id	sid	tid	token	lemma	pos
ejpam-534	1	1	2_534_geeta.dvi	2_534_geeta.dvi	NUM
ejpam-534	1	2	european	european	ADJ
ejpam-534	1	3	journal	journal	NOUN
ejpam-534	1	4	of	of	ADP
ejpam-534	1	5	pure	pure	ADJ
ejpam-534	1	6	and	and	CCONJ
ejpam-534	1	7	applied	apply	VERB
ejpam-534	1	8	mathematics	mathematic	NOUN
ejpam-534	1	9	vol	vol	NOUN
ejpam-534	1	10	.	.	PUNCT
ejpam-534	2	1	3	3	NUM
ejpam-534	2	2	,	,	PUNCT
ejpam-534	2	3	no	no	INTJ
ejpam-534	2	4	.	.	NOUN
ejpam-534	2	5	5	5	NUM
ejpam-534	2	6	,	,	PUNCT
ejpam-534	2	7	2010	2010	NUM
ejpam-534	2	8	,	,	PUNCT
ejpam-534	2	9	786	786	NUM
ejpam-534	2	10	-	-	SYM
ejpam-534	2	11	805	805	NUM
ejpam-534	2	12	issn	issn	PROPN
ejpam-534	2	13	1307	1307	NUM
ejpam-534	2	14	-	-	SYM
ejpam-534	2	15	5543	5543	NUM
ejpam-534	2	16	–	–	PUNCT
ejpam-534	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-534	2	18	optimality	optimality	NOUN
ejpam-534	2	19	and	and	CCONJ
ejpam-534	2	20	duality	duality	NOUN
ejpam-534	2	21	for	for	ADP
ejpam-534	2	22	second	second	ADJ
ejpam-534	2	23	-	-	PUNCT
ejpam-534	2	24	order	order	NOUN
ejpam-534	2	25	multiobjective	multiobjective	ADJ
ejpam-534	2	26	variational	variational	ADJ
ejpam-534	2	27	problems	problem	NOUN
ejpam-534	2	28	t.	t.	PROPN
ejpam-534	2	29	r.	r.	PROPN
ejpam-534	2	30	gulati	gulati	PROPN
ejpam-534	2	31	and	and	CCONJ
ejpam-534	2	32	geeta	geeta	PROPN
ejpam-534	2	33	mehndiratta∗	mehndiratta∗	PROPN
ejpam-534	2	34	department	department	PROPN
ejpam-534	2	35	of	of	ADP
ejpam-534	2	36	mathematics	mathematics	PROPN
ejpam-534	2	37	,	,	PUNCT
ejpam-534	2	38	indian	indian	PROPN
ejpam-534	2	39	institute	institute	PROPN
ejpam-534	2	40	of	of	ADP
ejpam-534	2	41	technology	technology	PROPN
ejpam-534	2	42	roorkee	roorkee	NOUN
ejpam-534	2	43	,	,	PUNCT
ejpam-534	2	44	roorkee-247	roorkee-247	NOUN
ejpam-534	2	45	667	667	NUM
ejpam-534	2	46	,	,	PUNCT
ejpam-534	2	47	india	india	PROPN
ejpam-534	2	48	abstract	abstract	NOUN
ejpam-534	2	49	.	.	PUNCT
ejpam-534	3	1	in	in	ADP
ejpam-534	3	2	this	this	DET
ejpam-534	3	3	work	work	NOUN
ejpam-534	3	4	,	,	PUNCT
ejpam-534	3	5	we	we	PRON
ejpam-534	3	6	first	first	ADV
ejpam-534	3	7	modify	modify	VERB
ejpam-534	3	8	a	a	DET
ejpam-534	3	9	converse	converse	NOUN
ejpam-534	3	10	duality	duality	NOUN
ejpam-534	3	11	theorem	theorem	VERB
ejpam-534	3	12	for	for	ADP
ejpam-534	3	13	second	second	ADJ
ejpam-534	3	14	-	-	PUNCT
ejpam-534	3	15	order	order	NOUN
ejpam-534	3	16	dual	dual	ADJ
ejpam-534	3	17	of	of	ADP
ejpam-534	3	18	a	a	DET
ejpam-534	3	19	scalar	scalar	ADJ
ejpam-534	3	20	variational	variational	ADJ
ejpam-534	3	21	problem	problem	NOUN
ejpam-534	3	22	.	.	PUNCT
ejpam-534	4	1	we	we	PRON
ejpam-534	4	2	then	then	ADV
ejpam-534	4	3	consider	consider	VERB
ejpam-534	4	4	its	its	PRON
ejpam-534	4	5	multiobjective	multiobjective	ADJ
ejpam-534	4	6	analogue	analogue	NOUN
ejpam-534	4	7	and	and	CCONJ
ejpam-534	4	8	obtain	obtain	VERB
ejpam-534	4	9	necessary	necessary	ADJ
ejpam-534	4	10	optimality	optimality	NOUN
ejpam-534	4	11	conditions	condition	NOUN
ejpam-534	4	12	and	and	CCONJ
ejpam-534	4	13	duality	duality	NOUN
ejpam-534	4	14	relations	relation	NOUN
ejpam-534	4	15	.	.	PUNCT
ejpam-534	5	1	at	at	ADP
ejpam-534	5	2	the	the	DET
ejpam-534	5	3	end	end	NOUN
ejpam-534	5	4	,	,	PUNCT
ejpam-534	5	5	the	the	DET
ejpam-534	5	6	static	static	ADJ
ejpam-534	5	7	case	case	NOUN
ejpam-534	5	8	of	of	ADP
ejpam-534	5	9	our	our	PRON
ejpam-534	5	10	problems	problem	NOUN
ejpam-534	5	11	has	have	AUX
ejpam-534	5	12	also	also	ADV
ejpam-534	5	13	been	be	AUX
ejpam-534	5	14	discussed	discuss	VERB
ejpam-534	5	15	.	.	PUNCT
ejpam-534	6	1	2000	2000	NUM
ejpam-534	6	2	mathematics	mathematic	NOUN
ejpam-534	6	3	subject	subject	NOUN
ejpam-534	6	4	classifications	classification	NOUN
ejpam-534	6	5	:	:	PUNCT
ejpam-534	6	6	90c26	90c26	NUM
ejpam-534	6	7	,	,	PUNCT
ejpam-534	6	8	90c29	90c29	NUM
ejpam-534	6	9	,	,	PUNCT
ejpam-534	6	10	90c30	90c30	NUM
ejpam-534	6	11	,	,	PUNCT
ejpam-534	6	12	90c46	90c46	NUM
ejpam-534	6	13	key	key	ADJ
ejpam-534	6	14	words	word	NOUN
ejpam-534	6	15	and	and	CCONJ
ejpam-534	6	16	phrases	phrase	NOUN
ejpam-534	6	17	:	:	PUNCT
ejpam-534	6	18	multiobjective	multiobjective	ADJ
ejpam-534	6	19	programming	programming	NOUN
ejpam-534	6	20	;	;	PUNCT
ejpam-534	6	21	variational	variational	ADJ
ejpam-534	6	22	problem	problem	NOUN
ejpam-534	6	23	;	;	PUNCT
ejpam-534	6	24	second	second	ADJ
ejpam-534	6	25	-	-	PUNCT
ejpam-534	6	26	order	order	NOUN
ejpam-534	6	27	duality	duality	NOUN
ejpam-534	6	28	;	;	PUNCT
ejpam-534	6	29	efficient	efficient	ADJ
ejpam-534	6	30	solutions	solution	NOUN
ejpam-534	6	31	;	;	PUNCT
ejpam-534	6	32	necessary	necessary	ADJ
ejpam-534	6	33	optimality	optimality	NOUN
ejpam-534	6	34	conditions	condition	NOUN
ejpam-534	6	35	1	1	NUM
ejpam-534	6	36	.	.	PUNCT
ejpam-534	7	1	introduction	introduction	NOUN
ejpam-534	7	2	consider	consider	VERB
ejpam-534	7	3	the	the	DET
ejpam-534	7	4	variational	variational	ADJ
ejpam-534	7	5	problem	problem	NOUN
ejpam-534	7	6	:	:	PUNCT
ejpam-534	7	7	(	(	PUNCT
ejpam-534	7	8	cp	cp	X
ejpam-534	7	9	)	)	PUNCT
ejpam-534	7	10	minimize	minimize	VERB
ejpam-534	7	11	b∫	b∫	NOUN
ejpam-534	7	12	a	a	DET
ejpam-534	7	13	f	f	X
ejpam-534	7	14	(	(	PUNCT
ejpam-534	7	15	t	t	PROPN
ejpam-534	7	16	,	,	PUNCT
ejpam-534	7	17	x	x	X
ejpam-534	7	18	,	,	PUNCT
ejpam-534	7	19	ẋ)d	ẋ)d	PROPN
ejpam-534	7	20	t	t	PROPN
ejpam-534	7	21	subject	subject	VERB
ejpam-534	7	22	to	to	ADP
ejpam-534	7	23	x(a	x(a	NOUN
ejpam-534	7	24	)	)	PUNCT
ejpam-534	7	25	=	=	SYM
ejpam-534	8	1	0=	0=	NUM
ejpam-534	8	2	x(b	x(b	PROPN
ejpam-534	8	3	)	)	PUNCT
ejpam-534	8	4	,	,	PUNCT
ejpam-534	8	5	g(t	g(t	PROPN
ejpam-534	8	6	,	,	PUNCT
ejpam-534	8	7	x	x	PRON
ejpam-534	8	8	,	,	PUNCT
ejpam-534	8	9	ẋ)≦	ẋ)≦	PROPN
ejpam-534	8	10	0	0	PROPN
ejpam-534	8	11	,	,	PUNCT
ejpam-534	8	12	t	t	PROPN
ejpam-534	8	13	∈	∈	PROPN
ejpam-534	9	1	i	i	PRON
ejpam-534	9	2	,	,	PUNCT
ejpam-534	9	3	where	where	SCONJ
ejpam-534	9	4	i	i	PRON
ejpam-534	9	5	=	=	PUNCT
ejpam-534	10	1	[	[	X
ejpam-534	10	2	a	a	X
ejpam-534	10	3	,	,	PUNCT
ejpam-534	10	4	b	b	X
ejpam-534	10	5	]	]	X
ejpam-534	10	6	is	be	AUX
ejpam-534	10	7	a	a	DET
ejpam-534	10	8	real	real	ADJ
ejpam-534	10	9	interval	interval	NOUN
ejpam-534	10	10	,	,	PUNCT
ejpam-534	10	11	f	f	X
ejpam-534	10	12	:	:	PUNCT
ejpam-534	11	1	i	i	PRON
ejpam-534	11	2	×	×	VERB
ejpam-534	11	3	rn	rn	PROPN
ejpam-534	11	4	×	×	PROPN
ejpam-534	11	5	rn	rn	PROPN
ejpam-534	11	6	→	→	SYM
ejpam-534	11	7	r	r	PROPN
ejpam-534	11	8	,	,	PUNCT
ejpam-534	11	9	g	g	NOUN
ejpam-534	11	10	:	:	PUNCT
ejpam-534	11	11	i	i	PRON
ejpam-534	11	12	×	×	VERB
ejpam-534	11	13	rn	rn	PROPN
ejpam-534	11	14	×	×	PROPN
ejpam-534	11	15	rn	rn	PROPN
ejpam-534	11	16	→	→	PROPN
ejpam-534	11	17	rm	rm	PROPN
ejpam-534	11	18	,	,	PUNCT
ejpam-534	11	19	x(t	x(t	PROPN
ejpam-534	11	20	)	)	PUNCT
ejpam-534	11	21	is	be	AUX
ejpam-534	11	22	an	an	DET
ejpam-534	11	23	n	n	ADV
ejpam-534	11	24	-	-	PUNCT
ejpam-534	11	25	dimensional	dimensional	ADJ
ejpam-534	11	26	piecewise	piecewise	NOUN
ejpam-534	11	27	smooth	smooth	ADJ
ejpam-534	11	28	function	function	NOUN
ejpam-534	11	29	of	of	ADP
ejpam-534	11	30	t	t	PROPN
ejpam-534	11	31	and	and	CCONJ
ejpam-534	11	32	ẋ(t	ẋ(t	NOUN
ejpam-534	11	33	)	)	PUNCT
ejpam-534	11	34	is	be	AUX
ejpam-534	11	35	the	the	DET
ejpam-534	11	36	derivative	derivative	NOUN
ejpam-534	11	37	of	of	ADP
ejpam-534	11	38	x(t	x(t	PROPN
ejpam-534	11	39	)	)	PUNCT
ejpam-534	11	40	with	with	ADP
ejpam-534	11	41	respect	respect	NOUN
ejpam-534	11	42	to	to	ADP
ejpam-534	11	43	t	t	NOUN
ejpam-534	11	44	in	in	ADP
ejpam-534	11	45	i	i	PRON
ejpam-534	11	46	.	.	PUNCT
ejpam-534	12	1	for	for	ADP
ejpam-534	12	2	notational	notational	ADJ
ejpam-534	12	3	simplicity	simplicity	NOUN
ejpam-534	12	4	,	,	PUNCT
ejpam-534	12	5	we	we	PRON
ejpam-534	12	6	write	write	VERB
ejpam-534	12	7	x(t	x(t	PROPN
ejpam-534	12	8	)	)	PUNCT
ejpam-534	12	9	and	and	CCONJ
ejpam-534	12	10	ẋ(t	ẋ(t	NOUN
ejpam-534	12	11	)	)	PUNCT
ejpam-534	12	12	as	as	ADP
ejpam-534	12	13	x	x	PROPN
ejpam-534	12	14	and	and	CCONJ
ejpam-534	12	15	ẋ	ẋ	PROPN
ejpam-534	12	16	,	,	PUNCT
ejpam-534	12	17	respectively	respectively	ADV
ejpam-534	12	18	.	.	PUNCT
ejpam-534	13	1	mond	mond	NOUN
ejpam-534	13	2	and	and	CCONJ
ejpam-534	13	3	hanson	hanson	NOUN
ejpam-534	14	1	[	[	X
ejpam-534	14	2	11	11	NUM
ejpam-534	14	3	]	]	PUNCT
ejpam-534	14	4	studied	study	VERB
ejpam-534	14	5	duality	duality	NOUN
ejpam-534	14	6	for	for	ADP
ejpam-534	14	7	the	the	DET
ejpam-534	14	8	above	above	ADJ
ejpam-534	14	9	problem	problem	NOUN
ejpam-534	14	10	under	under	ADP
ejpam-534	14	11	convexity	convexity	NOUN
ejpam-534	14	12	.	.	PUNCT
ejpam-534	15	1	the	the	DET
ejpam-534	15	2	work	work	NOUN
ejpam-534	15	3	in	in	ADP
ejpam-534	15	4	[	[	X
ejpam-534	15	5	11	11	NUM
ejpam-534	15	6	]	]	PUNCT
ejpam-534	15	7	was	be	AUX
ejpam-534	15	8	generalized	generalize	VERB
ejpam-534	15	9	to	to	ADP
ejpam-534	15	10	invex	invex	NOUN
ejpam-534	15	11	functions	function	NOUN
ejpam-534	15	12	in	in	ADP
ejpam-534	15	13	[	[	X
ejpam-534	15	14	10	10	NUM
ejpam-534	15	15	,	,	PUNCT
ejpam-534	15	16	12	12	NUM
ejpam-534	15	17	]	]	PUNCT
ejpam-534	15	18	and	and	CCONJ
ejpam-534	15	19	to	to	ADP
ejpam-534	15	20	multiobjective	multiobjective	ADJ
ejpam-534	15	21	variational	variational	ADJ
ejpam-534	15	22	problems	problem	NOUN
ejpam-534	15	23	by	by	ADP
ejpam-534	15	24	bector	bector	NOUN
ejpam-534	15	25	and	and	CCONJ
ejpam-534	15	26	husain	husain	NOUN
ejpam-534	16	1	[	[	X
ejpam-534	16	2	2	2	NUM
ejpam-534	16	3	]	]	PUNCT
ejpam-534	16	4	,	,	PUNCT
ejpam-534	16	5	bhatia	bhatia	PROPN
ejpam-534	16	6	and	and	CCONJ
ejpam-534	16	7	mehra	mehra	PROPN
ejpam-534	17	1	[	[	X
ejpam-534	17	2	3	3	NUM
ejpam-534	17	3	]	]	PUNCT
ejpam-534	17	4	,	,	PUNCT
ejpam-534	17	5	kim	kim	PROPN
ejpam-534	17	6	and	and	CCONJ
ejpam-534	17	7	kim	kim	PROPN
ejpam-534	18	1	[	[	X
ejpam-534	18	2	9	9	NUM
ejpam-534	18	3	]	]	PUNCT
ejpam-534	18	4	,	,	PUNCT
ejpam-534	18	5	ahmad	ahmad	PROPN
ejpam-534	18	6	and	and	CCONJ
ejpam-534	18	7	gulati	gulati	PROPN
ejpam-534	19	1	[	[	X
ejpam-534	19	2	1	1	X
ejpam-534	19	3	]	]	PUNCT
ejpam-534	19	4	among	among	ADP
ejpam-534	19	5	others	other	NOUN
ejpam-534	19	6	.	.	PUNCT
ejpam-534	20	1	in	in	ADP
ejpam-534	20	2	the	the	DET
ejpam-534	20	3	work	work	NOUN
ejpam-534	20	4	mentioned	mention	VERB
ejpam-534	20	5	above	above	ADV
ejpam-534	20	6	,	,	PUNCT
ejpam-534	20	7	the	the	DET
ejpam-534	20	8	boundary	boundary	ADJ
ejpam-534	20	9	conditions	condition	NOUN
ejpam-534	20	10	are	be	AUX
ejpam-534	20	11	∗corresponding	∗corresponde	VERB
ejpam-534	20	12	author	author	NOUN
ejpam-534	20	13	.	.	PUNCT
ejpam-534	21	1	email	email	NOUN
ejpam-534	21	2	addresses	address	NOUN
ejpam-534	21	3	:	:	PUNCT
ejpam-534	21	4	trgulati	trgulati	NUM
ejpam-534	21	5	�	�	NOUN
ejpam-534	21	6	gmail	gmail	NOUN
ejpam-534	21	7	.	.	PUNCT
ejpam-534	22	1	om	om	PROPN
ejpam-534	22	2	(	(	PUNCT
ejpam-534	22	3	t.	t.	PROPN
ejpam-534	22	4	gulati	gulati	PROPN
ejpam-534	22	5	)	)	PUNCT
ejpam-534	22	6	,	,	PUNCT
ejpam-534	22	7	geeta.mehndiratta	geeta.mehndiratta	PROPN
ejpam-534	22	8	�	�	PROPN
ejpam-534	22	9	rediffmail	rediffmail	NOUN
ejpam-534	22	10	.	.	PUNCT
ejpam-534	23	1	om	om	PROPN
ejpam-534	23	2	(	(	PUNCT
ejpam-534	23	3	g.	g.	PROPN
ejpam-534	23	4	mehndiratta	mehndiratta	PROPN
ejpam-534	23	5	)	)	PUNCT
ejpam-534	23	6	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-534	24	1	786	786	NUM
ejpam-534	25	1	c	c	NOUN
ejpam-534	25	2	©	©	PROPN
ejpam-534	25	3	2010	2010	NUM
ejpam-534	25	4	ejpam	ejpam	NOUN
ejpam-534	25	5	all	all	DET
ejpam-534	25	6	rights	right	NOUN
ejpam-534	25	7	reserved	reserve	VERB
ejpam-534	25	8	.	.	PUNCT
ejpam-534	26	1	t.	t.	PROPN
ejpam-534	26	2	gulati	gulati	PROPN
ejpam-534	26	3	and	and	CCONJ
ejpam-534	26	4	g.	g.	PROPN
ejpam-534	26	5	mehndiratta	mehndiratta	PROPN
ejpam-534	26	6	/	/	SYM
ejpam-534	26	7	eur	eur	PROPN
ejpam-534	26	8	.	.	PUNCT
ejpam-534	27	1	j.	j.	PROPN
ejpam-534	27	2	pure	pure	PROPN
ejpam-534	27	3	appl	appl	PROPN
ejpam-534	27	4	.	.	PROPN
ejpam-534	27	5	math	math	PROPN
ejpam-534	27	6	,	,	PUNCT
ejpam-534	27	7	3	3	NUM
ejpam-534	27	8	(	(	PUNCT
ejpam-534	27	9	2010	2010	NUM
ejpam-534	27	10	)	)	PUNCT
ejpam-534	27	11	,	,	PUNCT
ejpam-534	27	12	786	786	NUM
ejpam-534	27	13	-	-	SYM
ejpam-534	27	14	805	805	NUM
ejpam-534	27	15	787	787	NUM
ejpam-534	27	16	x(a	x(a	NOUN
ejpam-534	27	17	)	)	PUNCT
ejpam-534	27	18	=	=	SYM
ejpam-534	27	19	α	α	PROPN
ejpam-534	27	20	,	,	PUNCT
ejpam-534	27	21	x(b	x(b	PROPN
ejpam-534	27	22	)	)	PUNCT
ejpam-534	27	23	=	=	PUNCT
ejpam-534	28	1	β	β	X
ejpam-534	28	2	.	.	PUNCT
ejpam-534	29	1	recently	recently	ADV
ejpam-534	29	2	,	,	PUNCT
ejpam-534	29	3	husain	husain	PROPN
ejpam-534	29	4	et	et	PROPN
ejpam-534	29	5	al	al	PROPN
ejpam-534	29	6	.	.	PUNCT
ejpam-534	30	1	[	[	X
ejpam-534	30	2	8	8	NUM
ejpam-534	30	3	]	]	PUNCT
ejpam-534	30	4	formulated	formulate	VERB
ejpam-534	30	5	the	the	DET
ejpam-534	30	6	following	follow	VERB
ejpam-534	30	7	second	second	ADJ
ejpam-534	30	8	-	-	PUNCT
ejpam-534	30	9	order	order	NOUN
ejpam-534	30	10	dual	dual	ADJ
ejpam-534	30	11	(	(	PUNCT
ejpam-534	30	12	cd	cd	PROPN
ejpam-534	30	13	)	)	PUNCT
ejpam-534	30	14	for	for	ADP
ejpam-534	30	15	(	(	PUNCT
ejpam-534	30	16	cp	cp	NOUN
ejpam-534	30	17	):	):	PUNCT
ejpam-534	30	18	(	(	PUNCT
ejpam-534	30	19	cd	cd	PROPN
ejpam-534	30	20	)	)	PUNCT
ejpam-534	30	21	maximize	maximize	VERB
ejpam-534	30	22	b∫	b∫	PROPN
ejpam-534	30	23	a	a	DET
ejpam-534	30	24	{	{	PUNCT
ejpam-534	30	25	f	f	PROPN
ejpam-534	30	26	(	(	PUNCT
ejpam-534	30	27	t	t	PROPN
ejpam-534	30	28	,	,	PUNCT
ejpam-534	30	29	u	u	NOUN
ejpam-534	30	30	,	,	PUNCT
ejpam-534	30	31	u̇)−	u̇)−	PROPN
ejpam-534	30	32	1	1	NUM
ejpam-534	30	33	2	2	NUM
ejpam-534	30	34	β(t)t	β(t)t	NUM
ejpam-534	30	35	fβ(t)}d	fβ(t)}d	PROPN
ejpam-534	30	36	t	t	PROPN
ejpam-534	30	37	subject	subject	NOUN
ejpam-534	30	38	to	to	ADP
ejpam-534	30	39	u(a	u(a	PROPN
ejpam-534	30	40	)	)	PUNCT
ejpam-534	30	41	=	=	SYM
ejpam-534	30	42	0=	0=	PUNCT
ejpam-534	30	43	u(b	u(b	NOUN
ejpam-534	30	44	)	)	PUNCT
ejpam-534	30	45	,	,	PUNCT
ejpam-534	30	46	(	(	PUNCT
ejpam-534	30	47	1	1	X
ejpam-534	30	48	)	)	PUNCT
ejpam-534	30	49	fu	fu	NOUN
ejpam-534	30	50	+	+	CCONJ
ejpam-534	30	51	y(t)t	y(t)t	PROPN
ejpam-534	30	52	gu−	gu−	SYM
ejpam-534	30	53	d	d	X
ejpam-534	30	54	(	(	PUNCT
ejpam-534	30	55	fu̇	fu̇	PROPN
ejpam-534	30	56	+	+	NUM
ejpam-534	30	57	y(t)t	y(t)t	PROPN
ejpam-534	30	58	gu̇	gu̇	NOUN
ejpam-534	30	59	)	)	PUNCT
ejpam-534	31	1	+	+	CCONJ
ejpam-534	31	2	(	(	PUNCT
ejpam-534	31	3	f	f	X
ejpam-534	31	4	+	+	NOUN
ejpam-534	31	5	h)β(t	h)β(t	NOUN
ejpam-534	31	6	)	)	PUNCT
ejpam-534	31	7	=	=	SYM
ejpam-534	31	8	0	0	NUM
ejpam-534	31	9	,	,	PUNCT
ejpam-534	31	10	t	t	PROPN
ejpam-534	31	11	∈	∈	PROPN
ejpam-534	31	12	i	i	PRON
ejpam-534	31	13	,	,	PUNCT
ejpam-534	31	14	(	(	PUNCT
ejpam-534	31	15	2	2	X
ejpam-534	31	16	)	)	PUNCT
ejpam-534	31	17	b∫	b∫	NOUN
ejpam-534	31	18	a	a	DET
ejpam-534	31	19	{	{	PUNCT
ejpam-534	31	20	y(t)t	y(t)t	PROPN
ejpam-534	31	21	g(t	g(t	PROPN
ejpam-534	31	22	,	,	PUNCT
ejpam-534	31	23	u	u	NOUN
ejpam-534	31	24	,	,	PUNCT
ejpam-534	31	25	u̇)−	u̇)−	PROPN
ejpam-534	31	26	1	1	NUM
ejpam-534	31	27	2	2	NUM
ejpam-534	31	28	β(t)t	β(t)t	PUNCT
ejpam-534	31	29	hβ(t)}d	hβ(t)}d	PROPN
ejpam-534	31	30	t	t	NOUN
ejpam-534	31	31	≧	≧	NUM
ejpam-534	31	32	0	0	PUNCT
ejpam-534	32	1	(	(	PUNCT
ejpam-534	32	2	3	3	NUM
ejpam-534	32	3	)	)	PUNCT
ejpam-534	32	4	y(t	y(t	NUM
ejpam-534	32	5	)	)	PUNCT
ejpam-534	32	6	≧	≧	X
ejpam-534	33	1	0	0	NUM
ejpam-534	33	2	,	,	PUNCT
ejpam-534	33	3	t	t	PROPN
ejpam-534	33	4	∈	∈	PROPN
ejpam-534	34	1	i	i	PRON
ejpam-534	34	2	,	,	PUNCT
ejpam-534	34	3	(	(	PUNCT
ejpam-534	34	4	4	4	X
ejpam-534	34	5	)	)	PUNCT
ejpam-534	34	6	where	where	SCONJ
ejpam-534	34	7	the	the	DET
ejpam-534	34	8	symbols	symbol	NOUN
ejpam-534	34	9	are	be	AUX
ejpam-534	34	10	as	as	ADV
ejpam-534	34	11	defined	define	VERB
ejpam-534	34	12	in	in	ADP
ejpam-534	34	13	[	[	X
ejpam-534	34	14	8	8	NUM
ejpam-534	34	15	]	]	PUNCT
ejpam-534	34	16	.	.	PUNCT
ejpam-534	35	1	they	they	PRON
ejpam-534	35	2	established	establish	VERB
ejpam-534	35	3	the	the	DET
ejpam-534	35	4	following	follow	VERB
ejpam-534	35	5	converse	converse	NOUN
ejpam-534	35	6	duality	duality	NOUN
ejpam-534	35	7	theorem	theorem	NOUN
ejpam-534	35	8	:	:	PUNCT
ejpam-534	35	9	theorem	theorem	NOUN
ejpam-534	35	10	1	1	NUM
ejpam-534	35	11	.	.	PUNCT
ejpam-534	36	1	[	[	X
ejpam-534	36	2	converse	converse	NOUN
ejpam-534	36	3	duality	duality	NOUN
ejpam-534	36	4	]	]	PUNCT
ejpam-534	36	5	suppose	suppose	VERB
ejpam-534	36	6	that	that	SCONJ
ejpam-534	36	7	f	f	PROPN
ejpam-534	36	8	and	and	CCONJ
ejpam-534	36	9	g	g	PROPN
ejpam-534	36	10	are	be	AUX
ejpam-534	36	11	thrice	thrice	NOUN
ejpam-534	36	12	continuously	continuously	ADV
ejpam-534	36	13	differentiable	differentiable	ADJ
ejpam-534	36	14	.	.	PUNCT
ejpam-534	37	1	let	let	VERB
ejpam-534	37	2	(	(	PUNCT
ejpam-534	37	3	x̄(t	x̄(t	PROPN
ejpam-534	37	4	)	)	PUNCT
ejpam-534	37	5	,	,	PUNCT
ejpam-534	37	6	ȳ(t	ȳ(t	PROPN
ejpam-534	37	7	)	)	PUNCT
ejpam-534	37	8	,	,	PUNCT
ejpam-534	37	9	β̄(t	β̄(t	NOUN
ejpam-534	37	10	)	)	PUNCT
ejpam-534	37	11	)	)	PUNCT
ejpam-534	38	1	be	be	AUX
ejpam-534	38	2	an	an	DET
ejpam-534	38	3	optimal	optimal	ADJ
ejpam-534	38	4	solution	solution	NOUN
ejpam-534	38	5	of	of	ADP
ejpam-534	38	6	(	(	PUNCT
ejpam-534	38	7	cd	cd	PROPN
ejpam-534	38	8	)	)	PUNCT
ejpam-534	38	9	at	at	ADP
ejpam-534	38	10	which	which	PRON
ejpam-534	38	11	(	(	PUNCT
ejpam-534	38	12	a1	a1	PROPN
ejpam-534	38	13	)	)	PUNCT
ejpam-534	38	14	the	the	DET
ejpam-534	38	15	hessian	hessian	ADJ
ejpam-534	38	16	matrices	matrice	VERB
ejpam-534	38	17	f	f	PROPN
ejpam-534	38	18	and	and	CCONJ
ejpam-534	38	19	h	h	NOUN
ejpam-534	38	20	are	be	AUX
ejpam-534	38	21	not	not	PART
ejpam-534	38	22	the	the	DET
ejpam-534	38	23	multiple	multiple	NOUN
ejpam-534	38	24	of	of	ADP
ejpam-534	38	25	each	each	DET
ejpam-534	38	26	other	other	ADJ
ejpam-534	38	27	,	,	PUNCT
ejpam-534	38	28	(	(	PUNCT
ejpam-534	38	29	a2	a2	PROPN
ejpam-534	38	30	)	)	PUNCT
ejpam-534	38	31	ȳ(t)t	ȳ(t)t	PROPN
ejpam-534	39	1	gx	gx	PROPN
ejpam-534	39	2	−	−	PROPN
ejpam-534	40	1	d	d	NOUN
ejpam-534	40	2	ȳ(t)t	ȳ(t)t	NOUN
ejpam-534	40	3	g	g	PROPN
ejpam-534	40	4	ẋ	ẋ	PROPN
ejpam-534	41	1	6=	6=	ADP
ejpam-534	41	2	0	0	NUM
ejpam-534	41	3	,	,	PUNCT
ejpam-534	41	4	(	(	PUNCT
ejpam-534	41	5	a3	a3	NOUN
ejpam-534	41	6	)	)	PUNCT
ejpam-534	41	7	(	(	PUNCT
ejpam-534	41	8	i	i	NOUN
ejpam-534	41	9	)	)	PUNCT
ejpam-534	41	10	b∫	b∫	PROPN
ejpam-534	41	11	a	a	DET
ejpam-534	41	12	β̄(t)t	β̄(t)t	NOUN
ejpam-534	41	13	(	(	PUNCT
ejpam-534	41	14	ȳ(t)t	ȳ(t)t	PROPN
ejpam-534	41	15	gx	gx	PROPN
ejpam-534	42	1	−	−	PROPN
ejpam-534	43	1	d	d	NOUN
ejpam-534	43	2	ȳ(t)t	ȳ(t)t	NOUN
ejpam-534	43	3	g	g	PROPN
ejpam-534	43	4	ẋ)d	ẋ)d	PROPN
ejpam-534	43	5	t	t	PROPN
ejpam-534	43	6	≧	≧	PUNCT
ejpam-534	43	7	0	0	PUNCT
ejpam-534	44	1	and	and	CCONJ
ejpam-534	44	2	b∫	b∫	PROPN
ejpam-534	44	3	a	a	DET
ejpam-534	44	4	β̄(t)t	β̄(t)t	NOUN
ejpam-534	44	5	hβ̄(t)d	hβ̄(t)d	PROPN
ejpam-534	44	6	t	t	X
ejpam-534	44	7	>	>	X
ejpam-534	44	8	0	0	NUM
ejpam-534	44	9	,	,	PUNCT
ejpam-534	44	10	or	or	CCONJ
ejpam-534	44	11	(	(	PUNCT
ejpam-534	44	12	ii	ii	NOUN
ejpam-534	44	13	)	)	PUNCT
ejpam-534	44	14	b∫	b∫	PROPN
ejpam-534	44	15	a	a	DET
ejpam-534	44	16	β̄(t)t	β̄(t)t	NOUN
ejpam-534	44	17	(	(	PUNCT
ejpam-534	44	18	ȳ(t)t	ȳ(t)t	PROPN
ejpam-534	44	19	gx	gx	PROPN
ejpam-534	44	20	−	−	PROPN
ejpam-534	45	1	d	d	NOUN
ejpam-534	45	2	ȳ(t)t	ȳ(t)t	NOUN
ejpam-534	45	3	g	g	PROPN
ejpam-534	45	4	ẋ)d	ẋ)d	PROPN
ejpam-534	45	5	t	t	PROPN
ejpam-534	45	6	≦	≦	PROPN
ejpam-534	45	7	0	0	PUNCT
ejpam-534	45	8	and	and	CCONJ
ejpam-534	45	9	b∫	b∫	PROPN
ejpam-534	45	10	a	a	DET
ejpam-534	45	11	β̄(t)t	β̄(t)t	NOUN
ejpam-534	46	1	hβ̄(t)d	hβ̄(t)d	PROPN
ejpam-534	46	2	t	t	X
ejpam-534	46	3	<	<	X
ejpam-534	46	4	0	0	NUM
ejpam-534	46	5	.	.	PUNCT
ejpam-534	47	1	if	if	SCONJ
ejpam-534	47	2	,	,	PUNCT
ejpam-534	47	3	for	for	ADP
ejpam-534	47	4	all	all	PRON
ejpam-534	47	5	feasible	feasible	ADJ
ejpam-534	47	6	(	(	PUNCT
ejpam-534	47	7	x(t	x(t	PROPN
ejpam-534	47	8	)	)	PUNCT
ejpam-534	47	9	,	,	PUNCT
ejpam-534	47	10	y(t),β(t	y(t),β(t	NOUN
ejpam-534	47	11	)	)	PUNCT
ejpam-534	47	12	)	)	PUNCT
ejpam-534	47	13	,	,	PUNCT
ejpam-534	47	14	b∫	b∫	NOUN
ejpam-534	47	15	a	a	DET
ejpam-534	47	16	f	f	X
ejpam-534	47	17	(	(	PUNCT
ejpam-534	47	18	t	t	PROPN
ejpam-534	47	19	,	,	PUNCT
ejpam-534	47	20	.	.	PUNCT
ejpam-534	47	21	,	,	PUNCT
ejpam-534	47	22	.)d	.)d	PROPN
ejpam-534	47	23	t	t	PROPN
ejpam-534	47	24	is	be	AUX
ejpam-534	47	25	second	second	ADJ
ejpam-534	47	26	-	-	PUNCT
ejpam-534	47	27	order	order	NOUN
ejpam-534	47	28	pseudoinvex	pseudoinvex	NOUN
ejpam-534	47	29	and	and	CCONJ
ejpam-534	47	30	b∫	b∫	NOUN
ejpam-534	47	31	a	a	DET
ejpam-534	47	32	y(t)t	y(t)t	PROPN
ejpam-534	47	33	g(t	g(t	PROPN
ejpam-534	47	34	,	,	PUNCT
ejpam-534	47	35	.	.	PUNCT
ejpam-534	47	36	,	,	PUNCT
ejpam-534	47	37	.)d	.)d	PROPN
ejpam-534	47	38	t	t	PROPN
ejpam-534	47	39	is	be	AUX
ejpam-534	47	40	second	second	ADJ
ejpam-534	47	41	-	-	PUNCT
ejpam-534	47	42	order	order	NOUN
ejpam-534	47	43	quasiinvex	quasiinvex	NOUN
ejpam-534	47	44	with	with	ADP
ejpam-534	47	45	respect	respect	NOUN
ejpam-534	47	46	to	to	ADP
ejpam-534	47	47	the	the	DET
ejpam-534	47	48	same	same	ADJ
ejpam-534	47	49	η	η	PROPN
ejpam-534	47	50	,	,	PUNCT
ejpam-534	47	51	then	then	ADV
ejpam-534	47	52	x̄(t	x̄(t	NUM
ejpam-534	47	53	)	)	PUNCT
ejpam-534	47	54	is	be	AUX
ejpam-534	47	55	an	an	DET
ejpam-534	47	56	optimal	optimal	ADJ
ejpam-534	47	57	solution	solution	NOUN
ejpam-534	47	58	of	of	ADP
ejpam-534	47	59	(	(	PUNCT
ejpam-534	47	60	cp	cp	NOUN
ejpam-534	47	61	)	)	PUNCT
ejpam-534	47	62	.	.	PUNCT
ejpam-534	48	1	this	this	DET
ejpam-534	48	2	result	result	NOUN
ejpam-534	48	3	has	have	AUX
ejpam-534	48	4	been	be	AUX
ejpam-534	48	5	established	establish	VERB
ejpam-534	48	6	by	by	ADP
ejpam-534	48	7	first	first	ADV
ejpam-534	48	8	proving	prove	VERB
ejpam-534	48	9	that	that	SCONJ
ejpam-534	48	10	β̄(t	β̄(t	NUM
ejpam-534	48	11	)	)	PUNCT
ejpam-534	48	12	=	=	SYM
ejpam-534	48	13	0	0	NUM
ejpam-534	48	14	,	,	PUNCT
ejpam-534	48	15	t	t	PROPN
ejpam-534	49	1	∈	∈	PROPN
ejpam-534	50	1	i	i	PRON
ejpam-534	50	2	.	.	PUNCT
ejpam-534	51	1	it	it	PRON
ejpam-534	51	2	is	be	AUX
ejpam-534	51	3	obvious	obvious	ADJ
ejpam-534	51	4	that	that	SCONJ
ejpam-534	51	5	the	the	DET
ejpam-534	51	6	assumption	assumption	NOUN
ejpam-534	51	7	b∫	b∫	PROPN
ejpam-534	51	8	a	a	DET
ejpam-534	51	9	β̄(t)t	β̄(t)t	NOUN
ejpam-534	51	10	hβ̄(t)d	hβ̄(t)d	PROPN
ejpam-534	51	11	t	t	X
ejpam-534	51	12	>	>	X
ejpam-534	51	13	0	0	PUNCT
ejpam-534	52	1	(	(	PUNCT
ejpam-534	52	2	or	or	CCONJ
ejpam-534	52	3	<	<	X
ejpam-534	52	4	0	0	NUM
ejpam-534	52	5	)	)	PUNCT
ejpam-534	53	1	and	and	CCONJ
ejpam-534	53	2	the	the	DET
ejpam-534	53	3	conclusion	conclusion	NOUN
ejpam-534	53	4	β̄(t	β̄(t	NUM
ejpam-534	53	5	)	)	PUNCT
ejpam-534	53	6	=	=	SYM
ejpam-534	53	7	0	0	NUM
ejpam-534	53	8	,	,	PUNCT
ejpam-534	53	9	t	t	PROPN
ejpam-534	53	10	∈	∈	PROPN
ejpam-534	54	1	i	i	PRON
ejpam-534	54	2	,	,	PUNCT
ejpam-534	54	3	are	be	AUX
ejpam-534	54	4	inconsistent	inconsistent	ADJ
ejpam-534	54	5	.	.	PUNCT
ejpam-534	55	1	moreover	moreover	ADV
ejpam-534	55	2	,	,	PUNCT
ejpam-534	55	3	assumption	assumption	NOUN
ejpam-534	55	4	(	(	PUNCT
ejpam-534	55	5	a1	a1	NOUN
ejpam-534	55	6	)	)	PUNCT
ejpam-534	55	7	and	and	CCONJ
ejpam-534	55	8	equation	equation	NOUN
ejpam-534	55	9	(	(	PUNCT
ejpam-534	55	10	3.11	3.11	NUM
ejpam-534	55	11	)	)	PUNCT
ejpam-534	55	12	in	in	ADP
ejpam-534	55	13	[	[	X
ejpam-534	55	14	8	8	NUM
ejpam-534	55	15	]	]	PUNCT
ejpam-534	55	16	,	,	PUNCT
ejpam-534	55	17	namely	namely	ADV
ejpam-534	55	18	(	(	PUNCT
ejpam-534	55	19	λ(t	λ(t	NOUN
ejpam-534	55	20	)	)	PUNCT
ejpam-534	56	1	+	+	CCONJ
ejpam-534	56	2	αβ̄(t))t	αβ̄(t))t	NOUN
ejpam-534	56	3	f	f	X
ejpam-534	57	1	+	+	CCONJ
ejpam-534	57	2	(	(	PUNCT
ejpam-534	57	3	λ(t	λ(t	NOUN
ejpam-534	57	4	)	)	PUNCT
ejpam-534	58	1	+	+	CCONJ
ejpam-534	58	2	γβ̄(t))t	γβ̄(t))t	NUM
ejpam-534	58	3	h	h	NOUN
ejpam-534	59	1	=	=	SYM
ejpam-534	59	2	0	0	PROPN
ejpam-534	59	3	,	,	PUNCT
ejpam-534	59	4	t	t	PROPN
ejpam-534	59	5	∈	∈	PROPN
ejpam-534	60	1	i	i	PRON
ejpam-534	60	2	,	,	PUNCT
ejpam-534	60	3	do	do	AUX
ejpam-534	60	4	not	not	PART
ejpam-534	60	5	imply	imply	VERB
ejpam-534	60	6	λ(t	λ(t	PRON
ejpam-534	60	7	)	)	PUNCT
ejpam-534	61	1	+	+	X
ejpam-534	62	1	αβ̄(t	αβ̄(t	X
ejpam-534	62	2	)	)	PUNCT
ejpam-534	62	3	=	=	SYM
ejpam-534	62	4	0	0	NUM
ejpam-534	62	5	,	,	PUNCT
ejpam-534	62	6	t	t	PROPN
ejpam-534	62	7	∈	∈	PROPN
ejpam-534	63	1	i	i	PRON
ejpam-534	63	2	and	and	CCONJ
ejpam-534	63	3	λ(t	λ(t	NOUN
ejpam-534	63	4	)	)	PUNCT
ejpam-534	64	1	+	+	CCONJ
ejpam-534	64	2	γβ̄(t	γβ̄(t	NOUN
ejpam-534	64	3	)	)	PUNCT
ejpam-534	64	4	=	=	SYM
ejpam-534	64	5	0	0	NUM
ejpam-534	64	6	,	,	PUNCT
ejpam-534	65	1	t	t	PROPN
ejpam-534	65	2	∈	∈	PROPN
ejpam-534	66	1	i	i	PRON
ejpam-534	66	2	.	.	PUNCT
ejpam-534	67	1	one	one	NUM
ejpam-534	67	2	needs	need	VERB
ejpam-534	67	3	to	to	PART
ejpam-534	67	4	assume	assume	VERB
ejpam-534	67	5	that	that	SCONJ
ejpam-534	67	6	the	the	DET
ejpam-534	67	7	rows	row	NOUN
ejpam-534	67	8	of	of	ADP
ejpam-534	67	9	f	f	PROPN
ejpam-534	67	10	and	and	CCONJ
ejpam-534	67	11	h	h	NOUN
ejpam-534	67	12	are	be	AUX
ejpam-534	67	13	linearly	linearly	ADV
ejpam-534	67	14	independent	independent	ADJ
ejpam-534	67	15	.	.	PUNCT
ejpam-534	68	1	t.	t.	PROPN
ejpam-534	68	2	gulati	gulati	PROPN
ejpam-534	68	3	and	and	CCONJ
ejpam-534	68	4	g.	g.	PROPN
ejpam-534	68	5	mehndiratta	mehndiratta	PROPN
ejpam-534	68	6	/	/	SYM
ejpam-534	68	7	eur	eur	PROPN
ejpam-534	68	8	.	.	PUNCT
ejpam-534	69	1	j.	j.	PROPN
ejpam-534	69	2	pure	pure	PROPN
ejpam-534	69	3	appl	appl	PROPN
ejpam-534	69	4	.	.	PROPN
ejpam-534	69	5	math	math	PROPN
ejpam-534	69	6	,	,	PUNCT
ejpam-534	69	7	3	3	NUM
ejpam-534	69	8	(	(	PUNCT
ejpam-534	69	9	2010	2010	NUM
ejpam-534	69	10	)	)	PUNCT
ejpam-534	69	11	,	,	PUNCT
ejpam-534	69	12	786	786	NUM
ejpam-534	69	13	-	-	SYM
ejpam-534	69	14	805	805	NUM
ejpam-534	69	15	788	788	NUM
ejpam-534	69	16	this	this	DET
ejpam-534	69	17	paper	paper	NOUN
ejpam-534	69	18	is	be	AUX
ejpam-534	69	19	organized	organize	VERB
ejpam-534	69	20	as	as	SCONJ
ejpam-534	69	21	follows	follow	VERB
ejpam-534	69	22	.	.	PUNCT
ejpam-534	70	1	in	in	ADP
ejpam-534	70	2	section	section	NOUN
ejpam-534	70	3	2	2	NUM
ejpam-534	70	4	,	,	PUNCT
ejpam-534	70	5	we	we	PRON
ejpam-534	70	6	prove	prove	VERB
ejpam-534	70	7	a	a	DET
ejpam-534	70	8	converse	converse	NOUN
ejpam-534	70	9	duality	duality	NOUN
ejpam-534	70	10	theorem	theorem	VERB
ejpam-534	70	11	modifying	modify	VERB
ejpam-534	70	12	theorem	theorem	NOUN
ejpam-534	70	13	1	1	NUM
ejpam-534	70	14	.	.	PUNCT
ejpam-534	71	1	in	in	ADP
ejpam-534	71	2	section	section	NOUN
ejpam-534	71	3	3	3	NUM
ejpam-534	71	4	,	,	PUNCT
ejpam-534	71	5	we	we	PRON
ejpam-534	71	6	consider	consider	VERB
ejpam-534	71	7	the	the	DET
ejpam-534	71	8	multiobjective	multiobjective	ADJ
ejpam-534	71	9	analogue	analogue	NOUN
ejpam-534	71	10	of	of	ADP
ejpam-534	71	11	problem	problem	NOUN
ejpam-534	71	12	(	(	PUNCT
ejpam-534	71	13	cp	cp	NOUN
ejpam-534	71	14	)	)	PUNCT
ejpam-534	71	15	.	.	PUNCT
ejpam-534	72	1	this	this	DET
ejpam-534	72	2	section	section	NOUN
ejpam-534	72	3	also	also	ADV
ejpam-534	72	4	contains	contain	VERB
ejpam-534	72	5	notations	notation	NOUN
ejpam-534	72	6	and	and	CCONJ
ejpam-534	72	7	preliminaries	preliminary	NOUN
ejpam-534	72	8	.	.	PUNCT
ejpam-534	73	1	the	the	DET
ejpam-534	73	2	necessary	necessary	ADJ
ejpam-534	73	3	optimality	optimality	NOUN
ejpam-534	73	4	conditions	condition	NOUN
ejpam-534	73	5	for	for	ADP
ejpam-534	73	6	an	an	DET
ejpam-534	73	7	efficient	efficient	ADJ
ejpam-534	73	8	solution	solution	NOUN
ejpam-534	73	9	are	be	AUX
ejpam-534	73	10	obtained	obtain	VERB
ejpam-534	73	11	in	in	ADP
ejpam-534	73	12	section	section	NOUN
ejpam-534	73	13	4	4	NUM
ejpam-534	73	14	.	.	PUNCT
ejpam-534	74	1	the	the	DET
ejpam-534	74	2	duality	duality	NOUN
ejpam-534	74	3	results	result	NOUN
ejpam-534	74	4	are	be	AUX
ejpam-534	74	5	established	establish	VERB
ejpam-534	74	6	in	in	ADP
ejpam-534	74	7	section	section	NOUN
ejpam-534	74	8	5	5	NUM
ejpam-534	74	9	.	.	PUNCT
ejpam-534	75	1	the	the	DET
ejpam-534	75	2	static	static	ADJ
ejpam-534	75	3	case	case	NOUN
ejpam-534	75	4	of	of	ADP
ejpam-534	75	5	our	our	PRON
ejpam-534	75	6	problems	problem	NOUN
ejpam-534	75	7	has	have	AUX
ejpam-534	75	8	been	be	AUX
ejpam-534	75	9	given	give	VERB
ejpam-534	75	10	in	in	ADP
ejpam-534	75	11	the	the	DET
ejpam-534	75	12	last	last	ADJ
ejpam-534	75	13	section	section	NOUN
ejpam-534	75	14	.	.	PUNCT
ejpam-534	76	1	2	2	X
ejpam-534	76	2	.	.	X
ejpam-534	76	3	converse	converse	NOUN
ejpam-534	76	4	duality	duality	NOUN
ejpam-534	76	5	we	we	PRON
ejpam-534	76	6	denote	denote	VERB
ejpam-534	76	7	the	the	DET
ejpam-534	76	8	first	first	ADJ
ejpam-534	76	9	partial	partial	ADJ
ejpam-534	76	10	derivatives	derivative	NOUN
ejpam-534	76	11	of	of	ADP
ejpam-534	76	12	f	f	PROPN
ejpam-534	76	13	with	with	ADP
ejpam-534	76	14	respect	respect	NOUN
ejpam-534	76	15	to	to	ADP
ejpam-534	76	16	t	t	PROPN
ejpam-534	76	17	,	,	PUNCT
ejpam-534	76	18	x	x	PUNCT
ejpam-534	76	19	and	and	CCONJ
ejpam-534	76	20	ẋ	ẋ	PROPN
ejpam-534	76	21	,	,	PUNCT
ejpam-534	76	22	respectively	respectively	ADV
ejpam-534	76	23	,	,	PUNCT
ejpam-534	76	24	by	by	ADP
ejpam-534	76	25	ft	ft	PRON
ejpam-534	76	26	,	,	PUNCT
ejpam-534	76	27	fx	fx	PROPN
ejpam-534	76	28	and	and	CCONJ
ejpam-534	76	29	f	f	PROPN
ejpam-534	76	30	ẋ	ẋ	PROPN
ejpam-534	77	1	such	such	ADJ
ejpam-534	77	2	that	that	DET
ejpam-534	77	3	fx	fx	NOUN
ejpam-534	77	4	=	=	SYM
ejpam-534	77	5	(	(	PUNCT
ejpam-534	77	6	∂	∂	NUM
ejpam-534	77	7	f	f	PROPN
ejpam-534	77	8	∂	∂	NUM
ejpam-534	77	9	x1	x1	PROPN
ejpam-534	77	10	,	,	PUNCT
ejpam-534	77	11	∂	∂	NUM
ejpam-534	77	12	f	f	PROPN
ejpam-534	77	13	∂	∂	NUM
ejpam-534	77	14	x2	x2	NOUN
ejpam-534	77	15	,	,	PUNCT
ejpam-534	77	16	.	.	PUNCT
ejpam-534	77	17	.	.	PUNCT
ejpam-534	78	1	.	.	PUNCT
ejpam-534	79	1	,	,	PUNCT
ejpam-534	79	2	∂	∂	NUM
ejpam-534	79	3	f	f	PROPN
ejpam-534	79	4	∂	∂	PROPN
ejpam-534	79	5	xn	xn	PROPN
ejpam-534	79	6	)	)	PUNCT
ejpam-534	79	7	t	t	PROPN
ejpam-534	79	8	and	and	CCONJ
ejpam-534	79	9	f	f	PROPN
ejpam-534	79	10	ẋ	ẋ	PROPN
ejpam-534	80	1	=	=	PRON
ejpam-534	80	2	(	(	PUNCT
ejpam-534	80	3	∂	∂	NOUN
ejpam-534	80	4	f	f	NOUN
ejpam-534	80	5	∂	∂	NOUN
ejpam-534	81	1	ẋ1	ẋ1	PROPN
ejpam-534	81	2	,	,	PUNCT
ejpam-534	81	3	∂	∂	NOUN
ejpam-534	81	4	f	f	NOUN
ejpam-534	81	5	∂	∂	NUM
ejpam-534	82	1	ẋ2	ẋ2	PROPN
ejpam-534	82	2	,	,	PUNCT
ejpam-534	82	3	.	.	PUNCT
ejpam-534	82	4	.	.	PUNCT
ejpam-534	83	1	.	.	PUNCT
ejpam-534	84	1	,	,	PUNCT
ejpam-534	84	2	∂	∂	NUM
ejpam-534	84	3	f	f	NOUN
ejpam-534	84	4	∂	∂	PROPN
ejpam-534	84	5	ẋn	ẋn	PROPN
ejpam-534	84	6	)	)	PUNCT
ejpam-534	84	7	t	t	PROPN
ejpam-534	84	8	.	.	PUNCT
ejpam-534	85	1	the	the	DET
ejpam-534	85	2	matrices	matrix	NOUN
ejpam-534	85	3	fx	fx	NOUN
ejpam-534	85	4	x	x	PUNCT
ejpam-534	85	5	and	and	CCONJ
ejpam-534	85	6	gx	gx	PROPN
ejpam-534	85	7	are	be	AUX
ejpam-534	85	8	of	of	ADP
ejpam-534	85	9	order	order	NOUN
ejpam-534	85	10	n×n	n×n	PROPN
ejpam-534	85	11	and	and	CCONJ
ejpam-534	85	12	n×m	n×m	PROPN
ejpam-534	85	13	,	,	PUNCT
ejpam-534	85	14	respectively	respectively	ADV
ejpam-534	85	15	.	.	PUNCT
ejpam-534	86	1	similarly	similarly	ADV
ejpam-534	86	2	fx	fx	ADP
ejpam-534	86	3	ẋ	ẋ	PROPN
ejpam-534	87	1	,	,	PUNCT
ejpam-534	87	2	f	f	PROPN
ejpam-534	87	3	ẋ	ẋ	PROPN
ejpam-534	87	4	ẋ	ẋ	PROPN
ejpam-534	87	5	and	and	CCONJ
ejpam-534	87	6	the	the	DET
ejpam-534	87	7	partial	partial	ADJ
ejpam-534	87	8	derivatives	derivative	NOUN
ejpam-534	87	9	of	of	ADP
ejpam-534	87	10	g	g	PROPN
ejpam-534	87	11	j	j	PROPN
ejpam-534	87	12	are	be	AUX
ejpam-534	87	13	also	also	ADV
ejpam-534	87	14	defined	define	VERB
ejpam-534	87	15	.	.	PUNCT
ejpam-534	88	1	all	all	DET
ejpam-534	88	2	derivative	derivative	NOUN
ejpam-534	88	3	of	of	ADP
ejpam-534	88	4	x	x	X
ejpam-534	88	5	,	,	PUNCT
ejpam-534	88	6	and	and	CCONJ
ejpam-534	88	7	all	all	DET
ejpam-534	88	8	partial	partial	ADJ
ejpam-534	88	9	and	and	CCONJ
ejpam-534	88	10	total	total	ADJ
ejpam-534	88	11	derivatives	derivative	NOUN
ejpam-534	88	12	of	of	ADP
ejpam-534	88	13	f	f	PROPN
ejpam-534	88	14	and	and	CCONJ
ejpam-534	88	15	g	g	PROPN
ejpam-534	88	16	used	use	VERB
ejpam-534	88	17	in	in	ADP
ejpam-534	88	18	this	this	DET
ejpam-534	88	19	section	section	NOUN
ejpam-534	88	20	are	be	AUX
ejpam-534	88	21	assumed	assume	VERB
ejpam-534	88	22	to	to	PART
ejpam-534	88	23	be	be	AUX
ejpam-534	88	24	continuous	continuous	ADJ
ejpam-534	88	25	.	.	PUNCT
ejpam-534	89	1	let	let	VERB
ejpam-534	89	2	the	the	DET
ejpam-534	89	3	set	set	NOUN
ejpam-534	89	4	m	m	NOUN
ejpam-534	89	5	=	=	PUNCT
ejpam-534	89	6	{	{	PUNCT
ejpam-534	89	7	1,2	1,2	NUM
ejpam-534	89	8	,	,	PUNCT
ejpam-534	89	9	.	.	PUNCT
ejpam-534	89	10	.	.	PUNCT
ejpam-534	90	1	.	.	PUNCT
ejpam-534	91	1	,	,	PUNCT
ejpam-534	91	2	m	m	VERB
ejpam-534	91	3	}	}	PUNCT
ejpam-534	91	4	.	.	PUNCT
ejpam-534	92	1	remark	remark	NOUN
ejpam-534	92	2	1	1	NUM
ejpam-534	92	3	.	.	PUNCT
ejpam-534	93	1	it	it	PRON
ejpam-534	93	2	may	may	AUX
ejpam-534	93	3	be	be	AUX
ejpam-534	93	4	noted	note	VERB
ejpam-534	93	5	that	that	SCONJ
ejpam-534	93	6	if	if	SCONJ
ejpam-534	93	7	we	we	PRON
ejpam-534	93	8	write	write	VERB
ejpam-534	93	9	fx(t	fx(t	NOUN
ejpam-534	93	10	,	,	PUNCT
ejpam-534	93	11	x	x	X
ejpam-534	93	12	,	,	PUNCT
ejpam-534	93	13	ẋ)−	ẋ)−	PROPN
ejpam-534	94	1	d	d	PROPN
ejpam-534	94	2	d	d	PROPN
ejpam-534	94	3	t	t	PROPN
ejpam-534	94	4	f	f	PROPN
ejpam-534	94	5	ẋ	ẋ	PROPN
ejpam-534	94	6	(	(	PUNCT
ejpam-534	94	7	t	t	PROPN
ejpam-534	94	8	,	,	PUNCT
ejpam-534	94	9	x	x	X
ejpam-534	94	10	,	,	PUNCT
ejpam-534	94	11	ẋ	ẋ	PROPN
ejpam-534	94	12	)	)	PUNCT
ejpam-534	94	13	=	=	SYM
ejpam-534	94	14	l(t	l(t	PROPN
ejpam-534	94	15	,	,	PUNCT
ejpam-534	94	16	x	x	SYM
ejpam-534	94	17	,	,	PUNCT
ejpam-534	94	18	ẋ	ẋ	PROPN
ejpam-534	94	19	,	,	PUNCT
ejpam-534	94	20	ẍ	ẍ	PROPN
ejpam-534	94	21	)	)	PUNCT
ejpam-534	94	22	,	,	PUNCT
ejpam-534	94	23	then	then	ADV
ejpam-534	94	24	the	the	DET
ejpam-534	94	25	function	function	NOUN
ejpam-534	94	26	f	f	PROPN
ejpam-534	94	27	should	should	AUX
ejpam-534	94	28	be	be	AUX
ejpam-534	94	29	f	f	NOUN
ejpam-534	94	30	=	=	PUNCT
ejpam-534	94	31	lx	lx	NOUN
ejpam-534	94	32	(	(	PUNCT
ejpam-534	94	33	t	t	PROPN
ejpam-534	94	34	,	,	PUNCT
ejpam-534	94	35	x	x	X
ejpam-534	94	36	,	,	PUNCT
ejpam-534	94	37	ẋ	ẋ	PROPN
ejpam-534	94	38	,	,	PUNCT
ejpam-534	94	39	ẍ)−	ẍ)−	PROPN
ejpam-534	95	1	d	d	PROPN
ejpam-534	95	2	d	d	X
ejpam-534	95	3	t	t	PROPN
ejpam-534	95	4	l	l	PROPN
ejpam-534	95	5	ẋ(t	ẋ(t	PROPN
ejpam-534	95	6	,	,	PUNCT
ejpam-534	95	7	x	x	X
ejpam-534	95	8	,	,	PUNCT
ejpam-534	95	9	ẋ	ẋ	PROPN
ejpam-534	95	10	,	,	PUNCT
ejpam-534	95	11	ẍ	ẍ	X
ejpam-534	95	12	)	)	PUNCT
ejpam-534	96	1	+	+	CCONJ
ejpam-534	96	2	d2	d2	PROPN
ejpam-534	96	3	d	d	PROPN
ejpam-534	96	4	t2	t2	PROPN
ejpam-534	96	5	l	l	PROPN
ejpam-534	96	6	ẍ(t	ẍ(t	PROPN
ejpam-534	96	7	,	,	PUNCT
ejpam-534	96	8	x	x	X
ejpam-534	96	9	,	,	PUNCT
ejpam-534	96	10	ẋ	ẋ	PROPN
ejpam-534	96	11	,	,	PUNCT
ejpam-534	96	12	ẍ	ẍ	X
ejpam-534	96	13	)	)	PUNCT
ejpam-534	97	1	=	=	SYM
ejpam-534	97	2	∂	∂	NUM
ejpam-534	97	3	∂	∂	NOUN
ejpam-534	97	4	x	x	INTJ
ejpam-534	97	5	(	(	PUNCT
ejpam-534	97	6	fx(t	fx(t	PROPN
ejpam-534	97	7	,	,	PUNCT
ejpam-534	97	8	x	x	X
ejpam-534	97	9	,	,	PUNCT
ejpam-534	97	10	ẋ)−	ẋ)−	PROPN
ejpam-534	98	1	d	d	PROPN
ejpam-534	98	2	d	d	PROPN
ejpam-534	98	3	t	t	PROPN
ejpam-534	98	4	f	f	PROPN
ejpam-534	98	5	ẋ(t	ẋ(t	PROPN
ejpam-534	98	6	,	,	PUNCT
ejpam-534	98	7	x	x	X
ejpam-534	98	8	,	,	PUNCT
ejpam-534	98	9	ẋ))−	ẋ))−	PROPN
ejpam-534	99	1	d	d	PROPN
ejpam-534	99	2	d	d	X
ejpam-534	99	3	t	t	PROPN
ejpam-534	99	4	(	(	PUNCT
ejpam-534	99	5	∂	∂	NUM
ejpam-534	99	6	∂	∂	X
ejpam-534	99	7	ẋ	ẋ	PROPN
ejpam-534	99	8	(	(	PUNCT
ejpam-534	99	9	fx(t	fx(t	PROPN
ejpam-534	99	10	,	,	PUNCT
ejpam-534	99	11	x	x	X
ejpam-534	99	12	,	,	PUNCT
ejpam-534	99	13	ẋ)−	ẋ)−	PROPN
ejpam-534	99	14	d	d	PROPN
ejpam-534	100	1	d	d	PROPN
ejpam-534	100	2	t	t	PROPN
ejpam-534	100	3	f	f	PROPN
ejpam-534	100	4	ẋ	ẋ	PROPN
ejpam-534	100	5	(	(	PUNCT
ejpam-534	100	6	t	t	PROPN
ejpam-534	100	7	,	,	PUNCT
ejpam-534	100	8	x	x	X
ejpam-534	100	9	,	,	PUNCT
ejpam-534	100	10	ẋ	ẋ	PROPN
ejpam-534	100	11	)	)	PUNCT
ejpam-534	100	12	)	)	PUNCT
ejpam-534	100	13	)	)	PUNCT
ejpam-534	101	1	+	+	CCONJ
ejpam-534	101	2	d2	d2	PROPN
ejpam-534	101	3	d	d	PROPN
ejpam-534	101	4	t2	t2	PROPN
ejpam-534	101	5	(	(	PUNCT
ejpam-534	101	6	∂	∂	NUM
ejpam-534	101	7	∂	∂	NOUN
ejpam-534	101	8	ẍ	ẍ	PROPN
ejpam-534	102	1	(	(	PUNCT
ejpam-534	102	2	fx	fx	PROPN
ejpam-534	102	3	(	(	PUNCT
ejpam-534	102	4	t	t	PROPN
ejpam-534	102	5	,	,	PUNCT
ejpam-534	102	6	x	x	X
ejpam-534	102	7	,	,	PUNCT
ejpam-534	102	8	ẋ)−	ẋ)−	PROPN
ejpam-534	103	1	d	d	PROPN
ejpam-534	104	1	d	d	PROPN
ejpam-534	104	2	t	t	PROPN
ejpam-534	104	3	f	f	PROPN
ejpam-534	104	4	ẋ	ẋ	PROPN
ejpam-534	104	5	(	(	PUNCT
ejpam-534	104	6	t	t	PROPN
ejpam-534	104	7	,	,	PUNCT
ejpam-534	104	8	x	x	X
ejpam-534	104	9	,	,	PUNCT
ejpam-534	104	10	ẋ	ẋ	PROPN
ejpam-534	104	11	)	)	PUNCT
ejpam-534	104	12	)	)	PUNCT
ejpam-534	104	13	)	)	PUNCT
ejpam-534	105	1	=	=	SYM
ejpam-534	105	2	fx	fx	NOUN
ejpam-534	105	3	x	x	X
ejpam-534	105	4	−	−	PROPN
ejpam-534	106	1	d	d	X
ejpam-534	106	2	f	f	X
ejpam-534	106	3	ẋ	ẋ	PROPN
ejpam-534	107	1	x	x	X
ejpam-534	108	1	−	−	PROPN
ejpam-534	108	2	d	d	INTJ
ejpam-534	108	3	fx	fx	PROPN
ejpam-534	108	4	ẋ	ẋ	PROPN
ejpam-534	109	1	+	+	CCONJ
ejpam-534	109	2	d2	d2	PROPN
ejpam-534	109	3	f	f	PROPN
ejpam-534	109	4	ẋ	ẋ	PROPN
ejpam-534	109	5	ẋ	ẋ	PROPN
ejpam-534	110	1	−	−	PROPN
ejpam-534	110	2	d3	d3	PROPN
ejpam-534	110	3	f	f	PROPN
ejpam-534	110	4	ẋ	ẋ	PROPN
ejpam-534	110	5	ẍ	ẍ	PUNCT
ejpam-534	111	1	=	=	SYM
ejpam-534	111	2	fx	fx	PROPN
ejpam-534	111	3	x	x	X
ejpam-534	111	4	−	−	PROPN
ejpam-534	111	5	2d	2d	NUM
ejpam-534	111	6	fx	fx	PROPN
ejpam-534	111	7	ẋ	ẋ	PROPN
ejpam-534	112	1	+	+	CCONJ
ejpam-534	112	2	d2	d2	PROPN
ejpam-534	112	3	f	f	PROPN
ejpam-534	112	4	ẋ	ẋ	PROPN
ejpam-534	112	5	ẋ	ẋ	PROPN
ejpam-534	113	1	−	−	PROPN
ejpam-534	114	1	d3	d3	PROPN
ejpam-534	114	2	f	f	PROPN
ejpam-534	114	3	ẋ	ẋ	PROPN
ejpam-534	114	4	ẍ	ẍ	PROPN
ejpam-534	114	5	.	.	PUNCT
ejpam-534	115	1	thus	thus	ADV
ejpam-534	115	2	f	f	PROPN
ejpam-534	115	3	is	be	AUX
ejpam-534	115	4	a	a	DET
ejpam-534	115	5	function	function	NOUN
ejpam-534	115	6	of	of	ADP
ejpam-534	115	7	t	t	PROPN
ejpam-534	115	8	,	,	PUNCT
ejpam-534	115	9	x(t	x(t	PROPN
ejpam-534	115	10	)	)	PUNCT
ejpam-534	115	11	,	,	PUNCT
ejpam-534	115	12	ẋ(t	ẋ(t	NUM
ejpam-534	115	13	)	)	PUNCT
ejpam-534	115	14	,	,	PUNCT
ejpam-534	115	15	ẍ(t	ẍ(t	PROPN
ejpam-534	115	16	)	)	PUNCT
ejpam-534	115	17	,	,	PUNCT
ejpam-534	115	18	...	...	PUNCT
ejpam-534	116	1	x	x	X
ejpam-534	116	2	(	(	PUNCT
ejpam-534	116	3	t	t	NOUN
ejpam-534	116	4	)	)	PUNCT
ejpam-534	116	5	,	,	PUNCT
ejpam-534	116	6	....	....	PUNCT
ejpam-534	117	1	x	x	X
ejpam-534	117	2	(	(	PUNCT
ejpam-534	117	3	t	t	PROPN
ejpam-534	117	4	)	)	PUNCT
ejpam-534	117	5	and	and	CCONJ
ejpam-534	117	6	is	be	AUX
ejpam-534	117	7	given	give	VERB
ejpam-534	117	8	by	by	ADP
ejpam-534	117	9	f(t	f(t	NOUN
ejpam-534	117	10	,	,	PUNCT
ejpam-534	117	11	x	x	SYM
ejpam-534	117	12	,	,	PUNCT
ejpam-534	117	13	ẋ	ẋ	PROPN
ejpam-534	117	14	,	,	PUNCT
ejpam-534	117	15	ẍ	ẍ	PROPN
ejpam-534	117	16	,	,	PUNCT
ejpam-534	117	17	...	...	PUNCT
ejpam-534	118	1	x	x	X
ejpam-534	118	2	,	,	PUNCT
ejpam-534	118	3	....	....	PUNCT
ejpam-534	118	4	x	x	X
ejpam-534	118	5	)	)	PUNCT
ejpam-534	118	6	=	=	SYM
ejpam-534	118	7	fx	fx	NOUN
ejpam-534	118	8	x	x	SYM
ejpam-534	118	9	(	(	PUNCT
ejpam-534	118	10	t	t	PROPN
ejpam-534	118	11	,	,	PUNCT
ejpam-534	118	12	x	x	X
ejpam-534	118	13	,	,	PUNCT
ejpam-534	118	14	ẋ)−	ẋ)−	PROPN
ejpam-534	118	15	2d	2d	PROPN
ejpam-534	118	16	fx	fx	PROPN
ejpam-534	118	17	ẋ(t	ẋ(t	PROPN
ejpam-534	118	18	,	,	PUNCT
ejpam-534	118	19	x	x	X
ejpam-534	118	20	,	,	PUNCT
ejpam-534	118	21	ẋ	ẋ	PROPN
ejpam-534	118	22	)	)	PUNCT
ejpam-534	119	1	+	+	CCONJ
ejpam-534	119	2	d2	d2	PROPN
ejpam-534	119	3	f	f	PROPN
ejpam-534	119	4	ẋ	ẋ	PROPN
ejpam-534	120	1	ẋ(t	ẋ(t	PROPN
ejpam-534	120	2	,	,	PUNCT
ejpam-534	120	3	x	x	PRON
ejpam-534	120	4	,	,	PUNCT
ejpam-534	120	5	ẋ)−	ẋ)−	PROPN
ejpam-534	120	6	d3	d3	PROPN
ejpam-534	120	7	f	f	PROPN
ejpam-534	120	8	ẋ	ẋ	PROPN
ejpam-534	120	9	ẍ(t	ẍ(t	PROPN
ejpam-534	120	10	,	,	PUNCT
ejpam-534	120	11	x	x	X
ejpam-534	120	12	,	,	PUNCT
ejpam-534	120	13	ẋ	ẋ	PROPN
ejpam-534	120	14	)	)	PUNCT
ejpam-534	120	15	,	,	PUNCT
ejpam-534	120	16	t	t	PROPN
ejpam-534	120	17	∈	∈	PROPN
ejpam-534	121	1	i	i	PRON
ejpam-534	121	2	.	.	PUNCT
ejpam-534	122	1	therefore	therefore	ADV
ejpam-534	122	2	,	,	PUNCT
ejpam-534	122	3	it	it	PRON
ejpam-534	122	4	seems	seem	VERB
ejpam-534	122	5	to	to	ADP
ejpam-534	122	6	us	we	PRON
ejpam-534	122	7	,	,	PUNCT
ejpam-534	122	8	that	that	SCONJ
ejpam-534	122	9	the	the	DET
ejpam-534	122	10	function	function	NOUN
ejpam-534	122	11	f	f	PROPN
ejpam-534	122	12	should	should	AUX
ejpam-534	122	13	be	be	AUX
ejpam-534	122	14	as	as	SCONJ
ejpam-534	122	15	given	give	VERB
ejpam-534	122	16	above	above	ADV
ejpam-534	122	17	,	,	PUNCT
ejpam-534	122	18	while	while	SCONJ
ejpam-534	122	19	in	in	ADP
ejpam-534	122	20	chen	chen	PROPN
ejpam-534	123	1	[	[	X
ejpam-534	123	2	6	6	NUM
ejpam-534	123	3	]	]	PUNCT
ejpam-534	123	4	and	and	CCONJ
ejpam-534	123	5	husain	husain	PROPN
ejpam-534	123	6	et	et	PROPN
ejpam-534	123	7	al	al	PROPN
ejpam-534	123	8	.	.	PUNCT
ejpam-534	124	1	[	[	X
ejpam-534	124	2	8	8	NUM
ejpam-534	124	3	]	]	PUNCT
ejpam-534	124	4	,	,	PUNCT
ejpam-534	124	5	f	f	PROPN
ejpam-534	124	6	has	have	AUX
ejpam-534	124	7	been	be	AUX
ejpam-534	124	8	taken	take	VERB
ejpam-534	124	9	as	as	ADP
ejpam-534	124	10	fx	fx	PROPN
ejpam-534	124	11	x−2d	x−2d	INTJ
ejpam-534	124	12	fx	fx	PROPN
ejpam-534	124	13	ẋ+d2	ẋ+d2	PUNCT
ejpam-534	125	1	f	f	PROPN
ejpam-534	125	2	ẋ	ẋ	PROPN
ejpam-534	125	3	ẋ	ẋ	PROPN
ejpam-534	125	4	and	and	CCONJ
ejpam-534	125	5	fx	fx	PROPN
ejpam-534	125	6	x−d	x−d	PROPN
ejpam-534	125	7	fx	fx	PROPN
ejpam-534	125	8	ẋ+d2	ẋ+d2	PUNCT
ejpam-534	126	1	f	f	PROPN
ejpam-534	126	2	ẋ	ẋ	PROPN
ejpam-534	126	3	ẋ	ẋ	PROPN
ejpam-534	126	4	,	,	PUNCT
ejpam-534	126	5	respectively	respectively	ADV
ejpam-534	126	6	.	.	PUNCT
ejpam-534	127	1	we	we	PRON
ejpam-534	127	2	formulate	formulate	VERB
ejpam-534	127	3	the	the	DET
ejpam-534	127	4	following	follow	VERB
ejpam-534	127	5	dual	dual	ADJ
ejpam-534	127	6	problem	problem	NOUN
ejpam-534	127	7	for	for	ADP
ejpam-534	127	8	(	(	PUNCT
ejpam-534	127	9	cp	cp	NOUN
ejpam-534	127	10	)	)	PUNCT
ejpam-534	127	11	:	:	PUNCT
ejpam-534	127	12	(	(	PUNCT
ejpam-534	127	13	ócd	ócd	NOUN
ejpam-534	127	14	)	)	PUNCT
ejpam-534	127	15	maximize	maximize	VERB
ejpam-534	127	16	b∫	b∫	PROPN
ejpam-534	127	17	a	a	X
ejpam-534	127	18	(	(	PUNCT
ejpam-534	127	19	f	f	PROPN
ejpam-534	127	20	(	(	PUNCT
ejpam-534	127	21	t	t	PROPN
ejpam-534	127	22	,	,	PUNCT
ejpam-534	127	23	u	u	NOUN
ejpam-534	127	24	,	,	PUNCT
ejpam-534	127	25	u̇)−	u̇)−	PROPN
ejpam-534	127	26	1	1	NUM
ejpam-534	127	27	2	2	NUM
ejpam-534	127	28	β(t)t	β(t)t	PUNCT
ejpam-534	127	29	fβ(t))d	fβ(t))d	NOUN
ejpam-534	127	30	t	t	NOUN
ejpam-534	127	31	subject	subject	NOUN
ejpam-534	127	32	to	to	ADP
ejpam-534	127	33	u(a	u(a	NOUN
ejpam-534	127	34	)	)	PUNCT
ejpam-534	127	35	=	=	SYM
ejpam-534	127	36	0=	0=	PUNCT
ejpam-534	128	1	u(b	u(b	NOUN
ejpam-534	128	2	)	)	PUNCT
ejpam-534	128	3	,	,	PUNCT
ejpam-534	128	4	(	(	PUNCT
ejpam-534	128	5	5	5	X
ejpam-534	128	6	)	)	PUNCT
ejpam-534	128	7	t.	t.	NOUN
ejpam-534	128	8	gulati	gulati	PROPN
ejpam-534	128	9	and	and	CCONJ
ejpam-534	128	10	g.	g.	PROPN
ejpam-534	128	11	mehndiratta	mehndiratta	PROPN
ejpam-534	128	12	/	/	SYM
ejpam-534	128	13	eur	eur	PROPN
ejpam-534	128	14	.	.	PUNCT
ejpam-534	129	1	j.	j.	PROPN
ejpam-534	129	2	pure	pure	PROPN
ejpam-534	129	3	appl	appl	PROPN
ejpam-534	129	4	.	.	PROPN
ejpam-534	129	5	math	math	PROPN
ejpam-534	129	6	,	,	PUNCT
ejpam-534	129	7	3	3	NUM
ejpam-534	129	8	(	(	PUNCT
ejpam-534	129	9	2010	2010	NUM
ejpam-534	129	10	)	)	PUNCT
ejpam-534	129	11	,	,	PUNCT
ejpam-534	129	12	786	786	NUM
ejpam-534	129	13	-	-	SYM
ejpam-534	129	14	805	805	NUM
ejpam-534	129	15	789	789	NUM
ejpam-534	129	16	fx	fx	NOUN
ejpam-534	129	17	(	(	PUNCT
ejpam-534	129	18	t	t	PROPN
ejpam-534	129	19	,	,	PUNCT
ejpam-534	129	20	u	u	NOUN
ejpam-534	129	21	,	,	PUNCT
ejpam-534	129	22	u̇	u̇	PROPN
ejpam-534	129	23	)	)	PUNCT
ejpam-534	129	24	+	+	CCONJ
ejpam-534	129	25	gx(t	gx(t	PROPN
ejpam-534	129	26	,	,	PUNCT
ejpam-534	129	27	u	u	NOUN
ejpam-534	129	28	,	,	PUNCT
ejpam-534	129	29	u̇)y(t)−	u̇)y(t)−	PROPN
ejpam-534	129	30	d	d	PROPN
ejpam-534	129	31	(	(	PUNCT
ejpam-534	129	32	f	f	PROPN
ejpam-534	129	33	ẋ	ẋ	PROPN
ejpam-534	129	34	(	(	PUNCT
ejpam-534	129	35	t	t	PROPN
ejpam-534	129	36	,	,	PUNCT
ejpam-534	129	37	u	u	NOUN
ejpam-534	129	38	,	,	PUNCT
ejpam-534	129	39	u̇	u̇	PROPN
ejpam-534	129	40	)	)	PUNCT
ejpam-534	130	1	+	+	CCONJ
ejpam-534	130	2	g	g	PROPN
ejpam-534	130	3	ẋ(t	ẋ(t	PROPN
ejpam-534	130	4	,	,	PUNCT
ejpam-534	130	5	u	u	NOUN
ejpam-534	130	6	,	,	PUNCT
ejpam-534	130	7	u̇)y(t	u̇)y(t	PROPN
ejpam-534	130	8	)	)	PUNCT
ejpam-534	130	9	)	)	PUNCT
ejpam-534	131	1	+	+	CCONJ
ejpam-534	131	2	(	(	PUNCT
ejpam-534	131	3	f	f	X
ejpam-534	131	4	+	+	NOUN
ejpam-534	131	5	h)β(t	h)β(t	NOUN
ejpam-534	131	6	)	)	PUNCT
ejpam-534	131	7	=	=	SYM
ejpam-534	131	8	0	0	NUM
ejpam-534	131	9	,	,	PUNCT
ejpam-534	131	10	t	t	PROPN
ejpam-534	131	11	∈	∈	PROPN
ejpam-534	132	1	i	i	PRON
ejpam-534	132	2	,	,	PUNCT
ejpam-534	132	3	(	(	PUNCT
ejpam-534	132	4	6	6	NUM
ejpam-534	132	5	)	)	PUNCT
ejpam-534	132	6	y(t)t	y(t)t	NOUN
ejpam-534	132	7	g(t	g(t	PROPN
ejpam-534	132	8	,	,	PUNCT
ejpam-534	132	9	u	u	NOUN
ejpam-534	132	10	,	,	PUNCT
ejpam-534	132	11	u̇)−	u̇)−	PROPN
ejpam-534	132	12	1	1	NUM
ejpam-534	132	13	2	2	NUM
ejpam-534	132	14	β(t)t	β(t)t	PROPN
ejpam-534	132	15	hβ(t	hβ(t	NOUN
ejpam-534	132	16	)	)	PUNCT
ejpam-534	132	17	≧	≧	X
ejpam-534	132	18	0	0	NUM
ejpam-534	132	19	,	,	PUNCT
ejpam-534	132	20	t	t	PROPN
ejpam-534	132	21	∈	∈	PROPN
ejpam-534	133	1	i	i	PRON
ejpam-534	133	2	,	,	PUNCT
ejpam-534	133	3	(	(	PUNCT
ejpam-534	133	4	7	7	X
ejpam-534	133	5	)	)	PUNCT
ejpam-534	133	6	y(t	y(t	NUM
ejpam-534	133	7	)	)	PUNCT
ejpam-534	133	8	≧	≧	X
ejpam-534	133	9	0	0	NUM
ejpam-534	133	10	,	,	PUNCT
ejpam-534	133	11	t	t	PROPN
ejpam-534	133	12	∈	∈	PROPN
ejpam-534	134	1	i	i	PRON
ejpam-534	134	2	,	,	PUNCT
ejpam-534	134	3	(	(	PUNCT
ejpam-534	134	4	8)	8)	NUM
ejpam-534	134	5	where	where	SCONJ
ejpam-534	134	6	h(t	h(t	PROPN
ejpam-534	134	7	,	,	PUNCT
ejpam-534	134	8	u	u	NOUN
ejpam-534	134	9	,	,	PUNCT
ejpam-534	134	10	u̇	u̇	PROPN
ejpam-534	134	11	,	,	PUNCT
ejpam-534	134	12	ü	ü	NOUN
ejpam-534	134	13	,	,	PUNCT
ejpam-534	134	14	...	...	PUNCT
ejpam-534	134	15	u	u	NOUN
ejpam-534	134	16	,	,	PUNCT
ejpam-534	134	17	....	....	PUNCT
ejpam-534	134	18	u	u	INTJ
ejpam-534	134	19	,	,	PUNCT
ejpam-534	134	20	y(t	y(t	PROPN
ejpam-534	134	21	)	)	PUNCT
ejpam-534	134	22	,	,	PUNCT
ejpam-534	134	23	ẏ(t	ẏ(t	PROPN
ejpam-534	134	24	)	)	PUNCT
ejpam-534	134	25	,	,	PUNCT
ejpam-534	134	26	ÿ(t	ÿ(t	PROPN
ejpam-534	134	27	)	)	PUNCT
ejpam-534	134	28	,	,	PUNCT
ejpam-534	134	29	...	...	PUNCT
ejpam-534	135	1	y	y	PROPN
ejpam-534	135	2	(	(	PUNCT
ejpam-534	135	3	t	t	PROPN
ejpam-534	135	4	)	)	PUNCT
ejpam-534	135	5	)	)	PUNCT
ejpam-534	136	1	=	=	SYM
ejpam-534	136	2	(	(	PUNCT
ejpam-534	136	3	gx(t	gx(t	PROPN
ejpam-534	136	4	,	,	PUNCT
ejpam-534	136	5	u	u	NOUN
ejpam-534	136	6	,	,	PUNCT
ejpam-534	136	7	u̇)y(t))x	u̇)y(t))x	ADJ
ejpam-534	136	8	−	−	PROPN
ejpam-534	136	9	2d(gx(t	2d(gx(t	NUM
ejpam-534	136	10	,	,	PUNCT
ejpam-534	136	11	u	u	NOUN
ejpam-534	136	12	,	,	PUNCT
ejpam-534	136	13	u̇)y(t	u̇)y(t	PROPN
ejpam-534	136	14	)	)	PUNCT
ejpam-534	136	15	)	)	PUNCT
ejpam-534	137	1	ẋ	ẋ	PROPN
ejpam-534	138	1	+	+	PUNCT
ejpam-534	138	2	d2(g	d2(g	PROPN
ejpam-534	138	3	ẋ(t	ẋ(t	PROPN
ejpam-534	138	4	,	,	PUNCT
ejpam-534	138	5	u	u	NOUN
ejpam-534	138	6	,	,	PUNCT
ejpam-534	138	7	u̇)y(t	u̇)y(t	PROPN
ejpam-534	138	8	)	)	PUNCT
ejpam-534	138	9	)	)	PUNCT
ejpam-534	139	1	ẋ	ẋ	PROPN
ejpam-534	140	1	−	−	PROPN
ejpam-534	140	2	d3(g	d3(g	PROPN
ejpam-534	140	3	ẋ(t	ẋ(t	NUM
ejpam-534	140	4	,	,	PUNCT
ejpam-534	140	5	u	u	NOUN
ejpam-534	140	6	,	,	PUNCT
ejpam-534	140	7	u̇)y(t	u̇)y(t	PROPN
ejpam-534	140	8	)	)	PUNCT
ejpam-534	140	9	)	)	PUNCT
ejpam-534	140	10	ẍ	ẍ	X
ejpam-534	140	11	,	,	PUNCT
ejpam-534	140	12	t	t	PROPN
ejpam-534	140	13	∈	∈	PROPN
ejpam-534	141	1	i	i	PRON
ejpam-534	141	2	,	,	PUNCT
ejpam-534	141	3	and	and	CCONJ
ejpam-534	141	4	f(t	f(t	PROPN
ejpam-534	141	5	,	,	PUNCT
ejpam-534	141	6	u	u	NOUN
ejpam-534	141	7	,	,	PUNCT
ejpam-534	141	8	u̇	u̇	PROPN
ejpam-534	141	9	,	,	PUNCT
ejpam-534	141	10	ü	ü	NOUN
ejpam-534	141	11	,	,	PUNCT
ejpam-534	141	12	...	...	PUNCT
ejpam-534	141	13	u	u	NOUN
ejpam-534	141	14	,	,	PUNCT
ejpam-534	141	15	....	....	PUNCT
ejpam-534	141	16	u	u	NOUN
ejpam-534	141	17	)	)	PUNCT
ejpam-534	141	18	,	,	PUNCT
ejpam-534	141	19	t	t	PROPN
ejpam-534	141	20	∈	∈	PROPN
ejpam-534	142	1	i	i	PRON
ejpam-534	142	2	,	,	PUNCT
ejpam-534	142	3	is	be	AUX
ejpam-534	142	4	as	as	SCONJ
ejpam-534	142	5	given	give	VERB
ejpam-534	142	6	in	in	ADP
ejpam-534	142	7	remark	remark	NOUN
ejpam-534	142	8	1	1	NUM
ejpam-534	142	9	.	.	PUNCT
ejpam-534	143	1	like	like	ADP
ejpam-534	143	2	[	[	X
ejpam-534	143	3	8	8	NUM
ejpam-534	143	4	]	]	PUNCT
ejpam-534	143	5	,	,	PUNCT
ejpam-534	143	6	we	we	PRON
ejpam-534	143	7	shall	shall	AUX
ejpam-534	143	8	use	use	VERB
ejpam-534	143	9	fritz	fritz	PROPN
ejpam-534	143	10	john	john	PROPN
ejpam-534	143	11	necessary	necessary	ADJ
ejpam-534	143	12	optimality	optimality	NOUN
ejpam-534	143	13	conditions	condition	NOUN
ejpam-534	143	14	[	[	X
ejpam-534	143	15	4	4	X
ejpam-534	143	16	]	]	PUNCT
ejpam-534	143	17	for	for	ADP
ejpam-534	143	18	the	the	DET
ejpam-534	143	19	dual	dual	ADJ
ejpam-534	143	20	problem	problem	NOUN
ejpam-534	143	21	to	to	PART
ejpam-534	143	22	establish	establish	VERB
ejpam-534	143	23	the	the	DET
ejpam-534	143	24	converse	converse	NOUN
ejpam-534	143	25	duality	duality	NOUN
ejpam-534	143	26	theorem	theorem	VERB
ejpam-534	143	27	.	.	PUNCT
ejpam-534	144	1	since	since	SCONJ
ejpam-534	144	2	the	the	DET
ejpam-534	144	3	constraints	constraint	NOUN
ejpam-534	144	4	in	in	ADP
ejpam-534	144	5	the	the	DET
ejpam-534	144	6	problem	problem	NOUN
ejpam-534	144	7	considered	consider	VERB
ejpam-534	144	8	in	in	ADP
ejpam-534	144	9	[	[	X
ejpam-534	144	10	4	4	X
ejpam-534	144	11	]	]	PUNCT
ejpam-534	144	12	do	do	AUX
ejpam-534	144	13	not	not	PART
ejpam-534	144	14	involve	involve	VERB
ejpam-534	144	15	integrals	integral	NOUN
ejpam-534	144	16	,	,	PUNCT
ejpam-534	144	17	we	we	PRON
ejpam-534	144	18	have	have	AUX
ejpam-534	144	19	not	not	PART
ejpam-534	144	20	taken	take	VERB
ejpam-534	144	21	integral	integral	ADJ
ejpam-534	144	22	in	in	ADP
ejpam-534	144	23	the	the	DET
ejpam-534	144	24	dual	dual	ADJ
ejpam-534	144	25	constraint	constraint	NOUN
ejpam-534	144	26	(	(	PUNCT
ejpam-534	144	27	7	7	NUM
ejpam-534	144	28	)	)	PUNCT
ejpam-534	144	29	.	.	PUNCT
ejpam-534	145	1	moreover	moreover	ADV
ejpam-534	145	2	,	,	PUNCT
ejpam-534	145	3	some	some	DET
ejpam-534	145	4	terms	term	NOUN
ejpam-534	145	5	in	in	ADP
ejpam-534	145	6	(	(	PUNCT
ejpam-534	145	7	dc	dc	PROPN
ejpam-534	145	8	d	d	PROPN
ejpam-534	145	9	)	)	PUNCT
ejpam-534	145	10	are	be	AUX
ejpam-534	145	11	in	in	ADP
ejpam-534	145	12	different	different	ADJ
ejpam-534	145	13	form	form	NOUN
ejpam-534	145	14	than	than	ADP
ejpam-534	145	15	in	in	ADP
ejpam-534	145	16	(	(	PUNCT
ejpam-534	145	17	cd	cd	PROPN
ejpam-534	145	18	)	)	PUNCT
ejpam-534	145	19	.	.	PUNCT
ejpam-534	146	1	it	it	PRON
ejpam-534	146	2	has	have	AUX
ejpam-534	146	3	been	be	AUX
ejpam-534	146	4	done	do	VERB
ejpam-534	146	5	so	so	ADV
ejpam-534	146	6	to	to	PART
ejpam-534	146	7	make	make	VERB
ejpam-534	146	8	all	all	DET
ejpam-534	146	9	the	the	DET
ejpam-534	146	10	terms	term	NOUN
ejpam-534	146	11	in	in	ADP
ejpam-534	146	12	an	an	DET
ejpam-534	146	13	expression	expression	NOUN
ejpam-534	146	14	to	to	PART
ejpam-534	146	15	be	be	AUX
ejpam-534	146	16	of	of	ADP
ejpam-534	146	17	the	the	DET
ejpam-534	146	18	same	same	ADJ
ejpam-534	146	19	dimension	dimension	NOUN
ejpam-534	146	20	.	.	PUNCT
ejpam-534	147	1	however	however	ADV
ejpam-534	147	2	,	,	PUNCT
ejpam-534	147	3	the	the	DET
ejpam-534	147	4	weak	weak	ADJ
ejpam-534	147	5	duality	duality	NOUN
ejpam-534	147	6	theorem	theorem	NOUN
ejpam-534	147	7	given	give	VERB
ejpam-534	147	8	in	in	ADP
ejpam-534	147	9	[	[	NOUN
ejpam-534	147	10	8	8	NUM
ejpam-534	147	11	]	]	PUNCT
ejpam-534	147	12	holds	hold	VERB
ejpam-534	147	13	for	for	ADP
ejpam-534	147	14	problems	problem	NOUN
ejpam-534	147	15	(	(	PUNCT
ejpam-534	147	16	cp	cp	NOUN
ejpam-534	147	17	)	)	PUNCT
ejpam-534	147	18	and	and	CCONJ
ejpam-534	147	19	(	(	PUNCT
ejpam-534	147	20	dc	dc	PROPN
ejpam-534	147	21	d	d	PROPN
ejpam-534	147	22	)	)	PUNCT
ejpam-534	147	23	.	.	PUNCT
ejpam-534	148	1	theorem	theorem	NOUN
ejpam-534	148	2	2	2	NUM
ejpam-534	148	3	.	.	PUNCT
ejpam-534	149	1	[	[	X
ejpam-534	149	2	converse	converse	NOUN
ejpam-534	149	3	duality	duality	NOUN
ejpam-534	149	4	]	]	PUNCT
ejpam-534	149	5	let	let	VERB
ejpam-534	149	6	(	(	PUNCT
ejpam-534	149	7	ū(t	ū(t	ADJ
ejpam-534	149	8	)	)	PUNCT
ejpam-534	149	9	,	,	PUNCT
ejpam-534	149	10	ȳ(t	ȳ(t	PROPN
ejpam-534	149	11	)	)	PUNCT
ejpam-534	149	12	,	,	PUNCT
ejpam-534	149	13	β̄(t	β̄(t	NOUN
ejpam-534	149	14	)	)	PUNCT
ejpam-534	149	15	)	)	PUNCT
ejpam-534	149	16	be	be	AUX
ejpam-534	149	17	an	an	DET
ejpam-534	149	18	optimal	optimal	ADJ
ejpam-534	149	19	solution	solution	NOUN
ejpam-534	149	20	of	of	ADP
ejpam-534	149	21	(	(	PUNCT
ejpam-534	149	22	dc	dc	PROPN
ejpam-534	149	23	d	d	PROPN
ejpam-534	149	24	)	)	PUNCT
ejpam-534	149	25	.	.	PUNCT
ejpam-534	150	1	if	if	SCONJ
ejpam-534	150	2	for	for	ADP
ejpam-534	150	3	each	each	DET
ejpam-534	150	4	t	t	NOUN
ejpam-534	150	5	∈	∈	PROPN
ejpam-534	151	1	i	i	PRON
ejpam-534	151	2	,	,	PUNCT
ejpam-534	151	3	(	(	PUNCT
ejpam-534	151	4	b1	b1	PROPN
ejpam-534	151	5	)	)	PUNCT
ejpam-534	151	6	the	the	DET
ejpam-534	151	7	vectors	vector	NOUN
ejpam-534	151	8	{	{	PUNCT
ejpam-534	151	9	fi	fi	NOUN
ejpam-534	151	10	,	,	PUNCT
ejpam-534	151	11	hi	hi	INTJ
ejpam-534	151	12	,	,	PUNCT
ejpam-534	151	13	i	i	PRON
ejpam-534	151	14	=	=	NOUN
ejpam-534	151	15	1,2	1,2	NUM
ejpam-534	151	16	,	,	PUNCT
ejpam-534	151	17	.	.	PUNCT
ejpam-534	151	18	.	.	PUNCT
ejpam-534	151	19	.	.	PUNCT
ejpam-534	151	20	,	,	PUNCT
ejpam-534	151	21	n	n	CCONJ
ejpam-534	151	22	}	}	PUNCT
ejpam-534	151	23	are	be	AUX
ejpam-534	151	24	linearly	linearly	ADV
ejpam-534	151	25	independent	independent	ADJ
ejpam-534	151	26	,	,	PUNCT
ejpam-534	151	27	where	where	SCONJ
ejpam-534	151	28	fi	fi	NOUN
ejpam-534	152	1	and	and	CCONJ
ejpam-534	152	2	hi	hi	INTJ
ejpam-534	152	3	are	be	AUX
ejpam-534	152	4	the	the	DET
ejpam-534	152	5	ith	ith	NOUN
ejpam-534	152	6	rows	row	NOUN
ejpam-534	152	7	of	of	ADP
ejpam-534	152	8	f(t	f(t	PROPN
ejpam-534	152	9	,	,	PUNCT
ejpam-534	152	10	ū	ū	NOUN
ejpam-534	152	11	,	,	PUNCT
ejpam-534	152	12	˙̄u	˙̄u	NOUN
ejpam-534	152	13	,	,	PUNCT
ejpam-534	152	14	¨̄u	¨̄u	NOUN
ejpam-534	152	15	,	,	PUNCT
ejpam-534	152	16	...	...	PUNCT
ejpam-534	152	17	ū	ū	NOUN
ejpam-534	152	18	,	,	PUNCT
ejpam-534	152	19	....	....	PUNCT
ejpam-534	152	20	ū	ū	PROPN
ejpam-534	152	21	)	)	PUNCT
ejpam-534	152	22	and	and	CCONJ
ejpam-534	152	23	h(t	h(t	PROPN
ejpam-534	152	24	,	,	PUNCT
ejpam-534	152	25	ū	ū	NOUN
ejpam-534	152	26	,	,	PUNCT
ejpam-534	152	27	˙̄u	˙̄u	NOUN
ejpam-534	152	28	,	,	PUNCT
ejpam-534	152	29	¨̄u	¨̄u	NOUN
ejpam-534	152	30	,	,	PUNCT
ejpam-534	152	31	...	...	PUNCT
ejpam-534	152	32	ū	ū	NOUN
ejpam-534	152	33	,	,	PUNCT
ejpam-534	152	34	....	....	PUNCT
ejpam-534	152	35	ū	ū	NOUN
ejpam-534	152	36	,	,	PUNCT
ejpam-534	152	37	ȳ(t	ȳ(t	PROPN
ejpam-534	152	38	)	)	PUNCT
ejpam-534	152	39	,	,	PUNCT
ejpam-534	152	40	˙̄y(t	˙̄y(t	PUNCT
ejpam-534	152	41	)	)	PUNCT
ejpam-534	152	42	,	,	PUNCT
ejpam-534	152	43	¨̄y(t	¨̄y(t	NUM
ejpam-534	152	44	)	)	PUNCT
ejpam-534	152	45	,	,	PUNCT
ejpam-534	152	46	...	...	PUNCT
ejpam-534	153	1	ȳ	ȳ	PROPN
ejpam-534	153	2	(	(	PUNCT
ejpam-534	153	3	t	t	PROPN
ejpam-534	153	4	)	)	PUNCT
ejpam-534	153	5	)	)	PUNCT
ejpam-534	153	6	,	,	PUNCT
ejpam-534	153	7	respectively	respectively	ADV
ejpam-534	153	8	,	,	PUNCT
ejpam-534	153	9	(	(	PUNCT
ejpam-534	153	10	b2	b2	NOUN
ejpam-534	153	11	)	)	PUNCT
ejpam-534	153	12	gx(t	gx(t	NOUN
ejpam-534	153	13	,	,	PUNCT
ejpam-534	153	14	ū	ū	NOUN
ejpam-534	153	15	,	,	PUNCT
ejpam-534	153	16	˙̄u	˙̄u	X
ejpam-534	153	17	)	)	PUNCT
ejpam-534	153	18	ȳ(t)−	ȳ(t)−	PROPN
ejpam-534	153	19	d(g	d(g	PROPN
ejpam-534	153	20	ẋ(t	ẋ(t	PROPN
ejpam-534	153	21	,	,	PUNCT
ejpam-534	153	22	ū	ū	NOUN
ejpam-534	153	23	,	,	PUNCT
ejpam-534	153	24	˙̄u	˙̄u	NOUN
ejpam-534	153	25	)	)	PUNCT
ejpam-534	153	26	ȳ(t	ȳ(t	NOUN
ejpam-534	153	27	)	)	PUNCT
ejpam-534	153	28	)	)	PUNCT
ejpam-534	154	1	6=	6=	ADP
ejpam-534	154	2	0	0	NUM
ejpam-534	154	3	,	,	PUNCT
ejpam-534	154	4	and	and	CCONJ
ejpam-534	154	5	(	(	PUNCT
ejpam-534	154	6	b3	b3	PROPN
ejpam-534	154	7	)	)	PUNCT
ejpam-534	154	8	either	either	CCONJ
ejpam-534	154	9	(	(	PUNCT
ejpam-534	154	10	i	i	NOUN
ejpam-534	154	11	)	)	PUNCT
ejpam-534	154	12	the	the	DET
ejpam-534	154	13	n×n	n×n	PROPN
ejpam-534	154	14	matrix	matrix	NOUN
ejpam-534	154	15	h(t	h(t	PROPN
ejpam-534	154	16	,	,	PUNCT
ejpam-534	154	17	ū	ū	NOUN
ejpam-534	154	18	,	,	PUNCT
ejpam-534	154	19	˙̄u	˙̄u	NOUN
ejpam-534	154	20	,	,	PUNCT
ejpam-534	154	21	¨̄u	¨̄u	NOUN
ejpam-534	154	22	,	,	PUNCT
ejpam-534	154	23	...	...	PUNCT
ejpam-534	154	24	ū	ū	NOUN
ejpam-534	154	25	,	,	PUNCT
ejpam-534	154	26	....	....	PUNCT
ejpam-534	154	27	ū	ū	NOUN
ejpam-534	154	28	,	,	PUNCT
ejpam-534	154	29	ȳ(t	ȳ(t	PROPN
ejpam-534	154	30	)	)	PUNCT
ejpam-534	154	31	,	,	PUNCT
ejpam-534	154	32	˙̄y(t	˙̄y(t	PUNCT
ejpam-534	154	33	)	)	PUNCT
ejpam-534	154	34	,	,	PUNCT
ejpam-534	154	35	¨̄y(t	¨̄y(t	NUM
ejpam-534	154	36	)	)	PUNCT
ejpam-534	154	37	,	,	PUNCT
ejpam-534	154	38	...	...	PUNCT
ejpam-534	155	1	ȳ	ȳ	PROPN
ejpam-534	155	2	(	(	PUNCT
ejpam-534	155	3	t))+(gx(t	t))+(gx(t	PROPN
ejpam-534	155	4	,	,	PUNCT
ejpam-534	155	5	ū	ū	NOUN
ejpam-534	155	6	,	,	PUNCT
ejpam-534	155	7	˙̄u	˙̄u	X
ejpam-534	155	8	)	)	PUNCT
ejpam-534	156	1	ȳ(t))x	ȳ(t))x	NOUN
ejpam-534	156	2	is	be	AUX
ejpam-534	156	3	positive	positive	ADJ
ejpam-534	156	4	definite	definite	ADJ
ejpam-534	156	5	and	and	CCONJ
ejpam-534	156	6	β̄(t)t	β̄(t)t	NOUN
ejpam-534	156	7	(	(	PUNCT
ejpam-534	156	8	gx(t	gx(t	X
ejpam-534	156	9	,	,	PUNCT
ejpam-534	156	10	ū	ū	NOUN
ejpam-534	156	11	,	,	PUNCT
ejpam-534	156	12	˙̄u	˙̄u	NOUN
ejpam-534	156	13	)	)	PUNCT
ejpam-534	156	14	ȳ(t	ȳ(t	NOUN
ejpam-534	156	15	)	)	PUNCT
ejpam-534	156	16	)	)	PUNCT
ejpam-534	156	17	≧	≧	X
ejpam-534	157	1	0	0	NUM
ejpam-534	157	2	,	,	PUNCT
ejpam-534	157	3	or	or	CCONJ
ejpam-534	157	4	(	(	PUNCT
ejpam-534	157	5	ii	ii	NOUN
ejpam-534	157	6	)	)	PUNCT
ejpam-534	157	7	the	the	DET
ejpam-534	157	8	n×n	n×n	PROPN
ejpam-534	157	9	matrix	matrix	NOUN
ejpam-534	157	10	h(t	h(t	PROPN
ejpam-534	157	11	,	,	PUNCT
ejpam-534	157	12	ū	ū	NOUN
ejpam-534	157	13	,	,	PUNCT
ejpam-534	157	14	˙̄u	˙̄u	NOUN
ejpam-534	157	15	,	,	PUNCT
ejpam-534	157	16	¨̄u	¨̄u	NOUN
ejpam-534	157	17	,	,	PUNCT
ejpam-534	157	18	...	...	PUNCT
ejpam-534	157	19	ū	ū	NOUN
ejpam-534	157	20	,	,	PUNCT
ejpam-534	157	21	....	....	PUNCT
ejpam-534	157	22	ū	ū	NOUN
ejpam-534	157	23	,	,	PUNCT
ejpam-534	157	24	ȳ(t	ȳ(t	PROPN
ejpam-534	157	25	)	)	PUNCT
ejpam-534	157	26	,	,	PUNCT
ejpam-534	157	27	˙̄y(t	˙̄y(t	PUNCT
ejpam-534	157	28	)	)	PUNCT
ejpam-534	157	29	,	,	PUNCT
ejpam-534	157	30	¨̄y(t	¨̄y(t	NUM
ejpam-534	157	31	)	)	PUNCT
ejpam-534	157	32	,	,	PUNCT
ejpam-534	157	33	...	...	PUNCT
ejpam-534	158	1	ȳ	ȳ	PROPN
ejpam-534	158	2	(	(	PUNCT
ejpam-534	158	3	t))+(gx	t))+(gx	PROPN
ejpam-534	158	4	(	(	PUNCT
ejpam-534	158	5	t	t	PROPN
ejpam-534	158	6	,	,	PUNCT
ejpam-534	158	7	ū	ū	NOUN
ejpam-534	158	8	,	,	PUNCT
ejpam-534	158	9	˙̄u	˙̄u	X
ejpam-534	158	10	)	)	PUNCT
ejpam-534	159	1	ȳ(t))x	ȳ(t))x	NOUN
ejpam-534	159	2	is	be	AUX
ejpam-534	159	3	negative	negative	ADJ
ejpam-534	159	4	definite	definite	ADJ
ejpam-534	159	5	and	and	CCONJ
ejpam-534	159	6	β̄(t)t	β̄(t)t	NOUN
ejpam-534	159	7	(	(	PUNCT
ejpam-534	159	8	gx(t	gx(t	X
ejpam-534	159	9	,	,	PUNCT
ejpam-534	159	10	ū	ū	NOUN
ejpam-534	159	11	,	,	PUNCT
ejpam-534	159	12	˙̄u	˙̄u	NOUN
ejpam-534	159	13	)	)	PUNCT
ejpam-534	159	14	ȳ(t	ȳ(t	NOUN
ejpam-534	159	15	)	)	PUNCT
ejpam-534	159	16	)	)	PUNCT
ejpam-534	160	1	≦	≦	NUM
ejpam-534	160	2	0	0	NUM
ejpam-534	160	3	,	,	PUNCT
ejpam-534	160	4	then	then	ADV
ejpam-534	160	5	ū(t	ū(t	PROPN
ejpam-534	160	6	)	)	PUNCT
ejpam-534	160	7	is	be	AUX
ejpam-534	160	8	feasible	feasible	ADJ
ejpam-534	160	9	for	for	ADP
ejpam-534	160	10	(	(	PUNCT
ejpam-534	160	11	cp	cp	NOUN
ejpam-534	160	12	)	)	PUNCT
ejpam-534	160	13	and	and	CCONJ
ejpam-534	160	14	the	the	DET
ejpam-534	160	15	two	two	NUM
ejpam-534	160	16	objective	objective	ADJ
ejpam-534	160	17	functionals	functional	NOUN
ejpam-534	160	18	have	have	VERB
ejpam-534	160	19	same	same	ADJ
ejpam-534	160	20	value	value	NOUN
ejpam-534	160	21	.	.	PUNCT
ejpam-534	161	1	also	also	ADV
ejpam-534	161	2	,	,	PUNCT
ejpam-534	161	3	if	if	SCONJ
ejpam-534	161	4	the	the	DET
ejpam-534	161	5	weak	weak	ADJ
ejpam-534	161	6	duality	duality	NOUN
ejpam-534	161	7	theorem	theorem	VERB
ejpam-534	161	8	[	[	X
ejpam-534	161	9	8	8	NUM
ejpam-534	161	10	]	]	PUNCT
ejpam-534	161	11	holds	hold	VERB
ejpam-534	161	12	for	for	ADP
ejpam-534	161	13	all	all	DET
ejpam-534	161	14	feasible	feasible	ADJ
ejpam-534	161	15	solution	solution	NOUN
ejpam-534	161	16	of	of	ADP
ejpam-534	161	17	(	(	PUNCT
ejpam-534	161	18	cp	cp	NOUN
ejpam-534	161	19	)	)	PUNCT
ejpam-534	161	20	and	and	CCONJ
ejpam-534	161	21	(	(	PUNCT
ejpam-534	161	22	dc	dc	PROPN
ejpam-534	161	23	d	d	PROPN
ejpam-534	161	24	)	)	PUNCT
ejpam-534	161	25	,	,	PUNCT
ejpam-534	161	26	then	then	ADV
ejpam-534	161	27	ū(t	ū(t	PROPN
ejpam-534	161	28	)	)	PUNCT
ejpam-534	161	29	is	be	AUX
ejpam-534	161	30	an	an	DET
ejpam-534	161	31	optimal	optimal	ADJ
ejpam-534	161	32	solution	solution	NOUN
ejpam-534	161	33	of	of	ADP
ejpam-534	161	34	(	(	PUNCT
ejpam-534	161	35	cp	cp	NOUN
ejpam-534	161	36	)	)	PUNCT
ejpam-534	161	37	.	.	PUNCT
ejpam-534	162	1	proof	proof	NOUN
ejpam-534	162	2	.	.	PUNCT
ejpam-534	163	1	since	since	SCONJ
ejpam-534	163	2	(	(	PUNCT
ejpam-534	163	3	ū(t	ū(t	ADJ
ejpam-534	163	4	)	)	PUNCT
ejpam-534	163	5	,	,	PUNCT
ejpam-534	163	6	ȳ(t	ȳ(t	PROPN
ejpam-534	163	7	)	)	PUNCT
ejpam-534	163	8	,	,	PUNCT
ejpam-534	163	9	β̄(t	β̄(t	NOUN
ejpam-534	163	10	)	)	PUNCT
ejpam-534	163	11	)	)	PUNCT
ejpam-534	163	12	is	be	AUX
ejpam-534	163	13	an	an	DET
ejpam-534	163	14	optimal	optimal	ADJ
ejpam-534	163	15	solution	solution	NOUN
ejpam-534	163	16	of	of	ADP
ejpam-534	163	17	(	(	PUNCT
ejpam-534	163	18	dc	dc	PROPN
ejpam-534	163	19	d	d	PROPN
ejpam-534	163	20	)	)	PUNCT
ejpam-534	163	21	,	,	PUNCT
ejpam-534	163	22	there	there	PRON
ejpam-534	163	23	exist	exist	VERB
ejpam-534	163	24	α	α	DET
ejpam-534	163	25	∈	∈	NOUN
ejpam-534	163	26	r	r	NOUN
ejpam-534	163	27	and	and	CCONJ
ejpam-534	163	28	piecewise	piecewise	NOUN
ejpam-534	163	29	smooth	smooth	ADJ
ejpam-534	163	30	functions	function	NOUN
ejpam-534	164	1	λ	λ	X
ejpam-534	164	2	:	:	PUNCT
ejpam-534	164	3	i	i	PROPN
ejpam-534	164	4	→	→	SYM
ejpam-534	164	5	rn	rn	PROPN
ejpam-534	164	6	,	,	PUNCT
ejpam-534	164	7	γ	γ	X
ejpam-534	164	8	:	:	PUNCT
ejpam-534	164	9	i	i	PROPN
ejpam-534	164	10	→	→	SYM
ejpam-534	164	11	r	r	NOUN
ejpam-534	164	12	and	and	CCONJ
ejpam-534	164	13	µ	µ	NOUN
ejpam-534	164	14	:	:	PUNCT
ejpam-534	164	15	i	i	PROPN
ejpam-534	164	16	→	→	SYM
ejpam-534	164	17	rm	rm	NOUN
ejpam-534	164	18	such	such	ADJ
ejpam-534	164	19	that	that	SCONJ
ejpam-534	164	20	the	the	DET
ejpam-534	164	21	following	follow	VERB
ejpam-534	164	22	fritz	fritz	PROPN
ejpam-534	164	23	john	john	PROPN
ejpam-534	164	24	conditions	condition	NOUN
ejpam-534	165	1	[	[	X
ejpam-534	165	2	4	4	X
ejpam-534	165	3	]	]	PUNCT
ejpam-534	165	4	are	be	AUX
ejpam-534	165	5	satisfied	satisfied	ADJ
ejpam-534	165	6	at	at	ADP
ejpam-534	165	7	(	(	PUNCT
ejpam-534	165	8	ū(t	ū(t	ADJ
ejpam-534	165	9	)	)	PUNCT
ejpam-534	165	10	,	,	PUNCT
ejpam-534	165	11	ȳ(t	ȳ(t	PROPN
ejpam-534	165	12	)	)	PUNCT
ejpam-534	165	13	,	,	PUNCT
ejpam-534	165	14	β̄(t	β̄(t	NOUN
ejpam-534	165	15	)	)	PUNCT
ejpam-534	165	16	)	)	PUNCT
ejpam-534	166	1	(	(	PUNCT
ejpam-534	166	2	for	for	ADP
ejpam-534	166	3	brevity	brevity	NOUN
ejpam-534	166	4	,	,	PUNCT
ejpam-534	166	5	fx	fx	PROPN
ejpam-534	166	6	≡	≡	PROPN
ejpam-534	166	7	fx(t	fx(t	PROPN
ejpam-534	166	8	,	,	PUNCT
ejpam-534	166	9	ū	ū	NOUN
ejpam-534	166	10	,	,	PUNCT
ejpam-534	166	11	˙̄u	˙̄u	NOUN
ejpam-534	166	12	)	)	PUNCT
ejpam-534	166	13	,	,	PUNCT
ejpam-534	166	14	g	g	PROPN
ejpam-534	166	15	j	j	PROPN
ejpam-534	166	16	≡	≡	PROPN
ejpam-534	166	17	g	g	PROPN
ejpam-534	166	18	j(t	j(t	PROPN
ejpam-534	166	19	,	,	PUNCT
ejpam-534	166	20	ū	ū	NOUN
ejpam-534	166	21	,	,	PUNCT
ejpam-534	166	22	˙̄u	˙̄u	NOUN
ejpam-534	166	23	)	)	PUNCT
ejpam-534	166	24	,	,	PUNCT
ejpam-534	166	25	g	g	PROPN
ejpam-534	166	26	j	j	PROPN
ejpam-534	166	27	x	x	SYM
ejpam-534	166	28	≡	≡	PROPN
ejpam-534	166	29	g	g	PROPN
ejpam-534	166	30	j	j	PROPN
ejpam-534	166	31	x(t	x(t	PROPN
ejpam-534	166	32	,	,	PUNCT
ejpam-534	166	33	ū	ū	NOUN
ejpam-534	166	34	,	,	PUNCT
ejpam-534	166	35	˙̄u	˙̄u	X
ejpam-534	166	36	)	)	PUNCT
ejpam-534	166	37	etc	etc	X
ejpam-534	166	38	.	.	X
ejpam-534	166	39	):	):	PUNCT
ejpam-534	166	40	−α	−α	PROPN
ejpam-534	166	41	(	(	PUNCT
ejpam-534	166	42	fx	fx	NOUN
ejpam-534	166	43	−	−	PROPN
ejpam-534	167	1	d	d	X
ejpam-534	167	2	f	f	PROPN
ejpam-534	167	3	ẋ	ẋ	PROPN
ejpam-534	168	1	−	−	NOUN
ejpam-534	168	2	1	1	NUM
ejpam-534	168	3	2	2	NUM
ejpam-534	168	4	(	(	PUNCT
ejpam-534	168	5	β̄(t)t	β̄(t)t	PROPN
ejpam-534	168	6	f	f	AUX
ejpam-534	168	7	β̄(t))x	β̄(t))x	VERB
ejpam-534	169	1	+	+	CCONJ
ejpam-534	169	2	1	1	NUM
ejpam-534	169	3	2	2	NUM
ejpam-534	169	4	d(β̄(t)t	d(β̄(t)t	NOUN
ejpam-534	169	5	f	f	PROPN
ejpam-534	169	6	β̄(t	β̄(t	PROPN
ejpam-534	169	7	)	)	PUNCT
ejpam-534	169	8	)	)	PUNCT
ejpam-534	170	1	ẋ	ẋ	PROPN
ejpam-534	171	1	−	−	NOUN
ejpam-534	171	2	1	1	NUM
ejpam-534	171	3	2	2	NUM
ejpam-534	171	4	d2(β̄(t)t	d2(β̄(t)t	NOUN
ejpam-534	171	5	f	f	NOUN
ejpam-534	171	6	β̄(t	β̄(t	PROPN
ejpam-534	171	7	)	)	PUNCT
ejpam-534	171	8	)	)	PUNCT
ejpam-534	172	1	ẍ	ẍ	PROPN
ejpam-534	173	1	t.	t.	PROPN
ejpam-534	173	2	gulati	gulati	PROPN
ejpam-534	173	3	and	and	CCONJ
ejpam-534	173	4	g.	g.	PROPN
ejpam-534	173	5	mehndiratta	mehndiratta	PROPN
ejpam-534	173	6	/	/	SYM
ejpam-534	173	7	eur	eur	PROPN
ejpam-534	173	8	.	.	PUNCT
ejpam-534	174	1	j.	j.	PROPN
ejpam-534	174	2	pure	pure	PROPN
ejpam-534	174	3	appl	appl	PROPN
ejpam-534	174	4	.	.	PROPN
ejpam-534	174	5	math	math	PROPN
ejpam-534	174	6	,	,	PUNCT
ejpam-534	174	7	3	3	NUM
ejpam-534	174	8	(	(	PUNCT
ejpam-534	174	9	2010	2010	NUM
ejpam-534	174	10	)	)	PUNCT
ejpam-534	174	11	,	,	PUNCT
ejpam-534	174	12	786	786	NUM
ejpam-534	174	13	-	-	SYM
ejpam-534	174	14	805	805	NUM
ejpam-534	174	15	790	790	NUM
ejpam-534	174	16	+	+	CCONJ
ejpam-534	174	17	1	1	NUM
ejpam-534	174	18	2	2	NUM
ejpam-534	174	19	d3(β̄(t)t	d3(β̄(t)t	NOUN
ejpam-534	174	20	f	f	NOUN
ejpam-534	174	21	β̄(t))	β̄(t))	NOUN
ejpam-534	174	22	...	...	PUNCT
ejpam-534	174	23	x	x	X
ejpam-534	175	1	−	−	NOUN
ejpam-534	175	2	1	1	NUM
ejpam-534	175	3	2	2	NUM
ejpam-534	175	4	d4(β̄(t)t	d4(β̄(t)t	NOUN
ejpam-534	175	5	f	f	PROPN
ejpam-534	175	6	β̄(t))	β̄(t))	PROPN
ejpam-534	175	7	....	....	NOUN
ejpam-534	175	8	x	x	X
ejpam-534	175	9	)	)	PUNCT
ejpam-534	176	1	+	+	CCONJ
ejpam-534	176	2	(	(	PUNCT
ejpam-534	176	3	fx	fx	NOUN
ejpam-534	176	4	x	x	PUNCT
ejpam-534	176	5	−	−	PROPN
ejpam-534	176	6	d	d	INTJ
ejpam-534	176	7	fx	fx	PROPN
ejpam-534	176	8	ẋ	ẋ	PROPN
ejpam-534	177	1	+	+	CCONJ
ejpam-534	177	2	(	(	PUNCT
ejpam-534	177	3	gx	gx	PROPN
ejpam-534	177	4	ȳ(t))x	ȳ(t))x	PROPN
ejpam-534	177	5	−	−	PROPN
ejpam-534	177	6	d(gx	d(gx	PROPN
ejpam-534	177	7	ȳ(t	ȳ(t	NOUN
ejpam-534	177	8	)	)	PUNCT
ejpam-534	177	9	)	)	PUNCT
ejpam-534	178	1	ẋ	ẋ	PROPN
ejpam-534	178	2	−(d	−(d	NOUN
ejpam-534	178	3	(	(	PUNCT
ejpam-534	178	4	f	f	PROPN
ejpam-534	178	5	ẋ	ẋ	PROPN
ejpam-534	178	6	x	x	PUNCT
ejpam-534	179	1	+	+	PUNCT
ejpam-534	179	2	(	(	PUNCT
ejpam-534	179	3	g	g	PROPN
ejpam-534	179	4	ẋ	ẋ	PROPN
ejpam-534	179	5	ȳ(t))x)−	ȳ(t))x)−	PROPN
ejpam-534	179	6	d(d	d(d	PROPN
ejpam-534	179	7	(	(	PUNCT
ejpam-534	179	8	f	f	PROPN
ejpam-534	179	9	ẋ	ẋ	PROPN
ejpam-534	179	10	ẋ	ẋ	PROPN
ejpam-534	180	1	+	+	CCONJ
ejpam-534	180	2	(	(	PUNCT
ejpam-534	180	3	g	g	PROPN
ejpam-534	180	4	ẋ	ẋ	PROPN
ejpam-534	180	5	ȳ(t	ȳ(t	PROPN
ejpam-534	180	6	)	)	PUNCT
ejpam-534	180	7	)	)	PUNCT
ejpam-534	181	1	ẋ	ẋ	PROPN
ejpam-534	181	2	)	)	PUNCT
ejpam-534	181	3	)	)	PUNCT
ejpam-534	182	1	+	+	CCONJ
ejpam-534	183	1	d2(d	d2(d	PROPN
ejpam-534	183	2	(	(	PUNCT
ejpam-534	183	3	f	f	PROPN
ejpam-534	183	4	ẋ	ẋ	PROPN
ejpam-534	183	5	ẍ	ẍ	X
ejpam-534	184	1	+	+	CCONJ
ejpam-534	184	2	(	(	PUNCT
ejpam-534	184	3	g	g	PROPN
ejpam-534	184	4	ẋ	ẋ	PROPN
ejpam-534	184	5	ȳ(t	ȳ(t	PROPN
ejpam-534	184	6	)	)	PUNCT
ejpam-534	184	7	)	)	PUNCT
ejpam-534	185	1	ẍ	ẍ	X
ejpam-534	185	2	)	)	PUNCT
ejpam-534	185	3	)	)	PUNCT
ejpam-534	185	4	)	)	PUNCT
ejpam-534	186	1	+	+	X
ejpam-534	186	2	(	(	PUNCT
ejpam-534	186	3	(	(	PUNCT
ejpam-534	186	4	f	f	X
ejpam-534	186	5	+	+	ADV
ejpam-534	186	6	h)β̄(t))x	h)β̄(t))x	PROPN
ejpam-534	186	7	−	−	PROPN
ejpam-534	186	8	d((f	d((f	PUNCT
ejpam-534	186	9	+	+	NOUN
ejpam-534	186	10	h)β̄(t	h)β̄(t	ADJ
ejpam-534	186	11	)	)	PUNCT
ejpam-534	186	12	)	)	PUNCT
ejpam-534	186	13	ẋ	ẋ	PROPN
ejpam-534	187	1	+	+	CCONJ
ejpam-534	187	2	d2((f	d2((f	VERB
ejpam-534	187	3	+	+	ADJ
ejpam-534	187	4	h)β̄(t	h)β̄(t	ADJ
ejpam-534	187	5	)	)	PUNCT
ejpam-534	187	6	)	)	PUNCT
ejpam-534	187	7	ẍ	ẍ	PUNCT
ejpam-534	188	1	−	−	PROPN
ejpam-534	188	2	d3((f	d3((f	VERB
ejpam-534	188	3	+	+	NOUN
ejpam-534	188	4	h)β̄(t))	h)β̄(t))	ADJ
ejpam-534	188	5	...	...	PUNCT
ejpam-534	188	6	x	x	PUNCT
ejpam-534	189	1	+	+	PUNCT
ejpam-534	189	2	d4((f	d4((f	ADJ
ejpam-534	189	3	+	+	NOUN
ejpam-534	189	4	h)β̄(t))	h)β̄(t))	ADJ
ejpam-534	189	5	....	....	NOUN
ejpam-534	189	6	x	x	X
ejpam-534	189	7	)	)	PUNCT
ejpam-534	189	8	λ(t)−	λ(t)−	PROPN
ejpam-534	189	9	γ(t)(gx	γ(t)(gx	PROPN
ejpam-534	189	10	ȳ(t)−	ȳ(t)−	PROPN
ejpam-534	189	11	d(g	d(g	PROPN
ejpam-534	189	12	ẋ	ẋ	PROPN
ejpam-534	190	1	ȳ(t))−	ȳ(t))−	NOUN
ejpam-534	190	2	1	1	NUM
ejpam-534	190	3	2	2	NUM
ejpam-534	190	4	(	(	PUNCT
ejpam-534	190	5	β̄(t)t	β̄(t)t	PROPN
ejpam-534	190	6	hβ̄(t))x	hβ̄(t))x	PROPN
ejpam-534	191	1	+	+	CCONJ
ejpam-534	191	2	1	1	NUM
ejpam-534	191	3	2	2	NUM
ejpam-534	191	4	d(β̄(t)t	d(β̄(t)t	PROPN
ejpam-534	191	5	hβ̄(t	hβ̄(t	PROPN
ejpam-534	191	6	)	)	PUNCT
ejpam-534	191	7	)	)	PUNCT
ejpam-534	192	1	ẋ	ẋ	PROPN
ejpam-534	193	1	−	−	NOUN
ejpam-534	193	2	1	1	NUM
ejpam-534	193	3	2	2	NUM
ejpam-534	193	4	d2(β̄(t)t	d2(β̄(t)t	X
ejpam-534	193	5	hβ̄(t	hβ̄(t	PROPN
ejpam-534	193	6	)	)	PUNCT
ejpam-534	193	7	)	)	PUNCT
ejpam-534	193	8	ẍ	ẍ	PUNCT
ejpam-534	194	1	+	+	CCONJ
ejpam-534	194	2	1	1	NUM
ejpam-534	194	3	2	2	NUM
ejpam-534	194	4	d3(β̄(t)t	d3(β̄(t)t	NOUN
ejpam-534	194	5	hβ̄(t))	hβ̄(t))	PROPN
ejpam-534	194	6	...	...	PUNCT
ejpam-534	194	7	x	x	X
ejpam-534	194	8	−	−	NOUN
ejpam-534	194	9	1	1	NUM
ejpam-534	194	10	2	2	NUM
ejpam-534	194	11	d4(β̄(t)t	d4(β̄(t)t	X
ejpam-534	194	12	hβ̄(t))	hβ̄(t))	PROPN
ejpam-534	194	13	....	....	NOUN
ejpam-534	194	14	x	x	X
ejpam-534	194	15	)	)	PUNCT
ejpam-534	194	16	=	=	SYM
ejpam-534	194	17	0	0	NUM
ejpam-534	194	18	,	,	PUNCT
ejpam-534	194	19	t	t	PROPN
ejpam-534	194	20	∈	∈	PROPN
ejpam-534	195	1	i	i	PRON
ejpam-534	195	2	,	,	PUNCT
ejpam-534	195	3	(	(	PUNCT
ejpam-534	195	4	9	9	X
ejpam-534	195	5	)	)	PUNCT
ejpam-534	195	6	λ(t)t	λ(t)t	NOUN
ejpam-534	195	7	(	(	PUNCT
ejpam-534	195	8	g	g	NOUN
ejpam-534	195	9	j	j	PROPN
ejpam-534	195	10	x	x	PROPN
ejpam-534	196	1	+	+	CCONJ
ejpam-534	196	2	g	g	PROPN
ejpam-534	196	3	j	j	NOUN
ejpam-534	196	4	x	x	PUNCT
ejpam-534	196	5	x	x	PUNCT
ejpam-534	197	1	β̄(t))−	β̄(t))−	NOUN
ejpam-534	197	2	γ(t)(g	γ(t)(g	NUM
ejpam-534	197	3	j	j	NOUN
ejpam-534	198	1	−	−	NUM
ejpam-534	198	2	1	1	NUM
ejpam-534	198	3	2	2	NUM
ejpam-534	198	4	β̄(t)t	β̄(t)t	NOUN
ejpam-534	198	5	g	g	PROPN
ejpam-534	198	6	j	j	PROPN
ejpam-534	198	7	x	x	X
ejpam-534	198	8	x	x	PROPN
ejpam-534	198	9	β̄(t))−µ	β̄(t))−µ	PROPN
ejpam-534	198	10	j(t	j(t	PROPN
ejpam-534	198	11	)	)	PUNCT
ejpam-534	198	12	=	=	PUNCT
ejpam-534	199	1	0	0	NUM
ejpam-534	199	2	,	,	PUNCT
ejpam-534	199	3	t	t	PROPN
ejpam-534	199	4	∈	∈	PROPN
ejpam-534	200	1	i	i	PRON
ejpam-534	200	2	,	,	PUNCT
ejpam-534	200	3	j	j	PROPN
ejpam-534	200	4	∈	∈	PROPN
ejpam-534	200	5	m	m	PRON
ejpam-534	200	6	,	,	PUNCT
ejpam-534	200	7	(	(	PUNCT
ejpam-534	200	8	10	10	NUM
ejpam-534	200	9	)	)	PUNCT
ejpam-534	200	10	(	(	PUNCT
ejpam-534	200	11	λ(t	λ(t	X
ejpam-534	200	12	)	)	PUNCT
ejpam-534	201	1	+	+	ADP
ejpam-534	201	2	αβ̄(t))t	αβ̄(t))t	NOUN
ejpam-534	201	3	f	f	X
ejpam-534	202	1	+	+	CCONJ
ejpam-534	202	2	(	(	PUNCT
ejpam-534	202	3	λ(t	λ(t	NOUN
ejpam-534	202	4	)	)	PUNCT
ejpam-534	203	1	+	+	CCONJ
ejpam-534	203	2	γ(t)β̄(t))t	γ(t)β̄(t))t	PART
ejpam-534	203	3	h	h	NOUN
ejpam-534	203	4	=	=	SYM
ejpam-534	203	5	0	0	NUM
ejpam-534	203	6	,	,	PUNCT
ejpam-534	203	7	t	t	PROPN
ejpam-534	203	8	∈	∈	PROPN
ejpam-534	204	1	i	i	PRON
ejpam-534	204	2	,	,	PUNCT
ejpam-534	204	3	(	(	PUNCT
ejpam-534	204	4	11	11	NUM
ejpam-534	204	5	)	)	PUNCT
ejpam-534	204	6	γ(t	γ(t	NOUN
ejpam-534	204	7	)	)	PUNCT
ejpam-534	204	8	(	(	PUNCT
ejpam-534	204	9	ȳ(t)t	ȳ(t)t	NOUN
ejpam-534	204	10	g	g	NOUN
ejpam-534	204	11	−	−	PROPN
ejpam-534	204	12	1	1	NUM
ejpam-534	204	13	2	2	NUM
ejpam-534	204	14	β̄(t)t	β̄(t)t	PROPN
ejpam-534	204	15	hβ̄(t	hβ̄(t	PROPN
ejpam-534	204	16	)	)	PUNCT
ejpam-534	204	17	)	)	PUNCT
ejpam-534	205	1	=	=	SYM
ejpam-534	205	2	0	0	NUM
ejpam-534	205	3	,	,	PUNCT
ejpam-534	205	4	t	t	PROPN
ejpam-534	205	5	∈	∈	PROPN
ejpam-534	206	1	i	i	PRON
ejpam-534	206	2	,	,	PUNCT
ejpam-534	206	3	(	(	PUNCT
ejpam-534	206	4	12	12	NUM
ejpam-534	206	5	)	)	PUNCT
ejpam-534	206	6	µ(t)t	µ(t)t	NOUN
ejpam-534	206	7	ȳ(t	ȳ(t	NOUN
ejpam-534	206	8	)	)	PUNCT
ejpam-534	206	9	=	=	SYM
ejpam-534	206	10	0	0	NUM
ejpam-534	206	11	,	,	PUNCT
ejpam-534	206	12	t	t	PROPN
ejpam-534	206	13	∈	∈	PROPN
ejpam-534	207	1	i	i	PRON
ejpam-534	207	2	,	,	PUNCT
ejpam-534	207	3	(	(	PUNCT
ejpam-534	207	4	13	13	NUM
ejpam-534	207	5	)	)	PUNCT
ejpam-534	207	6	(	(	PUNCT
ejpam-534	207	7	α	α	NOUN
ejpam-534	207	8	,	,	PUNCT
ejpam-534	207	9	γ(t),µ(t	γ(t),µ(t	NUM
ejpam-534	207	10	)	)	PUNCT
ejpam-534	207	11	)	)	PUNCT
ejpam-534	207	12	≧	≧	X
ejpam-534	207	13	0	0	NUM
ejpam-534	207	14	,	,	PUNCT
ejpam-534	207	15	t	t	PROPN
ejpam-534	207	16	∈	∈	PROPN
ejpam-534	208	1	i	i	PRON
ejpam-534	208	2	,	,	PUNCT
ejpam-534	208	3	(	(	PUNCT
ejpam-534	208	4	14	14	NUM
ejpam-534	208	5	)	)	PUNCT
ejpam-534	208	6	(	(	PUNCT
ejpam-534	208	7	α	α	NOUN
ejpam-534	208	8	,	,	PUNCT
ejpam-534	208	9	λ(t),γ(t),µ(t	λ(t),γ(t),µ(t	NOUN
ejpam-534	208	10	)	)	PUNCT
ejpam-534	208	11	)	)	PUNCT
ejpam-534	209	1	6=	6=	ADP
ejpam-534	209	2	0	0	NUM
ejpam-534	209	3	,	,	PUNCT
ejpam-534	209	4	t	t	PROPN
ejpam-534	209	5	∈	∈	PROPN
ejpam-534	210	1	i	i	PRON
ejpam-534	210	2	.	.	PUNCT
ejpam-534	211	1	(	(	PUNCT
ejpam-534	211	2	15	15	NUM
ejpam-534	211	3	)	)	PUNCT
ejpam-534	211	4	by	by	ADP
ejpam-534	211	5	hypothesis	hypothesis	NOUN
ejpam-534	211	6	(	(	PUNCT
ejpam-534	211	7	b1	b1	NOUN
ejpam-534	211	8	)	)	PUNCT
ejpam-534	211	9	,	,	PUNCT
ejpam-534	211	10	equation	equation	NOUN
ejpam-534	211	11	(	(	PUNCT
ejpam-534	211	12	11	11	NUM
ejpam-534	211	13	)	)	PUNCT
ejpam-534	211	14	yields	yield	NOUN
ejpam-534	211	15	λ(t	λ(t	NOUN
ejpam-534	211	16	)	)	PUNCT
ejpam-534	211	17	+	+	NOUN
ejpam-534	211	18	αβ̄(t	αβ̄(t	X
ejpam-534	211	19	)	)	PUNCT
ejpam-534	211	20	=	=	SYM
ejpam-534	211	21	0	0	NUM
ejpam-534	211	22	,	,	PUNCT
ejpam-534	211	23	t	t	PROPN
ejpam-534	211	24	∈	∈	PROPN
ejpam-534	212	1	i	i	PRON
ejpam-534	212	2	and	and	CCONJ
ejpam-534	212	3	(	(	PUNCT
ejpam-534	212	4	16	16	NUM
ejpam-534	212	5	)	)	PUNCT
ejpam-534	212	6	λ(t	λ(t	NOUN
ejpam-534	212	7	)	)	PUNCT
ejpam-534	212	8	+	+	CCONJ
ejpam-534	212	9	γ(t)β̄(t	γ(t)β̄(t	NOUN
ejpam-534	212	10	)	)	PUNCT
ejpam-534	212	11	=	=	SYM
ejpam-534	212	12	0	0	NUM
ejpam-534	212	13	,	,	PUNCT
ejpam-534	212	14	t	t	PROPN
ejpam-534	212	15	∈	∈	PROPN
ejpam-534	213	1	i	i	PRON
ejpam-534	213	2	.	.	PUNCT
ejpam-534	214	1	(	(	PUNCT
ejpam-534	214	2	17	17	NUM
ejpam-534	214	3	)	)	PUNCT
ejpam-534	214	4	using	use	VERB
ejpam-534	214	5	(	(	PUNCT
ejpam-534	214	6	6	6	NUM
ejpam-534	214	7	)	)	PUNCT
ejpam-534	214	8	,	,	PUNCT
ejpam-534	214	9	(	(	PUNCT
ejpam-534	214	10	16	16	NUM
ejpam-534	214	11	)	)	PUNCT
ejpam-534	214	12	and	and	CCONJ
ejpam-534	214	13	(	(	PUNCT
ejpam-534	214	14	17	17	NUM
ejpam-534	214	15	)	)	PUNCT
ejpam-534	214	16	in	in	ADP
ejpam-534	214	17	(	(	PUNCT
ejpam-534	214	18	9	9	NUM
ejpam-534	214	19	)	)	PUNCT
ejpam-534	214	20	,	,	PUNCT
ejpam-534	214	21	we	we	PRON
ejpam-534	214	22	have	have	VERB
ejpam-534	214	23	(	(	PUNCT
ejpam-534	214	24	α−	α−	ADP
ejpam-534	214	25	γ(t))(gx	γ(t))(gx	NOUN
ejpam-534	214	26	ȳ(t)−	ȳ(t)−	PROPN
ejpam-534	214	27	d(g	d(g	PROPN
ejpam-534	214	28	ẋ	ẋ	PROPN
ejpam-534	214	29	ȳ(t	ȳ(t	PROPN
ejpam-534	214	30	)	)	PUNCT
ejpam-534	214	31	)	)	PUNCT
ejpam-534	215	1	+	+	NOUN
ejpam-534	215	2	hβ̄(t	hβ̄(t	NOUN
ejpam-534	215	3	)	)	PUNCT
ejpam-534	215	4	)	)	PUNCT
ejpam-534	216	1	+	+	CCONJ
ejpam-534	216	2	1	1	NUM
ejpam-534	216	3	2	2	NUM
ejpam-534	216	4	α((β̄(t)t	α((β̄(t)t	NUM
ejpam-534	216	5	f	f	NOUN
ejpam-534	216	6	β̄(t))x	β̄(t))x	NOUN
ejpam-534	216	7	−	−	PROPN
ejpam-534	216	8	d(β̄(t)t	d(β̄(t)t	PROPN
ejpam-534	216	9	f	f	PROPN
ejpam-534	216	10	β̄(t	β̄(t	PROPN
ejpam-534	216	11	)	)	PUNCT
ejpam-534	216	12	)	)	PUNCT
ejpam-534	216	13	ẋ	ẋ	PUNCT
ejpam-534	217	1	+	+	ADJ
ejpam-534	217	2	d2(β̄(t)t	d2(β̄(t)t	X
ejpam-534	217	3	f	f	NOUN
ejpam-534	217	4	β̄(t	β̄(t	PROPN
ejpam-534	217	5	)	)	PUNCT
ejpam-534	217	6	)	)	PUNCT
ejpam-534	217	7	ẍ	ẍ	PUNCT
ejpam-534	218	1	−	−	PROPN
ejpam-534	218	2	d3(β̄(t)t	d3(β̄(t)t	NOUN
ejpam-534	218	3	f	f	PROPN
ejpam-534	218	4	β̄(t))	β̄(t))	PROPN
ejpam-534	218	5	...	...	PUNCT
ejpam-534	218	6	x	x	X
ejpam-534	219	1	+	+	PUNCT
ejpam-534	219	2	d4(β̄(t)t	d4(β̄(t)t	X
ejpam-534	219	3	f	f	NOUN
ejpam-534	219	4	β̄(t))	β̄(t))	PROPN
ejpam-534	219	5	....	....	NOUN
ejpam-534	219	6	x	x	X
ejpam-534	219	7	)	)	PUNCT
ejpam-534	220	1	+	+	CCONJ
ejpam-534	220	2	(	(	PUNCT
ejpam-534	220	3	(	(	PUNCT
ejpam-534	220	4	(	(	PUNCT
ejpam-534	220	5	f	f	X
ejpam-534	220	6	+	+	ADV
ejpam-534	220	7	h)β̄(t))x	h)β̄(t))x	PROPN
ejpam-534	220	8	−	−	PROPN
ejpam-534	220	9	d((f	d((f	PUNCT
ejpam-534	220	10	+	+	NOUN
ejpam-534	220	11	h)β̄(t	h)β̄(t	ADJ
ejpam-534	220	12	)	)	PUNCT
ejpam-534	220	13	)	)	PUNCT
ejpam-534	220	14	ẋ	ẋ	PROPN
ejpam-534	221	1	+	+	CCONJ
ejpam-534	221	2	d2((f	d2((f	VERB
ejpam-534	221	3	+	+	ADJ
ejpam-534	221	4	h)β̄(t	h)β̄(t	ADJ
ejpam-534	221	5	)	)	PUNCT
ejpam-534	221	6	)	)	PUNCT
ejpam-534	221	7	ẍ	ẍ	PUNCT
ejpam-534	222	1	−	−	PROPN
ejpam-534	222	2	d3((f	d3((f	VERB
ejpam-534	222	3	+	+	NOUN
ejpam-534	222	4	h)β̄(t))	h)β̄(t))	ADJ
ejpam-534	222	5	...	...	PUNCT
ejpam-534	222	6	x	x	X
ejpam-534	223	1	+	+	X
ejpam-534	223	2	d4((f	d4((f	VERB
ejpam-534	223	3	+	+	ADJ
ejpam-534	223	4	h)β̄(t))	h)β̄(t))	ADJ
ejpam-534	223	5	....	....	NOUN
ejpam-534	223	6	x	x	X
ejpam-534	223	7	)	)	PUNCT
ejpam-534	223	8	λ(t	λ(t	NOUN
ejpam-534	223	9	)	)	PUNCT
ejpam-534	224	1	+	+	CCONJ
ejpam-534	224	2	1	1	NUM
ejpam-534	224	3	2	2	NUM
ejpam-534	224	4	γ(t)((β̄(t)t	γ(t)((β̄(t)t	X
ejpam-534	224	5	hβ̄(t))x	hβ̄(t))x	NOUN
ejpam-534	225	1	−	−	PROPN
ejpam-534	225	2	d(β̄(t)t	d(β̄(t)t	PROPN
ejpam-534	225	3	hβ̄(t	hβ̄(t	PROPN
ejpam-534	225	4	)	)	PUNCT
ejpam-534	225	5	)	)	PUNCT
ejpam-534	226	1	ẋ	ẋ	PUNCT
ejpam-534	227	1	+	+	NUM
ejpam-534	227	2	d2(β̄(t)t	d2(β̄(t)t	ADJ
ejpam-534	227	3	hβ̄(t	hβ̄(t	PROPN
ejpam-534	227	4	)	)	PUNCT
ejpam-534	227	5	)	)	PUNCT
ejpam-534	227	6	ẍ	ẍ	PUNCT
ejpam-534	228	1	−	−	PROPN
ejpam-534	228	2	d3(β̄(t)t	d3(β̄(t)t	NOUN
ejpam-534	228	3	hβ̄(t))	hβ̄(t))	PROPN
ejpam-534	228	4	...	...	PUNCT
ejpam-534	228	5	x	x	X
ejpam-534	229	1	+	+	X
ejpam-534	229	2	d4(β̄(t)t	d4(β̄(t)t	ADJ
ejpam-534	229	3	hβ̄(t))	hβ̄(t))	PROPN
ejpam-534	229	4	....	....	NOUN
ejpam-534	229	5	x	x	X
ejpam-534	229	6	)	)	PUNCT
ejpam-534	229	7	=	=	SYM
ejpam-534	229	8	0	0	NUM
ejpam-534	229	9	,	,	PUNCT
ejpam-534	229	10	t	t	PROPN
ejpam-534	229	11	∈	∈	PROPN
ejpam-534	230	1	i	i	PRON
ejpam-534	230	2	.	.	PUNCT
ejpam-534	231	1	(	(	PUNCT
ejpam-534	231	2	18	18	NUM
ejpam-534	231	3	)	)	PUNCT
ejpam-534	231	4	let	let	VERB
ejpam-534	231	5	γ(t	γ(t	NOUN
ejpam-534	231	6	)	)	PUNCT
ejpam-534	232	1	=	=	SYM
ejpam-534	232	2	0	0	NUM
ejpam-534	232	3	for	for	ADP
ejpam-534	232	4	some	some	DET
ejpam-534	232	5	t.	t.	NOUN
ejpam-534	232	6	suppose	suppose	VERB
ejpam-534	232	7	t0	t0	PROPN
ejpam-534	232	8	∈	∈	PROPN
ejpam-534	232	9	i	i	PRON
ejpam-534	232	10	and	and	CCONJ
ejpam-534	232	11	γ(t0	γ(t0	NOUN
ejpam-534	232	12	)	)	PUNCT
ejpam-534	233	1	=	=	SYM
ejpam-534	234	1	0	0	X
ejpam-534	234	2	.	.	PUNCT
ejpam-534	234	3	then	then	ADV
ejpam-534	234	4	by	by	ADP
ejpam-534	234	5	(	(	PUNCT
ejpam-534	234	6	17	17	NUM
ejpam-534	234	7	)	)	PUNCT
ejpam-534	234	8	,	,	PUNCT
ejpam-534	234	9	we	we	PRON
ejpam-534	234	10	get	get	VERB
ejpam-534	234	11	λ(t0	λ(t0	NOUN
ejpam-534	234	12	)	)	PUNCT
ejpam-534	235	1	=	=	SYM
ejpam-534	235	2	0	0	NUM
ejpam-534	236	1	and	and	CCONJ
ejpam-534	236	2	so	so	ADV
ejpam-534	236	3	αβ̄(t0	αβ̄(t0	NUM
ejpam-534	236	4	)	)	PUNCT
ejpam-534	237	1	=	=	PUNCT
ejpam-534	237	2	0	0	NUM
ejpam-534	237	3	,	,	PUNCT
ejpam-534	237	4	by	by	ADP
ejpam-534	237	5	(	(	PUNCT
ejpam-534	237	6	16	16	NUM
ejpam-534	237	7	)	)	PUNCT
ejpam-534	237	8	.	.	PUNCT
ejpam-534	238	1	thus	thus	ADV
ejpam-534	238	2	(	(	PUNCT
ejpam-534	238	3	18	18	NUM
ejpam-534	238	4	)	)	PUNCT
ejpam-534	238	5	yields	yield	VERB
ejpam-534	238	6	α(gx	α(gx	PROPN
ejpam-534	238	7	ȳ(t0)−	ȳ(t0)−	PROPN
ejpam-534	238	8	d(g	d(g	PROPN
ejpam-534	238	9	ẋ	ẋ	PROPN
ejpam-534	238	10	ȳ(t0	ȳ(t0	PROPN
ejpam-534	238	11	)	)	PUNCT
ejpam-534	238	12	)	)	PUNCT
ejpam-534	238	13	)	)	PUNCT
ejpam-534	239	1	=	=	PUNCT
ejpam-534	239	2	0	0	NUM
ejpam-534	239	3	,	,	PUNCT
ejpam-534	239	4	which	which	PRON
ejpam-534	239	5	by	by	ADP
ejpam-534	239	6	hypothesis	hypothesis	NOUN
ejpam-534	239	7	(	(	PUNCT
ejpam-534	239	8	b2	b2	NOUN
ejpam-534	239	9	)	)	PUNCT
ejpam-534	239	10	implies	imply	VERB
ejpam-534	239	11	α	α	X
ejpam-534	239	12	=	=	SYM
ejpam-534	239	13	0	0	PROPN
ejpam-534	239	14	.	.	PUNCT
ejpam-534	239	15	since	since	SCONJ
ejpam-534	239	16	λ(t0	λ(t0	NOUN
ejpam-534	239	17	)	)	PUNCT
ejpam-534	240	1	=	=	SYM
ejpam-534	240	2	0	0	NUM
ejpam-534	240	3	and	and	CCONJ
ejpam-534	240	4	γ(t0	γ(t0	NUM
ejpam-534	240	5	)	)	PUNCT
ejpam-534	241	1	=	=	SYM
ejpam-534	241	2	0	0	NUM
ejpam-534	241	3	,	,	PUNCT
ejpam-534	241	4	from	from	ADP
ejpam-534	241	5	(	(	PUNCT
ejpam-534	241	6	10	10	NUM
ejpam-534	241	7	)	)	PUNCT
ejpam-534	241	8	,	,	PUNCT
ejpam-534	241	9	we	we	PRON
ejpam-534	241	10	obtain	obtain	VERB
ejpam-534	241	11	µ	µ	X
ejpam-534	241	12	j(t0	j(t0	NOUN
ejpam-534	241	13	)	)	PUNCT
ejpam-534	242	1	=	=	SYM
ejpam-534	242	2	0	0	NUM
ejpam-534	242	3	,	,	PUNCT
ejpam-534	242	4	j	j	PROPN
ejpam-534	242	5	∈	∈	PROPN
ejpam-534	242	6	m	m	VERB
ejpam-534	242	7	.	.	PUNCT
ejpam-534	243	1	therefore	therefore	ADV
ejpam-534	243	2	(	(	PUNCT
ejpam-534	243	3	α	α	X
ejpam-534	243	4	,	,	PUNCT
ejpam-534	243	5	λ(t0),γ(t0),µ(t0	λ(t0),γ(t0),µ(t0	PROPN
ejpam-534	243	6	)	)	PUNCT
ejpam-534	243	7	)	)	PUNCT
ejpam-534	244	1	=	=	SYM
ejpam-534	244	2	0	0	NUM
ejpam-534	244	3	,	,	PUNCT
ejpam-534	244	4	contradicting	contradict	VERB
ejpam-534	244	5	(	(	PUNCT
ejpam-534	244	6	15	15	NUM
ejpam-534	244	7	)	)	PUNCT
ejpam-534	244	8	.	.	PUNCT
ejpam-534	245	1	hence	hence	ADV
ejpam-534	245	2	γ(t	γ(t	NOUN
ejpam-534	245	3	)	)	PUNCT
ejpam-534	245	4	>	>	X
ejpam-534	246	1	0	0	NUM
ejpam-534	246	2	,	,	PUNCT
ejpam-534	246	3	t	t	PROPN
ejpam-534	246	4	∈	∈	PROPN
ejpam-534	247	1	i	i	PRON
ejpam-534	247	2	.	.	PUNCT
ejpam-534	248	1	now	now	ADV
ejpam-534	248	2	,	,	PUNCT
ejpam-534	248	3	multiplying	multiply	VERB
ejpam-534	248	4	(	(	PUNCT
ejpam-534	248	5	10	10	NUM
ejpam-534	248	6	)	)	PUNCT
ejpam-534	248	7	by	by	ADP
ejpam-534	248	8	ȳ	ȳ	PROPN
ejpam-534	248	9	j(t	j(t	PROPN
ejpam-534	248	10	)	)	PUNCT
ejpam-534	248	11	,	,	PUNCT
ejpam-534	248	12	t	t	PROPN
ejpam-534	248	13	∈	∈	PROPN
ejpam-534	249	1	i	i	PRON
ejpam-534	249	2	,	,	PUNCT
ejpam-534	249	3	summing	sum	VERB
ejpam-534	249	4	over	over	ADP
ejpam-534	249	5	j	j	PROPN
ejpam-534	249	6	,	,	PUNCT
ejpam-534	249	7	and	and	CCONJ
ejpam-534	249	8	then	then	ADV
ejpam-534	249	9	using	use	VERB
ejpam-534	249	10	(	(	PUNCT
ejpam-534	249	11	12	12	NUM
ejpam-534	249	12	)	)	PUNCT
ejpam-534	249	13	,	,	PUNCT
ejpam-534	249	14	(	(	PUNCT
ejpam-534	249	15	13	13	NUM
ejpam-534	249	16	)	)	PUNCT
ejpam-534	249	17	,	,	PUNCT
ejpam-534	249	18	(	(	PUNCT
ejpam-534	249	19	17	17	NUM
ejpam-534	249	20	)	)	PUNCT
ejpam-534	249	21	and	and	CCONJ
ejpam-534	249	22	γ(t	γ(t	NOUN
ejpam-534	249	23	)	)	PUNCT
ejpam-534	249	24	>	>	X
ejpam-534	249	25	0	0	NUM
ejpam-534	249	26	,	,	PUNCT
ejpam-534	249	27	t	t	PROPN
ejpam-534	249	28	∈	∈	PROPN
ejpam-534	250	1	i	i	PRON
ejpam-534	250	2	,	,	PUNCT
ejpam-534	250	3	we	we	PRON
ejpam-534	250	4	get	get	VERB
ejpam-534	250	5	2β̄(t)t	2β̄(t)t	NUM
ejpam-534	250	6	(	(	PUNCT
ejpam-534	250	7	gx	gx	PROPN
ejpam-534	250	8	ȳ(t	ȳ(t	PROPN
ejpam-534	250	9	)	)	PUNCT
ejpam-534	250	10	)	)	PUNCT
ejpam-534	251	1	+	+	CCONJ
ejpam-534	252	1	β̄(t)t	β̄(t)t	NOUN
ejpam-534	252	2	(	(	PUNCT
ejpam-534	252	3	h	h	NOUN
ejpam-534	252	4	+	+	CCONJ
ejpam-534	252	5	(	(	PUNCT
ejpam-534	252	6	gx	gx	PROPN
ejpam-534	252	7	ȳ(t))x)β̄(t	ȳ(t))x)β̄(t	PROPN
ejpam-534	252	8	)	)	PUNCT
ejpam-534	252	9	=	=	SYM
ejpam-534	252	10	0	0	NUM
ejpam-534	252	11	,	,	PUNCT
ejpam-534	252	12	t	t	PROPN
ejpam-534	252	13	∈	∈	PROPN
ejpam-534	253	1	i	i	PRON
ejpam-534	253	2	,	,	PUNCT
ejpam-534	253	3	t.	t.	PROPN
ejpam-534	253	4	gulati	gulati	PROPN
ejpam-534	253	5	and	and	CCONJ
ejpam-534	253	6	g.	g.	PROPN
ejpam-534	253	7	mehndiratta	mehndiratta	PROPN
ejpam-534	253	8	/	/	SYM
ejpam-534	253	9	eur	eur	PROPN
ejpam-534	253	10	.	.	PUNCT
ejpam-534	254	1	j.	j.	PROPN
ejpam-534	254	2	pure	pure	PROPN
ejpam-534	254	3	appl	appl	PROPN
ejpam-534	254	4	.	.	PROPN
ejpam-534	254	5	math	math	PROPN
ejpam-534	254	6	,	,	PUNCT
ejpam-534	254	7	3	3	NUM
ejpam-534	254	8	(	(	PUNCT
ejpam-534	254	9	2010	2010	NUM
ejpam-534	254	10	)	)	PUNCT
ejpam-534	254	11	,	,	PUNCT
ejpam-534	254	12	786	786	NUM
ejpam-534	254	13	-	-	SYM
ejpam-534	254	14	805	805	NUM
ejpam-534	254	15	791	791	NUM
ejpam-534	254	16	which	which	PRON
ejpam-534	254	17	contradicts	contradict	VERB
ejpam-534	254	18	hypothesis	hypothesis	NOUN
ejpam-534	254	19	(	(	PUNCT
ejpam-534	254	20	b3	b3	PROPN
ejpam-534	254	21	)	)	PUNCT
ejpam-534	254	22	unless	unless	SCONJ
ejpam-534	254	23	β̄(t	β̄(t	NUM
ejpam-534	254	24	)	)	PUNCT
ejpam-534	254	25	=	=	SYM
ejpam-534	254	26	0	0	NUM
ejpam-534	254	27	,	,	PUNCT
ejpam-534	254	28	t	t	PROPN
ejpam-534	254	29	∈	∈	PROPN
ejpam-534	255	1	i	i	PRON
ejpam-534	255	2	.	.	PUNCT
ejpam-534	256	1	(	(	PUNCT
ejpam-534	256	2	19	19	NUM
ejpam-534	256	3	)	)	PUNCT
ejpam-534	256	4	thus	thus	ADV
ejpam-534	256	5	from	from	ADP
ejpam-534	256	6	(	(	PUNCT
ejpam-534	256	7	16	16	NUM
ejpam-534	256	8	)	)	PUNCT
ejpam-534	256	9	,	,	PUNCT
ejpam-534	256	10	λ(t	λ(t	X
ejpam-534	256	11	)	)	PUNCT
ejpam-534	256	12	=	=	SYM
ejpam-534	257	1	0	0	NUM
ejpam-534	257	2	,	,	PUNCT
ejpam-534	257	3	t	t	PROPN
ejpam-534	257	4	∈	∈	PROPN
ejpam-534	258	1	i	i	PRON
ejpam-534	258	2	.	.	PUNCT
ejpam-534	259	1	therefore	therefore	ADV
ejpam-534	259	2	for	for	ADP
ejpam-534	259	3	j	j	PROPN
ejpam-534	259	4	∈	∈	PROPN
ejpam-534	259	5	m	m	PROPN
ejpam-534	259	6	,	,	PUNCT
ejpam-534	259	7	equation	equation	NOUN
ejpam-534	259	8	(	(	PUNCT
ejpam-534	259	9	10	10	NUM
ejpam-534	259	10	)	)	PUNCT
ejpam-534	259	11	gives	give	VERB
ejpam-534	259	12	g	g	PRON
ejpam-534	259	13	j	j	PROPN
ejpam-534	259	14	=	=	SYM
ejpam-534	259	15	−	−	PROPN
ejpam-534	259	16	µ	µ	X
ejpam-534	259	17	j(t	j(t	PROPN
ejpam-534	259	18	)	)	PUNCT
ejpam-534	259	19	γ(t	γ(t	NOUN
ejpam-534	259	20	)	)	PUNCT
ejpam-534	259	21	≦	≦	NUM
ejpam-534	259	22	0	0	NUM
ejpam-534	259	23	,	,	PUNCT
ejpam-534	259	24	t	t	PROPN
ejpam-534	259	25	∈	∈	PROPN
ejpam-534	260	1	i	i	PRON
ejpam-534	260	2	.	.	PUNCT
ejpam-534	261	1	thus	thus	ADV
ejpam-534	261	2	ū(t	ū(t	ADJ
ejpam-534	261	3	)	)	PUNCT
ejpam-534	261	4	is	be	AUX
ejpam-534	261	5	feasible	feasible	ADJ
ejpam-534	261	6	for	for	ADP
ejpam-534	261	7	(	(	PUNCT
ejpam-534	261	8	cp	cp	NOUN
ejpam-534	261	9	)	)	PUNCT
ejpam-534	261	10	.	.	PUNCT
ejpam-534	262	1	also	also	ADV
ejpam-534	262	2	,	,	PUNCT
ejpam-534	262	3	in	in	ADP
ejpam-534	262	4	view	view	NOUN
ejpam-534	262	5	of	of	ADP
ejpam-534	262	6	(	(	PUNCT
ejpam-534	262	7	19	19	NUM
ejpam-534	262	8	)	)	PUNCT
ejpam-534	262	9	,	,	PUNCT
ejpam-534	262	10	the	the	DET
ejpam-534	262	11	two	two	NUM
ejpam-534	262	12	objectives	objective	NOUN
ejpam-534	262	13	are	be	AUX
ejpam-534	262	14	equal	equal	ADJ
ejpam-534	262	15	.	.	PUNCT
ejpam-534	263	1	now	now	ADV
ejpam-534	263	2	,	,	PUNCT
ejpam-534	263	3	assume	assume	VERB
ejpam-534	263	4	that	that	SCONJ
ejpam-534	263	5	ū(t	ū(t	NOUN
ejpam-534	263	6	)	)	PUNCT
ejpam-534	263	7	is	be	AUX
ejpam-534	263	8	not	not	PART
ejpam-534	263	9	an	an	DET
ejpam-534	263	10	optimal	optimal	ADJ
ejpam-534	263	11	solution	solution	NOUN
ejpam-534	263	12	of	of	ADP
ejpam-534	263	13	(	(	PUNCT
ejpam-534	263	14	cp	cp	NOUN
ejpam-534	263	15	)	)	PUNCT
ejpam-534	263	16	.	.	PUNCT
ejpam-534	264	1	then	then	ADV
ejpam-534	264	2	,	,	PUNCT
ejpam-534	264	3	there	there	PRON
ejpam-534	264	4	exists	exist	VERB
ejpam-534	264	5	û(t	û(t	NOUN
ejpam-534	264	6	)	)	PUNCT
ejpam-534	264	7	∈	∈	PROPN
ejpam-534	264	8	x	x	PUNCT
ejpam-534	265	1	such	such	ADJ
ejpam-534	265	2	that	that	SCONJ
ejpam-534	265	3	b∫	b∫	NOUN
ejpam-534	265	4	a	a	DET
ejpam-534	265	5	f	f	X
ejpam-534	265	6	(	(	PUNCT
ejpam-534	265	7	t	t	PROPN
ejpam-534	265	8	,	,	PUNCT
ejpam-534	265	9	û	û	NUM
ejpam-534	265	10	,	,	PUNCT
ejpam-534	265	11	˙̂u)d	˙̂u)d	PROPN
ejpam-534	265	12	t	t	PROPN
ejpam-534	265	13	<	<	X
ejpam-534	265	14	b∫	b∫	PROPN
ejpam-534	265	15	a	a	DET
ejpam-534	265	16	f	f	X
ejpam-534	265	17	(	(	PUNCT
ejpam-534	265	18	t	t	PROPN
ejpam-534	265	19	,	,	PUNCT
ejpam-534	265	20	ū	ū	NOUN
ejpam-534	265	21	,	,	PUNCT
ejpam-534	265	22	˙̄u)d	˙̄u)d	PUNCT
ejpam-534	266	1	t.	t.	PROPN
ejpam-534	266	2	as	as	ADP
ejpam-534	266	3	β̄(t	β̄(t	PROPN
ejpam-534	266	4	)	)	PUNCT
ejpam-534	266	5	=	=	SYM
ejpam-534	266	6	0	0	NUM
ejpam-534	266	7	,	,	PUNCT
ejpam-534	266	8	t	t	PROPN
ejpam-534	266	9	∈	∈	PROPN
ejpam-534	267	1	i	i	PRON
ejpam-534	267	2	,	,	PUNCT
ejpam-534	267	3	we	we	PRON
ejpam-534	267	4	have	have	VERB
ejpam-534	267	5	b∫	b∫	NOUN
ejpam-534	267	6	a	a	PRON
ejpam-534	267	7	f	f	X
ejpam-534	267	8	(	(	PUNCT
ejpam-534	267	9	t	t	PROPN
ejpam-534	267	10	,	,	PUNCT
ejpam-534	267	11	û	û	NUM
ejpam-534	267	12	,	,	PUNCT
ejpam-534	267	13	˙̂u)d	˙̂u)d	PROPN
ejpam-534	267	14	t	t	PROPN
ejpam-534	267	15	<	<	X
ejpam-534	267	16	b∫	b∫	PROPN
ejpam-534	267	17	a	a	X
ejpam-534	267	18	(	(	PUNCT
ejpam-534	267	19	f	f	PROPN
ejpam-534	267	20	(	(	PUNCT
ejpam-534	267	21	t	t	PROPN
ejpam-534	267	22	,	,	PUNCT
ejpam-534	267	23	ū	ū	NOUN
ejpam-534	267	24	,	,	PUNCT
ejpam-534	267	25	˙̄u)−	˙̄u)−	PROPN
ejpam-534	267	26	1	1	NUM
ejpam-534	267	27	2	2	NUM
ejpam-534	267	28	β̄(t)t	β̄(t)t	NOUN
ejpam-534	267	29	f	f	PROPN
ejpam-534	267	30	β̄(t))d	β̄(t))d	SYM
ejpam-534	267	31	t	t	PROPN
ejpam-534	267	32	,	,	PUNCT
ejpam-534	267	33	a	a	DET
ejpam-534	267	34	contradiction	contradiction	NOUN
ejpam-534	267	35	to	to	ADP
ejpam-534	267	36	the	the	DET
ejpam-534	267	37	weak	weak	ADJ
ejpam-534	267	38	duality	duality	NOUN
ejpam-534	267	39	theorem	theorem	VERB
ejpam-534	267	40	[	[	X
ejpam-534	267	41	8	8	NUM
ejpam-534	267	42	]	]	PUNCT
ejpam-534	267	43	.	.	PUNCT
ejpam-534	268	1	hence	hence	ADV
ejpam-534	268	2	ū(t	ū(t	NOUN
ejpam-534	268	3	)	)	PUNCT
ejpam-534	268	4	is	be	AUX
ejpam-534	268	5	an	an	DET
ejpam-534	268	6	optimal	optimal	ADJ
ejpam-534	268	7	solution	solution	NOUN
ejpam-534	268	8	for	for	ADP
ejpam-534	268	9	(	(	PUNCT
ejpam-534	268	10	cp	cp	NOUN
ejpam-534	268	11	)	)	PUNCT
ejpam-534	268	12	.	.	PUNCT
ejpam-534	269	1	3	3	X
ejpam-534	269	2	.	.	X
ejpam-534	269	3	multiobjective	multiobjective	ADJ
ejpam-534	269	4	variational	variational	ADJ
ejpam-534	269	5	problem	problem	NOUN
ejpam-534	269	6	we	we	PRON
ejpam-534	269	7	consider	consider	VERB
ejpam-534	269	8	the	the	DET
ejpam-534	269	9	following	follow	VERB
ejpam-534	269	10	multiobjective	multiobjective	ADJ
ejpam-534	269	11	variational	variational	ADJ
ejpam-534	269	12	problem	problem	NOUN
ejpam-534	269	13	(	(	PUNCT
ejpam-534	269	14	p	p	NOUN
ejpam-534	269	15	):	):	PUNCT
ejpam-534	269	16	(	(	PUNCT
ejpam-534	269	17	p	p	X
ejpam-534	269	18	)	)	PUNCT
ejpam-534	269	19	minimize	minimize	NOUN
ejpam-534	269	20	(	(	PUNCT
ejpam-534	269	21	b∫	b∫	NOUN
ejpam-534	269	22	a	a	DET
ejpam-534	269	23	f	f	X
ejpam-534	269	24	1(t	1(t	NUM
ejpam-534	269	25	,	,	PUNCT
ejpam-534	269	26	x	x	PRON
ejpam-534	269	27	,	,	PUNCT
ejpam-534	269	28	ẋ)d	ẋ)d	PROPN
ejpam-534	269	29	t	t	PROPN
ejpam-534	269	30	,	,	PUNCT
ejpam-534	269	31	b∫	b∫	PROPN
ejpam-534	269	32	a	a	DET
ejpam-534	269	33	f	f	PROPN
ejpam-534	269	34	2(t	2(t	NUM
ejpam-534	269	35	,	,	PUNCT
ejpam-534	269	36	x	x	SYM
ejpam-534	269	37	,	,	PUNCT
ejpam-534	269	38	ẋ)d	ẋ)d	PROPN
ejpam-534	269	39	t	t	PROPN
ejpam-534	269	40	,	,	PUNCT
ejpam-534	269	41	.	.	PUNCT
ejpam-534	269	42	.	.	PUNCT
ejpam-534	270	1	.	.	PUNCT
ejpam-534	271	1	,	,	PUNCT
ejpam-534	271	2	b∫	b∫	PROPN
ejpam-534	271	3	a	a	PRON
ejpam-534	271	4	f	f	X
ejpam-534	271	5	k(t	k(t	PROPN
ejpam-534	271	6	,	,	PUNCT
ejpam-534	271	7	x	x	SYM
ejpam-534	271	8	,	,	PUNCT
ejpam-534	271	9	ẋ)d	ẋ)d	PROPN
ejpam-534	271	10	t	t	PROPN
ejpam-534	271	11	)	)	PUNCT
ejpam-534	271	12	subject	subject	NOUN
ejpam-534	271	13	to	to	ADP
ejpam-534	271	14	x(a	x(a	NOUN
ejpam-534	271	15	)	)	PUNCT
ejpam-534	271	16	=	=	SYM
ejpam-534	271	17	α	α	PROPN
ejpam-534	271	18	,	,	PUNCT
ejpam-534	271	19	x(b	x(b	PROPN
ejpam-534	271	20	)	)	PUNCT
ejpam-534	272	1	=	=	SYM
ejpam-534	272	2	β	β	X
ejpam-534	272	3	,	,	PUNCT
ejpam-534	272	4	(	(	PUNCT
ejpam-534	272	5	20	20	NUM
ejpam-534	272	6	)	)	PUNCT
ejpam-534	272	7	g(t	g(t	PROPN
ejpam-534	272	8	,	,	PUNCT
ejpam-534	272	9	x	x	PRON
ejpam-534	272	10	,	,	PUNCT
ejpam-534	272	11	ẋ)≦	ẋ)≦	PROPN
ejpam-534	272	12	0	0	PROPN
ejpam-534	272	13	,	,	PUNCT
ejpam-534	272	14	t	t	PROPN
ejpam-534	272	15	∈	∈	PROPN
ejpam-534	273	1	i	i	PRON
ejpam-534	273	2	,	,	PUNCT
ejpam-534	273	3	(	(	PUNCT
ejpam-534	273	4	21	21	NUM
ejpam-534	273	5	)	)	PUNCT
ejpam-534	273	6	where	where	SCONJ
ejpam-534	273	7	f	f	PROPN
ejpam-534	273	8	i	i	PRON
ejpam-534	273	9	:	:	PUNCT
ejpam-534	273	10	i	i	PRON
ejpam-534	273	11	×	×	VERB
ejpam-534	273	12	s	s	PART
ejpam-534	273	13	×	×	NOUN
ejpam-534	273	14	s	s	X
ejpam-534	273	15	→	→	SYM
ejpam-534	273	16	r(i	r(i	PROPN
ejpam-534	273	17	∈	∈	PROPN
ejpam-534	273	18	k	k	PROPN
ejpam-534	273	19	)	)	PUNCT
ejpam-534	273	20	,	,	PUNCT
ejpam-534	273	21	g	g	PROPN
ejpam-534	273	22	=	=	SYM
ejpam-534	273	23	(	(	PUNCT
ejpam-534	273	24	g1	g1	PROPN
ejpam-534	273	25	,	,	PUNCT
ejpam-534	273	26	g2	g2	PROPN
ejpam-534	273	27	,	,	PUNCT
ejpam-534	273	28	.	.	PUNCT
ejpam-534	273	29	.	.	PUNCT
ejpam-534	273	30	.	.	PUNCT
ejpam-534	274	1	,	,	PUNCT
ejpam-534	274	2	gm	gm	PROPN
ejpam-534	274	3	)	)	PUNCT
ejpam-534	274	4	:	:	PUNCT
ejpam-534	275	1	i	i	PRON
ejpam-534	275	2	×	×	VERB
ejpam-534	275	3	s	s	PART
ejpam-534	275	4	×	×	PROPN
ejpam-534	275	5	s	s	X
ejpam-534	275	6	→	→	SYM
ejpam-534	275	7	rm	rm	PROPN
ejpam-534	275	8	and	and	CCONJ
ejpam-534	275	9	s	s	PROPN
ejpam-534	275	10	is	be	AUX
ejpam-534	275	11	an	an	DET
ejpam-534	275	12	open	open	ADJ
ejpam-534	275	13	set	set	NOUN
ejpam-534	275	14	in	in	ADP
ejpam-534	275	15	rn	rn	PROPN
ejpam-534	275	16	.	.	PUNCT
ejpam-534	276	1	we	we	PRON
ejpam-534	276	2	denote	denote	VERB
ejpam-534	276	3	the	the	DET
ejpam-534	276	4	first	first	ADJ
ejpam-534	276	5	partial	partial	ADJ
ejpam-534	276	6	derivatives	derivative	NOUN
ejpam-534	276	7	of	of	ADP
ejpam-534	276	8	f	f	PROPN
ejpam-534	276	9	i	i	PROPN
ejpam-534	276	10	,	,	PUNCT
ejpam-534	276	11	with	with	ADP
ejpam-534	276	12	respect	respect	NOUN
ejpam-534	276	13	to	to	ADP
ejpam-534	276	14	t	t	PROPN
ejpam-534	276	15	,	,	PUNCT
ejpam-534	276	16	x	x	PUNCT
ejpam-534	276	17	and	and	CCONJ
ejpam-534	276	18	ẋ	ẋ	PROPN
ejpam-534	276	19	respectively	respectively	ADV
ejpam-534	276	20	by	by	ADP
ejpam-534	276	21	f	f	PROPN
ejpam-534	277	1	i	i	PRON
ejpam-534	277	2	t	t	PROPN
ejpam-534	277	3	,	,	PUNCT
ejpam-534	277	4	f	f	PROPN
ejpam-534	278	1	i	i	PROPN
ejpam-534	278	2	x	x	PROPN
ejpam-534	278	3	and	and	CCONJ
ejpam-534	278	4	f	f	PROPN
ejpam-534	279	1	i	i	PRON
ejpam-534	279	2	ẋ	ẋ	PROPN
ejpam-534	280	1	such	such	ADJ
ejpam-534	280	2	that	that	SCONJ
ejpam-534	280	3	f	f	PROPN
ejpam-534	280	4	i	i	NOUN
ejpam-534	280	5	x	x	PROPN
ejpam-534	280	6	=	=	PUNCT
ejpam-534	280	7	(	(	PUNCT
ejpam-534	280	8	∂	∂	NUM
ejpam-534	280	9	f	f	NOUN
ejpam-534	281	1	i	i	PROPN
ejpam-534	281	2	∂	∂	NOUN
ejpam-534	281	3	x1	x1	NUM
ejpam-534	281	4	,	,	PUNCT
ejpam-534	281	5	∂	∂	NUM
ejpam-534	281	6	f	f	NOUN
ejpam-534	282	1	i	i	PROPN
ejpam-534	282	2	∂	∂	ADV
ejpam-534	282	3	x2	x2	INTJ
ejpam-534	282	4	,	,	PUNCT
ejpam-534	282	5	.	.	PUNCT
ejpam-534	282	6	.	.	PUNCT
ejpam-534	282	7	.	.	PUNCT
ejpam-534	283	1	,	,	PUNCT
ejpam-534	283	2	∂	∂	NUM
ejpam-534	283	3	f	f	NOUN
ejpam-534	284	1	i	i	PROPN
ejpam-534	284	2	∂	∂	PROPN
ejpam-534	284	3	xn	xn	PROPN
ejpam-534	284	4	)	)	PUNCT
ejpam-534	285	1	t	t	PROPN
ejpam-534	285	2	and	and	CCONJ
ejpam-534	285	3	f	f	PROPN
ejpam-534	286	1	i	i	PRON
ejpam-534	286	2	ẋ	ẋ	PROPN
ejpam-534	286	3	=	=	PRON
ejpam-534	286	4	(	(	PUNCT
ejpam-534	286	5	∂	∂	NUM
ejpam-534	286	6	f	f	NOUN
ejpam-534	287	1	i	i	PROPN
ejpam-534	287	2	∂	∂	AUX
ejpam-534	287	3	ẋ1	ẋ1	PROPN
ejpam-534	287	4	,	,	PUNCT
ejpam-534	287	5	∂	∂	NUM
ejpam-534	287	6	f	f	NOUN
ejpam-534	288	1	i	i	PROPN
ejpam-534	288	2	∂	∂	PUNCT
ejpam-534	288	3	ẋ2	ẋ2	NOUN
ejpam-534	288	4	,	,	PUNCT
ejpam-534	288	5	.	.	PUNCT
ejpam-534	288	6	.	.	PUNCT
ejpam-534	288	7	.	.	PUNCT
ejpam-534	289	1	,	,	PUNCT
ejpam-534	289	2	∂	∂	NUM
ejpam-534	289	3	f	f	X
ejpam-534	290	1	i	i	PROPN
ejpam-534	290	2	∂	∂	PROPN
ejpam-534	290	3	ẋn	ẋn	PROPN
ejpam-534	290	4	)	)	PUNCT
ejpam-534	290	5	t	t	PROPN
ejpam-534	290	6	.	.	PUNCT
ejpam-534	291	1	the	the	DET
ejpam-534	291	2	hessian	hessian	ADJ
ejpam-534	291	3	matrix	matrix	NOUN
ejpam-534	291	4	f	f	NOUN
ejpam-534	291	5	i	i	NOUN
ejpam-534	291	6	x	x	PROPN
ejpam-534	291	7	x	x	X
ejpam-534	291	8	,	,	PUNCT
ejpam-534	291	9	is	be	AUX
ejpam-534	291	10	an	an	PRON
ejpam-534	291	11	n	n	NUM
ejpam-534	291	12	×	×	NOUN
ejpam-534	291	13	n	n	CCONJ
ejpam-534	291	14	symmetric	symmetric	ADJ
ejpam-534	291	15	matrix	matrix	NOUN
ejpam-534	291	16	.	.	PUNCT
ejpam-534	292	1	similarly	similarly	ADV
ejpam-534	292	2	f	f	X
ejpam-534	292	3	i	i	NOUN
ejpam-534	292	4	x	x	PROPN
ejpam-534	292	5	ẋ	ẋ	PROPN
ejpam-534	292	6	,	,	PUNCT
ejpam-534	292	7	f	f	PROPN
ejpam-534	293	1	i	i	PRON
ejpam-534	293	2	ẋ	ẋ	PROPN
ejpam-534	293	3	ẋ	ẋ	PROPN
ejpam-534	293	4	and	and	CCONJ
ejpam-534	293	5	the	the	DET
ejpam-534	293	6	partial	partial	ADJ
ejpam-534	293	7	derivatives	derivative	NOUN
ejpam-534	293	8	of	of	ADP
ejpam-534	293	9	g	g	PROPN
ejpam-534	293	10	j	j	PROPN
ejpam-534	293	11	are	be	AUX
ejpam-534	293	12	also	also	ADV
ejpam-534	293	13	defined	define	VERB
ejpam-534	293	14	.	.	PUNCT
ejpam-534	294	1	all	all	DET
ejpam-534	294	2	the	the	DET
ejpam-534	294	3	partial	partial	ADJ
ejpam-534	294	4	and	and	CCONJ
ejpam-534	294	5	total	total	ADJ
ejpam-534	294	6	derivatives	derivative	NOUN
ejpam-534	294	7	of	of	ADP
ejpam-534	294	8	f	f	PROPN
ejpam-534	294	9	i	i	PROPN
ejpam-534	294	10	and	and	CCONJ
ejpam-534	294	11	g	g	PROPN
ejpam-534	294	12	used	use	VERB
ejpam-534	294	13	here	here	ADV
ejpam-534	294	14	onwards	onward	NOUN
ejpam-534	294	15	are	be	AUX
ejpam-534	294	16	assumed	assume	VERB
ejpam-534	294	17	to	to	PART
ejpam-534	294	18	be	be	AUX
ejpam-534	294	19	continuous	continuous	ADJ
ejpam-534	294	20	.	.	PUNCT
ejpam-534	295	1	we	we	PRON
ejpam-534	295	2	shall	shall	AUX
ejpam-534	295	3	use	use	VERB
ejpam-534	295	4	x	x	PUNCT
ejpam-534	295	5	for	for	ADP
ejpam-534	295	6	the	the	DET
ejpam-534	295	7	set	set	NOUN
ejpam-534	295	8	of	of	ADP
ejpam-534	295	9	all	all	DET
ejpam-534	295	10	feasible	feasible	ADJ
ejpam-534	295	11	solutions	solution	NOUN
ejpam-534	295	12	of	of	ADP
ejpam-534	295	13	(	(	PUNCT
ejpam-534	295	14	p	p	NOUN
ejpam-534	295	15	)	)	PUNCT
ejpam-534	295	16	.	.	PUNCT
ejpam-534	296	1	for	for	ADP
ejpam-534	296	2	the	the	DET
ejpam-534	296	3	sake	sake	NOUN
ejpam-534	296	4	of	of	ADP
ejpam-534	296	5	convenience	convenience	NOUN
ejpam-534	296	6	,	,	PUNCT
ejpam-534	296	7	we	we	PRON
ejpam-534	296	8	shall	shall	AUX
ejpam-534	296	9	not	not	PART
ejpam-534	296	10	write	write	VERB
ejpam-534	296	11	the	the	DET
ejpam-534	296	12	limits	limit	NOUN
ejpam-534	296	13	a	a	PRON
ejpam-534	296	14	and	and	CCONJ
ejpam-534	296	15	b	b	NOUN
ejpam-534	296	16	in	in	ADP
ejpam-534	296	17	the	the	DET
ejpam-534	296	18	integrals	integral	NOUN
ejpam-534	296	19	,	,	PUNCT
ejpam-534	296	20	i.e.	i.e.	X
ejpam-534	296	21	,	,	PUNCT
ejpam-534	296	22	∫	∫	PROPN
ejpam-534	296	23	f	f	PROPN
ejpam-534	296	24	i	i	PROPN
ejpam-534	296	25	d	d	PROPN
ejpam-534	296	26	t	t	PROPN
ejpam-534	296	27	shall	shall	AUX
ejpam-534	296	28	t.	t.	PROPN
ejpam-534	296	29	gulati	gulati	PROPN
ejpam-534	296	30	and	and	CCONJ
ejpam-534	296	31	g.	g.	PROPN
ejpam-534	296	32	mehndiratta	mehndiratta	PROPN
ejpam-534	296	33	/	/	SYM
ejpam-534	296	34	eur	eur	PROPN
ejpam-534	296	35	.	.	PUNCT
ejpam-534	297	1	j.	j.	PROPN
ejpam-534	297	2	pure	pure	PROPN
ejpam-534	297	3	appl	appl	PROPN
ejpam-534	297	4	.	.	PROPN
ejpam-534	297	5	math	math	PROPN
ejpam-534	297	6	,	,	PUNCT
ejpam-534	297	7	3	3	NUM
ejpam-534	297	8	(	(	PUNCT
ejpam-534	297	9	2010	2010	NUM
ejpam-534	297	10	)	)	PUNCT
ejpam-534	297	11	,	,	PUNCT
ejpam-534	297	12	786	786	NUM
ejpam-534	297	13	-	-	SYM
ejpam-534	297	14	805	805	NUM
ejpam-534	297	15	792	792	NUM
ejpam-534	297	16	mean	mean	NOUN
ejpam-534	297	17	b∫	b∫	NOUN
ejpam-534	298	1	a	a	DET
ejpam-534	298	2	f	f	X
ejpam-534	298	3	i	i	NOUN
ejpam-534	298	4	d	d	PROPN
ejpam-534	298	5	t.	t.	PROPN
ejpam-534	298	6	let	let	VERB
ejpam-534	298	7	k	k	X
ejpam-534	298	8	=	=	PUNCT
ejpam-534	298	9	{	{	PUNCT
ejpam-534	298	10	1,2	1,2	NUM
ejpam-534	298	11	,	,	PUNCT
ejpam-534	298	12	.	.	PUNCT
ejpam-534	298	13	.	.	PUNCT
ejpam-534	299	1	.	.	PUNCT
ejpam-534	300	1	,	,	PUNCT
ejpam-534	300	2	k	k	X
ejpam-534	300	3	}	}	PUNCT
ejpam-534	300	4	and	and	CCONJ
ejpam-534	300	5	for	for	ADP
ejpam-534	300	6	r	r	PROPN
ejpam-534	300	7	∈	∈	PROPN
ejpam-534	300	8	k	k	PROPN
ejpam-534	300	9	,	,	PUNCT
ejpam-534	300	10	the	the	DET
ejpam-534	300	11	set	set	NOUN
ejpam-534	300	12	kr	kr	PROPN
ejpam-534	300	13	=	=	SYM
ejpam-534	300	14	k	k	PROPN
ejpam-534	300	15	−	−	PROPN
ejpam-534	300	16	r.	r.	PROPN
ejpam-534	300	17	for	for	ADP
ejpam-534	300	18	a	a	PRON
ejpam-534	300	19	and	and	CCONJ
ejpam-534	300	20	b	b	NOUN
ejpam-534	300	21	in	in	ADP
ejpam-534	300	22	rn	rn	PROPN
ejpam-534	300	23	,	,	PUNCT
ejpam-534	300	24	we	we	PRON
ejpam-534	300	25	shall	shall	AUX
ejpam-534	300	26	use	use	VERB
ejpam-534	300	27	the	the	DET
ejpam-534	300	28	following	follow	VERB
ejpam-534	300	29	three	three	NUM
ejpam-534	300	30	inequalities	inequality	NOUN
ejpam-534	300	31	:	:	PUNCT
ejpam-534	300	32	a	a	DET
ejpam-534	300	33	≧	≧	PUNCT
ejpam-534	300	34	b⇔	b⇔	PROPN
ejpam-534	300	35	ai	ai	VERB
ejpam-534	300	36	≧	≧	NOUN
ejpam-534	300	37	bi	bi	NOUN
ejpam-534	301	1	(	(	PUNCT
ejpam-534	301	2	i	i	NOUN
ejpam-534	301	3	=	=	SYM
ejpam-534	301	4	1,2	1,2	NUM
ejpam-534	301	5	,	,	PUNCT
ejpam-534	301	6	.	.	PUNCT
ejpam-534	301	7	.	.	PUNCT
ejpam-534	302	1	.	.	PUNCT
ejpam-534	303	1	,	,	PUNCT
ejpam-534	303	2	n	n	CCONJ
ejpam-534	303	3	)	)	PUNCT
ejpam-534	303	4	a	a	DET
ejpam-534	303	5	≥	≥	NOUN
ejpam-534	303	6	b⇔	b⇔	NOUN
ejpam-534	303	7	(	(	PUNCT
ejpam-534	303	8	a	a	DET
ejpam-534	303	9	≧	≧	SYM
ejpam-534	303	10	b	b	NOUN
ejpam-534	303	11	,	,	PUNCT
ejpam-534	303	12	a	a	DET
ejpam-534	303	13	6=	6=	NUM
ejpam-534	303	14	b	b	NOUN
ejpam-534	303	15	)	)	PUNCT
ejpam-534	303	16	a	a	DET
ejpam-534	303	17	>	>	X
ejpam-534	303	18	b⇔	b⇔	PROPN
ejpam-534	303	19	ai	ai	VERB
ejpam-534	303	20	>	>	X
ejpam-534	303	21	bi	bi	NOUN
ejpam-534	303	22	(	(	PUNCT
ejpam-534	303	23	i	i	NOUN
ejpam-534	303	24	=	=	SYM
ejpam-534	303	25	1,2	1,2	NUM
ejpam-534	303	26	,	,	PUNCT
ejpam-534	303	27	.	.	PUNCT
ejpam-534	303	28	.	.	PUNCT
ejpam-534	304	1	.	.	PUNCT
ejpam-534	304	2	,	,	PUNCT
ejpam-534	304	3	n	n	CCONJ
ejpam-534	304	4	)	)	PUNCT
ejpam-534	304	5	.	.	PUNCT
ejpam-534	305	1	definition	definition	NOUN
ejpam-534	305	2	1	1	NUM
ejpam-534	305	3	.	.	PUNCT
ejpam-534	306	1	a	a	DET
ejpam-534	306	2	point	point	NOUN
ejpam-534	306	3	x̄(t	x̄(t	NUM
ejpam-534	306	4	)	)	PUNCT
ejpam-534	306	5	∈	∈	PROPN
ejpam-534	306	6	x	x	PUNCT
ejpam-534	306	7	is	be	AUX
ejpam-534	306	8	said	say	VERB
ejpam-534	306	9	to	to	PART
ejpam-534	306	10	be	be	AUX
ejpam-534	306	11	an	an	DET
ejpam-534	306	12	efficient	efficient	ADJ
ejpam-534	306	13	solution	solution	NOUN
ejpam-534	306	14	of	of	ADP
ejpam-534	306	15	(	(	PUNCT
ejpam-534	306	16	p	p	X
ejpam-534	306	17	)	)	PUNCT
ejpam-534	306	18	if	if	SCONJ
ejpam-534	306	19	there	there	PRON
ejpam-534	306	20	exists	exist	VERB
ejpam-534	306	21	no	no	DET
ejpam-534	306	22	x(t	x(t	PROPN
ejpam-534	306	23	)	)	PUNCT
ejpam-534	306	24	∈	∈	PROPN
ejpam-534	306	25	x	x	PUNCT
ejpam-534	306	26	such	such	ADJ
ejpam-534	306	27	that	that	DET
ejpam-534	306	28	∫	∫	PROPN
ejpam-534	306	29	f	f	PROPN
ejpam-534	306	30	r(t	r(t	PROPN
ejpam-534	306	31	,	,	PUNCT
ejpam-534	306	32	x	x	PRON
ejpam-534	306	33	,	,	PUNCT
ejpam-534	306	34	ẋ)d	ẋ)d	PROPN
ejpam-534	307	1	t	t	PROPN
ejpam-534	307	2	<	<	X
ejpam-534	307	3	∫	∫	PROPN
ejpam-534	307	4	f	f	PROPN
ejpam-534	307	5	r(t	r(t	PROPN
ejpam-534	307	6	,	,	PUNCT
ejpam-534	307	7	x̄	x̄	NOUN
ejpam-534	307	8	,	,	PUNCT
ejpam-534	307	9	˙̄x)d	˙̄x)d	PROPN
ejpam-534	307	10	t	t	PROPN
ejpam-534	307	11	for	for	ADP
ejpam-534	307	12	some	some	DET
ejpam-534	307	13	r	r	NOUN
ejpam-534	307	14	∈	∈	PROPN
ejpam-534	307	15	k	k	PROPN
ejpam-534	307	16	and	and	CCONJ
ejpam-534	307	17	∫	∫	PROPN
ejpam-534	307	18	f	f	PROPN
ejpam-534	307	19	i(t	i(t	PROPN
ejpam-534	307	20	,	,	PUNCT
ejpam-534	307	21	x	x	X
ejpam-534	307	22	,	,	PUNCT
ejpam-534	307	23	ẋ)d	ẋ)d	PROPN
ejpam-534	307	24	t	t	PROPN
ejpam-534	307	25	≦	≦	PROPN
ejpam-534	307	26	∫	∫	PROPN
ejpam-534	307	27	f	f	PROPN
ejpam-534	307	28	i(t	i(t	PROPN
ejpam-534	307	29	,	,	PUNCT
ejpam-534	307	30	x̄	x̄	NOUN
ejpam-534	307	31	,	,	PUNCT
ejpam-534	307	32	˙̄x)d	˙̄x)d	PROPN
ejpam-534	307	33	t	t	PROPN
ejpam-534	307	34	for	for	ADP
ejpam-534	307	35	i	i	PROPN
ejpam-534	307	36	∈	∈	PROPN
ejpam-534	307	37	kr	kr	PROPN
ejpam-534	307	38	.	.	PUNCT
ejpam-534	308	1	let	let	VERB
ejpam-534	308	2	p	p	NOUN
ejpam-534	308	3	:	:	PUNCT
ejpam-534	308	4	i	i	PROPN
ejpam-534	308	5	→	→	SYM
ejpam-534	308	6	rn	rn	PROPN
ejpam-534	308	7	and	and	CCONJ
ejpam-534	308	8	ai(t	ai(t	NOUN
ejpam-534	308	9	,	,	PUNCT
ejpam-534	308	10	x	x	X
ejpam-534	308	11	,	,	PUNCT
ejpam-534	308	12	ẋ	ẋ	PROPN
ejpam-534	308	13	,	,	PUNCT
ejpam-534	308	14	ẍ	ẍ	PROPN
ejpam-534	308	15	,	,	PUNCT
ejpam-534	308	16	...	...	PUNCT
ejpam-534	309	1	x	x	X
ejpam-534	309	2	,	,	PUNCT
ejpam-534	309	3	....	....	PUNCT
ejpam-534	309	4	x	x	X
ejpam-534	309	5	)	)	PUNCT
ejpam-534	310	1	=	=	PUNCT
ejpam-534	310	2	f	f	X
ejpam-534	311	1	i	i	NOUN
ejpam-534	311	2	x	x	PUNCT
ejpam-534	311	3	x(t	x(t	PROPN
ejpam-534	311	4	,	,	PUNCT
ejpam-534	311	5	x	x	X
ejpam-534	311	6	,	,	PUNCT
ejpam-534	311	7	ẋ	ẋ	PROPN
ejpam-534	311	8	)	)	PUNCT
ejpam-534	312	1	−	−	NOUN
ejpam-534	312	2	2d	2d	NUM
ejpam-534	312	3	f	f	NOUN
ejpam-534	313	1	i	i	NOUN
ejpam-534	313	2	x	x	PROPN
ejpam-534	313	3	ẋ	ẋ	PROPN
ejpam-534	313	4	(	(	PUNCT
ejpam-534	313	5	t	t	PROPN
ejpam-534	313	6	,	,	PUNCT
ejpam-534	313	7	x	x	X
ejpam-534	313	8	,	,	PUNCT
ejpam-534	313	9	ẋ	ẋ	PROPN
ejpam-534	313	10	)	)	PUNCT
ejpam-534	314	1	+	+	CCONJ
ejpam-534	315	1	d2	d2	PROPN
ejpam-534	315	2	f	f	PROPN
ejpam-534	316	1	i	i	PRON
ejpam-534	316	2	ẋ	ẋ	PROPN
ejpam-534	316	3	ẋ	ẋ	PROPN
ejpam-534	317	1	(	(	PUNCT
ejpam-534	317	2	t	t	PROPN
ejpam-534	317	3	,	,	PUNCT
ejpam-534	317	4	x	x	X
ejpam-534	317	5	,	,	PUNCT
ejpam-534	317	6	ẋ	ẋ	PROPN
ejpam-534	317	7	)	)	PUNCT
ejpam-534	318	1	−	−	PROPN
ejpam-534	318	2	d3	d3	PROPN
ejpam-534	318	3	f	f	PROPN
ejpam-534	319	1	i	i	PRON
ejpam-534	319	2	ẋ	ẋ	PROPN
ejpam-534	319	3	ẍ	ẍ	PROPN
ejpam-534	320	1	(	(	PUNCT
ejpam-534	320	2	t	t	PROPN
ejpam-534	320	3	,	,	PUNCT
ejpam-534	320	4	x	x	X
ejpam-534	320	5	,	,	PUNCT
ejpam-534	320	6	ẋ	ẋ	PROPN
ejpam-534	320	7	)	)	PUNCT
ejpam-534	320	8	,	,	PUNCT
ejpam-534	321	1	t	t	PROPN
ejpam-534	321	2	∈	∈	PROPN
ejpam-534	322	1	i	i	PRON
ejpam-534	322	2	,	,	PUNCT
ejpam-534	322	3	i	i	PROPN
ejpam-534	322	4	∈	∈	PROPN
ejpam-534	322	5	k	k	X
ejpam-534	322	6	.	.	PUNCT
ejpam-534	323	1	definition	definition	NOUN
ejpam-534	323	2	2	2	NUM
ejpam-534	323	3	.	.	PUNCT
ejpam-534	324	1	a	a	DET
ejpam-534	324	2	functional	functional	ADJ
ejpam-534	324	3	g	g	NOUN
ejpam-534	324	4	:	:	PUNCT
ejpam-534	324	5	i	i	NOUN
ejpam-534	324	6	×s×s×rn→	×s×s×rn→	PUNCT
ejpam-534	324	7	r	r	NOUN
ejpam-534	324	8	is	be	AUX
ejpam-534	324	9	said	say	VERB
ejpam-534	324	10	to	to	PART
ejpam-534	324	11	be	be	AUX
ejpam-534	324	12	sublinear	sublinear	ADJ
ejpam-534	324	13	,	,	PUNCT
ejpam-534	324	14	if	if	SCONJ
ejpam-534	324	15	for	for	ADP
ejpam-534	324	16	all	all	DET
ejpam-534	324	17	x(t),u(t	x(t),u(t	NOUN
ejpam-534	324	18	)	)	PUNCT
ejpam-534	324	19	∈	∈	PROPN
ejpam-534	324	20	s	s	PROPN
ejpam-534	324	21	,	,	PUNCT
ejpam-534	324	22	g(t	g(t	PROPN
ejpam-534	324	23	,	,	PUNCT
ejpam-534	324	24	x	x	X
ejpam-534	324	25	,	,	PUNCT
ejpam-534	324	26	u;ξ1	u;ξ1	PROPN
ejpam-534	324	27	+	+	PROPN
ejpam-534	324	28	ξ2)≦	ξ2)≦	PROPN
ejpam-534	324	29	g(t	g(t	PROPN
ejpam-534	324	30	,	,	PUNCT
ejpam-534	324	31	x	x	X
ejpam-534	324	32	,	,	PUNCT
ejpam-534	324	33	u;ξ1	u;ξ1	NOUN
ejpam-534	324	34	)	)	PUNCT
ejpam-534	324	35	+	+	CCONJ
ejpam-534	325	1	g(t	g(t	PROPN
ejpam-534	325	2	,	,	PUNCT
ejpam-534	325	3	x	x	NOUN
ejpam-534	325	4	,	,	PUNCT
ejpam-534	325	5	u;ξ2	u;ξ2	NOUN
ejpam-534	325	6	)	)	PUNCT
ejpam-534	325	7	for	for	ADP
ejpam-534	325	8	all	all	DET
ejpam-534	325	9	ξ1,ξ2	ξ1,ξ2	PROPN
ejpam-534	325	10	∈	∈	PROPN
ejpam-534	325	11	rn	rn	NOUN
ejpam-534	325	12	(	(	PUNCT
ejpam-534	325	13	22	22	NUM
ejpam-534	325	14	)	)	PUNCT
ejpam-534	325	15	and	and	CCONJ
ejpam-534	325	16	g(t	g(t	PROPN
ejpam-534	325	17	,	,	PUNCT
ejpam-534	325	18	x	x	X
ejpam-534	325	19	,	,	PUNCT
ejpam-534	325	20	u	u	NOUN
ejpam-534	325	21	;	;	PUNCT
ejpam-534	325	22	aξ	aξ	VERB
ejpam-534	325	23	)	)	PUNCT
ejpam-534	325	24	=	=	SYM
ejpam-534	326	1	ag(t	ag(t	NOUN
ejpam-534	326	2	,	,	PUNCT
ejpam-534	326	3	x	x	X
ejpam-534	326	4	,	,	PUNCT
ejpam-534	326	5	u;ξ	u;ξ	PROPN
ejpam-534	326	6	)	)	PUNCT
ejpam-534	326	7	for	for	ADP
ejpam-534	326	8	all	all	DET
ejpam-534	326	9	a	a	DET
ejpam-534	326	10	∈	∈	PROPN
ejpam-534	326	11	r	r	NOUN
ejpam-534	326	12	,	,	PUNCT
ejpam-534	326	13	a	a	DET
ejpam-534	326	14	≧	≧	NOUN
ejpam-534	326	15	0	0	NUM
ejpam-534	326	16	and	and	CCONJ
ejpam-534	326	17	ξ	ξ	PROPN
ejpam-534	326	18	∈	∈	PROPN
ejpam-534	326	19	rn	rn	PROPN
ejpam-534	326	20	.	.	PROPN
ejpam-534	327	1	(	(	PUNCT
ejpam-534	327	2	23	23	NUM
ejpam-534	327	3	)	)	PUNCT
ejpam-534	327	4	from	from	ADP
ejpam-534	327	5	(	(	PUNCT
ejpam-534	327	6	23	23	NUM
ejpam-534	327	7	)	)	PUNCT
ejpam-534	327	8	,	,	PUNCT
ejpam-534	327	9	it	it	PRON
ejpam-534	327	10	follows	follow	VERB
ejpam-534	327	11	that	that	SCONJ
ejpam-534	327	12	g(t	g(t	PROPN
ejpam-534	327	13	,	,	PUNCT
ejpam-534	327	14	x	x	INTJ
ejpam-534	327	15	,	,	PUNCT
ejpam-534	327	16	u	u	NOUN
ejpam-534	327	17	;	;	PUNCT
ejpam-534	327	18	0	0	NUM
ejpam-534	327	19	)	)	PUNCT
ejpam-534	327	20	=	=	SYM
ejpam-534	328	1	0	0	X
ejpam-534	328	2	.	.	PUNCT
ejpam-534	329	1	let	let	VERB
ejpam-534	329	2	ρ	ρ	NUM
ejpam-534	329	3	∈	∈	PROPN
ejpam-534	329	4	r	r	NOUN
ejpam-534	329	5	and	and	CCONJ
ejpam-534	329	6	d	d	NOUN
ejpam-534	329	7	:	:	PUNCT
ejpam-534	330	1	i	i	PRON
ejpam-534	330	2	×	×	VERB
ejpam-534	330	3	s	s	PART
ejpam-534	330	4	×	×	PROPN
ejpam-534	330	5	s→	s→	PRON
ejpam-534	330	6	rn	rn	AUX
ejpam-534	330	7	be	be	AUX
ejpam-534	330	8	a	a	DET
ejpam-534	330	9	pseudometric	pseudometric	NOUN
ejpam-534	330	10	on	on	ADP
ejpam-534	330	11	rn	rn	PROPN
ejpam-534	330	12	.	.	PUNCT
ejpam-534	330	13	definition	definition	NOUN
ejpam-534	330	14	3	3	NUM
ejpam-534	330	15	.	.	PUNCT
ejpam-534	331	1	the	the	DET
ejpam-534	331	2	functional	functional	ADJ
ejpam-534	331	3	∫	∫	PROPN
ejpam-534	331	4	f	f	PROPN
ejpam-534	331	5	i(t	i(t	PROPN
ejpam-534	331	6	,	,	PUNCT
ejpam-534	331	7	x	x	SYM
ejpam-534	331	8	,	,	PUNCT
ejpam-534	331	9	ẋ)d	ẋ)d	PROPN
ejpam-534	331	10	t	t	PROPN
ejpam-534	331	11	is	be	AUX
ejpam-534	331	12	said	say	VERB
ejpam-534	331	13	to	to	PART
ejpam-534	331	14	be	be	AUX
ejpam-534	331	15	second	second	ADJ
ejpam-534	331	16	-	-	PUNCT
ejpam-534	331	17	order	order	NOUN
ejpam-534	331	18	(	(	PUNCT
ejpam-534	331	19	g	g	NOUN
ejpam-534	331	20	,	,	PUNCT
ejpam-534	331	21	ρ)-convex	ρ)-convex	NOUN
ejpam-534	331	22	at	at	ADP
ejpam-534	331	23	u(t	u(t	NOUN
ejpam-534	331	24	)	)	PUNCT
ejpam-534	331	25	∈	∈	PROPN
ejpam-534	331	26	s	s	PART
ejpam-534	331	27	,	,	PUNCT
ejpam-534	331	28	if	if	SCONJ
ejpam-534	331	29	there	there	PRON
ejpam-534	331	30	exists	exist	VERB
ejpam-534	331	31	a	a	DET
ejpam-534	331	32	sublinear	sublinear	NOUN
ejpam-534	331	33	functional	functional	ADJ
ejpam-534	331	34	g	g	NOUN
ejpam-534	331	35	:	:	PUNCT
ejpam-534	331	36	i	i	NOUN
ejpam-534	331	37	×s×s×rn→	×s×s×rn→	PUNCT
ejpam-534	331	38	r	r	NOUN
ejpam-534	331	39	such	such	ADJ
ejpam-534	331	40	that	that	PRON
ejpam-534	331	41	for	for	ADP
ejpam-534	331	42	all	all	DET
ejpam-534	331	43	x(t	x(t	NOUN
ejpam-534	331	44	)	)	PUNCT
ejpam-534	331	45	∈	∈	PROPN
ejpam-534	331	46	s	s	NOUN
ejpam-534	331	47	,	,	PUNCT
ejpam-534	331	48	p(t	p(t	NOUN
ejpam-534	331	49	)	)	PUNCT
ejpam-534	331	50	∈	∈	PROPN
ejpam-534	331	51	rn	rn	PROPN
ejpam-534	331	52	,	,	PUNCT
ejpam-534	331	53	∫	∫	PROPN
ejpam-534	331	54	f	f	PROPN
ejpam-534	331	55	i(t	i(t	PROPN
ejpam-534	331	56	,	,	PUNCT
ejpam-534	331	57	x	x	X
ejpam-534	331	58	,	,	PUNCT
ejpam-534	331	59	ẋ)d	ẋ)d	PROPN
ejpam-534	331	60	t	t	PROPN
ejpam-534	332	1	−	−	PROPN
ejpam-534	332	2	∫	∫	PROPN
ejpam-534	332	3	f	f	PROPN
ejpam-534	332	4	i(t	i(t	PROPN
ejpam-534	332	5	,	,	PUNCT
ejpam-534	332	6	u	u	NOUN
ejpam-534	332	7	,	,	PUNCT
ejpam-534	332	8	u̇)d	u̇)d	PROPN
ejpam-534	332	9	t	t	NOUN
ejpam-534	332	10	+	+	CCONJ
ejpam-534	332	11	1	1	NUM
ejpam-534	332	12	2	2	NUM
ejpam-534	332	13	∫	∫	NOUN
ejpam-534	332	14	p(t)t	p(t)t	NOUN
ejpam-534	332	15	ai	ai	VERB
ejpam-534	332	16	p(t)d	p(t)d	PROPN
ejpam-534	332	17	t	t	PROPN
ejpam-534	332	18	≧	≧	X
ejpam-534	332	19	∫	∫	PROPN
ejpam-534	332	20	g(t	g(t	PROPN
ejpam-534	332	21	,	,	PUNCT
ejpam-534	332	22	x	x	X
ejpam-534	332	23	,	,	PUNCT
ejpam-534	332	24	u	u	NOUN
ejpam-534	332	25	;	;	PUNCT
ejpam-534	332	26	f	f	PROPN
ejpam-534	332	27	i	i	NOUN
ejpam-534	332	28	x	x	X
ejpam-534	332	29	(	(	PUNCT
ejpam-534	332	30	t	t	PROPN
ejpam-534	332	31	,	,	PUNCT
ejpam-534	332	32	u	u	NOUN
ejpam-534	332	33	,	,	PUNCT
ejpam-534	332	34	u̇)−	u̇)−	PROPN
ejpam-534	333	1	d	d	X
ejpam-534	333	2	f	f	PROPN
ejpam-534	334	1	i	i	PRON
ejpam-534	334	2	ẋ	ẋ	PROPN
ejpam-534	335	1	(	(	PUNCT
ejpam-534	335	2	t	t	PROPN
ejpam-534	335	3	,	,	PUNCT
ejpam-534	335	4	u	u	NOUN
ejpam-534	335	5	,	,	PUNCT
ejpam-534	335	6	u̇	u̇	PROPN
ejpam-534	335	7	)	)	PUNCT
ejpam-534	336	1	+	+	CCONJ
ejpam-534	336	2	ai	ai	VERB
ejpam-534	336	3	p(t))d	p(t))d	NOUN
ejpam-534	336	4	t	t	NOUN
ejpam-534	336	5	+	+	NOUN
ejpam-534	336	6	ρ	ρ	NOUN
ejpam-534	336	7	∫	∫	PROPN
ejpam-534	336	8	d2(t	d2(t	PROPN
ejpam-534	336	9	,	,	PUNCT
ejpam-534	336	10	x	x	X
ejpam-534	336	11	,	,	PUNCT
ejpam-534	336	12	u)d	u)d	X
ejpam-534	337	1	t.	t.	PROPN
ejpam-534	337	2	if	if	SCONJ
ejpam-534	337	3	in	in	ADP
ejpam-534	337	4	the	the	DET
ejpam-534	337	5	above	above	ADJ
ejpam-534	337	6	definition	definition	NOUN
ejpam-534	337	7	,	,	PUNCT
ejpam-534	337	8	inequality	inequality	NOUN
ejpam-534	337	9	is	be	AUX
ejpam-534	337	10	satisfied	satisfied	ADJ
ejpam-534	337	11	as	as	ADP
ejpam-534	337	12	strict	strict	ADJ
ejpam-534	337	13	inequality	inequality	NOUN
ejpam-534	337	14	,	,	PUNCT
ejpam-534	337	15	then	then	ADV
ejpam-534	337	16	we	we	PRON
ejpam-534	337	17	say	say	VERB
ejpam-534	337	18	that	that	SCONJ
ejpam-534	337	19	the	the	DET
ejpam-534	337	20	functional∫	functional∫	NOUN
ejpam-534	337	21	f	f	PROPN
ejpam-534	337	22	i(t	i(t	PROPN
ejpam-534	337	23	,	,	PUNCT
ejpam-534	337	24	x	x	SYM
ejpam-534	337	25	,	,	PUNCT
ejpam-534	337	26	ẋ)d	ẋ)d	PROPN
ejpam-534	337	27	t	t	PROPN
ejpam-534	337	28	is	be	AUX
ejpam-534	337	29	second	second	ADJ
ejpam-534	337	30	-	-	PUNCT
ejpam-534	337	31	order	order	NOUN
ejpam-534	337	32	strictly	strictly	ADV
ejpam-534	337	33	(	(	PUNCT
ejpam-534	337	34	g	g	NOUN
ejpam-534	337	35	,	,	PUNCT
ejpam-534	337	36	ρ)-convex	ρ)-convex	NOUN
ejpam-534	337	37	at	at	ADP
ejpam-534	337	38	u(t	u(t	NOUN
ejpam-534	337	39	)	)	PUNCT
ejpam-534	337	40	∈	∈	PROPN
ejpam-534	337	41	s.	s.	PROPN
ejpam-534	337	42	definition	definition	NOUN
ejpam-534	337	43	4	4	NUM
ejpam-534	337	44	.	.	PUNCT
ejpam-534	338	1	the	the	DET
ejpam-534	338	2	functional	functional	ADJ
ejpam-534	338	3	∫	∫	PROPN
ejpam-534	338	4	f	f	PROPN
ejpam-534	338	5	i(t	i(t	PROPN
ejpam-534	338	6	,	,	PUNCT
ejpam-534	338	7	x	x	SYM
ejpam-534	338	8	,	,	PUNCT
ejpam-534	338	9	ẋ)d	ẋ)d	PROPN
ejpam-534	338	10	t	t	PROPN
ejpam-534	338	11	is	be	AUX
ejpam-534	338	12	said	say	VERB
ejpam-534	338	13	to	to	PART
ejpam-534	338	14	be	be	AUX
ejpam-534	338	15	second	second	ADJ
ejpam-534	338	16	-	-	PUNCT
ejpam-534	338	17	order	order	NOUN
ejpam-534	338	18	(	(	PUNCT
ejpam-534	338	19	g	g	NOUN
ejpam-534	338	20	,	,	PUNCT
ejpam-534	338	21	ρ)-pseudoconvex	ρ)-pseudoconvex	PUNCT
ejpam-534	338	22	at	at	ADP
ejpam-534	338	23	u(t	u(t	NOUN
ejpam-534	338	24	)	)	PUNCT
ejpam-534	338	25	∈	∈	PROPN
ejpam-534	338	26	s	s	PART
ejpam-534	338	27	,	,	PUNCT
ejpam-534	338	28	if	if	SCONJ
ejpam-534	338	29	there	there	PRON
ejpam-534	338	30	exists	exist	VERB
ejpam-534	338	31	a	a	DET
ejpam-534	338	32	sublinear	sublinear	NOUN
ejpam-534	338	33	functional	functional	ADJ
ejpam-534	338	34	g	g	NOUN
ejpam-534	338	35	:	:	PUNCT
ejpam-534	338	36	i	i	PRON
ejpam-534	338	37	×	×	VERB
ejpam-534	338	38	s	s	PART
ejpam-534	338	39	×	×	PROPN
ejpam-534	338	40	s	s	PART
ejpam-534	338	41	×	×	PROPN
ejpam-534	338	42	rn	rn	PROPN
ejpam-534	338	43	→	→	PUNCT
ejpam-534	338	44	r	r	NOUN
ejpam-534	338	45	such	such	ADJ
ejpam-534	338	46	that	that	PRON
ejpam-534	338	47	for	for	ADP
ejpam-534	338	48	all	all	DET
ejpam-534	338	49	x(t	x(t	NOUN
ejpam-534	338	50	)	)	PUNCT
ejpam-534	338	51	∈	∈	PROPN
ejpam-534	338	52	s	s	NOUN
ejpam-534	338	53	,	,	PUNCT
ejpam-534	338	54	p(t	p(t	NOUN
ejpam-534	338	55	)	)	PUNCT
ejpam-534	338	56	∈	∈	PROPN
ejpam-534	338	57	rn	rn	PROPN
ejpam-534	338	58	,	,	PUNCT
ejpam-534	338	59	∫	∫	PROPN
ejpam-534	338	60	g(t	g(t	PROPN
ejpam-534	338	61	,	,	PUNCT
ejpam-534	338	62	x	x	X
ejpam-534	338	63	,	,	PUNCT
ejpam-534	338	64	u	u	NOUN
ejpam-534	338	65	;	;	PUNCT
ejpam-534	339	1	f	f	PROPN
ejpam-534	339	2	i	i	NOUN
ejpam-534	339	3	x	x	X
ejpam-534	339	4	(	(	PUNCT
ejpam-534	339	5	t	t	PROPN
ejpam-534	339	6	,	,	PUNCT
ejpam-534	339	7	u	u	NOUN
ejpam-534	339	8	,	,	PUNCT
ejpam-534	339	9	u̇	u̇	PROPN
ejpam-534	339	10	)	)	PUNCT
ejpam-534	339	11	−	−	PROPN
ejpam-534	340	1	d	d	X
ejpam-534	340	2	f	f	X
ejpam-534	341	1	i	i	PRON
ejpam-534	341	2	ẋ	ẋ	PROPN
ejpam-534	342	1	(	(	PUNCT
ejpam-534	342	2	t	t	PROPN
ejpam-534	342	3	,	,	PUNCT
ejpam-534	342	4	u	u	NOUN
ejpam-534	342	5	,	,	PUNCT
ejpam-534	342	6	u̇	u̇	PROPN
ejpam-534	342	7	)	)	PUNCT
ejpam-534	343	1	+	+	CCONJ
ejpam-534	343	2	ai	ai	VERB
ejpam-534	343	3	p(t))d	p(t))d	NOUN
ejpam-534	343	4	t	t	NOUN
ejpam-534	343	5	+	+	NOUN
ejpam-534	343	6	ρ	ρ	NOUN
ejpam-534	343	7	∫	∫	PROPN
ejpam-534	343	8	d2(t	d2(t	PROPN
ejpam-534	343	9	,	,	PUNCT
ejpam-534	343	10	x	x	X
ejpam-534	343	11	,	,	PUNCT
ejpam-534	343	12	u)d	u)d	PROPN
ejpam-534	343	13	t	t	PROPN
ejpam-534	343	14	≧	≧	NOUN
ejpam-534	343	15	0	0	PUNCT
ejpam-534	343	16	t.	t.	PROPN
ejpam-534	343	17	gulati	gulati	PROPN
ejpam-534	343	18	and	and	CCONJ
ejpam-534	343	19	g.	g.	PROPN
ejpam-534	343	20	mehndiratta	mehndiratta	PROPN
ejpam-534	343	21	/	/	SYM
ejpam-534	343	22	eur	eur	PROPN
ejpam-534	343	23	.	.	PUNCT
ejpam-534	344	1	j.	j.	PROPN
ejpam-534	344	2	pure	pure	PROPN
ejpam-534	344	3	appl	appl	PROPN
ejpam-534	344	4	.	.	PROPN
ejpam-534	344	5	math	math	PROPN
ejpam-534	344	6	,	,	PUNCT
ejpam-534	344	7	3	3	NUM
ejpam-534	344	8	(	(	PUNCT
ejpam-534	344	9	2010	2010	NUM
ejpam-534	344	10	)	)	PUNCT
ejpam-534	344	11	,	,	PUNCT
ejpam-534	344	12	786	786	NUM
ejpam-534	344	13	-	-	SYM
ejpam-534	344	14	805	805	NUM
ejpam-534	344	15	793	793	NUM
ejpam-534	344	16	⇒	⇒	NOUN
ejpam-534	344	17	∫	∫	PROPN
ejpam-534	344	18	f	f	PROPN
ejpam-534	344	19	i(t	i(t	PROPN
ejpam-534	344	20	,	,	PUNCT
ejpam-534	344	21	x	x	X
ejpam-534	344	22	,	,	PUNCT
ejpam-534	344	23	ẋ)d	ẋ)d	PROPN
ejpam-534	344	24	t	t	PROPN
ejpam-534	344	25	≧	≧	X
ejpam-534	344	26	∫	∫	PROPN
ejpam-534	344	27	f	f	PROPN
ejpam-534	344	28	i(t	i(t	PROPN
ejpam-534	344	29	,	,	PUNCT
ejpam-534	344	30	u	u	NOUN
ejpam-534	344	31	,	,	PUNCT
ejpam-534	344	32	u̇)d	u̇)d	PROPN
ejpam-534	344	33	t	t	NOUN
ejpam-534	344	34	−	−	PROPN
ejpam-534	344	35	1	1	NUM
ejpam-534	344	36	2	2	NUM
ejpam-534	344	37	∫	∫	NOUN
ejpam-534	344	38	p(t)t	p(t)t	NOUN
ejpam-534	344	39	ai	ai	VERB
ejpam-534	344	40	p(t)d	p(t)d	PROPN
ejpam-534	344	41	t.	t.	ADJ
ejpam-534	344	42	definition	definition	NOUN
ejpam-534	344	43	5	5	NUM
ejpam-534	344	44	.	.	PUNCT
ejpam-534	345	1	the	the	DET
ejpam-534	345	2	functional	functional	ADJ
ejpam-534	345	3	∫	∫	PROPN
ejpam-534	345	4	f	f	PROPN
ejpam-534	345	5	i(t	i(t	PROPN
ejpam-534	345	6	,	,	PUNCT
ejpam-534	345	7	x	x	SYM
ejpam-534	345	8	,	,	PUNCT
ejpam-534	345	9	ẋ)d	ẋ)d	PROPN
ejpam-534	345	10	t	t	PROPN
ejpam-534	345	11	is	be	AUX
ejpam-534	345	12	said	say	VERB
ejpam-534	345	13	to	to	PART
ejpam-534	345	14	be	be	AUX
ejpam-534	345	15	second	second	ADJ
ejpam-534	345	16	-	-	PUNCT
ejpam-534	345	17	order	order	NOUN
ejpam-534	345	18	(	(	PUNCT
ejpam-534	345	19	g	g	NOUN
ejpam-534	345	20	,	,	PUNCT
ejpam-534	345	21	ρ)-quasiconvex	ρ)-quasiconvex	X
ejpam-534	345	22	at	at	ADP
ejpam-534	345	23	u(t	u(t	NOUN
ejpam-534	345	24	)	)	PUNCT
ejpam-534	345	25	∈	∈	PROPN
ejpam-534	345	26	s	s	PART
ejpam-534	345	27	,	,	PUNCT
ejpam-534	345	28	if	if	SCONJ
ejpam-534	345	29	there	there	PRON
ejpam-534	345	30	exists	exist	VERB
ejpam-534	345	31	a	a	DET
ejpam-534	345	32	sublinear	sublinear	NOUN
ejpam-534	345	33	functional	functional	ADJ
ejpam-534	345	34	g	g	NOUN
ejpam-534	345	35	:	:	PUNCT
ejpam-534	345	36	i	i	PRON
ejpam-534	345	37	×	×	VERB
ejpam-534	345	38	s	s	PART
ejpam-534	345	39	×	×	PROPN
ejpam-534	345	40	s	s	PART
ejpam-534	345	41	×	×	NOUN
ejpam-534	345	42	rn→	rn→	PROPN
ejpam-534	345	43	r	r	NOUN
ejpam-534	345	44	such	such	ADJ
ejpam-534	345	45	that	that	PRON
ejpam-534	345	46	for	for	ADP
ejpam-534	345	47	all	all	DET
ejpam-534	345	48	x(t	x(t	NOUN
ejpam-534	345	49	)	)	PUNCT
ejpam-534	345	50	∈	∈	PROPN
ejpam-534	345	51	s	s	NOUN
ejpam-534	345	52	,	,	PUNCT
ejpam-534	345	53	p(t	p(t	NOUN
ejpam-534	345	54	)	)	PUNCT
ejpam-534	345	55	∈	∈	PROPN
ejpam-534	345	56	rn	rn	PROPN
ejpam-534	345	57	,	,	PUNCT
ejpam-534	345	58	∫	∫	PROPN
ejpam-534	345	59	f	f	PROPN
ejpam-534	345	60	i(t	i(t	PROPN
ejpam-534	345	61	,	,	PUNCT
ejpam-534	345	62	x	x	X
ejpam-534	345	63	,	,	PUNCT
ejpam-534	346	1	ẋ)d	ẋ)d	PROPN
ejpam-534	346	2	t	t	PROPN
ejpam-534	346	3	≦	≦	PROPN
ejpam-534	346	4	∫	∫	PROPN
ejpam-534	346	5	f	f	PROPN
ejpam-534	346	6	i(t	i(t	PROPN
ejpam-534	346	7	,	,	PUNCT
ejpam-534	346	8	u	u	NOUN
ejpam-534	346	9	,	,	PUNCT
ejpam-534	346	10	u̇)d	u̇)d	PROPN
ejpam-534	346	11	t	t	NOUN
ejpam-534	346	12	−	−	PROPN
ejpam-534	346	13	1	1	NUM
ejpam-534	346	14	2	2	NUM
ejpam-534	346	15	∫	∫	NOUN
ejpam-534	346	16	p(t)t	p(t)t	NOUN
ejpam-534	346	17	ai	ai	VERB
ejpam-534	346	18	p(t)d	p(t)d	PROPN
ejpam-534	346	19	t	t	PROPN
ejpam-534	346	20	⇒	⇒	PROPN
ejpam-534	346	21	∫	∫	PROPN
ejpam-534	346	22	g(t	g(t	PROPN
ejpam-534	346	23	,	,	PUNCT
ejpam-534	346	24	x	x	X
ejpam-534	346	25	,	,	PUNCT
ejpam-534	346	26	u	u	NOUN
ejpam-534	346	27	;	;	PUNCT
ejpam-534	347	1	f	f	PROPN
ejpam-534	347	2	i	i	NOUN
ejpam-534	347	3	x	x	X
ejpam-534	347	4	(	(	PUNCT
ejpam-534	347	5	t	t	PROPN
ejpam-534	347	6	,	,	PUNCT
ejpam-534	347	7	u	u	NOUN
ejpam-534	347	8	,	,	PUNCT
ejpam-534	347	9	u̇)−	u̇)−	PROPN
ejpam-534	348	1	d	d	X
ejpam-534	348	2	f	f	PROPN
ejpam-534	349	1	i	i	PRON
ejpam-534	349	2	ẋ	ẋ	PROPN
ejpam-534	350	1	(	(	PUNCT
ejpam-534	350	2	t	t	PROPN
ejpam-534	350	3	,	,	PUNCT
ejpam-534	350	4	u	u	NOUN
ejpam-534	350	5	,	,	PUNCT
ejpam-534	350	6	u̇	u̇	PROPN
ejpam-534	350	7	)	)	PUNCT
ejpam-534	351	1	+	+	NUM
ejpam-534	352	1	aip(t))d	aip(t))d	NOUN
ejpam-534	352	2	t	t	PROPN
ejpam-534	352	3	+	+	NOUN
ejpam-534	352	4	ρ	ρ	NOUN
ejpam-534	352	5	∫	∫	PROPN
ejpam-534	352	6	d2(t	d2(t	PROPN
ejpam-534	352	7	,	,	PUNCT
ejpam-534	352	8	x	x	X
ejpam-534	352	9	,	,	PUNCT
ejpam-534	352	10	u)d	u)d	PROPN
ejpam-534	352	11	t	t	PROPN
ejpam-534	352	12	≦	≦	PROPN
ejpam-534	352	13	0	0	NUM
ejpam-534	352	14	.	.	PROPN
ejpam-534	353	1	4	4	NUM
ejpam-534	353	2	.	.	NOUN
ejpam-534	353	3	necessary	necessary	ADJ
ejpam-534	353	4	optimality	optimality	NOUN
ejpam-534	353	5	conditions	condition	NOUN
ejpam-534	353	6	we	we	PRON
ejpam-534	353	7	now	now	ADV
ejpam-534	353	8	prove	prove	VERB
ejpam-534	353	9	three	three	NUM
ejpam-534	353	10	results	result	NOUN
ejpam-534	353	11	.	.	PUNCT
ejpam-534	354	1	the	the	DET
ejpam-534	354	2	first	first	ADJ
ejpam-534	354	3	gives	give	VERB
ejpam-534	354	4	fritz	fritz	PROPN
ejpam-534	354	5	john	john	PROPN
ejpam-534	354	6	type	type	PROPN
ejpam-534	354	7	necessary	necessary	ADJ
ejpam-534	354	8	conditions	condition	NOUN
ejpam-534	354	9	for	for	ADP
ejpam-534	354	10	(	(	PUNCT
ejpam-534	354	11	p	p	NOUN
ejpam-534	354	12	)	)	PUNCT
ejpam-534	354	13	and	and	CCONJ
ejpam-534	354	14	the	the	DET
ejpam-534	354	15	remaining	remain	VERB
ejpam-534	354	16	two	two	NUM
ejpam-534	354	17	are	be	AUX
ejpam-534	354	18	kuhn	kuhn	PROPN
ejpam-534	354	19	-	-	PUNCT
ejpam-534	354	20	tucker	tucker	PROPN
ejpam-534	354	21	type	type	VERB
ejpam-534	354	22	necessary	necessary	ADJ
ejpam-534	354	23	conditions	condition	NOUN
ejpam-534	354	24	for	for	ADP
ejpam-534	354	25	(	(	PUNCT
ejpam-534	354	26	p	p	NOUN
ejpam-534	354	27	)	)	PUNCT
ejpam-534	354	28	.	.	PUNCT
ejpam-534	355	1	to	to	PART
ejpam-534	355	2	establish	establish	VERB
ejpam-534	355	3	these	these	DET
ejpam-534	355	4	necessary	necessary	ADJ
ejpam-534	355	5	conditions	condition	NOUN
ejpam-534	355	6	,	,	PUNCT
ejpam-534	355	7	we	we	PRON
ejpam-534	355	8	shall	shall	AUX
ejpam-534	355	9	use	use	VERB
ejpam-534	355	10	the	the	DET
ejpam-534	355	11	corresponding	corresponding	ADJ
ejpam-534	355	12	result	result	NOUN
ejpam-534	355	13	for	for	ADP
ejpam-534	355	14	single	single	ADJ
ejpam-534	355	15	objective	objective	ADJ
ejpam-534	355	16	variational	variational	ADJ
ejpam-534	355	17	problems	problem	NOUN
ejpam-534	355	18	obtained	obtain	VERB
ejpam-534	355	19	by	by	ADP
ejpam-534	355	20	chandra	chandra	PROPN
ejpam-534	355	21	et	et	PROPN
ejpam-534	355	22	al	al	PROPN
ejpam-534	355	23	.	.	PUNCT
ejpam-534	356	1	[	[	X
ejpam-534	356	2	4	4	X
ejpam-534	356	3	]	]	PUNCT
ejpam-534	356	4	in	in	ADP
ejpam-534	356	5	their	their	PRON
ejpam-534	356	6	theorem	theorem	NOUN
ejpam-534	356	7	1	1	NUM
ejpam-534	356	8	.	.	PUNCT
ejpam-534	356	9	as	as	SCONJ
ejpam-534	356	10	stated	state	VERB
ejpam-534	356	11	in	in	ADP
ejpam-534	356	12	the	the	DET
ejpam-534	356	13	remarks	remark	NOUN
ejpam-534	356	14	after	after	ADP
ejpam-534	356	15	theorem	theorem	NOUN
ejpam-534	356	16	1	1	NUM
ejpam-534	356	17	in	in	ADP
ejpam-534	356	18	[	[	X
ejpam-534	356	19	4	4	NUM
ejpam-534	356	20	]	]	PUNCT
ejpam-534	356	21	,	,	PUNCT
ejpam-534	356	22	to	to	PART
ejpam-534	356	23	use	use	VERB
ejpam-534	356	24	their	their	PRON
ejpam-534	356	25	kuhn	kuhn	PROPN
ejpam-534	356	26	-	-	PUNCT
ejpam-534	356	27	tucker	tucker	PROPN
ejpam-534	356	28	conditions	condition	NOUN
ejpam-534	356	29	,	,	PUNCT
ejpam-534	356	30	we	we	PRON
ejpam-534	356	31	shall	shall	AUX
ejpam-534	356	32	assume	assume	VERB
ejpam-534	356	33	slater	slater	PROPN
ejpam-534	356	34	’s	’s	PART
ejpam-534	356	35	or	or	CCONJ
ejpam-534	356	36	robinson	robinson	PROPN
ejpam-534	356	37	condition	condition	NOUN
ejpam-534	356	38	.	.	PUNCT
ejpam-534	357	1	the	the	DET
ejpam-534	357	2	following	following	ADJ
ejpam-534	357	3	result	result	NOUN
ejpam-534	357	4	relates	relate	VERB
ejpam-534	357	5	an	an	DET
ejpam-534	357	6	efficient	efficient	ADJ
ejpam-534	357	7	solution	solution	NOUN
ejpam-534	357	8	of	of	ADP
ejpam-534	357	9	(	(	PUNCT
ejpam-534	357	10	p	p	NOUN
ejpam-534	357	11	)	)	PUNCT
ejpam-534	357	12	with	with	ADP
ejpam-534	357	13	an	an	DET
ejpam-534	357	14	optimal	optimal	ADJ
ejpam-534	357	15	solution	solution	NOUN
ejpam-534	357	16	of	of	ADP
ejpam-534	357	17	k	k	ADJ
ejpam-534	357	18	-	-	ADJ
ejpam-534	357	19	scalar	scalar	ADJ
ejpam-534	357	20	objective	objective	ADJ
ejpam-534	357	21	variational	variational	ADJ
ejpam-534	357	22	problems	problem	NOUN
ejpam-534	357	23	.	.	PUNCT
ejpam-534	358	1	lemma	lemma	PROPN
ejpam-534	358	2	1	1	NUM
ejpam-534	358	3	(	(	PUNCT
ejpam-534	358	4	chankong	chankong	NOUN
ejpam-534	358	5	and	and	CCONJ
ejpam-534	358	6	haimes	haime	NOUN
ejpam-534	358	7	[	[	X
ejpam-534	358	8	5	5	NUM
ejpam-534	358	9	]	]	NUM
ejpam-534	358	10	)	)	PUNCT
ejpam-534	358	11	.	.	PUNCT
ejpam-534	359	1	a	a	DET
ejpam-534	359	2	point	point	NOUN
ejpam-534	359	3	x̄(t	x̄(t	NUM
ejpam-534	359	4	)	)	PUNCT
ejpam-534	359	5	∈	∈	PROPN
ejpam-534	359	6	x	x	X
ejpam-534	359	7	is	be	AUX
ejpam-534	359	8	an	an	DET
ejpam-534	359	9	efficient	efficient	ADJ
ejpam-534	359	10	solution	solution	NOUN
ejpam-534	359	11	of	of	ADP
ejpam-534	359	12	(	(	PUNCT
ejpam-534	359	13	p	p	NOUN
ejpam-534	359	14	)	)	PUNCT
ejpam-534	359	15	if	if	SCONJ
ejpam-534	360	1	and	and	CCONJ
ejpam-534	360	2	only	only	ADV
ejpam-534	360	3	if	if	SCONJ
ejpam-534	360	4	x̄(t	x̄(t	NOUN
ejpam-534	360	5	)	)	PUNCT
ejpam-534	360	6	is	be	AUX
ejpam-534	360	7	an	an	DET
ejpam-534	360	8	optimal	optimal	ADJ
ejpam-534	360	9	solution	solution	NOUN
ejpam-534	360	10	of	of	ADP
ejpam-534	360	11	(	(	PUNCT
ejpam-534	360	12	pr	pr	NOUN
ejpam-534	360	13	)	)	PUNCT
ejpam-534	360	14	for	for	ADP
ejpam-534	360	15	each	each	DET
ejpam-534	360	16	r	r	NOUN
ejpam-534	360	17	∈	∈	PROPN
ejpam-534	360	18	k.	k.	NOUN
ejpam-534	360	19	(	(	PUNCT
ejpam-534	360	20	pr	pr	NOUN
ejpam-534	360	21	)	)	PUNCT
ejpam-534	360	22	minimize	minimize	VERB
ejpam-534	360	23	∫	∫	PROPN
ejpam-534	360	24	f	f	PROPN
ejpam-534	360	25	r(t	r(t	PROPN
ejpam-534	360	26	,	,	PUNCT
ejpam-534	360	27	x	x	PRON
ejpam-534	360	28	,	,	PUNCT
ejpam-534	360	29	ẋ)d	ẋ)d	PROPN
ejpam-534	360	30	t	t	PROPN
ejpam-534	360	31	subject	subject	VERB
ejpam-534	360	32	to	to	ADP
ejpam-534	360	33	x(a	x(a	NOUN
ejpam-534	360	34	)	)	PUNCT
ejpam-534	360	35	=	=	SYM
ejpam-534	360	36	α	α	PROPN
ejpam-534	360	37	,	,	PUNCT
ejpam-534	360	38	x(b	x(b	PROPN
ejpam-534	360	39	)	)	PUNCT
ejpam-534	361	1	=	=	SYM
ejpam-534	361	2	β	β	X
ejpam-534	361	3	,	,	PUNCT
ejpam-534	361	4	g(t	g(t	PROPN
ejpam-534	361	5	,	,	PUNCT
ejpam-534	361	6	x	x	PRON
ejpam-534	361	7	,	,	PUNCT
ejpam-534	361	8	ẋ)≦	ẋ)≦	PROPN
ejpam-534	361	9	0	0	PROPN
ejpam-534	361	10	,	,	PUNCT
ejpam-534	361	11	t	t	PROPN
ejpam-534	361	12	∈	∈	PROPN
ejpam-534	362	1	i	i	PRON
ejpam-534	362	2	,	,	PUNCT
ejpam-534	362	3	∫	∫	PROPN
ejpam-534	362	4	f	f	PROPN
ejpam-534	362	5	i(t	i(t	PROPN
ejpam-534	362	6	,	,	PUNCT
ejpam-534	362	7	x	x	X
ejpam-534	362	8	,	,	PUNCT
ejpam-534	362	9	ẋ)d	ẋ)d	PROPN
ejpam-534	362	10	t	t	PROPN
ejpam-534	362	11	≦	≦	PROPN
ejpam-534	362	12	∫	∫	PROPN
ejpam-534	362	13	f	f	PROPN
ejpam-534	362	14	i(t	i(t	PROPN
ejpam-534	362	15	,	,	PUNCT
ejpam-534	362	16	x̄	x̄	NOUN
ejpam-534	362	17	,	,	PUNCT
ejpam-534	362	18	˙̄x)d	˙̄x)d	PROPN
ejpam-534	362	19	t	t	PROPN
ejpam-534	362	20	,	,	PUNCT
ejpam-534	362	21	i	i	PRON
ejpam-534	362	22	∈	∈	PROPN
ejpam-534	362	23	kr	kr	PROPN
ejpam-534	362	24	.	.	PUNCT
ejpam-534	363	1	the	the	DET
ejpam-534	363	2	k	k	NOUN
ejpam-534	363	3	-	-	PUNCT
ejpam-534	363	4	problems	problem	NOUN
ejpam-534	363	5	(	(	PUNCT
ejpam-534	363	6	pr	pr	NOUN
ejpam-534	363	7	)	)	PUNCT
ejpam-534	363	8	involve	involve	VERB
ejpam-534	363	9	integral	integral	ADJ
ejpam-534	363	10	in	in	ADP
ejpam-534	363	11	the	the	DET
ejpam-534	363	12	constraints	constraint	NOUN
ejpam-534	363	13	,	,	PUNCT
ejpam-534	363	14	while	while	SCONJ
ejpam-534	363	15	to	to	PART
ejpam-534	363	16	obtain	obtain	VERB
ejpam-534	363	17	necessary	necessary	ADJ
ejpam-534	363	18	optimality	optimality	NOUN
ejpam-534	363	19	conditions	condition	NOUN
ejpam-534	363	20	for	for	ADP
ejpam-534	363	21	(	(	PUNCT
ejpam-534	363	22	p	p	NOUN
ejpam-534	363	23	)	)	PUNCT
ejpam-534	363	24	via	via	ADP
ejpam-534	363	25	(	(	PUNCT
ejpam-534	363	26	pr	pr	X
ejpam-534	363	27	)	)	PUNCT
ejpam-534	363	28	we	we	PRON
ejpam-534	363	29	need	need	VERB
ejpam-534	363	30	necessary	necessary	ADJ
ejpam-534	363	31	optimality	optimality	NOUN
ejpam-534	363	32	conditions	condition	NOUN
ejpam-534	363	33	for	for	ADP
ejpam-534	363	34	scalar	scalar	ADJ
ejpam-534	363	35	variational	variational	ADJ
ejpam-534	363	36	problem	problem	NOUN
ejpam-534	363	37	[	[	X
ejpam-534	363	38	4	4	NUM
ejpam-534	363	39	]	]	PUNCT
ejpam-534	363	40	.	.	PUNCT
ejpam-534	364	1	since	since	SCONJ
ejpam-534	364	2	the	the	DET
ejpam-534	364	3	variational	variational	ADJ
ejpam-534	364	4	problem	problem	NOUN
ejpam-534	364	5	in	in	ADP
ejpam-534	364	6	[	[	X
ejpam-534	364	7	4	4	X
ejpam-534	364	8	]	]	PUNCT
ejpam-534	364	9	does	do	AUX
ejpam-534	364	10	not	not	PART
ejpam-534	364	11	involve	involve	VERB
ejpam-534	364	12	the	the	DET
ejpam-534	364	13	integral	integral	ADJ
ejpam-534	364	14	in	in	ADP
ejpam-534	364	15	the	the	DET
ejpam-534	364	16	constraints	constraint	NOUN
ejpam-534	364	17	,	,	PUNCT
ejpam-534	364	18	we	we	PRON
ejpam-534	364	19	first	first	ADV
ejpam-534	364	20	derive	derive	VERB
ejpam-534	364	21	the	the	DET
ejpam-534	364	22	result	result	NOUN
ejpam-534	364	23	relating	relate	VERB
ejpam-534	364	24	an	an	DET
ejpam-534	364	25	efficient	efficient	ADJ
ejpam-534	364	26	solution	solution	NOUN
ejpam-534	364	27	of	of	ADP
ejpam-534	364	28	(	(	PUNCT
ejpam-534	364	29	p	p	NOUN
ejpam-534	364	30	)	)	PUNCT
ejpam-534	364	31	with	with	ADP
ejpam-534	364	32	the	the	DET
ejpam-534	364	33	optimal	optimal	ADJ
ejpam-534	364	34	solution	solution	NOUN
ejpam-534	364	35	of	of	ADP
ejpam-534	364	36	the	the	DET
ejpam-534	364	37	following	follow	VERB
ejpam-534	364	38	k	k	ADJ
ejpam-534	364	39	-	-	ADJ
ejpam-534	364	40	single	single	ADJ
ejpam-534	364	41	objective	objective	ADJ
ejpam-534	364	42	problems	problem	NOUN
ejpam-534	364	43	:	:	PUNCT
ejpam-534	364	44	(	(	PUNCT
ejpam-534	364	45	p̂r	p̂r	NOUN
ejpam-534	364	46	)	)	PUNCT
ejpam-534	364	47	minimize	minimize	VERB
ejpam-534	364	48	∫	∫	PROPN
ejpam-534	364	49	f	f	PROPN
ejpam-534	364	50	r(t	r(t	PROPN
ejpam-534	364	51	,	,	PUNCT
ejpam-534	364	52	x	x	PRON
ejpam-534	364	53	,	,	PUNCT
ejpam-534	364	54	ẋ)d	ẋ)d	PROPN
ejpam-534	364	55	t	t	PROPN
ejpam-534	364	56	subject	subject	VERB
ejpam-534	364	57	to	to	ADP
ejpam-534	364	58	x(a	x(a	NOUN
ejpam-534	364	59	)	)	PUNCT
ejpam-534	364	60	=	=	SYM
ejpam-534	364	61	α	α	PROPN
ejpam-534	364	62	,	,	PUNCT
ejpam-534	364	63	x(b	x(b	PROPN
ejpam-534	364	64	)	)	PUNCT
ejpam-534	365	1	=	=	SYM
ejpam-534	365	2	β	β	X
ejpam-534	365	3	,	,	PUNCT
ejpam-534	365	4	g(t	g(t	PROPN
ejpam-534	365	5	,	,	PUNCT
ejpam-534	365	6	x	x	PRON
ejpam-534	365	7	,	,	PUNCT
ejpam-534	365	8	ẋ)≦	ẋ)≦	PROPN
ejpam-534	365	9	0	0	PROPN
ejpam-534	365	10	,	,	PUNCT
ejpam-534	365	11	t	t	PROPN
ejpam-534	365	12	∈	∈	PROPN
ejpam-534	366	1	i	i	PRON
ejpam-534	366	2	,	,	PUNCT
ejpam-534	366	3	f	f	PROPN
ejpam-534	366	4	i(t	i(t	PROPN
ejpam-534	366	5	,	,	PUNCT
ejpam-534	366	6	x	x	X
ejpam-534	366	7	,	,	PUNCT
ejpam-534	366	8	ẋ)≦	ẋ)≦	PROPN
ejpam-534	366	9	f	f	PROPN
ejpam-534	366	10	i(t	i(t	PROPN
ejpam-534	366	11	,	,	PUNCT
ejpam-534	366	12	x̄	x̄	NOUN
ejpam-534	366	13	,	,	PUNCT
ejpam-534	366	14	˙̄x	˙̄x	PRON
ejpam-534	366	15	)	)	PUNCT
ejpam-534	366	16	,	,	PUNCT
ejpam-534	366	17	t	t	PROPN
ejpam-534	366	18	∈	∈	PROPN
ejpam-534	367	1	i	i	PRON
ejpam-534	367	2	,	,	PUNCT
ejpam-534	367	3	i	i	PROPN
ejpam-534	367	4	∈	∈	PROPN
ejpam-534	367	5	kr	kr	PROPN
ejpam-534	367	6	.	.	PUNCT
ejpam-534	368	1	lemma	lemma	PROPN
ejpam-534	368	2	2	2	X
ejpam-534	368	3	.	.	PUNCT
ejpam-534	369	1	let	let	VERB
ejpam-534	369	2	x̄(t	x̄(t	NOUN
ejpam-534	369	3	)	)	PUNCT
ejpam-534	370	1	∈	∈	PROPN
ejpam-534	370	2	x	x	VERB
ejpam-534	370	3	be	be	AUX
ejpam-534	370	4	an	an	DET
ejpam-534	370	5	efficient	efficient	ADJ
ejpam-534	370	6	solution	solution	NOUN
ejpam-534	370	7	of	of	ADP
ejpam-534	370	8	(	(	PUNCT
ejpam-534	370	9	p	p	NOUN
ejpam-534	370	10	)	)	PUNCT
ejpam-534	370	11	.	.	PUNCT
ejpam-534	371	1	then	then	ADV
ejpam-534	371	2	x̄(t	x̄(t	NUM
ejpam-534	371	3	)	)	PUNCT
ejpam-534	371	4	is	be	AUX
ejpam-534	371	5	an	an	DET
ejpam-534	371	6	optimal	optimal	ADJ
ejpam-534	371	7	solution	solution	NOUN
ejpam-534	371	8	of	of	ADP
ejpam-534	371	9	(	(	PUNCT
ejpam-534	371	10	p̂r	p̂r	NUM
ejpam-534	371	11	)	)	PUNCT
ejpam-534	371	12	for	for	ADP
ejpam-534	371	13	each	each	DET
ejpam-534	371	14	r	r	NOUN
ejpam-534	371	15	∈	∈	PROPN
ejpam-534	371	16	k.	k.	NOUN
ejpam-534	371	17	t.	t.	PROPN
ejpam-534	371	18	gulati	gulati	PROPN
ejpam-534	371	19	and	and	CCONJ
ejpam-534	371	20	g.	g.	PROPN
ejpam-534	371	21	mehndiratta	mehndiratta	PROPN
ejpam-534	371	22	/	/	SYM
ejpam-534	371	23	eur	eur	PROPN
ejpam-534	371	24	.	.	PUNCT
ejpam-534	372	1	j.	j.	PROPN
ejpam-534	372	2	pure	pure	PROPN
ejpam-534	372	3	appl	appl	PROPN
ejpam-534	372	4	.	.	PROPN
ejpam-534	372	5	math	math	PROPN
ejpam-534	372	6	,	,	PUNCT
ejpam-534	372	7	3	3	NUM
ejpam-534	372	8	(	(	PUNCT
ejpam-534	372	9	2010	2010	NUM
ejpam-534	372	10	)	)	PUNCT
ejpam-534	372	11	,	,	PUNCT
ejpam-534	372	12	786	786	NUM
ejpam-534	372	13	-	-	SYM
ejpam-534	372	14	805	805	NUM
ejpam-534	372	15	794	794	NUM
ejpam-534	372	16	proof	proof	NOUN
ejpam-534	372	17	.	.	PUNCT
ejpam-534	373	1	let	let	AUX
ejpam-534	373	2	x̄(t	x̄(t	PRON
ejpam-534	373	3	)	)	PUNCT
ejpam-534	373	4	be	be	AUX
ejpam-534	373	5	an	an	DET
ejpam-534	373	6	efficient	efficient	ADJ
ejpam-534	373	7	solution	solution	NOUN
ejpam-534	373	8	of	of	ADP
ejpam-534	373	9	(	(	PUNCT
ejpam-534	373	10	p	p	NOUN
ejpam-534	373	11	)	)	PUNCT
ejpam-534	373	12	and	and	CCONJ
ejpam-534	373	13	suppose	suppose	VERB
ejpam-534	373	14	,	,	PUNCT
ejpam-534	373	15	to	to	ADP
ejpam-534	373	16	the	the	DET
ejpam-534	373	17	contrary	contrary	NOUN
ejpam-534	373	18	,	,	PUNCT
ejpam-534	373	19	that	that	SCONJ
ejpam-534	373	20	x̄(t	x̄(t	PROPN
ejpam-534	373	21	)	)	PUNCT
ejpam-534	373	22	is	be	AUX
ejpam-534	373	23	not	not	PART
ejpam-534	373	24	an	an	DET
ejpam-534	373	25	optimal	optimal	ADJ
ejpam-534	373	26	solution	solution	NOUN
ejpam-534	373	27	of	of	ADP
ejpam-534	373	28	(	(	PUNCT
ejpam-534	373	29	p̂r	p̂r	NUM
ejpam-534	373	30	)	)	PUNCT
ejpam-534	373	31	,	,	PUNCT
ejpam-534	373	32	for	for	ADP
ejpam-534	373	33	some	some	DET
ejpam-534	373	34	r	r	NOUN
ejpam-534	373	35	∈	∈	PROPN
ejpam-534	373	36	k	k	X
ejpam-534	373	37	.	.	PUNCT
ejpam-534	374	1	then	then	ADV
ejpam-534	374	2	there	there	PRON
ejpam-534	374	3	exists	exist	VERB
ejpam-534	374	4	an	an	DET
ejpam-534	374	5	x̂(t	x̂(t	NOUN
ejpam-534	374	6	)	)	PUNCT
ejpam-534	374	7	∈	∈	PROPN
ejpam-534	374	8	x	x	PUNCT
ejpam-534	374	9	such	such	ADJ
ejpam-534	374	10	that	that	SCONJ
ejpam-534	374	11	g(t	g(t	PROPN
ejpam-534	374	12	,	,	PUNCT
ejpam-534	374	13	x̂	x̂	NUM
ejpam-534	374	14	,	,	PUNCT
ejpam-534	374	15	˙̂x)≦	˙̂x)≦	PROPN
ejpam-534	374	16	0	0	NUM
ejpam-534	374	17	,	,	PUNCT
ejpam-534	374	18	t	t	PROPN
ejpam-534	374	19	∈	∈	PROPN
ejpam-534	375	1	i	i	PRON
ejpam-534	375	2	,	,	PUNCT
ejpam-534	375	3	(	(	PUNCT
ejpam-534	375	4	24	24	NUM
ejpam-534	375	5	)	)	PUNCT
ejpam-534	375	6	f	f	PROPN
ejpam-534	375	7	i(t	i(t	PROPN
ejpam-534	375	8	,	,	PUNCT
ejpam-534	375	9	x̂	x̂	NUM
ejpam-534	375	10	,	,	PUNCT
ejpam-534	375	11	˙̂x)≦	˙̂x)≦	PROPN
ejpam-534	375	12	f	f	PROPN
ejpam-534	375	13	i(t	i(t	PROPN
ejpam-534	375	14	,	,	PUNCT
ejpam-534	375	15	x̄	x̄	NOUN
ejpam-534	375	16	,	,	PUNCT
ejpam-534	375	17	˙̄x	˙̄x	PRON
ejpam-534	375	18	)	)	PUNCT
ejpam-534	375	19	,	,	PUNCT
ejpam-534	376	1	t	t	PROPN
ejpam-534	376	2	∈	∈	PROPN
ejpam-534	377	1	i	i	PRON
ejpam-534	377	2	,	,	PUNCT
ejpam-534	377	3	i	i	PROPN
ejpam-534	377	4	∈	∈	PROPN
ejpam-534	377	5	kr	kr	PROPN
ejpam-534	377	6	,	,	PUNCT
ejpam-534	377	7	(	(	PUNCT
ejpam-534	377	8	25	25	NUM
ejpam-534	377	9	)	)	PUNCT
ejpam-534	377	10	and	and	CCONJ
ejpam-534	377	11	∫	∫	PROPN
ejpam-534	377	12	f	f	PROPN
ejpam-534	377	13	r(t	r(t	PROPN
ejpam-534	377	14	,	,	PUNCT
ejpam-534	377	15	x̂	x̂	NUM
ejpam-534	377	16	,	,	PUNCT
ejpam-534	377	17	˙̂x)d	˙̂x)d	PROPN
ejpam-534	377	18	t	t	PROPN
ejpam-534	377	19	<	<	X
ejpam-534	377	20	∫	∫	PROPN
ejpam-534	377	21	f	f	PROPN
ejpam-534	377	22	r(t	r(t	PROPN
ejpam-534	377	23	,	,	PUNCT
ejpam-534	377	24	x̄	x̄	NOUN
ejpam-534	377	25	,	,	PUNCT
ejpam-534	377	26	˙̄x)d	˙̄x)d	PRON
ejpam-534	377	27	t.	t.	PROPN
ejpam-534	377	28	(	(	PUNCT
ejpam-534	377	29	26	26	NUM
ejpam-534	377	30	)	)	PUNCT
ejpam-534	377	31	inequality	inequality	NOUN
ejpam-534	377	32	(	(	PUNCT
ejpam-534	377	33	25	25	NUM
ejpam-534	377	34	)	)	PUNCT
ejpam-534	377	35	implies	imply	VERB
ejpam-534	377	36	∫	∫	PROPN
ejpam-534	377	37	f	f	PROPN
ejpam-534	377	38	i(t	i(t	PROPN
ejpam-534	377	39	,	,	PUNCT
ejpam-534	377	40	x̂	x̂	NUM
ejpam-534	377	41	,	,	PUNCT
ejpam-534	377	42	˙̂x)d	˙̂x)d	PROPN
ejpam-534	377	43	t	t	PROPN
ejpam-534	377	44	≦	≦	PROPN
ejpam-534	377	45	∫	∫	PROPN
ejpam-534	377	46	f	f	PROPN
ejpam-534	377	47	i(t	i(t	PROPN
ejpam-534	377	48	,	,	PUNCT
ejpam-534	377	49	x̄	x̄	NOUN
ejpam-534	377	50	,	,	PUNCT
ejpam-534	377	51	˙̄x)d	˙̄x)d	PROPN
ejpam-534	377	52	t	t	PROPN
ejpam-534	377	53	,	,	PUNCT
ejpam-534	377	54	i	i	PRON
ejpam-534	377	55	∈	∈	PROPN
ejpam-534	377	56	kr	kr	PROPN
ejpam-534	377	57	.	.	PUNCT
ejpam-534	378	1	(	(	PUNCT
ejpam-534	378	2	27	27	NUM
ejpam-534	378	3	)	)	PUNCT
ejpam-534	378	4	inequalities	inequality	NOUN
ejpam-534	378	5	(	(	PUNCT
ejpam-534	378	6	26	26	NUM
ejpam-534	378	7	)	)	PUNCT
ejpam-534	378	8	and	and	CCONJ
ejpam-534	378	9	(	(	PUNCT
ejpam-534	378	10	27	27	NUM
ejpam-534	378	11	)	)	PUNCT
ejpam-534	378	12	contradict	contradict	VERB
ejpam-534	378	13	the	the	DET
ejpam-534	378	14	fact	fact	NOUN
ejpam-534	378	15	that	that	SCONJ
ejpam-534	378	16	x̄(t	x̄(t	PROPN
ejpam-534	378	17	)	)	PUNCT
ejpam-534	378	18	is	be	AUX
ejpam-534	378	19	an	an	DET
ejpam-534	378	20	efficient	efficient	ADJ
ejpam-534	378	21	solution	solution	NOUN
ejpam-534	378	22	of	of	ADP
ejpam-534	378	23	(	(	PUNCT
ejpam-534	378	24	p	p	NOUN
ejpam-534	378	25	)	)	PUNCT
ejpam-534	378	26	.	.	PUNCT
ejpam-534	379	1	hence	hence	ADV
ejpam-534	379	2	x̄(t	x̄(t	NUM
ejpam-534	379	3	)	)	PUNCT
ejpam-534	379	4	is	be	AUX
ejpam-534	379	5	an	an	DET
ejpam-534	379	6	optimal	optimal	ADJ
ejpam-534	379	7	solution	solution	NOUN
ejpam-534	379	8	of	of	ADP
ejpam-534	379	9	(	(	PUNCT
ejpam-534	379	10	p̂r	p̂r	NUM
ejpam-534	379	11	)	)	PUNCT
ejpam-534	379	12	for	for	ADP
ejpam-534	379	13	each	each	DET
ejpam-534	379	14	r	r	NOUN
ejpam-534	379	15	∈	∈	PROPN
ejpam-534	379	16	k	k	X
ejpam-534	379	17	.	.	PUNCT
ejpam-534	380	1	theorem	theorem	NOUN
ejpam-534	380	2	3	3	NUM
ejpam-534	380	3	(	(	PUNCT
ejpam-534	380	4	fritz	fritz	PROPN
ejpam-534	380	5	john	john	PROPN
ejpam-534	380	6	type	type	VERB
ejpam-534	380	7	necessary	necessary	ADJ
ejpam-534	380	8	conditions	condition	NOUN
ejpam-534	380	9	)	)	PUNCT
ejpam-534	380	10	.	.	PUNCT
ejpam-534	381	1	let	let	AUX
ejpam-534	381	2	x̄(t	x̄(t	PRON
ejpam-534	381	3	)	)	PUNCT
ejpam-534	381	4	be	be	AUX
ejpam-534	381	5	an	an	DET
ejpam-534	381	6	efficient	efficient	ADJ
ejpam-534	381	7	solution	solution	NOUN
ejpam-534	381	8	of	of	ADP
ejpam-534	381	9	(	(	PUNCT
ejpam-534	381	10	p	p	NOUN
ejpam-534	381	11	)	)	PUNCT
ejpam-534	381	12	.	.	PUNCT
ejpam-534	382	1	then	then	ADV
ejpam-534	382	2	there	there	PRON
ejpam-534	382	3	exist	exist	VERB
ejpam-534	382	4	λ̄i	λ̄i	NUM
ejpam-534	382	5	∈	∈	PROPN
ejpam-534	382	6	r	r	NOUN
ejpam-534	382	7	,	,	PUNCT
ejpam-534	382	8	i	i	PROPN
ejpam-534	382	9	∈	∈	PROPN
ejpam-534	382	10	k	k	PROPN
ejpam-534	382	11	and	and	CCONJ
ejpam-534	382	12	a	a	DET
ejpam-534	382	13	piecewise	piecewise	NOUN
ejpam-534	382	14	smooth	smooth	ADJ
ejpam-534	382	15	function	function	NOUN
ejpam-534	382	16	ȳ	ȳ	NOUN
ejpam-534	382	17	:	:	PUNCT
ejpam-534	382	18	i	i	PRON
ejpam-534	382	19	→	→	PUNCT
ejpam-534	382	20	rm	rm	PROPN
ejpam-534	382	21	such	such	ADJ
ejpam-534	382	22	that	that	PRON
ejpam-534	382	23	k∑	k∑	VERB
ejpam-534	382	24	i=1	i=1	PROPN
ejpam-534	383	1	λ̄i	λ̄i	PROPN
ejpam-534	383	2	(	(	PUNCT
ejpam-534	383	3	f	f	NOUN
ejpam-534	383	4	i	i	PRON
ejpam-534	383	5	x	x	X
ejpam-534	383	6	(	(	PUNCT
ejpam-534	383	7	t	t	PROPN
ejpam-534	383	8	,	,	PUNCT
ejpam-534	383	9	x̄	x̄	NOUN
ejpam-534	383	10	,	,	PUNCT
ejpam-534	383	11	˙̄x)−	˙̄x)−	PROPN
ejpam-534	384	1	d	d	X
ejpam-534	384	2	f	f	X
ejpam-534	385	1	i	i	PRON
ejpam-534	385	2	ẋ	ẋ	PROPN
ejpam-534	386	1	(	(	PUNCT
ejpam-534	386	2	t	t	PROPN
ejpam-534	386	3	,	,	PUNCT
ejpam-534	386	4	x̄	x̄	NOUN
ejpam-534	386	5	,	,	PUNCT
ejpam-534	386	6	˙̄x))+	˙̄x))+	ADP
ejpam-534	386	7	gx(t	gx(t	PROPN
ejpam-534	386	8	,	,	PUNCT
ejpam-534	386	9	x̄	x̄	NOUN
ejpam-534	386	10	,	,	PUNCT
ejpam-534	386	11	˙̄x	˙̄x	PRON
ejpam-534	386	12	)	)	PUNCT
ejpam-534	386	13	ȳ(t)−	ȳ(t)−	PROPN
ejpam-534	386	14	d(g	d(g	PROPN
ejpam-534	386	15	ẋ(t	ẋ(t	PROPN
ejpam-534	386	16	,	,	PUNCT
ejpam-534	386	17	x̄	x̄	NOUN
ejpam-534	386	18	,	,	PUNCT
ejpam-534	386	19	˙̄x	˙̄x	NOUN
ejpam-534	386	20	)	)	PUNCT
ejpam-534	386	21	ȳ(t	ȳ(t	NOUN
ejpam-534	386	22	)	)	PUNCT
ejpam-534	386	23	)	)	PUNCT
ejpam-534	387	1	=	=	PUNCT
ejpam-534	387	2	0	0	NUM
ejpam-534	387	3	,	,	PUNCT
ejpam-534	387	4	t	t	PROPN
ejpam-534	387	5	∈	∈	PROPN
ejpam-534	388	1	i	i	PRON
ejpam-534	388	2	,	,	PUNCT
ejpam-534	388	3	(	(	PUNCT
ejpam-534	388	4	28	28	NUM
ejpam-534	388	5	)	)	PUNCT
ejpam-534	388	6	ȳ(t)t	ȳ(t)t	PROPN
ejpam-534	388	7	g(t	g(t	PROPN
ejpam-534	388	8	,	,	PUNCT
ejpam-534	388	9	x̄	x̄	NOUN
ejpam-534	388	10	,	,	PUNCT
ejpam-534	388	11	˙̄x	˙̄x	PRON
ejpam-534	388	12	)	)	PUNCT
ejpam-534	388	13	=	=	SYM
ejpam-534	388	14	0	0	NUM
ejpam-534	388	15	,	,	PUNCT
ejpam-534	388	16	t	t	PROPN
ejpam-534	388	17	∈	∈	PROPN
ejpam-534	389	1	i	i	PRON
ejpam-534	389	2	,	,	PUNCT
ejpam-534	389	3	(	(	PUNCT
ejpam-534	389	4	29	29	NUM
ejpam-534	389	5	)	)	PUNCT
ejpam-534	389	6	(	(	PUNCT
ejpam-534	389	7	λ̄	λ̄	ADP
ejpam-534	389	8	,	,	PUNCT
ejpam-534	389	9	ȳ(t	ȳ(t	NOUN
ejpam-534	389	10	)	)	PUNCT
ejpam-534	389	11	)	)	PUNCT
ejpam-534	389	12	≥	≥	NOUN
ejpam-534	389	13	0	0	NUM
ejpam-534	389	14	,	,	PUNCT
ejpam-534	389	15	t	t	PROPN
ejpam-534	389	16	∈	∈	PROPN
ejpam-534	390	1	i	i	PRON
ejpam-534	390	2	.	.	PUNCT
ejpam-534	391	1	(	(	PUNCT
ejpam-534	391	2	30	30	X
ejpam-534	391	3	)	)	PUNCT
ejpam-534	391	4	proof	proof	NOUN
ejpam-534	391	5	.	.	PUNCT
ejpam-534	392	1	since	since	SCONJ
ejpam-534	392	2	x̄(t	x̄(t	PROPN
ejpam-534	392	3	)	)	PUNCT
ejpam-534	392	4	is	be	AUX
ejpam-534	392	5	an	an	DET
ejpam-534	392	6	efficient	efficient	ADJ
ejpam-534	392	7	solution	solution	NOUN
ejpam-534	392	8	of	of	ADP
ejpam-534	392	9	(	(	PUNCT
ejpam-534	392	10	p	p	NOUN
ejpam-534	392	11	)	)	PUNCT
ejpam-534	392	12	,	,	PUNCT
ejpam-534	392	13	by	by	ADP
ejpam-534	392	14	lemma	lemma	PROPN
ejpam-534	392	15	2	2	NUM
ejpam-534	392	16	,	,	PUNCT
ejpam-534	392	17	x̄(t	x̄(t	NUM
ejpam-534	392	18	)	)	PUNCT
ejpam-534	393	1	is	be	AUX
ejpam-534	393	2	an	an	DET
ejpam-534	393	3	optimal	optimal	ADJ
ejpam-534	393	4	solution	solution	NOUN
ejpam-534	393	5	of	of	ADP
ejpam-534	393	6	(	(	PUNCT
ejpam-534	393	7	p̂r	p̂r	NUM
ejpam-534	393	8	)	)	PUNCT
ejpam-534	393	9	for	for	ADP
ejpam-534	393	10	each	each	DET
ejpam-534	393	11	r	r	NOUN
ejpam-534	393	12	∈	∈	PROPN
ejpam-534	393	13	k	k	NOUN
ejpam-534	393	14	and	and	CCONJ
ejpam-534	393	15	hence	hence	ADV
ejpam-534	393	16	in	in	ADP
ejpam-534	393	17	particular	particular	ADJ
ejpam-534	393	18	of	of	ADP
ejpam-534	393	19	(	(	PUNCT
ejpam-534	393	20	p̂1	p̂1	ADJ
ejpam-534	393	21	)	)	PUNCT
ejpam-534	393	22	.	.	PUNCT
ejpam-534	394	1	therefore	therefore	ADV
ejpam-534	394	2	,	,	PUNCT
ejpam-534	394	3	by	by	ADP
ejpam-534	394	4	[	[	X
ejpam-534	394	5	4	4	NUM
ejpam-534	394	6	]	]	PUNCT
ejpam-534	394	7	,	,	PUNCT
ejpam-534	394	8	there	there	PRON
ejpam-534	394	9	exist	exist	VERB
ejpam-534	394	10	λ̄i	λ̄i	ADP
ejpam-534	394	11	,	,	PUNCT
ejpam-534	394	12	i	i	PROPN
ejpam-534	394	13	∈	∈	PROPN
ejpam-534	394	14	k	k	PROPN
ejpam-534	394	15	and	and	CCONJ
ejpam-534	394	16	a	a	DET
ejpam-534	394	17	piecewise	piecewise	NOUN
ejpam-534	394	18	smooth	smooth	ADJ
ejpam-534	394	19	function	function	NOUN
ejpam-534	394	20	ȳ(t	ȳ(t	NOUN
ejpam-534	394	21	)	)	PUNCT
ejpam-534	394	22	∈	∈	PROPN
ejpam-534	394	23	rm	rm	NOUN
ejpam-534	394	24	such	such	ADJ
ejpam-534	394	25	that	that	SCONJ
ejpam-534	394	26	gx(t	gx(t	NOUN
ejpam-534	394	27	,	,	PUNCT
ejpam-534	394	28	x̄	x̄	NOUN
ejpam-534	394	29	,	,	PUNCT
ejpam-534	394	30	˙̄x	˙̄x	PRON
ejpam-534	394	31	)	)	PUNCT
ejpam-534	395	1	ȳ(t)−	ȳ(t)−	PROPN
ejpam-534	395	2	d(g	d(g	PROPN
ejpam-534	395	3	ẋ(t	ẋ(t	PROPN
ejpam-534	395	4	,	,	PUNCT
ejpam-534	395	5	x̄	x̄	NOUN
ejpam-534	395	6	,	,	PUNCT
ejpam-534	395	7	˙̄x	˙̄x	NOUN
ejpam-534	395	8	)	)	PUNCT
ejpam-534	395	9	ȳ(t	ȳ(t	NOUN
ejpam-534	395	10	)	)	PUNCT
ejpam-534	395	11	)	)	PUNCT
ejpam-534	396	1	=	=	PUNCT
ejpam-534	396	2	0	0	NUM
ejpam-534	396	3	,	,	PUNCT
ejpam-534	396	4	t	t	PROPN
ejpam-534	396	5	∈	∈	PROPN
ejpam-534	397	1	i	i	PRON
ejpam-534	397	2	,	,	PUNCT
ejpam-534	397	3	ȳ(t)t	ȳ(t)t	PROPN
ejpam-534	397	4	g(t	g(t	PROPN
ejpam-534	397	5	,	,	PUNCT
ejpam-534	397	6	x̄	x̄	NOUN
ejpam-534	397	7	,	,	PUNCT
ejpam-534	397	8	˙̄x	˙̄x	PRON
ejpam-534	397	9	)	)	PUNCT
ejpam-534	397	10	=	=	SYM
ejpam-534	397	11	0	0	NUM
ejpam-534	397	12	,	,	PUNCT
ejpam-534	397	13	t	t	PROPN
ejpam-534	397	14	∈	∈	PROPN
ejpam-534	398	1	i	i	PRON
ejpam-534	398	2	,	,	PUNCT
ejpam-534	398	3	(	(	PUNCT
ejpam-534	398	4	λ̄1	λ̄1	X
ejpam-534	398	5	,	,	PUNCT
ejpam-534	398	6	λ̄2	λ̄2	X
ejpam-534	398	7	,	,	PUNCT
ejpam-534	398	8	.	.	PUNCT
ejpam-534	398	9	.	.	PUNCT
ejpam-534	398	10	.	.	PUNCT
ejpam-534	399	1	,	,	PUNCT
ejpam-534	399	2	λ̄k	λ̄k	PROPN
ejpam-534	399	3	,	,	PUNCT
ejpam-534	399	4	ȳ(t	ȳ(t	PROPN
ejpam-534	399	5	)	)	PUNCT
ejpam-534	399	6	)	)	PUNCT
ejpam-534	399	7	≥	≥	NOUN
ejpam-534	399	8	0	0	NUM
ejpam-534	399	9	,	,	PUNCT
ejpam-534	399	10	t	t	PROPN
ejpam-534	399	11	∈	∈	PROPN
ejpam-534	400	1	i	i	PRON
ejpam-534	400	2	,	,	PUNCT
ejpam-534	400	3	which	which	PRON
ejpam-534	400	4	give	give	VERB
ejpam-534	400	5	(	(	PUNCT
ejpam-534	400	6	28	28	NUM
ejpam-534	400	7	)	)	PUNCT
ejpam-534	400	8	to	to	ADP
ejpam-534	400	9	(	(	PUNCT
ejpam-534	400	10	30	30	NUM
ejpam-534	400	11	)	)	PUNCT
ejpam-534	400	12	.	.	PUNCT
ejpam-534	401	1	theorem	theorem	ADJ
ejpam-534	401	2	4	4	NUM
ejpam-534	401	3	(	(	PUNCT
ejpam-534	401	4	kuhn	kuhn	PROPN
ejpam-534	401	5	-	-	PUNCT
ejpam-534	401	6	tucker	tucker	PROPN
ejpam-534	401	7	type	type	VERB
ejpam-534	401	8	necessary	necessary	ADJ
ejpam-534	401	9	conditions	condition	NOUN
ejpam-534	401	10	)	)	PUNCT
ejpam-534	401	11	.	.	PUNCT
ejpam-534	402	1	let	let	AUX
ejpam-534	402	2	x̄(t	x̄(t	PRON
ejpam-534	402	3	)	)	PUNCT
ejpam-534	402	4	be	be	AUX
ejpam-534	402	5	an	an	DET
ejpam-534	402	6	efficient	efficient	ADJ
ejpam-534	402	7	solution	solution	NOUN
ejpam-534	402	8	of	of	ADP
ejpam-534	402	9	(	(	PUNCT
ejpam-534	402	10	p	p	NOUN
ejpam-534	402	11	)	)	PUNCT
ejpam-534	402	12	and	and	CCONJ
ejpam-534	402	13	let	let	VERB
ejpam-534	402	14	for	for	ADP
ejpam-534	402	15	some	some	DET
ejpam-534	402	16	r	r	NOUN
ejpam-534	402	17	∈	∈	PROPN
ejpam-534	402	18	k	k	NOUN
ejpam-534	402	19	,	,	PUNCT
ejpam-534	402	20	the	the	DET
ejpam-534	402	21	constraints	constraint	NOUN
ejpam-534	402	22	of	of	ADP
ejpam-534	402	23	(	(	PUNCT
ejpam-534	402	24	p̂r	p̂r	NOUN
ejpam-534	402	25	)	)	PUNCT
ejpam-534	402	26	satisfy	satisfy	PROPN
ejpam-534	402	27	slater	slater	PROPN
ejpam-534	402	28	’s	’s	PART
ejpam-534	402	29	or	or	CCONJ
ejpam-534	402	30	robinson	robinson	PROPN
ejpam-534	402	31	condition	condition	NOUN
ejpam-534	402	32	at	at	ADP
ejpam-534	402	33	x̄(t	x̄(t	PROPN
ejpam-534	402	34	)	)	PUNCT
ejpam-534	402	35	.	.	PUNCT
ejpam-534	403	1	then	then	ADV
ejpam-534	403	2	there	there	PRON
ejpam-534	403	3	exist	exist	VERB
ejpam-534	403	4	λ̄	λ̄	ADP
ejpam-534	403	5	∈	∈	PROPN
ejpam-534	403	6	rk	rk	NOUN
ejpam-534	403	7	and	and	CCONJ
ejpam-534	403	8	a	a	DET
ejpam-534	403	9	piecewise	piecewise	NOUN
ejpam-534	403	10	smooth	smooth	ADJ
ejpam-534	403	11	function	function	NOUN
ejpam-534	403	12	ȳ	ȳ	NOUN
ejpam-534	403	13	:	:	PUNCT
ejpam-534	404	1	i	i	PRON
ejpam-534	404	2	→	→	PUNCT
ejpam-534	404	3	rm	rm	PROPN
ejpam-534	404	4	such	such	ADJ
ejpam-534	404	5	that	that	PRON
ejpam-534	404	6	k∑	k∑	VERB
ejpam-534	404	7	i=1	i=1	PROPN
ejpam-534	405	1	λ̄i	λ̄i	PROPN
ejpam-534	405	2	(	(	PUNCT
ejpam-534	405	3	f	f	NOUN
ejpam-534	405	4	i	i	PRON
ejpam-534	405	5	x	x	X
ejpam-534	405	6	(	(	PUNCT
ejpam-534	405	7	t	t	PROPN
ejpam-534	405	8	,	,	PUNCT
ejpam-534	405	9	x̄	x̄	NOUN
ejpam-534	405	10	,	,	PUNCT
ejpam-534	405	11	˙̄x)−	˙̄x)−	PROPN
ejpam-534	406	1	d	d	X
ejpam-534	406	2	f	f	X
ejpam-534	407	1	i	i	PRON
ejpam-534	407	2	ẋ	ẋ	PROPN
ejpam-534	408	1	(	(	PUNCT
ejpam-534	408	2	t	t	PROPN
ejpam-534	408	3	,	,	PUNCT
ejpam-534	408	4	x̄	x̄	NOUN
ejpam-534	408	5	,	,	PUNCT
ejpam-534	408	6	˙̄x))+	˙̄x))+	ADP
ejpam-534	408	7	gx(t	gx(t	PROPN
ejpam-534	408	8	,	,	PUNCT
ejpam-534	408	9	x̄	x̄	NOUN
ejpam-534	408	10	,	,	PUNCT
ejpam-534	408	11	˙̄x	˙̄x	PRON
ejpam-534	408	12	)	)	PUNCT
ejpam-534	408	13	ȳ(t)−	ȳ(t)−	PROPN
ejpam-534	408	14	d(g	d(g	PROPN
ejpam-534	408	15	ẋ(t	ẋ(t	PROPN
ejpam-534	408	16	,	,	PUNCT
ejpam-534	408	17	x̄	x̄	NOUN
ejpam-534	408	18	,	,	PUNCT
ejpam-534	408	19	˙̄x	˙̄x	NOUN
ejpam-534	408	20	)	)	PUNCT
ejpam-534	408	21	ȳ(t	ȳ(t	NOUN
ejpam-534	408	22	)	)	PUNCT
ejpam-534	408	23	)	)	PUNCT
ejpam-534	409	1	=	=	PUNCT
ejpam-534	409	2	0	0	NUM
ejpam-534	409	3	,	,	PUNCT
ejpam-534	409	4	t	t	PROPN
ejpam-534	409	5	∈	∈	PROPN
ejpam-534	410	1	i	i	PRON
ejpam-534	410	2	,	,	PUNCT
ejpam-534	410	3	ȳ(t)t	ȳ(t)t	PROPN
ejpam-534	410	4	g(t	g(t	PROPN
ejpam-534	410	5	,	,	PUNCT
ejpam-534	410	6	x̄	x̄	NOUN
ejpam-534	410	7	,	,	PUNCT
ejpam-534	410	8	˙̄x	˙̄x	PRON
ejpam-534	410	9	)	)	PUNCT
ejpam-534	410	10	=	=	SYM
ejpam-534	410	11	0	0	NUM
ejpam-534	410	12	,	,	PUNCT
ejpam-534	410	13	t	t	PROPN
ejpam-534	410	14	∈	∈	PROPN
ejpam-534	411	1	i	i	PRON
ejpam-534	411	2	,	,	PUNCT
ejpam-534	411	3	λ̄≥	λ̄≥	NOUN
ejpam-534	411	4	0	0	NUM
ejpam-534	411	5	ȳ(t)≧	ȳ(t)≧	NOUN
ejpam-534	411	6	0	0	PROPN
ejpam-534	411	7	,	,	PUNCT
ejpam-534	411	8	t	t	PROPN
ejpam-534	411	9	∈	∈	PROPN
ejpam-534	412	1	i	i	PRON
ejpam-534	412	2	.	.	PUNCT
ejpam-534	413	1	t.	t.	PROPN
ejpam-534	413	2	gulati	gulati	PROPN
ejpam-534	413	3	and	and	CCONJ
ejpam-534	413	4	g.	g.	PROPN
ejpam-534	413	5	mehndiratta	mehndiratta	PROPN
ejpam-534	413	6	/	/	SYM
ejpam-534	413	7	eur	eur	PROPN
ejpam-534	413	8	.	.	PUNCT
ejpam-534	414	1	j.	j.	PROPN
ejpam-534	414	2	pure	pure	PROPN
ejpam-534	414	3	appl	appl	PROPN
ejpam-534	414	4	.	.	PROPN
ejpam-534	414	5	math	math	PROPN
ejpam-534	414	6	,	,	PUNCT
ejpam-534	414	7	3	3	NUM
ejpam-534	414	8	(	(	PUNCT
ejpam-534	414	9	2010	2010	NUM
ejpam-534	414	10	)	)	PUNCT
ejpam-534	414	11	,	,	PUNCT
ejpam-534	414	12	786	786	NUM
ejpam-534	414	13	-	-	SYM
ejpam-534	414	14	805	805	NUM
ejpam-534	414	15	795	795	NUM
ejpam-534	414	16	proof	proof	NOUN
ejpam-534	414	17	.	.	PUNCT
ejpam-534	415	1	since	since	SCONJ
ejpam-534	415	2	x̄(t	x̄(t	PROPN
ejpam-534	415	3	)	)	PUNCT
ejpam-534	415	4	is	be	AUX
ejpam-534	415	5	an	an	DET
ejpam-534	415	6	efficient	efficient	ADJ
ejpam-534	415	7	solution	solution	NOUN
ejpam-534	415	8	of	of	ADP
ejpam-534	415	9	(	(	PUNCT
ejpam-534	415	10	p	p	NOUN
ejpam-534	415	11	)	)	PUNCT
ejpam-534	415	12	,	,	PUNCT
ejpam-534	415	13	by	by	ADP
ejpam-534	415	14	lemma	lemma	PROPN
ejpam-534	415	15	2	2	NUM
ejpam-534	415	16	,	,	PUNCT
ejpam-534	415	17	x̄(t	x̄(t	NUM
ejpam-534	415	18	)	)	PUNCT
ejpam-534	416	1	is	be	AUX
ejpam-534	416	2	an	an	DET
ejpam-534	416	3	optimal	optimal	ADJ
ejpam-534	416	4	solution	solution	NOUN
ejpam-534	416	5	of	of	ADP
ejpam-534	416	6	(	(	PUNCT
ejpam-534	416	7	p̂r	p̂r	NUM
ejpam-534	416	8	)	)	PUNCT
ejpam-534	416	9	for	for	ADP
ejpam-534	416	10	each	each	DET
ejpam-534	416	11	r.	r.	PROPN
ejpam-534	416	12	as	as	ADP
ejpam-534	416	13	for	for	ADP
ejpam-534	416	14	some	some	DET
ejpam-534	416	15	r	r	NOUN
ejpam-534	416	16	,	,	PUNCT
ejpam-534	416	17	the	the	DET
ejpam-534	416	18	constraints	constraint	NOUN
ejpam-534	416	19	of	of	ADP
ejpam-534	416	20	(	(	PUNCT
ejpam-534	416	21	p̂r	p̂r	NOUN
ejpam-534	416	22	)	)	PUNCT
ejpam-534	416	23	satisfy	satisfy	PROPN
ejpam-534	416	24	slater	slater	PROPN
ejpam-534	416	25	’s	’s	PART
ejpam-534	416	26	or	or	CCONJ
ejpam-534	416	27	robinson	robinson	PROPN
ejpam-534	416	28	condition	condition	NOUN
ejpam-534	416	29	at	at	ADP
ejpam-534	416	30	x̄(t	x̄(t	PROPN
ejpam-534	416	31	)	)	PUNCT
ejpam-534	416	32	,	,	PUNCT
ejpam-534	416	33	by	by	ADP
ejpam-534	416	34	the	the	DET
ejpam-534	416	35	kuhn	kuhn	PROPN
ejpam-534	416	36	-	-	PUNCT
ejpam-534	416	37	tucker	tucker	PROPN
ejpam-534	416	38	necessary	necessary	ADJ
ejpam-534	416	39	conditions	condition	NOUN
ejpam-534	416	40	in	in	ADP
ejpam-534	416	41	[	[	X
ejpam-534	416	42	4	4	NUM
ejpam-534	416	43	]	]	PUNCT
ejpam-534	416	44	,	,	PUNCT
ejpam-534	416	45	there	there	PRON
ejpam-534	416	46	exist	exist	VERB
ejpam-534	416	47	0	0	NUM
ejpam-534	416	48	<	<	X
ejpam-534	416	49	λ̄r	λ̄r	PROPN
ejpam-534	416	50	∈r	∈r	NOUN
ejpam-534	416	51	,	,	PUNCT
ejpam-534	417	1	0	0	NUM
ejpam-534	417	2	≦	≦	NUM
ejpam-534	417	3	λ̄i	λ̄i	NOUN
ejpam-534	417	4	∈	∈	NOUN
ejpam-534	417	5	r	r	NOUN
ejpam-534	417	6	,	,	PUNCT
ejpam-534	417	7	i	i	PROPN
ejpam-534	417	8	∈	∈	PROPN
ejpam-534	417	9	kr	kr	PROPN
ejpam-534	417	10	and	and	CCONJ
ejpam-534	417	11	a	a	DET
ejpam-534	417	12	piecewise	piecewise	NOUN
ejpam-534	417	13	smooth	smooth	ADJ
ejpam-534	417	14	function	function	NOUN
ejpam-534	417	15	ȳ(t	ȳ(t	NOUN
ejpam-534	417	16	)	)	PUNCT
ejpam-534	417	17	∈	∈	PROPN
ejpam-534	417	18	rm	rm	NOUN
ejpam-534	418	1	such	such	ADJ
ejpam-534	418	2	that	that	SCONJ
ejpam-534	418	3	λ̄r	λ̄r	PROPN
ejpam-534	418	4	(	(	PUNCT
ejpam-534	418	5	f	f	NOUN
ejpam-534	418	6	r	r	NOUN
ejpam-534	418	7	x	x	X
ejpam-534	418	8	(	(	PUNCT
ejpam-534	418	9	t	t	PROPN
ejpam-534	418	10	,	,	PUNCT
ejpam-534	418	11	x̄	x̄	NOUN
ejpam-534	418	12	,	,	PUNCT
ejpam-534	418	13	˙̄x)−	˙̄x)−	PROPN
ejpam-534	418	14	d	d	X
ejpam-534	418	15	f	f	PROPN
ejpam-534	418	16	r	r	NOUN
ejpam-534	418	17	ẋ	ẋ	PROPN
ejpam-534	418	18	(	(	PUNCT
ejpam-534	418	19	t	t	PROPN
ejpam-534	418	20	,	,	PUNCT
ejpam-534	418	21	x̄	x̄	NOUN
ejpam-534	418	22	,	,	PUNCT
ejpam-534	418	23	˙̄x))+	˙̄x))+	PROPN
ejpam-534	418	24	∑	∑	PROPN
ejpam-534	418	25	i∈kr	i∈kr	PROPN
ejpam-534	418	26	λ̄i	λ̄i	PROPN
ejpam-534	418	27	(	(	PUNCT
ejpam-534	418	28	f	f	NOUN
ejpam-534	418	29	i	i	PRON
ejpam-534	418	30	x	x	X
ejpam-534	418	31	(	(	PUNCT
ejpam-534	418	32	t	t	PROPN
ejpam-534	418	33	,	,	PUNCT
ejpam-534	418	34	x̄	x̄	NOUN
ejpam-534	418	35	,	,	PUNCT
ejpam-534	418	36	˙̄x)−	˙̄x)−	PROPN
ejpam-534	418	37	d	d	X
ejpam-534	418	38	f	f	X
ejpam-534	419	1	i	i	PRON
ejpam-534	419	2	ẋ	ẋ	PROPN
ejpam-534	420	1	(	(	PUNCT
ejpam-534	420	2	t	t	PROPN
ejpam-534	420	3	,	,	PUNCT
ejpam-534	420	4	x̄	x̄	NOUN
ejpam-534	420	5	,	,	PUNCT
ejpam-534	420	6	˙̄x))+	˙̄x))+	ADP
ejpam-534	420	7	gx(t	gx(t	PROPN
ejpam-534	420	8	,	,	PUNCT
ejpam-534	420	9	x̄	x̄	NOUN
ejpam-534	420	10	,	,	PUNCT
ejpam-534	420	11	˙̄x	˙̄x	PRON
ejpam-534	420	12	)	)	PUNCT
ejpam-534	420	13	ȳ(t)−	ȳ(t)−	PROPN
ejpam-534	420	14	d(g	d(g	PROPN
ejpam-534	420	15	ẋ(t	ẋ(t	PROPN
ejpam-534	420	16	,	,	PUNCT
ejpam-534	420	17	x̄	x̄	NOUN
ejpam-534	420	18	,	,	PUNCT
ejpam-534	420	19	˙̄x	˙̄x	NOUN
ejpam-534	420	20	)	)	PUNCT
ejpam-534	420	21	ȳ(t	ȳ(t	NOUN
ejpam-534	420	22	)	)	PUNCT
ejpam-534	420	23	)	)	PUNCT
ejpam-534	421	1	=	=	PUNCT
ejpam-534	421	2	0	0	NUM
ejpam-534	421	3	,	,	PUNCT
ejpam-534	421	4	t	t	PROPN
ejpam-534	421	5	∈	∈	PROPN
ejpam-534	422	1	i	i	PRON
ejpam-534	422	2	,	,	PUNCT
ejpam-534	422	3	ȳ(t)t	ȳ(t)t	PROPN
ejpam-534	422	4	g(t	g(t	PROPN
ejpam-534	422	5	,	,	PUNCT
ejpam-534	422	6	x̄	x̄	NOUN
ejpam-534	422	7	,	,	PUNCT
ejpam-534	422	8	˙̄x	˙̄x	PRON
ejpam-534	422	9	)	)	PUNCT
ejpam-534	422	10	=	=	SYM
ejpam-534	422	11	0	0	NUM
ejpam-534	422	12	,	,	PUNCT
ejpam-534	422	13	t	t	PROPN
ejpam-534	422	14	∈	∈	PROPN
ejpam-534	423	1	i	i	PRON
ejpam-534	423	2	,	,	PUNCT
ejpam-534	423	3	λ̄r	λ̄r	PROPN
ejpam-534	423	4	>	>	X
ejpam-534	423	5	0,0≦	0,0≦	PROPN
ejpam-534	423	6	λ̄i	λ̄i	X
ejpam-534	423	7	∈	∈	NOUN
ejpam-534	423	8	r	r	NOUN
ejpam-534	423	9	,	,	PUNCT
ejpam-534	423	10	i	i	PROPN
ejpam-534	423	11	∈	∈	PROPN
ejpam-534	423	12	kr	kr	PROPN
ejpam-534	423	13	,	,	PUNCT
ejpam-534	423	14	ȳ(t)≧	ȳ(t)≧	NOUN
ejpam-534	423	15	0	0	NUM
ejpam-534	423	16	,	,	PUNCT
ejpam-534	423	17	t	t	PROPN
ejpam-534	423	18	∈	∈	PROPN
ejpam-534	424	1	i	i	PRON
ejpam-534	424	2	.	.	PUNCT
ejpam-534	425	1	or	or	CCONJ
ejpam-534	425	2	equivalently	equivalently	ADV
ejpam-534	425	3	k∑	k∑	VERB
ejpam-534	425	4	i=1	i=1	PROPN
ejpam-534	426	1	λ̄i	λ̄i	PROPN
ejpam-534	426	2	(	(	PUNCT
ejpam-534	426	3	f	f	NOUN
ejpam-534	426	4	i	i	PRON
ejpam-534	426	5	x	x	X
ejpam-534	426	6	(	(	PUNCT
ejpam-534	426	7	t	t	PROPN
ejpam-534	426	8	,	,	PUNCT
ejpam-534	426	9	x̄	x̄	NOUN
ejpam-534	426	10	,	,	PUNCT
ejpam-534	426	11	˙̄x)−	˙̄x)−	PROPN
ejpam-534	427	1	d	d	X
ejpam-534	427	2	f	f	X
ejpam-534	428	1	i	i	PRON
ejpam-534	428	2	ẋ	ẋ	PROPN
ejpam-534	429	1	(	(	PUNCT
ejpam-534	429	2	t	t	PROPN
ejpam-534	429	3	,	,	PUNCT
ejpam-534	429	4	x̄	x̄	NOUN
ejpam-534	429	5	,	,	PUNCT
ejpam-534	429	6	˙̄x))+	˙̄x))+	ADP
ejpam-534	429	7	gx(t	gx(t	PROPN
ejpam-534	429	8	,	,	PUNCT
ejpam-534	429	9	x̄	x̄	NOUN
ejpam-534	429	10	,	,	PUNCT
ejpam-534	429	11	˙̄x	˙̄x	PRON
ejpam-534	429	12	)	)	PUNCT
ejpam-534	429	13	ȳ(t)−	ȳ(t)−	PROPN
ejpam-534	429	14	d(g	d(g	PROPN
ejpam-534	429	15	ẋ(t	ẋ(t	PROPN
ejpam-534	429	16	,	,	PUNCT
ejpam-534	429	17	x̄	x̄	NOUN
ejpam-534	429	18	,	,	PUNCT
ejpam-534	429	19	˙̄x	˙̄x	NOUN
ejpam-534	429	20	)	)	PUNCT
ejpam-534	429	21	ȳ(t	ȳ(t	NOUN
ejpam-534	429	22	)	)	PUNCT
ejpam-534	429	23	)	)	PUNCT
ejpam-534	430	1	=	=	PUNCT
ejpam-534	430	2	0	0	NUM
ejpam-534	430	3	,	,	PUNCT
ejpam-534	430	4	t	t	PROPN
ejpam-534	430	5	∈	∈	PROPN
ejpam-534	431	1	i	i	PRON
ejpam-534	431	2	,	,	PUNCT
ejpam-534	431	3	ȳ(t)t	ȳ(t)t	PROPN
ejpam-534	431	4	g(t	g(t	PROPN
ejpam-534	431	5	,	,	PUNCT
ejpam-534	431	6	x̄	x̄	NOUN
ejpam-534	431	7	,	,	PUNCT
ejpam-534	431	8	˙̄x	˙̄x	PRON
ejpam-534	431	9	)	)	PUNCT
ejpam-534	431	10	=	=	SYM
ejpam-534	431	11	0	0	NUM
ejpam-534	431	12	,	,	PUNCT
ejpam-534	431	13	t	t	PROPN
ejpam-534	431	14	∈	∈	PROPN
ejpam-534	432	1	i	i	PRON
ejpam-534	432	2	,	,	PUNCT
ejpam-534	432	3	λ̄≥	λ̄≥	NOUN
ejpam-534	432	4	0	0	NUM
ejpam-534	432	5	,	,	PUNCT
ejpam-534	432	6	λ̄	λ̄	ADP
ejpam-534	432	7	∈	∈	PROPN
ejpam-534	432	8	rk	rk	NOUN
ejpam-534	432	9	,	,	PUNCT
ejpam-534	432	10	ȳ(t)≧	ȳ(t)≧	NOUN
ejpam-534	432	11	0	0	NUM
ejpam-534	432	12	,	,	PUNCT
ejpam-534	432	13	t	t	PROPN
ejpam-534	432	14	∈	∈	PROPN
ejpam-534	433	1	i	i	PRON
ejpam-534	433	2	.	.	PUNCT
ejpam-534	434	1	in	in	ADP
ejpam-534	434	2	theorem	theorem	NOUN
ejpam-534	434	3	4	4	NUM
ejpam-534	434	4	,	,	PUNCT
ejpam-534	434	5	we	we	PRON
ejpam-534	434	6	assumed	assume	VERB
ejpam-534	434	7	slater	slater	PROPN
ejpam-534	434	8	’s	’s	PART
ejpam-534	434	9	or	or	CCONJ
ejpam-534	434	10	robinson	robinson	VERB
ejpam-534	434	11	condition	condition	NOUN
ejpam-534	434	12	for	for	ADP
ejpam-534	434	13	some	some	PRON
ejpam-534	434	14	(	(	PUNCT
ejpam-534	434	15	p̂r	p̂r	NUM
ejpam-534	434	16	)	)	PUNCT
ejpam-534	434	17	,	,	PUNCT
ejpam-534	434	18	which	which	PRON
ejpam-534	434	19	gave	give	VERB
ejpam-534	434	20	us	we	PRON
ejpam-534	434	21	λ̄	λ̄	DET
ejpam-534	434	22	≥	≥	NOUN
ejpam-534	434	23	0	0	NUM
ejpam-534	434	24	.	.	PUNCT
ejpam-534	435	1	in	in	ADP
ejpam-534	435	2	the	the	DET
ejpam-534	435	3	following	following	NOUN
ejpam-534	435	4	theorem	theorem	NOUN
ejpam-534	435	5	,	,	PUNCT
ejpam-534	435	6	we	we	PRON
ejpam-534	435	7	assume	assume	VERB
ejpam-534	435	8	slater	slater	PROPN
ejpam-534	435	9	’s	’s	PART
ejpam-534	435	10	or	or	CCONJ
ejpam-534	435	11	robinson	robinson	PROPN
ejpam-534	435	12	condition	condition	NOUN
ejpam-534	435	13	for	for	ADP
ejpam-534	435	14	every	every	PRON
ejpam-534	435	15	(	(	PUNCT
ejpam-534	435	16	p̂r	p̂r	NUM
ejpam-534	435	17	)	)	PUNCT
ejpam-534	435	18	and	and	CCONJ
ejpam-534	435	19	obtain	obtain	VERB
ejpam-534	435	20	λ̄	λ̄	PRON
ejpam-534	435	21	>	>	X
ejpam-534	435	22	0	0	X
ejpam-534	435	23	.	.	PUNCT
ejpam-534	435	24	theorem	theorem	ADJ
ejpam-534	435	25	5	5	NUM
ejpam-534	435	26	(	(	PUNCT
ejpam-534	435	27	kuhn	kuhn	PROPN
ejpam-534	435	28	-	-	PUNCT
ejpam-534	435	29	tucker	tucker	PROPN
ejpam-534	435	30	type	type	VERB
ejpam-534	435	31	necessary	necessary	ADJ
ejpam-534	435	32	conditions	condition	NOUN
ejpam-534	435	33	)	)	PUNCT
ejpam-534	435	34	.	.	PUNCT
ejpam-534	436	1	let	let	AUX
ejpam-534	436	2	x̄(t	x̄(t	PRON
ejpam-534	436	3	)	)	PUNCT
ejpam-534	436	4	be	be	AUX
ejpam-534	436	5	an	an	DET
ejpam-534	436	6	efficient	efficient	ADJ
ejpam-534	436	7	solution	solution	NOUN
ejpam-534	436	8	of	of	ADP
ejpam-534	436	9	(	(	PUNCT
ejpam-534	436	10	p	p	NOUN
ejpam-534	436	11	)	)	PUNCT
ejpam-534	436	12	and	and	CCONJ
ejpam-534	436	13	let	let	VERB
ejpam-534	436	14	for	for	ADP
ejpam-534	436	15	each	each	DET
ejpam-534	436	16	r	r	NOUN
ejpam-534	436	17	∈	∈	PROPN
ejpam-534	436	18	k	k	NOUN
ejpam-534	436	19	,	,	PUNCT
ejpam-534	436	20	the	the	DET
ejpam-534	436	21	constraints	constraint	NOUN
ejpam-534	436	22	of	of	ADP
ejpam-534	436	23	(	(	PUNCT
ejpam-534	436	24	p̂r	p̂r	NOUN
ejpam-534	436	25	)	)	PUNCT
ejpam-534	436	26	satisfy	satisfy	PROPN
ejpam-534	436	27	slater	slater	PROPN
ejpam-534	436	28	’s	’s	PART
ejpam-534	436	29	or	or	CCONJ
ejpam-534	436	30	robinson	robinson	PROPN
ejpam-534	436	31	condition	condition	NOUN
ejpam-534	436	32	at	at	ADP
ejpam-534	436	33	x̄(t	x̄(t	PROPN
ejpam-534	436	34	)	)	PUNCT
ejpam-534	436	35	.	.	PUNCT
ejpam-534	437	1	then	then	ADV
ejpam-534	437	2	there	there	PRON
ejpam-534	437	3	exist	exist	VERB
ejpam-534	437	4	λ̄	λ̄	ADP
ejpam-534	437	5	∈	∈	PROPN
ejpam-534	437	6	rk	rk	NOUN
ejpam-534	437	7	and	and	CCONJ
ejpam-534	437	8	a	a	DET
ejpam-534	437	9	piecewise	piecewise	NOUN
ejpam-534	437	10	smooth	smooth	ADJ
ejpam-534	437	11	function	function	NOUN
ejpam-534	437	12	ȳ	ȳ	NOUN
ejpam-534	437	13	:	:	PUNCT
ejpam-534	438	1	i	i	PRON
ejpam-534	438	2	→	→	PUNCT
ejpam-534	438	3	rm	rm	PROPN
ejpam-534	438	4	such	such	ADJ
ejpam-534	438	5	that	that	PRON
ejpam-534	438	6	k∑	k∑	VERB
ejpam-534	438	7	i=1	i=1	PROPN
ejpam-534	439	1	λ̄i	λ̄i	PROPN
ejpam-534	439	2	(	(	PUNCT
ejpam-534	439	3	f	f	NOUN
ejpam-534	439	4	i	i	PRON
ejpam-534	439	5	x	x	X
ejpam-534	439	6	(	(	PUNCT
ejpam-534	439	7	t	t	PROPN
ejpam-534	439	8	,	,	PUNCT
ejpam-534	439	9	x̄	x̄	NOUN
ejpam-534	439	10	,	,	PUNCT
ejpam-534	439	11	˙̄x)−	˙̄x)−	PROPN
ejpam-534	440	1	d	d	X
ejpam-534	440	2	f	f	X
ejpam-534	441	1	i	i	PRON
ejpam-534	441	2	ẋ	ẋ	PROPN
ejpam-534	442	1	(	(	PUNCT
ejpam-534	442	2	t	t	PROPN
ejpam-534	442	3	,	,	PUNCT
ejpam-534	442	4	x̄	x̄	NOUN
ejpam-534	442	5	,	,	PUNCT
ejpam-534	442	6	˙̄x))+	˙̄x))+	ADP
ejpam-534	442	7	gx(t	gx(t	PROPN
ejpam-534	442	8	,	,	PUNCT
ejpam-534	442	9	x̄	x̄	NOUN
ejpam-534	442	10	,	,	PUNCT
ejpam-534	442	11	˙̄x	˙̄x	PRON
ejpam-534	442	12	)	)	PUNCT
ejpam-534	442	13	ȳ(t)−	ȳ(t)−	PROPN
ejpam-534	442	14	d(g	d(g	PROPN
ejpam-534	442	15	ẋ(t	ẋ(t	PROPN
ejpam-534	442	16	,	,	PUNCT
ejpam-534	442	17	x̄	x̄	NOUN
ejpam-534	442	18	,	,	PUNCT
ejpam-534	442	19	˙̄x	˙̄x	NOUN
ejpam-534	442	20	)	)	PUNCT
ejpam-534	442	21	ȳ(t	ȳ(t	NOUN
ejpam-534	442	22	)	)	PUNCT
ejpam-534	442	23	)	)	PUNCT
ejpam-534	443	1	=	=	PUNCT
ejpam-534	443	2	0	0	NUM
ejpam-534	443	3	,	,	PUNCT
ejpam-534	443	4	t	t	PROPN
ejpam-534	443	5	∈	∈	PROPN
ejpam-534	444	1	i	i	PRON
ejpam-534	444	2	,	,	PUNCT
ejpam-534	444	3	ȳ(t)t	ȳ(t)t	PROPN
ejpam-534	444	4	g(t	g(t	PROPN
ejpam-534	444	5	,	,	PUNCT
ejpam-534	444	6	x̄	x̄	NOUN
ejpam-534	444	7	,	,	PUNCT
ejpam-534	444	8	˙̄x	˙̄x	PRON
ejpam-534	444	9	)	)	PUNCT
ejpam-534	444	10	=	=	SYM
ejpam-534	444	11	0	0	NUM
ejpam-534	444	12	,	,	PUNCT
ejpam-534	444	13	t	t	PROPN
ejpam-534	444	14	∈	∈	PROPN
ejpam-534	445	1	i	i	PRON
ejpam-534	445	2	,	,	PUNCT
ejpam-534	445	3	λ̄	λ̄	X
ejpam-534	445	4	>	>	X
ejpam-534	445	5	0	0	NUM
ejpam-534	445	6	,	,	PUNCT
ejpam-534	445	7	k∑	k∑	VERB
ejpam-534	445	8	i=1	i=1	PROPN
ejpam-534	446	1	λ̄i	λ̄i	X
ejpam-534	446	2	=	=	SYM
ejpam-534	446	3	1	1	NUM
ejpam-534	446	4	,	,	PUNCT
ejpam-534	446	5	ȳ(t)≧	ȳ(t)≧	NOUN
ejpam-534	446	6	0	0	NUM
ejpam-534	446	7	,	,	PUNCT
ejpam-534	446	8	t	t	PROPN
ejpam-534	446	9	∈	∈	PROPN
ejpam-534	447	1	i	i	PRON
ejpam-534	447	2	.	.	PUNCT
ejpam-534	448	1	proof	proof	NOUN
ejpam-534	448	2	.	.	PUNCT
ejpam-534	449	1	since	since	SCONJ
ejpam-534	449	2	x̄(t	x̄(t	PROPN
ejpam-534	449	3	)	)	PUNCT
ejpam-534	449	4	is	be	AUX
ejpam-534	449	5	an	an	DET
ejpam-534	449	6	efficient	efficient	ADJ
ejpam-534	449	7	solution	solution	NOUN
ejpam-534	449	8	of	of	ADP
ejpam-534	449	9	(	(	PUNCT
ejpam-534	449	10	p	p	NOUN
ejpam-534	449	11	)	)	PUNCT
ejpam-534	449	12	,	,	PUNCT
ejpam-534	449	13	by	by	ADP
ejpam-534	449	14	lemma	lemma	PROPN
ejpam-534	449	15	2	2	NUM
ejpam-534	449	16	,	,	PUNCT
ejpam-534	449	17	x̄(t	x̄(t	NUM
ejpam-534	449	18	)	)	PUNCT
ejpam-534	450	1	is	be	AUX
ejpam-534	450	2	an	an	DET
ejpam-534	450	3	optimal	optimal	ADJ
ejpam-534	450	4	solution	solution	NOUN
ejpam-534	450	5	of	of	ADP
ejpam-534	450	6	(	(	PUNCT
ejpam-534	450	7	p̂r	p̂r	NUM
ejpam-534	450	8	)	)	PUNCT
ejpam-534	450	9	for	for	ADP
ejpam-534	450	10	each	each	DET
ejpam-534	450	11	r	r	NOUN
ejpam-534	450	12	∈	∈	PROPN
ejpam-534	450	13	k	k	X
ejpam-534	450	14	.	.	PUNCT
ejpam-534	451	1	as	as	ADP
ejpam-534	451	2	for	for	ADP
ejpam-534	451	3	each	each	DET
ejpam-534	451	4	r	r	NOUN
ejpam-534	451	5	,	,	PUNCT
ejpam-534	451	6	the	the	DET
ejpam-534	451	7	constraints	constraint	NOUN
ejpam-534	451	8	of	of	ADP
ejpam-534	451	9	(	(	PUNCT
ejpam-534	451	10	p̂r	p̂r	NOUN
ejpam-534	451	11	)	)	PUNCT
ejpam-534	451	12	satisfy	satisfy	PROPN
ejpam-534	451	13	slater	slater	PROPN
ejpam-534	451	14	’s	’s	PART
ejpam-534	451	15	or	or	CCONJ
ejpam-534	451	16	robinson	robinson	PROPN
ejpam-534	451	17	condition	condition	NOUN
ejpam-534	451	18	at	at	ADP
ejpam-534	451	19	x̄(t	x̄(t	PROPN
ejpam-534	451	20	)	)	PUNCT
ejpam-534	451	21	,	,	PUNCT
ejpam-534	451	22	by	by	ADP
ejpam-534	451	23	the	the	DET
ejpam-534	451	24	kuhn	kuhn	PROPN
ejpam-534	451	25	-	-	PUNCT
ejpam-534	451	26	tucker	tucker	PROPN
ejpam-534	451	27	necessary	necessary	ADJ
ejpam-534	451	28	conditions	condition	NOUN
ejpam-534	451	29	in	in	ADP
ejpam-534	451	30	[	[	X
ejpam-534	451	31	4	4	NUM
ejpam-534	451	32	]	]	PUNCT
ejpam-534	451	33	,	,	PUNCT
ejpam-534	451	34	for	for	ADP
ejpam-534	451	35	each	each	DET
ejpam-534	451	36	r	r	NOUN
ejpam-534	451	37	∈	∈	PROPN
ejpam-534	451	38	k	k	NOUN
ejpam-534	451	39	,	,	PUNCT
ejpam-534	451	40	there	there	PRON
ejpam-534	451	41	exist	exist	VERB
ejpam-534	451	42	v̄	v̄	NOUN
ejpam-534	452	1	i	i	PRON
ejpam-534	452	2	r	r	NOUN
ejpam-534	452	3	∈	∈	NOUN
ejpam-534	452	4	r	r	NOUN
ejpam-534	452	5	(	(	PUNCT
ejpam-534	452	6	i	i	PROPN
ejpam-534	452	7	∈	∈	PROPN
ejpam-534	452	8	kr	kr	PROPN
ejpam-534	452	9	)	)	PUNCT
ejpam-534	452	10	and	and	CCONJ
ejpam-534	452	11	piecewise	piecewise	VERB
ejpam-534	452	12	smooth	smooth	ADJ
ejpam-534	452	13	functions	function	NOUN
ejpam-534	452	14	µ̄	µ̄	PROPN
ejpam-534	452	15	j	j	PROPN
ejpam-534	452	16	r(t	r(t	PROPN
ejpam-534	452	17	)	)	PUNCT
ejpam-534	452	18	∈	∈	PROPN
ejpam-534	452	19	r	r	NOUN
ejpam-534	452	20	(	(	PUNCT
ejpam-534	452	21	j	j	PROPN
ejpam-534	452	22	∈	∈	PROPN
ejpam-534	452	23	m	m	PROPN
ejpam-534	452	24	)	)	PUNCT
ejpam-534	452	25	such	such	ADJ
ejpam-534	452	26	that	that	SCONJ
ejpam-534	452	27	t.	t.	PROPN
ejpam-534	452	28	gulati	gulati	PROPN
ejpam-534	452	29	and	and	CCONJ
ejpam-534	452	30	g.	g.	PROPN
ejpam-534	452	31	mehndiratta	mehndiratta	PROPN
ejpam-534	452	32	/	/	SYM
ejpam-534	452	33	eur	eur	PROPN
ejpam-534	452	34	.	.	PUNCT
ejpam-534	453	1	j.	j.	PROPN
ejpam-534	453	2	pure	pure	PROPN
ejpam-534	453	3	appl	appl	PROPN
ejpam-534	453	4	.	.	PROPN
ejpam-534	453	5	math	math	PROPN
ejpam-534	453	6	,	,	PUNCT
ejpam-534	453	7	3	3	NUM
ejpam-534	453	8	(	(	PUNCT
ejpam-534	453	9	2010	2010	NUM
ejpam-534	453	10	)	)	PUNCT
ejpam-534	453	11	,	,	PUNCT
ejpam-534	453	12	786	786	NUM
ejpam-534	453	13	-	-	SYM
ejpam-534	453	14	805	805	NUM
ejpam-534	453	15	796	796	NUM
ejpam-534	453	16	f	f	NOUN
ejpam-534	453	17	r	r	NOUN
ejpam-534	453	18	x	x	X
ejpam-534	453	19	(	(	PUNCT
ejpam-534	453	20	t	t	PROPN
ejpam-534	453	21	,	,	PUNCT
ejpam-534	453	22	x̄	x̄	NOUN
ejpam-534	453	23	,	,	PUNCT
ejpam-534	453	24	˙̄x)−	˙̄x)−	PROPN
ejpam-534	454	1	d	d	X
ejpam-534	454	2	f	f	PROPN
ejpam-534	454	3	r	r	NOUN
ejpam-534	454	4	ẋ	ẋ	PROPN
ejpam-534	454	5	(	(	PUNCT
ejpam-534	454	6	t	t	PROPN
ejpam-534	454	7	,	,	PUNCT
ejpam-534	454	8	x̄	x̄	NOUN
ejpam-534	454	9	,	,	PUNCT
ejpam-534	454	10	˙̄x)+	˙̄x)+	NOUN
ejpam-534	454	11	∑	∑	PUNCT
ejpam-534	454	12	i∈kr	i∈kr	NOUN
ejpam-534	454	13	v̄	v̄	NOUN
ejpam-534	455	1	i	i	PRON
ejpam-534	455	2	r	r	PROPN
ejpam-534	455	3	(	(	PUNCT
ejpam-534	455	4	f	f	NOUN
ejpam-534	455	5	i	i	PRON
ejpam-534	455	6	x	x	X
ejpam-534	455	7	(	(	PUNCT
ejpam-534	455	8	t	t	PROPN
ejpam-534	455	9	,	,	PUNCT
ejpam-534	455	10	x̄	x̄	NOUN
ejpam-534	455	11	,	,	PUNCT
ejpam-534	455	12	˙̄x)−	˙̄x)−	PROPN
ejpam-534	456	1	d	d	X
ejpam-534	456	2	f	f	X
ejpam-534	457	1	i	i	PRON
ejpam-534	457	2	ẋ	ẋ	PROPN
ejpam-534	458	1	(	(	PUNCT
ejpam-534	458	2	t	t	PROPN
ejpam-534	458	3	,	,	PUNCT
ejpam-534	458	4	x̄	x̄	NOUN
ejpam-534	458	5	,	,	PUNCT
ejpam-534	458	6	˙̄x))+	˙̄x))+	PROPN
ejpam-534	458	7	m∑	m∑	ADV
ejpam-534	459	1	j=1	j=1	PROPN
ejpam-534	460	1	(	(	PUNCT
ejpam-534	460	2	g	g	PROPN
ejpam-534	460	3	j	j	PROPN
ejpam-534	460	4	x(t	x(t	PROPN
ejpam-534	460	5	,	,	PUNCT
ejpam-534	460	6	x̄	x̄	NOUN
ejpam-534	460	7	,	,	PUNCT
ejpam-534	460	8	˙̄x)µ̄	˙̄x)µ̄	PROPN
ejpam-534	460	9	j	j	PROPN
ejpam-534	460	10	r(t)−	r(t)−	PROPN
ejpam-534	460	11	d(g	d(g	PROPN
ejpam-534	461	1	j	j	PROPN
ejpam-534	461	2	ẋ	ẋ	PROPN
ejpam-534	461	3	(	(	PUNCT
ejpam-534	461	4	t	t	PROPN
ejpam-534	461	5	,	,	PUNCT
ejpam-534	461	6	x̄	x̄	NOUN
ejpam-534	461	7	,	,	PUNCT
ejpam-534	461	8	˙̄x)µ̄	˙̄x)µ̄	PROPN
ejpam-534	461	9	j	j	PROPN
ejpam-534	461	10	r(t	r(t	NOUN
ejpam-534	461	11	)	)	PUNCT
ejpam-534	461	12	)	)	PUNCT
ejpam-534	461	13	)	)	PUNCT
ejpam-534	462	1	=	=	PUNCT
ejpam-534	462	2	0	0	NUM
ejpam-534	462	3	,	,	PUNCT
ejpam-534	462	4	t	t	PROPN
ejpam-534	462	5	∈	∈	PROPN
ejpam-534	463	1	i	i	PRON
ejpam-534	463	2	,	,	PUNCT
ejpam-534	463	3	m∑	m∑	SCONJ
ejpam-534	463	4	j=1	j=1	PROPN
ejpam-534	463	5	µ̄	µ̄	PROPN
ejpam-534	463	6	j	j	PROPN
ejpam-534	463	7	r(t)g	r(t)g	PROPN
ejpam-534	463	8	j(t	j(t	PROPN
ejpam-534	463	9	,	,	PUNCT
ejpam-534	463	10	x̄	x̄	PRON
ejpam-534	463	11	,	,	PUNCT
ejpam-534	463	12	˙̄x	˙̄x	PRON
ejpam-534	463	13	)	)	PUNCT
ejpam-534	463	14	=	=	SYM
ejpam-534	463	15	0	0	NUM
ejpam-534	463	16	,	,	PUNCT
ejpam-534	463	17	t	t	PROPN
ejpam-534	463	18	∈	∈	PROPN
ejpam-534	464	1	i	i	PRON
ejpam-534	464	2	,	,	PUNCT
ejpam-534	464	3	v̄	v̄	NOUN
ejpam-534	465	1	i	i	PRON
ejpam-534	465	2	r	r	VERB
ejpam-534	465	3	≧	≧	NOUN
ejpam-534	465	4	0	0	NUM
ejpam-534	465	5	,	,	PUNCT
ejpam-534	465	6	i	i	PRON
ejpam-534	465	7	∈	∈	PROPN
ejpam-534	465	8	kr	kr	PROPN
ejpam-534	465	9	,	,	PUNCT
ejpam-534	465	10	ȳ(t)≧	ȳ(t)≧	NOUN
ejpam-534	465	11	0	0	NUM
ejpam-534	465	12	,	,	PUNCT
ejpam-534	465	13	t	t	PROPN
ejpam-534	465	14	∈	∈	PROPN
ejpam-534	466	1	i	i	PRON
ejpam-534	466	2	.	.	PUNCT
ejpam-534	467	1	summing	sum	VERB
ejpam-534	467	2	over	over	ADP
ejpam-534	467	3	r	r	NOUN
ejpam-534	467	4	∈	∈	PROPN
ejpam-534	467	5	k	k	NOUN
ejpam-534	467	6	,	,	PUNCT
ejpam-534	467	7	we	we	PRON
ejpam-534	467	8	get	get	VERB
ejpam-534	467	9	k∑	k∑	VERB
ejpam-534	467	10	i=1	i=1	X
ejpam-534	468	1	(	(	PUNCT
ejpam-534	468	2	v̄	v̄	NOUN
ejpam-534	468	3	i	i	NOUN
ejpam-534	468	4	1	1	NUM
ejpam-534	468	5	+	+	NUM
ejpam-534	468	6	v̄	v̄	NOUN
ejpam-534	468	7	i	i	NOUN
ejpam-534	468	8	2	2	NUM
ejpam-534	468	9	+	+	CCONJ
ejpam-534	468	10	...	...	PUNCT
ejpam-534	469	1	+	+	CCONJ
ejpam-534	469	2	v̄	v̄	NOUN
ejpam-534	470	1	i	i	NOUN
ejpam-534	470	2	k	k	PROPN
ejpam-534	470	3	)	)	PUNCT
ejpam-534	471	1	(	(	PUNCT
ejpam-534	471	2	f	f	X
ejpam-534	471	3	i	i	NOUN
ejpam-534	471	4	x	x	X
ejpam-534	471	5	(	(	PUNCT
ejpam-534	471	6	t	t	PROPN
ejpam-534	471	7	,	,	PUNCT
ejpam-534	471	8	x̄	x̄	NOUN
ejpam-534	471	9	,	,	PUNCT
ejpam-534	471	10	˙̄x)−	˙̄x)−	PROPN
ejpam-534	472	1	d	d	X
ejpam-534	472	2	f	f	X
ejpam-534	473	1	i	i	PRON
ejpam-534	473	2	ẋ	ẋ	PROPN
ejpam-534	474	1	(	(	PUNCT
ejpam-534	474	2	t	t	PROPN
ejpam-534	474	3	,	,	PUNCT
ejpam-534	474	4	x̄	x̄	NOUN
ejpam-534	474	5	,	,	PUNCT
ejpam-534	474	6	˙̄x))+	˙̄x))+	PROPN
ejpam-534	474	7	m∑	m∑	ADV
ejpam-534	475	1	j=1	j=1	PROPN
ejpam-534	476	1	(	(	PUNCT
ejpam-534	476	2	g	g	PROPN
ejpam-534	476	3	j	j	PROPN
ejpam-534	476	4	x(t	x(t	PROPN
ejpam-534	476	5	,	,	PUNCT
ejpam-534	476	6	x̄	x̄	NOUN
ejpam-534	476	7	,	,	PUNCT
ejpam-534	476	8	˙̄x)(µ̄	˙̄x)(µ̄	PROPN
ejpam-534	476	9	j	j	PROPN
ejpam-534	476	10	1(t	1(t	NUM
ejpam-534	476	11	)	)	PUNCT
ejpam-534	477	1	+	+	CCONJ
ejpam-534	477	2	µ̄	µ̄	PROPN
ejpam-534	477	3	j	j	PROPN
ejpam-534	477	4	2(t	2(t	NUM
ejpam-534	477	5	)	)	PUNCT
ejpam-534	477	6	+	+	CCONJ
ejpam-534	477	7	.	.	PUNCT
ejpam-534	477	8	.	.	PUNCT
ejpam-534	478	1	.+	.+	NOUN
ejpam-534	478	2	µ̄	µ̄	PROPN
ejpam-534	478	3	j	j	PROPN
ejpam-534	478	4	k	k	PROPN
ejpam-534	478	5	(	(	PUNCT
ejpam-534	478	6	t))−	t))−	NOUN
ejpam-534	478	7	d(g	d(g	PROPN
ejpam-534	478	8	j	j	PROPN
ejpam-534	478	9	ẋ	ẋ	PROPN
ejpam-534	478	10	(	(	PUNCT
ejpam-534	478	11	t	t	PROPN
ejpam-534	478	12	,	,	PUNCT
ejpam-534	478	13	x̄	x̄	PRON
ejpam-534	478	14	,	,	PUNCT
ejpam-534	478	15	˙̄x)(µ̄	˙̄x)(µ̄	PROPN
ejpam-534	478	16	j	j	PROPN
ejpam-534	478	17	1(t	1(t	NUM
ejpam-534	478	18	)	)	PUNCT
ejpam-534	479	1	+	+	CCONJ
ejpam-534	479	2	µ̄	µ̄	PROPN
ejpam-534	479	3	j	j	PROPN
ejpam-534	479	4	2(t	2(t	NUM
ejpam-534	479	5	)	)	PUNCT
ejpam-534	479	6	+	+	CCONJ
ejpam-534	479	7	.	.	PUNCT
ejpam-534	479	8	.	.	PUNCT
ejpam-534	480	1	.+	.+	NOUN
ejpam-534	480	2	µ̄	µ̄	PROPN
ejpam-534	480	3	j	j	PROPN
ejpam-534	480	4	k	k	PROPN
ejpam-534	480	5	(	(	PUNCT
ejpam-534	480	6	t	t	PROPN
ejpam-534	480	7	)	)	PUNCT
ejpam-534	480	8	)	)	PUNCT
ejpam-534	480	9	)	)	PUNCT
ejpam-534	480	10	)	)	PUNCT
ejpam-534	481	1	=	=	PUNCT
ejpam-534	481	2	0	0	NUM
ejpam-534	481	3	,	,	PUNCT
ejpam-534	481	4	t	t	PROPN
ejpam-534	481	5	∈	∈	PROPN
ejpam-534	482	1	i	i	PRON
ejpam-534	482	2	,	,	PUNCT
ejpam-534	482	3	m∑	m∑	CCONJ
ejpam-534	482	4	j=1	j=1	PROPN
ejpam-534	482	5	(	(	PUNCT
ejpam-534	482	6	µ̄	µ̄	PROPN
ejpam-534	482	7	j	j	PROPN
ejpam-534	482	8	1	1	NUM
ejpam-534	482	9	(	(	PUNCT
ejpam-534	482	10	t	t	PROPN
ejpam-534	482	11	)	)	PUNCT
ejpam-534	482	12	+	+	CCONJ
ejpam-534	482	13	µ̄	µ̄	PROPN
ejpam-534	482	14	j	j	PROPN
ejpam-534	482	15	2	2	NUM
ejpam-534	482	16	(	(	PUNCT
ejpam-534	482	17	t	t	PROPN
ejpam-534	482	18	)	)	PUNCT
ejpam-534	482	19	+	+	CCONJ
ejpam-534	482	20	.	.	PUNCT
ejpam-534	482	21	.	.	PUNCT
ejpam-534	483	1	.+	.+	NOUN
ejpam-534	483	2	µ̄	µ̄	PROPN
ejpam-534	483	3	j	j	PROPN
ejpam-534	483	4	k	k	PROPN
ejpam-534	483	5	(	(	PUNCT
ejpam-534	483	6	t))g	t))g	PROPN
ejpam-534	483	7	j(t	j(t	PROPN
ejpam-534	483	8	,	,	PUNCT
ejpam-534	483	9	x̄	x̄	NOUN
ejpam-534	483	10	,	,	PUNCT
ejpam-534	483	11	˙̄x	˙̄x	PRON
ejpam-534	483	12	)	)	PUNCT
ejpam-534	483	13	=	=	SYM
ejpam-534	483	14	0	0	NUM
ejpam-534	483	15	,	,	PUNCT
ejpam-534	483	16	t	t	PROPN
ejpam-534	483	17	∈	∈	PROPN
ejpam-534	484	1	i	i	PRON
ejpam-534	484	2	,	,	PUNCT
ejpam-534	484	3	where	where	SCONJ
ejpam-534	484	4	v̄	v̄	NOUN
ejpam-534	485	1	i	i	PRON
ejpam-534	485	2	i	i	VERB
ejpam-534	485	3	=	=	NOUN
ejpam-534	485	4	1	1	NUM
ejpam-534	485	5	for	for	ADP
ejpam-534	485	6	each	each	DET
ejpam-534	485	7	i	i	PRON
ejpam-534	485	8	∈	∈	PROPN
ejpam-534	485	9	k	k	X
ejpam-534	485	10	.	.	PUNCT
ejpam-534	486	1	equivalently	equivalently	ADV
ejpam-534	486	2	,	,	PUNCT
ejpam-534	486	3	k∑	k∑	VERB
ejpam-534	486	4	i=1	i=1	PROPN
ejpam-534	487	1	v̄	v̄	PROPN
ejpam-534	488	1	i	i	PRON
ejpam-534	488	2	(	(	PUNCT
ejpam-534	488	3	f	f	PROPN
ejpam-534	488	4	i	i	PRON
ejpam-534	488	5	x	x	X
ejpam-534	488	6	(	(	PUNCT
ejpam-534	488	7	t	t	PROPN
ejpam-534	488	8	,	,	PUNCT
ejpam-534	488	9	x̄	x̄	PROPN
ejpam-534	488	10	,	,	PUNCT
ejpam-534	488	11	˙̄x)−d	˙̄x)−d	PROPN
ejpam-534	488	12	f	f	PROPN
ejpam-534	488	13	i	i	PROPN
ejpam-534	488	14	ẋ(t	ẋ(t	PROPN
ejpam-534	488	15	,	,	PUNCT
ejpam-534	488	16	x̄	x̄	NOUN
ejpam-534	488	17	,	,	PUNCT
ejpam-534	488	18	˙̄x))+	˙̄x))+	PROPN
ejpam-534	488	19	m∑	m∑	ADV
ejpam-534	488	20	j=1	j=1	PROPN
ejpam-534	488	21	(	(	PUNCT
ejpam-534	488	22	g	g	PROPN
ejpam-534	488	23	j	j	PROPN
ejpam-534	488	24	x(t	x(t	PROPN
ejpam-534	488	25	,	,	PUNCT
ejpam-534	488	26	x̄	x̄	NOUN
ejpam-534	488	27	,	,	PUNCT
ejpam-534	488	28	˙̄x)µ̄	˙̄x)µ̄	PROPN
ejpam-534	488	29	j(t)−d(g	j(t)−d(g	PROPN
ejpam-534	489	1	j	j	PROPN
ejpam-534	489	2	ẋ	ẋ	PROPN
ejpam-534	489	3	(	(	PUNCT
ejpam-534	489	4	t	t	PROPN
ejpam-534	489	5	,	,	PUNCT
ejpam-534	489	6	x̄	x̄	NOUN
ejpam-534	489	7	,	,	PUNCT
ejpam-534	489	8	˙̄x)µ̄	˙̄x)µ̄	PROPN
ejpam-534	489	9	j(t	j(t	PROPN
ejpam-534	489	10	)	)	PUNCT
ejpam-534	489	11	)	)	PUNCT
ejpam-534	489	12	)	)	PUNCT
ejpam-534	490	1	=	=	PUNCT
ejpam-534	490	2	0	0	NUM
ejpam-534	490	3	,	,	PUNCT
ejpam-534	490	4	t	t	PROPN
ejpam-534	490	5	∈	∈	PROPN
ejpam-534	491	1	i	i	PRON
ejpam-534	491	2	,	,	PUNCT
ejpam-534	491	3	(	(	PUNCT
ejpam-534	491	4	31	31	NUM
ejpam-534	491	5	)	)	PUNCT
ejpam-534	491	6	m∑	m∑	VERB
ejpam-534	491	7	j=1	j=1	PROPN
ejpam-534	491	8	µ̄	µ̄	PROPN
ejpam-534	491	9	j(t)g	j(t)g	PROPN
ejpam-534	491	10	j(t	j(t	PROPN
ejpam-534	491	11	,	,	PUNCT
ejpam-534	491	12	x̄	x̄	NOUN
ejpam-534	491	13	,	,	PUNCT
ejpam-534	491	14	˙̄x	˙̄x	PRON
ejpam-534	491	15	)	)	PUNCT
ejpam-534	492	1	=	=	SYM
ejpam-534	492	2	0	0	NUM
ejpam-534	492	3	,	,	PUNCT
ejpam-534	492	4	t	t	PROPN
ejpam-534	492	5	∈	∈	PROPN
ejpam-534	493	1	i	i	PRON
ejpam-534	493	2	,	,	PUNCT
ejpam-534	493	3	(	(	PUNCT
ejpam-534	493	4	32	32	NUM
ejpam-534	493	5	)	)	PUNCT
ejpam-534	493	6	where	where	SCONJ
ejpam-534	493	7	v̄	v̄	NOUN
ejpam-534	494	1	i	i	NOUN
ejpam-534	494	2	=	=	NOUN
ejpam-534	494	3	1	1	NUM
ejpam-534	494	4	+	+	CCONJ
ejpam-534	494	5	∑	∑	ADV
ejpam-534	494	6	r∈ki	r∈ki	VERB
ejpam-534	494	7	v̄	v̄	NOUN
ejpam-534	495	1	i	i	PRON
ejpam-534	495	2	r	r	VERB
ejpam-534	495	3	>	>	X
ejpam-534	495	4	0,i	0,i	NUM
ejpam-534	495	5	∈	∈	PROPN
ejpam-534	495	6	k	k	NOUN
ejpam-534	495	7	,	,	PUNCT
ejpam-534	495	8	and	and	CCONJ
ejpam-534	495	9	µ̄	µ̄	PROPN
ejpam-534	495	10	j(t	j(t	PROPN
ejpam-534	495	11	)	)	PUNCT
ejpam-534	496	1	=	=	SYM
ejpam-534	496	2	k∑	k∑	PUNCT
ejpam-534	497	1	r=1	r=1	NOUN
ejpam-534	497	2	µ̄	µ̄	PROPN
ejpam-534	497	3	j	j	PROPN
ejpam-534	497	4	r(t	r(t	PROPN
ejpam-534	497	5	)	)	PUNCT
ejpam-534	497	6	≧	≧	X
ejpam-534	497	7	0	0	NUM
ejpam-534	497	8	,	,	PUNCT
ejpam-534	497	9	t	t	PROPN
ejpam-534	497	10	∈	∈	PROPN
ejpam-534	498	1	i	i	PRON
ejpam-534	498	2	,	,	PUNCT
ejpam-534	498	3	j	j	PROPN
ejpam-534	498	4	∈	∈	PROPN
ejpam-534	498	5	m	m	VERB
ejpam-534	498	6	.	.	PUNCT
ejpam-534	499	1	dividing	divide	VERB
ejpam-534	499	2	(	(	PUNCT
ejpam-534	499	3	31	31	NUM
ejpam-534	499	4	)	)	PUNCT
ejpam-534	499	5	and	and	CCONJ
ejpam-534	499	6	(	(	PUNCT
ejpam-534	499	7	32	32	NUM
ejpam-534	499	8	)	)	PUNCT
ejpam-534	499	9	by	by	ADP
ejpam-534	499	10	k∑	k∑	PROPN
ejpam-534	499	11	i=1	i=1	PROPN
ejpam-534	500	1	v̄	v̄	NOUN
ejpam-534	501	1	i	i	PRON
ejpam-534	501	2	and	and	CCONJ
ejpam-534	501	3	setting	set	VERB
ejpam-534	501	4	λ̄i	λ̄i	NOUN
ejpam-534	501	5	=	=	SYM
ejpam-534	501	6	v̄	v̄	NOUN
ejpam-534	502	1	i	i	PRON
ejpam-534	502	2	k∑	k∑	VERB
ejpam-534	502	3	i=1	i=1	PRON
ejpam-534	503	1	v̄	v̄	NOUN
ejpam-534	504	1	i	i	PRON
ejpam-534	504	2	,	,	PUNCT
ejpam-534	504	3	i	i	PROPN
ejpam-534	504	4	∈	∈	PROPN
ejpam-534	504	5	k	k	PROPN
ejpam-534	504	6	,	,	PUNCT
ejpam-534	504	7	ȳ	ȳ	PROPN
ejpam-534	504	8	j(t	j(t	PROPN
ejpam-534	504	9	)	)	PUNCT
ejpam-534	504	10	=	=	SYM
ejpam-534	504	11	µ̄	µ̄	PROPN
ejpam-534	504	12	j(t	j(t	PROPN
ejpam-534	504	13	)	)	PUNCT
ejpam-534	504	14	k∑	k∑	VERB
ejpam-534	505	1	i=1	i=1	PRON
ejpam-534	506	1	v̄	v̄	NOUN
ejpam-534	507	1	i	i	PRON
ejpam-534	507	2	,	,	PUNCT
ejpam-534	507	3	j	j	PROPN
ejpam-534	507	4	∈	∈	PROPN
ejpam-534	507	5	m	m	VERB
ejpam-534	507	6	,	,	PUNCT
ejpam-534	507	7	we	we	PRON
ejpam-534	507	8	get	get	AUX
ejpam-534	507	9	k∑	k∑	VERB
ejpam-534	507	10	i=1	i=1	PROPN
ejpam-534	508	1	λ̄i	λ̄i	PROPN
ejpam-534	508	2	(	(	PUNCT
ejpam-534	508	3	f	f	NOUN
ejpam-534	508	4	i	i	PRON
ejpam-534	508	5	x	x	X
ejpam-534	508	6	(	(	PUNCT
ejpam-534	508	7	t	t	PROPN
ejpam-534	508	8	,	,	PUNCT
ejpam-534	508	9	x̄	x̄	NOUN
ejpam-534	508	10	,	,	PUNCT
ejpam-534	508	11	˙̄x)−	˙̄x)−	PROPN
ejpam-534	509	1	d	d	X
ejpam-534	509	2	f	f	X
ejpam-534	510	1	i	i	PRON
ejpam-534	510	2	ẋ	ẋ	PROPN
ejpam-534	511	1	(	(	PUNCT
ejpam-534	511	2	t	t	PROPN
ejpam-534	511	3	,	,	PUNCT
ejpam-534	511	4	x̄	x̄	NOUN
ejpam-534	511	5	,	,	PUNCT
ejpam-534	511	6	˙̄x	˙̄x	NOUN
ejpam-534	511	7	)	)	PUNCT
ejpam-534	511	8	)	)	PUNCT
ejpam-534	512	1	+	+	CCONJ
ejpam-534	512	2	m∑	m∑	ADV
ejpam-534	512	3	j=1	j=1	NOUN
ejpam-534	512	4	(	(	PUNCT
ejpam-534	512	5	g	g	PROPN
ejpam-534	512	6	j	j	PROPN
ejpam-534	512	7	x(t	x(t	PROPN
ejpam-534	512	8	,	,	PUNCT
ejpam-534	512	9	x̄	x̄	NOUN
ejpam-534	512	10	,	,	PUNCT
ejpam-534	512	11	˙̄x	˙̄x	PRON
ejpam-534	512	12	)	)	PUNCT
ejpam-534	512	13	ȳ	ȳ	PROPN
ejpam-534	513	1	j(t)−	j(t)−	PROPN
ejpam-534	513	2	d(g	d(g	PROPN
ejpam-534	514	1	j	j	PROPN
ejpam-534	514	2	ẋ	ẋ	PROPN
ejpam-534	514	3	(	(	PUNCT
ejpam-534	514	4	t	t	PROPN
ejpam-534	514	5	,	,	PUNCT
ejpam-534	514	6	x̄	x̄	NOUN
ejpam-534	514	7	,	,	PUNCT
ejpam-534	514	8	˙̄x	˙̄x	PRON
ejpam-534	514	9	)	)	PUNCT
ejpam-534	514	10	ȳ	ȳ	PROPN
ejpam-534	514	11	j(t	j(t	PROPN
ejpam-534	514	12	)	)	PUNCT
ejpam-534	514	13	)	)	PUNCT
ejpam-534	514	14	)	)	PUNCT
ejpam-534	515	1	=	=	PUNCT
ejpam-534	515	2	0	0	NUM
ejpam-534	515	3	,	,	PUNCT
ejpam-534	515	4	t	t	PROPN
ejpam-534	515	5	∈	∈	PROPN
ejpam-534	516	1	i	i	PRON
ejpam-534	516	2	,	,	PUNCT
ejpam-534	516	3	t.	t.	PROPN
ejpam-534	516	4	gulati	gulati	PROPN
ejpam-534	516	5	and	and	CCONJ
ejpam-534	516	6	g.	g.	PROPN
ejpam-534	516	7	mehndiratta	mehndiratta	PROPN
ejpam-534	516	8	/	/	SYM
ejpam-534	516	9	eur	eur	PROPN
ejpam-534	516	10	.	.	PUNCT
ejpam-534	517	1	j.	j.	PROPN
ejpam-534	517	2	pure	pure	PROPN
ejpam-534	517	3	appl	appl	PROPN
ejpam-534	517	4	.	.	PROPN
ejpam-534	517	5	math	math	PROPN
ejpam-534	517	6	,	,	PUNCT
ejpam-534	517	7	3	3	NUM
ejpam-534	517	8	(	(	PUNCT
ejpam-534	517	9	2010	2010	NUM
ejpam-534	517	10	)	)	PUNCT
ejpam-534	517	11	,	,	PUNCT
ejpam-534	517	12	786	786	NUM
ejpam-534	517	13	-	-	SYM
ejpam-534	517	14	805	805	NUM
ejpam-534	517	15	797	797	NUM
ejpam-534	517	16	m∑	m∑	ADV
ejpam-534	517	17	j=1	j=1	PROPN
ejpam-534	517	18	ȳ	ȳ	PROPN
ejpam-534	517	19	j(t)g	j(t)g	PROPN
ejpam-534	517	20	j(t	j(t	PROPN
ejpam-534	517	21	,	,	PUNCT
ejpam-534	517	22	x̄	x̄	NOUN
ejpam-534	517	23	,	,	PUNCT
ejpam-534	517	24	˙̄x	˙̄x	PRON
ejpam-534	517	25	)	)	PUNCT
ejpam-534	517	26	=	=	SYM
ejpam-534	517	27	0	0	NUM
ejpam-534	517	28	,	,	PUNCT
ejpam-534	517	29	t	t	PROPN
ejpam-534	518	1	∈	∈	PROPN
ejpam-534	519	1	i	i	PRON
ejpam-534	519	2	,	,	PUNCT
ejpam-534	519	3	or	or	CCONJ
ejpam-534	519	4	k∑	k∑	VERB
ejpam-534	519	5	i=1	i=1	PROPN
ejpam-534	519	6	λ̄i	λ̄i	PROPN
ejpam-534	519	7	(	(	PUNCT
ejpam-534	519	8	f	f	NOUN
ejpam-534	519	9	i	i	PRON
ejpam-534	519	10	x	x	X
ejpam-534	519	11	(	(	PUNCT
ejpam-534	519	12	t	t	PROPN
ejpam-534	519	13	,	,	PUNCT
ejpam-534	519	14	x̄	x̄	NOUN
ejpam-534	519	15	,	,	PUNCT
ejpam-534	519	16	˙̄x)−	˙̄x)−	PROPN
ejpam-534	520	1	d	d	X
ejpam-534	520	2	f	f	X
ejpam-534	521	1	i	i	PRON
ejpam-534	521	2	ẋ	ẋ	PROPN
ejpam-534	522	1	(	(	PUNCT
ejpam-534	522	2	t	t	PROPN
ejpam-534	522	3	,	,	PUNCT
ejpam-534	522	4	x̄	x̄	NOUN
ejpam-534	522	5	,	,	PUNCT
ejpam-534	522	6	˙̄x))+	˙̄x))+	ADP
ejpam-534	522	7	gx(t	gx(t	PROPN
ejpam-534	522	8	,	,	PUNCT
ejpam-534	522	9	x̄	x̄	NOUN
ejpam-534	522	10	,	,	PUNCT
ejpam-534	522	11	˙̄x	˙̄x	PRON
ejpam-534	522	12	)	)	PUNCT
ejpam-534	522	13	ȳ(t)−	ȳ(t)−	PROPN
ejpam-534	522	14	d(g	d(g	PROPN
ejpam-534	522	15	ẋ(t	ẋ(t	PROPN
ejpam-534	522	16	,	,	PUNCT
ejpam-534	522	17	x̄	x̄	NOUN
ejpam-534	522	18	,	,	PUNCT
ejpam-534	522	19	˙̄x	˙̄x	NOUN
ejpam-534	522	20	)	)	PUNCT
ejpam-534	522	21	ȳ(t	ȳ(t	NOUN
ejpam-534	522	22	)	)	PUNCT
ejpam-534	522	23	)	)	PUNCT
ejpam-534	523	1	=	=	PUNCT
ejpam-534	523	2	0	0	NUM
ejpam-534	523	3	,	,	PUNCT
ejpam-534	523	4	t	t	PROPN
ejpam-534	523	5	∈	∈	PROPN
ejpam-534	524	1	i	i	PRON
ejpam-534	524	2	,	,	PUNCT
ejpam-534	524	3	ȳ(t)t	ȳ(t)t	PROPN
ejpam-534	524	4	g(t	g(t	PROPN
ejpam-534	524	5	,	,	PUNCT
ejpam-534	524	6	x̄	x̄	NOUN
ejpam-534	524	7	,	,	PUNCT
ejpam-534	524	8	˙̄x	˙̄x	PRON
ejpam-534	524	9	)	)	PUNCT
ejpam-534	524	10	=	=	SYM
ejpam-534	524	11	0	0	NUM
ejpam-534	524	12	,	,	PUNCT
ejpam-534	524	13	t	t	PROPN
ejpam-534	524	14	∈	∈	PROPN
ejpam-534	525	1	i	i	PRON
ejpam-534	525	2	,	,	PUNCT
ejpam-534	525	3	λ̄=	λ̄=	X
ejpam-534	525	4	(	(	PUNCT
ejpam-534	525	5	λ̄1	λ̄1	X
ejpam-534	525	6	,	,	PUNCT
ejpam-534	525	7	λ̄2	λ̄2	X
ejpam-534	525	8	,	,	PUNCT
ejpam-534	525	9	.	.	PUNCT
ejpam-534	525	10	.	.	PUNCT
ejpam-534	525	11	.	.	PUNCT
ejpam-534	526	1	,	,	PUNCT
ejpam-534	526	2	λ̄k	λ̄k	PROPN
ejpam-534	526	3	)	)	PUNCT
ejpam-534	526	4	>	>	X
ejpam-534	527	1	0	0	PROPN
ejpam-534	527	2	,	,	PUNCT
ejpam-534	527	3	k∑	k∑	VERB
ejpam-534	527	4	i=1	i=1	PROPN
ejpam-534	528	1	λ̄i	λ̄i	X
ejpam-534	528	2	=	=	SYM
ejpam-534	528	3	1	1	NUM
ejpam-534	528	4	,	,	PUNCT
ejpam-534	528	5	ȳ(t	ȳ(t	NOUN
ejpam-534	528	6	)	)	PUNCT
ejpam-534	528	7	=	=	PUNCT
ejpam-534	529	1	(	(	PUNCT
ejpam-534	529	2	ȳ1(t	ȳ1(t	NUM
ejpam-534	529	3	)	)	PUNCT
ejpam-534	529	4	,	,	PUNCT
ejpam-534	529	5	ȳ2(t	ȳ2(t	PROPN
ejpam-534	529	6	)	)	PUNCT
ejpam-534	529	7	,	,	PUNCT
ejpam-534	529	8	.	.	PUNCT
ejpam-534	529	9	.	.	PUNCT
ejpam-534	530	1	.	.	PUNCT
ejpam-534	531	1	,	,	PUNCT
ejpam-534	531	2	ȳm(t	ȳm(t	NOUN
ejpam-534	531	3	)	)	PUNCT
ejpam-534	531	4	)	)	PUNCT
ejpam-534	532	1	≧	≧	X
ejpam-534	533	1	0	0	NUM
ejpam-534	533	2	,	,	PUNCT
ejpam-534	533	3	t	t	PROPN
ejpam-534	533	4	∈	∈	PROPN
ejpam-534	534	1	i	i	PRON
ejpam-534	534	2	.	.	PUNCT
ejpam-534	535	1	5	5	X
ejpam-534	535	2	.	.	X
ejpam-534	535	3	second	second	ADJ
ejpam-534	535	4	-	-	PUNCT
ejpam-534	535	5	order	order	NOUN
ejpam-534	535	6	mond	mond	NOUN
ejpam-534	535	7	-	-	PUNCT
ejpam-534	535	8	weir	weir	PROPN
ejpam-534	535	9	type	type	NOUN
ejpam-534	535	10	duality	duality	NOUN
ejpam-534	535	11	we	we	PRON
ejpam-534	535	12	present	present	VERB
ejpam-534	535	13	the	the	DET
ejpam-534	535	14	following	follow	VERB
ejpam-534	535	15	multiobjective	multiobjective	ADJ
ejpam-534	535	16	variational	variational	ADJ
ejpam-534	535	17	dual	dual	ADJ
ejpam-534	535	18	problem	problem	NOUN
ejpam-534	535	19	for	for	ADP
ejpam-534	535	20	(	(	PUNCT
ejpam-534	535	21	p	p	NOUN
ejpam-534	535	22	):	):	PUNCT
ejpam-534	535	23	(	(	PUNCT
ejpam-534	535	24	mwd	mwd	PROPN
ejpam-534	535	25	)	)	PUNCT
ejpam-534	535	26	maximize	maximize	NOUN
ejpam-534	535	27	(	(	PUNCT
ejpam-534	535	28	∫	∫	PROPN
ejpam-534	535	29	(	(	PUNCT
ejpam-534	535	30	f	f	PROPN
ejpam-534	535	31	1(t	1(t	NUM
ejpam-534	535	32	,	,	PUNCT
ejpam-534	535	33	u	u	NOUN
ejpam-534	535	34	,	,	PUNCT
ejpam-534	535	35	u̇)−	u̇)−	PROPN
ejpam-534	535	36	1	1	NUM
ejpam-534	535	37	2	2	NUM
ejpam-534	535	38	p(t)t	p(t)t	NOUN
ejpam-534	535	39	a1p(t))d	a1p(t))d	PROPN
ejpam-534	535	40	t	t	PROPN
ejpam-534	535	41	,	,	PUNCT
ejpam-534	535	42	.	.	PUNCT
ejpam-534	535	43	.	.	PUNCT
ejpam-534	536	1	.	.	PUNCT
ejpam-534	537	1	,	,	PUNCT
ejpam-534	537	2	∫	∫	PROPN
ejpam-534	537	3	(	(	PUNCT
ejpam-534	537	4	f	f	PROPN
ejpam-534	537	5	k(t	k(t	PROPN
ejpam-534	537	6	,	,	PUNCT
ejpam-534	537	7	u	u	NOUN
ejpam-534	537	8	,	,	PUNCT
ejpam-534	537	9	u̇)−	u̇)−	PROPN
ejpam-534	537	10	1	1	NUM
ejpam-534	537	11	2	2	NUM
ejpam-534	537	12	p(t)t	p(t)t	NOUN
ejpam-534	537	13	akp(t))d	akp(t))d	PROPN
ejpam-534	537	14	t	t	PROPN
ejpam-534	537	15	)	)	PUNCT
ejpam-534	537	16	subject	subject	NOUN
ejpam-534	537	17	to	to	ADP
ejpam-534	537	18	u(a	u(a	PROPN
ejpam-534	537	19	)	)	PUNCT
ejpam-534	537	20	=	=	SYM
ejpam-534	537	21	α	α	PROPN
ejpam-534	537	22	,	,	PUNCT
ejpam-534	537	23	u(b	u(b	NOUN
ejpam-534	537	24	)	)	PUNCT
ejpam-534	538	1	=	=	SYM
ejpam-534	538	2	β	β	X
ejpam-534	538	3	,	,	PUNCT
ejpam-534	538	4	(	(	PUNCT
ejpam-534	538	5	33	33	NUM
ejpam-534	538	6	)	)	PUNCT
ejpam-534	538	7	k∑	k∑	VERB
ejpam-534	538	8	i=1	i=1	PROPN
ejpam-534	539	1	λi	λi	PROPN
ejpam-534	539	2	(	(	PUNCT
ejpam-534	539	3	f	f	NOUN
ejpam-534	539	4	i	i	NOUN
ejpam-534	539	5	x	x	X
ejpam-534	539	6	(	(	PUNCT
ejpam-534	539	7	t	t	PROPN
ejpam-534	539	8	,	,	PUNCT
ejpam-534	539	9	u	u	NOUN
ejpam-534	539	10	,	,	PUNCT
ejpam-534	539	11	u̇)−	u̇)−	PROPN
ejpam-534	540	1	d	d	X
ejpam-534	540	2	f	f	PROPN
ejpam-534	541	1	i	i	PRON
ejpam-534	541	2	ẋ	ẋ	PROPN
ejpam-534	542	1	(	(	PUNCT
ejpam-534	542	2	t	t	PROPN
ejpam-534	542	3	,	,	PUNCT
ejpam-534	542	4	u	u	NOUN
ejpam-534	542	5	,	,	PUNCT
ejpam-534	542	6	u̇	u̇	PROPN
ejpam-534	542	7	)	)	PUNCT
ejpam-534	543	1	+	+	CCONJ
ejpam-534	543	2	aip(t	aip(t	NOUN
ejpam-534	543	3	)	)	PUNCT
ejpam-534	543	4	)	)	PUNCT
ejpam-534	544	1	+	+	CCONJ
ejpam-534	544	2	gx(t	gx(t	PROPN
ejpam-534	544	3	,	,	PUNCT
ejpam-534	544	4	u	u	NOUN
ejpam-534	544	5	,	,	PUNCT
ejpam-534	544	6	u̇)y(t)−	u̇)y(t)−	PROPN
ejpam-534	544	7	d(g	d(g	PROPN
ejpam-534	544	8	ẋ(t	ẋ(t	PROPN
ejpam-534	544	9	,	,	PUNCT
ejpam-534	544	10	u	u	NOUN
ejpam-534	544	11	,	,	PUNCT
ejpam-534	544	12	u̇)y(t	u̇)y(t	PROPN
ejpam-534	544	13	)	)	PUNCT
ejpam-534	544	14	)	)	PUNCT
ejpam-534	544	15	+	+	CCONJ
ejpam-534	544	16	bp(t	bp(t	NOUN
ejpam-534	544	17	)	)	PUNCT
ejpam-534	544	18	=	=	SYM
ejpam-534	544	19	0	0	NUM
ejpam-534	544	20	,	,	PUNCT
ejpam-534	544	21	t	t	PROPN
ejpam-534	544	22	∈	∈	PROPN
ejpam-534	545	1	i	i	PRON
ejpam-534	545	2	,	,	PUNCT
ejpam-534	545	3	(	(	PUNCT
ejpam-534	545	4	34	34	NUM
ejpam-534	545	5	)	)	PUNCT
ejpam-534	545	6	y(t)t	y(t)t	PROPN
ejpam-534	545	7	g(t	g(t	PROPN
ejpam-534	545	8	,	,	PUNCT
ejpam-534	545	9	u	u	NOUN
ejpam-534	545	10	,	,	PUNCT
ejpam-534	545	11	u̇)−	u̇)−	PROPN
ejpam-534	545	12	1	1	NUM
ejpam-534	545	13	2	2	NUM
ejpam-534	545	14	p(t)t	p(t)t	NOUN
ejpam-534	545	15	bp(t	bp(t	NOUN
ejpam-534	545	16	)	)	PUNCT
ejpam-534	545	17	≧	≧	X
ejpam-534	545	18	0	0	NUM
ejpam-534	545	19	,	,	PUNCT
ejpam-534	545	20	t	t	PROPN
ejpam-534	545	21	∈	∈	PROPN
ejpam-534	546	1	i	i	PRON
ejpam-534	546	2	,	,	PUNCT
ejpam-534	546	3	(	(	PUNCT
ejpam-534	546	4	35	35	NUM
ejpam-534	546	5	)	)	PUNCT
ejpam-534	546	6	λ	λ	NOUN
ejpam-534	546	7	≥	≥	NOUN
ejpam-534	546	8	0	0	NUM
ejpam-534	546	9	,	,	PUNCT
ejpam-534	546	10	(	(	PUNCT
ejpam-534	546	11	36	36	NUM
ejpam-534	546	12	)	)	PUNCT
ejpam-534	546	13	y(t	y(t	NUM
ejpam-534	546	14	)	)	PUNCT
ejpam-534	546	15	≧	≧	X
ejpam-534	546	16	0	0	NUM
ejpam-534	546	17	,	,	PUNCT
ejpam-534	546	18	t	t	PROPN
ejpam-534	546	19	∈	∈	PROPN
ejpam-534	547	1	i	i	PRON
ejpam-534	547	2	,	,	PUNCT
ejpam-534	547	3	(	(	PUNCT
ejpam-534	547	4	37	37	NUM
ejpam-534	547	5	)	)	PUNCT
ejpam-534	547	6	where	where	SCONJ
ejpam-534	547	7	y	y	NOUN
ejpam-534	547	8	:	:	PUNCT
ejpam-534	547	9	i	i	PROPN
ejpam-534	547	10	→	→	SYM
ejpam-534	547	11	rm	rm	PROPN
ejpam-534	547	12	,	,	PUNCT
ejpam-534	547	13	p	p	X
ejpam-534	547	14	:	:	PUNCT
ejpam-534	547	15	i	i	PROPN
ejpam-534	547	16	→	→	SYM
ejpam-534	547	17	rn	rn	PROPN
ejpam-534	547	18	,	,	PUNCT
ejpam-534	547	19	λ	λ	PROPN
ejpam-534	547	20	=	=	PRON
ejpam-534	547	21	(	(	PUNCT
ejpam-534	547	22	λ1,λ2	λ1,λ2	PROPN
ejpam-534	547	23	,	,	PUNCT
ejpam-534	547	24	.	.	PUNCT
ejpam-534	547	25	.	.	PUNCT
ejpam-534	547	26	.	.	PUNCT
ejpam-534	548	1	,	,	PUNCT
ejpam-534	548	2	λk	λk	X
ejpam-534	548	3	)	)	PUNCT
ejpam-534	548	4	∈	∈	PROPN
ejpam-534	548	5	rk	rk	NOUN
ejpam-534	548	6	,	,	PUNCT
ejpam-534	548	7	ai(t	ai(t	NOUN
ejpam-534	548	8	,	,	PUNCT
ejpam-534	548	9	u	u	NOUN
ejpam-534	548	10	,	,	PUNCT
ejpam-534	548	11	u̇	u̇	PROPN
ejpam-534	548	12	,	,	PUNCT
ejpam-534	548	13	ü	ü	NOUN
ejpam-534	548	14	,	,	PUNCT
ejpam-534	548	15	...	...	PUNCT
ejpam-534	549	1	u	u	NOUN
ejpam-534	549	2	,	,	PUNCT
ejpam-534	549	3	....	....	PUNCT
ejpam-534	549	4	u	u	NOUN
ejpam-534	549	5	)	)	PUNCT
ejpam-534	549	6	,	,	PUNCT
ejpam-534	549	7	t	t	PROPN
ejpam-534	549	8	∈	∈	PROPN
ejpam-534	550	1	i	i	PRON
ejpam-534	550	2	,	,	PUNCT
ejpam-534	550	3	i	i	PROPN
ejpam-534	550	4	∈	∈	PROPN
ejpam-534	550	5	k	k	X
ejpam-534	550	6	(	(	PUNCT
ejpam-534	550	7	as	as	SCONJ
ejpam-534	550	8	defined	define	VERB
ejpam-534	550	9	earlier	early	ADV
ejpam-534	550	10	)	)	PUNCT
ejpam-534	550	11	and	and	CCONJ
ejpam-534	550	12	b(t	b(t	PROPN
ejpam-534	550	13	,	,	PUNCT
ejpam-534	550	14	u	u	NOUN
ejpam-534	550	15	,	,	PUNCT
ejpam-534	550	16	u̇	u̇	PROPN
ejpam-534	550	17	,	,	PUNCT
ejpam-534	550	18	ü	ü	NOUN
ejpam-534	550	19	,	,	PUNCT
ejpam-534	550	20	...	...	PUNCT
ejpam-534	550	21	u	u	NOUN
ejpam-534	550	22	,	,	PUNCT
ejpam-534	550	23	....	....	PUNCT
ejpam-534	550	24	u	u	INTJ
ejpam-534	550	25	,	,	PUNCT
ejpam-534	550	26	y(t	y(t	PROPN
ejpam-534	550	27	)	)	PUNCT
ejpam-534	550	28	,	,	PUNCT
ejpam-534	550	29	ẏ(t	ẏ(t	PROPN
ejpam-534	550	30	)	)	PUNCT
ejpam-534	550	31	,	,	PUNCT
ejpam-534	550	32	ÿ(t	ÿ(t	PROPN
ejpam-534	550	33	)	)	PUNCT
ejpam-534	550	34	,	,	PUNCT
ejpam-534	550	35	...	...	PUNCT
ejpam-534	551	1	y	y	PROPN
ejpam-534	551	2	(	(	PUNCT
ejpam-534	551	3	t	t	PROPN
ejpam-534	551	4	)	)	PUNCT
ejpam-534	551	5	)	)	PUNCT
ejpam-534	552	1	=	=	PUNCT
ejpam-534	552	2	(	(	PUNCT
ejpam-534	552	3	gx	gx	PROPN
ejpam-534	552	4	y(t))x−2d(gx	y(t))x−2d(gx	PROPN
ejpam-534	552	5	y(t	y(t	PROPN
ejpam-534	552	6	)	)	PUNCT
ejpam-534	552	7	)	)	PUNCT
ejpam-534	553	1	ẋ+d2(g	ẋ+d2(g	PROPN
ejpam-534	553	2	ẋ	ẋ	PROPN
ejpam-534	553	3	y(t	y(t	PROPN
ejpam-534	553	4	)	)	PUNCT
ejpam-534	553	5	)	)	PUNCT
ejpam-534	554	1	ẋ−d3(g	ẋ−d3(g	PROPN
ejpam-534	554	2	ẋ	ẋ	PROPN
ejpam-534	554	3	y(t	y(t	NOUN
ejpam-534	554	4	)	)	PUNCT
ejpam-534	554	5	)	)	PUNCT
ejpam-534	555	1	ẍ	ẍ	X
ejpam-534	555	2	,	,	PUNCT
ejpam-534	555	3	t	t	PROPN
ejpam-534	555	4	∈	∈	PROPN
ejpam-534	556	1	i	i	PRON
ejpam-534	556	2	,	,	PUNCT
ejpam-534	556	3	are	be	AUX
ejpam-534	556	4	n×	n×	PRON
ejpam-534	556	5	n	n	PRON
ejpam-534	556	6	symmetric	symmetric	ADJ
ejpam-534	556	7	matrices	matrix	NOUN
ejpam-534	556	8	.	.	PUNCT
ejpam-534	557	1	let	let	VERB
ejpam-534	557	2	y	y	PRON
ejpam-534	557	3	be	be	AUX
ejpam-534	557	4	the	the	DET
ejpam-534	557	5	set	set	NOUN
ejpam-534	557	6	of	of	ADP
ejpam-534	557	7	all	all	DET
ejpam-534	557	8	feasible	feasible	ADJ
ejpam-534	557	9	solutions	solution	NOUN
ejpam-534	557	10	of	of	ADP
ejpam-534	557	11	the	the	DET
ejpam-534	557	12	above	above	ADJ
ejpam-534	557	13	problem	problem	NOUN
ejpam-534	557	14	.	.	PUNCT
ejpam-534	558	1	theorem	theorem	ADJ
ejpam-534	558	2	6	6	NUM
ejpam-534	558	3	.	.	PUNCT
ejpam-534	559	1	(	(	PUNCT
ejpam-534	559	2	weak	weak	ADJ
ejpam-534	559	3	duality	duality	NOUN
ejpam-534	559	4	)	)	PUNCT
ejpam-534	559	5	let	let	VERB
ejpam-534	559	6	x(t	x(t	NOUN
ejpam-534	559	7	)	)	PUNCT
ejpam-534	559	8	∈	∈	PROPN
ejpam-534	559	9	x	x	X
ejpam-534	559	10	and	and	CCONJ
ejpam-534	559	11	(	(	PUNCT
ejpam-534	559	12	u(t),λ	u(t),λ	PROPN
ejpam-534	559	13	,	,	PUNCT
ejpam-534	559	14	y(t	y(t	PROPN
ejpam-534	559	15	)	)	PUNCT
ejpam-534	559	16	,	,	PUNCT
ejpam-534	559	17	p(t	p(t	NOUN
ejpam-534	559	18	)	)	PUNCT
ejpam-534	559	19	)	)	PUNCT
ejpam-534	560	1	∈	∈	PROPN
ejpam-534	560	2	y	y	PROPN
ejpam-534	560	3	such	such	ADJ
ejpam-534	560	4	that	that	SCONJ
ejpam-534	560	5	t.	t.	PROPN
ejpam-534	560	6	gulati	gulati	PROPN
ejpam-534	560	7	and	and	CCONJ
ejpam-534	560	8	g.	g.	PROPN
ejpam-534	560	9	mehndiratta	mehndiratta	PROPN
ejpam-534	560	10	/	/	SYM
ejpam-534	560	11	eur	eur	PROPN
ejpam-534	560	12	.	.	PUNCT
ejpam-534	561	1	j.	j.	PROPN
ejpam-534	561	2	pure	pure	PROPN
ejpam-534	561	3	appl	appl	PROPN
ejpam-534	561	4	.	.	PROPN
ejpam-534	561	5	math	math	PROPN
ejpam-534	561	6	,	,	PUNCT
ejpam-534	561	7	3	3	NUM
ejpam-534	561	8	(	(	PUNCT
ejpam-534	561	9	2010	2010	NUM
ejpam-534	561	10	)	)	PUNCT
ejpam-534	561	11	,	,	PUNCT
ejpam-534	561	12	786	786	NUM
ejpam-534	561	13	-	-	SYM
ejpam-534	561	14	805	805	NUM
ejpam-534	561	15	798	798	NUM
ejpam-534	561	16	(	(	PUNCT
ejpam-534	561	17	i	i	NOUN
ejpam-534	561	18	)	)	PUNCT
ejpam-534	561	19	∫	∫	PROPN
ejpam-534	562	1	k∑	k∑	PROPN
ejpam-534	563	1	i=1	i=1	PROPN
ejpam-534	563	2	λi	λi	ADP
ejpam-534	563	3	f	f	PROPN
ejpam-534	563	4	i(t	i(t	PROPN
ejpam-534	563	5	,	,	PUNCT
ejpam-534	563	6	.	.	PUNCT
ejpam-534	563	7	,	,	PUNCT
ejpam-534	563	8	.)d	.)d	PROPN
ejpam-534	563	9	t	t	PROPN
ejpam-534	563	10	is	be	AUX
ejpam-534	563	11	second	second	ADJ
ejpam-534	563	12	-	-	PUNCT
ejpam-534	563	13	order	order	NOUN
ejpam-534	563	14	(	(	PUNCT
ejpam-534	563	15	g	g	NOUN
ejpam-534	563	16	,	,	PUNCT
ejpam-534	563	17	ρ1)-pseudoconvex	ρ1)-pseudoconvex	PROPN
ejpam-534	563	18	at	at	ADP
ejpam-534	563	19	u(t	u(t	NOUN
ejpam-534	563	20	)	)	PUNCT
ejpam-534	563	21	,	,	PUNCT
ejpam-534	563	22	(	(	PUNCT
ejpam-534	563	23	ii	ii	NOUN
ejpam-534	563	24	)	)	PUNCT
ejpam-534	563	25	∫	∫	PROPN
ejpam-534	563	26	y(t)t	y(t)t	PROPN
ejpam-534	563	27	g(t	g(t	PROPN
ejpam-534	563	28	,	,	PUNCT
ejpam-534	563	29	.	.	PUNCT
ejpam-534	563	30	,	,	PUNCT
ejpam-534	564	1	.)d	.)d	PROPN
ejpam-534	564	2	t	t	PROPN
ejpam-534	564	3	is	be	AUX
ejpam-534	564	4	second	second	ADJ
ejpam-534	564	5	-	-	PUNCT
ejpam-534	564	6	order	order	NOUN
ejpam-534	564	7	(	(	PUNCT
ejpam-534	564	8	g	g	NOUN
ejpam-534	564	9	,	,	PUNCT
ejpam-534	564	10	ρ2)-quasiconvex	ρ2)-quasiconvex	NOUN
ejpam-534	564	11	at	at	ADP
ejpam-534	564	12	u(t	u(t	NOUN
ejpam-534	564	13	)	)	PUNCT
ejpam-534	564	14	,	,	PUNCT
ejpam-534	564	15	(	(	PUNCT
ejpam-534	564	16	iii	iii	X
ejpam-534	564	17	)	)	PUNCT
ejpam-534	564	18	λ	λ	NOUN
ejpam-534	564	19	>	>	X
ejpam-534	564	20	0	0	PUNCT
ejpam-534	564	21	and	and	CCONJ
ejpam-534	564	22	ρ1+ρ2	ρ1+ρ2	PROPN
ejpam-534	564	23	≧	≧	NOUN
ejpam-534	564	24	0	0	X
ejpam-534	564	25	.	.	PUNCT
ejpam-534	565	1	then	then	ADV
ejpam-534	565	2	∫	∫	PROPN
ejpam-534	565	3	f	f	PROPN
ejpam-534	565	4	r(t	r(t	PROPN
ejpam-534	565	5	,	,	PUNCT
ejpam-534	565	6	x	x	PRON
ejpam-534	565	7	,	,	PUNCT
ejpam-534	565	8	ẋ)d	ẋ)d	PROPN
ejpam-534	565	9	t	t	PROPN
ejpam-534	565	10	<	<	X
ejpam-534	565	11	∫	∫	PROPN
ejpam-534	565	12	(	(	PUNCT
ejpam-534	565	13	f	f	PROPN
ejpam-534	565	14	r(t	r(t	PROPN
ejpam-534	565	15	,	,	PUNCT
ejpam-534	565	16	u	u	NOUN
ejpam-534	565	17	,	,	PUNCT
ejpam-534	565	18	u̇)−	u̇)−	PROPN
ejpam-534	565	19	1	1	NUM
ejpam-534	565	20	2	2	NUM
ejpam-534	565	21	p(t)t	p(t)t	NOUN
ejpam-534	565	22	ar	ar	NOUN
ejpam-534	565	23	p(t))d	p(t))d	NOUN
ejpam-534	565	24	t	t	NOUN
ejpam-534	565	25	for	for	ADP
ejpam-534	565	26	some	some	DET
ejpam-534	565	27	r	r	NOUN
ejpam-534	565	28	∈	∈	NOUN
ejpam-534	565	29	k	k	X
ejpam-534	565	30	(	(	PUNCT
ejpam-534	565	31	38	38	NUM
ejpam-534	565	32	)	)	PUNCT
ejpam-534	565	33	and	and	CCONJ
ejpam-534	565	34	∫	∫	PROPN
ejpam-534	565	35	f	f	PROPN
ejpam-534	565	36	i(t	i(t	PROPN
ejpam-534	565	37	,	,	PUNCT
ejpam-534	565	38	x	x	X
ejpam-534	565	39	,	,	PUNCT
ejpam-534	565	40	ẋ)d	ẋ)d	PROPN
ejpam-534	565	41	t	t	PROPN
ejpam-534	566	1	≦	≦	PROPN
ejpam-534	566	2	∫	∫	PROPN
ejpam-534	566	3	(	(	PUNCT
ejpam-534	566	4	f	f	PROPN
ejpam-534	566	5	i(t	i(t	PROPN
ejpam-534	566	6	,	,	PUNCT
ejpam-534	566	7	u	u	NOUN
ejpam-534	566	8	,	,	PUNCT
ejpam-534	566	9	u̇)−	u̇)−	PROPN
ejpam-534	566	10	1	1	NUM
ejpam-534	566	11	2	2	NUM
ejpam-534	566	12	p(t)t	p(t)t	NOUN
ejpam-534	566	13	aip(t))d	aip(t))d	PROPN
ejpam-534	566	14	t	t	PROPN
ejpam-534	566	15	,	,	PUNCT
ejpam-534	566	16	i	i	PROPN
ejpam-534	566	17	∈	∈	PROPN
ejpam-534	566	18	kr	kr	PROPN
ejpam-534	566	19	(	(	PUNCT
ejpam-534	566	20	39	39	NUM
ejpam-534	566	21	)	)	PUNCT
ejpam-534	566	22	can	can	AUX
ejpam-534	566	23	not	not	PART
ejpam-534	566	24	hold	hold	VERB
ejpam-534	566	25	.	.	PUNCT
ejpam-534	567	1	proof	proof	NOUN
ejpam-534	567	2	.	.	PUNCT
ejpam-534	568	1	suppose	suppose	VERB
ejpam-534	568	2	,	,	PUNCT
ejpam-534	568	3	to	to	ADP
ejpam-534	568	4	the	the	DET
ejpam-534	568	5	contrary	contrary	NOUN
ejpam-534	568	6	,	,	PUNCT
ejpam-534	568	7	that	that	SCONJ
ejpam-534	568	8	(	(	PUNCT
ejpam-534	568	9	38	38	NUM
ejpam-534	568	10	)	)	PUNCT
ejpam-534	568	11	and	and	CCONJ
ejpam-534	568	12	(	(	PUNCT
ejpam-534	568	13	39	39	NUM
ejpam-534	568	14	)	)	PUNCT
ejpam-534	568	15	hold	hold	VERB
ejpam-534	568	16	.	.	PUNCT
ejpam-534	569	1	since	since	SCONJ
ejpam-534	569	2	λ	λ	PROPN
ejpam-534	569	3	>	>	X
ejpam-534	569	4	0	0	PROPN
ejpam-534	569	5	,	,	PUNCT
ejpam-534	569	6	the	the	DET
ejpam-534	569	7	above	above	ADJ
ejpam-534	569	8	inequalities	inequality	NOUN
ejpam-534	569	9	give	give	VERB
ejpam-534	569	10	∫	∫	PROPN
ejpam-534	569	11	k∑	k∑	PROPN
ejpam-534	570	1	i=1	i=1	PROPN
ejpam-534	570	2	λi	λi	ADP
ejpam-534	570	3	f	f	PROPN
ejpam-534	570	4	i(t	i(t	PROPN
ejpam-534	570	5	,	,	PUNCT
ejpam-534	570	6	x	x	X
ejpam-534	570	7	,	,	PUNCT
ejpam-534	570	8	ẋ)d	ẋ)d	PROPN
ejpam-534	571	1	t	t	PROPN
ejpam-534	571	2	<	<	X
ejpam-534	571	3	∫	∫	PROPN
ejpam-534	571	4	k∑	k∑	PROPN
ejpam-534	571	5	i=1	i=1	PROPN
ejpam-534	571	6	λi	λi	PROPN
ejpam-534	571	7	(	(	PUNCT
ejpam-534	571	8	f	f	PROPN
ejpam-534	571	9	i(t	i(t	PROPN
ejpam-534	571	10	,	,	PUNCT
ejpam-534	571	11	u	u	NOUN
ejpam-534	571	12	,	,	PUNCT
ejpam-534	571	13	u̇)−	u̇)−	PROPN
ejpam-534	571	14	1	1	NUM
ejpam-534	571	15	2	2	NUM
ejpam-534	571	16	p(t)t	p(t)t	NOUN
ejpam-534	571	17	ai	ai	VERB
ejpam-534	571	18	p(t))d	p(t))d	NOUN
ejpam-534	571	19	t.	t.	NOUN
ejpam-534	571	20	(	(	PUNCT
ejpam-534	571	21	40	40	NUM
ejpam-534	571	22	)	)	PUNCT
ejpam-534	571	23	now	now	ADV
ejpam-534	571	24	,	,	PUNCT
ejpam-534	571	25	by	by	ADP
ejpam-534	571	26	the	the	DET
ejpam-534	571	27	constraints	constraint	NOUN
ejpam-534	571	28	(	(	PUNCT
ejpam-534	571	29	21	21	NUM
ejpam-534	571	30	)	)	PUNCT
ejpam-534	571	31	,	,	PUNCT
ejpam-534	571	32	(	(	PUNCT
ejpam-534	571	33	35	35	NUM
ejpam-534	571	34	)	)	PUNCT
ejpam-534	571	35	and	and	CCONJ
ejpam-534	571	36	(	(	PUNCT
ejpam-534	571	37	37	37	NUM
ejpam-534	571	38	)	)	PUNCT
ejpam-534	571	39	,	,	PUNCT
ejpam-534	571	40	we	we	PRON
ejpam-534	571	41	have	have	VERB
ejpam-534	571	42	∫	∫	PROPN
ejpam-534	571	43	y(t)t	y(t)t	PROPN
ejpam-534	571	44	g(t	g(t	PROPN
ejpam-534	571	45	,	,	PUNCT
ejpam-534	571	46	x	x	PRON
ejpam-534	571	47	,	,	PUNCT
ejpam-534	571	48	ẋ)d	ẋ)d	PROPN
ejpam-534	571	49	t	t	PROPN
ejpam-534	572	1	≦	≦	PROPN
ejpam-534	572	2	∫	∫	PROPN
ejpam-534	572	3	(	(	PUNCT
ejpam-534	572	4	y(t)t	y(t)t	PROPN
ejpam-534	572	5	g(t	g(t	PROPN
ejpam-534	572	6	,	,	PUNCT
ejpam-534	572	7	u	u	NOUN
ejpam-534	572	8	,	,	PUNCT
ejpam-534	572	9	u̇)−	u̇)−	PROPN
ejpam-534	572	10	1	1	NUM
ejpam-534	572	11	2	2	NUM
ejpam-534	572	12	p(t)t	p(t)t	NOUN
ejpam-534	572	13	bp(t))d	bp(t))d	NOUN
ejpam-534	572	14	t	t	NOUN
ejpam-534	572	15	as	as	ADP
ejpam-534	572	16	∫	∫	PROPN
ejpam-534	572	17	y(t)t	y(t)t	PROPN
ejpam-534	572	18	g(t	g(t	PROPN
ejpam-534	572	19	,	,	PUNCT
ejpam-534	572	20	.	.	PUNCT
ejpam-534	572	21	,	,	PUNCT
ejpam-534	572	22	.)d	.)d	PROPN
ejpam-534	572	23	t	t	PROPN
ejpam-534	572	24	is	be	AUX
ejpam-534	572	25	second	second	ADJ
ejpam-534	572	26	-	-	PUNCT
ejpam-534	572	27	order	order	NOUN
ejpam-534	572	28	(	(	PUNCT
ejpam-534	572	29	g	g	NOUN
ejpam-534	572	30	,	,	PUNCT
ejpam-534	572	31	ρ2)-quasiconvex	ρ2)-quasiconvex	NOUN
ejpam-534	572	32	at	at	ADP
ejpam-534	572	33	u(t	u(t	NOUN
ejpam-534	572	34	)	)	PUNCT
ejpam-534	572	35	,	,	PUNCT
ejpam-534	572	36	we	we	PRON
ejpam-534	572	37	get	get	VERB
ejpam-534	572	38	∫	∫	PROPN
ejpam-534	572	39	(	(	PUNCT
ejpam-534	572	40	g(t	g(t	PROPN
ejpam-534	572	41	,	,	PUNCT
ejpam-534	572	42	x	x	INTJ
ejpam-534	572	43	,	,	PUNCT
ejpam-534	572	44	u	u	NOUN
ejpam-534	572	45	;	;	PUNCT
ejpam-534	572	46	gx	gx	PROPN
ejpam-534	572	47	(	(	PUNCT
ejpam-534	572	48	t	t	PROPN
ejpam-534	572	49	,	,	PUNCT
ejpam-534	572	50	u	u	NOUN
ejpam-534	572	51	,	,	PUNCT
ejpam-534	572	52	u̇)y(t)−	u̇)y(t)−	PROPN
ejpam-534	572	53	d(g	d(g	PROPN
ejpam-534	572	54	ẋ(t	ẋ(t	PROPN
ejpam-534	572	55	,	,	PUNCT
ejpam-534	572	56	u	u	NOUN
ejpam-534	572	57	,	,	PUNCT
ejpam-534	572	58	u̇)y(t	u̇)y(t	PROPN
ejpam-534	572	59	)	)	PUNCT
ejpam-534	572	60	)	)	PUNCT
ejpam-534	573	1	+	+	CCONJ
ejpam-534	573	2	bp(t	bp(t	NOUN
ejpam-534	573	3	)	)	PUNCT
ejpam-534	573	4	)	)	PUNCT
ejpam-534	574	1	+	+	VERB
ejpam-534	574	2	ρ2d2(t	ρ2d2(t	PROPN
ejpam-534	574	3	,	,	PUNCT
ejpam-534	574	4	x	x	INTJ
ejpam-534	574	5	,	,	PUNCT
ejpam-534	574	6	u))d	u))d	ADJ
ejpam-534	574	7	t	t	PROPN
ejpam-534	574	8	≦	≦	PROPN
ejpam-534	574	9	0	0	NUM
ejpam-534	574	10	.	.	PUNCT
ejpam-534	575	1	(	(	PUNCT
ejpam-534	575	2	41	41	NUM
ejpam-534	575	3	)	)	PUNCT
ejpam-534	575	4	from	from	ADP
ejpam-534	575	5	the	the	DET
ejpam-534	575	6	constraint	constraint	NOUN
ejpam-534	575	7	(	(	PUNCT
ejpam-534	575	8	34	34	NUM
ejpam-534	575	9	)	)	PUNCT
ejpam-534	575	10	and	and	CCONJ
ejpam-534	575	11	the	the	DET
ejpam-534	575	12	fact	fact	NOUN
ejpam-534	575	13	that	that	SCONJ
ejpam-534	575	14	g(t	g(t	PROPN
ejpam-534	575	15	,	,	PUNCT
ejpam-534	575	16	x	x	X
ejpam-534	575	17	,	,	PUNCT
ejpam-534	575	18	u	u	NOUN
ejpam-534	575	19	;	;	PUNCT
ejpam-534	575	20	0	0	NUM
ejpam-534	575	21	)	)	PUNCT
ejpam-534	575	22	=	=	SYM
ejpam-534	576	1	0	0	NUM
ejpam-534	576	2	,	,	PUNCT
ejpam-534	576	3	we	we	PRON
ejpam-534	576	4	have	have	VERB
ejpam-534	576	5	∫	∫	PROPN
ejpam-534	576	6	(	(	PUNCT
ejpam-534	576	7	g(t	g(t	PROPN
ejpam-534	576	8	,	,	PUNCT
ejpam-534	576	9	x	x	INTJ
ejpam-534	576	10	,	,	PUNCT
ejpam-534	576	11	u	u	NOUN
ejpam-534	576	12	;	;	PUNCT
ejpam-534	576	13	k∑	k∑	VERB
ejpam-534	576	14	i=1	i=1	PROPN
ejpam-534	577	1	λi	λi	PROPN
ejpam-534	577	2	(	(	PUNCT
ejpam-534	577	3	f	f	NOUN
ejpam-534	577	4	i	i	NOUN
ejpam-534	577	5	x	x	X
ejpam-534	577	6	(	(	PUNCT
ejpam-534	577	7	t	t	PROPN
ejpam-534	577	8	,	,	PUNCT
ejpam-534	577	9	u	u	NOUN
ejpam-534	577	10	,	,	PUNCT
ejpam-534	577	11	u̇	u̇	PROPN
ejpam-534	577	12	)	)	PUNCT
ejpam-534	577	13	−	−	PROPN
ejpam-534	578	1	d	d	X
ejpam-534	578	2	f	f	X
ejpam-534	579	1	i	i	PRON
ejpam-534	579	2	ẋ	ẋ	PROPN
ejpam-534	580	1	(	(	PUNCT
ejpam-534	580	2	t	t	PROPN
ejpam-534	580	3	,	,	PUNCT
ejpam-534	580	4	u	u	NOUN
ejpam-534	580	5	,	,	PUNCT
ejpam-534	580	6	u̇	u̇	PROPN
ejpam-534	580	7	)	)	PUNCT
ejpam-534	581	1	+	+	CCONJ
ejpam-534	581	2	ai	ai	VERB
ejpam-534	581	3	p(t	p(t	NOUN
ejpam-534	581	4	)	)	PUNCT
ejpam-534	581	5	)	)	PUNCT
ejpam-534	582	1	+	+	CCONJ
ejpam-534	582	2	gx(t	gx(t	PROPN
ejpam-534	582	3	,	,	PUNCT
ejpam-534	582	4	u	u	NOUN
ejpam-534	582	5	,	,	PUNCT
ejpam-534	582	6	u̇)y(t	u̇)y(t	PROPN
ejpam-534	582	7	)	)	PUNCT
ejpam-534	583	1	−	−	PROPN
ejpam-534	584	1	d(g	d(g	PROPN
ejpam-534	584	2	ẋ(t	ẋ(t	PROPN
ejpam-534	584	3	,	,	PUNCT
ejpam-534	584	4	u	u	NOUN
ejpam-534	584	5	,	,	PUNCT
ejpam-534	584	6	u̇)y(t	u̇)y(t	PROPN
ejpam-534	584	7	)	)	PUNCT
ejpam-534	584	8	)	)	PUNCT
ejpam-534	585	1	+	+	NUM
ejpam-534	585	2	bp(t)))d	bp(t)))d	NOUN
ejpam-534	585	3	t	t	NOUN
ejpam-534	585	4	=	=	SYM
ejpam-534	585	5	0	0	PROPN
ejpam-534	585	6	,	,	PUNCT
ejpam-534	585	7	which	which	PRON
ejpam-534	585	8	on	on	ADP
ejpam-534	585	9	using	use	VERB
ejpam-534	585	10	inequality	inequality	NOUN
ejpam-534	585	11	(	(	PUNCT
ejpam-534	585	12	41	41	NUM
ejpam-534	585	13	)	)	PUNCT
ejpam-534	585	14	,	,	PUNCT
ejpam-534	585	15	hypothesis	hypothesis	NOUN
ejpam-534	585	16	(	(	PUNCT
ejpam-534	585	17	iii	iii	NOUN
ejpam-534	585	18	)	)	PUNCT
ejpam-534	585	19	and	and	CCONJ
ejpam-534	585	20	the	the	DET
ejpam-534	585	21	sublinearity	sublinearity	NOUN
ejpam-534	585	22	of	of	ADP
ejpam-534	585	23	g	g	NOUN
ejpam-534	585	24	,	,	PUNCT
ejpam-534	585	25	yield	yield	NOUN
ejpam-534	585	26	∫	∫	PROPN
ejpam-534	585	27	g(t	g(t	PROPN
ejpam-534	585	28	,	,	PUNCT
ejpam-534	585	29	x	x	X
ejpam-534	585	30	,	,	PUNCT
ejpam-534	585	31	u	u	NOUN
ejpam-534	585	32	;	;	PUNCT
ejpam-534	585	33	k∑	k∑	VERB
ejpam-534	585	34	i=1	i=1	PROPN
ejpam-534	585	35	λi	λi	PROPN
ejpam-534	585	36	(	(	PUNCT
ejpam-534	585	37	f	f	NOUN
ejpam-534	585	38	i	i	NOUN
ejpam-534	585	39	x	x	X
ejpam-534	585	40	(	(	PUNCT
ejpam-534	585	41	t	t	PROPN
ejpam-534	585	42	,	,	PUNCT
ejpam-534	585	43	u	u	NOUN
ejpam-534	585	44	,	,	PUNCT
ejpam-534	585	45	u̇)−	u̇)−	PROPN
ejpam-534	586	1	d	d	X
ejpam-534	586	2	f	f	PROPN
ejpam-534	587	1	i	i	PRON
ejpam-534	587	2	ẋ	ẋ	PROPN
ejpam-534	588	1	(	(	PUNCT
ejpam-534	588	2	t	t	PROPN
ejpam-534	588	3	,	,	PUNCT
ejpam-534	588	4	u	u	NOUN
ejpam-534	588	5	,	,	PUNCT
ejpam-534	588	6	u̇	u̇	PROPN
ejpam-534	588	7	)	)	PUNCT
ejpam-534	589	1	+	+	CCONJ
ejpam-534	589	2	ai	ai	VERB
ejpam-534	589	3	p(t)))d	p(t)))d	NOUN
ejpam-534	589	4	t	t	NOUN
ejpam-534	589	5	+	+	CCONJ
ejpam-534	589	6	∫	∫	PROPN
ejpam-534	589	7	ρ1d2(t	ρ1d2(t	PROPN
ejpam-534	589	8	,	,	PUNCT
ejpam-534	589	9	x	x	X
ejpam-534	589	10	,	,	PUNCT
ejpam-534	589	11	u)d	u)d	PROPN
ejpam-534	589	12	t	t	PROPN
ejpam-534	589	13	≧	≧	NOUN
ejpam-534	589	14	0	0	X
ejpam-534	589	15	.	.	PUNCT
ejpam-534	590	1	by	by	ADP
ejpam-534	590	2	hypothesis	hypothesis	NOUN
ejpam-534	590	3	(	(	PUNCT
ejpam-534	590	4	i	i	NOUN
ejpam-534	590	5	)	)	PUNCT
ejpam-534	590	6	,	,	PUNCT
ejpam-534	590	7	it	it	PRON
ejpam-534	590	8	implies	imply	VERB
ejpam-534	590	9	∫	∫	PROPN
ejpam-534	590	10	k∑	k∑	PROPN
ejpam-534	591	1	i=1	i=1	PROPN
ejpam-534	592	1	λi	λi	ADP
ejpam-534	592	2	f	f	PROPN
ejpam-534	592	3	i(t	i(t	PROPN
ejpam-534	592	4	,	,	PUNCT
ejpam-534	592	5	x	x	X
ejpam-534	592	6	,	,	PUNCT
ejpam-534	592	7	ẋ)d	ẋ)d	PROPN
ejpam-534	592	8	t	t	PROPN
ejpam-534	592	9	≧	≧	X
ejpam-534	592	10	∫	∫	PROPN
ejpam-534	592	11	k∑	k∑	PROPN
ejpam-534	592	12	i=1	i=1	PROPN
ejpam-534	593	1	λi	λi	PROPN
ejpam-534	593	2	(	(	PUNCT
ejpam-534	593	3	f	f	PROPN
ejpam-534	593	4	i(t	i(t	PROPN
ejpam-534	593	5	,	,	PUNCT
ejpam-534	593	6	u	u	NOUN
ejpam-534	593	7	,	,	PUNCT
ejpam-534	593	8	u̇)−	u̇)−	PROPN
ejpam-534	593	9	1	1	NUM
ejpam-534	593	10	2	2	NUM
ejpam-534	593	11	p(t)t	p(t)t	NOUN
ejpam-534	593	12	ai	ai	VERB
ejpam-534	593	13	p(t))d	p(t))d	PROPN
ejpam-534	593	14	t	t	PROPN
ejpam-534	593	15	,	,	PUNCT
ejpam-534	593	16	a	a	DET
ejpam-534	593	17	contradiction	contradiction	NOUN
ejpam-534	593	18	to	to	ADP
ejpam-534	593	19	(	(	PUNCT
ejpam-534	593	20	40	40	NUM
ejpam-534	593	21	)	)	PUNCT
ejpam-534	593	22	.	.	PUNCT
ejpam-534	594	1	hence	hence	ADV
ejpam-534	594	2	the	the	DET
ejpam-534	594	3	result	result	NOUN
ejpam-534	594	4	.	.	PUNCT
ejpam-534	595	1	t.	t.	PROPN
ejpam-534	595	2	gulati	gulati	PROPN
ejpam-534	595	3	and	and	CCONJ
ejpam-534	595	4	g.	g.	PROPN
ejpam-534	595	5	mehndiratta	mehndiratta	PROPN
ejpam-534	595	6	/	/	SYM
ejpam-534	595	7	eur	eur	PROPN
ejpam-534	595	8	.	.	PUNCT
ejpam-534	596	1	j.	j.	PROPN
ejpam-534	596	2	pure	pure	PROPN
ejpam-534	596	3	appl	appl	PROPN
ejpam-534	596	4	.	.	PROPN
ejpam-534	596	5	math	math	PROPN
ejpam-534	596	6	,	,	PUNCT
ejpam-534	596	7	3	3	NUM
ejpam-534	596	8	(	(	PUNCT
ejpam-534	596	9	2010	2010	NUM
ejpam-534	596	10	)	)	PUNCT
ejpam-534	596	11	,	,	PUNCT
ejpam-534	596	12	786	786	NUM
ejpam-534	596	13	-	-	SYM
ejpam-534	596	14	805	805	NUM
ejpam-534	596	15	799	799	NUM
ejpam-534	596	16	remark	remark	NOUN
ejpam-534	596	17	2	2	NUM
ejpam-534	596	18	.	.	PUNCT
ejpam-534	597	1	if	if	SCONJ
ejpam-534	597	2	we	we	PRON
ejpam-534	597	3	drop	drop	VERB
ejpam-534	597	4	the	the	DET
ejpam-534	597	5	assumption	assumption	NOUN
ejpam-534	597	6	λ	λ	X
ejpam-534	597	7	>	>	X
ejpam-534	597	8	0	0	PUNCT
ejpam-534	597	9	from	from	ADP
ejpam-534	597	10	theorem	theorem	ADJ
ejpam-534	597	11	6	6	NUM
ejpam-534	597	12	,	,	PUNCT
ejpam-534	597	13	then	then	ADV
ejpam-534	597	14	we	we	PRON
ejpam-534	597	15	need	need	VERB
ejpam-534	597	16	to	to	PART
ejpam-534	597	17	replace	replace	VERB
ejpam-534	597	18	hypothesis	hypothesis	NOUN
ejpam-534	597	19	(	(	PUNCT
ejpam-534	597	20	i	i	NOUN
ejpam-534	597	21	)	)	PUNCT
ejpam-534	597	22	by	by	ADP
ejpam-534	597	23	:	:	PUNCT
ejpam-534	597	24	∫	∫	PROPN
ejpam-534	597	25	k∑	k∑	PROPN
ejpam-534	597	26	i=1	i=1	PROPN
ejpam-534	597	27	λi	λi	ADP
ejpam-534	597	28	f	f	PROPN
ejpam-534	597	29	i(t	i(t	PROPN
ejpam-534	597	30	,	,	PUNCT
ejpam-534	597	31	.	.	PUNCT
ejpam-534	597	32	,	,	PUNCT
ejpam-534	597	33	.)d	.)d	PROPN
ejpam-534	597	34	t	t	PROPN
ejpam-534	597	35	is	be	AUX
ejpam-534	597	36	second	second	ADJ
ejpam-534	597	37	-	-	PUNCT
ejpam-534	597	38	order	order	NOUN
ejpam-534	597	39	strictly	strictly	ADV
ejpam-534	597	40	(	(	PUNCT
ejpam-534	597	41	g	g	NOUN
ejpam-534	597	42	,	,	PUNCT
ejpam-534	597	43	ρ1)-pseudoconvex	ρ1)-pseudoconvex	PROPN
ejpam-534	597	44	at	at	ADP
ejpam-534	597	45	u(t	u(t	NOUN
ejpam-534	597	46	)	)	PUNCT
ejpam-534	597	47	.	.	PUNCT
ejpam-534	598	1	theorem	theorem	VERB
ejpam-534	598	2	7	7	NUM
ejpam-534	598	3	(	(	PUNCT
ejpam-534	598	4	strong	strong	ADJ
ejpam-534	598	5	duality	duality	NOUN
ejpam-534	598	6	)	)	PUNCT
ejpam-534	598	7	.	.	PUNCT
ejpam-534	599	1	let	let	AUX
ejpam-534	599	2	x̄(t	x̄(t	PRON
ejpam-534	599	3	)	)	PUNCT
ejpam-534	599	4	be	be	AUX
ejpam-534	599	5	normal	normal	ADJ
ejpam-534	599	6	and	and	CCONJ
ejpam-534	599	7	is	be	AUX
ejpam-534	599	8	an	an	DET
ejpam-534	599	9	efficient	efficient	ADJ
ejpam-534	599	10	solution	solution	NOUN
ejpam-534	599	11	of	of	ADP
ejpam-534	599	12	(	(	PUNCT
ejpam-534	599	13	p	p	NOUN
ejpam-534	599	14	)	)	PUNCT
ejpam-534	599	15	.	.	PUNCT
ejpam-534	600	1	then	then	ADV
ejpam-534	600	2	,	,	PUNCT
ejpam-534	600	3	there	there	PRON
ejpam-534	600	4	exist	exist	VERB
ejpam-534	600	5	λ̄	λ̄	DET
ejpam-534	600	6	∈	∈	PROPN
ejpam-534	600	7	rk	rk	NOUN
ejpam-534	600	8	,	,	PUNCT
ejpam-534	600	9	a	a	DET
ejpam-534	600	10	piecewise	piecewise	NOUN
ejpam-534	600	11	smooth	smooth	ADJ
ejpam-534	600	12	function	function	NOUN
ejpam-534	600	13	ȳ	ȳ	NOUN
ejpam-534	600	14	:	:	PUNCT
ejpam-534	601	1	i	i	PRON
ejpam-534	601	2	→	→	PUNCT
ejpam-534	601	3	rm	rm	NOUN
ejpam-534	601	4	such	such	ADJ
ejpam-534	601	5	that	that	PRON
ejpam-534	601	6	(	(	PUNCT
ejpam-534	601	7	x̄(t	x̄(t	PROPN
ejpam-534	601	8	)	)	PUNCT
ejpam-534	601	9	,	,	PUNCT
ejpam-534	601	10	λ̄	λ̄	ADP
ejpam-534	601	11	,	,	PUNCT
ejpam-534	601	12	ȳ(t	ȳ(t	NOUN
ejpam-534	601	13	)	)	PUNCT
ejpam-534	601	14	,	,	PUNCT
ejpam-534	601	15	p̄(t	p̄(t	PROPN
ejpam-534	601	16	)	)	PUNCT
ejpam-534	601	17	=	=	SYM
ejpam-534	601	18	0	0	X
ejpam-534	601	19	)	)	PUNCT
ejpam-534	601	20	is	be	AUX
ejpam-534	601	21	feasible	feasible	ADJ
ejpam-534	601	22	for	for	ADP
ejpam-534	601	23	(	(	PUNCT
ejpam-534	601	24	mwd	mwd	PROPN
ejpam-534	601	25	)	)	PUNCT
ejpam-534	601	26	and	and	CCONJ
ejpam-534	601	27	the	the	DET
ejpam-534	601	28	two	two	NUM
ejpam-534	601	29	objective	objective	ADJ
ejpam-534	601	30	functionals	functional	NOUN
ejpam-534	601	31	are	be	AUX
ejpam-534	601	32	equal	equal	ADJ
ejpam-534	601	33	.	.	PUNCT
ejpam-534	602	1	furthermore	furthermore	ADV
ejpam-534	602	2	,	,	PUNCT
ejpam-534	602	3	if	if	SCONJ
ejpam-534	602	4	the	the	DET
ejpam-534	602	5	weak	weak	ADJ
ejpam-534	602	6	duality	duality	NOUN
ejpam-534	602	7	holds	hold	VERB
ejpam-534	602	8	for	for	ADP
ejpam-534	602	9	all	all	DET
ejpam-534	602	10	feasible	feasible	ADJ
ejpam-534	602	11	solutions	solution	NOUN
ejpam-534	602	12	of	of	ADP
ejpam-534	602	13	(	(	PUNCT
ejpam-534	602	14	p	p	NOUN
ejpam-534	602	15	)	)	PUNCT
ejpam-534	602	16	and	and	CCONJ
ejpam-534	602	17	(	(	PUNCT
ejpam-534	602	18	mwd	mwd	PROPN
ejpam-534	602	19	)	)	PUNCT
ejpam-534	602	20	,	,	PUNCT
ejpam-534	602	21	then	then	ADV
ejpam-534	602	22	(	(	PUNCT
ejpam-534	602	23	x̄(t	x̄(t	PROPN
ejpam-534	602	24	)	)	PUNCT
ejpam-534	602	25	,	,	PUNCT
ejpam-534	602	26	λ̄	λ̄	ADP
ejpam-534	602	27	,	,	PUNCT
ejpam-534	602	28	ȳ(t	ȳ(t	NOUN
ejpam-534	602	29	)	)	PUNCT
ejpam-534	602	30	,	,	PUNCT
ejpam-534	602	31	p̄(t	p̄(t	PROPN
ejpam-534	602	32	)	)	PUNCT
ejpam-534	602	33	=	=	SYM
ejpam-534	603	1	0	0	X
ejpam-534	603	2	)	)	PUNCT
ejpam-534	603	3	is	be	AUX
ejpam-534	603	4	an	an	DET
ejpam-534	603	5	efficient	efficient	ADJ
ejpam-534	603	6	solution	solution	NOUN
ejpam-534	603	7	of	of	ADP
ejpam-534	603	8	the	the	DET
ejpam-534	603	9	problem	problem	NOUN
ejpam-534	603	10	(	(	PUNCT
ejpam-534	603	11	mwd	mwd	PROPN
ejpam-534	603	12	)	)	PUNCT
ejpam-534	603	13	.	.	PUNCT
ejpam-534	604	1	proof	proof	NOUN
ejpam-534	604	2	.	.	PUNCT
ejpam-534	605	1	since	since	SCONJ
ejpam-534	605	2	x̄(t	x̄(t	PROPN
ejpam-534	605	3	)	)	PUNCT
ejpam-534	605	4	is	be	AUX
ejpam-534	605	5	normal	normal	ADJ
ejpam-534	605	6	and	and	CCONJ
ejpam-534	605	7	an	an	DET
ejpam-534	605	8	efficient	efficient	ADJ
ejpam-534	605	9	solution	solution	NOUN
ejpam-534	605	10	of	of	ADP
ejpam-534	605	11	(	(	PUNCT
ejpam-534	605	12	p	p	NOUN
ejpam-534	605	13	)	)	PUNCT
ejpam-534	605	14	,	,	PUNCT
ejpam-534	605	15	therefore	therefore	ADV
ejpam-534	605	16	by	by	ADP
ejpam-534	605	17	theorem	theorem	NOUN
ejpam-534	605	18	4	4	NUM
ejpam-534	605	19	,	,	PUNCT
ejpam-534	605	20	there	there	PRON
ejpam-534	605	21	exist	exist	VERB
ejpam-534	605	22	λ̄	λ̄	DET
ejpam-534	605	23	∈	∈	PROPN
ejpam-534	605	24	rk	rk	NOUN
ejpam-534	605	25	and	and	CCONJ
ejpam-534	605	26	a	a	DET
ejpam-534	605	27	piecewise	piecewise	NOUN
ejpam-534	605	28	smooth	smooth	ADJ
ejpam-534	605	29	function	function	NOUN
ejpam-534	605	30	ȳ(t	ȳ(t	NOUN
ejpam-534	605	31	)	)	PUNCT
ejpam-534	605	32	∈	∈	PROPN
ejpam-534	605	33	rm	rm	NOUN
ejpam-534	605	34	satisfying	satisfying	PROPN
ejpam-534	606	1	k∑	k∑	PROPN
ejpam-534	606	2	i=1	i=1	PROPN
ejpam-534	607	1	λ̄i	λ̄i	PROPN
ejpam-534	607	2	(	(	PUNCT
ejpam-534	607	3	f	f	NOUN
ejpam-534	607	4	i	i	PRON
ejpam-534	607	5	x	x	X
ejpam-534	607	6	(	(	PUNCT
ejpam-534	607	7	t	t	PROPN
ejpam-534	607	8	,	,	PUNCT
ejpam-534	607	9	x̄	x̄	NOUN
ejpam-534	607	10	,	,	PUNCT
ejpam-534	607	11	˙̄x)−	˙̄x)−	PROPN
ejpam-534	608	1	d	d	X
ejpam-534	608	2	f	f	X
ejpam-534	609	1	i	i	PRON
ejpam-534	609	2	ẋ	ẋ	PROPN
ejpam-534	610	1	(	(	PUNCT
ejpam-534	610	2	t	t	PROPN
ejpam-534	610	3	,	,	PUNCT
ejpam-534	610	4	x̄	x̄	NOUN
ejpam-534	610	5	,	,	PUNCT
ejpam-534	610	6	˙̄x))+	˙̄x))+	ADP
ejpam-534	610	7	gx(t	gx(t	PROPN
ejpam-534	610	8	,	,	PUNCT
ejpam-534	610	9	x̄	x̄	NOUN
ejpam-534	610	10	,	,	PUNCT
ejpam-534	610	11	˙̄x	˙̄x	PRON
ejpam-534	610	12	)	)	PUNCT
ejpam-534	610	13	ȳ(t)−	ȳ(t)−	PROPN
ejpam-534	610	14	d(g	d(g	PROPN
ejpam-534	610	15	ẋ(t	ẋ(t	PROPN
ejpam-534	610	16	,	,	PUNCT
ejpam-534	610	17	x̄	x̄	NOUN
ejpam-534	610	18	,	,	PUNCT
ejpam-534	610	19	˙̄x	˙̄x	NOUN
ejpam-534	610	20	)	)	PUNCT
ejpam-534	610	21	ȳ(t	ȳ(t	NOUN
ejpam-534	610	22	)	)	PUNCT
ejpam-534	610	23	)	)	PUNCT
ejpam-534	611	1	=	=	PUNCT
ejpam-534	611	2	0	0	NUM
ejpam-534	611	3	,	,	PUNCT
ejpam-534	611	4	t	t	PROPN
ejpam-534	611	5	∈	∈	PROPN
ejpam-534	612	1	i	i	PRON
ejpam-534	612	2	,	,	PUNCT
ejpam-534	612	3	ȳ(t)t	ȳ(t)t	PROPN
ejpam-534	612	4	g(t	g(t	PROPN
ejpam-534	612	5	,	,	PUNCT
ejpam-534	612	6	x̄	x̄	NOUN
ejpam-534	612	7	,	,	PUNCT
ejpam-534	612	8	˙̄x	˙̄x	PRON
ejpam-534	612	9	)	)	PUNCT
ejpam-534	612	10	=	=	SYM
ejpam-534	612	11	0	0	NUM
ejpam-534	612	12	,	,	PUNCT
ejpam-534	612	13	t	t	PROPN
ejpam-534	612	14	∈	∈	PROPN
ejpam-534	613	1	i	i	PRON
ejpam-534	613	2	,	,	PUNCT
ejpam-534	613	3	λ̄≥	λ̄≥	NOUN
ejpam-534	613	4	0	0	NUM
ejpam-534	613	5	,	,	PUNCT
ejpam-534	613	6	t	t	PROPN
ejpam-534	613	7	∈	∈	PROPN
ejpam-534	614	1	i	i	PRON
ejpam-534	614	2	,	,	PUNCT
ejpam-534	614	3	ȳ(t)≧	ȳ(t)≧	PROPN
ejpam-534	614	4	0	0	NUM
ejpam-534	614	5	,	,	PUNCT
ejpam-534	614	6	t	t	PROPN
ejpam-534	614	7	∈	∈	PROPN
ejpam-534	615	1	i	i	PRON
ejpam-534	615	2	.	.	PUNCT
ejpam-534	616	1	hence	hence	ADV
ejpam-534	616	2	(	(	PUNCT
ejpam-534	616	3	x̄(t	x̄(t	PROPN
ejpam-534	616	4	)	)	PUNCT
ejpam-534	616	5	,	,	PUNCT
ejpam-534	616	6	λ̄	λ̄	ADP
ejpam-534	616	7	,	,	PUNCT
ejpam-534	616	8	ȳ(t	ȳ(t	NOUN
ejpam-534	616	9	)	)	PUNCT
ejpam-534	616	10	,	,	PUNCT
ejpam-534	616	11	p̄(t	p̄(t	PROPN
ejpam-534	616	12	)	)	PUNCT
ejpam-534	616	13	=	=	SYM
ejpam-534	616	14	0	0	X
ejpam-534	616	15	)	)	PUNCT
ejpam-534	616	16	satisfies	satisfy	VERB
ejpam-534	616	17	the	the	DET
ejpam-534	616	18	constraints	constraint	NOUN
ejpam-534	616	19	of	of	ADP
ejpam-534	616	20	(	(	PUNCT
ejpam-534	616	21	mwd	mwd	PROPN
ejpam-534	616	22	)	)	PUNCT
ejpam-534	616	23	and	and	CCONJ
ejpam-534	616	24	thus	thus	ADV
ejpam-534	616	25	the	the	DET
ejpam-534	616	26	two	two	NUM
ejpam-534	616	27	objective	objective	ADJ
ejpam-534	616	28	functionals	functional	NOUN
ejpam-534	616	29	have	have	VERB
ejpam-534	616	30	the	the	DET
ejpam-534	616	31	same	same	ADJ
ejpam-534	616	32	value	value	NOUN
ejpam-534	616	33	.	.	PUNCT
ejpam-534	617	1	now	now	ADV
ejpam-534	617	2	,	,	PUNCT
ejpam-534	617	3	we	we	PRON
ejpam-534	617	4	claim	claim	VERB
ejpam-534	617	5	that	that	SCONJ
ejpam-534	617	6	(	(	PUNCT
ejpam-534	617	7	x̄(t	x̄(t	NOUN
ejpam-534	617	8	)	)	PUNCT
ejpam-534	617	9	,	,	PUNCT
ejpam-534	617	10	λ̄	λ̄	ADP
ejpam-534	617	11	,	,	PUNCT
ejpam-534	617	12	ȳ(t	ȳ(t	NOUN
ejpam-534	617	13	)	)	PUNCT
ejpam-534	617	14	,	,	PUNCT
ejpam-534	617	15	p̄(t	p̄(t	PROPN
ejpam-534	617	16	)	)	PUNCT
ejpam-534	617	17	=	=	SYM
ejpam-534	617	18	0	0	X
ejpam-534	617	19	)	)	PUNCT
ejpam-534	617	20	is	be	AUX
ejpam-534	617	21	an	an	DET
ejpam-534	617	22	efficient	efficient	ADJ
ejpam-534	617	23	solution	solution	NOUN
ejpam-534	617	24	of	of	ADP
ejpam-534	617	25	(	(	PUNCT
ejpam-534	617	26	mwd	mwd	PROPN
ejpam-534	617	27	)	)	PUNCT
ejpam-534	617	28	.	.	PUNCT
ejpam-534	618	1	if	if	SCONJ
ejpam-534	618	2	not	not	PART
ejpam-534	618	3	,	,	PUNCT
ejpam-534	618	4	then	then	ADV
ejpam-534	618	5	there	there	PRON
ejpam-534	618	6	exists	exist	VERB
ejpam-534	618	7	(	(	PUNCT
ejpam-534	618	8	û(t	û(t	NOUN
ejpam-534	618	9	)	)	PUNCT
ejpam-534	618	10	,	,	PUNCT
ejpam-534	618	11	λ̂	λ̂	NUM
ejpam-534	618	12	,	,	PUNCT
ejpam-534	618	13	ŷ(t	ŷ(t	NOUN
ejpam-534	618	14	)	)	PUNCT
ejpam-534	618	15	,	,	PUNCT
ejpam-534	618	16	p̂(t	p̂(t	NOUN
ejpam-534	618	17	)	)	PUNCT
ejpam-534	618	18	)	)	PUNCT
ejpam-534	619	1	∈	∈	PROPN
ejpam-534	619	2	y	y	PROPN
ejpam-534	619	3	,	,	PUNCT
ejpam-534	619	4	such	such	ADJ
ejpam-534	619	5	that	that	SCONJ
ejpam-534	619	6	(	(	PUNCT
ejpam-534	619	7	∫	∫	PROPN
ejpam-534	619	8	(	(	PUNCT
ejpam-534	619	9	f	f	PROPN
ejpam-534	619	10	1(t	1(t	NUM
ejpam-534	619	11	,	,	PUNCT
ejpam-534	619	12	û	û	NUM
ejpam-534	619	13	,	,	PUNCT
ejpam-534	619	14	˙̂u)−	˙̂u)−	NOUN
ejpam-534	619	15	1	1	NUM
ejpam-534	619	16	2	2	NUM
ejpam-534	619	17	p̂(t)t	p̂(t)t	PROPN
ejpam-534	619	18	a1(t	a1(t	PROPN
ejpam-534	619	19	,	,	PUNCT
ejpam-534	619	20	û	û	PROPN
ejpam-534	619	21	,	,	PUNCT
ejpam-534	619	22	˙̂u	˙̂u	PROPN
ejpam-534	619	23	,	,	PUNCT
ejpam-534	619	24	¨̂u	¨̂u	ADV
ejpam-534	619	25	,	,	PUNCT
ejpam-534	619	26	...	...	PUNCT
ejpam-534	619	27	û	û	NUM
ejpam-534	619	28	,	,	PUNCT
ejpam-534	619	29	....	....	PUNCT
ejpam-534	619	30	û	û	NUM
ejpam-534	619	31	)	)	PUNCT
ejpam-534	619	32	p̂(t))d	p̂(t))d	NOUN
ejpam-534	619	33	t	t	PROPN
ejpam-534	619	34	,	,	PUNCT
ejpam-534	619	35	.	.	PUNCT
ejpam-534	619	36	.	.	PUNCT
ejpam-534	619	37	.	.	PUNCT
ejpam-534	620	1	,	,	PUNCT
ejpam-534	620	2	∫	∫	PROPN
ejpam-534	620	3	(	(	PUNCT
ejpam-534	620	4	f	f	PROPN
ejpam-534	620	5	k(t	k(t	PROPN
ejpam-534	620	6	,	,	PUNCT
ejpam-534	620	7	û	û	NUM
ejpam-534	620	8	,	,	PUNCT
ejpam-534	620	9	˙̂u)−	˙̂u)−	NOUN
ejpam-534	620	10	1	1	NUM
ejpam-534	620	11	2	2	NUM
ejpam-534	620	12	p̂(t)t	p̂(t)t	PROPN
ejpam-534	620	13	ak(t	ak(t	X
ejpam-534	620	14	,	,	PUNCT
ejpam-534	620	15	û	û	NUM
ejpam-534	620	16	,	,	PUNCT
ejpam-534	620	17	˙̂u	˙̂u	PROPN
ejpam-534	620	18	,	,	PUNCT
ejpam-534	620	19	¨̂u	¨̂u	ADV
ejpam-534	620	20	,	,	PUNCT
ejpam-534	620	21	...	...	PUNCT
ejpam-534	620	22	û	û	NUM
ejpam-534	620	23	,	,	PUNCT
ejpam-534	620	24	....	....	PUNCT
ejpam-534	620	25	û	û	NUM
ejpam-534	620	26	)	)	PUNCT
ejpam-534	620	27	p̂(t))d	p̂(t))d	NOUN
ejpam-534	620	28	t	t	PROPN
ejpam-534	620	29	)	)	PUNCT
ejpam-534	620	30	≥	≥	PROPN
ejpam-534	620	31	(	(	PUNCT
ejpam-534	620	32	∫	∫	PROPN
ejpam-534	620	33	(	(	PUNCT
ejpam-534	620	34	f	f	PROPN
ejpam-534	620	35	1(t	1(t	NUM
ejpam-534	620	36	,	,	PUNCT
ejpam-534	620	37	x̄	x̄	NOUN
ejpam-534	620	38	,	,	PUNCT
ejpam-534	620	39	˙̄x)−	˙̄x)−	PROPN
ejpam-534	620	40	1	1	NUM
ejpam-534	620	41	2	2	NUM
ejpam-534	620	42	p̄(t)t	p̄(t)t	NOUN
ejpam-534	620	43	a1(t	a1(t	PROPN
ejpam-534	620	44	,	,	PUNCT
ejpam-534	620	45	x̄	x̄	NOUN
ejpam-534	620	46	,	,	PUNCT
ejpam-534	620	47	˙̄x	˙̄x	X
ejpam-534	620	48	,	,	PUNCT
ejpam-534	620	49	¨̄x	¨̄x	VERB
ejpam-534	620	50	,	,	PUNCT
ejpam-534	620	51	...	...	PUNCT
ejpam-534	621	1	x̄	x̄	NOUN
ejpam-534	621	2	,	,	PUNCT
ejpam-534	621	3	....	....	PUNCT
ejpam-534	621	4	x̄	x̄	X
ejpam-534	621	5	)	)	PUNCT
ejpam-534	621	6	p̄(t))d	p̄(t))d	NOUN
ejpam-534	621	7	t	t	NOUN
ejpam-534	621	8	,	,	PUNCT
ejpam-534	621	9	.	.	PUNCT
ejpam-534	621	10	.	.	PUNCT
ejpam-534	621	11	.	.	PUNCT
ejpam-534	622	1	,	,	PUNCT
ejpam-534	622	2	∫	∫	PROPN
ejpam-534	622	3	(	(	PUNCT
ejpam-534	622	4	f	f	PROPN
ejpam-534	622	5	k(t	k(t	PROPN
ejpam-534	622	6	,	,	PUNCT
ejpam-534	622	7	x̄	x̄	NOUN
ejpam-534	622	8	,	,	PUNCT
ejpam-534	622	9	˙̄x)−	˙̄x)−	PROPN
ejpam-534	622	10	1	1	NUM
ejpam-534	622	11	2	2	NUM
ejpam-534	622	12	p̄(t)t	p̄(t)t	NOUN
ejpam-534	622	13	ak(t	ak(t	PUNCT
ejpam-534	622	14	,	,	PUNCT
ejpam-534	622	15	x̄	x̄	NOUN
ejpam-534	622	16	,	,	PUNCT
ejpam-534	622	17	˙̄x	˙̄x	X
ejpam-534	622	18	,	,	PUNCT
ejpam-534	622	19	¨̄x	¨̄x	VERB
ejpam-534	622	20	,	,	PUNCT
ejpam-534	622	21	...	...	PUNCT
ejpam-534	623	1	x̄	x̄	NOUN
ejpam-534	623	2	,	,	PUNCT
ejpam-534	623	3	....	....	PUNCT
ejpam-534	623	4	x̄	x̄	X
ejpam-534	623	5	)	)	PUNCT
ejpam-534	623	6	p̄(t))d	p̄(t))d	NOUN
ejpam-534	623	7	t	t	NOUN
ejpam-534	623	8	)	)	PUNCT
ejpam-534	623	9	.	.	PUNCT
ejpam-534	624	1	as	as	ADP
ejpam-534	624	2	p̄(t	p̄(t	ADJ
ejpam-534	624	3	)	)	PUNCT
ejpam-534	624	4	=	=	SYM
ejpam-534	624	5	0	0	NUM
ejpam-534	624	6	,	,	PUNCT
ejpam-534	624	7	we	we	PRON
ejpam-534	624	8	have	have	VERB
ejpam-534	624	9	(	(	PUNCT
ejpam-534	624	10	∫	∫	PROPN
ejpam-534	624	11	(	(	PUNCT
ejpam-534	624	12	f	f	PROPN
ejpam-534	624	13	1(t	1(t	NUM
ejpam-534	624	14	,	,	PUNCT
ejpam-534	624	15	û	û	NUM
ejpam-534	624	16	,	,	PUNCT
ejpam-534	624	17	˙̂u)−	˙̂u)−	NOUN
ejpam-534	624	18	1	1	NUM
ejpam-534	624	19	2	2	NUM
ejpam-534	624	20	p̂(t)t	p̂(t)t	PROPN
ejpam-534	624	21	a1(t	a1(t	PROPN
ejpam-534	624	22	,	,	PUNCT
ejpam-534	624	23	û	û	PROPN
ejpam-534	624	24	,	,	PUNCT
ejpam-534	624	25	˙̂u	˙̂u	PROPN
ejpam-534	624	26	,	,	PUNCT
ejpam-534	624	27	¨̂u	¨̂u	ADV
ejpam-534	624	28	,	,	PUNCT
ejpam-534	624	29	...	...	PUNCT
ejpam-534	624	30	û	û	NUM
ejpam-534	624	31	,	,	PUNCT
ejpam-534	624	32	....	....	PUNCT
ejpam-534	624	33	û	û	NUM
ejpam-534	624	34	)	)	PUNCT
ejpam-534	624	35	p̂(t))d	p̂(t))d	NOUN
ejpam-534	624	36	t	t	PROPN
ejpam-534	624	37	,	,	PUNCT
ejpam-534	624	38	.	.	PUNCT
ejpam-534	624	39	.	.	PUNCT
ejpam-534	624	40	.	.	PUNCT
ejpam-534	625	1	,	,	PUNCT
ejpam-534	625	2	∫	∫	PROPN
ejpam-534	625	3	(	(	PUNCT
ejpam-534	625	4	f	f	PROPN
ejpam-534	625	5	k(t	k(t	PROPN
ejpam-534	625	6	,	,	PUNCT
ejpam-534	625	7	û	û	NUM
ejpam-534	625	8	,	,	PUNCT
ejpam-534	625	9	˙̂u)−	˙̂u)−	NOUN
ejpam-534	625	10	1	1	NUM
ejpam-534	625	11	2	2	NUM
ejpam-534	625	12	p̂(t)t	p̂(t)t	PROPN
ejpam-534	625	13	ak(t	ak(t	X
ejpam-534	625	14	,	,	PUNCT
ejpam-534	625	15	û	û	NUM
ejpam-534	625	16	,	,	PUNCT
ejpam-534	625	17	˙̂u	˙̂u	PROPN
ejpam-534	625	18	,	,	PUNCT
ejpam-534	625	19	¨̂u	¨̂u	ADV
ejpam-534	625	20	,	,	PUNCT
ejpam-534	625	21	...	...	PUNCT
ejpam-534	625	22	û	û	NUM
ejpam-534	625	23	,	,	PUNCT
ejpam-534	625	24	....	....	PUNCT
ejpam-534	625	25	û	û	NUM
ejpam-534	625	26	)	)	PUNCT
ejpam-534	625	27	p̂(t))d	p̂(t))d	NOUN
ejpam-534	625	28	t	t	PROPN
ejpam-534	625	29	)	)	PUNCT
ejpam-534	625	30	≥	≥	PROPN
ejpam-534	625	31	(	(	PUNCT
ejpam-534	625	32	∫	∫	PROPN
ejpam-534	625	33	f	f	PROPN
ejpam-534	625	34	1(t	1(t	NUM
ejpam-534	625	35	,	,	PUNCT
ejpam-534	625	36	x̄	x̄	NOUN
ejpam-534	625	37	,	,	PUNCT
ejpam-534	625	38	˙̄x)d	˙̄x)d	PROPN
ejpam-534	625	39	t	t	PROPN
ejpam-534	625	40	,	,	PUNCT
ejpam-534	625	41	.	.	PUNCT
ejpam-534	625	42	.	.	PUNCT
ejpam-534	626	1	.	.	PUNCT
ejpam-534	627	1	,	,	PUNCT
ejpam-534	627	2	∫	∫	PROPN
ejpam-534	627	3	f	f	PROPN
ejpam-534	627	4	k(t	k(t	PROPN
ejpam-534	627	5	,	,	PUNCT
ejpam-534	627	6	x̄	x̄	NOUN
ejpam-534	627	7	,	,	PUNCT
ejpam-534	627	8	˙̄x)d	˙̄x)d	PROPN
ejpam-534	627	9	t	t	PROPN
ejpam-534	627	10	)	)	PUNCT
ejpam-534	627	11	,	,	PUNCT
ejpam-534	627	12	t.	t.	PROPN
ejpam-534	627	13	gulati	gulati	PROPN
ejpam-534	627	14	and	and	CCONJ
ejpam-534	627	15	g.	g.	PROPN
ejpam-534	627	16	mehndiratta	mehndiratta	PROPN
ejpam-534	627	17	/	/	SYM
ejpam-534	627	18	eur	eur	PROPN
ejpam-534	627	19	.	.	PUNCT
ejpam-534	628	1	j.	j.	PROPN
ejpam-534	628	2	pure	pure	PROPN
ejpam-534	628	3	appl	appl	PROPN
ejpam-534	628	4	.	.	PROPN
ejpam-534	628	5	math	math	PROPN
ejpam-534	628	6	,	,	PUNCT
ejpam-534	628	7	3	3	NUM
ejpam-534	628	8	(	(	PUNCT
ejpam-534	628	9	2010	2010	NUM
ejpam-534	628	10	)	)	PUNCT
ejpam-534	628	11	,	,	PUNCT
ejpam-534	628	12	786	786	NUM
ejpam-534	628	13	-	-	SYM
ejpam-534	628	14	805	805	NUM
ejpam-534	628	15	800	800	NUM
ejpam-534	628	16	which	which	PRON
ejpam-534	628	17	contradicts	contradict	VERB
ejpam-534	628	18	the	the	DET
ejpam-534	628	19	weak	weak	ADJ
ejpam-534	628	20	duality	duality	NOUN
ejpam-534	628	21	theorem	theorem	VERB
ejpam-534	628	22	.	.	PUNCT
ejpam-534	629	1	hence	hence	ADV
ejpam-534	629	2	(	(	PUNCT
ejpam-534	629	3	x̄(t	x̄(t	PROPN
ejpam-534	629	4	)	)	PUNCT
ejpam-534	629	5	,	,	PUNCT
ejpam-534	629	6	λ̄	λ̄	ADP
ejpam-534	629	7	,	,	PUNCT
ejpam-534	629	8	ȳ(t	ȳ(t	NOUN
ejpam-534	629	9	)	)	PUNCT
ejpam-534	629	10	,	,	PUNCT
ejpam-534	629	11	p̄(t	p̄(t	PROPN
ejpam-534	629	12	)	)	PUNCT
ejpam-534	629	13	=	=	SYM
ejpam-534	630	1	0	0	X
ejpam-534	630	2	)	)	PUNCT
ejpam-534	630	3	is	be	AUX
ejpam-534	630	4	an	an	DET
ejpam-534	630	5	efficient	efficient	ADJ
ejpam-534	630	6	solution	solution	NOUN
ejpam-534	630	7	of	of	ADP
ejpam-534	630	8	(	(	PUNCT
ejpam-534	630	9	mwd	mwd	PROPN
ejpam-534	630	10	)	)	PUNCT
ejpam-534	630	11	.	.	PUNCT
ejpam-534	631	1	theorem	theorem	ADJ
ejpam-534	631	2	8	8	NUM
ejpam-534	631	3	(	(	PUNCT
ejpam-534	631	4	converse	converse	NOUN
ejpam-534	631	5	duality	duality	NOUN
ejpam-534	631	6	)	)	PUNCT
ejpam-534	631	7	.	.	PUNCT
ejpam-534	632	1	let	let	VERB
ejpam-534	632	2	(	(	PUNCT
ejpam-534	632	3	ū(t	ū(t	ADJ
ejpam-534	632	4	)	)	PUNCT
ejpam-534	632	5	,	,	PUNCT
ejpam-534	632	6	λ̄	λ̄	ADP
ejpam-534	632	7	,	,	PUNCT
ejpam-534	632	8	ȳ(t	ȳ(t	NOUN
ejpam-534	632	9	)	)	PUNCT
ejpam-534	632	10	,	,	PUNCT
ejpam-534	632	11	p̄(t	p̄(t	PROPN
ejpam-534	632	12	)	)	PUNCT
ejpam-534	632	13	)	)	PUNCT
ejpam-534	633	1	be	be	AUX
ejpam-534	633	2	an	an	DET
ejpam-534	633	3	efficient	efficient	ADJ
ejpam-534	633	4	solution	solution	NOUN
ejpam-534	633	5	of	of	ADP
ejpam-534	633	6	(	(	PUNCT
ejpam-534	633	7	mwd	mwd	PROPN
ejpam-534	633	8	)	)	PUNCT
ejpam-534	633	9	for	for	ADP
ejpam-534	633	10	which	which	PRON
ejpam-534	633	11	(	(	PUNCT
ejpam-534	633	12	c1	c1	PROPN
ejpam-534	633	13	)	)	PUNCT
ejpam-534	633	14	the	the	DET
ejpam-534	633	15	vectors	vector	NOUN
ejpam-534	633	16	{	{	PUNCT
ejpam-534	633	17	ai	ai	VERB
ejpam-534	633	18	m	m	PROPN
ejpam-534	633	19	,	,	PUNCT
ejpam-534	633	20	bm	bm	PROPN
ejpam-534	633	21	,	,	PUNCT
ejpam-534	633	22	t	t	PROPN
ejpam-534	633	23	∈	∈	PROPN
ejpam-534	634	1	i	i	PRON
ejpam-534	634	2	,	,	PUNCT
ejpam-534	634	3	i	i	PROPN
ejpam-534	634	4	∈	∈	PROPN
ejpam-534	634	5	k	k	PROPN
ejpam-534	634	6	,	,	PUNCT
ejpam-534	634	7	m	m	VERB
ejpam-534	634	8	=	=	SYM
ejpam-534	634	9	1,2	1,2	NUM
ejpam-534	634	10	,	,	PUNCT
ejpam-534	634	11	.	.	PUNCT
ejpam-534	634	12	.	.	PUNCT
ejpam-534	634	13	.	.	PUNCT
ejpam-534	635	1	,	,	PUNCT
ejpam-534	635	2	n	n	CCONJ
ejpam-534	635	3	}	}	PUNCT
ejpam-534	635	4	are	be	AUX
ejpam-534	635	5	linearly	linearly	ADV
ejpam-534	635	6	independent	independent	ADJ
ejpam-534	635	7	,	,	PUNCT
ejpam-534	635	8	where	where	SCONJ
ejpam-534	635	9	ai	ai	AUX
ejpam-534	635	10	m	m	VERB
ejpam-534	635	11	is	be	AUX
ejpam-534	635	12	the	the	DET
ejpam-534	635	13	mth	mth	NOUN
ejpam-534	635	14	row	row	NOUN
ejpam-534	635	15	of	of	ADP
ejpam-534	635	16	ai(t	ai(t	NOUN
ejpam-534	635	17	,	,	PUNCT
ejpam-534	635	18	ū	ū	NOUN
ejpam-534	635	19	,	,	PUNCT
ejpam-534	635	20	˙̄u	˙̄u	NOUN
ejpam-534	635	21	,	,	PUNCT
ejpam-534	635	22	¨̄u	¨̄u	NOUN
ejpam-534	635	23	,	,	PUNCT
ejpam-534	635	24	...	...	PUNCT
ejpam-534	635	25	ū	ū	NOUN
ejpam-534	635	26	,	,	PUNCT
ejpam-534	635	27	....	....	PUNCT
ejpam-534	635	28	ū	ū	PROPN
ejpam-534	635	29	)	)	PUNCT
ejpam-534	635	30	and	and	CCONJ
ejpam-534	635	31	bm	bm	PROPN
ejpam-534	635	32	is	be	AUX
ejpam-534	635	33	the	the	DET
ejpam-534	635	34	mth	mth	NOUN
ejpam-534	635	35	row	row	NOUN
ejpam-534	635	36	of	of	ADP
ejpam-534	635	37	b(t	b(t	PROPN
ejpam-534	635	38	,	,	PUNCT
ejpam-534	635	39	ū	ū	NOUN
ejpam-534	635	40	,	,	PUNCT
ejpam-534	635	41	˙̄u	˙̄u	NOUN
ejpam-534	635	42	,	,	PUNCT
ejpam-534	635	43	¨̄u	¨̄u	NOUN
ejpam-534	635	44	,	,	PUNCT
ejpam-534	635	45	...	...	PUNCT
ejpam-534	635	46	ū	ū	NOUN
ejpam-534	635	47	,	,	PUNCT
ejpam-534	635	48	....	....	PUNCT
ejpam-534	635	49	ū	ū	NOUN
ejpam-534	635	50	,	,	PUNCT
ejpam-534	635	51	ȳ(t	ȳ(t	PROPN
ejpam-534	635	52	)	)	PUNCT
ejpam-534	635	53	,	,	PUNCT
ejpam-534	635	54	˙̄y(t	˙̄y(t	PUNCT
ejpam-534	635	55	)	)	PUNCT
ejpam-534	635	56	,	,	PUNCT
ejpam-534	635	57	¨̄y(t	¨̄y(t	NUM
ejpam-534	635	58	)	)	PUNCT
ejpam-534	635	59	,	,	PUNCT
ejpam-534	635	60	...	...	PUNCT
ejpam-534	636	1	ȳ	ȳ	PROPN
ejpam-534	636	2	(	(	PUNCT
ejpam-534	636	3	t	t	PROPN
ejpam-534	636	4	)	)	PUNCT
ejpam-534	636	5	)	)	PUNCT
ejpam-534	636	6	,	,	PUNCT
ejpam-534	636	7	(	(	PUNCT
ejpam-534	636	8	c2	c2	PROPN
ejpam-534	636	9	)	)	PUNCT
ejpam-534	636	10	f	f	PROPN
ejpam-534	637	1	i	i	PRON
ejpam-534	637	2	x	x	X
ejpam-534	637	3	(	(	PUNCT
ejpam-534	637	4	t	t	PROPN
ejpam-534	637	5	,	,	PUNCT
ejpam-534	637	6	ū	ū	NOUN
ejpam-534	637	7	,	,	PUNCT
ejpam-534	637	8	˙̄u)−	˙̄u)−	PROPN
ejpam-534	637	9	d	d	PROPN
ejpam-534	637	10	f	f	PROPN
ejpam-534	638	1	i	i	PRON
ejpam-534	638	2	ẋ	ẋ	PROPN
ejpam-534	639	1	(	(	PUNCT
ejpam-534	639	2	t	t	PROPN
ejpam-534	639	3	,	,	PUNCT
ejpam-534	639	4	ū	ū	NOUN
ejpam-534	639	5	,	,	PUNCT
ejpam-534	639	6	˙̄u	˙̄u	NOUN
ejpam-534	639	7	)	)	PUNCT
ejpam-534	639	8	,	,	PUNCT
ejpam-534	640	1	t	t	PROPN
ejpam-534	640	2	∈	∈	PROPN
ejpam-534	641	1	i	i	PRON
ejpam-534	641	2	,	,	PUNCT
ejpam-534	641	3	i	i	PROPN
ejpam-534	641	4	∈	∈	PROPN
ejpam-534	641	5	k	k	PROPN
ejpam-534	641	6	,	,	PUNCT
ejpam-534	641	7	are	be	AUX
ejpam-534	641	8	linearly	linearly	ADV
ejpam-534	641	9	independent	independent	ADJ
ejpam-534	641	10	,	,	PUNCT
ejpam-534	641	11	and	and	CCONJ
ejpam-534	641	12	(	(	PUNCT
ejpam-534	641	13	c3	c3	PROPN
ejpam-534	641	14	)	)	PUNCT
ejpam-534	641	15	for	for	ADP
ejpam-534	641	16	t	t	PROPN
ejpam-534	641	17	∈	∈	PROPN
ejpam-534	642	1	i	i	PRON
ejpam-534	642	2	,	,	PUNCT
ejpam-534	642	3	either	either	CCONJ
ejpam-534	642	4	(	(	PUNCT
ejpam-534	642	5	a	a	X
ejpam-534	642	6	)	)	PUNCT
ejpam-534	642	7	the	the	DET
ejpam-534	642	8	n×n	n×n	PROPN
ejpam-534	642	9	matrix	matrix	NOUN
ejpam-534	642	10	b(t	b(t	NOUN
ejpam-534	642	11	,	,	PUNCT
ejpam-534	642	12	ū	ū	NOUN
ejpam-534	642	13	,	,	PUNCT
ejpam-534	642	14	˙̄u	˙̄u	NOUN
ejpam-534	642	15	,	,	PUNCT
ejpam-534	642	16	¨̄u	¨̄u	NOUN
ejpam-534	642	17	,	,	PUNCT
ejpam-534	642	18	...	...	PUNCT
ejpam-534	642	19	ū	ū	NOUN
ejpam-534	642	20	,	,	PUNCT
ejpam-534	642	21	....	....	PUNCT
ejpam-534	642	22	ū	ū	NOUN
ejpam-534	642	23	,	,	PUNCT
ejpam-534	642	24	ȳ(t	ȳ(t	PROPN
ejpam-534	642	25	)	)	PUNCT
ejpam-534	642	26	,	,	PUNCT
ejpam-534	642	27	˙̄y(t	˙̄y(t	PUNCT
ejpam-534	642	28	)	)	PUNCT
ejpam-534	642	29	,	,	PUNCT
ejpam-534	642	30	¨̄y(t	¨̄y(t	NUM
ejpam-534	642	31	)	)	PUNCT
ejpam-534	642	32	,	,	PUNCT
ejpam-534	642	33	...	...	PUNCT
ejpam-534	643	1	ȳ	ȳ	PROPN
ejpam-534	643	2	(	(	PUNCT
ejpam-534	643	3	t))+(gx(t	t))+(gx(t	PROPN
ejpam-534	643	4	,	,	PUNCT
ejpam-534	643	5	ū	ū	NOUN
ejpam-534	643	6	,	,	PUNCT
ejpam-534	643	7	˙̄u	˙̄u	X
ejpam-534	643	8	)	)	PUNCT
ejpam-534	644	1	ȳ(t))x	ȳ(t))x	NOUN
ejpam-534	644	2	is	be	AUX
ejpam-534	644	3	positive	positive	ADJ
ejpam-534	644	4	definite	definite	ADJ
ejpam-534	644	5	and	and	CCONJ
ejpam-534	644	6	p̄(t)t	p̄(t)t	PROPN
ejpam-534	644	7	(	(	PUNCT
ejpam-534	644	8	gx(t	gx(t	X
ejpam-534	644	9	,	,	PUNCT
ejpam-534	644	10	ū	ū	NOUN
ejpam-534	644	11	,	,	PUNCT
ejpam-534	644	12	˙̄u	˙̄u	NOUN
ejpam-534	644	13	)	)	PUNCT
ejpam-534	644	14	ȳ(t	ȳ(t	NOUN
ejpam-534	644	15	)	)	PUNCT
ejpam-534	644	16	)	)	PUNCT
ejpam-534	644	17	≧	≧	X
ejpam-534	645	1	0	0	NUM
ejpam-534	645	2	,	,	PUNCT
ejpam-534	645	3	or	or	CCONJ
ejpam-534	645	4	(	(	PUNCT
ejpam-534	645	5	b	b	X
ejpam-534	645	6	)	)	PUNCT
ejpam-534	645	7	the	the	DET
ejpam-534	645	8	n×n	n×n	PROPN
ejpam-534	645	9	matrix	matrix	NOUN
ejpam-534	645	10	b(t	b(t	NOUN
ejpam-534	645	11	,	,	PUNCT
ejpam-534	645	12	ū	ū	NOUN
ejpam-534	645	13	,	,	PUNCT
ejpam-534	645	14	˙̄u	˙̄u	NOUN
ejpam-534	645	15	,	,	PUNCT
ejpam-534	645	16	¨̄u	¨̄u	NOUN
ejpam-534	645	17	,	,	PUNCT
ejpam-534	645	18	...	...	PUNCT
ejpam-534	645	19	ū	ū	NOUN
ejpam-534	645	20	,	,	PUNCT
ejpam-534	645	21	....	....	PUNCT
ejpam-534	645	22	ū	ū	NOUN
ejpam-534	645	23	,	,	PUNCT
ejpam-534	645	24	ȳ(t	ȳ(t	PROPN
ejpam-534	645	25	)	)	PUNCT
ejpam-534	645	26	,	,	PUNCT
ejpam-534	645	27	˙̄y(t	˙̄y(t	PUNCT
ejpam-534	645	28	)	)	PUNCT
ejpam-534	645	29	,	,	PUNCT
ejpam-534	645	30	¨̄y(t	¨̄y(t	NUM
ejpam-534	645	31	)	)	PUNCT
ejpam-534	645	32	,	,	PUNCT
ejpam-534	645	33	...	...	PUNCT
ejpam-534	646	1	ȳ	ȳ	PROPN
ejpam-534	646	2	(	(	PUNCT
ejpam-534	646	3	t))+(gx(t	t))+(gx(t	PROPN
ejpam-534	646	4	,	,	PUNCT
ejpam-534	646	5	ū	ū	NOUN
ejpam-534	646	6	,	,	PUNCT
ejpam-534	646	7	˙̄u	˙̄u	X
ejpam-534	646	8	)	)	PUNCT
ejpam-534	647	1	ȳ(t))x	ȳ(t))x	NOUN
ejpam-534	647	2	is	be	AUX
ejpam-534	647	3	negative	negative	ADJ
ejpam-534	647	4	definite	definite	ADJ
ejpam-534	647	5	and	and	CCONJ
ejpam-534	647	6	p̄(t)t	p̄(t)t	PROPN
ejpam-534	647	7	(	(	PUNCT
ejpam-534	647	8	gx(t	gx(t	X
ejpam-534	647	9	,	,	PUNCT
ejpam-534	647	10	ū	ū	NOUN
ejpam-534	647	11	,	,	PUNCT
ejpam-534	647	12	˙̄u	˙̄u	X
ejpam-534	647	13	)	)	PUNCT
ejpam-534	647	14	ȳ(t))≦	ȳ(t))≦	PROPN
ejpam-534	647	15	0	0	NUM
ejpam-534	647	16	.	.	PUNCT
ejpam-534	648	1	then	then	ADV
ejpam-534	648	2	ū(t	ū(t	PROPN
ejpam-534	648	3	)	)	PUNCT
ejpam-534	648	4	is	be	AUX
ejpam-534	648	5	feasible	feasible	ADJ
ejpam-534	648	6	for	for	ADP
ejpam-534	648	7	(	(	PUNCT
ejpam-534	648	8	p	p	NOUN
ejpam-534	648	9	)	)	PUNCT
ejpam-534	648	10	and	and	CCONJ
ejpam-534	648	11	the	the	DET
ejpam-534	648	12	two	two	NUM
ejpam-534	648	13	objective	objective	ADJ
ejpam-534	648	14	functionals	functional	NOUN
ejpam-534	648	15	have	have	VERB
ejpam-534	648	16	same	same	ADJ
ejpam-534	648	17	value	value	NOUN
ejpam-534	648	18	.	.	PUNCT
ejpam-534	649	1	also	also	ADV
ejpam-534	649	2	,	,	PUNCT
ejpam-534	649	3	if	if	SCONJ
ejpam-534	649	4	the	the	DET
ejpam-534	649	5	weak	weak	ADJ
ejpam-534	649	6	duality	duality	NOUN
ejpam-534	649	7	theorem	theorem	VERB
ejpam-534	649	8	holds	hold	VERB
ejpam-534	649	9	for	for	ADP
ejpam-534	649	10	all	all	DET
ejpam-534	649	11	feasible	feasible	ADJ
ejpam-534	649	12	solutions	solution	NOUN
ejpam-534	649	13	of	of	ADP
ejpam-534	649	14	(	(	PUNCT
ejpam-534	649	15	p	p	NOUN
ejpam-534	649	16	)	)	PUNCT
ejpam-534	649	17	and	and	CCONJ
ejpam-534	649	18	(	(	PUNCT
ejpam-534	649	19	mwd	mwd	PROPN
ejpam-534	649	20	)	)	PUNCT
ejpam-534	649	21	,	,	PUNCT
ejpam-534	649	22	then	then	ADV
ejpam-534	649	23	ū(t	ū(t	PROPN
ejpam-534	649	24	)	)	PUNCT
ejpam-534	649	25	is	be	AUX
ejpam-534	649	26	an	an	DET
ejpam-534	649	27	efficient	efficient	ADJ
ejpam-534	649	28	solution	solution	NOUN
ejpam-534	649	29	of	of	ADP
ejpam-534	649	30	(	(	PUNCT
ejpam-534	649	31	p	p	NOUN
ejpam-534	649	32	)	)	PUNCT
ejpam-534	649	33	.	.	PUNCT
ejpam-534	650	1	proof	proof	NOUN
ejpam-534	650	2	.	.	PUNCT
ejpam-534	651	1	since	since	SCONJ
ejpam-534	651	2	(	(	PUNCT
ejpam-534	651	3	ū(t	ū(t	ADJ
ejpam-534	651	4	)	)	PUNCT
ejpam-534	651	5	,	,	PUNCT
ejpam-534	651	6	λ̄	λ̄	ADP
ejpam-534	651	7	,	,	PUNCT
ejpam-534	651	8	ȳ(t	ȳ(t	NOUN
ejpam-534	651	9	)	)	PUNCT
ejpam-534	651	10	,	,	PUNCT
ejpam-534	651	11	p̄(t	p̄(t	PROPN
ejpam-534	651	12	)	)	PUNCT
ejpam-534	651	13	)	)	PUNCT
ejpam-534	651	14	is	be	AUX
ejpam-534	651	15	an	an	DET
ejpam-534	651	16	efficient	efficient	ADJ
ejpam-534	651	17	solution	solution	NOUN
ejpam-534	651	18	of	of	ADP
ejpam-534	651	19	(	(	PUNCT
ejpam-534	651	20	mwd	mwd	PROPN
ejpam-534	651	21	)	)	PUNCT
ejpam-534	651	22	,	,	PUNCT
ejpam-534	651	23	there	there	PRON
ejpam-534	651	24	exist	exist	VERB
ejpam-534	651	25	α	α	PRON
ejpam-534	651	26	,	,	PUNCT
ejpam-534	651	27	η	η	PROPN
ejpam-534	651	28	∈	∈	NOUN
ejpam-534	651	29	rk	rk	NOUN
ejpam-534	651	30	and	and	CCONJ
ejpam-534	651	31	piecewise	piecewise	VERB
ejpam-534	651	32	smooth	smooth	ADJ
ejpam-534	651	33	functions	function	NOUN
ejpam-534	651	34	β	β	NOUN
ejpam-534	651	35	:	:	PUNCT
ejpam-534	651	36	i	i	PROPN
ejpam-534	651	37	→	→	SYM
ejpam-534	651	38	rn	rn	PROPN
ejpam-534	651	39	,	,	PUNCT
ejpam-534	651	40	γ	γ	X
ejpam-534	651	41	:	:	PUNCT
ejpam-534	651	42	i	i	PROPN
ejpam-534	651	43	→	→	SYM
ejpam-534	651	44	r	r	NOUN
ejpam-534	651	45	,	,	PUNCT
ejpam-534	651	46	µ	µ	X
ejpam-534	651	47	:	:	PUNCT
ejpam-534	651	48	i	i	PROPN
ejpam-534	651	49	→	→	SYM
ejpam-534	651	50	rm	rm	PROPN
ejpam-534	651	51	,	,	PUNCT
ejpam-534	651	52	such	such	ADJ
ejpam-534	651	53	that	that	SCONJ
ejpam-534	651	54	the	the	DET
ejpam-534	651	55	following	follow	VERB
ejpam-534	651	56	fritz	fritz	PROPN
ejpam-534	651	57	john	john	PROPN
ejpam-534	651	58	conditions	condition	NOUN
ejpam-534	651	59	(	(	PUNCT
ejpam-534	651	60	theorem	theorem	NOUN
ejpam-534	651	61	3	3	NUM
ejpam-534	651	62	)	)	PUNCT
ejpam-534	651	63	are	be	AUX
ejpam-534	651	64	satisfied	satisfied	ADJ
ejpam-534	651	65	at	at	ADP
ejpam-534	651	66	(	(	PUNCT
ejpam-534	651	67	ū(t	ū(t	ADJ
ejpam-534	651	68	)	)	PUNCT
ejpam-534	651	69	,	,	PUNCT
ejpam-534	651	70	λ̄	λ̄	ADP
ejpam-534	651	71	,	,	PUNCT
ejpam-534	651	72	ȳ(t	ȳ(t	NOUN
ejpam-534	651	73	)	)	PUNCT
ejpam-534	651	74	,	,	PUNCT
ejpam-534	651	75	p̄(t	p̄(t	PROPN
ejpam-534	651	76	)	)	PUNCT
ejpam-534	651	77	)	)	PUNCT
ejpam-534	652	1	(	(	PUNCT
ejpam-534	652	2	for	for	ADP
ejpam-534	652	3	brevity	brevity	NOUN
ejpam-534	652	4	,	,	PUNCT
ejpam-534	652	5	f	f	PROPN
ejpam-534	652	6	i	i	NOUN
ejpam-534	653	1	x	x	PROPN
ejpam-534	653	2	≡	≡	PROPN
ejpam-534	653	3	f	f	PROPN
ejpam-534	654	1	i	i	PRON
ejpam-534	654	2	x	x	X
ejpam-534	654	3	(	(	PUNCT
ejpam-534	654	4	t	t	PROPN
ejpam-534	654	5	,	,	PUNCT
ejpam-534	654	6	ū	ū	NOUN
ejpam-534	654	7	,	,	PUNCT
ejpam-534	654	8	˙̄u	˙̄u	NOUN
ejpam-534	654	9	)	)	PUNCT
ejpam-534	654	10	,	,	PUNCT
ejpam-534	654	11	g	g	PROPN
ejpam-534	654	12	j	j	PROPN
ejpam-534	654	13	≡	≡	PROPN
ejpam-534	654	14	g	g	PROPN
ejpam-534	654	15	j(t	j(t	PROPN
ejpam-534	654	16	,	,	PUNCT
ejpam-534	654	17	ū	ū	NOUN
ejpam-534	654	18	,	,	PUNCT
ejpam-534	654	19	˙̄u	˙̄u	NOUN
ejpam-534	654	20	)	)	PUNCT
ejpam-534	654	21	,	,	PUNCT
ejpam-534	654	22	g	g	PROPN
ejpam-534	654	23	j	j	PROPN
ejpam-534	654	24	x	x	SYM
ejpam-534	654	25	≡	≡	PROPN
ejpam-534	654	26	g	g	PROPN
ejpam-534	654	27	j	j	PROPN
ejpam-534	654	28	x(t	x(t	PROPN
ejpam-534	654	29	,	,	PUNCT
ejpam-534	654	30	ū	ū	NOUN
ejpam-534	654	31	,	,	PUNCT
ejpam-534	654	32	˙̄u	˙̄u	NUM
ejpam-534	654	33	)	)	PUNCT
ejpam-534	654	34	,	,	PUNCT
ejpam-534	654	35	ai	ai	VERB
ejpam-534	654	36	≡	≡	PROPN
ejpam-534	654	37	ai(t	ai(t	NOUN
ejpam-534	654	38	,	,	PUNCT
ejpam-534	654	39	ū	ū	NOUN
ejpam-534	654	40	,	,	PUNCT
ejpam-534	654	41	˙̄u	˙̄u	NOUN
ejpam-534	654	42	,	,	PUNCT
ejpam-534	654	43	¨̄u	¨̄u	NOUN
ejpam-534	654	44	,	,	PUNCT
ejpam-534	654	45	...	...	PUNCT
ejpam-534	654	46	ū	ū	NOUN
ejpam-534	654	47	,	,	PUNCT
ejpam-534	654	48	....	....	PUNCT
ejpam-534	654	49	ū	ū	PROPN
ejpam-534	654	50	)	)	PUNCT
ejpam-534	654	51	,	,	PUNCT
ejpam-534	654	52	b	b	PROPN
ejpam-534	654	53	≡	≡	PROPN
ejpam-534	654	54	b(t	b(t	PROPN
ejpam-534	654	55	,	,	PUNCT
ejpam-534	654	56	ū	ū	NOUN
ejpam-534	654	57	,	,	PUNCT
ejpam-534	654	58	˙̄u	˙̄u	NOUN
ejpam-534	654	59	,	,	PUNCT
ejpam-534	654	60	¨̄u	¨̄u	NOUN
ejpam-534	654	61	,	,	PUNCT
ejpam-534	654	62	...	...	PUNCT
ejpam-534	654	63	ū	ū	NOUN
ejpam-534	654	64	,	,	PUNCT
ejpam-534	654	65	....	....	PUNCT
ejpam-534	654	66	ū	ū	NOUN
ejpam-534	654	67	,	,	PUNCT
ejpam-534	654	68	ȳ(t	ȳ(t	PROPN
ejpam-534	654	69	)	)	PUNCT
ejpam-534	654	70	,	,	PUNCT
ejpam-534	654	71	˙̄y(t	˙̄y(t	PUNCT
ejpam-534	654	72	)	)	PUNCT
ejpam-534	654	73	,	,	PUNCT
ejpam-534	654	74	¨̄y(t	¨̄y(t	NUM
ejpam-534	654	75	)	)	PUNCT
ejpam-534	654	76	,	,	PUNCT
ejpam-534	654	77	...	...	PUNCT
ejpam-534	655	1	ȳ	ȳ	PROPN
ejpam-534	655	2	(	(	PUNCT
ejpam-534	655	3	t	t	PROPN
ejpam-534	655	4	)	)	PUNCT
ejpam-534	655	5	)	)	PUNCT
ejpam-534	655	6	etc	etc	X
ejpam-534	655	7	.	.	X
ejpam-534	655	8	):	):	PUNCT
ejpam-534	655	9	k∑	k∑	PROPN
ejpam-534	655	10	i=1	i=1	PROPN
ejpam-534	656	1	αi	αi	PROPN
ejpam-534	656	2	(	(	PUNCT
ejpam-534	656	3	f	f	NOUN
ejpam-534	656	4	i	i	NOUN
ejpam-534	656	5	x	x	PROPN
ejpam-534	657	1	−	−	PROPN
ejpam-534	658	1	d	d	X
ejpam-534	658	2	f	f	X
ejpam-534	659	1	i	i	PRON
ejpam-534	659	2	ẋ	ẋ	PUNCT
ejpam-534	660	1	−	−	NOUN
ejpam-534	660	2	1	1	NUM
ejpam-534	660	3	2	2	NUM
ejpam-534	660	4	(	(	PUNCT
ejpam-534	660	5	p̄(t)t	p̄(t)t	PROPN
ejpam-534	660	6	ai	ai	VERB
ejpam-534	660	7	p̄(t))x	p̄(t))x	PROPN
ejpam-534	660	8	+	+	CCONJ
ejpam-534	660	9	1	1	NUM
ejpam-534	660	10	2	2	NUM
ejpam-534	660	11	d(p̄(t)t	d(p̄(t)t	NOUN
ejpam-534	660	12	ai	ai	VERB
ejpam-534	660	13	p̄(t	p̄(t	ADJ
ejpam-534	660	14	)	)	PUNCT
ejpam-534	660	15	)	)	PUNCT
ejpam-534	661	1	ẋ	ẋ	PROPN
ejpam-534	662	1	−	−	NOUN
ejpam-534	662	2	1	1	NUM
ejpam-534	662	3	2	2	NUM
ejpam-534	662	4	d2(p̄(t)t	d2(p̄(t)t	NOUN
ejpam-534	662	5	ai	ai	VERB
ejpam-534	662	6	p̄(t	p̄(t	ADJ
ejpam-534	662	7	)	)	PUNCT
ejpam-534	662	8	)	)	PUNCT
ejpam-534	662	9	ẍ	ẍ	PUNCT
ejpam-534	663	1	+	+	CCONJ
ejpam-534	663	2	1	1	NUM
ejpam-534	663	3	2	2	NUM
ejpam-534	663	4	d3(p̄(t)t	d3(p̄(t)t	NOUN
ejpam-534	663	5	ai	ai	AUX
ejpam-534	663	6	p̄(t))	p̄(t))	VERB
ejpam-534	663	7	...	...	PUNCT
ejpam-534	663	8	x	x	X
ejpam-534	663	9	−	−	PROPN
ejpam-534	663	10	1	1	NUM
ejpam-534	663	11	2	2	NUM
ejpam-534	663	12	d4(p̄(t)t	d4(p̄(t)t	NOUN
ejpam-534	663	13	ai	ai	AUX
ejpam-534	663	14	p̄(t))	p̄(t))	PROPN
ejpam-534	663	15	....	....	PROPN
ejpam-534	663	16	x	x	X
ejpam-534	663	17	)	)	PUNCT
ejpam-534	663	18	−	−	PROPN
ejpam-534	664	1	(	(	PUNCT
ejpam-534	664	2	k∑	k∑	NOUN
ejpam-534	664	3	i=1	i=1	PROPN
ejpam-534	665	1	λ̄i(ai	λ̄i(ai	PROPN
ejpam-534	666	1	+	+	CCONJ
ejpam-534	666	2	(	(	PUNCT
ejpam-534	666	3	ai	ai	VERB
ejpam-534	666	4	p̄(t))x	p̄(t))x	PROPN
ejpam-534	666	5	−	−	PROPN
ejpam-534	666	6	d(ai	d(ai	PROPN
ejpam-534	666	7	p̄(t	p̄(t	PROPN
ejpam-534	666	8	)	)	PUNCT
ejpam-534	666	9	)	)	PUNCT
ejpam-534	667	1	ẋ	ẋ	PROPN
ejpam-534	668	1	+	+	CCONJ
ejpam-534	668	2	d2(ai	d2(ai	PROPN
ejpam-534	668	3	p̄(t	p̄(t	PROPN
ejpam-534	668	4	)	)	PUNCT
ejpam-534	668	5	)	)	PUNCT
ejpam-534	669	1	ẍ	ẍ	X
ejpam-534	670	1	−	−	PROPN
ejpam-534	670	2	d3(ai	d3(ai	PROPN
ejpam-534	670	3	p̄(t))	p̄(t))	NUM
ejpam-534	670	4	...	...	PUNCT
ejpam-534	670	5	x	x	X
ejpam-534	670	6	+	+	CCONJ
ejpam-534	670	7	d4(ai	d4(ai	PROPN
ejpam-534	670	8	p̄(t))	p̄(t))	NUM
ejpam-534	670	9	....	....	NOUN
ejpam-534	670	10	x	x	X
ejpam-534	670	11	)	)	PUNCT
ejpam-534	671	1	+	+	NUM
ejpam-534	671	2	b	b	X
ejpam-534	671	3	+	+	CCONJ
ejpam-534	671	4	(	(	PUNCT
ejpam-534	671	5	bp̄(t))x	bp̄(t))x	NOUN
ejpam-534	671	6	−	−	PROPN
ejpam-534	671	7	d(bp̄(t	d(bp̄(t	NOUN
ejpam-534	671	8	)	)	PUNCT
ejpam-534	671	9	)	)	PUNCT
ejpam-534	672	1	ẋ	ẋ	PROPN
ejpam-534	673	1	+	+	PUNCT
ejpam-534	673	2	d2(bp̄(t	d2(bp̄(t	PROPN
ejpam-534	673	3	)	)	PUNCT
ejpam-534	673	4	)	)	PUNCT
ejpam-534	674	1	ẍ	ẍ	X
ejpam-534	675	1	−	−	PROPN
ejpam-534	675	2	d3(bp̄(t))	d3(bp̄(t))	PROPN
ejpam-534	675	3	...	...	PUNCT
ejpam-534	675	4	x	x	SYM
ejpam-534	676	1	+	+	CCONJ
ejpam-534	676	2	d4(bp̄(t))	d4(bp̄(t))	ADJ
ejpam-534	676	3	....	....	PUNCT
ejpam-534	676	4	x	x	X
ejpam-534	676	5	)	)	PUNCT
ejpam-534	676	6	β(t	β(t	PROPN
ejpam-534	676	7	)	)	PUNCT
ejpam-534	677	1	+	+	CCONJ
ejpam-534	677	2	γ(t)(gx	γ(t)(gx	NUM
ejpam-534	677	3	y(t)−	y(t)−	PROPN
ejpam-534	677	4	d(g	d(g	PROPN
ejpam-534	678	1	ẋ	ẋ	PROPN
ejpam-534	679	1	ȳ(t))−	ȳ(t))−	NOUN
ejpam-534	679	2	1	1	NUM
ejpam-534	679	3	2	2	NUM
ejpam-534	679	4	(	(	PUNCT
ejpam-534	679	5	p̄(t)t	p̄(t)t	NOUN
ejpam-534	679	6	bp̄(t))x	bp̄(t))x	NOUN
ejpam-534	680	1	+	+	CCONJ
ejpam-534	680	2	1	1	NUM
ejpam-534	680	3	2	2	NUM
ejpam-534	680	4	d(p̄(t)t	d(p̄(t)t	NOUN
ejpam-534	680	5	bp̄(t	bp̄(t	NUM
ejpam-534	680	6	)	)	PUNCT
ejpam-534	680	7	)	)	PUNCT
ejpam-534	681	1	ẋ	ẋ	PROPN
ejpam-534	682	1	−	−	NOUN
ejpam-534	682	2	1	1	NUM
ejpam-534	682	3	2	2	NUM
ejpam-534	682	4	d2(p̄(t)t	d2(p̄(t)t	NOUN
ejpam-534	682	5	bp̄(t	bp̄(t	NUM
ejpam-534	682	6	)	)	PUNCT
ejpam-534	682	7	)	)	PUNCT
ejpam-534	682	8	ẍ	ẍ	PUNCT
ejpam-534	683	1	+	+	CCONJ
ejpam-534	683	2	1	1	NUM
ejpam-534	683	3	2	2	NUM
ejpam-534	683	4	d3(p̄(t)t	d3(p̄(t)t	NOUN
ejpam-534	683	5	bp̄(t))	bp̄(t))	NOUN
ejpam-534	683	6	...	...	PUNCT
ejpam-534	683	7	x	x	SYM
ejpam-534	683	8	−	−	PROPN
ejpam-534	683	9	1	1	NUM
ejpam-534	683	10	2	2	NUM
ejpam-534	683	11	d4(p̄(t)t	d4(p̄(t)t	VERB
ejpam-534	683	12	bp̄(t))	bp̄(t))	PROPN
ejpam-534	683	13	....	....	PUNCT
ejpam-534	683	14	x	x	X
ejpam-534	683	15	)	)	PUNCT
ejpam-534	684	1	=	=	SYM
ejpam-534	684	2	0	0	NUM
ejpam-534	684	3	,	,	PUNCT
ejpam-534	684	4	t	t	PROPN
ejpam-534	684	5	∈	∈	PROPN
ejpam-534	685	1	i	i	PRON
ejpam-534	685	2	,	,	PUNCT
ejpam-534	685	3	(	(	PUNCT
ejpam-534	685	4	42	42	NUM
ejpam-534	685	5	)	)	PUNCT
ejpam-534	685	6	β(t)t	β(t)t	NOUN
ejpam-534	685	7	(	(	PUNCT
ejpam-534	685	8	f	f	X
ejpam-534	685	9	i	i	NOUN
ejpam-534	685	10	x	x	X
ejpam-534	685	11	−	−	PROPN
ejpam-534	686	1	d	d	X
ejpam-534	686	2	f	f	X
ejpam-534	687	1	i	i	PRON
ejpam-534	687	2	ẋ	ẋ	PROPN
ejpam-534	688	1	+	+	CCONJ
ejpam-534	688	2	ai	ai	VERB
ejpam-534	688	3	p̄(t))−ηi	p̄(t))−ηi	NOUN
ejpam-534	688	4	=	=	SYM
ejpam-534	688	5	0	0	NUM
ejpam-534	688	6	,	,	PUNCT
ejpam-534	688	7	t	t	PROPN
ejpam-534	688	8	∈	∈	PROPN
ejpam-534	689	1	i	i	PRON
ejpam-534	689	2	,	,	PUNCT
ejpam-534	689	3	i	i	PROPN
ejpam-534	689	4	∈	∈	PROPN
ejpam-534	689	5	k	k	X
ejpam-534	689	6	,	,	PUNCT
ejpam-534	689	7	(	(	PUNCT
ejpam-534	689	8	43	43	NUM
ejpam-534	689	9	)	)	PUNCT
ejpam-534	689	10	β(t)t	β(t)t	NOUN
ejpam-534	689	11	(	(	PUNCT
ejpam-534	689	12	g	g	NOUN
ejpam-534	689	13	j	j	PROPN
ejpam-534	689	14	x	x	PROPN
ejpam-534	690	1	+	+	CCONJ
ejpam-534	690	2	g	g	PROPN
ejpam-534	690	3	j	j	PROPN
ejpam-534	690	4	x	x	PUNCT
ejpam-534	690	5	x	x	PUNCT
ejpam-534	690	6	p̄(t))−	p̄(t))−	NOUN
ejpam-534	690	7	γ(t)(g	γ(t)(g	NUM
ejpam-534	690	8	j	j	NOUN
ejpam-534	690	9	−	−	NUM
ejpam-534	690	10	1	1	NUM
ejpam-534	690	11	2	2	NUM
ejpam-534	690	12	p̄(t)t	p̄(t)t	NOUN
ejpam-534	690	13	g	g	PROPN
ejpam-534	690	14	j	j	PROPN
ejpam-534	690	15	x	x	X
ejpam-534	690	16	x	x	SYM
ejpam-534	690	17	p̄(t))−µ	p̄(t))−µ	X
ejpam-534	690	18	j(t	j(t	PROPN
ejpam-534	690	19	)	)	PUNCT
ejpam-534	690	20	=	=	SYM
ejpam-534	690	21	0	0	NUM
ejpam-534	690	22	,	,	PUNCT
ejpam-534	690	23	t	t	PROPN
ejpam-534	690	24	∈	∈	PROPN
ejpam-534	691	1	i	i	PRON
ejpam-534	691	2	,	,	PUNCT
ejpam-534	691	3	j	j	PROPN
ejpam-534	691	4	∈	∈	PROPN
ejpam-534	691	5	m	m	PROPN
ejpam-534	691	6	,	,	PUNCT
ejpam-534	691	7	(	(	PUNCT
ejpam-534	691	8	44	44	NUM
ejpam-534	691	9	)	)	PUNCT
ejpam-534	691	10	t.	t.	NOUN
ejpam-534	691	11	gulati	gulati	PROPN
ejpam-534	691	12	and	and	CCONJ
ejpam-534	691	13	g.	g.	PROPN
ejpam-534	691	14	mehndiratta	mehndiratta	PROPN
ejpam-534	691	15	/	/	SYM
ejpam-534	691	16	eur	eur	PROPN
ejpam-534	691	17	.	.	PUNCT
ejpam-534	692	1	j.	j.	PROPN
ejpam-534	692	2	pure	pure	PROPN
ejpam-534	692	3	appl	appl	PROPN
ejpam-534	692	4	.	.	PROPN
ejpam-534	692	5	math	math	PROPN
ejpam-534	692	6	,	,	PUNCT
ejpam-534	692	7	3	3	NUM
ejpam-534	692	8	(	(	PUNCT
ejpam-534	692	9	2010	2010	NUM
ejpam-534	692	10	)	)	PUNCT
ejpam-534	692	11	,	,	PUNCT
ejpam-534	692	12	786	786	NUM
ejpam-534	692	13	-	-	SYM
ejpam-534	692	14	805	805	NUM
ejpam-534	692	15	801	801	NUM
ejpam-534	692	16	k∑	k∑	VERB
ejpam-534	692	17	i=1	i=1	PROPN
ejpam-534	692	18	αiai	αiai	PROPN
ejpam-534	692	19	p̄(t	p̄(t	PROPN
ejpam-534	692	20	)	)	PUNCT
ejpam-534	693	1	+	+	CCONJ
ejpam-534	693	2	(	(	PUNCT
ejpam-534	693	3	k∑	k∑	VERB
ejpam-534	693	4	i=1	i=1	X
ejpam-534	693	5	λ̄iai	λ̄iai	X
ejpam-534	694	1	+	+	NUM
ejpam-534	694	2	b)β(t	b)β(t	NOUN
ejpam-534	694	3	)	)	PUNCT
ejpam-534	695	1	+	+	X
ejpam-534	695	2	γ(t)bp̄(t	γ(t)bp̄(t	X
ejpam-534	695	3	)	)	PUNCT
ejpam-534	695	4	=	=	SYM
ejpam-534	695	5	0	0	NUM
ejpam-534	695	6	,	,	PUNCT
ejpam-534	695	7	t	t	PROPN
ejpam-534	695	8	∈	∈	PROPN
ejpam-534	696	1	i	i	PRON
ejpam-534	696	2	,	,	PUNCT
ejpam-534	696	3	(	(	PUNCT
ejpam-534	696	4	45	45	NUM
ejpam-534	696	5	)	)	PUNCT
ejpam-534	696	6	γ(t	γ(t	NOUN
ejpam-534	696	7	)	)	PUNCT
ejpam-534	696	8	(	(	PUNCT
ejpam-534	696	9	ȳ(t)t	ȳ(t)t	NOUN
ejpam-534	696	10	g	g	NOUN
ejpam-534	696	11	−	−	PROPN
ejpam-534	696	12	1	1	NUM
ejpam-534	696	13	2	2	NUM
ejpam-534	696	14	p̄(t)t	p̄(t)t	NOUN
ejpam-534	696	15	bp̄(t	bp̄(t	NOUN
ejpam-534	696	16	)	)	PUNCT
ejpam-534	696	17	)	)	PUNCT
ejpam-534	697	1	=	=	PUNCT
ejpam-534	697	2	0	0	NUM
ejpam-534	697	3	,	,	PUNCT
ejpam-534	697	4	t	t	PROPN
ejpam-534	697	5	∈	∈	PROPN
ejpam-534	698	1	i	i	PRON
ejpam-534	698	2	,	,	PUNCT
ejpam-534	698	3	(	(	PUNCT
ejpam-534	698	4	46	46	NUM
ejpam-534	698	5	)	)	PUNCT
ejpam-534	698	6	µ(t)t	µ(t)t	NOUN
ejpam-534	698	7	ȳ(t	ȳ(t	NOUN
ejpam-534	698	8	)	)	PUNCT
ejpam-534	698	9	=	=	SYM
ejpam-534	698	10	0	0	NUM
ejpam-534	698	11	,	,	PUNCT
ejpam-534	698	12	t	t	PROPN
ejpam-534	698	13	∈	∈	PROPN
ejpam-534	699	1	i	i	PRON
ejpam-534	699	2	,	,	PUNCT
ejpam-534	699	3	(	(	PUNCT
ejpam-534	699	4	47	47	NUM
ejpam-534	699	5	)	)	PUNCT
ejpam-534	699	6	ηt	ηt	ADP
ejpam-534	699	7	λ̄	λ̄	NOUN
ejpam-534	699	8	=	=	SYM
ejpam-534	699	9	0	0	NUM
ejpam-534	699	10	,	,	PUNCT
ejpam-534	699	11	(	(	PUNCT
ejpam-534	699	12	48	48	NUM
ejpam-534	699	13	)	)	PUNCT
ejpam-534	699	14	(	(	PUNCT
ejpam-534	699	15	α	α	NOUN
ejpam-534	699	16	,	,	PUNCT
ejpam-534	699	17	β(t),γ(t),µ(t),η	β(t),γ(t),µ(t),η	ADJ
ejpam-534	699	18	)	)	PUNCT
ejpam-534	699	19	6=	6=	ADP
ejpam-534	699	20	0	0	NUM
ejpam-534	699	21	,	,	PUNCT
ejpam-534	699	22	t	t	PROPN
ejpam-534	699	23	∈	∈	PROPN
ejpam-534	700	1	i	i	PRON
ejpam-534	700	2	,	,	PUNCT
ejpam-534	700	3	(	(	PUNCT
ejpam-534	700	4	49	49	NUM
ejpam-534	700	5	)	)	PUNCT
ejpam-534	700	6	(	(	PUNCT
ejpam-534	700	7	α	α	NOUN
ejpam-534	700	8	,	,	PUNCT
ejpam-534	700	9	γ(t),µ(t),η	γ(t),µ(t),η	ADJ
ejpam-534	700	10	)	)	PUNCT
ejpam-534	700	11	≥	≥	NOUN
ejpam-534	700	12	0	0	NUM
ejpam-534	700	13	,	,	PUNCT
ejpam-534	700	14	t	t	PROPN
ejpam-534	700	15	∈	∈	PROPN
ejpam-534	701	1	i	i	PRON
ejpam-534	701	2	.	.	PUNCT
ejpam-534	702	1	(	(	PUNCT
ejpam-534	702	2	50	50	NUM
ejpam-534	702	3	)	)	PUNCT
ejpam-534	702	4	on	on	ADP
ejpam-534	702	5	rearranging	rearrange	VERB
ejpam-534	702	6	(	(	PUNCT
ejpam-534	702	7	45	45	NUM
ejpam-534	702	8	)	)	PUNCT
ejpam-534	702	9	,	,	PUNCT
ejpam-534	702	10	we	we	PRON
ejpam-534	702	11	get	get	AUX
ejpam-534	702	12	k∑	k∑	VERB
ejpam-534	702	13	i=1	i=1	PROPN
ejpam-534	702	14	ai(αi	ai(αi	PROPN
ejpam-534	702	15	p̄(t	p̄(t	PROPN
ejpam-534	702	16	)	)	PUNCT
ejpam-534	703	1	+	+	CCONJ
ejpam-534	703	2	λ̄iβ(t	λ̄iβ(t	NOUN
ejpam-534	703	3	)	)	PUNCT
ejpam-534	703	4	)	)	PUNCT
ejpam-534	704	1	+	+	X
ejpam-534	705	1	b(β(t	b(β(t	NOUN
ejpam-534	705	2	)	)	PUNCT
ejpam-534	706	1	+	+	X
ejpam-534	706	2	γ(t)p̄(t	γ(t)p̄(t	ADJ
ejpam-534	706	3	)	)	PUNCT
ejpam-534	706	4	)	)	PUNCT
ejpam-534	707	1	=	=	PUNCT
ejpam-534	707	2	0	0	NUM
ejpam-534	707	3	,	,	PUNCT
ejpam-534	707	4	t	t	PROPN
ejpam-534	707	5	∈	∈	PROPN
ejpam-534	708	1	i	i	PRON
ejpam-534	708	2	,	,	PUNCT
ejpam-534	708	3	which	which	PRON
ejpam-534	708	4	by	by	ADP
ejpam-534	708	5	hypothesis	hypothesis	NOUN
ejpam-534	708	6	(	(	PUNCT
ejpam-534	708	7	c1	c1	PROPN
ejpam-534	708	8	)	)	PUNCT
ejpam-534	708	9	,	,	PUNCT
ejpam-534	708	10	yield	yield	VERB
ejpam-534	708	11	αi	αi	NOUN
ejpam-534	708	12	p̄(t	p̄(t	PROPN
ejpam-534	708	13	)	)	PUNCT
ejpam-534	709	1	+	+	CCONJ
ejpam-534	709	2	λ̄iβ(t	λ̄iβ(t	NOUN
ejpam-534	709	3	)	)	PUNCT
ejpam-534	709	4	=	=	SYM
ejpam-534	709	5	0	0	NUM
ejpam-534	709	6	,	,	PUNCT
ejpam-534	709	7	t	t	PROPN
ejpam-534	709	8	∈	∈	PROPN
ejpam-534	710	1	i	i	PRON
ejpam-534	710	2	,	,	PUNCT
ejpam-534	710	3	i	i	PROPN
ejpam-534	710	4	∈	∈	PROPN
ejpam-534	710	5	k	k	X
ejpam-534	710	6	,	,	PUNCT
ejpam-534	710	7	(	(	PUNCT
ejpam-534	710	8	51	51	NUM
ejpam-534	710	9	)	)	PUNCT
ejpam-534	710	10	and	and	CCONJ
ejpam-534	710	11	β(t	β(t	PROPN
ejpam-534	710	12	)	)	PUNCT
ejpam-534	711	1	+	+	X
ejpam-534	711	2	γ(t)p̄(t	γ(t)p̄(t	ADJ
ejpam-534	711	3	)	)	PUNCT
ejpam-534	711	4	=	=	SYM
ejpam-534	711	5	0	0	NUM
ejpam-534	711	6	,	,	PUNCT
ejpam-534	711	7	t	t	PROPN
ejpam-534	711	8	∈	∈	PROPN
ejpam-534	712	1	i	i	PRON
ejpam-534	712	2	.	.	PUNCT
ejpam-534	713	1	(	(	PUNCT
ejpam-534	713	2	52	52	NUM
ejpam-534	713	3	)	)	PUNCT
ejpam-534	713	4	now	now	ADV
ejpam-534	713	5	,	,	PUNCT
ejpam-534	713	6	suppose	suppose	VERB
ejpam-534	713	7	γ(t	γ(t	NOUN
ejpam-534	713	8	)	)	PUNCT
ejpam-534	713	9	=	=	SYM
ejpam-534	713	10	0	0	NUM
ejpam-534	713	11	for	for	ADP
ejpam-534	713	12	some	some	DET
ejpam-534	713	13	t	t	PROPN
ejpam-534	713	14	,	,	PUNCT
ejpam-534	713	15	i.e.	i.e.	X
ejpam-534	713	16	,	,	PUNCT
ejpam-534	713	17	γ(t0	γ(t0	PROPN
ejpam-534	713	18	)	)	PUNCT
ejpam-534	714	1	=	=	SYM
ejpam-534	714	2	0	0	NUM
ejpam-534	714	3	for	for	ADP
ejpam-534	714	4	some	some	DET
ejpam-534	714	5	t0	t0	PROPN
ejpam-534	714	6	∈	∈	PROPN
ejpam-534	715	1	i	i	PRON
ejpam-534	715	2	.	.	PUNCT
ejpam-534	716	1	then	then	ADV
ejpam-534	716	2	equation	equation	NOUN
ejpam-534	716	3	(	(	PUNCT
ejpam-534	716	4	52	52	NUM
ejpam-534	716	5	)	)	PUNCT
ejpam-534	716	6	gives	give	VERB
ejpam-534	716	7	β(t0	β(t0	NOUN
ejpam-534	716	8	)	)	PUNCT
ejpam-534	717	1	=	=	SYM
ejpam-534	717	2	0	0	NUM
ejpam-534	718	1	and	and	CCONJ
ejpam-534	718	2	so	so	ADV
ejpam-534	718	3	equation	equation	NOUN
ejpam-534	718	4	(	(	PUNCT
ejpam-534	718	5	51	51	NUM
ejpam-534	718	6	)	)	PUNCT
ejpam-534	718	7	implies	imply	VERB
ejpam-534	718	8	αi	αi	NOUN
ejpam-534	718	9	p̄(t0	p̄(t0	NOUN
ejpam-534	718	10	)	)	PUNCT
ejpam-534	719	1	=	=	PUNCT
ejpam-534	719	2	0	0	X
ejpam-534	719	3	.	.	PUNCT
ejpam-534	720	1	therefore	therefore	ADV
ejpam-534	720	2	for	for	ADP
ejpam-534	720	3	t	t	PROPN
ejpam-534	720	4	=	=	SYM
ejpam-534	720	5	t0	t0	PROPN
ejpam-534	720	6	,	,	PUNCT
ejpam-534	720	7	equation	equation	NOUN
ejpam-534	720	8	(	(	PUNCT
ejpam-534	720	9	42	42	NUM
ejpam-534	720	10	)	)	PUNCT
ejpam-534	720	11	reduces	reduce	VERB
ejpam-534	720	12	to	to	PART
ejpam-534	720	13	k∑	k∑	VERB
ejpam-534	720	14	i=1	i=1	PROPN
ejpam-534	720	15	αi	αi	PROPN
ejpam-534	720	16	(	(	PUNCT
ejpam-534	720	17	f	f	NOUN
ejpam-534	720	18	i	i	NOUN
ejpam-534	720	19	x	x	PROPN
ejpam-534	721	1	−	−	PROPN
ejpam-534	722	1	d	d	X
ejpam-534	722	2	f	f	PROPN
ejpam-534	723	1	i	i	PRON
ejpam-534	723	2	ẋ	ẋ	PROPN
ejpam-534	723	3	)	)	PUNCT
ejpam-534	724	1	=	=	PUNCT
ejpam-534	724	2	0	0	X
ejpam-534	724	3	.	.	PUNCT
ejpam-534	725	1	on	on	ADP
ejpam-534	725	2	using	use	VERB
ejpam-534	725	3	hypothesis	hypothesis	NOUN
ejpam-534	725	4	(	(	PUNCT
ejpam-534	725	5	c2	c2	PROPN
ejpam-534	725	6	)	)	PUNCT
ejpam-534	725	7	in	in	ADP
ejpam-534	725	8	the	the	DET
ejpam-534	725	9	above	above	ADJ
ejpam-534	725	10	equation	equation	NOUN
ejpam-534	725	11	,	,	PUNCT
ejpam-534	725	12	we	we	PRON
ejpam-534	725	13	obtain	obtain	VERB
ejpam-534	725	14	αi	αi	NOUN
ejpam-534	725	15	=	=	SYM
ejpam-534	725	16	0	0	PROPN
ejpam-534	725	17	,	,	PUNCT
ejpam-534	726	1	i	i	PRON
ejpam-534	726	2	∈	∈	PROPN
ejpam-534	726	3	k	k	X
ejpam-534	726	4	.	.	PUNCT
ejpam-534	727	1	also	also	ADV
ejpam-534	727	2	,	,	PUNCT
ejpam-534	727	3	equations	equation	NOUN
ejpam-534	727	4	(	(	PUNCT
ejpam-534	727	5	43	43	NUM
ejpam-534	727	6	)	)	PUNCT
ejpam-534	727	7	and	and	CCONJ
ejpam-534	727	8	(	(	PUNCT
ejpam-534	727	9	44	44	NUM
ejpam-534	727	10	)	)	PUNCT
ejpam-534	727	11	give	give	VERB
ejpam-534	727	12	ηi	ηi	NOUN
ejpam-534	727	13	=	=	SYM
ejpam-534	727	14	0	0	NUM
ejpam-534	727	15	,	,	PUNCT
ejpam-534	727	16	i	i	PRON
ejpam-534	727	17	∈	∈	PROPN
ejpam-534	727	18	k	k	PROPN
ejpam-534	727	19	and	and	CCONJ
ejpam-534	727	20	µ	µ	PROPN
ejpam-534	727	21	j(t0	j(t0	NOUN
ejpam-534	727	22	)	)	PUNCT
ejpam-534	728	1	=	=	SYM
ejpam-534	728	2	0	0	NUM
ejpam-534	728	3	,	,	PUNCT
ejpam-534	728	4	j	j	PROPN
ejpam-534	728	5	∈	∈	PROPN
ejpam-534	728	6	m	m	PROPN
ejpam-534	728	7	,	,	PUNCT
ejpam-534	728	8	respectively	respectively	ADV
ejpam-534	728	9	.	.	PUNCT
ejpam-534	729	1	hence	hence	ADV
ejpam-534	729	2	(	(	PUNCT
ejpam-534	729	3	α	α	X
ejpam-534	729	4	,	,	PUNCT
ejpam-534	729	5	β(t0),γ(t0),µ(t0),η	β(t0),γ(t0),µ(t0),η	PROPN
ejpam-534	729	6	)	)	PUNCT
ejpam-534	730	1	=	=	SYM
ejpam-534	730	2	0	0	NUM
ejpam-534	730	3	,	,	PUNCT
ejpam-534	730	4	which	which	PRON
ejpam-534	730	5	contradicts	contradict	VERB
ejpam-534	730	6	(	(	PUNCT
ejpam-534	730	7	49	49	NUM
ejpam-534	730	8	)	)	PUNCT
ejpam-534	730	9	.	.	PUNCT
ejpam-534	731	1	therefore	therefore	ADV
ejpam-534	731	2	γ(t	γ(t	NOUN
ejpam-534	731	3	)	)	PUNCT
ejpam-534	731	4	>	>	X
ejpam-534	732	1	0	0	NUM
ejpam-534	732	2	,	,	PUNCT
ejpam-534	732	3	t	t	PROPN
ejpam-534	732	4	∈	∈	PROPN
ejpam-534	733	1	i	i	PRON
ejpam-534	733	2	.	.	PUNCT
ejpam-534	734	1	(	(	PUNCT
ejpam-534	734	2	53	53	NUM
ejpam-534	734	3	)	)	PUNCT
ejpam-534	734	4	multiplying	multiplying	NOUN
ejpam-534	734	5	(	(	PUNCT
ejpam-534	734	6	44	44	NUM
ejpam-534	734	7	)	)	PUNCT
ejpam-534	734	8	by	by	ADP
ejpam-534	734	9	ȳ	ȳ	PROPN
ejpam-534	734	10	j(t	j(t	PROPN
ejpam-534	734	11	)	)	PUNCT
ejpam-534	734	12	,	,	PUNCT
ejpam-534	734	13	summing	sum	VERB
ejpam-534	734	14	over	over	ADP
ejpam-534	734	15	j	j	PROPN
ejpam-534	734	16	and	and	CCONJ
ejpam-534	734	17	then	then	ADV
ejpam-534	734	18	using	use	VERB
ejpam-534	734	19	(	(	PUNCT
ejpam-534	734	20	46	46	NUM
ejpam-534	734	21	)	)	PUNCT
ejpam-534	734	22	,	,	PUNCT
ejpam-534	734	23	(	(	PUNCT
ejpam-534	734	24	47	47	NUM
ejpam-534	734	25	)	)	PUNCT
ejpam-534	734	26	,	,	PUNCT
ejpam-534	734	27	(	(	PUNCT
ejpam-534	734	28	52	52	NUM
ejpam-534	734	29	)	)	PUNCT
ejpam-534	734	30	and	and	CCONJ
ejpam-534	734	31	γ(t	γ(t	NOUN
ejpam-534	734	32	)	)	PUNCT
ejpam-534	734	33	>	>	X
ejpam-534	734	34	0	0	NUM
ejpam-534	734	35	,	,	PUNCT
ejpam-534	734	36	we	we	PRON
ejpam-534	734	37	have	have	VERB
ejpam-534	734	38	2p̄(t)t	2p̄(t)t	NUM
ejpam-534	734	39	(	(	PUNCT
ejpam-534	734	40	gx	gx	PROPN
ejpam-534	734	41	ȳ(t	ȳ(t	PROPN
ejpam-534	734	42	)	)	PUNCT
ejpam-534	734	43	)	)	PUNCT
ejpam-534	735	1	+	+	CCONJ
ejpam-534	735	2	p̄(t)t	p̄(t)t	NOUN
ejpam-534	735	3	(	(	PUNCT
ejpam-534	735	4	b+	b+	X
ejpam-534	735	5	(	(	PUNCT
ejpam-534	735	6	gx	gx	PROPN
ejpam-534	735	7	ȳ(t))x)p̄(t	ȳ(t))x)p̄(t	PROPN
ejpam-534	735	8	)	)	PUNCT
ejpam-534	735	9	=	=	SYM
ejpam-534	735	10	0	0	NUM
ejpam-534	735	11	,	,	PUNCT
ejpam-534	735	12	t	t	PROPN
ejpam-534	735	13	∈	∈	PROPN
ejpam-534	736	1	i	i	PRON
ejpam-534	736	2	,	,	PUNCT
ejpam-534	736	3	which	which	PRON
ejpam-534	736	4	contradicts	contradict	VERB
ejpam-534	736	5	hypothesis	hypothesis	NOUN
ejpam-534	736	6	(	(	PUNCT
ejpam-534	736	7	c3	c3	PROPN
ejpam-534	736	8	)	)	PUNCT
ejpam-534	736	9	unless	unless	SCONJ
ejpam-534	736	10	p̄(t	p̄(t	ADJ
ejpam-534	736	11	)	)	PUNCT
ejpam-534	736	12	=	=	SYM
ejpam-534	736	13	0	0	NUM
ejpam-534	736	14	,	,	PUNCT
ejpam-534	736	15	t	t	PROPN
ejpam-534	736	16	∈	∈	PROPN
ejpam-534	737	1	i	i	PRON
ejpam-534	737	2	.	.	PUNCT
ejpam-534	738	1	(	(	PUNCT
ejpam-534	738	2	54	54	NUM
ejpam-534	738	3	)	)	PUNCT
ejpam-534	738	4	t.	t.	NOUN
ejpam-534	738	5	gulati	gulati	PROPN
ejpam-534	738	6	and	and	CCONJ
ejpam-534	738	7	g.	g.	PROPN
ejpam-534	738	8	mehndiratta	mehndiratta	PROPN
ejpam-534	738	9	/	/	SYM
ejpam-534	738	10	eur	eur	PROPN
ejpam-534	738	11	.	.	PUNCT
ejpam-534	739	1	j.	j.	PROPN
ejpam-534	739	2	pure	pure	PROPN
ejpam-534	739	3	appl	appl	PROPN
ejpam-534	739	4	.	.	PROPN
ejpam-534	739	5	math	math	PROPN
ejpam-534	739	6	,	,	PUNCT
ejpam-534	739	7	3	3	NUM
ejpam-534	739	8	(	(	PUNCT
ejpam-534	739	9	2010	2010	NUM
ejpam-534	739	10	)	)	PUNCT
ejpam-534	739	11	,	,	PUNCT
ejpam-534	739	12	786	786	NUM
ejpam-534	739	13	-	-	SYM
ejpam-534	739	14	805	805	NUM
ejpam-534	739	15	802	802	NUM
ejpam-534	739	16	and	and	CCONJ
ejpam-534	739	17	thus	thus	ADV
ejpam-534	739	18	relation	relation	NOUN
ejpam-534	739	19	(	(	PUNCT
ejpam-534	739	20	52	52	NUM
ejpam-534	739	21	)	)	PUNCT
ejpam-534	739	22	gives	give	VERB
ejpam-534	739	23	β(t	β(t	PROPN
ejpam-534	739	24	)	)	PUNCT
ejpam-534	740	1	=	=	SYM
ejpam-534	740	2	0	0	NUM
ejpam-534	740	3	,	,	PUNCT
ejpam-534	740	4	t	t	PROPN
ejpam-534	740	5	∈	∈	PROPN
ejpam-534	741	1	i	i	PRON
ejpam-534	741	2	.	.	PUNCT
ejpam-534	742	1	for	for	ADP
ejpam-534	742	2	j	j	PROPN
ejpam-534	742	3	∈	∈	PROPN
ejpam-534	742	4	m	m	PROPN
ejpam-534	742	5	,	,	PUNCT
ejpam-534	742	6	equation	equation	NOUN
ejpam-534	742	7	(	(	PUNCT
ejpam-534	742	8	44	44	NUM
ejpam-534	742	9	)	)	PUNCT
ejpam-534	742	10	yield	yield	NOUN
ejpam-534	742	11	g	g	PROPN
ejpam-534	742	12	j	j	PROPN
ejpam-534	742	13	=	=	PROPN
ejpam-534	742	14	−µ	−µ	PROPN
ejpam-534	742	15	j(t	j(t	PROPN
ejpam-534	742	16	)	)	PUNCT
ejpam-534	743	1	γ(t	γ(t	NOUN
ejpam-534	743	2	)	)	PUNCT
ejpam-534	743	3	≦	≦	NUM
ejpam-534	743	4	0	0	NUM
ejpam-534	743	5	,	,	PUNCT
ejpam-534	743	6	t	t	PROPN
ejpam-534	743	7	∈	∈	PROPN
ejpam-534	744	1	i	i	PRON
ejpam-534	744	2	,	,	PUNCT
ejpam-534	744	3	j	j	PROPN
ejpam-534	744	4	∈	∈	PROPN
ejpam-534	744	5	m	m	VERB
ejpam-534	744	6	.	.	PUNCT
ejpam-534	745	1	thus	thus	ADV
ejpam-534	745	2	ū(t	ū(t	ADJ
ejpam-534	745	3	)	)	PUNCT
ejpam-534	745	4	is	be	AUX
ejpam-534	745	5	feasible	feasible	ADJ
ejpam-534	745	6	for	for	ADP
ejpam-534	745	7	(	(	PUNCT
ejpam-534	745	8	p	p	NOUN
ejpam-534	745	9	)	)	PUNCT
ejpam-534	745	10	.	.	PUNCT
ejpam-534	746	1	as	as	ADP
ejpam-534	746	2	p̄(t	p̄(t	ADJ
ejpam-534	746	3	)	)	PUNCT
ejpam-534	746	4	=	=	SYM
ejpam-534	746	5	0	0	NUM
ejpam-534	746	6	,	,	PUNCT
ejpam-534	746	7	t	t	PROPN
ejpam-534	746	8	∈	∈	PROPN
ejpam-534	746	9	i	i	PRON
ejpam-534	746	10	,	,	PUNCT
ejpam-534	746	11	the	the	DET
ejpam-534	746	12	two	two	NUM
ejpam-534	746	13	objectives	objective	NOUN
ejpam-534	746	14	functionals	functional	NOUN
ejpam-534	746	15	are	be	AUX
ejpam-534	746	16	equal	equal	ADJ
ejpam-534	746	17	.	.	PUNCT
ejpam-534	747	1	now	now	ADV
ejpam-534	747	2	,	,	PUNCT
ejpam-534	747	3	suppose	suppose	VERB
ejpam-534	747	4	that	that	SCONJ
ejpam-534	747	5	ū(t	ū(t	NOUN
ejpam-534	747	6	)	)	PUNCT
ejpam-534	747	7	is	be	AUX
ejpam-534	747	8	not	not	PART
ejpam-534	747	9	an	an	DET
ejpam-534	747	10	efficient	efficient	ADJ
ejpam-534	747	11	solution	solution	NOUN
ejpam-534	747	12	of	of	ADP
ejpam-534	747	13	(	(	PUNCT
ejpam-534	747	14	p	p	NOUN
ejpam-534	747	15	)	)	PUNCT
ejpam-534	747	16	.	.	PUNCT
ejpam-534	748	1	then	then	ADV
ejpam-534	748	2	,	,	PUNCT
ejpam-534	748	3	there	there	PRON
ejpam-534	748	4	exists	exist	VERB
ejpam-534	748	5	û(t	û(t	NOUN
ejpam-534	748	6	)	)	PUNCT
ejpam-534	748	7	∈	∈	PROPN
ejpam-534	748	8	x	x	PUNCT
ejpam-534	748	9	such	such	ADJ
ejpam-534	748	10	that	that	DET
ejpam-534	748	11	∫	∫	PROPN
ejpam-534	748	12	f	f	PROPN
ejpam-534	748	13	r(t	r(t	PROPN
ejpam-534	748	14	,	,	PUNCT
ejpam-534	748	15	û	û	NUM
ejpam-534	748	16	,	,	PUNCT
ejpam-534	748	17	˙̂u)d	˙̂u)d	PROPN
ejpam-534	748	18	t	t	PROPN
ejpam-534	748	19	<	<	X
ejpam-534	748	20	∫	∫	PROPN
ejpam-534	748	21	f	f	PROPN
ejpam-534	748	22	r(t	r(t	PROPN
ejpam-534	748	23	,	,	PUNCT
ejpam-534	748	24	ū	ū	NOUN
ejpam-534	748	25	,	,	PUNCT
ejpam-534	748	26	˙̄u)d	˙̄u)d	PROPN
ejpam-534	748	27	t	t	PROPN
ejpam-534	748	28	for	for	ADP
ejpam-534	748	29	some	some	DET
ejpam-534	748	30	r	r	NOUN
ejpam-534	748	31	∈	∈	PROPN
ejpam-534	748	32	k	k	PROPN
ejpam-534	748	33	and	and	CCONJ
ejpam-534	748	34	∫	∫	PROPN
ejpam-534	748	35	f	f	PROPN
ejpam-534	748	36	i(t	i(t	PROPN
ejpam-534	748	37	,	,	PUNCT
ejpam-534	748	38	û	û	NUM
ejpam-534	748	39	,	,	PUNCT
ejpam-534	749	1	˙̂u)d	˙̂u)d	PROPN
ejpam-534	749	2	t	t	PROPN
ejpam-534	749	3	≦	≦	PROPN
ejpam-534	749	4	∫	∫	PROPN
ejpam-534	749	5	f	f	PROPN
ejpam-534	749	6	i(t	i(t	PROPN
ejpam-534	749	7	,	,	PUNCT
ejpam-534	749	8	ū	ū	NOUN
ejpam-534	749	9	,	,	PUNCT
ejpam-534	749	10	˙̄u)d	˙̄u)d	PROPN
ejpam-534	749	11	t	t	PROPN
ejpam-534	749	12	,	,	PUNCT
ejpam-534	749	13	i	i	PRON
ejpam-534	749	14	∈	∈	PROPN
ejpam-534	749	15	kr	kr	PROPN
ejpam-534	749	16	.	.	PUNCT
ejpam-534	750	1	using	use	VERB
ejpam-534	750	2	(	(	PUNCT
ejpam-534	750	3	54	54	NUM
ejpam-534	750	4	)	)	PUNCT
ejpam-534	750	5	,	,	PUNCT
ejpam-534	750	6	we	we	PRON
ejpam-534	750	7	get	get	VERB
ejpam-534	750	8	∫	∫	PROPN
ejpam-534	750	9	f	f	PROPN
ejpam-534	750	10	r(t	r(t	PROPN
ejpam-534	750	11	,	,	PUNCT
ejpam-534	750	12	û	û	NUM
ejpam-534	750	13	,	,	PUNCT
ejpam-534	750	14	˙̂u)d	˙̂u)d	PROPN
ejpam-534	750	15	t	t	PROPN
ejpam-534	750	16	<	<	X
ejpam-534	750	17	∫	∫	PROPN
ejpam-534	750	18	(	(	PUNCT
ejpam-534	750	19	f	f	PROPN
ejpam-534	750	20	r(t	r(t	PROPN
ejpam-534	750	21	,	,	PUNCT
ejpam-534	750	22	ū	ū	NOUN
ejpam-534	750	23	,	,	PUNCT
ejpam-534	750	24	˙̄u)−	˙̄u)−	PROPN
ejpam-534	750	25	1	1	NUM
ejpam-534	750	26	2	2	NUM
ejpam-534	750	27	p̄(t)t	p̄(t)t	NOUN
ejpam-534	750	28	ar(t	ar(t	NOUN
ejpam-534	750	29	,	,	PUNCT
ejpam-534	750	30	ū	ū	NOUN
ejpam-534	750	31	,	,	PUNCT
ejpam-534	750	32	˙̄u	˙̄u	NOUN
ejpam-534	750	33	,	,	PUNCT
ejpam-534	750	34	¨̄u	¨̄u	NOUN
ejpam-534	750	35	,	,	PUNCT
ejpam-534	750	36	...	...	PUNCT
ejpam-534	750	37	ū	ū	NOUN
ejpam-534	750	38	,	,	PUNCT
ejpam-534	750	39	....	....	PUNCT
ejpam-534	751	1	ū	ū	NOUN
ejpam-534	751	2	)	)	PUNCT
ejpam-534	751	3	p̄(t))d	p̄(t))d	NOUN
ejpam-534	751	4	t	t	NOUN
ejpam-534	751	5	for	for	ADP
ejpam-534	751	6	some	some	DET
ejpam-534	751	7	r	r	NOUN
ejpam-534	751	8	∈	∈	PROPN
ejpam-534	751	9	k	k	PROPN
ejpam-534	751	10	and	and	CCONJ
ejpam-534	751	11	∫	∫	PROPN
ejpam-534	751	12	f	f	PROPN
ejpam-534	751	13	i(t	i(t	PROPN
ejpam-534	751	14	,	,	PUNCT
ejpam-534	751	15	û	û	NUM
ejpam-534	751	16	,	,	PUNCT
ejpam-534	751	17	˙̂u)d	˙̂u)d	PROPN
ejpam-534	751	18	t	t	PROPN
ejpam-534	751	19	≦	≦	PROPN
ejpam-534	751	20	∫	∫	PROPN
ejpam-534	751	21	(	(	PUNCT
ejpam-534	751	22	f	f	PROPN
ejpam-534	751	23	i(t	i(t	PROPN
ejpam-534	751	24	,	,	PUNCT
ejpam-534	751	25	ū	ū	NOUN
ejpam-534	751	26	,	,	PUNCT
ejpam-534	751	27	˙̄u)−	˙̄u)−	PROPN
ejpam-534	751	28	1	1	NUM
ejpam-534	751	29	2	2	NUM
ejpam-534	751	30	p̄(t)t	p̄(t)t	NOUN
ejpam-534	751	31	ai(t	ai(t	NOUN
ejpam-534	751	32	,	,	PUNCT
ejpam-534	751	33	ū	ū	NOUN
ejpam-534	751	34	,	,	PUNCT
ejpam-534	751	35	˙̄u	˙̄u	NOUN
ejpam-534	751	36	,	,	PUNCT
ejpam-534	751	37	¨̄u	¨̄u	NOUN
ejpam-534	751	38	,	,	PUNCT
ejpam-534	751	39	...	...	PUNCT
ejpam-534	751	40	ū	ū	NOUN
ejpam-534	751	41	,	,	PUNCT
ejpam-534	751	42	....	....	PUNCT
ejpam-534	751	43	ū	ū	NOUN
ejpam-534	751	44	)	)	PUNCT
ejpam-534	751	45	p̄(t))d	p̄(t))d	NOUN
ejpam-534	751	46	t	t	PROPN
ejpam-534	751	47	,	,	PUNCT
ejpam-534	751	48	i	i	PRON
ejpam-534	751	49	∈	∈	PROPN
ejpam-534	751	50	kr	kr	PROPN
ejpam-534	751	51	,	,	PUNCT
ejpam-534	751	52	which	which	PRON
ejpam-534	751	53	contradicts	contradict	VERB
ejpam-534	751	54	the	the	DET
ejpam-534	751	55	weak	weak	ADJ
ejpam-534	751	56	duality	duality	NOUN
ejpam-534	751	57	theorem	theorem	VERB
ejpam-534	751	58	.	.	PUNCT
ejpam-534	751	59	hence	hence	ADV
ejpam-534	751	60	ū(t	ū(t	NOUN
ejpam-534	751	61	)	)	PUNCT
ejpam-534	751	62	is	be	AUX
ejpam-534	751	63	an	an	DET
ejpam-534	751	64	efficient	efficient	ADJ
ejpam-534	751	65	solution	solution	NOUN
ejpam-534	751	66	for	for	ADP
ejpam-534	751	67	(	(	PUNCT
ejpam-534	751	68	p	p	NOUN
ejpam-534	751	69	)	)	PUNCT
ejpam-534	751	70	.	.	PUNCT
ejpam-534	752	1	remark	remark	PROPN
ejpam-534	752	2	3	3	NUM
ejpam-534	752	3	.	.	PUNCT
ejpam-534	753	1	for	for	ADP
ejpam-534	753	2	the	the	DET
ejpam-534	753	3	single	single	ADJ
ejpam-534	753	4	objective	objective	ADJ
ejpam-534	753	5	problems	problem	NOUN
ejpam-534	753	6	in	in	ADP
ejpam-534	753	7	section	section	NOUN
ejpam-534	753	8	2	2	NUM
ejpam-534	753	9	,	,	PUNCT
ejpam-534	753	10	the	the	DET
ejpam-534	753	11	hypothesis	hypothesis	NOUN
ejpam-534	753	12	(	(	PUNCT
ejpam-534	753	13	c2	c2	PROPN
ejpam-534	753	14	)	)	PUNCT
ejpam-534	753	15	reduces	reduce	VERB
ejpam-534	753	16	to	to	PART
ejpam-534	753	17	(	(	PUNCT
ejpam-534	753	18	c2′	c2′	PROPN
ejpam-534	753	19	)	)	PUNCT
ejpam-534	753	20	fx	fx	NOUN
ejpam-534	754	1	−	−	PROPN
ejpam-534	755	1	d	d	X
ejpam-534	755	2	f	f	PROPN
ejpam-534	755	3	ẋ	ẋ	PROPN
ejpam-534	756	1	6=	6=	PROPN
ejpam-534	756	2	0	0	NUM
ejpam-534	756	3	,	,	PUNCT
ejpam-534	756	4	t	t	PROPN
ejpam-534	756	5	∈	∈	PROPN
ejpam-534	757	1	i	i	PRON
ejpam-534	757	2	.	.	PUNCT
ejpam-534	758	1	therefore	therefore	ADV
ejpam-534	758	2	following	follow	VERB
ejpam-534	758	3	the	the	DET
ejpam-534	758	4	above	above	ADJ
ejpam-534	758	5	proof	proof	NOUN
ejpam-534	758	6	,	,	PUNCT
ejpam-534	758	7	theorem	theorem	VERB
ejpam-534	758	8	2	2	NUM
ejpam-534	758	9	can	can	AUX
ejpam-534	758	10	also	also	ADV
ejpam-534	758	11	be	be	AUX
ejpam-534	758	12	proved	prove	VERB
ejpam-534	758	13	if	if	SCONJ
ejpam-534	758	14	hypothesis	hypothesis	NOUN
ejpam-534	758	15	(	(	PUNCT
ejpam-534	758	16	b2	b2	NOUN
ejpam-534	758	17	)	)	PUNCT
ejpam-534	758	18	is	be	AUX
ejpam-534	758	19	replaced	replace	VERB
ejpam-534	758	20	by	by	ADP
ejpam-534	758	21	(	(	PUNCT
ejpam-534	758	22	c2′	c2′	PROPN
ejpam-534	758	23	)	)	PUNCT
ejpam-534	758	24	.	.	PUNCT
ejpam-534	759	1	this	this	PRON
ejpam-534	759	2	also	also	ADV
ejpam-534	759	3	makes	make	VERB
ejpam-534	759	4	the	the	DET
ejpam-534	759	5	proof	proof	NOUN
ejpam-534	759	6	simpler	simple	ADJ
ejpam-534	759	7	as	as	SCONJ
ejpam-534	759	8	it	it	PRON
ejpam-534	759	9	does	do	AUX
ejpam-534	759	10	not	not	PART
ejpam-534	759	11	require	require	VERB
ejpam-534	759	12	equation	equation	NOUN
ejpam-534	759	13	(	(	PUNCT
ejpam-534	759	14	18	18	NUM
ejpam-534	759	15	)	)	PUNCT
ejpam-534	759	16	.	.	PUNCT
ejpam-534	760	1	however	however	ADV
ejpam-534	760	2	,	,	PUNCT
ejpam-534	760	3	we	we	PRON
ejpam-534	760	4	proved	prove	VERB
ejpam-534	760	5	theorem	theorem	ADJ
ejpam-534	760	6	2	2	NUM
ejpam-534	760	7	assuming	assume	VERB
ejpam-534	760	8	(	(	PUNCT
ejpam-534	760	9	b2	b2	NOUN
ejpam-534	760	10	)	)	PUNCT
ejpam-534	760	11	,	,	PUNCT
ejpam-534	760	12	which	which	PRON
ejpam-534	760	13	is	be	AUX
ejpam-534	760	14	same	same	ADJ
ejpam-534	760	15	as	as	ADP
ejpam-534	760	16	hypothesis	hypothesis	NOUN
ejpam-534	760	17	(	(	PUNCT
ejpam-534	760	18	a2	a2	PROPN
ejpam-534	760	19	)	)	PUNCT
ejpam-534	760	20	in	in	ADP
ejpam-534	760	21	[	[	X
ejpam-534	760	22	8	8	NUM
ejpam-534	760	23	]	]	PUNCT
ejpam-534	760	24	.	.	PUNCT
ejpam-534	761	1	theorem	theorem	ADJ
ejpam-534	761	2	9	9	NUM
ejpam-534	761	3	(	(	PUNCT
ejpam-534	761	4	strict	strict	ADJ
ejpam-534	761	5	converse	converse	NOUN
ejpam-534	761	6	duality	duality	NOUN
ejpam-534	761	7	)	)	PUNCT
ejpam-534	761	8	.	.	PUNCT
ejpam-534	762	1	let	let	VERB
ejpam-534	762	2	x̄(t	x̄(t	PRON
ejpam-534	762	3	)	)	PUNCT
ejpam-534	762	4	and	and	CCONJ
ejpam-534	762	5	(	(	PUNCT
ejpam-534	762	6	ū(t	ū(t	PROPN
ejpam-534	762	7	)	)	PUNCT
ejpam-534	762	8	,	,	PUNCT
ejpam-534	762	9	λ̄	λ̄	ADP
ejpam-534	762	10	,	,	PUNCT
ejpam-534	762	11	ȳ(t	ȳ(t	NOUN
ejpam-534	762	12	)	)	PUNCT
ejpam-534	762	13	,	,	PUNCT
ejpam-534	762	14	p̄(t	p̄(t	PROPN
ejpam-534	762	15	)	)	PUNCT
ejpam-534	762	16	)	)	PUNCT
ejpam-534	763	1	be	be	AUX
ejpam-534	763	2	efficient	efficient	ADJ
ejpam-534	763	3	solutions	solution	NOUN
ejpam-534	763	4	of	of	ADP
ejpam-534	763	5	(	(	PUNCT
ejpam-534	763	6	p	p	NOUN
ejpam-534	763	7	)	)	PUNCT
ejpam-534	763	8	and	and	CCONJ
ejpam-534	763	9	(	(	PUNCT
ejpam-534	763	10	mwd	mwd	PROPN
ejpam-534	763	11	)	)	PUNCT
ejpam-534	763	12	respectively	respectively	ADV
ejpam-534	763	13	,	,	PUNCT
ejpam-534	763	14	such	such	ADJ
ejpam-534	763	15	that	that	DET
ejpam-534	763	16	∫	∫	PROPN
ejpam-534	763	17	k∑	k∑	PROPN
ejpam-534	763	18	i=1	i=1	PROPN
ejpam-534	764	1	λ̄i	λ̄i	PROPN
ejpam-534	764	2	f	f	PROPN
ejpam-534	764	3	i(t	i(t	PROPN
ejpam-534	764	4	,	,	PUNCT
ejpam-534	764	5	x̄	x̄	NOUN
ejpam-534	764	6	,	,	PUNCT
ejpam-534	764	7	˙̄x)d	˙̄x)d	PROPN
ejpam-534	764	8	t	t	PROPN
ejpam-534	764	9	=	=	SYM
ejpam-534	764	10	∫	∫	PROPN
ejpam-534	764	11	k∑	k∑	PROPN
ejpam-534	764	12	i=1	i=1	PROPN
ejpam-534	765	1	λ̄i	λ̄i	PROPN
ejpam-534	765	2	(	(	PUNCT
ejpam-534	765	3	f	f	PROPN
ejpam-534	765	4	i(t	i(t	PROPN
ejpam-534	765	5	,	,	PUNCT
ejpam-534	765	6	ū	ū	NOUN
ejpam-534	765	7	,	,	PUNCT
ejpam-534	765	8	˙̄u)−	˙̄u)−	PROPN
ejpam-534	765	9	1	1	NUM
ejpam-534	765	10	2	2	NUM
ejpam-534	765	11	p̄(t)t	p̄(t)t	NOUN
ejpam-534	765	12	ai(t	ai(t	NOUN
ejpam-534	765	13	,	,	PUNCT
ejpam-534	765	14	ū	ū	NOUN
ejpam-534	765	15	,	,	PUNCT
ejpam-534	765	16	˙̄u	˙̄u	NOUN
ejpam-534	765	17	,	,	PUNCT
ejpam-534	765	18	¨̄u	¨̄u	NOUN
ejpam-534	765	19	,	,	PUNCT
ejpam-534	765	20	...	...	PUNCT
ejpam-534	765	21	ū	ū	NOUN
ejpam-534	765	22	,	,	PUNCT
ejpam-534	765	23	....	....	PUNCT
ejpam-534	765	24	ū	ū	NOUN
ejpam-534	765	25	)	)	PUNCT
ejpam-534	765	26	p̄(t))d	p̄(t))d	NOUN
ejpam-534	765	27	t	t	NOUN
ejpam-534	765	28	(	(	PUNCT
ejpam-534	765	29	55	55	NUM
ejpam-534	765	30	)	)	PUNCT
ejpam-534	766	1	if	if	SCONJ
ejpam-534	766	2	(	(	PUNCT
ejpam-534	766	3	i	i	NOUN
ejpam-534	766	4	)	)	PUNCT
ejpam-534	766	5	∫	∫	PROPN
ejpam-534	766	6	k∑	k∑	PROPN
ejpam-534	766	7	i=1	i=1	PROPN
ejpam-534	767	1	λ̄i	λ̄i	PROPN
ejpam-534	767	2	f	f	PROPN
ejpam-534	767	3	i(t	i(t	PROPN
ejpam-534	767	4	,	,	PUNCT
ejpam-534	767	5	.	.	PUNCT
ejpam-534	767	6	,	,	PUNCT
ejpam-534	767	7	.)d	.)d	PROPN
ejpam-534	767	8	t	t	PROPN
ejpam-534	767	9	is	be	AUX
ejpam-534	767	10	second	second	ADJ
ejpam-534	767	11	-	-	PUNCT
ejpam-534	767	12	order	order	NOUN
ejpam-534	767	13	strictly	strictly	ADV
ejpam-534	767	14	(	(	PUNCT
ejpam-534	767	15	g	g	NOUN
ejpam-534	767	16	,	,	PUNCT
ejpam-534	767	17	ρ1)-convex	ρ1)-convex	NOUN
ejpam-534	767	18	at	at	ADP
ejpam-534	767	19	ū(t	ū(t	NOUN
ejpam-534	767	20	)	)	PUNCT
ejpam-534	767	21	,	,	PUNCT
ejpam-534	767	22	(	(	PUNCT
ejpam-534	767	23	ii	ii	NOUN
ejpam-534	767	24	)	)	PUNCT
ejpam-534	767	25	∫	∫	PROPN
ejpam-534	767	26	ȳ(t)t	ȳ(t)t	PROPN
ejpam-534	767	27	g(t	g(t	PROPN
ejpam-534	767	28	,	,	PUNCT
ejpam-534	767	29	.	.	PUNCT
ejpam-534	767	30	,	,	PUNCT
ejpam-534	768	1	.)d	.)d	PROPN
ejpam-534	768	2	t	t	PROPN
ejpam-534	768	3	is	be	AUX
ejpam-534	768	4	second	second	ADJ
ejpam-534	768	5	-	-	PUNCT
ejpam-534	768	6	order	order	NOUN
ejpam-534	768	7	(	(	PUNCT
ejpam-534	768	8	g	g	NOUN
ejpam-534	768	9	,	,	PUNCT
ejpam-534	768	10	ρ2)-convex	ρ2)-convex	NOUN
ejpam-534	768	11	at	at	ADP
ejpam-534	768	12	ū(t	ū(t	NOUN
ejpam-534	768	13	)	)	PUNCT
ejpam-534	768	14	,	,	PUNCT
ejpam-534	768	15	and	and	CCONJ
ejpam-534	768	16	t.	t.	PROPN
ejpam-534	768	17	gulati	gulati	PROPN
ejpam-534	768	18	and	and	CCONJ
ejpam-534	768	19	g.	g.	PROPN
ejpam-534	768	20	mehndiratta	mehndiratta	PROPN
ejpam-534	768	21	/	/	SYM
ejpam-534	768	22	eur	eur	PROPN
ejpam-534	768	23	.	.	PUNCT
ejpam-534	769	1	j.	j.	PROPN
ejpam-534	769	2	pure	pure	PROPN
ejpam-534	769	3	appl	appl	PROPN
ejpam-534	769	4	.	.	PROPN
ejpam-534	769	5	math	math	PROPN
ejpam-534	769	6	,	,	PUNCT
ejpam-534	769	7	3	3	NUM
ejpam-534	769	8	(	(	PUNCT
ejpam-534	769	9	2010	2010	NUM
ejpam-534	769	10	)	)	PUNCT
ejpam-534	769	11	,	,	PUNCT
ejpam-534	769	12	786	786	NUM
ejpam-534	769	13	-	-	SYM
ejpam-534	769	14	805	805	NUM
ejpam-534	769	15	803	803	NUM
ejpam-534	769	16	(	(	PUNCT
ejpam-534	769	17	iii	iii	NOUN
ejpam-534	769	18	)	)	PUNCT
ejpam-534	769	19	ρ1	ρ1	NOUN
ejpam-534	769	20	+	+	NOUN
ejpam-534	769	21	ρ2	ρ2	NOUN
ejpam-534	769	22	≧	≧	NOUN
ejpam-534	769	23	0	0	X
ejpam-534	769	24	.	.	PUNCT
ejpam-534	770	1	then	then	ADV
ejpam-534	770	2	x̄(t	x̄(t	NUM
ejpam-534	770	3	)	)	PUNCT
ejpam-534	771	1	=	=	SYM
ejpam-534	771	2	ū(t	ū(t	NOUN
ejpam-534	771	3	)	)	PUNCT
ejpam-534	771	4	.	.	PUNCT
ejpam-534	772	1	proof	proof	NOUN
ejpam-534	772	2	.	.	PUNCT
ejpam-534	773	1	suppose	suppose	VERB
ejpam-534	773	2	x̄(t0	x̄(t0	PROPN
ejpam-534	773	3	)	)	PUNCT
ejpam-534	773	4	6=	6=	X
ejpam-534	774	1	ū(t0	ū(t0	NOUN
ejpam-534	774	2	)	)	PUNCT
ejpam-534	774	3	for	for	ADP
ejpam-534	774	4	some	some	DET
ejpam-534	774	5	t0	t0	PROPN
ejpam-534	774	6	∈	∈	PROPN
ejpam-534	775	1	i	i	PRON
ejpam-534	775	2	.	.	PUNCT
ejpam-534	776	1	by	by	ADP
ejpam-534	776	2	hypothesis	hypothesis	NOUN
ejpam-534	776	3	(	(	PUNCT
ejpam-534	776	4	i	i	NOUN
ejpam-534	776	5	)	)	PUNCT
ejpam-534	776	6	,	,	PUNCT
ejpam-534	776	7	we	we	PRON
ejpam-534	776	8	have	have	VERB
ejpam-534	776	9	∫	∫	PROPN
ejpam-534	776	10	k∑	k∑	PROPN
ejpam-534	776	11	i=1	i=1	PROPN
ejpam-534	777	1	λ̄i	λ̄i	PROPN
ejpam-534	777	2	f	f	PROPN
ejpam-534	777	3	i(t0	i(t0	PROPN
ejpam-534	777	4	,	,	PUNCT
ejpam-534	777	5	x̄	x̄	NOUN
ejpam-534	777	6	,	,	PUNCT
ejpam-534	777	7	˙̄x)d	˙̄x)d	PROPN
ejpam-534	777	8	t	t	PROPN
ejpam-534	777	9	−	−	PROPN
ejpam-534	777	10	∫	∫	PROPN
ejpam-534	778	1	k∑	k∑	PROPN
ejpam-534	778	2	i=1	i=1	PROPN
ejpam-534	779	1	λ̄i	λ̄i	PROPN
ejpam-534	779	2	f	f	PROPN
ejpam-534	779	3	i(t0	i(t0	PROPN
ejpam-534	779	4	,	,	PUNCT
ejpam-534	779	5	ū	ū	PROPN
ejpam-534	779	6	,	,	PUNCT
ejpam-534	779	7	˙̄u)d	˙̄u)d	PROPN
ejpam-534	780	1	t	t	PROPN
ejpam-534	780	2	>	>	X
ejpam-534	780	3	∫	∫	PROPN
ejpam-534	780	4	(	(	PUNCT
ejpam-534	780	5	g(t0	g(t0	PROPN
ejpam-534	780	6	,	,	PUNCT
ejpam-534	780	7	x̄	x̄	PROPN
ejpam-534	780	8	,	,	PUNCT
ejpam-534	780	9	ū	ū	PROPN
ejpam-534	780	10	;	;	PUNCT
ejpam-534	780	11	k∑	k∑	PROPN
ejpam-534	780	12	i=1	i=1	PROPN
ejpam-534	781	1	λ̄i	λ̄i	PROPN
ejpam-534	781	2	(	(	PUNCT
ejpam-534	781	3	f	f	NOUN
ejpam-534	781	4	i	i	NOUN
ejpam-534	781	5	x	x	PROPN
ejpam-534	781	6	(	(	PUNCT
ejpam-534	781	7	t0	t0	NOUN
ejpam-534	781	8	,	,	PUNCT
ejpam-534	781	9	ū	ū	NOUN
ejpam-534	781	10	,	,	PUNCT
ejpam-534	781	11	˙̄u)−	˙̄u)−	PROPN
ejpam-534	781	12	d	d	PROPN
ejpam-534	782	1	f	f	PROPN
ejpam-534	783	1	i	i	PRON
ejpam-534	783	2	ẋ	ẋ	PROPN
ejpam-534	783	3	(	(	PUNCT
ejpam-534	783	4	t0	t0	NOUN
ejpam-534	783	5	,	,	PUNCT
ejpam-534	783	6	ū	ū	NOUN
ejpam-534	783	7	,	,	PUNCT
ejpam-534	783	8	˙̄u	˙̄u	X
ejpam-534	783	9	)	)	PUNCT
ejpam-534	784	1	+	+	ADJ
ejpam-534	784	2	ai(t0	ai(t0	ADJ
ejpam-534	784	3	,	,	PUNCT
ejpam-534	784	4	ū	ū	NOUN
ejpam-534	784	5	,	,	PUNCT
ejpam-534	784	6	˙̄u	˙̄u	NOUN
ejpam-534	784	7	,	,	PUNCT
ejpam-534	784	8	¨̄u	¨̄u	NOUN
ejpam-534	784	9	,	,	PUNCT
ejpam-534	784	10	...	...	PUNCT
ejpam-534	784	11	ū	ū	NOUN
ejpam-534	784	12	,	,	PUNCT
ejpam-534	784	13	....	....	PUNCT
ejpam-534	784	14	ū	ū	NOUN
ejpam-534	784	15	)	)	PUNCT
ejpam-534	784	16	p̄(t0)))−	p̄(t0)))−	NOUN
ejpam-534	784	17	1	1	NUM
ejpam-534	784	18	2	2	NUM
ejpam-534	784	19	k∑	k∑	NOUN
ejpam-534	784	20	i=1	i=1	PROPN
ejpam-534	784	21	λ̄i	λ̄i	PROPN
ejpam-534	784	22	p̄(t0	p̄(t0	NOUN
ejpam-534	784	23	)	)	PUNCT
ejpam-534	784	24	t	t	PROPN
ejpam-534	784	25	ai(t0	ai(t0	PROPN
ejpam-534	784	26	,	,	PUNCT
ejpam-534	784	27	ū	ū	NOUN
ejpam-534	784	28	,	,	PUNCT
ejpam-534	784	29	˙̄u	˙̄u	NOUN
ejpam-534	784	30	,	,	PUNCT
ejpam-534	784	31	¨̄u	¨̄u	NOUN
ejpam-534	784	32	,	,	PUNCT
ejpam-534	784	33	...	...	PUNCT
ejpam-534	784	34	ū	ū	NOUN
ejpam-534	784	35	,	,	PUNCT
ejpam-534	784	36	....	....	PUNCT
ejpam-534	784	37	ū	ū	PROPN
ejpam-534	784	38	)	)	PUNCT
ejpam-534	784	39	p̄(t0	p̄(t0	NOUN
ejpam-534	784	40	)	)	PUNCT
ejpam-534	785	1	+	+	NOUN
ejpam-534	785	2	ρ1d2(t0	ρ1d2(t0	NOUN
ejpam-534	785	3	,	,	PUNCT
ejpam-534	785	4	x̄	x̄	NOUN
ejpam-534	785	5	,	,	PUNCT
ejpam-534	785	6	ū))d	ū))d	INTJ
ejpam-534	785	7	t.	t.	NOUN
ejpam-534	785	8	(	(	PUNCT
ejpam-534	785	9	56	56	NUM
ejpam-534	785	10	)	)	PUNCT
ejpam-534	785	11	by	by	ADP
ejpam-534	785	12	hypothesis	hypothesis	NOUN
ejpam-534	785	13	(	(	PUNCT
ejpam-534	785	14	ii	ii	NOUN
ejpam-534	785	15	)	)	PUNCT
ejpam-534	785	16	,	,	PUNCT
ejpam-534	785	17	we	we	PRON
ejpam-534	785	18	get	get	VERB
ejpam-534	785	19	∫	∫	PROPN
ejpam-534	785	20	ȳ(t0	ȳ(t0	PROPN
ejpam-534	785	21	)	)	PUNCT
ejpam-534	785	22	t	t	PROPN
ejpam-534	785	23	g(t0	g(t0	PROPN
ejpam-534	785	24	,	,	PUNCT
ejpam-534	785	25	x̄	x̄	PROPN
ejpam-534	785	26	,	,	PUNCT
ejpam-534	785	27	˙̄x)d	˙̄x)d	PROPN
ejpam-534	785	28	t	t	PROPN
ejpam-534	786	1	−	−	PROPN
ejpam-534	786	2	∫	∫	PROPN
ejpam-534	786	3	ȳ(t0	ȳ(t0	PROPN
ejpam-534	786	4	)	)	PUNCT
ejpam-534	786	5	t	t	PROPN
ejpam-534	786	6	g(t0	g(t0	PROPN
ejpam-534	786	7	,	,	PUNCT
ejpam-534	786	8	ū	ū	PROPN
ejpam-534	786	9	,	,	PUNCT
ejpam-534	786	10	˙̄u)d	˙̄u)d	PROPN
ejpam-534	787	1	t	t	PROPN
ejpam-534	787	2	≧	≧	NUM
ejpam-534	787	3	∫	∫	PROPN
ejpam-534	787	4	(	(	PUNCT
ejpam-534	787	5	g(t0	g(t0	PROPN
ejpam-534	787	6	,	,	PUNCT
ejpam-534	787	7	x̄	x̄	PROPN
ejpam-534	787	8	,	,	PUNCT
ejpam-534	787	9	ū	ū	PROPN
ejpam-534	787	10	;	;	PUNCT
ejpam-534	787	11	gx(t0	gx(t0	PROPN
ejpam-534	787	12	,	,	PUNCT
ejpam-534	787	13	ū	ū	NOUN
ejpam-534	787	14	,	,	PUNCT
ejpam-534	787	15	˙̄u	˙̄u	NOUN
ejpam-534	787	16	)	)	PUNCT
ejpam-534	787	17	ȳ(t0)−	ȳ(t0)−	PROPN
ejpam-534	788	1	d(g	d(g	PROPN
ejpam-534	788	2	ẋ(t0	ẋ(t0	PROPN
ejpam-534	788	3	,	,	PUNCT
ejpam-534	788	4	ū	ū	NOUN
ejpam-534	788	5	,	,	PUNCT
ejpam-534	788	6	˙̄u	˙̄u	X
ejpam-534	788	7	)	)	PUNCT
ejpam-534	788	8	ȳ(t0))+	ȳ(t0))+	ADJ
ejpam-534	788	9	b(t0	b(t0	NOUN
ejpam-534	788	10	,	,	PUNCT
ejpam-534	788	11	ū	ū	NOUN
ejpam-534	788	12	,	,	PUNCT
ejpam-534	788	13	˙̄u	˙̄u	NOUN
ejpam-534	788	14	,	,	PUNCT
ejpam-534	788	15	¨̄u	¨̄u	NOUN
ejpam-534	788	16	,	,	PUNCT
ejpam-534	788	17	...	...	PUNCT
ejpam-534	788	18	ū	ū	NOUN
ejpam-534	788	19	,	,	PUNCT
ejpam-534	788	20	....	....	PUNCT
ejpam-534	788	21	ū	ū	PROPN
ejpam-534	788	22	,	,	PUNCT
ejpam-534	788	23	ȳ(t0	ȳ(t0	PROPN
ejpam-534	788	24	)	)	PUNCT
ejpam-534	788	25	,	,	PUNCT
ejpam-534	788	26	˙̄y(t0	˙̄y(t0	NUM
ejpam-534	788	27	)	)	PUNCT
ejpam-534	788	28	,	,	PUNCT
ejpam-534	788	29	¨̄y(t0	¨̄y(t0	NOUN
ejpam-534	788	30	)	)	PUNCT
ejpam-534	788	31	,	,	PUNCT
ejpam-534	788	32	...	...	PUNCT
ejpam-534	789	1	ȳ	ȳ	INTJ
ejpam-534	789	2	(	(	PUNCT
ejpam-534	789	3	t0))p̄(t0))−	t0))p̄(t0))−	ADP
ejpam-534	789	4	1	1	NUM
ejpam-534	789	5	2	2	NUM
ejpam-534	789	6	p̄(t0	p̄(t0	NOUN
ejpam-534	789	7	)	)	PUNCT
ejpam-534	789	8	t	t	PROPN
ejpam-534	789	9	b(t0	b(t0	PROPN
ejpam-534	789	10	,	,	PUNCT
ejpam-534	789	11	ū	ū	NOUN
ejpam-534	789	12	,	,	PUNCT
ejpam-534	789	13	˙̄u	˙̄u	NOUN
ejpam-534	789	14	,	,	PUNCT
ejpam-534	789	15	¨̄u	¨̄u	NOUN
ejpam-534	789	16	,	,	PUNCT
ejpam-534	789	17	...	...	PUNCT
ejpam-534	789	18	ū	ū	NOUN
ejpam-534	789	19	,	,	PUNCT
ejpam-534	789	20	....	....	PUNCT
ejpam-534	789	21	ū	ū	PROPN
ejpam-534	789	22	,	,	PUNCT
ejpam-534	789	23	ȳ(t0	ȳ(t0	PROPN
ejpam-534	789	24	)	)	PUNCT
ejpam-534	789	25	,	,	PUNCT
ejpam-534	789	26	˙̄y(t0	˙̄y(t0	NUM
ejpam-534	789	27	)	)	PUNCT
ejpam-534	789	28	,	,	PUNCT
ejpam-534	789	29	¨̄y(t0	¨̄y(t0	NOUN
ejpam-534	789	30	)	)	PUNCT
ejpam-534	789	31	,	,	PUNCT
ejpam-534	789	32	...	...	PUNCT
ejpam-534	790	1	ȳ	ȳ	PROPN
ejpam-534	790	2	(	(	PUNCT
ejpam-534	790	3	t0))p̄(t0	t0))p̄(t0	PROPN
ejpam-534	790	4	)	)	PUNCT
ejpam-534	791	1	+	+	NOUN
ejpam-534	791	2	ρ2d2(t0	ρ2d2(t0	NOUN
ejpam-534	791	3	,	,	PUNCT
ejpam-534	791	4	x̄	x̄	NOUN
ejpam-534	791	5	,	,	PUNCT
ejpam-534	791	6	ū))d	ū))d	INTJ
ejpam-534	791	7	t.	t.	NOUN
ejpam-534	791	8	(	(	PUNCT
ejpam-534	791	9	57	57	NUM
ejpam-534	791	10	)	)	PUNCT
ejpam-534	791	11	adding	add	VERB
ejpam-534	791	12	(	(	PUNCT
ejpam-534	791	13	56	56	NUM
ejpam-534	791	14	)	)	PUNCT
ejpam-534	791	15	,	,	PUNCT
ejpam-534	791	16	(	(	PUNCT
ejpam-534	791	17	57	57	NUM
ejpam-534	791	18	)	)	PUNCT
ejpam-534	791	19	and	and	CCONJ
ejpam-534	791	20	using	use	VERB
ejpam-534	791	21	hypothesis	hypothesis	NOUN
ejpam-534	791	22	(	(	PUNCT
ejpam-534	791	23	iii	iii	NOUN
ejpam-534	791	24	)	)	PUNCT
ejpam-534	791	25	,	,	PUNCT
ejpam-534	791	26	(	(	PUNCT
ejpam-534	791	27	21	21	NUM
ejpam-534	791	28	)	)	PUNCT
ejpam-534	791	29	,	,	PUNCT
ejpam-534	791	30	(	(	PUNCT
ejpam-534	791	31	35	35	NUM
ejpam-534	791	32	)	)	PUNCT
ejpam-534	791	33	,	,	PUNCT
ejpam-534	791	34	(	(	PUNCT
ejpam-534	791	35	37	37	NUM
ejpam-534	791	36	)	)	PUNCT
ejpam-534	791	37	,	,	PUNCT
ejpam-534	791	38	(	(	PUNCT
ejpam-534	791	39	55	55	NUM
ejpam-534	791	40	)	)	PUNCT
ejpam-534	791	41	,	,	PUNCT
ejpam-534	791	42	we	we	PRON
ejpam-534	791	43	obtain	obtain	VERB
ejpam-534	791	44	∫	∫	PROPN
ejpam-534	791	45	g(t0	g(t0	PROPN
ejpam-534	791	46	,	,	PUNCT
ejpam-534	791	47	x̄	x̄	PROPN
ejpam-534	791	48	,	,	PUNCT
ejpam-534	791	49	ū	ū	PROPN
ejpam-534	791	50	;	;	PUNCT
ejpam-534	791	51	k∑	k∑	PROPN
ejpam-534	791	52	i=1	i=1	PROPN
ejpam-534	792	1	λ̄i	λ̄i	PROPN
ejpam-534	792	2	(	(	PUNCT
ejpam-534	792	3	f	f	NOUN
ejpam-534	792	4	i	i	NOUN
ejpam-534	792	5	x	x	PROPN
ejpam-534	792	6	(	(	PUNCT
ejpam-534	792	7	t0	t0	NOUN
ejpam-534	792	8	,	,	PUNCT
ejpam-534	792	9	ū	ū	NOUN
ejpam-534	792	10	,	,	PUNCT
ejpam-534	792	11	˙̄u)−	˙̄u)−	PROPN
ejpam-534	792	12	d	d	PROPN
ejpam-534	793	1	f	f	PROPN
ejpam-534	794	1	i	i	PRON
ejpam-534	794	2	ẋ	ẋ	PROPN
ejpam-534	794	3	(	(	PUNCT
ejpam-534	794	4	t0	t0	NOUN
ejpam-534	794	5	,	,	PUNCT
ejpam-534	794	6	ū	ū	NOUN
ejpam-534	794	7	,	,	PUNCT
ejpam-534	794	8	˙̄u	˙̄u	X
ejpam-534	794	9	)	)	PUNCT
ejpam-534	794	10	+	+	CCONJ
ejpam-534	794	11	ai(t0	ai(t0	PROPN
ejpam-534	794	12	,	,	PUNCT
ejpam-534	794	13	ū	ū	NOUN
ejpam-534	794	14	,	,	PUNCT
ejpam-534	794	15	˙̄u	˙̄u	NOUN
ejpam-534	794	16	,	,	PUNCT
ejpam-534	794	17	¨̄u	¨̄u	NOUN
ejpam-534	794	18	,	,	PUNCT
ejpam-534	794	19	...	...	PUNCT
ejpam-534	794	20	ū	ū	NOUN
ejpam-534	794	21	,	,	PUNCT
ejpam-534	794	22	....	....	PUNCT
ejpam-534	794	23	ū	ū	PROPN
ejpam-534	794	24	)	)	PUNCT
ejpam-534	794	25	p̄(t0	p̄(t0	NOUN
ejpam-534	794	26	)	)	PUNCT
ejpam-534	794	27	)	)	PUNCT
ejpam-534	795	1	+	+	CCONJ
ejpam-534	795	2	gx(t0	gx(t0	PROPN
ejpam-534	795	3	,	,	PUNCT
ejpam-534	795	4	ū	ū	NOUN
ejpam-534	795	5	,	,	PUNCT
ejpam-534	795	6	˙̄u	˙̄u	NOUN
ejpam-534	795	7	)	)	PUNCT
ejpam-534	795	8	ȳ(t0)−	ȳ(t0)−	PROPN
ejpam-534	795	9	d(g	d(g	PROPN
ejpam-534	795	10	ẋ(t0	ẋ(t0	PROPN
ejpam-534	795	11	,	,	PUNCT
ejpam-534	795	12	ū	ū	NOUN
ejpam-534	795	13	,	,	PUNCT
ejpam-534	795	14	˙̄u	˙̄u	NOUN
ejpam-534	795	15	)	)	PUNCT
ejpam-534	795	16	ȳ(t0	ȳ(t0	NOUN
ejpam-534	795	17	)	)	PUNCT
ejpam-534	795	18	)	)	PUNCT
ejpam-534	796	1	+	+	CCONJ
ejpam-534	796	2	b(t0	b(t0	NOUN
ejpam-534	796	3	,	,	PUNCT
ejpam-534	796	4	ū	ū	NOUN
ejpam-534	796	5	,	,	PUNCT
ejpam-534	796	6	˙̄u	˙̄u	NOUN
ejpam-534	796	7	,	,	PUNCT
ejpam-534	796	8	¨̄u	¨̄u	NOUN
ejpam-534	796	9	,	,	PUNCT
ejpam-534	796	10	...	...	PUNCT
ejpam-534	796	11	ū	ū	NOUN
ejpam-534	796	12	,	,	PUNCT
ejpam-534	796	13	....	....	PUNCT
ejpam-534	796	14	ū	ū	PROPN
ejpam-534	796	15	,	,	PUNCT
ejpam-534	796	16	ȳ(t0	ȳ(t0	PROPN
ejpam-534	796	17	)	)	PUNCT
ejpam-534	796	18	,	,	PUNCT
ejpam-534	796	19	˙̄y(t0	˙̄y(t0	NUM
ejpam-534	796	20	)	)	PUNCT
ejpam-534	796	21	,	,	PUNCT
ejpam-534	796	22	¨̄y(t0	¨̄y(t0	NOUN
ejpam-534	796	23	)	)	PUNCT
ejpam-534	796	24	,	,	PUNCT
ejpam-534	796	25	...	...	PUNCT
ejpam-534	797	1	ȳ	ȳ	NOUN
ejpam-534	797	2	(	(	PUNCT
ejpam-534	797	3	t0))p̄(t0))d	t0))p̄(t0))d	NOUN
ejpam-534	797	4	t	t	X
ejpam-534	797	5	<	<	X
ejpam-534	797	6	0	0	NUM
ejpam-534	797	7	,	,	PUNCT
ejpam-534	797	8	which	which	PRON
ejpam-534	797	9	by	by	ADP
ejpam-534	797	10	(	(	PUNCT
ejpam-534	797	11	34	34	NUM
ejpam-534	797	12	)	)	PUNCT
ejpam-534	797	13	implies	imply	VERB
ejpam-534	797	14	∫	∫	PROPN
ejpam-534	797	15	g(t0	g(t0	PROPN
ejpam-534	797	16	,	,	PUNCT
ejpam-534	797	17	x̄	x̄	PROPN
ejpam-534	797	18	,	,	PUNCT
ejpam-534	797	19	ū	ū	PROPN
ejpam-534	797	20	;	;	PUNCT
ejpam-534	797	21	0)d	0)d	PROPN
ejpam-534	797	22	t	t	PROPN
ejpam-534	797	23	<	<	X
ejpam-534	797	24	0	0	PROPN
ejpam-534	797	25	,	,	PUNCT
ejpam-534	797	26	a	a	DET
ejpam-534	797	27	contradiction	contradiction	NOUN
ejpam-534	797	28	to	to	ADP
ejpam-534	797	29	the	the	DET
ejpam-534	797	30	fact	fact	NOUN
ejpam-534	797	31	that	that	SCONJ
ejpam-534	797	32	g(t	g(t	PROPN
ejpam-534	797	33	,	,	PUNCT
ejpam-534	797	34	x̄	x̄	NOUN
ejpam-534	797	35	,	,	PUNCT
ejpam-534	797	36	ū	ū	NOUN
ejpam-534	797	37	;	;	PUNCT
ejpam-534	797	38	0	0	NUM
ejpam-534	797	39	)	)	PUNCT
ejpam-534	797	40	=	=	SYM
ejpam-534	797	41	0	0	NUM
ejpam-534	797	42	,	,	PUNCT
ejpam-534	797	43	t	t	PROPN
ejpam-534	797	44	∈	∈	PROPN
ejpam-534	798	1	i	i	PRON
ejpam-534	798	2	.	.	PUNCT
ejpam-534	799	1	hence	hence	ADV
ejpam-534	799	2	x̄(t	x̄(t	NUM
ejpam-534	799	3	)	)	PUNCT
ejpam-534	799	4	=	=	SYM
ejpam-534	799	5	ū(t	ū(t	NOUN
ejpam-534	799	6	)	)	PUNCT
ejpam-534	799	7	,	,	PUNCT
ejpam-534	799	8	t	t	PROPN
ejpam-534	799	9	∈	∈	PROPN
ejpam-534	800	1	i	i	PRON
ejpam-534	800	2	.	.	PUNCT
ejpam-534	801	1	remark	remark	PROPN
ejpam-534	801	2	4	4	NUM
ejpam-534	801	3	.	.	PUNCT
ejpam-534	802	1	the	the	DET
ejpam-534	802	2	above	above	ADJ
ejpam-534	802	3	theorem	theorem	NOUN
ejpam-534	802	4	also	also	ADV
ejpam-534	802	5	holds	hold	VERB
ejpam-534	802	6	true	true	ADJ
ejpam-534	802	7	if	if	SCONJ
ejpam-534	802	8	we	we	PRON
ejpam-534	802	9	replace	replace	VERB
ejpam-534	802	10	“	"	PUNCT
ejpam-534	802	11	efficient	efficient	ADJ
ejpam-534	802	12	solutions	solution	NOUN
ejpam-534	802	13	”	"	PUNCT
ejpam-534	802	14	by	by	ADP
ejpam-534	802	15	“	"	PUNCT
ejpam-534	802	16	feasible	feasible	ADJ
ejpam-534	802	17	solutions	solution	NOUN
ejpam-534	802	18	”	"	PUNCT
ejpam-534	802	19	.	.	PUNCT
ejpam-534	803	1	6	6	X
ejpam-534	803	2	.	.	X
ejpam-534	803	3	related	relate	VERB
ejpam-534	803	4	problem	problem	NOUN
ejpam-534	803	5	if	if	SCONJ
ejpam-534	803	6	the	the	DET
ejpam-534	803	7	time	time	NOUN
ejpam-534	803	8	dependency	dependency	NOUN
ejpam-534	803	9	of	of	ADP
ejpam-534	803	10	problems	problem	NOUN
ejpam-534	803	11	(	(	PUNCT
ejpam-534	803	12	p	p	NOUN
ejpam-534	803	13	)	)	PUNCT
ejpam-534	803	14	and	and	CCONJ
ejpam-534	803	15	(	(	PUNCT
ejpam-534	803	16	mwd	mwd	PROPN
ejpam-534	803	17	)	)	PUNCT
ejpam-534	803	18	is	be	AUX
ejpam-534	803	19	removed	remove	VERB
ejpam-534	803	20	,	,	PUNCT
ejpam-534	803	21	then	then	ADV
ejpam-534	803	22	these	these	DET
ejpam-534	803	23	problems	problem	NOUN
ejpam-534	803	24	reduce	reduce	VERB
ejpam-534	803	25	to	to	ADP
ejpam-534	803	26	the	the	DET
ejpam-534	803	27	following	follow	VERB
ejpam-534	803	28	second	second	ADJ
ejpam-534	803	29	-	-	PUNCT
ejpam-534	803	30	order	order	NOUN
ejpam-534	803	31	multiobjective	multiobjective	ADJ
ejpam-534	803	32	nonlinear	nonlinear	ADJ
ejpam-534	803	33	problems	problem	NOUN
ejpam-534	803	34	studied	study	VERB
ejpam-534	803	35	in	in	ADP
ejpam-534	803	36	mond	mond	PROPN
ejpam-534	803	37	and	and	CCONJ
ejpam-534	803	38	zhang	zhang	PROPN
ejpam-534	804	1	[	[	X
ejpam-534	804	2	13	13	NUM
ejpam-534	804	3	]	]	PUNCT
ejpam-534	804	4	and	and	CCONJ
ejpam-534	804	5	gulati	gulati	PROPN
ejpam-534	804	6	and	and	CCONJ
ejpam-534	804	7	agarwal	agarwal	PROPN
ejpam-534	805	1	[	[	X
ejpam-534	805	2	7	7	NUM
ejpam-534	805	3	]	]	PUNCT
ejpam-534	805	4	.	.	PUNCT
ejpam-534	806	1	the	the	DET
ejpam-534	806	2	assumptions	assumption	NOUN
ejpam-534	806	3	in	in	ADP
ejpam-534	806	4	our	our	PRON
ejpam-534	806	5	converse	converse	NOUN
ejpam-534	806	6	duality	duality	NOUN
ejpam-534	806	7	theorem	theorem	VERB
ejpam-534	806	8	are	be	AUX
ejpam-534	806	9	similar	similar	ADJ
ejpam-534	806	10	to	to	ADP
ejpam-534	806	11	the	the	DET
ejpam-534	806	12	assumptions	assumption	NOUN
ejpam-534	806	13	in	in	ADP
ejpam-534	806	14	[	[	X
ejpam-534	806	15	7	7	NUM
ejpam-534	806	16	]	]	PUNCT
ejpam-534	806	17	.	.	PUNCT
ejpam-534	807	1	(	(	PUNCT
ejpam-534	807	2	np	np	X
ejpam-534	807	3	)	)	PUNCT
ejpam-534	807	4	minimize	minimize	NOUN
ejpam-534	807	5	(	(	PUNCT
ejpam-534	807	6	f	f	PROPN
ejpam-534	807	7	1(x	1(x	NUM
ejpam-534	807	8	)	)	PUNCT
ejpam-534	807	9	,	,	PUNCT
ejpam-534	807	10	f	f	PROPN
ejpam-534	807	11	2(x	2(x	NUM
ejpam-534	807	12	)	)	PUNCT
ejpam-534	807	13	,	,	PUNCT
ejpam-534	807	14	.	.	PUNCT
ejpam-534	807	15	.	.	PUNCT
ejpam-534	808	1	.	.	PUNCT
ejpam-534	809	1	,	,	PUNCT
ejpam-534	809	2	f	f	PROPN
ejpam-534	809	3	k(x	k(x	PROPN
ejpam-534	809	4	)	)	PUNCT
ejpam-534	809	5	)	)	PUNCT
ejpam-534	810	1	subject	subject	ADJ
ejpam-534	810	2	to	to	ADP
ejpam-534	810	3	g(x)≦	g(x)≦	NOUN
ejpam-534	810	4	0	0	NUM
ejpam-534	810	5	,	,	PUNCT
ejpam-534	810	6	references	reference	NOUN
ejpam-534	810	7	804	804	NUM
ejpam-534	810	8	(	(	PUNCT
ejpam-534	810	9	nd	nd	NOUN
ejpam-534	810	10	)	)	PUNCT
ejpam-534	810	11	minimize	minimize	NOUN
ejpam-534	810	12	(	(	PUNCT
ejpam-534	810	13	f	f	PROPN
ejpam-534	810	14	1(u)−	1(u)−	NUM
ejpam-534	810	15	1	1	NUM
ejpam-534	810	16	2	2	NUM
ejpam-534	810	17	pt∇2	pt∇2	NOUN
ejpam-534	810	18	f	f	PROPN
ejpam-534	810	19	1(u)p	1(u)p	NOUN
ejpam-534	810	20	,	,	PUNCT
ejpam-534	810	21	f	f	PROPN
ejpam-534	810	22	2(u)−	2(u)−	NUM
ejpam-534	810	23	1	1	NUM
ejpam-534	810	24	2	2	NUM
ejpam-534	810	25	pt∇2	pt∇2	NOUN
ejpam-534	810	26	f	f	NOUN
ejpam-534	810	27	2(u)p	2(u)p	ADJ
ejpam-534	810	28	,	,	PUNCT
ejpam-534	810	29	.	.	PUNCT
ejpam-534	810	30	.	.	PUNCT
ejpam-534	811	1	.	.	PUNCT
ejpam-534	812	1	,	,	PUNCT
ejpam-534	812	2	f	f	PROPN
ejpam-534	812	3	k(u)−	k(u)−	PROPN
ejpam-534	812	4	1	1	NUM
ejpam-534	812	5	2	2	NUM
ejpam-534	812	6	pt∇2	pt∇2	NOUN
ejpam-534	812	7	f	f	PROPN
ejpam-534	812	8	k(u)p	k(u)p	PROPN
ejpam-534	812	9	)	)	PUNCT
ejpam-534	812	10	subject	subject	NOUN
ejpam-534	812	11	to	to	ADP
ejpam-534	812	12	k∑	k∑	PROPN
ejpam-534	812	13	i=1	i=1	PROPN
ejpam-534	813	1	λi(∇	λi(∇	PROPN
ejpam-534	813	2	f	f	PROPN
ejpam-534	813	3	i(u	i(u	PROPN
ejpam-534	813	4	)	)	PUNCT
ejpam-534	814	1	+	+	ADP
ejpam-534	814	2	∇2	∇2	PROPN
ejpam-534	814	3	f	f	PROPN
ejpam-534	814	4	i(u)p	i(u)p	PROPN
ejpam-534	814	5	)	)	PUNCT
ejpam-534	814	6	+	+	CCONJ
ejpam-534	814	7	m∑	m∑	PROPN
ejpam-534	814	8	j=1	j=1	PROPN
ejpam-534	814	9	y	y	PROPN
ejpam-534	814	10	j(∇g	j(∇g	NUM
ejpam-534	814	11	j(u	j(u	PROPN
ejpam-534	814	12	)	)	PUNCT
ejpam-534	815	1	+	+	ADJ
ejpam-534	815	2	∇2	∇2	PROPN
ejpam-534	815	3	g	g	PROPN
ejpam-534	815	4	j(u)p	j(u)p	PROPN
ejpam-534	815	5	)	)	PUNCT
ejpam-534	815	6	=	=	SYM
ejpam-534	815	7	0	0	NUM
ejpam-534	815	8	,	,	PUNCT
ejpam-534	815	9	yt	yt	PROPN
ejpam-534	815	10	g(u)−	g(u)−	PROPN
ejpam-534	815	11	1	1	NUM
ejpam-534	815	12	2	2	NUM
ejpam-534	815	13	pt∇2(yt	pt∇2(yt	NUM
ejpam-534	815	14	g(u))p	g(u))p	PROPN
ejpam-534	815	15	≧	≧	NOUN
ejpam-534	815	16	0	0	NUM
ejpam-534	815	17	,	,	PUNCT
ejpam-534	815	18	λ≥	λ≥	ADP
ejpam-534	815	19	0	0	NUM
ejpam-534	815	20	,	,	PUNCT
ejpam-534	815	21	y	y	PROPN
ejpam-534	815	22	≧	≧	NOUN
ejpam-534	815	23	0	0	X
ejpam-534	815	24	.	.	PUNCT
ejpam-534	816	1	acknowledgements	acknowledgement	VERB
ejpam-534	816	2	the	the	DET
ejpam-534	816	3	second	second	ADJ
ejpam-534	816	4	author	author	NOUN
ejpam-534	816	5	is	be	AUX
ejpam-534	816	6	thankful	thankful	ADJ
ejpam-534	816	7	to	to	ADP
ejpam-534	816	8	the	the	DET
ejpam-534	816	9	university	university	NOUN
ejpam-534	816	10	grants	grant	NOUN
ejpam-534	816	11	commission	commission	PROPN
ejpam-534	816	12	,	,	PUNCT
ejpam-534	816	13	new	new	ADJ
ejpam-534	816	14	delhi	delhi	PROPN
ejpam-534	816	15	(	(	PUNCT
ejpam-534	816	16	india	india	PROPN
ejpam-534	816	17	)	)	PUNCT
ejpam-534	816	18	for	for	ADP
ejpam-534	816	19	providing	provide	VERB
ejpam-534	816	20	financial	financial	ADJ
ejpam-534	816	21	support	support	NOUN
ejpam-534	816	22	.	.	PUNCT
ejpam-534	817	1	references	reference	NOUN
ejpam-534	817	2	[	[	X
ejpam-534	817	3	1	1	NUM
ejpam-534	817	4	]	]	PUNCT
ejpam-534	817	5	i.	i.	PROPN
ejpam-534	817	6	ahmad	ahmad	PROPN
ejpam-534	817	7	,	,	PUNCT
ejpam-534	817	8	t.	t.	PROPN
ejpam-534	817	9	r.	r.	PROPN
ejpam-534	817	10	gulati	gulati	PROPN
ejpam-534	817	11	,	,	PUNCT
ejpam-534	817	12	mixed	mixed	ADJ
ejpam-534	817	13	type	type	NOUN
ejpam-534	817	14	duality	duality	NOUN
ejpam-534	817	15	for	for	ADP
ejpam-534	817	16	multiobjective	multiobjective	ADJ
ejpam-534	817	17	variational	variational	ADJ
ejpam-534	817	18	problems	problem	NOUN
ejpam-534	817	19	with	with	ADP
ejpam-534	817	20	generalized	generalized	ADJ
ejpam-534	817	21	(	(	PUNCT
ejpam-534	817	22	f	f	NOUN
ejpam-534	817	23	,	,	PUNCT
ejpam-534	817	24	ρ)-convexity	ρ)-convexity	NOUN
ejpam-534	817	25	,	,	PUNCT
ejpam-534	817	26	journal	journal	NOUN
ejpam-534	817	27	of	of	ADP
ejpam-534	817	28	mathematical	mathematical	ADJ
ejpam-534	817	29	analysis	analysis	NOUN
ejpam-534	817	30	and	and	CCONJ
ejpam-534	817	31	applications	application	NOUN
ejpam-534	817	32	306	306	NUM
ejpam-534	817	33	(	(	PUNCT
ejpam-534	817	34	2005	2005	NUM
ejpam-534	817	35	)	)	PUNCT
ejpam-534	817	36	669	669	NUM
ejpam-534	817	37	-	-	SYM
ejpam-534	817	38	683	683	NUM
ejpam-534	817	39	.	.	PUNCT
ejpam-534	818	1	[	[	X
ejpam-534	818	2	2	2	NUM
ejpam-534	818	3	]	]	PUNCT
ejpam-534	818	4	c.	c.	PROPN
ejpam-534	818	5	r.	r.	PROPN
ejpam-534	818	6	bector	bector	PROPN
ejpam-534	818	7	,	,	PUNCT
ejpam-534	818	8	i.	i.	PROPN
ejpam-534	818	9	husain	husain	PROPN
ejpam-534	818	10	,	,	PUNCT
ejpam-534	818	11	duality	duality	NOUN
ejpam-534	818	12	for	for	ADP
ejpam-534	818	13	multiobjective	multiobjective	ADJ
ejpam-534	818	14	variational	variational	ADJ
ejpam-534	818	15	problems	problem	NOUN
ejpam-534	818	16	,	,	PUNCT
ejpam-534	818	17	journal	journal	NOUN
ejpam-534	818	18	of	of	ADP
ejpam-534	818	19	mathematical	mathematical	ADJ
ejpam-534	818	20	analysis	analysis	NOUN
ejpam-534	818	21	and	and	CCONJ
ejpam-534	818	22	applications	application	NOUN
ejpam-534	818	23	166	166	NUM
ejpam-534	818	24	(	(	PUNCT
ejpam-534	818	25	1992	1992	NUM
ejpam-534	818	26	)	)	PUNCT
ejpam-534	818	27	214	214	NUM
ejpam-534	818	28	-	-	SYM
ejpam-534	818	29	229	229	NUM
ejpam-534	818	30	.	.	PUNCT
ejpam-534	819	1	[	[	X
ejpam-534	819	2	3	3	X
ejpam-534	819	3	]	]	X
ejpam-534	819	4	d.	d.	PROPN
ejpam-534	819	5	bhatia	bhatia	PROPN
ejpam-534	819	6	,	,	PUNCT
ejpam-534	819	7	a.	a.	PROPN
ejpam-534	819	8	mehra	mehra	PROPN
ejpam-534	819	9	,	,	PUNCT
ejpam-534	819	10	optimality	optimality	NOUN
ejpam-534	819	11	conditions	condition	NOUN
ejpam-534	819	12	and	and	CCONJ
ejpam-534	819	13	duality	duality	NOUN
ejpam-534	819	14	for	for	ADP
ejpam-534	819	15	multiobjective	multiobjective	ADJ
ejpam-534	819	16	variational	variational	ADJ
ejpam-534	819	17	problems	problem	NOUN
ejpam-534	819	18	with	with	ADP
ejpam-534	819	19	generalized	generalized	ADJ
ejpam-534	819	20	b	b	NOUN
ejpam-534	819	21	-	-	PUNCT
ejpam-534	819	22	invexity	invexity	NOUN
ejpam-534	819	23	,	,	PUNCT
ejpam-534	819	24	journal	journal	NOUN
ejpam-534	819	25	of	of	ADP
ejpam-534	819	26	mathematical	mathematical	ADJ
ejpam-534	819	27	analysis	analysis	NOUN
ejpam-534	819	28	and	and	CCONJ
ejpam-534	819	29	applications	application	NOUN
ejpam-534	819	30	234	234	NUM
ejpam-534	819	31	(	(	PUNCT
ejpam-534	819	32	1999	1999	NUM
ejpam-534	819	33	)	)	PUNCT
ejpam-534	819	34	341	341	NUM
ejpam-534	819	35	-	-	SYM
ejpam-534	819	36	360	360	NUM
ejpam-534	819	37	.	.	PUNCT
ejpam-534	820	1	[	[	X
ejpam-534	820	2	4	4	X
ejpam-534	820	3	]	]	PUNCT
ejpam-534	820	4	s.	s.	PROPN
ejpam-534	820	5	chandra	chandra	PROPN
ejpam-534	820	6	,	,	PUNCT
ejpam-534	820	7	b.	b.	PROPN
ejpam-534	820	8	d.	d.	PROPN
ejpam-534	820	9	craven	craven	PROPN
ejpam-534	820	10	,	,	PUNCT
ejpam-534	820	11	i.	i.	PROPN
ejpam-534	820	12	husain	husain	PROPN
ejpam-534	820	13	,	,	PUNCT
ejpam-534	820	14	a	a	DET
ejpam-534	820	15	class	class	NOUN
ejpam-534	820	16	of	of	ADP
ejpam-534	820	17	nondifferentiable	nondifferentiable	ADJ
ejpam-534	820	18	continuous	continuous	ADJ
ejpam-534	820	19	programming	programming	NOUN
ejpam-534	820	20	problems	problem	NOUN
ejpam-534	820	21	,	,	PUNCT
ejpam-534	820	22	journal	journal	NOUN
ejpam-534	820	23	of	of	ADP
ejpam-534	820	24	mathematical	mathematical	ADJ
ejpam-534	820	25	analysis	analysis	NOUN
ejpam-534	820	26	and	and	CCONJ
ejpam-534	820	27	applications	application	NOUN
ejpam-534	820	28	107	107	NUM
ejpam-534	820	29	(	(	PUNCT
ejpam-534	820	30	1985	1985	NUM
ejpam-534	820	31	)	)	PUNCT
ejpam-534	820	32	122	122	NUM
ejpam-534	820	33	-	-	SYM
ejpam-534	820	34	131	131	NUM
ejpam-534	820	35	.	.	PUNCT
ejpam-534	821	1	[	[	X
ejpam-534	821	2	5	5	X
ejpam-534	821	3	]	]	PUNCT
ejpam-534	821	4	v.	v.	CCONJ
ejpam-534	821	5	chankong	chankong	NOUN
ejpam-534	821	6	,	,	PUNCT
ejpam-534	821	7	y.	y.	PROPN
ejpam-534	821	8	y.	y.	PROPN
ejpam-534	821	9	haimes	haimes	PROPN
ejpam-534	821	10	,	,	PUNCT
ejpam-534	821	11	"	"	PUNCT
ejpam-534	821	12	multiobjective	multiobjective	ADJ
ejpam-534	821	13	decision	decision	NOUN
ejpam-534	821	14	making	making	NOUN
ejpam-534	821	15	:	:	PUNCT
ejpam-534	821	16	theory	theory	NOUN
ejpam-534	821	17	and	and	CCONJ
ejpam-534	821	18	methodology	methodology	NOUN
ejpam-534	821	19	,	,	PUNCT
ejpam-534	821	20	"	"	PUNCT
ejpam-534	821	21	north	north	NOUN
ejpam-534	821	22	-	-	PUNCT
ejpam-534	821	23	holland	holland	PROPN
ejpam-534	821	24	,	,	PUNCT
ejpam-534	821	25	new	new	PROPN
ejpam-534	821	26	york	york	PROPN
ejpam-534	821	27	,	,	PUNCT
ejpam-534	821	28	1983	1983	NUM
ejpam-534	821	29	.	.	PUNCT
ejpam-534	822	1	[	[	X
ejpam-534	822	2	6	6	NUM
ejpam-534	822	3	]	]	PUNCT
ejpam-534	822	4	x.	x.	NOUN
ejpam-534	822	5	h.	h.	PROPN
ejpam-534	822	6	chen	chen	PROPN
ejpam-534	822	7	,	,	PUNCT
ejpam-534	822	8	second	second	ADJ
ejpam-534	822	9	-	-	PUNCT
ejpam-534	822	10	order	order	NOUN
ejpam-534	822	11	duality	duality	NOUN
ejpam-534	822	12	for	for	ADP
ejpam-534	822	13	the	the	DET
ejpam-534	822	14	variational	variational	ADJ
ejpam-534	822	15	problems	problem	NOUN
ejpam-534	822	16	,	,	PUNCT
ejpam-534	822	17	journal	journal	NOUN
ejpam-534	822	18	of	of	ADP
ejpam-534	822	19	mathematical	mathematical	ADJ
ejpam-534	822	20	analysis	analysis	NOUN
ejpam-534	822	21	and	and	CCONJ
ejpam-534	822	22	applications	application	NOUN
ejpam-534	822	23	286	286	NUM
ejpam-534	822	24	(	(	PUNCT
ejpam-534	822	25	2003	2003	NUM
ejpam-534	822	26	)	)	PUNCT
ejpam-534	822	27	261	261	NUM
ejpam-534	822	28	-	-	SYM
ejpam-534	822	29	270	270	NUM
ejpam-534	822	30	.	.	PUNCT
ejpam-534	823	1	[	[	X
ejpam-534	823	2	7	7	X
ejpam-534	823	3	]	]	PUNCT
ejpam-534	823	4	t.	t.	PROPN
ejpam-534	823	5	r.	r.	PROPN
ejpam-534	823	6	gulati	gulati	PROPN
ejpam-534	823	7	,	,	PUNCT
ejpam-534	823	8	d.	d.	PROPN
ejpam-534	823	9	agarwal	agarwal	PROPN
ejpam-534	823	10	,	,	PUNCT
ejpam-534	823	11	on	on	ADP
ejpam-534	823	12	huard	huard	PROPN
ejpam-534	823	13	type	type	NOUN
ejpam-534	823	14	second	second	ADJ
ejpam-534	823	15	-	-	PUNCT
ejpam-534	823	16	order	order	NOUN
ejpam-534	823	17	converse	converse	NOUN
ejpam-534	823	18	duality	duality	NOUN
ejpam-534	823	19	in	in	ADP
ejpam-534	823	20	nonlinear	nonlinear	ADJ
ejpam-534	823	21	programming	programming	NOUN
ejpam-534	823	22	,	,	PUNCT
ejpam-534	823	23	applied	apply	VERB
ejpam-534	823	24	mathematics	mathematics	NOUN
ejpam-534	823	25	letters	letter	NOUN
ejpam-534	823	26	20	20	NUM
ejpam-534	823	27	(	(	PUNCT
ejpam-534	823	28	2007	2007	NUM
ejpam-534	823	29	)	)	PUNCT
ejpam-534	823	30	1057	1057	NUM
ejpam-534	823	31	-	-	SYM
ejpam-534	823	32	1063	1063	NUM
ejpam-534	823	33	.	.	PUNCT
ejpam-534	824	1	[	[	X
ejpam-534	824	2	8	8	NUM
ejpam-534	824	3	]	]	X
ejpam-534	824	4	i.	i.	PROPN
ejpam-534	824	5	husain	husain	PROPN
ejpam-534	824	6	,	,	PUNCT
ejpam-534	824	7	a.	a.	PROPN
ejpam-534	824	8	ahmed	ahmed	PROPN
ejpam-534	824	9	,	,	PUNCT
ejpam-534	824	10	m.	m.	NOUN
ejpam-534	824	11	masoodi	masoodi	PROPN
ejpam-534	824	12	,	,	PUNCT
ejpam-534	824	13	second	second	ADJ
ejpam-534	824	14	-	-	PUNCT
ejpam-534	824	15	order	order	NOUN
ejpam-534	824	16	duality	duality	NOUN
ejpam-534	824	17	for	for	ADP
ejpam-534	824	18	variational	variational	ADJ
ejpam-534	824	19	problems	problem	NOUN
ejpam-534	824	20	,	,	PUNCT
ejpam-534	824	21	european	european	PROPN
ejpam-534	824	22	journal	journal	PROPN
ejpam-534	824	23	of	of	ADP
ejpam-534	824	24	pure	pure	ADJ
ejpam-534	824	25	and	and	CCONJ
ejpam-534	824	26	applied	applied	ADJ
ejpam-534	824	27	mathematics	mathematic	NOUN
ejpam-534	824	28	2	2	NUM
ejpam-534	824	29	(	(	PUNCT
ejpam-534	824	30	2009	2009	NUM
ejpam-534	824	31	)	)	PUNCT
ejpam-534	824	32	278	278	NUM
ejpam-534	824	33	-	-	SYM
ejpam-534	824	34	295	295	NUM
ejpam-534	824	35	.	.	PUNCT
ejpam-534	825	1	[	[	X
ejpam-534	825	2	9	9	NUM
ejpam-534	825	3	]	]	PUNCT
ejpam-534	825	4	d.	d.	PROPN
ejpam-534	825	5	s.	s.	PROPN
ejpam-534	825	6	kim	kim	PROPN
ejpam-534	825	7	,	,	PUNCT
ejpam-534	825	8	a.	a.	PROPN
ejpam-534	825	9	l.	l.	PROPN
ejpam-534	825	10	kim	kim	PROPN
ejpam-534	825	11	,	,	PUNCT
ejpam-534	825	12	optimality	optimality	NOUN
ejpam-534	825	13	and	and	CCONJ
ejpam-534	825	14	duality	duality	NOUN
ejpam-534	825	15	for	for	ADP
ejpam-534	825	16	nondifferentiable	nondifferentiable	ADJ
ejpam-534	825	17	multiobjective	multiobjective	ADJ
ejpam-534	825	18	variational	variational	ADJ
ejpam-534	825	19	problems	problem	NOUN
ejpam-534	825	20	,	,	PUNCT
ejpam-534	825	21	journal	journal	NOUN
ejpam-534	825	22	of	of	ADP
ejpam-534	825	23	mathematical	mathematical	ADJ
ejpam-534	825	24	analysis	analysis	NOUN
ejpam-534	825	25	and	and	CCONJ
ejpam-534	825	26	applications	application	NOUN
ejpam-534	825	27	274	274	NUM
ejpam-534	825	28	(	(	PUNCT
ejpam-534	825	29	2002	2002	NUM
ejpam-534	825	30	)	)	PUNCT
ejpam-534	825	31	255278	255278	NUM
ejpam-534	825	32	.	.	PUNCT
ejpam-534	826	1	[	[	X
ejpam-534	826	2	10	10	NUM
ejpam-534	826	3	]	]	X
ejpam-534	826	4	b.	b.	PROPN
ejpam-534	826	5	mond	mond	PROPN
ejpam-534	826	6	,	,	PUNCT
ejpam-534	826	7	s.	s.	PROPN
ejpam-534	826	8	chandra	chandra	PROPN
ejpam-534	826	9	,	,	PUNCT
ejpam-534	826	10	i.	i.	PROPN
ejpam-534	826	11	husain	husain	PROPN
ejpam-534	826	12	,	,	PUNCT
ejpam-534	826	13	duality	duality	NOUN
ejpam-534	826	14	for	for	ADP
ejpam-534	826	15	variational	variational	ADJ
ejpam-534	826	16	problems	problem	NOUN
ejpam-534	826	17	with	with	ADP
ejpam-534	826	18	invexity	invexity	NOUN
ejpam-534	826	19	,	,	PUNCT
ejpam-534	826	20	journal	journal	NOUN
ejpam-534	826	21	of	of	ADP
ejpam-534	826	22	mathematical	mathematical	ADJ
ejpam-534	826	23	analysis	analysis	NOUN
ejpam-534	826	24	and	and	CCONJ
ejpam-534	826	25	applications	application	NOUN
ejpam-534	826	26	134	134	NUM
ejpam-534	826	27	(	(	PUNCT
ejpam-534	826	28	1988	1988	NUM
ejpam-534	826	29	)	)	PUNCT
ejpam-534	826	30	322	322	NUM
ejpam-534	826	31	-	-	SYM
ejpam-534	826	32	328	328	NUM
ejpam-534	826	33	.	.	PUNCT
ejpam-534	827	1	references	reference	NOUN
ejpam-534	827	2	805	805	NUM
ejpam-534	827	3	[	[	X
ejpam-534	827	4	11	11	NUM
ejpam-534	827	5	]	]	X
ejpam-534	827	6	b.	b.	PROPN
ejpam-534	827	7	mond	mond	PROPN
ejpam-534	827	8	,	,	PUNCT
ejpam-534	827	9	m.	m.	NOUN
ejpam-534	827	10	a.	a.	PROPN
ejpam-534	827	11	hanson	hanson	PROPN
ejpam-534	827	12	,	,	PUNCT
ejpam-534	827	13	duality	duality	NOUN
ejpam-534	827	14	for	for	ADP
ejpam-534	827	15	variational	variational	ADJ
ejpam-534	827	16	problems	problem	NOUN
ejpam-534	827	17	,	,	PUNCT
ejpam-534	827	18	journal	journal	NOUN
ejpam-534	827	19	of	of	ADP
ejpam-534	827	20	mathematical	mathematical	ADJ
ejpam-534	827	21	analysis	analysis	NOUN
ejpam-534	827	22	and	and	CCONJ
ejpam-534	827	23	applications	application	NOUN
ejpam-534	827	24	18	18	NUM
ejpam-534	827	25	(	(	PUNCT
ejpam-534	827	26	1967	1967	NUM
ejpam-534	827	27	)	)	PUNCT
ejpam-534	827	28	355	355	NUM
ejpam-534	827	29	-	-	SYM
ejpam-534	827	30	364	364	NUM
ejpam-534	827	31	.	.	PUNCT
ejpam-534	828	1	[	[	X
ejpam-534	828	2	12	12	NUM
ejpam-534	828	3	]	]	X
ejpam-534	828	4	b.	b.	PROPN
ejpam-534	828	5	mond	mond	PROPN
ejpam-534	828	6	,	,	PUNCT
ejpam-534	828	7	i.	i.	PROPN
ejpam-534	828	8	smart	smart	PROPN
ejpam-534	828	9	,	,	PUNCT
ejpam-534	828	10	duality	duality	NOUN
ejpam-534	828	11	and	and	CCONJ
ejpam-534	828	12	sufficiency	sufficiency	NOUN
ejpam-534	828	13	in	in	ADP
ejpam-534	828	14	control	control	NOUN
ejpam-534	828	15	problems	problem	NOUN
ejpam-534	828	16	with	with	ADP
ejpam-534	828	17	invexity	invexity	NOUN
ejpam-534	828	18	,	,	PUNCT
ejpam-534	828	19	journal	journal	NOUN
ejpam-534	828	20	of	of	ADP
ejpam-534	828	21	mathematical	mathematical	ADJ
ejpam-534	828	22	analysis	analysis	NOUN
ejpam-534	828	23	and	and	CCONJ
ejpam-534	828	24	applications	application	NOUN
ejpam-534	828	25	136	136	NUM
ejpam-534	828	26	(	(	PUNCT
ejpam-534	828	27	1988	1988	NUM
ejpam-534	828	28	)	)	PUNCT
ejpam-534	828	29	325	325	NUM
ejpam-534	828	30	-	-	SYM
ejpam-534	828	31	333	333	NUM
ejpam-534	828	32	.	.	PUNCT
ejpam-534	829	1	[	[	X
ejpam-534	829	2	13	13	NUM
ejpam-534	829	3	]	]	X
ejpam-534	829	4	b.	b.	PROPN
ejpam-534	829	5	mond	mond	PROPN
ejpam-534	829	6	,	,	PUNCT
ejpam-534	829	7	j.	j.	PROPN
ejpam-534	829	8	zhang	zhang	PROPN
ejpam-534	829	9	,	,	PUNCT
ejpam-534	829	10	duality	duality	NOUN
ejpam-534	829	11	for	for	ADP
ejpam-534	829	12	multiobjective	multiobjective	ADJ
ejpam-534	829	13	programming	programming	NOUN
ejpam-534	829	14	involving	involve	VERB
ejpam-534	829	15	second	second	ADJ
ejpam-534	829	16	order	order	NOUN
ejpam-534	829	17	vinvex	vinvex	NOUN
ejpam-534	829	18	functions	function	NOUN
ejpam-534	829	19	,	,	PUNCT
ejpam-534	829	20	proceedings	proceeding	NOUN
ejpam-534	829	21	of	of	ADP
ejpam-534	829	22	the	the	DET
ejpam-534	829	23	optimization	optimization	NOUN
ejpam-534	829	24	miniconference	miniconference	NOUN
ejpam-534	829	25	,	,	PUNCT
ejpam-534	829	26	b.	b.	PROPN
ejpam-534	829	27	m.	m.	PROPN
ejpam-534	829	28	glover	glover	PROPN
ejpam-534	829	29	and	and	CCONJ
ejpam-534	829	30	v.	v.	ADP
ejpam-534	829	31	jeyakumar	jeyakumar	PROPN
ejpam-534	829	32	,	,	PUNCT
ejpam-534	829	33	editors	editor	NOUN
ejpam-534	829	34	,	,	PUNCT
ejpam-534	829	35	university	university	NOUN
ejpam-534	829	36	of	of	ADP
ejpam-534	829	37	new	new	ADJ
ejpam-534	829	38	south	south	PROPN
ejpam-534	829	39	wales	wales	PROPN
ejpam-534	829	40	,	,	PUNCT
ejpam-534	829	41	sydney	sydney	PROPN
ejpam-534	829	42	,	,	PUNCT
ejpam-534	829	43	australia	australia	PROPN
ejpam-534	829	44	(	(	PUNCT
ejpam-534	829	45	1985	1985	NUM
ejpam-534	829	46	)	)	PUNCT
ejpam-534	829	47	89	89	NUM
ejpam-534	829	48	-	-	SYM
ejpam-534	829	49	100	100	NUM
ejpam-534	829	50	.	.	PUNCT