id	sid	tid	token	lemma	pos
ap-1362	1	1	wykresx.eps	wykresx.eps	X
ap-1362	1	2	acta	acta	PROPN
ap-1362	1	3	polytechnica	polytechnica	PROPN
ap-1362	1	4	vol	vol	NOUN
ap-1362	1	5	.	.	PUNCT
ap-1362	2	1	51	51	NUM
ap-1362	2	2	no	no	NOUN
ap-1362	2	3	.	.	PUNCT
ap-1362	3	1	1/2011	1/2011	NUM
ap-1362	3	2	infinitesimal	infinitesimal	ADJ
ap-1362	3	3	algebraic	algebraic	ADJ
ap-1362	3	4	skeletons	skeleton	NOUN
ap-1362	3	5	for	for	ADP
ap-1362	3	6	a	a	DET
ap-1362	3	7	(	(	PUNCT
ap-1362	3	8	2	2	NUM
ap-1362	3	9	+	+	NUM
ap-1362	3	10	1)-dimensional	1)-dimensional	NUM
ap-1362	3	11	toda	toda	NOUN
ap-1362	3	12	type	type	NOUN
ap-1362	3	13	system	system	NOUN
ap-1362	3	14	m.	m.	NOUN
ap-1362	3	15	palese	palese	PROPN
ap-1362	3	16	,	,	PUNCT
ap-1362	3	17	e.	e.	PROPN
ap-1362	3	18	winterroth	winterroth	PROPN
ap-1362	3	19	abstract	abstract	VERB
ap-1362	3	20	a	a	DET
ap-1362	3	21	tower	tower	NOUN
ap-1362	3	22	for	for	ADP
ap-1362	3	23	a	a	DET
ap-1362	3	24	(	(	PUNCT
ap-1362	3	25	2	2	NUM
ap-1362	3	26	+	+	NUM
ap-1362	3	27	1)-dimensional	1)-dimensional	NUM
ap-1362	3	28	toda	toda	NOUN
ap-1362	3	29	type	type	NOUN
ap-1362	3	30	system	system	NOUN
ap-1362	3	31	is	be	AUX
ap-1362	3	32	constructed	construct	VERB
ap-1362	3	33	in	in	ADP
ap-1362	3	34	terms	term	NOUN
ap-1362	3	35	of	of	ADP
ap-1362	3	36	a	a	DET
ap-1362	3	37	series	series	NOUN
ap-1362	3	38	expansion	expansion	NOUN
ap-1362	3	39	of	of	ADP
ap-1362	3	40	operators	operator	NOUN
ap-1362	3	41	which	which	PRON
ap-1362	3	42	can	can	AUX
ap-1362	3	43	be	be	AUX
ap-1362	3	44	interpreted	interpret	VERB
ap-1362	3	45	as	as	ADP
ap-1362	3	46	generalized	generalized	ADJ
ap-1362	3	47	bessel	bessel	ADJ
ap-1362	3	48	coefficients	coefficient	NOUN
ap-1362	3	49	;	;	PUNCT
ap-1362	3	50	the	the	DET
ap-1362	3	51	result	result	NOUN
ap-1362	3	52	is	be	AUX
ap-1362	3	53	formulated	formulate	VERB
ap-1362	3	54	as	as	ADP
ap-1362	3	55	an	an	DET
ap-1362	3	56	analog	analog	NOUN
ap-1362	3	57	of	of	ADP
ap-1362	3	58	the	the	DET
ap-1362	3	59	baker	baker	PROPN
ap-1362	3	60	-	-	PUNCT
ap-1362	3	61	campbell	campbell	PROPN
ap-1362	3	62	-	-	PUNCT
ap-1362	3	63	hausdorff	hausdorff	NOUN
ap-1362	3	64	formula	formula	NOUN
ap-1362	3	65	.	.	PUNCT
ap-1362	4	1	we	we	PRON
ap-1362	4	2	tackle	tackle	VERB
ap-1362	4	3	the	the	DET
ap-1362	4	4	problem	problem	NOUN
ap-1362	4	5	of	of	ADP
ap-1362	4	6	the	the	DET
ap-1362	4	7	construction	construction	NOUN
ap-1362	4	8	of	of	ADP
ap-1362	4	9	infinitesimal	infinitesimal	ADJ
ap-1362	4	10	algebraic	algebraic	ADJ
ap-1362	4	11	skeletons	skeleton	NOUN
ap-1362	4	12	for	for	ADP
ap-1362	4	13	such	such	DET
ap-1362	4	14	a	a	DET
ap-1362	4	15	tower	tower	NOUN
ap-1362	4	16	and	and	CCONJ
ap-1362	4	17	discuss	discuss	VERB
ap-1362	4	18	some	some	DET
ap-1362	4	19	open	open	ADJ
ap-1362	4	20	problems	problem	NOUN
ap-1362	4	21	arising	arise	VERB
ap-1362	4	22	along	along	ADP
ap-1362	4	23	our	our	PRON
ap-1362	4	24	approach	approach	NOUN
ap-1362	4	25	.	.	PUNCT
ap-1362	5	1	keywords	keyword	NOUN
ap-1362	5	2	:	:	PUNCT
ap-1362	5	3	toda	toda	PROPN
ap-1362	5	4	type	type	NOUN
ap-1362	5	5	system	system	NOUN
ap-1362	5	6	,	,	PUNCT
ap-1362	5	7	integrability	integrability	NOUN
ap-1362	5	8	,	,	PUNCT
ap-1362	5	9	infinitesimal	infinitesimal	ADJ
ap-1362	5	10	skeleton	skeleton	NOUN
ap-1362	5	11	,	,	PUNCT
ap-1362	5	12	tower	tower	NOUN
ap-1362	5	13	,	,	PUNCT
ap-1362	5	14	cartan	cartan	ADJ
ap-1362	5	15	connection	connection	NOUN
ap-1362	5	16	.	.	PUNCT
ap-1362	6	1	1	1	NUM
ap-1362	6	2	introduction	introduction	NOUN
ap-1362	6	3	nonlinear	nonlinear	ADJ
ap-1362	6	4	models	model	NOUN
ap-1362	6	5	,	,	PUNCT
ap-1362	6	6	and	and	CCONJ
ap-1362	6	7	in	in	ADP
ap-1362	6	8	particular	particular	ADJ
ap-1362	6	9	toda	toda	PROPN
ap-1362	6	10	type	type	NOUN
ap-1362	6	11	systems	system	NOUN
ap-1362	6	12	,	,	PUNCT
ap-1362	6	13	play	play	VERB
ap-1362	6	14	a	a	DET
ap-1362	6	15	role	role	NOUN
ap-1362	6	16	in	in	ADP
ap-1362	6	17	a	a	DET
ap-1362	6	18	variety	variety	NOUN
ap-1362	6	19	of	of	ADP
ap-1362	6	20	physical	physical	ADJ
ap-1362	6	21	phenomena	phenomenon	NOUN
ap-1362	6	22	.	.	PUNCT
ap-1362	7	1	as	as	SCONJ
ap-1362	7	2	is	be	AUX
ap-1362	7	3	well	well	ADV
ap-1362	7	4	known	know	VERB
ap-1362	7	5	,	,	PUNCT
ap-1362	7	6	the	the	DET
ap-1362	7	7	problem	problem	NOUN
ap-1362	7	8	of	of	ADP
ap-1362	7	9	their	their	PRON
ap-1362	7	10	integrability	integrability	NOUN
ap-1362	7	11	is	be	AUX
ap-1362	7	12	far	far	ADV
ap-1362	7	13	from	from	ADP
ap-1362	7	14	being	be	AUX
ap-1362	7	15	trivial	trivial	ADJ
ap-1362	7	16	.	.	PUNCT
ap-1362	8	1	it	it	PRON
ap-1362	8	2	is	be	AUX
ap-1362	8	3	nowadays	nowadays	ADV
ap-1362	8	4	well	well	ADV
ap-1362	8	5	recognized	recognize	VERB
ap-1362	8	6	that	that	SCONJ
ap-1362	8	7	the	the	DET
ap-1362	8	8	algebraic	algebraic	ADJ
ap-1362	8	9	properties	property	NOUN
ap-1362	8	10	of	of	ADP
ap-1362	8	11	nonlinear	nonlinear	ADJ
ap-1362	8	12	systems	system	NOUN
ap-1362	8	13	are	be	AUX
ap-1362	8	14	relevant	relevant	ADJ
ap-1362	8	15	from	from	ADP
ap-1362	8	16	the	the	DET
ap-1362	8	17	point	point	NOUN
ap-1362	8	18	of	of	ADP
ap-1362	8	19	view	view	NOUN
ap-1362	8	20	of	of	ADP
ap-1362	8	21	integrability	integrability	NOUN
ap-1362	8	22	.	.	PUNCT
ap-1362	9	1	a	a	DET
ap-1362	9	2	huge	huge	ADJ
ap-1362	9	3	scientific	scientific	ADJ
ap-1362	9	4	production	production	NOUN
ap-1362	9	5	within	within	ADP
ap-1362	9	6	this	this	DET
ap-1362	9	7	topic	topic	NOUN
ap-1362	9	8	has	have	AUX
ap-1362	9	9	developed	develop	VERB
ap-1362	9	10	in	in	ADP
ap-1362	9	11	both	both	CCONJ
ap-1362	9	12	discrete	discrete	ADJ
ap-1362	9	13	and	and	CCONJ
ap-1362	9	14	continuous	continuous	ADJ
ap-1362	9	15	,	,	PUNCT
ap-1362	9	16	as	as	ADV
ap-1362	9	17	well	well	ADV
ap-1362	9	18	as	as	ADP
ap-1362	9	19	,	,	PUNCT
ap-1362	9	20	classical	classical	ADJ
ap-1362	9	21	and	and	CCONJ
ap-1362	9	22	quantistic	quantistic	ADJ
ap-1362	9	23	models	model	NOUN
ap-1362	9	24	.	.	PUNCT
ap-1362	10	1	it	it	PRON
ap-1362	10	2	is	be	AUX
ap-1362	10	3	nevertheless	nevertheless	ADV
ap-1362	10	4	important	important	ADJ
ap-1362	10	5	not	not	PART
ap-1362	10	6	to	to	PART
ap-1362	10	7	forget	forget	VERB
ap-1362	10	8	the	the	DET
ap-1362	10	9	origin	origin	NOUN
ap-1362	10	10	of	of	ADP
ap-1362	10	11	this	this	DET
ap-1362	10	12	interest	interest	NOUN
ap-1362	10	13	:	:	PUNCT
ap-1362	10	14	for	for	ADP
ap-1362	10	15	a	a	DET
ap-1362	10	16	nonlinear	nonlinear	ADJ
ap-1362	10	17	system	system	NOUN
ap-1362	10	18	,	,	PUNCT
ap-1362	10	19	it	it	PRON
ap-1362	10	20	lies	lie	VERB
ap-1362	10	21	in	in	ADP
ap-1362	10	22	the	the	DET
ap-1362	10	23	concept	concept	NOUN
ap-1362	10	24	of	of	ADP
ap-1362	10	25	integrability	integrability	NOUN
ap-1362	10	26	as	as	ADP
ap-1362	10	27	of	of	ADP
ap-1362	10	28	having	have	VERB
ap-1362	10	29	‘	'	PUNCT
ap-1362	10	30	enough	enough	ADJ
ap-1362	10	31	’	'	PUNCT
ap-1362	10	32	conservation	conservation	NOUN
ap-1362	10	33	laws	law	NOUN
ap-1362	10	34	to	to	PART
ap-1362	10	35	exaustively	exaustively	ADV
ap-1362	10	36	describe	describe	VERB
ap-1362	10	37	the	the	DET
ap-1362	10	38	dynamics	dynamic	NOUN
ap-1362	10	39	(	(	PUNCT
ap-1362	10	40	an	an	DET
ap-1362	10	41	idea	idea	NOUN
ap-1362	10	42	which	which	PRON
ap-1362	10	43	originates	originate	VERB
ap-1362	10	44	in	in	ADP
ap-1362	10	45	the	the	DET
ap-1362	10	46	inverse	inverse	NOUN
ap-1362	10	47	of	of	ADP
ap-1362	10	48	the	the	DET
ap-1362	10	49	noether	noether	PROPN
ap-1362	10	50	theorem	theorem	PROPN
ap-1362	10	51	ii	ii	PROPN
ap-1362	10	52	in	in	ADP
ap-1362	10	53	the	the	DET
ap-1362	10	54	calculus	calculus	NOUN
ap-1362	10	55	of	of	ADP
ap-1362	10	56	variations	variation	NOUN
ap-1362	10	57	)	)	PUNCT
ap-1362	10	58	.	.	PUNCT
ap-1362	11	1	historically	historically	ADV
ap-1362	11	2	,	,	PUNCT
ap-1362	11	3	the	the	DET
ap-1362	11	4	algebraicgeometric	algebraicgeometric	ADJ
ap-1362	11	5	approach	approach	NOUN
ap-1362	11	6	is	be	AUX
ap-1362	11	7	based	base	VERB
ap-1362	11	8	on	on	ADP
ap-1362	11	9	the	the	DET
ap-1362	11	10	requirement	requirement	NOUN
ap-1362	11	11	for	for	ADP
ap-1362	11	12	the	the	DET
ap-1362	11	13	existence	existence	NOUN
ap-1362	11	14	of	of	ADP
ap-1362	11	15	conservation	conservation	NOUN
ap-1362	11	16	laws	law	NOUN
ap-1362	11	17	which	which	PRON
ap-1362	11	18	leads	lead	VERB
ap-1362	11	19	to	to	ADP
ap-1362	11	20	the	the	DET
ap-1362	11	21	existence	existence	NOUN
ap-1362	11	22	of	of	ADP
ap-1362	11	23	symmetries	symmetry	NOUN
ap-1362	11	24	(	(	PUNCT
ap-1362	11	25	in	in	ADP
ap-1362	11	26	terms	term	NOUN
ap-1362	11	27	of	of	ADP
ap-1362	11	28	algebraic	algebraic	ADJ
ap-1362	11	29	structures	structure	NOUN
ap-1362	11	30	)	)	PUNCT
ap-1362	11	31	.	.	PUNCT
ap-1362	12	1	in	in	ADP
ap-1362	12	2	this	this	DET
ap-1362	12	3	light	light	NOUN
ap-1362	12	4	,	,	PUNCT
ap-1362	12	5	wahlquist	wahlquist	NOUN
ap-1362	12	6	and	and	CCONJ
ap-1362	12	7	estabrook	estabrook	NOUN
ap-1362	12	8	[	[	X
ap-1362	12	9	15	15	NUM
ap-1362	12	10	,	,	PUNCT
ap-1362	12	11	5	5	NUM
ap-1362	12	12	]	]	PUNCT
ap-1362	12	13	proposed	propose	VERB
ap-1362	12	14	a	a	DET
ap-1362	12	15	technique	technique	NOUN
ap-1362	12	16	for	for	ADP
ap-1362	12	17	systematically	systematically	ADV
ap-1362	12	18	deriving	derive	VERB
ap-1362	12	19	what	what	PRON
ap-1362	12	20	they	they	PRON
ap-1362	12	21	called	call	VERB
ap-1362	12	22	a	a	DET
ap-1362	12	23	‘	'	PUNCT
ap-1362	12	24	prolongation	prolongation	NOUN
ap-1362	12	25	structure	structure	NOUN
ap-1362	12	26	’	'	PUNCT
ap-1362	12	27	in	in	ADP
ap-1362	12	28	terms	term	NOUN
ap-1362	12	29	of	of	ADP
ap-1362	12	30	a	a	DET
ap-1362	12	31	set	set	NOUN
ap-1362	12	32	of	of	ADP
ap-1362	12	33	‘	'	PUNCT
ap-1362	12	34	pseudopotentials	pseudopotential	NOUN
ap-1362	12	35	’	'	PUNCT
ap-1362	12	36	related	relate	VERB
ap-1362	12	37	with	with	ADP
ap-1362	12	38	the	the	DET
ap-1362	12	39	existence	existence	NOUN
ap-1362	12	40	of	of	ADP
ap-1362	12	41	an	an	DET
ap-1362	12	42	infinite	infinite	ADJ
ap-1362	12	43	set	set	NOUN
ap-1362	12	44	of	of	ADP
ap-1362	12	45	associated	associated	ADJ
ap-1362	12	46	conservation	conservation	NOUN
ap-1362	12	47	laws	law	NOUN
ap-1362	12	48	,	,	PUNCT
ap-1362	12	49	and	and	CCONJ
ap-1362	12	50	they	they	PRON
ap-1362	12	51	also	also	ADV
ap-1362	12	52	conjectured	conjecture	VERB
ap-1362	12	53	that	that	SCONJ
ap-1362	12	54	the	the	DET
ap-1362	12	55	structure	structure	NOUN
ap-1362	12	56	was	be	AUX
ap-1362	12	57	‘	'	PUNCT
ap-1362	12	58	open	open	ADJ
ap-1362	12	59	’	'	PUNCT
ap-1362	12	60	i.e.	i.e.	X
ap-1362	12	61	not	not	PART
ap-1362	12	62	a	a	DET
ap-1362	12	63	set	set	NOUN
ap-1362	12	64	of	of	ADP
ap-1362	12	65	structure	structure	NOUN
ap-1362	12	66	relations	relation	NOUN
ap-1362	12	67	of	of	ADP
ap-1362	12	68	a	a	DET
ap-1362	12	69	finite	finite	ADJ
ap-1362	12	70	-	-	ADJ
ap-1362	12	71	dimensional	dimensional	ADJ
ap-1362	12	72	lie	lie	NOUN
ap-1362	12	73	group	group	NOUN
ap-1362	12	74	.	.	PUNCT
ap-1362	13	1	since	since	SCONJ
ap-1362	13	2	then	then	ADV
ap-1362	13	3	,	,	PUNCT
ap-1362	13	4	‘	'	PUNCT
ap-1362	13	5	open	open	ADJ
ap-1362	13	6	’	'	PUNCT
ap-1362	13	7	lie	lie	NOUN
ap-1362	13	8	algebras	algebra	NOUN
ap-1362	13	9	have	have	AUX
ap-1362	13	10	been	be	AUX
ap-1362	13	11	extensively	extensively	ADV
ap-1362	13	12	studied	study	VERB
ap-1362	13	13	in	in	ADP
ap-1362	13	14	order	order	NOUN
ap-1362	13	15	to	to	PART
ap-1362	13	16	distinguish	distinguish	VERB
ap-1362	13	17	them	they	PRON
ap-1362	13	18	from	from	ADP
ap-1362	13	19	freely	freely	ADV
ap-1362	13	20	generated	generate	VERB
ap-1362	13	21	infinite	infinite	ADJ
ap-1362	13	22	-	-	PUNCT
ap-1362	13	23	dimensional	dimensional	ADJ
ap-1362	13	24	lie	lie	NOUN
ap-1362	13	25	algebras	algebra	NOUN
ap-1362	13	26	.	.	PUNCT
ap-1362	14	1	in	in	ADP
ap-1362	14	2	their	their	PRON
ap-1362	14	3	approach	approach	NOUN
ap-1362	14	4	,	,	PUNCT
ap-1362	14	5	conservation	conservation	NOUN
ap-1362	14	6	laws	law	NOUN
ap-1362	14	7	are	be	AUX
ap-1362	14	8	written	write	VERB
ap-1362	14	9	in	in	ADP
ap-1362	14	10	terms	term	NOUN
ap-1362	14	11	of	of	ADP
ap-1362	14	12	‘	'	PUNCT
ap-1362	14	13	prolongation	prolongation	NOUN
ap-1362	14	14	’	'	PUNCT
ap-1362	14	15	forms	form	NOUN
ap-1362	14	16	and	and	CCONJ
ap-1362	14	17	integrability	integrability	NOUN
ap-1362	14	18	is	be	AUX
ap-1362	14	19	intended	intend	VERB
ap-1362	14	20	as	as	ADP
ap-1362	14	21	an	an	DET
ap-1362	14	22	integrability	integrability	NOUN
ap-1362	14	23	condition	condition	NOUN
ap-1362	14	24	for	for	ADP
ap-1362	14	25	a	a	DET
ap-1362	14	26	‘	'	PUNCT
ap-1362	14	27	prolonged	prolonged	ADJ
ap-1362	14	28	’	'	PUNCT
ap-1362	14	29	differential	differential	ADJ
ap-1362	14	30	ideal	ideal	NOUN
ap-1362	14	31	.	.	PUNCT
ap-1362	15	1	attempting	attempt	VERB
ap-1362	15	2	a	a	DET
ap-1362	15	3	description	description	NOUN
ap-1362	15	4	of	of	ADP
ap-1362	15	5	symmetries	symmetry	NOUN
ap-1362	15	6	in	in	ADP
ap-1362	15	7	terms	term	NOUN
ap-1362	15	8	of	of	ADP
ap-1362	15	9	lie	lie	NOUN
ap-1362	15	10	algebras	algebra	NOUN
ap-1362	15	11	implies	imply	VERB
ap-1362	15	12	the	the	DET
ap-1362	15	13	appearance	appearance	NOUN
ap-1362	15	14	of	of	ADP
ap-1362	15	15	an	an	DET
ap-1362	15	16	homogeneous	homogeneous	ADJ
ap-1362	15	17	space	space	NOUN
ap-1362	15	18	and	and	CCONJ
ap-1362	15	19	thus	thus	ADV
ap-1362	15	20	the	the	DET
ap-1362	15	21	interpretation	interpretation	NOUN
ap-1362	15	22	of	of	ADP
ap-1362	15	23	prolongation	prolongation	NOUN
ap-1362	15	24	forms	form	NOUN
ap-1362	15	25	as	as	ADP
ap-1362	15	26	cartanehresmann	cartanehresmann	NOUN
ap-1362	15	27	connections	connection	NOUN
ap-1362	15	28	.	.	PUNCT
ap-1362	16	1	it	it	PRON
ap-1362	16	2	should	should	AUX
ap-1362	16	3	be	be	AUX
ap-1362	16	4	stressed	stress	VERB
ap-1362	16	5	that	that	SCONJ
ap-1362	16	6	the	the	DET
ap-1362	16	7	unknowns	unknown	NOUN
ap-1362	16	8	are	be	AUX
ap-1362	16	9	both	both	PRON
ap-1362	16	10	conservation	conservation	NOUN
ap-1362	16	11	laws	law	NOUN
ap-1362	16	12	and	and	CCONJ
ap-1362	16	13	symmetries	symmetry	NOUN
ap-1362	16	14	,	,	PUNCT
ap-1362	16	15	and	and	CCONJ
ap-1362	16	16	it	it	PRON
ap-1362	16	17	is	be	AUX
ap-1362	16	18	clear	clear	ADJ
ap-1362	16	19	that	that	SCONJ
ap-1362	16	20	the	the	DET
ap-1362	16	21	main	main	ADJ
ap-1362	16	22	point	point	NOUN
ap-1362	16	23	in	in	ADP
ap-1362	16	24	this	this	PRON
ap-1362	16	25	is	be	AUX
ap-1362	16	26	how	how	SCONJ
ap-1362	16	27	to	to	PART
ap-1362	16	28	realize	realize	VERB
ap-1362	16	29	the	the	DET
ap-1362	16	30	form	form	NOUN
ap-1362	16	31	of	of	ADP
ap-1362	16	32	the	the	DET
ap-1362	16	33	conservation	conservation	NOUN
ap-1362	16	34	laws	law	NOUN
ap-1362	16	35	and	and	CCONJ
ap-1362	16	36	thus	thus	ADV
ap-1362	16	37	the	the	DET
ap-1362	16	38	explicit	explicit	ADJ
ap-1362	16	39	expression	expression	NOUN
ap-1362	16	40	of	of	ADP
ap-1362	16	41	the	the	DET
ap-1362	16	42	prolongation	prolongation	NOUN
ap-1362	16	43	forms	form	NOUN
ap-1362	16	44	.	.	PUNCT
ap-1362	17	1	different	different	ADJ
ap-1362	17	2	formulations	formulation	NOUN
ap-1362	17	3	of	of	ADP
ap-1362	17	4	the	the	DET
ap-1362	17	5	prolongation	prolongation	NOUN
ap-1362	17	6	ideal	ideal	NOUN
ap-1362	17	7	bring	bring	VERB
ap-1362	17	8	to	to	ADP
ap-1362	17	9	both	both	CCONJ
ap-1362	17	10	different	different	ADJ
ap-1362	17	11	algebraic	algebraic	ADJ
ap-1362	17	12	structures	structure	NOUN
ap-1362	17	13	(	(	PUNCT
ap-1362	17	14	symmetries	symmetry	NOUN
ap-1362	17	15	)	)	PUNCT
ap-1362	17	16	and	and	CCONJ
ap-1362	17	17	corresponding	correspond	VERB
ap-1362	17	18	conservation	conservation	NOUN
ap-1362	17	19	laws	law	NOUN
ap-1362	17	20	:	:	PUNCT
ap-1362	17	21	of	of	ADP
ap-1362	17	22	course	course	NOUN
ap-1362	17	23	,	,	PUNCT
ap-1362	17	24	the	the	DET
ap-1362	17	25	structure	structure	NOUN
ap-1362	17	26	with	with	ADP
ap-1362	17	27	which	which	PRON
ap-1362	17	28	prolongation	prolongation	NOUN
ap-1362	17	29	forms	form	NOUN
ap-1362	17	30	are	be	AUX
ap-1362	17	31	postulated	postulate	VERB
ap-1362	17	32	can	can	AUX
ap-1362	17	33	produce	produce	VERB
ap-1362	17	34	lie	lie	NOUN
ap-1362	17	35	algebras	algebra	NOUN
ap-1362	17	36	or	or	CCONJ
ap-1362	17	37	more	more	ADV
ap-1362	17	38	general	general	ADJ
ap-1362	17	39	algebraic	algebraic	ADJ
ap-1362	17	40	structures	structure	NOUN
ap-1362	17	41	.	.	PUNCT
ap-1362	18	1	we	we	PRON
ap-1362	18	2	use	use	VERB
ap-1362	18	3	the	the	DET
ap-1362	18	4	algebraic	algebraic	ADJ
ap-1362	18	5	properties	property	NOUN
ap-1362	18	6	of	of	ADP
ap-1362	18	7	toda	toda	PROPN
ap-1362	18	8	type	type	NOUN
ap-1362	18	9	systems	system	NOUN
ap-1362	18	10	as	as	ADP
ap-1362	18	11	a	a	DET
ap-1362	18	12	‘	'	PUNCT
ap-1362	18	13	laboratory	laboratory	NOUN
ap-1362	18	14	’	'	PUNCT
ap-1362	18	15	to	to	PART
ap-1362	18	16	explicate	explicate	VERB
ap-1362	18	17	an	an	DET
ap-1362	18	18	algebraic	algebraic	ADJ
ap-1362	18	19	-	-	PUNCT
ap-1362	18	20	geometric	geometric	ADJ
ap-1362	18	21	interpretation	interpretation	NOUN
ap-1362	18	22	of	of	ADP
ap-1362	18	23	the	the	DET
ap-1362	18	24	above	above	ADJ
ap-1362	18	25	mentioned	mention	VERB
ap-1362	18	26	‘	'	PUNCT
ap-1362	18	27	prolongation	prolongation	NOUN
ap-1362	18	28	’	'	PUNCT
ap-1362	18	29	procedure	procedure	NOUN
ap-1362	18	30	in	in	ADP
ap-1362	18	31	terms	term	NOUN
ap-1362	18	32	of	of	ADP
ap-1362	18	33	towers	tower	NOUN
ap-1362	18	34	with	with	ADP
ap-1362	18	35	infinitesimal	infinitesimal	ADJ
ap-1362	18	36	algebraic	algebraic	ADJ
ap-1362	18	37	skeletons	skeleton	NOUN
ap-1362	18	38	[	[	X
ap-1362	18	39	9	9	NUM
ap-1362	18	40	]	]	PUNCT
ap-1362	18	41	.	.	PUNCT
ap-1362	19	1	consider	consider	VERB
ap-1362	19	2	the	the	DET
ap-1362	19	3	(	(	PUNCT
ap-1362	19	4	2	2	NUM
ap-1362	19	5	+	+	NUM
ap-1362	19	6	1)-dimensional	1)-dimensional	NUM
ap-1362	19	7	system	system	NOUN
ap-1362	19	8	,	,	PUNCT
ap-1362	19	9	a	a	DET
ap-1362	19	10	continuous	continuous	ADJ
ap-1362	19	11	(	(	PUNCT
ap-1362	19	12	or	or	CCONJ
ap-1362	19	13	long	long	ADJ
ap-1362	19	14	-	-	PUNCT
ap-1362	19	15	wave	wave	NOUN
ap-1362	19	16	)	)	PUNCT
ap-1362	19	17	approximation	approximation	NOUN
ap-1362	19	18	of	of	ADP
ap-1362	19	19	a	a	DET
ap-1362	19	20	spatially	spatially	ADV
ap-1362	19	21	two	two	NUM
ap-1362	19	22	-	-	PUNCT
ap-1362	19	23	dimensional	dimensional	ADJ
ap-1362	19	24	toda	toda	NOUN
ap-1362	19	25	lattice	lattice	NOUN
ap-1362	20	1	[	[	X
ap-1362	20	2	14	14	NUM
ap-1362	20	3	]	]	SYM
ap-1362	20	4	:	:	PUNCT
ap-1362	20	5	uxx	uxx	PROPN
ap-1362	20	6	+	+	CCONJ
ap-1362	20	7	uyy	uyy	PROPN
ap-1362	20	8	+	+	CCONJ
ap-1362	20	9	(	(	PUNCT
ap-1362	20	10	e	e	X
ap-1362	20	11	u)zz	u)zz	PROPN
ap-1362	20	12	=	=	SYM
ap-1362	20	13	0	0	NUM
ap-1362	20	14	,	,	PUNCT
ap-1362	20	15	(	(	PUNCT
ap-1362	20	16	1	1	X
ap-1362	20	17	)	)	PUNCT
ap-1362	20	18	where	where	SCONJ
ap-1362	20	19	u	u	NOUN
ap-1362	20	20	=	=	SYM
ap-1362	20	21	u(x	u(x	PROPN
ap-1362	20	22	,	,	PUNCT
ap-1362	20	23	y	y	PROPN
ap-1362	20	24	,	,	PUNCT
ap-1362	20	25	z	z	NOUN
ap-1362	20	26	)	)	PUNCT
ap-1362	20	27	is	be	AUX
ap-1362	20	28	a	a	DET
ap-1362	20	29	real	real	ADJ
ap-1362	20	30	field	field	NOUN
ap-1362	20	31	,	,	PUNCT
ap-1362	20	32	x	x	X
ap-1362	20	33	,	,	PUNCT
ap-1362	20	34	y	y	PROPN
ap-1362	20	35	,	,	PUNCT
ap-1362	20	36	z	z	PROPN
ap-1362	20	37	are	be	AUX
ap-1362	20	38	real	real	ADJ
ap-1362	20	39	local	local	ADJ
ap-1362	20	40	coordinates	coordinate	NOUN
ap-1362	20	41	(	(	PUNCT
ap-1362	20	42	if	if	SCONJ
ap-1362	20	43	we	we	PRON
ap-1362	20	44	want	want	VERB
ap-1362	20	45	,	,	PUNCT
ap-1362	20	46	z	z	NOUN
ap-1362	20	47	playing	play	VERB
ap-1362	20	48	the	the	DET
ap-1362	20	49	rôle	rôle	NOUN
ap-1362	20	50	of	of	ADP
ap-1362	20	51	a	a	DET
ap-1362	20	52	‘	'	PUNCT
ap-1362	20	53	time	time	NOUN
ap-1362	20	54	’	'	PUNCT
ap-1362	20	55	)	)	PUNCT
ap-1362	20	56	and	and	CCONJ
ap-1362	20	57	the	the	DET
ap-1362	20	58	subscripts	subscript	NOUN
ap-1362	20	59	mean	mean	VERB
ap-1362	20	60	partial	partial	ADJ
ap-1362	20	61	derivatives	derivative	NOUN
ap-1362	20	62	.	.	PUNCT
ap-1362	21	1	it	it	PRON
ap-1362	21	2	can	can	AUX
ap-1362	21	3	be	be	AUX
ap-1362	21	4	seen	see	VERB
ap-1362	21	5	as	as	ADP
ap-1362	21	6	the	the	DET
ap-1362	21	7	limit	limit	NOUN
ap-1362	21	8	for	for	ADP
ap-1362	21	9	γ	γ	X
ap-1362	21	10	→∞	→∞	PROPN
ap-1362	21	11	of	of	ADP
ap-1362	21	12	the	the	DET
ap-1362	21	13	more	more	ADV
ap-1362	21	14	general	general	ADJ
ap-1362	21	15	model	model	NOUN
ap-1362	21	16	uxx+uyy+	uxx+uyy+	X
ap-1362	22	1	[	[	PUNCT
ap-1362	22	2	(	(	PUNCT
ap-1362	22	3	1	1	NUM
ap-1362	22	4	+	+	NUM
ap-1362	22	5	u	u	NOUN
ap-1362	22	6	/	/	SYM
ap-1362	22	7	γ)γ−1	γ)γ−1	ADJ
ap-1362	22	8	]	]	PUNCT
ap-1362	22	9	zz	zz	PROPN
ap-1362	22	10	=	=	SYM
ap-1362	22	11	0	0	PROPN
ap-1362	22	12	,	,	PUNCT
ap-1362	22	13	covering	cover	VERB
ap-1362	22	14	(	(	PUNCT
ap-1362	22	15	for	for	ADP
ap-1362	22	16	γ	γ	NOUN
ap-1362	22	17	different	different	ADJ
ap-1362	22	18	from	from	ADP
ap-1362	22	19	0	0	NUM
ap-1362	22	20	,	,	PUNCT
ap-1362	22	21	1	1	X
ap-1362	22	22	)	)	PUNCT
ap-1362	22	23	various	various	ADJ
ap-1362	22	24	continuous	continuous	ADJ
ap-1362	22	25	approximations	approximation	NOUN
ap-1362	22	26	of	of	ADP
ap-1362	22	27	lattice	lattice	NOUN
ap-1362	22	28	models	model	NOUN
ap-1362	22	29	,	,	PUNCT
ap-1362	22	30	among	among	ADP
ap-1362	22	31	them	they	PRON
ap-1362	22	32	the	the	DET
ap-1362	22	33	fermi	fermi	NOUN
ap-1362	22	34	-	-	PUNCT
ap-1362	22	35	pasta	pasta	NOUN
ap-1362	22	36	-	-	PUNCT
ap-1362	22	37	ulam	ulam	NOUN
ap-1362	22	38	(	(	PUNCT
ap-1362	22	39	γ	γ	X
ap-1362	22	40	=	=	SYM
ap-1362	22	41	3	3	NUM
ap-1362	22	42	)	)	PUNCT
ap-1362	22	43	.	.	PUNCT
ap-1362	23	1	it	it	PRON
ap-1362	23	2	appears	appear	VERB
ap-1362	23	3	in	in	ADP
ap-1362	23	4	differential	differential	ADJ
ap-1362	23	5	geometry	geometry	NOUN
ap-1362	23	6	:	:	PUNCT
ap-1362	23	7	kaehler	kaehler	NOUN
ap-1362	23	8	metrics	metric	NOUN
ap-1362	23	9	[	[	X
ap-1362	23	10	8	8	NUM
ap-1362	23	11	]	]	PUNCT
ap-1362	23	12	;	;	PUNCT
ap-1362	23	13	in	in	ADP
ap-1362	23	14	mathematical	mathematical	ADJ
ap-1362	23	15	and	and	CCONJ
ap-1362	23	16	theoretical	theoretical	ADJ
ap-1362	23	17	physics	physics	NOUN
ap-1362	23	18	(	(	PUNCT
ap-1362	23	19	see	see	VERB
ap-1362	23	20	,	,	PUNCT
ap-1362	23	21	e.g.	e.g.	ADV
ap-1362	23	22	newman	newman	PROPN
ap-1362	23	23	and	and	CCONJ
ap-1362	23	24	penrose	penrose	PROPN
ap-1362	23	25	as	as	ADV
ap-1362	23	26	well	well	ADV
ap-1362	23	27	as	as	ADP
ap-1362	23	28	[	[	X
ap-1362	23	29	12	12	NUM
ap-1362	23	30	]	]	PUNCT
ap-1362	23	31	)	)	PUNCT
ap-1362	23	32	;	;	PUNCT
ap-1362	23	33	in	in	ADP
ap-1362	23	34	the	the	DET
ap-1362	23	35	theory	theory	NOUN
ap-1362	23	36	of	of	ADP
ap-1362	23	37	hamiltonian	hamiltonian	ADJ
ap-1362	23	38	systems	system	NOUN
ap-1362	23	39	,	,	PUNCT
ap-1362	23	40	in	in	ADP
ap-1362	23	41	general	general	ADJ
ap-1362	23	42	relativity	relativity	NOUN
ap-1362	23	43	:	:	PUNCT
ap-1362	23	44	heavenly	heavenly	ADJ
ap-1362	23	45	spaces	space	NOUN
ap-1362	23	46	(	(	PUNCT
ap-1362	23	47	real	real	ADJ
ap-1362	23	48	,	,	PUNCT
ap-1362	23	49	self	self	NOUN
ap-1362	23	50	-	-	PUNCT
ap-1362	23	51	dual	dual	ADJ
ap-1362	23	52	,	,	PUNCT
ap-1362	23	53	euclidean	euclidean	PROPN
ap-1362	23	54	einstein	einstein	PROPN
ap-1362	23	55	spaces	space	VERB
ap-1362	23	56	with	with	ADP
ap-1362	23	57	one	one	NUM
ap-1362	23	58	rotational	rotational	ADJ
ap-1362	23	59	killing	killing	NOUN
ap-1362	23	60	symmetry	symmetry	NOUN
ap-1362	23	61	,	,	PUNCT
ap-1362	23	62	[	[	X
ap-1362	23	63	12	12	NUM
ap-1362	23	64	,	,	PUNCT
ap-1362	23	65	4	4	NUM
ap-1362	23	66	]	]	NUM
ap-1362	23	67	)	)	PUNCT
ap-1362	23	68	;	;	PUNCT
ap-1362	23	69	in	in	ADP
ap-1362	23	70	the	the	DET
ap-1362	23	71	large	large	ADJ
ap-1362	23	72	n	n	NUM
ap-1362	23	73	limit	limit	NOUN
ap-1362	23	74	of	of	ADP
ap-1362	23	75	the	the	PRON
ap-1362	23	76	sl(n	sl(n	PUNCT
ap-1362	23	77	)	)	PUNCT
ap-1362	23	78	toda	toda	PROPN
ap-1362	23	79	lattice	lattice	PROPN
ap-1362	24	1	[	[	X
ap-1362	24	2	11	11	NUM
ap-1362	24	3	]	]	PUNCT
ap-1362	24	4	(	(	PUNCT
ap-1362	24	5	from	from	ADP
ap-1362	24	6	the	the	DET
ap-1362	24	7	constrainedwess	constrainedwess	NOUN
ap-1362	24	8	-	-	PUNCT
ap-1362	24	9	zuminosupported	zuminosupporte	VERB
ap-1362	24	10	by	by	ADP
ap-1362	24	11	the	the	DET
ap-1362	24	12	university	university	NOUN
ap-1362	24	13	of	of	ADP
ap-1362	24	14	torino	torino	NOUN
ap-1362	24	15	through	through	ADP
ap-1362	24	16	2009	2009	NUM
ap-1362	24	17	research	research	NOUN
ap-1362	24	18	project	project	NOUN
ap-1362	24	19	‘	'	PUNCT
ap-1362	24	20	conservation	conservation	NOUN
ap-1362	24	21	laws	law	NOUN
ap-1362	24	22	in	in	ADP
ap-1362	24	23	classical	classical	ADJ
ap-1362	24	24	and	and	CCONJ
ap-1362	24	25	quantum	quantum	NOUN
ap-1362	24	26	gravity	gravity	NOUN
ap-1362	24	27	’	'	PUNCT
ap-1362	24	28	.	.	PUNCT
ap-1362	25	1	54	54	NUM
ap-1362	25	2	acta	acta	PROPN
ap-1362	25	3	polytechnica	polytechnica	PROPN
ap-1362	25	4	vol	vol	NOUN
ap-1362	25	5	.	.	PUNCT
ap-1362	26	1	51	51	NUM
ap-1362	26	2	no	no	NOUN
ap-1362	26	3	.	.	PUNCT
ap-1362	27	1	1/2011	1/2011	NUM
ap-1362	27	2	novikov	novikov	NOUN
ap-1362	27	3	-	-	PUNCT
ap-1362	27	4	witten	witten	NOUN
ap-1362	27	5	model	model	NOUN
ap-1362	27	6	):	):	PUNCT
ap-1362	27	7	extended	extend	VERB
ap-1362	27	8	conformal	conformal	ADJ
ap-1362	27	9	symmetries	symmetry	NOUN
ap-1362	27	10	(	(	PUNCT
ap-1362	27	11	2d	2d	NUM
ap-1362	27	12	cft	cft	PROPN
ap-1362	27	13	)	)	PUNCT
ap-1362	27	14	and	and	CCONJ
ap-1362	27	15	reductions	reduction	NOUN
ap-1362	27	16	of	of	ADP
ap-1362	27	17	four	four	NUM
ap-1362	27	18	dimensional	dimensional	ADJ
ap-1362	27	19	theory	theory	NOUN
ap-1362	27	20	of	of	ADP
ap-1362	27	21	gravitational	gravitational	ADJ
ap-1362	27	22	instantons	instanton	NOUN
ap-1362	27	23	;	;	PUNCT
ap-1362	27	24	in	in	ADP
ap-1362	27	25	strings	string	NOUN
ap-1362	27	26	theory	theory	NOUN
ap-1362	27	27	and	and	CCONJ
ap-1362	27	28	statistical	statistical	ADJ
ap-1362	27	29	mechanics	mechanic	NOUN
ap-1362	27	30	.	.	PUNCT
ap-1362	28	1	it	it	PRON
ap-1362	28	2	can	can	AUX
ap-1362	28	3	be	be	AUX
ap-1362	28	4	seen	see	VERB
ap-1362	28	5	as	as	ADP
ap-1362	28	6	the	the	DET
ap-1362	28	7	particular	particular	ADJ
ap-1362	28	8	case	case	NOUN
ap-1362	28	9	with	with	ADP
ap-1362	28	10	d	d	PROPN
ap-1362	28	11	=	=	SYM
ap-1362	28	12	1	1	NUM
ap-1362	28	13	of	of	ADP
ap-1362	28	14	so	so	ADV
ap-1362	28	15	-	-	PUNCT
ap-1362	28	16	called	call	VERB
ap-1362	28	17	2d	2d	NOUN
ap-1362	28	18	-	-	PUNCT
ap-1362	28	19	dimensional	dimensional	ADJ
ap-1362	28	20	toda	toda	NOUN
ap-1362	28	21	-	-	PUNCT
ap-1362	28	22	type	type	NOUN
ap-1362	28	23	systems	system	NOUN
ap-1362	28	24	[	[	X
ap-1362	28	25	13	13	NUM
ap-1362	28	26	]	]	PUNCT
ap-1362	28	27	from	from	ADP
ap-1362	28	28	a	a	DET
ap-1362	28	29	‘	'	PUNCT
ap-1362	28	30	continuum	continuum	ADJ
ap-1362	28	31	lie	lie	NOUN
ap-1362	28	32	algebra	algebra	NOUN
ap-1362	28	33	’	'	PUNCT
ap-1362	28	34	by	by	ADP
ap-1362	28	35	means	mean	NOUN
ap-1362	28	36	of	of	ADP
ap-1362	28	37	a	a	DET
ap-1362	28	38	zero	zero	NUM
ap-1362	28	39	curvature	curvature	NOUN
ap-1362	28	40	representation	representation	NOUN
ap-1362	28	41	uww̄	uww̄	NOUN
ap-1362	29	1	=	=	PUNCT
ap-1362	29	2	k(eu	k(eu	PROPN
ap-1362	29	3	)	)	PUNCT
ap-1362	29	4	,	,	PUNCT
ap-1362	29	5	(	(	PUNCT
ap-1362	29	6	in	in	ADP
ap-1362	29	7	our	our	PRON
ap-1362	29	8	particular	particular	ADJ
ap-1362	29	9	case	case	NOUN
ap-1362	29	10	w	w	NOUN
ap-1362	29	11	=	=	PUNCT
ap-1362	29	12	x+	x+	PROPN
ap-1362	29	13	iy	iy	PROPN
ap-1362	29	14	and	and	CCONJ
ap-1362	29	15	k	k	PROPN
ap-1362	29	16	is	be	AUX
ap-1362	29	17	the	the	DET
ap-1362	29	18	differential	differential	ADJ
ap-1362	29	19	operator	operator	NOUN
ap-1362	29	20	given	give	VERB
ap-1362	29	21	by	by	ADP
ap-1362	29	22	k	k	PROPN
ap-1362	29	23	=	=	SYM
ap-1362	29	24	∂2	∂2	PROPN
ap-1362	29	25	∂z2	∂z2	PROPN
ap-1362	29	26	)	)	PUNCT
ap-1362	29	27	.	.	PUNCT
ap-1362	30	1	in	in	ADP
ap-1362	30	2	particular	particular	ADJ
ap-1362	30	3	,	,	PUNCT
ap-1362	30	4	it	it	PRON
ap-1362	30	5	has	have	AUX
ap-1362	30	6	been	be	AUX
ap-1362	30	7	studied	study	VERB
ap-1362	30	8	in	in	ADP
ap-1362	30	9	the	the	DET
ap-1362	30	10	context	context	NOUN
ap-1362	30	11	of	of	ADP
ap-1362	30	12	symmetry	symmetry	NOUN
ap-1362	30	13	reductions	reduction	NOUN
ap-1362	30	14	[	[	X
ap-1362	30	15	1	1	NUM
ap-1362	30	16	,	,	PUNCT
ap-1362	30	17	6	6	NUM
ap-1362	30	18	]	]	PUNCT
ap-1362	30	19	and	and	CCONJ
ap-1362	30	20	a	a	DET
ap-1362	30	21	(	(	PUNCT
ap-1362	30	22	1	1	NUM
ap-1362	30	23	+	+	NOUN
ap-1362	30	24	1)-dimensional	1)-dimensional	ADJ
ap-1362	30	25	version	version	NOUN
ap-1362	30	26	in	in	ADP
ap-1362	30	27	the	the	DET
ap-1362	30	28	context	context	NOUN
ap-1362	30	29	of	of	ADP
ap-1362	30	30	prolongation	prolongation	NOUN
ap-1362	30	31	structures	structure	NOUN
ap-1362	30	32	which	which	PRON
ap-1362	30	33	only	only	ADV
ap-1362	30	34	partially	partially	ADV
ap-1362	30	35	lead	lead	VERB
ap-1362	30	36	to	to	ADP
ap-1362	30	37	results	result	NOUN
ap-1362	30	38	[	[	X
ap-1362	30	39	2	2	NUM
ap-1362	30	40	]	]	PUNCT
ap-1362	30	41	.	.	PUNCT
ap-1362	31	1	2	2	NUM
ap-1362	31	2	towers	tower	NOUN
ap-1362	31	3	with	with	ADP
ap-1362	31	4	skeletons	skeleton	NOUN
ap-1362	31	5	for	for	ADP
ap-1362	31	6	toda	toda	PROPN
ap-1362	31	7	type	type	NOUN
ap-1362	31	8	systems	system	NOUN
ap-1362	31	9	the	the	DET
ap-1362	31	10	notion	notion	NOUN
ap-1362	31	11	of	of	ADP
ap-1362	31	12	an	an	DET
ap-1362	31	13	(	(	PUNCT
ap-1362	31	14	infinitesimal	infinitesimal	ADJ
ap-1362	31	15	)	)	PUNCT
ap-1362	31	16	algebraic	algebraic	ADJ
ap-1362	31	17	skeleton	skeleton	NOUN
ap-1362	31	18	is	be	AUX
ap-1362	31	19	an	an	DET
ap-1362	31	20	abstraction	abstraction	NOUN
ap-1362	31	21	of	of	ADP
ap-1362	31	22	some	some	DET
ap-1362	31	23	algebraic	algebraic	ADJ
ap-1362	31	24	aspects	aspect	NOUN
ap-1362	31	25	of	of	ADP
ap-1362	31	26	homogeneous	homogeneous	ADJ
ap-1362	31	27	spaces	space	NOUN
ap-1362	31	28	.	.	PUNCT
ap-1362	32	1	let	let	VERB
ap-1362	32	2	then	then	ADV
ap-1362	32	3	v	v	NOUN
ap-1362	32	4	denote	denote	VERB
ap-1362	32	5	a	a	DET
ap-1362	32	6	finite	finite	ADJ
ap-1362	32	7	-	-	ADJ
ap-1362	32	8	dimensional	dimensional	ADJ
ap-1362	32	9	vector	vector	NOUN
ap-1362	32	10	space	space	NOUN
ap-1362	32	11	.	.	PUNCT
ap-1362	33	1	an	an	DET
ap-1362	33	2	algebraic	algebraic	ADJ
ap-1362	33	3	skeleton	skeleton	NOUN
ap-1362	33	4	on	on	ADP
ap-1362	33	5	v	v	NUM
ap-1362	33	6	is	be	AUX
ap-1362	33	7	a	a	DET
ap-1362	33	8	triple	triple	ADJ
ap-1362	33	9	(	(	PUNCT
ap-1362	33	10	e	e	NOUN
ap-1362	33	11	,	,	PUNCT
ap-1362	33	12	g	g	PROPN
ap-1362	33	13	,	,	PUNCT
ap-1362	33	14	ρ	ρ	PROPN
ap-1362	33	15	)	)	PUNCT
ap-1362	33	16	,	,	PUNCT
ap-1362	33	17	with	with	ADP
ap-1362	33	18	g	g	PROPN
ap-1362	33	19	a	a	DET
ap-1362	33	20	(	(	PUNCT
ap-1362	33	21	possibly	possibly	ADV
ap-1362	33	22	infinite	infinite	ADJ
ap-1362	33	23	-	-	PUNCT
ap-1362	33	24	dimensional	dimensional	ADJ
ap-1362	33	25	)	)	PUNCT
ap-1362	33	26	lie	lie	NOUN
ap-1362	33	27	group	group	NOUN
ap-1362	33	28	,	,	PUNCT
ap-1362	33	29	e	e	PROPN
ap-1362	33	30	=	=	SYM
ap-1362	33	31	v	v	ADP
ap-1362	33	32	⊕	⊕	PROPN
ap-1362	33	33	g	g	NOUN
ap-1362	33	34	,	,	PUNCT
ap-1362	33	35	g	g	PROPN
ap-1362	33	36	the	the	DET
ap-1362	33	37	lie	lie	NOUN
ap-1362	33	38	algebra	algebra	NOUN
ap-1362	33	39	of	of	ADP
ap-1362	33	40	g	g	NOUN
ap-1362	33	41	,	,	PUNCT
ap-1362	33	42	and	and	CCONJ
ap-1362	33	43	ρ	ρ	DET
ap-1362	33	44	a	a	DET
ap-1362	33	45	representation	representation	NOUN
ap-1362	33	46	of	of	ADP
ap-1362	33	47	g	g	NOUN
ap-1362	33	48	on	on	ADP
ap-1362	33	49	e	e	X
ap-1362	33	50	(	(	PUNCT
ap-1362	33	51	infinitesimally	infinitesimally	ADV
ap-1362	33	52	of	of	ADP
ap-1362	33	53	g	g	NOUN
ap-1362	33	54	on	on	ADP
ap-1362	33	55	e	e	NOUN
ap-1362	33	56	)	)	PUNCT
ap-1362	33	57	such	such	ADJ
ap-1362	33	58	that	that	SCONJ
ap-1362	33	59	ρ(g)x	ρ(g)x	PROPN
ap-1362	33	60	=	=	SYM
ap-1362	33	61	ad(g)x	ad(g)x	PROPN
ap-1362	33	62	,	,	PUNCT
ap-1362	33	63	for	for	ADP
ap-1362	33	64	g	g	PROPN
ap-1362	33	65	∈	∈	PROPN
ap-1362	33	66	g	g	PROPN
ap-1362	33	67	,	,	PUNCT
ap-1362	33	68	x	x	SYM
ap-1362	33	69	∈	∈	PROPN
ap-1362	33	70	g.	g.	NOUN
ap-1362	33	71	let	let	VERB
ap-1362	33	72	z	z	PRON
ap-1362	33	73	be	be	AUX
ap-1362	33	74	a	a	DET
ap-1362	33	75	manifold	manifold	NOUN
ap-1362	33	76	of	of	ADP
ap-1362	33	77	type	type	NOUN
ap-1362	33	78	v	v	NOUN
ap-1362	33	79	(	(	PUNCT
ap-1362	33	80	i.e.	i.e.	X
ap-1362	33	81	∀z	∀z	X
ap-1362	33	82	∈	∈	PROPN
ap-1362	33	83	z	z	PROPN
ap-1362	33	84	,	,	PUNCT
ap-1362	33	85	tzz	tzz	PROPN
ap-1362	33	86	�	�	PROPN
ap-1362	33	87	v	v	PROPN
ap-1362	33	88	)	)	PUNCT
ap-1362	33	89	.	.	PUNCT
ap-1362	34	1	we	we	PRON
ap-1362	34	2	say	say	VERB
ap-1362	34	3	that	that	SCONJ
ap-1362	34	4	a	a	DET
ap-1362	34	5	principal	principal	ADJ
ap-1362	34	6	fibre	fibre	NOUN
ap-1362	34	7	bundle	bundle	NOUN
ap-1362	34	8	p	p	X
ap-1362	34	9	(	(	PUNCT
ap-1362	34	10	z	z	NOUN
ap-1362	34	11	,	,	PUNCT
ap-1362	34	12	g	g	NOUN
ap-1362	34	13	)	)	PUNCT
ap-1362	34	14	provided	provide	VERB
ap-1362	34	15	with	with	ADP
ap-1362	34	16	an	an	DET
ap-1362	34	17	absolute	absolute	ADJ
ap-1362	34	18	parallelism	parallelism	NOUN
ap-1362	34	19	ω	ω	NOUN
ap-1362	34	20	on	on	ADP
ap-1362	34	21	p	p	PROPN
ap-1362	34	22	is	be	AUX
ap-1362	34	23	a	a	DET
ap-1362	34	24	tower	tower	NOUN
ap-1362	34	25	on	on	ADP
ap-1362	34	26	z	z	NOUN
ap-1362	34	27	with	with	ADP
ap-1362	34	28	skeleton	skeleton	NOUN
ap-1362	34	29	(	(	PUNCT
ap-1362	34	30	e	e	NOUN
ap-1362	34	31	,	,	PUNCT
ap-1362	34	32	g	g	PROPN
ap-1362	34	33	,	,	PUNCT
ap-1362	34	34	ρ	ρ	PROPN
ap-1362	34	35	)	)	PUNCT
ap-1362	34	36	if	if	SCONJ
ap-1362	34	37	ω	ω	NOUN
ap-1362	34	38	takes	take	VERB
ap-1362	34	39	values	value	NOUN
ap-1362	34	40	in	in	ADP
ap-1362	34	41	e	e	NOUN
ap-1362	34	42	and	and	CCONJ
ap-1362	34	43	satisfies	satisfie	NOUN
ap-1362	34	44	:	:	PUNCT
ap-1362	34	45	r∗	r∗	VERB
ap-1362	34	46	gω	gω	PROPN
ap-1362	34	47	=	=	SYM
ap-1362	34	48	ρ(g)−1ω	ρ(g)−1ω	PROPN
ap-1362	34	49	,	,	PUNCT
ap-1362	34	50	for	for	ADP
ap-1362	34	51	g	g	PROPN
ap-1362	34	52	∈	∈	PROPN
ap-1362	34	53	g	g	PROPN
ap-1362	34	54	;	;	PUNCT
ap-1362	34	55	ω(ã	ω(ã	NUM
ap-1362	34	56	)	)	PUNCT
ap-1362	34	57	=	=	SYM
ap-1362	34	58	a	a	X
ap-1362	34	59	,	,	PUNCT
ap-1362	34	60	for	for	ADP
ap-1362	34	61	a	a	DET
ap-1362	34	62	∈	∈	PROPN
ap-1362	34	63	g	g	NOUN
ap-1362	34	64	;	;	PUNCT
ap-1362	34	65	here	here	ADV
ap-1362	34	66	rg	rg	PROPN
ap-1362	34	67	denotes	denote	VERB
ap-1362	34	68	the	the	DET
ap-1362	34	69	right	right	ADJ
ap-1362	34	70	translation	translation	NOUN
ap-1362	34	71	and	and	CCONJ
ap-1362	34	72	ã	ã	PROPN
ap-1362	34	73	the	the	DET
ap-1362	34	74	fundamental	fundamental	ADJ
ap-1362	34	75	vector	vector	NOUN
ap-1362	34	76	field	field	NOUN
ap-1362	34	77	induced	induce	VERB
ap-1362	34	78	on	on	ADP
ap-1362	34	79	p	p	NOUN
ap-1362	34	80	from	from	ADP
ap-1362	34	81	a.	a.	NOUN
ap-1362	34	82	in	in	ADP
ap-1362	34	83	general	general	ADJ
ap-1362	34	84	,	,	PUNCT
ap-1362	34	85	the	the	DET
ap-1362	34	86	absolute	absolute	ADJ
ap-1362	34	87	parallelism	parallelism	NOUN
ap-1362	34	88	does	do	AUX
ap-1362	34	89	not	not	PART
ap-1362	34	90	define	define	VERB
ap-1362	34	91	a	a	DET
ap-1362	34	92	lie	lie	NOUN
ap-1362	34	93	algebra	algebra	NOUN
ap-1362	34	94	homomorphism	homomorphism	NOUN
ap-1362	34	95	.	.	PUNCT
ap-1362	35	1	let	let	VERB
ap-1362	35	2	g	g	PRON
ap-1362	35	3	be	be	AUX
ap-1362	35	4	a	a	DET
ap-1362	35	5	lie	lie	NOUN
ap-1362	35	6	algebra	algebra	NOUN
ap-1362	35	7	and	and	CCONJ
ap-1362	35	8	k	k	PROPN
ap-1362	35	9	be	be	AUX
ap-1362	35	10	a	a	DET
ap-1362	35	11	lie	lie	NOUN
ap-1362	35	12	subalgebra	subalgebra	NOUN
ap-1362	35	13	of	of	ADP
ap-1362	35	14	g.	g.	PROPN
ap-1362	35	15	let	let	VERB
ap-1362	35	16	k	k	PROPN
ap-1362	35	17	be	be	AUX
ap-1362	35	18	a	a	DET
ap-1362	35	19	lie	lie	NOUN
ap-1362	35	20	group	group	NOUN
ap-1362	35	21	with	with	ADP
ap-1362	35	22	lie	lie	NOUN
ap-1362	35	23	algebra	algebra	PROPN
ap-1362	35	24	k	k	PROPN
ap-1362	35	25	and	and	CCONJ
ap-1362	35	26	let	let	VERB
ap-1362	35	27	p	p	PROPN
ap-1362	35	28	(	(	PUNCT
ap-1362	35	29	z	z	PROPN
ap-1362	35	30	,	,	PUNCT
ap-1362	35	31	k	k	NOUN
ap-1362	35	32	)	)	PUNCT
ap-1362	35	33	be	be	AUX
ap-1362	35	34	a	a	DET
ap-1362	35	35	principal	principal	ADJ
ap-1362	35	36	fibre	fibre	NOUN
ap-1362	35	37	bundle	bundle	NOUN
ap-1362	35	38	with	with	ADP
ap-1362	35	39	structure	structure	NOUN
ap-1362	35	40	groupk	groupk	NOUN
ap-1362	35	41	over	over	ADP
ap-1362	35	42	a	a	DET
ap-1362	35	43	manifold	manifold	ADJ
ap-1362	35	44	z	z	NOUN
ap-1362	35	45	,	,	PUNCT
ap-1362	35	46	as	as	ADP
ap-1362	35	47	above	above	ADV
ap-1362	35	48	.	.	PUNCT
ap-1362	36	1	a	a	DET
ap-1362	36	2	cartan	cartan	ADJ
ap-1362	36	3	connection	connection	NOUN
ap-1362	36	4	in	in	ADP
ap-1362	36	5	p	p	NOUN
ap-1362	36	6	of	of	ADP
ap-1362	36	7	type	type	NOUN
ap-1362	36	8	(	(	PUNCT
ap-1362	36	9	g	g	NOUN
ap-1362	36	10	,	,	PUNCT
ap-1362	36	11	k	k	NOUN
ap-1362	36	12	)	)	PUNCT
ap-1362	36	13	is	be	AUX
ap-1362	36	14	a	a	DET
ap-1362	36	15	1	1	NUM
ap-1362	36	16	-	-	PUNCT
ap-1362	36	17	form	form	NOUN
ap-1362	36	18	ω	ω	NOUN
ap-1362	36	19	on	on	ADP
ap-1362	36	20	p	p	NOUN
ap-1362	36	21	with	with	ADP
ap-1362	36	22	values	value	NOUN
ap-1362	36	23	in	in	ADP
ap-1362	36	24	g	g	NOUN
ap-1362	36	25	satisfying	satisfy	VERB
ap-1362	36	26	the	the	DET
ap-1362	36	27	following	follow	VERB
ap-1362	36	28	conditions	condition	NOUN
ap-1362	36	29	:	:	PUNCT
ap-1362	36	30	–	–	PUNCT
ap-1362	36	31	ω|tup	ω|tup	VERB
ap-1362	36	32	:	:	PUNCT
ap-1362	36	33	tup	tup	INTJ
ap-1362	36	34	→	→	SYM
ap-1362	36	35	g	g	PROPN
ap-1362	36	36	is	be	AUX
ap-1362	36	37	an	an	DET
ap-1362	36	38	isomorphism	isomorphism	NOUN
ap-1362	36	39	∀u	∀u	NOUN
ap-1362	36	40	∈	∈	NOUN
ap-1362	36	41	p	p	NOUN
ap-1362	36	42	;	;	PUNCT
ap-1362	36	43	–	–	PUNCT
ap-1362	36	44	r∗	r∗	VERB
ap-1362	36	45	gω	gω	PROPN
ap-1362	36	46	=	=	PUNCT
ap-1362	36	47	ad(g)−1ω	ad(g)−1ω	PROPN
ap-1362	36	48	for	for	ADP
ap-1362	36	49	g	g	PROPN
ap-1362	36	50	∈	∈	PROPN
ap-1362	36	51	k	k	PROPN
ap-1362	36	52	;	;	PUNCT
ap-1362	36	53	–	–	PUNCT
ap-1362	36	54	ω(ã	ω(ã	NOUN
ap-1362	36	55	)	)	PUNCT
ap-1362	36	56	=	=	PUNCT
ap-1362	36	57	a	a	PRON
ap-1362	36	58	for	for	ADP
ap-1362	36	59	a	a	DET
ap-1362	36	60	∈	∈	PROPN
ap-1362	36	61	k.	k.	NOUN
ap-1362	37	1	a	a	DET
ap-1362	37	2	cartan	cartan	ADJ
ap-1362	37	3	connection	connection	NOUN
ap-1362	37	4	(	(	PUNCT
ap-1362	37	5	p	p	X
ap-1362	37	6	,	,	PUNCT
ap-1362	37	7	z	z	PROPN
ap-1362	37	8	,	,	PUNCT
ap-1362	37	9	k	k	PROPN
ap-1362	37	10	,	,	PUNCT
ap-1362	37	11	ω	ω	NOUN
ap-1362	37	12	)	)	PUNCT
ap-1362	37	13	of	of	ADP
ap-1362	37	14	type	type	NOUN
ap-1362	37	15	(	(	PUNCT
ap-1362	37	16	g	g	NOUN
ap-1362	37	17	,	,	PUNCT
ap-1362	37	18	k	k	NOUN
ap-1362	37	19	)	)	PUNCT
ap-1362	37	20	is	be	AUX
ap-1362	37	21	a	a	DET
ap-1362	37	22	tower	tower	NOUN
ap-1362	37	23	on	on	ADP
ap-1362	37	24	z.	z.	PROPN
ap-1362	37	25	remark	remark	PROPN
ap-1362	37	26	that	that	SCONJ
ap-1362	37	27	since	since	SCONJ
ap-1362	37	28	,	,	PUNCT
ap-1362	37	29	a	a	PRON
ap-1362	37	30	priori	priori	X
ap-1362	37	31	,	,	PUNCT
ap-1362	37	32	the	the	DET
ap-1362	37	33	prolongation	prolongation	NOUN
ap-1362	37	34	algebra	algebra	NOUN
ap-1362	37	35	does	do	AUX
ap-1362	37	36	not	not	PART
ap-1362	37	37	close	close	VERB
ap-1362	37	38	into	into	ADP
ap-1362	37	39	a	a	DET
ap-1362	37	40	lie	lie	NOUN
ap-1362	37	41	algebra	algebra	NOUN
ap-1362	37	42	the	the	DET
ap-1362	37	43	starting	starting	NOUN
ap-1362	37	44	point	point	NOUN
ap-1362	37	45	for	for	ADP
ap-1362	37	46	the	the	DET
ap-1362	37	47	prolongation	prolongation	NOUN
ap-1362	37	48	procedure	procedure	NOUN
ap-1362	37	49	is	be	AUX
ap-1362	37	50	only	only	ADV
ap-1362	37	51	a	a	DET
ap-1362	37	52	tower	tower	NOUN
ap-1362	37	53	with	with	ADP
ap-1362	37	54	an	an	DET
ap-1362	37	55	absolute	absolute	ADJ
ap-1362	37	56	parallelism	parallelism	NOUN
ap-1362	37	57	,	,	PUNCT
ap-1362	37	58	and	and	CCONJ
ap-1362	37	59	not	not	PART
ap-1362	37	60	a	a	DET
ap-1362	37	61	cartan	cartan	ADJ
ap-1362	37	62	connection	connection	NOUN
ap-1362	37	63	.	.	PUNCT
ap-1362	38	1	thus	thus	ADV
ap-1362	38	2	,	,	PUNCT
ap-1362	38	3	in	in	ADP
ap-1362	38	4	principle	principle	ADJ
ap-1362	38	5	,	,	PUNCT
ap-1362	38	6	estabrook	estabrook	NOUN
ap-1362	38	7	-	-	PUNCT
ap-1362	38	8	wahlquist	wahlquist	NOUN
ap-1362	38	9	prolongation	prolongation	NOUN
ap-1362	38	10	forms	form	NOUN
ap-1362	38	11	are	be	AUX
ap-1362	38	12	absolute	absolute	ADJ
ap-1362	38	13	parallelism	parallelism	NOUN
ap-1362	38	14	forms	form	NOUN
ap-1362	38	15	.	.	PUNCT
ap-1362	39	1	the	the	DET
ap-1362	39	2	corresponding	corresponding	ADJ
ap-1362	39	3	open	open	ADJ
ap-1362	39	4	lie	lie	NOUN
ap-1362	39	5	algebra	algebra	NOUN
ap-1362	39	6	structure	structure	NOUN
ap-1362	39	7	can	can	AUX
ap-1362	39	8	be	be	AUX
ap-1362	39	9	provided	provide	VERB
ap-1362	39	10	with	with	ADP
ap-1362	39	11	the	the	DET
ap-1362	39	12	structure	structure	NOUN
ap-1362	39	13	of	of	ADP
ap-1362	39	14	an	an	DET
ap-1362	39	15	infinitesimal	infinitesimal	ADJ
ap-1362	39	16	algebraic	algebraic	ADJ
ap-1362	39	17	skeleton	skeleton	NOUN
ap-1362	39	18	on	on	ADP
ap-1362	39	19	a	a	DET
ap-1362	39	20	suitable	suitable	ADJ
ap-1362	39	21	space	space	NOUN
ap-1362	39	22	.	.	PUNCT
ap-1362	40	1	first	first	ADV
ap-1362	40	2	we	we	PRON
ap-1362	40	3	have	have	VERB
ap-1362	40	4	to	to	PART
ap-1362	40	5	prove	prove	VERB
ap-1362	40	6	that	that	SCONJ
ap-1362	40	7	a	a	DET
ap-1362	40	8	finite	finite	ADJ
ap-1362	40	9	dimensional	dimensional	ADJ
ap-1362	40	10	space	space	NOUN
ap-1362	40	11	v	v	NOUN
ap-1362	40	12	and	and	CCONJ
ap-1362	40	13	a	a	DET
ap-1362	40	14	lie	lie	NOUN
ap-1362	40	15	algebra	algebra	NOUN
ap-1362	40	16	g	g	PRON
ap-1362	40	17	exist	exist	VERB
ap-1362	40	18	satisfying	satisfy	VERB
ap-1362	40	19	the	the	DET
ap-1362	40	20	definition	definition	NOUN
ap-1362	40	21	of	of	ADP
ap-1362	40	22	a	a	DET
ap-1362	40	23	skeleton	skeleton	NOUN
ap-1362	40	24	,	,	PUNCT
ap-1362	40	25	i.e.	i.e.	X
ap-1362	40	26	in	in	ADP
ap-1362	40	27	particular	particular	ADJ
ap-1362	40	28	that	that	SCONJ
ap-1362	40	29	a	a	DET
ap-1362	40	30	suitable	suitable	ADJ
ap-1362	40	31	representation	representation	NOUN
ap-1362	40	32	ρ	ρ	NOUN
ap-1362	40	33	can	can	AUX
ap-1362	40	34	be	be	AUX
ap-1362	40	35	defined	define	VERB
ap-1362	40	36	.	.	PUNCT
ap-1362	41	1	the	the	DET
ap-1362	41	2	representation	representation	NOUN
ap-1362	41	3	is	be	AUX
ap-1362	41	4	obtained	obtain	VERB
ap-1362	41	5	by	by	ADP
ap-1362	41	6	means	mean	NOUN
ap-1362	41	7	of	of	ADP
ap-1362	41	8	an	an	DET
ap-1362	41	9	integrability	integrability	NOUN
ap-1362	41	10	condition	condition	NOUN
ap-1362	41	11	for	for	ADP
ap-1362	41	12	the	the	DET
ap-1362	41	13	absolute	absolute	ADJ
ap-1362	41	14	parallelism	parallelism	NOUN
ap-1362	41	15	of	of	ADP
ap-1362	41	16	a	a	DET
ap-1362	41	17	tower	tower	NOUN
ap-1362	41	18	on	on	ADP
ap-1362	41	19	a	a	DET
ap-1362	41	20	manifold	manifold	ADJ
ap-1362	41	21	z	z	NOUN
ap-1362	41	22	(	(	PUNCT
ap-1362	41	23	of	of	ADP
ap-1362	41	24	type	type	NOUN
ap-1362	41	25	v	v	NOUN
ap-1362	41	26	)	)	PUNCT
ap-1362	41	27	,	,	PUNCT
ap-1362	41	28	with	with	ADP
ap-1362	41	29	skeleton	skeleton	NOUN
ap-1362	41	30	(	(	PUNCT
ap-1362	41	31	e	e	NOUN
ap-1362	41	32	,	,	PUNCT
ap-1362	41	33	v	v	INTJ
ap-1362	41	34	,	,	PUNCT
ap-1362	41	35	g	g	NOUN
ap-1362	41	36	)	)	PUNCT
ap-1362	41	37	.	.	PUNCT
ap-1362	42	1	note	note	VERB
ap-1362	42	2	that	that	SCONJ
ap-1362	42	3	if	if	SCONJ
ap-1362	42	4	e	e	NOUN
ap-1362	42	5	has	have	VERB
ap-1362	42	6	in	in	ADP
ap-1362	42	7	addition	addition	NOUN
ap-1362	42	8	the	the	DET
ap-1362	42	9	structure	structure	NOUN
ap-1362	42	10	of	of	ADP
ap-1362	42	11	a	a	DET
ap-1362	42	12	lie	lie	NOUN
ap-1362	42	13	algebra	algebra	NOUN
ap-1362	42	14	this	this	PRON
ap-1362	42	15	is	be	AUX
ap-1362	42	16	exactly	exactly	ADV
ap-1362	42	17	a	a	DET
ap-1362	42	18	cartan	cartan	ADJ
ap-1362	42	19	connection	connection	NOUN
ap-1362	42	20	of	of	ADP
ap-1362	42	21	type	type	NOUN
ap-1362	42	22	(	(	PUNCT
ap-1362	42	23	e	e	NOUN
ap-1362	42	24	,	,	PUNCT
ap-1362	42	25	g	g	NOUN
ap-1362	42	26	)	)	PUNCT
ap-1362	42	27	;	;	PUNCT
ap-1362	42	28	in	in	ADP
ap-1362	42	29	fact	fact	NOUN
ap-1362	42	30	,	,	PUNCT
ap-1362	42	31	the	the	DET
ap-1362	42	32	spectral	spectral	ADJ
ap-1362	42	33	linear	linear	ADJ
ap-1362	42	34	problem	problem	NOUN
ap-1362	42	35	is	be	AUX
ap-1362	42	36	nothing	nothing	PRON
ap-1362	42	37	but	but	SCONJ
ap-1362	42	38	the	the	DET
ap-1362	42	39	construction	construction	NOUN
ap-1362	42	40	of	of	ADP
ap-1362	42	41	a	a	DET
ap-1362	42	42	cartan	cartan	ADJ
ap-1362	42	43	connection	connection	NOUN
ap-1362	42	44	from	from	ADP
ap-1362	42	45	this	this	DET
ap-1362	42	46	absolute	absolute	ADJ
ap-1362	42	47	parallelism	parallelism	NOUN
ap-1362	42	48	.	.	PUNCT
ap-1362	43	1	as	as	ADP
ap-1362	43	2	an	an	DET
ap-1362	43	3	example	example	NOUN
ap-1362	43	4	,	,	PUNCT
ap-1362	43	5	let	let	VERB
ap-1362	43	6	us	we	PRON
ap-1362	43	7	now	now	ADV
ap-1362	43	8	introduce	introduce	VERB
ap-1362	43	9	on	on	ADP
ap-1362	43	10	a	a	DET
ap-1362	43	11	manifold	manifold	NOUN
ap-1362	43	12	with	with	ADP
ap-1362	43	13	local	local	ADJ
ap-1362	43	14	coordinates	coordinate	NOUN
ap-1362	43	15	(	(	PUNCT
ap-1362	43	16	x	x	X
ap-1362	43	17	,	,	PUNCT
ap-1362	43	18	y	y	PROPN
ap-1362	43	19	,	,	PUNCT
ap-1362	43	20	z	z	PROPN
ap-1362	43	21	,	,	PUNCT
ap-1362	43	22	u	u	NOUN
ap-1362	43	23	,	,	PUNCT
ap-1362	43	24	p	p	X
ap-1362	43	25	,	,	PUNCT
ap-1362	43	26	q	q	ADJ
ap-1362	43	27	,	,	PUNCT
ap-1362	43	28	r	r	NOUN
ap-1362	43	29	)	)	PUNCT
ap-1362	43	30	the	the	DET
ap-1362	43	31	closed	close	VERB
ap-1362	43	32	differential	differential	ADJ
ap-1362	43	33	ideal	ideal	NOUN
ap-1362	43	34	defined	define	VERB
ap-1362	43	35	by	by	ADP
ap-1362	43	36	the	the	DET
ap-1362	43	37	set	set	NOUN
ap-1362	43	38	of	of	ADP
ap-1362	43	39	3	3	NUM
ap-1362	43	40	-	-	PUNCT
ap-1362	43	41	forms	form	NOUN
ap-1362	43	42	:	:	PUNCT
ap-1362	43	43	θ1	θ1	NOUN
ap-1362	43	44	=	=	PROPN
ap-1362	43	45	du∧	du∧	PROPN
ap-1362	43	46	dx∧dy−rdx∧dy∧dz	dx∧dy−rdx∧dy∧dz	PROPN
ap-1362	43	47	,	,	PUNCT
ap-1362	43	48	θ2	θ2	PROPN
ap-1362	43	49	=	=	SYM
ap-1362	43	50	du∧dy∧dz−pdx∧dy∧dz	du∧dy∧dz−pdx∧dy∧dz	PROPN
ap-1362	43	51	,	,	PUNCT
ap-1362	43	52	θ3	θ3	NOUN
ap-1362	43	53	=	=	PROPN
ap-1362	43	54	du∧dx∧dz+	du∧dx∧dz+	PROPN
ap-1362	43	55	qdx∧dy∧dz	qdx∧dy∧dz	PROPN
ap-1362	43	56	,	,	PUNCT
ap-1362	43	57	θ4	θ4	NOUN
ap-1362	43	58	=	=	SYM
ap-1362	44	1	dp∧dy∧dz−	dp∧dy∧dz−	ADJ
ap-1362	44	2	dq	dq	NUM
ap-1362	44	3	∧	∧	PROPN
ap-1362	44	4	dx∧	dx∧	PROPN
ap-1362	44	5	dz	dz	NOUN
ap-1362	44	6	+	+	NUM
ap-1362	44	7	eudr	eudr	NOUN
ap-1362	44	8	∧	∧	PROPN
ap-1362	44	9	dx	dx	PROPN
ap-1362	44	10	∧	∧	PROPN
ap-1362	44	11	dy+	dy+	NOUN
ap-1362	44	12	eur2dx∧	eur2dx∧	NOUN
ap-1362	44	13	dy	dy	NOUN
ap-1362	44	14	∧	∧	PROPN
ap-1362	44	15	dz	dz	PROPN
ap-1362	44	16	.	.	PUNCT
ap-1362	45	1	it	it	PRON
ap-1362	45	2	is	be	AUX
ap-1362	45	3	easy	easy	ADJ
ap-1362	45	4	to	to	PART
ap-1362	45	5	verify	verify	VERB
ap-1362	45	6	that	that	SCONJ
ap-1362	45	7	on	on	ADP
ap-1362	45	8	every	every	DET
ap-1362	45	9	integral	integral	ADJ
ap-1362	45	10	submanifold	submanifold	NOUN
ap-1362	45	11	defined	define	VERB
ap-1362	45	12	by	by	ADP
ap-1362	45	13	u	u	NOUN
ap-1362	45	14	=	=	SYM
ap-1362	45	15	u(x	u(x	PROPN
ap-1362	45	16	,	,	PUNCT
ap-1362	45	17	y	y	PROPN
ap-1362	45	18	,	,	PUNCT
ap-1362	45	19	z	z	NOUN
ap-1362	45	20	)	)	PUNCT
ap-1362	45	21	,	,	PUNCT
ap-1362	45	22	p	p	NOUN
ap-1362	45	23	=	=	SYM
ap-1362	45	24	ux	ux	PROPN
ap-1362	45	25	,	,	PUNCT
ap-1362	45	26	q	q	X
ap-1362	45	27	=	=	PUNCT
ap-1362	45	28	uy	uy	PROPN
ap-1362	45	29	,	,	PUNCT
ap-1362	45	30	r	r	NOUN
ap-1362	45	31	=	=	SYM
ap-1362	45	32	uz	uz	PROPN
ap-1362	45	33	,	,	PUNCT
ap-1362	45	34	with	with	ADP
ap-1362	45	35	dx	dx	PROPN
ap-1362	45	36	∧	∧	PROPN
ap-1362	45	37	dy	dy	NOUN
ap-1362	45	38	∧	∧	PROPN
ap-1362	45	39	dz	dz	PROPN
ap-1362	45	40	�	�	PROPN
ap-1362	45	41	=	=	SYM
ap-1362	45	42	0	0	PROPN
ap-1362	45	43	,	,	PUNCT
ap-1362	45	44	the	the	DET
ap-1362	45	45	above	above	ADJ
ap-1362	45	46	ideal	ideal	NOUN
ap-1362	45	47	is	be	AUX
ap-1362	45	48	equivalent	equivalent	ADJ
ap-1362	45	49	to	to	ADP
ap-1362	45	50	the	the	DET
ap-1362	45	51	toda	toda	PROPN
ap-1362	45	52	system	system	NOUN
ap-1362	45	53	under	under	ADP
ap-1362	45	54	study	study	NOUN
ap-1362	45	55	.	.	PUNCT
ap-1362	46	1	in	in	ADP
ap-1362	46	2	terms	term	NOUN
ap-1362	46	3	of	of	ADP
ap-1362	46	4	absolute	absolute	ADJ
ap-1362	46	5	parallelism	parallelism	NOUN
ap-1362	46	6	forms	form	NOUN
ap-1362	46	7	,	,	PUNCT
ap-1362	46	8	2	2	NUM
ap-1362	46	9	-	-	PUNCT
ap-1362	46	10	forms	form	NOUN
ap-1362	46	11	generating	generate	VERB
ap-1362	46	12	associated	associate	VERB
ap-1362	46	13	conservation	conservation	NOUN
ap-1362	46	14	laws	law	NOUN
ap-1362	46	15	can	can	AUX
ap-1362	46	16	be	be	AUX
ap-1362	46	17	defined	define	VERB
ap-1362	46	18	as	as	SCONJ
ap-1362	46	19	follows	follow	VERB
ap-1362	46	20	:	:	PUNCT
ap-1362	46	21	ωk	ωk	ADP
ap-1362	46	22	=	=	PRON
ap-1362	46	23	hk(u	hk(u	X
ap-1362	46	24	,	,	PUNCT
ap-1362	46	25	ux	ux	PROPN
ap-1362	46	26	,	,	PUNCT
ap-1362	46	27	uy	uy	PROPN
ap-1362	46	28	,	,	PUNCT
ap-1362	46	29	uz	uz	PROPN
ap-1362	46	30	;	;	PUNCT
ap-1362	46	31	ξ	ξ	X
ap-1362	46	32	m)dx	m)dx	NOUN
ap-1362	46	33	∧	∧	NOUN
ap-1362	46	34	dy	dy	NOUN
ap-1362	46	35	+	+	X
ap-1362	46	36	f	f	PROPN
ap-1362	46	37	k(u	k(u	X
ap-1362	46	38	,	,	PUNCT
ap-1362	46	39	ux	ux	PROPN
ap-1362	46	40	,	,	PUNCT
ap-1362	46	41	uy	uy	PROPN
ap-1362	46	42	,	,	PUNCT
ap-1362	46	43	uz	uz	PROPN
ap-1362	46	44	;	;	PUNCT
ap-1362	46	45	ξm)dx	ξm)dx	NUM
ap-1362	46	46	∧	∧	NOUN
ap-1362	46	47	dz	dz	X
ap-1362	46	48	+	+	CCONJ
ap-1362	46	49	gk(u	gk(u	X
ap-1362	46	50	,	,	PUNCT
ap-1362	46	51	ux	ux	PROPN
ap-1362	46	52	,	,	PUNCT
ap-1362	46	53	uy	uy	PROPN
ap-1362	46	54	,	,	PUNCT
ap-1362	46	55	uz	uz	PROPN
ap-1362	46	56	;	;	PUNCT
ap-1362	46	57	ξ	ξ	PROPN
ap-1362	46	58	m)dy	m)dy	PROPN
ap-1362	46	59	∧	∧	PROPN
ap-1362	46	60	dz	dz	PROPN
ap-1362	46	61	+	+	CCONJ
ap-1362	46	62	ak	ak	PROPN
ap-1362	46	63	mdξm	mdξm	ADJ
ap-1362	46	64	∧	∧	PROPN
ap-1362	46	65	dx+bk	dx+bk	NOUN
ap-1362	46	66	mdξm	mdξm	ADJ
ap-1362	46	67	∧	∧	PROPN
ap-1362	46	68	dz	dz	X
ap-1362	46	69	+	+	CCONJ
ap-1362	46	70	dξk	dξk	NOUN
ap-1362	46	71	∧	∧	NOUN
ap-1362	46	72	dy	dy	NOUN
ap-1362	46	73	,	,	PUNCT
ap-1362	46	74	where	where	SCONJ
ap-1362	46	75	ξ	ξ	X
ap-1362	46	76	=	=	PRON
ap-1362	46	77	{	{	PUNCT
ap-1362	46	78	ξm	ξm	PROPN
ap-1362	46	79	}	}	PUNCT
ap-1362	46	80	,	,	PUNCT
ap-1362	46	81	k	k	PROPN
ap-1362	46	82	,	,	PUNCT
ap-1362	46	83	m	m	VERB
ap-1362	46	84	=	=	NOUN
ap-1362	46	85	1	1	NUM
ap-1362	46	86	,	,	PUNCT
ap-1362	46	87	2	2	NUM
ap-1362	46	88	,	,	PUNCT
ap-1362	46	89	.	.	PUNCT
ap-1362	46	90	.	.	PUNCT
ap-1362	46	91	.	.	PUNCT
ap-1362	47	1	,	,	PUNCT
ap-1362	47	2	n	n	X
ap-1362	47	3	(	(	PUNCT
ap-1362	47	4	n	n	CCONJ
ap-1362	47	5	arbitrary	arbitrary	ADJ
ap-1362	47	6	)	)	PUNCT
ap-1362	47	7	,	,	PUNCT
ap-1362	47	8	and	and	CCONJ
ap-1362	47	9	hk	hk	PROPN
ap-1362	47	10	,	,	PUNCT
ap-1362	47	11	f	f	PROPN
ap-1362	47	12	k	k	PROPN
ap-1362	47	13	and	and	CCONJ
ap-1362	47	14	gk	gk	PROPN
ap-1362	47	15	are	be	AUX
ap-1362	47	16	,	,	PUNCT
ap-1362	47	17	respectively	respectively	ADV
ap-1362	47	18	,	,	PUNCT
ap-1362	48	1	the	the	DET
ap-1362	48	2	pseudopotential	pseudopotential	NOUN
ap-1362	48	3	(	(	PUNCT
ap-1362	48	4	coordinates	coordinate	NOUN
ap-1362	48	5	in	in	ADP
ap-1362	48	6	the	the	DET
ap-1362	48	7	space	space	NOUN
ap-1362	48	8	v	v	NOUN
ap-1362	48	9	)	)	PUNCT
ap-1362	48	10	and	and	CCONJ
ap-1362	48	11	functions	function	NOUN
ap-1362	48	12	to	to	PART
ap-1362	48	13	be	be	AUX
ap-1362	48	14	determined	determine	VERB
ap-1362	48	15	,	,	PUNCT
ap-1362	48	16	while	while	SCONJ
ap-1362	48	17	ak	ak	PROPN
ap-1362	48	18	m	m	PROPN
ap-1362	48	19	and	and	CCONJ
ap-1362	48	20	bk	bk	PROPN
ap-1362	48	21	m	m	VERB
ap-1362	48	22	denote	denote	VERB
ap-1362	48	23	the	the	DET
ap-1362	48	24	elements	element	NOUN
ap-1362	48	25	of	of	ADP
ap-1362	48	26	two	two	NUM
ap-1362	48	27	n	n	NUM
ap-1362	48	28	×	×	NOUN
ap-1362	48	29	n	n	CCONJ
ap-1362	48	30	constant	constant	ADJ
ap-1362	48	31	regular	regular	ADJ
ap-1362	48	32	matrices	matrix	NOUN
ap-1362	48	33	.	.	PUNCT
ap-1362	49	1	in	in	ADP
ap-1362	49	2	fact	fact	NOUN
ap-1362	49	3	,	,	PUNCT
ap-1362	49	4	we	we	PRON
ap-1362	49	5	remark	remark	VERB
ap-1362	49	6	that	that	SCONJ
ap-1362	49	7	ωk	ωk	ADP
ap-1362	49	8	=	=	NOUN
ap-1362	49	9	θk	θk	NOUN
ap-1362	49	10	m	m	NOUN
ap-1362	49	11	∧	∧	NOUN
ap-1362	49	12	ωm	ωm	NOUN
ap-1362	49	13	,	,	PUNCT
ap-1362	49	14	where	where	SCONJ
ap-1362	49	15	θk	θk	NOUN
ap-1362	49	16	m	m	VERB
ap-1362	49	17	=	=	PUNCT
ap-1362	49	18	−āk	−āk	NUM
ap-1362	49	19	mdx−b̄k	mdx−b̄k	PROPN
ap-1362	49	20	mdy−	mdy−	PROPN
ap-1362	49	21	c̄k	c̄k	PROPN
ap-1362	49	22	mdz	mdz	PROPN
ap-1362	49	23	,	,	PUNCT
ap-1362	49	24	and	and	CCONJ
ap-1362	49	25	the	the	DET
ap-1362	49	26	absolute	absolute	ADJ
ap-1362	49	27	parallelism	parallelism	NOUN
ap-1362	49	28	forms	form	NOUN
ap-1362	49	29	are	be	AUX
ap-1362	49	30	given	give	VERB
ap-1362	49	31	by1	by1	PROPN
ap-1362	49	32	ωm	ωm	PUNCT
ap-1362	49	33	=	=	SYM
ap-1362	49	34	dξ̄m	dξ̄m	NOUN
ap-1362	49	35	+	+	CCONJ
ap-1362	49	36	f̄mdx+	f̄mdx+	X
ap-1362	49	37	ḡmdy	ḡmdy	NOUN
ap-1362	49	38	+	+	CCONJ
ap-1362	49	39	h̄mdz	h̄mdz	PROPN
ap-1362	49	40	.	.	PUNCT
ap-1362	50	1	the	the	DET
ap-1362	50	2	integrability	integrability	NOUN
ap-1362	50	3	condition	condition	NOUN
ap-1362	50	4	for	for	ADP
ap-1362	50	5	the	the	DET
ap-1362	50	6	ideal	ideal	NOUN
ap-1362	50	7	generated	generate	VERB
ap-1362	50	8	by	by	ADP
ap-1362	50	9	forms	form	NOUN
ap-1362	50	10	θj	θj	NOUN
ap-1362	50	11	and	and	CCONJ
ap-1362	50	12	ω	ω	NOUN
ap-1362	50	13	k	k	PROPN
ap-1362	50	14	finally	finally	ADV
ap-1362	50	15	yields	yield	VERB
ap-1362	50	16	hk	hk	PROPN
ap-1362	50	17	=	=	PUNCT
ap-1362	50	18	euuzl	euuzl	ADJ
ap-1362	50	19	k(ξm)+	k(ξm)+	PROPN
ap-1362	50	20	p	p	X
ap-1362	50	21	k(u	k(u	X
ap-1362	50	22	,	,	PUNCT
ap-1362	50	23	ξm	ξm	PROPN
ap-1362	50	24	)	)	PUNCT
ap-1362	50	25	,	,	PUNCT
ap-1362	50	26	f	f	PROPN
ap-1362	50	27	k	k	PROPN
ap-1362	50	28	=	=	PUNCT
ap-1362	50	29	−	−	PROPN
ap-1362	50	30	uyl	uyl	ADJ
ap-1362	50	31	k(ξm	k(ξm	NOUN
ap-1362	50	32	)	)	PUNCT
ap-1362	51	1	+	+	NUM
ap-1362	51	2	nk(ξm	nk(ξm	NOUN
ap-1362	51	3	)	)	PUNCT
ap-1362	51	4	,	,	PUNCT
ap-1362	51	5	gk	gk	PROPN
ap-1362	51	6	=	=	PUNCT
ap-1362	51	7	uxlk(ξm	uxlk(ξm	PROPN
ap-1362	51	8	)	)	PUNCT
ap-1362	51	9	+	+	NOUN
ap-1362	51	10	mk(u	mk(u	X
ap-1362	51	11	,	,	PUNCT
ap-1362	51	12	ξm	ξm	PROPN
ap-1362	51	13	)	)	PUNCT
ap-1362	51	14	,	,	PUNCT
ap-1362	51	15	where	where	SCONJ
ap-1362	51	16	lk	lk	PROPN
ap-1362	51	17	,	,	PUNCT
ap-1362	51	18	p	p	PROPN
ap-1362	51	19	k	k	PROPN
ap-1362	51	20	,	,	PUNCT
ap-1362	51	21	nk	nk	PROPN
ap-1362	51	22	,	,	PUNCT
ap-1362	51	23	mk	mk	PROPN
ap-1362	51	24	are	be	AUX
ap-1362	51	25	functions	function	NOUN
ap-1362	51	26	of	of	ADP
ap-1362	51	27	integration	integration	NOUN
ap-1362	51	28	.	.	PUNCT
ap-1362	52	1	as	as	ADP
ap-1362	52	2	a	a	DET
ap-1362	52	3	consequence	consequence	NOUN
ap-1362	52	4	,	,	PUNCT
ap-1362	52	5	the	the	DET
ap-1362	52	6	desired	desire	VERB
ap-1362	52	7	representation	representation	NOUN
ap-1362	52	8	for	for	ADP
ap-1362	52	9	the	the	DET
ap-1362	52	10	skeleton	skeleton	NOUN
ap-1362	52	11	is	be	AUX
ap-1362	52	12	provided	provide	VERB
ap-1362	52	13	by	by	ADP
ap-1362	52	14	the	the	DET
ap-1362	52	15	following	follow	VERB
ap-1362	52	16	equations	equation	NOUN
ap-1362	52	17	(	(	PUNCT
ap-1362	52	18	we	we	PRON
ap-1362	52	19	omit	omit	VERB
ap-1362	52	20	the	the	DET
ap-1362	52	21	indices	index	NOUN
ap-1362	52	22	for	for	ADP
ap-1362	52	23	simplicity	simplicity	NOUN
ap-1362	52	24	)	)	PUNCT
ap-1362	52	25	.	.	PUNCT
ap-1362	53	1	pu	pu	PROPN
ap-1362	53	2	=	=	SYM
ap-1362	53	3	eu[l	eu[l	PROPN
ap-1362	53	4	,	,	PUNCT
ap-1362	53	5	m	m	VERB
ap-1362	53	6	]	]	PUNCT
ap-1362	53	7	,	,	PUNCT
ap-1362	53	8	mu	mu	PROPN
ap-1362	53	9	=	=	PUNCT
ap-1362	53	10	−[l	−[l	PROPN
ap-1362	53	11	,	,	PUNCT
ap-1362	53	12	p	p	X
ap-1362	53	13	]	]	PUNCT
ap-1362	53	14	,	,	PUNCT
ap-1362	53	15	[	[	X
ap-1362	53	16	m	m	X
ap-1362	53	17	,	,	PUNCT
ap-1362	53	18	p	p	X
ap-1362	53	19	]	]	X
ap-1362	53	20	=	=	SYM
ap-1362	53	21	0	0	NUM
ap-1362	53	22	.(2	.(2	NUM
ap-1362	53	23	)	)	PUNCT
ap-1362	54	1	we	we	PRON
ap-1362	54	2	will	will	AUX
ap-1362	54	3	consider	consider	VERB
ap-1362	54	4	l	l	NOUN
ap-1362	54	5	,	,	PUNCT
ap-1362	54	6	p	p	X
ap-1362	54	7	,	,	PUNCT
ap-1362	54	8	m	m	VERB
ap-1362	54	9	as	as	ADP
ap-1362	54	10	regular	regular	ADJ
ap-1362	54	11	operators	operator	NOUN
ap-1362	54	12	so	so	SCONJ
ap-1362	54	13	that	that	DET
ap-1362	54	14	lie	lie	NOUN
ap-1362	54	15	brackets	bracket	NOUN
ap-1362	54	16	can	can	AUX
ap-1362	54	17	be	be	AUX
ap-1362	54	18	interpreted	interpret	VERB
ap-1362	54	19	as	as	ADP
ap-1362	54	20	commutators	commutator	NOUN
ap-1362	54	21	.	.	PUNCT
ap-1362	55	1	we	we	PRON
ap-1362	55	2	can	can	AUX
ap-1362	55	3	now	now	ADV
ap-1362	55	4	look	look	VERB
ap-1362	55	5	for	for	ADP
ap-1362	55	6	an	an	DET
ap-1362	55	7	exact	exact	ADJ
ap-1362	55	8	solution	solution	NOUN
ap-1362	55	9	in	in	ADP
ap-1362	55	10	1f	1f	NUM
ap-1362	55	11	k	k	X
ap-1362	56	1	=	=	PUNCT
ap-1362	56	2	c̄k	c̄k	VERB
ap-1362	56	3	mf̄	mf̄	PROPN
ap-1362	56	4	m	m	VERB
ap-1362	56	5	−	−	PROPN
ap-1362	56	6	āk	āk	PROPN
ap-1362	56	7	mh̄m	mh̄m	NOUN
ap-1362	56	8	,	,	PUNCT
ap-1362	56	9	gk	gk	PROPN
ap-1362	56	10	=	=	SYM
ap-1362	56	11	c̄k	c̄k	PROPN
ap-1362	56	12	mḡm	mḡm	NOUN
ap-1362	56	13	−	−	PROPN
ap-1362	56	14	b̄k	b̄k	PROPN
ap-1362	56	15	mh̄m	mh̄m	NOUN
ap-1362	56	16	,	,	PUNCT
ap-1362	56	17	hk	hk	NOUN
ap-1362	56	18	=	=	PUNCT
ap-1362	57	1	b̄k	b̄k	NOUN
ap-1362	57	2	mf̄	mf̄	PROPN
ap-1362	57	3	m	m	VERB
ap-1362	57	4	−	−	PROPN
ap-1362	57	5	āk	āk	PROPN
ap-1362	57	6	mḡm	mḡm	NOUN
ap-1362	57	7	,	,	PUNCT
ap-1362	57	8	ξk	ξk	ADP
ap-1362	57	9	=	=	PUNCT
ap-1362	57	10	c̄k	c̄k	NUM
ap-1362	57	11	mξ̄m	mξ̄m	NOUN
ap-1362	57	12	55	55	NUM
ap-1362	57	13	acta	acta	PROPN
ap-1362	57	14	polytechnica	polytechnica	PROPN
ap-1362	57	15	vol	vol	NOUN
ap-1362	57	16	.	.	PUNCT
ap-1362	58	1	51	51	NUM
ap-1362	58	2	no	no	NOUN
ap-1362	58	3	.	.	PUNCT
ap-1362	59	1	1/2011	1/2011	NUM
ap-1362	59	2	order	order	NOUN
ap-1362	59	3	to	to	PART
ap-1362	59	4	give	give	VERB
ap-1362	59	5	the	the	DET
ap-1362	59	6	representation	representation	NOUN
ap-1362	59	7	explicitly	explicitly	ADV
ap-1362	59	8	.	.	PUNCT
ap-1362	60	1	for	for	ADP
ap-1362	60	2	any	any	DET
ap-1362	60	3	operator	operator	NOUN
ap-1362	60	4	d	d	NOUN
ap-1362	60	5	=	=	SYM
ap-1362	60	6	dj	dj	NOUN
ap-1362	60	7	∂	∂	NOUN
ap-1362	60	8	∂ξj	∂ξj	NOUN
ap-1362	60	9	,	,	PUNCT
ap-1362	60	10	by	by	ADP
ap-1362	60	11	introducing	introduce	VERB
ap-1362	60	12	l[d	l[d	NOUN
ap-1362	60	13	]	]	PUNCT
ap-1362	60	14	=	=	PUNCT
ap-1362	61	1	[	[	X
ap-1362	61	2	l	l	NOUN
ap-1362	61	3	,	,	PUNCT
ap-1362	61	4	d	d	X
ap-1362	61	5	]	]	X
ap-1362	61	6	,	,	PUNCT
ap-1362	61	7	we	we	PRON
ap-1362	61	8	define	define	VERB
ap-1362	61	9	the	the	DET
ap-1362	61	10	n	n	ADV
ap-1362	61	11	-	-	PUNCT
ap-1362	61	12	th	th	NOUN
ap-1362	61	13	power	power	NOUN
ap-1362	61	14	of	of	ADP
ap-1362	61	15	the	the	DET
ap-1362	61	16	operator	operator	NOUN
ap-1362	61	17	l	l	NOUN
ap-1362	61	18	by	by	ADP
ap-1362	61	19	setting	set	VERB
ap-1362	61	20	ln[d	ln[d	NOUN
ap-1362	61	21	]	]	PUNCT
ap-1362	61	22	=	=	PUNCT
ap-1362	62	1	[	[	X
ap-1362	62	2	l	l	NOUN
ap-1362	62	3	,	,	PUNCT
ap-1362	62	4	[	[	X
ap-1362	62	5	l	l	NOUN
ap-1362	62	6	,	,	PUNCT
ap-1362	62	7	.	.	PUNCT
ap-1362	62	8	.	.	PUNCT
ap-1362	62	9	.	.	PUNCT
ap-1362	63	1	,	,	PUNCT
ap-1362	64	1	[	[	X
ap-1362	64	2	l	l	X
ap-1362	64	3	,	,	PUNCT
ap-1362	64	4	d	d	X
ap-1362	64	5	]	]	PUNCT
ap-1362	64	6	.	.	PUNCT
ap-1362	64	7	.	.	PUNCT
ap-1362	65	1	.	.	PUNCT
ap-1362	66	1	]	]	X
ap-1362	66	2	,	,	PUNCT
ap-1362	66	3	where	where	SCONJ
ap-1362	66	4	l	l	NOUN
ap-1362	66	5	appears	appear	VERB
ap-1362	66	6	n	n	NOUN
ap-1362	66	7	-	-	PUNCT
ap-1362	66	8	times	time	NOUN
ap-1362	66	9	,	,	PUNCT
ap-1362	66	10	and	and	CCONJ
ap-1362	66	11	l0[d	l0[d	NOUN
ap-1362	66	12	]	]	PUNCT
ap-1362	67	1	=	=	SYM
ap-1362	67	2	d.	d.	PROPN
ap-1362	67	3	put	put	VERB
ap-1362	67	4	t	t	PROPN
ap-1362	67	5	=	=	SYM
ap-1362	67	6	2e	2e	PROPN
ap-1362	67	7	u	u	NOUN
ap-1362	67	8	2	2	NUM
ap-1362	67	9	.	.	PUNCT
ap-1362	68	1	a	a	DET
ap-1362	68	2	solution	solution	NOUN
ap-1362	68	3	of	of	ADP
ap-1362	68	4	the	the	DET
ap-1362	68	5	prolongation	prolongation	NOUN
ap-1362	68	6	equations	equation	NOUN
ap-1362	68	7	regular	regular	ADJ
ap-1362	68	8	at	at	ADP
ap-1362	68	9	t	t	PROPN
ap-1362	68	10	=	=	SYM
ap-1362	68	11	0	0	PUNCT
ap-1362	68	12	(	(	PUNCT
ap-1362	68	13	i.e.	i.e.	X
ap-1362	68	14	at	at	ADP
ap-1362	68	15	u	u	NOUN
ap-1362	68	16	→	→	SYM
ap-1362	68	17	−∞	−∞	NOUN
ap-1362	68	18	)	)	PUNCT
ap-1362	68	19	is	be	AUX
ap-1362	68	20	then	then	ADV
ap-1362	68	21	given	give	VERB
ap-1362	68	22	by	by	ADP
ap-1362	68	23	p	p	PROPN
ap-1362	68	24	=	=	PROPN
ap-1362	68	25	t	t	PROPN
ap-1362	68	26	2	2	NUM
ap-1362	68	27	j1(tl[p0	j1(tl[p0	NOUN
ap-1362	68	28	]	]	PUNCT
ap-1362	68	29	)	)	PUNCT
ap-1362	68	30	,	,	PUNCT
ap-1362	68	31	m	m	VERB
ap-1362	68	32	=	=	ADJ
ap-1362	68	33	j0(tl[m0	j0(tl[m0	PROPN
ap-1362	68	34	]	]	PUNCT
ap-1362	68	35	)	)	PUNCT
ap-1362	68	36	,	,	PUNCT
ap-1362	68	37	(	(	PUNCT
ap-1362	68	38	3	3	X
ap-1362	68	39	)	)	PUNCT
ap-1362	68	40	where	where	SCONJ
ap-1362	68	41	j0	j0	PROPN
ap-1362	68	42	(	(	PUNCT
ap-1362	68	43	·	·	PUNCT
ap-1362	68	44	)	)	PUNCT
ap-1362	68	45	and	and	CCONJ
ap-1362	68	46	j1	j1	PROPN
ap-1362	68	47	(	(	PUNCT
ap-1362	68	48	·	·	PUNCT
ap-1362	68	49	)	)	PUNCT
ap-1362	68	50	are	be	AUX
ap-1362	68	51	formal	formal	ADJ
ap-1362	68	52	operator	operator	NOUN
ap-1362	68	53	expansions	expansion	NOUN
ap-1362	68	54	given	give	VERB
ap-1362	68	55	by	by	ADP
ap-1362	68	56	j0(tl[m0	j0(tl[m0	PROPN
ap-1362	68	57	]	]	PUNCT
ap-1362	68	58	)	)	PUNCT
ap-1362	69	1	=	=	SYM
ap-1362	70	1	∞∑	∞∑	NUM
ap-1362	70	2	m=0	m=0	PROPN
ap-1362	70	3	(	(	PUNCT
ap-1362	70	4	−1)m	−1)m	PROPN
ap-1362	70	5	(	(	PUNCT
ap-1362	70	6	m!)2	m!)2	PROPN
ap-1362	70	7	(	(	PUNCT
ap-1362	70	8	t	t	PROPN
ap-1362	70	9	2	2	NUM
ap-1362	70	10	)	)	PUNCT
ap-1362	70	11	2	2	NUM
ap-1362	70	12	m	m	NOUN
ap-1362	70	13	l2m[m0	l2m[m0	NOUN
ap-1362	70	14	]	]	PUNCT
ap-1362	70	15	,	,	PUNCT
ap-1362	70	16	j1(tl[p0	j1(tl[p0	NOUN
ap-1362	70	17	]	]	PUNCT
ap-1362	70	18	)	)	PUNCT
ap-1362	70	19	=	=	SYM
ap-1362	71	1	∞∑	∞∑	NUM
ap-1362	71	2	m=0	m=0	PROPN
ap-1362	71	3	(	(	PUNCT
ap-1362	71	4	−1)m	−1)m	PROPN
ap-1362	71	5	m!(m+	m!(m+	NOUN
ap-1362	71	6	1	1	NUM
ap-1362	71	7	)	)	PUNCT
ap-1362	71	8	!	!	PUNCT
ap-1362	72	1	(	(	PUNCT
ap-1362	72	2	t	t	NOUN
ap-1362	72	3	2	2	NUM
ap-1362	72	4	)	)	PUNCT
ap-1362	72	5	1	1	NUM
ap-1362	73	1	+	+	NUM
ap-1362	73	2	2	2	NUM
ap-1362	73	3	m	m	NOUN
ap-1362	73	4	l1	l1	NOUN
ap-1362	73	5	+	+	NOUN
ap-1362	73	6	2m[p0	2m[p0	NUM
ap-1362	73	7	]	]	PUNCT
ap-1362	73	8	and	and	CCONJ
ap-1362	73	9	m0	m0	PROPN
ap-1362	73	10	≡	≡	PROPN
ap-1362	73	11	m0(ξ	m0(ξ	AUX
ap-1362	73	12	)	)	PUNCT
ap-1362	73	13	=	=	SYM
ap-1362	73	14	m(t	m(t	NOUN
ap-1362	73	15	;	;	PUNCT
ap-1362	73	16	ξ	ξ	X
ap-1362	73	17	)	)	PUNCT
ap-1362	73	18	|t=0	|t=0	PROPN
ap-1362	73	19	and	and	CCONJ
ap-1362	73	20	p0	p0	NOUN
ap-1362	73	21	≡	≡	PROPN
ap-1362	73	22	p0(ξ	p0(ξ	X
ap-1362	73	23	)	)	PUNCT
ap-1362	73	24	is	be	AUX
ap-1362	73	25	such	such	ADJ
ap-1362	73	26	that	that	SCONJ
ap-1362	73	27	[	[	X
ap-1362	73	28	l	l	NOUN
ap-1362	73	29	,	,	PUNCT
ap-1362	73	30	p0	p0	NOUN
ap-1362	73	31	]	]	PUNCT
ap-1362	73	32	=	=	PUNCT
ap-1362	74	1	[	[	X
ap-1362	74	2	l	l	NOUN
ap-1362	74	3	,	,	PUNCT
ap-1362	74	4	m0	m0	NOUN
ap-1362	74	5	]	]	PUNCT
ap-1362	75	1	[	[	X
ap-1362	75	2	10	10	NUM
ap-1362	75	3	]	]	PUNCT
ap-1362	75	4	.	.	PUNCT
ap-1362	76	1	by	by	ADP
ap-1362	76	2	defining	define	VERB
ap-1362	76	3	operator	operator	NOUN
ap-1362	76	4	bessel	bessel	NOUN
ap-1362	76	5	coefficients	coefficient	NOUN
ap-1362	76	6	jm(tx	jm(tx	PROPN
ap-1362	76	7	)	)	PUNCT
ap-1362	76	8	,	,	PUNCT
ap-1362	76	9	as	as	ADP
ap-1362	76	10	the	the	DET
ap-1362	76	11	coefficients	coefficient	NOUN
ap-1362	76	12	of	of	ADP
ap-1362	76	13	the	the	DET
ap-1362	76	14	formal	formal	ADJ
ap-1362	76	15	expansion	expansion	NOUN
ap-1362	76	16	e	e	NOUN
ap-1362	76	17	t	t	NOUN
ap-1362	76	18	2x(z−1	2x(z−1	NUM
ap-1362	76	19	/	/	SYM
ap-1362	76	20	z	z	NOUN
ap-1362	76	21	)	)	PUNCT
ap-1362	76	22	=	=	NOUN
ap-1362	77	1	∞∑	∞∑	NUM
ap-1362	77	2	m=−∞	m=−∞	X
ap-1362	77	3	zmjm(tx	zmjm(tx	NOUN
ap-1362	77	4	)	)	PUNCT
ap-1362	77	5	(	(	PUNCT
ap-1362	77	6	for	for	ADP
ap-1362	77	7	bessel	bessel	NOUN
ap-1362	77	8	functions	function	NOUN
ap-1362	77	9	a	a	DET
ap-1362	77	10	standard	standard	ADJ
ap-1362	77	11	reference	reference	NOUN
ap-1362	77	12	is	be	AUX
ap-1362	77	13	[	[	X
ap-1362	77	14	16	16	NUM
ap-1362	77	15	]	]	PUNCT
ap-1362	77	16	)	)	PUNCT
ap-1362	77	17	,	,	PUNCT
ap-1362	77	18	we	we	PRON
ap-1362	77	19	can	can	AUX
ap-1362	77	20	prove	prove	VERB
ap-1362	77	21	recurrence	recurrence	NOUN
ap-1362	77	22	and	and	CCONJ
ap-1362	77	23	derivation	derivation	NOUN
ap-1362	77	24	formulae	formulae	NOUN
ap-1362	77	25	by	by	ADP
ap-1362	77	26	means	mean	NOUN
ap-1362	77	27	of	of	ADP
ap-1362	77	28	which	which	PRON
ap-1362	77	29	we	we	PRON
ap-1362	77	30	provide	provide	VERB
ap-1362	77	31	an	an	DET
ap-1362	77	32	equivalent	equivalent	ADJ
ap-1362	77	33	solution	solution	NOUN
ap-1362	77	34	to	to	ADP
ap-1362	77	35	our	our	PRON
ap-1362	77	36	prolongation	prolongation	NOUN
ap-1362	77	37	equations	equation	NOUN
ap-1362	77	38	in	in	ADP
ap-1362	77	39	terms	term	NOUN
ap-1362	77	40	of	of	ADP
ap-1362	77	41	l	l	NOUN
ap-1362	77	42	:	:	PUNCT
ap-1362	77	43	p	p	X
ap-1362	77	44	=	=	PUNCT
ap-1362	77	45	t	t	PROPN
ap-1362	77	46	2	2	NUM
ap-1362	77	47	∞∑	∞∑	PROPN
ap-1362	77	48	k=−∞	k=−∞	X
ap-1362	77	49	jk+1(tl)p0jk(tl	jk+1(tl)p0jk(tl	PROPN
ap-1362	77	50	)	)	PUNCT
ap-1362	77	51	,	,	PUNCT
ap-1362	77	52	m	m	VERB
ap-1362	77	53	=	=	SYM
ap-1362	77	54	∞∑	∞∑	NUM
ap-1362	77	55	k=−∞	k=−∞	X
ap-1362	77	56	jk(tl)m0jk(tl	jk(tl)m0jk(tl	ADJ
ap-1362	77	57	)	)	PUNCT
ap-1362	77	58	,	,	PUNCT
ap-1362	77	59	based	base	VERB
ap-1362	77	60	on	on	ADP
ap-1362	77	61	the	the	DET
ap-1362	77	62	formulae	formulae	ADJ
ap-1362	77	63	j1(tl[p0	j1(tl[p0	NOUN
ap-1362	77	64	]	]	PUNCT
ap-1362	77	65	)	)	PUNCT
ap-1362	77	66	=	=	SYM
ap-1362	78	1	∞∑	∞∑	NUM
ap-1362	78	2	k=−∞	k=−∞	PROPN
ap-1362	78	3	jk+1(tl)p0jk(tl	jk+1(tl)p0jk(tl	PROPN
ap-1362	78	4	)	)	PUNCT
ap-1362	78	5	,	,	PUNCT
ap-1362	78	6	j0(tl[m0	j0(tl[m0	PROPN
ap-1362	78	7	]	]	PUNCT
ap-1362	78	8	)	)	PUNCT
ap-1362	78	9	=	=	PUNCT
ap-1362	79	1	∞∑	∞∑	NUM
ap-1362	79	2	k=−∞	k=−∞	PROPN
ap-1362	79	3	jk(tl)m0jk(tl	jk(tl)m0jk(tl	PROPN
ap-1362	79	4	)	)	PUNCT
ap-1362	79	5	,	,	PUNCT
ap-1362	79	6	which	which	PRON
ap-1362	79	7	are	be	AUX
ap-1362	79	8	in	in	ADP
ap-1362	79	9	fact	fact	NOUN
ap-1362	79	10	analogous	analogous	ADJ
ap-1362	79	11	to	to	ADP
ap-1362	79	12	the	the	DET
ap-1362	79	13	baker	baker	NOUN
ap-1362	79	14	-	-	PUNCT
ap-1362	79	15	campbellhausdorff	campbellhausdorff	ADJ
ap-1362	79	16	expansion	expansion	NOUN
ap-1362	79	17	[	[	X
ap-1362	79	18	10	10	NUM
ap-1362	79	19	]	]	PUNCT
ap-1362	79	20	.	.	PUNCT
ap-1362	80	1	these	these	DET
ap-1362	80	2	expansions	expansion	NOUN
ap-1362	80	3	together	together	ADV
ap-1362	80	4	with	with	ADP
ap-1362	80	5	[	[	X
ap-1362	80	6	m	m	NOUN
ap-1362	80	7	,	,	PUNCT
ap-1362	80	8	p	p	X
ap-1362	80	9	]	]	X
ap-1362	80	10	=	=	SYM
ap-1362	80	11	0	0	PUNCT
ap-1362	80	12	provide	provide	VERB
ap-1362	80	13	the	the	DET
ap-1362	80	14	desired	desire	VERB
ap-1362	80	15	representation	representation	NOUN
ap-1362	80	16	and	and	CCONJ
ap-1362	80	17	at	at	ADP
ap-1362	80	18	the	the	DET
ap-1362	80	19	same	same	ADJ
ap-1362	80	20	time	time	NOUN
ap-1362	80	21	define	define	VERB
ap-1362	80	22	a	a	DET
ap-1362	80	23	tower	tower	NOUN
ap-1362	80	24	with	with	ADP
ap-1362	80	25	absolute	absolute	ADJ
ap-1362	80	26	parallelism	parallelism	NOUN
ap-1362	80	27	.	.	PUNCT
ap-1362	81	1	the	the	DET
ap-1362	81	2	main	main	ADJ
ap-1362	81	3	problem	problem	NOUN
ap-1362	81	4	with	with	ADP
ap-1362	81	5	this	this	DET
ap-1362	81	6	tower	tower	NOUN
ap-1362	81	7	(	(	PUNCT
ap-1362	81	8	which	which	PRON
ap-1362	81	9	is	be	AUX
ap-1362	81	10	somehow	somehow	ADV
ap-1362	81	11	the	the	DET
ap-1362	81	12	most	most	ADV
ap-1362	81	13	general	general	ADJ
ap-1362	81	14	one	one	NUM
ap-1362	81	15	)	)	PUNCT
ap-1362	81	16	is	be	AUX
ap-1362	81	17	that	that	SCONJ
ap-1362	81	18	it	it	PRON
ap-1362	81	19	is	be	AUX
ap-1362	81	20	a	a	DET
ap-1362	81	21	non	non	ADJ
ap-1362	81	22	trivial	trivial	ADJ
ap-1362	81	23	task	task	NOUN
ap-1362	81	24	to	to	PART
ap-1362	81	25	characterize	characterize	VERB
ap-1362	81	26	explicitly	explicitly	ADV
ap-1362	81	27	its	its	PRON
ap-1362	81	28	algebraic	algebraic	ADJ
ap-1362	81	29	skeleton	skeleton	NOUN
ap-1362	81	30	by	by	ADP
ap-1362	81	31	means	mean	NOUN
ap-1362	81	32	of	of	ADP
ap-1362	81	33	the	the	DET
ap-1362	81	34	representation	representation	NOUN
ap-1362	81	35	provided	provide	VERB
ap-1362	81	36	by	by	ADP
ap-1362	81	37	the	the	DET
ap-1362	81	38	relations	relation	NOUN
ap-1362	81	39	[	[	X
ap-1362	81	40	m	m	X
ap-1362	81	41	,	,	PUNCT
ap-1362	81	42	p	p	X
ap-1362	81	43	]	]	X
ap-1362	81	44	=	=	PUNCT
ap-1362	81	45	0	0	X
ap-1362	81	46	.	.	PUNCT
ap-1362	82	1	on	on	ADP
ap-1362	82	2	the	the	DET
ap-1362	82	3	other	other	ADJ
ap-1362	82	4	hand	hand	NOUN
ap-1362	82	5	,	,	PUNCT
ap-1362	82	6	it	it	PRON
ap-1362	82	7	is	be	AUX
ap-1362	82	8	well	well	ADV
ap-1362	82	9	known	know	VERB
ap-1362	82	10	that	that	SCONJ
ap-1362	82	11	the	the	DET
ap-1362	82	12	toda	toda	PROPN
ap-1362	82	13	equation	equation	NOUN
ap-1362	82	14	can	can	AUX
ap-1362	82	15	be	be	AUX
ap-1362	82	16	solved	solve	VERB
ap-1362	82	17	by	by	ADP
ap-1362	82	18	the	the	DET
ap-1362	82	19	inverse	inverse	NOUN
ap-1362	82	20	scattering	scattering	NOUN
ap-1362	82	21	transform	transform	NOUN
ap-1362	82	22	[	[	X
ap-1362	82	23	7	7	NUM
ap-1362	82	24	]	]	PUNCT
ap-1362	82	25	.	.	PUNCT
ap-1362	83	1	however	however	ADV
ap-1362	83	2	,	,	PUNCT
ap-1362	83	3	the	the	DET
ap-1362	83	4	associated	associated	ADJ
ap-1362	83	5	linear	linear	PROPN
ap-1362	83	6	spectral	spectral	ADJ
ap-1362	83	7	problem	problem	NOUN
ap-1362	83	8	was	be	AUX
ap-1362	83	9	never	never	ADV
ap-1362	83	10	derived	derive	VERB
ap-1362	83	11	from	from	ADP
ap-1362	83	12	an	an	DET
ap-1362	83	13	infinitesimal	infinitesimal	ADJ
ap-1362	83	14	algebraic	algebraic	ADJ
ap-1362	83	15	skeleton	skeleton	NOUN
ap-1362	83	16	and	and	CCONJ
ap-1362	83	17	in	in	ADP
ap-1362	83	18	particular	particular	ADJ
ap-1362	83	19	as	as	ADP
ap-1362	83	20	the	the	DET
ap-1362	83	21	construction	construction	NOUN
ap-1362	83	22	of	of	ADP
ap-1362	83	23	a	a	DET
ap-1362	83	24	cartan	cartan	ADJ
ap-1362	83	25	connection	connection	NOUN
ap-1362	83	26	from	from	ADP
ap-1362	83	27	a	a	DET
ap-1362	83	28	tower	tower	NOUN
ap-1362	83	29	with	with	ADP
ap-1362	83	30	algebraic	algebraic	PROPN
ap-1362	83	31	skeleton	skeleton	NOUN
ap-1362	83	32	;	;	PUNCT
ap-1362	83	33	thus	thus	ADV
ap-1362	83	34	it	it	PRON
ap-1362	83	35	would	would	AUX
ap-1362	83	36	be	be	AUX
ap-1362	83	37	important	important	ADJ
ap-1362	83	38	to	to	PART
ap-1362	83	39	derive	derive	VERB
ap-1362	83	40	both	both	CCONJ
ap-1362	83	41	the	the	DET
ap-1362	83	42	toda	toda	PROPN
ap-1362	83	43	system	system	NOUN
ap-1362	83	44	and	and	CCONJ
ap-1362	83	45	related	relate	VERB
ap-1362	83	46	spectral	spectral	ADJ
ap-1362	83	47	problem(s	problem(s	NOUN
ap-1362	83	48	)	)	PUNCT
ap-1362	83	49	(	(	PUNCT
ap-1362	83	50	i.e.	i.e.	X
ap-1362	83	51	conservation	conservation	NOUN
ap-1362	83	52	laws	law	NOUN
ap-1362	83	53	and	and	CCONJ
ap-1362	83	54	symmetries	symmetry	NOUN
ap-1362	83	55	)	)	PUNCT
ap-1362	83	56	starting	start	VERB
ap-1362	83	57	from	from	ADP
ap-1362	83	58	a	a	DET
ap-1362	83	59	tower	tower	NOUN
ap-1362	83	60	with	with	ADP
ap-1362	83	61	an	an	DET
ap-1362	83	62	algebraic	algebraic	ADJ
ap-1362	83	63	skeleton	skeleton	NOUN
ap-1362	83	64	.	.	PUNCT
ap-1362	84	1	in	in	ADP
ap-1362	84	2	this	this	DET
ap-1362	84	3	perspective	perspective	NOUN
ap-1362	84	4	,	,	PUNCT
ap-1362	84	5	particular	particular	ADJ
ap-1362	84	6	solutions	solution	NOUN
ap-1362	84	7	of	of	ADP
ap-1362	84	8	the	the	DET
ap-1362	84	9	corresponding	corresponding	ADJ
ap-1362	84	10	estabrook	estabrook	NOUN
ap-1362	84	11	-	-	PUNCT
ap-1362	84	12	wahlquist	wahlquist	NOUN
ap-1362	84	13	prolongation	prolongation	NOUN
ap-1362	84	14	problem	problem	NOUN
ap-1362	84	15	can	can	AUX
ap-1362	84	16	assume	assume	VERB
ap-1362	84	17	a	a	DET
ap-1362	84	18	relevant	relevant	ADJ
ap-1362	84	19	role	role	NOUN
ap-1362	84	20	:	:	PUNCT
ap-1362	84	21	they	they	PRON
ap-1362	84	22	correspond	correspond	VERB
ap-1362	84	23	to	to	ADP
ap-1362	84	24	particular	particular	ADJ
ap-1362	84	25	choices	choice	NOUN
ap-1362	84	26	for	for	ADP
ap-1362	84	27	the	the	DET
ap-1362	84	28	absolute	absolute	ADJ
ap-1362	84	29	parallelism	parallelism	NOUN
ap-1362	84	30	and	and	CCONJ
ap-1362	84	31	can	can	AUX
ap-1362	84	32	provide	provide	VERB
ap-1362	84	33	us	we	PRON
ap-1362	84	34	explicit	explicit	ADJ
ap-1362	84	35	representations	representation	NOUN
ap-1362	84	36	of	of	ADP
ap-1362	84	37	the	the	DET
ap-1362	84	38	prolongation	prolongation	NOUN
ap-1362	84	39	skeleton	skeleton	NOUN
ap-1362	84	40	.	.	PUNCT
ap-1362	85	1	2.1	2.1	NUM
ap-1362	85	2	skeletons	skeleton	NOUN
ap-1362	85	3	if	if	SCONJ
ap-1362	85	4	we	we	PRON
ap-1362	85	5	look	look	VERB
ap-1362	85	6	for	for	ADP
ap-1362	85	7	operators	operator	NOUN
ap-1362	85	8	p	p	X
ap-1362	85	9	(	(	PUNCT
ap-1362	85	10	u	u	NOUN
ap-1362	85	11	,	,	PUNCT
ap-1362	85	12	ξ	ξ	NOUN
ap-1362	85	13	)	)	PUNCT
ap-1362	85	14	and	and	CCONJ
ap-1362	85	15	m(u	m(u	PROPN
ap-1362	85	16	,	,	PUNCT
ap-1362	85	17	ξ	ξ	NOUN
ap-1362	85	18	)	)	PUNCT
ap-1362	85	19	depending	depend	VERB
ap-1362	85	20	on	on	ADP
ap-1362	85	21	u	u	NOUN
ap-1362	85	22	only	only	ADV
ap-1362	85	23	through	through	ADP
ap-1362	85	24	the	the	DET
ap-1362	85	25	exponential	exponential	ADJ
ap-1362	85	26	function	function	NOUN
ap-1362	85	27	,	,	PUNCT
ap-1362	85	28	i.e.	i.e.	X
ap-1362	85	29	p	p	X
ap-1362	85	30	(	(	PUNCT
ap-1362	85	31	u	u	NOUN
ap-1362	85	32	,	,	PUNCT
ap-1362	85	33	ξ	ξ	X
ap-1362	85	34	)	)	PUNCT
ap-1362	85	35	=	=	SYM
ap-1362	85	36	eup̄	eup̄	X
ap-1362	85	37	(	(	PUNCT
ap-1362	85	38	ξ	ξ	NOUN
ap-1362	85	39	)	)	PUNCT
ap-1362	85	40	,	,	PUNCT
ap-1362	85	41	m(u	m(u	PROPN
ap-1362	85	42	,	,	PUNCT
ap-1362	85	43	ξ	ξ	NOUN
ap-1362	85	44	)	)	PUNCT
ap-1362	85	45	=	=	SYM
ap-1362	85	46	m(eu	m(eu	SYM
ap-1362	85	47	,	,	PUNCT
ap-1362	85	48	ξ	ξ	NOUN
ap-1362	85	49	)	)	PUNCT
ap-1362	85	50	,	,	PUNCT
ap-1362	85	51	the	the	DET
ap-1362	85	52	prolongation	prolongation	NOUN
ap-1362	85	53	equations	equation	NOUN
ap-1362	85	54	can	can	AUX
ap-1362	85	55	now	now	ADV
ap-1362	85	56	be	be	AUX
ap-1362	85	57	written	write	VERB
ap-1362	85	58	as	as	ADP
ap-1362	85	59	:	:	PUNCT
ap-1362	85	60	pu	pu	PROPN
ap-1362	85	61	=	=	SYM
ap-1362	85	62	eu[l	eu[l	PROPN
ap-1362	85	63	,	,	PUNCT
ap-1362	85	64	m	m	VERB
ap-1362	85	65	]	]	PUNCT
ap-1362	85	66	=	=	PUNCT
ap-1362	85	67	∂p	∂p	PROPN
ap-1362	85	68	∂eu	∂eu	PROPN
ap-1362	85	69	eu	eu	PROPN
ap-1362	85	70	,	,	PUNCT
ap-1362	85	71	mu	mu	PROPN
ap-1362	85	72	=	=	PUNCT
ap-1362	85	73	−[l	−[l	PROPN
ap-1362	85	74	,	,	PUNCT
ap-1362	85	75	p	p	X
ap-1362	85	76	]	]	X
ap-1362	85	77	=	=	SYM
ap-1362	85	78	∂m	∂m	PROPN
ap-1362	85	79	∂eu	∂eu	PROPN
ap-1362	85	80	eu	eu	PROPN
ap-1362	85	81	;	;	PUNCT
ap-1362	85	82	on	on	ADP
ap-1362	85	83	the	the	DET
ap-1362	85	84	other	other	ADJ
ap-1362	85	85	hand	hand	NOUN
ap-1362	85	86	,	,	PUNCT
ap-1362	85	87	we	we	PRON
ap-1362	85	88	have	have	VERB
ap-1362	85	89	∂p	∂p	PROPN
ap-1362	85	90	∂eu	∂eu	PROPN
ap-1362	85	91	=	=	SYM
ap-1362	85	92	p̄	p̄	NOUN
ap-1362	85	93	(	(	PUNCT
ap-1362	85	94	ξ	ξ	X
ap-1362	85	95	)	)	PUNCT
ap-1362	85	96	=	=	NOUN
ap-1362	86	1	[	[	X
ap-1362	86	2	l(ξ	l(ξ	NOUN
ap-1362	86	3	)	)	PUNCT
ap-1362	86	4	,	,	PUNCT
ap-1362	86	5	m(eu	m(eu	NUM
ap-1362	86	6	;	;	PUNCT
ap-1362	86	7	ξ	ξ	X
ap-1362	86	8	)	)	PUNCT
ap-1362	86	9	]	]	PUNCT
ap-1362	86	10	,	,	PUNCT
ap-1362	86	11	∂m	∂m	PROPN
ap-1362	86	12	∂eu	∂eu	PROPN
ap-1362	86	13	=	=	SYM
ap-1362	86	14	−[l(ξ	−[l(ξ	PROPN
ap-1362	86	15	)	)	PUNCT
ap-1362	86	16	,	,	PUNCT
ap-1362	86	17	p̄	p̄	X
ap-1362	86	18	(	(	PUNCT
ap-1362	86	19	ξ	ξ	NOUN
ap-1362	86	20	)	)	PUNCT
ap-1362	86	21	]	]	PUNCT
ap-1362	86	22	.	.	PUNCT
ap-1362	87	1	from	from	ADP
ap-1362	87	2	the	the	DET
ap-1362	87	3	second	second	ADJ
ap-1362	87	4	equation	equation	NOUN
ap-1362	87	5	,	,	PUNCT
ap-1362	87	6	we	we	PRON
ap-1362	87	7	get	get	VERB
ap-1362	87	8	m(eu	m(eu	NOUN
ap-1362	87	9	;	;	PUNCT
ap-1362	87	10	ξ	ξ	X
ap-1362	87	11	)	)	PUNCT
ap-1362	87	12	=	=	SYM
ap-1362	87	13	−eu[l(ξ	−eu[l(ξ	NOUN
ap-1362	87	14	)	)	PUNCT
ap-1362	87	15	,	,	PUNCT
ap-1362	87	16	p̄	p̄	X
ap-1362	87	17	(	(	PUNCT
ap-1362	87	18	ξ	ξ	NOUN
ap-1362	87	19	)	)	PUNCT
ap-1362	87	20	]	]	PUNCT
ap-1362	88	1	+	+	CCONJ
ap-1362	88	2	m̄(ξ	m̄(ξ	NOUN
ap-1362	88	3	)	)	PUNCT
ap-1362	88	4	and	and	CCONJ
ap-1362	88	5	thus	thus	ADV
ap-1362	88	6	p̄	p̄	X
ap-1362	88	7	(	(	PUNCT
ap-1362	88	8	ξ	ξ	NOUN
ap-1362	88	9	)	)	PUNCT
ap-1362	88	10	=	=	SYM
ap-1362	88	11	−eu[l(ξ	−eu[l(ξ	NOUN
ap-1362	88	12	)	)	PUNCT
ap-1362	88	13	,	,	PUNCT
ap-1362	89	1	[	[	X
ap-1362	89	2	l(ξ	l(ξ	NOUN
ap-1362	89	3	)	)	PUNCT
ap-1362	89	4	,	,	PUNCT
ap-1362	89	5	p̄	p̄	X
ap-1362	89	6	(	(	PUNCT
ap-1362	89	7	ξ	ξ	NOUN
ap-1362	89	8	)	)	PUNCT
ap-1362	89	9	]	]	PUNCT
ap-1362	89	10	]	]	PUNCT
ap-1362	90	1	+	+	CCONJ
ap-1362	90	2	[	[	X
ap-1362	90	3	l(ξ	l(ξ	NOUN
ap-1362	90	4	)	)	PUNCT
ap-1362	90	5	,	,	PUNCT
ap-1362	90	6	m̄(ξ	m̄(ξ	NOUN
ap-1362	90	7	)	)	PUNCT
ap-1362	90	8	]	]	PUNCT
ap-1362	90	9	.	.	PUNCT
ap-1362	91	1	we	we	PRON
ap-1362	91	2	see	see	VERB
ap-1362	91	3	then	then	ADV
ap-1362	91	4	that	that	SCONJ
ap-1362	91	5	we	we	PRON
ap-1362	91	6	are	be	AUX
ap-1362	91	7	able	able	ADJ
ap-1362	91	8	to	to	PART
ap-1362	91	9	obtain	obtain	VERB
ap-1362	91	10	commutation	commutation	NOUN
ap-1362	91	11	relations	relation	NOUN
ap-1362	91	12	:	:	PUNCT
ap-1362	91	13	p̄	p̄	X
ap-1362	91	14	(	(	PUNCT
ap-1362	91	15	ξ	ξ	X
ap-1362	91	16	)	)	PUNCT
ap-1362	91	17	=	=	NOUN
ap-1362	92	1	[	[	X
ap-1362	92	2	l(ξ	l(ξ	NOUN
ap-1362	92	3	)	)	PUNCT
ap-1362	92	4	,	,	PUNCT
ap-1362	92	5	m̄(ξ	m̄(ξ	NOUN
ap-1362	92	6	)	)	PUNCT
ap-1362	92	7	]	]	PUNCT
ap-1362	92	8	,	,	PUNCT
ap-1362	93	1	[	[	X
ap-1362	93	2	l(ξ	l(ξ	NOUN
ap-1362	93	3	)	)	PUNCT
ap-1362	93	4	,	,	PUNCT
ap-1362	94	1	[	[	X
ap-1362	94	2	l(ξ	l(ξ	NOUN
ap-1362	94	3	)	)	PUNCT
ap-1362	94	4	,	,	PUNCT
ap-1362	94	5	p̄	p̄	X
ap-1362	94	6	(	(	PUNCT
ap-1362	94	7	ξ	ξ	NOUN
ap-1362	94	8	)	)	PUNCT
ap-1362	94	9	]	]	X
ap-1362	94	10	]	]	X
ap-1362	95	1	=	=	PUNCT
ap-1362	95	2	0	0	X
ap-1362	95	3	.	.	PUNCT
ap-1362	96	1	there	there	PRON
ap-1362	96	2	are	be	VERB
ap-1362	96	3	additional	additional	ADJ
ap-1362	96	4	relations	relation	NOUN
ap-1362	96	5	determined	determine	VERB
ap-1362	96	6	by	by	ADP
ap-1362	96	7	the	the	DET
ap-1362	96	8	third	third	ADJ
ap-1362	96	9	prolongation	prolongation	NOUN
ap-1362	96	10	equation	equation	NOUN
ap-1362	96	11	[	[	X
ap-1362	96	12	−eu[l(ξ	−eu[l(ξ	NOUN
ap-1362	96	13	)	)	PUNCT
ap-1362	96	14	,	,	PUNCT
ap-1362	96	15	p̄	p̄	X
ap-1362	96	16	(	(	PUNCT
ap-1362	96	17	ξ	ξ	NOUN
ap-1362	96	18	)	)	PUNCT
ap-1362	96	19	]	]	PUNCT
ap-1362	97	1	+	+	CCONJ
ap-1362	97	2	m̄(ξ	m̄(ξ	NOUN
ap-1362	97	3	)	)	PUNCT
ap-1362	97	4	,	,	PUNCT
ap-1362	97	5	eup̄	eup̄	X
ap-1362	97	6	(	(	PUNCT
ap-1362	97	7	ξ	ξ	NOUN
ap-1362	97	8	)	)	PUNCT
ap-1362	97	9	]	]	PUNCT
ap-1362	98	1	=	=	PUNCT
ap-1362	98	2	0	0	NUM
ap-1362	98	3	,	,	PUNCT
ap-1362	98	4	so	so	SCONJ
ap-1362	98	5	that	that	SCONJ
ap-1362	98	6	we	we	PRON
ap-1362	98	7	have	have	VERB
ap-1362	98	8	[	[	X
ap-1362	98	9	[	[	X
ap-1362	98	10	l	l	NOUN
ap-1362	98	11	,	,	PUNCT
ap-1362	98	12	p̄	p̄	NOUN
ap-1362	98	13	]	]	PUNCT
ap-1362	98	14	,	,	PUNCT
ap-1362	98	15	p̄	p̄	PROPN
ap-1362	98	16	]	]	PUNCT
ap-1362	99	1	=	=	PUNCT
ap-1362	99	2	0	0	NUM
ap-1362	99	3	,	,	PUNCT
ap-1362	99	4	[	[	X
ap-1362	99	5	m̄	m̄	NOUN
ap-1362	99	6	,	,	PUNCT
ap-1362	99	7	p̄	p̄	VERB
ap-1362	99	8	]	]	PUNCT
ap-1362	99	9	=	=	PUNCT
ap-1362	100	1	0	0	X
ap-1362	100	2	.	.	PUNCT
ap-1362	101	1	for	for	ADP
ap-1362	101	2	the	the	DET
ap-1362	101	3	sake	sake	NOUN
ap-1362	101	4	of	of	ADP
ap-1362	101	5	convenience	convenience	NOUN
ap-1362	101	6	we	we	PRON
ap-1362	101	7	put	put	VERB
ap-1362	101	8	l	l	NOUN
ap-1362	101	9	=	=	SYM
ap-1362	101	10	x1	x1	PROPN
ap-1362	101	11	,	,	PUNCT
ap-1362	101	12	m̄	m̄	NOUN
ap-1362	101	13	=	=	SYM
ap-1362	101	14	x2	x2	PROPN
ap-1362	101	15	,	,	PUNCT
ap-1362	101	16	p̄	p̄	PROPN
ap-1362	101	17	=	=	SYM
ap-1362	101	18	x3	x3	PROPN
ap-1362	101	19	,	,	PUNCT
ap-1362	102	1	[	[	X
ap-1362	102	2	x1	x1	ADJ
ap-1362	102	3	,	,	PUNCT
ap-1362	102	4	x3	x3	ADJ
ap-1362	102	5	]	]	PUNCT
ap-1362	102	6	=	=	PUNCT
ap-1362	102	7	x4	x4	PROPN
ap-1362	102	8	and	and	CCONJ
ap-1362	102	9	we	we	PRON
ap-1362	102	10	then	then	ADV
ap-1362	102	11	have	have	VERB
ap-1362	102	12	the	the	DET
ap-1362	102	13	following	follow	VERB
ap-1362	102	14	prolongation	prolongation	NOUN
ap-1362	102	15	closed	close	VERB
ap-1362	102	16	lie	lie	NOUN
ap-1362	102	17	algebra	algebra	NOUN
ap-1362	102	18	:	:	PUNCT
ap-1362	103	1	[	[	X
ap-1362	103	2	x1	x1	X
ap-1362	103	3	,	,	PUNCT
ap-1362	103	4	x2	x2	PROPN
ap-1362	103	5	]	]	X
ap-1362	103	6	=	=	SYM
ap-1362	103	7	x3	x3	ADJ
ap-1362	103	8	,	,	PUNCT
ap-1362	103	9	[	[	X
ap-1362	103	10	x1	x1	ADJ
ap-1362	103	11	,	,	PUNCT
ap-1362	103	12	x3	x3	ADJ
ap-1362	103	13	]	]	PUNCT
ap-1362	103	14	=	=	SYM
ap-1362	103	15	x4	x4	PROPN
ap-1362	104	1	[	[	X
ap-1362	104	2	x1	x1	PROPN
ap-1362	104	3	,	,	PUNCT
ap-1362	104	4	x4	x4	PROPN
ap-1362	104	5	]	]	PUNCT
ap-1362	104	6	=	=	PUNCT
ap-1362	105	1	[	[	X
ap-1362	105	2	x2	x2	X
ap-1362	105	3	,	,	PUNCT
ap-1362	105	4	x3	x3	ADJ
ap-1362	105	5	]	]	PUNCT
ap-1362	105	6	=	=	PUNCT
ap-1362	106	1	[	[	X
ap-1362	106	2	x2	x2	PROPN
ap-1362	106	3	,	,	PUNCT
ap-1362	106	4	x4	x4	PROPN
ap-1362	106	5	]	]	PUNCT
ap-1362	106	6	=	=	PUNCT
ap-1362	107	1	[	[	X
ap-1362	107	2	x3	x3	ADJ
ap-1362	107	3	,	,	PUNCT
ap-1362	107	4	x4	x4	PROPN
ap-1362	107	5	]	]	X
ap-1362	107	6	=	=	SYM
ap-1362	107	7	0	0	NUM
ap-1362	107	8	,	,	PUNCT
ap-1362	107	9	note	note	VERB
ap-1362	107	10	that	that	SCONJ
ap-1362	107	11	if	if	SCONJ
ap-1362	107	12	x4	x4	PROPN
ap-1362	107	13	=	=	SYM
ap-1362	107	14	μx2	μx2	NUM
ap-1362	107	15	we	we	PRON
ap-1362	107	16	obtain	obtain	VERB
ap-1362	107	17	a	a	DET
ap-1362	107	18	quotient	quotient	NOUN
ap-1362	107	19	lie	lie	NOUN
ap-1362	107	20	algebra	algebra	NOUN
ap-1362	107	21	corresponding	correspond	VERB
ap-1362	107	22	to	to	ADP
ap-1362	107	23	the	the	DET
ap-1362	107	24	euclidean	euclidean	ADJ
ap-1362	107	25	group	group	NOUN
ap-1362	107	26	in	in	ADP
ap-1362	107	27	the	the	DET
ap-1362	107	28	plane	plane	NOUN
ap-1362	107	29	and	and	CCONJ
ap-1362	107	30	we	we	PRON
ap-1362	107	31	get	get	VERB
ap-1362	107	32	a	a	DET
ap-1362	107	33	cartan	cartan	ADJ
ap-1362	107	34	connection	connection	NOUN
ap-1362	107	35	.	.	PUNCT
ap-1362	108	1	suppose	suppose	VERB
ap-1362	108	2	now	now	ADV
ap-1362	109	1	that	that	SCONJ
ap-1362	109	2	p	p	X
ap-1362	109	3	(	(	PUNCT
ap-1362	109	4	u	u	NOUN
ap-1362	109	5	,	,	PUNCT
ap-1362	109	6	ξ	ξ	X
ap-1362	109	7	)	)	PUNCT
ap-1362	109	8	=	=	SYM
ap-1362	109	9	lnup̄	lnup̄	PROPN
ap-1362	109	10	(	(	PUNCT
ap-1362	109	11	ξ	ξ	NOUN
ap-1362	109	12	)	)	PUNCT
ap-1362	109	13	,	,	PUNCT
ap-1362	109	14	m(u	m(u	PROPN
ap-1362	109	15	,	,	PUNCT
ap-1362	109	16	ξ	ξ	NOUN
ap-1362	109	17	)	)	PUNCT
ap-1362	109	18	=	=	SYM
ap-1362	109	19	m(eu	m(eu	SYM
ap-1362	109	20	,	,	PUNCT
ap-1362	109	21	ξ	ξ	NOUN
ap-1362	109	22	)	)	PUNCT
ap-1362	109	23	.	.	PUNCT
ap-1362	110	1	we	we	PRON
ap-1362	110	2	derive	derive	VERB
ap-1362	110	3	then	then	ADV
ap-1362	110	4	pu	pu	PROPN
ap-1362	110	5	=	=	SYM
ap-1362	110	6	eu[l	eu[l	PROPN
ap-1362	110	7	,	,	PUNCT
ap-1362	110	8	m	m	VERB
ap-1362	110	9	]	]	X
ap-1362	110	10	=	=	PUNCT
ap-1362	110	11	d(ln	d(ln	PROPN
ap-1362	110	12	up̄	up̄	X
ap-1362	110	13	(	(	PUNCT
ap-1362	110	14	ξ	ξ	NOUN
ap-1362	110	15	)	)	PUNCT
ap-1362	110	16	)	)	PUNCT
ap-1362	110	17	deu	deu	PROPN
ap-1362	110	18	eu	eu	PROPN
ap-1362	110	19	=	=	SYM
ap-1362	110	20	1	1	NUM
ap-1362	110	21	u	u	NOUN
ap-1362	110	22	p̄	p̄	X
ap-1362	110	23	(	(	PUNCT
ap-1362	110	24	ξ	ξ	NOUN
ap-1362	110	25	)	)	PUNCT
ap-1362	110	26	,	,	PUNCT
ap-1362	110	27	mu	mu	PROPN
ap-1362	110	28	=	=	SYM
ap-1362	110	29	∂m	∂m	PROPN
ap-1362	110	30	∂eu	∂eu	PROPN
ap-1362	110	31	eu	eu	PROPN
ap-1362	110	32	=	=	PROPN
ap-1362	110	33	−[l	−[l	PROPN
ap-1362	110	34	,	,	PUNCT
ap-1362	110	35	p	p	X
ap-1362	110	36	]	]	X
ap-1362	110	37	=	=	SYM
ap-1362	110	38	−[l	−[l	PROPN
ap-1362	110	39	,	,	PUNCT
ap-1362	110	40	lnup̄	lnup̄	PROPN
ap-1362	110	41	(	(	PUNCT
ap-1362	110	42	ξ	ξ	PROPN
ap-1362	110	43	)	)	PUNCT
ap-1362	110	44	]	]	PUNCT
ap-1362	110	45	;	;	PUNCT
ap-1362	110	46	so	so	SCONJ
ap-1362	110	47	that	that	SCONJ
ap-1362	110	48	∂m	∂m	PROPN
ap-1362	110	49	∂eu	∂eu	PROPN
ap-1362	110	50	=	=	SYM
ap-1362	110	51	−	−	PROPN
ap-1362	110	52	lnu	lnu	NOUN
ap-1362	110	53	eu	eu	PROPN
ap-1362	111	1	[	[	X
ap-1362	111	2	l	l	NOUN
ap-1362	111	3	,	,	PUNCT
ap-1362	111	4	p̄	p̄	X
ap-1362	111	5	(	(	PUNCT
ap-1362	111	6	ξ	ξ	NOUN
ap-1362	111	7	)	)	PUNCT
ap-1362	111	8	]	]	PUNCT
ap-1362	111	9	,	,	PUNCT
ap-1362	111	10	from	from	ADP
ap-1362	111	11	which	which	PRON
ap-1362	111	12	we	we	PRON
ap-1362	111	13	get	get	VERB
ap-1362	111	14	m(eu	m(eu	ADP
ap-1362	111	15	,	,	PUNCT
ap-1362	111	16	ξ	ξ	NOUN
ap-1362	111	17	)	)	PUNCT
ap-1362	111	18	=	=	SYM
ap-1362	111	19	−(lnu	−(lnu	PROPN
ap-1362	111	20	−	−	PROPN
ap-1362	111	21	1)u[l(ξ	1)u[l(ξ	NUM
ap-1362	111	22	)	)	PUNCT
ap-1362	111	23	,	,	PUNCT
ap-1362	111	24	p̄	p̄	X
ap-1362	111	25	(	(	PUNCT
ap-1362	111	26	ξ	ξ	NOUN
ap-1362	111	27	)	)	PUNCT
ap-1362	111	28	]	]	PUNCT
ap-1362	112	1	+	+	CCONJ
ap-1362	112	2	m̄(ξ	m̄(ξ	NOUN
ap-1362	112	3	)	)	PUNCT
ap-1362	112	4	,	,	PUNCT
ap-1362	112	5	and	and	CCONJ
ap-1362	112	6	p	p	X
ap-1362	112	7	(	(	PUNCT
ap-1362	112	8	u	u	NOUN
ap-1362	112	9	,	,	PUNCT
ap-1362	112	10	ξ	ξ	X
ap-1362	112	11	)	)	PUNCT
ap-1362	112	12	=	=	SYM
ap-1362	112	13	ueu	ueu	NOUN
ap-1362	112	14	lnu[l	lnu[l	PROPN
ap-1362	112	15	,	,	PUNCT
ap-1362	112	16	m	m	VERB
ap-1362	112	17	]	]	X
ap-1362	112	18	.	.	PUNCT
ap-1362	113	1	from	from	ADP
ap-1362	113	2	[	[	X
ap-1362	113	3	p	p	X
ap-1362	113	4	,	,	PUNCT
ap-1362	113	5	m	m	VERB
ap-1362	113	6	]	]	PUNCT
ap-1362	113	7	=	=	SYM
ap-1362	113	8	0	0	NUM
ap-1362	113	9	we	we	PRON
ap-1362	113	10	get	get	VERB
ap-1362	113	11	,	,	PUNCT
ap-1362	113	12	for	for	ADP
ap-1362	113	13	u	u	PROPN
ap-1362	113	14	�	�	PROPN
ap-1362	113	15	=	=	SYM
ap-1362	113	16	0	0	NUM
ap-1362	113	17	,	,	PUNCT
ap-1362	113	18	1	1	NUM
ap-1362	113	19	(	(	PUNCT
ap-1362	113	20	which	which	PRON
ap-1362	113	21	are	be	AUX
ap-1362	113	22	trivial	trivial	ADJ
ap-1362	113	23	solutions	solution	NOUN
ap-1362	113	24	of	of	ADP
ap-1362	113	25	the	the	DET
ap-1362	113	26	toda	toda	PROPN
ap-1362	113	27	system	system	NOUN
ap-1362	113	28	)	)	PUNCT
ap-1362	113	29	,	,	PUNCT
ap-1362	114	1	[	[	X
ap-1362	114	2	[	[	X
ap-1362	114	3	l	l	NOUN
ap-1362	114	4	,	,	PUNCT
ap-1362	114	5	m	m	VERB
ap-1362	114	6	]	]	X
ap-1362	114	7	,	,	PUNCT
ap-1362	114	8	m	m	VERB
ap-1362	114	9	]	]	X
ap-1362	114	10	=	=	PUNCT
ap-1362	114	11	0	0	NUM
ap-1362	114	12	;	;	PUNCT
ap-1362	114	13	on	on	ADP
ap-1362	114	14	the	the	DET
ap-1362	114	15	other	other	ADJ
ap-1362	114	16	hand	hand	NOUN
ap-1362	114	17	substituting	substitute	VERB
ap-1362	114	18	the	the	DET
ap-1362	114	19	above	above	ADJ
ap-1362	114	20	expression	expression	NOUN
ap-1362	114	21	for	for	ADP
ap-1362	114	22	m	m	VERB
ap-1362	114	23	we	we	PRON
ap-1362	114	24	get	get	VERB
ap-1362	114	25	[	[	X
ap-1362	114	26	[	[	X
ap-1362	114	27	l	l	NOUN
ap-1362	114	28	,	,	PUNCT
ap-1362	114	29	m̄	m̄	PROPN
ap-1362	114	30	]	]	PUNCT
ap-1362	114	31	,	,	PUNCT
ap-1362	114	32	m̄	m̄	PROPN
ap-1362	114	33	]	]	PUNCT
ap-1362	115	1	=	=	SYM
ap-1362	115	2	0	0	NUM
ap-1362	115	3	,	,	PUNCT
ap-1362	115	4	56	56	NUM
ap-1362	115	5	acta	acta	PROPN
ap-1362	115	6	polytechnica	polytechnica	PROPN
ap-1362	115	7	vol	vol	NOUN
ap-1362	115	8	.	.	PUNCT
ap-1362	116	1	51	51	NUM
ap-1362	116	2	no	no	INTJ
ap-1362	116	3	.	.	PUNCT
ap-1362	116	4	1/2011	1/2011	NUM
ap-1362	117	1	[	[	X
ap-1362	117	2	[	[	X
ap-1362	117	3	l	l	NOUN
ap-1362	117	4	,	,	PUNCT
ap-1362	117	5	[	[	X
ap-1362	117	6	l	l	NOUN
ap-1362	117	7	,	,	PUNCT
ap-1362	117	8	p̄	p̄	NOUN
ap-1362	117	9	]	]	X
ap-1362	117	10	]	]	X
ap-1362	117	11	,	,	PUNCT
ap-1362	117	12	m̄	m̄	PROPN
ap-1362	117	13	]	]	PUNCT
ap-1362	118	1	+	+	PUNCT
ap-1362	119	1	[	[	X
ap-1362	119	2	[	[	X
ap-1362	119	3	l	l	NOUN
ap-1362	119	4	,	,	PUNCT
ap-1362	119	5	m̄	m̄	PROPN
ap-1362	119	6	]	]	PUNCT
ap-1362	119	7	,	,	PUNCT
ap-1362	120	1	[	[	X
ap-1362	120	2	l	l	NOUN
ap-1362	120	3	,	,	PUNCT
ap-1362	120	4	p̄	p̄	NOUN
ap-1362	120	5	]	]	X
ap-1362	120	6	]	]	X
ap-1362	121	1	=	=	SYM
ap-1362	121	2	0	0	PUNCT
ap-1362	121	3	,	,	PUNCT
ap-1362	121	4	[	[	X
ap-1362	121	5	[	[	X
ap-1362	121	6	l	l	X
ap-1362	121	7	,	,	PUNCT
ap-1362	121	8	[	[	X
ap-1362	121	9	l	l	NOUN
ap-1362	121	10	,	,	PUNCT
ap-1362	121	11	p̄	p̄	NOUN
ap-1362	121	12	]	]	X
ap-1362	121	13	]	]	X
ap-1362	121	14	,	,	PUNCT
ap-1362	121	15	[	[	X
ap-1362	121	16	l	l	NOUN
ap-1362	121	17	,	,	PUNCT
ap-1362	121	18	p̄	p̄	NOUN
ap-1362	121	19	]	]	X
ap-1362	121	20	]	]	X
ap-1362	121	21	=	=	SYM
ap-1362	121	22	0	0	PUNCT
ap-1362	121	23	.	.	PUNCT
ap-1362	122	1	by	by	ADP
ap-1362	122	2	putting	put	VERB
ap-1362	122	3	again	again	ADV
ap-1362	122	4	for	for	ADP
ap-1362	122	5	the	the	DET
ap-1362	122	6	sake	sake	NOUN
ap-1362	122	7	of	of	ADP
ap-1362	122	8	convenience	convenience	NOUN
ap-1362	122	9	l	l	NOUN
ap-1362	122	10	=	=	SYM
ap-1362	122	11	x1	x1	PROPN
ap-1362	122	12	,	,	PUNCT
ap-1362	122	13	m̄	m̄	NOUN
ap-1362	122	14	=	=	SYM
ap-1362	122	15	x2	x2	PROPN
ap-1362	122	16	,	,	PUNCT
ap-1362	122	17	p̄	p̄	PROPN
ap-1362	122	18	=	=	SYM
ap-1362	122	19	x3	x3	PROPN
ap-1362	122	20	,	,	PUNCT
ap-1362	122	21	then	then	ADV
ap-1362	122	22	we	we	PRON
ap-1362	122	23	get	get	VERB
ap-1362	122	24	the	the	DET
ap-1362	122	25	following	follow	VERB
ap-1362	122	26	infinitesimal	infinitesimal	ADJ
ap-1362	122	27	algebraic	algebraic	ADJ
ap-1362	122	28	skeleton	skeleton	NOUN
ap-1362	122	29	with	with	ADP
ap-1362	122	30	the	the	DET
ap-1362	122	31	structure	structure	NOUN
ap-1362	122	32	of	of	ADP
ap-1362	122	33	an	an	DET
ap-1362	122	34	open	open	ADJ
ap-1362	122	35	lie	lie	NOUN
ap-1362	122	36	algebra	algebra	NOUN
ap-1362	122	37	:	:	PUNCT
ap-1362	123	1	[	[	X
ap-1362	123	2	x1	x1	X
ap-1362	123	3	,	,	PUNCT
ap-1362	123	4	x2	x2	PROPN
ap-1362	123	5	]	]	X
ap-1362	123	6	=	=	PUNCT
ap-1362	123	7	x4	x4	PROPN
ap-1362	123	8	,	,	PUNCT
ap-1362	123	9	[	[	X
ap-1362	123	10	x1	x1	ADJ
ap-1362	123	11	,	,	PUNCT
ap-1362	123	12	x3	x3	ADJ
ap-1362	123	13	]	]	PUNCT
ap-1362	123	14	=	=	SYM
ap-1362	123	15	x5	x5	PROPN
ap-1362	123	16	,	,	PUNCT
ap-1362	123	17	[	[	X
ap-1362	123	18	x4	x4	PROPN
ap-1362	123	19	,	,	PUNCT
ap-1362	123	20	x5	x5	NOUN
ap-1362	123	21	]	]	X
ap-1362	123	22	=	=	PUNCT
ap-1362	124	1	[	[	X
ap-1362	124	2	x2	x2	X
ap-1362	124	3	,	,	PUNCT
ap-1362	124	4	x7	x7	NOUN
ap-1362	124	5	]	]	PUNCT
ap-1362	124	6	,	,	PUNCT
ap-1362	125	1	[	[	X
ap-1362	125	2	x3	x3	ADJ
ap-1362	125	3	,	,	PUNCT
ap-1362	125	4	x4	x4	PROPN
ap-1362	125	5	]	]	PUNCT
ap-1362	125	6	=	=	PUNCT
ap-1362	126	1	[	[	X
ap-1362	126	2	x2	x2	PROPN
ap-1362	126	3	,	,	PUNCT
ap-1362	126	4	x5	x5	PROPN
ap-1362	126	5	]	]	PUNCT
ap-1362	126	6	,	,	PUNCT
ap-1362	126	7	[	[	X
ap-1362	126	8	x1	x1	X
ap-1362	126	9	,	,	PUNCT
ap-1362	126	10	x4	x4	PROPN
ap-1362	126	11	]	]	X
ap-1362	126	12	=	=	SYM
ap-1362	126	13	x6	x6	PROPN
ap-1362	126	14	,	,	PUNCT
ap-1362	126	15	[	[	X
ap-1362	126	16	x1	x1	PROPN
ap-1362	126	17	,	,	PUNCT
ap-1362	126	18	x5	x5	NOUN
ap-1362	126	19	]	]	X
ap-1362	126	20	=	=	SYM
ap-1362	126	21	x7	x7	NOUN
ap-1362	126	22	,	,	PUNCT
ap-1362	126	23	[	[	X
ap-1362	126	24	x2	x2	X
ap-1362	126	25	,	,	PUNCT
ap-1362	126	26	x3	x3	ADJ
ap-1362	126	27	]	]	PUNCT
ap-1362	126	28	=	=	SYM
ap-1362	126	29	x8	x8	PROPN
ap-1362	126	30	,	,	PUNCT
ap-1362	126	31	[	[	X
ap-1362	126	32	x1	x1	PROPN
ap-1362	126	33	,	,	PUNCT
ap-1362	126	34	x8	x8	PROPN
ap-1362	126	35	]	]	X
ap-1362	127	1	=	=	PUNCT
ap-1362	128	1	[	[	X
ap-1362	128	2	x2	x2	PROPN
ap-1362	128	3	,	,	PUNCT
ap-1362	128	4	x4	x4	PROPN
ap-1362	128	5	]	]	PUNCT
ap-1362	128	6	=	=	PUNCT
ap-1362	129	1	[	[	X
ap-1362	129	2	x2	x2	PROPN
ap-1362	129	3	,	,	PUNCT
ap-1362	129	4	x6	x6	PROPN
ap-1362	129	5	]	]	PUNCT
ap-1362	129	6	=	=	PUNCT
ap-1362	130	1	[	[	X
ap-1362	130	2	x3	x3	ADJ
ap-1362	130	3	,	,	PUNCT
ap-1362	130	4	x7	x7	NOUN
ap-1362	130	5	]	]	X
ap-1362	130	6	=	=	SYM
ap-1362	130	7	0	0	NUM
ap-1362	130	8	,	,	PUNCT
ap-1362	130	9	.	.	PUNCT
ap-1362	130	10	.	.	PUNCT
ap-1362	131	1	.	.	PUNCT
ap-1362	132	1	we	we	PRON
ap-1362	132	2	observe	observe	VERB
ap-1362	132	3	that	that	SCONJ
ap-1362	132	4	by	by	ADP
ap-1362	132	5	the	the	DET
ap-1362	132	6	homomorphismx4	homomorphismx4	NOUN
ap-1362	132	7	=	=	SYM
ap-1362	132	8	x5	x5	PROPN
ap-1362	132	9	=	=	SYM
ap-1362	132	10	0	0	NUM
ap-1362	132	11	and	and	CCONJ
ap-1362	132	12	x8	x8	PROPN
ap-1362	132	13	=	=	SYM
ap-1362	132	14	νx3	νx3	NOUN
ap-1362	132	15	we	we	PRON
ap-1362	132	16	get	get	VERB
ap-1362	132	17	a	a	DET
ap-1362	132	18	closed	closed	ADJ
ap-1362	132	19	lie	lie	NOUN
ap-1362	132	20	algebra	algebra	NOUN
ap-1362	132	21	(	(	PUNCT
ap-1362	132	22	which	which	PRON
ap-1362	132	23	is	be	AUX
ap-1362	132	24	different	different	ADJ
ap-1362	132	25	from	from	ADP
ap-1362	132	26	the	the	DET
ap-1362	132	27	lie	lie	NOUN
ap-1362	132	28	algebra	algebra	NOUN
ap-1362	132	29	corresponding	correspond	VERB
ap-1362	132	30	to	to	ADP
ap-1362	132	31	the	the	DET
ap-1362	132	32	euclidean	euclidean	ADJ
ap-1362	132	33	group	group	NOUN
ap-1362	132	34	in	in	ADP
ap-1362	132	35	the	the	DET
ap-1362	132	36	plane	plane	NOUN
ap-1362	132	37	obtained	obtain	VERB
ap-1362	132	38	above	above	ADV
ap-1362	132	39	):	):	PUNCT
ap-1362	133	1	[	[	X
ap-1362	133	2	x1	x1	X
ap-1362	133	3	,	,	PUNCT
ap-1362	133	4	x2	x2	PROPN
ap-1362	133	5	]	]	X
ap-1362	133	6	=	=	SYM
ap-1362	133	7	0	0	PUNCT
ap-1362	133	8	,	,	PUNCT
ap-1362	134	1	[	[	X
ap-1362	134	2	x1	x1	X
ap-1362	134	3	,	,	PUNCT
ap-1362	134	4	x3	x3	ADJ
ap-1362	134	5	]	]	PUNCT
ap-1362	134	6	=	=	SYM
ap-1362	134	7	0	0	NUM
ap-1362	134	8	,	,	PUNCT
ap-1362	135	1	[	[	X
ap-1362	135	2	x2	x2	X
ap-1362	135	3	,	,	PUNCT
ap-1362	135	4	x3	x3	ADJ
ap-1362	135	5	]	]	X
ap-1362	135	6	=	=	SYM
ap-1362	135	7	νx3	νx3	NOUN
ap-1362	135	8	.	.	PUNCT
ap-1362	136	1	which	which	PRON
ap-1362	136	2	,	,	PUNCT
ap-1362	136	3	by	by	ADP
ap-1362	136	4	means	mean	NOUN
ap-1362	136	5	of	of	ADP
ap-1362	136	6	a	a	DET
ap-1362	136	7	suitable	suitable	ADJ
ap-1362	136	8	realization	realization	NOUN
ap-1362	136	9	,	,	PUNCT
ap-1362	136	10	can	can	AUX
ap-1362	136	11	also	also	ADV
ap-1362	136	12	provide	provide	VERB
ap-1362	136	13	us	we	PRON
ap-1362	136	14	with	with	ADP
ap-1362	136	15	a	a	DET
ap-1362	136	16	different	different	ADJ
ap-1362	136	17	cartan	cartan	ADJ
ap-1362	136	18	connection	connection	NOUN
ap-1362	136	19	(	(	PUNCT
ap-1362	136	20	thus	thus	ADV
ap-1362	136	21	a	a	DET
ap-1362	136	22	different	different	ADJ
ap-1362	136	23	spectral	spectral	ADJ
ap-1362	136	24	problem	problem	NOUN
ap-1362	136	25	and	and	CCONJ
ap-1362	136	26	different	different	ADJ
ap-1362	136	27	conservation	conservation	NOUN
ap-1362	136	28	laws	law	NOUN
ap-1362	136	29	)	)	PUNCT
ap-1362	136	30	;	;	PUNCT
ap-1362	136	31	on	on	ADP
ap-1362	136	32	the	the	DET
ap-1362	136	33	other	other	ADJ
ap-1362	136	34	hand	hand	NOUN
ap-1362	136	35	,	,	PUNCT
ap-1362	136	36	we	we	PRON
ap-1362	136	37	can	can	AUX
ap-1362	136	38	find	find	VERB
ap-1362	136	39	a	a	DET
ap-1362	136	40	closed	closed	ADJ
ap-1362	136	41	lie	lie	NOUN
ap-1362	136	42	algebra	algebra	NOUN
ap-1362	136	43	by	by	ADP
ap-1362	136	44	means	mean	NOUN
ap-1362	136	45	of	of	ADP
ap-1362	136	46	the	the	DET
ap-1362	136	47	following	follow	VERB
ap-1362	136	48	homomorphism	homomorphism	PROPN
ap-1362	136	49	x4	x4	PROPN
ap-1362	136	50	=	=	SYM
ap-1362	136	51	x2	x2	PROPN
ap-1362	136	52	and	and	CCONJ
ap-1362	136	53	x5	x5	PROPN
ap-1362	136	54	=	=	SYM
ap-1362	136	55	x3	x3	PROPN
ap-1362	136	56	,	,	PUNCT
ap-1362	136	57	and	and	CCONJ
ap-1362	136	58	then	then	ADV
ap-1362	136	59	we	we	PRON
ap-1362	136	60	have	have	VERB
ap-1362	136	61	[	[	X
ap-1362	136	62	x1	x1	PROPN
ap-1362	136	63	,	,	PUNCT
ap-1362	136	64	x2	x2	PROPN
ap-1362	136	65	]	]	X
ap-1362	137	1	=	=	SYM
ap-1362	137	2	x2	x2	INTJ
ap-1362	137	3	,	,	PUNCT
ap-1362	138	1	[	[	X
ap-1362	138	2	x1	x1	ADJ
ap-1362	138	3	,	,	PUNCT
ap-1362	138	4	x3	x3	ADJ
ap-1362	138	5	]	]	PUNCT
ap-1362	138	6	=	=	SYM
ap-1362	138	7	x3	x3	ADJ
ap-1362	138	8	,	,	PUNCT
ap-1362	138	9	[	[	X
ap-1362	138	10	x4	x4	PROPN
ap-1362	138	11	,	,	PUNCT
ap-1362	138	12	x5	x5	NOUN
ap-1362	138	13	]	]	X
ap-1362	138	14	=	=	PUNCT
ap-1362	139	1	[	[	X
ap-1362	139	2	x2	x2	X
ap-1362	139	3	,	,	PUNCT
ap-1362	139	4	x3	x3	ADJ
ap-1362	139	5	]	]	PUNCT
ap-1362	139	6	=	=	SYM
ap-1362	139	7	x8	x8	PROPN
ap-1362	139	8	=	=	SYM
ap-1362	139	9	0	0	NUM
ap-1362	139	10	,	,	PUNCT
ap-1362	140	1	[	[	X
ap-1362	140	2	x3	x3	ADJ
ap-1362	140	3	,	,	PUNCT
ap-1362	140	4	x4	x4	PROPN
ap-1362	140	5	]	]	PUNCT
ap-1362	140	6	=	=	PUNCT
ap-1362	141	1	[	[	X
ap-1362	141	2	x3	x3	ADJ
ap-1362	141	3	,	,	PUNCT
ap-1362	141	4	x2	x2	PROPN
ap-1362	141	5	]	]	X
ap-1362	141	6	=	=	SYM
ap-1362	141	7	−[x2	−[x2	PROPN
ap-1362	141	8	,	,	PUNCT
ap-1362	141	9	x3	x3	ADJ
ap-1362	141	10	]	]	PUNCT
ap-1362	142	1	=	=	PUNCT
ap-1362	143	1	[	[	X
ap-1362	143	2	x2	x2	PROPN
ap-1362	143	3	,	,	PUNCT
ap-1362	143	4	x5	x5	NOUN
ap-1362	143	5	]	]	X
ap-1362	143	6	=	=	PUNCT
ap-1362	144	1	[	[	X
ap-1362	144	2	x2	x2	X
ap-1362	144	3	,	,	PUNCT
ap-1362	144	4	x3	x3	ADJ
ap-1362	144	5	]	]	PUNCT
ap-1362	144	6	,	,	PUNCT
ap-1362	144	7	and	and	CCONJ
ap-1362	144	8	we	we	PRON
ap-1362	144	9	also	also	ADV
ap-1362	144	10	deduce	deduce	VERB
ap-1362	144	11	that	that	DET
ap-1362	144	12	x6	x6	NOUN
ap-1362	144	13	=	=	SYM
ap-1362	144	14	x4	x4	PROPN
ap-1362	144	15	=	=	SYM
ap-1362	144	16	x2	x2	PROPN
ap-1362	144	17	,	,	PUNCT
ap-1362	144	18	x7	x7	NOUN
ap-1362	144	19	=	=	SYM
ap-1362	144	20	x3	x3	ADJ
ap-1362	144	21	and	and	CCONJ
ap-1362	144	22	that	that	SCONJ
ap-1362	144	23	[	[	X
ap-1362	144	24	x1	x1	PROPN
ap-1362	144	25	,	,	PUNCT
ap-1362	144	26	x8	x8	PROPN
ap-1362	144	27	]	]	X
ap-1362	144	28	=	=	PUNCT
ap-1362	145	1	[	[	X
ap-1362	145	2	x2	x2	PROPN
ap-1362	145	3	,	,	PUNCT
ap-1362	145	4	x4	x4	PROPN
ap-1362	145	5	]	]	PUNCT
ap-1362	145	6	=	=	PUNCT
ap-1362	146	1	[	[	X
ap-1362	146	2	x2	x2	PROPN
ap-1362	146	3	,	,	PUNCT
ap-1362	146	4	x6	x6	PROPN
ap-1362	146	5	]	]	PUNCT
ap-1362	146	6	=	=	PUNCT
ap-1362	147	1	[	[	X
ap-1362	147	2	x3	x3	ADJ
ap-1362	147	3	,	,	PUNCT
ap-1362	147	4	x7	x7	NOUN
ap-1362	147	5	]	]	X
ap-1362	147	6	=	=	SYM
ap-1362	147	7	0	0	NUM
ap-1362	147	8	are	be	AUX
ap-1362	147	9	all	all	ADV
ap-1362	147	10	identically	identically	ADV
ap-1362	147	11	satisfied	satisfied	ADJ
ap-1362	147	12	.	.	PUNCT
ap-1362	148	1	it	it	PRON
ap-1362	148	2	is	be	AUX
ap-1362	148	3	easy	easy	ADJ
ap-1362	148	4	to	to	PART
ap-1362	148	5	see	see	VERB
ap-1362	148	6	that	that	SCONJ
ap-1362	148	7	the	the	DET
ap-1362	148	8	two	two	NUM
ap-1362	148	9	different	different	ADJ
ap-1362	148	10	cases	case	NOUN
ap-1362	148	11	above	above	ADV
ap-1362	148	12	are	be	AUX
ap-1362	148	13	both	both	PRON
ap-1362	148	14	given	give	VERB
ap-1362	148	15	by	by	ADP
ap-1362	148	16	the	the	DET
ap-1362	148	17	homomorphism	homomorphism	NOUN
ap-1362	148	18	given	give	VERB
ap-1362	148	19	by	by	ADP
ap-1362	148	20	requiring	require	VERB
ap-1362	148	21	x4	x4	PROPN
ap-1362	148	22	=	=	SYM
ap-1362	148	23	λx2	λx2	NOUN
ap-1362	148	24	and	and	CCONJ
ap-1362	148	25	x5	x5	PROPN
ap-1362	148	26	=	=	SYM
ap-1362	148	27	μx3	μx3	NOUN
ap-1362	148	28	.	.	PUNCT
ap-1362	149	1	it	it	PRON
ap-1362	149	2	is	be	AUX
ap-1362	149	3	easy	easy	ADJ
ap-1362	149	4	to	to	PART
ap-1362	149	5	realize	realize	VERB
ap-1362	149	6	that	that	SCONJ
ap-1362	149	7	μ	μ	NOUN
ap-1362	149	8	=	=	SYM
ap-1362	149	9	−λ	−λ	PROPN
ap-1362	149	10	must	must	AUX
ap-1362	149	11	old	old	ADJ
ap-1362	149	12	and	and	CCONJ
ap-1362	149	13	there	there	PRON
ap-1362	149	14	are	be	VERB
ap-1362	149	15	the	the	DET
ap-1362	149	16	two	two	NUM
ap-1362	149	17	cases	case	NOUN
ap-1362	149	18	λ	λ	X
ap-1362	149	19	=	=	SYM
ap-1362	149	20	0	0	NUM
ap-1362	149	21	with	with	ADP
ap-1362	149	22	x8	x8	PROPN
ap-1362	149	23	=	=	SYM
ap-1362	149	24	νx3	νx3	PROPN
ap-1362	149	25	giving	give	VERB
ap-1362	149	26	the	the	DET
ap-1362	149	27	first	first	ADJ
ap-1362	149	28	case	case	NOUN
ap-1362	149	29	,	,	PUNCT
ap-1362	149	30	and	and	CCONJ
ap-1362	149	31	x8	x8	PROPN
ap-1362	149	32	=	=	SYM
ap-1362	149	33	0	0	NUM
ap-1362	149	34	with	with	ADP
ap-1362	149	35	λ	λ	NOUN
ap-1362	149	36	=	=	SYM
ap-1362	149	37	1	1	NUM
ap-1362	149	38	giving	give	VERB
ap-1362	149	39	the	the	DET
ap-1362	149	40	second	second	ADJ
ap-1362	149	41	case	case	NOUN
ap-1362	149	42	,	,	PUNCT
ap-1362	149	43	respectively	respectively	ADV
ap-1362	149	44	.	.	PUNCT
ap-1362	150	1	for	for	ADP
ap-1362	150	2	any	any	DET
ap-1362	150	3	λ	λ	NOUN
ap-1362	150	4	�	�	PROPN
ap-1362	150	5	=	=	SYM
ap-1362	150	6	0	0	NUM
ap-1362	150	7	we	we	PRON
ap-1362	150	8	have	have	VERB
ap-1362	150	9	a	a	DET
ap-1362	150	10	closed	closed	ADJ
ap-1362	150	11	lie	lie	NOUN
ap-1362	150	12	algebra	algebra	NOUN
ap-1362	150	13	depending	depend	VERB
ap-1362	150	14	on	on	ADP
ap-1362	150	15	the	the	DET
ap-1362	150	16	parameter	parameter	NOUN
ap-1362	150	17	λ	λ	PROPN
ap-1362	150	18	:	:	PUNCT
ap-1362	151	1	[	[	X
ap-1362	151	2	x1	x1	X
ap-1362	151	3	,	,	PUNCT
ap-1362	151	4	x2	x2	PROPN
ap-1362	151	5	]	]	X
ap-1362	151	6	=	=	PUNCT
ap-1362	152	1	λx2	λx2	NOUN
ap-1362	152	2	,	,	PUNCT
ap-1362	152	3	[	[	X
ap-1362	152	4	x1	x1	X
ap-1362	152	5	,	,	PUNCT
ap-1362	152	6	x3	x3	ADJ
ap-1362	152	7	]	]	PUNCT
ap-1362	152	8	=	=	SYM
ap-1362	152	9	−λx3	−λx3	X
ap-1362	152	10	,	,	PUNCT
ap-1362	152	11	[	[	X
ap-1362	152	12	x2	x2	X
ap-1362	152	13	,	,	PUNCT
ap-1362	152	14	x3	x3	ADJ
ap-1362	152	15	]	]	PUNCT
ap-1362	152	16	=	=	SYM
ap-1362	152	17	0	0	NUM
ap-1362	152	18	.	.	PUNCT
ap-1362	153	1	furthermore	furthermore	ADV
ap-1362	153	2	,	,	PUNCT
ap-1362	153	3	by	by	ADP
ap-1362	153	4	putting	put	VERB
ap-1362	153	5	in	in	ADP
ap-1362	153	6	the	the	DET
ap-1362	153	7	prolongation	prolongation	NOUN
ap-1362	153	8	skeleton	skeleton	NOUN
ap-1362	153	9	x4	x4	PROPN
ap-1362	154	1	=	=	SYM
ap-1362	155	1	x2	x2	PROPN
ap-1362	155	2	and	and	CCONJ
ap-1362	155	3	x5	x5	PROPN
ap-1362	155	4	=	=	SYM
ap-1362	155	5	−x3	−x3	PROPN
ap-1362	155	6	it	it	PRON
ap-1362	155	7	is	be	AUX
ap-1362	155	8	possible	possible	ADJ
ap-1362	155	9	to	to	PART
ap-1362	155	10	realize	realize	VERB
ap-1362	155	11	the	the	DET
ap-1362	155	12	prolongation	prolongation	NOUN
ap-1362	155	13	skeleton	skeleton	NOUN
ap-1362	155	14	as	as	ADP
ap-1362	155	15	a	a	DET
ap-1362	155	16	kač-moody	kač-moody	NOUN
ap-1362	155	17	lie	lie	NOUN
ap-1362	155	18	algebra	algebra	NOUN
ap-1362	155	19	of	of	ADP
ap-1362	155	20	the	the	DET
ap-1362	155	21	type	type	NOUN
ap-1362	156	1	[	[	X
ap-1362	156	2	hi	hi	INTJ
ap-1362	156	3	,	,	PUNCT
ap-1362	156	4	hj	hj	X
ap-1362	156	5	]	]	PUNCT
ap-1362	156	6	=	=	PUNCT
ap-1362	156	7	0	0	PUNCT
ap-1362	156	8	,	,	PUNCT
ap-1362	157	1	[	[	X
ap-1362	157	2	hi	hi	INTJ
ap-1362	157	3	,	,	PUNCT
ap-1362	157	4	x+j	x+j	X
ap-1362	157	5	]	]	PUNCT
ap-1362	157	6	=	=	SYM
ap-1362	157	7	κijx+j	κijx+j	NOUN
ap-1362	157	8	,	,	PUNCT
ap-1362	158	1	[	[	X
ap-1362	158	2	hi	hi	INTJ
ap-1362	158	3	,	,	PUNCT
ap-1362	158	4	x−j	x−j	PROPN
ap-1362	158	5	]	]	PUNCT
ap-1362	159	1	=	=	PUNCT
ap-1362	159	2	−κijx−j	−κijx−j	NOUN
ap-1362	159	3	,	,	PUNCT
ap-1362	159	4	[	[	X
ap-1362	159	5	x+i	x+i	NUM
ap-1362	159	6	,	,	PUNCT
ap-1362	159	7	x−j	x−j	NOUN
ap-1362	159	8	]	]	X
ap-1362	160	1	=	=	SYM
ap-1362	160	2	δijhi	δijhi	NOUN
ap-1362	160	3	,	,	PUNCT
ap-1362	160	4	where	where	SCONJ
ap-1362	160	5	we	we	PRON
ap-1362	160	6	put	put	VERB
ap-1362	160	7	[	[	X
ap-1362	160	8	x2	x2	PROPN
ap-1362	160	9	,	,	PUNCT
ap-1362	160	10	x3	x3	ADJ
ap-1362	160	11	]	]	PUNCT
ap-1362	160	12	=	=	SYM
ap-1362	160	13	x8	x8	PROPN
ap-1362	160	14	,	,	PUNCT
ap-1362	160	15	[	[	X
ap-1362	160	16	x8	x8	X
ap-1362	160	17	,	,	PUNCT
ap-1362	160	18	x2	x2	PROPN
ap-1362	160	19	]	]	X
ap-1362	160	20	=	=	SYM
ap-1362	160	21	x9	x9	NOUN
ap-1362	160	22	,	,	PUNCT
ap-1362	160	23	[	[	X
ap-1362	160	24	x8	x8	X
ap-1362	160	25	,	,	PUNCT
ap-1362	160	26	x3	x3	ADJ
ap-1362	160	27	]	]	PUNCT
ap-1362	160	28	=	=	SYM
ap-1362	160	29	x10	x10	NOUN
ap-1362	160	30	,	,	PUNCT
ap-1362	160	31	[	[	X
ap-1362	160	32	x8	x8	PROPN
ap-1362	160	33	,	,	PUNCT
ap-1362	160	34	x9	x9	NOUN
ap-1362	160	35	]	]	X
ap-1362	160	36	=	=	SYM
ap-1362	160	37	x11	x11	X
ap-1362	161	1	[	[	X
ap-1362	161	2	x8	x8	PROPN
ap-1362	161	3	,	,	PUNCT
ap-1362	161	4	x10	x10	NOUN
ap-1362	161	5	]	]	X
ap-1362	161	6	=	=	SYM
ap-1362	161	7	x12	x12	NUM
ap-1362	161	8	and	and	CCONJ
ap-1362	161	9	{	{	PUNCT
ap-1362	161	10	x1	x1	PROPN
ap-1362	161	11	,	,	PUNCT
ap-1362	161	12	x13	x13	PROPN
ap-1362	161	13	,	,	PUNCT
ap-1362	161	14	.	.	PUNCT
ap-1362	161	15	.	.	PUNCT
ap-1362	162	1	.	.	PUNCT
ap-1362	162	2	}	}	PUNCT
ap-1362	163	1	=	=	SYM
ap-1362	163	2	hi	hi	INTJ
ap-1362	163	3	,	,	PUNCT
ap-1362	163	4	{	{	PUNCT
ap-1362	163	5	x8	x8	PROPN
ap-1362	163	6	,	,	PUNCT
ap-1362	163	7	.	.	PUNCT
ap-1362	163	8	.	.	PUNCT
ap-1362	163	9	.	.	PUNCT
ap-1362	163	10	}	}	PUNCT
ap-1362	164	1	=	=	SYM
ap-1362	164	2	hj	hj	PROPN
ap-1362	164	3	,	,	PUNCT
ap-1362	164	4	{	{	PUNCT
ap-1362	164	5	x2	x2	PROPN
ap-1362	164	6	,	,	PUNCT
ap-1362	164	7	x9	x9	PROPN
ap-1362	164	8	,	,	PUNCT
ap-1362	164	9	x11	x11	NOUN
ap-1362	164	10	,	,	PUNCT
ap-1362	164	11	.	.	PUNCT
ap-1362	164	12	.	.	PUNCT
ap-1362	164	13	.	.	PUNCT
ap-1362	164	14	}	}	PUNCT
ap-1362	165	1	=	=	SYM
ap-1362	165	2	x+i	x+i	PROPN
ap-1362	165	3	,	,	PUNCT
ap-1362	165	4	{	{	PUNCT
ap-1362	165	5	x3	x3	ADJ
ap-1362	165	6	,	,	PUNCT
ap-1362	165	7	x10	x10	NOUN
ap-1362	165	8	,	,	PUNCT
ap-1362	165	9	x12	x12	NUM
ap-1362	165	10	,	,	PUNCT
ap-1362	165	11	.	.	PUNCT
ap-1362	165	12	.	.	PUNCT
ap-1362	165	13	.	.	PUNCT
ap-1362	165	14	}	}	PUNCT
ap-1362	166	1	=	=	PUNCT
ap-1362	166	2	x−j	x−j	NOUN
ap-1362	166	3	.	.	PUNCT
ap-1362	167	1	we	we	PRON
ap-1362	167	2	also	also	ADV
ap-1362	167	3	put	put	VERB
ap-1362	167	4	[	[	X
ap-1362	167	5	x8	x8	PROPN
ap-1362	167	6	,	,	PUNCT
ap-1362	167	7	x11	x11	NOUN
ap-1362	167	8	]	]	X
ap-1362	167	9	=	=	SYM
ap-1362	167	10	x11	x11	NOUN
ap-1362	167	11	,	,	PUNCT
ap-1362	167	12	[	[	X
ap-1362	167	13	x8	x8	PROPN
ap-1362	167	14	,	,	PUNCT
ap-1362	167	15	x12	x12	NUM
ap-1362	167	16	]	]	X
ap-1362	167	17	=	=	PUNCT
ap-1362	167	18	−x12	−x12	X
ap-1362	167	19	,	,	PUNCT
ap-1362	167	20	and	and	CCONJ
ap-1362	167	21	so	so	ADV
ap-1362	167	22	on	on	ADV
ap-1362	167	23	.	.	PUNCT
ap-1362	168	1	we	we	PRON
ap-1362	168	2	then	then	ADV
ap-1362	168	3	also	also	ADV
ap-1362	168	4	have	have	VERB
ap-1362	168	5	[	[	X
ap-1362	168	6	x8	x8	PROPN
ap-1362	168	7	,	,	PUNCT
ap-1362	168	8	x13	x13	PROPN
ap-1362	168	9	]	]	X
ap-1362	168	10	=	=	SYM
ap-1362	168	11	0	0	PUNCT
ap-1362	168	12	and	and	CCONJ
ap-1362	168	13	it	it	PRON
ap-1362	168	14	is	be	AUX
ap-1362	168	15	easy	easy	ADJ
ap-1362	168	16	to	to	PART
ap-1362	168	17	realize	realize	VERB
ap-1362	168	18	that	that	PRON
ap-1362	168	19	[	[	X
ap-1362	168	20	x1	x1	ADJ
ap-1362	168	21	,	,	PUNCT
ap-1362	168	22	x9	x9	NOUN
ap-1362	168	23	]	]	PUNCT
ap-1362	168	24	=	=	SYM
ap-1362	168	25	x9	x9	NOUN
ap-1362	168	26	,	,	PUNCT
ap-1362	168	27	[	[	X
ap-1362	168	28	x1	x1	X
ap-1362	168	29	,	,	PUNCT
ap-1362	168	30	x10	x10	NOUN
ap-1362	168	31	]	]	X
ap-1362	168	32	=	=	SYM
ap-1362	168	33	−x10	−x10	PROPN
ap-1362	168	34	,	,	PUNCT
ap-1362	169	1	[	[	X
ap-1362	169	2	x1	x1	PROPN
ap-1362	169	3	,	,	PUNCT
ap-1362	169	4	x11	x11	NOUN
ap-1362	169	5	]	]	X
ap-1362	169	6	=	=	SYM
ap-1362	169	7	x11	x11	NOUN
ap-1362	169	8	,	,	PUNCT
ap-1362	170	1	[	[	X
ap-1362	170	2	x1	x1	PROPN
ap-1362	170	3	,	,	PUNCT
ap-1362	170	4	x12	x12	PROPN
ap-1362	170	5	]	]	X
ap-1362	170	6	=	=	PUNCT
ap-1362	170	7	−x12	−x12	X
ap-1362	170	8	,	,	PUNCT
ap-1362	170	9	and	and	CCONJ
ap-1362	170	10	so	so	ADV
ap-1362	170	11	on	on	ADV
ap-1362	170	12	;	;	PUNCT
ap-1362	170	13	thus	thus	ADV
ap-1362	170	14	characterizing	characterize	VERB
ap-1362	170	15	the	the	DET
ap-1362	170	16	cartan	cartan	ADJ
ap-1362	170	17	matrix	matrix	NOUN
ap-1362	170	18	κij	κij	PROPN
ap-1362	170	19	.	.	PUNCT
ap-1362	171	1	it	it	PRON
ap-1362	171	2	would	would	AUX
ap-1362	171	3	be	be	AUX
ap-1362	171	4	of	of	ADP
ap-1362	171	5	interest	interest	NOUN
ap-1362	171	6	to	to	PART
ap-1362	171	7	study	study	VERB
ap-1362	171	8	the	the	DET
ap-1362	171	9	relation	relation	NOUN
ap-1362	171	10	of	of	ADP
ap-1362	171	11	skeletons	skeleton	NOUN
ap-1362	171	12	with	with	ADP
ap-1362	171	13	generalization	generalization	NOUN
ap-1362	171	14	of	of	ADP
ap-1362	171	15	continuum	continuum	ADJ
ap-1362	171	16	lie	lie	NOUN
ap-1362	171	17	algebras	algebra	NOUN
ap-1362	171	18	to	to	ADP
ap-1362	171	19	the	the	DET
ap-1362	171	20	case	case	NOUN
ap-1362	171	21	when	when	SCONJ
ap-1362	171	22	the	the	DET
ap-1362	171	23	local	local	ADJ
ap-1362	171	24	algebra	algebra	NOUN
ap-1362	171	25	does	do	AUX
ap-1362	171	26	not	not	PART
ap-1362	171	27	generate	generate	VERB
ap-1362	171	28	g(e;k	g(e;k	PROPN
ap-1362	171	29	,	,	PUNCT
ap-1362	171	30	s	s	X
ap-1362	171	31	)	)	PUNCT
ap-1362	171	32	as	as	ADP
ap-1362	171	33	a	a	DET
ap-1362	171	34	whole	whole	NOUN
ap-1362	171	35	,	,	PUNCT
ap-1362	171	36	where	where	SCONJ
ap-1362	171	37	g(e;k	g(e;k	PROPN
ap-1362	171	38	,	,	PUNCT
ap-1362	171	39	s	s	X
ap-1362	171	40	)	)	PUNCT
ap-1362	171	41	are	be	AUX
ap-1362	171	42	saveliev	saveliev	PROPN
ap-1362	171	43	’s	’s	PART
ap-1362	171	44	continuum	continuum	ADJ
ap-1362	171	45	lie	lie	NOUN
ap-1362	171	46	algebras	algebra	NOUN
ap-1362	171	47	and	and	CCONJ
ap-1362	171	48	they	they	PRON
ap-1362	171	49	are	be	AUX
ap-1362	171	50	defined	define	VERB
ap-1362	171	51	as	as	SCONJ
ap-1362	171	52	follows	follow	VERB
ap-1362	171	53	.	.	PUNCT
ap-1362	172	1	let	let	VERB
ap-1362	172	2	e	e	PRON
ap-1362	172	3	be	be	AUX
ap-1362	172	4	a	a	DET
ap-1362	172	5	vector	vector	NOUN
ap-1362	172	6	space	space	NOUN
ap-1362	172	7	parametrizing	parametrize	VERB
ap-1362	172	8	lie	lie	NOUN
ap-1362	172	9	algebras	algebras	PROPN
ap-1362	172	10	gi	gi	PROPN
ap-1362	172	11	,	,	PUNCT
ap-1362	172	12	i	i	PRON
ap-1362	172	13	=	=	PUNCT
ap-1362	172	14	0,+1,−1	0,+1,−1	ADV
ap-1362	172	15	,	,	PUNCT
ap-1362	172	16	ĝ	ĝ	PROPN
ap-1362	172	17	≡	≡	PROPN
ap-1362	172	18	g−1	g−1	PROPN
ap-1362	172	19	⊕	⊕	PROPN
ap-1362	172	20	g0	g0	PROPN
ap-1362	172	21	⊕	⊕	PROPN
ap-1362	172	22	g+1	g+1	PROPN
ap-1362	172	23	,	,	PUNCT
ap-1362	172	24	such	such	ADJ
ap-1362	172	25	that	that	SCONJ
ap-1362	172	26	[	[	X
ap-1362	172	27	x0(φ	x0(φ	NOUN
ap-1362	172	28	)	)	PUNCT
ap-1362	172	29	,	,	PUNCT
ap-1362	172	30	x0(ψ	x0(ψ	NUM
ap-1362	172	31	)	)	PUNCT
ap-1362	172	32	]	]	PUNCT
ap-1362	173	1	=	=	PUNCT
ap-1362	173	2	0	0	NUM
ap-1362	173	3	,	,	PUNCT
ap-1362	173	4	[	[	X
ap-1362	173	5	x+1(φ	x+1(φ	PROPN
ap-1362	173	6	)	)	PUNCT
ap-1362	173	7	,	,	PUNCT
ap-1362	173	8	x−1(ψ	x−1(ψ	PROPN
ap-1362	173	9	)	)	PUNCT
ap-1362	173	10	]	]	PUNCT
ap-1362	173	11	=	=	SYM
ap-1362	173	12	x0(s(φ	x0(s(φ	PROPN
ap-1362	173	13	,	,	PUNCT
ap-1362	173	14	ψ	ψ	NOUN
ap-1362	173	15	)	)	PUNCT
ap-1362	173	16	)	)	PUNCT
ap-1362	173	17	,	,	PUNCT
ap-1362	174	1	[	[	X
ap-1362	174	2	x0(φ	x0(φ	X
ap-1362	174	3	)	)	PUNCT
ap-1362	174	4	,	,	PUNCT
ap-1362	174	5	x+1(ψ	x+1(ψ	PROPN
ap-1362	174	6	)	)	PUNCT
ap-1362	174	7	]	]	PUNCT
ap-1362	175	1	=	=	PUNCT
ap-1362	175	2	x+1(k(φ	x+1(k(φ	X
ap-1362	175	3	,	,	PUNCT
ap-1362	175	4	ψ	ψ	NOUN
ap-1362	175	5	)	)	PUNCT
ap-1362	175	6	)	)	PUNCT
ap-1362	175	7	,	,	PUNCT
ap-1362	176	1	[	[	X
ap-1362	176	2	x0(φ	x0(φ	X
ap-1362	176	3	)	)	PUNCT
ap-1362	176	4	,	,	PUNCT
ap-1362	176	5	x−1(ψ	x−1(ψ	PROPN
ap-1362	176	6	)	)	PUNCT
ap-1362	176	7	]	]	PUNCT
ap-1362	177	1	=	=	SYM
ap-1362	177	2	−x−1(k(φ	−x−1(k(φ	X
ap-1362	177	3	,	,	PUNCT
ap-1362	177	4	ψ	ψ	NOUN
ap-1362	177	5	)	)	PUNCT
ap-1362	177	6	)	)	PUNCT
ap-1362	177	7	,	,	PUNCT
ap-1362	177	8	with	with	ADP
ap-1362	177	9	k	k	PROPN
ap-1362	177	10	,	,	PUNCT
ap-1362	177	11	s	s	VERB
ap-1362	177	12	bilinear	bilinear	NOUN
ap-1362	177	13	maps	map	NOUN
ap-1362	177	14	e	e	X
ap-1362	177	15	×	×	NOUN
ap-1362	177	16	e	e	PROPN
ap-1362	177	17	→	→	SYM
ap-1362	177	18	e	e	X
ap-1362	177	19	satisfying	satisfy	VERB
ap-1362	177	20	conditions	condition	NOUN
ap-1362	177	21	equivalent	equivalent	ADJ
ap-1362	177	22	to	to	ADP
ap-1362	177	23	the	the	DET
ap-1362	177	24	jacobi	jacobi	PROPN
ap-1362	177	25	identity	identity	NOUN
ap-1362	177	26	.	.	PUNCT
ap-1362	178	1	take	take	VERB
ap-1362	178	2	g′(e;k	g′(e;k	NOUN
ap-1362	178	3	,	,	PUNCT
ap-1362	178	4	s	s	NOUN
ap-1362	178	5	)	)	PUNCT
ap-1362	178	6	as	as	ADP
ap-1362	178	7	the	the	DET
ap-1362	178	8	lie	lie	NOUN
ap-1362	178	9	algebra	algebra	NOUN
ap-1362	178	10	freely	freely	ADV
ap-1362	178	11	generated	generate	VERB
ap-1362	178	12	by	by	ADP
ap-1362	178	13	a	a	DET
ap-1362	178	14	local	local	ADJ
ap-1362	178	15	part	part	NOUN
ap-1362	178	16	ĝ	ĝ	NOUN
ap-1362	178	17	and	and	CCONJ
ap-1362	178	18	then	then	ADV
ap-1362	178	19	the	the	DET
ap-1362	178	20	quotient	quotient	NOUN
ap-1362	178	21	g(e;k	g(e;k	PROPN
ap-1362	178	22	,	,	PUNCT
ap-1362	178	23	s	s	X
ap-1362	178	24	)	)	PUNCT
ap-1362	178	25	=	=	SYM
ap-1362	178	26	g′(e;k	g′(e;k	NOUN
ap-1362	178	27	,	,	PUNCT
ap-1362	178	28	s)/j	s)/j	PUNCT
ap-1362	178	29	,	,	PUNCT
ap-1362	178	30	j	j	PROPN
ap-1362	178	31	the	the	DET
ap-1362	178	32	largest	large	ADJ
ap-1362	178	33	homogeneous	homogeneous	ADJ
ap-1362	178	34	ideal	ideal	NOUN
ap-1362	178	35	having	have	VERB
ap-1362	178	36	a	a	DET
ap-1362	178	37	trivial	trivial	ADJ
ap-1362	178	38	intersection	intersection	NOUN
ap-1362	178	39	with	with	ADP
ap-1362	178	40	g0	g0	PROPN
ap-1362	178	41	.	.	PUNCT
ap-1362	179	1	in	in	ADP
ap-1362	179	2	fact	fact	NOUN
ap-1362	179	3	,	,	PUNCT
ap-1362	179	4	such	such	DET
ap-1362	179	5	an	an	DET
ap-1362	179	6	algebra	algebra	NOUN
ap-1362	179	7	becomes	become	VERB
ap-1362	179	8	the	the	DET
ap-1362	179	9	kač-moody	kač-moody	NOUN
ap-1362	179	10	algebra	algebra	NOUN
ap-1362	179	11	above	above	ADP
ap-1362	179	12	when	when	SCONJ
ap-1362	179	13	e	e	PROPN
ap-1362	179	14	=	=	SYM
ap-1362	179	15	c	c	PROPN
ap-1362	179	16	n	n	CCONJ
ap-1362	179	17	,	,	PUNCT
ap-1362	179	18	k	k	PROPN
ap-1362	179	19	=	=	PUNCT
ap-1362	179	20	cartan	cartan	PROPN
ap-1362	179	21	matrix	matrix	NOUN
ap-1362	179	22	k	k	PROPN
ap-1362	179	23	,	,	PUNCT
ap-1362	179	24	s	s	PART
ap-1362	179	25	=	=	X
ap-1362	179	26	i.	i.	NOUN
ap-1362	179	27	the	the	DET
ap-1362	179	28	relation	relation	NOUN
ap-1362	179	29	with	with	ADP
ap-1362	179	30	the	the	DET
ap-1362	179	31	virasoro	virasoro	NOUN
ap-1362	179	32	algebra	algebra	PROPN
ap-1362	179	33	without	without	ADP
ap-1362	179	34	a	a	DET
ap-1362	179	35	central	central	ADJ
ap-1362	179	36	charge	charge	NOUN
ap-1362	179	37	could	could	AUX
ap-1362	179	38	be	be	AUX
ap-1362	179	39	also	also	ADV
ap-1362	179	40	considered	consider	VERB
ap-1362	179	41	in	in	ADP
ap-1362	179	42	this	this	DET
ap-1362	179	43	light	light	NOUN
ap-1362	179	44	.	.	PUNCT
ap-1362	180	1	this	this	DET
ap-1362	180	2	topic	topic	NOUN
ap-1362	180	3	will	will	AUX
ap-1362	180	4	be	be	AUX
ap-1362	180	5	the	the	DET
ap-1362	180	6	object	object	NOUN
ap-1362	180	7	of	of	ADP
ap-1362	180	8	further	further	ADJ
ap-1362	180	9	investigations	investigation	NOUN
ap-1362	180	10	.	.	PUNCT
ap-1362	181	1	references	reference	NOUN
ap-1362	181	2	[	[	X
ap-1362	181	3	1	1	NUM
ap-1362	181	4	]	]	PUNCT
ap-1362	181	5	alfinito	alfinito	ADJ
ap-1362	181	6	,	,	PUNCT
ap-1362	181	7	e.	e.	PROPN
ap-1362	181	8	,	,	PUNCT
ap-1362	181	9	soliani	soliani	PROPN
ap-1362	181	10	,	,	PUNCT
ap-1362	181	11	g.	g.	PROPN
ap-1362	181	12	,	,	PUNCT
ap-1362	181	13	solombrino	solombrino	PROPN
ap-1362	181	14	,	,	PUNCT
ap-1362	181	15	l.	l.	PROPN
ap-1362	181	16	:	:	PUNCT
ap-1362	181	17	the	the	DET
ap-1362	181	18	symmetry	symmetry	NOUN
ap-1362	181	19	structure	structure	NOUN
ap-1362	181	20	of	of	ADP
ap-1362	181	21	the	the	DET
ap-1362	181	22	heavenly	heavenly	ADJ
ap-1362	181	23	equation	equation	NOUN
ap-1362	181	24	,	,	PUNCT
ap-1362	181	25	lett	lett	PROPN
ap-1362	181	26	.	.	PUNCT
ap-1362	181	27	math	math	NOUN
ap-1362	181	28	.	.	PUNCT
ap-1362	182	1	phys	phy	NOUN
ap-1362	182	2	.	.	PUNCT
ap-1362	183	1	41	41	NUM
ap-1362	183	2	,	,	PUNCT
ap-1362	183	3	379–389	379–389	NUM
ap-1362	183	4	(	(	PUNCT
ap-1362	183	5	1997	1997	NUM
ap-1362	183	6	)	)	PUNCT
ap-1362	183	7	.	.	PUNCT
ap-1362	184	1	[	[	X
ap-1362	184	2	2	2	NUM
ap-1362	184	3	]	]	PUNCT
ap-1362	184	4	alfinito	alfinito	ADJ
ap-1362	184	5	,	,	PUNCT
ap-1362	184	6	e.	e.	PROPN
ap-1362	184	7	,	,	PUNCT
ap-1362	184	8	causo	causo	PROPN
ap-1362	184	9	,	,	PUNCT
ap-1362	184	10	m.	m.	NOUN
ap-1362	184	11	s.	s.	PROPN
ap-1362	184	12	,	,	PUNCT
ap-1362	184	13	profilo	profilo	PROPN
ap-1362	184	14	,	,	PUNCT
ap-1362	184	15	g.	g.	PROPN
ap-1362	184	16	,	,	PUNCT
ap-1362	184	17	soliani	soliani	NOUN
ap-1362	184	18	,	,	PUNCT
ap-1362	184	19	g.	g.	PROPN
ap-1362	184	20	:	:	PUNCT
ap-1362	184	21	a	a	DET
ap-1362	184	22	class	class	NOUN
ap-1362	184	23	of	of	ADP
ap-1362	184	24	nonlinear	nonlinear	ADJ
ap-1362	184	25	wave	wave	NOUN
ap-1362	184	26	equations	equation	NOUN
ap-1362	184	27	containing	contain	VERB
ap-1362	184	28	the	the	DET
ap-1362	184	29	continuous	continuous	ADJ
ap-1362	184	30	toda	toda	NOUN
ap-1362	184	31	case	case	NOUN
ap-1362	184	32	,	,	PUNCT
ap-1362	184	33	j.	j.	PROPN
ap-1362	184	34	phys	phys	PROPN
ap-1362	184	35	.	.	PUNCT
ap-1362	185	1	a	a	DET
ap-1362	185	2	31	31	NUM
ap-1362	185	3	(	(	PUNCT
ap-1362	185	4	9	9	NUM
ap-1362	185	5	)	)	PUNCT
ap-1362	185	6	(	(	PUNCT
ap-1362	185	7	1998	1998	NUM
ap-1362	185	8	)	)	PUNCT
ap-1362	185	9	2173–2189	2173–2189	NUM
ap-1362	185	10	.	.	PUNCT
ap-1362	186	1	[	[	X
ap-1362	186	2	3	3	NUM
ap-1362	186	3	]	]	X
ap-1362	186	4	baker	baker	PROPN
ap-1362	186	5	,	,	PUNCT
ap-1362	186	6	h.	h.	PROPN
ap-1362	186	7	f.	f.	PROPN
ap-1362	186	8	:	:	PUNCT
ap-1362	186	9	alternant	alternant	ADJ
ap-1362	186	10	and	and	CCONJ
ap-1362	186	11	continuous	continuous	ADJ
ap-1362	186	12	group	group	NOUN
ap-1362	186	13	,	,	PUNCT
ap-1362	186	14	proc	proc	NOUN
ap-1362	186	15	.	.	PUNCT
ap-1362	187	1	london	london	PROPN
ap-1362	187	2	math	math	PROPN
ap-1362	187	3	.	.	PUNCT
ap-1362	188	1	soc	soc	PROPN
ap-1362	188	2	.	.	PUNCT
ap-1362	189	1	(	(	PUNCT
ap-1362	189	2	2	2	NUM
ap-1362	189	3	)	)	PUNCT
ap-1362	189	4	,	,	PUNCT
ap-1362	189	5	3	3	NUM
ap-1362	189	6	,	,	PUNCT
ap-1362	189	7	24–47	24–47	NUM
ap-1362	189	8	(	(	PUNCT
ap-1362	189	9	1904	1904	NUM
ap-1362	189	10	)	)	PUNCT
ap-1362	189	11	;	;	PUNCT
ap-1362	190	1	campbell	campbell	PROPN
ap-1362	190	2	,	,	PUNCT
ap-1362	190	3	j.	j.	PROPN
ap-1362	190	4	e.	e.	PROPN
ap-1362	190	5	:	:	PUNCT
ap-1362	190	6	on	on	ADP
ap-1362	190	7	a	a	DET
ap-1362	190	8	law	law	NOUN
ap-1362	190	9	of	of	ADP
ap-1362	190	10	combination	combination	NOUN
ap-1362	190	11	of	of	ADP
ap-1362	190	12	operators	operator	NOUN
ap-1362	190	13	,	,	PUNCT
ap-1362	190	14	proc	proc	NOUN
ap-1362	190	15	.	.	PUNCT
ap-1362	191	1	london	london	PROPN
ap-1362	191	2	math	math	PROPN
ap-1362	191	3	.	.	PUNCT
ap-1362	192	1	soc	soc	PROPN
ap-1362	192	2	.	.	PUNCT
ap-1362	193	1	29	29	NUM
ap-1362	193	2	,	,	PUNCT
ap-1362	193	3	14–32	14–32	NUM
ap-1362	193	4	(	(	PUNCT
ap-1362	193	5	1898	1898	NUM
ap-1362	193	6	)	)	PUNCT
ap-1362	193	7	;	;	PUNCT
ap-1362	194	1	hausdorff	hausdorff	NOUN
ap-1362	194	2	,	,	PUNCT
ap-1362	194	3	f.	f.	PROPN
ap-1362	194	4	:	:	PUNCT
ap-1362	194	5	the	the	DET
ap-1362	194	6	symbolic	symbolic	ADJ
ap-1362	194	7	exponential	exponential	ADJ
ap-1362	194	8	formula	formula	NOUN
ap-1362	194	9	in	in	ADP
ap-1362	194	10	group	group	NOUN
ap-1362	194	11	theory	theory	NOUN
ap-1362	194	12	,	,	PUNCT
ap-1362	194	13	ber	ber	PROPN
ap-1362	194	14	.	.	PUNCT
ap-1362	195	1	verh.sächs	verh.sächs	PROPN
ap-1362	195	2	.	.	PUNCT
ap-1362	196	1	gess	gess	PROPN
ap-1362	196	2	.	.	PUNCT
ap-1362	197	1	wiss	wiss	PROPN
ap-1362	197	2	.	.	PUNCT
ap-1362	198	1	leipzig	leipzig	PROPN
ap-1362	198	2	.	.	PUNCT
ap-1362	199	1	math.-phys	math.-phys	PROPN
ap-1362	199	2	.	.	PUNCT
ap-1362	200	1	kl	kl	PROPN
ap-1362	200	2	.	.	PROPN
ap-1362	200	3	58	58	NUM
ap-1362	200	4	,	,	PUNCT
ap-1362	200	5	19–48	19–48	NUM
ap-1362	200	6	(	(	PUNCT
ap-1362	200	7	1906	1906	NUM
ap-1362	200	8	)	)	PUNCT
ap-1362	200	9	.	.	PUNCT
ap-1362	201	1	[	[	X
ap-1362	201	2	4	4	NUM
ap-1362	201	3	]	]	X
ap-1362	201	4	boyer	boyer	PROPN
ap-1362	201	5	,	,	PUNCT
ap-1362	201	6	c.	c.	PROPN
ap-1362	201	7	,	,	PUNCT
ap-1362	201	8	finley	finley	PROPN
ap-1362	201	9	,	,	PUNCT
ap-1362	201	10	j.	j.	PROPN
ap-1362	201	11	d.	d.	PROPN
ap-1362	201	12	:	:	PUNCT
ap-1362	201	13	killing	kill	VERB
ap-1362	201	14	vectors	vector	NOUN
ap-1362	201	15	in	in	ADP
ap-1362	201	16	selfdual	selfdual	ADJ
ap-1362	201	17	,	,	PUNCT
ap-1362	201	18	euclidean	euclidean	PROPN
ap-1362	201	19	einstein	einstein	PROPN
ap-1362	201	20	spaces	spaces	PROPN
ap-1362	201	21	,	,	PUNCT
ap-1362	201	22	j.	j.	PROPN
ap-1362	201	23	math	math	PROPN
ap-1362	201	24	.	.	PUNCT
ap-1362	202	1	phys	phy	NOUN
ap-1362	202	2	.	.	PUNCT
ap-1362	203	1	23	23	NUM
ap-1362	203	2	,	,	PUNCT
ap-1362	203	3	1	1	NUM
ap-1362	203	4	126–1128	126–1128	NUM
ap-1362	203	5	(	(	PUNCT
ap-1362	203	6	1982	1982	NUM
ap-1362	203	7	)	)	PUNCT
ap-1362	203	8	.	.	PUNCT
ap-1362	204	1	[	[	X
ap-1362	204	2	5	5	NUM
ap-1362	204	3	]	]	X
ap-1362	204	4	estabrook	estabrook	NOUN
ap-1362	204	5	,	,	PUNCT
ap-1362	204	6	f.	f.	PROPN
ap-1362	204	7	b.	b.	PROPN
ap-1362	204	8	,	,	PUNCT
ap-1362	204	9	wahlquist	wahlquist	NOUN
ap-1362	204	10	,	,	PUNCT
ap-1362	204	11	h.	h.	PROPN
ap-1362	204	12	d.	d.	PROPN
ap-1362	204	13	:	:	PUNCT
ap-1362	204	14	prolongation	prolongation	NOUN
ap-1362	204	15	structures	structure	NOUN
ap-1362	204	16	of	of	ADP
ap-1362	204	17	nonlinear	nonlinear	ADJ
ap-1362	204	18	evolution	evolution	NOUN
ap-1362	204	19	equations	equation	NOUN
ap-1362	204	20	.	.	PUNCT
ap-1362	205	1	ii	ii	PROPN
ap-1362	205	2	,	,	PUNCT
ap-1362	205	3	j.	j.	PROPN
ap-1362	205	4	math	math	PROPN
ap-1362	205	5	.	.	PUNCT
ap-1362	206	1	phys	phy	NOUN
ap-1362	206	2	.	.	PUNCT
ap-1362	207	1	17	17	NUM
ap-1362	207	2	,	,	PUNCT
ap-1362	207	3	1	1	NUM
ap-1362	207	4	293–1297	293–1297	NUM
ap-1362	207	5	(	(	PUNCT
ap-1362	207	6	1976	1976	NUM
ap-1362	207	7	)	)	PUNCT
ap-1362	207	8	.	.	PUNCT
ap-1362	208	1	57	57	NUM
ap-1362	208	2	acta	acta	PROPN
ap-1362	208	3	polytechnica	polytechnica	PROPN
ap-1362	208	4	vol	vol	NOUN
ap-1362	208	5	.	.	PUNCT
ap-1362	209	1	51	51	NUM
ap-1362	209	2	no	no	INTJ
ap-1362	209	3	.	.	PUNCT
ap-1362	210	1	1/2011	1/2011	NUM
ap-1362	211	1	[	[	X
ap-1362	211	2	6	6	NUM
ap-1362	211	3	]	]	X
ap-1362	211	4	grassi	grassi	NOUN
ap-1362	211	5	,	,	PUNCT
ap-1362	211	6	v.	v.	PROPN
ap-1362	211	7	,	,	PUNCT
ap-1362	211	8	leo	leo	PROPN
ap-1362	211	9	,	,	PUNCT
ap-1362	211	10	r.	r.	PROPN
ap-1362	211	11	a.	a.	PROPN
ap-1362	211	12	,	,	PUNCT
ap-1362	211	13	soliani	soliani	NOUN
ap-1362	211	14	,	,	PUNCT
ap-1362	211	15	g.	g.	PROPN
ap-1362	211	16	,	,	PUNCT
ap-1362	211	17	solombrino	solombrino	PROPN
ap-1362	211	18	,	,	PUNCT
ap-1362	211	19	l.	l.	PROPN
ap-1362	211	20	:	:	PUNCT
ap-1362	211	21	continuous	continuous	ADJ
ap-1362	211	22	approximation	approximation	NOUN
ap-1362	211	23	of	of	ADP
ap-1362	211	24	binomial	binomial	ADJ
ap-1362	211	25	lattices	lattice	NOUN
ap-1362	211	26	,	,	PUNCT
ap-1362	211	27	internat	internat	PROPN
ap-1362	211	28	.	.	PUNCT
ap-1362	212	1	j.	j.	PROPN
ap-1362	212	2	modern	modern	PROPN
ap-1362	212	3	phys	phys	PROPN
ap-1362	212	4	.	.	PUNCT
ap-1362	213	1	a	a	DET
ap-1362	213	2	14	14	NUM
ap-1362	213	3	(	(	PUNCT
ap-1362	213	4	15	15	NUM
ap-1362	213	5	)	)	PUNCT
ap-1362	213	6	(	(	PUNCT
ap-1362	213	7	1999	1999	NUM
ap-1362	213	8	)	)	PUNCT
ap-1362	213	9	2	2	NUM
ap-1362	213	10	357–2384	357–2384	NUM
ap-1362	213	11	.	.	PUNCT
ap-1362	214	1	[	[	X
ap-1362	214	2	7	7	NUM
ap-1362	214	3	]	]	X
ap-1362	214	4	kodama	kodama	X
ap-1362	214	5	,	,	PUNCT
ap-1362	214	6	y.	y.	NOUN
ap-1362	214	7	:	:	PUNCT
ap-1362	214	8	solutions	solution	NOUN
ap-1362	214	9	of	of	ADP
ap-1362	214	10	the	the	DET
ap-1362	214	11	dispersionless	dispersionless	NOUN
ap-1362	214	12	toda	toda	PROPN
ap-1362	214	13	equation	equation	NOUN
ap-1362	214	14	,	,	PUNCT
ap-1362	214	15	phys	phy	NOUN
ap-1362	214	16	.	.	PUNCT
ap-1362	215	1	lett	lett	PROPN
ap-1362	215	2	.	.	PUNCT
ap-1362	216	1	a	a	DET
ap-1362	216	2	147	147	NUM
ap-1362	216	3	(	(	PUNCT
ap-1362	216	4	8–9	8–9	NOUN
ap-1362	216	5	)	)	PUNCT
ap-1362	216	6	(	(	PUNCT
ap-1362	216	7	1990	1990	NUM
ap-1362	216	8	)	)	PUNCT
ap-1362	216	9	477–482	477–482	NUM
ap-1362	216	10	.	.	PUNCT
ap-1362	217	1	[	[	X
ap-1362	217	2	8	8	NUM
ap-1362	217	3	]	]	X
ap-1362	217	4	lebrun	lebrun	NOUN
ap-1362	217	5	,	,	PUNCT
ap-1362	217	6	c.	c.	NOUN
ap-1362	217	7	:	:	PUNCT
ap-1362	217	8	explicit	explicit	ADJ
ap-1362	217	9	self	self	NOUN
ap-1362	217	10	-	-	PUNCT
ap-1362	217	11	dual	dual	ADJ
ap-1362	217	12	metrics	metric	NOUN
ap-1362	217	13	on	on	ADP
ap-1362	217	14	cp2	cp2	NOUN
ap-1362	217	15	#	#	NOUN
ap-1362	217	16	.	.	PUNCT
ap-1362	217	17	.	.	PUNCT
ap-1362	218	1	.#cp2	.#cp2	PROPN
ap-1362	218	2	,	,	PUNCT
ap-1362	218	3	,	,	PUNCT
ap-1362	218	4	j.	j.	PROPN
ap-1362	218	5	diff	diff	PROPN
ap-1362	218	6	.	.	PUNCT
ap-1362	219	1	geom	geom	PROPN
ap-1362	219	2	.	.	PUNCT
ap-1362	220	1	34	34	NUM
ap-1362	220	2	(	(	PUNCT
ap-1362	220	3	1	1	NUM
ap-1362	220	4	)	)	PUNCT
ap-1362	220	5	(	(	PUNCT
ap-1362	220	6	1991	1991	NUM
ap-1362	220	7	)	)	PUNCT
ap-1362	221	1	223–253	223–253	NUM
ap-1362	221	2	.	.	PUNCT
ap-1362	222	1	[	[	X
ap-1362	222	2	9	9	NUM
ap-1362	222	3	]	]	SYM
ap-1362	222	4	morimoto	morimoto	NOUN
ap-1362	222	5	,	,	PUNCT
ap-1362	222	6	t.	t.	PROPN
ap-1362	222	7	:	:	PUNCT
ap-1362	222	8	geometric	geometric	ADJ
ap-1362	222	9	structures	structure	NOUN
ap-1362	222	10	on	on	ADP
ap-1362	222	11	filtered	filter	VERB
ap-1362	222	12	manifolds	manifold	NOUN
ap-1362	222	13	,	,	PUNCT
ap-1362	222	14	hokkaido	hokkaido	PROPN
ap-1362	222	15	math	math	PROPN
ap-1362	222	16	.	.	PUNCT
ap-1362	223	1	j.	j.	PROPN
ap-1362	223	2	22(3	22(3	PROPN
ap-1362	223	3	)	)	PUNCT
ap-1362	223	4	(	(	PUNCT
ap-1362	223	5	1993	1993	NUM
ap-1362	223	6	)	)	PUNCT
ap-1362	224	1	263–347	263–347	NUM
ap-1362	224	2	.	.	PUNCT
ap-1362	225	1	[	[	X
ap-1362	225	2	10	10	NUM
ap-1362	225	3	]	]	X
ap-1362	225	4	palese	palese	NOUN
ap-1362	225	5	,	,	PUNCT
ap-1362	225	6	m.	m.	NOUN
ap-1362	225	7	,	,	PUNCT
ap-1362	225	8	leo	leo	PROPN
ap-1362	225	9	,	,	PUNCT
ap-1362	225	10	r.	r.	PROPN
ap-1362	225	11	a.	a.	PROPN
ap-1362	225	12	,	,	PUNCT
ap-1362	225	13	soliani	soliani	PROPN
ap-1362	225	14	,	,	PUNCT
ap-1362	225	15	g.	g.	PROPN
ap-1362	225	16	:	:	PUNCT
ap-1362	225	17	the	the	DET
ap-1362	225	18	prolongation	prolongation	NOUN
ap-1362	225	19	problem	problem	NOUN
ap-1362	225	20	for	for	ADP
ap-1362	225	21	the	the	DET
ap-1362	225	22	heavenly	heavenly	ADJ
ap-1362	225	23	equation	equation	NOUN
ap-1362	225	24	;	;	PUNCT
ap-1362	225	25	in	in	ADP
ap-1362	225	26	recent	recent	ADJ
ap-1362	225	27	developments	development	NOUN
ap-1362	225	28	in	in	ADP
ap-1362	225	29	general	general	ADJ
ap-1362	225	30	relativity	relativity	NOUN
ap-1362	225	31	(	(	PUNCT
ap-1362	225	32	bari	bari	NOUN
ap-1362	225	33	,	,	PUNCT
ap-1362	225	34	1998	1998	NUM
ap-1362	225	35	)	)	PUNCT
ap-1362	225	36	springer	springer	NOUN
ap-1362	225	37	italia	italia	PROPN
ap-1362	225	38	,	,	PUNCT
ap-1362	225	39	milan	milan	PROPN
ap-1362	225	40	(	(	PUNCT
ap-1362	225	41	2000	2000	NUM
ap-1362	225	42	)	)	PUNCT
ap-1362	225	43	337–344	337–344	NUM
ap-1362	225	44	.	.	PUNCT
ap-1362	226	1	[	[	X
ap-1362	226	2	11	11	NUM
ap-1362	226	3	]	]	PUNCT
ap-1362	226	4	park	park	NOUN
ap-1362	226	5	,	,	PUNCT
ap-1362	226	6	q	q	PROPN
ap-1362	226	7	-	-	PUNCT
ap-1362	226	8	han	han	ADJ
ap-1362	226	9	:	:	PUNCT
ap-1362	226	10	extended	extend	VERB
ap-1362	226	11	conformal	conformal	ADJ
ap-1362	226	12	symmetries	symmetry	NOUN
ap-1362	226	13	in	in	ADP
ap-1362	226	14	real	real	ADJ
ap-1362	226	15	heavens	heaven	NOUN
ap-1362	226	16	,	,	PUNCT
ap-1362	226	17	phys	phy	NOUN
ap-1362	226	18	.	.	PUNCT
ap-1362	227	1	lett	lett	PROPN
ap-1362	227	2	.	.	PUNCT
ap-1362	228	1	236b	236b	NUM
ap-1362	228	2	,	,	PUNCT
ap-1362	228	3	429–432	429–432	NUM
ap-1362	228	4	(	(	PUNCT
ap-1362	228	5	1990	1990	NUM
ap-1362	228	6	)	)	PUNCT
ap-1362	228	7	.	.	PUNCT
ap-1362	229	1	[	[	X
ap-1362	229	2	12	12	NUM
ap-1362	229	3	]	]	X
ap-1362	229	4	plebanski	plebanski	PROPN
ap-1362	229	5	,	,	PUNCT
ap-1362	229	6	j.	j.	PROPN
ap-1362	229	7	f.	f.	PROPN
ap-1362	229	8	:	:	PUNCT
ap-1362	229	9	some	some	DET
ap-1362	229	10	solutions	solution	NOUN
ap-1362	229	11	of	of	ADP
ap-1362	229	12	complex	complex	ADJ
ap-1362	229	13	einstein	einstein	PROPN
ap-1362	229	14	equations	equation	NOUN
ap-1362	229	15	,	,	PUNCT
ap-1362	229	16	j.	j.	PROPN
ap-1362	229	17	math	math	PROPN
ap-1362	229	18	.	.	PUNCT
ap-1362	230	1	phys	phy	NOUN
ap-1362	230	2	.	.	PUNCT
ap-1362	231	1	16	16	NUM
ap-1362	231	2	,	,	PUNCT
ap-1362	231	3	2	2	NUM
ap-1362	231	4	395–2402	395–2402	NUM
ap-1362	231	5	(	(	PUNCT
ap-1362	231	6	1975	1975	NUM
ap-1362	231	7	)	)	PUNCT
ap-1362	231	8	.	.	PUNCT
ap-1362	232	1	[	[	X
ap-1362	232	2	13	13	NUM
ap-1362	232	3	]	]	X
ap-1362	232	4	saveliev	saveliev	PROPN
ap-1362	232	5	,	,	PUNCT
ap-1362	232	6	m.	m.	NOUN
ap-1362	232	7	v.	v.	NOUN
ap-1362	232	8	:	:	PUNCT
ap-1362	232	9	integro	integro	ADJ
ap-1362	232	10	-	-	PUNCT
ap-1362	232	11	differential	differential	NOUN
ap-1362	232	12	nonlinear	nonlinear	ADJ
ap-1362	232	13	equations	equation	NOUN
ap-1362	232	14	and	and	CCONJ
ap-1362	232	15	continual	continual	ADJ
ap-1362	232	16	lie	lie	NOUN
ap-1362	232	17	algebras	algebra	NOUN
ap-1362	232	18	,	,	PUNCT
ap-1362	232	19	comm	comm	NOUN
ap-1362	232	20	.	.	PUNCT
ap-1362	232	21	math	math	NOUN
ap-1362	232	22	.	.	PUNCT
ap-1362	233	1	phys	phy	NOUN
ap-1362	233	2	.	.	PUNCT
ap-1362	234	1	121	121	NUM
ap-1362	234	2	(	(	PUNCT
ap-1362	234	3	2)(1989	2)(1989	NUM
ap-1362	234	4	)	)	PUNCT
ap-1362	234	5	283–290	283–290	NUM
ap-1362	234	6	;	;	PUNCT
ap-1362	234	7	saveliev	saveliev	ADV
ap-1362	234	8	,	,	PUNCT
ap-1362	234	9	m.	m.	NOUN
ap-1362	235	1	v.	v.	CCONJ
ap-1362	235	2	:	:	PUNCT
ap-1362	235	3	on	on	ADP
ap-1362	235	4	the	the	DET
ap-1362	235	5	integrability	integrability	NOUN
ap-1362	235	6	problem	problem	NOUN
ap-1362	235	7	of	of	ADP
ap-1362	235	8	a	a	DET
ap-1362	235	9	continuous	continuous	ADJ
ap-1362	235	10	toda	toda	NOUN
ap-1362	235	11	system	system	NOUN
ap-1362	235	12	,	,	PUNCT
ap-1362	235	13	theoret	theoret	ADJ
ap-1362	235	14	.	.	PUNCT
ap-1362	236	1	and	and	CCONJ
ap-1362	236	2	math	math	NOUN
ap-1362	236	3	.	.	PUNCT
ap-1362	237	1	phys	phy	NOUN
ap-1362	237	2	.	.	PUNCT
ap-1362	238	1	(	(	PUNCT
ap-1362	238	2	1992	1992	NUM
ap-1362	238	3	)	)	PUNCT
ap-1362	238	4	92	92	NUM
ap-1362	238	5	(	(	PUNCT
ap-1362	238	6	3	3	NUM
ap-1362	238	7	)	)	PUNCT
ap-1362	238	8	1	1	NUM
ap-1362	238	9	024–1	024–1	NUM
ap-1362	238	10	031	031	NUM
ap-1362	238	11	(	(	PUNCT
ap-1362	238	12	1993	1993	NUM
ap-1362	238	13	)	)	PUNCT
ap-1362	238	14	;	;	PUNCT
ap-1362	238	15	razumov	razumov	VERB
ap-1362	238	16	,	,	PUNCT
ap-1362	238	17	a.	a.	NOUN
ap-1362	238	18	v.	v.	PROPN
ap-1362	238	19	,	,	PUNCT
ap-1362	238	20	saveliev	saveliev	ADV
ap-1362	238	21	,	,	PUNCT
ap-1362	238	22	m.	m.	NOUN
ap-1362	239	1	v.	v.	NOUN
ap-1362	239	2	:	:	PUNCT
ap-1362	239	3	multidimensional	multidimensional	ADJ
ap-1362	239	4	systems	system	NOUN
ap-1362	239	5	of	of	ADP
ap-1362	239	6	toda	toda	PROPN
ap-1362	239	7	type	type	NOUN
ap-1362	239	8	,	,	PUNCT
ap-1362	239	9	theoret	theoret	ADJ
ap-1362	239	10	.	.	PUNCT
ap-1362	240	1	and	and	CCONJ
ap-1362	240	2	math	math	NOUN
ap-1362	240	3	.	.	PUNCT
ap-1362	241	1	phys	phy	NOUN
ap-1362	241	2	.	.	PUNCT
ap-1362	242	1	(	(	PUNCT
ap-1362	242	2	1997	1997	NUM
ap-1362	242	3	)	)	PUNCT
ap-1362	242	4	112	112	NUM
ap-1362	242	5	(	(	PUNCT
ap-1362	242	6	2	2	NUM
ap-1362	242	7	)	)	PUNCT
ap-1362	242	8	999–1022	999–1022	NUM
ap-1362	242	9	(	(	PUNCT
ap-1362	242	10	1998	1998	NUM
ap-1362	242	11	)	)	PUNCT
ap-1362	242	12	.	.	PUNCT
ap-1362	243	1	[	[	X
ap-1362	243	2	14	14	NUM
ap-1362	243	3	]	]	SYM
ap-1362	243	4	toda	toda	PROPN
ap-1362	243	5	,	,	PUNCT
ap-1362	243	6	m.	m.	NOUN
ap-1362	243	7	:	:	PUNCT
ap-1362	243	8	theory	theory	NOUN
ap-1362	243	9	of	of	ADP
ap-1362	243	10	nonlinear	nonlinear	ADJ
ap-1362	243	11	lattices	lattice	NOUN
ap-1362	243	12	,	,	PUNCT
ap-1362	243	13	springer	springer	NOUN
ap-1362	243	14	series	series	NOUN
ap-1362	243	15	in	in	ADP
ap-1362	243	16	solid	solid	ADJ
ap-1362	243	17	-	-	PUNCT
ap-1362	243	18	state	state	NOUN
ap-1362	243	19	sciences	science	NOUN
ap-1362	243	20	20	20	NUM
ap-1362	243	21	springerverlag	springerverlag	NOUN
ap-1362	243	22	,	,	PUNCT
ap-1362	243	23	berlin	berlin	PROPN
ap-1362	243	24	-	-	PUNCT
ap-1362	243	25	new	new	PROPN
ap-1362	243	26	york	york	PROPN
ap-1362	243	27	(	(	PUNCT
ap-1362	243	28	1981	1981	NUM
ap-1362	243	29	)	)	PUNCT
ap-1362	243	30	.	.	PUNCT
ap-1362	244	1	[	[	X
ap-1362	244	2	15	15	NUM
ap-1362	244	3	]	]	X
ap-1362	244	4	whalquist	whalquist	NOUN
ap-1362	244	5	,	,	PUNCT
ap-1362	244	6	h.	h.	PROPN
ap-1362	244	7	d.	d.	PROPN
ap-1362	244	8	,	,	PUNCT
ap-1362	244	9	estabrook	estabrook	PROPN
ap-1362	244	10	,	,	PUNCT
ap-1362	244	11	f.	f.	PROPN
ap-1362	244	12	b.	b.	PROPN
ap-1362	244	13	:	:	PUNCT
ap-1362	244	14	prolongation	prolongation	NOUN
ap-1362	244	15	structures	structure	NOUN
ap-1362	244	16	of	of	ADP
ap-1362	244	17	nonlinear	nonlinear	ADJ
ap-1362	244	18	evolution	evolution	NOUN
ap-1362	244	19	equations	equation	NOUN
ap-1362	244	20	,	,	PUNCT
ap-1362	244	21	j.	j.	PROPN
ap-1362	244	22	math	math	PROPN
ap-1362	244	23	.	.	PUNCT
ap-1362	245	1	phys	phy	NOUN
ap-1362	245	2	.	.	PUNCT
ap-1362	246	1	16	16	NUM
ap-1362	246	2	,	,	PUNCT
ap-1362	246	3	1–7	1–7	NUM
ap-1362	246	4	(	(	PUNCT
ap-1362	246	5	1975	1975	NUM
ap-1362	246	6	)	)	PUNCT
ap-1362	246	7	.	.	PUNCT
ap-1362	247	1	[	[	X
ap-1362	247	2	16	16	NUM
ap-1362	247	3	]	]	X
ap-1362	247	4	watson	watson	PROPN
ap-1362	247	5	,	,	PUNCT
ap-1362	247	6	g.	g.	PROPN
ap-1362	247	7	n.	n.	PROPN
ap-1362	247	8	:	:	PUNCT
ap-1362	247	9	a	a	DET
ap-1362	247	10	treatise	treatise	NOUN
ap-1362	247	11	on	on	ADP
ap-1362	247	12	the	the	DET
ap-1362	247	13	theory	theory	NOUN
ap-1362	247	14	of	of	ADP
ap-1362	247	15	bessel	bessel	NOUN
ap-1362	247	16	functions	function	NOUN
ap-1362	247	17	,	,	PUNCT
ap-1362	247	18	cambridge	cambridge	PROPN
ap-1362	247	19	university	university	PROPN
ap-1362	247	20	press	press	PROPN
ap-1362	247	21	,	,	PUNCT
ap-1362	247	22	cambridge	cambridge	PROPN
ap-1362	247	23	(	(	PUNCT
ap-1362	247	24	1952	1952	NUM
ap-1362	247	25	)	)	PUNCT
ap-1362	247	26	.	.	PUNCT
ap-1362	248	1	marcella	marcella	PROPN
ap-1362	248	2	palese	palese	PROPN
ap-1362	249	1	e	e	NOUN
ap-1362	249	2	-	-	NOUN
ap-1362	249	3	mail	mail	NOUN
ap-1362	249	4	:	:	PUNCT
ap-1362	249	5	marcella.palese@unito.it	marcella.palese@unito.it	PROPN
ap-1362	249	6	department	department	NOUN
ap-1362	249	7	of	of	ADP
ap-1362	249	8	mathematics	mathematics	PROPN
ap-1362	249	9	university	university	PROPN
ap-1362	249	10	of	of	ADP
ap-1362	249	11	torino	torino	NOUN
ap-1362	249	12	via	via	ADP
ap-1362	249	13	c.	c.	PROPN
ap-1362	249	14	alberto	alberto	PROPN
ap-1362	249	15	10	10	NUM
ap-1362	249	16	,	,	PUNCT
ap-1362	249	17	10123	10123	NUM
ap-1362	249	18	torino	torino	NOUN
ap-1362	249	19	,	,	PUNCT
ap-1362	249	20	italy	italy	PROPN
ap-1362	249	21	ekkehart	ekkehart	VERB
ap-1362	249	22	winterroth	winterroth	ADJ
ap-1362	249	23	e	e	NOUN
ap-1362	249	24	-	-	NOUN
ap-1362	249	25	mail	mail	NOUN
ap-1362	249	26	:	:	PUNCT
ap-1362	249	27	ekkehart.winterroth@unito.it	ekkehart.winterroth@unito.it	PROPN
ap-1362	249	28	department	department	NOUN
ap-1362	249	29	of	of	ADP
ap-1362	249	30	mathematics	mathematics	PROPN
ap-1362	249	31	university	university	PROPN
ap-1362	249	32	of	of	ADP
ap-1362	249	33	torino	torino	NOUN
ap-1362	249	34	via	via	ADP
ap-1362	249	35	c.	c.	PROPN
ap-1362	249	36	alberto	alberto	PROPN
ap-1362	249	37	10	10	NUM
ap-1362	249	38	,	,	PUNCT
ap-1362	249	39	10123	10123	NUM
ap-1362	249	40	torino	torino	NOUN
ap-1362	249	41	,	,	PUNCT
ap-1362	249	42	italy	italy	PROPN
ap-1362	249	43	58	58	NUM