id	sid	tid	token	lemma	pos
ap-10701	1	1	acta	acta	PROPN
ap-10701	1	2	polytechnica	polytechnica	PROPN
ap-10701	1	3	https://doi.org/10.14311/ap.2025.65.0566	https://doi.org/10.14311/ap.2025.65.0566	PROPN
ap-10701	1	4	acta	acta	PROPN
ap-10701	1	5	polytechnica	polytechnica	PROPN
ap-10701	1	6	65(5):566–577	65(5):566–577	PROPN
ap-10701	1	7	,	,	PUNCT
ap-10701	1	8	2025	2025	NUM
ap-10701	1	9	©	©	ADP
ap-10701	1	10	2025	2025	NUM
ap-10701	1	11	the	the	DET
ap-10701	1	12	author(s	author(s	NOUN
ap-10701	1	13	)	)	PUNCT
ap-10701	1	14	.	.	PUNCT
ap-10701	2	1	licensed	license	VERB
ap-10701	2	2	under	under	ADP
ap-10701	2	3	a	a	DET
ap-10701	2	4	cc	cc	NOUN
ap-10701	2	5	-	-	PUNCT
ap-10701	2	6	by	by	ADP
ap-10701	2	7	4.0	4.0	NUM
ap-10701	2	8	licence	licence	NOUN
ap-10701	2	9	published	publish	VERB
ap-10701	2	10	by	by	ADP
ap-10701	2	11	the	the	DET
ap-10701	2	12	czech	czech	PROPN
ap-10701	2	13	technical	technical	PROPN
ap-10701	2	14	university	university	PROPN
ap-10701	2	15	in	in	ADP
ap-10701	2	16	prague	prague	PROPN
ap-10701	2	17	method	method	NOUN
ap-10701	2	18	of	of	ADP
ap-10701	2	19	lines	line	NOUN
ap-10701	2	20	for	for	ADP
ap-10701	2	21	reaction	reaction	NOUN
ap-10701	2	22	-	-	PUNCT
ap-10701	2	23	diffusion	diffusion	NOUN
ap-10701	2	24	systems	system	NOUN
ap-10701	2	25	admitting	admit	VERB
ap-10701	2	26	invariant	invariant	ADJ
ap-10701	2	27	regions	region	NOUN
ap-10701	2	28	niels	niels	PROPN
ap-10701	2	29	van	van	PROPN
ap-10701	2	30	der	der	PROPN
ap-10701	2	31	meer	meer	PROPN
ap-10701	2	32	,	,	PUNCT
ap-10701	2	33	michal	michal	PROPN
ap-10701	2	34	beneš∗	beneš∗	PROPN
ap-10701	2	35	czech	czech	PROPN
ap-10701	2	36	technical	technical	PROPN
ap-10701	2	37	university	university	PROPN
ap-10701	2	38	in	in	ADP
ap-10701	2	39	prague	prague	PROPN
ap-10701	2	40	,	,	PUNCT
ap-10701	2	41	faculty	faculty	NOUN
ap-10701	2	42	of	of	ADP
ap-10701	2	43	nuclear	nuclear	ADJ
ap-10701	2	44	sciences	science	NOUN
ap-10701	2	45	and	and	CCONJ
ap-10701	2	46	physical	physical	ADJ
ap-10701	2	47	engineering	engineering	NOUN
ap-10701	2	48	,	,	PUNCT
ap-10701	2	49	department	department	NOUN
ap-10701	2	50	of	of	ADP
ap-10701	2	51	mathematics	mathematic	NOUN
ap-10701	2	52	,	,	PUNCT
ap-10701	2	53	trojanova	trojanova	X
ap-10701	2	54	13	13	NUM
ap-10701	2	55	,	,	PUNCT
ap-10701	2	56	120	120	NUM
ap-10701	2	57	00	00	NUM
ap-10701	2	58	prague	prague	PROPN
ap-10701	2	59	,	,	PUNCT
ap-10701	2	60	czech	czech	PROPN
ap-10701	2	61	republic	republic	NOUN
ap-10701	2	62	∗	∗	NOUN
ap-10701	2	63	corresponding	correspond	VERB
ap-10701	2	64	author	author	NOUN
ap-10701	2	65	:	:	PUNCT
ap-10701	2	66	michal.benes@fjfi.cvut.cz	michal.benes@fjfi.cvut.cz	NOUN
ap-10701	2	67	abstract	abstract	ADJ
ap-10701	2	68	.	.	PUNCT
ap-10701	3	1	systems	system	NOUN
ap-10701	3	2	of	of	ADP
ap-10701	3	3	nonlinear	nonlinear	ADJ
ap-10701	3	4	reaction	reaction	NOUN
ap-10701	3	5	-	-	PUNCT
ap-10701	3	6	diffusion	diffusion	NOUN
ap-10701	3	7	equations	equation	NOUN
ap-10701	3	8	arise	arise	VERB
ap-10701	3	9	in	in	ADP
ap-10701	3	10	various	various	ADJ
ap-10701	3	11	fields	field	NOUN
ap-10701	3	12	,	,	PUNCT
ap-10701	3	13	including	include	VERB
ap-10701	3	14	chemistry	chemistry	NOUN
ap-10701	3	15	,	,	PUNCT
ap-10701	3	16	population	population	NOUN
ap-10701	3	17	dynamics	dynamic	NOUN
ap-10701	3	18	,	,	PUNCT
ap-10701	3	19	pattern	pattern	NOUN
ap-10701	3	20	formation	formation	NOUN
ap-10701	3	21	,	,	PUNCT
ap-10701	3	22	phase	phase	NOUN
ap-10701	3	23	transitions	transition	NOUN
ap-10701	3	24	,	,	PUNCT
ap-10701	3	25	and	and	CCONJ
ap-10701	3	26	image	image	NOUN
ap-10701	3	27	processing	processing	NOUN
ap-10701	3	28	.	.	PUNCT
ap-10701	4	1	with	with	ADP
ap-10701	4	2	the	the	DET
ap-10701	4	3	exception	exception	NOUN
ap-10701	4	4	of	of	ADP
ap-10701	4	5	few	few	ADJ
ap-10701	4	6	analytically	analytically	ADV
ap-10701	4	7	solvable	solvable	ADJ
ap-10701	4	8	cases	case	NOUN
ap-10701	4	9	,	,	PUNCT
ap-10701	4	10	they	they	PRON
ap-10701	4	11	are	be	AUX
ap-10701	4	12	treated	treat	VERB
ap-10701	4	13	by	by	ADP
ap-10701	4	14	numerical	numerical	ADJ
ap-10701	4	15	methods	method	NOUN
ap-10701	4	16	carefully	carefully	ADV
ap-10701	4	17	adjusted	adjust	VERB
ap-10701	4	18	to	to	PART
ap-10701	4	19	capture	capture	VERB
ap-10701	4	20	the	the	DET
ap-10701	4	21	nonlinear	nonlinear	ADJ
ap-10701	4	22	phenomena	phenomenon	NOUN
ap-10701	4	23	exhibited	exhibit	VERB
ap-10701	4	24	by	by	ADP
ap-10701	4	25	the	the	DET
ap-10701	4	26	solution	solution	NOUN
ap-10701	4	27	.	.	PUNCT
ap-10701	5	1	this	this	DET
ap-10701	5	2	article	article	NOUN
ap-10701	5	3	shows	show	VERB
ap-10701	5	4	how	how	SCONJ
ap-10701	5	5	to	to	PART
ap-10701	5	6	extend	extend	VERB
ap-10701	5	7	the	the	DET
ap-10701	5	8	notion	notion	NOUN
ap-10701	5	9	of	of	ADP
ap-10701	5	10	invariant	invariant	ADJ
ap-10701	5	11	regions	region	NOUN
ap-10701	5	12	generalizing	generalize	VERB
ap-10701	5	13	the	the	DET
ap-10701	5	14	maximum	maximum	ADJ
ap-10701	5	15	principle	principle	NOUN
ap-10701	5	16	for	for	ADP
ap-10701	5	17	diffusion	diffusion	NOUN
ap-10701	5	18	equations	equation	NOUN
ap-10701	5	19	to	to	ADP
ap-10701	5	20	the	the	DET
ap-10701	5	21	finite	finite	ADJ
ap-10701	5	22	-	-	PUNCT
ap-10701	5	23	difference	difference	NOUN
ap-10701	5	24	method	method	NOUN
ap-10701	5	25	of	of	ADP
ap-10701	5	26	lines	line	NOUN
ap-10701	5	27	,	,	PUNCT
ap-10701	5	28	and	and	CCONJ
ap-10701	5	29	how	how	SCONJ
ap-10701	5	30	to	to	PART
ap-10701	5	31	consequently	consequently	ADV
ap-10701	5	32	prove	prove	VERB
ap-10701	5	33	convergence	convergence	NOUN
ap-10701	5	34	of	of	ADP
ap-10701	5	35	the	the	DET
ap-10701	5	36	underlying	underlying	ADJ
ap-10701	5	37	numerical	numerical	ADJ
ap-10701	5	38	scheme	scheme	NOUN
ap-10701	5	39	.	.	PUNCT
ap-10701	6	1	we	we	PRON
ap-10701	6	2	also	also	ADV
ap-10701	6	3	provide	provide	VERB
ap-10701	6	4	two	two	NUM
ap-10701	6	5	particular	particular	ADJ
ap-10701	6	6	examples	example	NOUN
ap-10701	6	7	of	of	ADP
ap-10701	6	8	reaction	reaction	NOUN
ap-10701	6	9	-	-	PUNCT
ap-10701	6	10	diffusion	diffusion	NOUN
ap-10701	6	11	systems	system	NOUN
ap-10701	6	12	in	in	ADP
ap-10701	6	13	one	one	NUM
ap-10701	6	14	-	-	PUNCT
ap-10701	6	15	dimensional	dimensional	ADJ
ap-10701	6	16	space	space	NOUN
ap-10701	6	17	with	with	ADP
ap-10701	6	18	a	a	DET
ap-10701	6	19	diagonal	diagonal	ADJ
ap-10701	6	20	diffusion	diffusion	NOUN
ap-10701	6	21	operator	operator	NOUN
ap-10701	6	22	,	,	PUNCT
ap-10701	6	23	which	which	PRON
ap-10701	6	24	are	be	AUX
ap-10701	6	25	solved	solve	VERB
ap-10701	6	26	by	by	ADP
ap-10701	6	27	the	the	DET
ap-10701	6	28	presented	present	VERB
ap-10701	6	29	numerical	numerical	ADJ
ap-10701	6	30	method	method	NOUN
ap-10701	6	31	.	.	PUNCT
ap-10701	7	1	keywords	keyword	NOUN
ap-10701	7	2	:	:	PUNCT
ap-10701	7	3	reaction	reaction	NOUN
ap-10701	7	4	-	-	PUNCT
ap-10701	7	5	diffusion	diffusion	NOUN
ap-10701	7	6	dynamics	dynamic	NOUN
ap-10701	7	7	,	,	PUNCT
ap-10701	7	8	finite	finite	ADJ
ap-10701	7	9	-	-	PUNCT
ap-10701	7	10	difference	difference	NOUN
ap-10701	7	11	method	method	NOUN
ap-10701	7	12	,	,	PUNCT
ap-10701	7	13	method	method	NOUN
ap-10701	7	14	of	of	ADP
ap-10701	7	15	lines	line	NOUN
ap-10701	7	16	,	,	PUNCT
ap-10701	7	17	invariant	invariant	ADJ
ap-10701	7	18	regions	region	NOUN
ap-10701	7	19	.	.	PUNCT
ap-10701	8	1	1	1	X
ap-10701	8	2	.	.	X
ap-10701	8	3	introduction	introduction	NOUN
ap-10701	8	4	reaction	reaction	NOUN
ap-10701	8	5	-	-	PUNCT
ap-10701	8	6	diffusion	diffusion	NOUN
ap-10701	8	7	systems	system	NOUN
ap-10701	8	8	arise	arise	VERB
ap-10701	8	9	in	in	ADP
ap-10701	8	10	a	a	DET
ap-10701	8	11	variety	variety	NOUN
ap-10701	8	12	of	of	ADP
ap-10701	8	13	natural	natural	ADJ
ap-10701	8	14	science	science	NOUN
ap-10701	8	15	disciplines	discipline	NOUN
ap-10701	8	16	.	.	PUNCT
ap-10701	9	1	originally	originally	ADV
ap-10701	9	2	,	,	PUNCT
ap-10701	9	3	the	the	DET
ap-10701	9	4	reaction	reaction	NOUN
ap-10701	9	5	of	of	ADP
ap-10701	9	6	several	several	ADJ
ap-10701	9	7	chemical	chemical	ADJ
ap-10701	9	8	components	component	NOUN
ap-10701	9	9	in	in	ADP
ap-10701	9	10	a	a	DET
ap-10701	9	11	volume	volume	NOUN
ap-10701	9	12	of	of	ADP
ap-10701	9	13	space	space	NOUN
ap-10701	9	14	is	be	AUX
ap-10701	9	15	described	describe	VERB
ap-10701	9	16	in	in	ADP
ap-10701	9	17	terms	term	NOUN
ap-10701	9	18	of	of	ADP
ap-10701	9	19	the	the	DET
ap-10701	9	20	mass	mass	NOUN
ap-10701	9	21	balance	balance	NOUN
ap-10701	9	22	by	by	ADP
ap-10701	9	23	a	a	DET
ap-10701	9	24	system	system	NOUN
ap-10701	9	25	of	of	ADP
ap-10701	9	26	reaction	reaction	NOUN
ap-10701	9	27	equations	equation	NOUN
ap-10701	9	28	with	with	ADP
ap-10701	9	29	spatial	spatial	ADJ
ap-10701	9	30	transport	transport	NOUN
ap-10701	9	31	by	by	ADP
ap-10701	9	32	diffusion	diffusion	NOUN
ap-10701	9	33	.	.	PUNCT
ap-10701	10	1	this	this	PRON
ap-10701	10	2	is	be	AUX
ap-10701	10	3	summarized	summarize	VERB
ap-10701	10	4	,	,	PUNCT
ap-10701	10	5	for	for	ADP
ap-10701	10	6	example	example	NOUN
ap-10701	10	7	in	in	ADP
ap-10701	10	8	[	[	X
ap-10701	10	9	1–3	1–3	NOUN
ap-10701	10	10	]	]	X
ap-10701	10	11	.	.	PUNCT
ap-10701	11	1	similarly	similarly	ADV
ap-10701	11	2	,	,	PUNCT
ap-10701	11	3	such	such	ADJ
ap-10701	11	4	systems	system	NOUN
ap-10701	11	5	describe	describe	VERB
ap-10701	11	6	the	the	DET
ap-10701	11	7	competitive	competitive	ADJ
ap-10701	11	8	coexistence	coexistence	NOUN
ap-10701	11	9	of	of	ADP
ap-10701	11	10	several	several	ADJ
ap-10701	11	11	biological	biological	ADJ
ap-10701	11	12	species	specie	NOUN
ap-10701	11	13	within	within	ADP
ap-10701	11	14	a	a	DET
ap-10701	11	15	spatial	spatial	ADJ
ap-10701	11	16	volume	volume	NOUN
ap-10701	11	17	(	(	PUNCT
ap-10701	11	18	see	see	VERB
ap-10701	11	19	,	,	PUNCT
ap-10701	11	20	e.g.	e.g.	ADV
ap-10701	12	1	[	[	X
ap-10701	12	2	4	4	NUM
ap-10701	12	3	–	–	PUNCT
ap-10701	12	4	6	6	NUM
ap-10701	12	5	]	]	NUM
ap-10701	12	6	)	)	PUNCT
ap-10701	12	7	.	.	PUNCT
ap-10701	13	1	phase	phase	NOUN
ap-10701	13	2	transitions	transition	NOUN
ap-10701	13	3	such	such	ADJ
ap-10701	13	4	as	as	ADP
ap-10701	13	5	those	those	PRON
ap-10701	13	6	during	during	ADP
ap-10701	13	7	metal	metal	NOUN
ap-10701	13	8	solidification	solidification	NOUN
ap-10701	13	9	at	at	ADP
ap-10701	13	10	microscale	microscale	NOUN
ap-10701	13	11	,	,	PUNCT
ap-10701	13	12	or	or	CCONJ
ap-10701	13	13	the	the	DET
ap-10701	13	14	conversion	conversion	NOUN
ap-10701	13	15	of	of	ADP
ap-10701	13	16	crystalline	crystalline	NOUN
ap-10701	13	17	lattice	lattice	NOUN
ap-10701	13	18	can	can	AUX
ap-10701	13	19	also	also	ADV
ap-10701	13	20	lead	lead	VERB
ap-10701	13	21	to	to	ADP
ap-10701	13	22	systems	system	NOUN
ap-10701	13	23	of	of	ADP
ap-10701	13	24	reaction	reaction	NOUN
ap-10701	13	25	-	-	PUNCT
ap-10701	13	26	diffusion	diffusion	NOUN
ap-10701	13	27	equations	equation	NOUN
ap-10701	13	28	known	know	VERB
ap-10701	13	29	as	as	ADP
ap-10701	13	30	phase	phase	NOUN
ap-10701	13	31	-	-	PUNCT
ap-10701	13	32	field	field	NOUN
ap-10701	14	1	[	[	X
ap-10701	14	2	7–10	7–10	X
ap-10701	14	3	]	]	PUNCT
ap-10701	14	4	.	.	PUNCT
ap-10701	15	1	geometric	geometric	ADJ
ap-10701	15	2	methods	method	NOUN
ap-10701	15	3	of	of	ADP
ap-10701	15	4	image	image	NOUN
ap-10701	15	5	processing	processing	NOUN
ap-10701	15	6	based	base	VERB
ap-10701	15	7	on	on	ADP
ap-10701	15	8	the	the	DET
ap-10701	15	9	motion	motion	NOUN
ap-10701	15	10	of	of	ADP
ap-10701	15	11	level	level	NOUN
ap-10701	15	12	sets	set	NOUN
ap-10701	15	13	employ	employ	VERB
ap-10701	15	14	a	a	DET
ap-10701	15	15	reaction	reaction	NOUN
ap-10701	15	16	-	-	PUNCT
ap-10701	15	17	diffusion	diffusion	NOUN
ap-10701	15	18	equation	equation	NOUN
ap-10701	15	19	of	of	ADP
ap-10701	15	20	the	the	DET
ap-10701	15	21	allen	allen	ADJ
ap-10701	15	22	-	-	PUNCT
ap-10701	15	23	cahn	cahn	NOUN
ap-10701	15	24	type	type	NOUN
ap-10701	16	1	[	[	X
ap-10701	16	2	11	11	NUM
ap-10701	16	3	]	]	PUNCT
ap-10701	16	4	.	.	PUNCT
ap-10701	17	1	numerical	numerical	ADJ
ap-10701	17	2	solution	solution	NOUN
ap-10701	17	3	of	of	ADP
ap-10701	17	4	such	such	ADJ
ap-10701	17	5	systems	system	NOUN
ap-10701	17	6	is	be	AUX
ap-10701	17	7	being	be	AUX
ap-10701	17	8	performed	perform	VERB
ap-10701	17	9	using	use	VERB
ap-10701	17	10	a	a	DET
ap-10701	17	11	variety	variety	NOUN
ap-10701	17	12	of	of	ADP
ap-10701	17	13	methods	method	NOUN
ap-10701	17	14	.	.	PUNCT
ap-10701	18	1	the	the	DET
ap-10701	18	2	full	full	ADJ
ap-10701	18	3	finitedifference	finitedifference	NOUN
ap-10701	18	4	discretization	discretization	NOUN
ap-10701	18	5	is	be	AUX
ap-10701	18	6	summarized	summarize	VERB
ap-10701	18	7	,	,	PUNCT
ap-10701	18	8	for	for	ADP
ap-10701	18	9	example	example	NOUN
ap-10701	18	10	,	,	PUNCT
ap-10701	18	11	in	in	ADP
ap-10701	18	12	[	[	PUNCT
ap-10701	18	13	2	2	NUM
ap-10701	18	14	,	,	PUNCT
ap-10701	18	15	12	12	NUM
ap-10701	18	16	]	]	PUNCT
ap-10701	18	17	,	,	PUNCT
ap-10701	18	18	the	the	DET
ap-10701	18	19	finite	finite	ADJ
ap-10701	18	20	-	-	ADJ
ap-10701	18	21	element	element	ADJ
ap-10701	18	22	method	method	NOUN
ap-10701	18	23	is	be	AUX
ap-10701	18	24	used	use	VERB
ap-10701	18	25	e.g.	e.g.	ADV
ap-10701	18	26	in	in	ADP
ap-10701	18	27	[	[	NOUN
ap-10701	18	28	13	13	NUM
ap-10701	18	29	,	,	PUNCT
ap-10701	18	30	14	14	NUM
ap-10701	18	31	]	]	PUNCT
ap-10701	18	32	,	,	PUNCT
ap-10701	18	33	the	the	DET
ap-10701	18	34	non	non	ADJ
ap-10701	18	35	-	-	ADJ
ap-10701	18	36	linear	linear	ADJ
ap-10701	18	37	spectral	spectral	ADJ
ap-10701	18	38	galerkin	galerkin	ADJ
ap-10701	18	39	method	method	NOUN
ap-10701	18	40	is	be	AUX
ap-10701	18	41	discussed	discuss	VERB
ap-10701	18	42	,	,	PUNCT
ap-10701	18	43	for	for	ADP
ap-10701	18	44	example	example	NOUN
ap-10701	18	45	,	,	PUNCT
ap-10701	18	46	in	in	ADP
ap-10701	18	47	[	[	X
ap-10701	18	48	15	15	NUM
ap-10701	18	49	,	,	PUNCT
ap-10701	18	50	16	16	NUM
ap-10701	18	51	]	]	PUNCT
ap-10701	18	52	.	.	PUNCT
ap-10701	19	1	this	this	DET
ap-10701	19	2	article	article	NOUN
ap-10701	19	3	is	be	AUX
ap-10701	19	4	devoted	devote	VERB
ap-10701	19	5	to	to	ADP
ap-10701	19	6	the	the	DET
ap-10701	19	7	method	method	NOUN
ap-10701	19	8	of	of	ADP
ap-10701	19	9	lines	line	NOUN
ap-10701	19	10	based	base	VERB
ap-10701	19	11	on	on	ADP
ap-10701	19	12	space	space	NOUN
ap-10701	19	13	discretization	discretization	NOUN
ap-10701	19	14	by	by	ADP
ap-10701	19	15	the	the	DET
ap-10701	19	16	finite	finite	ADJ
ap-10701	19	17	-	-	PUNCT
ap-10701	19	18	difference	difference	NOUN
ap-10701	19	19	method	method	NOUN
ap-10701	19	20	and	and	CCONJ
ap-10701	19	21	subsequent	subsequent	ADJ
ap-10701	19	22	treatment	treatment	NOUN
ap-10701	19	23	of	of	ADP
ap-10701	19	24	the	the	DET
ap-10701	19	25	ode	ode	ADJ
ap-10701	19	26	system	system	NOUN
ap-10701	19	27	in	in	ADP
ap-10701	19	28	time	time	NOUN
ap-10701	19	29	.	.	PUNCT
ap-10701	20	1	we	we	PRON
ap-10701	20	2	show	show	VERB
ap-10701	20	3	that	that	SCONJ
ap-10701	20	4	the	the	DET
ap-10701	20	5	property	property	NOUN
ap-10701	20	6	of	of	ADP
ap-10701	20	7	invariant	invariant	ADJ
ap-10701	20	8	regions	region	NOUN
ap-10701	20	9	propagates	propagate	VERB
ap-10701	20	10	to	to	ADP
ap-10701	20	11	the	the	DET
ap-10701	20	12	same	same	ADJ
ap-10701	20	13	property	property	NOUN
ap-10701	20	14	for	for	ADP
ap-10701	20	15	such	such	DET
ap-10701	20	16	a	a	DET
ap-10701	20	17	system	system	NOUN
ap-10701	20	18	of	of	ADP
ap-10701	20	19	ode	ode	PROPN
ap-10701	20	20	’s	’	VERB
ap-10701	20	21	generated	generate	VERB
ap-10701	20	22	by	by	ADP
ap-10701	20	23	the	the	DET
ap-10701	20	24	finite	finite	ADJ
ap-10701	20	25	-	-	PUNCT
ap-10701	20	26	difference	difference	NOUN
ap-10701	20	27	method	method	NOUN
ap-10701	20	28	and	and	CCONJ
ap-10701	20	29	allows	allow	VERB
ap-10701	20	30	to	to	PART
ap-10701	20	31	show	show	VERB
ap-10701	20	32	sufficient	sufficient	ADJ
ap-10701	20	33	a	a	DET
ap-10701	20	34	priori	priori	ADJ
ap-10701	20	35	estimates	estimate	NOUN
ap-10701	20	36	needed	need	VERB
ap-10701	20	37	for	for	ADP
ap-10701	20	38	convergence	convergence	NOUN
ap-10701	20	39	of	of	ADP
ap-10701	20	40	the	the	DET
ap-10701	20	41	numerical	numerical	ADJ
ap-10701	20	42	scheme	scheme	NOUN
ap-10701	20	43	.	.	PUNCT
ap-10701	21	1	the	the	DET
ap-10701	21	2	text	text	NOUN
ap-10701	21	3	is	be	AUX
ap-10701	21	4	organized	organize	VERB
ap-10701	21	5	into	into	ADP
ap-10701	21	6	a	a	DET
ap-10701	21	7	mathematical	mathematical	ADJ
ap-10701	21	8	introduction	introduction	NOUN
ap-10701	21	9	with	with	ADP
ap-10701	21	10	the	the	DET
ap-10701	21	11	state	state	NOUN
ap-10701	21	12	of	of	ADP
ap-10701	21	13	the	the	DET
ap-10701	21	14	art	art	NOUN
ap-10701	21	15	,	,	PUNCT
ap-10701	21	16	design	design	NOUN
ap-10701	21	17	of	of	ADP
ap-10701	21	18	the	the	DET
ap-10701	21	19	method	method	NOUN
ap-10701	21	20	of	of	ADP
ap-10701	21	21	lines	line	NOUN
ap-10701	21	22	,	,	PUNCT
ap-10701	21	23	a	a	DET
ap-10701	21	24	demonstration	demonstration	NOUN
ap-10701	21	25	of	of	ADP
ap-10701	21	26	the	the	DET
ap-10701	21	27	invariant	invariant	ADJ
ap-10701	21	28	-	-	PUNCT
ap-10701	21	29	region	region	NOUN
ap-10701	21	30	property	property	NOUN
ap-10701	21	31	,	,	PUNCT
ap-10701	21	32	convergence	convergence	NOUN
ap-10701	21	33	analysis	analysis	NOUN
ap-10701	21	34	and	and	CCONJ
ap-10701	21	35	applications	application	NOUN
ap-10701	21	36	to	to	ADP
ap-10701	21	37	two	two	NUM
ap-10701	21	38	different	different	ADJ
ap-10701	21	39	systems	system	NOUN
ap-10701	21	40	of	of	ADP
ap-10701	21	41	reaction	reaction	NOUN
ap-10701	21	42	-	-	PUNCT
ap-10701	21	43	diffusion	diffusion	NOUN
ap-10701	21	44	equations	equation	NOUN
ap-10701	21	45	,	,	PUNCT
ap-10701	21	46	including	include	VERB
ap-10701	21	47	computational	computational	ADJ
ap-10701	21	48	results	result	NOUN
ap-10701	21	49	.	.	PUNCT
ap-10701	22	1	we	we	PRON
ap-10701	22	2	also	also	ADV
ap-10701	22	3	indicate	indicate	VERB
ap-10701	22	4	possible	possible	ADJ
ap-10701	22	5	generalizations	generalization	NOUN
ap-10701	22	6	of	of	ADP
ap-10701	22	7	the	the	DET
ap-10701	22	8	presented	present	VERB
ap-10701	22	9	approach	approach	NOUN
ap-10701	22	10	.	.	PUNCT
ap-10701	23	1	2	2	X
ap-10701	23	2	.	.	X
ap-10701	23	3	reaction	reaction	NOUN
ap-10701	23	4	-	-	PUNCT
ap-10701	23	5	diffusion	diffusion	NOUN
ap-10701	23	6	systems	system	NOUN
ap-10701	23	7	in	in	ADP
ap-10701	23	8	the	the	DET
ap-10701	23	9	following	following	NOUN
ap-10701	23	10	,	,	PUNCT
ap-10701	23	11	we	we	PRON
ap-10701	23	12	consider	consider	VERB
ap-10701	23	13	an	an	DET
ap-10701	23	14	initial	initial	ADJ
ap-10701	23	15	-	-	PUNCT
ap-10701	23	16	boundary	boundary	ADJ
ap-10701	23	17	-	-	PUNCT
ap-10701	23	18	value	value	NOUN
ap-10701	23	19	problem	problem	NOUN
ap-10701	23	20	for	for	ADP
ap-10701	23	21	a	a	DET
ap-10701	23	22	system	system	NOUN
ap-10701	23	23	of	of	ADP
ap-10701	23	24	d	d	PROPN
ap-10701	23	25	reaction	reaction	NOUN
ap-10701	23	26	-	-	PUNCT
ap-10701	23	27	diffusion	diffusion	NOUN
ap-10701	23	28	equations	equation	NOUN
ap-10701	23	29	on	on	ADP
ap-10701	23	30	a	a	DET
ap-10701	23	31	space	space	NOUN
ap-10701	23	32	interval	interval	NOUN
ap-10701	23	33	(	(	PUNCT
ap-10701	23	34	a	a	DET
ap-10701	23	35	,	,	PUNCT
ap-10701	23	36	b	b	NOUN
ap-10701	23	37	)	)	PUNCT
ap-10701	23	38	and	and	CCONJ
ap-10701	23	39	a	a	DET
ap-10701	23	40	time	time	NOUN
ap-10701	23	41	interval	interval	NOUN
ap-10701	23	42	(	(	PUNCT
ap-10701	23	43	0	0	NUM
ap-10701	23	44	,	,	PUNCT
ap-10701	23	45	t	t	NOUN
ap-10701	23	46	)	)	PUNCT
ap-10701	23	47	in	in	ADP
ap-10701	23	48	the	the	DET
ap-10701	23	49	form	form	NOUN
ap-10701	23	50	:	:	PUNCT
ap-10701	23	51	∂tu	∂tu	ADV
ap-10701	23	52	=	=	SYM
ap-10701	23	53	d∂2	d∂2	PROPN
ap-10701	23	54	xxu	xxu	PROPN
ap-10701	23	55	+	+	X
ap-10701	23	56	f(u	f(u	ADJ
ap-10701	23	57	)	)	PUNCT
ap-10701	23	58	in	in	ADP
ap-10701	23	59	(	(	PUNCT
ap-10701	23	60	0	0	NUM
ap-10701	23	61	,	,	PUNCT
ap-10701	23	62	t	t	NOUN
ap-10701	23	63	)	)	PUNCT
ap-10701	23	64	×	×	NOUN
ap-10701	23	65	(	(	PUNCT
ap-10701	23	66	a	a	DET
ap-10701	23	67	,	,	PUNCT
ap-10701	23	68	b	b	NOUN
ap-10701	23	69	)	)	PUNCT
ap-10701	23	70	,	,	PUNCT
ap-10701	23	71	u	u	NOUN
ap-10701	23	72	|x	|x	NOUN
ap-10701	23	73	=	=	SYM
ap-10701	23	74	a	a	NOUN
ap-10701	23	75	=	=	SYM
ap-10701	23	76	0	0	NUM
ap-10701	23	77	,	,	PUNCT
ap-10701	23	78	u	u	NOUN
ap-10701	23	79	|x	|x	NOUN
ap-10701	23	80	=	=	SYM
ap-10701	23	81	b	b	NOUN
ap-10701	23	82	=	=	SYM
ap-10701	23	83	0	0	PROPN
ap-10701	23	84	,	,	PUNCT
ap-10701	23	85	u	u	PROPN
ap-10701	23	86	|t=0	|t=0	PROPN
ap-10701	23	87	=	=	PUNCT
ap-10701	23	88	uini	uini	NOUN
ap-10701	23	89	,	,	PUNCT
ap-10701	23	90	(	(	PUNCT
ap-10701	23	91	1	1	X
ap-10701	23	92	)	)	PUNCT
ap-10701	23	93	where	where	SCONJ
ap-10701	23	94	d	d	PROPN
ap-10701	23	95	∈	∈	PROPN
ap-10701	23	96	rd×d	rd×d	PROPN
ap-10701	23	97	,	,	PUNCT
ap-10701	23	98	d	d	PROPN
ap-10701	23	99	∈	∈	PROPN
ap-10701	23	100	n	n	CCONJ
ap-10701	23	101	,	,	PUNCT
ap-10701	23	102	is	be	AUX
ap-10701	23	103	the	the	DET
ap-10701	23	104	positive	positive	ADJ
ap-10701	23	105	definite	definite	ADJ
ap-10701	23	106	,	,	PUNCT
ap-10701	23	107	for	for	ADP
ap-10701	23	108	simplicity	simplicity	NOUN
ap-10701	23	109	diagonal	diagonal	ADJ
ap-10701	23	110	,	,	PUNCT
ap-10701	23	111	matrix	matrix	NOUN
ap-10701	23	112	,	,	PUNCT
ap-10701	23	113	f	f	X
ap-10701	23	114	:	:	PUNCT
ap-10701	23	115	rd	rd	PROPN
ap-10701	23	116	→	→	SYM
ap-10701	23	117	rd	rd	PROPN
ap-10701	23	118	is	be	AUX
ap-10701	23	119	the	the	DET
ap-10701	23	120	vectorvalued	vectorvalue	VERB
ap-10701	23	121	c(1)(rd	c(1)(rd	PROPN
ap-10701	23	122	)	)	PUNCT
ap-10701	23	123	map	map	NOUN
ap-10701	23	124	,	,	PUNCT
ap-10701	23	125	u	u	NOUN
ap-10701	23	126	:	:	PUNCT
ap-10701	23	127	[	[	X
ap-10701	23	128	0	0	NUM
ap-10701	23	129	,	,	PUNCT
ap-10701	23	130	t	t	X
ap-10701	23	131	]	]	PUNCT
ap-10701	23	132	×	×	NOUN
ap-10701	24	1	[	[	X
ap-10701	24	2	a	a	X
ap-10701	24	3	,	,	PUNCT
ap-10701	24	4	b	b	NOUN
ap-10701	24	5	]	]	PUNCT
ap-10701	24	6	→	→	SYM
ap-10701	24	7	rd	rd	NOUN
ap-10701	24	8	is	be	AUX
ap-10701	24	9	the	the	DET
ap-10701	24	10	solution	solution	NOUN
ap-10701	24	11	.	.	PUNCT
ap-10701	25	1	as	as	SCONJ
ap-10701	25	2	discussed	discuss	VERB
ap-10701	25	3	in	in	ADP
ap-10701	25	4	literature	literature	NOUN
ap-10701	25	5	(	(	PUNCT
ap-10701	25	6	see	see	VERB
ap-10701	25	7	e.g.	e.g.	ADV
ap-10701	25	8	[	[	X
ap-10701	25	9	1	1	NUM
ap-10701	25	10	,	,	PUNCT
ap-10701	25	11	3	3	NUM
ap-10701	25	12	,	,	PUNCT
ap-10701	25	13	13	13	NUM
ap-10701	25	14	,	,	PUNCT
ap-10701	25	15	15	15	NUM
ap-10701	25	16	,	,	PUNCT
ap-10701	25	17	17	17	NUM
ap-10701	25	18	]	]	NUM
ap-10701	25	19	)	)	PUNCT
ap-10701	25	20	,	,	PUNCT
ap-10701	25	21	the	the	DET
ap-10701	25	22	system	system	NOUN
ap-10701	25	23	(	(	PUNCT
ap-10701	25	24	1	1	X
ap-10701	25	25	)	)	PUNCT
ap-10701	25	26	is	be	AUX
ap-10701	25	27	studied	study	VERB
ap-10701	25	28	using	use	VERB
ap-10701	25	29	the	the	DET
ap-10701	25	30	weak	weak	ADJ
ap-10701	25	31	formulation	formulation	NOUN
ap-10701	25	32	.	.	PUNCT
ap-10701	26	1	for	for	ADP
ap-10701	26	2	this	this	DET
ap-10701	26	3	purpose	purpose	NOUN
ap-10701	26	4	,	,	PUNCT
ap-10701	26	5	we	we	PRON
ap-10701	26	6	introduce	introduce	VERB
ap-10701	26	7	the	the	DET
ap-10701	26	8	lebesgue	lebesgue	NOUN
ap-10701	26	9	space	space	NOUN
ap-10701	26	10	h	h	PROPN
ap-10701	26	11	=	=	PROPN
ap-10701	26	12	l2((a	l2((a	PROPN
ap-10701	26	13	,	,	PUNCT
ap-10701	26	14	b);rd	b);rd	NOUN
ap-10701	26	15	)	)	PUNCT
ap-10701	26	16	of	of	ADP
ap-10701	26	17	square	square	ADJ
ap-10701	26	18	-	-	PUNCT
ap-10701	26	19	integrable	integrable	ADJ
ap-10701	26	20	vector	vector	NOUN
ap-10701	26	21	functions	function	NOUN
ap-10701	26	22	u	u	NOUN
ap-10701	26	23	,	,	PUNCT
ap-10701	26	24	v	v	INTJ
ap-10701	26	25	,	,	PUNCT
ap-10701	26	26	with	with	ADP
ap-10701	26	27	the	the	DET
ap-10701	26	28	scalar	scalar	ADJ
ap-10701	26	29	product	product	NOUN
ap-10701	26	30	:	:	PUNCT
ap-10701	26	31	(	(	PUNCT
ap-10701	26	32	u	u	NOUN
ap-10701	26	33	,	,	PUNCT
ap-10701	26	34	v	v	NOUN
ap-10701	26	35	)	)	PUNCT
ap-10701	26	36	=	=	SYM
ap-10701	27	1	d∑	d∑	PROPN
ap-10701	28	1	i=1	i=1	PROPN
ap-10701	28	2	∫	∫	PROPN
ap-10701	29	1	b	b	PROPN
ap-10701	29	2	a	a	DET
ap-10701	29	3	ui(x)vi(x)dx	ui(x)vi(x)dx	PROPN
ap-10701	29	4	,	,	PUNCT
ap-10701	29	5	and	and	CCONJ
ap-10701	29	6	the	the	DET
ap-10701	29	7	sobolev	sobolev	ADJ
ap-10701	29	8	space	space	NOUN
ap-10701	29	9	of	of	ADP
ap-10701	29	10	vector	vector	NOUN
ap-10701	29	11	-	-	PUNCT
ap-10701	29	12	valued	value	VERB
ap-10701	29	13	functions	function	NOUN
ap-10701	29	14	v	v	NOUN
ap-10701	29	15	=	=	PUNCT
ap-10701	29	16	ẘ	ẘ	VERB
ap-10701	29	17	(	(	PUNCT
ap-10701	29	18	1	1	NUM
ap-10701	29	19	)	)	SYM
ap-10701	29	20	2	2	NUM
ap-10701	29	21	(	(	PUNCT
ap-10701	29	22	(	(	PUNCT
ap-10701	29	23	a	a	PRON
ap-10701	29	24	,	,	PUNCT
ap-10701	29	25	b);rd	b);rd	VERB
ap-10701	29	26	)	)	PUNCT
ap-10701	29	27	with	with	ADP
ap-10701	29	28	the	the	DET
ap-10701	29	29	scalar	scalar	ADJ
ap-10701	29	30	product	product	NOUN
ap-10701	29	31	:	:	PUNCT
ap-10701	29	32	(	(	PUNCT
ap-10701	29	33	u	u	NOUN
ap-10701	29	34	,	,	PUNCT
ap-10701	29	35	v	v	NOUN
ap-10701	29	36	)	)	PUNCT
ap-10701	29	37	v	v	NOUN
ap-10701	29	38	=	=	SYM
ap-10701	29	39	d∑	d∑	PROPN
ap-10701	30	1	i=1	i=1	PROPN
ap-10701	30	2	∫	∫	PROPN
ap-10701	31	1	b	b	PROPN
ap-10701	31	2	a	a	DET
ap-10701	31	3	dui(x	dui(x	PROPN
ap-10701	31	4	)	)	PUNCT
ap-10701	31	5	dx	dx	PROPN
ap-10701	31	6	dvi(x	dvi(x	PROPN
ap-10701	31	7	)	)	PUNCT
ap-10701	31	8	dx	dx	PROPN
ap-10701	31	9	dx	dx	PROPN
ap-10701	31	10	,	,	PUNCT
ap-10701	31	11	for	for	ADP
ap-10701	31	12	u	u	NOUN
ap-10701	31	13	=	=	PUNCT
ap-10701	32	1	[	[	X
ap-10701	32	2	u1	u1	NOUN
ap-10701	32	3	,	,	PUNCT
ap-10701	32	4	.	.	PUNCT
ap-10701	32	5	.	.	PUNCT
ap-10701	33	1	.	.	PUNCT
ap-10701	34	1	,	,	PUNCT
ap-10701	34	2	ud]t	ud]t	PROPN
ap-10701	34	3	,	,	PUNCT
ap-10701	34	4	v	v	NOUN
ap-10701	34	5	=	=	SYM
ap-10701	35	1	[	[	X
ap-10701	35	2	v1	v1	NOUN
ap-10701	35	3	,	,	PUNCT
ap-10701	35	4	.	.	PUNCT
ap-10701	35	5	.	.	PUNCT
ap-10701	36	1	.	.	PUNCT
ap-10701	37	1	,	,	PUNCT
ap-10701	37	2	vd]t	vd]t	PROPN
ap-10701	37	3	.	.	PUNCT
ap-10701	38	1	as	as	ADP
ap-10701	38	2	in	in	ADP
ap-10701	38	3	literature	literature	NOUN
ap-10701	38	4	(	(	PUNCT
ap-10701	38	5	see	see	VERB
ap-10701	38	6	e.g.	e.g.	ADV
ap-10701	38	7	[	[	X
ap-10701	38	8	3	3	NUM
ap-10701	38	9	,	,	PUNCT
ap-10701	38	10	15	15	NUM
ap-10701	38	11	]	]	NUM
ap-10701	38	12	)	)	PUNCT
ap-10701	38	13	,	,	PUNCT
ap-10701	38	14	problem	problem	NOUN
ap-10701	38	15	(	(	PUNCT
ap-10701	38	16	1	1	X
ap-10701	38	17	)	)	PUNCT
ap-10701	38	18	has	have	VERB
ap-10701	38	19	the	the	DET
ap-10701	38	20	weak	weak	ADJ
ap-10701	38	21	solution	solution	NOUN
ap-10701	38	22	u	u	NOUN
ap-10701	38	23	:	:	PUNCT
ap-10701	38	24	(	(	PUNCT
ap-10701	38	25	0	0	NUM
ap-10701	38	26	,	,	PUNCT
ap-10701	38	27	t	t	NOUN
ap-10701	38	28	)	)	PUNCT
ap-10701	38	29	→	→	SYM
ap-10701	38	30	v	v	NOUN
ap-10701	38	31	,	,	PUNCT
ap-10701	38	32	provided	provide	VERB
ap-10701	38	33	:	:	PUNCT
ap-10701	38	34	d	d	X
ap-10701	38	35	dt	dt	X
ap-10701	38	36	(	(	PUNCT
ap-10701	38	37	u	u	NOUN
ap-10701	38	38	,	,	PUNCT
ap-10701	38	39	v	v	NOUN
ap-10701	38	40	)	)	PUNCT
ap-10701	39	1	+	+	CCONJ
ap-10701	39	2	(	(	PUNCT
ap-10701	39	3	du	du	X
ap-10701	39	4	,	,	PUNCT
ap-10701	39	5	v	v	NOUN
ap-10701	39	6	)	)	PUNCT
ap-10701	39	7	v	v	NOUN
ap-10701	39	8	=	=	PUNCT
ap-10701	39	9	(	(	PUNCT
ap-10701	39	10	f(u	f(u	PROPN
ap-10701	39	11	)	)	PUNCT
ap-10701	39	12	,	,	PUNCT
ap-10701	39	13	v	v	NOUN
ap-10701	39	14	)	)	PUNCT
ap-10701	39	15	,	,	PUNCT
ap-10701	39	16	for	for	ADP
ap-10701	39	17	all	all	DET
ap-10701	39	18	v	v	ADP
ap-10701	39	19	∈	∈	PROPN
ap-10701	39	20	v	v	NOUN
ap-10701	39	21	,	,	PUNCT
ap-10701	39	22	in	in	ADP
ap-10701	39	23	the	the	DET
ap-10701	39	24	sense	sense	NOUN
ap-10701	39	25	of	of	ADP
ap-10701	39	26	d′((0	d′((0	PROPN
ap-10701	39	27	,	,	PUNCT
ap-10701	39	28	t	t	NOUN
ap-10701	39	29	)	)	PUNCT
ap-10701	39	30	)	)	PUNCT
ap-10701	39	31	,	,	PUNCT
ap-10701	39	32	(	(	PUNCT
ap-10701	39	33	2	2	X
ap-10701	39	34	)	)	PUNCT
ap-10701	39	35	u	u	NOUN
ap-10701	39	36	|t=0	|t=0	PROPN
ap-10701	39	37	=	=	SYM
ap-10701	39	38	uini	uini	NOUN
ap-10701	39	39	.	.	PUNCT
ap-10701	40	1	566	566	NUM
ap-10701	40	2	https://doi.org/10.14311/ap.2025.65.0566	https://doi.org/10.14311/ap.2025.65.0566	PROPN
ap-10701	40	3	https://creativecommons.org/licenses/by/4.0/	https://creativecommons.org/licenses/by/4.0/	PROPN
ap-10701	40	4	https://www.cvut.cz/en	https://www.cvut.cz/en	PROPN
ap-10701	40	5	vol	vol	NOUN
ap-10701	40	6	.	.	PROPN
ap-10701	41	1	65	65	NUM
ap-10701	41	2	no	no	NOUN
ap-10701	41	3	.	.	PUNCT
ap-10701	42	1	5/2025	5/2025	NUM
ap-10701	42	2	method	method	NOUN
ap-10701	42	3	of	of	ADP
ap-10701	42	4	lines	line	NOUN
ap-10701	42	5	for	for	ADP
ap-10701	42	6	reaction	reaction	NOUN
ap-10701	42	7	-	-	PUNCT
ap-10701	42	8	diffusion	diffusion	NOUN
ap-10701	42	9	systems	system	NOUN
ap-10701	42	10	.	.	PUNCT
ap-10701	42	11	.	.	PUNCT
ap-10701	42	12	.	.	PUNCT
ap-10701	43	1	remark	remark	NOUN
ap-10701	43	2	in	in	ADP
ap-10701	43	3	the	the	DET
ap-10701	43	4	given	give	VERB
ap-10701	43	5	framework	framework	NOUN
ap-10701	43	6	,	,	PUNCT
ap-10701	43	7	the	the	DET
ap-10701	43	8	weak	weak	ADJ
ap-10701	43	9	solution	solution	NOUN
ap-10701	43	10	,	,	PUNCT
ap-10701	43	11	provided	provide	VERB
ap-10701	43	12	it	it	PRON
ap-10701	43	13	exists	exist	VERB
ap-10701	43	14	,	,	PUNCT
ap-10701	43	15	is	be	AUX
ap-10701	43	16	in	in	ADP
ap-10701	43	17	fact	fact	NOUN
ap-10701	43	18	a	a	DET
ap-10701	43	19	continuous	continuous	ADJ
ap-10701	43	20	map	map	NOUN
ap-10701	43	21	,	,	PUNCT
ap-10701	43	22	due	due	ADP
ap-10701	43	23	to	to	ADP
ap-10701	43	24	the	the	DET
ap-10701	43	25	corresponding	corresponding	ADJ
ap-10701	43	26	embedding	embedding	NOUN
ap-10701	43	27	of	of	ADP
ap-10701	43	28	the	the	DET
ap-10701	43	29	sobolev	sobolev	NOUN
ap-10701	43	30	space	space	NOUN
ap-10701	43	31	(	(	PUNCT
ap-10701	43	32	see	see	VERB
ap-10701	43	33	[	[	X
ap-10701	43	34	3	3	NUM
ap-10701	43	35	]	]	NUM
ap-10701	43	36	)	)	PUNCT
ap-10701	43	37	.	.	PUNCT
ap-10701	44	1	the	the	DET
ap-10701	44	2	existence	existence	NOUN
ap-10701	44	3	as	as	ADV
ap-10701	44	4	well	well	ADV
ap-10701	44	5	as	as	ADP
ap-10701	44	6	convergence	convergence	NOUN
ap-10701	44	7	of	of	ADP
ap-10701	44	8	the	the	DET
ap-10701	44	9	numerical	numerical	ADJ
ap-10701	44	10	solution	solution	NOUN
ap-10701	44	11	are	be	AUX
ap-10701	44	12	studied	study	VERB
ap-10701	44	13	using	use	VERB
ap-10701	44	14	suitable	suitable	ADJ
ap-10701	44	15	bounds	bound	NOUN
ap-10701	44	16	for	for	ADP
ap-10701	44	17	norms	norm	NOUN
ap-10701	44	18	of	of	ADP
ap-10701	44	19	the	the	DET
ap-10701	44	20	solution	solution	NOUN
ap-10701	44	21	(	(	PUNCT
ap-10701	44	22	see	see	VERB
ap-10701	44	23	[	[	X
ap-10701	44	24	10	10	NUM
ap-10701	44	25	,	,	PUNCT
ap-10701	44	26	15	15	NUM
ap-10701	44	27	]	]	NUM
ap-10701	44	28	)	)	PUNCT
ap-10701	44	29	.	.	PUNCT
ap-10701	45	1	one	one	NUM
ap-10701	45	2	way	way	NOUN
ap-10701	45	3	to	to	PART
ap-10701	45	4	obtain	obtain	VERB
ap-10701	45	5	them	they	PRON
ap-10701	45	6	is	be	AUX
ap-10701	45	7	based	base	VERB
ap-10701	45	8	on	on	ADP
ap-10701	45	9	a	a	DET
ap-10701	45	10	contractive	contractive	ADJ
ap-10701	45	11	property	property	NOUN
ap-10701	45	12	of	of	ADP
ap-10701	45	13	the	the	DET
ap-10701	45	14	reaction	reaction	NOUN
ap-10701	45	15	field	field	NOUN
ap-10701	45	16	(	(	PUNCT
ap-10701	45	17	f(u	f(u	PROPN
ap-10701	45	18	)	)	PUNCT
ap-10701	45	19	,	,	PUNCT
ap-10701	45	20	v	v	NOUN
ap-10701	45	21	)	)	PUNCT
ap-10701	45	22	,	,	PUNCT
ap-10701	45	23	known	know	VERB
ap-10701	45	24	as	as	ADP
ap-10701	45	25	the	the	DET
ap-10701	45	26	invariant	invariant	ADJ
ap-10701	45	27	region	region	NOUN
ap-10701	45	28	(	(	PUNCT
ap-10701	45	29	see	see	VERB
ap-10701	45	30	e.g.	e.g.	ADV
ap-10701	45	31	[	[	X
ap-10701	45	32	1	1	NUM
ap-10701	45	33	]	]	NUM
ap-10701	45	34	)	)	PUNCT
ap-10701	45	35	.	.	PUNCT
ap-10701	46	1	definition	definition	NOUN
ap-10701	46	2	1	1	NUM
ap-10701	46	3	.	.	PUNCT
ap-10701	47	1	the	the	DET
ap-10701	47	2	system	system	NOUN
ap-10701	47	3	(	(	PUNCT
ap-10701	47	4	1	1	X
ap-10701	47	5	)	)	PUNCT
ap-10701	47	6	is	be	AUX
ap-10701	47	7	said	say	VERB
ap-10701	47	8	to	to	PART
ap-10701	47	9	possess	possess	VERB
ap-10701	47	10	an	an	DET
ap-10701	47	11	invariant	invariant	ADJ
ap-10701	47	12	region	region	NOUN
ap-10701	47	13	o	o	PROPN
ap-10701	47	14	⊂	⊂	PROPN
ap-10701	47	15	rd	rd	PROPN
ap-10701	47	16	,	,	PUNCT
ap-10701	47	17	provided	provide	VERB
ap-10701	47	18	o	o	PROPN
ap-10701	47	19	is	be	AUX
ap-10701	47	20	a	a	DET
ap-10701	47	21	bounded	bound	VERB
ap-10701	47	22	closed	closed	ADJ
ap-10701	47	23	convex	convex	NOUN
ap-10701	47	24	set	set	NOUN
ap-10701	47	25	,	,	PUNCT
ap-10701	47	26	and	and	CCONJ
ap-10701	47	27	for	for	ADP
ap-10701	47	28	each	each	DET
ap-10701	47	29	initial	initial	ADJ
ap-10701	47	30	condition	condition	NOUN
ap-10701	47	31	uini	uini	PROPN
ap-10701	47	32	∈	∈	PROPN
ap-10701	47	33	c((a	c((a	PROPN
ap-10701	47	34	,	,	PUNCT
ap-10701	47	35	b);rd	b);rd	NOUN
ap-10701	47	36	)	)	PUNCT
ap-10701	47	37	,	,	PUNCT
ap-10701	47	38	with	with	ADP
ap-10701	47	39	values	value	NOUN
ap-10701	47	40	in	in	ADP
ap-10701	47	41	o	o	NOUN
ap-10701	47	42	,	,	PUNCT
ap-10701	47	43	the	the	DET
ap-10701	47	44	solution	solution	NOUN
ap-10701	47	45	values	value	VERB
ap-10701	47	46	u(t	u(t	NOUN
ap-10701	47	47	,	,	PUNCT
ap-10701	47	48	x	x	X
ap-10701	47	49	)	)	PUNCT
ap-10701	47	50	also	also	ADV
ap-10701	47	51	are	be	AUX
ap-10701	47	52	in	in	ADP
ap-10701	47	53	o	o	NOUN
ap-10701	47	54	for	for	ADP
ap-10701	47	55	all	all	DET
ap-10701	47	56	x	x	SYM
ap-10701	47	57	∈	∈	PROPN
ap-10701	47	58	(	(	PUNCT
ap-10701	47	59	a	a	DET
ap-10701	47	60	,	,	PUNCT
ap-10701	47	61	b	b	NOUN
ap-10701	47	62	)	)	PUNCT
ap-10701	47	63	and	and	CCONJ
ap-10701	47	64	all	all	DET
ap-10701	47	65	t	t	NOUN
ap-10701	47	66	>	>	X
ap-10701	47	67	0	0	PUNCT
ap-10701	48	1	for	for	ADP
ap-10701	48	2	which	which	PRON
ap-10701	48	3	the	the	DET
ap-10701	48	4	solution	solution	NOUN
ap-10701	48	5	exists	exist	VERB
ap-10701	48	6	.	.	PUNCT
ap-10701	49	1	we	we	PRON
ap-10701	49	2	aim	aim	VERB
ap-10701	49	3	to	to	PART
ap-10701	49	4	show	show	VERB
ap-10701	49	5	that	that	SCONJ
ap-10701	49	6	such	such	DET
ap-10701	49	7	a	a	DET
ap-10701	49	8	property	property	NOUN
ap-10701	49	9	valid	valid	NOUN
ap-10701	49	10	for	for	ADP
ap-10701	49	11	the	the	DET
ap-10701	49	12	numerical	numerical	ADJ
ap-10701	49	13	solution	solution	NOUN
ap-10701	49	14	guarantees	guarantee	VERB
ap-10701	49	15	the	the	DET
ap-10701	49	16	convergence	convergence	NOUN
ap-10701	49	17	of	of	ADP
ap-10701	49	18	the	the	DET
ap-10701	49	19	numerical	numerical	ADJ
ap-10701	49	20	solution	solution	NOUN
ap-10701	49	21	to	to	ADP
ap-10701	49	22	the	the	DET
ap-10701	49	23	weak	weak	ADJ
ap-10701	49	24	solution	solution	NOUN
ap-10701	49	25	.	.	PUNCT
ap-10701	50	1	3	3	X
ap-10701	50	2	.	.	X
ap-10701	50	3	method	method	NOUN
ap-10701	50	4	of	of	ADP
ap-10701	50	5	lines	line	NOUN
ap-10701	50	6	3.1	3.1	NUM
ap-10701	50	7	.	.	PUNCT
ap-10701	51	1	finite	finite	ADJ
ap-10701	51	2	-	-	PUNCT
ap-10701	51	3	difference	difference	ADJ
ap-10701	51	4	discretization	discretization	NOUN
ap-10701	51	5	here	here	ADV
ap-10701	51	6	,	,	PUNCT
ap-10701	51	7	we	we	PRON
ap-10701	51	8	summarize	summarize	VERB
ap-10701	51	9	the	the	DET
ap-10701	51	10	use	use	NOUN
ap-10701	51	11	of	of	ADP
ap-10701	51	12	the	the	DET
ap-10701	51	13	finite	finite	ADJ
ap-10701	51	14	-	-	PUNCT
ap-10701	51	15	difference	difference	NOUN
ap-10701	51	16	method	method	NOUN
ap-10701	51	17	for	for	ADP
ap-10701	51	18	space	space	NOUN
ap-10701	51	19	discretization	discretization	NOUN
ap-10701	51	20	of	of	ADP
ap-10701	51	21	(	(	PUNCT
ap-10701	51	22	1	1	NUM
ap-10701	51	23	)	)	PUNCT
ap-10701	51	24	,	,	PUNCT
ap-10701	51	25	while	while	SCONJ
ap-10701	51	26	the	the	DET
ap-10701	51	27	time	time	NOUN
ap-10701	51	28	variable	variable	ADJ
ap-10701	51	29	remains	remain	VERB
ap-10701	51	30	continuous	continuous	ADJ
ap-10701	51	31	.	.	PUNCT
ap-10701	52	1	this	this	DET
ap-10701	52	2	widely	widely	ADV
ap-10701	52	3	used	use	VERB
ap-10701	52	4	approach	approach	NOUN
ap-10701	52	5	is	be	AUX
ap-10701	52	6	known	know	VERB
ap-10701	52	7	as	as	ADP
ap-10701	52	8	the	the	DET
ap-10701	52	9	method	method	NOUN
ap-10701	52	10	of	of	ADP
ap-10701	52	11	lines	line	NOUN
ap-10701	52	12	(	(	PUNCT
ap-10701	52	13	see	see	VERB
ap-10701	52	14	[	[	X
ap-10701	52	15	2	2	NUM
ap-10701	52	16	,	,	PUNCT
ap-10701	52	17	5	5	NUM
ap-10701	52	18	,	,	PUNCT
ap-10701	52	19	15	15	NUM
ap-10701	52	20	,	,	PUNCT
ap-10701	52	21	18	18	NUM
ap-10701	52	22	–	–	SYM
ap-10701	52	23	20	20	NUM
ap-10701	52	24	]	]	PUNCT
ap-10701	52	25	)	)	PUNCT
ap-10701	52	26	.	.	PUNCT
ap-10701	53	1	for	for	ADP
ap-10701	53	2	this	this	DET
ap-10701	53	3	purpose	purpose	NOUN
ap-10701	53	4	we	we	PRON
ap-10701	53	5	introduce	introduce	VERB
ap-10701	53	6	corresponding	correspond	VERB
ap-10701	53	7	notations	notation	NOUN
ap-10701	53	8	(	(	PUNCT
ap-10701	53	9	as	as	ADP
ap-10701	53	10	in	in	ADP
ap-10701	53	11	[	[	PUNCT
ap-10701	53	12	11	11	NUM
ap-10701	53	13	,	,	PUNCT
ap-10701	53	14	21	21	NUM
ap-10701	53	15	,	,	PUNCT
ap-10701	53	16	22	22	NUM
ap-10701	53	17	]	]	PUNCT
ap-10701	53	18	)	)	PUNCT
ap-10701	53	19	.	.	PUNCT
ap-10701	54	1	using	use	VERB
ap-10701	54	2	m	m	PROPN
ap-10701	54	3	∈	∈	NOUN
ap-10701	54	4	n	n	PRON
ap-10701	54	5	as	as	ADP
ap-10701	54	6	the	the	DET
ap-10701	54	7	number	number	NOUN
ap-10701	54	8	of	of	ADP
ap-10701	54	9	meshes	mesh	NOUN
ap-10701	54	10	,	,	PUNCT
ap-10701	54	11	and	and	CCONJ
ap-10701	54	12	h	h	NOUN
ap-10701	54	13	=	=	NOUN
ap-10701	54	14	b−a	b−a	X
ap-10701	54	15	m	m	VERB
ap-10701	54	16	as	as	ADP
ap-10701	54	17	the	the	DET
ap-10701	54	18	mesh	mesh	NOUN
ap-10701	54	19	size	size	NOUN
ap-10701	54	20	,	,	PUNCT
ap-10701	54	21	we	we	PRON
ap-10701	54	22	denote	denote	VERB
ap-10701	54	23	ωh	ωh	ADP
ap-10701	54	24	=	=	PUNCT
ap-10701	54	25	{	{	PUNCT
ap-10701	54	26	a	a	PROPN
ap-10701	54	27	+	+	X
ap-10701	54	28	jh	jh	PROPN
ap-10701	54	29	|	|	ADV
ap-10701	54	30	j	j	PROPN
ap-10701	54	31	=	=	PUNCT
ap-10701	54	32	0	0	PROPN
ap-10701	54	33	,	,	PUNCT
ap-10701	54	34	.	.	PUNCT
ap-10701	54	35	.	.	PUNCT
ap-10701	55	1	.	.	PUNCT
ap-10701	56	1	,	,	PUNCT
ap-10701	56	2	m	m	VERB
ap-10701	56	3	}	}	PUNCT
ap-10701	56	4	the	the	DET
ap-10701	56	5	finitedifference	finitedifference	NOUN
ap-10701	56	6	grid	grid	NOUN
ap-10701	56	7	,	,	PUNCT
ap-10701	56	8	ωh	ωh	ADP
ap-10701	56	9	:	:	PUNCT
ap-10701	56	10	=	=	X
ap-10701	56	11	{	{	PUNCT
ap-10701	56	12	a	a	PROPN
ap-10701	56	13	+	+	X
ap-10701	56	14	jh	jh	PROPN
ap-10701	56	15	|	|	ADV
ap-10701	56	16	j	j	PROPN
ap-10701	56	17	=	=	NOUN
ap-10701	56	18	1	1	NUM
ap-10701	56	19	,	,	PUNCT
ap-10701	56	20	.	.	PUNCT
ap-10701	56	21	.	.	PUNCT
ap-10701	57	1	.	.	PUNCT
ap-10701	58	1	,	,	PUNCT
ap-10701	58	2	m	m	VERB
ap-10701	58	3	−	−	PROPN
ap-10701	58	4	1	1	NUM
ap-10701	58	5	}	}	PUNCT
ap-10701	58	6	the	the	DET
ap-10701	58	7	internal	internal	ADJ
ap-10701	58	8	nodes	node	NOUN
ap-10701	58	9	.	.	PUNCT
ap-10701	59	1	we	we	PRON
ap-10701	59	2	abbreviate	abbreviate	VERB
ap-10701	59	3	the	the	DET
ap-10701	59	4	notation	notation	NOUN
ap-10701	59	5	of	of	ADP
ap-10701	59	6	values	value	NOUN
ap-10701	59	7	of	of	ADP
ap-10701	59	8	functions	function	NOUN
ap-10701	59	9	v	v	NOUN
ap-10701	59	10	:	:	PUNCT
ap-10701	59	11	ωh	ωh	ADP
ap-10701	59	12	→	→	SYM
ap-10701	59	13	rd	rd	NOUN
ap-10701	59	14	defined	define	VERB
ap-10701	59	15	on	on	ADP
ap-10701	59	16	ωh	ωh	DET
ap-10701	59	17	–	–	PUNCT
ap-10701	59	18	grid	grid	NOUN
ap-10701	59	19	functions	function	NOUN
ap-10701	59	20	–	–	PUNCT
ap-10701	59	21	as	as	ADP
ap-10701	59	22	vj	vj	PROPN
ap-10701	59	23	=	=	SYM
ap-10701	59	24	v	v	PROPN
ap-10701	59	25	(	(	PUNCT
ap-10701	59	26	a+	a+	X
ap-10701	59	27	jh	jh	PROPN
ap-10701	59	28	)	)	PUNCT
ap-10701	59	29	.	.	PUNCT
ap-10701	60	1	the	the	DET
ap-10701	60	2	space	space	NOUN
ap-10701	60	3	of	of	ADP
ap-10701	60	4	all	all	DET
ap-10701	60	5	grid	grid	NOUN
ap-10701	60	6	functions	function	NOUN
ap-10701	60	7	with	with	ADP
ap-10701	60	8	zero	zero	NUM
ap-10701	60	9	boundary	boundary	ADJ
ap-10701	60	10	values	value	NOUN
ap-10701	60	11	is	be	AUX
ap-10701	60	12	denoted	denote	VERB
ap-10701	60	13	as	as	ADP
ap-10701	60	14	hh	hh	PROPN
ap-10701	60	15	=	=	PRON
ap-10701	60	16	{	{	PUNCT
ap-10701	60	17	v	v	NOUN
ap-10701	60	18	:	:	PUNCT
ap-10701	60	19	ωh	ωh	PROPN
ap-10701	60	20	→	→	SYM
ap-10701	60	21	rd	rd	NOUN
ap-10701	60	22	|	|	NOUN
ap-10701	60	23	v0	v0	NOUN
ap-10701	60	24	=	=	SYM
ap-10701	60	25	0	0	NUM
ap-10701	60	26	,	,	PUNCT
ap-10701	60	27	vm	vm	X
ap-10701	60	28	=	=	NOUN
ap-10701	60	29	0	0	NUM
ap-10701	60	30	}	}	PUNCT
ap-10701	60	31	.	.	PUNCT
ap-10701	61	1	discretization	discretization	NOUN
ap-10701	61	2	of	of	ADP
ap-10701	61	3	the	the	DET
ap-10701	61	4	second	second	ADJ
ap-10701	61	5	space	space	NOUN
ap-10701	61	6	derivatives	derivative	NOUN
ap-10701	61	7	is	be	AUX
ap-10701	61	8	obtained	obtain	VERB
ap-10701	61	9	by	by	ADP
ap-10701	61	10	the	the	DET
ap-10701	61	11	central	central	ADJ
ap-10701	61	12	difference	difference	NOUN
ap-10701	61	13	with	with	ADP
ap-10701	61	14	corresponding	corresponding	ADJ
ap-10701	61	15	error	error	NOUN
ap-10701	61	16	of	of	ADP
ap-10701	61	17	approximation	approximation	NOUN
ap-10701	61	18	o(h2	o(h2	NOUN
ap-10701	61	19	)	)	PUNCT
ap-10701	61	20	.	.	PUNCT
ap-10701	62	1	vx	vx	PROPN
ap-10701	62	2	,	,	PUNCT
ap-10701	62	3	j	j	PROPN
ap-10701	62	4	=	=	NOUN
ap-10701	62	5	vj+1	vj+1	PROPN
ap-10701	62	6	−	−	PROPN
ap-10701	62	7	vj	vj	PROPN
ap-10701	62	8	h	h	PROPN
ap-10701	62	9	,	,	PUNCT
ap-10701	62	10	vx̄,j	vx̄,j	PUNCT
ap-10701	63	1	=	=	PRON
ap-10701	63	2	vj	vj	INTJ
ap-10701	64	1	−	−	PROPN
ap-10701	64	2	vj−1	vj−1	PROPN
ap-10701	64	3	h	h	PROPN
ap-10701	64	4	,	,	PUNCT
ap-10701	64	5	vx̄x	vx̄x	PROPN
ap-10701	64	6	,	,	PUNCT
ap-10701	64	7	j	j	X
ap-10701	64	8	=	=	NOUN
ap-10701	64	9	vj+1	vj+1	PROPN
ap-10701	65	1	−	−	NUM
ap-10701	65	2	2vj	2vj	X
ap-10701	65	3	+	+	NUM
ap-10701	65	4	vj−1	vj−1	PROPN
ap-10701	65	5	h2	h2	NOUN
ap-10701	65	6	.	.	PUNCT
ap-10701	66	1	next	next	ADV
ap-10701	66	2	,	,	PUNCT
ap-10701	66	3	for	for	ADP
ap-10701	66	4	the	the	DET
ap-10701	66	5	grid	grid	NOUN
ap-10701	66	6	functions	function	NOUN
ap-10701	66	7	v	v	NOUN
ap-10701	66	8	,	,	PUNCT
ap-10701	66	9	w	w	PROPN
ap-10701	66	10	∈	∈	NOUN
ap-10701	66	11	hh	hh	NOUN
ap-10701	66	12	,	,	PUNCT
ap-10701	66	13	we	we	PRON
ap-10701	66	14	denote	denote	VERB
ap-10701	66	15	the	the	DET
ap-10701	66	16	products	product	NOUN
ap-10701	66	17	and	and	CCONJ
ap-10701	66	18	norms	norm	NOUN
ap-10701	66	19	on	on	ADP
ap-10701	66	20	the	the	DET
ap-10701	66	21	grid	grid	NOUN
ap-10701	66	22	:	:	PUNCT
ap-10701	66	23	(	(	PUNCT
ap-10701	66	24	v	v	NOUN
ap-10701	66	25	,	,	PUNCT
ap-10701	66	26	w	w	NOUN
ap-10701	66	27	)	)	PUNCT
ap-10701	66	28	h	h	NOUN
ap-10701	67	1	=	=	SYM
ap-10701	67	2	m−1∑	m−1∑	PROPN
ap-10701	67	3	j=1	j=1	PROPN
ap-10701	67	4	hvjwj	hvjwj	ADV
ap-10701	67	5	,	,	PUNCT
ap-10701	67	6	∥v	∥v	PROPN
ap-10701	67	7	∥h	∥h	PROPN
ap-10701	67	8	=	=	NOUN
ap-10701	67	9	√	√	PROPN
ap-10701	67	10	(	(	PUNCT
ap-10701	67	11	v	v	NOUN
ap-10701	67	12	,	,	PUNCT
ap-10701	67	13	v	v	NOUN
ap-10701	67	14	)	)	PUNCT
ap-10701	67	15	h	h	NOUN
ap-10701	67	16	,	,	PUNCT
ap-10701	67	17	(	(	PUNCT
ap-10701	67	18	v	v	NOUN
ap-10701	67	19	,	,	PUNCT
ap-10701	67	20	w	w	NOUN
ap-10701	67	21	]	]	X
ap-10701	67	22	=	=	PUNCT
ap-10701	67	23	m∑	m∑	PROPN
ap-10701	67	24	j=1	j=1	PROPN
ap-10701	67	25	hvjwj	hvjwj	PROPN
ap-10701	67	26	,	,	PUNCT
ap-10701	67	27	||v	||v	NOUN
ap-10701	67	28	]	]	PUNCT
ap-10701	67	29	|	|	NOUN
ap-10701	67	30	=	=	SYM
ap-10701	67	31	√	√	PROPN
ap-10701	67	32	(	(	PUNCT
ap-10701	67	33	v	v	NOUN
ap-10701	67	34	,	,	PUNCT
ap-10701	67	35	v	v	X
ap-10701	67	36	]	]	PUNCT
ap-10701	67	37	.	.	PUNCT
ap-10701	68	1	we	we	PRON
ap-10701	68	2	notice	notice	VERB
ap-10701	68	3	that	that	SCONJ
ap-10701	68	4	the	the	DET
ap-10701	68	5	integration	integration	NOUN
ap-10701	68	6	by	by	ADP
ap-10701	68	7	parts	part	NOUN
ap-10701	68	8	can	can	AUX
ap-10701	68	9	be	be	AUX
ap-10701	68	10	used	use	VERB
ap-10701	68	11	:	:	PUNCT
ap-10701	68	12	(	(	PUNCT
ap-10701	68	13	v	v	NOUN
ap-10701	68	14	,	,	PUNCT
ap-10701	68	15	wx)h	wx)h	PROPN
ap-10701	68	16	=	=	PUNCT
ap-10701	68	17	vmwm	vmwm	NOUN
ap-10701	68	18	−	−	NOUN
ap-10701	68	19	v0w1	v0w1	ADP
ap-10701	68	20	−	−	PROPN
ap-10701	68	21	(	(	PUNCT
ap-10701	68	22	vx̄,w	vx̄,w	X
ap-10701	68	23	]	]	PUNCT
ap-10701	68	24	,	,	PUNCT
ap-10701	68	25	which	which	PRON
ap-10701	68	26	obviously	obviously	ADV
ap-10701	68	27	simplifies	simplify	VERB
ap-10701	68	28	on	on	ADP
ap-10701	68	29	hh	hh	PROPN
ap-10701	68	30	.	.	PUNCT
ap-10701	69	1	we	we	PRON
ap-10701	69	2	also	also	ADV
ap-10701	69	3	recall	recall	VERB
ap-10701	69	4	the	the	DET
ap-10701	69	5	maximum	maximum	ADJ
ap-10701	69	6	norm	norm	NOUN
ap-10701	69	7	:	:	PUNCT
ap-10701	69	8	∥v	∥v	PROPN
ap-10701	69	9	∥0,h	∥0,h	PROPN
ap-10701	69	10	=	=	SYM
ap-10701	69	11	max{|vj	max{|vj	NOUN
ap-10701	70	1	|	|	ADV
ap-10701	70	2	|	|	ADV
ap-10701	70	3	j	j	PROPN
ap-10701	70	4	=	=	SYM
ap-10701	70	5	0	0	PROPN
ap-10701	70	6	,	,	PUNCT
ap-10701	70	7	.	.	PUNCT
ap-10701	70	8	.	.	PUNCT
ap-10701	70	9	.	.	PUNCT
ap-10701	71	1	,	,	PUNCT
ap-10701	71	2	m	m	VERB
ap-10701	71	3	}	}	PUNCT
ap-10701	71	4	,	,	PUNCT
ap-10701	71	5	and	and	CCONJ
ap-10701	71	6	the	the	DET
ap-10701	71	7	embedding	embed	VERB
ap-10701	71	8	inequalities	inequality	NOUN
ap-10701	71	9	discussed	discuss	VERB
ap-10701	71	10	in	in	ADP
ap-10701	71	11	[	[	X
ap-10701	71	12	11	11	NUM
ap-10701	71	13	,	,	PUNCT
ap-10701	71	14	22	22	NUM
ap-10701	71	15	]	]	PUNCT
ap-10701	71	16	:	:	PUNCT
ap-10701	71	17	∥v	∥v	PROPN
ap-10701	71	18	∥0,h	∥0,h	PROPN
ap-10701	71	19	≤	≤	PROPN
ap-10701	71	20	c(a	c(a	PROPN
ap-10701	71	21	,	,	PUNCT
ap-10701	71	22	b)||v	b)||v	NOUN
ap-10701	71	23	]	]	PUNCT
ap-10701	71	24	|	|	ADV
ap-10701	71	25	.	.	PUNCT
ap-10701	72	1	(	(	PUNCT
ap-10701	72	2	3	3	X
ap-10701	72	3	)	)	PUNCT
ap-10701	72	4	we	we	PRON
ap-10701	72	5	then	then	ADV
ap-10701	72	6	discretize	discretize	VERB
ap-10701	72	7	(	(	PUNCT
ap-10701	72	8	1	1	NUM
ap-10701	72	9	)	)	PUNCT
ap-10701	72	10	and	and	CCONJ
ap-10701	72	11	design	design	VERB
ap-10701	72	12	the	the	DET
ap-10701	72	13	semi	semi	ADJ
ap-10701	72	14	-	-	ADJ
ap-10701	72	15	discrete	discrete	ADJ
ap-10701	72	16	scheme	scheme	NOUN
ap-10701	72	17	:	:	PUNCT
ap-10701	72	18	dz	dz	ADJ
ap-10701	72	19	dt	dt	NOUN
ap-10701	72	20	=	=	SYM
ap-10701	72	21	dzx̄x	dzx̄x	PROPN
ap-10701	72	22	+	+	NUM
ap-10701	72	23	f(z	f(z	NOUN
ap-10701	72	24	)	)	PUNCT
ap-10701	72	25	,	,	PUNCT
ap-10701	72	26	in	in	ADP
ap-10701	72	27	(	(	PUNCT
ap-10701	72	28	0	0	NUM
ap-10701	72	29	,	,	PUNCT
ap-10701	72	30	t	t	NOUN
ap-10701	72	31	)	)	PUNCT
ap-10701	72	32	×	×	PROPN
ap-10701	72	33	ωh	ωh	PROPN
ap-10701	72	34	,	,	PUNCT
ap-10701	72	35	z|t=0=	z|t=0=	PROPN
ap-10701	72	36	zini	zini	PROPN
ap-10701	72	37	,	,	PUNCT
ap-10701	72	38	in	in	ADP
ap-10701	72	39	ωh	ωh	ADP
ap-10701	72	40	,	,	PUNCT
ap-10701	72	41	(	(	PUNCT
ap-10701	72	42	4	4	X
ap-10701	72	43	)	)	PUNCT
ap-10701	72	44	z0	z0	NOUN
ap-10701	72	45	=	=	SYM
ap-10701	72	46	0	0	PROPN
ap-10701	72	47	,	,	PUNCT
ap-10701	72	48	zm	zm	PROPN
ap-10701	72	49	=	=	SYM
ap-10701	72	50	0	0	PROPN
ap-10701	72	51	,	,	PUNCT
ap-10701	72	52	in	in	ADP
ap-10701	72	53	(	(	PUNCT
ap-10701	72	54	0	0	NUM
ap-10701	72	55	,	,	PUNCT
ap-10701	72	56	t	t	PROPN
ap-10701	72	57	)	)	PUNCT
ap-10701	72	58	,	,	PUNCT
ap-10701	72	59	whose	whose	DET
ap-10701	72	60	solution	solution	NOUN
ap-10701	72	61	is	be	AUX
ap-10701	72	62	a	a	DET
ap-10701	72	63	time	time	NOUN
ap-10701	72	64	dependent	dependent	ADJ
ap-10701	72	65	vector	vector	NOUN
ap-10701	72	66	-	-	PUNCT
ap-10701	72	67	valued	value	VERB
ap-10701	72	68	function	function	NOUN
ap-10701	72	69	z	z	NOUN
ap-10701	72	70	=	=	SYM
ap-10701	72	71	z(t	z(t	NOUN
ap-10701	72	72	)	)	PUNCT
ap-10701	72	73	with	with	ADP
ap-10701	72	74	values	value	NOUN
ap-10701	72	75	in	in	ADP
ap-10701	72	76	hh	hh	PROPN
ap-10701	72	77	.	.	PROPN
ap-10701	72	78	3.2	3.2	NUM
ap-10701	72	79	.	.	PUNCT
ap-10701	73	1	invariant	invariant	ADJ
ap-10701	73	2	regions	region	NOUN
ap-10701	73	3	for	for	ADP
ap-10701	73	4	the	the	DET
ap-10701	73	5	semi	semi	ADJ
ap-10701	73	6	-	-	ADJ
ap-10701	73	7	discrete	discrete	ADJ
ap-10701	73	8	scheme	scheme	NOUN
ap-10701	73	9	we	we	PRON
ap-10701	73	10	now	now	ADV
ap-10701	73	11	show	show	VERB
ap-10701	73	12	that	that	SCONJ
ap-10701	73	13	the	the	DET
ap-10701	73	14	idea	idea	NOUN
ap-10701	73	15	of	of	ADP
ap-10701	73	16	an	an	DET
ap-10701	73	17	invariant	invariant	ADJ
ap-10701	73	18	region	region	NOUN
ap-10701	73	19	for	for	ADP
ap-10701	73	20	the	the	DET
ap-10701	73	21	original	original	ADJ
ap-10701	73	22	system	system	NOUN
ap-10701	73	23	(	(	PUNCT
ap-10701	73	24	1	1	X
ap-10701	73	25	)	)	PUNCT
ap-10701	73	26	can	can	AUX
ap-10701	73	27	be	be	AUX
ap-10701	73	28	extended	extend	VERB
ap-10701	73	29	to	to	ADP
ap-10701	73	30	semidiscrete	semidiscrete	ADJ
ap-10701	73	31	scheme	scheme	NOUN
ap-10701	73	32	(	(	PUNCT
ap-10701	73	33	4	4	NUM
ap-10701	73	34	)	)	PUNCT
ap-10701	73	35	.	.	PUNCT
ap-10701	74	1	for	for	ADP
ap-10701	74	2	simplicity	simplicity	NOUN
ap-10701	74	3	,	,	PUNCT
ap-10701	74	4	we	we	PRON
ap-10701	74	5	consider	consider	VERB
ap-10701	74	6	a	a	DET
ap-10701	74	7	prismatic	prismatic	ADJ
ap-10701	74	8	shape	shape	NOUN
ap-10701	74	9	of	of	ADP
ap-10701	74	10	the	the	DET
ap-10701	74	11	invariant	invariant	ADJ
ap-10701	74	12	region	region	NOUN
ap-10701	74	13	,	,	PUNCT
ap-10701	74	14	even	even	ADV
ap-10701	74	15	though	though	SCONJ
ap-10701	74	16	a	a	DET
ap-10701	74	17	general	general	ADJ
ap-10701	74	18	shape	shape	NOUN
ap-10701	74	19	as	as	ADP
ap-10701	74	20	in	in	ADP
ap-10701	74	21	[	[	X
ap-10701	74	22	1	1	NUM
ap-10701	74	23	]	]	PUNCT
ap-10701	74	24	can	can	AUX
ap-10701	74	25	be	be	AUX
ap-10701	74	26	treated	treat	VERB
ap-10701	74	27	correspondingly	correspondingly	ADV
ap-10701	74	28	.	.	PUNCT
ap-10701	75	1	to	to	ADP
ap-10701	75	2	this	this	DET
ap-10701	75	3	end	end	NOUN
ap-10701	75	4	,	,	PUNCT
ap-10701	75	5	we	we	PRON
ap-10701	75	6	denote	denote	VERB
ap-10701	75	7	,	,	PUNCT
ap-10701	75	8	for	for	ADP
ap-10701	75	9	given	give	VERB
ap-10701	75	10	constants	constant	NOUN
ap-10701	75	11	ak	ak	PROPN
ap-10701	75	12	<	<	X
ap-10701	75	13	bk	bk	PROPN
ap-10701	75	14	,	,	PUNCT
ap-10701	75	15	k	k	PROPN
ap-10701	75	16	=	=	SYM
ap-10701	75	17	1	1	NUM
ap-10701	75	18	,	,	PUNCT
ap-10701	75	19	.	.	PUNCT
ap-10701	75	20	.	.	PUNCT
ap-10701	76	1	.	.	PUNCT
ap-10701	77	1	,	,	PUNCT
ap-10701	77	2	d	d	X
ap-10701	77	3	,	,	PUNCT
ap-10701	77	4	the	the	DET
ap-10701	77	5	set	set	NOUN
ap-10701	77	6	:	:	PUNCT
ap-10701	77	7	σ	σ	X
ap-10701	77	8	=	=	PUNCT
ap-10701	77	9	{	{	PUNCT
ap-10701	77	10	w	w	PROPN
ap-10701	77	11	∈	∈	PROPN
ap-10701	77	12	rd|ak	rd|ak	NOUN
ap-10701	77	13	≤	≤	NUM
ap-10701	77	14	wk	wk	NOUN
ap-10701	77	15	≤	≤	PROPN
ap-10701	77	16	bk	bk	PROPN
ap-10701	77	17	,	,	PUNCT
ap-10701	77	18	k	k	PROPN
ap-10701	77	19	=	=	SYM
ap-10701	77	20	1	1	NUM
ap-10701	77	21	,	,	PUNCT
ap-10701	77	22	.	.	PUNCT
ap-10701	77	23	.	.	PUNCT
ap-10701	77	24	.	.	PUNCT
ap-10701	78	1	,	,	PUNCT
ap-10701	78	2	d	d	X
ap-10701	78	3	}	}	PUNCT
ap-10701	78	4	.	.	PUNCT
ap-10701	79	1	we	we	PRON
ap-10701	79	2	say	say	VERB
ap-10701	79	3	that	that	SCONJ
ap-10701	79	4	σ	σ	PROPN
ap-10701	79	5	is	be	AUX
ap-10701	79	6	the	the	DET
ap-10701	79	7	invariant	invariant	ADJ
ap-10701	79	8	region	region	NOUN
ap-10701	79	9	for	for	ADP
ap-10701	79	10	system	system	NOUN
ap-10701	79	11	(	(	PUNCT
ap-10701	79	12	4	4	NUM
ap-10701	79	13	)	)	PUNCT
ap-10701	79	14	,	,	PUNCT
ap-10701	79	15	provided	provide	VERB
ap-10701	79	16	for	for	ADP
ap-10701	79	17	each	each	DET
ap-10701	79	18	initial	initial	ADJ
ap-10701	79	19	condition	condition	NOUN
ap-10701	79	20	zini	zini	PROPN
ap-10701	79	21	:	:	PUNCT
ap-10701	79	22	ωh	ωh	X
ap-10701	79	23	→	→	SYM
ap-10701	79	24	rd	rd	NOUN
ap-10701	79	25	having	have	VERB
ap-10701	79	26	values	value	NOUN
ap-10701	79	27	in	in	ADP
ap-10701	79	28	σ	σ	PROPN
ap-10701	79	29	,	,	PUNCT
ap-10701	79	30	the	the	DET
ap-10701	79	31	solution	solution	NOUN
ap-10701	79	32	of	of	ADP
ap-10701	79	33	(	(	PUNCT
ap-10701	79	34	4	4	NUM
ap-10701	79	35	)	)	PUNCT
ap-10701	79	36	available	available	ADJ
ap-10701	79	37	for	for	ADP
ap-10701	79	38	t	t	PROPN
ap-10701	79	39	∈	∈	PROPN
ap-10701	80	1	[	[	X
ap-10701	80	2	0	0	NUM
ap-10701	80	3	,	,	PUNCT
ap-10701	80	4	t	t	NOUN
ap-10701	80	5	)	)	PUNCT
ap-10701	80	6	(	(	PUNCT
ap-10701	80	7	including	include	VERB
ap-10701	80	8	t	t	X
ap-10701	80	9	=	=	PUNCT
ap-10701	80	10	+	+	NOUN
ap-10701	80	11	∞	∞	NOUN
ap-10701	80	12	)	)	PUNCT
ap-10701	80	13	also	also	ADV
ap-10701	80	14	has	have	VERB
ap-10701	80	15	values	value	NOUN
ap-10701	80	16	in	in	ADP
ap-10701	80	17	σ	σ	PROPN
ap-10701	80	18	.	.	PUNCT
ap-10701	81	1	consequently	consequently	ADV
ap-10701	81	2	,	,	PUNCT
ap-10701	81	3	we	we	PRON
ap-10701	81	4	formulate	formulate	VERB
ap-10701	81	5	the	the	DET
ap-10701	81	6	statement	statement	NOUN
ap-10701	81	7	related	relate	VERB
ap-10701	81	8	to	to	ADP
ap-10701	81	9	it	it	PRON
ap-10701	81	10	.	.	PUNCT
ap-10701	82	1	lemma	lemma	PROPN
ap-10701	82	2	1	1	X
ap-10701	82	3	.	.	PUNCT
ap-10701	83	1	consider	consider	VERB
ap-10701	83	2	the	the	DET
ap-10701	83	3	semi	semi	ADJ
ap-10701	83	4	-	-	ADJ
ap-10701	83	5	discrete	discrete	ADJ
ap-10701	83	6	scheme	scheme	NOUN
ap-10701	83	7	(	(	PUNCT
ap-10701	83	8	4	4	NUM
ap-10701	83	9	)	)	PUNCT
ap-10701	83	10	and	and	CCONJ
ap-10701	83	11	the	the	DET
ap-10701	83	12	region	region	NOUN
ap-10701	83	13	σ	σ	PROPN
ap-10701	83	14	.	.	PUNCT
ap-10701	84	1	if	if	SCONJ
ap-10701	84	2	f	f	PROPN
ap-10701	84	3	points	point	VERB
ap-10701	84	4	strictly	strictly	ADV
ap-10701	84	5	into	into	ADP
ap-10701	84	6	σ	σ	PROPN
ap-10701	84	7	along	along	ADP
ap-10701	84	8	∂σ	∂σ	PROPN
ap-10701	84	9	,	,	PUNCT
ap-10701	84	10	then	then	ADV
ap-10701	84	11	σ	σ	PROPN
ap-10701	84	12	is	be	AUX
ap-10701	84	13	the	the	DET
ap-10701	84	14	invariant	invariant	ADJ
ap-10701	84	15	region	region	NOUN
ap-10701	84	16	.	.	PUNCT
ap-10701	85	1	proof	proof	NOUN
ap-10701	85	2	.	.	PUNCT
ap-10701	86	1	we	we	PRON
ap-10701	86	2	denote	denote	VERB
ap-10701	86	3	f(v	f(v	PRON
ap-10701	86	4	)	)	PUNCT
ap-10701	86	5	=	=	PUNCT
ap-10701	87	1	[	[	X
ap-10701	87	2	f	f	X
ap-10701	87	3	1(v	1(v	NUM
ap-10701	87	4	)	)	PUNCT
ap-10701	87	5	,	,	PUNCT
ap-10701	87	6	.	.	PUNCT
ap-10701	87	7	.	.	PUNCT
ap-10701	87	8	.	.	PUNCT
ap-10701	88	1	,	,	PUNCT
ap-10701	88	2	f	f	PROPN
ap-10701	88	3	d(v	d(v	PROPN
ap-10701	88	4	)	)	PUNCT
ap-10701	88	5	]	]	PUNCT
ap-10701	88	6	,	,	PUNCT
ap-10701	88	7	d	d	X
ap-10701	88	8	=	=	PUNCT
ap-10701	88	9	diag(d1	diag(d1	NOUN
ap-10701	88	10	,	,	PUNCT
ap-10701	88	11	.	.	PUNCT
ap-10701	88	12	.	.	PUNCT
ap-10701	89	1	.	.	PUNCT
ap-10701	90	1	,	,	PUNCT
ap-10701	90	2	dd	dd	NOUN
ap-10701	90	3	)	)	PUNCT
ap-10701	90	4	.	.	PUNCT
ap-10701	91	1	by	by	ADP
ap-10701	91	2	contradiction	contradiction	NOUN
ap-10701	91	3	,	,	PUNCT
ap-10701	91	4	we	we	PRON
ap-10701	91	5	assume	assume	VERB
ap-10701	91	6	that	that	SCONJ
ap-10701	91	7	zini	zini	PROPN
ap-10701	91	8	has	have	VERB
ap-10701	91	9	values	value	NOUN
ap-10701	91	10	in	in	ADP
ap-10701	91	11	σ	σ	PROPN
ap-10701	91	12	,	,	PUNCT
ap-10701	91	13	however	however	ADV
ap-10701	91	14	,	,	PUNCT
ap-10701	91	15	there	there	PRON
ap-10701	91	16	is	be	VERB
ap-10701	91	17	t1	t1	PROPN
ap-10701	91	18	∈	∈	PROPN
ap-10701	91	19	(	(	PUNCT
ap-10701	91	20	0	0	NUM
ap-10701	91	21	,	,	PUNCT
ap-10701	91	22	t	t	NOUN
ap-10701	91	23	)	)	PUNCT
ap-10701	91	24	at	at	ADP
ap-10701	91	25	which	which	PRON
ap-10701	91	26	the	the	DET
ap-10701	91	27	solution	solution	NOUN
ap-10701	91	28	z(t	z(t	NOUN
ap-10701	91	29	)	)	PUNCT
ap-10701	91	30	of	of	ADP
ap-10701	91	31	(	(	PUNCT
ap-10701	91	32	4	4	X
ap-10701	91	33	)	)	PUNCT
ap-10701	91	34	leaves	leave	VERB
ap-10701	91	35	σ	σ	PROPN
ap-10701	91	36	.	.	PROPN
ap-10701	92	1	assume	assume	VERB
ap-10701	92	2	that	that	SCONJ
ap-10701	92	3	this	this	PRON
ap-10701	92	4	happens	happen	VERB
ap-10701	92	5	on	on	ADP
ap-10701	92	6	the	the	DET
ap-10701	92	7	boundary	boundary	NOUN
ap-10701	92	8	of	of	ADP
ap-10701	92	9	σ	σ	PROPN
ap-10701	92	10	given	give	VERB
ap-10701	92	11	by	by	ADP
ap-10701	92	12	the	the	DET
ap-10701	92	13	value	value	NOUN
ap-10701	92	14	zk0	zk0	NOUN
ap-10701	92	15	=	=	PUNCT
ap-10701	92	16	bk0	bk0	NOUN
ap-10701	92	17	for	for	ADP
ap-10701	92	18	a	a	DET
ap-10701	92	19	specific	specific	ADJ
ap-10701	92	20	k0	k0	PROPN
ap-10701	92	21	.	.	PUNCT
ap-10701	93	1	as	as	ADP
ap-10701	93	2	f	f	PROPN
ap-10701	93	3	k0(z	k0(z	PROPN
ap-10701	93	4	)	)	PUNCT
ap-10701	93	5	<	<	X
ap-10701	93	6	0	0	PUNCT
ap-10701	93	7	along	along	ADP
ap-10701	93	8	this	this	DET
ap-10701	93	9	edge	edge	NOUN
ap-10701	93	10	of	of	ADP
ap-10701	93	11	σ	σ	NOUN
ap-10701	93	12	,	,	PUNCT
ap-10701	93	13	there	there	PRON
ap-10701	93	14	is	be	VERB
ap-10701	93	15	a	a	DET
ap-10701	93	16	band	band	NOUN
ap-10701	93	17	of	of	ADP
ap-10701	93	18	values	value	NOUN
ap-10701	93	19	of	of	ADP
ap-10701	93	20	thickness	thickness	NOUN
ap-10701	93	21	δ	δ	PROPN
ap-10701	93	22	>	>	X
ap-10701	93	23	0	0	NUM
ap-10701	93	24	such	such	ADJ
ap-10701	93	25	that	that	DET
ap-10701	93	26	fk0(z	fk0(z	NOUN
ap-10701	93	27	)	)	PUNCT
ap-10701	93	28	<	<	X
ap-10701	93	29	0	0	NUM
ap-10701	93	30	for	for	ADP
ap-10701	93	31	zk0	zk0	NOUN
ap-10701	93	32	∈	∈	PROPN
ap-10701	94	1	[	[	X
ap-10701	94	2	bk0	bk0	NOUN
ap-10701	94	3	,	,	PUNCT
ap-10701	94	4	bk0	bk0	PROPN
ap-10701	94	5	+	+	CCONJ
ap-10701	94	6	δ	δ	X
ap-10701	94	7	]	]	X
ap-10701	94	8	.	.	PUNCT
ap-10701	95	1	this	this	PRON
ap-10701	95	2	means	mean	VERB
ap-10701	95	3	that	that	SCONJ
ap-10701	95	4	there	there	PRON
ap-10701	95	5	is	be	VERB
ap-10701	95	6	a	a	DET
ap-10701	95	7	time	time	NOUN
ap-10701	95	8	t0	t0	PROPN
ap-10701	95	9	≤	≤	PROPN
ap-10701	95	10	t1	t1	VERB
ap-10701	95	11	a	a	DET
ap-10701	95	12	node	node	PROPN
ap-10701	95	13	j0	j0	PROPN
ap-10701	95	14	for	for	ADP
ap-10701	95	15	which	which	PRON
ap-10701	95	16	:	:	PUNCT
ap-10701	95	17	zk0	zk0	PROPN
ap-10701	95	18	j0	j0	PROPN
ap-10701	95	19	(	(	PUNCT
ap-10701	95	20	t0	t0	PROPN
ap-10701	95	21	)	)	PUNCT
ap-10701	95	22	>	>	X
ap-10701	95	23	bk0	bk0	NOUN
ap-10701	95	24	,	,	PUNCT
ap-10701	95	25	and	and	CCONJ
ap-10701	95	26	such	such	DET
ap-10701	95	27	a	a	DET
ap-10701	95	28	value	value	NOUN
ap-10701	95	29	zk0	zk0	NOUN
ap-10701	95	30	j0	j0	PROPN
ap-10701	95	31	(	(	PUNCT
ap-10701	95	32	t0	t0	PROPN
ap-10701	95	33	)	)	PUNCT
ap-10701	95	34	is	be	AUX
ap-10701	95	35	maximal	maximal	ADJ
ap-10701	95	36	on	on	ADP
ap-10701	95	37	ωh	ωh	SYM
ap-10701	95	38	,	,	PUNCT
ap-10701	95	39	i.e.	i.e.	X
ap-10701	95	40	zk0	zk0	PROPN
ap-10701	95	41	j0	j0	PROPN
ap-10701	95	42	(	(	PUNCT
ap-10701	95	43	t0	t0	PROPN
ap-10701	95	44	)	)	PUNCT
ap-10701	95	45	≥	≥	NOUN
ap-10701	95	46	zk0	zk0	PROPN
ap-10701	95	47	j	j	PROPN
ap-10701	95	48	(	(	PUNCT
ap-10701	95	49	t0	t0	PROPN
ap-10701	95	50	)	)	PUNCT
ap-10701	95	51	,	,	PUNCT
ap-10701	95	52	j	j	PROPN
ap-10701	95	53	=	=	SYM
ap-10701	95	54	0	0	PROPN
ap-10701	95	55	,	,	PUNCT
ap-10701	95	56	.	.	PUNCT
ap-10701	95	57	.	.	PUNCT
ap-10701	95	58	.	.	PUNCT
ap-10701	96	1	,	,	PUNCT
ap-10701	96	2	m.	m.	NOUN
ap-10701	96	3	the	the	DET
ap-10701	96	4	central	central	ADJ
ap-10701	96	5	second	second	ADJ
ap-10701	96	6	difference	difference	NOUN
ap-10701	96	7	zk0	zk0	NOUN
ap-10701	96	8	x̄x(t0	x̄x(t0	NOUN
ap-10701	96	9	)	)	PUNCT
ap-10701	96	10	is	be	AUX
ap-10701	96	11	,	,	PUNCT
ap-10701	96	12	therefore	therefore	ADV
ap-10701	96	13	,	,	PUNCT
ap-10701	96	14	non	non	ADJ
ap-10701	96	15	-	-	ADJ
ap-10701	96	16	positive	positive	ADJ
ap-10701	96	17	:	:	PUNCT
ap-10701	96	18	zk0	zk0	PROPN
ap-10701	96	19	x̄x	x̄x	PROPN
ap-10701	96	20	,	,	PUNCT
ap-10701	96	21	j0	j0	PROPN
ap-10701	96	22	(	(	PUNCT
ap-10701	96	23	t0	t0	PROPN
ap-10701	96	24	)	)	PUNCT
ap-10701	96	25	=	=	SYM
ap-10701	97	1	zk0	zk0	PROPN
ap-10701	97	2	j0	j0	PROPN
ap-10701	97	3	+	+	PROPN
ap-10701	97	4	1(t0	1(t0	NUM
ap-10701	97	5	)	)	PUNCT
ap-10701	97	6	−	−	PROPN
ap-10701	97	7	2zk0	2zk0	NUM
ap-10701	97	8	j0	j0	PROPN
ap-10701	97	9	(	(	PUNCT
ap-10701	97	10	t0	t0	PROPN
ap-10701	97	11	)	)	PUNCT
ap-10701	98	1	+	+	CCONJ
ap-10701	98	2	zk0	zk0	PROPN
ap-10701	98	3	j0−1(t0	j0−1(t0	NOUN
ap-10701	98	4	)	)	PUNCT
ap-10701	98	5	h2	h2	NOUN
ap-10701	98	6	≤	≤	ADV
ap-10701	98	7	0	0	X
ap-10701	98	8	.	.	PUNCT
ap-10701	99	1	as	as	SCONJ
ap-10701	99	2	zk0	zk0	PROPN
ap-10701	99	3	j0	j0	PROPN
ap-10701	99	4	∈	∈	PROPN
ap-10701	99	5	[	[	X
ap-10701	99	6	bk0	bk0	NOUN
ap-10701	99	7	,	,	PUNCT
ap-10701	99	8	bk0	bk0	PROPN
ap-10701	99	9	+	+	CCONJ
ap-10701	99	10	δ	δ	PROPN
ap-10701	99	11	]	]	X
ap-10701	99	12	,	,	PUNCT
ap-10701	99	13	the	the	DET
ap-10701	99	14	inward	inward	ADJ
ap-10701	99	15	pointing	pointing	NOUN
ap-10701	99	16	field	field	NOUN
ap-10701	99	17	f	f	PROPN
ap-10701	99	18	satisfies	satisfie	NOUN
ap-10701	99	19	:	:	PUNCT
ap-10701	99	20	f	f	PROPN
ap-10701	99	21	k0(zj0(t0	k0(zj0(t0	PROPN
ap-10701	99	22	)	)	PUNCT
ap-10701	99	23	)	)	PUNCT
ap-10701	100	1	<	<	X
ap-10701	100	2	0	0	X
ap-10701	100	3	.	.	PROPN
ap-10701	100	4	567	567	NUM
ap-10701	100	5	niels	niels	PROPN
ap-10701	100	6	van	van	PROPN
ap-10701	100	7	der	der	PROPN
ap-10701	100	8	meer	meer	PROPN
ap-10701	100	9	,	,	PUNCT
ap-10701	100	10	michal	michal	PROPN
ap-10701	100	11	beneš	beneš	PROPN
ap-10701	100	12	acta	acta	PROPN
ap-10701	100	13	polytechnica	polytechnica	PROPN
ap-10701	100	14	we	we	PRON
ap-10701	100	15	then	then	ADV
ap-10701	100	16	obtain	obtain	VERB
ap-10701	100	17	:	:	PUNCT
ap-10701	100	18	dzk0	dzk0	PROPN
ap-10701	100	19	j0	j0	PROPN
ap-10701	100	20	dt	dt	PROPN
ap-10701	100	21	(	(	PUNCT
ap-10701	100	22	t0	t0	NOUN
ap-10701	100	23	)	)	PUNCT
ap-10701	100	24	=	=	SYM
ap-10701	100	25	dk0zk0	dk0zk0	NOUN
ap-10701	100	26	x̄x	x̄x	PROPN
ap-10701	100	27	,	,	PUNCT
ap-10701	100	28	j0	j0	PROPN
ap-10701	100	29	(	(	PUNCT
ap-10701	100	30	t0	t0	PROPN
ap-10701	100	31	)	)	PUNCT
ap-10701	101	1	+	+	CCONJ
ap-10701	101	2	f	f	PROPN
ap-10701	101	3	k0(zj0(t0	k0(zj0(t0	PROPN
ap-10701	101	4	)	)	PUNCT
ap-10701	101	5	)	)	PUNCT
ap-10701	102	1	<	<	X
ap-10701	102	2	0	0	NUM
ap-10701	102	3	,	,	PUNCT
ap-10701	102	4	which	which	PRON
ap-10701	102	5	means	mean	VERB
ap-10701	102	6	that	that	SCONJ
ap-10701	102	7	zk0	zk0	PROPN
ap-10701	102	8	j0	j0	PROPN
ap-10701	102	9	(	(	PUNCT
ap-10701	102	10	t	t	PROPN
ap-10701	102	11	)	)	PUNCT
ap-10701	102	12	can	can	AUX
ap-10701	102	13	not	not	PART
ap-10701	102	14	grow	grow	VERB
ap-10701	102	15	to	to	ADP
ap-10701	102	16	any	any	DET
ap-10701	102	17	higher	high	ADJ
ap-10701	102	18	value	value	NOUN
ap-10701	102	19	,	,	PUNCT
ap-10701	102	20	and	and	CCONJ
ap-10701	102	21	is	be	AUX
ap-10701	102	22	still	still	ADV
ap-10701	102	23	maximal	maximal	ADJ
ap-10701	102	24	over	over	ADP
ap-10701	102	25	all	all	DET
ap-10701	102	26	other	other	ADJ
ap-10701	102	27	nodes	node	NOUN
ap-10701	102	28	.	.	PUNCT
ap-10701	103	1	such	such	ADJ
ap-10701	103	2	values	value	NOUN
ap-10701	103	3	,	,	PUNCT
ap-10701	103	4	therefore	therefore	ADV
ap-10701	103	5	,	,	PUNCT
ap-10701	103	6	can	can	AUX
ap-10701	103	7	not	not	PART
ap-10701	103	8	reach	reach	VERB
ap-10701	103	9	zk0(t1	zk0(t1	NOUN
ap-10701	103	10	)	)	PUNCT
ap-10701	103	11	>	>	X
ap-10701	104	1	bk0	bk0	INTJ
ap-10701	104	2	.	.	PUNCT
ap-10701	105	1	this	this	DET
ap-10701	105	2	lemma	lemma	PROPN
ap-10701	105	3	will	will	AUX
ap-10701	105	4	be	be	AUX
ap-10701	105	5	used	use	VERB
ap-10701	105	6	in	in	ADP
ap-10701	105	7	the	the	DET
ap-10701	105	8	following	follow	VERB
ap-10701	105	9	section	section	NOUN
ap-10701	105	10	to	to	PART
ap-10701	105	11	derive	derive	VERB
ap-10701	105	12	estimates	estimate	NOUN
ap-10701	105	13	of	of	ADP
ap-10701	105	14	the	the	DET
ap-10701	105	15	grid	grid	NOUN
ap-10701	105	16	function	function	NOUN
ap-10701	105	17	found	find	VERB
ap-10701	105	18	by	by	ADP
ap-10701	105	19	semidiscrete	semidiscrete	ADJ
ap-10701	105	20	scheme	scheme	NOUN
ap-10701	105	21	(	(	PUNCT
ap-10701	105	22	4	4	NUM
ap-10701	105	23	)	)	PUNCT
ap-10701	105	24	,	,	PUNCT
ap-10701	105	25	and	and	CCONJ
ap-10701	105	26	then	then	ADV
ap-10701	105	27	facilitate	facilitate	VERB
ap-10701	105	28	the	the	DET
ap-10701	105	29	proof	proof	NOUN
ap-10701	105	30	of	of	ADP
ap-10701	105	31	convergence	convergence	NOUN
ap-10701	105	32	for	for	ADP
ap-10701	105	33	scheme	scheme	NOUN
ap-10701	105	34	(	(	PUNCT
ap-10701	105	35	4	4	NUM
ap-10701	105	36	)	)	PUNCT
ap-10701	105	37	.	.	PUNCT
ap-10701	106	1	4	4	X
ap-10701	106	2	.	.	X
ap-10701	106	3	numerical	numerical	ADJ
ap-10701	106	4	analysis	analysis	NOUN
ap-10701	106	5	of	of	ADP
ap-10701	106	6	method	method	NOUN
ap-10701	106	7	of	of	ADP
ap-10701	106	8	lines	line	NOUN
ap-10701	106	9	scheme	scheme	NOUN
ap-10701	106	10	(	(	PUNCT
ap-10701	106	11	4	4	NUM
ap-10701	106	12	)	)	PUNCT
ap-10701	106	13	,	,	PUNCT
ap-10701	106	14	as	as	ADP
ap-10701	106	15	a	a	DET
ap-10701	106	16	system	system	NOUN
ap-10701	106	17	of	of	ADP
ap-10701	106	18	first	first	ADJ
ap-10701	106	19	order	order	NOUN
ap-10701	106	20	ode	ode	NOUN
ap-10701	106	21	’s	’s	NOUN
ap-10701	106	22	with	with	ADP
ap-10701	106	23	a	a	DET
ap-10701	106	24	convenient	convenient	ADJ
ap-10701	106	25	right	right	ADJ
ap-10701	106	26	-	-	PUNCT
ap-10701	106	27	hand	hand	NOUN
ap-10701	106	28	side	side	NOUN
ap-10701	106	29	,	,	PUNCT
ap-10701	106	30	possesses	possess	VERB
ap-10701	106	31	the	the	DET
ap-10701	106	32	unique	unique	ADJ
ap-10701	106	33	solution	solution	NOUN
ap-10701	106	34	z	z	NOUN
ap-10701	106	35	=	=	SYM
ap-10701	106	36	z(t	z(t	NOUN
ap-10701	106	37	)	)	PUNCT
ap-10701	106	38	defined	define	VERB
ap-10701	106	39	on	on	ADP
ap-10701	106	40	(	(	PUNCT
ap-10701	106	41	0	0	NUM
ap-10701	106	42	,	,	PUNCT
ap-10701	106	43	tm	tm	NOUN
ap-10701	106	44	)	)	PUNCT
ap-10701	106	45	for	for	ADP
ap-10701	106	46	a	a	DET
ap-10701	106	47	tm	tm	NOUN
ap-10701	106	48	>	>	X
ap-10701	106	49	0	0	NUM
ap-10701	106	50	,	,	PUNCT
ap-10701	106	51	following	follow	VERB
ap-10701	106	52	the	the	DET
ap-10701	106	53	picard	picard	NOUN
ap-10701	106	54	theorem	theorem	NOUN
ap-10701	106	55	.	.	PUNCT
ap-10701	107	1	due	due	ADP
ap-10701	107	2	to	to	ADP
ap-10701	107	3	lemma	lemma	PROPN
ap-10701	107	4	1	1	NUM
ap-10701	107	5	with	with	ADP
ap-10701	107	6	the	the	DET
ap-10701	107	7	invariant	invariant	ADJ
ap-10701	107	8	region	region	NOUN
ap-10701	107	9	σ	σ	PROPN
ap-10701	107	10	independent	independent	ADJ
ap-10701	107	11	of	of	ADP
ap-10701	107	12	m	m	PROPN
ap-10701	107	13	,	,	PUNCT
ap-10701	107	14	we	we	PRON
ap-10701	107	15	see	see	VERB
ap-10701	107	16	that	that	SCONJ
ap-10701	107	17	all	all	DET
ap-10701	107	18	solutions	solution	NOUN
ap-10701	107	19	of	of	ADP
ap-10701	107	20	(	(	PUNCT
ap-10701	107	21	4	4	NUM
ap-10701	107	22	)	)	PUNCT
ap-10701	107	23	are	be	AUX
ap-10701	107	24	uniformly	uniformly	ADV
ap-10701	107	25	bounded	bound	VERB
ap-10701	107	26	in	in	ADP
ap-10701	107	27	their	their	PRON
ap-10701	107	28	values	value	NOUN
ap-10701	107	29	.	.	PUNCT
ap-10701	108	1	the	the	DET
ap-10701	108	2	theory	theory	NOUN
ap-10701	108	3	of	of	ADP
ap-10701	108	4	ode	ode	PROPN
ap-10701	108	5	’s	’s	PART
ap-10701	108	6	[	[	X
ap-10701	108	7	23	23	NUM
ap-10701	108	8	]	]	PUNCT
ap-10701	108	9	then	then	ADV
ap-10701	108	10	yields	yield	VERB
ap-10701	108	11	tm	tm	NOUN
ap-10701	108	12	=	=	PROPN
ap-10701	109	1	+	+	PROPN
ap-10701	109	2	∞.	∞.	PROPN
ap-10701	109	3	solutions	solution	NOUN
ap-10701	109	4	of	of	ADP
ap-10701	109	5	(	(	PUNCT
ap-10701	109	6	4	4	NUM
ap-10701	109	7	)	)	PUNCT
ap-10701	109	8	are	be	AUX
ap-10701	109	9	then	then	ADV
ap-10701	109	10	available	available	ADJ
ap-10701	109	11	on	on	ADP
ap-10701	109	12	a	a	DET
ap-10701	109	13	selected	select	VERB
ap-10701	109	14	time	time	NOUN
ap-10701	109	15	interval	interval	NOUN
ap-10701	109	16	(	(	PUNCT
ap-10701	109	17	0	0	NUM
ap-10701	109	18	,	,	PUNCT
ap-10701	109	19	t	t	NOUN
ap-10701	109	20	)	)	PUNCT
ap-10701	109	21	for	for	ADP
ap-10701	109	22	all	all	DET
ap-10701	109	23	h.	h.	PROPN
ap-10701	109	24	4.1	4.1	NUM
ap-10701	109	25	.	.	PUNCT
ap-10701	110	1	a	a	DET
ap-10701	110	2	priori	priori	ADJ
ap-10701	110	3	estimates	estimate	NOUN
ap-10701	110	4	we	we	PRON
ap-10701	110	5	multiply	multiply	VERB
ap-10701	110	6	(	(	PUNCT
ap-10701	110	7	4	4	NUM
ap-10701	110	8	)	)	PUNCT
ap-10701	110	9	by	by	ADP
ap-10701	110	10	its	its	PRON
ap-10701	110	11	solution	solution	NOUN
ap-10701	110	12	in	in	ADP
ap-10701	110	13	terms	term	NOUN
ap-10701	110	14	of	of	ADP
ap-10701	110	15	the	the	DET
ap-10701	110	16	scalar	scalar	ADJ
ap-10701	110	17	product	product	NOUN
ap-10701	110	18	(	(	PUNCT
ap-10701	110	19	.	.	PUNCT
ap-10701	110	20	,	,	PUNCT
ap-10701	110	21	.)h	.)h	NOUN
ap-10701	110	22	,	,	PUNCT
ap-10701	110	23	use	use	VERB
ap-10701	110	24	the	the	DET
ap-10701	110	25	integration	integration	NOUN
ap-10701	110	26	by	by	ADP
ap-10701	110	27	parts	part	NOUN
ap-10701	110	28	over	over	ADP
ap-10701	110	29	ωh	ωh	ADP
ap-10701	110	30	,	,	PUNCT
ap-10701	110	31	and	and	CCONJ
ap-10701	110	32	obtain	obtain	VERB
ap-10701	110	33	:	:	PUNCT
ap-10701	110	34	1	1	NUM
ap-10701	110	35	2	2	NUM
ap-10701	110	36	d∥z∥2	d∥z∥2	NOUN
ap-10701	110	37	h	h	NOUN
ap-10701	110	38	dt	dt	X
ap-10701	111	1	+	+	CCONJ
ap-10701	111	2	(	(	PUNCT
ap-10701	111	3	dzx̄	dzx̄	NOUN
ap-10701	111	4	,	,	PUNCT
ap-10701	111	5	zx̄	zx̄	NOUN
ap-10701	111	6	]	]	X
ap-10701	111	7	=	=	SYM
ap-10701	111	8	(	(	PUNCT
ap-10701	111	9	f(z	f(z	PROPN
ap-10701	111	10	)	)	PUNCT
ap-10701	111	11	,	,	PUNCT
ap-10701	111	12	z)h	z)h	X
ap-10701	111	13	.	.	PUNCT
ap-10701	112	1	due	due	ADP
ap-10701	112	2	to	to	ADP
ap-10701	112	3	lemma	lemma	PROPN
ap-10701	112	4	1	1	NUM
ap-10701	112	5	,	,	PUNCT
ap-10701	112	6	the	the	DET
ap-10701	112	7	c1	c1	NOUN
ap-10701	112	8	map	map	NOUN
ap-10701	112	9	f	f	PROPN
ap-10701	112	10	is	be	AUX
ap-10701	112	11	bounded	bound	VERB
ap-10701	112	12	with	with	ADP
ap-10701	112	13	bounded	bounded	ADJ
ap-10701	112	14	derivative	derivative	NOUN
ap-10701	112	15	on	on	ADP
ap-10701	112	16	σ	σ	PROPN
ap-10701	112	17	,	,	PUNCT
ap-10701	112	18	i.e.	i.e.	X
ap-10701	112	19	|f(z)|	|f(z)|	ADJ
ap-10701	112	20	≤	≤	NOUN
ap-10701	112	21	l|z|	l|z|	NOUN
ap-10701	112	22	for	for	ADP
ap-10701	112	23	an	an	DET
ap-10701	112	24	l	l	NOUN
ap-10701	112	25	>	>	X
ap-10701	112	26	0	0	X
ap-10701	112	27	.	.	PUNCT
ap-10701	113	1	as	as	SCONJ
ap-10701	113	2	d	d	PROPN
ap-10701	113	3	is	be	AUX
ap-10701	113	4	a	a	DET
ap-10701	113	5	positive	positive	ADJ
ap-10701	113	6	diagonal	diagonal	ADJ
ap-10701	113	7	matrix	matrix	NOUN
ap-10701	113	8	with	with	ADP
ap-10701	113	9	values	value	NOUN
ap-10701	113	10	bounded	bound	VERB
ap-10701	113	11	from	from	ADP
ap-10701	113	12	below	below	ADV
ap-10701	113	13	by	by	ADP
ap-10701	113	14	d0	d0	PROPN
ap-10701	113	15	>	>	X
ap-10701	113	16	0	0	PROPN
ap-10701	113	17	,	,	PUNCT
ap-10701	113	18	we	we	PRON
ap-10701	113	19	have	have	VERB
ap-10701	113	20	:	:	PUNCT
ap-10701	113	21	1	1	NUM
ap-10701	113	22	2	2	NUM
ap-10701	113	23	d∥z∥2	d∥z∥2	NOUN
ap-10701	113	24	h	h	NOUN
ap-10701	113	25	dt	dt	NOUN
ap-10701	114	1	+	+	CCONJ
ap-10701	114	2	d0||zx̄]|2	d0||zx̄]|2	NUM
ap-10701	114	3	≤	≤	NUM
ap-10701	114	4	l∥z∥2	l∥z∥2	PROPN
ap-10701	114	5	h.	h.	NOUN
ap-10701	114	6	the	the	DET
ap-10701	114	7	grönwall	grönwall	NOUN
ap-10701	114	8	argument	argument	NOUN
ap-10701	114	9	then	then	ADV
ap-10701	114	10	yields	yield	VERB
ap-10701	114	11	:	:	PUNCT
ap-10701	114	12	∥z∥2	∥z∥2	VERB
ap-10701	114	13	h(t)+2d0	h(t)+2d0	ADJ
ap-10701	114	14	∫	∫	PROPN
ap-10701	114	15	t	t	PROPN
ap-10701	114	16	0	0	NUM
ap-10701	114	17	||zx̄]|2(t)dt	||zx̄]|2(t)dt	PROPN
ap-10701	114	18	≤	≤	PROPN
ap-10701	114	19	∥z∥2	∥z∥2	VERB
ap-10701	114	20	h(0)(1+e2lt	h(0)(1+e2lt	NOUN
ap-10701	114	21	)	)	PUNCT
ap-10701	114	22	.	.	PUNCT
ap-10701	115	1	(	(	PUNCT
ap-10701	115	2	5	5	X
ap-10701	115	3	)	)	PUNCT
ap-10701	115	4	multiplying	multiplying	NOUN
ap-10701	115	5	(	(	PUNCT
ap-10701	115	6	4	4	NUM
ap-10701	115	7	)	)	PUNCT
ap-10701	115	8	by	by	ADP
ap-10701	115	9	dz	dz	ADJ
ap-10701	115	10	dt	dt	NOUN
ap-10701	116	1	=	=	SYM
ap-10701	116	2	ż	ż	NOUN
ap-10701	116	3	in	in	ADP
ap-10701	116	4	terms	term	NOUN
ap-10701	116	5	of	of	ADP
ap-10701	116	6	the	the	DET
ap-10701	116	7	scalar	scalar	ADJ
ap-10701	116	8	product	product	NOUN
ap-10701	116	9	(	(	PUNCT
ap-10701	116	10	.	.	PUNCT
ap-10701	116	11	,	,	PUNCT
ap-10701	116	12	.)h	.)h	NOUN
ap-10701	116	13	,	,	PUNCT
ap-10701	116	14	and	and	CCONJ
ap-10701	116	15	using	use	VERB
ap-10701	116	16	the	the	DET
ap-10701	116	17	integration	integration	NOUN
ap-10701	116	18	by	by	ADP
ap-10701	116	19	parts	part	NOUN
ap-10701	116	20	over	over	ADP
ap-10701	116	21	ωh	ωh	ADP
ap-10701	116	22	yield	yield	NOUN
ap-10701	116	23	:	:	PUNCT
ap-10701	116	24	∥ż∥2	∥ż∥2	X
ap-10701	116	25	h(t	h(t	X
ap-10701	116	26	)	)	PUNCT
ap-10701	117	1	+	+	CCONJ
ap-10701	117	2	1	1	NUM
ap-10701	117	3	2	2	NUM
ap-10701	117	4	d(dzx̄	d(dzx̄	PROPN
ap-10701	117	5	,	,	PUNCT
ap-10701	117	6	zx̄	zx̄	NOUN
ap-10701	117	7	]	]	X
ap-10701	117	8	dt	dt	X
ap-10701	117	9	=	=	SYM
ap-10701	117	10	(	(	PUNCT
ap-10701	117	11	f(z	f(z	PROPN
ap-10701	117	12	)	)	PUNCT
ap-10701	117	13	,	,	PUNCT
ap-10701	117	14	ż	ż	NOUN
ap-10701	117	15	)	)	PUNCT
ap-10701	117	16	h	h	NOUN
ap-10701	117	17	.	.	PUNCT
ap-10701	118	1	again	again	ADV
ap-10701	118	2	,	,	PUNCT
ap-10701	118	3	due	due	ADP
ap-10701	118	4	to	to	ADP
ap-10701	118	5	lemma	lemma	PROPN
ap-10701	118	6	1	1	NUM
ap-10701	118	7	,	,	PUNCT
ap-10701	118	8	|f(z)|	|f(z)|	PROPN
ap-10701	118	9	≤	≤	NUM
ap-10701	118	10	l|z|	l|z|	NOUN
ap-10701	118	11	for	for	ADP
ap-10701	118	12	an	an	DET
ap-10701	118	13	l	l	NOUN
ap-10701	118	14	>	>	X
ap-10701	118	15	0	0	X
ap-10701	118	16	.	.	PUNCT
ap-10701	119	1	using	use	VERB
ap-10701	119	2	the	the	DET
ap-10701	119	3	cauchy	cauchy	NOUN
ap-10701	119	4	-	-	PUNCT
ap-10701	119	5	schwarz	schwarz	PROPN
ap-10701	119	6	and	and	CCONJ
ap-10701	119	7	young	young	ADJ
ap-10701	119	8	inequalities	inequality	NOUN
ap-10701	119	9	,	,	PUNCT
ap-10701	119	10	we	we	PRON
ap-10701	119	11	have	have	VERB
ap-10701	119	12	:	:	PUNCT
ap-10701	119	13	∥ż∥2	∥ż∥2	VERB
ap-10701	119	14	h(t	h(t	NUM
ap-10701	119	15	)	)	PUNCT
ap-10701	120	1	+	+	CCONJ
ap-10701	120	2	1	1	NUM
ap-10701	120	3	2	2	NUM
ap-10701	120	4	d(dzx̄	d(dzx̄	PROPN
ap-10701	120	5	,	,	PUNCT
ap-10701	120	6	zx̄	zx̄	NOUN
ap-10701	120	7	]	]	X
ap-10701	120	8	dt	dt	X
ap-10701	120	9	≤	≤	NUM
ap-10701	120	10	l2	l2	NOUN
ap-10701	120	11	2	2	NUM
ap-10701	120	12	∥z∥2	∥z∥2	NOUN
ap-10701	120	13	h	h	NOUN
ap-10701	120	14	+	+	CCONJ
ap-10701	120	15	1	1	NUM
ap-10701	120	16	2∥ż∥2	2∥ż∥2	NUM
ap-10701	120	17	h	h	NOUN
ap-10701	120	18	,	,	PUNCT
ap-10701	120	19	and	and	CCONJ
ap-10701	120	20	:	:	PUNCT
ap-10701	120	21	∥ż∥2	∥ż∥2	VERB
ap-10701	120	22	h(t	h(t	NUM
ap-10701	120	23	)	)	PUNCT
ap-10701	121	1	+	+	CCONJ
ap-10701	121	2	d(dzx̄	d(dzx̄	PROPN
ap-10701	121	3	,	,	PUNCT
ap-10701	121	4	zx̄	zx̄	NOUN
ap-10701	121	5	]	]	X
ap-10701	121	6	dt	dt	X
ap-10701	121	7	≤	≤	PROPN
ap-10701	121	8	l2∥z∥2	l2∥z∥2	NOUN
ap-10701	121	9	h.	h.	NOUN
ap-10701	121	10	the	the	DET
ap-10701	121	11	integration	integration	NOUN
ap-10701	121	12	and	and	CCONJ
ap-10701	121	13	the	the	DET
ap-10701	121	14	grönwall	grönwall	NOUN
ap-10701	121	15	argument	argument	NOUN
ap-10701	121	16	then	then	ADV
ap-10701	121	17	yield:∫	yield:∫	PROPN
ap-10701	121	18	t	t	PROPN
ap-10701	121	19	0	0	NUM
ap-10701	121	20	∥ż∥2	∥ż∥2	NOUN
ap-10701	121	21	h(t)dt+	h(t)dt+	PRON
ap-10701	121	22	(	(	PUNCT
ap-10701	121	23	dzx̄	dzx̄	NOUN
ap-10701	121	24	,	,	PUNCT
ap-10701	121	25	zx̄	zx̄	NOUN
ap-10701	121	26	]	]	X
ap-10701	121	27	(	(	PUNCT
ap-10701	121	28	t	t	NOUN
ap-10701	121	29	)	)	PUNCT
ap-10701	121	30	≤	≤	NOUN
ap-10701	121	31	(	(	PUNCT
ap-10701	121	32	dzx̄	dzx̄	NOUN
ap-10701	121	33	,	,	PUNCT
ap-10701	121	34	zx̄	zx̄	NOUN
ap-10701	121	35	]	]	X
ap-10701	121	36	(	(	PUNCT
ap-10701	121	37	0	0	NUM
ap-10701	121	38	)	)	PUNCT
ap-10701	121	39	+	+	NUM
ap-10701	121	40	l2∥z∥2	l2∥z∥2	NOUN
ap-10701	121	41	h(0)e2lt	h(0)e2lt	NOUN
ap-10701	121	42	.	.	PUNCT
ap-10701	122	1	(	(	PUNCT
ap-10701	122	2	6	6	NUM
ap-10701	122	3	)	)	PUNCT
ap-10701	122	4	4.2	4.2	NUM
ap-10701	122	5	.	.	PUNCT
ap-10701	123	1	interpolation	interpolation	NOUN
ap-10701	123	2	results	result	NOUN
ap-10701	123	3	as	as	ADP
ap-10701	123	4	in	in	ADP
ap-10701	123	5	[	[	X
ap-10701	123	6	21	21	NUM
ap-10701	123	7	,	,	PUNCT
ap-10701	123	8	22	22	NUM
ap-10701	123	9	]	]	PUNCT
ap-10701	123	10	,	,	PUNCT
ap-10701	123	11	we	we	PRON
ap-10701	123	12	introduce	introduce	VERB
ap-10701	123	13	the	the	DET
ap-10701	123	14	interpolation	interpolation	NOUN
ap-10701	123	15	operators	operator	NOUN
ap-10701	123	16	mapping	map	VERB
ap-10701	123	17	the	the	DET
ap-10701	123	18	grid	grid	NOUN
ap-10701	123	19	functions	function	NOUN
ap-10701	123	20	defined	define	VERB
ap-10701	123	21	on	on	ADP
ap-10701	123	22	ωh	ωh	ADP
ap-10701	123	23	to	to	PART
ap-10701	123	24	convenient	convenient	ADJ
ap-10701	123	25	lebesgue	lebesgue	NOUN
ap-10701	123	26	-	-	PUNCT
ap-10701	123	27	integrable	integrable	ADJ
ap-10701	123	28	functions	function	NOUN
ap-10701	123	29	on	on	ADP
ap-10701	123	30	(	(	PUNCT
ap-10701	123	31	a	a	DET
ap-10701	123	32	,	,	PUNCT
ap-10701	123	33	b	b	NOUN
ap-10701	123	34	)	)	PUNCT
ap-10701	123	35	.	.	PUNCT
ap-10701	124	1	we	we	PRON
ap-10701	124	2	define	define	VERB
ap-10701	124	3	:	:	PUNCT
ap-10701	124	4	•	•	NUM
ap-10701	124	5	qh	qh	NOUN
ap-10701	124	6	:	:	PUNCT
ap-10701	124	7	hh	hh	PROPN
ap-10701	124	8	→	→	SYM
ap-10701	124	9	c([a	c([a	PROPN
ap-10701	124	10	,	,	PUNCT
ap-10701	124	11	b	b	NOUN
ap-10701	124	12	]	]	X
ap-10701	124	13	)	)	PUNCT
ap-10701	124	14	such	such	ADJ
ap-10701	124	15	that	that	PRON
ap-10701	124	16	for	for	ADP
ap-10701	124	17	each	each	DET
ap-10701	124	18	u	u	NOUN
ap-10701	124	19	∈	∈	PROPN
ap-10701	124	20	hh	hh	X
ap-10701	124	21	(	(	PUNCT
ap-10701	124	22	qhu)(x	qhu)(x	PROPN
ap-10701	124	23	)	)	PUNCT
ap-10701	124	24	=	=	SYM
ap-10701	125	1	uj−1	uj−1	NOUN
ap-10701	125	2	+	+	CCONJ
ap-10701	125	3	ux̄,j−1(x−	ux̄,j−1(x−	PROPN
ap-10701	125	4	a−	a−	PROPN
ap-10701	125	5	(	(	PUNCT
ap-10701	125	6	j	j	PROPN
ap-10701	125	7	−	−	PROPN
ap-10701	125	8	1)h	1)h	NUM
ap-10701	125	9	)	)	PUNCT
ap-10701	125	10	,	,	PUNCT
ap-10701	125	11	for	for	ADP
ap-10701	125	12	x	x	PROPN
ap-10701	125	13	∈	∈	PROPN
ap-10701	126	1	[	[	X
ap-10701	126	2	a+	a+	X
ap-10701	126	3	(	(	PUNCT
ap-10701	126	4	j	j	PROPN
ap-10701	126	5	−	−	PROPN
ap-10701	126	6	1)h	1)h	PROPN
ap-10701	126	7	,	,	PUNCT
ap-10701	126	8	a+	a+	PUNCT
ap-10701	126	9	jh	jh	PROPN
ap-10701	126	10	]	]	X
ap-10701	126	11	;	;	PUNCT
ap-10701	126	12	•	•	X
ap-10701	126	13	sh	sh	INTJ
ap-10701	126	14	:	:	PUNCT
ap-10701	126	15	hh	hh	PROPN
ap-10701	126	16	→	→	SYM
ap-10701	126	17	lp((a	lp((a	PROPN
ap-10701	126	18	,	,	PUNCT
ap-10701	126	19	b	b	NOUN
ap-10701	126	20	)	)	PUNCT
ap-10701	126	21	)	)	PUNCT
ap-10701	126	22	for	for	ADP
ap-10701	126	23	a	a	DET
ap-10701	126	24	given	give	VERB
ap-10701	126	25	p	p	PRON
ap-10701	126	26	≥	≥	NUM
ap-10701	126	27	1	1	NUM
ap-10701	126	28	such	such	ADJ
ap-10701	126	29	that	that	PRON
ap-10701	126	30	for	for	ADP
ap-10701	126	31	each	each	DET
ap-10701	126	32	u	u	NOUN
ap-10701	126	33	∈	∈	PROPN
ap-10701	126	34	hh	hh	PROPN
ap-10701	126	35	(	(	PUNCT
ap-10701	126	36	shu)(x	shu)(x	NOUN
ap-10701	126	37	)	)	PUNCT
ap-10701	126	38	=	=	SYM
ap-10701	126	39	uj	uj	PROPN
ap-10701	126	40	,	,	PUNCT
ap-10701	126	41	for	for	ADP
ap-10701	126	42	x	x	PROPN
ap-10701	126	43	∈	∈	PROPN
ap-10701	126	44	(	(	PUNCT
ap-10701	126	45	a+	a+	X
ap-10701	126	46	(	(	PUNCT
ap-10701	126	47	j	j	NOUN
ap-10701	126	48	−	−	NOUN
ap-10701	126	49	1	1	NUM
ap-10701	126	50	2	2	NUM
ap-10701	126	51	)	)	PUNCT
ap-10701	126	52	h	h	NOUN
ap-10701	126	53	,	,	PUNCT
ap-10701	126	54	a+	a+	PUNCT
ap-10701	126	55	(	(	PUNCT
ap-10701	126	56	j	j	NOUN
ap-10701	126	57	+	+	CCONJ
ap-10701	126	58	1	1	NUM
ap-10701	126	59	2	2	NUM
ap-10701	126	60	)	)	PUNCT
ap-10701	126	61	h	h	NOUN
ap-10701	126	62	)	)	PUNCT
ap-10701	126	63	;	;	PUNCT
ap-10701	126	64	•	•	X
ap-10701	126	65	ph	ph	NOUN
ap-10701	126	66	:	:	PUNCT
ap-10701	126	67	c([a	c([a	PROPN
ap-10701	126	68	,	,	PUNCT
ap-10701	126	69	b	b	NOUN
ap-10701	126	70	]	]	X
ap-10701	126	71	)	)	PUNCT
ap-10701	126	72	→	→	SYM
ap-10701	126	73	hh	hh	VERB
ap-10701	126	74	such	such	ADJ
ap-10701	126	75	that	that	PRON
ap-10701	126	76	for	for	ADP
ap-10701	126	77	each	each	DET
ap-10701	126	78	u	u	PROPN
ap-10701	126	79	∈	∈	PROPN
ap-10701	126	80	h	h	NOUN
ap-10701	126	81	(	(	PUNCT
ap-10701	126	82	phu)j	phu)j	PROPN
ap-10701	126	83	=	=	SYM
ap-10701	126	84	u(a+	u(a+	PROPN
ap-10701	126	85	jh	jh	PROPN
ap-10701	126	86	)	)	PUNCT
ap-10701	126	87	,	,	PUNCT
ap-10701	126	88	for	for	ADP
ap-10701	126	89	j	j	PROPN
ap-10701	126	90	=	=	SYM
ap-10701	126	91	0	0	PROPN
ap-10701	126	92	,	,	PUNCT
ap-10701	126	93	.	.	PUNCT
ap-10701	126	94	.	.	PUNCT
ap-10701	126	95	.	.	PUNCT
ap-10701	127	1	,	,	PUNCT
ap-10701	127	2	m.	m.	NOUN
ap-10701	127	3	remark	remark	VERB
ap-10701	127	4	the	the	DET
ap-10701	127	5	operator	operator	NOUN
ap-10701	127	6	ph	ph	NOUN
ap-10701	127	7	is	be	AUX
ap-10701	127	8	linear	linear	ADJ
ap-10701	127	9	and	and	CCONJ
ap-10701	127	10	continuous	continuous	ADJ
ap-10701	127	11	from	from	ADP
ap-10701	127	12	c([a	c([a	PROPN
ap-10701	127	13	,	,	PUNCT
ap-10701	127	14	b	b	NOUN
ap-10701	127	15	]	]	X
ap-10701	127	16	)	)	PUNCT
ap-10701	127	17	to	to	ADP
ap-10701	127	18	hh	hh	PROPN
ap-10701	127	19	,	,	PUNCT
ap-10701	127	20	and	and	CCONJ
ap-10701	127	21	can	can	AUX
ap-10701	127	22	be	be	AUX
ap-10701	127	23	extended	extend	VERB
ap-10701	127	24	to	to	ADP
ap-10701	127	25	w	w	PROPN
ap-10701	127	26	(	(	PUNCT
ap-10701	127	27	1	1	NUM
ap-10701	127	28	)	)	SYM
ap-10701	127	29	2	2	NUM
ap-10701	127	30	(	(	PUNCT
ap-10701	127	31	(	(	PUNCT
ap-10701	127	32	a	a	DET
ap-10701	127	33	,	,	PUNCT
ap-10701	127	34	b	b	NOUN
ap-10701	127	35	)	)	PUNCT
ap-10701	127	36	)	)	PUNCT
ap-10701	127	37	via	via	ADP
ap-10701	127	38	density	density	NOUN
ap-10701	127	39	argument	argument	NOUN
ap-10701	127	40	.	.	PUNCT
ap-10701	128	1	qhu	qhu	PROPN
ap-10701	128	2	is	be	AUX
ap-10701	128	3	a	a	DET
ap-10701	128	4	continuous	continuous	ADJ
ap-10701	128	5	piecewise	piecewise	NOUN
ap-10701	128	6	linear	linear	NOUN
ap-10701	128	7	function	function	NOUN
ap-10701	128	8	,	,	PUNCT
ap-10701	128	9	∂x(qhu	∂x(qhu	NOUN
ap-10701	128	10	)	)	PUNCT
ap-10701	128	11	exists	exist	VERB
ap-10701	128	12	a.e	a.e	PROPN
ap-10701	128	13	.	.	PROPN
ap-10701	129	1	in	in	ADP
ap-10701	129	2	(	(	PUNCT
ap-10701	129	3	a	a	DET
ap-10701	129	4	,	,	PUNCT
ap-10701	129	5	b	b	NOUN
ap-10701	129	6	)	)	PUNCT
ap-10701	129	7	.	.	PUNCT
ap-10701	130	1	we	we	PRON
ap-10701	130	2	proceed	proceed	VERB
ap-10701	130	3	by	by	ADP
ap-10701	130	4	determining	determine	VERB
ap-10701	130	5	basic	basic	ADJ
ap-10701	130	6	properties	property	NOUN
ap-10701	130	7	of	of	ADP
ap-10701	130	8	the	the	DET
ap-10701	130	9	above	above	ADV
ap-10701	130	10	defined	define	VERB
ap-10701	130	11	maps	map	NOUN
ap-10701	130	12	as	as	SCONJ
ap-10701	130	13	proven	prove	VERB
ap-10701	130	14	in	in	ADP
ap-10701	130	15	[	[	X
ap-10701	130	16	21	21	NUM
ap-10701	130	17	]	]	PUNCT
ap-10701	130	18	,	,	PUNCT
ap-10701	130	19	taking	take	VERB
ap-10701	130	20	v	v	NOUN
ap-10701	130	21	,	,	PUNCT
ap-10701	130	22	w	w	PROPN
ap-10701	130	23	∈	∈	PROPN
ap-10701	130	24	hh	hh	VERB
ap-10701	130	25	:	:	PUNCT
ap-10701	130	26	(	(	PUNCT
ap-10701	130	27	1	1	NUM
ap-10701	130	28	.	.	PUNCT
ap-10701	130	29	)	)	PUNCT
ap-10701	131	1	the	the	DET
ap-10701	131	2	scalar	scalar	ADJ
ap-10701	131	3	products	product	NOUN
ap-10701	131	4	in	in	ADP
ap-10701	131	5	l2	l2	NOUN
ap-10701	131	6	and	and	CCONJ
ap-10701	131	7	hh	hh	NOUN
ap-10701	131	8	are	be	AUX
ap-10701	131	9	related	relate	VERB
ap-10701	131	10	as:∫	as:∫	PROPN
ap-10701	131	11	b	b	PROPN
ap-10701	131	12	a	a	DET
ap-10701	131	13	shv	shv	PROPN
ap-10701	131	14	shwdx	shwdx	NOUN
ap-10701	131	15	=	=	SYM
ap-10701	131	16	(	(	PUNCT
ap-10701	131	17	v	v	NOUN
ap-10701	131	18	,	,	PUNCT
ap-10701	131	19	w	w	NOUN
ap-10701	131	20	)	)	PUNCT
ap-10701	131	21	h.	h.	PROPN
ap-10701	131	22	(	(	PUNCT
ap-10701	131	23	7	7	NUM
ap-10701	131	24	)	)	PUNCT
ap-10701	131	25	(	(	PUNCT
ap-10701	131	26	2	2	NUM
ap-10701	131	27	.	.	PUNCT
ap-10701	131	28	)	)	PUNCT
ap-10701	132	1	the	the	DET
ap-10701	132	2	products	product	NOUN
ap-10701	132	3	of	of	ADP
ap-10701	132	4	gradients	gradient	NOUN
ap-10701	132	5	are	be	AUX
ap-10701	132	6	related	relate	VERB
ap-10701	132	7	as:∫	as:∫	PROPN
ap-10701	132	8	b	b	PROPN
ap-10701	132	9	a	a	DET
ap-10701	132	10	∂x(qhv	∂x(qhv	PROPN
ap-10701	132	11	)	)	PUNCT
ap-10701	132	12	∂x(qhw	∂x(qhw	PROPN
ap-10701	132	13	)	)	PUNCT
ap-10701	133	1	dx	dx	PROPN
ap-10701	134	1	=	=	SYM
ap-10701	134	2	(	(	PUNCT
ap-10701	134	3	vx̄,wx̄	vx̄,wx̄	PROPN
ap-10701	134	4	]	]	PUNCT
ap-10701	134	5	.	.	PUNCT
ap-10701	135	1	(	(	PUNCT
ap-10701	135	2	8)	8)	NUM
ap-10701	135	3	(	(	PUNCT
ap-10701	135	4	3	3	NUM
ap-10701	135	5	.	.	PUNCT
ap-10701	135	6	)	)	PUNCT
ap-10701	136	1	the	the	DET
ap-10701	136	2	relation	relation	NOUN
ap-10701	136	3	of	of	ADP
ap-10701	136	4	norms	norm	NOUN
ap-10701	136	5	is	be	AUX
ap-10701	136	6	:	:	PUNCT
ap-10701	136	7	∥qhv	∥qhv	NUM
ap-10701	136	8	∥l2((a	∥l2((a	PROPN
ap-10701	136	9	,	,	PUNCT
ap-10701	136	10	b	b	NOUN
ap-10701	136	11	)	)	PUNCT
ap-10701	136	12	)	)	PUNCT
ap-10701	136	13	≤	≤	NUM
ap-10701	137	1	∥shv	∥shv	NOUN
ap-10701	137	2	∥l2((a	∥l2((a	PROPN
ap-10701	137	3	,	,	PUNCT
ap-10701	137	4	b	b	NOUN
ap-10701	137	5	)	)	PUNCT
ap-10701	137	6	)	)	PUNCT
ap-10701	137	7	.	.	PUNCT
ap-10701	138	1	(	(	PUNCT
ap-10701	138	2	9	9	NUM
ap-10701	138	3	)	)	PUNCT
ap-10701	138	4	(	(	PUNCT
ap-10701	138	5	4	4	NUM
ap-10701	138	6	.	.	PUNCT
ap-10701	138	7	)	)	PUNCT
ap-10701	139	1	the	the	DET
ap-10701	139	2	difference	difference	NOUN
ap-10701	139	3	of	of	ADP
ap-10701	139	4	extrapolation	extrapolation	NOUN
ap-10701	139	5	operators	operator	NOUN
ap-10701	139	6	is:∫	is:∫	NOUN
ap-10701	139	7	b	b	PROPN
ap-10701	139	8	a	a	DET
ap-10701	139	9	|qhv	|qhv	NOUN
ap-10701	139	10	−	−	NOUN
ap-10701	139	11	shv	shv	NOUN
ap-10701	139	12	|2dx	|2dx	PROPN
ap-10701	139	13	≤	≤	PROPN
ap-10701	139	14	h2	h2	NOUN
ap-10701	139	15	6	6	NUM
ap-10701	139	16	∥vx̄]|2	∥vx̄]|2	NOUN
ap-10701	139	17	.	.	PUNCT
ap-10701	140	1	(	(	PUNCT
ap-10701	140	2	10	10	NUM
ap-10701	140	3	)	)	PUNCT
ap-10701	140	4	(	(	PUNCT
ap-10701	140	5	5	5	NUM
ap-10701	140	6	.	.	PUNCT
ap-10701	140	7	)	)	PUNCT
ap-10701	140	8	let	let	VERB
ap-10701	140	9	v	v	NUM
ap-10701	140	10	∈	∈	PROPN
ap-10701	140	11	c0,ν((a	c0,ν((a	NOUN
ap-10701	140	12	,	,	PUNCT
ap-10701	140	13	b);rd	b);rd	NOUN
ap-10701	140	14	)	)	PUNCT
ap-10701	140	15	,	,	PUNCT
ap-10701	140	16	ν	ν	PROPN
ap-10701	140	17	∈	∈	PROPN
ap-10701	140	18	(	(	PUNCT
ap-10701	140	19	0	0	NUM
ap-10701	140	20	,	,	PUNCT
ap-10701	140	21	1	1	NUM
ap-10701	140	22	)	)	PUNCT
ap-10701	140	23	.	.	PUNCT
ap-10701	141	1	then	then	ADV
ap-10701	141	2	:	:	PUNCT
ap-10701	141	3	sh(phv	sh(phv	NOUN
ap-10701	141	4	)	)	PUNCT
ap-10701	142	1	→	→	SYM
ap-10701	142	2	v	v	NOUN
ap-10701	142	3	in	in	ADP
ap-10701	142	4	ls((a	ls((a	PROPN
ap-10701	142	5	,	,	PUNCT
ap-10701	142	6	b);rd	b);rd	NOUN
ap-10701	142	7	)	)	PUNCT
ap-10701	142	8	,	,	PUNCT
ap-10701	142	9	whenever	whenever	SCONJ
ap-10701	142	10	h	h	NOUN
ap-10701	142	11	→	→	SYM
ap-10701	142	12	0	0	NUM
ap-10701	142	13	,	,	PUNCT
ap-10701	142	14	(	(	PUNCT
ap-10701	142	15	11	11	NUM
ap-10701	142	16	)	)	PUNCT
ap-10701	142	17	for	for	ADP
ap-10701	142	18	s	s	PROPN
ap-10701	142	19	>	>	X
ap-10701	142	20	1	1	NUM
ap-10701	142	21	.	.	NOUN
ap-10701	142	22	568	568	NUM
ap-10701	142	23	vol	vol	NOUN
ap-10701	142	24	.	.	PUNCT
ap-10701	143	1	65	65	NUM
ap-10701	143	2	no	no	NOUN
ap-10701	143	3	.	.	PUNCT
ap-10701	144	1	5/2025	5/2025	NUM
ap-10701	144	2	method	method	NOUN
ap-10701	144	3	of	of	ADP
ap-10701	144	4	lines	line	NOUN
ap-10701	144	5	for	for	ADP
ap-10701	144	6	reaction	reaction	NOUN
ap-10701	144	7	-	-	PUNCT
ap-10701	144	8	diffusion	diffusion	NOUN
ap-10701	144	9	systems	system	NOUN
ap-10701	144	10	.	.	PUNCT
ap-10701	144	11	.	.	PUNCT
ap-10701	144	12	.	.	PUNCT
ap-10701	145	1	(	(	PUNCT
ap-10701	145	2	6	6	NUM
ap-10701	145	3	.	.	PUNCT
ap-10701	145	4	)	)	PUNCT
ap-10701	145	5	let	let	VERB
ap-10701	145	6	v	v	NUM
ap-10701	145	7	∈	∈	PRON
ap-10701	145	8	v	v	ADP
ap-10701	145	9	∩w	∩w	NOUN
ap-10701	145	10	(	(	PUNCT
ap-10701	145	11	2	2	NUM
ap-10701	145	12	)	)	SYM
ap-10701	145	13	2	2	NUM
ap-10701	145	14	(	(	PUNCT
ap-10701	145	15	(	(	PUNCT
ap-10701	145	16	a	a	PRON
ap-10701	145	17	,	,	PUNCT
ap-10701	145	18	b);rd	b);rd	NOUN
ap-10701	145	19	)	)	PUNCT
ap-10701	145	20	.	.	PUNCT
ap-10701	146	1	then	then	ADV
ap-10701	146	2	:	:	PUNCT
ap-10701	146	3	qh(phv	qh(phv	X
ap-10701	146	4	)	)	PUNCT
ap-10701	146	5	→	→	SYM
ap-10701	146	6	v	v	X
ap-10701	146	7	(	(	PUNCT
ap-10701	146	8	12	12	NUM
ap-10701	146	9	)	)	PUNCT
ap-10701	146	10	in	in	ADP
ap-10701	146	11	v	v	NOUN
ap-10701	146	12	,	,	PUNCT
ap-10701	146	13	if	if	SCONJ
ap-10701	146	14	h	h	NOUN
ap-10701	146	15	→	→	SYM
ap-10701	146	16	0	0	X
ap-10701	146	17	.	.	X
ap-10701	147	1	extending	extend	VERB
ap-10701	147	2	the	the	DET
ap-10701	147	3	results	result	NOUN
ap-10701	147	4	of	of	ADP
ap-10701	147	5	section	section	NOUN
ap-10701	147	6	4.1	4.1	NUM
ap-10701	147	7	to	to	ADP
ap-10701	147	8	the	the	DET
ap-10701	147	9	continuum	continuum	NOUN
ap-10701	147	10	of	of	ADP
ap-10701	147	11	(	(	PUNCT
ap-10701	147	12	a	a	DET
ap-10701	147	13	,	,	PUNCT
ap-10701	147	14	b	b	NOUN
ap-10701	147	15	)	)	PUNCT
ap-10701	147	16	,	,	PUNCT
ap-10701	147	17	we	we	PRON
ap-10701	147	18	see	see	VERB
ap-10701	147	19	that	that	PRON
ap-10701	147	20	∂xqh(phuini	∂xqh(phuini	NUM
ap-10701	147	21	)	)	PUNCT
ap-10701	147	22	are	be	AUX
ap-10701	147	23	bounded	bound	VERB
ap-10701	147	24	in	in	ADP
ap-10701	147	25	l2((a	l2((a	PROPN
ap-10701	147	26	,	,	PUNCT
ap-10701	147	27	b	b	NOUN
ap-10701	147	28	)	)	PUNCT
ap-10701	147	29	)	)	PUNCT
ap-10701	147	30	(	(	PUNCT
ap-10701	147	31	by	by	ADP
ap-10701	147	32	equation	equation	NOUN
ap-10701	147	33	(	(	PUNCT
ap-10701	147	34	12	12	NUM
ap-10701	147	35	)	)	PUNCT
ap-10701	147	36	)	)	PUNCT
ap-10701	147	37	,	,	PUNCT
ap-10701	147	38	and	and	CCONJ
ap-10701	147	39	sh(phuini	sh(phuini	PROPN
ap-10701	147	40	)	)	PUNCT
ap-10701	147	41	is	be	AUX
ap-10701	147	42	bounded	bound	VERB
ap-10701	147	43	in	in	ADP
ap-10701	147	44	l2((a	l2((a	PROPN
ap-10701	147	45	,	,	PUNCT
ap-10701	147	46	b	b	NOUN
ap-10701	147	47	)	)	PUNCT
ap-10701	147	48	)	)	PUNCT
ap-10701	147	49	(	(	PUNCT
ap-10701	147	50	by	by	ADP
ap-10701	147	51	equation	equation	NOUN
ap-10701	147	52	(	(	PUNCT
ap-10701	147	53	7	7	NUM
ap-10701	147	54	)	)	PUNCT
ap-10701	147	55	)	)	PUNCT
ap-10701	147	56	independently	independently	ADV
ap-10701	147	57	of	of	ADP
ap-10701	147	58	h.	h.	PROPN
ap-10701	147	59	therefore	therefore	ADV
ap-10701	147	60	,	,	PUNCT
ap-10701	147	61	solution	solution	NOUN
ap-10701	147	62	of	of	ADP
ap-10701	147	63	equation	equation	NOUN
ap-10701	147	64	(	(	PUNCT
ap-10701	147	65	4	4	NUM
ap-10701	147	66	)	)	PUNCT
ap-10701	147	67	obtained	obtain	VERB
ap-10701	147	68	for	for	ADP
ap-10701	147	69	zini	zini	NOUN
ap-10701	147	70	=	=	SYM
ap-10701	147	71	phuini	phuini	NOUN
ap-10701	147	72	satisfies	satisfie	NOUN
ap-10701	147	73	:	:	PUNCT
ap-10701	147	74	∂xqhz	∂xqhz	PROPN
ap-10701	147	75	∈	∈	PROPN
ap-10701	147	76	l∞(0	l∞(0	PROPN
ap-10701	147	77	,	,	PUNCT
ap-10701	147	78	t	t	PROPN
ap-10701	147	79	;	;	PUNCT
ap-10701	147	80	l2((a	l2((a	PROPN
ap-10701	147	81	,	,	PUNCT
ap-10701	147	82	b	b	NOUN
ap-10701	147	83	)	)	PUNCT
ap-10701	147	84	)	)	PUNCT
ap-10701	147	85	)	)	PUNCT
ap-10701	147	86	,	,	PUNCT
ap-10701	147	87	shz	shz	AUX
ap-10701	147	88	∈	∈	PROPN
ap-10701	147	89	l∞(0	l∞(0	PRON
ap-10701	147	90	,	,	PUNCT
ap-10701	147	91	t	t	PROPN
ap-10701	147	92	;	;	PUNCT
ap-10701	147	93	l2((a	l2((a	PROPN
ap-10701	147	94	,	,	PUNCT
ap-10701	147	95	b	b	NOUN
ap-10701	147	96	)	)	PUNCT
ap-10701	147	97	)	)	PUNCT
ap-10701	147	98	)	)	PUNCT
ap-10701	147	99	,	,	PUNCT
ap-10701	147	100	from	from	ADP
ap-10701	147	101	which	which	PRON
ap-10701	147	102	:	:	PUNCT
ap-10701	147	103	∂xqhz	∂xqhz	PROPN
ap-10701	147	104	∈	∈	PROPN
ap-10701	147	105	l2(0	l2(0	PROPN
ap-10701	147	106	,	,	PUNCT
ap-10701	147	107	t	t	PROPN
ap-10701	147	108	;	;	PUNCT
ap-10701	147	109	l2((a	l2((a	PROPN
ap-10701	147	110	,	,	PUNCT
ap-10701	147	111	b	b	NOUN
ap-10701	147	112	)	)	PUNCT
ap-10701	147	113	)	)	PUNCT
ap-10701	147	114	)	)	PUNCT
ap-10701	147	115	,	,	PUNCT
ap-10701	147	116	shz	shz	AUX
ap-10701	147	117	∈	∈	PROPN
ap-10701	147	118	l2(0	l2(0	NOUN
ap-10701	147	119	,	,	PUNCT
ap-10701	147	120	t	t	PROPN
ap-10701	147	121	;	;	PUNCT
ap-10701	147	122	l2((a	l2((a	PROPN
ap-10701	147	123	,	,	PUNCT
ap-10701	147	124	b	b	NOUN
ap-10701	147	125	)	)	PUNCT
ap-10701	147	126	)	)	PUNCT
ap-10701	147	127	)	)	PUNCT
ap-10701	147	128	,	,	PUNCT
ap-10701	147	129	are	be	AUX
ap-10701	147	130	bounded	bound	VERB
ap-10701	147	131	independently	independently	ADV
ap-10701	147	132	of	of	ADP
ap-10701	147	133	h.	h.	PROPN
ap-10701	147	134	moreover	moreover	ADV
ap-10701	147	135	,	,	PUNCT
ap-10701	147	136	we	we	PRON
ap-10701	147	137	obtain	obtain	VERB
ap-10701	147	138	that	that	PRON
ap-10701	147	139	:	:	PUNCT
ap-10701	147	140	shż	shż	PROPN
ap-10701	147	141	∈	∈	PROPN
ap-10701	147	142	l2(0	l2(0	NOUN
ap-10701	147	143	,	,	PUNCT
ap-10701	147	144	t	t	PROPN
ap-10701	147	145	;	;	PUNCT
ap-10701	147	146	l2((a	l2((a	PROPN
ap-10701	147	147	,	,	PUNCT
ap-10701	147	148	b	b	NOUN
ap-10701	147	149	)	)	PUNCT
ap-10701	147	150	)	)	PUNCT
ap-10701	147	151	)	)	PUNCT
ap-10701	147	152	,	,	PUNCT
ap-10701	147	153	are	be	AUX
ap-10701	147	154	bounded	bound	VERB
ap-10701	147	155	independently	independently	ADV
ap-10701	147	156	of	of	ADP
ap-10701	147	157	h	h	NOUN
ap-10701	147	158	as	as	SCONJ
ap-10701	147	159	follows	follow	VERB
ap-10701	147	160	from	from	ADP
ap-10701	147	161	(	(	PUNCT
ap-10701	147	162	6	6	NUM
ap-10701	147	163	)	)	PUNCT
ap-10701	147	164	.	.	PUNCT
ap-10701	148	1	we	we	PRON
ap-10701	148	2	conclude	conclude	VERB
ap-10701	148	3	that	that	PRON
ap-10701	148	4	:	:	PUNCT
ap-10701	148	5	qhz	qhz	PROPN
ap-10701	148	6	∈	∈	PROPN
ap-10701	148	7	l∞(0	l∞(0	PROPN
ap-10701	148	8	,	,	PUNCT
ap-10701	148	9	t	t	PROPN
ap-10701	148	10	;	;	PUNCT
ap-10701	148	11	h1	h1	PROPN
ap-10701	148	12	0((a	0((a	PROPN
ap-10701	148	13	,	,	PUNCT
ap-10701	148	14	b	b	NOUN
ap-10701	148	15	)	)	PUNCT
ap-10701	148	16	)	)	PUNCT
ap-10701	148	17	)	)	PUNCT
ap-10701	148	18	,	,	PUNCT
ap-10701	148	19	qhz	qhz	PROPN
ap-10701	148	20	∈	∈	PROPN
ap-10701	148	21	l2(0	l2(0	NOUN
ap-10701	148	22	,	,	PUNCT
ap-10701	148	23	t	t	PROPN
ap-10701	148	24	;	;	PUNCT
ap-10701	148	25	h1	h1	PROPN
ap-10701	148	26	0((a	0((a	PROPN
ap-10701	148	27	,	,	PUNCT
ap-10701	148	28	b	b	NOUN
ap-10701	148	29	)	)	PUNCT
ap-10701	148	30	)	)	PUNCT
ap-10701	148	31	)	)	PUNCT
ap-10701	148	32	,	,	PUNCT
ap-10701	148	33	are	be	AUX
ap-10701	148	34	bounded	bound	VERB
ap-10701	148	35	independently	independently	ADV
ap-10701	148	36	on	on	ADP
ap-10701	148	37	h.	h.	NOUN
ap-10701	148	38	according	accord	VERB
ap-10701	148	39	to	to	ADP
ap-10701	148	40	(	(	PUNCT
ap-10701	148	41	9	9	NUM
ap-10701	148	42	)	)	PUNCT
ap-10701	148	43	,	,	PUNCT
ap-10701	148	44	qhż	qhż	PROPN
ap-10701	148	45	∈	∈	PROPN
ap-10701	148	46	l2(0	l2(0	PROPN
ap-10701	148	47	,	,	PUNCT
ap-10701	148	48	t	t	PROPN
ap-10701	148	49	;	;	PUNCT
ap-10701	148	50	l2((a	l2((a	PROPN
ap-10701	148	51	,	,	PUNCT
ap-10701	148	52	b	b	NOUN
ap-10701	148	53	)	)	PUNCT
ap-10701	148	54	)	)	PUNCT
ap-10701	148	55	)	)	PUNCT
ap-10701	148	56	.	.	PUNCT
ap-10701	149	1	4.3	4.3	NUM
ap-10701	149	2	.	.	PUNCT
ap-10701	149	3	passage	passage	NOUN
ap-10701	149	4	to	to	ADP
ap-10701	149	5	the	the	DET
ap-10701	149	6	limit	limit	NOUN
ap-10701	149	7	passing	pass	VERB
ap-10701	149	8	to	to	ADP
ap-10701	149	9	a	a	DET
ap-10701	149	10	subsequence	subsequence	NOUN
ap-10701	149	11	,	,	PUNCT
ap-10701	149	12	we	we	PRON
ap-10701	149	13	have	have	VERB
ap-10701	149	14	:	:	PUNCT
ap-10701	149	15	•	•	NUM
ap-10701	149	16	qhnz	qhnz	NOUN
ap-10701	149	17	⇀	⇀	PROPN
ap-10701	149	18	u	u	NOUN
ap-10701	149	19	in	in	ADP
ap-10701	149	20	l2(0	l2(0	PROPN
ap-10701	149	21	,	,	PUNCT
ap-10701	149	22	t	t	NOUN
ap-10701	149	23	;	;	PUNCT
ap-10701	149	24	v	v	NOUN
ap-10701	149	25	)	)	PUNCT
ap-10701	149	26	;	;	PUNCT
ap-10701	149	27	•	•	NUM
ap-10701	149	28	shnż	shnż	NOUN
ap-10701	150	1	⇀	⇀	PROPN
ap-10701	150	2	∂tu	∂tu	ADV
ap-10701	150	3	in	in	ADP
ap-10701	150	4	l2(0	l2(0	PROPN
ap-10701	150	5	,	,	PUNCT
ap-10701	150	6	t	t	NOUN
ap-10701	150	7	;	;	PUNCT
ap-10701	150	8	v−1	v−1	PROPN
ap-10701	150	9	)	)	PUNCT
ap-10701	150	10	;	;	PUNCT
ap-10701	150	11	•	•	NUM
ap-10701	150	12	shn	shn	PROPN
ap-10701	150	13	z	z	NOUN
ap-10701	150	14	⇀	⇀	PUNCT
ap-10701	151	1	u	u	NOUN
ap-10701	151	2	in	in	ADP
ap-10701	151	3	l2(0	l2(0	NOUN
ap-10701	151	4	,	,	PUNCT
ap-10701	151	5	t	t	NOUN
ap-10701	151	6	;	;	PUNCT
ap-10701	151	7	h	h	X
ap-10701	151	8	)	)	PUNCT
ap-10701	151	9	.	.	PUNCT
ap-10701	152	1	the	the	DET
ap-10701	152	2	non	non	ADJ
ap-10701	152	3	-	-	ADJ
ap-10701	152	4	linear	linear	ADJ
ap-10701	152	5	terms	term	NOUN
ap-10701	152	6	in	in	ADP
ap-10701	152	7	equation	equation	NOUN
ap-10701	152	8	(	(	PUNCT
ap-10701	152	9	1	1	X
ap-10701	152	10	)	)	PUNCT
ap-10701	152	11	require	require	VERB
ap-10701	152	12	a	a	DET
ap-10701	152	13	stronger	strong	ADJ
ap-10701	152	14	convergence	convergence	NOUN
ap-10701	152	15	result	result	NOUN
ap-10701	152	16	.	.	PUNCT
ap-10701	153	1	using	use	VERB
ap-10701	153	2	the	the	DET
ap-10701	153	3	lemma	lemma	PROPN
ap-10701	153	4	on	on	ADP
ap-10701	153	5	the	the	DET
ap-10701	153	6	compact	compact	ADJ
ap-10701	153	7	embedding	embed	VERB
ap-10701	153	8	(	(	PUNCT
ap-10701	153	9	see	see	VERB
ap-10701	153	10	e.g.	e.g.	ADV
ap-10701	153	11	[	[	X
ap-10701	153	12	3	3	NUM
ap-10701	153	13	,	,	PUNCT
ap-10701	153	14	24	24	NUM
ap-10701	153	15	]	]	PUNCT
ap-10701	153	16	)	)	PUNCT
ap-10701	153	17	,	,	PUNCT
ap-10701	153	18	we	we	PRON
ap-10701	153	19	conclude	conclude	VERB
ap-10701	153	20	that	that	SCONJ
ap-10701	153	21	qhnz	qhnz	PROPN
ap-10701	153	22	converges	converge	VERB
ap-10701	153	23	strongly	strongly	ADV
ap-10701	153	24	in	in	ADP
ap-10701	153	25	l2(0	l2(0	NOUN
ap-10701	153	26	,	,	PUNCT
ap-10701	153	27	t	t	NOUN
ap-10701	153	28	;	;	PUNCT
ap-10701	153	29	h	h	X
ap-10701	153	30	)	)	PUNCT
ap-10701	153	31	.	.	PUNCT
ap-10701	154	1	denote	denote	VERB
ap-10701	154	2	their	their	PRON
ap-10701	154	3	common	common	ADJ
ap-10701	154	4	limit	limit	NOUN
ap-10701	154	5	as	as	ADP
ap-10701	154	6	u	u	NOUN
ap-10701	154	7	and	and	CCONJ
ap-10701	154	8	the	the	DET
ap-10701	154	9	weak	weak	ADJ
ap-10701	154	10	limit	limit	NOUN
ap-10701	154	11	of	of	ADP
ap-10701	154	12	shnż	shnż	NOUN
ap-10701	154	13	in	in	ADP
ap-10701	154	14	l2(0	l2(0	NOUN
ap-10701	154	15	,	,	PUNCT
ap-10701	154	16	t	t	NOUN
ap-10701	154	17	;	;	PUNCT
ap-10701	154	18	h	h	X
ap-10701	154	19	)	)	PUNCT
ap-10701	154	20	as	as	ADP
ap-10701	154	21	u	u	NOUN
ap-10701	154	22	(	(	PUNCT
ap-10701	154	23	1	1	NUM
ap-10701	154	24	)	)	PUNCT
ap-10701	154	25	.	.	PUNCT
ap-10701	155	1	these	these	DET
ap-10701	155	2	limits	limit	NOUN
ap-10701	155	3	exist	exist	VERB
ap-10701	155	4	as	as	ADP
ap-10701	155	5	a	a	DET
ap-10701	155	6	consequence	consequence	NOUN
ap-10701	155	7	of	of	ADP
ap-10701	155	8	the	the	DET
ap-10701	155	9	above	above	ADV
ap-10701	155	10	-	-	PUNCT
ap-10701	155	11	mentioned	mention	VERB
ap-10701	155	12	facts	fact	NOUN
ap-10701	155	13	.	.	PUNCT
ap-10701	156	1	the	the	DET
ap-10701	156	2	fact	fact	NOUN
ap-10701	156	3	that	that	SCONJ
ap-10701	156	4	u	u	NOUN
ap-10701	156	5	(	(	PUNCT
ap-10701	156	6	1	1	NUM
ap-10701	156	7	)	)	PUNCT
ap-10701	156	8	=	=	VERB
ap-10701	156	9	∂tu	∂tu	ADV
ap-10701	156	10	is	be	AUX
ap-10701	156	11	implied	imply	VERB
ap-10701	156	12	by	by	ADP
ap-10701	156	13	the	the	DET
ap-10701	156	14	uniquenes	uniquene	NOUN
ap-10701	156	15	of	of	ADP
ap-10701	156	16	the	the	DET
ap-10701	156	17	limit	limit	NOUN
ap-10701	156	18	in	in	ADP
ap-10701	156	19	d′(0	d′(0	NOUN
ap-10701	156	20	,	,	PUNCT
ap-10701	156	21	t	t	PROPN
ap-10701	156	22	)	)	PUNCT
ap-10701	156	23	,	,	PUNCT
ap-10701	156	24	as:∫	as:∫	PROPN
ap-10701	156	25	t	t	PROPN
ap-10701	156	26	0	0	NUM
ap-10701	156	27	(	(	PUNCT
ap-10701	156	28	shn	shn	NOUN
ap-10701	156	29	ż	ż	NOUN
ap-10701	156	30	−	−	PROPN
ap-10701	156	31	qhn	qhn	NOUN
ap-10701	156	32	ż	ż	NOUN
ap-10701	156	33	,	,	PUNCT
ap-10701	156	34	q)ψ(t)dt	q)ψ(t)dt	NOUN
ap-10701	156	35	=	=	PUNCT
ap-10701	156	36	−	−	PROPN
ap-10701	156	37	∫	∫	PROPN
ap-10701	156	38	t	t	PROPN
ap-10701	156	39	0	0	NUM
ap-10701	156	40	(	(	PUNCT
ap-10701	156	41	shn	shn	PROPN
ap-10701	156	42	z	z	NOUN
ap-10701	156	43	−	−	PROPN
ap-10701	156	44	qhn	qhn	NOUN
ap-10701	156	45	z	z	NOUN
ap-10701	156	46	,	,	PUNCT
ap-10701	156	47	q)ψ̇(t)dt	q)ψ̇(t)dt	PROPN
ap-10701	156	48	,	,	PUNCT
ap-10701	156	49	where	where	SCONJ
ap-10701	156	50	q	q	PROPN
ap-10701	156	51	∈	∈	PROPN
ap-10701	156	52	d((a	d((a	PROPN
ap-10701	156	53	,	,	PUNCT
ap-10701	156	54	b	b	NOUN
ap-10701	156	55	)	)	PUNCT
ap-10701	156	56	)	)	PUNCT
ap-10701	156	57	,	,	PUNCT
ap-10701	156	58	ψ	ψ	X
ap-10701	156	59	∈	∈	PROPN
ap-10701	156	60	d(0	d(0	PROPN
ap-10701	156	61	,	,	PUNCT
ap-10701	156	62	t	t	PROPN
ap-10701	156	63	)	)	PUNCT
ap-10701	156	64	.	.	PUNCT
ap-10701	157	1	lemma	lemma	PROPN
ap-10701	157	2	2	2	X
ap-10701	157	3	.	.	PUNCT
ap-10701	158	1	if	if	SCONJ
ap-10701	158	2	u	u	PRON
ap-10701	158	3	denotes	denote	VERB
ap-10701	158	4	the	the	DET
ap-10701	158	5	weak	weak	ADJ
ap-10701	158	6	limit	limit	NOUN
ap-10701	158	7	of	of	ADP
ap-10701	158	8	shn	shn	PROPN
ap-10701	158	9	z	z	PROPN
ap-10701	158	10	in	in	ADP
ap-10701	158	11	l2(0	l2(0	PROPN
ap-10701	158	12	,	,	PUNCT
ap-10701	158	13	t	t	NOUN
ap-10701	158	14	;	;	PUNCT
ap-10701	158	15	h	h	NOUN
ap-10701	158	16	)	)	PUNCT
ap-10701	158	17	,	,	PUNCT
ap-10701	158	18	and	and	CCONJ
ap-10701	158	19	the	the	DET
ap-10701	158	20	strong	strong	ADJ
ap-10701	158	21	limit	limit	NOUN
ap-10701	158	22	of	of	ADP
ap-10701	158	23	qhn	qhn	NOUN
ap-10701	158	24	z	z	PROPN
ap-10701	158	25	in	in	ADP
ap-10701	158	26	l2(0	l2(0	PROPN
ap-10701	158	27	,	,	PUNCT
ap-10701	158	28	t	t	NOUN
ap-10701	158	29	;	;	PUNCT
ap-10701	158	30	h	h	X
ap-10701	158	31	)	)	PUNCT
ap-10701	158	32	,	,	PUNCT
ap-10701	158	33	then	then	ADV
ap-10701	158	34	:	:	PUNCT
ap-10701	158	35	f(shn	f(shn	PROPN
ap-10701	158	36	z	z	PROPN
ap-10701	158	37	)	)	PUNCT
ap-10701	158	38	→	→	PUNCT
ap-10701	158	39	f(u	f(u	ADJ
ap-10701	158	40	)	)	PUNCT
ap-10701	158	41	weakly	weakly	ADJ
ap-10701	158	42	in	in	ADP
ap-10701	158	43	l2(0	l2(0	NOUN
ap-10701	158	44	,	,	PUNCT
ap-10701	158	45	t	t	NOUN
ap-10701	158	46	;	;	PUNCT
ap-10701	158	47	h	h	X
ap-10701	158	48	)	)	PUNCT
ap-10701	158	49	.	.	PUNCT
ap-10701	159	1	proof	proof	NOUN
ap-10701	159	2	.	.	PUNCT
ap-10701	160	1	the	the	DET
ap-10701	160	2	argument	argument	NOUN
ap-10701	160	3	is	be	AUX
ap-10701	160	4	provided	provide	VERB
ap-10701	160	5	by	by	ADP
ap-10701	160	6	the	the	DET
ap-10701	160	7	lipschitz	lipschitz	ADJ
ap-10701	160	8	continuity	continuity	NOUN
ap-10701	160	9	of	of	ADP
ap-10701	160	10	f	f	PROPN
ap-10701	160	11	within	within	ADP
ap-10701	160	12	the	the	DET
ap-10701	160	13	invariant	invariant	ADJ
ap-10701	160	14	region	region	NOUN
ap-10701	160	15	.	.	PUNCT
ap-10701	161	1	to	to	PART
ap-10701	161	2	pass	pass	VERB
ap-10701	161	3	to	to	ADP
ap-10701	161	4	the	the	DET
ap-10701	161	5	limit	limit	NOUN
ap-10701	161	6	,	,	PUNCT
ap-10701	161	7	we	we	PRON
ap-10701	161	8	proceed	proceed	VERB
ap-10701	161	9	as	as	ADP
ap-10701	161	10	in	in	ADP
ap-10701	161	11	[	[	X
ap-10701	161	12	3	3	NUM
ap-10701	161	13	,	,	PUNCT
ap-10701	161	14	25	25	NUM
ap-10701	161	15	,	,	PUNCT
ap-10701	161	16	26	26	NUM
ap-10701	161	17	]	]	PUNCT
ap-10701	161	18	,	,	PUNCT
ap-10701	161	19	and	and	CCONJ
ap-10701	161	20	multiply	multiply	ADV
ap-10701	161	21	(	(	PUNCT
ap-10701	161	22	4	4	NUM
ap-10701	161	23	)	)	PUNCT
ap-10701	161	24	by	by	ADP
ap-10701	161	25	the	the	DET
ap-10701	161	26	test	test	NOUN
ap-10701	161	27	functions	function	NOUN
ap-10701	161	28	phnv	phnv	NOUN
ap-10701	161	29	,	,	PUNCT
ap-10701	161	30	where	where	SCONJ
ap-10701	161	31	v	v	X
ap-10701	161	32	∈	∈	PROPN
ap-10701	161	33	d((a	d((a	PROPN
ap-10701	161	34	,	,	PUNCT
ap-10701	161	35	b	b	NOUN
ap-10701	161	36	)	)	PUNCT
ap-10701	161	37	)	)	PUNCT
ap-10701	161	38	.	.	PUNCT
ap-10701	162	1	we	we	PRON
ap-10701	162	2	integrate	integrate	VERB
ap-10701	162	3	it	it	PRON
ap-10701	162	4	over	over	ADP
ap-10701	162	5	ωh	ωh	PROPN
ap-10701	162	6	.	.	PUNCT
ap-10701	163	1	then	then	ADV
ap-10701	163	2	,	,	PUNCT
ap-10701	163	3	we	we	PRON
ap-10701	163	4	have	have	VERB
ap-10701	163	5	,	,	PUNCT
ap-10701	163	6	in	in	ADP
ap-10701	163	7	terms	term	NOUN
ap-10701	163	8	of	of	ADP
ap-10701	163	9	h	h	NOUN
ap-10701	163	10	:	:	PUNCT
ap-10701	163	11	(	(	PUNCT
ap-10701	163	12	shn	shn	PROPN
ap-10701	163	13	ż,shn	ż,shn	PROPN
ap-10701	163	14	phn	phn	PROPN
ap-10701	163	15	v	v	NOUN
ap-10701	163	16	)	)	PUNCT
ap-10701	164	1	+	+	CCONJ
ap-10701	164	2	(	(	PUNCT
ap-10701	164	3	∂xqhn	∂xqhn	ADP
ap-10701	164	4	z	z	NOUN
ap-10701	164	5	,	,	PUNCT
ap-10701	164	6	∂xqhn	∂xqhn	PRON
ap-10701	164	7	phn	phn	ADJ
ap-10701	164	8	v	v	NOUN
ap-10701	164	9	)	)	PUNCT
ap-10701	164	10	=	=	SYM
ap-10701	164	11	(	(	PUNCT
ap-10701	164	12	f(shn	f(shn	PROPN
ap-10701	164	13	z),shn	z),shn	PROPN
ap-10701	165	1	phn	phn	PROPN
ap-10701	165	2	v	v	NOUN
ap-10701	165	3	)	)	PUNCT
ap-10701	165	4	.	.	PUNCT
ap-10701	166	1	(	(	PUNCT
ap-10701	166	2	13	13	X
ap-10701	166	3	)	)	PUNCT
ap-10701	166	4	knowing	know	VERB
ap-10701	166	5	that	that	SCONJ
ap-10701	166	6	(	(	PUNCT
ap-10701	166	7	1	1	NUM
ap-10701	166	8	.	.	PUNCT
ap-10701	166	9	)	)	PUNCT
ap-10701	166	10	shn	shn	PROPN
ap-10701	166	11	ż	ż	NOUN
ap-10701	166	12	converges	converge	VERB
ap-10701	166	13	weakly	weakly	ADV
ap-10701	166	14	in	in	ADP
ap-10701	166	15	l2(0	l2(0	NOUN
ap-10701	166	16	,	,	PUNCT
ap-10701	166	17	t	t	NOUN
ap-10701	166	18	;	;	PUNCT
ap-10701	166	19	h	h	X
ap-10701	166	20	)	)	PUNCT
ap-10701	166	21	to	to	PART
ap-10701	166	22	∂tu	∂tu	ADV
ap-10701	166	23	;	;	PUNCT
ap-10701	166	24	(	(	PUNCT
ap-10701	166	25	2	2	NUM
ap-10701	166	26	.	.	NUM
ap-10701	166	27	)	)	PUNCT
ap-10701	167	1	∂xqhn	∂xqhn	ADP
ap-10701	167	2	z	z	NOUN
ap-10701	167	3	converges	converge	VERB
ap-10701	167	4	strongly	strongly	ADV
ap-10701	167	5	in	in	ADP
ap-10701	167	6	l2(0	l2(0	NOUN
ap-10701	167	7	,	,	PUNCT
ap-10701	167	8	t	t	NOUN
ap-10701	167	9	;	;	PUNCT
ap-10701	167	10	h	h	X
ap-10701	167	11	)	)	PUNCT
ap-10701	167	12	to	to	ADP
ap-10701	167	13	∂xu	∂xu	NOUN
ap-10701	167	14	;	;	PUNCT
ap-10701	167	15	(	(	PUNCT
ap-10701	167	16	3	3	NUM
ap-10701	167	17	.	.	PUNCT
ap-10701	167	18	)	)	PUNCT
ap-10701	167	19	shn	shn	PROPN
ap-10701	167	20	phn	phn	PROPN
ap-10701	167	21	uini	uini	NOUN
ap-10701	167	22	converges	converge	VERB
ap-10701	167	23	strongly	strongly	ADV
ap-10701	167	24	to	to	ADP
ap-10701	167	25	uini	uini	NOUN
ap-10701	167	26	in	in	ADP
ap-10701	167	27	h	h	NOUN
ap-10701	167	28	,	,	PUNCT
ap-10701	167	29	we	we	PRON
ap-10701	167	30	multiply	multiply	VERB
ap-10701	167	31	(	(	PUNCT
ap-10701	167	32	13	13	NUM
ap-10701	167	33	)	)	PUNCT
ap-10701	167	34	by	by	ADP
ap-10701	167	35	a	a	DET
ap-10701	167	36	scalar	scalar	ADJ
ap-10701	167	37	function	function	NOUN
ap-10701	167	38	ψ(t	ψ(t	PROPN
ap-10701	167	39	)	)	PUNCT
ap-10701	167	40	∈	∈	PROPN
ap-10701	167	41	c1([0	c1([0	PROPN
ap-10701	167	42	,	,	PUNCT
ap-10701	167	43	t	t	NOUN
ap-10701	167	44	]	]	PUNCT
ap-10701	167	45	)	)	PUNCT
ap-10701	167	46	,	,	PUNCT
ap-10701	167	47	for	for	ADP
ap-10701	167	48	which	which	PRON
ap-10701	167	49	ψ(t	ψ(t	X
ap-10701	167	50	)	)	PUNCT
ap-10701	167	51	=	=	SYM
ap-10701	167	52	0	0	NUM
ap-10701	167	53	,	,	PUNCT
ap-10701	167	54	and	and	CCONJ
ap-10701	167	55	integrate	integrate	VERB
ap-10701	167	56	by	by	ADP
ap-10701	167	57	parts	part	NOUN
ap-10701	167	58	.	.	PUNCT
ap-10701	168	1	taking	take	VERB
ap-10701	168	2	into	into	ADP
ap-10701	168	3	account	account	NOUN
ap-10701	168	4	all	all	DET
ap-10701	168	5	previous	previous	ADJ
ap-10701	168	6	results	result	NOUN
ap-10701	168	7	,	,	PUNCT
ap-10701	168	8	the	the	DET
ap-10701	168	9	fact	fact	NOUN
ap-10701	168	10	that	that	SCONJ
ap-10701	168	11	:	:	PUNCT
ap-10701	168	12	shn	shn	NOUN
ap-10701	168	13	z(0	z(0	AUX
ap-10701	168	14	)	)	PUNCT
ap-10701	168	15	=	=	SYM
ap-10701	168	16	shn	shn	PROPN
ap-10701	168	17	phn	phn	PROPN
ap-10701	168	18	uini	uini	NOUN
ap-10701	168	19	,	,	PUNCT
ap-10701	168	20	and	and	CCONJ
ap-10701	168	21	the	the	DET
ap-10701	168	22	lebesgue	lebesgue	NOUN
ap-10701	168	23	theorem	theorem	PROPN
ap-10701	168	24	,	,	PUNCT
ap-10701	168	25	we	we	PRON
ap-10701	168	26	are	be	AUX
ap-10701	168	27	able	able	ADJ
ap-10701	168	28	to	to	PART
ap-10701	168	29	pass	pass	VERB
ap-10701	168	30	to	to	ADP
ap-10701	168	31	the	the	DET
ap-10701	168	32	limit	limit	NOUN
ap-10701	168	33	:	:	PUNCT
ap-10701	168	34	(	(	PUNCT
ap-10701	168	35	uini	uini	X
ap-10701	168	36	,	,	PUNCT
ap-10701	168	37	v	v	NOUN
ap-10701	168	38	)	)	PUNCT
ap-10701	168	39	ψ(0	ψ(0	NOUN
ap-10701	168	40	)	)	PUNCT
ap-10701	169	1	−	−	NOUN
ap-10701	170	1	∫	∫	PROPN
ap-10701	170	2	t	t	PROPN
ap-10701	170	3	0	0	NUM
ap-10701	171	1	(	(	PUNCT
ap-10701	171	2	u	u	NOUN
ap-10701	171	3	,	,	PUNCT
ap-10701	171	4	v	v	NOUN
ap-10701	171	5	)	)	PUNCT
ap-10701	171	6	ψ̇dt	ψ̇dt	PROPN
ap-10701	171	7	=	=	SYM
ap-10701	172	1	∫	∫	PROPN
ap-10701	172	2	t	t	NOUN
ap-10701	172	3	0	0	NUM
ap-10701	172	4	ψ(t	ψ(t	PROPN
ap-10701	172	5	)	)	PUNCT
ap-10701	172	6	(	(	PUNCT
ap-10701	172	7	−(∂xu	−(∂xu	NOUN
ap-10701	172	8	,	,	PUNCT
ap-10701	172	9	∂xv	∂xv	NOUN
ap-10701	172	10	)	)	PUNCT
ap-10701	172	11	+	+	CCONJ
ap-10701	172	12	(	(	PUNCT
ap-10701	172	13	f(u	f(u	PROPN
ap-10701	172	14	)	)	PUNCT
ap-10701	172	15	,	,	PUNCT
ap-10701	172	16	v	v	NOUN
ap-10701	172	17	)	)	PUNCT
ap-10701	172	18	)	)	PUNCT
ap-10701	173	1	dt	dt	X
ap-10701	173	2	.	.	PUNCT
ap-10701	174	1	(	(	PUNCT
ap-10701	174	2	14	14	NUM
ap-10701	174	3	)	)	PUNCT
ap-10701	174	4	if	if	SCONJ
ap-10701	174	5	ψ	ψ	X
ap-10701	174	6	∈	∈	PROPN
ap-10701	174	7	d(0	d(0	PROPN
ap-10701	174	8	,	,	PUNCT
ap-10701	174	9	t	t	PROPN
ap-10701	174	10	)	)	PUNCT
ap-10701	174	11	,	,	PUNCT
ap-10701	174	12	we	we	PRON
ap-10701	174	13	have	have	VERB
ap-10701	174	14	:	:	PUNCT
ap-10701	174	15	d(u	d(u	PROPN
ap-10701	174	16	,	,	PUNCT
ap-10701	174	17	v	v	NOUN
ap-10701	174	18	)	)	PUNCT
ap-10701	174	19	dt	dt	X
ap-10701	175	1	+	+	CCONJ
ap-10701	175	2	(	(	PUNCT
ap-10701	175	3	∂xu	∂xu	NOUN
ap-10701	175	4	,	,	PUNCT
ap-10701	175	5	∂xv	∂xv	NOUN
ap-10701	175	6	)	)	PUNCT
ap-10701	175	7	=	=	SYM
ap-10701	175	8	(	(	PUNCT
ap-10701	175	9	f(u	f(u	PROPN
ap-10701	175	10	)	)	PUNCT
ap-10701	175	11	,	,	PUNCT
ap-10701	175	12	v	v	NOUN
ap-10701	175	13	)	)	PUNCT
ap-10701	175	14	,	,	PUNCT
ap-10701	175	15	u	u	PROPN
ap-10701	175	16	|t=0	|t=0	PROPN
ap-10701	175	17	=	=	PUNCT
ap-10701	175	18	uini	uini	NOUN
ap-10701	175	19	.	.	PUNCT
ap-10701	176	1	(	(	PUNCT
ap-10701	176	2	15	15	NUM
ap-10701	176	3	)	)	PUNCT
ap-10701	176	4	it	it	PRON
ap-10701	176	5	remains	remain	VERB
ap-10701	176	6	to	to	PART
ap-10701	176	7	show	show	VERB
ap-10701	176	8	that	that	SCONJ
ap-10701	176	9	the	the	DET
ap-10701	176	10	weak	weak	ADJ
ap-10701	176	11	solution	solution	NOUN
ap-10701	176	12	satisfies	satisfy	VERB
ap-10701	176	13	the	the	DET
ap-10701	176	14	initial	initial	ADJ
ap-10701	176	15	condition	condition	NOUN
ap-10701	176	16	.	.	PUNCT
ap-10701	177	1	multiplying	multiply	VERB
ap-10701	177	2	(	(	PUNCT
ap-10701	177	3	15	15	NUM
ap-10701	177	4	)	)	PUNCT
ap-10701	177	5	by	by	ADP
ap-10701	177	6	a	a	DET
ap-10701	177	7	scalar	scalar	ADJ
ap-10701	177	8	function	function	NOUN
ap-10701	177	9	ψ(t	ψ(t	PROPN
ap-10701	177	10	)	)	PUNCT
ap-10701	177	11	∈	∈	PROPN
ap-10701	177	12	c1([0	c1([0	PROPN
ap-10701	177	13	,	,	PUNCT
ap-10701	177	14	t	t	NOUN
ap-10701	177	15	]	]	PUNCT
ap-10701	177	16	)	)	PUNCT
ap-10701	177	17	,	,	PUNCT
ap-10701	177	18	for	for	ADP
ap-10701	177	19	which	which	PRON
ap-10701	177	20	ψ(t	ψ(t	X
ap-10701	177	21	)	)	PUNCT
ap-10701	177	22	=	=	SYM
ap-10701	177	23	0	0	NUM
ap-10701	177	24	,	,	PUNCT
ap-10701	177	25	and	and	CCONJ
ap-10701	177	26	integrating	integrate	VERB
ap-10701	177	27	by	by	ADP
ap-10701	177	28	parts	part	NOUN
ap-10701	177	29	,	,	PUNCT
ap-10701	177	30	we	we	PRON
ap-10701	177	31	obtain	obtain	VERB
ap-10701	177	32	:	:	PUNCT
ap-10701	177	33	(	(	PUNCT
ap-10701	177	34	u	u	NOUN
ap-10701	177	35	,	,	PUNCT
ap-10701	177	36	v	v	NOUN
ap-10701	177	37	)	)	PUNCT
ap-10701	177	38	|t=0ψ(0	|t=0ψ(0	NOUN
ap-10701	177	39	)	)	PUNCT
ap-10701	178	1	−	−	NOUN
ap-10701	179	1	∫	∫	PROPN
ap-10701	179	2	t	t	PROPN
ap-10701	179	3	0	0	NUM
ap-10701	179	4	(	(	PUNCT
ap-10701	179	5	u	u	NOUN
ap-10701	179	6	,	,	PUNCT
ap-10701	179	7	v	v	NOUN
ap-10701	179	8	)	)	PUNCT
ap-10701	179	9	ψ̇dt	ψ̇dt	PROPN
ap-10701	179	10	=	=	SYM
ap-10701	179	11	∫	∫	PROPN
ap-10701	179	12	t	t	NOUN
ap-10701	179	13	0	0	NUM
ap-10701	179	14	ψ(t	ψ(t	PROPN
ap-10701	179	15	)	)	PUNCT
ap-10701	179	16	(	(	PUNCT
ap-10701	179	17	−(∂xu	−(∂xu	NOUN
ap-10701	179	18	,	,	PUNCT
ap-10701	179	19	∂xv	∂xv	NOUN
ap-10701	179	20	)	)	PUNCT
ap-10701	179	21	+	+	CCONJ
ap-10701	179	22	(	(	PUNCT
ap-10701	179	23	f(z	f(z	NOUN
ap-10701	179	24	)	)	PUNCT
ap-10701	179	25	,	,	PUNCT
ap-10701	179	26	v	v	NOUN
ap-10701	179	27	)	)	PUNCT
ap-10701	179	28	)	)	PUNCT
ap-10701	180	1	dt	dt	X
ap-10701	180	2	.	.	PUNCT
ap-10701	181	1	(	(	PUNCT
ap-10701	181	2	16	16	NUM
ap-10701	181	3	)	)	PUNCT
ap-10701	181	4	subtracting	subtract	VERB
ap-10701	181	5	(	(	PUNCT
ap-10701	181	6	16	16	NUM
ap-10701	181	7	)	)	PUNCT
ap-10701	181	8	from	from	ADP
ap-10701	181	9	(	(	PUNCT
ap-10701	181	10	14	14	NUM
ap-10701	181	11	)	)	PUNCT
ap-10701	181	12	,	,	PUNCT
ap-10701	181	13	we	we	PRON
ap-10701	181	14	get	get	VERB
ap-10701	181	15	:	:	PUNCT
ap-10701	181	16	(	(	PUNCT
ap-10701	181	17	uini	uini	NOUN
ap-10701	181	18	−	−	PROPN
ap-10701	181	19	u	u	PROPN
ap-10701	181	20	|t=0	|t=0	PROPN
ap-10701	181	21	,	,	PUNCT
ap-10701	181	22	v	v	NOUN
ap-10701	181	23	)	)	PUNCT
ap-10701	181	24	ψ(0	ψ(0	NOUN
ap-10701	181	25	)	)	PUNCT
ap-10701	181	26	=	=	SYM
ap-10701	182	1	0	0	NUM
ap-10701	182	2	,	,	PUNCT
ap-10701	182	3	for	for	ADP
ap-10701	182	4	all	all	DET
ap-10701	182	5	v	v	ADP
ap-10701	182	6	∈	∈	PROPN
ap-10701	182	7	d((a	d((a	NOUN
ap-10701	182	8	,	,	PUNCT
ap-10701	182	9	b	b	NOUN
ap-10701	182	10	)	)	PUNCT
ap-10701	182	11	)	)	PUNCT
ap-10701	182	12	.	.	PUNCT
ap-10701	183	1	from	from	ADP
ap-10701	183	2	this	this	PRON
ap-10701	183	3	we	we	PRON
ap-10701	183	4	see	see	VERB
ap-10701	183	5	that	that	SCONJ
ap-10701	183	6	u	u	PROPN
ap-10701	183	7	|t=0	|t=0	PROPN
ap-10701	183	8	=	=	PUNCT
ap-10701	183	9	uini	uini	NOUN
ap-10701	183	10	in	in	ADP
ap-10701	183	11	l2((a	l2((a	PROPN
ap-10701	183	12	,	,	PUNCT
ap-10701	183	13	b	b	NOUN
ap-10701	183	14	)	)	PUNCT
ap-10701	183	15	)	)	PUNCT
ap-10701	183	16	.	.	PUNCT
ap-10701	184	1	to	to	PART
ap-10701	184	2	prove	prove	VERB
ap-10701	184	3	uniqueness	uniqueness	NOUN
ap-10701	184	4	,	,	PUNCT
ap-10701	184	5	consider	consider	VERB
ap-10701	184	6	two	two	NUM
ap-10701	184	7	solutions	solution	NOUN
ap-10701	184	8	of	of	ADP
ap-10701	184	9	the	the	DET
ap-10701	184	10	problem	problem	NOUN
ap-10701	184	11	(	(	PUNCT
ap-10701	184	12	2	2	NUM
ap-10701	184	13	)	)	PUNCT
ap-10701	184	14	,	,	PUNCT
ap-10701	184	15	denoted	denote	VERB
ap-10701	184	16	as	as	ADP
ap-10701	184	17	z	z	PROPN
ap-10701	184	18	and	and	CCONJ
ap-10701	184	19	z̄.	z̄.	NUM
ap-10701	184	20	subtracting	subtract	VERB
ap-10701	184	21	two	two	NUM
ap-10701	184	22	systems	system	NOUN
ap-10701	184	23	of	of	ADP
ap-10701	184	24	equations	equation	NOUN
ap-10701	184	25	and	and	CCONJ
ap-10701	184	26	denoting	denote	VERB
ap-10701	184	27	r	r	NOUN
ap-10701	184	28	=	=	PUNCT
ap-10701	184	29	z	z	NOUN
ap-10701	184	30	−	−	PROPN
ap-10701	184	31	z̄	z̄	NOUN
ap-10701	184	32	,	,	PUNCT
ap-10701	184	33	multiplying	multiply	VERB
ap-10701	184	34	the	the	DET
ap-10701	184	35	system	system	NOUN
ap-10701	184	36	by	by	ADP
ap-10701	184	37	r	r	NOUN
ap-10701	184	38	via	via	ADP
ap-10701	184	39	the	the	DET
ap-10701	184	40	semi	semi	ADJ
ap-10701	184	41	-	-	ADJ
ap-10701	184	42	discrete	discrete	ADJ
ap-10701	184	43	scheme	scheme	NOUN
ap-10701	184	44	(	(	PUNCT
ap-10701	184	45	4	4	NUM
ap-10701	184	46	)	)	PUNCT
ap-10701	184	47	,	,	PUNCT
ap-10701	184	48	we	we	PRON
ap-10701	184	49	have	have	VERB
ap-10701	184	50	:	:	PUNCT
ap-10701	184	51	1	1	NUM
ap-10701	184	52	2	2	NUM
ap-10701	184	53	d∥r∥2	d∥r∥2	PROPN
ap-10701	184	54	dt	dt	NOUN
ap-10701	184	55	+	+	CCONJ
ap-10701	184	56	(	(	PUNCT
ap-10701	184	57	∂xr	∂xr	PROPN
ap-10701	184	58	,	,	PUNCT
ap-10701	184	59	∂xr	∂xr	PROPN
ap-10701	184	60	)	)	PUNCT
ap-10701	185	1	=	=	PUNCT
ap-10701	185	2	(	(	PUNCT
ap-10701	185	3	f(z	f(z	PROPN
ap-10701	185	4	)	)	PUNCT
ap-10701	185	5	−	−	PROPN
ap-10701	185	6	f(z̄	f(z̄	NUM
ap-10701	185	7	)	)	PUNCT
ap-10701	185	8	,	,	PUNCT
ap-10701	185	9	r	r	NOUN
ap-10701	185	10	)	)	PUNCT
ap-10701	185	11	,	,	PUNCT
ap-10701	185	12	r(0	r(0	PROPN
ap-10701	185	13	)	)	PUNCT
ap-10701	185	14	=	=	SYM
ap-10701	186	1	0	0	X
ap-10701	186	2	.	.	PUNCT
ap-10701	187	1	(	(	PUNCT
ap-10701	187	2	17	17	NUM
ap-10701	187	3	)	)	PUNCT
ap-10701	187	4	as	as	ADP
ap-10701	187	5	:	:	PUNCT
ap-10701	187	6	|(f(z	|(f(z	NUM
ap-10701	187	7	)	)	PUNCT
ap-10701	187	8	−	−	PROPN
ap-10701	187	9	f(z̄	f(z̄	NUM
ap-10701	187	10	)	)	PUNCT
ap-10701	187	11	,	,	PUNCT
ap-10701	187	12	r)|	r)|	PROPN
ap-10701	187	13	≤	≤	PROPN
ap-10701	187	14	l∥r∥2	l∥r∥2	PROPN
ap-10701	187	15	,	,	PUNCT
ap-10701	187	16	equation	equation	NOUN
ap-10701	187	17	(	(	PUNCT
ap-10701	187	18	17	17	NUM
ap-10701	187	19	)	)	PUNCT
ap-10701	187	20	can	can	AUX
ap-10701	187	21	be	be	AUX
ap-10701	187	22	integrated	integrate	VERB
ap-10701	187	23	by	by	ADP
ap-10701	187	24	the	the	DET
ap-10701	187	25	grönwall	grönwall	NOUN
ap-10701	187	26	argument	argument	NOUN
ap-10701	187	27	to	to	PART
ap-10701	187	28	see	see	VERB
ap-10701	187	29	that	that	DET
ap-10701	187	30	r	r	NOUN
ap-10701	187	31	=	=	SYM
ap-10701	187	32	0	0	NUM
ap-10701	187	33	.	.	PUNCT
ap-10701	188	1	569	569	NUM
ap-10701	188	2	niels	niels	PROPN
ap-10701	188	3	van	van	PROPN
ap-10701	188	4	der	der	PROPN
ap-10701	188	5	meer	meer	PROPN
ap-10701	188	6	,	,	PUNCT
ap-10701	188	7	michal	michal	PROPN
ap-10701	188	8	beneš	beneš	PROPN
ap-10701	188	9	acta	acta	PROPN
ap-10701	188	10	polytechnica	polytechnica	PROPN
ap-10701	188	11	4.4	4.4	NUM
ap-10701	188	12	.	.	PUNCT
ap-10701	189	1	regularity	regularity	PROPN
ap-10701	189	2	lemma	lemma	PROPN
ap-10701	189	3	3	3	X
ap-10701	189	4	.	.	PUNCT
ap-10701	190	1	the	the	DET
ap-10701	190	2	solution	solution	NOUN
ap-10701	190	3	u	u	NOUN
ap-10701	190	4	of	of	ADP
ap-10701	190	5	(	(	PUNCT
ap-10701	190	6	2	2	NUM
ap-10701	190	7	)	)	PUNCT
ap-10701	190	8	is	be	AUX
ap-10701	190	9	in	in	ADP
ap-10701	190	10	l2(0	l2(0	NOUN
ap-10701	190	11	,	,	PUNCT
ap-10701	190	12	t	t	NOUN
ap-10701	190	13	;	;	PUNCT
ap-10701	190	14	w	w	X
ap-10701	190	15	(	(	PUNCT
ap-10701	190	16	2	2	NUM
ap-10701	190	17	)	)	SYM
ap-10701	190	18	2	2	NUM
ap-10701	190	19	(	(	PUNCT
ap-10701	190	20	(	(	PUNCT
ap-10701	190	21	a	a	PRON
ap-10701	190	22	,	,	PUNCT
ap-10701	190	23	b);rd	b);rd	NOUN
ap-10701	190	24	)	)	PUNCT
ap-10701	190	25	,	,	PUNCT
ap-10701	190	26	its	its	PRON
ap-10701	190	27	time	time	NOUN
ap-10701	190	28	derivative	derivative	ADJ
ap-10701	190	29	in	in	ADP
ap-10701	190	30	l2(0	l2(0	PROPN
ap-10701	190	31	,	,	PUNCT
ap-10701	190	32	t	t	NOUN
ap-10701	190	33	;	;	PUNCT
ap-10701	190	34	h	h	NOUN
ap-10701	190	35	)	)	PUNCT
ap-10701	190	36	,	,	PUNCT
ap-10701	190	37	and	and	CCONJ
ap-10701	190	38	due	due	ADP
ap-10701	190	39	to	to	ADP
ap-10701	190	40	the	the	DET
ap-10701	190	41	embedding	embed	VERB
ap-10701	190	42	property	property	NOUN
ap-10701	190	43	,	,	PUNCT
ap-10701	190	44	it	it	PRON
ap-10701	190	45	is	be	AUX
ap-10701	190	46	in	in	ADP
ap-10701	190	47	c(0	c(0	PROPN
ap-10701	190	48	,	,	PUNCT
ap-10701	190	49	t	t	PROPN
ap-10701	190	50	;	;	PUNCT
ap-10701	190	51	c1([a	c1([a	PROPN
ap-10701	190	52	,	,	PUNCT
ap-10701	190	53	b	b	NOUN
ap-10701	190	54	]	]	X
ap-10701	190	55	)	)	PUNCT
ap-10701	190	56	)	)	PUNCT
ap-10701	190	57	.	.	PUNCT
ap-10701	191	1	proof	proof	NOUN
ap-10701	191	2	.	.	PUNCT
ap-10701	192	1	from	from	ADP
ap-10701	192	2	the	the	DET
ap-10701	192	3	above	above	ADJ
ap-10701	192	4	facts	fact	NOUN
ap-10701	192	5	,	,	PUNCT
ap-10701	192	6	we	we	PRON
ap-10701	192	7	see	see	VERB
ap-10701	192	8	that	that	SCONJ
ap-10701	192	9	∂tu	∂tu	ADV
ap-10701	192	10	∈	∈	PROPN
ap-10701	192	11	l2(0	l2(0	NOUN
ap-10701	192	12	,	,	PUNCT
ap-10701	192	13	t	t	NOUN
ap-10701	192	14	;	;	PUNCT
ap-10701	192	15	h	h	X
ap-10701	192	16	)	)	PUNCT
ap-10701	192	17	.	.	PUNCT
ap-10701	193	1	then	then	ADV
ap-10701	193	2	from	from	ADP
ap-10701	193	3	(	(	PUNCT
ap-10701	193	4	15	15	NUM
ap-10701	193	5	)	)	PUNCT
ap-10701	193	6	,	,	PUNCT
ap-10701	193	7	we	we	PRON
ap-10701	193	8	obtain	obtain	VERB
ap-10701	193	9	:	:	PUNCT
ap-10701	193	10	(	(	PUNCT
ap-10701	193	11	∂xu	∂xu	NOUN
ap-10701	193	12	,	,	PUNCT
ap-10701	193	13	∂xv	∂xv	NOUN
ap-10701	193	14	)	)	PUNCT
ap-10701	193	15	=	=	SYM
ap-10701	193	16	(	(	PUNCT
ap-10701	193	17	f(u	f(u	PROPN
ap-10701	193	18	)	)	PUNCT
ap-10701	193	19	,	,	PUNCT
ap-10701	193	20	v	v	NOUN
ap-10701	193	21	)	)	PUNCT
ap-10701	193	22	−	−	PROPN
ap-10701	194	1	(	(	PUNCT
ap-10701	194	2	du	du	PROPN
ap-10701	194	3	dt	dt	PROPN
ap-10701	194	4	,	,	PUNCT
ap-10701	194	5	v	v	NOUN
ap-10701	194	6	)	)	PUNCT
ap-10701	194	7	,	,	PUNCT
ap-10701	194	8	which	which	PRON
ap-10701	194	9	in	in	ADP
ap-10701	194	10	terms	term	NOUN
ap-10701	194	11	of	of	ADP
ap-10701	194	12	d((a	d((a	PROPN
ap-10701	194	13	,	,	PUNCT
ap-10701	194	14	b	b	NOUN
ap-10701	194	15	)	)	PUNCT
ap-10701	194	16	)	)	PUNCT
ap-10701	194	17	yields	yield	NOUN
ap-10701	194	18	:	:	PUNCT
ap-10701	194	19	∂xxu	∂xxu	PROPN
ap-10701	194	20	=	=	SYM
ap-10701	194	21	f(u	f(u	PROPN
ap-10701	194	22	)	)	PUNCT
ap-10701	194	23	−	−	PROPN
ap-10701	194	24	du	du	NOUN
ap-10701	194	25	dt	dt	NOUN
ap-10701	194	26	,	,	PUNCT
ap-10701	194	27	and	and	CCONJ
ap-10701	194	28	then	then	ADV
ap-10701	194	29	∂xxu	∂xxu	NUM
ap-10701	194	30	∈	∈	PROPN
ap-10701	194	31	l2(0	l2(0	NOUN
ap-10701	194	32	,	,	PUNCT
ap-10701	194	33	t	t	NOUN
ap-10701	194	34	;	;	PUNCT
ap-10701	194	35	h	h	X
ap-10701	194	36	)	)	PUNCT
ap-10701	194	37	.	.	PUNCT
ap-10701	195	1	the	the	DET
ap-10701	195	2	embedding	embed	VERB
ap-10701	195	3	then	then	ADV
ap-10701	195	4	provides	provide	VERB
ap-10701	195	5	continuity	continuity	NOUN
ap-10701	195	6	.	.	PUNCT
ap-10701	196	1	4.5	4.5	NUM
ap-10701	196	2	.	.	PUNCT
ap-10701	197	1	error	error	NOUN
ap-10701	197	2	estimates	estimate	NOUN
ap-10701	197	3	consider	consider	VERB
ap-10701	197	4	the	the	DET
ap-10701	197	5	weak	weak	ADJ
ap-10701	197	6	solution	solution	NOUN
ap-10701	197	7	u	u	NOUN
ap-10701	197	8	of	of	ADP
ap-10701	197	9	equation	equation	NOUN
ap-10701	197	10	(	(	PUNCT
ap-10701	197	11	2	2	NUM
ap-10701	197	12	)	)	PUNCT
ap-10701	197	13	,	,	PUNCT
ap-10701	197	14	and	and	CCONJ
ap-10701	197	15	the	the	DET
ap-10701	197	16	solution	solution	NOUN
ap-10701	197	17	z	z	PROPN
ap-10701	197	18	of	of	ADP
ap-10701	197	19	the	the	DET
ap-10701	197	20	semi	semi	ADJ
ap-10701	197	21	-	-	ADJ
ap-10701	197	22	discrete	discrete	ADJ
ap-10701	197	23	scheme	scheme	NOUN
ap-10701	197	24	equation	equation	NOUN
ap-10701	197	25	(	(	PUNCT
ap-10701	197	26	4	4	NUM
ap-10701	197	27	)	)	PUNCT
ap-10701	197	28	.	.	PUNCT
ap-10701	198	1	we	we	PRON
ap-10701	198	2	project	project	VERB
ap-10701	198	3	u	u	NOUN
ap-10701	198	4	onto	onto	ADP
ap-10701	198	5	ωh	ωh	PRON
ap-10701	198	6	within	within	ADP
ap-10701	198	7	the	the	DET
ap-10701	198	8	weak	weak	ADJ
ap-10701	198	9	equality	equality	NOUN
ap-10701	198	10	equation	equation	NOUN
ap-10701	198	11	(	(	PUNCT
ap-10701	198	12	15	15	NUM
ap-10701	198	13	)	)	PUNCT
ap-10701	198	14	,	,	PUNCT
ap-10701	198	15	producing	produce	VERB
ap-10701	198	16	the	the	DET
ap-10701	198	17	approximation	approximation	NOUN
ap-10701	198	18	error	error	NOUN
ap-10701	198	19	ψ	ψ	NOUN
ap-10701	198	20	:	:	PUNCT
ap-10701	198	21	d(phnu	d(phnu	ADJ
ap-10701	198	22	,	,	PUNCT
ap-10701	198	23	phnv	phnv	NOUN
ap-10701	198	24	)	)	PUNCT
ap-10701	198	25	dt	dt	X
ap-10701	199	1	+	+	CCONJ
ap-10701	199	2	(	(	PUNCT
ap-10701	199	3	phn	phn	INTJ
ap-10701	199	4	u	u	NOUN
ap-10701	199	5	x̄,phn	x̄,phn	PROPN
ap-10701	199	6	v	v	NUM
ap-10701	199	7	x̄	x̄	PROPN
ap-10701	199	8	)	)	PUNCT
ap-10701	199	9	=	=	PRON
ap-10701	199	10	(	(	PUNCT
ap-10701	199	11	f(phn	f(phn	INTJ
ap-10701	199	12	u),phn	u),phn	ADJ
ap-10701	199	13	v	v	NOUN
ap-10701	199	14	)	)	PUNCT
ap-10701	200	1	+	+	CCONJ
ap-10701	200	2	ψ	ψ	X
ap-10701	200	3	,	,	PUNCT
ap-10701	200	4	(	(	PUNCT
ap-10701	200	5	18	18	NUM
ap-10701	200	6	)	)	PUNCT
ap-10701	200	7	phn	phn	PROPN
ap-10701	200	8	u	u	PROPN
ap-10701	200	9	|t=0	|t=0	PROPN
ap-10701	200	10	=	=	PUNCT
ap-10701	200	11	phn	phn	PROPN
ap-10701	200	12	uini	uini	NOUN
ap-10701	200	13	.	.	PUNCT
ap-10701	201	1	then	then	ADV
ap-10701	201	2	we	we	PRON
ap-10701	201	3	subtract	subtract	VERB
ap-10701	201	4	it	it	PRON
ap-10701	201	5	from	from	ADP
ap-10701	201	6	(	(	PUNCT
ap-10701	201	7	4	4	NUM
ap-10701	201	8	)	)	PUNCT
ap-10701	201	9	to	to	PART
ap-10701	201	10	obtain	obtain	VERB
ap-10701	201	11	:(	:(	PUNCT
ap-10701	201	12	d(phn	d(phn	VERB
ap-10701	201	13	u	u	NOUN
ap-10701	201	14	−	−	PROPN
ap-10701	201	15	z	z	PROPN
ap-10701	201	16	)	)	PUNCT
ap-10701	201	17	dt	dt	NOUN
ap-10701	201	18	,	,	PUNCT
ap-10701	201	19	phn	phn	PROPN
ap-10701	201	20	v	v	NOUN
ap-10701	201	21	)	)	PUNCT
ap-10701	201	22	+	+	CCONJ
ap-10701	201	23	(	(	PUNCT
ap-10701	201	24	(	(	PUNCT
ap-10701	201	25	phn	phn	PROPN
ap-10701	201	26	u	u	NOUN
ap-10701	201	27	−	−	PROPN
ap-10701	201	28	z)x̄,phn	z)x̄,phn	NUM
ap-10701	201	29	v	v	NOUN
ap-10701	201	30	x̄	x̄	PROPN
ap-10701	201	31	)	)	PUNCT
ap-10701	201	32	=	=	SYM
ap-10701	201	33	(	(	PUNCT
ap-10701	201	34	f(phn	f(phn	PROPN
ap-10701	201	35	u	u	NOUN
ap-10701	201	36	)	)	PUNCT
ap-10701	201	37	−	−	ADP
ap-10701	202	1	f(z),phn	f(z),phn	PROPN
ap-10701	202	2	v	v	NOUN
ap-10701	202	3	)	)	PUNCT
ap-10701	203	1	+	+	PUNCT
ap-10701	203	2	ψ	ψ	NOUN
ap-10701	203	3	,	,	PUNCT
ap-10701	203	4	phnu	phnu	ADV
ap-10701	203	5	−	−	PROPN
ap-10701	204	1	z|t=0	z|t=0	NUM
ap-10701	204	2	=	=	SYM
ap-10701	204	3	0	0	X
ap-10701	204	4	.	.	X
ap-10701	205	1	selecting	select	VERB
ap-10701	205	2	phn	phn	PROPN
ap-10701	205	3	v	v	NOUN
ap-10701	205	4	=	=	X
ap-10701	205	5	phn	phn	ADJ
ap-10701	205	6	u	u	NOUN
ap-10701	206	1	−	−	PROPN
ap-10701	206	2	z	z	PROPN
ap-10701	206	3	,	,	PUNCT
ap-10701	206	4	we	we	PRON
ap-10701	206	5	get	get	VERB
ap-10701	206	6	:(	:(	PUNCT
ap-10701	206	7	d(phn	d(phn	NOUN
ap-10701	206	8	u	u	NOUN
ap-10701	206	9	−	−	PROPN
ap-10701	206	10	z	z	PROPN
ap-10701	206	11	)	)	PUNCT
ap-10701	206	12	dt	dt	NOUN
ap-10701	206	13	,	,	PUNCT
ap-10701	206	14	phn	phn	ADJ
ap-10701	206	15	u	u	NOUN
ap-10701	206	16	−	−	PROPN
ap-10701	206	17	z	z	NOUN
ap-10701	206	18	)	)	PUNCT
ap-10701	207	1	+	+	CCONJ
ap-10701	207	2	(	(	PUNCT
ap-10701	207	3	(	(	PUNCT
ap-10701	207	4	phn	phn	PROPN
ap-10701	207	5	u	u	NOUN
ap-10701	207	6	−	−	PROPN
ap-10701	207	7	z)x̄,phn	z)x̄,phn	PROPN
ap-10701	207	8	(	(	PUNCT
ap-10701	207	9	phn	phn	PROPN
ap-10701	207	10	u	u	NOUN
ap-10701	207	11	−	−	PROPN
ap-10701	207	12	z)x̄	z)x̄	NUM
ap-10701	207	13	)	)	PUNCT
ap-10701	207	14	=	=	SYM
ap-10701	207	15	(	(	PUNCT
ap-10701	207	16	f(phn	f(phn	PROPN
ap-10701	207	17	u	u	NOUN
ap-10701	207	18	)	)	PUNCT
ap-10701	207	19	−	−	ADP
ap-10701	208	1	f(z),phn	f(z),phn	PROPN
ap-10701	208	2	u	u	NOUN
ap-10701	208	3	−	−	PROPN
ap-10701	208	4	z	z	PROPN
ap-10701	208	5	)	)	PUNCT
ap-10701	209	1	+	+	PUNCT
ap-10701	209	2	ψ	ψ	NOUN
ap-10701	209	3	,	,	PUNCT
ap-10701	209	4	phnu	phnu	ADV
ap-10701	209	5	−	−	PROPN
ap-10701	209	6	z|t=0	z|t=0	NUM
ap-10701	209	7	=	=	SYM
ap-10701	209	8	0	0	NUM
ap-10701	209	9	.	.	PUNCT
ap-10701	210	1	from	from	ADP
ap-10701	210	2	which	which	PRON
ap-10701	210	3	the	the	DET
ap-10701	210	4	grönwall	grönwall	NOUN
ap-10701	210	5	argument	argument	NOUN
ap-10701	210	6	yields	yield	VERB
ap-10701	210	7	:	:	PUNCT
ap-10701	210	8	∥phnu	∥phnu	NOUN
ap-10701	210	9	−	−	PROPN
ap-10701	210	10	z∥2(t	z∥2(t	PROPN
ap-10701	210	11	)	)	PUNCT
ap-10701	210	12	≤	≤	NUM
ap-10701	211	1	∫	∫	PROPN
ap-10701	211	2	t	t	PROPN
ap-10701	211	3	0	0	NUM
ap-10701	211	4	∥ψ(t)∥2el(t	∥ψ(t)∥2el(t	X
ap-10701	211	5	−t)dt	−t)dt	X
ap-10701	211	6	.	.	PUNCT
ap-10701	212	1	as	as	SCONJ
ap-10701	212	2	the	the	DET
ap-10701	212	3	difference	difference	NOUN
ap-10701	212	4	and	and	CCONJ
ap-10701	212	5	interpolation	interpolation	NOUN
ap-10701	212	6	approximation	approximation	NOUN
ap-10701	212	7	errors	error	NOUN
ap-10701	212	8	imply	imply	VERB
ap-10701	212	9	∥ψ(t)∥2	∥ψ(t)∥2	PROPN
ap-10701	213	1	≈	≈	PROPN
ap-10701	213	2	o(h4	o(h4	PROPN
ap-10701	213	3	)	)	PUNCT
ap-10701	214	1	,	,	PUNCT
ap-10701	214	2	we	we	PRON
ap-10701	214	3	obtain	obtain	VERB
ap-10701	214	4	that	that	SCONJ
ap-10701	214	5	∥phn	∥phn	PROPN
ap-10701	214	6	u	u	NOUN
ap-10701	214	7	−	−	PROPN
ap-10701	214	8	z∥(t	z∥(t	NUM
ap-10701	214	9	)	)	PUNCT
ap-10701	215	1	≈	≈	PROPN
ap-10701	215	2	o(h2	o(h2	NOUN
ap-10701	215	3	)	)	PUNCT
ap-10701	215	4	.	.	PUNCT
ap-10701	216	1	we	we	PRON
ap-10701	216	2	then	then	ADV
ap-10701	216	3	conclude	conclude	VERB
ap-10701	216	4	by	by	ADP
ap-10701	216	5	stating	state	VERB
ap-10701	216	6	the	the	DET
ap-10701	216	7	convergence	convergence	NOUN
ap-10701	216	8	property	property	NOUN
ap-10701	216	9	.	.	PUNCT
ap-10701	217	1	theorem	theorem	NOUN
ap-10701	217	2	1	1	NUM
ap-10701	217	3	.	.	PUNCT
ap-10701	218	1	let	let	VERB
ap-10701	218	2	the	the	DET
ap-10701	218	3	above	above	ADJ
ap-10701	218	4	assumption	assumption	NOUN
ap-10701	218	5	hold	hold	NOUN
ap-10701	218	6	and	and	CCONJ
ap-10701	218	7	uini	uini	NOUN
ap-10701	218	8	∈	∈	PROPN
ap-10701	219	1	v.	v.	CCONJ
ap-10701	219	2	then	then	ADV
ap-10701	219	3	the	the	DET
ap-10701	219	4	solution	solution	NOUN
ap-10701	219	5	of	of	ADP
ap-10701	219	6	scheme	scheme	NOUN
ap-10701	219	7	(	(	PUNCT
ap-10701	219	8	4	4	NUM
ap-10701	219	9	)	)	PUNCT
ap-10701	219	10	converges	converge	NOUN
ap-10701	219	11	to	to	ADP
ap-10701	219	12	the	the	DET
ap-10701	219	13	weak	weak	ADJ
ap-10701	219	14	solution	solution	NOUN
ap-10701	219	15	of	of	ADP
ap-10701	219	16	(	(	PUNCT
ap-10701	219	17	2	2	NUM
ap-10701	219	18	)	)	PUNCT
ap-10701	219	19	.	.	PUNCT
ap-10701	220	1	remark	remark	VERB
ap-10701	220	2	the	the	DET
ap-10701	220	3	analysis	analysis	NOUN
ap-10701	220	4	of	of	ADP
ap-10701	220	5	the	the	DET
ap-10701	220	6	method	method	NOUN
ap-10701	220	7	using	use	VERB
ap-10701	220	8	invariant	invariant	ADJ
ap-10701	220	9	regions	region	NOUN
ap-10701	220	10	can	can	AUX
ap-10701	220	11	be	be	AUX
ap-10701	220	12	extended	extend	VERB
ap-10701	220	13	,	,	PUNCT
ap-10701	220	14	namely	namely	ADV
ap-10701	220	15	to	to	ADP
ap-10701	220	16	the	the	DET
ap-10701	220	17	following	following	ADJ
ap-10701	220	18	cases	case	NOUN
ap-10701	220	19	.	.	PUNCT
ap-10701	221	1	the	the	DET
ap-10701	221	2	spatial	spatial	ADJ
ap-10701	221	3	domain	domain	NOUN
ap-10701	221	4	can	can	AUX
ap-10701	221	5	have	have	VERB
ap-10701	221	6	a	a	DET
ap-10701	221	7	higher	high	ADJ
ap-10701	221	8	dimension	dimension	NOUN
ap-10701	221	9	than	than	ADP
ap-10701	221	10	1	1	NUM
ap-10701	221	11	and	and	CCONJ
ap-10701	221	12	the	the	DET
ap-10701	221	13	diffusion	diffusion	NOUN
ap-10701	221	14	terms	term	NOUN
ap-10701	221	15	will	will	AUX
ap-10701	221	16	contain	contain	VERB
ap-10701	221	17	the	the	DET
ap-10701	221	18	laplace	laplace	NOUN
ap-10701	221	19	operator	operator	NOUN
ap-10701	221	20	.	.	PUNCT
ap-10701	222	1	in	in	ADP
ap-10701	222	2	that	that	DET
ap-10701	222	3	case	case	NOUN
ap-10701	222	4	,	,	PUNCT
ap-10701	222	5	we	we	PRON
ap-10701	222	6	would	would	AUX
ap-10701	222	7	assume	assume	VERB
ap-10701	222	8	the	the	DET
ap-10701	222	9	domain	domain	NOUN
ap-10701	222	10	to	to	PART
ap-10701	222	11	be	be	AUX
ap-10701	222	12	bounded	bound	VERB
ap-10701	222	13	with	with	ADP
ap-10701	222	14	the	the	DET
ap-10701	222	15	lipschitz	lipschitz	ADJ
ap-10701	222	16	boundary	boundary	NOUN
ap-10701	222	17	(	(	PUNCT
ap-10701	222	18	e.g.	e.g.	ADV
ap-10701	222	19	see	see	VERB
ap-10701	222	20	[	[	X
ap-10701	222	21	5	5	NUM
ap-10701	222	22	,	,	PUNCT
ap-10701	222	23	27	27	NUM
ap-10701	222	24	]	]	NUM
ap-10701	222	25	)	)	PUNCT
ap-10701	222	26	.	.	PUNCT
ap-10701	223	1	the	the	DET
ap-10701	223	2	positive	positive	ADJ
ap-10701	223	3	definite	definite	ADJ
ap-10701	223	4	matrix	matrix	NOUN
ap-10701	223	5	d	d	NOUN
ap-10701	223	6	in	in	ADP
ap-10701	223	7	equation	equation	NOUN
ap-10701	223	8	(	(	PUNCT
ap-10701	223	9	1	1	X
ap-10701	223	10	)	)	PUNCT
ap-10701	223	11	does	do	AUX
ap-10701	223	12	not	not	PART
ap-10701	223	13	have	have	VERB
ap-10701	223	14	to	to	PART
ap-10701	223	15	be	be	AUX
ap-10701	223	16	diagonal	diagonal	ADJ
ap-10701	223	17	,	,	PUNCT
ap-10701	223	18	as	as	SCONJ
ap-10701	223	19	described	describe	VERB
ap-10701	223	20	in	in	ADP
ap-10701	223	21	[	[	X
ap-10701	223	22	1	1	NUM
ap-10701	223	23	]	]	PUNCT
ap-10701	223	24	.	.	PUNCT
ap-10701	224	1	however	however	ADV
ap-10701	224	2	,	,	PUNCT
ap-10701	224	3	the	the	DET
ap-10701	224	4	invariant	invariant	ADJ
ap-10701	224	5	region	region	NOUN
ap-10701	224	6	can	can	AUX
ap-10701	224	7	then	then	ADV
ap-10701	224	8	have	have	VERB
ap-10701	224	9	a	a	DET
ap-10701	224	10	more	more	ADV
ap-10701	224	11	general	general	ADJ
ap-10701	224	12	shape	shape	NOUN
ap-10701	224	13	than	than	ADP
ap-10701	224	14	prismatic	prismatic	ADJ
ap-10701	224	15	.	.	PUNCT
ap-10701	225	1	this	this	PRON
ap-10701	225	2	would	would	AUX
ap-10701	225	3	cover	cover	VERB
ap-10701	225	4	the	the	DET
ap-10701	225	5	processes	process	NOUN
ap-10701	225	6	including	include	VERB
ap-10701	225	7	cross	cross	NOUN
ap-10701	225	8	-	-	NOUN
ap-10701	225	9	diffusion	diffusion	NOUN
ap-10701	225	10	(	(	PUNCT
ap-10701	225	11	e.g.	e.g.	ADV
ap-10701	225	12	in	in	ADP
ap-10701	225	13	the	the	DET
ap-10701	225	14	phase	phase	NOUN
ap-10701	225	15	-	-	PUNCT
ap-10701	225	16	field	field	NOUN
ap-10701	225	17	models	model	NOUN
ap-10701	225	18	[	[	X
ap-10701	225	19	8	8	NUM
ap-10701	225	20	]	]	PUNCT
ap-10701	225	21	,	,	PUNCT
ap-10701	225	22	or	or	CCONJ
ap-10701	225	23	the	the	DET
ap-10701	225	24	fitzhugh	fitzhugh	PROPN
ap-10701	225	25	-	-	PUNCT
ap-10701	225	26	nagumo	nagumo	ADJ
ap-10701	225	27	systems	system	NOUN
ap-10701	225	28	[	[	X
ap-10701	225	29	28	28	NUM
ap-10701	225	30	]	]	NUM
ap-10701	225	31	)	)	PUNCT
ap-10701	225	32	.	.	PUNCT
ap-10701	226	1	the	the	DET
ap-10701	226	2	dirichlet	dirichlet	PROPN
ap-10701	226	3	boundary	boundary	PROPN
ap-10701	226	4	conditions	condition	NOUN
ap-10701	226	5	are	be	AUX
ap-10701	226	6	used	use	VERB
ap-10701	226	7	in	in	ADP
ap-10701	226	8	a	a	DET
ap-10701	226	9	variety	variety	NOUN
ap-10701	226	10	of	of	ADP
ap-10701	226	11	reaction	reaction	NOUN
ap-10701	226	12	-	-	PUNCT
ap-10701	226	13	diffusion	diffusion	NOUN
ap-10701	226	14	models	model	NOUN
ap-10701	226	15	to	to	PART
ap-10701	226	16	capture	capture	VERB
ap-10701	226	17	fixed	fix	VERB
ap-10701	226	18	solution	solution	NOUN
ap-10701	226	19	values	value	NOUN
ap-10701	226	20	at	at	ADP
ap-10701	226	21	the	the	DET
ap-10701	226	22	domain	domain	NOUN
ap-10701	226	23	boundary	boundary	NOUN
ap-10701	226	24	(	(	PUNCT
ap-10701	226	25	e.g.	e.g.	ADV
ap-10701	226	26	concentration	concentration	NOUN
ap-10701	226	27	,	,	PUNCT
ap-10701	226	28	voltage	voltage	NOUN
ap-10701	226	29	,	,	PUNCT
ap-10701	226	30	phase	phase	NOUN
ap-10701	226	31	state	state	NOUN
ap-10701	226	32	–	–	PUNCT
ap-10701	226	33	see	see	VERB
ap-10701	226	34	e.g.	e.g.	ADV
ap-10701	226	35	[	[	X
ap-10701	226	36	1	1	NUM
ap-10701	226	37	,	,	PUNCT
ap-10701	226	38	3	3	NUM
ap-10701	226	39	,	,	PUNCT
ap-10701	226	40	5	5	NUM
ap-10701	226	41	,	,	PUNCT
ap-10701	226	42	10	10	NUM
ap-10701	226	43	,	,	PUNCT
ap-10701	226	44	29	29	NUM
ap-10701	226	45	]	]	PUNCT
ap-10701	226	46	)	)	PUNCT
ap-10701	226	47	.	.	PUNCT
ap-10701	227	1	as	as	SCONJ
ap-10701	227	2	the	the	DET
ap-10701	227	3	neumann	neumann	PROPN
ap-10701	227	4	boundary	boundary	PROPN
ap-10701	227	5	conditions	condition	NOUN
ap-10701	227	6	also	also	ADV
ap-10701	227	7	serve	serve	VERB
ap-10701	227	8	in	in	ADP
ap-10701	227	9	such	such	ADJ
ap-10701	227	10	models	model	NOUN
ap-10701	227	11	,	,	PUNCT
ap-10701	227	12	e.g.	e.g.	ADV
ap-10701	227	13	to	to	PART
ap-10701	227	14	express	express	VERB
ap-10701	227	15	quantity	quantity	NOUN
ap-10701	227	16	conservation	conservation	NOUN
ap-10701	227	17	or	or	CCONJ
ap-10701	227	18	reflexion	reflexion	NOUN
ap-10701	227	19	,	,	PUNCT
ap-10701	227	20	they	they	PRON
ap-10701	227	21	can	can	AUX
ap-10701	227	22	be	be	AUX
ap-10701	227	23	processed	process	VERB
ap-10701	227	24	by	by	ADP
ap-10701	227	25	the	the	DET
ap-10701	227	26	described	describe	VERB
ap-10701	227	27	method	method	NOUN
ap-10701	227	28	as	as	ADV
ap-10701	227	29	well	well	ADV
ap-10701	227	30	,	,	PUNCT
ap-10701	227	31	influencing	influence	VERB
ap-10701	227	32	the	the	DET
ap-10701	227	33	choice	choice	NOUN
ap-10701	227	34	of	of	ADP
ap-10701	227	35	space	space	NOUN
ap-10701	227	36	v	v	NOUN
ap-10701	227	37	=	=	SYM
ap-10701	227	38	w	w	PROPN
ap-10701	227	39	(	(	PUNCT
ap-10701	227	40	1	1	NUM
ap-10701	227	41	)	)	SYM
ap-10701	227	42	2	2	NUM
ap-10701	227	43	(	(	PUNCT
ap-10701	227	44	(	(	PUNCT
ap-10701	227	45	a	a	PRON
ap-10701	227	46	,	,	PUNCT
ap-10701	227	47	b);rd	b);rd	NOUN
ap-10701	227	48	)	)	PUNCT
ap-10701	227	49	and	and	CCONJ
ap-10701	227	50	hh	hh	X
ap-10701	227	51	.	.	PROPN
ap-10701	228	1	for	for	ADP
ap-10701	228	2	details	detail	NOUN
ap-10701	228	3	,	,	PUNCT
ap-10701	228	4	see	see	VERB
ap-10701	228	5	[	[	X
ap-10701	228	6	11	11	NUM
ap-10701	228	7	,	,	PUNCT
ap-10701	228	8	30	30	NUM
ap-10701	228	9	,	,	PUNCT
ap-10701	228	10	31	31	NUM
ap-10701	228	11	]	]	PUNCT
ap-10701	228	12	.	.	PUNCT
ap-10701	229	1	however	however	ADV
ap-10701	229	2	,	,	PUNCT
ap-10701	229	3	the	the	DET
ap-10701	229	4	convergence	convergence	NOUN
ap-10701	229	5	rate	rate	NOUN
ap-10701	229	6	in	in	ADP
ap-10701	229	7	section	section	NOUN
ap-10701	229	8	4.5	4.5	NUM
ap-10701	229	9	will	will	AUX
ap-10701	229	10	be	be	AUX
ap-10701	229	11	just	just	ADV
ap-10701	229	12	o(h	o(h	ADJ
ap-10701	229	13	)	)	PUNCT
ap-10701	229	14	,	,	PUNCT
ap-10701	229	15	provided	provide	VERB
ap-10701	229	16	the	the	DET
ap-10701	229	17	usual	usual	ADJ
ap-10701	229	18	one	one	NUM
ap-10701	229	19	-	-	PUNCT
ap-10701	229	20	sided	sided	ADJ
ap-10701	229	21	differences	difference	NOUN
ap-10701	229	22	have	have	AUX
ap-10701	229	23	been	be	AUX
ap-10701	229	24	used	use	VERB
ap-10701	229	25	to	to	PART
ap-10701	229	26	approximate	approximate	VERB
ap-10701	229	27	the	the	DET
ap-10701	229	28	neumann	neumann	PROPN
ap-10701	229	29	boundary	boundary	ADJ
ap-10701	229	30	conditions	condition	NOUN
ap-10701	229	31	.	.	PUNCT
ap-10701	230	1	more	more	ADV
ap-10701	230	2	recently	recently	ADV
ap-10701	230	3	,	,	PUNCT
ap-10701	230	4	the	the	DET
ap-10701	230	5	reaction	reaction	NOUN
ap-10701	230	6	-	-	PUNCT
ap-10701	230	7	diffusion	diffusion	NOUN
ap-10701	230	8	systems	system	NOUN
ap-10701	230	9	are	be	AUX
ap-10701	230	10	considered	consider	VERB
ap-10701	230	11	on	on	ADP
ap-10701	230	12	curves	curve	NOUN
ap-10701	230	13	or	or	CCONJ
ap-10701	230	14	surfaces	surface	NOUN
ap-10701	230	15	(	(	PUNCT
ap-10701	230	16	see	see	VERB
ap-10701	230	17	e.g.	e.g.	ADV
ap-10701	230	18	[	[	X
ap-10701	230	19	14	14	NUM
ap-10701	230	20	,	,	PUNCT
ap-10701	230	21	32	32	NUM
ap-10701	230	22	]	]	PUNCT
ap-10701	230	23	)	)	PUNCT
ap-10701	230	24	.	.	PUNCT
ap-10701	231	1	5	5	X
ap-10701	231	2	.	.	X
ap-10701	231	3	examples	example	NOUN
ap-10701	231	4	we	we	PRON
ap-10701	231	5	accompany	accompany	VERB
ap-10701	231	6	the	the	DET
ap-10701	231	7	numerical	numerical	ADJ
ap-10701	231	8	analysis	analysis	NOUN
ap-10701	231	9	of	of	ADP
ap-10701	231	10	the	the	DET
ap-10701	231	11	method	method	NOUN
ap-10701	231	12	of	of	ADP
ap-10701	231	13	lines	line	NOUN
ap-10701	231	14	by	by	ADP
ap-10701	231	15	selecting	select	VERB
ap-10701	231	16	two	two	NUM
ap-10701	231	17	distinct	distinct	ADJ
ap-10701	231	18	examples	example	NOUN
ap-10701	231	19	of	of	ADP
ap-10701	231	20	systems	system	NOUN
ap-10701	231	21	–	–	PUNCT
ap-10701	231	22	the	the	DET
ap-10701	231	23	brusselator	brusselator	NOUN
ap-10701	231	24	reaction	reaction	NOUN
ap-10701	231	25	diffusion	diffusion	NOUN
ap-10701	231	26	model	model	NOUN
ap-10701	231	27	from	from	ADP
ap-10701	231	28	chemistry	chemistry	NOUN
ap-10701	231	29	introduced	introduce	VERB
ap-10701	231	30	in	in	ADP
ap-10701	231	31	[	[	X
ap-10701	231	32	33	33	NUM
ap-10701	231	33	]	]	PUNCT
ap-10701	231	34	and	and	CCONJ
ap-10701	231	35	discussed	discuss	VERB
ap-10701	231	36	in	in	ADP
ap-10701	231	37	[	[	X
ap-10701	231	38	2	2	NUM
ap-10701	231	39	,	,	PUNCT
ap-10701	231	40	34	34	NUM
ap-10701	231	41	]	]	PUNCT
ap-10701	231	42	,	,	PUNCT
ap-10701	231	43	and	and	CCONJ
ap-10701	231	44	the	the	DET
ap-10701	231	45	fitzhugh	fitzhugh	PROPN
ap-10701	231	46	-	-	PUNCT
ap-10701	231	47	nagumo	nagumo	ADJ
ap-10701	231	48	model	model	NOUN
ap-10701	231	49	of	of	ADP
ap-10701	231	50	excitable	excitable	ADJ
ap-10701	231	51	medium	medium	NOUN
ap-10701	231	52	from	from	ADP
ap-10701	231	53	biophysical	biophysical	ADJ
ap-10701	231	54	context	context	NOUN
ap-10701	231	55	introduced	introduce	VERB
ap-10701	231	56	in	in	ADP
ap-10701	231	57	[	[	X
ap-10701	231	58	35	35	NUM
ap-10701	231	59	,	,	PUNCT
ap-10701	231	60	36	36	NUM
ap-10701	231	61	]	]	PUNCT
ap-10701	231	62	,	,	PUNCT
ap-10701	231	63	and	and	CCONJ
ap-10701	231	64	recently	recently	ADV
ap-10701	231	65	discussed	discuss	VERB
ap-10701	231	66	,	,	PUNCT
ap-10701	231	67	for	for	ADP
ap-10701	231	68	example	example	NOUN
ap-10701	231	69	,	,	PUNCT
ap-10701	231	70	in	in	ADP
ap-10701	231	71	[	[	PUNCT
ap-10701	231	72	5	5	NUM
ap-10701	231	73	,	,	PUNCT
ap-10701	231	74	28	28	NUM
ap-10701	231	75	]	]	PUNCT
ap-10701	231	76	.	.	PUNCT
ap-10701	232	1	the	the	DET
ap-10701	232	2	method	method	NOUN
ap-10701	232	3	is	be	AUX
ap-10701	232	4	well	well	ADV
ap-10701	232	5	applicable	applicable	ADJ
ap-10701	232	6	to	to	ADP
ap-10701	232	7	any	any	DET
ap-10701	232	8	other	other	ADJ
ap-10701	232	9	reaction	reaction	NOUN
ap-10701	232	10	-	-	PUNCT
ap-10701	232	11	diffusion	diffusion	NOUN
ap-10701	232	12	model	model	NOUN
ap-10701	232	13	satisfying	satisfy	VERB
ap-10701	232	14	underlying	underlie	VERB
ap-10701	232	15	assumptions	assumption	NOUN
ap-10701	232	16	,	,	PUNCT
ap-10701	232	17	e.g.	e.g.	ADV
ap-10701	232	18	to	to	ADP
ap-10701	232	19	the	the	DET
ap-10701	232	20	greyscott	greyscott	NOUN
ap-10701	232	21	model	model	NOUN
ap-10701	232	22	(	(	PUNCT
ap-10701	232	23	see	see	VERB
ap-10701	232	24	[	[	X
ap-10701	232	25	13	13	NUM
ap-10701	232	26	]	]	NUM
ap-10701	232	27	)	)	PUNCT
ap-10701	232	28	,	,	PUNCT
ap-10701	232	29	the	the	DET
ap-10701	232	30	phase	phase	NOUN
ap-10701	232	31	-	-	PUNCT
ap-10701	232	32	field	field	NOUN
ap-10701	232	33	model	model	NOUN
ap-10701	232	34	[	[	X
ap-10701	232	35	10	10	NUM
ap-10701	232	36	]	]	PUNCT
ap-10701	232	37	,	,	PUNCT
ap-10701	232	38	or	or	CCONJ
ap-10701	232	39	the	the	DET
ap-10701	232	40	competition	competition	NOUN
ap-10701	232	41	-	-	PUNCT
ap-10701	232	42	diffusion	diffusion	NOUN
ap-10701	232	43	systems	system	NOUN
ap-10701	232	44	such	such	ADJ
ap-10701	232	45	as	as	ADP
ap-10701	232	46	[	[	X
ap-10701	232	47	37	37	NUM
ap-10701	232	48	]	]	SYM
ap-10701	232	49	.	.	PUNCT
ap-10701	233	1	5.1	5.1	NUM
ap-10701	233	2	.	.	PUNCT
ap-10701	234	1	numerical	numerical	PROPN
ap-10701	234	2	error	error	NOUN
ap-10701	234	3	measurement	measurement	NOUN
ap-10701	234	4	to	to	PART
ap-10701	234	5	study	study	VERB
ap-10701	234	6	convergence	convergence	NOUN
ap-10701	234	7	of	of	ADP
ap-10701	234	8	the	the	DET
ap-10701	234	9	numerical	numerical	ADJ
ap-10701	234	10	solution	solution	NOUN
ap-10701	234	11	obtained	obtain	VERB
ap-10701	234	12	by	by	ADP
ap-10701	234	13	scheme	scheme	NOUN
ap-10701	234	14	(	(	PUNCT
ap-10701	234	15	4	4	NUM
ap-10701	234	16	)	)	PUNCT
ap-10701	234	17	,	,	PUNCT
ap-10701	234	18	the	the	DET
ap-10701	234	19	numerical	numerical	ADJ
ap-10701	234	20	solution	solution	NOUN
ap-10701	234	21	is	be	AUX
ap-10701	234	22	computed	compute	VERB
ap-10701	234	23	using	use	VERB
ap-10701	234	24	several	several	ADJ
ap-10701	234	25	grids	grid	NOUN
ap-10701	234	26	with	with	ADP
ap-10701	234	27	decreasing	decrease	VERB
ap-10701	234	28	mesh	mesh	NOUN
ap-10701	234	29	size	size	NOUN
ap-10701	234	30	h	h	NOUN
ap-10701	234	31	,	,	PUNCT
ap-10701	234	32	(	(	PUNCT
ap-10701	234	33	increasing	increase	VERB
ap-10701	234	34	number	number	NOUN
ap-10701	234	35	of	of	ADP
ap-10701	234	36	meshes	mesh	NOUN
ap-10701	234	37	m	m	NOUN
ap-10701	234	38	=	=	NOUN
ap-10701	234	39	b−a	b−a	NOUN
ap-10701	234	40	h	h	NOUN
ap-10701	234	41	)	)	PUNCT
ap-10701	234	42	,	,	PUNCT
ap-10701	234	43	and	and	CCONJ
ap-10701	234	44	compared	compare	VERB
ap-10701	234	45	to	to	ADP
ap-10701	234	46	the	the	DET
ap-10701	234	47	numerical	numerical	ADJ
ap-10701	234	48	solution	solution	NOUN
ap-10701	234	49	computed	compute	VERB
ap-10701	234	50	on	on	ADP
ap-10701	234	51	a	a	DET
ap-10701	234	52	very	very	ADV
ap-10701	234	53	fine	fine	ADJ
ap-10701	234	54	mesh	mesh	NOUN
ap-10701	234	55	with	with	ADP
ap-10701	234	56	h̄	h̄	NOUN
ap-10701	234	57	,	,	PUNCT
ap-10701	234	58	m̄	m̄	NOUN
ap-10701	234	59	=	=	SYM
ap-10701	234	60	b−a	b−a	NUM
ap-10701	234	61	h̄	h̄	PROPN
ap-10701	234	62	while	while	SCONJ
ap-10701	234	63	projecting	project	VERB
ap-10701	234	64	solutions	solution	NOUN
ap-10701	234	65	on	on	ADP
ap-10701	234	66	sparser	sparse	ADJ
ap-10701	234	67	meshes	mesh	NOUN
ap-10701	234	68	to	to	ADP
ap-10701	234	69	the	the	DET
ap-10701	234	70	finest	fine	ADJ
ap-10701	234	71	mesh	mesh	NOUN
ap-10701	234	72	using	use	VERB
ap-10701	234	73	linear	linear	ADJ
ap-10701	234	74	interpolation	interpolation	NOUN
ap-10701	234	75	.	.	PUNCT
ap-10701	235	1	the	the	DET
ap-10701	235	2	solution	solution	NOUN
ap-10701	235	3	on	on	ADP
ap-10701	235	4	each	each	DET
ap-10701	235	5	mesh	mesh	NOUN
ap-10701	235	6	is	be	AUX
ap-10701	235	7	stored	store	VERB
ap-10701	235	8	at	at	ADP
ap-10701	235	9	fixed	fix	VERB
ap-10701	235	10	time	time	NOUN
ap-10701	235	11	levels	level	NOUN
ap-10701	235	12	using	use	VERB
ap-10701	235	13	the	the	DET
ap-10701	235	14	output	output	NOUN
ap-10701	235	15	time	time	NOUN
ap-10701	235	16	step	step	NOUN
ap-10701	235	17	τ̄	τ̄	INTJ
ap-10701	235	18	,	,	PUNCT
ap-10701	235	19	nt	not	PART
ap-10701	235	20	=	=	SYM
ap-10701	235	21	t	t	PROPN
ap-10701	235	22	τ̄	τ̄	INTJ
ap-10701	235	23	.	.	PUNCT
ap-10701	236	1	denoting	denote	VERB
ap-10701	236	2	zk	zk	PROPN
ap-10701	236	3	=	=	SYM
ap-10701	236	4	zk(t	zk(t	PROPN
ap-10701	236	5	)	)	PUNCT
ap-10701	236	6	the	the	DET
ap-10701	236	7	vector	vector	NOUN
ap-10701	236	8	-	-	PUNCT
ap-10701	236	9	valued	value	VERB
ap-10701	236	10	grid	grid	NOUN
ap-10701	236	11	function	function	NOUN
ap-10701	236	12	representing	represent	VERB
ap-10701	236	13	the	the	DET
ap-10701	236	14	finest	fine	ADJ
ap-10701	236	15	grid	grid	NOUN
ap-10701	236	16	projection	projection	NOUN
ap-10701	236	17	of	of	ADP
ap-10701	236	18	the	the	DET
ap-10701	236	19	numerical	numerical	ADJ
ap-10701	236	20	solution	solution	NOUN
ap-10701	236	21	computed	compute	VERB
ap-10701	236	22	on	on	ADP
ap-10701	236	23	the	the	DET
ap-10701	236	24	grid	grid	NOUN
ap-10701	236	25	with	with	ADP
ap-10701	236	26	parameters	parameter	NOUN
ap-10701	236	27	hk	hk	PROPN
ap-10701	236	28	,	,	PUNCT
ap-10701	236	29	mk	mk	PROPN
ap-10701	236	30	,	,	PUNCT
ap-10701	236	31	and	and	CCONJ
ap-10701	236	32	zd	zd	PROPN
ap-10701	236	33	=	=	PUNCT
ap-10701	236	34	zd(t	zd(t	CCONJ
ap-10701	236	35	)	)	PUNCT
ap-10701	236	36	the	the	DET
ap-10701	236	37	numerical	numerical	ADJ
ap-10701	236	38	solution	solution	NOUN
ap-10701	236	39	on	on	ADP
ap-10701	236	40	the	the	DET
ap-10701	236	41	very	very	ADV
ap-10701	236	42	fine	fine	ADJ
ap-10701	236	43	mesh	mesh	NOUN
ap-10701	236	44	,	,	PUNCT
ap-10701	236	45	we	we	PRON
ap-10701	236	46	can	can	AUX
ap-10701	236	47	express	express	VERB
ap-10701	236	48	their	their	PRON
ap-10701	236	49	distance	distance	NOUN
ap-10701	236	50	measured	measure	VERB
ap-10701	236	51	570	570	NUM
ap-10701	236	52	vol	vol	NOUN
ap-10701	236	53	.	.	PUNCT
ap-10701	237	1	65	65	NUM
ap-10701	237	2	no	no	NOUN
ap-10701	237	3	.	.	PUNCT
ap-10701	238	1	5/2025	5/2025	NUM
ap-10701	238	2	method	method	NOUN
ap-10701	238	3	of	of	ADP
ap-10701	238	4	lines	line	NOUN
ap-10701	238	5	for	for	ADP
ap-10701	238	6	reaction	reaction	NOUN
ap-10701	238	7	-	-	PUNCT
ap-10701	238	8	diffusion	diffusion	NOUN
ap-10701	238	9	systems	system	NOUN
ap-10701	238	10	.	.	PUNCT
ap-10701	238	11	.	.	PUNCT
ap-10701	238	12	.	.	PUNCT
ap-10701	239	1	in	in	ADP
ap-10701	239	2	corresponding	corresponding	ADJ
ap-10701	239	3	norm	norm	NOUN
ap-10701	239	4	as	as	ADP
ap-10701	239	5	:	:	PUNCT
ap-10701	239	6	e2(hk	e2(hk	PROPN
ap-10701	239	7	)	)	PUNCT
ap-10701	239	8	=	=	SYM
ap-10701	239	9	max	max	PROPN
ap-10701	239	10	0≤l≤nt	0≤l≤nt	NUM
ap-10701	239	11			PROPN
ap-10701	239	12	m̄∑	m̄∑	NOUN
ap-10701	239	13	j=1	j=1	NOUN
ap-10701	239	14	|zk	|zk	PRON
ap-10701	239	15	j	j	PROPN
ap-10701	239	16	(	(	PUNCT
ap-10701	239	17	lτ̄	lτ̄	PROPN
ap-10701	239	18	)	)	PUNCT
ap-10701	239	19	−	−	PROPN
ap-10701	240	1	zd	zd	PROPN
ap-10701	240	2	j	j	PROPN
ap-10701	240	3	(	(	PUNCT
ap-10701	240	4	lτ̄)|2h̄	lτ̄)|2h̄	PROPN
ap-10701	240	5	1	1	VERB
ap-10701	240	6	2	2	X
ap-10701	240	7	.	.	PUNCT
ap-10701	240	8	convergence	convergence	NOUN
ap-10701	240	9	of	of	ADP
ap-10701	240	10	the	the	DET
ap-10701	240	11	numerical	numerical	ADJ
ap-10701	240	12	solution	solution	NOUN
ap-10701	240	13	is	be	AUX
ap-10701	240	14	assessed	assess	VERB
ap-10701	240	15	using	use	VERB
ap-10701	240	16	the	the	DET
ap-10701	240	17	experimental	experimental	ADJ
ap-10701	240	18	order	order	NOUN
ap-10701	240	19	of	of	ADP
ap-10701	240	20	convergence	convergence	NOUN
ap-10701	240	21	(	(	PUNCT
ap-10701	240	22	eoc	eoc	PROPN
ap-10701	240	23	)	)	PUNCT
ap-10701	240	24	,	,	PUNCT
ap-10701	240	25	as	as	ADP
ap-10701	240	26	in	in	ADP
ap-10701	240	27	[	[	X
ap-10701	240	28	38	38	NUM
ap-10701	240	29	]	]	PUNCT
ap-10701	240	30	,	,	PUNCT
ap-10701	240	31	calculated	calculate	VERB
ap-10701	240	32	from	from	ADP
ap-10701	240	33	two	two	NUM
ap-10701	240	34	numerical	numerical	ADJ
ap-10701	240	35	solutions	solution	NOUN
ap-10701	240	36	obtained	obtain	VERB
ap-10701	240	37	on	on	ADP
ap-10701	240	38	grids	grid	NOUN
ap-10701	240	39	with	with	ADP
ap-10701	240	40	meshes	mesh	NOUN
ap-10701	240	41	h1	h1	PROPN
ap-10701	240	42	,	,	PUNCT
ap-10701	240	43	h2	h2	PROPN
ap-10701	240	44	as	as	ADP
ap-10701	240	45	:	:	PUNCT
ap-10701	240	46	eoc(h1	eoc(h1	PROPN
ap-10701	240	47	,	,	PUNCT
ap-10701	240	48	h2	h2	NOUN
ap-10701	240	49	)	)	PUNCT
ap-10701	240	50	=	=	PRON
ap-10701	240	51	log	log	VERB
ap-10701	240	52	e2(h1	e2(h1	NUM
ap-10701	240	53	)	)	PUNCT
ap-10701	240	54	e2(h2	e2(h2	NOUN
ap-10701	240	55	)	)	PUNCT
ap-10701	240	56	.	.	PUNCT
ap-10701	241	1	5.2	5.2	NUM
ap-10701	241	2	.	.	PUNCT
ap-10701	241	3	brusselator	brusselator	NOUN
ap-10701	241	4	model	model	NOUN
ap-10701	241	5	as	as	ADP
ap-10701	241	6	an	an	DET
ap-10701	241	7	example	example	NOUN
ap-10701	241	8	of	of	ADP
ap-10701	241	9	a	a	DET
ap-10701	241	10	reaction	reaction	NOUN
ap-10701	241	11	diffusion	diffusion	NOUN
ap-10701	241	12	system	system	NOUN
ap-10701	241	13	admitting	admit	VERB
ap-10701	241	14	invariant	invariant	ADJ
ap-10701	241	15	region	region	NOUN
ap-10701	241	16	,	,	PUNCT
ap-10701	241	17	we	we	PRON
ap-10701	241	18	recall	recall	VERB
ap-10701	241	19	the	the	DET
ap-10701	241	20	brusselator	brusselator	NOUN
ap-10701	241	21	system	system	NOUN
ap-10701	241	22	,	,	PUNCT
ap-10701	241	23	which	which	PRON
ap-10701	241	24	describes	describe	VERB
ap-10701	241	25	the	the	DET
ap-10701	241	26	following	follow	VERB
ap-10701	241	27	fictitious	fictitious	ADJ
ap-10701	241	28	system	system	NOUN
ap-10701	241	29	of	of	ADP
ap-10701	241	30	chemical	chemical	ADJ
ap-10701	241	31	reactions	reaction	NOUN
ap-10701	241	32	of	of	ADP
ap-10701	241	33	two	two	NUM
ap-10701	241	34	chemicals	chemical	NOUN
ap-10701	241	35	a	a	PRON
ap-10701	241	36	and	and	CCONJ
ap-10701	241	37	b	b	NOUN
ap-10701	241	38	,	,	PUNCT
ap-10701	241	39	transforming	transform	VERB
ap-10701	241	40	to	to	ADP
ap-10701	241	41	the	the	DET
ap-10701	241	42	chemicals	chemical	NOUN
ap-10701	241	43	d	d	NOUN
ap-10701	241	44	and	and	CCONJ
ap-10701	241	45	e	e	NOUN
ap-10701	241	46	with	with	ADP
ap-10701	241	47	the	the	DET
ap-10701	241	48	side	side	NOUN
ap-10701	241	49	products	product	NOUN
ap-10701	241	50	x	x	PUNCT
ap-10701	241	51	and	and	CCONJ
ap-10701	241	52	y	y	PROPN
ap-10701	241	53	in	in	ADP
ap-10701	241	54	an	an	DET
ap-10701	241	55	inert	inert	ADJ
ap-10701	241	56	medium	medium	NOUN
ap-10701	241	57	(	(	PUNCT
ap-10701	241	58	see	see	VERB
ap-10701	241	59	[	[	X
ap-10701	241	60	2	2	NUM
ap-10701	241	61	]	]	PUNCT
ap-10701	241	62	):	):	PUNCT
ap-10701	241	63	a	a	DET
ap-10701	241	64	k1−→	k1−→	PROPN
ap-10701	241	65	x	x	PROPN
ap-10701	241	66	,	,	PUNCT
ap-10701	241	67	b	b	PROPN
ap-10701	242	1	+	+	CCONJ
ap-10701	242	2	x	x	SYM
ap-10701	242	3	k2−→	k2−→	NOUN
ap-10701	242	4	y	y	PROPN
ap-10701	242	5	+	+	PROPN
ap-10701	242	6	d	d	PROPN
ap-10701	242	7	,	,	PUNCT
ap-10701	242	8	2x	2x	NUM
ap-10701	242	9	+	+	CCONJ
ap-10701	242	10	y	y	PROPN
ap-10701	242	11	k3−→	k3−→	NOUN
ap-10701	242	12	3x	3x	NUM
ap-10701	242	13	,	,	PUNCT
ap-10701	242	14	x	x	PUNCT
ap-10701	242	15	k4−→	k4−→	PROPN
ap-10701	242	16	e.	e.	PROPN
ap-10701	243	1	the	the	DET
ap-10701	243	2	reaction	reaction	NOUN
ap-10701	243	3	takes	take	VERB
ap-10701	243	4	place	place	NOUN
ap-10701	243	5	in	in	ADP
ap-10701	243	6	a	a	DET
ap-10701	243	7	reactor	reactor	NOUN
ap-10701	243	8	,	,	PUNCT
ap-10701	243	9	characterized	characterize	VERB
ap-10701	243	10	by	by	ADP
ap-10701	243	11	the	the	DET
ap-10701	243	12	length	length	NOUN
ap-10701	243	13	l.	l.	PROPN
ap-10701	243	14	the	the	DET
ap-10701	243	15	mentioned	mention	VERB
ap-10701	243	16	system	system	NOUN
ap-10701	243	17	of	of	ADP
ap-10701	243	18	rde	rde	PROPN
ap-10701	243	19	has	have	AUX
ap-10701	243	20	been	be	AUX
ap-10701	243	21	proposed	propose	VERB
ap-10701	243	22	in	in	ADP
ap-10701	243	23	[	[	X
ap-10701	243	24	39	39	NUM
ap-10701	243	25	]	]	PUNCT
ap-10701	243	26	,	,	PUNCT
ap-10701	243	27	and	and	CCONJ
ap-10701	243	28	widely	widely	ADV
ap-10701	243	29	studied	study	VERB
ap-10701	243	30	by	by	ADP
ap-10701	243	31	many	many	ADJ
ap-10701	243	32	authors	author	NOUN
ap-10701	243	33	.	.	PUNCT
ap-10701	244	1	we	we	PRON
ap-10701	244	2	refer	refer	VERB
ap-10701	244	3	,	,	PUNCT
ap-10701	244	4	for	for	ADP
ap-10701	244	5	example	example	NOUN
ap-10701	244	6	,	,	PUNCT
ap-10701	244	7	to	to	ADP
ap-10701	244	8	[	[	X
ap-10701	244	9	34	34	NUM
ap-10701	244	10	,	,	PUNCT
ap-10701	244	11	40	40	NUM
ap-10701	244	12	,	,	PUNCT
ap-10701	244	13	41	41	NUM
ap-10701	244	14	]	]	PUNCT
ap-10701	244	15	.	.	PUNCT
ap-10701	245	1	the	the	DET
ap-10701	245	2	brusselator	brusselator	NOUN
ap-10701	245	3	equations	equation	NOUN
ap-10701	245	4	have	have	VERB
ap-10701	245	5	the	the	DET
ap-10701	245	6	form	form	NOUN
ap-10701	245	7	:	:	PUNCT
ap-10701	245	8	∂u	∂u	PROPN
ap-10701	245	9	∂t	∂t	PROPN
ap-10701	245	10	=	=	SYM
ap-10701	245	11	du	du	PROPN
ap-10701	245	12	l2	l2	PROPN
ap-10701	245	13	∂2u	∂2u	PROPN
ap-10701	245	14	∂x2	∂x2	PROPN
ap-10701	245	15	+	+	PROPN
ap-10701	245	16	a−	a−	PROPN
ap-10701	245	17	(	(	PUNCT
ap-10701	245	18	b	b	NOUN
ap-10701	245	19	+	+	CCONJ
ap-10701	245	20	1)u+	1)u+	NUM
ap-10701	245	21	u2v	u2v	ADJ
ap-10701	245	22	,	,	PUNCT
ap-10701	245	23	∂v	∂v	PROPN
ap-10701	245	24	∂t	∂t	PROPN
ap-10701	245	25	=	=	SYM
ap-10701	245	26	dv	dv	PROPN
ap-10701	245	27	l2	l2	PROPN
ap-10701	245	28	∂2v	∂2v	PROPN
ap-10701	245	29	∂x2	∂x2	PROPN
ap-10701	245	30	+	+	PROPN
ap-10701	245	31	bu−	bu−	X
ap-10701	245	32	u2v	u2v	ADJ
ap-10701	245	33	,	,	PUNCT
ap-10701	245	34	(	(	PUNCT
ap-10701	245	35	19	19	NUM
ap-10701	245	36	)	)	PUNCT
ap-10701	245	37	where	where	SCONJ
ap-10701	245	38	a	a	DET
ap-10701	245	39	,	,	PUNCT
ap-10701	245	40	b	b	NOUN
ap-10701	245	41	,	,	PUNCT
ap-10701	245	42	du	du	PROPN
ap-10701	245	43	,	,	PUNCT
ap-10701	245	44	dv	dv	PROPN
ap-10701	245	45	,	,	PUNCT
ap-10701	245	46	and	and	CCONJ
ap-10701	245	47	l	l	NOUN
ap-10701	245	48	are	be	AUX
ap-10701	245	49	positive	positive	ADJ
ap-10701	245	50	constants	constant	NOUN
ap-10701	245	51	,	,	PUNCT
ap-10701	245	52	t	t	PROPN
ap-10701	245	53	∈	∈	PROPN
ap-10701	246	1	[	[	X
ap-10701	246	2	0,+∞	0,+∞	NUM
ap-10701	246	3	)	)	PUNCT
ap-10701	246	4	,	,	PUNCT
ap-10701	246	5	x	x	PUNCT
ap-10701	246	6	∈	∈	PROPN
ap-10701	247	1	[	[	X
ap-10701	247	2	0	0	NUM
ap-10701	247	3	,	,	PUNCT
ap-10701	247	4	1	1	NUM
ap-10701	247	5	]	]	PUNCT
ap-10701	247	6	.	.	PUNCT
ap-10701	248	1	the	the	DET
ap-10701	248	2	equations	equation	NOUN
ap-10701	248	3	are	be	AUX
ap-10701	248	4	endowed	endow	VERB
ap-10701	248	5	by	by	ADP
ap-10701	248	6	the	the	DET
ap-10701	248	7	boundary	boundary	ADJ
ap-10701	248	8	conditions	condition	NOUN
ap-10701	248	9	:	:	PUNCT
ap-10701	248	10	u(t	u(t	NOUN
ap-10701	248	11	,	,	PUNCT
ap-10701	248	12	0	0	NUM
ap-10701	248	13	)	)	PUNCT
ap-10701	248	14	=	=	SYM
ap-10701	248	15	a	a	PRON
ap-10701	248	16	,	,	PUNCT
ap-10701	248	17	u(t	u(t	NOUN
ap-10701	248	18	,	,	PUNCT
ap-10701	248	19	1	1	NUM
ap-10701	248	20	)	)	PUNCT
ap-10701	248	21	=	=	SYM
ap-10701	249	1	a	a	PRON
ap-10701	249	2	,	,	PUNCT
ap-10701	249	3	v(t	v(t	NOUN
ap-10701	249	4	,	,	PUNCT
ap-10701	249	5	0	0	NUM
ap-10701	249	6	)	)	PUNCT
ap-10701	249	7	=	=	SYM
ap-10701	250	1	b	b	PROPN
ap-10701	250	2	a	a	PRON
ap-10701	250	3	,	,	PUNCT
ap-10701	250	4	v(t	v(t	PROPN
ap-10701	250	5	,	,	PUNCT
ap-10701	250	6	1	1	NUM
ap-10701	250	7	)	)	PUNCT
ap-10701	250	8	=	=	SYM
ap-10701	250	9	b	b	PROPN
ap-10701	250	10	a	a	DET
ap-10701	250	11	,	,	PUNCT
ap-10701	250	12	(	(	PUNCT
ap-10701	250	13	20	20	NUM
ap-10701	250	14	)	)	PUNCT
ap-10701	250	15	and	and	CCONJ
ap-10701	250	16	the	the	DET
ap-10701	250	17	initial	initial	ADJ
ap-10701	250	18	conditions	condition	NOUN
ap-10701	250	19	:	:	PUNCT
ap-10701	250	20	u(0	u(0	NOUN
ap-10701	250	21	,	,	PUNCT
ap-10701	250	22	x	x	NOUN
ap-10701	250	23	)	)	PUNCT
ap-10701	250	24	=	=	SYM
ap-10701	250	25	u0(x	u0(x	NOUN
ap-10701	250	26	)	)	PUNCT
ap-10701	250	27	,	,	PUNCT
ap-10701	250	28	v(0	v(0	PROPN
ap-10701	250	29	,	,	PUNCT
ap-10701	250	30	x	x	NOUN
ap-10701	250	31	)	)	PUNCT
ap-10701	250	32	=	=	SYM
ap-10701	250	33	v0(x	v0(x	PROPN
ap-10701	250	34	)	)	PUNCT
ap-10701	250	35	.	.	PUNCT
ap-10701	251	1	(	(	PUNCT
ap-10701	251	2	21	21	NUM
ap-10701	251	3	)	)	PUNCT
ap-10701	251	4	the	the	DET
ap-10701	251	5	parameters	parameter	NOUN
ap-10701	251	6	a	a	PRON
ap-10701	251	7	,	,	PUNCT
ap-10701	251	8	b	b	AUX
ap-10701	251	9	express	express	VERB
ap-10701	251	10	the	the	DET
ap-10701	251	11	rescaled	rescaled	ADJ
ap-10701	251	12	constant	constant	ADJ
ap-10701	251	13	concentrations	concentration	NOUN
ap-10701	251	14	of	of	ADP
ap-10701	251	15	the	the	DET
ap-10701	251	16	reactants	reactant	NOUN
ap-10701	251	17	in	in	ADP
ap-10701	251	18	the	the	DET
ap-10701	251	19	reactor	reactor	NOUN
ap-10701	251	20	,	,	PUNCT
ap-10701	251	21	du	du	PROPN
ap-10701	251	22	,	,	PUNCT
ap-10701	251	23	dv	dv	PROPN
ap-10701	251	24	are	be	AUX
ap-10701	251	25	the	the	DET
ap-10701	251	26	diffusion	diffusion	NOUN
ap-10701	251	27	coefficients	coefficient	NOUN
ap-10701	251	28	of	of	ADP
ap-10701	251	29	x	x	X
ap-10701	251	30	and	and	CCONJ
ap-10701	251	31	y.	y.	NOUN
ap-10701	251	32	the	the	DET
ap-10701	251	33	functions	function	NOUN
ap-10701	251	34	u(t	u(t	NOUN
ap-10701	251	35	,	,	PUNCT
ap-10701	251	36	x	x	NOUN
ap-10701	251	37	)	)	PUNCT
ap-10701	251	38	,	,	PUNCT
ap-10701	251	39	v(t	v(t	NOUN
ap-10701	251	40	,	,	PUNCT
ap-10701	251	41	x	x	X
ap-10701	251	42	)	)	PUNCT
ap-10701	251	43	are	be	AUX
ap-10701	251	44	the	the	DET
ap-10701	251	45	concentrations	concentration	NOUN
ap-10701	251	46	of	of	ADP
ap-10701	251	47	x	x	X
ap-10701	251	48	and	and	CCONJ
ap-10701	251	49	y	y	PROPN
ap-10701	251	50	rescaled	rescale	VERB
ap-10701	251	51	with	with	ADP
ap-10701	251	52	respect	respect	NOUN
ap-10701	251	53	to	to	ADP
ap-10701	251	54	a	a	DET
ap-10701	251	55	,	,	PUNCT
ap-10701	251	56	b	b	NOUN
ap-10701	251	57	,	,	PUNCT
ap-10701	251	58	and	and	CCONJ
ap-10701	251	59	the	the	DET
ap-10701	251	60	reaction	reaction	NOUN
ap-10701	251	61	rates	rate	NOUN
ap-10701	251	62	ki	ki	PROPN
ap-10701	251	63	.	.	PUNCT
ap-10701	252	1	we	we	PRON
ap-10701	252	2	convert	convert	VERB
ap-10701	252	3	problem	problem	NOUN
ap-10701	252	4	(	(	PUNCT
ap-10701	252	5	19)–(21	19)–(21	NOUN
ap-10701	252	6	)	)	PUNCT
ap-10701	252	7	to	to	PART
ap-10701	252	8	have	have	VERB
ap-10701	252	9	homogeneous	homogeneous	ADJ
ap-10701	252	10	boundary	boundary	ADJ
ap-10701	252	11	conditions	condition	NOUN
ap-10701	252	12	.	.	PUNCT
ap-10701	253	1	defining	define	VERB
ap-10701	253	2	the	the	DET
ap-10701	253	3	transformation	transformation	NOUN
ap-10701	253	4	:	:	PUNCT
ap-10701	253	5	x(t	x(t	PROPN
ap-10701	253	6	,	,	PUNCT
ap-10701	253	7	x	x	NOUN
ap-10701	253	8	)	)	PUNCT
ap-10701	253	9	=	=	SYM
ap-10701	253	10	u(t	u(t	NOUN
ap-10701	253	11	,	,	PUNCT
ap-10701	253	12	x	x	X
ap-10701	253	13	)	)	PUNCT
ap-10701	253	14	−a	−a	NOUN
ap-10701	253	15	,	,	PUNCT
ap-10701	253	16	y	y	PROPN
ap-10701	253	17	(	(	PUNCT
ap-10701	253	18	t	t	PROPN
ap-10701	253	19	,	,	PUNCT
ap-10701	253	20	x	x	NOUN
ap-10701	253	21	)	)	PUNCT
ap-10701	253	22	=	=	SYM
ap-10701	253	23	v(t	v(t	VERB
ap-10701	253	24	,	,	PUNCT
ap-10701	253	25	x	x	NOUN
ap-10701	253	26	)	)	PUNCT
ap-10701	253	27	−	−	PROPN
ap-10701	253	28	b	b	PROPN
ap-10701	253	29	a	a	PRON
ap-10701	253	30	,	,	PUNCT
ap-10701	253	31	(	(	PUNCT
ap-10701	253	32	22	22	NUM
ap-10701	253	33	)	)	PUNCT
ap-10701	253	34	we	we	PRON
ap-10701	253	35	obtain	obtain	VERB
ap-10701	253	36	:	:	PUNCT
ap-10701	253	37	∂x	∂x	PROPN
ap-10701	253	38	∂t	∂t	PROPN
ap-10701	253	39	=	=	NOUN
ap-10701	253	40	du	du	PROPN
ap-10701	253	41	l2	l2	PROPN
ap-10701	253	42	∂2x	∂2x	NOUN
ap-10701	253	43	∂x2	∂x2	NOUN
ap-10701	253	44	+	+	CCONJ
ap-10701	253	45	(	(	PUNCT
ap-10701	253	46	b	b	X
ap-10701	253	47	−	−	ADP
ap-10701	253	48	1)x	1)x	NUM
ap-10701	254	1	+	+	NOUN
ap-10701	254	2	a2y	a2y	X
ap-10701	254	3	+	+	CCONJ
ap-10701	255	1	2axy	2axy	NUM
ap-10701	255	2	+	+	SYM
ap-10701	255	3	b	b	NOUN
ap-10701	255	4	a	a	DET
ap-10701	255	5	x2	x2	PROPN
ap-10701	256	1	+	+	NOUN
ap-10701	256	2	x2y	x2y	PROPN
ap-10701	256	3	,	,	PUNCT
ap-10701	256	4	∂y	∂y	PROPN
ap-10701	256	5	∂t	∂t	PROPN
ap-10701	256	6	=	=	SYM
ap-10701	256	7	dv	dv	PROPN
ap-10701	256	8	l2	l2	PROPN
ap-10701	256	9	∂2y	∂2y	VERB
ap-10701	256	10	∂x2	∂x2	NOUN
ap-10701	256	11	−bx	−bx	NOUN
ap-10701	256	12	−a2y	−a2y	PROPN
ap-10701	256	13	−	−	PROPN
ap-10701	257	1	2axy	2axy	NUM
ap-10701	257	2	−	−	NOUN
ap-10701	257	3	b	b	NOUN
ap-10701	257	4	a	a	DET
ap-10701	257	5	x2	x2	PROPN
ap-10701	257	6	−x2y	−x2y	NOUN
ap-10701	257	7	,	,	PUNCT
ap-10701	257	8	(	(	PUNCT
ap-10701	257	9	23	23	NUM
ap-10701	257	10	)	)	PUNCT
ap-10701	257	11	with	with	ADP
ap-10701	257	12	homogeneous	homogeneous	ADJ
ap-10701	257	13	boundary	boundary	ADJ
ap-10701	257	14	conditions	condition	NOUN
ap-10701	257	15	and	and	CCONJ
ap-10701	257	16	with	with	ADP
ap-10701	257	17	initial	initial	ADJ
ap-10701	257	18	conditions	condition	NOUN
ap-10701	257	19	in	in	ADP
ap-10701	257	20	the	the	DET
ap-10701	257	21	form	form	NOUN
ap-10701	257	22	:	:	PUNCT
ap-10701	257	23	x|t=0	x|t=0	PROPN
ap-10701	257	24	=	=	PUNCT
ap-10701	257	25	u0	u0	PROPN
ap-10701	257	26	−a	−a	NOUN
ap-10701	257	27	,	,	PUNCT
ap-10701	257	28	y	y	PROPN
ap-10701	257	29	|t=0	|t=0	PROPN
ap-10701	257	30	=	=	PUNCT
ap-10701	257	31	v0	v0	PROPN
ap-10701	257	32	−	−	PROPN
ap-10701	257	33	b	b	PROPN
ap-10701	257	34	a	a	PRON
ap-10701	257	35	.	.	PUNCT
ap-10701	258	1	(	(	PUNCT
ap-10701	258	2	24	24	NUM
ap-10701	258	3	)	)	PUNCT
ap-10701	258	4	denoting	denote	VERB
ap-10701	258	5	:	:	PUNCT
ap-10701	258	6	u(t	u(t	NOUN
ap-10701	258	7	)	)	PUNCT
ap-10701	258	8	=	=	NOUN
ap-10701	258	9	(	(	PUNCT
ap-10701	258	10	x(t	x(t	PROPN
ap-10701	258	11	,	,	PUNCT
ap-10701	258	12	·	·	PUNCT
ap-10701	258	13	)	)	PUNCT
ap-10701	259	1	y	y	PROPN
ap-10701	259	2	(	(	PUNCT
ap-10701	259	3	t	t	PROPN
ap-10701	259	4	,	,	PUNCT
ap-10701	259	5	·	·	PUNCT
ap-10701	259	6	)	)	PUNCT
ap-10701	259	7	)	)	PUNCT
ap-10701	259	8	,	,	PUNCT
ap-10701	259	9	f(u	f(u	PROPN
ap-10701	259	10	)	)	PUNCT
ap-10701	259	11	=	=	SYM
ap-10701	259	12	cu	cu	PROPN
ap-10701	259	13	+	+	PUNCT
ap-10701	259	14	b(u	b(u	PROPN
ap-10701	259	15	)	)	PUNCT
ap-10701	259	16	+	+	NUM
ap-10701	259	17	t(u	t(u	NUM
ap-10701	259	18	)	)	PUNCT
ap-10701	259	19	,	,	PUNCT
ap-10701	260	1	d	d	NOUN
ap-10701	260	2	=	=	PRON
ap-10701	260	3	(	(	PUNCT
ap-10701	260	4	du	du	X
ap-10701	260	5	l2	l2	NOUN
ap-10701	260	6	,	,	PUNCT
ap-10701	260	7	0	0	NUM
ap-10701	260	8	0	0	NUM
ap-10701	260	9	,	,	PUNCT
ap-10701	260	10	dv	dv	PROPN
ap-10701	260	11	l2	l2	PROPN
ap-10701	260	12	)	)	PUNCT
ap-10701	260	13	,	,	PUNCT
ap-10701	260	14	c	c	X
ap-10701	260	15	=	=	PRON
ap-10701	260	16	(	(	PUNCT
ap-10701	260	17	b−1	b−1	PROPN
ap-10701	260	18	,	,	PUNCT
ap-10701	260	19	a2	a2	PROPN
ap-10701	260	20	−b	−b	VERB
ap-10701	260	21	,	,	PUNCT
ap-10701	260	22	−a2	−a2	PROPN
ap-10701	260	23	)	)	PUNCT
ap-10701	260	24	,	,	PUNCT
ap-10701	260	25	b(u	b(u	PROPN
ap-10701	260	26	)	)	PUNCT
ap-10701	260	27	=	=	PUNCT
ap-10701	261	1	(	(	PUNCT
ap-10701	261	2	2axy	2axy	NUM
ap-10701	261	3	+	+	SYM
ap-10701	261	4	b	b	NOUN
ap-10701	261	5	ax	ax	NOUN
ap-10701	261	6	2	2	NUM
ap-10701	261	7	−2axy	−2axy	NOUN
ap-10701	261	8	−	−	PROPN
ap-10701	261	9	b	b	NOUN
ap-10701	261	10	ax	ax	NOUN
ap-10701	261	11	2	2	NUM
ap-10701	261	12	)	)	PUNCT
ap-10701	261	13	,	,	PUNCT
ap-10701	261	14	t(u	t(u	NUM
ap-10701	261	15	)	)	PUNCT
ap-10701	261	16	=	=	PRON
ap-10701	261	17	(	(	PUNCT
ap-10701	261	18	x2y	x2y	X
ap-10701	261	19	−x2y	−x2y	X
ap-10701	261	20	)	)	PUNCT
ap-10701	261	21	,	,	PUNCT
ap-10701	261	22	problem	problem	NOUN
ap-10701	261	23	(	(	PUNCT
ap-10701	261	24	23)–(24	23)–(24	NUM
ap-10701	261	25	)	)	PUNCT
ap-10701	261	26	can	can	AUX
ap-10701	261	27	be	be	AUX
ap-10701	261	28	written	write	VERB
ap-10701	261	29	as	as	ADP
ap-10701	261	30	:	:	PUNCT
ap-10701	261	31	∂u	∂u	PROPN
ap-10701	261	32	∂t	∂t	PROPN
ap-10701	261	33	=	=	SYM
ap-10701	261	34	d∆u	d∆u	PROPN
ap-10701	261	35	+	+	CCONJ
ap-10701	261	36	cu	cu	PROPN
ap-10701	261	37	+	+	CCONJ
ap-10701	261	38	b(u	b(u	PROPN
ap-10701	261	39	)	)	PUNCT
ap-10701	261	40	+	+	NUM
ap-10701	261	41	t(u	t(u	NUM
ap-10701	261	42	)	)	PUNCT
ap-10701	261	43	,	,	PUNCT
ap-10701	261	44	u	u	NOUN
ap-10701	261	45	|∂ω	|∂ω	PROPN
ap-10701	261	46	=	=	SYM
ap-10701	261	47	0	0	NUM
ap-10701	261	48	,	,	PUNCT
ap-10701	261	49	(	(	PUNCT
ap-10701	261	50	25	25	NUM
ap-10701	261	51	)	)	PUNCT
ap-10701	261	52	u	u	NOUN
ap-10701	261	53	|t=0	|t=0	PROPN
ap-10701	261	54	=	=	PUNCT
ap-10701	261	55	uini	uini	NOUN
ap-10701	261	56	.	.	PUNCT
ap-10701	262	1	the	the	DET
ap-10701	262	2	invariant	invariant	ADJ
ap-10701	262	3	regions	region	NOUN
ap-10701	262	4	for	for	ADP
ap-10701	262	5	system	system	NOUN
ap-10701	262	6	(	(	PUNCT
ap-10701	262	7	25	25	NUM
ap-10701	262	8	)	)	PUNCT
ap-10701	262	9	have	have	AUX
ap-10701	262	10	been	be	AUX
ap-10701	262	11	found	find	VERB
ap-10701	262	12	by	by	ADP
ap-10701	262	13	several	several	ADJ
ap-10701	262	14	authors	author	NOUN
ap-10701	262	15	,	,	PUNCT
ap-10701	262	16	e.g.	e.g.	ADV
ap-10701	262	17	by	by	ADP
ap-10701	262	18	eslerová	eslerová	NOUN
ap-10701	262	19	in	in	ADP
ap-10701	262	20	[	[	X
ap-10701	262	21	42	42	NUM
ap-10701	262	22	]	]	PUNCT
ap-10701	262	23	or	or	CCONJ
ap-10701	262	24	by	by	ADP
ap-10701	262	25	[	[	X
ap-10701	262	26	43	43	NUM
ap-10701	262	27	,	,	PUNCT
ap-10701	262	28	44	44	NUM
ap-10701	262	29	]	]	PUNCT
ap-10701	262	30	.	.	PUNCT
ap-10701	263	1	under	under	ADP
ap-10701	263	2	such	such	ADJ
ap-10701	263	3	circumstances	circumstance	NOUN
ap-10701	263	4	,	,	PUNCT
ap-10701	263	5	convergence	convergence	NOUN
ap-10701	263	6	of	of	ADP
ap-10701	263	7	numerical	numerical	ADJ
ap-10701	263	8	methods	method	NOUN
ap-10701	263	9	have	have	AUX
ap-10701	263	10	been	be	AUX
ap-10701	263	11	analyzed	analyze	VERB
ap-10701	263	12	,	,	PUNCT
ap-10701	263	13	for	for	ADP
ap-10701	263	14	example	example	NOUN
ap-10701	263	15	,	,	PUNCT
ap-10701	263	16	the	the	DET
ap-10701	263	17	nonlinear	nonlinear	ADJ
ap-10701	263	18	galerkin	galerkin	PROPN
ap-10701	263	19	method	method	NOUN
ap-10701	263	20	has	have	AUX
ap-10701	263	21	been	be	AUX
ap-10701	263	22	studied	study	VERB
ap-10701	263	23	in	in	ADP
ap-10701	263	24	[	[	PUNCT
ap-10701	263	25	13	13	NUM
ap-10701	263	26	,	,	PUNCT
ap-10701	263	27	15	15	NUM
ap-10701	263	28	,	,	PUNCT
ap-10701	263	29	17	17	NUM
ap-10701	263	30	]	]	PUNCT
ap-10701	263	31	.	.	PUNCT
ap-10701	264	1	for	for	ADP
ap-10701	264	2	an	an	DET
ap-10701	264	3	example	example	NOUN
ap-10701	264	4	of	of	ADP
ap-10701	264	5	numerical	numerical	ADJ
ap-10701	264	6	solution	solution	NOUN
ap-10701	264	7	,	,	PUNCT
ap-10701	264	8	we	we	PRON
ap-10701	264	9	set	set	VERB
ap-10701	264	10	the	the	DET
ap-10701	264	11	space	space	NOUN
ap-10701	264	12	and	and	CCONJ
ap-10701	264	13	time	time	NOUN
ap-10701	264	14	intervals	interval	NOUN
ap-10701	264	15	as	as	ADP
ap-10701	264	16	(	(	PUNCT
ap-10701	264	17	a	a	DET
ap-10701	264	18	,	,	PUNCT
ap-10701	264	19	b	b	NOUN
ap-10701	264	20	)	)	PUNCT
ap-10701	264	21	=	=	SYM
ap-10701	264	22	(	(	PUNCT
ap-10701	264	23	0	0	NUM
ap-10701	264	24	,	,	PUNCT
ap-10701	264	25	1	1	NUM
ap-10701	264	26	)	)	PUNCT
ap-10701	264	27	,	,	PUNCT
ap-10701	264	28	(	(	PUNCT
ap-10701	264	29	0	0	NUM
ap-10701	264	30	,	,	PUNCT
ap-10701	264	31	t	t	NOUN
ap-10701	264	32	)	)	PUNCT
ap-10701	264	33	=	=	PUNCT
ap-10701	265	1	(	(	PUNCT
ap-10701	265	2	0	0	NUM
ap-10701	265	3	,	,	PUNCT
ap-10701	265	4	100	100	NUM
ap-10701	265	5	)	)	PUNCT
ap-10701	265	6	,	,	PUNCT
ap-10701	265	7	the	the	DET
ap-10701	265	8	reaction	reaction	NOUN
ap-10701	265	9	parameters	parameter	VERB
ap-10701	265	10	a	a	PRON
ap-10701	265	11	=	=	SYM
ap-10701	265	12	2.0	2.0	NUM
ap-10701	265	13	,	,	PUNCT
ap-10701	265	14	b	b	NOUN
ap-10701	265	15	=	=	SYM
ap-10701	265	16	5.45	5.45	NUM
ap-10701	265	17	,	,	PUNCT
ap-10701	266	1	the	the	DET
ap-10701	266	2	diffusion	diffusion	NOUN
ap-10701	266	3	parameters	parameter	NOUN
ap-10701	266	4	du	du	PROPN
ap-10701	266	5	=	=	SYM
ap-10701	266	6	0.008	0.008	PROPN
ap-10701	266	7	,	,	PUNCT
ap-10701	266	8	dv	dv	PROPN
ap-10701	266	9	=	=	PROPN
ap-10701	266	10	0.004	0.004	NUM
ap-10701	266	11	,	,	PUNCT
ap-10701	266	12	and	and	CCONJ
ap-10701	266	13	l	l	NOUN
ap-10701	266	14	=	=	NOUN
ap-10701	266	15	1.42	1.42	NUM
ap-10701	266	16	.	.	PUNCT
ap-10701	267	1	this	this	DET
ap-10701	267	2	choice	choice	NOUN
ap-10701	267	3	is	be	AUX
ap-10701	267	4	motivated	motivate	VERB
ap-10701	267	5	by	by	ADP
ap-10701	267	6	computational	computational	ADJ
ap-10701	267	7	studies	study	NOUN
ap-10701	267	8	,	,	PUNCT
ap-10701	267	9	for	for	ADP
ap-10701	267	10	example	example	NOUN
ap-10701	267	11	,	,	PUNCT
ap-10701	267	12	in	in	ADP
ap-10701	267	13	[	[	PUNCT
ap-10701	267	14	34	34	NUM
ap-10701	267	15	,	,	PUNCT
ap-10701	267	16	40	40	NUM
ap-10701	267	17	,	,	PUNCT
ap-10701	267	18	42	42	NUM
ap-10701	267	19	]	]	PUNCT
ap-10701	267	20	.	.	PUNCT
ap-10701	268	1	more	more	ADV
ap-10701	268	2	specifically	specifically	ADV
ap-10701	268	3	,	,	PUNCT
ap-10701	268	4	the	the	DET
ap-10701	268	5	selected	select	VERB
ap-10701	268	6	value	value	NOUN
ap-10701	268	7	of	of	ADP
ap-10701	268	8	l	l	NOUN
ap-10701	268	9	generates	generate	VERB
ap-10701	268	10	an	an	DET
ap-10701	268	11	oscillatory	oscillatory	ADJ
ap-10701	268	12	behavior	behavior	NOUN
ap-10701	268	13	of	of	ADP
ap-10701	268	14	the	the	DET
ap-10701	268	15	solution	solution	NOUN
ap-10701	268	16	in	in	ADP
ap-10701	268	17	time	time	NOUN
ap-10701	268	18	.	.	PUNCT
ap-10701	269	1	the	the	DET
ap-10701	269	2	initial	initial	ADJ
ap-10701	269	3	condition	condition	NOUN
ap-10701	269	4	is	be	AUX
ap-10701	269	5	set	set	VERB
ap-10701	269	6	to	to	PART
ap-10701	269	7	:	:	PUNCT
ap-10701	269	8	u0(x	u0(x	NUM
ap-10701	269	9	)	)	PUNCT
ap-10701	269	10	=	=	SYM
ap-10701	269	11	a+	a+	PUNCT
ap-10701	269	12	sin(2πx	sin(2πx	NOUN
ap-10701	269	13	)	)	PUNCT
ap-10701	269	14	,	,	PUNCT
ap-10701	269	15	v0(x	v0(x	X
ap-10701	269	16	)	)	PUNCT
ap-10701	269	17	=	=	SYM
ap-10701	270	1	b	b	X
ap-10701	270	2	a	a	DET
ap-10701	270	3	+	+	NOUN
ap-10701	270	4	sin(2πx	sin(2πx	NUM
ap-10701	270	5	)	)	PUNCT
ap-10701	270	6	.	.	PUNCT
ap-10701	271	1	it	it	PRON
ap-10701	271	2	means	mean	VERB
ap-10701	271	3	that	that	SCONJ
ap-10701	271	4	it	it	PRON
ap-10701	271	5	is	be	AUX
ap-10701	271	6	a	a	DET
ap-10701	271	7	sinusoidal	sinusoidal	ADJ
ap-10701	271	8	perturbation	perturbation	NOUN
ap-10701	271	9	of	of	ADP
ap-10701	271	10	the	the	DET
ap-10701	271	11	fixed	fix	VERB
ap-10701	271	12	point	point	NOUN
ap-10701	272	1	[	[	X
ap-10701	272	2	a	a	X
ap-10701	272	3	,	,	PUNCT
ap-10701	272	4	b	b	X
ap-10701	272	5	a	a	PRON
ap-10701	272	6	]	]	X
ap-10701	272	7	.	.	PUNCT
ap-10701	273	1	as	as	SCONJ
ap-10701	273	2	known	know	VERB
ap-10701	273	3	from	from	ADP
ap-10701	273	4	[	[	X
ap-10701	273	5	27	27	NUM
ap-10701	273	6	,	,	PUNCT
ap-10701	273	7	34	34	NUM
ap-10701	273	8	,	,	PUNCT
ap-10701	273	9	40	40	NUM
ap-10701	273	10	,	,	PUNCT
ap-10701	273	11	42	42	NUM
ap-10701	273	12	,	,	PUNCT
ap-10701	273	13	44	44	NUM
ap-10701	273	14	]	]	PUNCT
ap-10701	273	15	,	,	PUNCT
ap-10701	273	16	the	the	DET
ap-10701	273	17	solution	solution	NOUN
ap-10701	273	18	approaches	approach	VERB
ap-10701	273	19	a	a	DET
ap-10701	273	20	periodic	periodic	ADJ
ap-10701	273	21	trajectory	trajectory	NOUN
ap-10701	273	22	for	for	ADP
ap-10701	273	23	t	t	PROPN
ap-10701	273	24	→	→	PUNCT
ap-10701	273	25	+	+	PROPN
ap-10701	273	26	∞.	∞.	PROPN
ap-10701	273	27	we	we	PRON
ap-10701	273	28	remark	remark	VERB
ap-10701	273	29	that	that	SCONJ
ap-10701	273	30	the	the	DET
ap-10701	273	31	amplitude	amplitude	NOUN
ap-10701	273	32	,	,	PUNCT
ap-10701	273	33	the	the	DET
ap-10701	273	34	frequency	frequency	NOUN
ap-10701	273	35	of	of	ADP
ap-10701	273	36	this	this	DET
ap-10701	273	37	perturbation	perturbation	NOUN
ap-10701	273	38	,	,	PUNCT
ap-10701	273	39	the	the	DET
ap-10701	273	40	spatial	spatial	ADJ
ap-10701	273	41	symmetry	symmetry	NOUN
ap-10701	273	42	of	of	ADP
ap-10701	273	43	the	the	DET
ap-10701	273	44	initial	initial	ADJ
ap-10701	273	45	condition	condition	NOUN
ap-10701	273	46	,	,	PUNCT
ap-10701	273	47	or	or	CCONJ
ap-10701	273	48	localization	localization	NOUN
ap-10701	273	49	of	of	ADP
ap-10701	273	50	its	its	PRON
ap-10701	273	51	profile	profile	NOUN
ap-10701	273	52	can	can	AUX
ap-10701	273	53	influence	influence	VERB
ap-10701	273	54	the	the	DET
ap-10701	273	55	dynamics	dynamic	NOUN
ap-10701	273	56	of	of	ADP
ap-10701	273	57	the	the	DET
ap-10701	273	58	solution	solution	NOUN
ap-10701	273	59	.	.	PUNCT
ap-10701	274	1	convergence	convergence	NOUN
ap-10701	274	2	with	with	ADP
ap-10701	274	3	respect	respect	NOUN
ap-10701	274	4	to	to	ADP
ap-10701	274	5	a	a	DET
ap-10701	274	6	very	very	ADV
ap-10701	274	7	fine	fine	ADJ
ap-10701	274	8	solution	solution	NOUN
ap-10701	274	9	obtained	obtain	VERB
ap-10701	274	10	for	for	ADP
ap-10701	274	11	m	m	PROPN
ap-10701	274	12	=	=	SYM
ap-10701	274	13	2	2	NUM
ap-10701	274	14	000	000	NUM
ap-10701	274	15	is	be	AUX
ap-10701	274	16	summarized	summarize	VERB
ap-10701	274	17	in	in	ADP
ap-10701	274	18	terms	term	NOUN
ap-10701	274	19	of	of	ADP
ap-10701	274	20	571	571	NUM
ap-10701	274	21	niels	niels	PROPN
ap-10701	274	22	van	van	PROPN
ap-10701	274	23	der	der	PROPN
ap-10701	274	24	meer	meer	PROPN
ap-10701	274	25	,	,	PUNCT
ap-10701	274	26	michal	michal	PROPN
ap-10701	274	27	beneš	beneš	PROPN
ap-10701	274	28	acta	acta	PROPN
ap-10701	274	29	polytechnica	polytechnica	PROPN
ap-10701	274	30	mesh	mesh	NOUN
ap-10701	274	31	level	level	NOUN
ap-10701	275	1	i	i	PRON
ap-10701	275	2	m	m	VERB
ap-10701	275	3	e2(hi	e2(hi	PROPN
ap-10701	275	4	)	)	PUNCT
ap-10701	275	5	eoc(hi−1	eoc(hi−1	PROPN
ap-10701	275	6	,	,	PUNCT
ap-10701	275	7	hi	hi	ADJ
ap-10701	275	8	)	)	PUNCT
ap-10701	275	9	0	0	NUM
ap-10701	275	10	50	50	NUM
ap-10701	275	11	0.0688107	0.0688107	NUM
ap-10701	275	12	–	–	PUNCT
ap-10701	275	13	1	1	NUM
ap-10701	275	14	100	100	NUM
ap-10701	275	15	0.0165081	0.0165081	NUM
ap-10701	275	16	2.059	2.059	NUM
ap-10701	275	17	2	2	NUM
ap-10701	275	18	200	200	NUM
ap-10701	275	19	0.0040801	0.0040801	NUM
ap-10701	275	20	2.016	2.016	NUM
ap-10701	275	21	3	3	NUM
ap-10701	275	22	400	400	NUM
ap-10701	275	23	0.0009881	0.0009881	NUM
ap-10701	275	24	2.046	2.046	NUM
ap-10701	275	25	4	4	NUM
ap-10701	275	26	800	800	NUM
ap-10701	275	27	0.0002161	0.0002161	NUM
ap-10701	275	28	2.193	2.193	NUM
ap-10701	275	29	table	table	NOUN
ap-10701	275	30	1	1	NUM
ap-10701	275	31	.	.	PUNCT
ap-10701	275	32	brusselator	brusselator	NOUN
ap-10701	275	33	model	model	NOUN
ap-10701	275	34	–	–	PUNCT
ap-10701	275	35	variable	variable	ADJ
ap-10701	275	36	u	u	NOUN
ap-10701	275	37	:	:	PUNCT
ap-10701	275	38	table	table	NOUN
ap-10701	275	39	of	of	ADP
ap-10701	275	40	numerical	numerical	ADJ
ap-10701	275	41	parameters	parameter	NOUN
ap-10701	275	42	and	and	CCONJ
ap-10701	275	43	convergence	convergence	NOUN
ap-10701	275	44	errors	error	NOUN
ap-10701	275	45	.	.	PUNCT
ap-10701	276	1	mesh	mesh	NOUN
ap-10701	276	2	level	level	NOUN
ap-10701	277	1	i	i	PRON
ap-10701	277	2	m	m	VERB
ap-10701	277	3	e2(hi	e2(hi	PROPN
ap-10701	277	4	)	)	PUNCT
ap-10701	277	5	eoc(hi−1	eoc(hi−1	PROPN
ap-10701	277	6	,	,	PUNCT
ap-10701	277	7	hi	hi	ADJ
ap-10701	277	8	)	)	PUNCT
ap-10701	277	9	0	0	NUM
ap-10701	277	10	50	50	NUM
ap-10701	277	11	0.0789331	0.0789331	NUM
ap-10701	277	12	–	–	PUNCT
ap-10701	277	13	1	1	NUM
ap-10701	277	14	100	100	NUM
ap-10701	277	15	0.0188665	0.0188665	NUM
ap-10701	277	16	2.065	2.065	NUM
ap-10701	277	17	2	2	NUM
ap-10701	277	18	200	200	NUM
ap-10701	277	19	0.0046606	0.0046606	NUM
ap-10701	277	20	2.017	2.017	NUM
ap-10701	277	21	3	3	NUM
ap-10701	277	22	400	400	NUM
ap-10701	277	23	0.0011289	0.0011289	NUM
ap-10701	277	24	2.046	2.046	NUM
ap-10701	277	25	4	4	NUM
ap-10701	277	26	800	800	NUM
ap-10701	277	27	0.0002469	0.0002469	NUM
ap-10701	277	28	2.193	2.193	NUM
ap-10701	277	29	table	table	NOUN
ap-10701	277	30	2	2	NUM
ap-10701	277	31	.	.	X
ap-10701	277	32	brusselator	brusselator	NOUN
ap-10701	277	33	model	model	NOUN
ap-10701	277	34	–	–	PUNCT
ap-10701	277	35	variable	variable	ADJ
ap-10701	277	36	v	v	NOUN
ap-10701	277	37	:	:	PUNCT
ap-10701	277	38	table	table	NOUN
ap-10701	277	39	of	of	ADP
ap-10701	277	40	numerical	numerical	ADJ
ap-10701	277	41	parameters	parameter	NOUN
ap-10701	277	42	and	and	CCONJ
ap-10701	277	43	convergence	convergence	NOUN
ap-10701	277	44	errors	error	NOUN
ap-10701	277	45	.	.	PUNCT
ap-10701	278	1	figure	figure	VERB
ap-10701	278	2	1	1	NUM
ap-10701	278	3	.	.	PUNCT
ap-10701	279	1	brusselator	brusselator	NOUN
ap-10701	279	2	dynamics	dynamic	NOUN
ap-10701	279	3	.	.	PUNCT
ap-10701	280	1	time	time	NOUN
ap-10701	280	2	evolution	evolution	NOUN
ap-10701	280	3	of	of	ADP
ap-10701	280	4	the	the	DET
ap-10701	280	5	u(t	u(t	NOUN
ap-10701	280	6	,	,	PUNCT
ap-10701	280	7	0.5)-component	0.5)-component	NUM
ap-10701	280	8	of	of	ADP
ap-10701	280	9	the	the	DET
ap-10701	280	10	solution	solution	NOUN
ap-10701	280	11	.	.	PUNCT
ap-10701	281	1	errors	error	NOUN
ap-10701	281	2	and	and	CCONJ
ap-10701	281	3	the	the	DET
ap-10701	281	4	experimental	experimental	ADJ
ap-10701	281	5	order	order	NOUN
ap-10701	281	6	of	of	ADP
ap-10701	281	7	convergence	convergence	NOUN
ap-10701	281	8	in	in	ADP
ap-10701	281	9	tables	table	NOUN
ap-10701	281	10	1	1	NUM
ap-10701	281	11	and	and	CCONJ
ap-10701	281	12	2	2	NUM
ap-10701	281	13	.	.	PUNCT
ap-10701	281	14	as	as	SCONJ
ap-10701	281	15	expected	expect	VERB
ap-10701	281	16	,	,	PUNCT
ap-10701	281	17	the	the	DET
ap-10701	281	18	convergence	convergence	NOUN
ap-10701	281	19	rate	rate	NOUN
ap-10701	281	20	is	be	AUX
ap-10701	281	21	close	close	ADJ
ap-10701	281	22	to	to	ADP
ap-10701	281	23	2	2	NUM
ap-10701	281	24	given	give	VERB
ap-10701	281	25	by	by	ADP
ap-10701	281	26	the	the	DET
ap-10701	281	27	order	order	NOUN
ap-10701	281	28	of	of	ADP
ap-10701	281	29	approximation	approximation	NOUN
ap-10701	281	30	of	of	ADP
ap-10701	281	31	the	the	DET
ap-10701	281	32	second	second	ADJ
ap-10701	281	33	derivative	derivative	NOUN
ap-10701	281	34	.	.	PUNCT
ap-10701	282	1	the	the	DET
ap-10701	282	2	profile	profile	NOUN
ap-10701	282	3	of	of	ADP
ap-10701	282	4	the	the	DET
ap-10701	282	5	solution	solution	NOUN
ap-10701	282	6	components	component	NOUN
ap-10701	282	7	u	u	PROPN
ap-10701	282	8	,	,	PUNCT
ap-10701	282	9	and	and	CCONJ
ap-10701	282	10	v	v	NOUN
ap-10701	282	11	is	be	AUX
ap-10701	282	12	shown	show	VERB
ap-10701	282	13	in	in	ADP
ap-10701	282	14	figures	figure	NOUN
ap-10701	282	15	1	1	NUM
ap-10701	282	16	,	,	PUNCT
ap-10701	282	17	and	and	CCONJ
ap-10701	282	18	2	2	X
ap-10701	282	19	.	.	X
ap-10701	282	20	convergence	convergence	NOUN
ap-10701	282	21	in	in	ADP
ap-10701	282	22	space	space	NOUN
ap-10701	282	23	profiles	profile	NOUN
ap-10701	282	24	is	be	AUX
ap-10701	282	25	depicted	depict	VERB
ap-10701	282	26	in	in	ADP
ap-10701	282	27	figures	figure	NOUN
ap-10701	282	28	3	3	NUM
ap-10701	282	29	and	and	CCONJ
ap-10701	282	30	4	4	NUM
ap-10701	282	31	.	.	NOUN
ap-10701	282	32	5.3	5.3	NUM
ap-10701	282	33	.	.	PUNCT
ap-10701	283	1	fitzhugh	fitzhugh	PROPN
ap-10701	283	2	nagumo	nagumo	ADJ
ap-10701	283	3	model	model	NOUN
ap-10701	283	4	some	some	PRON
ap-10701	283	5	of	of	ADP
ap-10701	283	6	mathematical	mathematical	ADJ
ap-10701	283	7	models	model	NOUN
ap-10701	283	8	used	use	VERB
ap-10701	283	9	in	in	ADP
ap-10701	283	10	electrocardiology	electrocardiology	NOUN
ap-10701	283	11	and	and	CCONJ
ap-10701	283	12	electrophysiology	electrophysiology	NOUN
ap-10701	283	13	,	,	PUNCT
ap-10701	283	14	are	be	AUX
ap-10701	283	15	systems	system	NOUN
ap-10701	283	16	of	of	ADP
ap-10701	283	17	reactiondiffusion	reactiondiffusion	NOUN
ap-10701	283	18	equations	equation	NOUN
ap-10701	283	19	.	.	PUNCT
ap-10701	284	1	one	one	NUM
ap-10701	284	2	of	of	ADP
ap-10701	284	3	them	they	PRON
ap-10701	284	4	designed	design	VERB
ap-10701	284	5	for	for	ADP
ap-10701	284	6	the	the	DET
ap-10701	284	7	conduction	conduction	NOUN
ap-10701	284	8	of	of	ADP
ap-10701	284	9	nerve	nerve	NOUN
ap-10701	284	10	impulses	impulse	NOUN
ap-10701	284	11	along	along	ADP
ap-10701	284	12	an	an	DET
ap-10701	284	13	axon	axon	NOUN
ap-10701	284	14	is	be	AUX
ap-10701	284	15	the	the	DET
ap-10701	284	16	fitzhugh	fitzhugh	PROPN
ap-10701	284	17	-	-	PUNCT
ap-10701	284	18	nagumo	nagumo	ADJ
ap-10701	284	19	(	(	PUNCT
ap-10701	284	20	fhn	fhn	ADJ
ap-10701	284	21	)	)	PUNCT
ap-10701	284	22	model	model	NOUN
ap-10701	284	23	.	.	PUNCT
ap-10701	285	1	first	first	ADV
ap-10701	285	2	proposed	propose	VERB
ap-10701	285	3	in	in	ADP
ap-10701	285	4	1961	1961	NUM
ap-10701	285	5	by	by	ADP
ap-10701	285	6	fitzhugh	fitzhugh	PROPN
ap-10701	285	7	[	[	X
ap-10701	285	8	35	35	NUM
ap-10701	285	9	]	]	PUNCT
ap-10701	285	10	,	,	PUNCT
ap-10701	285	11	it	it	PRON
ap-10701	285	12	is	be	AUX
ap-10701	285	13	a	a	DET
ap-10701	285	14	simplification	simplification	NOUN
ap-10701	285	15	of	of	ADP
ap-10701	285	16	the	the	DET
ap-10701	285	17	pioneering	pioneering	ADJ
ap-10701	285	18	hodgkin	hodgkin	PROPN
ap-10701	285	19	-	-	PUNCT
ap-10701	285	20	huxley	huxley	PROPN
ap-10701	285	21	model	model	NOUN
ap-10701	285	22	from	from	ADP
ap-10701	285	23	1956	1956	NUM
ap-10701	285	24	(	(	PUNCT
ap-10701	285	25	see	see	VERB
ap-10701	285	26	the	the	DET
ap-10701	285	27	original	original	ADJ
ap-10701	285	28	work	work	NOUN
ap-10701	285	29	[	[	X
ap-10701	285	30	45	45	NUM
ap-10701	285	31	]	]	PUNCT
ap-10701	285	32	)	)	PUNCT
ap-10701	285	33	.	.	PUNCT
ap-10701	286	1	in	in	ADP
ap-10701	286	2	1962	1962	NUM
ap-10701	286	3	,	,	PUNCT
ap-10701	286	4	nagumo	nagumo	PROPN
ap-10701	286	5	et	et	PROPN
ap-10701	286	6	al	al	PROPN
ap-10701	286	7	.	.	PUNCT
ap-10701	287	1	[	[	X
ap-10701	287	2	36	36	NUM
ap-10701	287	3	]	]	PUNCT
ap-10701	287	4	derived	derive	VERB
ap-10701	287	5	the	the	DET
ap-10701	287	6	equations	equation	NOUN
ap-10701	287	7	from	from	ADP
ap-10701	287	8	an	an	DET
ap-10701	287	9	active	active	ADJ
ap-10701	287	10	pulse	pulse	NOUN
ap-10701	287	11	transmission	transmission	NOUN
ap-10701	287	12	line	line	NOUN
ap-10701	287	13	simulating	simulate	VERB
ap-10701	287	14	an	an	DET
ap-10701	287	15	animal	animal	NOUN
ap-10701	287	16	nerve	nerve	NOUN
ap-10701	287	17	axon	axon	NOUN
ap-10701	287	18	.	.	PUNCT
ap-10701	288	1	since	since	SCONJ
ap-10701	288	2	then	then	ADV
ap-10701	288	3	,	,	PUNCT
ap-10701	288	4	many	many	ADJ
ap-10701	288	5	results	result	NOUN
ap-10701	288	6	regarding	regard	VERB
ap-10701	288	7	the	the	DET
ap-10701	288	8	qualitative	qualitative	ADJ
ap-10701	288	9	behaviour	behaviour	NOUN
ap-10701	288	10	of	of	ADP
ap-10701	288	11	the	the	DET
ap-10701	288	12	fhn	fhn	ADJ
ap-10701	288	13	model	model	NOUN
ap-10701	288	14	have	have	AUX
ap-10701	288	15	been	be	AUX
ap-10701	288	16	published	publish	VERB
ap-10701	288	17	,	,	PUNCT
ap-10701	288	18	for	for	ADP
ap-10701	288	19	example	example	NOUN
ap-10701	288	20	,	,	PUNCT
ap-10701	288	21	by	by	ADP
ap-10701	288	22	keener	keener	NOUN
ap-10701	288	23	[	[	X
ap-10701	288	24	46	46	NUM
ap-10701	288	25	]	]	PUNCT
ap-10701	288	26	,	,	PUNCT
ap-10701	288	27	and	and	CCONJ
ap-10701	288	28	in	in	ADP
ap-10701	288	29	[	[	X
ap-10701	288	30	47	47	NUM
ap-10701	288	31	,	,	PUNCT
ap-10701	288	32	48	48	NUM
ap-10701	288	33	]	]	PUNCT
ap-10701	288	34	.	.	PUNCT
ap-10701	289	1	in	in	ADP
ap-10701	289	2	this	this	DET
ap-10701	289	3	work	work	NOUN
ap-10701	289	4	,	,	PUNCT
ap-10701	289	5	we	we	PRON
ap-10701	289	6	consider	consider	VERB
ap-10701	289	7	the	the	DET
ap-10701	289	8	fitzhugh	fitzhugh	PROPN
ap-10701	289	9	-	-	PUNCT
ap-10701	289	10	nagumo	nagumo	ADJ
ap-10701	289	11	system	system	NOUN
ap-10701	289	12	in	in	ADP
ap-10701	289	13	the	the	DET
ap-10701	289	14	form	form	NOUN
ap-10701	289	15	∂tv	∂tv	PROPN
ap-10701	289	16	=	=	SYM
ap-10701	289	17	d∂2	d∂2	PROPN
ap-10701	289	18	xxv	xxv	PROPN
ap-10701	289	19	+	+	NUM
ap-10701	289	20	f(v	f(v	NOUN
ap-10701	289	21	)	)	PUNCT
ap-10701	289	22	−	−	PROPN
ap-10701	290	1	w	w	PROPN
ap-10701	291	1	+	+	CCONJ
ap-10701	291	2	iext	iext	ADJ
ap-10701	291	3	,	,	PUNCT
ap-10701	291	4	∂tw	∂tw	PROPN
ap-10701	291	5	=	=	NOUN
ap-10701	291	6	δd∂2	δd∂2	NOUN
ap-10701	291	7	xxw	xxw	NOUN
ap-10701	291	8	+	+	CCONJ
ap-10701	292	1	ϵ(βv	ϵ(βv	NUM
ap-10701	292	2	−	−	NOUN
ap-10701	292	3	γw	γw	NOUN
ap-10701	292	4	)	)	PUNCT
ap-10701	292	5	,	,	PUNCT
ap-10701	292	6	(	(	PUNCT
ap-10701	292	7	26	26	NUM
ap-10701	292	8	)	)	PUNCT
ap-10701	292	9	v|x	v|x	NOUN
ap-10701	293	1	=	=	SYM
ap-10701	293	2	a	a	DET
ap-10701	293	3	=	=	SYM
ap-10701	293	4	g1	g1	NOUN
ap-10701	293	5	,	,	PUNCT
ap-10701	293	6	v|x	v|x	NOUN
ap-10701	293	7	=	=	SYM
ap-10701	293	8	b	b	NOUN
ap-10701	293	9	=	=	SYM
ap-10701	293	10	g1	g1	PROPN
ap-10701	293	11	,	,	PUNCT
ap-10701	293	12	w|x	w|x	PUNCT
ap-10701	293	13	=	=	SYM
ap-10701	293	14	a	a	PRON
ap-10701	293	15	=	=	SYM
ap-10701	293	16	g2	g2	PROPN
ap-10701	293	17	,	,	PUNCT
ap-10701	293	18	w|x	w|x	PUNCT
ap-10701	293	19	=	=	SYM
ap-10701	293	20	b	b	NOUN
ap-10701	293	21	=	=	SYM
ap-10701	293	22	g2	g2	PROPN
ap-10701	293	23	,	,	PUNCT
ap-10701	293	24	v|t=0	v|t=0	NUM
ap-10701	293	25	=	=	SYM
ap-10701	293	26	vini	vini	PROPN
ap-10701	293	27	,	,	PUNCT
ap-10701	293	28	w|t=0	w|t=0	PROPN
ap-10701	293	29	=	=	SYM
ap-10701	293	30	wini	wini	PROPN
ap-10701	293	31	,	,	PUNCT
ap-10701	293	32	where	where	SCONJ
ap-10701	293	33	d	d	NOUN
ap-10701	293	34	,	,	PUNCT
ap-10701	293	35	δ	δ	PROPN
ap-10701	293	36	,	,	PUNCT
ap-10701	293	37	ϵ	ϵ	X
ap-10701	293	38	,	,	PUNCT
ap-10701	293	39	β	β	X
ap-10701	293	40	,	,	PUNCT
ap-10701	293	41	γ	γ	X
ap-10701	293	42	>	>	X
ap-10701	293	43	0	0	NUM
ap-10701	293	44	,	,	PUNCT
ap-10701	293	45	and	and	CCONJ
ap-10701	293	46	f	f	PROPN
ap-10701	293	47	is	be	AUX
ap-10701	293	48	the	the	DET
ap-10701	293	49	reaction	reaction	NOUN
ap-10701	293	50	term	term	NOUN
ap-10701	293	51	,	,	PUNCT
ap-10701	293	52	f(v	f(v	PROPN
ap-10701	293	53	)	)	PUNCT
ap-10701	293	54	=	=	SYM
ap-10701	293	55	v(1	v(1	ADJ
ap-10701	293	56	−	−	PROPN
ap-10701	293	57	v)(v	v)(v	NOUN
ap-10701	293	58	−	−	PROPN
ap-10701	293	59	α	α	X
ap-10701	293	60	)	)	PUNCT
ap-10701	293	61	,	,	PUNCT
ap-10701	293	62	α	α	PROPN
ap-10701	293	63	∈	∈	PROPN
ap-10701	293	64	(	(	PUNCT
ap-10701	293	65	0	0	NUM
ap-10701	293	66	,	,	PUNCT
ap-10701	293	67	1	1	NUM
ap-10701	293	68	)	)	PUNCT
ap-10701	293	69	.	.	PUNCT
ap-10701	294	1	572	572	NUM
ap-10701	294	2	vol	vol	NOUN
ap-10701	294	3	.	.	PUNCT
ap-10701	295	1	65	65	NUM
ap-10701	295	2	no	no	NOUN
ap-10701	295	3	.	.	PUNCT
ap-10701	296	1	5/2025	5/2025	NUM
ap-10701	296	2	method	method	NOUN
ap-10701	296	3	of	of	ADP
ap-10701	296	4	lines	line	NOUN
ap-10701	296	5	for	for	ADP
ap-10701	296	6	reaction	reaction	NOUN
ap-10701	296	7	-	-	PUNCT
ap-10701	296	8	diffusion	diffusion	NOUN
ap-10701	296	9	systems	system	NOUN
ap-10701	296	10	.	.	PUNCT
ap-10701	296	11	.	.	PUNCT
ap-10701	296	12	.	.	PUNCT
ap-10701	297	1	figure	figure	NOUN
ap-10701	297	2	2	2	NUM
ap-10701	297	3	.	.	PUNCT
ap-10701	297	4	brusselator	brusselator	NOUN
ap-10701	297	5	dynamics	dynamic	NOUN
ap-10701	297	6	.	.	PUNCT
ap-10701	298	1	time	time	NOUN
ap-10701	298	2	evolution	evolution	NOUN
ap-10701	298	3	of	of	ADP
ap-10701	298	4	the	the	DET
ap-10701	298	5	v(t	v(t	NOUN
ap-10701	298	6	,	,	PUNCT
ap-10701	298	7	0.5)-component	0.5)-component	NUM
ap-10701	298	8	of	of	ADP
ap-10701	298	9	the	the	DET
ap-10701	298	10	solution	solution	NOUN
ap-10701	298	11	.	.	PUNCT
ap-10701	299	1	figure	figure	NOUN
ap-10701	299	2	3	3	NUM
ap-10701	299	3	.	.	PUNCT
ap-10701	299	4	brusselator	brusselator	NOUN
ap-10701	299	5	dynamics	dynamic	NOUN
ap-10701	299	6	.	.	PUNCT
ap-10701	300	1	convergence	convergence	NOUN
ap-10701	300	2	of	of	ADP
ap-10701	300	3	the	the	DET
ap-10701	300	4	space	space	NOUN
ap-10701	300	5	profile	profile	NOUN
ap-10701	300	6	of	of	ADP
ap-10701	300	7	the	the	DET
ap-10701	300	8	u	u	NOUN
ap-10701	300	9	-	-	NOUN
ap-10701	300	10	component	component	NOUN
ap-10701	300	11	of	of	ADP
ap-10701	300	12	the	the	DET
ap-10701	300	13	solution	solution	NOUN
ap-10701	300	14	for	for	ADP
ap-10701	300	15	t	t	NOUN
ap-10701	300	16	=	=	SYM
ap-10701	300	17	100	100	NUM
ap-10701	300	18	.	.	PUNCT
ap-10701	301	1	the	the	DET
ap-10701	301	2	external	external	ADJ
ap-10701	301	3	excitation	excitation	NOUN
ap-10701	301	4	current	current	ADJ
ap-10701	301	5	iext	iext	PROPN
ap-10701	301	6	∈	∈	PROPN
ap-10701	301	7	r	r	NOUN
ap-10701	301	8	can	can	AUX
ap-10701	301	9	provide	provide	VERB
ap-10701	301	10	signal	signal	NOUN
ap-10701	301	11	from	from	ADP
ap-10701	301	12	neighbouring	neighbouring	ADJ
ap-10701	301	13	neurons	neuron	NOUN
ap-10701	301	14	.	.	PUNCT
ap-10701	302	1	the	the	DET
ap-10701	302	2	model	model	NOUN
ap-10701	302	3	reflects	reflect	VERB
ap-10701	302	4	important	important	ADJ
ap-10701	302	5	qualitative	qualitative	ADJ
ap-10701	302	6	properties	property	NOUN
ap-10701	302	7	of	of	ADP
ap-10701	302	8	excitable	excitable	ADJ
ap-10701	302	9	medium	medium	NOUN
ap-10701	302	10	:	:	PUNCT
ap-10701	302	11	•	•	NUM
ap-10701	302	12	excitability	excitability	NOUN
ap-10701	302	13	:	:	PUNCT
ap-10701	302	14	small	small	ADJ
ap-10701	302	15	stimulus	stimulus	NOUN
ap-10701	302	16	of	of	ADP
ap-10701	302	17	a	a	DET
ap-10701	302	18	suitable	suitable	ADJ
ap-10701	302	19	form	form	NOUN
ap-10701	302	20	generates	generate	VERB
ap-10701	302	21	a	a	DET
ap-10701	302	22	larger	large	ADJ
ap-10701	302	23	response	response	NOUN
ap-10701	302	24	of	of	ADP
ap-10701	302	25	medium	medium	ADJ
ap-10701	302	26	leading	leading	NOUN
ap-10701	302	27	,	,	PUNCT
ap-10701	302	28	after	after	ADP
ap-10701	302	29	a	a	DET
ap-10701	302	30	while	while	NOUN
ap-10701	302	31	,	,	PUNCT
ap-10701	302	32	to	to	ADP
ap-10701	302	33	the	the	DET
ap-10701	302	34	initial	initial	ADJ
ap-10701	302	35	state	state	NOUN
ap-10701	302	36	.	.	PUNCT
ap-10701	303	1	•	•	NUM
ap-10701	303	2	refractoriness	refractoriness	NOUN
ap-10701	303	3	:	:	PUNCT
ap-10701	303	4	if	if	SCONJ
ap-10701	303	5	such	such	DET
ap-10701	303	6	a	a	DET
ap-10701	303	7	reaction	reaction	NOUN
ap-10701	303	8	occurs	occur	VERB
ap-10701	303	9	,	,	PUNCT
ap-10701	303	10	the	the	DET
ap-10701	303	11	medium	medium	NOUN
ap-10701	303	12	can	can	AUX
ap-10701	303	13	not	not	PART
ap-10701	303	14	be	be	AUX
ap-10701	303	15	excited	excite	VERB
ap-10701	303	16	again	again	ADV
ap-10701	303	17	for	for	ADP
ap-10701	303	18	some	some	DET
ap-10701	303	19	time	time	NOUN
ap-10701	303	20	.	.	PUNCT
ap-10701	304	1	variable	variable	ADJ
ap-10701	304	2	v	v	PROPN
ap-10701	304	3	represents	represent	VERB
ap-10701	304	4	a	a	DET
ap-10701	304	5	(	(	PUNCT
ap-10701	304	6	normalized	normalize	VERB
ap-10701	304	7	)	)	PUNCT
ap-10701	304	8	membrane	membrane	NOUN
ap-10701	304	9	potential	potential	NOUN
ap-10701	304	10	and	and	CCONJ
ap-10701	304	11	is	be	AUX
ap-10701	304	12	called	call	VERB
ap-10701	304	13	the	the	DET
ap-10701	304	14	excitable	excitable	ADJ
ap-10701	304	15	.	.	PUNCT
ap-10701	305	1	the	the	DET
ap-10701	305	2	variable	variable	ADJ
ap-10701	305	3	w	w	PROPN
ap-10701	305	4	serves	serve	VERB
ap-10701	305	5	as	as	ADP
ap-10701	305	6	a	a	DET
ap-10701	305	7	gating	gate	VERB
ap-10701	305	8	variable	variable	NOUN
ap-10701	305	9	(	(	PUNCT
ap-10701	305	10	see	see	VERB
ap-10701	305	11	[	[	X
ap-10701	305	12	46	46	NUM
ap-10701	305	13	]	]	PUNCT
ap-10701	305	14	)	)	PUNCT
ap-10701	305	15	.	.	PUNCT
ap-10701	306	1	we	we	PRON
ap-10701	306	2	also	also	ADV
ap-10701	306	3	remark	remark	VERB
ap-10701	306	4	that	that	SCONJ
ap-10701	306	5	system	system	NOUN
ap-10701	306	6	(	(	PUNCT
ap-10701	306	7	26	26	NUM
ap-10701	306	8	)	)	PUNCT
ap-10701	306	9	can	can	AUX
ap-10701	306	10	be	be	AUX
ap-10701	306	11	formulated	formulate	VERB
ap-10701	306	12	in	in	ADP
ap-10701	306	13	several	several	ADJ
ap-10701	306	14	different	different	ADJ
ap-10701	306	15	forms	form	NOUN
ap-10701	306	16	in	in	ADP
ap-10701	306	17	literature	literature	NOUN
ap-10701	306	18	.	.	PUNCT
ap-10701	307	1	the	the	DET
ap-10701	307	2	small	small	ADJ
ap-10701	307	3	parameter	parameter	NOUN
ap-10701	307	4	ϵ	ϵ	ADP
ap-10701	307	5	quantifies	quantifie	NOUN
ap-10701	307	6	relative	relative	ADJ
ap-10701	307	7	rates	rate	NOUN
ap-10701	307	8	of	of	ADP
ap-10701	307	9	excitation	excitation	NOUN
ap-10701	307	10	and	and	CCONJ
ap-10701	307	11	recovery	recovery	NOUN
ap-10701	307	12	.	.	PUNCT
ap-10701	308	1	the	the	DET
ap-10701	308	2	invariant	invariant	ADJ
ap-10701	308	3	regions	region	NOUN
ap-10701	308	4	for	for	ADP
ap-10701	308	5	(	(	PUNCT
ap-10701	308	6	26	26	NUM
ap-10701	308	7	)	)	PUNCT
ap-10701	308	8	are	be	AUX
ap-10701	308	9	available	available	ADJ
ap-10701	308	10	and	and	CCONJ
ap-10701	308	11	have	have	AUX
ap-10701	308	12	been	be	AUX
ap-10701	308	13	studied	study	VERB
ap-10701	308	14	by	by	ADP
ap-10701	308	15	several	several	ADJ
ap-10701	308	16	authors	author	NOUN
ap-10701	308	17	,	,	PUNCT
ap-10701	308	18	for	for	ADP
ap-10701	308	19	example	example	NOUN
ap-10701	308	20	,	,	PUNCT
ap-10701	308	21	in	in	ADP
ap-10701	308	22	[	[	X
ap-10701	308	23	1	1	NUM
ap-10701	308	24	]	]	PUNCT
ap-10701	308	25	and	and	CCONJ
ap-10701	308	26	recently	recently	ADV
ap-10701	308	27	in	in	ADP
ap-10701	308	28	[	[	X
ap-10701	308	29	5	5	NUM
ap-10701	308	30	]	]	PUNCT
ap-10701	308	31	.	.	PUNCT
ap-10701	309	1	we	we	PRON
ap-10701	309	2	,	,	PUNCT
ap-10701	309	3	therefore	therefore	ADV
ap-10701	309	4	,	,	PUNCT
ap-10701	309	5	apply	apply	VERB
ap-10701	309	6	the	the	DET
ap-10701	309	7	approach	approach	NOUN
ap-10701	309	8	described	describe	VERB
ap-10701	309	9	in	in	ADP
ap-10701	309	10	this	this	DET
ap-10701	309	11	text	text	NOUN
ap-10701	309	12	and	and	CCONJ
ap-10701	309	13	have	have	VERB
ap-10701	309	14	the	the	DET
ap-10701	309	15	convergence	convergence	NOUN
ap-10701	309	16	of	of	ADP
ap-10701	309	17	the	the	DET
ap-10701	309	18	numerical	numerical	ADJ
ap-10701	309	19	scheme	scheme	NOUN
ap-10701	309	20	guaranteed	guarantee	VERB
ap-10701	309	21	.	.	PUNCT
ap-10701	310	1	a	a	DET
ap-10701	310	2	computational	computational	ADJ
ap-10701	310	3	example	example	NOUN
ap-10701	310	4	has	have	AUX
ap-10701	310	5	been	be	AUX
ap-10701	310	6	performed	perform	VERB
ap-10701	310	7	on	on	ADP
ap-10701	310	8	the	the	DET
ap-10701	310	9	space	space	NOUN
ap-10701	310	10	interval	interval	NOUN
ap-10701	310	11	(	(	PUNCT
ap-10701	310	12	0	0	NUM
ap-10701	310	13	,	,	PUNCT
ap-10701	310	14	50	50	NUM
ap-10701	310	15	)	)	PUNCT
ap-10701	310	16	for	for	ADP
ap-10701	310	17	the	the	DET
ap-10701	310	18	initial	initial	ADJ
ap-10701	310	19	conditions	condition	NOUN
ap-10701	310	20	:	:	PUNCT
ap-10701	310	21	vini(x	vini(x	NUM
ap-10701	310	22	)	)	PUNCT
ap-10701	310	23	=	=	SYM
ap-10701	310	24	1	1	NUM
ap-10701	310	25	2	2	NUM
ap-10701	310	26	exp	exp	NOUN
ap-10701	310	27	(	(	PUNCT
ap-10701	310	28	−	−	PROPN
ap-10701	310	29	(	(	PUNCT
ap-10701	310	30	x−	x−	PROPN
ap-10701	310	31	9)2	9)2	PROPN
ap-10701	310	32	3	3	NUM
ap-10701	310	33	)	)	PUNCT
ap-10701	310	34	,	,	PUNCT
ap-10701	310	35	wini(x	wini(x	NOUN
ap-10701	310	36	)	)	PUNCT
ap-10701	310	37	=	=	SYM
ap-10701	310	38	1	1	NUM
ap-10701	310	39	5	5	NUM
ap-10701	310	40	exp	exp	NOUN
ap-10701	310	41	(	(	PUNCT
ap-10701	310	42	−	−	PROPN
ap-10701	310	43	(	(	PUNCT
ap-10701	310	44	x−	x−	PROPN
ap-10701	310	45	7)2	7)2	PROPN
ap-10701	310	46	3	3	NUM
ap-10701	310	47	)	)	PUNCT
ap-10701	310	48	,	,	PUNCT
ap-10701	310	49	573	573	NUM
ap-10701	310	50	niels	niels	PROPN
ap-10701	310	51	van	van	PROPN
ap-10701	310	52	der	der	PROPN
ap-10701	310	53	meer	meer	PROPN
ap-10701	310	54	,	,	PUNCT
ap-10701	310	55	michal	michal	PROPN
ap-10701	310	56	beneš	beneš	PROPN
ap-10701	310	57	acta	acta	PROPN
ap-10701	310	58	polytechnica	polytechnica	PROPN
ap-10701	310	59	figure	figure	NOUN
ap-10701	310	60	4	4	NUM
ap-10701	310	61	.	.	PUNCT
ap-10701	310	62	brusselator	brusselator	NOUN
ap-10701	310	63	dynamics	dynamic	NOUN
ap-10701	310	64	.	.	PUNCT
ap-10701	311	1	convergence	convergence	NOUN
ap-10701	311	2	of	of	ADP
ap-10701	311	3	the	the	DET
ap-10701	311	4	space	space	NOUN
ap-10701	311	5	profile	profile	NOUN
ap-10701	311	6	of	of	ADP
ap-10701	311	7	the	the	DET
ap-10701	311	8	v	v	NOUN
ap-10701	311	9	-	-	PUNCT
ap-10701	311	10	component	component	NOUN
ap-10701	311	11	of	of	ADP
ap-10701	311	12	the	the	DET
ap-10701	311	13	solution	solution	NOUN
ap-10701	311	14	for	for	ADP
ap-10701	311	15	t	t	NOUN
ap-10701	311	16	=	=	SYM
ap-10701	311	17	100	100	NUM
ap-10701	311	18	.	.	PUNCT
ap-10701	312	1	mesh	mesh	NOUN
ap-10701	312	2	level	level	NOUN
ap-10701	313	1	i	i	PRON
ap-10701	313	2	m	m	VERB
ap-10701	313	3	e2(hi	e2(hi	PROPN
ap-10701	313	4	)	)	PUNCT
ap-10701	313	5	eoc(hi−1	eoc(hi−1	PROPN
ap-10701	313	6	,	,	PUNCT
ap-10701	313	7	hi	hi	ADJ
ap-10701	313	8	)	)	PUNCT
ap-10701	313	9	0	0	NUM
ap-10701	313	10	50	50	NUM
ap-10701	313	11	37.66	37.66	NUM
ap-10701	313	12	–	–	PUNCT
ap-10701	313	13	1	1	NUM
ap-10701	313	14	100	100	NUM
ap-10701	313	15	7.89	7.89	NUM
ap-10701	313	16	2.25	2.25	NUM
ap-10701	313	17	2	2	NUM
ap-10701	313	18	200	200	NUM
ap-10701	313	19	1.39	1.39	NUM
ap-10701	313	20	2.50	2.50	NUM
ap-10701	313	21	3	3	NUM
ap-10701	313	22	400	400	NUM
ap-10701	313	23	0.246	0.246	NUM
ap-10701	313	24	2.50	2.50	NUM
ap-10701	313	25	4	4	NUM
ap-10701	313	26	800	800	NUM
ap-10701	313	27	0.0433	0.0433	NUM
ap-10701	313	28	2.50	2.50	NUM
ap-10701	313	29	5	5	NUM
ap-10701	313	30	1	1	NUM
ap-10701	313	31	600	600	NUM
ap-10701	313	32	0.0107	0.0107	NUM
ap-10701	313	33	2.01	2.01	NUM
ap-10701	313	34	6	6	NUM
ap-10701	313	35	3	3	NUM
ap-10701	313	36	200	200	NUM
ap-10701	313	37	0.0035	0.0035	NUM
ap-10701	313	38	1.61	1.61	NUM
ap-10701	313	39	7	7	NUM
ap-10701	313	40	6	6	NUM
ap-10701	313	41	400	400	NUM
ap-10701	313	42	0.00106	0.00106	NUM
ap-10701	313	43	1.73	1.73	NUM
ap-10701	313	44	table	table	NOUN
ap-10701	313	45	3	3	NUM
ap-10701	313	46	.	.	PUNCT
ap-10701	313	47	fhn	fhn	ADJ
ap-10701	313	48	model	model	NOUN
ap-10701	313	49	–	–	PUNCT
ap-10701	313	50	variable	variable	ADJ
ap-10701	313	51	v	v	NOUN
ap-10701	313	52	:	:	PUNCT
ap-10701	313	53	table	table	NOUN
ap-10701	313	54	of	of	ADP
ap-10701	313	55	numerical	numerical	ADJ
ap-10701	313	56	parameters	parameter	NOUN
ap-10701	313	57	and	and	CCONJ
ap-10701	313	58	convergence	convergence	NOUN
ap-10701	313	59	errors	error	NOUN
ap-10701	313	60	.	.	PUNCT
ap-10701	314	1	mesh	mesh	NOUN
ap-10701	314	2	level	level	NOUN
ap-10701	315	1	i	i	PRON
ap-10701	315	2	m	m	VERB
ap-10701	315	3	e2(hi	e2(hi	PROPN
ap-10701	315	4	)	)	PUNCT
ap-10701	315	5	eoc(hi−1	eoc(hi−1	PROPN
ap-10701	315	6	,	,	PUNCT
ap-10701	315	7	hi	hi	ADJ
ap-10701	315	8	)	)	PUNCT
ap-10701	315	9	0	0	NUM
ap-10701	315	10	50	50	NUM
ap-10701	315	11	2.29	2.29	NUM
ap-10701	315	12	–	–	PUNCT
ap-10701	315	13	1	1	NUM
ap-10701	315	14	100	100	NUM
ap-10701	315	15	0.409	0.409	NUM
ap-10701	315	16	2.48	2.48	NUM
ap-10701	315	17	2	2	NUM
ap-10701	315	18	200	200	NUM
ap-10701	315	19	0.0728	0.0728	NUM
ap-10701	315	20	2.49	2.49	NUM
ap-10701	315	21	3	3	NUM
ap-10701	315	22	400	400	NUM
ap-10701	315	23	0.0139	0.0139	NUM
ap-10701	315	24	2.39	2.39	NUM
ap-10701	315	25	4	4	NUM
ap-10701	315	26	800	800	NUM
ap-10701	315	27	0.00368	0.00368	NUM
ap-10701	315	28	1.92	1.92	NUM
ap-10701	315	29	5	5	NUM
ap-10701	315	30	1	1	NUM
ap-10701	315	31	600	600	NUM
ap-10701	315	32	0.00121	0.00121	NUM
ap-10701	315	33	1.60	1.60	NUM
ap-10701	315	34	6	6	NUM
ap-10701	315	35	3	3	NUM
ap-10701	315	36	200	200	NUM
ap-10701	315	37	0.000393	0.000393	NUM
ap-10701	315	38	1.62	1.62	NUM
ap-10701	315	39	7	7	NUM
ap-10701	315	40	6	6	NUM
ap-10701	315	41	400	400	NUM
ap-10701	315	42	0.000119	0.000119	NUM
ap-10701	315	43	1.73	1.73	NUM
ap-10701	315	44	table	table	NOUN
ap-10701	315	45	4	4	NUM
ap-10701	315	46	.	.	PUNCT
ap-10701	315	47	fhn	fhn	ADJ
ap-10701	315	48	model	model	NOUN
ap-10701	315	49	–	–	PUNCT
ap-10701	315	50	variable	variable	ADJ
ap-10701	315	51	w	w	NOUN
ap-10701	315	52	:	:	PUNCT
ap-10701	315	53	table	table	NOUN
ap-10701	315	54	of	of	ADP
ap-10701	315	55	numerical	numerical	ADJ
ap-10701	315	56	parameters	parameter	NOUN
ap-10701	315	57	and	and	CCONJ
ap-10701	315	58	convergence	convergence	NOUN
ap-10701	315	59	errors	error	NOUN
ap-10701	315	60	.	.	PUNCT
ap-10701	316	1	and	and	CCONJ
ap-10701	316	2	for	for	ADP
ap-10701	316	3	the	the	DET
ap-10701	316	4	boundary	boundary	ADJ
ap-10701	316	5	conditions	condition	NOUN
ap-10701	316	6	:	:	PUNCT
ap-10701	316	7	v(0	v(0	PROPN
ap-10701	316	8	,	,	PUNCT
ap-10701	316	9	t	t	PROPN
ap-10701	316	10	)	)	PUNCT
ap-10701	316	11	=	=	SYM
ap-10701	316	12	0	0	NUM
ap-10701	316	13	,	,	PUNCT
ap-10701	316	14	v(50	v(50	NOUN
ap-10701	316	15	,	,	PUNCT
ap-10701	316	16	t	t	PROPN
ap-10701	316	17	)	)	PUNCT
ap-10701	316	18	=	=	SYM
ap-10701	316	19	0	0	NUM
ap-10701	316	20	,	,	PUNCT
ap-10701	316	21	w(0	w(0	PROPN
ap-10701	316	22	,	,	PUNCT
ap-10701	316	23	t	t	PROPN
ap-10701	316	24	)	)	PUNCT
ap-10701	316	25	=	=	SYM
ap-10701	316	26	0	0	NUM
ap-10701	316	27	,	,	PUNCT
ap-10701	316	28	w(50	w(50	ADJ
ap-10701	316	29	,	,	PUNCT
ap-10701	316	30	t	t	PROPN
ap-10701	316	31	)	)	PUNCT
ap-10701	316	32	=	=	SYM
ap-10701	316	33	0	0	X
ap-10701	316	34	.	.	PUNCT
ap-10701	317	1	the	the	DET
ap-10701	317	2	remaining	remain	VERB
ap-10701	317	3	settings	setting	NOUN
ap-10701	317	4	for	for	ADP
ap-10701	317	5	this	this	DET
ap-10701	317	6	computation	computation	NOUN
ap-10701	317	7	are	be	AUX
ap-10701	317	8	:	:	PUNCT
ap-10701	317	9	d	d	X
ap-10701	317	10	=	=	SYM
ap-10701	317	11	0.1	0.1	NUM
ap-10701	317	12	,	,	PUNCT
ap-10701	317	13	α	α	NOUN
ap-10701	317	14	=	=	SYM
ap-10701	317	15	0.1	0.1	NUM
ap-10701	317	16	,	,	PUNCT
ap-10701	317	17	β	β	X
ap-10701	317	18	=	=	SYM
ap-10701	317	19	0.3	0.3	NUM
ap-10701	317	20	,	,	PUNCT
ap-10701	317	21	γ	γ	X
ap-10701	317	22	=	=	SYM
ap-10701	317	23	1.0	1.0	NUM
ap-10701	317	24	,	,	PUNCT
ap-10701	317	25	δ	δ	PROPN
ap-10701	317	26	=	=	SYM
ap-10701	317	27	0.001	0.001	NUM
ap-10701	317	28	,	,	PUNCT
ap-10701	317	29	ϵ	ϵ	X
ap-10701	317	30	=	=	PUNCT
ap-10701	317	31	0.01	0.01	NUM
ap-10701	317	32	,	,	PUNCT
ap-10701	317	33	iext	iext	PROPN
ap-10701	317	34	=	=	SYM
ap-10701	317	35	0.0	0.0	NUM
ap-10701	317	36	.	.	PUNCT
ap-10701	318	1	the	the	DET
ap-10701	318	2	time	time	NOUN
ap-10701	318	3	extent	extent	NOUN
ap-10701	318	4	is	be	AUX
ap-10701	318	5	(	(	PUNCT
ap-10701	318	6	0	0	NUM
ap-10701	318	7	,	,	PUNCT
ap-10701	318	8	200	200	NUM
ap-10701	318	9	)	)	PUNCT
ap-10701	318	10	.	.	PUNCT
ap-10701	319	1	the	the	DET
ap-10701	319	2	choice	choice	NOUN
ap-10701	319	3	of	of	ADP
ap-10701	319	4	the	the	DET
ap-10701	319	5	initial	initial	ADJ
ap-10701	319	6	condition	condition	NOUN
ap-10701	319	7	is	be	AUX
ap-10701	319	8	motivated	motivate	VERB
ap-10701	319	9	by	by	ADP
ap-10701	319	10	modeling	model	VERB
ap-10701	319	11	excitation	excitation	NOUN
ap-10701	319	12	in	in	ADP
ap-10701	319	13	myocardium	myocardium	NOUN
ap-10701	319	14	[	[	X
ap-10701	319	15	5	5	NUM
ap-10701	319	16	,	,	PUNCT
ap-10701	319	17	46	46	NUM
ap-10701	319	18	]	]	PUNCT
ap-10701	319	19	.	.	PUNCT
ap-10701	320	1	the	the	DET
ap-10701	320	2	convergence	convergence	NOUN
ap-10701	320	3	with	with	ADP
ap-10701	320	4	respect	respect	NOUN
ap-10701	320	5	to	to	ADP
ap-10701	320	6	a	a	DET
ap-10701	320	7	very	very	ADV
ap-10701	320	8	fine	fine	ADJ
ap-10701	320	9	solution	solution	NOUN
ap-10701	320	10	obtained	obtain	VERB
ap-10701	320	11	for	for	ADP
ap-10701	320	12	m	m	PROPN
ap-10701	320	13	=	=	NOUN
ap-10701	320	14	25	25	NUM
ap-10701	320	15	600	600	NUM
ap-10701	320	16	is	be	AUX
ap-10701	320	17	summarized	summarize	VERB
ap-10701	320	18	in	in	ADP
ap-10701	320	19	terms	term	NOUN
ap-10701	320	20	of	of	ADP
ap-10701	320	21	errors	error	NOUN
ap-10701	320	22	in	in	ADP
ap-10701	320	23	table	table	NOUN
ap-10701	320	24	3	3	NUM
ap-10701	320	25	,	,	PUNCT
ap-10701	320	26	and	and	CCONJ
ap-10701	320	27	in	in	ADP
ap-10701	320	28	terms	term	NOUN
ap-10701	320	29	of	of	ADP
ap-10701	320	30	the	the	DET
ap-10701	320	31	experimental	experimental	ADJ
ap-10701	320	32	order	order	NOUN
ap-10701	320	33	of	of	ADP
ap-10701	320	34	convergence	convergence	NOUN
ap-10701	320	35	in	in	ADP
ap-10701	320	36	table	table	NOUN
ap-10701	320	37	4	4	NUM
ap-10701	320	38	.	.	PUNCT
ap-10701	320	39	convergence	convergence	NOUN
ap-10701	320	40	in	in	ADP
ap-10701	320	41	space	space	NOUN
ap-10701	320	42	profiles	profile	NOUN
ap-10701	320	43	is	be	AUX
ap-10701	320	44	depicted	depict	VERB
ap-10701	320	45	in	in	ADP
ap-10701	320	46	figures	figure	NOUN
ap-10701	320	47	5	5	NUM
ap-10701	320	48	and	and	CCONJ
ap-10701	320	49	6	6	NUM
ap-10701	320	50	.	.	PUNCT
ap-10701	320	51	again	again	ADV
ap-10701	320	52	,	,	PUNCT
ap-10701	320	53	as	as	SCONJ
ap-10701	320	54	expected	expect	VERB
ap-10701	320	55	,	,	PUNCT
ap-10701	320	56	the	the	DET
ap-10701	320	57	convergence	convergence	NOUN
ap-10701	320	58	rate	rate	NOUN
ap-10701	320	59	is	be	AUX
ap-10701	320	60	close	close	ADJ
ap-10701	320	61	to	to	ADP
ap-10701	320	62	2	2	NUM
ap-10701	320	63	given	give	VERB
ap-10701	320	64	by	by	ADP
ap-10701	320	65	the	the	DET
ap-10701	320	66	order	order	NOUN
ap-10701	320	67	of	of	ADP
ap-10701	320	68	approximation	approximation	NOUN
ap-10701	320	69	of	of	ADP
ap-10701	320	70	the	the	DET
ap-10701	320	71	second	second	ADJ
ap-10701	320	72	derivative	derivative	NOUN
ap-10701	320	73	.	.	PUNCT
ap-10701	321	1	6	6	NUM
ap-10701	321	2	.	.	X
ap-10701	321	3	conclusion	conclusion	VERB
ap-10701	321	4	the	the	DET
ap-10701	321	5	finite	finite	ADJ
ap-10701	321	6	-	-	PUNCT
ap-10701	321	7	difference	difference	ADJ
ap-10701	321	8	method	method	NOUN
ap-10701	321	9	of	of	ADP
ap-10701	321	10	lines	line	NOUN
ap-10701	321	11	turns	turn	VERB
ap-10701	321	12	out	out	ADP
ap-10701	321	13	to	to	PART
ap-10701	321	14	be	be	AUX
ap-10701	321	15	efficient	efficient	ADJ
ap-10701	321	16	,	,	PUNCT
ap-10701	321	17	easy	easy	ADJ
ap-10701	321	18	to	to	PART
ap-10701	321	19	implement	implement	VERB
ap-10701	321	20	,	,	PUNCT
ap-10701	321	21	and	and	CCONJ
ap-10701	321	22	accurate	accurate	ADJ
ap-10701	321	23	in	in	ADP
ap-10701	321	24	approximating	approximate	VERB
ap-10701	321	25	nonlinear	nonlinear	ADJ
ap-10701	321	26	dynamics	dynamic	NOUN
ap-10701	321	27	of	of	ADP
ap-10701	321	28	reaction	reaction	NOUN
ap-10701	321	29	diffusion	diffusion	NOUN
ap-10701	321	30	systems	system	NOUN
ap-10701	321	31	.	.	PUNCT
ap-10701	322	1	its	its	PRON
ap-10701	322	2	convergence	convergence	NOUN
ap-10701	322	3	is	be	AUX
ap-10701	322	4	shown	show	VERB
ap-10701	322	5	by	by	ADP
ap-10701	322	6	means	mean	NOUN
ap-10701	322	7	of	of	ADP
ap-10701	322	8	the	the	DET
ap-10701	322	9	generalized	generalized	ADJ
ap-10701	322	10	574	574	NUM
ap-10701	322	11	vol	vol	NOUN
ap-10701	322	12	.	.	PUNCT
ap-10701	323	1	65	65	NUM
ap-10701	323	2	no	no	NOUN
ap-10701	323	3	.	.	PUNCT
ap-10701	324	1	5/2025	5/2025	NUM
ap-10701	324	2	method	method	NOUN
ap-10701	324	3	of	of	ADP
ap-10701	324	4	lines	line	NOUN
ap-10701	324	5	for	for	ADP
ap-10701	324	6	reaction	reaction	NOUN
ap-10701	324	7	-	-	PUNCT
ap-10701	324	8	diffusion	diffusion	NOUN
ap-10701	324	9	systems	system	NOUN
ap-10701	324	10	.	.	PUNCT
ap-10701	324	11	.	.	PUNCT
ap-10701	324	12	.	.	PUNCT
ap-10701	325	1	figure	figure	VERB
ap-10701	325	2	5	5	NUM
ap-10701	325	3	.	.	PUNCT
ap-10701	325	4	fhn	fhn	ADJ
ap-10701	325	5	dynamics	dynamic	NOUN
ap-10701	325	6	.	.	PUNCT
ap-10701	326	1	convergence	convergence	NOUN
ap-10701	326	2	of	of	ADP
ap-10701	326	3	the	the	DET
ap-10701	326	4	space	space	NOUN
ap-10701	326	5	profile	profile	NOUN
ap-10701	326	6	of	of	ADP
ap-10701	326	7	the	the	DET
ap-10701	326	8	v	v	NOUN
ap-10701	326	9	-	-	PUNCT
ap-10701	326	10	component	component	NOUN
ap-10701	326	11	of	of	ADP
ap-10701	326	12	the	the	DET
ap-10701	326	13	solution	solution	NOUN
ap-10701	326	14	for	for	ADP
ap-10701	326	15	t	t	NOUN
ap-10701	326	16	=	=	SYM
ap-10701	326	17	160	160	NUM
ap-10701	326	18	.	.	PUNCT
ap-10701	326	19	figure	figure	NOUN
ap-10701	326	20	6	6	NUM
ap-10701	326	21	.	.	PUNCT
ap-10701	326	22	fhn	fhn	ADJ
ap-10701	326	23	dynamics	dynamic	NOUN
ap-10701	326	24	.	.	PUNCT
ap-10701	327	1	convergence	convergence	NOUN
ap-10701	327	2	of	of	ADP
ap-10701	327	3	the	the	DET
ap-10701	327	4	space	space	NOUN
ap-10701	327	5	profile	profile	NOUN
ap-10701	327	6	of	of	ADP
ap-10701	327	7	the	the	DET
ap-10701	327	8	w	w	NOUN
ap-10701	327	9	-	-	PUNCT
ap-10701	327	10	component	component	NOUN
ap-10701	327	11	of	of	ADP
ap-10701	327	12	the	the	DET
ap-10701	327	13	solution	solution	NOUN
ap-10701	327	14	for	for	ADP
ap-10701	327	15	t	t	NOUN
ap-10701	327	16	=	=	SYM
ap-10701	327	17	160	160	NUM
ap-10701	327	18	.	.	PUNCT
ap-10701	328	1	maximum	maximum	ADJ
ap-10701	328	2	principle	principle	NOUN
ap-10701	328	3	known	know	VERB
ap-10701	328	4	as	as	ADP
ap-10701	328	5	the	the	DET
ap-10701	328	6	invariant	invariant	ADJ
ap-10701	328	7	-	-	PUNCT
ap-10701	328	8	region	region	NOUN
ap-10701	328	9	concept	concept	NOUN
ap-10701	328	10	.	.	PUNCT
ap-10701	329	1	we	we	PRON
ap-10701	329	2	have	have	AUX
ap-10701	329	3	shown	show	VERB
ap-10701	329	4	that	that	SCONJ
ap-10701	329	5	the	the	DET
ap-10701	329	6	invariant	invariant	ADJ
ap-10701	329	7	-	-	PUNCT
ap-10701	329	8	region	region	NOUN
ap-10701	329	9	property	property	NOUN
ap-10701	329	10	carries	carry	VERB
ap-10701	329	11	over	over	ADP
ap-10701	329	12	to	to	ADP
ap-10701	329	13	the	the	DET
ap-10701	329	14	method	method	NOUN
ap-10701	329	15	of	of	ADP
ap-10701	329	16	lines	line	NOUN
ap-10701	329	17	,	,	PUNCT
ap-10701	329	18	thereby	thereby	ADV
ap-10701	329	19	facilitating	facilitate	VERB
ap-10701	329	20	the	the	DET
ap-10701	329	21	proofs	proof	NOUN
ap-10701	329	22	.	.	PUNCT
ap-10701	330	1	in	in	ADP
ap-10701	330	2	two	two	NUM
ap-10701	330	3	examples	example	NOUN
ap-10701	330	4	,	,	PUNCT
ap-10701	330	5	we	we	PRON
ap-10701	330	6	show	show	VERB
ap-10701	330	7	how	how	SCONJ
ap-10701	330	8	the	the	DET
ap-10701	330	9	method	method	NOUN
ap-10701	330	10	can	can	AUX
ap-10701	330	11	be	be	AUX
ap-10701	330	12	applied	apply	VERB
ap-10701	330	13	.	.	PUNCT
ap-10701	331	1	7	7	X
ap-10701	331	2	.	.	X
ap-10701	331	3	dedication	dedication	NOUN
ap-10701	331	4	the	the	DET
ap-10701	331	5	authors	author	NOUN
ap-10701	331	6	devote	devote	VERB
ap-10701	331	7	the	the	DET
ap-10701	331	8	text	text	NOUN
ap-10701	331	9	to	to	ADP
ap-10701	331	10	the	the	DET
ap-10701	331	11	memory	memory	NOUN
ap-10701	331	12	of	of	ADP
ap-10701	331	13	prof	prof	PROPN
ap-10701	331	14	.	.	PUNCT
ap-10701	332	1	ing	ing	PROPN
ap-10701	332	2	.	.	PUNCT
ap-10701	333	1	miloslav	miloslav	PROPN
ap-10701	333	2	havlíček	havlíček	PROPN
ap-10701	333	3	,	,	PUNCT
ap-10701	333	4	drsc	drsc	PROPN
ap-10701	333	5	.	.	PUNCT
ap-10701	334	1	acknowledgements	acknowledgement	NOUN
ap-10701	334	2	the	the	DET
ap-10701	334	3	authors	author	NOUN
ap-10701	334	4	were	be	AUX
ap-10701	334	5	partly	partly	ADV
ap-10701	334	6	supported	support	VERB
ap-10701	334	7	by	by	ADP
ap-10701	334	8	the	the	DET
ap-10701	334	9	project	project	NOUN
ap-10701	334	10	2518265s	2518265s	NUM
ap-10701	334	11	of	of	ADP
ap-10701	334	12	the	the	DET
ap-10701	334	13	czech	czech	PROPN
ap-10701	334	14	science	science	NOUN
ap-10701	334	15	foundation	foundation	PROPN
ap-10701	334	16	,	,	PUNCT
ap-10701	334	17	and	and	CCONJ
ap-10701	334	18	by	by	ADP
ap-10701	334	19	the	the	DET
ap-10701	334	20	ctu	ctu	NOUN
ap-10701	334	21	under	under	ADP
ap-10701	334	22	the	the	DET
ap-10701	334	23	grant	grant	NOUN
ap-10701	334	24	no	no	INTJ
ap-10701	334	25	.	.	PUNCT
ap-10701	335	1	sgs23/188	sgs23/188	NOUN
ap-10701	335	2	/	/	SYM
ap-10701	335	3	ohk4/3t/14	ohk4/3t/14	PROPN
ap-10701	335	4	.	.	PUNCT
ap-10701	336	1	the	the	DET
ap-10701	336	2	second	second	ADJ
ap-10701	336	3	author	author	NOUN
ap-10701	336	4	is	be	AUX
ap-10701	336	5	grateful	grateful	ADJ
ap-10701	336	6	to	to	PART
ap-10701	336	7	prof	prof	VERB
ap-10701	336	8	.	.	PUNCT
ap-10701	337	1	ing	ing	PROPN
ap-10701	337	2	.	.	PUNCT
ap-10701	338	1	miloslav	miloslav	PROPN
ap-10701	338	2	havlíček	havlíček	PROPN
ap-10701	338	3	,	,	PUNCT
ap-10701	338	4	drsc	drsc	PROPN
ap-10701	338	5	.	.	PUNCT
ap-10701	339	1	for	for	ADP
ap-10701	339	2	his	his	PRON
ap-10701	339	3	encouragement	encouragement	NOUN
ap-10701	339	4	,	,	PUNCT
ap-10701	339	5	interest	interest	NOUN
ap-10701	339	6	in	in	ADP
ap-10701	339	7	results	result	NOUN
ap-10701	339	8	of	of	ADP
ap-10701	339	9	the	the	DET
ap-10701	339	10	research	research	NOUN
ap-10701	339	11	,	,	PUNCT
ap-10701	339	12	kind	kind	ADJ
ap-10701	339	13	and	and	CCONJ
ap-10701	339	14	friendly	friendly	ADJ
ap-10701	339	15	attitude	attitude	NOUN
ap-10701	339	16	,	,	PUNCT
ap-10701	339	17	and	and	CCONJ
ap-10701	339	18	mediation	mediation	NOUN
ap-10701	339	19	of	of	ADP
ap-10701	339	20	international	international	ADJ
ap-10701	339	21	contacts	contact	NOUN
ap-10701	339	22	which	which	PRON
ap-10701	339	23	led	lead	VERB
ap-10701	339	24	to	to	ADP
ap-10701	339	25	many	many	ADJ
ap-10701	339	26	results	result	NOUN
ap-10701	339	27	at	at	ADP
ap-10701	339	28	the	the	DET
ap-10701	339	29	scientific	scientific	ADJ
ap-10701	339	30	as	as	ADV
ap-10701	339	31	well	well	ADV
ap-10701	339	32	as	as	ADP
ap-10701	339	33	educational	educational	ADJ
ap-10701	339	34	level	level	NOUN
ap-10701	339	35	.	.	PUNCT
ap-10701	340	1	references	reference	NOUN
ap-10701	340	2	[	[	X
ap-10701	340	3	1	1	X
ap-10701	340	4	]	]	PUNCT
ap-10701	340	5	j.	j.	PROPN
ap-10701	340	6	smoller	smoller	PROPN
ap-10701	340	7	.	.	PUNCT
ap-10701	341	1	shock	shock	NOUN
ap-10701	341	2	waves	wave	NOUN
ap-10701	341	3	and	and	CCONJ
ap-10701	341	4	reaction	reaction	NOUN
ap-10701	341	5	–	–	PUNCT
ap-10701	341	6	diffusion	diffusion	NOUN
ap-10701	341	7	equations	equation	NOUN
ap-10701	341	8	.	.	PUNCT
ap-10701	342	1	springer	springer	NOUN
ap-10701	342	2	,	,	PUNCT
ap-10701	342	3	new	new	PROPN
ap-10701	342	4	york	york	PROPN
ap-10701	342	5	,	,	PUNCT
ap-10701	342	6	2nd	2nd	PROPN
ap-10701	342	7	edn	edn	PROPN
ap-10701	342	8	.	.	PUNCT
ap-10701	342	9	,	,	PUNCT
ap-10701	342	10	1994	1994	NUM
ap-10701	342	11	.	.	PUNCT
ap-10701	343	1	https://doi.org/10.1007/978-1-4612-0873-0	https://doi.org/10.1007/978-1-4612-0873-0	PROPN
ap-10701	343	2	[	[	X
ap-10701	343	3	2	2	NUM
ap-10701	343	4	]	]	PUNCT
ap-10701	343	5	m.	m.	NOUN
ap-10701	343	6	holodniok	holodniok	PROPN
ap-10701	343	7	,	,	PUNCT
ap-10701	343	8	m.	m.	NOUN
ap-10701	343	9	kubíček	kubíček	PROPN
ap-10701	343	10	,	,	PUNCT
ap-10701	343	11	m.	m.	NOUN
ap-10701	343	12	marek	marek	PROPN
ap-10701	343	13	.	.	PUNCT
ap-10701	344	1	metody	metody	ADJ
ap-10701	344	2	analýzy	analýzy	NOUN
ap-10701	344	3	nelineárních	nelineárních	ADJ
ap-10701	344	4	dynamických	dynamických	NOUN
ap-10701	344	5	modelů	modelů	NOUN
ap-10701	345	1	[	[	X
ap-10701	345	2	in	in	ADP
ap-10701	345	3	czech	czech	PROPN
ap-10701	345	4	;	;	PUNCT
ap-10701	345	5	methods	method	NOUN
ap-10701	345	6	of	of	ADP
ap-10701	345	7	the	the	DET
ap-10701	345	8	analysis	analysis	NOUN
ap-10701	345	9	of	of	ADP
ap-10701	345	10	nonlinear	nonlinear	ADJ
ap-10701	345	11	dynamical	dynamical	ADJ
ap-10701	345	12	models	model	NOUN
ap-10701	345	13	]	]	PUNCT
ap-10701	345	14	.	.	PUNCT
ap-10701	346	1	academia	academia	PROPN
ap-10701	346	2	,	,	PUNCT
ap-10701	346	3	prague	prague	PROPN
ap-10701	346	4	,	,	PUNCT
ap-10701	346	5	1986	1986	NUM
ap-10701	346	6	.	.	PUNCT
ap-10701	347	1	575	575	NUM
ap-10701	347	2	https://doi.org/10.1007/978-1-4612-0873-0	https://doi.org/10.1007/978-1-4612-0873-0	PROPN
ap-10701	347	3	niels	niels	PROPN
ap-10701	347	4	van	van	PROPN
ap-10701	347	5	der	der	PROPN
ap-10701	347	6	meer	meer	PROPN
ap-10701	347	7	,	,	PUNCT
ap-10701	347	8	michal	michal	PROPN
ap-10701	347	9	beneš	beneš	PROPN
ap-10701	347	10	acta	acta	PROPN
ap-10701	347	11	polytechnica	polytechnica	PROPN
ap-10701	348	1	[	[	X
ap-10701	348	2	3	3	NUM
ap-10701	348	3	]	]	PUNCT
ap-10701	348	4	r.	r.	NOUN
ap-10701	348	5	temam	temam	NOUN
ap-10701	348	6	.	.	PUNCT
ap-10701	349	1	infinite	infinite	ADJ
ap-10701	349	2	-	-	PUNCT
ap-10701	349	3	dimensional	dimensional	ADJ
ap-10701	349	4	dynamical	dynamical	ADJ
ap-10701	349	5	systems	system	NOUN
ap-10701	349	6	in	in	ADP
ap-10701	349	7	mechanics	mechanic	NOUN
ap-10701	349	8	and	and	CCONJ
ap-10701	349	9	physics	physics	PROPN
ap-10701	349	10	.	.	PUNCT
ap-10701	350	1	springer	springer	PROPN
ap-10701	350	2	,	,	PUNCT
ap-10701	350	3	new	new	PROPN
ap-10701	350	4	york	york	PROPN
ap-10701	350	5	,	,	PUNCT
ap-10701	350	6	1988	1988	NUM
ap-10701	350	7	.	.	PUNCT
ap-10701	351	1	isbn	isbn	ADJ
ap-10701	351	2	0	0	NUM
ap-10701	351	3	-	-	SYM
ap-10701	351	4	387	387	NUM
ap-10701	351	5	-	-	PUNCT
ap-10701	351	6	96638	96638	NUM
ap-10701	351	7	-	-	SYM
ap-10701	351	8	2	2	NUM
ap-10701	351	9	.	.	PUNCT
ap-10701	352	1	[	[	X
ap-10701	352	2	4	4	X
ap-10701	352	3	]	]	PUNCT
ap-10701	352	4	j.	j.	PROPN
ap-10701	352	5	d.	d.	PROPN
ap-10701	352	6	murray	murray	PROPN
ap-10701	352	7	.	.	PUNCT
ap-10701	353	1	mathematical	mathematical	ADJ
ap-10701	353	2	biology	biology	NOUN
ap-10701	353	3	.	.	PUNCT
ap-10701	354	1	springer	springer	NOUN
ap-10701	354	2	,	,	PUNCT
ap-10701	354	3	berlin	berlin	PROPN
ap-10701	354	4	,	,	PUNCT
ap-10701	354	5	heidelberg	heidelberg	PROPN
ap-10701	354	6	,	,	PUNCT
ap-10701	354	7	1993	1993	NUM
ap-10701	354	8	.	.	PUNCT
ap-10701	355	1	https://doi.org/10.1007/978-3-662-08542-4	https://doi.org/10.1007/978-3-662-08542-4	PRON
ap-10701	355	2	[	[	X
ap-10701	355	3	5	5	X
ap-10701	355	4	]	]	PUNCT
ap-10701	355	5	j.	j.	PROPN
ap-10701	355	6	kantner	kantner	PROPN
ap-10701	355	7	,	,	PUNCT
ap-10701	355	8	m.	m.	NOUN
ap-10701	355	9	beneš	beneš	PROPN
ap-10701	355	10	.	.	PUNCT
ap-10701	356	1	mathematical	mathematical	ADJ
ap-10701	356	2	model	model	NOUN
ap-10701	356	3	of	of	ADP
ap-10701	356	4	signal	signal	ADJ
ap-10701	356	5	propagation	propagation	NOUN
ap-10701	356	6	in	in	ADP
ap-10701	356	7	excitable	excitable	ADJ
ap-10701	356	8	media	medium	NOUN
ap-10701	356	9	.	.	PUNCT
ap-10701	357	1	discrete	discrete	ADJ
ap-10701	357	2	and	and	CCONJ
ap-10701	357	3	continuous	continuous	ADJ
ap-10701	357	4	dynamical	dynamical	ADJ
ap-10701	357	5	systems	system	NOUN
ap-10701	357	6	–	–	PUNCT
ap-10701	357	7	series	series	NOUN
ap-10701	357	8	s	s	PROPN
ap-10701	357	9	14(3):935	14(3):935	PROPN
ap-10701	357	10	–	–	PUNCT
ap-10701	357	11	951	951	NUM
ap-10701	357	12	,	,	PUNCT
ap-10701	357	13	2021	2021	NUM
ap-10701	357	14	.	.	PUNCT
ap-10701	358	1	https://doi.org/10.3934/dcdss.2020382	https://doi.org/10.3934/dcdss.2020382	NOUN
ap-10701	359	1	[	[	X
ap-10701	359	2	6	6	NUM
ap-10701	359	3	]	]	PUNCT
ap-10701	359	4	f.	f.	PROPN
ap-10701	359	5	verhulst	verhulst	PROPN
ap-10701	359	6	.	.	PUNCT
ap-10701	360	1	nonlinear	nonlinear	ADJ
ap-10701	360	2	differential	differential	ADJ
ap-10701	360	3	equations	equation	NOUN
ap-10701	360	4	and	and	CCONJ
ap-10701	360	5	dynamical	dynamical	ADJ
ap-10701	360	6	systems	system	NOUN
ap-10701	360	7	.	.	PUNCT
ap-10701	361	1	springer	springer	NOUN
ap-10701	361	2	,	,	PUNCT
ap-10701	361	3	berlin	berlin	PROPN
ap-10701	361	4	,	,	PUNCT
ap-10701	361	5	heidelberg	heidelberg	PROPN
ap-10701	361	6	,	,	PUNCT
ap-10701	361	7	1996	1996	NUM
ap-10701	361	8	.	.	PUNCT
ap-10701	362	1	https://doi.org/10.1007/978-3-642-61453-8	https://doi.org/10.1007/978-3-642-61453-8	NUM
ap-10701	363	1	[	[	X
ap-10701	363	2	7	7	X
ap-10701	363	3	]	]	X
ap-10701	363	4	t.	t.	NOUN
ap-10701	363	5	ohta	ohta	PROPN
ap-10701	363	6	,	,	PUNCT
ap-10701	363	7	m.	m.	NOUN
ap-10701	363	8	mimura	mimura	PROPN
ap-10701	363	9	,	,	PUNCT
ap-10701	363	10	r.	r.	PROPN
ap-10701	363	11	kobayashi	kobayashi	PROPN
ap-10701	363	12	.	.	PUNCT
ap-10701	364	1	higherdimensional	higherdimensional	ADJ
ap-10701	364	2	localized	localize	VERB
ap-10701	364	3	patterns	pattern	NOUN
ap-10701	364	4	in	in	ADP
ap-10701	364	5	excitable	excitable	ADJ
ap-10701	364	6	media	medium	NOUN
ap-10701	364	7	.	.	PUNCT
ap-10701	365	1	physica	physica	NOUN
ap-10701	365	2	d	d	NOUN
ap-10701	365	3	:	:	PUNCT
ap-10701	365	4	nonlinear	nonlinear	ADJ
ap-10701	365	5	phenomena	phenomena	NOUN
ap-10701	365	6	34(1):115–144	34(1):115–144	NUM
ap-10701	365	7	,	,	PUNCT
ap-10701	365	8	1989	1989	NUM
ap-10701	365	9	.	.	PUNCT
ap-10701	366	1	https://doi.org/10.1016/0167-2789(89)90230-3	https://doi.org/10.1016/0167-2789(89)90230-3	NUM
ap-10701	367	1	[	[	X
ap-10701	367	2	8	8	NUM
ap-10701	367	3	]	]	X
ap-10701	367	4	o.	o.	NOUN
ap-10701	367	5	penrose	penrose	PROPN
ap-10701	367	6	,	,	PUNCT
ap-10701	367	7	p.	p.	PROPN
ap-10701	367	8	c.	c.	PROPN
ap-10701	367	9	fife	fife	PROPN
ap-10701	367	10	.	.	PUNCT
ap-10701	368	1	on	on	ADP
ap-10701	368	2	the	the	DET
ap-10701	368	3	relation	relation	NOUN
ap-10701	368	4	between	between	ADP
ap-10701	368	5	the	the	DET
ap-10701	368	6	standard	standard	ADJ
ap-10701	368	7	phase	phase	NOUN
ap-10701	368	8	-	-	PUNCT
ap-10701	368	9	field	field	NOUN
ap-10701	368	10	model	model	NOUN
ap-10701	368	11	and	and	CCONJ
ap-10701	368	12	a	a	DET
ap-10701	368	13	“	"	PUNCT
ap-10701	368	14	thermodynamically	thermodynamically	ADV
ap-10701	368	15	consistent	consistent	ADJ
ap-10701	368	16	”	"	PUNCT
ap-10701	368	17	phase	phase	NOUN
ap-10701	368	18	-	-	PUNCT
ap-10701	368	19	field	field	NOUN
ap-10701	368	20	model	model	NOUN
ap-10701	368	21	.	.	PUNCT
ap-10701	369	1	physica	physica	NOUN
ap-10701	369	2	d	d	NOUN
ap-10701	369	3	:	:	PUNCT
ap-10701	369	4	nonlinear	nonlinear	ADJ
ap-10701	369	5	phenomena	phenomenon	NOUN
ap-10701	369	6	69(1):107–113	69(1):107–113	NUM
ap-10701	369	7	,	,	PUNCT
ap-10701	369	8	1993	1993	NUM
ap-10701	369	9	.	.	PUNCT
ap-10701	370	1	https://doi.org/10.1016/0167-2789(93)90183-2	https://doi.org/10.1016/0167-2789(93)90183-2	PROPN
ap-10701	371	1	[	[	PUNCT
ap-10701	371	2	9	9	NUM
ap-10701	371	3	]	]	PUNCT
ap-10701	371	4	m.	m.	NOUN
ap-10701	371	5	beneš	beneš	PROPN
ap-10701	371	6	.	.	PUNCT
ap-10701	372	1	numerical	numerical	ADJ
ap-10701	372	2	solution	solution	NOUN
ap-10701	372	3	of	of	ADP
ap-10701	372	4	phase	phase	NOUN
ap-10701	372	5	-	-	PUNCT
ap-10701	372	6	field	field	NOUN
ap-10701	372	7	equations	equation	NOUN
ap-10701	372	8	with	with	ADP
ap-10701	372	9	a	a	DET
ap-10701	372	10	gradient	gradient	ADJ
ap-10701	372	11	coupling	coupling	NOUN
ap-10701	372	12	term	term	NOUN
ap-10701	372	13	.	.	PUNCT
ap-10701	373	1	in	in	ADP
ap-10701	373	2	w.	w.	PROPN
ap-10701	373	3	jäger	jäger	PROPN
ap-10701	373	4	,	,	PUNCT
ap-10701	373	5	j.	j.	PROPN
ap-10701	373	6	nečas	nečas	PROPN
ap-10701	373	7	,	,	PUNCT
ap-10701	373	8	o.	o.	PROPN
ap-10701	373	9	john	john	PROPN
ap-10701	373	10	,	,	PUNCT
ap-10701	373	11	et	et	PROPN
ap-10701	373	12	al	al	PROPN
ap-10701	373	13	.	.	PUNCT
ap-10701	374	1	(	(	PUNCT
ap-10701	374	2	eds	ed	NOUN
ap-10701	374	3	.	.	PUNCT
ap-10701	374	4	)	)	PUNCT
ap-10701	374	5	,	,	PUNCT
ap-10701	374	6	partial	partial	ADJ
ap-10701	374	7	differential	differential	NOUN
ap-10701	374	8	equations	equation	NOUN
ap-10701	374	9	–	–	PUNCT
ap-10701	374	10	theory	theory	NOUN
ap-10701	374	11	and	and	CCONJ
ap-10701	374	12	numerical	numerical	ADJ
ap-10701	374	13	solution	solution	NOUN
ap-10701	374	14	,	,	PUNCT
ap-10701	374	15	pp	pp	ADV
ap-10701	374	16	.	.	PUNCT
ap-10701	375	1	25–33	25–33	NUM
ap-10701	375	2	.	.	PUNCT
ap-10701	376	1	new	new	PROPN
ap-10701	376	2	york	york	PROPN
ap-10701	376	3	,	,	PUNCT
ap-10701	376	4	2000	2000	NUM
ap-10701	376	5	.	.	PUNCT
ap-10701	377	1	[	[	X
ap-10701	377	2	10	10	NUM
ap-10701	377	3	]	]	PUNCT
ap-10701	377	4	m.	m.	NOUN
ap-10701	377	5	beneš	beneš	NOUN
ap-10701	377	6	.	.	PUNCT
ap-10701	378	1	mathematical	mathematical	ADJ
ap-10701	378	2	analysis	analysis	NOUN
ap-10701	378	3	of	of	ADP
ap-10701	378	4	phase	phase	NOUN
ap-10701	378	5	-	-	PUNCT
ap-10701	378	6	field	field	NOUN
ap-10701	378	7	equations	equation	NOUN
ap-10701	378	8	with	with	ADP
ap-10701	378	9	numerically	numerically	ADV
ap-10701	378	10	efficient	efficient	ADJ
ap-10701	378	11	coupling	coupling	NOUN
ap-10701	378	12	terms	term	NOUN
ap-10701	378	13	.	.	PUNCT
ap-10701	379	1	interfaces	interface	NOUN
ap-10701	379	2	and	and	CCONJ
ap-10701	379	3	free	free	ADJ
ap-10701	379	4	boundaries	boundary	NOUN
ap-10701	379	5	3(2):201–212	3(2):201–212	NUM
ap-10701	379	6	,	,	PUNCT
ap-10701	379	7	2001	2001	NUM
ap-10701	379	8	.	.	PUNCT
ap-10701	380	1	https://doi.org/10.4171/ifb/38	https://doi.org/10.4171/ifb/38	X
ap-10701	380	2	[	[	X
ap-10701	380	3	11	11	NUM
ap-10701	380	4	]	]	PUNCT
ap-10701	380	5	m.	m.	NOUN
ap-10701	380	6	beneš	beneš	NOUN
ap-10701	380	7	,	,	PUNCT
ap-10701	380	8	v.	v.	ADP
ap-10701	380	9	chalupecký	chalupecký	NOUN
ap-10701	380	10	,	,	PUNCT
ap-10701	380	11	k.	k.	PROPN
ap-10701	380	12	mikula	mikula	PROPN
ap-10701	380	13	.	.	PUNCT
ap-10701	381	1	geometrical	geometrical	ADJ
ap-10701	381	2	image	image	NOUN
ap-10701	381	3	segmentation	segmentation	NOUN
ap-10701	381	4	by	by	ADP
ap-10701	381	5	the	the	DET
ap-10701	381	6	allen	allen	PROPN
ap-10701	381	7	-	-	PUNCT
ap-10701	381	8	cahn	cahn	NOUN
ap-10701	381	9	equation	equation	NOUN
ap-10701	381	10	.	.	PUNCT
ap-10701	382	1	applied	apply	VERB
ap-10701	382	2	numerical	numerical	ADJ
ap-10701	382	3	mathematics	mathematics	PROPN
ap-10701	382	4	51(2–3):187–205	51(2–3):187–205	NOUN
ap-10701	382	5	,	,	PUNCT
ap-10701	382	6	2004	2004	NUM
ap-10701	382	7	.	.	PUNCT
ap-10701	383	1	https://doi.org/10.1016/j.apnum.2004.05.001	https://doi.org/10.1016/j.apnum.2004.05.001	VERB
ap-10701	383	2	[	[	X
ap-10701	383	3	12	12	NUM
ap-10701	383	4	]	]	PUNCT
ap-10701	383	5	d.	d.	PROPN
ap-10701	383	6	hoff	hoff	PROPN
ap-10701	383	7	.	.	PUNCT
ap-10701	384	1	stability	stability	NOUN
ap-10701	384	2	and	and	CCONJ
ap-10701	384	3	convergence	convergence	NOUN
ap-10701	384	4	of	of	ADP
ap-10701	384	5	finite	finite	ADJ
ap-10701	384	6	difference	difference	NOUN
ap-10701	384	7	methods	method	NOUN
ap-10701	384	8	for	for	ADP
ap-10701	384	9	systems	system	NOUN
ap-10701	384	10	of	of	ADP
ap-10701	384	11	nonlinear	nonlinear	ADJ
ap-10701	384	12	reaction	reaction	NOUN
ap-10701	384	13	-	-	PUNCT
ap-10701	384	14	diffusion	diffusion	NOUN
ap-10701	384	15	equations	equation	NOUN
ap-10701	384	16	.	.	PUNCT
ap-10701	385	1	siam	siam	PROPN
ap-10701	385	2	journal	journal	PROPN
ap-10701	385	3	on	on	ADP
ap-10701	385	4	numerical	numerical	ADJ
ap-10701	385	5	analysis	analysis	NOUN
ap-10701	385	6	15(6):1161–1177	15(6):1161–1177	NUM
ap-10701	385	7	,	,	PUNCT
ap-10701	385	8	1978	1978	NUM
ap-10701	385	9	.	.	PUNCT
ap-10701	386	1	https://doi.org/10.1137/0715077	https://doi.org/10.1137/0715077	PROPN
ap-10701	387	1	[	[	X
ap-10701	387	2	13	13	NUM
ap-10701	387	3	]	]	PUNCT
ap-10701	387	4	j.	j.	PROPN
ap-10701	387	5	mach	mach	PROPN
ap-10701	387	6	,	,	PUNCT
ap-10701	387	7	m.	m.	NOUN
ap-10701	387	8	beneš	beneš	NOUN
ap-10701	387	9	,	,	PUNCT
ap-10701	387	10	p.	p.	NOUN
ap-10701	387	11	strachota	strachota	NOUN
ap-10701	387	12	.	.	PUNCT
ap-10701	388	1	nonlinear	nonlinear	ADJ
ap-10701	388	2	galerkin	galerkin	PROPN
ap-10701	388	3	finite	finite	PROPN
ap-10701	388	4	element	element	NOUN
ap-10701	388	5	method	method	NOUN
ap-10701	388	6	applied	apply	VERB
ap-10701	388	7	to	to	ADP
ap-10701	388	8	the	the	DET
ap-10701	388	9	system	system	NOUN
ap-10701	388	10	of	of	ADP
ap-10701	388	11	reactiondiffusion	reactiondiffusion	NOUN
ap-10701	388	12	equations	equation	NOUN
ap-10701	388	13	in	in	ADP
ap-10701	388	14	one	one	NUM
ap-10701	388	15	space	space	NOUN
ap-10701	388	16	dimension	dimension	NOUN
ap-10701	388	17	.	.	PUNCT
ap-10701	389	1	computers	computer	NOUN
ap-10701	389	2	&	&	CCONJ
ap-10701	389	3	mathematics	mathematic	NOUN
ap-10701	389	4	with	with	ADP
ap-10701	389	5	applications	application	NOUN
ap-10701	389	6	73(9):2053–2065	73(9):2053–2065	PROPN
ap-10701	389	7	,	,	PUNCT
ap-10701	389	8	2017	2017	NUM
ap-10701	389	9	.	.	PUNCT
ap-10701	390	1	https://doi.org/10.1016/j.camwa.2017.02.032	https://doi.org/10.1016/j.camwa.2017.02.032	NUM
ap-10701	390	2	[	[	X
ap-10701	390	3	14	14	NUM
ap-10701	390	4	]	]	PUNCT
ap-10701	390	5	m.	m.	NOUN
ap-10701	390	6	frittelli	frittelli	PROPN
ap-10701	390	7	,	,	PUNCT
ap-10701	390	8	a.	a.	NOUN
ap-10701	390	9	madzvamuse	madzvamuse	PROPN
ap-10701	390	10	,	,	PUNCT
ap-10701	390	11	i.	i.	PROPN
ap-10701	390	12	sgura	sgura	PROPN
ap-10701	390	13	,	,	PUNCT
ap-10701	390	14	c.	c.	PROPN
ap-10701	390	15	venkataraman	venkataraman	NOUN
ap-10701	390	16	.	.	PUNCT
ap-10701	391	1	preserving	preserve	VERB
ap-10701	391	2	invariance	invariance	NOUN
ap-10701	391	3	properties	property	NOUN
ap-10701	391	4	of	of	ADP
ap-10701	391	5	reaction	reaction	NOUN
ap-10701	391	6	–	–	PUNCT
ap-10701	391	7	diffusion	diffusion	NOUN
ap-10701	391	8	systems	system	NOUN
ap-10701	391	9	on	on	ADP
ap-10701	391	10	stationary	stationary	ADJ
ap-10701	391	11	surfaces	surface	NOUN
ap-10701	391	12	.	.	PUNCT
ap-10701	392	1	i	i	PRON
ap-10701	392	2	m	m	VERB
ap-10701	392	3	a	a	DET
ap-10701	392	4	journal	journal	NOUN
ap-10701	392	5	of	of	ADP
ap-10701	392	6	numerical	numerical	ADJ
ap-10701	392	7	analysis	analysis	NOUN
ap-10701	392	8	39(1):235–270	39(1):235–270	NUM
ap-10701	392	9	,	,	PUNCT
ap-10701	392	10	2017	2017	NUM
ap-10701	392	11	.	.	PUNCT
ap-10701	393	1	https://doi.org/10.1093/imanum/drx058	https://doi.org/10.1093/imanum/drx058	NOUN
ap-10701	393	2	[	[	X
ap-10701	393	3	15	15	NUM
ap-10701	393	4	]	]	X
ap-10701	393	5	j.	j.	PROPN
ap-10701	393	6	šembera	šembera	PROPN
ap-10701	393	7	,	,	PUNCT
ap-10701	393	8	m.	m.	NOUN
ap-10701	393	9	beneš	beneš	PROPN
ap-10701	393	10	.	.	PUNCT
ap-10701	394	1	nonlinear	nonlinear	ADJ
ap-10701	394	2	galerkin	galerkin	PROPN
ap-10701	394	3	method	method	NOUN
ap-10701	394	4	for	for	ADP
ap-10701	394	5	reaction	reaction	NOUN
ap-10701	394	6	–	–	PUNCT
ap-10701	394	7	diffusion	diffusion	NOUN
ap-10701	394	8	systems	system	NOUN
ap-10701	394	9	admitting	admit	VERB
ap-10701	394	10	invariant	invariant	ADJ
ap-10701	394	11	regions	region	NOUN
ap-10701	394	12	.	.	PUNCT
ap-10701	395	1	journal	journal	NOUN
ap-10701	395	2	of	of	ADP
ap-10701	395	3	computational	computational	ADJ
ap-10701	395	4	and	and	CCONJ
ap-10701	395	5	applied	applied	ADJ
ap-10701	395	6	mathematics	mathematic	NOUN
ap-10701	395	7	136(1–2):163–176	136(1–2):163–176	NUM
ap-10701	395	8	,	,	PUNCT
ap-10701	395	9	2001	2001	NUM
ap-10701	395	10	.	.	PUNCT
ap-10701	396	1	https://doi.org/10.1016/s0377-0427(00)00582-3	https://doi.org/10.1016/s0377-0427(00)00582-3	PROPN
ap-10701	397	1	[	[	X
ap-10701	397	2	16	16	NUM
ap-10701	397	3	]	]	PUNCT
ap-10701	397	4	m.	m.	NOUN
ap-10701	397	5	kolář	kolář	NOUN
ap-10701	397	6	.	.	PUNCT
ap-10701	398	1	computational	computational	ADJ
ap-10701	398	2	studies	study	NOUN
ap-10701	398	3	of	of	ADP
ap-10701	398	4	reaction	reaction	NOUN
ap-10701	398	5	-	-	PUNCT
ap-10701	398	6	diffusion	diffusion	NOUN
ap-10701	398	7	systems	system	NOUN
ap-10701	398	8	by	by	ADP
ap-10701	398	9	nonlinear	nonlinear	ADJ
ap-10701	398	10	galerkin	galerkin	PROPN
ap-10701	398	11	method	method	NOUN
ap-10701	398	12	.	.	PUNCT
ap-10701	399	1	american	american	PROPN
ap-10701	399	2	journal	journal	PROPN
ap-10701	399	3	of	of	ADP
ap-10701	399	4	computational	computational	ADJ
ap-10701	399	5	mathematics	mathematic	NOUN
ap-10701	399	6	3(2):137–146	3(2):137–146	NUM
ap-10701	399	7	,	,	PUNCT
ap-10701	399	8	2013	2013	NUM
ap-10701	399	9	.	.	PUNCT
ap-10701	400	1	https://doi.org/10.4236/ajcm.2013.32022	https://doi.org/10.4236/ajcm.2013.32022	PROPN
ap-10701	401	1	[	[	X
ap-10701	401	2	17	17	NUM
ap-10701	401	3	]	]	X
ap-10701	401	4	j.	j.	PROPN
ap-10701	401	5	mach	mach	PROPN
ap-10701	401	6	.	.	PUNCT
ap-10701	402	1	application	application	NOUN
ap-10701	402	2	of	of	ADP
ap-10701	402	3	the	the	DET
ap-10701	402	4	nonlinear	nonlinear	ADJ
ap-10701	402	5	galerkin	galerkin	ADJ
ap-10701	402	6	fem	fem	NOUN
ap-10701	402	7	method	method	NOUN
ap-10701	402	8	to	to	ADP
ap-10701	402	9	the	the	DET
ap-10701	402	10	numerical	numerical	ADJ
ap-10701	402	11	solution	solution	NOUN
ap-10701	402	12	of	of	ADP
ap-10701	402	13	a	a	DET
ap-10701	402	14	reaction	reaction	NOUN
ap-10701	402	15	-	-	PUNCT
ap-10701	402	16	diffusion	diffusion	NOUN
ap-10701	402	17	system	system	NOUN
ap-10701	402	18	in	in	ADP
ap-10701	402	19	two	two	NUM
ap-10701	402	20	dimensions	dimension	NOUN
ap-10701	402	21	.	.	PUNCT
ap-10701	403	1	rims	rims	PROPN
ap-10701	403	2	kokyuroku	kokyuroku	PROPN
ap-10701	403	3	bessatsu	bessatsu	PROPN
ap-10701	403	4	b35:95–113	b35:95–113	PROPN
ap-10701	403	5	,	,	PUNCT
ap-10701	403	6	2012	2012	NUM
ap-10701	403	7	.	.	PUNCT
ap-10701	404	1	[	[	X
ap-10701	404	2	18	18	NUM
ap-10701	404	3	]	]	PUNCT
ap-10701	404	4	m.	m.	NOUN
ap-10701	404	5	beneš	beneš	PROPN
ap-10701	404	6	,	,	PUNCT
ap-10701	404	7	k.	k.	PROPN
ap-10701	404	8	mikula	mikula	PROPN
ap-10701	404	9	,	,	PUNCT
ap-10701	404	10	t.	t.	NOUN
ap-10701	404	11	oberhuber	oberhuber	PROPN
ap-10701	404	12	,	,	PUNCT
ap-10701	404	13	d.	d.	PROPN
ap-10701	404	14	ševčovič	ševčovič	PROPN
ap-10701	404	15	.	.	PUNCT
ap-10701	405	1	comparison	comparison	NOUN
ap-10701	405	2	study	study	NOUN
ap-10701	405	3	for	for	ADP
ap-10701	405	4	level	level	NOUN
ap-10701	405	5	set	set	VERB
ap-10701	405	6	and	and	CCONJ
ap-10701	405	7	direct	direct	ADJ
ap-10701	405	8	lagrangian	lagrangian	ADJ
ap-10701	405	9	methods	method	NOUN
ap-10701	405	10	for	for	ADP
ap-10701	405	11	computing	computing	NOUN
ap-10701	405	12	willmore	willmore	NOUN
ap-10701	405	13	flow	flow	NOUN
ap-10701	405	14	of	of	ADP
ap-10701	405	15	closed	closed	ADJ
ap-10701	405	16	planar	planar	ADJ
ap-10701	405	17	curves	curve	NOUN
ap-10701	405	18	.	.	PUNCT
ap-10701	406	1	computing	computing	NOUN
ap-10701	406	2	and	and	CCONJ
ap-10701	406	3	visualization	visualization	NOUN
ap-10701	406	4	in	in	ADP
ap-10701	406	5	science	science	NOUN
ap-10701	406	6	12(6):307–317	12(6):307–317	NOUN
ap-10701	406	7	,	,	PUNCT
ap-10701	406	8	2009	2009	NUM
ap-10701	406	9	.	.	PUNCT
ap-10701	407	1	https://doi.org/10.1007/s00791-008-0112-2	https://doi.org/10.1007/s00791-008-0112-2	PUNCT
ap-10701	408	1	[	[	X
ap-10701	408	2	19	19	NUM
ap-10701	408	3	]	]	PUNCT
ap-10701	408	4	p.	p.	PROPN
ap-10701	408	5	pauš	pauš	PROPN
ap-10701	408	6	.	.	PUNCT
ap-10701	409	1	numerical	numerical	PROPN
ap-10701	409	2	simulation	simulation	PROPN
ap-10701	409	3	of	of	ADP
ap-10701	409	4	dislocation	dislocation	NOUN
ap-10701	409	5	dynamics	dynamic	NOUN
ap-10701	409	6	.	.	PUNCT
ap-10701	410	1	in	in	ADP
ap-10701	410	2	m.	m.	NOUN
ap-10701	410	3	vajsáblová	vajsáblová	NOUN
ap-10701	410	4	,	,	PUNCT
ap-10701	410	5	p.	p.	PROPN
ap-10701	410	6	struk	struk	PROPN
ap-10701	410	7	(	(	PUNCT
ap-10701	410	8	eds	ed	NOUN
ap-10701	410	9	.	.	PUNCT
ap-10701	410	10	)	)	PUNCT
ap-10701	410	11	,	,	PUNCT
ap-10701	410	12	proceedings	proceeding	NOUN
ap-10701	410	13	of	of	ADP
ap-10701	410	14	slovak	slovak	ADJ
ap-10701	410	15	–	–	PUNCT
ap-10701	410	16	austrian	austrian	ADJ
ap-10701	410	17	congress	congress	PROPN
ap-10701	410	18	,	,	PUNCT
ap-10701	410	19	magia	magia	PROPN
ap-10701	410	20	,	,	PUNCT
ap-10701	410	21	pp	pp	ADJ
ap-10701	410	22	.	.	PUNCT
ap-10701	411	1	45–52	45–52	NUM
ap-10701	411	2	.	.	PUNCT
ap-10701	412	1	bratislava	bratislava	PROPN
ap-10701	412	2	,	,	PUNCT
ap-10701	412	3	2007	2007	NUM
ap-10701	412	4	.	.	PUNCT
ap-10701	413	1	isbn	isbn	ADJ
ap-10701	413	2	978	978	NUM
ap-10701	413	3	-	-	SYM
ap-10701	413	4	80	80	NUM
ap-10701	413	5	-	-	PUNCT
ap-10701	413	6	227	227	NUM
ap-10701	413	7	-	-	PUNCT
ap-10701	413	8	2796	2796	NUM
ap-10701	413	9	-	-	SYM
ap-10701	413	10	9	9	NUM
ap-10701	413	11	.	.	PUNCT
ap-10701	414	1	[	[	X
ap-10701	414	2	20	20	NUM
ap-10701	414	3	]	]	PUNCT
ap-10701	414	4	m.	m.	NOUN
ap-10701	414	5	kolář	kolář	NOUN
ap-10701	414	6	,	,	PUNCT
ap-10701	414	7	d.	d.	PROPN
ap-10701	414	8	ševčovič	ševčovič	PROPN
ap-10701	414	9	.	.	PUNCT
ap-10701	415	1	evolution	evolution	NOUN
ap-10701	415	2	of	of	ADP
ap-10701	415	3	multiple	multiple	ADJ
ap-10701	415	4	closed	closed	ADJ
ap-10701	415	5	knotted	knotted	ADJ
ap-10701	415	6	curves	curve	NOUN
ap-10701	415	7	in	in	ADP
ap-10701	415	8	space	space	NOUN
ap-10701	415	9	.	.	PUNCT
ap-10701	416	1	in	in	ADP
ap-10701	416	2	p.	p.	PROPN
ap-10701	416	3	frolkovič	frolkovič	PROPN
ap-10701	416	4	,	,	PUNCT
ap-10701	416	5	k.	k.	PROPN
ap-10701	416	6	mikula	mikula	PROPN
ap-10701	416	7	,	,	PUNCT
ap-10701	416	8	d.	d.	PROPN
ap-10701	416	9	ševčovič	ševčovič	PROPN
ap-10701	416	10	(	(	PUNCT
ap-10701	416	11	eds	ed	NOUN
ap-10701	416	12	.	.	PUNCT
ap-10701	416	13	)	)	PUNCT
ap-10701	416	14	,	,	PUNCT
ap-10701	416	15	proceedings	proceeding	NOUN
ap-10701	416	16	of	of	ADP
ap-10701	416	17	the	the	DET
ap-10701	416	18	algoritmy	algoritmy	NOUN
ap-10701	416	19	2024	2024	NUM
ap-10701	416	20	conference	conference	NOUN
ap-10701	416	21	,	,	PUNCT
ap-10701	416	22	pp	pp	ADP
ap-10701	416	23	.	.	PUNCT
ap-10701	417	1	129–138	129–138	NUM
ap-10701	417	2	.	.	PUNCT
ap-10701	418	1	bratislava	bratislava	PROPN
ap-10701	418	2	,	,	PUNCT
ap-10701	418	3	2024	2024	NUM
ap-10701	418	4	.	.	PUNCT
ap-10701	419	1	[	[	X
ap-10701	419	2	21	21	NUM
ap-10701	419	3	]	]	PUNCT
ap-10701	419	4	m.	m.	NOUN
ap-10701	419	5	beneš	beneš	NOUN
ap-10701	419	6	.	.	PUNCT
ap-10701	419	7	phase	phase	NOUN
ap-10701	419	8	-	-	PUNCT
ap-10701	419	9	field	field	NOUN
ap-10701	419	10	model	model	NOUN
ap-10701	419	11	of	of	ADP
ap-10701	419	12	microstructure	microstructure	ADJ
ap-10701	419	13	growth	growth	NOUN
ap-10701	419	14	in	in	ADP
ap-10701	419	15	solidification	solidification	NOUN
ap-10701	419	16	of	of	ADP
ap-10701	419	17	pure	pure	ADJ
ap-10701	419	18	substances	substance	NOUN
ap-10701	419	19	.	.	PUNCT
ap-10701	420	1	ph.d	ph.d	PROPN
ap-10701	420	2	.	.	PUNCT
ap-10701	421	1	thesis	thesis	NOUN
ap-10701	421	2	,	,	PUNCT
ap-10701	421	3	czech	czech	PROPN
ap-10701	421	4	technical	technical	PROPN
ap-10701	421	5	university	university	PROPN
ap-10701	421	6	in	in	ADP
ap-10701	421	7	prague	prague	PROPN
ap-10701	421	8	,	,	PUNCT
ap-10701	421	9	faculty	faculty	NOUN
ap-10701	421	10	of	of	ADP
ap-10701	421	11	nuclear	nuclear	ADJ
ap-10701	421	12	sciences	science	NOUN
ap-10701	421	13	and	and	CCONJ
ap-10701	421	14	physical	physical	ADJ
ap-10701	421	15	engineering	engineering	NOUN
ap-10701	421	16	,	,	PUNCT
ap-10701	421	17	1997	1997	NUM
ap-10701	421	18	.	.	PUNCT
ap-10701	422	1	[	[	X
ap-10701	422	2	22	22	NUM
ap-10701	422	3	]	]	PUNCT
ap-10701	422	4	m.	m.	NOUN
ap-10701	422	5	beneš	beneš	NOUN
ap-10701	422	6	.	.	PUNCT
ap-10701	423	1	analysis	analysis	NOUN
ap-10701	423	2	of	of	ADP
ap-10701	423	3	equations	equation	NOUN
ap-10701	423	4	in	in	ADP
ap-10701	423	5	the	the	DET
ap-10701	423	6	phase	phase	NOUN
ap-10701	423	7	field	field	NOUN
ap-10701	423	8	model	model	NOUN
ap-10701	423	9	.	.	PUNCT
ap-10701	424	1	in	in	ADP
ap-10701	424	2	z.	z.	PROPN
ap-10701	424	3	došlá	došlá	PROPN
ap-10701	424	4	,	,	PUNCT
ap-10701	424	5	j.	j.	PROPN
ap-10701	424	6	kuben	kuben	PROPN
ap-10701	424	7	,	,	PUNCT
ap-10701	424	8	j.	j.	PROPN
ap-10701	424	9	vosmanský	vosmanský	PROPN
ap-10701	424	10	(	(	PUNCT
ap-10701	424	11	eds	ed	NOUN
ap-10701	424	12	.	.	PUNCT
ap-10701	424	13	)	)	PUNCT
ap-10701	424	14	,	,	PUNCT
ap-10701	424	15	proceedings	proceeding	NOUN
ap-10701	424	16	of	of	ADP
ap-10701	424	17	equadiff	equadiff	NOUN
ap-10701	424	18	9	9	NUM
ap-10701	424	19	,	,	PUNCT
ap-10701	424	20	pp	pp	ADJ
ap-10701	424	21	.	.	PUNCT
ap-10701	425	1	17–35	17–35	NUM
ap-10701	425	2	.	.	PUNCT
ap-10701	425	3	brno	brno	NOUN
ap-10701	425	4	,	,	PUNCT
ap-10701	425	5	1998	1998	NUM
ap-10701	425	6	.	.	PUNCT
ap-10701	426	1	[	[	X
ap-10701	426	2	2025	2025	NUM
ap-10701	426	3	-	-	SYM
ap-10701	426	4	06	06	NUM
ap-10701	426	5	-	-	SYM
ap-10701	426	6	30	30	NUM
ap-10701	426	7	]	]	PUNCT
ap-10701	426	8	.	.	PUNCT
ap-10701	427	1	https://dml.cz/handle/10338.dmlcz/700304	https://dml.cz/handle/10338.dmlcz/700304	PUNCT
ap-10701	428	1	[	[	X
ap-10701	428	2	23	23	NUM
ap-10701	428	3	]	]	PUNCT
ap-10701	428	4	l.	l.	PROPN
ap-10701	428	5	s.	s.	PROPN
ap-10701	428	6	pontryagin	pontryagin	PROPN
ap-10701	428	7	.	.	PUNCT
ap-10701	429	1	ordinary	ordinary	ADJ
ap-10701	429	2	differential	differential	ADJ
ap-10701	429	3	equations	equation	NOUN
ap-10701	429	4	.	.	PUNCT
ap-10701	430	1	addisson	addisson	PROPN
ap-10701	430	2	wesley	wesley	PROPN
ap-10701	430	3	publishing	publishing	PROPN
ap-10701	430	4	,	,	PUNCT
ap-10701	430	5	palo	palo	PROPN
ap-10701	430	6	alto	alto	PROPN
ap-10701	430	7	,	,	PUNCT
ap-10701	430	8	1962	1962	NUM
ap-10701	430	9	.	.	PUNCT
ap-10701	431	1	[	[	X
ap-10701	431	2	24	24	NUM
ap-10701	431	3	]	]	PUNCT
ap-10701	431	4	t.	t.	NOUN
ap-10701	431	5	roubíček	roubíček	NOUN
ap-10701	431	6	.	.	PUNCT
ap-10701	432	1	a	a	DET
ap-10701	432	2	generalization	generalization	NOUN
ap-10701	432	3	of	of	ADP
ap-10701	432	4	the	the	DET
ap-10701	432	5	lions	lion	NOUN
ap-10701	432	6	-	-	PUNCT
ap-10701	432	7	temam	temam	NOUN
ap-10701	432	8	compact	compact	ADJ
ap-10701	432	9	imbedding	imbedding	NOUN
ap-10701	432	10	theorem	theorem	VERB
ap-10701	432	11	.	.	PUNCT
ap-10701	433	1	časopis	časopis	ADJ
ap-10701	433	2	pro	pro	PROPN
ap-10701	433	3	pěstování	pěstování	PROPN
ap-10701	433	4	matematiky	matematiky	PROPN
ap-10701	433	5	115(4):338–342	115(4):338–342	PROPN
ap-10701	433	6	,	,	PUNCT
ap-10701	433	7	1990	1990	NUM
ap-10701	433	8	.	.	PUNCT
ap-10701	434	1	[	[	X
ap-10701	434	2	2025	2025	NUM
ap-10701	434	3	-	-	SYM
ap-10701	434	4	06	06	NUM
ap-10701	434	5	-	-	SYM
ap-10701	434	6	30	30	NUM
ap-10701	434	7	]	]	PUNCT
ap-10701	434	8	.	.	PUNCT
ap-10701	435	1	http://eudml.org/doc/21776	http://eudml.org/doc/21776	PROPN
ap-10701	436	1	[	[	X
ap-10701	436	2	25	25	NUM
ap-10701	436	3	]	]	X
ap-10701	436	4	j.-l	j.-l	ADJ
ap-10701	436	5	.	.	PUNCT
ap-10701	437	1	lions	lion	NOUN
ap-10701	437	2	.	.	PUNCT
ap-10701	438	1	quelques	quelques	PROPN
ap-10701	438	2	méthodes	méthode	NOUN
ap-10701	438	3	de	de	X
ap-10701	438	4	résolution	résolution	PROPN
ap-10701	438	5	des	des	X
ap-10701	438	6	problèmes	problèmes	PROPN
ap-10701	438	7	aux	aux	PROPN
ap-10701	438	8	limites	limites	PROPN
ap-10701	438	9	non	non	X
ap-10701	438	10	linéaires	linéaires	PROPN
ap-10701	439	1	[	[	X
ap-10701	439	2	in	in	ADP
ap-10701	439	3	french	french	NOUN
ap-10701	439	4	;	;	PUNCT
ap-10701	439	5	several	several	ADJ
ap-10701	439	6	solution	solution	NOUN
ap-10701	439	7	methods	method	NOUN
ap-10701	439	8	of	of	ADP
ap-10701	439	9	nonlinear	nonlinear	ADJ
ap-10701	439	10	boundary	boundary	ADJ
ap-10701	439	11	-	-	PUNCT
ap-10701	439	12	value	value	NOUN
ap-10701	439	13	problems	problem	NOUN
ap-10701	439	14	]	]	PUNCT
ap-10701	439	15	.	.	PUNCT
ap-10701	440	1	dunod	dunod	PROPN
ap-10701	440	2	,	,	PUNCT
ap-10701	440	3	gauthiers	gauthier	NOUN
ap-10701	440	4	-	-	PUNCT
ap-10701	440	5	villars	villar	NOUN
ap-10701	440	6	,	,	PUNCT
ap-10701	440	7	paris	paris	PROPN
ap-10701	440	8	,	,	PUNCT
ap-10701	440	9	1969	1969	NUM
ap-10701	440	10	.	.	PUNCT
ap-10701	441	1	[	[	X
ap-10701	441	2	26	26	NUM
ap-10701	441	3	]	]	X
ap-10701	441	4	r.	r.	NOUN
ap-10701	441	5	temam	temam	NOUN
ap-10701	441	6	.	.	PUNCT
ap-10701	442	1	navier	navier	NOUN
ap-10701	442	2	-	-	PUNCT
ap-10701	442	3	stokes	stoke	NOUN
ap-10701	442	4	equations	equation	NOUN
ap-10701	442	5	,	,	PUNCT
ap-10701	442	6	theory	theory	NOUN
ap-10701	442	7	and	and	CCONJ
ap-10701	442	8	numerical	numerical	ADJ
ap-10701	442	9	analysis	analysis	NOUN
ap-10701	442	10	.	.	PUNCT
ap-10701	443	1	north	north	NOUN
ap-10701	443	2	-	-	PUNCT
ap-10701	443	3	holland	holland	PROPN
ap-10701	443	4	,	,	PUNCT
ap-10701	443	5	amsterdam	amsterdam	PROPN
ap-10701	443	6	,	,	PUNCT
ap-10701	443	7	1979	1979	NUM
ap-10701	443	8	.	.	PUNCT
ap-10701	444	1	[	[	X
ap-10701	444	2	27	27	NUM
ap-10701	444	3	]	]	X
ap-10701	444	4	y.	y.	PROPN
ap-10701	444	5	ji	ji	PROPN
ap-10701	444	6	,	,	PUNCT
ap-10701	444	7	j.	j.	PROPN
ap-10701	444	8	shen	shen	PROPN
ap-10701	444	9	,	,	PUNCT
ap-10701	444	10	x.	x.	PROPN
ap-10701	444	11	mao	mao	PROPN
ap-10701	444	12	.	.	PUNCT
ap-10701	445	1	pattern	pattern	NOUN
ap-10701	445	2	formation	formation	NOUN
ap-10701	445	3	of	of	ADP
ap-10701	445	4	brusselator	brusselator	NOUN
ap-10701	445	5	in	in	ADP
ap-10701	445	6	the	the	DET
ap-10701	445	7	reaction	reaction	NOUN
ap-10701	445	8	-	-	PUNCT
ap-10701	445	9	diffusion	diffusion	NOUN
ap-10701	445	10	system	system	NOUN
ap-10701	445	11	.	.	PUNCT
ap-10701	446	1	discrete	discrete	ADJ
ap-10701	446	2	and	and	CCONJ
ap-10701	446	3	continuous	continuous	ADJ
ap-10701	446	4	dynamical	dynamical	ADJ
ap-10701	446	5	systems	system	NOUN
ap-10701	446	6	–	–	PUNCT
ap-10701	446	7	series	series	NOUN
ap-10701	446	8	s	s	PART
ap-10701	446	9	16(3–4):434	16(3–4):434	NOUN
ap-10701	446	10	–	–	PUNCT
ap-10701	446	11	459	459	NUM
ap-10701	446	12	,	,	PUNCT
ap-10701	446	13	2023	2023	NUM
ap-10701	446	14	.	.	PUNCT
ap-10701	446	15	https://doi.org/10.3934/dcdss.2022103	https://doi.org/10.3934/dcdss.2022103	PUNCT
ap-10701	447	1	[	[	X
ap-10701	447	2	28	28	NUM
ap-10701	447	3	]	]	X
ap-10701	447	4	g.	g.	PROPN
ap-10701	447	5	gambino	gambino	PROPN
ap-10701	447	6	,	,	PUNCT
ap-10701	447	7	v.	v.	PROPN
ap-10701	447	8	giunta	giunta	PROPN
ap-10701	447	9	,	,	PUNCT
ap-10701	447	10	m.	m.	NOUN
ap-10701	447	11	c.	c.	PROPN
ap-10701	447	12	lombardo	lombardo	PROPN
ap-10701	447	13	,	,	PUNCT
ap-10701	447	14	g.	g.	PROPN
ap-10701	447	15	rubino	rubino	PROPN
ap-10701	447	16	.	.	PUNCT
ap-10701	448	1	cross	cross	ADJ
ap-10701	448	2	-	-	ADJ
ap-10701	448	3	diffusion	diffusion	NOUN
ap-10701	448	4	effects	effect	NOUN
ap-10701	448	5	on	on	ADP
ap-10701	448	6	stationary	stationary	ADJ
ap-10701	448	7	pattern	pattern	NOUN
ap-10701	448	8	formation	formation	NOUN
ap-10701	448	9	in	in	ADP
ap-10701	448	10	the	the	DET
ap-10701	448	11	fitzhugh	fitzhugh	PROPN
ap-10701	448	12	-	-	PUNCT
ap-10701	448	13	nagumo	nagumo	ADJ
ap-10701	448	14	model	model	NOUN
ap-10701	448	15	.	.	PUNCT
ap-10701	449	1	discrete	discrete	ADJ
ap-10701	449	2	and	and	CCONJ
ap-10701	449	3	continuous	continuous	ADJ
ap-10701	449	4	dynamical	dynamical	ADJ
ap-10701	449	5	systems	system	NOUN
ap-10701	449	6	–	–	PUNCT
ap-10701	449	7	series	series	NOUN
ap-10701	449	8	b	b	PROPN
ap-10701	449	9	27(12):7783	27(12):7783	PROPN
ap-10701	449	10	–	–	PUNCT
ap-10701	449	11	7816	7816	NUM
ap-10701	449	12	,	,	PUNCT
ap-10701	449	13	2022	2022	NUM
ap-10701	449	14	.	.	PUNCT
ap-10701	450	1	https://doi.org/10.3934/dcdsb.2022063	https://doi.org/10.3934/dcdsb.2022063	ADJ
ap-10701	450	2	[	[	X
ap-10701	450	3	29	29	NUM
ap-10701	450	4	]	]	X
ap-10701	450	5	v.	v.	CCONJ
ap-10701	450	6	thomée	thomée	PROPN
ap-10701	450	7	,	,	PUNCT
ap-10701	450	8	l.	l.	PROPN
ap-10701	450	9	b.	b.	PROPN
ap-10701	450	10	wahlbin	wahlbin	PROPN
ap-10701	450	11	.	.	PUNCT
ap-10701	451	1	on	on	ADP
ap-10701	451	2	the	the	DET
ap-10701	451	3	existence	existence	NOUN
ap-10701	451	4	of	of	ADP
ap-10701	451	5	maximum	maximum	ADJ
ap-10701	451	6	principles	principle	NOUN
ap-10701	451	7	in	in	ADP
ap-10701	451	8	parabolic	parabolic	PROPN
ap-10701	451	9	finite	finite	PROPN
ap-10701	451	10	element	element	NOUN
ap-10701	451	11	equations	equation	NOUN
ap-10701	451	12	.	.	PUNCT
ap-10701	452	1	mathematics	mathematic	NOUN
ap-10701	452	2	of	of	ADP
ap-10701	452	3	computation	computation	NOUN
ap-10701	452	4	77(261):11–19	77(261):11–19	NOUN
ap-10701	452	5	,	,	PUNCT
ap-10701	452	6	2008	2008	NUM
ap-10701	452	7	.	.	PUNCT
ap-10701	452	8	https://doi.org/10.1090/s0025-5718-07-02021-2	https://doi.org/10.1090/s0025-5718-07-02021-2	PRON
ap-10701	453	1	[	[	X
ap-10701	453	2	30	30	NUM
ap-10701	453	3	]	]	X
ap-10701	453	4	a.	a.	NOUN
ap-10701	453	5	a.	a.	PROPN
ap-10701	453	6	samarskii	samarskii	PROPN
ap-10701	453	7	,	,	PUNCT
ap-10701	453	8	v.	v.	PROPN
ap-10701	453	9	b.	b.	PROPN
ap-10701	453	10	andreev	andreev	PROPN
ap-10701	453	11	.	.	PUNCT
ap-10701	454	1	raznostnyje	raznostnyje	PROPN
ap-10701	454	2	metody	metody	ADJ
ap-10701	454	3	dlja	dlja	ADJ
ap-10701	454	4	ellipticeskich	ellipticeskich	PROPN
ap-10701	454	5	uravnenij	uravnenij	VERB
ap-10701	455	1	[	[	X
ap-10701	455	2	in	in	ADP
ap-10701	455	3	russian	russian	ADJ
ap-10701	455	4	;	;	PUNCT
ap-10701	455	5	difference	difference	NOUN
ap-10701	455	6	methods	method	NOUN
ap-10701	455	7	for	for	ADP
ap-10701	455	8	elliptic	elliptic	ADJ
ap-10701	455	9	equations	equation	NOUN
ap-10701	455	10	]	]	PUNCT
ap-10701	455	11	.	.	PUNCT
ap-10701	456	1	nauka	nauka	PROPN
ap-10701	456	2	,	,	PUNCT
ap-10701	456	3	moscow	moscow	PROPN
ap-10701	456	4	,	,	PUNCT
ap-10701	456	5	1976	1976	NUM
ap-10701	456	6	.	.	PUNCT
ap-10701	457	1	[	[	X
ap-10701	457	2	31	31	NUM
ap-10701	457	3	]	]	PUNCT
ap-10701	457	4	a.	a.	NOUN
ap-10701	457	5	a.	a.	PROPN
ap-10701	457	6	samarskii	samarskii	PROPN
ap-10701	457	7	.	.	PUNCT
ap-10701	458	1	teorija	teorija	PROPN
ap-10701	458	2	raznostnych	raznostnych	PROPN
ap-10701	458	3	schem	schem	NOUN
ap-10701	459	1	[	[	X
ap-10701	459	2	in	in	ADP
ap-10701	459	3	russian	russian	NOUN
ap-10701	459	4	;	;	PUNCT
ap-10701	459	5	theory	theory	NOUN
ap-10701	459	6	of	of	ADP
ap-10701	459	7	difference	difference	NOUN
ap-10701	459	8	schemes	scheme	NOUN
ap-10701	459	9	]	]	PUNCT
ap-10701	459	10	.	.	PUNCT
ap-10701	460	1	nauka	nauka	PROPN
ap-10701	460	2	,	,	PUNCT
ap-10701	460	3	moscow	moscow	PROPN
ap-10701	460	4	,	,	PUNCT
ap-10701	460	5	1977	1977	NUM
ap-10701	460	6	.	.	PUNCT
ap-10701	461	1	576	576	NUM
ap-10701	461	2	https://doi.org/10.1007/978-3-662-08542-4	https://doi.org/10.1007/978-3-662-08542-4	NOUN
ap-10701	461	3	https://doi.org/10.3934/dcdss.2020382	https://doi.org/10.3934/dcdss.2020382	NOUN
ap-10701	461	4	https://doi.org/10.1007/978-3-642-61453-8	https://doi.org/10.1007/978-3-642-61453-8	PROPN
ap-10701	461	5	https://doi.org/10.1016/0167-2789(89)90230-3	https://doi.org/10.1016/0167-2789(89)90230-3	NOUN
ap-10701	461	6	https://doi.org/10.1016/0167-2789(93)90183-2	https://doi.org/10.1016/0167-2789(93)90183-2	PROPN
ap-10701	461	7	https://doi.org/10.4171/ifb/38	https://doi.org/10.4171/ifb/38	NOUN
ap-10701	461	8	https://doi.org/10.1016/j.apnum.2004.05.001	https://doi.org/10.1016/j.apnum.2004.05.001	VERB
ap-10701	461	9	https://doi.org/10.1137/0715077	https://doi.org/10.1137/0715077	PROPN
ap-10701	461	10	https://doi.org/10.1016/j.camwa.2017.02.032	https://doi.org/10.1016/j.camwa.2017.02.032	NUM
ap-10701	461	11	https://doi.org/10.1093/imanum/drx058	https://doi.org/10.1093/imanum/drx058	NOUN
ap-10701	461	12	https://doi.org/10.1016/s0377-0427(00)00582-3	https://doi.org/10.1016/s0377-0427(00)00582-3	PROPN
ap-10701	461	13	https://doi.org/10.4236/ajcm.2013.32022	https://doi.org/10.4236/ajcm.2013.32022	PROPN
ap-10701	461	14	https://doi.org/10.1007/s00791-008-0112-2	https://doi.org/10.1007/s00791-008-0112-2	PUNCT
ap-10701	461	15	https://dml.cz/handle/10338.dmlcz/700304	https://dml.cz/handle/10338.dmlcz/700304	PUNCT
ap-10701	461	16	http://eudml.org/doc/21776	http://eudml.org/doc/21776	PROPN
ap-10701	461	17	https://doi.org/10.3934/dcdss.2022103	https://doi.org/10.3934/dcdss.2022103	PUNCT
ap-10701	461	18	https://doi.org/10.3934/dcdsb.2022063	https://doi.org/10.3934/dcdsb.2022063	NOUN
ap-10701	461	19	https://doi.org/10.1090/s0025-5718-07-02021-2	https://doi.org/10.1090/s0025-5718-07-02021-2	NUM
ap-10701	461	20	vol	vol	NOUN
ap-10701	461	21	.	.	PUNCT
ap-10701	462	1	65	65	NUM
ap-10701	462	2	no	no	NOUN
ap-10701	462	3	.	.	PUNCT
ap-10701	463	1	5/2025	5/2025	NUM
ap-10701	463	2	method	method	NOUN
ap-10701	463	3	of	of	ADP
ap-10701	463	4	lines	line	NOUN
ap-10701	463	5	for	for	ADP
ap-10701	463	6	reaction	reaction	NOUN
ap-10701	463	7	-	-	PUNCT
ap-10701	463	8	diffusion	diffusion	NOUN
ap-10701	463	9	systems	system	NOUN
ap-10701	463	10	.	.	PUNCT
ap-10701	463	11	.	.	PUNCT
ap-10701	463	12	.	.	PUNCT
ap-10701	464	1	[	[	X
ap-10701	464	2	32	32	NUM
ap-10701	464	3	]	]	PUNCT
ap-10701	464	4	d.	d.	NOUN
ap-10701	464	5	žurek	žurek	PROPN
ap-10701	464	6	.	.	PUNCT
ap-10701	465	1	electromechanical	electromechanical	ADJ
ap-10701	465	2	model	model	NOUN
ap-10701	465	3	of	of	ADP
ap-10701	465	4	excitable	excitable	ADJ
ap-10701	465	5	medium	medium	NOUN
ap-10701	465	6	.	.	PUNCT
ap-10701	466	1	master	master	NOUN
ap-10701	466	2	’s	’s	PART
ap-10701	466	3	thesis	thesis	NOUN
ap-10701	466	4	,	,	PUNCT
ap-10701	466	5	czech	czech	PROPN
ap-10701	466	6	technical	technical	PROPN
ap-10701	466	7	university	university	PROPN
ap-10701	466	8	in	in	ADP
ap-10701	466	9	prague	prague	PROPN
ap-10701	466	10	,	,	PUNCT
ap-10701	466	11	faculty	faculty	NOUN
ap-10701	466	12	of	of	ADP
ap-10701	466	13	nuclear	nuclear	ADJ
ap-10701	466	14	sciences	science	NOUN
ap-10701	466	15	and	and	CCONJ
ap-10701	466	16	physical	physical	ADJ
ap-10701	466	17	engineering	engineering	NOUN
ap-10701	466	18	,	,	PUNCT
ap-10701	466	19	prague	prague	NOUN
ap-10701	466	20	,	,	PUNCT
ap-10701	466	21	2024	2024	NUM
ap-10701	466	22	.	.	PUNCT
ap-10701	467	1	[	[	X
ap-10701	467	2	33	33	NUM
ap-10701	467	3	]	]	PUNCT
ap-10701	467	4	i.	i.	NOUN
ap-10701	467	5	prigogine	prigogine	PROPN
ap-10701	467	6	,	,	PUNCT
ap-10701	467	7	r.	r.	PROPN
ap-10701	467	8	lefever	lefever	PROPN
ap-10701	467	9	.	.	PUNCT
ap-10701	468	1	symmetry	symmetry	NOUN
ap-10701	468	2	breaking	break	VERB
ap-10701	468	3	instabilities	instability	NOUN
ap-10701	468	4	in	in	ADP
ap-10701	468	5	dissipative	dissipative	ADJ
ap-10701	468	6	systems	system	NOUN
ap-10701	468	7	.	.	PUNCT
ap-10701	469	1	ii	ii	PROPN
ap-10701	469	2	.	.	PUNCT
ap-10701	470	1	the	the	DET
ap-10701	470	2	journal	journal	PROPN
ap-10701	470	3	of	of	ADP
ap-10701	470	4	chemical	chemical	PROPN
ap-10701	470	5	physics	physics	PROPN
ap-10701	470	6	48(4):1695–1700	48(4):1695–1700	NUM
ap-10701	470	7	,	,	PUNCT
ap-10701	470	8	1968	1968	NUM
ap-10701	470	9	.	.	PUNCT
ap-10701	471	1	https://doi.org/10.1063/1.1668896	https://doi.org/10.1063/1.1668896	X
ap-10701	472	1	[	[	X
ap-10701	472	2	34	34	NUM
ap-10701	472	3	]	]	PUNCT
ap-10701	472	4	m.	m.	NOUN
ap-10701	472	5	marek	marek	PROPN
ap-10701	472	6	,	,	PUNCT
ap-10701	472	7	i.	i.	PROPN
ap-10701	472	8	schreiber	schreiber	PROPN
ap-10701	472	9	.	.	PUNCT
ap-10701	473	1	chaotic	chaotic	ADJ
ap-10701	473	2	behaviour	behaviour	NOUN
ap-10701	473	3	of	of	ADP
ap-10701	473	4	deterministic	deterministic	ADJ
ap-10701	473	5	dissipative	dissipative	NOUN
ap-10701	473	6	systems	system	NOUN
ap-10701	473	7	,	,	PUNCT
ap-10701	473	8	vol	vol	NOUN
ap-10701	473	9	.	.	PROPN
ap-10701	474	1	1	1	NUM
ap-10701	474	2	.	.	X
ap-10701	474	3	cambridge	cambridge	PROPN
ap-10701	474	4	university	university	PROPN
ap-10701	474	5	press	press	PROPN
ap-10701	474	6	&	&	CCONJ
ap-10701	474	7	academia	academia	PROPN
ap-10701	474	8	prague	prague	PROPN
ap-10701	474	9	,	,	PUNCT
ap-10701	474	10	1991	1991	NUM
ap-10701	474	11	.	.	PUNCT
ap-10701	475	1	https://doi.org/10.1017/cbo9780511608162	https://doi.org/10.1017/cbo9780511608162	NOUN
ap-10701	476	1	[	[	X
ap-10701	476	2	35	35	NUM
ap-10701	476	3	]	]	X
ap-10701	476	4	r.	r.	PROPN
ap-10701	476	5	fitzhugh	fitzhugh	PROPN
ap-10701	476	6	.	.	PUNCT
ap-10701	476	7	impulses	impulse	NOUN
ap-10701	476	8	and	and	CCONJ
ap-10701	476	9	physiological	physiological	ADJ
ap-10701	476	10	states	state	NOUN
ap-10701	476	11	in	in	ADP
ap-10701	476	12	theoretical	theoretical	ADJ
ap-10701	476	13	models	model	NOUN
ap-10701	476	14	of	of	ADP
ap-10701	476	15	nerve	nerve	NOUN
ap-10701	476	16	membrane	membrane	NOUN
ap-10701	476	17	.	.	PUNCT
ap-10701	477	1	biophysical	biophysical	ADJ
ap-10701	477	2	journal	journal	NOUN
ap-10701	477	3	1(6):445–466	1(6):445–466	NUM
ap-10701	477	4	,	,	PUNCT
ap-10701	477	5	1961	1961	NUM
ap-10701	477	6	.	.	PUNCT
ap-10701	478	1	https://doi.org/10.1016/s0006-3495(61)86902-6	https://doi.org/10.1016/s0006-3495(61)86902-6	PROPN
ap-10701	479	1	[	[	X
ap-10701	479	2	36	36	NUM
ap-10701	479	3	]	]	PUNCT
ap-10701	479	4	j.	j.	PROPN
ap-10701	479	5	nagumo	nagumo	PROPN
ap-10701	479	6	,	,	PUNCT
ap-10701	479	7	s.	s.	PROPN
ap-10701	479	8	arimoto	arimoto	PROPN
ap-10701	479	9	,	,	PUNCT
ap-10701	479	10	s.	s.	PROPN
ap-10701	479	11	yoshizawa	yoshizawa	PROPN
ap-10701	479	12	.	.	PUNCT
ap-10701	480	1	an	an	DET
ap-10701	480	2	active	active	ADJ
ap-10701	480	3	pulse	pulse	NOUN
ap-10701	480	4	transmission	transmission	NOUN
ap-10701	480	5	line	line	NOUN
ap-10701	480	6	simulating	simulate	VERB
ap-10701	480	7	nerve	nerve	NOUN
ap-10701	480	8	axon	axon	NOUN
ap-10701	480	9	.	.	PUNCT
ap-10701	481	1	proceedings	proceeding	NOUN
ap-10701	481	2	of	of	ADP
ap-10701	481	3	the	the	DET
ap-10701	481	4	ire	ire	NOUN
ap-10701	481	5	50(10):2061–2070	50(10):2061–2070	NUM
ap-10701	481	6	,	,	PUNCT
ap-10701	481	7	1962	1962	NUM
ap-10701	481	8	.	.	PUNCT
ap-10701	482	1	https://doi.org/10.1109/jrproc.1962.288235	https://doi.org/10.1109/jrproc.1962.288235	PROPN
ap-10701	482	2	[	[	X
ap-10701	482	3	37	37	NUM
ap-10701	482	4	]	]	PUNCT
ap-10701	482	5	s.-i	s.-i	PROPN
ap-10701	482	6	.	.	PUNCT
ap-10701	483	1	ei	ei	PROPN
ap-10701	483	2	,	,	PUNCT
ap-10701	483	3	r.	r.	PROPN
ap-10701	483	4	ikota	ikota	PROPN
ap-10701	483	5	,	,	PUNCT
ap-10701	483	6	m.	m.	NOUN
ap-10701	483	7	mimura	mimura	NOUN
ap-10701	483	8	.	.	PUNCT
ap-10701	484	1	segregating	segregate	VERB
ap-10701	484	2	partition	partition	NOUN
ap-10701	484	3	problem	problem	NOUN
ap-10701	484	4	in	in	ADP
ap-10701	484	5	competition	competition	NOUN
ap-10701	484	6	-	-	PUNCT
ap-10701	484	7	diffusion	diffusion	NOUN
ap-10701	484	8	systems	system	NOUN
ap-10701	484	9	.	.	PUNCT
ap-10701	485	1	interfaces	interface	NOUN
ap-10701	485	2	and	and	CCONJ
ap-10701	485	3	free	free	ADJ
ap-10701	485	4	boundaries	boundary	NOUN
ap-10701	485	5	1(1):57–80	1(1):57–80	NUM
ap-10701	485	6	,	,	PUNCT
ap-10701	485	7	1999	1999	NUM
ap-10701	485	8	.	.	PUNCT
ap-10701	486	1	https://doi.org/10.4171/ifb/4	https://doi.org/10.4171/ifb/4	X
ap-10701	487	1	[	[	X
ap-10701	487	2	38	38	NUM
ap-10701	487	3	]	]	PUNCT
ap-10701	487	4	g.	g.	PROPN
ap-10701	487	5	dziuk	dziuk	PROPN
ap-10701	487	6	.	.	PUNCT
ap-10701	488	1	convergence	convergence	NOUN
ap-10701	488	2	of	of	ADP
ap-10701	488	3	a	a	DET
ap-10701	488	4	semi	semi	ADJ
ap-10701	488	5	-	-	ADJ
ap-10701	488	6	discrete	discrete	ADJ
ap-10701	488	7	scheme	scheme	NOUN
ap-10701	488	8	for	for	ADP
ap-10701	488	9	the	the	DET
ap-10701	488	10	curve	curve	NOUN
ap-10701	488	11	shortening	shortening	NOUN
ap-10701	488	12	flow	flow	NOUN
ap-10701	488	13	.	.	PUNCT
ap-10701	489	1	mathematical	mathematical	ADJ
ap-10701	489	2	models	model	NOUN
ap-10701	489	3	and	and	CCONJ
ap-10701	489	4	methods	method	NOUN
ap-10701	489	5	in	in	ADP
ap-10701	489	6	applied	apply	VERB
ap-10701	489	7	sciences	science	NOUN
ap-10701	489	8	4(4):589–606	4(4):589–606	NUM
ap-10701	489	9	,	,	PUNCT
ap-10701	489	10	1994	1994	NUM
ap-10701	489	11	.	.	PUNCT
ap-10701	490	1	https://doi.org/10.1142/s0218202594000339	https://doi.org/10.1142/s0218202594000339	PROPN
ap-10701	491	1	[	[	X
ap-10701	491	2	39	39	NUM
ap-10701	491	3	]	]	PUNCT
ap-10701	491	4	g.	g.	PROPN
ap-10701	491	5	nicolis	nicolis	PROPN
ap-10701	491	6	,	,	PUNCT
ap-10701	491	7	i.	i.	PROPN
ap-10701	491	8	prigogine	prigogine	PROPN
ap-10701	491	9	.	.	PUNCT
ap-10701	492	1	self	self	NOUN
ap-10701	492	2	-	-	PUNCT
ap-10701	492	3	organisation	organisation	NOUN
ap-10701	492	4	in	in	ADP
ap-10701	492	5	nonequilibrium	nonequilibrium	NOUN
ap-10701	492	6	systems	system	NOUN
ap-10701	492	7	.	.	PUNCT
ap-10701	493	1	wiley	wiley	PROPN
ap-10701	493	2	and	and	CCONJ
ap-10701	493	3	sons	son	NOUN
ap-10701	493	4	,	,	PUNCT
ap-10701	493	5	new	new	PROPN
ap-10701	493	6	york	york	PROPN
ap-10701	493	7	,	,	PUNCT
ap-10701	493	8	1977	1977	NUM
ap-10701	493	9	.	.	PUNCT
ap-10701	494	1	[	[	X
ap-10701	494	2	40	40	NUM
ap-10701	494	3	]	]	PUNCT
ap-10701	494	4	p.	p.	NOUN
ap-10701	494	5	raschman	raschman	PROPN
ap-10701	494	6	,	,	PUNCT
ap-10701	494	7	m.	m.	NOUN
ap-10701	494	8	kubíček	kubíček	PROPN
ap-10701	494	9	,	,	PUNCT
ap-10701	494	10	m.	m.	NOUN
ap-10701	494	11	marek	marek	PROPN
ap-10701	494	12	.	.	PUNCT
ap-10701	495	1	concentration	concentration	NOUN
ap-10701	495	2	waves	wave	NOUN
ap-10701	495	3	in	in	ADP
ap-10701	495	4	reaction	reaction	NOUN
ap-10701	495	5	-	-	PUNCT
ap-10701	495	6	diffusion	diffusion	NOUN
ap-10701	495	7	systems	system	NOUN
ap-10701	495	8	.	.	PUNCT
ap-10701	496	1	scientific	scientific	ADJ
ap-10701	496	2	papers	paper	NOUN
ap-10701	496	3	of	of	ADP
ap-10701	496	4	the	the	DET
ap-10701	496	5	prague	prague	PROPN
ap-10701	496	6	institute	institute	PROPN
ap-10701	496	7	of	of	ADP
ap-10701	496	8	chemical	chemical	PROPN
ap-10701	496	9	technology	technology	PROPN
ap-10701	496	10	k17:151–175	k17:151–175	PROPN
ap-10701	496	11	,	,	PUNCT
ap-10701	496	12	1982	1982	NUM
ap-10701	496	13	.	.	PUNCT
ap-10701	497	1	[	[	X
ap-10701	497	2	41	41	NUM
ap-10701	497	3	]	]	PUNCT
ap-10701	497	4	m.	m.	NOUN
ap-10701	497	5	holodniok	holodniok	PROPN
ap-10701	497	6	,	,	PUNCT
ap-10701	497	7	p.	p.	PROPN
ap-10701	497	8	knedlík	knedlík	PROPN
ap-10701	497	9	,	,	PUNCT
ap-10701	497	10	m.	m.	NOUN
ap-10701	497	11	kubíček	kubíček	PROPN
ap-10701	497	12	.	.	PROPN
ap-10701	498	1	continuation	continuation	NOUN
ap-10701	498	2	of	of	ADP
ap-10701	498	3	periodic	periodic	ADJ
ap-10701	498	4	solutions	solution	NOUN
ap-10701	498	5	in	in	ADP
ap-10701	498	6	parabolic	parabolic	ADJ
ap-10701	498	7	partial	partial	ADJ
ap-10701	498	8	differential	differential	NOUN
ap-10701	498	9	equations	equation	NOUN
ap-10701	498	10	.	.	PUNCT
ap-10701	499	1	in	in	ADP
ap-10701	499	2	t.	t.	PROPN
ap-10701	499	3	küpper	küpper	PROPN
ap-10701	499	4	,	,	PUNCT
ap-10701	499	5	r.	r.	PROPN
ap-10701	499	6	seydel	seydel	PROPN
ap-10701	499	7	,	,	PUNCT
ap-10701	499	8	h.	h.	PROPN
ap-10701	499	9	troger	troger	PROPN
ap-10701	499	10	(	(	PUNCT
ap-10701	499	11	eds	ed	NOUN
ap-10701	499	12	.	.	PUNCT
ap-10701	499	13	)	)	PUNCT
ap-10701	499	14	,	,	PUNCT
ap-10701	499	15	bifurcation	bifurcation	NOUN
ap-10701	499	16	:	:	PUNCT
ap-10701	499	17	analysis	analysis	NOUN
ap-10701	499	18	,	,	PUNCT
ap-10701	499	19	algorithms	algorithm	NOUN
ap-10701	499	20	,	,	PUNCT
ap-10701	499	21	applications	application	NOUN
ap-10701	499	22	,	,	PUNCT
ap-10701	499	23	pp	pp	ADJ
ap-10701	499	24	.	.	PUNCT
ap-10701	500	1	122–130	122–130	NUM
ap-10701	500	2	.	.	PUNCT
ap-10701	501	1	birkhäuser	birkhäuser	PROPN
ap-10701	501	2	,	,	PUNCT
ap-10701	501	3	basel	basel	PROPN
ap-10701	501	4	,	,	PUNCT
ap-10701	501	5	1987	1987	NUM
ap-10701	501	6	.	.	PUNCT
ap-10701	502	1	https://doi.org/10.1007/978-3-0348-7241-6_13	https://doi.org/10.1007/978-3-0348-7241-6_13	PROPN
ap-10701	503	1	[	[	X
ap-10701	503	2	42	42	NUM
ap-10701	503	3	]	]	X
ap-10701	503	4	l.	l.	PROPN
ap-10701	503	5	čížková	čížková	PROPN
ap-10701	503	6	-	-	PUNCT
ap-10701	503	7	eslerová	eslerová	PROPN
ap-10701	503	8	.	.	PUNCT
ap-10701	504	1	numerická	numerická	PROPN
ap-10701	504	2	analýza	analýza	NOUN
ap-10701	504	3	dynamiky	dynamiky	VERB
ap-10701	504	4	reakčně	reakčně	ADJ
ap-10701	504	5	-	-	PUNCT
ap-10701	504	6	difúzních	difúzních	PROPN
ap-10701	504	7	rovnic	rovnic	ADJ
ap-10701	504	8	brusselátor	brusselátor	NOUN
ap-10701	504	9	[	[	X
ap-10701	504	10	in	in	ADP
ap-10701	504	11	czech	czech	PROPN
ap-10701	504	12	;	;	PUNCT
ap-10701	504	13	numerical	numerical	ADJ
ap-10701	504	14	analysis	analysis	NOUN
ap-10701	504	15	of	of	ADP
ap-10701	504	16	dynamics	dynamic	NOUN
ap-10701	504	17	of	of	ADP
ap-10701	504	18	brusselator	brusselator	NOUN
ap-10701	504	19	reaction	reaction	NOUN
ap-10701	504	20	-	-	PUNCT
ap-10701	504	21	diffusion	diffusion	NOUN
ap-10701	504	22	equations	equation	NOUN
ap-10701	504	23	]	]	PUNCT
ap-10701	504	24	.	.	PUNCT
ap-10701	505	1	master	master	PROPN
ap-10701	505	2	’s	’s	PART
ap-10701	505	3	thesis	thesis	NOUN
ap-10701	505	4	,	,	PUNCT
ap-10701	505	5	czech	czech	PROPN
ap-10701	505	6	technical	technical	PROPN
ap-10701	505	7	university	university	PROPN
ap-10701	505	8	in	in	ADP
ap-10701	505	9	prague	prague	PROPN
ap-10701	505	10	,	,	PUNCT
ap-10701	505	11	faculty	faculty	NOUN
ap-10701	505	12	of	of	ADP
ap-10701	505	13	nuclear	nuclear	ADJ
ap-10701	505	14	sciences	science	NOUN
ap-10701	505	15	and	and	CCONJ
ap-10701	505	16	physical	physical	ADJ
ap-10701	505	17	engineering	engineering	NOUN
ap-10701	505	18	,	,	PUNCT
ap-10701	505	19	prague	prague	NOUN
ap-10701	505	20	,	,	PUNCT
ap-10701	505	21	1996	1996	NUM
ap-10701	505	22	.	.	PUNCT
ap-10701	506	1	https://doi.org/10.13140/rg.2.2.16452.37765	https://doi.org/10.13140/rg.2.2.16452.37765	PROPN
ap-10701	507	1	[	[	X
ap-10701	507	2	43	43	NUM
ap-10701	507	3	]	]	X
ap-10701	507	4	s.	s.	PROPN
ap-10701	507	5	kouachi	kouachi	PROPN
ap-10701	507	6	.	.	PUNCT
ap-10701	508	1	global	global	ADJ
ap-10701	508	2	existence	existence	NOUN
ap-10701	508	3	for	for	ADP
ap-10701	508	4	some	some	DET
ap-10701	508	5	strongly	strongly	ADV
ap-10701	508	6	coupled	couple	VERB
ap-10701	508	7	reaction	reaction	NOUN
ap-10701	508	8	-	-	PUNCT
ap-10701	508	9	diffusion	diffusion	NOUN
ap-10701	508	10	systems	system	NOUN
ap-10701	508	11	non	non	ADJ
ap-10701	508	12	-	-	ADJ
ap-10701	508	13	dissipative	dissipative	ADJ
ap-10701	508	14	via	via	ADP
ap-10701	508	15	invariant	invariant	ADJ
ap-10701	508	16	regions	region	NOUN
ap-10701	508	17	techniques	technique	NOUN
ap-10701	508	18	.	.	PUNCT
ap-10701	509	1	tech	tech	NOUN
ap-10701	509	2	.	.	PUNCT
ap-10701	509	3	rep	rep	PROPN
ap-10701	509	4	.	.	PROPN
ap-10701	509	5	hal-01429082	hal-01429082	PROPN
ap-10701	509	6	,	,	PUNCT
ap-10701	509	7	hal	hal	PROPN
ap-10701	509	8	,	,	PUNCT
ap-10701	509	9	open	open	ADJ
ap-10701	509	10	science	science	NOUN
ap-10701	509	11	,	,	PUNCT
ap-10701	509	12	2017	2017	NUM
ap-10701	509	13	.	.	PUNCT
ap-10701	510	1	[	[	X
ap-10701	510	2	2025	2025	NUM
ap-10701	510	3	-	-	SYM
ap-10701	510	4	06	06	NUM
ap-10701	510	5	-	-	SYM
ap-10701	510	6	30	30	NUM
ap-10701	510	7	]	]	PUNCT
ap-10701	510	8	.	.	PUNCT
ap-10701	510	9	https://hal.archives-ouvertes.fr/hal-01429082	https://hal.archives-ouvertes.fr/hal-01429082	PROPN
ap-10701	511	1	[	[	X
ap-10701	511	2	44	44	NUM
ap-10701	511	3	]	]	PUNCT
ap-10701	511	4	s.	s.	PROPN
ap-10701	511	5	m.	m.	PROPN
ap-10701	511	6	stoltz	stoltz	PROPN
ap-10701	511	7	.	.	PUNCT
ap-10701	511	8	pattern	pattern	NOUN
ap-10701	511	9	formation	formation	NOUN
ap-10701	511	10	in	in	ADP
ap-10701	511	11	the	the	DET
ap-10701	511	12	brusselator	brusselator	NOUN
ap-10701	511	13	model	model	NOUN
ap-10701	511	14	of	of	ADP
ap-10701	511	15	chemical	chemical	NOUN
ap-10701	511	16	reactions	reaction	NOUN
ap-10701	511	17	.	.	PUNCT
ap-10701	512	1	master	master	NOUN
ap-10701	512	2	’s	’s	PART
ap-10701	512	3	thesis	thesis	NOUN
ap-10701	512	4	,	,	PUNCT
ap-10701	512	5	university	university	NOUN
ap-10701	512	6	of	of	ADP
ap-10701	512	7	pretoria	pretoria	PROPN
ap-10701	512	8	,	,	PUNCT
ap-10701	512	9	pretoria	pretoria	PROPN
ap-10701	512	10	,	,	PUNCT
ap-10701	512	11	2016	2016	NUM
ap-10701	512	12	.	.	PUNCT
ap-10701	513	1	[	[	X
ap-10701	513	2	45	45	NUM
ap-10701	513	3	]	]	PUNCT
ap-10701	513	4	a.	a.	NOUN
ap-10701	513	5	l.	l.	PROPN
ap-10701	513	6	hodgkin	hodgkin	PROPN
ap-10701	513	7	,	,	PUNCT
ap-10701	513	8	a.	a.	PROPN
ap-10701	513	9	f.	f.	PROPN
ap-10701	513	10	huxley	huxley	PROPN
ap-10701	513	11	,	,	PUNCT
ap-10701	513	12	b.	b.	PROPN
ap-10701	513	13	katz	katz	PROPN
ap-10701	513	14	.	.	PUNCT
ap-10701	514	1	measurement	measurement	PROPN
ap-10701	514	2	of	of	ADP
ap-10701	514	3	current	current	ADJ
ap-10701	514	4	-	-	PUNCT
ap-10701	514	5	voltage	voltage	NOUN
ap-10701	514	6	relations	relation	NOUN
ap-10701	514	7	in	in	ADP
ap-10701	514	8	the	the	DET
ap-10701	514	9	membrane	membrane	NOUN
ap-10701	514	10	of	of	ADP
ap-10701	514	11	the	the	DET
ap-10701	514	12	giant	giant	ADJ
ap-10701	514	13	axon	axon	NOUN
ap-10701	514	14	of	of	ADP
ap-10701	514	15	loligo	loligo	PROPN
ap-10701	514	16	.	.	PUNCT
ap-10701	515	1	the	the	DET
ap-10701	515	2	journal	journal	NOUN
ap-10701	515	3	of	of	ADP
ap-10701	515	4	physiology	physiology	NOUN
ap-10701	515	5	116(4):424–448	116(4):424–448	NUM
ap-10701	515	6	,	,	PUNCT
ap-10701	515	7	1952	1952	NUM
ap-10701	515	8	.	.	PUNCT
ap-10701	516	1	https://doi.org/10.1113/jphysiol.1952.sp004716	https://doi.org/10.1113/jphysiol.1952.sp004716	NOUN
ap-10701	517	1	[	[	X
ap-10701	517	2	46	46	NUM
ap-10701	517	3	]	]	X
ap-10701	517	4	j.	j.	PROPN
ap-10701	517	5	keener	keener	PROPN
ap-10701	517	6	,	,	PUNCT
ap-10701	517	7	j.	j.	PROPN
ap-10701	517	8	sneyd	sneyd	PROPN
ap-10701	517	9	.	.	PUNCT
ap-10701	518	1	mathematical	mathematical	ADJ
ap-10701	518	2	physiology	physiology	NOUN
ap-10701	518	3	.	.	PUNCT
ap-10701	519	1	springer	springer	NOUN
ap-10701	519	2	,	,	PUNCT
ap-10701	519	3	new	new	PROPN
ap-10701	519	4	york	york	PROPN
ap-10701	519	5	,	,	PUNCT
ap-10701	519	6	1998	1998	NUM
ap-10701	519	7	.	.	PUNCT
ap-10701	520	1	https://doi.org/10.1007/b98841	https://doi.org/10.1007/b98841	PRON
ap-10701	521	1	[	[	X
ap-10701	521	2	47	47	NUM
ap-10701	521	3	]	]	PUNCT
ap-10701	521	4	b.	b.	PROPN
ap-10701	521	5	deng	deng	PROPN
ap-10701	521	6	.	.	PUNCT
ap-10701	522	1	the	the	DET
ap-10701	522	2	existence	existence	NOUN
ap-10701	522	3	of	of	ADP
ap-10701	522	4	infinitely	infinitely	ADV
ap-10701	522	5	many	many	ADJ
ap-10701	522	6	traveling	travel	VERB
ap-10701	522	7	front	front	ADJ
ap-10701	522	8	and	and	CCONJ
ap-10701	522	9	back	back	ADJ
ap-10701	522	10	waves	wave	NOUN
ap-10701	522	11	in	in	ADP
ap-10701	522	12	the	the	DET
ap-10701	522	13	fitzhugh	fitzhugh	PROPN
ap-10701	522	14	–	–	PUNCT
ap-10701	522	15	nagumo	nagumo	ADJ
ap-10701	522	16	equations	equation	NOUN
ap-10701	522	17	.	.	PUNCT
ap-10701	523	1	siam	siam	PROPN
ap-10701	523	2	journal	journal	PROPN
ap-10701	523	3	on	on	ADP
ap-10701	523	4	mathematical	mathematical	ADJ
ap-10701	523	5	analysis	analysis	NOUN
ap-10701	523	6	22(6):1631	22(6):1631	NUM
ap-10701	523	7	–	–	PUNCT
ap-10701	523	8	1650	1650	NUM
ap-10701	523	9	,	,	PUNCT
ap-10701	523	10	1991	1991	NUM
ap-10701	523	11	.	.	PUNCT
ap-10701	524	1	https://doi.org/10.1137/0522102	https://doi.org/10.1137/0522102	X
ap-10701	525	1	[	[	X
ap-10701	525	2	48	48	NUM
ap-10701	525	3	]	]	PUNCT
ap-10701	525	4	j.	j.	PROPN
ap-10701	525	5	rauch	rauch	PROPN
ap-10701	525	6	,	,	PUNCT
ap-10701	525	7	j.	j.	PROPN
ap-10701	525	8	smoller	smoller	PROPN
ap-10701	525	9	.	.	PUNCT
ap-10701	526	1	qualitative	qualitative	ADJ
ap-10701	526	2	theory	theory	NOUN
ap-10701	526	3	of	of	ADP
ap-10701	526	4	the	the	DET
ap-10701	526	5	fitzhugh	fitzhugh	PROPN
ap-10701	526	6	-	-	PUNCT
ap-10701	526	7	nagumo	nagumo	ADJ
ap-10701	526	8	equations	equation	NOUN
ap-10701	526	9	.	.	PUNCT
ap-10701	527	1	advances	advance	NOUN
ap-10701	527	2	in	in	ADP
ap-10701	527	3	mathematics	mathematics	PROPN
ap-10701	527	4	27(1):12–24	27(1):12–24	NUM
ap-10701	527	5	,	,	PUNCT
ap-10701	527	6	1978	1978	NUM
ap-10701	527	7	.	.	PUNCT
ap-10701	528	1	https://doi.org/10.1016/0001-8708(78)90075-0	https://doi.org/10.1016/0001-8708(78)90075-0	NOUN
ap-10701	528	2	577	577	NUM
ap-10701	529	1	https://doi.org/10.1063/1.1668896	https://doi.org/10.1063/1.1668896	NOUN
ap-10701	529	2	https://doi.org/10.1017/cbo9780511608162	https://doi.org/10.1017/cbo9780511608162	ADJ
ap-10701	529	3	https://doi.org/10.1016/s0006-3495(61)86902-6	https://doi.org/10.1016/s0006-3495(61)86902-6	PROPN
ap-10701	530	1	https://doi.org/10.1109/jrproc.1962.288235	https://doi.org/10.1109/jrproc.1962.288235	PROPN
ap-10701	530	2	https://doi.org/10.4171/ifb/4	https://doi.org/10.4171/ifb/4	INTJ
ap-10701	530	3	https://doi.org/10.1142/s0218202594000339	https://doi.org/10.1142/s0218202594000339	PROPN
ap-10701	530	4	https://doi.org/10.1007/978-3-0348-7241-6_13	https://doi.org/10.1007/978-3-0348-7241-6_13	PROPN
ap-10701	530	5	https://doi.org/10.13140/rg.2.2.16452.37765	https://doi.org/10.13140/rg.2.2.16452.37765	PROPN
ap-10701	530	6	https://hal.archives-ouvertes.fr/hal-01429082	https://hal.archives-ouvertes.fr/hal-01429082	PROPN
ap-10701	530	7	https://doi.org/10.1113/jphysiol.1952.sp004716	https://doi.org/10.1113/jphysiol.1952.sp004716	PROPN
ap-10701	530	8	https://doi.org/10.1007/b98841	https://doi.org/10.1007/b98841	NUM
ap-10701	530	9	https://doi.org/10.1137/0522102	https://doi.org/10.1137/0522102	NUM
ap-10701	530	10	https://doi.org/10.1016/0001-8708(78)90075-0	https://doi.org/10.1016/0001-8708(78)90075-0	PROPN
ap-10701	530	11	acta	acta	PROPN
ap-10701	530	12	polytechnica	polytechnica	PROPN
ap-10701	530	13	65(5):566–577	65(5):566–577	PROPN
ap-10701	530	14	,	,	PUNCT
ap-10701	530	15	2025	2025	NUM
ap-10701	530	16	1	1	NUM
ap-10701	530	17	introduction	introduction	NOUN
ap-10701	530	18	2	2	NUM
ap-10701	530	19	reaction	reaction	NOUN
ap-10701	530	20	-	-	PUNCT
ap-10701	530	21	diffusion	diffusion	NOUN
ap-10701	530	22	systems	system	NOUN
ap-10701	530	23	3	3	NUM
ap-10701	530	24	method	method	NOUN
ap-10701	530	25	of	of	ADP
ap-10701	530	26	lines	line	NOUN
ap-10701	530	27	3.1	3.1	NUM
ap-10701	530	28	finite	finite	ADJ
ap-10701	530	29	-	-	PUNCT
ap-10701	530	30	difference	difference	ADJ
ap-10701	530	31	discretization	discretization	NOUN
ap-10701	530	32	3.2	3.2	NUM
ap-10701	530	33	invariant	invariant	ADJ
ap-10701	530	34	regions	region	NOUN
ap-10701	530	35	for	for	ADP
ap-10701	530	36	the	the	DET
ap-10701	530	37	semi	semi	ADJ
ap-10701	530	38	-	-	ADJ
ap-10701	530	39	discrete	discrete	ADJ
ap-10701	530	40	scheme	scheme	NOUN
ap-10701	530	41	4	4	NUM
ap-10701	530	42	numerical	numerical	ADJ
ap-10701	530	43	analysis	analysis	NOUN
ap-10701	530	44	of	of	ADP
ap-10701	530	45	method	method	NOUN
ap-10701	530	46	of	of	ADP
ap-10701	530	47	lines	line	NOUN
ap-10701	530	48	4.1	4.1	NUM
ap-10701	530	49	a	a	DET
ap-10701	530	50	priori	priori	ADJ
ap-10701	530	51	estimates	estimate	VERB
ap-10701	530	52	4.2	4.2	NUM
ap-10701	530	53	interpolation	interpolation	NOUN
ap-10701	530	54	results	result	VERB
ap-10701	530	55	4.3	4.3	NUM
ap-10701	530	56	passage	passage	NOUN
ap-10701	530	57	to	to	ADP
ap-10701	530	58	the	the	DET
ap-10701	530	59	limit	limit	NOUN
ap-10701	530	60	4.4	4.4	NUM
ap-10701	530	61	regularity	regularity	NOUN
ap-10701	530	62	4.5	4.5	NUM
ap-10701	530	63	error	error	NOUN
ap-10701	530	64	estimates	estimate	NOUN
ap-10701	530	65	5	5	NUM
ap-10701	530	66	examples	example	NOUN
ap-10701	530	67	5.1	5.1	NUM
ap-10701	530	68	numerical	numerical	ADJ
ap-10701	530	69	error	error	NOUN
ap-10701	530	70	measurement	measurement	NOUN
ap-10701	530	71	5.2	5.2	NUM
ap-10701	530	72	brusselator	brusselator	NOUN
ap-10701	530	73	model	model	NOUN
ap-10701	530	74	5.3	5.3	NUM
ap-10701	530	75	fitzhugh	fitzhugh	PROPN
ap-10701	530	76	nagumo	nagumo	ADJ
ap-10701	530	77	model	model	NOUN
ap-10701	530	78	6	6	NUM
ap-10701	530	79	conclusion	conclusion	NOUN
ap-10701	530	80	7	7	NUM
ap-10701	530	81	dedication	dedication	NOUN
ap-10701	530	82	acknowledgements	acknowledgement	NOUN
ap-10701	530	83	references	reference	NOUN