id	sid	tid	token	lemma	pos
ap-1352	1	1	wykresx.eps	wykresx.eps	X
ap-1352	1	2	acta	acta	PROPN
ap-1352	1	3	polytechnica	polytechnica	PROPN
ap-1352	1	4	vol	vol	NOUN
ap-1352	1	5	.	.	PUNCT
ap-1352	2	1	51	51	NUM
ap-1352	2	2	no	no	NOUN
ap-1352	2	3	.	.	PUNCT
ap-1352	3	1	1/2011	1/2011	NUM
ap-1352	3	2	bidifferential	bidifferential	ADJ
ap-1352	3	3	calculus	calculus	NOUN
ap-1352	3	4	,	,	PUNCT
ap-1352	3	5	matrix	matrix	NOUN
ap-1352	3	6	sit	sit	NOUN
ap-1352	3	7	and	and	CCONJ
ap-1352	3	8	sine	sine	NOUN
ap-1352	3	9	-	-	PUNCT
ap-1352	3	10	gordon	gordon	PROPN
ap-1352	3	11	equations	equation	NOUN
ap-1352	3	12	a.	a.	NOUN
ap-1352	3	13	dimakis	dimakis	PROPN
ap-1352	3	14	,	,	PUNCT
ap-1352	3	15	n.	n.	PROPN
ap-1352	3	16	kanning	kanning	PROPN
ap-1352	3	17	,	,	PUNCT
ap-1352	3	18	f.	f.	PROPN
ap-1352	3	19	müller	müller	PROPN
ap-1352	3	20	-	-	PUNCT
ap-1352	3	21	hoissen	hoissen	NOUN
ap-1352	3	22	abstract	abstract	NOUN
ap-1352	3	23	we	we	PRON
ap-1352	3	24	express	express	VERB
ap-1352	3	25	a	a	DET
ap-1352	3	26	matrix	matrix	NOUN
ap-1352	3	27	version	version	NOUN
ap-1352	3	28	of	of	ADP
ap-1352	3	29	the	the	DET
ap-1352	3	30	self	self	NOUN
ap-1352	3	31	-	-	PUNCT
ap-1352	3	32	induced	induce	VERB
ap-1352	3	33	transparency	transparency	NOUN
ap-1352	3	34	(	(	PUNCT
ap-1352	3	35	sit	sit	NOUN
ap-1352	3	36	)	)	PUNCT
ap-1352	3	37	equations	equation	NOUN
ap-1352	3	38	in	in	ADP
ap-1352	3	39	the	the	DET
ap-1352	3	40	bidifferential	bidifferential	ADJ
ap-1352	3	41	calculus	calculus	NOUN
ap-1352	3	42	framework	framework	NOUN
ap-1352	3	43	.	.	PUNCT
ap-1352	4	1	an	an	DET
ap-1352	4	2	infinite	infinite	ADJ
ap-1352	4	3	family	family	NOUN
ap-1352	4	4	of	of	ADP
ap-1352	4	5	exact	exact	ADJ
ap-1352	4	6	solutions	solution	NOUN
ap-1352	4	7	is	be	AUX
ap-1352	4	8	then	then	ADV
ap-1352	4	9	obtained	obtain	VERB
ap-1352	4	10	by	by	ADP
ap-1352	4	11	application	application	NOUN
ap-1352	4	12	of	of	ADP
ap-1352	4	13	a	a	DET
ap-1352	4	14	general	general	ADJ
ap-1352	4	15	result	result	NOUN
ap-1352	4	16	that	that	PRON
ap-1352	4	17	generates	generate	VERB
ap-1352	4	18	exact	exact	ADJ
ap-1352	4	19	solutions	solution	NOUN
ap-1352	4	20	from	from	ADP
ap-1352	4	21	solutions	solution	NOUN
ap-1352	4	22	of	of	ADP
ap-1352	4	23	a	a	DET
ap-1352	4	24	linear	linear	ADJ
ap-1352	4	25	system	system	NOUN
ap-1352	4	26	of	of	ADP
ap-1352	4	27	arbitrary	arbitrary	ADJ
ap-1352	4	28	matrix	matrix	NOUN
ap-1352	4	29	size	size	NOUN
ap-1352	4	30	.	.	PUNCT
ap-1352	5	1	a	a	DET
ap-1352	5	2	side	side	NOUN
ap-1352	5	3	result	result	NOUN
ap-1352	5	4	is	be	AUX
ap-1352	5	5	a	a	DET
ap-1352	5	6	solution	solution	NOUN
ap-1352	5	7	formula	formula	NOUN
ap-1352	5	8	for	for	ADP
ap-1352	5	9	the	the	DET
ap-1352	5	10	sine	sine	NOUN
ap-1352	5	11	-	-	PUNCT
ap-1352	5	12	gordon	gordon	PROPN
ap-1352	5	13	equation	equation	NOUN
ap-1352	5	14	.	.	PUNCT
ap-1352	6	1	keywords	keyword	NOUN
ap-1352	6	2	:	:	PUNCT
ap-1352	6	3	bidifferential	bidifferential	ADJ
ap-1352	6	4	calculus	calculus	NOUN
ap-1352	6	5	,	,	PUNCT
ap-1352	6	6	integrable	integrable	ADJ
ap-1352	6	7	system	system	NOUN
ap-1352	6	8	,	,	PUNCT
ap-1352	6	9	self	self	NOUN
ap-1352	6	10	-	-	PUNCT
ap-1352	6	11	induced	induce	VERB
ap-1352	6	12	transparency	transparency	NOUN
ap-1352	6	13	,	,	PUNCT
ap-1352	6	14	sine	sine	NOUN
ap-1352	6	15	-	-	PUNCT
ap-1352	6	16	gordon	gordon	NOUN
ap-1352	6	17	.	.	PUNCT
ap-1352	7	1	1	1	NUM
ap-1352	7	2	introduction	introduction	NOUN
ap-1352	7	3	the	the	DET
ap-1352	7	4	bidifferential	bidifferential	ADJ
ap-1352	7	5	calculus	calculus	NOUN
ap-1352	7	6	approach	approach	NOUN
ap-1352	7	7	(	(	PUNCT
ap-1352	7	8	see	see	VERB
ap-1352	7	9	[	[	X
ap-1352	7	10	1	1	X
ap-1352	7	11	]	]	PUNCT
ap-1352	7	12	and	and	CCONJ
ap-1352	7	13	the	the	DET
ap-1352	7	14	references	reference	NOUN
ap-1352	7	15	therein	therein	ADV
ap-1352	7	16	)	)	PUNCT
ap-1352	7	17	aims	aim	VERB
ap-1352	7	18	to	to	PART
ap-1352	7	19	extract	extract	VERB
ap-1352	7	20	the	the	DET
ap-1352	7	21	essence	essence	NOUN
ap-1352	7	22	of	of	ADP
ap-1352	7	23	integrability	integrability	NOUN
ap-1352	7	24	aspects	aspect	NOUN
ap-1352	7	25	of	of	ADP
ap-1352	7	26	integrable	integrable	ADJ
ap-1352	7	27	partial	partial	ADJ
ap-1352	7	28	differential	differential	NOUN
ap-1352	7	29	or	or	CCONJ
ap-1352	7	30	difference	difference	NOUN
ap-1352	7	31	equations	equation	NOUN
ap-1352	7	32	(	(	PUNCT
ap-1352	7	33	pddes	pdde	NOUN
ap-1352	7	34	)	)	PUNCT
ap-1352	7	35	and	and	CCONJ
ap-1352	7	36	to	to	PART
ap-1352	7	37	express	express	VERB
ap-1352	7	38	them	they	PRON
ap-1352	7	39	,	,	PUNCT
ap-1352	7	40	and	and	CCONJ
ap-1352	7	41	relations	relation	NOUN
ap-1352	7	42	between	between	ADP
ap-1352	7	43	them	they	PRON
ap-1352	7	44	,	,	PUNCT
ap-1352	7	45	in	in	ADP
ap-1352	7	46	a	a	DET
ap-1352	7	47	universal	universal	ADJ
ap-1352	7	48	way	way	NOUN
ap-1352	7	49	,	,	PUNCT
ap-1352	7	50	i.e.	i.e.	X
ap-1352	7	51	resolved	resolve	VERB
ap-1352	7	52	from	from	ADP
ap-1352	7	53	specific	specific	ADJ
ap-1352	7	54	examples	example	NOUN
ap-1352	7	55	.	.	PUNCT
ap-1352	8	1	a	a	DET
ap-1352	8	2	powerful	powerful	ADJ
ap-1352	8	3	,	,	PUNCT
ap-1352	8	4	though	though	SCONJ
ap-1352	8	5	simple	simple	ADJ
ap-1352	8	6	to	to	PART
ap-1352	8	7	prove	prove	VERB
ap-1352	8	8	,	,	PUNCT
ap-1352	8	9	result	result	VERB
ap-1352	8	10	[	[	X
ap-1352	8	11	1	1	NUM
ap-1352	8	12	,	,	PUNCT
ap-1352	8	13	2	2	NUM
ap-1352	8	14	,	,	PUNCT
ap-1352	8	15	3	3	NUM
ap-1352	8	16	]	]	PUNCT
ap-1352	8	17	(	(	PUNCT
ap-1352	8	18	see	see	VERB
ap-1352	8	19	section	section	NOUN
ap-1352	8	20	6	6	NUM
ap-1352	8	21	)	)	PUNCT
ap-1352	8	22	generates	generate	VERB
ap-1352	8	23	families	family	NOUN
ap-1352	8	24	of	of	ADP
ap-1352	8	25	exact	exact	ADJ
ap-1352	8	26	solutions	solution	NOUN
ap-1352	8	27	from	from	ADP
ap-1352	8	28	a	a	DET
ap-1352	8	29	matrix	matrix	NOUN
ap-1352	8	30	linear	linear	NOUN
ap-1352	8	31	system	system	NOUN
ap-1352	8	32	.	.	PUNCT
ap-1352	9	1	in	in	ADP
ap-1352	9	2	the	the	DET
ap-1352	9	3	following	following	NOUN
ap-1352	9	4	we	we	PRON
ap-1352	9	5	briefly	briefly	ADV
ap-1352	9	6	recall	recall	VERB
ap-1352	9	7	the	the	DET
ap-1352	9	8	basic	basic	ADJ
ap-1352	9	9	framework	framework	NOUN
ap-1352	9	10	and	and	CCONJ
ap-1352	9	11	then	then	ADV
ap-1352	9	12	apply	apply	VERB
ap-1352	9	13	the	the	DET
ap-1352	9	14	latter	latter	ADJ
ap-1352	9	15	result	result	NOUN
ap-1352	9	16	to	to	ADP
ap-1352	9	17	a	a	DET
ap-1352	9	18	matrix	matrix	NOUN
ap-1352	9	19	generalization	generalization	NOUN
ap-1352	9	20	of	of	ADP
ap-1352	9	21	the	the	DET
ap-1352	9	22	sit	sit	NOUN
ap-1352	9	23	equations	equation	NOUN
ap-1352	9	24	.	.	PUNCT
ap-1352	10	1	2	2	NUM
ap-1352	10	2	bidifferential	bidifferential	ADJ
ap-1352	10	3	calculus	calculus	NOUN
ap-1352	10	4	a	a	DET
ap-1352	10	5	graded	grade	VERB
ap-1352	10	6	algebra	algebra	NOUN
ap-1352	10	7	is	be	AUX
ap-1352	10	8	an	an	DET
ap-1352	10	9	associative	associative	ADJ
ap-1352	10	10	algebra	algebra	NOUN
ap-1352	10	11	ω	ω	NOUN
ap-1352	10	12	over	over	ADP
ap-1352	10	13	c	c	NOUN
ap-1352	10	14	with	with	ADP
ap-1352	10	15	a	a	DET
ap-1352	10	16	direct	direct	ADJ
ap-1352	10	17	sum	sum	NOUN
ap-1352	10	18	decomposition	decomposition	NOUN
ap-1352	10	19	ω	ω	X
ap-1352	10	20	=	=	SYM
ap-1352	10	21	⊕	⊕	PROPN
ap-1352	10	22	r≥0	r≥0	PROPN
ap-1352	10	23	ωr	ωr	VERB
ap-1352	10	24	into	into	ADP
ap-1352	10	25	a	a	DET
ap-1352	10	26	subalgebra	subalgebra	NOUN
ap-1352	10	27	a	a	DET
ap-1352	10	28	:	:	PUNCT
ap-1352	10	29	=	=	NOUN
ap-1352	10	30	ω0	ω0	PROPN
ap-1352	10	31	and	and	CCONJ
ap-1352	10	32	a	a	DET
ap-1352	10	33	-	-	PUNCT
ap-1352	10	34	bimodules	bimodule	NOUN
ap-1352	10	35	ωr	ωr	ADJ
ap-1352	10	36	,	,	PUNCT
ap-1352	10	37	such	such	ADJ
ap-1352	10	38	that	that	SCONJ
ap-1352	10	39	ωr	ωr	ADP
ap-1352	10	40	ωs	ωs	DET
ap-1352	10	41	⊆	⊆	NUM
ap-1352	10	42	ωr+s	ωr+s	PROPN
ap-1352	10	43	.	.	PUNCT
ap-1352	11	1	a	a	DET
ap-1352	11	2	bidifferential	bidifferential	ADJ
ap-1352	11	3	calculus	calculus	NOUN
ap-1352	11	4	(	(	PUNCT
ap-1352	11	5	or	or	CCONJ
ap-1352	11	6	bidifferential	bidifferential	ADJ
ap-1352	11	7	graded	grade	VERB
ap-1352	11	8	algebra	algebra	NOUN
ap-1352	11	9	)	)	PUNCT
ap-1352	11	10	is	be	AUX
ap-1352	11	11	a	a	DET
ap-1352	11	12	unital	unital	ADJ
ap-1352	11	13	graded	grade	VERB
ap-1352	11	14	algebra	algebra	NOUN
ap-1352	11	15	ω	ω	PROPN
ap-1352	11	16	equipped	equip	VERB
ap-1352	11	17	with	with	ADP
ap-1352	11	18	two	two	NUM
ap-1352	11	19	(	(	PUNCT
ap-1352	11	20	c	c	NOUN
ap-1352	11	21	-	-	PUNCT
ap-1352	11	22	linear	linear	NOUN
ap-1352	11	23	)	)	PUNCT
ap-1352	11	24	graded	grade	VERB
ap-1352	11	25	derivations	derivation	NOUN
ap-1352	11	26	d	d	NOUN
ap-1352	11	27	,	,	PUNCT
ap-1352	11	28	d̄	d̄	PROPN
ap-1352	11	29	:	:	PUNCT
ap-1352	11	30	ω	ω	PROPN
ap-1352	11	31	→	→	SYM
ap-1352	11	32	ω	ω	PROPN
ap-1352	11	33	of	of	ADP
ap-1352	11	34	degree	degree	NOUN
ap-1352	11	35	one	one	NUM
ap-1352	11	36	(	(	PUNCT
ap-1352	11	37	hence	hence	ADV
ap-1352	11	38	dωr	dωr	PROPN
ap-1352	11	39	⊆	⊆	NUM
ap-1352	11	40	ωr+1	ωr+1	NUM
ap-1352	11	41	,	,	PUNCT
ap-1352	11	42	d̄ωr	d̄ωr	PROPN
ap-1352	11	43	⊆	⊆	NUM
ap-1352	11	44	ωr+1	ωr+1	NUM
ap-1352	11	45	)	)	PUNCT
ap-1352	11	46	,	,	PUNCT
ap-1352	11	47	with	with	ADP
ap-1352	11	48	the	the	DET
ap-1352	11	49	properties	property	NOUN
ap-1352	11	50	d2z	d2z	PUNCT
ap-1352	11	51	=	=	PUNCT
ap-1352	11	52	0	0	PUNCT
ap-1352	11	53	∀z	∀z	PROPN
ap-1352	11	54	∈	∈	PROPN
ap-1352	11	55	c	c	NOUN
ap-1352	11	56	,	,	PUNCT
ap-1352	11	57	where	where	SCONJ
ap-1352	11	58	dz	dz	ADJ
ap-1352	11	59	:	:	PUNCT
ap-1352	11	60	=	=	PUNCT
ap-1352	11	61	d̄−	d̄−	VERB
ap-1352	11	62	z	z	NOUN
ap-1352	11	63	d	d	NOUN
ap-1352	11	64	,	,	PUNCT
ap-1352	11	65	(	(	PUNCT
ap-1352	11	66	1	1	NUM
ap-1352	11	67	)	)	PUNCT
ap-1352	11	68	and	and	CCONJ
ap-1352	11	69	the	the	DET
ap-1352	11	70	graded	grade	VERB
ap-1352	11	71	leibniz	leibniz	PROPN
ap-1352	11	72	rule	rule	NOUN
ap-1352	11	73	dz(χ	dz(χ	X
ap-1352	11	74	χ′	χ′	PROPN
ap-1352	11	75	)	)	PUNCT
ap-1352	11	76	=	=	PUNCT
ap-1352	11	77	(	(	PUNCT
ap-1352	11	78	dzχ)χ′	dzχ)χ′	VERB
ap-1352	11	79	+	+	CCONJ
ap-1352	11	80	(	(	PUNCT
ap-1352	11	81	−1)r	−1)r	X
ap-1352	11	82	χ	χ	DET
ap-1352	11	83	dzχ	dzχ	NOUN
ap-1352	11	84	′	′	NOUN
ap-1352	11	85	,	,	PUNCT
ap-1352	11	86	for	for	ADP
ap-1352	11	87	all	all	PRON
ap-1352	11	88	χ	χ	PRON
ap-1352	11	89	∈	∈	PROPN
ap-1352	11	90	ωr	ωr	ADJ
ap-1352	11	91	and	and	CCONJ
ap-1352	11	92	χ′	χ′	PROPN
ap-1352	11	93	∈	∈	PROPN
ap-1352	11	94	ω	ω	PROPN
ap-1352	11	95	.	.	PROPN
ap-1352	11	96	3	3	NUM
ap-1352	11	97	dressing	dress	VERB
ap-1352	11	98	a	a	DET
ap-1352	11	99	bidifferential	bidifferential	ADJ
ap-1352	11	100	calculus	calculus	NOUN
ap-1352	11	101	let	let	VERB
ap-1352	11	102	(	(	PUNCT
ap-1352	11	103	ω	ω	NOUN
ap-1352	11	104	,	,	PUNCT
ap-1352	11	105	d	d	PROPN
ap-1352	11	106	,	,	PUNCT
ap-1352	11	107	d̄	d̄	PROPN
ap-1352	11	108	)	)	PUNCT
ap-1352	11	109	be	be	VERB
ap-1352	11	110	a	a	DET
ap-1352	11	111	bidifferential	bidifferential	ADJ
ap-1352	11	112	calculus	calculus	NOUN
ap-1352	11	113	.	.	PUNCT
ap-1352	12	1	replacing	replace	VERB
ap-1352	12	2	dz	dz	NOUN
ap-1352	12	3	in	in	ADP
ap-1352	12	4	(	(	PUNCT
ap-1352	12	5	1	1	NUM
ap-1352	12	6	)	)	PUNCT
ap-1352	12	7	by	by	ADP
ap-1352	12	8	dz	dz	X
ap-1352	12	9	:	:	PUNCT
ap-1352	12	10	=	=	SYM
ap-1352	12	11	d̄−a−	d̄−a−	PROPN
ap-1352	12	12	z	z	PROPN
ap-1352	12	13	d	d	PROPN
ap-1352	12	14	with	with	ADP
ap-1352	12	15	a	a	DET
ap-1352	12	16	1	1	NUM
ap-1352	12	17	-	-	PUNCT
ap-1352	12	18	form	form	NOUN
ap-1352	12	19	a	a	DET
ap-1352	12	20	∈	∈	PROPN
ap-1352	12	21	ω1	ω1	PROPN
ap-1352	12	22	(	(	PUNCT
ap-1352	12	23	in	in	ADP
ap-1352	12	24	the	the	DET
ap-1352	12	25	expression	expression	NOUN
ap-1352	12	26	for	for	SCONJ
ap-1352	12	27	dz	dz	NOUN
ap-1352	12	28	to	to	PART
ap-1352	12	29	be	be	AUX
ap-1352	12	30	regarded	regard	VERB
ap-1352	12	31	as	as	ADP
ap-1352	12	32	a	a	DET
ap-1352	12	33	multiplication	multiplication	NOUN
ap-1352	12	34	operator	operator	NOUN
ap-1352	12	35	)	)	PUNCT
ap-1352	12	36	,	,	PUNCT
ap-1352	12	37	the	the	DET
ap-1352	12	38	resulting	result	VERB
ap-1352	12	39	condition	condition	NOUN
ap-1352	12	40	d2z	d2z	PUNCT
ap-1352	12	41	=	=	PUNCT
ap-1352	12	42	0	0	PUNCT
ap-1352	12	43	(	(	PUNCT
ap-1352	12	44	for	for	ADP
ap-1352	12	45	all	all	DET
ap-1352	12	46	z	z	NOUN
ap-1352	12	47	∈	∈	PROPN
ap-1352	12	48	c	c	NOUN
ap-1352	12	49	)	)	PUNCT
ap-1352	12	50	can	can	AUX
ap-1352	12	51	be	be	AUX
ap-1352	12	52	expressed	express	VERB
ap-1352	12	53	as	as	ADP
ap-1352	12	54	da	da	NOUN
ap-1352	12	55	=	=	SYM
ap-1352	12	56	0	0	PUNCT
ap-1352	13	1	=	=	SYM
ap-1352	13	2	d̄a	d̄a	NOUN
ap-1352	13	3	−aa	−aa	NOUN
ap-1352	13	4	.	.	PUNCT
ap-1352	14	1	(	(	PUNCT
ap-1352	14	2	2	2	X
ap-1352	14	3	)	)	PUNCT
ap-1352	14	4	if	if	SCONJ
ap-1352	14	5	(	(	PUNCT
ap-1352	14	6	2	2	X
ap-1352	14	7	)	)	PUNCT
ap-1352	14	8	is	be	AUX
ap-1352	14	9	equivalent	equivalent	ADJ
ap-1352	14	10	to	to	ADP
ap-1352	14	11	a	a	DET
ap-1352	14	12	pdde	pdde	NOUN
ap-1352	14	13	,	,	PUNCT
ap-1352	14	14	we	we	PRON
ap-1352	14	15	have	have	VERB
ap-1352	14	16	a	a	DET
ap-1352	14	17	bidifferential	bidifferential	ADJ
ap-1352	14	18	calculus	calculus	NOUN
ap-1352	14	19	formulation	formulation	NOUN
ap-1352	14	20	for	for	ADP
ap-1352	14	21	it	it	PRON
ap-1352	14	22	.	.	PUNCT
ap-1352	15	1	this	this	PRON
ap-1352	15	2	requires	require	VERB
ap-1352	15	3	that	that	SCONJ
ap-1352	15	4	a	a	PRON
ap-1352	15	5	depends	depend	VERB
ap-1352	15	6	on	on	ADP
ap-1352	15	7	independent	independent	ADJ
ap-1352	15	8	variables	variable	NOUN
ap-1352	15	9	and	and	CCONJ
ap-1352	15	10	the	the	DET
ap-1352	15	11	derivations	derivation	NOUN
ap-1352	15	12	d	d	NOUN
ap-1352	15	13	,	,	PUNCT
ap-1352	15	14	d̄	d̄	PROPN
ap-1352	15	15	involve	involve	VERB
ap-1352	15	16	differential	differential	NOUN
ap-1352	15	17	or	or	CCONJ
ap-1352	15	18	difference	difference	NOUN
ap-1352	15	19	operators	operator	NOUN
ap-1352	15	20	.	.	PUNCT
ap-1352	16	1	several	several	ADJ
ap-1352	16	2	ways	way	NOUN
ap-1352	16	3	exist	exist	VERB
ap-1352	16	4	to	to	PART
ap-1352	16	5	reduce	reduce	VERB
ap-1352	16	6	the	the	DET
ap-1352	16	7	two	two	NUM
ap-1352	16	8	equations	equation	NOUN
ap-1352	16	9	(	(	PUNCT
ap-1352	16	10	2	2	NUM
ap-1352	16	11	)	)	PUNCT
ap-1352	16	12	to	to	ADP
ap-1352	16	13	a	a	DET
ap-1352	16	14	single	single	ADJ
ap-1352	16	15	one	one	NOUN
ap-1352	16	16	:	:	PUNCT
ap-1352	16	17	(	(	PUNCT
ap-1352	16	18	1	1	X
ap-1352	16	19	)	)	PUNCT
ap-1352	16	20	we	we	PRON
ap-1352	16	21	can	can	AUX
ap-1352	16	22	solve	solve	VERB
ap-1352	16	23	the	the	DET
ap-1352	16	24	first	first	ADJ
ap-1352	16	25	of	of	ADP
ap-1352	16	26	(	(	PUNCT
ap-1352	16	27	2	2	NUM
ap-1352	16	28	)	)	PUNCT
ap-1352	16	29	by	by	ADP
ap-1352	16	30	setting	set	VERB
ap-1352	16	31	a	a	DET
ap-1352	16	32	=	=	NOUN
ap-1352	16	33	dφ	dφ	ADJ
ap-1352	16	34	.	.	PUNCT
ap-1352	17	1	this	this	PRON
ap-1352	17	2	converts	convert	VERB
ap-1352	17	3	the	the	DET
ap-1352	17	4	second	second	ADJ
ap-1352	17	5	of	of	ADP
ap-1352	17	6	(	(	PUNCT
ap-1352	17	7	2	2	NUM
ap-1352	17	8	)	)	PUNCT
ap-1352	17	9	into	into	ADP
ap-1352	17	10	d̄	d̄	PROPN
ap-1352	17	11	dφ	dφ	ADP
ap-1352	17	12	=	=	NOUN
ap-1352	17	13	dφ	dφ	X
ap-1352	17	14	dφ	dφ	INTJ
ap-1352	17	15	.	.	PUNCT
ap-1352	18	1	(	(	PUNCT
ap-1352	18	2	3	3	X
ap-1352	18	3	)	)	PUNCT
ap-1352	18	4	(	(	PUNCT
ap-1352	18	5	2	2	X
ap-1352	18	6	)	)	PUNCT
ap-1352	18	7	the	the	DET
ap-1352	18	8	second	second	NOUN
ap-1352	18	9	of	of	ADP
ap-1352	18	10	(	(	PUNCT
ap-1352	18	11	2	2	X
ap-1352	18	12	)	)	PUNCT
ap-1352	18	13	can	can	AUX
ap-1352	18	14	be	be	AUX
ap-1352	18	15	solved	solve	VERB
ap-1352	18	16	by	by	ADP
ap-1352	18	17	setting	set	VERB
ap-1352	18	18	a	a	DET
ap-1352	18	19	=	=	X
ap-1352	18	20	(	(	PUNCT
ap-1352	18	21	d̄g	d̄g	PROPN
ap-1352	18	22	)	)	PUNCT
ap-1352	18	23	g−1	g−1	PROPN
ap-1352	18	24	.	.	PUNCT
ap-1352	19	1	the	the	DET
ap-1352	19	2	first	first	ADJ
ap-1352	19	3	equation	equation	NOUN
ap-1352	19	4	then	then	ADV
ap-1352	19	5	reads	read	VERB
ap-1352	19	6	d	d	X
ap-1352	19	7	(	(	PUNCT
ap-1352	19	8	(	(	PUNCT
ap-1352	19	9	d̄g	d̄g	ADJ
ap-1352	19	10	)	)	PUNCT
ap-1352	19	11	g−1	g−1	PROPN
ap-1352	19	12	)	)	PUNCT
ap-1352	20	1	=	=	SYM
ap-1352	20	2	0	0	X
ap-1352	20	3	.	.	PUNCT
ap-1352	21	1	(	(	PUNCT
ap-1352	21	2	4	4	NUM
ap-1352	21	3	)	)	PUNCT
ap-1352	21	4	(	(	PUNCT
ap-1352	21	5	3	3	X
ap-1352	21	6	)	)	PUNCT
ap-1352	21	7	more	more	ADV
ap-1352	21	8	generally	generally	ADV
ap-1352	21	9	,	,	PUNCT
ap-1352	21	10	setting	set	VERB
ap-1352	21	11	a	a	PRON
ap-1352	21	12	=	=	PUNCT
ap-1352	22	1	[	[	X
ap-1352	22	2	d̄g	d̄g	NOUN
ap-1352	22	3	−	−	PROPN
ap-1352	22	4	(	(	PUNCT
ap-1352	22	5	dg)δ	dg)δ	PROPN
ap-1352	22	6	]	]	X
ap-1352	22	7	g−1	g−1	PROPN
ap-1352	22	8	,	,	PUNCT
ap-1352	22	9	with	with	ADP
ap-1352	22	10	some	some	DET
ap-1352	22	11	δ	δ	PROPN
ap-1352	22	12	∈	∈	PROPN
ap-1352	22	13	a	a	PRON
ap-1352	22	14	,	,	PUNCT
ap-1352	22	15	we	we	PRON
ap-1352	22	16	have	have	VERB
ap-1352	22	17	d̄a−aa	d̄a−aa	PROPN
ap-1352	22	18	=	=	SYM
ap-1352	22	19	(	(	PUNCT
ap-1352	22	20	da	da	NOUN
ap-1352	22	21	)	)	PUNCT
ap-1352	23	1	gδg−1	gδg−1	NOUN
ap-1352	23	2	+	+	CCONJ
ap-1352	23	3	(	(	PUNCT
ap-1352	23	4	dg	dg	NOUN
ap-1352	23	5	)	)	PUNCT
ap-1352	23	6	(	(	PUNCT
ap-1352	23	7	d̄δ	d̄δ	PROPN
ap-1352	23	8	−	−	PROPN
ap-1352	23	9	(	(	PUNCT
ap-1352	23	10	dδ)δ	dδ)δ	PROPN
ap-1352	23	11	)	)	PUNCT
ap-1352	23	12	g−1	g−1	PROPN
ap-1352	23	13	.	.	PUNCT
ap-1352	24	1	as	as	ADP
ap-1352	24	2	a	a	DET
ap-1352	24	3	consequence	consequence	NOUN
ap-1352	24	4	,	,	PUNCT
ap-1352	24	5	if	if	SCONJ
ap-1352	24	6	δ	δ	PROPN
ap-1352	24	7	is	be	AUX
ap-1352	24	8	chosen	choose	VERB
ap-1352	24	9	such	such	ADJ
ap-1352	24	10	that	that	SCONJ
ap-1352	24	11	d̄δ	d̄δ	NOUN
ap-1352	24	12	=	=	SYM
ap-1352	24	13	(	(	PUNCT
ap-1352	24	14	dδ)δ	dδ)δ	PROPN
ap-1352	24	15	,	,	PUNCT
ap-1352	24	16	then	then	ADV
ap-1352	24	17	the	the	DET
ap-1352	24	18	two	two	NUM
ap-1352	24	19	equations	equation	NOUN
ap-1352	24	20	(	(	PUNCT
ap-1352	24	21	2	2	X
ap-1352	24	22	)	)	PUNCT
ap-1352	24	23	reduce	reduce	VERB
ap-1352	24	24	to	to	ADP
ap-1352	24	25	d	d	PROPN
ap-1352	24	26	(	(	PUNCT
ap-1352	24	27	[	[	X
ap-1352	24	28	d̄g	d̄g	ADP
ap-1352	24	29	−	−	PROPN
ap-1352	24	30	(	(	PUNCT
ap-1352	24	31	dg)δ	dg)δ	PROPN
ap-1352	24	32	]	]	X
ap-1352	24	33	g−1	g−1	PROPN
ap-1352	24	34	)	)	PUNCT
ap-1352	25	1	=	=	SYM
ap-1352	25	2	0	0	X
ap-1352	25	3	.	.	PUNCT
ap-1352	26	1	(	(	PUNCT
ap-1352	26	2	5	5	NUM
ap-1352	26	3	)	)	PUNCT
ap-1352	26	4	with	with	ADP
ap-1352	26	5	the	the	DET
ap-1352	26	6	choice	choice	NOUN
ap-1352	26	7	of	of	ADP
ap-1352	26	8	a	a	DET
ap-1352	26	9	suitable	suitable	ADJ
ap-1352	26	10	bidifferential	bidifferential	ADJ
ap-1352	26	11	calculus	calculus	NOUN
ap-1352	26	12	,	,	PUNCT
ap-1352	26	13	(	(	PUNCT
ap-1352	26	14	3	3	NUM
ap-1352	26	15	)	)	PUNCT
ap-1352	26	16	and	and	CCONJ
ap-1352	26	17	(	(	PUNCT
ap-1352	26	18	4	4	NUM
ap-1352	26	19	)	)	PUNCT
ap-1352	26	20	,	,	PUNCT
ap-1352	26	21	or	or	CCONJ
ap-1352	26	22	more	more	ADV
ap-1352	26	23	generally	generally	ADV
ap-1352	26	24	(	(	PUNCT
ap-1352	26	25	5	5	NUM
ap-1352	26	26	)	)	PUNCT
ap-1352	26	27	,	,	PUNCT
ap-1352	26	28	have	have	AUX
ap-1352	26	29	been	be	AUX
ap-1352	26	30	shown	show	VERB
ap-1352	26	31	to	to	PART
ap-1352	26	32	reproduce	reproduce	VERB
ap-1352	26	33	quite	quite	DET
ap-1352	26	34	a	a	DET
ap-1352	26	35	number	number	NOUN
ap-1352	26	36	of	of	ADP
ap-1352	26	37	integrable	integrable	ADJ
ap-1352	26	38	pddes	pdde	NOUN
ap-1352	26	39	.	.	PUNCT
ap-1352	27	1	this	this	PRON
ap-1352	27	2	includes	include	VERB
ap-1352	27	3	the	the	DET
ap-1352	27	4	self	self	NOUN
ap-1352	27	5	-	-	PUNCT
ap-1352	27	6	dual	dual	ADJ
ap-1352	27	7	yang	yang	PROPN
ap-1352	27	8	-	-	PUNCT
ap-1352	27	9	mills	mill	NOUN
ap-1352	27	10	equation	equation	NOUN
ap-1352	27	11	,	,	PUNCT
ap-1352	27	12	in	in	ADP
ap-1352	27	13	which	which	DET
ap-1352	27	14	case	case	NOUN
ap-1352	27	15	(	(	PUNCT
ap-1352	27	16	3	3	NUM
ap-1352	27	17	)	)	PUNCT
ap-1352	27	18	and	and	CCONJ
ap-1352	27	19	(	(	PUNCT
ap-1352	27	20	4	4	X
ap-1352	27	21	)	)	PUNCT
ap-1352	27	22	correspond	correspond	VERB
ap-1352	27	23	to	to	ADP
ap-1352	27	24	wellknown	wellknown	ADJ
ap-1352	27	25	potential	potential	ADJ
ap-1352	27	26	forms	form	NOUN
ap-1352	27	27	[	[	X
ap-1352	27	28	1	1	NUM
ap-1352	27	29	]	]	PUNCT
ap-1352	27	30	.	.	PUNCT
ap-1352	28	1	having	having	AUX
ap-1352	28	2	found	find	VERB
ap-1352	28	3	a	a	DET
ap-1352	28	4	bidifferential	bidifferential	ADJ
ap-1352	28	5	calculus	calculus	NOUN
ap-1352	28	6	in	in	ADP
ap-1352	28	7	terms	term	NOUN
ap-1352	28	8	of	of	ADP
ap-1352	28	9	which	which	PRON
ap-1352	28	10	e.g.	e.g.	ADV
ap-1352	28	11	(	(	PUNCT
ap-1352	28	12	3	3	X
ap-1352	28	13	)	)	PUNCT
ap-1352	28	14	is	be	AUX
ap-1352	28	15	equivalent	equivalent	ADJ
ap-1352	28	16	to	to	ADP
ap-1352	28	17	a	a	DET
ap-1352	28	18	certain	certain	ADJ
ap-1352	28	19	pdde	pdde	NOUN
ap-1352	28	20	,	,	PUNCT
ap-1352	28	21	it	it	PRON
ap-1352	28	22	is	be	AUX
ap-1352	28	23	not	not	PART
ap-1352	28	24	in	in	ADP
ap-1352	28	25	general	general	ADJ
ap-1352	28	26	guaranteed	guarantee	VERB
ap-1352	28	27	that	that	SCONJ
ap-1352	28	28	also	also	ADV
ap-1352	28	29	(	(	PUNCT
ap-1352	28	30	4	4	X
ap-1352	28	31	)	)	PUNCT
ap-1352	28	32	represents	represent	VERB
ap-1352	28	33	a	a	DET
ap-1352	28	34	decent	decent	ADJ
ap-1352	28	35	pdde	pdde	NOUN
ap-1352	28	36	.	.	PUNCT
ap-1352	29	1	then	then	ADV
ap-1352	29	2	the	the	DET
ap-1352	29	3	generalization	generalization	NOUN
ap-1352	29	4	(	(	PUNCT
ap-1352	29	5	5	5	NUM
ap-1352	29	6	)	)	PUNCT
ap-1352	29	7	has	have	VERB
ap-1352	29	8	a	a	DET
ap-1352	29	9	chance	chance	NOUN
ap-1352	29	10	to	to	PART
ap-1352	29	11	work	work	VERB
ap-1352	29	12	(	(	PUNCT
ap-1352	29	13	cf	cf	NOUN
ap-1352	29	14	.	.	PUNCT
ap-1352	30	1	[	[	X
ap-1352	30	2	1	1	NUM
ap-1352	30	3	]	]	PUNCT
ap-1352	30	4	)	)	PUNCT
ap-1352	30	5	.	.	PUNCT
ap-1352	31	1	in	in	ADP
ap-1352	31	2	such	such	DET
ap-1352	31	3	a	a	DET
ap-1352	31	4	case	case	NOUN
ap-1352	31	5	,	,	PUNCT
ap-1352	31	6	the	the	DET
ap-1352	31	7	miura	miura	PROPN
ap-1352	31	8	transformation	transformation	NOUN
ap-1352	32	1	[	[	X
ap-1352	32	2	d̄g	d̄g	VERB
ap-1352	32	3	−	−	PROPN
ap-1352	32	4	(	(	PUNCT
ap-1352	32	5	dg)δ	dg)δ	PROPN
ap-1352	32	6	]	]	X
ap-1352	32	7	g−1	g−1	PROPN
ap-1352	32	8	=	=	PUNCT
ap-1352	32	9	dφ	dφ	X
ap-1352	32	10	(	(	PUNCT
ap-1352	32	11	6	6	NUM
ap-1352	32	12	)	)	PUNCT
ap-1352	32	13	is	be	AUX
ap-1352	32	14	a	a	DET
ap-1352	32	15	hetero	hetero	NOUN
ap-1352	32	16	-	-	PUNCT
ap-1352	32	17	bäcklund	bäcklund	NOUN
ap-1352	32	18	transformation	transformation	NOUN
ap-1352	32	19	relating	relate	VERB
ap-1352	32	20	solutions	solution	NOUN
ap-1352	32	21	of	of	ADP
ap-1352	32	22	the	the	DET
ap-1352	32	23	two	two	NUM
ap-1352	32	24	pddes	pdde	NOUN
ap-1352	32	25	.	.	PUNCT
ap-1352	33	1	bäcklund	bäcklund	NOUN
ap-1352	33	2	,	,	PUNCT
ap-1352	33	3	darboux	darboux	VERB
ap-1352	33	4	and	and	CCONJ
ap-1352	33	5	binary	binary	ADJ
ap-1352	33	6	darboux	darboux	NOUN
ap-1352	33	7	transformations	transformation	NOUN
ap-1352	33	8	can	can	AUX
ap-1352	33	9	be	be	AUX
ap-1352	33	10	understood	understand	VERB
ap-1352	33	11	in	in	ADP
ap-1352	33	12	this	this	DET
ap-1352	33	13	general	general	ADJ
ap-1352	33	14	framework	framework	NOUN
ap-1352	33	15	[	[	X
ap-1352	33	16	1	1	NUM
ap-1352	33	17	]	]	PUNCT
ap-1352	33	18	,	,	PUNCT
ap-1352	33	19	and	and	CCONJ
ap-1352	33	20	there	there	PRON
ap-1352	33	21	is	be	VERB
ap-1352	33	22	a	a	DET
ap-1352	33	23	construction	construction	NOUN
ap-1352	33	24	of	of	ADP
ap-1352	33	25	an	an	DET
ap-1352	33	26	infinite	infinite	ADJ
ap-1352	33	27	33	33	NUM
ap-1352	33	28	acta	acta	PROPN
ap-1352	33	29	polytechnica	polytechnica	PROPN
ap-1352	33	30	vol	vol	NOUN
ap-1352	33	31	.	.	PUNCT
ap-1352	34	1	51	51	NUM
ap-1352	34	2	no	no	NOUN
ap-1352	34	3	.	.	PUNCT
ap-1352	35	1	1/2011	1/2011	NUM
ap-1352	35	2	set	set	NOUN
ap-1352	35	3	of	of	ADP
ap-1352	35	4	(	(	PUNCT
ap-1352	35	5	generalized	generalized	ADJ
ap-1352	35	6	)	)	PUNCT
ap-1352	35	7	conservation	conservation	NOUN
ap-1352	35	8	laws	law	NOUN
ap-1352	35	9	.	.	PUNCT
ap-1352	36	1	exchanging	exchange	VERB
ap-1352	36	2	d	d	PROPN
ap-1352	36	3	and	and	CCONJ
ap-1352	36	4	d̄	d̄	PROPN
ap-1352	36	5	leads	lead	VERB
ap-1352	36	6	to	to	ADP
ap-1352	36	7	what	what	PRON
ap-1352	36	8	is	be	AUX
ap-1352	36	9	known	know	VERB
ap-1352	36	10	in	in	ADP
ap-1352	36	11	the	the	DET
ap-1352	36	12	literature	literature	NOUN
ap-1352	36	13	as	as	ADP
ap-1352	36	14	‘	'	PUNCT
ap-1352	36	15	negative	negative	ADJ
ap-1352	36	16	flows	flow	NOUN
ap-1352	36	17	’	'	PUNCT
ap-1352	37	1	[	[	X
ap-1352	37	2	3	3	NUM
ap-1352	37	3	]	]	PUNCT
ap-1352	37	4	.	.	PUNCT
ap-1352	38	1	4	4	NUM
ap-1352	38	2	a	a	DET
ap-1352	38	3	matrix	matrix	NOUN
ap-1352	38	4	generalization	generalization	NOUN
ap-1352	38	5	of	of	ADP
ap-1352	38	6	sit	sit	NOUN
ap-1352	38	7	equations	equation	NOUN
ap-1352	38	8	and	and	CCONJ
ap-1352	38	9	its	its	PRON
ap-1352	38	10	miura	miura	NOUN
ap-1352	38	11	-	-	PUNCT
ap-1352	38	12	dual	dual	ADV
ap-1352	38	13	let	let	VERB
ap-1352	38	14	a	a	DET
ap-1352	38	15	=	=	PUNCT
ap-1352	38	16	mat	mat	NOUN
ap-1352	38	17	(	(	PUNCT
ap-1352	38	18	n	n	X
ap-1352	38	19	,	,	PUNCT
ap-1352	38	20	n	n	CCONJ
ap-1352	38	21	,	,	PUNCT
ap-1352	38	22	c∞(r2	c∞(r2	NOUN
ap-1352	38	23	)	)	PUNCT
ap-1352	38	24	)	)	PUNCT
ap-1352	38	25	,	,	PUNCT
ap-1352	38	26	the	the	DET
ap-1352	38	27	algebra	algebra	NOUN
ap-1352	38	28	of	of	ADP
ap-1352	38	29	n×n	n×n	PROPN
ap-1352	38	30	matrices	matrix	NOUN
ap-1352	38	31	of	of	ADP
ap-1352	38	32	smooth	smooth	ADJ
ap-1352	38	33	functions	function	NOUN
ap-1352	38	34	on	on	ADP
ap-1352	38	35	r	r	NOUN
ap-1352	38	36	2	2	NUM
ap-1352	38	37	.	.	PUNCT
ap-1352	39	1	let	let	VERB
ap-1352	39	2	ω	ω	NOUN
ap-1352	39	3	=	=	PUNCT
ap-1352	39	4	a⊗	a⊗	PROPN
ap-1352	39	5	∧	∧	PROPN
ap-1352	39	6	(	(	PUNCT
ap-1352	39	7	c2	c2	PROPN
ap-1352	39	8	)	)	PUNCT
ap-1352	39	9	with	with	ADP
ap-1352	39	10	the	the	DET
ap-1352	39	11	exterior	exterior	ADJ
ap-1352	39	12	algebra	algebra	NOUN
ap-1352	39	13	∧	∧	PROPN
ap-1352	39	14	(	(	PUNCT
ap-1352	39	15	c2	c2	PROPN
ap-1352	39	16	)	)	PUNCT
ap-1352	39	17	of	of	ADP
ap-1352	39	18	c	c	PROPN
ap-1352	39	19	2	2	NUM
ap-1352	39	20	.	.	PUNCT
ap-1352	40	1	in	in	ADP
ap-1352	40	2	terms	term	NOUN
ap-1352	40	3	of	of	ADP
ap-1352	40	4	coordinates	coordinate	NOUN
ap-1352	40	5	x	x	SYM
ap-1352	40	6	,	,	PUNCT
ap-1352	40	7	y	y	PROPN
ap-1352	40	8	of	of	ADP
ap-1352	40	9	r2	r2	PROPN
ap-1352	40	10	,	,	PUNCT
ap-1352	40	11	a	a	DET
ap-1352	40	12	basis	basis	NOUN
ap-1352	40	13	ζ1	ζ1	NOUN
ap-1352	40	14	,	,	PUNCT
ap-1352	40	15	ζ2	ζ2	NOUN
ap-1352	40	16	of	of	ADP
ap-1352	40	17	1∧	1∧	NUM
ap-1352	40	18	(	(	PUNCT
ap-1352	40	19	c2	c2	PROPN
ap-1352	40	20	)	)	PUNCT
ap-1352	40	21	,	,	PUNCT
ap-1352	40	22	and	and	CCONJ
ap-1352	40	23	a	a	DET
ap-1352	40	24	constant	constant	ADJ
ap-1352	40	25	n	n	NUM
ap-1352	40	26	×	×	NOUN
ap-1352	40	27	n	n	CCONJ
ap-1352	40	28	matrix	matrix	NOUN
ap-1352	40	29	j	j	PROPN
ap-1352	40	30	,	,	PUNCT
ap-1352	40	31	maps	maps	PROPN
ap-1352	40	32	d	d	PROPN
ap-1352	40	33	and	and	CCONJ
ap-1352	40	34	d̄	d̄	PROPN
ap-1352	40	35	are	be	AUX
ap-1352	40	36	defined	define	VERB
ap-1352	40	37	as	as	SCONJ
ap-1352	40	38	follows	follow	VERB
ap-1352	40	39	on	on	ADP
ap-1352	40	40	a	a	DET
ap-1352	40	41	,	,	PUNCT
ap-1352	40	42	df	df	PROPN
ap-1352	40	43	=	=	SYM
ap-1352	40	44	1	1	NUM
ap-1352	40	45	2	2	NUM
ap-1352	41	1	[	[	X
ap-1352	41	2	j	j	PROPN
ap-1352	41	3	,	,	PUNCT
ap-1352	41	4	f	f	PROPN
ap-1352	41	5	]	]	X
ap-1352	41	6	⊗	⊗	PROPN
ap-1352	41	7	ζ1	ζ1	PROPN
ap-1352	41	8	+	+	CCONJ
ap-1352	41	9	fy	fy	PROPN
ap-1352	41	10	⊗	⊗	ADJ
ap-1352	41	11	ζ2	ζ2	NOUN
ap-1352	41	12	,	,	PUNCT
ap-1352	41	13	d̄f	d̄f	PROPN
ap-1352	41	14	=	=	PUNCT
ap-1352	41	15	fx	fx	PROPN
ap-1352	41	16	⊗	⊗	NUM
ap-1352	41	17	ζ1	ζ1	PROPN
ap-1352	41	18	+	+	CCONJ
ap-1352	41	19	1	1	NUM
ap-1352	41	20	2	2	NUM
ap-1352	41	21	[	[	X
ap-1352	41	22	j	j	PROPN
ap-1352	41	23	,	,	PUNCT
ap-1352	41	24	f	f	PROPN
ap-1352	41	25	]	]	X
ap-1352	41	26	⊗	⊗	ADJ
ap-1352	41	27	ζ2	ζ2	NOUN
ap-1352	41	28	(	(	PUNCT
ap-1352	41	29	see	see	VERB
ap-1352	41	30	also	also	ADV
ap-1352	41	31	[	[	X
ap-1352	41	32	4	4	NUM
ap-1352	41	33	]	]	PUNCT
ap-1352	41	34	)	)	PUNCT
ap-1352	41	35	.	.	PUNCT
ap-1352	42	1	they	they	PRON
ap-1352	42	2	extend	extend	VERB
ap-1352	42	3	in	in	ADP
ap-1352	42	4	an	an	DET
ap-1352	42	5	obvious	obvious	ADJ
ap-1352	42	6	way	way	NOUN
ap-1352	42	7	(	(	PUNCT
ap-1352	42	8	with	with	ADP
ap-1352	42	9	dζi	dζi	NOUN
ap-1352	42	10	=	=	SYM
ap-1352	42	11	d̄ζi	d̄ζi	NOUN
ap-1352	42	12	=	=	SYM
ap-1352	42	13	0	0	NUM
ap-1352	42	14	)	)	PUNCT
ap-1352	42	15	to	to	ADP
ap-1352	42	16	ω	ω	NUM
ap-1352	42	17	such	such	ADJ
ap-1352	42	18	that	that	SCONJ
ap-1352	42	19	(	(	PUNCT
ap-1352	42	20	ω	ω	NOUN
ap-1352	42	21	,	,	PUNCT
ap-1352	42	22	d	d	PROPN
ap-1352	42	23	,	,	PUNCT
ap-1352	42	24	d̄	d̄	NOUN
ap-1352	42	25	)	)	PUNCT
ap-1352	42	26	becomes	become	VERB
ap-1352	42	27	a	a	DET
ap-1352	42	28	bidifferential	bidifferential	ADJ
ap-1352	42	29	calculus	calculus	NOUN
ap-1352	42	30	.	.	PUNCT
ap-1352	43	1	we	we	PRON
ap-1352	43	2	find	find	VERB
ap-1352	43	3	that	that	SCONJ
ap-1352	43	4	(	(	PUNCT
ap-1352	43	5	3	3	X
ap-1352	43	6	)	)	PUNCT
ap-1352	43	7	is	be	AUX
ap-1352	43	8	equivalent	equivalent	ADJ
ap-1352	43	9	to	to	ADP
ap-1352	43	10	φxy	φxy	NOUN
ap-1352	43	11	=	=	SYM
ap-1352	43	12	1	1	NUM
ap-1352	43	13	2	2	NUM
ap-1352	43	14	[	[	PUNCT
ap-1352	43	15	[	[	X
ap-1352	43	16	j	j	PROPN
ap-1352	43	17	,	,	PUNCT
ap-1352	43	18	φ	φ	PROPN
ap-1352	43	19	]	]	X
ap-1352	43	20	,	,	PUNCT
ap-1352	43	21	φy	φy	ADP
ap-1352	43	22	−	−	PROPN
ap-1352	43	23	1	1	NUM
ap-1352	43	24	2	2	NUM
ap-1352	43	25	j	j	NOUN
ap-1352	43	26	]	]	PUNCT
ap-1352	43	27	.	.	PUNCT
ap-1352	44	1	(	(	PUNCT
ap-1352	44	2	7	7	X
ap-1352	44	3	)	)	PUNCT
ap-1352	44	4	let	let	VERB
ap-1352	44	5	n	n	NOUN
ap-1352	44	6	=	=	SYM
ap-1352	44	7	2	2	NUM
ap-1352	44	8	m	m	NOUN
ap-1352	44	9	and	and	CCONJ
ap-1352	44	10	j	j	NOUN
ap-1352	44	11	=	=	SYM
ap-1352	44	12	block	block	NOUN
ap-1352	44	13	-	-	PUNCT
ap-1352	44	14	diag(i,−i	diag(i,−i	PROPN
ap-1352	44	15	)	)	PUNCT
ap-1352	44	16	,	,	PUNCT
ap-1352	44	17	where	where	SCONJ
ap-1352	44	18	i	i	PRON
ap-1352	44	19	=	=	VERB
ap-1352	45	1	i	i	PRON
ap-1352	45	2	m	m	VERB
ap-1352	45	3	denotes	denote	VERB
ap-1352	45	4	the	the	DET
ap-1352	45	5	m	m	PROPN
ap-1352	45	6	×	×	NOUN
ap-1352	45	7	m	m	NOUN
ap-1352	45	8	identity	identity	NOUN
ap-1352	45	9	matrix	matrix	NOUN
ap-1352	45	10	.	.	PUNCT
ap-1352	46	1	decomposing	decompose	VERB
ap-1352	46	2	φ	φ	NOUN
ap-1352	46	3	into	into	ADP
ap-1352	46	4	m×m	m×m	ADJ
ap-1352	46	5	blocks	block	NOUN
ap-1352	46	6	,	,	PUNCT
ap-1352	46	7	and	and	CCONJ
ap-1352	46	8	constraining	constrain	VERB
ap-1352	46	9	it	it	PRON
ap-1352	46	10	as	as	SCONJ
ap-1352	46	11	follows	follow	VERB
ap-1352	46	12	,	,	PUNCT
ap-1352	46	13	φ	φ	PROPN
ap-1352	46	14	=	=	PUNCT
ap-1352	46	15	(	(	PUNCT
ap-1352	46	16	p	p	X
ap-1352	46	17	q	q	X
ap-1352	46	18	q	q	PUNCT
ap-1352	46	19	−p	−p	NOUN
ap-1352	46	20	)	)	PUNCT
ap-1352	46	21	,	,	PUNCT
ap-1352	46	22	(	(	PUNCT
ap-1352	46	23	8)	8)	NUM
ap-1352	46	24	(	(	PUNCT
ap-1352	46	25	7	7	NUM
ap-1352	46	26	)	)	PUNCT
ap-1352	46	27	splits	split	VERB
ap-1352	46	28	into	into	ADP
ap-1352	46	29	the	the	DET
ap-1352	46	30	two	two	NUM
ap-1352	46	31	equations	equation	NOUN
ap-1352	46	32	pxy	pxy	AUX
ap-1352	46	33	=	=	PUNCT
ap-1352	46	34	(	(	PUNCT
ap-1352	46	35	q2)y	q2)y	INTJ
ap-1352	46	36	,	,	PUNCT
ap-1352	46	37	qxy	qxy	PROPN
ap-1352	46	38	=	=	SYM
ap-1352	46	39	q	q	NOUN
ap-1352	47	1	−	−	PROPN
ap-1352	47	2	pyq	pyq	NOUN
ap-1352	47	3	−	−	PROPN
ap-1352	47	4	qpy	qpy	NOUN
ap-1352	47	5	.	.	PUNCT
ap-1352	48	1	(	(	PUNCT
ap-1352	48	2	9	9	X
ap-1352	48	3	)	)	PUNCT
ap-1352	48	4	we	we	PRON
ap-1352	48	5	refer	refer	VERB
ap-1352	48	6	to	to	ADP
ap-1352	48	7	them	they	PRON
ap-1352	48	8	as	as	ADP
ap-1352	48	9	matrix	matrix	NOUN
ap-1352	48	10	-	-	PUNCT
ap-1352	48	11	sit	sit	NOUN
ap-1352	48	12	equations	equation	NOUN
ap-1352	48	13	(	(	PUNCT
ap-1352	48	14	see	see	VERB
ap-1352	48	15	section	section	NOUN
ap-1352	48	16	5	5	NUM
ap-1352	48	17	)	)	PUNCT
ap-1352	48	18	,	,	PUNCT
ap-1352	48	19	not	not	PART
ap-1352	48	20	purporting	purport	VERB
ap-1352	48	21	that	that	SCONJ
ap-1352	48	22	they	they	PRON
ap-1352	48	23	have	have	VERB
ap-1352	48	24	a	a	DET
ap-1352	48	25	similar	similar	ADJ
ap-1352	48	26	physical	physical	ADJ
ap-1352	48	27	relevance	relevance	NOUN
ap-1352	48	28	as	as	ADP
ap-1352	48	29	in	in	ADP
ap-1352	48	30	the	the	DET
ap-1352	48	31	scalar	scalar	ADJ
ap-1352	48	32	case	case	NOUN
ap-1352	48	33	.	.	PUNCT
ap-1352	49	1	the	the	DET
ap-1352	49	2	miura	miura	PROPN
ap-1352	49	3	transformation	transformation	NOUN
ap-1352	49	4	(	(	PUNCT
ap-1352	49	5	6	6	NUM
ap-1352	49	6	)	)	PUNCT
ap-1352	49	7	(	(	PUNCT
ap-1352	49	8	with	with	ADP
ap-1352	49	9	δ	δ	PROPN
ap-1352	49	10	=	=	SYM
ap-1352	49	11	0	0	NUM
ap-1352	49	12	)	)	PUNCT
ap-1352	49	13	now	now	ADV
ap-1352	49	14	reads	read	VERB
ap-1352	49	15	gx	gx	PROPN
ap-1352	49	16	g−1	g−1	PROPN
ap-1352	49	17	=	=	NOUN
ap-1352	49	18	1	1	NUM
ap-1352	49	19	2	2	NUM
ap-1352	49	20	[	[	X
ap-1352	49	21	j	j	PROPN
ap-1352	49	22	,	,	PUNCT
ap-1352	49	23	φ	φ	PROPN
ap-1352	49	24	]	]	X
ap-1352	49	25	,	,	PUNCT
ap-1352	49	26	1	1	NUM
ap-1352	49	27	2	2	NUM
ap-1352	49	28	[	[	X
ap-1352	49	29	j	j	NOUN
ap-1352	49	30	,	,	PUNCT
ap-1352	49	31	g	g	NOUN
ap-1352	49	32	]	]	X
ap-1352	49	33	g−1	g−1	PROPN
ap-1352	49	34	=	=	NOUN
ap-1352	49	35	φy	φy	NOUN
ap-1352	49	36	.	.	PUNCT
ap-1352	50	1	(	(	PUNCT
ap-1352	50	2	10	10	NUM
ap-1352	50	3	)	)	PUNCT
ap-1352	50	4	writing	write	VERB
ap-1352	50	5	g	g	NOUN
ap-1352	50	6	=	=	PUNCT
ap-1352	50	7	(	(	PUNCT
ap-1352	50	8	a	a	DET
ap-1352	50	9	b	b	NOUN
ap-1352	50	10	c	c	NOUN
ap-1352	50	11	d	d	NOUN
ap-1352	50	12	)	)	PUNCT
ap-1352	50	13	,	,	PUNCT
ap-1352	50	14	with	with	ADP
ap-1352	50	15	m	m	PROPN
ap-1352	50	16	×	×	PROPN
ap-1352	50	17	m	m	NOUN
ap-1352	50	18	matrices	matrix	NOUN
ap-1352	50	19	a	a	DET
ap-1352	50	20	,	,	PUNCT
ap-1352	50	21	b	b	NOUN
ap-1352	50	22	,	,	PUNCT
ap-1352	50	23	c	c	NOUN
ap-1352	50	24	,	,	PUNCT
ap-1352	50	25	d	d	NOUN
ap-1352	50	26	,	,	PUNCT
ap-1352	50	27	and	and	CCONJ
ap-1352	50	28	assuming	assume	VERB
ap-1352	50	29	that	that	SCONJ
ap-1352	50	30	a	a	PRON
ap-1352	50	31	and	and	CCONJ
ap-1352	50	32	its	its	PRON
ap-1352	50	33	schur	schur	NOUN
ap-1352	50	34	complement	complement	PROPN
ap-1352	50	35	s(a	s(a	PROPN
ap-1352	50	36	)	)	PUNCT
ap-1352	50	37	=	=	PUNCT
ap-1352	51	1	d−c	d−c	VERB
ap-1352	51	2	a−1b	a−1b	NOUN
ap-1352	51	3	is	be	AUX
ap-1352	51	4	invertible	invertible	ADJ
ap-1352	51	5	(	(	PUNCT
ap-1352	51	6	which	which	PRON
ap-1352	51	7	implies	imply	VERB
ap-1352	51	8	that	that	SCONJ
ap-1352	51	9	g	g	PROPN
ap-1352	51	10	is	be	AUX
ap-1352	51	11	invertible	invertible	ADJ
ap-1352	51	12	)	)	PUNCT
ap-1352	51	13	,	,	PUNCT
ap-1352	51	14	(	(	PUNCT
ap-1352	51	15	10	10	NUM
ap-1352	51	16	)	)	PUNCT
ap-1352	51	17	with	with	ADP
ap-1352	51	18	(	(	PUNCT
ap-1352	51	19	8)	8)	NUM
ap-1352	51	20	requires	require	VERB
ap-1352	51	21	b	b	NOUN
ap-1352	51	22	=	=	NOUN
ap-1352	51	23	−c	−c	ADJ
ap-1352	51	24	a−1d	a−1d	NOUN
ap-1352	51	25	,	,	PUNCT
ap-1352	51	26	ax	ax	NOUN
ap-1352	51	27	=	=	PUNCT
ap-1352	51	28	−cx	−cx	PROPN
ap-1352	51	29	a−1c	a−1c	VERB
ap-1352	51	30	,	,	PUNCT
ap-1352	51	31	(	(	PUNCT
ap-1352	51	32	11	11	NUM
ap-1352	51	33	)	)	PUNCT
ap-1352	51	34	dx	dx	PROPN
ap-1352	52	1	=	=	PROPN
ap-1352	52	2	−cx	−cx	PROPN
ap-1352	52	3	a−1c	a−1c	VERB
ap-1352	52	4	a−1d	a−1d	NOUN
ap-1352	52	5	.	.	PUNCT
ap-1352	53	1	the	the	DET
ap-1352	53	2	last	last	ADJ
ap-1352	53	3	equation	equation	NOUN
ap-1352	53	4	can	can	AUX
ap-1352	53	5	be	be	AUX
ap-1352	53	6	replaced	replace	VERB
ap-1352	53	7	by	by	ADP
ap-1352	53	8	dx	dx	PROPN
ap-1352	53	9	d−1	d−1	PROPN
ap-1352	53	10	=	=	PROPN
ap-1352	53	11	ax	ax	PROPN
ap-1352	53	12	a−1	a−1	PROPN
ap-1352	53	13	.	.	PUNCT
ap-1352	54	1	invertibility	invertibility	NOUN
ap-1352	54	2	of	of	ADP
ap-1352	54	3	s(a	s(a	PROPN
ap-1352	54	4	)	)	PUNCT
ap-1352	54	5	implies	imply	VERB
ap-1352	54	6	that	that	SCONJ
ap-1352	54	7	d	d	PROPN
ap-1352	54	8	and	and	CCONJ
ap-1352	54	9	i+r2	i+r2	PROPN
ap-1352	54	10	are	be	AUX
ap-1352	54	11	invertible	invertible	ADJ
ap-1352	54	12	,	,	PUNCT
ap-1352	54	13	where	where	SCONJ
ap-1352	54	14	r	r	NOUN
ap-1352	54	15	:	:	PUNCT
ap-1352	54	16	=	=	SYM
ap-1352	54	17	c	c	X
ap-1352	54	18	a−1	a−1	PROPN
ap-1352	54	19	.	.	PUNCT
ap-1352	55	1	the	the	DET
ap-1352	55	2	conditions	condition	NOUN
ap-1352	55	3	(	(	PUNCT
ap-1352	55	4	11	11	NUM
ap-1352	55	5	)	)	PUNCT
ap-1352	55	6	are	be	AUX
ap-1352	55	7	necessary	necessary	ADJ
ap-1352	55	8	in	in	ADP
ap-1352	55	9	order	order	NOUN
ap-1352	55	10	that	that	SCONJ
ap-1352	55	11	the	the	DET
ap-1352	55	12	miura	miura	PROPN
ap-1352	55	13	transformation	transformation	NOUN
ap-1352	55	14	relates	relate	VERB
ap-1352	55	15	solutions	solution	NOUN
ap-1352	55	16	of	of	ADP
ap-1352	55	17	(	(	PUNCT
ap-1352	55	18	9	9	NUM
ap-1352	55	19	)	)	PUNCT
ap-1352	55	20	to	to	ADP
ap-1352	55	21	solutions	solution	NOUN
ap-1352	55	22	of	of	ADP
ap-1352	55	23	its	its	PRON
ap-1352	55	24	‘	'	PUNCT
ap-1352	55	25	dual	dual	ADJ
ap-1352	55	26	’	'	PUNCT
ap-1352	55	27	(	(	PUNCT
ap-1352	55	28	gx	gx	PROPN
ap-1352	55	29	g−1)y	g−1)y	X
ap-1352	55	30	=	=	SYM
ap-1352	55	31	1	1	NUM
ap-1352	55	32	4	4	NUM
ap-1352	55	33	[	[	X
ap-1352	55	34	gjg−1	gjg−1	PROPN
ap-1352	55	35	,	,	PUNCT
ap-1352	55	36	j	j	PROPN
ap-1352	55	37	]	]	PUNCT
ap-1352	55	38	,	,	PUNCT
ap-1352	55	39	(	(	PUNCT
ap-1352	55	40	12	12	NUM
ap-1352	55	41	)	)	PUNCT
ap-1352	55	42	obtained	obtain	VERB
ap-1352	55	43	from	from	ADP
ap-1352	55	44	(	(	PUNCT
ap-1352	55	45	4	4	NUM
ap-1352	55	46	)	)	PUNCT
ap-1352	55	47	.	.	PUNCT
ap-1352	56	1	taking	take	VERB
ap-1352	56	2	(	(	PUNCT
ap-1352	56	3	11	11	NUM
ap-1352	56	4	)	)	PUNCT
ap-1352	56	5	into	into	ADP
ap-1352	56	6	account	account	NOUN
ap-1352	56	7	,	,	PUNCT
ap-1352	56	8	the	the	DET
ap-1352	56	9	miura	miura	PROPN
ap-1352	56	10	transformation	transformation	NOUN
ap-1352	56	11	reads	read	VERB
ap-1352	56	12	q	q	NOUN
ap-1352	56	13	=	=	SYM
ap-1352	57	1	−cx	−cx	NOUN
ap-1352	57	2	a−1	a−1	PROPN
ap-1352	57	3	=	=	SYM
ap-1352	57	4	−rx	−rx	NOUN
ap-1352	57	5	−	−	NOUN
ap-1352	57	6	r	r	NOUN
ap-1352	57	7	ax	ax	NOUN
ap-1352	57	8	a−1	a−1	PROPN
ap-1352	57	9	,	,	PUNCT
ap-1352	57	10	qy	qy	PROPN
ap-1352	57	11	=	=	PROPN
ap-1352	57	12	−r	−r	PROPN
ap-1352	57	13	(	(	PUNCT
ap-1352	57	14	i	i	NOUN
ap-1352	57	15	+	+	NUM
ap-1352	57	16	r2)−1	r2)−1	NOUN
ap-1352	57	17	,	,	PUNCT
ap-1352	57	18	(	(	PUNCT
ap-1352	57	19	13	13	NUM
ap-1352	57	20	)	)	PUNCT
ap-1352	57	21	py	py	NOUN
ap-1352	58	1	=	=	NOUN
ap-1352	59	1	i	i	PRON
ap-1352	59	2	−	−	PROPN
ap-1352	60	1	(	(	PUNCT
ap-1352	60	2	i	i	PRON
ap-1352	60	3	+	+	NUM
ap-1352	60	4	r2)−1	r2)−1	NOUN
ap-1352	60	5	.	.	PUNCT
ap-1352	61	1	as	as	ADP
ap-1352	61	2	a	a	DET
ap-1352	61	3	consequence	consequence	NOUN
ap-1352	61	4	,	,	PUNCT
ap-1352	61	5	we	we	PRON
ap-1352	61	6	have	have	VERB
ap-1352	61	7	qy	qy	NOUN
ap-1352	61	8	2	2	NUM
ap-1352	61	9	+	+	CCONJ
ap-1352	61	10	py	py	PROPN
ap-1352	61	11	2	2	NUM
ap-1352	61	12	=	=	SYM
ap-1352	61	13	py	py	PROPN
ap-1352	61	14	.	.	PUNCT
ap-1352	62	1	(	(	PUNCT
ap-1352	62	2	14	14	NUM
ap-1352	62	3	)	)	PUNCT
ap-1352	62	4	furthermore	furthermore	ADV
ap-1352	62	5	,	,	PUNCT
ap-1352	62	6	the	the	DET
ap-1352	62	7	second	second	ADJ
ap-1352	62	8	of	of	ADP
ap-1352	62	9	(	(	PUNCT
ap-1352	62	10	11	11	NUM
ap-1352	62	11	)	)	PUNCT
ap-1352	62	12	and	and	CCONJ
ap-1352	62	13	the	the	DET
ap-1352	62	14	first	first	ADJ
ap-1352	62	15	of	of	ADP
ap-1352	62	16	(	(	PUNCT
ap-1352	62	17	13	13	NUM
ap-1352	62	18	)	)	PUNCT
ap-1352	62	19	imply	imply	VERB
ap-1352	62	20	axa−1	axa−1	PROPN
ap-1352	62	21	=	=	PUNCT
ap-1352	62	22	qr	qr	PROPN
ap-1352	62	23	.	.	PUNCT
ap-1352	63	1	hence	hence	ADV
ap-1352	63	2	we	we	PRON
ap-1352	63	3	obtain	obtain	VERB
ap-1352	63	4	the	the	DET
ap-1352	63	5	system	system	NOUN
ap-1352	63	6	rx	rx	VERB
ap-1352	63	7	=	=	NOUN
ap-1352	63	8	−q	−q	ADJ
ap-1352	63	9	−	−	NOUN
ap-1352	63	10	r	r	NOUN
ap-1352	63	11	q	q	NOUN
ap-1352	63	12	r	r	NOUN
ap-1352	63	13	,	,	PUNCT
ap-1352	63	14	qy	qy	PROPN
ap-1352	63	15	=	=	PROPN
ap-1352	63	16	−r	−r	PROPN
ap-1352	63	17	(	(	PUNCT
ap-1352	63	18	i	i	NOUN
ap-1352	63	19	+	+	NUM
ap-1352	63	20	r2)−1	r2)−1	NOUN
ap-1352	63	21	,	,	PUNCT
ap-1352	63	22	(	(	PUNCT
ap-1352	63	23	15	15	NUM
ap-1352	63	24	)	)	PUNCT
ap-1352	63	25	which	which	PRON
ap-1352	63	26	may	may	AUX
ap-1352	63	27	be	be	AUX
ap-1352	63	28	regarded	regard	VERB
ap-1352	63	29	as	as	ADP
ap-1352	63	30	a	a	DET
ap-1352	63	31	matrix	matrix	NOUN
ap-1352	63	32	or	or	CCONJ
ap-1352	63	33	‘	'	PUNCT
ap-1352	63	34	noncommutative	noncommutative	ADJ
ap-1352	63	35	’	'	PUNCT
ap-1352	63	36	generalization	generalization	NOUN
ap-1352	63	37	of	of	ADP
ap-1352	63	38	the	the	DET
ap-1352	63	39	sine	sine	NOUN
ap-1352	63	40	-	-	PUNCT
ap-1352	63	41	gordon	gordon	PROPN
ap-1352	63	42	equation	equation	NOUN
ap-1352	63	43	.	.	PUNCT
ap-1352	64	1	there	there	PRON
ap-1352	64	2	are	be	VERB
ap-1352	64	3	various	various	ADJ
ap-1352	64	4	such	such	ADJ
ap-1352	64	5	generalizations	generalization	NOUN
ap-1352	64	6	in	in	ADP
ap-1352	64	7	the	the	DET
ap-1352	64	8	literature	literature	NOUN
ap-1352	64	9	.	.	PUNCT
ap-1352	65	1	the	the	DET
ap-1352	65	2	first	first	ADJ
ap-1352	65	3	equation	equation	NOUN
ap-1352	65	4	has	have	VERB
ap-1352	65	5	the	the	DET
ap-1352	65	6	solution	solution	NOUN
ap-1352	65	7	q	q	NOUN
ap-1352	66	1	=	=	SYM
ap-1352	66	2	−	−	PROPN
ap-1352	66	3	∞∑	∞∑	PROPN
ap-1352	66	4	k=0	k=0	PROPN
ap-1352	66	5	(	(	PUNCT
ap-1352	66	6	−1)k	−1)k	NOUN
ap-1352	66	7	rk	rk	NOUN
ap-1352	66	8	rx	rx	VERB
ap-1352	66	9	rk	rk	NOUN
ap-1352	66	10	,	,	PUNCT
ap-1352	66	11	if	if	SCONJ
ap-1352	66	12	the	the	DET
ap-1352	66	13	sum	sum	NOUN
ap-1352	66	14	exists	exist	VERB
ap-1352	66	15	.	.	PUNCT
ap-1352	67	1	alternatively	alternatively	ADV
ap-1352	67	2	,	,	PUNCT
ap-1352	67	3	we	we	PRON
ap-1352	67	4	can	can	AUX
ap-1352	67	5	express	express	VERB
ap-1352	67	6	this	this	PRON
ap-1352	67	7	as	as	ADP
ap-1352	67	8	q	q	NOUN
ap-1352	67	9	=	=	SYM
ap-1352	67	10	−(i	−(i	PROPN
ap-1352	67	11	+	+	CCONJ
ap-1352	67	12	rlrr	rlrr	NOUN
ap-1352	67	13	)	)	PUNCT
ap-1352	67	14	−1(rx	−1(rx	PROPN
ap-1352	67	15	)	)	PUNCT
ap-1352	67	16	,	,	PUNCT
ap-1352	67	17	where	where	SCONJ
ap-1352	67	18	rl	rl	PROPN
ap-1352	67	19	(	(	PUNCT
ap-1352	67	20	rr	rr	NOUN
ap-1352	67	21	)	)	PUNCT
ap-1352	67	22	denotes	denote	VERB
ap-1352	67	23	the	the	DET
ap-1352	67	24	map	map	NOUN
ap-1352	67	25	of	of	ADP
ap-1352	67	26	left	left	ADJ
ap-1352	67	27	(	(	PUNCT
ap-1352	67	28	right	right	ADJ
ap-1352	67	29	)	)	PUNCT
ap-1352	67	30	multiplication	multiplication	NOUN
ap-1352	67	31	by	by	ADP
ap-1352	67	32	r.	r.	PROPN
ap-1352	67	33	this	this	PRON
ap-1352	67	34	can	can	AUX
ap-1352	67	35	be	be	AUX
ap-1352	67	36	used	use	VERB
ap-1352	67	37	to	to	PART
ap-1352	67	38	eliminate	eliminate	VERB
ap-1352	67	39	q	q	NOUN
ap-1352	67	40	from	from	ADP
ap-1352	67	41	the	the	DET
ap-1352	67	42	second	second	ADJ
ap-1352	67	43	equation	equation	NOUN
ap-1352	67	44	,	,	PUNCT
ap-1352	67	45	resulting	result	VERB
ap-1352	67	46	in	in	ADP
ap-1352	67	47	(	(	PUNCT
ap-1352	67	48	(	(	PUNCT
ap-1352	67	49	i	i	NOUN
ap-1352	67	50	+	+	X
ap-1352	67	51	rlrr)−1(rx	rlrr)−1(rx	PROPN
ap-1352	67	52	)	)	PUNCT
ap-1352	67	53	)	)	PUNCT
ap-1352	68	1	y	y	NOUN
ap-1352	68	2	=	=	PUNCT
ap-1352	68	3	r	r	NOUN
ap-1352	68	4	(	(	PUNCT
ap-1352	68	5	i	i	NOUN
ap-1352	68	6	+	+	NUM
ap-1352	68	7	r2)−1	r2)−1	NOUN
ap-1352	68	8	.	.	PUNCT
ap-1352	69	1	(	(	PUNCT
ap-1352	69	2	16	16	NUM
ap-1352	69	3	)	)	PUNCT
ap-1352	69	4	if	if	SCONJ
ap-1352	69	5	r	r	NOUN
ap-1352	69	6	=	=	PUNCT
ap-1352	69	7	tan(θ/2)π	tan(θ/2)π	ADV
ap-1352	69	8	with	with	ADP
ap-1352	69	9	a	a	DET
ap-1352	69	10	constant	constant	ADJ
ap-1352	69	11	projection	projection	NOUN
ap-1352	69	12	π	π	PROPN
ap-1352	69	13	(	(	PUNCT
ap-1352	69	14	i.e.	i.e.	X
ap-1352	69	15	π2	π2	X
ap-1352	69	16	=	=	SYM
ap-1352	69	17	π	π	NOUN
ap-1352	69	18	)	)	PUNCT
ap-1352	69	19	and	and	CCONJ
ap-1352	69	20	a	a	DET
ap-1352	69	21	function	function	NOUN
ap-1352	69	22	θ	θ	NOUN
ap-1352	69	23	,	,	PUNCT
ap-1352	69	24	then	then	ADV
ap-1352	69	25	(	(	PUNCT
ap-1352	69	26	16	16	NUM
ap-1352	69	27	)	)	PUNCT
ap-1352	69	28	reduces	reduce	VERB
ap-1352	69	29	to	to	ADP
ap-1352	69	30	the	the	DET
ap-1352	69	31	sine	sine	NOUN
ap-1352	69	32	-	-	PUNCT
ap-1352	69	33	gordon	gordon	PROPN
ap-1352	69	34	equation	equation	NOUN
ap-1352	69	35	θxy	θxy	NOUN
ap-1352	69	36	=	=	PUNCT
ap-1352	69	37	sin	sin	NOUN
ap-1352	69	38	θ	θ	PROPN
ap-1352	69	39	.	.	PUNCT
ap-1352	70	1	(	(	PUNCT
ap-1352	70	2	17	17	NUM
ap-1352	70	3	)	)	PUNCT
ap-1352	70	4	(	(	PUNCT
ap-1352	70	5	15	15	NUM
ap-1352	70	6	)	)	PUNCT
ap-1352	70	7	can	can	AUX
ap-1352	70	8	be	be	AUX
ap-1352	70	9	obtained	obtain	VERB
ap-1352	70	10	directly	directly	ADV
ap-1352	70	11	from	from	ADP
ap-1352	70	12	(	(	PUNCT
ap-1352	70	13	12	12	NUM
ap-1352	70	14	)	)	PUNCT
ap-1352	70	15	as	as	SCONJ
ap-1352	70	16	follows	follow	VERB
ap-1352	70	17	,	,	PUNCT
ap-1352	70	18	by	by	ADP
ap-1352	70	19	setting	set	VERB
ap-1352	70	20	g	g	NOUN
ap-1352	70	21	=	=	PUNCT
ap-1352	70	22	(	(	PUNCT
ap-1352	70	23	a	a	DET
ap-1352	70	24	−c	−c	NOUN
ap-1352	70	25	c	c	PROPN
ap-1352	70	26	a	a	PRON
ap-1352	70	27	)	)	PUNCT
ap-1352	71	1	=	=	SYM
ap-1352	71	2	(	(	PUNCT
ap-1352	71	3	i	i	PRON
ap-1352	71	4	−r	−r	VERB
ap-1352	71	5	r	r	NOUN
ap-1352	71	6	i	i	NOUN
ap-1352	71	7	)	)	PUNCT
ap-1352	71	8	a	a	PRON
ap-1352	71	9	,	,	PUNCT
ap-1352	71	10	hence	hence	ADV
ap-1352	71	11	g−1	g−1	PROPN
ap-1352	71	12	=	=	SYM
ap-1352	71	13	a−1	a−1	PROPN
ap-1352	71	14	(	(	PUNCT
ap-1352	71	15	i	i	NOUN
ap-1352	71	16	r	r	PROPN
ap-1352	71	17	−r	−r	PROPN
ap-1352	71	18	i	i	PROPN
ap-1352	71	19	)	)	PUNCT
ap-1352	72	1	(	(	PUNCT
ap-1352	72	2	i	i	PRON
ap-1352	72	3	+	+	NUM
ap-1352	72	4	r2)−1	r2)−1	NOUN
ap-1352	72	5	.	.	PUNCT
ap-1352	73	1	this	this	PRON
ap-1352	73	2	leads	lead	VERB
ap-1352	73	3	to	to	ADP
ap-1352	73	4	(	(	PUNCT
ap-1352	73	5	(	(	PUNCT
ap-1352	73	6	rx	rx	VERB
ap-1352	73	7	r	r	NOUN
ap-1352	73	8	+	+	NOUN
ap-1352	73	9	rρ	rρ	NOUN
ap-1352	73	10	r	r	NOUN
ap-1352	73	11	+	+	NOUN
ap-1352	73	12	ρ)(i	ρ)(i	NOUN
ap-1352	73	13	+	+	NUM
ap-1352	73	14	r2)−1	r2)−1	NOUN
ap-1352	73	15	)	)	PUNCT
ap-1352	74	1	y	y	PROPN
ap-1352	75	1	=	=	SYM
ap-1352	76	1	0	0	NUM
ap-1352	77	1	,	,	PUNCT
ap-1352	77	2	(	(	PUNCT
ap-1352	77	3	(	(	PUNCT
ap-1352	77	4	rx	rx	VERB
ap-1352	77	5	+	+	CCONJ
ap-1352	77	6	rρ	rρ	INTJ
ap-1352	77	7	−	−	PROPN
ap-1352	77	8	ρ	ρ	PROPN
ap-1352	77	9	r)(i	r)(i	NOUN
ap-1352	77	10	+	+	NUM
ap-1352	77	11	r2)−1	r2)−1	NOUN
ap-1352	77	12	)	)	PUNCT
ap-1352	78	1	y	y	PROPN
ap-1352	78	2	=	=	PUNCT
ap-1352	79	1	r(i	r(i	NOUN
ap-1352	79	2	+	+	CCONJ
ap-1352	79	3	r2)−1	r2)−1	NOUN
ap-1352	79	4	,	,	PUNCT
ap-1352	79	5	34	34	NUM
ap-1352	79	6	acta	acta	PROPN
ap-1352	79	7	polytechnica	polytechnica	PROPN
ap-1352	79	8	vol	vol	NOUN
ap-1352	79	9	.	.	PUNCT
ap-1352	80	1	51	51	NUM
ap-1352	80	2	no	no	NOUN
ap-1352	80	3	.	.	PUNCT
ap-1352	81	1	1/2011	1/2011	NUM
ap-1352	81	2	where	where	SCONJ
ap-1352	81	3	ρ	ρ	NOUN
ap-1352	81	4	:	:	PUNCT
ap-1352	81	5	=	=	SYM
ap-1352	81	6	axa−1	axa−1	NOUN
ap-1352	81	7	.	.	PUNCT
ap-1352	82	1	setting	set	VERB
ap-1352	82	2	an	an	DET
ap-1352	82	3	integration	integration	NOUN
ap-1352	82	4	‘	'	PUNCT
ap-1352	82	5	constant	constant	ADJ
ap-1352	82	6	’	'	PUNCT
ap-1352	82	7	to	to	ADP
ap-1352	82	8	zero	zero	NUM
ap-1352	82	9	,	,	PUNCT
ap-1352	82	10	the	the	DET
ap-1352	82	11	first	first	ADJ
ap-1352	82	12	equation	equation	NOUN
ap-1352	82	13	integrates	integrate	NOUN
ap-1352	82	14	to	to	ADP
ap-1352	82	15	ρ	ρ	PROPN
ap-1352	82	16	=	=	SYM
ap-1352	82	17	−rxr−rρ	−rxr−rρ	PROPN
ap-1352	82	18	r.	r.	NOUN
ap-1352	82	19	with	with	ADP
ap-1352	82	20	its	its	PRON
ap-1352	82	21	help	help	NOUN
ap-1352	82	22	,	,	PUNCT
ap-1352	82	23	the	the	DET
ap-1352	82	24	second	second	NOUN
ap-1352	82	25	can	can	AUX
ap-1352	82	26	be	be	AUX
ap-1352	82	27	written	write	VERB
ap-1352	82	28	as	as	ADP
ap-1352	82	29	(	(	PUNCT
ap-1352	82	30	rx	rx	VERB
ap-1352	82	31	+	+	PUNCT
ap-1352	82	32	rρ)y	rρ)y	NOUN
ap-1352	82	33	=	=	SYM
ap-1352	82	34	r(i	r(i	NOUN
ap-1352	82	35	+	+	CCONJ
ap-1352	82	36	r2)−1	r2)−1	NOUN
ap-1352	82	37	.	.	PUNCT
ap-1352	83	1	since	since	SCONJ
ap-1352	83	2	q	q	NOUN
ap-1352	83	3	=	=	PUNCT
ap-1352	83	4	−(ra)x	−(ra)x	PUNCT
ap-1352	83	5	a−1	a−1	PROPN
ap-1352	83	6	=	=	SYM
ap-1352	83	7	−rx	−rx	NOUN
ap-1352	83	8	−	−	NOUN
ap-1352	83	9	r	r	NOUN
ap-1352	83	10	ρ	ρ	PROPN
ap-1352	83	11	,	,	PUNCT
ap-1352	83	12	this	this	PRON
ap-1352	83	13	is	be	AUX
ap-1352	83	14	the	the	DET
ap-1352	83	15	second	second	ADJ
ap-1352	83	16	of	of	ADP
ap-1352	83	17	(	(	PUNCT
ap-1352	83	18	15	15	NUM
ap-1352	83	19	)	)	PUNCT
ap-1352	83	20	.	.	PUNCT
ap-1352	84	1	the	the	DET
ap-1352	84	2	first	first	ADV
ap-1352	84	3	follows	follow	VERB
ap-1352	84	4	noting	note	VERB
ap-1352	84	5	that	that	SCONJ
ap-1352	84	6	qr	qr	PROPN
ap-1352	84	7	=	=	SYM
ap-1352	84	8	ρ	ρ	PROPN
ap-1352	84	9	.	.	PROPN
ap-1352	84	10	5	5	NUM
ap-1352	84	11	sharp	sharp	ADJ
ap-1352	84	12	line	line	NOUN
ap-1352	84	13	sit	sit	NOUN
ap-1352	84	14	equations	equation	NOUN
ap-1352	84	15	and	and	CCONJ
ap-1352	84	16	sine	sine	NOUN
ap-1352	84	17	-	-	PUNCT
ap-1352	84	18	gordon	gordon	PROPN
ap-1352	84	19	we	we	PRON
ap-1352	84	20	consider	consider	VERB
ap-1352	84	21	the	the	DET
ap-1352	84	22	scalar	scalar	ADJ
ap-1352	84	23	case	case	NOUN
ap-1352	84	24	,	,	PUNCT
ap-1352	84	25	i.e.	i.e.	X
ap-1352	84	26	m	m	NOUN
ap-1352	84	27	=	=	ADJ
ap-1352	84	28	1	1	X
ap-1352	84	29	.	.	X
ap-1352	84	30	introducing	introduce	VERB
ap-1352	84	31	e	e	NOUN
ap-1352	84	32	=	=	SYM
ap-1352	84	33	2	2	NUM
ap-1352	84	34	√	√	NUM
ap-1352	84	35	αq	αq	NOUN
ap-1352	84	36	with	with	ADP
ap-1352	84	37	a	a	DET
ap-1352	84	38	positive	positive	ADJ
ap-1352	84	39	constant	constant	ADJ
ap-1352	84	40	α	α	NOUN
ap-1352	84	41	,	,	PUNCT
ap-1352	84	42	p	p	NOUN
ap-1352	84	43	=	=	PROPN
ap-1352	84	44	2qy	2qy	NOUN
ap-1352	84	45	,	,	PUNCT
ap-1352	84	46	n	n	NOUN
ap-1352	84	47	=	=	SYM
ap-1352	84	48	2py	2py	NOUN
ap-1352	84	49	−	−	NOUN
ap-1352	84	50	1	1	NUM
ap-1352	84	51	,	,	PUNCT
ap-1352	84	52	and	and	CCONJ
ap-1352	84	53	new	new	ADJ
ap-1352	84	54	coordinates	coordinate	NOUN
ap-1352	84	55	z	z	PROPN
ap-1352	84	56	,	,	PUNCT
ap-1352	84	57	t	t	PROPN
ap-1352	84	58	via	via	ADP
ap-1352	84	59	x	x	X
ap-1352	84	60	=	=	PUNCT
ap-1352	84	61	√	√	PROPN
ap-1352	84	62	α(z	α(z	PROPN
ap-1352	84	63	−	−	PROPN
ap-1352	84	64	t	t	PROPN
ap-1352	84	65	)	)	PUNCT
ap-1352	84	66	and	and	CCONJ
ap-1352	84	67	y	y	PROPN
ap-1352	84	68	=	=	PUNCT
ap-1352	84	69	√	√	NUM
ap-1352	84	70	αz	αz	PROPN
ap-1352	84	71	,	,	PUNCT
ap-1352	84	72	the	the	DET
ap-1352	84	73	system	system	NOUN
ap-1352	84	74	(	(	PUNCT
ap-1352	84	75	9	9	NUM
ap-1352	84	76	)	)	PUNCT
ap-1352	84	77	is	be	AUX
ap-1352	84	78	transformed	transform	VERB
ap-1352	84	79	into	into	ADP
ap-1352	84	80	pt	pt	NOUN
ap-1352	84	81	=	=	SYM
ap-1352	84	82	e	e	PROPN
ap-1352	84	83	n	n	NOUN
ap-1352	84	84	,	,	PUNCT
ap-1352	84	85	nt	not	PART
ap-1352	84	86	=	=	PRON
ap-1352	84	87	−e	−e	NOUN
ap-1352	84	88	p	p	NOUN
ap-1352	84	89	,	,	PUNCT
ap-1352	84	90	and	and	CCONJ
ap-1352	84	91	the	the	DET
ap-1352	84	92	relation	relation	NOUN
ap-1352	84	93	between	between	ADP
ap-1352	84	94	e	e	NOUN
ap-1352	84	95	and	and	CCONJ
ap-1352	84	96	p	p	NOUN
ap-1352	84	97	takes	take	VERB
ap-1352	84	98	the	the	DET
ap-1352	84	99	form	form	NOUN
ap-1352	84	100	ez	ez	NOUN
ap-1352	84	101	+	+	CCONJ
ap-1352	84	102	et	et	X
ap-1352	84	103	=	=	NOUN
ap-1352	84	104	αp	αp	NOUN
ap-1352	84	105	.	.	PUNCT
ap-1352	85	1	these	these	PRON
ap-1352	85	2	are	be	AUX
ap-1352	85	3	the	the	DET
ap-1352	85	4	sharp	sharp	ADJ
ap-1352	85	5	line	line	NOUN
ap-1352	85	6	self	self	NOUN
ap-1352	85	7	-	-	PUNCT
ap-1352	85	8	induced	induce	VERB
ap-1352	85	9	transparency	transparency	NOUN
ap-1352	85	10	(	(	PUNCT
ap-1352	85	11	sit	sit	NOUN
ap-1352	85	12	)	)	PUNCT
ap-1352	85	13	equations	equation	NOUN
ap-1352	85	14	[	[	X
ap-1352	85	15	5	5	NUM
ap-1352	85	16	,	,	PUNCT
ap-1352	85	17	6	6	NUM
ap-1352	85	18	,	,	PUNCT
ap-1352	85	19	7	7	NUM
ap-1352	85	20	]	]	PUNCT
ap-1352	85	21	.	.	PUNCT
ap-1352	86	1	we	we	PRON
ap-1352	86	2	note	note	VERB
ap-1352	86	3	that	that	SCONJ
ap-1352	86	4	p2	p2	PROPN
ap-1352	86	5	+	+	CCONJ
ap-1352	86	6	n	n	NUM
ap-1352	86	7	2	2	NUM
ap-1352	86	8	is	be	AUX
ap-1352	86	9	conserved	conserve	VERB
ap-1352	86	10	.	.	PUNCT
ap-1352	87	1	indeed	indeed	ADV
ap-1352	87	2	,	,	PUNCT
ap-1352	87	3	as	as	ADP
ap-1352	87	4	a	a	DET
ap-1352	87	5	consequence	consequence	NOUN
ap-1352	87	6	of	of	ADP
ap-1352	87	7	(	(	PUNCT
ap-1352	87	8	14	14	NUM
ap-1352	87	9	)	)	PUNCT
ap-1352	87	10	,	,	PUNCT
ap-1352	87	11	we	we	PRON
ap-1352	87	12	have	have	AUX
ap-1352	87	13	p2	p2	VERB
ap-1352	87	14	+	+	NOUN
ap-1352	87	15	n	n	ADJ
ap-1352	87	16	2	2	NUM
ap-1352	87	17	=	=	SYM
ap-1352	87	18	1	1	X
ap-1352	87	19	.	.	X
ap-1352	87	20	writing	write	VERB
ap-1352	87	21	p	p	NOUN
ap-1352	87	22	=	=	NOUN
ap-1352	87	23	−	−	PROPN
ap-1352	87	24	sin	sin	NOUN
ap-1352	87	25	θ	θ	PROPN
ap-1352	87	26	and	and	CCONJ
ap-1352	87	27	n	n	NOUN
ap-1352	87	28	=	=	SYM
ap-1352	87	29	−	−	PROPN
ap-1352	87	30	cos	cos	PROPN
ap-1352	87	31	θ	θ	PROPN
ap-1352	87	32	,	,	PUNCT
ap-1352	87	33	reduces	reduce	VERB
ap-1352	87	34	the	the	DET
ap-1352	87	35	first	first	ADJ
ap-1352	87	36	two	two	NUM
ap-1352	87	37	equations	equation	NOUN
ap-1352	87	38	to	to	ADP
ap-1352	87	39	e	e	PROPN
ap-1352	87	40	=	=	PUNCT
ap-1352	87	41	θt	θt	AUX
ap-1352	87	42	.	.	PROPN
ap-1352	87	43	expressed	express	VERB
ap-1352	87	44	in	in	ADP
ap-1352	87	45	the	the	DET
ap-1352	87	46	coordinates	coordinate	NOUN
ap-1352	87	47	x	x	SYM
ap-1352	87	48	,	,	PUNCT
ap-1352	87	49	y	y	PROPN
ap-1352	87	50	,	,	PUNCT
ap-1352	87	51	the	the	DET
ap-1352	87	52	third	third	NOUN
ap-1352	87	53	then	then	ADV
ap-1352	87	54	becomes	become	VERB
ap-1352	87	55	the	the	DET
ap-1352	87	56	sine	sine	ADJ
ap-1352	87	57	-	-	PUNCT
ap-1352	87	58	gordon	gordon	NOUN
ap-1352	87	59	equation	equation	NOUN
ap-1352	87	60	(	(	PUNCT
ap-1352	87	61	17	17	NUM
ap-1352	87	62	)	)	PUNCT
ap-1352	87	63	(	(	PUNCT
ap-1352	87	64	cf	cf	NOUN
ap-1352	87	65	.	.	PUNCT
ap-1352	88	1	[	[	X
ap-1352	88	2	6	6	NUM
ap-1352	88	3	]	]	PUNCT
ap-1352	88	4	)	)	PUNCT
ap-1352	88	5	.	.	PUNCT
ap-1352	89	1	as	as	ADP
ap-1352	89	2	a	a	DET
ap-1352	89	3	consequence	consequence	NOUN
ap-1352	89	4	of	of	ADP
ap-1352	89	5	the	the	DET
ap-1352	89	6	above	above	ADJ
ap-1352	89	7	relations	relation	NOUN
ap-1352	89	8	,	,	PUNCT
ap-1352	89	9	q	q	NOUN
ap-1352	89	10	and	and	CCONJ
ap-1352	89	11	p	p	PROPN
ap-1352	89	12	depend	depend	VERB
ap-1352	89	13	as	as	SCONJ
ap-1352	89	14	follows	follow	VERB
ap-1352	89	15	on	on	ADP
ap-1352	89	16	θ	θ	PROPN
ap-1352	89	17	,	,	PUNCT
ap-1352	89	18	q	q	NOUN
ap-1352	89	19	=	=	PUNCT
ap-1352	89	20	−1	−1	NOUN
ap-1352	89	21	2	2	NUM
ap-1352	89	22	θx	θx	NOUN
ap-1352	89	23	,	,	PUNCT
ap-1352	89	24	qy	qy	NOUN
ap-1352	89	25	=	=	SYM
ap-1352	89	26	−1	−1	NOUN
ap-1352	89	27	2	2	NUM
ap-1352	89	28	sin	sin	NOUN
ap-1352	89	29	θ	θ	PROPN
ap-1352	89	30	,	,	PUNCT
ap-1352	89	31	(	(	PUNCT
ap-1352	89	32	18	18	NUM
ap-1352	89	33	)	)	PUNCT
ap-1352	89	34	py	py	NOUN
ap-1352	89	35	=	=	NOUN
ap-1352	89	36	1	1	NUM
ap-1352	89	37	2	2	NUM
ap-1352	89	38	(	(	PUNCT
ap-1352	89	39	1−	1−	NUM
ap-1352	89	40	cos	cos	PROPN
ap-1352	89	41	θ	θ	PROPN
ap-1352	89	42	)	)	PUNCT
ap-1352	89	43	.	.	PUNCT
ap-1352	90	1	these	these	PRON
ap-1352	90	2	are	be	AUX
ap-1352	90	3	precisely	precisely	ADV
ap-1352	90	4	the	the	DET
ap-1352	90	5	equations	equation	NOUN
ap-1352	90	6	that	that	PRON
ap-1352	90	7	result	result	VERB
ap-1352	90	8	from	from	ADP
ap-1352	90	9	the	the	DET
ap-1352	90	10	miura	miura	PROPN
ap-1352	90	11	transformation	transformation	NOUN
ap-1352	90	12	(	(	PUNCT
ap-1352	90	13	10	10	NUM
ap-1352	90	14	)	)	PUNCT
ap-1352	90	15	(	(	PUNCT
ap-1352	90	16	or	or	CCONJ
ap-1352	90	17	from	from	ADP
ap-1352	90	18	(	(	PUNCT
ap-1352	90	19	13	13	NUM
ap-1352	90	20	)	)	PUNCT
ap-1352	90	21	)	)	PUNCT
ap-1352	90	22	,	,	PUNCT
ap-1352	90	23	choosing	choose	VERB
ap-1352	90	24	g	g	NOUN
ap-1352	90	25	=	=	SYM
ap-1352	90	26	⎛⎜⎜⎝	⎛⎜⎜⎝	NOUN
ap-1352	90	27	cos	cos	ADP
ap-1352	90	28	θ	θ	PROPN
ap-1352	90	29	2	2	NUM
ap-1352	90	30	−	−	NOUN
ap-1352	90	31	sin	sin	NOUN
ap-1352	90	32	θ	θ	PROPN
ap-1352	90	33	2	2	NUM
ap-1352	90	34	sin	sin	NOUN
ap-1352	90	35	θ	θ	PROPN
ap-1352	90	36	2	2	NUM
ap-1352	90	37	cos	cos	ADP
ap-1352	90	38	θ	θ	PROPN
ap-1352	90	39	2	2	NUM
ap-1352	90	40	⎞⎟⎟⎠	⎞⎟⎟⎠	NOUN
ap-1352	90	41	,	,	PUNCT
ap-1352	90	42	and	and	CCONJ
ap-1352	90	43	(	(	PUNCT
ap-1352	90	44	12	12	NUM
ap-1352	90	45	)	)	PUNCT
ap-1352	90	46	becomes	become	VERB
ap-1352	90	47	the	the	DET
ap-1352	90	48	sine	sine	ADJ
ap-1352	90	49	-	-	PUNCT
ap-1352	90	50	gordon	gordon	NOUN
ap-1352	90	51	equation	equation	NOUN
ap-1352	90	52	(	(	PUNCT
ap-1352	90	53	17	17	NUM
ap-1352	90	54	)	)	PUNCT
ap-1352	90	55	.	.	PUNCT
ap-1352	91	1	the	the	DET
ap-1352	91	2	conditions	condition	NOUN
ap-1352	91	3	(	(	PUNCT
ap-1352	91	4	11	11	NUM
ap-1352	91	5	)	)	PUNCT
ap-1352	91	6	are	be	AUX
ap-1352	91	7	identically	identically	ADV
ap-1352	91	8	satisfied	satisfied	ADJ
ap-1352	91	9	as	as	ADP
ap-1352	91	10	a	a	DET
ap-1352	91	11	consequence	consequence	NOUN
ap-1352	91	12	of	of	ADP
ap-1352	91	13	the	the	DET
ap-1352	91	14	form	form	NOUN
ap-1352	91	15	of	of	ADP
ap-1352	91	16	g.	g.	PROPN
ap-1352	91	17	6	6	NUM
ap-1352	91	18	a	a	DET
ap-1352	91	19	universal	universal	ADJ
ap-1352	91	20	method	method	NOUN
ap-1352	91	21	of	of	ADP
ap-1352	91	22	generating	generate	VERB
ap-1352	91	23	solutions	solution	NOUN
ap-1352	91	24	from	from	ADP
ap-1352	91	25	a	a	DET
ap-1352	91	26	matrix	matrix	NOUN
ap-1352	91	27	linear	linear	NOUN
ap-1352	91	28	system	system	NOUN
ap-1352	91	29	theorem	theorem	VERB
ap-1352	91	30	1	1	NUM
ap-1352	91	31	let	let	VERB
ap-1352	91	32	(	(	PUNCT
ap-1352	91	33	ω	ω	NOUN
ap-1352	91	34	,	,	PUNCT
ap-1352	91	35	d	d	PROPN
ap-1352	91	36	,	,	PUNCT
ap-1352	91	37	d̄	d̄	PROPN
ap-1352	91	38	)	)	PUNCT
ap-1352	91	39	be	be	VERB
ap-1352	91	40	a	a	DET
ap-1352	91	41	bidifferential	bidifferential	ADJ
ap-1352	91	42	calculus	calculus	NOUN
ap-1352	91	43	with	with	ADP
ap-1352	91	44	ω	ω	PROPN
ap-1352	91	45	=	=	SYM
ap-1352	91	46	a⊗	a⊗	PROPN
ap-1352	91	47	∧	∧	PROPN
ap-1352	91	48	(	(	PUNCT
ap-1352	91	49	c2	c2	PROPN
ap-1352	91	50	)	)	PUNCT
ap-1352	91	51	,	,	PUNCT
ap-1352	91	52	where	where	SCONJ
ap-1352	91	53	a	a	PRON
ap-1352	91	54	is	be	AUX
ap-1352	91	55	the	the	DET
ap-1352	91	56	algebra	algebra	NOUN
ap-1352	91	57	of	of	ADP
ap-1352	91	58	matrices	matrix	NOUN
ap-1352	91	59	with	with	ADP
ap-1352	91	60	entries	entry	NOUN
ap-1352	91	61	in	in	ADP
ap-1352	91	62	some	some	DET
ap-1352	91	63	algebra	algebra	NOUN
ap-1352	91	64	b	b	NOUN
ap-1352	91	65	(	(	PUNCT
ap-1352	91	66	where	where	SCONJ
ap-1352	91	67	the	the	DET
ap-1352	91	68	product	product	NOUN
ap-1352	91	69	of	of	ADP
ap-1352	91	70	two	two	NUM
ap-1352	91	71	matrices	matrix	NOUN
ap-1352	91	72	is	be	AUX
ap-1352	91	73	defined	define	VERB
ap-1352	91	74	to	to	PART
ap-1352	91	75	be	be	AUX
ap-1352	91	76	zero	zero	NUM
ap-1352	91	77	if	if	SCONJ
ap-1352	91	78	the	the	DET
ap-1352	91	79	sizes	size	NOUN
ap-1352	91	80	of	of	ADP
ap-1352	91	81	the	the	DET
ap-1352	91	82	two	two	NUM
ap-1352	91	83	matrices	matrix	NOUN
ap-1352	91	84	do	do	AUX
ap-1352	91	85	not	not	PART
ap-1352	91	86	match	match	VERB
ap-1352	91	87	)	)	PUNCT
ap-1352	91	88	.	.	PUNCT
ap-1352	92	1	for	for	ADP
ap-1352	92	2	fixed	fixed	ADJ
ap-1352	92	3	n	n	CCONJ
ap-1352	92	4	,	,	PUNCT
ap-1352	92	5	n	n	PROPN
ap-1352	92	6	′	′	NUM
ap-1352	92	7	,	,	PUNCT
ap-1352	92	8	let	let	VERB
ap-1352	92	9	x	x	X
ap-1352	92	10	∈	∈	PROPN
ap-1352	92	11	mat	mat	NOUN
ap-1352	92	12	(	(	PUNCT
ap-1352	92	13	n	n	X
ap-1352	92	14	,	,	PUNCT
ap-1352	92	15	n	n	CCONJ
ap-1352	92	16	,	,	PUNCT
ap-1352	92	17	b	b	NOUN
ap-1352	92	18	)	)	PUNCT
ap-1352	92	19	and	and	CCONJ
ap-1352	92	20	y	y	PROPN
ap-1352	92	21	∈	∈	PROPN
ap-1352	92	22	mat	mat	NOUN
ap-1352	92	23	(	(	PUNCT
ap-1352	92	24	n	n	NOUN
ap-1352	92	25	′	′	NUM
ap-1352	92	26	,	,	PUNCT
ap-1352	92	27	n	n	CCONJ
ap-1352	92	28	,	,	PUNCT
ap-1352	92	29	b	b	X
ap-1352	92	30	)	)	PUNCT
ap-1352	92	31	be	be	AUX
ap-1352	92	32	solutions	solution	NOUN
ap-1352	92	33	of	of	ADP
ap-1352	92	34	the	the	DET
ap-1352	92	35	linear	linear	ADJ
ap-1352	92	36	equations	equation	NOUN
ap-1352	93	1	d̄x	d̄x	X
ap-1352	93	2	=	=	PUNCT
ap-1352	93	3	(	(	PUNCT
ap-1352	93	4	dx)p	dx)p	PROPN
ap-1352	93	5	,	,	PUNCT
ap-1352	93	6	d̄y	d̄y	PROPN
ap-1352	93	7	=	=	SYM
ap-1352	93	8	(	(	PUNCT
ap-1352	93	9	dy	dy	NOUN
ap-1352	93	10	)	)	PUNCT
ap-1352	93	11	p	p	NOUN
ap-1352	93	12	,	,	PUNCT
ap-1352	93	13	r	r	NOUN
ap-1352	93	14	x	x	SYM
ap-1352	93	15	−x	−x	NOUN
ap-1352	93	16	p	p	NOUN
ap-1352	93	17	=	=	NOUN
ap-1352	93	18	−q	−q	ADJ
ap-1352	93	19	y	y	PROPN
ap-1352	93	20	,	,	PUNCT
ap-1352	93	21	with	with	ADP
ap-1352	93	22	d	d	NOUN
ap-1352	93	23	-	-	ADJ
ap-1352	93	24	constant	constant	ADJ
ap-1352	93	25	and	and	CCONJ
ap-1352	93	26	d̄-constant	d̄-constant	PROPN
ap-1352	93	27	matrices	matrix	NOUN
ap-1352	93	28	p	p	NOUN
ap-1352	93	29	,	,	PUNCT
ap-1352	93	30	r	r	NOUN
ap-1352	93	31	∈	∈	PROPN
ap-1352	93	32	mat	mat	NOUN
ap-1352	93	33	(	(	PUNCT
ap-1352	93	34	n	n	X
ap-1352	93	35	,	,	PUNCT
ap-1352	93	36	n	n	CCONJ
ap-1352	93	37	,	,	PUNCT
ap-1352	93	38	b	b	NOUN
ap-1352	93	39	)	)	PUNCT
ap-1352	93	40	,	,	PUNCT
ap-1352	93	41	and	and	CCONJ
ap-1352	93	42	q	q	NOUN
ap-1352	93	43	=	=	PROPN
ap-1352	93	44	ṽ	ṽ	PROPN
ap-1352	93	45	ũ	ũ	PROPN
ap-1352	93	46	,	,	PUNCT
ap-1352	93	47	where	where	SCONJ
ap-1352	93	48	ũ	ũ	PROPN
ap-1352	93	49	∈	∈	PROPN
ap-1352	93	50	mat	mat	NOUN
ap-1352	93	51	(	(	PUNCT
ap-1352	93	52	n	n	X
ap-1352	93	53	,	,	PUNCT
ap-1352	93	54	n	n	PRON
ap-1352	93	55	′,b	′,b	PRON
ap-1352	93	56	)	)	PUNCT
ap-1352	93	57	and	and	CCONJ
ap-1352	93	58	ṽ	ṽ	PROPN
ap-1352	93	59	∈	∈	PROPN
ap-1352	93	60	mat	mat	NOUN
ap-1352	93	61	(	(	PUNCT
ap-1352	93	62	n	n	X
ap-1352	93	63	,	,	PUNCT
ap-1352	93	64	n	n	CCONJ
ap-1352	93	65	,	,	PUNCT
ap-1352	93	66	b	b	NOUN
ap-1352	93	67	)	)	PUNCT
ap-1352	93	68	are	be	AUX
ap-1352	93	69	dand	dand	PROPN
ap-1352	93	70	d̄constant	d̄constant	ADJ
ap-1352	93	71	.	.	PUNCT
ap-1352	94	1	ifx	ifx	PROPN
ap-1352	94	2	is	be	AUX
ap-1352	94	3	invertible	invertible	ADJ
ap-1352	94	4	,	,	PUNCT
ap-1352	94	5	the	the	DET
ap-1352	94	6	n×n	n×n	PROPN
ap-1352	94	7	matrix	matrix	NOUN
ap-1352	94	8	variable	variable	NOUN
ap-1352	94	9	φ	φ	NOUN
ap-1352	94	10	=	=	PUNCT
ap-1352	95	1	ũy	ũy	PROPN
ap-1352	95	2	x−1ṽ	x−1ṽ	PUNCT
ap-1352	96	1	∈	∈	PROPN
ap-1352	96	2	mat	mat	NOUN
ap-1352	96	3	(	(	PUNCT
ap-1352	96	4	n	n	X
ap-1352	96	5	,	,	PUNCT
ap-1352	96	6	n	n	CCONJ
ap-1352	96	7	,	,	PUNCT
ap-1352	96	8	b	b	X
ap-1352	96	9	)	)	PUNCT
ap-1352	96	10	solves	solve	VERB
ap-1352	96	11	d̄φ	d̄φ	PROPN
ap-1352	96	12	=	=	PUNCT
ap-1352	96	13	(	(	PUNCT
ap-1352	96	14	dφ)φ+dϑ	dφ)φ+dϑ	VERB
ap-1352	96	15	with	with	ADP
ap-1352	96	16	ϑ	ϑ	X
ap-1352	96	17	=	=	SYM
ap-1352	96	18	ũy	ũy	PROPN
ap-1352	96	19	x−1rṽ	x−1rṽ	X
ap-1352	96	20	,	,	PUNCT
ap-1352	96	21	hence	hence	ADV
ap-1352	96	22	(	(	PUNCT
ap-1352	96	23	by	by	ADP
ap-1352	96	24	application	application	NOUN
ap-1352	96	25	of	of	ADP
ap-1352	96	26	d	d	NOUN
ap-1352	96	27	)	)	PUNCT
ap-1352	96	28	also	also	ADV
ap-1352	96	29	(	(	PUNCT
ap-1352	96	30	3	3	NUM
ap-1352	96	31	)	)	PUNCT
ap-1352	96	32	.	.	PUNCT
ap-1352	97	1	�	�	PROPN
ap-1352	97	2	there	there	PRON
ap-1352	97	3	is	be	VERB
ap-1352	97	4	a	a	DET
ap-1352	97	5	similar	similar	ADJ
ap-1352	97	6	result	result	NOUN
ap-1352	97	7	for	for	ADP
ap-1352	97	8	(	(	PUNCT
ap-1352	97	9	5	5	NUM
ap-1352	97	10	)	)	PUNCT
ap-1352	97	11	[	[	X
ap-1352	97	12	3	3	NUM
ap-1352	97	13	]	]	PUNCT
ap-1352	97	14	.	.	PUNCT
ap-1352	98	1	the	the	DET
ap-1352	98	2	miura	miura	PROPN
ap-1352	98	3	transformation	transformation	NOUN
ap-1352	98	4	is	be	AUX
ap-1352	98	5	a	a	DET
ap-1352	98	6	corresponding	corresponding	ADJ
ap-1352	98	7	bridge	bridge	NOUN
ap-1352	98	8	.	.	PUNCT
ap-1352	99	1	7	7	NUM
ap-1352	99	2	solutions	solution	NOUN
ap-1352	99	3	of	of	ADP
ap-1352	99	4	the	the	DET
ap-1352	99	5	matrix	matrix	NOUN
ap-1352	99	6	sit	sit	NOUN
ap-1352	99	7	equations	equation	NOUN
ap-1352	99	8	from	from	ADP
ap-1352	99	9	theorem	theorem	NOUN
ap-1352	99	10	1	1	NUM
ap-1352	99	11	we	we	PRON
ap-1352	99	12	can	can	AUX
ap-1352	99	13	deduce	deduce	VERB
ap-1352	99	14	the	the	DET
ap-1352	99	15	following	follow	VERB
ap-1352	99	16	result	result	NOUN
ap-1352	99	17	,	,	PUNCT
ap-1352	99	18	using	use	VERB
ap-1352	99	19	straightforward	straightforward	ADJ
ap-1352	99	20	calculations	calculation	NOUN
ap-1352	99	21	[	[	X
ap-1352	99	22	8	8	NUM
ap-1352	99	23	]	]	PUNCT
ap-1352	99	24	,	,	PUNCT
ap-1352	99	25	analogous	analogous	ADJ
ap-1352	99	26	to	to	ADP
ap-1352	99	27	those	those	PRON
ap-1352	99	28	in	in	ADP
ap-1352	99	29	[	[	X
ap-1352	99	30	2	2	NUM
ap-1352	99	31	]	]	PUNCT
ap-1352	99	32	(	(	PUNCT
ap-1352	99	33	see	see	VERB
ap-1352	99	34	also	also	ADV
ap-1352	99	35	[	[	X
ap-1352	99	36	3	3	NUM
ap-1352	99	37	]	]	NUM
ap-1352	99	38	)	)	PUNCT
ap-1352	99	39	.	.	PUNCT
ap-1352	100	1	proposition	proposition	NOUN
ap-1352	100	2	2	2	NUM
ap-1352	100	3	let	let	VERB
ap-1352	100	4	s	s	PRON
ap-1352	100	5	∈	∈	PROPN
ap-1352	100	6	mat	mat	NOUN
ap-1352	100	7	(	(	PUNCT
ap-1352	100	8	m	m	PROPN
ap-1352	100	9	,	,	PUNCT
ap-1352	100	10	m	m	PROPN
ap-1352	100	11	,	,	PUNCT
ap-1352	100	12	c	c	X
ap-1352	100	13	)	)	PUNCT
ap-1352	100	14	be	be	AUX
ap-1352	100	15	invertible	invertible	ADJ
ap-1352	100	16	,	,	PUNCT
ap-1352	100	17	u	u	PROPN
ap-1352	100	18	∈	∈	PROPN
ap-1352	100	19	mat	mat	NOUN
ap-1352	100	20	(	(	PUNCT
ap-1352	100	21	m	m	PROPN
ap-1352	100	22	,	,	PUNCT
ap-1352	100	23	m	m	PROPN
ap-1352	100	24	,	,	PUNCT
ap-1352	100	25	c	c	NOUN
ap-1352	100	26	)	)	PUNCT
ap-1352	100	27	,	,	PUNCT
ap-1352	100	28	v	v	PROPN
ap-1352	100	29	∈	∈	PROPN
ap-1352	100	30	mat	mat	NOUN
ap-1352	100	31	(	(	PUNCT
ap-1352	100	32	m	m	PROPN
ap-1352	100	33	,	,	PUNCT
ap-1352	100	34	m	m	PROPN
ap-1352	100	35	,	,	PUNCT
ap-1352	100	36	c	c	NOUN
ap-1352	100	37	)	)	PUNCT
ap-1352	100	38	,	,	PUNCT
ap-1352	100	39	and	and	CCONJ
ap-1352	100	40	k	k	PROPN
ap-1352	100	41	∈	∈	PROPN
ap-1352	100	42	mat	mat	NOUN
ap-1352	100	43	(	(	PUNCT
ap-1352	100	44	m	m	PROPN
ap-1352	100	45	,	,	PUNCT
ap-1352	100	46	m	m	PROPN
ap-1352	100	47	,	,	PUNCT
ap-1352	100	48	c	c	NOUN
ap-1352	100	49	)	)	PUNCT
ap-1352	100	50	a	a	DET
ap-1352	100	51	solution	solution	NOUN
ap-1352	100	52	of	of	ADP
ap-1352	100	53	the	the	DET
ap-1352	100	54	sylvester	sylvest	ADJ
ap-1352	100	55	equation	equation	NOUN
ap-1352	100	56	sk	sk	VERB
ap-1352	100	57	+	+	PROPN
ap-1352	100	58	ks	ks	X
ap-1352	100	59	=	=	SYM
ap-1352	100	60	v	v	NUM
ap-1352	100	61	u	u	NOUN
ap-1352	100	62	.	.	PUNCT
ap-1352	101	1	(	(	PUNCT
ap-1352	101	2	19	19	NUM
ap-1352	101	3	)	)	PUNCT
ap-1352	101	4	then	then	ADV
ap-1352	101	5	,	,	PUNCT
ap-1352	101	6	with	with	ADP
ap-1352	101	7	ξ	ξ	PROPN
ap-1352	101	8	=	=	SYM
ap-1352	101	9	e−sx−s−1	e−sx−s−1	PROPN
ap-1352	101	10	y	y	PROPN
ap-1352	101	11	and	and	CCONJ
ap-1352	101	12	any	any	DET
ap-1352	101	13	p0	p0	NOUN
ap-1352	101	14	∈	∈	PROPN
ap-1352	101	15	mat	mat	NOUN
ap-1352	101	16	(	(	PUNCT
ap-1352	101	17	m	m	PROPN
ap-1352	101	18	,	,	PUNCT
ap-1352	101	19	m	m	PROPN
ap-1352	101	20	,	,	PUNCT
ap-1352	101	21	c	c	NOUN
ap-1352	101	22	)	)	PUNCT
ap-1352	101	23	(	(	PUNCT
ap-1352	101	24	more	more	ADV
ap-1352	101	25	generally	generally	ADV
ap-1352	101	26	x	x	ADJ
ap-1352	101	27	-	-	ADJ
ap-1352	101	28	dependent	dependent	ADJ
ap-1352	101	29	)	)	PUNCT
ap-1352	101	30	,	,	PUNCT
ap-1352	101	31	q	q	NOUN
ap-1352	101	32	=	=	PRON
ap-1352	101	33	uξ	uξ	NOUN
ap-1352	101	34	(	(	PUNCT
ap-1352	101	35	i	i	PRON
ap-1352	101	36	m	m	VERB
ap-1352	101	37	+	+	ADJ
ap-1352	101	38	(	(	PUNCT
ap-1352	101	39	kξ)2)−1v	kξ)2)−1v	NOUN
ap-1352	101	40	,	,	PUNCT
ap-1352	101	41	p=	p=	ADJ
ap-1352	101	42	p0	p0	NOUN
ap-1352	101	43	−uξkξ	−uξkξ	NOUN
ap-1352	101	44	(	(	PUNCT
ap-1352	101	45	i	i	PRON
ap-1352	101	46	m	m	VERB
ap-1352	101	47	+	+	ADJ
ap-1352	101	48	(	(	PUNCT
ap-1352	101	49	kξ)2)−1v	kξ)2)−1v	NOUN
ap-1352	101	50	(	(	PUNCT
ap-1352	101	51	20	20	NUM
ap-1352	101	52	)	)	PUNCT
ap-1352	101	53	(	(	PUNCT
ap-1352	101	54	assuming	assume	VERB
ap-1352	101	55	the	the	DET
ap-1352	101	56	inverse	inverse	NOUN
ap-1352	101	57	exists	exist	VERB
ap-1352	101	58	)	)	PUNCT
ap-1352	101	59	is	be	AUX
ap-1352	101	60	a	a	DET
ap-1352	101	61	solution	solution	NOUN
ap-1352	101	62	of	of	ADP
ap-1352	101	63	(	(	PUNCT
ap-1352	101	64	9	9	NUM
ap-1352	101	65	)	)	PUNCT
ap-1352	101	66	.	.	PUNCT
ap-1352	102	1	�	�	PROPN
ap-1352	102	2	if	if	SCONJ
ap-1352	102	3	the	the	DET
ap-1352	102	4	matrix	matrix	NOUN
ap-1352	102	5	s	s	PART
ap-1352	102	6	satisfies	satisfy	VERB
ap-1352	102	7	the	the	DET
ap-1352	102	8	spectrum	spectrum	NOUN
ap-1352	102	9	condition	condition	NOUN
ap-1352	102	10	σ(s	σ(s	NOUN
ap-1352	102	11	)	)	PUNCT
ap-1352	102	12	∩	∩	NOUN
ap-1352	102	13	σ(−s	σ(−	NOUN
ap-1352	102	14	)	)	PUNCT
ap-1352	102	15	=	=	SYM
ap-1352	102	16	∅	∅	NOUN
ap-1352	102	17	(	(	PUNCT
ap-1352	102	18	21	21	NUM
ap-1352	102	19	)	)	PUNCT
ap-1352	102	20	(	(	PUNCT
ap-1352	102	21	where	where	SCONJ
ap-1352	102	22	σ(s	σ(s	NOUN
ap-1352	102	23	)	)	PUNCT
ap-1352	102	24	denotes	denote	VERB
ap-1352	102	25	the	the	DET
ap-1352	102	26	set	set	NOUN
ap-1352	102	27	of	of	ADP
ap-1352	102	28	eigenvalues	eigenvalue	NOUN
ap-1352	102	29	of	of	ADP
ap-1352	102	30	s	s	NOUN
ap-1352	102	31	)	)	PUNCT
ap-1352	102	32	,	,	PUNCT
ap-1352	102	33	then	then	ADV
ap-1352	102	34	the	the	DET
ap-1352	102	35	sylvester	sylvester	ADJ
ap-1352	102	36	equation	equation	NOUN
ap-1352	102	37	(	(	PUNCT
ap-1352	102	38	19	19	NUM
ap-1352	102	39	)	)	PUNCT
ap-1352	102	40	has	have	VERB
ap-1352	102	41	a	a	DET
ap-1352	102	42	unique	unique	ADJ
ap-1352	102	43	solution	solution	NOUN
ap-1352	102	44	k	k	PROPN
ap-1352	102	45	(	(	PUNCT
ap-1352	102	46	for	for	ADP
ap-1352	102	47	any	any	DET
ap-1352	102	48	choice	choice	NOUN
ap-1352	102	49	of	of	ADP
ap-1352	102	50	the	the	DET
ap-1352	102	51	matrices	matrix	NOUN
ap-1352	102	52	u	u	NOUN
ap-1352	102	53	,	,	PUNCT
ap-1352	102	54	v	v	NOUN
ap-1352	102	55	)	)	PUNCT
ap-1352	102	56	,	,	PUNCT
ap-1352	102	57	see	see	VERB
ap-1352	103	1	e.g.	e.g.	ADV
ap-1352	103	2	[	[	X
ap-1352	103	3	9	9	NUM
ap-1352	103	4	]	]	PUNCT
ap-1352	103	5	.	.	PUNCT
ap-1352	104	1	by	by	ADP
ap-1352	104	2	a	a	DET
ap-1352	104	3	lengthy	lengthy	ADJ
ap-1352	104	4	calculation	calculation	NOUN
ap-1352	104	5	[	[	X
ap-1352	104	6	8	8	X
ap-1352	104	7	]	]	PUNCT
ap-1352	104	8	one	one	PRON
ap-1352	104	9	can	can	AUX
ap-1352	104	10	verify	verify	VERB
ap-1352	104	11	directly	directly	ADV
ap-1352	104	12	that	that	SCONJ
ap-1352	104	13	the	the	DET
ap-1352	104	14	solutions	solution	NOUN
ap-1352	104	15	in	in	ADP
ap-1352	104	16	proposition	proposition	NOUN
ap-1352	104	17	2	2	NUM
ap-1352	104	18	satisfy	satisfy	NOUN
ap-1352	104	19	(	(	PUNCT
ap-1352	104	20	14	14	NUM
ap-1352	104	21	)	)	PUNCT
ap-1352	104	22	.	.	PUNCT
ap-1352	105	1	alternatively	alternatively	ADV
ap-1352	105	2	,	,	PUNCT
ap-1352	105	3	one	one	PRON
ap-1352	105	4	can	can	AUX
ap-1352	105	5	show	show	VERB
ap-1352	105	6	that	that	SCONJ
ap-1352	105	7	these	these	DET
ap-1352	105	8	solutions	solution	NOUN
ap-1352	105	9	actually	actually	ADV
ap-1352	105	10	determine	determine	VERB
ap-1352	105	11	solutions	solution	NOUN
ap-1352	105	12	of	of	ADP
ap-1352	105	13	the	the	DET
ap-1352	105	14	miura	miura	PROPN
ap-1352	105	15	transformation	transformation	NOUN
ap-1352	105	16	(	(	PUNCT
ap-1352	105	17	cf	cf	NOUN
ap-1352	105	18	.	.	PUNCT
ap-1352	106	1	[	[	X
ap-1352	106	2	3	3	NUM
ap-1352	106	3	]	]	NUM
ap-1352	106	4	)	)	PUNCT
ap-1352	106	5	,	,	PUNCT
ap-1352	106	6	and	and	CCONJ
ap-1352	106	7	we	we	PRON
ap-1352	106	8	have	have	AUX
ap-1352	106	9	seen	see	VERB
ap-1352	106	10	that	that	SCONJ
ap-1352	106	11	(	(	PUNCT
ap-1352	106	12	14	14	NUM
ap-1352	106	13	)	)	PUNCT
ap-1352	106	14	is	be	AUX
ap-1352	106	15	a	a	DET
ap-1352	106	16	consequence	consequence	NOUN
ap-1352	106	17	.	.	PUNCT
ap-1352	107	1	there	there	PRON
ap-1352	107	2	is	be	VERB
ap-1352	107	3	a	a	DET
ap-1352	107	4	certain	certain	ADJ
ap-1352	107	5	redundancy	redundancy	NOUN
ap-1352	107	6	in	in	ADP
ap-1352	107	7	the	the	DET
ap-1352	107	8	matrix	matrix	NOUN
ap-1352	107	9	data	datum	NOUN
ap-1352	107	10	that	that	PRON
ap-1352	107	11	determine	determine	VERB
ap-1352	107	12	the	the	DET
ap-1352	107	13	solutions	solution	NOUN
ap-1352	107	14	(	(	PUNCT
ap-1352	107	15	20	20	NUM
ap-1352	107	16	)	)	PUNCT
ap-1352	107	17	of	of	ADP
ap-1352	107	18	(	(	PUNCT
ap-1352	107	19	9	9	NUM
ap-1352	107	20	)	)	PUNCT
ap-1352	107	21	.	.	PUNCT
ap-1352	108	1	this	this	PRON
ap-1352	108	2	can	can	AUX
ap-1352	108	3	be	be	AUX
ap-1352	108	4	35	35	NUM
ap-1352	108	5	acta	acta	PROPN
ap-1352	108	6	polytechnica	polytechnica	PROPN
ap-1352	108	7	vol	vol	NOUN
ap-1352	108	8	.	.	PUNCT
ap-1352	109	1	51	51	NUM
ap-1352	109	2	no	no	NOUN
ap-1352	109	3	.	.	PUNCT
ap-1352	110	1	1/2011	1/2011	NUM
ap-1352	110	2	narrowed	narrow	VERB
ap-1352	110	3	down	down	ADP
ap-1352	110	4	by	by	ADP
ap-1352	110	5	observing	observe	VERB
ap-1352	110	6	that	that	SCONJ
ap-1352	110	7	the	the	DET
ap-1352	110	8	following	follow	VERB
ap-1352	110	9	transformations	transformation	NOUN
ap-1352	110	10	leave	leave	VERB
ap-1352	110	11	(	(	PUNCT
ap-1352	110	12	19	19	NUM
ap-1352	110	13	)	)	PUNCT
ap-1352	110	14	and	and	CCONJ
ap-1352	110	15	(	(	PUNCT
ap-1352	110	16	20	20	NUM
ap-1352	110	17	)	)	PUNCT
ap-1352	110	18	invariant	invariant	ADJ
ap-1352	110	19	(	(	PUNCT
ap-1352	110	20	see	see	VERB
ap-1352	110	21	also	also	ADV
ap-1352	110	22	the	the	DET
ap-1352	110	23	nls	nls	NOUN
ap-1352	110	24	case	case	NOUN
ap-1352	110	25	treated	treat	VERB
ap-1352	110	26	in	in	ADP
ap-1352	110	27	[	[	X
ap-1352	110	28	2	2	NUM
ap-1352	110	29	]	]	PUNCT
ap-1352	110	30	)	)	PUNCT
ap-1352	110	31	.	.	PUNCT
ap-1352	111	1	(	(	PUNCT
ap-1352	111	2	1	1	X
ap-1352	111	3	)	)	PUNCT
ap-1352	111	4	similarity	similarity	NOUN
ap-1352	111	5	transformation	transformation	NOUN
ap-1352	111	6	with	with	ADP
ap-1352	111	7	an	an	DET
ap-1352	111	8	invertiblem	invertiblem	NOUN
ap-1352	111	9	∈	∈	PROPN
ap-1352	111	10	mat	mat	NOUN
ap-1352	111	11	(	(	PUNCT
ap-1352	111	12	m	m	PROPN
ap-1352	111	13	,	,	PUNCT
ap-1352	111	14	m	m	PROPN
ap-1352	111	15	,	,	PUNCT
ap-1352	111	16	c	c	X
ap-1352	111	17	):	):	PUNCT
ap-1352	111	18	s	s	NOUN
ap-1352	111	19	�	�	PROPN
ap-1352	111	20	→	→	SYM
ap-1352	111	21	msm−1	msm−1	PROPN
ap-1352	111	22	,	,	PUNCT
ap-1352	111	23	k	k	PROPN
ap-1352	111	24	�	�	PROPN
ap-1352	111	25	→	→	SYM
ap-1352	111	26	mkm−1	mkm−1	PROPN
ap-1352	111	27	,	,	PUNCT
ap-1352	111	28	v	v	NUM
ap-1352	111	29	�	�	PROPN
ap-1352	111	30	→	→	SYM
ap-1352	111	31	mv	mv	PROPN
ap-1352	111	32	,	,	PUNCT
ap-1352	111	33	u	u	PROPN
ap-1352	111	34	�	�	PROPN
ap-1352	111	35	→	→	SYM
ap-1352	111	36	um−1	um−1	PROPN
ap-1352	111	37	.	.	PUNCT
ap-1352	112	1	as	as	ADP
ap-1352	112	2	a	a	DET
ap-1352	112	3	consequence	consequence	NOUN
ap-1352	112	4	,	,	PUNCT
ap-1352	112	5	we	we	PRON
ap-1352	112	6	can	can	AUX
ap-1352	112	7	choose	choose	VERB
ap-1352	112	8	s	s	PROPN
ap-1352	112	9	in	in	ADP
ap-1352	112	10	jordan	jordan	PROPN
ap-1352	112	11	normal	normal	ADJ
ap-1352	112	12	form	form	NOUN
ap-1352	112	13	without	without	ADP
ap-1352	112	14	restriction	restriction	NOUN
ap-1352	112	15	of	of	ADP
ap-1352	112	16	generality	generality	NOUN
ap-1352	112	17	.	.	PUNCT
ap-1352	113	1	(	(	PUNCT
ap-1352	113	2	2	2	NUM
ap-1352	113	3	)	)	PUNCT
ap-1352	113	4	reparametrization	reparametrization	NOUN
ap-1352	113	5	transformation	transformation	NOUN
ap-1352	113	6	with	with	ADP
ap-1352	113	7	invertible	invertible	ADJ
ap-1352	113	8	a	a	DET
ap-1352	113	9	,	,	PUNCT
ap-1352	113	10	b	b	PROPN
ap-1352	113	11	∈	∈	PROPN
ap-1352	113	12	mat	mat	NOUN
ap-1352	113	13	(	(	PUNCT
ap-1352	113	14	m	m	PROPN
ap-1352	113	15	,	,	PUNCT
ap-1352	113	16	m	m	PROPN
ap-1352	113	17	,	,	PUNCT
ap-1352	113	18	c	c	X
ap-1352	113	19	):	):	PUNCT
ap-1352	113	20	s	s	NOUN
ap-1352	113	21	�	�	PROPN
ap-1352	113	22	→	→	SYM
ap-1352	113	23	s	s	PART
ap-1352	113	24	,	,	PUNCT
ap-1352	113	25	k	k	PROPN
ap-1352	113	26	�	�	PROPN
ap-1352	113	27	→	→	SYM
ap-1352	113	28	b−1ka−1	b−1ka−1	PROPN
ap-1352	113	29	,	,	PUNCT
ap-1352	113	30	v	v	ADP
ap-1352	113	31	�	�	PROPN
ap-1352	113	32	→	→	SYM
ap-1352	113	33	b−1v	b−1v	NOUN
ap-1352	113	34	,	,	PUNCT
ap-1352	113	35	u	u	PROPN
ap-1352	113	36	�	�	PROPN
ap-1352	113	37	→	→	SYM
ap-1352	113	38	ua−1	ua−1	PROPN
ap-1352	113	39	,	,	PUNCT
ap-1352	113	40	ξ	ξ	PROPN
ap-1352	113	41	�	�	PROPN
ap-1352	113	42	→	→	SYM
ap-1352	113	43	abξ	abξ	NOUN
ap-1352	113	44	.	.	PUNCT
ap-1352	114	1	(	(	PUNCT
ap-1352	114	2	3	3	X
ap-1352	114	3	)	)	PUNCT
ap-1352	114	4	reflexion	reflexion	NOUN
ap-1352	114	5	symmetry	symmetry	NOUN
ap-1352	114	6	:	:	PUNCT
ap-1352	114	7	s	s	PART
ap-1352	114	8	�	�	PROPN
ap-1352	114	9	→	→	SYM
ap-1352	114	10	−s	−s	NOUN
ap-1352	114	11	,	,	PUNCT
ap-1352	114	12	k	k	PROPN
ap-1352	114	13	�	�	PROPN
ap-1352	114	14	→	→	SYM
ap-1352	114	15	−k−1	−k−1	NUM
ap-1352	114	16	,	,	PUNCT
ap-1352	114	17	v	v	ADP
ap-1352	114	18	�	�	PROPN
ap-1352	114	19	→	→	SYM
ap-1352	114	20	k−1v	k−1v	PROPN
ap-1352	114	21	,	,	PUNCT
ap-1352	114	22	u	u	PROPN
ap-1352	114	23	�	�	PROPN
ap-1352	114	24	→	→	SYM
ap-1352	114	25	uk−1	uk−1	INTJ
ap-1352	114	26	,	,	PUNCT
ap-1352	114	27	p0	p0	PROPN
ap-1352	114	28	�	�	PROPN
ap-1352	114	29	→	→	SYM
ap-1352	114	30	p0	p0	PROPN
ap-1352	114	31	−uk−1v	−uk−1v	PROPN
ap-1352	114	32	.	.	PUNCT
ap-1352	115	1	this	this	PRON
ap-1352	115	2	requires	require	VERB
ap-1352	115	3	that	that	SCONJ
ap-1352	115	4	k	k	PROPN
ap-1352	115	5	is	be	AUX
ap-1352	115	6	invertible	invertible	ADJ
ap-1352	115	7	.	.	PUNCT
ap-1352	116	1	more	more	ADV
ap-1352	116	2	generally	generally	ADV
ap-1352	116	3	,	,	PUNCT
ap-1352	116	4	such	such	DET
ap-1352	116	5	a	a	DET
ap-1352	116	6	reflexion	reflexion	NOUN
ap-1352	116	7	can	can	AUX
ap-1352	116	8	be	be	AUX
ap-1352	116	9	applied	apply	VERB
ap-1352	116	10	to	to	ADP
ap-1352	116	11	any	any	DET
ap-1352	116	12	jordan	jordan	PROPN
ap-1352	116	13	block	block	NOUN
ap-1352	116	14	of	of	ADP
ap-1352	116	15	s	s	PRON
ap-1352	116	16	and	and	CCONJ
ap-1352	116	17	then	then	ADV
ap-1352	116	18	changes	change	VERB
ap-1352	116	19	the	the	DET
ap-1352	116	20	sign	sign	NOUN
ap-1352	116	21	of	of	ADP
ap-1352	116	22	its	its	PRON
ap-1352	116	23	eigenvalue	eigenvalue	NOUN
ap-1352	117	1	[	[	X
ap-1352	117	2	8	8	NUM
ap-1352	117	3	]	]	PUNCT
ap-1352	117	4	(	(	PUNCT
ap-1352	117	5	see	see	VERB
ap-1352	117	6	also	also	ADV
ap-1352	117	7	[	[	X
ap-1352	117	8	10	10	NUM
ap-1352	117	9	,	,	PUNCT
ap-1352	117	10	2	2	NUM
ap-1352	117	11	]	]	NUM
ap-1352	117	12	)	)	PUNCT
ap-1352	117	13	.	.	PUNCT
ap-1352	118	1	the	the	DET
ap-1352	118	2	jordan	jordan	PROPN
ap-1352	118	3	normal	normal	ADJ
ap-1352	118	4	form	form	NOUN
ap-1352	118	5	can	can	AUX
ap-1352	118	6	be	be	AUX
ap-1352	118	7	restored	restore	VERB
ap-1352	118	8	afterwards	afterwards	ADV
ap-1352	118	9	via	via	ADP
ap-1352	118	10	a	a	DET
ap-1352	118	11	similarity	similarity	NOUN
ap-1352	118	12	transformation	transformation	NOUN
ap-1352	118	13	.	.	PUNCT
ap-1352	119	1	the	the	DET
ap-1352	119	2	following	following	ADJ
ap-1352	119	3	result	result	NOUN
ap-1352	119	4	is	be	AUX
ap-1352	119	5	easily	easily	ADV
ap-1352	119	6	verified	verify	VERB
ap-1352	119	7	[	[	X
ap-1352	119	8	8	8	NUM
ap-1352	119	9	]	]	PUNCT
ap-1352	119	10	.	.	PUNCT
ap-1352	120	1	proposition	proposition	NOUN
ap-1352	120	2	3	3	NUM
ap-1352	120	3	let	let	VERB
ap-1352	120	4	s	s	NOUN
ap-1352	120	5	,	,	PUNCT
ap-1352	120	6	u	u	NOUN
ap-1352	120	7	,	,	PUNCT
ap-1352	120	8	v	v	PART
ap-1352	120	9	be	be	AUX
ap-1352	120	10	as	as	ADP
ap-1352	120	11	in	in	ADP
ap-1352	120	12	proposition	proposition	NOUN
ap-1352	120	13	2	2	NUM
ap-1352	120	14	and	and	CCONJ
ap-1352	120	15	t	t	PROPN
ap-1352	120	16	∈mat	∈mat	PROPN
ap-1352	120	17	(	(	PUNCT
ap-1352	120	18	m	m	PROPN
ap-1352	120	19	,	,	PUNCT
ap-1352	120	20	m	m	PROPN
ap-1352	120	21	,	,	PUNCT
ap-1352	120	22	c	c	NOUN
ap-1352	120	23	)	)	PUNCT
ap-1352	120	24	invertible	invertible	ADJ
ap-1352	120	25	.	.	PUNCT
ap-1352	121	1	(	(	PUNCT
ap-1352	121	2	1	1	X
ap-1352	121	3	)	)	PUNCT
ap-1352	121	4	let	let	VERB
ap-1352	121	5	t	t	NOUN
ap-1352	121	6	be	be	AUX
ap-1352	121	7	hermitian	hermitian	ADJ
ap-1352	121	8	(	(	PUNCT
ap-1352	121	9	i.e.	i.e.	X
ap-1352	121	10	t	t	X
ap-1352	121	11	†	†	X
ap-1352	121	12	=	=	PROPN
ap-1352	121	13	t	t	PROPN
ap-1352	121	14	)	)	PUNCT
ap-1352	121	15	and	and	CCONJ
ap-1352	121	16	such	such	ADJ
ap-1352	121	17	that	that	PRON
ap-1352	121	18	s†	s†	NOUN
ap-1352	121	19	=	=	SYM
ap-1352	121	20	tst−1	tst−1	PROPN
ap-1352	121	21	,	,	PUNCT
ap-1352	121	22	u	u	NOUN
ap-1352	121	23	=	=	PROPN
ap-1352	121	24	v	v	X
ap-1352	121	25	†t	†t	ADJ
ap-1352	121	26	.	.	PUNCT
ap-1352	122	1	let	let	VERB
ap-1352	122	2	k	k	PRON
ap-1352	122	3	be	be	AUX
ap-1352	122	4	a	a	DET
ap-1352	122	5	solution	solution	NOUN
ap-1352	122	6	of	of	ADP
ap-1352	122	7	(	(	PUNCT
ap-1352	122	8	19	19	NUM
ap-1352	122	9	)	)	PUNCT
ap-1352	122	10	,	,	PUNCT
ap-1352	122	11	which	which	PRON
ap-1352	122	12	can	can	AUX
ap-1352	122	13	then	then	ADV
ap-1352	122	14	be	be	AUX
ap-1352	122	15	chosen	choose	VERB
ap-1352	122	16	such	such	ADJ
ap-1352	122	17	that	that	DET
ap-1352	122	18	k†	k†	PROPN
ap-1352	122	19	=	=	SYM
ap-1352	122	20	t	t	PROPN
ap-1352	122	21	kt−1	kt−1	PROPN
ap-1352	122	22	.	.	PUNCT
ap-1352	123	1	then	then	ADV
ap-1352	123	2	q	q	X
ap-1352	123	3	and	and	CCONJ
ap-1352	123	4	p	p	X
ap-1352	123	5	given	give	VERB
ap-1352	123	6	by	by	ADP
ap-1352	123	7	(	(	PUNCT
ap-1352	123	8	20	20	NUM
ap-1352	123	9	)	)	PUNCT
ap-1352	123	10	with	with	ADP
ap-1352	123	11	p†0	p†0	NOUN
ap-1352	123	12	=	=	SYM
ap-1352	124	1	p0	p0	NOUN
ap-1352	124	2	are	be	AUX
ap-1352	124	3	both	both	PRON
ap-1352	124	4	hermitian	hermitian	ADJ
ap-1352	124	5	and	and	CCONJ
ap-1352	124	6	thus	thus	ADV
ap-1352	124	7	solve	solve	VERB
ap-1352	124	8	the	the	DET
ap-1352	124	9	hermitian	hermitian	ADJ
ap-1352	124	10	reduction	reduction	NOUN
ap-1352	124	11	of	of	ADP
ap-1352	124	12	(	(	PUNCT
ap-1352	124	13	9	9	NUM
ap-1352	124	14	)	)	PUNCT
ap-1352	124	15	.	.	PUNCT
ap-1352	125	1	(	(	PUNCT
ap-1352	125	2	2	2	X
ap-1352	125	3	)	)	PUNCT
ap-1352	125	4	let	let	VERB
ap-1352	125	5	t̄	t̄	NOUN
ap-1352	125	6	=	=	SYM
ap-1352	125	7	t−1	t−1	PROPN
ap-1352	125	8	(	(	PUNCT
ap-1352	125	9	where	where	SCONJ
ap-1352	125	10	the	the	DET
ap-1352	125	11	bar	bar	NOUN
ap-1352	125	12	means	mean	VERB
ap-1352	125	13	complex	complex	ADJ
ap-1352	125	14	conjugation	conjugation	NOUN
ap-1352	125	15	)	)	PUNCT
ap-1352	125	16	and	and	CCONJ
ap-1352	125	17	s̄	s̄	NOUN
ap-1352	125	18	=	=	SYM
ap-1352	125	19	tst−1	tst−1	PROPN
ap-1352	125	20	,	,	PUNCT
ap-1352	125	21	ū	ū	NOUN
ap-1352	125	22	=	=	SYM
ap-1352	125	23	ut−1	ut−1	PROPN
ap-1352	125	24	and	and	CCONJ
ap-1352	125	25	v̄	v̄	NOUN
ap-1352	125	26	=	=	NOUN
ap-1352	125	27	tv	tv	NOUN
ap-1352	125	28	.	.	PUNCT
ap-1352	126	1	let	let	VERB
ap-1352	126	2	k	k	PRON
ap-1352	126	3	be	be	AUX
ap-1352	126	4	a	a	DET
ap-1352	126	5	solution	solution	NOUN
ap-1352	126	6	of	of	ADP
ap-1352	126	7	(	(	PUNCT
ap-1352	126	8	19	19	NUM
ap-1352	126	9	)	)	PUNCT
ap-1352	126	10	,	,	PUNCT
ap-1352	126	11	which	which	PRON
ap-1352	126	12	can	can	AUX
ap-1352	126	13	then	then	ADV
ap-1352	126	14	be	be	AUX
ap-1352	126	15	chosen	choose	VERB
ap-1352	126	16	such	such	ADJ
ap-1352	126	17	that	that	SCONJ
ap-1352	126	18	k̄	k̄	PROPN
ap-1352	126	19	=	=	SYM
ap-1352	126	20	tkt−1	tkt−1	PROPN
ap-1352	126	21	.	.	PUNCT
ap-1352	127	1	then	then	ADV
ap-1352	127	2	q	q	X
ap-1352	127	3	and	and	CCONJ
ap-1352	127	4	p	p	X
ap-1352	127	5	given	give	VERB
ap-1352	127	6	by	by	ADP
ap-1352	127	7	(	(	PUNCT
ap-1352	127	8	20	20	NUM
ap-1352	127	9	)	)	PUNCT
ap-1352	127	10	with	with	ADP
ap-1352	127	11	p̄0	p̄0	NOUN
ap-1352	127	12	=	=	PUNCT
ap-1352	127	13	p0	p0	NOUN
ap-1352	127	14	satisfy	satisfy	VERB
ap-1352	127	15	q̄	q̄	NOUN
ap-1352	127	16	=	=	PUNCT
ap-1352	127	17	q	q	NOUN
ap-1352	128	1	and	and	CCONJ
ap-1352	128	2	p̄	p̄	NOUN
ap-1352	128	3	=	=	SYM
ap-1352	128	4	p	p	X
ap-1352	128	5	,	,	PUNCT
ap-1352	128	6	and	and	CCONJ
ap-1352	128	7	thus	thus	ADV
ap-1352	128	8	solve	solve	VERB
ap-1352	128	9	the	the	DET
ap-1352	128	10	complex	complex	ADJ
ap-1352	128	11	conjugation	conjugation	NOUN
ap-1352	128	12	reduction	reduction	NOUN
ap-1352	128	13	of	of	ADP
ap-1352	128	14	(	(	PUNCT
ap-1352	128	15	9	9	NUM
ap-1352	128	16	)	)	PUNCT
ap-1352	128	17	.	.	PUNCT
ap-1352	129	1	�	�	PROPN
ap-1352	129	2	8	8	NUM
ap-1352	129	3	rank	rank	NOUN
ap-1352	129	4	one	one	NUM
ap-1352	129	5	solutions	solution	NOUN
ap-1352	129	6	let	let	VERB
ap-1352	129	7	m	m	VERB
ap-1352	129	8	=	=	NOUN
ap-1352	129	9	1	1	X
ap-1352	129	10	.	.	PUNCT
ap-1352	130	1	we	we	PRON
ap-1352	130	2	write	write	VERB
ap-1352	130	3	s	s	PROPN
ap-1352	130	4	=	=	SYM
ap-1352	130	5	s	s	PROPN
ap-1352	130	6	,	,	PUNCT
ap-1352	130	7	u	u	NOUN
ap-1352	130	8	=	=	SYM
ap-1352	130	9	u	u	PROPN
ap-1352	130	10	,	,	PUNCT
ap-1352	130	11	v	v	NOUN
ap-1352	130	12	=	=	SYM
ap-1352	130	13	vt	vt	PROPN
ap-1352	130	14	,	,	PUNCT
ap-1352	130	15	k	k	PROPN
ap-1352	130	16	=	=	SYM
ap-1352	130	17	k	k	PROPN
ap-1352	130	18	(	(	PUNCT
ap-1352	130	19	where	where	SCONJ
ap-1352	130	20	t	t	PROPN
ap-1352	130	21	means	mean	VERB
ap-1352	130	22	the	the	DET
ap-1352	130	23	transpose	transpose	NOUN
ap-1352	130	24	)	)	PUNCT
ap-1352	130	25	and	and	CCONJ
ap-1352	130	26	ξ	ξ	X
ap-1352	130	27	=	=	SYM
ap-1352	130	28	ξ	ξ	X
ap-1352	130	29	=	=	SYM
ap-1352	130	30	e−sx−s−1y	e−sx−s−1y	PROPN
ap-1352	130	31	.	.	PUNCT
ap-1352	131	1	then	then	ADV
ap-1352	131	2	(	(	PUNCT
ap-1352	131	3	19	19	NUM
ap-1352	131	4	)	)	PUNCT
ap-1352	131	5	yields	yield	NOUN
ap-1352	131	6	k	k	NOUN
ap-1352	132	1	=	=	PUNCT
ap-1352	132	2	(	(	PUNCT
ap-1352	132	3	vtu)/(2s	vtu)/(2s	NOUN
ap-1352	132	4	)	)	PUNCT
ap-1352	132	5	.	.	PUNCT
ap-1352	133	1	from	from	ADP
ap-1352	133	2	(	(	PUNCT
ap-1352	133	3	20	20	NUM
ap-1352	133	4	)	)	PUNCT
ap-1352	133	5	we	we	PRON
ap-1352	133	6	obtain	obtain	VERB
ap-1352	133	7	q	q	NOUN
ap-1352	133	8	=	=	SYM
ap-1352	133	9	2	2	NUM
ap-1352	133	10	s	s	NOUN
ap-1352	133	11	k	k	X
ap-1352	133	12	ξ	ξ	PROPN
ap-1352	133	13	1	1	NUM
ap-1352	133	14	+	+	CCONJ
ap-1352	133	15	(	(	PUNCT
ap-1352	133	16	kξ)2	kξ)2	PROPN
ap-1352	133	17	π	π	PROPN
ap-1352	133	18	,	,	PUNCT
ap-1352	133	19	p	p	X
ap-1352	133	20	=	=	PUNCT
ap-1352	133	21	p̃0	p̃0	PROPN
ap-1352	133	22	+	+	CCONJ
ap-1352	133	23	2	2	NUM
ap-1352	133	24	s	s	NOUN
ap-1352	133	25	1	1	NUM
ap-1352	133	26	+	+	CCONJ
ap-1352	133	27	(	(	PUNCT
ap-1352	133	28	kξ)2	kξ)2	PROPN
ap-1352	133	29	π	π	PROPN
ap-1352	133	30	,	,	PUNCT
ap-1352	133	31	p̃0	p̃0	PROPN
ap-1352	133	32	:	:	PUNCT
ap-1352	133	33	=	=	PUNCT
ap-1352	133	34	p0	p0	NOUN
ap-1352	134	1	−	−	NOUN
ap-1352	134	2	2s	2s	PROPN
ap-1352	134	3	π	π	X
ap-1352	134	4	,	,	PUNCT
ap-1352	134	5	π	π	X
ap-1352	134	6	:	:	PUNCT
ap-1352	134	7	=	=	NUM
ap-1352	134	8	uvt	uvt	PROPN
ap-1352	134	9	vtu	vtu	NOUN
ap-1352	134	10	.	.	PUNCT
ap-1352	135	1	the	the	DET
ap-1352	135	2	miura	miura	PROPN
ap-1352	135	3	transformation	transformation	NOUN
ap-1352	135	4	(	(	PUNCT
ap-1352	135	5	13	13	NUM
ap-1352	135	6	)	)	PUNCT
ap-1352	135	7	implies	imply	VERB
ap-1352	135	8	r	r	NOUN
ap-1352	135	9	=	=	SYM
ap-1352	135	10	−qy	−qy	PROPN
ap-1352	135	11	(	(	PUNCT
ap-1352	135	12	i	i	PRON
ap-1352	135	13	−	−	PROPN
ap-1352	135	14	py)−1	py)−1	NOUN
ap-1352	135	15	,	,	PUNCT
ap-1352	135	16	and	and	CCONJ
ap-1352	135	17	we	we	PRON
ap-1352	135	18	obtain	obtain	VERB
ap-1352	135	19	r	r	NOUN
ap-1352	135	20	=	=	SYM
ap-1352	135	21	−	−	PROPN
ap-1352	135	22	2	2	NUM
ap-1352	135	23	kξ	kξ	NOUN
ap-1352	135	24	1−	1−	NUM
ap-1352	136	1	(	(	PUNCT
ap-1352	136	2	kξ)2	kξ)2	PROPN
ap-1352	136	3	π	π	PROPN
ap-1352	136	4	,	,	PUNCT
ap-1352	136	5	which	which	PRON
ap-1352	136	6	is	be	AUX
ap-1352	136	7	singular	singular	ADJ
ap-1352	136	8	.	.	PUNCT
ap-1352	137	1	but	but	CCONJ
ap-1352	137	2	θ	θ	X
ap-1352	137	3	=	=	PUNCT
ap-1352	138	1	−2	−2	X
ap-1352	138	2	arctan(2kξ/[1−(kξ)2	arctan(2kξ/[1−(kξ)2	PROPN
ap-1352	138	3	]	]	PUNCT
ap-1352	138	4	)	)	PUNCT
ap-1352	138	5	is	be	AUX
ap-1352	138	6	the	the	DET
ap-1352	138	7	single	single	ADJ
ap-1352	138	8	kink	kink	NOUN
ap-1352	138	9	solution	solution	NOUN
ap-1352	138	10	of	of	ADP
ap-1352	138	11	the	the	DET
ap-1352	138	12	sine	sine	NOUN
ap-1352	138	13	-	-	PUNCT
ap-1352	138	14	gordon	gordon	NOUN
ap-1352	138	15	equation	equation	NOUN
ap-1352	138	16	(	(	PUNCT
ap-1352	138	17	17	17	NUM
ap-1352	138	18	)	)	PUNCT
ap-1352	138	19	.	.	PUNCT
ap-1352	139	1	9	9	NUM
ap-1352	139	2	solutions	solution	NOUN
ap-1352	139	3	of	of	ADP
ap-1352	139	4	the	the	DET
ap-1352	139	5	scalar	scalar	ADJ
ap-1352	139	6	(	(	PUNCT
ap-1352	139	7	sharp	sharp	ADJ
ap-1352	139	8	line	line	NOUN
ap-1352	139	9	)	)	PUNCT
ap-1352	139	10	sit	sit	VERB
ap-1352	139	11	equations	equation	NOUN
ap-1352	139	12	we	we	PRON
ap-1352	139	13	rewrite	rewrite	VERB
ap-1352	139	14	p	p	PRON
ap-1352	139	15	in	in	ADP
ap-1352	139	16	(	(	PUNCT
ap-1352	139	17	20	20	NUM
ap-1352	139	18	)	)	PUNCT
ap-1352	139	19	,	,	PUNCT
ap-1352	139	20	where	where	SCONJ
ap-1352	139	21	now	now	ADV
ap-1352	139	22	m	m	VERB
ap-1352	139	23	=	=	ADJ
ap-1352	139	24	1	1	NUM
ap-1352	139	25	,	,	PUNCT
ap-1352	139	26	as	as	SCONJ
ap-1352	139	27	follows	follow	VERB
ap-1352	139	28	,	,	PUNCT
ap-1352	139	29	p	p	NOUN
ap-1352	139	30	=	=	PROPN
ap-1352	139	31	p0	p0	NOUN
ap-1352	139	32	−	−	PROPN
ap-1352	139	33	tr	tr	PUNCT
ap-1352	139	34	(	(	PUNCT
ap-1352	139	35	(	(	PUNCT
ap-1352	139	36	sk	sk	X
ap-1352	139	37	+	+	NOUN
ap-1352	139	38	ks)ξkξ	ks)ξkξ	X
ap-1352	139	39	(	(	PUNCT
ap-1352	139	40	i	i	PRON
ap-1352	139	41	m	m	VERB
ap-1352	139	42	+	+	PUNCT
ap-1352	139	43	(	(	PUNCT
ap-1352	139	44	kξ)2)−1	kξ)2)−1	X
ap-1352	139	45	)	)	PUNCT
ap-1352	140	1	=	=	NOUN
ap-1352	140	2	p0	p0	NOUN
ap-1352	140	3	+	+	CCONJ
ap-1352	140	4	tr	tr	VERB
ap-1352	140	5	(	(	PUNCT
ap-1352	140	6	(	(	PUNCT
ap-1352	140	7	i	i	PRON
ap-1352	140	8	m	m	VERB
ap-1352	140	9	+	+	ADJ
ap-1352	141	1	(	(	PUNCT
ap-1352	141	2	kξ)2)x	kξ)2)x	X
ap-1352	141	3	(	(	PUNCT
ap-1352	141	4	i	i	NOUN
ap-1352	141	5	m	m	VERB
ap-1352	141	6	+	+	PUNCT
ap-1352	141	7	(	(	PUNCT
ap-1352	141	8	kξ)2)−1	kξ)2)−1	X
ap-1352	141	9	)	)	PUNCT
ap-1352	141	10	=	=	NOUN
ap-1352	141	11	p0	p0	NOUN
ap-1352	141	12	+	+	CCONJ
ap-1352	141	13	(	(	PUNCT
ap-1352	141	14	log	log	PROPN
ap-1352	141	15	det	det	PROPN
ap-1352	141	16	(	(	PUNCT
ap-1352	141	17	i	i	PRON
ap-1352	141	18	m	m	VERB
ap-1352	141	19	+	+	ADJ
ap-1352	141	20	(	(	PUNCT
ap-1352	141	21	kξ)2	kξ)2	PROPN
ap-1352	141	22	)	)	PUNCT
ap-1352	141	23	)	)	PUNCT
ap-1352	142	1	x	x	X
ap-1352	142	2	,	,	PUNCT
ap-1352	142	3	(	(	PUNCT
ap-1352	142	4	22	22	NUM
ap-1352	142	5	)	)	PUNCT
ap-1352	142	6	using	use	VERB
ap-1352	142	7	(	(	PUNCT
ap-1352	142	8	19	19	NUM
ap-1352	142	9	)	)	PUNCT
ap-1352	142	10	and	and	CCONJ
ap-1352	142	11	the	the	DET
ap-1352	142	12	identity	identity	NOUN
ap-1352	142	13	(	(	PUNCT
ap-1352	142	14	detm)x	detm)x	NOUN
ap-1352	142	15	=	=	SYM
ap-1352	142	16	tr(mxm−1	tr(mxm−1	PROPN
ap-1352	142	17	)	)	PUNCT
ap-1352	142	18	detm	detm	NOUN
ap-1352	142	19	for	for	ADP
ap-1352	142	20	an	an	DET
ap-1352	142	21	invertible	invertible	ADJ
ap-1352	142	22	matrix	matrix	NOUN
ap-1352	142	23	functionm	functionm	NOUN
ap-1352	142	24	.	.	PUNCT
ap-1352	143	1	q	q	PUNCT
ap-1352	144	1	in	in	ADP
ap-1352	144	2	(	(	PUNCT
ap-1352	144	3	20	20	NUM
ap-1352	144	4	)	)	PUNCT
ap-1352	144	5	can	can	AUX
ap-1352	144	6	be	be	AUX
ap-1352	144	7	expressed	express	VERB
ap-1352	144	8	as	as	ADP
ap-1352	144	9	q	q	NOUN
ap-1352	144	10	=	=	SYM
ap-1352	144	11	2	2	NUM
ap-1352	144	12	tr	tr	NOUN
ap-1352	144	13	(	(	PUNCT
ap-1352	144	14	skξ	skξ	X
ap-1352	144	15	(	(	PUNCT
ap-1352	144	16	i	i	NOUN
ap-1352	144	17	m	m	VERB
ap-1352	144	18	+	+	PUNCT
ap-1352	144	19	(	(	PUNCT
ap-1352	144	20	kξ)2)−1	kξ)2)−1	X
ap-1352	144	21	)	)	PUNCT
ap-1352	144	22	.	.	PUNCT
ap-1352	145	1	in	in	ADP
ap-1352	145	2	particular	particular	ADJ
ap-1352	145	3	,	,	PUNCT
ap-1352	145	4	if	if	SCONJ
ap-1352	145	5	s	s	VERB
ap-1352	145	6	is	be	AUX
ap-1352	145	7	diagonal	diagonal	ADJ
ap-1352	145	8	with	with	ADP
ap-1352	145	9	eigenvalues	eigenvalue	NOUN
ap-1352	145	10	si	si	PROPN
ap-1352	145	11	,	,	PUNCT
ap-1352	145	12	i	i	NOUN
ap-1352	145	13	=	=	NOUN
ap-1352	145	14	1	1	NUM
ap-1352	145	15	,	,	PUNCT
ap-1352	145	16	.	.	PUNCT
ap-1352	145	17	.	.	PUNCT
ap-1352	146	1	.	.	PUNCT
ap-1352	147	1	,	,	PUNCT
ap-1352	147	2	m	m	VERB
ap-1352	147	3	,	,	PUNCT
ap-1352	147	4	and	and	CCONJ
ap-1352	147	5	satisfies	satisfie	NOUN
ap-1352	147	6	(	(	PUNCT
ap-1352	147	7	21	21	NUM
ap-1352	147	8	)	)	PUNCT
ap-1352	147	9	,	,	PUNCT
ap-1352	147	10	then	then	ADV
ap-1352	147	11	the	the	DET
ap-1352	147	12	solution	solution	NOUN
ap-1352	147	13	k	k	PROPN
ap-1352	147	14	of	of	ADP
ap-1352	147	15	the	the	DET
ap-1352	147	16	sylvester	sylvest	ADJ
ap-1352	147	17	equation	equation	NOUN
ap-1352	147	18	(	(	PUNCT
ap-1352	147	19	19	19	NUM
ap-1352	147	20	)	)	PUNCT
ap-1352	147	21	,	,	PUNCT
ap-1352	147	22	which	which	PRON
ap-1352	147	23	now	now	ADV
ap-1352	147	24	amounts	amount	VERB
ap-1352	147	25	to	to	ADP
ap-1352	147	26	rank	rank	NOUN
ap-1352	147	27	(	(	PUNCT
ap-1352	147	28	sk	sk	INTJ
ap-1352	147	29	+	+	CCONJ
ap-1352	147	30	ks	ks	NOUN
ap-1352	147	31	)	)	PUNCT
ap-1352	147	32	=	=	SYM
ap-1352	147	33	1	1	NUM
ap-1352	147	34	,	,	PUNCT
ap-1352	147	35	is	be	AUX
ap-1352	147	36	the	the	DET
ap-1352	147	37	cauchy	cauchy	NOUN
ap-1352	147	38	-	-	PUNCT
ap-1352	147	39	type	type	NOUN
ap-1352	147	40	matrix	matrix	NOUN
ap-1352	147	41	with	with	ADP
ap-1352	147	42	components	component	NOUN
ap-1352	147	43	kij	kij	PROPN
ap-1352	147	44	=	=	SYM
ap-1352	147	45	vi	vi	PROPN
ap-1352	147	46	uj/(si	uj/(si	PROPN
ap-1352	147	47	+	+	CCONJ
ap-1352	147	48	sj	sj	PROPN
ap-1352	147	49	)	)	PUNCT
ap-1352	147	50	,	,	PUNCT
ap-1352	147	51	where	where	SCONJ
ap-1352	147	52	ui	ui	PROPN
ap-1352	147	53	,	,	PUNCT
ap-1352	147	54	vi	vi	PROPN
ap-1352	147	55	∈	∈	PROPN
ap-1352	147	56	c.	c.	NOUN
ap-1352	147	57	figs	fig	NOUN
ap-1352	147	58	.	.	PUNCT
ap-1352	148	1	1	1	NUM
ap-1352	148	2	and	and	CCONJ
ap-1352	148	3	2	2	NUM
ap-1352	148	4	show	show	NOUN
ap-1352	148	5	plots	plot	NOUN
ap-1352	148	6	of	of	ADP
ap-1352	148	7	two	two	NUM
ap-1352	148	8	examples	example	NOUN
ap-1352	148	9	from	from	ADP
ap-1352	148	10	the	the	DET
ap-1352	148	11	above	above	ADJ
ap-1352	148	12	family	family	NOUN
ap-1352	148	13	of	of	ADP
ap-1352	148	14	solutions	solution	NOUN
ap-1352	148	15	.	.	PUNCT
ap-1352	149	1	fig	fig	NOUN
ap-1352	149	2	.	.	PUNCT
ap-1352	150	1	1	1	NUM
ap-1352	150	2	:	:	PUNCT
ap-1352	150	3	a	a	DET
ap-1352	150	4	scalar	scalar	ADJ
ap-1352	150	5	2	2	NUM
ap-1352	150	6	-	-	PUNCT
ap-1352	150	7	soliton	soliton	NOUN
ap-1352	150	8	solution	solution	NOUN
ap-1352	150	9	with	with	ADP
ap-1352	150	10	s	s	NOUN
ap-1352	150	11	=	=	VERB
ap-1352	150	12	diag	diag	X
ap-1352	150	13	(	(	PUNCT
ap-1352	150	14	1	1	NUM
ap-1352	150	15	,	,	PUNCT
ap-1352	150	16	2	2	NUM
ap-1352	150	17	)	)	PUNCT
ap-1352	150	18	and	and	CCONJ
ap-1352	150	19	ui	ui	NOUN
ap-1352	150	20	=	=	NOUN
ap-1352	150	21	vi	vi	PROPN
ap-1352	150	22	=	=	SYM
ap-1352	150	23	1	1	NUM
ap-1352	150	24	fig	fig	NOUN
ap-1352	150	25	.	.	PUNCT
ap-1352	151	1	2	2	NUM
ap-1352	151	2	:	:	PUNCT
ap-1352	151	3	a	a	DET
ap-1352	151	4	scalar	scalar	ADJ
ap-1352	151	5	breather	breather	NOUN
ap-1352	151	6	solution	solution	NOUN
ap-1352	151	7	with	with	ADP
ap-1352	151	8	s	s	NOUN
ap-1352	151	9	=	=	VERB
ap-1352	151	10	diag	diag	NOUN
ap-1352	151	11	(	(	PUNCT
ap-1352	151	12	1	1	NUM
ap-1352	151	13	+	+	CCONJ
ap-1352	151	14	i	i	PRON
ap-1352	151	15	,	,	PUNCT
ap-1352	151	16	1−	1−	NUM
ap-1352	151	17	i	i	NOUN
ap-1352	151	18	)	)	PUNCT
ap-1352	151	19	and	and	CCONJ
ap-1352	151	20	ui	ui	NOUN
ap-1352	151	21	=	=	NOUN
ap-1352	151	22	vi	vi	PROPN
ap-1352	152	1	=	=	NOUN
ap-1352	152	2	1	1	NUM
ap-1352	152	3	10	10	NUM
ap-1352	152	4	a	a	DET
ap-1352	152	5	family	family	NOUN
ap-1352	152	6	of	of	ADP
ap-1352	152	7	solutions	solution	NOUN
ap-1352	152	8	of	of	ADP
ap-1352	152	9	the	the	DET
ap-1352	152	10	real	real	ADJ
ap-1352	152	11	sine	sine	ADJ
ap-1352	152	12	-	-	PUNCT
ap-1352	152	13	gordon	gordon	NOUN
ap-1352	152	14	equation	equation	NOUN
ap-1352	152	15	via	via	ADP
ap-1352	152	16	the	the	DET
ap-1352	152	17	miura	miura	PROPN
ap-1352	152	18	transformation	transformation	NOUN
ap-1352	152	19	(	(	PUNCT
ap-1352	152	20	18	18	NUM
ap-1352	152	21	)	)	PUNCT
ap-1352	152	22	,	,	PUNCT
ap-1352	152	23	proposition	proposition	NOUN
ap-1352	152	24	2	2	NUM
ap-1352	152	25	determines	determine	VERB
ap-1352	152	26	a	a	DET
ap-1352	152	27	family	family	NOUN
ap-1352	152	28	of	of	ADP
ap-1352	152	29	sine	sine	NOUN
ap-1352	152	30	-	-	PUNCT
ap-1352	152	31	gordon	gordon	PROPN
ap-1352	152	32	solutions	solution	NOUN
ap-1352	152	33	(	(	PUNCT
ap-1352	152	34	see	see	VERB
ap-1352	152	35	also	also	ADV
ap-1352	152	36	36	36	NUM
ap-1352	152	37	acta	acta	PROPN
ap-1352	152	38	polytechnica	polytechnica	PROPN
ap-1352	152	39	vol	vol	NOUN
ap-1352	152	40	.	.	PUNCT
ap-1352	153	1	51	51	NUM
ap-1352	153	2	no	no	NOUN
ap-1352	153	3	.	.	PUNCT
ap-1352	154	1	1/2011	1/2011	X
ap-1352	154	2	e.g.	e.g.	ADV
ap-1352	154	3	[	[	X
ap-1352	154	4	6	6	NUM
ap-1352	154	5	,	,	PUNCT
ap-1352	154	6	11	11	NUM
ap-1352	154	7	,	,	PUNCT
ap-1352	154	8	12	12	NUM
ap-1352	154	9	,	,	PUNCT
ap-1352	154	10	13	13	NUM
ap-1352	154	11	,	,	PUNCT
ap-1352	154	12	14	14	NUM
ap-1352	154	13	,	,	PUNCT
ap-1352	154	14	15	15	NUM
ap-1352	154	15	,	,	PUNCT
ap-1352	154	16	16	16	NUM
ap-1352	154	17	]	]	PUNCT
ap-1352	154	18	for	for	ADP
ap-1352	154	19	related	related	ADJ
ap-1352	154	20	results	result	NOUN
ap-1352	154	21	obtained	obtain	VERB
ap-1352	154	22	by	by	ADP
ap-1352	154	23	different	different	ADJ
ap-1352	154	24	methods	method	NOUN
ap-1352	154	25	)	)	PUNCT
ap-1352	154	26	.	.	PUNCT
ap-1352	155	1	proposition	proposition	NOUN
ap-1352	155	2	4	4	NUM
ap-1352	155	3	let	let	VERB
ap-1352	155	4	s	s	PRON
ap-1352	155	5	∈	∈	PROPN
ap-1352	155	6	mat	mat	NOUN
ap-1352	155	7	(	(	PUNCT
ap-1352	155	8	m	m	PROPN
ap-1352	155	9	,	,	PUNCT
ap-1352	155	10	m	m	PROPN
ap-1352	155	11	,	,	PUNCT
ap-1352	155	12	c	c	AUX
ap-1352	155	13	)	)	PUNCT
ap-1352	155	14	be	be	AUX
ap-1352	155	15	invertible	invertible	ADJ
ap-1352	155	16	and	and	CCONJ
ap-1352	155	17	k	k	PROPN
ap-1352	155	18	∈	∈	PROPN
ap-1352	155	19	mat	mat	NOUN
ap-1352	155	20	(	(	PUNCT
ap-1352	155	21	m	m	PROPN
ap-1352	155	22	,	,	PUNCT
ap-1352	155	23	m	m	PROPN
ap-1352	155	24	,	,	PUNCT
ap-1352	155	25	c	c	NOUN
ap-1352	155	26	)	)	PUNCT
ap-1352	155	27	such	such	ADJ
ap-1352	155	28	that	that	DET
ap-1352	155	29	rank	rank	NOUN
ap-1352	155	30	(	(	PUNCT
ap-1352	155	31	sk	sk	X
ap-1352	155	32	+	+	CCONJ
ap-1352	155	33	ks	ks	NOUN
ap-1352	155	34	)	)	PUNCT
ap-1352	155	35	=	=	SYM
ap-1352	155	36	1	1	NUM
ap-1352	155	37	,	,	PUNCT
ap-1352	155	38	det(im	det(im	NOUN
ap-1352	155	39	+	+	CCONJ
ap-1352	155	40	(	(	PUNCT
ap-1352	155	41	kξ)2	kξ)2	PROPN
ap-1352	155	42	)	)	PUNCT
ap-1352	155	43	∈	∈	PROPN
ap-1352	155	44	r	r	NOUN
ap-1352	155	45	with	with	ADP
ap-1352	155	46	ξ	ξ	PROPN
ap-1352	155	47	=	=	SYM
ap-1352	155	48	e−sx−s−1	e−sx−s−1	PROPN
ap-1352	155	49	y	y	PROPN
ap-1352	155	50	,	,	PUNCT
ap-1352	155	51	and	and	CCONJ
ap-1352	155	52	tr	tr	VERB
ap-1352	155	53	(	(	PUNCT
ap-1352	155	54	skξ	skξ	X
ap-1352	155	55	(	(	PUNCT
ap-1352	155	56	i	i	NOUN
ap-1352	155	57	m	m	VERB
ap-1352	155	58	+	+	ADJ
ap-1352	155	59	(	(	PUNCT
ap-1352	155	60	kξ)2)−1	kξ)2)−1	NOUN
ap-1352	155	61	)	)	PUNCT
ap-1352	155	62	�	�	PROPN
ap-1352	155	63	∈	∈	PROPN
ap-1352	155	64	ir	ir	NOUN
ap-1352	155	65	(	(	PUNCT
ap-1352	155	66	where	where	SCONJ
ap-1352	155	67	i	i	PRON
ap-1352	155	68	is	be	AUX
ap-1352	155	69	the	the	DET
ap-1352	155	70	imaginary	imaginary	ADJ
ap-1352	155	71	unit	unit	NOUN
ap-1352	155	72	)	)	PUNCT
ap-1352	155	73	.	.	PUNCT
ap-1352	156	1	then	then	ADV
ap-1352	156	2	θ	θ	X
ap-1352	156	3	=	=	SYM
ap-1352	156	4	4	4	NUM
ap-1352	156	5	arctan	arctan	NOUN
ap-1352	156	6	(	(	PUNCT
ap-1352	156	7	√	√	PROPN
ap-1352	156	8	β	β	SYM
ap-1352	156	9	1	1	NUM
ap-1352	156	10	+	+	CCONJ
ap-1352	156	11	√	√	PROPN
ap-1352	156	12	1−	1−	NUM
ap-1352	156	13	β	β	X
ap-1352	156	14	)	)	PUNCT
ap-1352	156	15	with	with	ADP
ap-1352	156	16	β	β	PRON
ap-1352	156	17	:	:	PUNCT
ap-1352	156	18	=	=	SYM
ap-1352	156	19	(	(	PUNCT
ap-1352	156	20	log	log	VERB
ap-1352	156	21	|	|	ADV
ap-1352	156	22	det(im	det(im	NOUN
ap-1352	156	23	+	+	CCONJ
ap-1352	156	24	(	(	PUNCT
ap-1352	156	25	kξ)2)|	kξ)2)|	PROPN
ap-1352	156	26	)	)	PUNCT
ap-1352	156	27	xy	xy	PROPN
ap-1352	157	1	(	(	PUNCT
ap-1352	157	2	23	23	NUM
ap-1352	157	3	)	)	PUNCT
ap-1352	157	4	solves	solve	VERB
ap-1352	157	5	the	the	DET
ap-1352	157	6	sine	sine	NOUN
ap-1352	157	7	-	-	PUNCT
ap-1352	157	8	gordon	gordon	PROPN
ap-1352	157	9	equation	equation	NOUN
ap-1352	157	10	θxy	θxy	NOUN
ap-1352	157	11	=	=	PUNCT
ap-1352	157	12	sin	sin	NOUN
ap-1352	157	13	θ	θ	PROPN
ap-1352	157	14	in	in	ADP
ap-1352	157	15	any	any	DET
ap-1352	157	16	open	open	ADJ
ap-1352	157	17	set	set	NOUN
ap-1352	157	18	of	of	ADP
ap-1352	157	19	r	r	NOUN
ap-1352	157	20	2	2	NUM
ap-1352	158	1	where	where	SCONJ
ap-1352	158	2	det(im	det(im	NOUN
ap-1352	158	3	+	+	CCONJ
ap-1352	158	4	(	(	PUNCT
ap-1352	158	5	kξ)2	kξ)2	PROPN
ap-1352	158	6	)	)	PUNCT
ap-1352	158	7	�	�	PROPN
ap-1352	158	8	=	=	SYM
ap-1352	158	9	0	0	NUM
ap-1352	158	10	.	.	PUNCT
ap-1352	158	11	proof	proof	NOUN
ap-1352	158	12	:	:	PUNCT
ap-1352	158	13	let	let	VERB
ap-1352	158	14	p	p	PRON
ap-1352	158	15	be	be	AUX
ap-1352	158	16	given	give	VERB
ap-1352	158	17	by	by	ADP
ap-1352	158	18	(	(	PUNCT
ap-1352	158	19	22	22	NUM
ap-1352	158	20	)	)	PUNCT
ap-1352	158	21	.	.	PUNCT
ap-1352	159	1	due	due	ADP
ap-1352	159	2	to	to	ADP
ap-1352	159	3	the	the	DET
ap-1352	159	4	assumption	assumption	NOUN
ap-1352	159	5	det(im	det(im	NOUN
ap-1352	159	6	+	+	PROPN
ap-1352	159	7	(	(	PUNCT
ap-1352	159	8	kξ)2	kξ)2	PROPN
ap-1352	159	9	)	)	PUNCT
ap-1352	159	10	∈	∈	PROPN
ap-1352	159	11	r	r	NOUN
ap-1352	159	12	,	,	PUNCT
ap-1352	159	13	py	py	PROPN
ap-1352	159	14	is	be	AUX
ap-1352	159	15	real	real	ADJ
ap-1352	159	16	,	,	PUNCT
ap-1352	159	17	hence	hence	ADV
ap-1352	159	18	(	(	PUNCT
ap-1352	159	19	14	14	NUM
ap-1352	159	20	)	)	PUNCT
ap-1352	159	21	implies	imply	VERB
ap-1352	159	22	|1	|1	DET
ap-1352	159	23	−	−	NUM
ap-1352	159	24	2py|2	2py|2	NUM
ap-1352	159	25	=	=	SYM
ap-1352	159	26	1	1	NUM
ap-1352	159	27	−	−	PROPN
ap-1352	159	28	4qy	4qy	NOUN
ap-1352	159	29	2	2	NUM
ap-1352	159	30	.	.	PUNCT
ap-1352	160	1	it	it	PRON
ap-1352	160	2	follows	follow	VERB
ap-1352	160	3	that	that	SCONJ
ap-1352	160	4	qy	qy	NOUN
ap-1352	160	5	2	2	NUM
ap-1352	160	6	is	be	AUX
ap-1352	160	7	real	real	ADJ
ap-1352	160	8	.	.	PUNCT
ap-1352	161	1	since	since	SCONJ
ap-1352	161	2	another	another	PRON
ap-1352	161	3	of	of	ADP
ap-1352	161	4	our	our	PRON
ap-1352	161	5	assumptions	assumption	NOUN
ap-1352	161	6	excludes	exclude	NOUN
ap-1352	161	7	that	that	SCONJ
ap-1352	161	8	qy	qy	NOUN
ap-1352	161	9	is	be	AUX
ap-1352	161	10	imaginary	imaginary	ADJ
ap-1352	161	11	,	,	PUNCT
ap-1352	161	12	it	it	PRON
ap-1352	161	13	follows	follow	VERB
ap-1352	161	14	that	that	SCONJ
ap-1352	161	15	|1	|1	NUM
ap-1352	162	1	−	−	NUM
ap-1352	162	2	2py|	2py|	NUM
ap-1352	162	3	≤	≤	NUM
ap-1352	162	4	1	1	NUM
ap-1352	162	5	.	.	PUNCT
ap-1352	163	1	hence	hence	ADV
ap-1352	163	2	the	the	DET
ap-1352	163	3	equation	equation	NOUN
ap-1352	163	4	cos	cos	ADP
ap-1352	163	5	θ	θ	PROPN
ap-1352	163	6	=	=	SYM
ap-1352	164	1	1	1	NUM
ap-1352	164	2	−	−	PROPN
ap-1352	164	3	2py	2py	ADJ
ap-1352	164	4	(	(	PUNCT
ap-1352	164	5	second	second	ADJ
ap-1352	164	6	of	of	ADP
ap-1352	164	7	(	(	PUNCT
ap-1352	164	8	18	18	NUM
ap-1352	164	9	)	)	PUNCT
ap-1352	164	10	)	)	PUNCT
ap-1352	164	11	has	have	VERB
ap-1352	164	12	a	a	DET
ap-1352	164	13	real	real	ADJ
ap-1352	164	14	solution	solution	NOUN
ap-1352	164	15	θ	θ	NOUN
ap-1352	164	16	.	.	PUNCT
ap-1352	164	17	inserting	insert	VERB
ap-1352	164	18	expression	expression	NOUN
ap-1352	164	19	(	(	PUNCT
ap-1352	164	20	22	22	NUM
ap-1352	164	21	)	)	PUNCT
ap-1352	164	22	for	for	ADP
ap-1352	164	23	p	p	PRON
ap-1352	164	24	,	,	PUNCT
ap-1352	164	25	we	we	PRON
ap-1352	164	26	arrive	arrive	VERB
ap-1352	164	27	at	at	ADP
ap-1352	164	28	cos	cos	PROPN
ap-1352	165	1	θ	θ	PROPN
ap-1352	165	2	=	=	SYM
ap-1352	165	3	1−2	1−2	NUM
ap-1352	165	4	(	(	PUNCT
ap-1352	165	5	log	log	NOUN
ap-1352	165	6	det(im	det(im	NOUN
ap-1352	165	7	+	+	CCONJ
ap-1352	165	8	(	(	PUNCT
ap-1352	165	9	kξ)2	kξ)2	PROPN
ap-1352	165	10	)	)	PUNCT
ap-1352	165	11	)	)	PUNCT
ap-1352	166	1	xy	xy	INTJ
ap-1352	166	2	.	.	PUNCT
ap-1352	167	1	moreover	moreover	ADV
ap-1352	167	2	,	,	PUNCT
ap-1352	167	3	(	(	PUNCT
ap-1352	167	4	14	14	NUM
ap-1352	167	5	)	)	PUNCT
ap-1352	167	6	shows	show	VERB
ap-1352	167	7	that	that	SCONJ
ap-1352	167	8	py	py	PROPN
ap-1352	167	9	≥	≥	PRON
ap-1352	167	10	0	0	NUM
ap-1352	167	11	and	and	CCONJ
ap-1352	167	12	thus	thus	ADV
ap-1352	167	13	0	0	NUM
ap-1352	167	14	≤	≤	NUM
ap-1352	167	15	py	py	X
ap-1352	167	16	≤	≤	ADJ
ap-1352	167	17	1	1	NUM
ap-1352	167	18	.	.	PUNCT
ap-1352	167	19	using	use	VERB
ap-1352	167	20	identities	identity	NOUN
ap-1352	167	21	for	for	ADP
ap-1352	167	22	the	the	DET
ap-1352	167	23	inverse	inverse	NOUN
ap-1352	167	24	trigonometric	trigonometric	NOUN
ap-1352	167	25	functions	function	NOUN
ap-1352	167	26	,	,	PUNCT
ap-1352	167	27	we	we	PRON
ap-1352	167	28	find	find	VERB
ap-1352	167	29	(	(	PUNCT
ap-1352	167	30	23	23	NUM
ap-1352	167	31	)	)	PUNCT
ap-1352	167	32	,	,	PUNCT
ap-1352	167	33	where	where	SCONJ
ap-1352	167	34	β	β	X
ap-1352	167	35	=	=	SYM
ap-1352	167	36	py	py	PROPN
ap-1352	167	37	.	.	PUNCT
ap-1352	167	38	�	�	PROPN
ap-1352	167	39	proposition	proposition	VERB
ap-1352	167	40	3	3	NUM
ap-1352	167	41	yields	yield	NOUN
ap-1352	167	42	sufficient	sufficient	ADJ
ap-1352	167	43	conditions	condition	NOUN
ap-1352	167	44	on	on	ADP
ap-1352	167	45	the	the	DET
ap-1352	167	46	matrix	matrix	NOUN
ap-1352	167	47	data	datum	NOUN
ap-1352	167	48	for	for	ADP
ap-1352	167	49	which	which	PRON
ap-1352	167	50	the	the	DET
ap-1352	167	51	last	last	ADJ
ap-1352	167	52	two	two	NUM
ap-1352	167	53	assumptions	assumption	NOUN
ap-1352	167	54	in	in	ADP
ap-1352	167	55	proposition	proposition	NOUN
ap-1352	167	56	4	4	NUM
ap-1352	167	57	are	be	AUX
ap-1352	167	58	satisfied	satisfied	ADJ
ap-1352	167	59	.	.	PUNCT
ap-1352	168	1	references	reference	NOUN
ap-1352	168	2	[	[	X
ap-1352	168	3	1	1	NUM
ap-1352	168	4	]	]	PUNCT
ap-1352	168	5	dimakis	dimaki	NOUN
ap-1352	168	6	,	,	PUNCT
ap-1352	168	7	a.	a.	NOUN
ap-1352	168	8	,	,	PUNCT
ap-1352	168	9	müller	müller	NOUN
ap-1352	168	10	-	-	PUNCT
ap-1352	168	11	hoissen	hoissen	NOUN
ap-1352	168	12	,	,	PUNCT
ap-1352	168	13	f.	f.	PROPN
ap-1352	168	14	:	:	PUNCT
ap-1352	168	15	bidifferential	bidifferential	PROPN
ap-1352	168	16	graded	grade	VERB
ap-1352	168	17	algebras	algebra	NOUN
ap-1352	168	18	and	and	CCONJ
ap-1352	168	19	integrable	integrable	ADJ
ap-1352	168	20	systems	system	NOUN
ap-1352	168	21	.	.	PUNCT
ap-1352	169	1	discr	discr	PROPN
ap-1352	169	2	.	.	PUNCT
ap-1352	170	1	cont	cont	PROPN
ap-1352	170	2	.	.	PUNCT
ap-1352	171	1	dyn	dyn	NOUN
ap-1352	171	2	.	.	PUNCT
ap-1352	172	1	systems	system	NOUN
ap-1352	172	2	suppl	suppl	PROPN
ap-1352	172	3	.	.	PROPN
ap-1352	172	4	,	,	PUNCT
ap-1352	172	5	2009	2009	NUM
ap-1352	172	6	,	,	PUNCT
ap-1352	172	7	2009	2009	NUM
ap-1352	172	8	,	,	PUNCT
ap-1352	172	9	p.	p.	NOUN
ap-1352	172	10	208–219	208–219	NUM
ap-1352	172	11	.	.	PUNCT
ap-1352	173	1	[	[	X
ap-1352	173	2	2	2	NUM
ap-1352	173	3	]	]	PUNCT
ap-1352	173	4	dimakis	dimaki	NOUN
ap-1352	173	5	,	,	PUNCT
ap-1352	173	6	a.	a.	NOUN
ap-1352	173	7	,	,	PUNCT
ap-1352	173	8	müller	müller	NOUN
ap-1352	173	9	-	-	PUNCT
ap-1352	173	10	hoissen	hoissen	NOUN
ap-1352	173	11	,	,	PUNCT
ap-1352	173	12	f.	f.	PROPN
ap-1352	173	13	:	:	PUNCT
ap-1352	173	14	solutions	solution	NOUN
ap-1352	173	15	of	of	ADP
ap-1352	173	16	matrix	matrix	NOUN
ap-1352	173	17	nls	nls	NOUN
ap-1352	173	18	systems	system	NOUN
ap-1352	173	19	and	and	CCONJ
ap-1352	173	20	their	their	PRON
ap-1352	173	21	discretizations	discretization	NOUN
ap-1352	173	22	:	:	PUNCT
ap-1352	173	23	a	a	DET
ap-1352	173	24	unified	unified	ADJ
ap-1352	173	25	treatment	treatment	NOUN
ap-1352	173	26	.	.	PUNCT
ap-1352	174	1	inverse	inverse	NOUN
ap-1352	174	2	problems	problem	NOUN
ap-1352	174	3	,	,	PUNCT
ap-1352	174	4	26	26	NUM
ap-1352	174	5	,	,	PUNCT
ap-1352	174	6	2010	2010	NUM
ap-1352	174	7	,	,	PUNCT
ap-1352	174	8	095007	095007	NUM
ap-1352	174	9	.	.	PUNCT
ap-1352	175	1	[	[	X
ap-1352	175	2	3	3	NUM
ap-1352	175	3	]	]	PUNCT
ap-1352	175	4	dimakis	dimaki	NOUN
ap-1352	175	5	,	,	PUNCT
ap-1352	175	6	a.	a.	NOUN
ap-1352	175	7	,	,	PUNCT
ap-1352	175	8	müller	müller	NOUN
ap-1352	175	9	-	-	PUNCT
ap-1352	175	10	hoissen	hoissen	NOUN
ap-1352	175	11	,	,	PUNCT
ap-1352	175	12	f.	f.	PROPN
ap-1352	175	13	:	:	PUNCT
ap-1352	175	14	bidifferential	bidifferential	ADJ
ap-1352	175	15	calculus	calculus	NOUN
ap-1352	175	16	approach	approach	NOUN
ap-1352	175	17	to	to	ADP
ap-1352	175	18	akns	akns	NOUN
ap-1352	175	19	hierarchies	hierarchy	NOUN
ap-1352	175	20	and	and	CCONJ
ap-1352	175	21	their	their	PRON
ap-1352	175	22	solutions	solution	NOUN
ap-1352	175	23	.	.	PUNCT
ap-1352	176	1	sigma	sigma	PROPN
ap-1352	176	2	,	,	PUNCT
ap-1352	176	3	6	6	NUM
ap-1352	176	4	,	,	PUNCT
ap-1352	176	5	2010	2010	NUM
ap-1352	176	6	,	,	PUNCT
ap-1352	176	7	2010055	2010055	NUM
ap-1352	176	8	.	.	PUNCT
ap-1352	177	1	[	[	X
ap-1352	177	2	4	4	NUM
ap-1352	177	3	]	]	X
ap-1352	177	4	grisaru	grisaru	NOUN
ap-1352	177	5	,	,	PUNCT
ap-1352	177	6	m.	m.	NOUN
ap-1352	177	7	,	,	PUNCT
ap-1352	177	8	penati	penati	PROPN
ap-1352	177	9	,	,	PUNCT
ap-1352	177	10	s.	s.	PROPN
ap-1352	177	11	:	:	PUNCT
ap-1352	177	12	an	an	DET
ap-1352	177	13	integrable	integrable	ADJ
ap-1352	177	14	noncommutative	noncommutative	ADJ
ap-1352	177	15	version	version	NOUN
ap-1352	177	16	of	of	ADP
ap-1352	177	17	the	the	DET
ap-1352	177	18	sine	sine	NOUN
ap-1352	177	19	-	-	PUNCT
ap-1352	177	20	gordon	gordon	PROPN
ap-1352	177	21	system	system	NOUN
ap-1352	177	22	.	.	PUNCT
ap-1352	178	1	nucl	nucl	PROPN
ap-1352	178	2	.	.	PUNCT
ap-1352	179	1	phys	phy	NOUN
ap-1352	179	2	.	.	PUNCT
ap-1352	180	1	b	b	X
ap-1352	180	2	,	,	PUNCT
ap-1352	180	3	655	655	NUM
ap-1352	180	4	,	,	PUNCT
ap-1352	180	5	2003	2003	NUM
ap-1352	180	6	,	,	PUNCT
ap-1352	180	7	p.	p.	NOUN
ap-1352	180	8	250–276	250–276	NUM
ap-1352	180	9	.	.	PUNCT
ap-1352	181	1	[	[	X
ap-1352	181	2	5	5	NUM
ap-1352	181	3	]	]	X
ap-1352	181	4	lamb	lamb	PROPN
ap-1352	181	5	,	,	PUNCT
ap-1352	181	6	g.	g.	PROPN
ap-1352	181	7	:	:	PUNCT
ap-1352	181	8	analytical	analytical	ADJ
ap-1352	181	9	descriptions	description	NOUN
ap-1352	181	10	of	of	ADP
ap-1352	181	11	ultrashort	ultrashort	ADJ
ap-1352	181	12	optical	optical	ADJ
ap-1352	181	13	pulse	pulse	NOUN
ap-1352	181	14	propagation	propagation	NOUN
ap-1352	181	15	in	in	ADP
ap-1352	181	16	a	a	DET
ap-1352	181	17	resonant	resonant	ADJ
ap-1352	181	18	medium	medium	NOUN
ap-1352	181	19	.	.	PUNCT
ap-1352	182	1	rev	rev	PROPN
ap-1352	182	2	.	.	PUNCT
ap-1352	183	1	mod	mod	PROPN
ap-1352	183	2	.	.	PUNCT
ap-1352	184	1	phys	phys	PROPN
ap-1352	184	2	.	.	PUNCT
ap-1352	184	3	,	,	PUNCT
ap-1352	184	4	43	43	NUM
ap-1352	184	5	,	,	PUNCT
ap-1352	184	6	1971	1971	NUM
ap-1352	184	7	,	,	PUNCT
ap-1352	184	8	p.	p.	NOUN
ap-1352	184	9	99–124	99–124	NUM
ap-1352	184	10	.	.	PUNCT
ap-1352	185	1	[	[	X
ap-1352	185	2	6	6	NUM
ap-1352	185	3	]	]	SYM
ap-1352	185	4	caudrey	caudrey	PROPN
ap-1352	185	5	,	,	PUNCT
ap-1352	185	6	p.	p.	NOUN
ap-1352	185	7	,	,	PUNCT
ap-1352	185	8	gibbon	gibbon	PROPN
ap-1352	185	9	,	,	PUNCT
ap-1352	185	10	j.	j.	PROPN
ap-1352	185	11	,	,	PUNCT
ap-1352	185	12	eilbeck	eilbeck	PROPN
ap-1352	185	13	,	,	PUNCT
ap-1352	185	14	j.	j.	PROPN
ap-1352	185	15	,	,	PUNCT
ap-1352	185	16	bullough	bullough	ADV
ap-1352	185	17	,	,	PUNCT
ap-1352	185	18	r.	r.	PROPN
ap-1352	185	19	:	:	PUNCT
ap-1352	185	20	exact	exact	ADJ
ap-1352	185	21	multi	multi	ADJ
ap-1352	185	22	-	-	ADJ
ap-1352	185	23	soliton	soliton	ADJ
ap-1352	185	24	solutions	solution	NOUN
ap-1352	185	25	of	of	ADP
ap-1352	185	26	the	the	DET
ap-1352	185	27	self	self	NOUN
ap-1352	185	28	-	-	PUNCT
ap-1352	185	29	induced	induce	VERB
ap-1352	185	30	transparency	transparency	NOUN
ap-1352	185	31	and	and	CCONJ
ap-1352	185	32	sine	sine	NOUN
ap-1352	185	33	-	-	PUNCT
ap-1352	185	34	gordon	gordon	PROPN
ap-1352	185	35	equations	equation	NOUN
ap-1352	185	36	.	.	PUNCT
ap-1352	186	1	phys	phy	NOUN
ap-1352	186	2	.	.	PUNCT
ap-1352	187	1	rev	rev	PROPN
ap-1352	187	2	.	.	PROPN
ap-1352	187	3	lett	lett	PROPN
ap-1352	187	4	.	.	PROPN
ap-1352	187	5	,	,	PUNCT
ap-1352	187	6	30	30	NUM
ap-1352	187	7	,	,	PUNCT
ap-1352	187	8	1973	1973	NUM
ap-1352	187	9	,	,	PUNCT
ap-1352	187	10	p.	p.	NOUN
ap-1352	187	11	237–238	237–238	NUM
ap-1352	187	12	.	.	PUNCT
ap-1352	188	1	[	[	X
ap-1352	188	2	7	7	NUM
ap-1352	188	3	]	]	SYM
ap-1352	188	4	bullough	bullough	NOUN
ap-1352	188	5	,	,	PUNCT
ap-1352	188	6	r.	r.	PROPN
ap-1352	188	7	,	,	PUNCT
ap-1352	188	8	caudrey	caudrey	PROPN
ap-1352	188	9	,	,	PUNCT
ap-1352	188	10	p.	p.	NOUN
ap-1352	188	11	,	,	PUNCT
ap-1352	188	12	eilbeck	eilbeck	PROPN
ap-1352	188	13	,	,	PUNCT
ap-1352	188	14	j.	j.	PROPN
ap-1352	188	15	,	,	PUNCT
ap-1352	188	16	gibbon	gibbon	PROPN
ap-1352	188	17	,	,	PUNCT
ap-1352	188	18	j.	j.	PROPN
ap-1352	188	19	:	:	PUNCT
ap-1352	188	20	a	a	DET
ap-1352	188	21	general	general	ADJ
ap-1352	188	22	theory	theory	NOUN
ap-1352	188	23	of	of	ADP
ap-1352	188	24	self	self	NOUN
ap-1352	188	25	-	-	PUNCT
ap-1352	188	26	induced	induce	VERB
ap-1352	188	27	transparency	transparency	NOUN
ap-1352	188	28	.	.	PUNCT
ap-1352	189	1	opto	opto	ADJ
ap-1352	189	2	-	-	PUNCT
ap-1352	189	3	electronics	electronic	NOUN
ap-1352	189	4	,	,	PUNCT
ap-1352	189	5	6	6	NUM
ap-1352	189	6	,	,	PUNCT
ap-1352	189	7	1974	1974	NUM
ap-1352	189	8	,	,	PUNCT
ap-1352	189	9	p.	p.	NOUN
ap-1352	189	10	121–140	121–140	NUM
ap-1352	189	11	.	.	PUNCT
ap-1352	190	1	[	[	X
ap-1352	190	2	8	8	NUM
ap-1352	190	3	]	]	X
ap-1352	190	4	kanning	kanning	NOUN
ap-1352	190	5	,	,	PUNCT
ap-1352	190	6	n.	n.	NOUN
ap-1352	190	7	:	:	PUNCT
ap-1352	190	8	integrable	integrable	ADJ
ap-1352	190	9	systeme	systeme	NOUN
ap-1352	190	10	in	in	ADP
ap-1352	190	11	der	der	ADJ
ap-1352	190	12	allgemeinen	allgemeinen	NOUN
ap-1352	190	13	relativitätstheorie	relativitätstheorie	NOUN
ap-1352	190	14	:	:	PUNCT
ap-1352	190	15	ein	ein	PROPN
ap-1352	190	16	bidifferentialkalkül	bidifferentialkalkül	PROPN
ap-1352	190	17	-	-	PUNCT
ap-1352	190	18	zugang	zugang	PROPN
ap-1352	190	19	.	.	PUNCT
ap-1352	191	1	diploma	diploma	NOUN
ap-1352	191	2	thesis	thesis	NOUN
ap-1352	191	3	.	.	PUNCT
ap-1352	192	1	göttingen	göttingen	NOUN
ap-1352	192	2	:	:	PUNCT
ap-1352	192	3	university	university	NOUN
ap-1352	192	4	of	of	ADP
ap-1352	192	5	göttingen	göttingen	PROPN
ap-1352	192	6	,	,	PUNCT
ap-1352	192	7	2010	2010	NUM
ap-1352	192	8	.	.	PUNCT
ap-1352	193	1	[	[	X
ap-1352	193	2	9	9	NUM
ap-1352	193	3	]	]	PUNCT
ap-1352	193	4	horn	horn	NOUN
ap-1352	193	5	,	,	PUNCT
ap-1352	193	6	r.	r.	PROPN
ap-1352	193	7	,	,	PUNCT
ap-1352	193	8	johnson	johnson	PROPN
ap-1352	193	9	,	,	PUNCT
ap-1352	193	10	c.	c.	PROPN
ap-1352	193	11	:	:	PUNCT
ap-1352	193	12	topics	topic	NOUN
ap-1352	193	13	in	in	ADP
ap-1352	193	14	matrix	matrix	NOUN
ap-1352	193	15	analysis	analysis	NOUN
ap-1352	193	16	.	.	PUNCT
ap-1352	194	1	cambridge	cambridge	NOUN
ap-1352	194	2	:	:	PUNCT
ap-1352	194	3	cambridge	cambridge	PROPN
ap-1352	194	4	univ	univ	PROPN
ap-1352	194	5	.	.	PUNCT
ap-1352	195	1	press	press	PROPN
ap-1352	195	2	,	,	PUNCT
ap-1352	195	3	1991	1991	NUM
ap-1352	195	4	.	.	PUNCT
ap-1352	196	1	[	[	X
ap-1352	196	2	10	10	NUM
ap-1352	196	3	]	]	X
ap-1352	196	4	aktosun	aktosun	NOUN
ap-1352	196	5	,	,	PUNCT
ap-1352	196	6	t.	t.	PROPN
ap-1352	196	7	,	,	PUNCT
ap-1352	196	8	busse	busse	PROPN
ap-1352	196	9	,	,	PUNCT
ap-1352	196	10	t.	t.	PROPN
ap-1352	196	11	,	,	PUNCT
ap-1352	196	12	demontis	demontis	PROPN
ap-1352	196	13	,	,	PUNCT
ap-1352	196	14	f.	f.	PROPN
ap-1352	196	15	,	,	PUNCT
ap-1352	196	16	van	van	PROPN
ap-1352	196	17	der	der	PROPN
ap-1352	196	18	mee	mee	PROPN
ap-1352	196	19	,	,	PUNCT
ap-1352	196	20	c.	c.	PROPN
ap-1352	196	21	:	:	PUNCT
ap-1352	196	22	symmetries	symmetry	NOUN
ap-1352	196	23	for	for	ADP
ap-1352	196	24	exact	exact	ADJ
ap-1352	196	25	solutions	solution	NOUN
ap-1352	196	26	to	to	ADP
ap-1352	196	27	the	the	DET
ap-1352	196	28	nonlinear	nonlinear	ADJ
ap-1352	196	29	schrödinger	schrödinger	NOUN
ap-1352	196	30	equation	equation	NOUN
ap-1352	196	31	.	.	PUNCT
ap-1352	197	1	j.	j.	PROPN
ap-1352	197	2	phys	phys	PROPN
ap-1352	197	3	.	.	PUNCT
ap-1352	198	1	a	a	DET
ap-1352	198	2	:	:	PUNCT
ap-1352	198	3	theor	theor	PROPN
ap-1352	198	4	.	.	PUNCT
ap-1352	198	5	math	math	PROPN
ap-1352	198	6	.	.	PUNCT
ap-1352	198	7	,	,	PUNCT
ap-1352	198	8	43	43	NUM
ap-1352	198	9	,	,	PUNCT
ap-1352	198	10	2010	2010	NUM
ap-1352	198	11	,	,	PUNCT
ap-1352	198	12	025202	025202	NUM
ap-1352	198	13	.	.	PUNCT
ap-1352	199	1	[	[	X
ap-1352	199	2	11	11	NUM
ap-1352	199	3	]	]	SYM
ap-1352	199	4	hirota	hirota	PROPN
ap-1352	199	5	,	,	PUNCT
ap-1352	199	6	r.	r.	PROPN
ap-1352	199	7	:	:	PUNCT
ap-1352	199	8	exact	exact	ADJ
ap-1352	199	9	solution	solution	NOUN
ap-1352	199	10	of	of	ADP
ap-1352	199	11	the	the	DET
ap-1352	199	12	sine	sine	NOUN
ap-1352	199	13	-	-	PUNCT
ap-1352	199	14	gordon	gordon	NOUN
ap-1352	199	15	equation	equation	NOUN
ap-1352	199	16	for	for	ADP
ap-1352	199	17	multiple	multiple	ADJ
ap-1352	199	18	collisions	collision	NOUN
ap-1352	199	19	of	of	ADP
ap-1352	199	20	solitons	soliton	NOUN
ap-1352	199	21	.	.	PUNCT
ap-1352	200	1	j.	j.	PROPN
ap-1352	200	2	phys	phys	PROPN
ap-1352	200	3	.	.	PUNCT
ap-1352	201	1	soc	soc	PROPN
ap-1352	201	2	.	.	PUNCT
ap-1352	202	1	japan	japan	PROPN
ap-1352	202	2	,	,	PUNCT
ap-1352	202	3	33	33	NUM
ap-1352	202	4	,	,	PUNCT
ap-1352	202	5	1972	1972	NUM
ap-1352	202	6	,	,	PUNCT
ap-1352	202	7	p.	p.	NOUN
ap-1352	202	8	1	1	NUM
ap-1352	202	9	459–1	459–1	NUM
ap-1352	202	10	463	463	NUM
ap-1352	202	11	.	.	PUNCT
ap-1352	203	1	[	[	X
ap-1352	203	2	12	12	NUM
ap-1352	203	3	]	]	SYM
ap-1352	203	4	ablowitz	ablowitz	NOUN
ap-1352	203	5	,	,	PUNCT
ap-1352	203	6	m.	m.	NOUN
ap-1352	203	7	,	,	PUNCT
ap-1352	203	8	kaup	kaup	PROPN
ap-1352	203	9	,	,	PUNCT
ap-1352	203	10	d.	d.	PROPN
ap-1352	203	11	,	,	PUNCT
ap-1352	203	12	newell	newell	PROPN
ap-1352	203	13	,	,	PUNCT
ap-1352	203	14	a.	a.	PROPN
ap-1352	203	15	,	,	PUNCT
ap-1352	203	16	segur	segur	PROPN
ap-1352	203	17	,	,	PUNCT
ap-1352	203	18	h.	h.	NOUN
ap-1352	203	19	:	:	PUNCT
ap-1352	203	20	method	method	NOUN
ap-1352	203	21	for	for	ADP
ap-1352	203	22	solving	solve	VERB
ap-1352	203	23	the	the	DET
ap-1352	203	24	sine	sine	NOUN
ap-1352	203	25	-	-	PUNCT
ap-1352	203	26	gordon	gordon	PROPN
ap-1352	203	27	equation	equation	NOUN
ap-1352	203	28	.	.	PUNCT
ap-1352	204	1	phys	phy	NOUN
ap-1352	204	2	.	.	PUNCT
ap-1352	205	1	rev	rev	PROPN
ap-1352	205	2	.	.	PROPN
ap-1352	205	3	lett	lett	PROPN
ap-1352	205	4	.	.	PROPN
ap-1352	205	5	,	,	PUNCT
ap-1352	205	6	30	30	NUM
ap-1352	205	7	,	,	PUNCT
ap-1352	205	8	1973	1973	NUM
ap-1352	205	9	,	,	PUNCT
ap-1352	205	10	p.	p.	NOUN
ap-1352	205	11	1	1	NUM
ap-1352	205	12	262–1264	262–1264	NUM
ap-1352	205	13	.	.	PUNCT
ap-1352	206	1	[	[	X
ap-1352	206	2	13	13	NUM
ap-1352	206	3	]	]	SYM
ap-1352	206	4	pöppe	pöppe	PROPN
ap-1352	206	5	,	,	PUNCT
ap-1352	206	6	c.	c.	NOUN
ap-1352	206	7	:	:	PUNCT
ap-1352	206	8	construction	construction	NOUN
ap-1352	206	9	of	of	ADP
ap-1352	206	10	solutions	solution	NOUN
ap-1352	206	11	of	of	ADP
ap-1352	206	12	the	the	DET
ap-1352	206	13	sinegordon	sinegordon	ADJ
ap-1352	206	14	equation	equation	NOUN
ap-1352	206	15	by	by	ADP
ap-1352	206	16	means	mean	NOUN
ap-1352	206	17	of	of	ADP
ap-1352	206	18	fredholm	fredholm	NOUN
ap-1352	206	19	determinants	determinant	NOUN
ap-1352	206	20	.	.	PUNCT
ap-1352	207	1	physica	physica	PROPN
ap-1352	207	2	d	d	PROPN
ap-1352	207	3	,	,	PUNCT
ap-1352	207	4	9	9	NUM
ap-1352	207	5	,	,	PUNCT
ap-1352	207	6	1983	1983	NUM
ap-1352	207	7	,	,	PUNCT
ap-1352	207	8	p.	p.	NOUN
ap-1352	207	9	103–139	103–139	NUM
ap-1352	207	10	.	.	PUNCT
ap-1352	208	1	[	[	X
ap-1352	208	2	14	14	NUM
ap-1352	208	3	]	]	X
ap-1352	208	4	zheng	zheng	PROPN
ap-1352	208	5	,	,	PUNCT
ap-1352	208	6	w.	w.	PROPN
ap-1352	208	7	:	:	PUNCT
ap-1352	208	8	the	the	DET
ap-1352	208	9	sine	sine	ADJ
ap-1352	208	10	-	-	PUNCT
ap-1352	208	11	gordon	gordon	NOUN
ap-1352	208	12	equation	equation	NOUN
ap-1352	208	13	and	and	CCONJ
ap-1352	208	14	the	the	DET
ap-1352	208	15	trace	trace	NOUN
ap-1352	208	16	method	method	NOUN
ap-1352	208	17	.	.	PUNCT
ap-1352	209	1	j.	j.	PROPN
ap-1352	209	2	phys	phys	PROPN
ap-1352	209	3	.	.	PUNCT
ap-1352	210	1	a	a	DET
ap-1352	210	2	:	:	PUNCT
ap-1352	210	3	math	math	NOUN
ap-1352	210	4	.	.	PUNCT
ap-1352	211	1	gen	gen	PROPN
ap-1352	211	2	.	.	PROPN
ap-1352	211	3	,	,	PUNCT
ap-1352	211	4	19	19	NUM
ap-1352	211	5	,	,	PUNCT
ap-1352	211	6	1986	1986	NUM
ap-1352	211	7	,	,	PUNCT
ap-1352	211	8	p.	p.	NOUN
ap-1352	212	1	l485	l485	PROPN
ap-1352	212	2	–	–	PUNCT
ap-1352	212	3	l489	l489	PROPN
ap-1352	212	4	.	.	PUNCT
ap-1352	213	1	[	[	X
ap-1352	213	2	15	15	NUM
ap-1352	213	3	]	]	X
ap-1352	213	4	schiebold	schiebold	ADJ
ap-1352	213	5	,	,	PUNCT
ap-1352	213	6	c.	c.	NOUN
ap-1352	213	7	:	:	PUNCT
ap-1352	213	8	noncommutative	noncommutative	ADJ
ap-1352	213	9	akns	akns	NOUN
ap-1352	213	10	system	system	NOUN
ap-1352	213	11	and	and	CCONJ
ap-1352	213	12	multisoliton	multisoliton	NOUN
ap-1352	213	13	solutions	solution	NOUN
ap-1352	213	14	to	to	ADP
ap-1352	213	15	the	the	DET
ap-1352	213	16	matrix	matrix	NOUN
ap-1352	213	17	sinegordon	sinegordon	ADJ
ap-1352	213	18	equation	equation	NOUN
ap-1352	213	19	.	.	PUNCT
ap-1352	214	1	discr	discr	PROPN
ap-1352	214	2	.	.	PUNCT
ap-1352	215	1	cont	cont	PROPN
ap-1352	215	2	.	.	PUNCT
ap-1352	216	1	dyn	dyn	NOUN
ap-1352	216	2	.	.	PUNCT
ap-1352	217	1	systems	system	NOUN
ap-1352	217	2	suppl	suppl	PROPN
ap-1352	217	3	.	.	PROPN
ap-1352	217	4	,	,	PUNCT
ap-1352	217	5	2009	2009	NUM
ap-1352	217	6	,	,	PUNCT
ap-1352	217	7	2009	2009	NUM
ap-1352	217	8	,	,	PUNCT
ap-1352	217	9	p.	p.	NOUN
ap-1352	217	10	678–690	678–690	NUM
ap-1352	217	11	.	.	PUNCT
ap-1352	218	1	[	[	X
ap-1352	218	2	16	16	NUM
ap-1352	218	3	]	]	X
ap-1352	218	4	aktosun	aktosun	NOUN
ap-1352	218	5	,	,	PUNCT
ap-1352	218	6	t.	t.	PROPN
ap-1352	218	7	,	,	PUNCT
ap-1352	218	8	demontis	demontis	PROPN
ap-1352	218	9	,	,	PUNCT
ap-1352	218	10	f.	f.	PROPN
ap-1352	218	11	,	,	PUNCT
ap-1352	218	12	van	van	PROPN
ap-1352	218	13	der	der	PROPN
ap-1352	218	14	mee	mee	PROPN
ap-1352	218	15	,	,	PUNCT
ap-1352	218	16	c.	c.	NOUN
ap-1352	218	17	:	:	PUNCT
ap-1352	218	18	exact	exact	ADJ
ap-1352	218	19	solutions	solution	NOUN
ap-1352	218	20	to	to	ADP
ap-1352	218	21	the	the	DET
ap-1352	218	22	sine	sine	NOUN
ap-1352	218	23	-	-	PUNCT
ap-1352	218	24	gordon	gordon	PROPN
ap-1352	218	25	equation	equation	NOUN
ap-1352	218	26	.	.	PUNCT
ap-1352	219	1	arxiv:1003.2453	arxiv:1003.2453	NOUN
ap-1352	219	2	,	,	PUNCT
ap-1352	219	3	2010	2010	NUM
ap-1352	219	4	.	.	PUNCT
ap-1352	220	1	aristophanes	aristophane	NOUN
ap-1352	220	2	dimakis	dimaki	NOUN
ap-1352	220	3	e	e	NOUN
ap-1352	220	4	-	-	NOUN
ap-1352	220	5	mail	mail	NOUN
ap-1352	220	6	:	:	PUNCT
ap-1352	220	7	dimakis@aegean.gr	dimakis@aegean.gr	NOUN
ap-1352	220	8	department	department	NOUN
ap-1352	220	9	of	of	ADP
ap-1352	220	10	financial	financial	ADJ
ap-1352	220	11	and	and	CCONJ
ap-1352	220	12	management	management	NOUN
ap-1352	220	13	engineering	engineering	PROPN
ap-1352	220	14	university	university	PROPN
ap-1352	220	15	of	of	ADP
ap-1352	220	16	the	the	DET
ap-1352	220	17	aegean	aegean	PROPN
ap-1352	220	18	,	,	PUNCT
ap-1352	220	19	41	41	NUM
ap-1352	220	20	kountourioti	kountourioti	PROPN
ap-1352	220	21	str	str	PROPN
ap-1352	220	22	.	.	PUNCT
ap-1352	221	1	gr-82100	gr-82100	PROPN
ap-1352	221	2	chios	chios	PROPN
ap-1352	221	3	,	,	PUNCT
ap-1352	221	4	greece	greece	PROPN
ap-1352	221	5	nils	nils	PROPN
ap-1352	221	6	kanning	kanne	VERB
ap-1352	221	7	e	e	NOUN
ap-1352	221	8	-	-	NOUN
ap-1352	221	9	mail	mail	NOUN
ap-1352	221	10	:	:	PUNCT
ap-1352	221	11	nils.kanning@ds.mpg.de	nils.kanning@ds.mpg.de	ADV
ap-1352	221	12	max	max	PROPN
ap-1352	221	13	-	-	PUNCT
ap-1352	221	14	planck	planck	NOUN
ap-1352	221	15	-	-	PUNCT
ap-1352	221	16	institute	institute	NOUN
ap-1352	221	17	for	for	ADP
ap-1352	221	18	dynamics	dynamic	NOUN
ap-1352	221	19	and	and	CCONJ
ap-1352	221	20	self	self	NOUN
ap-1352	221	21	-	-	PUNCT
ap-1352	221	22	organization	organization	NOUN
ap-1352	221	23	bunsenstrasse	bunsenstrasse	NOUN
ap-1352	221	24	10	10	NUM
ap-1352	221	25	,	,	PUNCT
ap-1352	221	26	d-37073	d-37073	PROPN
ap-1352	221	27	göttingen	göttingen	PROPN
ap-1352	221	28	,	,	PUNCT
ap-1352	221	29	germany	germany	PROPN
ap-1352	221	30	folkert	folkert	PROPN
ap-1352	221	31	müller	müller	NOUN
ap-1352	221	32	-	-	PUNCT
ap-1352	221	33	hoissen	hoissen	ADJ
ap-1352	221	34	e	e	NOUN
ap-1352	221	35	-	-	NOUN
ap-1352	221	36	mail	mail	NOUN
ap-1352	221	37	:	:	PUNCT
ap-1352	221	38	folkert.mueller-hoissen@ds.mpg.de	folkert.mueller-hoissen@ds.mpg.de	NUM
ap-1352	221	39	max	max	PROPN
ap-1352	221	40	-	-	PUNCT
ap-1352	221	41	planck	planck	NOUN
ap-1352	221	42	-	-	PUNCT
ap-1352	221	43	institute	institute	NOUN
ap-1352	221	44	for	for	ADP
ap-1352	221	45	dynamics	dynamic	NOUN
ap-1352	221	46	and	and	CCONJ
ap-1352	221	47	self	self	NOUN
ap-1352	221	48	-	-	PUNCT
ap-1352	221	49	organization	organization	NOUN
ap-1352	221	50	bunsenstrasse	bunsenstrasse	NOUN
ap-1352	221	51	10	10	NUM
ap-1352	221	52	,	,	PUNCT
ap-1352	221	53	d-37073	d-37073	PROPN
ap-1352	221	54	göttingen	göttingen	PROPN
ap-1352	221	55	,	,	PUNCT
ap-1352	221	56	germany	germany	PROPN
ap-1352	221	57	37	37	NUM