id	sid	tid	token	lemma	pos
ejpam-1475	1	1	1_1163215_remsing.dvi	1_1163215_remsing.dvi	PROPN
ejpam-1475	1	2	european	european	PROPN
ejpam-1475	1	3	journal	journal	PROPN
ejpam-1475	1	4	of	of	ADP
ejpam-1475	1	5	pure	pure	ADJ
ejpam-1475	1	6	and	and	CCONJ
ejpam-1475	1	7	applied	apply	VERB
ejpam-1475	1	8	mathematics	mathematic	NOUN
ejpam-1475	1	9	vol	vol	NOUN
ejpam-1475	1	10	.	.	PROPN
ejpam-1475	1	11	5	5	NUM
ejpam-1475	1	12	,	,	PUNCT
ejpam-1475	1	13	no	no	INTJ
ejpam-1475	1	14	.	.	NOUN
ejpam-1475	1	15	1	1	NUM
ejpam-1475	1	16	,	,	PUNCT
ejpam-1475	1	17	2012	2012	NUM
ejpam-1475	1	18	,	,	PUNCT
ejpam-1475	1	19	1	1	NUM
ejpam-1475	1	20	-	-	SYM
ejpam-1475	1	21	15	15	NUM
ejpam-1475	1	22	issn	issn	PROPN
ejpam-1475	1	23	1307	1307	NUM
ejpam-1475	1	24	-	-	SYM
ejpam-1475	1	25	5543	5543	NUM
ejpam-1475	1	26	–	–	PUNCT
ejpam-1475	1	27	www.ejpam.com	www.ejpam.com	X
ejpam-1475	1	28	special	special	ADJ
ejpam-1475	1	29	issue	issue	NOUN
ejpam-1475	1	30	for	for	ADP
ejpam-1475	1	31	the	the	DET
ejpam-1475	1	32	international	international	ADJ
ejpam-1475	1	33	conference	conference	NOUN
ejpam-1475	1	34	on	on	ADP
ejpam-1475	1	35	applied	apply	VERB
ejpam-1475	1	36	analysis	analysis	NOUN
ejpam-1475	1	37	and	and	CCONJ
ejpam-1475	1	38	algebra	algebra	NOUN
ejpam-1475	1	39	29	29	NUM
ejpam-1475	1	40	june	june	PROPN
ejpam-1475	1	41	02	02	NUM
ejpam-1475	1	42	july	july	PROPN
ejpam-1475	1	43	2011	2011	NUM
ejpam-1475	1	44	,	,	PUNCT
ejpam-1475	1	45	istanbul	istanbul	PROPN
ejpam-1475	1	46	turkey	turkey	PROPN
ejpam-1475	1	47	single	single	ADJ
ejpam-1475	1	48	-	-	PUNCT
ejpam-1475	1	49	input	input	NOUN
ejpam-1475	1	50	control	control	NOUN
ejpam-1475	1	51	systems	system	NOUN
ejpam-1475	1	52	on	on	ADP
ejpam-1475	1	53	the	the	DET
ejpam-1475	1	54	euclidean	euclidean	ADJ
ejpam-1475	1	55	group	group	NOUN
ejpam-1475	1	56	se(2	se(2	PROPN
ejpam-1475	1	57	)	)	PUNCT
ejpam-1475	1	58	ross	ross	PROPN
ejpam-1475	1	59	m.	m.	PROPN
ejpam-1475	1	60	adams	adams	PROPN
ejpam-1475	1	61	,	,	PUNCT
ejpam-1475	1	62	rory	rory	PROPN
ejpam-1475	1	63	biggs	biggs	PROPN
ejpam-1475	1	64	,	,	PUNCT
ejpam-1475	1	65	claudiu	claudiu	ADJ
ejpam-1475	1	66	c.	c.	PROPN
ejpam-1475	1	67	remsing∗	remsing∗	NOUN
ejpam-1475	1	68	department	department	PROPN
ejpam-1475	1	69	of	of	ADP
ejpam-1475	1	70	mathematics	mathematics	PROPN
ejpam-1475	1	71	(	(	PUNCT
ejpam-1475	1	72	pure	pure	ADJ
ejpam-1475	1	73	and	and	CCONJ
ejpam-1475	1	74	applied	apply	VERB
ejpam-1475	1	75	)	)	PUNCT
ejpam-1475	1	76	,	,	PUNCT
ejpam-1475	1	77	rhodes	rhode	VERB
ejpam-1475	1	78	university	university	PROPN
ejpam-1475	1	79	,	,	PUNCT
ejpam-1475	1	80	grahamstown	grahamstown	ADJ
ejpam-1475	1	81	6140	6140	NUM
ejpam-1475	1	82	,	,	PUNCT
ejpam-1475	1	83	south	south	PROPN
ejpam-1475	1	84	africa	africa	PROPN
ejpam-1475	1	85	abstract	abstract	PROPN
ejpam-1475	1	86	.	.	PUNCT
ejpam-1475	2	1	we	we	PRON
ejpam-1475	2	2	consider	consider	VERB
ejpam-1475	2	3	a	a	DET
ejpam-1475	2	4	general	general	ADJ
ejpam-1475	2	5	single	single	ADJ
ejpam-1475	2	6	-	-	PUNCT
ejpam-1475	2	7	input	input	NOUN
ejpam-1475	2	8	left	left	ADJ
ejpam-1475	2	9	-	-	PUNCT
ejpam-1475	2	10	invariant	invariant	ADJ
ejpam-1475	2	11	control	control	NOUN
ejpam-1475	2	12	affine	affine	NOUN
ejpam-1475	2	13	system	system	NOUN
ejpam-1475	2	14	,	,	PUNCT
ejpam-1475	2	15	evolving	evolve	VERB
ejpam-1475	2	16	on	on	ADP
ejpam-1475	2	17	the	the	DET
ejpam-1475	2	18	euclidean	euclidean	ADJ
ejpam-1475	2	19	group	group	NOUN
ejpam-1475	2	20	se(2	se(2	PROPN
ejpam-1475	2	21	)	)	PUNCT
ejpam-1475	2	22	.	.	PUNCT
ejpam-1475	3	1	any	any	DET
ejpam-1475	3	2	such	such	ADJ
ejpam-1475	3	3	controllable	controllable	ADJ
ejpam-1475	3	4	control	control	NOUN
ejpam-1475	3	5	system	system	NOUN
ejpam-1475	3	6	is	be	AUX
ejpam-1475	3	7	(	(	PUNCT
ejpam-1475	3	8	detached	detached	ADJ
ejpam-1475	3	9	feedback	feedback	NOUN
ejpam-1475	3	10	)	)	PUNCT
ejpam-1475	3	11	equivalent	equivalent	ADJ
ejpam-1475	3	12	to	to	ADP
ejpam-1475	3	13	one	one	NUM
ejpam-1475	3	14	of	of	ADP
ejpam-1475	3	15	two	two	NUM
ejpam-1475	3	16	typical	typical	ADJ
ejpam-1475	3	17	cases	case	NOUN
ejpam-1475	3	18	.	.	PUNCT
ejpam-1475	4	1	in	in	ADP
ejpam-1475	4	2	each	each	DET
ejpam-1475	4	3	case	case	NOUN
ejpam-1475	4	4	,	,	PUNCT
ejpam-1475	4	5	we	we	PRON
ejpam-1475	4	6	consider	consider	VERB
ejpam-1475	4	7	an	an	DET
ejpam-1475	4	8	optimal	optimal	ADJ
ejpam-1475	4	9	control	control	NOUN
ejpam-1475	4	10	problem	problem	NOUN
ejpam-1475	4	11	(	(	PUNCT
ejpam-1475	4	12	with	with	ADP
ejpam-1475	4	13	quadratic	quadratic	ADJ
ejpam-1475	4	14	cost	cost	NOUN
ejpam-1475	4	15	)	)	PUNCT
ejpam-1475	4	16	which	which	PRON
ejpam-1475	4	17	is	be	AUX
ejpam-1475	4	18	then	then	ADV
ejpam-1475	4	19	lifted	lift	VERB
ejpam-1475	4	20	,	,	PUNCT
ejpam-1475	4	21	via	via	ADP
ejpam-1475	4	22	the	the	DET
ejpam-1475	4	23	pontryagin	pontryagin	NOUN
ejpam-1475	4	24	maximum	maximum	PROPN
ejpam-1475	4	25	principle	principle	NOUN
ejpam-1475	4	26	,	,	PUNCT
ejpam-1475	4	27	to	to	ADP
ejpam-1475	4	28	a	a	DET
ejpam-1475	4	29	hamiltonian	hamiltonian	ADJ
ejpam-1475	4	30	system	system	NOUN
ejpam-1475	4	31	on	on	ADP
ejpam-1475	4	32	the	the	DET
ejpam-1475	4	33	dual	dual	ADJ
ejpam-1475	4	34	space	space	NOUN
ejpam-1475	4	35	se(2)∗.	se(2)∗.	NOUN
ejpam-1475	4	36	the	the	DET
ejpam-1475	4	37	reduced	reduce	VERB
ejpam-1475	4	38	hamilton	hamilton	PROPN
ejpam-1475	4	39	equations	equation	NOUN
ejpam-1475	4	40	are	be	AUX
ejpam-1475	4	41	derived	derive	VERB
ejpam-1475	4	42	and	and	CCONJ
ejpam-1475	4	43	the	the	DET
ejpam-1475	4	44	stability	stability	NOUN
ejpam-1475	4	45	nature	nature	NOUN
ejpam-1475	4	46	of	of	ADP
ejpam-1475	4	47	all	all	DET
ejpam-1475	4	48	equilibrium	equilibrium	NOUN
ejpam-1475	4	49	states	state	NOUN
ejpam-1475	4	50	is	be	AUX
ejpam-1475	4	51	then	then	ADV
ejpam-1475	4	52	investigated	investigate	VERB
ejpam-1475	4	53	.	.	PUNCT
ejpam-1475	5	1	finally	finally	ADV
ejpam-1475	5	2	,	,	PUNCT
ejpam-1475	5	3	these	these	DET
ejpam-1475	5	4	equations	equation	NOUN
ejpam-1475	5	5	are	be	AUX
ejpam-1475	5	6	explicitly	explicitly	ADV
ejpam-1475	5	7	integrated	integrate	VERB
ejpam-1475	5	8	by	by	ADP
ejpam-1475	5	9	elliptic	elliptic	ADJ
ejpam-1475	5	10	functions	function	NOUN
ejpam-1475	5	11	.	.	PUNCT
ejpam-1475	6	1	2000	2000	NUM
ejpam-1475	6	2	mathematics	mathematic	NOUN
ejpam-1475	6	3	subject	subject	NOUN
ejpam-1475	6	4	classifications	classification	NOUN
ejpam-1475	6	5	:	:	PUNCT
ejpam-1475	6	6	49j15	49j15	NUM
ejpam-1475	6	7	,	,	PUNCT
ejpam-1475	6	8	93d05	93d05	NUM
ejpam-1475	6	9	,	,	PUNCT
ejpam-1475	6	10	22e60	22e60	NUM
ejpam-1475	6	11	,	,	PUNCT
ejpam-1475	6	12	53d17	53d17	NUM
ejpam-1475	6	13	key	key	ADJ
ejpam-1475	6	14	words	word	NOUN
ejpam-1475	6	15	and	and	CCONJ
ejpam-1475	6	16	phrases	phrase	NOUN
ejpam-1475	6	17	:	:	PUNCT
ejpam-1475	6	18	left	left	ADJ
ejpam-1475	6	19	-	-	PUNCT
ejpam-1475	6	20	invariant	invariant	ADJ
ejpam-1475	6	21	control	control	NOUN
ejpam-1475	6	22	system	system	NOUN
ejpam-1475	6	23	,	,	PUNCT
ejpam-1475	6	24	(	(	PUNCT
ejpam-1475	6	25	detached	detached	ADJ
ejpam-1475	6	26	)	)	PUNCT
ejpam-1475	6	27	feedback	feedback	NOUN
ejpam-1475	6	28	equivalence	equivalence	NOUN
ejpam-1475	6	29	,	,	PUNCT
ejpam-1475	6	30	lie	lie	NOUN
ejpam-1475	6	31	-	-	PUNCT
ejpam-1475	6	32	poisson	poisson	NOUN
ejpam-1475	6	33	structure	structure	NOUN
ejpam-1475	6	34	,	,	PUNCT
ejpam-1475	6	35	elliptic	elliptic	ADJ
ejpam-1475	6	36	function	function	NOUN
ejpam-1475	6	37	,	,	PUNCT
ejpam-1475	6	38	lyapunov	lyapunov	NOUN
ejpam-1475	6	39	stability	stability	NOUN
ejpam-1475	6	40	1	1	NUM
ejpam-1475	6	41	.	.	PUNCT
ejpam-1475	7	1	introduction	introduction	NOUN
ejpam-1475	7	2	in	in	ADP
ejpam-1475	7	3	recent	recent	ADJ
ejpam-1475	7	4	decades	decade	NOUN
ejpam-1475	7	5	,	,	PUNCT
ejpam-1475	7	6	attention	attention	NOUN
ejpam-1475	7	7	has	have	AUX
ejpam-1475	7	8	been	be	AUX
ejpam-1475	7	9	drawn	draw	VERB
ejpam-1475	7	10	to	to	ADP
ejpam-1475	7	11	invariant	invariant	VERB
ejpam-1475	7	12	control	control	NOUN
ejpam-1475	7	13	systems	system	NOUN
ejpam-1475	7	14	evolving	evolve	VERB
ejpam-1475	7	15	on	on	ADP
ejpam-1475	7	16	matrix	matrix	NOUN
ejpam-1475	7	17	lie	lie	NOUN
ejpam-1475	7	18	groups	group	NOUN
ejpam-1475	7	19	of	of	ADP
ejpam-1475	7	20	low	low	ADJ
ejpam-1475	7	21	dimension	dimension	NOUN
ejpam-1475	7	22	.	.	PUNCT
ejpam-1475	8	1	such	such	ADJ
ejpam-1475	8	2	systems	system	NOUN
ejpam-1475	8	3	arise	arise	VERB
ejpam-1475	8	4	,	,	PUNCT
ejpam-1475	8	5	for	for	ADP
ejpam-1475	8	6	instance	instance	NOUN
ejpam-1475	8	7	,	,	PUNCT
ejpam-1475	8	8	in	in	ADP
ejpam-1475	8	9	the	the	DET
ejpam-1475	8	10	airplane	airplane	NOUN
ejpam-1475	8	11	landing	landing	NOUN
ejpam-1475	8	12	problem	problem	NOUN
ejpam-1475	8	13	,	,	PUNCT
ejpam-1475	8	14	the	the	DET
ejpam-1475	8	15	motion	motion	NOUN
ejpam-1475	8	16	planning	planning	NOUN
ejpam-1475	8	17	for	for	ADP
ejpam-1475	8	18	wheeled	wheeled	ADJ
ejpam-1475	8	19	robots	robot	NOUN
ejpam-1475	8	20	,	,	PUNCT
ejpam-1475	8	21	and	and	CCONJ
ejpam-1475	8	22	the	the	DET
ejpam-1475	8	23	control	control	NOUN
ejpam-1475	8	24	of	of	ADP
ejpam-1475	8	25	underactuated	underactuated	ADJ
ejpam-1475	8	26	underwater	underwater	ADJ
ejpam-1475	8	27	vehicles	vehicle	NOUN
ejpam-1475	8	28	(	(	PUNCT
ejpam-1475	8	29	see	see	VERB
ejpam-1475	8	30	,	,	PUNCT
ejpam-1475	8	31	e.g.	e.g.	ADV
ejpam-1475	8	32	,	,	PUNCT
ejpam-1475	8	33	[	[	X
ejpam-1475	8	34	31	31	NUM
ejpam-1475	8	35	,	,	PUNCT
ejpam-1475	8	36	21	21	NUM
ejpam-1475	8	37	,	,	PUNCT
ejpam-1475	8	38	20	20	NUM
ejpam-1475	8	39	,	,	PUNCT
ejpam-1475	8	40	22	22	NUM
ejpam-1475	8	41	,	,	PUNCT
ejpam-1475	8	42	15	15	NUM
ejpam-1475	8	43	]	]	PUNCT
ejpam-1475	8	44	and	and	CCONJ
ejpam-1475	8	45	the	the	DET
ejpam-1475	8	46	references	reference	NOUN
ejpam-1475	8	47	therein	therein	ADV
ejpam-1475	8	48	)	)	PUNCT
ejpam-1475	8	49	.	.	PUNCT
ejpam-1475	9	1	an	an	DET
ejpam-1475	9	2	arbitrary	arbitrary	ADJ
ejpam-1475	9	3	left	left	ADJ
ejpam-1475	9	4	-	-	PUNCT
ejpam-1475	9	5	invariant	invariant	ADJ
ejpam-1475	9	6	control	control	NOUN
ejpam-1475	9	7	affine	affine	NOUN
ejpam-1475	9	8	system	system	NOUN
ejpam-1475	9	9	on	on	ADP
ejpam-1475	9	10	the	the	DET
ejpam-1475	9	11	euclidean	euclidean	ADJ
ejpam-1475	9	12	group	group	NOUN
ejpam-1475	9	13	se(2	se(2	PROPN
ejpam-1475	9	14	)	)	PUNCT
ejpam-1475	9	15	has	have	VERB
ejpam-1475	9	16	the	the	DET
ejpam-1475	9	17	form	form	NOUN
ejpam-1475	9	18	ġ	ġ	NOUN
ejpam-1475	9	19	=	=	PUNCT
ejpam-1475	9	20	g	g	PROPN
ejpam-1475	9	21	�	�	PROPN
ejpam-1475	9	22	a+	a+	PUNCT
ejpam-1475	9	23	u1b1	u1b1	X
ejpam-1475	9	24	+	+	CCONJ
ejpam-1475	9	25	·	·	PUNCT
ejpam-1475	9	26	·	·	PUNCT
ejpam-1475	9	27	·	·	PUNCT
ejpam-1475	9	28	+	+	NUM
ejpam-1475	9	29	uℓbℓ	uℓbℓ	ADJ
ejpam-1475	9	30	�	�	PROPN
ejpam-1475	9	31	,	,	PUNCT
ejpam-1475	9	32	where	where	SCONJ
ejpam-1475	9	33	a	a	PRON
ejpam-1475	9	34	,	,	PUNCT
ejpam-1475	9	35	b1	b1	NOUN
ejpam-1475	9	36	,	,	PUNCT
ejpam-1475	9	37	.	.	PUNCT
ejpam-1475	9	38	.	.	PUNCT
ejpam-1475	10	1	.	.	PUNCT
ejpam-1475	11	1	,	,	PUNCT
ejpam-1475	11	2	bℓ	bℓ	PROPN
ejpam-1475	11	3	∈	∈	PROPN
ejpam-1475	11	4	se(2	se(2	PROPN
ejpam-1475	11	5	)	)	PUNCT
ejpam-1475	11	6	,	,	PUNCT
ejpam-1475	11	7	1	1	NUM
ejpam-1475	11	8	≤	≤	NUM
ejpam-1475	11	9	ℓ	ℓ	NOUN
ejpam-1475	11	10	≤	≤	NOUN
ejpam-1475	11	11	3	3	NUM
ejpam-1475	11	12	.	.	PUNCT
ejpam-1475	12	1	(	(	PUNCT
ejpam-1475	12	2	the	the	DET
ejpam-1475	12	3	elements	element	NOUN
ejpam-1475	12	4	b1	b1	VERB
ejpam-1475	12	5	,	,	PUNCT
ejpam-1475	12	6	.	.	PUNCT
ejpam-1475	12	7	.	.	PUNCT
ejpam-1475	13	1	.	.	PUNCT
ejpam-1475	14	1	,	,	PUNCT
ejpam-1475	14	2	bℓ	bℓ	PROPN
ejpam-1475	14	3	are	be	AUX
ejpam-1475	14	4	assumed	assume	VERB
ejpam-1475	14	5	to	to	PART
ejpam-1475	14	6	be	be	AUX
ejpam-1475	14	7	linearly	linearly	ADV
ejpam-1475	14	8	independent	independent	ADJ
ejpam-1475	14	9	.	.	PUNCT
ejpam-1475	14	10	)	)	PUNCT
ejpam-1475	15	1	specific	specific	ADJ
ejpam-1475	15	2	(	(	PUNCT
ejpam-1475	15	3	left	left	ADJ
ejpam-1475	15	4	-	-	PUNCT
ejpam-1475	15	5	invariant	invariant	ADJ
ejpam-1475	15	6	)	)	PUNCT
ejpam-1475	15	7	optimal	optimal	ADJ
ejpam-1475	15	8	control	control	NOUN
ejpam-1475	15	9	problems	problem	NOUN
ejpam-1475	15	10	on	on	ADP
ejpam-1475	15	11	the	the	DET
ejpam-1475	15	12	euclidean	euclidean	ADJ
ejpam-1475	15	13	group	group	NOUN
ejpam-1475	15	14	se(2	se(2	PROPN
ejpam-1475	15	15	)	)	PUNCT
ejpam-1475	15	16	,	,	PUNCT
ejpam-1475	15	17	associated	associate	VERB
ejpam-1475	15	18	with	with	ADP
ejpam-1475	15	19	above	above	ADP
ejpam-1475	15	20	mentioned	mention	VERB
ejpam-1475	15	21	control	control	NOUN
ejpam-1475	15	22	systems	system	NOUN
ejpam-1475	15	23	,	,	PUNCT
ejpam-1475	15	24	have	have	AUX
ejpam-1475	15	25	been	be	AUX
ejpam-1475	15	26	studied	study	VERB
ejpam-1475	15	27	by	by	ADP
ejpam-1475	15	28	several	several	ADJ
ejpam-1475	15	29	authors	author	NOUN
ejpam-1475	15	30	(	(	PUNCT
ejpam-1475	15	31	see	see	VERB
ejpam-1475	15	32	,	,	PUNCT
ejpam-1475	15	33	e.g.	e.g.	ADV
ejpam-1475	15	34	,	,	PUNCT
ejpam-1475	15	35	[	[	X
ejpam-1475	15	36	11	11	NUM
ejpam-1475	15	37	,	,	PUNCT
ejpam-1475	15	38	10	10	NUM
ejpam-1475	15	39	,	,	PUNCT
ejpam-1475	15	40	29	29	NUM
ejpam-1475	15	41	,	,	PUNCT
ejpam-1475	15	42	24	24	NUM
ejpam-1475	15	43	,	,	PUNCT
ejpam-1475	15	44	23	23	NUM
ejpam-1475	15	45	,	,	PUNCT
ejpam-1475	15	46	28	28	NUM
ejpam-1475	15	47	]	]	PUNCT
ejpam-1475	15	48	)	)	PUNCT
ejpam-1475	15	49	.	.	PUNCT
ejpam-1475	16	1	in	in	ADP
ejpam-1475	16	2	this	this	DET
ejpam-1475	16	3	paper	paper	NOUN
ejpam-1475	16	4	,	,	PUNCT
ejpam-1475	16	5	we	we	PRON
ejpam-1475	16	6	consider	consider	VERB
ejpam-1475	16	7	only	only	ADV
ejpam-1475	16	8	single	single	ADJ
ejpam-1475	16	9	-	-	PUNCT
ejpam-1475	16	10	input	input	NOUN
ejpam-1475	16	11	control	control	NOUN
ejpam-1475	16	12	systems	system	NOUN
ejpam-1475	16	13	(	(	PUNCT
ejpam-1475	16	14	i.e.	i.e.	X
ejpam-1475	16	15	,	,	PUNCT
ejpam-1475	16	16	systems	system	NOUN
ejpam-1475	16	17	of	of	ADP
ejpam-1475	16	18	the	the	DET
ejpam-1475	16	19	form	form	NOUN
ejpam-1475	16	20	ġ	ġ	NOUN
ejpam-1475	16	21	=	=	NOUN
ejpam-1475	16	22	g	g	PROPN
ejpam-1475	16	23	(	(	PUNCT
ejpam-1475	16	24	a+	a+	PUNCT
ejpam-1475	16	25	ub	ub	ADJ
ejpam-1475	16	26	)	)	PUNCT
ejpam-1475	16	27	)	)	PUNCT
ejpam-1475	16	28	.	.	PUNCT
ejpam-1475	17	1	such	such	DET
ejpam-1475	17	2	a	a	DET
ejpam-1475	17	3	system	system	NOUN
ejpam-1475	17	4	is	be	AUX
ejpam-1475	17	5	controllable	controllable	ADJ
ejpam-1475	17	6	if	if	SCONJ
ejpam-1475	17	7	and	and	CCONJ
ejpam-1475	17	8	only	only	ADV
ejpam-1475	17	9	if	if	SCONJ
ejpam-1475	17	10	it	it	PRON
ejpam-1475	17	11	has	have	VERB
ejpam-1475	17	12	full	full	ADJ
ejpam-1475	17	13	rank	rank	NOUN
ejpam-1475	17	14	.	.	PUNCT
ejpam-1475	18	1	moreover	moreover	ADV
ejpam-1475	18	2	,	,	PUNCT
ejpam-1475	18	3	∗corresponding	∗corresponde	VERB
ejpam-1475	18	4	author	author	NOUN
ejpam-1475	18	5	.	.	PUNCT
ejpam-1475	19	1	email	email	NOUN
ejpam-1475	19	2	addresses	address	NOUN
ejpam-1475	19	3	:	:	PUNCT
ejpam-1475	19	4	dros	dros	PROPN
ejpam-1475	19	5	�	�	PROPN
ejpam-1475	19	6	webmail	webmail	NOUN
ejpam-1475	19	7	.	.	PUNCT
ejpam-1475	20	1	o.za	o.za	PROPN
ejpam-1475	20	2	(	(	PUNCT
ejpam-1475	20	3	r.	r.	PROPN
ejpam-1475	20	4	adams	adams	PROPN
ejpam-1475	20	5	)	)	PUNCT
ejpam-1475	20	6	,	,	PUNCT
ejpam-1475	20	7	rorybiggs	rorybigg	NOUN
ejpam-1475	20	8	�	�	NOUN
ejpam-1475	20	9	gmail	gmail	NOUN
ejpam-1475	20	10	.	.	PUNCT
ejpam-1475	21	1	om	om	PROPN
ejpam-1475	21	2	(	(	PUNCT
ejpam-1475	21	3	r.	r.	PROPN
ejpam-1475	21	4	biggs	biggs	PROPN
ejpam-1475	21	5	)	)	PUNCT
ejpam-1475	21	6	,	,	PUNCT
ejpam-1475	21	7	.	.	PUNCT
ejpam-1475	22	1	.remsing	.remse	VERB
ejpam-1475	22	2	�	�	PROPN
ejpam-1475	22	3	ru.a	ru.a	PROPN
ejpam-1475	22	4	.za	.za	PUNCT
ejpam-1475	23	1	(	(	PUNCT
ejpam-1475	23	2	c.	c.	NOUN
ejpam-1475	23	3	remsing	remsing	NOUN
ejpam-1475	23	4	)	)	PUNCT
ejpam-1475	23	5	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-1475	24	1	1	1	NUM
ejpam-1475	24	2	c	c	X
ejpam-1475	24	3	©	©	PROPN
ejpam-1475	24	4	2012	2012	NUM
ejpam-1475	24	5	ejpam	ejpam	VERB
ejpam-1475	24	6	all	all	DET
ejpam-1475	24	7	rights	right	NOUN
ejpam-1475	24	8	reserved	reserve	VERB
ejpam-1475	24	9	.	.	PUNCT
ejpam-1475	25	1	r.	r.	PROPN
ejpam-1475	25	2	adams	adams	PROPN
ejpam-1475	25	3	,	,	PUNCT
ejpam-1475	25	4	r.	r.	PROPN
ejpam-1475	25	5	biggs	biggs	PROPN
ejpam-1475	25	6	,	,	PUNCT
ejpam-1475	25	7	c.	c.	PROPN
ejpam-1475	25	8	remsing	remsing	NOUN
ejpam-1475	25	9	/	/	SYM
ejpam-1475	25	10	eur	eur	NOUN
ejpam-1475	25	11	.	.	PUNCT
ejpam-1475	26	1	j.	j.	PROPN
ejpam-1475	26	2	pure	pure	PROPN
ejpam-1475	26	3	appl	appl	PROPN
ejpam-1475	26	4	.	.	PROPN
ejpam-1475	26	5	math	math	PROPN
ejpam-1475	26	6	,	,	PUNCT
ejpam-1475	26	7	5	5	NUM
ejpam-1475	26	8	(	(	PUNCT
ejpam-1475	26	9	2012	2012	NUM
ejpam-1475	26	10	)	)	PUNCT
ejpam-1475	26	11	,	,	PUNCT
ejpam-1475	26	12	1	1	NUM
ejpam-1475	26	13	-	-	SYM
ejpam-1475	26	14	15	15	NUM
ejpam-1475	26	15	2	2	NUM
ejpam-1475	26	16	any	any	DET
ejpam-1475	26	17	such	such	ADJ
ejpam-1475	26	18	controllable	controllable	ADJ
ejpam-1475	26	19	control	control	NOUN
ejpam-1475	26	20	system	system	NOUN
ejpam-1475	26	21	is	be	AUX
ejpam-1475	26	22	(	(	PUNCT
ejpam-1475	26	23	detached	detached	ADJ
ejpam-1475	26	24	feedback	feedback	NOUN
ejpam-1475	26	25	)	)	PUNCT
ejpam-1475	26	26	equivalent	equivalent	ADJ
ejpam-1475	26	27	to	to	ADP
ejpam-1475	26	28	exactly	exactly	ADV
ejpam-1475	26	29	one	one	NUM
ejpam-1475	26	30	of	of	ADP
ejpam-1475	26	31	the	the	DET
ejpam-1475	26	32	following	follow	VERB
ejpam-1475	26	33	control	control	NOUN
ejpam-1475	26	34	systems	system	NOUN
ejpam-1475	26	35	:	:	PUNCT
ejpam-1475	26	36	σ1	σ1	NOUN
ejpam-1475	26	37	or	or	CCONJ
ejpam-1475	26	38	σ2,α	σ2,α	PROPN
ejpam-1475	26	39	(	(	PUNCT
ejpam-1475	26	40	α	α	NOUN
ejpam-1475	26	41	>	>	X
ejpam-1475	26	42	0	0	NUM
ejpam-1475	26	43	)	)	PUNCT
ejpam-1475	26	44	with	with	ADP
ejpam-1475	26	45	trace	trace	NOUN
ejpam-1475	26	46	γ1	γ1	NOUN
ejpam-1475	26	47	=	=	SYM
ejpam-1475	26	48	e1	e1	PROPN
ejpam-1475	26	49	+	+	CCONJ
ejpam-1475	26	50	〈	〈	NOUN
ejpam-1475	26	51	e3	e3	NOUN
ejpam-1475	26	52	〉	〉	NOUN
ejpam-1475	26	53	or	or	CCONJ
ejpam-1475	26	54	γ2,α	γ2,α	PROPN
ejpam-1475	26	55	=	=	SYM
ejpam-1475	26	56	αe3	αe3	PROPN
ejpam-1475	26	57	+	+	CCONJ
ejpam-1475	26	58	〈	〈	PROPN
ejpam-1475	26	59	e1	e1	NOUN
ejpam-1475	26	60	〉	〉	NOUN
ejpam-1475	26	61	,	,	PUNCT
ejpam-1475	26	62	respectively	respectively	ADV
ejpam-1475	26	63	.	.	PUNCT
ejpam-1475	27	1	(	(	PUNCT
ejpam-1475	27	2	here	here	ADV
ejpam-1475	27	3	e1	e1	PROPN
ejpam-1475	27	4	and	and	CCONJ
ejpam-1475	27	5	e3	e3	NOUN
ejpam-1475	27	6	denote	denote	NOUN
ejpam-1475	27	7	elements	element	NOUN
ejpam-1475	27	8	of	of	ADP
ejpam-1475	27	9	the	the	DET
ejpam-1475	27	10	standard	standard	ADJ
ejpam-1475	27	11	basis	basis	NOUN
ejpam-1475	27	12	for	for	ADP
ejpam-1475	27	13	se(2	se(2	NOUN
ejpam-1475	27	14	)	)	PUNCT
ejpam-1475	27	15	.	.	PUNCT
ejpam-1475	27	16	)	)	PUNCT
ejpam-1475	28	1	in	in	ADP
ejpam-1475	28	2	each	each	DET
ejpam-1475	28	3	typical	typical	ADJ
ejpam-1475	28	4	case	case	NOUN
ejpam-1475	28	5	,	,	PUNCT
ejpam-1475	28	6	we	we	PRON
ejpam-1475	28	7	consider	consider	VERB
ejpam-1475	28	8	an	an	DET
ejpam-1475	28	9	optimal	optimal	ADJ
ejpam-1475	28	10	control	control	NOUN
ejpam-1475	28	11	problem	problem	NOUN
ejpam-1475	28	12	(	(	PUNCT
ejpam-1475	28	13	with	with	ADP
ejpam-1475	28	14	quadratic	quadratic	ADJ
ejpam-1475	28	15	cost	cost	NOUN
ejpam-1475	28	16	)	)	PUNCT
ejpam-1475	28	17	of	of	ADP
ejpam-1475	28	18	the	the	DET
ejpam-1475	28	19	form	form	NOUN
ejpam-1475	28	20	ġ	ġ	NOUN
ejpam-1475	28	21	=	=	NOUN
ejpam-1475	28	22	g	g	PROPN
ejpam-1475	28	23	(	(	PUNCT
ejpam-1475	28	24	a+	a+	PUNCT
ejpam-1475	28	25	ub	ub	PROPN
ejpam-1475	28	26	)	)	PUNCT
ejpam-1475	28	27	,	,	PUNCT
ejpam-1475	28	28	g	g	PROPN
ejpam-1475	28	29	∈	∈	PROPN
ejpam-1475	28	30	se(2	se(2	PROPN
ejpam-1475	28	31	)	)	PUNCT
ejpam-1475	28	32	,	,	PUNCT
ejpam-1475	28	33	u	u	PROPN
ejpam-1475	28	34	∈	∈	PROPN
ejpam-1475	28	35	r	r	NOUN
ejpam-1475	28	36	g(0	g(0	PROPN
ejpam-1475	28	37	)	)	PUNCT
ejpam-1475	28	38	=	=	SYM
ejpam-1475	28	39	g0	g0	PROPN
ejpam-1475	28	40	,	,	PUNCT
ejpam-1475	28	41	g(t	g(t	PROPN
ejpam-1475	28	42	)	)	PUNCT
ejpam-1475	29	1	=	=	PUNCT
ejpam-1475	30	1	gt	gt	PROPN
ejpam-1475	30	2	j	j	NOUN
ejpam-1475	31	1	=	=	NOUN
ejpam-1475	31	2	1	1	NUM
ejpam-1475	31	3	2	2	NUM
ejpam-1475	31	4	∫	∫	NOUN
ejpam-1475	31	5	t	t	NOUN
ejpam-1475	31	6	0	0	NUM
ejpam-1475	31	7	u2(t)d	u2(t)d	PROPN
ejpam-1475	31	8	t	t	X
ejpam-1475	31	9	→min	→min	PROPN
ejpam-1475	31	10	.	.	PUNCT
ejpam-1475	32	1	each	each	DET
ejpam-1475	32	2	problem	problem	NOUN
ejpam-1475	32	3	is	be	AUX
ejpam-1475	32	4	lifted	lift	VERB
ejpam-1475	32	5	,	,	PUNCT
ejpam-1475	32	6	via	via	ADP
ejpam-1475	32	7	the	the	DET
ejpam-1475	32	8	pontryagin	pontryagin	NOUN
ejpam-1475	32	9	maximum	maximum	PROPN
ejpam-1475	32	10	principle	principle	NOUN
ejpam-1475	32	11	,	,	PUNCT
ejpam-1475	32	12	to	to	ADP
ejpam-1475	32	13	a	a	DET
ejpam-1475	32	14	hamiltonian	hamiltonian	ADJ
ejpam-1475	32	15	system	system	NOUN
ejpam-1475	32	16	on	on	ADP
ejpam-1475	32	17	the	the	DET
ejpam-1475	32	18	dual	dual	ADJ
ejpam-1475	32	19	of	of	ADP
ejpam-1475	32	20	the	the	DET
ejpam-1475	32	21	lie	lie	NOUN
ejpam-1475	32	22	algebra	algebra	PROPN
ejpam-1475	32	23	se(2	se(2	PROPN
ejpam-1475	32	24	)	)	PUNCT
ejpam-1475	32	25	.	.	PUNCT
ejpam-1475	33	1	then	then	ADV
ejpam-1475	33	2	the	the	DET
ejpam-1475	33	3	(	(	PUNCT
ejpam-1475	33	4	minus	minus	NOUN
ejpam-1475	33	5	)	)	PUNCT
ejpam-1475	33	6	lie	lie	NOUN
ejpam-1475	33	7	-	-	PUNCT
ejpam-1475	33	8	poisson	poisson	NOUN
ejpam-1475	33	9	structure	structure	NOUN
ejpam-1475	33	10	on	on	ADP
ejpam-1475	33	11	se(2)∗	se(2)∗	NOUN
ejpam-1475	33	12	is	be	AUX
ejpam-1475	33	13	used	use	VERB
ejpam-1475	33	14	to	to	PART
ejpam-1475	33	15	derive	derive	VERB
ejpam-1475	33	16	the	the	DET
ejpam-1475	33	17	equations	equation	NOUN
ejpam-1475	33	18	for	for	ADP
ejpam-1475	33	19	extrema	extrema	NOUN
ejpam-1475	33	20	(	(	PUNCT
ejpam-1475	33	21	cf	cf	NOUN
ejpam-1475	33	22	.	.	PUNCT
ejpam-1475	34	1	[	[	X
ejpam-1475	34	2	11	11	NUM
ejpam-1475	34	3	,	,	PUNCT
ejpam-1475	34	4	1	1	NUM
ejpam-1475	34	5	,	,	PUNCT
ejpam-1475	34	6	13	13	NUM
ejpam-1475	34	7	]	]	PUNCT
ejpam-1475	34	8	;	;	PUNCT
ejpam-1475	34	9	see	see	VERB
ejpam-1475	34	10	also	also	ADV
ejpam-1475	34	11	[	[	X
ejpam-1475	34	12	25	25	NUM
ejpam-1475	34	13	,	,	PUNCT
ejpam-1475	34	14	26	26	NUM
ejpam-1475	34	15	]	]	PUNCT
ejpam-1475	34	16	for	for	ADP
ejpam-1475	34	17	similar	similar	ADJ
ejpam-1475	34	18	computations	computation	NOUN
ejpam-1475	34	19	on	on	ADP
ejpam-1475	34	20	the	the	DET
ejpam-1475	34	21	rotation	rotation	NOUN
ejpam-1475	34	22	group	group	NOUN
ejpam-1475	34	23	so(3	so(3	PROPN
ejpam-1475	34	24	)	)	PUNCT
ejpam-1475	34	25	)	)	PUNCT
ejpam-1475	34	26	.	.	PUNCT
ejpam-1475	35	1	the	the	DET
ejpam-1475	35	2	(	(	PUNCT
ejpam-1475	35	3	lyapunov	lyapunov	NOUN
ejpam-1475	35	4	)	)	PUNCT
ejpam-1475	35	5	stability	stability	NOUN
ejpam-1475	35	6	nature	nature	NOUN
ejpam-1475	35	7	of	of	ADP
ejpam-1475	35	8	all	all	DET
ejpam-1475	35	9	equilibrium	equilibrium	NOUN
ejpam-1475	35	10	states	state	NOUN
ejpam-1475	35	11	is	be	AUX
ejpam-1475	35	12	then	then	ADV
ejpam-1475	35	13	investigated	investigate	VERB
ejpam-1475	35	14	(	(	PUNCT
ejpam-1475	35	15	by	by	ADP
ejpam-1475	35	16	the	the	DET
ejpam-1475	35	17	energy	energy	NOUN
ejpam-1475	35	18	-	-	PUNCT
ejpam-1475	35	19	casimir	casimir	NOUN
ejpam-1475	35	20	method	method	NOUN
ejpam-1475	35	21	)	)	PUNCT
ejpam-1475	35	22	.	.	PUNCT
ejpam-1475	36	1	finally	finally	ADV
ejpam-1475	36	2	,	,	PUNCT
ejpam-1475	36	3	these	these	DET
ejpam-1475	36	4	equations	equation	NOUN
ejpam-1475	36	5	are	be	AUX
ejpam-1475	36	6	explicitly	explicitly	ADV
ejpam-1475	36	7	integrated	integrate	VERB
ejpam-1475	36	8	by	by	ADP
ejpam-1475	36	9	elliptic	elliptic	ADJ
ejpam-1475	36	10	functions	function	NOUN
ejpam-1475	36	11	.	.	PUNCT
ejpam-1475	37	1	2	2	X
ejpam-1475	37	2	.	.	NUM
ejpam-1475	37	3	preliminaries	preliminary	NOUN
ejpam-1475	37	4	2.1	2.1	NUM
ejpam-1475	37	5	.	.	PUNCT
ejpam-1475	37	6	invariant	invariant	PROPN
ejpam-1475	37	7	control	control	NOUN
ejpam-1475	37	8	systems	system	NOUN
ejpam-1475	37	9	invariant	invariant	PROPN
ejpam-1475	37	10	control	control	NOUN
ejpam-1475	37	11	systems	system	NOUN
ejpam-1475	37	12	on	on	ADP
ejpam-1475	37	13	lie	lie	NOUN
ejpam-1475	37	14	groups	group	NOUN
ejpam-1475	37	15	were	be	AUX
ejpam-1475	37	16	first	first	ADV
ejpam-1475	37	17	considered	consider	VERB
ejpam-1475	37	18	in	in	ADP
ejpam-1475	37	19	1972	1972	NUM
ejpam-1475	37	20	by	by	ADP
ejpam-1475	37	21	brockett	brockett	PROPN
ejpam-1475	38	1	[	[	X
ejpam-1475	38	2	8	8	NUM
ejpam-1475	38	3	]	]	PUNCT
ejpam-1475	38	4	and	and	CCONJ
ejpam-1475	38	5	by	by	ADP
ejpam-1475	38	6	jurdjevic	jurdjevic	PROPN
ejpam-1475	38	7	and	and	CCONJ
ejpam-1475	38	8	sussmann	sussmann	NOUN
ejpam-1475	38	9	[	[	X
ejpam-1475	38	10	12	12	NUM
ejpam-1475	38	11	]	]	PUNCT
ejpam-1475	38	12	.	.	PUNCT
ejpam-1475	39	1	a	a	DET
ejpam-1475	39	2	left	left	ADJ
ejpam-1475	39	3	-	-	PUNCT
ejpam-1475	39	4	invariant	invariant	ADJ
ejpam-1475	39	5	control	control	NOUN
ejpam-1475	39	6	system	system	NOUN
ejpam-1475	39	7	σ	σ	PROPN
ejpam-1475	39	8	is	be	AUX
ejpam-1475	39	9	a	a	DET
ejpam-1475	39	10	(	(	PUNCT
ejpam-1475	39	11	smooth	smooth	ADJ
ejpam-1475	39	12	)	)	PUNCT
ejpam-1475	39	13	control	control	NOUN
ejpam-1475	39	14	system	system	NOUN
ejpam-1475	39	15	evolving	evolve	VERB
ejpam-1475	39	16	on	on	ADP
ejpam-1475	39	17	a	a	DET
ejpam-1475	39	18	(	(	PUNCT
ejpam-1475	39	19	real	real	ADJ
ejpam-1475	39	20	,	,	PUNCT
ejpam-1475	39	21	finite	finite	ADJ
ejpam-1475	39	22	-	-	ADJ
ejpam-1475	39	23	dimensional	dimensional	ADJ
ejpam-1475	39	24	)	)	PUNCT
ejpam-1475	39	25	lie	lie	NOUN
ejpam-1475	39	26	group	group	NOUN
ejpam-1475	39	27	g	g	PROPN
ejpam-1475	39	28	,	,	PUNCT
ejpam-1475	39	29	whose	whose	DET
ejpam-1475	39	30	dynamics	dynamic	NOUN
ejpam-1475	39	31	ξ	ξ	X
ejpam-1475	39	32	:	:	PUNCT
ejpam-1475	39	33	g×u	g×u	PROPN
ejpam-1475	39	34	→	→	PUNCT
ejpam-1475	39	35	tg	tg	PROPN
ejpam-1475	39	36	is	be	AUX
ejpam-1475	39	37	invariant	invariant	ADJ
ejpam-1475	39	38	under	under	ADP
ejpam-1475	39	39	left	left	ADJ
ejpam-1475	39	40	translations	translation	NOUN
ejpam-1475	39	41	.	.	PUNCT
ejpam-1475	40	1	(	(	PUNCT
ejpam-1475	40	2	the	the	DET
ejpam-1475	40	3	tangent	tangent	NOUN
ejpam-1475	40	4	bundle	bundle	NOUN
ejpam-1475	40	5	tg	tg	PROPN
ejpam-1475	40	6	is	be	AUX
ejpam-1475	40	7	identified	identify	VERB
ejpam-1475	40	8	with	with	ADP
ejpam-1475	40	9	g×	g×	PROPN
ejpam-1475	40	10	g	g	NOUN
ejpam-1475	40	11	,	,	PUNCT
ejpam-1475	40	12	where	where	SCONJ
ejpam-1475	40	13	g	g	PROPN
ejpam-1475	40	14	is	be	AUX
ejpam-1475	40	15	the	the	DET
ejpam-1475	40	16	lie	lie	NOUN
ejpam-1475	40	17	algebra	algebra	NOUN
ejpam-1475	40	18	of	of	ADP
ejpam-1475	40	19	g	g	NOUN
ejpam-1475	40	20	)	)	PUNCT
ejpam-1475	40	21	.	.	PUNCT
ejpam-1475	41	1	for	for	ADP
ejpam-1475	41	2	the	the	DET
ejpam-1475	41	3	sake	sake	NOUN
ejpam-1475	41	4	of	of	ADP
ejpam-1475	41	5	convenience	convenience	NOUN
ejpam-1475	41	6	,	,	PUNCT
ejpam-1475	41	7	we	we	PRON
ejpam-1475	41	8	shall	shall	AUX
ejpam-1475	41	9	assume	assume	VERB
ejpam-1475	41	10	that	that	SCONJ
ejpam-1475	41	11	(	(	PUNCT
ejpam-1475	41	12	the	the	DET
ejpam-1475	41	13	state	state	NOUN
ejpam-1475	41	14	space	space	NOUN
ejpam-1475	41	15	of	of	ADP
ejpam-1475	41	16	the	the	DET
ejpam-1475	41	17	system	system	NOUN
ejpam-1475	41	18	)	)	PUNCT
ejpam-1475	41	19	g	g	NOUN
ejpam-1475	41	20	is	be	AUX
ejpam-1475	41	21	a	a	DET
ejpam-1475	41	22	matrix	matrix	NOUN
ejpam-1475	41	23	lie	lie	NOUN
ejpam-1475	41	24	group	group	NOUN
ejpam-1475	41	25	.	.	PUNCT
ejpam-1475	42	1	for	for	ADP
ejpam-1475	42	2	the	the	DET
ejpam-1475	42	3	purposes	purpose	NOUN
ejpam-1475	42	4	of	of	ADP
ejpam-1475	42	5	this	this	DET
ejpam-1475	42	6	paper	paper	NOUN
ejpam-1475	42	7	,	,	PUNCT
ejpam-1475	42	8	we	we	PRON
ejpam-1475	42	9	may	may	AUX
ejpam-1475	42	10	also	also	ADV
ejpam-1475	42	11	assume	assume	VERB
ejpam-1475	42	12	that	that	SCONJ
ejpam-1475	42	13	(	(	PUNCT
ejpam-1475	42	14	the	the	DET
ejpam-1475	42	15	input	input	NOUN
ejpam-1475	42	16	space	space	NOUN
ejpam-1475	42	17	)	)	PUNCT
ejpam-1475	42	18	u	u	NOUN
ejpam-1475	42	19	=	=	PUNCT
ejpam-1475	42	20	rℓ.	rℓ.	VERB
ejpam-1475	42	21	such	such	DET
ejpam-1475	42	22	a	a	DET
ejpam-1475	42	23	control	control	NOUN
ejpam-1475	42	24	system	system	NOUN
ejpam-1475	42	25	is	be	AUX
ejpam-1475	42	26	described	describe	VERB
ejpam-1475	42	27	as	as	ADP
ejpam-1475	42	28	follows	follow	VERB
ejpam-1475	42	29	(	(	PUNCT
ejpam-1475	42	30	cf	cf	NOUN
ejpam-1475	42	31	.	.	PUNCT
ejpam-1475	43	1	[	[	X
ejpam-1475	43	2	11	11	NUM
ejpam-1475	43	3	,	,	PUNCT
ejpam-1475	43	4	1	1	NUM
ejpam-1475	43	5	,	,	PUNCT
ejpam-1475	43	6	27	27	NUM
ejpam-1475	43	7	]	]	PUNCT
ejpam-1475	43	8	)	)	PUNCT
ejpam-1475	43	9	ġ	ġ	NOUN
ejpam-1475	43	10	=	=	SYM
ejpam-1475	43	11	ξ(g	ξ(g	PROPN
ejpam-1475	43	12	,	,	PUNCT
ejpam-1475	43	13	u	u	NOUN
ejpam-1475	43	14	)	)	PUNCT
ejpam-1475	43	15	,	,	PUNCT
ejpam-1475	43	16	g	g	PROPN
ejpam-1475	43	17	∈	∈	PROPN
ejpam-1475	43	18	g	g	PROPN
ejpam-1475	43	19	,	,	PUNCT
ejpam-1475	43	20	u	u	PROPN
ejpam-1475	43	21	∈	∈	PROPN
ejpam-1475	43	22	rℓ	rℓ	NOUN
ejpam-1475	43	23	(	(	PUNCT
ejpam-1475	43	24	1	1	NUM
ejpam-1475	43	25	)	)	PUNCT
ejpam-1475	43	26	where	where	SCONJ
ejpam-1475	43	27	ξ(g	ξ(g	PROPN
ejpam-1475	43	28	,	,	PUNCT
ejpam-1475	43	29	u	u	NOUN
ejpam-1475	43	30	)	)	PUNCT
ejpam-1475	43	31	=	=	SYM
ejpam-1475	43	32	gξ(1,u	gξ(1,u	PROPN
ejpam-1475	43	33	)	)	PUNCT
ejpam-1475	43	34	∈	∈	PROPN
ejpam-1475	43	35	tgg	tgg	PROPN
ejpam-1475	43	36	.	.	PUNCT
ejpam-1475	43	37	admissible	admissible	ADJ
ejpam-1475	43	38	controls	control	NOUN
ejpam-1475	43	39	are	be	AUX
ejpam-1475	43	40	bounded	bound	VERB
ejpam-1475	43	41	and	and	CCONJ
ejpam-1475	43	42	measurable	measurable	ADJ
ejpam-1475	43	43	maps	map	NOUN
ejpam-1475	43	44	u	u	PROPN
ejpam-1475	43	45	(	(	PUNCT
ejpam-1475	43	46	·	·	PUNCT
ejpam-1475	43	47	)	)	PUNCT
ejpam-1475	43	48	:	:	PUNCT
ejpam-1475	44	1	[	[	X
ejpam-1475	44	2	0	0	NUM
ejpam-1475	44	3	,	,	PUNCT
ejpam-1475	44	4	t	t	PROPN
ejpam-1475	44	5	]	]	PUNCT
ejpam-1475	44	6	→	→	PUNCT
ejpam-1475	44	7	rℓ.	rℓ.	AUX
ejpam-1475	44	8	we	we	PRON
ejpam-1475	44	9	further	far	ADV
ejpam-1475	44	10	assume	assume	VERB
ejpam-1475	44	11	that	that	SCONJ
ejpam-1475	44	12	the	the	DET
ejpam-1475	44	13	parametrisation	parametrisation	NOUN
ejpam-1475	44	14	map	map	NOUN
ejpam-1475	44	15	ξ(1	ξ(1	PROPN
ejpam-1475	44	16	,	,	PUNCT
ejpam-1475	44	17	·	·	PUNCT
ejpam-1475	44	18	)	)	PUNCT
ejpam-1475	44	19	:	:	PUNCT
ejpam-1475	44	20	rℓ	rℓ	NOUN
ejpam-1475	44	21	→	→	SYM
ejpam-1475	44	22	g	g	NOUN
ejpam-1475	44	23	is	be	AUX
ejpam-1475	44	24	an	an	DET
ejpam-1475	44	25	embedding	embedding	NOUN
ejpam-1475	44	26	.	.	PUNCT
ejpam-1475	45	1	hence	hence	ADV
ejpam-1475	45	2	,	,	PUNCT
ejpam-1475	45	3	the	the	DET
ejpam-1475	45	4	trace	trace	NOUN
ejpam-1475	45	5	γ	γ	X
ejpam-1475	45	6	=	=	SYM
ejpam-1475	45	7	imξ(1	imξ(1	ADJ
ejpam-1475	45	8	,	,	PUNCT
ejpam-1475	45	9	·	·	PUNCT
ejpam-1475	45	10	)	)	PUNCT
ejpam-1475	45	11	is	be	AUX
ejpam-1475	45	12	a	a	DET
ejpam-1475	45	13	submanifold	submanifold	NOUN
ejpam-1475	45	14	of	of	ADP
ejpam-1475	45	15	g.	g.	PROPN
ejpam-1475	45	16	we	we	PRON
ejpam-1475	45	17	have	have	VERB
ejpam-1475	45	18	that	that	PRON
ejpam-1475	45	19	γ	γ	PROPN
ejpam-1475	45	20	=	=	SYM
ejpam-1475	45	21	¦	¦	X
ejpam-1475	45	22	ξu	ξu	PROPN
ejpam-1475	45	23	=	=	SYM
ejpam-1475	45	24	ξ(1,u	ξ(1,u	PROPN
ejpam-1475	45	25	)	)	PUNCT
ejpam-1475	45	26	:	:	PUNCT
ejpam-1475	45	27	u	u	NOUN
ejpam-1475	45	28	∈	∈	NOUN
ejpam-1475	45	29	rℓ	rℓ	NOUN
ejpam-1475	45	30	©	©	PROPN
ejpam-1475	45	31	(	(	PUNCT
ejpam-1475	45	32	cf	cf	NOUN
ejpam-1475	45	33	.	.	PUNCT
ejpam-1475	46	1	[	[	X
ejpam-1475	46	2	5	5	NUM
ejpam-1475	46	3	,	,	PUNCT
ejpam-1475	46	4	6	6	NUM
ejpam-1475	46	5	]	]	NUM
ejpam-1475	46	6	)	)	PUNCT
ejpam-1475	46	7	.	.	PUNCT
ejpam-1475	47	1	a	a	DET
ejpam-1475	47	2	trajectory	trajectory	NOUN
ejpam-1475	47	3	for	for	ADP
ejpam-1475	47	4	an	an	DET
ejpam-1475	47	5	admissible	admissible	ADJ
ejpam-1475	47	6	control	control	NOUN
ejpam-1475	47	7	u	u	NOUN
ejpam-1475	47	8	(	(	PUNCT
ejpam-1475	47	9	·	·	PUNCT
ejpam-1475	47	10	)	)	PUNCT
ejpam-1475	47	11	:	:	PUNCT
ejpam-1475	48	1	[	[	X
ejpam-1475	48	2	0	0	NUM
ejpam-1475	48	3	,	,	PUNCT
ejpam-1475	48	4	t]→	t]→	DET
ejpam-1475	48	5	rℓ	rℓ	NOUN
ejpam-1475	48	6	is	be	AUX
ejpam-1475	48	7	an	an	DET
ejpam-1475	48	8	absolutely	absolutely	ADV
ejpam-1475	48	9	continuous	continuous	ADJ
ejpam-1475	48	10	curve	curve	NOUN
ejpam-1475	48	11	g	g	PROPN
ejpam-1475	48	12	(	(	PUNCT
ejpam-1475	48	13	·	·	PUNCT
ejpam-1475	48	14	)	)	PUNCT
ejpam-1475	48	15	:	:	PUNCT
ejpam-1475	49	1	[	[	X
ejpam-1475	49	2	0	0	NUM
ejpam-1475	49	3	,	,	PUNCT
ejpam-1475	49	4	t]→	t]→	PRON
ejpam-1475	49	5	g	g	NOUN
ejpam-1475	49	6	such	such	ADJ
ejpam-1475	49	7	that	that	DET
ejpam-1475	49	8	ġ(t	ġ(t	NOUN
ejpam-1475	49	9	)	)	PUNCT
ejpam-1475	49	10	=	=	NOUN
ejpam-1475	49	11	g(t)ξ(1,u(t	g(t)ξ(1,u(t	VERB
ejpam-1475	49	12	)	)	PUNCT
ejpam-1475	49	13	)	)	PUNCT
ejpam-1475	49	14	for	for	ADP
ejpam-1475	49	15	almost	almost	ADV
ejpam-1475	49	16	every	every	PRON
ejpam-1475	49	17	t	t	NOUN
ejpam-1475	49	18	∈	∈	PROPN
ejpam-1475	50	1	[	[	X
ejpam-1475	50	2	0	0	NUM
ejpam-1475	50	3	,	,	PUNCT
ejpam-1475	50	4	t	t	PROPN
ejpam-1475	50	5	]	]	PUNCT
ejpam-1475	50	6	.	.	PUNCT
ejpam-1475	51	1	a	a	DET
ejpam-1475	51	2	left	left	ADJ
ejpam-1475	51	3	-	-	PUNCT
ejpam-1475	51	4	invariant	invariant	ADJ
ejpam-1475	51	5	control	control	NOUN
ejpam-1475	51	6	system	system	NOUN
ejpam-1475	51	7	σ	σ	PROPN
ejpam-1475	51	8	is	be	AUX
ejpam-1475	51	9	said	say	VERB
ejpam-1475	51	10	to	to	PART
ejpam-1475	51	11	be	be	AUX
ejpam-1475	51	12	controllable	controllable	ADJ
ejpam-1475	51	13	if	if	SCONJ
ejpam-1475	51	14	for	for	ADP
ejpam-1475	51	15	any	any	DET
ejpam-1475	51	16	g0	g0	NOUN
ejpam-1475	51	17	,	,	PUNCT
ejpam-1475	51	18	g1	g1	PROPN
ejpam-1475	51	19	∈	∈	PROPN
ejpam-1475	51	20	g	g	NOUN
ejpam-1475	51	21	,	,	PUNCT
ejpam-1475	51	22	there	there	PRON
ejpam-1475	51	23	exists	exist	VERB
ejpam-1475	51	24	a	a	DET
ejpam-1475	51	25	trajectory	trajectory	NOUN
ejpam-1475	51	26	g	g	NOUN
ejpam-1475	51	27	(	(	PUNCT
ejpam-1475	51	28	·	·	PUNCT
ejpam-1475	51	29	)	)	PUNCT
ejpam-1475	51	30	:	:	PUNCT
ejpam-1475	52	1	[	[	X
ejpam-1475	52	2	0	0	NUM
ejpam-1475	52	3	,	,	PUNCT
ejpam-1475	52	4	t	t	PROPN
ejpam-1475	52	5	]	]	PUNCT
ejpam-1475	52	6	→	→	PUNCT
ejpam-1475	52	7	rℓ	rℓ	ADP
ejpam-1475	52	8	such	such	ADJ
ejpam-1475	52	9	that	that	PRON
ejpam-1475	52	10	g(0	g(0	NOUN
ejpam-1475	52	11	)	)	PUNCT
ejpam-1475	52	12	=	=	PROPN
ejpam-1475	52	13	g0	g0	NOUN
ejpam-1475	52	14	and	and	CCONJ
ejpam-1475	52	15	g(t	g(t	PROPN
ejpam-1475	52	16	)	)	PUNCT
ejpam-1475	52	17	=	=	PUNCT
ejpam-1475	52	18	g1	g1	PROPN
ejpam-1475	52	19	.	.	PUNCT
ejpam-1475	53	1	controllable	controllable	ADJ
ejpam-1475	53	2	systems	system	NOUN
ejpam-1475	53	3	on	on	ADP
ejpam-1475	53	4	connected	connected	ADJ
ejpam-1475	53	5	(	(	PUNCT
ejpam-1475	53	6	matrix	matrix	NOUN
ejpam-1475	53	7	)	)	PUNCT
ejpam-1475	53	8	lie	lie	NOUN
ejpam-1475	53	9	groups	group	NOUN
ejpam-1475	53	10	must	must	AUX
ejpam-1475	53	11	have	have	VERB
ejpam-1475	53	12	full	full	ADJ
ejpam-1475	53	13	rank	rank	NOUN
ejpam-1475	53	14	;	;	PUNCT
ejpam-1475	53	15	this	this	PRON
ejpam-1475	53	16	means	mean	VERB
ejpam-1475	53	17	that	that	SCONJ
ejpam-1475	53	18	the	the	DET
ejpam-1475	53	19	lie	lie	NOUN
ejpam-1475	53	20	algebra	algebra	NOUN
ejpam-1475	53	21	generated	generate	VERB
ejpam-1475	53	22	by	by	ADP
ejpam-1475	53	23	the	the	DET
ejpam-1475	53	24	trace	trace	NOUN
ejpam-1475	53	25	of	of	ADP
ejpam-1475	53	26	the	the	DET
ejpam-1475	53	27	system	system	NOUN
ejpam-1475	53	28	,	,	PUNCT
ejpam-1475	53	29	lie(γ	lie(γ	PROPN
ejpam-1475	53	30	)	)	PUNCT
ejpam-1475	53	31	,	,	PUNCT
ejpam-1475	53	32	is	be	AUX
ejpam-1475	53	33	g.	g.	PROPN
ejpam-1475	53	34	the	the	DET
ejpam-1475	53	35	following	following	ADJ
ejpam-1475	53	36	result	result	NOUN
ejpam-1475	53	37	is	be	AUX
ejpam-1475	53	38	well	well	ADV
ejpam-1475	53	39	known	know	VERB
ejpam-1475	53	40	(	(	PUNCT
ejpam-1475	53	41	see	see	VERB
ejpam-1475	53	42	,	,	PUNCT
ejpam-1475	53	43	also	also	ADV
ejpam-1475	53	44	,	,	PUNCT
ejpam-1475	53	45	[	[	X
ejpam-1475	53	46	30	30	NUM
ejpam-1475	53	47	]	]	NUM
ejpam-1475	53	48	)	)	PUNCT
ejpam-1475	53	49	.	.	PUNCT
ejpam-1475	54	1	theorem	theorem	ADJ
ejpam-1475	54	2	1	1	NUM
ejpam-1475	54	3	(	(	PUNCT
ejpam-1475	54	4	[	[	X
ejpam-1475	54	5	7	7	NUM
ejpam-1475	54	6	]	]	NUM
ejpam-1475	54	7	)	)	PUNCT
ejpam-1475	54	8	.	.	PUNCT
ejpam-1475	55	1	a	a	DET
ejpam-1475	55	2	left	left	ADJ
ejpam-1475	55	3	-	-	PUNCT
ejpam-1475	55	4	invariant	invariant	ADJ
ejpam-1475	55	5	control	control	NOUN
ejpam-1475	55	6	system	system	NOUN
ejpam-1475	55	7	on	on	ADP
ejpam-1475	55	8	the	the	DET
ejpam-1475	55	9	euclidean	euclidean	ADJ
ejpam-1475	55	10	group	group	NOUN
ejpam-1475	55	11	se(n	se(n	PROPN
ejpam-1475	55	12	)	)	PUNCT
ejpam-1475	55	13	is	be	AUX
ejpam-1475	55	14	controllable	controllable	ADJ
ejpam-1475	55	15	if	if	SCONJ
ejpam-1475	55	16	and	and	CCONJ
ejpam-1475	55	17	only	only	ADV
ejpam-1475	55	18	if	if	SCONJ
ejpam-1475	55	19	it	it	PRON
ejpam-1475	55	20	has	have	VERB
ejpam-1475	55	21	full	full	ADJ
ejpam-1475	55	22	rank	rank	NOUN
ejpam-1475	55	23	.	.	PUNCT
ejpam-1475	56	1	r.	r.	PROPN
ejpam-1475	56	2	adams	adams	PROPN
ejpam-1475	56	3	,	,	PUNCT
ejpam-1475	56	4	r.	r.	PROPN
ejpam-1475	56	5	biggs	biggs	PROPN
ejpam-1475	56	6	,	,	PUNCT
ejpam-1475	56	7	c.	c.	PROPN
ejpam-1475	56	8	remsing	remsing	NOUN
ejpam-1475	56	9	/	/	SYM
ejpam-1475	56	10	eur	eur	NOUN
ejpam-1475	56	11	.	.	PUNCT
ejpam-1475	57	1	j.	j.	PROPN
ejpam-1475	57	2	pure	pure	PROPN
ejpam-1475	57	3	appl	appl	PROPN
ejpam-1475	57	4	.	.	PROPN
ejpam-1475	57	5	math	math	PROPN
ejpam-1475	57	6	,	,	PUNCT
ejpam-1475	57	7	5	5	NUM
ejpam-1475	57	8	(	(	PUNCT
ejpam-1475	57	9	2012	2012	NUM
ejpam-1475	57	10	)	)	PUNCT
ejpam-1475	57	11	,	,	PUNCT
ejpam-1475	57	12	1	1	NUM
ejpam-1475	57	13	-	-	SYM
ejpam-1475	57	14	15	15	NUM
ejpam-1475	57	15	3	3	NUM
ejpam-1475	57	16	we	we	PRON
ejpam-1475	57	17	shall	shall	AUX
ejpam-1475	57	18	denote	denote	VERB
ejpam-1475	57	19	a	a	DET
ejpam-1475	57	20	(	(	PUNCT
ejpam-1475	57	21	left	left	ADJ
ejpam-1475	57	22	-	-	PUNCT
ejpam-1475	57	23	invariant	invariant	ADJ
ejpam-1475	57	24	control	control	NOUN
ejpam-1475	57	25	)	)	PUNCT
ejpam-1475	57	26	system	system	NOUN
ejpam-1475	57	27	σ	σ	PUNCT
ejpam-1475	57	28	by	by	ADP
ejpam-1475	57	29	(	(	PUNCT
ejpam-1475	57	30	g	g	PROPN
ejpam-1475	57	31	,	,	PUNCT
ejpam-1475	57	32	ξ	ξ	NOUN
ejpam-1475	57	33	)	)	PUNCT
ejpam-1475	57	34	(	(	PUNCT
ejpam-1475	57	35	see	see	VERB
ejpam-1475	57	36	,	,	PUNCT
ejpam-1475	57	37	e.g.	e.g.	ADV
ejpam-1475	57	38	,	,	PUNCT
ejpam-1475	57	39	[	[	X
ejpam-1475	57	40	5	5	NUM
ejpam-1475	57	41	,	,	PUNCT
ejpam-1475	57	42	6	6	NUM
ejpam-1475	57	43	]	]	NUM
ejpam-1475	57	44	)	)	PUNCT
ejpam-1475	57	45	.	.	PUNCT
ejpam-1475	58	1	we	we	PRON
ejpam-1475	58	2	say	say	VERB
ejpam-1475	58	3	that	that	SCONJ
ejpam-1475	58	4	a	a	DET
ejpam-1475	58	5	system	system	NOUN
ejpam-1475	58	6	σ	σ	NOUN
ejpam-1475	58	7	=	=	SYM
ejpam-1475	58	8	(	(	PUNCT
ejpam-1475	58	9	g	g	PROPN
ejpam-1475	58	10	,	,	PUNCT
ejpam-1475	58	11	ξ	ξ	NOUN
ejpam-1475	58	12	)	)	PUNCT
ejpam-1475	58	13	is	be	AUX
ejpam-1475	58	14	connected	connect	VERB
ejpam-1475	58	15	if	if	SCONJ
ejpam-1475	58	16	its	its	PRON
ejpam-1475	58	17	state	state	NOUN
ejpam-1475	58	18	space	space	NOUN
ejpam-1475	58	19	g	g	NOUN
ejpam-1475	58	20	is	be	AUX
ejpam-1475	58	21	connected	connect	VERB
ejpam-1475	58	22	.	.	PUNCT
ejpam-1475	59	1	let	let	VERB
ejpam-1475	59	2	σ	σ	NOUN
ejpam-1475	59	3	=	=	SYM
ejpam-1475	59	4	(	(	PUNCT
ejpam-1475	59	5	g	g	PROPN
ejpam-1475	59	6	,	,	PUNCT
ejpam-1475	59	7	ξ	ξ	NOUN
ejpam-1475	59	8	)	)	PUNCT
ejpam-1475	59	9	and	and	CCONJ
ejpam-1475	59	10	σ′	σ′	PROPN
ejpam-1475	59	11	=	=	SYM
ejpam-1475	59	12	(	(	PUNCT
ejpam-1475	59	13	g′,ξ′	g′,ξ′	PROPN
ejpam-1475	59	14	)	)	PUNCT
ejpam-1475	59	15	be	be	VERB
ejpam-1475	59	16	two	two	NUM
ejpam-1475	59	17	connected	connected	ADJ
ejpam-1475	59	18	full	full	ADJ
ejpam-1475	59	19	-	-	PUNCT
ejpam-1475	59	20	rank	rank	NOUN
ejpam-1475	59	21	systems	system	NOUN
ejpam-1475	59	22	with	with	ADP
ejpam-1475	59	23	traces	trace	NOUN
ejpam-1475	59	24	γ	γ	PROPN
ejpam-1475	59	25	⊆	⊆	NUM
ejpam-1475	59	26	g	g	NOUN
ejpam-1475	59	27	and	and	CCONJ
ejpam-1475	59	28	γ′	γ′	NOUN
ejpam-1475	59	29	⊆	⊆	NUM
ejpam-1475	59	30	g	g	NOUN
ejpam-1475	59	31	′	′	NUM
ejpam-1475	59	32	,	,	PUNCT
ejpam-1475	59	33	respectively	respectively	ADV
ejpam-1475	59	34	.	.	PUNCT
ejpam-1475	60	1	we	we	PRON
ejpam-1475	60	2	say	say	VERB
ejpam-1475	60	3	that	that	SCONJ
ejpam-1475	60	4	σ	σ	PROPN
ejpam-1475	60	5	and	and	CCONJ
ejpam-1475	60	6	σ′	σ′	PROPN
ejpam-1475	60	7	are	be	AUX
ejpam-1475	60	8	(	(	PUNCT
ejpam-1475	60	9	locally	locally	ADV
ejpam-1475	60	10	)	)	PUNCT
ejpam-1475	60	11	detached	detach	VERB
ejpam-1475	60	12	feedback	feedback	NOUN
ejpam-1475	60	13	equivalent	equivalent	ADJ
ejpam-1475	60	14	if	if	SCONJ
ejpam-1475	60	15	there	there	PRON
ejpam-1475	60	16	exist	exist	VERB
ejpam-1475	60	17	open	open	ADJ
ejpam-1475	60	18	neighbourhoods	neighbourhood	NOUN
ejpam-1475	60	19	n	n	CCONJ
ejpam-1475	60	20	and	and	CCONJ
ejpam-1475	60	21	n	n	NUM
ejpam-1475	60	22	′	′	NUM
ejpam-1475	60	23	of	of	ADP
ejpam-1475	60	24	(	(	PUNCT
ejpam-1475	60	25	the	the	DET
ejpam-1475	60	26	unit	unit	NOUN
ejpam-1475	60	27	elements	element	NOUN
ejpam-1475	60	28	)	)	PUNCT
ejpam-1475	60	29	1	1	NUM
ejpam-1475	60	30	and	and	CCONJ
ejpam-1475	60	31	1′	1′	NUM
ejpam-1475	60	32	,	,	PUNCT
ejpam-1475	60	33	respectively	respectively	ADV
ejpam-1475	60	34	,	,	PUNCT
ejpam-1475	60	35	and	and	CCONJ
ejpam-1475	60	36	a	a	DET
ejpam-1475	60	37	(	(	PUNCT
ejpam-1475	60	38	local	local	ADJ
ejpam-1475	60	39	)	)	PUNCT
ejpam-1475	60	40	diffeomorphism	diffeomorphism	NOUN
ejpam-1475	60	41	φ	φ	NOUN
ejpam-1475	60	42	=	=	SYM
ejpam-1475	60	43	φ	φ	PROPN
ejpam-1475	60	44	×ϕ	×ϕ	PROPN
ejpam-1475	60	45	:	:	PUNCT
ejpam-1475	60	46	n	n	PRON
ejpam-1475	60	47	×rℓ	×rℓ	PROPN
ejpam-1475	60	48	→	→	SYM
ejpam-1475	60	49	n	n	CCONJ
ejpam-1475	60	50	′	′	NUM
ejpam-1475	60	51	×rℓ	×rℓ	NOUN
ejpam-1475	60	52	such	such	ADJ
ejpam-1475	60	53	that	that	SCONJ
ejpam-1475	60	54	φ(1	φ(1	PROPN
ejpam-1475	60	55	)	)	PUNCT
ejpam-1475	60	56	=	=	SYM
ejpam-1475	60	57	1′	1′	NUM
ejpam-1475	60	58	and	and	CCONJ
ejpam-1475	60	59	tgφ	tgφ	NOUN
ejpam-1475	60	60	·	·	PUNCT
ejpam-1475	60	61	ξ(g	ξ(g	PROPN
ejpam-1475	60	62	,	,	PUNCT
ejpam-1475	60	63	u	u	NOUN
ejpam-1475	60	64	)	)	PUNCT
ejpam-1475	60	65	=	=	SYM
ejpam-1475	60	66	ξ′(φ(g),ϕ(u	ξ′(φ(g),ϕ(u	NOUN
ejpam-1475	60	67	)	)	PUNCT
ejpam-1475	60	68	)	)	PUNCT
ejpam-1475	60	69	for	for	ADP
ejpam-1475	60	70	g	g	PROPN
ejpam-1475	60	71	∈	∈	PROPN
ejpam-1475	60	72	n	n	NOUN
ejpam-1475	60	73	and	and	CCONJ
ejpam-1475	60	74	u	u	PROPN
ejpam-1475	60	75	∈	∈	PROPN
ejpam-1475	60	76	rℓ.	rℓ.	VERB
ejpam-1475	60	77	two	two	NUM
ejpam-1475	60	78	detached	detach	VERB
ejpam-1475	60	79	feedback	feedback	NOUN
ejpam-1475	60	80	equivalent	equivalent	ADJ
ejpam-1475	60	81	systems	system	NOUN
ejpam-1475	60	82	have	have	VERB
ejpam-1475	60	83	the	the	DET
ejpam-1475	60	84	same	same	ADJ
ejpam-1475	60	85	trajectories	trajectory	NOUN
ejpam-1475	60	86	(	(	PUNCT
ejpam-1475	60	87	up	up	ADP
ejpam-1475	60	88	to	to	ADP
ejpam-1475	60	89	a	a	DET
ejpam-1475	60	90	diffeomorphism	diffeomorphism	NOUN
ejpam-1475	60	91	in	in	ADP
ejpam-1475	60	92	the	the	DET
ejpam-1475	60	93	state	state	NOUN
ejpam-1475	60	94	space	space	NOUN
ejpam-1475	60	95	)	)	PUNCT
ejpam-1475	60	96	,	,	PUNCT
ejpam-1475	60	97	which	which	PRON
ejpam-1475	60	98	are	be	AUX
ejpam-1475	60	99	parametrised	parametrise	VERB
ejpam-1475	60	100	differently	differently	ADV
ejpam-1475	60	101	by	by	ADP
ejpam-1475	60	102	admissible	admissible	ADJ
ejpam-1475	60	103	controls	control	NOUN
ejpam-1475	60	104	.	.	PUNCT
ejpam-1475	61	1	we	we	PRON
ejpam-1475	61	2	recall	recall	VERB
ejpam-1475	61	3	the	the	DET
ejpam-1475	61	4	following	follow	VERB
ejpam-1475	61	5	result	result	NOUN
ejpam-1475	61	6	.	.	PUNCT
ejpam-1475	62	1	theorem	theorem	ADJ
ejpam-1475	62	2	2	2	NUM
ejpam-1475	62	3	(	(	PUNCT
ejpam-1475	62	4	[	[	X
ejpam-1475	62	5	6	6	NUM
ejpam-1475	62	6	]	]	NUM
ejpam-1475	62	7	)	)	PUNCT
ejpam-1475	62	8	.	.	PUNCT
ejpam-1475	63	1	σ	σ	NOUN
ejpam-1475	63	2	=	=	PUNCT
ejpam-1475	63	3	(	(	PUNCT
ejpam-1475	63	4	g	g	PROPN
ejpam-1475	63	5	,	,	PUNCT
ejpam-1475	63	6	ξ	ξ	NOUN
ejpam-1475	63	7	)	)	PUNCT
ejpam-1475	63	8	and	and	CCONJ
ejpam-1475	63	9	σ′	σ′	PROPN
ejpam-1475	63	10	=	=	SYM
ejpam-1475	63	11	(	(	PUNCT
ejpam-1475	63	12	g′,ξ′	g′,ξ′	ADJ
ejpam-1475	63	13	)	)	PUNCT
ejpam-1475	63	14	are	be	AUX
ejpam-1475	63	15	(	(	PUNCT
ejpam-1475	63	16	locally	locally	ADV
ejpam-1475	63	17	)	)	PUNCT
ejpam-1475	63	18	detached	detach	VERB
ejpam-1475	63	19	feedback	feedback	NOUN
ejpam-1475	63	20	equivalent	equivalent	ADJ
ejpam-1475	63	21	if	if	SCONJ
ejpam-1475	63	22	and	and	CCONJ
ejpam-1475	63	23	only	only	ADV
ejpam-1475	63	24	if	if	SCONJ
ejpam-1475	63	25	there	there	PRON
ejpam-1475	63	26	exists	exist	VERB
ejpam-1475	63	27	a	a	DET
ejpam-1475	63	28	lie	lie	NOUN
ejpam-1475	63	29	algebra	algebra	VERB
ejpam-1475	63	30	isomorphism	isomorphism	NOUN
ejpam-1475	63	31	ψ	ψ	X
ejpam-1475	63	32	:	:	PUNCT
ejpam-1475	63	33	g→	g→	NOUN
ejpam-1475	63	34	g	g	NOUN
ejpam-1475	63	35	′	′	NUM
ejpam-1475	63	36	such	such	ADJ
ejpam-1475	63	37	that	that	SCONJ
ejpam-1475	63	38	ψ	ψ	NOUN
ejpam-1475	63	39	·	·	PUNCT
ejpam-1475	63	40	γ	γ	X
ejpam-1475	63	41	=	=	SYM
ejpam-1475	63	42	γ′.	γ′.	VERB
ejpam-1475	63	43	2.2	2.2	NUM
ejpam-1475	63	44	.	.	PUNCT
ejpam-1475	64	1	invariant	invariant	ADJ
ejpam-1475	64	2	optimal	optimal	ADJ
ejpam-1475	64	3	control	control	NOUN
ejpam-1475	64	4	problems	problem	NOUN
ejpam-1475	64	5	consider	consider	VERB
ejpam-1475	64	6	a	a	DET
ejpam-1475	64	7	left	left	ADJ
ejpam-1475	64	8	-	-	PUNCT
ejpam-1475	64	9	invariant	invariant	ADJ
ejpam-1475	64	10	control	control	NOUN
ejpam-1475	64	11	system	system	NOUN
ejpam-1475	64	12	(	(	PUNCT
ejpam-1475	64	13	1	1	X
ejpam-1475	64	14	)	)	PUNCT
ejpam-1475	64	15	evolving	evolve	VERB
ejpam-1475	64	16	on	on	ADP
ejpam-1475	64	17	some	some	DET
ejpam-1475	64	18	matrix	matrix	NOUN
ejpam-1475	64	19	lie	lie	NOUN
ejpam-1475	64	20	group	group	NOUN
ejpam-1475	64	21	g	g	PROPN
ejpam-1475	64	22	≤	≤	PROPN
ejpam-1475	64	23	gl(n	gl(n	PUNCT
ejpam-1475	64	24	,	,	PUNCT
ejpam-1475	64	25	r	r	NOUN
ejpam-1475	64	26	)	)	PUNCT
ejpam-1475	64	27	of	of	ADP
ejpam-1475	64	28	dimension	dimension	NOUN
ejpam-1475	64	29	m.	m.	NOUN
ejpam-1475	64	30	in	in	ADP
ejpam-1475	64	31	addition	addition	NOUN
ejpam-1475	64	32	,	,	PUNCT
ejpam-1475	64	33	it	it	PRON
ejpam-1475	64	34	is	be	AUX
ejpam-1475	64	35	assumed	assume	VERB
ejpam-1475	64	36	that	that	SCONJ
ejpam-1475	64	37	there	there	PRON
ejpam-1475	64	38	is	be	VERB
ejpam-1475	64	39	a	a	DET
ejpam-1475	64	40	prescribed	prescribe	VERB
ejpam-1475	64	41	(	(	PUNCT
ejpam-1475	64	42	smooth	smooth	ADJ
ejpam-1475	64	43	)	)	PUNCT
ejpam-1475	64	44	cost	cost	NOUN
ejpam-1475	64	45	function	function	NOUN
ejpam-1475	64	46	l	l	NOUN
ejpam-1475	64	47	:	:	PUNCT
ejpam-1475	64	48	rℓ	rℓ	NOUN
ejpam-1475	64	49	→	→	SYM
ejpam-1475	64	50	r	r	NOUN
ejpam-1475	64	51	(	(	PUNCT
ejpam-1475	64	52	which	which	PRON
ejpam-1475	64	53	is	be	AUX
ejpam-1475	64	54	also	also	ADV
ejpam-1475	64	55	called	call	VERB
ejpam-1475	64	56	a	a	DET
ejpam-1475	64	57	lagrangian	lagrangian	ADJ
ejpam-1475	64	58	)	)	PUNCT
ejpam-1475	64	59	.	.	PUNCT
ejpam-1475	65	1	let	let	VERB
ejpam-1475	65	2	g0	g0	NOUN
ejpam-1475	65	3	and	and	CCONJ
ejpam-1475	65	4	g1	g1	PROPN
ejpam-1475	65	5	be	be	AUX
ejpam-1475	65	6	arbitrary	arbitrary	ADJ
ejpam-1475	65	7	but	but	CCONJ
ejpam-1475	65	8	fixed	fix	VERB
ejpam-1475	65	9	points	point	NOUN
ejpam-1475	65	10	of	of	ADP
ejpam-1475	65	11	g.	g.	NOUN
ejpam-1475	65	12	we	we	PRON
ejpam-1475	65	13	shall	shall	AUX
ejpam-1475	65	14	be	be	AUX
ejpam-1475	65	15	interested	interested	ADJ
ejpam-1475	65	16	in	in	ADP
ejpam-1475	65	17	finding	find	VERB
ejpam-1475	65	18	a	a	DET
ejpam-1475	65	19	trajectory	trajectory	NOUN
ejpam-1475	65	20	-	-	PUNCT
ejpam-1475	65	21	control	control	NOUN
ejpam-1475	65	22	pair	pair	NOUN
ejpam-1475	65	23	(	(	PUNCT
ejpam-1475	65	24	g(·),u	g(·),u	NOUN
ejpam-1475	65	25	(	(	PUNCT
ejpam-1475	65	26	·	·	PUNCT
ejpam-1475	65	27	)	)	PUNCT
ejpam-1475	65	28	)	)	PUNCT
ejpam-1475	65	29	which	which	PRON
ejpam-1475	65	30	satisfies	satisfy	VERB
ejpam-1475	65	31	g(0	g(0	NOUN
ejpam-1475	65	32	)	)	PUNCT
ejpam-1475	65	33	=	=	SYM
ejpam-1475	65	34	g0	g0	PROPN
ejpam-1475	65	35	,	,	PUNCT
ejpam-1475	65	36	g(t	g(t	PROPN
ejpam-1475	65	37	)	)	PUNCT
ejpam-1475	66	1	=	=	PUNCT
ejpam-1475	66	2	g1	g1	PROPN
ejpam-1475	66	3	(	(	PUNCT
ejpam-1475	66	4	2	2	NUM
ejpam-1475	66	5	)	)	PUNCT
ejpam-1475	66	6	and	and	CCONJ
ejpam-1475	66	7	in	in	ADP
ejpam-1475	66	8	addition	addition	NOUN
ejpam-1475	66	9	minimizes	minimize	VERB
ejpam-1475	66	10	the	the	DET
ejpam-1475	66	11	total	total	ADJ
ejpam-1475	66	12	cost	cost	NOUN
ejpam-1475	66	13	functional	functional	ADJ
ejpam-1475	66	14	j	j	PROPN
ejpam-1475	66	15	=	=	SYM
ejpam-1475	66	16	∫	∫	PROPN
ejpam-1475	67	1	t	t	PROPN
ejpam-1475	67	2	0	0	NUM
ejpam-1475	67	3	l(u(t))d	l(u(t))d	PROPN
ejpam-1475	67	4	t	t	NOUN
ejpam-1475	67	5	among	among	ADP
ejpam-1475	67	6	all	all	DET
ejpam-1475	67	7	trajectories	trajectory	NOUN
ejpam-1475	67	8	of	of	ADP
ejpam-1475	67	9	(	(	PUNCT
ejpam-1475	67	10	1	1	X
ejpam-1475	67	11	)	)	PUNCT
ejpam-1475	67	12	which	which	PRON
ejpam-1475	67	13	satisfy	satisfy	VERB
ejpam-1475	67	14	the	the	DET
ejpam-1475	67	15	same	same	ADJ
ejpam-1475	67	16	boundary	boundary	ADJ
ejpam-1475	67	17	conditions	condition	NOUN
ejpam-1475	67	18	(	(	PUNCT
ejpam-1475	67	19	2	2	NUM
ejpam-1475	67	20	)	)	PUNCT
ejpam-1475	67	21	.	.	PUNCT
ejpam-1475	68	1	the	the	DET
ejpam-1475	68	2	terminal	terminal	ADJ
ejpam-1475	68	3	time	time	NOUN
ejpam-1475	68	4	t	t	PROPN
ejpam-1475	68	5	>	>	X
ejpam-1475	68	6	0	0	NUM
ejpam-1475	68	7	can	can	AUX
ejpam-1475	68	8	be	be	AUX
ejpam-1475	68	9	either	either	ADV
ejpam-1475	68	10	fixed	fix	VERB
ejpam-1475	68	11	or	or	CCONJ
ejpam-1475	68	12	it	it	PRON
ejpam-1475	68	13	can	can	AUX
ejpam-1475	68	14	be	be	AUX
ejpam-1475	68	15	free	free	ADJ
ejpam-1475	68	16	.	.	PUNCT
ejpam-1475	69	1	the	the	DET
ejpam-1475	69	2	pontryagin	pontryagin	NOUN
ejpam-1475	69	3	maximum	maximum	ADJ
ejpam-1475	69	4	principle	principle	NOUN
ejpam-1475	69	5	is	be	AUX
ejpam-1475	69	6	a	a	DET
ejpam-1475	69	7	necessary	necessary	ADJ
ejpam-1475	69	8	condition	condition	NOUN
ejpam-1475	69	9	for	for	ADP
ejpam-1475	69	10	optimality	optimality	NOUN
ejpam-1475	69	11	which	which	PRON
ejpam-1475	69	12	is	be	AUX
ejpam-1475	69	13	most	most	ADV
ejpam-1475	69	14	naturally	naturally	ADV
ejpam-1475	69	15	expressed	express	VERB
ejpam-1475	69	16	in	in	ADP
ejpam-1475	69	17	the	the	DET
ejpam-1475	69	18	language	language	NOUN
ejpam-1475	69	19	of	of	ADP
ejpam-1475	69	20	the	the	DET
ejpam-1475	69	21	geometry	geometry	NOUN
ejpam-1475	69	22	of	of	ADP
ejpam-1475	69	23	the	the	DET
ejpam-1475	69	24	cotangent	cotangent	NOUN
ejpam-1475	69	25	bundle	bundle	NOUN
ejpam-1475	69	26	t	t	PROPN
ejpam-1475	69	27	∗g	∗g	NOUN
ejpam-1475	69	28	of	of	ADP
ejpam-1475	69	29	g	g	PROPN
ejpam-1475	69	30	(	(	PUNCT
ejpam-1475	69	31	cf	cf	NOUN
ejpam-1475	69	32	.	.	PUNCT
ejpam-1475	70	1	[	[	X
ejpam-1475	70	2	1	1	NUM
ejpam-1475	70	3	,	,	PUNCT
ejpam-1475	70	4	11	11	NUM
ejpam-1475	70	5	]	]	NUM
ejpam-1475	70	6	)	)	PUNCT
ejpam-1475	70	7	.	.	PUNCT
ejpam-1475	71	1	the	the	DET
ejpam-1475	71	2	cotangent	cotangent	NOUN
ejpam-1475	71	3	bundle	bundle	NOUN
ejpam-1475	71	4	t	t	PROPN
ejpam-1475	71	5	∗g	∗g	PROPN
ejpam-1475	71	6	can	can	AUX
ejpam-1475	71	7	be	be	AUX
ejpam-1475	71	8	trivialized	trivialize	VERB
ejpam-1475	71	9	(	(	PUNCT
ejpam-1475	71	10	from	from	ADP
ejpam-1475	71	11	the	the	DET
ejpam-1475	71	12	left	left	NOUN
ejpam-1475	71	13	)	)	PUNCT
ejpam-1475	72	1	such	such	ADJ
ejpam-1475	72	2	that	that	SCONJ
ejpam-1475	72	3	t	t	NOUN
ejpam-1475	72	4	∗g	∗g	PROPN
ejpam-1475	72	5	=	=	PUNCT
ejpam-1475	72	6	g×g∗	g×g∗	PROPN
ejpam-1475	72	7	,	,	PUNCT
ejpam-1475	72	8	where	where	SCONJ
ejpam-1475	72	9	g	g	PROPN
ejpam-1475	72	10	∗	∗	NOUN
ejpam-1475	72	11	is	be	AUX
ejpam-1475	72	12	the	the	DET
ejpam-1475	72	13	dual	dual	ADJ
ejpam-1475	72	14	space	space	NOUN
ejpam-1475	72	15	of	of	ADP
ejpam-1475	72	16	the	the	DET
ejpam-1475	72	17	lie	lie	NOUN
ejpam-1475	72	18	algebra	algebra	NOUN
ejpam-1475	72	19	g.	g.	NOUN
ejpam-1475	72	20	the	the	DET
ejpam-1475	72	21	dual	dual	ADJ
ejpam-1475	72	22	space	space	NOUN
ejpam-1475	72	23	g	g	PROPN
ejpam-1475	72	24	∗	∗	NOUN
ejpam-1475	72	25	has	have	VERB
ejpam-1475	72	26	a	a	DET
ejpam-1475	72	27	natural	natural	ADJ
ejpam-1475	72	28	poisson	poisson	NOUN
ejpam-1475	72	29	structure	structure	NOUN
ejpam-1475	72	30	,	,	PUNCT
ejpam-1475	72	31	called	call	VERB
ejpam-1475	72	32	the	the	DET
ejpam-1475	72	33	“	"	PUNCT
ejpam-1475	72	34	minus	minus	CCONJ
ejpam-1475	72	35	lie	lie	NOUN
ejpam-1475	72	36	-	-	PUNCT
ejpam-1475	72	37	poisson	poisson	NOUN
ejpam-1475	72	38	structure	structure	NOUN
ejpam-1475	72	39	”	"	PUNCT
ejpam-1475	72	40	,	,	PUNCT
ejpam-1475	72	41	given	give	VERB
ejpam-1475	72	42	by	by	ADP
ejpam-1475	72	43	{	{	PUNCT
ejpam-1475	72	44	f	f	PROPN
ejpam-1475	72	45	,	,	PUNCT
ejpam-1475	72	46	g}−	g}−	PROPN
ejpam-1475	72	47	(	(	PUNCT
ejpam-1475	72	48	p	p	NOUN
ejpam-1475	72	49	)	)	PUNCT
ejpam-1475	72	50	=	=	SYM
ejpam-1475	72	51	−p	−p	PROPN
ejpam-1475	72	52	�	�	PROPN
ejpam-1475	72	53	�	�	PROPN
ejpam-1475	72	54	df(p	df(p	NUM
ejpam-1475	72	55	)	)	PUNCT
ejpam-1475	72	56	,	,	PUNCT
ejpam-1475	72	57	dg(p	dg(p	X
ejpam-1475	72	58	)	)	PUNCT
ejpam-1475	72	59	�	�	PROPN
ejpam-1475	72	60	�	�	PROPN
ejpam-1475	72	61	for	for	ADP
ejpam-1475	72	62	p	p	PROPN
ejpam-1475	72	63	∈	∈	PROPN
ejpam-1475	72	64	g∗	g∗	NOUN
ejpam-1475	72	65	and	and	CCONJ
ejpam-1475	72	66	f	f	NOUN
ejpam-1475	72	67	,	,	PUNCT
ejpam-1475	72	68	g	g	PROPN
ejpam-1475	72	69	∈	∈	PROPN
ejpam-1475	72	70	c∞(g∗	c∞(g∗	NOUN
ejpam-1475	72	71	)	)	PUNCT
ejpam-1475	72	72	.	.	PUNCT
ejpam-1475	73	1	(	(	PUNCT
ejpam-1475	73	2	note	note	VERB
ejpam-1475	73	3	that	that	SCONJ
ejpam-1475	73	4	df(p	df(p	PRON
ejpam-1475	73	5	)	)	PUNCT
ejpam-1475	73	6	is	be	AUX
ejpam-1475	73	7	a	a	DET
ejpam-1475	73	8	linear	linear	ADJ
ejpam-1475	73	9	function	function	NOUN
ejpam-1475	73	10	on	on	ADP
ejpam-1475	73	11	g	g	PROPN
ejpam-1475	73	12	∗	∗	NOUN
ejpam-1475	73	13	and	and	CCONJ
ejpam-1475	73	14	so	so	ADV
ejpam-1475	73	15	is	be	AUX
ejpam-1475	73	16	an	an	DET
ejpam-1475	73	17	element	element	NOUN
ejpam-1475	73	18	of	of	ADP
ejpam-1475	73	19	g.	g.	PROPN
ejpam-1475	73	20	)	)	PUNCT
ejpam-1475	73	21	the	the	DET
ejpam-1475	73	22	poisson	poisson	PROPN
ejpam-1475	73	23	manifold	manifold	NOUN
ejpam-1475	73	24	(	(	PUNCT
ejpam-1475	73	25	g∗	g∗	PROPN
ejpam-1475	73	26	,	,	PUNCT
ejpam-1475	73	27	{	{	PUNCT
ejpam-1475	73	28	·	·	PUNCT
ejpam-1475	73	29	,	,	PUNCT
ejpam-1475	73	30	·	·	PUNCT
ejpam-1475	73	31	}	}	PUNCT
ejpam-1475	73	32	)	)	PUNCT
ejpam-1475	73	33	is	be	AUX
ejpam-1475	73	34	denoted	denote	VERB
ejpam-1475	73	35	by	by	ADP
ejpam-1475	73	36	g	g	NOUN
ejpam-1475	73	37	∗	∗	NOUN
ejpam-1475	73	38	−.	−.	NOUN
ejpam-1475	73	39	each	each	DET
ejpam-1475	73	40	left	left	ADJ
ejpam-1475	73	41	-	-	PUNCT
ejpam-1475	73	42	invariant	invariant	ADJ
ejpam-1475	73	43	hamiltonian	hamiltonian	NOUN
ejpam-1475	73	44	on	on	ADP
ejpam-1475	73	45	the	the	DET
ejpam-1475	73	46	cotangent	cotangent	NOUN
ejpam-1475	73	47	bundle	bundle	NOUN
ejpam-1475	73	48	t	t	PROPN
ejpam-1475	73	49	∗g	∗g	PROPN
ejpam-1475	73	50	is	be	AUX
ejpam-1475	73	51	identified	identify	VERB
ejpam-1475	73	52	with	with	ADP
ejpam-1475	73	53	its	its	PRON
ejpam-1475	73	54	reduction	reduction	NOUN
ejpam-1475	73	55	on	on	ADP
ejpam-1475	73	56	the	the	DET
ejpam-1475	73	57	dual	dual	ADJ
ejpam-1475	73	58	space	space	NOUN
ejpam-1475	73	59	g	g	NOUN
ejpam-1475	73	60	∗	∗	VERB
ejpam-1475	73	61	−.	−.	ADJ
ejpam-1475	73	62	to	to	ADP
ejpam-1475	73	63	an	an	DET
ejpam-1475	73	64	optimal	optimal	ADJ
ejpam-1475	73	65	control	control	NOUN
ejpam-1475	73	66	problem	problem	NOUN
ejpam-1475	73	67	(	(	PUNCT
ejpam-1475	73	68	with	with	ADP
ejpam-1475	73	69	fixed	fix	VERB
ejpam-1475	73	70	terminal	terminal	ADJ
ejpam-1475	73	71	time	time	NOUN
ejpam-1475	73	72	)	)	PUNCT
ejpam-1475	74	1	∫	∫	PROPN
ejpam-1475	74	2	t	t	NOUN
ejpam-1475	74	3	0	0	NUM
ejpam-1475	74	4	l(u(t))d	l(u(t))d	PROPN
ejpam-1475	74	5	t	t	PROPN
ejpam-1475	74	6	→min	→min	PROPN
ejpam-1475	74	7	(	(	PUNCT
ejpam-1475	74	8	3	3	NUM
ejpam-1475	74	9	)	)	PUNCT
ejpam-1475	74	10	subject	subject	NOUN
ejpam-1475	74	11	to	to	ADP
ejpam-1475	74	12	(	(	PUNCT
ejpam-1475	74	13	1	1	NUM
ejpam-1475	74	14	)	)	PUNCT
ejpam-1475	74	15	and	and	CCONJ
ejpam-1475	74	16	(	(	PUNCT
ejpam-1475	74	17	2	2	NUM
ejpam-1475	74	18	)	)	PUNCT
ejpam-1475	74	19	,	,	PUNCT
ejpam-1475	74	20	we	we	PRON
ejpam-1475	74	21	associate	associate	VERB
ejpam-1475	74	22	,	,	PUNCT
ejpam-1475	74	23	for	for	ADP
ejpam-1475	74	24	each	each	DET
ejpam-1475	74	25	real	real	ADJ
ejpam-1475	74	26	number	number	NOUN
ejpam-1475	74	27	λ	λ	NOUN
ejpam-1475	74	28	and	and	CCONJ
ejpam-1475	74	29	each	each	DET
ejpam-1475	74	30	control	control	NOUN
ejpam-1475	74	31	parameter	parameter	NOUN
ejpam-1475	74	32	u	u	PROPN
ejpam-1475	74	33	∈	∈	PROPN
ejpam-1475	74	34	rℓ	rℓ	PROPN
ejpam-1475	74	35	,	,	PUNCT
ejpam-1475	74	36	a	a	DET
ejpam-1475	74	37	hamiltonian	hamiltonian	ADJ
ejpam-1475	74	38	function	function	NOUN
ejpam-1475	74	39	on	on	ADP
ejpam-1475	74	40	t	t	PROPN
ejpam-1475	74	41	∗g	∗g	PROPN
ejpam-1475	74	42	=	=	PUNCT
ejpam-1475	75	1	g×	g×	PROPN
ejpam-1475	75	2	g	g	NOUN
ejpam-1475	75	3	∗	∗	NOUN
ejpam-1475	75	4	:	:	PUNCT
ejpam-1475	75	5	hλu	hλu	NOUN
ejpam-1475	75	6	(	(	PUNCT
ejpam-1475	75	7	ξ	ξ	NOUN
ejpam-1475	75	8	)	)	PUNCT
ejpam-1475	75	9	=	=	SYM
ejpam-1475	75	10	λl(u	λl(u	X
ejpam-1475	75	11	)	)	PUNCT
ejpam-1475	75	12	+	+	CCONJ
ejpam-1475	75	13	ξ	ξ	PROPN
ejpam-1475	75	14	�	�	PROPN
ejpam-1475	75	15	gξ(1,u	gξ(1,u	PROPN
ejpam-1475	75	16	)	)	PUNCT
ejpam-1475	75	17	�	�	PROPN
ejpam-1475	75	18	=	=	SYM
ejpam-1475	75	19	λl(u	λl(u	X
ejpam-1475	75	20	)	)	PUNCT
ejpam-1475	76	1	+	+	CCONJ
ejpam-1475	76	2	p	p	X
ejpam-1475	76	3	(	(	PUNCT
ejpam-1475	76	4	ξ(1,u	ξ(1,u	NOUN
ejpam-1475	76	5	)	)	PUNCT
ejpam-1475	76	6	)	)	PUNCT
ejpam-1475	76	7	,	,	PUNCT
ejpam-1475	76	8	ξ=	ξ=	X
ejpam-1475	76	9	(	(	PUNCT
ejpam-1475	76	10	g	g	NOUN
ejpam-1475	76	11	,	,	PUNCT
ejpam-1475	76	12	p	p	NOUN
ejpam-1475	76	13	)	)	PUNCT
ejpam-1475	76	14	∈	∈	PROPN
ejpam-1475	76	15	t	t	PROPN
ejpam-1475	76	16	∗g	∗g	PROPN
ejpam-1475	76	17	.	.	PUNCT
ejpam-1475	77	1	the	the	DET
ejpam-1475	77	2	maximum	maximum	ADJ
ejpam-1475	77	3	principle	principle	NOUN
ejpam-1475	77	4	can	can	AUX
ejpam-1475	77	5	be	be	AUX
ejpam-1475	77	6	stated	state	VERB
ejpam-1475	77	7	,	,	PUNCT
ejpam-1475	77	8	in	in	ADP
ejpam-1475	77	9	terms	term	NOUN
ejpam-1475	77	10	of	of	ADP
ejpam-1475	77	11	the	the	DET
ejpam-1475	77	12	above	above	ADJ
ejpam-1475	77	13	hamiltonians	hamiltonian	NOUN
ejpam-1475	77	14	,	,	PUNCT
ejpam-1475	77	15	as	as	SCONJ
ejpam-1475	77	16	follows	follow	VERB
ejpam-1475	77	17	.	.	PUNCT
ejpam-1475	78	1	r.	r.	PROPN
ejpam-1475	78	2	adams	adams	PROPN
ejpam-1475	78	3	,	,	PUNCT
ejpam-1475	78	4	r.	r.	PROPN
ejpam-1475	78	5	biggs	biggs	PROPN
ejpam-1475	78	6	,	,	PUNCT
ejpam-1475	78	7	c.	c.	PROPN
ejpam-1475	78	8	remsing	remsing	NOUN
ejpam-1475	78	9	/	/	SYM
ejpam-1475	78	10	eur	eur	NOUN
ejpam-1475	78	11	.	.	PUNCT
ejpam-1475	79	1	j.	j.	PROPN
ejpam-1475	79	2	pure	pure	PROPN
ejpam-1475	79	3	appl	appl	PROPN
ejpam-1475	79	4	.	.	PROPN
ejpam-1475	79	5	math	math	PROPN
ejpam-1475	79	6	,	,	PUNCT
ejpam-1475	79	7	5	5	NUM
ejpam-1475	79	8	(	(	PUNCT
ejpam-1475	79	9	2012	2012	NUM
ejpam-1475	79	10	)	)	PUNCT
ejpam-1475	79	11	,	,	PUNCT
ejpam-1475	79	12	1	1	NUM
ejpam-1475	79	13	-	-	SYM
ejpam-1475	79	14	15	15	NUM
ejpam-1475	79	15	4	4	NUM
ejpam-1475	79	16	maximum	maximum	NOUN
ejpam-1475	79	17	principle	principle	NOUN
ejpam-1475	79	18	.	.	PUNCT
ejpam-1475	80	1	suppose	suppose	VERB
ejpam-1475	80	2	the	the	DET
ejpam-1475	80	3	trajectory	trajectory	NOUN
ejpam-1475	80	4	-	-	PUNCT
ejpam-1475	80	5	control	control	NOUN
ejpam-1475	80	6	pair	pair	NOUN
ejpam-1475	80	7	(	(	PUNCT
ejpam-1475	80	8	ḡ	ḡ	VERB
ejpam-1475	80	9	(	(	PUNCT
ejpam-1475	80	10	·	·	PUNCT
ejpam-1475	80	11	)	)	PUNCT
ejpam-1475	80	12	,	,	PUNCT
ejpam-1475	80	13	ū	ū	NOUN
ejpam-1475	80	14	(	(	PUNCT
ejpam-1475	80	15	·	·	PUNCT
ejpam-1475	80	16	)	)	PUNCT
ejpam-1475	80	17	)	)	PUNCT
ejpam-1475	80	18	defined	define	VERB
ejpam-1475	80	19	over	over	ADP
ejpam-1475	80	20	the	the	DET
ejpam-1475	80	21	interval	interval	NOUN
ejpam-1475	80	22	[	[	X
ejpam-1475	80	23	0	0	NUM
ejpam-1475	80	24	,	,	PUNCT
ejpam-1475	80	25	t	t	PROPN
ejpam-1475	80	26	]	]	PUNCT
ejpam-1475	80	27	is	be	AUX
ejpam-1475	80	28	a	a	DET
ejpam-1475	80	29	solution	solution	NOUN
ejpam-1475	80	30	for	for	ADP
ejpam-1475	80	31	the	the	DET
ejpam-1475	80	32	optimal	optimal	ADJ
ejpam-1475	80	33	control	control	NOUN
ejpam-1475	80	34	problem	problem	NOUN
ejpam-1475	80	35	(	(	PUNCT
ejpam-1475	80	36	1)-(2)-(3	1)-(2)-(3	NUM
ejpam-1475	80	37	)	)	PUNCT
ejpam-1475	80	38	.	.	PUNCT
ejpam-1475	81	1	then	then	ADV
ejpam-1475	81	2	,	,	PUNCT
ejpam-1475	81	3	there	there	PRON
ejpam-1475	81	4	exists	exist	VERB
ejpam-1475	81	5	a	a	DET
ejpam-1475	81	6	curve	curve	NOUN
ejpam-1475	81	7	ξ	ξ	PROPN
ejpam-1475	81	8	(	(	PUNCT
ejpam-1475	81	9	·	·	PUNCT
ejpam-1475	81	10	)	)	PUNCT
ejpam-1475	81	11	:	:	PUNCT
ejpam-1475	82	1	[	[	X
ejpam-1475	82	2	0	0	NUM
ejpam-1475	82	3	,	,	PUNCT
ejpam-1475	82	4	t	t	PROPN
ejpam-1475	82	5	]	]	PUNCT
ejpam-1475	82	6	→	→	SYM
ejpam-1475	82	7	t	t	PROPN
ejpam-1475	82	8	∗g	∗g	NOUN
ejpam-1475	82	9	with	with	ADP
ejpam-1475	82	10	ξ(t	ξ(t	NOUN
ejpam-1475	82	11	)	)	PUNCT
ejpam-1475	82	12	∈	∈	PROPN
ejpam-1475	82	13	t	t	PROPN
ejpam-1475	82	14	∗	∗	X
ejpam-1475	82	15	ḡ(t	ḡ(t	PROPN
ejpam-1475	82	16	)	)	PUNCT
ejpam-1475	82	17	g	g	NOUN
ejpam-1475	82	18	,	,	PUNCT
ejpam-1475	82	19	t	t	PROPN
ejpam-1475	82	20	∈	∈	PROPN
ejpam-1475	83	1	[	[	X
ejpam-1475	83	2	0	0	NUM
ejpam-1475	83	3	,	,	PUNCT
ejpam-1475	83	4	t	t	PROPN
ejpam-1475	83	5	]	]	PUNCT
ejpam-1475	83	6	,	,	PUNCT
ejpam-1475	83	7	and	and	CCONJ
ejpam-1475	83	8	a	a	DET
ejpam-1475	83	9	real	real	ADJ
ejpam-1475	83	10	number	number	NOUN
ejpam-1475	83	11	λ	λ	NOUN
ejpam-1475	83	12	≤	≤	NOUN
ejpam-1475	83	13	0	0	NUM
ejpam-1475	83	14	,	,	PUNCT
ejpam-1475	83	15	such	such	ADJ
ejpam-1475	83	16	that	that	SCONJ
ejpam-1475	83	17	the	the	DET
ejpam-1475	83	18	following	follow	VERB
ejpam-1475	83	19	conditions	condition	NOUN
ejpam-1475	83	20	hold	hold	VERB
ejpam-1475	83	21	for	for	ADP
ejpam-1475	83	22	almost	almost	ADV
ejpam-1475	83	23	every	every	PRON
ejpam-1475	83	24	t	t	NOUN
ejpam-1475	83	25	∈	∈	PROPN
ejpam-1475	84	1	[	[	X
ejpam-1475	84	2	0	0	NUM
ejpam-1475	84	3	,	,	PUNCT
ejpam-1475	84	4	t	t	PROPN
ejpam-1475	84	5	]	]	PUNCT
ejpam-1475	84	6	:	:	PUNCT
ejpam-1475	84	7	(	(	PUNCT
ejpam-1475	84	8	λ	λ	X
ejpam-1475	84	9	,	,	PUNCT
ejpam-1475	84	10	ξ(t	ξ(t	NOUN
ejpam-1475	84	11	)	)	PUNCT
ejpam-1475	84	12	)	)	PUNCT
ejpam-1475	84	13	6≡	6≡	NUM
ejpam-1475	84	14	(	(	PUNCT
ejpam-1475	84	15	0,0	0,0	NOUN
ejpam-1475	84	16	)	)	PUNCT
ejpam-1475	84	17	(	(	PUNCT
ejpam-1475	84	18	4	4	X
ejpam-1475	84	19	)	)	PUNCT
ejpam-1475	84	20	ξ̇(t	ξ̇(t	NOUN
ejpam-1475	84	21	)	)	PUNCT
ejpam-1475	84	22	=	=	PUNCT
ejpam-1475	84	23	~hλ	~hλ	PUNCT
ejpam-1475	84	24	ū(t	ū(t	NOUN
ejpam-1475	84	25	)	)	PUNCT
ejpam-1475	84	26	(	(	PUNCT
ejpam-1475	84	27	ξ(t	ξ(t	NOUN
ejpam-1475	84	28	)	)	PUNCT
ejpam-1475	84	29	)	)	PUNCT
ejpam-1475	84	30	(	(	PUNCT
ejpam-1475	84	31	5	5	X
ejpam-1475	84	32	)	)	PUNCT
ejpam-1475	84	33	hλ	hλ	X
ejpam-1475	84	34	ū(t	ū(t	NOUN
ejpam-1475	84	35	)	)	PUNCT
ejpam-1475	84	36	(	(	PUNCT
ejpam-1475	84	37	ξ(t	ξ(t	NOUN
ejpam-1475	84	38	)	)	PUNCT
ejpam-1475	84	39	)	)	PUNCT
ejpam-1475	85	1	=	=	PRON
ejpam-1475	85	2	max	max	NOUN
ejpam-1475	85	3	u	u	PROPN
ejpam-1475	85	4	hλu	hλu	NOUN
ejpam-1475	85	5	(	(	PUNCT
ejpam-1475	85	6	ξ(t	ξ(t	NOUN
ejpam-1475	85	7	)	)	PUNCT
ejpam-1475	85	8	)	)	PUNCT
ejpam-1475	85	9	=	=	PUNCT
ejpam-1475	85	10	constant	constant	ADJ
ejpam-1475	85	11	.	.	PUNCT
ejpam-1475	86	1	(	(	PUNCT
ejpam-1475	86	2	6	6	NUM
ejpam-1475	86	3	)	)	PUNCT
ejpam-1475	86	4	an	an	DET
ejpam-1475	86	5	optimal	optimal	ADJ
ejpam-1475	86	6	trajectory	trajectory	NOUN
ejpam-1475	86	7	ḡ	ḡ	VERB
ejpam-1475	86	8	(	(	PUNCT
ejpam-1475	86	9	·	·	PUNCT
ejpam-1475	86	10	)	)	PUNCT
ejpam-1475	86	11	:	:	PUNCT
ejpam-1475	87	1	[	[	X
ejpam-1475	87	2	0	0	NUM
ejpam-1475	87	3	,	,	PUNCT
ejpam-1475	87	4	t	t	PROPN
ejpam-1475	87	5	]	]	PUNCT
ejpam-1475	87	6	→	→	PUNCT
ejpam-1475	87	7	g	g	PROPN
ejpam-1475	87	8	is	be	AUX
ejpam-1475	87	9	the	the	DET
ejpam-1475	87	10	projection	projection	NOUN
ejpam-1475	87	11	of	of	ADP
ejpam-1475	87	12	an	an	DET
ejpam-1475	87	13	integral	integral	ADJ
ejpam-1475	87	14	curve	curve	NOUN
ejpam-1475	87	15	ξ	ξ	PROPN
ejpam-1475	87	16	(	(	PUNCT
ejpam-1475	87	17	·	·	PUNCT
ejpam-1475	87	18	)	)	PUNCT
ejpam-1475	87	19	of	of	ADP
ejpam-1475	87	20	the	the	DET
ejpam-1475	87	21	(	(	PUNCT
ejpam-1475	87	22	time	time	NOUN
ejpam-1475	87	23	-	-	PUNCT
ejpam-1475	87	24	varying	vary	VERB
ejpam-1475	87	25	)	)	PUNCT
ejpam-1475	87	26	hamiltonian	hamiltonian	ADJ
ejpam-1475	87	27	vector	vector	NOUN
ejpam-1475	87	28	field	field	NOUN
ejpam-1475	87	29	~hλ	~hλ	PROPN
ejpam-1475	87	30	ū(t	ū(t	NOUN
ejpam-1475	87	31	)	)	PUNCT
ejpam-1475	87	32	defined	define	VERB
ejpam-1475	87	33	for	for	ADP
ejpam-1475	87	34	all	all	DET
ejpam-1475	87	35	t	t	NOUN
ejpam-1475	87	36	∈	∈	PROPN
ejpam-1475	88	1	[	[	X
ejpam-1475	88	2	0	0	NUM
ejpam-1475	88	3	,	,	PUNCT
ejpam-1475	88	4	t	t	PROPN
ejpam-1475	88	5	]	]	PUNCT
ejpam-1475	88	6	.	.	PUNCT
ejpam-1475	89	1	a	a	DET
ejpam-1475	89	2	trajectory	trajectory	NOUN
ejpam-1475	89	3	-	-	PUNCT
ejpam-1475	89	4	control	control	NOUN
ejpam-1475	89	5	pair	pair	NOUN
ejpam-1475	89	6	(	(	PUNCT
ejpam-1475	89	7	ξ(·),u	ξ(·),u	PROPN
ejpam-1475	89	8	(	(	PUNCT
ejpam-1475	89	9	·	·	PUNCT
ejpam-1475	89	10	)	)	PUNCT
ejpam-1475	89	11	)	)	PUNCT
ejpam-1475	89	12	defined	define	VERB
ejpam-1475	89	13	on	on	ADP
ejpam-1475	89	14	[	[	X
ejpam-1475	89	15	0	0	NUM
ejpam-1475	89	16	,	,	PUNCT
ejpam-1475	89	17	t	t	PROPN
ejpam-1475	89	18	]	]	PUNCT
ejpam-1475	89	19	is	be	AUX
ejpam-1475	89	20	said	say	VERB
ejpam-1475	89	21	to	to	PART
ejpam-1475	89	22	be	be	AUX
ejpam-1475	89	23	an	an	DET
ejpam-1475	89	24	extremal	extremal	ADJ
ejpam-1475	89	25	pair	pair	NOUN
ejpam-1475	89	26	if	if	SCONJ
ejpam-1475	89	27	ξ	ξ	X
ejpam-1475	89	28	(	(	PUNCT
ejpam-1475	89	29	·	·	PUNCT
ejpam-1475	89	30	)	)	PUNCT
ejpam-1475	89	31	satisfies	satisfy	VERB
ejpam-1475	89	32	the	the	DET
ejpam-1475	89	33	conditions	condition	NOUN
ejpam-1475	89	34	(	(	PUNCT
ejpam-1475	89	35	4	4	NUM
ejpam-1475	89	36	)	)	PUNCT
ejpam-1475	89	37	,	,	PUNCT
ejpam-1475	89	38	(	(	PUNCT
ejpam-1475	89	39	5	5	NUM
ejpam-1475	89	40	)	)	PUNCT
ejpam-1475	89	41	and	and	CCONJ
ejpam-1475	89	42	(	(	PUNCT
ejpam-1475	89	43	6	6	NUM
ejpam-1475	89	44	)	)	PUNCT
ejpam-1475	89	45	.	.	PUNCT
ejpam-1475	90	1	the	the	DET
ejpam-1475	90	2	projection	projection	PROPN
ejpam-1475	90	3	ξ	ξ	PROPN
ejpam-1475	90	4	(	(	PUNCT
ejpam-1475	90	5	·	·	PUNCT
ejpam-1475	90	6	)	)	PUNCT
ejpam-1475	90	7	of	of	ADP
ejpam-1475	90	8	an	an	DET
ejpam-1475	90	9	extremal	extremal	ADJ
ejpam-1475	90	10	pair	pair	NOUN
ejpam-1475	90	11	is	be	AUX
ejpam-1475	90	12	called	call	VERB
ejpam-1475	90	13	an	an	DET
ejpam-1475	90	14	extremal	extremal	NOUN
ejpam-1475	90	15	.	.	PUNCT
ejpam-1475	91	1	an	an	DET
ejpam-1475	91	2	extremal	extremal	ADJ
ejpam-1475	91	3	curve	curve	NOUN
ejpam-1475	91	4	is	be	AUX
ejpam-1475	91	5	called	call	VERB
ejpam-1475	91	6	normal	normal	ADJ
ejpam-1475	91	7	if	if	SCONJ
ejpam-1475	91	8	λ	λ	NOUN
ejpam-1475	91	9	=	=	VERB
ejpam-1475	91	10	−1	−1	NOUN
ejpam-1475	91	11	and	and	CCONJ
ejpam-1475	91	12	abnormal	abnormal	ADJ
ejpam-1475	91	13	if	if	SCONJ
ejpam-1475	91	14	λ	λ	X
ejpam-1475	91	15	=	=	NOUN
ejpam-1475	91	16	0	0	X
ejpam-1475	91	17	.	.	PUNCT
ejpam-1475	92	1	in	in	ADP
ejpam-1475	92	2	this	this	DET
ejpam-1475	92	3	paper	paper	NOUN
ejpam-1475	92	4	,	,	PUNCT
ejpam-1475	92	5	we	we	PRON
ejpam-1475	92	6	shall	shall	AUX
ejpam-1475	92	7	be	be	AUX
ejpam-1475	92	8	concerned	concern	VERB
ejpam-1475	92	9	only	only	ADV
ejpam-1475	92	10	with	with	ADP
ejpam-1475	92	11	normal	normal	ADJ
ejpam-1475	92	12	extremals	extremal	NOUN
ejpam-1475	92	13	.	.	PUNCT
ejpam-1475	93	1	suppose	suppose	VERB
ejpam-1475	93	2	the	the	DET
ejpam-1475	93	3	maximum	maximum	ADJ
ejpam-1475	93	4	condition	condition	NOUN
ejpam-1475	93	5	(	(	PUNCT
ejpam-1475	93	6	6	6	NUM
ejpam-1475	93	7	)	)	PUNCT
ejpam-1475	93	8	eliminates	eliminate	VERB
ejpam-1475	93	9	the	the	DET
ejpam-1475	93	10	parameter	parameter	NOUN
ejpam-1475	93	11	u	u	NOUN
ejpam-1475	93	12	from	from	ADP
ejpam-1475	93	13	the	the	DET
ejpam-1475	93	14	family	family	NOUN
ejpam-1475	93	15	of	of	ADP
ejpam-1475	93	16	hamiltonians	hamiltonians	PROPN
ejpam-1475	93	17	�	�	PROPN
ejpam-1475	93	18	hu	hu	PROPN
ejpam-1475	93	19	�	�	PROPN
ejpam-1475	93	20	,	,	PUNCT
ejpam-1475	93	21	and	and	CCONJ
ejpam-1475	93	22	as	as	ADP
ejpam-1475	93	23	a	a	DET
ejpam-1475	93	24	result	result	NOUN
ejpam-1475	93	25	of	of	ADP
ejpam-1475	93	26	this	this	DET
ejpam-1475	93	27	elimination	elimination	NOUN
ejpam-1475	93	28	,	,	PUNCT
ejpam-1475	93	29	we	we	PRON
ejpam-1475	93	30	obtain	obtain	VERB
ejpam-1475	93	31	a	a	DET
ejpam-1475	93	32	smooth	smooth	ADJ
ejpam-1475	93	33	function	function	NOUN
ejpam-1475	93	34	h	h	NOUN
ejpam-1475	93	35	(	(	PUNCT
ejpam-1475	93	36	without	without	ADP
ejpam-1475	93	37	parameters	parameter	NOUN
ejpam-1475	93	38	)	)	PUNCT
ejpam-1475	93	39	on	on	ADP
ejpam-1475	93	40	t	t	PROPN
ejpam-1475	93	41	∗g	∗g	PROPN
ejpam-1475	93	42	(	(	PUNCT
ejpam-1475	93	43	in	in	ADP
ejpam-1475	93	44	fact	fact	NOUN
ejpam-1475	93	45	,	,	PUNCT
ejpam-1475	93	46	on	on	ADP
ejpam-1475	93	47	g	g	ADP
ejpam-1475	93	48	∗	∗	NOUN
ejpam-1475	93	49	−	−	NUM
ejpam-1475	93	50	)	)	PUNCT
ejpam-1475	93	51	.	.	PUNCT
ejpam-1475	94	1	then	then	ADV
ejpam-1475	94	2	the	the	DET
ejpam-1475	94	3	whole	whole	ADJ
ejpam-1475	94	4	(	(	PUNCT
ejpam-1475	94	5	left	leave	VERB
ejpam-1475	94	6	-	-	PUNCT
ejpam-1475	94	7	invariant	invariant	ADJ
ejpam-1475	94	8	)	)	PUNCT
ejpam-1475	94	9	optimal	optimal	ADJ
ejpam-1475	94	10	control	control	NOUN
ejpam-1475	94	11	problem	problem	NOUN
ejpam-1475	94	12	reduces	reduce	VERB
ejpam-1475	94	13	to	to	ADP
ejpam-1475	94	14	the	the	DET
ejpam-1475	94	15	study	study	NOUN
ejpam-1475	94	16	of	of	ADP
ejpam-1475	94	17	trajectories	trajectory	NOUN
ejpam-1475	94	18	of	of	ADP
ejpam-1475	94	19	a	a	DET
ejpam-1475	94	20	fixed	fix	VERB
ejpam-1475	94	21	hamiltonian	hamiltonian	ADJ
ejpam-1475	94	22	vector	vector	NOUN
ejpam-1475	94	23	field	field	NOUN
ejpam-1475	94	24	~h	~h	PROPN
ejpam-1475	94	25	.	.	PUNCT
ejpam-1475	95	1	the	the	DET
ejpam-1475	95	2	following	follow	VERB
ejpam-1475	95	3	result	result	NOUN
ejpam-1475	95	4	holds	hold	VERB
ejpam-1475	95	5	.	.	PUNCT
ejpam-1475	96	1	theorem	theorem	ADJ
ejpam-1475	96	2	3	3	NUM
ejpam-1475	96	3	(	(	PUNCT
ejpam-1475	96	4	[	[	X
ejpam-1475	96	5	13	13	NUM
ejpam-1475	96	6	]	]	NUM
ejpam-1475	96	7	)	)	PUNCT
ejpam-1475	96	8	.	.	PUNCT
ejpam-1475	97	1	for	for	ADP
ejpam-1475	97	2	the	the	DET
ejpam-1475	97	3	left	left	ADJ
ejpam-1475	97	4	-	-	PUNCT
ejpam-1475	97	5	invariant	invariant	ADJ
ejpam-1475	97	6	control	control	NOUN
ejpam-1475	97	7	problem	problem	NOUN
ejpam-1475	97	8	ġ	ġ	NOUN
ejpam-1475	97	9	=	=	PUNCT
ejpam-1475	97	10	g	g	PROPN
ejpam-1475	97	11	�	�	PROPN
ejpam-1475	97	12	a+	a+	PUNCT
ejpam-1475	97	13	u1b1	u1b1	X
ejpam-1475	97	14	+	+	CCONJ
ejpam-1475	97	15	·	·	PUNCT
ejpam-1475	97	16	·	·	PUNCT
ejpam-1475	97	17	·	·	PUNCT
ejpam-1475	97	18	+	+	NUM
ejpam-1475	97	19	uℓbℓ	uℓbℓ	ADJ
ejpam-1475	97	20	�	�	NOUN
ejpam-1475	97	21	,	,	PUNCT
ejpam-1475	97	22	g	g	PROPN
ejpam-1475	97	23	∈	∈	PROPN
ejpam-1475	97	24	g	g	PROPN
ejpam-1475	97	25	,	,	PUNCT
ejpam-1475	97	26	u	u	PROPN
ejpam-1475	97	27	∈	∈	PROPN
ejpam-1475	97	28	rℓ	rℓ	NOUN
ejpam-1475	97	29	g(0	g(0	PROPN
ejpam-1475	97	30	)	)	PUNCT
ejpam-1475	97	31	=	=	PROPN
ejpam-1475	97	32	g0	g0	PROPN
ejpam-1475	97	33	,	,	PUNCT
ejpam-1475	97	34	g(t	g(t	PROPN
ejpam-1475	97	35	)	)	PUNCT
ejpam-1475	98	1	=	=	PUNCT
ejpam-1475	99	1	gt	gt	PROPN
ejpam-1475	99	2	j	j	NOUN
ejpam-1475	99	3	=	=	NOUN
ejpam-1475	99	4	1	1	NUM
ejpam-1475	99	5	2	2	NUM
ejpam-1475	99	6	∫	∫	NOUN
ejpam-1475	99	7	t	t	PROPN
ejpam-1475	99	8	0	0	NUM
ejpam-1475	99	9	�	�	PROPN
ejpam-1475	99	10	c1u2	c1u2	X
ejpam-1475	99	11	1(t	1(t	NUM
ejpam-1475	99	12	)	)	PUNCT
ejpam-1475	100	1	+	+	CCONJ
ejpam-1475	100	2	·	·	PUNCT
ejpam-1475	100	3	·	·	PUNCT
ejpam-1475	100	4	·	·	PUNCT
ejpam-1475	100	5	+	+	CCONJ
ejpam-1475	100	6	cℓu	cℓu	ADJ
ejpam-1475	100	7	2	2	NUM
ejpam-1475	100	8	ℓ(t	ℓ(t	PROPN
ejpam-1475	100	9	)	)	PUNCT
ejpam-1475	100	10	�	�	PROPN
ejpam-1475	100	11	d	d	PROPN
ejpam-1475	100	12	t	t	PROPN
ejpam-1475	100	13	→min	→min	PROPN
ejpam-1475	100	14	(	(	PUNCT
ejpam-1475	100	15	t	t	PROPN
ejpam-1475	100	16	is	be	AUX
ejpam-1475	100	17	fixed	fix	VERB
ejpam-1475	100	18	)	)	PUNCT
ejpam-1475	100	19	every	every	DET
ejpam-1475	100	20	(	(	PUNCT
ejpam-1475	100	21	normal	normal	ADJ
ejpam-1475	100	22	)	)	PUNCT
ejpam-1475	100	23	extremal	extremal	ADJ
ejpam-1475	100	24	control	control	NOUN
ejpam-1475	100	25	is	be	AUX
ejpam-1475	100	26	given	give	VERB
ejpam-1475	100	27	by	by	ADP
ejpam-1475	100	28	ui(t	ui(t	NOUN
ejpam-1475	100	29	)	)	PUNCT
ejpam-1475	100	30	=	=	SYM
ejpam-1475	100	31	1	1	NUM
ejpam-1475	100	32	ci	ci	NOUN
ejpam-1475	100	33	p(t)(bi	p(t)(bi	PROPN
ejpam-1475	100	34	)	)	PUNCT
ejpam-1475	100	35	,	,	PUNCT
ejpam-1475	100	36	i	i	PRON
ejpam-1475	100	37	=	=	NOUN
ejpam-1475	100	38	1	1	NUM
ejpam-1475	100	39	,	,	PUNCT
ejpam-1475	100	40	.	.	PUNCT
ejpam-1475	100	41	.	.	PUNCT
ejpam-1475	100	42	.	.	PUNCT
ejpam-1475	101	1	,	,	PUNCT
ejpam-1475	101	2	ℓ	ℓ	INTJ
ejpam-1475	101	3	where	where	SCONJ
ejpam-1475	101	4	p	p	X
ejpam-1475	101	5	(	(	PUNCT
ejpam-1475	101	6	·	·	PUNCT
ejpam-1475	101	7	)	)	PUNCT
ejpam-1475	101	8	:	:	PUNCT
ejpam-1475	102	1	[	[	X
ejpam-1475	102	2	0	0	NUM
ejpam-1475	102	3	,	,	PUNCT
ejpam-1475	102	4	t]→	t]→	PRON
ejpam-1475	102	5	g	g	PROPN
ejpam-1475	102	6	∗	∗	NOUN
ejpam-1475	102	7	is	be	AUX
ejpam-1475	102	8	an	an	DET
ejpam-1475	102	9	integral	integral	ADJ
ejpam-1475	102	10	curve	curve	NOUN
ejpam-1475	102	11	of	of	ADP
ejpam-1475	102	12	the	the	DET
ejpam-1475	102	13	hamiltonian	hamiltonian	ADJ
ejpam-1475	102	14	vector	vector	NOUN
ejpam-1475	102	15	field	field	NOUN
ejpam-1475	102	16	~h	~h	PUNCT
ejpam-1475	102	17	on	on	ADP
ejpam-1475	102	18	g	g	PROPN
ejpam-1475	102	19	∗	∗	NOUN
ejpam-1475	102	20	−	−	PROPN
ejpam-1475	102	21	corresponding	correspond	VERB
ejpam-1475	102	22	to	to	ADP
ejpam-1475	102	23	the	the	DET
ejpam-1475	102	24	reduced	reduce	VERB
ejpam-1475	102	25	hamiltonian	hamiltonian	ADJ
ejpam-1475	102	26	h(p	h(p	NOUN
ejpam-1475	102	27	)	)	PUNCT
ejpam-1475	102	28	=	=	SYM
ejpam-1475	102	29	p(a	p(a	PROPN
ejpam-1475	102	30	)	)	PUNCT
ejpam-1475	102	31	+	+	CCONJ
ejpam-1475	102	32	1	1	NUM
ejpam-1475	102	33	2	2	NUM
ejpam-1475	102	34	�	�	PROPN
ejpam-1475	102	35	1	1	NUM
ejpam-1475	102	36	c1	c1	PROPN
ejpam-1475	102	37	p(b1	p(b1	PROPN
ejpam-1475	102	38	)	)	PUNCT
ejpam-1475	102	39	2	2	NUM
ejpam-1475	102	40	+	+	CCONJ
ejpam-1475	102	41	·	·	PUNCT
ejpam-1475	102	42	·	·	PUNCT
ejpam-1475	102	43	·	·	PUNCT
ejpam-1475	103	1	+	+	SYM
ejpam-1475	103	2	1	1	NUM
ejpam-1475	103	3	cℓ	cℓ	ADP
ejpam-1475	103	4	p(bℓ	p(bℓ	NUM
ejpam-1475	103	5	)	)	PUNCT
ejpam-1475	103	6	2	2	NUM
ejpam-1475	103	7	�	�	PROPN
ejpam-1475	103	8	.	.	PUNCT
ejpam-1475	104	1	remark	remark	PROPN
ejpam-1475	104	2	1	1	NUM
ejpam-1475	104	3	.	.	PUNCT
ejpam-1475	105	1	in	in	ADP
ejpam-1475	105	2	coordinates	coordinate	NOUN
ejpam-1475	105	3	on	on	ADP
ejpam-1475	105	4	g	g	PROPN
ejpam-1475	105	5	∗	∗	NOUN
ejpam-1475	105	6	−	−	PROPN
ejpam-1475	105	7	,	,	PUNCT
ejpam-1475	105	8	the	the	DET
ejpam-1475	105	9	(	(	PUNCT
ejpam-1475	105	10	components	component	NOUN
ejpam-1475	105	11	of	of	ADP
ejpam-1475	105	12	the	the	PRON
ejpam-1475	105	13	)	)	PUNCT
ejpam-1475	105	14	integral	integral	ADJ
ejpam-1475	105	15	curves	curve	NOUN
ejpam-1475	105	16	satisfy	satisfy	VERB
ejpam-1475	105	17	ṗi	ṗi	PROPN
ejpam-1475	106	1	=	=	PUNCT
ejpam-1475	106	2	−	−	PROPN
ejpam-1475	106	3	m	m	PROPN
ejpam-1475	106	4	∑	∑	PROPN
ejpam-1475	106	5	j	j	PROPN
ejpam-1475	106	6	,	,	PUNCT
ejpam-1475	106	7	k=1	k=1	PROPN
ejpam-1475	107	1	ck	ck	INTJ
ejpam-1475	108	1	i	i	PRON
ejpam-1475	108	2	j	j	PROPN
ejpam-1475	108	3	pk	pk	PROPN
ejpam-1475	108	4	∂	∂	NUM
ejpam-1475	108	5	h	h	NOUN
ejpam-1475	108	6	∂	∂	PROPN
ejpam-1475	109	1	p	p	PROPN
ejpam-1475	109	2	j	j	PROPN
ejpam-1475	109	3	,	,	PUNCT
ejpam-1475	109	4	i	i	PRON
ejpam-1475	109	5	=	=	NOUN
ejpam-1475	109	6	1	1	NUM
ejpam-1475	109	7	,	,	PUNCT
ejpam-1475	109	8	.	.	PUNCT
ejpam-1475	109	9	.	.	PUNCT
ejpam-1475	109	10	.	.	PUNCT
ejpam-1475	110	1	,	,	PUNCT
ejpam-1475	110	2	m.	m.	NOUN
ejpam-1475	110	3	here	here	ADV
ejpam-1475	110	4	,	,	PUNCT
ejpam-1475	110	5	ck	ck	INTJ
ejpam-1475	111	1	i	i	PRON
ejpam-1475	111	2	j	j	PROPN
ejpam-1475	111	3	denote	denote	VERB
ejpam-1475	111	4	the	the	DET
ejpam-1475	111	5	structure	structure	NOUN
ejpam-1475	111	6	constants	constant	NOUN
ejpam-1475	111	7	of	of	ADP
ejpam-1475	111	8	g	g	NOUN
ejpam-1475	111	9	with	with	ADP
ejpam-1475	111	10	respect	respect	NOUN
ejpam-1475	111	11	to	to	ADP
ejpam-1475	111	12	a	a	DET
ejpam-1475	111	13	basis	basis	NOUN
ejpam-1475	111	14	�	�	NOUN
ejpam-1475	111	15	ek	ek	PROPN
ejpam-1475	111	16	�	�	PROPN
ejpam-1475	111	17	1≤k≤m	1≤k≤m	NUM
ejpam-1475	111	18	for	for	ADP
ejpam-1475	111	19	g	g	PROPN
ejpam-1475	111	20	(	(	PUNCT
ejpam-1475	111	21	i.e.	i.e.	X
ejpam-1475	111	22	,	,	PUNCT
ejpam-1475	111	23	[	[	X
ejpam-1475	111	24	ei	ei	X
ejpam-1475	111	25	,	,	PUNCT
ejpam-1475	111	26	e	e	X
ejpam-1475	111	27	j	j	NOUN
ejpam-1475	111	28	]	]	X
ejpam-1475	112	1	=	=	PUNCT
ejpam-1475	112	2	∑m	∑m	INTJ
ejpam-1475	112	3	k=1	k=1	X
ejpam-1475	113	1	ck	ck	INTJ
ejpam-1475	114	1	i	i	PRON
ejpam-1475	114	2	j	j	PROPN
ejpam-1475	114	3	ek	ek	PROPN
ejpam-1475	114	4	)	)	PUNCT
ejpam-1475	114	5	and	and	CCONJ
ejpam-1475	114	6	pi	pi	NOUN
ejpam-1475	114	7	=	=	SYM
ejpam-1475	114	8	p(ei	p(ei	NOUN
ejpam-1475	114	9	)	)	PUNCT
ejpam-1475	114	10	.	.	PUNCT
ejpam-1475	115	1	r.	r.	PROPN
ejpam-1475	115	2	adams	adams	PROPN
ejpam-1475	115	3	,	,	PUNCT
ejpam-1475	115	4	r.	r.	PROPN
ejpam-1475	115	5	biggs	biggs	PROPN
ejpam-1475	115	6	,	,	PUNCT
ejpam-1475	115	7	c.	c.	PROPN
ejpam-1475	115	8	remsing	remsing	NOUN
ejpam-1475	115	9	/	/	SYM
ejpam-1475	115	10	eur	eur	NOUN
ejpam-1475	115	11	.	.	PUNCT
ejpam-1475	116	1	j.	j.	PROPN
ejpam-1475	116	2	pure	pure	PROPN
ejpam-1475	116	3	appl	appl	PROPN
ejpam-1475	116	4	.	.	PROPN
ejpam-1475	116	5	math	math	PROPN
ejpam-1475	116	6	,	,	PUNCT
ejpam-1475	116	7	5	5	NUM
ejpam-1475	116	8	(	(	PUNCT
ejpam-1475	116	9	2012	2012	NUM
ejpam-1475	116	10	)	)	PUNCT
ejpam-1475	116	11	,	,	PUNCT
ejpam-1475	116	12	1	1	NUM
ejpam-1475	116	13	-	-	SYM
ejpam-1475	116	14	15	15	NUM
ejpam-1475	116	15	5	5	NUM
ejpam-1475	116	16	2.3	2.3	NUM
ejpam-1475	116	17	.	.	PUNCT
ejpam-1475	117	1	jacobi	jacobi	PROPN
ejpam-1475	117	2	elliptic	elliptic	ADJ
ejpam-1475	117	3	functions	function	NOUN
ejpam-1475	117	4	given	give	VERB
ejpam-1475	117	5	the	the	DET
ejpam-1475	117	6	modulus	modulus	NOUN
ejpam-1475	117	7	k	k	PROPN
ejpam-1475	117	8	∈	∈	PROPN
ejpam-1475	118	1	[	[	X
ejpam-1475	118	2	0,1	0,1	NUM
ejpam-1475	118	3	]	]	PUNCT
ejpam-1475	118	4	,	,	PUNCT
ejpam-1475	118	5	the	the	DET
ejpam-1475	118	6	basic	basic	ADJ
ejpam-1475	118	7	jacobi	jacobi	PROPN
ejpam-1475	118	8	elliptic	elliptic	PROPN
ejpam-1475	118	9	functions	function	NOUN
ejpam-1475	118	10	sn	sn	X
ejpam-1475	118	11	(	(	PUNCT
ejpam-1475	118	12	·	·	PUNCT
ejpam-1475	118	13	,	,	PUNCT
ejpam-1475	118	14	k	k	NOUN
ejpam-1475	118	15	)	)	PUNCT
ejpam-1475	118	16	,	,	PUNCT
ejpam-1475	118	17	cn	cn	PROPN
ejpam-1475	118	18	(	(	PUNCT
ejpam-1475	118	19	·	·	PUNCT
ejpam-1475	118	20	,	,	PUNCT
ejpam-1475	118	21	k	k	NOUN
ejpam-1475	118	22	)	)	PUNCT
ejpam-1475	118	23	and	and	CCONJ
ejpam-1475	118	24	dn	dn	PROPN
ejpam-1475	118	25	(	(	PUNCT
ejpam-1475	118	26	·	·	PUNCT
ejpam-1475	118	27	,	,	PUNCT
ejpam-1475	118	28	k	k	NOUN
ejpam-1475	118	29	)	)	PUNCT
ejpam-1475	118	30	can	can	AUX
ejpam-1475	118	31	be	be	AUX
ejpam-1475	118	32	defined	define	VERB
ejpam-1475	118	33	as	as	ADP
ejpam-1475	118	34	sn(x	sn(x	PUNCT
ejpam-1475	118	35	,	,	PUNCT
ejpam-1475	118	36	k	k	X
ejpam-1475	118	37	)	)	PUNCT
ejpam-1475	118	38	=	=	SYM
ejpam-1475	118	39	sin	sin	NOUN
ejpam-1475	118	40	am(x	am(x	X
ejpam-1475	118	41	,	,	PUNCT
ejpam-1475	118	42	k	k	NOUN
ejpam-1475	118	43	)	)	PUNCT
ejpam-1475	118	44	cn(x	cn(x	PUNCT
ejpam-1475	118	45	,	,	PUNCT
ejpam-1475	118	46	k	k	X
ejpam-1475	118	47	)	)	PUNCT
ejpam-1475	119	1	=	=	SYM
ejpam-1475	119	2	cosam(x	cosam(x	NUM
ejpam-1475	119	3	,	,	PUNCT
ejpam-1475	119	4	k	k	NOUN
ejpam-1475	119	5	)	)	PUNCT
ejpam-1475	119	6	dn(x	dn(x	PUNCT
ejpam-1475	119	7	,	,	PUNCT
ejpam-1475	119	8	k	k	X
ejpam-1475	119	9	)	)	PUNCT
ejpam-1475	119	10	=	=	SYM
ejpam-1475	120	1	p	p	X
ejpam-1475	120	2	1−	1−	NUM
ejpam-1475	120	3	k2	k2	PROPN
ejpam-1475	120	4	sin2	sin2	PROPN
ejpam-1475	120	5	am(x	am(x	PUNCT
ejpam-1475	120	6	,	,	PUNCT
ejpam-1475	120	7	k	k	NOUN
ejpam-1475	120	8	)	)	PUNCT
ejpam-1475	120	9	where	where	SCONJ
ejpam-1475	120	10	am	be	AUX
ejpam-1475	120	11	(	(	PUNCT
ejpam-1475	120	12	·	·	PUNCT
ejpam-1475	120	13	,	,	PUNCT
ejpam-1475	120	14	k	k	NOUN
ejpam-1475	120	15	)	)	PUNCT
ejpam-1475	120	16	=	=	SYM
ejpam-1475	121	1	f	f	X
ejpam-1475	121	2	(	(	PUNCT
ejpam-1475	121	3	·	·	PUNCT
ejpam-1475	121	4	,	,	PUNCT
ejpam-1475	121	5	k)−1	k)−1	PROPN
ejpam-1475	121	6	is	be	AUX
ejpam-1475	121	7	the	the	DET
ejpam-1475	121	8	amplitude	amplitude	NOUN
ejpam-1475	121	9	and	and	CCONJ
ejpam-1475	121	10	f(ϕ	f(ϕ	PROPN
ejpam-1475	121	11	,	,	PUNCT
ejpam-1475	121	12	k	k	NOUN
ejpam-1475	121	13	)	)	PUNCT
ejpam-1475	121	14	=	=	SYM
ejpam-1475	122	1	∫	∫	PROPN
ejpam-1475	123	1	ϕ	ϕ	NOUN
ejpam-1475	123	2	0	0	PUNCT
ejpam-1475	124	1	d	d	NOUN
ejpam-1475	124	2	tp	tp	ADP
ejpam-1475	124	3	1−k2	1−k2	NUM
ejpam-1475	124	4	sin2	sin2	NOUN
ejpam-1475	124	5	t	t	PROPN
ejpam-1475	124	6	·	·	PUNCT
ejpam-1475	124	7	(	(	PUNCT
ejpam-1475	124	8	for	for	ADP
ejpam-1475	124	9	the	the	DET
ejpam-1475	124	10	degenerate	degenerate	ADJ
ejpam-1475	124	11	cases	case	NOUN
ejpam-1475	124	12	k	k	NOUN
ejpam-1475	124	13	=	=	SYM
ejpam-1475	124	14	0	0	PROPN
ejpam-1475	124	15	and	and	CCONJ
ejpam-1475	124	16	k	k	X
ejpam-1475	124	17	=	=	SYM
ejpam-1475	124	18	1	1	NUM
ejpam-1475	124	19	,	,	PUNCT
ejpam-1475	124	20	we	we	PRON
ejpam-1475	124	21	recover	recover	VERB
ejpam-1475	124	22	the	the	DET
ejpam-1475	124	23	circular	circular	ADJ
ejpam-1475	124	24	functions	function	NOUN
ejpam-1475	124	25	and	and	CCONJ
ejpam-1475	124	26	the	the	DET
ejpam-1475	124	27	hyperbolic	hyperbolic	ADJ
ejpam-1475	124	28	functions	function	NOUN
ejpam-1475	124	29	,	,	PUNCT
ejpam-1475	124	30	respectively	respectively	ADV
ejpam-1475	124	31	.	.	PUNCT
ejpam-1475	124	32	)	)	PUNCT
ejpam-1475	125	1	nine	nine	NUM
ejpam-1475	125	2	other	other	ADJ
ejpam-1475	125	3	elliptic	elliptic	ADJ
ejpam-1475	125	4	functions	function	NOUN
ejpam-1475	125	5	are	be	AUX
ejpam-1475	125	6	defined	define	VERB
ejpam-1475	125	7	by	by	ADP
ejpam-1475	125	8	taking	take	VERB
ejpam-1475	125	9	reciprocals	reciprocal	NOUN
ejpam-1475	125	10	and	and	CCONJ
ejpam-1475	125	11	quotients	quotient	NOUN
ejpam-1475	125	12	;	;	PUNCT
ejpam-1475	125	13	in	in	ADP
ejpam-1475	125	14	particular	particular	ADJ
ejpam-1475	125	15	,	,	PUNCT
ejpam-1475	125	16	we	we	PRON
ejpam-1475	125	17	get	get	AUX
ejpam-1475	125	18	ns	ns	ADJ
ejpam-1475	125	19	(	(	PUNCT
ejpam-1475	125	20	·	·	PUNCT
ejpam-1475	125	21	,	,	PUNCT
ejpam-1475	125	22	k	k	NOUN
ejpam-1475	125	23	)	)	PUNCT
ejpam-1475	125	24	=	=	SYM
ejpam-1475	125	25	1	1	NUM
ejpam-1475	125	26	sn(·,k	sn(·,k	NOUN
ejpam-1475	125	27	)	)	PUNCT
ejpam-1475	125	28	·	·	PUNCT
ejpam-1475	126	1	simple	simple	ADJ
ejpam-1475	126	2	elliptic	elliptic	ADJ
ejpam-1475	126	3	integrals	integral	NOUN
ejpam-1475	126	4	can	can	AUX
ejpam-1475	126	5	be	be	AUX
ejpam-1475	126	6	expressed	express	VERB
ejpam-1475	126	7	in	in	ADP
ejpam-1475	126	8	terms	term	NOUN
ejpam-1475	126	9	of	of	ADP
ejpam-1475	126	10	appropriate	appropriate	ADJ
ejpam-1475	126	11	inverse	inverse	NOUN
ejpam-1475	126	12	(	(	PUNCT
ejpam-1475	126	13	elliptic	elliptic	ADJ
ejpam-1475	126	14	)	)	PUNCT
ejpam-1475	126	15	functions	function	NOUN
ejpam-1475	126	16	.	.	PUNCT
ejpam-1475	127	1	the	the	DET
ejpam-1475	127	2	following	follow	VERB
ejpam-1475	127	3	formulas	formula	NOUN
ejpam-1475	127	4	hold	hold	VERB
ejpam-1475	127	5	true	true	ADJ
ejpam-1475	127	6	for	for	ADP
ejpam-1475	127	7	b	b	NOUN
ejpam-1475	127	8	<	<	X
ejpam-1475	127	9	a	a	DET
ejpam-1475	127	10	≤	≤	PROPN
ejpam-1475	127	11	x	x	PUNCT
ejpam-1475	127	12	and	and	CCONJ
ejpam-1475	127	13	b	b	NOUN
ejpam-1475	127	14	≤	≤	NUM
ejpam-1475	127	15	x	x	SYM
ejpam-1475	127	16	≤	≤	NUM
ejpam-1475	127	17	a	a	PRON
ejpam-1475	127	18	,	,	PUNCT
ejpam-1475	127	19	respectively	respectively	ADV
ejpam-1475	127	20	(	(	PUNCT
ejpam-1475	127	21	see	see	VERB
ejpam-1475	127	22	[	[	X
ejpam-1475	127	23	2	2	NUM
ejpam-1475	127	24	]	]	PUNCT
ejpam-1475	127	25	or	or	CCONJ
ejpam-1475	127	26	[	[	X
ejpam-1475	127	27	14	14	NUM
ejpam-1475	127	28	]	]	SYM
ejpam-1475	127	29	):	):	PUNCT
ejpam-1475	127	30	∫	∫	PROPN
ejpam-1475	127	31	∞	∞	NUM
ejpam-1475	127	32	x	x	PUNCT
ejpam-1475	128	1	d	d	NOUN
ejpam-1475	128	2	t	t	X
ejpam-1475	128	3	p	p	X
ejpam-1475	128	4	(	(	PUNCT
ejpam-1475	128	5	t2	t2	NOUN
ejpam-1475	128	6	−	−	PROPN
ejpam-1475	128	7	a2)(t2	a2)(t2	NOUN
ejpam-1475	128	8	−	−	NOUN
ejpam-1475	128	9	b2	b2	NOUN
ejpam-1475	128	10	)	)	PUNCT
ejpam-1475	128	11	=	=	SYM
ejpam-1475	129	1	1	1	NUM
ejpam-1475	129	2	a	a	DET
ejpam-1475	129	3	ns−1	ns−1	PROPN
ejpam-1475	129	4	�	�	PROPN
ejpam-1475	129	5	1	1	NUM
ejpam-1475	129	6	a	a	DET
ejpam-1475	129	7	x	x	X
ejpam-1475	129	8	,	,	PUNCT
ejpam-1475	129	9	b	b	PROPN
ejpam-1475	129	10	a	a	DET
ejpam-1475	129	11	�	�	PROPN
ejpam-1475	129	12	(	(	PUNCT
ejpam-1475	129	13	7	7	NUM
ejpam-1475	129	14	)	)	PUNCT
ejpam-1475	129	15	∫	∫	NOUN
ejpam-1475	130	1	a	a	DET
ejpam-1475	130	2	x	x	X
ejpam-1475	130	3	d	d	NOUN
ejpam-1475	130	4	t	t	X
ejpam-1475	130	5	p	p	X
ejpam-1475	130	6	(	(	PUNCT
ejpam-1475	130	7	a2−	a2−	PROPN
ejpam-1475	130	8	t2)(t2	t2)(t2	NOUN
ejpam-1475	130	9	−	−	PROPN
ejpam-1475	130	10	b2	b2	NOUN
ejpam-1475	130	11	)	)	PUNCT
ejpam-1475	130	12	=	=	SYM
ejpam-1475	131	1	1	1	NUM
ejpam-1475	131	2	a	a	DET
ejpam-1475	131	3	dn−1	dn−1	ADJ
ejpam-1475	131	4	�	�	PROPN
ejpam-1475	131	5	1	1	NUM
ejpam-1475	131	6	a	a	PRON
ejpam-1475	131	7	x	x	X
ejpam-1475	131	8	,	,	PUNCT
ejpam-1475	131	9	p	p	X
ejpam-1475	131	10	a2−b2	a2−b2	PROPN
ejpam-1475	131	11	a	a	DET
ejpam-1475	131	12	�	�	PROPN
ejpam-1475	131	13	·	·	PUNCT
ejpam-1475	131	14	(	(	PUNCT
ejpam-1475	131	15	8)	8)	NUM
ejpam-1475	131	16	2.4	2.4	NUM
ejpam-1475	131	17	.	.	PUNCT
ejpam-1475	132	1	the	the	DET
ejpam-1475	132	2	energy	energy	NOUN
ejpam-1475	132	3	-	-	PUNCT
ejpam-1475	132	4	casimir	casimir	NOUN
ejpam-1475	132	5	method	method	NOUN
ejpam-1475	132	6	the	the	DET
ejpam-1475	132	7	energy	energy	NOUN
ejpam-1475	132	8	-	-	PUNCT
ejpam-1475	132	9	casimir	casimir	NOUN
ejpam-1475	132	10	method	method	NOUN
ejpam-1475	132	11	[	[	X
ejpam-1475	132	12	9	9	NUM
ejpam-1475	132	13	]	]	PUNCT
ejpam-1475	132	14	gives	give	VERB
ejpam-1475	132	15	sufficient	sufficient	ADJ
ejpam-1475	132	16	conditions	condition	NOUN
ejpam-1475	132	17	for	for	ADP
ejpam-1475	132	18	lyapunov	lyapunov	ADJ
ejpam-1475	132	19	stability	stability	NOUN
ejpam-1475	132	20	of	of	ADP
ejpam-1475	132	21	equilibrium	equilibrium	NOUN
ejpam-1475	132	22	states	state	NOUN
ejpam-1475	132	23	for	for	ADP
ejpam-1475	132	24	certain	certain	ADJ
ejpam-1475	132	25	types	type	NOUN
ejpam-1475	132	26	of	of	ADP
ejpam-1475	132	27	hamilton	hamilton	PROPN
ejpam-1475	132	28	-	-	PUNCT
ejpam-1475	132	29	poisson	poisson	PROPN
ejpam-1475	132	30	dynamical	dynamical	ADJ
ejpam-1475	132	31	systems	system	NOUN
ejpam-1475	132	32	(	(	PUNCT
ejpam-1475	132	33	cf	cf	NOUN
ejpam-1475	132	34	.	.	PUNCT
ejpam-1475	133	1	[	[	X
ejpam-1475	133	2	16	16	NUM
ejpam-1475	133	3	,	,	PUNCT
ejpam-1475	133	4	19	19	NUM
ejpam-1475	133	5	]	]	NUM
ejpam-1475	133	6	)	)	PUNCT
ejpam-1475	133	7	.	.	PUNCT
ejpam-1475	134	1	the	the	DET
ejpam-1475	134	2	method	method	NOUN
ejpam-1475	134	3	is	be	AUX
ejpam-1475	134	4	restricted	restrict	VERB
ejpam-1475	134	5	to	to	ADP
ejpam-1475	134	6	certain	certain	ADJ
ejpam-1475	134	7	types	type	NOUN
ejpam-1475	134	8	of	of	ADP
ejpam-1475	134	9	systems	system	NOUN
ejpam-1475	134	10	,	,	PUNCT
ejpam-1475	134	11	since	since	SCONJ
ejpam-1475	134	12	its	its	PRON
ejpam-1475	134	13	implementation	implementation	NOUN
ejpam-1475	134	14	relies	rely	VERB
ejpam-1475	134	15	on	on	ADP
ejpam-1475	134	16	an	an	DET
ejpam-1475	134	17	abundant	abundant	ADJ
ejpam-1475	134	18	supply	supply	NOUN
ejpam-1475	134	19	of	of	ADP
ejpam-1475	134	20	casimir	casimir	NOUN
ejpam-1475	134	21	functions	function	NOUN
ejpam-1475	134	22	.	.	PUNCT
ejpam-1475	135	1	the	the	DET
ejpam-1475	135	2	standard	standard	ADJ
ejpam-1475	135	3	energy	energy	NOUN
ejpam-1475	135	4	-	-	PUNCT
ejpam-1475	135	5	casimir	casimir	NOUN
ejpam-1475	135	6	method	method	NOUN
ejpam-1475	135	7	states	state	VERB
ejpam-1475	135	8	that	that	SCONJ
ejpam-1475	135	9	if	if	SCONJ
ejpam-1475	135	10	ze	ze	PROPN
ejpam-1475	135	11	is	be	AUX
ejpam-1475	135	12	an	an	DET
ejpam-1475	135	13	equilibrium	equilibrium	NOUN
ejpam-1475	135	14	point	point	NOUN
ejpam-1475	135	15	of	of	ADP
ejpam-1475	135	16	a	a	DET
ejpam-1475	135	17	hamiltonian	hamiltonian	ADJ
ejpam-1475	135	18	vector	vector	NOUN
ejpam-1475	135	19	field	field	NOUN
ejpam-1475	135	20	~h	~h	PUNCT
ejpam-1475	135	21	(	(	PUNCT
ejpam-1475	135	22	associated	associate	VERB
ejpam-1475	135	23	with	with	ADP
ejpam-1475	135	24	an	an	DET
ejpam-1475	135	25	energy	energy	NOUN
ejpam-1475	135	26	function	function	NOUN
ejpam-1475	135	27	h	h	NOUN
ejpam-1475	135	28	)	)	PUNCT
ejpam-1475	135	29	and	and	CCONJ
ejpam-1475	135	30	if	if	SCONJ
ejpam-1475	135	31	there	there	PRON
ejpam-1475	135	32	exists	exist	VERB
ejpam-1475	135	33	a	a	DET
ejpam-1475	135	34	casimir	casimir	NOUN
ejpam-1475	135	35	function	function	NOUN
ejpam-1475	135	36	c	c	PROPN
ejpam-1475	135	37	such	such	ADJ
ejpam-1475	135	38	that	that	DET
ejpam-1475	135	39	ze	ze	PROPN
ejpam-1475	135	40	is	be	AUX
ejpam-1475	135	41	a	a	DET
ejpam-1475	135	42	critical	critical	ADJ
ejpam-1475	135	43	point	point	NOUN
ejpam-1475	135	44	of	of	ADP
ejpam-1475	135	45	h+c	h+c	X
ejpam-1475	135	46	(	(	PUNCT
ejpam-1475	135	47	on	on	ADP
ejpam-1475	135	48	the	the	DET
ejpam-1475	135	49	whole	whole	ADJ
ejpam-1475	135	50	state	state	NOUN
ejpam-1475	135	51	space	space	NOUN
ejpam-1475	135	52	)	)	PUNCT
ejpam-1475	135	53	and	and	CCONJ
ejpam-1475	135	54	d2(h	d2(h	PROPN
ejpam-1475	135	55	+	+	NOUN
ejpam-1475	135	56	c)(ze	c)(ze	NOUN
ejpam-1475	135	57	)	)	PUNCT
ejpam-1475	135	58	is	be	AUX
ejpam-1475	135	59	(	(	PUNCT
ejpam-1475	135	60	positive	positive	ADJ
ejpam-1475	135	61	or	or	CCONJ
ejpam-1475	135	62	negative	negative	ADJ
ejpam-1475	135	63	)	)	PUNCT
ejpam-1475	135	64	definite	definite	ADJ
ejpam-1475	135	65	,	,	PUNCT
ejpam-1475	135	66	then	then	ADV
ejpam-1475	135	67	ze	ze	PROPN
ejpam-1475	135	68	is	be	AUX
ejpam-1475	135	69	lyapunov	lyapunov	PROPN
ejpam-1475	135	70	stable	stable	ADJ
ejpam-1475	135	71	.	.	PUNCT
ejpam-1475	136	1	ortega	ortega	PROPN
ejpam-1475	136	2	and	and	CCONJ
ejpam-1475	136	3	ratiu	ratiu	NOUN
ejpam-1475	136	4	have	have	AUX
ejpam-1475	136	5	obtained	obtain	VERB
ejpam-1475	136	6	a	a	DET
ejpam-1475	136	7	generalisation	generalisation	NOUN
ejpam-1475	136	8	of	of	ADP
ejpam-1475	136	9	the	the	DET
ejpam-1475	136	10	standard	standard	ADJ
ejpam-1475	136	11	energy	energy	NOUN
ejpam-1475	136	12	-	-	PUNCT
ejpam-1475	136	13	casimir	casimir	NOUN
ejpam-1475	136	14	method	method	NOUN
ejpam-1475	136	15	(	(	PUNCT
ejpam-1475	136	16	cf	cf	NOUN
ejpam-1475	136	17	.	.	PUNCT
ejpam-1475	137	1	[	[	X
ejpam-1475	137	2	18	18	NUM
ejpam-1475	137	3	,	,	PUNCT
ejpam-1475	137	4	17	17	NUM
ejpam-1475	137	5	]	]	PUNCT
ejpam-1475	137	6	)	)	PUNCT
ejpam-1475	137	7	.	.	PUNCT
ejpam-1475	138	1	this	this	DET
ejpam-1475	138	2	extended	extend	VERB
ejpam-1475	138	3	version	version	NOUN
ejpam-1475	138	4	states	state	NOUN
ejpam-1475	138	5	that	that	SCONJ
ejpam-1475	138	6	if	if	SCONJ
ejpam-1475	138	7	c	c	NOUN
ejpam-1475	138	8	=	=	SYM
ejpam-1475	138	9	λ1c1	λ1c1	X
ejpam-1475	138	10	+	+	PROPN
ejpam-1475	138	11	·	·	PUNCT
ejpam-1475	138	12	·	·	PUNCT
ejpam-1475	138	13	·	·	PUNCT
ejpam-1475	138	14	+	+	PUNCT
ejpam-1475	138	15	λkck	λkck	NOUN
ejpam-1475	138	16	,	,	PUNCT
ejpam-1475	138	17	where	where	SCONJ
ejpam-1475	138	18	λ1	λ1	ADJ
ejpam-1475	138	19	,	,	PUNCT
ejpam-1475	138	20	.	.	PUNCT
ejpam-1475	138	21	.	.	PUNCT
ejpam-1475	138	22	.	.	PUNCT
ejpam-1475	139	1	,	,	PUNCT
ejpam-1475	139	2	λk	λk	PROPN
ejpam-1475	139	3	∈	∈	PROPN
ejpam-1475	139	4	r	r	NOUN
ejpam-1475	139	5	and	and	CCONJ
ejpam-1475	139	6	c1	c1	PROPN
ejpam-1475	139	7	,	,	PUNCT
ejpam-1475	139	8	.	.	PUNCT
ejpam-1475	139	9	.	.	PUNCT
ejpam-1475	140	1	.	.	PUNCT
ejpam-1475	141	1	,	,	PUNCT
ejpam-1475	141	2	ck	ck	INTJ
ejpam-1475	141	3	are	be	AUX
ejpam-1475	141	4	conserved	conserved	ADJ
ejpam-1475	141	5	quantities	quantity	NOUN
ejpam-1475	141	6	(	(	PUNCT
ejpam-1475	141	7	i.e.	i.e.	X
ejpam-1475	141	8	,	,	PUNCT
ejpam-1475	141	9	they	they	PRON
ejpam-1475	141	10	poisson	poisson	PROPN
ejpam-1475	141	11	commute	commute	VERB
ejpam-1475	141	12	with	with	ADP
ejpam-1475	141	13	the	the	DET
ejpam-1475	141	14	energy	energy	NOUN
ejpam-1475	141	15	function	function	NOUN
ejpam-1475	141	16	h	h	PROPN
ejpam-1475	141	17	)	)	PUNCT
ejpam-1475	141	18	,	,	PUNCT
ejpam-1475	141	19	then	then	ADV
ejpam-1475	141	20	definiteness	definiteness	NOUN
ejpam-1475	141	21	of	of	ADP
ejpam-1475	141	22	d2(λ0h	d2(λ0h	PROPN
ejpam-1475	141	23	+	+	CCONJ
ejpam-1475	141	24	c)(ze),λ0	c)(ze),λ0	PROPN
ejpam-1475	141	25	∈	∈	PROPN
ejpam-1475	141	26	r	r	NOUN
ejpam-1475	141	27	is	be	AUX
ejpam-1475	141	28	only	only	ADV
ejpam-1475	141	29	required	require	VERB
ejpam-1475	141	30	on	on	ADP
ejpam-1475	141	31	the	the	DET
ejpam-1475	141	32	intersection	intersection	NOUN
ejpam-1475	141	33	(	(	PUNCT
ejpam-1475	141	34	subspace	subspace	PROPN
ejpam-1475	141	35	)	)	PUNCT
ejpam-1475	141	36	w	w	PROPN
ejpam-1475	142	1	=	=	PUNCT
ejpam-1475	142	2	ker	ker	PROPN
ejpam-1475	142	3	dh(ze)∩	dh(ze)∩	ADJ
ejpam-1475	142	4	ker	ker	PROPN
ejpam-1475	142	5	dc1(ze)∩	dc1(ze)∩	X
ejpam-1475	142	6	·	·	PUNCT
ejpam-1475	142	7	·	·	PUNCT
ejpam-1475	142	8	·	·	PUNCT
ejpam-1475	142	9	∩	∩	NOUN
ejpam-1475	142	10	dck(ze	dck(ze	NOUN
ejpam-1475	142	11	)	)	PUNCT
ejpam-1475	142	12	.	.	PUNCT
ejpam-1475	143	1	3	3	X
ejpam-1475	143	2	.	.	X
ejpam-1475	143	3	the	the	DET
ejpam-1475	143	4	euclidean	euclidean	ADJ
ejpam-1475	143	5	group	group	NOUN
ejpam-1475	143	6	se(2	se(2	PROPN
ejpam-1475	143	7	)	)	PUNCT
ejpam-1475	143	8	the	the	DET
ejpam-1475	143	9	euclidean	euclidean	ADJ
ejpam-1475	143	10	group	group	NOUN
ejpam-1475	143	11	se(2	se(2	PROPN
ejpam-1475	143	12	)	)	PUNCT
ejpam-1475	143	13	=	=	SYM
ejpam-1475	144	1	¨	¨	NOUN
ejpam-1475	144	2	�	�	PROPN
ejpam-1475	144	3	1	1	NUM
ejpam-1475	144	4	0	0	NUM
ejpam-1475	144	5	v	v	NOUN
ejpam-1475	144	6	r	r	PROPN
ejpam-1475	144	7	�	�	NOUN
ejpam-1475	144	8	:	:	PUNCT
ejpam-1475	144	9	v	v	NUM
ejpam-1475	144	10	∈	∈	PROPN
ejpam-1475	144	11	r2×1	r2×1	NOUN
ejpam-1475	144	12	,	,	PUNCT
ejpam-1475	144	13	r	r	NOUN
ejpam-1475	144	14	∈	∈	PROPN
ejpam-1475	144	15	so(2	so(2	NOUN
ejpam-1475	144	16	)	)	PUNCT
ejpam-1475	144	17	«	«	PUNCT
ejpam-1475	144	18	r.	r.	PROPN
ejpam-1475	144	19	adams	adams	PROPN
ejpam-1475	144	20	,	,	PUNCT
ejpam-1475	144	21	r.	r.	PROPN
ejpam-1475	144	22	biggs	biggs	PROPN
ejpam-1475	144	23	,	,	PUNCT
ejpam-1475	144	24	c.	c.	PROPN
ejpam-1475	144	25	remsing	remsing	NOUN
ejpam-1475	144	26	/	/	SYM
ejpam-1475	144	27	eur	eur	NOUN
ejpam-1475	144	28	.	.	PUNCT
ejpam-1475	145	1	j.	j.	PROPN
ejpam-1475	145	2	pure	pure	PROPN
ejpam-1475	145	3	appl	appl	PROPN
ejpam-1475	145	4	.	.	PROPN
ejpam-1475	145	5	math	math	PROPN
ejpam-1475	145	6	,	,	PUNCT
ejpam-1475	145	7	5	5	NUM
ejpam-1475	145	8	(	(	PUNCT
ejpam-1475	145	9	2012	2012	NUM
ejpam-1475	145	10	)	)	PUNCT
ejpam-1475	145	11	,	,	PUNCT
ejpam-1475	145	12	1	1	NUM
ejpam-1475	145	13	-	-	SYM
ejpam-1475	145	14	15	15	NUM
ejpam-1475	145	15	6	6	NUM
ejpam-1475	145	16	is	be	AUX
ejpam-1475	145	17	a	a	DET
ejpam-1475	145	18	(	(	PUNCT
ejpam-1475	145	19	real	real	ADJ
ejpam-1475	145	20	)	)	PUNCT
ejpam-1475	145	21	three	three	NUM
ejpam-1475	145	22	-	-	PUNCT
ejpam-1475	145	23	dimensional	dimensional	ADJ
ejpam-1475	145	24	connected	connected	ADJ
ejpam-1475	145	25	matrix	matrix	NOUN
ejpam-1475	145	26	lie	lie	NOUN
ejpam-1475	145	27	group	group	NOUN
ejpam-1475	145	28	.	.	PUNCT
ejpam-1475	146	1	the	the	DET
ejpam-1475	146	2	group	group	NOUN
ejpam-1475	146	3	is	be	AUX
ejpam-1475	146	4	solvable	solvable	ADJ
ejpam-1475	146	5	and	and	CCONJ
ejpam-1475	146	6	unimodular	unimodular	ADJ
ejpam-1475	146	7	.	.	PUNCT
ejpam-1475	147	1	the	the	DET
ejpam-1475	147	2	associated	associated	ADJ
ejpam-1475	147	3	lie	lie	NOUN
ejpam-1475	147	4	algebra	algebra	NOUN
ejpam-1475	147	5	is	be	AUX
ejpam-1475	147	6	given	give	VERB
ejpam-1475	147	7	by	by	ADP
ejpam-1475	147	8	se(2	se(2	NOUN
ejpam-1475	147	9	)	)	PUNCT
ejpam-1475	147	10	=	=	PUNCT
ejpam-1475	148	1			PROPN
ejpam-1475	148	2			ADP
ejpam-1475	148	3			ADJ
ejpam-1475	148	4			NOUN
ejpam-1475	148	5			NOUN
ejpam-1475	148	6			NOUN
ejpam-1475	148	7	0	0	NUM
ejpam-1475	148	8	0	0	NUM
ejpam-1475	148	9	0	0	NUM
ejpam-1475	149	1	x1	x1	NOUN
ejpam-1475	149	2	0	0	NUM
ejpam-1475	150	1	−x3	−x3	PROPN
ejpam-1475	150	2	x2	x2	PROPN
ejpam-1475	150	3	x3	x3	ADJ
ejpam-1475	150	4	0	0	PUNCT
ejpam-1475	151	1			PROPN
ejpam-1475	151	2			PROPN
ejpam-1475	151	3			PROPN
ejpam-1475	151	4	:	:	PUNCT
ejpam-1475	151	5	x1	x1	NUM
ejpam-1475	151	6	,	,	PUNCT
ejpam-1475	151	7	x2	x2	PROPN
ejpam-1475	151	8	,	,	PUNCT
ejpam-1475	151	9	x3	x3	PROPN
ejpam-1475	151	10	∈	∈	PROPN
ejpam-1475	151	11	r	r	NOUN
ejpam-1475	151	12			PROPN
ejpam-1475	151	13			PROPN
ejpam-1475	151	14			NOUN
ejpam-1475	151	15	.	.	PUNCT
ejpam-1475	152	1	let	let	VERB
ejpam-1475	152	2	e1	e1	NOUN
ejpam-1475	152	3	=	=	NOUN
ejpam-1475	152	4			NOUN
ejpam-1475	152	5			ADJ
ejpam-1475	152	6			NOUN
ejpam-1475	152	7	0	0	NUM
ejpam-1475	152	8	0	0	NUM
ejpam-1475	152	9	0	0	NUM
ejpam-1475	152	10	1	1	NUM
ejpam-1475	152	11	0	0	NUM
ejpam-1475	152	12	0	0	NUM
ejpam-1475	152	13	0	0	NUM
ejpam-1475	152	14	0	0	NUM
ejpam-1475	152	15	0	0	NUM
ejpam-1475	152	16			PROPN
ejpam-1475	152	17			PROPN
ejpam-1475	152	18			PROPN
ejpam-1475	152	19	,	,	PUNCT
ejpam-1475	153	1	e2	e2	NOUN
ejpam-1475	153	2	=	=	PUNCT
ejpam-1475	153	3			PROPN
ejpam-1475	153	4			ADJ
ejpam-1475	153	5			NOUN
ejpam-1475	153	6	0	0	NUM
ejpam-1475	153	7	0	0	NUM
ejpam-1475	153	8	0	0	NUM
ejpam-1475	153	9	0	0	NUM
ejpam-1475	153	10	0	0	NUM
ejpam-1475	153	11	0	0	NUM
ejpam-1475	153	12	1	1	NUM
ejpam-1475	153	13	0	0	NUM
ejpam-1475	153	14	0	0	NUM
ejpam-1475	153	15			PROPN
ejpam-1475	153	16			PROPN
ejpam-1475	153	17			PROPN
ejpam-1475	153	18	,	,	PUNCT
ejpam-1475	153	19	e3	e3	NOUN
ejpam-1475	153	20	=	=	SYM
ejpam-1475	153	21			NOUN
ejpam-1475	153	22			ADJ
ejpam-1475	153	23			NOUN
ejpam-1475	153	24	0	0	NUM
ejpam-1475	153	25	0	0	NUM
ejpam-1475	153	26	0	0	NUM
ejpam-1475	153	27	0	0	NUM
ejpam-1475	153	28	0	0	NUM
ejpam-1475	153	29	−1	−1	NOUN
ejpam-1475	153	30	0	0	NUM
ejpam-1475	153	31	1	1	NUM
ejpam-1475	153	32	0	0	NUM
ejpam-1475	153	33			PROPN
ejpam-1475	153	34			PROPN
ejpam-1475	153	35			PROPN
ejpam-1475	153	36	be	be	AUX
ejpam-1475	153	37	the	the	DET
ejpam-1475	153	38	standard	standard	ADJ
ejpam-1475	153	39	basis	basis	NOUN
ejpam-1475	153	40	of	of	ADP
ejpam-1475	153	41	se(2	se(2	NOUN
ejpam-1475	153	42	)	)	PUNCT
ejpam-1475	153	43	with	with	ADP
ejpam-1475	153	44	the	the	DET
ejpam-1475	153	45	following	follow	VERB
ejpam-1475	153	46	table	table	NOUN
ejpam-1475	153	47	for	for	ADP
ejpam-1475	153	48	the	the	DET
ejpam-1475	153	49	bracket	bracket	NOUN
ejpam-1475	153	50	operation	operation	NOUN
ejpam-1475	153	51	[	[	X
ejpam-1475	153	52	·	·	PUNCT
ejpam-1475	153	53	,	,	PUNCT
ejpam-1475	153	54	·	·	PUNCT
ejpam-1475	153	55	]	]	PUNCT
ejpam-1475	153	56	e1	e1	PROPN
ejpam-1475	153	57	e2	e2	PROPN
ejpam-1475	153	58	e3	e3	NOUN
ejpam-1475	153	59	e1	e1	NOUN
ejpam-1475	153	60	0	0	NUM
ejpam-1475	153	61	0	0	NUM
ejpam-1475	153	62	−e2	−e2	PROPN
ejpam-1475	153	63	e2	e2	PROPN
ejpam-1475	153	64	0	0	NUM
ejpam-1475	153	65	0	0	NUM
ejpam-1475	153	66	e1	e1	NOUN
ejpam-1475	153	67	e3	e3	NOUN
ejpam-1475	153	68	e2	e2	NOUN
ejpam-1475	153	69	−e1	−e1	PROPN
ejpam-1475	153	70	0	0	NUM
ejpam-1475	153	71	with	with	ADP
ejpam-1475	153	72	respect	respect	NOUN
ejpam-1475	153	73	to	to	ADP
ejpam-1475	153	74	this	this	DET
ejpam-1475	153	75	basis	basis	NOUN
ejpam-1475	153	76	,	,	PUNCT
ejpam-1475	153	77	the	the	DET
ejpam-1475	153	78	group	group	NOUN
ejpam-1475	153	79	aut(se(2	aut(se(2	NOUN
ejpam-1475	153	80	)	)	PUNCT
ejpam-1475	153	81	)	)	PUNCT
ejpam-1475	153	82	of	of	ADP
ejpam-1475	153	83	lie	lie	NOUN
ejpam-1475	153	84	algebra	algebra	NOUN
ejpam-1475	153	85	automorphisms	automorphism	NOUN
ejpam-1475	153	86	of	of	ADP
ejpam-1475	153	87	se(2	se(2	PROPN
ejpam-1475	153	88	)	)	PUNCT
ejpam-1475	153	89	is	be	AUX
ejpam-1475	153	90	given	give	VERB
ejpam-1475	153	91	by	by	ADP
ejpam-1475	153	92			PROPN
ejpam-1475	153	93			NOUN
ejpam-1475	153	94			ADJ
ejpam-1475	153	95			NOUN
ejpam-1475	153	96			NOUN
ejpam-1475	153	97			NOUN
ejpam-1475	154	1	x	x	PUNCT
ejpam-1475	155	1	y	y	NOUN
ejpam-1475	155	2	v	v	INTJ
ejpam-1475	155	3	−ςy	−ςy	INTJ
ejpam-1475	155	4	ςx	ςx	INTJ
ejpam-1475	156	1	w	w	NOUN
ejpam-1475	156	2	0	0	NUM
ejpam-1475	156	3	0	0	NUM
ejpam-1475	157	1	ς	ς	PROPN
ejpam-1475	157	2			PROPN
ejpam-1475	157	3			PROPN
ejpam-1475	157	4			PROPN
ejpam-1475	157	5	:	:	PUNCT
ejpam-1475	157	6	x	x	X
ejpam-1475	157	7	,	,	PUNCT
ejpam-1475	157	8	y	y	PROPN
ejpam-1475	157	9	,	,	PUNCT
ejpam-1475	157	10	v	v	NOUN
ejpam-1475	157	11	,	,	PUNCT
ejpam-1475	157	12	w	w	PROPN
ejpam-1475	157	13	∈	∈	PROPN
ejpam-1475	157	14	r	r	NOUN
ejpam-1475	157	15	,	,	PUNCT
ejpam-1475	157	16	x2	x2	PROPN
ejpam-1475	157	17	+	+	X
ejpam-1475	157	18	y2	y2	PROPN
ejpam-1475	157	19	6=	6=	ADP
ejpam-1475	157	20	0,ς=	0,ς=	PROPN
ejpam-1475	157	21	±1	±1	VERB
ejpam-1475	157	22			PROPN
ejpam-1475	157	23			PROPN
ejpam-1475	157	24			NOUN
ejpam-1475	157	25	.	.	PUNCT
ejpam-1475	158	1	(	(	PUNCT
ejpam-1475	158	2	9	9	NUM
ejpam-1475	158	3	)	)	PUNCT
ejpam-1475	158	4	as	as	ADP
ejpam-1475	158	5	se(2	se(2	NOUN
ejpam-1475	158	6	)	)	PUNCT
ejpam-1475	158	7	is	be	AUX
ejpam-1475	158	8	not	not	PART
ejpam-1475	158	9	semisimple	semisimple	ADJ
ejpam-1475	158	10	,	,	PUNCT
ejpam-1475	158	11	the	the	DET
ejpam-1475	158	12	killing	killing	NOUN
ejpam-1475	158	13	form	form	NOUN
ejpam-1475	158	14	is	be	AUX
ejpam-1475	158	15	degenerate	degenerate	ADJ
ejpam-1475	158	16	.	.	PUNCT
ejpam-1475	159	1	moreover	moreover	ADV
ejpam-1475	159	2	,	,	PUNCT
ejpam-1475	159	3	it	it	PRON
ejpam-1475	159	4	can	can	AUX
ejpam-1475	159	5	be	be	AUX
ejpam-1475	159	6	shown	show	VERB
ejpam-1475	159	7	that	that	SCONJ
ejpam-1475	159	8	there	there	PRON
ejpam-1475	159	9	does	do	AUX
ejpam-1475	159	10	not	not	PART
ejpam-1475	159	11	exist	exist	VERB
ejpam-1475	159	12	any	any	DET
ejpam-1475	159	13	non	non	ADJ
ejpam-1475	159	14	-	-	ADJ
ejpam-1475	159	15	degenerate	degenerate	ADJ
ejpam-1475	159	16	invariant	invariant	ADJ
ejpam-1475	159	17	scalar	scalar	ADJ
ejpam-1475	159	18	product	product	NOUN
ejpam-1475	159	19	on	on	ADP
ejpam-1475	159	20	se(2	se(2	NOUN
ejpam-1475	159	21	)	)	PUNCT
ejpam-1475	159	22	.	.	PUNCT
ejpam-1475	160	1	therefore	therefore	ADV
ejpam-1475	160	2	,	,	PUNCT
ejpam-1475	160	3	we	we	PRON
ejpam-1475	160	4	use	use	VERB
ejpam-1475	160	5	the	the	DET
ejpam-1475	160	6	non	non	ADJ
ejpam-1475	160	7	-	-	ADJ
ejpam-1475	160	8	degenerate	degenerate	ADJ
ejpam-1475	160	9	bilinear	bilinear	NOUN
ejpam-1475	160	10	form	form	NOUN
ejpam-1475	160	11	*	*	PUNCT
ejpam-1475	160	12			NOUN
ejpam-1475	160	13			ADJ
ejpam-1475	160	14			NOUN
ejpam-1475	160	15	0	0	NUM
ejpam-1475	160	16	0	0	NUM
ejpam-1475	160	17	0	0	NUM
ejpam-1475	161	1	x1	x1	NOUN
ejpam-1475	161	2	0	0	NUM
ejpam-1475	162	1	−x3	−x3	PROPN
ejpam-1475	162	2	x2	x2	PROPN
ejpam-1475	162	3	x3	x3	ADJ
ejpam-1475	162	4	0	0	PUNCT
ejpam-1475	163	1			PROPN
ejpam-1475	163	2			PROPN
ejpam-1475	163	3			PROPN
ejpam-1475	163	4	,	,	PUNCT
ejpam-1475	163	5			NOUN
ejpam-1475	163	6			ADJ
ejpam-1475	163	7			NOUN
ejpam-1475	163	8	0	0	NUM
ejpam-1475	164	1	0	0	NUM
ejpam-1475	164	2	0	0	NUM
ejpam-1475	164	3	y1	y1	NOUN
ejpam-1475	164	4	0	0	NUM
ejpam-1475	164	5	−y3	−y3	NOUN
ejpam-1475	164	6	y2	y2	NOUN
ejpam-1475	164	7	y3	y3	NOUN
ejpam-1475	164	8	0	0	NUM
ejpam-1475	164	9			PROPN
ejpam-1475	164	10			PROPN
ejpam-1475	164	11			PROPN
ejpam-1475	164	12	+	+	NUM
ejpam-1475	164	13	=	=	SYM
ejpam-1475	164	14	x1	x1	NUM
ejpam-1475	164	15	y1	y1	NOUN
ejpam-1475	165	1	+	+	CCONJ
ejpam-1475	165	2	x2	x2	ADJ
ejpam-1475	165	3	y2	y2	PROPN
ejpam-1475	165	4	+	+	CCONJ
ejpam-1475	165	5	x3	x3	ADJ
ejpam-1475	165	6	y3	y3	NOUN
ejpam-1475	165	7	(	(	PUNCT
ejpam-1475	165	8	on	on	ADP
ejpam-1475	165	9	se(2	se(2	NOUN
ejpam-1475	165	10	)	)	PUNCT
ejpam-1475	165	11	)	)	PUNCT
ejpam-1475	165	12	to	to	PART
ejpam-1475	165	13	identify	identify	VERB
ejpam-1475	165	14	se(2	se(2	PROPN
ejpam-1475	165	15	)	)	PUNCT
ejpam-1475	165	16	with	with	ADP
ejpam-1475	165	17	se(2)∗	se(2)∗	PROPN
ejpam-1475	165	18	(	(	PUNCT
ejpam-1475	165	19	cf	cf	NOUN
ejpam-1475	165	20	.	.	PUNCT
ejpam-1475	166	1	[	[	X
ejpam-1475	166	2	11	11	NUM
ejpam-1475	166	3	]	]	NUM
ejpam-1475	166	4	)	)	PUNCT
ejpam-1475	166	5	.	.	PUNCT
ejpam-1475	167	1	that	that	PRON
ejpam-1475	167	2	is	is	ADV
ejpam-1475	167	3	,	,	PUNCT
ejpam-1475	167	4	we	we	PRON
ejpam-1475	167	5	identify	identify	VERB
ejpam-1475	167	6	p	p	PROPN
ejpam-1475	167	7	∈	∈	PROPN
ejpam-1475	167	8	se(2	se(2	NOUN
ejpam-1475	167	9	)	)	PUNCT
ejpam-1475	167	10	with	with	ADP
ejpam-1475	167	11	〈	〈	PROPN
ejpam-1475	167	12	p	p	NOUN
ejpam-1475	167	13	,	,	PUNCT
ejpam-1475	167	14	·	·	PUNCT
ejpam-1475	167	15	〉	〉	NOUN
ejpam-1475	167	16	∈	∈	PROPN
ejpam-1475	167	17	se(2)∗.	se(2)∗.	NOUN
ejpam-1475	167	18	then	then	ADV
ejpam-1475	167	19	each	each	DET
ejpam-1475	167	20	extremal	extremal	ADJ
ejpam-1475	167	21	curve	curve	NOUN
ejpam-1475	167	22	p	p	X
ejpam-1475	167	23	(	(	PUNCT
ejpam-1475	167	24	·	·	PUNCT
ejpam-1475	167	25	)	)	PUNCT
ejpam-1475	167	26	in	in	ADP
ejpam-1475	167	27	se(2)∗	se(2)∗	ADJ
ejpam-1475	167	28	is	be	AUX
ejpam-1475	167	29	identified	identify	VERB
ejpam-1475	167	30	with	with	ADP
ejpam-1475	167	31	a	a	DET
ejpam-1475	167	32	curve	curve	NOUN
ejpam-1475	167	33	p	p	X
ejpam-1475	167	34	(	(	PUNCT
ejpam-1475	167	35	·	·	PUNCT
ejpam-1475	167	36	)	)	PUNCT
ejpam-1475	167	37	in	in	ADP
ejpam-1475	167	38	se(2	se(2	NOUN
ejpam-1475	167	39	)	)	PUNCT
ejpam-1475	167	40	via	via	ADP
ejpam-1475	167	41	the	the	DET
ejpam-1475	167	42	formula	formula	NOUN
ejpam-1475	167	43	〈	〈	NOUN
ejpam-1475	167	44	p(t	p(t	NOUN
ejpam-1475	167	45	)	)	PUNCT
ejpam-1475	167	46	,	,	PUNCT
ejpam-1475	167	47	x	x	SYM
ejpam-1475	167	48	〉	〉	NOUN
ejpam-1475	167	49	=	=	NOUN
ejpam-1475	167	50	p(t)(x	p(t)(x	NUM
ejpam-1475	167	51	)	)	PUNCT
ejpam-1475	167	52	for	for	ADP
ejpam-1475	167	53	all	all	DET
ejpam-1475	167	54	x	x	SYM
ejpam-1475	167	55	∈	∈	PROPN
ejpam-1475	167	56	se(2	se(2	NOUN
ejpam-1475	167	57	)	)	PUNCT
ejpam-1475	167	58	.	.	PUNCT
ejpam-1475	168	1	thus	thus	ADV
ejpam-1475	168	2	p(t	p(t	NOUN
ejpam-1475	168	3	)	)	PUNCT
ejpam-1475	169	1	=	=	NOUN
ejpam-1475	169	2			VERB
ejpam-1475	169	3			ADJ
ejpam-1475	169	4			NOUN
ejpam-1475	169	5	0	0	NUM
ejpam-1475	169	6	0	0	NUM
ejpam-1475	169	7	0	0	NUM
ejpam-1475	169	8	p1(t	p1(t	PROPN
ejpam-1475	169	9	)	)	PUNCT
ejpam-1475	169	10	0	0	NUM
ejpam-1475	170	1	−p3(t	−p3(t	PROPN
ejpam-1475	170	2	)	)	PUNCT
ejpam-1475	170	3	p2(t	p2(t	PROPN
ejpam-1475	170	4	)	)	PUNCT
ejpam-1475	170	5	p3(t	p3(t	PROPN
ejpam-1475	170	6	)	)	PUNCT
ejpam-1475	170	7	0	0	NUM
ejpam-1475	171	1			PROPN
ejpam-1475	171	2			PROPN
ejpam-1475	171	3			PROPN
ejpam-1475	171	4	where	where	SCONJ
ejpam-1475	171	5	pi(t	pi(t	NOUN
ejpam-1475	171	6	)	)	PUNCT
ejpam-1475	171	7	=	=	PUNCT
ejpam-1475	172	1	〈	〈	NOUN
ejpam-1475	172	2	p(t	p(t	NOUN
ejpam-1475	172	3	)	)	PUNCT
ejpam-1475	172	4	,	,	PUNCT
ejpam-1475	172	5	ei	ei	ADP
ejpam-1475	172	6	〉	〉	NOUN
ejpam-1475	172	7	=	=	SYM
ejpam-1475	172	8	p(t)(ei	p(t)(ei	NUM
ejpam-1475	172	9	)	)	PUNCT
ejpam-1475	172	10	=	=	SYM
ejpam-1475	172	11	pi(t	pi(t	NOUN
ejpam-1475	172	12	)	)	PUNCT
ejpam-1475	172	13	,	,	PUNCT
ejpam-1475	172	14	i	i	PRON
ejpam-1475	172	15	=	=	NOUN
ejpam-1475	173	1	1,2,3	1,2,3	X
ejpam-1475	173	2	.	.	PUNCT
ejpam-1475	173	3	now	now	ADV
ejpam-1475	173	4	consider	consider	VERB
ejpam-1475	173	5	a	a	DET
ejpam-1475	173	6	hamiltonian	hamiltonian	ADJ
ejpam-1475	173	7	h	h	NOUN
ejpam-1475	173	8	on	on	ADP
ejpam-1475	173	9	the	the	DET
ejpam-1475	173	10	(	(	PUNCT
ejpam-1475	173	11	minus	minus	NOUN
ejpam-1475	173	12	)	)	PUNCT
ejpam-1475	173	13	lie	lie	NOUN
ejpam-1475	173	14	-	-	PUNCT
ejpam-1475	173	15	poison	poison	NOUN
ejpam-1475	173	16	structure	structure	NOUN
ejpam-1475	173	17	for	for	ADP
ejpam-1475	173	18	se(2)∗.	se(2)∗.	PRON
ejpam-1475	173	19	the	the	DET
ejpam-1475	173	20	equations	equation	NOUN
ejpam-1475	173	21	of	of	ADP
ejpam-1475	173	22	motion	motion	NOUN
ejpam-1475	173	23	take	take	VERB
ejpam-1475	173	24	the	the	DET
ejpam-1475	173	25	following	following	ADJ
ejpam-1475	173	26	form	form	NOUN
ejpam-1475	173	27	ṗi	ṗi	PROPN
ejpam-1475	173	28	=	=	SYM
ejpam-1475	173	29	−p	−p	PROPN
ejpam-1475	173	30	(	(	PUNCT
ejpam-1475	173	31	�	�	PROPN
ejpam-1475	173	32	ei	ei	PROPN
ejpam-1475	173	33	,	,	PUNCT
ejpam-1475	173	34	dh(p	dh(p	NOUN
ejpam-1475	173	35	)	)	PUNCT
ejpam-1475	173	36	�	�	PROPN
ejpam-1475	173	37	)	)	PUNCT
ejpam-1475	173	38	,	,	PUNCT
ejpam-1475	174	1	i	i	PRON
ejpam-1475	174	2	=	=	NOUN
ejpam-1475	174	3	1,2,3	1,2,3	NUM
ejpam-1475	174	4	r.	r.	PROPN
ejpam-1475	174	5	adams	adams	PROPN
ejpam-1475	174	6	,	,	PUNCT
ejpam-1475	174	7	r.	r.	PROPN
ejpam-1475	174	8	biggs	biggs	PROPN
ejpam-1475	174	9	,	,	PUNCT
ejpam-1475	174	10	c.	c.	PROPN
ejpam-1475	174	11	remsing	remsing	NOUN
ejpam-1475	174	12	/	/	SYM
ejpam-1475	174	13	eur	eur	NOUN
ejpam-1475	174	14	.	.	PUNCT
ejpam-1475	175	1	j.	j.	PROPN
ejpam-1475	175	2	pure	pure	PROPN
ejpam-1475	175	3	appl	appl	PROPN
ejpam-1475	175	4	.	.	PROPN
ejpam-1475	175	5	math	math	PROPN
ejpam-1475	175	6	,	,	PUNCT
ejpam-1475	175	7	5	5	NUM
ejpam-1475	175	8	(	(	PUNCT
ejpam-1475	175	9	2012	2012	NUM
ejpam-1475	175	10	)	)	PUNCT
ejpam-1475	175	11	,	,	PUNCT
ejpam-1475	175	12	1	1	NUM
ejpam-1475	175	13	-	-	SYM
ejpam-1475	175	14	15	15	NUM
ejpam-1475	175	15	7	7	NUM
ejpam-1475	175	16	or	or	CCONJ
ejpam-1475	175	17	,	,	PUNCT
ejpam-1475	175	18	explicitly	explicitly	ADV
ejpam-1475	175	19	,	,	PUNCT
ejpam-1475	175	20			PROPN
ejpam-1475	175	21			PROPN
ejpam-1475	175	22			PROPN
ejpam-1475	175	23			PROPN
ejpam-1475	175	24			PROPN
ejpam-1475	175	25			PROPN
ejpam-1475	175	26			NOUN
ejpam-1475	175	27			PROPN
ejpam-1475	175	28			PROPN
ejpam-1475	175	29			PROPN
ejpam-1475	175	30			PROPN
ejpam-1475	175	31			PROPN
ejpam-1475	175	32			NOUN
ejpam-1475	175	33	ṗ1	ṗ1	PROPN
ejpam-1475	175	34	=	=	SYM
ejpam-1475	175	35	∂	∂	NUM
ejpam-1475	175	36	h	h	NOUN
ejpam-1475	175	37	∂	∂	NOUN
ejpam-1475	175	38	p3	p3	PROPN
ejpam-1475	175	39	p2	p2	VERB
ejpam-1475	175	40	ṗ2	ṗ2	PROPN
ejpam-1475	175	41	=	=	PUNCT
ejpam-1475	176	1	−	−	PROPN
ejpam-1475	176	2	∂	∂	NUM
ejpam-1475	176	3	h	h	NOUN
ejpam-1475	176	4	∂	∂	NOUN
ejpam-1475	176	5	p3	p3	PROPN
ejpam-1475	176	6	p1	p1	PROPN
ejpam-1475	176	7	ṗ3	ṗ3	PROPN
ejpam-1475	176	8	=	=	PROPN
ejpam-1475	176	9	∂	∂	NUM
ejpam-1475	176	10	h	h	NOUN
ejpam-1475	176	11	∂	∂	NOUN
ejpam-1475	176	12	p2	p2	PROPN
ejpam-1475	176	13	p1	p1	PROPN
ejpam-1475	176	14	−	−	PROPN
ejpam-1475	176	15	∂	∂	NOUN
ejpam-1475	176	16	h	h	NOUN
ejpam-1475	176	17	∂	∂	NOUN
ejpam-1475	176	18	p1	p1	NOUN
ejpam-1475	176	19	p2	p2	NOUN
ejpam-1475	176	20	·	·	PUNCT
ejpam-1475	176	21	(	(	PUNCT
ejpam-1475	176	22	10	10	NUM
ejpam-1475	176	23	)	)	PUNCT
ejpam-1475	176	24	we	we	PRON
ejpam-1475	176	25	note	note	VERB
ejpam-1475	176	26	that	that	SCONJ
ejpam-1475	176	27	c	c	NOUN
ejpam-1475	176	28	:	:	PUNCT
ejpam-1475	176	29	se(2)∗→	se(2)∗→	PROPN
ejpam-1475	176	30	r	r	NOUN
ejpam-1475	176	31	,	,	PUNCT
ejpam-1475	176	32	c(p	c(p	NOUN
ejpam-1475	176	33	)	)	PUNCT
ejpam-1475	176	34	=	=	PUNCT
ejpam-1475	176	35	p2	p2	PROPN
ejpam-1475	176	36	1	1	NUM
ejpam-1475	176	37	+	+	NUM
ejpam-1475	176	38	p2	p2	NOUN
ejpam-1475	176	39	2	2	NUM
ejpam-1475	176	40	is	be	AUX
ejpam-1475	176	41	a	a	DET
ejpam-1475	176	42	casimir	casimir	NOUN
ejpam-1475	176	43	function	function	NOUN
ejpam-1475	176	44	.	.	PUNCT
ejpam-1475	177	1	4	4	X
ejpam-1475	177	2	.	.	X
ejpam-1475	177	3	classification	classification	NOUN
ejpam-1475	177	4	of	of	ADP
ejpam-1475	177	5	systems	system	NOUN
ejpam-1475	177	6	consider	consider	VERB
ejpam-1475	177	7	a	a	DET
ejpam-1475	177	8	general	general	ADJ
ejpam-1475	177	9	single	single	ADJ
ejpam-1475	177	10	-	-	PUNCT
ejpam-1475	177	11	input	input	NOUN
ejpam-1475	177	12	left	left	ADJ
ejpam-1475	177	13	-	-	PUNCT
ejpam-1475	177	14	invariant	invariant	ADJ
ejpam-1475	177	15	control	control	NOUN
ejpam-1475	177	16	affine	affine	NOUN
ejpam-1475	177	17	system	system	NOUN
ejpam-1475	177	18	σ	σ	PROPN
ejpam-1475	177	19	with	with	ADP
ejpam-1475	177	20	trace	trace	NOUN
ejpam-1475	177	21	γ	γ	X
ejpam-1475	177	22	=	=	SYM
ejpam-1475	177	23	a+	a+	PUNCT
ejpam-1475	177	24	〈	〈	PROPN
ejpam-1475	177	25	b	b	SYM
ejpam-1475	177	26	〉	〉	NOUN
ejpam-1475	177	27	⊂	⊂	PROPN
ejpam-1475	177	28	se(2	se(2	NOUN
ejpam-1475	177	29	)	)	PUNCT
ejpam-1475	177	30	.	.	PUNCT
ejpam-1475	178	1	we	we	PRON
ejpam-1475	178	2	shall	shall	AUX
ejpam-1475	178	3	assume	assume	VERB
ejpam-1475	178	4	that	that	SCONJ
ejpam-1475	178	5	σ	σ	PROPN
ejpam-1475	178	6	has	have	VERB
ejpam-1475	178	7	full	full	ADJ
ejpam-1475	178	8	rank	rank	NOUN
ejpam-1475	178	9	(	(	PUNCT
ejpam-1475	178	10	i.e.	i.e.	X
ejpam-1475	178	11	,	,	PUNCT
ejpam-1475	178	12	lie{a	lie{a	NOUN
ejpam-1475	178	13	,	,	PUNCT
ejpam-1475	178	14	b	b	NOUN
ejpam-1475	178	15	}	}	PUNCT
ejpam-1475	178	16	=	=	SYM
ejpam-1475	178	17	se(2	se(2	NOUN
ejpam-1475	178	18	)	)	PUNCT
ejpam-1475	178	19	)	)	PUNCT
ejpam-1475	178	20	.	.	PUNCT
ejpam-1475	179	1	this	this	PRON
ejpam-1475	179	2	means	mean	VERB
ejpam-1475	179	3	(	(	PUNCT
ejpam-1475	179	4	by	by	ADP
ejpam-1475	179	5	proposition	proposition	NOUN
ejpam-1475	179	6	1	1	NUM
ejpam-1475	179	7	)	)	PUNCT
ejpam-1475	179	8	that	that	SCONJ
ejpam-1475	179	9	σ	σ	PROPN
ejpam-1475	179	10	is	be	AUX
ejpam-1475	179	11	precisely	precisely	ADV
ejpam-1475	179	12	a	a	DET
ejpam-1475	179	13	controllable	controllable	ADJ
ejpam-1475	179	14	system	system	NOUN
ejpam-1475	179	15	.	.	PUNCT
ejpam-1475	180	1	note	note	VERB
ejpam-1475	180	2	that	that	SCONJ
ejpam-1475	180	3	the	the	DET
ejpam-1475	180	4	lie	lie	NOUN
ejpam-1475	180	5	algebra	algebra	NOUN
ejpam-1475	180	6	rank	rank	NOUN
ejpam-1475	180	7	condition	condition	NOUN
ejpam-1475	180	8	is	be	AUX
ejpam-1475	180	9	equivalent	equivalent	ADJ
ejpam-1475	180	10	to	to	ADP
ejpam-1475	180	11	the	the	DET
ejpam-1475	180	12	conditions	condition	NOUN
ejpam-1475	180	13	(	(	PUNCT
ejpam-1475	180	14	i	i	NOUN
ejpam-1475	180	15	)	)	PUNCT
ejpam-1475	180	16	a	a	PRON
ejpam-1475	180	17	and	and	CCONJ
ejpam-1475	180	18	b	b	NOUN
ejpam-1475	180	19	are	be	AUX
ejpam-1475	180	20	linearly	linearly	ADV
ejpam-1475	180	21	independent	independent	ADJ
ejpam-1475	180	22	and	and	CCONJ
ejpam-1475	180	23	(	(	PUNCT
ejpam-1475	180	24	ii	ii	NOUN
ejpam-1475	180	25	)	)	PUNCT
ejpam-1475	180	26	{	{	PUNCT
ejpam-1475	180	27	a	a	PRON
ejpam-1475	180	28	,	,	PUNCT
ejpam-1475	180	29	b	b	NOUN
ejpam-1475	180	30	}	}	PUNCT
ejpam-1475	180	31	6⊂	6⊂	NUM
ejpam-1475	180	32	〈	〈	PROPN
ejpam-1475	180	33	e1	e1	NOUN
ejpam-1475	180	34	,	,	PUNCT
ejpam-1475	180	35	e2	e2	NOUN
ejpam-1475	180	36	〉	〉	NOUN
ejpam-1475	180	37	(	(	PUNCT
ejpam-1475	180	38	cf	cf	NOUN
ejpam-1475	180	39	.	.	PUNCT
ejpam-1475	181	1	[	[	X
ejpam-1475	181	2	30	30	NUM
ejpam-1475	181	3	]	]	NUM
ejpam-1475	181	4	)	)	PUNCT
ejpam-1475	181	5	.	.	PUNCT
ejpam-1475	182	1	the	the	DET
ejpam-1475	182	2	following	follow	VERB
ejpam-1475	182	3	result	result	NOUN
ejpam-1475	182	4	gives	give	VERB
ejpam-1475	182	5	a	a	DET
ejpam-1475	182	6	classification	classification	NOUN
ejpam-1475	182	7	of	of	ADP
ejpam-1475	182	8	all	all	DET
ejpam-1475	182	9	such	such	ADJ
ejpam-1475	182	10	control	control	NOUN
ejpam-1475	182	11	systems	system	NOUN
ejpam-1475	182	12	under	under	ADP
ejpam-1475	182	13	the	the	DET
ejpam-1475	182	14	detached	detach	VERB
ejpam-1475	182	15	feedback	feedback	NOUN
ejpam-1475	182	16	equivalence	equivalence	NOUN
ejpam-1475	182	17	(	(	PUNCT
ejpam-1475	182	18	see	see	VERB
ejpam-1475	182	19	,	,	PUNCT
ejpam-1475	182	20	also	also	ADV
ejpam-1475	182	21	,	,	PUNCT
ejpam-1475	182	22	[	[	X
ejpam-1475	182	23	6	6	NUM
ejpam-1475	182	24	,	,	PUNCT
ejpam-1475	182	25	4	4	NUM
ejpam-1475	182	26	,	,	PUNCT
ejpam-1475	182	27	3	3	NUM
ejpam-1475	182	28	]	]	NUM
ejpam-1475	182	29	)	)	PUNCT
ejpam-1475	182	30	.	.	PUNCT
ejpam-1475	183	1	theorem	theorem	ADJ
ejpam-1475	183	2	4	4	NUM
ejpam-1475	183	3	.	.	PUNCT
ejpam-1475	184	1	any	any	DET
ejpam-1475	184	2	controllable	controllable	ADJ
ejpam-1475	184	3	single	single	ADJ
ejpam-1475	184	4	-	-	PUNCT
ejpam-1475	184	5	input	input	NOUN
ejpam-1475	184	6	(	(	PUNCT
ejpam-1475	184	7	left	leave	VERB
ejpam-1475	184	8	-	-	PUNCT
ejpam-1475	184	9	invariant	invariant	ADJ
ejpam-1475	184	10	control	control	NOUN
ejpam-1475	184	11	affine	affine	NOUN
ejpam-1475	184	12	)	)	PUNCT
ejpam-1475	184	13	system	system	NOUN
ejpam-1475	184	14	σ	σ	X
ejpam-1475	184	15	is	be	AUX
ejpam-1475	184	16	(	(	PUNCT
ejpam-1475	184	17	locally	locally	ADV
ejpam-1475	184	18	)	)	PUNCT
ejpam-1475	184	19	detached	detach	VERB
ejpam-1475	184	20	feedback	feedback	NOUN
ejpam-1475	184	21	equivalent	equivalent	ADJ
ejpam-1475	184	22	to	to	ADP
ejpam-1475	184	23	exactly	exactly	ADV
ejpam-1475	184	24	one	one	NUM
ejpam-1475	184	25	of	of	ADP
ejpam-1475	184	26	the	the	DET
ejpam-1475	184	27	following	follow	VERB
ejpam-1475	184	28	systems	system	NOUN
ejpam-1475	184	29	:	:	PUNCT
ejpam-1475	184	30	σ1	σ1	NOUN
ejpam-1475	184	31	or	or	CCONJ
ejpam-1475	184	32	σ2,α	σ2,α	PROPN
ejpam-1475	184	33	(	(	PUNCT
ejpam-1475	184	34	α	α	NOUN
ejpam-1475	184	35	>	>	X
ejpam-1475	184	36	0	0	NUM
ejpam-1475	184	37	)	)	PUNCT
ejpam-1475	184	38	with	with	ADP
ejpam-1475	184	39	respective	respective	ADJ
ejpam-1475	184	40	parametrisations	parametrisation	NOUN
ejpam-1475	184	41	ξ1(1,u	ξ1(1,u	NUM
ejpam-1475	184	42	)	)	PUNCT
ejpam-1475	185	1	=	=	SYM
ejpam-1475	185	2	e1	e1	NOUN
ejpam-1475	185	3	+	+	CCONJ
ejpam-1475	185	4	ue3	ue3	ADJ
ejpam-1475	185	5	,	,	PUNCT
ejpam-1475	185	6	ξ2,α(1,u	ξ2,α(1,u	NUM
ejpam-1475	185	7	)	)	PUNCT
ejpam-1475	185	8	=	=	SYM
ejpam-1475	185	9	αe3	αe3	NOUN
ejpam-1475	185	10	+	+	CCONJ
ejpam-1475	185	11	ue1	ue1	PROPN
ejpam-1475	185	12	.	.	PUNCT
ejpam-1475	186	1	proof	proof	NOUN
ejpam-1475	186	2	.	.	PUNCT
ejpam-1475	187	1	throughout	throughout	ADV
ejpam-1475	187	2	,	,	PUNCT
ejpam-1475	187	3	we	we	PRON
ejpam-1475	187	4	use	use	VERB
ejpam-1475	187	5	the	the	DET
ejpam-1475	187	6	algebraic	algebraic	ADJ
ejpam-1475	187	7	characterisation	characterisation	NOUN
ejpam-1475	187	8	from	from	ADP
ejpam-1475	187	9	proposition	proposition	NOUN
ejpam-1475	187	10	2	2	NUM
ejpam-1475	187	11	.	.	PUNCT
ejpam-1475	187	12	let	let	VERB
ejpam-1475	187	13	the	the	DET
ejpam-1475	187	14	trace	trace	NOUN
ejpam-1475	187	15	of	of	ADP
ejpam-1475	187	16	the	the	DET
ejpam-1475	187	17	system	system	NOUN
ejpam-1475	187	18	σ	σ	NOUN
ejpam-1475	187	19	be	be	AUX
ejpam-1475	187	20	given	give	VERB
ejpam-1475	187	21	by	by	ADP
ejpam-1475	187	22	γ	γ	PROPN
ejpam-1475	187	23	=	=	SYM
ejpam-1475	187	24	∑3	∑3	PROPN
ejpam-1475	187	25	i=1	i=1	PROPN
ejpam-1475	187	26	ai	ai	VERB
ejpam-1475	187	27	ei	ei	X
ejpam-1475	188	1	+	+	CCONJ
ejpam-1475	188	2	d	d	NUM
ejpam-1475	188	3	∑3	∑3	PROPN
ejpam-1475	188	4	i=1	i=1	PROPN
ejpam-1475	188	5	bi	bi	NOUN
ejpam-1475	188	6	ei	ei	PROPN
ejpam-1475	188	7	e	e	PROPN
ejpam-1475	188	8	.	.	PUNCT
ejpam-1475	189	1	first	first	ADV
ejpam-1475	189	2	,	,	PUNCT
ejpam-1475	189	3	consider	consider	VERB
ejpam-1475	189	4	the	the	DET
ejpam-1475	189	5	case	case	NOUN
ejpam-1475	189	6	b3	b3	PROPN
ejpam-1475	189	7	6=	6=	ADP
ejpam-1475	189	8	0	0	NUM
ejpam-1475	189	9	.	.	PUNCT
ejpam-1475	190	1	then	then	ADV
ejpam-1475	190	2	γ	γ	X
ejpam-1475	190	3	=	=	SYM
ejpam-1475	190	4	(	(	PUNCT
ejpam-1475	190	5	a1	a1	NOUN
ejpam-1475	190	6	−	−	NOUN
ejpam-1475	190	7	b1a3	b1a3	NOUN
ejpam-1475	190	8	b3	b3	NOUN
ejpam-1475	190	9	)	)	PUNCT
ejpam-1475	190	10	e1	e1	PROPN
ejpam-1475	190	11	+	+	CCONJ
ejpam-1475	190	12	(	(	PUNCT
ejpam-1475	190	13	a2−	a2−	PROPN
ejpam-1475	190	14	b2a3	b2a3	PROPN
ejpam-1475	190	15	b3	b3	PROPN
ejpam-1475	190	16	)	)	PUNCT
ejpam-1475	190	17	e2	e2	PROPN
ejpam-1475	190	18	+	+	CCONJ
ejpam-1475	190	19	d	d	PROPN
ejpam-1475	190	20	b1	b1	PROPN
ejpam-1475	190	21	b3	b3	PROPN
ejpam-1475	190	22	e1	e1	PROPN
ejpam-1475	190	23	+	+	CCONJ
ejpam-1475	190	24	b2	b2	NOUN
ejpam-1475	190	25	b3	b3	PROPN
ejpam-1475	190	26	e2	e2	NOUN
ejpam-1475	190	27	+	+	CCONJ
ejpam-1475	190	28	e3	e3	NOUN
ejpam-1475	190	29	e	e	NOUN
ejpam-1475	190	30	=	=	SYM
ejpam-1475	190	31	a′1e1	a′1e1	PROPN
ejpam-1475	190	32	+	+	CCONJ
ejpam-1475	190	33	a′2e2	a′2e2	PROPN
ejpam-1475	190	34	+	+	CCONJ
ejpam-1475	190	35	¬	¬	PROPN
ejpam-1475	190	36	b′1e1	b′1e1	NOUN
ejpam-1475	190	37	+	+	CCONJ
ejpam-1475	190	38	b′2e2	b′2e2	PROPN
ejpam-1475	190	39	+	+	CCONJ
ejpam-1475	190	40	e3	e3	VERB
ejpam-1475	190	41	¶	¶	NOUN
ejpam-1475	190	42	for	for	ADP
ejpam-1475	190	43	some	some	DET
ejpam-1475	190	44	corresponding	corresponding	ADJ
ejpam-1475	190	45	constants	constant	NOUN
ejpam-1475	190	46	a′i	a′i	PROPN
ejpam-1475	190	47	,	,	PUNCT
ejpam-1475	190	48	b′i	b′i	PROPN
ejpam-1475	190	49	∈	∈	PROPN
ejpam-1475	190	50	r	r	PROPN
ejpam-1475	190	51	,	,	PUNCT
ejpam-1475	190	52	i	i	NOUN
ejpam-1475	190	53	=	=	NOUN
ejpam-1475	190	54	1,2	1,2	NUM
ejpam-1475	190	55	.	.	PUNCT
ejpam-1475	191	1	hence	hence	ADV
ejpam-1475	191	2	,	,	PUNCT
ejpam-1475	191	3	ψ	ψ	X
ejpam-1475	191	4	=	=	NOUN
ejpam-1475	191	5			X
ejpam-1475	191	6			ADJ
ejpam-1475	191	7			X
ejpam-1475	191	8	a′1	a′1	PROPN
ejpam-1475	191	9	−a′2	−a′2	PUNCT
ejpam-1475	191	10	b′1	b′1	VERB
ejpam-1475	191	11	a′2	a′2	CCONJ
ejpam-1475	192	1	a′1	a′1	PROPN
ejpam-1475	192	2	b′2	b′2	PROPN
ejpam-1475	192	3	0	0	NUM
ejpam-1475	192	4	0	0	NUM
ejpam-1475	192	5	1	1	NUM
ejpam-1475	192	6			PROPN
ejpam-1475	192	7			PROPN
ejpam-1475	192	8			PROPN
ejpam-1475	192	9	is	be	AUX
ejpam-1475	192	10	a	a	DET
ejpam-1475	192	11	lie	lie	NOUN
ejpam-1475	192	12	algebra	algebra	NOUN
ejpam-1475	192	13	automorphism	automorphism	NOUN
ejpam-1475	192	14	mapping	mapping	NOUN
ejpam-1475	192	15	γ1	γ1	NOUN
ejpam-1475	192	16	to	to	ADP
ejpam-1475	192	17	γ	γ	PROPN
ejpam-1475	192	18	.	.	PUNCT
ejpam-1475	193	1	(	(	PUNCT
ejpam-1475	193	2	note	note	VERB
ejpam-1475	193	3	that	that	SCONJ
ejpam-1475	193	4	detψ=	detψ=	VERB
ejpam-1475	193	5	0	0	PUNCT
ejpam-1475	194	1	if	if	SCONJ
ejpam-1475	194	2	and	and	CCONJ
ejpam-1475	194	3	only	only	ADV
ejpam-1475	194	4	if	if	SCONJ
ejpam-1475	194	5	a′1	a′1	PROPN
ejpam-1475	194	6	=	=	PUNCT
ejpam-1475	194	7	a′2	a′2	NOUN
ejpam-1475	194	8	=	=	SYM
ejpam-1475	194	9	0	0	PROPN
ejpam-1475	194	10	,	,	PUNCT
ejpam-1475	194	11	a	a	DET
ejpam-1475	194	12	contradiction	contradiction	NOUN
ejpam-1475	194	13	.	.	PUNCT
ejpam-1475	194	14	)	)	PUNCT
ejpam-1475	195	1	next	next	ADV
ejpam-1475	195	2	,	,	PUNCT
ejpam-1475	195	3	consider	consider	VERB
ejpam-1475	195	4	the	the	DET
ejpam-1475	195	5	case	case	NOUN
ejpam-1475	195	6	b3	b3	NOUN
ejpam-1475	195	7	=	=	SYM
ejpam-1475	195	8	0	0	X
ejpam-1475	195	9	.	.	PUNCT
ejpam-1475	196	1	since	since	SCONJ
ejpam-1475	196	2	a3	a3	NOUN
ejpam-1475	196	3	6=	6=	PRON
ejpam-1475	196	4	0	0	NUM
ejpam-1475	197	1	(	(	PUNCT
ejpam-1475	197	2	as	as	SCONJ
ejpam-1475	197	3	σ	σ	PROPN
ejpam-1475	197	4	is	be	AUX
ejpam-1475	197	5	of	of	ADP
ejpam-1475	197	6	full	full	ADJ
ejpam-1475	197	7	rank	rank	NOUN
ejpam-1475	197	8	)	)	PUNCT
ejpam-1475	197	9	,	,	PUNCT
ejpam-1475	197	10	and	and	CCONJ
ejpam-1475	197	11	either	either	PRON
ejpam-1475	197	12	b1	b1	NOUN
ejpam-1475	197	13	6=	6=	PRON
ejpam-1475	197	14	0	0	NUM
ejpam-1475	197	15	or	or	CCONJ
ejpam-1475	197	16	b2	b2	NOUN
ejpam-1475	197	17	6=	6=	ADP
ejpam-1475	197	18	0	0	NUM
ejpam-1475	197	19	,	,	PUNCT
ejpam-1475	197	20	we	we	PRON
ejpam-1475	197	21	get	get	VERB
ejpam-1475	197	22	that	that	PRON
ejpam-1475	197	23	ψ=	ψ=	NOUN
ejpam-1475	197	24			NOUN
ejpam-1475	197	25			NOUN
ejpam-1475	197	26			NUM
ejpam-1475	197	27	b1	b1	NOUN
ejpam-1475	197	28	−sgn(a3)b2	−sgn(a3)b2	PROPN
ejpam-1475	197	29	a1	a1	NOUN
ejpam-1475	197	30	α	α	NOUN
ejpam-1475	197	31	b2	b2	NOUN
ejpam-1475	197	32	sgn(a3)b1	sgn(a3)b1	NOUN
ejpam-1475	197	33	a2	a2	NOUN
ejpam-1475	197	34	α	α	NOUN
ejpam-1475	197	35	0	0	NUM
ejpam-1475	197	36	0	0	NUM
ejpam-1475	197	37	sgn(a3	sgn(a3	NOUN
ejpam-1475	197	38	)	)	PUNCT
ejpam-1475	197	39			PROPN
ejpam-1475	198	1			PROPN
ejpam-1475	198	2			PROPN
ejpam-1475	198	3	r.	r.	PROPN
ejpam-1475	198	4	adams	adams	PROPN
ejpam-1475	198	5	,	,	PUNCT
ejpam-1475	198	6	r.	r.	PROPN
ejpam-1475	198	7	biggs	biggs	PROPN
ejpam-1475	198	8	,	,	PUNCT
ejpam-1475	198	9	c.	c.	PROPN
ejpam-1475	198	10	remsing	remsing	NOUN
ejpam-1475	198	11	/	/	SYM
ejpam-1475	198	12	eur	eur	NOUN
ejpam-1475	198	13	.	.	PUNCT
ejpam-1475	199	1	j.	j.	PROPN
ejpam-1475	199	2	pure	pure	PROPN
ejpam-1475	199	3	appl	appl	PROPN
ejpam-1475	199	4	.	.	PROPN
ejpam-1475	199	5	math	math	PROPN
ejpam-1475	199	6	,	,	PUNCT
ejpam-1475	199	7	5	5	NUM
ejpam-1475	199	8	(	(	PUNCT
ejpam-1475	199	9	2012	2012	NUM
ejpam-1475	199	10	)	)	PUNCT
ejpam-1475	199	11	,	,	PUNCT
ejpam-1475	199	12	1	1	NUM
ejpam-1475	199	13	-	-	SYM
ejpam-1475	199	14	15	15	NUM
ejpam-1475	199	15	8	8	NUM
ejpam-1475	199	16	is	be	AUX
ejpam-1475	199	17	a	a	DET
ejpam-1475	199	18	lie	lie	NOUN
ejpam-1475	199	19	algebra	algebra	NOUN
ejpam-1475	199	20	automorphism	automorphism	NOUN
ejpam-1475	199	21	.	.	PUNCT
ejpam-1475	200	1	let	let	VERB
ejpam-1475	200	2	α	α	NOUN
ejpam-1475	200	3	=	=	SYM
ejpam-1475	200	4	|a3|	|a3|	NOUN
ejpam-1475	200	5	,	,	PUNCT
ejpam-1475	200	6	then	then	ADV
ejpam-1475	200	7	ψ·γ2,α	ψ·γ2,α	PROPN
ejpam-1475	200	8	=	=	SYM
ejpam-1475	200	9	γ	γ	PROPN
ejpam-1475	200	10	.	.	PUNCT
ejpam-1475	201	1	a	a	DET
ejpam-1475	201	2	simple	simple	ADJ
ejpam-1475	201	3	argument	argument	NOUN
ejpam-1475	201	4	shows	show	VERB
ejpam-1475	201	5	that	that	SCONJ
ejpam-1475	201	6	σ1	σ1	PROPN
ejpam-1475	201	7	is	be	AUX
ejpam-1475	201	8	not	not	PART
ejpam-1475	201	9	equivalent	equivalent	ADJ
ejpam-1475	201	10	to	to	ADP
ejpam-1475	201	11	any	any	DET
ejpam-1475	201	12	system	system	NOUN
ejpam-1475	201	13	σ2,α	σ2,α	NOUN
ejpam-1475	201	14	and	and	CCONJ
ejpam-1475	201	15	that	that	SCONJ
ejpam-1475	201	16	σ2,α	σ2,α	PROPN
ejpam-1475	201	17	is	be	AUX
ejpam-1475	201	18	not	not	PART
ejpam-1475	201	19	equivalent	equivalent	ADJ
ejpam-1475	201	20	to	to	ADP
ejpam-1475	201	21	σ2,β	σ2,β	PROPN
ejpam-1475	201	22	for	for	ADP
ejpam-1475	201	23	any	any	DET
ejpam-1475	201	24	α	α	NOUN
ejpam-1475	201	25	6=	6=	ADP
ejpam-1475	201	26	β	β	PROPN
ejpam-1475	201	27	,	,	PUNCT
ejpam-1475	201	28	α	α	PROPN
ejpam-1475	201	29	,	,	PUNCT
ejpam-1475	201	30	β	β	X
ejpam-1475	201	31	>	>	X
ejpam-1475	201	32	0	0	X
ejpam-1475	201	33	.	.	PUNCT
ejpam-1475	201	34	left	leave	VERB
ejpam-1475	201	35	-	-	PUNCT
ejpam-1475	201	36	invariant	invariant	ADJ
ejpam-1475	201	37	control	control	NOUN
ejpam-1475	201	38	problems	problem	NOUN
ejpam-1475	201	39	henceforth	henceforth	ADV
ejpam-1475	201	40	,	,	PUNCT
ejpam-1475	201	41	we	we	PRON
ejpam-1475	201	42	consider	consider	VERB
ejpam-1475	201	43	only	only	ADV
ejpam-1475	201	44	the	the	DET
ejpam-1475	201	45	systems	system	NOUN
ejpam-1475	201	46	σ1	σ1	PROPN
ejpam-1475	201	47	and	and	CCONJ
ejpam-1475	201	48	σ2,α	σ2,α	PROPN
ejpam-1475	201	49	.	.	PROPN
ejpam-1475	202	1	in	in	ADP
ejpam-1475	202	2	each	each	PRON
ejpam-1475	202	3	of	of	ADP
ejpam-1475	202	4	these	these	DET
ejpam-1475	202	5	typical	typical	ADJ
ejpam-1475	202	6	cases	case	NOUN
ejpam-1475	202	7	,	,	PUNCT
ejpam-1475	202	8	we	we	PRON
ejpam-1475	202	9	investigate	investigate	VERB
ejpam-1475	202	10	an	an	DET
ejpam-1475	202	11	optimal	optimal	ADJ
ejpam-1475	202	12	control	control	NOUN
ejpam-1475	202	13	problem	problem	NOUN
ejpam-1475	202	14	(	(	PUNCT
ejpam-1475	202	15	with	with	ADP
ejpam-1475	202	16	quadratic	quadratic	ADJ
ejpam-1475	202	17	cost	cost	NOUN
ejpam-1475	202	18	):	):	PUNCT
ejpam-1475	202	19	ġ	ġ	NOUN
ejpam-1475	202	20	=	=	SYM
ejpam-1475	202	21	g	g	PROPN
ejpam-1475	202	22	�	�	PROPN
ejpam-1475	202	23	e1	e1	PROPN
ejpam-1475	202	24	+	+	CCONJ
ejpam-1475	202	25	ue3	ue3	ADJ
ejpam-1475	202	26	�	�	PROPN
ejpam-1475	202	27	g(0	g(0	PROPN
ejpam-1475	202	28	)	)	PUNCT
ejpam-1475	202	29	=	=	PROPN
ejpam-1475	202	30	g0	g0	PROPN
ejpam-1475	202	31	,	,	PUNCT
ejpam-1475	202	32	g(t	g(t	PROPN
ejpam-1475	202	33	)	)	PUNCT
ejpam-1475	203	1	=	=	PUNCT
ejpam-1475	204	1	gt	gt	PROPN
ejpam-1475	204	2	j	j	NOUN
ejpam-1475	205	1	=	=	NOUN
ejpam-1475	205	2	1	1	NUM
ejpam-1475	205	3	2	2	NUM
ejpam-1475	205	4	∫	∫	NOUN
ejpam-1475	205	5	t	t	NOUN
ejpam-1475	205	6	0	0	NUM
ejpam-1475	205	7	u2(t)d	u2(t)d	PROPN
ejpam-1475	205	8	t	t	PROPN
ejpam-1475	205	9	→min	→min	NOUN
ejpam-1475	205	10			PROPN
ejpam-1475	205	11			PROPN
ejpam-1475	205	12			PROPN
ejpam-1475	205	13			PROPN
ejpam-1475	205	14			ADJ
ejpam-1475	205	15			ADJ
ejpam-1475	205	16			NOUN
ejpam-1475	205	17	licp(1	licp(1	NOUN
ejpam-1475	205	18	)	)	PUNCT
ejpam-1475	205	19	and	and	CCONJ
ejpam-1475	205	20	ġ	ġ	NOUN
ejpam-1475	205	21	=	=	PUNCT
ejpam-1475	205	22	g	g	PROPN
ejpam-1475	205	23	�	�	PROPN
ejpam-1475	205	24	αe3	αe3	NOUN
ejpam-1475	205	25	+	+	CCONJ
ejpam-1475	205	26	ue1	ue1	PROPN
ejpam-1475	205	27	�	�	PROPN
ejpam-1475	205	28	g(0	g(0	PROPN
ejpam-1475	205	29	)	)	PUNCT
ejpam-1475	205	30	=	=	PROPN
ejpam-1475	205	31	g0	g0	PROPN
ejpam-1475	205	32	,	,	PUNCT
ejpam-1475	205	33	g(t	g(t	PROPN
ejpam-1475	205	34	)	)	PUNCT
ejpam-1475	206	1	=	=	PUNCT
ejpam-1475	207	1	gt	gt	PROPN
ejpam-1475	207	2	j	j	NOUN
ejpam-1475	208	1	=	=	NOUN
ejpam-1475	208	2	1	1	NUM
ejpam-1475	208	3	2	2	NUM
ejpam-1475	208	4	∫	∫	NOUN
ejpam-1475	208	5	t	t	NOUN
ejpam-1475	208	6	0	0	NUM
ejpam-1475	208	7	u2(t)d	u2(t)d	PROPN
ejpam-1475	208	8	t	t	PROPN
ejpam-1475	208	9	→min	→min	NOUN
ejpam-1475	208	10			PROPN
ejpam-1475	208	11			PROPN
ejpam-1475	208	12			PROPN
ejpam-1475	208	13			PROPN
ejpam-1475	208	14			ADJ
ejpam-1475	208	15			ADJ
ejpam-1475	208	16			NOUN
ejpam-1475	208	17	licp(2	licp(2	NOUN
ejpam-1475	208	18	)	)	PUNCT
ejpam-1475	209	1	the	the	DET
ejpam-1475	209	2	following	follow	VERB
ejpam-1475	209	3	two	two	NUM
ejpam-1475	209	4	results	result	NOUN
ejpam-1475	209	5	follow	follow	VERB
ejpam-1475	209	6	easily	easily	ADV
ejpam-1475	209	7	from	from	ADP
ejpam-1475	209	8	proposition	proposition	NOUN
ejpam-1475	209	9	3	3	NUM
ejpam-1475	209	10	.	.	PUNCT
ejpam-1475	210	1	theorem	theorem	NOUN
ejpam-1475	210	2	5	5	NUM
ejpam-1475	210	3	(	(	PUNCT
ejpam-1475	210	4	[	[	X
ejpam-1475	210	5	31	31	NUM
ejpam-1475	210	6	]	]	PUNCT
ejpam-1475	210	7	)	)	PUNCT
ejpam-1475	210	8	.	.	PUNCT
ejpam-1475	211	1	for	for	ADP
ejpam-1475	211	2	the	the	DET
ejpam-1475	211	3	licp(1	licp(1	NOUN
ejpam-1475	211	4	)	)	PUNCT
ejpam-1475	211	5	,	,	PUNCT
ejpam-1475	211	6	the	the	DET
ejpam-1475	211	7	extremal	extremal	ADJ
ejpam-1475	211	8	control	control	NOUN
ejpam-1475	211	9	is	be	AUX
ejpam-1475	211	10	given	give	VERB
ejpam-1475	211	11	by	by	ADP
ejpam-1475	211	12	u=	u=	ADJ
ejpam-1475	211	13	p3	p3	NOUN
ejpam-1475	211	14	,	,	PUNCT
ejpam-1475	211	15	where	where	SCONJ
ejpam-1475	211	16	h(p	h(p	NOUN
ejpam-1475	211	17	)	)	PUNCT
ejpam-1475	211	18	=	=	SYM
ejpam-1475	211	19	p1	p1	NOUN
ejpam-1475	211	20	+	+	CCONJ
ejpam-1475	211	21	1	1	NUM
ejpam-1475	211	22	2	2	NUM
ejpam-1475	211	23	p2	p2	NOUN
ejpam-1475	211	24	3	3	NUM
ejpam-1475	211	25	and	and	CCONJ
ejpam-1475	211	26			VERB
ejpam-1475	212	1			PRON
ejpam-1475	212	2			NOUN
ejpam-1475	212	3	ṗ1	ṗ1	NOUN
ejpam-1475	212	4	=	=	PUNCT
ejpam-1475	212	5	p2p3	p2p3	PROPN
ejpam-1475	212	6	ṗ2	ṗ2	NOUN
ejpam-1475	212	7	=	=	PUNCT
ejpam-1475	213	1	−p1p3	−p1p3	PROPN
ejpam-1475	213	2	ṗ3	ṗ3	NOUN
ejpam-1475	213	3	=	=	PUNCT
ejpam-1475	213	4	−p2	−p2	PROPN
ejpam-1475	213	5	.	.	PUNCT
ejpam-1475	214	1	(	(	PUNCT
ejpam-1475	214	2	11	11	NUM
ejpam-1475	214	3	)	)	PUNCT
ejpam-1475	214	4	theorem	theorem	NOUN
ejpam-1475	214	5	6	6	NUM
ejpam-1475	214	6	.	.	PUNCT
ejpam-1475	214	7	for	for	ADP
ejpam-1475	214	8	the	the	DET
ejpam-1475	214	9	licp(2	licp(2	NOUN
ejpam-1475	214	10	)	)	PUNCT
ejpam-1475	214	11	,	,	PUNCT
ejpam-1475	214	12	the	the	DET
ejpam-1475	214	13	extremal	extremal	ADJ
ejpam-1475	214	14	control	control	NOUN
ejpam-1475	214	15	is	be	AUX
ejpam-1475	214	16	given	give	VERB
ejpam-1475	214	17	by	by	ADP
ejpam-1475	214	18	u	u	NOUN
ejpam-1475	214	19	=	=	PROPN
ejpam-1475	214	20	p1	p1	PROPN
ejpam-1475	214	21	,	,	PUNCT
ejpam-1475	214	22	where	where	SCONJ
ejpam-1475	214	23	h(p	h(p	NOUN
ejpam-1475	214	24	)	)	PUNCT
ejpam-1475	214	25	=	=	SYM
ejpam-1475	214	26	1	1	NUM
ejpam-1475	214	27	2	2	NUM
ejpam-1475	214	28	p2	p2	NOUN
ejpam-1475	214	29	1	1	NUM
ejpam-1475	214	30	+	+	NOUN
ejpam-1475	214	31	αp3	αp3	NOUN
ejpam-1475	214	32	and	and	CCONJ
ejpam-1475	214	33			VERB
ejpam-1475	214	34			PRON
ejpam-1475	214	35			NOUN
ejpam-1475	214	36	ṗ1	ṗ1	NOUN
ejpam-1475	214	37	=	=	SYM
ejpam-1475	214	38	αp2	αp2	NOUN
ejpam-1475	214	39	ṗ2	ṗ2	PROPN
ejpam-1475	214	40	=	=	PUNCT
ejpam-1475	214	41	−αp1	−αp1	PROPN
ejpam-1475	215	1	ṗ3	ṗ3	PROPN
ejpam-1475	215	2	=	=	PUNCT
ejpam-1475	215	3	−p1p2	−p1p2	PROPN
ejpam-1475	215	4	.	.	PUNCT
ejpam-1475	216	1	(	(	PUNCT
ejpam-1475	216	2	12	12	NUM
ejpam-1475	216	3	)	)	PUNCT
ejpam-1475	216	4	5	5	NUM
ejpam-1475	216	5	.	.	X
ejpam-1475	216	6	stability	stability	NOUN
ejpam-1475	216	7	the	the	DET
ejpam-1475	216	8	equilibrium	equilibrium	NOUN
ejpam-1475	216	9	states	state	NOUN
ejpam-1475	216	10	for	for	ADP
ejpam-1475	216	11	(	(	PUNCT
ejpam-1475	216	12	11	11	NUM
ejpam-1475	216	13	)	)	PUNCT
ejpam-1475	216	14	are	be	AUX
ejpam-1475	216	15	e	e	X
ejpam-1475	216	16	µ	µ	X
ejpam-1475	216	17	1	1	NUM
ejpam-1475	216	18	=	=	SYM
ejpam-1475	216	19	(	(	PUNCT
ejpam-1475	216	20	µ	µ	NOUN
ejpam-1475	216	21	,	,	PUNCT
ejpam-1475	216	22	0,0	0,0	NOUN
ejpam-1475	216	23	)	)	PUNCT
ejpam-1475	216	24	and	and	CCONJ
ejpam-1475	216	25	eν2	eν2	NOUN
ejpam-1475	216	26	=	=	PRON
ejpam-1475	216	27	(	(	PUNCT
ejpam-1475	216	28	0,0,ν	0,0,ν	NUM
ejpam-1475	216	29	)	)	PUNCT
ejpam-1475	216	30	where	where	SCONJ
ejpam-1475	216	31	µ,ν	µ,ν	ADP
ejpam-1475	216	32	∈	∈	PROPN
ejpam-1475	216	33	r	r	NOUN
ejpam-1475	216	34	,	,	PUNCT
ejpam-1475	216	35	ν	ν	X
ejpam-1475	216	36	6=	6=	ADP
ejpam-1475	216	37	0	0	NUM
ejpam-1475	216	38	.	.	PUNCT
ejpam-1475	217	1	theorem	theorem	NOUN
ejpam-1475	217	2	7	7	NUM
ejpam-1475	217	3	.	.	PUNCT
ejpam-1475	218	1	the	the	DET
ejpam-1475	218	2	equilibrium	equilibrium	NOUN
ejpam-1475	218	3	states	state	NOUN
ejpam-1475	218	4	have	have	VERB
ejpam-1475	218	5	the	the	DET
ejpam-1475	218	6	following	follow	VERB
ejpam-1475	218	7	behaviour	behaviour	NOUN
ejpam-1475	218	8	.	.	PUNCT
ejpam-1475	219	1	r.	r.	PROPN
ejpam-1475	219	2	adams	adams	PROPN
ejpam-1475	219	3	,	,	PUNCT
ejpam-1475	219	4	r.	r.	PROPN
ejpam-1475	219	5	biggs	biggs	PROPN
ejpam-1475	219	6	,	,	PUNCT
ejpam-1475	219	7	c.	c.	PROPN
ejpam-1475	219	8	remsing	remsing	NOUN
ejpam-1475	219	9	/	/	SYM
ejpam-1475	219	10	eur	eur	NOUN
ejpam-1475	219	11	.	.	PUNCT
ejpam-1475	220	1	j.	j.	PROPN
ejpam-1475	220	2	pure	pure	PROPN
ejpam-1475	220	3	appl	appl	PROPN
ejpam-1475	220	4	.	.	PROPN
ejpam-1475	220	5	math	math	PROPN
ejpam-1475	220	6	,	,	PUNCT
ejpam-1475	220	7	5	5	NUM
ejpam-1475	220	8	(	(	PUNCT
ejpam-1475	220	9	2012	2012	NUM
ejpam-1475	220	10	)	)	PUNCT
ejpam-1475	220	11	,	,	PUNCT
ejpam-1475	220	12	1	1	NUM
ejpam-1475	220	13	-	-	SYM
ejpam-1475	220	14	15	15	NUM
ejpam-1475	220	15	9	9	NUM
ejpam-1475	220	16	(	(	PUNCT
ejpam-1475	220	17	i	i	NOUN
ejpam-1475	220	18	)	)	PUNCT
ejpam-1475	220	19	the	the	DET
ejpam-1475	220	20	equilibrium	equilibrium	NOUN
ejpam-1475	220	21	state	state	NOUN
ejpam-1475	220	22	e	e	PROPN
ejpam-1475	220	23	µ	µ	X
ejpam-1475	220	24	1	1	NUM
ejpam-1475	220	25	is	be	AUX
ejpam-1475	220	26	stable	stable	ADJ
ejpam-1475	220	27	if	if	SCONJ
ejpam-1475	220	28	µ	µ	X
ejpam-1475	220	29	<	<	X
ejpam-1475	220	30	0	0	PUNCT
ejpam-1475	220	31	and	and	CCONJ
ejpam-1475	220	32	unstable	unstable	ADJ
ejpam-1475	220	33	if	if	SCONJ
ejpam-1475	220	34	µ≥	µ≥	PROPN
ejpam-1475	220	35	0	0	NUM
ejpam-1475	220	36	.	.	PUNCT
ejpam-1475	221	1	(	(	PUNCT
ejpam-1475	221	2	ii	ii	NOUN
ejpam-1475	221	3	)	)	PUNCT
ejpam-1475	221	4	each	each	DET
ejpam-1475	221	5	equilibrium	equilibrium	NOUN
ejpam-1475	221	6	state	state	NOUN
ejpam-1475	221	7	eν2	eν2	PROPN
ejpam-1475	221	8	is	be	AUX
ejpam-1475	221	9	stable	stable	ADJ
ejpam-1475	221	10	.	.	PUNCT
ejpam-1475	222	1	proof	proof	NOUN
ejpam-1475	222	2	.	.	PUNCT
ejpam-1475	223	1	the	the	DET
ejpam-1475	223	2	linearization	linearization	NOUN
ejpam-1475	223	3	of	of	ADP
ejpam-1475	223	4	the	the	DET
ejpam-1475	223	5	system	system	NOUN
ejpam-1475	223	6	is	be	AUX
ejpam-1475	223	7	given	give	VERB
ejpam-1475	223	8	by	by	ADP
ejpam-1475	223	9			NOUN
ejpam-1475	223	10			ADJ
ejpam-1475	223	11			NOUN
ejpam-1475	223	12	0	0	NUM
ejpam-1475	224	1	p3	p3	NOUN
ejpam-1475	224	2	p2	p2	NOUN
ejpam-1475	224	3	−p3	−p3	PROPN
ejpam-1475	224	4	0	0	PUNCT
ejpam-1475	225	1	−p1	−p1	X
ejpam-1475	225	2	0	0	NUM
ejpam-1475	225	3	−1	−1	NOUN
ejpam-1475	225	4	0	0	PUNCT
ejpam-1475	225	5			PROPN
ejpam-1475	225	6			PROPN
ejpam-1475	225	7			PROPN
ejpam-1475	225	8	.	.	PUNCT
ejpam-1475	226	1	(	(	PUNCT
ejpam-1475	226	2	i	i	NOUN
ejpam-1475	226	3	)	)	PUNCT
ejpam-1475	226	4	assume	assume	VERB
ejpam-1475	226	5	µ	µ	X
ejpam-1475	226	6	>	>	X
ejpam-1475	226	7	0	0	NUM
ejpam-1475	226	8	.	.	PUNCT
ejpam-1475	227	1	the	the	DET
ejpam-1475	227	2	linearization	linearization	NOUN
ejpam-1475	227	3	of	of	ADP
ejpam-1475	227	4	the	the	DET
ejpam-1475	227	5	system	system	NOUN
ejpam-1475	227	6	(	(	PUNCT
ejpam-1475	227	7	at	at	ADP
ejpam-1475	227	8	e	e	PROPN
ejpam-1475	227	9	µ	µ	X
ejpam-1475	227	10	1	1	NUM
ejpam-1475	227	11	)	)	PUNCT
ejpam-1475	227	12	has	have	AUX
ejpam-1475	227	13	eigenvalues	eigenvalue	VERB
ejpam-1475	227	14	λ1	λ1	ADJ
ejpam-1475	227	15	=	=	SYM
ejpam-1475	227	16	0	0	NUM
ejpam-1475	227	17	,	,	PUNCT
ejpam-1475	227	18	λ2,3	λ2,3	X
ejpam-1475	227	19	=	=	X
ejpam-1475	227	20	±pµ.	±pµ.	NUM
ejpam-1475	227	21	thus	thus	ADV
ejpam-1475	227	22	e	e	X
ejpam-1475	227	23	µ	µ	X
ejpam-1475	227	24	1	1	NUM
ejpam-1475	227	25	is	be	AUX
ejpam-1475	227	26	unstable	unstable	ADJ
ejpam-1475	227	27	.	.	PUNCT
ejpam-1475	228	1	now	now	ADV
ejpam-1475	228	2	,	,	PUNCT
ejpam-1475	228	3	assume	assume	VERB
ejpam-1475	228	4	µ	µ	X
ejpam-1475	228	5	=	=	SYM
ejpam-1475	228	6	0	0	NUM
ejpam-1475	228	7	.	.	PUNCT
ejpam-1475	229	1	then	then	ADV
ejpam-1475	229	2	the	the	DET
ejpam-1475	229	3	linearization	linearization	NOUN
ejpam-1475	229	4	of	of	ADP
ejpam-1475	229	5	the	the	DET
ejpam-1475	229	6	system	system	NOUN
ejpam-1475	229	7	has	have	AUX
ejpam-1475	229	8	eigenvalues	eigenvalue	VERB
ejpam-1475	229	9	λ1,2,3	λ1,2,3	NOUN
ejpam-1475	229	10	=	=	NOUN
ejpam-1475	229	11	0	0	NUM
ejpam-1475	229	12	.	.	PUNCT
ejpam-1475	230	1	thus	thus	ADV
ejpam-1475	230	2	,	,	PUNCT
ejpam-1475	230	3	as	as	SCONJ
ejpam-1475	230	4	the	the	DET
ejpam-1475	230	5	geometric	geometric	ADJ
ejpam-1475	230	6	multiplicity	multiplicity	NOUN
ejpam-1475	230	7	is	be	AUX
ejpam-1475	230	8	strictly	strictly	ADV
ejpam-1475	230	9	less	less	ADJ
ejpam-1475	230	10	than	than	ADP
ejpam-1475	230	11	the	the	DET
ejpam-1475	230	12	algebraic	algebraic	ADJ
ejpam-1475	230	13	multiplicity	multiplicity	NOUN
ejpam-1475	230	14	,	,	PUNCT
ejpam-1475	230	15	e	e	X
ejpam-1475	230	16	µ	µ	X
ejpam-1475	230	17	1	1	NUM
ejpam-1475	230	18	is	be	AUX
ejpam-1475	230	19	unstable	unstable	ADJ
ejpam-1475	230	20	.	.	PUNCT
ejpam-1475	231	1	assume	assume	VERB
ejpam-1475	231	2	µ	µ	X
ejpam-1475	231	3	<	<	X
ejpam-1475	231	4	0	0	X
ejpam-1475	231	5	.	.	PUNCT
ejpam-1475	232	1	let	let	VERB
ejpam-1475	232	2	hχ	hχ	VERB
ejpam-1475	232	3	=	=	NOUN
ejpam-1475	232	4	h	h	NOUN
ejpam-1475	233	1	+	+	NOUN
ejpam-1475	233	2	χ(c	χ(c	NOUN
ejpam-1475	233	3	)	)	PUNCT
ejpam-1475	233	4	be	be	AUX
ejpam-1475	233	5	an	an	DET
ejpam-1475	233	6	energy	energy	NOUN
ejpam-1475	233	7	-	-	PUNCT
ejpam-1475	233	8	casimir	casimir	NOUN
ejpam-1475	233	9	function	function	NOUN
ejpam-1475	233	10	,	,	PUNCT
ejpam-1475	233	11	i.e.	i.e.	X
ejpam-1475	233	12	,	,	PUNCT
ejpam-1475	233	13	hχ(p1	hχ(p1	NOUN
ejpam-1475	233	14	,	,	PUNCT
ejpam-1475	233	15	p2	p2	X
ejpam-1475	233	16	,	,	PUNCT
ejpam-1475	233	17	p3	p3	NOUN
ejpam-1475	233	18	)	)	PUNCT
ejpam-1475	234	1	=	=	SYM
ejpam-1475	234	2	1	1	NUM
ejpam-1475	234	3	2	2	NUM
ejpam-1475	234	4	p2	p2	X
ejpam-1475	234	5	3	3	NUM
ejpam-1475	234	6	+	+	NOUN
ejpam-1475	234	7	p1	p1	PROPN
ejpam-1475	234	8	+	+	PROPN
ejpam-1475	234	9	χ	χ	DET
ejpam-1475	234	10	�	�	PROPN
ejpam-1475	234	11	p2	p2	PROPN
ejpam-1475	234	12	1	1	NUM
ejpam-1475	234	13	+	+	NUM
ejpam-1475	234	14	p2	p2	PROPN
ejpam-1475	234	15	2	2	NUM
ejpam-1475	234	16	�	�	PROPN
ejpam-1475	234	17	,	,	PUNCT
ejpam-1475	234	18	where	where	SCONJ
ejpam-1475	234	19	χ	χ	PRON
ejpam-1475	234	20	∈	∈	PROPN
ejpam-1475	234	21	c∞(r	c∞(r	NOUN
ejpam-1475	234	22	)	)	PUNCT
ejpam-1475	234	23	.	.	PUNCT
ejpam-1475	235	1	the	the	DET
ejpam-1475	235	2	derivative	derivative	ADJ
ejpam-1475	235	3	dhχ	dhχ	NOUN
ejpam-1475	235	4	=	=	SYM
ejpam-1475	235	5	�	�	PROPN
ejpam-1475	235	6	1	1	NUM
ejpam-1475	235	7	+	+	NUM
ejpam-1475	235	8	2p1χ̇	2p1χ̇	NUM
ejpam-1475	235	9	�	�	NOUN
ejpam-1475	235	10	p2	p2	VERB
ejpam-1475	235	11	1	1	NUM
ejpam-1475	235	12	+	+	NUM
ejpam-1475	235	13	p2	p2	PROPN
ejpam-1475	235	14	2	2	NUM
ejpam-1475	235	15	�	�	PROPN
ejpam-1475	235	16	2p2χ̇	2p2χ̇	NUM
ejpam-1475	235	17	�	�	PROPN
ejpam-1475	235	18	p2	p2	PROPN
ejpam-1475	235	19	1	1	NUM
ejpam-1475	235	20	+	+	NUM
ejpam-1475	235	21	p2	p2	PROPN
ejpam-1475	235	22	2	2	NUM
ejpam-1475	235	23	�	�	PROPN
ejpam-1475	235	24	p3	p3	PROPN
ejpam-1475	235	25	�	�	PROPN
ejpam-1475	235	26	vanishes	vanish	VERB
ejpam-1475	235	27	at	at	ADP
ejpam-1475	235	28	e	e	PROPN
ejpam-1475	235	29	µ	µ	X
ejpam-1475	235	30	1	1	NUM
ejpam-1475	235	31	if	if	SCONJ
ejpam-1475	235	32	and	and	CCONJ
ejpam-1475	235	33	only	only	ADV
ejpam-1475	235	34	if	if	SCONJ
ejpam-1475	235	35	χ̇	χ̇	PROPN
ejpam-1475	235	36	�	�	PROPN
ejpam-1475	235	37	µ2	µ2	PROPN
ejpam-1475	235	38	�	�	PROPN
ejpam-1475	235	39	=	=	SYM
ejpam-1475	235	40	−	−	PROPN
ejpam-1475	235	41	1	1	NUM
ejpam-1475	235	42	2µ	2µ	NUM
ejpam-1475	235	43	·	·	PUNCT
ejpam-1475	235	44	then	then	ADV
ejpam-1475	235	45	,	,	PUNCT
ejpam-1475	235	46	the	the	DET
ejpam-1475	235	47	hessian	hessian	NOUN
ejpam-1475	235	48	(	(	PUNCT
ejpam-1475	235	49	at	at	ADP
ejpam-1475	235	50	e	e	PROPN
ejpam-1475	235	51	µ	µ	X
ejpam-1475	235	52	1	1	NUM
ejpam-1475	235	53	)	)	PUNCT
ejpam-1475	235	54	d2hχ(µ	d2hχ(µ	PROPN
ejpam-1475	235	55	,	,	PUNCT
ejpam-1475	235	56	0,0	0,0	NUM
ejpam-1475	235	57	)	)	PUNCT
ejpam-1475	236	1	=	=	SYM
ejpam-1475	236	2	diag	diag	PROPN
ejpam-1475	236	3	�	�	PROPN
ejpam-1475	236	4	4µ2χ̈	4µ2χ̈	PROPN
ejpam-1475	236	5	�	�	PROPN
ejpam-1475	236	6	µ2	µ2	PROPN
ejpam-1475	236	7	�	�	PROPN
ejpam-1475	236	8	−	−	PROPN
ejpam-1475	236	9	1	1	NUM
ejpam-1475	236	10	µ	µ	NOUN
ejpam-1475	236	11	,	,	PUNCT
ejpam-1475	236	12	−	−	PROPN
ejpam-1475	236	13	1	1	NUM
ejpam-1475	236	14	µ	µ	NOUN
ejpam-1475	236	15	,	,	PUNCT
ejpam-1475	236	16	1	1	NUM
ejpam-1475	236	17	�	�	PROPN
ejpam-1475	236	18	is	be	AUX
ejpam-1475	236	19	positive	positive	ADJ
ejpam-1475	236	20	definite	definite	ADJ
ejpam-1475	236	21	if	if	SCONJ
ejpam-1475	237	1	and	and	CCONJ
ejpam-1475	237	2	only	only	ADV
ejpam-1475	237	3	if	if	SCONJ
ejpam-1475	237	4	χ̈	χ̈	PROPN
ejpam-1475	237	5	�	�	PROPN
ejpam-1475	237	6	µ2	µ2	PROPN
ejpam-1475	237	7	�	�	PROPN
ejpam-1475	237	8	>	>	X
ejpam-1475	237	9	1	1	NUM
ejpam-1475	237	10	4µ3	4µ3	NUM
ejpam-1475	237	11	·	·	PUNCT
ejpam-1475	237	12	the	the	DET
ejpam-1475	237	13	function	function	NOUN
ejpam-1475	237	14	χ(x	χ(x	PROPN
ejpam-1475	237	15	)	)	PUNCT
ejpam-1475	238	1	=	=	PUNCT
ejpam-1475	239	1	−	−	PROPN
ejpam-1475	239	2	1	1	NUM
ejpam-1475	239	3	4µ3	4µ3	NUM
ejpam-1475	239	4	x2	x2	PROPN
ejpam-1475	239	5	satisfies	satisfy	VERB
ejpam-1475	239	6	these	these	DET
ejpam-1475	239	7	requirements	requirement	NOUN
ejpam-1475	239	8	.	.	PUNCT
ejpam-1475	240	1	hence	hence	ADV
ejpam-1475	240	2	,	,	PUNCT
ejpam-1475	240	3	by	by	ADP
ejpam-1475	240	4	the	the	DET
ejpam-1475	240	5	standard	standard	ADJ
ejpam-1475	240	6	energy	energy	NOUN
ejpam-1475	240	7	-	-	PUNCT
ejpam-1475	240	8	casimir	casimir	NOUN
ejpam-1475	240	9	method	method	NOUN
ejpam-1475	240	10	,	,	PUNCT
ejpam-1475	240	11	e	e	X
ejpam-1475	240	12	µ	µ	X
ejpam-1475	240	13	1	1	NUM
ejpam-1475	240	14	is	be	AUX
ejpam-1475	240	15	stable	stable	ADJ
ejpam-1475	240	16	.	.	PUNCT
ejpam-1475	241	1	(	(	PUNCT
ejpam-1475	241	2	ii	ii	NOUN
ejpam-1475	241	3	)	)	PUNCT
ejpam-1475	241	4	let	let	VERB
ejpam-1475	241	5	hλ	hλ	ADP
ejpam-1475	241	6	=	=	PUNCT
ejpam-1475	241	7	λ0h	λ0h	PROPN
ejpam-1475	242	1	+	+	ADP
ejpam-1475	242	2	λ1c	λ1c	X
ejpam-1475	242	3	,	,	PUNCT
ejpam-1475	242	4	where	where	SCONJ
ejpam-1475	242	5	λ0	λ0	NOUN
ejpam-1475	242	6	=	=	SYM
ejpam-1475	242	7	0	0	NUM
ejpam-1475	242	8	,	,	PUNCT
ejpam-1475	242	9	λ1	λ1	NOUN
ejpam-1475	242	10	=	=	SYM
ejpam-1475	242	11	1	1	X
ejpam-1475	242	12	.	.	PUNCT
ejpam-1475	243	1	then	then	ADV
ejpam-1475	243	2	we	we	PRON
ejpam-1475	243	3	get	get	VERB
ejpam-1475	243	4	dhλ(0,0,ν	dhλ(0,0,ν	PROPN
ejpam-1475	243	5	)	)	PUNCT
ejpam-1475	243	6	=	=	SYM
ejpam-1475	243	7	�	�	PROPN
ejpam-1475	243	8	2p1	2p1	NUM
ejpam-1475	243	9	2p2	2p2	NUM
ejpam-1475	243	10	0	0	NUM
ejpam-1475	243	11	�	�	PROPN
ejpam-1475	243	12	|(0,0,ν	|(0,0,ν	NUM
ejpam-1475	243	13	)	)	PUNCT
ejpam-1475	243	14	=	=	SYM
ejpam-1475	243	15	0	0	NUM
ejpam-1475	243	16	and	and	CCONJ
ejpam-1475	243	17	d2hλ(0,0,ν	d2hλ(0,0,ν	ADJ
ejpam-1475	243	18	)	)	PUNCT
ejpam-1475	244	1	=	=	NOUN
ejpam-1475	244	2	diag	diag	NOUN
ejpam-1475	244	3	(	(	PUNCT
ejpam-1475	244	4	2	2	NUM
ejpam-1475	244	5	,	,	PUNCT
ejpam-1475	244	6	2	2	NUM
ejpam-1475	244	7	,	,	PUNCT
ejpam-1475	244	8	0	0	NUM
ejpam-1475	244	9	)	)	PUNCT
ejpam-1475	244	10	.	.	PUNCT
ejpam-1475	245	1	also	also	ADV
ejpam-1475	245	2	,	,	PUNCT
ejpam-1475	245	3	ker	ker	NOUN
ejpam-1475	245	4	dh(eν2)∩	dh(eν2)∩	PROPN
ejpam-1475	245	5	ker	ker	NOUN
ejpam-1475	245	6	dc(eν2	dc(eν2	PUNCT
ejpam-1475	245	7	)	)	PUNCT
ejpam-1475	245	8	=	=	PRON
ejpam-1475	245	9	span	span	NOUN
ejpam-1475	245	10	{	{	PUNCT
ejpam-1475	245	11	(	(	PUNCT
ejpam-1475	245	12	−ν	−ν	ADJ
ejpam-1475	245	13	,	,	PUNCT
ejpam-1475	245	14	0,1	0,1	NUM
ejpam-1475	245	15	)	)	PUNCT
ejpam-1475	245	16	,	,	PUNCT
ejpam-1475	245	17	(	(	PUNCT
ejpam-1475	245	18	0,1,0	0,1,0	NUM
ejpam-1475	245	19	)	)	PUNCT
ejpam-1475	245	20	}	}	PUNCT
ejpam-1475	245	21	and	and	CCONJ
ejpam-1475	245	22	so	so	ADV
ejpam-1475	245	23	d2hλ(0,0,ν	d2hλ(0,0,ν	PROPN
ejpam-1475	245	24	)	)	PUNCT
ejpam-1475	245	25	�	�	PROPN
ejpam-1475	245	26	�	�	PROPN
ejpam-1475	245	27	w×w	w×w	PROPN
ejpam-1475	245	28	=	=	PROPN
ejpam-1475	245	29	diag	diag	PROPN
ejpam-1475	245	30	�	�	PROPN
ejpam-1475	245	31	2ν2	2ν2	PROPN
ejpam-1475	245	32	,	,	PUNCT
ejpam-1475	245	33	2	2	NUM
ejpam-1475	245	34	�	�	NOUN
ejpam-1475	245	35	is	be	AUX
ejpam-1475	245	36	positive	positive	ADJ
ejpam-1475	245	37	definite	definite	ADJ
ejpam-1475	245	38	.	.	PUNCT
ejpam-1475	246	1	hence	hence	ADV
ejpam-1475	246	2	,	,	PUNCT
ejpam-1475	246	3	by	by	ADP
ejpam-1475	246	4	the	the	DET
ejpam-1475	246	5	extended	extend	VERB
ejpam-1475	246	6	energy	energy	NOUN
ejpam-1475	246	7	-	-	PUNCT
ejpam-1475	246	8	casimir	casimir	NOUN
ejpam-1475	246	9	method	method	NOUN
ejpam-1475	246	10	,	,	PUNCT
ejpam-1475	246	11	eν2	eν2	PROPN
ejpam-1475	246	12	is	be	AUX
ejpam-1475	246	13	stable	stable	ADJ
ejpam-1475	246	14	.	.	PUNCT
ejpam-1475	247	1	the	the	DET
ejpam-1475	247	2	equilibrium	equilibrium	NOUN
ejpam-1475	247	3	states	state	NOUN
ejpam-1475	247	4	for	for	ADP
ejpam-1475	247	5	(	(	PUNCT
ejpam-1475	247	6	12	12	NUM
ejpam-1475	247	7	)	)	PUNCT
ejpam-1475	247	8	are	be	AUX
ejpam-1475	247	9	e	e	PROPN
ejpam-1475	247	10	µ	µ	X
ejpam-1475	247	11	3	3	NUM
ejpam-1475	247	12	=	=	SYM
ejpam-1475	247	13	(	(	PUNCT
ejpam-1475	247	14	0,0,µ	0,0,µ	NOUN
ejpam-1475	247	15	)	)	PUNCT
ejpam-1475	247	16	,	,	PUNCT
ejpam-1475	247	17	µ	µ	PROPN
ejpam-1475	247	18	∈	∈	PROPN
ejpam-1475	247	19	r.	r.	PROPN
ejpam-1475	247	20	again	again	ADV
ejpam-1475	247	21	,	,	PUNCT
ejpam-1475	247	22	using	use	VERB
ejpam-1475	247	23	the	the	DET
ejpam-1475	247	24	extended	extended	ADJ
ejpam-1475	247	25	energy	energy	NOUN
ejpam-1475	247	26	-	-	PUNCT
ejpam-1475	247	27	casimir	casimir	NOUN
ejpam-1475	247	28	method	method	NOUN
ejpam-1475	247	29	(	(	PUNCT
ejpam-1475	247	30	as	as	ADP
ejpam-1475	247	31	in	in	ADP
ejpam-1475	247	32	theorem	theorem	NOUN
ejpam-1475	247	33	7	7	NUM
ejpam-1475	247	34	)	)	PUNCT
ejpam-1475	247	35	,	,	PUNCT
ejpam-1475	247	36	we	we	PRON
ejpam-1475	247	37	obtain	obtain	VERB
ejpam-1475	247	38	the	the	DET
ejpam-1475	247	39	following	follow	VERB
ejpam-1475	247	40	result	result	NOUN
ejpam-1475	247	41	.	.	PUNCT
ejpam-1475	248	1	theorem	theorem	ADJ
ejpam-1475	248	2	8	8	NUM
ejpam-1475	248	3	.	.	PUNCT
ejpam-1475	249	1	each	each	DET
ejpam-1475	249	2	equilibrium	equilibrium	NOUN
ejpam-1475	249	3	state	state	NOUN
ejpam-1475	249	4	e	e	PROPN
ejpam-1475	249	5	µ	µ	X
ejpam-1475	249	6	3	3	NUM
ejpam-1475	249	7	is	be	AUX
ejpam-1475	249	8	stable	stable	ADJ
ejpam-1475	249	9	.	.	PUNCT
ejpam-1475	250	1	r.	r.	PROPN
ejpam-1475	250	2	adams	adams	PROPN
ejpam-1475	250	3	,	,	PUNCT
ejpam-1475	250	4	r.	r.	PROPN
ejpam-1475	250	5	biggs	biggs	PROPN
ejpam-1475	250	6	,	,	PUNCT
ejpam-1475	250	7	c.	c.	PROPN
ejpam-1475	250	8	remsing	remsing	NOUN
ejpam-1475	250	9	/	/	SYM
ejpam-1475	250	10	eur	eur	NOUN
ejpam-1475	250	11	.	.	PUNCT
ejpam-1475	251	1	j.	j.	PROPN
ejpam-1475	251	2	pure	pure	PROPN
ejpam-1475	251	3	appl	appl	PROPN
ejpam-1475	251	4	.	.	PROPN
ejpam-1475	251	5	math	math	PROPN
ejpam-1475	251	6	,	,	PUNCT
ejpam-1475	251	7	5	5	NUM
ejpam-1475	251	8	(	(	PUNCT
ejpam-1475	251	9	2012	2012	NUM
ejpam-1475	251	10	)	)	PUNCT
ejpam-1475	251	11	,	,	PUNCT
ejpam-1475	251	12	1	1	NUM
ejpam-1475	251	13	-	-	SYM
ejpam-1475	251	14	15	15	NUM
ejpam-1475	251	15	10	10	NUM
ejpam-1475	251	16	6	6	NUM
ejpam-1475	251	17	.	.	PUNCT
ejpam-1475	252	1	explicit	explicit	ADJ
ejpam-1475	252	2	integration	integration	NOUN
ejpam-1475	252	3	first	first	ADV
ejpam-1475	252	4	,	,	PUNCT
ejpam-1475	252	5	let	let	VERB
ejpam-1475	252	6	us	we	PRON
ejpam-1475	252	7	consider	consider	VERB
ejpam-1475	252	8	the	the	DET
ejpam-1475	252	9	invariant	invariant	ADJ
ejpam-1475	252	10	control	control	NOUN
ejpam-1475	252	11	problem	problem	NOUN
ejpam-1475	252	12	licp(1	licp(1	NOUN
ejpam-1475	252	13	)	)	PUNCT
ejpam-1475	252	14	.	.	PUNCT
ejpam-1475	253	1	there	there	PRON
ejpam-1475	253	2	are	be	VERB
ejpam-1475	253	3	three	three	NUM
ejpam-1475	253	4	typical	typical	ADJ
ejpam-1475	253	5	cases	case	NOUN
ejpam-1475	253	6	for	for	ADP
ejpam-1475	253	7	the	the	DET
ejpam-1475	253	8	reduced	reduce	VERB
ejpam-1475	253	9	extremal	extremal	ADJ
ejpam-1475	253	10	equations	equation	NOUN
ejpam-1475	253	11	(	(	PUNCT
ejpam-1475	253	12	11	11	NUM
ejpam-1475	253	13	)	)	PUNCT
ejpam-1475	253	14	,	,	PUNCT
ejpam-1475	253	15	corresponding	correspond	VERB
ejpam-1475	253	16	to	to	ADP
ejpam-1475	253	17	h	h	PROPN
ejpam-1475	253	18	>	>	X
ejpam-1475	253	19	p	p	PROPN
ejpam-1475	253	20	c	c	NOUN
ejpam-1475	253	21	,	,	PUNCT
ejpam-1475	253	22	h	h	NOUN
ejpam-1475	254	1	=	=	NOUN
ejpam-1475	254	2	p	p	PROPN
ejpam-1475	254	3	c	c	PROPN
ejpam-1475	254	4	and	and	CCONJ
ejpam-1475	254	5	−pc	−pc	NUM
ejpam-1475	254	6	<	<	X
ejpam-1475	254	7	h	h	NOUN
ejpam-1475	254	8	<	<	X
ejpam-1475	254	9	p	p	X
ejpam-1475	254	10	c	c	PROPN
ejpam-1475	254	11	.	.	PUNCT
ejpam-1475	255	1	(	(	PUNCT
ejpam-1475	255	2	note	note	VERB
ejpam-1475	255	3	that	that	SCONJ
ejpam-1475	255	4	h	h	NOUN
ejpam-1475	256	1	=	=	SYM
ejpam-1475	256	2	−pc	−pc	PROPN
ejpam-1475	256	3	and	and	CCONJ
ejpam-1475	256	4	c	c	NOUN
ejpam-1475	256	5	=	=	SYM
ejpam-1475	256	6	0	0	PROPN
ejpam-1475	256	7	correspond	correspond	VERB
ejpam-1475	256	8	to	to	ADP
ejpam-1475	256	9	constant	constant	ADJ
ejpam-1475	256	10	solutions	solution	NOUN
ejpam-1475	256	11	,	,	PUNCT
ejpam-1475	256	12	whereas	whereas	SCONJ
ejpam-1475	256	13	the	the	DET
ejpam-1475	256	14	situation	situation	NOUN
ejpam-1475	256	15	h	h	NOUN
ejpam-1475	256	16	<	<	X
ejpam-1475	257	1	p	p	X
ejpam-1475	257	2	c	c	NOUN
ejpam-1475	257	3	is	be	AUX
ejpam-1475	257	4	impossible	impossible	ADJ
ejpam-1475	257	5	.	.	PUNCT
ejpam-1475	257	6	)	)	PUNCT
ejpam-1475	258	1	in	in	ADP
ejpam-1475	258	2	figure	figure	NOUN
ejpam-1475	258	3	1	1	NUM
ejpam-1475	258	4	,	,	PUNCT
ejpam-1475	258	5	we	we	PRON
ejpam-1475	258	6	graph	graph	VERB
ejpam-1475	258	7	the	the	DET
ejpam-1475	258	8	level	level	NOUN
ejpam-1475	258	9	sets	set	NOUN
ejpam-1475	258	10	of	of	ADP
ejpam-1475	258	11	h	h	NOUN
ejpam-1475	258	12	and	and	CCONJ
ejpam-1475	258	13	c	c	PROPN
ejpam-1475	258	14	and	and	CCONJ
ejpam-1475	258	15	their	their	PRON
ejpam-1475	258	16	intersection	intersection	NOUN
ejpam-1475	258	17	.	.	PUNCT
ejpam-1475	259	1	we	we	PRON
ejpam-1475	259	2	also	also	ADV
ejpam-1475	259	3	graph	graph	VERB
ejpam-1475	259	4	the	the	DET
ejpam-1475	259	5	stable	stable	ADJ
ejpam-1475	259	6	equilibrium	equilibrium	NOUN
ejpam-1475	259	7	points	point	NOUN
ejpam-1475	259	8	(	(	PUNCT
ejpam-1475	259	9	illustrated	illustrate	VERB
ejpam-1475	259	10	in	in	ADP
ejpam-1475	259	11	blue	blue	ADJ
ejpam-1475	259	12	)	)	PUNCT
ejpam-1475	259	13	and	and	CCONJ
ejpam-1475	259	14	unstable	unstable	ADJ
ejpam-1475	259	15	equilibrium	equilibrium	NOUN
ejpam-1475	259	16	points	point	NOUN
ejpam-1475	259	17	(	(	PUNCT
ejpam-1475	259	18	illustrated	illustrate	VERB
ejpam-1475	259	19	in	in	ADP
ejpam-1475	259	20	red	red	PROPN
ejpam-1475	259	21	)	)	PUNCT
ejpam-1475	259	22	,	,	PUNCT
ejpam-1475	259	23	as	as	SCONJ
ejpam-1475	259	24	presented	present	VERB
ejpam-1475	259	25	in	in	ADP
ejpam-1475	259	26	theorem	theorem	NOUN
ejpam-1475	259	27	7	7	NUM
ejpam-1475	259	28	.	.	PUNCT
ejpam-1475	260	1	the	the	DET
ejpam-1475	260	2	reduced	reduce	VERB
ejpam-1475	260	3	hamilton	hamilton	PROPN
ejpam-1475	260	4	-2	-2	INTJ
ejpam-1475	260	5	0	0	NUM
ejpam-1475	260	6	2	2	NUM
ejpam-1475	260	7	e1	e1	NOUN
ejpam-1475	260	8	*	*	PUNCT
ejpam-1475	260	9	-2	-2	NOUN
ejpam-1475	260	10	0	0	NUM
ejpam-1475	260	11	2	2	NUM
ejpam-1475	260	12	e2	e2	NOUN
ejpam-1475	260	13	*	*	PUNCT
ejpam-1475	260	14	-2	-2	NOUN
ejpam-1475	260	15	0	0	NUM
ejpam-1475	260	16	2	2	NUM
ejpam-1475	260	17	e3	e3	VERB
ejpam-1475	260	18	*	*	PUNCT
ejpam-1475	260	19	-2	-2	NOUN
ejpam-1475	260	20	0	0	NUM
ejpam-1475	260	21	2	2	NUM
ejpam-1475	260	22	e1	e1	NOUN
ejpam-1475	260	23	*	*	PUNCT
ejpam-1475	260	24	-2	-2	NOUN
ejpam-1475	260	25	0	0	NUM
ejpam-1475	260	26	2	2	NUM
ejpam-1475	260	27	e2	e2	NOUN
ejpam-1475	260	28	*	*	PUNCT
ejpam-1475	260	29	-2	-2	NOUN
ejpam-1475	260	30	0	0	NUM
ejpam-1475	260	31	2	2	NUM
ejpam-1475	260	32	e3	e3	VERB
ejpam-1475	260	33	*	*	PUNCT
ejpam-1475	260	34	(	(	PUNCT
ejpam-1475	260	35	a	a	X
ejpam-1475	260	36	)	)	PUNCT
ejpam-1475	260	37	h	h	NOUN
ejpam-1475	260	38	>	>	X
ejpam-1475	260	39	p	p	X
ejpam-1475	261	1	c	c	X
ejpam-1475	261	2	-2	-2	NOUN
ejpam-1475	261	3	0	0	NUM
ejpam-1475	261	4	2	2	NUM
ejpam-1475	261	5	e1	e1	NOUN
ejpam-1475	261	6	*	*	PUNCT
ejpam-1475	262	1	-2	-2	NOUN
ejpam-1475	262	2	0	0	NUM
ejpam-1475	262	3	2	2	NUM
ejpam-1475	262	4	e2	e2	NOUN
ejpam-1475	262	5	*	*	PUNCT
ejpam-1475	263	1	-2	-2	NOUN
ejpam-1475	263	2	0	0	NUM
ejpam-1475	263	3	2	2	NUM
ejpam-1475	263	4	e3	e3	VERB
ejpam-1475	263	5	*	*	PUNCT
ejpam-1475	264	1	-2	-2	NOUN
ejpam-1475	264	2	0	0	NUM
ejpam-1475	264	3	2	2	NUM
ejpam-1475	264	4	e1	e1	NOUN
ejpam-1475	264	5	*	*	PUNCT
ejpam-1475	264	6	-2	-2	NOUN
ejpam-1475	264	7	0	0	NUM
ejpam-1475	264	8	2	2	NUM
ejpam-1475	264	9	e2	e2	NOUN
ejpam-1475	264	10	*	*	PUNCT
ejpam-1475	265	1	-2	-2	NOUN
ejpam-1475	265	2	0	0	NUM
ejpam-1475	265	3	2	2	NUM
ejpam-1475	265	4	e3	e3	NOUN
ejpam-1475	265	5	*	*	PUNCT
ejpam-1475	265	6	(	(	PUNCT
ejpam-1475	265	7	b	b	NOUN
ejpam-1475	265	8	)	)	PUNCT
ejpam-1475	265	9	h	h	NOUN
ejpam-1475	266	1	=	=	NOUN
ejpam-1475	267	1	p	p	X
ejpam-1475	267	2	c	c	X
ejpam-1475	267	3	-2	-2	NOUN
ejpam-1475	267	4	0	0	NUM
ejpam-1475	267	5	2	2	NUM
ejpam-1475	267	6	e1	e1	NOUN
ejpam-1475	267	7	*	*	PUNCT
ejpam-1475	268	1	-2	-2	NOUN
ejpam-1475	268	2	0	0	NUM
ejpam-1475	268	3	2	2	NUM
ejpam-1475	268	4	e2	e2	NOUN
ejpam-1475	268	5	*	*	PUNCT
ejpam-1475	269	1	-2	-2	NOUN
ejpam-1475	269	2	0	0	NUM
ejpam-1475	269	3	2	2	NUM
ejpam-1475	269	4	e3	e3	VERB
ejpam-1475	269	5	*	*	PUNCT
ejpam-1475	270	1	-2	-2	NOUN
ejpam-1475	270	2	0	0	NUM
ejpam-1475	270	3	2	2	NUM
ejpam-1475	270	4	e1	e1	NOUN
ejpam-1475	270	5	*	*	PUNCT
ejpam-1475	270	6	-2	-2	NOUN
ejpam-1475	270	7	0	0	NUM
ejpam-1475	270	8	2	2	NUM
ejpam-1475	270	9	e2	e2	NOUN
ejpam-1475	270	10	*	*	PUNCT
ejpam-1475	271	1	-2	-2	NOUN
ejpam-1475	271	2	0	0	NUM
ejpam-1475	271	3	2	2	NUM
ejpam-1475	271	4	e3	e3	NOUN
ejpam-1475	271	5	*	*	PUNCT
ejpam-1475	271	6	(	(	PUNCT
ejpam-1475	271	7	c	c	X
ejpam-1475	271	8	)	)	PUNCT
ejpam-1475	271	9	−pc	−pc	PROPN
ejpam-1475	271	10	<	<	X
ejpam-1475	271	11	h	h	NOUN
ejpam-1475	271	12	<	<	X
ejpam-1475	271	13	p	p	X
ejpam-1475	271	14	c	c	PROPN
ejpam-1475	271	15	figure	figure	NOUN
ejpam-1475	271	16	1	1	NUM
ejpam-1475	271	17	:	:	PUNCT
ejpam-1475	271	18	typical	typical	ADJ
ejpam-1475	271	19	cases	case	NOUN
ejpam-1475	271	20	of	of	ADP
ejpam-1475	271	21	reduced	reduce	VERB
ejpam-1475	271	22	extremals	extremal	NOUN
ejpam-1475	271	23	of	of	ADP
ejpam-1475	271	24	licp(1	licp(1	NOUN
ejpam-1475	271	25	)	)	PUNCT
ejpam-1475	271	26	.	.	PUNCT
ejpam-1475	272	1	equations	equation	NOUN
ejpam-1475	272	2	(	(	PUNCT
ejpam-1475	272	3	11	11	NUM
ejpam-1475	272	4	)	)	PUNCT
ejpam-1475	272	5	can	can	AUX
ejpam-1475	272	6	be	be	AUX
ejpam-1475	272	7	integrated	integrate	VERB
ejpam-1475	272	8	by	by	ADP
ejpam-1475	272	9	jacobi	jacobi	PROPN
ejpam-1475	272	10	elliptic	elliptic	ADJ
ejpam-1475	272	11	functions	function	NOUN
ejpam-1475	272	12	.	.	PUNCT
ejpam-1475	273	1	in	in	ADP
ejpam-1475	273	2	each	each	PRON
ejpam-1475	273	3	of	of	ADP
ejpam-1475	273	4	the	the	DET
ejpam-1475	273	5	typical	typical	ADJ
ejpam-1475	273	6	cases	case	NOUN
ejpam-1475	273	7	,	,	PUNCT
ejpam-1475	273	8	we	we	PRON
ejpam-1475	273	9	obtain	obtain	VERB
ejpam-1475	273	10	explicit	explicit	ADJ
ejpam-1475	273	11	expressions	expression	NOUN
ejpam-1475	273	12	for	for	ADP
ejpam-1475	273	13	the	the	DET
ejpam-1475	273	14	integral	integral	ADJ
ejpam-1475	273	15	curves	curve	NOUN
ejpam-1475	273	16	of	of	ADP
ejpam-1475	273	17	~h	~h	PROPN
ejpam-1475	273	18	.	.	PUNCT
ejpam-1475	274	1	we	we	PRON
ejpam-1475	274	2	start	start	VERB
ejpam-1475	274	3	by	by	ADP
ejpam-1475	274	4	considering	consider	VERB
ejpam-1475	274	5	the	the	DET
ejpam-1475	274	6	case	case	NOUN
ejpam-1475	274	7	h	h	NOUN
ejpam-1475	274	8	>	>	X
ejpam-1475	274	9	p	p	PROPN
ejpam-1475	274	10	c	c	PROPN
ejpam-1475	274	11	.	.	PUNCT
ejpam-1475	275	1	theorem	theorem	NOUN
ejpam-1475	275	2	9	9	NUM
ejpam-1475	275	3	.	.	PUNCT
ejpam-1475	276	1	suppose	suppose	VERB
ejpam-1475	276	2	p	p	X
ejpam-1475	276	3	(	(	PUNCT
ejpam-1475	276	4	·	·	PUNCT
ejpam-1475	276	5	)	)	PUNCT
ejpam-1475	276	6	:	:	PUNCT
ejpam-1475	276	7	(	(	PUNCT
ejpam-1475	276	8	−ǫ	−ǫ	NOUN
ejpam-1475	276	9	,	,	PUNCT
ejpam-1475	276	10	ǫ)→	ǫ)→	NOUN
ejpam-1475	276	11	se(2)∗	se(2)∗	NOUN
ejpam-1475	276	12	is	be	AUX
ejpam-1475	276	13	an	an	DET
ejpam-1475	276	14	integral	integral	ADJ
ejpam-1475	276	15	curve	curve	NOUN
ejpam-1475	276	16	of	of	ADP
ejpam-1475	276	17	~h	~h	PROPN
ejpam-1475	276	18	such	such	ADJ
ejpam-1475	276	19	that	that	DET
ejpam-1475	276	20	h(p(0	h(p(0	NOUN
ejpam-1475	276	21	)	)	PUNCT
ejpam-1475	276	22	)	)	PUNCT
ejpam-1475	277	1	=	=	SYM
ejpam-1475	277	2	h0	h0	PROPN
ejpam-1475	277	3	,	,	PUNCT
ejpam-1475	277	4	c(p(0	c(p(0	NOUN
ejpam-1475	277	5	)	)	PUNCT
ejpam-1475	277	6	)	)	PUNCT
ejpam-1475	278	1	=	=	SYM
ejpam-1475	278	2	c0	c0	X
ejpam-1475	278	3	>	>	X
ejpam-1475	278	4	0	0	PUNCT
ejpam-1475	278	5	and	and	CCONJ
ejpam-1475	278	6	h2	h2	PROPN
ejpam-1475	278	7	0	0	NUM
ejpam-1475	279	1	−	−	PROPN
ejpam-1475	279	2	c0	c0	PROPN
ejpam-1475	279	3	>	>	X
ejpam-1475	279	4	0	0	X
ejpam-1475	279	5	.	.	PUNCT
ejpam-1475	280	1	then	then	ADV
ejpam-1475	280	2	there	there	PRON
ejpam-1475	280	3	exists	exist	VERB
ejpam-1475	280	4	t0	t0	PROPN
ejpam-1475	280	5	∈	∈	PROPN
ejpam-1475	280	6	r	r	NOUN
ejpam-1475	280	7	and	and	CCONJ
ejpam-1475	280	8	σ	σ	NOUN
ejpam-1475	280	9	∈	∈	PROPN
ejpam-1475	280	10	{	{	PUNCT
ejpam-1475	280	11	−1,1	−1,1	NOUN
ejpam-1475	280	12	}	}	PUNCT
ejpam-1475	280	13	such	such	ADJ
ejpam-1475	280	14	that	that	SCONJ
ejpam-1475	280	15	r.	r.	PROPN
ejpam-1475	280	16	adams	adams	PROPN
ejpam-1475	280	17	,	,	PUNCT
ejpam-1475	280	18	r.	r.	PROPN
ejpam-1475	280	19	biggs	biggs	PROPN
ejpam-1475	280	20	,	,	PUNCT
ejpam-1475	280	21	c.	c.	PROPN
ejpam-1475	280	22	remsing	remsing	NOUN
ejpam-1475	280	23	/	/	SYM
ejpam-1475	280	24	eur	eur	NOUN
ejpam-1475	280	25	.	.	PUNCT
ejpam-1475	281	1	j.	j.	PROPN
ejpam-1475	281	2	pure	pure	PROPN
ejpam-1475	281	3	appl	appl	PROPN
ejpam-1475	281	4	.	.	PROPN
ejpam-1475	281	5	math	math	PROPN
ejpam-1475	281	6	,	,	PUNCT
ejpam-1475	281	7	5	5	NUM
ejpam-1475	281	8	(	(	PUNCT
ejpam-1475	281	9	2012	2012	NUM
ejpam-1475	281	10	)	)	PUNCT
ejpam-1475	281	11	,	,	PUNCT
ejpam-1475	281	12	1	1	NUM
ejpam-1475	281	13	-	-	SYM
ejpam-1475	281	14	15	15	NUM
ejpam-1475	281	15	11	11	NUM
ejpam-1475	281	16	p(t	p(t	NOUN
ejpam-1475	281	17	)	)	PUNCT
ejpam-1475	281	18	=	=	SYM
ejpam-1475	282	1	p̄(t	p̄(t	PROPN
ejpam-1475	282	2	+	+	CCONJ
ejpam-1475	282	3	t0	t0	NOUN
ejpam-1475	282	4	)	)	PUNCT
ejpam-1475	282	5	for	for	ADP
ejpam-1475	282	6	t	t	PROPN
ejpam-1475	282	7	∈	∈	PROPN
ejpam-1475	282	8	(	(	PUNCT
ejpam-1475	282	9	−ǫ	−ǫ	NOUN
ejpam-1475	282	10	,	,	PUNCT
ejpam-1475	282	11	ǫ	ǫ	NOUN
ejpam-1475	282	12	)	)	PUNCT
ejpam-1475	282	13	,	,	PUNCT
ejpam-1475	282	14	where	where	SCONJ
ejpam-1475	282	15			PROPN
ejpam-1475	282	16			PROPN
ejpam-1475	282	17			PROPN
ejpam-1475	282	18			PROPN
ejpam-1475	282	19			PROPN
ejpam-1475	282	20			PROPN
ejpam-1475	282	21			NOUN
ejpam-1475	282	22			PROPN
ejpam-1475	282	23			PROPN
ejpam-1475	282	24			PROPN
ejpam-1475	282	25			PROPN
ejpam-1475	282	26			PROPN
ejpam-1475	282	27			NOUN
ejpam-1475	282	28	p̄1(t	p̄1(t	NUM
ejpam-1475	282	29	)	)	PUNCT
ejpam-1475	282	30	=	=	SYM
ejpam-1475	283	1	p	p	PROPN
ejpam-1475	283	2	c0	c0	PROPN
ejpam-1475	283	3	k−	k−	PROPN
ejpam-1475	283	4	sn	sn	PROPN
ejpam-1475	283	5	(	(	PUNCT
ejpam-1475	283	6	ωt	ωt	PROPN
ejpam-1475	283	7	,	,	PUNCT
ejpam-1475	283	8	k	k	NOUN
ejpam-1475	283	9	)	)	PUNCT
ejpam-1475	283	10	1−	1−	NUM
ejpam-1475	284	1	k	k	PROPN
ejpam-1475	284	2	sn	sn	PROPN
ejpam-1475	284	3	(	(	PUNCT
ejpam-1475	284	4	ωt	ωt	PROPN
ejpam-1475	284	5	,	,	PUNCT
ejpam-1475	284	6	k	k	NOUN
ejpam-1475	284	7	)	)	PUNCT
ejpam-1475	284	8	p̄2(t	p̄2(t	NOUN
ejpam-1475	284	9	)	)	PUNCT
ejpam-1475	284	10	=	=	SYM
ejpam-1475	285	1	σ	σ	PROPN
ejpam-1475	285	2	p	p	PROPN
ejpam-1475	285	3	c0	c0	PROPN
ejpam-1475	285	4	k′cn	k′cn	PROPN
ejpam-1475	285	5	(	(	PUNCT
ejpam-1475	285	6	ωt	ωt	PROPN
ejpam-1475	285	7	,	,	PUNCT
ejpam-1475	285	8	k	k	NOUN
ejpam-1475	285	9	)	)	PUNCT
ejpam-1475	285	10	1−	1−	NUM
ejpam-1475	286	1	k	k	PROPN
ejpam-1475	286	2	sn	sn	PROPN
ejpam-1475	286	3	(	(	PUNCT
ejpam-1475	286	4	ωt	ωt	PROPN
ejpam-1475	286	5	,	,	PUNCT
ejpam-1475	286	6	k	k	NOUN
ejpam-1475	286	7	)	)	PUNCT
ejpam-1475	286	8	p̄3(t	p̄3(t	NUM
ejpam-1475	286	9	)	)	PUNCT
ejpam-1475	286	10	=	=	SYM
ejpam-1475	287	1	−σ	−σ	NOUN
ejpam-1475	288	1	p	p	NOUN
ejpam-1475	288	2	2δ	2δ	NUM
ejpam-1475	288	3	dn	dn	PROPN
ejpam-1475	288	4	(	(	PUNCT
ejpam-1475	288	5	ωt	ωt	PROPN
ejpam-1475	288	6	,	,	PUNCT
ejpam-1475	288	7	k	k	NOUN
ejpam-1475	288	8	)	)	PUNCT
ejpam-1475	288	9	1−	1−	NUM
ejpam-1475	289	1	k	k	PROPN
ejpam-1475	289	2	sn	sn	PROPN
ejpam-1475	289	3	(	(	PUNCT
ejpam-1475	289	4	ωt	ωt	PROPN
ejpam-1475	289	5	,	,	PUNCT
ejpam-1475	289	6	k	k	NOUN
ejpam-1475	289	7	)	)	PUNCT
ejpam-1475	289	8	·	·	PUNCT
ejpam-1475	289	9	here	here	ADV
ejpam-1475	289	10	δ	δ	X
ejpam-1475	289	11	=	=	PUNCT
ejpam-1475	290	1	p	p	PROPN
ejpam-1475	290	2	h2	h2	PROPN
ejpam-1475	290	3	0	0	NUM
ejpam-1475	290	4	−	−	PROPN
ejpam-1475	290	5	c0	c0	PROPN
ejpam-1475	290	6	,	,	PUNCT
ejpam-1475	290	7	ω	ω	PROPN
ejpam-1475	290	8	=	=	SYM
ejpam-1475	290	9	p	p	PROPN
ejpam-1475	290	10	h0	h0	PROPN
ejpam-1475	290	11	+	+	PROPN
ejpam-1475	290	12	δ	δ	PROPN
ejpam-1475	290	13	,	,	PUNCT
ejpam-1475	290	14	k	k	X
ejpam-1475	290	15	=	=	PUNCT
ejpam-1475	290	16	q	q	PROPN
ejpam-1475	290	17	h0−δ	h0−δ	PROPN
ejpam-1475	290	18	h0+δ	h0+δ	PROPN
ejpam-1475	290	19	and	and	CCONJ
ejpam-1475	290	20	k′	k′	PROPN
ejpam-1475	290	21	=	=	SYM
ejpam-1475	290	22	q	q	PROPN
ejpam-1475	290	23	2δ	2δ	NUM
ejpam-1475	290	24	h0+δ	h0+δ	PROPN
ejpam-1475	290	25	·	·	PUNCT
ejpam-1475	290	26	proof	proof	NOUN
ejpam-1475	290	27	.	.	PUNCT
ejpam-1475	291	1	we	we	PRON
ejpam-1475	291	2	start	start	VERB
ejpam-1475	291	3	by	by	ADP
ejpam-1475	291	4	explaining	explain	VERB
ejpam-1475	291	5	how	how	SCONJ
ejpam-1475	291	6	the	the	DET
ejpam-1475	291	7	expression	expression	NOUN
ejpam-1475	291	8	for	for	ADP
ejpam-1475	291	9	p̄	p̄	PROPN
ejpam-1475	291	10	(	(	PUNCT
ejpam-1475	291	11	·	·	PUNCT
ejpam-1475	291	12	)	)	PUNCT
ejpam-1475	291	13	can	can	AUX
ejpam-1475	291	14	be	be	AUX
ejpam-1475	291	15	found	find	VERB
ejpam-1475	291	16	.	.	PUNCT
ejpam-1475	292	1	assume	assume	VERB
ejpam-1475	292	2	p̄	p̄	PROPN
ejpam-1475	292	3	(	(	PUNCT
ejpam-1475	292	4	·	·	PUNCT
ejpam-1475	292	5	)	)	PUNCT
ejpam-1475	292	6	is	be	AUX
ejpam-1475	292	7	an	an	DET
ejpam-1475	292	8	integral	integral	ADJ
ejpam-1475	292	9	curve	curve	NOUN
ejpam-1475	292	10	of	of	ADP
ejpam-1475	292	11	~h	~h	NUM
ejpam-1475	292	12	satisfying	satisfying	ADJ
ejpam-1475	292	13	h(p̄(0	h(p̄(0	NOUN
ejpam-1475	292	14	)	)	PUNCT
ejpam-1475	292	15	)	)	PUNCT
ejpam-1475	293	1	=	=	SYM
ejpam-1475	293	2	h0	h0	PROPN
ejpam-1475	293	3	,	,	PUNCT
ejpam-1475	293	4	c(p̄(0	c(p̄(0	NOUN
ejpam-1475	293	5	)	)	PUNCT
ejpam-1475	293	6	)	)	PUNCT
ejpam-1475	294	1	=	=	SYM
ejpam-1475	294	2	c0	c0	X
ejpam-1475	294	3	>	>	X
ejpam-1475	294	4	0	0	PUNCT
ejpam-1475	294	5	and	and	CCONJ
ejpam-1475	294	6	δ2	δ2	VERB
ejpam-1475	294	7	=	=	SYM
ejpam-1475	294	8	h2	h2	NOUN
ejpam-1475	294	9	0	0	NUM
ejpam-1475	295	1	−	−	PROPN
ejpam-1475	295	2	c0	c0	PROPN
ejpam-1475	295	3	>	>	X
ejpam-1475	295	4	0	0	X
ejpam-1475	295	5	.	.	PUNCT
ejpam-1475	296	1	then	then	ADV
ejpam-1475	296	2	,	,	PUNCT
ejpam-1475	296	3	as	as	ADP
ejpam-1475	296	4	p̄	p̄	X
ejpam-1475	296	5	(	(	PUNCT
ejpam-1475	296	6	·	·	PUNCT
ejpam-1475	296	7	)	)	PUNCT
ejpam-1475	296	8	solves	solve	NOUN
ejpam-1475	296	9	(	(	PUNCT
ejpam-1475	296	10	11	11	NUM
ejpam-1475	296	11	)	)	PUNCT
ejpam-1475	296	12	,	,	PUNCT
ejpam-1475	296	13	we	we	PRON
ejpam-1475	296	14	get	get	VERB
ejpam-1475	296	15	that	that	PRON
ejpam-1475	297	1	d	d	PROPN
ejpam-1475	297	2	d	d	X
ejpam-1475	297	3	t	t	PROPN
ejpam-1475	297	4	p̄1(t	p̄1(t	NUM
ejpam-1475	297	5	)	)	PUNCT
ejpam-1475	298	1	=	=	SYM
ejpam-1475	298	2	±	±	NUM
ejpam-1475	298	3	p	p	NOUN
ejpam-1475	298	4	2	2	NUM
ejpam-1475	298	5	�	�	PROPN
ejpam-1475	298	6	c0	c0	PROPN
ejpam-1475	298	7	−	−	PROPN
ejpam-1475	298	8	p̄1(t	p̄1(t	SYM
ejpam-1475	298	9	)	)	PUNCT
ejpam-1475	298	10	2	2	NUM
ejpam-1475	298	11	�	�	PROPN
ejpam-1475	298	12	�	�	PROPN
ejpam-1475	298	13	h0	h0	NOUN
ejpam-1475	298	14	−	−	PROPN
ejpam-1475	298	15	p̄1(t	p̄1(t	SYM
ejpam-1475	298	16	)	)	PUNCT
ejpam-1475	298	17	�	�	PROPN
ejpam-1475	298	18	.	.	PUNCT
ejpam-1475	299	1	(	(	PUNCT
ejpam-1475	299	2	13	13	NUM
ejpam-1475	299	3	)	)	PUNCT
ejpam-1475	299	4	this	this	DET
ejpam-1475	299	5	(	(	PUNCT
ejpam-1475	299	6	separable	separable	ADJ
ejpam-1475	299	7	)	)	PUNCT
ejpam-1475	299	8	differential	differential	NOUN
ejpam-1475	299	9	equation	equation	NOUN
ejpam-1475	299	10	is	be	AUX
ejpam-1475	299	11	transformed	transform	VERB
ejpam-1475	299	12	into	into	ADP
ejpam-1475	299	13	standard	standard	ADJ
ejpam-1475	299	14	form	form	NOUN
ejpam-1475	299	15	(	(	PUNCT
ejpam-1475	299	16	see	see	VERB
ejpam-1475	299	17	[	[	X
ejpam-1475	299	18	2	2	NUM
ejpam-1475	299	19	]	]	PUNCT
ejpam-1475	299	20	)	)	PUNCT
ejpam-1475	299	21	and	and	CCONJ
ejpam-1475	299	22	formula	formula	NOUN
ejpam-1475	299	23	(	(	PUNCT
ejpam-1475	299	24	7	7	X
ejpam-1475	299	25	)	)	PUNCT
ejpam-1475	299	26	is	be	AUX
ejpam-1475	299	27	then	then	ADV
ejpam-1475	299	28	applied	apply	VERB
ejpam-1475	299	29	.	.	PUNCT
ejpam-1475	300	1	after	after	ADP
ejpam-1475	300	2	further	further	ADJ
ejpam-1475	300	3	simplification	simplification	NOUN
ejpam-1475	300	4	,	,	PUNCT
ejpam-1475	300	5	this	this	DET
ejpam-1475	300	6	yields	yield	NOUN
ejpam-1475	300	7	p̄1(t	p̄1(t	PRON
ejpam-1475	300	8	)	)	PUNCT
ejpam-1475	300	9	as	as	SCONJ
ejpam-1475	300	10	specified	specify	VERB
ejpam-1475	300	11	.	.	PUNCT
ejpam-1475	301	1	then	then	ADV
ejpam-1475	301	2	,	,	PUNCT
ejpam-1475	301	3	as	as	ADP
ejpam-1475	301	4	c(p̄(t	c(p̄(t	NOUN
ejpam-1475	301	5	)	)	PUNCT
ejpam-1475	301	6	)	)	PUNCT
ejpam-1475	302	1	=	=	SYM
ejpam-1475	302	2	c0	c0	NOUN
ejpam-1475	302	3	,	,	PUNCT
ejpam-1475	302	4	we	we	PRON
ejpam-1475	302	5	get	get	VERB
ejpam-1475	302	6	that	that	PRON
ejpam-1475	302	7	p̄2(t	p̄2(t	NOUN
ejpam-1475	302	8	)	)	PUNCT
ejpam-1475	302	9	2	2	NUM
ejpam-1475	302	10	=	=	SYM
ejpam-1475	302	11	c0	c0	PROPN
ejpam-1475	302	12	−	−	PROPN
ejpam-1475	302	13	p̄1(t	p̄1(t	PART
ejpam-1475	302	14	)	)	PUNCT
ejpam-1475	302	15	2	2	NUM
ejpam-1475	302	16	=	=	SYM
ejpam-1475	302	17	2c0δ	2c0δ	NUM
ejpam-1475	302	18	�	�	PROPN
ejpam-1475	302	19	1−	1−	NUM
ejpam-1475	302	20	sn	sn	PROPN
ejpam-1475	302	21	(	(	PUNCT
ejpam-1475	302	22	ωt	ωt	PROPN
ejpam-1475	302	23	,	,	PUNCT
ejpam-1475	302	24	k)2	k)2	PROPN
ejpam-1475	302	25	�	�	PROPN
ejpam-1475	302	26	�	�	PROPN
ejpam-1475	302	27	h0	h0	PROPN
ejpam-1475	302	28	+	+	PROPN
ejpam-1475	302	29	δ	δ	PROPN
ejpam-1475	302	30	�	�	PROPN
ejpam-1475	302	31	(	(	PUNCT
ejpam-1475	302	32	1−	1−	NUM
ejpam-1475	302	33	ksn	ksn	NOUN
ejpam-1475	302	34	(	(	PUNCT
ejpam-1475	302	35	ωt	ωt	PROPN
ejpam-1475	302	36	,	,	PUNCT
ejpam-1475	302	37	k))2	k))2	NOUN
ejpam-1475	302	38	=	=	PUNCT
ejpam-1475	302	39	c0(k	c0(k	PRON
ejpam-1475	302	40	′)2cn	′)2cn	ADJ
ejpam-1475	302	41	(	(	PUNCT
ejpam-1475	302	42	ωt	ωt	PROPN
ejpam-1475	302	43	,	,	PUNCT
ejpam-1475	302	44	k)2	k)2	PROPN
ejpam-1475	302	45	(	(	PUNCT
ejpam-1475	302	46	1−	1−	NUM
ejpam-1475	302	47	ksn	ksn	NOUN
ejpam-1475	302	48	(	(	PUNCT
ejpam-1475	302	49	ωt	ωt	PROPN
ejpam-1475	302	50	,	,	PUNCT
ejpam-1475	302	51	k))2	k))2	NOUN
ejpam-1475	302	52	yielding	yield	VERB
ejpam-1475	302	53	p̄2(t	p̄2(t	NOUN
ejpam-1475	302	54	)	)	PUNCT
ejpam-1475	302	55	as	as	SCONJ
ejpam-1475	302	56	specified	specify	VERB
ejpam-1475	302	57	,	,	PUNCT
ejpam-1475	302	58	for	for	ADP
ejpam-1475	302	59	some	some	DET
ejpam-1475	302	60	σ	σ	NUM
ejpam-1475	302	61	∈	∈	PROPN
ejpam-1475	302	62	{	{	PUNCT
ejpam-1475	302	63	−1,1	−1,1	NOUN
ejpam-1475	302	64	}	}	PUNCT
ejpam-1475	302	65	.	.	PUNCT
ejpam-1475	303	1	finally	finally	ADV
ejpam-1475	303	2	,	,	PUNCT
ejpam-1475	303	3	as	as	ADP
ejpam-1475	303	4	d	d	PROPN
ejpam-1475	303	5	d	d	PROPN
ejpam-1475	303	6	t	t	PROPN
ejpam-1475	303	7	p̄3(t	p̄3(t	PROPN
ejpam-1475	303	8	)	)	PUNCT
ejpam-1475	303	9	=	=	PRON
ejpam-1475	304	1	−p̄2	−p̄2	PROPN
ejpam-1475	304	2	and	and	CCONJ
ejpam-1475	304	3	−σpc0	−σpc0	PROPN
ejpam-1475	304	4	∫	∫	PROPN
ejpam-1475	304	5	k′cn	k′cn	PROPN
ejpam-1475	304	6	(	(	PUNCT
ejpam-1475	304	7	ωt	ωt	PROPN
ejpam-1475	304	8	,	,	PUNCT
ejpam-1475	304	9	k	k	NOUN
ejpam-1475	304	10	)	)	PUNCT
ejpam-1475	305	1	1−	1−	NUM
ejpam-1475	305	2	k	k	PROPN
ejpam-1475	305	3	sn	sn	PROPN
ejpam-1475	305	4	(	(	PUNCT
ejpam-1475	305	5	ωt	ωt	PROPN
ejpam-1475	305	6	,	,	PUNCT
ejpam-1475	305	7	k	k	NOUN
ejpam-1475	305	8	)	)	PUNCT
ejpam-1475	305	9	d	d	NOUN
ejpam-1475	305	10	t	t	NOUN
ejpam-1475	305	11	=	=	PUNCT
ejpam-1475	305	12	−σpc0	−σpc0	PROPN
ejpam-1475	305	13	k′	k′	PROPN
ejpam-1475	305	14	kω	kω	INTJ
ejpam-1475	305	15	dn	dn	PROPN
ejpam-1475	305	16	(	(	PUNCT
ejpam-1475	305	17	ωt	ωt	PROPN
ejpam-1475	305	18	,	,	PUNCT
ejpam-1475	305	19	k	k	NOUN
ejpam-1475	305	20	)	)	PUNCT
ejpam-1475	305	21	1−	1−	NUM
ejpam-1475	306	1	k	k	PROPN
ejpam-1475	306	2	sn	sn	PROPN
ejpam-1475	306	3	(	(	PUNCT
ejpam-1475	306	4	ωt	ωt	PROPN
ejpam-1475	306	5	,	,	PUNCT
ejpam-1475	306	6	k	k	NOUN
ejpam-1475	306	7	)	)	PUNCT
ejpam-1475	306	8	we	we	PRON
ejpam-1475	306	9	get	get	VERB
ejpam-1475	306	10	p̄3(t	p̄3(t	NOUN
ejpam-1475	306	11	)	)	PUNCT
ejpam-1475	306	12	as	as	SCONJ
ejpam-1475	306	13	prescribed	prescribe	VERB
ejpam-1475	306	14	.	.	PUNCT
ejpam-1475	307	1	this	this	PRON
ejpam-1475	307	2	motivates	motivate	VERB
ejpam-1475	307	3	p̄	p̄	PROPN
ejpam-1475	307	4	(	(	PUNCT
ejpam-1475	307	5	·	·	PUNCT
ejpam-1475	307	6	)	)	PUNCT
ejpam-1475	307	7	as	as	ADP
ejpam-1475	307	8	a	a	DET
ejpam-1475	307	9	prospective	prospective	ADJ
ejpam-1475	307	10	integral	integral	ADJ
ejpam-1475	307	11	curve	curve	NOUN
ejpam-1475	307	12	of	of	ADP
ejpam-1475	307	13	~h	~h	PROPN
ejpam-1475	307	14	.	.	PUNCT
ejpam-1475	308	1	now	now	ADV
ejpam-1475	308	2	notice	notice	VERB
ejpam-1475	308	3	,	,	PUNCT
ejpam-1475	308	4	as	as	ADP
ejpam-1475	308	5	δ2	δ2	VERB
ejpam-1475	308	6	=	=	SYM
ejpam-1475	308	7	h2	h2	NOUN
ejpam-1475	308	8	0	0	NUM
ejpam-1475	309	1	−	−	PROPN
ejpam-1475	309	2	c0	c0	PROPN
ejpam-1475	309	3	>	>	X
ejpam-1475	309	4	0	0	PROPN
ejpam-1475	309	5	,	,	PUNCT
ejpam-1475	309	6	that	that	SCONJ
ejpam-1475	309	7	0	0	NUM
ejpam-1475	309	8	<	<	X
ejpam-1475	309	9	k	k	X
ejpam-1475	309	10	<	<	X
ejpam-1475	309	11	1	1	NUM
ejpam-1475	309	12	and	and	CCONJ
ejpam-1475	309	13	so	so	ADV
ejpam-1475	309	14	1−	1−	NUM
ejpam-1475	309	15	k	k	PROPN
ejpam-1475	309	16	sn	sn	PROPN
ejpam-1475	309	17	(	(	PUNCT
ejpam-1475	309	18	ωt	ωt	PROPN
ejpam-1475	309	19	,	,	PUNCT
ejpam-1475	309	20	k	k	NOUN
ejpam-1475	309	21	)	)	PUNCT
ejpam-1475	309	22	>	>	X
ejpam-1475	310	1	0	0	X
ejpam-1475	310	2	.	.	PUNCT
ejpam-1475	310	3	hence	hence	ADV
ejpam-1475	310	4	p̄(t	p̄(t	PROPN
ejpam-1475	310	5	)	)	PUNCT
ejpam-1475	310	6	is	be	AUX
ejpam-1475	310	7	well	well	ADV
ejpam-1475	310	8	defined	define	VERB
ejpam-1475	310	9	and	and	CCONJ
ejpam-1475	310	10	smooth	smooth	ADJ
ejpam-1475	310	11	for	for	ADP
ejpam-1475	310	12	all	all	DET
ejpam-1475	310	13	t	t	NOUN
ejpam-1475	310	14	∈	∈	NOUN
ejpam-1475	310	15	r	r	NOUN
ejpam-1475	310	16	(	(	PUNCT
ejpam-1475	310	17	and	and	CCONJ
ejpam-1475	310	18	all	all	DET
ejpam-1475	310	19	h0	h0	PROPN
ejpam-1475	310	20	,	,	PUNCT
ejpam-1475	310	21	c0	c0	NOUN
ejpam-1475	310	22	such	such	ADJ
ejpam-1475	310	23	that	that	DET
ejpam-1475	310	24	h2	h2	PROPN
ejpam-1475	310	25	0−	0−	NUM
ejpam-1475	310	26	c0	c0	X
ejpam-1475	310	27	>	>	X
ejpam-1475	310	28	0	0	PROPN
ejpam-1475	310	29	,	,	PUNCT
ejpam-1475	310	30	c0	c0	NOUN
ejpam-1475	310	31	>	>	X
ejpam-1475	310	32	0	0	NUM
ejpam-1475	310	33	)	)	PUNCT
ejpam-1475	310	34	.	.	PUNCT
ejpam-1475	311	1	we	we	PRON
ejpam-1475	311	2	now	now	ADV
ejpam-1475	311	3	verify	verify	VERB
ejpam-1475	311	4	that	that	SCONJ
ejpam-1475	311	5	p̄	p̄	PROPN
ejpam-1475	311	6	(	(	PUNCT
ejpam-1475	311	7	·	·	PUNCT
ejpam-1475	311	8	)	)	PUNCT
ejpam-1475	311	9	is	be	AUX
ejpam-1475	311	10	a	a	DET
ejpam-1475	311	11	solution	solution	NOUN
ejpam-1475	311	12	to	to	ADP
ejpam-1475	311	13	(	(	PUNCT
ejpam-1475	311	14	11	11	NUM
ejpam-1475	311	15	)	)	PUNCT
ejpam-1475	311	16	.	.	PUNCT
ejpam-1475	312	1	we	we	PRON
ejpam-1475	312	2	get	get	VERB
ejpam-1475	312	3	that	that	PRON
ejpam-1475	313	1	d	d	PROPN
ejpam-1475	313	2	d	d	X
ejpam-1475	313	3	t	t	PROPN
ejpam-1475	313	4	p̄1(t)−	p̄1(t)−	PUNCT
ejpam-1475	313	5	p̄2(t)p̄3(t	p̄2(t)p̄3(t	PROPN
ejpam-1475	313	6	)	)	PUNCT
ejpam-1475	313	7	=	=	SYM
ejpam-1475	313	8	�	�	PROPN
ejpam-1475	313	9	−pc0(k	−pc0(k	VERB
ejpam-1475	314	1	′)2ω+	′)2ω+	PROPN
ejpam-1475	314	2	p	p	ADJ
ejpam-1475	314	3	2c0δ	2c0δ	NUM
ejpam-1475	314	4	�	�	PROPN
ejpam-1475	314	5	cn	cn	PROPN
ejpam-1475	314	6	(	(	PUNCT
ejpam-1475	314	7	ωt	ωt	PROPN
ejpam-1475	314	8	,	,	PUNCT
ejpam-1475	314	9	k)dn	k)dn	PROPN
ejpam-1475	314	10	(	(	PUNCT
ejpam-1475	314	11	ωt	ωt	PROPN
ejpam-1475	314	12	,	,	PUNCT
ejpam-1475	314	13	k	k	NOUN
ejpam-1475	314	14	)	)	PUNCT
ejpam-1475	314	15	(	(	PUNCT
ejpam-1475	314	16	1−	1−	NUM
ejpam-1475	314	17	ksn	ksn	NOUN
ejpam-1475	314	18	(	(	PUNCT
ejpam-1475	314	19	ωt	ωt	PROPN
ejpam-1475	314	20	,	,	PUNCT
ejpam-1475	314	21	k))2	k))2	NOUN
ejpam-1475	314	22	·	·	PUNCT
ejpam-1475	314	23	substitution	substitution	NOUN
ejpam-1475	314	24	and	and	CCONJ
ejpam-1475	314	25	simplification	simplification	NOUN
ejpam-1475	314	26	then	then	ADV
ejpam-1475	314	27	yields	yield	VERB
ejpam-1475	314	28	d	d	PROPN
ejpam-1475	314	29	d	d	X
ejpam-1475	314	30	t	t	PROPN
ejpam-1475	314	31	p̄1(t	p̄1(t	X
ejpam-1475	314	32	)	)	PUNCT
ejpam-1475	314	33	=	=	SYM
ejpam-1475	314	34	p̄2(t)p̄3(t	p̄2(t)p̄3(t	PROPN
ejpam-1475	314	35	)	)	PUNCT
ejpam-1475	314	36	.	.	PUNCT
ejpam-1475	315	1	likewise	likewise	ADV
ejpam-1475	315	2	,	,	PUNCT
ejpam-1475	315	3	we	we	PRON
ejpam-1475	315	4	get	get	VERB
ejpam-1475	315	5	d	d	PROPN
ejpam-1475	315	6	d	d	X
ejpam-1475	315	7	t	t	PROPN
ejpam-1475	315	8	p̄2(t	p̄2(t	NOUN
ejpam-1475	315	9	)	)	PUNCT
ejpam-1475	315	10	=	=	PUNCT
ejpam-1475	315	11	−p̄1(t)p̄3(t	−p̄1(t)p̄3(t	X
ejpam-1475	315	12	)	)	PUNCT
ejpam-1475	315	13	and	and	CCONJ
ejpam-1475	315	14	d	d	PROPN
ejpam-1475	315	15	d	d	PROPN
ejpam-1475	315	16	t	t	PROPN
ejpam-1475	315	17	p̄3(t	p̄3(t	PROPN
ejpam-1475	315	18	)	)	PUNCT
ejpam-1475	315	19	=	=	SYM
ejpam-1475	315	20	−p̄2(t	−p̄2(t	PROPN
ejpam-1475	315	21	)	)	PUNCT
ejpam-1475	315	22	.	.	PUNCT
ejpam-1475	316	1	hence	hence	ADV
ejpam-1475	316	2	p̄	p̄	PROPN
ejpam-1475	316	3	(	(	PUNCT
ejpam-1475	316	4	·	·	PUNCT
ejpam-1475	316	5	)	)	PUNCT
ejpam-1475	316	6	:	:	PUNCT
ejpam-1475	317	1	r→	r→	NOUN
ejpam-1475	317	2	se(2)∗	se(2)∗	NOUN
ejpam-1475	317	3	is	be	AUX
ejpam-1475	317	4	a	a	DET
ejpam-1475	317	5	periodic	periodic	ADJ
ejpam-1475	317	6	integral	integral	ADJ
ejpam-1475	317	7	curve	curve	NOUN
ejpam-1475	317	8	of	of	ADP
ejpam-1475	317	9	~h	~h	PROPN
ejpam-1475	317	10	.	.	PUNCT
ejpam-1475	318	1	any	any	DET
ejpam-1475	318	2	integral	integral	ADJ
ejpam-1475	318	3	curve	curve	NOUN
ejpam-1475	318	4	p	p	X
ejpam-1475	318	5	(	(	PUNCT
ejpam-1475	318	6	·	·	PUNCT
ejpam-1475	318	7	)	)	PUNCT
ejpam-1475	318	8	developing	develop	VERB
ejpam-1475	318	9	on	on	ADP
ejpam-1475	318	10	h−1(h0)∩	h−1(h0)∩	PROPN
ejpam-1475	318	11	c−1(c0	c−1(c0	NOUN
ejpam-1475	318	12	)	)	PUNCT
ejpam-1475	318	13	must	must	AUX
ejpam-1475	318	14	be	be	AUX
ejpam-1475	318	15	of	of	ADP
ejpam-1475	318	16	the	the	DET
ejpam-1475	318	17	form	form	NOUN
ejpam-1475	318	18	p(t	p(t	NOUN
ejpam-1475	318	19	)	)	PUNCT
ejpam-1475	319	1	=	=	SYM
ejpam-1475	319	2	p̄(t	p̄(t	PROPN
ejpam-1475	319	3	+	+	CCONJ
ejpam-1475	319	4	t0	t0	NOUN
ejpam-1475	319	5	)	)	PUNCT
ejpam-1475	319	6	for	for	ADP
ejpam-1475	319	7	some	some	PRON
ejpam-1475	319	8	σ	σ	NUM
ejpam-1475	319	9	∈	∈	PROPN
ejpam-1475	319	10	{	{	PUNCT
ejpam-1475	319	11	−1,1	−1,1	NOUN
ejpam-1475	319	12	}	}	PUNCT
ejpam-1475	319	13	and	and	CCONJ
ejpam-1475	319	14	t0	t0	PROPN
ejpam-1475	319	15	∈	∈	PROPN
ejpam-1475	319	16	r	r	NOUN
ejpam-1475	319	17	(	(	PUNCT
ejpam-1475	319	18	see	see	VERB
ejpam-1475	319	19	figure	figure	NOUN
ejpam-1475	319	20	1a	1a	NOUN
ejpam-1475	319	21	)	)	PUNCT
ejpam-1475	319	22	.	.	PUNCT
ejpam-1475	320	1	we	we	PRON
ejpam-1475	320	2	now	now	ADV
ejpam-1475	320	3	prove	prove	VERB
ejpam-1475	320	4	this	this	DET
ejpam-1475	320	5	fact	fact	NOUN
ejpam-1475	320	6	.	.	PUNCT
ejpam-1475	321	1	r.	r.	PROPN
ejpam-1475	321	2	adams	adams	PROPN
ejpam-1475	321	3	,	,	PUNCT
ejpam-1475	321	4	r.	r.	PROPN
ejpam-1475	321	5	biggs	biggs	PROPN
ejpam-1475	321	6	,	,	PUNCT
ejpam-1475	321	7	c.	c.	PROPN
ejpam-1475	321	8	remsing	remsing	NOUN
ejpam-1475	321	9	/	/	SYM
ejpam-1475	321	10	eur	eur	NOUN
ejpam-1475	321	11	.	.	PUNCT
ejpam-1475	322	1	j.	j.	PROPN
ejpam-1475	322	2	pure	pure	PROPN
ejpam-1475	322	3	appl	appl	PROPN
ejpam-1475	322	4	.	.	PROPN
ejpam-1475	322	5	math	math	PROPN
ejpam-1475	322	6	,	,	PUNCT
ejpam-1475	322	7	5	5	NUM
ejpam-1475	322	8	(	(	PUNCT
ejpam-1475	322	9	2012	2012	NUM
ejpam-1475	322	10	)	)	PUNCT
ejpam-1475	322	11	,	,	PUNCT
ejpam-1475	322	12	1	1	NUM
ejpam-1475	322	13	-	-	SYM
ejpam-1475	322	14	15	15	NUM
ejpam-1475	322	15	12	12	NUM
ejpam-1475	322	16	let	let	VERB
ejpam-1475	322	17	σ	σ	NOUN
ejpam-1475	322	18	=	=	SYM
ejpam-1475	322	19	sgn(p3(0	sgn(p3(0	PROPN
ejpam-1475	322	20	)	)	PUNCT
ejpam-1475	322	21	)	)	PUNCT
ejpam-1475	322	22	.	.	PUNCT
ejpam-1475	323	1	we	we	PRON
ejpam-1475	323	2	may	may	AUX
ejpam-1475	323	3	assume	assume	VERB
ejpam-1475	323	4	σ	σ	PROPN
ejpam-1475	323	5	6=	6=	PROPN
ejpam-1475	323	6	0	0	NUM
ejpam-1475	323	7	.	.	PUNCT
ejpam-1475	324	1	next	next	ADV
ejpam-1475	324	2	we	we	PRON
ejpam-1475	324	3	note	note	VERB
ejpam-1475	324	4	that	that	SCONJ
ejpam-1475	324	5	(	(	PUNCT
ejpam-1475	324	6	p̄1(t	p̄1(t	NUM
ejpam-1475	324	7	)	)	PUNCT
ejpam-1475	324	8	,	,	PUNCT
ejpam-1475	324	9	p̄2(t	p̄2(t	NOUN
ejpam-1475	324	10	)	)	PUNCT
ejpam-1475	324	11	)	)	PUNCT
ejpam-1475	324	12	parametrises	parametrise	VERB
ejpam-1475	324	13	the	the	DET
ejpam-1475	324	14	circle	circle	NOUN
ejpam-1475	324	15	s	s	PART
ejpam-1475	324	16	=	=	X
ejpam-1475	324	17	{	{	PUNCT
ejpam-1475	324	18	(	(	PUNCT
ejpam-1475	324	19	x	x	INTJ
ejpam-1475	324	20	,	,	PUNCT
ejpam-1475	324	21	y	y	PROPN
ejpam-1475	324	22	)	)	PUNCT
ejpam-1475	324	23	:	:	PUNCT
ejpam-1475	325	1	x2	x2	X
ejpam-1475	325	2	+	+	CCONJ
ejpam-1475	325	3	y2	y2	NOUN
ejpam-1475	325	4	=	=	SYM
ejpam-1475	325	5	c0	c0	NOUN
ejpam-1475	325	6	}	}	PUNCT
ejpam-1475	325	7	.	.	PUNCT
ejpam-1475	326	1	but	but	CCONJ
ejpam-1475	326	2	p1(0	p1(0	PROPN
ejpam-1475	326	3	)	)	PUNCT
ejpam-1475	327	1	2	2	NUM
ejpam-1475	327	2	+	+	NUM
ejpam-1475	327	3	p2(0	p2(0	NOUN
ejpam-1475	327	4	)	)	PUNCT
ejpam-1475	327	5	2	2	NUM
ejpam-1475	327	6	=	=	SYM
ejpam-1475	327	7	c0	c0	NOUN
ejpam-1475	327	8	,	,	PUNCT
ejpam-1475	327	9	i.e.	i.e.	X
ejpam-1475	327	10	,	,	PUNCT
ejpam-1475	327	11	(	(	PUNCT
ejpam-1475	327	12	p1(0	p1(0	PROPN
ejpam-1475	327	13	)	)	PUNCT
ejpam-1475	327	14	,	,	PUNCT
ejpam-1475	327	15	p2(0	p2(0	NOUN
ejpam-1475	327	16	)	)	PUNCT
ejpam-1475	327	17	)	)	PUNCT
ejpam-1475	328	1	∈	∈	PROPN
ejpam-1475	328	2	s.	s.	PROPN
ejpam-1475	328	3	therefore	therefore	ADV
ejpam-1475	328	4	,	,	PUNCT
ejpam-1475	328	5	there	there	PRON
ejpam-1475	328	6	exists	exist	VERB
ejpam-1475	328	7	t0	t0	PROPN
ejpam-1475	328	8	∈	∈	PROPN
ejpam-1475	328	9	r	r	NOUN
ejpam-1475	328	10	such	such	ADJ
ejpam-1475	328	11	that	that	DET
ejpam-1475	328	12	p̄1(t0	p̄1(t0	NOUN
ejpam-1475	328	13	)	)	PUNCT
ejpam-1475	328	14	=	=	SYM
ejpam-1475	328	15	p1(0	p1(0	PROPN
ejpam-1475	328	16	)	)	PUNCT
ejpam-1475	328	17	and	and	CCONJ
ejpam-1475	328	18	p̄2(t0	p̄2(t0	PROPN
ejpam-1475	328	19	)	)	PUNCT
ejpam-1475	328	20	=	=	SYM
ejpam-1475	328	21	p2(0	p2(0	NOUN
ejpam-1475	328	22	)	)	PUNCT
ejpam-1475	328	23	.	.	PUNCT
ejpam-1475	329	1	then	then	ADV
ejpam-1475	329	2	we	we	PRON
ejpam-1475	329	3	have	have	VERB
ejpam-1475	329	4	that	that	DET
ejpam-1475	329	5	p3(0	p3(0	PROPN
ejpam-1475	329	6	)	)	PUNCT
ejpam-1475	329	7	2	2	NUM
ejpam-1475	329	8	=	=	SYM
ejpam-1475	329	9	2(h0	2(h0	NUM
ejpam-1475	329	10	−	−	PROPN
ejpam-1475	329	11	p1(0	p1(0	PROPN
ejpam-1475	329	12	)	)	PUNCT
ejpam-1475	329	13	)	)	PUNCT
ejpam-1475	330	1	=	=	PUNCT
ejpam-1475	330	2	2(h0	2(h0	NUM
ejpam-1475	330	3	−	−	PROPN
ejpam-1475	330	4	p̄1(t0	p̄1(t0	NOUN
ejpam-1475	330	5	)	)	PUNCT
ejpam-1475	330	6	)	)	PUNCT
ejpam-1475	331	1	=	=	SYM
ejpam-1475	331	2	p̄3(t0	p̄3(t0	PROPN
ejpam-1475	331	3	)	)	PUNCT
ejpam-1475	332	1	2	2	NUM
ejpam-1475	332	2	.	.	X
ejpam-1475	333	1	hence	hence	ADV
ejpam-1475	333	2	,	,	PUNCT
ejpam-1475	333	3	as	as	ADP
ejpam-1475	333	4	sgn(p3(t0	sgn(p3(t0	PROPN
ejpam-1475	333	5	)	)	PUNCT
ejpam-1475	333	6	)	)	PUNCT
ejpam-1475	334	1	=	=	PUNCT
ejpam-1475	334	2	σ	σ	NOUN
ejpam-1475	334	3	=	=	SYM
ejpam-1475	334	4	sgn(p3(0	sgn(p3(0	PROPN
ejpam-1475	334	5	)	)	PUNCT
ejpam-1475	334	6	)	)	PUNCT
ejpam-1475	334	7	,	,	PUNCT
ejpam-1475	334	8	we	we	PRON
ejpam-1475	334	9	get	get	VERB
ejpam-1475	334	10	that	that	DET
ejpam-1475	334	11	p3(0	p3(0	PROPN
ejpam-1475	334	12	)	)	PUNCT
ejpam-1475	335	1	=	=	SYM
ejpam-1475	335	2	p̄3(t0	p̄3(t0	PROPN
ejpam-1475	335	3	)	)	PUNCT
ejpam-1475	335	4	.	.	PUNCT
ejpam-1475	336	1	thus	thus	ADV
ejpam-1475	336	2	the	the	DET
ejpam-1475	336	3	integral	integral	ADJ
ejpam-1475	336	4	curves	curve	NOUN
ejpam-1475	336	5	t	t	NOUN
ejpam-1475	336	6	7→	7→	NUM
ejpam-1475	336	7	p(t	p(t	NOUN
ejpam-1475	336	8	)	)	PUNCT
ejpam-1475	336	9	and	and	CCONJ
ejpam-1475	336	10	t	t	PROPN
ejpam-1475	336	11	7→	7→	PROPN
ejpam-1475	336	12	p̄(t	p̄(t	PROPN
ejpam-1475	336	13	+	+	CCONJ
ejpam-1475	336	14	t0	t0	NOUN
ejpam-1475	336	15	)	)	PUNCT
ejpam-1475	336	16	solve	solve	VERB
ejpam-1475	336	17	the	the	DET
ejpam-1475	336	18	same	same	ADJ
ejpam-1475	336	19	cauchy	cauchy	NOUN
ejpam-1475	336	20	problem	problem	NOUN
ejpam-1475	336	21	,	,	PUNCT
ejpam-1475	336	22	and	and	CCONJ
ejpam-1475	336	23	therefore	therefore	ADV
ejpam-1475	336	24	are	be	AUX
ejpam-1475	336	25	identical	identical	ADJ
ejpam-1475	336	26	.	.	PUNCT
ejpam-1475	337	1	(	(	PUNCT
ejpam-1475	337	2	throughout	throughout	ADP
ejpam-1475	337	3	this	this	DET
ejpam-1475	337	4	proof	proof	NOUN
ejpam-1475	337	5	we	we	PRON
ejpam-1475	337	6	used	use	VERB
ejpam-1475	337	7	mathematica	mathematica	PROPN
ejpam-1475	337	8	to	to	PART
ejpam-1475	337	9	facilitate	facilitate	VERB
ejpam-1475	337	10	calculations	calculation	NOUN
ejpam-1475	337	11	.	.	PUNCT
ejpam-1475	337	12	)	)	PUNCT
ejpam-1475	337	13	remark	remark	VERB
ejpam-1475	337	14	2	2	NUM
ejpam-1475	337	15	.	.	PUNCT
ejpam-1475	337	16	note	note	VERB
ejpam-1475	337	17	that	that	SCONJ
ejpam-1475	337	18	,	,	PUNCT
ejpam-1475	337	19	for	for	ADP
ejpam-1475	337	20	any	any	DET
ejpam-1475	337	21	h0	h0	NOUN
ejpam-1475	337	22	,	,	PUNCT
ejpam-1475	337	23	c0	c0	PROPN
ejpam-1475	337	24	∈	∈	PROPN
ejpam-1475	337	25	r	r	PROPN
ejpam-1475	337	26	,	,	PUNCT
ejpam-1475	337	27	h2	h2	NOUN
ejpam-1475	337	28	0	0	NUM
ejpam-1475	337	29	−	−	PROPN
ejpam-1475	337	30	c0	c0	PROPN
ejpam-1475	337	31	>	>	X
ejpam-1475	337	32	0	0	PROPN
ejpam-1475	337	33	,	,	PUNCT
ejpam-1475	337	34	c0	c0	NOUN
ejpam-1475	337	35	>	>	X
ejpam-1475	337	36	0	0	PUNCT
ejpam-1475	338	1	and	and	CCONJ
ejpam-1475	338	2	σ	σ	PROPN
ejpam-1475	338	3	∈	∈	PROPN
ejpam-1475	338	4	{	{	PUNCT
ejpam-1475	338	5	−1,1	−1,1	NOUN
ejpam-1475	338	6	}	}	PUNCT
ejpam-1475	338	7	,	,	PUNCT
ejpam-1475	338	8	we	we	PRON
ejpam-1475	338	9	have	have	VERB
ejpam-1475	338	10	that	that	DET
ejpam-1475	338	11	p̄	p̄	PROPN
ejpam-1475	338	12	(	(	PUNCT
ejpam-1475	338	13	·	·	PUNCT
ejpam-1475	338	14	)	)	PUNCT
ejpam-1475	338	15	:	:	PUNCT
ejpam-1475	339	1	r	r	NOUN
ejpam-1475	339	2	→	→	SYM
ejpam-1475	339	3	se(2)∗	se(2)∗	ADJ
ejpam-1475	339	4	is	be	AUX
ejpam-1475	339	5	a	a	DET
ejpam-1475	339	6	periodic	periodic	ADJ
ejpam-1475	339	7	integral	integral	ADJ
ejpam-1475	339	8	curve	curve	NOUN
ejpam-1475	339	9	of	of	ADP
ejpam-1475	339	10	~h	~h	PROPN
ejpam-1475	339	11	.	.	PUNCT
ejpam-1475	340	1	consequently	consequently	ADV
ejpam-1475	340	2	,	,	PUNCT
ejpam-1475	340	3	any	any	DET
ejpam-1475	340	4	integral	integral	ADJ
ejpam-1475	340	5	curve	curve	NOUN
ejpam-1475	340	6	p	p	X
ejpam-1475	340	7	(	(	PUNCT
ejpam-1475	340	8	·	·	PUNCT
ejpam-1475	340	9	)	)	PUNCT
ejpam-1475	340	10	of	of	ADP
ejpam-1475	340	11	~h	~h	PROPN
ejpam-1475	340	12	(	(	PUNCT
ejpam-1475	340	13	satisfying	satisfy	VERB
ejpam-1475	340	14	the	the	DET
ejpam-1475	340	15	conditions	condition	NOUN
ejpam-1475	340	16	of	of	ADP
ejpam-1475	340	17	theorem	theorem	NOUN
ejpam-1475	340	18	9	9	NUM
ejpam-1475	340	19	)	)	PUNCT
ejpam-1475	340	20	has	have	VERB
ejpam-1475	340	21	maximal	maximal	ADJ
ejpam-1475	340	22	domain	domain	NOUN
ejpam-1475	340	23	r	r	NOUN
ejpam-1475	340	24	and	and	CCONJ
ejpam-1475	340	25	is	be	AUX
ejpam-1475	340	26	periodic	periodic	ADJ
ejpam-1475	340	27	(	(	PUNCT
ejpam-1475	340	28	on	on	ADP
ejpam-1475	340	29	r	r	NOUN
ejpam-1475	340	30	)	)	PUNCT
ejpam-1475	340	31	.	.	PUNCT
ejpam-1475	341	1	we	we	PRON
ejpam-1475	341	2	now	now	ADV
ejpam-1475	341	3	proceed	proceed	VERB
ejpam-1475	341	4	to	to	ADP
ejpam-1475	341	5	the	the	DET
ejpam-1475	341	6	case	case	NOUN
ejpam-1475	341	7	−pc	−pc	ADP
ejpam-1475	341	8	<	<	X
ejpam-1475	341	9	h	h	NOUN
ejpam-1475	341	10	<	<	X
ejpam-1475	341	11	p	p	X
ejpam-1475	341	12	c	c	PROPN
ejpam-1475	341	13	.	.	PUNCT
ejpam-1475	342	1	theorem	theorem	ADJ
ejpam-1475	342	2	10	10	NUM
ejpam-1475	342	3	.	.	PUNCT
ejpam-1475	343	1	suppose	suppose	VERB
ejpam-1475	343	2	p	p	X
ejpam-1475	343	3	(	(	PUNCT
ejpam-1475	343	4	·	·	PUNCT
ejpam-1475	343	5	)	)	PUNCT
ejpam-1475	343	6	:	:	PUNCT
ejpam-1475	343	7	(	(	PUNCT
ejpam-1475	343	8	−ǫ	−ǫ	NOUN
ejpam-1475	343	9	,	,	PUNCT
ejpam-1475	343	10	ǫ)→	ǫ)→	NOUN
ejpam-1475	343	11	se(2)∗	se(2)∗	NOUN
ejpam-1475	343	12	is	be	AUX
ejpam-1475	343	13	an	an	DET
ejpam-1475	343	14	integral	integral	ADJ
ejpam-1475	343	15	curve	curve	NOUN
ejpam-1475	343	16	of	of	ADP
ejpam-1475	343	17	~h	~h	PROPN
ejpam-1475	343	18	such	such	ADJ
ejpam-1475	343	19	that	that	DET
ejpam-1475	343	20	h(p(0	h(p(0	NOUN
ejpam-1475	343	21	)	)	PUNCT
ejpam-1475	343	22	)	)	PUNCT
ejpam-1475	344	1	=	=	SYM
ejpam-1475	344	2	h0	h0	PROPN
ejpam-1475	344	3	,	,	PUNCT
ejpam-1475	344	4	c(p(0	c(p(0	NOUN
ejpam-1475	344	5	)	)	PUNCT
ejpam-1475	344	6	)	)	PUNCT
ejpam-1475	345	1	=	=	SYM
ejpam-1475	345	2	c0	c0	X
ejpam-1475	345	3	>	>	X
ejpam-1475	345	4	0	0	PUNCT
ejpam-1475	345	5	and	and	CCONJ
ejpam-1475	345	6	h2	h2	PROPN
ejpam-1475	345	7	0	0	NUM
ejpam-1475	346	1	−	−	PROPN
ejpam-1475	346	2	c0	c0	NOUN
ejpam-1475	346	3	<	<	X
ejpam-1475	346	4	0	0	X
ejpam-1475	346	5	.	.	PUNCT
ejpam-1475	347	1	then	then	ADV
ejpam-1475	347	2	there	there	PRON
ejpam-1475	347	3	exists	exist	VERB
ejpam-1475	347	4	t0	t0	PROPN
ejpam-1475	347	5	∈	∈	PROPN
ejpam-1475	347	6	r	r	NOUN
ejpam-1475	347	7	such	such	ADJ
ejpam-1475	347	8	that	that	DET
ejpam-1475	347	9	p(t	p(t	NOUN
ejpam-1475	347	10	)	)	PUNCT
ejpam-1475	348	1	=	=	SYM
ejpam-1475	348	2	p̄(t	p̄(t	PROPN
ejpam-1475	348	3	+	+	CCONJ
ejpam-1475	348	4	t0	t0	NOUN
ejpam-1475	348	5	)	)	PUNCT
ejpam-1475	348	6	for	for	ADP
ejpam-1475	348	7	t	t	PROPN
ejpam-1475	348	8	∈	∈	PROPN
ejpam-1475	348	9	(	(	PUNCT
ejpam-1475	348	10	−ǫ	−ǫ	NOUN
ejpam-1475	348	11	,	,	PUNCT
ejpam-1475	348	12	ǫ	ǫ	NOUN
ejpam-1475	348	13	)	)	PUNCT
ejpam-1475	348	14	,	,	PUNCT
ejpam-1475	348	15	where	where	SCONJ
ejpam-1475	348	16			PROPN
ejpam-1475	348	17			PROPN
ejpam-1475	348	18			PROPN
ejpam-1475	348	19			PROPN
ejpam-1475	348	20			PROPN
ejpam-1475	348	21			PROPN
ejpam-1475	348	22			PROPN
ejpam-1475	348	23			PROPN
ejpam-1475	348	24			NOUN
ejpam-1475	348	25			PROPN
ejpam-1475	348	26			PROPN
ejpam-1475	348	27			PROPN
ejpam-1475	348	28			PROPN
ejpam-1475	348	29			PROPN
ejpam-1475	348	30			PROPN
ejpam-1475	348	31			PROPN
ejpam-1475	348	32			NOUN
ejpam-1475	348	33	p̄1(t	p̄1(t	NUM
ejpam-1475	348	34	)	)	PUNCT
ejpam-1475	348	35	=	=	SYM
ejpam-1475	348	36	−	−	PROPN
ejpam-1475	348	37	p	p	PROPN
ejpam-1475	348	38	c0	c0	PROPN
ejpam-1475	348	39	−	−	PROPN
ejpam-1475	348	40	2δ+	2δ+	NUM
ejpam-1475	348	41	�	�	PROPN
ejpam-1475	348	42	p	p	PROPN
ejpam-1475	348	43	c0	c0	NOUN
ejpam-1475	348	44	+	+	CCONJ
ejpam-1475	348	45	2δ	2δ	NUM
ejpam-1475	348	46	�	�	PROPN
ejpam-1475	348	47	dn	dn	PROPN
ejpam-1475	348	48	(	(	PUNCT
ejpam-1475	348	49	ωt	ωt	PROPN
ejpam-1475	348	50	,	,	PUNCT
ejpam-1475	348	51	k	k	NOUN
ejpam-1475	348	52	)	)	PUNCT
ejpam-1475	348	53	1	1	NUM
ejpam-1475	348	54	+	+	NUM
ejpam-1475	348	55	dn	dn	ADJ
ejpam-1475	348	56	(	(	PUNCT
ejpam-1475	348	57	ωt	ωt	PROPN
ejpam-1475	348	58	,	,	PUNCT
ejpam-1475	348	59	k	k	NOUN
ejpam-1475	348	60	)	)	PUNCT
ejpam-1475	348	61	p̄2(t	p̄2(t	NOUN
ejpam-1475	348	62	)	)	PUNCT
ejpam-1475	348	63	=	=	SYM
ejpam-1475	348	64	4	4	NUM
ejpam-1475	348	65	4	4	NUM
ejpam-1475	348	66	p	p	NOUN
ejpam-1475	348	67	c0δ	c0δ	PROPN
ejpam-1475	348	68	pp	pp	NOUN
ejpam-1475	348	69	c0	c0	PROPN
ejpam-1475	348	70	+	+	CCONJ
ejpam-1475	348	71	δ	δ	PROPN
ejpam-1475	349	1	p	p	NOUN
ejpam-1475	349	2	k′+	k′+	PROPN
ejpam-1475	349	3	dn	dn	PROPN
ejpam-1475	349	4	(	(	PUNCT
ejpam-1475	349	5	ωt	ωt	PROPN
ejpam-1475	349	6	,	,	PUNCT
ejpam-1475	349	7	k)sn	k)sn	PROPN
ejpam-1475	349	8	(	(	PUNCT
ejpam-1475	349	9	ωt	ωt	PROPN
ejpam-1475	349	10	,	,	PUNCT
ejpam-1475	349	11	k	k	NOUN
ejpam-1475	349	12	)	)	PUNCT
ejpam-1475	349	13	p	p	NOUN
ejpam-1475	349	14	(	(	PUNCT
ejpam-1475	349	15	1	1	NUM
ejpam-1475	349	16	+	+	NUM
ejpam-1475	349	17	dn	dn	ADJ
ejpam-1475	349	18	(	(	PUNCT
ejpam-1475	349	19	ωt	ωt	PROPN
ejpam-1475	349	20	,	,	PUNCT
ejpam-1475	349	21	k))3	k))3	X
ejpam-1475	349	22	p̄3(t	p̄3(t	X
ejpam-1475	349	23	)	)	PUNCT
ejpam-1475	349	24	=	=	SYM
ejpam-1475	349	25	4δ	4δ	NOUN
ejpam-1475	349	26	pp	pp	ADP
ejpam-1475	349	27	c0	c0	PROPN
ejpam-1475	349	28	+	+	CCONJ
ejpam-1475	349	29	δ	δ	PROPN
ejpam-1475	349	30	cn	cn	PROPN
ejpam-1475	349	31	(	(	PUNCT
ejpam-1475	349	32	ωt	ωt	PROPN
ejpam-1475	349	33	,	,	PUNCT
ejpam-1475	349	34	k	k	NOUN
ejpam-1475	349	35	)	)	PUNCT
ejpam-1475	349	36	p	p	NOUN
ejpam-1475	349	37	k′+	k′+	PROPN
ejpam-1475	349	38	dn	dn	PROPN
ejpam-1475	349	39	(	(	PUNCT
ejpam-1475	349	40	ωt	ωt	PROPN
ejpam-1475	349	41	,	,	PUNCT
ejpam-1475	349	42	k	k	NOUN
ejpam-1475	349	43	)	)	PUNCT
ejpam-1475	349	44	p	p	NOUN
ejpam-1475	349	45	1	1	NUM
ejpam-1475	349	46	+	+	NUM
ejpam-1475	349	47	dn	dn	PROPN
ejpam-1475	349	48	(	(	PUNCT
ejpam-1475	349	49	ωt	ωt	PROPN
ejpam-1475	349	50	,	,	PUNCT
ejpam-1475	349	51	k	k	NOUN
ejpam-1475	349	52	)	)	PUNCT
ejpam-1475	349	53	·	·	PUNCT
ejpam-1475	349	54	here	here	ADV
ejpam-1475	349	55	δ	δ	X
ejpam-1475	349	56	=	=	SYM
ejpam-1475	349	57	1p	1p	NUM
ejpam-1475	349	58	2	2	NUM
ejpam-1475	349	59	4	4	NUM
ejpam-1475	349	60	p	p	PROPN
ejpam-1475	349	61	c0	c0	PROPN
ejpam-1475	349	62	p	p	PROPN
ejpam-1475	349	63	h0	h0	PROPN
ejpam-1475	349	64	+	+	PROPN
ejpam-1475	349	65	p	p	PROPN
ejpam-1475	349	66	c0	c0	NOUN
ejpam-1475	349	67	,	,	PUNCT
ejpam-1475	349	68	ω	ω	PROPN
ejpam-1475	349	69	=	=	PUNCT
ejpam-1475	350	1	p	p	X
ejpam-1475	350	2	c0+δ	c0+δ	PROPN
ejpam-1475	350	3	4pc0	4pc0	NUM
ejpam-1475	350	4	,	,	PUNCT
ejpam-1475	351	1	k	k	PROPN
ejpam-1475	351	2	=	=	SYM
ejpam-1475	351	3	2	2	NUM
ejpam-1475	351	4	pp	pp	NOUN
ejpam-1475	351	5	c0δp	c0δp	PUNCT
ejpam-1475	351	6	c0+δ	c0+δ	PROPN
ejpam-1475	351	7	and	and	CCONJ
ejpam-1475	351	8	k′	k′	PROPN
ejpam-1475	351	9	=	=	SYM
ejpam-1475	352	1	p	p	NOUN
ejpam-1475	352	2	c0−δp	c0−δp	PUNCT
ejpam-1475	352	3	c0+δ	c0+δ	PROPN
ejpam-1475	352	4	·	·	PUNCT
ejpam-1475	352	5	remark	remark	NOUN
ejpam-1475	352	6	3	3	NUM
ejpam-1475	352	7	.	.	PUNCT
ejpam-1475	353	1	the	the	DET
ejpam-1475	353	2	proof	proof	NOUN
ejpam-1475	353	3	of	of	ADP
ejpam-1475	353	4	this	this	DET
ejpam-1475	353	5	theorem	theorem	NOUN
ejpam-1475	353	6	is	be	AUX
ejpam-1475	353	7	similar	similar	ADJ
ejpam-1475	353	8	to	to	ADP
ejpam-1475	353	9	that	that	PRON
ejpam-1475	353	10	of	of	ADP
ejpam-1475	353	11	theorem	theorem	NOUN
ejpam-1475	353	12	9	9	NUM
ejpam-1475	353	13	.	.	PUNCT
ejpam-1475	354	1	the	the	DET
ejpam-1475	354	2	crucial	crucial	ADJ
ejpam-1475	354	3	difference	difference	NOUN
ejpam-1475	354	4	is	be	AUX
ejpam-1475	354	5	that	that	SCONJ
ejpam-1475	354	6	before	before	ADP
ejpam-1475	354	7	solving	solve	VERB
ejpam-1475	354	8	equation	equation	NOUN
ejpam-1475	354	9	(	(	PUNCT
ejpam-1475	354	10	13	13	NUM
ejpam-1475	354	11	)	)	PUNCT
ejpam-1475	354	12	,	,	PUNCT
ejpam-1475	354	13	one	one	PRON
ejpam-1475	354	14	needs	need	VERB
ejpam-1475	354	15	to	to	PART
ejpam-1475	354	16	deinterlace	deinterlace	VERB
ejpam-1475	354	17	the	the	DET
ejpam-1475	354	18	roots	root	NOUN
ejpam-1475	354	19	of	of	ADP
ejpam-1475	354	20	the	the	DET
ejpam-1475	354	21	two	two	NUM
ejpam-1475	354	22	quadratics	quadratic	NOUN
ejpam-1475	354	23	involved	involve	VERB
ejpam-1475	354	24	.	.	PUNCT
ejpam-1475	355	1	(	(	PUNCT
ejpam-1475	355	2	this	this	PRON
ejpam-1475	355	3	leads	lead	VERB
ejpam-1475	355	4	to	to	ADP
ejpam-1475	355	5	a	a	DET
ejpam-1475	355	6	somewhat	somewhat	ADV
ejpam-1475	355	7	more	more	ADV
ejpam-1475	355	8	involved	involved	ADJ
ejpam-1475	355	9	computation	computation	NOUN
ejpam-1475	355	10	which	which	PRON
ejpam-1475	355	11	relies	rely	VERB
ejpam-1475	355	12	on	on	ADP
ejpam-1475	355	13	formula	formula	NOUN
ejpam-1475	355	14	(	(	PUNCT
ejpam-1475	355	15	8)	8)	NUM
ejpam-1475	355	16	.	.	PUNCT
ejpam-1475	355	17	)	)	PUNCT
ejpam-1475	356	1	again	again	ADV
ejpam-1475	356	2	,	,	PUNCT
ejpam-1475	356	3	we	we	PRON
ejpam-1475	356	4	note	note	VERB
ejpam-1475	356	5	that	that	SCONJ
ejpam-1475	356	6	p̄	p̄	PROPN
ejpam-1475	356	7	(	(	PUNCT
ejpam-1475	356	8	·	·	PUNCT
ejpam-1475	356	9	)	)	PUNCT
ejpam-1475	356	10	is	be	AUX
ejpam-1475	356	11	always	always	ADV
ejpam-1475	356	12	a	a	DET
ejpam-1475	356	13	periodic	periodic	ADJ
ejpam-1475	356	14	integral	integral	ADJ
ejpam-1475	356	15	curve	curve	NOUN
ejpam-1475	356	16	and	and	CCONJ
ejpam-1475	356	17	that	that	SCONJ
ejpam-1475	356	18	any	any	DET
ejpam-1475	356	19	integral	integral	ADJ
ejpam-1475	356	20	curve	curve	NOUN
ejpam-1475	356	21	p	p	X
ejpam-1475	356	22	(	(	PUNCT
ejpam-1475	356	23	·	·	PUNCT
ejpam-1475	356	24	)	)	PUNCT
ejpam-1475	356	25	has	have	VERB
ejpam-1475	356	26	maximal	maximal	ADJ
ejpam-1475	356	27	domain	domain	NOUN
ejpam-1475	356	28	r	r	NOUN
ejpam-1475	356	29	,	,	PUNCT
ejpam-1475	356	30	on	on	ADP
ejpam-1475	356	31	which	which	PRON
ejpam-1475	356	32	it	it	PRON
ejpam-1475	356	33	is	be	AUX
ejpam-1475	356	34	periodic	periodic	ADJ
ejpam-1475	356	35	.	.	PUNCT
ejpam-1475	357	1	we	we	PRON
ejpam-1475	357	2	finish	finish	VERB
ejpam-1475	357	3	with	with	ADP
ejpam-1475	357	4	the	the	DET
ejpam-1475	357	5	case	case	NOUN
ejpam-1475	357	6	h	h	NOUN
ejpam-1475	358	1	=	=	NOUN
ejpam-1475	358	2	p	p	X
ejpam-1475	358	3	c	c	PROPN
ejpam-1475	358	4	.	.	PUNCT
ejpam-1475	359	1	theorem	theorem	NOUN
ejpam-1475	359	2	11	11	NUM
ejpam-1475	359	3	.	.	PUNCT
ejpam-1475	360	1	suppose	suppose	VERB
ejpam-1475	360	2	p	p	X
ejpam-1475	360	3	(	(	PUNCT
ejpam-1475	360	4	·	·	PUNCT
ejpam-1475	360	5	)	)	PUNCT
ejpam-1475	360	6	:	:	PUNCT
ejpam-1475	360	7	(	(	PUNCT
ejpam-1475	360	8	−ǫ	−ǫ	NOUN
ejpam-1475	360	9	,	,	PUNCT
ejpam-1475	360	10	ǫ)→	ǫ)→	NOUN
ejpam-1475	360	11	se(2)∗	se(2)∗	NOUN
ejpam-1475	360	12	is	be	AUX
ejpam-1475	360	13	an	an	DET
ejpam-1475	360	14	integral	integral	ADJ
ejpam-1475	360	15	curve	curve	NOUN
ejpam-1475	360	16	of	of	ADP
ejpam-1475	360	17	~h	~h	PROPN
ejpam-1475	360	18	such	such	ADJ
ejpam-1475	360	19	that	that	DET
ejpam-1475	360	20	h(p(0	h(p(0	NOUN
ejpam-1475	360	21	)	)	PUNCT
ejpam-1475	360	22	)	)	PUNCT
ejpam-1475	361	1	=	=	SYM
ejpam-1475	361	2	h0	h0	PROPN
ejpam-1475	361	3	,	,	PUNCT
ejpam-1475	361	4	c(p(0	c(p(0	NOUN
ejpam-1475	361	5	)	)	PUNCT
ejpam-1475	361	6	)	)	PUNCT
ejpam-1475	362	1	=	=	SYM
ejpam-1475	362	2	c0	c0	X
ejpam-1475	362	3	>	>	X
ejpam-1475	362	4	0	0	PUNCT
ejpam-1475	362	5	and	and	CCONJ
ejpam-1475	362	6	h0	h0	NOUN
ejpam-1475	362	7	=	=	PROPN
ejpam-1475	362	8	p	p	PROPN
ejpam-1475	362	9	c0	c0	NOUN
ejpam-1475	362	10	.	.	PUNCT
ejpam-1475	363	1	then	then	ADV
ejpam-1475	363	2	there	there	PRON
ejpam-1475	363	3	exists	exist	VERB
ejpam-1475	363	4	t0	t0	PROPN
ejpam-1475	363	5	∈	∈	PROPN
ejpam-1475	363	6	r	r	NOUN
ejpam-1475	363	7	and	and	CCONJ
ejpam-1475	363	8	σ	σ	NOUN
ejpam-1475	363	9	∈	∈	PROPN
ejpam-1475	363	10	{	{	PUNCT
ejpam-1475	363	11	−1,1	−1,1	NOUN
ejpam-1475	363	12	}	}	PUNCT
ejpam-1475	363	13	such	such	ADJ
ejpam-1475	363	14	that	that	DET
ejpam-1475	363	15	p(t	p(t	NOUN
ejpam-1475	363	16	)	)	PUNCT
ejpam-1475	364	1	=	=	SYM
ejpam-1475	364	2	p̄(t	p̄(t	PROPN
ejpam-1475	364	3	+	+	CCONJ
ejpam-1475	364	4	t0	t0	NOUN
ejpam-1475	364	5	)	)	PUNCT
ejpam-1475	364	6	for	for	ADP
ejpam-1475	364	7	t	t	PROPN
ejpam-1475	364	8	∈	∈	PROPN
ejpam-1475	364	9	(	(	PUNCT
ejpam-1475	364	10	−ǫ	−ǫ	NOUN
ejpam-1475	364	11	,	,	PUNCT
ejpam-1475	364	12	ǫ	ǫ	NOUN
ejpam-1475	364	13	)	)	PUNCT
ejpam-1475	364	14	,	,	PUNCT
ejpam-1475	364	15	where	where	SCONJ
ejpam-1475	364	16			NOUN
ejpam-1475	364	17			VERB
ejpam-1475	364	18			NOUN
ejpam-1475	364	19			ADJ
ejpam-1475	364	20			NOUN
ejpam-1475	364	21	p̄1(t	p̄1(t	NUM
ejpam-1475	364	22	)	)	PUNCT
ejpam-1475	364	23	=	=	SYM
ejpam-1475	364	24	1	1	NUM
ejpam-1475	364	25	2	2	NUM
ejpam-1475	364	26	h0(cosh(2	h0(cosh(2	PROPN
ejpam-1475	364	27	p	p	PROPN
ejpam-1475	364	28	h0	h0	NOUN
ejpam-1475	364	29	t)−	t)−	PROPN
ejpam-1475	364	30	3)sech2	3)sech2	NUM
ejpam-1475	364	31	(	(	PUNCT
ejpam-1475	364	32	p	p	PROPN
ejpam-1475	364	33	h0	h0	PROPN
ejpam-1475	364	34	t	t	PROPN
ejpam-1475	364	35	)	)	PUNCT
ejpam-1475	364	36	p̄2(t	p̄2(t	NOUN
ejpam-1475	364	37	)	)	PUNCT
ejpam-1475	365	1	=	=	SYM
ejpam-1475	365	2	σh0sinh(2	σh0sinh(2	NOUN
ejpam-1475	365	3	p	p	PROPN
ejpam-1475	365	4	h0	h0	PROPN
ejpam-1475	365	5	t)sech3	t)sech3	PROPN
ejpam-1475	365	6	(	(	PUNCT
ejpam-1475	365	7	p	p	PROPN
ejpam-1475	365	8	h0	h0	PROPN
ejpam-1475	365	9	t	t	PROPN
ejpam-1475	365	10	)	)	PUNCT
ejpam-1475	365	11	p̄3(t	p̄3(t	NUM
ejpam-1475	365	12	)	)	PUNCT
ejpam-1475	366	1	=	=	PUNCT
ejpam-1475	366	2	2σ	2σ	NOUN
ejpam-1475	367	1	p	p	PROPN
ejpam-1475	367	2	h0sech	h0sech	PROPN
ejpam-1475	367	3	(	(	PUNCT
ejpam-1475	367	4	p	p	PROPN
ejpam-1475	367	5	h0	h0	PROPN
ejpam-1475	367	6	t	t	PROPN
ejpam-1475	367	7	)	)	PUNCT
ejpam-1475	367	8	.	.	PUNCT
ejpam-1475	368	1	references	reference	NOUN
ejpam-1475	368	2	13	13	NUM
ejpam-1475	368	3	remark	remark	NOUN
ejpam-1475	368	4	4	4	NUM
ejpam-1475	368	5	.	.	PUNCT
ejpam-1475	369	1	this	this	DET
ejpam-1475	369	2	result	result	NOUN
ejpam-1475	369	3	can	can	AUX
ejpam-1475	369	4	be	be	AUX
ejpam-1475	369	5	obtained	obtain	VERB
ejpam-1475	369	6	by	by	ADP
ejpam-1475	369	7	limiting	limit	VERB
ejpam-1475	369	8	h0	h0	NOUN
ejpam-1475	369	9	→	→	SYM
ejpam-1475	369	10	pc0	pc0	PROPN
ejpam-1475	369	11	from	from	ADP
ejpam-1475	369	12	the	the	DET
ejpam-1475	369	13	left	left	NOUN
ejpam-1475	369	14	(	(	PUNCT
ejpam-1475	369	15	i.e.	i.e.	X
ejpam-1475	369	16	,	,	PUNCT
ejpam-1475	369	17	using	use	VERB
ejpam-1475	369	18	theorem	theorem	NOUN
ejpam-1475	369	19	10	10	NUM
ejpam-1475	369	20	)	)	PUNCT
ejpam-1475	369	21	and	and	CCONJ
ejpam-1475	369	22	adding	add	VERB
ejpam-1475	369	23	possible	possible	ADJ
ejpam-1475	369	24	changes	change	NOUN
ejpam-1475	369	25	in	in	ADP
ejpam-1475	369	26	sign	sign	NOUN
ejpam-1475	369	27	.	.	PUNCT
ejpam-1475	370	1	note	note	VERB
ejpam-1475	370	2	however	however	ADV
ejpam-1475	370	3	that	that	SCONJ
ejpam-1475	370	4	this	this	PRON
ejpam-1475	370	5	can	can	AUX
ejpam-1475	370	6	not	not	PART
ejpam-1475	370	7	be	be	AUX
ejpam-1475	370	8	done	do	VERB
ejpam-1475	370	9	from	from	ADP
ejpam-1475	370	10	the	the	DET
ejpam-1475	370	11	right	right	NOUN
ejpam-1475	370	12	(	(	PUNCT
ejpam-1475	370	13	i.e.	i.e.	X
ejpam-1475	370	14	,	,	PUNCT
ejpam-1475	370	15	using	use	VERB
ejpam-1475	370	16	theorem	theorem	NOUN
ejpam-1475	370	17	9	9	NUM
ejpam-1475	370	18	)	)	PUNCT
ejpam-1475	370	19	.	.	PUNCT
ejpam-1475	371	1	finally	finally	ADV
ejpam-1475	371	2	,	,	PUNCT
ejpam-1475	371	3	for	for	ADP
ejpam-1475	371	4	the	the	DET
ejpam-1475	371	5	invariant	invariant	ADJ
ejpam-1475	371	6	control	control	PROPN
ejpam-1475	371	7	problem	problem	NOUN
ejpam-1475	371	8	licp(2	licp(2	PROPN
ejpam-1475	371	9	)	)	PUNCT
ejpam-1475	371	10	,	,	PUNCT
ejpam-1475	371	11	there	there	PRON
ejpam-1475	371	12	is	be	VERB
ejpam-1475	371	13	only	only	ADV
ejpam-1475	371	14	one	one	NUM
ejpam-1475	371	15	typical	typical	ADJ
ejpam-1475	371	16	case	case	NOUN
ejpam-1475	371	17	.	.	PUNCT
ejpam-1475	372	1	as	as	ADP
ejpam-1475	372	2	before	before	ADV
ejpam-1475	372	3	,	,	PUNCT
ejpam-1475	372	4	we	we	PRON
ejpam-1475	372	5	graph	graph	VERB
ejpam-1475	372	6	the	the	DET
ejpam-1475	372	7	level	level	NOUN
ejpam-1475	372	8	sets	set	NOUN
ejpam-1475	372	9	of	of	ADP
ejpam-1475	372	10	h	h	NOUN
ejpam-1475	372	11	and	and	CCONJ
ejpam-1475	372	12	c	c	PROPN
ejpam-1475	372	13	and	and	CCONJ
ejpam-1475	372	14	their	their	PRON
ejpam-1475	372	15	intersection	intersection	NOUN
ejpam-1475	372	16	in	in	ADP
ejpam-1475	372	17	figure	figure	NOUN
ejpam-1475	372	18	2	2	NUM
ejpam-1475	372	19	.	.	PUNCT
ejpam-1475	373	1	a	a	DET
ejpam-1475	373	2	simple	simple	ADJ
ejpam-1475	373	3	computation	computation	NOUN
ejpam-1475	373	4	then	then	ADV
ejpam-1475	373	5	gives	give	VERB
ejpam-1475	373	6	the	the	DET
ejpam-1475	373	7	solutions	solution	NOUN
ejpam-1475	373	8	in	in	ADP
ejpam-1475	373	9	this	this	DET
ejpam-1475	373	10	case	case	NOUN
ejpam-1475	373	11	.	.	PUNCT
ejpam-1475	374	1	-2	-2	NOUN
ejpam-1475	374	2	0	0	NUM
ejpam-1475	374	3	2	2	NUM
ejpam-1475	374	4	e1	e1	NOUN
ejpam-1475	374	5	*	*	PUNCT
ejpam-1475	375	1	-2	-2	NOUN
ejpam-1475	375	2	0	0	NUM
ejpam-1475	375	3	2	2	NUM
ejpam-1475	375	4	e2	e2	NOUN
ejpam-1475	375	5	*	*	PUNCT
ejpam-1475	376	1	-2	-2	NOUN
ejpam-1475	376	2	0	0	NUM
ejpam-1475	376	3	2	2	NUM
ejpam-1475	376	4	e3	e3	VERB
ejpam-1475	376	5	*	*	PUNCT
ejpam-1475	377	1	-2	-2	NOUN
ejpam-1475	377	2	0	0	NUM
ejpam-1475	377	3	2	2	NUM
ejpam-1475	377	4	e1	e1	NOUN
ejpam-1475	377	5	*	*	PUNCT
ejpam-1475	377	6	-2	-2	NOUN
ejpam-1475	377	7	0	0	NUM
ejpam-1475	377	8	2	2	NUM
ejpam-1475	377	9	e2	e2	NOUN
ejpam-1475	377	10	*	*	PUNCT
ejpam-1475	378	1	-2	-2	NOUN
ejpam-1475	378	2	0	0	NUM
ejpam-1475	378	3	2	2	NUM
ejpam-1475	378	4	e3	e3	NOUN
ejpam-1475	378	5	*	*	PUNCT
ejpam-1475	378	6	figure	figure	NOUN
ejpam-1475	378	7	2	2	NUM
ejpam-1475	378	8	:	:	PUNCT
ejpam-1475	378	9	typical	typical	ADJ
ejpam-1475	378	10	reduced	reduced	ADJ
ejpam-1475	378	11	extremal	extremal	ADJ
ejpam-1475	378	12	of	of	ADP
ejpam-1475	378	13	licp(2	licp(2	NOUN
ejpam-1475	378	14	)	)	PUNCT
ejpam-1475	378	15	.	.	PUNCT
ejpam-1475	379	1	theorem	theorem	NOUN
ejpam-1475	379	2	12	12	NUM
ejpam-1475	379	3	.	.	PUNCT
ejpam-1475	380	1	the	the	DET
ejpam-1475	380	2	reduced	reduce	VERB
ejpam-1475	380	3	hamilton	hamilton	PROPN
ejpam-1475	380	4	equations	equations	PROPN
ejpam-1475	380	5	(	(	PUNCT
ejpam-1475	380	6	12	12	NUM
ejpam-1475	380	7	)	)	PUNCT
ejpam-1475	380	8	have	have	VERB
ejpam-1475	380	9	the	the	DET
ejpam-1475	380	10	solutions	solution	NOUN
ejpam-1475	380	11			NOUN
ejpam-1475	380	12			PRON
ejpam-1475	380	13			NOUN
ejpam-1475	380	14	p1(t	p1(t	PART
ejpam-1475	380	15	)	)	PUNCT
ejpam-1475	380	16	=	=	SYM
ejpam-1475	381	1	p	p	PROPN
ejpam-1475	381	2	c0	c0	PROPN
ejpam-1475	381	3	sin	sin	PROPN
ejpam-1475	381	4	�	�	PROPN
ejpam-1475	381	5	αt	αt	PROPN
ejpam-1475	381	6	+	+	CCONJ
ejpam-1475	381	7	t0	t0	PROPN
ejpam-1475	381	8	�	�	PROPN
ejpam-1475	381	9	p2(t	p2(t	PROPN
ejpam-1475	381	10	)	)	PUNCT
ejpam-1475	381	11	=	=	PUNCT
ejpam-1475	382	1	p	p	PROPN
ejpam-1475	382	2	c0	c0	PROPN
ejpam-1475	382	3	cos	cos	PROPN
ejpam-1475	382	4	�	�	PROPN
ejpam-1475	382	5	αt	αt	PROPN
ejpam-1475	382	6	+	+	PROPN
ejpam-1475	382	7	t0	t0	PROPN
ejpam-1475	382	8	�	�	PROPN
ejpam-1475	382	9	p3(t	p3(t	PROPN
ejpam-1475	382	10	)	)	PUNCT
ejpam-1475	382	11	=	=	SYM
ejpam-1475	382	12	h0	h0	NOUN
ejpam-1475	382	13	α	α	NOUN
ejpam-1475	382	14	−	−	PROPN
ejpam-1475	382	15	c0	c0	PROPN
ejpam-1475	382	16	2α	2α	PROPN
ejpam-1475	382	17	sin2	sin2	PROPN
ejpam-1475	382	18	�	�	PROPN
ejpam-1475	383	1	αt	αt	PROPN
ejpam-1475	383	2	+	+	PROPN
ejpam-1475	383	3	t0	t0	PROPN
ejpam-1475	383	4	�	�	PROPN
ejpam-1475	383	5	where	where	SCONJ
ejpam-1475	383	6	c0	c0	PROPN
ejpam-1475	383	7	=	=	SYM
ejpam-1475	383	8	c(p(0	c(p(0	NOUN
ejpam-1475	383	9	)	)	PUNCT
ejpam-1475	383	10	)	)	PUNCT
ejpam-1475	383	11	,	,	PUNCT
ejpam-1475	383	12	h0	h0	PROPN
ejpam-1475	383	13	=	=	SYM
ejpam-1475	383	14	h(p(0	h(p(0	PROPN
ejpam-1475	383	15	)	)	PUNCT
ejpam-1475	383	16	)	)	PUNCT
ejpam-1475	383	17	and	and	CCONJ
ejpam-1475	383	18	t0	t0	PROPN
ejpam-1475	383	19	∈	∈	PROPN
ejpam-1475	383	20	r.	r.	PROPN
ejpam-1475	383	21	references	reference	NOUN
ejpam-1475	384	1	[	[	X
ejpam-1475	384	2	1	1	X
ejpam-1475	384	3	]	]	PUNCT
ejpam-1475	384	4	a	a	DET
ejpam-1475	384	5	agrachev	agrachev	NOUN
ejpam-1475	384	6	and	and	CCONJ
ejpam-1475	384	7	y	y	PROPN
ejpam-1475	384	8	sachkov	sachkov	PROPN
ejpam-1475	384	9	.	.	PUNCT
ejpam-1475	385	1	control	control	PROPN
ejpam-1475	385	2	theory	theory	NOUN
ejpam-1475	385	3	from	from	ADP
ejpam-1475	385	4	the	the	DET
ejpam-1475	385	5	geometric	geometric	ADJ
ejpam-1475	385	6	viewpoint	viewpoint	NOUN
ejpam-1475	385	7	.	.	PUNCT
ejpam-1475	386	1	springerverlag	springerverlag	PROPN
ejpam-1475	386	2	,	,	PUNCT
ejpam-1475	386	3	berlin	berlin	PROPN
ejpam-1475	386	4	,	,	PUNCT
ejpam-1475	386	5	2004	2004	NUM
ejpam-1475	386	6	.	.	PUNCT
ejpam-1475	387	1	[	[	X
ejpam-1475	387	2	2	2	X
ejpam-1475	387	3	]	]	X
ejpam-1475	387	4	j	j	PROPN
ejpam-1475	387	5	armitage	armitage	PROPN
ejpam-1475	387	6	and	and	CCONJ
ejpam-1475	387	7	w	w	PROPN
ejpam-1475	387	8	eberlein	eberlein	PROPN
ejpam-1475	387	9	.	.	PUNCT
ejpam-1475	388	1	elliptic	elliptic	ADJ
ejpam-1475	388	2	functions	function	NOUN
ejpam-1475	388	3	.	.	PUNCT
ejpam-1475	389	1	cambridge	cambridge	PROPN
ejpam-1475	389	2	university	university	PROPN
ejpam-1475	389	3	press	press	PROPN
ejpam-1475	389	4	,	,	PUNCT
ejpam-1475	389	5	cambridge	cambridge	PROPN
ejpam-1475	389	6	,	,	PUNCT
ejpam-1475	389	7	2006	2006	NUM
ejpam-1475	389	8	.	.	PUNCT
ejpam-1475	390	1	[	[	X
ejpam-1475	390	2	3	3	NUM
ejpam-1475	390	3	]	]	X
ejpam-1475	390	4	r	r	NOUN
ejpam-1475	390	5	biggs	biggs	PROPN
ejpam-1475	390	6	and	and	CCONJ
ejpam-1475	390	7	c	c	PROPN
ejpam-1475	390	8	remsing	remsing	NOUN
ejpam-1475	390	9	.	.	PUNCT
ejpam-1475	391	1	control	control	NOUN
ejpam-1475	391	2	affine	affine	NOUN
ejpam-1475	391	3	systems	system	NOUN
ejpam-1475	391	4	on	on	ADP
ejpam-1475	391	5	solvable	solvable	ADJ
ejpam-1475	391	6	three	three	NUM
ejpam-1475	391	7	-	-	PUNCT
ejpam-1475	391	8	dimensional	dimensional	ADJ
ejpam-1475	391	9	lie	lie	NOUN
ejpam-1475	391	10	groups	group	NOUN
ejpam-1475	391	11	,	,	PUNCT
ejpam-1475	391	12	ii	ii	PROPN
ejpam-1475	391	13	(	(	PUNCT
ejpam-1475	391	14	submitted	submit	VERB
ejpam-1475	391	15	)	)	PUNCT
ejpam-1475	391	16	.	.	PUNCT
ejpam-1475	392	1	[	[	X
ejpam-1475	392	2	4	4	NUM
ejpam-1475	392	3	]	]	X
ejpam-1475	392	4	r	r	NOUN
ejpam-1475	392	5	biggs	biggs	PROPN
ejpam-1475	392	6	and	and	CCONJ
ejpam-1475	392	7	c	c	PROPN
ejpam-1475	392	8	remsing	remsing	NOUN
ejpam-1475	392	9	.	.	PUNCT
ejpam-1475	393	1	a	a	DET
ejpam-1475	393	2	note	note	NOUN
ejpam-1475	393	3	on	on	ADP
ejpam-1475	393	4	the	the	DET
ejpam-1475	393	5	affine	affine	NOUN
ejpam-1475	393	6	subspaces	subspace	NOUN
ejpam-1475	393	7	of	of	ADP
ejpam-1475	393	8	three	three	NUM
ejpam-1475	393	9	-	-	PUNCT
ejpam-1475	393	10	dimensional	dimensional	ADJ
ejpam-1475	393	11	lie	lie	NOUN
ejpam-1475	393	12	algebras	algebra	NOUN
ejpam-1475	393	13	(	(	PUNCT
ejpam-1475	393	14	submitted	submit	VERB
ejpam-1475	393	15	)	)	PUNCT
ejpam-1475	393	16	.	.	PUNCT
ejpam-1475	394	1	[	[	X
ejpam-1475	394	2	5	5	NUM
ejpam-1475	394	3	]	]	X
ejpam-1475	394	4	r	r	NOUN
ejpam-1475	394	5	biggs	biggs	PROPN
ejpam-1475	394	6	and	and	CCONJ
ejpam-1475	394	7	c	c	PROPN
ejpam-1475	394	8	remsing	remsing	NOUN
ejpam-1475	394	9	.	.	PUNCT
ejpam-1475	395	1	a	a	DET
ejpam-1475	395	2	category	category	NOUN
ejpam-1475	395	3	of	of	ADP
ejpam-1475	395	4	control	control	NOUN
ejpam-1475	395	5	systems	system	NOUN
ejpam-1475	395	6	.	.	PUNCT
ejpam-1475	396	1	to	to	PART
ejpam-1475	396	2	appear	appear	VERB
ejpam-1475	396	3	in	in	ADP
ejpam-1475	396	4	an	an	PRON
ejpam-1475	396	5	.	.	PUNCT
ejpam-1475	397	1	şt	şt	PROPN
ejpam-1475	397	2	.	.	PROPN
ejpam-1475	397	3	univ	univ	PROPN
ejpam-1475	397	4	.	.	PUNCT
ejpam-1475	398	1	ovidius	ovidius	PROPN
ejpam-1475	398	2	constanţa	constanţa	NOUN
ejpam-1475	398	3	,	,	PUNCT
ejpam-1475	398	4	20(1	20(1	NUM
ejpam-1475	398	5	)	)	PUNCT
ejpam-1475	398	6	,	,	PUNCT
ejpam-1475	398	7	2012	2012	NUM
ejpam-1475	398	8	.	.	PUNCT
ejpam-1475	399	1	references	reference	NOUN
ejpam-1475	399	2	14	14	NUM
ejpam-1475	400	1	[	[	X
ejpam-1475	400	2	6	6	NUM
ejpam-1475	400	3	]	]	X
ejpam-1475	400	4	r	r	NOUN
ejpam-1475	400	5	biggs	biggs	PROPN
ejpam-1475	400	6	and	and	CCONJ
ejpam-1475	400	7	c	c	PROPN
ejpam-1475	400	8	remsing	remsing	NOUN
ejpam-1475	400	9	.	.	PUNCT
ejpam-1475	401	1	on	on	ADP
ejpam-1475	401	2	the	the	DET
ejpam-1475	401	3	equivalence	equivalence	NOUN
ejpam-1475	401	4	of	of	ADP
ejpam-1475	401	5	control	control	NOUN
ejpam-1475	401	6	systems	system	NOUN
ejpam-1475	401	7	on	on	ADP
ejpam-1475	401	8	lie	lie	NOUN
ejpam-1475	401	9	groups	group	NOUN
ejpam-1475	401	10	.	.	PUNCT
ejpam-1475	402	1	to	to	PART
ejpam-1475	402	2	appear	appear	VERB
ejpam-1475	402	3	in	in	ADP
ejpam-1475	402	4	balkan	balkan	PROPN
ejpam-1475	402	5	j.	j.	PROPN
ejpam-1475	402	6	geometry	geometry	PROPN
ejpam-1475	402	7	appl	appl	PROPN
ejpam-1475	402	8	.	.	PROPN
ejpam-1475	402	9	,	,	PUNCT
ejpam-1475	402	10	17(1	17(1	NUM
ejpam-1475	402	11	)	)	PUNCT
ejpam-1475	402	12	,	,	PUNCT
ejpam-1475	402	13	2012	2012	NUM
ejpam-1475	402	14	.	.	PUNCT
ejpam-1475	403	1	[	[	X
ejpam-1475	403	2	7	7	NUM
ejpam-1475	403	3	]	]	SYM
ejpam-1475	403	4	b	b	X
ejpam-1475	403	5	bonnard	bonnard	NOUN
ejpam-1475	403	6	,	,	PUNCT
ejpam-1475	403	7	v	v	ADP
ejpam-1475	403	8	jurdjevic	jurdjevic	PROPN
ejpam-1475	403	9	,	,	PUNCT
ejpam-1475	403	10	i	i	PRON
ejpam-1475	403	11	kupka	kupka	PROPN
ejpam-1475	403	12	,	,	PUNCT
ejpam-1475	403	13	and	and	CCONJ
ejpam-1475	403	14	g	g	PROPN
ejpam-1475	403	15	sallet	sallet	NOUN
ejpam-1475	403	16	.	.	PUNCT
ejpam-1475	404	1	transitivity	transitivity	NOUN
ejpam-1475	404	2	of	of	ADP
ejpam-1475	404	3	families	family	NOUN
ejpam-1475	404	4	of	of	ADP
ejpam-1475	404	5	invariant	invariant	ADJ
ejpam-1475	404	6	vector	vector	NOUN
ejpam-1475	404	7	fields	field	NOUN
ejpam-1475	404	8	on	on	ADP
ejpam-1475	404	9	the	the	DET
ejpam-1475	404	10	semidirect	semidirect	NOUN
ejpam-1475	404	11	product	product	NOUN
ejpam-1475	404	12	of	of	ADP
ejpam-1475	404	13	lie	lie	NOUN
ejpam-1475	404	14	groups	group	NOUN
ejpam-1475	404	15	.	.	PUNCT
ejpam-1475	405	1	trans	trans	PROPN
ejpam-1475	405	2	.	.	PUNCT
ejpam-1475	406	1	amer	amer	PROPN
ejpam-1475	406	2	.	.	PUNCT
ejpam-1475	406	3	math	math	PROPN
ejpam-1475	406	4	.	.	PUNCT
ejpam-1475	407	1	soc	soc	PROPN
ejpam-1475	407	2	.	.	PUNCT
ejpam-1475	407	3	,	,	PUNCT
ejpam-1475	407	4	271(2):525–535	271(2):525–535	NUM
ejpam-1475	407	5	,	,	PUNCT
ejpam-1475	407	6	1982	1982	NUM
ejpam-1475	407	7	.	.	PUNCT
ejpam-1475	408	1	[	[	X
ejpam-1475	408	2	8	8	NUM
ejpam-1475	408	3	]	]	X
ejpam-1475	408	4	r	r	NOUN
ejpam-1475	408	5	brockett	brockett	PROPN
ejpam-1475	408	6	.	.	PUNCT
ejpam-1475	409	1	system	system	NOUN
ejpam-1475	409	2	theory	theory	NOUN
ejpam-1475	409	3	on	on	ADP
ejpam-1475	409	4	group	group	NOUN
ejpam-1475	409	5	manifolds	manifold	NOUN
ejpam-1475	409	6	and	and	CCONJ
ejpam-1475	409	7	coset	coset	NOUN
ejpam-1475	409	8	spaces	space	NOUN
ejpam-1475	409	9	.	.	PUNCT
ejpam-1475	410	1	siam	siam	PROPN
ejpam-1475	410	2	j.	j.	PROPN
ejpam-1475	410	3	control	control	PROPN
ejpam-1475	410	4	,	,	PUNCT
ejpam-1475	410	5	10(2):265–284	10(2):265–284	PROPN
ejpam-1475	410	6	,	,	PUNCT
ejpam-1475	410	7	1972	1972	NUM
ejpam-1475	410	8	.	.	PUNCT
ejpam-1475	411	1	[	[	X
ejpam-1475	411	2	9	9	NUM
ejpam-1475	411	3	]	]	X
ejpam-1475	411	4	d	d	X
ejpam-1475	411	5	holm	holm	PROPN
ejpam-1475	411	6	,	,	PUNCT
ejpam-1475	411	7	j	j	PROPN
ejpam-1475	411	8	marsden	marsden	PROPN
ejpam-1475	411	9	,	,	PUNCT
ejpam-1475	411	10	t	t	PROPN
ejpam-1475	411	11	ratiu	ratiu	NOUN
ejpam-1475	411	12	,	,	PUNCT
ejpam-1475	411	13	and	and	CCONJ
ejpam-1475	411	14	a	a	DET
ejpam-1475	411	15	weinstein	weinstein	NOUN
ejpam-1475	411	16	.	.	PUNCT
ejpam-1475	412	1	nonlinear	nonlinear	ADJ
ejpam-1475	412	2	stability	stability	NOUN
ejpam-1475	412	3	of	of	ADP
ejpam-1475	412	4	fluid	fluid	NOUN
ejpam-1475	412	5	and	and	CCONJ
ejpam-1475	412	6	plasma	plasma	NOUN
ejpam-1475	412	7	equilibrium	equilibrium	NOUN
ejpam-1475	412	8	.	.	PUNCT
ejpam-1475	413	1	phys	phy	NOUN
ejpam-1475	413	2	.	.	PUNCT
ejpam-1475	414	1	rep	rep	PROPN
ejpam-1475	414	2	.	.	PROPN
ejpam-1475	414	3	,	,	PUNCT
ejpam-1475	414	4	123:1–116	123:1–116	NUM
ejpam-1475	414	5	,	,	PUNCT
ejpam-1475	414	6	1985	1985	NUM
ejpam-1475	414	7	.	.	PUNCT
ejpam-1475	415	1	[	[	X
ejpam-1475	415	2	10	10	NUM
ejpam-1475	415	3	]	]	SYM
ejpam-1475	415	4	v	v	ADP
ejpam-1475	415	5	jurdjevic	jurdjevic	PROPN
ejpam-1475	415	6	.	.	PUNCT
ejpam-1475	416	1	non	non	ADJ
ejpam-1475	416	2	-	-	ADJ
ejpam-1475	416	3	euclidean	euclidean	ADJ
ejpam-1475	416	4	elastica	elastica	PROPN
ejpam-1475	416	5	.	.	PUNCT
ejpam-1475	417	1	amer	amer	PROPN
ejpam-1475	417	2	.	.	PUNCT
ejpam-1475	418	1	j.	j.	PROPN
ejpam-1475	418	2	math	math	PROPN
ejpam-1475	418	3	.	.	PUNCT
ejpam-1475	418	4	,	,	PUNCT
ejpam-1475	418	5	117(1):93–124	117(1):93–124	PROPN
ejpam-1475	418	6	,	,	PUNCT
ejpam-1475	418	7	1995	1995	NUM
ejpam-1475	418	8	.	.	PUNCT
ejpam-1475	419	1	[	[	X
ejpam-1475	419	2	11	11	NUM
ejpam-1475	419	3	]	]	SYM
ejpam-1475	419	4	v	v	ADP
ejpam-1475	419	5	jurdjevic	jurdjevic	PROPN
ejpam-1475	419	6	.	.	PUNCT
ejpam-1475	420	1	geometric	geometric	ADJ
ejpam-1475	420	2	control	control	NOUN
ejpam-1475	420	3	theory	theory	NOUN
ejpam-1475	420	4	.	.	PUNCT
ejpam-1475	421	1	cambridge	cambridge	PROPN
ejpam-1475	421	2	university	university	PROPN
ejpam-1475	421	3	press	press	PROPN
ejpam-1475	421	4	,	,	PUNCT
ejpam-1475	421	5	cambridge	cambridge	PROPN
ejpam-1475	421	6	,	,	PUNCT
ejpam-1475	421	7	1997	1997	NUM
ejpam-1475	421	8	.	.	PUNCT
ejpam-1475	422	1	[	[	X
ejpam-1475	422	2	12	12	NUM
ejpam-1475	422	3	]	]	PUNCT
ejpam-1475	422	4	v	v	ADP
ejpam-1475	422	5	jurdjevic	jurdjevic	ADJ
ejpam-1475	422	6	and	and	CCONJ
ejpam-1475	422	7	h	h	PROPN
ejpam-1475	422	8	sussmann	sussmann	PROPN
ejpam-1475	422	9	.	.	PUNCT
ejpam-1475	423	1	control	control	NOUN
ejpam-1475	423	2	systems	system	NOUN
ejpam-1475	423	3	on	on	ADP
ejpam-1475	423	4	lie	lie	NOUN
ejpam-1475	423	5	groups	group	NOUN
ejpam-1475	423	6	.	.	PUNCT
ejpam-1475	424	1	j.	j.	PROPN
ejpam-1475	424	2	diff	diff	PROPN
ejpam-1475	424	3	.	.	PUNCT
ejpam-1475	425	1	equations	equation	NOUN
ejpam-1475	425	2	,	,	PUNCT
ejpam-1475	425	3	12:313	12:313	NUM
ejpam-1475	425	4	–	–	PUNCT
ejpam-1475	425	5	329	329	NUM
ejpam-1475	425	6	,	,	PUNCT
ejpam-1475	425	7	1972	1972	NUM
ejpam-1475	425	8	.	.	PUNCT
ejpam-1475	426	1	[	[	X
ejpam-1475	426	2	13	13	NUM
ejpam-1475	426	3	]	]	X
ejpam-1475	426	4	p	p	X
ejpam-1475	426	5	krishnaprasad	krishnaprasad	ADJ
ejpam-1475	426	6	.	.	PUNCT
ejpam-1475	426	7	optimal	optimal	ADJ
ejpam-1475	426	8	control	control	NOUN
ejpam-1475	426	9	and	and	CCONJ
ejpam-1475	426	10	poisson	poisson	NOUN
ejpam-1475	426	11	reduction	reduction	NOUN
ejpam-1475	426	12	.	.	PUNCT
ejpam-1475	427	1	technical	technical	ADJ
ejpam-1475	427	2	research	research	PROPN
ejpam-1475	427	3	report	report	PROPN
ejpam-1475	427	4	t.r.93	t.r.93	PROPN
ejpam-1475	427	5	-	-	PUNCT
ejpam-1475	427	6	87	87	NUM
ejpam-1475	427	7	,	,	PUNCT
ejpam-1475	427	8	inst	inst	NOUN
ejpam-1475	427	9	.	.	PUNCT
ejpam-1475	428	1	systems	system	NOUN
ejpam-1475	428	2	research	research	PROPN
ejpam-1475	428	3	,	,	PUNCT
ejpam-1475	428	4	univ	univ	PROPN
ejpam-1475	428	5	.	.	PROPN
ejpam-1475	428	6	of	of	ADP
ejpam-1475	428	7	maryland	maryland	PROPN
ejpam-1475	428	8	,	,	PUNCT
ejpam-1475	428	9	1993	1993	NUM
ejpam-1475	428	10	.	.	PUNCT
ejpam-1475	429	1	[	[	X
ejpam-1475	429	2	14	14	NUM
ejpam-1475	429	3	]	]	X
ejpam-1475	429	4	d	d	X
ejpam-1475	429	5	lawden	lawden	PROPN
ejpam-1475	429	6	.	.	PUNCT
ejpam-1475	430	1	elliptic	elliptic	ADJ
ejpam-1475	430	2	functions	function	NOUN
ejpam-1475	430	3	and	and	CCONJ
ejpam-1475	430	4	applications	application	NOUN
ejpam-1475	430	5	.	.	PUNCT
ejpam-1475	431	1	springer	springer	NOUN
ejpam-1475	431	2	-	-	PUNCT
ejpam-1475	431	3	verlag	verlag	PROPN
ejpam-1475	431	4	,	,	PUNCT
ejpam-1475	431	5	new	new	PROPN
ejpam-1475	431	6	york	york	PROPN
ejpam-1475	431	7	,	,	PUNCT
ejpam-1475	431	8	1989	1989	NUM
ejpam-1475	431	9	.	.	PUNCT
ejpam-1475	432	1	[	[	X
ejpam-1475	432	2	15	15	NUM
ejpam-1475	432	3	]	]	X
ejpam-1475	432	4	n	n	PRON
ejpam-1475	432	5	leonard	leonard	PROPN
ejpam-1475	432	6	.	.	PUNCT
ejpam-1475	433	1	stability	stability	NOUN
ejpam-1475	433	2	of	of	ADP
ejpam-1475	433	3	a	a	DET
ejpam-1475	433	4	bottom	bottom	ADJ
ejpam-1475	433	5	-	-	PUNCT
ejpam-1475	433	6	heavy	heavy	ADJ
ejpam-1475	433	7	underwater	underwater	ADJ
ejpam-1475	433	8	vehicle	vehicle	NOUN
ejpam-1475	433	9	.	.	PUNCT
ejpam-1475	434	1	automatica	automatica	PROPN
ejpam-1475	434	2	,	,	PUNCT
ejpam-1475	434	3	33(3):331–346	33(3):331–346	PROPN
ejpam-1475	434	4	,	,	PUNCT
ejpam-1475	434	5	1997	1997	NUM
ejpam-1475	434	6	.	.	PUNCT
ejpam-1475	435	1	[	[	X
ejpam-1475	435	2	16	16	NUM
ejpam-1475	435	3	]	]	X
ejpam-1475	435	4	j	j	PROPN
ejpam-1475	435	5	marsden	marsden	PROPN
ejpam-1475	435	6	and	and	CCONJ
ejpam-1475	435	7	t	t	PROPN
ejpam-1475	435	8	ratiu	ratiu	NOUN
ejpam-1475	435	9	.	.	PUNCT
ejpam-1475	436	1	introduction	introduction	NOUN
ejpam-1475	436	2	to	to	ADP
ejpam-1475	436	3	mechanics	mechanic	NOUN
ejpam-1475	436	4	and	and	CCONJ
ejpam-1475	436	5	symmetry	symmetry	NOUN
ejpam-1475	436	6	.	.	PUNCT
ejpam-1475	437	1	springer	springer	NOUN
ejpam-1475	437	2	-	-	PUNCT
ejpam-1475	437	3	verlag	verlag	PROPN
ejpam-1475	437	4	,	,	PUNCT
ejpam-1475	437	5	new	new	PROPN
ejpam-1475	437	6	york	york	PROPN
ejpam-1475	437	7	,	,	PUNCT
ejpam-1475	437	8	second	second	ADJ
ejpam-1475	437	9	edition	edition	NOUN
ejpam-1475	437	10	,	,	PUNCT
ejpam-1475	437	11	1999	1999	NUM
ejpam-1475	437	12	.	.	PUNCT
ejpam-1475	438	1	[	[	X
ejpam-1475	438	2	17	17	NUM
ejpam-1475	438	3	]	]	X
ejpam-1475	438	4	j	j	PROPN
ejpam-1475	438	5	-	-	PUNCT
ejpam-1475	438	6	p	p	PROPN
ejpam-1475	438	7	ortega	ortega	PROPN
ejpam-1475	438	8	,	,	PUNCT
ejpam-1475	438	9	v	v	ADP
ejpam-1475	438	10	planas	planas	PROPN
ejpam-1475	438	11	-	-	PUNCT
ejpam-1475	438	12	bielsa	bielsa	NOUN
ejpam-1475	438	13	,	,	PUNCT
ejpam-1475	438	14	and	and	CCONJ
ejpam-1475	438	15	t	t	PROPN
ejpam-1475	438	16	ratiu	ratiu	NOUN
ejpam-1475	438	17	.	.	PUNCT
ejpam-1475	439	1	asymptotic	asymptotic	ADJ
ejpam-1475	439	2	and	and	CCONJ
ejpam-1475	439	3	lyapunov	lyapunov	ADJ
ejpam-1475	439	4	stability	stability	NOUN
ejpam-1475	439	5	of	of	ADP
ejpam-1475	439	6	constrained	constrain	VERB
ejpam-1475	439	7	and	and	CCONJ
ejpam-1475	439	8	poisson	poisson	PROPN
ejpam-1475	439	9	equilibria	equilibria	PROPN
ejpam-1475	439	10	.	.	PUNCT
ejpam-1475	440	1	j.	j.	PROPN
ejpam-1475	440	2	diff	diff	PROPN
ejpam-1475	440	3	.	.	PUNCT
ejpam-1475	441	1	equations	equation	NOUN
ejpam-1475	441	2	,	,	PUNCT
ejpam-1475	441	3	214:92–127	214:92–127	NUM
ejpam-1475	441	4	,	,	PUNCT
ejpam-1475	441	5	2005	2005	NUM
ejpam-1475	441	6	.	.	PUNCT
ejpam-1475	442	1	[	[	X
ejpam-1475	442	2	18	18	NUM
ejpam-1475	442	3	]	]	X
ejpam-1475	442	4	j	j	PROPN
ejpam-1475	442	5	-	-	PROPN
ejpam-1475	442	6	p	p	PROPN
ejpam-1475	442	7	ortega	ortega	PROPN
ejpam-1475	442	8	and	and	CCONJ
ejpam-1475	442	9	t	t	PROPN
ejpam-1475	442	10	ratiu	ratiu	NOUN
ejpam-1475	442	11	.	.	PUNCT
ejpam-1475	443	1	non	non	ADJ
ejpam-1475	443	2	-	-	ADJ
ejpam-1475	443	3	linear	linear	ADJ
ejpam-1475	443	4	stability	stability	NOUN
ejpam-1475	443	5	of	of	ADP
ejpam-1475	443	6	singular	singular	PROPN
ejpam-1475	443	7	relative	relative	ADJ
ejpam-1475	443	8	periodic	periodic	ADJ
ejpam-1475	443	9	orbits	orbit	NOUN
ejpam-1475	443	10	in	in	ADP
ejpam-1475	443	11	hamiltonian	hamiltonian	ADJ
ejpam-1475	443	12	systems	system	NOUN
ejpam-1475	443	13	with	with	ADP
ejpam-1475	443	14	symmetry	symmetry	NOUN
ejpam-1475	443	15	.	.	PUNCT
ejpam-1475	444	1	j.	j.	PROPN
ejpam-1475	444	2	geom	geom	PROPN
ejpam-1475	444	3	.	.	PUNCT
ejpam-1475	445	1	phys	phy	NOUN
ejpam-1475	445	2	.	.	PUNCT
ejpam-1475	445	3	,	,	PUNCT
ejpam-1475	445	4	32:160–188	32:160–188	NUM
ejpam-1475	445	5	,	,	PUNCT
ejpam-1475	445	6	1999	1999	NUM
ejpam-1475	445	7	.	.	PUNCT
ejpam-1475	446	1	[	[	X
ejpam-1475	446	2	19	19	NUM
ejpam-1475	446	3	]	]	X
ejpam-1475	446	4	m	m	VERB
ejpam-1475	446	5	puta	puta	ADJ
ejpam-1475	446	6	.	.	PUNCT
ejpam-1475	447	1	hamiltonian	hamiltonian	ADJ
ejpam-1475	447	2	mechanical	mechanical	ADJ
ejpam-1475	447	3	systems	system	NOUN
ejpam-1475	447	4	and	and	CCONJ
ejpam-1475	447	5	geometric	geometric	ADJ
ejpam-1475	447	6	quantization	quantization	NOUN
ejpam-1475	447	7	.	.	PUNCT
ejpam-1475	448	1	kluwer	kluwer	NOUN
ejpam-1475	448	2	,	,	PUNCT
ejpam-1475	448	3	dordrecht	dordrecht	PROPN
ejpam-1475	448	4	,	,	PUNCT
ejpam-1475	448	5	1993	1993	NUM
ejpam-1475	448	6	.	.	PUNCT
ejpam-1475	449	1	[	[	X
ejpam-1475	449	2	20	20	NUM
ejpam-1475	449	3	]	]	X
ejpam-1475	449	4	m	m	VERB
ejpam-1475	449	5	puta	puta	ADJ
ejpam-1475	449	6	.	.	PUNCT
ejpam-1475	450	1	optimal	optimal	ADJ
ejpam-1475	450	2	control	control	NOUN
ejpam-1475	450	3	problems	problem	NOUN
ejpam-1475	450	4	on	on	ADP
ejpam-1475	450	5	matrix	matrix	NOUN
ejpam-1475	450	6	lie	lie	NOUN
ejpam-1475	450	7	groups	group	NOUN
ejpam-1475	450	8	.	.	PUNCT
ejpam-1475	451	1	quad	quad	ADJ
ejpam-1475	451	2	.	.	PUNCT
ejpam-1475	452	1	sem	sem	PROPN
ejpam-1475	452	2	.	.	PUNCT
ejpam-1475	452	3	top	top	PROPN
ejpam-1475	452	4	.	.	PUNCT
ejpam-1475	453	1	alg	alg	PROPN
ejpam-1475	453	2	.	.	PUNCT
ejpam-1475	454	1	e	e	PROPN
ejpam-1475	454	2	diff	diff	PROPN
ejpam-1475	454	3	.	.	PROPN
ejpam-1475	454	4	,	,	PUNCT
ejpam-1475	454	5	univ	univ	PROPN
ejpam-1475	454	6	.	.	PUNCT
ejpam-1475	454	7	di	di	PROPN
ejpam-1475	454	8	roma	roma	PROPN
ejpam-1475	454	9	“	"	PUNCT
ejpam-1475	454	10	la	la	X
ejpam-1475	454	11	sapienza	sapienza	PROPN
ejpam-1475	454	12	”	"	PUNCT
ejpam-1475	454	13	,	,	PUNCT
ejpam-1475	454	14	1996	1996	NUM
ejpam-1475	454	15	.	.	PUNCT
ejpam-1475	455	1	[	[	X
ejpam-1475	455	2	21	21	NUM
ejpam-1475	455	3	]	]	X
ejpam-1475	455	4	m	m	VERB
ejpam-1475	455	5	puta	puta	ADJ
ejpam-1475	455	6	.	.	PUNCT
ejpam-1475	456	1	stability	stability	NOUN
ejpam-1475	456	2	and	and	CCONJ
ejpam-1475	456	3	control	control	NOUN
ejpam-1475	456	4	in	in	ADP
ejpam-1475	456	5	spacecraft	spacecraft	NOUN
ejpam-1475	456	6	dynamics	dynamic	NOUN
ejpam-1475	456	7	.	.	PUNCT
ejpam-1475	457	1	j.	j.	PROPN
ejpam-1475	457	2	lie	lie	PROPN
ejpam-1475	457	3	theory	theory	NOUN
ejpam-1475	457	4	,	,	PUNCT
ejpam-1475	457	5	7:269–278	7:269–278	NOUN
ejpam-1475	457	6	,	,	PUNCT
ejpam-1475	457	7	1997	1997	NUM
ejpam-1475	457	8	.	.	PUNCT
ejpam-1475	458	1	[	[	X
ejpam-1475	458	2	22	22	NUM
ejpam-1475	458	3	]	]	X
ejpam-1475	458	4	m	m	VERB
ejpam-1475	458	5	puta	puta	ADJ
ejpam-1475	458	6	,	,	PUNCT
ejpam-1475	458	7	p	p	PROPN
ejpam-1475	458	8	birtea	birtea	PROPN
ejpam-1475	458	9	,	,	PUNCT
ejpam-1475	458	10	c	c	PROPN
ejpam-1475	458	11	lăzureanu	lăzureanu	PROPN
ejpam-1475	458	12	,	,	PUNCT
ejpam-1475	458	13	c	c	NOUN
ejpam-1475	458	14	pop	pop	NOUN
ejpam-1475	458	15	,	,	PUNCT
ejpam-1475	458	16	and	and	CCONJ
ejpam-1475	458	17	r	r	NOUN
ejpam-1475	458	18	tudoran	tudoran	VERB
ejpam-1475	458	19	.	.	PUNCT
ejpam-1475	459	1	control	control	NOUN
ejpam-1475	459	2	,	,	PUNCT
ejpam-1475	459	3	integrability	integrability	NOUN
ejpam-1475	459	4	and	and	CCONJ
ejpam-1475	459	5	stability	stability	NOUN
ejpam-1475	459	6	in	in	ADP
ejpam-1475	459	7	some	some	DET
ejpam-1475	459	8	concrete	concrete	ADJ
ejpam-1475	459	9	mechanical	mechanical	ADJ
ejpam-1475	459	10	problems	problem	NOUN
ejpam-1475	459	11	on	on	ADP
ejpam-1475	459	12	matrix	matrix	NOUN
ejpam-1475	459	13	lie	lie	NOUN
ejpam-1475	459	14	groups	group	NOUN
ejpam-1475	459	15	.	.	PUNCT
ejpam-1475	460	1	quad	quad	ADJ
ejpam-1475	460	2	.	.	PUNCT
ejpam-1475	461	1	sem	sem	PROPN
ejpam-1475	461	2	.	.	PUNCT
ejpam-1475	461	3	top	top	PROPN
ejpam-1475	461	4	.	.	PUNCT
ejpam-1475	462	1	alg	alg	PROPN
ejpam-1475	462	2	.	.	PUNCT
ejpam-1475	463	1	e	e	PROPN
ejpam-1475	463	2	diff	diff	PROPN
ejpam-1475	463	3	.	.	PROPN
ejpam-1475	463	4	,	,	PUNCT
ejpam-1475	463	5	univ	univ	PROPN
ejpam-1475	463	6	.	.	PUNCT
ejpam-1475	463	7	di	di	PROPN
ejpam-1475	463	8	roma	roma	PROPN
ejpam-1475	463	9	“	"	PUNCT
ejpam-1475	463	10	la	la	X
ejpam-1475	463	11	sapienza	sapienza	PROPN
ejpam-1475	463	12	”	"	PUNCT
ejpam-1475	463	13	,	,	PUNCT
ejpam-1475	463	14	1998	1998	NUM
ejpam-1475	463	15	.	.	PUNCT
ejpam-1475	464	1	references	reference	NOUN
ejpam-1475	464	2	15	15	NUM
ejpam-1475	465	1	[	[	X
ejpam-1475	465	2	23	23	NUM
ejpam-1475	465	3	]	]	X
ejpam-1475	465	4	m	m	VERB
ejpam-1475	465	5	puta	puta	ADJ
ejpam-1475	465	6	,	,	PUNCT
ejpam-1475	465	7	s	s	PART
ejpam-1475	465	8	chirici	chirici	NOUN
ejpam-1475	465	9	,	,	PUNCT
ejpam-1475	465	10	and	and	CCONJ
ejpam-1475	465	11	a	a	DET
ejpam-1475	465	12	voitecovici	voitecovici	NOUN
ejpam-1475	465	13	.	.	PUNCT
ejpam-1475	466	1	an	an	DET
ejpam-1475	466	2	optimal	optimal	ADJ
ejpam-1475	466	3	control	control	NOUN
ejpam-1475	466	4	problem	problem	NOUN
ejpam-1475	466	5	on	on	ADP
ejpam-1475	466	6	the	the	DET
ejpam-1475	466	7	lie	lie	NOUN
ejpam-1475	466	8	group	group	NOUN
ejpam-1475	466	9	se	se	PROPN
ejpam-1475	466	10	(	(	PUNCT
ejpam-1475	466	11	2,r	2,r	NUM
ejpam-1475	466	12	)	)	PUNCT
ejpam-1475	466	13	.	.	PUNCT
ejpam-1475	467	1	publ	publ	PROPN
ejpam-1475	467	2	.	.	PUNCT
ejpam-1475	468	1	math	math	NOUN
ejpam-1475	468	2	.	.	PUNCT
ejpam-1475	469	1	debrecen	debrecen	PROPN
ejpam-1475	469	2	,	,	PUNCT
ejpam-1475	469	3	60:15–22	60:15–22	PROPN
ejpam-1475	469	4	,	,	PUNCT
ejpam-1475	469	5	2002	2002	NUM
ejpam-1475	469	6	.	.	PUNCT
ejpam-1475	470	1	[	[	X
ejpam-1475	470	2	24	24	NUM
ejpam-1475	470	3	]	]	X
ejpam-1475	470	4	m	m	VERB
ejpam-1475	470	5	puta	puta	ADJ
ejpam-1475	470	6	,	,	PUNCT
ejpam-1475	470	7	g	g	PROPN
ejpam-1475	470	8	schwab	schwab	NOUN
ejpam-1475	470	9	,	,	PUNCT
ejpam-1475	470	10	and	and	CCONJ
ejpam-1475	470	11	a	a	DET
ejpam-1475	470	12	voitecovici	voitecovici	NOUN
ejpam-1475	470	13	.	.	PUNCT
ejpam-1475	471	1	some	some	DET
ejpam-1475	471	2	remarks	remark	NOUN
ejpam-1475	471	3	on	on	ADP
ejpam-1475	471	4	an	an	DET
ejpam-1475	471	5	optimal	optimal	ADJ
ejpam-1475	471	6	control	control	NOUN
ejpam-1475	471	7	problem	problem	NOUN
ejpam-1475	471	8	on	on	ADP
ejpam-1475	471	9	the	the	DET
ejpam-1475	471	10	lie	lie	NOUN
ejpam-1475	471	11	group	group	NOUN
ejpam-1475	471	12	se	se	PROPN
ejpam-1475	471	13	(	(	PUNCT
ejpam-1475	471	14	2,r	2,r	NUM
ejpam-1475	471	15	)	)	PUNCT
ejpam-1475	471	16	.	.	PUNCT
ejpam-1475	472	1	an	an	PRON
ejpam-1475	472	2	.	.	PUNCT
ejpam-1475	473	1	şt	şt	PROPN
ejpam-1475	473	2	.	.	PROPN
ejpam-1475	473	3	univ	univ	PROPN
ejpam-1475	473	4	.	.	PUNCT
ejpam-1475	474	1	“	"	PUNCT
ejpam-1475	474	2	a.i	a.i	PROPN
ejpam-1475	474	3	.	.	PROPN
ejpam-1475	474	4	cuza	cuza	PROPN
ejpam-1475	474	5	”	"	PUNCT
ejpam-1475	474	6	iaşi	iaşi	NOUN
ejpam-1475	474	7	,	,	PUNCT
ejpam-1475	474	8	ser	ser	NOUN
ejpam-1475	474	9	.	.	PROPN
ejpam-1475	474	10	mat	mat	PROPN
ejpam-1475	474	11	.	.	PROPN
ejpam-1475	474	12	,	,	PUNCT
ejpam-1475	474	13	49(2):249–256	49(2):249–256	PROPN
ejpam-1475	474	14	,	,	PUNCT
ejpam-1475	474	15	2003	2003	NUM
ejpam-1475	474	16	.	.	PUNCT
ejpam-1475	475	1	[	[	X
ejpam-1475	475	2	25	25	NUM
ejpam-1475	475	3	]	]	X
ejpam-1475	475	4	c	c	NOUN
ejpam-1475	475	5	remsing	remsing	NOUN
ejpam-1475	475	6	.	.	PUNCT
ejpam-1475	476	1	control	control	NOUN
ejpam-1475	476	2	and	and	CCONJ
ejpam-1475	476	3	integrability	integrability	NOUN
ejpam-1475	476	4	on	on	ADP
ejpam-1475	476	5	so	so	ADV
ejpam-1475	476	6	(	(	PUNCT
ejpam-1475	476	7	3	3	NUM
ejpam-1475	476	8	)	)	PUNCT
ejpam-1475	476	9	.	.	PUNCT
ejpam-1475	477	1	in	in	ADP
ejpam-1475	477	2	lect	lect	PROPN
ejpam-1475	477	3	.	.	PUNCT
ejpam-1475	478	1	notes	note	VERB
ejpam-1475	478	2	eng	eng	PROPN
ejpam-1475	478	3	.	.	PROPN
ejpam-1475	478	4	comp	comp	PROPN
ejpam-1475	478	5	.	.	PUNCT
ejpam-1475	479	1	sci	sci	PROPN
ejpam-1475	479	2	.	.	PROPN
ejpam-1475	479	3	,	,	PUNCT
ejpam-1475	479	4	pages	page	NOUN
ejpam-1475	479	5	1705–1710	1705–1710	NUM
ejpam-1475	479	6	,	,	PUNCT
ejpam-1475	479	7	london	london	PROPN
ejpam-1475	479	8	,	,	PUNCT
ejpam-1475	479	9	u.k	u.k	PROPN
ejpam-1475	479	10	.	.	PROPN
ejpam-1475	479	11	,	,	PUNCT
ejpam-1475	479	12	2010	2010	NUM
ejpam-1475	479	13	.	.	PUNCT
ejpam-1475	480	1	[	[	X
ejpam-1475	480	2	26	26	NUM
ejpam-1475	480	3	]	]	X
ejpam-1475	480	4	c	c	NOUN
ejpam-1475	480	5	remsing	remsing	NOUN
ejpam-1475	480	6	.	.	PUNCT
ejpam-1475	481	1	integrability	integrability	NOUN
ejpam-1475	481	2	and	and	CCONJ
ejpam-1475	481	3	optimal	optimal	ADJ
ejpam-1475	481	4	control	control	NOUN
ejpam-1475	481	5	.	.	PUNCT
ejpam-1475	482	1	in	in	ADP
ejpam-1475	482	2	19th	19th	ADJ
ejpam-1475	482	3	int	int	NOUN
ejpam-1475	482	4	.	.	PUNCT
ejpam-1475	483	1	symp	symp	PROPN
ejpam-1475	483	2	.	.	PUNCT
ejpam-1475	484	1	math	math	PROPN
ejpam-1475	484	2	.	.	PUNCT
ejpam-1475	485	1	theory	theory	NOUN
ejpam-1475	485	2	of	of	ADP
ejpam-1475	485	3	networks	network	NOUN
ejpam-1475	485	4	&	&	CCONJ
ejpam-1475	485	5	syst	syst	PROPN
ejpam-1475	485	6	.	.	PROPN
ejpam-1475	485	7	,	,	PUNCT
ejpam-1475	485	8	pages	page	NOUN
ejpam-1475	485	9	1749–1754	1749–1754	NUM
ejpam-1475	485	10	,	,	PUNCT
ejpam-1475	485	11	budapest	budapest	NOUN
ejpam-1475	485	12	,	,	PUNCT
ejpam-1475	485	13	hungary	hungary	PROPN
ejpam-1475	485	14	,	,	PUNCT
ejpam-1475	485	15	2010	2010	NUM
ejpam-1475	485	16	.	.	PUNCT
ejpam-1475	486	1	[	[	X
ejpam-1475	486	2	27	27	NUM
ejpam-1475	486	3	]	]	X
ejpam-1475	486	4	c	c	NOUN
ejpam-1475	486	5	remsing	remse	VERB
ejpam-1475	486	6	.	.	PUNCT
ejpam-1475	487	1	optimal	optimal	ADJ
ejpam-1475	487	2	control	control	NOUN
ejpam-1475	487	3	and	and	CCONJ
ejpam-1475	487	4	hamilton	hamilton	PROPN
ejpam-1475	487	5	-	-	PUNCT
ejpam-1475	487	6	poisson	poisson	PROPN
ejpam-1475	487	7	formalism	formalism	NOUN
ejpam-1475	487	8	.	.	PUNCT
ejpam-1475	488	1	int	int	NOUN
ejpam-1475	488	2	.	.	PUNCT
ejpam-1475	489	1	j.	j.	PROPN
ejpam-1475	489	2	pure	pure	PROPN
ejpam-1475	489	3	appl	appl	PROPN
ejpam-1475	489	4	.	.	PUNCT
ejpam-1475	489	5	math	math	PROPN
ejpam-1475	489	6	.	.	PUNCT
ejpam-1475	489	7	,	,	PUNCT
ejpam-1475	490	1	59(1):11–17	59(1):11–17	NUM
ejpam-1475	490	2	,	,	PUNCT
ejpam-1475	490	3	2010	2010	NUM
ejpam-1475	490	4	.	.	PUNCT
ejpam-1475	491	1	[	[	X
ejpam-1475	491	2	28	28	NUM
ejpam-1475	491	3	]	]	X
ejpam-1475	491	4	c	c	NOUN
ejpam-1475	491	5	remsing	remsing	NOUN
ejpam-1475	491	6	.	.	PUNCT
ejpam-1475	492	1	control	control	NOUN
ejpam-1475	492	2	and	and	CCONJ
ejpam-1475	492	3	stability	stability	NOUN
ejpam-1475	492	4	on	on	ADP
ejpam-1475	492	5	the	the	DET
ejpam-1475	492	6	euclidean	euclidean	ADJ
ejpam-1475	492	7	group	group	NOUN
ejpam-1475	492	8	se	se	X
ejpam-1475	492	9	(	(	PUNCT
ejpam-1475	492	10	2	2	NUM
ejpam-1475	492	11	)	)	PUNCT
ejpam-1475	492	12	.	.	PUNCT
ejpam-1475	493	1	in	in	ADP
ejpam-1475	493	2	lect	lect	PROPN
ejpam-1475	493	3	.	.	PUNCT
ejpam-1475	494	1	notes	note	VERB
ejpam-1475	494	2	eng	eng	PROPN
ejpam-1475	494	3	.	.	PROPN
ejpam-1475	494	4	comp	comp	PROPN
ejpam-1475	494	5	.	.	PUNCT
ejpam-1475	495	1	sci	sci	PROPN
ejpam-1475	495	2	.	.	PROPN
ejpam-1475	495	3	,	,	PUNCT
ejpam-1475	495	4	pages	page	NOUN
ejpam-1475	495	5	225–230	225–230	NUM
ejpam-1475	495	6	,	,	PUNCT
ejpam-1475	495	7	london	london	PROPN
ejpam-1475	495	8	,	,	PUNCT
ejpam-1475	495	9	u.k	u.k	PROPN
ejpam-1475	495	10	.	.	PROPN
ejpam-1475	495	11	,	,	PUNCT
ejpam-1475	495	12	2011	2011	NUM
ejpam-1475	495	13	.	.	PUNCT
ejpam-1475	496	1	[	[	X
ejpam-1475	496	2	29	29	NUM
ejpam-1475	496	3	]	]	X
ejpam-1475	496	4	y	y	PROPN
ejpam-1475	496	5	sachkov	sachkov	PROPN
ejpam-1475	496	6	.	.	PUNCT
ejpam-1475	497	1	maxwell	maxwell	PROPN
ejpam-1475	497	2	strata	strata	PROPN
ejpam-1475	497	3	in	in	ADP
ejpam-1475	497	4	the	the	DET
ejpam-1475	497	5	euler	euler	NOUN
ejpam-1475	497	6	elastic	elastic	ADJ
ejpam-1475	497	7	problem	problem	NOUN
ejpam-1475	497	8	.	.	PUNCT
ejpam-1475	498	1	j.	j.	PROPN
ejpam-1475	498	2	dynam	dynam	PROPN
ejpam-1475	498	3	.	.	PUNCT
ejpam-1475	499	1	control	control	PROPN
ejpam-1475	499	2	syst	syst	PROPN
ejpam-1475	499	3	.	.	PUNCT
ejpam-1475	499	4	,	,	PUNCT
ejpam-1475	499	5	14(2):169–234	14(2):169–234	NUM
ejpam-1475	499	6	,	,	PUNCT
ejpam-1475	499	7	2008	2008	NUM
ejpam-1475	499	8	.	.	PUNCT
ejpam-1475	500	1	[	[	X
ejpam-1475	500	2	30	30	NUM
ejpam-1475	500	3	]	]	X
ejpam-1475	500	4	y	y	PROPN
ejpam-1475	500	5	sachkov	sachkov	PROPN
ejpam-1475	500	6	.	.	PUNCT
ejpam-1475	501	1	control	control	PROPN
ejpam-1475	501	2	theory	theory	NOUN
ejpam-1475	501	3	on	on	ADP
ejpam-1475	501	4	lie	lie	NOUN
ejpam-1475	501	5	groups	group	NOUN
ejpam-1475	501	6	.	.	PUNCT
ejpam-1475	502	1	j.	j.	PROPN
ejpam-1475	502	2	math	math	PROPN
ejpam-1475	502	3	.	.	PUNCT
ejpam-1475	503	1	sci	sci	PROPN
ejpam-1475	503	2	.	.	PROPN
ejpam-1475	503	3	,	,	PUNCT
ejpam-1475	503	4	156(3):381–439	156(3):381–439	NUM
ejpam-1475	503	5	,	,	PUNCT
ejpam-1475	503	6	2009	2009	NUM
ejpam-1475	503	7	.	.	PUNCT
ejpam-1475	504	1	[	[	X
ejpam-1475	504	2	31	31	NUM
ejpam-1475	504	3	]	]	X
ejpam-1475	504	4	g	g	PROPN
ejpam-1475	504	5	walsh	walsh	PROPN
ejpam-1475	504	6	,	,	PUNCT
ejpam-1475	504	7	r	r	NOUN
ejpam-1475	504	8	montgomery	montgomery	NOUN
ejpam-1475	504	9	,	,	PUNCT
ejpam-1475	504	10	and	and	CCONJ
ejpam-1475	504	11	s	s	VERB
ejpam-1475	504	12	sastry	sastry	NOUN
ejpam-1475	504	13	.	.	PUNCT
ejpam-1475	505	1	optimal	optimal	ADJ
ejpam-1475	505	2	path	path	NOUN
ejpam-1475	505	3	planning	planning	NOUN
ejpam-1475	505	4	on	on	ADP
ejpam-1475	505	5	matrix	matrix	NOUN
ejpam-1475	505	6	lie	lie	NOUN
ejpam-1475	505	7	groups	group	NOUN
ejpam-1475	505	8	.	.	PUNCT
ejpam-1475	506	1	in	in	ADP
ejpam-1475	506	2	33rd	33rd	ADJ
ejpam-1475	506	3	conf	conf	NOUN
ejpam-1475	506	4	.	.	PUNCT
ejpam-1475	506	5	decision	decision	NOUN
ejpam-1475	506	6	&	&	CCONJ
ejpam-1475	506	7	control	control	PROPN
ejpam-1475	506	8	,	,	PUNCT
ejpam-1475	506	9	pages	page	NOUN
ejpam-1475	506	10	1258–1263	1258–1263	NUM
ejpam-1475	506	11	,	,	PUNCT
ejpam-1475	506	12	lake	lake	PROPN
ejpam-1475	506	13	buena	buena	PROPN
ejpam-1475	506	14	vista	vista	PROPN
ejpam-1475	506	15	,	,	PUNCT
ejpam-1475	506	16	fl	fl	PROPN
ejpam-1475	506	17	,	,	PUNCT
ejpam-1475	506	18	u.s.a	u.s.a	PROPN
ejpam-1475	506	19	.	.	PROPN
ejpam-1475	506	20	,	,	PUNCT
ejpam-1475	506	21	1994	1994	NUM
ejpam-1475	506	22	.	.	PUNCT