id	sid	tid	token	lemma	pos
ap-3524	1	1	acta	acta	PROPN
ap-3524	1	2	polytechnica	polytechnica	PROPN
ap-3524	1	3	doi:10.14311	doi:10.14311	PROPN
ap-3524	1	4	/	/	SYM
ap-3524	1	5	ap.2016.56.0236	ap.2016.56.0236	PROPN
ap-3524	1	6	acta	acta	PROPN
ap-3524	1	7	polytechnica	polytechnica	PROPN
ap-3524	1	8	56(3):236–244	56(3):236–244	PROPN
ap-3524	1	9	,	,	PUNCT
ap-3524	1	10	2016	2016	NUM
ap-3524	1	11	©	©	PROPN
ap-3524	1	12	czech	czech	PROPN
ap-3524	1	13	technical	technical	PROPN
ap-3524	1	14	university	university	PROPN
ap-3524	1	15	in	in	ADP
ap-3524	1	16	prague	prague	PROPN
ap-3524	1	17	,	,	PUNCT
ap-3524	1	18	2016	2016	NUM
ap-3524	1	19	available	available	ADJ
ap-3524	1	20	online	online	ADV
ap-3524	1	21	at	at	ADP
ap-3524	1	22	http://ojs.cvut.cz/ojs/index.php/ap	http://ojs.cvut.cz/ojs/index.php/ap	PROPN
ap-3524	1	23	on	on	ADP
ap-3524	1	24	the	the	DET
ap-3524	1	25	construction	construction	NOUN
ap-3524	1	26	of	of	ADP
ap-3524	1	27	partial	partial	ADJ
ap-3524	1	28	difference	difference	NOUN
ap-3524	1	29	schemes	scheme	NOUN
ap-3524	1	30	ii	ii	NOUN
ap-3524	1	31	:	:	PUNCT
ap-3524	1	32	discrete	discrete	ADJ
ap-3524	1	33	variables	variable	NOUN
ap-3524	1	34	and	and	CCONJ
ap-3524	1	35	schwarzian	schwarzian	NOUN
ap-3524	1	36	lattices	lattice	NOUN
ap-3524	1	37	decio	decio	PROPN
ap-3524	1	38	levia,∗	levia,∗	PROPN
ap-3524	1	39	,	,	PUNCT
ap-3524	1	40	miguel	miguel	PROPN
ap-3524	1	41	a.	a.	PROPN
ap-3524	1	42	rodríguezb	rodríguezb	VERB
ap-3524	1	43	a	a	DET
ap-3524	1	44	dipartimento	dipartimento	PROPN
ap-3524	1	45	di	di	X
ap-3524	1	46	matematica	matematica	PROPN
ap-3524	1	47	e	e	PROPN
ap-3524	1	48	fisica	fisica	PROPN
ap-3524	1	49	,	,	PUNCT
ap-3524	1	50	università	università	PROPN
ap-3524	1	51	degli	degli	PROPN
ap-3524	1	52	studi	studi	PROPN
ap-3524	1	53	roma	roma	PROPN
ap-3524	1	54	tre	tre	PROPN
ap-3524	1	55	and	and	CCONJ
ap-3524	1	56	infn	infn	PROPN
ap-3524	1	57	sezione	sezione	PROPN
ap-3524	1	58	di	di	PROPN
ap-3524	1	59	roma	roma	PROPN
ap-3524	1	60	tre	tre	PROPN
ap-3524	1	61	,	,	PUNCT
ap-3524	1	62	via	via	ADP
ap-3524	1	63	della	della	PROPN
ap-3524	1	64	vasca	vasca	PROPN
ap-3524	1	65	navale	navale	PROPN
ap-3524	1	66	84	84	NUM
ap-3524	1	67	,	,	PUNCT
ap-3524	1	68	00146	00146	NUM
ap-3524	1	69	roma	roma	PROPN
ap-3524	1	70	,	,	PUNCT
ap-3524	1	71	italy	italy	PROPN
ap-3524	1	72	b	b	PROPN
ap-3524	1	73	departamento	departamento	PROPN
ap-3524	1	74	de	de	PROPN
ap-3524	1	75	física	física	PROPN
ap-3524	1	76	teórica	teórica	PROPN
ap-3524	1	77	ii	ii	PROPN
ap-3524	1	78	,	,	PUNCT
ap-3524	1	79	facultad	facultad	PROPN
ap-3524	1	80	de	de	PROPN
ap-3524	1	81	físicas	físicas	PROPN
ap-3524	1	82	,	,	PUNCT
ap-3524	1	83	universidad	universidad	PROPN
ap-3524	1	84	complutense	complutense	NOUN
ap-3524	1	85	,	,	PUNCT
ap-3524	1	86	28040	28040	NUM
ap-3524	1	87	madrid	madrid	PROPN
ap-3524	1	88	,	,	PUNCT
ap-3524	1	89	spain	spain	PROPN
ap-3524	1	90	∗	∗	NOUN
ap-3524	1	91	corresponding	correspond	VERB
ap-3524	1	92	author	author	NOUN
ap-3524	1	93	:	:	PUNCT
ap-3524	1	94	decio.levi@roma3.infn.it	decio.levi@roma3.infn.it	PROPN
ap-3524	1	95	abstract	abstract	NOUN
ap-3524	1	96	.	.	PUNCT
ap-3524	2	1	in	in	ADP
ap-3524	2	2	the	the	DET
ap-3524	2	3	process	process	NOUN
ap-3524	2	4	of	of	ADP
ap-3524	2	5	constructing	construct	VERB
ap-3524	2	6	invariant	invariant	ADJ
ap-3524	2	7	difference	difference	NOUN
ap-3524	2	8	schemes	scheme	NOUN
ap-3524	2	9	which	which	PRON
ap-3524	2	10	approximate	approximate	VERB
ap-3524	2	11	partial	partial	ADJ
ap-3524	2	12	differential	differential	ADJ
ap-3524	2	13	equations	equation	NOUN
ap-3524	2	14	we	we	PRON
ap-3524	2	15	write	write	VERB
ap-3524	2	16	down	down	ADP
ap-3524	2	17	a	a	DET
ap-3524	2	18	procedure	procedure	NOUN
ap-3524	2	19	for	for	ADP
ap-3524	2	20	discretizing	discretize	VERB
ap-3524	2	21	a	a	DET
ap-3524	2	22	partial	partial	ADJ
ap-3524	2	23	differential	differential	NOUN
ap-3524	2	24	equation	equation	NOUN
ap-3524	2	25	on	on	ADP
ap-3524	2	26	an	an	DET
ap-3524	2	27	arbitrary	arbitrary	ADJ
ap-3524	2	28	lattice	lattice	NOUN
ap-3524	2	29	.	.	PUNCT
ap-3524	3	1	an	an	DET
ap-3524	3	2	open	open	ADJ
ap-3524	3	3	problem	problem	NOUN
ap-3524	3	4	is	be	AUX
ap-3524	3	5	the	the	DET
ap-3524	3	6	meaning	meaning	NOUN
ap-3524	3	7	of	of	ADP
ap-3524	3	8	a	a	DET
ap-3524	3	9	lattice	lattice	NOUN
ap-3524	3	10	which	which	PRON
ap-3524	3	11	does	do	AUX
ap-3524	3	12	not	not	PART
ap-3524	3	13	satisfy	satisfy	VERB
ap-3524	3	14	the	the	DET
ap-3524	3	15	clairaut	clairaut	NOUN
ap-3524	3	16	–	–	PUNCT
ap-3524	3	17	schwarz	schwarz	PROPN
ap-3524	3	18	–	–	PUNCT
ap-3524	3	19	young	young	ADJ
ap-3524	3	20	theorem	theorem	NOUN
ap-3524	3	21	.	.	PUNCT
ap-3524	3	22	to	to	PART
ap-3524	3	23	analyze	analyze	VERB
ap-3524	3	24	it	it	PRON
ap-3524	3	25	we	we	PRON
ap-3524	3	26	apply	apply	VERB
ap-3524	3	27	the	the	DET
ap-3524	3	28	procedure	procedure	NOUN
ap-3524	3	29	on	on	ADP
ap-3524	3	30	a	a	DET
ap-3524	3	31	simple	simple	ADJ
ap-3524	3	32	example	example	NOUN
ap-3524	3	33	,	,	PUNCT
ap-3524	3	34	the	the	DET
ap-3524	3	35	potential	potential	ADJ
ap-3524	3	36	burgers	burger	NOUN
ap-3524	3	37	equation	equation	NOUN
ap-3524	3	38	with	with	ADP
ap-3524	3	39	two	two	NUM
ap-3524	3	40	different	different	ADJ
ap-3524	3	41	lattices	lattice	NOUN
ap-3524	3	42	,	,	PUNCT
ap-3524	3	43	an	an	DET
ap-3524	3	44	orthogonal	orthogonal	ADJ
ap-3524	3	45	lattice	lattice	NOUN
ap-3524	3	46	which	which	PRON
ap-3524	3	47	is	be	AUX
ap-3524	3	48	invariant	invariant	ADJ
ap-3524	3	49	under	under	ADP
ap-3524	3	50	the	the	DET
ap-3524	3	51	symmetries	symmetry	NOUN
ap-3524	3	52	of	of	ADP
ap-3524	3	53	the	the	DET
ap-3524	3	54	equation	equation	NOUN
ap-3524	3	55	and	and	CCONJ
ap-3524	3	56	satisfies	satisfy	VERB
ap-3524	3	57	the	the	DET
ap-3524	3	58	commutativity	commutativity	NOUN
ap-3524	3	59	of	of	ADP
ap-3524	3	60	the	the	DET
ap-3524	3	61	partial	partial	ADJ
ap-3524	3	62	difference	difference	NOUN
ap-3524	3	63	operators	operator	NOUN
ap-3524	3	64	and	and	CCONJ
ap-3524	3	65	an	an	DET
ap-3524	3	66	exponential	exponential	ADJ
ap-3524	3	67	lattice	lattice	NOUN
ap-3524	3	68	which	which	PRON
ap-3524	3	69	is	be	AUX
ap-3524	3	70	not	not	PART
ap-3524	3	71	invariant	invariant	ADJ
ap-3524	3	72	and	and	CCONJ
ap-3524	3	73	does	do	AUX
ap-3524	3	74	not	not	PART
ap-3524	3	75	satisfy	satisfy	VERB
ap-3524	3	76	the	the	DET
ap-3524	3	77	clairaut	clairaut	NOUN
ap-3524	3	78	–	–	PUNCT
ap-3524	3	79	schwarz	schwarz	PROPN
ap-3524	3	80	–	–	PUNCT
ap-3524	3	81	young	young	ADJ
ap-3524	3	82	theorem	theorem	NOUN
ap-3524	3	83	.	.	PUNCT
ap-3524	4	1	a	a	DET
ap-3524	4	2	discussion	discussion	NOUN
ap-3524	4	3	on	on	ADP
ap-3524	4	4	the	the	DET
ap-3524	4	5	numerical	numerical	ADJ
ap-3524	4	6	results	result	NOUN
ap-3524	4	7	is	be	AUX
ap-3524	4	8	presented	present	VERB
ap-3524	4	9	showing	show	VERB
ap-3524	4	10	the	the	DET
ap-3524	4	11	different	different	ADJ
ap-3524	4	12	behavior	behavior	NOUN
ap-3524	4	13	of	of	ADP
ap-3524	4	14	both	both	DET
ap-3524	4	15	schemes	scheme	NOUN
ap-3524	4	16	for	for	ADP
ap-3524	4	17	two	two	NUM
ap-3524	4	18	different	different	ADJ
ap-3524	4	19	exact	exact	ADJ
ap-3524	4	20	solutions	solution	NOUN
ap-3524	4	21	and	and	CCONJ
ap-3524	4	22	their	their	PRON
ap-3524	4	23	numerical	numerical	ADJ
ap-3524	4	24	approximations	approximation	NOUN
ap-3524	4	25	.	.	PUNCT
ap-3524	5	1	keywords	keyword	NOUN
ap-3524	5	2	:	:	PUNCT
ap-3524	5	3	partial	partial	ADJ
ap-3524	5	4	differential	differential	NOUN
ap-3524	5	5	and	and	CCONJ
ap-3524	5	6	difference	difference	NOUN
ap-3524	5	7	equations	equation	NOUN
ap-3524	5	8	;	;	PUNCT
ap-3524	5	9	discretization	discretization	NOUN
ap-3524	5	10	;	;	PUNCT
ap-3524	5	11	clairaut	clairaut	PROPN
ap-3524	5	12	–	–	PUNCT
ap-3524	5	13	schwarz	schwarz	NOUN
ap-3524	5	14	–	–	PUNCT
ap-3524	5	15	young	young	ADJ
ap-3524	5	16	theorem	theorem	NOUN
ap-3524	5	17	.	.	PUNCT
ap-3524	6	1	ams	ams	PROPN
ap-3524	6	2	mathematics	mathematics	PROPN
ap-3524	6	3	subject	subject	ADJ
ap-3524	6	4	classification	classification	NOUN
ap-3524	6	5	:	:	PUNCT
ap-3524	6	6	39a14	39a14	NUM
ap-3524	6	7	,	,	PUNCT
ap-3524	6	8	35f05	35f05	NUM
ap-3524	6	9	.	.	PUNCT
ap-3524	7	1	1	1	X
ap-3524	7	2	.	.	X
ap-3524	7	3	introduction	introduction	NOUN
ap-3524	7	4	the	the	DET
ap-3524	7	5	construction	construction	NOUN
ap-3524	7	6	of	of	ADP
ap-3524	7	7	difference	difference	NOUN
ap-3524	7	8	equations	equation	NOUN
ap-3524	7	9	,	,	PUNCT
ap-3524	7	10	written	write	VERB
ap-3524	7	11	as	as	ADP
ap-3524	7	12	invariants	invariant	NOUN
ap-3524	7	13	of	of	ADP
ap-3524	7	14	the	the	DET
ap-3524	7	15	continuous	continuous	ADJ
ap-3524	7	16	group	group	NOUN
ap-3524	7	17	of	of	ADP
ap-3524	7	18	symmetries	symmetry	NOUN
ap-3524	7	19	of	of	ADP
ap-3524	7	20	differential	differential	ADJ
ap-3524	7	21	equations	equation	NOUN
ap-3524	7	22	,	,	PUNCT
ap-3524	7	23	is	be	AUX
ap-3524	7	24	part	part	NOUN
ap-3524	7	25	of	of	ADP
ap-3524	7	26	a	a	DET
ap-3524	7	27	project	project	NOUN
ap-3524	7	28	to	to	PART
ap-3524	7	29	apply	apply	VERB
ap-3524	7	30	symmetry	symmetry	NOUN
ap-3524	7	31	group	group	NOUN
ap-3524	7	32	methods	method	NOUN
ap-3524	7	33	to	to	ADP
ap-3524	7	34	the	the	DET
ap-3524	7	35	numerical	numerical	ADJ
ap-3524	7	36	solution	solution	NOUN
ap-3524	7	37	of	of	ADP
ap-3524	7	38	differential	differential	ADJ
ap-3524	7	39	equations	equation	NOUN
ap-3524	8	1	[	[	X
ap-3524	8	2	2	2	NUM
ap-3524	8	3	,	,	PUNCT
ap-3524	8	4	3	3	NUM
ap-3524	8	5	,	,	PUNCT
ap-3524	8	6	6–9	6–9	PROPN
ap-3524	8	7	,	,	PUNCT
ap-3524	8	8	11–13	11–13	NUM
ap-3524	8	9	,	,	PUNCT
ap-3524	8	10	15–17	15–17	NUM
ap-3524	8	11	,	,	PUNCT
ap-3524	8	12	19–23	19–23	NUM
ap-3524	8	13	]	]	PUNCT
ap-3524	8	14	.	.	PUNCT
ap-3524	9	1	this	this	DET
ap-3524	9	2	project	project	NOUN
ap-3524	9	3	has	have	AUX
ap-3524	9	4	accomplished	accomplish	VERB
ap-3524	9	5	a	a	DET
ap-3524	9	6	significative	significative	ADJ
ap-3524	9	7	advance	advance	NOUN
ap-3524	9	8	since	since	SCONJ
ap-3524	9	9	its	its	PRON
ap-3524	9	10	first	first	ADJ
ap-3524	9	11	introduction	introduction	NOUN
ap-3524	9	12	last	last	ADJ
ap-3524	9	13	century	century	NOUN
ap-3524	9	14	.	.	PUNCT
ap-3524	10	1	in	in	ADP
ap-3524	10	2	particular	particular	ADJ
ap-3524	10	3	,	,	PUNCT
ap-3524	10	4	the	the	DET
ap-3524	10	5	construction	construction	NOUN
ap-3524	10	6	of	of	ADP
ap-3524	10	7	invariant	invariant	ADJ
ap-3524	10	8	schemes	scheme	NOUN
ap-3524	10	9	has	have	AUX
ap-3524	10	10	proven	prove	VERB
ap-3524	10	11	to	to	PART
ap-3524	10	12	be	be	AUX
ap-3524	10	13	a	a	DET
ap-3524	10	14	very	very	ADV
ap-3524	10	15	fruitful	fruitful	ADJ
ap-3524	10	16	approach	approach	NOUN
ap-3524	10	17	in	in	ADP
ap-3524	10	18	the	the	DET
ap-3524	10	19	construction	construction	NOUN
ap-3524	10	20	of	of	ADP
ap-3524	10	21	numerical	numerical	ADJ
ap-3524	10	22	schemes	scheme	NOUN
ap-3524	10	23	for	for	ADP
ap-3524	10	24	ordinary	ordinary	ADJ
ap-3524	10	25	differential	differential	ADJ
ap-3524	10	26	equations	equation	NOUN
ap-3524	10	27	[	[	X
ap-3524	10	28	2	2	NUM
ap-3524	10	29	,	,	PUNCT
ap-3524	10	30	3	3	NUM
ap-3524	10	31	]	]	PUNCT
ap-3524	10	32	,	,	PUNCT
ap-3524	10	33	in	in	ADP
ap-3524	10	34	cases	case	NOUN
ap-3524	10	35	when	when	SCONJ
ap-3524	10	36	the	the	DET
ap-3524	10	37	usual	usual	ADJ
ap-3524	10	38	approaches	approach	NOUN
ap-3524	10	39	present	present	VERB
ap-3524	10	40	serious	serious	ADJ
ap-3524	10	41	problems	problem	NOUN
ap-3524	10	42	of	of	ADP
ap-3524	10	43	convergence	convergence	NOUN
ap-3524	10	44	and	and	CCONJ
ap-3524	10	45	accuracy	accuracy	NOUN
ap-3524	10	46	,	,	PUNCT
ap-3524	10	47	for	for	ADP
ap-3524	10	48	instance	instance	NOUN
ap-3524	10	49	,	,	PUNCT
ap-3524	10	50	in	in	ADP
ap-3524	10	51	the	the	DET
ap-3524	10	52	behavior	behavior	NOUN
ap-3524	10	53	of	of	ADP
ap-3524	10	54	the	the	DET
ap-3524	10	55	solutions	solution	NOUN
ap-3524	10	56	in	in	ADP
ap-3524	10	57	the	the	DET
ap-3524	10	58	neighborhood	neighborhood	NOUN
ap-3524	10	59	of	of	ADP
ap-3524	10	60	a	a	DET
ap-3524	10	61	singularity	singularity	NOUN
ap-3524	10	62	.	.	PUNCT
ap-3524	11	1	in	in	ADP
ap-3524	11	2	this	this	DET
ap-3524	11	3	problem	problem	NOUN
ap-3524	11	4	a	a	DET
ap-3524	11	5	deeper	deep	ADJ
ap-3524	11	6	understanding	understanding	NOUN
ap-3524	11	7	of	of	ADP
ap-3524	11	8	the	the	DET
ap-3524	11	9	mathematics	mathematic	NOUN
ap-3524	11	10	involved	involve	VERB
ap-3524	11	11	in	in	ADP
ap-3524	11	12	its	its	PRON
ap-3524	11	13	relation	relation	NOUN
ap-3524	11	14	with	with	ADP
ap-3524	11	15	numerics	numeric	NOUN
ap-3524	11	16	can	can	AUX
ap-3524	11	17	provide	provide	VERB
ap-3524	11	18	results	result	NOUN
ap-3524	11	19	important	important	ADJ
ap-3524	11	20	for	for	ADP
ap-3524	11	21	their	their	PRON
ap-3524	11	22	applications	application	NOUN
ap-3524	11	23	to	to	ADP
ap-3524	11	24	problems	problem	NOUN
ap-3524	11	25	in	in	ADP
ap-3524	11	26	physics	physics	NOUN
ap-3524	11	27	and	and	CCONJ
ap-3524	11	28	mathematics	mathematic	NOUN
ap-3524	11	29	.	.	PUNCT
ap-3524	12	1	the	the	DET
ap-3524	12	2	usual	usual	ADJ
ap-3524	12	3	procedure	procedure	NOUN
ap-3524	12	4	in	in	ADP
ap-3524	12	5	this	this	DET
ap-3524	12	6	framework	framework	NOUN
ap-3524	12	7	is	be	AUX
ap-3524	12	8	to	to	PART
ap-3524	12	9	compute	compute	VERB
ap-3524	12	10	the	the	DET
ap-3524	12	11	symmetry	symmetry	NOUN
ap-3524	12	12	group	group	NOUN
ap-3524	12	13	of	of	ADP
ap-3524	12	14	the	the	DET
ap-3524	12	15	differential	differential	ADJ
ap-3524	12	16	equation	equation	NOUN
ap-3524	12	17	and	and	CCONJ
ap-3524	12	18	then	then	ADV
ap-3524	12	19	compute	compute	VERB
ap-3524	12	20	the	the	DET
ap-3524	12	21	invariant	invariant	ADJ
ap-3524	12	22	lattice	lattice	NOUN
ap-3524	12	23	and	and	CCONJ
ap-3524	12	24	invariant	invariant	ADJ
ap-3524	12	25	difference	difference	NOUN
ap-3524	12	26	equation	equation	NOUN
ap-3524	12	27	with	with	ADP
ap-3524	12	28	respect	respect	NOUN
ap-3524	12	29	to	to	ADP
ap-3524	12	30	the	the	DET
ap-3524	12	31	symmetry	symmetry	NOUN
ap-3524	12	32	group	group	NOUN
ap-3524	12	33	.	.	PUNCT
ap-3524	13	1	however	however	ADV
ap-3524	13	2	,	,	PUNCT
ap-3524	13	3	since	since	SCONJ
ap-3524	13	4	the	the	DET
ap-3524	13	5	differential	differential	NOUN
ap-3524	13	6	and	and	CCONJ
ap-3524	13	7	difference	difference	NOUN
ap-3524	13	8	calculus	calculus	NOUN
ap-3524	13	9	present	present	ADJ
ap-3524	13	10	substantial	substantial	ADJ
ap-3524	13	11	differences	difference	NOUN
ap-3524	13	12	,	,	PUNCT
ap-3524	13	13	a	a	DET
ap-3524	13	14	special	special	ADJ
ap-3524	13	15	care	care	NOUN
ap-3524	13	16	has	have	VERB
ap-3524	13	17	to	to	PART
ap-3524	13	18	be	be	AUX
ap-3524	13	19	taken	take	VERB
ap-3524	13	20	to	to	PART
ap-3524	13	21	assure	assure	VERB
ap-3524	13	22	the	the	DET
ap-3524	13	23	consistency	consistency	NOUN
ap-3524	13	24	of	of	ADP
ap-3524	13	25	the	the	DET
ap-3524	13	26	approach	approach	NOUN
ap-3524	13	27	.	.	PUNCT
ap-3524	14	1	for	for	ADP
ap-3524	14	2	example	example	NOUN
ap-3524	14	3	,	,	PUNCT
ap-3524	14	4	the	the	DET
ap-3524	14	5	clairaut	clairaut	NOUN
ap-3524	14	6	–	–	PUNCT
ap-3524	14	7	schwarz	schwarz	PROPN
ap-3524	14	8	–	–	PUNCT
ap-3524	14	9	young	young	ADJ
ap-3524	14	10	theorem	theorem	NOUN
ap-3524	14	11	on	on	ADP
ap-3524	14	12	the	the	DET
ap-3524	14	13	equality	equality	NOUN
ap-3524	14	14	of	of	ADP
ap-3524	14	15	the	the	DET
ap-3524	14	16	cross	cross	NOUN
ap-3524	14	17	derivatives	derivative	NOUN
ap-3524	14	18	,	,	PUNCT
ap-3524	14	19	which	which	PRON
ap-3524	14	20	is	be	AUX
ap-3524	14	21	satisfied	satisfied	ADJ
ap-3524	14	22	in	in	ADP
ap-3524	14	23	the	the	DET
ap-3524	14	24	continuous	continuous	ADJ
ap-3524	14	25	case	case	NOUN
ap-3524	14	26	under	under	ADP
ap-3524	14	27	some	some	DET
ap-3524	14	28	mild	mild	ADJ
ap-3524	14	29	conditions	condition	NOUN
ap-3524	14	30	on	on	ADP
ap-3524	14	31	the	the	DET
ap-3524	14	32	functions	function	NOUN
ap-3524	14	33	,	,	PUNCT
ap-3524	14	34	is	be	AUX
ap-3524	14	35	not	not	PART
ap-3524	14	36	valid	valid	ADJ
ap-3524	14	37	in	in	ADP
ap-3524	14	38	the	the	DET
ap-3524	14	39	discrete	discrete	ADJ
ap-3524	14	40	case	case	NOUN
ap-3524	14	41	for	for	ADP
ap-3524	14	42	a	a	DET
ap-3524	14	43	general	general	ADJ
ap-3524	14	44	lattice	lattice	NOUN
ap-3524	14	45	.	.	PUNCT
ap-3524	15	1	recently	recently	ADV
ap-3524	15	2	it	it	PRON
ap-3524	15	3	has	have	AUX
ap-3524	15	4	been	be	AUX
ap-3524	15	5	shown	show	VERB
ap-3524	15	6	[	[	PUNCT
ap-3524	15	7	14	14	NUM
ap-3524	15	8	]	]	PUNCT
ap-3524	15	9	that	that	SCONJ
ap-3524	15	10	the	the	DET
ap-3524	15	11	discrete	discrete	ADJ
ap-3524	15	12	clairaut	clairaut	NOUN
ap-3524	15	13	–	–	PUNCT
ap-3524	15	14	schwarz	schwarz	NOUN
ap-3524	15	15	–	–	PUNCT
ap-3524	15	16	young	young	ADJ
ap-3524	15	17	theorem	theorem	NOUN
ap-3524	15	18	,	,	PUNCT
ap-3524	15	19	equality	equality	NOUN
ap-3524	15	20	of	of	ADP
ap-3524	15	21	the	the	DET
ap-3524	15	22	cross	cross	NOUN
ap-3524	15	23	differences	difference	NOUN
ap-3524	15	24	,	,	PUNCT
ap-3524	15	25	imposes	impose	VERB
ap-3524	15	26	strong	strong	ADJ
ap-3524	15	27	restrictions	restriction	NOUN
ap-3524	15	28	on	on	ADP
ap-3524	15	29	the	the	DET
ap-3524	15	30	lattice	lattice	NOUN
ap-3524	15	31	.	.	PUNCT
ap-3524	16	1	moreover	moreover	ADV
ap-3524	16	2	,	,	PUNCT
ap-3524	16	3	the	the	DET
ap-3524	16	4	construction	construction	NOUN
ap-3524	16	5	of	of	ADP
ap-3524	16	6	the	the	DET
ap-3524	16	7	discrete	discrete	ADJ
ap-3524	16	8	invariant	invariant	ADJ
ap-3524	16	9	scheme	scheme	NOUN
ap-3524	16	10	starting	start	VERB
ap-3524	16	11	from	from	ADP
ap-3524	16	12	the	the	DET
ap-3524	16	13	discrete	discrete	ADJ
ap-3524	16	14	invariants	invariant	NOUN
ap-3524	16	15	is	be	AUX
ap-3524	16	16	not	not	PART
ap-3524	16	17	at	at	ADV
ap-3524	16	18	all	all	ADV
ap-3524	16	19	obvious	obvious	ADJ
ap-3524	16	20	as	as	SCONJ
ap-3524	16	21	it	it	PRON
ap-3524	16	22	is	be	AUX
ap-3524	16	23	usually	usually	ADV
ap-3524	16	24	obtained	obtain	VERB
ap-3524	16	25	by	by	ADP
ap-3524	16	26	finding	find	VERB
ap-3524	16	27	a	a	DET
ap-3524	16	28	proper	proper	ADJ
ap-3524	16	29	combination	combination	NOUN
ap-3524	16	30	of	of	ADP
ap-3524	16	31	the	the	DET
ap-3524	16	32	continuous	continuous	ADJ
ap-3524	16	33	limits	limit	NOUN
ap-3524	16	34	of	of	ADP
ap-3524	16	35	the	the	DET
ap-3524	16	36	various	various	ADJ
ap-3524	16	37	discrete	discrete	ADJ
ap-3524	16	38	invariants	invariant	NOUN
ap-3524	16	39	.	.	PUNCT
ap-3524	17	1	the	the	DET
ap-3524	17	2	main	main	ADJ
ap-3524	17	3	idea	idea	NOUN
ap-3524	17	4	guiding	guide	VERB
ap-3524	17	5	the	the	DET
ap-3524	17	6	construction	construction	NOUN
ap-3524	17	7	of	of	ADP
ap-3524	17	8	the	the	DET
ap-3524	17	9	whole	whole	ADJ
ap-3524	17	10	scheme	scheme	NOUN
ap-3524	17	11	,	,	PUNCT
ap-3524	17	12	that	that	PRON
ap-3524	17	13	is	be	AUX
ap-3524	17	14	the	the	DET
ap-3524	17	15	difference	difference	NOUN
ap-3524	17	16	equations	equation	NOUN
ap-3524	17	17	and	and	CCONJ
ap-3524	17	18	the	the	DET
ap-3524	17	19	equations	equation	NOUN
ap-3524	17	20	defining	define	VERB
ap-3524	17	21	the	the	DET
ap-3524	17	22	lattice	lattice	NOUN
ap-3524	17	23	,	,	PUNCT
ap-3524	17	24	which	which	PRON
ap-3524	17	25	in	in	ADP
ap-3524	17	26	some	some	DET
ap-3524	17	27	cases	case	NOUN
ap-3524	17	28	are	be	AUX
ap-3524	17	29	mixed	mixed	ADJ
ap-3524	17	30	,	,	PUNCT
ap-3524	17	31	is	be	AUX
ap-3524	17	32	that	that	SCONJ
ap-3524	17	33	the	the	DET
ap-3524	17	34	continuous	continuous	ADJ
ap-3524	17	35	limit	limit	NOUN
ap-3524	17	36	yields	yield	VERB
ap-3524	17	37	the	the	DET
ap-3524	17	38	differential	differential	ADJ
ap-3524	17	39	equation	equation	NOUN
ap-3524	17	40	and	and	CCONJ
ap-3524	17	41	trivial	trivial	ADJ
ap-3524	17	42	identities	identity	NOUN
ap-3524	17	43	.	.	PUNCT
ap-3524	18	1	this	this	DET
ap-3524	18	2	article	article	NOUN
ap-3524	18	3	is	be	AUX
ap-3524	18	4	a	a	DET
ap-3524	18	5	continuation	continuation	NOUN
ap-3524	18	6	of	of	ADP
ap-3524	18	7	our	our	PRON
ap-3524	18	8	work	work	NOUN
ap-3524	18	9	on	on	ADP
ap-3524	18	10	the	the	DET
ap-3524	18	11	construction	construction	NOUN
ap-3524	18	12	of	of	ADP
ap-3524	18	13	partial	partial	ADJ
ap-3524	18	14	difference	difference	NOUN
ap-3524	18	15	schemes	scheme	NOUN
ap-3524	18	16	[	[	X
ap-3524	18	17	14	14	NUM
ap-3524	18	18	]	]	PUNCT
ap-3524	18	19	.	.	PUNCT
ap-3524	19	1	in	in	ADP
ap-3524	19	2	the	the	DET
ap-3524	19	3	previous	previous	ADJ
ap-3524	19	4	work	work	NOUN
ap-3524	19	5	we	we	PRON
ap-3524	19	6	concentrated	concentrate	VERB
ap-3524	19	7	on	on	ADP
ap-3524	19	8	the	the	DET
ap-3524	19	9	clairaut	clairaut	NOUN
ap-3524	19	10	–	–	PUNCT
ap-3524	19	11	schwarz	schwarz	PROPN
ap-3524	19	12	–	–	PUNCT
ap-3524	19	13	young	young	ADJ
ap-3524	19	14	theorem	theorem	NOUN
ap-3524	19	15	.	.	PUNCT
ap-3524	20	1	here	here	ADV
ap-3524	20	2	we	we	PRON
ap-3524	20	3	introduce	introduce	VERB
ap-3524	20	4	by	by	ADP
ap-3524	20	5	a	a	DET
ap-3524	20	6	one	one	NOUN
ap-3524	20	7	to	to	ADP
ap-3524	20	8	one	one	NUM
ap-3524	20	9	correspondence	correspondence	NOUN
ap-3524	20	10	a	a	DET
ap-3524	20	11	new	new	ADJ
ap-3524	20	12	set	set	NOUN
ap-3524	20	13	of	of	ADP
ap-3524	20	14	discrete	discrete	ADJ
ap-3524	20	15	coordinates	coordinate	NOUN
ap-3524	20	16	which	which	PRON
ap-3524	20	17	describe	describe	VERB
ap-3524	20	18	the	the	DET
ap-3524	20	19	partial	partial	ADJ
ap-3524	20	20	difference	difference	NOUN
ap-3524	20	21	equation	equation	NOUN
ap-3524	20	22	on	on	ADP
ap-3524	20	23	the	the	DET
ap-3524	20	24	lattice	lattice	NOUN
ap-3524	20	25	.	.	PUNCT
ap-3524	21	1	in	in	ADP
ap-3524	21	2	terms	term	NOUN
ap-3524	21	3	of	of	ADP
ap-3524	21	4	these	these	DET
ap-3524	21	5	coordinate	coordinate	NOUN
ap-3524	21	6	systems	system	NOUN
ap-3524	21	7	we	we	PRON
ap-3524	21	8	can	can	AUX
ap-3524	21	9	write	write	VERB
ap-3524	21	10	immediately	immediately	ADV
ap-3524	21	11	the	the	DET
ap-3524	21	12	discrete	discrete	ADJ
ap-3524	21	13	counterpart	counterpart	NOUN
ap-3524	21	14	of	of	ADP
ap-3524	21	15	any	any	DET
ap-3524	21	16	continuous	continuous	ADJ
ap-3524	21	17	invariant	invariant	NOUN
ap-3524	21	18	.	.	PUNCT
ap-3524	22	1	so	so	ADV
ap-3524	22	2	we	we	PRON
ap-3524	22	3	can	can	AUX
ap-3524	22	4	discretize	discretize	VERB
ap-3524	22	5	in	in	ADP
ap-3524	22	6	a	a	DET
ap-3524	22	7	straightforward	straightforward	ADJ
ap-3524	22	8	way	way	NOUN
ap-3524	22	9	any	any	DET
ap-3524	22	10	partial	partial	ADJ
ap-3524	22	11	differential	differential	NOUN
ap-3524	22	12	equation	equation	NOUN
ap-3524	22	13	described	describe	VERB
ap-3524	22	14	in	in	ADP
ap-3524	22	15	terms	term	NOUN
ap-3524	22	16	of	of	ADP
ap-3524	22	17	the	the	DET
ap-3524	22	18	invariants	invariant	NOUN
ap-3524	22	19	of	of	ADP
ap-3524	22	20	a	a	DET
ap-3524	22	21	group	group	NOUN
ap-3524	22	22	of	of	ADP
ap-3524	22	23	symmetries	symmetry	NOUN
ap-3524	22	24	.	.	PUNCT
ap-3524	23	1	a	a	DET
ap-3524	23	2	particular	particular	ADJ
ap-3524	23	3	role	role	NOUN
ap-3524	23	4	in	in	ADP
ap-3524	23	5	the	the	DET
ap-3524	23	6	construction	construction	NOUN
ap-3524	23	7	of	of	ADP
ap-3524	23	8	discrete	discrete	ADJ
ap-3524	23	9	invariant	invariant	ADJ
ap-3524	23	10	schemes	scheme	NOUN
ap-3524	23	11	is	be	AUX
ap-3524	23	12	played	play	VERB
ap-3524	23	13	by	by	ADP
ap-3524	23	14	the	the	DET
ap-3524	23	15	lattice	lattice	NOUN
ap-3524	23	16	.	.	PUNCT
ap-3524	24	1	consequently	consequently	ADV
ap-3524	24	2	the	the	DET
ap-3524	24	3	clairaut	clairaut	NOUN
ap-3524	24	4	–	–	PUNCT
ap-3524	24	5	schwarz	schwarz	NOUN
ap-3524	24	6	–	–	PUNCT
ap-3524	24	7	young	young	ADJ
ap-3524	24	8	theorem	theorem	NOUN
ap-3524	24	9	can	can	AUX
ap-3524	24	10	play	play	VERB
ap-3524	24	11	an	an	DET
ap-3524	24	12	important	important	ADJ
ap-3524	24	13	role	role	NOUN
ap-3524	24	14	in	in	ADP
ap-3524	24	15	discriminating	discriminate	VERB
ap-3524	24	16	lattice	lattice	NOUN
ap-3524	24	17	schemes	scheme	NOUN
ap-3524	24	18	,	,	PUNCT
ap-3524	24	19	i.e.	i.e.	X
ap-3524	24	20	,	,	PUNCT
ap-3524	24	21	the	the	DET
ap-3524	24	22	combination	combination	NOUN
ap-3524	24	23	of	of	ADP
ap-3524	24	24	the	the	DET
ap-3524	24	25	discrete	discrete	ADJ
ap-3524	24	26	equation	equation	NOUN
ap-3524	24	27	and	and	CCONJ
ap-3524	24	28	its	its	PRON
ap-3524	24	29	lattice	lattice	NOUN
ap-3524	24	30	.	.	PUNCT
ap-3524	25	1	in	in	ADP
ap-3524	25	2	section	section	NOUN
ap-3524	25	3	2	2	NUM
ap-3524	25	4	we	we	PRON
ap-3524	25	5	study	study	VERB
ap-3524	25	6	schemes	scheme	NOUN
ap-3524	25	7	for	for	ADP
ap-3524	25	8	scalar	scalar	ADJ
ap-3524	25	9	partial	partial	ADJ
ap-3524	25	10	differential	differential	NOUN
ap-3524	25	11	equations	equation	NOUN
ap-3524	25	12	and	and	CCONJ
ap-3524	25	13	show	show	VERB
ap-3524	25	14	the	the	DET
ap-3524	25	15	constraints	constraint	NOUN
ap-3524	25	16	on	on	ADP
ap-3524	25	17	the	the	DET
ap-3524	25	18	group	group	NOUN
ap-3524	25	19	transformations	transformation	NOUN
ap-3524	25	20	due	due	ADP
ap-3524	25	21	to	to	ADP
ap-3524	25	22	the	the	DET
ap-3524	25	23	clairaut	clairaut	NOUN
ap-3524	25	24	–	–	PUNCT
ap-3524	25	25	schwarz	schwarz	PROPN
ap-3524	25	26	–	–	PUNCT
ap-3524	25	27	young	young	ADJ
ap-3524	25	28	theorem	theorem	NOUN
ap-3524	25	29	.	.	PUNCT
ap-3524	26	1	using	use	VERB
ap-3524	26	2	these	these	DET
ap-3524	26	3	results	result	NOUN
ap-3524	26	4	,	,	PUNCT
ap-3524	26	5	in	in	ADP
ap-3524	26	6	section	section	NOUN
ap-3524	26	7	3	3	NUM
ap-3524	26	8	we	we	PRON
ap-3524	26	9	construct	construct	VERB
ap-3524	26	10	236	236	NUM
ap-3524	26	11	http://dx.doi.org/10.14311/ap.2016.56.0236	http://dx.doi.org/10.14311/ap.2016.56.0236	PUNCT
ap-3524	26	12	http://ojs.cvut.cz/ojs/index.php/ap	http://ojs.cvut.cz/ojs/index.php/ap	PROPN
ap-3524	26	13	vol	vol	NOUN
ap-3524	26	14	.	.	PUNCT
ap-3524	27	1	56	56	NUM
ap-3524	27	2	no	no	NOUN
ap-3524	27	3	.	.	PUNCT
ap-3524	28	1	3/2016	3/2016	NUM
ap-3524	28	2	on	on	ADP
ap-3524	28	3	the	the	DET
ap-3524	28	4	construction	construction	NOUN
ap-3524	28	5	of	of	ADP
ap-3524	28	6	partial	partial	ADJ
ap-3524	28	7	difference	difference	NOUN
ap-3524	28	8	schemes	scheme	NOUN
ap-3524	28	9	ii	ii	NOUN
ap-3524	28	10	in	in	ADP
ap-3524	28	11	a	a	DET
ap-3524	28	12	standard	standard	ADJ
ap-3524	28	13	way	way	NOUN
ap-3524	28	14	the	the	DET
ap-3524	28	15	invariant	invariant	ADJ
ap-3524	28	16	discrete	discrete	ADJ
ap-3524	28	17	potential	potential	ADJ
ap-3524	28	18	burgers	burger	NOUN
ap-3524	28	19	and	and	CCONJ
ap-3524	28	20	in	in	ADP
ap-3524	28	21	section	section	NOUN
ap-3524	28	22	4	4	NUM
ap-3524	28	23	,	,	PUNCT
ap-3524	28	24	we	we	PRON
ap-3524	28	25	study	study	VERB
ap-3524	28	26	it	it	PRON
ap-3524	28	27	numerically	numerically	ADV
ap-3524	28	28	for	for	ADP
ap-3524	28	29	two	two	NUM
ap-3524	28	30	different	different	ADJ
ap-3524	28	31	lattices	lattice	NOUN
ap-3524	28	32	,	,	PUNCT
ap-3524	28	33	one	one	NUM
ap-3524	28	34	invariant	invariant	ADJ
ap-3524	28	35	and	and	CCONJ
ap-3524	28	36	schwarzian	schwarzian	NOUN
ap-3524	28	37	and	and	CCONJ
ap-3524	28	38	one	one	NUM
ap-3524	28	39	not	not	PART
ap-3524	28	40	,	,	PUNCT
ap-3524	28	41	for	for	ADP
ap-3524	28	42	two	two	NUM
ap-3524	28	43	different	different	ADJ
ap-3524	28	44	exact	exact	ADJ
ap-3524	28	45	solutions	solution	NOUN
ap-3524	28	46	of	of	ADP
ap-3524	28	47	the	the	DET
ap-3524	28	48	differential	differential	ADJ
ap-3524	28	49	equation	equation	NOUN
ap-3524	28	50	.	.	PUNCT
ap-3524	29	1	some	some	DET
ap-3524	29	2	concluding	conclude	VERB
ap-3524	29	3	remarks	remark	NOUN
ap-3524	29	4	are	be	AUX
ap-3524	29	5	presented	present	VERB
ap-3524	29	6	in	in	ADP
ap-3524	29	7	section	section	NOUN
ap-3524	29	8	5	5	NUM
ap-3524	29	9	.	.	NOUN
ap-3524	29	10	2	2	NUM
ap-3524	29	11	.	.	PUNCT
ap-3524	30	1	schemes	scheme	NOUN
ap-3524	30	2	for	for	ADP
ap-3524	30	3	partial	partial	ADJ
ap-3524	30	4	difference	difference	NOUN
ap-3524	30	5	equations	equation	NOUN
ap-3524	30	6	in	in	ADP
ap-3524	30	7	the	the	DET
ap-3524	30	8	case	case	NOUN
ap-3524	30	9	of	of	ADP
ap-3524	30	10	ordinary	ordinary	ADJ
ap-3524	30	11	difference	difference	NOUN
ap-3524	30	12	equations	equation	NOUN
ap-3524	30	13	of	of	ADP
ap-3524	30	14	order	order	NOUN
ap-3524	30	15	k	k	PROPN
ap-3524	30	16	for	for	ADP
ap-3524	30	17	one	one	NUM
ap-3524	30	18	dependent	dependent	ADJ
ap-3524	30	19	variable	variable	ADJ
ap-3524	30	20	un	un	NOUN
ap-3524	30	21	and	and	CCONJ
ap-3524	30	22	one	one	NUM
ap-3524	30	23	independent	independent	ADJ
ap-3524	30	24	variable	variable	NOUN
ap-3524	30	25	xn	xn	PROPN
ap-3524	30	26	,	,	PUNCT
ap-3524	30	27	a	a	DET
ap-3524	30	28	natural	natural	ADJ
ap-3524	30	29	scheme	scheme	NOUN
ap-3524	30	30	is	be	AUX
ap-3524	30	31	given	give	VERB
ap-3524	30	32	by	by	ADP
ap-3524	30	33	the	the	DET
ap-3524	30	34	points	point	NOUN
ap-3524	30	35	{	{	PUNCT
ap-3524	30	36	xn+k−1	xn+k−1	PROPN
ap-3524	30	37	,	,	PUNCT
ap-3524	30	38	un+k−1	un+k−1	PROPN
ap-3524	30	39	,	,	PUNCT
ap-3524	30	40	1	1	NUM
ap-3524	30	41	≤	≤	NUM
ap-3524	30	42	k	k	NOUN
ap-3524	30	43	≤	≤	PROPN
ap-3524	31	1	k	k	PROPN
ap-3524	32	1	+	+	CCONJ
ap-3524	32	2	1	1	X
ap-3524	32	3	}	}	PUNCT
ap-3524	32	4	for	for	ADP
ap-3524	32	5	some	some	DET
ap-3524	32	6	fixed	fix	VERB
ap-3524	32	7	n.	n.	NOUN
ap-3524	32	8	an	an	DET
ap-3524	32	9	alternative	alternative	ADJ
ap-3524	32	10	equivalent	equivalent	ADJ
ap-3524	32	11	set	set	NOUN
ap-3524	32	12	of	of	ADP
ap-3524	32	13	coordinates	coordinate	NOUN
ap-3524	32	14	on	on	ADP
ap-3524	32	15	the	the	DET
ap-3524	32	16	scheme	scheme	NOUN
ap-3524	32	17	is	be	AUX
ap-3524	32	18	given	give	VERB
ap-3524	32	19	by	by	ADP
ap-3524	32	20	[	[	X
ap-3524	32	21	14	14	NUM
ap-3524	32	22	,	,	PUNCT
ap-3524	32	23	23	23	NUM
ap-3524	32	24	]	]	PUNCT
ap-3524	32	25	:	:	PUNCT
ap-3524	32	26	{	{	PUNCT
ap-3524	32	27	xn	xn	PROPN
ap-3524	32	28	,	,	PUNCT
ap-3524	32	29	un	un	PROPN
ap-3524	32	30	,	,	PUNCT
ap-3524	32	31	p(1	p(1	PROPN
ap-3524	32	32	)	)	PUNCT
ap-3524	32	33	n+1	n+1	PROPN
ap-3524	32	34	,	,	PUNCT
ap-3524	32	35	p	p	X
ap-3524	32	36	(	(	PUNCT
ap-3524	32	37	2	2	NUM
ap-3524	32	38	)	)	PUNCT
ap-3524	32	39	n+2	n+2	NUM
ap-3524	32	40	,	,	PUNCT
ap-3524	32	41	p	p	X
ap-3524	32	42	(	(	PUNCT
ap-3524	32	43	3	3	NUM
ap-3524	32	44	)	)	PUNCT
ap-3524	32	45	n+3	n+3	PROPN
ap-3524	32	46	,	,	PUNCT
ap-3524	32	47	p	p	X
ap-3524	32	48	(	(	PUNCT
ap-3524	32	49	4	4	NUM
ap-3524	32	50	)	)	PUNCT
ap-3524	32	51	n+4	n+4	NUM
ap-3524	32	52	,	,	PUNCT
ap-3524	32	53	.	.	PUNCT
ap-3524	32	54	.	.	PUNCT
ap-3524	32	55	.	.	PUNCT
ap-3524	33	1	p	p	X
ap-3524	33	2	(	(	PUNCT
ap-3524	33	3	k−1	k−1	PROPN
ap-3524	33	4	)	)	PUNCT
ap-3524	33	5	n+k−1	n+k−1	PROPN
ap-3524	33	6	,	,	PUNCT
ap-3524	33	7	p	p	X
ap-3524	33	8	(	(	PUNCT
ap-3524	33	9	k	k	NOUN
ap-3524	33	10	)	)	PUNCT
ap-3524	33	11	n+k	n+k	PROPN
ap-3524	33	12	,	,	PUNCT
ap-3524	33	13	hn+1	hn+1	PROPN
ap-3524	33	14	,	,	PUNCT
ap-3524	33	15	hn+2	hn+2	NOUN
ap-3524	33	16	,	,	PUNCT
ap-3524	33	17	.	.	PUNCT
ap-3524	33	18	.	.	PUNCT
ap-3524	33	19	.	.	PUNCT
ap-3524	34	1	hn+k	hn+k	INTJ
ap-3524	34	2	}	}	PUNCT
ap-3524	34	3	(	(	PUNCT
ap-3524	34	4	1	1	NUM
ap-3524	34	5	)	)	PUNCT
ap-3524	34	6	with	with	ADP
ap-3524	34	7	hn+k	hn+k	PROPN
ap-3524	34	8	=	=	PUNCT
ap-3524	34	9	xn+k	xn+k	PROPN
ap-3524	34	10	−	−	PROPN
ap-3524	35	1	xn+k−1	xn+k−1	PROPN
ap-3524	35	2	,	,	PUNCT
ap-3524	36	1	1	1	NUM
ap-3524	36	2	≤	≤	NUM
ap-3524	36	3	k	k	X
ap-3524	36	4	≤	≤	PROPN
ap-3524	36	5	k	k	PROPN
ap-3524	36	6	,	,	PUNCT
ap-3524	36	7	p	p	X
ap-3524	36	8	(	(	PUNCT
ap-3524	36	9	k	k	NOUN
ap-3524	36	10	)	)	PUNCT
ap-3524	36	11	n+k	n+k	PROPN
ap-3524	36	12	=	=	PUNCT
ap-3524	37	1	[	[	X
ap-3524	37	2	dx]kun	dx]kun	X
ap-3524	37	3	,	,	PUNCT
ap-3524	37	4	where	where	SCONJ
ap-3524	37	5	dx	dx	PROPN
ap-3524	37	6	=	=	NOUN
ap-3524	37	7	1	1	NUM
ap-3524	37	8	hn+1	hn+1	X
ap-3524	38	1	[	[	X
ap-3524	38	2	tx	tx	PROPN
ap-3524	38	3	−	−	NUM
ap-3524	38	4	1	1	NUM
ap-3524	38	5	]	]	PUNCT
ap-3524	38	6	,	,	PUNCT
ap-3524	38	7	txun	txun	NOUN
ap-3524	38	8	=	=	SYM
ap-3524	38	9	un+1	un+1	PROPN
ap-3524	38	10	,	,	PUNCT
ap-3524	38	11	k	k	PROPN
ap-3524	38	12	∈	∈	PROPN
ap-3524	38	13	z+	z+	NUM
ap-3524	38	14	(	(	PUNCT
ap-3524	38	15	2	2	NUM
ap-3524	38	16	)	)	PUNCT
ap-3524	38	17	in	in	ADP
ap-3524	38	18	the	the	DET
ap-3524	38	19	continuous	continuous	ADJ
ap-3524	38	20	limit	limit	NOUN
ap-3524	38	21	hn+k	hn+k	PROPN
ap-3524	38	22	→	→	SYM
ap-3524	38	23	0	0	NUM
ap-3524	38	24	and	and	CCONJ
ap-3524	38	25	p(k	p(k	NOUN
ap-3524	38	26	)	)	PUNCT
ap-3524	38	27	n+k	n+k	NOUN
ap-3524	38	28	→	→	SYM
ap-3524	38	29	dku(x	dku(x	PROPN
ap-3524	38	30	)	)	PUNCT
ap-3524	38	31	dxk	dxk	NOUN
ap-3524	38	32	.	.	PUNCT
ap-3524	39	1	if	if	SCONJ
ap-3524	39	2	we	we	PRON
ap-3524	39	3	transform	transform	VERB
ap-3524	39	4	the	the	DET
ap-3524	39	5	standard	standard	ADJ
ap-3524	39	6	discrete	discrete	ADJ
ap-3524	39	7	prolongation	prolongation	NOUN
ap-3524	39	8	[	[	X
ap-3524	39	9	17	17	NUM
ap-3524	39	10	]	]	PUNCT
ap-3524	39	11	pr(k	pr(k	NOUN
ap-3524	39	12	)	)	PUNCT
ap-3524	39	13	x̂	x̂	PUNCT
ap-3524	40	1	=	=	PUNCT
ap-3524	40	2	n+k∑	n+k∑	PROPN
ap-3524	40	3	k	k	NOUN
ap-3524	40	4	=	=	NOUN
ap-3524	40	5	n	n	X
ap-3524	40	6	(	(	PUNCT
ap-3524	40	7	ξk(xk	ξk(xk	PROPN
ap-3524	40	8	,	,	PUNCT
ap-3524	40	9	uk)∂xk	uk)∂xk	PROPN
ap-3524	40	10	+	+	CCONJ
ap-3524	40	11	φk(xk	φk(xk	NOUN
ap-3524	40	12	,	,	PUNCT
ap-3524	40	13	uk)∂uk	uk)∂uk	ADJ
ap-3524	40	14	)	)	PUNCT
ap-3524	40	15	(	(	PUNCT
ap-3524	40	16	3	3	X
ap-3524	40	17	)	)	PUNCT
ap-3524	40	18	of	of	ADP
ap-3524	40	19	the	the	DET
ap-3524	40	20	vector	vector	NOUN
ap-3524	40	21	field	field	NOUN
ap-3524	40	22	x̂	x̂	PUNCT
ap-3524	41	1	=	=	PUNCT
ap-3524	41	2	ξn(xn	ξn(xn	NOUN
ap-3524	41	3	,	,	PUNCT
ap-3524	41	4	un)∂xn	un)∂xn	PROPN
ap-3524	41	5	+	+	NUM
ap-3524	41	6	φn(xn	φn(xn	PROPN
ap-3524	41	7	,	,	PUNCT
ap-3524	41	8	un)∂un	un)∂un	PROPN
ap-3524	41	9	(	(	PUNCT
ap-3524	41	10	4	4	NUM
ap-3524	41	11	)	)	PUNCT
ap-3524	41	12	to	to	ADP
ap-3524	41	13	the	the	DET
ap-3524	41	14	new	new	ADJ
ap-3524	41	15	variables	variable	NOUN
ap-3524	41	16	(	(	PUNCT
ap-3524	41	17	1	1	NUM
ap-3524	41	18	)	)	PUNCT
ap-3524	41	19	,	,	PUNCT
ap-3524	41	20	we	we	PRON
ap-3524	41	21	obtain	obtain	VERB
ap-3524	41	22	pr	pr	NOUN
ap-3524	41	23	x̂	x̂	PUNCT
ap-3524	42	1	=	=	PUNCT
ap-3524	42	2	ξn(xn	ξn(xn	NOUN
ap-3524	42	3	,	,	PUNCT
ap-3524	42	4	un)∂xn	un)∂xn	PROPN
ap-3524	42	5	+	+	NUM
ap-3524	42	6	φn(xn	φn(xn	PROPN
ap-3524	42	7	,	,	PUNCT
ap-3524	42	8	un)∂un	un)∂un	PROPN
ap-3524	42	9	+	+	CCONJ
ap-3524	42	10	k∑	k∑	VERB
ap-3524	42	11	k=1	k=1	PROPN
ap-3524	42	12	κ(k)∂hn+k	κ(k)∂hn+k	PROPN
ap-3524	43	1	+	+	CCONJ
ap-3524	43	2	k∑	k∑	PROPN
ap-3524	44	1	k=1	k=1	PROPN
ap-3524	45	1	φ	φ	PROPN
ap-3524	45	2	(	(	PUNCT
ap-3524	45	3	k	k	NOUN
ap-3524	45	4	)	)	PUNCT
ap-3524	45	5	n+k∂p(k	n+k∂p(k	NOUN
ap-3524	45	6	)	)	PUNCT
ap-3524	45	7	n+k	n+k	PROPN
ap-3524	45	8	.	.	PUNCT
ap-3524	46	1	(	(	PUNCT
ap-3524	46	2	5	5	X
ap-3524	46	3	)	)	PUNCT
ap-3524	46	4	the	the	DET
ap-3524	46	5	general	general	ADJ
ap-3524	46	6	formulas	formula	NOUN
ap-3524	46	7	for	for	ADP
ap-3524	46	8	the	the	DET
ap-3524	46	9	coefficients	coefficient	NOUN
ap-3524	46	10	κ(k	κ(k	PROPN
ap-3524	46	11	)	)	PUNCT
ap-3524	46	12	and	and	CCONJ
ap-3524	46	13	φ(k	φ(k	PROPN
ap-3524	46	14	)	)	PUNCT
ap-3524	46	15	are	be	AUX
ap-3524	46	16	κ(k	κ(k	PROPN
ap-3524	46	17	)	)	PUNCT
ap-3524	47	1	=	=	SYM
ap-3524	47	2	ξn+k	ξn+k	PROPN
ap-3524	48	1	−	−	PROPN
ap-3524	48	2	ξn+k−1	ξn+k−1	PROPN
ap-3524	48	3	,	,	PUNCT
ap-3524	48	4	φ	φ	PROPN
ap-3524	48	5	(	(	PUNCT
ap-3524	48	6	k	k	NOUN
ap-3524	48	7	)	)	PUNCT
ap-3524	48	8	n+k	n+k	PROPN
ap-3524	48	9	=	=	SYM
ap-3524	48	10	dxφ	dxφ	NOUN
ap-3524	48	11	(	(	PUNCT
ap-3524	48	12	k−1	k−1	PROPN
ap-3524	48	13	)	)	PUNCT
ap-3524	48	14	n+k−1	n+k−1	PROPN
ap-3524	49	1	−	−	PROPN
ap-3524	49	2	p	p	NOUN
ap-3524	49	3	(	(	PUNCT
ap-3524	49	4	k	k	NOUN
ap-3524	49	5	)	)	PUNCT
ap-3524	49	6	n+kdxξn	n+kdxξn	PROPN
ap-3524	49	7	,	,	PUNCT
ap-3524	49	8	k	k	X
ap-3524	49	9	=	=	SYM
ap-3524	49	10	1	1	NUM
ap-3524	49	11	,	,	PUNCT
ap-3524	49	12	2	2	NUM
ap-3524	49	13	,	,	PUNCT
ap-3524	49	14	.	.	PUNCT
ap-3524	49	15	.	.	PUNCT
ap-3524	49	16	.	.	PUNCT
ap-3524	50	1	,	,	PUNCT
ap-3524	50	2	k.	k.	PROPN
ap-3524	50	3	(	(	PUNCT
ap-3524	50	4	6	6	X
ap-3524	50	5	)	)	PUNCT
ap-3524	50	6	it	it	PRON
ap-3524	50	7	is	be	AUX
ap-3524	50	8	worthwhile	worthwhile	ADJ
ap-3524	50	9	to	to	PART
ap-3524	50	10	notice	notice	VERB
ap-3524	50	11	that	that	SCONJ
ap-3524	50	12	both	both	CCONJ
ap-3524	50	13	the	the	DET
ap-3524	50	14	higher	high	ADJ
ap-3524	50	15	order	order	NOUN
ap-3524	50	16	discrete	discrete	ADJ
ap-3524	50	17	derivatives	derivative	NOUN
ap-3524	50	18	and	and	CCONJ
ap-3524	50	19	their	their	PRON
ap-3524	50	20	corresponding	corresponding	ADJ
ap-3524	50	21	prolongations	prolongation	NOUN
ap-3524	50	22	are	be	AUX
ap-3524	50	23	written	write	VERB
ap-3524	50	24	in	in	ADP
ap-3524	50	25	terms	term	NOUN
ap-3524	50	26	of	of	ADP
ap-3524	50	27	xn	xn	PROPN
ap-3524	50	28	,	,	PUNCT
ap-3524	50	29	un	un	PROPN
ap-3524	50	30	,	,	PUNCT
ap-3524	50	31	ξn(xn	ξn(xn	NOUN
ap-3524	50	32	,	,	PUNCT
ap-3524	50	33	un	un	PROPN
ap-3524	50	34	)	)	PUNCT
ap-3524	50	35	,	,	PUNCT
ap-3524	50	36	φn(xn	φn(xn	PROPN
ap-3524	50	37	,	,	PUNCT
ap-3524	50	38	un	un	PROPN
ap-3524	50	39	)	)	PUNCT
ap-3524	50	40	and	and	CCONJ
ap-3524	50	41	their	their	PRON
ap-3524	50	42	difference	difference	NOUN
ap-3524	50	43	consequences	consequence	NOUN
ap-3524	50	44	obtained	obtain	VERB
ap-3524	50	45	by	by	ADP
ap-3524	50	46	applying	apply	VERB
ap-3524	50	47	the	the	DET
ap-3524	50	48	operator	operator	NOUN
ap-3524	50	49	dx	dx	PROPN
ap-3524	50	50	given	give	VERB
ap-3524	50	51	in	in	ADP
ap-3524	50	52	(	(	PUNCT
ap-3524	50	53	2	2	NUM
ap-3524	50	54	)	)	PUNCT
ap-3524	50	55	.	.	PUNCT
ap-3524	51	1	this	this	DET
ap-3524	51	2	way	way	NOUN
ap-3524	51	3	of	of	ADP
ap-3524	51	4	constructing	construct	VERB
ap-3524	51	5	invariant	invariant	ADJ
ap-3524	51	6	ordinary	ordinary	ADJ
ap-3524	51	7	difference	difference	NOUN
ap-3524	51	8	equation	equation	NOUN
ap-3524	51	9	is	be	AUX
ap-3524	51	10	different	different	ADJ
ap-3524	51	11	from	from	ADP
ap-3524	51	12	that	that	PRON
ap-3524	51	13	considered	consider	VERB
ap-3524	51	14	in	in	ADP
ap-3524	51	15	[	[	X
ap-3524	51	16	13	13	NUM
ap-3524	51	17	]	]	PUNCT
ap-3524	51	18	but	but	CCONJ
ap-3524	51	19	is	be	AUX
ap-3524	51	20	easily	easily	ADV
ap-3524	51	21	extendible	extendible	ADJ
ap-3524	51	22	to	to	ADP
ap-3524	51	23	the	the	DET
ap-3524	51	24	case	case	NOUN
ap-3524	51	25	of	of	ADP
ap-3524	51	26	partial	partial	ADJ
ap-3524	51	27	difference	difference	NOUN
ap-3524	51	28	equations	equation	NOUN
ap-3524	51	29	.	.	PUNCT
ap-3524	52	1	for	for	ADP
ap-3524	52	2	partial	partial	ADJ
ap-3524	52	3	difference	difference	NOUN
ap-3524	52	4	equations	equation	NOUN
ap-3524	52	5	we	we	PRON
ap-3524	52	6	consider	consider	VERB
ap-3524	52	7	here	here	ADV
ap-3524	52	8	only	only	ADV
ap-3524	52	9	,	,	PUNCT
ap-3524	52	10	for	for	ADP
ap-3524	52	11	simplicity	simplicity	NOUN
ap-3524	52	12	,	,	PUNCT
ap-3524	52	13	the	the	DET
ap-3524	52	14	case	case	NOUN
ap-3524	52	15	of	of	ADP
ap-3524	52	16	one	one	NUM
ap-3524	52	17	dependent	dependent	ADJ
ap-3524	52	18	variable	variable	NOUN
ap-3524	52	19	and	and	CCONJ
ap-3524	52	20	two	two	NUM
ap-3524	52	21	independent	independent	ADJ
ap-3524	52	22	variables	variable	NOUN
ap-3524	52	23	as	as	SCONJ
ap-3524	52	24	will	will	AUX
ap-3524	52	25	be	be	AUX
ap-3524	52	26	the	the	DET
ap-3524	52	27	example	example	NOUN
ap-3524	52	28	we	we	PRON
ap-3524	52	29	will	will	AUX
ap-3524	52	30	discuss	discuss	VERB
ap-3524	52	31	in	in	ADP
ap-3524	52	32	the	the	DET
ap-3524	52	33	following	follow	VERB
ap-3524	52	34	section	section	NOUN
ap-3524	52	35	.	.	PUNCT
ap-3524	53	1	moreover	moreover	ADV
ap-3524	53	2	,	,	PUNCT
ap-3524	53	3	as	as	SCONJ
ap-3524	53	4	we	we	PRON
ap-3524	53	5	will	will	AUX
ap-3524	53	6	deal	deal	VERB
ap-3524	53	7	with	with	ADP
ap-3524	53	8	a	a	DET
ap-3524	53	9	nonlinear	nonlinear	ADJ
ap-3524	53	10	partial	partial	ADJ
ap-3524	53	11	difference	difference	NOUN
ap-3524	53	12	equation	equation	NOUN
ap-3524	53	13	of	of	ADP
ap-3524	53	14	second	second	ADJ
ap-3524	53	15	order	order	NOUN
ap-3524	53	16	we	we	PRON
ap-3524	53	17	limit	limit	VERB
ap-3524	53	18	ourselves	ourselves	PRON
ap-3524	53	19	to	to	ADP
ap-3524	53	20	a	a	DET
ap-3524	53	21	scheme	scheme	NOUN
ap-3524	53	22	of	of	ADP
ap-3524	53	23	six	six	NUM
ap-3524	53	24	points	point	NOUN
ap-3524	53	25	(	(	PUNCT
ap-3524	53	26	n	n	CCONJ
ap-3524	53	27	,	,	PUNCT
ap-3524	53	28	m	m	NOUN
ap-3524	53	29	)	)	PUNCT
ap-3524	53	30	,	,	PUNCT
ap-3524	53	31	(	(	PUNCT
ap-3524	53	32	n+	n+	X
ap-3524	53	33	1,m	1,m	NUM
ap-3524	53	34	)	)	PUNCT
ap-3524	53	35	,	,	PUNCT
ap-3524	53	36	(	(	PUNCT
ap-3524	53	37	n	n	CCONJ
ap-3524	53	38	,	,	PUNCT
ap-3524	53	39	m+	m+	NOUN
ap-3524	53	40	1	1	NUM
ap-3524	53	41	)	)	PUNCT
ap-3524	53	42	,	,	PUNCT
ap-3524	53	43	(	(	PUNCT
ap-3524	53	44	n+	n+	X
ap-3524	53	45	2,m	2,m	NOUN
ap-3524	53	46	)	)	PUNCT
ap-3524	53	47	,	,	PUNCT
ap-3524	53	48	(	(	PUNCT
ap-3524	53	49	n	n	CCONJ
ap-3524	53	50	,	,	PUNCT
ap-3524	53	51	m+	m+	NOUN
ap-3524	53	52	2	2	NUM
ap-3524	53	53	)	)	PUNCT
ap-3524	53	54	,	,	PUNCT
ap-3524	53	55	(	(	PUNCT
ap-3524	53	56	n+	n+	NUM
ap-3524	53	57	1,m+	1,m+	NUM
ap-3524	53	58	1	1	NUM
ap-3524	53	59	)	)	PUNCT
ap-3524	53	60	,	,	PUNCT
ap-3524	53	61	the	the	DET
ap-3524	53	62	minimum	minimum	ADJ
ap-3524	53	63	number	number	NOUN
ap-3524	53	64	of	of	ADP
ap-3524	53	65	points	point	NOUN
ap-3524	53	66	necessary	necessary	ADJ
ap-3524	53	67	to	to	PART
ap-3524	53	68	get	get	VERB
ap-3524	53	69	all	all	DET
ap-3524	53	70	partial	partial	ADJ
ap-3524	53	71	second	second	ADJ
ap-3524	53	72	derivatives	derivative	NOUN
ap-3524	53	73	as	as	ADP
ap-3524	53	74	first	first	ADJ
ap-3524	53	75	order	order	NOUN
ap-3524	53	76	approximations	approximation	NOUN
ap-3524	53	77	.	.	PUNCT
ap-3524	54	1	the	the	DET
ap-3524	54	2	variables	variable	NOUN
ap-3524	54	3	x	x	NOUN
ap-3524	54	4	,	,	PUNCT
ap-3524	54	5	y	y	PROPN
ap-3524	54	6	and	and	CCONJ
ap-3524	54	7	u(x	u(x	PROPN
ap-3524	54	8	,	,	PUNCT
ap-3524	54	9	y	y	NOUN
ap-3524	54	10	)	)	PUNCT
ap-3524	54	11	in	in	ADP
ap-3524	54	12	all	all	DET
ap-3524	54	13	points	point	NOUN
ap-3524	54	14	correspond	correspond	VERB
ap-3524	54	15	to	to	ADP
ap-3524	54	16	18	18	NUM
ap-3524	54	17	data	datum	NOUN
ap-3524	54	18	,	,	PUNCT
ap-3524	54	19	12	12	NUM
ap-3524	54	20	related	relate	VERB
ap-3524	54	21	to	to	ADP
ap-3524	54	22	the	the	DET
ap-3524	54	23	independent	independent	ADJ
ap-3524	54	24	variables	variable	NOUN
ap-3524	54	25	and	and	CCONJ
ap-3524	54	26	6	6	NUM
ap-3524	54	27	to	to	ADP
ap-3524	54	28	the	the	DET
ap-3524	54	29	dependent	dependent	ADJ
ap-3524	54	30	one	one	NUM
ap-3524	54	31	.	.	PUNCT
ap-3524	55	1	the	the	DET
ap-3524	55	2	extension	extension	NOUN
ap-3524	55	3	to	to	ADP
ap-3524	55	4	more	more	ADJ
ap-3524	55	5	variables	variable	NOUN
ap-3524	55	6	and	and	CCONJ
ap-3524	55	7	higher	high	ADJ
ap-3524	55	8	order	order	NOUN
ap-3524	55	9	equations	equation	NOUN
ap-3524	55	10	requires	require	VERB
ap-3524	55	11	just	just	ADV
ap-3524	55	12	more	more	ADJ
ap-3524	55	13	points	point	NOUN
ap-3524	55	14	but	but	CCONJ
ap-3524	55	15	it	it	PRON
ap-3524	55	16	is	be	AUX
ap-3524	55	17	straightforward	straightforward	ADJ
ap-3524	55	18	.	.	PUNCT
ap-3524	56	1	having	have	VERB
ap-3524	56	2	12	12	NUM
ap-3524	56	3	data	datum	NOUN
ap-3524	56	4	for	for	ADP
ap-3524	56	5	the	the	DET
ap-3524	56	6	independent	independent	ADJ
ap-3524	56	7	variables	variable	NOUN
ap-3524	56	8	we	we	PRON
ap-3524	56	9	can	can	AUX
ap-3524	56	10	construct	construct	VERB
ap-3524	56	11	from	from	ADP
ap-3524	56	12	them	they	PRON
ap-3524	56	13	10	10	NUM
ap-3524	56	14	differences	difference	NOUN
ap-3524	56	15	x0,0	x0,0	NOUN
ap-3524	56	16	,	,	PUNCT
ap-3524	56	17	y0,0	y0,0	NOUN
ap-3524	56	18	,	,	PUNCT
ap-3524	56	19	hx0,0	hx0,0	NOUN
ap-3524	56	20	=	=	SYM
ap-3524	56	21	x1,0	x1,0	PROPN
ap-3524	56	22	−	−	PROPN
ap-3524	56	23	x0,0	x0,0	NOUN
ap-3524	56	24	,	,	PUNCT
ap-3524	56	25	hy0,0	hy0,0	NOUN
ap-3524	56	26	=	=	PUNCT
ap-3524	56	27	y0,1	y0,1	PROPN
ap-3524	56	28	−	−	PROPN
ap-3524	56	29	y0,0	y0,0	NOUN
ap-3524	56	30	,	,	PUNCT
ap-3524	56	31	σx0,0	σx0,0	NOUN
ap-3524	57	1	=	=	SYM
ap-3524	57	2	x0,1	x0,1	PROPN
ap-3524	57	3	−	−	PROPN
ap-3524	58	1	x0,0	x0,0	NOUN
ap-3524	58	2	,	,	PUNCT
ap-3524	58	3	σy0,0	σy0,0	NOUN
ap-3524	58	4	=	=	PUNCT
ap-3524	58	5	y1,0	y1,0	PROPN
ap-3524	58	6	−	−	PROPN
ap-3524	58	7	y0,0	y0,0	NOUN
ap-3524	58	8	,	,	PUNCT
ap-3524	58	9	hx1,0	hx1,0	NOUN
ap-3524	58	10	=	=	PUNCT
ap-3524	59	1	x2,0	x2,0	PROPN
ap-3524	60	1	−	−	PROPN
ap-3524	60	2	x1,0	x1,0	PROPN
ap-3524	60	3	,	,	PUNCT
ap-3524	60	4	hy0,1	hy0,1	NOUN
ap-3524	60	5	=	=	SYM
ap-3524	60	6	y0,2	y0,2	PROPN
ap-3524	60	7	−	−	PROPN
ap-3524	60	8	y0,1	y0,1	NOUN
ap-3524	60	9	,	,	PUNCT
ap-3524	60	10	σx0,1	σx0,1	NOUN
ap-3524	60	11	=	=	SYM
ap-3524	60	12	x0,2	x0,2	PROPN
ap-3524	60	13	−	−	PROPN
ap-3524	60	14	x0,1	x0,1	NOUN
ap-3524	60	15	,	,	PUNCT
ap-3524	60	16	σy1,0	σy1,0	VERB
ap-3524	60	17	=	=	PUNCT
ap-3524	60	18	y2,0	y2,0	PROPN
ap-3524	60	19	−	−	PROPN
ap-3524	60	20	y1,0	y1,0	PROPN
ap-3524	60	21	,	,	PUNCT
ap-3524	60	22	hx0,1	hx0,1	NOUN
ap-3524	60	23	=	=	SYM
ap-3524	60	24	x1,1	x1,1	PROPN
ap-3524	61	1	−	−	PROPN
ap-3524	61	2	x0,1	x0,1	NOUN
ap-3524	61	3	,	,	PUNCT
ap-3524	61	4	hy1,0	hy1,0	X
ap-3524	61	5	=	=	PUNCT
ap-3524	61	6	y1,1	y1,1	PROPN
ap-3524	61	7	−	−	PROPN
ap-3524	61	8	y1,0	y1,0	PROPN
ap-3524	61	9	,	,	PUNCT
ap-3524	61	10	(	(	PUNCT
ap-3524	61	11	7	7	X
ap-3524	61	12	)	)	PUNCT
ap-3524	61	13	where	where	SCONJ
ap-3524	61	14	for	for	ADP
ap-3524	61	15	convenience	convenience	NOUN
ap-3524	61	16	of	of	ADP
ap-3524	61	17	notation	notation	NOUN
ap-3524	61	18	here	here	ADV
ap-3524	61	19	and	and	CCONJ
ap-3524	61	20	in	in	ADP
ap-3524	61	21	the	the	DET
ap-3524	61	22	following	following	NOUN
ap-3524	61	23	,	,	PUNCT
ap-3524	61	24	whenever	whenever	SCONJ
ap-3524	61	25	it	it	PRON
ap-3524	61	26	may	may	AUX
ap-3524	61	27	not	not	PART
ap-3524	61	28	create	create	VERB
ap-3524	61	29	misunderstanding	misunderstanding	NOUN
ap-3524	61	30	,	,	PUNCT
ap-3524	61	31	we	we	PRON
ap-3524	61	32	have	have	AUX
ap-3524	61	33	indicated	indicate	VERB
ap-3524	61	34	just	just	ADV
ap-3524	61	35	the	the	DET
ap-3524	61	36	distance	distance	NOUN
ap-3524	61	37	from	from	ADP
ap-3524	61	38	the	the	DET
ap-3524	61	39	values	value	NOUN
ap-3524	61	40	n	n	CCONJ
ap-3524	61	41	,	,	PUNCT
ap-3524	61	42	m	m	NOUN
ap-3524	61	43	of	of	ADP
ap-3524	61	44	the	the	DET
ap-3524	61	45	indices	index	NOUN
ap-3524	61	46	.	.	PUNCT
ap-3524	62	1	from	from	ADP
ap-3524	62	2	the	the	DET
ap-3524	62	3	values	value	NOUN
ap-3524	62	4	of	of	ADP
ap-3524	62	5	the	the	DET
ap-3524	62	6	dependent	dependent	ADJ
ap-3524	62	7	variables	variable	NOUN
ap-3524	62	8	in	in	ADP
ap-3524	62	9	the	the	DET
ap-3524	62	10	6	6	NUM
ap-3524	62	11	points	point	NOUN
ap-3524	62	12	we	we	PRON
ap-3524	62	13	can	can	AUX
ap-3524	62	14	calculate	calculate	VERB
ap-3524	62	15	the	the	DET
ap-3524	62	16	6	6	NUM
ap-3524	62	17	quantities	quantity	NOUN
ap-3524	62	18	u0,0	u0,0	NOUN
ap-3524	62	19	,	,	PUNCT
ap-3524	62	20	dxu0,0	dxu0,0	NOUN
ap-3524	62	21	,	,	PUNCT
ap-3524	62	22	dyu0,0	dyu0,0	NOUN
ap-3524	62	23	,	,	PUNCT
ap-3524	62	24	[	[	X
ap-3524	62	25	dx]2u0,0	dx]2u0,0	NOUN
ap-3524	62	26	,	,	PUNCT
ap-3524	62	27	[	[	X
ap-3524	62	28	dy]2u0,0	dy]2u0,0	NOUN
ap-3524	62	29	,	,	PUNCT
ap-3524	62	30	dxdyu0,0	dxdyu0,0	PROPN
ap-3524	62	31	,	,	PUNCT
ap-3524	62	32	(	(	PUNCT
ap-3524	62	33	8)	8)	NUM
ap-3524	62	34	where	where	SCONJ
ap-3524	62	35	the	the	DET
ap-3524	62	36	operators	operator	NOUN
ap-3524	62	37	dx	dx	PROPN
ap-3524	62	38	and	and	CCONJ
ap-3524	62	39	dy	dy	PROPN
ap-3524	62	40	,	,	PUNCT
ap-3524	62	41	introduced	introduce	VERB
ap-3524	62	42	in	in	ADP
ap-3524	62	43	[	[	X
ap-3524	62	44	14	14	NUM
ap-3524	62	45	]	]	PUNCT
ap-3524	62	46	,	,	PUNCT
ap-3524	62	47	are	be	AUX
ap-3524	62	48	given	give	VERB
ap-3524	62	49	by	by	ADP
ap-3524	62	50	dx	dx	PROPN
ap-3524	62	51	=	=	SYM
ap-3524	62	52	1	1	NUM
ap-3524	62	53	hx0,0h	hx0,0h	VERB
ap-3524	62	54	y	y	PROPN
ap-3524	62	55	0,0	0,0	NUM
ap-3524	62	56	−	−	ADP
ap-3524	62	57	σx0,0σ	σx0,0σ	NOUN
ap-3524	62	58	y	y	PROPN
ap-3524	62	59	0,0	0,0	NUM
ap-3524	62	60	(	(	PUNCT
ap-3524	62	61	hy0,0∆n	hy0,0∆n	PROPN
ap-3524	62	62	−	−	PROPN
ap-3524	62	63	σy0,0∆m	σy0,0∆m	PROPN
ap-3524	62	64	)	)	PUNCT
ap-3524	62	65	,	,	PUNCT
ap-3524	62	66	dy	dy	NOUN
ap-3524	62	67	=	=	SYM
ap-3524	62	68	1	1	NUM
ap-3524	62	69	hx0,0h	hx0,0h	VERB
ap-3524	62	70	y	y	PROPN
ap-3524	62	71	0,0	0,0	NUM
ap-3524	62	72	−	−	ADP
ap-3524	62	73	σx0,0σ	σx0,0σ	NOUN
ap-3524	62	74	y	y	PROPN
ap-3524	62	75	0,0	0,0	NUM
ap-3524	62	76	(	(	PUNCT
ap-3524	62	77	−σx0,0∆n	−σx0,0∆n	NOUN
ap-3524	62	78	+	+	CCONJ
ap-3524	62	79	hx0,0∆m	hx0,0∆m	NOUN
ap-3524	62	80	)	)	PUNCT
ap-3524	62	81	(	(	PUNCT
ap-3524	62	82	9	9	X
ap-3524	62	83	)	)	SYM
ap-3524	62	84	237	237	NUM
ap-3524	62	85	decio	decio	NOUN
ap-3524	62	86	levi	levi	PROPN
ap-3524	62	87	,	,	PUNCT
ap-3524	62	88	miguel	miguel	PROPN
ap-3524	62	89	a.	a.	PROPN
ap-3524	62	90	rodríguez	rodríguez	PROPN
ap-3524	62	91	acta	acta	PROPN
ap-3524	62	92	polytechnica	polytechnica	PROPN
ap-3524	62	93	with	with	ADP
ap-3524	62	94	tnfn	tnfn	PROPN
ap-3524	62	95	,	,	PUNCT
ap-3524	62	96	m	m	NOUN
ap-3524	62	97	=	=	ADJ
ap-3524	62	98	fn+1,m	fn+1,m	PROPN
ap-3524	62	99	,	,	PUNCT
ap-3524	63	1	∆n	∆n	PROPN
ap-3524	63	2	=	=	PUNCT
ap-3524	63	3	tn	tn	PROPN
ap-3524	63	4	−	−	NOUN
ap-3524	63	5	1	1	NUM
ap-3524	63	6	,	,	PUNCT
ap-3524	63	7	tmfn	tmfn	NOUN
ap-3524	63	8	,	,	PUNCT
ap-3524	63	9	m	m	PROPN
ap-3524	63	10	=	=	SYM
ap-3524	63	11	fn	fn	NOUN
ap-3524	63	12	,	,	PUNCT
ap-3524	63	13	m+1	m+1	NUM
ap-3524	63	14	,	,	PUNCT
ap-3524	63	15	∆m	∆m	PROPN
ap-3524	63	16	=	=	PROPN
ap-3524	63	17	tm	tm	PROPN
ap-3524	63	18	−	−	PROPN
ap-3524	63	19	1	1	NUM
ap-3524	63	20	.	.	PUNCT
ap-3524	64	1	these	these	DET
ap-3524	64	2	operators	operator	NOUN
ap-3524	64	3	are	be	AUX
ap-3524	64	4	the	the	DET
ap-3524	64	5	discrete	discrete	ADJ
ap-3524	64	6	counterpart	counterpart	NOUN
ap-3524	64	7	of	of	ADP
ap-3524	64	8	the	the	DET
ap-3524	64	9	partial	partial	ADJ
ap-3524	64	10	derivatives	derivative	NOUN
ap-3524	64	11	in	in	ADP
ap-3524	64	12	the	the	DET
ap-3524	64	13	x	x	NOUN
ap-3524	64	14	,	,	PUNCT
ap-3524	64	15	y	y	PROPN
ap-3524	64	16	axes	axis	NOUN
ap-3524	64	17	directions	direction	NOUN
ap-3524	64	18	,	,	PUNCT
ap-3524	64	19	written	write	VERB
ap-3524	64	20	in	in	ADP
ap-3524	64	21	terms	term	NOUN
ap-3524	64	22	of	of	ADP
ap-3524	64	23	the	the	DET
ap-3524	64	24	partial	partial	ADJ
ap-3524	64	25	difference	difference	NOUN
ap-3524	64	26	operators	operator	NOUN
ap-3524	64	27	in	in	ADP
ap-3524	64	28	the	the	DET
ap-3524	64	29	lattice	lattice	NOUN
ap-3524	64	30	directions	direction	NOUN
ap-3524	64	31	,	,	PUNCT
ap-3524	64	32	which	which	PRON
ap-3524	64	33	,	,	PUNCT
ap-3524	64	34	generically	generically	ADV
ap-3524	64	35	,	,	PUNCT
ap-3524	64	36	do	do	AUX
ap-3524	64	37	not	not	PART
ap-3524	64	38	coincide	coincide	VERB
ap-3524	64	39	with	with	ADP
ap-3524	64	40	the	the	DET
ap-3524	64	41	cartesian	cartesian	ADJ
ap-3524	64	42	axes	axis	NOUN
ap-3524	64	43	.	.	PUNCT
ap-3524	65	1	see	see	VERB
ap-3524	65	2	[	[	X
ap-3524	65	3	14	14	NUM
ap-3524	65	4	]	]	PUNCT
ap-3524	65	5	for	for	ADP
ap-3524	65	6	a	a	DET
ap-3524	65	7	more	more	ADV
ap-3524	65	8	detailed	detailed	ADJ
ap-3524	65	9	description	description	NOUN
ap-3524	65	10	.	.	PUNCT
ap-3524	66	1	note	note	VERB
ap-3524	66	2	that	that	SCONJ
ap-3524	66	3	dydxu0,0	dydxu0,0	NOUN
ap-3524	66	4	is	be	AUX
ap-3524	66	5	not	not	PART
ap-3524	66	6	independent	independent	ADJ
ap-3524	66	7	from	from	ADP
ap-3524	66	8	the	the	DET
ap-3524	66	9	6	6	NUM
ap-3524	66	10	quantities	quantity	NOUN
ap-3524	66	11	(	(	PUNCT
ap-3524	66	12	8)	8)	NUM
ap-3524	66	13	.	.	PUNCT
ap-3524	67	1	it	it	PRON
ap-3524	67	2	can	can	AUX
ap-3524	67	3	be	be	AUX
ap-3524	67	4	written	write	VERB
ap-3524	67	5	in	in	ADP
ap-3524	67	6	term	term	NOUN
ap-3524	67	7	of	of	ADP
ap-3524	67	8	(	(	PUNCT
ap-3524	67	9	7	7	NUM
ap-3524	67	10	)	)	PUNCT
ap-3524	67	11	and	and	CCONJ
ap-3524	67	12	(	(	PUNCT
ap-3524	67	13	8)	8)	NUM
ap-3524	67	14	.	.	PUNCT
ap-3524	68	1	for	for	ADP
ap-3524	68	2	a	a	DET
ap-3524	68	3	generic	generic	ADJ
ap-3524	68	4	lattice	lattice	NOUN
ap-3524	68	5	we	we	PRON
ap-3524	68	6	have	have	VERB
ap-3524	68	7	:	:	PUNCT
ap-3524	68	8	dydxu0,0	dydxu0,0	NOUN
ap-3524	68	9	=	=	PUNCT
ap-3524	68	10	−dxdxu0,0	−dxdxu0,0	X
ap-3524	68	11	(	(	PUNCT
ap-3524	68	12	hx0,0	hx0,0	NOUN
ap-3524	68	13	−	−	NOUN
ap-3524	68	14	hx0,1)(hx0,0	hx0,1)(hx0,0	NOUN
ap-3524	68	15	−	−	PROPN
ap-3524	68	16	σx0,0	σx0,0	NOUN
ap-3524	68	17	)	)	PUNCT
ap-3524	68	18	hx0,1h	hx0,1h	ADP
ap-3524	68	19	y	y	NOUN
ap-3524	68	20	0,0	0,0	NOUN
ap-3524	68	21	+	+	CCONJ
ap-3524	68	22	hx0,0σ	hx0,0σ	NOUN
ap-3524	68	23	y	y	NOUN
ap-3524	68	24	0,0	0,0	NOUN
ap-3524	68	25	−	−	ADP
ap-3524	68	26	hx0,1σ	hx0,1σ	ADJ
ap-3524	68	27	y	y	PROPN
ap-3524	68	28	0,0	0,0	NUM
ap-3524	68	29	−	−	ADP
ap-3524	68	30	σx0,0σ	σx0,0σ	NOUN
ap-3524	68	31	y	y	PROPN
ap-3524	68	32	0,0	0,0	NUM
ap-3524	68	33	+	+	ADJ
ap-3524	68	34	dydyu0,0	dydyu0,0	NOUN
ap-3524	68	35	(	(	PUNCT
ap-3524	68	36	hy0,0	hy0,0	NOUN
ap-3524	68	37	−	−	PROPN
ap-3524	68	38	h	h	NOUN
ap-3524	68	39	y	y	PROPN
ap-3524	68	40	1,0)(hy0,0	1,0)(hy0,0	NUM
ap-3524	68	41	−	−	PROPN
ap-3524	68	42	σ	σ	NUM
ap-3524	68	43	y	y	PROPN
ap-3524	68	44	0,0	0,0	NOUN
ap-3524	68	45	)	)	PUNCT
ap-3524	68	46	hx0,1h	hx0,1h	ADP
ap-3524	68	47	y	y	NOUN
ap-3524	68	48	0,0	0,0	NOUN
ap-3524	68	49	+	+	CCONJ
ap-3524	68	50	hx0,0σ	hx0,0σ	NOUN
ap-3524	68	51	y	y	NOUN
ap-3524	68	52	0,0	0,0	NOUN
ap-3524	68	53	−	−	ADP
ap-3524	68	54	hx0,1σ	hx0,1σ	ADJ
ap-3524	68	55	y	y	PROPN
ap-3524	68	56	0,0	0,0	NUM
ap-3524	68	57	−	−	ADP
ap-3524	68	58	σx0,0σ	σx0,0σ	NOUN
ap-3524	68	59	y	y	PROPN
ap-3524	68	60	0,0	0,0	NUM
ap-3524	68	61	+	+	ADJ
ap-3524	68	62	dxdyu0,0	dxdyu0,0	NOUN
ap-3524	68	63	hx0,0h	hx0,0h	VERB
ap-3524	68	64	y	y	PROPN
ap-3524	68	65	1,0	1,0	NUM
ap-3524	68	66	+	+	CCONJ
ap-3524	68	67	hy0,0σ	hy0,0σ	NOUN
ap-3524	68	68	x	x	SYM
ap-3524	68	69	0,0	0,0	NUM
ap-3524	68	70	−	−	NOUN
ap-3524	68	71	h	h	NOUN
ap-3524	68	72	y	y	NOUN
ap-3524	68	73	1,0σ	1,0σ	NUM
ap-3524	68	74	x	x	SYM
ap-3524	68	75	0,0	0,0	NUM
ap-3524	68	76	−	−	NOUN
ap-3524	68	77	σx0,0σ	σx0,0σ	NOUN
ap-3524	68	78	y	y	PROPN
ap-3524	68	79	0,0	0,0	NUM
ap-3524	68	80	hx0,1h	hx0,1h	ADP
ap-3524	68	81	y	y	NOUN
ap-3524	68	82	0,0	0,0	NOUN
ap-3524	68	83	+	+	CCONJ
ap-3524	68	84	hx0,0σ	hx0,0σ	NOUN
ap-3524	68	85	y	y	NOUN
ap-3524	68	86	0,0	0,0	NOUN
ap-3524	68	87	−	−	ADP
ap-3524	68	88	hx0,1σ	hx0,1σ	ADJ
ap-3524	68	89	y	y	PROPN
ap-3524	68	90	0,0	0,0	NUM
ap-3524	68	91	−	−	ADP
ap-3524	68	92	σx0,0σ	σx0,0σ	NOUN
ap-3524	68	93	y	y	PROPN
ap-3524	68	94	0,0	0,0	NUM
ap-3524	68	95	(	(	PUNCT
ap-3524	68	96	10	10	NUM
ap-3524	68	97	)	)	PUNCT
ap-3524	68	98	formulas	formula	NOUN
ap-3524	68	99	(	(	PUNCT
ap-3524	68	100	7)–(10	7)–(10	NUM
ap-3524	68	101	)	)	PUNCT
ap-3524	68	102	can	can	AUX
ap-3524	68	103	be	be	AUX
ap-3524	68	104	simplified	simplify	VERB
ap-3524	68	105	if	if	SCONJ
ap-3524	68	106	we	we	PRON
ap-3524	68	107	require	require	VERB
ap-3524	68	108	the	the	DET
ap-3524	68	109	validity	validity	NOUN
ap-3524	68	110	of	of	ADP
ap-3524	68	111	the	the	DET
ap-3524	68	112	clairaut	clairaut	NOUN
ap-3524	68	113	–	–	PUNCT
ap-3524	68	114	schwarz	schwarz	PROPN
ap-3524	68	115	–	–	PUNCT
ap-3524	68	116	young	young	ADJ
ap-3524	68	117	theorem	theorem	VERB
ap-3524	68	118	,	,	PUNCT
ap-3524	68	119	i.e.	i.e.	X
ap-3524	68	120	,	,	PUNCT
ap-3524	68	121	dxdyu0,0	dxdyu0,0	NOUN
ap-3524	68	122	=	=	SYM
ap-3524	68	123	dydxu0,0	dydxu0,0	PROPN
ap-3524	68	124	.	.	PUNCT
ap-3524	69	1	this	this	PRON
ap-3524	69	2	is	be	AUX
ap-3524	69	3	true	true	ADJ
ap-3524	69	4	when	when	SCONJ
ap-3524	69	5	the	the	DET
ap-3524	69	6	following	follow	VERB
ap-3524	69	7	constraint	constraint	NOUN
ap-3524	69	8	for	for	ADP
ap-3524	69	9	the	the	DET
ap-3524	69	10	lattice	lattice	NOUN
ap-3524	69	11	holds	hold	VERB
ap-3524	69	12	[	[	X
ap-3524	69	13	14	14	NUM
ap-3524	69	14	]	]	SYM
ap-3524	69	15	:	:	PUNCT
ap-3524	69	16	σxn	σxn	PROPN
ap-3524	69	17	,	,	PUNCT
ap-3524	69	18	m	m	PROPN
ap-3524	69	19	=	=	SYM
ap-3524	69	20	σxn+1,m	σxn+1,m	PROPN
ap-3524	69	21	≡	≡	PROPN
ap-3524	69	22	σxm	σxm	PROPN
ap-3524	69	23	,	,	PUNCT
ap-3524	69	24	hxn	hxn	NOUN
ap-3524	69	25	,	,	PUNCT
ap-3524	69	26	m	m	NOUN
ap-3524	69	27	=	=	NOUN
ap-3524	69	28	hxn	hxn	NOUN
ap-3524	69	29	,	,	PUNCT
ap-3524	69	30	m+1	m+1	NUM
ap-3524	69	31	≡	≡	PROPN
ap-3524	69	32	hxn	hxn	NOUN
ap-3524	69	33	,	,	PUNCT
ap-3524	69	34	σyn	σyn	PROPN
ap-3524	69	35	,	,	PUNCT
ap-3524	69	36	m	m	NOUN
ap-3524	69	37	=	=	SYM
ap-3524	69	38	σyn	σyn	ADJ
ap-3524	69	39	,	,	PUNCT
ap-3524	69	40	m+1	m+1	PROPN
ap-3524	69	41	≡	≡	PROPN
ap-3524	69	42	σyn	σyn	PROPN
ap-3524	69	43	,	,	PUNCT
ap-3524	69	44	hyn	hyn	PROPN
ap-3524	69	45	,	,	PUNCT
ap-3524	69	46	m	m	PROPN
ap-3524	69	47	=	=	NUM
ap-3524	69	48	hyn+1,m	hyn+1,m	PROPN
ap-3524	69	49	≡	≡	PROPN
ap-3524	69	50	hym	hym	PROPN
ap-3524	69	51	.	.	PUNCT
ap-3524	70	1	(	(	PUNCT
ap-3524	70	2	11	11	NUM
ap-3524	70	3	)	)	PUNCT
ap-3524	70	4	using	use	VERB
ap-3524	70	5	the	the	DET
ap-3524	70	6	operators	operator	NOUN
ap-3524	70	7	dx	dx	PROPN
ap-3524	70	8	and	and	CCONJ
ap-3524	70	9	dy	dy	NOUN
ap-3524	70	10	given	give	VERB
ap-3524	70	11	in	in	ADP
ap-3524	70	12	(	(	PUNCT
ap-3524	70	13	9	9	X
ap-3524	70	14	)	)	PUNCT
ap-3524	70	15	we	we	PRON
ap-3524	70	16	can	can	AUX
ap-3524	70	17	transform	transform	VERB
ap-3524	70	18	the	the	DET
ap-3524	70	19	standard	standard	ADJ
ap-3524	70	20	discrete	discrete	ADJ
ap-3524	70	21	prolongation	prolongation	NOUN
ap-3524	70	22	[	[	X
ap-3524	70	23	17	17	NUM
ap-3524	70	24	]	]	PUNCT
ap-3524	70	25	pr	pr	NOUN
ap-3524	70	26	x̂n	x̂n	NOUN
ap-3524	70	27	,	,	PUNCT
ap-3524	70	28	m	m	VERB
ap-3524	70	29	=	=	ADJ
ap-3524	70	30	x̂n	x̂n	NOUN
ap-3524	70	31	,	,	PUNCT
ap-3524	70	32	m	m	VERB
ap-3524	70	33	+	+	ADJ
ap-3524	70	34	x̂n+1,m	x̂n+1,m	PROPN
ap-3524	71	1	+	+	PROPN
ap-3524	71	2	x̂n+2,m	x̂n+2,m	PROPN
ap-3524	71	3	+	+	NUM
ap-3524	71	4	x̂n	x̂n	NOUN
ap-3524	71	5	,	,	PUNCT
ap-3524	71	6	m+1	m+1	NUM
ap-3524	71	7	+	+	NUM
ap-3524	71	8	x̂n	x̂n	NOUN
ap-3524	71	9	,	,	PUNCT
ap-3524	71	10	m+2	m+2	X
ap-3524	71	11	+	+	PROPN
ap-3524	71	12	x̂n+1,m+1	x̂n+1,m+1	PROPN
ap-3524	71	13	(	(	PUNCT
ap-3524	71	14	12	12	NUM
ap-3524	71	15	)	)	PUNCT
ap-3524	71	16	of	of	ADP
ap-3524	71	17	the	the	DET
ap-3524	71	18	vector	vector	NOUN
ap-3524	71	19	field	field	NOUN
ap-3524	71	20	x̂n	x̂n	NOUN
ap-3524	71	21	,	,	PUNCT
ap-3524	71	22	m	m	VERB
ap-3524	71	23	=	=	ADJ
ap-3524	71	24	ξn	ξn	PROPN
ap-3524	71	25	,	,	PUNCT
ap-3524	71	26	m∂xn	m∂xn	PROPN
ap-3524	71	27	,	,	PUNCT
ap-3524	71	28	m	m	VERB
ap-3524	71	29	+	+	X
ap-3524	71	30	τn	τn	ADJ
ap-3524	71	31	,	,	PUNCT
ap-3524	71	32	m∂yn	m∂yn	PROPN
ap-3524	71	33	,	,	PUNCT
ap-3524	71	34	m	m	VERB
ap-3524	71	35	+	+	X
ap-3524	71	36	φn	φn	ADJ
ap-3524	71	37	,	,	PUNCT
ap-3524	71	38	m∂un	m∂un	ADJ
ap-3524	71	39	,	,	PUNCT
ap-3524	71	40	m	m	PROPN
ap-3524	71	41	(	(	PUNCT
ap-3524	71	42	13	13	NUM
ap-3524	71	43	)	)	PUNCT
ap-3524	71	44	to	to	ADP
ap-3524	71	45	the	the	DET
ap-3524	71	46	new	new	ADJ
ap-3524	71	47	set	set	NOUN
ap-3524	71	48	of	of	ADP
ap-3524	71	49	independent	independent	ADJ
ap-3524	71	50	variables	variable	NOUN
ap-3524	71	51	(	(	PUNCT
ap-3524	71	52	7	7	NUM
ap-3524	71	53	)	)	PUNCT
ap-3524	71	54	,	,	PUNCT
ap-3524	71	55	(	(	PUNCT
ap-3524	71	56	8)	8)	X
ap-3524	71	57	.	.	PUNCT
ap-3524	72	1	we	we	PRON
ap-3524	72	2	get	get	VERB
ap-3524	72	3	pr	pr	ADP
ap-3524	72	4	x̂n	x̂n	NOUN
ap-3524	72	5	,	,	PUNCT
ap-3524	72	6	m	m	VERB
ap-3524	72	7	=	=	ADJ
ap-3524	72	8	x̂n	x̂n	NOUN
ap-3524	72	9	,	,	PUNCT
ap-3524	72	10	m	m	VERB
ap-3524	72	11	+	+	ADJ
ap-3524	72	12	∑	∑	PUNCT
ap-3524	72	13	(	(	PUNCT
ap-3524	72	14	i	i	INTJ
ap-3524	72	15	,	,	PUNCT
ap-3524	72	16	j)=0,1	j)=0,1	PROPN
ap-3524	72	17	[	[	PUNCT
ap-3524	72	18	η	η	X
ap-3524	72	19	(	(	PUNCT
ap-3524	72	20	x	x	NOUN
ap-3524	72	21	)	)	PUNCT
ap-3524	72	22	n+i	n+i	NUM
ap-3524	72	23	,	,	PUNCT
ap-3524	72	24	m+j∂hx	m+j∂hx	X
ap-3524	72	25	n+i	n+i	NUM
ap-3524	72	26	,	,	PUNCT
ap-3524	72	27	m+j	m+j	NUM
ap-3524	72	28	+	+	NUM
ap-3524	72	29	χ	χ	X
ap-3524	72	30	(	(	PUNCT
ap-3524	72	31	x	x	X
ap-3524	72	32	)	)	PUNCT
ap-3524	72	33	n+i	n+i	NUM
ap-3524	72	34	,	,	PUNCT
ap-3524	72	35	m+j∂σx	m+j∂σx	PROPN
ap-3524	72	36	n+i	n+i	NUM
ap-3524	72	37	,	,	PUNCT
ap-3524	72	38	m+j	m+j	PROPN
ap-3524	72	39	+	+	NUM
ap-3524	72	40	η	η	PROPN
ap-3524	72	41	(	(	PUNCT
ap-3524	72	42	y	y	NOUN
ap-3524	72	43	)	)	PUNCT
ap-3524	72	44	n+i	n+i	NUM
ap-3524	72	45	,	,	PUNCT
ap-3524	72	46	m+j∂hy	m+j∂hy	NOUN
ap-3524	72	47	n+i	n+i	NUM
ap-3524	72	48	,	,	PUNCT
ap-3524	72	49	m+j	m+j	NUM
ap-3524	72	50	+	+	NUM
ap-3524	72	51	χ	χ	X
ap-3524	72	52	(	(	PUNCT
ap-3524	72	53	y	y	NOUN
ap-3524	72	54	)	)	PUNCT
ap-3524	72	55	n+i	n+i	NUM
ap-3524	72	56	,	,	PUNCT
ap-3524	72	57	m+j∂σy	m+j∂σy	NOUN
ap-3524	72	58	n+i	n+i	NUM
ap-3524	72	59	,	,	PUNCT
ap-3524	72	60	m+j	m+j	NUM
ap-3524	72	61	]	]	PUNCT
ap-3524	72	62	+	+	PUNCT
ap-3524	72	63	φ(1,x	φ(1,x	NOUN
ap-3524	72	64	)	)	PUNCT
ap-3524	72	65	n	n	CCONJ
ap-3524	72	66	,	,	PUNCT
ap-3524	72	67	m	m	NOUN
ap-3524	72	68	∂dxun	∂dxun	NOUN
ap-3524	72	69	,	,	PUNCT
ap-3524	72	70	m	m	PROPN
ap-3524	72	71	+	+	X
ap-3524	72	72	φ(1,y	φ(1,y	NOUN
ap-3524	72	73	)	)	PUNCT
ap-3524	72	74	n	n	CCONJ
ap-3524	72	75	,	,	PUNCT
ap-3524	72	76	m	m	VERB
ap-3524	72	77	∂dyun	∂dyun	NOUN
ap-3524	72	78	,	,	PUNCT
ap-3524	72	79	m	m	VERB
ap-3524	72	80	+	+	ADJ
ap-3524	72	81	φ(2,xx	φ(2,xx	NOUN
ap-3524	72	82	)	)	PUNCT
ap-3524	72	83	n	n	CCONJ
ap-3524	72	84	,	,	PUNCT
ap-3524	72	85	m	m	PROPN
ap-3524	72	86	∂[dx]2un	∂[dx]2un	NUM
ap-3524	72	87	,	,	PUNCT
ap-3524	72	88	m	m	VERB
ap-3524	72	89	+	+	ADJ
ap-3524	72	90	φ(2,xy	φ(2,xy	PROPN
ap-3524	72	91	)	)	PUNCT
ap-3524	72	92	n	n	CCONJ
ap-3524	72	93	,	,	PUNCT
ap-3524	72	94	m	m	VERB
ap-3524	72	95	∂dydxun	∂dydxun	NOUN
ap-3524	72	96	,	,	PUNCT
ap-3524	72	97	m	m	VERB
ap-3524	72	98	+	+	ADJ
ap-3524	72	99	φ(2,yy	φ(2,yy	NOUN
ap-3524	72	100	)	)	PUNCT
ap-3524	72	101	n	n	CCONJ
ap-3524	72	102	,	,	PUNCT
ap-3524	72	103	m	m	VERB
ap-3524	72	104	∂[dy	∂[dy	X
ap-3524	72	105	]	]	X
ap-3524	72	106	2un	2un	ADJ
ap-3524	72	107	,	,	PUNCT
ap-3524	72	108	m	m	PRON
ap-3524	72	109	,	,	PUNCT
ap-3524	72	110	(	(	PUNCT
ap-3524	72	111	14	14	NUM
ap-3524	72	112	)	)	PUNCT
ap-3524	72	113	where	where	SCONJ
ap-3524	72	114	η	η	PROPN
ap-3524	72	115	(	(	PUNCT
ap-3524	72	116	x	x	NOUN
ap-3524	72	117	)	)	PUNCT
ap-3524	72	118	n+i	n+i	NUM
ap-3524	72	119	,	,	PUNCT
ap-3524	72	120	m+j	m+j	NOUN
ap-3524	72	121	=	=	SYM
ap-3524	72	122	ξn+1+i	ξn+1+i	NOUN
ap-3524	72	123	,	,	PUNCT
ap-3524	72	124	m+j	m+j	NUM
ap-3524	72	125	−	−	PROPN
ap-3524	72	126	ξn+i	ξn+i	PROPN
ap-3524	72	127	,	,	PUNCT
ap-3524	72	128	m+j	m+j	NUM
ap-3524	72	129	,	,	PUNCT
ap-3524	72	130	η	η	PROPN
ap-3524	72	131	(	(	PUNCT
ap-3524	72	132	y	y	NOUN
ap-3524	72	133	)	)	PUNCT
ap-3524	72	134	n+i	n+i	NUM
ap-3524	72	135	,	,	PUNCT
ap-3524	72	136	m+j	m+j	NOUN
ap-3524	72	137	=	=	SYM
ap-3524	72	138	τn+i	τn+i	PROPN
ap-3524	72	139	,	,	PUNCT
ap-3524	72	140	m+1+j	m+1+j	NOUN
ap-3524	72	141	−	−	PROPN
ap-3524	72	142	τn+i	τn+i	PROPN
ap-3524	72	143	,	,	PUNCT
ap-3524	72	144	m+j	m+j	NUM
ap-3524	72	145	,	,	PUNCT
ap-3524	72	146	χ	χ	X
ap-3524	72	147	(	(	PUNCT
ap-3524	72	148	x	x	X
ap-3524	72	149	)	)	PUNCT
ap-3524	72	150	n+i	n+i	NUM
ap-3524	72	151	,	,	PUNCT
ap-3524	72	152	m+j	m+j	NOUN
ap-3524	72	153	=	=	SYM
ap-3524	72	154	ξn+i	ξn+i	NUM
ap-3524	72	155	,	,	PUNCT
ap-3524	72	156	m+1+j	m+1+j	NOUN
ap-3524	72	157	−	−	PROPN
ap-3524	72	158	ξn+i	ξn+i	PROPN
ap-3524	72	159	,	,	PUNCT
ap-3524	72	160	m+j	m+j	NUM
ap-3524	72	161	,	,	PUNCT
ap-3524	72	162	χ	χ	X
ap-3524	72	163	(	(	PUNCT
ap-3524	72	164	y	y	NOUN
ap-3524	72	165	)	)	PUNCT
ap-3524	72	166	n+i	n+i	NUM
ap-3524	72	167	,	,	PUNCT
ap-3524	72	168	m+j	m+j	NOUN
ap-3524	72	169	=	=	PUNCT
ap-3524	72	170	τn+1+i	τn+1+i	NOUN
ap-3524	72	171	,	,	PUNCT
ap-3524	72	172	m+j	m+j	NUM
ap-3524	72	173	−	−	PROPN
ap-3524	72	174	τn+i	τn+i	ADJ
ap-3524	72	175	,	,	PUNCT
ap-3524	72	176	m+j	m+j	NUM
ap-3524	72	177	,	,	PUNCT
ap-3524	72	178	φ(1,x	φ(1,x	ADJ
ap-3524	72	179	)	)	PUNCT
ap-3524	72	180	n	n	CCONJ
ap-3524	72	181	,	,	PUNCT
ap-3524	72	182	m	m	VERB
ap-3524	72	183	=	=	ADJ
ap-3524	72	184	dxφn	dxφn	NOUN
ap-3524	72	185	,	,	PUNCT
ap-3524	72	186	m	m	VERB
ap-3524	72	187	−dxun	−dxun	NOUN
ap-3524	72	188	,	,	PUNCT
ap-3524	72	189	mdxξn	mdxξn	NOUN
ap-3524	72	190	,	,	PUNCT
ap-3524	72	191	m	m	VERB
ap-3524	72	192	−dyun	−dyun	ADV
ap-3524	72	193	,	,	PUNCT
ap-3524	72	194	mdxτn	mdxτn	NOUN
ap-3524	72	195	,	,	PUNCT
ap-3524	72	196	m	m	PROPN
ap-3524	72	197	,	,	PUNCT
ap-3524	72	198	φ(1,y	φ(1,y	NOUN
ap-3524	72	199	)	)	PUNCT
ap-3524	72	200	n	n	CCONJ
ap-3524	72	201	,	,	PUNCT
ap-3524	72	202	m	m	PROPN
ap-3524	72	203	=	=	ADJ
ap-3524	72	204	dyφn	dyφn	NOUN
ap-3524	72	205	,	,	PUNCT
ap-3524	72	206	m	m	VERB
ap-3524	72	207	−dxun	−dxun	NOUN
ap-3524	72	208	,	,	PUNCT
ap-3524	72	209	mdyξn	mdyξn	NOUN
ap-3524	72	210	,	,	PUNCT
ap-3524	72	211	m	m	VERB
ap-3524	72	212	−dyun	−dyun	ADV
ap-3524	72	213	,	,	PUNCT
ap-3524	72	214	mdyτn	mdyτn	NOUN
ap-3524	72	215	,	,	PUNCT
ap-3524	72	216	m	m	PROPN
ap-3524	72	217	,	,	PUNCT
ap-3524	72	218	φ(2,xx	φ(2,xx	NOUN
ap-3524	72	219	)	)	PUNCT
ap-3524	72	220	n	n	CCONJ
ap-3524	72	221	,	,	PUNCT
ap-3524	72	222	m	m	VERB
ap-3524	72	223	=	=	X
ap-3524	72	224	dxφ	dxφ	X
ap-3524	72	225	(	(	PUNCT
ap-3524	72	226	1,x	1,x	NUM
ap-3524	72	227	)	)	PUNCT
ap-3524	72	228	n	n	CCONJ
ap-3524	72	229	,	,	PUNCT
ap-3524	72	230	m	m	VERB
ap-3524	72	231	−	−	NOUN
ap-3524	73	1	[	[	X
ap-3524	73	2	dx]2un	dx]2un	ADJ
ap-3524	73	3	,	,	PUNCT
ap-3524	73	4	mdxξn	mdxξn	NOUN
ap-3524	73	5	,	,	PUNCT
ap-3524	73	6	m	m	VERB
ap-3524	73	7	−dydxun	−dydxun	NOUN
ap-3524	73	8	,	,	PUNCT
ap-3524	73	9	mdxτn	mdxτn	NOUN
ap-3524	73	10	,	,	PUNCT
ap-3524	73	11	m	m	PROPN
ap-3524	73	12	,	,	PUNCT
ap-3524	73	13	φ(2,xy	φ(2,xy	PROPN
ap-3524	73	14	)	)	PUNCT
ap-3524	73	15	n	n	CCONJ
ap-3524	73	16	,	,	PUNCT
ap-3524	73	17	m	m	VERB
ap-3524	73	18	=	=	X
ap-3524	73	19	dxφ	dxφ	X
ap-3524	73	20	(	(	PUNCT
ap-3524	73	21	1,y	1,y	NUM
ap-3524	73	22	)	)	PUNCT
ap-3524	73	23	n	n	CCONJ
ap-3524	73	24	,	,	PUNCT
ap-3524	73	25	m	m	VERB
ap-3524	73	26	−dxdyun	−dxdyun	NOUN
ap-3524	73	27	,	,	PUNCT
ap-3524	73	28	mdxξn	mdxξn	NOUN
ap-3524	73	29	,	,	PUNCT
ap-3524	73	30	m	m	VERB
ap-3524	73	31	−	−	NOUN
ap-3524	74	1	[	[	X
ap-3524	74	2	dy]2un	dy]2un	PROPN
ap-3524	74	3	,	,	PUNCT
ap-3524	74	4	mdxτn	mdxτn	NOUN
ap-3524	74	5	,	,	PUNCT
ap-3524	74	6	m	m	PROPN
ap-3524	74	7	,	,	PUNCT
ap-3524	74	8	φ(2,yy	φ(2,yy	NOUN
ap-3524	74	9	)	)	PUNCT
ap-3524	74	10	n	n	CCONJ
ap-3524	74	11	,	,	PUNCT
ap-3524	74	12	m	m	VERB
ap-3524	74	13	=	=	VERB
ap-3524	74	14	dyφ	dyφ	X
ap-3524	74	15	(	(	PUNCT
ap-3524	74	16	1,y	1,y	NUM
ap-3524	74	17	)	)	PUNCT
ap-3524	74	18	n	n	CCONJ
ap-3524	74	19	,	,	PUNCT
ap-3524	74	20	m	m	VERB
ap-3524	74	21	−dxdyun	−dxdyun	NOUN
ap-3524	74	22	,	,	PUNCT
ap-3524	74	23	mdyξn	mdyξn	NOUN
ap-3524	74	24	,	,	PUNCT
ap-3524	74	25	m	m	VERB
ap-3524	74	26	−	−	NOUN
ap-3524	75	1	[	[	X
ap-3524	75	2	dy]2un	dy]2un	PROPN
ap-3524	75	3	,	,	PUNCT
ap-3524	75	4	mdyτn	mdyτn	NOUN
ap-3524	75	5	,	,	PUNCT
ap-3524	75	6	m.	m.	NOUN
ap-3524	75	7	(	(	PUNCT
ap-3524	75	8	15	15	NUM
ap-3524	75	9	)	)	PUNCT
ap-3524	75	10	in	in	ADP
ap-3524	75	11	the	the	DET
ap-3524	75	12	continuous	continuous	ADJ
ap-3524	75	13	limit	limit	NOUN
ap-3524	75	14	,	,	PUNCT
ap-3524	75	15	when	when	SCONJ
ap-3524	75	16	hxn+i	hxn+i	NUM
ap-3524	75	17	,	,	PUNCT
ap-3524	75	18	m+j	m+j	NUM
ap-3524	75	19	,	,	PUNCT
ap-3524	75	20	h	h	NOUN
ap-3524	75	21	y	y	PROPN
ap-3524	75	22	n+i	n+i	PROPN
ap-3524	75	23	,	,	PUNCT
ap-3524	75	24	m+j	m+j	NUM
ap-3524	75	25	,	,	PUNCT
ap-3524	75	26	σxn+i	σxn+i	PROPN
ap-3524	75	27	,	,	PUNCT
ap-3524	75	28	m+j	m+j	NUM
ap-3524	75	29	and	and	CCONJ
ap-3524	75	30	σ	σ	PROPN
ap-3524	75	31	y	y	PROPN
ap-3524	75	32	n+i	n+i	PROPN
ap-3524	75	33	,	,	PUNCT
ap-3524	75	34	m+j	m+j	NUM
ap-3524	75	35	go	go	VERB
ap-3524	75	36	to	to	ADP
ap-3524	75	37	0	0	NUM
ap-3524	75	38	,	,	PUNCT
ap-3524	75	39	η(x	η(x	X
ap-3524	75	40	)	)	PUNCT
ap-3524	75	41	n+i	n+i	NUM
ap-3524	75	42	,	,	PUNCT
ap-3524	75	43	m+j	m+j	NUM
ap-3524	75	44	,	,	PUNCT
ap-3524	75	45	η	η	PROPN
ap-3524	75	46	(	(	PUNCT
ap-3524	75	47	y	y	NOUN
ap-3524	75	48	)	)	PUNCT
ap-3524	75	49	n+i	n+i	NUM
ap-3524	75	50	,	,	PUNCT
ap-3524	75	51	m+j	m+j	NUM
ap-3524	75	52	,	,	PUNCT
ap-3524	75	53	χ	χ	X
ap-3524	75	54	(	(	PUNCT
ap-3524	75	55	x	x	X
ap-3524	75	56	)	)	PUNCT
ap-3524	75	57	n+i	n+i	NUM
ap-3524	75	58	,	,	PUNCT
ap-3524	75	59	m+j	m+j	NUM
ap-3524	75	60	and	and	CCONJ
ap-3524	75	61	χ(y	χ(y	NOUN
ap-3524	75	62	)	)	PUNCT
ap-3524	75	63	n+i	n+i	NUM
ap-3524	75	64	,	,	PUNCT
ap-3524	75	65	m+j	m+j	NUM
ap-3524	75	66	go	go	VERB
ap-3524	75	67	also	also	ADV
ap-3524	75	68	to	to	ADP
ap-3524	75	69	0	0	NUM
ap-3524	75	70	while	while	SCONJ
ap-3524	75	71	φ(1,x	φ(1,x	NOUN
ap-3524	75	72	)	)	PUNCT
ap-3524	75	73	n	n	CCONJ
ap-3524	75	74	,	,	PUNCT
ap-3524	75	75	m	m	PROPN
ap-3524	75	76	,	,	PUNCT
ap-3524	75	77	φ(1,y	φ(1,y	NOUN
ap-3524	75	78	)	)	PUNCT
ap-3524	75	79	n	n	CCONJ
ap-3524	75	80	,	,	PUNCT
ap-3524	75	81	m	m	PRON
ap-3524	75	82	,	,	PUNCT
ap-3524	75	83	φ(2,xx	φ(2,xx	NOUN
ap-3524	75	84	)	)	PUNCT
ap-3524	75	85	n	n	CCONJ
ap-3524	75	86	,	,	PUNCT
ap-3524	75	87	m	m	PROPN
ap-3524	75	88	,	,	PUNCT
ap-3524	75	89	φ(2,xy	φ(2,xy	PROPN
ap-3524	75	90	)	)	PUNCT
ap-3524	75	91	n	n	CCONJ
ap-3524	75	92	,	,	PUNCT
ap-3524	75	93	m	m	PROPN
ap-3524	75	94	and	and	CCONJ
ap-3524	75	95	φ(2,yy	φ(2,yy	PROPN
ap-3524	75	96	)	)	PUNCT
ap-3524	75	97	n	n	CCONJ
ap-3524	75	98	,	,	PUNCT
ap-3524	75	99	m	m	VERB
ap-3524	75	100	go	go	VERB
ap-3524	75	101	to	to	ADP
ap-3524	75	102	the	the	DET
ap-3524	75	103	corresponding	corresponding	ADJ
ap-3524	75	104	continuous	continuous	ADJ
ap-3524	75	105	prolongations	prolongation	NOUN
ap-3524	75	106	.	.	PUNCT
ap-3524	76	1	applying	apply	VERB
ap-3524	76	2	the	the	DET
ap-3524	76	3	infinitesimal	infinitesimal	ADJ
ap-3524	76	4	generator	generator	NOUN
ap-3524	76	5	(	(	PUNCT
ap-3524	76	6	14	14	NUM
ap-3524	76	7	)	)	PUNCT
ap-3524	76	8	onto	onto	ADP
ap-3524	76	9	(	(	PUNCT
ap-3524	76	10	11	11	NUM
ap-3524	76	11	)	)	PUNCT
ap-3524	76	12	we	we	PRON
ap-3524	76	13	get	get	VERB
ap-3524	76	14	that	that	SCONJ
ap-3524	76	15	both	both	PRON
ap-3524	76	16	functions	function	NOUN
ap-3524	76	17	ξn	ξn	NOUN
ap-3524	76	18	,	,	PUNCT
ap-3524	76	19	m(xn	m(xn	PROPN
ap-3524	76	20	,	,	PUNCT
ap-3524	76	21	m	m	PROPN
ap-3524	76	22	,	,	PUNCT
ap-3524	76	23	yn	yn	PROPN
ap-3524	76	24	,	,	PUNCT
ap-3524	76	25	m	m	PROPN
ap-3524	76	26	,	,	PUNCT
ap-3524	76	27	un	un	PROPN
ap-3524	76	28	,	,	PUNCT
ap-3524	76	29	m	m	NOUN
ap-3524	76	30	)	)	PUNCT
ap-3524	76	31	and	and	CCONJ
ap-3524	76	32	τn	τn	ADP
ap-3524	76	33	,	,	PUNCT
ap-3524	76	34	m(xn	m(xn	PROPN
ap-3524	76	35	,	,	PUNCT
ap-3524	76	36	m	m	PROPN
ap-3524	76	37	,	,	PUNCT
ap-3524	76	38	yn	yn	PROPN
ap-3524	76	39	,	,	PUNCT
ap-3524	76	40	m	m	PROPN
ap-3524	76	41	,	,	PUNCT
ap-3524	76	42	un	un	PROPN
ap-3524	76	43	,	,	PUNCT
ap-3524	76	44	m	m	VERB
ap-3524	76	45	)	)	PUNCT
ap-3524	76	46	must	must	AUX
ap-3524	76	47	satisfy	satisfy	VERB
ap-3524	76	48	the	the	DET
ap-3524	76	49	discrete	discrete	ADJ
ap-3524	76	50	wave	wave	NOUN
ap-3524	76	51	equations	equation	NOUN
ap-3524	76	52	ξn	ξn	PROPN
ap-3524	76	53	,	,	PUNCT
ap-3524	76	54	m+1	m+1	NUM
ap-3524	76	55	−	−	PROPN
ap-3524	76	56	ξn	ξn	PROPN
ap-3524	76	57	,	,	PUNCT
ap-3524	76	58	m	m	VERB
ap-3524	76	59	−	−	NOUN
ap-3524	76	60	ξn+1,m+1	ξn+1,m+1	PUNCT
ap-3524	77	1	+	+	NUM
ap-3524	77	2	ξn+1,m	ξn+1,m	NOUN
ap-3524	77	3	=	=	SYM
ap-3524	77	4	0	0	NUM
ap-3524	77	5	,	,	PUNCT
ap-3524	77	6	τn	τn	NOUN
ap-3524	77	7	,	,	PUNCT
ap-3524	77	8	m+1	m+1	NUM
ap-3524	77	9	−	−	NOUN
ap-3524	77	10	τn	τn	NOUN
ap-3524	77	11	,	,	PUNCT
ap-3524	77	12	m	m	VERB
ap-3524	77	13	−	−	NOUN
ap-3524	77	14	τn+1,m+1	τn+1,m+1	PUNCT
ap-3524	78	1	+	+	CCONJ
ap-3524	78	2	τn+1,m	τn+1,m	NOUN
ap-3524	78	3	=	=	NOUN
ap-3524	78	4	0	0	X
ap-3524	78	5	.	.	PUNCT
ap-3524	79	1	(	(	PUNCT
ap-3524	79	2	16	16	NUM
ap-3524	79	3	)	)	PUNCT
ap-3524	79	4	this	this	PRON
ap-3524	79	5	is	be	AUX
ap-3524	79	6	a	a	DET
ap-3524	79	7	constraint	constraint	NOUN
ap-3524	79	8	for	for	ADP
ap-3524	79	9	the	the	DET
ap-3524	79	10	symmetry	symmetry	NOUN
ap-3524	79	11	coefficients	coefficient	VERB
ap-3524	79	12	if	if	SCONJ
ap-3524	79	13	the	the	DET
ap-3524	79	14	clairaut	clairaut	NOUN
ap-3524	79	15	–	–	PUNCT
ap-3524	79	16	schwarz	schwarz	NOUN
ap-3524	79	17	–	–	PUNCT
ap-3524	79	18	young	young	ADJ
ap-3524	79	19	theorem	theorem	NOUN
ap-3524	79	20	is	be	AUX
ap-3524	79	21	to	to	PART
ap-3524	79	22	be	be	AUX
ap-3524	79	23	satisfied	satisfied	ADJ
ap-3524	79	24	,	,	PUNCT
ap-3524	79	25	i.e.	i.e.	X
ap-3524	79	26	,	,	PUNCT
ap-3524	79	27	(	(	PUNCT
ap-3524	79	28	16	16	NUM
ap-3524	79	29	)	)	PUNCT
ap-3524	79	30	are	be	AUX
ap-3524	79	31	to	to	PART
ap-3524	79	32	be	be	AUX
ap-3524	79	33	added	add	VERB
ap-3524	79	34	to	to	ADP
ap-3524	79	35	the	the	DET
ap-3524	79	36	determining	determine	VERB
ap-3524	79	37	equations	equation	NOUN
ap-3524	79	38	if	if	SCONJ
ap-3524	79	39	we	we	PRON
ap-3524	79	40	want	want	VERB
ap-3524	79	41	to	to	PART
ap-3524	79	42	have	have	VERB
ap-3524	79	43	a	a	DET
ap-3524	79	44	lattice	lattice	NOUN
ap-3524	79	45	satisfying	satisfy	VERB
ap-3524	79	46	the	the	DET
ap-3524	79	47	clairaut	clairaut	NOUN
ap-3524	79	48	–	–	PUNCT
ap-3524	79	49	schwarz	schwarz	PROPN
ap-3524	79	50	–	–	PUNCT
ap-3524	79	51	young	young	ADJ
ap-3524	79	52	theorem	theorem	NOUN
ap-3524	79	53	.	.	PUNCT
ap-3524	80	1	in	in	ADP
ap-3524	80	2	this	this	DET
ap-3524	80	3	case	case	NOUN
ap-3524	80	4	,	,	PUNCT
ap-3524	80	5	if	if	SCONJ
ap-3524	80	6	,	,	PUNCT
ap-3524	80	7	for	for	ADP
ap-3524	80	8	example	example	NOUN
ap-3524	80	9	,	,	PUNCT
ap-3524	80	10	the	the	DET
ap-3524	80	11	difference	difference	NOUN
ap-3524	80	12	equation	equation	NOUN
ap-3524	80	13	for	for	ADP
ap-3524	80	14	un	un	PROPN
ap-3524	80	15	,	,	PUNCT
ap-3524	80	16	m	m	VERB
ap-3524	80	17	involves	involve	VERB
ap-3524	80	18	second	second	ADJ
ap-3524	80	19	order	order	NOUN
ap-3524	80	20	shifts	shift	NOUN
ap-3524	80	21	like	like	ADP
ap-3524	80	22	un+2,m	un+2,m	NOUN
ap-3524	80	23	or	or	CCONJ
ap-3524	80	24	un	un	PROPN
ap-3524	80	25	,	,	PUNCT
ap-3524	80	26	m+2	m+2	NOUN
ap-3524	80	27	so	so	SCONJ
ap-3524	80	28	that	that	SCONJ
ap-3524	80	29	un	un	PROPN
ap-3524	80	30	,	,	PUNCT
ap-3524	80	31	m	m	PROPN
ap-3524	80	32	,	,	PUNCT
ap-3524	80	33	un	un	PROPN
ap-3524	80	34	,	,	PUNCT
ap-3524	80	35	m+1	m+1	NUM
ap-3524	80	36	and	and	CCONJ
ap-3524	80	37	un+1,m	un+1,m	PROPN
ap-3524	80	38	are	be	AUX
ap-3524	80	39	independent	independent	ADJ
ap-3524	80	40	variables	variable	NOUN
ap-3524	80	41	,	,	PUNCT
ap-3524	80	42	then	then	ADV
ap-3524	80	43	from	from	ADP
ap-3524	80	44	(	(	PUNCT
ap-3524	80	45	16	16	NUM
ap-3524	80	46	)	)	PUNCT
ap-3524	80	47	we	we	PRON
ap-3524	80	48	get	get	VERB
ap-3524	80	49	ξn	ξn	NOUN
ap-3524	80	50	,	,	PUNCT
ap-3524	80	51	m(xn	m(xn	PROPN
ap-3524	80	52	,	,	PUNCT
ap-3524	80	53	m	m	PROPN
ap-3524	80	54	,	,	PUNCT
ap-3524	80	55	yn	yn	PROPN
ap-3524	80	56	,	,	PUNCT
ap-3524	80	57	m	m	PROPN
ap-3524	80	58	,	,	PUNCT
ap-3524	80	59	un	un	PROPN
ap-3524	80	60	,	,	PUNCT
ap-3524	80	61	m	m	NOUN
ap-3524	80	62	)	)	PUNCT
ap-3524	81	1	=	=	SYM
ap-3524	81	2	ξn	ξn	PROPN
ap-3524	81	3	,	,	PUNCT
ap-3524	81	4	m(xn	m(xn	PROPN
ap-3524	81	5	,	,	PUNCT
ap-3524	81	6	m	m	PROPN
ap-3524	81	7	,	,	PUNCT
ap-3524	81	8	yn	yn	PROPN
ap-3524	81	9	,	,	PUNCT
ap-3524	81	10	m	m	PROPN
ap-3524	81	11	)	)	PUNCT
ap-3524	81	12	.	.	PUNCT
ap-3524	82	1	if	if	SCONJ
ap-3524	82	2	the	the	DET
ap-3524	82	3	lattice	lattice	PROPN
ap-3524	82	4	equations	equation	NOUN
ap-3524	82	5	in	in	ADP
ap-3524	82	6	our	our	PRON
ap-3524	82	7	scheme	scheme	NOUN
ap-3524	82	8	involve	involve	VERB
ap-3524	82	9	the	the	DET
ap-3524	82	10	points	point	NOUN
ap-3524	82	11	xn+2,m	xn+2,m	PROPN
ap-3524	82	12	,	,	PUNCT
ap-3524	82	13	yn+2,m	yn+2,m	NOUN
ap-3524	82	14	or	or	CCONJ
ap-3524	82	15	xn	xn	PROPN
ap-3524	82	16	,	,	PUNCT
ap-3524	82	17	m+2	m+2	NOUN
ap-3524	82	18	,	,	PUNCT
ap-3524	82	19	yn	yn	PROPN
ap-3524	82	20	,	,	PUNCT
ap-3524	82	21	m+2	m+2	NOUN
ap-3524	82	22	,	,	PUNCT
ap-3524	82	23	so	so	SCONJ
ap-3524	82	24	that	that	SCONJ
ap-3524	82	25	xn	xn	PROPN
ap-3524	82	26	,	,	PUNCT
ap-3524	82	27	m	m	PROPN
ap-3524	82	28	,	,	PUNCT
ap-3524	82	29	xn	xn	PROPN
ap-3524	82	30	,	,	PUNCT
ap-3524	82	31	m+1	m+1	NUM
ap-3524	82	32	,	,	PUNCT
ap-3524	82	33	xn+1,m	xn+1,m	PROPN
ap-3524	82	34	,	,	PUNCT
ap-3524	82	35	yn	yn	PROPN
ap-3524	82	36	,	,	PUNCT
ap-3524	82	37	m	m	PROPN
ap-3524	82	38	,	,	PUNCT
ap-3524	82	39	yn	yn	PROPN
ap-3524	82	40	,	,	PUNCT
ap-3524	82	41	m+1	m+1	NUM
ap-3524	82	42	and	and	CCONJ
ap-3524	82	43	yn+1,m	yn+1,m	PROPN
ap-3524	82	44	are	be	AUX
ap-3524	82	45	independent	independent	ADJ
ap-3524	82	46	variables	variable	NOUN
ap-3524	82	47	,	,	PUNCT
ap-3524	82	48	then	then	ADV
ap-3524	82	49	ξn	ξn	PROPN
ap-3524	82	50	,	,	PUNCT
ap-3524	82	51	m(xn	m(xn	PROPN
ap-3524	82	52	,	,	PUNCT
ap-3524	82	53	m	m	PROPN
ap-3524	82	54	,	,	PUNCT
ap-3524	82	55	yn	yn	PROPN
ap-3524	82	56	,	,	PUNCT
ap-3524	82	57	m	m	PROPN
ap-3524	82	58	,	,	PUNCT
ap-3524	82	59	un	un	PROPN
ap-3524	82	60	,	,	PUNCT
ap-3524	82	61	m	m	NOUN
ap-3524	82	62	)	)	PUNCT
ap-3524	83	1	=	=	SYM
ap-3524	83	2	ξn	ξn	PROPN
ap-3524	83	3	,	,	PUNCT
ap-3524	83	4	m.	m.	NOUN
ap-3524	83	5	then	then	ADV
ap-3524	83	6	,	,	PUNCT
ap-3524	83	7	as	as	SCONJ
ap-3524	83	8	it	it	PRON
ap-3524	83	9	is	be	AUX
ap-3524	83	10	the	the	DET
ap-3524	83	11	case	case	NOUN
ap-3524	83	12	of	of	ADP
ap-3524	83	13	the	the	DET
ap-3524	83	14	continuous	continuous	ADJ
ap-3524	83	15	wave	wave	NOUN
ap-3524	83	16	equation	equation	NOUN
ap-3524	83	17	,	,	PUNCT
ap-3524	83	18	the	the	DET
ap-3524	83	19	238	238	NUM
ap-3524	83	20	vol	vol	NOUN
ap-3524	83	21	.	.	PUNCT
ap-3524	84	1	56	56	NUM
ap-3524	84	2	no	no	NOUN
ap-3524	84	3	.	.	PUNCT
ap-3524	85	1	3/2016	3/2016	NUM
ap-3524	85	2	on	on	ADP
ap-3524	85	3	the	the	DET
ap-3524	85	4	construction	construction	NOUN
ap-3524	85	5	of	of	ADP
ap-3524	85	6	partial	partial	ADJ
ap-3524	85	7	difference	difference	NOUN
ap-3524	85	8	schemes	scheme	NOUN
ap-3524	85	9	ii	ii	PROPN
ap-3524	85	10	general	general	ADJ
ap-3524	85	11	solution	solution	NOUN
ap-3524	85	12	of	of	ADP
ap-3524	85	13	(	(	PUNCT
ap-3524	85	14	16	16	NUM
ap-3524	85	15	)	)	PUNCT
ap-3524	85	16	is	be	AUX
ap-3524	85	17	given	give	VERB
ap-3524	85	18	by	by	ADP
ap-3524	85	19	ξn	ξn	PROPN
ap-3524	85	20	,	,	PUNCT
ap-3524	85	21	m	m	PROPN
ap-3524	85	22	=	=	ADJ
ap-3524	85	23	f	f	X
ap-3524	85	24	(	(	PUNCT
ap-3524	85	25	x	x	NOUN
ap-3524	85	26	)	)	PUNCT
ap-3524	85	27	n	n	PROPN
ap-3524	85	28	+	+	CCONJ
ap-3524	85	29	g	g	PROPN
ap-3524	85	30	(	(	PUNCT
ap-3524	85	31	x	x	NOUN
ap-3524	85	32	)	)	PUNCT
ap-3524	85	33	m	m	PROPN
ap-3524	85	34	and	and	CCONJ
ap-3524	85	35	τn	τn	ADP
ap-3524	85	36	,	,	PUNCT
ap-3524	85	37	m	m	VERB
ap-3524	85	38	=	=	SYM
ap-3524	85	39	f	f	X
ap-3524	85	40	(	(	PUNCT
ap-3524	85	41	y	y	NOUN
ap-3524	85	42	)	)	PUNCT
ap-3524	85	43	n	n	PROPN
ap-3524	85	44	+	+	CCONJ
ap-3524	85	45	g	g	PROPN
ap-3524	85	46	(	(	PUNCT
ap-3524	85	47	y	y	NOUN
ap-3524	85	48	)	)	PUNCT
ap-3524	85	49	m	m	VERB
ap-3524	85	50	,	,	PUNCT
ap-3524	85	51	i.e.	i.e.	X
ap-3524	85	52	,	,	PUNCT
ap-3524	85	53	the	the	DET
ap-3524	85	54	sum	sum	NOUN
ap-3524	85	55	of	of	ADP
ap-3524	85	56	an	an	DET
ap-3524	85	57	arbitrary	arbitrary	ADJ
ap-3524	85	58	function	function	NOUN
ap-3524	85	59	of	of	ADP
ap-3524	85	60	n	n	PROPN
ap-3524	85	61	and	and	CCONJ
ap-3524	85	62	one	one	NUM
ap-3524	85	63	of	of	ADP
ap-3524	85	64	m.	m.	NOUN
ap-3524	85	65	it	it	PRON
ap-3524	85	66	is	be	AUX
ap-3524	85	67	worthwhile	worthwhile	ADJ
ap-3524	85	68	,	,	PUNCT
ap-3524	85	69	in	in	ADP
ap-3524	85	70	view	view	NOUN
ap-3524	85	71	of	of	ADP
ap-3524	85	72	the	the	DET
ap-3524	85	73	application	application	NOUN
ap-3524	85	74	to	to	PART
ap-3524	85	75	be	be	AUX
ap-3524	85	76	carried	carry	VERB
ap-3524	85	77	out	out	ADP
ap-3524	85	78	in	in	ADP
ap-3524	85	79	next	next	ADJ
ap-3524	85	80	section	section	NOUN
ap-3524	85	81	,	,	PUNCT
ap-3524	85	82	to	to	PART
ap-3524	85	83	compute	compute	VERB
ap-3524	85	84	the	the	DET
ap-3524	85	85	lowest	low	ADJ
ap-3524	85	86	order	order	NOUN
ap-3524	85	87	discrete	discrete	ADJ
ap-3524	85	88	derivatives	derivative	NOUN
ap-3524	85	89	of	of	ADP
ap-3524	85	90	monomials	monomial	NOUN
ap-3524	85	91	in	in	ADP
ap-3524	85	92	x	x	PUNCT
ap-3524	85	93	and	and	CCONJ
ap-3524	85	94	y	y	PROPN
ap-3524	85	95	:	:	PUNCT
ap-3524	85	96	dxxn	dxxn	VERB
ap-3524	85	97	,	,	PUNCT
ap-3524	85	98	m	m	VERB
ap-3524	85	99	=	=	NOUN
ap-3524	85	100	1	1	NUM
ap-3524	85	101	,	,	PUNCT
ap-3524	85	102	dxyn	dxyn	ADJ
ap-3524	85	103	,	,	PUNCT
ap-3524	85	104	m	m	VERB
ap-3524	85	105	=	=	ADJ
ap-3524	85	106	0	0	NUM
ap-3524	85	107	,	,	PUNCT
ap-3524	85	108	dyxn	dyxn	NOUN
ap-3524	85	109	,	,	PUNCT
ap-3524	85	110	m	m	NOUN
ap-3524	85	111	=	=	SYM
ap-3524	85	112	0	0	NUM
ap-3524	85	113	,	,	PUNCT
ap-3524	85	114	dyyn	dyyn	ADV
ap-3524	85	115	,	,	PUNCT
ap-3524	85	116	m	m	VERB
ap-3524	85	117	=	=	NOUN
ap-3524	85	118	1	1	NUM
ap-3524	85	119	,	,	PUNCT
ap-3524	85	120	dxx	dxx	PROPN
ap-3524	85	121	2	2	NUM
ap-3524	85	122	n	n	CCONJ
ap-3524	85	123	,	,	PUNCT
ap-3524	85	124	m	m	VERB
ap-3524	85	125	=	=	NOUN
ap-3524	85	126	2xn	2xn	ADJ
ap-3524	85	127	,	,	PUNCT
ap-3524	85	128	m	m	VERB
ap-3524	85	129	+	+	CCONJ
ap-3524	85	130	hyn	hyn	PROPN
ap-3524	85	131	,	,	PUNCT
ap-3524	85	132	m(hxn	m(hxn	NOUN
ap-3524	85	133	,	,	PUNCT
ap-3524	85	134	m)2	m)2	NOUN
ap-3524	85	135	−	−	PROPN
ap-3524	85	136	σyn	σyn	ADJ
ap-3524	85	137	,	,	PUNCT
ap-3524	85	138	m(σxn	m(σxn	PROPN
ap-3524	85	139	,	,	PUNCT
ap-3524	85	140	m)2	m)2	PROPN
ap-3524	85	141	hyn	hyn	PROPN
ap-3524	85	142	,	,	PUNCT
ap-3524	85	143	mhxn	mhxn	PROPN
ap-3524	85	144	,	,	PUNCT
ap-3524	85	145	m	m	VERB
ap-3524	85	146	−	−	PROPN
ap-3524	85	147	σ	σ	PROPN
ap-3524	85	148	y	y	PROPN
ap-3524	85	149	n	n	PROPN
ap-3524	85	150	,	,	PUNCT
ap-3524	85	151	mσxn	mσxn	PROPN
ap-3524	85	152	,	,	PUNCT
ap-3524	85	153	m	m	VERB
ap-3524	85	154	=	=	NOUN
ap-3524	85	155	2xn	2xn	ADJ
ap-3524	85	156	,	,	PUNCT
ap-3524	85	157	m	m	VERB
ap-3524	85	158	+	+	PROPN
ap-3524	85	159	∆x	∆x	PROPN
ap-3524	85	160	xx	xx	PROPN
ap-3524	85	161	,	,	PUNCT
ap-3524	85	162	dxxn	dxxn	ADJ
ap-3524	85	163	,	,	PUNCT
ap-3524	85	164	myn	myn	PROPN
ap-3524	85	165	,	,	PUNCT
ap-3524	85	166	m	m	VERB
ap-3524	85	167	=	=	SYM
ap-3524	85	168	yn	yn	PROPN
ap-3524	85	169	,	,	PUNCT
ap-3524	85	170	m	m	VERB
ap-3524	85	171	+	+	X
ap-3524	85	172	hyn	hyn	PROPN
ap-3524	85	173	,	,	PUNCT
ap-3524	85	174	mσ	mσ	PROPN
ap-3524	85	175	y	y	PROPN
ap-3524	85	176	n	n	PROPN
ap-3524	85	177	,	,	PUNCT
ap-3524	85	178	m(hxn	m(hxn	NOUN
ap-3524	85	179	,	,	PUNCT
ap-3524	85	180	m	m	NOUN
ap-3524	85	181	−	−	NOUN
ap-3524	85	182	σxn	σxn	PROPN
ap-3524	85	183	,	,	PUNCT
ap-3524	85	184	m	m	NOUN
ap-3524	85	185	)	)	PUNCT
ap-3524	85	186	hyn	hyn	PROPN
ap-3524	85	187	,	,	PUNCT
ap-3524	85	188	mhxn	mhxn	PROPN
ap-3524	85	189	,	,	PUNCT
ap-3524	85	190	m	m	VERB
ap-3524	85	191	−	−	PROPN
ap-3524	85	192	σ	σ	PROPN
ap-3524	85	193	y	y	PROPN
ap-3524	85	194	n	n	PROPN
ap-3524	85	195	,	,	PUNCT
ap-3524	85	196	mσxn	mσxn	PROPN
ap-3524	85	197	,	,	PUNCT
ap-3524	85	198	m	m	PROPN
ap-3524	85	199	=	=	SYM
ap-3524	85	200	yn	yn	PROPN
ap-3524	85	201	,	,	PUNCT
ap-3524	85	202	m	m	VERB
ap-3524	85	203	+	+	PROPN
ap-3524	86	1	∆x	∆x	PROPN
ap-3524	86	2	xy	xy	PROPN
ap-3524	86	3	,	,	PUNCT
ap-3524	86	4	dxy	dxy	PROPN
ap-3524	86	5	2	2	NUM
ap-3524	86	6	n	n	NUM
ap-3524	86	7	,	,	PUNCT
ap-3524	86	8	m	m	PROPN
ap-3524	86	9	=	=	SYM
ap-3524	87	1	−	−	PROPN
ap-3524	87	2	hyn	hyn	PROPN
ap-3524	87	3	,	,	PUNCT
ap-3524	87	4	mσ	mσ	PROPN
ap-3524	87	5	y	y	PROPN
ap-3524	87	6	n	n	PROPN
ap-3524	87	7	,	,	PUNCT
ap-3524	87	8	m(hyn	m(hyn	PROPN
ap-3524	87	9	,	,	PUNCT
ap-3524	87	10	m	m	NOUN
ap-3524	87	11	−	−	NOUN
ap-3524	87	12	σyn	σyn	ADJ
ap-3524	87	13	,	,	PUNCT
ap-3524	87	14	m	m	NOUN
ap-3524	87	15	)	)	PUNCT
ap-3524	87	16	hyn	hyn	PROPN
ap-3524	87	17	,	,	PUNCT
ap-3524	87	18	mhxn	mhxn	PROPN
ap-3524	87	19	,	,	PUNCT
ap-3524	87	20	m	m	VERB
ap-3524	87	21	−	−	PROPN
ap-3524	87	22	σ	σ	PROPN
ap-3524	87	23	y	y	PROPN
ap-3524	87	24	n	n	PROPN
ap-3524	87	25	,	,	PUNCT
ap-3524	87	26	mσxn	mσxn	PROPN
ap-3524	87	27	,	,	PUNCT
ap-3524	87	28	m	m	PROPN
ap-3524	87	29	=	=	PROPN
ap-3524	87	30	∆x	∆x	PROPN
ap-3524	87	31	yy	yy	PROPN
ap-3524	87	32	,	,	PUNCT
ap-3524	87	33	dyx	dyx	VERB
ap-3524	87	34	2	2	NUM
ap-3524	87	35	n	n	NOUN
ap-3524	87	36	,	,	PUNCT
ap-3524	87	37	m	m	NOUN
ap-3524	87	38	=	=	NOUN
ap-3524	87	39	−	−	NOUN
ap-3524	87	40	hxn	hxn	NOUN
ap-3524	87	41	,	,	PUNCT
ap-3524	87	42	mσ	mσ	INTJ
ap-3524	87	43	x	x	SYM
ap-3524	87	44	n	n	CCONJ
ap-3524	87	45	,	,	PUNCT
ap-3524	87	46	m(hxn	m(hxn	NOUN
ap-3524	87	47	,	,	PUNCT
ap-3524	87	48	m	m	NOUN
ap-3524	87	49	−	−	NOUN
ap-3524	87	50	σxn	σxn	PROPN
ap-3524	87	51	,	,	PUNCT
ap-3524	87	52	m	m	NOUN
ap-3524	87	53	)	)	PUNCT
ap-3524	87	54	hyn	hyn	PROPN
ap-3524	87	55	,	,	PUNCT
ap-3524	87	56	mhxn	mhxn	PROPN
ap-3524	87	57	,	,	PUNCT
ap-3524	87	58	m	m	VERB
ap-3524	87	59	−	−	PROPN
ap-3524	87	60	σ	σ	PROPN
ap-3524	87	61	y	y	PROPN
ap-3524	87	62	n	n	PROPN
ap-3524	87	63	,	,	PUNCT
ap-3524	87	64	mσxn	mσxn	PROPN
ap-3524	87	65	,	,	PUNCT
ap-3524	87	66	m	m	VERB
ap-3524	87	67	=	=	SYM
ap-3524	87	68	∆y	∆y	PROPN
ap-3524	87	69	xx	xx	NUM
ap-3524	87	70	,	,	PUNCT
ap-3524	87	71	dyxn	dyxn	PROPN
ap-3524	87	72	,	,	PUNCT
ap-3524	87	73	myn	myn	PROPN
ap-3524	87	74	,	,	PUNCT
ap-3524	87	75	m	m	VERB
ap-3524	87	76	=	=	SYM
ap-3524	87	77	xn	xn	PROPN
ap-3524	87	78	,	,	PUNCT
ap-3524	87	79	m	m	VERB
ap-3524	87	80	+	+	X
ap-3524	87	81	hxn	hxn	NOUN
ap-3524	87	82	,	,	PUNCT
ap-3524	87	83	mσ	mσ	INTJ
ap-3524	87	84	x	x	SYM
ap-3524	87	85	n	n	CCONJ
ap-3524	87	86	,	,	PUNCT
ap-3524	87	87	m(hyn	m(hyn	PROPN
ap-3524	87	88	,	,	PUNCT
ap-3524	87	89	m	m	NOUN
ap-3524	87	90	−	−	NOUN
ap-3524	87	91	σyn	σyn	ADJ
ap-3524	87	92	,	,	PUNCT
ap-3524	87	93	m	m	NOUN
ap-3524	87	94	)	)	PUNCT
ap-3524	87	95	hyn	hyn	PROPN
ap-3524	87	96	,	,	PUNCT
ap-3524	87	97	mhxn	mhxn	PROPN
ap-3524	87	98	,	,	PUNCT
ap-3524	87	99	m	m	VERB
ap-3524	87	100	−	−	PROPN
ap-3524	87	101	σ	σ	PROPN
ap-3524	87	102	y	y	PROPN
ap-3524	87	103	n	n	PROPN
ap-3524	87	104	,	,	PUNCT
ap-3524	87	105	mσxn	mσxn	PROPN
ap-3524	87	106	,	,	PUNCT
ap-3524	87	107	m	m	PROPN
ap-3524	87	108	=	=	SYM
ap-3524	87	109	xn	xn	PROPN
ap-3524	87	110	,	,	PUNCT
ap-3524	87	111	m	m	VERB
ap-3524	87	112	+	+	X
ap-3524	87	113	∆y	∆y	PROPN
ap-3524	88	1	xy	xy	INTJ
ap-3524	88	2	,	,	PUNCT
ap-3524	88	3	dyy	dyy	PROPN
ap-3524	88	4	2	2	NUM
ap-3524	88	5	n	n	NOUN
ap-3524	88	6	,	,	PUNCT
ap-3524	88	7	m	m	NOUN
ap-3524	88	8	=	=	ADJ
ap-3524	88	9	2yn	2yn	ADJ
ap-3524	88	10	,	,	PUNCT
ap-3524	88	11	m	m	VERB
ap-3524	88	12	+	+	X
ap-3524	88	13	hxn	hxn	NOUN
ap-3524	88	14	,	,	PUNCT
ap-3524	88	15	m(hyn	m(hyn	PROPN
ap-3524	88	16	,	,	PUNCT
ap-3524	88	17	m)2	m)2	PROPN
ap-3524	88	18	−	−	PROPN
ap-3524	88	19	σxn	σxn	NOUN
ap-3524	88	20	,	,	PUNCT
ap-3524	88	21	m(σyn	m(σyn	PROPN
ap-3524	88	22	,	,	PUNCT
ap-3524	88	23	m)2	m)2	PROPN
ap-3524	88	24	hyn	hyn	PROPN
ap-3524	88	25	,	,	PUNCT
ap-3524	88	26	mhxn	mhxn	PROPN
ap-3524	88	27	,	,	PUNCT
ap-3524	88	28	m	m	VERB
ap-3524	88	29	−	−	PROPN
ap-3524	88	30	σ	σ	PROPN
ap-3524	88	31	y	y	PROPN
ap-3524	88	32	n	n	PROPN
ap-3524	88	33	,	,	PUNCT
ap-3524	88	34	mσxn	mσxn	PROPN
ap-3524	88	35	,	,	PUNCT
ap-3524	88	36	m	m	PROPN
ap-3524	88	37	=	=	ADJ
ap-3524	88	38	2yn	2yn	ADJ
ap-3524	88	39	,	,	PUNCT
ap-3524	88	40	m	m	VERB
ap-3524	88	41	+	+	X
ap-3524	88	42	∆y	∆y	PROPN
ap-3524	88	43	yy	yy	PROPN
ap-3524	88	44	.	.	PUNCT
ap-3524	89	1	(	(	PUNCT
ap-3524	89	2	17	17	NUM
ap-3524	89	3	)	)	PUNCT
ap-3524	89	4	where	where	SCONJ
ap-3524	89	5	the	the	DET
ap-3524	89	6	quantities	quantity	NOUN
ap-3524	89	7	∆x	∆x	PROPN
ap-3524	89	8	xx	xx	PROPN
ap-3524	89	9	,	,	PUNCT
ap-3524	89	10	∆x	∆x	PROPN
ap-3524	89	11	xy	xy	PROPN
ap-3524	89	12	,	,	PUNCT
ap-3524	89	13	∆x	∆x	PROPN
ap-3524	89	14	yy	yy	PROPN
ap-3524	89	15	,	,	PUNCT
ap-3524	89	16	∆y	∆y	PROPN
ap-3524	89	17	xx	xx	NUM
ap-3524	89	18	,	,	PUNCT
ap-3524	89	19	∆y	∆y	PROPN
ap-3524	89	20	xy	xy	PROPN
ap-3524	89	21	and	and	CCONJ
ap-3524	89	22	∆y	∆y	PROPN
ap-3524	89	23	yy	yy	PROPN
ap-3524	89	24	go	go	VERB
ap-3524	89	25	to	to	ADP
ap-3524	89	26	zero	zero	NUM
ap-3524	89	27	in	in	ADP
ap-3524	89	28	the	the	DET
ap-3524	89	29	continuous	continuous	ADJ
ap-3524	89	30	limit	limit	NOUN
ap-3524	89	31	when	when	SCONJ
ap-3524	89	32	h	h	PROPN
ap-3524	89	33	and	and	CCONJ
ap-3524	89	34	σ	σ	PROPN
ap-3524	89	35	go	go	VERB
ap-3524	89	36	to	to	ADP
ap-3524	89	37	zero	zero	NUM
ap-3524	89	38	.	.	PUNCT
ap-3524	90	1	3	3	X
ap-3524	90	2	.	.	X
ap-3524	90	3	example	example	NOUN
ap-3524	90	4	:	:	PUNCT
ap-3524	90	5	the	the	DET
ap-3524	90	6	potential	potential	ADJ
ap-3524	90	7	burgers	burger	NOUN
ap-3524	90	8	equation	equation	NOUN
ap-3524	90	9	the	the	DET
ap-3524	90	10	burgers	burger	NOUN
ap-3524	90	11	equation	equation	NOUN
ap-3524	90	12	ut	ut	PROPN
ap-3524	90	13	=	=	PROPN
ap-3524	90	14	νuxx	νuxx	PROPN
ap-3524	90	15	+	+	CCONJ
ap-3524	90	16	uux	uux	PROPN
ap-3524	90	17	,	,	PUNCT
ap-3524	90	18	(	(	PUNCT
ap-3524	90	19	18	18	NUM
ap-3524	90	20	)	)	PUNCT
ap-3524	90	21	a	a	DET
ap-3524	90	22	very	very	ADV
ap-3524	90	23	well	well	ADV
ap-3524	90	24	known	know	VERB
ap-3524	90	25	partial	partial	ADJ
ap-3524	90	26	differential	differential	NOUN
ap-3524	90	27	equation	equation	NOUN
ap-3524	90	28	,	,	PUNCT
ap-3524	90	29	appears	appear	VERB
ap-3524	90	30	as	as	ADP
ap-3524	90	31	a	a	DET
ap-3524	90	32	simplification	simplification	NOUN
ap-3524	90	33	of	of	ADP
ap-3524	90	34	the	the	DET
ap-3524	90	35	navier	navier	NOUN
ap-3524	90	36	–	–	PUNCT
ap-3524	90	37	stokes	stoke	NOUN
ap-3524	90	38	equation	equation	NOUN
ap-3524	90	39	and	and	CCONJ
ap-3524	90	40	has	have	AUX
ap-3524	90	41	been	be	AUX
ap-3524	90	42	studied	study	VERB
ap-3524	90	43	from	from	ADP
ap-3524	90	44	many	many	ADJ
ap-3524	90	45	,	,	PUNCT
ap-3524	90	46	if	if	SCONJ
ap-3524	90	47	not	not	PART
ap-3524	90	48	all	all	PRON
ap-3524	90	49	,	,	PUNCT
ap-3524	90	50	points	point	NOUN
ap-3524	90	51	of	of	ADP
ap-3524	90	52	view	view	NOUN
ap-3524	90	53	[	[	X
ap-3524	90	54	4	4	NUM
ap-3524	90	55	]	]	PUNCT
ap-3524	90	56	.	.	PUNCT
ap-3524	91	1	it	it	PRON
ap-3524	91	2	was	be	AUX
ap-3524	91	3	proposed	propose	VERB
ap-3524	91	4	as	as	ADP
ap-3524	91	5	a	a	DET
ap-3524	91	6	model	model	NOUN
ap-3524	91	7	for	for	ADP
ap-3524	91	8	a	a	DET
ap-3524	91	9	viscous	viscous	ADJ
ap-3524	91	10	fluid	fluid	NOUN
ap-3524	91	11	,	,	PUNCT
ap-3524	91	12	with	with	ADP
ap-3524	91	13	a	a	DET
ap-3524	91	14	viscosity	viscosity	NOUN
ap-3524	91	15	parameter	parameter	NOUN
ap-3524	91	16	ν	ν	NOUN
ap-3524	91	17	.	.	PUNCT
ap-3524	92	1	when	when	SCONJ
ap-3524	92	2	the	the	DET
ap-3524	92	3	viscosity	viscosity	NOUN
ap-3524	92	4	parameter	parameter	NOUN
ap-3524	92	5	ν	ν	PROPN
ap-3524	92	6	is	be	AUX
ap-3524	92	7	set	set	VERB
ap-3524	92	8	equal	equal	ADJ
ap-3524	92	9	to	to	ADP
ap-3524	92	10	zero	zero	NUM
ap-3524	92	11	,	,	PUNCT
ap-3524	92	12	the	the	DET
ap-3524	92	13	burgers	burger	NOUN
ap-3524	92	14	equation	equation	NOUN
ap-3524	92	15	degenerates	degenerate	NOUN
ap-3524	92	16	into	into	ADP
ap-3524	92	17	a	a	DET
ap-3524	92	18	quasilinear	quasilinear	NOUN
ap-3524	92	19	first	first	ADJ
ap-3524	92	20	order	order	NOUN
ap-3524	92	21	equation	equation	NOUN
ap-3524	92	22	which	which	PRON
ap-3524	92	23	is	be	AUX
ap-3524	92	24	the	the	DET
ap-3524	92	25	prototype	prototype	NOUN
ap-3524	92	26	of	of	ADP
ap-3524	92	27	a	a	DET
ap-3524	92	28	class	class	NOUN
ap-3524	92	29	of	of	ADP
ap-3524	92	30	equations	equation	NOUN
ap-3524	92	31	which	which	PRON
ap-3524	92	32	presents	present	VERB
ap-3524	92	33	nonlinear	nonlinear	ADJ
ap-3524	92	34	phenomena	phenomenon	NOUN
ap-3524	92	35	such	such	ADJ
ap-3524	92	36	as	as	ADP
ap-3524	92	37	shock	shock	NOUN
ap-3524	92	38	waves	wave	NOUN
ap-3524	92	39	.	.	PUNCT
ap-3524	93	1	in	in	ADP
ap-3524	93	2	fact	fact	NOUN
ap-3524	93	3	,	,	PUNCT
ap-3524	93	4	the	the	DET
ap-3524	93	5	limit	limit	NOUN
ap-3524	93	6	ν	ν	X
ap-3524	93	7	→	→	SYM
ap-3524	93	8	0	0	NUM
ap-3524	93	9	allows	allow	VERB
ap-3524	93	10	the	the	DET
ap-3524	93	11	study	study	NOUN
ap-3524	93	12	of	of	ADP
ap-3524	93	13	these	these	DET
ap-3524	93	14	shock	shock	NOUN
ap-3524	93	15	wave	wave	NOUN
ap-3524	93	16	solutions	solution	NOUN
ap-3524	93	17	as	as	ADP
ap-3524	93	18	limits	limit	NOUN
ap-3524	93	19	of	of	ADP
ap-3524	93	20	the	the	DET
ap-3524	93	21	solutions	solution	NOUN
ap-3524	93	22	of	of	ADP
ap-3524	93	23	the	the	DET
ap-3524	93	24	viscous	viscous	ADJ
ap-3524	93	25	burgers	burger	NOUN
ap-3524	93	26	equation	equation	NOUN
ap-3524	93	27	.	.	PUNCT
ap-3524	94	1	in	in	ADP
ap-3524	94	2	particular	particular	ADJ
ap-3524	94	3	,	,	PUNCT
ap-3524	94	4	although	although	SCONJ
ap-3524	94	5	the	the	DET
ap-3524	94	6	inviscid	inviscid	ADJ
ap-3524	94	7	burgers	burger	NOUN
ap-3524	94	8	equation	equation	NOUN
ap-3524	94	9	has	have	VERB
ap-3524	94	10	an	an	DET
ap-3524	94	11	infinite	infinite	ADJ
ap-3524	94	12	dimensional	dimensional	ADJ
ap-3524	94	13	group	group	NOUN
ap-3524	94	14	of	of	ADP
ap-3524	94	15	symmetries	symmetry	NOUN
ap-3524	94	16	(	(	PUNCT
ap-3524	94	17	being	be	AUX
ap-3524	94	18	a	a	DET
ap-3524	94	19	first	first	ADJ
ap-3524	94	20	order	order	NOUN
ap-3524	94	21	equation	equation	NOUN
ap-3524	94	22	)	)	PUNCT
ap-3524	94	23	,	,	PUNCT
ap-3524	94	24	the	the	DET
ap-3524	94	25	limit	limit	NOUN
ap-3524	94	26	of	of	ADP
ap-3524	94	27	the	the	DET
ap-3524	94	28	symmetry	symmetry	NOUN
ap-3524	94	29	group	group	NOUN
ap-3524	94	30	of	of	ADP
ap-3524	94	31	the	the	DET
ap-3524	94	32	viscous	viscous	ADJ
ap-3524	94	33	burgers	burger	NOUN
ap-3524	94	34	equations	equation	NOUN
ap-3524	94	35	provides	provide	VERB
ap-3524	94	36	a	a	DET
ap-3524	94	37	subgroup	subgroup	NOUN
ap-3524	94	38	of	of	ADP
ap-3524	94	39	the	the	DET
ap-3524	94	40	whole	whole	ADJ
ap-3524	94	41	group	group	NOUN
ap-3524	94	42	of	of	ADP
ap-3524	94	43	symmetries	symmetry	NOUN
ap-3524	94	44	of	of	ADP
ap-3524	94	45	the	the	DET
ap-3524	94	46	inviscid	inviscid	ADJ
ap-3524	94	47	burgers	burger	NOUN
ap-3524	94	48	equation	equation	NOUN
ap-3524	94	49	which	which	PRON
ap-3524	94	50	is	be	AUX
ap-3524	94	51	a	a	DET
ap-3524	94	52	useful	useful	ADJ
ap-3524	94	53	tool	tool	NOUN
ap-3524	94	54	in	in	ADP
ap-3524	94	55	the	the	DET
ap-3524	94	56	study	study	NOUN
ap-3524	94	57	of	of	ADP
ap-3524	94	58	the	the	DET
ap-3524	94	59	equation	equation	NOUN
ap-3524	94	60	and	and	CCONJ
ap-3524	94	61	in	in	ADP
ap-3524	94	62	particular	particular	ADJ
ap-3524	94	63	its	its	PRON
ap-3524	94	64	discretization	discretization	NOUN
ap-3524	94	65	using	use	VERB
ap-3524	94	66	invariant	invariant	ADJ
ap-3524	94	67	techniques	technique	NOUN
ap-3524	94	68	.	.	PUNCT
ap-3524	95	1	several	several	ADJ
ap-3524	95	2	invariant	invariant	ADJ
ap-3524	95	3	discretization	discretization	NOUN
ap-3524	95	4	approaches	approach	NOUN
ap-3524	95	5	have	have	AUX
ap-3524	95	6	been	be	AUX
ap-3524	95	7	proposed	propose	VERB
ap-3524	95	8	to	to	PART
ap-3524	95	9	construct	construct	VERB
ap-3524	95	10	explicit	explicit	ADJ
ap-3524	95	11	numerical	numerical	ADJ
ap-3524	95	12	schemes	scheme	NOUN
ap-3524	95	13	for	for	ADP
ap-3524	95	14	finding	find	VERB
ap-3524	95	15	numerical	numerical	ADJ
ap-3524	95	16	solutions	solution	NOUN
ap-3524	95	17	on	on	ADP
ap-3524	95	18	invariant	invariant	ADJ
ap-3524	95	19	lattices	lattice	NOUN
ap-3524	95	20	[	[	X
ap-3524	95	21	1	1	NUM
ap-3524	95	22	,	,	PUNCT
ap-3524	95	23	10	10	NUM
ap-3524	95	24	]	]	PUNCT
ap-3524	95	25	.	.	PUNCT
ap-3524	96	1	in	in	ADP
ap-3524	96	2	some	some	PRON
ap-3524	96	3	of	of	ADP
ap-3524	96	4	these	these	DET
ap-3524	96	5	works	work	NOUN
ap-3524	96	6	,	,	PUNCT
ap-3524	96	7	explicit	explicit	ADJ
ap-3524	96	8	comparison	comparison	NOUN
ap-3524	96	9	has	have	AUX
ap-3524	96	10	been	be	AUX
ap-3524	96	11	made	make	VERB
ap-3524	96	12	,	,	PUNCT
ap-3524	96	13	showing	show	VERB
ap-3524	96	14	the	the	DET
ap-3524	96	15	higher	high	ADJ
ap-3524	96	16	accuracy	accuracy	NOUN
ap-3524	96	17	and	and	CCONJ
ap-3524	96	18	stability	stability	NOUN
ap-3524	96	19	of	of	ADP
ap-3524	96	20	these	these	DET
ap-3524	96	21	methods	method	NOUN
ap-3524	96	22	[	[	X
ap-3524	96	23	5	5	NUM
ap-3524	96	24	]	]	PUNCT
ap-3524	96	25	.	.	PUNCT
ap-3524	97	1	it	it	PRON
ap-3524	97	2	is	be	AUX
ap-3524	97	3	not	not	PART
ap-3524	97	4	our	our	PRON
ap-3524	97	5	intention	intention	NOUN
ap-3524	97	6	in	in	ADP
ap-3524	97	7	this	this	DET
ap-3524	97	8	paper	paper	NOUN
ap-3524	97	9	to	to	PART
ap-3524	97	10	present	present	VERB
ap-3524	97	11	this	this	DET
ap-3524	97	12	kind	kind	NOUN
ap-3524	97	13	of	of	ADP
ap-3524	97	14	numerical	numerical	ADJ
ap-3524	97	15	results	result	NOUN
ap-3524	97	16	but	but	CCONJ
ap-3524	97	17	rather	rather	ADV
ap-3524	97	18	to	to	PART
ap-3524	97	19	prove	prove	VERB
ap-3524	97	20	the	the	DET
ap-3524	97	21	possibility	possibility	NOUN
ap-3524	97	22	of	of	ADP
ap-3524	97	23	constructing	construct	VERB
ap-3524	97	24	in	in	ADP
ap-3524	97	25	an	an	DET
ap-3524	97	26	easy	easy	ADJ
ap-3524	97	27	way	way	NOUN
ap-3524	97	28	such	such	ADJ
ap-3524	97	29	invariant	invariant	ADJ
ap-3524	97	30	discrete	discrete	ADJ
ap-3524	97	31	schemes	scheme	NOUN
ap-3524	97	32	and	and	CCONJ
ap-3524	97	33	discuss	discuss	VERB
ap-3524	97	34	the	the	DET
ap-3524	97	35	properties	property	NOUN
ap-3524	97	36	of	of	ADP
ap-3524	97	37	a	a	DET
ap-3524	97	38	lattice	lattice	NOUN
ap-3524	97	39	satisfying	satisfy	VERB
ap-3524	97	40	the	the	DET
ap-3524	97	41	clairaut	clairaut	NOUN
ap-3524	97	42	–	–	PUNCT
ap-3524	97	43	schwarz	schwarz	PROPN
ap-3524	97	44	–	–	PUNCT
ap-3524	97	45	young	young	ADJ
ap-3524	97	46	theorem	theorem	NOUN
ap-3524	97	47	from	from	ADP
ap-3524	97	48	the	the	DET
ap-3524	97	49	numerical	numerical	ADJ
ap-3524	97	50	point	point	NOUN
ap-3524	97	51	of	of	ADP
ap-3524	97	52	view	view	NOUN
ap-3524	97	53	.	.	PUNCT
ap-3524	98	1	for	for	ADP
ap-3524	98	2	the	the	DET
ap-3524	98	3	control	control	NOUN
ap-3524	98	4	of	of	ADP
ap-3524	98	5	the	the	DET
ap-3524	98	6	numerical	numerical	ADJ
ap-3524	98	7	calculations	calculation	NOUN
ap-3524	98	8	we	we	PRON
ap-3524	98	9	will	will	AUX
ap-3524	98	10	study	study	VERB
ap-3524	98	11	the	the	DET
ap-3524	98	12	time	time	NOUN
ap-3524	98	13	evolution	evolution	NOUN
ap-3524	98	14	of	of	ADP
ap-3524	98	15	the	the	DET
ap-3524	98	16	initial	initial	ADJ
ap-3524	98	17	condition	condition	NOUN
ap-3524	98	18	provided	provide	VERB
ap-3524	98	19	by	by	ADP
ap-3524	98	20	exact	exact	ADJ
ap-3524	98	21	solutions	solution	NOUN
ap-3524	98	22	of	of	ADP
ap-3524	98	23	the	the	DET
ap-3524	98	24	burgers	burger	NOUN
ap-3524	98	25	equation	equation	NOUN
ap-3524	98	26	.	.	PUNCT
ap-3524	99	1	to	to	PART
ap-3524	99	2	simplify	simplify	VERB
ap-3524	99	3	the	the	DET
ap-3524	99	4	presentation	presentation	NOUN
ap-3524	99	5	and	and	CCONJ
ap-3524	99	6	with	with	ADP
ap-3524	99	7	no	no	DET
ap-3524	99	8	loss	loss	NOUN
ap-3524	99	9	of	of	ADP
ap-3524	99	10	generality	generality	NOUN
ap-3524	99	11	we	we	PRON
ap-3524	99	12	will	will	AUX
ap-3524	99	13	go	go	VERB
ap-3524	99	14	over	over	ADP
ap-3524	99	15	to	to	PART
ap-3524	99	16	consider	consider	VERB
ap-3524	99	17	the	the	DET
ap-3524	99	18	potential	potential	ADJ
ap-3524	99	19	burgers	burger	NOUN
ap-3524	99	20	equation	equation	NOUN
ap-3524	99	21	as	as	SCONJ
ap-3524	99	22	this	this	PRON
ap-3524	99	23	is	be	AUX
ap-3524	99	24	point	point	NOUN
ap-3524	99	25	transformable	transformable	ADJ
ap-3524	99	26	into	into	ADP
ap-3524	99	27	the	the	DET
ap-3524	99	28	linear	linear	ADJ
ap-3524	99	29	heat	heat	NOUN
ap-3524	99	30	equation	equation	NOUN
ap-3524	99	31	for	for	ADP
ap-3524	99	32	which	which	PRON
ap-3524	99	33	many	many	ADJ
ap-3524	99	34	exact	exact	ADJ
ap-3524	99	35	solutions	solution	NOUN
ap-3524	99	36	are	be	AUX
ap-3524	99	37	known	know	VERB
ap-3524	99	38	.	.	PUNCT
ap-3524	100	1	let	let	VERB
ap-3524	100	2	us	we	PRON
ap-3524	100	3	construct	construct	VERB
ap-3524	100	4	using	use	VERB
ap-3524	100	5	the	the	DET
ap-3524	100	6	formulas	formula	NOUN
ap-3524	100	7	introduced	introduce	VERB
ap-3524	100	8	in	in	ADP
ap-3524	100	9	the	the	DET
ap-3524	100	10	previous	previous	ADJ
ap-3524	100	11	section	section	NOUN
ap-3524	100	12	the	the	DET
ap-3524	100	13	discrete	discrete	ADJ
ap-3524	100	14	scheme	scheme	NOUN
ap-3524	100	15	which	which	PRON
ap-3524	100	16	preserves	preserve	VERB
ap-3524	100	17	the	the	DET
ap-3524	100	18	point	point	NOUN
ap-3524	100	19	symmetries	symmetry	NOUN
ap-3524	100	20	of	of	ADP
ap-3524	100	21	the	the	DET
ap-3524	100	22	potential	potential	ADJ
ap-3524	100	23	burgers	burger	NOUN
ap-3524	100	24	equation	equation	NOUN
ap-3524	100	25	uy	uy	PROPN
ap-3524	100	26	−	−	PROPN
ap-3524	100	27	uxx	uxx	PROPN
ap-3524	100	28	−	−	PROPN
ap-3524	100	29	u2	u2	NOUN
ap-3524	100	30	x	x	PROPN
ap-3524	100	31	=	=	NOUN
ap-3524	100	32	0	0	PROPN
ap-3524	100	33	.	.	PUNCT
ap-3524	101	1	(	(	PUNCT
ap-3524	101	2	19	19	NUM
ap-3524	101	3	)	)	PUNCT
ap-3524	101	4	the	the	DET
ap-3524	101	5	point	point	NOUN
ap-3524	101	6	symmetries	symmetry	NOUN
ap-3524	101	7	of	of	ADP
ap-3524	101	8	(	(	PUNCT
ap-3524	101	9	19	19	NUM
ap-3524	101	10	)	)	PUNCT
ap-3524	101	11	are	be	AUX
ap-3524	101	12	[	[	X
ap-3524	101	13	18	18	NUM
ap-3524	101	14	]	]	PUNCT
ap-3524	101	15	v̂1	v̂1	X
ap-3524	101	16	=	=	SYM
ap-3524	101	17	∂x	∂x	PROPN
ap-3524	101	18	,	,	PUNCT
ap-3524	101	19	v̂2	v̂2	NOUN
ap-3524	101	20	=	=	SYM
ap-3524	101	21	∂y	∂y	SYM
ap-3524	101	22	,	,	PUNCT
ap-3524	101	23	v̂3	v̂3	NOUN
ap-3524	101	24	=	=	SYM
ap-3524	101	25	∂u	∂u	PROPN
ap-3524	101	26	,	,	PUNCT
ap-3524	101	27	v̂4	v̂4	PUNCT
ap-3524	102	1	=	=	PUNCT
ap-3524	102	2	x∂x	x∂x	X
ap-3524	103	1	+	+	PUNCT
ap-3524	103	2	2y∂y	2y∂y	NUM
ap-3524	103	3	,	,	PUNCT
ap-3524	103	4	v̂5	v̂5	NOUN
ap-3524	104	1	=	=	PUNCT
ap-3524	104	2	2y∂x	2y∂x	NUM
ap-3524	105	1	−	−	NOUN
ap-3524	105	2	x∂u	x∂u	NOUN
ap-3524	105	3	,	,	PUNCT
ap-3524	105	4	v̂6	v̂6	ADP
ap-3524	105	5	=	=	SYM
ap-3524	105	6	4yx∂x	4yx∂x	PROPN
ap-3524	106	1	+	+	CCONJ
ap-3524	107	1	4y2∂y	4y2∂y	NOUN
ap-3524	107	2	−	−	PROPN
ap-3524	108	1	(	(	PUNCT
ap-3524	108	2	x2	x2	PROPN
ap-3524	109	1	+	+	CCONJ
ap-3524	109	2	2y)∂u	2y)∂u	NUM
ap-3524	109	3	,	,	PUNCT
ap-3524	109	4	v̂α	v̂α	ADP
ap-3524	109	5	=	=	PROPN
ap-3524	109	6	α(x	α(x	PROPN
ap-3524	109	7	,	,	PUNCT
ap-3524	109	8	y)e−u∂u	y)e−u∂u	PROPN
ap-3524	109	9	,	,	PUNCT
ap-3524	109	10	(	(	PUNCT
ap-3524	109	11	20	20	NUM
ap-3524	109	12	)	)	PUNCT
ap-3524	109	13	where	where	SCONJ
ap-3524	109	14	the	the	DET
ap-3524	109	15	function	function	NOUN
ap-3524	109	16	α(x	α(x	PROPN
ap-3524	109	17	,	,	PUNCT
ap-3524	109	18	y	y	PROPN
ap-3524	109	19	)	)	PUNCT
ap-3524	109	20	satisfies	satisfy	VERB
ap-3524	109	21	the	the	DET
ap-3524	109	22	heat	heat	NOUN
ap-3524	109	23	equation	equation	NOUN
ap-3524	109	24	αy	αy	NOUN
ap-3524	109	25	=	=	SYM
ap-3524	109	26	αxx	αxx	PROPN
ap-3524	109	27	.	.	PUNCT
ap-3524	110	1	(	(	PUNCT
ap-3524	110	2	21	21	NUM
ap-3524	110	3	)	)	PUNCT
ap-3524	110	4	239	239	NUM
ap-3524	110	5	decio	decio	NOUN
ap-3524	110	6	levi	levi	PROPN
ap-3524	110	7	,	,	PUNCT
ap-3524	110	8	miguel	miguel	PROPN
ap-3524	110	9	a.	a.	PROPN
ap-3524	110	10	rodríguez	rodríguez	PROPN
ap-3524	110	11	acta	acta	PROPN
ap-3524	110	12	polytechnica	polytechnica	PROPN
ap-3524	110	13	the	the	DET
ap-3524	110	14	infinitesimal	infinitesimal	ADJ
ap-3524	110	15	generator	generator	NOUN
ap-3524	110	16	v̂α	v̂α	ADP
ap-3524	110	17	is	be	AUX
ap-3524	110	18	the	the	DET
ap-3524	110	19	one	one	NUM
ap-3524	110	20	responsible	responsible	ADJ
ap-3524	110	21	for	for	ADP
ap-3524	110	22	the	the	DET
ap-3524	110	23	linearizability	linearizability	NOUN
ap-3524	110	24	of	of	ADP
ap-3524	110	25	the	the	DET
ap-3524	110	26	potential	potential	ADJ
ap-3524	110	27	burgers	burger	NOUN
ap-3524	110	28	equation	equation	NOUN
ap-3524	110	29	as	as	SCONJ
ap-3524	110	30	it	it	PRON
ap-3524	110	31	provides	provide	VERB
ap-3524	110	32	its	its	PRON
ap-3524	110	33	linearizing	linearize	VERB
ap-3524	110	34	transformation	transformation	NOUN
ap-3524	110	35	α	α	X
ap-3524	110	36	=	=	SYM
ap-3524	110	37	eu	eu	PROPN
ap-3524	110	38	.	.	PROPN
ap-3524	111	1	(	(	PUNCT
ap-3524	111	2	22	22	NUM
ap-3524	111	3	)	)	PUNCT
ap-3524	111	4	a	a	DET
ap-3524	111	5	function	function	NOUN
ap-3524	111	6	f	f	X
ap-3524	111	7	(	(	PUNCT
ap-3524	111	8	x	x	PROPN
ap-3524	111	9	,	,	PUNCT
ap-3524	111	10	y	y	PROPN
ap-3524	111	11	,	,	PUNCT
ap-3524	111	12	u	u	NOUN
ap-3524	111	13	,	,	PUNCT
ap-3524	111	14	ux	ux	PROPN
ap-3524	111	15	,	,	PUNCT
ap-3524	111	16	uy	uy	PROPN
ap-3524	111	17	,	,	PUNCT
ap-3524	111	18	uxx	uxx	PROPN
ap-3524	111	19	)	)	PUNCT
ap-3524	111	20	is	be	AUX
ap-3524	111	21	invariant	invariant	ADJ
ap-3524	111	22	under	under	ADP
ap-3524	111	23	the	the	DET
ap-3524	111	24	infinitesimal	infinitesimal	ADJ
ap-3524	111	25	generators	generator	NOUN
ap-3524	111	26	v̂1	v̂1	PROPN
ap-3524	111	27	,	,	PUNCT
ap-3524	111	28	v̂2	v̂2	NOUN
ap-3524	111	29	,	,	PUNCT
ap-3524	111	30	v̂3	v̂3	ADJ
ap-3524	111	31	v̂4	v̂4	X
ap-3524	111	32	,	,	PUNCT
ap-3524	111	33	v̂5	v̂5	ADV
ap-3524	111	34	if	if	SCONJ
ap-3524	111	35	it	it	PRON
ap-3524	111	36	depends	depend	VERB
ap-3524	111	37	on	on	ADP
ap-3524	111	38	i(1	i(1	NOUN
ap-3524	111	39	)	)	PUNCT
ap-3524	112	1	=	=	PRON
ap-3524	112	2	uy	uy	PROPN
ap-3524	112	3	−	−	PROPN
ap-3524	112	4	u2	u2	PROPN
ap-3524	112	5	x	x	PROPN
ap-3524	112	6	uxx	uxx	PROPN
ap-3524	112	7	.	.	PUNCT
ap-3524	113	1	(	(	PUNCT
ap-3524	113	2	23	23	NUM
ap-3524	113	3	)	)	PUNCT
ap-3524	113	4	it	it	PRON
ap-3524	113	5	is	be	AUX
ap-3524	113	6	then	then	ADV
ap-3524	113	7	easy	easy	ADJ
ap-3524	113	8	to	to	PART
ap-3524	113	9	see	see	VERB
ap-3524	113	10	that	that	PRON
ap-3524	113	11	(	(	PUNCT
ap-3524	113	12	23	23	NUM
ap-3524	113	13	)	)	PUNCT
ap-3524	113	14	is	be	AUX
ap-3524	113	15	weakly	weakly	ADV
ap-3524	113	16	invariant	invariant	ADJ
ap-3524	113	17	also	also	ADV
ap-3524	113	18	under	under	ADP
ap-3524	113	19	v̂6	v̂6	NOUN
ap-3524	113	20	and	and	CCONJ
ap-3524	113	21	v̂α	v̂α	ADP
ap-3524	113	22	,	,	PUNCT
ap-3524	113	23	i.e.	i.e.	X
ap-3524	113	24	,	,	PUNCT
ap-3524	113	25	pr(2	pr(2	NOUN
ap-3524	113	26	)	)	PUNCT
ap-3524	113	27	v̂6	v̂6	NOUN
ap-3524	114	1	i	i	PRON
ap-3524	114	2	(	(	PUNCT
ap-3524	114	3	1	1	X
ap-3524	114	4	)	)	PUNCT
ap-3524	114	5	=	=	SYM
ap-3524	114	6	2	2	NUM
ap-3524	114	7	uxx	uxx	X
ap-3524	114	8	(	(	PUNCT
ap-3524	114	9	i(1	i(1	PROPN
ap-3524	114	10	)	)	PUNCT
ap-3524	114	11	−	−	PROPN
ap-3524	114	12	1	1	NUM
ap-3524	114	13	)	)	PUNCT
ap-3524	114	14	,	,	PUNCT
ap-3524	114	15	pr(2	pr(2	NOUN
ap-3524	114	16	)	)	PUNCT
ap-3524	114	17	v̂α	v̂α	ADP
ap-3524	114	18	i	i	PRON
ap-3524	114	19	(	(	PUNCT
ap-3524	114	20	1	1	X
ap-3524	114	21	)	)	PUNCT
ap-3524	114	22	=	=	NOUN
ap-3524	114	23	−e	−e	NOUN
ap-3524	114	24	−u	−u	PROPN
ap-3524	114	25	uxx	uxx	NOUN
ap-3524	114	26	(	(	PUNCT
ap-3524	114	27	αu2	αu2	NOUN
ap-3524	114	28	x	x	X
ap-3524	114	29	+	+	PUNCT
ap-3524	114	30	2αxux	2αxux	NUM
ap-3524	114	31	+	+	CCONJ
ap-3524	114	32	αy	αy	NOUN
ap-3524	114	33	)	)	PUNCT
ap-3524	114	34	(	(	PUNCT
ap-3524	114	35	i(1	i(1	PROPN
ap-3524	114	36	)	)	PUNCT
ap-3524	114	37	−	−	PROPN
ap-3524	114	38	1	1	NUM
ap-3524	114	39	)	)	PUNCT
ap-3524	114	40	.	.	PUNCT
ap-3524	115	1	the	the	DET
ap-3524	115	2	potential	potential	ADJ
ap-3524	115	3	burgers	burger	NOUN
ap-3524	115	4	equation	equation	NOUN
ap-3524	115	5	(	(	PUNCT
ap-3524	115	6	19	19	NUM
ap-3524	115	7	)	)	PUNCT
ap-3524	115	8	is	be	AUX
ap-3524	115	9	then	then	ADV
ap-3524	115	10	given	give	VERB
ap-3524	115	11	by	by	ADP
ap-3524	115	12	i(1	i(1	NOUN
ap-3524	115	13	)	)	PUNCT
ap-3524	115	14	=	=	SYM
ap-3524	115	15	1	1	NUM
ap-3524	115	16	(	(	PUNCT
ap-3524	115	17	24	24	NUM
ap-3524	115	18	)	)	PUNCT
ap-3524	115	19	taking	take	VERB
ap-3524	115	20	into	into	ADP
ap-3524	115	21	account	account	NOUN
ap-3524	115	22	the	the	DET
ap-3524	115	23	discrete	discrete	ADJ
ap-3524	115	24	prolongation	prolongation	NOUN
ap-3524	115	25	(	(	PUNCT
ap-3524	115	26	14	14	NUM
ap-3524	115	27	)	)	PUNCT
ap-3524	115	28	and	and	CCONJ
ap-3524	115	29	the	the	DET
ap-3524	115	30	definition	definition	NOUN
ap-3524	115	31	of	of	ADP
ap-3524	115	32	the	the	DET
ap-3524	115	33	infinitesimal	infinitesimal	ADJ
ap-3524	115	34	coefficients	coefficient	NOUN
ap-3524	115	35	(	(	PUNCT
ap-3524	115	36	15	15	NUM
ap-3524	115	37	)	)	PUNCT
ap-3524	115	38	we	we	PRON
ap-3524	115	39	can	can	AUX
ap-3524	115	40	construct	construct	VERB
ap-3524	115	41	the	the	DET
ap-3524	115	42	discrete	discrete	ADJ
ap-3524	115	43	prolongation	prolongation	NOUN
ap-3524	115	44	of	of	ADP
ap-3524	115	45	the	the	DET
ap-3524	115	46	vector	vector	NOUN
ap-3524	115	47	fields	field	NOUN
ap-3524	115	48	(	(	PUNCT
ap-3524	115	49	20	20	NUM
ap-3524	115	50	)	)	PUNCT
ap-3524	115	51	.	.	PUNCT
ap-3524	116	1	it	it	PRON
ap-3524	116	2	is	be	AUX
ap-3524	116	3	easy	easy	ADJ
ap-3524	116	4	to	to	PART
ap-3524	116	5	show	show	VERB
ap-3524	116	6	that	that	SCONJ
ap-3524	116	7	the	the	DET
ap-3524	116	8	conditions	condition	NOUN
ap-3524	116	9	(	(	PUNCT
ap-3524	116	10	16	16	NUM
ap-3524	116	11	)	)	PUNCT
ap-3524	116	12	are	be	AUX
ap-3524	116	13	satisfied	satisfied	ADJ
ap-3524	116	14	for	for	ADP
ap-3524	116	15	all	all	DET
ap-3524	116	16	symmetries	symmetry	NOUN
ap-3524	116	17	(	(	PUNCT
ap-3524	116	18	20	20	NUM
ap-3524	116	19	)	)	PUNCT
ap-3524	116	20	except	except	SCONJ
ap-3524	116	21	for	for	ADP
ap-3524	116	22	v̂6	v̂6	NOUN
ap-3524	116	23	for	for	ADP
ap-3524	116	24	which	which	PRON
ap-3524	116	25	ξn	ξn	X
ap-3524	116	26	,	,	PUNCT
ap-3524	116	27	m+1	m+1	NUM
ap-3524	116	28	−	−	PROPN
ap-3524	116	29	ξn	ξn	PROPN
ap-3524	116	30	,	,	PUNCT
ap-3524	116	31	m	m	VERB
ap-3524	116	32	−	−	NOUN
ap-3524	116	33	ξn+1,m+1	ξn+1,m+1	PUNCT
ap-3524	116	34	+	+	NUM
ap-3524	116	35	ξn+1,m	ξn+1,m	NOUN
ap-3524	116	36	=	=	SYM
ap-3524	116	37	−4[hxn	−4[hxn	NOUN
ap-3524	116	38	,	,	PUNCT
ap-3524	116	39	mhyn	mhyn	ADJ
ap-3524	116	40	,	,	PUNCT
ap-3524	116	41	m	m	VERB
ap-3524	116	42	+	+	X
ap-3524	116	43	σxn	σxn	ADJ
ap-3524	116	44	,	,	PUNCT
ap-3524	116	45	mσ	mσ	PROPN
ap-3524	116	46	y	y	PROPN
ap-3524	116	47	n	n	PROPN
ap-3524	116	48	,	,	PUNCT
ap-3524	116	49	m	m	PROPN
ap-3524	116	50	]	]	X
ap-3524	116	51	6=	6=	ADP
ap-3524	116	52	0	0	NUM
ap-3524	116	53	and	and	CCONJ
ap-3524	116	54	τn	τn	ADP
ap-3524	116	55	,	,	PUNCT
ap-3524	116	56	m+1	m+1	NUM
ap-3524	116	57	−	−	NOUN
ap-3524	116	58	τn	τn	NOUN
ap-3524	116	59	,	,	PUNCT
ap-3524	116	60	m	m	VERB
ap-3524	116	61	−	−	NOUN
ap-3524	116	62	τn+1,m+1	τn+1,m+1	PUNCT
ap-3524	117	1	+	+	CCONJ
ap-3524	117	2	τn+1,m	τn+1,m	NOUN
ap-3524	117	3	=	=	SYM
ap-3524	117	4	−8hxn	−8hxn	NOUN
ap-3524	117	5	,	,	PUNCT
ap-3524	117	6	mσxn	mσxn	NOUN
ap-3524	117	7	,	,	PUNCT
ap-3524	117	8	m	m	PROPN
ap-3524	117	9	6=	6=	PROPN
ap-3524	117	10	0	0	NUM
ap-3524	117	11	.	.	PUNCT
ap-3524	118	1	since	since	SCONJ
ap-3524	118	2	we	we	PRON
ap-3524	118	3	are	be	AUX
ap-3524	118	4	presently	presently	ADV
ap-3524	118	5	interested	interested	ADJ
ap-3524	118	6	in	in	ADP
ap-3524	118	7	analyzing	analyze	VERB
ap-3524	118	8	the	the	DET
ap-3524	118	9	role	role	NOUN
ap-3524	118	10	of	of	ADP
ap-3524	118	11	the	the	DET
ap-3524	118	12	schwarz	schwarz	PROPN
ap-3524	118	13	condition	condition	NOUN
ap-3524	118	14	on	on	ADP
ap-3524	118	15	the	the	DET
ap-3524	118	16	construction	construction	NOUN
ap-3524	118	17	of	of	ADP
ap-3524	118	18	lattices	lattice	NOUN
ap-3524	118	19	and	and	CCONJ
ap-3524	118	20	its	its	PRON
ap-3524	118	21	consequences	consequence	NOUN
ap-3524	118	22	in	in	ADP
ap-3524	118	23	numerical	numerical	ADJ
ap-3524	118	24	computations	computation	NOUN
ap-3524	118	25	,	,	PUNCT
ap-3524	118	26	we	we	PRON
ap-3524	118	27	will	will	AUX
ap-3524	118	28	not	not	PART
ap-3524	118	29	consider	consider	VERB
ap-3524	118	30	the	the	DET
ap-3524	118	31	symmetry	symmetry	NOUN
ap-3524	118	32	with	with	ADP
ap-3524	118	33	generator	generator	NOUN
ap-3524	118	34	v̂6	v̂6	PROPN
ap-3524	118	35	in	in	ADP
ap-3524	118	36	the	the	DET
ap-3524	118	37	following	following	NOUN
ap-3524	118	38	,	,	PUNCT
ap-3524	118	39	that	that	ADV
ap-3524	118	40	is	is	ADV
ap-3524	118	41	,	,	PUNCT
ap-3524	118	42	we	we	PRON
ap-3524	118	43	restrict	restrict	VERB
ap-3524	118	44	ourselves	ourselves	PRON
ap-3524	118	45	to	to	ADP
ap-3524	118	46	a	a	DET
ap-3524	118	47	sugbroup	sugbroup	NOUN
ap-3524	118	48	of	of	ADP
ap-3524	118	49	the	the	DET
ap-3524	118	50	whole	whole	ADJ
ap-3524	118	51	symmetry	symmetry	NOUN
ap-3524	118	52	group	group	NOUN
ap-3524	118	53	(	(	PUNCT
ap-3524	118	54	note	note	VERB
ap-3524	118	55	that	that	SCONJ
ap-3524	118	56	we	we	PRON
ap-3524	118	57	have	have	AUX
ap-3524	118	58	also	also	ADV
ap-3524	118	59	disregard	disregard	VERB
ap-3524	118	60	in	in	ADP
ap-3524	118	61	our	our	PRON
ap-3524	118	62	analysis	analysis	NOUN
ap-3524	118	63	the	the	DET
ap-3524	118	64	operator	operator	NOUN
ap-3524	118	65	v̂α	v̂α	ADP
ap-3524	118	66	,	,	PUNCT
ap-3524	118	67	which	which	PRON
ap-3524	118	68	,	,	PUNCT
ap-3524	118	69	as	as	SCONJ
ap-3524	118	70	we	we	PRON
ap-3524	118	71	have	have	AUX
ap-3524	118	72	remarked	remark	VERB
ap-3524	118	73	above	above	ADV
ap-3524	118	74	,	,	PUNCT
ap-3524	118	75	is	be	AUX
ap-3524	118	76	related	relate	VERB
ap-3524	118	77	to	to	ADP
ap-3524	118	78	the	the	DET
ap-3524	118	79	linearization	linearization	NOUN
ap-3524	118	80	of	of	ADP
ap-3524	118	81	the	the	DET
ap-3524	118	82	equation	equation	NOUN
ap-3524	118	83	under	under	ADP
ap-3524	118	84	study	study	NOUN
ap-3524	118	85	)	)	PUNCT
ap-3524	118	86	.	.	PUNCT
ap-3524	119	1	taking	take	VERB
ap-3524	119	2	into	into	ADP
ap-3524	119	3	account	account	NOUN
ap-3524	119	4	(	(	PUNCT
ap-3524	119	5	17	17	NUM
ap-3524	119	6	)	)	PUNCT
ap-3524	119	7	we	we	PRON
ap-3524	119	8	have	have	VERB
ap-3524	119	9	:	:	PUNCT
ap-3524	119	10	prd	prd	NOUN
ap-3524	119	11	v̂1	v̂1	NOUN
ap-3524	119	12	=	=	PUNCT
ap-3524	119	13	∂xn	∂xn	PROPN
ap-3524	119	14	,	,	PUNCT
ap-3524	119	15	m	m	NOUN
ap-3524	119	16	,	,	PUNCT
ap-3524	119	17	prd	prd	NOUN
ap-3524	119	18	v̂2	v̂2	NOUN
ap-3524	119	19	=	=	SYM
ap-3524	120	1	∂yn	∂yn	PROPN
ap-3524	120	2	,	,	PUNCT
ap-3524	120	3	m	m	NOUN
ap-3524	120	4	,	,	PUNCT
ap-3524	120	5	prd	prd	NOUN
ap-3524	120	6	v̂3	v̂3	NOUN
ap-3524	120	7	=	=	SYM
ap-3524	120	8	∂un	∂un	PROPN
ap-3524	120	9	,	,	PUNCT
ap-3524	120	10	m	m	VERB
ap-3524	120	11	,	,	PUNCT
ap-3524	120	12	prd	prd	NOUN
ap-3524	120	13	v̂4	v̂4	PUNCT
ap-3524	120	14	=	=	PUNCT
ap-3524	120	15	xn	xn	PROPN
ap-3524	120	16	,	,	PUNCT
ap-3524	120	17	m∂xn	m∂xn	PROPN
ap-3524	120	18	,	,	PUNCT
ap-3524	120	19	m	m	VERB
ap-3524	120	20	+	+	CCONJ
ap-3524	120	21	2yn	2yn	ADJ
ap-3524	120	22	,	,	PUNCT
ap-3524	120	23	m∂yn	m∂yn	PROPN
ap-3524	120	24	,	,	PUNCT
ap-3524	120	25	m	m	VERB
ap-3524	120	26	+	+	X
ap-3524	120	27	hxn	hxn	NOUN
ap-3524	120	28	,	,	PUNCT
ap-3524	120	29	m∂hx	m∂hx	NOUN
ap-3524	120	30	n	n	CCONJ
ap-3524	120	31	,	,	PUNCT
ap-3524	120	32	m	m	VERB
ap-3524	120	33	+	+	ADJ
ap-3524	120	34	hxn+1,m∂hx	hxn+1,m∂hx	ADP
ap-3524	120	35	n+1,m	n+1,m	NOUN
ap-3524	120	36	+	+	CCONJ
ap-3524	120	37	hxn	hxn	NOUN
ap-3524	120	38	,	,	PUNCT
ap-3524	120	39	m+1∂hx	m+1∂hx	NOUN
ap-3524	120	40	n	n	CCONJ
ap-3524	120	41	,	,	PUNCT
ap-3524	120	42	m+1	m+1	PRON
ap-3524	120	43	+	+	CCONJ
ap-3524	120	44	σxn	σxn	NOUN
ap-3524	120	45	,	,	PUNCT
ap-3524	120	46	m∂σx	m∂σx	PROPN
ap-3524	120	47	n	n	PART
ap-3524	120	48	,	,	PUNCT
ap-3524	120	49	m	m	PROPN
ap-3524	120	50	+	+	ADJ
ap-3524	120	51	σxn	σxn	ADJ
ap-3524	120	52	,	,	PUNCT
ap-3524	120	53	m+1∂σx	m+1∂σx	ADP
ap-3524	120	54	n	n	CCONJ
ap-3524	120	55	,	,	PUNCT
ap-3524	120	56	m+1	m+1	PROPN
ap-3524	120	57	+	+	NUM
ap-3524	120	58	2	2	NUM
ap-3524	120	59	(	(	PUNCT
ap-3524	120	60	hyn	hyn	PROPN
ap-3524	120	61	,	,	PUNCT
ap-3524	120	62	m∂hy	m∂hy	PROPN
ap-3524	120	63	n	n	CCONJ
ap-3524	120	64	,	,	PUNCT
ap-3524	120	65	m	m	VERB
ap-3524	120	66	+	+	ADJ
ap-3524	120	67	hyn+1,m∂hy	hyn+1,m∂hy	ADJ
ap-3524	120	68	n+1,m	n+1,m	PROPN
ap-3524	120	69	+	+	CCONJ
ap-3524	120	70	hyn	hyn	PROPN
ap-3524	120	71	,	,	PUNCT
ap-3524	120	72	m+1∂hy	m+1∂hy	NOUN
ap-3524	120	73	n	n	CCONJ
ap-3524	120	74	,	,	PUNCT
ap-3524	120	75	m+1	m+1	PROPN
ap-3524	120	76	+	+	CCONJ
ap-3524	120	77	σyn	σyn	ADJ
ap-3524	120	78	,	,	PUNCT
ap-3524	120	79	m∂σy	m∂σy	PROPN
ap-3524	120	80	n	n	CCONJ
ap-3524	120	81	,	,	PUNCT
ap-3524	120	82	m	m	VERB
ap-3524	120	83	+	+	ADJ
ap-3524	120	84	σyn+1,m∂σy	σyn+1,m∂σy	NOUN
ap-3524	120	85	n+1,m	n+1,m	NOUN
ap-3524	120	86	)	)	PUNCT
ap-3524	120	87	−dxun	−dxun	ADP
ap-3524	120	88	,	,	PUNCT
ap-3524	120	89	m∂dxun	m∂dxun	PROPN
ap-3524	120	90	,	,	PUNCT
ap-3524	120	91	m	m	VERB
ap-3524	120	92	−	−	NOUN
ap-3524	120	93	2dyun	2dyun	NUM
ap-3524	120	94	,	,	PUNCT
ap-3524	120	95	m∂dyun	m∂dyun	NOUN
ap-3524	120	96	,	,	PUNCT
ap-3524	120	97	m	m	VERB
ap-3524	120	98	−	−	NOUN
ap-3524	120	99	2[dx]2un	2[dx]2un	NUM
ap-3524	120	100	,	,	PUNCT
ap-3524	120	101	m∂d2	m∂d2	PROPN
ap-3524	120	102	xun	xun	PROPN
ap-3524	120	103	,	,	PUNCT
ap-3524	120	104	m	m	PROPN
ap-3524	120	105	,	,	PUNCT
ap-3524	120	106	prd	prd	NOUN
ap-3524	120	107	v̂5	v̂5	NOUN
ap-3524	120	108	=	=	PUNCT
ap-3524	120	109	2yn	2yn	ADJ
ap-3524	120	110	,	,	PUNCT
ap-3524	120	111	m∂xn	m∂xn	PROPN
ap-3524	120	112	,	,	PUNCT
ap-3524	120	113	m	m	VERB
ap-3524	120	114	−	−	NOUN
ap-3524	120	115	xn	xn	PROPN
ap-3524	120	116	,	,	PUNCT
ap-3524	120	117	m∂un	m∂un	ADJ
ap-3524	120	118	,	,	PUNCT
ap-3524	120	119	m	m	VERB
ap-3524	120	120	+	+	X
ap-3524	120	121	2σyn	2σyn	NUM
ap-3524	120	122	,	,	PUNCT
ap-3524	120	123	m∂hx	m∂hx	NOUN
ap-3524	120	124	n	n	CCONJ
ap-3524	120	125	,	,	PUNCT
ap-3524	120	126	m	m	VERB
ap-3524	120	127	+	+	PROPN
ap-3524	120	128	2σyn+1,m∂hx	2σyn+1,m∂hx	NUM
ap-3524	120	129	n+1,m	n+1,m	NOUN
ap-3524	120	130	+	+	CCONJ
ap-3524	120	131	2(hyn+1,m	2(hyn+1,m	NUM
ap-3524	120	132	+	+	CCONJ
ap-3524	120	133	σyn	σyn	ADJ
ap-3524	120	134	,	,	PUNCT
ap-3524	120	135	m	m	VERB
ap-3524	120	136	−	−	PROPN
ap-3524	120	137	hyn	hyn	PROPN
ap-3524	120	138	,	,	PUNCT
ap-3524	120	139	m)∂hx	m)∂hx	X
ap-3524	120	140	n	n	CCONJ
ap-3524	120	141	,	,	PUNCT
ap-3524	120	142	m+1	m+1	PROPN
ap-3524	120	143	+2hyn	+2hyn	PROPN
ap-3524	120	144	,	,	PUNCT
ap-3524	120	145	m∂σx	m∂σx	PROPN
ap-3524	120	146	n	n	CCONJ
ap-3524	120	147	,	,	PUNCT
ap-3524	120	148	m	m	PROPN
ap-3524	120	149	+	+	NOUN
ap-3524	120	150	2hyn	2hyn	NUM
ap-3524	120	151	,	,	PUNCT
ap-3524	120	152	m+1∂σx	m+1∂σx	ADP
ap-3524	120	153	n	n	CCONJ
ap-3524	120	154	,	,	PUNCT
ap-3524	120	155	m+1	m+1	NUM
ap-3524	120	156	−	−	PROPN
ap-3524	120	157	∂dxun	∂dxun	NOUN
ap-3524	120	158	,	,	PUNCT
ap-3524	120	159	m	m	VERB
ap-3524	120	160	−	−	PROPN
ap-3524	120	161	2dxun	2dxun	NUM
ap-3524	120	162	,	,	PUNCT
ap-3524	120	163	m∂dyun	m∂dyun	NOUN
ap-3524	120	164	,	,	PUNCT
ap-3524	120	165	m	m	PROPN
ap-3524	120	166	.	.	PUNCT
ap-3524	121	1	(	(	PUNCT
ap-3524	121	2	25	25	NUM
ap-3524	121	3	)	)	PUNCT
ap-3524	121	4	the	the	DET
ap-3524	121	5	commutation	commutation	NOUN
ap-3524	121	6	table	table	NOUN
ap-3524	121	7	of	of	ADP
ap-3524	121	8	this	this	DET
ap-3524	121	9	algebra	algebra	NOUN
ap-3524	121	10	appears	appear	VERB
ap-3524	121	11	in	in	ADP
ap-3524	121	12	table	table	NOUN
ap-3524	121	13	1	1	NUM
ap-3524	121	14	(	(	PUNCT
ap-3524	121	15	it	it	PRON
ap-3524	121	16	is	be	AUX
ap-3524	121	17	,	,	PUNCT
ap-3524	121	18	obviously	obviously	ADV
ap-3524	121	19	the	the	DET
ap-3524	121	20	same	same	ADJ
ap-3524	121	21	as	as	ADP
ap-3524	121	22	in	in	ADP
ap-3524	121	23	the	the	DET
ap-3524	121	24	continuous	continuous	ADJ
ap-3524	121	25	case	case	NOUN
ap-3524	121	26	)	)	PUNCT
ap-3524	121	27	.	.	PUNCT
ap-3524	122	1	it	it	PRON
ap-3524	122	2	is	be	AUX
ap-3524	122	3	immediate	immediate	ADJ
ap-3524	122	4	to	to	PART
ap-3524	122	5	see	see	VERB
ap-3524	122	6	that	that	SCONJ
ap-3524	122	7	a	a	DET
ap-3524	122	8	discrete	discrete	ADJ
ap-3524	122	9	potential	potential	ADJ
ap-3524	122	10	burgers	burger	NOUN
ap-3524	122	11	equation	equation	NOUN
ap-3524	122	12	preserving	preserve	VERB
ap-3524	122	13	the	the	DET
ap-3524	122	14	lie	lie	NOUN
ap-3524	122	15	algebra	algebra	NOUN
ap-3524	122	16	of	of	ADP
ap-3524	122	17	(	(	PUNCT
ap-3524	122	18	19	19	NUM
ap-3524	122	19	)	)	PUNCT
ap-3524	122	20	given	give	VERB
ap-3524	122	21	by	by	ADP
ap-3524	122	22	the	the	DET
ap-3524	122	23	generators	generator	NOUN
ap-3524	122	24	v̂1	v̂1	PROPN
ap-3524	122	25	,	,	PUNCT
ap-3524	122	26	v̂2	v̂2	NOUN
ap-3524	122	27	,	,	PUNCT
ap-3524	122	28	v̂3	v̂3	ADJ
ap-3524	122	29	v̂4	v̂4	X
ap-3524	122	30	,	,	PUNCT
ap-3524	122	31	v̂5	v̂5	PROPN
ap-3524	122	32	is	be	AUX
ap-3524	122	33	:	:	PUNCT
ap-3524	122	34	i(1	i(1	PROPN
ap-3524	122	35	)	)	PUNCT
ap-3524	122	36	=	=	NOUN
ap-3524	123	1	[	[	X
ap-3524	123	2	dx]2un	dx]2un	PROPN
ap-3524	123	3	,	,	PUNCT
ap-3524	123	4	m	m	VERB
ap-3524	123	5	dyun	dyun	NOUN
ap-3524	123	6	,	,	PUNCT
ap-3524	123	7	m	m	VERB
ap-3524	123	8	−	−	PROPN
ap-3524	123	9	(	(	PUNCT
ap-3524	123	10	dxun	dxun	NOUN
ap-3524	123	11	,	,	PUNCT
ap-3524	123	12	m)2	m)2	PROPN
ap-3524	123	13	=	=	SYM
ap-3524	123	14	1	1	NUM
ap-3524	123	15	,	,	PUNCT
ap-3524	123	16	i.e.	i.e.	X
ap-3524	123	17	,	,	PUNCT
ap-3524	123	18	dyun	dyun	NOUN
ap-3524	123	19	,	,	PUNCT
ap-3524	123	20	m	m	VERB
ap-3524	123	21	−	−	NOUN
ap-3524	124	1	[	[	X
ap-3524	124	2	dx]2un	dx]2un	ADJ
ap-3524	124	3	,	,	PUNCT
ap-3524	124	4	m	m	VERB
ap-3524	124	5	−	−	NOUN
ap-3524	124	6	(	(	PUNCT
ap-3524	124	7	dxun	dxun	NOUN
ap-3524	124	8	,	,	PUNCT
ap-3524	124	9	m)2	m)2	PROPN
ap-3524	124	10	=	=	SYM
ap-3524	124	11	0	0	NUM
ap-3524	124	12	.	.	PUNCT
ap-3524	125	1	(	(	PUNCT
ap-3524	125	2	26	26	NUM
ap-3524	125	3	)	)	PUNCT
ap-3524	125	4	the	the	DET
ap-3524	125	5	continuous	continuous	ADJ
ap-3524	125	6	limit	limit	NOUN
ap-3524	125	7	of	of	ADP
ap-3524	125	8	(	(	PUNCT
ap-3524	125	9	26	26	NUM
ap-3524	125	10	)	)	PUNCT
ap-3524	125	11	is	be	AUX
ap-3524	125	12	trivially	trivially	ADV
ap-3524	125	13	given	give	VERB
ap-3524	125	14	by	by	ADP
ap-3524	125	15	(	(	PUNCT
ap-3524	125	16	19	19	NUM
ap-3524	125	17	)	)	PUNCT
ap-3524	125	18	when	when	SCONJ
ap-3524	125	19	hx	hx	PROPN
ap-3524	125	20	,	,	PUNCT
ap-3524	125	21	hy	hy	PROPN
ap-3524	125	22	,	,	PUNCT
ap-3524	125	23	σx	σx	NOUN
ap-3524	125	24	and	and	CCONJ
ap-3524	125	25	σy	σy	PRON
ap-3524	125	26	go	go	VERB
ap-3524	125	27	to	to	ADP
ap-3524	125	28	zero	zero	NUM
ap-3524	125	29	preserving	preserve	VERB
ap-3524	125	30	the	the	DET
ap-3524	125	31	structure	structure	NOUN
ap-3524	125	32	of	of	ADP
ap-3524	125	33	the	the	DET
ap-3524	125	34	lattice	lattice	NOUN
ap-3524	125	35	.	.	PUNCT
ap-3524	126	1	eq	eq	X
ap-3524	126	2	.	.	PUNCT
ap-3524	127	1	(	(	PUNCT
ap-3524	127	2	26	26	NUM
ap-3524	127	3	)	)	PUNCT
ap-3524	127	4	involves	involve	VERB
ap-3524	127	5	6	6	NUM
ap-3524	127	6	lattice	lattice	NOUN
ap-3524	127	7	points	point	NOUN
ap-3524	127	8	centered	center	VERB
ap-3524	127	9	around	around	ADP
ap-3524	127	10	(	(	PUNCT
ap-3524	127	11	n	n	CCONJ
ap-3524	127	12	,	,	PUNCT
ap-3524	127	13	m	m	NOUN
ap-3524	127	14	)	)	PUNCT
ap-3524	127	15	,	,	PUNCT
ap-3524	127	16	i.e.	i.e.	X
ap-3524	127	17	,	,	PUNCT
ap-3524	127	18	(	(	PUNCT
ap-3524	127	19	n	n	X
ap-3524	127	20	,	,	PUNCT
ap-3524	127	21	m	m	NOUN
ap-3524	127	22	)	)	PUNCT
ap-3524	127	23	,	,	PUNCT
ap-3524	127	24	(	(	PUNCT
ap-3524	127	25	n	n	X
ap-3524	127	26	+	+	CCONJ
ap-3524	127	27	1,m	1,m	NUM
ap-3524	127	28	)	)	PUNCT
ap-3524	127	29	,	,	PUNCT
ap-3524	127	30	(	(	PUNCT
ap-3524	127	31	n	n	CCONJ
ap-3524	127	32	,	,	PUNCT
ap-3524	127	33	m	m	VERB
ap-3524	127	34	+	+	ADJ
ap-3524	127	35	1	1	NUM
ap-3524	127	36	)	)	PUNCT
ap-3524	127	37	,	,	PUNCT
ap-3524	127	38	(	(	PUNCT
ap-3524	127	39	n+	n+	X
ap-3524	127	40	2,m	2,m	NOUN
ap-3524	127	41	)	)	PUNCT
ap-3524	127	42	,	,	PUNCT
ap-3524	127	43	(	(	PUNCT
ap-3524	127	44	n+	n+	NUM
ap-3524	127	45	1,m+	1,m+	NUM
ap-3524	127	46	1	1	NUM
ap-3524	127	47	)	)	PUNCT
ap-3524	127	48	,	,	PUNCT
ap-3524	127	49	(	(	PUNCT
ap-3524	127	50	n	n	CCONJ
ap-3524	127	51	,	,	PUNCT
ap-3524	127	52	m+	m+	NOUN
ap-3524	127	53	2	2	NUM
ap-3524	127	54	)	)	PUNCT
ap-3524	127	55	.	.	PUNCT
ap-3524	128	1	it	it	PRON
ap-3524	128	2	explicitly	explicitly	ADV
ap-3524	128	3	reads	read	VERB
ap-3524	128	4	:	:	PUNCT
ap-3524	128	5	−σxm(un+1,m	−σxm(un+1,m	NUM
ap-3524	129	1	−	−	NOUN
ap-3524	129	2	un	un	PROPN
ap-3524	129	3	,	,	PUNCT
ap-3524	129	4	m	m	PRON
ap-3524	129	5	)	)	PUNCT
ap-3524	130	1	+	+	CCONJ
ap-3524	130	2	hxn(un	hxn(un	NOUN
ap-3524	130	3	,	,	PUNCT
ap-3524	130	4	m+1	m+1	NUM
ap-3524	130	5	−	−	NUM
ap-3524	130	6	un	un	PROPN
ap-3524	130	7	,	,	PUNCT
ap-3524	130	8	m	m	NOUN
ap-3524	130	9	)	)	PUNCT
ap-3524	130	10	hxnh	hxnh	ADJ
ap-3524	130	11	y	y	PROPN
ap-3524	130	12	m	m	NOUN
ap-3524	130	13	−	−	PROPN
ap-3524	130	14	σxmσ	σxmσ	PROPN
ap-3524	130	15	y	y	PROPN
ap-3524	130	16	n	n	ADV
ap-3524	130	17	−	−	PROPN
ap-3524	130	18	[	[	PUNCT
ap-3524	130	19	hym	hym	PROPN
ap-3524	130	20	(	(	PUNCT
ap-3524	130	21	hym(un+2,m	hym(un+2,m	ADJ
ap-3524	130	22	−	−	PROPN
ap-3524	130	23	un+1,m)−	un+1,m)−	ADJ
ap-3524	130	24	σyn+1(un+1,m+1	σyn+1(un+1,m+1	PROPN
ap-3524	130	25	−	−	PROPN
ap-3524	131	1	un+1,m	un+1,m	PROPN
ap-3524	131	2	)	)	PUNCT
ap-3524	131	3	hxn+1h	hxn+1h	VERB
ap-3524	131	4	y	y	PROPN
ap-3524	131	5	m	m	VERB
ap-3524	131	6	−	−	PROPN
ap-3524	131	7	σxmσ	σxmσ	NOUN
ap-3524	131	8	y	y	PROPN
ap-3524	131	9	n+1	n+1	PROPN
ap-3524	131	10	−	−	PROPN
ap-3524	132	1	hym(un+1,m	hym(un+1,m	NOUN
ap-3524	132	2	−	−	PROPN
ap-3524	132	3	un	un	PROPN
ap-3524	132	4	,	,	PUNCT
ap-3524	132	5	m)−	m)−	PROPN
ap-3524	132	6	σyn(un	σyn(un	NOUN
ap-3524	132	7	,	,	PUNCT
ap-3524	132	8	m+1	m+1	NUM
ap-3524	132	9	−	−	NUM
ap-3524	132	10	un	un	PROPN
ap-3524	132	11	,	,	PUNCT
ap-3524	132	12	m	m	NOUN
ap-3524	132	13	)	)	PUNCT
ap-3524	132	14	hxnh	hxnh	ADJ
ap-3524	133	1	y	y	PROPN
ap-3524	133	2	m	m	NOUN
ap-3524	133	3	−	−	PROPN
ap-3524	133	4	σxmσ	σxmσ	PROPN
ap-3524	133	5	y	y	PROPN
ap-3524	133	6	n	n	PROPN
ap-3524	133	7	)	)	PUNCT
ap-3524	134	1	−	−	ADP
ap-3524	134	2	σyn	σyn	NOUN
ap-3524	134	3	(	(	PUNCT
ap-3524	134	4	hym+1(un+1,m+1	hym+1(un+1,m+1	PROPN
ap-3524	134	5	−	−	PROPN
ap-3524	134	6	un	un	PROPN
ap-3524	134	7	,	,	PUNCT
ap-3524	134	8	m+1)−	m+1)−	ADJ
ap-3524	134	9	σyn(un	σyn(un	NOUN
ap-3524	134	10	,	,	PUNCT
ap-3524	134	11	m+2	m+2	NOUN
ap-3524	134	12	−	−	PROPN
ap-3524	134	13	un	un	PROPN
ap-3524	134	14	,	,	PUNCT
ap-3524	134	15	m+1	m+1	NUM
ap-3524	134	16	)	)	PUNCT
ap-3524	134	17	hxnh	hxnh	ADJ
ap-3524	134	18	y	y	PROPN
ap-3524	134	19	m+1	m+1	NUM
ap-3524	134	20	−	−	NOUN
ap-3524	134	21	σxm+1σ	σxm+1σ	VERB
ap-3524	134	22	y	y	PROPN
ap-3524	134	23	n	n	CCONJ
ap-3524	134	24	−	−	PROPN
ap-3524	134	25	hym(un+1,m	hym(un+1,m	PROPN
ap-3524	134	26	−	−	PROPN
ap-3524	134	27	un	un	PROPN
ap-3524	134	28	,	,	PUNCT
ap-3524	134	29	m)−	m)−	PROPN
ap-3524	134	30	σyn(un	σyn(un	NOUN
ap-3524	134	31	,	,	PUNCT
ap-3524	134	32	m+1	m+1	NUM
ap-3524	134	33	−	−	NUM
ap-3524	134	34	un	un	PROPN
ap-3524	134	35	,	,	PUNCT
ap-3524	134	36	m	m	NOUN
ap-3524	134	37	)	)	PUNCT
ap-3524	134	38	hxnh	hxnh	ADJ
ap-3524	134	39	y	y	PROPN
ap-3524	134	40	m	m	NOUN
ap-3524	134	41	−	−	PROPN
ap-3524	134	42	σxmσ	σxmσ	PROPN
ap-3524	134	43	y	y	PROPN
ap-3524	134	44	n	n	PROPN
ap-3524	134	45	)	)	PUNCT
ap-3524	134	46	]	]	PUNCT
ap-3524	134	47	(	(	PUNCT
ap-3524	134	48	hxnh	hxnh	ADJ
ap-3524	134	49	y	y	PROPN
ap-3524	134	50	m	m	VERB
ap-3524	134	51	−	−	NOUN
ap-3524	134	52	σxmσyn	σxmσyn	NOUN
ap-3524	134	53	)	)	PUNCT
ap-3524	134	54	−1	−1	NOUN
ap-3524	134	55	−	−	PROPN
ap-3524	134	56	(	(	PUNCT
ap-3524	134	57	hym(un+1,m	hym(un+1,m	PROPN
ap-3524	134	58	−	−	PROPN
ap-3524	134	59	un	un	PROPN
ap-3524	134	60	,	,	PUNCT
ap-3524	134	61	m)−	m)−	PROPN
ap-3524	134	62	σyn(un	σyn(un	NOUN
ap-3524	134	63	,	,	PUNCT
ap-3524	134	64	m+1	m+1	NUM
ap-3524	134	65	−	−	NOUN
ap-3524	134	66	un	un	PROPN
ap-3524	134	67	,	,	PUNCT
ap-3524	134	68	m))2	m))2	PROPN
ap-3524	134	69	(	(	PUNCT
ap-3524	134	70	hxnh	hxnh	PROPN
ap-3524	134	71	y	y	PROPN
ap-3524	134	72	m	m	NOUN
ap-3524	134	73	−	−	PROPN
ap-3524	134	74	σxmσ	σxmσ	NOUN
ap-3524	134	75	y	y	PROPN
ap-3524	134	76	n)2	n)2	PROPN
ap-3524	134	77	=	=	PUNCT
ap-3524	134	78	0	0	X
ap-3524	134	79	.	.	PUNCT
ap-3524	135	1	(	(	PUNCT
ap-3524	135	2	27	27	NUM
ap-3524	135	3	)	)	PUNCT
ap-3524	135	4	240	240	NUM
ap-3524	135	5	vol	vol	NOUN
ap-3524	135	6	.	.	PUNCT
ap-3524	136	1	56	56	NUM
ap-3524	136	2	no	no	NOUN
ap-3524	136	3	.	.	PUNCT
ap-3524	137	1	3/2016	3/2016	NUM
ap-3524	137	2	on	on	ADP
ap-3524	137	3	the	the	DET
ap-3524	137	4	construction	construction	NOUN
ap-3524	137	5	of	of	ADP
ap-3524	137	6	partial	partial	ADJ
ap-3524	137	7	difference	difference	NOUN
ap-3524	137	8	schemes	scheme	NOUN
ap-3524	137	9	ii	ii	PROPN
ap-3524	137	10	v̂1	v̂1	PROPN
ap-3524	137	11	v̂2	v̂2	PROPN
ap-3524	137	12	v̂3	v̂3	PROPN
ap-3524	138	1	v̂4	v̂4	X
ap-3524	138	2	v̂5	v̂5	NOUN
ap-3524	138	3	v̂1	v̂1	X
ap-3524	138	4	0	0	NUM
ap-3524	138	5	0	0	NUM
ap-3524	138	6	0	0	NUM
ap-3524	138	7	v̂1	v̂1	NOUN
ap-3524	138	8	−v̂3	−v̂3	X
ap-3524	138	9	v̂2	v̂2	NOUN
ap-3524	138	10	0	0	NUM
ap-3524	138	11	0	0	NUM
ap-3524	138	12	0	0	NUM
ap-3524	139	1	2v̂2	2v̂2	NUM
ap-3524	139	2	2v̂1	2v̂1	NUM
ap-3524	139	3	v̂3	v̂3	NOUN
ap-3524	139	4	0	0	NUM
ap-3524	139	5	0	0	NUM
ap-3524	139	6	0	0	NUM
ap-3524	139	7	0	0	NUM
ap-3524	139	8	0	0	NUM
ap-3524	139	9	v̂4	v̂4	PRON
ap-3524	139	10	−v̂1	−v̂1	PROPN
ap-3524	140	1	−2v̂2	−2v̂2	NOUN
ap-3524	140	2	0	0	NUM
ap-3524	140	3	0	0	NUM
ap-3524	140	4	v̂5	v̂5	PROPN
ap-3524	140	5	v̂5	v̂5	ADJ
ap-3524	140	6	v̂3	v̂3	ADJ
ap-3524	141	1	−2v̂1	−2v̂1	PROPN
ap-3524	141	2	0	0	PUNCT
ap-3524	141	3	−v̂5	−v̂5	NOUN
ap-3524	141	4	0	0	NUM
ap-3524	141	5	table	table	NOUN
ap-3524	141	6	1	1	NUM
ap-3524	141	7	.	.	PUNCT
ap-3524	142	1	commutation	commutation	NOUN
ap-3524	142	2	table	table	NOUN
ap-3524	142	3	of	of	ADP
ap-3524	142	4	the	the	DET
ap-3524	142	5	discrete	discrete	ADJ
ap-3524	142	6	invariance	invariance	NOUN
ap-3524	142	7	algebra	algebra	NOUN
ap-3524	142	8	.	.	PUNCT
ap-3524	143	1	to	to	PART
ap-3524	143	2	complete	complete	VERB
ap-3524	143	3	the	the	DET
ap-3524	143	4	difference	difference	NOUN
ap-3524	143	5	scheme	scheme	NOUN
ap-3524	143	6	we	we	PRON
ap-3524	143	7	have	have	VERB
ap-3524	143	8	to	to	PART
ap-3524	143	9	associate	associate	VERB
ap-3524	143	10	to	to	ADP
ap-3524	143	11	it	it	PRON
ap-3524	143	12	a	a	DET
ap-3524	143	13	lattice	lattice	NOUN
ap-3524	143	14	equation	equation	NOUN
ap-3524	143	15	which	which	PRON
ap-3524	143	16	preserve	preserve	VERB
ap-3524	143	17	the	the	DET
ap-3524	143	18	symmetries	symmetry	NOUN
ap-3524	143	19	(	(	PUNCT
ap-3524	143	20	25	25	NUM
ap-3524	143	21	)	)	PUNCT
ap-3524	143	22	or	or	CCONJ
ap-3524	143	23	part	part	NOUN
ap-3524	143	24	of	of	ADP
ap-3524	143	25	them	they	PRON
ap-3524	143	26	.	.	PUNCT
ap-3524	144	1	the	the	DET
ap-3524	144	2	complete	complete	ADJ
ap-3524	144	3	list	list	NOUN
ap-3524	144	4	of	of	ADP
ap-3524	144	5	discrete	discrete	ADJ
ap-3524	144	6	invariant	invariant	NOUN
ap-3524	144	7	of	of	ADP
ap-3524	144	8	(	(	PUNCT
ap-3524	144	9	25	25	NUM
ap-3524	144	10	)	)	PUNCT
ap-3524	144	11	,	,	PUNCT
ap-3524	144	12	obtained	obtain	VERB
ap-3524	144	13	as	as	ADP
ap-3524	144	14	usual	usual	ADJ
ap-3524	144	15	,	,	PUNCT
ap-3524	144	16	as	as	ADP
ap-3524	144	17	solutions	solution	NOUN
ap-3524	144	18	of	of	ADP
ap-3524	144	19	the	the	DET
ap-3524	144	20	equations	equation	NOUN
ap-3524	144	21	prd	prd	PROPN
ap-3524	144	22	v̂i(k	v̂i(k	PROPN
ap-3524	144	23	)	)	PUNCT
ap-3524	145	1	=	=	SYM
ap-3524	145	2	0	0	NUM
ap-3524	145	3	,	,	PUNCT
ap-3524	145	4	are	be	AUX
ap-3524	145	5	:	:	PUNCT
ap-3524	145	6	k1	k1	PROPN
ap-3524	145	7	=	=	SYM
ap-3524	145	8	hyn+1,m	hyn+1,m	PROPN
ap-3524	145	9	hyn	hyn	PROPN
ap-3524	145	10	,	,	PUNCT
ap-3524	145	11	m	m	PROPN
ap-3524	145	12	,	,	PUNCT
ap-3524	145	13	k2	k2	PROPN
ap-3524	145	14	=	=	SYM
ap-3524	145	15	hyn	hyn	PROPN
ap-3524	145	16	,	,	PUNCT
ap-3524	145	17	m+1	m+1	PROPN
ap-3524	145	18	hyn	hyn	PROPN
ap-3524	145	19	,	,	PUNCT
ap-3524	145	20	m	m	PRON
ap-3524	145	21	,	,	PUNCT
ap-3524	145	22	k3	k3	PROPN
ap-3524	145	23	=	=	SYM
ap-3524	145	24	σyn	σyn	PROPN
ap-3524	145	25	,	,	PUNCT
ap-3524	145	26	m	m	PROPN
ap-3524	145	27	hyn	hyn	PROPN
ap-3524	145	28	,	,	PUNCT
ap-3524	145	29	m	m	VERB
ap-3524	145	30	,	,	PUNCT
ap-3524	145	31	k4	k4	PROPN
ap-3524	145	32	=	=	SYM
ap-3524	145	33	σyn+1,m	σyn+1,m	PROPN
ap-3524	145	34	hyn	hyn	PROPN
ap-3524	145	35	,	,	PUNCT
ap-3524	145	36	m	m	PROPN
ap-3524	145	37	,	,	PUNCT
ap-3524	145	38	k5	k5	PROPN
ap-3524	145	39	=	=	PROPN
ap-3524	145	40	1	1	NUM
ap-3524	145	41	(	(	PUNCT
ap-3524	145	42	hyn	hyn	PROPN
ap-3524	145	43	,	,	PUNCT
ap-3524	145	44	m)3/2	m)3/2	PROPN
ap-3524	146	1	(	(	PUNCT
ap-3524	146	2	hxn	hxn	NOUN
ap-3524	146	3	,	,	PUNCT
ap-3524	146	4	mh	mh	PROPN
ap-3524	146	5	y	y	PROPN
ap-3524	146	6	n	n	PROPN
ap-3524	146	7	,	,	PUNCT
ap-3524	146	8	m	m	VERB
ap-3524	146	9	−	−	PROPN
ap-3524	146	10	σxn	σxn	NOUN
ap-3524	146	11	,	,	PUNCT
ap-3524	146	12	mσyn	mσyn	NOUN
ap-3524	146	13	,	,	PUNCT
ap-3524	146	14	m	m	PROPN
ap-3524	146	15	)	)	PUNCT
ap-3524	146	16	,	,	PUNCT
ap-3524	146	17	k6	k6	NOUN
ap-3524	146	18	=	=	SYM
ap-3524	146	19	1	1	NUM
ap-3524	146	20	(	(	PUNCT
ap-3524	146	21	hyn	hyn	PROPN
ap-3524	146	22	,	,	PUNCT
ap-3524	146	23	m)3/2	m)3/2	PROPN
ap-3524	146	24	(	(	PUNCT
ap-3524	146	25	hyn	hyn	PROPN
ap-3524	146	26	,	,	PUNCT
ap-3524	146	27	m+1σ	m+1σ	PROPN
ap-3524	146	28	x	x	SYM
ap-3524	146	29	n	n	CCONJ
ap-3524	146	30	,	,	PUNCT
ap-3524	146	31	m	m	VERB
ap-3524	146	32	−	−	PROPN
ap-3524	146	33	hyn	hyn	PROPN
ap-3524	146	34	,	,	PUNCT
ap-3524	146	35	mσxn	mσxn	PROPN
ap-3524	146	36	,	,	PUNCT
ap-3524	146	37	m+1	m+1	NUM
ap-3524	146	38	)	)	PUNCT
ap-3524	146	39	,	,	PUNCT
ap-3524	146	40	k7	k7	PROPN
ap-3524	146	41	=	=	PUNCT
ap-3524	146	42	1	1	NUM
ap-3524	146	43	(	(	PUNCT
ap-3524	146	44	hyn	hyn	PROPN
ap-3524	146	45	,	,	PUNCT
ap-3524	146	46	m)3/2	m)3/2	PROPN
ap-3524	147	1	(	(	PUNCT
ap-3524	147	2	hxn	hxn	NOUN
ap-3524	147	3	,	,	PUNCT
ap-3524	147	4	m(hyn+1,m	m(hyn+1,m	PROPN
ap-3524	147	5	−	−	PROPN
ap-3524	147	6	hyn	hyn	PROPN
ap-3524	147	7	,	,	PUNCT
ap-3524	147	8	m)−	m)−	PROPN
ap-3524	147	9	σyn	σyn	PROPN
ap-3524	147	10	,	,	PUNCT
ap-3524	147	11	m(hxn	m(hxn	NOUN
ap-3524	147	12	,	,	PUNCT
ap-3524	147	13	m+1	m+1	NUM
ap-3524	147	14	−	−	PROPN
ap-3524	147	15	hxn	hxn	NOUN
ap-3524	147	16	,	,	PUNCT
ap-3524	147	17	m	m	NOUN
ap-3524	147	18	)	)	PUNCT
ap-3524	147	19	)	)	PUNCT
ap-3524	147	20	,	,	PUNCT
ap-3524	147	21	k8	k8	NOUN
ap-3524	147	22	=	=	SYM
ap-3524	147	23	1	1	NUM
ap-3524	147	24	(	(	PUNCT
ap-3524	147	25	hyn	hyn	PROPN
ap-3524	147	26	,	,	PUNCT
ap-3524	147	27	m)3/2	m)3/2	PROPN
ap-3524	148	1	(	(	PUNCT
ap-3524	148	2	hxn	hxn	NOUN
ap-3524	148	3	,	,	PUNCT
ap-3524	148	4	mσ	mσ	PROPN
ap-3524	148	5	y	y	PROPN
ap-3524	148	6	n+1,m	n+1,m	PROPN
ap-3524	148	7	−	−	PROPN
ap-3524	148	8	hxn+1,mσ	hxn+1,mσ	NUM
ap-3524	148	9	y	y	PROPN
ap-3524	148	10	n	n	PROPN
ap-3524	148	11	,	,	PUNCT
ap-3524	148	12	m	m	PROPN
ap-3524	148	13	)	)	PUNCT
ap-3524	148	14	,	,	PUNCT
ap-3524	148	15	k9	k9	PROPN
ap-3524	148	16	=	=	PROPN
ap-3524	148	17	1	1	NUM
ap-3524	148	18	(	(	PUNCT
ap-3524	148	19	hyn	hyn	PROPN
ap-3524	148	20	,	,	PUNCT
ap-3524	148	21	m)1/2	m)1/2	PUNCT
ap-3524	149	1	(	(	PUNCT
ap-3524	149	2	hxn	hxn	NOUN
ap-3524	149	3	,	,	PUNCT
ap-3524	149	4	m	m	VERB
ap-3524	149	5	+	+	X
ap-3524	149	6	2σyn	2σyn	NUM
ap-3524	149	7	,	,	PUNCT
ap-3524	149	8	mdxun	mdxun	ADJ
ap-3524	149	9	,	,	PUNCT
ap-3524	149	10	m	m	PROPN
ap-3524	149	11	)	)	PUNCT
ap-3524	149	12	,	,	PUNCT
ap-3524	149	13	k10	k10	NOUN
ap-3524	149	14	=	=	PUNCT
ap-3524	149	15	dyun	dyun	NOUN
ap-3524	149	16	,	,	PUNCT
ap-3524	149	17	m	m	VERB
ap-3524	149	18	−	−	PROPN
ap-3524	149	19	(	(	PUNCT
ap-3524	149	20	dxun	dxun	NOUN
ap-3524	149	21	,	,	PUNCT
ap-3524	149	22	m)2	m)2	PROPN
ap-3524	150	1	[	[	X
ap-3524	150	2	dx]2un	dx]2un	ADJ
ap-3524	150	3	,	,	PUNCT
ap-3524	150	4	m	m	PROPN
ap-3524	150	5	.	.	PUNCT
ap-3524	151	1	(	(	PUNCT
ap-3524	151	2	28	28	NUM
ap-3524	151	3	)	)	PUNCT
ap-3524	151	4	our	our	PRON
ap-3524	151	5	first	first	ADJ
ap-3524	151	6	choice	choice	NOUN
ap-3524	151	7	for	for	ADP
ap-3524	151	8	the	the	DET
ap-3524	151	9	difference	difference	NOUN
ap-3524	151	10	scheme	scheme	NOUN
ap-3524	151	11	is	be	AUX
ap-3524	151	12	an	an	DET
ap-3524	151	13	orthogonal	orthogonal	ADJ
ap-3524	151	14	cartesian	cartesian	ADJ
ap-3524	151	15	lattice	lattice	NOUN
ap-3524	151	16	given	give	VERB
ap-3524	151	17	,	,	PUNCT
ap-3524	151	18	in	in	ADP
ap-3524	151	19	the	the	DET
ap-3524	151	20	coordinates	coordinate	NOUN
ap-3524	151	21	hn	hn	PROPN
ap-3524	151	22	,	,	PUNCT
ap-3524	151	23	m	m	PROPN
ap-3524	151	24	and	and	CCONJ
ap-3524	151	25	σn	σn	NOUN
ap-3524	151	26	,	,	PUNCT
ap-3524	151	27	m	m	VERB
ap-3524	151	28	by	by	ADP
ap-3524	151	29	hyn	hyn	PROPN
ap-3524	151	30	,	,	PUNCT
ap-3524	151	31	m	m	PROPN
ap-3524	151	32	=	=	SYM
ap-3524	151	33	b	b	PROPN
ap-3524	151	34	,	,	PUNCT
ap-3524	151	35	σyn	σyn	ADJ
ap-3524	151	36	,	,	PUNCT
ap-3524	151	37	m	m	VERB
ap-3524	151	38	=	=	SYM
ap-3524	151	39	0	0	NUM
ap-3524	151	40	,	,	PUNCT
ap-3524	151	41	hxn	hxn	NOUN
ap-3524	151	42	,	,	PUNCT
ap-3524	151	43	m	m	VERB
ap-3524	151	44	=	=	SYM
ap-3524	151	45	a	a	PRON
ap-3524	151	46	,	,	PUNCT
ap-3524	151	47	σxn	σxn	PROPN
ap-3524	151	48	,	,	PUNCT
ap-3524	151	49	m	m	VERB
ap-3524	151	50	=	=	NOUN
ap-3524	151	51	0	0	NUM
ap-3524	151	52	,	,	PUNCT
ap-3524	151	53	(	(	PUNCT
ap-3524	151	54	29	29	NUM
ap-3524	151	55	)	)	PUNCT
ap-3524	151	56	where	where	SCONJ
ap-3524	151	57	a	a	PRON
ap-3524	151	58	and	and	CCONJ
ap-3524	151	59	b	b	NOUN
ap-3524	151	60	are	be	AUX
ap-3524	151	61	arbitrary	arbitrary	ADJ
ap-3524	151	62	constants	constant	NOUN
ap-3524	151	63	,	,	PUNCT
ap-3524	151	64	which	which	PRON
ap-3524	151	65	in	in	ADP
ap-3524	151	66	the	the	DET
ap-3524	151	67	continuous	continuous	ADJ
ap-3524	151	68	limit	limit	NOUN
ap-3524	151	69	go	go	VERB
ap-3524	151	70	to	to	ADP
ap-3524	151	71	zero	zero	NUM
ap-3524	151	72	.	.	PUNCT
ap-3524	152	1	this	this	DET
ap-3524	152	2	lattice	lattice	NOUN
ap-3524	152	3	,	,	PUNCT
ap-3524	152	4	which	which	PRON
ap-3524	152	5	is	be	AUX
ap-3524	152	6	clearly	clearly	ADV
ap-3524	152	7	invariant	invariant	ADJ
ap-3524	152	8	under	under	ADP
ap-3524	152	9	all	all	DET
ap-3524	152	10	the	the	DET
ap-3524	152	11	symmetries	symmetry	NOUN
ap-3524	152	12	which	which	PRON
ap-3524	152	13	satisfy	satisfy	VERB
ap-3524	152	14	the	the	DET
ap-3524	152	15	commutativity	commutativity	NOUN
ap-3524	152	16	constraint	constraint	NOUN
ap-3524	152	17	,	,	PUNCT
ap-3524	152	18	corresponds	correspond	VERB
ap-3524	152	19	to	to	ADP
ap-3524	152	20	the	the	DET
ap-3524	152	21	lie	lie	NOUN
ap-3524	152	22	point	point	NOUN
ap-3524	152	23	symmetry	symmetry	NOUN
ap-3524	152	24	infinitesimal	infinitesimal	ADJ
ap-3524	152	25	generators	generator	NOUN
ap-3524	152	26	ξn	ξn	PROPN
ap-3524	152	27	,	,	PUNCT
ap-3524	152	28	m	m	VERB
ap-3524	152	29	=	=	SYM
ap-3524	152	30	τn	τn	ADJ
ap-3524	152	31	,	,	PUNCT
ap-3524	152	32	m	m	VERB
ap-3524	152	33	=	=	ADJ
ap-3524	152	34	1	1	NUM
ap-3524	152	35	(	(	PUNCT
ap-3524	152	36	30	30	NUM
ap-3524	152	37	)	)	PUNCT
ap-3524	152	38	these	these	DET
ap-3524	152	39	generators	generator	NOUN
ap-3524	152	40	comply	comply	VERB
ap-3524	152	41	with	with	ADP
ap-3524	152	42	the	the	DET
ap-3524	152	43	constraints	constraint	NOUN
ap-3524	152	44	in	in	ADP
ap-3524	152	45	(	(	PUNCT
ap-3524	152	46	16	16	NUM
ap-3524	152	47	)	)	PUNCT
ap-3524	152	48	and	and	CCONJ
ap-3524	152	49	the	the	DET
ap-3524	152	50	orthogonal	orthogonal	ADJ
ap-3524	152	51	lattice	lattice	NOUN
ap-3524	152	52	(	(	PUNCT
ap-3524	152	53	29	29	NUM
ap-3524	152	54	)	)	PUNCT
ap-3524	152	55	satisfies	satisfy	VERB
ap-3524	152	56	the	the	DET
ap-3524	152	57	clairaut	clairaut	NOUN
ap-3524	152	58	–	–	PUNCT
ap-3524	152	59	schwarz	schwarz	PROPN
ap-3524	152	60	–	–	PUNCT
ap-3524	152	61	young	young	ADJ
ap-3524	152	62	theorem	theorem	NOUN
ap-3524	152	63	.	.	PUNCT
ap-3524	152	64	to	to	PART
ap-3524	152	65	carry	carry	VERB
ap-3524	152	66	out	out	ADP
ap-3524	152	67	a	a	DET
ap-3524	152	68	comparison	comparison	NOUN
ap-3524	152	69	between	between	ADP
ap-3524	152	70	this	this	DET
ap-3524	152	71	invariant	invariant	PROPN
ap-3524	152	72	schwarzian	schwarzian	NOUN
ap-3524	152	73	lattice	lattice	NOUN
ap-3524	152	74	with	with	ADP
ap-3524	152	75	other	other	ADJ
ap-3524	152	76	lattices	lattice	NOUN
ap-3524	152	77	which	which	PRON
ap-3524	152	78	lack	lack	VERB
ap-3524	152	79	these	these	DET
ap-3524	152	80	properties	property	NOUN
ap-3524	152	81	,	,	PUNCT
ap-3524	152	82	we	we	PRON
ap-3524	152	83	will	will	AUX
ap-3524	152	84	consider	consider	VERB
ap-3524	152	85	an	an	DET
ap-3524	152	86	exponential	exponential	ADJ
ap-3524	152	87	non	non	PROPN
ap-3524	152	88	schwarzian	schwarzian	PROPN
ap-3524	152	89	lattice	lattice	VERB
ap-3524	152	90	as	as	SCONJ
ap-3524	152	91	given	give	VERB
ap-3524	152	92	in	in	ADP
ap-3524	152	93	[	[	NOUN
ap-3524	152	94	14	14	NUM
ap-3524	152	95	]	]	PUNCT
ap-3524	152	96	by	by	ADP
ap-3524	152	97	yn	yn	PROPN
ap-3524	152	98	,	,	PUNCT
ap-3524	152	99	m	m	PROPN
ap-3524	152	100	=	=	PROPN
ap-3524	152	101	bm+	bm+	PROPN
ap-3524	152	102	b0	b0	PROPN
ap-3524	152	103	,	,	PUNCT
ap-3524	152	104	xn	xn	PROPN
ap-3524	152	105	,	,	PUNCT
ap-3524	152	106	m	m	VERB
ap-3524	152	107	=	=	PUNCT
ap-3524	152	108	(	(	PUNCT
ap-3524	152	109	1	1	NUM
ap-3524	152	110	+	+	NUM
ap-3524	152	111	c)m(an+	c)m(an+	NOUN
ap-3524	152	112	a0	a0	PROPN
ap-3524	152	113	)	)	PUNCT
ap-3524	152	114	,	,	PUNCT
ap-3524	152	115	(	(	PUNCT
ap-3524	152	116	31	31	NUM
ap-3524	152	117	)	)	PUNCT
ap-3524	152	118	where	where	SCONJ
ap-3524	152	119	a	a	PRON
ap-3524	152	120	,	,	PUNCT
ap-3524	152	121	a0	a0	PROPN
ap-3524	152	122	,	,	PUNCT
ap-3524	152	123	b	b	PROPN
ap-3524	152	124	,	,	PUNCT
ap-3524	152	125	b0	b0	NOUN
ap-3524	152	126	and	and	CCONJ
ap-3524	152	127	c	c	NOUN
ap-3524	152	128	are	be	AUX
ap-3524	152	129	arbitrary	arbitrary	ADJ
ap-3524	152	130	constants	constant	NOUN
ap-3524	152	131	.	.	PUNCT
ap-3524	153	1	b	b	NOUN
ap-3524	153	2	and	and	CCONJ
ap-3524	153	3	a	a	PRON
ap-3524	153	4	are	be	AUX
ap-3524	153	5	the	the	DET
ap-3524	153	6	lattice	lattice	NOUN
ap-3524	153	7	spacing	spacing	NOUN
ap-3524	153	8	and	and	CCONJ
ap-3524	153	9	c	c	NOUN
ap-3524	153	10	is	be	AUX
ap-3524	153	11	a	a	DET
ap-3524	153	12	dilation	dilation	NOUN
ap-3524	153	13	parameter	parameter	NOUN
ap-3524	153	14	which	which	PRON
ap-3524	153	15	,	,	PUNCT
ap-3524	153	16	when	when	SCONJ
ap-3524	153	17	set	set	VERB
ap-3524	153	18	equal	equal	ADJ
ap-3524	153	19	to	to	ADP
ap-3524	153	20	zero	zero	NUM
ap-3524	153	21	reduces	reduce	VERB
ap-3524	153	22	this	this	DET
ap-3524	153	23	lattice	lattice	NOUN
ap-3524	153	24	to	to	ADP
ap-3524	153	25	an	an	DET
ap-3524	153	26	orthogonal	orthogonal	ADJ
ap-3524	153	27	lattice	lattice	NOUN
ap-3524	153	28	.	.	PUNCT
ap-3524	154	1	this	this	DET
ap-3524	154	2	lattice	lattice	NOUN
ap-3524	154	3	corresponds	correspond	VERB
ap-3524	154	4	to	to	ADP
ap-3524	154	5	the	the	DET
ap-3524	154	6	lie	lie	NOUN
ap-3524	154	7	point	point	NOUN
ap-3524	154	8	symmetry	symmetry	NOUN
ap-3524	154	9	infinitesimal	infinitesimal	ADJ
ap-3524	154	10	generators	generator	NOUN
ap-3524	154	11	ξn	ξn	PROPN
ap-3524	154	12	,	,	PUNCT
ap-3524	154	13	m	m	VERB
ap-3524	154	14	=	=	PUNCT
ap-3524	154	15	(	(	PUNCT
ap-3524	154	16	1	1	NUM
ap-3524	154	17	+	+	CCONJ
ap-3524	154	18	c)m(k1n+	c)m(k1n+	X
ap-3524	154	19	k2	k2	NOUN
ap-3524	154	20	)	)	PUNCT
ap-3524	154	21	+	+	CCONJ
ap-3524	155	1	k0	k0	PROPN
ap-3524	155	2	xn	xn	PROPN
ap-3524	155	3	,	,	PUNCT
ap-3524	155	4	m	m	PROPN
ap-3524	155	5	,	,	PUNCT
ap-3524	155	6	τn	τn	ADJ
ap-3524	155	7	,	,	PUNCT
ap-3524	155	8	m	m	VERB
ap-3524	155	9	=	=	NOUN
ap-3524	155	10	k3	k3	ADJ
ap-3524	155	11	(	(	PUNCT
ap-3524	155	12	32	32	NUM
ap-3524	155	13	)	)	PUNCT
ap-3524	155	14	which	which	PRON
ap-3524	155	15	clearly	clearly	ADV
ap-3524	155	16	do	do	AUX
ap-3524	155	17	not	not	PART
ap-3524	155	18	satisfy	satisfy	VERB
ap-3524	155	19	(	(	PUNCT
ap-3524	155	20	16	16	NUM
ap-3524	155	21	)	)	PUNCT
ap-3524	155	22	.	.	PUNCT
ap-3524	156	1	the	the	DET
ap-3524	156	2	non	non	PROPN
ap-3524	156	3	schwarzian	schwarzian	PROPN
ap-3524	156	4	property	property	NOUN
ap-3524	156	5	of	of	ADP
ap-3524	156	6	this	this	DET
ap-3524	156	7	lattice	lattice	NOUN
ap-3524	156	8	can	can	AUX
ap-3524	156	9	also	also	ADV
ap-3524	156	10	be	be	AUX
ap-3524	156	11	seen	see	VERB
ap-3524	156	12	by	by	ADP
ap-3524	156	13	considering	consider	VERB
ap-3524	156	14	the	the	DET
ap-3524	156	15	lattice	lattice	PROPN
ap-3524	156	16	differences	differences	PROPN
ap-3524	156	17	hyn	hyn	PROPN
ap-3524	156	18	,	,	PUNCT
ap-3524	156	19	m	m	PROPN
ap-3524	156	20	=	=	SYM
ap-3524	156	21	b	b	PROPN
ap-3524	156	22	,	,	PUNCT
ap-3524	156	23	σyn	σyn	ADJ
ap-3524	156	24	,	,	PUNCT
ap-3524	156	25	m	m	VERB
ap-3524	156	26	=	=	SYM
ap-3524	156	27	0	0	NUM
ap-3524	156	28	,	,	PUNCT
ap-3524	156	29	hxn	hxn	NOUN
ap-3524	156	30	,	,	PUNCT
ap-3524	156	31	m	m	VERB
ap-3524	156	32	=	=	PUNCT
ap-3524	156	33	(	(	PUNCT
ap-3524	156	34	1	1	NUM
ap-3524	156	35	+	+	CCONJ
ap-3524	156	36	c)ma	c)ma	PROPN
ap-3524	156	37	,	,	PUNCT
ap-3524	156	38	σxn	σxn	NOUN
ap-3524	156	39	,	,	PUNCT
ap-3524	156	40	m	m	VERB
ap-3524	156	41	=	=	PROPN
ap-3524	156	42	c(1	c(1	PROPN
ap-3524	156	43	+	+	PROPN
ap-3524	156	44	c)man	c)man	PROPN
ap-3524	156	45	.	.	PUNCT
ap-3524	157	1	(	(	PUNCT
ap-3524	157	2	33	33	NUM
ap-3524	157	3	)	)	PUNCT
ap-3524	157	4	and	and	CCONJ
ap-3524	157	5	comparing	compare	VERB
ap-3524	157	6	them	they	PRON
ap-3524	157	7	with	with	ADP
ap-3524	157	8	(	(	PUNCT
ap-3524	157	9	11	11	NUM
ap-3524	157	10	)	)	PUNCT
ap-3524	157	11	.	.	PUNCT
ap-3524	158	1	this	this	DET
ap-3524	158	2	non	non	PROPN
ap-3524	158	3	schwarzian	schwarzian	PROPN
ap-3524	158	4	lattice	lattice	PROPN
ap-3524	158	5	is	be	AUX
ap-3524	158	6	not	not	PART
ap-3524	158	7	invariant	invariant	ADJ
ap-3524	158	8	under	under	ADP
ap-3524	158	9	the	the	DET
ap-3524	158	10	potential	potential	ADJ
ap-3524	158	11	burgers	burger	NOUN
ap-3524	158	12	symmetry	symmetry	NOUN
ap-3524	158	13	group	group	NOUN
ap-3524	158	14	(	(	PUNCT
ap-3524	158	15	20	20	NUM
ap-3524	158	16	)	)	PUNCT
ap-3524	158	17	;	;	PUNCT
ap-3524	158	18	k5	k5	PROPN
ap-3524	158	19	,	,	PUNCT
ap-3524	158	20	k6	k6	PROPN
ap-3524	158	21	,	,	PUNCT
ap-3524	158	22	k7	k7	PROPN
ap-3524	158	23	and	and	CCONJ
ap-3524	158	24	k9	k9	PROPN
ap-3524	158	25	are	be	AUX
ap-3524	158	26	non	non	NOUN
ap-3524	158	27	constants	constant	NOUN
ap-3524	158	28	.	.	PUNCT
ap-3524	159	1	in	in	ADP
ap-3524	159	2	the	the	DET
ap-3524	159	3	following	follow	VERB
ap-3524	159	4	section	section	NOUN
ap-3524	159	5	we	we	PRON
ap-3524	159	6	will	will	AUX
ap-3524	159	7	provide	provide	VERB
ap-3524	159	8	a	a	DET
ap-3524	159	9	numerical	numerical	ADJ
ap-3524	159	10	test	test	NOUN
ap-3524	159	11	about	about	ADP
ap-3524	159	12	the	the	DET
ap-3524	159	13	possible	possible	ADJ
ap-3524	159	14	importance	importance	NOUN
ap-3524	159	15	of	of	ADP
ap-3524	159	16	the	the	DET
ap-3524	159	17	clairaut	clairaut	NOUN
ap-3524	159	18	–	–	PUNCT
ap-3524	159	19	schwarz	schwarz	PROPN
ap-3524	159	20	–	–	PUNCT
ap-3524	159	21	young	young	ADJ
ap-3524	159	22	theorem	theorem	NOUN
ap-3524	159	23	,	,	PUNCT
ap-3524	159	24	by	by	ADP
ap-3524	159	25	studying	study	VERB
ap-3524	159	26	numerically	numerically	ADV
ap-3524	159	27	the	the	DET
ap-3524	159	28	evolution	evolution	NOUN
ap-3524	159	29	provided	provide	VERB
ap-3524	159	30	by	by	ADP
ap-3524	159	31	the	the	DET
ap-3524	159	32	symmetry	symmetry	NOUN
ap-3524	159	33	preserving	preserve	VERB
ap-3524	159	34	discretized	discretize	VERB
ap-3524	159	35	potential	potential	ADJ
ap-3524	159	36	burgers	burger	NOUN
ap-3524	159	37	equation	equation	NOUN
ap-3524	159	38	(	(	PUNCT
ap-3524	159	39	27	27	NUM
ap-3524	159	40	)	)	PUNCT
ap-3524	159	41	on	on	ADP
ap-3524	159	42	the	the	DET
ap-3524	159	43	two	two	NUM
ap-3524	159	44	different	different	ADJ
ap-3524	159	45	lattices	lattice	NOUN
ap-3524	159	46	we	we	PRON
ap-3524	159	47	introduced	introduce	VERB
ap-3524	159	48	above	above	ADV
ap-3524	159	49	,	,	PUNCT
ap-3524	159	50	i.e.	i.e.	X
ap-3524	159	51	,	,	PUNCT
ap-3524	159	52	the	the	DET
ap-3524	159	53	schwarzian	schwarzian	PROPN
ap-3524	159	54	and	and	CCONJ
ap-3524	159	55	non	non	ADJ
ap-3524	159	56	schwarzian	schwarzian	NOUN
ap-3524	159	57	lattices	lattice	NOUN
ap-3524	159	58	(	(	PUNCT
ap-3524	159	59	29	29	NUM
ap-3524	159	60	,	,	PUNCT
ap-3524	159	61	33	33	NUM
ap-3524	159	62	)	)	PUNCT
ap-3524	159	63	.	.	PUNCT
ap-3524	160	1	4	4	X
ap-3524	160	2	.	.	X
ap-3524	160	3	numerical	numerical	ADJ
ap-3524	160	4	calculation	calculation	NOUN
ap-3524	160	5	results	result	VERB
ap-3524	160	6	for	for	ADP
ap-3524	160	7	the	the	DET
ap-3524	160	8	discrete	discrete	ADJ
ap-3524	160	9	potential	potential	ADJ
ap-3524	160	10	burgers	burger	NOUN
ap-3524	160	11	equation	equation	NOUN
ap-3524	160	12	in	in	ADP
ap-3524	160	13	order	order	NOUN
ap-3524	160	14	to	to	PART
ap-3524	160	15	compare	compare	VERB
ap-3524	160	16	the	the	DET
ap-3524	160	17	precision	precision	NOUN
ap-3524	160	18	and	and	CCONJ
ap-3524	160	19	accuracy	accuracy	NOUN
ap-3524	160	20	of	of	ADP
ap-3524	160	21	different	different	ADJ
ap-3524	160	22	lattices	lattice	NOUN
ap-3524	160	23	used	use	VERB
ap-3524	160	24	to	to	PART
ap-3524	160	25	compute	compute	VERB
ap-3524	160	26	numerically	numerically	ADV
ap-3524	160	27	the	the	DET
ap-3524	160	28	solution	solution	NOUN
ap-3524	160	29	of	of	ADP
ap-3524	160	30	the	the	DET
ap-3524	160	31	potential	potential	ADJ
ap-3524	160	32	burgers	burger	NOUN
ap-3524	160	33	equation	equation	NOUN
ap-3524	160	34	,	,	PUNCT
ap-3524	160	35	we	we	PRON
ap-3524	160	36	will	will	AUX
ap-3524	160	37	construct	construct	VERB
ap-3524	160	38	two	two	NUM
ap-3524	160	39	of	of	ADP
ap-3524	160	40	its	its	PRON
ap-3524	160	41	exact	exact	ADJ
ap-3524	160	42	solutions	solution	NOUN
ap-3524	160	43	(	(	PUNCT
ap-3524	160	44	associated	associate	VERB
ap-3524	160	45	to	to	ADP
ap-3524	160	46	different	different	ADJ
ap-3524	160	47	symmetries	symmetry	NOUN
ap-3524	160	48	241	241	NUM
ap-3524	160	49	decio	decio	PROPN
ap-3524	160	50	levi	levi	PROPN
ap-3524	160	51	,	,	PUNCT
ap-3524	160	52	miguel	miguel	PROPN
ap-3524	160	53	a.	a.	PROPN
ap-3524	160	54	rodríguez	rodríguez	PROPN
ap-3524	160	55	acta	acta	PROPN
ap-3524	160	56	polytechnica	polytechnica	PROPN
ap-3524	160	57	of	of	ADP
ap-3524	160	58	the	the	DET
ap-3524	160	59	heat	heat	NOUN
ap-3524	160	60	equation	equation	NOUN
ap-3524	160	61	)	)	PUNCT
ap-3524	160	62	and	and	CCONJ
ap-3524	160	63	use	use	VERB
ap-3524	160	64	them	they	PRON
ap-3524	160	65	as	as	ADP
ap-3524	160	66	initial	initial	ADJ
ap-3524	160	67	conditions	condition	NOUN
ap-3524	160	68	for	for	ADP
ap-3524	160	69	the	the	DET
ap-3524	160	70	evolution	evolution	NOUN
ap-3524	160	71	of	of	ADP
ap-3524	160	72	the	the	DET
ap-3524	160	73	burgers	burger	NOUN
ap-3524	160	74	map	map	NOUN
ap-3524	160	75	(	(	PUNCT
ap-3524	160	76	27	27	NUM
ap-3524	160	77	)	)	PUNCT
ap-3524	160	78	.	.	PUNCT
ap-3524	161	1	in	in	ADP
ap-3524	161	2	fact	fact	NOUN
ap-3524	161	3	,	,	PUNCT
ap-3524	161	4	we	we	PRON
ap-3524	161	5	will	will	AUX
ap-3524	161	6	not	not	PART
ap-3524	161	7	do	do	VERB
ap-3524	161	8	a	a	DET
ap-3524	161	9	direct	direct	ADJ
ap-3524	161	10	comparison	comparison	NOUN
ap-3524	161	11	of	of	ADP
ap-3524	161	12	the	the	DET
ap-3524	161	13	evolution	evolution	NOUN
ap-3524	161	14	of	of	ADP
ap-3524	161	15	this	this	DET
ap-3524	161	16	map	map	NOUN
ap-3524	161	17	in	in	ADP
ap-3524	161	18	the	the	DET
ap-3524	161	19	two	two	NUM
ap-3524	161	20	lattices	lattice	NOUN
ap-3524	161	21	(	(	PUNCT
ap-3524	161	22	29	29	NUM
ap-3524	161	23	)	)	PUNCT
ap-3524	161	24	and	and	CCONJ
ap-3524	161	25	(	(	PUNCT
ap-3524	161	26	33	33	NUM
ap-3524	161	27	)	)	PUNCT
ap-3524	161	28	but	but	CCONJ
ap-3524	161	29	compare	compare	VERB
ap-3524	161	30	the	the	DET
ap-3524	161	31	solution	solution	NOUN
ap-3524	161	32	of	of	ADP
ap-3524	161	33	the	the	DET
ap-3524	161	34	map	map	NOUN
ap-3524	161	35	in	in	ADP
ap-3524	161	36	each	each	DET
ap-3524	161	37	lattice	lattice	NOUN
ap-3524	161	38	with	with	ADP
ap-3524	161	39	the	the	DET
ap-3524	161	40	exact	exact	ADJ
ap-3524	161	41	solution	solution	NOUN
ap-3524	161	42	of	of	ADP
ap-3524	161	43	the	the	DET
ap-3524	161	44	continuous	continuous	ADJ
ap-3524	161	45	equation	equation	NOUN
ap-3524	161	46	.	.	PUNCT
ap-3524	162	1	we	we	PRON
ap-3524	162	2	introduce	introduce	VERB
ap-3524	162	3	two	two	NUM
ap-3524	162	4	invariant	invariant	ADJ
ap-3524	162	5	solutions	solution	NOUN
ap-3524	162	6	of	of	ADP
ap-3524	162	7	(	(	PUNCT
ap-3524	162	8	21	21	NUM
ap-3524	162	9	)	)	PUNCT
ap-3524	162	10	and	and	CCONJ
ap-3524	162	11	transform	transform	VERB
ap-3524	162	12	them	they	PRON
ap-3524	162	13	into	into	ADP
ap-3524	162	14	solutions	solution	NOUN
ap-3524	162	15	of	of	ADP
ap-3524	162	16	the	the	DET
ap-3524	162	17	potential	potential	ADJ
ap-3524	162	18	burgers	burger	NOUN
ap-3524	162	19	equation	equation	NOUN
ap-3524	162	20	[	[	X
ap-3524	162	21	14	14	NUM
ap-3524	162	22	]	]	X
ap-3524	162	23	using	use	VERB
ap-3524	162	24	(	(	PUNCT
ap-3524	162	25	22	22	NUM
ap-3524	162	26	)	)	PUNCT
ap-3524	162	27	.	.	PUNCT
ap-3524	163	1	starting	start	VERB
ap-3524	163	2	from	from	ADP
ap-3524	163	3	the	the	DET
ap-3524	163	4	traveling	travel	VERB
ap-3524	163	5	wave	wave	NOUN
ap-3524	163	6	solution	solution	NOUN
ap-3524	163	7	of	of	ADP
ap-3524	163	8	the	the	DET
ap-3524	163	9	heat	heat	NOUN
ap-3524	163	10	equation	equation	NOUN
ap-3524	163	11	(	(	PUNCT
ap-3524	163	12	invariant	invariant	ADJ
ap-3524	163	13	under	under	ADP
ap-3524	163	14	a	a	DET
ap-3524	163	15	combination	combination	NOUN
ap-3524	163	16	of	of	ADP
ap-3524	163	17	x	x	SYM
ap-3524	163	18	and	and	CCONJ
ap-3524	163	19	y	y	PROPN
ap-3524	163	20	translations	translation	NOUN
ap-3524	163	21	)	)	PUNCT
ap-3524	163	22	we	we	PRON
ap-3524	163	23	get	get	VERB
ap-3524	163	24	as	as	ADP
ap-3524	163	25	a	a	DET
ap-3524	163	26	simple	simple	ADJ
ap-3524	163	27	solution	solution	NOUN
ap-3524	163	28	,	,	PUNCT
ap-3524	163	29	bounded	bound	VERB
ap-3524	163	30	for	for	ADP
ap-3524	163	31	x	x	PROPN
ap-3524	163	32	∈	∈	PROPN
ap-3524	163	33	r+	r+	NOUN
ap-3524	163	34	for	for	ADP
ap-3524	163	35	each	each	DET
ap-3524	163	36	y	y	PROPN
ap-3524	163	37	,	,	PUNCT
ap-3524	163	38	f1(x	f1(x	PROPN
ap-3524	163	39	,	,	PUNCT
ap-3524	163	40	y	y	NOUN
ap-3524	163	41	)	)	PUNCT
ap-3524	163	42	=	=	SYM
ap-3524	163	43	log(1	log(1	NOUN
ap-3524	163	44	+	+	CCONJ
ap-3524	163	45	e−(x−y	e−(x−y	NOUN
ap-3524	163	46	)	)	PUNCT
ap-3524	163	47	)	)	PUNCT
ap-3524	163	48	.	.	PUNCT
ap-3524	164	1	(	(	PUNCT
ap-3524	164	2	34	34	NUM
ap-3524	164	3	)	)	PUNCT
ap-3524	164	4	a	a	DET
ap-3524	164	5	second	second	ADJ
ap-3524	164	6	exact	exact	ADJ
ap-3524	164	7	solution	solution	NOUN
ap-3524	164	8	(	(	PUNCT
ap-3524	164	9	the	the	DET
ap-3524	164	10	fundamental	fundamental	ADJ
ap-3524	164	11	solution	solution	NOUN
ap-3524	164	12	)	)	PUNCT
ap-3524	164	13	is	be	AUX
ap-3524	164	14	given	give	VERB
ap-3524	164	15	by	by	ADP
ap-3524	164	16	the	the	DET
ap-3524	164	17	galilei	galilei	NOUN
ap-3524	164	18	–	–	PUNCT
ap-3524	164	19	invariant	invariant	ADJ
ap-3524	164	20	solution	solution	NOUN
ap-3524	164	21	of	of	ADP
ap-3524	164	22	the	the	DET
ap-3524	164	23	heat	heat	NOUN
ap-3524	164	24	equation	equation	NOUN
ap-3524	164	25	f2(x	f2(x	PROPN
ap-3524	164	26	,	,	PUNCT
ap-3524	164	27	y	y	NOUN
ap-3524	164	28	)	)	PUNCT
ap-3524	164	29	=	=	VERB
ap-3524	165	1	log	log	NOUN
ap-3524	165	2	(	(	PUNCT
ap-3524	165	3	1	1	NUM
ap-3524	165	4	+	+	CCONJ
ap-3524	165	5	e−x2/(4y	e−x2/(4y	PROPN
ap-3524	165	6	)	)	PUNCT
ap-3524	165	7	√	√	PROPN
ap-3524	165	8	y	y	PROPN
ap-3524	165	9	)	)	PUNCT
ap-3524	165	10	.	.	PUNCT
ap-3524	166	1	(	(	PUNCT
ap-3524	166	2	35	35	NUM
ap-3524	166	3	)	)	PUNCT
ap-3524	166	4	to	to	PART
ap-3524	166	5	compare	compare	VERB
ap-3524	166	6	the	the	DET
ap-3524	166	7	results	result	NOUN
ap-3524	166	8	given	give	VERB
ap-3524	166	9	by	by	ADP
ap-3524	166	10	the	the	DET
ap-3524	166	11	evolution	evolution	NOUN
ap-3524	166	12	of	of	ADP
ap-3524	166	13	the	the	DET
ap-3524	166	14	map	map	NOUN
ap-3524	166	15	on	on	ADP
ap-3524	166	16	a	a	DET
ap-3524	166	17	given	give	VERB
ap-3524	166	18	lattice	lattice	NOUN
ap-3524	166	19	to	to	ADP
ap-3524	166	20	the	the	DET
ap-3524	166	21	evolution	evolution	NOUN
ap-3524	166	22	given	give	VERB
ap-3524	166	23	by	by	ADP
ap-3524	166	24	the	the	DET
ap-3524	166	25	exact	exact	ADJ
ap-3524	166	26	solution	solution	NOUN
ap-3524	166	27	we	we	PRON
ap-3524	166	28	introduce	introduce	VERB
ap-3524	166	29	a	a	DET
ap-3524	166	30	global	global	ADJ
ap-3524	166	31	estimator	estimator	NOUN
ap-3524	166	32	,	,	PUNCT
ap-3524	166	33	the	the	DET
ap-3524	166	34	usual	usual	ADJ
ap-3524	166	35	(	(	PUNCT
ap-3524	166	36	relative	relative	ADJ
ap-3524	166	37	)	)	PUNCT
ap-3524	166	38	distance	distance	NOUN
ap-3524	166	39	in	in	ADP
ap-3524	166	40	the	the	DET
ap-3524	166	41	discrete	discrete	ADJ
ap-3524	166	42	analog	analog	NOUN
ap-3524	166	43	of	of	ADP
ap-3524	166	44	the	the	DET
ap-3524	166	45	l2	l2	NOUN
ap-3524	166	46	space	space	NOUN
ap-3524	166	47	:	:	PUNCT
ap-3524	166	48	χlattice(f	χlattice(f	NOUN
ap-3524	166	49	)	)	PUNCT
ap-3524	166	50	=	=	PRON
ap-3524	166	51	√∑	√∑	PROPN
ap-3524	166	52	n	n	CCONJ
ap-3524	166	53	,	,	PUNCT
ap-3524	166	54	m(f	m(f	PROPN
ap-3524	166	55	lattice	lattice	PROPN
ap-3524	166	56	n	n	PRON
ap-3524	166	57	,	,	PUNCT
ap-3524	166	58	m	m	VERB
ap-3524	166	59	−	−	PROPN
ap-3524	166	60	fn	fn	PROPN
ap-3524	166	61	,	,	PUNCT
ap-3524	166	62	m)2∑	m)2∑	NUM
ap-3524	166	63	n	n	CCONJ
ap-3524	166	64	,	,	PUNCT
ap-3524	166	65	m	m	PROPN
ap-3524	166	66	f	f	NOUN
ap-3524	166	67	2	2	NUM
ap-3524	166	68	n	n	NOUN
ap-3524	166	69	,	,	PUNCT
ap-3524	166	70	m	m	PROPN
ap-3524	166	71	(	(	PUNCT
ap-3524	166	72	36	36	NUM
ap-3524	166	73	)	)	PUNCT
ap-3524	166	74	where	where	SCONJ
ap-3524	166	75	fn	fn	NOUN
ap-3524	166	76	,	,	PUNCT
ap-3524	166	77	m	m	PROPN
ap-3524	166	78	and	and	CCONJ
ap-3524	166	79	f	f	PROPN
ap-3524	166	80	lattice	lattice	PROPN
ap-3524	166	81	n	n	PROPN
ap-3524	166	82	,	,	PUNCT
ap-3524	166	83	m	m	VERB
ap-3524	166	84	are	be	AUX
ap-3524	166	85	the	the	DET
ap-3524	166	86	values	value	NOUN
ap-3524	166	87	of	of	ADP
ap-3524	166	88	the	the	DET
ap-3524	166	89	exact	exact	ADJ
ap-3524	166	90	solution	solution	NOUN
ap-3524	166	91	and	and	CCONJ
ap-3524	166	92	the	the	DET
ap-3524	166	93	numerical	numerical	ADJ
ap-3524	166	94	one	one	NUM
ap-3524	166	95	,	,	PUNCT
ap-3524	166	96	respectively	respectively	ADV
ap-3524	166	97	,	,	PUNCT
ap-3524	166	98	computed	compute	VERB
ap-3524	166	99	in	in	ADP
ap-3524	166	100	the	the	DET
ap-3524	166	101	points	point	NOUN
ap-3524	166	102	of	of	ADP
ap-3524	166	103	the	the	DET
ap-3524	166	104	lattices	lattice	NOUN
ap-3524	166	105	(	(	PUNCT
ap-3524	166	106	29	29	NUM
ap-3524	166	107	,	,	PUNCT
ap-3524	166	108	33	33	NUM
ap-3524	166	109	)	)	PUNCT
ap-3524	166	110	.	.	PUNCT
ap-3524	167	1	since	since	SCONJ
ap-3524	167	2	our	our	PRON
ap-3524	167	3	intention	intention	NOUN
ap-3524	167	4	is	be	AUX
ap-3524	167	5	to	to	PART
ap-3524	167	6	compare	compare	VERB
ap-3524	167	7	the	the	DET
ap-3524	167	8	lattices	lattice	NOUN
ap-3524	167	9	,	,	PUNCT
ap-3524	167	10	we	we	PRON
ap-3524	167	11	will	will	AUX
ap-3524	167	12	not	not	PART
ap-3524	167	13	insist	insist	VERB
ap-3524	167	14	on	on	ADP
ap-3524	167	15	improving	improve	VERB
ap-3524	167	16	the	the	DET
ap-3524	167	17	precision	precision	NOUN
ap-3524	167	18	and	and	CCONJ
ap-3524	167	19	accuracy	accuracy	NOUN
ap-3524	167	20	of	of	ADP
ap-3524	167	21	the	the	DET
ap-3524	167	22	solution	solution	NOUN
ap-3524	167	23	by	by	ADP
ap-3524	167	24	modifying	modify	VERB
ap-3524	167	25	in	in	ADP
ap-3524	167	26	an	an	DET
ap-3524	167	27	optimal	optimal	ADJ
ap-3524	167	28	way	way	NOUN
ap-3524	167	29	the	the	DET
ap-3524	167	30	parameters	parameter	NOUN
ap-3524	167	31	involved	involve	VERB
ap-3524	167	32	in	in	ADP
ap-3524	167	33	the	the	DET
ap-3524	167	34	computation	computation	NOUN
ap-3524	167	35	.	.	PUNCT
ap-3524	168	1	for	for	ADP
ap-3524	168	2	the	the	DET
ap-3524	168	3	orthogonal	orthogonal	ADJ
ap-3524	168	4	lattice	lattice	NOUN
ap-3524	168	5	we	we	PRON
ap-3524	168	6	will	will	AUX
ap-3524	168	7	take	take	VERB
ap-3524	168	8	(	(	PUNCT
ap-3524	168	9	for	for	ADP
ap-3524	168	10	f1	f1	NOUN
ap-3524	168	11	and	and	CCONJ
ap-3524	168	12	f2	f2	PROPN
ap-3524	168	13	)	)	PUNCT
ap-3524	168	14	a	a	DET
ap-3524	168	15	=	=	SYM
ap-3524	168	16	b	b	NOUN
ap-3524	168	17	=	=	SYM
ap-3524	168	18	0.1	0.1	NUM
ap-3524	168	19	in	in	ADP
ap-3524	168	20	a	a	DET
ap-3524	168	21	square	square	ADJ
ap-3524	168	22	d	d	NOUN
ap-3524	168	23	of	of	ADP
ap-3524	168	24	8×	8×	NUM
ap-3524	168	25	8	8	NUM
ap-3524	168	26	points	point	NOUN
ap-3524	168	27	in	in	ADP
ap-3524	168	28	the	the	DET
ap-3524	168	29	x	x	NOUN
ap-3524	168	30	,	,	PUNCT
ap-3524	168	31	y	y	PROPN
ap-3524	168	32	plane	plane	NOUN
ap-3524	168	33	.	.	PUNCT
ap-3524	169	1	we	we	PRON
ap-3524	169	2	will	will	AUX
ap-3524	169	3	use	use	VERB
ap-3524	169	4	the	the	DET
ap-3524	169	5	same	same	ADJ
ap-3524	169	6	number	number	NOUN
ap-3524	169	7	of	of	ADP
ap-3524	169	8	points	point	NOUN
ap-3524	169	9	in	in	ADP
ap-3524	169	10	all	all	DET
ap-3524	169	11	the	the	DET
ap-3524	169	12	cases	case	NOUN
ap-3524	169	13	we	we	PRON
ap-3524	169	14	will	will	AUX
ap-3524	169	15	consider	consider	VERB
ap-3524	169	16	,	,	PUNCT
ap-3524	169	17	in	in	ADP
ap-3524	169	18	order	order	NOUN
ap-3524	169	19	to	to	PART
ap-3524	169	20	keep	keep	VERB
ap-3524	169	21	as	as	ADV
ap-3524	169	22	far	far	ADV
ap-3524	169	23	as	as	ADP
ap-3524	169	24	possible	possible	ADJ
ap-3524	169	25	the	the	DET
ap-3524	169	26	same	same	ADJ
ap-3524	169	27	round	round	NOUN
ap-3524	169	28	off	off	ADP
ap-3524	169	29	errors	error	NOUN
ap-3524	169	30	due	due	ADP
ap-3524	169	31	to	to	ADP
ap-3524	169	32	machine	machine	NOUN
ap-3524	169	33	precision	precision	NOUN
ap-3524	169	34	.	.	PUNCT
ap-3524	170	1	augmenting	augment	VERB
ap-3524	170	2	the	the	DET
ap-3524	170	3	number	number	NOUN
ap-3524	170	4	of	of	ADP
ap-3524	170	5	points	point	NOUN
ap-3524	170	6	enlarges	enlarge	VERB
ap-3524	170	7	the	the	DET
ap-3524	170	8	numerical	numerical	ADJ
ap-3524	170	9	instabilities	instability	NOUN
ap-3524	170	10	which	which	PRON
ap-3524	170	11	could	could	AUX
ap-3524	170	12	be	be	AUX
ap-3524	170	13	reduced	reduce	VERB
ap-3524	170	14	by	by	ADP
ap-3524	170	15	increasing	increase	VERB
ap-3524	170	16	the	the	DET
ap-3524	170	17	precision	precision	NOUN
ap-3524	170	18	of	of	ADP
ap-3524	170	19	the	the	DET
ap-3524	170	20	calculations	calculation	NOUN
ap-3524	170	21	at	at	ADP
ap-3524	170	22	the	the	DET
ap-3524	170	23	cost	cost	NOUN
ap-3524	170	24	of	of	ADP
ap-3524	170	25	the	the	DET
ap-3524	170	26	time	time	NOUN
ap-3524	170	27	of	of	ADP
ap-3524	170	28	calculus	calculus	NOUN
ap-3524	170	29	.	.	PUNCT
ap-3524	171	1	these	these	DET
ap-3524	171	2	instabilities	instability	NOUN
ap-3524	171	3	are	be	AUX
ap-3524	171	4	non	non	ADJ
ap-3524	171	5	–	–	PUNCT
ap-3524	171	6	physical	physical	ADJ
ap-3524	171	7	and	and	CCONJ
ap-3524	171	8	we	we	PRON
ap-3524	171	9	decide	decide	VERB
ap-3524	171	10	to	to	PART
ap-3524	171	11	avoid	avoid	VERB
ap-3524	171	12	them	they	PRON
ap-3524	171	13	by	by	ADP
ap-3524	171	14	reducing	reduce	VERB
ap-3524	171	15	appropriately	appropriately	ADV
ap-3524	171	16	the	the	DET
ap-3524	171	17	number	number	NOUN
ap-3524	171	18	of	of	ADP
ap-3524	171	19	points	point	NOUN
ap-3524	171	20	.	.	PUNCT
ap-3524	172	1	the	the	DET
ap-3524	172	2	region	region	NOUN
ap-3524	172	3	covered	cover	VERB
ap-3524	172	4	by	by	ADP
ap-3524	172	5	the	the	DET
ap-3524	172	6	lattice	lattice	NOUN
ap-3524	172	7	in	in	ADP
ap-3524	172	8	the	the	DET
ap-3524	172	9	two	two	NUM
ap-3524	172	10	cases	case	NOUN
ap-3524	172	11	(	(	PUNCT
ap-3524	172	12	orthogonal	orthogonal	ADJ
ap-3524	172	13	and	and	CCONJ
ap-3524	172	14	exponential	exponential	NOUN
ap-3524	172	15	)	)	PUNCT
ap-3524	172	16	can	can	AUX
ap-3524	172	17	be	be	AUX
ap-3524	172	18	different	different	ADJ
ap-3524	172	19	for	for	ADP
ap-3524	172	20	the	the	DET
ap-3524	172	21	same	same	ADJ
ap-3524	172	22	lattice	lattice	NOUN
ap-3524	172	23	spacing	spacing	NOUN
ap-3524	172	24	.	.	PUNCT
ap-3524	173	1	see	see	VERB
ap-3524	173	2	for	for	ADP
ap-3524	173	3	example	example	NOUN
ap-3524	173	4	in	in	ADP
ap-3524	173	5	figure	figure	NOUN
ap-3524	173	6	1	1	NUM
ap-3524	173	7	the	the	DET
ap-3524	173	8	cases	case	NOUN
ap-3524	173	9	(	(	PUNCT
ap-3524	173	10	1	1	NUM
ap-3524	173	11	)	)	PUNCT
ap-3524	173	12	and	and	CCONJ
ap-3524	173	13	(	(	PUNCT
ap-3524	173	14	2	2	NUM
ap-3524	173	15	)	)	PUNCT
ap-3524	173	16	.	.	PUNCT
ap-3524	174	1	in	in	ADP
ap-3524	174	2	the	the	DET
ap-3524	174	3	exponential	exponential	ADJ
ap-3524	174	4	lattice	lattice	NOUN
ap-3524	174	5	we	we	PRON
ap-3524	174	6	will	will	AUX
ap-3524	174	7	consider	consider	VERB
ap-3524	174	8	two	two	NUM
ap-3524	174	9	different	different	ADJ
ap-3524	174	10	situations	situation	NOUN
ap-3524	174	11	:	:	PUNCT
ap-3524	174	12	(	(	PUNCT
ap-3524	174	13	i	i	NOUN
ap-3524	174	14	)	)	PUNCT
ap-3524	174	15	the	the	DET
ap-3524	174	16	spacing	spacing	NOUN
ap-3524	174	17	is	be	AUX
ap-3524	174	18	the	the	DET
ap-3524	174	19	same	same	ADJ
ap-3524	174	20	as	as	ADP
ap-3524	174	21	in	in	ADP
ap-3524	174	22	the	the	DET
ap-3524	174	23	orthogonal	orthogonal	ADJ
ap-3524	174	24	case	case	NOUN
ap-3524	174	25	(	(	PUNCT
ap-3524	174	26	a	a	DET
ap-3524	174	27	=	=	X
ap-3524	174	28	b	b	NOUN
ap-3524	174	29	=	=	SYM
ap-3524	174	30	0.1	0.1	NUM
ap-3524	174	31	)	)	PUNCT
ap-3524	174	32	,	,	PUNCT
ap-3524	174	33	and	and	CCONJ
ap-3524	174	34	thus	thus	ADV
ap-3524	174	35	for	for	ADP
ap-3524	174	36	the	the	DET
ap-3524	174	37	exponential	exponential	ADJ
ap-3524	174	38	lattice	lattice	NOUN
ap-3524	174	39	the	the	DET
ap-3524	174	40	region	region	NOUN
ap-3524	174	41	is	be	AUX
ap-3524	174	42	deformed	deform	VERB
ap-3524	174	43	and	and	CCONJ
ap-3524	174	44	enlarged	enlarge	VERB
ap-3524	174	45	with	with	ADP
ap-3524	174	46	respect	respect	NOUN
ap-3524	174	47	to	to	ADP
ap-3524	174	48	the	the	DET
ap-3524	174	49	square	square	ADJ
ap-3524	175	1	d	d	NOUN
ap-3524	175	2	considered	consider	VERB
ap-3524	175	3	in	in	ADP
ap-3524	175	4	the	the	DET
ap-3524	175	5	orthogonal	orthogonal	ADJ
ap-3524	175	6	lattice	lattice	NOUN
ap-3524	175	7	,	,	PUNCT
ap-3524	175	8	(	(	PUNCT
ap-3524	175	9	ii	ii	NOUN
ap-3524	175	10	)	)	PUNCT
ap-3524	175	11	we	we	PRON
ap-3524	175	12	will	will	AUX
ap-3524	175	13	modify	modify	VERB
ap-3524	175	14	a	a	PRON
ap-3524	175	15	in	in	ADP
ap-3524	175	16	such	such	DET
ap-3524	175	17	a	a	DET
ap-3524	175	18	way	way	NOUN
ap-3524	175	19	that	that	PRON
ap-3524	175	20	the	the	DET
ap-3524	175	21	64	64	NUM
ap-3524	175	22	points	point	NOUN
ap-3524	175	23	of	of	ADP
ap-3524	175	24	the	the	DET
ap-3524	175	25	lattice	lattice	NOUN
ap-3524	175	26	are	be	AUX
ap-3524	175	27	inside	inside	ADP
ap-3524	175	28	the	the	DET
ap-3524	175	29	square	square	PROPN
ap-3524	175	30	d.	d.	PROPN
ap-3524	175	31	let	let	VERB
ap-3524	175	32	us	we	PRON
ap-3524	175	33	notice	notice	VERB
ap-3524	175	34	that	that	SCONJ
ap-3524	175	35	in	in	ADP
ap-3524	175	36	this	this	DET
ap-3524	175	37	case	case	NOUN
ap-3524	175	38	part	part	NOUN
ap-3524	175	39	of	of	ADP
ap-3524	175	40	d	d	PROPN
ap-3524	175	41	is	be	AUX
ap-3524	175	42	not	not	PART
ap-3524	175	43	covered	cover	VERB
ap-3524	175	44	by	by	ADP
ap-3524	175	45	the	the	DET
ap-3524	175	46	lattice	lattice	NOUN
ap-3524	175	47	,	,	PUNCT
ap-3524	175	48	and	and	CCONJ
ap-3524	175	49	this	this	PRON
ap-3524	175	50	may	may	AUX
ap-3524	175	51	create	create	VERB
ap-3524	175	52	problems	problem	NOUN
ap-3524	175	53	as	as	SCONJ
ap-3524	175	54	we	we	PRON
ap-3524	175	55	will	will	AUX
ap-3524	175	56	see	see	VERB
ap-3524	175	57	later	later	ADV
ap-3524	175	58	.	.	PUNCT
ap-3524	176	1	the	the	DET
ap-3524	176	2	exponential	exponential	ADJ
ap-3524	176	3	lattice	lattice	NOUN
ap-3524	176	4	has	have	VERB
ap-3524	176	5	a	a	DET
ap-3524	176	6	parameter	parameter	NOUN
ap-3524	176	7	c	c	NOUN
ap-3524	176	8	controlling	control	VERB
ap-3524	176	9	the	the	DET
ap-3524	176	10	dilation	dilation	NOUN
ap-3524	176	11	of	of	ADP
ap-3524	176	12	the	the	DET
ap-3524	176	13	x	x	NOUN
ap-3524	176	14	variable	variable	NOUN
ap-3524	176	15	.	.	PUNCT
ap-3524	177	1	as	as	SCONJ
ap-3524	177	2	we	we	PRON
ap-3524	177	3	said	say	VERB
ap-3524	177	4	above	above	ADV
ap-3524	177	5	,	,	PUNCT
ap-3524	177	6	when	when	SCONJ
ap-3524	177	7	c	c	NOUN
ap-3524	177	8	=	=	SYM
ap-3524	177	9	0	0	PROPN
ap-3524	177	10	the	the	DET
ap-3524	177	11	lattice	lattice	NOUN
ap-3524	177	12	is	be	AUX
ap-3524	177	13	orthogonal	orthogonal	ADJ
ap-3524	177	14	.	.	PUNCT
ap-3524	178	1	we	we	PRON
ap-3524	178	2	have	have	AUX
ap-3524	178	3	considered	consider	VERB
ap-3524	178	4	in	in	ADP
ap-3524	178	5	these	these	DET
ap-3524	178	6	numerical	numerical	ADJ
ap-3524	178	7	calculations	calculation	NOUN
ap-3524	178	8	two	two	NUM
ap-3524	178	9	cases	case	NOUN
ap-3524	178	10	,	,	PUNCT
ap-3524	178	11	c	c	NOUN
ap-3524	178	12	=	=	SYM
ap-3524	178	13	0.1	0.1	NUM
ap-3524	178	14	and	and	CCONJ
ap-3524	178	15	c	c	NOUN
ap-3524	178	16	=	=	SYM
ap-3524	178	17	0.15	0.15	NUM
ap-3524	178	18	,	,	PUNCT
ap-3524	178	19	to	to	PART
ap-3524	178	20	compare	compare	VERB
ap-3524	178	21	the	the	DET
ap-3524	178	22	different	different	ADJ
ap-3524	178	23	behavior	behavior	NOUN
ap-3524	178	24	of	of	ADP
ap-3524	178	25	the	the	DET
ap-3524	178	26	exponential	exponential	ADJ
ap-3524	178	27	lattice	lattice	NOUN
ap-3524	178	28	when	when	SCONJ
ap-3524	178	29	it	it	PRON
ap-3524	178	30	turns	turn	VERB
ap-3524	178	31	into	into	ADP
ap-3524	178	32	an	an	DET
ap-3524	178	33	orthogonal	orthogonal	ADJ
ap-3524	178	34	one	one	NUM
ap-3524	178	35	.	.	PUNCT
ap-3524	179	1	in	in	ADP
ap-3524	179	2	these	these	DET
ap-3524	179	3	two	two	NUM
ap-3524	179	4	cases	case	NOUN
ap-3524	179	5	,	,	PUNCT
ap-3524	179	6	the	the	DET
ap-3524	179	7	parameter	parameter	NOUN
ap-3524	179	8	a	a	PRON
ap-3524	179	9	is	be	AUX
ap-3524	179	10	taken	take	VERB
ap-3524	179	11	as	as	ADP
ap-3524	179	12	a	a	DET
ap-3524	179	13	=	=	SYM
ap-3524	179	14	0.0375	0.0375	NUM
ap-3524	179	15	and	and	CCONJ
ap-3524	179	16	a	a	DET
ap-3524	179	17	=	=	NOUN
ap-3524	179	18	0.0513	0.0513	NUM
ap-3524	179	19	respectively	respectively	ADV
ap-3524	179	20	,	,	PUNCT
ap-3524	179	21	when	when	SCONJ
ap-3524	179	22	we	we	PRON
ap-3524	179	23	keep	keep	VERB
ap-3524	179	24	the	the	DET
ap-3524	179	25	64	64	NUM
ap-3524	179	26	point	point	NOUN
ap-3524	179	27	of	of	ADP
ap-3524	179	28	the	the	DET
ap-3524	179	29	lattice	lattice	NOUN
ap-3524	179	30	inside	inside	ADP
ap-3524	179	31	d	d	PROPN
ap-3524	179	32	(	(	PUNCT
ap-3524	179	33	see	see	VERB
ap-3524	179	34	figure	figure	NOUN
ap-3524	179	35	1	1	NUM
ap-3524	179	36	for	for	ADP
ap-3524	179	37	a	a	DET
ap-3524	179	38	graphical	graphical	ADJ
ap-3524	179	39	description	description	NOUN
ap-3524	179	40	of	of	ADP
ap-3524	179	41	the	the	DET
ap-3524	179	42	four	four	NUM
ap-3524	179	43	lattices	lattice	NOUN
ap-3524	179	44	under	under	ADP
ap-3524	179	45	study	study	NOUN
ap-3524	179	46	)	)	PUNCT
ap-3524	179	47	.	.	PUNCT
ap-3524	180	1	the	the	DET
ap-3524	180	2	χ	χ	PROPN
ap-3524	180	3	estimator	estimator	NOUN
ap-3524	180	4	is	be	AUX
ap-3524	180	5	given	give	VERB
ap-3524	180	6	in	in	ADP
ap-3524	180	7	table	table	NOUN
ap-3524	180	8	2	2	NUM
ap-3524	180	9	and	and	CCONJ
ap-3524	180	10	gives	give	VERB
ap-3524	180	11	raise	raise	VERB
ap-3524	180	12	to	to	ADP
ap-3524	180	13	the	the	DET
ap-3524	180	14	following	follow	VERB
ap-3524	180	15	conclusions	conclusion	NOUN
ap-3524	180	16	:	:	PUNCT
ap-3524	180	17	(	(	PUNCT
ap-3524	180	18	1	1	NUM
ap-3524	180	19	.	.	PUNCT
ap-3524	180	20	)	)	PUNCT
ap-3524	181	1	the	the	DET
ap-3524	181	2	orthogonal	orthogonal	ADJ
ap-3524	181	3	lattice	lattice	NOUN
ap-3524	181	4	(	(	PUNCT
ap-3524	181	5	schwarzian	schwarzian	PROPN
ap-3524	181	6	lattice	lattice	PROPN
ap-3524	181	7	)	)	PUNCT
ap-3524	181	8	provides	provide	VERB
ap-3524	181	9	better	well	ADJ
ap-3524	181	10	results	result	NOUN
ap-3524	181	11	than	than	ADP
ap-3524	181	12	the	the	DET
ap-3524	181	13	exponential	exponential	ADJ
ap-3524	181	14	one	one	NOUN
ap-3524	181	15	(	(	PUNCT
ap-3524	181	16	non	non	X
ap-3524	181	17	schwarzian	schwarzian	PROPN
ap-3524	181	18	lattice	lattice	PROPN
ap-3524	181	19	)	)	PUNCT
ap-3524	181	20	in	in	ADP
ap-3524	181	21	all	all	DET
ap-3524	181	22	cases	case	NOUN
ap-3524	181	23	except	except	SCONJ
ap-3524	181	24	one	one	NUM
ap-3524	181	25	.	.	PUNCT
ap-3524	182	1	(	(	PUNCT
ap-3524	182	2	2	2	NUM
ap-3524	182	3	.	.	PUNCT
ap-3524	182	4	)	)	PUNCT
ap-3524	183	1	the	the	DET
ap-3524	183	2	results	result	NOUN
ap-3524	183	3	for	for	ADP
ap-3524	183	4	the	the	DET
ap-3524	183	5	exponential	exponential	ADJ
ap-3524	183	6	lattice	lattice	NOUN
ap-3524	183	7	with	with	ADP
ap-3524	183	8	different	different	ADJ
ap-3524	183	9	values	value	NOUN
ap-3524	183	10	of	of	ADP
ap-3524	183	11	c	c	PROPN
ap-3524	183	12	show	show	VERB
ap-3524	183	13	that	that	SCONJ
ap-3524	183	14	the	the	DET
ap-3524	183	15	approximation	approximation	NOUN
ap-3524	183	16	is	be	AUX
ap-3524	183	17	better	well	ADJ
ap-3524	183	18	when	when	SCONJ
ap-3524	183	19	the	the	DET
ap-3524	183	20	lattice	lattice	NOUN
ap-3524	183	21	is	be	AUX
ap-3524	183	22	closer	close	ADJ
ap-3524	183	23	to	to	ADP
ap-3524	183	24	a	a	DET
ap-3524	183	25	schwarzian	schwarzian	NOUN
ap-3524	183	26	lattice	lattice	NOUN
ap-3524	183	27	(	(	PUNCT
ap-3524	183	28	recall	recall	VERB
ap-3524	183	29	that	that	SCONJ
ap-3524	183	30	when	when	SCONJ
ap-3524	183	31	c→	c→	X
ap-3524	183	32	0	0	NUM
ap-3524	183	33	the	the	DET
ap-3524	183	34	exponential	exponential	ADJ
ap-3524	183	35	lattice	lattice	NOUN
ap-3524	183	36	becomes	become	VERB
ap-3524	183	37	orthogonal	orthogonal	ADJ
ap-3524	183	38	)	)	PUNCT
ap-3524	183	39	,	,	PUNCT
ap-3524	183	40	for	for	ADP
ap-3524	183	41	the	the	DET
ap-3524	183	42	two	two	NUM
ap-3524	183	43	solutions	solution	NOUN
ap-3524	183	44	considered	consider	VERB
ap-3524	183	45	.	.	PUNCT
ap-3524	184	1	(	(	PUNCT
ap-3524	184	2	3	3	NUM
ap-3524	184	3	.	.	PUNCT
ap-3524	184	4	)	)	PUNCT
ap-3524	185	1	the	the	DET
ap-3524	185	2	value	value	NOUN
ap-3524	185	3	of	of	ADP
ap-3524	185	4	the	the	DET
ap-3524	185	5	χ	χ	PROPN
ap-3524	185	6	estimator	estimator	NOUN
ap-3524	185	7	for	for	ADP
ap-3524	185	8	the	the	DET
ap-3524	185	9	traveling	travel	VERB
ap-3524	185	10	wave	wave	NOUN
ap-3524	185	11	solution	solution	NOUN
ap-3524	185	12	in	in	ADP
ap-3524	185	13	the	the	DET
ap-3524	185	14	exponential	exponential	ADJ
ap-3524	185	15	lattice	lattice	NOUN
ap-3524	185	16	when	when	SCONJ
ap-3524	185	17	a	a	DET
ap-3524	185	18	=	=	SYM
ap-3524	185	19	0.0513	0.0513	NUM
ap-3524	185	20	and	and	CCONJ
ap-3524	185	21	c	c	NOUN
ap-3524	185	22	=	=	SYM
ap-3524	185	23	0.1	0.1	NUM
ap-3524	185	24	is	be	AUX
ap-3524	185	25	lower	low	ADJ
ap-3524	185	26	than	than	ADP
ap-3524	185	27	the	the	DET
ap-3524	185	28	corresponding	corresponding	ADJ
ap-3524	185	29	value	value	NOUN
ap-3524	185	30	for	for	ADP
ap-3524	185	31	the	the	DET
ap-3524	185	32	orthogonal	orthogonal	ADJ
ap-3524	185	33	case	case	NOUN
ap-3524	185	34	.	.	PUNCT
ap-3524	186	1	in	in	ADP
ap-3524	186	2	this	this	DET
ap-3524	186	3	case	case	NOUN
ap-3524	186	4	(	(	PUNCT
ap-3524	186	5	figure	figure	NOUN
ap-3524	186	6	1.3	1.3	NUM
ap-3524	186	7	)	)	PUNCT
ap-3524	186	8	the	the	DET
ap-3524	186	9	lattice	lattice	NOUN
ap-3524	186	10	is	be	AUX
ap-3524	186	11	close	close	ADJ
ap-3524	186	12	to	to	ADP
ap-3524	186	13	the	the	DET
ap-3524	186	14	orthogonal	orthogonal	ADJ
ap-3524	186	15	one	one	NOUN
ap-3524	186	16	but	but	CCONJ
ap-3524	186	17	there	there	PRON
ap-3524	186	18	is	be	VERB
ap-3524	186	19	a	a	DET
ap-3524	186	20	region	region	NOUN
ap-3524	186	21	in	in	ADP
ap-3524	186	22	d	d	PROPN
ap-3524	186	23	which	which	PRON
ap-3524	186	24	is	be	AUX
ap-3524	186	25	not	not	PART
ap-3524	186	26	covered	cover	VERB
ap-3524	186	27	by	by	ADP
ap-3524	186	28	the	the	DET
ap-3524	186	29	exponential	exponential	ADJ
ap-3524	186	30	lattice	lattice	NOUN
ap-3524	186	31	.	.	PUNCT
ap-3524	187	1	this	this	PRON
ap-3524	187	2	is	be	AUX
ap-3524	187	3	the	the	DET
ap-3524	187	4	region	region	NOUN
ap-3524	187	5	where	where	SCONJ
ap-3524	187	6	the	the	DET
ap-3524	187	7	round	round	NOUN
ap-3524	187	8	off	off	ADP
ap-3524	187	9	errors	error	NOUN
ap-3524	187	10	the	the	DET
ap-3524	187	11	computer	computer	NOUN
ap-3524	187	12	makes	make	VERB
ap-3524	187	13	in	in	ADP
ap-3524	187	14	calculating	calculate	VERB
ap-3524	187	15	the	the	DET
ap-3524	187	16	points	point	NOUN
ap-3524	187	17	in	in	ADP
ap-3524	187	18	the	the	DET
ap-3524	187	19	orthogonal	orthogonal	ADJ
ap-3524	187	20	lattice	lattice	NOUN
ap-3524	187	21	are	be	AUX
ap-3524	187	22	greater	great	ADJ
ap-3524	187	23	.	.	PUNCT
ap-3524	188	1	this	this	PRON
ap-3524	188	2	is	be	AUX
ap-3524	188	3	the	the	DET
ap-3524	188	4	reason	reason	NOUN
ap-3524	188	5	for	for	ADP
ap-3524	188	6	this	this	DET
ap-3524	188	7	unsatisfactory	unsatisfactory	ADJ
ap-3524	188	8	value	value	NOUN
ap-3524	188	9	.	.	PUNCT
ap-3524	189	1	when	when	SCONJ
ap-3524	189	2	c	c	X
ap-3524	189	3	=	=	SYM
ap-3524	189	4	0.15	0.15	NUM
ap-3524	189	5	the	the	DET
ap-3524	189	6	lattice	lattice	NOUN
ap-3524	189	7	is	be	AUX
ap-3524	189	8	far	far	ADV
ap-3524	189	9	from	from	ADP
ap-3524	189	10	the	the	DET
ap-3524	189	11	orthogonal	orthogonal	ADJ
ap-3524	189	12	one	one	NOUN
ap-3524	189	13	and	and	CCONJ
ap-3524	189	14	thus	thus	ADV
ap-3524	189	15	χ	χ	PRON
ap-3524	189	16	is	be	AUX
ap-3524	189	17	greater	great	ADJ
ap-3524	189	18	than	than	ADP
ap-3524	189	19	in	in	ADP
ap-3524	189	20	the	the	DET
ap-3524	189	21	orthogonal	orthogonal	ADJ
ap-3524	189	22	case	case	NOUN
ap-3524	189	23	.	.	PUNCT
ap-3524	190	1	5	5	X
ap-3524	190	2	.	.	X
ap-3524	190	3	conclusions	conclusion	NOUN
ap-3524	190	4	in	in	ADP
ap-3524	190	5	this	this	DET
ap-3524	190	6	work	work	NOUN
ap-3524	190	7	we	we	PRON
ap-3524	190	8	have	have	AUX
ap-3524	190	9	shown	show	VERB
ap-3524	190	10	that	that	SCONJ
ap-3524	190	11	also	also	ADV
ap-3524	190	12	in	in	ADP
ap-3524	190	13	the	the	DET
ap-3524	190	14	case	case	NOUN
ap-3524	190	15	of	of	ADP
ap-3524	190	16	partial	partial	ADJ
ap-3524	190	17	difference	difference	NOUN
ap-3524	190	18	equations	equation	NOUN
ap-3524	190	19	we	we	PRON
ap-3524	190	20	can	can	AUX
ap-3524	190	21	introduce	introduce	VERB
ap-3524	190	22	a	a	DET
ap-3524	190	23	set	set	NOUN
ap-3524	190	24	of	of	ADP
ap-3524	190	25	variables	variable	NOUN
ap-3524	190	26	which	which	PRON
ap-3524	190	27	are	be	AUX
ap-3524	190	28	in	in	ADP
ap-3524	190	29	one	one	NUM
ap-3524	190	30	to	to	ADP
ap-3524	190	31	one	one	NUM
ap-3524	190	32	correspondence	correspondence	NOUN
ap-3524	190	33	with	with	ADP
ap-3524	190	34	the	the	DET
ap-3524	190	35	grid	grid	NOUN
ap-3524	190	36	points	point	NOUN
ap-3524	190	37	when	when	SCONJ
ap-3524	190	38	we	we	PRON
ap-3524	190	39	substitute	substitute	VERB
ap-3524	190	40	them	they	PRON
ap-3524	190	41	by	by	ADP
ap-3524	190	42	the	the	DET
ap-3524	190	43	lattice	lattice	PROPN
ap-3524	190	44	differences	difference	NOUN
ap-3524	190	45	and	and	CCONJ
ap-3524	190	46	the	the	DET
ap-3524	190	47	derivatives	derivative	NOUN
ap-3524	190	48	on	on	ADP
ap-3524	190	49	the	the	DET
ap-3524	190	50	lattice	lattice	NOUN
ap-3524	190	51	of	of	ADP
ap-3524	190	52	the	the	DET
ap-3524	190	53	dependent	dependent	ADJ
ap-3524	190	54	function	function	NOUN
ap-3524	190	55	.	.	PUNCT
ap-3524	191	1	this	this	DET
ap-3524	191	2	correspondence	correspondence	NOUN
ap-3524	191	3	allows	allow	VERB
ap-3524	191	4	us	we	PRON
ap-3524	191	5	to	to	PART
ap-3524	191	6	write	write	VERB
ap-3524	191	7	down	down	ADP
ap-3524	191	8	the	the	DET
ap-3524	191	9	invariance	invariance	NOUN
ap-3524	191	10	equations	equation	NOUN
ap-3524	191	11	by	by	ADP
ap-3524	191	12	using	use	VERB
ap-3524	191	13	only	only	ADV
ap-3524	191	14	the	the	DET
ap-3524	191	15	knowledge	knowledge	NOUN
ap-3524	191	16	of	of	ADP
ap-3524	191	17	the	the	DET
ap-3524	191	18	continuous	continuous	ADJ
ap-3524	191	19	invariants	invariant	NOUN
ap-3524	191	20	.	.	PUNCT
ap-3524	192	1	242	242	NUM
ap-3524	192	2	vol	vol	NOUN
ap-3524	192	3	.	.	PUNCT
ap-3524	193	1	56	56	NUM
ap-3524	193	2	no	no	NOUN
ap-3524	193	3	.	.	PUNCT
ap-3524	194	1	3/2016	3/2016	NUM
ap-3524	194	2	on	on	ADP
ap-3524	194	3	the	the	DET
ap-3524	194	4	construction	construction	NOUN
ap-3524	194	5	of	of	ADP
ap-3524	194	6	partial	partial	ADJ
ap-3524	194	7	difference	difference	NOUN
ap-3524	194	8	schemes	scheme	NOUN
ap-3524	194	9	ii	ii	PROPN
ap-3524	194	10	y	y	PROPN
ap-3524	194	11	x	x	PROPN
ap-3524	194	12	�	�	PROPN
ap-3524	194	13	0.1	0.1	NUM
ap-3524	194	14	0.2	0.2	NUM
ap-3524	194	15	0.3	0.3	NUM
ap-3524	194	16	0.4	0.4	NUM
ap-3524	194	17	0.5	0.5	NUM
ap-3524	194	18	0.6	0.6	NUM
ap-3524	194	19	0.7	0.7	NUM
ap-3524	194	20	0.1	0.1	NUM
ap-3524	194	21	0.2	0.2	NUM
ap-3524	194	22	0.3	0.3	NUM
ap-3524	194	23	0.4	0.4	NUM
ap-3524	194	24	0.5	0.5	NUM
ap-3524	194	25	0.6	0.6	NUM
ap-3524	194	26	0.7	0.7	NUM
ap-3524	194	27	x	x	SYM
ap-3524	194	28	y	y	PROPN
ap-3524	194	29	0.5	0.5	NUM
ap-3524	194	30	1.0	1.0	NUM
ap-3524	194	31	1.5	1.5	NUM
ap-3524	194	32	0.2	0.2	NUM
ap-3524	194	33	0.4	0.4	NUM
ap-3524	194	34	0.6	0.6	NUM
ap-3524	194	35	0.8	0.8	NUM
ap-3524	194	36	(	(	PUNCT
ap-3524	194	37	1	1	NUM
ap-3524	194	38	)	)	PUNCT
ap-3524	194	39	(	(	PUNCT
ap-3524	194	40	2	2	X
ap-3524	194	41	)	)	PUNCT
ap-3524	194	42	x	x	SYM
ap-3524	195	1	y	y	NOUN
ap-3524	195	2	0.1	0.1	NUM
ap-3524	195	3	0.2	0.2	NUM
ap-3524	195	4	0.3	0.3	NUM
ap-3524	195	5	0.4	0.4	NUM
ap-3524	195	6	0.5	0.5	NUM
ap-3524	195	7	0.6	0.6	NUM
ap-3524	195	8	0.7	0.7	NUM
ap-3524	195	9	0.1	0.1	NUM
ap-3524	195	10	0.2	0.2	NUM
ap-3524	195	11	0.3	0.3	NUM
ap-3524	195	12	0.4	0.4	NUM
ap-3524	195	13	0.5	0.5	NUM
ap-3524	195	14	0.6	0.6	NUM
ap-3524	195	15	0.7	0.7	NUM
ap-3524	195	16	x	x	SYM
ap-3524	195	17	y	y	NOUN
ap-3524	195	18	0.1	0.1	NUM
ap-3524	195	19	0.2	0.2	NUM
ap-3524	195	20	0.3	0.3	NUM
ap-3524	195	21	0.4	0.4	NUM
ap-3524	195	22	0.5	0.5	NUM
ap-3524	195	23	0.6	0.6	NUM
ap-3524	195	24	0.7	0.7	NUM
ap-3524	195	25	0.1	0.1	NUM
ap-3524	195	26	0.2	0.2	NUM
ap-3524	195	27	0.3	0.3	NUM
ap-3524	195	28	0.4	0.4	NUM
ap-3524	195	29	0.5	0.5	NUM
ap-3524	195	30	0.6	0.6	NUM
ap-3524	195	31	0.7	0.7	NUM
ap-3524	195	32	(	(	PUNCT
ap-3524	195	33	3	3	NUM
ap-3524	195	34	)	)	PUNCT
ap-3524	195	35	(	(	PUNCT
ap-3524	195	36	4	4	X
ap-3524	195	37	)	)	PUNCT
ap-3524	195	38	figure	figure	NOUN
ap-3524	195	39	1	1	NUM
ap-3524	195	40	.	.	PUNCT
ap-3524	195	41	(	(	PUNCT
ap-3524	195	42	1	1	X
ap-3524	195	43	)	)	PUNCT
ap-3524	195	44	orthogonal	orthogonal	ADJ
ap-3524	195	45	lattice	lattice	NOUN
ap-3524	195	46	:	:	PUNCT
ap-3524	195	47	a	a	DET
ap-3524	195	48	=	=	SYM
ap-3524	195	49	0.1	0.1	NUM
ap-3524	195	50	,	,	PUNCT
ap-3524	195	51	b	b	NOUN
ap-3524	195	52	=	=	SYM
ap-3524	195	53	0.1	0.1	NUM
ap-3524	195	54	.	.	PUNCT
ap-3524	196	1	(	(	PUNCT
ap-3524	196	2	2	2	X
ap-3524	196	3	)	)	PUNCT
ap-3524	196	4	exponential	exponential	ADJ
ap-3524	196	5	lattice	lattice	NOUN
ap-3524	196	6	:	:	PUNCT
ap-3524	196	7	a	a	DET
ap-3524	196	8	=	=	SYM
ap-3524	196	9	0.1	0.1	NUM
ap-3524	196	10	,	,	PUNCT
ap-3524	196	11	b	b	NOUN
ap-3524	196	12	=	=	SYM
ap-3524	196	13	0.1	0.1	NUM
ap-3524	196	14	,	,	PUNCT
ap-3524	196	15	c	c	NOUN
ap-3524	196	16	=	=	PUNCT
ap-3524	196	17	0.15	0.15	NUM
ap-3524	196	18	.	.	PUNCT
ap-3524	197	1	(	(	PUNCT
ap-3524	197	2	3	3	X
ap-3524	197	3	)	)	PUNCT
ap-3524	197	4	exponential	exponential	ADJ
ap-3524	197	5	lattice	lattice	NOUN
ap-3524	197	6	:	:	PUNCT
ap-3524	197	7	a	a	DET
ap-3524	197	8	=	=	SYM
ap-3524	197	9	0.0513	0.0513	NUM
ap-3524	197	10	,	,	PUNCT
ap-3524	197	11	b	b	NOUN
ap-3524	197	12	=	=	SYM
ap-3524	197	13	0.1	0.1	NUM
ap-3524	197	14	,	,	PUNCT
ap-3524	197	15	c	c	NOUN
ap-3524	197	16	=	=	SYM
ap-3524	197	17	0.1	0.1	NUM
ap-3524	197	18	.	.	PUNCT
ap-3524	198	1	(	(	PUNCT
ap-3524	198	2	4	4	X
ap-3524	198	3	)	)	PUNCT
ap-3524	198	4	exponential	exponential	ADJ
ap-3524	198	5	lattice	lattice	NOUN
ap-3524	198	6	:	:	PUNCT
ap-3524	198	7	a	a	DET
ap-3524	198	8	=	=	SYM
ap-3524	198	9	0.0375	0.0375	NUM
ap-3524	198	10	,	,	PUNCT
ap-3524	198	11	b	b	NOUN
ap-3524	198	12	=	=	SYM
ap-3524	198	13	0.1	0.1	NUM
ap-3524	198	14	,	,	PUNCT
ap-3524	198	15	c	c	NOUN
ap-3524	198	16	=	=	SYM
ap-3524	198	17	0.15	0.15	NUM
ap-3524	198	18	.	.	PUNCT
ap-3524	199	1	dimension	dimension	NOUN
ap-3524	199	2	:	:	PUNCT
ap-3524	199	3	8	8	NUM
ap-3524	199	4	×	×	NOUN
ap-3524	199	5	8	8	NUM
ap-3524	199	6	points	point	NOUN
ap-3524	199	7	.	.	PUNCT
ap-3524	200	1	χort	χort	NOUN
ap-3524	200	2	χexp	χexp	PROPN
ap-3524	200	3	,	,	PUNCT
ap-3524	200	4	c	c	NOUN
ap-3524	200	5	=	=	SYM
ap-3524	200	6	0.1	0.1	NUM
ap-3524	200	7	χexp	χexp	NOUN
ap-3524	200	8	,	,	PUNCT
ap-3524	200	9	c	c	NOUN
ap-3524	200	10	=	=	SYM
ap-3524	200	11	0.15	0.15	NUM
ap-3524	200	12	f1	f1	NOUN
ap-3524	200	13	(	(	PUNCT
ap-3524	200	14	1	1	NUM
ap-3524	200	15	)	)	PUNCT
ap-3524	200	16	0.01267	0.01267	NUM
ap-3524	200	17	(	(	PUNCT
ap-3524	200	18	5	5	NUM
ap-3524	200	19	)	)	PUNCT
ap-3524	200	20	0.01437	0.01437	NUM
ap-3524	200	21	(	(	PUNCT
ap-3524	200	22	2	2	NUM
ap-3524	200	23	)	)	PUNCT
ap-3524	200	24	0.01651	0.01651	NUM
ap-3524	200	25	(	(	PUNCT
ap-3524	200	26	3	3	X
ap-3524	200	27	)	)	PUNCT
ap-3524	200	28	0.01147	0.01147	NUM
ap-3524	200	29	(	(	PUNCT
ap-3524	200	30	4	4	NUM
ap-3524	200	31	)	)	PUNCT
ap-3524	200	32	0.01408	0.01408	NUM
ap-3524	200	33	f2	f2	PRON
ap-3524	200	34	(	(	PUNCT
ap-3524	200	35	1	1	NUM
ap-3524	200	36	)	)	PUNCT
ap-3524	200	37	0.00249	0.00249	NUM
ap-3524	200	38	(	(	PUNCT
ap-3524	200	39	5	5	NUM
ap-3524	200	40	)	)	PUNCT
ap-3524	200	41	0.00430	0.00430	NUM
ap-3524	200	42	(	(	PUNCT
ap-3524	200	43	2	2	NUM
ap-3524	200	44	)	)	PUNCT
ap-3524	200	45	0.00610	0.00610	NUM
ap-3524	200	46	(	(	PUNCT
ap-3524	200	47	3	3	NUM
ap-3524	200	48	)	)	PUNCT
ap-3524	200	49	0.00642	0.00642	NUM
ap-3524	200	50	(	(	PUNCT
ap-3524	200	51	4	4	NUM
ap-3524	200	52	)	)	PUNCT
ap-3524	200	53	0.00913	0.00913	NUM
ap-3524	200	54	table	table	NOUN
ap-3524	200	55	2	2	NUM
ap-3524	200	56	.	.	X
ap-3524	201	1	χ	χ	DET
ap-3524	201	2	estimator	estimator	NOUN
ap-3524	201	3	values	value	NOUN
ap-3524	201	4	for	for	ADP
ap-3524	201	5	the	the	DET
ap-3524	201	6	functions	function	NOUN
ap-3524	201	7	f1	f1	NOUN
ap-3524	201	8	and	and	CCONJ
ap-3524	201	9	f2	f2	PROPN
ap-3524	201	10	given	give	VERB
ap-3524	201	11	by	by	ADP
ap-3524	201	12	(	(	PUNCT
ap-3524	201	13	34	34	NUM
ap-3524	201	14	)	)	PUNCT
ap-3524	201	15	and	and	CCONJ
ap-3524	201	16	(	(	PUNCT
ap-3524	201	17	35	35	NUM
ap-3524	201	18	)	)	PUNCT
ap-3524	201	19	,	,	PUNCT
ap-3524	201	20	respectively	respectively	ADV
ap-3524	201	21	.	.	PUNCT
ap-3524	202	1	(	(	PUNCT
ap-3524	202	2	1	1	NUM
ap-3524	202	3	):	):	PUNCT
ap-3524	202	4	a	a	DET
ap-3524	202	5	=	=	SYM
ap-3524	202	6	0.1	0.1	NUM
ap-3524	202	7	,	,	PUNCT
ap-3524	202	8	lattice	lattice	NOUN
ap-3524	202	9	(	(	PUNCT
ap-3524	202	10	1	1	NUM
ap-3524	202	11	)	)	PUNCT
ap-3524	202	12	in	in	ADP
ap-3524	202	13	figure	figure	NOUN
ap-3524	202	14	1	1	NUM
ap-3524	202	15	.	.	PUNCT
ap-3524	203	1	(	(	PUNCT
ap-3524	203	2	2	2	NUM
ap-3524	203	3	):	):	PUNCT
ap-3524	203	4	a	a	DET
ap-3524	203	5	=	=	SYM
ap-3524	203	6	0.1	0.1	NUM
ap-3524	203	7	,	,	PUNCT
ap-3524	203	8	lattice	lattice	NOUN
ap-3524	203	9	(	(	PUNCT
ap-3524	203	10	2	2	NUM
ap-3524	203	11	)	)	PUNCT
ap-3524	203	12	in	in	ADP
ap-3524	203	13	figure	figure	NOUN
ap-3524	203	14	1	1	NUM
ap-3524	203	15	.	.	PUNCT
ap-3524	204	1	(	(	PUNCT
ap-3524	204	2	3	3	NUM
ap-3524	204	3	):	):	PUNCT
ap-3524	204	4	a	a	DET
ap-3524	204	5	=	=	SYM
ap-3524	204	6	0.0513	0.0513	NUM
ap-3524	204	7	,	,	PUNCT
ap-3524	204	8	lattice	lattice	NOUN
ap-3524	204	9	(	(	PUNCT
ap-3524	204	10	3	3	NUM
ap-3524	204	11	)	)	PUNCT
ap-3524	204	12	in	in	ADP
ap-3524	204	13	figure	figure	NOUN
ap-3524	204	14	1	1	NUM
ap-3524	204	15	.	.	PUNCT
ap-3524	205	1	(	(	PUNCT
ap-3524	205	2	4	4	NUM
ap-3524	205	3	):	):	PUNCT
ap-3524	205	4	a	a	DET
ap-3524	205	5	=	=	SYM
ap-3524	205	6	0.0375	0.0375	NUM
ap-3524	205	7	,	,	PUNCT
ap-3524	205	8	lattice	lattice	NOUN
ap-3524	205	9	(	(	PUNCT
ap-3524	205	10	4	4	NUM
ap-3524	205	11	)	)	PUNCT
ap-3524	205	12	in	in	ADP
ap-3524	205	13	figure	figure	NOUN
ap-3524	205	14	1	1	NUM
ap-3524	205	15	.	.	PUNCT
ap-3524	206	1	(	(	PUNCT
ap-3524	206	2	5	5	NUM
ap-3524	206	3	):	):	PUNCT
ap-3524	206	4	a	a	DET
ap-3524	206	5	=	=	SYM
ap-3524	206	6	0.1	0.1	NUM
ap-3524	206	7	,	,	PUNCT
ap-3524	206	8	the	the	DET
ap-3524	206	9	exponential	exponential	ADJ
ap-3524	206	10	lattice	lattice	NOUN
ap-3524	206	11	is	be	AUX
ap-3524	206	12	similar	similar	ADJ
ap-3524	206	13	to	to	ADP
ap-3524	206	14	the	the	DET
ap-3524	206	15	lattice	lattice	NOUN
ap-3524	206	16	(	(	PUNCT
ap-3524	206	17	2	2	NUM
ap-3524	206	18	)	)	PUNCT
ap-3524	206	19	in	in	ADP
ap-3524	206	20	figure	figure	NOUN
ap-3524	206	21	1	1	NUM
ap-3524	206	22	.	.	PUNCT
ap-3524	207	1	the	the	DET
ap-3524	207	2	numerical	numerical	ADJ
ap-3524	207	3	calculation	calculation	NOUN
ap-3524	207	4	we	we	PRON
ap-3524	207	5	carried	carry	VERB
ap-3524	207	6	out	out	ADP
ap-3524	207	7	in	in	ADP
ap-3524	207	8	section	section	NOUN
ap-3524	207	9	4	4	NUM
ap-3524	207	10	shows	show	VERB
ap-3524	207	11	that	that	SCONJ
ap-3524	207	12	the	the	DET
ap-3524	207	13	schwarzian	schwarzian	PROPN
ap-3524	207	14	property	property	NOUN
ap-3524	207	15	seems	seem	VERB
ap-3524	207	16	important	important	ADJ
ap-3524	207	17	in	in	ADP
ap-3524	207	18	providing	provide	VERB
ap-3524	207	19	better	well	ADJ
ap-3524	207	20	numerical	numerical	ADJ
ap-3524	207	21	results	result	NOUN
ap-3524	207	22	.	.	PUNCT
ap-3524	208	1	more	more	ADJ
ap-3524	208	2	examples	example	NOUN
ap-3524	208	3	should	should	AUX
ap-3524	208	4	be	be	AUX
ap-3524	208	5	done	do	VERB
ap-3524	208	6	,	,	PUNCT
ap-3524	208	7	both	both	PRON
ap-3524	208	8	to	to	PART
ap-3524	208	9	understand	understand	VERB
ap-3524	208	10	the	the	DET
ap-3524	208	11	stability	stability	NOUN
ap-3524	208	12	of	of	ADP
ap-3524	208	13	the	the	DET
ap-3524	208	14	models	model	NOUN
ap-3524	208	15	we	we	PRON
ap-3524	208	16	construct	construct	VERB
ap-3524	208	17	in	in	ADP
ap-3524	208	18	this	this	DET
ap-3524	208	19	way	way	NOUN
ap-3524	208	20	and	and	CCONJ
ap-3524	208	21	the	the	DET
ap-3524	208	22	analysis	analysis	NOUN
ap-3524	208	23	of	of	ADP
ap-3524	208	24	the	the	DET
ap-3524	208	25	lattices	lattice	NOUN
ap-3524	208	26	in	in	ADP
ap-3524	208	27	the	the	DET
ap-3524	208	28	schwarzian	schwarzian	NOUN
ap-3524	208	29	and	and	CCONJ
ap-3524	208	30	non	non	ADJ
ap-3524	208	31	schwarzian	schwarzian	NOUN
ap-3524	208	32	case	case	NOUN
ap-3524	208	33	.	.	PUNCT
ap-3524	209	1	there	there	PRON
ap-3524	209	2	might	might	AUX
ap-3524	209	3	be	be	AUX
ap-3524	209	4	boundary	boundary	ADJ
ap-3524	209	5	value	value	NOUN
ap-3524	209	6	problems	problem	NOUN
ap-3524	209	7	where	where	SCONJ
ap-3524	209	8	a	a	DET
ap-3524	209	9	non	non	X
ap-3524	209	10	schwarzian	schwarzian	PROPN
ap-3524	209	11	lattice	lattice	PROPN
ap-3524	209	12	adapted	adapt	VERB
ap-3524	209	13	to	to	ADP
ap-3524	209	14	the	the	DET
ap-3524	209	15	geometry	geometry	NOUN
ap-3524	209	16	of	of	ADP
ap-3524	209	17	the	the	DET
ap-3524	209	18	problem	problem	NOUN
ap-3524	209	19	could	could	AUX
ap-3524	209	20	be	be	AUX
ap-3524	209	21	better	well	ADJ
ap-3524	209	22	than	than	ADP
ap-3524	209	23	a	a	DET
ap-3524	209	24	schwarzian	schwarzian	NOUN
ap-3524	209	25	one	one	NUM
ap-3524	209	26	.	.	PUNCT
ap-3524	210	1	acknowledgements	acknowledgement	NOUN
ap-3524	210	2	dl	dl	PROPN
ap-3524	210	3	has	have	AUX
ap-3524	210	4	been	be	AUX
ap-3524	210	5	partly	partly	ADV
ap-3524	210	6	supported	support	VERB
ap-3524	210	7	by	by	ADP
ap-3524	210	8	the	the	DET
ap-3524	210	9	italian	italian	PROPN
ap-3524	210	10	ministry	ministry	PROPN
ap-3524	210	11	of	of	ADP
ap-3524	210	12	education	education	PROPN
ap-3524	210	13	and	and	CCONJ
ap-3524	210	14	research	research	NOUN
ap-3524	210	15	,	,	PUNCT
ap-3524	210	16	2010	2010	NUM
ap-3524	210	17	prin	prin	NOUN
ap-3524	210	18	continuous	continuous	ADJ
ap-3524	210	19	and	and	CCONJ
ap-3524	210	20	discrete	discrete	ADJ
ap-3524	210	21	nonlinear	nonlinear	ADJ
ap-3524	210	22	integrable	integrable	ADJ
ap-3524	210	23	evolutions	evolution	NOUN
ap-3524	210	24	:	:	PUNCT
ap-3524	210	25	from	from	ADP
ap-3524	210	26	water	water	NOUN
ap-3524	210	27	waves	wave	NOUN
ap-3524	210	28	to	to	ADP
ap-3524	210	29	symplectic	symplectic	ADJ
ap-3524	210	30	maps	map	NOUN
ap-3524	210	31	and	and	CCONJ
ap-3524	210	32	by	by	ADP
ap-3524	210	33	infn	infn	PROPN
ap-3524	210	34	is	be	AUX
ap-3524	210	35	-	-	PUNCT
ap-3524	210	36	csn4	csn4	ADJ
ap-3524	210	37	mathematical	mathematical	ADJ
ap-3524	210	38	methods	method	NOUN
ap-3524	210	39	of	of	ADP
ap-3524	210	40	nonlinear	nonlinear	ADJ
ap-3524	210	41	physics	physics	NOUN
ap-3524	210	42	.	.	PUNCT
ap-3524	211	1	dl	dl	PROPN
ap-3524	211	2	thanks	thank	NOUN
ap-3524	211	3	the	the	DET
ap-3524	211	4	departamento	departamento	PROPN
ap-3524	211	5	de	de	PROPN
ap-3524	211	6	física	física	PROPN
ap-3524	211	7	teórica	teórica	PROPN
ap-3524	211	8	ii	ii	PROPN
ap-3524	211	9	of	of	ADP
ap-3524	211	10	the	the	DET
ap-3524	211	11	complutense	complutense	NOUN
ap-3524	211	12	university	university	NOUN
ap-3524	211	13	in	in	ADP
ap-3524	211	14	madrid	madrid	PROPN
ap-3524	211	15	for	for	ADP
ap-3524	211	16	its	its	PRON
ap-3524	211	17	hospitality	hospitality	NOUN
ap-3524	211	18	.	.	PUNCT
ap-3524	212	1	mar	mar	PROPN
ap-3524	212	2	was	be	AUX
ap-3524	212	3	supported	support	VERB
ap-3524	212	4	by	by	ADP
ap-3524	212	5	the	the	DET
ap-3524	212	6	spanish	spanish	ADJ
ap-3524	212	7	mineco	mineco	PROPN
ap-3524	212	8	under	under	ADP
ap-3524	212	9	project	project	NOUN
ap-3524	212	10	fis2015	fis2015	PROPN
ap-3524	212	11	-	-	PUNCT
ap-3524	212	12	63966	63966	NUM
ap-3524	212	13	.	.	PUNCT
ap-3524	213	1	the	the	DET
ap-3524	213	2	authors	author	NOUN
ap-3524	213	3	would	would	AUX
ap-3524	213	4	like	like	VERB
ap-3524	213	5	to	to	PART
ap-3524	213	6	thank	thank	VERB
ap-3524	213	7	the	the	DET
ap-3524	213	8	referees	referee	NOUN
ap-3524	213	9	for	for	ADP
ap-3524	213	10	their	their	PRON
ap-3524	213	11	useful	useful	ADJ
ap-3524	213	12	comments	comment	NOUN
ap-3524	213	13	.	.	PUNCT
ap-3524	214	1	references	reference	NOUN
ap-3524	214	2	[	[	X
ap-3524	214	3	1	1	NUM
ap-3524	214	4	]	]	PUNCT
ap-3524	214	5	bihlo	bihlo	NOUN
ap-3524	214	6	a	a	PRON
ap-3524	214	7	and	and	CCONJ
ap-3524	214	8	nave	nave	PROPN
ap-3524	214	9	j	j	PROPN
ap-3524	214	10	-	-	PROPN
ap-3524	214	11	c	c	PROPN
ap-3524	214	12	2014	2014	NUM
ap-3524	214	13	convecting	convecting	NOUN
ap-3524	214	14	reference	reference	NOUN
ap-3524	214	15	frames	frame	NOUN
ap-3524	214	16	and	and	CCONJ
ap-3524	214	17	invariant	invariant	ADJ
ap-3524	214	18	numerical	numerical	ADJ
ap-3524	214	19	models	model	NOUN
ap-3524	214	20	j.	j.	PROPN
ap-3524	214	21	comput	comput	PROPN
ap-3524	214	22	.	.	PUNCT
ap-3524	215	1	phys	phy	NOUN
ap-3524	215	2	.	.	PUNCT
ap-3524	216	1	272	272	NUM
ap-3524	216	2	656–663	656–663	NUM
ap-3524	216	3	;	;	PUNCT
ap-3524	216	4	doi:10.1016	doi:10.1016	PROPN
ap-3524	216	5	/	/	SYM
ap-3524	217	1	j.jcp.2014.04.042	j.jcp.2014.04.042	NOUN
ap-3524	217	2	[	[	X
ap-3524	217	3	2	2	X
ap-3524	217	4	]	]	PUNCT
ap-3524	217	5	bourlioux	bourlioux	NOUN
ap-3524	217	6	a	a	PROPN
ap-3524	217	7	,	,	PUNCT
ap-3524	217	8	cyr	cyr	PROPN
ap-3524	217	9	-	-	PUNCT
ap-3524	217	10	gagnon	gagnon	PROPN
ap-3524	217	11	c	c	PROPN
ap-3524	217	12	,	,	PUNCT
ap-3524	217	13	and	and	CCONJ
ap-3524	217	14	winternitz	winternitz	VERB
ap-3524	217	15	p	p	ADJ
ap-3524	217	16	2006	2006	NUM
ap-3524	217	17	difference	difference	NOUN
ap-3524	217	18	schemes	scheme	NOUN
ap-3524	217	19	with	with	ADP
ap-3524	217	20	point	point	NOUN
ap-3524	217	21	symmetries	symmetry	NOUN
ap-3524	217	22	and	and	CCONJ
ap-3524	217	23	their	their	PRON
ap-3524	217	24	numerical	numerical	ADJ
ap-3524	217	25	tests	test	NOUN
ap-3524	217	26	j.	j.	PROPN
ap-3524	217	27	phys	phys	PROPN
ap-3524	217	28	.	.	PUNCT
ap-3524	218	1	a	a	DET
ap-3524	218	2	:	:	PUNCT
ap-3524	218	3	math	math	NOUN
ap-3524	218	4	.	.	PUNCT
ap-3524	219	1	gen	gen	PROPN
ap-3524	219	2	.	.	PROPN
ap-3524	219	3	39	39	NUM
ap-3524	219	4	6877–6896	6877–6896	NUM
ap-3524	219	5	;	;	PUNCT
ap-3524	219	6	doi:10.1088/0305	doi:10.1088/0305	ADJ
ap-3524	219	7	-	-	PUNCT
ap-3524	219	8	4470/39/22/006	4470/39/22/006	ADJ
ap-3524	219	9	243	243	NUM
ap-3524	219	10	http://dx.doi.org/10.1016/j.jcp.2014.04.042	http://dx.doi.org/10.1016/j.jcp.2014.04.042	PROPN
ap-3524	219	11	http://dx.doi.org/10.1088/0305-4470/39/22/006	http://dx.doi.org/10.1088/0305-4470/39/22/006	VERB
ap-3524	219	12	decio	decio	NOUN
ap-3524	219	13	levi	levi	PROPN
ap-3524	219	14	,	,	PUNCT
ap-3524	219	15	miguel	miguel	PROPN
ap-3524	219	16	a.	a.	PROPN
ap-3524	219	17	rodríguez	rodríguez	PROPN
ap-3524	219	18	acta	acta	PROPN
ap-3524	219	19	polytechnica	polytechnica	PROPN
ap-3524	220	1	[	[	X
ap-3524	220	2	3	3	X
ap-3524	220	3	]	]	PUNCT
ap-3524	220	4	bourlioux	bourlioux	NOUN
ap-3524	220	5	a	a	PRON
ap-3524	220	6	,	,	PUNCT
ap-3524	220	7	rebelo	rebelo	NOUN
ap-3524	220	8	r	r	NOUN
ap-3524	220	9	,	,	PUNCT
ap-3524	220	10	and	and	CCONJ
ap-3524	220	11	winternitz	winternitz	PROPN
ap-3524	220	12	p	p	PROPN
ap-3524	220	13	2008	2008	NUM
ap-3524	220	14	symmetry	symmetry	NOUN
ap-3524	220	15	preserving	preserve	VERB
ap-3524	220	16	discretization	discretization	NOUN
ap-3524	220	17	of	of	ADP
ap-3524	220	18	sl(2,r	sl(2,r	NOUN
ap-3524	220	19	)	)	PUNCT
ap-3524	220	20	invariant	invariant	ADJ
ap-3524	220	21	equations	equation	NOUN
ap-3524	220	22	j.	j.	PROPN
ap-3524	220	23	nonlinear	nonlinear	PROPN
ap-3524	220	24	math	math	PROPN
ap-3524	220	25	.	.	PUNCT
ap-3524	221	1	phys	phy	NOUN
ap-3524	221	2	.	.	PUNCT
ap-3524	222	1	15	15	NUM
ap-3524	222	2	(	(	PUNCT
ap-3524	222	3	suppl.3	suppl.3	NOUN
ap-3524	222	4	)	)	PUNCT
ap-3524	222	5	362–372	362–372	NUM
ap-3524	222	6	[	[	X
ap-3524	222	7	4	4	NUM
ap-3524	222	8	]	]	PUNCT
ap-3524	222	9	burgers	burger	NOUN
ap-3524	222	10	j	j	PROPN
ap-3524	222	11	m	m	VERB
ap-3524	222	12	1974	1974	NUM
ap-3524	222	13	the	the	DET
ap-3524	222	14	nonlinear	nonlinear	ADJ
ap-3524	222	15	diffusion	diffusion	NOUN
ap-3524	222	16	equation	equation	NOUN
ap-3524	222	17	,	,	PUNCT
ap-3524	222	18	asymptotic	asymptotic	ADJ
ap-3524	222	19	solutions	solution	NOUN
ap-3524	222	20	and	and	CCONJ
ap-3524	222	21	statistical	statistical	ADJ
ap-3524	222	22	problems	problem	NOUN
ap-3524	222	23	,	,	PUNCT
ap-3524	222	24	springer	springer	NOUN
ap-3524	222	25	,	,	PUNCT
ap-3524	222	26	dordrecht	dordrecht	PROPN
ap-3524	222	27	.	.	PUNCT
ap-3524	223	1	[	[	X
ap-3524	223	2	5	5	NUM
ap-3524	223	3	]	]	PUNCT
ap-3524	223	4	chhay	chhay	NOUN
ap-3524	223	5	m	m	PROPN
ap-3524	223	6	and	and	CCONJ
ap-3524	223	7	hamdouni	hamdouni	PROPN
ap-3524	223	8	a	a	DET
ap-3524	223	9	2010	2010	NUM
ap-3524	223	10	a	a	DET
ap-3524	223	11	new	new	ADJ
ap-3524	223	12	construction	construction	NOUN
ap-3524	223	13	for	for	ADP
ap-3524	223	14	invariant	invariant	ADJ
ap-3524	223	15	numerical	numerical	ADJ
ap-3524	223	16	schemes	scheme	NOUN
ap-3524	223	17	using	use	VERB
ap-3524	223	18	moving	moving	NOUN
ap-3524	223	19	frames	frame	NOUN
ap-3524	223	20	c.r	c.r	PROPN
ap-3524	223	21	.	.	PUNCT
ap-3524	224	1	mecanique	mecanique	PROPN
ap-3524	224	2	338	338	NUM
ap-3524	224	3	97–101	97–101	NUM
ap-3524	224	4	;	;	PUNCT
ap-3524	224	5	doi:10.1016	doi:10.1016	PROPN
ap-3524	224	6	/	/	SYM
ap-3524	224	7	j.crme.2010.01.001	j.crme.2010.01.001	PROPN
ap-3524	225	1	[	[	X
ap-3524	225	2	6	6	NUM
ap-3524	225	3	]	]	PUNCT
ap-3524	225	4	dorodnitsyn	dorodnitsyn	PROPN
ap-3524	225	5	v	v	ADP
ap-3524	225	6	a	a	DET
ap-3524	225	7	1991	1991	NUM
ap-3524	225	8	transformation	transformation	NOUN
ap-3524	225	9	groups	group	NOUN
ap-3524	225	10	in	in	ADP
ap-3524	225	11	difference	difference	NOUN
ap-3524	225	12	spaces	space	NOUN
ap-3524	225	13	,	,	PUNCT
ap-3524	225	14	j.	j.	PROPN
ap-3524	225	15	soviet	soviet	PROPN
ap-3524	225	16	math	math	PROPN
ap-3524	225	17	.	.	PUNCT
ap-3524	226	1	55	55	NUM
ap-3524	226	2	1490–1517	1490–1517	NUM
ap-3524	226	3	[	[	X
ap-3524	226	4	7	7	NUM
ap-3524	226	5	]	]	X
ap-3524	226	6	dorodnitsyn	dorodnitsyn	NOUN
ap-3524	226	7	v	v	ADP
ap-3524	226	8	a	a	DET
ap-3524	226	9	2011	2011	NUM
ap-3524	226	10	applications	application	NOUN
ap-3524	226	11	of	of	ADP
ap-3524	226	12	lie	lie	NOUN
ap-3524	226	13	groups	group	NOUN
ap-3524	226	14	to	to	ADP
ap-3524	226	15	difference	difference	NOUN
ap-3524	226	16	equations	equation	NOUN
ap-3524	226	17	,	,	PUNCT
ap-3524	226	18	crc	crc	NOUN
ap-3524	226	19	press	press	PROPN
ap-3524	226	20	,	,	PUNCT
ap-3524	226	21	boca	boca	PROPN
ap-3524	226	22	raton	raton	PROPN
ap-3524	227	1	[	[	X
ap-3524	227	2	8	8	NUM
ap-3524	227	3	]	]	X
ap-3524	227	4	dorodnitsyn	dorodnitsyn	PROPN
ap-3524	227	5	v	v	ADP
ap-3524	227	6	a	a	PRON
ap-3524	227	7	and	and	CCONJ
ap-3524	227	8	winternitz	winternitz	PROPN
ap-3524	227	9	p	p	PROPN
ap-3524	227	10	2000	2000	NUM
ap-3524	227	11	lie	lie	NOUN
ap-3524	227	12	point	point	NOUN
ap-3524	227	13	symmetry	symmetry	NOUN
ap-3524	227	14	preserving	preserve	VERB
ap-3524	227	15	discretizations	discretization	NOUN
ap-3524	227	16	for	for	ADP
ap-3524	227	17	variable	variable	ADJ
ap-3524	227	18	coefficient	coefficient	NOUN
ap-3524	227	19	korteweg	korteweg	NOUN
ap-3524	227	20	-	-	PUNCT
ap-3524	227	21	de	de	PROPN
ap-3524	227	22	vries	vries	PROPN
ap-3524	227	23	equations	equation	NOUN
ap-3524	227	24	nonlinear	nonlinear	ADJ
ap-3524	227	25	dynamics	dynamic	NOUN
ap-3524	227	26	22	22	NUM
ap-3524	227	27	49–59	49–59	NOUN
ap-3524	228	1	[	[	X
ap-3524	228	2	9	9	NUM
ap-3524	228	3	]	]	X
ap-3524	228	4	kim	kim	PROPN
ap-3524	228	5	p	p	PROPN
ap-3524	228	6	and	and	CCONJ
ap-3524	228	7	olver	olver	NOUN
ap-3524	228	8	p	p	PROPN
ap-3524	228	9	j	j	PROPN
ap-3524	228	10	2004	2004	NUM
ap-3524	228	11	geometric	geometric	ADJ
ap-3524	228	12	integration	integration	NOUN
ap-3524	228	13	via	via	ADP
ap-3524	228	14	multi	multi	ADJ
ap-3524	228	15	-	-	ADJ
ap-3524	228	16	space	space	ADJ
ap-3524	228	17	regular	regular	ADJ
ap-3524	228	18	and	and	CCONJ
ap-3524	228	19	chaotic	chaotic	ADJ
ap-3524	228	20	dynamics	dynamic	NOUN
ap-3524	228	21	9	9	NUM
ap-3524	228	22	213–226	213–226	NUM
ap-3524	228	23	[	[	PUNCT
ap-3524	228	24	10	10	NUM
ap-3524	228	25	]	]	X
ap-3524	228	26	kim	kim	PROPN
ap-3524	228	27	p	p	PROPN
ap-3524	228	28	2008	2008	NUM
ap-3524	228	29	invariantization	invariantization	NOUN
ap-3524	228	30	of	of	ADP
ap-3524	228	31	the	the	DET
ap-3524	228	32	crank	crank	NOUN
ap-3524	228	33	-	-	PUNCT
ap-3524	228	34	nicolson	nicolson	PROPN
ap-3524	228	35	method	method	NOUN
ap-3524	228	36	for	for	ADP
ap-3524	228	37	burgers	burger	NOUN
ap-3524	228	38	’	'	PUNCT
ap-3524	228	39	equation	equation	NOUN
ap-3524	228	40	physica	physica	NOUN
ap-3524	228	41	d	d	PROPN
ap-3524	228	42	237	237	NUM
ap-3524	228	43	243–254	243–254	NUM
ap-3524	228	44	;	;	PUNCT
ap-3524	228	45	doi:10.1016	doi:10.1016	PROPN
ap-3524	228	46	/	/	SYM
ap-3524	228	47	j.physd.2007.09.001	j.physd.2007.09.001	PROPN
ap-3524	229	1	[	[	X
ap-3524	229	2	11	11	NUM
ap-3524	229	3	]	]	X
ap-3524	229	4	levi	levi	PROPN
ap-3524	229	5	d	d	PROPN
ap-3524	229	6	,	,	PUNCT
ap-3524	229	7	olver	olver	NOUN
ap-3524	229	8	p	p	X
ap-3524	229	9	,	,	PUNCT
ap-3524	229	10	thomova	thomova	X
ap-3524	229	11	z	z	NOUN
ap-3524	229	12	and	and	CCONJ
ap-3524	229	13	winternitz	winternitz	PROPN
ap-3524	229	14	p	p	PROPN
ap-3524	229	15	(	(	PUNCT
ap-3524	229	16	editors	editor	NOUN
ap-3524	229	17	)	)	PUNCT
ap-3524	229	18	2011	2011	NUM
ap-3524	229	19	symmetries	symmetry	NOUN
ap-3524	229	20	and	and	CCONJ
ap-3524	229	21	integrability	integrability	NOUN
ap-3524	229	22	of	of	ADP
ap-3524	229	23	difference	difference	NOUN
ap-3524	229	24	equations	equation	NOUN
ap-3524	229	25	,	,	PUNCT
ap-3524	229	26	cup	cup	NOUN
ap-3524	229	27	,	,	PUNCT
ap-3524	229	28	lms	lm	NOUN
ap-3524	229	29	lecture	lecture	NOUN
ap-3524	229	30	series	series	NOUN
ap-3524	229	31	.	.	PUNCT
ap-3524	230	1	[	[	X
ap-3524	230	2	12	12	NUM
ap-3524	230	3	]	]	X
ap-3524	230	4	levi	levi	PROPN
ap-3524	230	5	d	d	PROPN
ap-3524	230	6	,	,	PUNCT
ap-3524	230	7	scimiterna	scimiterna	VERB
ap-3524	230	8	c	c	NOUN
ap-3524	230	9	,	,	PUNCT
ap-3524	230	10	thomova	thomova	X
ap-3524	230	11	z	z	NOUN
ap-3524	230	12	and	and	CCONJ
ap-3524	230	13	winternitz	winternitz	PROPN
ap-3524	230	14	p	p	PROPN
ap-3524	230	15	2012	2012	NUM
ap-3524	230	16	contact	contact	NOUN
ap-3524	230	17	transformations	transformation	NOUN
ap-3524	230	18	for	for	ADP
ap-3524	230	19	difference	difference	NOUN
ap-3524	230	20	schemes	scheme	NOUN
ap-3524	230	21	j.	j.	PROPN
ap-3524	230	22	phys	phys	PROPN
ap-3524	230	23	.	.	PUNCT
ap-3524	231	1	a	a	DET
ap-3524	231	2	:	:	PUNCT
ap-3524	231	3	math	math	NOUN
ap-3524	231	4	.	.	PUNCT
ap-3524	232	1	theor	theor	PROPN
ap-3524	232	2	.	.	PUNCT
ap-3524	233	1	45	45	NUM
ap-3524	233	2	022001	022001	NUM
ap-3524	233	3	;	;	PUNCT
ap-3524	233	4	doi:10.1088/1751	doi:10.1088/1751	ADV
ap-3524	233	5	-	-	PUNCT
ap-3524	233	6	8113/45/2/022001	8113/45/2/022001	NUM
ap-3524	234	1	[	[	PUNCT
ap-3524	234	2	13	13	NUM
ap-3524	234	3	]	]	X
ap-3524	234	4	levi	levi	PROPN
ap-3524	234	5	d	d	PROPN
ap-3524	234	6	,	,	PUNCT
ap-3524	234	7	thomova	thomova	PROPN
ap-3524	234	8	z	z	NOUN
ap-3524	234	9	and	and	CCONJ
ap-3524	234	10	winternitz	winternitz	PROPN
ap-3524	234	11	p	p	PROPN
ap-3524	234	12	2011	2011	NUM
ap-3524	234	13	are	be	AUX
ap-3524	234	14	there	there	PRON
ap-3524	234	15	contact	contact	NOUN
ap-3524	234	16	transformations	transformation	NOUN
ap-3524	234	17	for	for	ADP
ap-3524	234	18	discrete	discrete	ADJ
ap-3524	234	19	equations	equation	NOUN
ap-3524	234	20	?	?	PUNCT
ap-3524	235	1	j.	j.	PROPN
ap-3524	235	2	phys	phys	PROPN
ap-3524	235	3	.	.	PUNCT
ap-3524	236	1	a	a	DET
ap-3524	236	2	:	:	PUNCT
ap-3524	236	3	math	math	NOUN
ap-3524	236	4	.	.	PUNCT
ap-3524	237	1	theor	theor	PROPN
ap-3524	237	2	.	.	PUNCT
ap-3524	238	1	44	44	NUM
ap-3524	238	2	265201	265201	NUM
ap-3524	238	3	;	;	PUNCT
ap-3524	238	4	doi:10.1088/1751	doi:10.1088/1751	ADV
ap-3524	238	5	-	-	PUNCT
ap-3524	238	6	8113/44/26/265201	8113/44/26/265201	VERB
ap-3524	238	7	[	[	X
ap-3524	238	8	14	14	NUM
ap-3524	238	9	]	]	X
ap-3524	238	10	levi	levi	PROPN
ap-3524	238	11	d	d	PROPN
ap-3524	238	12	and	and	CCONJ
ap-3524	238	13	rodríguez	rodríguez	VERB
ap-3524	238	14	m	m	PROPN
ap-3524	238	15	a	a	DET
ap-3524	238	16	2013	2013	NUM
ap-3524	238	17	on	on	ADP
ap-3524	238	18	the	the	DET
ap-3524	238	19	construction	construction	NOUN
ap-3524	238	20	of	of	ADP
ap-3524	238	21	partial	partial	ADJ
ap-3524	238	22	difference	difference	NOUN
ap-3524	238	23	schemes	scheme	NOUN
ap-3524	239	1	i	i	PRON
ap-3524	239	2	:	:	PUNCT
ap-3524	239	3	the	the	DET
ap-3524	239	4	clairaut	clairaut	NOUN
ap-3524	239	5	,	,	PUNCT
ap-3524	239	6	schwarz	schwarz	PROPN
ap-3524	239	7	,	,	PUNCT
ap-3524	239	8	young	young	ADJ
ap-3524	239	9	theorem	theorem	NOUN
ap-3524	239	10	on	on	ADP
ap-3524	239	11	the	the	DET
ap-3524	239	12	lattice	lattice	NOUN
ap-3524	239	13	,	,	PUNCT
ap-3524	239	14	j.	j.	PROPN
ap-3524	239	15	phys	phys	PROPN
ap-3524	239	16	.	.	PUNCT
ap-3524	240	1	a	a	DET
ap-3524	240	2	:	:	PUNCT
ap-3524	240	3	math	math	NOUN
ap-3524	240	4	.	.	PUNCT
ap-3524	241	1	theor	theor	PROPN
ap-3524	241	2	.	.	PUNCT
ap-3524	242	1	46	46	NUM
ap-3524	242	2	295203	295203	NUM
ap-3524	242	3	;	;	PUNCT
ap-3524	242	4	doi:10.1088/1751	doi:10.1088/1751	ADV
ap-3524	242	5	-	-	PUNCT
ap-3524	242	6	8113/46/29/295203	8113/46/29/295203	NOUN
ap-3524	242	7	[	[	X
ap-3524	242	8	15	15	NUM
ap-3524	242	9	]	]	X
ap-3524	242	10	levi	levi	PROPN
ap-3524	242	11	d	d	PROPN
ap-3524	242	12	and	and	CCONJ
ap-3524	242	13	winternitz	winternitz	PROPN
ap-3524	242	14	p	p	NOUN
ap-3524	242	15	1991	1991	NUM
ap-3524	242	16	continuous	continuous	ADJ
ap-3524	242	17	symmetries	symmetry	NOUN
ap-3524	242	18	of	of	ADP
ap-3524	242	19	discrete	discrete	ADJ
ap-3524	242	20	equations	equation	NOUN
ap-3524	242	21	,	,	PUNCT
ap-3524	242	22	phys	phy	NOUN
ap-3524	242	23	.	.	PUNCT
ap-3524	243	1	lett	lett	PROPN
ap-3524	243	2	.	.	PUNCT
ap-3524	244	1	a	a	DET
ap-3524	244	2	152	152	NUM
ap-3524	244	3	335–338	335–338	NUM
ap-3524	244	4	;	;	PUNCT
ap-3524	244	5	doi:10.1016/0375	doi:10.1016/0375	ADJ
ap-3524	244	6	-	-	PUNCT
ap-3524	244	7	9601(91)90733	9601(91)90733	NUM
ap-3524	244	8	-	-	PUNCT
ap-3524	244	9	o	o	NOUN
ap-3524	245	1	[	[	X
ap-3524	245	2	16	16	NUM
ap-3524	245	3	]	]	X
ap-3524	245	4	levi	levi	PROPN
ap-3524	245	5	d	d	PROPN
ap-3524	245	6	and	and	CCONJ
ap-3524	245	7	winternitz	winternitz	PROPN
ap-3524	245	8	p	p	PROPN
ap-3524	245	9	1996	1996	NUM
ap-3524	245	10	symmetries	symmetry	NOUN
ap-3524	245	11	of	of	ADP
ap-3524	245	12	discrete	discrete	ADJ
ap-3524	245	13	dynamical	dynamical	ADJ
ap-3524	245	14	systems	system	NOUN
ap-3524	245	15	.	.	PUNCT
ap-3524	246	1	j.math	j.math	NOUN
ap-3524	246	2	.	.	PUNCT
ap-3524	247	1	phys	phy	NOUN
ap-3524	247	2	.	.	PUNCT
ap-3524	248	1	37	37	NUM
ap-3524	248	2	5551–5576	5551–5576	NUM
ap-3524	248	3	;	;	PUNCT
ap-3524	248	4	doi:10.1063/1.531722	doi:10.1063/1.531722	PROPN
ap-3524	248	5	[	[	X
ap-3524	248	6	17	17	NUM
ap-3524	248	7	]	]	X
ap-3524	248	8	levi	levi	PROPN
ap-3524	248	9	d	d	PROPN
ap-3524	248	10	and	and	CCONJ
ap-3524	248	11	winternitz	winternitz	PROPN
ap-3524	248	12	p	p	PROPN
ap-3524	248	13	2006	2006	NUM
ap-3524	248	14	continuous	continuous	ADJ
ap-3524	248	15	symmetries	symmetry	NOUN
ap-3524	248	16	of	of	ADP
ap-3524	248	17	difference	difference	NOUN
ap-3524	248	18	equations	equation	NOUN
ap-3524	248	19	j.	j.	PROPN
ap-3524	248	20	phys	phys	PROPN
ap-3524	248	21	.	.	PUNCT
ap-3524	249	1	a	a	DET
ap-3524	249	2	:	:	PUNCT
ap-3524	249	3	math	math	NOUN
ap-3524	249	4	.	.	PUNCT
ap-3524	250	1	gen	gen	PROPN
ap-3524	250	2	.	.	PROPN
ap-3524	250	3	39	39	NUM
ap-3524	250	4	r1	r1	NOUN
ap-3524	250	5	;	;	PUNCT
ap-3524	250	6	doi:10.1088/0305	doi:10.1088/0305	ADJ
ap-3524	250	7	-	-	PUNCT
ap-3524	250	8	4470/39/2	4470/39/2	NUM
ap-3524	250	9	/	/	SYM
ap-3524	250	10	r01	r01	PROPN
ap-3524	251	1	[	[	X
ap-3524	251	2	18	18	NUM
ap-3524	251	3	]	]	X
ap-3524	251	4	olver	olver	NOUN
ap-3524	251	5	p	p	X
ap-3524	251	6	j	j	PROPN
ap-3524	251	7	1993	1993	NUM
ap-3524	251	8	applications	application	NOUN
ap-3524	251	9	of	of	ADP
ap-3524	251	10	lie	lie	NOUN
ap-3524	251	11	groups	group	NOUN
ap-3524	251	12	to	to	PART
ap-3524	251	13	differential	differential	VERB
ap-3524	251	14	equations	equation	NOUN
ap-3524	251	15	,	,	PUNCT
ap-3524	251	16	springer	springer	NOUN
ap-3524	251	17	-	-	PUNCT
ap-3524	251	18	verlag	verlag	PROPN
ap-3524	251	19	,	,	PUNCT
ap-3524	251	20	new	new	PROPN
ap-3524	251	21	york	york	PROPN
ap-3524	251	22	[	[	X
ap-3524	251	23	19	19	NUM
ap-3524	251	24	]	]	X
ap-3524	251	25	rebelo	rebelo	NOUN
ap-3524	251	26	r	r	NOUN
ap-3524	251	27	and	and	CCONJ
ap-3524	251	28	valiquette	valiquette	PROPN
ap-3524	251	29	f	f	PROPN
ap-3524	251	30	2013	2013	NUM
ap-3524	251	31	symmetry	symmetry	NOUN
ap-3524	251	32	preserving	preserve	VERB
ap-3524	251	33	numerical	numerical	ADJ
ap-3524	251	34	schemes	scheme	NOUN
ap-3524	251	35	for	for	ADP
ap-3524	251	36	partial	partial	ADJ
ap-3524	251	37	differential	differential	ADJ
ap-3524	251	38	equations	equation	NOUN
ap-3524	251	39	and	and	CCONJ
ap-3524	251	40	their	their	PRON
ap-3524	251	41	numerical	numerical	ADJ
ap-3524	251	42	tests	test	NOUN
ap-3524	251	43	j.	j.	PROPN
ap-3524	251	44	difference	difference	PROPN
ap-3524	251	45	eq	eq	ADP
ap-3524	251	46	.	.	PROPN
ap-3524	251	47	appl	appl	PROPN
ap-3524	251	48	.	.	PROPN
ap-3524	252	1	19	19	NUM
ap-3524	252	2	737–757	737–757	PROPN
ap-3524	252	3	;	;	PUNCT
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ap-3524	254	1	[	[	X
ap-3524	254	2	20	20	NUM
ap-3524	254	3	]	]	PUNCT
ap-3524	254	4	rebelo	rebelo	NOUN
ap-3524	254	5	r	r	NOUN
ap-3524	254	6	and	and	CCONJ
ap-3524	254	7	valiquette	valiquette	PROPN
ap-3524	254	8	f	f	PROPN
ap-3524	254	9	2015	2015	NUM
ap-3524	254	10	invariant	invariant	ADJ
ap-3524	254	11	discretization	discretization	NOUN
ap-3524	254	12	of	of	ADP
ap-3524	254	13	partial	partial	ADJ
ap-3524	254	14	differential	differential	ADJ
ap-3524	254	15	equations	equation	NOUN
ap-3524	254	16	admitting	admit	VERB
ap-3524	254	17	infinite	infinite	ADJ
ap-3524	254	18	-	-	PUNCT
ap-3524	254	19	dimensional	dimensional	ADJ
ap-3524	254	20	symmetry	symmetry	NOUN
ap-3524	254	21	groups	group	NOUN
ap-3524	254	22	j.	j.	PROPN
ap-3524	254	23	difference	difference	PROPN
ap-3524	254	24	eq	eq	ADP
ap-3524	254	25	.	.	PROPN
ap-3524	254	26	appl	appl	PROPN
ap-3524	254	27	.	.	PUNCT
ap-3524	255	1	bf	bf	NOUN
ap-3524	255	2	21	21	NUM
ap-3524	255	3	285–318	285–318	NUM
ap-3524	255	4	;	;	PUNCT
ap-3524	256	1	doi:10.1080/10236198.2015.1007134	doi:10.1080/10236198.2015.1007134	PROPN
ap-3524	257	1	[	[	X
ap-3524	257	2	21	21	NUM
ap-3524	257	3	]	]	PUNCT
ap-3524	257	4	rebelo	rebelo	NOUN
ap-3524	257	5	r	r	NOUN
ap-3524	257	6	and	and	CCONJ
ap-3524	257	7	winternitz	winternitz	PROPN
ap-3524	257	8	p	p	PROPN
ap-3524	257	9	2009	2009	NUM
ap-3524	257	10	invariant	invariant	ADJ
ap-3524	257	11	difference	difference	NOUN
ap-3524	257	12	schemes	scheme	NOUN
ap-3524	257	13	and	and	CCONJ
ap-3524	257	14	their	their	PRON
ap-3524	257	15	applications	application	NOUN
ap-3524	257	16	to	to	PART
ap-3524	257	17	sl(2,r	sl(2,r	VERB
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ap-3524	257	19	invariant	invariant	ADJ
ap-3524	257	20	differential	differential	ADJ
ap-3524	257	21	equations	equation	NOUN
ap-3524	257	22	j.	j.	PROPN
ap-3524	257	23	phys	phys	PROPN
ap-3524	257	24	.	.	PUNCT
ap-3524	258	1	a	a	PRON
ap-3524	258	2	:	:	PUNCT
ap-3524	259	1	math.theor	math.theor	PROPN
ap-3524	259	2	.	.	PROPN
ap-3524	259	3	42	42	NUM
ap-3524	259	4	454016	454016	NUM
ap-3524	259	5	;	;	PUNCT
ap-3524	259	6	doi:10.1088/1751	doi:10.1088/1751	PROPN
ap-3524	259	7	-	-	PUNCT
ap-3524	259	8	8113/42/45/454016	8113/42/45/454016	NUM
ap-3524	259	9	[	[	X
ap-3524	259	10	22	22	NUM
ap-3524	259	11	]	]	X
ap-3524	259	12	winternitz	winternitz	NOUN
ap-3524	259	13	p	p	PROPN
ap-3524	259	14	2004	2004	NUM
ap-3524	259	15	symmetries	symmetry	NOUN
ap-3524	259	16	of	of	ADP
ap-3524	259	17	discrete	discrete	ADJ
ap-3524	259	18	systems	system	NOUN
ap-3524	259	19	.	.	PUNCT
ap-3524	260	1	discrete	discrete	VERB
ap-3524	260	2	integrable	integrable	ADJ
ap-3524	260	3	systems	system	NOUN
ap-3524	260	4	,	,	PUNCT
ap-3524	260	5	vol	vol	NOUN
ap-3524	260	6	.	.	PROPN
ap-3524	260	7	644	644	NUM
ap-3524	260	8	,	,	PUNCT
ap-3524	260	9	lecture	lecture	NOUN
ap-3524	260	10	notes	note	NOUN
ap-3524	260	11	in	in	ADP
ap-3524	260	12	physics	physics	NOUN
ap-3524	260	13	.	.	PUNCT
ap-3524	261	1	ed	ed	PROPN
ap-3524	261	2	b	b	PROPN
ap-3524	261	3	grammaticos	grammaticos	PROPN
ap-3524	261	4	,	,	PUNCT
ap-3524	261	5	y	y	PROPN
ap-3524	261	6	kosmann	kosmann	PROPN
ap-3524	261	7	-	-	PUNCT
ap-3524	261	8	schwarzbach	schwarzbach	NOUN
ap-3524	261	9	,	,	PUNCT
ap-3524	261	10	and	and	CCONJ
ap-3524	261	11	t	t	PROPN
ap-3524	261	12	tamizhmani	tamizhmani	NOUN
ap-3524	261	13	(	(	PUNCT
ap-3524	261	14	berlin	berlin	PROPN
ap-3524	261	15	,	,	PUNCT
ap-3524	261	16	springer	springer	NOUN
ap-3524	261	17	verlag	verlag	PROPN
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ap-3524	261	19	pp	pp	ADP
ap-3524	261	20	185–243	185–243	NUM
ap-3524	261	21	.	.	PUNCT
ap-3524	262	1	see	see	VERB
ap-3524	262	2	also	also	ADV
ap-3524	262	3	arxiv	arxiv	NOUN
ap-3524	262	4	:	:	PUNCT
ap-3524	262	5	nlin.si/0309058	nlin.si/0309058	NOUN
ap-3524	262	6	[	[	X
ap-3524	262	7	23	23	NUM
ap-3524	262	8	]	]	X
ap-3524	262	9	winternitz	winternitz	PROPN
ap-3524	262	10	p	p	PROPN
ap-3524	262	11	2011	2011	NUM
ap-3524	262	12	symmetry	symmetry	NOUN
ap-3524	262	13	preserving	preserve	VERB
ap-3524	262	14	discretization	discretization	NOUN
ap-3524	262	15	of	of	ADP
ap-3524	262	16	differential	differential	ADJ
ap-3524	262	17	equations	equation	NOUN
ap-3524	262	18	and	and	CCONJ
ap-3524	262	19	lie	lie	VERB
ap-3524	262	20	point	point	NOUN
ap-3524	262	21	symmetries	symmetry	NOUN
ap-3524	262	22	of	of	ADP
ap-3524	262	23	differential	differential	ADJ
ap-3524	262	24	-	-	PUNCT
ap-3524	262	25	difference	difference	NOUN
ap-3524	262	26	equations	equation	NOUN
ap-3524	262	27	.	.	PUNCT
ap-3524	263	1	symmetries	symmetry	NOUN
ap-3524	263	2	and	and	CCONJ
ap-3524	263	3	integrability	integrability	NOUN
ap-3524	263	4	of	of	ADP
ap-3524	263	5	difference	difference	NOUN
ap-3524	263	6	equations	equation	NOUN
ap-3524	263	7	.	.	PUNCT
ap-3524	264	1	lms	lm	NOUN
ap-3524	264	2	lecture	lecture	NOUN
ap-3524	264	3	series	series	NOUN
ap-3524	264	4	.	.	PUNCT
ap-3524	265	1	ed	ed	PROPN
ap-3524	266	1	d	d	PROPN
ap-3524	266	2	levi	levi	PROPN
ap-3524	266	3	,	,	PUNCT
ap-3524	266	4	p	p	PROPN
ap-3524	266	5	j	j	PROPN
ap-3524	266	6	olver	olver	ADV
ap-3524	266	7	,	,	PUNCT
ap-3524	266	8	z	z	NOUN
ap-3524	266	9	thomova	thomova	NOUN
ap-3524	266	10	and	and	CCONJ
ap-3524	266	11	p	p	X
ap-3524	266	12	winternitz	winternitz	NOUN
ap-3524	266	13	.	.	PUNCT
ap-3524	267	1	244	244	NUM
ap-3524	267	2	http://dx.doi.org/10.1016/j.crme.2010.01.001	http://dx.doi.org/10.1016/j.crme.2010.01.001	NOUN
ap-3524	267	3	http://dx.doi.org/10.1016/j.physd.2007.09.001	http://dx.doi.org/10.1016/j.physd.2007.09.001	PROPN
ap-3524	267	4	http://dx.doi.org/10.1088/1751-8113/45/2/022001	http://dx.doi.org/10.1088/1751-8113/45/2/022001	PROPN
ap-3524	267	5	http://dx.doi.org/10.1088/1751-8113/44/26/265201	http://dx.doi.org/10.1088/1751-8113/44/26/265201	ADJ
ap-3524	267	6	http://dx.doi.org/10.1088/1751-8113/46/29/295203	http://dx.doi.org/10.1088/1751-8113/46/29/295203	X
ap-3524	267	7	http://dx.doi.org/10.1016/0375-9601(91)90733-o	http://dx.doi.org/10.1016/0375-9601(91)90733-o	NOUN
ap-3524	267	8	http://dx.doi.org/10.1063/1.531722	http://dx.doi.org/10.1063/1.531722	NOUN
ap-3524	267	9	http://dx.doi.org/10.1088/0305-4470/39/2/r01	http://dx.doi.org/10.1088/0305-4470/39/2/r01	ADJ
ap-3524	267	10	http://dx.doi.org/10.1080/10236198.2012.685470	http://dx.doi.org/10.1080/10236198.2012.685470	NOUN
ap-3524	267	11	http://dx.doi.org/10.1080/10236198.2015.1007134	http://dx.doi.org/10.1080/10236198.2015.1007134	NOUN
ap-3524	267	12	http://dx.doi.org/10.1088/1751-8113/42/45/454016	http://dx.doi.org/10.1088/1751-8113/42/45/454016	PRON
ap-3524	267	13	http://arxiv.org/abs/nlin.si/0309058	http://arxiv.org/abs/nlin.si/0309058	PROPN
ap-3524	267	14	acta	acta	PROPN
ap-3524	267	15	polytechnica	polytechnica	PROPN
ap-3524	267	16	56(3):236–244	56(3):236–244	PROPN
ap-3524	267	17	,	,	PUNCT
ap-3524	267	18	2016	2016	NUM
ap-3524	267	19	1	1	NUM
ap-3524	267	20	introduction	introduction	NOUN
ap-3524	267	21	2	2	NUM
ap-3524	267	22	schemes	scheme	NOUN
ap-3524	267	23	for	for	ADP
ap-3524	267	24	partial	partial	ADJ
ap-3524	267	25	difference	difference	NOUN
ap-3524	267	26	equations	equation	NOUN
ap-3524	267	27	3	3	NUM
ap-3524	267	28	example	example	NOUN
ap-3524	267	29	:	:	PUNCT
ap-3524	267	30	the	the	DET
ap-3524	267	31	potential	potential	ADJ
ap-3524	267	32	burgers	burger	NOUN
ap-3524	267	33	equation	equation	NOUN
ap-3524	267	34	4	4	NUM
ap-3524	267	35	numerical	numerical	ADJ
ap-3524	267	36	calculation	calculation	NOUN
ap-3524	267	37	results	result	NOUN
ap-3524	267	38	for	for	ADP
ap-3524	267	39	the	the	DET
ap-3524	267	40	discrete	discrete	ADJ
ap-3524	267	41	potential	potential	ADJ
ap-3524	267	42	burgers	burger	NOUN
ap-3524	267	43	equation	equation	NOUN
ap-3524	267	44	5	5	NUM
ap-3524	267	45	conclusions	conclusion	NOUN
ap-3524	267	46	acknowledgements	acknowledgement	NOUN
ap-3524	267	47	references	reference	NOUN