X
ma-105	605	2	(	(	PUNCT
ma-105	605	3	µld3	µld3	NOUN
ma-105	605	4	+	+	CCONJ
ma-105	605	5	µ+	µ+	PROPN
ma-105	605	6	u	u	NOUN
ma-105	605	7	(	(	PUNCT
ma-105	605	8	1−	1−	NUM
ma-105	605	9	η)βλ	η)βλ	PROPN
ma-105	605	10	α0	α0	ADJ
ma-105	605	11	+	+	CCONJ
ma-105	605	12	α1λ	α1λ	NUM
ma-105	605	13	)	)	PUNCT
ma-105	606	1	+	+	CCONJ
ma-105	606	2	µld2	µld2	PROPN
ma-105	606	3	+	+	CCONJ
ma-105	606	4	(	(	PUNCT
ma-105	606	5	α+	α+	X
ma-105	606	6	ρ	ρ	NOUN
ma-105	606	7	)	)	PUNCT
ma-105	606	8	]	]	PUNCT
ma-105	606	9	.	.	PUNCT
ma-105	607	1	let	let	VERB
ma-105	607	2	c	c	NOUN
ma-105	607	3	=	=	SYM
ma-105	607	4	(	(	PUNCT
ma-105	607	5	µld2	µld2	PROPN
ma-105	607	6	+	+	CCONJ
ma-105	607	7	α+	α+	PUNCT
ma-105	607	8	ρ	ρ	NOUN
ma-105	607	9	)	)	PUNCT
ma-105	607	10	(	(	PUNCT
ma-105	607	11	µld3	µld3	NOUN
ma-105	607	12	+	+	CCONJ
ma-105	607	13	µ+	µ+	PROPN
ma-105	607	14	u	u	NOUN
ma-105	607	15	(	(	PUNCT
ma-105	607	16	1−	1−	NUM
ma-105	607	17	η)βλ	η)βλ	PROPN
ma-105	608	1	α0	α0	ADJ
ma-105	608	2	+	+	CCONJ
ma-105	608	3	α1λ	α1λ	NUM
ma-105	608	4	)	)	PUNCT
ma-105	609	1	−	−	PROPN
ma-105	610	1	(	(	PUNCT
ma-105	610	2	1−	1−	NUM
ma-105	610	3	ε)(1−	ε)(1−	NOUN
ma-105	610	4	η)kβλ	η)kβλ	PROPN
ma-105	610	5	α0	α0	PROPN
ma-105	610	6	+	+	CCONJ
ma-105	610	7	α1λ	α1λ	NUM
ma-105	610	8	.	.	PUNCT
ma-105	611	1	one	one	PRON
ma-105	611	2	has	have	VERB
ma-105	611	3	,	,	PUNCT
ma-105	611	4	c	c	PROPN
ma-105	611	5	=	=	PUNCT
ma-105	611	6	µld2	µld2	PROPN
ma-105	611	7	(	(	PUNCT
ma-105	611	8	µld3	µld3	PROPN
ma-105	611	9	+	+	CCONJ
ma-105	611	10	µ+	µ+	PROPN
ma-105	611	11	u	u	NOUN
ma-105	611	12	(	(	PUNCT
ma-105	611	13	1−	1−	NUM
ma-105	611	14	η)βλ	η)βλ	PROPN
ma-105	612	1	α0	α0	ADJ
ma-105	612	2	+	+	CCONJ
ma-105	612	3	α1λ	α1λ	NUM
ma-105	612	4	)	)	PUNCT
ma-105	613	1	+	+	CCONJ
ma-105	613	2	(	(	PUNCT
ma-105	613	3	α+	α+	X
ma-105	613	4	ρ)µld3	ρ)µld3	PROPN
ma-105	613	5	+	+	CCONJ
ma-105	613	6	(	(	PUNCT
ma-105	613	7	α+	α+	NOUN
ma-105	613	8	ρ	ρ	NOUN
ma-105	613	9	)	)	PUNCT
ma-105	613	10	(	(	PUNCT
ma-105	613	11	µ+	µ+	X
ma-105	613	12	u	u	NOUN
ma-105	613	13	(	(	PUNCT
ma-105	613	14	1−	1−	NUM
ma-105	613	15	η)βλ	η)βλ	PROPN
ma-105	614	1	α0	α0	ADJ
ma-105	614	2	+	+	CCONJ
ma-105	614	3	α1λ	α1λ	NUM
ma-105	614	4	)	)	PUNCT
ma-105	615	1	−	−	PROPN
ma-105	616	1	(	(	PUNCT
ma-105	616	2	1−	1−	NUM
ma-105	616	3	ε)(1−	ε)(1−	NOUN
ma-105	616	4	η)kβλ	η)kβλ	PROPN
ma-105	616	5	α0	α0	PROPN
ma-105	616	6	+	+	CCONJ
ma-105	616	7	α1λ	α1λ	NUM
ma-105	616	8	,	,	PUNCT
ma-105	616	9	=	=	SYM
ma-105	616	10	µld2	µld2	PROPN
ma-105	616	11	(	(	PUNCT
ma-105	616	12	µld3	µld3	PROPN
ma-105	616	13	+	+	CCONJ
ma-105	616	14	µ+	µ+	PROPN
ma-105	616	15	u	u	NOUN
ma-105	616	16	(	(	PUNCT
ma-105	616	17	1−	1−	NUM
ma-105	616	18	η)βλ	η)βλ	PROPN
ma-105	617	1	α0	α0	ADJ
ma-105	617	2	+	+	CCONJ
ma-105	617	3	α1λ	α1λ	NUM
ma-105	617	4	)	)	PUNCT
ma-105	618	1	+	+	CCONJ
ma-105	618	2	(	(	PUNCT
ma-105	618	3	α+	α+	X
ma-105	618	4	ρ)µld3	ρ)µld3	PROPN
ma-105	618	5	+	+	SYM
ma-105	618	6	1	1	NUM
ma-105	618	7	α0	α0	ADJ
ma-105	618	8	+	+	CCONJ
ma-105	618	9	α1λ	α1λ	PRON
ma-105	618	10	[	[	PUNCT
ma-105	618	11	(	(	PUNCT
ma-105	618	12	α+	α+	X
ma-105	618	13	ρ	ρ	NOUN
ma-105	618	14	)	)	PUNCT
ma-105	618	15	[	[	X
ma-105	618	16	µ(α0	µ(α0	ADV
ma-105	618	17	+	+	CCONJ
ma-105	618	18	α1λ	α1λ	NUM
ma-105	618	19	)	)	PUNCT
ma-105	618	20	+	+	CCONJ
ma-105	618	21	u(1−	u(1−	ADJ
ma-105	618	22	η)βλ]−	η)βλ]−	NOUN
ma-105	618	23	(	(	PUNCT
ma-105	618	24	1−	1−	NUM
ma-105	618	25	ε)(1−	ε)(1−	PROPN
ma-105	618	26	η)kβλ	η)kβλ	PROPN
ma-105	618	27	]	]	PUNCT
ma-105	618	28	,	,	PUNCT
ma-105	618	29	https://doi.org/10.28924/ada/ma.3.1	https://doi.org/10.28924/ada/ma.3.1	PROPN
ma-105	618	30	eur	eur	PROPN
ma-105	618	31	.	.	PUNCT
ma-105	619	1	j.	j.	PROPN
ma-105	619	2	math	math	PROPN
ma-105	619	3	.	.	PUNCT
ma-105	620	1	anal	anal	PROPN
ma-105	620	2	.	.	PUNCT
ma-105	621	1	10.28924	10.28924	NUM
ma-105	621	2	/	/	SYM
ma-105	621	3	ada	ada	PROPN
ma-105	621	4	/	/	SYM
ma-105	621	5	ma.3.1	ma.3.1	PROPN
ma-105	621	6	22	22	NUM
ma-105	621	7	=	=	SYM
ma-105	621	8	µld2	µld2	PROPN
ma-105	621	9	(	(	PUNCT
ma-105	621	10	µld3	µld3	PROPN
ma-105	621	11	+	+	CCONJ
ma-105	621	12	µ+	µ+	PROPN
ma-105	621	13	u	u	NOUN
ma-105	621	14	(	(	PUNCT
ma-105	621	15	1−	1−	NUM
ma-105	621	16	η)βλ	η)βλ	PROPN
ma-105	622	1	α0	α0	ADJ
ma-105	622	2	+	+	CCONJ
ma-105	622	3	α1λ	α1λ	NUM
ma-105	622	4	)	)	PUNCT
ma-105	623	1	+	+	CCONJ
ma-105	623	2	(	(	PUNCT
ma-105	623	3	α+	α+	X
ma-105	623	4	ρ)µld3	ρ)µld3	PROPN
ma-105	623	5	+	+	CCONJ
ma-105	623	6	(	(	PUNCT
ma-105	623	7	α+	α+	NOUN
ma-105	623	8	ρ	ρ	NOUN
ma-105	623	9	)	)	PUNCT
ma-105	624	1	[	[	X
ma-105	624	2	µ(α0	µ(α0	ADV
ma-105	624	3	+	+	CCONJ
ma-105	624	4	α1λ	α1λ	NUM
ma-105	624	5	)	)	PUNCT
ma-105	624	6	+	+	CCONJ
ma-105	624	7	u(1−	u(1−	PROPN
ma-105	624	8	η)βλ	η)βλ	PROPN
ma-105	624	9	]	]	X
ma-105	624	10	α0	α0	PROPN
ma-105	624	11	+	+	PUNCT
ma-105	624	12	α1λ	α1λ	PRON
ma-105	624	13	(	(	PUNCT
ma-105	624	14	1−r0	1−r0	NUM
ma-105	624	15	)	)	PUNCT
ma-105	624	16	.	.	PUNCT
ma-105	625	1	since	since	SCONJ
ma-105	625	2	b	b	PROPN
ma-105	625	3	>	>	X
ma-105	625	4	0	0	NUM
ma-105	625	5	,	,	PUNCT
ma-105	625	6	if	if	SCONJ
ma-105	625	7	r0	r0	NOUN
ma-105	625	8	≤	≤	NOUN
ma-105	625	9	1	1	NUM
ma-105	625	10	then	then	ADV
ma-105	625	11	c	c	PROPN
ma-105	625	12	is	be	AUX
ma-105	625	13	also	also	ADV
ma-105	625	14	positive	positive	ADJ
ma-105	625	15	.	.	PUNCT
ma-105	626	1	hence	hence	ADV
ma-105	626	2	by	by	ADP
ma-105	626	3	virtue	virtue	NOUN
ma-105	626	4	of	of	ADP
ma-105	626	5	the	the	DET
ma-105	626	6	routh	routh	PROPN
ma-105	626	7	-	-	PUNCT
ma-105	626	8	hurwitz	hurwitz	PROPN
ma-105	626	9	criterion	criterion	NOUN
ma-105	626	10	,	,	PUNCT
ma-105	626	11	equation	equation	NOUN
ma-105	626	12	(	(	PUNCT
ma-105	626	13	4.12	4.12	NUM
ma-105	626	14	)	)	PUNCT
ma-105	626	15	does	do	AUX
ma-105	626	16	not	not	PART
ma-105	626	17	admit	admit	VERB
ma-105	626	18	solution	solution	NOUN
ma-105	626	19	with	with	ADP
ma-105	626	20	positive	positive	ADJ
ma-105	626	21	real	real	ADJ
ma-105	626	22	part	part	NOUN
ma-105	626	23	.	.	PUNCT
ma-105	627	1	thus	thus	ADV
ma-105	627	2	none	none	NOUN
ma-105	627	3	characteristic	characteristic	ADJ
ma-105	627	4	eigenvaluehave	eigenvaluehave	VERB
ma-105	627	5	positive	positive	ADJ
ma-105	627	6	real	real	ADJ
ma-105	627	7	part	part	NOUN
ma-105	627	8	.	.	PUNCT
ma-105	628	1	therefore	therefore	ADV
ma-105	628	2	if	if	SCONJ
ma-105	628	3	r0	r0	NOUN
ma-105	628	4	≤	≤	NOUN
ma-105	628	5	1	1	NUM
ma-105	628	6	,	,	PUNCT
ma-105	628	7	the	the	DET
ma-105	628	8	spatially	spatially	ADV
ma-105	628	9	homogeneous	homogeneous	ADJ
ma-105	628	10	uninfected	uninfected	ADJ
ma-105	628	11	equilibrium	equilibrium	NOUN
ma-105	628	12	e0	e0	PROPN
ma-105	628	13	=	=	PUNCT
ma-105	628	14	(	(	PUNCT
ma-105	628	15	λ	λ	X
ma-105	628	16	d	d	PROPN
ma-105	628	17	,	,	PUNCT
ma-105	628	18	0	0	NUM
ma-105	628	19	,	,	PUNCT
ma-105	628	20	0	0	NUM
ma-105	628	21	)	)	PUNCT
ma-105	628	22	of	of	ADP
ma-105	628	23	(	(	PUNCT
ma-105	628	24	2.4	2.4	NUM
ma-105	628	25	)	)	PUNCT
ma-105	628	26	is	be	AUX
ma-105	628	27	locally	locally	ADV
ma-105	628	28	asymptotically	asymptotically	ADV
ma-105	628	29	stable.otherwise	stable.otherwise	NOUN
ma-105	628	30	if	if	SCONJ
ma-105	628	31	r0	r0	NOUN
ma-105	628	32	>	>	X
ma-105	628	33	1	1	NUM
ma-105	628	34	,	,	PUNCT
ma-105	628	35	then	then	ADV
ma-105	628	36	for	for	ADP
ma-105	628	37	l	l	NOUN
ma-105	628	38	=	=	SYM
ma-105	628	39	1	1	NUM
ma-105	628	40	,	,	PUNCT
ma-105	628	41	(	(	PUNCT
ma-105	628	42	in	in	ADP
ma-105	628	43	this	this	DET
ma-105	628	44	case	case	NOUN
ma-105	628	45	µ1	µ1	NOUN
ma-105	628	46	=	=	SYM
ma-105	628	47	0	0	NUM
ma-105	628	48	)	)	PUNCT
ma-105	628	49	one	one	NOUN
ma-105	628	50	has	have	VERB
ma-105	628	51	,	,	PUNCT
ma-105	628	52	c	c	NOUN
ma-105	628	53	=	=	SYM
ma-105	628	54	(	(	PUNCT
ma-105	628	55	α+	α+	NOUN
ma-105	628	56	ρ	ρ	NOUN
ma-105	628	57	)	)	PUNCT
ma-105	629	1	[	[	X
ma-105	629	2	µ(α0	µ(α0	ADV
ma-105	629	3	+	+	CCONJ
ma-105	629	4	α1λ	α1λ	NUM
ma-105	629	5	)	)	PUNCT
ma-105	629	6	+	+	CCONJ
ma-105	629	7	u(1−	u(1−	PROPN
ma-105	629	8	η)βλ	η)βλ	PROPN
ma-105	629	9	]	]	X
ma-105	629	10	α0	α0	PROPN
ma-105	629	11	+	+	PUNCT
ma-105	629	12	α1λ	α1λ	PRON
ma-105	629	13	(	(	PUNCT
ma-105	629	14	1−r0	1−r0	NUM
ma-105	629	15	)	)	PUNCT
ma-105	629	16	<	<	X
ma-105	629	17	0	0	X
ma-105	629	18	.	.	PUNCT
ma-105	630	1	hence	hence	ADV
ma-105	630	2	there	there	PRON
ma-105	630	3	is	be	VERB
ma-105	630	4	a	a	DET
ma-105	630	5	complex	complex	ADJ
ma-105	630	6	root	root	NOUN
ma-105	630	7	of	of	ADP
ma-105	630	8	equation	equation	NOUN
ma-105	630	9	(	(	PUNCT
ma-105	630	10	4.12	4.12	NUM
ma-105	630	11	)	)	PUNCT
ma-105	630	12	with	with	ADP
ma-105	630	13	positive	positive	ADJ
ma-105	630	14	real	real	ADJ
ma-105	630	15	part	part	NOUN
ma-105	630	16	in	in	ADP
ma-105	630	17	the	the	DET
ma-105	630	18	spectrum	spectrum	NOUN
ma-105	630	19	of	of	ADP
ma-105	630	20	kaccording	kaccording	NOUN
ma-105	630	21	to	to	ADP
ma-105	630	22	routh	routh	PROPN
ma-105	630	23	-	-	PUNCT
ma-105	630	24	hurwitz	hurwitz	PROPN
ma-105	630	25	criterion	criterion	NOUN
ma-105	630	26	.	.	PUNCT
ma-105	631	1	therefore	therefore	ADV
ma-105	631	2	the	the	DET
ma-105	631	3	uninfected	uninfected	ADJ
ma-105	631	4	equilibrium	equilibrium	NOUN
ma-105	631	5	e0	e0	PROPN
ma-105	631	6	=	=	PUNCT
ma-105	631	7	(	(	PUNCT
ma-105	631	8	λ	λ	X
ma-105	631	9	d	d	PROPN
ma-105	631	10	,	,	PUNCT
ma-105	631	11	0	0	NUM
ma-105	631	12	,	,	PUNCT
ma-105	631	13	0	0	NUM
ma-105	631	14	)	)	PUNCT
ma-105	631	15	of	of	ADP
ma-105	631	16	(	(	PUNCT
ma-105	631	17	2.4)is	2.4)is	ADJ
ma-105	631	18	unstable	unstable	ADJ
ma-105	631	19	.	.	PUNCT
ma-105	632	1	this	this	PRON
ma-105	632	2	completes	complete	VERB
ma-105	632	3	the	the	DET
ma-105	632	4	proof	proof	NOUN
ma-105	632	5	of	of	ADP
ma-105	632	6	theorem	theorem	ADJ
ma-105	632	7	4.2	4.2	NUM
ma-105	632	8	.	.	PUNCT
ma-105	632	9	�	�	PROPN
ma-105	632	10	4.5	4.5	NUM
ma-105	632	11	.	.	PUNCT
ma-105	633	1	global	global	ADJ
ma-105	633	2	stability	stability	NOUN
ma-105	633	3	of	of	ADP
ma-105	633	4	hcv	hcv	NOUN
ma-105	633	5	-	-	PUNCT
ma-105	633	6	uninfected	uninfected	ADJ
ma-105	633	7	equilibrium	equilibrium	NOUN
ma-105	633	8	.	.	PUNCT
ma-105	634	1	the	the	DET
ma-105	634	2	objective	objective	NOUN
ma-105	634	3	of	of	ADP
ma-105	634	4	this	this	DET
ma-105	634	5	section	section	NOUN
ma-105	634	6	is	be	AUX
ma-105	634	7	to	to	PART
ma-105	634	8	discuss	discuss	VERB
ma-105	634	9	theglobal	theglobal	ADJ
ma-105	634	10	stability	stability	NOUN
ma-105	634	11	of	of	ADP
ma-105	634	12	the	the	DET
ma-105	634	13	spatially	spatially	ADV
ma-105	634	14	homogeneous	homogeneous	ADJ
ma-105	634	15	uninfected	uninfected	ADJ
ma-105	634	16	equilibrium	equilibrium	NOUN
ma-105	634	17	for	for	ADP
ma-105	634	18	the	the	DET
ma-105	634	19	pde	pde	NOUN
ma-105	634	20	system	system	NOUN
ma-105	634	21	(	(	PUNCT
ma-105	634	22	2.4	2.4	NUM
ma-105	634	23	)	)	PUNCT
ma-105	634	24	.	.	PUNCT
ma-105	635	1	weaddress	weaddress	PROPN
ma-105	635	2	global	global	ADJ
ma-105	635	3	stability	stability	NOUN
ma-105	635	4	by	by	ADP
ma-105	635	5	using	use	VERB
ma-105	635	6	the	the	DET
ma-105	635	7	construction	construction	NOUN
ma-105	635	8	of	of	ADP
ma-105	635	9	lyapunov	lyapunov	ADJ
ma-105	635	10	functional	functional	ADJ
ma-105	635	11	method	method	NOUN
ma-105	635	12	.	.	PUNCT
ma-105	636	1	this	this	DET
ma-105	636	2	lyapunovfunctional	lyapunovfunctional	NOUN
ma-105	636	3	is	be	AUX
ma-105	636	4	obtained	obtain	VERB
ma-105	636	5	from	from	ADP
ma-105	636	6	those	those	PRON
ma-105	636	7	of	of	ADP
ma-105	636	8	differential	differential	ADJ
ma-105	636	9	equations	equation	NOUN
ma-105	636	10	by	by	ADP
ma-105	636	11	applying	apply	VERB
ma-105	636	12	the	the	DET
ma-105	636	13	method	method	NOUN
ma-105	636	14	presented	present	VERB
ma-105	636	15	in	in	ADP
ma-105	636	16	[	[	PUNCT
ma-105	636	17	15].for	15].for	ADP
ma-105	636	18	this	this	DET
ma-105	636	19	purpose	purpose	NOUN
ma-105	636	20	,	,	PUNCT
ma-105	636	21	we	we	PRON
ma-105	636	22	start	start	VERB
ma-105	636	23	by	by	ADP
ma-105	636	24	letting	let	VERB
ma-105	636	25	τ0	τ0	NOUN
ma-105	636	26	=	=	PUNCT
ma-105	636	27	(	(	PUNCT
ma-105	636	28	1−	1−	NUM
ma-105	636	29	ε)k(1−	ε)k(1−	PROPN
ma-105	636	30	η)βλ	η)βλ	PROPN
ma-105	636	31	µα0(α+	µα0(α+	CCONJ
ma-105	636	32	ρ	ρ	NOUN
ma-105	636	33	)	)	PUNCT
ma-105	636	34	.	.	PUNCT
ma-105	637	1	then	then	ADV
ma-105	637	2	,	,	PUNCT
ma-105	637	3	it	it	PRON
ma-105	637	4	is	be	AUX
ma-105	637	5	easy	easy	ADJ
ma-105	637	6	to	to	PART
ma-105	637	7	see	see	VERB
ma-105	637	8	that	that	PRON
ma-105	637	9	(	(	PUNCT
ma-105	637	10	1−	1−	NUM
ma-105	637	11	ε)(1−	ε)(1−	NOUN
ma-105	637	12	η)kβλ	η)kβλ	PROPN
ma-105	637	13	(	(	PUNCT
ma-105	637	14	α+	α+	NOUN
ma-105	637	15	ρ	ρ	NOUN
ma-105	637	16	)	)	PUNCT
ma-105	638	1	[	[	X
ma-105	638	2	µ(α0	µ(α0	ADV
ma-105	638	3	+	+	CCONJ
ma-105	638	4	α1λ	α1λ	NUM
ma-105	638	5	)	)	PUNCT
ma-105	638	6	+	+	CCONJ
ma-105	638	7	u(1−	u(1−	PROPN
ma-105	638	8	η)βλ	η)βλ	PROPN
ma-105	638	9	]	]	PUNCT
ma-105	638	10	≤	≤	NUM
ma-105	638	11	(	(	PUNCT
ma-105	638	12	1−	1−	NUM
ma-105	638	13	ε)k(1−	ε)k(1−	PROPN
ma-105	638	14	η)βλ	η)βλ	PROPN
ma-105	638	15	µα0(α+	µα0(α+	CCONJ
ma-105	638	16	ρ	ρ	NOUN
ma-105	638	17	)	)	PUNCT
ma-105	638	18	,	,	PUNCT
ma-105	638	19	i.e.	i.e.	X
ma-105	638	20	,	,	PUNCT
ma-105	638	21	r0	r0	NOUN
ma-105	638	22	≤	≤	NUM
ma-105	638	23	τ0.we	τ0.we	NOUN
ma-105	638	24	state	state	NOUN
ma-105	638	25	the	the	DET
ma-105	638	26	following	following	ADJ
ma-105	638	27	result	result	NOUN
ma-105	638	28	on	on	ADP
ma-105	638	29	global	global	ADJ
ma-105	638	30	stability	stability	NOUN
ma-105	638	31	at	at	ADP
ma-105	638	32	e0	e0	PROPN
ma-105	638	33	as	as	SCONJ
ma-105	638	34	follows	follow	VERB
ma-105	638	35	:	:	PUNCT
ma-105	638	36	theorem	theorem	VERB
ma-105	638	37	4.3	4.3	NUM
ma-105	638	38	.	.	PUNCT
ma-105	639	1	the	the	DET
ma-105	639	2	spatially	spatially	ADV
ma-105	639	3	homogeneous	homogeneous	ADJ
ma-105	639	4	uninfected	uninfected	ADJ
ma-105	639	5	equilibrium	equilibrium	NOUN
ma-105	639	6	e0	e0	PROPN
ma-105	639	7	of	of	ADP
ma-105	639	8	pde	pde	NOUN
ma-105	639	9	-	-	PUNCT
ma-105	639	10	model	model	NOUN
ma-105	639	11	system	system	NOUN
ma-105	639	12	(	(	PUNCT
ma-105	639	13	2.4	2.4	NUM
ma-105	639	14	)	)	PUNCT
ma-105	639	15	is	be	AUX
ma-105	639	16	globally	globally	ADV
ma-105	639	17	asymptotically	asymptotically	ADV
ma-105	639	18	stable	stable	ADJ
ma-105	639	19	in	in	ADP
ma-105	639	20	the	the	DET
ma-105	639	21	positively	positively	ADV
ma-105	639	22	-	-	PUNCT
ma-105	639	23	invariant	invariant	ADJ
ma-105	639	24	region	region	NOUN
ma-105	639	25	σ	σ	NOUN
ma-105	639	26	if	if	SCONJ
ma-105	639	27	τ0	τ0	NOUN
ma-105	639	28	<	<	X
ma-105	639	29	1	1	X
ma-105	639	30	.	.	PUNCT
ma-105	639	31	proof	proof	NOUN
ma-105	639	32	.	.	PUNCT
ma-105	640	1	let	let	VERB
ma-105	640	2	us	we	PRON
ma-105	640	3	consider	consider	VERB
ma-105	640	4	the	the	DET
ma-105	640	5	following	follow	VERB
ma-105	640	6	function	function	NOUN
ma-105	640	7	g1(t	g1(t	NOUN
ma-105	640	8	)	)	PUNCT
ma-105	640	9	=	=	SYM
ma-105	640	10	(	(	PUNCT
ma-105	640	11	1−	1−	NUM
ma-105	640	12	ε)k	ε)k	X
ma-105	640	13	α+	α+	PUNCT
ma-105	640	14	ρ	ρ	PROPN
ma-105	640	15	i(t	i(t	PROPN
ma-105	640	16	)	)	PUNCT
ma-105	641	1	+	+	NUM
ma-105	641	2	v	v	X
ma-105	641	3	(	(	PUNCT
ma-105	641	4	t	t	PROPN
ma-105	641	5	)	)	PUNCT
ma-105	641	6	.	.	PUNCT
ma-105	642	1	then	then	ADV
ma-105	642	2	,	,	PUNCT
ma-105	642	3	the	the	DET
ma-105	642	4	differentiation	differentiation	NOUN
ma-105	642	5	of	of	ADP
ma-105	642	6	g1	g1	NOUN
ma-105	642	7	with	with	ADP
ma-105	642	8	respect	respect	NOUN
ma-105	642	9	to	to	ADP
ma-105	642	10	t	t	PROPN
ma-105	642	11	gives	give	VERB
ma-105	642	12	dg1	dg1	INTJ
ma-105	642	13	dt	dt	NOUN
ma-105	642	14	=	=	PUNCT
ma-105	642	15	(	(	PUNCT
ma-105	642	16	(	(	PUNCT
ma-105	642	17	1−	1−	NUM
ma-105	642	18	ε)k	ε)k	NOUN
ma-105	642	19	−	−	PUNCT
ma-105	642	20	u(α+	u(α+	PROPN
ma-105	642	21	ρ	ρ	PROPN
ma-105	642	22	)	)	PUNCT
ma-105	642	23	µ(α+	µ(α+	PUNCT
ma-105	642	24	ρ)(α0	ρ)(α0	PROPN
ma-105	643	1	+	+	CCONJ
ma-105	643	2	α1h	α1h	PROPN
ma-105	643	3	+	+	SYM
ma-105	643	4	α2v	α2v	NOUN
ma-105	643	5	+	+	CCONJ
ma-105	643	6	α3hv	α3hv	NUM
ma-105	643	7	)	)	PUNCT
ma-105	643	8	(	(	PUNCT
ma-105	643	9	1−	1−	NUM
ma-105	643	10	η)βh	η)βh	PROPN
ma-105	643	11	−	−	PROPN
ma-105	643	12	1	1	NUM
ma-105	643	13	)	)	PUNCT
ma-105	643	14	µv	µv	PROPN
ma-105	643	15	.	.	PUNCT
ma-105	644	1	https://doi.org/10.28924/ada/ma.3.1	https://doi.org/10.28924/ada/ma.3.1	PROPN
ma-105	644	2	eur	eur	PROPN
ma-105	644	3	.	.	PUNCT
ma-105	645	1	j.	j.	PROPN
ma-105	645	2	math	math	PROPN
ma-105	645	3	.	.	PUNCT
ma-105	646	1	anal	anal	PROPN
ma-105	646	2	.	.	PUNCT
ma-105	647	1	10.28924	10.28924	NUM
ma-105	647	2	/	/	SYM
ma-105	647	3	ada	ada	PROPN
ma-105	647	4	/	/	SYM
ma-105	647	5	ma.3.1	ma.3.1	PROPN
ma-105	647	6	23since	23since	NUM
ma-105	647	7	h	h	NOUN
ma-105	647	8	≤	≤	NOUN
ma-105	648	1	λ	λ	X
ma-105	648	2	d	d	NOUN
ma-105	648	3	=	=	SYM
ma-105	648	4	λ	λ	PROPN
ma-105	648	5	in	in	ADP
ma-105	648	6	the	the	DET
ma-105	648	7	positively	positively	ADV
ma-105	648	8	-	-	PUNCT
ma-105	648	9	invariant	invariant	ADJ
ma-105	648	10	region	region	NOUN
ma-105	648	11	σ	σ	PROPN
ma-105	648	12	,	,	PUNCT
ma-105	648	13	one	one	NUM
ma-105	648	14	has	have	AUX
ma-105	648	15	dg1	dg1	VERB
ma-105	648	16	dt	dt	PRON
ma-105	648	17	≤	≤	X
ma-105	649	1	[	[	X
ma-105	649	2	[	[	PUNCT
ma-105	649	3	(	(	PUNCT
ma-105	649	4	1−	1−	NUM
ma-105	649	5	ε)k	ε)k	ADJ
ma-105	649	6	−	−	PUNCT
ma-105	649	7	u(α+	u(α+	PROPN
ma-105	649	8	ρ	ρ	PROPN
ma-105	649	9	)	)	PUNCT
ma-105	649	10	]	]	PUNCT
ma-105	650	1	(	(	PUNCT
ma-105	650	2	1−	1−	NUM
ma-105	650	3	η)βλ	η)βλ	PROPN
ma-105	650	4	µα0(α+	µα0(α+	NUM
ma-105	650	5	ρ	ρ	NOUN
ma-105	650	6	)	)	PUNCT
ma-105	650	7	−	−	PROPN
ma-105	650	8	1	1	NUM
ma-105	650	9	]	]	PUNCT
ma-105	650	10	µv	µv	PROPN
ma-105	650	11	,	,	PUNCT
ma-105	650	12	≤	≤	X
ma-105	651	1	[	[	X
ma-105	651	2	(	(	PUNCT
ma-105	651	3	1−	1−	NUM
ma-105	651	4	ε)(1−	ε)(1−	PROPN
ma-105	651	5	η)kβλ	η)kβλ	PROPN
ma-105	651	6	µα0(α+	µα0(α+	ADP
ma-105	651	7	ρ	ρ	PROPN
ma-105	651	8	)	)	PUNCT
ma-105	651	9	−	−	PROPN
ma-105	651	10	1	1	NUM
ma-105	651	11	]	]	PUNCT
ma-105	651	12	µv	µv	NOUN
ma-105	651	13	,	,	PUNCT
ma-105	651	14	≤	≤	NUM
ma-105	651	15	(	(	PUNCT
ma-105	651	16	τ0	τ0	NOUN
ma-105	651	17	−	−	PROPN
ma-105	651	18	1)µv	1)µv	NUM
ma-105	651	19	.	.	PUNCT
ma-105	652	1	now	now	ADV
ma-105	652	2	,	,	PUNCT
ma-105	652	3	we	we	PRON
ma-105	652	4	define	define	VERB
ma-105	652	5	the	the	DET
ma-105	652	6	lyapunov	lyapunov	ADJ
ma-105	652	7	function	function	NOUN
ma-105	652	8	as	as	SCONJ
ma-105	652	9	follows	follow	VERB
ma-105	652	10	l1	l1	PROPN
ma-105	652	11	=	=	SYM
ma-105	652	12	∫	∫	PROPN
ma-105	652	13	ω	ω	PROPN
ma-105	652	14	g1dx	g1dx	PROPN
ma-105	652	15	.	.	PUNCT
ma-105	653	1	the	the	DET
ma-105	653	2	computation	computation	NOUN
ma-105	653	3	of	of	ADP
ma-105	653	4	the	the	DET
ma-105	653	5	time	time	NOUN
ma-105	653	6	derivative	derivative	NOUN
ma-105	653	7	of	of	ADP
ma-105	653	8	l1	l1	PROPN
ma-105	653	9	along	along	ADP
ma-105	653	10	the	the	DET
ma-105	653	11	positive	positive	ADJ
ma-105	653	12	solutions	solution	NOUN
ma-105	653	13	of	of	ADP
ma-105	653	14	the	the	DET
ma-105	653	15	pde	pde	NOUN
ma-105	653	16	-	-	PUNCT
ma-105	653	17	model	model	NOUN
ma-105	653	18	system(2.4	system(2.4	NOUN
ma-105	653	19	)	)	PUNCT
ma-105	653	20	yields	yield	NOUN
ma-105	653	21	dl1	dl1	NOUN
ma-105	653	22	dt	dt	NOUN
ma-105	654	1	=	=	SYM
ma-105	654	2	d	d	X
ma-105	654	3	dt	dt	X
ma-105	654	4	[	[	PUNCT
ma-105	654	5	∫	∫	PROPN
ma-105	654	6	ω	ω	PROPN
ma-105	654	7	g1dx	g1dx	X
ma-105	654	8	]	]	PUNCT
ma-105	654	9	,	,	PUNCT
ma-105	654	10	=	=	SYM
ma-105	654	11	∫	∫	PROPN
ma-105	654	12	ω	ω	PROPN
ma-105	654	13	dg1	dg1	PROPN
ma-105	654	14	dt	dt	X
ma-105	654	15	dx	dx	PROPN
ma-105	654	16	,	,	PUNCT
ma-105	654	17	≤	≤	PROPN
ma-105	654	18	∫	∫	PROPN
ma-105	654	19	ω	ω	PROPN
ma-105	654	20	[	[	PUNCT
ma-105	654	21	(	(	PUNCT
ma-105	654	22	τ0	τ0	NOUN
ma-105	654	23	−	−	PROPN
ma-105	654	24	1)µv	1)µv	PROPN
ma-105	654	25	]	]	PUNCT
ma-105	654	26	dx	dx	PROPN
ma-105	654	27	.	.	PUNCT
ma-105	655	1	it	it	PRON
ma-105	655	2	is	be	AUX
ma-105	655	3	clear	clear	ADJ
ma-105	655	4	that	that	SCONJ
ma-105	655	5	the	the	DET
ma-105	655	6	condition	condition	NOUN
ma-105	655	7	τ0	τ0	VERB
ma-105	655	8	≤	≤	ADJ
ma-105	655	9	1	1	NUM
ma-105	655	10	gives	give	VERB
ma-105	655	11	dl1	dl1	NOUN
ma-105	655	12	dt	dt	NOUN
ma-105	655	13	≤	≤	NUM
ma-105	655	14	0	0	NUM
ma-105	655	15	for	for	ADP
ma-105	655	16	all	all	DET
ma-105	655	17	h	h	NOUN
ma-105	655	18	,	,	PUNCT
ma-105	655	19	i	i	PRON
ma-105	655	20	,	,	PUNCT
ma-105	655	21	v	v	X
ma-105	655	22	>	>	X
ma-105	655	23	0	0	NUM
ma-105	655	24	.	.	PUNCT
ma-105	656	1	we	we	PRON
ma-105	656	2	note	note	VERB
ma-105	656	3	that	that	SCONJ
ma-105	656	4	the	the	DET
ma-105	656	5	solutionsof	solutionsof	NOUN
ma-105	656	6	system	system	NOUN
ma-105	656	7	(	(	PUNCT
ma-105	656	8	2.4	2.4	NUM
ma-105	656	9	)	)	PUNCT
ma-105	656	10	are	be	AUX
ma-105	656	11	limited	limit	VERB
ma-105	656	12	by	by	ADP
ma-105	656	13	υ	υ	PROPN
ma-105	656	14	,	,	PUNCT
ma-105	656	15	the	the	DET
ma-105	656	16	greatest	great	ADJ
ma-105	656	17	invariant	invariant	ADJ
ma-105	656	18	subset	subset	NOUN
ma-105	656	19	of	of	ADP
ma-105	656	20	e={(h	e={(h	PROPN
ma-105	656	21	,	,	PUNCT
ma-105	656	22	i	i	PRON
ma-105	656	23	,	,	PUNCT
ma-105	656	24	v	v	NOUN
ma-105	656	25	)	)	PUNCT
ma-105	656	26	∈	∈	PROPN
ma-105	657	1	σ|dl1	σ|dl1	NOUN
ma-105	657	2	dt	dt	NOUN
ma-105	658	1	=	=	NOUN
ma-105	658	2	0	0	NUM
ma-105	658	3	}	}	PUNCT
ma-105	658	4	.we	.we	PUNCT
ma-105	659	1	realize	realize	VERB
ma-105	659	2	that	that	DET
ma-105	659	3	dl1	dl1	NOUN
ma-105	659	4	dt	dt	X
ma-105	660	1	=	=	SYM
ma-105	660	2	0	0	PUNCT
ma-105	661	1	if	if	SCONJ
ma-105	661	2	and	and	CCONJ
ma-105	661	3	only	only	ADV
ma-105	661	4	if	if	SCONJ
ma-105	661	5	v	v	NOUN
ma-105	661	6	=	=	SYM
ma-105	661	7	0	0	PUNCT
ma-105	662	1	and	and	CCONJ
ma-105	662	2	i	i	PRON
ma-105	662	3	=	=	NOUN
ma-105	662	4	0	0	X
ma-105	662	5	.	.	PUNCT
ma-105	663	1	each	each	DET
ma-105	663	2	element	element	NOUN
ma-105	663	3	of	of	ADP
ma-105	663	4	υ	υ	PROPN
ma-105	663	5	satisfies	satisfie	NOUN
ma-105	663	6	v	v	ADP
ma-105	663	7	=	=	SYM
ma-105	663	8	0	0	NUM
ma-105	663	9	andconsequently	andconsequently	ADV
ma-105	663	10	i=0	i=0	PROPN
ma-105	663	11	.	.	PUNCT
ma-105	663	12	by	by	ADP
ma-105	663	13	lyapunov	lyapunov	PROPN
ma-105	663	14	-	-	PUNCT
ma-105	663	15	lasalle	lasalle	PROPN
ma-105	663	16	invariance	invariance	NOUN
ma-105	663	17	principle	principle	NOUN
ma-105	664	1	[	[	X
ma-105	664	2	27	27	NUM
ma-105	664	3	]	]	PUNCT
ma-105	664	4	,	,	PUNCT
ma-105	664	5	e0	e0	PROPN
ma-105	664	6	is	be	AUX
ma-105	664	7	globally	globally	ADV
ma-105	664	8	asymptoticallystable	asymptoticallystable	ADJ
ma-105	664	9	if	if	SCONJ
ma-105	664	10	τ0	τ0	PROPN
ma-105	664	11	<	<	X
ma-105	664	12	1	1	X
ma-105	664	13	.	.	PUNCT
ma-105	665	1	so	so	ADV
ma-105	665	2	,	,	PUNCT
ma-105	665	3	we	we	PRON
ma-105	665	4	obtain	obtain	VERB
ma-105	665	5	a	a	DET
ma-105	665	6	sufficient	sufficient	ADJ
ma-105	665	7	condition	condition	NOUN
ma-105	665	8	r0	r0	NOUN
ma-105	665	9	≤	≤	PUNCT
ma-105	665	10	τ0	τ0	NOUN
ma-105	665	11	which	which	PRON
ma-105	665	12	ensures	ensure	VERB
ma-105	665	13	that	that	SCONJ
ma-105	665	14	the	the	DET
ma-105	665	15	hcv	hcv	PROPN
ma-105	665	16	spatiallyhomogeneous	spatiallyhomogeneous	PROPN
ma-105	665	17	equilibrium	equilibrium	PROPN
ma-105	665	18	e0	e0	PROPN
ma-105	665	19	of	of	ADP
ma-105	665	20	pde	pde	NOUN
ma-105	665	21	-	-	PUNCT
ma-105	665	22	model	model	NOUN
ma-105	665	23	system	system	NOUN
ma-105	665	24	(	(	PUNCT
ma-105	665	25	2.4	2.4	NUM
ma-105	665	26	)	)	PUNCT
ma-105	665	27	is	be	AUX
ma-105	665	28	globally	globally	ADV
ma-105	665	29	asymptotically	asymptotically	ADV
ma-105	665	30	stable	stable	ADJ
ma-105	665	31	if	if	SCONJ
ma-105	665	32	τ0	τ0	PROPN
ma-105	665	33	<	<	X
ma-105	665	34	1.this	1.this	NUM
ma-105	665	35	completes	complete	VERB
ma-105	665	36	the	the	DET
ma-105	665	37	proof	proof	NOUN
ma-105	665	38	of	of	ADP
ma-105	665	39	theorem	theorem	ADJ
ma-105	665	40	4.3	4.3	NUM
ma-105	665	41	.	.	PUNCT
ma-105	665	42	�	�	PROPN
ma-105	665	43	4.6	4.6	NUM
ma-105	665	44	.	.	PUNCT
ma-105	666	1	local	local	ADJ
ma-105	666	2	stability	stability	NOUN
ma-105	666	3	of	of	ADP
ma-105	666	4	hcv	hcv	X
ma-105	666	5	spatially	spatially	ADV
ma-105	666	6	homogeneous	homogeneous	ADJ
ma-105	666	7	infected	infected	ADJ
ma-105	666	8	equilibrium	equilibrium	NOUN
ma-105	666	9	.	.	PUNCT
ma-105	667	1	let	let	VERB
ma-105	667	2	us	we	PRON
ma-105	667	3	study	study	VERB
ma-105	667	4	the	the	DET
ma-105	667	5	localstability	localstability	NOUN
ma-105	667	6	of	of	ADP
ma-105	667	7	the	the	DET
ma-105	667	8	unique	unique	ADJ
ma-105	667	9	infected	infect	VERB
ma-105	667	10	spatially	spatially	ADV
ma-105	667	11	homogeneous	homogeneous	ADJ
ma-105	667	12	equilibrium	equilibrium	NOUN
ma-105	667	13	e∗	e∗	NOUN
ma-105	667	14	of	of	ADP
ma-105	667	15	our	our	PRON
ma-105	667	16	pde	pde	NOUN
ma-105	667	17	-	-	PUNCT
ma-105	667	18	model	model	NOUN
ma-105	667	19	system.consider	system.consider	NUM
ma-105	667	20	the	the	DET
ma-105	667	21	laplace	laplace	NOUN
ma-105	667	22	operator	operator	NOUN
ma-105	667	23	−∆	−∆	NOUN
ma-105	667	24	and	and	CCONJ
ma-105	667	25	let	let	VERB
ma-105	667	26	0	0	NUM
ma-105	667	27	=	=	SYM
ma-105	667	28	µ1	µ1	PROPN
ma-105	667	29	<	<	X
ma-105	667	30	µ2	µ2	PROPN
ma-105	667	31	<	<	X
ma-105	667	32	µ3	µ3	PROPN
ma-105	667	33	<	<	X
ma-105	667	34	·	·	PUNCT
ma-105	667	35	·	·	PUNCT
ma-105	667	36	·	·	PUNCT
ma-105	667	37	be	be	AUX
ma-105	667	38	its	its	PRON
ma-105	667	39	eigenvalues	eigenvalue	NOUN
ma-105	667	40	on	on	ADP
ma-105	667	41	ω	ω	NUM
ma-105	667	42	withthe	withthe	ADJ
ma-105	667	43	homogeneous	homogeneous	ADJ
ma-105	667	44	neumann	neumann	PROPN
ma-105	667	45	boundary	boundary	ADJ
ma-105	667	46	condition	condition	NOUN
ma-105	667	47	,	,	PUNCT
ma-105	667	48	and	and	CCONJ
ma-105	667	49	eµl	eµl	NOUN
ma-105	667	50	be	be	AUX
ma-105	667	51	the	the	DET
ma-105	667	52	eigenspace	eigenspace	NOUN
ma-105	667	53	corresponding	correspond	VERB
ma-105	667	54	to	to	ADP
ma-105	667	55	µlin	µlin	PROPN
ma-105	667	56	c1(ω	c1(ω	PROPN
ma-105	667	57	)	)	PUNCT
ma-105	667	58	.	.	PUNCT
ma-105	668	1	let	let	VERB
ma-105	668	2	also	also	ADV
ma-105	668	3	x	x	PUNCT
ma-105	668	4	=	=	SYM
ma-105	668	5	(	(	PUNCT
ma-105	668	6	c1(ω))3	c1(ω))3	PROPN
ma-105	668	7	,	,	PUNCT
ma-105	668	8	{	{	PUNCT
ma-105	668	9	ϕl	ϕl	PROPN
ma-105	668	10	j	j	PROPN
ma-105	668	11	,	,	PUNCT
ma-105	668	12	j	j	PROPN
ma-105	668	13	=	=	SYM
ma-105	668	14	1	1	NUM
ma-105	668	15	,	,	PUNCT
ma-105	668	16	2	2	NUM
ma-105	668	17	,	,	PUNCT
ma-105	668	18	·	·	PUNCT
ma-105	668	19	·	·	PUNCT
ma-105	668	20	·	·	PUNCT
ma-105	668	21	,	,	PUNCT
ma-105	668	22	d	d	PROPN
ma-105	668	23	imeµl	imeµl	PROPN
ma-105	668	24	}	}	PUNCT
ma-105	668	25	be	be	AUX
ma-105	668	26	an	an	DET
ma-105	668	27	orthogonal	orthogonal	ADJ
ma-105	668	28	basis	basis	NOUN
ma-105	668	29	of	of	ADP
ma-105	668	30	eµl	eµl	NOUN
ma-105	668	31	and	and	CCONJ
ma-105	668	32	xl	xl	PROPN
ma-105	668	33	j	j	PROPN
ma-105	669	1	=	=	PRON
ma-105	669	2	{	{	PUNCT
ma-105	669	3	ϕl	ϕl	PROPN
ma-105	669	4	jc	jc	PROPN
ma-105	669	5	/	/	SYM
ma-105	669	6	c	c	PROPN
ma-105	669	7	∈	∈	PROPN
ma-105	669	8	r3}.then	r3}.then	NOUN
ma-105	669	9	,	,	PUNCT
ma-105	669	10	x	x	PUNCT
ma-105	669	11	=	=	PUNCT
ma-105	669	12	∞⊕	∞⊕	PROPN
ma-105	670	1	l=1	l=1	X
ma-105	670	2	xl	xl	INTJ
ma-105	670	3	with	with	ADP
ma-105	670	4	xl	xl	PROPN
ma-105	670	5	=	=	PUNCT
ma-105	671	1	dimeµl⊕	dimeµl⊕	NOUN
ma-105	671	2	j=1	j=1	PROPN
ma-105	671	3	xl	xl	PROPN
ma-105	671	4	j	j	PROPN
ma-105	671	5	.	.	PUNCT
ma-105	672	1	now	now	ADV
ma-105	672	2	,	,	PUNCT
ma-105	672	3	let	let	VERB
ma-105	672	4	set	set	VERB
ma-105	672	5	w1	w1	NOUN
ma-105	672	6	=	=	SYM
ma-105	672	7	h	h	NOUN
ma-105	672	8	,	,	PUNCT
ma-105	672	9	w2	w2	NOUN
ma-105	672	10	=	=	PROPN
ma-105	672	11	i	i	PROPN
ma-105	672	12	,	,	PUNCT
ma-105	672	13	w3	w3	PROPN
ma-105	672	14	=	=	PROPN
ma-105	672	15	v	v	PROPN
ma-105	672	16	.	.	PUNCT
ma-105	673	1	further	far	ADV
ma-105	673	2	we	we	PRON
ma-105	673	3	use	use	VERB
ma-105	673	4	the	the	DET
ma-105	673	5	vector	vector	NOUN
ma-105	673	6	notation	notation	NOUN
ma-105	673	7	w	w	PROPN
ma-105	673	8	=	=	SYM
ma-105	673	9	(	(	PUNCT
ma-105	673	10	w1	w1	NOUN
ma-105	673	11	,	,	PUNCT
ma-105	673	12	w2	w2	NOUN
ma-105	673	13	,	,	PUNCT
ma-105	673	14	w3)t	w3)t	NOUN
ma-105	673	15	=	=	SYM
ma-105	673	16	(	(	PUNCT
ma-105	673	17	h	h	NOUN
ma-105	673	18	,	,	PUNCT
ma-105	673	19	i	i	PRON
ma-105	673	20	,	,	PUNCT
ma-105	673	21	v	v	NOUN
ma-105	673	22	)	)	PUNCT
ma-105	673	23	t	t	PROPN
ma-105	673	24	.	.	PUNCT
ma-105	674	1	then	then	ADV
ma-105	674	2	the	the	DET
ma-105	674	3	linearization	linearization	NOUN
ma-105	674	4	of	of	ADP
ma-105	674	5	the	the	DET
ma-105	674	6	pde	pde	NOUN
ma-105	674	7	system	system	NOUN
ma-105	674	8	at	at	ADP
ma-105	674	9	e∗	e∗	PROPN
ma-105	674	10	is	be	AUX
ma-105	674	11	of	of	ADP
ma-105	674	12	the	the	DET
ma-105	674	13	form	form	NOUN
ma-105	674	14	wt	wt	NOUN
ma-105	674	15	=	=	PUNCT
ma-105	674	16	lw	lw	NOUN
ma-105	674	17	=	=	PUNCT
ma-105	674	18	d∆w	d∆w	PROPN
ma-105	675	1	+	+	NOUN
ma-105	675	2	k(e∗)w	k(e∗)w	PROPN
ma-105	675	3	,	,	PUNCT
ma-105	675	4	https://doi.org/10.28924/ada/ma.3.1	https://doi.org/10.28924/ada/ma.3.1	PROPN
ma-105	675	5	eur	eur	PROPN
ma-105	675	6	.	.	PUNCT
ma-105	676	1	j.	j.	PROPN
ma-105	676	2	math	math	PROPN
ma-105	676	3	.	.	PUNCT
ma-105	677	1	anal	anal	PROPN
ma-105	677	2	.	.	PUNCT
ma-105	678	1	10.28924	10.28924	NUM
ma-105	678	2	/	/	SYM
ma-105	678	3	ada	ada	PROPN
ma-105	678	4	/	/	SYM
ma-105	678	5	ma.3.1	ma.3.1	PROPN
ma-105	678	6	24where	24where	X
ma-105	679	1	k(e∗)w	k(e∗)w	PROPN
ma-105	679	2	=	=	SYM
ma-105	680	1			PROPN
ma-105	680	2	−	−	X
ma-105	681	1	(	(	PUNCT
ma-105	681	2	d	d	NOUN
ma-105	681	3	+	+	PUNCT
ma-105	682	1	a)w1	a)w1	ADV
ma-105	682	2	+	+	PUNCT
ma-105	682	3	ρw2	ρw2	NOUN
ma-105	682	4	−	−	PROPN
ma-105	682	5	bw3	bw3	PROPN
ma-105	682	6	aw1	aw1	VERB
ma-105	682	7	−	−	PROPN
ma-105	682	8	(	(	PUNCT
ma-105	682	9	α+	α+	PROPN
ma-105	682	10	ρ)w2	ρ)w2	PROPN
ma-105	682	11	+	+	CCONJ
ma-105	682	12	bw3	bw3	PROPN
ma-105	682	13	−uaw1	−uaw1	PROPN
ma-105	683	1	+	+	PUNCT
ma-105	683	2	(	(	PUNCT
ma-105	683	3	1−	1−	NUM
ma-105	683	4	ε)kw2	ε)kw2	NOUN
ma-105	683	5	−	−	PROPN
ma-105	683	6	(	(	PUNCT
ma-105	683	7	µ+	µ+	X
ma-105	683	8	ub)w3	ub)w3	NOUN
ma-105	683	9			NOUN
ma-105	683	10	,	,	PUNCT
ma-105	683	11	(	(	PUNCT
ma-105	683	12	4.13	4.13	NUM
ma-105	683	13	)	)	PUNCT
ma-105	683	14	with	with	ADP
ma-105	683	15	a	a	PRON
ma-105	683	16	=	=	SYM
ma-105	683	17	(	(	PUNCT
ma-105	683	18	1−	1−	NUM
ma-105	683	19	η)(α0	η)(α0	NOUN
ma-105	683	20	+	+	CCONJ
ma-105	683	21	α2v	α2v	SYM
ma-105	683	22	∗)βv	∗)βv	NUM
ma-105	683	23	∗	∗	NOUN
ma-105	683	24	(	(	PUNCT
ma-105	683	25	α0	α0	ADJ
ma-105	683	26	+	+	NUM
ma-105	683	27	α1h∗	α1h∗	NUM
ma-105	683	28	+	+	CCONJ
ma-105	683	29	α2v	α2v	NOUN
ma-105	683	30	∗	∗	NOUN
ma-105	683	31	+	+	CCONJ
ma-105	683	32	α3h∗v	α3h∗v	PROPN
ma-105	683	33	∗)2and	∗)2and	PROPN
ma-105	683	34	b	b	PROPN
ma-105	683	35	=	=	SYM
ma-105	683	36	(	(	PUNCT
ma-105	683	37	1−	1−	NUM
ma-105	683	38	η)(α0	η)(α0	X
ma-105	683	39	+	+	CCONJ
ma-105	683	40	α1h	α1h	ADV
ma-105	683	41	∗)βh∗	∗)βh∗	ADV
ma-105	683	42	(	(	PUNCT
ma-105	683	43	α0	α0	ADJ
ma-105	683	44	+	+	NUM
ma-105	683	45	α1h∗	α1h∗	NUM
ma-105	683	46	+	+	CCONJ
ma-105	683	47	α2v	α2v	NOUN
ma-105	683	48	∗	∗	NOUN
ma-105	683	49	+	+	CCONJ
ma-105	683	50	α3h∗v	α3h∗v	NOUN
ma-105	683	51	∗)2	∗)2	PROPN
ma-105	683	52	.	.	PUNCT
ma-105	684	1	for	for	ADP
ma-105	684	2	each	each	DET
ma-105	684	3	l	l	NOUN
ma-105	684	4	≥	≥	NUM
ma-105	684	5	1	1	NUM
ma-105	684	6	,	,	PUNCT
ma-105	684	7	xl	xl	PROPN
ma-105	684	8	is	be	AUX
ma-105	684	9	invariant	invariant	ADJ
ma-105	684	10	under	under	ADP
ma-105	684	11	the	the	DET
ma-105	684	12	operator	operator	NOUN
ma-105	684	13	l	l	NOUN
ma-105	684	14	,	,	PUNCT
ma-105	684	15	and	and	CCONJ
ma-105	684	16	λ̃	λ̃	PROPN
ma-105	684	17	is	be	AUX
ma-105	684	18	an	an	DET
ma-105	684	19	eigenvalue	eigenvalue	ADJ
ma-105	684	20	l	l	NOUN
ma-105	684	21	if	if	SCONJ
ma-105	684	22	and	and	CCONJ
ma-105	684	23	only	only	ADV
ma-105	684	24	if	if	SCONJ
ma-105	684	25	it	it	PRON
ma-105	684	26	isan	isan	ADJ
ma-105	684	27	eigenvalue	eigenvalue	PROPN
ma-105	684	28	of	of	ADP
ma-105	684	29	the	the	DET
ma-105	684	30	matrix	matrix	NOUN
ma-105	684	31	−µld	−µld	VERB
ma-105	684	32	+	+	SYM
ma-105	684	33	k(e∗	k(e∗	X
ma-105	684	34	)	)	PUNCT
ma-105	684	35	for	for	ADP
ma-105	684	36	some	some	DET
ma-105	684	37	l	l	NOUN
ma-105	684	38	≥	≥	NOUN
ma-105	684	39	1	1	NUM
ma-105	684	40	,	,	PUNCT
ma-105	684	41	in	in	ADP
ma-105	684	42	which	which	DET
ma-105	684	43	case	case	NOUN
ma-105	684	44	,	,	PUNCT
ma-105	684	45	there	there	PRON
ma-105	684	46	is	be	VERB
ma-105	684	47	an	an	DET
ma-105	684	48	eigenvectorin	eigenvectorin	NOUN
ma-105	684	49	xl	xl	PROPN
ma-105	684	50	.	.	PUNCT
ma-105	685	1	therefore	therefore	ADV
ma-105	685	2	we	we	PRON
ma-105	685	3	get	get	VERB
ma-105	685	4	:	:	PUNCT
ma-105	685	5	det	det	X
ma-105	685	6	(	(	PUNCT
ma-105	685	7	−	−	PROPN
ma-105	685	8	µld+k(e∗)−	µld+k(e∗)−	PROPN
ma-105	685	9	λ̃id	λ̃id	X
ma-105	685	10	)	)	PUNCT
ma-105	685	11	=	=	PUNCT
ma-105	685	12	∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣	ADP
ma-105	685	13	−(µld1	−(µld1	NOUN
ma-105	685	14	+	+	X
ma-105	685	15	d	d	X
ma-105	685	16	+	+	CCONJ
ma-105	685	17	a)−	a)−	PROPN
ma-105	685	18	λ̃	λ̃	PROPN
ma-105	685	19	ρ	ρ	NOUN
ma-105	685	20	−b	−b	ADP
ma-105	685	21	a	a	DET
ma-105	685	22	−(µld2	−(µld2	ADJ
ma-105	685	23	+	+	CCONJ
ma-105	686	1	α+	α+	PUNCT
ma-105	686	2	ρ)−	ρ)−	PROPN
ma-105	686	3	λ̃	λ̃	PROPN
ma-105	686	4	b	b	PROPN
ma-105	686	5	−ua	−ua	NOUN
ma-105	686	6	(	(	PUNCT
ma-105	686	7	1−	1−	NUM
ma-105	686	8	ε)k	ε)k	ADJ
ma-105	686	9	−	−	PROPN
ma-105	686	10	(	(	PUNCT
ma-105	686	11	µld3	µld3	PROPN
ma-105	686	12	+	+	CCONJ
ma-105	686	13	µ+	µ+	PRON
ma-105	686	14	ub)−	ub)−	NOUN
ma-105	686	15	λ̃	λ̃	PROPN
ma-105	686	16	∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣	PROPN
ma-105	686	17	.	.	PUNCT
ma-105	687	1	the	the	DET
ma-105	687	2	characteristic	characteristic	ADJ
ma-105	687	3	equation	equation	NOUN
ma-105	687	4	of	of	ADP
ma-105	687	5	−µld	−µld	ADJ
ma-105	687	6	+	+	SYM
ma-105	687	7	k(e∗	k(e∗	NOUN
ma-105	687	8	)	)	PUNCT
ma-105	687	9	is	be	AUX
ma-105	687	10	on	on	ADP
ma-105	687	11	the	the	DET
ma-105	687	12	form	form	NOUN
ma-105	687	13	λ̃3	λ̃3	X
ma-105	687	14	+	+	CCONJ
ma-105	687	15	a2λ̃	a2λ̃	NOUN
ma-105	687	16	2	2	NUM
ma-105	687	17	+	+	CCONJ
ma-105	687	18	a1λ̃+	a1λ̃+	PROPN
ma-105	687	19	a0	a0	PROPN
ma-105	687	20	=	=	SYM
ma-105	687	21	0	0	NUM
ma-105	687	22	(	(	PUNCT
ma-105	687	23	4.14	4.14	NUM
ma-105	687	24	)	)	PUNCT
ma-105	687	25	where	where	SCONJ
ma-105	687	26	a2	a2	PROPN
ma-105	687	27	=	=	PUNCT
ma-105	687	28	(	(	PUNCT
ma-105	687	29	µld1	µld1	VERB
ma-105	687	30	+	+	CCONJ
ma-105	687	31	d	d	X
ma-105	687	32	+	+	CCONJ
ma-105	687	33	a+	a+	PUNCT
ma-105	687	34	µld2	µld2	PROPN
ma-105	687	35	+	+	CCONJ
ma-105	687	36	α+	α+	X
ma-105	687	37	ρ+	ρ+	NOUN
ma-105	687	38	µld3	µld3	NOUN
ma-105	687	39	+	+	CCONJ
ma-105	687	40	µ+	µ+	PROPN
ma-105	687	41	ub	ub	PROPN
ma-105	687	42	)	)	PUNCT
ma-105	687	43	>	>	X
ma-105	687	44	0	0	NUM
ma-105	687	45	,	,	PUNCT
ma-105	687	46	a1	a1	NOUN
ma-105	687	47	=	=	PUNCT
ma-105	687	48	(	(	PUNCT
ma-105	687	49	µld1	µld1	VERB
ma-105	687	50	+	+	PROPN
ma-105	687	51	d+a)(µld2	d+a)(µld2	X
ma-105	688	1	+	+	ADJ
ma-105	688	2	α+ρ+µld3	α+ρ+µld3	PROPN
ma-105	688	3	+	+	PROPN
ma-105	688	4	µ+ub	µ+ub	NOUN
ma-105	688	5	)	)	PUNCT
ma-105	689	1	+	+	CCONJ
ma-105	689	2	(	(	PUNCT
ma-105	689	3	µld2	µld2	PROPN
ma-105	689	4	+	+	NOUN
ma-105	689	5	α+ρ)(µld3	α+ρ)(µld3	X
ma-105	690	1	+	+	ADJ
ma-105	690	2	µ+ub)−(1−ε)kb	µ+ub)−(1−ε)kb	NUM
ma-105	690	3	,	,	PUNCT
ma-105	691	1	a0	a0	PROPN
ma-105	691	2	=	=	SYM
ma-105	691	3	(	(	PUNCT
ma-105	691	4	µld1	µld1	VERB
ma-105	691	5	+	+	CCONJ
ma-105	691	6	d	d	X
ma-105	691	7	+	+	CCONJ
ma-105	691	8	a)(µld2	a)(µld2	NOUN
ma-105	691	9	+	+	CCONJ
ma-105	691	10	α+	α+	PUNCT
ma-105	691	11	ρ)(µld3	ρ)(µld3	PROPN
ma-105	691	12	+	+	NUM
ma-105	691	13	µ+	µ+	PRON
ma-105	691	14	ub)−	ub)−	NOUN
ma-105	691	15	(	(	PUNCT
ma-105	691	16	µld1	µld1	VERB
ma-105	691	17	+	+	CCONJ
ma-105	691	18	d	d	PROPN
ma-105	692	1	+	+	CCONJ
ma-105	692	2	a)(1−	a)(1−	PROPN
ma-105	692	3	ε)kb.if	ε)kb.if	PROPN
ma-105	692	4	a1	a1	PROPN
ma-105	692	5	>	>	X
ma-105	692	6	0	0	PUNCT
ma-105	692	7	and	and	CCONJ
ma-105	692	8	a1a2	a1a2	INTJ
ma-105	692	9	>	>	X
ma-105	692	10	a0	a0	NOUN
ma-105	692	11	from	from	ADP
ma-105	692	12	the	the	DET
ma-105	692	13	above	above	ADJ
ma-105	692	14	investigations	investigation	NOUN
ma-105	692	15	,	,	PUNCT
ma-105	692	16	it	it	PRON
ma-105	692	17	then	then	ADV
ma-105	692	18	follows	follow	VERB
ma-105	692	19	from	from	ADP
ma-105	692	20	routh	routh	PROPN
ma-105	692	21	-	-	PUNCT
ma-105	692	22	hurwitz	hurwitz	PROPN
ma-105	692	23	criterionthat	criterionthat	PRON
ma-105	692	24	all	all	DET
ma-105	692	25	roots	root	NOUN
ma-105	692	26	of	of	ADP
ma-105	692	27	(	(	PUNCT
ma-105	692	28	4.14	4.14	NUM
ma-105	692	29	)	)	PUNCT
ma-105	692	30	have	have	VERB
ma-105	692	31	negative	negative	ADJ
ma-105	692	32	real	real	ADJ
ma-105	692	33	parts	part	NOUN
ma-105	692	34	and	and	CCONJ
ma-105	692	35	therefore	therefore	ADV
ma-105	692	36	we	we	PRON
ma-105	692	37	have	have	VERB
ma-105	692	38	the	the	DET
ma-105	692	39	following	follow	VERB
ma-105	692	40	result	result	NOUN
ma-105	692	41	.	.	PUNCT
ma-105	693	1	theorem	theorem	VERB
ma-105	693	2	4.4	4.4	NUM
ma-105	693	3	.	.	PUNCT
ma-105	694	1	if	if	SCONJ
ma-105	694	2	a1	a1	NOUN
ma-105	694	3	>	>	X
ma-105	694	4	0	0	PUNCT
ma-105	694	5	and	and	CCONJ
ma-105	694	6	a1a2	a1a2	INTJ
ma-105	694	7	>	>	X
ma-105	694	8	a0	a0	PROPN
ma-105	694	9	,	,	PUNCT
ma-105	694	10	then	then	ADV
ma-105	694	11	the	the	DET
ma-105	694	12	spatially	spatially	ADV
ma-105	694	13	homogeneous	homogeneous	ADJ
ma-105	694	14	infected	infected	ADJ
ma-105	694	15	equilibrium	equilibrium	NOUN
ma-105	694	16	e∗	e∗	NOUN
ma-105	695	1	=	=	SYM
ma-105	695	2	(	(	PUNCT
ma-105	695	3	h∗	h∗	PROPN
ma-105	695	4	,	,	PUNCT
ma-105	695	5	i∗	i∗	PROPN
ma-105	695	6	,	,	PUNCT
ma-105	695	7	v	v	NOUN
ma-105	695	8	∗	∗	NOUN
ma-105	695	9	)	)	PUNCT
ma-105	695	10	of	of	ADP
ma-105	695	11	the	the	DET
ma-105	695	12	pde	pde	NOUN
ma-105	695	13	-	-	PUNCT
ma-105	695	14	model	model	NOUN
ma-105	695	15	system	system	NOUN
ma-105	695	16	(	(	PUNCT
ma-105	695	17	2.4	2.4	NUM
ma-105	695	18	)	)	PUNCT
ma-105	695	19	is	be	AUX
ma-105	695	20	locally	locally	ADV
ma-105	695	21	asymptotically	asymptotically	ADV
ma-105	695	22	stable	stable	ADJ
ma-105	695	23	when	when	SCONJ
ma-105	695	24	it	it	PRON
ma-105	695	25	exists	exist	VERB
ma-105	695	26	.	.	PUNCT
ma-105	696	1	4.7	4.7	NUM
ma-105	696	2	.	.	PUNCT
ma-105	696	3	global	global	ADJ
ma-105	696	4	stability	stability	NOUN
ma-105	696	5	of	of	ADP
ma-105	696	6	hcv	hcv	NOUN
ma-105	696	7	-	-	PUNCT
ma-105	696	8	spatially	spatially	ADV
ma-105	696	9	homogeneous	homogeneous	ADJ
ma-105	696	10	infected	infected	ADJ
ma-105	696	11	equilibrium	equilibrium	NOUN
ma-105	696	12	.	.	PUNCT
ma-105	697	1	the	the	DET
ma-105	697	2	objective	objective	NOUN
ma-105	697	3	of	of	ADP
ma-105	697	4	thissection	thissection	NOUN
ma-105	697	5	is	be	AUX
ma-105	697	6	to	to	PART
ma-105	697	7	discuss	discuss	VERB
ma-105	697	8	the	the	DET
ma-105	697	9	global	global	ADJ
ma-105	697	10	stability	stability	NOUN
ma-105	697	11	of	of	ADP
ma-105	697	12	the	the	DET
ma-105	697	13	spatially	spatially	ADV
ma-105	697	14	homogeneous	homogeneous	ADJ
ma-105	697	15	infected	infect	VERB
ma-105	697	16	equilibrium	equilibrium	NOUN
ma-105	697	17	e∗	e∗	PROPN
ma-105	697	18	forthe	forthe	DET
ma-105	697	19	pde	pde	NOUN
ma-105	697	20	system	system	NOUN
ma-105	697	21	(	(	PUNCT
ma-105	697	22	2.4	2.4	NUM
ma-105	697	23	)	)	PUNCT
ma-105	697	24	.	.	PUNCT
ma-105	698	1	we	we	PRON
ma-105	698	2	address	address	VERB
ma-105	698	3	global	global	ADJ
ma-105	698	4	stability	stability	NOUN
ma-105	698	5	by	by	ADP
ma-105	698	6	using	use	VERB
ma-105	698	7	the	the	DET
ma-105	698	8	method	method	NOUN
ma-105	698	9	of	of	ADP
ma-105	698	10	construction	construction	NOUN
ma-105	698	11	of	of	ADP
ma-105	698	12	lyapunovfunctionals	lyapunovfunctional	NOUN
ma-105	698	13	.	.	PUNCT
ma-105	699	1	these	these	DET
ma-105	699	2	lyapunov	lyapunov	ADJ
ma-105	699	3	functional	functional	NOUN
ma-105	699	4	is	be	AUX
ma-105	699	5	obtained	obtain	VERB
ma-105	699	6	from	from	ADP
ma-105	699	7	those	those	PRON
ma-105	699	8	for	for	ADP
ma-105	699	9	differential	differential	ADJ
ma-105	699	10	equations	equation	NOUN
ma-105	699	11	by	by	ADP
ma-105	699	12	applyingthe	applyingthe	DET
ma-105	699	13	method	method	NOUN
ma-105	699	14	of	of	ADP
ma-105	699	15	hattaf	hattaf	NOUN
ma-105	699	16	and	and	CCONJ
ma-105	699	17	yousfi	yousfi	ADV
ma-105	699	18	presented	present	VERB
ma-105	699	19	in	in	ADP
ma-105	699	20	[	[	X
ma-105	699	21	15	15	NUM
ma-105	699	22	]	]	PUNCT
ma-105	699	23	.	.	PUNCT
ma-105	700	1	we	we	PRON
ma-105	700	2	address	address	VERB
ma-105	700	3	this	this	DET
ma-105	700	4	study	study	NOUN
ma-105	700	5	with	with	ADP
ma-105	700	6	certain	certain	ADJ
ma-105	700	7	assumptionsnamely	assumptionsnamely	ADV
ma-105	700	8	:	:	PUNCT
ma-105	700	9	u	u	NOUN
ma-105	700	10	=	=	NOUN
ma-105	700	11	0	0	PUNCT
ma-105	700	12	(	(	PUNCT
ma-105	700	13	i.e.	i.e.	X
ma-105	700	14	,	,	PUNCT
ma-105	700	15	there	there	PRON
ma-105	700	16	is	be	VERB
ma-105	700	17	no	no	DET
ma-105	700	18	absorption	absorption	NOUN
ma-105	700	19	effect	effect	NOUN
ma-105	700	20	)	)	PUNCT
ma-105	700	21	,	,	PUNCT
ma-105	700	22	α0	α0	ADJ
ma-105	700	23	=	=	SYM
ma-105	700	24	1	1	NUM
ma-105	700	25	et	et	NOUN
ma-105	700	26	α3	α3	NOUN
ma-105	700	27	=	=	PUNCT
ma-105	701	1	α1α2	α1α2	X
ma-105	701	2	.	.	PUNCT
ma-105	702	1	thus	thus	ADV
ma-105	702	2	we	we	PRON
ma-105	702	3	have	have	VERB
ma-105	702	4	thefollowing	thefollowing	NOUN
ma-105	702	5	results	result	NOUN
ma-105	702	6	.	.	PUNCT
ma-105	703	1	theorem	theorem	VERB
ma-105	703	2	4.5	4.5	NUM
ma-105	703	3	.	.	PUNCT
ma-105	704	1	the	the	DET
ma-105	704	2	spatially	spatially	ADV
ma-105	704	3	homogeneous	homogeneous	ADJ
ma-105	704	4	infected	infect	VERB
ma-105	704	5	equilibrium	equilibrium	NOUN
ma-105	704	6	e∗	e∗	PROPN
ma-105	704	7	of	of	ADP
ma-105	704	8	pde	pde	NOUN
ma-105	704	9	-	-	PUNCT
ma-105	704	10	model	model	NOUN
ma-105	704	11	system	system	NOUN
ma-105	704	12	(	(	PUNCT
ma-105	704	13	2.4	2.4	NUM
ma-105	704	14	)	)	PUNCT
ma-105	704	15	is	be	AUX
ma-105	704	16	globally	globally	ADV
ma-105	704	17	asymptotically	asymptotically	ADV
ma-105	704	18	stable	stable	ADJ
ma-105	704	19	when	when	SCONJ
ma-105	704	20	it	it	PRON
ma-105	704	21	exists	exist	VERB
ma-105	704	22	.	.	PUNCT
ma-105	705	1	https://doi.org/10.28924/ada/ma.3.1	https://doi.org/10.28924/ada/ma.3.1	PROPN
ma-105	705	2	eur	eur	PROPN
ma-105	705	3	.	.	PUNCT
ma-105	706	1	j.	j.	PROPN
ma-105	706	2	math	math	PROPN
ma-105	706	3	.	.	PUNCT
ma-105	707	1	anal	anal	PROPN
ma-105	707	2	.	.	PUNCT
ma-105	708	1	10.28924	10.28924	NUM
ma-105	708	2	/	/	SYM
ma-105	708	3	ada	ada	PROPN
ma-105	708	4	/	/	SYM
ma-105	708	5	ma.3.1	ma.3.1	PROPN
ma-105	708	6	25	25	NUM
ma-105	708	7	proof	proof	NOUN
ma-105	708	8	.	.	PUNCT
ma-105	709	1	we	we	PRON
ma-105	709	2	first	first	ADV
ma-105	709	3	define	define	VERB
ma-105	709	4	the	the	DET
ma-105	709	5	function	function	NOUN
ma-105	709	6	g2(h	g2(h	PROPN
ma-105	709	7	,	,	PUNCT
ma-105	709	8	i	i	PRON
ma-105	709	9	,	,	PUNCT
ma-105	709	10	v	v	NOUN
ma-105	709	11	)	)	PUNCT
ma-105	710	1	=	=	SYM
ma-105	710	2	h	h	NOUN
ma-105	711	1	−h∗	−h∗	NOUN
ma-105	711	2	−	−	PROPN
ma-105	711	3	∫	∫	PROPN
ma-105	711	4	h	h	PROPN
ma-105	711	5	h∗	h∗	PROPN
ma-105	711	6	(	(	PUNCT
ma-105	711	7	α+	α+	PROPN
ma-105	711	8	ρ)i∗	ρ)i∗	PROPN
ma-105	711	9	(	(	PUNCT
ma-105	711	10	1−η)βτv	1−η)βτv	NUM
ma-105	711	11	∗	∗	NOUN
ma-105	711	12	(	(	PUNCT
ma-105	711	13	1+α1τ)(1+α2v	1+α1τ)(1+α2v	NUM
ma-105	711	14	∗	∗	NOUN
ma-105	711	15	)	)	PUNCT
ma-105	711	16	dτ	dτ	NOUN
ma-105	712	1	+	+	CCONJ
ma-105	713	1	i	i	PRON
ma-105	713	2	−	−	PROPN
ma-105	713	3	i∗	i∗	NOUN
ma-105	713	4	−	−	NOUN
ma-105	714	1	i∗	i∗	NOUN
ma-105	714	2	ln	ln	NOUN
ma-105	714	3	(	(	PUNCT
ma-105	714	4	i	i	PRON
ma-105	714	5	i∗	i∗	VERB
ma-105	714	6	)	)	PUNCT
ma-105	715	1	+	+	CCONJ
ma-105	715	2	α+	α+	PROPN
ma-105	715	3	ρ	ρ	PROPN
ma-105	715	4	(	(	PUNCT
ma-105	715	5	1−	1−	NUM
ma-105	715	6	ε)k	ε)k	X
ma-105	715	7	(	(	PUNCT
ma-105	715	8	α0	α0	ADJ
ma-105	715	9	+	+	CCONJ
ma-105	715	10	α2v	α2v	NUM
ma-105	715	11	∗	∗	NOUN
ma-105	715	12	)	)	PUNCT
ma-105	715	13	v	v	ADP
ma-105	715	14	−	−	PROPN
ma-105	715	15	v	v	ADP
ma-105	715	16	∗	∗	NOUN
ma-105	715	17	−	−	PROPN
ma-105	715	18	∫	∫	PROPN
ma-105	715	19	v	v	NOUN
ma-105	715	20	v	v	NOUN
ma-105	715	21	∗	∗	NOUN
ma-105	715	22	(	(	PUNCT
ma-105	715	23	α+	α+	PROPN
ma-105	715	24	ρ)i∗	ρ)i∗	NOUN
ma-105	715	25	(	(	PUNCT
ma-105	715	26	1−η)βτh∗	1−η)βτh∗	NUM
ma-105	715	27	(	(	PUNCT
ma-105	715	28	1+α1h∗)(1+α2τ	1+α1h∗)(1+α2τ	NUM
ma-105	715	29	)	)	PUNCT
ma-105	715	30	dτ	dτ	NOUN
ma-105	715	31			PROPN
ma-105	715	32	.	.	PUNCT
ma-105	716	1	then	then	ADV
ma-105	716	2	,	,	PUNCT
ma-105	716	3	the	the	DET
ma-105	716	4	computation	computation	NOUN
ma-105	716	5	of	of	ADP
ma-105	716	6	the	the	DET
ma-105	716	7	derivative	derivative	NOUN
ma-105	716	8	of	of	ADP
ma-105	716	9	g2	g2	PROPN
ma-105	716	10	with	with	ADP
ma-105	716	11	respect	respect	NOUN
ma-105	716	12	to	to	ADP
ma-105	716	13	t	t	PROPN
ma-105	716	14	yields	yield	NOUN
ma-105	716	15	:	:	PUNCT
ma-105	716	16	dg2	dg2	PROPN
ma-105	716	17	dt	dt	X
ma-105	717	1	=	=	PUNCT
ma-105	717	2	[	[	PUNCT
ma-105	717	3	λ−	λ−	PROPN
ma-105	717	4	dh	dh	NOUN
ma-105	718	1	−	−	PROPN
ma-105	718	2	αi	αi	INTJ
ma-105	718	3	−	−	PROPN
ma-105	719	1	(	(	PUNCT
ma-105	719	2	α+	α+	X
ma-105	719	3	ρ)µ	ρ)µ	ADJ
ma-105	719	4	(	(	PUNCT
ma-105	719	5	1−	1−	NUM
ma-105	719	6	ε)k	ε)k	ADJ
ma-105	719	7	v	v	NOUN
ma-105	719	8	]	]	X
ma-105	719	9	−	−	PROPN
ma-105	719	10	(	(	PUNCT
ma-105	719	11	α+	α+	NUM
ma-105	719	12	ρ)i∗	ρ)i∗	PROPN
ma-105	719	13	(	(	PUNCT
ma-105	719	14	1	1	NUM
ma-105	719	15	+	+	NUM
ma-105	719	16	α1h)(1	α1h)(1	NUM
ma-105	719	17	+	+	CCONJ
ma-105	719	18	α2v	α2v	NOUN
ma-105	719	19	∗	∗	NOUN
ma-105	719	20	)	)	PUNCT
ma-105	719	21	(	(	PUNCT
ma-105	719	22	1−	1−	NUM
ma-105	719	23	η)βhv	η)βhv	PROPN
ma-105	719	24	∗	∗	NOUN
ma-105	719	25	[	[	PUNCT
ma-105	719	26	λ−	λ−	PROPN
ma-105	719	27	dh	dh	NOUN
ma-105	719	28	−	−	PROPN
ma-105	720	1	(	(	PUNCT
ma-105	720	2	1−	1−	NUM
ma-105	720	3	η)βhv	η)βhv	PROPN
ma-105	720	4	(	(	PUNCT
ma-105	720	5	1	1	NUM
ma-105	720	6	+	+	NUM
ma-105	720	7	α1h)(1	α1h)(1	NUM
ma-105	720	8	+	+	CCONJ
ma-105	720	9	α2v	α2v	NOUN
ma-105	720	10	)	)	PUNCT
ma-105	721	1	+	+	NUM
ma-105	721	2	ρi	ρi	X
ma-105	721	3	]	]	PUNCT
ma-105	721	4	−	−	PROPN
ma-105	721	5	i∗	i∗	NOUN
ma-105	722	1	i	i	PRON
ma-105	722	2	[	[	PUNCT
ma-105	722	3	(	(	PUNCT
ma-105	722	4	1−	1−	NUM
ma-105	722	5	η)βhv	η)βhv	PROPN
ma-105	722	6	(	(	PUNCT
ma-105	722	7	1	1	NUM
ma-105	722	8	+	+	NUM
ma-105	722	9	α1h)(1	α1h)(1	NUM
ma-105	722	10	+	+	CCONJ
ma-105	722	11	α2v	α2v	NOUN
ma-105	722	12	)	)	PUNCT
ma-105	722	13	−	−	PROPN
ma-105	722	14	(	(	PUNCT
ma-105	722	15	α+	α+	X
ma-105	722	16	ρ)i	ρ)i	NOUN
ma-105	722	17	]	]	PUNCT
ma-105	722	18	−	−	PROPN
ma-105	722	19	α+	α+	PUNCT
ma-105	722	20	ρ	ρ	PROPN
ma-105	722	21	(	(	PUNCT
ma-105	722	22	1−	1−	NUM
ma-105	722	23	ε)k	ε)k	ADJ
ma-105	722	24	v	v	ADP
ma-105	722	25	∗	∗	NOUN
ma-105	722	26	v	v	NOUN
ma-105	722	27	[	[	X
ma-105	722	28	(	(	PUNCT
ma-105	722	29	1−	1−	NUM
ma-105	722	30	ε)ki	ε)ki	PROPN
ma-105	722	31	−	−	NOUN
ma-105	722	32	µv	µv	NOUN
ma-105	722	33	]	]	PUNCT
ma-105	722	34	.	.	PUNCT
ma-105	723	1	since	since	SCONJ
ma-105	723	2	(	(	PUNCT
ma-105	723	3	1−	1−	NUM
ma-105	723	4	η)βh∗v	η)βh∗v	NOUN
ma-105	723	5	∗	∗	NOUN
ma-105	723	6	(	(	PUNCT
ma-105	723	7	1	1	NUM
ma-105	724	1	+	+	NUM
ma-105	724	2	α1h∗)(1	α1h∗)(1	PRON
ma-105	724	3	+	+	CCONJ
ma-105	724	4	α2v	α2v	NUM
ma-105	724	5	∗	∗	NOUN
ma-105	724	6	)	)	PUNCT
ma-105	724	7	=	=	SYM
ma-105	725	1	(	(	PUNCT
ma-105	725	2	α+	α+	PROPN
ma-105	725	3	ρ)i∗	ρ)i∗	NOUN
ma-105	725	4	,	,	PUNCT
ma-105	725	5	λ	λ	X
ma-105	725	6	=	=	PUNCT
ma-105	725	7	dh∗	dh∗	NOUN
ma-105	725	8	+	+	CCONJ
ma-105	725	9	αi∗	αi∗	NOUN
ma-105	725	10	,	,	PUNCT
ma-105	725	11	and	and	CCONJ
ma-105	725	12	(	(	PUNCT
ma-105	725	13	α+	α+	X
ma-105	725	14	ρ)µ	ρ)µ	ADJ
ma-105	725	15	(	(	PUNCT
ma-105	725	16	1−	1−	NUM
ma-105	725	17	ε)k	ε)k	X
ma-105	725	18	=	=	SYM
ma-105	725	19	(	(	PUNCT
ma-105	725	20	α+	α+	NOUN
ma-105	725	21	ρ)i∗	ρ)i∗	NUM
ma-105	725	22	v	v	ADP
ma-105	725	23	∗	∗	NOUN
ma-105	725	24	,	,	PUNCT
ma-105	725	25	we	we	PRON
ma-105	725	26	have	have	VERB
ma-105	725	27	dg2	dg2	PROPN
ma-105	725	28	dt	dt	NOUN
ma-105	725	29	=	=	PUNCT
ma-105	725	30	[	[	PUNCT
ma-105	725	31	dh∗	dh∗	X
ma-105	725	32	+	+	NUM
ma-105	725	33	αi∗	αi∗	NOUN
ma-105	725	34	−	−	X
ma-105	726	1	dh	dh	NOUN
ma-105	726	2	−	−	PROPN
ma-105	726	3	αi	αi	INTJ
ma-105	726	4	−	−	PROPN
ma-105	727	1	(	(	PUNCT
ma-105	727	2	α+	α+	NUM
ma-105	727	3	ρ)i∗	ρ)i∗	NUM
ma-105	727	4	v	v	NOUN
ma-105	727	5	v	v	NOUN
ma-105	727	6	∗	∗	NOUN
ma-105	727	7	]	]	PUNCT
ma-105	728	1	−(α+	−(α+	NUM
ma-105	728	2	ρ)i∗	ρ)i∗	PROPN
ma-105	728	3	(	(	PUNCT
ma-105	728	4	1	1	NUM
ma-105	728	5	+	+	NUM
ma-105	728	6	α1h)(1	α1h)(1	NUM
ma-105	728	7	+	+	CCONJ
ma-105	728	8	α2v	α2v	NOUN
ma-105	728	9	∗	∗	NOUN
ma-105	728	10	)	)	PUNCT
ma-105	728	11	(	(	PUNCT
ma-105	728	12	1−	1−	NUM
ma-105	728	13	η)βhv	η)βhv	PROPN
ma-105	728	14	∗	∗	NOUN
ma-105	728	15	[	[	PUNCT
ma-105	728	16	dh∗	dh∗	NOUN
ma-105	728	17	+	+	NUM
ma-105	728	18	αi∗	αi∗	NOUN
ma-105	728	19	−	−	NOUN
ma-105	728	20	dh	dh	NOUN
ma-105	728	21	−	−	PROPN
ma-105	728	22	(	(	PUNCT
ma-105	728	23	1−	1−	NUM
ma-105	728	24	η)βhv	η)βhv	PROPN
ma-105	728	25	(	(	PUNCT
ma-105	728	26	1	1	NUM
ma-105	728	27	+	+	NUM
ma-105	728	28	α1h)(1	α1h)(1	NUM
ma-105	728	29	+	+	CCONJ
ma-105	728	30	α2v	α2v	NOUN
ma-105	728	31	)	)	PUNCT
ma-105	729	1	+	+	NUM
ma-105	729	2	ρi	ρi	X
ma-105	729	3	]	]	PUNCT
ma-105	729	4	−	−	PROPN
ma-105	729	5	i∗	i∗	NOUN
ma-105	729	6	i	i	PRON
ma-105	729	7	(1−	(1−	PUNCT
ma-105	729	8	η	η	PROPN
ma-105	729	9	)	)	PUNCT
ma-105	729	10	(	(	PUNCT
ma-105	729	11	1+α1h	1+α1h	NUM
ma-105	729	12	∗)(1+α2v	∗)(1+α2v	NOUN
ma-105	729	13	∗)(α+ρ)i∗	∗)(α+ρ)i∗	PUNCT
ma-105	729	14	(	(	PUNCT
ma-105	729	15	1−η)h∗v	1−η)h∗v	NUM
ma-105	729	16	∗	∗	PROPN
ma-105	729	17	hv	hv	PROPN
ma-105	729	18	(	(	PUNCT
ma-105	729	19	1	1	NUM
ma-105	729	20	+	+	NUM
ma-105	729	21	α1h)(1	α1h)(1	NUM
ma-105	729	22	+	+	CCONJ
ma-105	729	23	α2v	α2v	NOUN
ma-105	729	24	)	)	PUNCT
ma-105	729	25	−	−	PROPN
ma-105	730	1	(	(	PUNCT
ma-105	730	2	α+	α+	X
ma-105	730	3	ρ)i	ρ)i	NOUN
ma-105	730	4	−	−	X
ma-105	730	5	(	(	PUNCT
ma-105	730	6	α+	α+	X
ma-105	730	7	ρ)i	ρ)i	NOUN
ma-105	730	8	v	v	ADP
ma-105	730	9	∗	∗	NOUN
ma-105	730	10	v	v	NOUN
ma-105	730	11	+	+	CCONJ
ma-105	730	12	(	(	PUNCT
ma-105	730	13	α+	α+	X
ma-105	730	14	ρ)µ	ρ)µ	ADJ
ma-105	730	15	(	(	PUNCT
ma-105	730	16	1−	1−	NUM
ma-105	730	17	ε)k	ε)k	NOUN
ma-105	730	18	v	v	ADP
ma-105	730	19	∗	∗	NOUN
ma-105	730	20	,	,	PUNCT
ma-105	730	21	=	=	PRON
ma-105	730	22	[	[	PUNCT
ma-105	730	23	dh∗	dh∗	NOUN
ma-105	730	24	+	+	CCONJ
ma-105	730	25	(	(	PUNCT
ma-105	730	26	α+	α+	PRON
ma-105	730	27	ρ)i∗	ρ)i∗	NUM
ma-105	730	28	−	−	PROPN
ma-105	730	29	ρi∗	ρi∗	ADJ
ma-105	730	30	−	−	PROPN
ma-105	730	31	dh	dh	NOUN
ma-105	730	32	−	−	PROPN
ma-105	730	33	αi	αi	INTJ
ma-105	730	34	−	−	PROPN
ma-105	731	1	(	(	PUNCT
ma-105	731	2	α+	α+	NUM
ma-105	731	3	ρ)i∗	ρ)i∗	NUM
ma-105	731	4	v	v	NOUN
ma-105	731	5	v	v	NOUN
ma-105	731	6	∗	∗	NOUN
ma-105	731	7	]	]	PUNCT
ma-105	731	8	−	−	PUNCT
ma-105	732	1	[	[	X
ma-105	732	2	h∗	h∗	NOUN
ma-105	732	3	h	h	NOUN
ma-105	732	4	1	1	NUM
ma-105	732	5	+	+	CCONJ
ma-105	732	6	α1h	α1h	ADV
ma-105	732	7	1	1	NUM
ma-105	732	8	+	+	NUM
ma-105	732	9	α1h∗	α1h∗	NUM
ma-105	732	10	dh∗	dh∗	NOUN
ma-105	732	11	+	+	CCONJ
ma-105	732	12	h∗	h∗	NOUN
ma-105	732	13	h	h	NOUN
ma-105	732	14	1	1	NUM
ma-105	732	15	+	+	CCONJ
ma-105	732	16	α1h	α1h	ADV
ma-105	732	17	1	1	NUM
ma-105	732	18	+	+	NUM
ma-105	732	19	α1h∗	α1h∗	PROPN
ma-105	732	20	αi∗	αi∗	NOUN
ma-105	732	21	−	−	NOUN
ma-105	732	22	1	1	NUM
ma-105	732	23	+	+	CCONJ
ma-105	732	24	α1h	α1h	ADV
ma-105	732	25	1	1	NUM
ma-105	732	26	+	+	NUM
ma-105	732	27	α1h∗	α1h∗	NOUN
ma-105	732	28	dh∗	dh∗	NOUN
ma-105	732	29	−	−	ADP
ma-105	732	30	v	v	NOUN
ma-105	732	31	v	v	NOUN
ma-105	732	32	∗	∗	NOUN
ma-105	732	33	1	1	NUM
ma-105	732	34	+	+	NUM
ma-105	732	35	α2v	α2v	NOUN
ma-105	732	36	∗	∗	NOUN
ma-105	732	37	1	1	NUM
ma-105	732	38	+	+	CCONJ
ma-105	732	39	α2v	α2v	NOUN
ma-105	732	40	(	(	PUNCT
ma-105	732	41	α+	α+	NOUN
ma-105	732	42	ρ)i∗	ρ)i∗	NOUN
ma-105	732	43	+	+	CCONJ
ma-105	732	44	h∗	h∗	PROPN
ma-105	732	45	h	h	NOUN
ma-105	732	46	1	1	NUM
ma-105	732	47	+	+	CCONJ
ma-105	732	48	α1h	α1h	ADV
ma-105	732	49	1	1	NUM
ma-105	732	50	+	+	NUM
ma-105	732	51	α1h∗	α1h∗	PROPN
ma-105	732	52	ρi	ρi	X
ma-105	732	53	]	]	PUNCT
ma-105	733	1	+	+	CCONJ
ma-105	733	2	(	(	PUNCT
ma-105	733	3	α+	α+	PRON
ma-105	733	4	ρ)i∗	ρ)i∗	PROPN
ma-105	733	5	[	[	PUNCT
ma-105	733	6	1−	1−	NUM
ma-105	733	7	hi∗v	hi∗v	X
ma-105	733	8	(	(	PUNCT
ma-105	733	9	1	1	NUM
ma-105	733	10	+	+	CCONJ
ma-105	733	11	α1h	α1h	PROPN
ma-105	733	12	∗)(1	∗)(1	NOUN
ma-105	733	13	+	+	CCONJ
ma-105	733	14	α2v	α2v	NUM
ma-105	733	15	∗	∗	NOUN
ma-105	733	16	)	)	PUNCT
ma-105	733	17	h∗iv	h∗iv	PROPN
ma-105	733	18	∗(1	∗(1	NOUN
ma-105	733	19	+	+	CCONJ
ma-105	733	20	α1h)(1	α1h)(1	NUM
ma-105	733	21	+	+	CCONJ
ma-105	733	22	α2v	α2v	NOUN
ma-105	733	23	)	)	PUNCT
ma-105	733	24	]	]	PUNCT
ma-105	734	1	+	+	CCONJ
ma-105	734	2	(	(	PUNCT
ma-105	734	3	α+	α+	PRON
ma-105	734	4	ρ)i∗	ρ)i∗	PROPN
ma-105	734	5	(	(	PUNCT
ma-105	734	6	1−	1−	NUM
ma-105	734	7	i	i	PRON
ma-105	734	8	i∗	i∗	VERB
ma-105	734	9	v	v	ADP
ma-105	734	10	∗	∗	NOUN
ma-105	734	11	v	v	NOUN
ma-105	734	12	)	)	PUNCT
ma-105	734	13	,	,	PUNCT
ma-105	734	14	https://doi.org/10.28924/ada/ma.3.1	https://doi.org/10.28924/ada/ma.3.1	PROPN
ma-105	734	15	eur	eur	PROPN
ma-105	734	16	.	.	PUNCT
ma-105	735	1	j.	j.	PROPN
ma-105	735	2	math	math	PROPN
ma-105	735	3	.	.	PUNCT
ma-105	736	1	anal	anal	PROPN
ma-105	736	2	.	.	PUNCT
ma-105	737	1	10.28924	10.28924	NUM
ma-105	737	2	/	/	SYM
ma-105	737	3	ada	ada	PROPN
ma-105	737	4	/	/	SYM
ma-105	737	5	ma.3.1	ma.3.1	PROPN
ma-105	737	6	26	26	NUM
ma-105	737	7	=	=	NOUN
ma-105	737	8	dh∗	dh∗	NOUN
ma-105	737	9	[	[	PUNCT
ma-105	737	10	1−	1−	NUM
ma-105	737	11	h	h	NOUN
ma-105	737	12	h∗	h∗	PROPN
ma-105	737	13	−	−	PROPN
ma-105	737	14	h∗	h∗	PROPN
ma-105	737	15	h	h	NOUN
ma-105	737	16	1	1	NUM
ma-105	737	17	+	+	CCONJ
ma-105	737	18	α1h	α1h	ADV
ma-105	737	19	1	1	NUM
ma-105	737	20	+	+	NUM
ma-105	737	21	α1h∗	α1h∗	PRON
ma-105	737	22	+	+	CCONJ
ma-105	737	23	1	1	NUM
ma-105	737	24	+	+	CCONJ
ma-105	737	25	α1h	α1h	ADV
ma-105	737	26	1	1	NUM
ma-105	737	27	+	+	NUM
ma-105	737	28	α1h∗	α1h∗	PRON
ma-105	737	29	]	]	PUNCT
ma-105	738	1	+	+	CCONJ
ma-105	738	2	(	(	PUNCT
ma-105	738	3	α+	α+	PRON
ma-105	738	4	ρ)i∗	ρ)i∗	PROPN
ma-105	738	5	[	[	PUNCT
ma-105	738	6	1−	1−	NUM
ma-105	738	7	hi∗v	hi∗v	X
ma-105	738	8	(	(	PUNCT
ma-105	738	9	1	1	NUM
ma-105	738	10	+	+	CCONJ
ma-105	738	11	α1h	α1h	PROPN
ma-105	738	12	∗)(1	∗)(1	NOUN
ma-105	738	13	+	+	CCONJ
ma-105	738	14	α2v	α2v	NUM
ma-105	738	15	∗	∗	NOUN
ma-105	738	16	)	)	PUNCT
ma-105	738	17	h∗iv	h∗iv	PROPN
ma-105	738	18	∗(1	∗(1	NOUN
ma-105	738	19	+	+	CCONJ
ma-105	738	20	α1h)(1	α1h)(1	NUM
ma-105	738	21	+	+	CCONJ
ma-105	738	22	α2v	α2v	NOUN
ma-105	738	23	)	)	PUNCT
ma-105	739	1	+	+	CCONJ
ma-105	740	1	v	v	NUM
ma-105	740	2	v	v	NOUN
ma-105	740	3	∗	∗	NOUN
ma-105	740	4	1	1	NUM
ma-105	740	5	+	+	NUM
ma-105	740	6	α2v	α2v	NOUN
ma-105	740	7	∗	∗	NOUN
ma-105	740	8	1	1	NUM
ma-105	740	9	+	+	CCONJ
ma-105	740	10	α2v	α2v	NOUN
ma-105	740	11	]	]	PUNCT
ma-105	741	1	+	+	CCONJ
ma-105	741	2	(	(	PUNCT
ma-105	741	3	α+	α+	PRON
ma-105	741	4	ρ)i∗	ρ)i∗	PROPN
ma-105	741	5	(	(	PUNCT
ma-105	741	6	2−	2−	NUM
ma-105	741	7	v	v	NOUN
ma-105	741	8	v	v	NOUN
ma-105	741	9	∗	∗	NOUN
ma-105	741	10	−	−	NOUN
ma-105	742	1	i	i	PRON
ma-105	742	2	i∗	i∗	VERB
ma-105	742	3	v	v	ADP
ma-105	742	4	∗	∗	NOUN
ma-105	742	5	v	v	NOUN
ma-105	742	6	)	)	PUNCT
ma-105	743	1	−	−	PROPN
ma-105	744	1	αi∗	αi∗	NOUN
ma-105	745	1	(	(	PUNCT
ma-105	745	2	ρ	ρ	NOUN
ma-105	745	3	α	α	PROPN
ma-105	746	1	+	+	X
ma-105	746	2	i	i	PRON
ma-105	746	3	i∗	i∗	NOUN
ma-105	746	4	)	)	PUNCT
ma-105	747	1	−	−	PROPN
ma-105	747	2	h∗	h∗	NOUN
ma-105	747	3	h	h	NOUN
ma-105	747	4	1	1	NUM
ma-105	748	1	+	+	CCONJ
ma-105	748	2	α1h	α1h	ADV
ma-105	748	3	1	1	NUM
ma-105	748	4	+	+	NUM
ma-105	748	5	α1h∗	α1h∗	PROPN
ma-105	748	6	αi∗	αi∗	NOUN
ma-105	748	7	−	−	PROPN
ma-105	748	8	h∗	h∗	PROPN
ma-105	748	9	h	h	NOUN
ma-105	748	10	1	1	NUM
ma-105	749	1	+	+	CCONJ
ma-105	749	2	α1h	α1h	ADV
ma-105	749	3	1	1	NUM
ma-105	749	4	+	+	NUM
ma-105	749	5	α1h∗	α1h∗	PROPN
ma-105	749	6	ρi	ρi	NOUN
ma-105	749	7	,	,	PUNCT
ma-105	749	8	=	=	NOUN
ma-105	749	9	−	−	PROPN
ma-105	749	10	d(h	d(h	PROPN
ma-105	749	11	−h∗)2	−h∗)2	PROPN
ma-105	750	1	h(1	h(1	PROPN
ma-105	750	2	+	+	CCONJ
ma-105	750	3	α1h∗	α1h∗	PROPN
ma-105	750	4	)	)	PUNCT
ma-105	751	1	+	+	CCONJ
ma-105	751	2	(	(	PUNCT
ma-105	751	3	α+	α+	PRON
ma-105	751	4	ρ)i∗	ρ)i∗	PROPN
ma-105	751	5	[	[	PUNCT
ma-105	751	6	−1−	−1−	PROPN
ma-105	751	7	v	v	NUM
ma-105	751	8	v	v	NOUN
ma-105	751	9	∗	∗	NOUN
ma-105	751	10	+	+	CCONJ
ma-105	751	11	v	v	NUM
ma-105	751	12	v	v	NOUN
ma-105	751	13	∗	∗	NOUN
ma-105	751	14	1	1	NUM
ma-105	751	15	+	+	NUM
ma-105	751	16	α2v	α2v	NOUN
ma-105	751	17	∗	∗	NOUN
ma-105	751	18	1	1	NUM
ma-105	751	19	+	+	CCONJ
ma-105	751	20	α2v	α2v	NOUN
ma-105	751	21	+	+	SYM
ma-105	751	22	1	1	NUM
ma-105	751	23	+	+	CCONJ
ma-105	751	24	α2v	α2v	NUM
ma-105	751	25	1	1	NUM
ma-105	751	26	+	+	NUM
ma-105	751	27	α2v	α2v	NOUN
ma-105	751	28	∗	∗	NOUN
ma-105	751	29	]	]	PUNCT
ma-105	752	1	+	+	CCONJ
ma-105	752	2	(	(	PUNCT
ma-105	752	3	α+	α+	PRON
ma-105	752	4	ρ)i∗	ρ)i∗	PROPN
ma-105	752	5	[	[	PUNCT
ma-105	752	6	4−	4−	NUM
ma-105	752	7	h∗	h∗	NOUN
ma-105	752	8	h	h	NOUN
ma-105	752	9	1	1	NUM
ma-105	752	10	+	+	CCONJ
ma-105	752	11	α1h	α1h	ADV
ma-105	752	12	1	1	NUM
ma-105	752	13	+	+	NUM
ma-105	752	14	α1h∗	α1h∗	PROPN
ma-105	752	15	−	−	PROPN
ma-105	752	16	hi∗v	hi∗v	PROPN
ma-105	752	17	(	(	PUNCT
ma-105	752	18	1	1	NUM
ma-105	752	19	+	+	CCONJ
ma-105	752	20	α1h	α1h	PROPN
ma-105	752	21	∗)(1	∗)(1	NOUN
ma-105	752	22	+	+	CCONJ
ma-105	752	23	α2v	α2v	NUM
ma-105	752	24	∗	∗	NOUN
ma-105	752	25	)	)	PUNCT
ma-105	752	26	h∗iv	h∗iv	PROPN
ma-105	752	27	∗(1	∗(1	NOUN
ma-105	752	28	+	+	CCONJ
ma-105	752	29	α1h)(1	α1h)(1	NUM
ma-105	752	30	+	+	CCONJ
ma-105	752	31	α2v	α2v	NOUN
ma-105	752	32	)	)	PUNCT
ma-105	752	33	−	−	PROPN
ma-105	753	1	i	i	PRON
ma-105	753	2	i∗	i∗	VERB
ma-105	753	3	v	v	ADP
ma-105	753	4	∗	∗	NOUN
ma-105	753	5	v	v	NOUN
ma-105	753	6	−	−	PROPN
ma-105	753	7	1	1	NUM
ma-105	753	8	+	+	CCONJ
ma-105	753	9	α2v	α2v	SYM
ma-105	753	10	1	1	NUM
ma-105	753	11	+	+	NUM
ma-105	753	12	α2v	α2v	NOUN
ma-105	753	13	∗	∗	NOUN
ma-105	753	14	]	]	PUNCT
ma-105	753	15	−	−	PROPN
ma-105	754	1	αi∗	αi∗	NOUN
ma-105	754	2	(	(	PUNCT
ma-105	754	3	ρ	ρ	NOUN
ma-105	754	4	α	α	PROPN
ma-105	755	1	+	+	X
ma-105	755	2	i	i	PRON
ma-105	755	3	i∗	i∗	NOUN
ma-105	755	4	)	)	PUNCT
ma-105	756	1	−	−	PROPN
ma-105	756	2	h∗	h∗	NOUN
ma-105	756	3	h	h	NOUN
ma-105	756	4	1	1	NUM
ma-105	757	1	+	+	CCONJ
ma-105	757	2	α1h	α1h	ADV
ma-105	757	3	1	1	NUM
ma-105	757	4	+	+	NUM
ma-105	757	5	α1h∗	α1h∗	PROPN
ma-105	757	6	αi∗	αi∗	NOUN
ma-105	757	7	−	−	PROPN
ma-105	757	8	h∗	h∗	PROPN
ma-105	757	9	h	h	NOUN
ma-105	757	10	1	1	NUM
ma-105	758	1	+	+	CCONJ
ma-105	758	2	α1h	α1h	ADV
ma-105	758	3	1	1	NUM
ma-105	758	4	+	+	NUM
ma-105	758	5	α1h∗	α1h∗	PROPN
ma-105	758	6	ρi	ρi	NOUN
ma-105	758	7	+	+	CCONJ
ma-105	758	8	(	(	PUNCT
ma-105	758	9	α+	α+	PRON
ma-105	758	10	ρ)i∗	ρ)i∗	PROPN
ma-105	758	11	h∗	h∗	PROPN
ma-105	758	12	h	h	NOUN
ma-105	758	13	1	1	NUM
ma-105	759	1	+	+	CCONJ
ma-105	759	2	α1h	α1h	ADV
ma-105	759	3	1	1	NUM
ma-105	759	4	+	+	NUM
ma-105	759	5	α1h∗	α1h∗	NOUN
ma-105	759	6	.	.	PUNCT
ma-105	760	1	therefore	therefore	ADV
ma-105	760	2	dg2	dg2	PROPN
ma-105	760	3	dt	dt	PROPN
ma-105	761	1	=	=	NOUN
ma-105	761	2	−	−	PROPN
ma-105	761	3	d(h	d(h	PROPN
ma-105	761	4	−h∗)2	−h∗)2	PROPN
ma-105	761	5	h(1	h(1	PROPN
ma-105	761	6	+	+	CCONJ
ma-105	761	7	α1h∗	α1h∗	NOUN
ma-105	761	8	)	)	PUNCT
ma-105	761	9	−	−	PROPN
ma-105	761	10	α2(α+	α2(α+	PROPN
ma-105	762	1	ρ)i∗(v	ρ)i∗(v	ADP
ma-105	762	2	−	−	NOUN
ma-105	762	3	v	v	ADP
ma-105	762	4	∗)2	∗)2	PROPN
ma-105	762	5	v	v	ADP
ma-105	762	6	∗(1	∗(1	NOUN
ma-105	762	7	+	+	CCONJ
ma-105	762	8	α2v	α2v	NOUN
ma-105	762	9	∗)(1	∗)(1	X
ma-105	762	10	+	+	NUM
ma-105	762	11	α2v	α2v	NUM
ma-105	762	12	)	)	PUNCT
ma-105	763	1	−	−	PROPN
ma-105	763	2	αi∗	αi∗	NOUN
ma-105	763	3	(	(	PUNCT
ma-105	763	4	ρ	ρ	NOUN
ma-105	763	5	α	α	PROPN
ma-105	764	1	+	+	X
ma-105	765	1	i	i	PRON
ma-105	765	2	i∗	i∗	NOUN
ma-105	765	3	)	)	PUNCT
ma-105	766	1	+	+	CCONJ
ma-105	766	2	(	(	PUNCT
ma-105	766	3	α+	α+	PRON
ma-105	766	4	ρ)i∗	ρ)i∗	PROPN
ma-105	766	5	[	[	PUNCT
ma-105	766	6	4−	4−	NUM
ma-105	766	7	h∗	h∗	NOUN
ma-105	766	8	h	h	NOUN
ma-105	766	9	1	1	NUM
ma-105	766	10	+	+	CCONJ
ma-105	766	11	α1h	α1h	ADV
ma-105	766	12	1	1	NUM
ma-105	766	13	+	+	NUM
ma-105	766	14	α1h∗	α1h∗	PROPN
ma-105	766	15	−	−	PROPN
ma-105	766	16	hi∗v	hi∗v	PROPN
ma-105	766	17	(	(	PUNCT
ma-105	766	18	1	1	NUM
ma-105	766	19	+	+	CCONJ
ma-105	766	20	α1h	α1h	PROPN
ma-105	766	21	∗)(1	∗)(1	NOUN
ma-105	766	22	+	+	CCONJ
ma-105	766	23	α2v	α2v	NUM
ma-105	766	24	∗	∗	NOUN
ma-105	766	25	)	)	PUNCT
ma-105	766	26	h∗iv	h∗iv	PROPN
ma-105	766	27	∗(1	∗(1	NOUN
ma-105	766	28	+	+	CCONJ
ma-105	766	29	α1h)(1	α1h)(1	NUM
ma-105	766	30	+	+	CCONJ
ma-105	766	31	α2v	α2v	NOUN
ma-105	766	32	)	)	PUNCT
ma-105	766	33	−	−	PROPN
ma-105	767	1	i	i	PRON
ma-105	767	2	i∗	i∗	VERB
ma-105	767	3	v	v	ADP
ma-105	767	4	∗	∗	NOUN
ma-105	767	5	v	v	NOUN
ma-105	767	6	−	−	PROPN
ma-105	767	7	1	1	NUM
ma-105	767	8	+	+	CCONJ
ma-105	767	9	α2v	α2v	SYM
ma-105	767	10	1	1	NUM
ma-105	767	11	+	+	NUM
ma-105	767	12	α2v	α2v	NOUN
ma-105	767	13	∗	∗	NOUN
ma-105	767	14	]	]	PUNCT
ma-105	767	15	.	.	PUNCT
ma-105	768	1	we	we	PRON
ma-105	768	2	have	have	VERB
ma-105	768	3	:	:	PUNCT
ma-105	768	4	(	(	PUNCT
ma-105	768	5	α+	α+	NUM
ma-105	768	6	ρ)i∗	ρ)i∗	PROPN
ma-105	768	7	[	[	PUNCT
ma-105	768	8	4−	4−	NUM
ma-105	768	9	h∗	h∗	NOUN
ma-105	768	10	h	h	NOUN
ma-105	768	11	1	1	NUM
ma-105	768	12	+	+	CCONJ
ma-105	768	13	α1h	α1h	ADV
ma-105	768	14	1	1	NUM
ma-105	768	15	+	+	NUM
ma-105	768	16	α1h∗	α1h∗	PROPN
ma-105	768	17	−	−	PROPN
ma-105	768	18	hi∗v	hi∗v	PROPN
ma-105	768	19	(	(	PUNCT
ma-105	768	20	1	1	NUM
ma-105	768	21	+	+	CCONJ
ma-105	768	22	α1h	α1h	PROPN
ma-105	768	23	∗)(1	∗)(1	NOUN
ma-105	768	24	+	+	CCONJ
ma-105	768	25	α2v	α2v	NUM
ma-105	768	26	∗	∗	NOUN
ma-105	768	27	)	)	PUNCT
ma-105	768	28	h∗iv	h∗iv	PROPN
ma-105	768	29	∗(1	∗(1	NOUN
ma-105	768	30	+	+	CCONJ
ma-105	768	31	α1h)(1	α1h)(1	NUM
ma-105	768	32	+	+	CCONJ
ma-105	768	33	α2v	α2v	NOUN
ma-105	768	34	)	)	PUNCT
ma-105	768	35	−	−	PROPN
ma-105	769	1	i	i	PRON
ma-105	769	2	i∗	i∗	VERB
ma-105	769	3	v	v	ADP
ma-105	769	4	∗	∗	NOUN
ma-105	769	5	v	v	NOUN
ma-105	769	6	−	−	PROPN
ma-105	769	7	1	1	NUM
ma-105	769	8	+	+	CCONJ
ma-105	769	9	α2v	α2v	SYM
ma-105	769	10	1	1	NUM
ma-105	769	11	+	+	NUM
ma-105	769	12	α2v	α2v	NOUN
ma-105	769	13	∗	∗	NOUN
ma-105	769	14	]	]	PUNCT
ma-105	769	15	≤	≤	NUM
ma-105	769	16	0	0	PUNCT
ma-105	769	17	since	since	SCONJ
ma-105	769	18	the	the	DET
ma-105	769	19	left	left	ADJ
ma-105	769	20	side	side	NOUN
ma-105	769	21	of	of	ADP
ma-105	769	22	the	the	DET
ma-105	769	23	latter	latter	ADJ
ma-105	769	24	inequality	inequality	NOUN
ma-105	769	25	is	be	AUX
ma-105	769	26	the	the	DET
ma-105	769	27	difference	difference	NOUN
ma-105	769	28	between	between	ADP
ma-105	769	29	the	the	DET
ma-105	769	30	geometric	geometric	ADJ
ma-105	769	31	mean	mean	NOUN
ma-105	769	32	and	and	CCONJ
ma-105	769	33	thearithmetic	thearithmetic	ADJ
ma-105	769	34	mean	mean	NOUN
ma-105	769	35	.	.	PUNCT
ma-105	770	1	that	that	PRON
ma-105	770	2	is	be	AUX
ma-105	770	3	dg2	dg2	PROPN
ma-105	770	4	dt	dt	X
ma-105	770	5	≤	≤	ADV
ma-105	770	6	0	0	NUM
ma-105	770	7	.	.	PUNCT
ma-105	771	1	otherwise	otherwise	ADV
ma-105	771	2	dg2	dg2	PROPN
ma-105	771	3	dt	dt	NOUN
ma-105	772	1	=	=	PUNCT
ma-105	772	2	0	0	PUNCT
ma-105	773	1	if	if	SCONJ
ma-105	773	2	and	and	CCONJ
ma-105	773	3	only	only	ADV
ma-105	773	4	if	if	SCONJ
ma-105	773	5	h	h	NOUN
ma-105	773	6	=	=	SYM
ma-105	773	7	h∗	h∗	PROPN
ma-105	773	8	,	,	PUNCT
ma-105	773	9	i	i	PRON
ma-105	773	10	=	=	VERB
ma-105	773	11	i∗	i∗	NOUN
ma-105	773	12	et	et	NOUN
ma-105	773	13	v	v	NOUN
ma-105	773	14	=	=	SYM
ma-105	773	15	v	v	NOUN
ma-105	773	16	∗.thus	∗.thus	PUNCT
ma-105	773	17	g2	g2	PROPN
ma-105	773	18	is	be	AUX
ma-105	773	19	a	a	DET
ma-105	773	20	lyapunov	lyapunov	ADJ
ma-105	773	21	functional	functional	NOUN
ma-105	773	22	of	of	ADP
ma-105	773	23	the	the	DET
ma-105	773	24	differential	differential	ADJ
ma-105	773	25	equation	equation	NOUN
ma-105	773	26	associated	associate	VERB
ma-105	773	27	to	to	ADP
ma-105	773	28	the	the	DET
ma-105	773	29	pde	pde	NOUN
ma-105	773	30	-	-	PUNCT
ma-105	773	31	model	model	NOUN
ma-105	773	32	system(2.4	system(2.4	NOUN
ma-105	773	33	)	)	PUNCT
ma-105	773	34	.	.	PUNCT
ma-105	774	1	therefore	therefore	ADV
ma-105	774	2	using	use	VERB
ma-105	774	3	lyapunov	lyapunov	PROPN
ma-105	774	4	-	-	PUNCT
ma-105	774	5	lasalle	lasalle	PROPN
ma-105	774	6	invariance	invariance	NOUN
ma-105	774	7	principle	principle	NOUN
ma-105	774	8	[	[	X
ma-105	774	9	27	27	NUM
ma-105	774	10	]	]	PUNCT
ma-105	774	11	combined	combine	VERB
ma-105	774	12	to	to	ADP
ma-105	774	13	the	the	DET
ma-105	774	14	method	method	NOUN
ma-105	774	15	presentedin	presentedin	VERB
ma-105	774	16	[	[	X
ma-105	774	17	15	15	NUM
ma-105	774	18	]	]	PUNCT
ma-105	774	19	,	,	PUNCT
ma-105	774	20	the	the	DET
ma-105	774	21	functional	functional	ADJ
ma-105	774	22	defined	define	VERB
ma-105	774	23	by	by	ADP
ma-105	774	24	l2(t	l2(t	PROPN
ma-105	774	25	)	)	PUNCT
ma-105	774	26	=	=	SYM
ma-105	775	1	∫	∫	PROPN
ma-105	775	2	ω	ω	PROPN
ma-105	775	3	g2(t)dxis	g2(t)dxis	PUNCT
ma-105	775	4	a	a	DET
ma-105	775	5	lyapunov	lyapunov	ADJ
ma-105	775	6	functional	functional	NOUN
ma-105	775	7	of	of	ADP
ma-105	775	8	the	the	DET
ma-105	775	9	pde	pde	NOUN
ma-105	775	10	-	-	PUNCT
ma-105	775	11	model	model	NOUN
ma-105	775	12	system	system	NOUN
ma-105	775	13	(	(	PUNCT
ma-105	775	14	2.4	2.4	NUM
ma-105	775	15	)	)	PUNCT
ma-105	775	16	at	at	ADP
ma-105	775	17	the	the	DET
ma-105	775	18	spatially	spatially	ADV
ma-105	775	19	homogeneous	homogeneous	ADJ
ma-105	775	20	infectedequilibrium	infectedequilibrium	NOUN
ma-105	775	21	e∗.	e∗.	NOUN
ma-105	775	22	therefore	therefore	ADV
ma-105	775	23	e∗	e∗	PROPN
ma-105	775	24	is	be	AUX
ma-105	775	25	globally	globally	ADV
ma-105	775	26	asymptotically	asymptotically	ADV
ma-105	775	27	stable	stable	ADJ
ma-105	775	28	.	.	PUNCT
ma-105	776	1	this	this	PRON
ma-105	776	2	completes	complete	VERB
ma-105	776	3	the	the	DET
ma-105	776	4	proof	proof	NOUN
ma-105	776	5	of	of	ADP
ma-105	776	6	theo	theo	PROPN
ma-105	776	7	-	-	PUNCT
ma-105	776	8	rem	rem	PROPN
ma-105	776	9	4.5	4.5	NUM
ma-105	776	10	.	.	PUNCT
ma-105	776	11	�	�	PROPN
ma-105	776	12	5	5	NUM
ma-105	776	13	.	.	PUNCT
ma-105	776	14	numerical	numerical	ADJ
ma-105	776	15	simulations	simulation	NOUN
ma-105	776	16	in	in	ADP
ma-105	776	17	this	this	DET
ma-105	776	18	section	section	NOUN
ma-105	776	19	,	,	PUNCT
ma-105	776	20	we	we	PRON
ma-105	776	21	present	present	VERB
ma-105	776	22	the	the	DET
ma-105	776	23	numerical	numerical	ADJ
ma-105	776	24	simulations	simulation	NOUN
ma-105	776	25	to	to	PART
ma-105	776	26	illustrate	illustrate	VERB
ma-105	776	27	our	our	PRON
ma-105	776	28	theoretical	theoretical	ADJ
ma-105	776	29	results	result	NOUN
ma-105	776	30	.	.	PUNCT
ma-105	777	1	tosimplify	tosimplify	VERB
ma-105	777	2	,	,	PUNCT
ma-105	777	3	we	we	PRON
ma-105	777	4	consider	consider	VERB
ma-105	777	5	ibvp	ibvp	NOUN
ma-105	777	6	(	(	PUNCT
ma-105	777	7	2.4	2.4	NUM
ma-105	777	8	)	)	PUNCT
ma-105	777	9	with	with	ADP
ma-105	777	10	ω	ω	PROPN
ma-105	777	11	=	=	SYM
ma-105	777	12	(	(	PUNCT
ma-105	777	13	1	1	NUM
ma-105	777	14	)	)	PUNCT
ma-105	777	15	under	under	ADP
ma-105	777	16	neumann	neumann	PROPN
ma-105	777	17	boundary	boundary	ADJ
ma-105	777	18	condition	condition	NOUN
ma-105	778	1	∂h	∂h	AUX
ma-105	778	2	∂ν	∂ν	X
ma-105	778	3	=	=	SYM
ma-105	778	4	0	0	PROPN
ma-105	778	5	,	,	PUNCT
ma-105	778	6	∂i	∂i	PROPN
ma-105	778	7	∂ν	∂ν	X
ma-105	778	8	=	=	PUNCT
ma-105	778	9	0	0	PROPN
ma-105	778	10	,	,	PUNCT
ma-105	778	11	∂v	∂v	PROPN
ma-105	778	12	∂ν	∂ν	X
ma-105	778	13	=	=	PUNCT
ma-105	778	14	0	0	PROPN
ma-105	778	15	t	t	PROPN
ma-105	778	16	>	>	X
ma-105	778	17	0	0	PROPN
ma-105	778	18	,	,	PUNCT
ma-105	778	19	x	x	SYM
ma-105	778	20	=	=	SYM
ma-105	778	21	1	1	NUM
ma-105	778	22	(	(	PUNCT
ma-105	778	23	5.1	5.1	NUM
ma-105	778	24	)	)	PUNCT
ma-105	778	25	and	and	CCONJ
ma-105	778	26	,	,	PUNCT
ma-105	778	27	following	follow	VERB
ma-105	778	28	initial	initial	ADJ
ma-105	778	29	conditions	condition	NOUN
ma-105	778	30	h(x	h(x	PROPN
ma-105	778	31	,	,	PUNCT
ma-105	778	32	0	0	NUM
ma-105	778	33	)	)	PUNCT
ma-105	778	34	=	=	SYM
ma-105	778	35	5	5	NUM
ma-105	778	36	,	,	PUNCT
ma-105	778	37	i(x	i(x	NOUN
ma-105	778	38	,	,	PUNCT
ma-105	778	39	0	0	NUM
ma-105	778	40	)	)	PUNCT
ma-105	778	41	=	=	SYM
ma-105	778	42	5	5	NUM
ma-105	778	43	,	,	PUNCT
ma-105	778	44	v	v	NOUN
ma-105	778	45	(	(	PUNCT
ma-105	778	46	x	x	NOUN
ma-105	778	47	,	,	PUNCT
ma-105	778	48	0	0	NUM
ma-105	778	49	)	)	PUNCT
ma-105	778	50	=	=	SYM
ma-105	778	51	5	5	NUM
ma-105	778	52	,	,	PUNCT
ma-105	778	53	(	(	PUNCT
ma-105	778	54	5.2	5.2	NUM
ma-105	778	55	)	)	PUNCT
ma-105	778	56	https://doi.org/10.28924/ada/ma.3.1	https://doi.org/10.28924/ada/ma.3.1	PROPN
ma-105	778	57	eur	eur	PROPN
ma-105	778	58	.	.	PUNCT
ma-105	779	1	j.	j.	PROPN
ma-105	779	2	math	math	PROPN
ma-105	779	3	.	.	PUNCT
ma-105	780	1	anal	anal	PROPN
ma-105	780	2	.	.	PUNCT
ma-105	781	1	10.28924	10.28924	NUM
ma-105	781	2	/	/	SYM
ma-105	781	3	ada	ada	PROPN
ma-105	781	4	/	/	SYM
ma-105	781	5	ma.3.1	ma.3.1	PROPN
ma-105	781	6	27and	27and	PROPN
ma-105	781	7	h(x	h(x	PROPN
ma-105	781	8	,	,	PUNCT
ma-105	781	9	0	0	NUM
ma-105	781	10	)	)	PUNCT
ma-105	781	11	=	=	SYM
ma-105	781	12	15	15	NUM
ma-105	781	13	,	,	PUNCT
ma-105	781	14	i(x	i(x	NOUN
ma-105	781	15	,	,	PUNCT
ma-105	781	16	0	0	NUM
ma-105	781	17	)	)	PUNCT
ma-105	781	18	=	=	SYM
ma-105	781	19	5	5	NUM
ma-105	781	20	,	,	PUNCT
ma-105	781	21	v	v	NOUN
ma-105	781	22	(	(	PUNCT
ma-105	781	23	x	x	NOUN
ma-105	781	24	,	,	PUNCT
ma-105	781	25	0	0	NUM
ma-105	781	26	)	)	PUNCT
ma-105	781	27	=	=	SYM
ma-105	781	28	5	5	X
ma-105	781	29	.	.	PUNCT
ma-105	782	1	(	(	PUNCT
ma-105	782	2	5.3)now	5.3)now	ADV
ma-105	782	3	we	we	PRON
ma-105	782	4	choose	choose	VERB
ma-105	782	5	the	the	DET
ma-105	782	6	numerical	numerical	ADJ
ma-105	782	7	values	value	NOUN
ma-105	782	8	of	of	ADP
ma-105	782	9	the	the	DET
ma-105	782	10	parameters	parameter	NOUN
ma-105	782	11	for	for	ADP
ma-105	782	12	the	the	DET
ma-105	782	13	pde	pde	NOUN
ma-105	782	14	-	-	PUNCT
ma-105	782	15	cellular	cellular	ADJ
ma-105	782	16	model	model	NOUN
ma-105	782	17	system	system	NOUN
ma-105	782	18	(	(	PUNCT
ma-105	782	19	2.4)as	2.4)as	PRON
ma-105	782	20	follows	follow	VERB
ma-105	782	21	:	:	PUNCT
ma-105	782	22	λ	λ	X
ma-105	782	23	=	=	NOUN
ma-105	782	24	50	50	NUM
ma-105	782	25	;	;	PUNCT
ma-105	782	26	d	d	NOUN
ma-105	782	27	=	=	SYM
ma-105	782	28	5	5	NUM
ma-105	782	29	;	;	PUNCT
ma-105	782	30	ρ	ρ	PROPN
ma-105	782	31	=	=	SYM
ma-105	782	32	0	0	NUM
ma-105	782	33	,	,	PUNCT
ma-105	782	34	01	01	NUM
ma-105	782	35	;	;	PUNCT
ma-105	782	36	α	α	NOUN
ma-105	782	37	=	=	SYM
ma-105	782	38	0	0	NUM
ma-105	782	39	,	,	PUNCT
ma-105	782	40	05	05	NUM
ma-105	782	41	;	;	PUNCT
ma-105	782	42	d1	d1	PROPN
ma-105	782	43	=	=	SYM
ma-105	782	44	d2	d2	PROPN
ma-105	782	45	=	=	PUNCT
ma-105	782	46	d3	d3	PROPN
ma-105	782	47	=	=	SYM
ma-105	782	48	0	0	NUM
ma-105	782	49	,	,	PUNCT
ma-105	782	50	1	1	NUM
ma-105	782	51	;	;	PUNCT
ma-105	782	52	η	η	PROPN
ma-105	782	53	=	=	SYM
ma-105	782	54	0	0	NUM
ma-105	782	55	,	,	PUNCT
ma-105	782	56	00004	00004	NUM
ma-105	782	57	;	;	PUNCT
ma-105	782	58	α3	α3	NOUN
ma-105	782	59	=	=	SYM
ma-105	782	60	0	0	NUM
ma-105	782	61	,	,	PUNCT
ma-105	782	62	03	03	NUM
ma-105	782	63	;	;	PUNCT
ma-105	782	64	ε	ε	PROPN
ma-105	782	65	=	=	SYM
ma-105	782	66	0	0	NUM
ma-105	782	67	,	,	PUNCT
ma-105	782	68	5	5	NUM
ma-105	782	69	;	;	PUNCT
ma-105	782	70	α2	α2	ADJ
ma-105	782	71	=	=	SYM
ma-105	782	72	0	0	NUM
ma-105	782	73	,	,	PUNCT
ma-105	782	74	02	02	NUM
ma-105	782	75	;	;	PUNCT
ma-105	782	76	k	k	PROPN
ma-105	782	77	=	=	SYM
ma-105	782	78	2	2	NUM
ma-105	782	79	;	;	PUNCT
ma-105	782	80	α1	α1	PROPN
ma-105	782	81	=	=	SYM
ma-105	782	82	0	0	NUM
ma-105	782	83	,	,	PUNCT
ma-105	782	84	1	1	NUM
ma-105	782	85	;	;	PUNCT
ma-105	782	86	µ	µ	X
ma-105	782	87	=	=	SYM
ma-105	782	88	20	20	NUM
ma-105	782	89	;	;	PUNCT
ma-105	782	90	α0	α0	ADJ
ma-105	782	91	=	=	SYM
ma-105	782	92	1	1	NUM
ma-105	782	93	;	;	PUNCT
ma-105	782	94	β	β	X
ma-105	782	95	=	=	SYM
ma-105	782	96	0	0	NUM
ma-105	782	97	,	,	PUNCT
ma-105	782	98	24	24	NUM
ma-105	782	99	et	et	NOUN
ma-105	782	100	u	u	NOUN
ma-105	782	101	=	=	PROPN
ma-105	782	102	1	1	NUM
ma-105	782	103	.	.	PUNCT
ma-105	783	1	by	by	ADP
ma-105	783	2	calculation	calculation	NOUN
ma-105	783	3	wehave	wehave	NOUN
ma-105	783	4	r0	r0	NOUN
ma-105	783	5	=	=	SYM
ma-105	783	6	0.943361	0.943361	PROPN
ma-105	783	7	.	.	PUNCT
ma-105	784	1	in	in	ADP
ma-105	784	2	this	this	DET
ma-105	784	3	case	case	NOUN
ma-105	784	4	,	,	PUNCT
ma-105	784	5	pde	pde	NOUN
ma-105	784	6	-	-	PUNCT
ma-105	784	7	cellular	cellular	ADJ
ma-105	784	8	model	model	NOUN
ma-105	784	9	system	system	NOUN
ma-105	784	10	(	(	PUNCT
ma-105	784	11	2.4	2.4	NUM
ma-105	784	12	)	)	PUNCT
ma-105	784	13	has	have	VERB
ma-105	784	14	a	a	DET
ma-105	784	15	spatially	spatially	ADV
ma-105	784	16	homogeneousequilibrium	homogeneousequilibrium	NOUN
ma-105	784	17	e0	e0	NOUN
ma-105	784	18	=	=	PUNCT
ma-105	784	19	(	(	PUNCT
ma-105	784	20	10	10	NUM
ma-105	784	21	,	,	PUNCT
ma-105	784	22	0	0	NUM
ma-105	784	23	,	,	PUNCT
ma-105	784	24	0	0	NUM
ma-105	784	25	)	)	PUNCT
ma-105	784	26	.	.	PUNCT
ma-105	785	1	hence	hence	ADV
ma-105	785	2	by	by	ADP
ma-105	785	3	theorem	theorem	VERB
ma-105	785	4	4.3	4.3	NUM
ma-105	785	5	e0	e0	PROPN
ma-105	785	6	is	be	AUX
ma-105	785	7	globally	globally	ADV
ma-105	785	8	asymptotically	asymptotically	ADV
ma-105	785	9	stable	stable	ADJ
ma-105	785	10	.	.	PUNCT
ma-105	786	1	numericalsimulation	numericalsimulation	NOUN
ma-105	786	2	illustrates	illustrate	VERB
ma-105	786	3	our	our	PRON
ma-105	786	4	result	result	NOUN
ma-105	786	5	(	(	PUNCT
ma-105	786	6	see	see	VERB
ma-105	786	7	figure	figure	NOUN
ma-105	786	8	1	1	NUM
ma-105	786	9	)	)	PUNCT
ma-105	786	10	.	.	PUNCT
ma-105	787	1	otherwise	otherwise	ADV
ma-105	787	2	we	we	PRON
ma-105	787	3	choose	choose	VERB
ma-105	787	4	the	the	DET
ma-105	787	5	numerical	numerical	ADJ
ma-105	787	6	values	value	NOUN
ma-105	787	7	of	of	ADP
ma-105	787	8	(	(	PUNCT
ma-105	787	9	a	a	NOUN
ma-105	787	10	)	)	PUNCT
ma-105	787	11	(	(	PUNCT
ma-105	787	12	b	b	X
ma-105	787	13	)	)	PUNCT
ma-105	787	14	(	(	PUNCT
ma-105	787	15	c	c	X
ma-105	787	16	)	)	PUNCT
ma-105	787	17	figure	figure	NOUN
ma-105	787	18	1	1	NUM
ma-105	787	19	.	.	PUNCT
ma-105	787	20	simulations	simulation	NOUN
ma-105	787	21	of	of	ADP
ma-105	787	22	ibvp	ibvp	NOUN
ma-105	787	23	(	(	PUNCT
ma-105	787	24	2.4	2.4	NUM
ma-105	787	25	)	)	PUNCT
ma-105	787	26	under	under	ADP
ma-105	787	27	neumann	neumann	PROPN
ma-105	787	28	boundary	boundary	ADJ
ma-105	787	29	conditions	condition	NOUN
ma-105	787	30	(	(	PUNCT
ma-105	787	31	5.1	5.1	NUM
ma-105	787	32	)	)	PUNCT
ma-105	787	33	andinitial	andinitial	ADJ
ma-105	787	34	condition	condition	NOUN
ma-105	787	35	(	(	PUNCT
ma-105	787	36	5.2	5.2	NUM
ma-105	787	37	)	)	PUNCT
ma-105	787	38	the	the	DET
ma-105	787	39	parameters	parameter	NOUN
ma-105	787	40	for	for	ADP
ma-105	787	41	the	the	DET
ma-105	787	42	pde	pde	NOUN
ma-105	787	43	-	-	PUNCT
ma-105	787	44	cellular	cellular	ADJ
ma-105	787	45	model	model	NOUN
ma-105	787	46	system	system	NOUN
ma-105	787	47	(	(	PUNCT
ma-105	787	48	2.4	2.4	NUM
ma-105	787	49	)	)	PUNCT
ma-105	787	50	as	as	SCONJ
ma-105	787	51	follows	follow	VERB
ma-105	787	52	:	:	PUNCT
ma-105	787	53	λ	λ	X
ma-105	787	54	=	=	NOUN
ma-105	787	55	50	50	NUM
ma-105	787	56	;	;	PUNCT
ma-105	787	57	d	d	NOUN
ma-105	787	58	=	=	SYM
ma-105	787	59	5	5	NUM
ma-105	787	60	;	;	PUNCT
ma-105	787	61	ρ	ρ	PROPN
ma-105	787	62	=	=	SYM
ma-105	787	63	0	0	NUM
ma-105	787	64	,	,	PUNCT
ma-105	787	65	01	01	NUM
ma-105	787	66	;	;	PUNCT
ma-105	787	67	α	α	NOUN
ma-105	787	68	=	=	SYM
ma-105	787	69	0	0	NUM
ma-105	787	70	,	,	PUNCT
ma-105	787	71	05	05	NUM
ma-105	787	72	;	;	PUNCT
ma-105	787	73	d1	d1	PROPN
ma-105	787	74	=	=	SYM
ma-105	787	75	d2	d2	PROPN
ma-105	787	76	=	=	PUNCT
ma-105	787	77	d3	d3	PROPN
ma-105	787	78	=	=	SYM
ma-105	787	79	0	0	NUM
ma-105	787	80	,	,	PUNCT
ma-105	787	81	1	1	NUM
ma-105	787	82	;	;	PUNCT
ma-105	787	83	η	η	PROPN
ma-105	787	84	=	=	SYM
ma-105	787	85	0	0	NUM
ma-105	787	86	,	,	PUNCT
ma-105	787	87	00004	00004	NUM
ma-105	787	88	;	;	PUNCT
ma-105	787	89	ε	ε	PROPN
ma-105	787	90	=	=	SYM
ma-105	787	91	0	0	NUM
ma-105	787	92	,	,	PUNCT
ma-105	787	93	5	5	NUM
ma-105	787	94	;	;	PUNCT
ma-105	787	95	α0	α0	ADJ
ma-105	787	96	=	=	SYM
ma-105	787	97	1	1	NUM
ma-105	787	98	;	;	PUNCT
ma-105	787	99	α1	α1	PROPN
ma-105	787	100	=	=	SYM
ma-105	787	101	0	0	NUM
ma-105	787	102	,	,	PUNCT
ma-105	787	103	1	1	NUM
ma-105	787	104	;	;	PUNCT
ma-105	787	105	α2	α2	ADJ
ma-105	787	106	=	=	SYM
ma-105	787	107	0	0	NUM
ma-105	787	108	,	,	PUNCT
ma-105	787	109	02	02	NUM
ma-105	787	110	;	;	PUNCT
ma-105	787	111	α3	α3	NOUN
ma-105	787	112	=	=	SYM
ma-105	787	113	0	0	NUM
ma-105	787	114	,	,	PUNCT
ma-105	787	115	03	03	NUM
ma-105	787	116	;	;	PUNCT
ma-105	787	117	k	k	PROPN
ma-105	787	118	=	=	SYM
ma-105	787	119	2	2	NUM
ma-105	787	120	;	;	PUNCT
ma-105	787	121	µ	µ	X
ma-105	787	122	=	=	SYM
ma-105	787	123	2	2	NUM
ma-105	787	124	;	;	PUNCT
ma-105	787	125	β	β	X
ma-105	787	126	=	=	SYM
ma-105	787	127	0	0	NUM
ma-105	787	128	,	,	PUNCT
ma-105	787	129	24	24	NUM
ma-105	787	130	et	et	NOUN
ma-105	787	131	u	u	NOUN
ma-105	787	132	=	=	PROPN
ma-105	787	133	1	1	NUM
ma-105	787	134	.	.	PUNCT
ma-105	787	135	by	by	ADP
ma-105	787	136	calculation	calculation	NOUN
ma-105	787	137	we	we	PRON
ma-105	787	138	have	have	VERB
ma-105	787	139	r0	r0	NOUN
ma-105	787	140	=	=	NOUN
ma-105	787	141	6.25009	6.25009	NUM
ma-105	787	142	.	.	PUNCT
ma-105	788	1	in	in	ADP
ma-105	788	2	this	this	DET
ma-105	788	3	case	case	NOUN
ma-105	788	4	,	,	PUNCT
ma-105	788	5	pde	pde	NOUN
ma-105	788	6	-	-	PUNCT
ma-105	788	7	cellular	cellular	ADJ
ma-105	788	8	model	model	NOUN
ma-105	788	9	system	system	NOUN
ma-105	788	10	(	(	PUNCT
ma-105	788	11	2.4	2.4	NUM
ma-105	788	12	)	)	PUNCT
ma-105	788	13	has	have	VERB
ma-105	788	14	a	a	DET
ma-105	788	15	spatially	spatially	ADV
ma-105	788	16	homogeneous	homogeneous	ADJ
ma-105	788	17	equilibrium	equilibrium	NOUN
ma-105	788	18	e∗	e∗	NOUN
ma-105	788	19	=	=	SYM
ma-105	788	20	(	(	PUNCT
ma-105	788	21	5	5	NUM
ma-105	788	22	;	;	PUNCT
ma-105	788	23	500	500	NUM
ma-105	788	24	;	;	PUNCT
ma-105	788	25	235	235	NUM
ma-105	788	26	)	)	PUNCT
ma-105	788	27	.	.	PUNCT
ma-105	789	1	https://doi.org/10.28924/ada/ma.3.1	https://doi.org/10.28924/ada/ma.3.1	PROPN
ma-105	789	2	eur	eur	PROPN
ma-105	789	3	.	.	PUNCT
ma-105	790	1	j.	j.	PROPN
ma-105	790	2	math	math	PROPN
ma-105	790	3	.	.	PUNCT
ma-105	791	1	anal	anal	PROPN
ma-105	791	2	.	.	PUNCT
ma-105	792	1	10.28924	10.28924	NUM
ma-105	792	2	/	/	SYM
ma-105	792	3	ada	ada	PROPN
ma-105	792	4	/	/	SYM
ma-105	792	5	ma.3.1	ma.3.1	PROPN
ma-105	792	6	28hence	28hence	NUM
ma-105	792	7	by	by	ADP
ma-105	792	8	theorem	theorem	VERB
ma-105	792	9	4.5	4.5	NUM
ma-105	792	10	e∗	e∗	PROPN
ma-105	792	11	is	be	AUX
ma-105	792	12	globally	globally	ADV
ma-105	792	13	asymptotically	asymptotically	ADV
ma-105	792	14	stable	stable	ADJ
ma-105	792	15	.	.	PUNCT
ma-105	793	1	numerical	numerical	PROPN
ma-105	793	2	simulation	simulation	PROPN
ma-105	793	3	illustrates	illustrate	VERB
ma-105	793	4	ourresult	ourresult	PROPN
ma-105	793	5	(	(	PUNCT
ma-105	793	6	see	see	VERB
ma-105	793	7	figure	figure	NOUN
ma-105	793	8	2	2	NUM
ma-105	793	9	)	)	PUNCT
ma-105	793	10	.	.	PUNCT
ma-105	794	1	(	(	PUNCT
ma-105	794	2	a	a	X
ma-105	794	3	)	)	PUNCT
ma-105	794	4	(	(	PUNCT
ma-105	794	5	b	b	X
ma-105	794	6	)	)	PUNCT
ma-105	794	7	(	(	PUNCT
ma-105	794	8	c	c	X
ma-105	794	9	)	)	PUNCT
ma-105	794	10	figure	figure	NOUN
ma-105	794	11	2	2	NUM
ma-105	794	12	.	.	PUNCT
ma-105	795	1	simulations	simulation	NOUN
ma-105	795	2	of	of	ADP
ma-105	795	3	ibvp	ibvp	NOUN
ma-105	795	4	(	(	PUNCT
ma-105	795	5	2.4	2.4	NUM
ma-105	795	6	)	)	PUNCT
ma-105	795	7	under	under	ADP
ma-105	795	8	neumann	neumann	PROPN
ma-105	795	9	boundary	boundary	ADJ
ma-105	795	10	conditions	condition	NOUN
ma-105	795	11	(	(	PUNCT
ma-105	795	12	5.1	5.1	NUM
ma-105	795	13	)	)	PUNCT
ma-105	795	14	andinitial	andinitial	ADJ
ma-105	795	15	condition	condition	NOUN
ma-105	795	16	(	(	PUNCT
ma-105	795	17	5.3	5.3	NUM
ma-105	795	18	)	)	PUNCT
ma-105	795	19	6	6	NUM
ma-105	795	20	.	.	PUNCT
ma-105	795	21	conclusion	conclusion	NOUN
ma-105	795	22	in	in	ADP
ma-105	795	23	this	this	DET
ma-105	795	24	work	work	NOUN
ma-105	796	1	,	,	PUNCT
ma-105	796	2	we	we	PRON
ma-105	796	3	addressed	address	VERB
ma-105	796	4	the	the	DET
ma-105	796	5	dynamics	dynamic	NOUN
ma-105	796	6	of	of	ADP
ma-105	796	7	a	a	DET
ma-105	796	8	reaction	reaction	NOUN
ma-105	796	9	diffusion	diffusion	NOUN
ma-105	796	10	hcv	hcv	X
ma-105	796	11	intra	intra	ADJ
ma-105	796	12	-	-	ADJ
ma-105	796	13	host	host	ADJ
ma-105	796	14	infection	infection	NOUN
ma-105	796	15	modelwith	modelwith	ADP
ma-105	796	16	the	the	DET
ma-105	796	17	hattaf	hattaf	NOUN
ma-105	796	18	-	-	PUNCT
ma-105	796	19	yousfi	yousfi	ADJ
ma-105	796	20	incidence	incidence	NOUN
ma-105	796	21	rate	rate	NOUN
ma-105	796	22	,	,	PUNCT
ma-105	796	23	which	which	PRON
ma-105	796	24	is	be	AUX
ma-105	796	25	a	a	DET
ma-105	796	26	generalized	generalized	ADJ
ma-105	796	27	non	non	ADJ
ma-105	796	28	-	-	ADJ
ma-105	796	29	linear	linear	ADJ
ma-105	796	30	incidence	incidence	NOUN
ma-105	796	31	rate	rate	NOUN
ma-105	796	32	.	.	PUNCT
ma-105	797	1	the	the	DET
ma-105	797	2	object	object	NOUN
ma-105	797	3	ofthis	ofthis	ADJ
ma-105	797	4	work	work	NOUN
ma-105	797	5	was	be	AUX
ma-105	797	6	to	to	PART
ma-105	797	7	make	make	VERB
ma-105	797	8	a	a	DET
ma-105	797	9	mathematical	mathematical	ADJ
ma-105	797	10	analysis	analysis	NOUN
ma-105	797	11	of	of	ADP
ma-105	797	12	a	a	DET
ma-105	797	13	cellular	cellular	ADJ
ma-105	797	14	model	model	NOUN
ma-105	797	15	of	of	ADP
ma-105	797	16	hcv	hcv	PROPN
ma-105	797	17	infection	infection	NOUN
ma-105	797	18	which	which	PRON
ma-105	797	19	assumesthat	assumesthat	NOUN
ma-105	797	20	virions	virion	NOUN
ma-105	797	21	diffuse	diffuse	VERB
ma-105	797	22	into	into	ADP
ma-105	797	23	the	the	DET
ma-105	797	24	liver	liver	NOUN
ma-105	797	25	,	,	PUNCT
ma-105	797	26	which	which	PRON
ma-105	797	27	uses	use	VERB
ma-105	797	28	the	the	DET
ma-105	797	29	hattaf	hattaf	NOUN
ma-105	797	30	-	-	PUNCT
ma-105	797	31	yousfi	yousfi	ADJ
ma-105	797	32	functional	functional	ADJ
ma-105	797	33	response	response	NOUN
ma-105	797	34	generalizingmost	generalizingmost	NOUN
ma-105	797	35	of	of	ADP
ma-105	797	36	the	the	DET
ma-105	797	37	functional	functional	ADJ
ma-105	797	38	responses	response	NOUN
ma-105	797	39	that	that	PRON
ma-105	797	40	exist	exist	VERB
ma-105	797	41	.	.	PUNCT
ma-105	798	1	our	our	PRON
ma-105	798	2	model	model	NOUN
ma-105	798	3	also	also	ADV
ma-105	798	4	takes	take	VERB
ma-105	798	5	into	into	ADP
ma-105	798	6	account	account	NOUN
ma-105	798	7	the	the	DET
ma-105	798	8	absorption	absorption	NOUN
ma-105	798	9	effectwhich	effectwhich	PRON
ma-105	798	10	is	be	AUX
ma-105	798	11	much	much	ADV
ma-105	798	12	neglected	neglect	VERB
ma-105	798	13	in	in	ADP
ma-105	798	14	the	the	DET
ma-105	798	15	literature	literature	NOUN
ma-105	798	16	.	.	PUNCT
ma-105	799	1	we	we	PRON
ma-105	799	2	first	first	ADV
ma-105	799	3	showed	show	VERB
ma-105	799	4	that	that	SCONJ
ma-105	799	5	the	the	DET
ma-105	799	6	initial	initial	ADJ
ma-105	799	7	value	value	NOUN
ma-105	799	8	and	and	CCONJ
ma-105	799	9	boundaryproblem	boundaryproblem	NOUN
ma-105	799	10	(	(	PUNCT
ma-105	799	11	2.4	2.4	NUM
ma-105	799	12	)	)	PUNCT
ma-105	799	13	admits	admit	VERB
ma-105	799	14	a	a	DET
ma-105	799	15	unique	unique	ADJ
ma-105	799	16	global	global	ADJ
ma-105	799	17	solution	solution	NOUN
ma-105	799	18	in	in	ADP
ma-105	799	19	time	time	NOUN
ma-105	799	20	.	.	PUNCT
ma-105	800	1	and	and	CCONJ
ma-105	800	2	secondly	secondly	ADV
ma-105	800	3	,	,	PUNCT
ma-105	800	4	we	we	PRON
ma-105	800	5	have	have	AUX
ma-105	800	6	shown	show	VERB
ma-105	800	7	that	that	SCONJ
ma-105	800	8	thisunique	thisunique	ADJ
ma-105	800	9	solution	solution	NOUN
ma-105	800	10	is	be	AUX
ma-105	800	11	positive	positive	ADJ
ma-105	800	12	and	and	CCONJ
ma-105	800	13	uniformly	uniformly	ADV
ma-105	800	14	bounded	bound	VERB
ma-105	800	15	.	.	PUNCT
ma-105	801	1	then	then	ADV
ma-105	801	2	,	,	PUNCT
ma-105	801	3	we	we	PRON
ma-105	801	4	determined	determine	VERB
ma-105	801	5	the	the	DET
ma-105	801	6	expression	expression	NOUN
ma-105	801	7	of	of	ADP
ma-105	801	8	basic	basic	ADJ
ma-105	801	9	https://doi.org/10.28924/ada/ma.3.1	https://doi.org/10.28924/ada/ma.3.1	PROPN
ma-105	801	10	eur	eur	PROPN
ma-105	801	11	.	.	PUNCT
ma-105	802	1	j.	j.	PROPN
ma-105	802	2	math	math	PROPN
ma-105	802	3	.	.	PUNCT
ma-105	803	1	anal	anal	PROPN
ma-105	803	2	.	.	PUNCT
ma-105	804	1	10.28924	10.28924	NUM
ma-105	804	2	/	/	SYM
ma-105	804	3	ada	ada	PROPN
ma-105	804	4	/	/	SYM
ma-105	804	5	ma.3.1	ma.3.1	PROPN
ma-105	804	6	29reproduction	29reproduction	NOUN
ma-105	804	7	number	number	NOUN
ma-105	804	8	r0	r0	NOUN
ma-105	804	9	which	which	PRON
ma-105	804	10	is	be	AUX
ma-105	804	11	the	the	DET
ma-105	804	12	parameter	parameter	NOUN
ma-105	804	13	from	from	ADP
ma-105	804	14	which	which	PRON
ma-105	804	15	we	we	PRON
ma-105	804	16	studied	study	VERB
ma-105	804	17	the	the	DET
ma-105	804	18	dynamics	dynamic	NOUN
ma-105	804	19	of	of	ADP
ma-105	804	20	our	our	PRON
ma-105	804	21	modelat	modelat	ADJ
ma-105	804	22	equilibria	equilibrium	NOUN
ma-105	804	23	whose	whose	DET
ma-105	804	24	existence	existence	NOUN
ma-105	804	25	and	and	CCONJ
ma-105	804	26	uniqueness	uniqueness	NOUN
ma-105	804	27	of	of	ADP
ma-105	804	28	these	these	PRON
ma-105	804	29	have	have	AUX
ma-105	804	30	been	be	AUX
ma-105	804	31	previously	previously	ADV
ma-105	804	32	proven	prove	VERB
ma-105	804	33	.	.	PUNCT
ma-105	805	1	more	more	ADV
ma-105	805	2	precisely	precisely	ADV
ma-105	805	3	,	,	PUNCT
ma-105	805	4	we	we	PRON
ma-105	805	5	have	have	AUX
ma-105	805	6	shown	show	VERB
ma-105	805	7	that	that	SCONJ
ma-105	805	8	,	,	PUNCT
ma-105	805	9	if	if	SCONJ
ma-105	805	10	r0	r0	NOUN
ma-105	805	11	<	<	X
ma-105	805	12	1	1	NUM
ma-105	805	13	,	,	PUNCT
ma-105	805	14	the	the	DET
ma-105	805	15	unique	unique	ADJ
ma-105	805	16	uninfected	uninfected	ADJ
ma-105	805	17	equilibrium	equilibrium	NOUN
ma-105	805	18	point	point	NOUN
ma-105	805	19	is	be	AUX
ma-105	805	20	locally	locally	ADV
ma-105	805	21	and	and	CCONJ
ma-105	805	22	globallyasymptotically	globallyasymptotically	ADV
ma-105	805	23	stable	stable	ADJ
ma-105	805	24	.	.	PUNCT
ma-105	806	1	this	this	PRON
ma-105	806	2	means	mean	VERB
ma-105	806	3	that	that	SCONJ
ma-105	806	4	,	,	PUNCT
ma-105	806	5	under	under	ADP
ma-105	806	6	this	this	DET
ma-105	806	7	condition	condition	NOUN
ma-105	806	8	,	,	PUNCT
ma-105	806	9	infection	infection	NOUN
ma-105	806	10	disappears	disappear	VERB
ma-105	806	11	.	.	PUNCT
ma-105	807	1	otherwise	otherwise	ADV
ma-105	807	2	,	,	PUNCT
ma-105	807	3	theuninfected	theuninfecte	VERB
ma-105	807	4	equilibrium	equilibrium	NOUN
ma-105	807	5	point	point	NOUN
ma-105	807	6	is	be	AUX
ma-105	807	7	unstable	unstable	ADJ
ma-105	807	8	;	;	PUNCT
ma-105	807	9	and	and	CCONJ
ma-105	807	10	in	in	ADP
ma-105	807	11	this	this	DET
ma-105	807	12	case	case	NOUN
ma-105	807	13	the	the	DET
ma-105	807	14	infection	infection	NOUN
ma-105	807	15	persists	persist	VERB
ma-105	807	16	in	in	ADP
ma-105	807	17	the	the	DET
ma-105	807	18	host	host	NOUN
ma-105	807	19	.	.	PUNCT
ma-105	808	1	it	it	PRON
ma-105	808	2	hasalso	hasalso	ADV
ma-105	808	3	been	be	AUX
ma-105	808	4	shown	show	VERB
ma-105	808	5	under	under	ADP
ma-105	808	6	the	the	DET
ma-105	808	7	hypothesis	hypothesis	NOUN
ma-105	808	8	r0	r0	NOUN
ma-105	808	9	>	>	X
ma-105	808	10	1	1	NUM
ma-105	808	11	,	,	PUNCT
ma-105	808	12	that	that	SCONJ
ma-105	808	13	the	the	DET
ma-105	808	14	infected	infected	ADJ
ma-105	808	15	equilibrium	equilibrium	NOUN
ma-105	808	16	point	point	NOUN
ma-105	808	17	is	be	AUX
ma-105	808	18	locally	locally	ADV
ma-105	808	19	andglobally	andglobally	ADV
ma-105	808	20	asymptotically	asymptotically	ADV
ma-105	808	21	stable	stable	ADJ
ma-105	808	22	.	.	PUNCT
ma-105	809	1	this	this	DET
ma-105	809	2	edifying	edifying	ADJ
ma-105	809	3	work	work	NOUN
ma-105	809	4	ended	end	VERB
ma-105	809	5	with	with	ADP
ma-105	809	6	numerical	numerical	ADJ
ma-105	809	7	simulations	simulation	NOUN
ma-105	809	8	,	,	PUNCT
ma-105	809	9	carried	carry	VERB
ma-105	809	10	outon	outon	NOUN
ma-105	809	11	the	the	DET
ma-105	809	12	mathematica	mathematica	PROPN
ma-105	809	13	software	software	PROPN
ma-105	809	14	,	,	PUNCT
ma-105	809	15	which	which	PRON
ma-105	809	16	confirmed	confirm	VERB
ma-105	809	17	our	our	PRON
ma-105	809	18	theoretical	theoretical	ADJ
ma-105	809	19	results	result	NOUN
ma-105	809	20	.	.	PUNCT
ma-105	810	1	in	in	ADP
ma-105	810	2	order	order	NOUN
ma-105	810	3	to	to	PART
ma-105	810	4	get	get	VERB
ma-105	810	5	as	as	ADV
ma-105	810	6	close	close	ADJ
ma-105	810	7	aspossible	aspossible	ADJ
ma-105	810	8	to	to	ADP
ma-105	810	9	complex	complex	ADJ
ma-105	810	10	reality	reality	NOUN
ma-105	810	11	of	of	ADP
ma-105	810	12	biological	biological	ADJ
ma-105	810	13	phenomena	phenomenon	NOUN
ma-105	810	14	,	,	PUNCT
ma-105	810	15	we	we	PRON
ma-105	810	16	envisage	envisage	VERB
ma-105	810	17	in	in	ADP
ma-105	810	18	the	the	DET
ma-105	810	19	future	future	NOUN
ma-105	810	20	,	,	PUNCT
ma-105	810	21	the	the	DET
ma-105	810	22	mathematicalanalysis	mathematicalanalysis	NOUN
ma-105	810	23	of	of	ADP
ma-105	810	24	models	model	NOUN
ma-105	810	25	taking	take	VERB
ma-105	810	26	into	into	ADP
ma-105	810	27	account	account	NOUN
ma-105	810	28	cell	cell	NOUN
ma-105	810	29	proliferation	proliferation	NOUN
ma-105	810	30	,	,	PUNCT
ma-105	810	31	the	the	DET
ma-105	810	32	delays	delay	NOUN
ma-105	810	33	and	and	CCONJ
ma-105	810	34	more	more	ADJ
ma-105	810	35	generalization	generalization	NOUN
ma-105	810	36	of	of	ADP
ma-105	810	37	theincident	theincident	NOUN
ma-105	810	38	rate	rate	NOUN
ma-105	810	39	function	function	NOUN
ma-105	810	40	.	.	PUNCT
ma-105	811	1	appendix	appendix	VERB
ma-105	811	2	a.	a.	NOUN
ma-105	811	3	proof	proof	NOUN
ma-105	811	4	of	of	ADP
ma-105	811	5	proposition	proposition	NOUN
ma-105	811	6	3.8	3.8	NUM
ma-105	811	7	the	the	DET
ma-105	811	8	proof	proof	NOUN
ma-105	811	9	is	be	AUX
ma-105	811	10	established	establish	VERB
ma-105	811	11	by	by	ADP
ma-105	811	12	using	use	VERB
ma-105	811	13	banach	banach	NOUN
ma-105	811	14	’s	’s	ADV
ma-105	811	15	fixed	fix	VERB
ma-105	811	16	point	point	NOUN
ma-105	811	17	theorem.choose	theorem.choose	NUM
ma-105	811	18	β	β	ADP
ma-105	811	19	such	such	ADJ
ma-105	811	20	that	that	SCONJ
ma-105	811	21	3	3	NUM
ma-105	811	22	4	4	NUM
ma-105	811	23	<	<	X
ma-105	811	24	β	β	X
ma-105	811	25	<	<	X
ma-105	811	26	1	1	NUM
ma-105	811	27	,	,	PUNCT
ma-105	811	28	then	then	ADV
ma-105	811	29	the	the	DET
ma-105	811	30	injection	injection	NOUN
ma-105	811	31	i	i	PRON
ma-105	811	32	:	:	PUNCT
ma-105	811	33	d(hβ	d(hβ	NUM
ma-105	811	34	)	)	PUNCT
ma-105	811	35	→	→	SYM
ma-105	811	36	c0	c0	PROPN
ma-105	811	37	b	b	PROPN
ma-105	811	38	is	be	AUX
ma-105	811	39	continuous	continuous	ADJ
ma-105	811	40	by	by	ADP
ma-105	811	41	lemma	lemma	PROPN
ma-105	811	42	3.3.for	3.3.for	PROPN
ma-105	811	43	r0	r0	PROPN
ma-105	811	44	>	>	X
ma-105	811	45	0	0	PUNCT
ma-105	812	1	and	and	CCONJ
ma-105	812	2	t	t	X
ma-105	812	3	>	>	X
ma-105	812	4	0	0	PROPN
ma-105	812	5	,	,	PUNCT
ma-105	812	6	the	the	DET
ma-105	812	7	following	follow	VERB
ma-105	812	8	closed	closed	ADJ
ma-105	812	9	ball	ball	NOUN
ma-105	812	10	is	be	AUX
ma-105	812	11	considered	consider	VERB
ma-105	812	12	:	:	PUNCT
ma-105	812	13	br0	br0	VERB
ma-105	812	14	(	(	PUNCT
ma-105	812	15	h0	h0	PROPN
ma-105	812	16	,	,	PUNCT
ma-105	812	17	i0	i0	PROPN
ma-105	812	18	,	,	PUNCT
ma-105	812	19	v0	v0	PROPN
ma-105	812	20	)	)	PUNCT
ma-105	812	21	=	=	PRON
ma-105	812	22	{	{	PUNCT
ma-105	812	23	(	(	PUNCT
ma-105	812	24	h	h	NOUN
ma-105	812	25	,	,	PUNCT
ma-105	812	26	i	i	PRON
ma-105	812	27	,	,	PUNCT
ma-105	812	28	v	v	NOUN
ma-105	812	29	)	)	PUNCT
ma-105	812	30	∈	∈	PROPN
ma-105	812	31	(	(	PUNCT
ma-105	812	32	c0	c0	PROPN
ma-105	812	33	b((0	b((0	PROPN
ma-105	812	34	,	,	PUNCT
ma-105	812	35	t	t	X
ma-105	812	36	]	]	PUNCT
ma-105	812	37	,	,	PUNCT
ma-105	812	38	d(hβ)))3	d(hβ)))3	X
ma-105	812	39	:	:	PUNCT
ma-105	812	40	‖h	‖h	NUM
ma-105	813	1	−h0‖β	−h0‖β	PROPN
ma-105	813	2	,	,	PUNCT
ma-105	813	3	‖i	‖i	NOUN
ma-105	813	4	−	−	NOUN
ma-105	813	5	i0‖β	i0‖β	NOUN
ma-105	813	6	,	,	PUNCT
ma-105	813	7	‖v	‖v	NOUN
ma-105	813	8	−	−	NOUN
ma-105	813	9	v0‖β	v0‖β	NOUN
ma-105	813	10	≤	≤	NUM
ma-105	813	11	r0	r0	NOUN
ma-105	813	12	}	}	PUNCT
ma-105	813	13	.(a.1)by	.(a.1)by	PUNCT
ma-105	814	1	proposition	proposition	NOUN
ma-105	814	2	3.1	3.1	NUM
ma-105	815	1	,	,	PUNCT
ma-105	815	2	we	we	PRON
ma-105	815	3	have	have	VERB
ma-105	815	4	the	the	DET
ma-105	815	5	local	local	ADJ
ma-105	815	6	lipschitz	lipschitz	NOUN
ma-105	815	7	properties	property	NOUN
ma-105	815	8	:	:	PUNCT
ma-105	815	9	‖f(t	‖f(t	NUM
ma-105	815	10	,	,	PUNCT
ma-105	815	11	h1	h1	PROPN
ma-105	815	12	,	,	PUNCT
ma-105	815	13	i1	i1	PROPN
ma-105	815	14	,	,	PUNCT
ma-105	815	15	v1)−f(t	v1)−f(t	PROPN
ma-105	815	16	,	,	PUNCT
ma-105	815	17	h2	h2	PROPN
ma-105	815	18	,	,	PUNCT
ma-105	815	19	i2	i2	PROPN
ma-105	815	20	,	,	PUNCT
ma-105	815	21	v2)‖2	v2)‖2	ADJ
ma-105	815	22	≤	≤	NUM
ma-105	815	23	k1	k1	NOUN
ma-105	815	24	1‖h1	1‖h1	NOUN
ma-105	815	25	−h2‖d(hβ	−h2‖d(hβ	NOUN
ma-105	815	26	)	)	PUNCT
ma-105	815	27	+	+	ADJ
ma-105	815	28	k1	k1	NOUN
ma-105	815	29	2‖i1	2‖i1	NUM
ma-105	815	30	−	−	ADP
ma-105	815	31	i2‖d(hβ	i2‖d(hβ	NOUN
ma-105	815	32	)	)	PUNCT
ma-105	815	33	+	+	ADJ
ma-105	815	34	k1	k1	NOUN
ma-105	815	35	3‖v1	3‖v1	NUM
ma-105	816	1	−	−	NOUN
ma-105	816	2	v2‖d(hβ	v2‖d(hβ	NOUN
ma-105	816	3	)	)	PUNCT
ma-105	816	4	,	,	PUNCT
ma-105	816	5	‖g(t	‖g(t	NOUN
ma-105	816	6	,	,	PUNCT
ma-105	816	7	h1	h1	PROPN
ma-105	816	8	,	,	PUNCT
ma-105	816	9	i1	i1	PROPN
ma-105	816	10	,	,	PUNCT
ma-105	816	11	v1)−	v1)−	PROPN
ma-105	816	12	g(t	g(t	PROPN
ma-105	816	13	,	,	PUNCT
ma-105	816	14	h2	h2	PROPN
ma-105	816	15	,	,	PUNCT
ma-105	816	16	i2	i2	PROPN
ma-105	816	17	,	,	PUNCT
ma-105	816	18	v2)‖2	v2)‖2	ADJ
ma-105	816	19	≤	≤	NUM
ma-105	816	20	k2	k2	ADJ
ma-105	816	21	1‖h1	1‖h1	PROPN
ma-105	816	22	−h2‖d(hβ	−h2‖d(hβ	NOUN
ma-105	816	23	)	)	PUNCT
ma-105	817	1	+	+	ADJ
ma-105	817	2	k2	k2	ADJ
ma-105	817	3	2‖i1	2‖i1	NUM
ma-105	817	4	−	−	ADP
ma-105	817	5	i2‖d(hβ	i2‖d(hβ	NOUN
ma-105	817	6	)	)	PUNCT
ma-105	817	7	+	+	ADJ
ma-105	817	8	k2	k2	ADJ
ma-105	817	9	3‖v1	3‖v1	VERB
ma-105	817	10	−	−	PROPN
ma-105	818	1	v2‖d(hβ	v2‖d(hβ	NOUN
ma-105	818	2	)	)	PUNCT
ma-105	818	3	,	,	PUNCT
ma-105	818	4	‖q(t	‖q(t	PROPN
ma-105	818	5	,	,	PUNCT
ma-105	818	6	h1	h1	PROPN
ma-105	818	7	,	,	PUNCT
ma-105	818	8	i1	i1	PROPN
ma-105	818	9	,	,	PUNCT
ma-105	818	10	v1)−q(t	v1)−q(t	NOUN
ma-105	818	11	,	,	PUNCT
ma-105	818	12	h2	h2	PROPN
ma-105	818	13	,	,	PUNCT
ma-105	818	14	i2	i2	PROPN
ma-105	818	15	,	,	PUNCT
ma-105	818	16	v2)‖2	v2)‖2	ADJ
ma-105	818	17	≤	≤	NOUN
ma-105	818	18	k3	k3	VERB
ma-105	818	19	1‖h1	1‖h1	NOUN
ma-105	818	20	−h2‖d(hβ	−h2‖d(hβ	NOUN
ma-105	818	21	)	)	PUNCT
ma-105	819	1	+	+	SYM
ma-105	819	2	k3	k3	ADJ
ma-105	819	3	2‖i1	2‖i1	NUM
ma-105	819	4	−	−	ADP
ma-105	819	5	i2‖d(hβ	i2‖d(hβ	NOUN
ma-105	819	6	)	)	PUNCT
ma-105	819	7	+	+	NOUN
ma-105	819	8	k3	k3	ADJ
ma-105	819	9	3‖v1	3‖v1	NOUN
ma-105	819	10	−	−	NOUN
ma-105	819	11	v2‖d(hβ),(a.2	v2‖d(hβ),(a.2	NOUN
ma-105	819	12	)	)	PUNCT
ma-105	819	13	for	for	ADP
ma-105	819	14	t	t	PROPN
ma-105	819	15	∈	∈	PROPN
ma-105	820	1	[	[	X
ma-105	820	2	0	0	NUM
ma-105	820	3	,	,	PUNCT
ma-105	820	4	t	t	X
ma-105	820	5	]	]	PUNCT
ma-105	820	6	,	,	PUNCT
ma-105	820	7	(	(	PUNCT
ma-105	820	8	h1	h1	PROPN
ma-105	820	9	,	,	PUNCT
ma-105	820	10	i1	i1	PROPN
ma-105	820	11	,	,	PUNCT
ma-105	820	12	v1	v1	PROPN
ma-105	820	13	)	)	PUNCT
ma-105	820	14	,	,	PUNCT
ma-105	820	15	(	(	PUNCT
ma-105	820	16	h2	h2	PROPN
ma-105	820	17	,	,	PUNCT
ma-105	820	18	i2	i2	PROPN
ma-105	820	19	,	,	PUNCT
ma-105	820	20	v2	v2	PROPN
ma-105	820	21	)	)	PUNCT
ma-105	820	22	∈	∈	PROPN
ma-105	820	23	br0	br0	NOUN
ma-105	820	24	(	(	PUNCT
ma-105	820	25	h0	h0	PROPN
ma-105	820	26	,	,	PUNCT
ma-105	820	27	i0	i0	PROPN
ma-105	820	28	,	,	PUNCT
ma-105	820	29	v0	v0	PROPN
ma-105	820	30	)	)	PUNCT
ma-105	820	31	and	and	CCONJ
ma-105	820	32	lipschitz	lipschitz	NOUN
ma-105	820	33	-	-	PUNCT
ma-105	820	34	constants	constant	NOUN
ma-105	820	35	k	k	NOUN
ma-105	820	36	ij	ij	INTJ
ma-105	820	37	>	>	X
ma-105	820	38	0	0	NUM
ma-105	820	39	,	,	PUNCT
ma-105	820	40	i	i	PRON
ma-105	820	41	,	,	PUNCT
ma-105	820	42	j	j	PROPN
ma-105	820	43	=	=	SYM
ma-105	820	44	1	1	NUM
ma-105	820	45	,	,	PUNCT
ma-105	820	46	2	2	NUM
ma-105	820	47	,	,	PUNCT
ma-105	820	48	3	3	NUM
ma-105	820	49	.	.	PUNCT
ma-105	821	1	in	in	ADP
ma-105	821	2	addition	addition	NOUN
ma-105	821	3	(	(	PUNCT
ma-105	821	4	y1	y1	INTJ
ma-105	821	5	,	,	PUNCT
ma-105	821	6	y2	y2	PROPN
ma-105	821	7	,	,	PUNCT
ma-105	821	8	y3	y3	PROPN
ma-105	821	9	)	)	PUNCT
ma-105	821	10	∈	∈	PROPN
ma-105	821	11	br0	br0	NOUN
ma-105	821	12	(	(	PUNCT
ma-105	821	13	h0	h0	PROPN
ma-105	821	14	,	,	PUNCT
ma-105	821	15	i0	i0	PROPN
ma-105	821	16	,	,	PUNCT
ma-105	821	17	v0	v0	PROPN
ma-105	821	18	)	)	PUNCT
ma-105	821	19	,	,	PUNCT
ma-105	821	20	define	define	VERB
ma-105	821	21	p	p	X
ma-105	821	22	:	:	PUNCT
ma-105	822	1	[	[	X
ma-105	822	2	0	0	NUM
ma-105	822	3	,	,	PUNCT
ma-105	822	4	t	t	X
ma-105	822	5	]	]	PUNCT
ma-105	822	6	→	→	SYM
ma-105	822	7	l2(ω	l2(ω	NUM
ma-105	822	8	)	)	PUNCT
ma-105	822	9	,	,	PUNCT
ma-105	822	10	q	q	NOUN
ma-105	822	11	:	:	PUNCT
ma-105	823	1	[	[	X
ma-105	823	2	0	0	NUM
ma-105	823	3	,	,	PUNCT
ma-105	823	4	t	t	NOUN
ma-105	823	5	]	]	PUNCT
ma-105	823	6	→	→	PUNCT
ma-105	823	7	l2(ω)and	l2(ω)and	NUM
ma-105	823	8	r	r	NOUN
ma-105	823	9	:	:	PUNCT
ma-105	824	1	[	[	X
ma-105	824	2	0	0	NUM
ma-105	824	3	,	,	PUNCT
ma-105	824	4	t	t	X
ma-105	824	5	]	]	PUNCT
ma-105	824	6	→	→	SYM
ma-105	824	7	l2(ω	l2(ω	CCONJ
ma-105	824	8	)	)	PUNCT
ma-105	824	9	as	as	SCONJ
ma-105	824	10	follows	follow	VERB
ma-105	824	11	py1(t	py1(t	VERB
ma-105	824	12	)	)	PUNCT
ma-105	824	13	=	=	PRON
ma-105	824	14	g1(t)h0	g1(t)h0	X
ma-105	825	1	+	+	CCONJ
ma-105	825	2	∫	∫	PROPN
ma-105	825	3	t	t	NOUN
ma-105	825	4	0	0	PUNCT
ma-105	826	1	g1(t	g1(t	ADP
ma-105	826	2	−	−	PROPN
ma-105	826	3	τ)f(t	τ)f(t	NOUN
ma-105	826	4	,	,	PUNCT
ma-105	826	5	y1(τ	y1(τ	PROPN
ma-105	826	6	)	)	PUNCT
ma-105	826	7	,	,	PUNCT
ma-105	826	8	y2(τ	y2(τ	PROPN
ma-105	826	9	)	)	PUNCT
ma-105	826	10	,	,	PUNCT
ma-105	826	11	y3(τ))dτ	y3(τ))dτ	PROPN
ma-105	826	12	,	,	PUNCT
ma-105	826	13	qy2(t	qy2(t	PROPN
ma-105	826	14	)	)	PUNCT
ma-105	826	15	=	=	SYM
ma-105	826	16	g2(t)i0	g2(t)i0	NOUN
ma-105	827	1	+	+	CCONJ
ma-105	828	1	∫	∫	PROPN
ma-105	828	2	t	t	NOUN
ma-105	828	3	0	0	NUM
ma-105	829	1	g2(t	g2(t	PROPN
ma-105	830	1	−	−	PROPN
ma-105	830	2	τ)g(t	τ)g(t	PROPN
ma-105	830	3	,	,	PUNCT
ma-105	830	4	y1(τ	y1(τ	PROPN
ma-105	830	5	)	)	PUNCT
ma-105	830	6	,	,	PUNCT
ma-105	830	7	y2(τ	y2(τ	PROPN
ma-105	830	8	)	)	PUNCT
ma-105	830	9	,	,	PUNCT
ma-105	830	10	y3(τ))dτ	y3(τ))dτ	PROPN
ma-105	830	11	,	,	PUNCT
ma-105	830	12	ry3(t	ry3(t	ADJ
ma-105	830	13	)	)	PUNCT
ma-105	830	14	=	=	NOUN
ma-105	830	15	g3(t)v0	g3(t)v0	NOUN
ma-105	831	1	+	+	CCONJ
ma-105	832	1	∫	∫	PROPN
ma-105	832	2	t	t	PROPN
ma-105	832	3	0	0	NUM
ma-105	832	4	g3(t	g3(t	NUM
ma-105	832	5	−	−	PROPN
ma-105	832	6	τ)q(t	τ)q(t	NOUN
ma-105	832	7	,	,	PUNCT
ma-105	832	8	y1(τ	y1(τ	PROPN
ma-105	832	9	)	)	PUNCT
ma-105	832	10	,	,	PUNCT
ma-105	832	11	y2(τ	y2(τ	PROPN
ma-105	832	12	)	)	PUNCT
ma-105	832	13	,	,	PUNCT
ma-105	832	14	y3(τ))dτ	y3(τ))dτ	PROPN
ma-105	832	15	.	.	PUNCT
ma-105	833	1	finally	finally	ADV
ma-105	833	2	,	,	PUNCT
ma-105	833	3	set	set	VERB
ma-105	833	4	m1	m1	NOUN
ma-105	833	5	=	=	PUNCT
ma-105	833	6	sup	sup	NOUN
ma-105	833	7	t∈[0,t	t∈[0,t	NOUN
ma-105	833	8	]	]	PUNCT
ma-105	834	1	‖f(t	‖f(t	X
ma-105	834	2	,	,	PUNCT
ma-105	834	3	y1(0	y1(0	PROPN
ma-105	834	4	)	)	PUNCT
ma-105	834	5	,	,	PUNCT
ma-105	834	6	y2(0	y2(0	PROPN
ma-105	834	7	)	)	PUNCT
ma-105	834	8	,	,	PUNCT
ma-105	834	9	y3(0))‖2	y3(0))‖2	NOUN
ma-105	834	10	,	,	PUNCT
ma-105	834	11	m2	m2	PROPN
ma-105	834	12	=	=	PROPN
ma-105	834	13	sup	sup	PROPN
ma-105	834	14	t∈[0,t	t∈[0,t	PROPN
ma-105	834	15	]	]	PUNCT
ma-105	834	16	‖g(t	‖g(t	ADJ
ma-105	834	17	,	,	PUNCT
ma-105	834	18	y1(0	y1(0	PROPN
ma-105	834	19	)	)	PUNCT
ma-105	834	20	,	,	PUNCT
ma-105	834	21	y2(0	y2(0	PROPN
ma-105	834	22	)	)	PUNCT
ma-105	834	23	,	,	PUNCT
ma-105	834	24	y3(0))‖2	y3(0))‖2	NOUN
ma-105	834	25	,	,	PUNCT
ma-105	834	26	m3	m3	PROPN
ma-105	834	27	=	=	PUNCT
ma-105	834	28	sup	sup	NOUN
ma-105	834	29	t∈[0,t	t∈[0,t	NOUN
ma-105	834	30	]	]	PUNCT
ma-105	834	31	‖q(t	‖q(t	PROPN
ma-105	834	32	,	,	PUNCT
ma-105	834	33	y1(0	y1(0	PROPN
ma-105	834	34	)	)	PUNCT
ma-105	834	35	,	,	PUNCT
ma-105	834	36	y2(0	y2(0	PROPN
ma-105	834	37	)	)	PUNCT
ma-105	834	38	,	,	PUNCT
ma-105	834	39	y3(0))‖2	y3(0))‖2	PRON
ma-105	834	40	and	and	CCONJ
ma-105	834	41	choose	choose	VERB
ma-105	834	42	t	t	NOUN
ma-105	834	43	so	so	SCONJ
ma-105	834	44	that	that	SCONJ
ma-105	834	45	:	:	PUNCT
ma-105	834	46	‖g1(h)h0	‖g1(h)h0	PROPN
ma-105	834	47	−h0‖β	−h0‖β	PROPN
ma-105	834	48	,	,	PUNCT
ma-105	834	49	‖g2(h)i0	‖g2(h)i0	NOUN
ma-105	834	50	−	−	NOUN
ma-105	834	51	i0‖β	i0‖β	NOUN
ma-105	834	52	,	,	PUNCT
ma-105	834	53	‖g3(h)v0	‖g3(h)v0	NOUN
ma-105	834	54	−	−	NOUN
ma-105	834	55	v0‖β	v0‖β	NOUN
ma-105	834	56	≤	≤	NOUN
ma-105	834	57	3r0	3r0	NUM
ma-105	834	58	4	4	NUM
ma-105	834	59	,	,	PUNCT
ma-105	834	60	0	0	NUM
ma-105	834	61	≤	≤	NUM
ma-105	834	62	h	h	NOUN
ma-105	834	63	≤	≤	PROPN
ma-105	834	64	t	t	PROPN
ma-105	834	65	,	,	PUNCT
ma-105	834	66	(	(	PUNCT
ma-105	834	67	a.3	a.3	NOUN
ma-105	834	68	)	)	PUNCT
ma-105	834	69	https://doi.org/10.28924/ada/ma.3.1	https://doi.org/10.28924/ada/ma.3.1	PROPN
ma-105	834	70	eur	eur	PROPN
ma-105	834	71	.	.	PUNCT
ma-105	835	1	j.	j.	PROPN
ma-105	835	2	math	math	PROPN
ma-105	835	3	.	.	PUNCT
ma-105	836	1	anal	anal	PROPN
ma-105	836	2	.	.	PUNCT
ma-105	837	1	10.28924	10.28924	NUM
ma-105	837	2	/	/	SYM
ma-105	837	3	ada	ada	PROPN
ma-105	837	4	/	/	SYM
ma-105	837	5	ma.3.1	ma.3.1	PROPN
ma-105	837	6	30	30	NUM
ma-105	837	7	c	c	NOUN
ma-105	837	8	iβ,2(mi	iβ,2(mi	NOUN
ma-105	837	9	+	+	CCONJ
ma-105	837	10	r0k	r0k	PROPN
ma-105	837	11	i	i	X
ma-105	837	12	1	1	NUM
ma-105	837	13	+	+	CCONJ
ma-105	837	14	r0k	r0k	PROPN
ma-105	837	15	i	i	NOUN
ma-105	837	16	2	2	NUM
ma-105	837	17	+	+	CCONJ
ma-105	837	18	r0k	r0k	PROPN
ma-105	837	19	i	i	NOUN
ma-105	837	20	3	3	X
ma-105	837	21	)	)	PUNCT
ma-105	838	1	∫	∫	PROPN
ma-105	838	2	t	t	PROPN
ma-105	838	3	0	0	NUM
ma-105	838	4	s−βds	s−βds	ADJ
ma-105	838	5	≤	≤	NUM
ma-105	838	6	r0	r0	NOUN
ma-105	838	7	4	4	NUM
ma-105	838	8	,	,	PUNCT
ma-105	838	9	i	i	PRON
ma-105	838	10	=	=	NOUN
ma-105	838	11	1	1	NUM
ma-105	838	12	,	,	PUNCT
ma-105	838	13	2	2	NUM
ma-105	838	14	,	,	PUNCT
ma-105	838	15	3	3	NUM
ma-105	838	16	,	,	PUNCT
ma-105	838	17	(	(	PUNCT
ma-105	838	18	a.4	a.4	X
ma-105	838	19	)	)	PUNCT
ma-105	838	20	where	where	SCONJ
ma-105	838	21	c	c	PROPN
ma-105	838	22	iβ,2	iβ,2	PROPN
ma-105	838	23	is	be	AUX
ma-105	838	24	the	the	DET
ma-105	838	25	constant	constant	ADJ
ma-105	838	26	in	in	ADP
ma-105	838	27	property	property	NOUN
ma-105	838	28	2	2	NUM
ma-105	838	29	)	)	PUNCT
ma-105	838	30	of	of	ADP
ma-105	838	31	corollary	corollary	ADJ
ma-105	838	32	3.5	3.5	NUM
ma-105	838	33	for	for	ADP
ma-105	838	34	operator	operator	NOUN
ma-105	838	35	a	a	DET
ma-105	838	36	(	(	PUNCT
ma-105	838	37	a	a	PRON
ma-105	838	38	is	be	AUX
ma-105	838	39	zero	zero	NUM
ma-105	838	40	for	for	ADP
ma-105	838	41	i	i	PROPN
ma-105	838	42	=	=	NOUN
ma-105	838	43	1	1	NUM
ma-105	838	44	,	,	PUNCT
ma-105	838	45	2).note	2).note	NUM
ma-105	838	46	that	that	PRON
ma-105	838	47	such	such	ADJ
ma-105	838	48	t	t	NOUN
ma-105	838	49	exists	exist	VERB
ma-105	838	50	since	since	SCONJ
ma-105	838	51	g1(h	g1(h	PROPN
ma-105	838	52	)	)	PUNCT
ma-105	838	53	,	,	PUNCT
ma-105	838	54	g2(h	g2(h	PROPN
ma-105	838	55	)	)	PUNCT
ma-105	838	56	and	and	CCONJ
ma-105	838	57	g3(h	g3(h	X
ma-105	838	58	)	)	PUNCT
ma-105	838	59	converge	converge	VERB
ma-105	838	60	to	to	ADP
ma-105	838	61	i	i	PROPN
ma-105	838	62	d	d	PROPN
ma-105	838	63	as	as	SCONJ
ma-105	838	64	h	h	NOUN
ma-105	838	65	tends	tend	VERB
ma-105	838	66	to	to	ADP
ma-105	838	67	0	0	NUM
ma-105	838	68	+	+	CCONJ
ma-105	838	69	by	by	ADP
ma-105	838	70	definitionof	definitionof	NOUN
ma-105	838	71	an	an	DET
ma-105	838	72	analytic	analytic	ADJ
ma-105	838	73	semigroup	semigroup	NOUN
ma-105	838	74	and∫	and∫	PROPN
ma-105	838	75	t	t	PROPN
ma-105	838	76	0	0	NUM
ma-105	838	77	s−βds	s−βds	NOUN
ma-105	838	78	=	=	NOUN
ma-105	838	79	1	1	NUM
ma-105	838	80	1−	1−	NUM
ma-105	838	81	βh	βh	ADP
ma-105	838	82	1−β	1−β	NUM
ma-105	838	83	→	→	SYM
ma-105	838	84	0	0	NUM
ma-105	838	85	,	,	PUNCT
ma-105	838	86	h	h	NOUN
ma-105	838	87	→	→	SYM
ma-105	838	88	0	0	NUM
ma-105	839	1	+	+	NUM
ma-105	839	2	f	f	NOUN
ma-105	839	3	or	or	CCONJ
ma-105	839	4	β	β	ADJ
ma-105	839	5	<	<	X
ma-105	839	6	1	1	NUM
ma-105	839	7	.	.	PUNCT
ma-105	840	1	then	then	ADV
ma-105	840	2	the	the	DET
ma-105	840	3	proof	proof	NOUN
ma-105	840	4	will	will	AUX
ma-105	840	5	continue	continue	VERB
ma-105	840	6	according	accord	VERB
ma-105	840	7	to	to	ADP
ma-105	840	8	the	the	DET
ma-105	840	9	following	follow	VERB
ma-105	840	10	two	two	NUM
ma-105	840	11	points	point	NOUN
ma-105	840	12	:	:	PUNCT
ma-105	840	13	(	(	PUNCT
ma-105	840	14	a	a	X
ma-105	840	15	):	):	PUNCT
ma-105	840	16	it	it	PRON
ma-105	840	17	is	be	AUX
ma-105	840	18	shown	show	VERB
ma-105	840	19	that	that	SCONJ
ma-105	840	20	(	(	PUNCT
ma-105	840	21	p	p	X
ma-105	840	22	,	,	PUNCT
ma-105	840	23	q	q	ADJ
ma-105	840	24	,	,	PUNCT
ma-105	840	25	r	r	NOUN
ma-105	840	26	)	)	PUNCT
ma-105	840	27	maps	map	NOUN
ma-105	840	28	br0	br0	VERB
ma-105	840	29	(	(	PUNCT
ma-105	840	30	h0	h0	PROPN
ma-105	840	31	,	,	PUNCT
ma-105	840	32	i0	i0	PROPN
ma-105	840	33	,	,	PUNCT
ma-105	840	34	v0	v0	PROPN
ma-105	840	35	)	)	PUNCT
ma-105	840	36	into	into	ADP
ma-105	840	37	itself	itself	PRON
ma-105	840	38	,	,	PUNCT
ma-105	840	39	(	(	PUNCT
ma-105	840	40	b	b	X
ma-105	840	41	):	):	PUNCT
ma-105	840	42	it	it	PRON
ma-105	840	43	is	be	AUX
ma-105	840	44	shown	show	VERB
ma-105	840	45	that	that	SCONJ
ma-105	840	46	(	(	PUNCT
ma-105	840	47	p	p	X
ma-105	840	48	,	,	PUNCT
ma-105	840	49	q	q	ADJ
ma-105	840	50	,	,	PUNCT
ma-105	840	51	r	r	NOUN
ma-105	840	52	)	)	PUNCT
ma-105	840	53	is	be	AUX
ma-105	840	54	a	a	DET
ma-105	840	55	strict	strict	ADJ
ma-105	840	56	contraction	contraction	NOUN
ma-105	840	57	on	on	ADP
ma-105	840	58	br0	br0	NOUN
ma-105	840	59	(	(	PUNCT
ma-105	840	60	h0	h0	PROPN
ma-105	840	61	,	,	PUNCT
ma-105	840	62	i0	i0	PROPN
ma-105	840	63	,	,	PUNCT
ma-105	840	64	v0	v0	PROPN
ma-105	840	65	)	)	PUNCT
ma-105	840	66	,	,	PUNCT
ma-105	840	67	allowing	allow	VERB
ma-105	840	68	the	the	DET
ma-105	840	69	use	use	NOUN
ma-105	840	70	ofbanach	ofbanach	NOUN
ma-105	840	71	’s	’s	PART
ma-105	840	72	fixed	fix	VERB
ma-105	840	73	point	point	NOUN
ma-105	840	74	theorem	theorem	VERB
ma-105	840	75	to	to	PART
ma-105	840	76	get	get	VERB
ma-105	840	77	the	the	DET
ma-105	840	78	existence	existence	NOUN
ma-105	840	79	of	of	ADP
ma-105	840	80	a	a	DET
ma-105	840	81	unique	unique	ADJ
ma-105	840	82	fixed	fix	VERB
ma-105	840	83	point	point	NOUN
ma-105	840	84	in	in	ADP
ma-105	840	85	br0	br0	NOUN
ma-105	840	86	(	(	PUNCT
ma-105	840	87	h0	h0	PROPN
ma-105	840	88	,	,	PUNCT
ma-105	840	89	i0	i0	PROPN
ma-105	840	90	,	,	PUNCT
ma-105	840	91	v0).let	v0).let	NUM
ma-105	840	92	(	(	PUNCT
ma-105	840	93	h	h	NOUN
ma-105	840	94	,	,	PUNCT
ma-105	840	95	i	i	PRON
ma-105	840	96	,	,	PUNCT
ma-105	840	97	v	v	NOUN
ma-105	840	98	)	)	PUNCT
ma-105	840	99	∈	∈	PROPN
ma-105	840	100	br0	br0	NOUN
ma-105	840	101	(	(	PUNCT
ma-105	840	102	h0	h0	PROPN
ma-105	840	103	,	,	PUNCT
ma-105	840	104	i0	i0	PROPN
ma-105	840	105	,	,	PUNCT
ma-105	840	106	v0	v0	PROPN
ma-105	840	107	)	)	PUNCT
ma-105	840	108	.	.	PUNCT
ma-105	841	1	then	then	ADV
ma-105	841	2	,	,	PUNCT
ma-105	841	3	using	use	VERB
ma-105	841	4	(	(	PUNCT
ma-105	841	5	a.3	a.3	NOUN
ma-105	841	6	)	)	PUNCT
ma-105	841	7	and	and	CCONJ
ma-105	841	8	property	property	NOUN
ma-105	841	9	2	2	NUM
ma-105	841	10	)	)	PUNCT
ma-105	841	11	of	of	ADP
ma-105	841	12	corollary	corollary	ADJ
ma-105	841	13	3.5	3.5	NUM
ma-105	841	14	,	,	PUNCT
ma-105	841	15	we	we	PRON
ma-105	841	16	have	have	VERB
ma-105	841	17	:	:	PUNCT
ma-105	841	18	‖ph(t)−h0‖d(hβ	‖ph(t)−h0‖d(hβ	PROPN
ma-105	841	19	)	)	PUNCT
ma-105	842	1	=	=	PRON
ma-105	842	2	∥∥∥g1(t)h0	∥∥∥g1(t)h0	PART
ma-105	843	1	−h0	−h0	VERB
ma-105	843	2	+	+	CCONJ
ma-105	844	1	∫	∫	PROPN
ma-105	844	2	t	t	PROPN
ma-105	844	3	0	0	PUNCT
ma-105	845	1	g1(t	g1(t	ADP
ma-105	845	2	−	−	PROPN
ma-105	845	3	τ)f(τ	τ)f(τ	NOUN
ma-105	845	4	,	,	PUNCT
ma-105	845	5	h(τ	h(τ	PROPN
ma-105	845	6	)	)	PUNCT
ma-105	845	7	,	,	PUNCT
ma-105	845	8	i(τ	i(τ	PROPN
ma-105	845	9	)	)	PUNCT
ma-105	845	10	,	,	PUNCT
ma-105	845	11	v	v	X
ma-105	845	12	(	(	PUNCT
ma-105	845	13	τ))dτ	τ))dτ	PROPN
ma-105	845	14	∥∥∥	∥∥∥	PROPN
ma-105	845	15	d(hβ	d(hβ	NUM
ma-105	845	16	)	)	PUNCT
ma-105	845	17	,	,	PUNCT
ma-105	845	18	≤	≤	ADJ
ma-105	845	19	‖g1(t)h0	‖g1(t)h0	NOUN
ma-105	845	20	−h0‖d(hβ	−h0‖d(hβ	NOUN
ma-105	845	21	)	)	PUNCT
ma-105	846	1	+	+	CCONJ
ma-105	846	2	∫	∫	PROPN
ma-105	846	3	t	t	NOUN
ma-105	846	4	0	0	NUM
ma-105	847	1	‖g1(t	‖g1(t	ADJ
ma-105	847	2	−	−	NOUN
ma-105	847	3	τ)f(τ	τ)f(τ	NOUN
ma-105	847	4	,	,	PUNCT
ma-105	847	5	h(τ	h(τ	PROPN
ma-105	847	6	)	)	PUNCT
ma-105	847	7	,	,	PUNCT
ma-105	847	8	i(τ	i(τ	PROPN
ma-105	847	9	)	)	PUNCT
ma-105	847	10	,	,	PUNCT
ma-105	847	11	v	v	X
ma-105	847	12	(	(	PUNCT
ma-105	847	13	τ))‖d(hβ)dτ	τ))‖d(hβ)dτ	NOUN
ma-105	847	14	,	,	PUNCT
ma-105	847	15	≤	≤	NUM
ma-105	847	16	3r0	3r0	NUM
ma-105	847	17	4	4	NUM
ma-105	847	18	+	+	NUM
ma-105	847	19	∫	∫	PROPN
ma-105	847	20	t	t	PROPN
ma-105	847	21	0	0	NUM
ma-105	848	1	c1	c1	PROPN
ma-105	848	2	β,2(t	β,2(t	PROPN
ma-105	849	1	−	−	PROPN
ma-105	849	2	s)−β	s)−β	ADV
ma-105	849	3	∥∥∥f(τ	∥∥∥f(τ	ADJ
ma-105	849	4	,	,	PUNCT
ma-105	849	5	h(τ	h(τ	PROPN
ma-105	849	6	)	)	PUNCT
ma-105	849	7	,	,	PUNCT
ma-105	849	8	i(τ	i(τ	PROPN
ma-105	849	9	)	)	PUNCT
ma-105	849	10	,	,	PUNCT
ma-105	849	11	v	v	X
ma-105	849	12	(	(	PUNCT
ma-105	849	13	τ	τ	NOUN
ma-105	849	14	)	)	PUNCT
ma-105	849	15	)	)	PUNCT
ma-105	849	16	∥∥∥	∥∥∥	PROPN
ma-105	849	17	2	2	NUM
ma-105	849	18	dτ	dτ	NOUN
ma-105	849	19	,	,	PUNCT
ma-105	849	20	≤	≤	NOUN
ma-105	849	21	3r0	3r0	NUM
ma-105	849	22	4	4	NUM
ma-105	850	1	+	+	NUM
ma-105	850	2	∫	∫	PROPN
ma-105	850	3	t	t	PROPN
ma-105	850	4	0	0	NUM
ma-105	850	5	c1	c1	PROPN
ma-105	850	6	β,2(t	β,2(t	PROPN
ma-105	851	1	−	−	PROPN
ma-105	851	2	s)−β	s)−β	ADV
ma-105	851	3	∥∥∥f(τ	∥∥∥f(τ	ADJ
ma-105	851	4	,	,	PUNCT
ma-105	851	5	h(τ	h(τ	PROPN
ma-105	851	6	)	)	PUNCT
ma-105	851	7	,	,	PUNCT
ma-105	851	8	i(τ	i(τ	PROPN
ma-105	851	9	)	)	PUNCT
ma-105	851	10	,	,	PUNCT
ma-105	851	11	v	v	X
ma-105	851	12	(	(	PUNCT
ma-105	851	13	τ))−f(τ	τ))−f(τ	X
ma-105	851	14	,	,	PUNCT
ma-105	851	15	h0	h0	PROPN
ma-105	851	16	,	,	PUNCT
ma-105	851	17	i0	i0	PROPN
ma-105	851	18	,	,	PUNCT
ma-105	851	19	v0	v0	PROPN
ma-105	851	20	)	)	PUNCT
ma-105	852	1	+	+	ADP
ma-105	852	2	f(τ	f(τ	PROPN
ma-105	852	3	,	,	PUNCT
ma-105	852	4	h0	h0	PROPN
ma-105	852	5	,	,	PUNCT
ma-105	852	6	i0	i0	PROPN
ma-105	852	7	,	,	PUNCT
ma-105	852	8	v0	v0	PROPN
ma-105	852	9	)	)	PUNCT
ma-105	852	10	∥∥∥	∥∥∥	PROPN
ma-105	852	11	2	2	NUM
ma-105	852	12	dτ	dτ	NOUN
ma-105	852	13	,	,	PUNCT
ma-105	852	14	≤	≤	NOUN
ma-105	852	15	3r0	3r0	NUM
ma-105	852	16	4	4	NUM
ma-105	853	1	+	+	NUM
ma-105	853	2	∫	∫	PROPN
ma-105	853	3	t	t	PROPN
ma-105	853	4	0	0	NUM
ma-105	853	5	c1	c1	PROPN
ma-105	853	6	β,2(t	β,2(t	PROPN
ma-105	854	1	−	−	NOUN
ma-105	855	1	s)−β	s)−β	CCONJ
ma-105	855	2	(	(	PUNCT
ma-105	855	3	∥∥∥f(τ	∥∥∥f(τ	ADJ
ma-105	855	4	,	,	PUNCT
ma-105	855	5	h(τ	h(τ	PROPN
ma-105	855	6	)	)	PUNCT
ma-105	855	7	,	,	PUNCT
ma-105	855	8	i(τ	i(τ	PROPN
ma-105	855	9	)	)	PUNCT
ma-105	855	10	,	,	PUNCT
ma-105	855	11	v	v	X
ma-105	855	12	(	(	PUNCT
ma-105	855	13	τ))−f(τ	τ))−f(τ	X
ma-105	855	14	,	,	PUNCT
ma-105	855	15	h0	h0	PROPN
ma-105	855	16	,	,	PUNCT
ma-105	855	17	i0	i0	PROPN
ma-105	855	18	,	,	PUNCT
ma-105	855	19	v0	v0	PROPN
ma-105	855	20	)	)	PUNCT
ma-105	855	21	∥∥∥	∥∥∥	PROPN
ma-105	855	22	2	2	NUM
ma-105	855	23	+	+	CCONJ
ma-105	855	24	∥∥∥f(τ	∥∥∥f(τ	ADJ
ma-105	855	25	,	,	PUNCT
ma-105	855	26	h0	h0	PROPN
ma-105	855	27	,	,	PUNCT
ma-105	855	28	i0	i0	PROPN
ma-105	855	29	,	,	PUNCT
ma-105	855	30	v0	v0	PROPN
ma-105	855	31	)	)	PUNCT
ma-105	855	32	∥∥∥	∥∥∥	PROPN
ma-105	855	33	2	2	NUM
ma-105	855	34	)	)	PUNCT
ma-105	855	35	dτ	dτ	PROPN
ma-105	855	36	,	,	PUNCT
ma-105	855	37	‖ph(t)−h0‖d(hβ	‖ph(t)−h0‖d(hβ	PROPN
ma-105	855	38	)	)	PUNCT
ma-105	855	39	≤	≤	NOUN
ma-105	855	40	3r0	3r0	NUM
ma-105	855	41	4	4	NUM
ma-105	856	1	+	+	NUM
ma-105	856	2	∫	∫	PROPN
ma-105	856	3	t	t	PROPN
ma-105	856	4	0	0	NUM
ma-105	856	5	c1	c1	PROPN
ma-105	856	6	β,2(t	β,2(t	PROPN
ma-105	857	1	−	−	PROPN
ma-105	857	2	s)−β	s)−β	ADV
ma-105	857	3	(	(	PUNCT
ma-105	857	4	k1	k1	NOUN
ma-105	857	5	1	1	NUM
ma-105	857	6	r0	r0	NOUN
ma-105	857	7	+	+	NOUN
ma-105	857	8	k1	k1	NOUN
ma-105	857	9	2	2	NUM
ma-105	857	10	r0	r0	NOUN
ma-105	857	11	+	+	NOUN
ma-105	857	12	k1	k1	NOUN
ma-105	857	13	3	3	NUM
ma-105	857	14	r0	r0	NOUN
ma-105	857	15	+	+	NOUN
ma-105	857	16	m1	m1	PROPN
ma-105	857	17	)	)	PUNCT
ma-105	857	18	dτ	dτ	PROPN
ma-105	857	19	,	,	PUNCT
ma-105	857	20	≤	≤	NOUN
ma-105	857	21	3r0	3r0	NUM
ma-105	857	22	4	4	NUM
ma-105	857	23	+	+	CCONJ
ma-105	857	24	c1	c1	PROPN
ma-105	857	25	β,2	β,2	PUNCT
ma-105	858	1	(	(	PUNCT
ma-105	858	2	k1	k1	NOUN
ma-105	858	3	1	1	NUM
ma-105	858	4	r0	r0	NOUN
ma-105	858	5	+	+	NOUN
ma-105	858	6	k1	k1	NOUN
ma-105	858	7	2	2	NUM
ma-105	858	8	r0	r0	NOUN
ma-105	858	9	+	+	NOUN
ma-105	858	10	k1	k1	NOUN
ma-105	858	11	3	3	NUM
ma-105	858	12	r0	r0	NOUN
ma-105	858	13	+	+	NOUN
ma-105	858	14	m1	m1	PROPN
ma-105	858	15	)	)	PUNCT
ma-105	859	1	∫	∫	PROPN
ma-105	859	2	t	t	PROPN
ma-105	859	3	0	0	NUM
ma-105	860	1	(	(	PUNCT
ma-105	860	2	t	t	NOUN
ma-105	860	3	−	−	PROPN
ma-105	860	4	s)−βdτ	s)−βdτ	NOUN
ma-105	860	5	,	,	PUNCT
ma-105	860	6	≤	≤	NOUN
ma-105	860	7	3r0	3r0	NUM
ma-105	860	8	4	4	NUM
ma-105	860	9	+	+	SYM
ma-105	860	10	0	0	NUM
ma-105	860	11	,	,	PUNCT
ma-105	860	12	≤	≤	NOUN
ma-105	860	13	r0	r0	NOUN
ma-105	860	14	for	for	ADP
ma-105	860	15	0	0	NUM
ma-105	860	16	≤	≤	NOUN
ma-105	860	17	t	t	PROPN
ma-105	860	18	≤	≤	PROPN
ma-105	860	19	t	t	PROPN
ma-105	860	20	,	,	PUNCT
ma-105	860	21	and	and	CCONJ
ma-105	860	22	similarly	similarly	ADV
ma-105	860	23	‖qi(t)−	‖qi(t)−	PROPN
ma-105	860	24	i0‖d(hβ	i0‖d(hβ	PROPN
ma-105	860	25	)	)	PUNCT
ma-105	860	26	≤	≤	NOUN
ma-105	860	27	r0	r0	NOUN
ma-105	860	28	and	and	CCONJ
ma-105	860	29	<	<	X
ma-105	860	30	‖rv	‖rv	PROPN
ma-105	860	31	(	(	PUNCT
ma-105	860	32	t)−	t)−	PROPN
ma-105	860	33	v0‖d(hβ	v0‖d(hβ	NOUN
ma-105	860	34	)	)	PUNCT
ma-105	860	35	≤	≤	NOUN
ma-105	860	36	r0.showing	r0.showe	VERB
ma-105	860	37	that	that	PRON
ma-105	860	38	(	(	PUNCT
ma-105	860	39	p	p	X
ma-105	860	40	,	,	PUNCT
ma-105	860	41	q	q	ADJ
ma-105	860	42	,	,	PUNCT
ma-105	860	43	r	r	NOUN
ma-105	860	44	)	)	PUNCT
ma-105	860	45	maps	map	NOUN
ma-105	860	46	br0	br0	VERB
ma-105	860	47	(	(	PUNCT
ma-105	860	48	h0	h0	PROPN
ma-105	860	49	,	,	PUNCT
ma-105	860	50	i0	i0	PROPN
ma-105	860	51	,	,	PUNCT
ma-105	860	52	v0	v0	PROPN
ma-105	860	53	)	)	PUNCT
ma-105	860	54	into	into	ADP
ma-105	860	55	itself	itself	PRON
ma-105	860	56	.	.	PUNCT
ma-105	861	1	furthermore	furthermore	ADV
ma-105	861	2	,	,	PUNCT
ma-105	861	3	from	from	ADP
ma-105	861	4	property	property	NOUN
ma-105	861	5	1	1	NUM
ma-105	861	6	)	)	PUNCT
ma-105	861	7	in	in	ADP
ma-105	861	8	corol	corol	PROPN
ma-105	861	9	-	-	PUNCT
ma-105	861	10	lary	lary	PROPN
ma-105	861	11	3.5	3.5	NUM
ma-105	861	12	and	and	CCONJ
ma-105	861	13	lemma	lemma	PROPN
ma-105	861	14	3.6	3.6	NUM
ma-105	861	15	we	we	PRON
ma-105	861	16	compute	compute	VERB
ma-105	861	17	:	:	PUNCT
ma-105	861	18	‖ph(t	‖ph(t	PROPN
ma-105	861	19	+	+	CCONJ
ma-105	861	20	h)−	h)−	PROPN
ma-105	861	21	ph(t)‖d(hβ	ph(t)‖d(hβ	NOUN
ma-105	861	22	)	)	PUNCT
ma-105	861	23	https://doi.org/10.28924/ada/ma.3.1	https://doi.org/10.28924/ada/ma.3.1	PROPN
ma-105	861	24	eur	eur	PROPN
ma-105	861	25	.	.	PUNCT
ma-105	862	1	j.	j.	PROPN
ma-105	862	2	math	math	PROPN
ma-105	862	3	.	.	PUNCT
ma-105	863	1	anal	anal	PROPN
ma-105	863	2	.	.	PUNCT
ma-105	864	1	10.28924	10.28924	NUM
ma-105	864	2	/	/	SYM
ma-105	864	3	ada	ada	PROPN
ma-105	864	4	/	/	SYM
ma-105	864	5	ma.3.1	ma.3.1	PROPN
ma-105	864	6	31	31	NUM
ma-105	864	7	=	=	SYM
ma-105	865	1	∥∥∥g1(t	∥∥∥g1(t	PUNCT
ma-105	866	1	+	+	PUNCT
ma-105	866	2	h)h0	h)h0	PROPN
ma-105	866	3	−	−	PROPN
ma-105	866	4	g1(t)h0	g1(t)h0	NOUN
ma-105	866	5	+	+	CCONJ
ma-105	866	6	∫	∫	PROPN
ma-105	866	7	t+h	t+h	NUM
ma-105	866	8	0	0	PUNCT
ma-105	867	1	g1(t	g1(t	X
ma-105	867	2	+	+	NUM
ma-105	867	3	h	h	NOUN
ma-105	867	4	−	−	NOUN
ma-105	867	5	τ)f(τ	τ)f(τ	NOUN
ma-105	867	6	,	,	PUNCT
ma-105	867	7	h(τ	h(τ	PROPN
ma-105	867	8	)	)	PUNCT
ma-105	867	9	,	,	PUNCT
ma-105	867	10	i(τ	i(τ	PROPN
ma-105	867	11	)	)	PUNCT
ma-105	867	12	,	,	PUNCT
ma-105	867	13	v	v	X
ma-105	867	14	(	(	PUNCT
ma-105	867	15	τ))dτ	τ))dτ	PROPN
ma-105	867	16	−	−	PROPN
ma-105	867	17	∫	∫	PROPN
ma-105	867	18	t	t	PROPN
ma-105	867	19	0	0	PUNCT
ma-105	868	1	g1(t	g1(t	ADP
ma-105	868	2	−	−	PROPN
ma-105	868	3	τ)f(τ	τ)f(τ	NOUN
ma-105	868	4	,	,	PUNCT
ma-105	868	5	h(τ	h(τ	PROPN
ma-105	868	6	)	)	PUNCT
ma-105	868	7	,	,	PUNCT
ma-105	868	8	i(τ	i(τ	PROPN
ma-105	868	9	)	)	PUNCT
ma-105	868	10	,	,	PUNCT
ma-105	868	11	v	v	X
ma-105	868	12	(	(	PUNCT
ma-105	868	13	τ))dτ	τ))dτ	PROPN
ma-105	868	14	∥∥∥	∥∥∥	PROPN
ma-105	868	15	d(hβ	d(hβ	NUM
ma-105	868	16	)	)	PUNCT
ma-105	868	17	,	,	PUNCT
ma-105	868	18	=	=	SYM
ma-105	868	19	∥∥∥g1(t)g1(h)h0	∥∥∥g1(t)g1(h)h0	NUM
ma-105	868	20	−	−	NOUN
ma-105	868	21	g1(t)h0	g1(t)h0	NOUN
ma-105	869	1	+	+	CCONJ
ma-105	869	2	∫	∫	PROPN
ma-105	869	3	t	t	PROPN
ma-105	869	4	0	0	NUM
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ma-105	869	6	−	−	NOUN
ma-105	869	7	τ)f(τ	τ)f(τ	NOUN
ma-105	869	8	,	,	PUNCT
ma-105	869	9	h(τ	h(τ	PROPN
ma-105	869	10	)	)	PUNCT
ma-105	869	11	,	,	PUNCT
ma-105	869	12	i(τ	i(τ	PROPN
ma-105	869	13	)	)	PUNCT
ma-105	869	14	,	,	PUNCT
ma-105	869	15	v	v	NOUN
ma-105	869	16	(	(	PUNCT
ma-105	869	17	τ))dτ	τ))dτ	PROPN
ma-105	869	18	+	+	CCONJ
ma-105	869	19	∫	∫	PROPN
ma-105	869	20	t+h	t+h	X
ma-105	869	21	t	t	PROPN
ma-105	869	22	g1(h)g1(t	g1(h)g1(t	PROPN
ma-105	869	23	−	−	PROPN
ma-105	869	24	τ)f(τ	τ)f(τ	NOUN
ma-105	869	25	,	,	PUNCT
ma-105	869	26	h(τ	h(τ	PROPN
ma-105	869	27	)	)	PUNCT
ma-105	869	28	,	,	PUNCT
ma-105	869	29	i(τ	i(τ	PROPN
ma-105	869	30	)	)	PUNCT
ma-105	869	31	,	,	PUNCT
ma-105	869	32	v	v	X
ma-105	869	33	(	(	PUNCT
ma-105	869	34	τ))dτ	τ))dτ	PROPN
ma-105	869	35	−	−	PROPN
ma-105	870	1	∫	∫	PROPN
ma-105	870	2	t	t	PROPN
ma-105	870	3	0	0	PUNCT
ma-105	871	1	g1(t	g1(t	ADP
ma-105	871	2	−	−	PROPN
ma-105	871	3	τ)f(τ	τ)f(τ	NOUN
ma-105	871	4	,	,	PUNCT
ma-105	871	5	h(τ	h(τ	PROPN
ma-105	871	6	)	)	PUNCT
ma-105	871	7	,	,	PUNCT
ma-105	871	8	i(τ	i(τ	PROPN
ma-105	871	9	)	)	PUNCT
ma-105	871	10	,	,	PUNCT
ma-105	871	11	v	v	X
ma-105	871	12	(	(	PUNCT
ma-105	871	13	τ))dτ	τ))dτ	PROPN
ma-105	871	14	∥∥∥	∥∥∥	PROPN
ma-105	871	15	d(hβ	d(hβ	NUM
ma-105	871	16	)	)	PUNCT
ma-105	871	17	,	,	PUNCT
ma-105	872	1	=	=	PUNCT
ma-105	872	2	∥∥∥g1(t)(g1(h)−	∥∥∥g1(t)(g1(h)−	PROPN
ma-105	872	3	id)h0	id)h0	PROPN
ma-105	872	4	+	+	CCONJ
ma-105	872	5	∫	∫	PROPN
ma-105	872	6	t	t	PROPN
ma-105	872	7	0	0	NUM
ma-105	872	8	(	(	PUNCT
ma-105	872	9	g1(h)−	g1(h)−	X
ma-105	872	10	id)g1(t	id)g1(t	PROPN
ma-105	872	11	−	−	PROPN
ma-105	872	12	τ)f(τ	τ)f(τ	NOUN
ma-105	872	13	,	,	PUNCT
ma-105	872	14	h(τ	h(τ	PROPN
ma-105	872	15	)	)	PUNCT
ma-105	872	16	,	,	PUNCT
ma-105	872	17	i(τ	i(τ	PROPN
ma-105	872	18	)	)	PUNCT
ma-105	872	19	,	,	PUNCT
ma-105	872	20	v	v	NOUN
ma-105	872	21	(	(	PUNCT
ma-105	872	22	τ))dτ	τ))dτ	PROPN
ma-105	872	23	+	+	CCONJ
ma-105	872	24	∫	∫	PROPN
ma-105	872	25	t+h	t+h	X
ma-105	872	26	t	t	NOUN
ma-105	872	27	g1(t	g1(t	X
ma-105	872	28	+	+	CCONJ
ma-105	872	29	h	h	NOUN
ma-105	872	30	−	−	NOUN
ma-105	872	31	τ)f(τ	τ)f(τ	NOUN
ma-105	872	32	,	,	PUNCT
ma-105	872	33	h(τ	h(τ	PROPN
ma-105	872	34	)	)	PUNCT
ma-105	872	35	,	,	PUNCT
ma-105	872	36	i(τ	i(τ	PROPN
ma-105	872	37	)	)	PUNCT
ma-105	872	38	,	,	PUNCT
ma-105	872	39	v	v	X
ma-105	872	40	(	(	PUNCT
ma-105	872	41	τ))dτ	τ))dτ	PROPN
ma-105	872	42	∥∥∥	∥∥∥	PROPN
ma-105	872	43	d(hβ	d(hβ	NUM
ma-105	872	44	)	)	PUNCT
ma-105	872	45	.	.	PUNCT
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ma-105	873	2	strong	strong	ADJ
ma-105	873	3	continuity	continuity	NOUN
ma-105	873	4	of	of	ADP
ma-105	873	5	the	the	DET
ma-105	873	6	semigroup	semigroup	NOUN
ma-105	873	7	and	and	CCONJ
ma-105	873	8	lemma	lemma	PROPN
ma-105	873	9	3.6	3.6	NUM
ma-105	873	10	yields	yield	NOUN
ma-105	873	11	‖ph(t	‖ph(t	PUNCT
ma-105	873	12	+	+	CCONJ
ma-105	873	13	h)−	h)−	PROPN
ma-105	873	14	ph(t)‖d(hβ	ph(t)‖d(hβ	X
ma-105	873	15	)	)	PUNCT
ma-105	873	16	→	→	SYM
ma-105	873	17	0	0	NUM
ma-105	873	18	as	as	ADP
ma-105	873	19	h	h	NOUN
ma-105	873	20	→	→	SYM
ma-105	873	21	0	0	NUM
ma-105	873	22	+	+	NOUN
ma-105	873	23	.	.	PUNCT
ma-105	874	1	therefore	therefore	ADV
ma-105	874	2	p	p	PROPN
ma-105	874	3	is	be	AUX
ma-105	874	4	continuous	continuous	ADJ
ma-105	874	5	from	from	ADP
ma-105	874	6	[	[	X
ma-105	874	7	0,t	0,t	X
ma-105	874	8	]	]	PUNCT
ma-105	874	9	into	into	ADP
ma-105	874	10	d(hβ).a	d(hβ).a	PROPN
ma-105	874	11	similar	similar	ADJ
ma-105	874	12	calculation	calculation	NOUN
ma-105	874	13	shows	show	VERB
ma-105	874	14	that	that	SCONJ
ma-105	874	15	q	q	PROPN
ma-105	874	16	and	and	CCONJ
ma-105	874	17	r	r	NOUN
ma-105	874	18	have	have	VERB
ma-105	874	19	the	the	DET
ma-105	874	20	same	same	ADJ
ma-105	874	21	properties	property	NOUN
ma-105	874	22	and	and	CCONJ
ma-105	874	23	item	item	NOUN
ma-105	874	24	(	(	PUNCT
ma-105	874	25	a	a	X
ma-105	874	26	)	)	PUNCT
ma-105	874	27	is	be	AUX
ma-105	874	28	proved.presently	proved.presently	ADV
ma-105	874	29	let	let	VERB
ma-105	874	30	us	we	PRON
ma-105	874	31	show	show	VERB
ma-105	874	32	that	that	SCONJ
ma-105	874	33	(	(	PUNCT
ma-105	874	34	p	p	X
ma-105	874	35	,	,	PUNCT
ma-105	874	36	q	q	ADJ
ma-105	874	37	,	,	PUNCT
ma-105	874	38	r	r	NOUN
ma-105	874	39	)	)	PUNCT
ma-105	874	40	is	be	AUX
ma-105	874	41	a	a	DET
ma-105	874	42	strict	strict	ADJ
ma-105	874	43	contraction	contraction	NOUN
ma-105	874	44	on	on	ADP
ma-105	874	45	br0	br0	NOUN
ma-105	874	46	(	(	PUNCT
ma-105	874	47	h0	h0	PROPN
ma-105	874	48	,	,	PUNCT
ma-105	874	49	i0	i0	PROPN
ma-105	874	50	,	,	PUNCT
ma-105	874	51	v0).let	v0).let	NUM
ma-105	874	52	(	(	PUNCT
ma-105	874	53	y1	y1	NOUN
ma-105	874	54	,	,	PUNCT
ma-105	874	55	y2	y2	PROPN
ma-105	874	56	,	,	PUNCT
ma-105	874	57	y3	y3	PROPN
ma-105	874	58	)	)	PUNCT
ma-105	874	59	,	,	PUNCT
ma-105	874	60	(	(	PUNCT
ma-105	874	61	z1	z1	PROPN
ma-105	874	62	,	,	PUNCT
ma-105	874	63	z2	z2	PROPN
ma-105	874	64	,	,	PUNCT
ma-105	874	65	z3	z3	PROPN
ma-105	874	66	)	)	PUNCT
ma-105	874	67	∈	∈	PROPN
ma-105	874	68	br0	br0	NOUN
ma-105	874	69	(	(	PUNCT
ma-105	874	70	h0	h0	PROPN
ma-105	874	71	,	,	PUNCT
ma-105	874	72	i0	i0	PROPN
ma-105	874	73	,	,	PUNCT
ma-105	874	74	v0	v0	PROPN
ma-105	874	75	)	)	PUNCT
ma-105	874	76	.	.	PUNCT
ma-105	875	1	then	then	ADV
ma-105	875	2	‖py1(t)−	‖py1(t)−	X
ma-105	875	3	pz1(t)‖d(hβ	pz1(t)‖d(hβ	X
ma-105	875	4	)	)	PUNCT
ma-105	875	5	=	=	PUNCT
ma-105	876	1	∥∥∥∫	∥∥∥∫	PROPN
ma-105	876	2	t	t	NOUN
ma-105	876	3	0	0	NUM
ma-105	877	1	g1(t	g1(t	ADP
ma-105	877	2	−	−	PROPN
ma-105	877	3	τ	τ	X
ma-105	877	4	)	)	PUNCT
ma-105	877	5	(	(	PUNCT
ma-105	877	6	f(τ	f(τ	PROPN
ma-105	877	7	,	,	PUNCT
ma-105	877	8	y1(τ	y1(τ	PROPN
ma-105	877	9	)	)	PUNCT
ma-105	877	10	,	,	PUNCT
ma-105	877	11	y2(τ	y2(τ	PROPN
ma-105	877	12	)	)	PUNCT
ma-105	877	13	,	,	PUNCT
ma-105	877	14	y3(τ))−f(τ	y3(τ))−f(τ	NUM
ma-105	877	15	,	,	PUNCT
ma-105	877	16	z1(τ	z1(τ	PROPN
ma-105	877	17	)	)	PUNCT
ma-105	877	18	,	,	PUNCT
ma-105	877	19	z2(τ	z2(τ	PROPN
ma-105	877	20	)	)	PUNCT
ma-105	877	21	,	,	PUNCT
ma-105	877	22	z3(τ	z3(τ	NUM
ma-105	877	23	)	)	PUNCT
ma-105	877	24	)	)	PUNCT
ma-105	877	25	)	)	PUNCT
ma-105	877	26	dτ	dτ	PROPN
ma-105	877	27	∥∥∥	∥∥∥	PROPN
ma-105	877	28	d(hβ	d(hβ	NUM
ma-105	877	29	)	)	PUNCT
ma-105	877	30	,	,	PUNCT
ma-105	877	31	≤	≤	NUM
ma-105	877	32	∫	∫	PROPN
ma-105	877	33	t	t	PROPN
ma-105	877	34	0	0	NUM
ma-105	878	1	∥∥∥g1(t	∥∥∥g1(t	PRON
ma-105	878	2	−	−	PROPN
ma-105	879	1	τ	τ	NOUN
ma-105	879	2	)	)	PUNCT
ma-105	879	3	(	(	PUNCT
ma-105	879	4	f(τ	f(τ	PROPN
ma-105	879	5	,	,	PUNCT
ma-105	879	6	y1(τ	y1(τ	PROPN
ma-105	879	7	)	)	PUNCT
ma-105	879	8	,	,	PUNCT
ma-105	879	9	y2(τ	y2(τ	PROPN
ma-105	879	10	)	)	PUNCT
ma-105	879	11	,	,	PUNCT
ma-105	879	12	y3(τ))−f(τ	y3(τ))−f(τ	NUM
ma-105	879	13	,	,	PUNCT
ma-105	879	14	z1(τ	z1(τ	PROPN
ma-105	879	15	)	)	PUNCT
ma-105	879	16	,	,	PUNCT
ma-105	879	17	z2(τ	z2(τ	PROPN
ma-105	879	18	)	)	PUNCT
ma-105	879	19	,	,	PUNCT
ma-105	879	20	z3(τ	z3(τ	NUM
ma-105	879	21	)	)	PUNCT
ma-105	879	22	)	)	PUNCT
ma-105	879	23	)	)	PUNCT
ma-105	880	1	∥∥∥	∥∥∥	NUM
ma-105	880	2	d(hβ	d(hβ	NUM
ma-105	880	3	)	)	PUNCT
ma-105	880	4	dτ	dτ	NOUN
ma-105	880	5	,	,	PUNCT
ma-105	880	6	≤	≤	NUM
ma-105	880	7	∫	∫	PROPN
ma-105	881	1	t	t	PROPN
ma-105	881	2	0	0	PROPN
ma-105	881	3	c1	c1	PROPN
ma-105	881	4	β,2(t	β,2(t	PROPN
ma-105	882	1	−	−	PROPN
ma-105	883	1	τ)−β	τ)−β	ADP
ma-105	883	2	∥∥∥f(τ	∥∥∥f(τ	ADJ
ma-105	883	3	,	,	PUNCT
ma-105	883	4	y1(τ	y1(τ	PROPN
ma-105	883	5	)	)	PUNCT
ma-105	883	6	,	,	PUNCT
ma-105	883	7	y2(τ	y2(τ	PROPN
ma-105	883	8	)	)	PUNCT
ma-105	883	9	,	,	PUNCT
ma-105	883	10	y3(τ))−f(τ	y3(τ))−f(τ	NUM
ma-105	883	11	,	,	PUNCT
ma-105	883	12	z1(τ	z1(τ	PROPN
ma-105	883	13	)	)	PUNCT
ma-105	883	14	,	,	PUNCT
ma-105	883	15	z2(τ	z2(τ	PROPN
ma-105	883	16	)	)	PUNCT
ma-105	883	17	,	,	PUNCT
ma-105	883	18	z3(τ	z3(τ	NUM
ma-105	883	19	)	)	PUNCT
ma-105	883	20	)	)	PUNCT
ma-105	883	21	∥∥∥	∥∥∥	PROPN
ma-105	883	22	2	2	NUM
ma-105	883	23	dτ	dτ	NOUN
ma-105	883	24	,	,	PUNCT
ma-105	883	25	≤	≤	NUM
ma-105	883	26	∫	∫	PROPN
ma-105	884	1	t	t	PROPN
ma-105	884	2	0	0	PROPN
ma-105	884	3	c1	c1	PROPN
ma-105	884	4	β,2(t	β,2(t	PROPN
ma-105	885	1	−	−	PROPN
ma-105	886	1	τ)−β	τ)−β	PUNCT
ma-105	886	2	(	(	PUNCT
ma-105	886	3	k1	k1	NOUN
ma-105	886	4	1‖y1	1‖y1	NOUN
ma-105	886	5	−	−	PROPN
ma-105	886	6	z1‖d(hβ	z1‖d(hβ	SYM
ma-105	886	7	)	)	PUNCT
ma-105	886	8	+	+	ADJ
ma-105	886	9	k1	k1	ADJ
ma-105	886	10	2‖y2	2‖y2	NOUN
ma-105	886	11	−	−	PROPN
ma-105	886	12	z2‖d(hβ	z2‖d(hβ	NOUN
ma-105	886	13	)	)	PUNCT
ma-105	886	14	+	+	NOUN
ma-105	886	15	k1	k1	NOUN
ma-105	886	16	3‖y3	3‖y3	NUM
ma-105	886	17	−	−	PROPN
ma-105	886	18	z3‖d(hβ	z3‖d(hβ	NOUN
ma-105	886	19	)	)	PUNCT
ma-105	886	20	)	)	PUNCT
ma-105	886	21	dτ	dτ	PROPN
ma-105	886	22	,	,	PUNCT
ma-105	886	23	≤	≤	PROPN
ma-105	886	24	c1	c1	PROPN
ma-105	886	25	β,2	β,2	PROPN
ma-105	887	1	(	(	PUNCT
ma-105	887	2	k1	k1	NOUN
ma-105	887	3	1	1	NUM
ma-105	887	4	sup	sup	NOUN
ma-105	887	5	τ∈[0,t	τ∈[0,t	PROPN
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ma-105	888	1	‖y1	‖y1	PRON
ma-105	888	2	−	−	PROPN
ma-105	888	3	z1‖d(hβ	z1‖d(hβ	X
ma-105	888	4	)	)	PUNCT
ma-105	888	5	+	+	NOUN
ma-105	888	6	k1	k1	NOUN
ma-105	888	7	2	2	NUM
ma-105	888	8	sup	sup	NOUN
ma-105	888	9	τ∈[0,t	τ∈[0,t	PROPN
ma-105	888	10	]	]	X
ma-105	888	11	‖y2	‖y2	ADJ
ma-105	888	12	−	−	PROPN
ma-105	888	13	z2‖d(hβ	z2‖d(hβ	NOUN
ma-105	888	14	)	)	PUNCT
ma-105	888	15	+	+	NUM
ma-105	888	16	k1	k1	NOUN
ma-105	888	17	3	3	NUM
ma-105	888	18	sup	sup	NOUN
ma-105	888	19	τ∈[0,t	τ∈[0,t	NOUN
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ma-105	888	21	‖y3	‖y3	ADJ
ma-105	889	1	−	−	PROPN
ma-105	889	2	z3‖d(hβ	z3‖d(hβ	NOUN
ma-105	889	3	)	)	PUNCT
ma-105	889	4	)	)	PUNCT
ma-105	890	1	∫	∫	PROPN
ma-105	890	2	t	t	PROPN
ma-105	890	3	0	0	NUM
ma-105	891	1	(	(	PUNCT
ma-105	891	2	t	t	NOUN
ma-105	891	3	−	−	PROPN
ma-105	891	4	τ)−βdτ	τ)−βdτ	PROPN
ma-105	891	5	.	.	PUNCT
ma-105	892	1	that	that	PRON
ma-105	892	2	is	be	AUX
ma-105	892	3	:	:	PUNCT
ma-105	892	4	‖py1(t)−	‖py1(t)−	PROPN
ma-105	892	5	pz1(t)‖d(hβ	pz1(t)‖d(hβ	NUM
ma-105	892	6	)	)	PUNCT
ma-105	892	7	https://doi.org/10.28924/ada/ma.3.1	https://doi.org/10.28924/ada/ma.3.1	PROPN
ma-105	892	8	eur	eur	PROPN
ma-105	892	9	.	.	PUNCT
ma-105	893	1	j.	j.	PROPN
ma-105	893	2	math	math	PROPN
ma-105	893	3	.	.	PUNCT
ma-105	894	1	anal	anal	PROPN
ma-105	894	2	.	.	PUNCT
ma-105	895	1	10.28924	10.28924	NUM
ma-105	895	2	/	/	SYM
ma-105	895	3	ada	ada	PROPN
ma-105	895	4	/	/	SYM
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ma-105	895	6	32	32	NUM
ma-105	895	7	≤	≤	PROPN
ma-105	895	8	c1	c1	PROPN
ma-105	895	9	β,2	β,2	PUNCT
ma-105	895	10	(	(	PUNCT
ma-105	895	11	k1	k1	PROPN
ma-105	895	12	1	1	NUM
ma-105	895	13	+	+	NOUN
ma-105	895	14	k1	k1	NOUN
ma-105	895	15	2	2	NUM
ma-105	895	16	+	+	NOUN
ma-105	895	17	k1	k1	NOUN
ma-105	895	18	3	3	NUM
ma-105	895	19	+	+	NOUN
ma-105	895	20	m1	m1	PROPN
ma-105	895	21	r0	r0	NOUN
ma-105	895	22	)	)	PUNCT
ma-105	895	23	(	(	PUNCT
ma-105	895	24	sup	sup	NOUN
ma-105	895	25	τ∈[0,t	τ∈[0,t	PROPN
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ma-105	896	1	‖y1	‖y1	DET
ma-105	896	2	−	−	PROPN
ma-105	896	3	z1‖d(hβ	z1‖d(hβ	X
ma-105	896	4	)	)	PUNCT
ma-105	896	5	+	+	NUM
ma-105	896	6	sup	sup	PROPN
ma-105	896	7	τ∈[0,t	τ∈[0,t	PROPN
ma-105	896	8	]	]	X
ma-105	896	9	‖y2	‖y2	ADJ
ma-105	896	10	−	−	PROPN
ma-105	896	11	z2‖d(hβ	z2‖d(hβ	NOUN
ma-105	896	12	)	)	PUNCT
ma-105	896	13	+	+	NUM
ma-105	896	14	sup	sup	PROPN
ma-105	896	15	τ∈[0,t	τ∈[0,t	PROPN
ma-105	896	16	]	]	X
ma-105	896	17	‖y3	‖y3	ADJ
ma-105	896	18	−	−	PROPN
ma-105	896	19	z3‖d(hβ	z3‖d(hβ	NOUN
ma-105	896	20	)	)	PUNCT
ma-105	896	21	)	)	PUNCT
ma-105	897	1	∫	∫	PROPN
ma-105	897	2	t	t	PROPN
ma-105	897	3	0	0	NUM
ma-105	898	1	(	(	PUNCT
ma-105	898	2	t	t	NOUN
ma-105	898	3	−	−	PROPN
ma-105	899	1	τ)−βdτ	τ)−βdτ	PROPN
ma-105	899	2	,	,	PUNCT
ma-105	899	3	≤	≤	NUM
ma-105	899	4	(	(	PUNCT
ma-105	899	5	sup	sup	NOUN
ma-105	899	6	τ∈[0,t	τ∈[0,t	PROPN
ma-105	899	7	]	]	X
ma-105	900	1	‖y1	‖y1	DET
ma-105	900	2	−	−	PROPN
ma-105	900	3	z1‖d(hβ	z1‖d(hβ	X
ma-105	900	4	)	)	PUNCT
ma-105	900	5	+	+	NUM
ma-105	900	6	sup	sup	PROPN
ma-105	900	7	τ∈[0,t	τ∈[0,t	PROPN
ma-105	900	8	]	]	X
ma-105	900	9	‖y2	‖y2	ADJ
ma-105	900	10	−	−	PROPN
ma-105	900	11	z2‖d(hβ	z2‖d(hβ	NOUN
ma-105	900	12	)	)	PUNCT
ma-105	900	13	+	+	NUM
ma-105	900	14	sup	sup	PROPN
ma-105	900	15	τ∈[0,t	τ∈[0,t	PROPN
ma-105	900	16	]	]	X
ma-105	900	17	‖y3	‖y3	ADJ
ma-105	900	18	−	−	PROPN
ma-105	900	19	z3‖d(hβ	z3‖d(hβ	NOUN
ma-105	900	20	)	)	PUNCT
ma-105	900	21	)	)	PUNCT
ma-105	901	1	×c1	×c1	PROPN
ma-105	901	2	β,2	β,2	PUNCT
ma-105	902	1	(	(	PUNCT
ma-105	902	2	k1	k1	NOUN
ma-105	902	3	1	1	NUM
ma-105	902	4	+	+	NOUN
ma-105	902	5	k1	k1	NOUN
ma-105	902	6	2	2	NUM
ma-105	902	7	+	+	NOUN
ma-105	902	8	k1	k1	NOUN
ma-105	902	9	3	3	NUM
ma-105	902	10	+	+	NOUN
ma-105	902	11	m1	m1	PROPN
ma-105	902	12	r0	r0	NOUN
ma-105	902	13	)	)	PUNCT
ma-105	902	14	∫	∫	PROPN
ma-105	902	15	t	t	PROPN
ma-105	902	16	0	0	NUM
ma-105	902	17	s−βds	s−βds	NOUN
ma-105	902	18	,	,	PUNCT
ma-105	902	19	≤	≤	NUM
ma-105	902	20	(	(	PUNCT
ma-105	902	21	sup	sup	NOUN
ma-105	902	22	τ∈[0,t	τ∈[0,t	PROPN
ma-105	902	23	]	]	X
ma-105	903	1	‖y1	‖y1	DET
ma-105	903	2	−	−	PROPN
ma-105	903	3	z1‖d(hβ	z1‖d(hβ	X
ma-105	903	4	)	)	PUNCT
ma-105	903	5	+	+	NUM
ma-105	903	6	sup	sup	PROPN
ma-105	903	7	τ∈[0,t	τ∈[0,t	PROPN
ma-105	903	8	]	]	X
ma-105	903	9	‖y2	‖y2	ADJ
ma-105	903	10	−	−	PROPN
ma-105	903	11	z2‖d(hβ	z2‖d(hβ	NOUN
ma-105	903	12	)	)	PUNCT
ma-105	903	13	+	+	NUM
ma-105	903	14	sup	sup	PROPN
ma-105	903	15	τ∈[0,t	τ∈[0,t	PROPN
ma-105	903	16	]	]	X
ma-105	903	17	‖y3	‖y3	ADJ
ma-105	903	18	−	−	PROPN
ma-105	903	19	z3‖d(hβ	z3‖d(hβ	NOUN
ma-105	903	20	)	)	PUNCT
ma-105	903	21	)	)	PUNCT
ma-105	903	22	×	×	NOUN
ma-105	903	23	1	1	NUM
ma-105	903	24	r0	r0	NOUN
ma-105	903	25	c1	c1	PROPN
ma-105	903	26	β,2	β,2	PROPN
ma-105	903	27	(	(	PUNCT
ma-105	903	28	r0k	r0k	NOUN
ma-105	903	29	1	1	NUM
ma-105	903	30	1	1	NUM
ma-105	903	31	+	+	CCONJ
ma-105	903	32	r0k	r0k	PROPN
ma-105	903	33	1	1	NUM
ma-105	903	34	2	2	NUM
ma-105	903	35	+	+	CCONJ
ma-105	903	36	r0k	r0k	NOUN
ma-105	903	37	1	1	NUM
ma-105	903	38	3	3	NUM
ma-105	903	39	+	+	PROPN
ma-105	903	40	m1	m1	PROPN
ma-105	903	41	)	)	PUNCT
ma-105	903	42	∫	∫	PROPN
ma-105	903	43	t	t	PROPN
ma-105	903	44	0	0	NUM
ma-105	903	45	s−βds	s−βds	NOUN
ma-105	903	46	,	,	PUNCT
ma-105	903	47	≤	≤	NUM
ma-105	903	48	(	(	PUNCT
ma-105	903	49	sup	sup	NOUN
ma-105	903	50	τ∈[0,t	τ∈[0,t	PROPN
ma-105	903	51	]	]	X
ma-105	904	1	‖y1	‖y1	DET
ma-105	904	2	−	−	PROPN
ma-105	904	3	z1‖d(hβ	z1‖d(hβ	X
ma-105	904	4	)	)	PUNCT
ma-105	904	5	+	+	NUM
ma-105	904	6	sup	sup	PROPN
ma-105	904	7	τ∈[0,t	τ∈[0,t	PROPN
ma-105	904	8	]	]	X
ma-105	904	9	‖y2	‖y2	ADJ
ma-105	904	10	−	−	PROPN
ma-105	904	11	z2‖d(hβ	z2‖d(hβ	NOUN
ma-105	904	12	)	)	PUNCT
ma-105	904	13	+	+	NUM
ma-105	904	14	sup	sup	PROPN
ma-105	904	15	τ∈[0,t	τ∈[0,t	PROPN
ma-105	904	16	]	]	X
ma-105	904	17	‖y3	‖y3	ADJ
ma-105	904	18	−	−	PROPN
ma-105	904	19	z3‖d(hβ	z3‖d(hβ	NOUN
ma-105	904	20	)	)	PUNCT
ma-105	904	21	)	)	PUNCT
ma-105	904	22	1	1	NUM
ma-105	904	23	r0	r0	NOUN
ma-105	904	24	×	×	NOUN
ma-105	904	25	r0	r0	NOUN
ma-105	904	26	4	4	NUM
ma-105	904	27	,	,	PUNCT
ma-105	904	28	≤	≤	NUM
ma-105	904	29	1	1	NUM
ma-105	904	30	4	4	NUM
ma-105	904	31	(	(	PUNCT
ma-105	904	32	sup	sup	NOUN
ma-105	904	33	τ∈[0,t	τ∈[0,t	PROPN
ma-105	904	34	]	]	X
ma-105	905	1	‖y1	‖y1	DET
ma-105	905	2	−	−	PROPN
ma-105	905	3	z1‖d(hβ	z1‖d(hβ	X
ma-105	905	4	)	)	PUNCT
ma-105	905	5	+	+	NUM
ma-105	905	6	sup	sup	PROPN
ma-105	905	7	τ∈[0,t	τ∈[0,t	PROPN
ma-105	905	8	]	]	X
ma-105	905	9	‖y2	‖y2	ADJ
ma-105	905	10	−	−	PROPN
ma-105	905	11	z2‖d(hβ	z2‖d(hβ	NOUN
ma-105	905	12	)	)	PUNCT
ma-105	905	13	+	+	NUM
ma-105	905	14	sup	sup	PROPN
ma-105	905	15	τ∈[0,t	τ∈[0,t	PROPN
ma-105	905	16	]	]	X
ma-105	905	17	‖y3	‖y3	ADJ
ma-105	905	18	−	−	PROPN
ma-105	905	19	z3‖d(hβ	z3‖d(hβ	NOUN
ma-105	905	20	)	)	PUNCT
ma-105	905	21	)	)	PUNCT
ma-105	905	22	,	,	PUNCT
ma-105	905	23	for	for	ADP
ma-105	905	24	every	every	DET
ma-105	905	25	t	t	NOUN
ma-105	905	26	∈	∈	PROPN
ma-105	906	1	[	[	X
ma-105	906	2	0	0	NUM
ma-105	906	3	,	,	PUNCT
ma-105	906	4	t	t	X
ma-105	906	5	]	]	PUNCT
ma-105	906	6	.	.	PUNCT
ma-105	907	1	hence	hence	ADV
ma-105	907	2	sup	sup	NOUN
ma-105	907	3	t∈[0,t	t∈[0,t	PROPN
ma-105	907	4	]	]	PUNCT
ma-105	907	5	‖py1(t)−	‖py1(t)−	PROPN
ma-105	907	6	pz1(t)‖d(hβ	pz1(t)‖d(hβ	X
ma-105	907	7	)	)	PUNCT
ma-105	907	8	≤	≤	NUM
ma-105	907	9	1	1	NUM
ma-105	907	10	4	4	NUM
ma-105	907	11	(	(	PUNCT
ma-105	907	12	sup	sup	NOUN
ma-105	907	13	τ∈[0,t	τ∈[0,t	PROPN
ma-105	907	14	]	]	X
ma-105	908	1	‖y1	‖y1	DET
ma-105	908	2	−	−	PROPN
ma-105	908	3	z1‖d(hβ	z1‖d(hβ	X
ma-105	908	4	)	)	PUNCT
ma-105	908	5	+	+	NUM
ma-105	908	6	sup	sup	PROPN
ma-105	908	7	τ∈[0,t	τ∈[0,t	PROPN
ma-105	908	8	]	]	X
ma-105	908	9	‖y2	‖y2	ADJ
ma-105	908	10	−	−	PROPN
ma-105	908	11	z2‖d(hβ	z2‖d(hβ	NOUN
ma-105	908	12	)	)	PUNCT
ma-105	908	13	+	+	NUM
ma-105	908	14	sup	sup	PROPN
ma-105	908	15	τ∈[0,t	τ∈[0,t	PROPN
ma-105	908	16	]	]	X
ma-105	908	17	‖y3	‖y3	ADJ
ma-105	908	18	−	−	PROPN
ma-105	908	19	z3‖d(hβ	z3‖d(hβ	NOUN
ma-105	908	20	)	)	PUNCT
ma-105	908	21	)	)	PUNCT
ma-105	908	22	.	.	PUNCT
ma-105	909	1	similarly	similarly	ADV
ma-105	909	2	sup	sup	NOUN
ma-105	909	3	t∈[0,t	t∈[0,t	NOUN
ma-105	909	4	]	]	PUNCT
ma-105	909	5	‖qy1(t)−qz1(t)‖d(hβ	‖qy1(t)−qz1(t)‖d(hβ	NOUN
ma-105	909	6	)	)	PUNCT
ma-105	909	7	≤	≤	NUM
ma-105	909	8	1	1	NUM
ma-105	909	9	4	4	NUM
ma-105	909	10	(	(	PUNCT
ma-105	909	11	sup	sup	NOUN
ma-105	909	12	τ∈[0,t	τ∈[0,t	PROPN
ma-105	909	13	]	]	X
ma-105	910	1	‖y1	‖y1	DET
ma-105	910	2	−	−	PROPN
ma-105	910	3	z1‖d(hβ	z1‖d(hβ	X
ma-105	910	4	)	)	PUNCT
ma-105	910	5	+	+	NUM
ma-105	910	6	sup	sup	PROPN
ma-105	910	7	τ∈[0,t	τ∈[0,t	PROPN
ma-105	910	8	]	]	X
ma-105	910	9	‖y2	‖y2	ADJ
ma-105	910	10	−	−	PROPN
ma-105	910	11	z2‖d(hβ	z2‖d(hβ	NOUN
ma-105	910	12	)	)	PUNCT
ma-105	910	13	+	+	NUM
ma-105	910	14	sup	sup	PROPN
ma-105	910	15	τ∈[0,t	τ∈[0,t	PROPN
ma-105	910	16	]	]	X
ma-105	910	17	‖y3	‖y3	ADJ
ma-105	910	18	−	−	PROPN
ma-105	910	19	z3‖d(hβ	z3‖d(hβ	NOUN
ma-105	910	20	)	)	PUNCT
ma-105	910	21	)	)	PUNCT
ma-105	910	22	and	and	CCONJ
ma-105	910	23	sup	sup	NOUN
ma-105	910	24	t∈[0,t	t∈[0,t	PROPN
ma-105	910	25	]	]	PUNCT
ma-105	910	26	‖ry1(t)−	‖ry1(t)−	X
ma-105	910	27	rz1(t)‖d(hβ	rz1(t)‖d(hβ	NUM
ma-105	910	28	)	)	PUNCT
ma-105	910	29	≤	≤	NUM
ma-105	910	30	1	1	NUM
ma-105	910	31	4	4	NUM
ma-105	910	32	(	(	PUNCT
ma-105	910	33	sup	sup	NOUN
ma-105	910	34	τ∈[0,t	τ∈[0,t	PROPN
ma-105	910	35	]	]	X
ma-105	910	36	‖y1	‖y1	PRON
ma-105	910	37	−	−	PROPN
ma-105	910	38	z1‖d(hβ	z1‖d(hβ	X
ma-105	910	39	)	)	PUNCT
ma-105	910	40	+	+	NUM
ma-105	910	41	sup	sup	PROPN
ma-105	910	42	τ∈[0,t	τ∈[0,t	PROPN
ma-105	910	43	]	]	X
ma-105	910	44	‖y2	‖y2	ADJ
ma-105	910	45	−	−	PROPN
ma-105	910	46	z2‖d(hβ	z2‖d(hβ	NOUN
ma-105	910	47	)	)	PUNCT
ma-105	910	48	+	+	NUM
ma-105	910	49	sup	sup	PROPN
ma-105	910	50	τ∈[0,t	τ∈[0,t	PROPN
ma-105	910	51	]	]	X
ma-105	910	52	‖y3	‖y3	ADJ
ma-105	910	53	−	−	PROPN
ma-105	910	54	z3‖d(hβ	z3‖d(hβ	NOUN
ma-105	910	55	)	)	PUNCT
ma-105	910	56	)	)	PUNCT
ma-105	910	57	.	.	PUNCT
ma-105	911	1	thus	thus	ADV
ma-105	911	2	sup	sup	NOUN
ma-105	911	3	t∈[0,t	t∈[0,t	NOUN
ma-105	911	4	]	]	PUNCT
ma-105	911	5	‖(p	‖(p	ADJ
ma-105	911	6	,	,	PUNCT
ma-105	911	7	q	q	NOUN
ma-105	911	8	,	,	PUNCT
ma-105	911	9	r)(y1(t	r)(y1(t	NUM
ma-105	911	10	)	)	PUNCT
ma-105	911	11	,	,	PUNCT
ma-105	911	12	y2(t	y2(t	PROPN
ma-105	911	13	)	)	PUNCT
ma-105	911	14	,	,	PUNCT
ma-105	911	15	y3(t))−	y3(t))−	PROPN
ma-105	911	16	(	(	PUNCT
ma-105	911	17	p	p	NOUN
ma-105	911	18	,	,	PUNCT
ma-105	911	19	q	q	ADJ
ma-105	911	20	,	,	PUNCT
ma-105	911	21	r)(z1(t	r)(z1(t	NUM
ma-105	911	22	)	)	PUNCT
ma-105	911	23	,	,	PUNCT
ma-105	911	24	z2(t	z2(t	PROPN
ma-105	911	25	)	)	PUNCT
ma-105	911	26	,	,	PUNCT
ma-105	911	27	z3(t))‖d(hβ)3	z3(t))‖d(hβ)3	NOUN
ma-105	911	28	≤	≤	NUM
ma-105	911	29	sup	sup	NOUN
ma-105	911	30	τ∈[0,t	τ∈[0,t	NOUN
ma-105	911	31	]	]	X
ma-105	911	32	(	(	PUNCT
ma-105	911	33	‖py1	‖py1	NOUN
ma-105	911	34	−	−	PROPN
ma-105	911	35	pz1‖d(hβ	pz1‖d(hβ	NUM
ma-105	911	36	)	)	PUNCT
ma-105	912	1	+	+	CCONJ
ma-105	912	2	‖qy2	‖qy2	ADJ
ma-105	912	3	−qz2‖d(hβ	−qz2‖d(hβ	ADJ
ma-105	912	4	)	)	PUNCT
ma-105	912	5	+	+	CCONJ
ma-105	912	6	‖ry3	‖ry3	ADJ
ma-105	912	7	−	−	NOUN
ma-105	912	8	rz3‖d(hβ	rz3‖d(hβ	NOUN
ma-105	912	9	)	)	PUNCT
ma-105	912	10	)	)	PUNCT
ma-105	912	11	,	,	PUNCT
ma-105	912	12	≤	≤	NUM
ma-105	912	13	sup	sup	NOUN
ma-105	912	14	τ∈[0,t	τ∈[0,t	NOUN
ma-105	912	15	]	]	PUNCT
ma-105	912	16	‖py1	‖py1	PROPN
ma-105	912	17	−	−	PROPN
ma-105	912	18	pz1‖d(hβ	pz1‖d(hβ	NUM
ma-105	912	19	)	)	PUNCT
ma-105	913	1	+	+	CCONJ
ma-105	913	2	sup	sup	NOUN
ma-105	913	3	τ∈[0,t	τ∈[0,t	NOUN
ma-105	913	4	]	]	PUNCT
ma-105	913	5	‖qy2	‖qy2	ADJ
ma-105	913	6	−qz2‖d(hβ	−qz2‖d(hβ	ADJ
ma-105	913	7	)	)	PUNCT
ma-105	914	1	+	+	CCONJ
ma-105	914	2	sup	sup	PROPN
ma-105	914	3	τ∈[0,t	τ∈[0,t	NOUN
ma-105	914	4	]	]	X
ma-105	914	5	‖ry3	‖ry3	ADJ
ma-105	914	6	−	−	NOUN
ma-105	914	7	rz3‖d(hβ	rz3‖d(hβ	NOUN
ma-105	914	8	)	)	PUNCT
ma-105	914	9	,	,	PUNCT
ma-105	914	10	≤	≤	NUM
ma-105	914	11	3	3	NUM
ma-105	914	12	4	4	NUM
ma-105	914	13	(	(	PUNCT
ma-105	914	14	sup	sup	NOUN
ma-105	914	15	τ∈[0,t	τ∈[0,t	PROPN
ma-105	914	16	]	]	X
ma-105	915	1	‖y1	‖y1	DET
ma-105	915	2	−	−	PROPN
ma-105	915	3	z1‖d(hβ	z1‖d(hβ	X
ma-105	915	4	)	)	PUNCT
ma-105	915	5	+	+	NUM
ma-105	915	6	sup	sup	PROPN
ma-105	915	7	τ∈[0,t	τ∈[0,t	PROPN
ma-105	915	8	]	]	X
ma-105	915	9	‖y2	‖y2	ADJ
ma-105	915	10	−	−	PROPN
ma-105	915	11	z2‖d(hβ	z2‖d(hβ	NOUN
ma-105	915	12	)	)	PUNCT
ma-105	915	13	+	+	NUM
ma-105	915	14	sup	sup	PROPN
ma-105	915	15	τ∈[0,t	τ∈[0,t	PROPN
ma-105	915	16	]	]	X
ma-105	915	17	‖y3	‖y3	ADJ
ma-105	915	18	−	−	PROPN
ma-105	915	19	z3‖d(hβ	z3‖d(hβ	NOUN
ma-105	915	20	)	)	PUNCT
ma-105	915	21	)	)	PUNCT
ma-105	915	22	,	,	PUNCT
ma-105	915	23	≤	≤	NUM
ma-105	915	24	3	3	NUM
ma-105	915	25	4	4	NUM
ma-105	915	26	sup	sup	NOUN
ma-105	915	27	t∈[0,t	t∈[0,t	NOUN
ma-105	915	28	]	]	PUNCT
ma-105	915	29	‖(y1(t	‖(y1(t	PROPN
ma-105	915	30	)	)	PUNCT
ma-105	915	31	,	,	PUNCT
ma-105	915	32	y2(t	y2(t	PROPN
ma-105	915	33	)	)	PUNCT
ma-105	915	34	,	,	PUNCT
ma-105	915	35	y3(t))−	y3(t))−	PROPN
ma-105	915	36	(	(	PUNCT
ma-105	915	37	z1(t	z1(t	NUM
ma-105	915	38	)	)	PUNCT
ma-105	915	39	,	,	PUNCT
ma-105	915	40	z2(t	z2(t	PROPN
ma-105	915	41	)	)	PUNCT
ma-105	915	42	,	,	PUNCT
ma-105	915	43	z3(t))‖d(hβ)3	z3(t))‖d(hβ)3	NOUN
ma-105	915	44	.	.	PUNCT
ma-105	916	1	hence	hence	ADV
ma-105	916	2	(	(	PUNCT
ma-105	916	3	p	p	X
ma-105	916	4	,	,	PUNCT
ma-105	916	5	q	q	ADJ
ma-105	916	6	,	,	PUNCT
ma-105	916	7	r	r	NOUN
ma-105	916	8	)	)	PUNCT
ma-105	916	9	is	be	AUX
ma-105	916	10	a	a	DET
ma-105	916	11	strict	strict	ADJ
ma-105	916	12	contraction	contraction	NOUN
ma-105	916	13	on	on	ADP
ma-105	916	14	br0	br0	NOUN
ma-105	916	15	(	(	PUNCT
ma-105	916	16	h0	h0	PROPN
ma-105	916	17	,	,	PUNCT
ma-105	916	18	i0	i0	PROPN
ma-105	916	19	,	,	PUNCT
ma-105	916	20	v0	v0	PROPN
ma-105	916	21	)	)	PUNCT
ma-105	916	22	and	and	CCONJ
ma-105	916	23	this	this	PRON
ma-105	916	24	proves	prove	VERB
ma-105	916	25	part	part	NOUN
ma-105	916	26	b	b	NOUN
ma-105	916	27	)	)	PUNCT
ma-105	916	28	.	.	PUNCT
ma-105	917	1	according	accord	VERB
ma-105	917	2	tobanach	tobanach	NOUN
ma-105	917	3	’s	’s	PART
ma-105	917	4	fixed	fix	VERB
ma-105	917	5	point	point	NOUN
ma-105	917	6	theorem	theorem	VERB
ma-105	917	7	,	,	PUNCT
ma-105	917	8	(	(	PUNCT
ma-105	917	9	p	p	X
ma-105	917	10	,	,	PUNCT
ma-105	917	11	q	q	ADJ
ma-105	917	12	,	,	PUNCT
ma-105	917	13	r	r	NOUN
ma-105	917	14	)	)	PUNCT
ma-105	917	15	has	have	VERB
ma-105	917	16	a	a	DET
ma-105	917	17	unique	unique	ADJ
ma-105	917	18	fixed	fix	VERB
ma-105	917	19	point	point	NOUN
ma-105	917	20	in	in	ADP
ma-105	917	21	br0	br0	NOUN
ma-105	917	22	(	(	PUNCT
ma-105	917	23	h0	h0	PROPN
ma-105	917	24	,	,	PUNCT
ma-105	917	25	i0	i0	PROPN
ma-105	917	26	,	,	PUNCT
ma-105	917	27	v0	v0	PROPN
ma-105	917	28	)	)	PUNCT
ma-105	917	29	.	.	PUNCT
ma-105	918	1	this	this	PRON
ma-105	918	2	is	be	AUX
ma-105	918	3	thesolution	thesolution	NOUN
ma-105	918	4	of	of	ADP
ma-105	918	5	(	(	PUNCT
ma-105	918	6	2.4	2.4	NUM
ma-105	918	7	)	)	PUNCT
ma-105	918	8	on	on	ADP
ma-105	918	9	[	[	X
ma-105	918	10	0,t	0,t	X
ma-105	918	11	]	]	PUNCT
ma-105	918	12	with	with	ADP
ma-105	918	13	initial	initial	ADJ
ma-105	918	14	value	value	NOUN
ma-105	918	15	(	(	PUNCT
ma-105	918	16	h(0	h(0	PROPN
ma-105	918	17	)	)	PUNCT
ma-105	918	18	,	,	PUNCT
ma-105	918	19	i(0	i(0	PROPN
ma-105	918	20	)	)	PUNCT
ma-105	918	21	,	,	PUNCT
ma-105	918	22	v	v	X
ma-105	918	23	(	(	PUNCT
ma-105	918	24	0	0	NUM
ma-105	918	25	)	)	PUNCT
ma-105	918	26	)	)	PUNCT
ma-105	919	1	=	=	PRON
ma-105	919	2	(	(	PUNCT
ma-105	919	3	h0	h0	PROPN
ma-105	919	4	,	,	PUNCT
ma-105	919	5	i0	i0	PROPN
ma-105	919	6	,	,	PUNCT
ma-105	919	7	v0	v0	PROPN
ma-105	919	8	)	)	PUNCT
ma-105	919	9	in	in	ADP
ma-105	919	10	(	(	PUNCT
ma-105	919	11	d(hβ))3	d(hβ))3	PROPN
ma-105	919	12	.	.	PROPN
ma-105	919	13	thiscompletes	thiscomplete	VERB
ma-105	919	14	the	the	DET
ma-105	919	15	proof	proof	NOUN
ma-105	919	16	of	of	ADP
ma-105	919	17	proposition	proposition	NOUN
ma-105	919	18	3.8	3.8	NUM
ma-105	919	19	.	.	PUNCT
ma-105	920	1	https://doi.org/10.28924/ada/ma.3.1	https://doi.org/10.28924/ada/ma.3.1	PROPN
ma-105	920	2	eur	eur	PROPN
ma-105	920	3	.	.	PUNCT
ma-105	921	1	j.	j.	PROPN
ma-105	921	2	math	math	PROPN
ma-105	921	3	.	.	PUNCT
ma-105	922	1	anal	anal	PROPN
ma-105	922	2	.	.	PUNCT
ma-105	923	1	10.28924	10.28924	NUM
ma-105	923	2	/	/	SYM
ma-105	923	3	ada	ada	PROPN
ma-105	923	4	/	/	SYM
ma-105	923	5	ma.3.1	ma.3.1	PROPN
ma-105	923	6	33appendix	33appendix	PROPN
ma-105	923	7	b.	b.	PROPN
ma-105	923	8	proof	proof	NOUN
ma-105	923	9	of	of	ADP
ma-105	923	10	theorem	theorem	NOUN
ma-105	923	11	3.11	3.11	NUM
ma-105	923	12	we	we	PRON
ma-105	923	13	first	first	ADV
ma-105	923	14	prove	prove	VERB
ma-105	923	15	the	the	DET
ma-105	923	16	existence	existence	NOUN
ma-105	923	17	and	and	CCONJ
ma-105	923	18	positivity	positivity	NOUN
ma-105	923	19	of	of	ADP
ma-105	923	20	the	the	DET
ma-105	923	21	solution	solution	NOUN
ma-105	923	22	.	.	PUNCT
ma-105	924	1	from	from	ADP
ma-105	924	2	theorem	theorem	ADJ
ma-105	924	3	3.10	3.10	NUM
ma-105	924	4	,	,	PUNCT
ma-105	924	5	there	there	PRON
ma-105	924	6	exist	exist	VERB
ma-105	924	7	asequence	asequence	NOUN
ma-105	924	8	(	(	PUNCT
ma-105	924	9	wmi	wmi	PROPN
ma-105	924	10	)	)	PUNCT
ma-105	924	11	and	and	CCONJ
ma-105	924	12	a	a	DET
ma-105	924	13	function	function	NOUN
ma-105	924	14	wi	wi	PROPN
ma-105	924	15	such	such	ADJ
ma-105	924	16	that	that	DET
ma-105	924	17	wmi	wmi	PROPN
ma-105	924	18	→	→	PUNCT
ma-105	924	19	wi	wi	PROPN
ma-105	924	20	in	in	ADP
ma-105	924	21	c0([0	c0([0	PROPN
ma-105	924	22	,	,	PUNCT
ma-105	924	23	t	t	X
ma-105	924	24	]	]	PUNCT
ma-105	924	25	,	,	PUNCT
ma-105	924	26	h	h	NOUN
ma-105	924	27	)	)	PUNCT
ma-105	924	28	,	,	PUNCT
ma-105	924	29	with	with	ADP
ma-105	924	30	wi	wi	PROPN
ma-105	924	31	≥	≥	NUM
ma-105	924	32	0	0	NUM
ma-105	924	33	and	and	CCONJ
ma-105	924	34	wi(0	wi(0	NOUN
ma-105	924	35	)	)	PUNCT
ma-105	925	1	=	=	SYM
ma-105	925	2	w0i	w0i	PROPN
ma-105	925	3	.we	.we	PUNCT
ma-105	925	4	check	check	VERB
ma-105	925	5	that	that	PRON
ma-105	925	6	qi(w	qi(w	VERB
ma-105	925	7	m−1)→	m−1)→	PRON
ma-105	925	8	qi(w	qi(w	PROPN
ma-105	925	9	)	)	PUNCT
ma-105	925	10	and	and	CCONJ
ma-105	925	11	qi(w	qi(w	X
ma-105	925	12	m−1)wmi	m−1)wmi	X
ma-105	925	13	→	→	SYM
ma-105	925	14	qi(w)wi	qi(w)wi	ADJ
ma-105	925	15	in	in	ADP
ma-105	925	16	c0([0	c0([0	PROPN
ma-105	925	17	,	,	PUNCT
ma-105	925	18	t	t	X
ma-105	925	19	]	]	PUNCT
ma-105	925	20	,	,	PUNCT
ma-105	925	21	h	h	NOUN
ma-105	925	22	)	)	PUNCT
ma-105	925	23	.	.	PUNCT
ma-105	926	1	we	we	PRON
ma-105	926	2	also	also	ADV
ma-105	926	3	have	have	VERB
ma-105	926	4	fi(w	fi(w	PUNCT
ma-105	926	5	m−1)→	m−1)→	NOUN
ma-105	926	6	fi(w	fi(w	PUNCT
ma-105	926	7	)	)	PUNCT
ma-105	926	8	in	in	ADP
ma-105	926	9	c0([0	c0([0	PROPN
ma-105	926	10	,	,	PUNCT
ma-105	926	11	t	t	X
ma-105	926	12	]	]	PUNCT
ma-105	926	13	,	,	PUNCT
ma-105	926	14	h	h	NOUN
ma-105	926	15	)	)	PUNCT
ma-105	926	16	⋂	⋂	PROPN
ma-105	926	17	l2((0	l2((0	PROPN
ma-105	926	18	,	,	PUNCT
ma-105	926	19	t	t	PROPN
ma-105	926	20	)	)	PUNCT
ma-105	926	21	,	,	PUNCT
ma-105	926	22	e′).but	e′).but	PROPN
ma-105	926	23	,	,	PUNCT
ma-105	926	24	wmi	wmi	PROPN
ma-105	926	25	is	be	AUX
ma-105	926	26	solution	solution	NOUN
ma-105	926	27	of〈∂wmi	of〈∂wmi	PROPN
ma-105	926	28	∂t	∂t	PROPN
ma-105	926	29	,	,	PUNCT
ma-105	926	30	vi	vi	NOUN
ma-105	926	31	〉	〉	NOUN
ma-105	926	32	+	+	CCONJ
ma-105	926	33	〈	〈	PROPN
ma-105	926	34	aiw	aiw	PROPN
ma-105	926	35	m	m	VERB
ma-105	926	36	i	i	NOUN
ma-105	926	37	,	,	PUNCT
ma-105	926	38	vi	vi	NOUN
ma-105	926	39	〉	〉	NOUN
ma-105	926	40	+	+	CCONJ
ma-105	926	41	(	(	PUNCT
ma-105	926	42	qi(w	qi(w	X
ma-105	926	43	m−1)wmi	m−1)wmi	X
ma-105	926	44	,	,	PUNCT
ma-105	926	45	vi	vi	NOUN
ma-105	926	46	)	)	PUNCT
ma-105	927	1	=	=	SYM
ma-105	927	2	〈	〈	PROPN
ma-105	927	3	fi(w	fi(w	PUNCT
ma-105	927	4	m−1	m−1	PROPN
ma-105	927	5	)	)	PUNCT
ma-105	927	6	,	,	PUNCT
ma-105	927	7	vi	vi	NOUN
ma-105	927	8	〉	〉	NOUN
ma-105	927	9	,	,	PUNCT
ma-105	927	10	∀vi	∀vi	PROPN
ma-105	927	11	∈	∈	PROPN
ma-105	927	12	e.	e.	PROPN
ma-105	927	13	(	(	PUNCT
ma-105	927	14	b.1	b.1	NOUN
ma-105	927	15	)	)	PUNCT
ma-105	927	16	we	we	PRON
ma-105	927	17	take	take	VERB
ma-105	927	18	φ	φ	PROPN
ma-105	927	19	∈	∈	PROPN
ma-105	927	20	d((0	d((0	PROPN
ma-105	927	21	,	,	PUNCT
ma-105	927	22	t	t	NOUN
ma-105	927	23	)	)	PUNCT
ma-105	927	24	)	)	PUNCT
ma-105	927	25	,	,	PUNCT
ma-105	928	1	such	such	ADJ
ma-105	928	2	that	that	PRON
ma-105	928	3	φvi	φvi	VERB
ma-105	928	4	∈	∈	PROPN
ma-105	928	5	l2((0	l2((0	PROPN
ma-105	928	6	,	,	PUNCT
ma-105	928	7	t	t	PROPN
ma-105	928	8	)	)	PUNCT
ma-105	928	9	,	,	PUNCT
ma-105	928	10	e),∫	e),∫	PROPN
ma-105	928	11	t	t	PROPN
ma-105	928	12	0	0	PUNCT
ma-105	928	13	〈	〈	NOUN
ma-105	928	14	∂wmi	∂wmi	NOUN
ma-105	928	15	∂t	∂t	PROPN
ma-105	928	16	,	,	PUNCT
ma-105	928	17	φvi	φvi	VERB
ma-105	928	18	〉	〉	NOUN
ma-105	928	19	dt+	dt+	NOUN
ma-105	928	20	∫	∫	PROPN
ma-105	928	21	t	t	PROPN
ma-105	928	22	0	0	NUM
ma-105	928	23	〈	〈	PROPN
ma-105	928	24	aiw	aiw	PROPN
ma-105	928	25	m	m	VERB
ma-105	928	26	i	i	PRON
ma-105	928	27	,	,	PUNCT
ma-105	928	28	φvi	φvi	VERB
ma-105	928	29	〉	〉	NOUN
ma-105	928	30	dt+	dt+	NOUN
ma-105	928	31	∫	∫	PROPN
ma-105	928	32	t	t	PROPN
ma-105	928	33	0	0	NUM
ma-105	928	34	(	(	PUNCT
ma-105	928	35	qi(w	qi(w	X
ma-105	928	36	m−1)wmi	m−1)wmi	X
ma-105	928	37	,	,	PUNCT
ma-105	928	38	φvi	φvi	NOUN
ma-105	928	39	)	)	PUNCT
ma-105	928	40	dt	dt	PUNCT
ma-105	929	1	=	=	SYM
ma-105	929	2	∫	∫	PROPN
ma-105	929	3	t	t	PROPN
ma-105	929	4	0	0	NUM
ma-105	929	5	〈	〈	PROPN
ma-105	929	6	fi(w	fi(w	NUM
ma-105	929	7	m−1	m−1	PROPN
ma-105	929	8	)	)	PUNCT
ma-105	929	9	,	,	PUNCT
ma-105	929	10	φvi	φvi	VERB
ma-105	929	11	〉	〉	NOUN
ma-105	929	12	dt.(b.2)the	dt.(b.2)the	DET
ma-105	929	13	second	second	ADJ
ma-105	929	14	term	term	NOUN
ma-105	929	15	in	in	ADP
ma-105	929	16	the	the	DET
ma-105	929	17	left	left	ADJ
ma-105	929	18	side	side	NOUN
ma-105	929	19	and	and	CCONJ
ma-105	929	20	the	the	DET
ma-105	929	21	right	right	ADJ
ma-105	929	22	side	side	NOUN
ma-105	929	23	of	of	ADP
ma-105	929	24	the	the	DET
ma-105	929	25	equality	equality	NOUN
ma-105	929	26	(	(	PUNCT
ma-105	929	27	b.2	b.2	NOUN
ma-105	929	28	)	)	PUNCT
ma-105	929	29	converges	converge	NOUN
ma-105	929	30	due	due	ADP
ma-105	929	31	to	to	ADP
ma-105	929	32	the	the	DET
ma-105	929	33	weakconvergence	weakconvergence	NOUN
ma-105	929	34	in	in	ADP
ma-105	929	35	l2((0	l2((0	PROPN
ma-105	929	36	,	,	PUNCT
ma-105	929	37	t	t	PROPN
ma-105	929	38	)	)	PUNCT
ma-105	929	39	,	,	PUNCT
ma-105	929	40	e′	e′	NOUN
ma-105	929	41	)	)	PUNCT
ma-105	929	42	.	.	PUNCT
ma-105	930	1	the	the	DET
ma-105	930	2	third	third	ADJ
ma-105	930	3	term	term	NOUN
ma-105	930	4	in	in	ADP
ma-105	930	5	the	the	DET
ma-105	930	6	left	left	ADJ
ma-105	930	7	-	-	PUNCT
ma-105	930	8	hand	hand	NOUN
ma-105	930	9	side	side	NOUN
ma-105	930	10	of	of	ADP
ma-105	930	11	(	(	PUNCT
ma-105	930	12	b.2	b.2	NOUN
ma-105	930	13	)	)	PUNCT
ma-105	930	14	also	also	ADV
ma-105	930	15	converges	converge	VERB
ma-105	930	16	,	,	PUNCT
ma-105	930	17	due	due	ADJ
ma-105	930	18	tothe	tothe	PRON
ma-105	930	19	convergence	convergence	NOUN
ma-105	930	20	in	in	ADP
ma-105	930	21	c([0	c([0	PROPN
ma-105	930	22	,	,	PUNCT
ma-105	930	23	t	t	X
ma-105	930	24	]	]	PUNCT
ma-105	930	25	,	,	PUNCT
ma-105	930	26	h	h	NOUN
ma-105	930	27	)	)	PUNCT
ma-105	930	28	.	.	PUNCT
ma-105	931	1	we	we	PRON
ma-105	931	2	deduce	deduce	VERB
ma-105	931	3	that	that	SCONJ
ma-105	931	4	∂wmi	∂wmi	VERB
ma-105	931	5	∂t	∂t	PROPN
ma-105	931	6	converges	converge	VERB
ma-105	931	7	weakly	weakly	ADV
ma-105	931	8	in	in	ADP
ma-105	931	9	l2((0	l2((0	PROPN
ma-105	931	10	,	,	PUNCT
ma-105	931	11	t	t	PROPN
ma-105	931	12	)	)	PUNCT
ma-105	931	13	,	,	PUNCT
ma-105	931	14	e′).but	e′).but	CCONJ
ma-105	931	15	we	we	PRON
ma-105	931	16	have	have	VERB
ma-105	931	17	wmi	wmi	PROPN
ma-105	931	18	→	→	SYM
ma-105	931	19	wi	wi	PROPN
ma-105	931	20	in	in	ADP
ma-105	931	21	c0([0	c0([0	PROPN
ma-105	931	22	,	,	PUNCT
ma-105	931	23	t	t	X
ma-105	931	24	]	]	PUNCT
ma-105	931	25	,	,	PUNCT
ma-105	931	26	h).then	h).then	PRON
ma-105	931	27	∂wmi	∂wmi	VERB
ma-105	931	28	∂t	∂t	PROPN
ma-105	931	29	→	→	SYM
ma-105	931	30	∂wi	∂wi	PROPN
ma-105	931	31	∂t	∂t	PROPN
ma-105	931	32	in	in	ADP
ma-105	931	33	d′((0	d′((0	PROPN
ma-105	931	34	,	,	PUNCT
ma-105	931	35	t	t	NOUN
ma-105	931	36	)	)	PUNCT
ma-105	931	37	,	,	PUNCT
ma-105	931	38	h)therefore	h)therefore	NOUN
ma-105	931	39	,	,	PUNCT
ma-105	931	40	we	we	PRON
ma-105	931	41	obtain	obtain	VERB
ma-105	931	42	∂wmi	∂wmi	ADJ
ma-105	931	43	∂t	∂t	PROPN
ma-105	931	44	→	→	SYM
ma-105	931	45	∂wi	∂wi	PROPN
ma-105	931	46	∂t	∂t	PROPN
ma-105	931	47	weakly	weakly	ADJ
ma-105	931	48	in	in	ADP
ma-105	931	49	l2((0	l2((0	PROPN
ma-105	931	50	,	,	PUNCT
ma-105	931	51	t	t	PROPN
ma-105	931	52	)	)	PUNCT
ma-105	931	53	,	,	PUNCT
ma-105	931	54	e′),and∫	e′),and∫	PROPN
ma-105	931	55	t	t	PROPN
ma-105	931	56	0	0	NUM
ma-105	932	1	〈	〈	PROPN
ma-105	932	2	∂wi	∂wi	PROPN
ma-105	932	3	∂t	∂t	PROPN
ma-105	932	4	,	,	PUNCT
ma-105	932	5	φvi	φvi	VERB
ma-105	932	6	〉	〉	NOUN
ma-105	932	7	dt	dt	NOUN
ma-105	932	8	+	+	CCONJ
ma-105	932	9	∫	∫	PROPN
ma-105	932	10	t	t	PROPN
ma-105	932	11	0	0	NUM
ma-105	932	12	〈	〈	PROPN
ma-105	932	13	aiwi	aiwi	NOUN
ma-105	932	14	,	,	PUNCT
ma-105	932	15	φvi	φvi	VERB
ma-105	932	16	〉	〉	NOUN
ma-105	932	17	dt	dt	NOUN
ma-105	932	18	+	+	CCONJ
ma-105	932	19	∫	∫	PROPN
ma-105	932	20	t	t	PROPN
ma-105	932	21	0	0	NUM
ma-105	932	22	(	(	PUNCT
ma-105	932	23	qi(w)wi	qi(w)wi	ADJ
ma-105	932	24	,	,	PUNCT
ma-105	932	25	φvi	φvi	NOUN
ma-105	932	26	)	)	PUNCT
ma-105	933	1	h	h	NOUN
ma-105	933	2	dt	dt	NOUN
ma-105	934	1	=	=	SYM
ma-105	934	2	∫	∫	PROPN
ma-105	934	3	t	t	PROPN
ma-105	934	4	0	0	NUM
ma-105	934	5	〈	〈	PROPN
ma-105	934	6	fi(w	fi(w	NOUN
ma-105	934	7	)	)	PUNCT
ma-105	934	8	,	,	PUNCT
ma-105	934	9	φvi	φvi	VERB
ma-105	934	10	〉	〉	NOUN
ma-105	934	11	dt	dt	NOUN
ma-105	934	12	.	.	PUNCT
ma-105	935	1	(	(	PUNCT
ma-105	935	2	b.3	b.3	PROPN
ma-105	935	3	)	)	PUNCT
ma-105	935	4	this	this	PRON
ma-105	935	5	being	be	AUX
ma-105	935	6	true	true	ADJ
ma-105	935	7	for	for	ADP
ma-105	935	8	all	all	DET
ma-105	935	9	φ	φ	NOUN
ma-105	935	10	,	,	PUNCT
ma-105	935	11	one	one	NUM
ma-105	935	12	has〈∂wi	has〈∂wi	PROPN
ma-105	935	13	∂t	∂t	PROPN
ma-105	935	14	,	,	PUNCT
ma-105	935	15	vi	vi	NOUN
ma-105	935	16	〉	〉	NOUN
ma-105	935	17	+	+	CCONJ
ma-105	935	18	〈	〈	PROPN
ma-105	935	19	aiwi	aiwi	NOUN
ma-105	935	20	,	,	PUNCT
ma-105	935	21	vi	vi	NOUN
ma-105	935	22	〉	〉	NOUN
ma-105	935	23	+	+	CCONJ
ma-105	935	24	(	(	PUNCT
ma-105	935	25	qi(w)wi	qi(w)wi	ADJ
ma-105	935	26	,	,	PUNCT
ma-105	935	27	vi	vi	NOUN
ma-105	935	28	)	)	PUNCT
ma-105	935	29	h	h	NOUN
ma-105	936	1	=	=	PUNCT
ma-105	936	2	〈	〈	PROPN
ma-105	936	3	fi(w	fi(w	NOUN
ma-105	936	4	)	)	PUNCT
ma-105	936	5	,	,	PUNCT
ma-105	936	6	vi	vi	NOUN
ma-105	936	7	〉	〉	NOUN
ma-105	936	8	,	,	PUNCT
ma-105	936	9	∀vi	∀vi	PROPN
ma-105	936	10	∈	∈	PROPN
ma-105	936	11	e.	e.	PROPN
ma-105	936	12	that	that	PRON
ma-105	936	13	is	be	AUX
ma-105	936	14	to	to	PART
ma-105	936	15	say	say	VERB
ma-105	936	16	,	,	PUNCT
ma-105	936	17	d	d	X
ma-105	936	18	dt	dt	X
ma-105	936	19	(	(	PUNCT
ma-105	936	20	wi	wi	PROPN
ma-105	936	21	,	,	PUNCT
ma-105	936	22	vi)h	vi)h	PROPN
ma-105	936	23	+	+	CCONJ
ma-105	936	24	a(wi	a(wi	PROPN
ma-105	936	25	,	,	PUNCT
ma-105	936	26	vi	vi	PROPN
ma-105	936	27	)	)	PUNCT
ma-105	937	1	+	+	CCONJ
ma-105	937	2	(	(	PUNCT
ma-105	937	3	qi(w)wi	qi(w)wi	ADJ
ma-105	937	4	,	,	PUNCT
ma-105	937	5	vi	vi	NOUN
ma-105	937	6	)	)	PUNCT
ma-105	937	7	h	h	NOUN
ma-105	938	1	=	=	PUNCT
ma-105	938	2	〈	〈	PROPN
ma-105	938	3	fi(w	fi(w	NOUN
ma-105	938	4	)	)	PUNCT
ma-105	938	5	,	,	PUNCT
ma-105	938	6	vi	vi	NOUN
ma-105	938	7	〉	〉	NOUN
ma-105	938	8	,	,	PUNCT
ma-105	938	9	∀vi	∀vi	PROPN
ma-105	938	10	∈	∈	PROPN
ma-105	938	11	e	e	NOUN
ma-105	938	12	,	,	PUNCT
ma-105	938	13	(	(	PUNCT
ma-105	938	14	b.4	b.4	NOUN
ma-105	938	15	)	)	PUNCT
ma-105	938	16	∂wi	∂wi	PROPN
ma-105	938	17	∂t	∂t	PROPN
ma-105	938	18	=	=	SYM
ma-105	938	19	fi(w)−	fi(w)−	PROPN
ma-105	938	20	aiwi	aiwi	NOUN
ma-105	938	21	−	−	PROPN
ma-105	938	22	qi(w)wi	qi(w)wi	NOUN
ma-105	938	23	in	in	ADP
ma-105	938	24	l2((0	l2((0	PROPN
ma-105	938	25	,	,	PUNCT
ma-105	938	26	t	t	PROPN
ma-105	938	27	)	)	PUNCT
ma-105	938	28	,	,	PUNCT
ma-105	938	29	e′	e′	NOUN
ma-105	938	30	)	)	PUNCT
ma-105	938	31	.	.	PUNCT
ma-105	939	1	(	(	PUNCT
ma-105	939	2	b.5	b.5	NOUN
ma-105	939	3	)	)	PUNCT
ma-105	939	4	https://doi.org/10.28924/ada/ma.3.1	https://doi.org/10.28924/ada/ma.3.1	PROPN
ma-105	939	5	eur	eur	PROPN
ma-105	939	6	.	.	PUNCT
ma-105	940	1	j.	j.	PROPN
ma-105	940	2	math	math	PROPN
ma-105	940	3	.	.	PUNCT
ma-105	941	1	anal	anal	PROPN
ma-105	941	2	.	.	PUNCT
ma-105	942	1	10.28924	10.28924	NUM
ma-105	942	2	/	/	SYM
ma-105	942	3	ada	ada	PROPN
ma-105	942	4	/	/	SYM
ma-105	942	5	ma.3.1	ma.3.1	PROPN
ma-105	942	6	34according	34accorde	VERB
ma-105	942	7	to	to	ADP
ma-105	942	8	(	(	PUNCT
ma-105	942	9	3.27	3.27	NUM
ma-105	942	10	)	)	PUNCT
ma-105	942	11	and	and	CCONJ
ma-105	942	12	(	(	PUNCT
ma-105	942	13	3.28	3.28	NUM
ma-105	942	14	)	)	PUNCT
ma-105	942	15	we	we	PRON
ma-105	942	16	have	have	VERB
ma-105	942	17	wmi	wmi	X
ma-105	942	18	(	(	PUNCT
ma-105	942	19	t	t	PROPN
ma-105	942	20	)	)	PUNCT
ma-105	942	21	=	=	NOUN
ma-105	942	22	gi(t)w0i	gi(t)w0i	VERB
ma-105	943	1	+	+	CCONJ
ma-105	943	2	∫	∫	PROPN
ma-105	943	3	t	t	PROPN
ma-105	943	4	0	0	NUM
ma-105	943	5	gi(t	gi(t	NOUN
ma-105	943	6	−	−	PROPN
ma-105	943	7	s)(−qi(wm−1)wmi	s)(−qi(wm−1)wmi	PROPN
ma-105	943	8	+	+	CCONJ
ma-105	943	9	fi(w	fi(w	PUNCT
ma-105	943	10	m−1))(s)ds	m−1))(s)ds	PROPN
ma-105	943	11	,	,	PUNCT
ma-105	943	12	(	(	PUNCT
ma-105	943	13	b.6	b.6	ADP
ma-105	943	14	)	)	PUNCT
ma-105	943	15	and	and	CCONJ
ma-105	943	16	in	in	ADP
ma-105	943	17	addition	addition	NOUN
ma-105	943	18	,	,	PUNCT
ma-105	943	19	as	as	ADP
ma-105	943	20	qi(wm−1)wmi	qi(wm−1)wmi	NOUN
ma-105	943	21	and	and	CCONJ
ma-105	943	22	fi(w	fi(w	PUNCT
ma-105	943	23	m−1	m−1	PROPN
ma-105	943	24	)	)	PUNCT
ma-105	943	25	converge	converge	VERB
ma-105	943	26	in	in	ADP
ma-105	943	27	c0([0	c0([0	PROPN
ma-105	943	28	,	,	PUNCT
ma-105	943	29	t	t	X
ma-105	943	30	]	]	PUNCT
ma-105	943	31	,	,	PUNCT
ma-105	943	32	h	h	NOUN
ma-105	943	33	)	)	PUNCT
ma-105	943	34	and	and	CCONJ
ma-105	943	35	the	the	DET
ma-105	943	36	operator	operator	NOUN
ma-105	943	37	gi	gi	NOUN
ma-105	943	38	,	,	PUNCT
ma-105	943	39	defined	define	VERB
ma-105	943	40	by	by	ADP
ma-105	943	41	the	the	DET
ma-105	943	42	relation	relation	NOUN
ma-105	943	43	(	(	PUNCT
ma-105	943	44	3.29	3.29	NUM
ma-105	943	45	)	)	PUNCT
ma-105	943	46	,	,	PUNCT
ma-105	943	47	is	be	AUX
ma-105	943	48	compact	compact	ADJ
ma-105	943	49	,	,	PUNCT
ma-105	943	50	using	use	VERB
ma-105	943	51	the	the	DET
ma-105	943	52	limit	limit	NOUN
ma-105	943	53	in	in	ADP
ma-105	943	54	(	(	PUNCT
ma-105	943	55	b.6	b.6	NOUN
ma-105	943	56	)	)	PUNCT
ma-105	943	57	one	one	NOUN
ma-105	943	58	has	have	VERB
ma-105	943	59	,	,	PUNCT
ma-105	943	60	wi(t	wi(t	NOUN
ma-105	943	61	)	)	PUNCT
ma-105	943	62	=	=	PUNCT
ma-105	943	63	gi(t)w0i	gi(t)w0i	VERB
ma-105	944	1	+	+	CCONJ
ma-105	944	2	∫	∫	PROPN
ma-105	944	3	t	t	PROPN
ma-105	944	4	0	0	NUM
ma-105	944	5	gi(t	gi(t	PROPN
ma-105	944	6	−	−	PROPN
ma-105	944	7	s)(−qi(w)wi	s)(−qi(w)wi	PROPN
ma-105	944	8	+	+	CCONJ
ma-105	944	9	fi(w))(s)ds	fi(w))(s)ds	X
ma-105	944	10	.	.	PUNCT
ma-105	945	1	(	(	PUNCT
ma-105	945	2	b.7	b.7	NOUN
ma-105	945	3	)	)	PUNCT
ma-105	945	4	it	it	PRON
ma-105	945	5	remains	remain	VERB
ma-105	945	6	to	to	PART
ma-105	945	7	prove	prove	VERB
ma-105	945	8	uniqueness.let	uniqueness.let	X
ma-105	945	9	v	v	NOUN
ma-105	945	10	be	be	AUX
ma-105	945	11	another	another	DET
ma-105	945	12	solution	solution	NOUN
ma-105	945	13	of	of	ADP
ma-105	945	14	ibvp	ibvp	NOUN
ma-105	945	15	(	(	PUNCT
ma-105	945	16	3.21	3.21	NUM
ma-105	945	17	)	)	PUNCT
ma-105	945	18	.	.	PUNCT
ma-105	946	1	then	then	ADV
ma-105	946	2	vi	vi	PROPN
ma-105	946	3	∈	∈	PROPN
ma-105	946	4	w	w	PROPN
ma-105	946	5	(	(	PUNCT
ma-105	946	6	0	0	NUM
ma-105	946	7	,	,	PUNCT
ma-105	946	8	t	t	PROPN
ma-105	946	9	,	,	PUNCT
ma-105	946	10	e	e	NOUN
ma-105	946	11	,	,	PUNCT
ma-105	946	12	e′)⇒	e′)⇒	PROPN
ma-105	946	13	vi	vi	NOUN
ma-105	946	14	∈	∈	PROPN
ma-105	946	15	c0([0	c0([0	PROPN
ma-105	946	16	,	,	PUNCT
ma-105	946	17	t	t	X
ma-105	946	18	]	]	PUNCT
ma-105	946	19	,	,	PUNCT
ma-105	946	20	h	h	NOUN
ma-105	946	21	)	)	PUNCT
ma-105	946	22	and	and	CCONJ
ma-105	946	23	vi	vi	PROPN
ma-105	946	24	≥	≥	NOUN
ma-105	946	25	0	0	NUM
ma-105	946	26	.	.	PUNCT
ma-105	947	1	consequently	consequently	ADV
ma-105	947	2	we	we	PRON
ma-105	947	3	obtain	obtain	VERB
ma-105	947	4	qi(v)vi	qi(v)vi	NOUN
ma-105	947	5	+	+	CCONJ
ma-105	947	6	fi(v	fi(v	PUNCT
ma-105	947	7	)	)	PUNCT
ma-105	947	8	∈	∈	PROPN
ma-105	947	9	l2((0	l2((0	PROPN
ma-105	947	10	,	,	PUNCT
ma-105	947	11	t	t	PROPN
ma-105	947	12	)	)	PUNCT
ma-105	947	13	,	,	PUNCT
ma-105	947	14	e′	e′	NOUN
ma-105	947	15	)	)	PUNCT
ma-105	947	16	.	.	PUNCT
ma-105	948	1	thus	thus	ADV
ma-105	948	2	,	,	PUNCT
ma-105	948	3	by	by	ADP
ma-105	948	4	proposition	proposition	NOUN
ma-105	948	5	2.11	2.11	NUM
ma-105	948	6	of	of	ADP
ma-105	948	7	[	[	X
ma-105	948	8	12	12	NUM
ma-105	948	9	]	]	PUNCT
ma-105	948	10	,	,	PUNCT
ma-105	948	11	one	one	PRON
ma-105	948	12	has	have	VERB
ma-105	948	13	vi(t	vi(t	NOUN
ma-105	948	14	)	)	PUNCT
ma-105	949	1	=	=	NOUN
ma-105	949	2	gi(t)w0i	gi(t)w0i	VERB
ma-105	950	1	+	+	CCONJ
ma-105	950	2	∫	∫	PROPN
ma-105	950	3	t	t	PROPN
ma-105	950	4	0	0	NUM
ma-105	950	5	gi(t	gi(t	PUNCT
ma-105	950	6	−	−	PROPN
ma-105	950	7	s)(−qi(v)vi	s)(−qi(v)vi	NOUN
ma-105	950	8	+	+	CCONJ
ma-105	950	9	fi(v))(s)ds	fi(v))(s)d	NOUN
ma-105	950	10	.	.	PUNCT
ma-105	951	1	subtracting	subtract	VERB
ma-105	951	2	,	,	PUNCT
ma-105	951	3	we	we	PRON
ma-105	951	4	have	have	VERB
ma-105	951	5	wi(t)−	wi(t)−	PROPN
ma-105	951	6	vi(t	vi(t	PUNCT
ma-105	951	7	)	)	PUNCT
ma-105	952	1	=	=	SYM
ma-105	953	1	∫	∫	PROPN
ma-105	953	2	t	t	PROPN
ma-105	953	3	0	0	NUM
ma-105	953	4	gi(t	gi(t	PROPN
ma-105	953	5	−	−	PROPN
ma-105	953	6	s	s	AUX
ma-105	953	7	)	)	PUNCT
ma-105	953	8	(	(	PUNCT
ma-105	953	9	−	−	PROPN
ma-105	953	10	(	(	PUNCT
ma-105	953	11	qi(w)wi	qi(w)wi	ADJ
ma-105	953	12	−	−	PROPN
ma-105	953	13	qi(v)vi	qi(v)vi	NOUN
ma-105	953	14	)	)	PUNCT
ma-105	953	15	+	+	CCONJ
ma-105	953	16	(	(	PUNCT
ma-105	953	17	fi(w)−	fi(w)−	PROPN
ma-105	953	18	fi(v	fi(v	PRON
ma-105	953	19	)	)	PUNCT
ma-105	953	20	)	)	PUNCT
ma-105	953	21	)	)	PUNCT
ma-105	954	1	(	(	PUNCT
ma-105	954	2	s)ds	s)ds	PROPN
ma-105	954	3	,	,	PUNCT
ma-105	954	4	(	(	PUNCT
ma-105	954	5	b.8	b.8	NOUN
ma-105	954	6	)	)	PUNCT
ma-105	954	7	with	with	ADP
ma-105	954	8	qi(w)wi	qi(w)wi	ADJ
ma-105	954	9	−	−	ADP
ma-105	954	10	qi(v)vi	qi(v)vi	NOUN
ma-105	954	11	=	=	PUNCT
ma-105	954	12	qi(w)wi	qi(w)wi	ADJ
ma-105	954	13	−	−	PROPN
ma-105	954	14	qi(w)vi	qi(w)vi	VERB
ma-105	954	15	+	+	CCONJ
ma-105	954	16	qi(w)vi	qi(w)vi	NOUN
ma-105	954	17	−	−	PROPN
ma-105	954	18	qi(v)vi	qi(v)vi	NOUN
ma-105	954	19	,	,	PUNCT
ma-105	954	20	=	=	PUNCT
ma-105	954	21	qi(w)(wi	qi(w)(wi	PROPN
ma-105	954	22	−	−	PROPN
ma-105	954	23	vi	vi	NOUN
ma-105	954	24	)	)	PUNCT
ma-105	954	25	+	+	CCONJ
ma-105	954	26	(	(	PUNCT
ma-105	954	27	qi(w)−	qi(w)−	ADJ
ma-105	954	28	qi(v))vi	qi(v))vi	NOUN
ma-105	954	29	.	.	PUNCT
ma-105	955	1	since	since	SCONJ
ma-105	955	2	wi	wi	PROPN
ma-105	955	3	is	be	AUX
ma-105	955	4	positive	positive	ADJ
ma-105	955	5	,	,	PUNCT
ma-105	955	6	one	one	NUM
ma-105	955	7	has∥∥∥∥∥	has∥∥∥∥∥	NOUN
ma-105	955	8	wj	wj	NOUN
ma-105	955	9	α0	α0	PROPN
ma-105	955	10	+	+	CCONJ
ma-105	955	11	α1wk	α1wk	X
ma-105	955	12	+	+	CCONJ
ma-105	955	13	α2wj	α2wj	PUNCT
ma-105	956	1	+	+	CCONJ
ma-105	956	2	α3wkwj	α3wkwj	NOUN
ma-105	956	3	∥∥∥∥∥	∥∥∥∥∥	VERB
ma-105	956	4	≤	≤	ADV
ma-105	956	5	1	1	NUM
ma-105	956	6	k	k	X
ma-105	956	7	‖wj‖∞	‖wj‖∞	X
ma-105	956	8	where	where	SCONJ
ma-105	956	9	‖wj‖∞	‖wj‖∞	X
ma-105	956	10	=	=	SYM
ma-105	956	11	‖wj‖l∞((0,t	‖wj‖l∞((0,t	PROPN
ma-105	956	12	)	)	PUNCT
ma-105	956	13	,	,	PUNCT
ma-105	956	14	h	h	NOUN
ma-105	956	15	)	)	PUNCT
ma-105	956	16	.	.	PUNCT
ma-105	957	1	if	if	SCONJ
ma-105	957	2	we	we	PRON
ma-105	957	3	define	define	VERB
ma-105	957	4	‖w‖∞	‖w‖∞	PROPN
ma-105	957	5	=	=	SYM
ma-105	957	6	3∑	3∑	NUM
ma-105	957	7	j=1	j=1	NOUN
ma-105	957	8	‖wj‖∞	‖wj‖∞	NUM
ma-105	957	9	,	,	PUNCT
ma-105	957	10	there	there	PRON
ma-105	957	11	is	be	VERB
ma-105	957	12	m1	m1	PROPN
ma-105	957	13	>	>	X
ma-105	957	14	0	0	NUM
ma-105	957	15	such	such	ADJ
ma-105	957	16	that	that	SCONJ
ma-105	957	17	‖q(w)‖∞	‖q(w)‖∞	ADJ
ma-105	957	18	≤	≤	NUM
ma-105	957	19	m1‖wj‖∞.	m1‖wj‖∞.	PROPN
ma-105	957	20	https://doi.org/10.28924/ada/ma.3.1	https://doi.org/10.28924/ada/ma.3.1	PROPN
ma-105	957	21	eur	eur	PROPN
ma-105	957	22	.	.	PUNCT
ma-105	958	1	j.	j.	PROPN
ma-105	958	2	math	math	PROPN
ma-105	958	3	.	.	PUNCT
ma-105	959	1	anal	anal	PROPN
ma-105	959	2	.	.	PUNCT
ma-105	960	1	10.28924	10.28924	NUM
ma-105	960	2	/	/	SYM
ma-105	960	3	ada	ada	PROPN
ma-105	960	4	/	/	SYM
ma-105	960	5	ma.3.1	ma.3.1	PROPN
ma-105	960	6	35so	35so	NOUN
ma-105	960	7	,	,	PUNCT
ma-105	960	8	for	for	ADP
ma-105	960	9	r	r	NOUN
ma-105	960	10	=	=	SYM
ma-105	960	11	1	1	NUM
ma-105	960	12	,	,	PUNCT
ma-105	960	13	2	2	NUM
ma-105	960	14	,	,	PUNCT
ma-105	960	15	3	3	NUM
ma-105	960	16	,	,	PUNCT
ma-105	960	17	the	the	DET
ma-105	960	18	numerator	numerator	NOUN
ma-105	960	19	of	of	ADP
ma-105	960	20	qr	qr	PROPN
ma-105	960	21	(	(	PUNCT
ma-105	960	22	w	w	NOUN
ma-105	960	23	)	)	PUNCT
ma-105	961	1	−	−	PROPN
ma-105	961	2	qr	qr	PROPN
ma-105	961	3	(	(	PUNCT
ma-105	961	4	v	v	NOUN
ma-105	961	5	)	)	PUNCT
ma-105	961	6	is	be	AUX
ma-105	961	7	the	the	DET
ma-105	961	8	sum	sum	NOUN
ma-105	961	9	of	of	ADP
ma-105	961	10	terms	term	NOUN
ma-105	961	11	of	of	ADP
ma-105	961	12	the	the	DET
ma-105	961	13	form	form	NOUN
ma-105	961	14	(	(	PUNCT
ma-105	961	15	wk	wk	ADP
ma-105	961	16	−	−	NOUN
ma-105	962	1	vk)vj	vk)vj	PUNCT
ma-105	963	1	or	or	CCONJ
ma-105	963	2	(	(	PUNCT
ma-105	963	3	wj	wj	PROPN
ma-105	963	4	−	−	PROPN
ma-105	963	5	vj)wk	vj)wk	NOUN
ma-105	963	6	,	,	PUNCT
ma-105	963	7	and	and	CCONJ
ma-105	963	8	we	we	PRON
ma-105	963	9	can	can	AUX
ma-105	963	10	find	find	VERB
ma-105	963	11	m2	m2	PROPN
ma-105	963	12	>	>	X
ma-105	963	13	0	0	NUM
ma-105	964	1	such	such	ADJ
ma-105	964	2	that	that	SCONJ
ma-105	964	3	∣∣qr	∣∣qr	PROPN
ma-105	964	4	(	(	PUNCT
ma-105	964	5	w)−	w)−	PROPN
ma-105	964	6	qr	qr	PROPN
ma-105	964	7	(	(	PUNCT
ma-105	964	8	v	v	NOUN
ma-105	964	9	)	)	PUNCT
ma-105	964	10	∣∣	∣∣	X
ma-105	964	11	h(s	h(	NOUN
ma-105	964	12	)	)	PUNCT
ma-105	964	13	≤	≤	NUM
ma-105	964	14	m2	m2	PROPN
ma-105	964	15	(	(	PUNCT
ma-105	964	16	3∑	3∑	NOUN
ma-105	964	17	j=1	j=1	NOUN
ma-105	964	18	|wj(s)−	|wj(s)−	NOUN
ma-105	964	19	vj(s)|h	vj(s)|h	PROPN
ma-105	964	20	)	)	PUNCT
ma-105	964	21	.	.	PUNCT
ma-105	965	1	also	also	ADV
ma-105	965	2	we	we	PRON
ma-105	965	3	can	can	AUX
ma-105	965	4	find	find	VERB
ma-105	965	5	m3	m3	PROPN
ma-105	965	6	>	>	X
ma-105	965	7	0	0	NUM
ma-105	966	1	such	such	ADJ
ma-105	966	2	that∣∣fr	that∣∣fr	NOUN
ma-105	966	3	(	(	PUNCT
ma-105	966	4	w)−	w)−	PROPN
ma-105	966	5	fr	fr	INTJ
ma-105	966	6	(	(	PUNCT
ma-105	966	7	v	v	NOUN
ma-105	966	8	)	)	PUNCT
ma-105	966	9	∣∣	∣∣	X
ma-105	966	10	h(s	h(	NOUN
ma-105	966	11	)	)	PUNCT
ma-105	966	12	≤	≤	NOUN
ma-105	966	13	m3	m3	NOUN
ma-105	966	14	(	(	PUNCT
ma-105	966	15	3∑	3∑	NOUN
ma-105	966	16	j=1	j=1	NOUN
ma-105	966	17	|wj(s)−	|wj(s)−	NOUN
ma-105	966	18	vj(s)|h	vj(s)|h	PROPN
ma-105	966	19	)	)	PUNCT
ma-105	966	20	.	.	PUNCT
ma-105	967	1	summing	sum	VERB
ma-105	967	2	up	up	ADP
ma-105	967	3	|wj(s	|wj(	NOUN
ma-105	967	4	)	)	PUNCT
ma-105	967	5	−	−	PROPN
ma-105	967	6	vj(s)|h	vj(s)|h	NOUN
ma-105	967	7	and	and	CCONJ
ma-105	967	8	noting	note	VERB
ma-105	967	9	that	that	SCONJ
ma-105	967	10	‖gj(t	‖gj(t	PROPN
ma-105	967	11	−	−	PROPN
ma-105	967	12	s)‖	s)‖	VERB
ma-105	967	13	≤	≤	NUM
ma-105	967	14	njeθjt	njeθjt	NOUN
ma-105	967	15	with	with	ADP
ma-105	967	16	nj	nj	PROPN
ma-105	967	17	,	,	PUNCT
ma-105	967	18	θj	θj	ADV
ma-105	967	19	>	>	X
ma-105	967	20	0	0	NUM
ma-105	967	21	,	,	PUNCT
ma-105	967	22	we	we	PRON
ma-105	967	23	can	can	AUX
ma-105	967	24	find	find	VERB
ma-105	967	25	m	m	VERB
ma-105	967	26	>	>	X
ma-105	967	27	0	0	NUM
ma-105	968	1	such	such	ADJ
ma-105	968	2	that	that	SCONJ
ma-105	968	3	3∑	3∑	NUM
ma-105	968	4	j=1	j=1	NOUN
ma-105	968	5	|wj(s)−	|wj(s)−	AUX
ma-105	968	6	vj(s)|h	vj(s)|h	NOUN
ma-105	968	7	≤	≤	ADJ
ma-105	968	8	m‖w	m‖w	ADJ
ma-105	968	9	−	−	PROPN
ma-105	968	10	v‖∞.	v‖∞.	ADJ
ma-105	968	11	replacing	replacing	NOUN
ma-105	968	12	in	in	ADP
ma-105	968	13	(	(	PUNCT
ma-105	968	14	b.8	b.8	NOUN
ma-105	968	15	)	)	PUNCT
ma-105	968	16	,	,	PUNCT
ma-105	968	17	we	we	PRON
ma-105	968	18	obtain	obtain	VERB
ma-105	968	19	3∑	3∑	NOUN
ma-105	968	20	j=1	j=1	NOUN
ma-105	968	21	|wj(s)−	|wj(s)−	NOUN
ma-105	969	1	vj(s)|h	vj(s)|h	NOUN
ma-105	969	2	≤	≤	ADV
ma-105	970	1	m2‖w	m2‖w	INTJ
ma-105	970	2	−	−	PROPN
ma-105	970	3	v‖∞	v‖∞	NOUN
ma-105	971	1	∫	∫	PROPN
ma-105	971	2	t	t	PROPN
ma-105	971	3	0	0	NUM
ma-105	971	4	sds	sds	PROPN
ma-105	971	5	=	=	PROPN
ma-105	971	6	m2	m2	PROPN
ma-105	971	7	t	t	PROPN
ma-105	971	8	2	2	NUM
ma-105	971	9	2	2	NUM
ma-105	971	10	‖w	‖w	NOUN
ma-105	971	11	−	−	PROPN
ma-105	971	12	v‖∞.	v‖∞.	NOUN
ma-105	971	13	by	by	ADP
ma-105	971	14	induction	induction	NOUN
ma-105	971	15	,	,	PUNCT
ma-105	971	16	we	we	PRON
ma-105	971	17	have	have	VERB
ma-105	971	18	3∑	3∑	NUM
ma-105	971	19	j=1	j=1	NOUN
ma-105	971	20	|wj(s)−	|wj(s)−	NOUN
ma-105	971	21	vj(s)|h	vj(s)|h	PROPN
ma-105	971	22	≤	≤	NUM
ma-105	971	23	mn	mn	PROPN
ma-105	971	24	n	n	X
ma-105	971	25	!	!	PROPN
ma-105	971	26	t	t	PROPN
ma-105	971	27	n‖w	n‖w	NOUN
ma-105	971	28	−	−	PROPN
ma-105	972	1	v‖∞	v‖∞	ADV
ma-105	972	2	,	,	PUNCT
ma-105	972	3	with	with	ADP
ma-105	972	4	lim	lim	PROPN
ma-105	972	5	n→+∞	n→+∞	PROPN
ma-105	972	6	mn	mn	PROPN
ma-105	972	7	n	n	PROPN
ma-105	972	8	!	!	PROPN
ma-105	972	9	t	t	PROPN
ma-105	972	10	n‖w	n‖w	NOUN
ma-105	972	11	−	−	PROPN
ma-105	972	12	v‖∞	v‖∞	X
ma-105	973	1	=	=	SYM
ma-105	973	2	0	0	X
ma-105	973	3	.	.	PUNCT
ma-105	974	1	therefore	therefore	ADV
ma-105	974	2	w	w	PROPN
ma-105	974	3	=	=	PUNCT
ma-105	974	4	v	v	PROPN
ma-105	974	5	.	.	PUNCT
ma-105	975	1	this	this	PRON
ma-105	975	2	ends	end	VERB
ma-105	975	3	the	the	DET
ma-105	975	4	proof	proof	NOUN
ma-105	975	5	of	of	ADP
ma-105	975	6	theorem	theorem	NOUN
ma-105	975	7	3.11	3.11	NUM
ma-105	975	8	.	.	PUNCT
ma-105	976	1	acknowledgmenta.nangue	acknowledgmenta.nangue	NOUN
ma-105	976	2	acknowledges	acknowledge	VERB
ma-105	976	3	support	support	NOUN
ma-105	976	4	from	from	ADP
ma-105	976	5	the	the	DET
ma-105	976	6	faculty	faculty	NOUN
ma-105	976	7	of	of	ADP
ma-105	976	8	sciences	science	NOUN
ma-105	976	9	of	of	ADP
ma-105	976	10	the	the	DET
ma-105	976	11	university	university	NOUN
ma-105	976	12	of	of	ADP
ma-105	976	13	maroua	maroua	PROPN
ma-105	976	14	,	,	PUNCT
ma-105	976	15	wherethis	wherethis	ADJ
ma-105	976	16	work	work	NOUN
ma-105	976	17	was	be	AUX
ma-105	976	18	initiated	initiate	VERB
ma-105	976	19	.	.	PUNCT
ma-105	977	1	conflict	conflict	NOUN
ma-105	977	2	of	of	ADP
ma-105	977	3	intereststhe	intereststhe	DET
ma-105	977	4	authors	author	NOUN
ma-105	977	5	declare	declare	VERB
ma-105	977	6	that	that	SCONJ
ma-105	977	7	they	they	PRON
ma-105	977	8	have	have	VERB
ma-105	977	9	no	no	DET
ma-105	977	10	conflict	conflict	NOUN
ma-105	977	11	of	of	ADP
ma-105	977	12	interests	interest	NOUN
ma-105	977	13	regarding	regard	VERB
ma-105	977	14	the	the	DET
ma-105	977	15	publication	publication	NOUN
ma-105	977	16	of	of	ADP
ma-105	977	17	this	this	DET
ma-105	977	18	paper	paper	NOUN
ma-105	977	19	.	.	PUNCT
ma-105	978	1	authors	author	NOUN
ma-105	978	2	’	'	PUNCT
ma-105	978	3	contributiona	contributiona	PROPN
ma-105	978	4	.	.	PUNCT
ma-105	979	1	nangue	nangue	PROPN
ma-105	979	2	provided	provide	VERB
ma-105	979	3	the	the	DET
ma-105	979	4	subject	subject	NOUN
ma-105	979	5	,	,	PUNCT
ma-105	979	6	wrote	write	VERB
ma-105	979	7	the	the	DET
ma-105	979	8	introduction	introduction	NOUN
ma-105	979	9	,	,	PUNCT
ma-105	979	10	the	the	DET
ma-105	979	11	conclusion	conclusion	NOUN
ma-105	979	12	,	,	PUNCT
ma-105	979	13	checked	check	VERB
ma-105	979	14	the	the	DET
ma-105	979	15	proofs	proof	NOUN
ma-105	979	16	andverified	andverifie	VERB
ma-105	979	17	the	the	DET
ma-105	979	18	calculation	calculation	NOUN
ma-105	979	19	.	.	PUNCT
ma-105	980	1	he	he	PRON
ma-105	980	2	also	also	ADV
ma-105	980	3	managed	manage	VERB
ma-105	980	4	the	the	DET
ma-105	980	5	wellposedness	wellposedness	NOUN
ma-105	980	6	of	of	ADP
ma-105	980	7	the	the	DET
ma-105	980	8	initial	initial	ADJ
ma-105	980	9	and	and	CCONJ
ma-105	980	10	boundary	boundary	ADJ
ma-105	980	11	valueproblem	valueproblem	NOUN
ma-105	980	12	.	.	PUNCT
ma-105	981	1	b.	b.	PROPN
ma-105	981	2	nde	nde	PROPN
ma-105	981	3	tchiffo	tchiffo	PROPN
ma-105	981	4	conceived	conceive	VERB
ma-105	981	5	the	the	DET
ma-105	981	6	study	study	NOUN
ma-105	981	7	and	and	CCONJ
ma-105	981	8	computed	compute	VERB
ma-105	981	9	equilibria	equilibrium	NOUN
ma-105	981	10	and	and	CCONJ
ma-105	981	11	their	their	PRON
ma-105	981	12	global	global	ADJ
ma-105	981	13	stabilities.the	stabilities.the	DET
ma-105	981	14	two	two	NUM
ma-105	981	15	authors	author	NOUN
ma-105	981	16	together	together	ADV
ma-105	981	17	undertook	undertake	VERB
ma-105	981	18	the	the	DET
ma-105	981	19	numerical	numerical	ADJ
ma-105	981	20	simulations	simulation	NOUN
ma-105	981	21	on	on	ADP
ma-105	981	22	mathematica	mathematica	PROPN
ma-105	981	23	.	.	PUNCT
ma-105	982	1	all	all	DET
ma-105	982	2	the	the	DET
ma-105	982	3	authorsread	authorsread	NOUN
ma-105	982	4	and	and	CCONJ
ma-105	982	5	approved	approve	VERB
ma-105	982	6	the	the	DET
ma-105	982	7	final	final	ADJ
ma-105	982	8	manuscript	manuscript	NOUN
ma-105	982	9	.	.	PUNCT
ma-105	983	1	https://doi.org/10.28924/ada/ma.3.1	https://doi.org/10.28924/ada/ma.3.1	PROPN
ma-105	983	2	eur	eur	PROPN
ma-105	983	3	.	.	PUNCT
ma-105	984	1	j.	j.	PROPN
ma-105	984	2	math	math	PROPN
ma-105	984	3	.	.	PUNCT
ma-105	985	1	anal	anal	PROPN
ma-105	985	2	.	.	PUNCT
ma-105	986	1	10.28924	10.28924	NUM
ma-105	986	2	/	/	SYM
ma-105	986	3	ada	ada	PROPN
ma-105	986	4	/	/	SYM
ma-105	986	5	ma.3.1	ma.3.1	PROPN
ma-105	986	6	36references	36reference	NOUN
ma-105	986	7	[	[	X
ma-105	986	8	1	1	NUM
ma-105	986	9	]	]	X
ma-105	986	10	r.a	r.a	PROPN
ma-105	986	11	.	.	PROPN
ma-105	986	12	adams	adams	PROPN
ma-105	986	13	,	,	PUNCT
ma-105	986	14	sobolev	sobolev	NOUN
ma-105	986	15	spaces	space	NOUN
ma-105	986	16	,	,	PUNCT
ma-105	986	17	academic	academic	ADJ
ma-105	986	18	press	press	NOUN
ma-105	986	19	,	,	PUNCT
ma-105	986	20	new	new	PROPN
ma-105	986	21	york	york	PROPN
ma-105	986	22	,	,	PUNCT
ma-105	986	23	(	(	PUNCT
ma-105	986	24	1975).[2	1975).[2	ADV
ma-105	986	25	]	]	X
ma-105	986	26	h.	h.	PROPN
ma-105	986	27	amann	amann	PROPN
ma-105	986	28	,	,	PUNCT
ma-105	986	29	dynamic	dynamic	ADJ
ma-105	986	30	theory	theory	NOUN
ma-105	986	31	of	of	ADP
ma-105	986	32	quasilinear	quasilinear	PROPN
ma-105	986	33	parabolic	parabolic	PROPN
ma-105	986	34	equations	equation	NOUN
ma-105	986	35	—	—	PUNCT
ma-105	986	36	i.	i.	PROPN
ma-105	986	37	abstract	abstract	PROPN
ma-105	986	38	evolution	evolution	PROPN
ma-105	986	39	equations	equation	NOUN
ma-105	986	40	,	,	PUNCT
ma-105	986	41	nonlinear	nonlinear	ADJ
ma-105	986	42	anal.:theory	anal.:theory	PROPN
ma-105	986	43	methods	method	NOUN
ma-105	986	44	appl	appl	PROPN
ma-105	986	45	.	.	PROPN
ma-105	987	1	12	12	NUM
ma-105	987	2	(	(	PUNCT
ma-105	987	3	1988	1988	NUM
ma-105	987	4	)	)	PUNCT
ma-105	987	5	895–919	895–919	NUM
ma-105	987	6	.	.	PUNCT
ma-105	988	1	https://doi.org/10.1016/0362-546x(88)90073-9.[3	https://doi.org/10.1016/0362-546x(88)90073-9.[3	NOUN
ma-105	988	2	]	]	X
ma-105	988	3	h.	h.	PROPN
ma-105	988	4	amann	amann	PROPN
ma-105	988	5	,	,	PUNCT
ma-105	988	6	dynamic	dynamic	ADJ
ma-105	988	7	theory	theory	NOUN
ma-105	988	8	of	of	ADP
ma-105	988	9	quasilinear	quasilinear	PROPN
ma-105	988	10	parabolic	parabolic	PROPN
ma-105	988	11	systems	system	NOUN
ma-105	988	12	,	,	PUNCT
ma-105	988	13	math	math	NOUN
ma-105	988	14	z.	z.	PROPN
ma-105	988	15	202	202	NUM
ma-105	988	16	(	(	PUNCT
ma-105	988	17	1989	1989	NUM
ma-105	988	18	)	)	PUNCT
ma-105	988	19	219–250	219–250	NUM
ma-105	988	20	.	.	PUNCT
ma-105	989	1	https://doi.org/10	https://doi.org/10	PROPN
ma-105	989	2	.	.	PUNCT
ma-105	989	3	1007	1007	NUM
ma-105	989	4	/	/	SYM
ma-105	989	5	bf01215256.[4	bf01215256.[4	PROPN
ma-105	989	6	]	]	X
ma-105	989	7	h.	h.	PROPN
ma-105	989	8	amann	amann	PROPN
ma-105	989	9	,	,	PUNCT
ma-105	989	10	dynamic	dynamic	ADJ
ma-105	989	11	theory	theory	NOUN
ma-105	989	12	of	of	ADP
ma-105	989	13	quasilinear	quasilinear	PROPN
ma-105	989	14	parabolic	parabolic	PROPN
ma-105	989	15	equations	equations	PROPN
ma-105	989	16	-	-	PUNCT
ma-105	989	17	ii	ii	NOUN
ma-105	989	18	.	.	PUNCT
ma-105	989	19	reaction	reaction	NOUN
ma-105	989	20	-	-	PUNCT
ma-105	989	21	diffusion	diffusion	NOUN
ma-105	989	22	systems	system	NOUN
ma-105	989	23	,	,	PUNCT
ma-105	989	24	differ	differ	VERB
ma-105	989	25	.	.	PUNCT
ma-105	990	1	integral	integral	PROPN
ma-105	990	2	equ	equ	PROPN
ma-105	990	3	.	.	PUNCT
ma-105	991	1	3(1990	3(1990	NUM
ma-105	991	2	)	)	PUNCT
ma-105	991	3	13	13	NUM
ma-105	991	4	-	-	SYM
ma-105	991	5	75.[5	75.[5	SYM
ma-105	991	6	]	]	X
ma-105	991	7	j.r	j.r	PROPN
ma-105	991	8	.	.	PROPN
ma-105	991	9	beddington	beddington	PROPN
ma-105	991	10	,	,	PUNCT
ma-105	991	11	mutual	mutual	ADJ
ma-105	991	12	interference	interference	NOUN
ma-105	991	13	between	between	ADP
ma-105	991	14	parasites	parasite	NOUN
ma-105	991	15	or	or	CCONJ
ma-105	991	16	predators	predator	NOUN
ma-105	991	17	and	and	CCONJ
ma-105	991	18	its	its	PRON
ma-105	991	19	effect	effect	NOUN
ma-105	991	20	on	on	ADP
ma-105	991	21	searching	search	VERB
ma-105	991	22	efficiency	efficiency	NOUN
ma-105	991	23	,	,	PUNCT
ma-105	991	24	j.	j.	PROPN
ma-105	991	25	animalecol	animalecol	PROPN
ma-105	991	26	.	.	PROPN
ma-105	992	1	44	44	NUM
ma-105	992	2	(	(	PUNCT
ma-105	992	3	1975	1975	NUM
ma-105	992	4	)	)	PUNCT
ma-105	993	1	331	331	NUM
ma-105	993	2	.	.	PUNCT
ma-105	994	1	https://doi.org/10.2307/3866.[6	https://doi.org/10.2307/3866.[6	CCONJ
ma-105	994	2	]	]	PUNCT
ma-105	994	3	a.	a.	NOUN
ma-105	994	4	chatterjee	chatterjee	PROPN
ma-105	994	5	,	,	PUNCT
ma-105	994	6	j.	j.	PROPN
ma-105	994	7	guedj	guedj	PROPN
ma-105	994	8	,	,	PUNCT
ma-105	994	9	a.s	a.s	PROPN
ma-105	994	10	.	.	PROPN
ma-105	994	11	perelson	perelson	PROPN
ma-105	994	12	,	,	PUNCT
ma-105	994	13	mathematical	mathematical	ADJ
ma-105	994	14	modelling	modelling	NOUN
ma-105	994	15	of	of	ADP
ma-105	994	16	hcv	hcv	NOUN
ma-105	994	17	infection	infection	NOUN
ma-105	995	1	:	:	PUNCT
ma-105	995	2	what	what	PRON
ma-105	995	3	can	can	AUX
ma-105	995	4	it	it	PRON
ma-105	995	5	teach	teach	VERB
ma-105	995	6	us	we	PRON
ma-105	995	7	in	in	ADP
ma-105	995	8	the	the	DET
ma-105	995	9	era	era	NOUN
ma-105	995	10	ofdirect	ofdirect	NOUN
ma-105	995	11	-	-	PUNCT
ma-105	995	12	acting	act	VERB
ma-105	995	13	antiviral	antiviral	ADJ
ma-105	995	14	agents	agent	NOUN
ma-105	995	15	?	?	PUNCT
ma-105	995	16	,	,	PUNCT
ma-105	995	17	antivir	antivir	PROPN
ma-105	995	18	.	.	PUNCT
ma-105	996	1	ther	ther	INTJ
ma-105	996	2	.	.	PUNCT
ma-105	997	1	17	17	NUM
ma-105	997	2	(	(	PUNCT
ma-105	997	3	2012	2012	NUM
ma-105	997	4	)	)	PUNCT
ma-105	997	5	1171–1182	1171–1182	NUM
ma-105	997	6	.	.	PUNCT
ma-105	998	1	https://doi.org/10.3851/imp2428.[7	https://doi.org/10.3851/imp2428.[7	PROPN
ma-105	998	2	]	]	X
ma-105	998	3	m.s.f	m.s.f	PROPN
ma-105	998	4	.	.	PUNCT
ma-105	998	5	chong	chong	PROPN
ma-105	998	6	,	,	PUNCT
ma-105	998	7	m.	m.	NOUN
ma-105	998	8	shahrill	shahrill	PROPN
ma-105	998	9	,	,	PUNCT
ma-105	998	10	l.	l.	PROPN
ma-105	998	11	crossley	crossley	PROPN
ma-105	998	12	,	,	PUNCT
ma-105	998	13	et	et	PROPN
ma-105	998	14	al	al	PROPN
ma-105	998	15	.	.	PUNCT
ma-105	999	1	the	the	DET
ma-105	999	2	stability	stability	NOUN
ma-105	999	3	analyses	analysis	NOUN
ma-105	999	4	of	of	ADP
ma-105	999	5	the	the	DET
ma-105	999	6	mathematical	mathematical	ADJ
ma-105	999	7	models	model	NOUN
ma-105	999	8	of	of	ADP
ma-105	999	9	hepatitis	hepatitis	PROPN
ma-105	999	10	c	c	PROPN
ma-105	999	11	virusinfection	virusinfection	PROPN
ma-105	999	12	,	,	PUNCT
ma-105	999	13	modern	modern	ADJ
ma-105	999	14	appl	appl	NOUN
ma-105	999	15	.	.	PUNCT
ma-105	1000	1	sci	sci	PROPN
ma-105	1000	2	.	.	PROPN
ma-105	1000	3	9	9	NUM
ma-105	1000	4	(	(	PUNCT
ma-105	1000	5	2015	2015	NUM
ma-105	1000	6	)	)	PUNCT
ma-105	1000	7	250	250	NUM
ma-105	1000	8	-	-	SYM
ma-105	1000	9	271	271	NUM
ma-105	1000	10	.	.	PUNCT
ma-105	1001	1	https://doi.org/10.5539/mas.v9n3p250.[8	https://doi.org/10.5539/mas.v9n3p250.[8	PROPN
ma-105	1001	2	]	]	X
ma-105	1001	3	s.m	s.m	PROPN
ma-105	1001	4	.	.	PROPN
ma-105	1001	5	ciupe	ciupe	PROPN
ma-105	1001	6	,	,	PUNCT
ma-105	1001	7	r.m	r.m	PROPN
ma-105	1001	8	.	.	PROPN
ma-105	1001	9	ribeiro	ribeiro	PROPN
ma-105	1001	10	,	,	PUNCT
ma-105	1001	11	p.w	p.w	PROPN
ma-105	1001	12	.	.	PROPN
ma-105	1001	13	nelson	nelson	PROPN
ma-105	1001	14	,	,	PUNCT
ma-105	1001	15	a.s	a.s	PROPN
ma-105	1001	16	.	.	PROPN
ma-105	1001	17	perelson	perelson	PROPN
ma-105	1001	18	,	,	PUNCT
ma-105	1001	19	modeling	model	VERB
ma-105	1001	20	the	the	DET
ma-105	1001	21	mechanisms	mechanism	NOUN
ma-105	1001	22	of	of	ADP
ma-105	1001	23	acute	acute	ADJ
ma-105	1001	24	hepatitis	hepatitis	PROPN
ma-105	1001	25	b	b	PROPN
ma-105	1001	26	virus	virus	NOUN
ma-105	1001	27	infection	infection	NOUN
ma-105	1001	28	,	,	PUNCT
ma-105	1001	29	j.	j.	PROPN
ma-105	1001	30	theor	theor	PROPN
ma-105	1001	31	.	.	PUNCT
ma-105	1002	1	biol	biol	PROPN
ma-105	1002	2	.	.	PUNCT
ma-105	1003	1	247	247	NUM
ma-105	1003	2	(	(	PUNCT
ma-105	1003	3	2007	2007	NUM
ma-105	1003	4	)	)	PUNCT
ma-105	1003	5	23–35	23–35	NUM
ma-105	1003	6	.	.	PUNCT
ma-105	1004	1	https://doi.org/10.1016/j.jtbi.2007.02.017.[9	https://doi.org/10.1016/j.jtbi.2007.02.017.[9	PROPN
ma-105	1004	2	]	]	PUNCT
ma-105	1004	3	p.h	p.h	PROPN
ma-105	1004	4	.	.	PROPN
ma-105	1004	5	crowley	crowley	PROPN
ma-105	1004	6	,	,	PUNCT
ma-105	1004	7	e.k	e.k	PROPN
ma-105	1004	8	.	.	PROPN
ma-105	1004	9	martin	martin	PROPN
ma-105	1004	10	,	,	PUNCT
ma-105	1004	11	functional	functional	ADJ
ma-105	1004	12	responses	response	NOUN
ma-105	1004	13	and	and	CCONJ
ma-105	1004	14	interference	interference	NOUN
ma-105	1004	15	within	within	ADP
ma-105	1004	16	and	and	CCONJ
ma-105	1004	17	between	between	ADP
ma-105	1004	18	year	year	NOUN
ma-105	1004	19	classes	class	NOUN
ma-105	1004	20	of	of	ADP
ma-105	1004	21	a	a	DET
ma-105	1004	22	dragonflypopulation	dragonflypopulation	NOUN
ma-105	1004	23	,	,	PUNCT
ma-105	1004	24	j.	j.	PROPN
ma-105	1004	25	north	north	PROPN
ma-105	1004	26	amer	amer	PROPN
ma-105	1004	27	.	.	PUNCT
ma-105	1004	28	benthol	benthol	PROPN
ma-105	1004	29	.	.	PUNCT
ma-105	1005	1	soc	soc	NOUN
ma-105	1005	2	.	.	PUNCT
ma-105	1006	1	8	8	NUM
ma-105	1006	2	(	(	PUNCT
ma-105	1006	3	1989	1989	NUM
ma-105	1006	4	)	)	PUNCT
ma-105	1006	5	211–221	211–221	NUM
ma-105	1006	6	.	.	PUNCT
ma-105	1007	1	https://doi.org/10.2307/1467324.[10	https://doi.org/10.2307/1467324.[10	NUM
ma-105	1007	2	]	]	X
ma-105	1007	3	h.	h.	PROPN
ma-105	1007	4	dahari	dahari	PROPN
ma-105	1007	5	,	,	PUNCT
ma-105	1007	6	r.m	r.m	PROPN
ma-105	1007	7	.	.	PROPN
ma-105	1007	8	ribeiro	ribeiro	PROPN
ma-105	1007	9	,	,	PUNCT
ma-105	1007	10	a.s	a.s	PROPN
ma-105	1007	11	.	.	PROPN
ma-105	1007	12	perelson	perelson	PROPN
ma-105	1007	13	,	,	PUNCT
ma-105	1007	14	triphasic	triphasic	ADJ
ma-105	1007	15	decline	decline	NOUN
ma-105	1007	16	of	of	ADP
ma-105	1007	17	hepatitis	hepatitis	PROPN
ma-105	1007	18	c	c	PROPN
ma-105	1007	19	virus	virus	PROPN
ma-105	1007	20	rna	rna	PROPN
ma-105	1007	21	during	during	ADP
ma-105	1007	22	antiviral	antiviral	ADJ
ma-105	1007	23	therapy	therapy	NOUN
ma-105	1007	24	,	,	PUNCT
ma-105	1007	25	hepa	hepa	NOUN
ma-105	1007	26	-	-	PUNCT
ma-105	1007	27	tology	tology	NOUN
ma-105	1007	28	.	.	PUNCT
ma-105	1008	1	46	46	NUM
ma-105	1008	2	(	(	PUNCT
ma-105	1008	3	2007	2007	NUM
ma-105	1008	4	)	)	PUNCT
ma-105	1008	5	16–21	16–21	NUM
ma-105	1008	6	.	.	PUNCT
ma-105	1009	1	https://doi.org/10.1002/hep.21657.[11	https://doi.org/10.1002/hep.21657.[11	PROPN
ma-105	1009	2	]	]	X
ma-105	1009	3	d.l	d.l	PROPN
ma-105	1009	4	.	.	PROPN
ma-105	1009	5	deangelis	deangelis	PROPN
ma-105	1009	6	,	,	PUNCT
ma-105	1009	7	r.a	r.a	PROPN
ma-105	1009	8	.	.	PROPN
ma-105	1009	9	goldstein	goldstein	PROPN
ma-105	1009	10	,	,	PUNCT
ma-105	1009	11	r.v	r.v	PROPN
ma-105	1009	12	.	.	PROPN
ma-105	1009	13	o’neill	o’neill	PROPN
ma-105	1009	14	,	,	PUNCT
ma-105	1009	15	a	a	DET
ma-105	1009	16	model	model	NOUN
ma-105	1009	17	for	for	ADP
ma-105	1009	18	tropic	tropic	NOUN
ma-105	1009	19	interaction	interaction	NOUN
ma-105	1009	20	,	,	PUNCT
ma-105	1009	21	ecology	ecology	NOUN
ma-105	1009	22	.	.	PUNCT
ma-105	1010	1	56	56	NUM
ma-105	1010	2	(	(	PUNCT
ma-105	1010	3	1975	1975	NUM
ma-105	1010	4	)	)	PUNCT
ma-105	1011	1	881–892	881–892	NUM
ma-105	1011	2	.	.	PUNCT
ma-105	1012	1	https	https	NOUN
ma-105	1012	2	:	:	PUNCT
ma-105	1012	3	//doi.org/10.2307/1936298.[12	//doi.org/10.2307/1936298.[12	PUNCT
ma-105	1012	4	]	]	PUNCT
ma-105	1012	5	c.	c.	PROPN
ma-105	1012	6	goudjo	goudjo	PROPN
ma-105	1012	7	,	,	PUNCT
ma-105	1012	8	b.	b.	PROPN
ma-105	1012	9	lèye	lèye	PROPN
ma-105	1012	10	,	,	PUNCT
ma-105	1012	11	m.	m.	NOUN
ma-105	1012	12	sy	sy	PROPN
ma-105	1012	13	,	,	PUNCT
ma-105	1012	14	weak	weak	ADJ
ma-105	1012	15	solution	solution	NOUN
ma-105	1012	16	to	to	ADP
ma-105	1012	17	a	a	DET
ma-105	1012	18	parabolic	parabolic	ADJ
ma-105	1012	19	nonlinear	nonlinear	ADJ
ma-105	1012	20	system	system	NOUN
ma-105	1012	21	arising	arise	VERB
ma-105	1012	22	in	in	ADP
ma-105	1012	23	biological	biological	ADJ
ma-105	1012	24	dynamic	dynamic	NOUN
ma-105	1012	25	in	in	ADP
ma-105	1012	26	the	the	DET
ma-105	1012	27	soil	soil	NOUN
ma-105	1012	28	,	,	PUNCT
ma-105	1012	29	int	int	NOUN
ma-105	1012	30	.	.	PUNCT
ma-105	1013	1	j.	j.	PROPN
ma-105	1013	2	differ	differ	VERB
ma-105	1013	3	.	.	PUNCT
ma-105	1014	1	equ	equ	PROPN
ma-105	1014	2	.	.	PROPN
ma-105	1014	3	2011	2011	NUM
ma-105	1014	4	(	(	PUNCT
ma-105	1014	5	2011	2011	NUM
ma-105	1014	6	)	)	PUNCT
ma-105	1014	7	831436	831436	NUM
ma-105	1014	8	.	.	PUNCT
ma-105	1015	1	https://doi.org/10.1155/2011/831436.[13	https://doi.org/10.1155/2011/831436.[13	ADJ
ma-105	1015	2	]	]	PUNCT
ma-105	1015	3	j.w.h	j.w.h	ADJ
ma-105	1015	4	.	.	PUNCT
ma-105	1016	1	so	so	ADV
ma-105	1016	2	,	,	PUNCT
ma-105	1016	3	s.a	s.a	PROPN
ma-105	1016	4	.	.	PROPN
ma-105	1016	5	gourley	gourley	PROPN
ma-105	1016	6	,	,	PUNCT
ma-105	1016	7	dynamics	dynamic	NOUN
ma-105	1016	8	of	of	ADP
ma-105	1016	9	a	a	DET
ma-105	1016	10	food	food	NOUN
ma-105	1016	11	-	-	PUNCT
ma-105	1016	12	limited	limit	VERB
ma-105	1016	13	population	population	NOUN
ma-105	1016	14	model	model	NOUN
ma-105	1016	15	incorporating	incorporate	VERB
ma-105	1016	16	nonlocal	nonlocal	ADJ
ma-105	1016	17	delays	delay	NOUN
ma-105	1016	18	on	on	ADP
ma-105	1016	19	a	a	DET
ma-105	1016	20	finitedomain	finitedomain	NOUN
ma-105	1016	21	,	,	PUNCT
ma-105	1016	22	j.	j.	PROPN
ma-105	1016	23	math	math	PROPN
ma-105	1016	24	.	.	PUNCT
ma-105	1017	1	biol	biol	PROPN
ma-105	1017	2	.	.	PUNCT
ma-105	1018	1	44	44	NUM
ma-105	1018	2	(	(	PUNCT
ma-105	1018	3	2002	2002	NUM
ma-105	1018	4	)	)	PUNCT
ma-105	1018	5	49–78	49–78	PROPN
ma-105	1018	6	.	.	PUNCT
ma-105	1018	7	https://doi.org/10.1007/s002850100109.[14	https://doi.org/10.1007/s002850100109.[14	PROPN
ma-105	1018	8	]	]	X
ma-105	1018	9	j.	j.	PROPN
ma-105	1018	10	guedj	guedj	PROPN
ma-105	1018	11	,	,	PUNCT
ma-105	1018	12	a.u	a.u	PROPN
ma-105	1018	13	.	.	PROPN
ma-105	1018	14	neumann	neumann	PROPN
ma-105	1018	15	,	,	PUNCT
ma-105	1018	16	understanding	understand	VERB
ma-105	1018	17	hepatitis	hepatitis	PROPN
ma-105	1018	18	c	c	PROPN
ma-105	1018	19	viral	viral	ADJ
ma-105	1018	20	dynamics	dynamic	NOUN
ma-105	1018	21	with	with	ADP
ma-105	1018	22	direct	direct	ADJ
ma-105	1018	23	-	-	PUNCT
ma-105	1018	24	acting	act	VERB
ma-105	1018	25	antiviral	antiviral	ADJ
ma-105	1018	26	agents	agent	NOUN
ma-105	1018	27	due	due	ADP
ma-105	1018	28	to	to	ADP
ma-105	1018	29	theinterplay	theinterplay	NOUN
ma-105	1018	30	between	between	ADP
ma-105	1018	31	intracellular	intracellular	ADJ
ma-105	1018	32	replication	replication	NOUN
ma-105	1018	33	and	and	CCONJ
ma-105	1018	34	cellular	cellular	ADJ
ma-105	1018	35	infection	infection	NOUN
ma-105	1018	36	dynamics	dynamic	NOUN
ma-105	1018	37	,	,	PUNCT
ma-105	1018	38	j.	j.	PROPN
ma-105	1018	39	theor	theor	PROPN
ma-105	1018	40	.	.	PUNCT
ma-105	1019	1	biol	biol	PROPN
ma-105	1019	2	.	.	PUNCT
ma-105	1020	1	267	267	NUM
ma-105	1020	2	(	(	PUNCT
ma-105	1020	3	2010	2010	NUM
ma-105	1020	4	)	)	PUNCT
ma-105	1020	5	330–340	330–340	NUM
ma-105	1020	6	.	.	PUNCT
ma-105	1021	1	https://doi.org/10.1016/j.jtbi.2010.08.036.[15	https://doi.org/10.1016/j.jtbi.2010.08.036.[15	NOUN
ma-105	1021	2	]	]	X
ma-105	1021	3	k.	k.	PROPN
ma-105	1021	4	hattaf	hattaf	PROPN
ma-105	1021	5	,	,	PUNCT
ma-105	1021	6	n.	n.	PROPN
ma-105	1021	7	yousfi	yousfi	NOUN
ma-105	1021	8	,	,	PUNCT
ma-105	1021	9	global	global	ADJ
ma-105	1021	10	stability	stability	NOUN
ma-105	1021	11	for	for	ADP
ma-105	1021	12	reaction	reaction	NOUN
ma-105	1021	13	–	–	PUNCT
ma-105	1021	14	diffusion	diffusion	NOUN
ma-105	1021	15	equations	equation	NOUN
ma-105	1021	16	in	in	ADP
ma-105	1021	17	biology	biology	NOUN
ma-105	1021	18	,	,	PUNCT
ma-105	1021	19	computers	computer	NOUN
ma-105	1021	20	math	math	NOUN
ma-105	1021	21	.	.	PUNCT
ma-105	1022	1	appl	appl	PROPN
ma-105	1022	2	.	.	PUNCT
ma-105	1023	1	66	66	NUM
ma-105	1023	2	(	(	PUNCT
ma-105	1023	3	2013)1488–1497	2013)1488–1497	NUM
ma-105	1023	4	.	.	PUNCT
ma-105	1024	1	https://doi.org/10.1016/j.camwa.2013.08.023.[16	https://doi.org/10.1016/j.camwa.2013.08.023.[16	PROPN
ma-105	1024	2	]	]	PUNCT
ma-105	1025	1	k.	k.	PROPN
ma-105	1025	2	hattaf	hattaf	PROPN
ma-105	1025	3	,	,	PUNCT
ma-105	1025	4	n.	n.	PROPN
ma-105	1025	5	yousfi	yousfi	NOUN
ma-105	1025	6	,	,	PUNCT
ma-105	1025	7	global	global	ADJ
ma-105	1025	8	stability	stability	NOUN
ma-105	1025	9	of	of	ADP
ma-105	1025	10	a	a	DET
ma-105	1025	11	virus	virus	NOUN
ma-105	1025	12	dynamics	dynamic	NOUN
ma-105	1025	13	model	model	NOUN
ma-105	1025	14	with	with	ADP
ma-105	1025	15	cure	cure	NOUN
ma-105	1025	16	rate	rate	NOUN
ma-105	1025	17	and	and	CCONJ
ma-105	1025	18	absorption	absorption	NOUN
ma-105	1025	19	,	,	PUNCT
ma-105	1025	20	j.	j.	PROPN
ma-105	1025	21	egypt	egypt	PROPN
ma-105	1025	22	.	.	PUNCT
ma-105	1026	1	math	math	PROPN
ma-105	1026	2	.	.	PUNCT
ma-105	1027	1	soc.22	soc.22	NOUN
ma-105	1027	2	(	(	PUNCT
ma-105	1027	3	2014	2014	NUM
ma-105	1027	4	)	)	PUNCT
ma-105	1027	5	386–389	386–389	NUM
ma-105	1027	6	.	.	PUNCT
ma-105	1028	1	https://doi.org/10.1016/j.joems.2013.12.010.[17	https://doi.org/10.1016/j.joems.2013.12.010.[17	PROPN
ma-105	1028	2	]	]	PUNCT
ma-105	1028	3	k.	k.	PROPN
ma-105	1028	4	hattaf	hattaf	PROPN
ma-105	1028	5	,	,	PUNCT
ma-105	1028	6	n.	n.	PROPN
ma-105	1028	7	yousfi	yousfi	NOUN
ma-105	1028	8	,	,	PUNCT
ma-105	1028	9	global	global	ADJ
ma-105	1028	10	dynamics	dynamic	NOUN
ma-105	1028	11	of	of	ADP
ma-105	1028	12	a	a	DET
ma-105	1028	13	delay	delay	NOUN
ma-105	1028	14	reaction	reaction	NOUN
ma-105	1028	15	–	–	PUNCT
ma-105	1028	16	diffusion	diffusion	NOUN
ma-105	1028	17	model	model	NOUN
ma-105	1028	18	for	for	ADP
ma-105	1028	19	viral	viral	ADJ
ma-105	1028	20	infection	infection	NOUN
ma-105	1028	21	with	with	ADP
ma-105	1028	22	specific	specific	ADJ
ma-105	1028	23	functionalresponse	functionalresponse	NOUN
ma-105	1028	24	,	,	PUNCT
ma-105	1028	25	comp	comp	NOUN
ma-105	1028	26	.	.	PUNCT
ma-105	1029	1	appl	appl	PROPN
ma-105	1029	2	.	.	PROPN
ma-105	1029	3	math	math	NOUN
ma-105	1029	4	.	.	PUNCT
ma-105	1030	1	34	34	NUM
ma-105	1030	2	(	(	PUNCT
ma-105	1030	3	2014	2014	NUM
ma-105	1030	4	)	)	PUNCT
ma-105	1031	1	807–818	807–818	NUM
ma-105	1031	2	.	.	PUNCT
ma-105	1032	1	https://doi.org/10.1007/s40314-014-0143-x.[18	https://doi.org/10.1007/s40314-014-0143-x.[18	PUNCT
ma-105	1032	2	]	]	PUNCT
ma-105	1032	3	k.	k.	PROPN
ma-105	1032	4	hattaf	hattaf	PROPN
ma-105	1032	5	,	,	PUNCT
ma-105	1032	6	n.	n.	PROPN
ma-105	1032	7	yousfi	yousfi	PROPN
ma-105	1032	8	,	,	PUNCT
ma-105	1032	9	a	a	DET
ma-105	1032	10	class	class	NOUN
ma-105	1032	11	of	of	ADP
ma-105	1032	12	delayed	delay	VERB
ma-105	1032	13	viral	viral	ADJ
ma-105	1032	14	infection	infection	NOUN
ma-105	1032	15	models	model	NOUN
ma-105	1032	16	with	with	ADP
ma-105	1032	17	general	general	ADJ
ma-105	1032	18	incidence	incidence	NOUN
ma-105	1032	19	rate	rate	NOUN
ma-105	1032	20	and	and	CCONJ
ma-105	1032	21	adaptive	adaptive	ADJ
ma-105	1032	22	immuneresponse	immuneresponse	NOUN
ma-105	1032	23	,	,	PUNCT
ma-105	1032	24	int	int	NOUN
ma-105	1032	25	.	.	PUNCT
ma-105	1033	1	j.	j.	PROPN
ma-105	1033	2	dynam	dynam	PROPN
ma-105	1033	3	.	.	PUNCT
ma-105	1034	1	control	control	NOUN
ma-105	1034	2	.	.	PUNCT
ma-105	1035	1	4	4	NUM
ma-105	1035	2	(	(	PUNCT
ma-105	1035	3	2015	2015	NUM
ma-105	1035	4	)	)	PUNCT
ma-105	1035	5	254–265	254–265	NUM
ma-105	1035	6	.	.	PUNCT
ma-105	1036	1	https://doi.org/10.1007/s40435-015-0158-1.[19	https://doi.org/10.1007/s40435-015-0158-1.[19	NOUN
ma-105	1036	2	]	]	PUNCT
ma-105	1036	3	k.	k.	PROPN
ma-105	1036	4	hattaf	hattaf	PROPN
ma-105	1036	5	,	,	PUNCT
ma-105	1036	6	n.	n.	PROPN
ma-105	1036	7	yousfi	yousfi	PROPN
ma-105	1036	8	,	,	PUNCT
ma-105	1036	9	a.	a.	NOUN
ma-105	1036	10	tridane	tridane	NOUN
ma-105	1036	11	,	,	PUNCT
ma-105	1036	12	mathematical	mathematical	ADJ
ma-105	1036	13	analysis	analysis	NOUN
ma-105	1036	14	of	of	ADP
ma-105	1036	15	a	a	DET
ma-105	1036	16	virus	virus	NOUN
ma-105	1036	17	dynamics	dynamic	NOUN
ma-105	1036	18	model	model	NOUN
ma-105	1036	19	with	with	ADP
ma-105	1036	20	general	general	ADJ
ma-105	1036	21	incidence	incidence	NOUN
ma-105	1036	22	rate	rate	NOUN
ma-105	1036	23	andcure	andcure	NOUN
ma-105	1036	24	rate	rate	NOUN
ma-105	1036	25	,	,	PUNCT
ma-105	1036	26	nonlinear	nonlinear	ADJ
ma-105	1036	27	anal	anal	NOUN
ma-105	1036	28	.	.	PUNCT
ma-105	1036	29	:	:	PUNCT
ma-105	1037	1	real	real	ADJ
ma-105	1037	2	world	world	NOUN
ma-105	1037	3	appl	appl	PROPN
ma-105	1037	4	.	.	PROPN
ma-105	1038	1	13	13	NUM
ma-105	1038	2	(	(	PUNCT
ma-105	1038	3	2012	2012	NUM
ma-105	1038	4	)	)	PUNCT
ma-105	1038	5	1866–1872	1866–1872	NUM
ma-105	1038	6	.	.	PUNCT
ma-105	1039	1	https://doi.org/10.1016/j.nonrwa.2011	https://doi.org/10.1016/j.nonrwa.2011	PROPN
ma-105	1039	2	.	.	PUNCT
ma-105	1040	1	12.015.[20	12.015.[20	NUM
ma-105	1040	2	]	]	X
ma-105	1040	3	k.	k.	PROPN
ma-105	1040	4	hattaf	hattaf	PROPN
ma-105	1040	5	,	,	PUNCT
ma-105	1040	6	n.	n.	PROPN
ma-105	1040	7	yousfi	yousfi	PROPN
ma-105	1040	8	,	,	PUNCT
ma-105	1040	9	a.	a.	NOUN
ma-105	1040	10	tridane	tridane	NOUN
ma-105	1040	11	,	,	PUNCT
ma-105	1040	12	a	a	DET
ma-105	1040	13	delay	delay	NOUN
ma-105	1040	14	virus	virus	NOUN
ma-105	1040	15	dynamics	dynamic	NOUN
ma-105	1040	16	model	model	NOUN
ma-105	1040	17	with	with	ADP
ma-105	1040	18	general	general	ADJ
ma-105	1040	19	incidence	incidence	NOUN
ma-105	1040	20	rate	rate	NOUN
ma-105	1040	21	,	,	PUNCT
ma-105	1040	22	differ	differ	VERB
ma-105	1040	23	.	.	PUNCT
ma-105	1041	1	equ	equ	PROPN
ma-105	1041	2	.	.	PUNCT
ma-105	1041	3	dyn	dyn	PROPN
ma-105	1041	4	.	.	PUNCT
ma-105	1042	1	syst.22	syst.22	PROPN
ma-105	1042	2	(	(	PUNCT
ma-105	1042	3	2013	2013	NUM
ma-105	1042	4	)	)	PUNCT
ma-105	1042	5	181–190	181–190	NUM
ma-105	1042	6	.	.	PUNCT
ma-105	1042	7	https://doi.org/10.1007/s12591-013-0167-5.[21	https://doi.org/10.1007/s12591-013-0167-5.[21	PROPN
ma-105	1042	8	]	]	PUNCT
ma-105	1043	1	k.	k.	PROPN
ma-105	1043	2	hattaf	hattaf	PROPN
ma-105	1043	3	,	,	PUNCT
ma-105	1043	4	n.	n.	PROPN
ma-105	1043	5	yousfi	yousfi	PROPN
ma-105	1043	6	,	,	PUNCT
ma-105	1043	7	a.	a.	NOUN
ma-105	1043	8	tridane	tridane	NOUN
ma-105	1043	9	,	,	PUNCT
ma-105	1043	10	stability	stability	NOUN
ma-105	1043	11	analysis	analysis	NOUN
ma-105	1043	12	of	of	ADP
ma-105	1043	13	a	a	DET
ma-105	1043	14	virus	virus	NOUN
ma-105	1043	15	dynamics	dynamic	NOUN
ma-105	1043	16	model	model	NOUN
ma-105	1043	17	with	with	ADP
ma-105	1043	18	general	general	ADJ
ma-105	1043	19	incidence	incidence	NOUN
ma-105	1043	20	rate	rate	NOUN
ma-105	1043	21	and	and	CCONJ
ma-105	1043	22	twodelays	twodelay	NOUN
ma-105	1043	23	,	,	PUNCT
ma-105	1043	24	appl	appl	PROPN
ma-105	1043	25	.	.	PROPN
ma-105	1043	26	math	math	PROPN
ma-105	1043	27	.	.	PUNCT
ma-105	1044	1	comput	comput	NOUN
ma-105	1044	2	.	.	PUNCT
ma-105	1045	1	221	221	NUM
ma-105	1045	2	(	(	PUNCT
ma-105	1045	3	2013	2013	NUM
ma-105	1045	4	)	)	PUNCT
ma-105	1046	1	514–521	514–521	NUM
ma-105	1046	2	.	.	PUNCT
ma-105	1047	1	https://doi.org/10.1016/j.amc.2013.07.005	https://doi.org/10.1016/j.amc.2013.07.005	PROPN
ma-105	1047	2	.	.	PUNCT
ma-105	1048	1	https://doi.org/10.28924/ada/ma.3.1	https://doi.org/10.28924/ada/ma.3.1	PROPN
ma-105	1048	2	https://doi.org/10.1016/0362-546x(88)90073-9	https://doi.org/10.1016/0362-546x(88)90073-9	PROPN
ma-105	1048	3	https://doi.org/10.1007/bf01215256	https://doi.org/10.1007/bf01215256	X
ma-105	1048	4	https://doi.org/10.1007/bf01215256	https://doi.org/10.1007/bf01215256	X
ma-105	1048	5	https://doi.org/10.2307/3866	https://doi.org/10.2307/3866	PROPN
ma-105	1048	6	https://doi.org/10.3851/imp2428	https://doi.org/10.3851/imp2428	PROPN
ma-105	1048	7	https://doi.org/10.5539/mas.v9n3p250	https://doi.org/10.5539/mas.v9n3p250	PROPN
ma-105	1048	8	https://doi.org/10.1016/j.jtbi.2007.02.017	https://doi.org/10.1016/j.jtbi.2007.02.017	PROPN
ma-105	1048	9	https://doi.org/10.2307/1467324	https://doi.org/10.2307/1467324	PROPN
ma-105	1048	10	https://doi.org/10.1002/hep.21657	https://doi.org/10.1002/hep.21657	PROPN
ma-105	1048	11	https://doi.org/10.2307/1936298	https://doi.org/10.2307/1936298	NOUN
ma-105	1048	12	https://doi.org/10.2307/1936298	https://doi.org/10.2307/1936298	X
ma-105	1049	1	https://doi.org/10.1155/2011/831436	https://doi.org/10.1155/2011/831436	X
ma-105	1049	2	https://doi.org/10.1007/s002850100109	https://doi.org/10.1007/s002850100109	NUM
ma-105	1049	3	https://doi.org/10.1016/j.jtbi.2010.08.036	https://doi.org/10.1016/j.jtbi.2010.08.036	PROPN
ma-105	1049	4	https://doi.org/10.1016/j.camwa.2013.08.023	https://doi.org/10.1016/j.camwa.2013.08.023	PROPN
ma-105	1049	5	https://doi.org/10.1016/j.joems.2013.12.010	https://doi.org/10.1016/j.joems.2013.12.010	ADJ
ma-105	1049	6	https://doi.org/10.1007/s40314-014-0143-x	https://doi.org/10.1007/s40314-014-0143-x	NOUN
ma-105	1049	7	https://doi.org/10.1007/s40435-015-0158-1	https://doi.org/10.1007/s40435-015-0158-1	NOUN
ma-105	1049	8	https://doi.org/10.1016/j.nonrwa.2011.12.015	https://doi.org/10.1016/j.nonrwa.2011.12.015	X
ma-105	1049	9	https://doi.org/10.1016/j.nonrwa.2011.12.015	https://doi.org/10.1016/j.nonrwa.2011.12.015	PROPN
ma-105	1049	10	https://doi.org/10.1007/s12591-013-0167-5	https://doi.org/10.1007/s12591-013-0167-5	NUM
ma-105	1049	11	https://doi.org/10.1016/j.amc.2013.07.005	https://doi.org/10.1016/j.amc.2013.07.005	NUM
ma-105	1049	12	eur	eur	PROPN
ma-105	1049	13	.	.	PUNCT
ma-105	1050	1	j.	j.	PROPN
ma-105	1050	2	math	math	PROPN
ma-105	1050	3	.	.	PUNCT
ma-105	1051	1	anal	anal	PROPN
ma-105	1051	2	.	.	PUNCT
ma-105	1052	1	10.28924	10.28924	NUM
ma-105	1052	2	/	/	SYM
ma-105	1052	3	ada	ada	PROPN
ma-105	1052	4	/	/	SYM
ma-105	1052	5	ma.3.1	ma.3.1	PROPN
ma-105	1052	6	37	37	NUM
ma-105	1053	1	[	[	X
ma-105	1053	2	22	22	NUM
ma-105	1053	3	]	]	X
ma-105	1053	4	d.	d.	PROPN
ma-105	1053	5	henry	henry	PROPN
ma-105	1053	6	,	,	PUNCT
ma-105	1053	7	geometric	geometric	ADJ
ma-105	1053	8	theory	theory	NOUN
ma-105	1053	9	of	of	ADP
ma-105	1053	10	semilinear	semilinear	PROPN
ma-105	1053	11	parabolic	parabolic	PROPN
ma-105	1053	12	equations	equation	NOUN
ma-105	1053	13	,	,	PUNCT
ma-105	1053	14	1st	1st	PROPN
ma-105	1053	15	edition	edition	NOUN
ma-105	1053	16	,	,	PUNCT
ma-105	1053	17	springer	springer	NOUN
ma-105	1053	18	-	-	PUNCT
ma-105	1053	19	verlag	verlag	PROPN
ma-105	1053	20	,	,	PUNCT
ma-105	1053	21	new	new	PROPN
ma-105	1053	22	york	york	PROPN
ma-105	1053	23	,	,	PUNCT
ma-105	1053	24	(	(	PUNCT
ma-105	1053	25	1981).[23	1981).[23	X
ma-105	1053	26	]	]	X
ma-105	1053	27	d.	d.	PROPN
ma-105	1053	28	henry	henry	PROPN
ma-105	1053	29	,	,	PUNCT
ma-105	1053	30	geometric	geometric	ADJ
ma-105	1053	31	theory	theory	NOUN
ma-105	1053	32	of	of	ADP
ma-105	1053	33	semilinear	semilinear	PROPN
ma-105	1053	34	parabolic	parabolic	PROPN
ma-105	1053	35	equations	equation	NOUN
ma-105	1053	36	,	,	PUNCT
ma-105	1053	37	840	840	NUM
ma-105	1053	38	of	of	ADP
ma-105	1053	39	lecture	lecture	NOUN
ma-105	1053	40	notes	note	NOUN
ma-105	1053	41	in	in	ADP
ma-105	1053	42	mathematics	mathematic	NOUN
ma-105	1053	43	,	,	PUNCT
ma-105	1053	44	new	new	PROPN
ma-105	1053	45	york	york	PROPN
ma-105	1053	46	,	,	PUNCT
ma-105	1053	47	usa	usa	PROPN
ma-105	1053	48	(	(	PUNCT
ma-105	1053	49	1993).[24	1993).[24	NUM
ma-105	1053	50	]	]	X
ma-105	1053	51	s.l	s.l	PROPN
ma-105	1053	52	.	.	PROPN
ma-105	1053	53	hollis	hollis	PROPN
ma-105	1053	54	,	,	PUNCT
ma-105	1053	55	r.h	r.h	PROPN
ma-105	1053	56	.	.	PROPN
ma-105	1053	57	martin	martin	PROPN
ma-105	1053	58	,	,	PUNCT
ma-105	1053	59	jr	jr	PROPN
ma-105	1053	60	.	.	PROPN
ma-105	1053	61	,	,	PUNCT
ma-105	1053	62	m.	m.	NOUN
ma-105	1053	63	pierre	pierre	PROPN
ma-105	1053	64	,	,	PUNCT
ma-105	1053	65	global	global	ADJ
ma-105	1053	66	existence	existence	NOUN
ma-105	1053	67	and	and	CCONJ
ma-105	1053	68	boundedness	boundedness	NOUN
ma-105	1053	69	in	in	ADP
ma-105	1053	70	reaction	reaction	NOUN
ma-105	1053	71	-	-	PUNCT
ma-105	1053	72	diffusion	diffusion	NOUN
ma-105	1053	73	systems	system	NOUN
ma-105	1053	74	,	,	PUNCT
ma-105	1053	75	siam	siam	ADJ
ma-105	1053	76	j.math	j.math	NOUN
ma-105	1053	77	.	.	PUNCT
ma-105	1054	1	anal	anal	PROPN
ma-105	1054	2	.	.	PUNCT
ma-105	1055	1	18	18	NUM
ma-105	1055	2	(	(	PUNCT
ma-105	1055	3	1987	1987	NUM
ma-105	1055	4	)	)	PUNCT
ma-105	1056	1	744–761	744–761	NUM
ma-105	1056	2	.	.	PUNCT
ma-105	1057	1	https://doi.org/10.1137/0518057.[25	https://doi.org/10.1137/0518057.[25	PROPN
ma-105	1057	2	]	]	X
ma-105	1057	3	g.	g.	PROPN
ma-105	1057	4	huang	huang	PROPN
ma-105	1057	5	,	,	PUNCT
ma-105	1057	6	w.	w.	PROPN
ma-105	1057	7	ma	ma	PROPN
ma-105	1057	8	,	,	PUNCT
ma-105	1057	9	y.	y.	PROPN
ma-105	1057	10	takeuchi	takeuchi	PROPN
ma-105	1057	11	,	,	PUNCT
ma-105	1057	12	global	global	ADJ
ma-105	1057	13	properties	property	NOUN
ma-105	1057	14	for	for	ADP
ma-105	1057	15	virus	virus	NOUN
ma-105	1057	16	dynamics	dynamic	NOUN
ma-105	1057	17	model	model	NOUN
ma-105	1057	18	with	with	ADP
ma-105	1057	19	beddington	beddington	PROPN
ma-105	1057	20	–	–	PUNCT
ma-105	1057	21	deangelis	deangelis	PROPN
ma-105	1057	22	functionalresponse	functionalresponse	PROPN
ma-105	1057	23	,	,	PUNCT
ma-105	1057	24	appl	appl	PROPN
ma-105	1057	25	.	.	PROPN
ma-105	1057	26	math	math	PROPN
ma-105	1057	27	.	.	PUNCT
ma-105	1058	1	lett	lett	PROPN
ma-105	1058	2	.	.	PUNCT
ma-105	1059	1	22	22	NUM
ma-105	1059	2	(	(	PUNCT
ma-105	1059	3	2009	2009	NUM
ma-105	1059	4	)	)	PUNCT
ma-105	1059	5	1690–1693	1690–1693	NUM
ma-105	1059	6	.	.	PUNCT
ma-105	1060	1	https://doi.org/10.1016/j.aml.2009.06.004.[26	https://doi.org/10.1016/j.aml.2009.06.004.[26	PROPN
ma-105	1060	2	]	]	PUNCT
ma-105	1060	3	g.	g.	PROPN
ma-105	1060	4	huang	huang	PROPN
ma-105	1060	5	,	,	PUNCT
ma-105	1060	6	w.	w.	PROPN
ma-105	1060	7	ma	ma	PROPN
ma-105	1060	8	,	,	PUNCT
ma-105	1060	9	y.	y.	PROPN
ma-105	1060	10	takeuchi	takeuchi	PROPN
ma-105	1060	11	,	,	PUNCT
ma-105	1060	12	global	global	ADJ
ma-105	1060	13	analysis	analysis	NOUN
ma-105	1060	14	for	for	ADP
ma-105	1060	15	delay	delay	NOUN
ma-105	1060	16	virus	virus	NOUN
ma-105	1060	17	dynamics	dynamic	NOUN
ma-105	1060	18	model	model	NOUN
ma-105	1060	19	with	with	ADP
ma-105	1060	20	beddington	beddington	PROPN
ma-105	1060	21	–	–	PUNCT
ma-105	1060	22	deangelis	deangelis	PROPN
ma-105	1060	23	functionalresponse	functionalresponse	PROPN
ma-105	1060	24	,	,	PUNCT
ma-105	1060	25	appl	appl	PROPN
ma-105	1060	26	.	.	PROPN
ma-105	1060	27	math	math	PROPN
ma-105	1060	28	.	.	PUNCT
ma-105	1061	1	lett	lett	PROPN
ma-105	1061	2	.	.	PROPN
ma-105	1062	1	24	24	NUM
ma-105	1062	2	(	(	PUNCT
ma-105	1062	3	2011	2011	NUM
ma-105	1062	4	)	)	PUNCT
ma-105	1062	5	1199–1203	1199–1203	NUM
ma-105	1062	6	.	.	PUNCT
ma-105	1063	1	https://doi.org/10.1016/j.aml.2011.02.007.[27	https://doi.org/10.1016/j.aml.2011.02.007.[27	PROPN
ma-105	1063	2	]	]	PUNCT
ma-105	1063	3	h.	h.	PROPN
ma-105	1063	4	khalil	khalil	PROPN
ma-105	1063	5	,	,	PUNCT
ma-105	1063	6	nonlinear	nonlinear	ADJ
ma-105	1063	7	systems	system	NOUN
ma-105	1063	8	,	,	PUNCT
ma-105	1063	9	3rd	3rd	ADJ
ma-105	1063	10	edn	edn	NOUN
ma-105	1063	11	.	.	PUNCT
ma-105	1064	1	prentice	prentice	PROPN
ma-105	1064	2	hall	hall	PROPN
ma-105	1064	3	,	,	PUNCT
ma-105	1064	4	new	new	PROPN
ma-105	1064	5	york	york	PROPN
ma-105	1064	6	,	,	PUNCT
ma-105	1064	7	(	(	PUNCT
ma-105	1064	8	2002).[28	2002).[28	X
ma-105	1064	9	]	]	X
ma-105	1064	10	d.	d.	PROPN
ma-105	1064	11	li	li	PROPN
ma-105	1064	12	,	,	PUNCT
ma-105	1064	13	w.	w.	PROPN
ma-105	1064	14	ma	ma	PROPN
ma-105	1064	15	,	,	PUNCT
ma-105	1064	16	asymptotic	asymptotic	ADJ
ma-105	1064	17	properties	property	NOUN
ma-105	1064	18	of	of	ADP
ma-105	1064	19	a	a	DET
ma-105	1064	20	hiv-1	hiv-1	ADJ
ma-105	1064	21	infection	infection	NOUN
ma-105	1064	22	model	model	NOUN
ma-105	1064	23	with	with	ADP
ma-105	1064	24	time	time	NOUN
ma-105	1064	25	delay	delay	NOUN
ma-105	1064	26	,	,	PUNCT
ma-105	1064	27	j.	j.	PROPN
ma-105	1064	28	math	math	PROPN
ma-105	1064	29	.	.	PUNCT
ma-105	1065	1	anal	anal	PROPN
ma-105	1065	2	.	.	PUNCT
ma-105	1066	1	appl	appl	PROPN
ma-105	1066	2	.	.	PUNCT
ma-105	1067	1	335	335	NUM
ma-105	1067	2	(	(	PUNCT
ma-105	1067	3	2007)683–691	2007)683–691	NUM
ma-105	1067	4	.	.	PUNCT
ma-105	1068	1	https://doi.org/10.1016/j.jmaa.2007.02.006.[29	https://doi.org/10.1016/j.jmaa.2007.02.006.[29	PROPN
ma-105	1068	2	]	]	X
ma-105	1068	3	l.	l.	PROPN
ma-105	1068	4	min	min	PROPN
ma-105	1068	5	,	,	PUNCT
ma-105	1068	6	y.	y.	PROPN
ma-105	1068	7	su	su	PROPN
ma-105	1068	8	,	,	PUNCT
ma-105	1068	9	y.	y.	PROPN
ma-105	1068	10	kuang	kuang	PROPN
ma-105	1068	11	,	,	PUNCT
ma-105	1068	12	mathematical	mathematical	ADJ
ma-105	1068	13	analysis	analysis	NOUN
ma-105	1068	14	of	of	ADP
ma-105	1068	15	a	a	DET
ma-105	1068	16	basic	basic	ADJ
ma-105	1068	17	model	model	NOUN
ma-105	1068	18	of	of	ADP
ma-105	1068	19	virus	virus	NOUN
ma-105	1068	20	infection	infection	NOUN
ma-105	1068	21	with	with	ADP
ma-105	1068	22	application	application	NOUN
ma-105	1068	23	to	to	ADP
ma-105	1068	24	hbv	hbv	NOUN
ma-105	1068	25	infection	infection	NOUN
ma-105	1068	26	,	,	PUNCT
ma-105	1068	27	rocky	rocky	ADJ
ma-105	1068	28	mount	mount	PROPN
ma-105	1068	29	.	.	PUNCT
ma-105	1069	1	j.	j.	PROPN
ma-105	1069	2	math	math	PROPN
ma-105	1069	3	.	.	PUNCT
ma-105	1070	1	38	38	NUM
ma-105	1070	2	(	(	PUNCT
ma-105	1070	3	2008	2008	NUM
ma-105	1070	4	)	)	PUNCT
ma-105	1070	5	1573	1573	NUM
ma-105	1070	6	-	-	SYM
ma-105	1070	7	1585	1585	NUM
ma-105	1070	8	.	.	PUNCT
ma-105	1071	1	https://www.jstor.org/stable/44239519.[30	https://www.jstor.org/stable/44239519.[30	NOUN
ma-105	1071	2	]	]	PUNCT
ma-105	1071	3	a.u	a.u	PROPN
ma-105	1071	4	.	.	PROPN
ma-105	1071	5	neumann	neumann	PROPN
ma-105	1071	6	,	,	PUNCT
ma-105	1071	7	n.p	n.p	PROPN
ma-105	1071	8	.	.	PROPN
ma-105	1071	9	lam	lam	PROPN
ma-105	1071	10	,	,	PUNCT
ma-105	1071	11	h.	h.	PROPN
ma-105	1071	12	dahari	dahari	PROPN
ma-105	1071	13	,	,	PUNCT
ma-105	1071	14	et	et	PROPN
ma-105	1071	15	al	al	PROPN
ma-105	1071	16	.	.	PUNCT
ma-105	1072	1	hepatitis	hepatitis	PROPN
ma-105	1072	2	c	c	PROPN
ma-105	1072	3	viral	viral	ADJ
ma-105	1072	4	dynamics	dynamic	NOUN
ma-105	1072	5	in	in	ADP
ma-105	1072	6	vivo	vivo	NOUN
ma-105	1072	7	and	and	CCONJ
ma-105	1072	8	the	the	DET
ma-105	1072	9	antiviral	antiviral	ADJ
ma-105	1072	10	efficacy	efficacy	NOUN
ma-105	1072	11	of	of	ADP
ma-105	1072	12	interferon	interferon	ADJ
ma-105	1072	13	-	-	PUNCT
ma-105	1072	14	αtherapy	αtherapy	NOUN
ma-105	1072	15	,	,	PUNCT
ma-105	1072	16	science	science	NOUN
ma-105	1072	17	.	.	PUNCT
ma-105	1073	1	282	282	NUM
ma-105	1073	2	(	(	PUNCT
ma-105	1073	3	1998	1998	NUM
ma-105	1073	4	)	)	PUNCT
ma-105	1074	1	103–107	103–107	NUM
ma-105	1074	2	.	.	PUNCT
ma-105	1075	1	https://doi.org/10.1126/science.282.5386.103.[31	https://doi.org/10.1126/science.282.5386.103.[31	X
ma-105	1075	2	]	]	X
ma-105	1075	3	m.a	m.a	PROPN
ma-105	1075	4	.	.	PROPN
ma-105	1075	5	nowak	nowak	PROPN
ma-105	1075	6	,	,	PUNCT
ma-105	1075	7	c.r.m	c.r.m	PROPN
ma-105	1075	8	.	.	PUNCT
ma-105	1075	9	bangham	bangham	PROPN
ma-105	1075	10	,	,	PUNCT
ma-105	1075	11	population	population	NOUN
ma-105	1075	12	dynamics	dynamic	NOUN
ma-105	1075	13	of	of	ADP
ma-105	1075	14	immune	immune	ADJ
ma-105	1075	15	responses	response	NOUN
ma-105	1075	16	to	to	ADP
ma-105	1075	17	persistent	persistent	ADJ
ma-105	1075	18	viruses	virus	NOUN
ma-105	1075	19	,	,	PUNCT
ma-105	1075	20	science	science	NOUN
ma-105	1075	21	.	.	PUNCT
ma-105	1076	1	272	272	NUM
ma-105	1076	2	(	(	PUNCT
ma-105	1076	3	1996)74–79	1996)74–79	NOUN
ma-105	1076	4	.	.	PUNCT
ma-105	1077	1	https://doi.org/10.1126/science.272.5258.74.[32	https://doi.org/10.1126/science.272.5258.74.[32	NOUN
ma-105	1077	2	]	]	X
ma-105	1077	3	m.a	m.a	PROPN
ma-105	1077	4	.	.	PROPN
ma-105	1077	5	nowak	nowak	PROPN
ma-105	1077	6	,	,	PUNCT
ma-105	1077	7	s.	s.	PROPN
ma-105	1077	8	bonhoeffer	bonhoeffer	PROPN
ma-105	1077	9	,	,	PUNCT
ma-105	1077	10	a.m.	a.m.	PROPN
ma-105	1077	11	hill	hill	PROPN
ma-105	1077	12	,	,	PUNCT
ma-105	1077	13	et	et	PROPN
ma-105	1077	14	al	al	PROPN
ma-105	1077	15	.	.	PROPN
ma-105	1077	16	viral	viral	ADJ
ma-105	1077	17	dynamics	dynamic	NOUN
ma-105	1077	18	in	in	ADP
ma-105	1077	19	hepatitis	hepatitis	PROPN
ma-105	1077	20	b	b	PROPN
ma-105	1077	21	virus	virus	NOUN
ma-105	1077	22	infection	infection	NOUN
ma-105	1077	23	.	.	PUNCT
ma-105	1077	24	,	,	PUNCT
ma-105	1077	25	proc	proc	PROPN
ma-105	1077	26	.	.	PUNCT
ma-105	1078	1	natl	natl	PROPN
ma-105	1078	2	.	.	PUNCT
ma-105	1079	1	acad	acad	PROPN
ma-105	1079	2	.	.	PUNCT
ma-105	1080	1	sci.u.s.a	sci.u.s.a	PROPN
ma-105	1080	2	.	.	PROPN
ma-105	1081	1	93	93	NUM
ma-105	1081	2	(	(	PUNCT
ma-105	1081	3	1996	1996	NUM
ma-105	1081	4	)	)	PUNCT
ma-105	1081	5	4398–4402	4398–4402	NOUN
ma-105	1081	6	.	.	PUNCT
ma-105	1082	1	https://doi.org/10.1073/pnas.93.9.4398.[33	https://doi.org/10.1073/pnas.93.9.4398.[33	NOUN
ma-105	1082	2	]	]	X
ma-105	1082	3	m.h	m.h	PROPN
ma-105	1082	4	.	.	PROPN
ma-105	1082	5	protter	protter	PROPN
ma-105	1082	6	,	,	PUNCT
ma-105	1082	7	h.p	h.p	PROPN
ma-105	1082	8	.	.	PROPN
ma-105	1082	9	weinberger	weinberger	PROPN
ma-105	1082	10	,	,	PUNCT
ma-105	1082	11	maximum	maximum	ADJ
ma-105	1082	12	principle	principle	NOUN
ma-105	1082	13	in	in	ADP
ma-105	1082	14	differential	differential	ADJ
ma-105	1082	15	equations	equation	NOUN
ma-105	1082	16	,	,	PUNCT
ma-105	1082	17	prentice	prentice	NOUN
ma-105	1082	18	-	-	PUNCT
ma-105	1082	19	hall	hall	NOUN
ma-105	1082	20	,	,	PUNCT
ma-105	1082	21	englewood	englewood	PROPN
ma-105	1082	22	cliffs	cliffs	PROPN
ma-105	1082	23	,	,	PUNCT
ma-105	1082	24	newjersey	newjersey	NOUN
ma-105	1082	25	,	,	PUNCT
ma-105	1082	26	usa	usa	PROPN
ma-105	1082	27	(	(	PUNCT
ma-105	1082	28	1967).[34	1967).[34	PROPN
ma-105	1082	29	]	]	X
ma-105	1082	30	d.	d.	PROPN
ma-105	1082	31	riad	riad	PROPN
ma-105	1082	32	,	,	PUNCT
ma-105	1082	33	k.	k.	PROPN
ma-105	1082	34	hattaf	hattaf	PROPN
ma-105	1082	35	,	,	PUNCT
ma-105	1082	36	n.	n.	PROPN
ma-105	1082	37	yousfi	yousfi	NOUN
ma-105	1082	38	,	,	PUNCT
ma-105	1082	39	dynamics	dynamic	NOUN
ma-105	1082	40	of	of	ADP
ma-105	1082	41	capital	capital	NOUN
ma-105	1082	42	-	-	PUNCT
ma-105	1082	43	labour	labour	NOUN
ma-105	1082	44	model	model	NOUN
ma-105	1082	45	with	with	ADP
ma-105	1082	46	hattaf	hattaf	NOUN
ma-105	1082	47	-	-	PUNCT
ma-105	1082	48	yousfi	yousfi	ADJ
ma-105	1082	49	functional	functional	ADJ
ma-105	1082	50	response	response	NOUN
ma-105	1082	51	,	,	PUNCT
ma-105	1082	52	br	br	PROPN
ma-105	1082	53	.	.	PUNCT
ma-105	1083	1	j.	j.	PROPN
ma-105	1083	2	math.computer	math.computer	PROPN
ma-105	1083	3	sci	sci	PROPN
ma-105	1083	4	.	.	PROPN
ma-105	1083	5	18	18	NUM
ma-105	1083	6	(	(	PUNCT
ma-105	1083	7	2016	2016	NUM
ma-105	1083	8	)	)	PUNCT
ma-105	1083	9	1–7	1–7	X
ma-105	1083	10	.	.	PUNCT
ma-105	1083	11	https://doi.org/10.9734/bjmcs/2016/28640.[35	https://doi.org/10.9734/bjmcs/2016/28640.[35	PROPN
ma-105	1083	12	]	]	X
ma-105	1083	13	l.	l.	PROPN
ma-105	1083	14	rong	rong	PROPN
ma-105	1083	15	,	,	PUNCT
ma-105	1083	16	a.s	a.s	PROPN
ma-105	1083	17	.	.	PROPN
ma-105	1083	18	perelson	perelson	PROPN
ma-105	1083	19	,	,	PUNCT
ma-105	1083	20	mathematical	mathematical	ADJ
ma-105	1083	21	analysis	analysis	NOUN
ma-105	1083	22	of	of	ADP
ma-105	1083	23	multiscale	multiscale	ADJ
ma-105	1083	24	models	model	NOUN
ma-105	1083	25	for	for	ADP
ma-105	1083	26	hepatitis	hepatitis	PROPN
ma-105	1083	27	c	c	PROPN
ma-105	1083	28	virus	virus	NOUN
ma-105	1083	29	dynamics	dynamic	NOUN
ma-105	1083	30	under	under	ADP
ma-105	1083	31	therapy	therapy	NOUN
ma-105	1083	32	withdirect	withdirect	ADV
ma-105	1083	33	-	-	PUNCT
ma-105	1083	34	acting	act	VERB
ma-105	1083	35	antiviral	antiviral	ADJ
ma-105	1083	36	agents	agent	NOUN
ma-105	1083	37	,	,	PUNCT
ma-105	1083	38	math	math	NOUN
ma-105	1083	39	.	.	PUNCT
ma-105	1083	40	biosc	biosc	PROPN
ma-105	1083	41	.	.	PUNCT
ma-105	1084	1	245	245	NUM
ma-105	1084	2	(	(	PUNCT
ma-105	1084	3	2013	2013	NUM
ma-105	1084	4	)	)	PUNCT
ma-105	1084	5	22–30	22–30	NUM
ma-105	1084	6	.	.	PUNCT
ma-105	1085	1	https://doi.org/10.1016/j.mbs.2013.04.012.[36	https://doi.org/10.1016/j.mbs.2013.04.012.[36	PROPN
ma-105	1085	2	]	]	PUNCT
ma-105	1085	3	x.	x.	NOUN
ma-105	1085	4	song	song	PROPN
ma-105	1085	5	,	,	PUNCT
ma-105	1085	6	a.u	a.u	PROPN
ma-105	1085	7	.	.	PROPN
ma-105	1085	8	neumann	neumann	PROPN
ma-105	1085	9	,	,	PUNCT
ma-105	1085	10	global	global	ADJ
ma-105	1085	11	stability	stability	NOUN
ma-105	1085	12	and	and	CCONJ
ma-105	1085	13	periodic	periodic	ADJ
ma-105	1085	14	solution	solution	NOUN
ma-105	1085	15	of	of	ADP
ma-105	1085	16	the	the	DET
ma-105	1085	17	viral	viral	ADJ
ma-105	1085	18	dynamics	dynamic	NOUN
ma-105	1085	19	,	,	PUNCT
ma-105	1085	20	j.	j.	PROPN
ma-105	1085	21	math	math	PROPN
ma-105	1085	22	.	.	PUNCT
ma-105	1086	1	anal	anal	PROPN
ma-105	1086	2	.	.	PUNCT
ma-105	1086	3	appl	appl	PROPN
ma-105	1086	4	.	.	PROPN
ma-105	1087	1	329	329	NUM
ma-105	1087	2	(	(	PUNCT
ma-105	1087	3	2007)281–297	2007)281–297	NUM
ma-105	1087	4	.	.	PUNCT
ma-105	1088	1	https://doi.org/10.1016/j.jmaa.2006.06.064.[37	https://doi.org/10.1016/j.jmaa.2006.06.064.[37	PROPN
ma-105	1088	2	]	]	X
ma-105	1088	3	h.r	h.r	PROPN
ma-105	1088	4	.	.	PROPN
ma-105	1088	5	thieme	thieme	PROPN
ma-105	1088	6	,	,	PUNCT
ma-105	1088	7	spectral	spectral	ADJ
ma-105	1088	8	bound	bind	VERB
ma-105	1088	9	and	and	CCONJ
ma-105	1088	10	reproduction	reproduction	NOUN
ma-105	1088	11	number	number	NOUN
ma-105	1088	12	for	for	ADP
ma-105	1088	13	infinite	infinite	ADJ
ma-105	1088	14	-	-	PUNCT
ma-105	1088	15	dimensional	dimensional	ADJ
ma-105	1088	16	population	population	NOUN
ma-105	1088	17	structure	structure	NOUN
ma-105	1088	18	and	and	CCONJ
ma-105	1088	19	time	time	NOUN
ma-105	1088	20	het	het	NOUN
ma-105	1088	21	-	-	PUNCT
ma-105	1088	22	erogeneity	erogeneity	NOUN
ma-105	1088	23	,	,	PUNCT
ma-105	1088	24	siam	siam	PROPN
ma-105	1088	25	j.	j.	PROPN
ma-105	1088	26	appl	appl	PROPN
ma-105	1088	27	.	.	PROPN
ma-105	1088	28	math	math	NOUN
ma-105	1088	29	.	.	PUNCT
ma-105	1089	1	70	70	NUM
ma-105	1089	2	(	(	PUNCT
ma-105	1089	3	2009	2009	NUM
ma-105	1089	4	)	)	PUNCT
ma-105	1090	1	188–211	188–211	NUM
ma-105	1090	2	.	.	PUNCT
ma-105	1091	1	https://doi.org/10.1137/080732870.[38	https://doi.org/10.1137/080732870.[38	PROPN
ma-105	1091	2	]	]	PUNCT
ma-105	1091	3	x.	x.	NOUN
ma-105	1091	4	wang	wang	PROPN
ma-105	1091	5	,	,	PUNCT
ma-105	1091	6	y.	y.	PROPN
ma-105	1091	7	tao	tao	PROPN
ma-105	1091	8	,	,	PUNCT
ma-105	1091	9	x.	x.	NOUN
ma-105	1091	10	song	song	NOUN
ma-105	1091	11	,	,	PUNCT
ma-105	1091	12	global	global	ADJ
ma-105	1091	13	stability	stability	NOUN
ma-105	1091	14	of	of	ADP
ma-105	1091	15	a	a	DET
ma-105	1091	16	virus	virus	NOUN
ma-105	1091	17	dynamics	dynamic	NOUN
ma-105	1091	18	model	model	NOUN
ma-105	1091	19	with	with	ADP
ma-105	1091	20	beddington	beddington	PROPN
ma-105	1091	21	–	–	PUNCT
ma-105	1091	22	deangelis	deangelis	PROPN
ma-105	1091	23	incidence	incidence	NOUN
ma-105	1091	24	rate	rate	NOUN
ma-105	1091	25	andctl	andctl	ADJ
ma-105	1091	26	immune	immune	ADJ
ma-105	1091	27	response	response	NOUN
ma-105	1091	28	,	,	PUNCT
ma-105	1091	29	nonlinear	nonlinear	ADJ
ma-105	1091	30	dyn	dyn	NOUN
ma-105	1091	31	.	.	PUNCT
ma-105	1092	1	66	66	NUM
ma-105	1092	2	(	(	PUNCT
ma-105	1092	3	2011	2011	NUM
ma-105	1092	4	)	)	PUNCT
ma-105	1093	1	825–830	825–830	NUM
ma-105	1093	2	.	.	PUNCT
ma-105	1094	1	https://doi.org/10.1007/s11071-011-9954-0.[39	https://doi.org/10.1007/s11071-011-9954-0.[39	PROPN
ma-105	1094	2	]	]	PUNCT
ma-105	1094	3	k.	k.	PROPN
ma-105	1094	4	wang	wang	PROPN
ma-105	1094	5	,	,	PUNCT
ma-105	1094	6	w.	w.	PROPN
ma-105	1094	7	wang	wang	PROPN
ma-105	1094	8	,	,	PUNCT
ma-105	1094	9	propagation	propagation	NOUN
ma-105	1094	10	of	of	ADP
ma-105	1094	11	hbv	hbv	NOUN
ma-105	1094	12	with	with	ADP
ma-105	1094	13	spatial	spatial	ADJ
ma-105	1094	14	dependence	dependence	NOUN
ma-105	1094	15	,	,	PUNCT
ma-105	1094	16	math	math	NOUN
ma-105	1094	17	.	.	PUNCT
ma-105	1095	1	biosci	biosci	PROPN
ma-105	1095	2	.	.	PUNCT
ma-105	1096	1	210	210	NUM
ma-105	1096	2	(	(	PUNCT
ma-105	1096	3	2007	2007	NUM
ma-105	1096	4	)	)	PUNCT
ma-105	1096	5	78–95	78–95	NUM
ma-105	1096	6	.	.	PUNCT
ma-105	1097	1	https://doi	https://doi	X
ma-105	1097	2	.	.	PUNCT
ma-105	1098	1	org/10.1016	org/10.1016	PROPN
ma-105	1098	2	/	/	SYM
ma-105	1098	3	j.mbs.2007.05.004.[40	j.mbs.2007.05.004.[40	NOUN
ma-105	1098	4	]	]	PUNCT
ma-105	1098	5	w.	w.	PROPN
ma-105	1098	6	wang	wang	PROPN
ma-105	1098	7	,	,	PUNCT
ma-105	1098	8	x.q	x.q	PROPN
ma-105	1098	9	.	.	PROPN
ma-105	1098	10	zhao	zhao	PROPN
ma-105	1098	11	,	,	PUNCT
ma-105	1098	12	basic	basic	ADJ
ma-105	1098	13	reproduction	reproduction	NOUN
ma-105	1098	14	numbers	number	NOUN
ma-105	1098	15	for	for	ADP
ma-105	1098	16	reaction	reaction	NOUN
ma-105	1098	17	-	-	PUNCT
ma-105	1098	18	diffusion	diffusion	NOUN
ma-105	1098	19	epidemic	epidemic	NOUN
ma-105	1098	20	models	model	NOUN
ma-105	1098	21	,	,	PUNCT
ma-105	1098	22	siam	siam	PROPN
ma-105	1098	23	j.	j.	PROPN
ma-105	1098	24	appl	appl	PROPN
ma-105	1098	25	.	.	PUNCT
ma-105	1099	1	dyn	dyn	PROPN
ma-105	1099	2	.	.	PUNCT
ma-105	1100	1	syst.11	syst.11	PROPN
ma-105	1100	2	(	(	PUNCT
ma-105	1100	3	2012	2012	NUM
ma-105	1100	4	)	)	PUNCT
ma-105	1100	5	1652–1673	1652–1673	NUM
ma-105	1100	6	.	.	PUNCT
ma-105	1101	1	https://doi.org/10.1137/120872942.[41	https://doi.org/10.1137/120872942.[41	PROPN
ma-105	1101	2	]	]	X
ma-105	1101	3	who	who	PRON
ma-105	1101	4	,	,	PUNCT
ma-105	1101	5	global	global	ADJ
ma-105	1101	6	hepatitis	hepatitis	NOUN
ma-105	1101	7	report	report	NOUN
ma-105	1101	8	,	,	PUNCT
ma-105	1101	9	world	world	PROPN
ma-105	1101	10	health	health	NOUN
ma-105	1101	11	organization	organization	PROPN
ma-105	1101	12	,	,	PUNCT
ma-105	1101	13	geneva	geneva	PROPN
ma-105	1101	14	,	,	PUNCT
ma-105	1101	15	2017	2017	NUM
ma-105	1101	16	.	.	PUNCT
ma-105	1102	1	http://apps.who.int/iris/	http://apps.who.int/iris/	PROPN
ma-105	1102	2	bitstream/10665/255016/1/9789241565455	bitstream/10665/255016/1/9789241565455	PROPN
ma-105	1102	3	-	-	PUNCT
ma-105	1102	4	eng.pdf	eng.pdf	NOUN
ma-105	1102	5	,	,	PUNCT
ma-105	1102	6	(	(	PUNCT
ma-105	1102	7	accessed	access	VERB
ma-105	1102	8	29	29	NUM
ma-105	1102	9	january	january	PROPN
ma-105	1102	10	2018).[42	2018).[42	NUM
ma-105	1102	11	]	]	X
ma-105	1103	1	y.	y.	PROPN
ma-105	1103	2	zhang	zhang	PROPN
ma-105	1103	3	,	,	PUNCT
ma-105	1103	4	z.	z.	PROPN
ma-105	1103	5	xu	xu	PROPN
ma-105	1103	6	,	,	PUNCT
ma-105	1103	7	dynamics	dynamic	NOUN
ma-105	1103	8	of	of	ADP
ma-105	1103	9	a	a	DET
ma-105	1103	10	diffusive	diffusive	ADJ
ma-105	1103	11	hbv	hbv	NOUN
ma-105	1103	12	model	model	NOUN
ma-105	1103	13	with	with	ADP
ma-105	1103	14	delayed	delay	VERB
ma-105	1103	15	beddington	beddington	PROPN
ma-105	1103	16	–	–	PUNCT
ma-105	1103	17	deangelis	deangelis	PROPN
ma-105	1103	18	response	response	NOUN
ma-105	1103	19	,	,	PUNCT
ma-105	1103	20	nonlinear	nonlinear	ADJ
ma-105	1103	21	anal.:real	anal.:real	ADJ
ma-105	1103	22	world	world	NOUN
ma-105	1103	23	appl	appl	NOUN
ma-105	1103	24	.	.	PROPN
ma-105	1103	25	15	15	NUM
ma-105	1103	26	(	(	PUNCT
ma-105	1103	27	2014	2014	NUM
ma-105	1103	28	)	)	PUNCT
ma-105	1103	29	118–139	118–139	NUM
ma-105	1103	30	.	.	PUNCT
ma-105	1104	1	https://doi.org/10.1016/j.nonrwa.2013.06.005.[43	https://doi.org/10.1016/j.nonrwa.2013.06.005.[43	ADP
ma-105	1104	2	]	]	X
ma-105	1104	3	x.	x.	NOUN
ma-105	1104	4	zhou	zhou	PROPN
ma-105	1104	5	,	,	PUNCT
ma-105	1104	6	j.	j.	PROPN
ma-105	1104	7	cui	cui	PROPN
ma-105	1104	8	,	,	PUNCT
ma-105	1104	9	global	global	ADJ
ma-105	1104	10	stability	stability	NOUN
ma-105	1104	11	of	of	ADP
ma-105	1104	12	the	the	DET
ma-105	1104	13	viral	viral	ADJ
ma-105	1104	14	dynamics	dynamic	NOUN
ma-105	1104	15	with	with	ADP
ma-105	1104	16	crowley	crowley	PROPN
ma-105	1104	17	martin	martin	PROPN
ma-105	1104	18	functional	functional	ADJ
ma-105	1104	19	response	response	NOUN
ma-105	1104	20	,	,	PUNCT
ma-105	1104	21	bull	bull	NOUN
ma-105	1104	22	.	.	PUNCT
ma-105	1105	1	korean	korean	PROPN
ma-105	1105	2	math.soc	math.soc	PROPN
ma-105	1105	3	.	.	PROPN
ma-105	1106	1	48	48	NUM
ma-105	1106	2	(	(	PUNCT
ma-105	1106	3	2011	2011	NUM
ma-105	1106	4	)	)	PUNCT
ma-105	1106	5	555	555	NUM
ma-105	1106	6	-	-	SYM
ma-105	1106	7	574	574	NUM
ma-105	1106	8	.	.	PUNCT
ma-105	1107	1	https://doi.org/10.4134/bkms.2011.48.3.555	https://doi.org/10.4134/bkms.2011.48.3.555	ADJ
ma-105	1107	2	.	.	PUNCT
ma-105	1108	1	https://doi.org/10.28924/ada/ma.3.1	https://doi.org/10.28924/ada/ma.3.1	PROPN
ma-105	1108	2	https://doi.org/10.1137/0518057	https://doi.org/10.1137/0518057	ADJ
ma-105	1108	3	https://doi.org/10.1016/j.aml.2009.06.004	https://doi.org/10.1016/j.aml.2009.06.004	PROPN
ma-105	1108	4	https://doi.org/10.1016/j.aml.2011.02.007	https://doi.org/10.1016/j.aml.2011.02.007	ADJ
ma-105	1108	5	https://doi.org/10.1016/j.jmaa.2007.02.006	https://doi.org/10.1016/j.jmaa.2007.02.006	ADJ
ma-105	1108	6	https://www.jstor.org/stable/44239519	https://www.jstor.org/stable/44239519	ADJ
ma-105	1108	7	https://doi.org/10.1126/science.282.5386.103	https://doi.org/10.1126/science.282.5386.103	PROPN
ma-105	1108	8	https://doi.org/10.1126/science.272.5258.74	https://doi.org/10.1126/science.272.5258.74	PROPN
ma-105	1108	9	https://doi.org/10.1073/pnas.93.9.4398	https://doi.org/10.1073/pnas.93.9.4398	PROPN
ma-105	1108	10	https://doi.org/10.9734/bjmcs/2016/28640	https://doi.org/10.9734/bjmcs/2016/28640	ADJ
ma-105	1108	11	https://doi.org/10.1016/j.mbs.2013.04.012	https://doi.org/10.1016/j.mbs.2013.04.012	NOUN
ma-105	1108	12	https://doi.org/10.1016/j.jmaa.2006.06.064	https://doi.org/10.1016/j.jmaa.2006.06.064	NOUN
ma-105	1108	13	https://doi.org/10.1137/080732870	https://doi.org/10.1137/080732870	NOUN
ma-105	1108	14	https://doi.org/10.1007/s11071-011-9954-0	https://doi.org/10.1007/s11071-011-9954-0	NUM
ma-105	1108	15	https://doi.org/10.1016/j.mbs.2007.05.004	https://doi.org/10.1016/j.mbs.2007.05.004	NOUN
ma-105	1108	16	https://doi.org/10.1016/j.mbs.2007.05.004	https://doi.org/10.1016/j.mbs.2007.05.004	PROPN
ma-105	1108	17	https://doi.org/10.1137/120872942	https://doi.org/10.1137/120872942	ADJ
ma-105	1108	18	http://apps.who.int/iris/bitstream/10665/255016/1/9789241565455eng.pdf	http://apps.who.int/iris/bitstream/10665/255016/1/9789241565455eng.pdf	PROPN
ma-105	1108	19	http://apps.who.int/iris/bitstream/10665/255016/1/9789241565455eng.pdf	http://apps.who.int/iris/bitstream/10665/255016/1/9789241565455eng.pdf	NOUN
ma-105	1108	20	https://doi.org/10.1016/j.nonrwa.2013.06.005	https://doi.org/10.1016/j.nonrwa.2013.06.005	VERB
ma-105	1108	21	https://doi.org/10.4134/bkms.2011.48.3.555	https://doi.org/10.4134/bkms.2011.48.3.555	ADV
ma-105	1108	22	1	1	NUM
ma-105	1108	23	.	.	PUNCT
ma-105	1109	1	introduction	introduction	NOUN
ma-105	1109	2	2	2	NUM
ma-105	1109	3	.	.	PUNCT
ma-105	1109	4	formulation	formulation	NOUN
ma-105	1109	5	of	of	ADP
ma-105	1109	6	the	the	DET
ma-105	1109	7	pde	pde	NOUN
ma-105	1109	8	-	-	PUNCT
ma-105	1109	9	cellular	cellular	ADJ
ma-105	1109	10	model	model	NOUN
ma-105	1109	11	2.1	2.1	NUM
ma-105	1109	12	.	.	PUNCT
ma-105	1110	1	fluctuation	fluctuation	NOUN
ma-105	1110	2	of	of	ADP
ma-105	1110	3	healthy	healthy	ADJ
ma-105	1110	4	hepatocytes	hepatocyte	NOUN
ma-105	1110	5	2.2	2.2	NUM
ma-105	1110	6	.	.	PUNCT
ma-105	1111	1	fluctuation	fluctuation	NOUN
ma-105	1111	2	of	of	ADP
ma-105	1111	3	hcv	hcv	PROPN
ma-105	1111	4	infected	infect	VERB
ma-105	1111	5	cells	cell	NOUN
ma-105	1111	6	2.3	2.3	NUM
ma-105	1111	7	.	.	PUNCT
ma-105	1112	1	fluctuation	fluctuation	NOUN
ma-105	1112	2	of	of	ADP
ma-105	1112	3	free	free	ADJ
ma-105	1112	4	hcv	hcv	X
ma-105	1112	5	virions	virion	NOUN
ma-105	1112	6	2.4	2.4	NUM
ma-105	1112	7	.	.	PUNCT
ma-105	1113	1	the	the	DET
ma-105	1113	2	initial	initial	ADJ
ma-105	1113	3	boundary	boundary	ADJ
ma-105	1113	4	value	value	NOUN
ma-105	1113	5	problem	problem	NOUN
ma-105	1113	6	associated	associate	VERB
ma-105	1113	7	to	to	ADP
ma-105	1113	8	pde	pde	NOUN
ma-105	1113	9	-	-	PUNCT
ma-105	1113	10	cellular	cellular	ADJ
ma-105	1113	11	model	model	NOUN
ma-105	1113	12	3	3	NUM
ma-105	1113	13	.	.	PUNCT
ma-105	1113	14	qualitative	qualitative	ADJ
ma-105	1113	15	and	and	CCONJ
ma-105	1113	16	quantitative	quantitative	ADJ
ma-105	1113	17	analysis	analysis	NOUN
ma-105	1113	18	and	and	CCONJ
ma-105	1113	19	some	some	DET
ma-105	1113	20	properties	property	NOUN
ma-105	1113	21	of	of	ADP
ma-105	1113	22	the	the	DET
ma-105	1113	23	solutions	solution	NOUN
ma-105	1113	24	for	for	ADP
ma-105	1113	25	ibvp	ibvp	NOUN
ma-105	1113	26	(	(	PUNCT
ma-105	1113	27	2.4	2.4	NUM
ma-105	1113	28	)	)	PUNCT
ma-105	1113	29	3.1	3.1	NUM
ma-105	1113	30	.	.	PUNCT
ma-105	1113	31	local	local	ADJ
ma-105	1113	32	existence	existence	NOUN
ma-105	1113	33	and	and	CCONJ
ma-105	1113	34	uniqueness	uniqueness	NOUN
ma-105	1113	35	of	of	ADP
ma-105	1113	36	solutions	solution	NOUN
ma-105	1113	37	for	for	ADP
ma-105	1113	38	the	the	DET
ma-105	1113	39	ibvp	ibvp	NOUN
ma-105	1113	40	(	(	PUNCT
ma-105	1113	41	2.4	2.4	NUM
ma-105	1113	42	)	)	PUNCT
ma-105	1113	43	3.2	3.2	NUM
ma-105	1113	44	.	.	PUNCT
ma-105	1114	1	boundedness	boundedness	NOUN
ma-105	1114	2	of	of	ADP
ma-105	1114	3	the	the	DET
ma-105	1114	4	solutions	solution	NOUN
ma-105	1114	5	for	for	ADP
ma-105	1114	6	ibvp	ibvp	NOUN
ma-105	1114	7	(	(	PUNCT
ma-105	1114	8	2.4	2.4	NUM
ma-105	1114	9	)	)	PUNCT
ma-105	1114	10	3.3	3.3	NUM
ma-105	1114	11	.	.	PUNCT
ma-105	1115	1	global	global	ADJ
ma-105	1115	2	existence	existence	NOUN
ma-105	1115	3	,	,	PUNCT
ma-105	1115	4	uniqueness	uniqueness	NOUN
ma-105	1115	5	and	and	CCONJ
ma-105	1115	6	positivity	positivity	NOUN
ma-105	1115	7	for	for	ADP
ma-105	1115	8	the	the	DET
ma-105	1115	9	ibvp	ibvp	NOUN
ma-105	1115	10	(	(	PUNCT
ma-105	1115	11	2.4	2.4	NUM
ma-105	1115	12	)	)	PUNCT
ma-105	1115	13	4	4	NUM
ma-105	1115	14	.	.	PUNCT
ma-105	1116	1	stability	stability	NOUN
ma-105	1116	2	analysis	analysis	NOUN
ma-105	1116	3	of	of	ADP
ma-105	1116	4	the	the	DET
ma-105	1116	5	spatially	spatially	ADV
ma-105	1116	6	homogeneous	homogeneous	ADJ
ma-105	1116	7	equilibria	equilibrium	NOUN
ma-105	1116	8	4.1	4.1	NUM
ma-105	1116	9	.	.	PUNCT
ma-105	1117	1	hcv	hcv	NOUN
ma-105	1117	2	-	-	PUNCT
ma-105	1117	3	spatial	spatial	ADJ
ma-105	1117	4	homogeneous	homogeneous	ADJ
ma-105	1117	5	uninfected	uninfected	ADJ
ma-105	1117	6	equilibrium	equilibrium	NOUN
ma-105	1117	7	e0	e0	PROPN
ma-105	1117	8	4.2	4.2	NUM
ma-105	1117	9	.	.	PUNCT
ma-105	1118	1	basic	basic	ADJ
ma-105	1118	2	reproduction	reproduction	NOUN
ma-105	1118	3	number	number	NOUN
ma-105	1118	4	r0	r0	NOUN
ma-105	1118	5	4.3	4.3	NUM
ma-105	1118	6	.	.	PUNCT
ma-105	1119	1	existence	existence	NOUN
ma-105	1119	2	and	and	CCONJ
ma-105	1119	3	uniqueness	uniqueness	NOUN
ma-105	1119	4	of	of	ADP
ma-105	1119	5	hcv	hcv	NOUN
ma-105	1119	6	-	-	PUNCT
ma-105	1119	7	spatial	spatial	ADJ
ma-105	1119	8	homogeneous	homogeneous	ADJ
ma-105	1119	9	infected	infected	ADJ
ma-105	1119	10	equilibrium	equilibrium	NOUN
ma-105	1119	11	e	e	PROPN
ma-105	1119	12	*	*	PROPN
ma-105	1119	13	4.4	4.4	NUM
ma-105	1119	14	.	.	PUNCT
ma-105	1120	1	local	local	ADJ
ma-105	1120	2	stability	stability	NOUN
ma-105	1120	3	of	of	ADP
ma-105	1120	4	hcv	hcv	NOUN
ma-105	1120	5	-	-	PUNCT
ma-105	1120	6	uninfected	uninfected	ADJ
ma-105	1120	7	equilibrium	equilibrium	NOUN
ma-105	1120	8	4.5	4.5	NUM
ma-105	1120	9	.	.	PUNCT
ma-105	1121	1	global	global	ADJ
ma-105	1121	2	stability	stability	NOUN
ma-105	1121	3	of	of	ADP
ma-105	1121	4	hcv	hcv	NOUN
ma-105	1121	5	-	-	PUNCT
ma-105	1121	6	uninfected	uninfected	ADJ
ma-105	1121	7	equilibrium	equilibrium	NOUN
ma-105	1121	8	4.6	4.6	NUM
ma-105	1121	9	.	.	PUNCT
ma-105	1122	1	local	local	ADJ
ma-105	1122	2	stability	stability	NOUN
ma-105	1122	3	of	of	ADP
ma-105	1122	4	hcv	hcv	X
ma-105	1122	5	spatially	spatially	ADV
ma-105	1122	6	homogeneous	homogeneous	ADJ
ma-105	1122	7	infected	infected	ADJ
ma-105	1122	8	equilibrium	equilibrium	NOUN
ma-105	1122	9	4.7	4.7	NUM
ma-105	1122	10	.	.	PUNCT
ma-105	1123	1	global	global	ADJ
ma-105	1123	2	stability	stability	NOUN
ma-105	1123	3	of	of	ADP
ma-105	1123	4	hcv	hcv	NOUN
ma-105	1123	5	-	-	PUNCT
ma-105	1123	6	spatially	spatially	ADV
ma-105	1123	7	homogeneous	homogeneous	ADJ
ma-105	1123	8	infected	infected	ADJ
ma-105	1123	9	equilibrium	equilibrium	NOUN
ma-105	1123	10	5	5	NUM
ma-105	1123	11	.	.	PUNCT
ma-105	1123	12	numerical	numerical	ADJ
ma-105	1123	13	simulations	simulation	NOUN
ma-105	1123	14	6	6	NUM
ma-105	1123	15	.	.	PUNCT
ma-105	1123	16	conclusion	conclusion	NOUN
ma-105	1123	17	appendix	appendix	VERB
ma-105	1123	18	a.	a.	NOUN
ma-105	1123	19	proof	proof	NOUN
ma-105	1123	20	of	of	ADP
ma-105	1123	21	proposition	proposition	NOUN
ma-105	1123	22	3.8	3.8	NUM
ma-105	1123	23	appendix	appendix	NOUN
ma-105	1123	24	b.	b.	NOUN
ma-105	1123	25	proof	proof	NOUN
ma-105	1123	26	of	of	ADP
ma-105	1123	27	theorem	theorem	ADJ
ma-105	1123	28	3.11	3.11	NUM
ma-105	1123	29	references	reference	NOUN