id	sid	tid	token	lemma	pos
ejpam-457	1	1	7_457_husain.dvi	7_457_husain.dvi	NUM
ejpam-457	1	2	european	european	ADJ
ejpam-457	1	3	journal	journal	NOUN
ejpam-457	1	4	of	of	ADP
ejpam-457	1	5	pure	pure	ADJ
ejpam-457	1	6	and	and	CCONJ
ejpam-457	1	7	applied	apply	VERB
ejpam-457	1	8	mathematics	mathematic	NOUN
ejpam-457	1	9	vol	vol	NOUN
ejpam-457	1	10	.	.	PUNCT
ejpam-457	2	1	3	3	NUM
ejpam-457	2	2	,	,	PUNCT
ejpam-457	2	3	no	no	INTJ
ejpam-457	2	4	.	.	NOUN
ejpam-457	2	5	1	1	NUM
ejpam-457	2	6	,	,	PUNCT
ejpam-457	2	7	2010	2010	NUM
ejpam-457	2	8	,	,	PUNCT
ejpam-457	2	9	81	81	NUM
ejpam-457	2	10	-	-	SYM
ejpam-457	2	11	97	97	NUM
ejpam-457	2	12	issn	issn	PROPN
ejpam-457	2	13	1307	1307	NUM
ejpam-457	2	14	-	-	SYM
ejpam-457	2	15	5543	5543	NUM
ejpam-457	2	16	–	–	PUNCT
ejpam-457	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-457	2	18	on	on	ADP
ejpam-457	2	19	mixed	mixed	ADJ
ejpam-457	2	20	type	type	NOUN
ejpam-457	2	21	duality	duality	NOUN
ejpam-457	2	22	for	for	ADP
ejpam-457	2	23	nondifferentiable	nondifferentiable	ADJ
ejpam-457	2	24	multiobjective	multiobjective	ADJ
ejpam-457	2	25	variational	variational	ADJ
ejpam-457	2	26	problems	problem	NOUN
ejpam-457	2	27	i.	i.	PROPN
ejpam-457	2	28	husain1∗	husain1∗	PROPN
ejpam-457	2	29	and	and	CCONJ
ejpam-457	2	30	rumana	rumana	PROPN
ejpam-457	2	31	g.	g.	PROPN
ejpam-457	2	32	mattoo2	mattoo2	PROPN
ejpam-457	3	1	1	1	NUM
ejpam-457	3	2	department	department	NOUN
ejpam-457	3	3	of	of	ADP
ejpam-457	3	4	mathematics	mathematics	PROPN
ejpam-457	3	5	,	,	PUNCT
ejpam-457	3	6	jaypee	jaypee	PROPN
ejpam-457	3	7	institute	institute	PROPN
ejpam-457	3	8	of	of	ADP
ejpam-457	3	9	engineering	engineering	NOUN
ejpam-457	3	10	and	and	CCONJ
ejpam-457	3	11	technology	technology	NOUN
ejpam-457	3	12	,	,	PUNCT
ejpam-457	3	13	guna	guna	PROPN
ejpam-457	3	14	,	,	PUNCT
ejpam-457	3	15	mp	mp	PROPN
ejpam-457	3	16	,	,	PUNCT
ejpam-457	3	17	india	india	PROPN
ejpam-457	3	18	.	.	PUNCT
ejpam-457	4	1	(	(	PUNCT
ejpam-457	4	2	a	a	DET
ejpam-457	4	3	constituent	constituent	ADJ
ejpam-457	4	4	centre	centre	NOUN
ejpam-457	4	5	of	of	ADP
ejpam-457	4	6	jaypee	jaypee	PROPN
ejpam-457	4	7	university	university	PROPN
ejpam-457	4	8	of	of	ADP
ejpam-457	4	9	information	information	NOUN
ejpam-457	4	10	technology	technology	PROPN
ejpam-457	4	11	,	,	PUNCT
ejpam-457	4	12	waknaghat	waknaghat	PROPN
ejpam-457	4	13	,	,	PUNCT
ejpam-457	4	14	solan	solan	PROPN
ejpam-457	4	15	,	,	PUNCT
ejpam-457	4	16	hp	hp	PROPN
ejpam-457	4	17	,	,	PUNCT
ejpam-457	4	18	india	india	PROPN
ejpam-457	4	19	)	)	PUNCT
ejpam-457	4	20	2	2	NUM
ejpam-457	4	21	department	department	NOUN
ejpam-457	4	22	of	of	ADP
ejpam-457	4	23	statistics	statistic	NOUN
ejpam-457	4	24	,	,	PUNCT
ejpam-457	4	25	university	university	PROPN
ejpam-457	4	26	of	of	ADP
ejpam-457	4	27	kashmir	kashmir	PROPN
ejpam-457	4	28	,	,	PUNCT
ejpam-457	4	29	srinagar	srinagar	PROPN
ejpam-457	4	30	,	,	PUNCT
ejpam-457	4	31	kashmir	kashmir	PROPN
ejpam-457	4	32	,	,	PUNCT
ejpam-457	4	33	india	india	PROPN
ejpam-457	4	34	.	.	PUNCT
ejpam-457	5	1	abstract	abstract	PROPN
ejpam-457	5	2	.	.	PUNCT
ejpam-457	6	1	a	a	DET
ejpam-457	6	2	mixed	mixed	ADJ
ejpam-457	6	3	type	type	NOUN
ejpam-457	6	4	dual	dual	ADJ
ejpam-457	6	5	to	to	ADP
ejpam-457	6	6	a	a	DET
ejpam-457	6	7	nondifferentiable	nondifferentiable	ADJ
ejpam-457	6	8	variational	variational	ADJ
ejpam-457	6	9	problem	problem	NOUN
ejpam-457	6	10	involving	involve	VERB
ejpam-457	6	11	higher	high	ADJ
ejpam-457	6	12	order	order	NOUN
ejpam-457	6	13	derivative	derivative	NOUN
ejpam-457	6	14	is	be	AUX
ejpam-457	6	15	formulated	formulate	VERB
ejpam-457	6	16	and	and	CCONJ
ejpam-457	6	17	duality	duality	NOUN
ejpam-457	6	18	results	result	NOUN
ejpam-457	6	19	are	be	AUX
ejpam-457	6	20	proved	prove	VERB
ejpam-457	6	21	under	under	ADP
ejpam-457	6	22	generalized	generalized	ADJ
ejpam-457	6	23	invexity	invexity	NOUN
ejpam-457	6	24	conditions	condition	NOUN
ejpam-457	6	25	.	.	PUNCT
ejpam-457	7	1	special	special	ADJ
ejpam-457	7	2	cases	case	NOUN
ejpam-457	7	3	are	be	AUX
ejpam-457	7	4	generated	generate	VERB
ejpam-457	7	5	from	from	ADP
ejpam-457	7	6	our	our	PRON
ejpam-457	7	7	results	result	NOUN
ejpam-457	7	8	.	.	PUNCT
ejpam-457	8	1	2000	2000	NUM
ejpam-457	8	2	mathematics	mathematic	NOUN
ejpam-457	8	3	subject	subject	NOUN
ejpam-457	8	4	classifications	classification	NOUN
ejpam-457	8	5	:	:	PUNCT
ejpam-457	8	6	primary	primary	ADJ
ejpam-457	8	7	90c30	90c30	NUM
ejpam-457	8	8	,	,	PUNCT
ejpam-457	8	9	secondary	secondary	ADJ
ejpam-457	8	10	90c11	90c11	NUM
ejpam-457	8	11	,	,	PUNCT
ejpam-457	8	12	90c20	90c20	NUM
ejpam-457	8	13	,	,	PUNCT
ejpam-457	8	14	90c26	90c26	NUM
ejpam-457	8	15	.	.	PUNCT
ejpam-457	9	1	key	key	ADJ
ejpam-457	9	2	words	word	NOUN
ejpam-457	9	3	and	and	CCONJ
ejpam-457	9	4	phrases	phrase	NOUN
ejpam-457	9	5	:	:	PUNCT
ejpam-457	9	6	mixed	mixed	ADJ
ejpam-457	9	7	type	type	NOUN
ejpam-457	9	8	dual	dual	ADJ
ejpam-457	9	9	;	;	PUNCT
ejpam-457	9	10	nondifferentiable	nondifferentiable	ADJ
ejpam-457	9	11	variational	variational	ADJ
ejpam-457	9	12	problem	problem	NOUN
ejpam-457	9	13	;	;	PUNCT
ejpam-457	9	14	duality	duality	NOUN
ejpam-457	9	15	;	;	PUNCT
ejpam-457	9	16	invexity	invexity	NOUN
ejpam-457	9	17	;	;	PUNCT
ejpam-457	9	18	generalized	generalized	ADJ
ejpam-457	9	19	invexity	invexity	NOUN
ejpam-457	9	20	.	.	PUNCT
ejpam-457	10	1	1	1	X
ejpam-457	10	2	.	.	X
ejpam-457	10	3	introduction	introduction	NOUN
ejpam-457	10	4	in	in	ADP
ejpam-457	10	5	[	[	X
ejpam-457	10	6	9	9	NUM
ejpam-457	10	7	]	]	PUNCT
ejpam-457	10	8	,	,	PUNCT
ejpam-457	10	9	husain	husain	PROPN
ejpam-457	10	10	et	et	PROPN
ejpam-457	10	11	al	al	PROPN
ejpam-457	10	12	considered	consider	VERB
ejpam-457	10	13	the	the	DET
ejpam-457	10	14	following	follow	VERB
ejpam-457	10	15	nondifferentiable	nondifferentiable	ADJ
ejpam-457	10	16	multiobjective	multiobjective	ADJ
ejpam-457	10	17	variational	variational	ADJ
ejpam-457	10	18	problem	problem	NOUN
ejpam-457	10	19	containing	contain	VERB
ejpam-457	10	20	square	square	ADJ
ejpam-457	10	21	root	root	NOUN
ejpam-457	10	22	terms	term	NOUN
ejpam-457	10	23	:	:	PUNCT
ejpam-457	10	24	(	(	PUNCT
ejpam-457	10	25	vp	vp	AUX
ejpam-457	10	26	)	)	PUNCT
ejpam-457	10	27	minimize	minimize	VERB
ejpam-457	10	28	�	�	PROPN
ejpam-457	10	29	∫	∫	PROPN
ejpam-457	11	1	i	i	PRON
ejpam-457	11	2	(	(	PUNCT
ejpam-457	11	3	f	f	PROPN
ejpam-457	11	4	1(t	1(t	NUM
ejpam-457	11	5	,	,	PUNCT
ejpam-457	11	6	x	x	PRON
ejpam-457	11	7	,	,	PUNCT
ejpam-457	11	8	ẋ	ẋ	PROPN
ejpam-457	11	9	,	,	PUNCT
ejpam-457	11	10	ẍ	ẍ	X
ejpam-457	11	11	)	)	PUNCT
ejpam-457	12	1	+	+	CCONJ
ejpam-457	12	2	(	(	PUNCT
ejpam-457	12	3	x(t)t	x(t)t	PROPN
ejpam-457	12	4	b1(t)x(t	b1(t)x(t	PROPN
ejpam-457	12	5	)	)	PUNCT
ejpam-457	12	6	)	)	PUNCT
ejpam-457	12	7	1	1	NUM
ejpam-457	12	8	2	2	NUM
ejpam-457	12	9	)	)	PUNCT
ejpam-457	12	10	d	d	PROPN
ejpam-457	12	11	t	t	PROPN
ejpam-457	12	12	,	,	PUNCT
ejpam-457	12	13	.	.	PUNCT
ejpam-457	12	14	.	.	PUNCT
ejpam-457	12	15	.	.	PUNCT
ejpam-457	13	1	,	,	PUNCT
ejpam-457	13	2	∫	∫	PROPN
ejpam-457	14	1	i	i	PRON
ejpam-457	14	2	(	(	PUNCT
ejpam-457	14	3	f	f	PROPN
ejpam-457	14	4	p(t	p(t	NOUN
ejpam-457	14	5	,	,	PUNCT
ejpam-457	14	6	x	x	SYM
ejpam-457	14	7	,	,	PUNCT
ejpam-457	14	8	ẋ	ẋ	PROPN
ejpam-457	14	9	,	,	PUNCT
ejpam-457	14	10	ẍ	ẍ	X
ejpam-457	14	11	)	)	PUNCT
ejpam-457	15	1	+	+	CCONJ
ejpam-457	15	2	(	(	PUNCT
ejpam-457	15	3	x(t)t	x(t)t	PROPN
ejpam-457	15	4	bp(t)x(t	bp(t)x(t	PROPN
ejpam-457	15	5	)	)	PUNCT
ejpam-457	15	6	)	)	PUNCT
ejpam-457	15	7	1	1	NUM
ejpam-457	15	8	2	2	NUM
ejpam-457	15	9	)	)	PUNCT
ejpam-457	15	10	d	d	NOUN
ejpam-457	15	11	t	t	PROPN
ejpam-457	15	12	�	�	PROPN
ejpam-457	15	13	subject	subject	ADJ
ejpam-457	15	14	to	to	ADP
ejpam-457	15	15	x(a	x(a	NOUN
ejpam-457	15	16	)	)	PUNCT
ejpam-457	15	17	=	=	SYM
ejpam-457	16	1	0=	0=	NUM
ejpam-457	16	2	x(b	x(b	PROPN
ejpam-457	16	3	)	)	PUNCT
ejpam-457	16	4	ẋ(a	ẋ(a	PROPN
ejpam-457	16	5	)	)	PUNCT
ejpam-457	16	6	=	=	PUNCT
ejpam-457	17	1	0=	0=	NUM
ejpam-457	17	2	ẋ(b	ẋ(b	PROPN
ejpam-457	17	3	)	)	PUNCT
ejpam-457	17	4	g(t	g(t	PROPN
ejpam-457	17	5	,	,	PUNCT
ejpam-457	17	6	x	x	SYM
ejpam-457	17	7	,	,	PUNCT
ejpam-457	17	8	ẋ	ẋ	PROPN
ejpam-457	17	9	,	,	PUNCT
ejpam-457	17	10	ẋ	ẋ	PROPN
ejpam-457	17	11	)	)	PUNCT
ejpam-457	17	12	≦	≦	NOUN
ejpam-457	17	13	0	0	NUM
ejpam-457	17	14	,	,	PUNCT
ejpam-457	17	15	t	t	PROPN
ejpam-457	17	16	∈	∈	PROPN
ejpam-457	18	1	i	i	PRON
ejpam-457	18	2	,	,	PUNCT
ejpam-457	18	3	where	where	SCONJ
ejpam-457	18	4	∗corresponding	∗corresponde	VERB
ejpam-457	18	5	author	author	NOUN
ejpam-457	18	6	.	.	PUNCT
ejpam-457	19	1	email	email	NOUN
ejpam-457	19	2	address	address	NOUN
ejpam-457	19	3	:	:	PUNCT
ejpam-457	19	4	iqbal.husain	iqbal.husain	X
ejpam-457	19	5	�	�	NOUN
ejpam-457	19	6	jiet.a	jiet.a	NOUN
ejpam-457	19	7	.in	.in	PUNCT
ejpam-457	19	8	(	(	PUNCT
ejpam-457	19	9	i.	i.	PROPN
ejpam-457	19	10	husain	husain	PROPN
ejpam-457	19	11	)	)	PUNCT
ejpam-457	19	12	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-457	20	1	81	81	NUM
ejpam-457	20	2	c	c	X
ejpam-457	20	3	©	©	PROPN
ejpam-457	20	4	2009	2009	NUM
ejpam-457	20	5	ejpam	ejpam	NOUN
ejpam-457	20	6	all	all	DET
ejpam-457	20	7	rights	right	NOUN
ejpam-457	20	8	reserved	reserve	VERB
ejpam-457	20	9	.	.	PUNCT
ejpam-457	21	1	i.	i.	PROPN
ejpam-457	21	2	husain	husain	PROPN
ejpam-457	21	3	,	,	PUNCT
ejpam-457	21	4	r.	r.	PROPN
ejpam-457	21	5	mattoo	mattoo	PROPN
ejpam-457	21	6	/	/	SYM
ejpam-457	21	7	eur	eur	PROPN
ejpam-457	21	8	.	.	PUNCT
ejpam-457	22	1	j.	j.	PROPN
ejpam-457	22	2	pure	pure	PROPN
ejpam-457	22	3	appl	appl	PROPN
ejpam-457	22	4	.	.	PROPN
ejpam-457	22	5	math	math	PROPN
ejpam-457	22	6	,	,	PUNCT
ejpam-457	22	7	3	3	NUM
ejpam-457	22	8	(	(	PUNCT
ejpam-457	22	9	2010	2010	NUM
ejpam-457	22	10	)	)	PUNCT
ejpam-457	22	11	,	,	PUNCT
ejpam-457	22	12	81	81	NUM
ejpam-457	22	13	-	-	SYM
ejpam-457	22	14	97	97	NUM
ejpam-457	22	15	82	82	NUM
ejpam-457	22	16	1	1	NUM
ejpam-457	22	17	f	f	NOUN
ejpam-457	23	1	i	i	PRON
ejpam-457	23	2	:	:	PUNCT
ejpam-457	24	1	i	i	PRON
ejpam-457	24	2	×	×	VERB
ejpam-457	24	3	rn	rn	PROPN
ejpam-457	24	4	×	×	PROPN
ejpam-457	24	5	rn	rn	PROPN
ejpam-457	24	6	×	×	PROPN
ejpam-457	24	7	rn	rn	PROPN
ejpam-457	24	8	→	→	SYM
ejpam-457	24	9	r	r	PROPN
ejpam-457	24	10	,	,	PUNCT
ejpam-457	24	11	(	(	PUNCT
ejpam-457	24	12	i	i	NOUN
ejpam-457	24	13	=	=	SYM
ejpam-457	24	14	1,2	1,2	NUM
ejpam-457	24	15	,	,	PUNCT
ejpam-457	24	16	.	.	PUNCT
ejpam-457	24	17	.	.	PUNCT
ejpam-457	24	18	.	.	PUNCT
ejpam-457	25	1	,	,	PUNCT
ejpam-457	25	2	p	p	X
ejpam-457	25	3	)	)	PUNCT
ejpam-457	25	4	,	,	PUNCT
ejpam-457	25	5	g	g	NOUN
ejpam-457	25	6	:	:	PUNCT
ejpam-457	26	1	i	i	PRON
ejpam-457	26	2	×	×	VERB
ejpam-457	26	3	rn	rn	PROPN
ejpam-457	26	4	×	×	PROPN
ejpam-457	26	5	rn	rn	PROPN
ejpam-457	26	6	×	×	PROPN
ejpam-457	26	7	rn	rn	PROPN
ejpam-457	26	8	→	→	PROPN
ejpam-457	26	9	rm	rm	PROPN
ejpam-457	26	10	,	,	PUNCT
ejpam-457	26	11	j	j	PROPN
ejpam-457	26	12	=	=	PROPN
ejpam-457	26	13	1	1	NUM
ejpam-457	26	14	,	,	PUNCT
ejpam-457	26	15	.	.	PUNCT
ejpam-457	26	16	.	.	PUNCT
ejpam-457	27	1	.	.	PUNCT
ejpam-457	28	1	,	,	PUNCT
ejpam-457	28	2	m	m	VERB
ejpam-457	28	3	are	be	AUX
ejpam-457	28	4	assumed	assume	VERB
ejpam-457	28	5	to	to	PART
ejpam-457	28	6	be	be	AUX
ejpam-457	28	7	continuously	continuously	ADV
ejpam-457	28	8	differentiable	differentiable	ADJ
ejpam-457	28	9	functions	function	NOUN
ejpam-457	28	10	,	,	PUNCT
ejpam-457	28	11	and	and	CCONJ
ejpam-457	28	12	for	for	ADP
ejpam-457	28	13	each	each	DET
ejpam-457	28	14	t	t	NOUN
ejpam-457	28	15	∈	∈	PROPN
ejpam-457	29	1	i	i	PRON
ejpam-457	29	2	,	,	PUNCT
ejpam-457	29	3	i	i	PROPN
ejpam-457	29	4	∈	∈	VERB
ejpam-457	29	5	p	p	NOUN
ejpam-457	30	1	=	=	X
ejpam-457	30	2	{	{	PUNCT
ejpam-457	30	3	1,2	1,2	NUM
ejpam-457	30	4	,	,	PUNCT
ejpam-457	30	5	.	.	PUNCT
ejpam-457	30	6	.	.	PUNCT
ejpam-457	31	1	.	.	PUNCT
ejpam-457	32	1	,	,	PUNCT
ejpam-457	32	2	p	p	X
ejpam-457	32	3	}	}	PUNCT
ejpam-457	32	4	,	,	PUNCT
ejpam-457	32	5	bi(t	bi(t	NOUN
ejpam-457	32	6	)	)	PUNCT
ejpam-457	32	7	is	be	AUX
ejpam-457	32	8	an	an	DET
ejpam-457	32	9	n×n	n×n	PROPN
ejpam-457	32	10	positive	positive	ADJ
ejpam-457	32	11	semidefinite	semidefinite	NOUN
ejpam-457	32	12	(	(	PUNCT
ejpam-457	32	13	symmetric	symmetric	ADJ
ejpam-457	32	14	)	)	PUNCT
ejpam-457	32	15	matrix	matrix	NOUN
ejpam-457	32	16	,	,	PUNCT
ejpam-457	32	17	with	with	ADP
ejpam-457	32	18	bi(·)continuous	bi(·)continuous	NOUN
ejpam-457	32	19	on	on	ADP
ejpam-457	32	20	i	i	PRON
ejpam-457	32	21	.	.	PUNCT
ejpam-457	33	1	the	the	DET
ejpam-457	33	2	following	follow	VERB
ejpam-457	33	3	wolfe	wolfe	PROPN
ejpam-457	33	4	type	type	NOUN
ejpam-457	33	5	dual	dual	ADJ
ejpam-457	33	6	to	to	ADP
ejpam-457	33	7	the	the	DET
ejpam-457	33	8	problem	problem	NOUN
ejpam-457	33	9	(	(	PUNCT
ejpam-457	33	10	vp	vp	NOUN
ejpam-457	33	11	)	)	PUNCT
ejpam-457	33	12	is	be	AUX
ejpam-457	33	13	presented	present	VERB
ejpam-457	33	14	in	in	ADP
ejpam-457	33	15	[	[	X
ejpam-457	33	16	9	9	NUM
ejpam-457	33	17	]	]	SYM
ejpam-457	33	18	:	:	PUNCT
ejpam-457	33	19	(	(	PUNCT
ejpam-457	33	20	mwd	mwd	PROPN
ejpam-457	33	21	)	)	PUNCT
ejpam-457	33	22	maximize	maximize	VERB
ejpam-457	33	23	�	�	PROPN
ejpam-457	33	24	∫	∫	PROPN
ejpam-457	34	1	i	i	PRON
ejpam-457	34	2	(	(	PUNCT
ejpam-457	34	3	f	f	PROPN
ejpam-457	34	4	1(t	1(t	NUM
ejpam-457	34	5	,	,	PUNCT
ejpam-457	34	6	u	u	NOUN
ejpam-457	34	7	,	,	PUNCT
ejpam-457	34	8	u̇	u̇	PROPN
ejpam-457	34	9	,	,	PUNCT
ejpam-457	34	10	ü	ü	PRON
ejpam-457	34	11	)	)	PUNCT
ejpam-457	35	1	+	+	CCONJ
ejpam-457	35	2	(	(	PUNCT
ejpam-457	35	3	u(t)t	u(t)t	X
ejpam-457	35	4	b1(t)z1(t	b1(t)z1(t	PROPN
ejpam-457	35	5	)	)	PUNCT
ejpam-457	35	6	)	)	PUNCT
ejpam-457	36	1	+	+	CCONJ
ejpam-457	36	2	y(t)t	y(t)t	PROPN
ejpam-457	36	3	g(t	g(t	PROPN
ejpam-457	36	4	,	,	PUNCT
ejpam-457	36	5	u	u	NOUN
ejpam-457	36	6	,	,	PUNCT
ejpam-457	36	7	u̇	u̇	PROPN
ejpam-457	36	8	,	,	PUNCT
ejpam-457	36	9	ü))d	ü))d	PROPN
ejpam-457	36	10	t	t	NOUN
ejpam-457	36	11	,	,	PUNCT
ejpam-457	36	12	.	.	PUNCT
ejpam-457	36	13	.	.	PUNCT
ejpam-457	36	14	.	.	PUNCT
ejpam-457	37	1	,	,	PUNCT
ejpam-457	37	2	∫	∫	PROPN
ejpam-457	38	1	i	i	PRON
ejpam-457	38	2	(	(	PUNCT
ejpam-457	38	3	f	f	PROPN
ejpam-457	38	4	p(t	p(t	PROPN
ejpam-457	38	5	,	,	PUNCT
ejpam-457	38	6	u	u	NOUN
ejpam-457	38	7	,	,	PUNCT
ejpam-457	38	8	u̇	u̇	PROPN
ejpam-457	38	9	,	,	PUNCT
ejpam-457	38	10	ü	ü	PRON
ejpam-457	38	11	)	)	PUNCT
ejpam-457	39	1	+	+	CCONJ
ejpam-457	39	2	(	(	PUNCT
ejpam-457	39	3	u(t)t	u(t)t	NOUN
ejpam-457	39	4	bp(t)zp(t	bp(t)zp(t	NOUN
ejpam-457	39	5	)	)	PUNCT
ejpam-457	39	6	)	)	PUNCT
ejpam-457	40	1	+	+	CCONJ
ejpam-457	40	2	y(t)t	y(t)t	PROPN
ejpam-457	40	3	g(t	g(t	PROPN
ejpam-457	40	4	,	,	PUNCT
ejpam-457	40	5	u	u	NOUN
ejpam-457	40	6	,	,	PUNCT
ejpam-457	40	7	u̇	u̇	PROPN
ejpam-457	40	8	,	,	PUNCT
ejpam-457	40	9	ü))d	ü))d	PROPN
ejpam-457	40	10	t	t	PROPN
ejpam-457	40	11	�	�	PROPN
ejpam-457	40	12	subject	subject	ADJ
ejpam-457	40	13	to	to	ADP
ejpam-457	40	14	u(a	u(a	NOUN
ejpam-457	40	15	)	)	PUNCT
ejpam-457	40	16	=	=	SYM
ejpam-457	41	1	0=	0=	PUNCT
ejpam-457	41	2	u(b	u(b	X
ejpam-457	41	3	)	)	PUNCT
ejpam-457	41	4	u̇(a	u̇(a	PROPN
ejpam-457	41	5	)	)	PUNCT
ejpam-457	41	6	=	=	NOUN
ejpam-457	42	1	0=	0=	NOUN
ejpam-457	42	2	u̇(b	u̇(b	NOUN
ejpam-457	42	3	)	)	PUNCT
ejpam-457	43	1	p	p	NOUN
ejpam-457	43	2	∑	∑	PUNCT
ejpam-457	43	3	i=1	i=1	PROPN
ejpam-457	43	4	λi	λi	PROPN
ejpam-457	43	5	�	�	PROPN
ejpam-457	43	6	f	f	PROPN
ejpam-457	44	1	i	i	PRON
ejpam-457	44	2	u	u	PROPN
ejpam-457	44	3	(	(	PUNCT
ejpam-457	44	4	t	t	PROPN
ejpam-457	44	5	,	,	PUNCT
ejpam-457	44	6	u	u	NOUN
ejpam-457	44	7	,	,	PUNCT
ejpam-457	44	8	u̇	u̇	PROPN
ejpam-457	44	9	,	,	PUNCT
ejpam-457	44	10	ü	ü	NUM
ejpam-457	44	11	)	)	PUNCT
ejpam-457	45	1	d	d	NOUN
ejpam-457	45	2	t	t	PROPN
ejpam-457	45	3	+	+	CCONJ
ejpam-457	45	4	bi	bi	NOUN
ejpam-457	45	5	(	(	PUNCT
ejpam-457	45	6	t	t	PROPN
ejpam-457	45	7	)	)	PUNCT
ejpam-457	46	1	z	z	NOUN
ejpam-457	47	1	i	i	PRON
ejpam-457	47	2	(	(	PUNCT
ejpam-457	47	3	t	t	PROPN
ejpam-457	47	4	)	)	PUNCT
ejpam-457	48	1	+	+	NOUN
ejpam-457	48	2	y	y	PROPN
ejpam-457	48	3	(	(	PUNCT
ejpam-457	48	4	t)t	t)t	X
ejpam-457	48	5	gu	gu	X
ejpam-457	48	6	(	(	PUNCT
ejpam-457	48	7	t	t	PROPN
ejpam-457	48	8	,	,	PUNCT
ejpam-457	48	9	u	u	NOUN
ejpam-457	48	10	,	,	PUNCT
ejpam-457	48	11	u̇	u̇	PROPN
ejpam-457	48	12	,	,	PUNCT
ejpam-457	48	13	ü	ü	NUM
ejpam-457	48	14	)	)	PUNCT
ejpam-457	48	15	�	�	PROPN
ejpam-457	48	16	−d	−d	PROPN
ejpam-457	48	17	�	�	PROPN
ejpam-457	48	18	λt	λt	ADP
ejpam-457	48	19	fu̇	fu̇	PROPN
ejpam-457	48	20	(	(	PUNCT
ejpam-457	48	21	t	t	PROPN
ejpam-457	48	22	,	,	PUNCT
ejpam-457	48	23	u	u	NOUN
ejpam-457	48	24	,	,	PUNCT
ejpam-457	48	25	u̇	u̇	PROPN
ejpam-457	48	26	,	,	PUNCT
ejpam-457	48	27	ü	ü	PRON
ejpam-457	48	28	)	)	PUNCT
ejpam-457	49	1	+	+	CCONJ
ejpam-457	49	2	y	y	PROPN
ejpam-457	49	3	(	(	PUNCT
ejpam-457	49	4	t)t	t)t	X
ejpam-457	49	5	gu̇	gu̇	X
ejpam-457	49	6	(	(	PUNCT
ejpam-457	49	7	t	t	PROPN
ejpam-457	49	8	,	,	PUNCT
ejpam-457	49	9	u	u	NOUN
ejpam-457	49	10	,	,	PUNCT
ejpam-457	49	11	u̇	u̇	PROPN
ejpam-457	49	12	,	,	PUNCT
ejpam-457	49	13	ü	ü	NOUN
ejpam-457	49	14	)	)	PUNCT
ejpam-457	49	15	�	�	PROPN
ejpam-457	50	1	+	+	NUM
ejpam-457	50	2	d2	d2	PROPN
ejpam-457	50	3	�	�	PROPN
ejpam-457	50	4	λt	λt	ADP
ejpam-457	50	5	fü	fü	X
ejpam-457	50	6	(	(	PUNCT
ejpam-457	50	7	t	t	PROPN
ejpam-457	50	8	,	,	PUNCT
ejpam-457	50	9	u	u	NOUN
ejpam-457	50	10	,	,	PUNCT
ejpam-457	50	11	u̇	u̇	PROPN
ejpam-457	50	12	,	,	PUNCT
ejpam-457	50	13	ü	ü	PRON
ejpam-457	50	14	)	)	PUNCT
ejpam-457	51	1	+	+	CCONJ
ejpam-457	51	2	y	y	PROPN
ejpam-457	51	3	(	(	PUNCT
ejpam-457	51	4	t)t	t)t	X
ejpam-457	51	5	gü	gü	X
ejpam-457	51	6	(	(	PUNCT
ejpam-457	51	7	t	t	PROPN
ejpam-457	51	8	,	,	PUNCT
ejpam-457	51	9	u	u	NOUN
ejpam-457	51	10	,	,	PUNCT
ejpam-457	51	11	u̇	u̇	PROPN
ejpam-457	51	12	,	,	PUNCT
ejpam-457	51	13	ü	ü	NOUN
ejpam-457	51	14	)	)	PUNCT
ejpam-457	51	15	�	�	PROPN
ejpam-457	51	16	=	=	SYM
ejpam-457	51	17	0	0	NUM
ejpam-457	51	18	,	,	PUNCT
ejpam-457	51	19	t	t	PROPN
ejpam-457	51	20	∈	∈	PROPN
ejpam-457	52	1	i	i	PRON
ejpam-457	52	2	,	,	PUNCT
ejpam-457	52	3	y(t	y(t	PROPN
ejpam-457	52	4	)	)	PUNCT
ejpam-457	52	5	≧	≧	X
ejpam-457	52	6	0	0	NUM
ejpam-457	52	7	,	,	PUNCT
ejpam-457	52	8	t	t	PROPN
ejpam-457	52	9	∈	∈	PROPN
ejpam-457	53	1	i	i	PRON
ejpam-457	53	2	,	,	PUNCT
ejpam-457	53	3	λ	λ	X
ejpam-457	53	4	>	>	X
ejpam-457	53	5	0	0	NUM
ejpam-457	53	6	,	,	PUNCT
ejpam-457	53	7	λt	λt	ADP
ejpam-457	53	8	e	e	NOUN
ejpam-457	53	9	=	=	SYM
ejpam-457	53	10	1	1	X
ejpam-457	53	11	.	.	X
ejpam-457	53	12	z̄	z̄	PROPN
ejpam-457	53	13	i(t)t	i(t)t	PROPN
ejpam-457	53	14	bi(t)z̄	bi(t)z̄	PROPN
ejpam-457	53	15	i(t)≦	i(t)≦	ADP
ejpam-457	53	16	1	1	NUM
ejpam-457	53	17	,	,	PUNCT
ejpam-457	53	18	t	t	PROPN
ejpam-457	53	19	∈	∈	PROPN
ejpam-457	54	1	i	i	PRON
ejpam-457	54	2	,	,	PUNCT
ejpam-457	54	3	i	i	PROPN
ejpam-457	54	4	∈	∈	VERB
ejpam-457	54	5	p	p	X
ejpam-457	54	6	,	,	PUNCT
ejpam-457	54	7	the	the	DET
ejpam-457	54	8	problem	problem	NOUN
ejpam-457	54	9	(	(	PUNCT
ejpam-457	54	10	mwd	mwd	PROPN
ejpam-457	54	11	)	)	PUNCT
ejpam-457	54	12	is	be	AUX
ejpam-457	54	13	a	a	DET
ejpam-457	54	14	dual	dual	ADJ
ejpam-457	54	15	to	to	ADP
ejpam-457	54	16	(	(	PUNCT
ejpam-457	54	17	vp	vp	X
ejpam-457	54	18	)	)	PUNCT
ejpam-457	54	19	assuming	assume	VERB
ejpam-457	54	20	that	that	SCONJ
ejpam-457	54	21	p	p	PROPN
ejpam-457	54	22	∑	∑	PROPN
ejpam-457	54	23	i=1	i=1	PROPN
ejpam-457	54	24	λi	λi	INTJ
ejpam-457	54	25	∫	∫	PROPN
ejpam-457	54	26	i	i	INTJ
ejpam-457	54	27	(	(	PUNCT
ejpam-457	54	28	f	f	PROPN
ejpam-457	54	29	i(t	i(t	PROPN
ejpam-457	54	30	,	,	PUNCT
ejpam-457	54	31	.	.	PUNCT
ejpam-457	54	32	,	,	PUNCT
ejpam-457	54	33	.	.	PUNCT
ejpam-457	54	34	,	,	PUNCT
ejpam-457	54	35	.	.	PUNCT
ejpam-457	54	36	)	)	PUNCT
ejpam-457	55	1	+	+	CCONJ
ejpam-457	55	2	(	(	PUNCT
ejpam-457	55	3	·	·	PUNCT
ejpam-457	55	4	)	)	PUNCT
ejpam-457	55	5	t	t	PROPN
ejpam-457	55	6	bi(t)z	bi(t)z	PROPN
ejpam-457	55	7	i(t	i(t	PROPN
ejpam-457	55	8	)	)	PUNCT
ejpam-457	55	9	+	+	NUM
ejpam-457	55	10	y(t)t	y(t)t	PROPN
ejpam-457	55	11	g(t	g(t	PROPN
ejpam-457	55	12	,	,	PUNCT
ejpam-457	55	13	.	.	PUNCT
ejpam-457	55	14	,	,	PUNCT
ejpam-457	55	15	.	.	PUNCT
ejpam-457	55	16	,	,	PUNCT
ejpam-457	55	17	.))d	.))d	PUNCT
ejpam-457	56	1	t	t	PROPN
ejpam-457	56	2	is	be	AUX
ejpam-457	56	3	pseudoinvex	pseudoinvex	NOUN
ejpam-457	56	4	with	with	ADP
ejpam-457	56	5	respect	respect	NOUN
ejpam-457	56	6	to	to	ADP
ejpam-457	56	7	η	η	PROPN
ejpam-457	56	8	.	.	PUNCT
ejpam-457	56	9	the	the	DET
ejpam-457	56	10	authors	author	NOUN
ejpam-457	56	11	in	in	ADP
ejpam-457	56	12	[	[	X
ejpam-457	56	13	9	9	NUM
ejpam-457	56	14	]	]	PUNCT
ejpam-457	56	15	further	far	ADV
ejpam-457	56	16	weakened	weaken	VERB
ejpam-457	56	17	the	the	DET
ejpam-457	56	18	invexity	invexity	NOUN
ejpam-457	56	19	required	require	VERB
ejpam-457	56	20	in	in	ADP
ejpam-457	56	21	wolfe	wolfe	PROPN
ejpam-457	56	22	type	type	NOUN
ejpam-457	56	23	duality	duality	NOUN
ejpam-457	56	24	by	by	ADP
ejpam-457	56	25	constructing	construct	VERB
ejpam-457	56	26	the	the	DET
ejpam-457	56	27	following	follow	VERB
ejpam-457	56	28	mondweir	mondweir	ADJ
ejpam-457	56	29	type	type	NOUN
ejpam-457	56	30	vector	vector	NOUN
ejpam-457	56	31	dual	dual	ADJ
ejpam-457	56	32	.	.	PUNCT
ejpam-457	57	1	the	the	DET
ejpam-457	57	2	following	follow	VERB
ejpam-457	57	3	is	be	AUX
ejpam-457	57	4	the	the	DET
ejpam-457	57	5	mond	mond	PROPN
ejpam-457	57	6	-	-	PUNCT
ejpam-457	57	7	weir	weir	PROPN
ejpam-457	57	8	vector	vector	NOUN
ejpam-457	57	9	type	type	NOUN
ejpam-457	57	10	dual	dual	ADJ
ejpam-457	57	11	to	to	ADP
ejpam-457	57	12	(	(	PUNCT
ejpam-457	57	13	vp	vp	PROPN
ejpam-457	57	14	):	):	PUNCT
ejpam-457	57	15	(	(	PUNCT
ejpam-457	57	16	m	m	NOUN
ejpam-457	57	17	-	-	PUNCT
ejpam-457	57	18	wvd	wvd	NOUN
ejpam-457	57	19	)	)	PUNCT
ejpam-457	57	20	maximize	maximize	VERB
ejpam-457	58	1	�	�	PROPN
ejpam-457	58	2	∫	∫	PROPN
ejpam-457	59	1	i	i	PRON
ejpam-457	59	2	(	(	PUNCT
ejpam-457	59	3	f	f	PROPN
ejpam-457	59	4	1(t	1(t	NUM
ejpam-457	59	5	,	,	PUNCT
ejpam-457	59	6	u	u	NOUN
ejpam-457	59	7	,	,	PUNCT
ejpam-457	59	8	u̇	u̇	PROPN
ejpam-457	59	9	,	,	PUNCT
ejpam-457	59	10	ü	ü	PRON
ejpam-457	59	11	)	)	PUNCT
ejpam-457	60	1	+	+	CCONJ
ejpam-457	60	2	(	(	PUNCT
ejpam-457	60	3	u(t)t	u(t)t	PROPN
ejpam-457	60	4	b1(t)z1(t)))d	b1(t)z1(t)))d	PROPN
ejpam-457	60	5	t	t	PROPN
ejpam-457	60	6	,	,	PUNCT
ejpam-457	60	7	.	.	PUNCT
ejpam-457	60	8	.	.	PUNCT
ejpam-457	60	9	.	.	PUNCT
ejpam-457	61	1	,	,	PUNCT
ejpam-457	61	2	∫	∫	PROPN
ejpam-457	62	1	i	i	PRON
ejpam-457	62	2	(	(	PUNCT
ejpam-457	62	3	f	f	PROPN
ejpam-457	62	4	p(t	p(t	PROPN
ejpam-457	62	5	,	,	PUNCT
ejpam-457	62	6	u	u	NOUN
ejpam-457	62	7	,	,	PUNCT
ejpam-457	62	8	u̇	u̇	PROPN
ejpam-457	62	9	,	,	PUNCT
ejpam-457	62	10	ü	ü	PRON
ejpam-457	62	11	)	)	PUNCT
ejpam-457	63	1	+	+	CCONJ
ejpam-457	63	2	(	(	PUNCT
ejpam-457	63	3	u(t)t	u(t)t	PROPN
ejpam-457	63	4	bp(t)zp(t)))d	bp(t)zp(t)))d	PROPN
ejpam-457	63	5	t	t	PROPN
ejpam-457	63	6	�	�	PROPN
ejpam-457	63	7	subject	subject	ADJ
ejpam-457	63	8	to	to	ADP
ejpam-457	63	9	u(a	u(a	NOUN
ejpam-457	63	10	)	)	PUNCT
ejpam-457	63	11	=	=	SYM
ejpam-457	63	12	0=	0=	PUNCT
ejpam-457	64	1	u(b	u(b	X
ejpam-457	64	2	)	)	PUNCT
ejpam-457	64	3	u̇(a	u̇(a	PROPN
ejpam-457	64	4	)	)	PUNCT
ejpam-457	64	5	=	=	NOUN
ejpam-457	64	6	0=	0=	NOUN
ejpam-457	65	1	u̇(b	u̇(b	NOUN
ejpam-457	65	2	)	)	PUNCT
ejpam-457	66	1	p	p	NOUN
ejpam-457	66	2	∑	∑	PUNCT
ejpam-457	66	3	i=1	i=1	PROPN
ejpam-457	66	4	λi	λi	PROPN
ejpam-457	66	5	�	�	PROPN
ejpam-457	66	6	f	f	PROPN
ejpam-457	67	1	i	i	PRON
ejpam-457	67	2	u	u	PROPN
ejpam-457	67	3	(	(	PUNCT
ejpam-457	67	4	t	t	PROPN
ejpam-457	67	5	,	,	PUNCT
ejpam-457	67	6	u	u	NOUN
ejpam-457	67	7	,	,	PUNCT
ejpam-457	67	8	u̇	u̇	PROPN
ejpam-457	67	9	,	,	PUNCT
ejpam-457	67	10	ü	ü	NUM
ejpam-457	67	11	)	)	PUNCT
ejpam-457	68	1	d	d	NOUN
ejpam-457	68	2	t	t	NOUN
ejpam-457	68	3	+	+	CCONJ
ejpam-457	68	4	bi(t)z	bi(t)z	NOUN
ejpam-457	68	5	i(t	i(t	NOUN
ejpam-457	68	6	)	)	PUNCT
ejpam-457	69	1	+	+	NUM
ejpam-457	69	2	y(t)t	y(t)t	NOUN
ejpam-457	69	3	gu(t	gu(t	PUNCT
ejpam-457	69	4	,	,	PUNCT
ejpam-457	69	5	u	u	NOUN
ejpam-457	69	6	,	,	PUNCT
ejpam-457	69	7	u̇	u̇	PROPN
ejpam-457	69	8	,	,	PUNCT
ejpam-457	69	9	ü	ü	NUM
ejpam-457	69	10	)	)	PUNCT
ejpam-457	69	11	�	�	PROPN
ejpam-457	69	12	i.	i.	PROPN
ejpam-457	69	13	husain	husain	PROPN
ejpam-457	69	14	,	,	PUNCT
ejpam-457	69	15	r.	r.	PROPN
ejpam-457	69	16	mattoo	mattoo	PROPN
ejpam-457	69	17	/	/	SYM
ejpam-457	69	18	eur	eur	PROPN
ejpam-457	69	19	.	.	PUNCT
ejpam-457	70	1	j.	j.	PROPN
ejpam-457	70	2	pure	pure	PROPN
ejpam-457	70	3	appl	appl	PROPN
ejpam-457	70	4	.	.	PROPN
ejpam-457	70	5	math	math	PROPN
ejpam-457	70	6	,	,	PUNCT
ejpam-457	70	7	3	3	NUM
ejpam-457	70	8	(	(	PUNCT
ejpam-457	70	9	2010	2010	NUM
ejpam-457	70	10	)	)	PUNCT
ejpam-457	70	11	,	,	PUNCT
ejpam-457	70	12	81	81	NUM
ejpam-457	70	13	-	-	SYM
ejpam-457	70	14	97	97	NUM
ejpam-457	70	15	83	83	NUM
ejpam-457	70	16	−d	−d	ADJ
ejpam-457	70	17	�	�	PROPN
ejpam-457	70	18	λt	λt	ADP
ejpam-457	70	19	fu̇(t	fu̇(t	PROPN
ejpam-457	70	20	,	,	PUNCT
ejpam-457	70	21	u	u	NOUN
ejpam-457	70	22	,	,	PUNCT
ejpam-457	70	23	u̇	u̇	PROPN
ejpam-457	70	24	,	,	PUNCT
ejpam-457	70	25	ü	ü	PRON
ejpam-457	70	26	)	)	PUNCT
ejpam-457	71	1	+	+	NUM
ejpam-457	71	2	y(t)t	y(t)t	NOUN
ejpam-457	71	3	gu̇(t	gu̇(t	NOUN
ejpam-457	71	4	,	,	PUNCT
ejpam-457	71	5	u	u	NOUN
ejpam-457	71	6	,	,	PUNCT
ejpam-457	71	7	u̇	u̇	PROPN
ejpam-457	71	8	,	,	PUNCT
ejpam-457	71	9	ü	ü	NOUN
ejpam-457	71	10	)	)	PUNCT
ejpam-457	71	11	�	�	PROPN
ejpam-457	71	12	+	+	NUM
ejpam-457	71	13	d2	d2	PROPN
ejpam-457	71	14	�	�	PROPN
ejpam-457	71	15	λt	λt	ADP
ejpam-457	71	16	fü(t	fü(t	NOUN
ejpam-457	71	17	,	,	PUNCT
ejpam-457	71	18	u	u	NOUN
ejpam-457	71	19	,	,	PUNCT
ejpam-457	71	20	u̇	u̇	PROPN
ejpam-457	71	21	,	,	PUNCT
ejpam-457	71	22	ü	ü	PRON
ejpam-457	71	23	)	)	PUNCT
ejpam-457	72	1	+	+	CCONJ
ejpam-457	72	2	y(t)t	y(t)t	PROPN
ejpam-457	72	3	gü(t	gü(t	NOUN
ejpam-457	72	4	,	,	PUNCT
ejpam-457	72	5	u	u	NOUN
ejpam-457	72	6	,	,	PUNCT
ejpam-457	72	7	u̇	u̇	PROPN
ejpam-457	72	8	,	,	PUNCT
ejpam-457	72	9	ü	ü	NOUN
ejpam-457	72	10	)	)	PUNCT
ejpam-457	72	11	�	�	PROPN
ejpam-457	72	12	=	=	SYM
ejpam-457	72	13	0	0	NUM
ejpam-457	72	14	,	,	PUNCT
ejpam-457	72	15	t	t	PROPN
ejpam-457	72	16	∈	∈	PROPN
ejpam-457	73	1	i	i	PRON
ejpam-457	73	2	,	,	PUNCT
ejpam-457	73	3	z̄	z̄	PROPN
ejpam-457	73	4	i(t)t	i(t)t	PROPN
ejpam-457	73	5	bi(t)z̄	bi(t)z̄	PROPN
ejpam-457	73	6	i(t	i(t	PROPN
ejpam-457	73	7	)	)	PUNCT
ejpam-457	73	8	≦	≦	NUM
ejpam-457	73	9	1	1	NUM
ejpam-457	73	10	,	,	PUNCT
ejpam-457	73	11	t	t	PROPN
ejpam-457	73	12	∈	∈	PROPN
ejpam-457	74	1	i	i	PRON
ejpam-457	74	2	,	,	PUNCT
ejpam-457	74	3	i	i	PROPN
ejpam-457	74	4	∈	∈	VERB
ejpam-457	75	1	p	p	NOUN
ejpam-457	75	2	∫	∫	PROPN
ejpam-457	75	3	i	i	PROPN
ejpam-457	75	4	y(t)t	y(t)t	PROPN
ejpam-457	75	5	g(t	g(t	PROPN
ejpam-457	75	6	,	,	PUNCT
ejpam-457	75	7	u	u	NOUN
ejpam-457	75	8	,	,	PUNCT
ejpam-457	75	9	u̇	u̇	PROPN
ejpam-457	75	10	,	,	PUNCT
ejpam-457	75	11	ü)d	ü)d	PROPN
ejpam-457	75	12	t	t	PROPN
ejpam-457	75	13	≧	≧	NUM
ejpam-457	75	14	0	0	NUM
ejpam-457	75	15	,	,	PUNCT
ejpam-457	75	16	y(t	y(t	NUM
ejpam-457	75	17	)	)	PUNCT
ejpam-457	75	18	≧	≧	X
ejpam-457	75	19	0	0	NUM
ejpam-457	75	20	,	,	PUNCT
ejpam-457	75	21	t	t	PROPN
ejpam-457	75	22	∈	∈	PROPN
ejpam-457	76	1	i	i	PRON
ejpam-457	76	2	,	,	PUNCT
ejpam-457	76	3	λ	λ	X
ejpam-457	76	4	>	>	X
ejpam-457	76	5	0	0	PROPN
ejpam-457	76	6	.	.	PUNCT
ejpam-457	76	7	mond	mond	PROPN
ejpam-457	76	8	-	-	PUNCT
ejpam-457	76	9	weir	weir	PROPN
ejpam-457	76	10	established	establish	VERB
ejpam-457	76	11	usual	usual	ADJ
ejpam-457	76	12	duality	duality	NOUN
ejpam-457	76	13	theorems	theorem	NOUN
ejpam-457	76	14	under	under	ADP
ejpam-457	76	15	the	the	DET
ejpam-457	76	16	hypotheses	hypothesis	NOUN
ejpam-457	76	17	that	that	SCONJ
ejpam-457	76	18	p	p	NOUN
ejpam-457	76	19	∑	∑	PROPN
ejpam-457	76	20	i=1	i=1	PROPN
ejpam-457	76	21	λi	λi	INTJ
ejpam-457	76	22	∫	∫	PROPN
ejpam-457	77	1	i	i	INTJ
ejpam-457	77	2	(	(	PUNCT
ejpam-457	77	3	f	f	PROPN
ejpam-457	77	4	i(t	i(t	PROPN
ejpam-457	77	5	,	,	PUNCT
ejpam-457	77	6	.	.	PUNCT
ejpam-457	77	7	,	,	PUNCT
ejpam-457	77	8	.	.	PUNCT
ejpam-457	77	9	,	,	PUNCT
ejpam-457	77	10	.	.	PUNCT
ejpam-457	77	11	)	)	PUNCT
ejpam-457	78	1	+	+	CCONJ
ejpam-457	78	2	(	(	PUNCT
ejpam-457	78	3	·	·	PUNCT
ejpam-457	78	4	)	)	PUNCT
ejpam-457	78	5	t	t	NOUN
ejpam-457	78	6	bi(t)z	bi(t)z	PROPN
ejpam-457	78	7	i(t))d	i(t))d	NOUN
ejpam-457	78	8	t	t	NOUN
ejpam-457	78	9	is	be	AUX
ejpam-457	78	10	pseudoinvex	pseudoinvex	NOUN
ejpam-457	78	11	and	and	CCONJ
ejpam-457	78	12	∫	∫	NOUN
ejpam-457	78	13	i	i	PROPN
ejpam-457	78	14	y(t)t	y(t)t	PROPN
ejpam-457	78	15	g(t	g(t	PROPN
ejpam-457	78	16	,	,	PUNCT
ejpam-457	78	17	.	.	PUNCT
ejpam-457	78	18	,	,	PUNCT
ejpam-457	78	19	.	.	PUNCT
ejpam-457	78	20	,	,	PUNCT
ejpam-457	79	1	.)d	.)d	PROPN
ejpam-457	79	2	t	t	PROPN
ejpam-457	79	3	is	be	AUX
ejpam-457	79	4	quasi	quasi	ADJ
ejpam-457	79	5	-	-	NOUN
ejpam-457	79	6	invex	invex	ADJ
ejpam-457	79	7	with	with	ADP
ejpam-457	79	8	respect	respect	NOUN
ejpam-457	79	9	to	to	ADP
ejpam-457	79	10	the	the	DET
ejpam-457	79	11	same	same	ADJ
ejpam-457	79	12	η	η	PROPN
ejpam-457	79	13	.	.	PROPN
ejpam-457	79	14	in	in	ADP
ejpam-457	79	15	this	this	DET
ejpam-457	79	16	paper	paper	NOUN
ejpam-457	79	17	,	,	PUNCT
ejpam-457	79	18	we	we	PRON
ejpam-457	79	19	propose	propose	VERB
ejpam-457	79	20	,	,	PUNCT
ejpam-457	79	21	in	in	ADP
ejpam-457	79	22	the	the	DET
ejpam-457	79	23	spirit	spirit	NOUN
ejpam-457	79	24	of	of	ADP
ejpam-457	79	25	husain	husain	PROPN
ejpam-457	79	26	and	and	CCONJ
ejpam-457	79	27	jabeen	jabeen	VERB
ejpam-457	79	28	[	[	X
ejpam-457	79	29	7	7	X
ejpam-457	79	30	]	]	PUNCT
ejpam-457	79	31	and	and	CCONJ
ejpam-457	79	32	xu	xu	X
ejpam-457	80	1	[	[	X
ejpam-457	80	2	18	18	NUM
ejpam-457	80	3	]	]	X
ejpam-457	80	4	,	,	PUNCT
ejpam-457	80	5	a	a	DET
ejpam-457	80	6	mixed	mixed	ADJ
ejpam-457	80	7	type	type	NOUN
ejpam-457	80	8	dual	dual	ADJ
ejpam-457	80	9	to	to	ADP
ejpam-457	80	10	(	(	PUNCT
ejpam-457	80	11	vp	vp	NOUN
ejpam-457	80	12	)	)	PUNCT
ejpam-457	80	13	and	and	CCONJ
ejpam-457	80	14	established	establish	VERB
ejpam-457	80	15	various	various	ADJ
ejpam-457	80	16	duality	duality	NOUN
ejpam-457	80	17	results	result	NOUN
ejpam-457	80	18	under	under	ADP
ejpam-457	80	19	generalized	generalized	ADJ
ejpam-457	80	20	invexity	invexity	NOUN
ejpam-457	80	21	requirements	requirement	NOUN
ejpam-457	80	22	.	.	PUNCT
ejpam-457	81	1	special	special	ADJ
ejpam-457	81	2	cases	case	NOUN
ejpam-457	81	3	are	be	AUX
ejpam-457	81	4	generalized	generalize	VERB
ejpam-457	81	5	and	and	CCONJ
ejpam-457	81	6	it	it	PRON
ejpam-457	81	7	is	be	AUX
ejpam-457	81	8	also	also	ADV
ejpam-457	81	9	pointed	point	VERB
ejpam-457	81	10	out	out	ADP
ejpam-457	81	11	that	that	SCONJ
ejpam-457	81	12	our	our	PRON
ejpam-457	81	13	duality	duality	NOUN
ejpam-457	81	14	results	result	NOUN
ejpam-457	81	15	can	can	AUX
ejpam-457	81	16	be	be	AUX
ejpam-457	81	17	viewed	view	VERB
ejpam-457	81	18	as	as	ADP
ejpam-457	81	19	dynamic	dynamic	ADJ
ejpam-457	81	20	generalizations	generalization	NOUN
ejpam-457	81	21	of	of	ADP
ejpam-457	81	22	those	those	PRON
ejpam-457	81	23	of	of	ADP
ejpam-457	81	24	static	static	ADJ
ejpam-457	81	25	case	case	NOUN
ejpam-457	81	26	,	,	PUNCT
ejpam-457	81	27	already	already	ADV
ejpam-457	81	28	existing	exist	VERB
ejpam-457	81	29	in	in	ADP
ejpam-457	81	30	the	the	DET
ejpam-457	81	31	literature	literature	NOUN
ejpam-457	81	32	.	.	PUNCT
ejpam-457	82	1	2	2	X
ejpam-457	82	2	.	.	X
ejpam-457	82	3	pre	pre	NOUN
ejpam-457	82	4	-	-	NOUN
ejpam-457	82	5	requisites	requisite	NOUN
ejpam-457	82	6	consider	consider	VERB
ejpam-457	82	7	the	the	DET
ejpam-457	82	8	real	real	ADJ
ejpam-457	82	9	interval	interval	NOUN
ejpam-457	83	1	i	i	PRON
ejpam-457	83	2	=	=	PUNCT
ejpam-457	84	1	[	[	X
ejpam-457	84	2	a	a	X
ejpam-457	84	3	,	,	PUNCT
ejpam-457	84	4	b	b	NOUN
ejpam-457	84	5	]	]	X
ejpam-457	84	6	,	,	PUNCT
ejpam-457	84	7	and	and	CCONJ
ejpam-457	84	8	the	the	DET
ejpam-457	84	9	continuously	continuously	ADV
ejpam-457	84	10	differentiable	differentiable	ADJ
ejpam-457	84	11	function	function	NOUN
ejpam-457	84	12	φ	φ	PROPN
ejpam-457	84	13	:	:	PUNCT
ejpam-457	84	14	i×rn×rn×rn→	i×rn×rn×rn→	VERB
ejpam-457	84	15	r.	r.	VERB
ejpam-457	84	16	in	in	ADP
ejpam-457	84	17	order	order	NOUN
ejpam-457	84	18	to	to	PART
ejpam-457	84	19	consider	consider	VERB
ejpam-457	84	20	φ(t	φ(t	PROPN
ejpam-457	84	21	,	,	PUNCT
ejpam-457	84	22	x	x	SYM
ejpam-457	84	23	,	,	PUNCT
ejpam-457	84	24	ẋ	ẋ	PROPN
ejpam-457	84	25	,	,	PUNCT
ejpam-457	84	26	ẍ	ẍ	PROPN
ejpam-457	84	27	)	)	PUNCT
ejpam-457	84	28	,	,	PUNCT
ejpam-457	84	29	where	where	SCONJ
ejpam-457	84	30	x	x	X
ejpam-457	84	31	:	:	PUNCT
ejpam-457	84	32	i	i	PRON
ejpam-457	84	33	→	→	SYM
ejpam-457	84	34	rn	rn	PROPN
ejpam-457	84	35	is	be	AUX
ejpam-457	84	36	twice	twice	ADV
ejpam-457	84	37	differentiable	differentiable	ADJ
ejpam-457	84	38	with	with	ADP
ejpam-457	84	39	its	its	PRON
ejpam-457	84	40	first	first	ADJ
ejpam-457	84	41	and	and	CCONJ
ejpam-457	84	42	second	second	ADJ
ejpam-457	84	43	order	order	NOUN
ejpam-457	84	44	derivatives	derivative	NOUN
ejpam-457	84	45	ẋ	ẋ	PROPN
ejpam-457	84	46	and	and	CCONJ
ejpam-457	84	47	ẍ	ẍ	PROPN
ejpam-457	84	48	respectively	respectively	ADV
ejpam-457	84	49	,	,	PUNCT
ejpam-457	84	50	we	we	PRON
ejpam-457	84	51	denote	denote	VERB
ejpam-457	84	52	the	the	DET
ejpam-457	84	53	partial	partial	ADJ
ejpam-457	84	54	derivative	derivative	NOUN
ejpam-457	84	55	φ	φ	NOUN
ejpam-457	84	56	by	by	ADP
ejpam-457	84	57	φt	φt	PROPN
ejpam-457	84	58	.	.	PUNCT
ejpam-457	85	1	φx	φx	PROPN
ejpam-457	85	2	=	=	SYM
ejpam-457	85	3	�	�	PROPN
ejpam-457	85	4	∂	∂	PROPN
ejpam-457	85	5	φ	φ	PROPN
ejpam-457	85	6	∂	∂	NOUN
ejpam-457	85	7	x1	x1	PROPN
ejpam-457	85	8	,	,	PUNCT
ejpam-457	85	9	.	.	PUNCT
ejpam-457	85	10	.	.	PUNCT
ejpam-457	86	1	.	.	PUNCT
ejpam-457	87	1	,	,	PUNCT
ejpam-457	87	2	∂	∂	NUM
ejpam-457	87	3	φ	φ	PROPN
ejpam-457	87	4	∂	∂	PROPN
ejpam-457	87	5	xn	xn	PROPN
ejpam-457	87	6	�	�	PROPN
ejpam-457	87	7	t	t	PROPN
ejpam-457	87	8	,	,	PUNCT
ejpam-457	87	9	φ	φ	PROPN
ejpam-457	87	10	ẋ	ẋ	PUNCT
ejpam-457	88	1	=	=	SYM
ejpam-457	88	2	�	�	PROPN
ejpam-457	88	3	∂	∂	PROPN
ejpam-457	88	4	φ	φ	PROPN
ejpam-457	88	5	∂	∂	NOUN
ejpam-457	89	1	ẋ1	ẋ1	PROPN
ejpam-457	89	2	,	,	PUNCT
ejpam-457	89	3	.	.	PUNCT
ejpam-457	89	4	.	.	PUNCT
ejpam-457	90	1	.	.	PUNCT
ejpam-457	91	1	,	,	PUNCT
ejpam-457	91	2	∂	∂	NUM
ejpam-457	91	3	φ	φ	PROPN
ejpam-457	91	4	∂	∂	PROPN
ejpam-457	91	5	ẋn	ẋn	PROPN
ejpam-457	91	6	�	�	PROPN
ejpam-457	91	7	t	t	PROPN
ejpam-457	91	8	,	,	PUNCT
ejpam-457	91	9	φ	φ	PROPN
ejpam-457	91	10	ẍ	ẍ	PUNCT
ejpam-457	92	1	=	=	SYM
ejpam-457	92	2	�	�	PROPN
ejpam-457	92	3	∂	∂	PROPN
ejpam-457	92	4	φ	φ	PROPN
ejpam-457	92	5	∂	∂	PROPN
ejpam-457	92	6	ẍ1	ẍ1	PROPN
ejpam-457	92	7	,	,	PUNCT
ejpam-457	92	8	.	.	PUNCT
ejpam-457	92	9	.	.	PUNCT
ejpam-457	93	1	.	.	PUNCT
ejpam-457	94	1	,	,	PUNCT
ejpam-457	94	2	∂	∂	NUM
ejpam-457	94	3	φ	φ	PROPN
ejpam-457	94	4	∂	∂	PROPN
ejpam-457	94	5	ẍn	ẍn	PROPN
ejpam-457	94	6	�	�	PROPN
ejpam-457	94	7	t	t	PROPN
ejpam-457	94	8	.	.	PUNCT
ejpam-457	95	1	the	the	DET
ejpam-457	95	2	partial	partial	ADJ
ejpam-457	95	3	derivative	derivative	NOUN
ejpam-457	95	4	of	of	ADP
ejpam-457	95	5	other	other	ADJ
ejpam-457	95	6	function	function	NOUN
ejpam-457	95	7	will	will	AUX
ejpam-457	95	8	be	be	AUX
ejpam-457	95	9	written	write	VERB
ejpam-457	95	10	similarly	similarly	ADV
ejpam-457	95	11	.	.	PUNCT
ejpam-457	96	1	let	let	VERB
ejpam-457	96	2	k	k	PROPN
ejpam-457	96	3	designates	designate	VERB
ejpam-457	96	4	the	the	DET
ejpam-457	96	5	space	space	NOUN
ejpam-457	96	6	of	of	ADP
ejpam-457	96	7	piecewise	piecewise	NOUN
ejpam-457	96	8	functions	function	NOUN
ejpam-457	96	9	x	x	PUNCT
ejpam-457	96	10	:	:	PUNCT
ejpam-457	96	11	i	i	PRON
ejpam-457	96	12	→	→	SYM
ejpam-457	96	13	rn	rn	X
ejpam-457	96	14	possessing	possess	VERB
ejpam-457	96	15	derivatives	derivative	NOUN
ejpam-457	96	16	ẋ	ẋ	PROPN
ejpam-457	96	17	and	and	CCONJ
ejpam-457	96	18	ẍ	ẍ	X
ejpam-457	96	19	with	with	ADP
ejpam-457	96	20	the	the	DET
ejpam-457	96	21	norm	norm	NOUN
ejpam-457	96	22	‖x‖	‖x‖	PROPN
ejpam-457	96	23	=	=	SYM
ejpam-457	96	24	‖x‖∞‖x‖∞	‖x‖∞‖x‖∞	PROPN
ejpam-457	96	25	+	+	CCONJ
ejpam-457	96	26	‖d	‖d	ADJ
ejpam-457	96	27	2	2	NUM
ejpam-457	96	28	x‖∞	x‖∞	NOUN
ejpam-457	96	29	,	,	PUNCT
ejpam-457	96	30	where	where	SCONJ
ejpam-457	96	31	the	the	DET
ejpam-457	96	32	differentiation	differentiation	NOUN
ejpam-457	96	33	operator	operator	NOUN
ejpam-457	96	34	d	d	NOUN
ejpam-457	96	35	is	be	AUX
ejpam-457	96	36	given	give	VERB
ejpam-457	96	37	by	by	ADP
ejpam-457	96	38	u	u	NOUN
ejpam-457	96	39	=	=	NOUN
ejpam-457	96	40	dx⇔	dx⇔	NOUN
ejpam-457	96	41	x(t	x(t	PROPN
ejpam-457	96	42	)	)	PUNCT
ejpam-457	96	43	=	=	SYM
ejpam-457	97	1	α+	α+	PUNCT
ejpam-457	97	2	∫	∫	PROPN
ejpam-457	97	3	t	t	PROPN
ejpam-457	97	4	a	a	DET
ejpam-457	97	5	u(s)ds	u(s)ds	PROPN
ejpam-457	97	6	,	,	PUNCT
ejpam-457	97	7	where	where	SCONJ
ejpam-457	97	8	α	α	NOUN
ejpam-457	97	9	is	be	AUX
ejpam-457	97	10	given	give	VERB
ejpam-457	97	11	boundary	boundary	ADJ
ejpam-457	97	12	value	value	NOUN
ejpam-457	97	13	;	;	PUNCT
ejpam-457	97	14	thus	thus	ADV
ejpam-457	97	15	d	d	X
ejpam-457	97	16	≡	≡	PROPN
ejpam-457	97	17	d	d	PROPN
ejpam-457	97	18	d	d	PROPN
ejpam-457	97	19	t	t	PROPN
ejpam-457	97	20	except	except	SCONJ
ejpam-457	97	21	at	at	ADP
ejpam-457	97	22	discontinuities	discontinuity	NOUN
ejpam-457	97	23	.	.	PUNCT
ejpam-457	98	1	in	in	ADP
ejpam-457	98	2	the	the	DET
ejpam-457	98	3	results	result	NOUN
ejpam-457	98	4	to	to	PART
ejpam-457	98	5	follow	follow	VERB
ejpam-457	98	6	,	,	PUNCT
ejpam-457	98	7	we	we	PRON
ejpam-457	98	8	use	use	VERB
ejpam-457	98	9	c(i	c(i	NOUN
ejpam-457	98	10	,	,	PUNCT
ejpam-457	98	11	rk	rk	NOUN
ejpam-457	98	12	)	)	PUNCT
ejpam-457	98	13	to	to	PART
ejpam-457	98	14	denote	denote	VERB
ejpam-457	98	15	the	the	DET
ejpam-457	98	16	space	space	NOUN
ejpam-457	98	17	of	of	ADP
ejpam-457	98	18	continuous	continuous	ADJ
ejpam-457	98	19	functions	function	NOUN
ejpam-457	98	20	with	with	ADP
ejpam-457	98	21	the	the	DET
ejpam-457	98	22	uniform	uniform	PROPN
ejpam-457	98	23	norm	norm	NOUN
ejpam-457	98	24	;	;	PUNCT
ejpam-457	98	25	superscript	superscript	PROPN
ejpam-457	98	26	t	t	PROPN
ejpam-457	98	27	denotes	denotes	PROPN
ejpam-457	98	28	matrix	matrix	NOUN
ejpam-457	98	29	transpose	transpose	PROPN
ejpam-457	98	30	.	.	PUNCT
ejpam-457	99	1	i.	i.	PROPN
ejpam-457	99	2	husain	husain	PROPN
ejpam-457	99	3	,	,	PUNCT
ejpam-457	99	4	r.	r.	PROPN
ejpam-457	99	5	mattoo	mattoo	PROPN
ejpam-457	99	6	/	/	SYM
ejpam-457	99	7	eur	eur	PROPN
ejpam-457	99	8	.	.	PUNCT
ejpam-457	100	1	j.	j.	PROPN
ejpam-457	100	2	pure	pure	PROPN
ejpam-457	100	3	appl	appl	PROPN
ejpam-457	100	4	.	.	PROPN
ejpam-457	100	5	math	math	PROPN
ejpam-457	100	6	,	,	PUNCT
ejpam-457	100	7	3	3	NUM
ejpam-457	100	8	(	(	PUNCT
ejpam-457	100	9	2010	2010	NUM
ejpam-457	100	10	)	)	PUNCT
ejpam-457	100	11	,	,	PUNCT
ejpam-457	100	12	81	81	NUM
ejpam-457	100	13	-	-	SYM
ejpam-457	100	14	97	97	NUM
ejpam-457	100	15	84	84	NUM
ejpam-457	100	16	before	before	ADP
ejpam-457	100	17	stating	state	VERB
ejpam-457	100	18	our	our	PRON
ejpam-457	100	19	mixed	mixed	ADJ
ejpam-457	100	20	type	type	NOUN
ejpam-457	100	21	multiobjective	multiobjective	ADJ
ejpam-457	100	22	variational	variational	ADJ
ejpam-457	100	23	problem	problem	NOUN
ejpam-457	101	1	,	,	PUNCT
ejpam-457	101	2	we	we	PRON
ejpam-457	101	3	mention	mention	VERB
ejpam-457	101	4	the	the	DET
ejpam-457	101	5	following	follow	VERB
ejpam-457	101	6	conventions	convention	NOUN
ejpam-457	101	7	for	for	ADP
ejpam-457	101	8	vectors	vector	NOUN
ejpam-457	101	9	x	x	PUNCT
ejpam-457	101	10	and	and	CCONJ
ejpam-457	101	11	y	y	PROPN
ejpam-457	101	12	in	in	ADP
ejpam-457	101	13	n	n	CCONJ
ejpam-457	101	14	-	-	PUNCT
ejpam-457	101	15	dimensional	dimensional	ADJ
ejpam-457	101	16	euclidian	euclidian	ADJ
ejpam-457	101	17	space	space	NOUN
ejpam-457	101	18	rn	rn	PROPN
ejpam-457	101	19	to	to	PART
ejpam-457	101	20	be	be	AUX
ejpam-457	101	21	used	use	VERB
ejpam-457	101	22	throughout	throughout	ADP
ejpam-457	101	23	the	the	DET
ejpam-457	101	24	analysis	analysis	NOUN
ejpam-457	101	25	of	of	ADP
ejpam-457	101	26	this	this	DET
ejpam-457	101	27	research	research	NOUN
ejpam-457	101	28	together	together	ADV
ejpam-457	101	29	with	with	ADP
ejpam-457	101	30	some	some	DET
ejpam-457	101	31	definitions	definition	NOUN
ejpam-457	101	32	of	of	ADP
ejpam-457	101	33	invexity	invexity	NOUN
ejpam-457	101	34	and	and	CCONJ
ejpam-457	101	35	generalized	generalized	ADJ
ejpam-457	101	36	invexity	invexity	NOUN
ejpam-457	101	37	for	for	ADP
ejpam-457	101	38	easy	easy	ADJ
ejpam-457	101	39	reference	reference	NOUN
ejpam-457	101	40	.	.	PUNCT
ejpam-457	102	1	x	x	X
ejpam-457	102	2	<	<	X
ejpam-457	102	3	y	y	PROPN
ejpam-457	102	4	,	,	PUNCT
ejpam-457	102	5	⇔	⇔	X
ejpam-457	102	6	x	x	PROPN
ejpam-457	102	7	i	i	PRON
ejpam-457	102	8	<	<	X
ejpam-457	102	9	yi	yi	PROPN
ejpam-457	102	10	,	,	PUNCT
ejpam-457	102	11	i	i	NOUN
ejpam-457	102	12	=	=	NOUN
ejpam-457	102	13	1,2	1,2	NUM
ejpam-457	102	14	,	,	PUNCT
ejpam-457	102	15	.	.	PUNCT
ejpam-457	102	16	.	.	PUNCT
ejpam-457	102	17	.	.	PUNCT
ejpam-457	103	1	,	,	PUNCT
ejpam-457	103	2	n.	n.	NOUN
ejpam-457	103	3	x	x	PUNCT
ejpam-457	104	1	≦	≦	NUM
ejpam-457	104	2	y	y	PROPN
ejpam-457	104	3	,	,	PUNCT
ejpam-457	104	4	⇔	⇔	X
ejpam-457	104	5	x	x	PROPN
ejpam-457	104	6	i	i	NOUN
ejpam-457	104	7	≤	≤	PUNCT
ejpam-457	104	8	yi	yi	NOUN
ejpam-457	104	9	,	,	PUNCT
ejpam-457	104	10	i	i	NOUN
ejpam-457	104	11	=	=	NOUN
ejpam-457	104	12	1,2	1,2	NUM
ejpam-457	104	13	,	,	PUNCT
ejpam-457	104	14	.	.	PUNCT
ejpam-457	104	15	.	.	PUNCT
ejpam-457	104	16	.	.	PUNCT
ejpam-457	105	1	,	,	PUNCT
ejpam-457	105	2	n.	n.	NOUN
ejpam-457	105	3	x	x	PUNCT
ejpam-457	105	4	≤	≤	PROPN
ejpam-457	105	5	y	y	PROPN
ejpam-457	105	6	,	,	PUNCT
ejpam-457	105	7	⇔	⇔	X
ejpam-457	105	8	x	x	PROPN
ejpam-457	105	9	i	i	PRON
ejpam-457	105	10	≦	≦	VERB
ejpam-457	105	11	yi	yi	INTJ
ejpam-457	105	12	,	,	PUNCT
ejpam-457	105	13	i	i	PRON
ejpam-457	105	14	=	=	NOUN
ejpam-457	105	15	1,2	1,2	NUM
ejpam-457	105	16	,	,	PUNCT
ejpam-457	105	17	.	.	PUNCT
ejpam-457	105	18	.	.	PUNCT
ejpam-457	105	19	.	.	PUNCT
ejpam-457	106	1	,	,	PUNCT
ejpam-457	106	2	n.	n.	NOUN
ejpam-457	106	3	but	but	CCONJ
ejpam-457	106	4	x	x	SYM
ejpam-457	106	5	6=	6=	NUM
ejpam-457	106	6	y	y	PROPN
ejpam-457	106	7	x	x	SYM
ejpam-457	106	8	�	�	PROPN
ejpam-457	106	9	y	y	PROPN
ejpam-457	106	10	,	,	PUNCT
ejpam-457	106	11	is	be	AUX
ejpam-457	106	12	the	the	DET
ejpam-457	106	13	negation	negation	NOUN
ejpam-457	106	14	of	of	ADP
ejpam-457	106	15	x	x	PUNCT
ejpam-457	106	16	≤	≤	NUM
ejpam-457	106	17	y	y	NOUN
ejpam-457	106	18	for	for	ADP
ejpam-457	106	19	x	x	X
ejpam-457	106	20	,	,	PUNCT
ejpam-457	106	21	y	y	PROPN
ejpam-457	106	22	∈	∈	PROPN
ejpam-457	106	23	r	r	NOUN
ejpam-457	106	24	,	,	PUNCT
ejpam-457	106	25	x	x	PUNCT
ejpam-457	106	26	≤	≤	ADJ
ejpam-457	106	27	y	y	PROPN
ejpam-457	106	28	and	and	CCONJ
ejpam-457	106	29	x	x	SYM
ejpam-457	106	30	<	<	X
ejpam-457	106	31	y	y	X
ejpam-457	106	32	have	have	VERB
ejpam-457	106	33	the	the	DET
ejpam-457	106	34	usual	usual	ADJ
ejpam-457	106	35	meaning	meaning	NOUN
ejpam-457	106	36	.	.	PUNCT
ejpam-457	107	1	definition	definition	NOUN
ejpam-457	107	2	1	1	NUM
ejpam-457	107	3	(	(	PUNCT
ejpam-457	107	4	invexity	invexity	NOUN
ejpam-457	107	5	)	)	PUNCT
ejpam-457	107	6	.	.	PUNCT
ejpam-457	108	1	if	if	SCONJ
ejpam-457	108	2	there	there	PRON
ejpam-457	108	3	exists	exist	VERB
ejpam-457	108	4	vector	vector	NOUN
ejpam-457	108	5	function	function	NOUN
ejpam-457	108	6	η(t	η(t	NOUN
ejpam-457	108	7	,	,	PUNCT
ejpam-457	108	8	x	x	SYM
ejpam-457	108	9	,	,	PUNCT
ejpam-457	108	10	u	u	NOUN
ejpam-457	108	11	)	)	PUNCT
ejpam-457	108	12	∈	∈	PROPN
ejpam-457	108	13	rn	rn	PROPN
ejpam-457	108	14	with	with	ADP
ejpam-457	108	15	η	η	PROPN
ejpam-457	108	16	=	=	PROPN
ejpam-457	108	17	0	0	PROPN
ejpam-457	108	18	and	and	CCONJ
ejpam-457	108	19	x(t	x(t	PROPN
ejpam-457	108	20	)	)	PUNCT
ejpam-457	108	21	=	=	SYM
ejpam-457	108	22	u(t	u(t	NOUN
ejpam-457	108	23	)	)	PUNCT
ejpam-457	108	24	,	,	PUNCT
ejpam-457	108	25	t	t	PROPN
ejpam-457	108	26	∈	∈	PROPN
ejpam-457	109	1	i	i	PRON
ejpam-457	109	2	and	and	CCONJ
ejpam-457	109	3	dη	dη	X
ejpam-457	109	4	=	=	NOUN
ejpam-457	109	5	0	0	NUM
ejpam-457	109	6	for	for	ADP
ejpam-457	109	7	ẋ(t	ẋ(t	NOUN
ejpam-457	109	8	)	)	PUNCT
ejpam-457	109	9	=	=	SYM
ejpam-457	109	10	u̇(t	u̇(t	NOUN
ejpam-457	109	11	)	)	PUNCT
ejpam-457	109	12	,	,	PUNCT
ejpam-457	109	13	t	t	PROPN
ejpam-457	109	14	∈	∈	PROPN
ejpam-457	109	15	i	i	PRON
ejpam-457	109	16	such	such	ADJ
ejpam-457	109	17	that	that	PRON
ejpam-457	109	18	for	for	ADP
ejpam-457	109	19	a	a	DET
ejpam-457	109	20	scalar	scalar	ADJ
ejpam-457	109	21	function	function	NOUN
ejpam-457	109	22	φ(t	φ(t	PROPN
ejpam-457	109	23	,	,	PUNCT
ejpam-457	109	24	x	x	SYM
ejpam-457	109	25	,	,	PUNCT
ejpam-457	109	26	ẋ	ẋ	PROPN
ejpam-457	109	27	,	,	PUNCT
ejpam-457	109	28	ẍ	ẍ	PROPN
ejpam-457	109	29	)	)	PUNCT
ejpam-457	109	30	,	,	PUNCT
ejpam-457	109	31	the	the	DET
ejpam-457	109	32	functional	functional	ADJ
ejpam-457	109	33	φ(x	φ(x	PROPN
ejpam-457	109	34	,	,	PUNCT
ejpam-457	109	35	ẋ	ẋ	PROPN
ejpam-457	109	36	,	,	PUNCT
ejpam-457	109	37	ẍ	ẍ	X
ejpam-457	109	38	)	)	PUNCT
ejpam-457	110	1	=	=	SYM
ejpam-457	110	2	∫	∫	PROPN
ejpam-457	111	1	i	i	PROPN
ejpam-457	111	2	φ(t	φ(t	PROPN
ejpam-457	111	3	,	,	PUNCT
ejpam-457	111	4	x	x	X
ejpam-457	111	5	,	,	PUNCT
ejpam-457	111	6	ẋ	ẋ	PROPN
ejpam-457	111	7	,	,	PUNCT
ejpam-457	111	8	ẍ)d	ẍ)d	PROPN
ejpam-457	111	9	t	t	NOUN
ejpam-457	111	10	satisfies	satisfy	VERB
ejpam-457	111	11	φ(x	φ(x	PROPN
ejpam-457	111	12	,	,	PUNCT
ejpam-457	111	13	u̇	u̇	PROPN
ejpam-457	111	14	,	,	PUNCT
ejpam-457	111	15	ü)−φ(x	ü)−φ(x	NOUN
ejpam-457	111	16	,	,	PUNCT
ejpam-457	111	17	ẋ	ẋ	PROPN
ejpam-457	111	18	,	,	PUNCT
ejpam-457	111	19	ẍ	ẍ	X
ejpam-457	111	20	)	)	PUNCT
ejpam-457	111	21	≧	≧	X
ejpam-457	112	1	∫	∫	PROPN
ejpam-457	113	1	i	i	PRON
ejpam-457	113	2	{	{	PUNCT
ejpam-457	113	3	ηtφx(t	ηtφx(t	PROPN
ejpam-457	113	4	,	,	PUNCT
ejpam-457	113	5	x	x	SYM
ejpam-457	113	6	,	,	PUNCT
ejpam-457	113	7	ẋ	ẋ	PROPN
ejpam-457	113	8	,	,	PUNCT
ejpam-457	113	9	ẍ	ẍ	X
ejpam-457	113	10	)	)	PUNCT
ejpam-457	114	1	+	+	CCONJ
ejpam-457	114	2	(	(	PUNCT
ejpam-457	114	3	dη)tφ	dη)tφ	NUM
ejpam-457	114	4	ẋ	ẋ	PROPN
ejpam-457	114	5	(	(	PUNCT
ejpam-457	114	6	t	t	PROPN
ejpam-457	114	7	,	,	PUNCT
ejpam-457	114	8	x	x	X
ejpam-457	114	9	,	,	PUNCT
ejpam-457	114	10	ẋ	ẋ	PROPN
ejpam-457	114	11	,	,	PUNCT
ejpam-457	114	12	ẍ	ẍ	X
ejpam-457	114	13	)	)	PUNCT
ejpam-457	115	1	+	+	CCONJ
ejpam-457	115	2	(	(	PUNCT
ejpam-457	115	3	d2η)tφ	d2η)tφ	PROPN
ejpam-457	115	4	ẍ	ẍ	PROPN
ejpam-457	115	5	(	(	PUNCT
ejpam-457	115	6	t	t	PROPN
ejpam-457	115	7	,	,	PUNCT
ejpam-457	115	8	x	x	X
ejpam-457	115	9	,	,	PUNCT
ejpam-457	115	10	ẋ	ẋ	PROPN
ejpam-457	115	11	,	,	PUNCT
ejpam-457	115	12	ẍ)}d	ẍ)}d	PROPN
ejpam-457	115	13	t	t	PROPN
ejpam-457	115	14	,	,	PUNCT
ejpam-457	115	15	φ	φ	PROPN
ejpam-457	115	16	is	be	AUX
ejpam-457	115	17	said	say	VERB
ejpam-457	115	18	to	to	PART
ejpam-457	115	19	be	be	AUX
ejpam-457	115	20	invex	invex	NOUN
ejpam-457	115	21	in	in	ADP
ejpam-457	115	22	x	x	SYM
ejpam-457	115	23	,	,	PUNCT
ejpam-457	115	24	ẋ	ẋ	PROPN
ejpam-457	115	25	and	and	CCONJ
ejpam-457	115	26	ẍ	ẍ	X
ejpam-457	115	27	on	on	ADP
ejpam-457	115	28	i	i	PRON
ejpam-457	115	29	with	with	ADP
ejpam-457	115	30	respect	respect	NOUN
ejpam-457	115	31	to	to	ADP
ejpam-457	115	32	η	η	PROPN
ejpam-457	115	33	.	.	PROPN
ejpam-457	115	34	definition	definition	NOUN
ejpam-457	115	35	2	2	NUM
ejpam-457	115	36	(	(	PUNCT
ejpam-457	115	37	pseudoinvexity	pseudoinvexity	NOUN
ejpam-457	115	38	)	)	PUNCT
ejpam-457	115	39	.	.	PUNCT
ejpam-457	116	1	φ	φ	PROPN
ejpam-457	116	2	is	be	AUX
ejpam-457	116	3	said	say	VERB
ejpam-457	116	4	to	to	PART
ejpam-457	116	5	be	be	AUX
ejpam-457	116	6	pseudoinvex	pseudoinvex	NOUN
ejpam-457	116	7	in	in	ADP
ejpam-457	116	8	x	x	X
ejpam-457	116	9	,	,	PUNCT
ejpam-457	116	10	ẋ	ẋ	PROPN
ejpam-457	116	11	and	and	CCONJ
ejpam-457	116	12	ẍ	ẍ	X
ejpam-457	116	13	with	with	ADP
ejpam-457	116	14	respect	respect	NOUN
ejpam-457	116	15	to	to	ADP
ejpam-457	116	16	η	η	PROPN
ejpam-457	116	17	if	if	SCONJ
ejpam-457	116	18	∫	∫	PROPN
ejpam-457	116	19	i	i	PRON
ejpam-457	116	20	{	{	PUNCT
ejpam-457	116	21	ηtφx	ηtφx	PROPN
ejpam-457	116	22	(	(	PUNCT
ejpam-457	116	23	t	t	PROPN
ejpam-457	116	24	,	,	PUNCT
ejpam-457	116	25	x	x	X
ejpam-457	116	26	,	,	PUNCT
ejpam-457	116	27	ẋ	ẋ	PROPN
ejpam-457	116	28	,	,	PUNCT
ejpam-457	116	29	ẍ	ẍ	X
ejpam-457	116	30	)	)	PUNCT
ejpam-457	117	1	+	+	CCONJ
ejpam-457	117	2	(	(	PUNCT
ejpam-457	117	3	dη)tφ	dη)tφ	NOUN
ejpam-457	117	4	ẋ(t	ẋ(t	NOUN
ejpam-457	117	5	,	,	PUNCT
ejpam-457	117	6	x	x	X
ejpam-457	117	7	,	,	PUNCT
ejpam-457	117	8	ẋ	ẋ	PROPN
ejpam-457	117	9	,	,	PUNCT
ejpam-457	117	10	ẍ	ẍ	X
ejpam-457	117	11	)	)	PUNCT
ejpam-457	118	1	+	+	CCONJ
ejpam-457	118	2	(	(	PUNCT
ejpam-457	118	3	d2η)tφ	d2η)tφ	PROPN
ejpam-457	118	4	ẍ	ẍ	PROPN
ejpam-457	118	5	(	(	PUNCT
ejpam-457	118	6	t	t	PROPN
ejpam-457	118	7	,	,	PUNCT
ejpam-457	118	8	x	x	X
ejpam-457	118	9	,	,	PUNCT
ejpam-457	118	10	ẋ	ẋ	PROPN
ejpam-457	118	11	,	,	PUNCT
ejpam-457	118	12	ẍ)}d	ẍ)}d	PROPN
ejpam-457	118	13	t	t	PROPN
ejpam-457	118	14	≧	≧	NOUN
ejpam-457	118	15	0	0	NUM
ejpam-457	118	16	implies	imply	VERB
ejpam-457	118	17	φ(x	φ(x	PROPN
ejpam-457	118	18	,	,	PUNCT
ejpam-457	118	19	u̇	u̇	PROPN
ejpam-457	118	20	,	,	PUNCT
ejpam-457	118	21	ü)≧	ü)≧	PROPN
ejpam-457	118	22	φ(x	φ(x	PROPN
ejpam-457	118	23	,	,	PUNCT
ejpam-457	118	24	ẋ	ẋ	PROPN
ejpam-457	118	25	,	,	PUNCT
ejpam-457	118	26	ẍ	ẍ	PROPN
ejpam-457	118	27	)	)	PUNCT
ejpam-457	118	28	.	.	PUNCT
ejpam-457	119	1	definition	definition	NOUN
ejpam-457	119	2	3	3	NUM
ejpam-457	119	3	(	(	PUNCT
ejpam-457	119	4	quasi	quasi	NOUN
ejpam-457	119	5	-	-	NOUN
ejpam-457	119	6	invex	invex	ADJ
ejpam-457	119	7	)	)	PUNCT
ejpam-457	119	8	.	.	PUNCT
ejpam-457	120	1	the	the	DET
ejpam-457	120	2	functional	functional	ADJ
ejpam-457	120	3	φ	φ	PROPN
ejpam-457	120	4	is	be	AUX
ejpam-457	120	5	said	say	VERB
ejpam-457	120	6	to	to	ADP
ejpam-457	120	7	quasi	quasi	NOUN
ejpam-457	120	8	-	-	NOUN
ejpam-457	120	9	invex	invex	ADJ
ejpam-457	120	10	in	in	ADP
ejpam-457	120	11	x	x	SYM
ejpam-457	120	12	,	,	PUNCT
ejpam-457	120	13	ẋ	ẋ	PROPN
ejpam-457	120	14	and	and	CCONJ
ejpam-457	120	15	ẍ	ẍ	X
ejpam-457	120	16	with	with	ADP
ejpam-457	120	17	respect	respect	NOUN
ejpam-457	120	18	to	to	ADP
ejpam-457	120	19	η	η	PROPN
ejpam-457	120	20	if	if	SCONJ
ejpam-457	120	21	φ(x	φ(x	PROPN
ejpam-457	120	22	,	,	PUNCT
ejpam-457	120	23	u̇	u̇	PROPN
ejpam-457	120	24	,	,	PUNCT
ejpam-457	120	25	ü)≦	ü)≦	NOUN
ejpam-457	120	26	φ(x	φ(x	PROPN
ejpam-457	120	27	,	,	PUNCT
ejpam-457	120	28	ẋ	ẋ	PROPN
ejpam-457	120	29	,	,	PUNCT
ejpam-457	120	30	ẍ	ẍ	PROPN
ejpam-457	120	31	)	)	PUNCT
ejpam-457	120	32	implies	imply	VERB
ejpam-457	120	33	∫	∫	PROPN
ejpam-457	120	34	i	i	PRON
ejpam-457	120	35	{	{	PUNCT
ejpam-457	120	36	ηtφx	ηtφx	PROPN
ejpam-457	120	37	(	(	PUNCT
ejpam-457	120	38	t	t	PROPN
ejpam-457	120	39	,	,	PUNCT
ejpam-457	120	40	x	x	X
ejpam-457	120	41	,	,	PUNCT
ejpam-457	120	42	ẋ	ẋ	PROPN
ejpam-457	120	43	,	,	PUNCT
ejpam-457	120	44	ẍ	ẍ	X
ejpam-457	120	45	)	)	PUNCT
ejpam-457	121	1	+	+	CCONJ
ejpam-457	121	2	(	(	PUNCT
ejpam-457	121	3	dη)tφ	dη)tφ	NOUN
ejpam-457	121	4	ẋ(t	ẋ(t	NOUN
ejpam-457	121	5	,	,	PUNCT
ejpam-457	121	6	x	x	X
ejpam-457	121	7	,	,	PUNCT
ejpam-457	121	8	ẋ	ẋ	PROPN
ejpam-457	121	9	,	,	PUNCT
ejpam-457	121	10	ẍ	ẍ	X
ejpam-457	121	11	)	)	PUNCT
ejpam-457	122	1	+	+	CCONJ
ejpam-457	122	2	(	(	PUNCT
ejpam-457	122	3	d2η)tφ	d2η)tφ	PROPN
ejpam-457	122	4	ẍ(t	ẍ(t	PROPN
ejpam-457	122	5	,	,	PUNCT
ejpam-457	122	6	x	x	X
ejpam-457	122	7	,	,	PUNCT
ejpam-457	122	8	ẋ	ẋ	PROPN
ejpam-457	122	9	,	,	PUNCT
ejpam-457	122	10	ẍ)}d	ẍ)}d	PROPN
ejpam-457	122	11	t	t	PROPN
ejpam-457	122	12	≦	≦	PROPN
ejpam-457	122	13	0	0	PUNCT
ejpam-457	122	14	.	.	PUNCT
ejpam-457	123	1	we	we	PRON
ejpam-457	123	2	require	require	VERB
ejpam-457	123	3	the	the	DET
ejpam-457	123	4	following	follow	VERB
ejpam-457	123	5	definition	definition	NOUN
ejpam-457	123	6	of	of	ADP
ejpam-457	123	7	efficient	efficient	ADJ
ejpam-457	123	8	solution	solution	NOUN
ejpam-457	123	9	for	for	ADP
ejpam-457	123	10	our	our	PRON
ejpam-457	123	11	further	further	ADJ
ejpam-457	123	12	analysis	analysis	NOUN
ejpam-457	123	13	.	.	PUNCT
ejpam-457	124	1	the	the	DET
ejpam-457	124	2	set	set	NOUN
ejpam-457	124	3	of	of	ADP
ejpam-457	124	4	feasible	feasible	ADJ
ejpam-457	124	5	solutions	solution	NOUN
ejpam-457	124	6	for	for	ADP
ejpam-457	124	7	(	(	PUNCT
ejpam-457	124	8	vp	vp	NOUN
ejpam-457	124	9	)	)	PUNCT
ejpam-457	124	10	is	be	AUX
ejpam-457	124	11	designated	designate	VERB
ejpam-457	124	12	by	by	ADP
ejpam-457	124	13	x	x	X
ejpam-457	124	14	.	.	PUNCT
ejpam-457	124	15	i.	i.	PROPN
ejpam-457	124	16	husain	husain	PROPN
ejpam-457	124	17	,	,	PUNCT
ejpam-457	124	18	r.	r.	PROPN
ejpam-457	124	19	mattoo	mattoo	PROPN
ejpam-457	124	20	/	/	SYM
ejpam-457	124	21	eur	eur	PROPN
ejpam-457	124	22	.	.	PUNCT
ejpam-457	125	1	j.	j.	PROPN
ejpam-457	125	2	pure	pure	PROPN
ejpam-457	125	3	appl	appl	PROPN
ejpam-457	125	4	.	.	PROPN
ejpam-457	125	5	math	math	PROPN
ejpam-457	125	6	,	,	PUNCT
ejpam-457	125	7	3	3	NUM
ejpam-457	125	8	(	(	PUNCT
ejpam-457	125	9	2010	2010	NUM
ejpam-457	125	10	)	)	PUNCT
ejpam-457	125	11	,	,	PUNCT
ejpam-457	125	12	81	81	NUM
ejpam-457	125	13	-	-	SYM
ejpam-457	125	14	97	97	NUM
ejpam-457	125	15	85	85	NUM
ejpam-457	125	16	definition	definition	NOUN
ejpam-457	125	17	4	4	NUM
ejpam-457	125	18	(	(	PUNCT
ejpam-457	125	19	efficiency	efficiency	NOUN
ejpam-457	125	20	)	)	PUNCT
ejpam-457	125	21	.	.	PUNCT
ejpam-457	126	1	a	a	DET
ejpam-457	126	2	point	point	NOUN
ejpam-457	126	3	x̄	x̄	X
ejpam-457	126	4	∈	∈	PROPN
ejpam-457	126	5	x	x	PUNCT
ejpam-457	126	6	is	be	AUX
ejpam-457	126	7	said	say	VERB
ejpam-457	126	8	to	to	PART
ejpam-457	126	9	be	be	AUX
ejpam-457	126	10	efficient	efficient	ADJ
ejpam-457	126	11	solution	solution	NOUN
ejpam-457	126	12	of	of	ADP
ejpam-457	126	13	(	(	PUNCT
ejpam-457	126	14	vp	vp	PROPN
ejpam-457	126	15	)	)	PUNCT
ejpam-457	126	16	if	if	SCONJ
ejpam-457	126	17	for	for	ADP
ejpam-457	126	18	all	all	PRON
ejpam-457	126	19	feasible	feasible	ADJ
ejpam-457	126	20	x̄	x̄	PRON
ejpam-457	126	21	∈	∈	PROPN
ejpam-457	127	1	x	x	PUNCT
ejpam-457	127	2	∫	∫	PROPN
ejpam-457	128	1	i	i	PRON
ejpam-457	128	2	(	(	PUNCT
ejpam-457	128	3	f	f	PROPN
ejpam-457	128	4	i(t	i(t	PROPN
ejpam-457	128	5	,	,	PUNCT
ejpam-457	128	6	x(t	x(t	PROPN
ejpam-457	128	7	)	)	PUNCT
ejpam-457	128	8	,	,	PUNCT
ejpam-457	128	9	ẋ(t	ẋ(t	NOUN
ejpam-457	128	10	)	)	PUNCT
ejpam-457	128	11	,	,	PUNCT
ejpam-457	128	12	ẍ(t))d	ẍ(t))d	PROPN
ejpam-457	128	13	t	t	PROPN
ejpam-457	128	14	+	+	CCONJ
ejpam-457	128	15	(	(	PUNCT
ejpam-457	128	16	x(t)t	x(t)t	PROPN
ejpam-457	128	17	bi(t)x(t	bi(t)x(t	PROPN
ejpam-457	128	18	)	)	PUNCT
ejpam-457	128	19	)	)	PUNCT
ejpam-457	128	20	1	1	NUM
ejpam-457	128	21	2	2	NUM
ejpam-457	128	22	)	)	PUNCT
ejpam-457	128	23	d	d	NOUN
ejpam-457	128	24	t	t	PROPN
ejpam-457	128	25	�	�	PROPN
ejpam-457	128	26	∫	∫	PROPN
ejpam-457	129	1	i	i	PRON
ejpam-457	129	2	(	(	PUNCT
ejpam-457	129	3	f	f	PROPN
ejpam-457	129	4	i(t	i(t	PROPN
ejpam-457	129	5	,	,	PUNCT
ejpam-457	129	6	x̄(t	x̄(t	NUM
ejpam-457	129	7	)	)	PUNCT
ejpam-457	129	8	,	,	PUNCT
ejpam-457	129	9	˙̄x(t	˙̄x(t	NOUN
ejpam-457	129	10	)	)	PUNCT
ejpam-457	129	11	,	,	PUNCT
ejpam-457	129	12	¨̄x(t))d	¨̄x(t))d	NOUN
ejpam-457	129	13	t	t	NOUN
ejpam-457	129	14	+	+	CCONJ
ejpam-457	129	15	(	(	PUNCT
ejpam-457	129	16	x̄(t)t	x̄(t)t	NOUN
ejpam-457	129	17	bi(t	bi(t	NOUN
ejpam-457	129	18	)	)	PUNCT
ejpam-457	129	19	x̄(t	x̄(t	PROPN
ejpam-457	129	20	)	)	PUNCT
ejpam-457	129	21	)	)	PUNCT
ejpam-457	129	22	1	1	NUM
ejpam-457	129	23	2	2	NUM
ejpam-457	129	24	)	)	PUNCT
ejpam-457	129	25	d	d	NOUN
ejpam-457	129	26	t	t	PROPN
ejpam-457	129	27	for	for	ADP
ejpam-457	129	28	all	all	DET
ejpam-457	129	29	i	i	PRON
ejpam-457	129	30	∈	∈	PROPN
ejpam-457	130	1	p.	p.	NOUN
ejpam-457	131	1	in	in	ADP
ejpam-457	131	2	order	order	NOUN
ejpam-457	131	3	to	to	PART
ejpam-457	131	4	prove	prove	VERB
ejpam-457	131	5	the	the	DET
ejpam-457	131	6	strong	strong	ADJ
ejpam-457	131	7	duality	duality	NOUN
ejpam-457	131	8	theorem	theorem	VERB
ejpam-457	131	9	we	we	PRON
ejpam-457	131	10	will	will	AUX
ejpam-457	131	11	invoke	invoke	VERB
ejpam-457	131	12	the	the	DET
ejpam-457	131	13	following	follow	VERB
ejpam-457	131	14	lemma	lemma	PROPN
ejpam-457	131	15	due	due	ADP
ejpam-457	131	16	to	to	ADP
ejpam-457	131	17	changkong	changkong	NOUN
ejpam-457	131	18	and	and	CCONJ
ejpam-457	131	19	haimes	haime	NOUN
ejpam-457	131	20	[	[	X
ejpam-457	131	21	5	5	NUM
ejpam-457	131	22	]	]	PUNCT
ejpam-457	131	23	.	.	PUNCT
ejpam-457	132	1	lemma	lemma	PROPN
ejpam-457	132	2	1	1	NUM
ejpam-457	132	3	.	.	PUNCT
ejpam-457	133	1	a	a	DET
ejpam-457	133	2	point	point	NOUN
ejpam-457	133	3	x̄	x̄	X
ejpam-457	133	4	∈	∈	PROPN
ejpam-457	133	5	x	x	PUNCT
ejpam-457	133	6	be	be	AUX
ejpam-457	133	7	an	an	DET
ejpam-457	133	8	efficient	efficient	ADJ
ejpam-457	133	9	solution	solution	NOUN
ejpam-457	133	10	of	of	ADP
ejpam-457	133	11	(	(	PUNCT
ejpam-457	133	12	vp	vp	PROPN
ejpam-457	133	13	)	)	PUNCT
ejpam-457	133	14	if	if	SCONJ
ejpam-457	133	15	and	and	CCONJ
ejpam-457	133	16	only	only	ADV
ejpam-457	133	17	if	if	SCONJ
ejpam-457	133	18	x̄	x̄	PRON
ejpam-457	133	19	∈	∈	PROPN
ejpam-457	133	20	x	x	X
ejpam-457	133	21	is	be	AUX
ejpam-457	133	22	an	an	DET
ejpam-457	133	23	optimal	optimal	ADJ
ejpam-457	133	24	solution	solution	NOUN
ejpam-457	133	25	of	of	ADP
ejpam-457	133	26	the	the	DET
ejpam-457	133	27	following	following	ADJ
ejpam-457	133	28	problem	problem	NOUN
ejpam-457	133	29	(	(	PUNCT
ejpam-457	133	30	pk	pk	NOUN
ejpam-457	133	31	(	(	PUNCT
ejpam-457	133	32	x̄	x̄	PROPN
ejpam-457	133	33	)	)	PUNCT
ejpam-457	133	34	)	)	PUNCT
ejpam-457	133	35	for	for	ADP
ejpam-457	133	36	all	all	PRON
ejpam-457	133	37	k	k	X
ejpam-457	133	38	(	(	PUNCT
ejpam-457	133	39	pk	pk	PROPN
ejpam-457	133	40	(	(	PUNCT
ejpam-457	133	41	x̄	x̄	NOUN
ejpam-457	133	42	)	)	PUNCT
ejpam-457	133	43	)	)	PUNCT
ejpam-457	133	44	minimize	minimize	VERB
ejpam-457	133	45	�	�	PROPN
ejpam-457	133	46	∫	∫	PROPN
ejpam-457	134	1	i	i	PROPN
ejpam-457	134	2	(	(	PUNCT
ejpam-457	134	3	f	f	PROPN
ejpam-457	134	4	k(t	k(t	PROPN
ejpam-457	134	5	,	,	PUNCT
ejpam-457	134	6	x	x	X
ejpam-457	134	7	,	,	PUNCT
ejpam-457	134	8	ẋ	ẋ	PROPN
ejpam-457	134	9	,	,	PUNCT
ejpam-457	134	10	ẍ)d	ẍ)d	PROPN
ejpam-457	134	11	t	t	PROPN
ejpam-457	134	12	+	+	CCONJ
ejpam-457	134	13	(	(	PUNCT
ejpam-457	134	14	x(t)t	x(t)t	PROPN
ejpam-457	134	15	bk(t)x(t	bk(t)x(t	PROPN
ejpam-457	134	16	)	)	PUNCT
ejpam-457	134	17	)	)	PUNCT
ejpam-457	134	18	1	1	NUM
ejpam-457	134	19	2	2	NUM
ejpam-457	134	20	�	�	PROPN
ejpam-457	134	21	d	d	PROPN
ejpam-457	134	22	t	t	PROPN
ejpam-457	134	23	subject	subject	NOUN
ejpam-457	134	24	to	to	ADP
ejpam-457	134	25	x(a	x(a	NOUN
ejpam-457	134	26	)	)	PUNCT
ejpam-457	134	27	=	=	SYM
ejpam-457	134	28	0=	0=	NUM
ejpam-457	134	29	x(b	x(b	PROPN
ejpam-457	134	30	)	)	PUNCT
ejpam-457	134	31	,	,	PUNCT
ejpam-457	134	32	ẋ(a	ẋ(a	PROPN
ejpam-457	134	33	)	)	PUNCT
ejpam-457	134	34	=	=	PUNCT
ejpam-457	134	35	0=	0=	NUM
ejpam-457	134	36	ẋ(b	ẋ(b	PROPN
ejpam-457	134	37	)	)	PUNCT
ejpam-457	134	38	,	,	PUNCT
ejpam-457	134	39	g(t	g(t	PROPN
ejpam-457	134	40	,	,	PUNCT
ejpam-457	134	41	x	x	SYM
ejpam-457	134	42	,	,	PUNCT
ejpam-457	134	43	ẋ	ẋ	PROPN
ejpam-457	134	44	,	,	PUNCT
ejpam-457	134	45	ẋ)≦	ẋ)≦	PROPN
ejpam-457	134	46	0	0	PROPN
ejpam-457	134	47	,	,	PUNCT
ejpam-457	134	48	t	t	PROPN
ejpam-457	134	49	∈	∈	PROPN
ejpam-457	135	1	i	i	PRON
ejpam-457	135	2	,	,	PUNCT
ejpam-457	135	3	∫	∫	PROPN
ejpam-457	135	4	i	i	PRON
ejpam-457	135	5	(	(	PUNCT
ejpam-457	135	6	f	f	PROPN
ejpam-457	135	7	i(t	i(t	PROPN
ejpam-457	135	8	,	,	PUNCT
ejpam-457	135	9	x(t	x(t	PROPN
ejpam-457	135	10	)	)	PUNCT
ejpam-457	135	11	,	,	PUNCT
ejpam-457	135	12	ẋ(t	ẋ(t	NOUN
ejpam-457	135	13	)	)	PUNCT
ejpam-457	135	14	,	,	PUNCT
ejpam-457	135	15	ẍ(t))d	ẍ(t))d	PROPN
ejpam-457	135	16	t	t	PROPN
ejpam-457	135	17	+	+	CCONJ
ejpam-457	135	18	(	(	PUNCT
ejpam-457	135	19	x(t)t	x(t)t	PROPN
ejpam-457	135	20	bi(t)x(t	bi(t)x(t	PROPN
ejpam-457	135	21	)	)	PUNCT
ejpam-457	135	22	)	)	PUNCT
ejpam-457	135	23	1	1	NUM
ejpam-457	135	24	2	2	NUM
ejpam-457	135	25	)	)	PUNCT
ejpam-457	135	26	d	d	SYM
ejpam-457	135	27	t	t	PROPN
ejpam-457	135	28	≤	≤	NUM
ejpam-457	135	29	∫	∫	PROPN
ejpam-457	136	1	i	i	PRON
ejpam-457	136	2	(	(	PUNCT
ejpam-457	136	3	f	f	PROPN
ejpam-457	136	4	i(t	i(t	PROPN
ejpam-457	136	5	,	,	PUNCT
ejpam-457	136	6	x̄(t	x̄(t	NUM
ejpam-457	136	7	)	)	PUNCT
ejpam-457	136	8	,	,	PUNCT
ejpam-457	136	9	˙̄x(t	˙̄x(t	NOUN
ejpam-457	136	10	)	)	PUNCT
ejpam-457	136	11	,	,	PUNCT
ejpam-457	136	12	¨̄x(t))d	¨̄x(t))d	NOUN
ejpam-457	136	13	t	t	NOUN
ejpam-457	136	14	+	+	CCONJ
ejpam-457	136	15	(	(	PUNCT
ejpam-457	136	16	x̄(t)t	x̄(t)t	NOUN
ejpam-457	136	17	bi(t	bi(t	NOUN
ejpam-457	136	18	)	)	PUNCT
ejpam-457	136	19	x̄(t	x̄(t	PROPN
ejpam-457	136	20	)	)	PUNCT
ejpam-457	136	21	)	)	PUNCT
ejpam-457	136	22	1	1	NUM
ejpam-457	136	23	2	2	NUM
ejpam-457	136	24	)	)	PUNCT
ejpam-457	136	25	d	d	SYM
ejpam-457	136	26	t	t	PROPN
ejpam-457	136	27	,	,	PUNCT
ejpam-457	136	28	i	i	PROPN
ejpam-457	136	29	6=	6=	PROPN
ejpam-457	136	30	k	k	PROPN
ejpam-457	136	31	3	3	X
ejpam-457	136	32	.	.	PUNCT
ejpam-457	136	33	mixed	mixed	ADJ
ejpam-457	136	34	type	type	NOUN
ejpam-457	136	35	duality	duality	NOUN
ejpam-457	136	36	we	we	PRON
ejpam-457	136	37	formulate	formulate	VERB
ejpam-457	136	38	the	the	DET
ejpam-457	136	39	following	follow	VERB
ejpam-457	136	40	type	type	NOUN
ejpam-457	136	41	dual	dual	ADJ
ejpam-457	136	42	(	(	PUNCT
ejpam-457	136	43	mix	mix	VERB
ejpam-457	136	44	d	d	NOUN
ejpam-457	136	45	)	)	PUNCT
ejpam-457	136	46	to	to	ADP
ejpam-457	136	47	(	(	PUNCT
ejpam-457	136	48	vp	vp	PROPN
ejpam-457	136	49	):	):	PUNCT
ejpam-457	136	50	(	(	PUNCT
ejpam-457	136	51	mix	mix	VERB
ejpam-457	136	52	d	d	NOUN
ejpam-457	136	53	)	)	PUNCT
ejpam-457	136	54	maximize	maximize	VERB
ejpam-457	136	55	�	�	PROPN
ejpam-457	136	56	∫	∫	PROPN
ejpam-457	137	1	i	i	PROPN
ejpam-457	137	2	�	�	PROPN
ejpam-457	137	3	f	f	PROPN
ejpam-457	137	4	1(t	1(t	NUM
ejpam-457	137	5	,	,	PUNCT
ejpam-457	137	6	u	u	NOUN
ejpam-457	137	7	,	,	PUNCT
ejpam-457	137	8	u̇	u̇	PROPN
ejpam-457	137	9	,	,	PUNCT
ejpam-457	137	10	ü	ü	PRON
ejpam-457	137	11	)	)	PUNCT
ejpam-457	138	1	+	+	CCONJ
ejpam-457	138	2	u(t)t	u(t)t	X
ejpam-457	138	3	b1(t)z1(t	b1(t)z1(t	X
ejpam-457	138	4	)	)	PUNCT
ejpam-457	139	1	+	+	CCONJ
ejpam-457	139	2	∑	∑	PUNCT
ejpam-457	139	3	j∈j	j∈j	NOUN
ejpam-457	139	4	◦	◦	NOUN
ejpam-457	139	5	y	y	PROPN
ejpam-457	139	6	j(t)g	j(t)g	PROPN
ejpam-457	139	7	j(t	j(t	PROPN
ejpam-457	139	8	,	,	PUNCT
ejpam-457	139	9	u	u	NOUN
ejpam-457	139	10	,	,	PUNCT
ejpam-457	139	11	u̇	u̇	PROPN
ejpam-457	139	12	,	,	PUNCT
ejpam-457	139	13	ü	ü	NOUN
ejpam-457	139	14	)	)	PUNCT
ejpam-457	139	15	�	�	PROPN
ejpam-457	139	16	d	d	PROPN
ejpam-457	139	17	t	t	PROPN
ejpam-457	139	18	,	,	PUNCT
ejpam-457	139	19	.	.	PUNCT
ejpam-457	139	20	.	.	PUNCT
ejpam-457	139	21	.	.	PUNCT
ejpam-457	140	1	,	,	PUNCT
ejpam-457	140	2	∫	∫	PROPN
ejpam-457	141	1	i	i	PRON
ejpam-457	141	2	�	�	PROPN
ejpam-457	142	1	f	f	PROPN
ejpam-457	142	2	p(t	p(t	PROPN
ejpam-457	142	3	,	,	PUNCT
ejpam-457	142	4	u	u	NOUN
ejpam-457	142	5	,	,	PUNCT
ejpam-457	142	6	u̇	u̇	PROPN
ejpam-457	142	7	,	,	PUNCT
ejpam-457	142	8	ü	ü	PRON
ejpam-457	142	9	)	)	PUNCT
ejpam-457	143	1	+	+	CCONJ
ejpam-457	143	2	(	(	PUNCT
ejpam-457	143	3	u(t)t	u(t)t	NOUN
ejpam-457	143	4	bp(t)zp(t	bp(t)zp(t	NOUN
ejpam-457	143	5	)	)	PUNCT
ejpam-457	143	6	)	)	PUNCT
ejpam-457	144	1	+	+	CCONJ
ejpam-457	144	2	∑	∑	PUNCT
ejpam-457	144	3	j∈j	j∈j	NOUN
ejpam-457	144	4	◦	◦	NOUN
ejpam-457	144	5	y	y	PROPN
ejpam-457	144	6	j(t)g	j(t)g	PROPN
ejpam-457	144	7	j(t	j(t	PROPN
ejpam-457	144	8	,	,	PUNCT
ejpam-457	144	9	u	u	NOUN
ejpam-457	144	10	,	,	PUNCT
ejpam-457	144	11	u̇	u̇	PROPN
ejpam-457	144	12	,	,	PUNCT
ejpam-457	144	13	ü	ü	NOUN
ejpam-457	144	14	)	)	PUNCT
ejpam-457	144	15	�	�	PROPN
ejpam-457	144	16	d	d	PROPN
ejpam-457	144	17	t	t	PROPN
ejpam-457	144	18	�	�	PROPN
ejpam-457	144	19	subject	subject	ADJ
ejpam-457	144	20	to	to	ADP
ejpam-457	144	21	u(a	u(a	NOUN
ejpam-457	144	22	)	)	PUNCT
ejpam-457	144	23	=	=	SYM
ejpam-457	144	24	0=	0=	PUNCT
ejpam-457	145	1	u(b	u(b	NOUN
ejpam-457	145	2	)	)	PUNCT
ejpam-457	145	3	,	,	PUNCT
ejpam-457	145	4	(	(	PUNCT
ejpam-457	145	5	1	1	X
ejpam-457	145	6	)	)	PUNCT
ejpam-457	145	7	u̇(a	u̇(a	NOUN
ejpam-457	145	8	)	)	PUNCT
ejpam-457	145	9	=	=	SYM
ejpam-457	146	1	0=	0=	NOUN
ejpam-457	146	2	u̇(b	u̇(b	NOUN
ejpam-457	146	3	)	)	PUNCT
ejpam-457	146	4	,	,	PUNCT
ejpam-457	146	5	(	(	PUNCT
ejpam-457	146	6	2	2	X
ejpam-457	146	7	)	)	PUNCT
ejpam-457	146	8	p	p	NOUN
ejpam-457	146	9	∑	∑	PUNCT
ejpam-457	146	10	i=1	i=1	PROPN
ejpam-457	146	11	λi	λi	PROPN
ejpam-457	146	12	(	(	PUNCT
ejpam-457	146	13	f	f	NOUN
ejpam-457	146	14	i	i	PRON
ejpam-457	146	15	u	u	PROPN
ejpam-457	146	16	(	(	PUNCT
ejpam-457	146	17	t	t	PROPN
ejpam-457	146	18	,	,	PUNCT
ejpam-457	146	19	u	u	NOUN
ejpam-457	146	20	,	,	PUNCT
ejpam-457	146	21	u̇	u̇	PROPN
ejpam-457	146	22	,	,	PUNCT
ejpam-457	146	23	ü)d	ü)d	PROPN
ejpam-457	146	24	t	t	NOUN
ejpam-457	146	25	+	+	CCONJ
ejpam-457	146	26	bi(t)z	bi(t)z	PROPN
ejpam-457	146	27	i(t	i(t	NOUN
ejpam-457	146	28	)	)	PUNCT
ejpam-457	146	29	+	+	NUM
ejpam-457	146	30	y(t)t	y(t)t	NOUN
ejpam-457	146	31	gu(t	gu(t	PUNCT
ejpam-457	146	32	,	,	PUNCT
ejpam-457	146	33	u	u	NOUN
ejpam-457	146	34	,	,	PUNCT
ejpam-457	146	35	u̇	u̇	PROPN
ejpam-457	146	36	,	,	PUNCT
ejpam-457	146	37	ü	ü	NUM
ejpam-457	146	38	)	)	PUNCT
ejpam-457	146	39	)	)	PUNCT
ejpam-457	146	40	i.	i.	PROPN
ejpam-457	146	41	husain	husain	PROPN
ejpam-457	146	42	,	,	PUNCT
ejpam-457	146	43	r.	r.	PROPN
ejpam-457	146	44	mattoo	mattoo	PROPN
ejpam-457	146	45	/	/	SYM
ejpam-457	146	46	eur	eur	PROPN
ejpam-457	146	47	.	.	PUNCT
ejpam-457	147	1	j.	j.	PROPN
ejpam-457	147	2	pure	pure	PROPN
ejpam-457	147	3	appl	appl	PROPN
ejpam-457	147	4	.	.	PROPN
ejpam-457	147	5	math	math	PROPN
ejpam-457	147	6	,	,	PUNCT
ejpam-457	147	7	3	3	NUM
ejpam-457	147	8	(	(	PUNCT
ejpam-457	147	9	2010	2010	NUM
ejpam-457	147	10	)	)	PUNCT
ejpam-457	147	11	,	,	PUNCT
ejpam-457	147	12	81	81	NUM
ejpam-457	147	13	-	-	SYM
ejpam-457	147	14	97	97	NUM
ejpam-457	147	15	86	86	NUM
ejpam-457	147	16	−d(λt	−d(λt	NOUN
ejpam-457	148	1	fu̇	fu̇	PROPN
ejpam-457	148	2	+	+	NUM
ejpam-457	148	3	y(t)t	y(t)t	PROPN
ejpam-457	148	4	gu̇	gu̇	NOUN
ejpam-457	148	5	)	)	PUNCT
ejpam-457	149	1	+	+	CCONJ
ejpam-457	149	2	d2(λt	d2(λt	PROPN
ejpam-457	149	3	fü	fü	PUNCT
ejpam-457	149	4	+	+	NUM
ejpam-457	149	5	y(t)t	y(t)t	NOUN
ejpam-457	149	6	gü	gü	X
ejpam-457	149	7	)	)	PUNCT
ejpam-457	149	8	=	=	PUNCT
ejpam-457	149	9	0	0	NUM
ejpam-457	149	10	,	,	PUNCT
ejpam-457	149	11	t	t	PROPN
ejpam-457	149	12	∈	∈	PROPN
ejpam-457	150	1	i	i	PRON
ejpam-457	150	2	(	(	PUNCT
ejpam-457	150	3	3	3	X
ejpam-457	150	4	)	)	PUNCT
ejpam-457	150	5	∑	∑	PUNCT
ejpam-457	150	6	j∈jα	j∈jα	PROPN
ejpam-457	150	7	∫	∫	PROPN
ejpam-457	151	1	i	i	PRON
ejpam-457	151	2	y	y	PROPN
ejpam-457	151	3	j(t)g	j(t)g	PROPN
ejpam-457	151	4	j(t	j(t	PROPN
ejpam-457	151	5	,	,	PUNCT
ejpam-457	151	6	u	u	NOUN
ejpam-457	151	7	,	,	PUNCT
ejpam-457	151	8	u̇	u̇	PROPN
ejpam-457	151	9	,	,	PUNCT
ejpam-457	151	10	ü)d	ü)d	PROPN
ejpam-457	151	11	t	t	PROPN
ejpam-457	151	12	≧	≧	NUM
ejpam-457	151	13	0	0	NUM
ejpam-457	151	14	,	,	PUNCT
ejpam-457	151	15	α	α	NOUN
ejpam-457	151	16	=	=	SYM
ejpam-457	151	17	1,2	1,2	NUM
ejpam-457	151	18	,	,	PUNCT
ejpam-457	151	19	.	.	PUNCT
ejpam-457	151	20	.	.	PUNCT
ejpam-457	152	1	.	.	PUNCT
ejpam-457	153	1	,	,	PUNCT
ejpam-457	153	2	r	r	NOUN
ejpam-457	153	3	(	(	PUNCT
ejpam-457	153	4	4	4	NUM
ejpam-457	153	5	)	)	PUNCT
ejpam-457	153	6	z̄	z̄	PROPN
ejpam-457	153	7	i(t)t	i(t)t	PROPN
ejpam-457	153	8	bi(t)z̄	bi(t)z̄	PROPN
ejpam-457	153	9	i(t	i(t	PROPN
ejpam-457	153	10	)	)	PUNCT
ejpam-457	153	11	≦	≦	NUM
ejpam-457	153	12	1	1	NUM
ejpam-457	153	13	,	,	PUNCT
ejpam-457	153	14	t	t	PROPN
ejpam-457	153	15	∈	∈	PROPN
ejpam-457	154	1	i	i	PRON
ejpam-457	154	2	,	,	PUNCT
ejpam-457	154	3	i	i	PROPN
ejpam-457	154	4	∈	∈	VERB
ejpam-457	154	5	p	p	X
ejpam-457	154	6	(	(	PUNCT
ejpam-457	154	7	5	5	NUM
ejpam-457	154	8	)	)	PUNCT
ejpam-457	154	9	y(t	y(t	NUM
ejpam-457	154	10	)	)	PUNCT
ejpam-457	154	11	≧	≧	X
ejpam-457	154	12	0	0	NUM
ejpam-457	154	13	,	,	PUNCT
ejpam-457	154	14	t	t	PROPN
ejpam-457	154	15	∈	∈	PROPN
ejpam-457	155	1	i	i	PRON
ejpam-457	155	2	,	,	PUNCT
ejpam-457	155	3	(	(	PUNCT
ejpam-457	155	4	6	6	X
ejpam-457	155	5	)	)	PUNCT
ejpam-457	155	6	λ	λ	PROPN
ejpam-457	155	7	∈	∈	PROPN
ejpam-457	155	8	λ+	λ+	PUNCT
ejpam-457	155	9	(	(	PUNCT
ejpam-457	155	10	7	7	NUM
ejpam-457	155	11	)	)	PUNCT
ejpam-457	155	12	where	where	SCONJ
ejpam-457	155	13	(	(	PUNCT
ejpam-457	155	14	i	i	NOUN
ejpam-457	155	15	)	)	PUNCT
ejpam-457	155	16	λ+	λ+	PUNCT
ejpam-457	155	17	=	=	PUNCT
ejpam-457	155	18	{	{	PUNCT
ejpam-457	155	19	λ	λ	X
ejpam-457	155	20	∈	∈	NOUN
ejpam-457	155	21	rp|λ	rp|λ	X
ejpam-457	155	22	>	>	X
ejpam-457	155	23	0,λt	0,λt	NUM
ejpam-457	155	24	e	e	X
ejpam-457	155	25	=	=	SYM
ejpam-457	155	26	1	1	NUM
ejpam-457	155	27	,	,	PUNCT
ejpam-457	155	28	e	e	X
ejpam-457	155	29	=	=	PUNCT
ejpam-457	155	30	(	(	PUNCT
ejpam-457	155	31	1,1	1,1	NUM
ejpam-457	155	32	,	,	PUNCT
ejpam-457	155	33	.	.	PUNCT
ejpam-457	155	34	.	.	PUNCT
ejpam-457	155	35	.	.	PUNCT
ejpam-457	156	1	,	,	PUNCT
ejpam-457	156	2	1)t	1)t	PROPN
ejpam-457	156	3	∈	∈	PROPN
ejpam-457	156	4	rp	rp	NOUN
ejpam-457	156	5	}	}	PUNCT
ejpam-457	156	6	(	(	PUNCT
ejpam-457	156	7	ii	ii	NOUN
ejpam-457	156	8	)	)	PUNCT
ejpam-457	156	9	jα	jα	NOUN
ejpam-457	156	10	⊆	⊆	NUM
ejpam-457	156	11	m	m	NOUN
ejpam-457	156	12	=	=	SYM
ejpam-457	156	13	{	{	PUNCT
ejpam-457	156	14	1,2	1,2	NUM
ejpam-457	156	15	,	,	PUNCT
ejpam-457	156	16	.	.	PUNCT
ejpam-457	156	17	.	.	PUNCT
ejpam-457	156	18	.	.	PUNCT
ejpam-457	157	1	,	,	PUNCT
ejpam-457	157	2	m	m	VERB
ejpam-457	157	3	}	}	PUNCT
ejpam-457	157	4	,	,	PUNCT
ejpam-457	157	5	α=	α=	NOUN
ejpam-457	157	6	0,1,2	0,1,2	NOUN
ejpam-457	157	7	,	,	PUNCT
ejpam-457	157	8	.	.	PUNCT
ejpam-457	157	9	.	.	PUNCT
ejpam-457	158	1	.	.	PUNCT
ejpam-457	159	1	,	,	PUNCT
ejpam-457	159	2	r	r	NOUN
ejpam-457	159	3	with	with	ADP
ejpam-457	159	4	r	r	NOUN
ejpam-457	159	5	⋃	⋃	PUNCT
ejpam-457	160	1	α=0	α=0	ADJ
ejpam-457	160	2	jα	jα	NOUN
ejpam-457	160	3	=	=	PUNCT
ejpam-457	160	4	m	m	PROPN
ejpam-457	160	5	and	and	CCONJ
ejpam-457	160	6	jα	jα	PROPN
ejpam-457	160	7	⋂	⋂	PROPN
ejpam-457	160	8	jβ	jβ	PROPN
ejpam-457	160	9	=	=	SYM
ejpam-457	160	10	φ	φ	PROPN
ejpam-457	160	11	,	,	PUNCT
ejpam-457	160	12	if	if	SCONJ
ejpam-457	160	13	α	α	PROPN
ejpam-457	160	14	6=	6=	ADP
ejpam-457	160	15	β	β	NOUN
ejpam-457	160	16	.	.	PUNCT
ejpam-457	161	1	if	if	SCONJ
ejpam-457	161	2	j	j	PROPN
ejpam-457	161	3	◦	◦	NOUN
ejpam-457	161	4	=	=	SYM
ejpam-457	161	5	m	m	PROPN
ejpam-457	161	6	,	,	PUNCT
ejpam-457	161	7	then	then	ADV
ejpam-457	161	8	(	(	PUNCT
ejpam-457	161	9	mix	mix	VERB
ejpam-457	161	10	d	d	NOUN
ejpam-457	161	11	)	)	PUNCT
ejpam-457	161	12	becomes	become	VERB
ejpam-457	161	13	wolfe	wolfe	PROPN
ejpam-457	161	14	type	type	NOUN
ejpam-457	161	15	dual	dual	ADV
ejpam-457	161	16	considered	consider	VERB
ejpam-457	161	17	in	in	ADP
ejpam-457	161	18	[	[	X
ejpam-457	161	19	9	9	NUM
ejpam-457	161	20	]	]	PUNCT
ejpam-457	161	21	,	,	PUNCT
ejpam-457	161	22	if	if	SCONJ
ejpam-457	161	23	j	j	PROPN
ejpam-457	161	24	◦	◦	NOUN
ejpam-457	161	25	=	=	SYM
ejpam-457	161	26	φ	φ	PROPN
ejpam-457	161	27	and	and	CCONJ
ejpam-457	161	28	jα	jα	NOUN
ejpam-457	161	29	=	=	PUNCT
ejpam-457	161	30	m	m	VERB
ejpam-457	161	31	for	for	ADP
ejpam-457	161	32	some	some	DET
ejpam-457	161	33	α	α	NOUN
ejpam-457	161	34	∈	∈	PROPN
ejpam-457	161	35	{	{	PUNCT
ejpam-457	161	36	1,2	1,2	NUM
ejpam-457	161	37	,	,	PUNCT
ejpam-457	161	38	.	.	PUNCT
ejpam-457	161	39	.	.	PUNCT
ejpam-457	162	1	.	.	PUNCT
ejpam-457	163	1	,	,	PUNCT
ejpam-457	163	2	r	r	X
ejpam-457	163	3	}	}	PUNCT
ejpam-457	163	4	,	,	PUNCT
ejpam-457	163	5	then	then	ADV
ejpam-457	163	6	(	(	PUNCT
ejpam-457	163	7	mix	mix	VERB
ejpam-457	163	8	d	d	NOUN
ejpam-457	163	9	)	)	PUNCT
ejpam-457	163	10	becomes	become	VERB
ejpam-457	163	11	mond	mond	PROPN
ejpam-457	163	12	-	-	PUNCT
ejpam-457	163	13	weir	weir	PROPN
ejpam-457	163	14	type	type	NOUN
ejpam-457	163	15	dual	dual	ADV
ejpam-457	163	16	considered	consider	VERB
ejpam-457	163	17	in	in	ADP
ejpam-457	163	18	[	[	X
ejpam-457	163	19	9	9	NUM
ejpam-457	163	20	]	]	PUNCT
ejpam-457	163	21	.	.	PUNCT
ejpam-457	164	1	theorem	theorem	ADJ
ejpam-457	164	2	1	1	NUM
ejpam-457	164	3	(	(	PUNCT
ejpam-457	164	4	weak	weak	ADJ
ejpam-457	164	5	duality	duality	NOUN
ejpam-457	164	6	)	)	PUNCT
ejpam-457	164	7	.	.	PUNCT
ejpam-457	165	1	let	let	VERB
ejpam-457	165	2	x̄	x̄	PRON
ejpam-457	165	3	be	be	AUX
ejpam-457	165	4	feasible	feasible	ADJ
ejpam-457	165	5	for	for	ADP
ejpam-457	165	6	(	(	PUNCT
ejpam-457	165	7	vp	vp	NOUN
ejpam-457	165	8	)	)	PUNCT
ejpam-457	165	9	and	and	CCONJ
ejpam-457	165	10	(	(	PUNCT
ejpam-457	165	11	u	u	NOUN
ejpam-457	165	12	,	,	PUNCT
ejpam-457	165	13	y	y	PROPN
ejpam-457	165	14	,	,	PUNCT
ejpam-457	165	15	z1	z1	PROPN
ejpam-457	165	16	,	,	PUNCT
ejpam-457	165	17	.	.	PUNCT
ejpam-457	165	18	.	.	PUNCT
ejpam-457	166	1	.	.	PUNCT
ejpam-457	167	1	,	,	PUNCT
ejpam-457	167	2	zp	zp	PROPN
ejpam-457	167	3	,	,	PUNCT
ejpam-457	167	4	λ	λ	PROPN
ejpam-457	167	5	)	)	PUNCT
ejpam-457	167	6	be	be	AUX
ejpam-457	167	7	feasible	feasible	ADJ
ejpam-457	167	8	for	for	ADP
ejpam-457	167	9	(	(	PUNCT
ejpam-457	167	10	mix	mix	VERB
ejpam-457	167	11	d	d	NOUN
ejpam-457	167	12	)	)	PUNCT
ejpam-457	167	13	.	.	PUNCT
ejpam-457	168	1	if	if	SCONJ
ejpam-457	168	2	for	for	ADP
ejpam-457	168	3	feasible	feasible	ADJ
ejpam-457	168	4	(	(	PUNCT
ejpam-457	168	5	x	x	INTJ
ejpam-457	168	6	,	,	PUNCT
ejpam-457	168	7	u	u	NOUN
ejpam-457	168	8	,	,	PUNCT
ejpam-457	168	9	z1	z1	NOUN
ejpam-457	168	10	,	,	PUNCT
ejpam-457	168	11	.	.	PUNCT
ejpam-457	168	12	.	.	PUNCT
ejpam-457	169	1	.	.	PUNCT
ejpam-457	170	1	,	,	PUNCT
ejpam-457	170	2	zp	zp	PROPN
ejpam-457	170	3	,	,	PUNCT
ejpam-457	170	4	λ	λ	PROPN
ejpam-457	170	5	)	)	PUNCT
ejpam-457	170	6	,	,	PUNCT
ejpam-457	170	7	p	p	X
ejpam-457	170	8	∑	∑	PUNCT
ejpam-457	170	9	i=1	i=1	PROPN
ejpam-457	171	1	λi	λi	X
ejpam-457	171	2	∫	∫	PROPN
ejpam-457	172	1	i	i	PROPN
ejpam-457	172	2	�	�	PROPN
ejpam-457	172	3	f	f	PROPN
ejpam-457	172	4	i(t	i(t	PROPN
ejpam-457	172	5	,	,	PUNCT
ejpam-457	172	6	.	.	PUNCT
ejpam-457	172	7	,	,	PUNCT
ejpam-457	172	8	.	.	PUNCT
ejpam-457	172	9	,	,	PUNCT
ejpam-457	172	10	.	.	PUNCT
ejpam-457	172	11	)	)	PUNCT
ejpam-457	173	1	+	+	CCONJ
ejpam-457	173	2	∑	∑	PUNCT
ejpam-457	173	3	j∈j	j∈j	NOUN
ejpam-457	173	4	◦	◦	NOUN
ejpam-457	173	5	y	y	PROPN
ejpam-457	173	6	j(t)g	j(t)g	PROPN
ejpam-457	173	7	j(t	j(t	PROPN
ejpam-457	173	8	,	,	PUNCT
ejpam-457	173	9	.	.	PUNCT
ejpam-457	173	10	,	,	PUNCT
ejpam-457	173	11	.	.	PUNCT
ejpam-457	173	12	,	,	PUNCT
ejpam-457	173	13	.	.	PUNCT
ejpam-457	173	14	)	)	PUNCT
ejpam-457	174	1	+	+	CCONJ
ejpam-457	174	2	(	(	PUNCT
ejpam-457	174	3	·	·	PUNCT
ejpam-457	174	4	)	)	PUNCT
ejpam-457	174	5	t	t	PROPN
ejpam-457	174	6	bi(t)z	bi(t)z	PROPN
ejpam-457	174	7	i(t	i(t	PROPN
ejpam-457	174	8	)	)	PUNCT
ejpam-457	174	9	�	�	PROPN
ejpam-457	175	1	d	d	PROPN
ejpam-457	175	2	t	t	PROPN
ejpam-457	175	3	is	be	AUX
ejpam-457	175	4	pseudoinvex	pseudoinvex	NOUN
ejpam-457	175	5	and	and	CCONJ
ejpam-457	175	6	∑	∑	ADV
ejpam-457	175	7	j∈jα	j∈jα	PROPN
ejpam-457	175	8	∫	∫	PROPN
ejpam-457	176	1	i	i	PRON
ejpam-457	176	2	y	y	PROPN
ejpam-457	176	3	j(t)g	j(t)g	PROPN
ejpam-457	176	4	j(t	j(t	PROPN
ejpam-457	176	5	,	,	PUNCT
ejpam-457	176	6	.	.	PUNCT
ejpam-457	176	7	,	,	PUNCT
ejpam-457	176	8	.	.	PUNCT
ejpam-457	176	9	,	,	PUNCT
ejpam-457	176	10	.)d	.)d	PROPN
ejpam-457	176	11	t	t	PROPN
ejpam-457	176	12	,	,	PUNCT
ejpam-457	176	13	α	α	NOUN
ejpam-457	176	14	=	=	SYM
ejpam-457	176	15	1,2	1,2	NUM
ejpam-457	176	16	,	,	PUNCT
ejpam-457	176	17	.	.	PUNCT
ejpam-457	176	18	.	.	PUNCT
ejpam-457	177	1	.	.	PUNCT
ejpam-457	178	1	,	,	PUNCT
ejpam-457	178	2	r	r	NOUN
ejpam-457	178	3	is	be	AUX
ejpam-457	178	4	quasi	quasi	ADJ
ejpam-457	178	5	-	-	NOUN
ejpam-457	178	6	invex	invex	ADJ
ejpam-457	178	7	with	with	ADP
ejpam-457	178	8	respect	respect	NOUN
ejpam-457	178	9	to	to	ADP
ejpam-457	178	10	same	same	ADJ
ejpam-457	178	11	η	η	PROPN
ejpam-457	178	12	,	,	PUNCT
ejpam-457	178	13	then	then	ADV
ejpam-457	178	14	the	the	DET
ejpam-457	178	15	following	following	NOUN
ejpam-457	178	16	can	can	AUX
ejpam-457	178	17	not	not	PART
ejpam-457	178	18	hold	hold	VERB
ejpam-457	178	19	:	:	PUNCT
ejpam-457	178	20	∫	∫	PROPN
ejpam-457	179	1	i	i	PRON
ejpam-457	179	2	(	(	PUNCT
ejpam-457	179	3	f	f	PROPN
ejpam-457	179	4	i(t	i(t	PROPN
ejpam-457	179	5	,	,	PUNCT
ejpam-457	179	6	x	x	X
ejpam-457	179	7	,	,	PUNCT
ejpam-457	179	8	ẋ	ẋ	PROPN
ejpam-457	179	9	,	,	PUNCT
ejpam-457	179	10	ẍ)d	ẍ)d	PROPN
ejpam-457	179	11	t	t	PROPN
ejpam-457	179	12	+	+	CCONJ
ejpam-457	179	13	(	(	PUNCT
ejpam-457	179	14	x(t)t	x(t)t	PROPN
ejpam-457	179	15	bi(t)x(t	bi(t)x(t	PROPN
ejpam-457	179	16	)	)	PUNCT
ejpam-457	179	17	)	)	PUNCT
ejpam-457	179	18	1	1	NUM
ejpam-457	179	19	2	2	NUM
ejpam-457	179	20	)	)	PUNCT
ejpam-457	179	21	d	d	NOUN
ejpam-457	179	22	t	t	PROPN
ejpam-457	179	23	≦	≦	VERB
ejpam-457	179	24	∫	∫	INTJ
ejpam-457	180	1	i	i	NOUN
ejpam-457	180	2	�	�	PROPN
ejpam-457	180	3	f	f	PROPN
ejpam-457	180	4	i(t	i(t	PROPN
ejpam-457	180	5	,	,	PUNCT
ejpam-457	180	6	u	u	NOUN
ejpam-457	180	7	,	,	PUNCT
ejpam-457	180	8	u̇	u̇	PROPN
ejpam-457	180	9	,	,	PUNCT
ejpam-457	180	10	ü)d	ü)d	PROPN
ejpam-457	180	11	t	t	NOUN
ejpam-457	180	12	+	+	CCONJ
ejpam-457	180	13	(	(	PUNCT
ejpam-457	180	14	u(t)t	u(t)t	PROPN
ejpam-457	180	15	bi(t)z	bi(t)z	PROPN
ejpam-457	180	16	i(t	i(t	NOUN
ejpam-457	180	17	)	)	PUNCT
ejpam-457	180	18	)	)	PUNCT
ejpam-457	181	1	+	+	CCONJ
ejpam-457	181	2	∑	∑	PUNCT
ejpam-457	181	3	j∈j	j∈j	NOUN
ejpam-457	181	4	◦	◦	NOUN
ejpam-457	181	5	y	y	PROPN
ejpam-457	181	6	j(t)g	j(t)g	PROPN
ejpam-457	181	7	j(t	j(t	PROPN
ejpam-457	181	8	,	,	PUNCT
ejpam-457	181	9	u	u	NOUN
ejpam-457	181	10	,	,	PUNCT
ejpam-457	181	11	u̇	u̇	PROPN
ejpam-457	181	12	,	,	PUNCT
ejpam-457	181	13	ü	ü	NOUN
ejpam-457	181	14	)	)	PUNCT
ejpam-457	181	15	�	�	PROPN
ejpam-457	181	16	d	d	PROPN
ejpam-457	181	17	t	t	PROPN
ejpam-457	181	18	(	(	PUNCT
ejpam-457	181	19	8)	8)	NUM
ejpam-457	181	20	for	for	ADP
ejpam-457	181	21	all	all	PRON
ejpam-457	181	22	i	i	PRON
ejpam-457	181	23	∈	∈	PROPN
ejpam-457	181	24	p	p	X
ejpam-457	181	25	,	,	PUNCT
ejpam-457	181	26	and	and	CCONJ
ejpam-457	181	27	∫	∫	PROPN
ejpam-457	182	1	i	i	PRON
ejpam-457	182	2	(	(	PUNCT
ejpam-457	182	3	f	f	PROPN
ejpam-457	182	4	k(t	k(t	PROPN
ejpam-457	182	5	,	,	PUNCT
ejpam-457	182	6	x	x	X
ejpam-457	182	7	,	,	PUNCT
ejpam-457	182	8	ẋ	ẋ	PROPN
ejpam-457	182	9	,	,	PUNCT
ejpam-457	182	10	ẍ)d	ẍ)d	PROPN
ejpam-457	182	11	t	t	PROPN
ejpam-457	182	12	+	+	CCONJ
ejpam-457	182	13	(	(	PUNCT
ejpam-457	182	14	x(t)t	x(t)t	PROPN
ejpam-457	182	15	bk(t)x(t	bk(t)x(t	PROPN
ejpam-457	182	16	)	)	PUNCT
ejpam-457	182	17	)	)	PUNCT
ejpam-457	182	18	1	1	NUM
ejpam-457	182	19	2	2	NUM
ejpam-457	182	20	)	)	PUNCT
ejpam-457	182	21	d	d	NOUN
ejpam-457	182	22	t	t	PROPN
ejpam-457	182	23	≦	≦	VERB
ejpam-457	182	24	∫	∫	INTJ
ejpam-457	183	1	i	i	PRON
ejpam-457	183	2	�	�	PROPN
ejpam-457	183	3	f	f	PROPN
ejpam-457	183	4	k(t	k(t	PROPN
ejpam-457	183	5	,	,	PUNCT
ejpam-457	183	6	u	u	NOUN
ejpam-457	183	7	,	,	PUNCT
ejpam-457	183	8	u̇	u̇	PROPN
ejpam-457	183	9	,	,	PUNCT
ejpam-457	183	10	ü)d	ü)d	PROPN
ejpam-457	183	11	t	t	NOUN
ejpam-457	183	12	+	+	CCONJ
ejpam-457	183	13	(	(	PUNCT
ejpam-457	183	14	u(t)t	u(t)t	X
ejpam-457	183	15	bk(t)zk(t	bk(t)zk(t	NOUN
ejpam-457	183	16	)	)	PUNCT
ejpam-457	183	17	)	)	PUNCT
ejpam-457	184	1	+	+	CCONJ
ejpam-457	184	2	∑	∑	PUNCT
ejpam-457	184	3	j∈j	j∈j	NOUN
ejpam-457	184	4	◦	◦	NOUN
ejpam-457	184	5	y	y	PROPN
ejpam-457	184	6	j(t)g	j(t)g	PROPN
ejpam-457	184	7	j(t	j(t	PROPN
ejpam-457	184	8	,	,	PUNCT
ejpam-457	184	9	u	u	NOUN
ejpam-457	184	10	,	,	PUNCT
ejpam-457	184	11	u̇	u̇	PROPN
ejpam-457	184	12	,	,	PUNCT
ejpam-457	184	13	ü	ü	NOUN
ejpam-457	184	14	)	)	PUNCT
ejpam-457	184	15	�	�	PROPN
ejpam-457	184	16	d	d	PROPN
ejpam-457	184	17	t	t	PROPN
ejpam-457	184	18	(	(	PUNCT
ejpam-457	184	19	9	9	NUM
ejpam-457	184	20	)	)	PUNCT
ejpam-457	184	21	for	for	ADP
ejpam-457	184	22	some	some	DET
ejpam-457	184	23	k.	k.	PROPN
ejpam-457	184	24	i.	i.	PROPN
ejpam-457	184	25	husain	husain	PROPN
ejpam-457	184	26	,	,	PUNCT
ejpam-457	184	27	r.	r.	PROPN
ejpam-457	184	28	mattoo	mattoo	PROPN
ejpam-457	184	29	/	/	SYM
ejpam-457	184	30	eur	eur	PROPN
ejpam-457	184	31	.	.	PUNCT
ejpam-457	185	1	j.	j.	PROPN
ejpam-457	185	2	pure	pure	PROPN
ejpam-457	185	3	appl	appl	PROPN
ejpam-457	185	4	.	.	PROPN
ejpam-457	185	5	math	math	PROPN
ejpam-457	185	6	,	,	PUNCT
ejpam-457	185	7	3	3	NUM
ejpam-457	185	8	(	(	PUNCT
ejpam-457	185	9	2010	2010	NUM
ejpam-457	185	10	)	)	PUNCT
ejpam-457	185	11	,	,	PUNCT
ejpam-457	185	12	81	81	NUM
ejpam-457	185	13	-	-	SYM
ejpam-457	185	14	97	97	NUM
ejpam-457	185	15	87	87	NUM
ejpam-457	185	16	proof	proof	NOUN
ejpam-457	185	17	.	.	PUNCT
ejpam-457	186	1	suppose	suppose	VERB
ejpam-457	186	2	contrary	contrary	ADV
ejpam-457	186	3	to	to	ADP
ejpam-457	186	4	the	the	DET
ejpam-457	186	5	result	result	NOUN
ejpam-457	186	6	,	,	PUNCT
ejpam-457	186	7	that	that	SCONJ
ejpam-457	186	8	(	(	PUNCT
ejpam-457	186	9	8)	8)	NUM
ejpam-457	186	10	and	and	CCONJ
ejpam-457	186	11	(	(	PUNCT
ejpam-457	186	12	9	9	X
ejpam-457	186	13	)	)	PUNCT
ejpam-457	186	14	hold	hold	NOUN
ejpam-457	186	15	.	.	PUNCT
ejpam-457	187	1	in	in	ADP
ejpam-457	187	2	view	view	NOUN
ejpam-457	187	3	of	of	ADP
ejpam-457	187	4	y(t	y(t	PROPN
ejpam-457	187	5	)	)	PUNCT
ejpam-457	187	6	≧	≧	X
ejpam-457	187	7	0	0	NUM
ejpam-457	187	8	,	,	PUNCT
ejpam-457	187	9	t	t	PROPN
ejpam-457	187	10	∈	∈	PROPN
ejpam-457	187	11	i	i	PRON
ejpam-457	187	12	,	,	PUNCT
ejpam-457	187	13	z̄	z̄	PROPN
ejpam-457	187	14	i(t)t	i(t)t	PROPN
ejpam-457	187	15	bi(t)z̄	bi(t)z̄	PROPN
ejpam-457	187	16	i(t	i(t	PROPN
ejpam-457	187	17	)	)	PUNCT
ejpam-457	187	18	≦	≦	NUM
ejpam-457	187	19	1	1	NUM
ejpam-457	187	20	,	,	PUNCT
ejpam-457	187	21	t	t	PROPN
ejpam-457	187	22	∈	∈	PROPN
ejpam-457	188	1	i	i	PRON
ejpam-457	188	2	,	,	PUNCT
ejpam-457	188	3	i	i	PROPN
ejpam-457	188	4	∈	∈	PROPN
ejpam-457	188	5	p	p	NOUN
ejpam-457	188	6	and	and	CCONJ
ejpam-457	188	7	g(t	g(t	PROPN
ejpam-457	188	8	,	,	PUNCT
ejpam-457	188	9	x	x	SYM
ejpam-457	188	10	,	,	PUNCT
ejpam-457	188	11	ẋ	ẋ	PROPN
ejpam-457	188	12	,	,	PUNCT
ejpam-457	188	13	ẋ)≦	ẋ)≦	PROPN
ejpam-457	188	14	0	0	PROPN
ejpam-457	188	15	,	,	PUNCT
ejpam-457	188	16	t	t	PROPN
ejpam-457	188	17	∈	∈	PROPN
ejpam-457	189	1	i	i	PRON
ejpam-457	189	2	,	,	PUNCT
ejpam-457	189	3	these	these	DET
ejpam-457	189	4	inequalities	inequality	NOUN
ejpam-457	189	5	yield	yield	VERB
ejpam-457	189	6	,	,	PUNCT
ejpam-457	189	7	∫	∫	PROPN
ejpam-457	190	1	i	i	PROPN
ejpam-457	190	2	�	�	PROPN
ejpam-457	190	3	f	f	PROPN
ejpam-457	190	4	i(t	i(t	PROPN
ejpam-457	190	5	,	,	PUNCT
ejpam-457	190	6	x	x	X
ejpam-457	190	7	,	,	PUNCT
ejpam-457	190	8	ẋ	ẋ	PROPN
ejpam-457	190	9	,	,	PUNCT
ejpam-457	190	10	ẍ)d	ẍ)d	PROPN
ejpam-457	190	11	t	t	PROPN
ejpam-457	190	12	+	+	CCONJ
ejpam-457	190	13	(	(	PUNCT
ejpam-457	190	14	x(t)t	x(t)t	PROPN
ejpam-457	190	15	bi(t)z	bi(t)z	PROPN
ejpam-457	190	16	i(t	i(t	PROPN
ejpam-457	190	17	)	)	PUNCT
ejpam-457	190	18	)	)	PUNCT
ejpam-457	191	1	+	+	CCONJ
ejpam-457	191	2	∑	∑	PUNCT
ejpam-457	191	3	j∈j	j∈j	NOUN
ejpam-457	191	4	◦	◦	NOUN
ejpam-457	191	5	y	y	PROPN
ejpam-457	191	6	j(t)g	j(t)g	PROPN
ejpam-457	191	7	j(t	j(t	PROPN
ejpam-457	191	8	,	,	PUNCT
ejpam-457	191	9	u	u	NOUN
ejpam-457	191	10	,	,	PUNCT
ejpam-457	191	11	u̇	u̇	PROPN
ejpam-457	191	12	,	,	PUNCT
ejpam-457	191	13	ü	ü	NOUN
ejpam-457	191	14	)	)	PUNCT
ejpam-457	191	15	�	�	PROPN
ejpam-457	192	1	d	d	PROPN
ejpam-457	192	2	t	t	PROPN
ejpam-457	192	3	≦	≦	PROPN
ejpam-457	192	4	∫	∫	INTJ
ejpam-457	192	5	i	i	NOUN
ejpam-457	192	6	�	�	PROPN
ejpam-457	192	7	f	f	PROPN
ejpam-457	192	8	i(t	i(t	PROPN
ejpam-457	192	9	,	,	PUNCT
ejpam-457	192	10	u	u	NOUN
ejpam-457	192	11	,	,	PUNCT
ejpam-457	192	12	u̇	u̇	PROPN
ejpam-457	192	13	,	,	PUNCT
ejpam-457	192	14	ü)d	ü)d	PROPN
ejpam-457	192	15	t	t	NOUN
ejpam-457	192	16	+	+	CCONJ
ejpam-457	192	17	(	(	PUNCT
ejpam-457	192	18	u(t)t	u(t)t	PROPN
ejpam-457	192	19	bi(t)z	bi(t)z	PROPN
ejpam-457	192	20	i(t	i(t	NOUN
ejpam-457	192	21	)	)	PUNCT
ejpam-457	192	22	)	)	PUNCT
ejpam-457	193	1	+	+	CCONJ
ejpam-457	193	2	∑	∑	PUNCT
ejpam-457	193	3	j∈j	j∈j	NOUN
ejpam-457	193	4	◦	◦	NOUN
ejpam-457	193	5	y	y	PROPN
ejpam-457	193	6	j(t)g	j(t)g	PROPN
ejpam-457	193	7	j(t	j(t	PROPN
ejpam-457	193	8	,	,	PUNCT
ejpam-457	193	9	u	u	NOUN
ejpam-457	193	10	,	,	PUNCT
ejpam-457	193	11	u̇	u̇	PROPN
ejpam-457	193	12	,	,	PUNCT
ejpam-457	193	13	ü	ü	NOUN
ejpam-457	193	14	)	)	PUNCT
ejpam-457	193	15	�	�	PROPN
ejpam-457	193	16	d	d	PROPN
ejpam-457	193	17	t	t	PROPN
ejpam-457	193	18	for	for	ADP
ejpam-457	193	19	all	all	PRON
ejpam-457	193	20	i	i	PRON
ejpam-457	193	21	∈	∈	PROPN
ejpam-457	193	22	p	p	X
ejpam-457	193	23	,	,	PUNCT
ejpam-457	193	24	and	and	CCONJ
ejpam-457	193	25	∫	∫	PROPN
ejpam-457	194	1	i	i	PRON
ejpam-457	194	2	�	�	PROPN
ejpam-457	194	3	f	f	PROPN
ejpam-457	194	4	k(t	k(t	PROPN
ejpam-457	194	5	,	,	PUNCT
ejpam-457	194	6	x	x	INTJ
ejpam-457	194	7	,	,	PUNCT
ejpam-457	194	8	ẋ	ẋ	PROPN
ejpam-457	194	9	,	,	PUNCT
ejpam-457	194	10	ẍ)d	ẍ)d	PROPN
ejpam-457	194	11	t	t	PROPN
ejpam-457	194	12	+	+	CCONJ
ejpam-457	194	13	(	(	PUNCT
ejpam-457	194	14	x(t)t	x(t)t	PROPN
ejpam-457	194	15	bk(t)zk(t	bk(t)zk(t	PROPN
ejpam-457	194	16	)	)	PUNCT
ejpam-457	194	17	)	)	PUNCT
ejpam-457	195	1	+	+	CCONJ
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ejpam-457	195	4	◦	◦	NOUN
ejpam-457	195	5	y	y	PROPN
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ejpam-457	195	7	j(t	j(t	PROPN
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ejpam-457	195	9	u	u	NOUN
ejpam-457	195	10	,	,	PUNCT
ejpam-457	195	11	u̇	u̇	PROPN
ejpam-457	195	12	,	,	PUNCT
ejpam-457	195	13	ü	ü	NOUN
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ejpam-457	195	15	�	�	PROPN
ejpam-457	196	1	d	d	PROPN
ejpam-457	196	2	t	t	PROPN
ejpam-457	196	3	≦	≦	PROPN
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ejpam-457	197	1	i	i	PRON
ejpam-457	197	2	�	�	PROPN
ejpam-457	197	3	f	f	PROPN
ejpam-457	197	4	k(t	k(t	PROPN
ejpam-457	197	5	,	,	PUNCT
ejpam-457	197	6	u	u	NOUN
ejpam-457	197	7	,	,	PUNCT
ejpam-457	197	8	u̇	u̇	PROPN
ejpam-457	197	9	,	,	PUNCT
ejpam-457	197	10	ü)d	ü)d	PROPN
ejpam-457	197	11	t	t	NOUN
ejpam-457	197	12	+	+	CCONJ
ejpam-457	197	13	(	(	PUNCT
ejpam-457	197	14	u(t)t	u(t)t	X
ejpam-457	197	15	bk(t)zk(t	bk(t)zk(t	NOUN
ejpam-457	197	16	)	)	PUNCT
ejpam-457	197	17	)	)	PUNCT
ejpam-457	198	1	+	+	CCONJ
ejpam-457	198	2	∑	∑	PUNCT
ejpam-457	198	3	j∈j	j∈j	NOUN
ejpam-457	198	4	◦	◦	NOUN
ejpam-457	198	5	y	y	PROPN
ejpam-457	198	6	j(t)g	j(t)g	PROPN
ejpam-457	198	7	j(t	j(t	PROPN
ejpam-457	198	8	,	,	PUNCT
ejpam-457	198	9	u	u	NOUN
ejpam-457	198	10	,	,	PUNCT
ejpam-457	198	11	u̇	u̇	PROPN
ejpam-457	198	12	,	,	PUNCT
ejpam-457	198	13	ü	ü	NOUN
ejpam-457	198	14	)	)	PUNCT
ejpam-457	198	15	�	�	PROPN
ejpam-457	198	16	d	d	PROPN
ejpam-457	198	17	t	t	PROPN
ejpam-457	198	18	for	for	ADP
ejpam-457	198	19	some	some	DET
ejpam-457	198	20	k.	k.	NOUN
ejpam-457	198	21	now	now	ADV
ejpam-457	198	22	using	use	VERB
ejpam-457	198	23	λ	λ	PROPN
ejpam-457	198	24	>	>	X
ejpam-457	198	25	0	0	PUNCT
ejpam-457	198	26	and	and	CCONJ
ejpam-457	198	27	λt	λt	ADP
ejpam-457	198	28	e	e	NOUN
ejpam-457	198	29	=	=	SYM
ejpam-457	198	30	1	1	NUM
ejpam-457	198	31	,	,	PUNCT
ejpam-457	198	32	these	these	DET
ejpam-457	198	33	inequalities	inequality	NOUN
ejpam-457	198	34	yield	yield	VERB
ejpam-457	198	35	p	p	NOUN
ejpam-457	198	36	∑	∑	PROPN
ejpam-457	198	37	i=1	i=1	PROPN
ejpam-457	198	38	λi	λi	INTJ
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ejpam-457	199	1	i	i	PROPN
ejpam-457	199	2	�	�	PROPN
ejpam-457	199	3	f	f	PROPN
ejpam-457	199	4	i(t	i(t	PROPN
ejpam-457	199	5	,	,	PUNCT
ejpam-457	199	6	x	x	X
ejpam-457	199	7	,	,	PUNCT
ejpam-457	199	8	ẋ	ẋ	PROPN
ejpam-457	199	9	,	,	PUNCT
ejpam-457	199	10	ẍ)d	ẍ)d	PROPN
ejpam-457	199	11	t	t	PROPN
ejpam-457	199	12	+	+	CCONJ
ejpam-457	199	13	(	(	PUNCT
ejpam-457	199	14	x(t)t	x(t)t	PROPN
ejpam-457	199	15	bi(t)z	bi(t)z	PROPN
ejpam-457	199	16	i(t	i(t	PROPN
ejpam-457	199	17	)	)	PUNCT
ejpam-457	199	18	)	)	PUNCT
ejpam-457	200	1	+	+	CCONJ
ejpam-457	200	2	∑	∑	PUNCT
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ejpam-457	200	4	◦	◦	NOUN
ejpam-457	200	5	y	y	PROPN
ejpam-457	200	6	j(t)g	j(t)g	PROPN
ejpam-457	200	7	j(t	j(t	PROPN
ejpam-457	200	8	,	,	PUNCT
ejpam-457	200	9	x	x	INTJ
ejpam-457	200	10	,	,	PUNCT
ejpam-457	200	11	ẋ	ẋ	PROPN
ejpam-457	200	12	,	,	PUNCT
ejpam-457	200	13	ẍ	ẍ	X
ejpam-457	200	14	)	)	PUNCT
ejpam-457	200	15	�	�	PROPN
ejpam-457	201	1	d	d	PROPN
ejpam-457	201	2	t	t	PROPN
ejpam-457	201	3	<	<	X
ejpam-457	201	4	p	p	X
ejpam-457	201	5	∑	∑	PROPN
ejpam-457	201	6	i=1	i=1	PROPN
ejpam-457	201	7	λi	λi	X
ejpam-457	201	8	∫	∫	PROPN
ejpam-457	202	1	i	i	PROPN
ejpam-457	202	2	�	�	PROPN
ejpam-457	202	3	f	f	PROPN
ejpam-457	202	4	i(t	i(t	PROPN
ejpam-457	202	5	,	,	PUNCT
ejpam-457	202	6	u	u	NOUN
ejpam-457	202	7	,	,	PUNCT
ejpam-457	202	8	u̇	u̇	PROPN
ejpam-457	202	9	,	,	PUNCT
ejpam-457	202	10	ü)d	ü)d	PROPN
ejpam-457	202	11	t	t	NOUN
ejpam-457	202	12	+	+	CCONJ
ejpam-457	202	13	(	(	PUNCT
ejpam-457	202	14	u(t)t	u(t)t	PROPN
ejpam-457	202	15	bi(t)z	bi(t)z	PROPN
ejpam-457	202	16	i(t	i(t	NOUN
ejpam-457	202	17	)	)	PUNCT
ejpam-457	202	18	)	)	PUNCT
ejpam-457	203	1	+	+	CCONJ
ejpam-457	203	2	∑	∑	PUNCT
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ejpam-457	203	4	◦	◦	NOUN
ejpam-457	203	5	y	y	PROPN
ejpam-457	203	6	j(t)g	j(t)g	PROPN
ejpam-457	203	7	j(t	j(t	PROPN
ejpam-457	203	8	,	,	PUNCT
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ejpam-457	203	10	,	,	PUNCT
ejpam-457	203	11	ẋ	ẋ	PROPN
ejpam-457	203	12	,	,	PUNCT
ejpam-457	203	13	ẍ	ẍ	X
ejpam-457	203	14	)	)	PUNCT
ejpam-457	203	15	�	�	PROPN
ejpam-457	203	16	d	d	PROPN
ejpam-457	203	17	t	t	PROPN
ejpam-457	203	18	by	by	ADP
ejpam-457	203	19	pseudo	pseudo	NOUN
ejpam-457	203	20	invexity	invexity	NOUN
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ejpam-457	203	22	p	p	NOUN
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ejpam-457	203	24	i=1	i=1	PROPN
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ejpam-457	204	1	i	i	PROPN
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ejpam-457	204	5	,	,	PUNCT
ejpam-457	204	6	.	.	PUNCT
ejpam-457	204	7	,	,	PUNCT
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ejpam-457	204	9	,	,	PUNCT
ejpam-457	204	10	.	.	PUNCT
ejpam-457	204	11	)	)	PUNCT
ejpam-457	205	1	+	+	CCONJ
ejpam-457	205	2	∑	∑	PUNCT
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ejpam-457	205	4	◦	◦	NOUN
ejpam-457	205	5	y	y	PROPN
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ejpam-457	205	10	,	,	PUNCT
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ejpam-457	205	12	,	,	PUNCT
ejpam-457	205	13	.	.	PUNCT
ejpam-457	205	14	)	)	PUNCT
ejpam-457	206	1	+	+	CCONJ
ejpam-457	206	2	(	(	PUNCT
ejpam-457	206	3	·	·	PUNCT
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ejpam-457	206	5	t	t	PROPN
ejpam-457	206	6	bi(t)z	bi(t)z	PROPN
ejpam-457	206	7	i(t	i(t	PROPN
ejpam-457	206	8	)	)	PUNCT
ejpam-457	206	9	�	�	PROPN
ejpam-457	207	1	d	d	PROPN
ejpam-457	207	2	t	t	PROPN
ejpam-457	207	3	with	with	ADP
ejpam-457	207	4	respect	respect	NOUN
ejpam-457	207	5	to	to	ADP
ejpam-457	207	6	η	η	PROPN
ejpam-457	207	7	,	,	PUNCT
ejpam-457	207	8	we	we	PRON
ejpam-457	207	9	have	have	VERB
ejpam-457	207	10	0	0	NUM
ejpam-457	207	11	>	>	X
ejpam-457	208	1	p	p	X
ejpam-457	209	1	∑	∑	PUNCT
ejpam-457	210	1	i=1	i=1	PROPN
ejpam-457	211	1	λi	λi	X
ejpam-457	211	2	∫	∫	PROPN
ejpam-457	211	3	i	i	PROPN
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ejpam-457	211	5	�	�	PROPN
ejpam-457	211	6	�	�	PROPN
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ejpam-457	211	8	i	i	NOUN
ejpam-457	211	9	x	x	PROPN
ejpam-457	211	10	+	+	NUM
ejpam-457	211	11	bi(t)z	bi(t)z	NOUN
ejpam-457	211	12	i(t	i(t	NOUN
ejpam-457	211	13	)	)	PUNCT
ejpam-457	212	1	+	+	CCONJ
ejpam-457	212	2	∑	∑	PUNCT
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ejpam-457	212	4	◦	◦	NOUN
ejpam-457	212	5	y	y	PROPN
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ejpam-457	212	7	j	j	PROPN
ejpam-457	212	8	x	x	SYM
ejpam-457	212	9	�	�	PROPN
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ejpam-457	213	2	(	(	PUNCT
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ejpam-457	214	1	i	i	PRON
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ejpam-457	215	1	+	+	CCONJ
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ejpam-457	215	4	◦	◦	NOUN
ejpam-457	215	5	y	y	PROPN
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ejpam-457	215	7	j	j	PROPN
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ejpam-457	215	9	�	�	PROPN
ejpam-457	215	10	+	+	CCONJ
ejpam-457	215	11	(	(	PUNCT
ejpam-457	215	12	d2η)t	d2η)t	NOUN
ejpam-457	215	13	�	�	X
ejpam-457	215	14	f	f	PROPN
ejpam-457	216	1	i	i	NOUN
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ejpam-457	217	1	+	+	CCONJ
ejpam-457	217	2	∑	∑	PROPN
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ejpam-457	217	4	◦	◦	NOUN
ejpam-457	217	5	y	y	PROPN
ejpam-457	217	6	j(t)g	j(t)g	PROPN
ejpam-457	217	7	j	j	PROPN
ejpam-457	217	8	ẍ	ẍ	PROPN
ejpam-457	217	9	�	�	PROPN
ejpam-457	217	10	�	�	PROPN
ejpam-457	217	11	d	d	PROPN
ejpam-457	217	12	t	t	PROPN
ejpam-457	217	13	this	this	PRON
ejpam-457	217	14	,	,	PUNCT
ejpam-457	217	15	by	by	ADP
ejpam-457	217	16	integration	integration	NOUN
ejpam-457	217	17	by	by	ADP
ejpam-457	217	18	parts	part	NOUN
ejpam-457	217	19	,	,	PUNCT
ejpam-457	217	20	gives	give	VERB
ejpam-457	217	21	,	,	PUNCT
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ejpam-457	217	24	∑	∑	PUNCT
ejpam-457	217	25	i=1	i=1	PROPN
ejpam-457	218	1	λi	λi	X
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ejpam-457	218	3	i	i	PROPN
ejpam-457	218	4	ηt	ηt	ADP
ejpam-457	218	5	�	�	PROPN
ejpam-457	218	6	�	�	PROPN
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ejpam-457	218	8	f	f	NOUN
ejpam-457	218	9	i	i	NOUN
ejpam-457	218	10	x	x	PROPN
ejpam-457	218	11	+	+	NUM
ejpam-457	218	12	bi(t)z	bi(t)z	NOUN
ejpam-457	218	13	i(t	i(t	NOUN
ejpam-457	218	14	)	)	PUNCT
ejpam-457	219	1	+	+	CCONJ
ejpam-457	219	2	∑	∑	PUNCT
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ejpam-457	219	4	◦	◦	NOUN
ejpam-457	219	5	y	y	PROPN
ejpam-457	220	1	j(t)g	j(t)g	PROPN
ejpam-457	220	2	j	j	PROPN
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ejpam-457	220	5	−	−	PROPN
ejpam-457	221	1	d	d	X
ejpam-457	221	2	�	�	PROPN
ejpam-457	221	3	f	f	PROPN
ejpam-457	222	1	i	i	PRON
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ejpam-457	223	1	+	+	CCONJ
ejpam-457	223	2	∑	∑	NOUN
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ejpam-457	223	4	◦	◦	NOUN
ejpam-457	223	5	y	y	PROPN
ejpam-457	223	6	j(t)g	j(t)g	PROPN
ejpam-457	223	7	j	j	PROPN
ejpam-457	223	8	ẋ	ẋ	PROPN
ejpam-457	223	9	�	�	PROPN
ejpam-457	223	10	�	�	PROPN
ejpam-457	223	11	d	d	PROPN
ejpam-457	223	12	t	t	PROPN
ejpam-457	223	13	+	+	NOUN
ejpam-457	223	14	ηt	ηt	ADP
ejpam-457	223	15	�	�	PROPN
ejpam-457	224	1	f	f	PROPN
ejpam-457	225	1	i	i	PRON
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ejpam-457	226	1	+	+	CCONJ
ejpam-457	226	2	∑	∑	NOUN
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ejpam-457	226	4	◦	◦	NOUN
ejpam-457	226	5	y	y	PROPN
ejpam-457	226	6	j(t)g	j(t)g	PROPN
ejpam-457	226	7	j	j	PROPN
ejpam-457	226	8	ẋ	ẋ	PROPN
ejpam-457	226	9	�	�	PROPN
ejpam-457	226	10	�	�	PROPN
ejpam-457	226	11	�	�	PROPN
ejpam-457	226	12	�	�	PROPN
ejpam-457	226	13	�	�	PROPN
ejpam-457	226	14	t	t	PROPN
ejpam-457	226	15	=	=	PROPN
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ejpam-457	226	20	+	+	X
ejpam-457	226	21	(	(	PUNCT
ejpam-457	226	22	dη)t	dη)t	PROPN
ejpam-457	226	23	�	�	PROPN
ejpam-457	226	24	f	f	PROPN
ejpam-457	227	1	i	i	NOUN
ejpam-457	227	2	ẍ	ẍ	PUNCT
ejpam-457	228	1	+	+	CCONJ
ejpam-457	228	2	∑	∑	PROPN
ejpam-457	228	3	j∈j	j∈j	NOUN
ejpam-457	228	4	◦	◦	NOUN
ejpam-457	228	5	y	y	PROPN
ejpam-457	228	6	j(t)g	j(t)g	PROPN
ejpam-457	228	7	j	j	PROPN
ejpam-457	228	8	ẍ	ẍ	PROPN
ejpam-457	228	9	�	�	PROPN
ejpam-457	228	10	�	�	PROPN
ejpam-457	228	11	�	�	PROPN
ejpam-457	228	12	�	�	PROPN
ejpam-457	228	13	�	�	PROPN
ejpam-457	228	14	t	t	PROPN
ejpam-457	228	15	=	=	PROPN
ejpam-457	228	16	b	b	PROPN
ejpam-457	228	17	t	t	PROPN
ejpam-457	228	18	=	=	PROPN
ejpam-457	228	19	a	a	DET
ejpam-457	228	20	i.	i.	PROPN
ejpam-457	228	21	husain	husain	PROPN
ejpam-457	228	22	,	,	PUNCT
ejpam-457	228	23	r.	r.	PROPN
ejpam-457	228	24	mattoo	mattoo	PROPN
ejpam-457	228	25	/	/	SYM
ejpam-457	228	26	eur	eur	PROPN
ejpam-457	228	27	.	.	PUNCT
ejpam-457	229	1	j.	j.	PROPN
ejpam-457	229	2	pure	pure	PROPN
ejpam-457	229	3	appl	appl	PROPN
ejpam-457	229	4	.	.	PROPN
ejpam-457	229	5	math	math	PROPN
ejpam-457	229	6	,	,	PUNCT
ejpam-457	229	7	3	3	NUM
ejpam-457	229	8	(	(	PUNCT
ejpam-457	229	9	2010	2010	NUM
ejpam-457	229	10	)	)	PUNCT
ejpam-457	229	11	,	,	PUNCT
ejpam-457	229	12	81	81	NUM
ejpam-457	229	13	-	-	SYM
ejpam-457	229	14	97	97	NUM
ejpam-457	229	15	88	88	NUM
ejpam-457	229	16	+	+	CCONJ
ejpam-457	229	17	∫	∫	PROPN
ejpam-457	229	18	i	i	INTJ
ejpam-457	229	19	(	(	PUNCT
ejpam-457	229	20	dη)t	dη)t	PROPN
ejpam-457	229	21	d	d	PROPN
ejpam-457	229	22	�	�	PROPN
ejpam-457	230	1	f	f	PROPN
ejpam-457	230	2	i	i	NOUN
ejpam-457	230	3	ẍ	ẍ	PUNCT
ejpam-457	231	1	+	+	CCONJ
ejpam-457	231	2	∑	∑	PROPN
ejpam-457	231	3	j∈j	j∈j	NOUN
ejpam-457	231	4	◦	◦	NOUN
ejpam-457	231	5	y	y	PROPN
ejpam-457	231	6	j(t)g	j(t)g	PROPN
ejpam-457	231	7	j	j	PROPN
ejpam-457	231	8	ẍ	ẍ	PROPN
ejpam-457	231	9	�	�	PROPN
ejpam-457	232	1	d	d	PROPN
ejpam-457	232	2	t	t	PROPN
ejpam-457	232	3	�	�	PROPN
ejpam-457	232	4	using	use	VERB
ejpam-457	232	5	the	the	DET
ejpam-457	232	6	boundary	boundary	ADJ
ejpam-457	232	7	conditions	condition	NOUN
ejpam-457	232	8	which	which	PRON
ejpam-457	232	9	at	at	ADP
ejpam-457	232	10	t	t	PROPN
ejpam-457	232	11	=	=	SYM
ejpam-457	232	12	a	a	X
ejpam-457	232	13	,	,	PUNCT
ejpam-457	232	14	t	t	PROPN
ejpam-457	232	15	=	=	SYM
ejpam-457	232	16	b	b	NOUN
ejpam-457	232	17	gives	give	VERB
ejpam-457	232	18	dη	dη	X
ejpam-457	232	19	=	=	PUNCT
ejpam-457	232	20	0=	0=	NUM
ejpam-457	232	21	η	η	X
ejpam-457	232	22	=	=	PROPN
ejpam-457	233	1	p	p	PROPN
ejpam-457	233	2	∑	∑	PROPN
ejpam-457	233	3	i=1	i=1	PROPN
ejpam-457	233	4	λi	λi	INTJ
ejpam-457	233	5	∫	∫	PROPN
ejpam-457	234	1	i	i	PRON
ejpam-457	234	2	�	�	PROPN
ejpam-457	234	3	ηt	ηt	ADP
ejpam-457	234	4	�	�	PROPN
ejpam-457	234	5	�	�	PROPN
ejpam-457	234	6	f	f	PROPN
ejpam-457	234	7	i	i	NOUN
ejpam-457	234	8	x	x	PROPN
ejpam-457	234	9	+	+	NUM
ejpam-457	234	10	bi(t)z	bi(t)z	NOUN
ejpam-457	234	11	i(t	i(t	NOUN
ejpam-457	234	12	)	)	PUNCT
ejpam-457	234	13	+	+	CCONJ
ejpam-457	234	14	∑	∑	PUNCT
ejpam-457	234	15	j∈j	j∈j	NOUN
ejpam-457	234	16	◦	◦	NOUN
ejpam-457	234	17	y	y	PROPN
ejpam-457	234	18	j(t)g	j(t)g	PROPN
ejpam-457	234	19	j	j	PROPN
ejpam-457	234	20	x	x	SYM
ejpam-457	234	21	�	�	PROPN
ejpam-457	234	22	−	−	PROPN
ejpam-457	235	1	d	d	PROPN
ejpam-457	235	2	�	�	PROPN
ejpam-457	235	3	f	f	PROPN
ejpam-457	236	1	i	i	PRON
ejpam-457	236	2	ẋ	ẋ	PUNCT
ejpam-457	237	1	+	+	CCONJ
ejpam-457	237	2	∑	∑	NOUN
ejpam-457	237	3	j∈j	j∈j	NOUN
ejpam-457	237	4	◦	◦	NOUN
ejpam-457	237	5	y	y	PROPN
ejpam-457	237	6	j(t)g	j(t)g	PROPN
ejpam-457	237	7	j	j	PROPN
ejpam-457	237	8	ẋ	ẋ	PROPN
ejpam-457	237	9	�	�	PROPN
ejpam-457	237	10	�	�	PROPN
ejpam-457	237	11	d	d	PROPN
ejpam-457	237	12	t	t	PROPN
ejpam-457	238	1	+	+	CCONJ
ejpam-457	238	2	∫	∫	PROPN
ejpam-457	239	1	i	i	INTJ
ejpam-457	239	2	(	(	PUNCT
ejpam-457	239	3	dη)t	dη)t	PROPN
ejpam-457	239	4	d	d	PROPN
ejpam-457	239	5	�	�	PROPN
ejpam-457	239	6	f	f	PROPN
ejpam-457	239	7	i	i	NOUN
ejpam-457	239	8	ẍ	ẍ	PUNCT
ejpam-457	240	1	+	+	CCONJ
ejpam-457	240	2	∑	∑	PROPN
ejpam-457	240	3	j∈j	j∈j	NOUN
ejpam-457	240	4	◦	◦	NOUN
ejpam-457	240	5	y	y	PROPN
ejpam-457	241	1	j(t)g	j(t)g	PROPN
ejpam-457	241	2	j	j	PROPN
ejpam-457	241	3	ẍ	ẍ	PROPN
ejpam-457	241	4	�	�	PROPN
ejpam-457	241	5	�	�	PROPN
ejpam-457	241	6	d	d	PROPN
ejpam-457	241	7	t	t	PROPN
ejpam-457	242	1	=	=	PUNCT
ejpam-457	242	2	p	p	NOUN
ejpam-457	242	3	∑	∑	PUNCT
ejpam-457	242	4	i=1	i=1	PROPN
ejpam-457	242	5	λi	λi	INTJ
ejpam-457	242	6	∫	∫	PROPN
ejpam-457	243	1	i	i	PRON
ejpam-457	243	2	�	�	PROPN
ejpam-457	243	3	ηt	ηt	ADP
ejpam-457	243	4	�	�	PROPN
ejpam-457	243	5	�	�	PROPN
ejpam-457	243	6	f	f	PROPN
ejpam-457	243	7	i	i	NOUN
ejpam-457	243	8	x	x	PROPN
ejpam-457	243	9	+	+	NUM
ejpam-457	243	10	bi(t)z	bi(t)z	NOUN
ejpam-457	243	11	i(t	i(t	NOUN
ejpam-457	243	12	)	)	PUNCT
ejpam-457	243	13	+	+	CCONJ
ejpam-457	243	14	∑	∑	PUNCT
ejpam-457	243	15	j∈j	j∈j	NOUN
ejpam-457	243	16	◦	◦	NOUN
ejpam-457	243	17	y	y	PROPN
ejpam-457	243	18	j(t)g	j(t)g	PROPN
ejpam-457	243	19	j	j	PROPN
ejpam-457	243	20	x	x	SYM
ejpam-457	243	21	�	�	PROPN
ejpam-457	243	22	−	−	PROPN
ejpam-457	244	1	d	d	PROPN
ejpam-457	244	2	�	�	PROPN
ejpam-457	244	3	f	f	PROPN
ejpam-457	245	1	i	i	PRON
ejpam-457	245	2	ẋ	ẋ	PUNCT
ejpam-457	246	1	+	+	CCONJ
ejpam-457	246	2	∑	∑	NOUN
ejpam-457	246	3	j∈j	j∈j	NOUN
ejpam-457	246	4	◦	◦	NOUN
ejpam-457	246	5	y	y	PROPN
ejpam-457	246	6	j(t)g	j(t)g	PROPN
ejpam-457	247	1	j	j	PROPN
ejpam-457	247	2	ẋ	ẋ	PROPN
ejpam-457	247	3	�	�	PROPN
ejpam-457	247	4	+	+	NUM
ejpam-457	247	5	d2	d2	PROPN
ejpam-457	247	6	�	�	PROPN
ejpam-457	247	7	f	f	PROPN
ejpam-457	247	8	i	i	PRON
ejpam-457	247	9	ẍ	ẍ	PUNCT
ejpam-457	248	1	+	+	CCONJ
ejpam-457	248	2	∑	∑	PROPN
ejpam-457	248	3	j∈j	j∈j	NOUN
ejpam-457	248	4	◦	◦	NOUN
ejpam-457	248	5	y	y	PROPN
ejpam-457	249	1	j(t)g	j(t)g	PROPN
ejpam-457	249	2	j	j	PROPN
ejpam-457	249	3	ẍ	ẍ	PROPN
ejpam-457	249	4	�	�	PROPN
ejpam-457	249	5	�	�	PROPN
ejpam-457	249	6	�	�	PROPN
ejpam-457	249	7	d	d	PROPN
ejpam-457	249	8	t	t	PROPN
ejpam-457	249	9	−ηt	−ηt	PROPN
ejpam-457	249	10	�	�	PROPN
ejpam-457	250	1	f	f	PROPN
ejpam-457	250	2	i	i	PRON
ejpam-457	250	3	ẍ	ẍ	PUNCT
ejpam-457	251	1	+	+	CCONJ
ejpam-457	251	2	∑	∑	PROPN
ejpam-457	251	3	j∈j	j∈j	NOUN
ejpam-457	251	4	◦	◦	NOUN
ejpam-457	251	5	y	y	PROPN
ejpam-457	251	6	j(t)g	j(t)g	PROPN
ejpam-457	251	7	j	j	PROPN
ejpam-457	251	8	ẍ	ẍ	PROPN
ejpam-457	251	9	�	�	PROPN
ejpam-457	251	10	�	�	PROPN
ejpam-457	251	11	�	�	PROPN
ejpam-457	251	12	�	�	PROPN
ejpam-457	251	13	�	�	PROPN
ejpam-457	251	14	t	t	PROPN
ejpam-457	251	15	=	=	PROPN
ejpam-457	251	16	b	b	PROPN
ejpam-457	251	17	t	t	PROPN
ejpam-457	251	18	=	=	PROPN
ejpam-457	251	19	a	a	DET
ejpam-457	251	20	0	0	NUM
ejpam-457	251	21	>	>	X
ejpam-457	251	22	p	p	X
ejpam-457	251	23	∑	∑	PUNCT
ejpam-457	251	24	i=1	i=1	PROPN
ejpam-457	251	25	λi	λi	X
ejpam-457	251	26	∫	∫	PROPN
ejpam-457	252	1	i	i	PRON
ejpam-457	252	2	�	�	PROPN
ejpam-457	252	3	ηt	ηt	ADP
ejpam-457	252	4	�	�	PROPN
ejpam-457	252	5	�	�	PROPN
ejpam-457	252	6	f	f	PROPN
ejpam-457	252	7	i	i	NOUN
ejpam-457	252	8	x	x	PROPN
ejpam-457	252	9	+	+	NUM
ejpam-457	252	10	bi(t)z	bi(t)z	NOUN
ejpam-457	252	11	i(t	i(t	NOUN
ejpam-457	252	12	)	)	PUNCT
ejpam-457	252	13	+	+	CCONJ
ejpam-457	252	14	∑	∑	PUNCT
ejpam-457	252	15	j∈j	j∈j	NOUN
ejpam-457	252	16	◦	◦	NOUN
ejpam-457	252	17	y	y	PROPN
ejpam-457	252	18	j(t)g	j(t)g	PROPN
ejpam-457	252	19	j	j	PROPN
ejpam-457	252	20	x	x	SYM
ejpam-457	252	21	�	�	PROPN
ejpam-457	252	22	−	−	PROPN
ejpam-457	253	1	d	d	PROPN
ejpam-457	253	2	�	�	PROPN
ejpam-457	253	3	f	f	PROPN
ejpam-457	254	1	i	i	PRON
ejpam-457	254	2	ẋ	ẋ	PUNCT
ejpam-457	255	1	+	+	CCONJ
ejpam-457	255	2	∑	∑	NOUN
ejpam-457	255	3	j∈j	j∈j	NOUN
ejpam-457	255	4	◦	◦	NOUN
ejpam-457	255	5	y	y	PROPN
ejpam-457	255	6	j(t)g	j(t)g	PROPN
ejpam-457	256	1	j	j	PROPN
ejpam-457	256	2	ẋ	ẋ	PROPN
ejpam-457	256	3	�	�	PROPN
ejpam-457	256	4	+	+	NUM
ejpam-457	256	5	d2	d2	PROPN
ejpam-457	256	6	�	�	PROPN
ejpam-457	256	7	f	f	PROPN
ejpam-457	256	8	i	i	PRON
ejpam-457	256	9	ẍ	ẍ	PUNCT
ejpam-457	257	1	+	+	CCONJ
ejpam-457	257	2	∑	∑	PROPN
ejpam-457	257	3	j∈j	j∈j	NOUN
ejpam-457	257	4	◦	◦	NOUN
ejpam-457	257	5	y	y	PROPN
ejpam-457	257	6	j(t)g	j(t)g	PROPN
ejpam-457	257	7	j	j	PROPN
ejpam-457	257	8	ẍ	ẍ	PROPN
ejpam-457	257	9	�	�	PROPN
ejpam-457	257	10	�	�	PROPN
ejpam-457	257	11	�	�	PROPN
ejpam-457	257	12	d	d	PROPN
ejpam-457	257	13	t	t	PROPN
ejpam-457	257	14	(	(	PUNCT
ejpam-457	257	15	10	10	NUM
ejpam-457	257	16	)	)	PUNCT
ejpam-457	257	17	now	now	ADV
ejpam-457	257	18	,	,	PUNCT
ejpam-457	257	19	from	from	ADP
ejpam-457	257	20	the	the	DET
ejpam-457	257	21	feasibility	feasibility	NOUN
ejpam-457	257	22	of	of	ADP
ejpam-457	257	23	(	(	PUNCT
ejpam-457	257	24	vp	vp	PROPN
ejpam-457	257	25	)	)	PUNCT
ejpam-457	257	26	and	and	CCONJ
ejpam-457	257	27	(	(	PUNCT
ejpam-457	257	28	mix	mix	VERB
ejpam-457	257	29	-	-	PUNCT
ejpam-457	257	30	d	d	NOUN
ejpam-457	257	31	)	)	PUNCT
ejpam-457	257	32	,	,	PUNCT
ejpam-457	257	33	we	we	PRON
ejpam-457	257	34	have	have	VERB
ejpam-457	257	35	∑	∑	ADV
ejpam-457	257	36	j∈jα	j∈jα	PROPN
ejpam-457	257	37	∫	∫	PROPN
ejpam-457	258	1	i	i	PRON
ejpam-457	258	2	y	y	PROPN
ejpam-457	258	3	j(t)g	j(t)g	PROPN
ejpam-457	258	4	j(t	j(t	PROPN
ejpam-457	258	5	,	,	PUNCT
ejpam-457	258	6	x	x	X
ejpam-457	258	7	,	,	PUNCT
ejpam-457	258	8	ẋ	ẋ	PROPN
ejpam-457	258	9	,	,	PUNCT
ejpam-457	258	10	ẍ)d	ẍ)d	PROPN
ejpam-457	258	11	t	t	PROPN
ejpam-457	258	12	≦	≦	VERB
ejpam-457	258	13	∑	∑	PROPN
ejpam-457	258	14	j∈jα	j∈jα	PROPN
ejpam-457	258	15	∫	∫	PROPN
ejpam-457	259	1	i	i	PRON
ejpam-457	259	2	y	y	PROPN
ejpam-457	259	3	j(t)g	j(t)g	PROPN
ejpam-457	259	4	j(t	j(t	PROPN
ejpam-457	259	5	,	,	PUNCT
ejpam-457	259	6	u	u	NOUN
ejpam-457	259	7	,	,	PUNCT
ejpam-457	259	8	u̇	u̇	PROPN
ejpam-457	259	9	,	,	PUNCT
ejpam-457	259	10	ü)d	ü)d	PROPN
ejpam-457	259	11	t	t	PROPN
ejpam-457	259	12	this	this	PRON
ejpam-457	259	13	,	,	PUNCT
ejpam-457	259	14	because	because	SCONJ
ejpam-457	259	15	of	of	ADP
ejpam-457	259	16	quasi	quasi	NOUN
ejpam-457	259	17	-	-	NOUN
ejpam-457	259	18	invexity	invexity	NOUN
ejpam-457	259	19	of	of	ADP
ejpam-457	259	20	∑	∑	PUNCT
ejpam-457	259	21	j∈jα	j∈jα	PROPN
ejpam-457	259	22	∫	∫	PROPN
ejpam-457	260	1	i	i	PRON
ejpam-457	260	2	y	y	PROPN
ejpam-457	260	3	j(t)g	j(t)g	PROPN
ejpam-457	260	4	j(t	j(t	PROPN
ejpam-457	260	5	,	,	PUNCT
ejpam-457	260	6	.	.	PUNCT
ejpam-457	260	7	,	,	PUNCT
ejpam-457	260	8	.	.	PUNCT
ejpam-457	260	9	,	,	PUNCT
ejpam-457	260	10	.)d	.)d	PROPN
ejpam-457	260	11	t	t	PROPN
ejpam-457	260	12	with	with	ADP
ejpam-457	260	13	η	η	PROPN
ejpam-457	260	14	implies	imply	VERB
ejpam-457	260	15	∑	∑	PROPN
ejpam-457	260	16	j∈jα	j∈jα	PROPN
ejpam-457	260	17	∫	∫	PROPN
ejpam-457	260	18	i	i	PRON
ejpam-457	260	19	{	{	PUNCT
ejpam-457	260	20	ηt	ηt	ADP
ejpam-457	260	21	(	(	PUNCT
ejpam-457	260	22	y	y	PROPN
ejpam-457	260	23	j(t)g	j(t)g	PROPN
ejpam-457	260	24	j	j	PROPN
ejpam-457	260	25	x	x	X
ejpam-457	260	26	)	)	PUNCT
ejpam-457	261	1	+	+	CCONJ
ejpam-457	261	2	(	(	PUNCT
ejpam-457	261	3	dη	dη	NOUN
ejpam-457	261	4	)	)	PUNCT
ejpam-457	261	5	t	t	PROPN
ejpam-457	261	6	y	y	PROPN
ejpam-457	262	1	j(t)g	j(t)g	PROPN
ejpam-457	262	2	j	j	PROPN
ejpam-457	262	3	ẋ	ẋ	PROPN
ejpam-457	263	1	+	+	CCONJ
ejpam-457	263	2	(	(	PUNCT
ejpam-457	263	3	d2η)t	d2η)t	NOUN
ejpam-457	263	4	y	y	PROPN
ejpam-457	263	5	j(t)g	j(t)g	PROPN
ejpam-457	263	6	j	j	PROPN
ejpam-457	263	7	ẍ}d	ẍ}d	PROPN
ejpam-457	263	8	t	t	PROPN
ejpam-457	263	9	≦	≦	VERB
ejpam-457	263	10	0	0	PUNCT
ejpam-457	263	11	as	as	ADP
ejpam-457	263	12	earlier	early	ADV
ejpam-457	263	13	,	,	PUNCT
ejpam-457	263	14	integrating	integrate	VERB
ejpam-457	263	15	by	by	ADP
ejpam-457	263	16	parts	part	NOUN
ejpam-457	263	17	and	and	CCONJ
ejpam-457	263	18	using	use	VERB
ejpam-457	263	19	the	the	DET
ejpam-457	263	20	boundary	boundary	ADJ
ejpam-457	263	21	conditions	condition	NOUN
ejpam-457	263	22	,	,	PUNCT
ejpam-457	263	23	we	we	PRON
ejpam-457	263	24	have	have	VERB
ejpam-457	263	25	∑	∑	ADV
ejpam-457	263	26	j∈jα	j∈jα	PROPN
ejpam-457	263	27	∫	∫	PROPN
ejpam-457	264	1	i	i	PRON
ejpam-457	264	2	ηt	ηt	ADP
ejpam-457	264	3	{	{	PUNCT
ejpam-457	264	4	(	(	PUNCT
ejpam-457	264	5	y	y	PROPN
ejpam-457	264	6	j(t)g	j(t)g	PROPN
ejpam-457	264	7	j	j	PROPN
ejpam-457	264	8	x	x	PUNCT
ejpam-457	264	9	)	)	PUNCT
ejpam-457	265	1	+	+	CCONJ
ejpam-457	265	2	dt	dt	X
ejpam-457	265	3	y	y	PROPN
ejpam-457	266	1	j(t)g	j(t)g	PROPN
ejpam-457	266	2	j	j	PROPN
ejpam-457	266	3	ẋ	ẋ	PROPN
ejpam-457	267	1	+	+	CCONJ
ejpam-457	267	2	d2	d2	PROPN
ejpam-457	267	3	y	y	PROPN
ejpam-457	267	4	j(t)g	j(t)g	PROPN
ejpam-457	267	5	j	j	PROPN
ejpam-457	267	6	ẍ	ẍ	PROPN
ejpam-457	267	7	}	}	PUNCT
ejpam-457	267	8	d	d	PROPN
ejpam-457	267	9	t	t	PROPN
ejpam-457	267	10	≦	≦	PROPN
ejpam-457	267	11	0	0	PUNCT
ejpam-457	267	12	(	(	PUNCT
ejpam-457	267	13	11	11	NUM
ejpam-457	267	14	)	)	PUNCT
ejpam-457	267	15	combining	combine	VERB
ejpam-457	267	16	(	(	PUNCT
ejpam-457	267	17	10	10	NUM
ejpam-457	267	18	)	)	PUNCT
ejpam-457	267	19	and	and	CCONJ
ejpam-457	267	20	(	(	PUNCT
ejpam-457	267	21	11	11	NUM
ejpam-457	267	22	)	)	PUNCT
ejpam-457	267	23	,	,	PUNCT
ejpam-457	267	24	we	we	PRON
ejpam-457	267	25	have	have	VERB
ejpam-457	267	26	∫	∫	PROPN
ejpam-457	268	1	i	i	PROPN
ejpam-457	268	2	ηt	ηt	ADP
ejpam-457	268	3	�	�	PROPN
ejpam-457	268	4	p	p	PROPN
ejpam-457	268	5	∑	∑	PROPN
ejpam-457	268	6	i=1	i=1	PROPN
ejpam-457	268	7	λi	λi	PROPN
ejpam-457	268	8	(	(	PUNCT
ejpam-457	268	9	f	f	NOUN
ejpam-457	268	10	i	i	NOUN
ejpam-457	268	11	x	x	PROPN
ejpam-457	269	1	+	+	NUM
ejpam-457	269	2	bi(t)z	bi(t)z	NOUN
ejpam-457	269	3	i(t	i(t	NOUN
ejpam-457	269	4	)	)	PUNCT
ejpam-457	270	1	+	+	NUM
ejpam-457	270	2	y(t)t	y(t)t	PROPN
ejpam-457	270	3	gx	gx	PROPN
ejpam-457	270	4	�	�	PROPN
ejpam-457	270	5	i.	i.	PROPN
ejpam-457	270	6	husain	husain	PROPN
ejpam-457	270	7	,	,	PUNCT
ejpam-457	270	8	r.	r.	PROPN
ejpam-457	270	9	mattoo	mattoo	PROPN
ejpam-457	270	10	/	/	SYM
ejpam-457	270	11	eur	eur	PROPN
ejpam-457	270	12	.	.	PUNCT
ejpam-457	271	1	j.	j.	PROPN
ejpam-457	271	2	pure	pure	PROPN
ejpam-457	271	3	appl	appl	PROPN
ejpam-457	271	4	.	.	PROPN
ejpam-457	271	5	math	math	PROPN
ejpam-457	271	6	,	,	PUNCT
ejpam-457	271	7	3	3	NUM
ejpam-457	271	8	(	(	PUNCT
ejpam-457	271	9	2010	2010	NUM
ejpam-457	271	10	)	)	PUNCT
ejpam-457	271	11	,	,	PUNCT
ejpam-457	271	12	81	81	NUM
ejpam-457	271	13	-	-	SYM
ejpam-457	271	14	97	97	NUM
ejpam-457	271	15	89	89	NUM
ejpam-457	271	16	−d(λt	−d(λt	NOUN
ejpam-457	271	17	f	f	X
ejpam-457	271	18	ẋ	ẋ	PROPN
ejpam-457	272	1	+	+	NUM
ejpam-457	272	2	y(t)t	y(t)t	PROPN
ejpam-457	272	3	g	g	PROPN
ejpam-457	272	4	ẋ	ẋ	PROPN
ejpam-457	272	5	)	)	PUNCT
ejpam-457	273	1	+	+	CCONJ
ejpam-457	273	2	d2(λt	d2(λt	PROPN
ejpam-457	273	3	f	f	X
ejpam-457	273	4	ẍ	ẍ	PUNCT
ejpam-457	274	1	+	+	CCONJ
ejpam-457	274	2	y(t)t	y(t)t	PROPN
ejpam-457	274	3	g	g	PROPN
ejpam-457	274	4	ẍ))d	ẍ))d	PROPN
ejpam-457	274	5	t	t	PROPN
ejpam-457	274	6	<	<	X
ejpam-457	274	7	0	0	NUM
ejpam-457	274	8	from	from	ADP
ejpam-457	274	9	the	the	DET
ejpam-457	274	10	equality	equality	NOUN
ejpam-457	274	11	constraint	constraint	NOUN
ejpam-457	274	12	of	of	ADP
ejpam-457	274	13	the	the	DET
ejpam-457	274	14	dual	dual	ADJ
ejpam-457	274	15	,	,	PUNCT
ejpam-457	274	16	we	we	PRON
ejpam-457	274	17	have	have	VERB
ejpam-457	274	18	∫	∫	PROPN
ejpam-457	275	1	i	i	PRON
ejpam-457	275	2	ηt	ηt	ADP
ejpam-457	275	3	(	(	PUNCT
ejpam-457	275	4	p	p	NOUN
ejpam-457	275	5	∑	∑	PROPN
ejpam-457	275	6	i=1	i=1	PROPN
ejpam-457	275	7	λi	λi	PROPN
ejpam-457	275	8	(	(	PUNCT
ejpam-457	275	9	f	f	NOUN
ejpam-457	275	10	i	i	NOUN
ejpam-457	275	11	x	x	PROPN
ejpam-457	275	12	+	+	NUM
ejpam-457	275	13	bi(t)z	bi(t)z	NOUN
ejpam-457	275	14	i(t	i(t	NOUN
ejpam-457	275	15	)	)	PUNCT
ejpam-457	275	16	+	+	NUM
ejpam-457	275	17	y(t)t	y(t)t	PROPN
ejpam-457	275	18	gx	gx	PROPN
ejpam-457	275	19	)	)	PUNCT
ejpam-457	275	20	−d(λt	−d(λt	NOUN
ejpam-457	275	21	f	f	PROPN
ejpam-457	275	22	ẋ	ẋ	PROPN
ejpam-457	276	1	+	+	NUM
ejpam-457	276	2	y(t)t	y(t)t	PROPN
ejpam-457	276	3	g	g	PROPN
ejpam-457	276	4	ẋ	ẋ	PROPN
ejpam-457	276	5	)	)	PUNCT
ejpam-457	277	1	+	+	CCONJ
ejpam-457	277	2	d2(λt	d2(λt	PROPN
ejpam-457	277	3	f	f	X
ejpam-457	277	4	ẍ	ẍ	PUNCT
ejpam-457	278	1	+	+	CCONJ
ejpam-457	278	2	y(t)t	y(t)t	PROPN
ejpam-457	278	3	g	g	PROPN
ejpam-457	278	4	ẍ))d	ẍ))d	PROPN
ejpam-457	278	5	t	t	PROPN
ejpam-457	278	6	=	=	SYM
ejpam-457	278	7	0	0	NUM
ejpam-457	278	8	which	which	PRON
ejpam-457	278	9	is	be	AUX
ejpam-457	278	10	a	a	DET
ejpam-457	278	11	contradiction	contradiction	NOUN
ejpam-457	278	12	.	.	PUNCT
ejpam-457	279	1	hence	hence	ADV
ejpam-457	279	2	the	the	DET
ejpam-457	279	3	conclusion	conclusion	NOUN
ejpam-457	279	4	of	of	ADP
ejpam-457	279	5	the	the	DET
ejpam-457	279	6	theorem	theorem	NOUN
ejpam-457	279	7	is	be	AUX
ejpam-457	279	8	true	true	ADJ
ejpam-457	279	9	.	.	PUNCT
ejpam-457	280	1	theorem	theorem	ADJ
ejpam-457	280	2	2	2	NUM
ejpam-457	280	3	(	(	PUNCT
ejpam-457	280	4	strong	strong	ADJ
ejpam-457	280	5	duality	duality	NOUN
ejpam-457	280	6	)	)	PUNCT
ejpam-457	280	7	.	.	PUNCT
ejpam-457	281	1	let	let	VERB
ejpam-457	281	2	x̄	x̄	PRON
ejpam-457	281	3	∈	∈	PROPN
ejpam-457	281	4	x	x	PUNCT
ejpam-457	281	5	be	be	AUX
ejpam-457	281	6	an	an	DET
ejpam-457	281	7	efficient	efficient	ADJ
ejpam-457	281	8	solution	solution	NOUN
ejpam-457	281	9	of	of	ADP
ejpam-457	281	10	(	(	PUNCT
ejpam-457	281	11	vp	vp	NOUN
ejpam-457	281	12	)	)	PUNCT
ejpam-457	281	13	and	and	CCONJ
ejpam-457	281	14	for	for	ADP
ejpam-457	281	15	at	at	ADV
ejpam-457	281	16	least	least	ADV
ejpam-457	281	17	one	one	NUM
ejpam-457	281	18	i	i	PRON
ejpam-457	281	19	∈	∈	PROPN
ejpam-457	282	1	p	p	X
ejpam-457	282	2	,	,	PUNCT
ejpam-457	282	3	x̄	x̄	PRON
ejpam-457	282	4	satisfies	satisfy	VERB
ejpam-457	282	5	the	the	DET
ejpam-457	282	6	regularity	regularity	NOUN
ejpam-457	282	7	condition	condition	NOUN
ejpam-457	283	1	[	[	X
ejpam-457	283	2	3	3	X
ejpam-457	283	3	]	]	PUNCT
ejpam-457	283	4	for	for	ADP
ejpam-457	283	5	the	the	DET
ejpam-457	283	6	problem	problem	NOUN
ejpam-457	283	7	(	(	PUNCT
ejpam-457	283	8	pk	pk	NOUN
ejpam-457	283	9	(	(	PUNCT
ejpam-457	283	10	x̄	x̄	PROPN
ejpam-457	283	11	)	)	PUNCT
ejpam-457	283	12	)	)	PUNCT
ejpam-457	283	13	.	.	PUNCT
ejpam-457	284	1	then	then	ADV
ejpam-457	284	2	there	there	PRON
ejpam-457	284	3	exist	exist	VERB
ejpam-457	284	4	multipliers	multiplier	NOUN
ejpam-457	284	5	λ̄	λ̄	ADP
ejpam-457	284	6	∈	∈	PROPN
ejpam-457	284	7	rp	rp	NOUN
ejpam-457	284	8	,	,	PUNCT
ejpam-457	284	9	piecewise	piecewise	NOUN
ejpam-457	284	10	smooth	smooth	ADJ
ejpam-457	284	11	ȳ	ȳ	PROPN
ejpam-457	284	12	∈	∈	PROPN
ejpam-457	284	13	rm	rm	PROPN
ejpam-457	284	14	and	and	CCONJ
ejpam-457	284	15	z	z	PROPN
ejpam-457	284	16	i(t	i(t	PROPN
ejpam-457	284	17	)	)	PUNCT
ejpam-457	284	18	∈	∈	PROPN
ejpam-457	284	19	rn	rn	PROPN
ejpam-457	284	20	,	,	PUNCT
ejpam-457	284	21	i	i	PRON
ejpam-457	284	22	=	=	PUNCT
ejpam-457	284	23	{	{	PUNCT
ejpam-457	284	24	1,2	1,2	NUM
ejpam-457	284	25	,	,	PUNCT
ejpam-457	284	26	.	.	PUNCT
ejpam-457	284	27	.	.	PUNCT
ejpam-457	285	1	.	.	PUNCT
ejpam-457	286	1	,	,	PUNCT
ejpam-457	286	2	p	p	X
ejpam-457	286	3	}	}	PUNCT
ejpam-457	286	4	such	such	ADJ
ejpam-457	286	5	that	that	SCONJ
ejpam-457	286	6	(	(	PUNCT
ejpam-457	286	7	x̄	x̄	NOUN
ejpam-457	286	8	,	,	PUNCT
ejpam-457	286	9	ȳ	ȳ	PROPN
ejpam-457	286	10	,	,	PUNCT
ejpam-457	286	11	z̄1	z̄1	PROPN
ejpam-457	286	12	,	,	PUNCT
ejpam-457	286	13	.	.	PUNCT
ejpam-457	286	14	.	.	PUNCT
ejpam-457	287	1	.	.	PUNCT
ejpam-457	288	1	,	,	PUNCT
ejpam-457	288	2	z̄p	z̄p	PROPN
ejpam-457	288	3	,	,	PUNCT
ejpam-457	288	4	λ	λ	X
ejpam-457	288	5	)	)	PUNCT
ejpam-457	288	6	is	be	AUX
ejpam-457	288	7	feasible	feasible	ADJ
ejpam-457	288	8	for	for	ADP
ejpam-457	288	9	(	(	PUNCT
ejpam-457	288	10	mix	mix	VERB
ejpam-457	288	11	d	d	NOUN
ejpam-457	288	12	)	)	PUNCT
ejpam-457	288	13	and	and	CCONJ
ejpam-457	288	14	the	the	DET
ejpam-457	288	15	objectives	objective	NOUN
ejpam-457	288	16	of	of	ADP
ejpam-457	288	17	(	(	PUNCT
ejpam-457	288	18	vp	vp	NOUN
ejpam-457	288	19	)	)	PUNCT
ejpam-457	288	20	and	and	CCONJ
ejpam-457	288	21	(	(	PUNCT
ejpam-457	288	22	mix	mix	VERB
ejpam-457	288	23	d	d	NOUN
ejpam-457	288	24	)	)	PUNCT
ejpam-457	288	25	are	be	AUX
ejpam-457	288	26	equal	equal	ADJ
ejpam-457	288	27	.	.	PUNCT
ejpam-457	289	1	further	far	ADV
ejpam-457	289	2	,	,	PUNCT
ejpam-457	289	3	if	if	SCONJ
ejpam-457	289	4	the	the	DET
ejpam-457	289	5	hypotheses	hypothesis	NOUN
ejpam-457	289	6	of	of	ADP
ejpam-457	289	7	theorem	theorem	NOUN
ejpam-457	289	8	1	1	NUM
ejpam-457	289	9	are	be	AUX
ejpam-457	289	10	met	meet	VERB
ejpam-457	289	11	,	,	PUNCT
ejpam-457	289	12	then	then	ADV
ejpam-457	289	13	(	(	PUNCT
ejpam-457	289	14	x̄	x̄	NOUN
ejpam-457	289	15	,	,	PUNCT
ejpam-457	289	16	ȳ	ȳ	PROPN
ejpam-457	289	17	,	,	PUNCT
ejpam-457	289	18	z̄1	z̄1	PROPN
ejpam-457	289	19	,	,	PUNCT
ejpam-457	289	20	.	.	PUNCT
ejpam-457	289	21	.	.	PUNCT
ejpam-457	289	22	.	.	PUNCT
ejpam-457	290	1	,	,	PUNCT
ejpam-457	290	2	z̄p	z̄p	PROPN
ejpam-457	290	3	,	,	PUNCT
ejpam-457	290	4	λ	λ	X
ejpam-457	290	5	)	)	PUNCT
ejpam-457	290	6	is	be	AUX
ejpam-457	290	7	an	an	DET
ejpam-457	290	8	efficient	efficient	ADJ
ejpam-457	290	9	solution	solution	NOUN
ejpam-457	290	10	of	of	ADP
ejpam-457	290	11	(	(	PUNCT
ejpam-457	290	12	mix	mix	VERB
ejpam-457	290	13	d	d	NOUN
ejpam-457	290	14	)	)	PUNCT
ejpam-457	290	15	.	.	PUNCT
ejpam-457	291	1	proof	proof	NOUN
ejpam-457	291	2	.	.	PUNCT
ejpam-457	292	1	x̄	x̄	X
ejpam-457	292	2	∈	∈	PROPN
ejpam-457	292	3	x	x	X
ejpam-457	292	4	is	be	AUX
ejpam-457	292	5	an	an	DET
ejpam-457	292	6	optimal	optimal	ADJ
ejpam-457	292	7	solution	solution	NOUN
ejpam-457	292	8	of	of	ADP
ejpam-457	292	9	(	(	PUNCT
ejpam-457	292	10	pk	pk	NOUN
ejpam-457	292	11	(	(	PUNCT
ejpam-457	292	12	x̄	x̄	PROPN
ejpam-457	292	13	)	)	PUNCT
ejpam-457	292	14	)	)	PUNCT
ejpam-457	292	15	.	.	PUNCT
ejpam-457	293	1	this	this	PRON
ejpam-457	293	2	implies	imply	VERB
ejpam-457	293	3	that	that	SCONJ
ejpam-457	293	4	there	there	PRON
ejpam-457	293	5	exist	exist	VERB
ejpam-457	293	6	ξ̄	ξ̄	ADJ
ejpam-457	293	7	∈	∈	PROPN
ejpam-457	293	8	rp	rp	NOUN
ejpam-457	293	9	with	with	ADP
ejpam-457	293	10	ξ̄1	ξ̄1	NUM
ejpam-457	293	11	,	,	PUNCT
ejpam-457	293	12	.	.	PUNCT
ejpam-457	293	13	.	.	PUNCT
ejpam-457	294	1	.	.	PUNCT
ejpam-457	295	1	,	,	PUNCT
ejpam-457	295	2	ξ̄p	ξ̄p	PROPN
ejpam-457	295	3	,	,	PUNCT
ejpam-457	295	4	z	z	PROPN
ejpam-457	295	5	i(t	i(t	PROPN
ejpam-457	295	6	)	)	PUNCT
ejpam-457	295	7	∈	∈	PROPN
ejpam-457	295	8	rn	rn	PROPN
ejpam-457	295	9	,	,	PUNCT
ejpam-457	295	10	i	i	PRON
ejpam-457	295	11	=	=	PUNCT
ejpam-457	295	12	{	{	PUNCT
ejpam-457	295	13	1,2	1,2	NUM
ejpam-457	295	14	,	,	PUNCT
ejpam-457	295	15	.	.	PUNCT
ejpam-457	295	16	.	.	PUNCT
ejpam-457	295	17	.	.	PUNCT
ejpam-457	296	1	,	,	PUNCT
ejpam-457	296	2	p	p	X
ejpam-457	296	3	}	}	PUNCT
ejpam-457	296	4	and	and	CCONJ
ejpam-457	296	5	piecewise	piecewise	VERB
ejpam-457	296	6	smooth	smooth	ADJ
ejpam-457	296	7	ῡ	ῡ	PROPN
ejpam-457	296	8	∈	∈	PROPN
ejpam-457	296	9	rmsuch	rmsuch	NOUN
ejpam-457	297	1	that	that	SCONJ
ejpam-457	297	2	,	,	PUNCT
ejpam-457	297	3	the	the	DET
ejpam-457	297	4	following	follow	VERB
ejpam-457	297	5	optimality	optimality	NOUN
ejpam-457	297	6	conditions	condition	NOUN
ejpam-457	297	7	[	[	X
ejpam-457	297	8	3	3	X
ejpam-457	297	9	]	]	PUNCT
ejpam-457	297	10	hold	hold	VERB
ejpam-457	297	11	:	:	PUNCT
ejpam-457	297	12	ξ̄k	ξ̄k	NUM
ejpam-457	297	13	(	(	PUNCT
ejpam-457	297	14	f	f	NOUN
ejpam-457	297	15	k	k	NOUN
ejpam-457	297	16	x	x	PUNCT
ejpam-457	298	1	+	+	CCONJ
ejpam-457	298	2	bk(t)zk(t)−	bk(t)zk(t)−	PROPN
ejpam-457	298	3	d	d	PROPN
ejpam-457	298	4	f	f	PROPN
ejpam-457	298	5	k	k	PROPN
ejpam-457	298	6	ẋ	ẋ	PROPN
ejpam-457	299	1	+	+	CCONJ
ejpam-457	299	2	d2	d2	PROPN
ejpam-457	299	3	f	f	PROPN
ejpam-457	299	4	k	k	PROPN
ejpam-457	299	5	ẍ	ẍ	PROPN
ejpam-457	299	6	)	)	PUNCT
ejpam-457	300	1	+	+	CCONJ
ejpam-457	301	1	p	p	X
ejpam-457	301	2	∑	∑	PUNCT
ejpam-457	301	3	i=1	i=1	PROPN
ejpam-457	301	4	i	i	PRON
ejpam-457	301	5	6	6	NUM
ejpam-457	301	6	=	=	SYM
ejpam-457	301	7	k	k	X
ejpam-457	301	8	ξ̄i	ξ̄i	PROPN
ejpam-457	301	9	(	(	PUNCT
ejpam-457	301	10	f	f	NOUN
ejpam-457	301	11	i	i	NOUN
ejpam-457	301	12	x	x	PUNCT
ejpam-457	302	1	+	+	NUM
ejpam-457	302	2	bi(t)z	bi(t)z	X
ejpam-457	302	3	i(t)−	i(t)−	PROPN
ejpam-457	302	4	d	d	PROPN
ejpam-457	302	5	f	f	PROPN
ejpam-457	303	1	i	i	PRON
ejpam-457	303	2	ẋ	ẋ	PROPN
ejpam-457	304	1	+	+	CCONJ
ejpam-457	304	2	d2	d2	PROPN
ejpam-457	304	3	f	f	PROPN
ejpam-457	304	4	i	i	PROPN
ejpam-457	304	5	ẍ	ẍ	PUNCT
ejpam-457	304	6	)	)	PUNCT
ejpam-457	305	1	+	+	PUNCT
ejpam-457	305	2	ῡ(t)t	ῡ(t)t	X
ejpam-457	305	3	gx	gx	PROPN
ejpam-457	305	4	−	−	PROPN
ejpam-457	305	5	d(ῡ(t)t	d(ῡ(t)t	ADV
ejpam-457	305	6	g	g	PROPN
ejpam-457	305	7	ẋ	ẋ	PROPN
ejpam-457	305	8	)	)	PUNCT
ejpam-457	305	9	+	+	CCONJ
ejpam-457	305	10	d2(ῡ(t)t	d2(ῡ(t)t	VERB
ejpam-457	305	11	g	g	PROPN
ejpam-457	305	12	ẍ	ẍ	PROPN
ejpam-457	305	13	)	)	PUNCT
ejpam-457	305	14	=	=	SYM
ejpam-457	305	15	0	0	PUNCT
ejpam-457	305	16	(	(	PUNCT
ejpam-457	305	17	12	12	NUM
ejpam-457	305	18	)	)	PUNCT
ejpam-457	305	19	ῡ(t)t	ῡ(t)t	PROPN
ejpam-457	305	20	g(t	g(t	PROPN
ejpam-457	305	21	,	,	PUNCT
ejpam-457	305	22	x̄	x̄	NOUN
ejpam-457	305	23	,	,	PUNCT
ejpam-457	305	24	˙̄x	˙̄x	X
ejpam-457	305	25	,	,	PUNCT
ejpam-457	305	26	¨̄x)d	¨̄x)d	NOUN
ejpam-457	305	27	t	t	NOUN
ejpam-457	305	28	=	=	SYM
ejpam-457	305	29	0	0	NUM
ejpam-457	305	30	(	(	PUNCT
ejpam-457	305	31	13	13	NUM
ejpam-457	305	32	)	)	PUNCT
ejpam-457	305	33	(	(	PUNCT
ejpam-457	305	34	x̄(t)t	x̄(t)t	NOUN
ejpam-457	305	35	bi(t	bi(t	NOUN
ejpam-457	305	36	)	)	PUNCT
ejpam-457	305	37	x̄(t	x̄(t	PROPN
ejpam-457	305	38	)	)	PUNCT
ejpam-457	305	39	)	)	PUNCT
ejpam-457	305	40	1	1	NUM
ejpam-457	305	41	2	2	NUM
ejpam-457	305	42	=	=	SYM
ejpam-457	305	43	(	(	PUNCT
ejpam-457	305	44	x̄(t)t	x̄(t)t	PROPN
ejpam-457	305	45	bi(t)z̄	bi(t)z̄	PROPN
ejpam-457	305	46	i(t	i(t	PROPN
ejpam-457	305	47	)	)	PUNCT
ejpam-457	305	48	)	)	PUNCT
ejpam-457	305	49	,	,	PUNCT
ejpam-457	305	50	i	i	PRON
ejpam-457	305	51	=	=	NOUN
ejpam-457	305	52	1	1	NUM
ejpam-457	305	53	,	,	PUNCT
ejpam-457	305	54	.	.	PUNCT
ejpam-457	305	55	.	.	PUNCT
ejpam-457	305	56	.	.	PUNCT
ejpam-457	306	1	,	,	PUNCT
ejpam-457	306	2	p	p	X
ejpam-457	306	3	(	(	PUNCT
ejpam-457	306	4	14	14	NUM
ejpam-457	306	5	)	)	PUNCT
ejpam-457	306	6	(	(	PUNCT
ejpam-457	306	7	z̄(t)t	z̄(t)t	NOUN
ejpam-457	306	8	bi(t)z̄	bi(t)z̄	PROPN
ejpam-457	306	9	i(t	i(t	PROPN
ejpam-457	306	10	)	)	PUNCT
ejpam-457	306	11	)	)	PUNCT
ejpam-457	306	12	≦	≦	NUM
ejpam-457	306	13	1	1	NUM
ejpam-457	306	14	,	,	PUNCT
ejpam-457	306	15	t	t	PROPN
ejpam-457	306	16	∈	∈	PROPN
ejpam-457	307	1	i	i	PRON
ejpam-457	307	2	,	,	PUNCT
ejpam-457	307	3	i	i	NOUN
ejpam-457	307	4	=	=	NOUN
ejpam-457	307	5	1,2	1,2	NUM
ejpam-457	307	6	,	,	PUNCT
ejpam-457	307	7	.	.	PUNCT
ejpam-457	307	8	.	.	PUNCT
ejpam-457	307	9	.	.	PUNCT
ejpam-457	308	1	,	,	PUNCT
ejpam-457	308	2	p	p	X
ejpam-457	308	3	(	(	PUNCT
ejpam-457	308	4	15	15	NUM
ejpam-457	308	5	)	)	PUNCT
ejpam-457	308	6	ξ̄	ξ̄	ADJ
ejpam-457	308	7	>	>	X
ejpam-457	308	8	0	0	NUM
ejpam-457	308	9	,	,	PUNCT
ejpam-457	308	10	ῡ(t	ῡ(t	NOUN
ejpam-457	308	11	)	)	PUNCT
ejpam-457	308	12	≧	≧	X
ejpam-457	308	13	0	0	NUM
ejpam-457	308	14	,	,	PUNCT
ejpam-457	308	15	t	t	PROPN
ejpam-457	308	16	∈	∈	PROPN
ejpam-457	308	17	i	i	PRON
ejpam-457	308	18	(	(	PUNCT
ejpam-457	308	19	16	16	NUM
ejpam-457	308	20	)	)	PUNCT
ejpam-457	308	21	dividing	dividing	NOUN
ejpam-457	308	22	(	(	PUNCT
ejpam-457	308	23	12	12	NUM
ejpam-457	308	24	)	)	PUNCT
ejpam-457	308	25	,	,	PUNCT
ejpam-457	308	26	(	(	PUNCT
ejpam-457	308	27	13	13	NUM
ejpam-457	308	28	)	)	PUNCT
ejpam-457	308	29	and	and	CCONJ
ejpam-457	308	30	(	(	PUNCT
ejpam-457	308	31	16	16	NUM
ejpam-457	308	32	)	)	PUNCT
ejpam-457	308	33	by	by	ADP
ejpam-457	308	34	p	p	PROPN
ejpam-457	308	35	∑	∑	PROPN
ejpam-457	308	36	i=1	i=1	PROPN
ejpam-457	308	37	ξ̄i	ξ̄i	PROPN
ejpam-457	308	38	,	,	PUNCT
ejpam-457	308	39	and	and	CCONJ
ejpam-457	308	40	setting	set	VERB
ejpam-457	308	41	λ̄i	λ̄i	NOUN
ejpam-457	308	42	=	=	SYM
ejpam-457	308	43	ξ̄	ξ̄	ADJ
ejpam-457	308	44	p	p	X
ejpam-457	308	45	∑	∑	PROPN
ejpam-457	308	46	i=1	i=1	PROPN
ejpam-457	308	47	ξ̄i	ξ̄i	PROPN
ejpam-457	308	48	,	,	PUNCT
ejpam-457	308	49	i	i	PRON
ejpam-457	308	50	=	=	NOUN
ejpam-457	308	51	1	1	NUM
ejpam-457	308	52	,	,	PUNCT
ejpam-457	308	53	.	.	PUNCT
ejpam-457	308	54	.	.	PUNCT
ejpam-457	309	1	.	.	PUNCT
ejpam-457	310	1	,	,	PUNCT
ejpam-457	310	2	p	p	NOUN
ejpam-457	310	3	and	and	CCONJ
ejpam-457	310	4	ȳ(t	ȳ(t	NOUN
ejpam-457	310	5	)	)	PUNCT
ejpam-457	310	6	=	=	SYM
ejpam-457	310	7	ῡ(t	ῡ(t	NOUN
ejpam-457	310	8	)	)	PUNCT
ejpam-457	311	1	p	p	NOUN
ejpam-457	311	2	∑	∑	PUNCT
ejpam-457	311	3	i=1	i=1	PROPN
ejpam-457	311	4	ξ̄i	ξ̄i	PROPN
ejpam-457	311	5	,	,	PUNCT
ejpam-457	311	6	we	we	PRON
ejpam-457	311	7	have	have	VERB
ejpam-457	311	8	p	p	NOUN
ejpam-457	311	9	∑	∑	PROPN
ejpam-457	311	10	i=1	i=1	PROPN
ejpam-457	311	11	λ̄i	λ̄i	PROPN
ejpam-457	311	12	(	(	PUNCT
ejpam-457	311	13	f	f	NOUN
ejpam-457	311	14	i	i	PROPN
ejpam-457	311	15	x	x	PROPN
ejpam-457	312	1	+	+	CCONJ
ejpam-457	312	2	bi(t)z̄	bi(t)z̄	PROPN
ejpam-457	312	3	i(t)−	i(t)−	PROPN
ejpam-457	313	1	d	d	PROPN
ejpam-457	313	2	f	f	PROPN
ejpam-457	314	1	i	i	PRON
ejpam-457	314	2	ẋ	ẋ	PROPN
ejpam-457	315	1	+	+	CCONJ
ejpam-457	315	2	d2	d2	PROPN
ejpam-457	315	3	f	f	PROPN
ejpam-457	315	4	i	i	PROPN
ejpam-457	315	5	ẍ	ẍ	PUNCT
ejpam-457	315	6	)	)	PUNCT
ejpam-457	316	1	+	+	CCONJ
ejpam-457	316	2	ȳ(t)t	ȳ(t)t	NOUN
ejpam-457	316	3	gx	gx	PROPN
ejpam-457	316	4	−	−	PROPN
ejpam-457	317	1	d	d	PROPN
ejpam-457	317	2	(	(	PUNCT
ejpam-457	317	3	ȳ(t)t	ȳ(t)t	NOUN
ejpam-457	317	4	g	g	PROPN
ejpam-457	317	5	ẋ	ẋ	PROPN
ejpam-457	317	6	)	)	PUNCT
ejpam-457	318	1	+	+	CCONJ
ejpam-457	318	2	d2	d2	PROPN
ejpam-457	318	3	(	(	PUNCT
ejpam-457	318	4	ȳ(t)t	ȳ(t)t	PROPN
ejpam-457	318	5	g	g	PROPN
ejpam-457	318	6	ẍ	ẍ	PROPN
ejpam-457	318	7	)	)	PUNCT
ejpam-457	319	1	=	=	SYM
ejpam-457	319	2	0	0	NUM
ejpam-457	319	3	(	(	PUNCT
ejpam-457	319	4	17	17	NUM
ejpam-457	319	5	)	)	PUNCT
ejpam-457	319	6	ȳ(t)t	ȳ(t)t	PROPN
ejpam-457	319	7	g(t	g(t	PROPN
ejpam-457	319	8	,	,	PUNCT
ejpam-457	319	9	x̄	x̄	NOUN
ejpam-457	319	10	,	,	PUNCT
ejpam-457	319	11	˙̄x	˙̄x	X
ejpam-457	319	12	,	,	PUNCT
ejpam-457	319	13	¨̄x)d	¨̄x)d	NOUN
ejpam-457	319	14	t	t	NOUN
ejpam-457	319	15	=	=	SYM
ejpam-457	319	16	0	0	NUM
ejpam-457	319	17	(	(	PUNCT
ejpam-457	319	18	18	18	NUM
ejpam-457	319	19	)	)	PUNCT
ejpam-457	319	20	λ̄	λ̄	VERB
ejpam-457	319	21	>	>	X
ejpam-457	319	22	0	0	NUM
ejpam-457	319	23	,	,	PUNCT
ejpam-457	319	24	ȳ(t	ȳ(t	PROPN
ejpam-457	319	25	)	)	PUNCT
ejpam-457	319	26	≧	≧	X
ejpam-457	319	27	0	0	NUM
ejpam-457	319	28	,	,	PUNCT
ejpam-457	319	29	t	t	PROPN
ejpam-457	319	30	∈	∈	PROPN
ejpam-457	320	1	i	i	PRON
ejpam-457	320	2	(	(	PUNCT
ejpam-457	320	3	19	19	NUM
ejpam-457	320	4	)	)	PUNCT
ejpam-457	320	5	i.	i.	NOUN
ejpam-457	320	6	husain	husain	PROPN
ejpam-457	320	7	,	,	PUNCT
ejpam-457	320	8	r.	r.	PROPN
ejpam-457	320	9	mattoo	mattoo	PROPN
ejpam-457	320	10	/	/	SYM
ejpam-457	320	11	eur	eur	PROPN
ejpam-457	320	12	.	.	PUNCT
ejpam-457	321	1	j.	j.	PROPN
ejpam-457	321	2	pure	pure	PROPN
ejpam-457	321	3	appl	appl	PROPN
ejpam-457	321	4	.	.	PROPN
ejpam-457	321	5	math	math	PROPN
ejpam-457	321	6	,	,	PUNCT
ejpam-457	321	7	3	3	NUM
ejpam-457	321	8	(	(	PUNCT
ejpam-457	321	9	2010	2010	NUM
ejpam-457	321	10	)	)	PUNCT
ejpam-457	321	11	,	,	PUNCT
ejpam-457	321	12	81	81	NUM
ejpam-457	321	13	-	-	SYM
ejpam-457	321	14	97	97	NUM
ejpam-457	321	15	90	90	NUM
ejpam-457	321	16	the	the	DET
ejpam-457	321	17	equation	equation	NOUN
ejpam-457	321	18	(	(	PUNCT
ejpam-457	321	19	18	18	NUM
ejpam-457	321	20	)	)	PUNCT
ejpam-457	321	21	implies	imply	VERB
ejpam-457	321	22	∑	∑	PROPN
ejpam-457	321	23	j∈j	j∈j	NOUN
ejpam-457	321	24	◦	◦	NOUN
ejpam-457	321	25	y	y	PROPN
ejpam-457	321	26	j(t)g	j(t)g	PROPN
ejpam-457	321	27	j(t	j(t	PROPN
ejpam-457	321	28	,	,	PUNCT
ejpam-457	321	29	x	x	INTJ
ejpam-457	321	30	,	,	PUNCT
ejpam-457	321	31	ẋ	ẋ	PROPN
ejpam-457	321	32	,	,	PUNCT
ejpam-457	321	33	ẍ	ẍ	X
ejpam-457	321	34	)	)	PUNCT
ejpam-457	322	1	=	=	SYM
ejpam-457	322	2	0	0	NUM
ejpam-457	322	3	and	and	CCONJ
ejpam-457	322	4	∑	∑	ADP
ejpam-457	322	5	j∈jα	j∈jα	PROPN
ejpam-457	322	6	y	y	PROPN
ejpam-457	322	7	j(t)g	j(t)g	PROPN
ejpam-457	322	8	j(t	j(t	PROPN
ejpam-457	322	9	,	,	PUNCT
ejpam-457	322	10	x	x	INTJ
ejpam-457	322	11	,	,	PUNCT
ejpam-457	322	12	ẋ	ẋ	PROPN
ejpam-457	322	13	,	,	PUNCT
ejpam-457	322	14	ẍ	ẍ	X
ejpam-457	322	15	)	)	PUNCT
ejpam-457	323	1	=	=	SYM
ejpam-457	323	2	0	0	NUM
ejpam-457	323	3	,	,	PUNCT
ejpam-457	323	4	α	α	NOUN
ejpam-457	323	5	=	=	SYM
ejpam-457	323	6	1	1	NUM
ejpam-457	323	7	,	,	PUNCT
ejpam-457	323	8	.	.	PUNCT
ejpam-457	323	9	.	.	PUNCT
ejpam-457	323	10	.	.	PUNCT
ejpam-457	324	1	,	,	PUNCT
ejpam-457	324	2	r	r	NOUN
ejpam-457	324	3	(	(	PUNCT
ejpam-457	324	4	20	20	NUM
ejpam-457	324	5	)	)	PUNCT
ejpam-457	324	6	this	this	PRON
ejpam-457	324	7	implies	imply	VERB
ejpam-457	324	8	,	,	PUNCT
ejpam-457	324	9	∑	∑	PUNCT
ejpam-457	324	10	j∈jα	j∈jα	PROPN
ejpam-457	324	11	∫	∫	PROPN
ejpam-457	325	1	i	i	PRON
ejpam-457	325	2	y	y	PROPN
ejpam-457	325	3	j(t)g	j(t)g	PROPN
ejpam-457	325	4	j(t	j(t	PROPN
ejpam-457	325	5	,	,	PUNCT
ejpam-457	325	6	x	x	INTJ
ejpam-457	325	7	,	,	PUNCT
ejpam-457	325	8	ẋ	ẋ	PROPN
ejpam-457	325	9	,	,	PUNCT
ejpam-457	325	10	ẍ	ẍ	X
ejpam-457	325	11	)	)	PUNCT
ejpam-457	326	1	=	=	SYM
ejpam-457	326	2	0	0	NUM
ejpam-457	326	3	,	,	PUNCT
ejpam-457	326	4	α=	α=	NOUN
ejpam-457	326	5	1	1	NUM
ejpam-457	326	6	,	,	PUNCT
ejpam-457	326	7	.	.	PUNCT
ejpam-457	326	8	.	.	PUNCT
ejpam-457	326	9	.	.	PUNCT
ejpam-457	327	1	,	,	PUNCT
ejpam-457	327	2	r	r	NOUN
ejpam-457	327	3	(	(	PUNCT
ejpam-457	327	4	21	21	NUM
ejpam-457	327	5	)	)	PUNCT
ejpam-457	327	6	consequently	consequently	ADV
ejpam-457	327	7	(	(	PUNCT
ejpam-457	327	8	15	15	NUM
ejpam-457	327	9	)	)	PUNCT
ejpam-457	327	10	,	,	PUNCT
ejpam-457	327	11	(	(	PUNCT
ejpam-457	327	12	17	17	NUM
ejpam-457	327	13	)	)	PUNCT
ejpam-457	327	14	,	,	PUNCT
ejpam-457	327	15	(	(	PUNCT
ejpam-457	327	16	19	19	NUM
ejpam-457	327	17	)	)	PUNCT
ejpam-457	327	18	and	and	CCONJ
ejpam-457	327	19	(	(	PUNCT
ejpam-457	327	20	21	21	NUM
ejpam-457	327	21	)	)	PUNCT
ejpam-457	327	22	implies	imply	VERB
ejpam-457	327	23	that	that	SCONJ
ejpam-457	327	24	(	(	PUNCT
ejpam-457	327	25	x̄	x̄	NOUN
ejpam-457	327	26	,	,	PUNCT
ejpam-457	327	27	ȳ	ȳ	PROPN
ejpam-457	327	28	,	,	PUNCT
ejpam-457	327	29	z̄1	z̄1	PROPN
ejpam-457	327	30	,	,	PUNCT
ejpam-457	327	31	.	.	PUNCT
ejpam-457	327	32	.	.	PUNCT
ejpam-457	328	1	.	.	PUNCT
ejpam-457	329	1	,	,	PUNCT
ejpam-457	329	2	z̄p	z̄p	PROPN
ejpam-457	329	3	,	,	PUNCT
ejpam-457	329	4	λ̄	λ̄	PRON
ejpam-457	329	5	)	)	PUNCT
ejpam-457	329	6	is	be	AUX
ejpam-457	329	7	feasible	feasible	ADJ
ejpam-457	329	8	for	for	ADP
ejpam-457	329	9	(	(	PUNCT
ejpam-457	329	10	mix	mix	VERB
ejpam-457	329	11	d	d	NOUN
ejpam-457	329	12	)	)	PUNCT
ejpam-457	329	13	.	.	PUNCT
ejpam-457	330	1	∫	∫	PROPN
ejpam-457	331	1	i	i	PRON
ejpam-457	331	2	�	�	PROPN
ejpam-457	331	3	f	f	PROPN
ejpam-457	331	4	i(t	i(t	PROPN
ejpam-457	331	5	,	,	PUNCT
ejpam-457	331	6	x̄	x̄	NOUN
ejpam-457	331	7	,	,	PUNCT
ejpam-457	331	8	˙̄x	˙̄x	X
ejpam-457	331	9	,	,	PUNCT
ejpam-457	331	10	¨̄x	¨̄x	X
ejpam-457	331	11	)	)	PUNCT
ejpam-457	332	1	+	+	CCONJ
ejpam-457	332	2	(	(	PUNCT
ejpam-457	332	3	x̄(t)t	x̄(t)t	NOUN
ejpam-457	332	4	bi(t	bi(t	NOUN
ejpam-457	332	5	)	)	PUNCT
ejpam-457	332	6	x̄(t	x̄(t	PROPN
ejpam-457	332	7	)	)	PUNCT
ejpam-457	332	8	)	)	PUNCT
ejpam-457	332	9	1	1	NUM
ejpam-457	332	10	2	2	NUM
ejpam-457	332	11	+	+	NUM
ejpam-457	332	12	∑	∑	NOUN
ejpam-457	332	13	j∈j	j∈j	NOUN
ejpam-457	332	14	◦	◦	NOUN
ejpam-457	332	15	y	y	PROPN
ejpam-457	332	16	j(t)g	j(t)g	PROPN
ejpam-457	332	17	j(t	j(t	PROPN
ejpam-457	332	18	,	,	PUNCT
ejpam-457	332	19	x̄	x̄	NOUN
ejpam-457	332	20	,	,	PUNCT
ejpam-457	332	21	˙̄x	˙̄x	X
ejpam-457	332	22	,	,	PUNCT
ejpam-457	332	23	¨̄x	¨̄x	ADJ
ejpam-457	332	24	)	)	PUNCT
ejpam-457	332	25	�	�	PROPN
ejpam-457	333	1	d	d	PROPN
ejpam-457	333	2	t	t	PROPN
ejpam-457	333	3	=	=	SYM
ejpam-457	333	4	∫	∫	PROPN
ejpam-457	334	1	i	i	PRON
ejpam-457	334	2	(	(	PUNCT
ejpam-457	334	3	f	f	PROPN
ejpam-457	334	4	i(t	i(t	PROPN
ejpam-457	334	5	,	,	PUNCT
ejpam-457	334	6	x̄	x̄	NOUN
ejpam-457	334	7	,	,	PUNCT
ejpam-457	334	8	˙̄x	˙̄x	X
ejpam-457	334	9	,	,	PUNCT
ejpam-457	334	10	¨̄x)+	¨̄x)+	PROPN
ejpam-457	334	11	(	(	PUNCT
ejpam-457	334	12	x̄(t)t	x̄(t)t	NOUN
ejpam-457	334	13	bi(t)z̄	bi(t)z̄	PROPN
ejpam-457	334	14	i(t)))d	i(t)))d	PROPN
ejpam-457	334	15	t	t	PROPN
ejpam-457	334	16	,	,	PUNCT
ejpam-457	334	17	i	i	NOUN
ejpam-457	334	18	=	=	NOUN
ejpam-457	334	19	1,2	1,2	NUM
ejpam-457	334	20	,	,	PUNCT
ejpam-457	334	21	.	.	PUNCT
ejpam-457	334	22	.	.	PUNCT
ejpam-457	334	23	.	.	PUNCT
ejpam-457	335	1	,	,	PUNCT
ejpam-457	335	2	p	p	X
ejpam-457	335	3	this	this	PRON
ejpam-457	335	4	in	in	ADP
ejpam-457	335	5	view	view	NOUN
ejpam-457	335	6	of	of	ADP
ejpam-457	335	7	theorem	theorem	NOUN
ejpam-457	335	8	1	1	NUM
ejpam-457	335	9	,	,	PUNCT
ejpam-457	335	10	the	the	DET
ejpam-457	335	11	efficiency	efficiency	NOUN
ejpam-457	335	12	of	of	ADP
ejpam-457	335	13	(	(	PUNCT
ejpam-457	335	14	x̄	x̄	NOUN
ejpam-457	335	15	,	,	PUNCT
ejpam-457	335	16	ȳ	ȳ	PROPN
ejpam-457	335	17	,	,	PUNCT
ejpam-457	335	18	z̄1	z̄1	PROPN
ejpam-457	335	19	,	,	PUNCT
ejpam-457	335	20	.	.	PUNCT
ejpam-457	335	21	.	.	PUNCT
ejpam-457	335	22	.	.	PUNCT
ejpam-457	336	1	,	,	PUNCT
ejpam-457	336	2	z̄p	z̄p	PROPN
ejpam-457	336	3	,	,	PUNCT
ejpam-457	336	4	λ̄	λ̄	PRON
ejpam-457	336	5	)	)	PUNCT
ejpam-457	336	6	follows	follow	VERB
ejpam-457	336	7	.	.	PUNCT
ejpam-457	337	1	as	as	ADP
ejpam-457	337	2	in	in	ADP
ejpam-457	337	3	[	[	X
ejpam-457	337	4	15	15	NUM
ejpam-457	337	5	]	]	PUNCT
ejpam-457	337	6	,	,	PUNCT
ejpam-457	337	7	by	by	ADP
ejpam-457	337	8	employing	employ	VERB
ejpam-457	337	9	chain	chain	NOUN
ejpam-457	337	10	rule	rule	NOUN
ejpam-457	337	11	in	in	ADP
ejpam-457	337	12	calculus	calculus	NOUN
ejpam-457	337	13	,	,	PUNCT
ejpam-457	337	14	it	it	PRON
ejpam-457	337	15	can	can	AUX
ejpam-457	337	16	be	be	AUX
ejpam-457	337	17	easily	easily	ADV
ejpam-457	337	18	seen	see	VERB
ejpam-457	337	19	that	that	SCONJ
ejpam-457	337	20	the	the	DET
ejpam-457	337	21	expression	expression	NOUN
ejpam-457	337	22	p	p	NOUN
ejpam-457	337	23	∑	∑	PROPN
ejpam-457	337	24	i=1	i=1	PROPN
ejpam-457	337	25	λi	λi	PROPN
ejpam-457	337	26	(	(	PUNCT
ejpam-457	337	27	f	f	NOUN
ejpam-457	337	28	i	i	NOUN
ejpam-457	337	29	x	x	X
ejpam-457	337	30	(	(	PUNCT
ejpam-457	337	31	t	t	PROPN
ejpam-457	337	32	,	,	PUNCT
ejpam-457	337	33	u	u	NOUN
ejpam-457	337	34	,	,	PUNCT
ejpam-457	337	35	u̇	u̇	PROPN
ejpam-457	337	36	,	,	PUNCT
ejpam-457	337	37	ü)d	ü)d	PROPN
ejpam-457	337	38	t	t	NOUN
ejpam-457	337	39	+	+	CCONJ
ejpam-457	337	40	bi(t)z	bi(t)z	PROPN
ejpam-457	337	41	i(t	i(t	NOUN
ejpam-457	337	42	)	)	PUNCT
ejpam-457	338	1	+	+	NUM
ejpam-457	338	2	y(t)t	y(t)t	NOUN
ejpam-457	338	3	gx(t	gx(t	NOUN
ejpam-457	338	4	,	,	PUNCT
ejpam-457	338	5	u	u	NOUN
ejpam-457	338	6	,	,	PUNCT
ejpam-457	338	7	u̇	u̇	PROPN
ejpam-457	338	8	,	,	PUNCT
ejpam-457	338	9	ü	ü	NUM
ejpam-457	338	10	)	)	PUNCT
ejpam-457	338	11	)	)	PUNCT
ejpam-457	339	1	−d(λt	−d(λt	NOUN
ejpam-457	339	2	f	f	X
ejpam-457	339	3	ẋ	ẋ	PROPN
ejpam-457	340	1	+	+	NUM
ejpam-457	340	2	y(t)t	y(t)t	PROPN
ejpam-457	340	3	g	g	PROPN
ejpam-457	340	4	ẋ	ẋ	PROPN
ejpam-457	340	5	)	)	PUNCT
ejpam-457	341	1	+	+	CCONJ
ejpam-457	341	2	d2(λt	d2(λt	PROPN
ejpam-457	341	3	f	f	X
ejpam-457	341	4	ẍ	ẍ	PUNCT
ejpam-457	342	1	+	+	CCONJ
ejpam-457	342	2	y(t)t	y(t)t	PROPN
ejpam-457	342	3	g	g	PROPN
ejpam-457	342	4	ẍ	ẍ	PROPN
ejpam-457	342	5	)	)	PUNCT
ejpam-457	342	6	=	=	SYM
ejpam-457	342	7	0	0	NUM
ejpam-457	342	8	,	,	PUNCT
ejpam-457	342	9	,	,	PUNCT
ejpam-457	342	10	t	t	PROPN
ejpam-457	342	11	∈	∈	PROPN
ejpam-457	342	12	i	i	PRON
ejpam-457	342	13	may	may	AUX
ejpam-457	342	14	be	be	AUX
ejpam-457	342	15	regarded	regard	VERB
ejpam-457	342	16	as	as	ADP
ejpam-457	342	17	a	a	DET
ejpam-457	342	18	function	function	NOUN
ejpam-457	342	19	θ	θ	PROPN
ejpam-457	342	20	of	of	ADP
ejpam-457	342	21	variables	variable	NOUN
ejpam-457	342	22	t	t	PROPN
ejpam-457	342	23	,	,	PUNCT
ejpam-457	342	24	x	x	X
ejpam-457	342	25	,	,	PUNCT
ejpam-457	342	26	ẋ	ẋ	PROPN
ejpam-457	342	27	,	,	PUNCT
ejpam-457	342	28	ẍ	ẍ	PROPN
ejpam-457	342	29	,	,	PUNCT
ejpam-457	342	30	...	...	PUNCT
ejpam-457	343	1	x	x	X
ejpam-457	343	2	,	,	PUNCT
ejpam-457	343	3	y	y	PROPN
ejpam-457	343	4	,	,	PUNCT
ejpam-457	343	5	ẏ	ẏ	PROPN
ejpam-457	343	6	,	,	PUNCT
ejpam-457	343	7	ÿ	ÿ	PROPN
ejpam-457	343	8	and	and	CCONJ
ejpam-457	343	9	λ	λ	PROPN
ejpam-457	343	10	,	,	PUNCT
ejpam-457	343	11	where	where	SCONJ
ejpam-457	343	12	...	...	PUNCT
ejpam-457	343	13	x	x	PUNCT
ejpam-457	343	14	=	=	PUNCT
ejpam-457	343	15	d3	d3	X
ejpam-457	343	16	x	x	X
ejpam-457	343	17	and	and	CCONJ
ejpam-457	343	18	ÿ	ÿ	PROPN
ejpam-457	343	19	=	=	PROPN
ejpam-457	343	20	d2	d2	PROPN
ejpam-457	343	21	y.	y.	PROPN
ejpam-457	343	22	that	that	PRON
ejpam-457	343	23	is	be	AUX
ejpam-457	343	24	,	,	PUNCT
ejpam-457	343	25	we	we	PRON
ejpam-457	343	26	can	can	AUX
ejpam-457	343	27	write	write	VERB
ejpam-457	343	28	θ(t	θ(t	PROPN
ejpam-457	343	29	,	,	PUNCT
ejpam-457	343	30	x	x	SYM
ejpam-457	343	31	,	,	PUNCT
ejpam-457	343	32	ẋ	ẋ	PROPN
ejpam-457	343	33	,	,	PUNCT
ejpam-457	343	34	ẍ	ẍ	PROPN
ejpam-457	343	35	,	,	PUNCT
ejpam-457	343	36	...	...	PUNCT
ejpam-457	344	1	x	x	X
ejpam-457	344	2	,	,	PUNCT
ejpam-457	344	3	y	y	PROPN
ejpam-457	344	4	,	,	PUNCT
ejpam-457	344	5	ẏ	ẏ	PROPN
ejpam-457	344	6	,	,	PUNCT
ejpam-457	344	7	ÿ	ÿ	PROPN
ejpam-457	344	8	,	,	PUNCT
ejpam-457	344	9	λ	λ	PROPN
ejpam-457	344	10	)	)	PUNCT
ejpam-457	344	11	=	=	PUNCT
ejpam-457	345	1	p	p	NOUN
ejpam-457	345	2	∑	∑	PUNCT
ejpam-457	345	3	i=1	i=1	PROPN
ejpam-457	345	4	λi	λi	PROPN
ejpam-457	345	5	(	(	PUNCT
ejpam-457	345	6	f	f	NOUN
ejpam-457	345	7	i	i	NOUN
ejpam-457	345	8	x	x	X
ejpam-457	345	9	(	(	PUNCT
ejpam-457	345	10	t	t	PROPN
ejpam-457	345	11	,	,	PUNCT
ejpam-457	345	12	u	u	NOUN
ejpam-457	345	13	,	,	PUNCT
ejpam-457	345	14	u̇	u̇	PROPN
ejpam-457	345	15	,	,	PUNCT
ejpam-457	345	16	ü)d	ü)d	PROPN
ejpam-457	345	17	t	t	NOUN
ejpam-457	345	18	+	+	CCONJ
ejpam-457	345	19	bi(t)z	bi(t)z	PROPN
ejpam-457	345	20	i(t	i(t	NOUN
ejpam-457	345	21	)	)	PUNCT
ejpam-457	346	1	+	+	NUM
ejpam-457	346	2	y(t)t	y(t)t	NOUN
ejpam-457	346	3	gx(t	gx(t	NOUN
ejpam-457	346	4	,	,	PUNCT
ejpam-457	346	5	u	u	NOUN
ejpam-457	346	6	,	,	PUNCT
ejpam-457	346	7	u̇	u̇	PROPN
ejpam-457	346	8	,	,	PUNCT
ejpam-457	346	9	ü	ü	NUM
ejpam-457	346	10	)	)	PUNCT
ejpam-457	346	11	)	)	PUNCT
ejpam-457	347	1	−d(λt	−d(λt	NOUN
ejpam-457	347	2	f	f	X
ejpam-457	347	3	ẋ	ẋ	PROPN
ejpam-457	348	1	+	+	NUM
ejpam-457	348	2	y(t)t	y(t)t	PROPN
ejpam-457	348	3	g	g	PROPN
ejpam-457	348	4	ẋ	ẋ	PROPN
ejpam-457	348	5	)	)	PUNCT
ejpam-457	349	1	+	+	CCONJ
ejpam-457	349	2	d2(λt	d2(λt	PROPN
ejpam-457	349	3	f	f	X
ejpam-457	349	4	ẍ	ẍ	PUNCT
ejpam-457	350	1	+	+	CCONJ
ejpam-457	350	2	y(t)t	y(t)t	PROPN
ejpam-457	350	3	g	g	PROPN
ejpam-457	350	4	ẍ	ẍ	PROPN
ejpam-457	350	5	)	)	PUNCT
ejpam-457	351	1	=	=	PUNCT
ejpam-457	351	2	0	0	NUM
ejpam-457	352	1	in	in	ADP
ejpam-457	352	2	order	order	NOUN
ejpam-457	352	3	to	to	PART
ejpam-457	352	4	prove	prove	VERB
ejpam-457	352	5	converse	converse	NOUN
ejpam-457	352	6	duality	duality	NOUN
ejpam-457	352	7	between	between	ADP
ejpam-457	352	8	(	(	PUNCT
ejpam-457	352	9	vp	vp	NOUN
ejpam-457	352	10	)	)	PUNCT
ejpam-457	352	11	and	and	CCONJ
ejpam-457	352	12	(	(	PUNCT
ejpam-457	352	13	mix	mix	VERB
ejpam-457	352	14	d	d	NOUN
ejpam-457	352	15	)	)	PUNCT
ejpam-457	352	16	,	,	PUNCT
ejpam-457	352	17	the	the	DET
ejpam-457	352	18	space	space	NOUN
ejpam-457	352	19	x	x	PUNCT
ejpam-457	352	20	is	be	AUX
ejpam-457	352	21	now	now	ADV
ejpam-457	352	22	replaced	replace	VERB
ejpam-457	352	23	by	by	ADP
ejpam-457	352	24	a	a	DET
ejpam-457	352	25	smaller	small	ADJ
ejpam-457	352	26	space	space	NOUN
ejpam-457	352	27	x2	x2	NOUN
ejpam-457	352	28	of	of	ADP
ejpam-457	352	29	piecewise	piecewise	PROPN
ejpam-457	352	30	smooth	smooth	ADJ
ejpam-457	352	31	thrice	thrice	PROPN
ejpam-457	352	32	differentiable	differentiable	ADJ
ejpam-457	352	33	function	function	NOUN
ejpam-457	352	34	x	x	X
ejpam-457	352	35	:	:	PUNCT
ejpam-457	353	1	i	i	PRON
ejpam-457	353	2	→	→	SYM
ejpam-457	353	3	rn	rn	PROPN
ejpam-457	353	4	with	with	ADP
ejpam-457	353	5	the	the	DET
ejpam-457	353	6	norm	norm	NOUN
ejpam-457	353	7	‖x‖∞+	‖x‖∞+	X
ejpam-457	353	8	‖dx‖∞+	‖dx‖∞+	PUNCT
ejpam-457	353	9	‖d	‖d	ADJ
ejpam-457	353	10	2	2	NUM
ejpam-457	353	11	x‖∞+	x‖∞+	NOUN
ejpam-457	353	12	‖d	‖d	ADJ
ejpam-457	353	13	3	3	NUM
ejpam-457	353	14	x‖∞.	x‖∞.	PROPN
ejpam-457	353	15	the	the	DET
ejpam-457	353	16	problem	problem	NOUN
ejpam-457	353	17	(	(	PUNCT
ejpam-457	353	18	mix	mix	VERB
ejpam-457	353	19	d	d	NOUN
ejpam-457	353	20	)	)	PUNCT
ejpam-457	353	21	may	may	AUX
ejpam-457	353	22	now	now	ADV
ejpam-457	353	23	be	be	AUX
ejpam-457	353	24	briefly	briefly	ADV
ejpam-457	353	25	written	write	VERB
ejpam-457	353	26	as	as	ADP
ejpam-457	353	27	,	,	PUNCT
ejpam-457	353	28	minimize	minimize	VERB
ejpam-457	353	29	�	�	PROPN
ejpam-457	353	30	−	−	PROPN
ejpam-457	354	1	∫	∫	NOUN
ejpam-457	355	1	i	i	PRON
ejpam-457	355	2	(	(	PUNCT
ejpam-457	355	3	f	f	PROPN
ejpam-457	355	4	1(t	1(t	NUM
ejpam-457	355	5	,	,	PUNCT
ejpam-457	355	6	u	u	NOUN
ejpam-457	355	7	,	,	PUNCT
ejpam-457	355	8	u̇	u̇	PROPN
ejpam-457	355	9	,	,	PUNCT
ejpam-457	355	10	ü	ü	PRON
ejpam-457	355	11	)	)	PUNCT
ejpam-457	356	1	+	+	CCONJ
ejpam-457	356	2	u(t)t	u(t)t	X
ejpam-457	356	3	b1(t)z1(t	b1(t)z1(t	X
ejpam-457	356	4	)	)	PUNCT
ejpam-457	357	1	+	+	CCONJ
ejpam-457	357	2	∑	∑	PUNCT
ejpam-457	357	3	j∈j	j∈j	NOUN
ejpam-457	357	4	◦	◦	NOUN
ejpam-457	357	5	y	y	PROPN
ejpam-457	357	6	j(t)g	j(t)g	PROPN
ejpam-457	357	7	j(t	j(t	PROPN
ejpam-457	357	8	,	,	PUNCT
ejpam-457	357	9	u	u	NOUN
ejpam-457	357	10	,	,	PUNCT
ejpam-457	357	11	u̇	u̇	PROPN
ejpam-457	357	12	,	,	PUNCT
ejpam-457	357	13	ü	ü	NOUN
ejpam-457	357	14	)	)	PUNCT
ejpam-457	357	15	�	�	PROPN
ejpam-457	357	16	d	d	PROPN
ejpam-457	357	17	t	t	PROPN
ejpam-457	357	18	,	,	PUNCT
ejpam-457	357	19	.	.	PUNCT
ejpam-457	357	20	.	.	PUNCT
ejpam-457	357	21	.	.	PUNCT
ejpam-457	358	1	,	,	PUNCT
ejpam-457	358	2	∫	∫	PROPN
ejpam-457	359	1	i	i	PRON
ejpam-457	359	2	−	−	PROPN
ejpam-457	359	3	(	(	PUNCT
ejpam-457	359	4	f	f	PROPN
ejpam-457	359	5	p(t	p(t	PROPN
ejpam-457	359	6	,	,	PUNCT
ejpam-457	359	7	u	u	NOUN
ejpam-457	359	8	,	,	PUNCT
ejpam-457	359	9	u̇	u̇	PROPN
ejpam-457	359	10	,	,	PUNCT
ejpam-457	359	11	ü	ü	PRON
ejpam-457	359	12	)	)	PUNCT
ejpam-457	360	1	+	+	CCONJ
ejpam-457	360	2	(	(	PUNCT
ejpam-457	360	3	u(t)t	u(t)t	NOUN
ejpam-457	360	4	bp(t)zp(t	bp(t)zp(t	NOUN
ejpam-457	360	5	)	)	PUNCT
ejpam-457	360	6	)	)	PUNCT
ejpam-457	361	1	+	+	CCONJ
ejpam-457	361	2	∑	∑	PUNCT
ejpam-457	361	3	j∈j	j∈j	NOUN
ejpam-457	361	4	◦	◦	NOUN
ejpam-457	361	5	y	y	PROPN
ejpam-457	361	6	j(t)g	j(t)g	PROPN
ejpam-457	361	7	j(t	j(t	PROPN
ejpam-457	361	8	,	,	PUNCT
ejpam-457	361	9	u	u	NOUN
ejpam-457	361	10	,	,	PUNCT
ejpam-457	361	11	u̇	u̇	PROPN
ejpam-457	361	12	,	,	PUNCT
ejpam-457	361	13	ü	ü	NOUN
ejpam-457	361	14	)	)	PUNCT
ejpam-457	361	15	�	�	PROPN
ejpam-457	361	16	d	d	PROPN
ejpam-457	361	17	t	t	PROPN
ejpam-457	361	18	�	�	PROPN
ejpam-457	361	19	subject	subject	ADJ
ejpam-457	361	20	to	to	ADP
ejpam-457	361	21	i.	i.	PROPN
ejpam-457	361	22	husain	husain	PROPN
ejpam-457	361	23	,	,	PUNCT
ejpam-457	361	24	r.	r.	PROPN
ejpam-457	361	25	mattoo	mattoo	PROPN
ejpam-457	361	26	/	/	SYM
ejpam-457	361	27	eur	eur	PROPN
ejpam-457	361	28	.	.	PUNCT
ejpam-457	362	1	j.	j.	PROPN
ejpam-457	362	2	pure	pure	PROPN
ejpam-457	362	3	appl	appl	PROPN
ejpam-457	362	4	.	.	PROPN
ejpam-457	362	5	math	math	PROPN
ejpam-457	362	6	,	,	PUNCT
ejpam-457	362	7	3	3	NUM
ejpam-457	362	8	(	(	PUNCT
ejpam-457	362	9	2010	2010	NUM
ejpam-457	362	10	)	)	PUNCT
ejpam-457	362	11	,	,	PUNCT
ejpam-457	362	12	81	81	NUM
ejpam-457	362	13	-	-	SYM
ejpam-457	362	14	97	97	NUM
ejpam-457	362	15	91	91	NUM
ejpam-457	362	16	u(a	u(a	NOUN
ejpam-457	362	17	)	)	PUNCT
ejpam-457	362	18	=	=	SYM
ejpam-457	362	19	0=	0=	PUNCT
ejpam-457	363	1	u(b	u(b	X
ejpam-457	363	2	)	)	PUNCT
ejpam-457	363	3	u̇(a	u̇(a	PROPN
ejpam-457	363	4	)	)	PUNCT
ejpam-457	363	5	=	=	SYM
ejpam-457	363	6	0=	0=	NOUN
ejpam-457	364	1	u̇(b	u̇(b	NOUN
ejpam-457	364	2	)	)	PUNCT
ejpam-457	364	3	θ(t	θ(t	PROPN
ejpam-457	364	4	,	,	PUNCT
ejpam-457	364	5	x	x	X
ejpam-457	364	6	,	,	PUNCT
ejpam-457	364	7	ẋ	ẋ	PROPN
ejpam-457	364	8	,	,	PUNCT
ejpam-457	364	9	ẍ	ẍ	PROPN
ejpam-457	364	10	,	,	PUNCT
ejpam-457	364	11	...	...	PUNCT
ejpam-457	365	1	x	x	X
ejpam-457	365	2	,	,	PUNCT
ejpam-457	365	3	y	y	PROPN
ejpam-457	365	4	,	,	PUNCT
ejpam-457	365	5	ẏ	ẏ	PROPN
ejpam-457	365	6	,	,	PUNCT
ejpam-457	365	7	ÿ	ÿ	PROPN
ejpam-457	365	8	,	,	PUNCT
ejpam-457	365	9	λ	λ	NOUN
ejpam-457	365	10	)	)	PUNCT
ejpam-457	365	11	=	=	SYM
ejpam-457	365	12	0	0	NUM
ejpam-457	365	13	,	,	PUNCT
ejpam-457	365	14	t	t	PROPN
ejpam-457	365	15	∈	∈	PROPN
ejpam-457	366	1	i	i	PRON
ejpam-457	366	2	∑	∑	PUNCT
ejpam-457	366	3	j∈jα	j∈jα	PROPN
ejpam-457	366	4	∫	∫	PROPN
ejpam-457	367	1	i	i	PRON
ejpam-457	367	2	y	y	PROPN
ejpam-457	367	3	j(t)g	j(t)g	PROPN
ejpam-457	367	4	j(t	j(t	PROPN
ejpam-457	367	5	,	,	PUNCT
ejpam-457	367	6	u	u	NOUN
ejpam-457	367	7	,	,	PUNCT
ejpam-457	367	8	u̇	u̇	PROPN
ejpam-457	367	9	,	,	PUNCT
ejpam-457	367	10	ü)d	ü)d	PROPN
ejpam-457	367	11	t	t	PROPN
ejpam-457	367	12	≧	≧	X
ejpam-457	367	13	0	0	NUM
ejpam-457	367	14	,	,	PUNCT
ejpam-457	367	15	α=	α=	NOUN
ejpam-457	367	16	1,2	1,2	NUM
ejpam-457	367	17	,	,	PUNCT
ejpam-457	367	18	.	.	PUNCT
ejpam-457	367	19	.	.	PUNCT
ejpam-457	368	1	.	.	PUNCT
ejpam-457	369	1	,	,	PUNCT
ejpam-457	369	2	r	r	NOUN
ejpam-457	369	3	z̄	z̄	PROPN
ejpam-457	369	4	i(t)t	i(t)t	PROPN
ejpam-457	369	5	bi(t)z̄	bi(t)z̄	PROPN
ejpam-457	369	6	i(t	i(t	PROPN
ejpam-457	369	7	)	)	PUNCT
ejpam-457	369	8	≦	≦	NUM
ejpam-457	369	9	1	1	NUM
ejpam-457	369	10	,	,	PUNCT
ejpam-457	369	11	t	t	PROPN
ejpam-457	369	12	∈	∈	PROPN
ejpam-457	370	1	i	i	PRON
ejpam-457	370	2	,	,	PUNCT
ejpam-457	370	3	i	i	PRON
ejpam-457	370	4	∈	∈	VERB
ejpam-457	370	5	p	p	ADJ
ejpam-457	370	6	y(t	y(t	PROPN
ejpam-457	370	7	)	)	PUNCT
ejpam-457	370	8	≧	≧	X
ejpam-457	371	1	0	0	NUM
ejpam-457	371	2	,	,	PUNCT
ejpam-457	371	3	t	t	PROPN
ejpam-457	371	4	∈	∈	PROPN
ejpam-457	372	1	i	i	PRON
ejpam-457	372	2	λ	λ	X
ejpam-457	372	3	>	>	X
ejpam-457	372	4	0	0	PROPN
ejpam-457	372	5	,	,	PUNCT
ejpam-457	372	6	λt	λt	ADP
ejpam-457	372	7	e	e	NOUN
ejpam-457	372	8	=	=	NOUN
ejpam-457	372	9	1	1	NUM
ejpam-457	372	10	where	where	SCONJ
ejpam-457	372	11	θ(t	θ(t	VERB
ejpam-457	372	12	,	,	PUNCT
ejpam-457	372	13	x	x	X
ejpam-457	372	14	,	,	PUNCT
ejpam-457	372	15	ẋ	ẋ	PROPN
ejpam-457	372	16	,	,	PUNCT
ejpam-457	372	17	ẍ	ẍ	PROPN
ejpam-457	372	18	,	,	PUNCT
ejpam-457	372	19	...	...	PUNCT
ejpam-457	373	1	x	x	X
ejpam-457	373	2	,	,	PUNCT
ejpam-457	373	3	y	y	PROPN
ejpam-457	373	4	,	,	PUNCT
ejpam-457	373	5	ẏ	ẏ	PROPN
ejpam-457	373	6	,	,	PUNCT
ejpam-457	373	7	ÿ	ÿ	PROPN
ejpam-457	373	8	,	,	PUNCT
ejpam-457	373	9	λ	λ	PROPN
ejpam-457	373	10	)	)	PUNCT
ejpam-457	373	11	=	=	PUNCT
ejpam-457	374	1	p	p	NOUN
ejpam-457	374	2	∑	∑	PUNCT
ejpam-457	374	3	i=1	i=1	PROPN
ejpam-457	374	4	λi	λi	PROPN
ejpam-457	374	5	(	(	PUNCT
ejpam-457	374	6	f	f	NOUN
ejpam-457	374	7	i	i	NOUN
ejpam-457	374	8	x	x	X
ejpam-457	374	9	(	(	PUNCT
ejpam-457	374	10	t	t	PROPN
ejpam-457	374	11	,	,	PUNCT
ejpam-457	374	12	u	u	NOUN
ejpam-457	374	13	,	,	PUNCT
ejpam-457	374	14	u̇	u̇	PROPN
ejpam-457	374	15	,	,	PUNCT
ejpam-457	374	16	ü	ü	PRON
ejpam-457	374	17	)	)	PUNCT
ejpam-457	375	1	+	+	NUM
ejpam-457	375	2	bi(t)z	bi(t)z	NOUN
ejpam-457	375	3	i(t	i(t	NOUN
ejpam-457	375	4	)	)	PUNCT
ejpam-457	375	5	+	+	NUM
ejpam-457	375	6	y(t)t	y(t)t	NOUN
ejpam-457	375	7	gx(t	gx(t	NOUN
ejpam-457	375	8	,	,	PUNCT
ejpam-457	375	9	u	u	NOUN
ejpam-457	375	10	,	,	PUNCT
ejpam-457	375	11	u̇	u̇	PROPN
ejpam-457	375	12	,	,	PUNCT
ejpam-457	375	13	ü	ü	NUM
ejpam-457	375	14	)	)	PUNCT
ejpam-457	375	15	)	)	PUNCT
ejpam-457	375	16	−d(λt	−d(λt	NOUN
ejpam-457	375	17	f	f	X
ejpam-457	375	18	ẋ	ẋ	PROPN
ejpam-457	376	1	+	+	NUM
ejpam-457	376	2	y(t)t	y(t)t	PROPN
ejpam-457	376	3	g	g	PROPN
ejpam-457	376	4	ẋ	ẋ	PROPN
ejpam-457	376	5	)	)	PUNCT
ejpam-457	377	1	+	+	CCONJ
ejpam-457	377	2	d2(λt	d2(λt	PROPN
ejpam-457	377	3	f	f	X
ejpam-457	377	4	ẍ	ẍ	PUNCT
ejpam-457	378	1	+	+	CCONJ
ejpam-457	378	2	y(t)t	y(t)t	PROPN
ejpam-457	378	3	g	g	PROPN
ejpam-457	378	4	ẍ	ẍ	PROPN
ejpam-457	378	5	)	)	PUNCT
ejpam-457	379	1	=	=	SYM
ejpam-457	379	2	0	0	NUM
ejpam-457	379	3	consider	consider	VERB
ejpam-457	379	4	θ(t	θ(t	NOUN
ejpam-457	379	5	,	,	PUNCT
ejpam-457	379	6	x	x	X
ejpam-457	379	7	(	(	PUNCT
ejpam-457	379	8	·	·	PUNCT
ejpam-457	379	9	)	)	PUNCT
ejpam-457	379	10	,	,	PUNCT
ejpam-457	379	11	ẋ	ẋ	PROPN
ejpam-457	379	12	(	(	PUNCT
ejpam-457	379	13	·	·	PUNCT
ejpam-457	379	14	)	)	PUNCT
ejpam-457	379	15	,	,	PUNCT
ejpam-457	379	16	ẍ	ẍ	PROPN
ejpam-457	379	17	(	(	PUNCT
ejpam-457	379	18	·	·	PUNCT
ejpam-457	379	19	)	)	PUNCT
ejpam-457	379	20	,	,	PUNCT
ejpam-457	379	21	...	...	PUNCT
ejpam-457	380	1	x	x	X
ejpam-457	380	2	(	(	PUNCT
ejpam-457	380	3	·	·	PUNCT
ejpam-457	380	4	)	)	PUNCT
ejpam-457	380	5	,	,	PUNCT
ejpam-457	380	6	y	y	PROPN
ejpam-457	380	7	(	(	PUNCT
ejpam-457	380	8	·	·	PUNCT
ejpam-457	380	9	)	)	PUNCT
ejpam-457	380	10	,	,	PUNCT
ejpam-457	380	11	ẏ	ẏ	PROPN
ejpam-457	380	12	(	(	PUNCT
ejpam-457	380	13	·	·	PUNCT
ejpam-457	380	14	)	)	PUNCT
ejpam-457	380	15	,	,	PUNCT
ejpam-457	380	16	ÿ(·),λ	ÿ(·),λ	NUM
ejpam-457	380	17	)	)	PUNCT
ejpam-457	380	18	=	=	SYM
ejpam-457	380	19	0	0	PUNCT
ejpam-457	380	20	as	as	ADP
ejpam-457	380	21	defining	define	VERB
ejpam-457	380	22	a	a	DET
ejpam-457	380	23	mapping	mapping	NOUN
ejpam-457	380	24	ψ	ψ	X
ejpam-457	380	25	:	:	PUNCT
ejpam-457	380	26	x	x	SYM
ejpam-457	380	27	×	×	NOUN
ejpam-457	380	28	y	y	PROPN
ejpam-457	380	29	×	×	NOUN
ejpam-457	380	30	rp	rp	PROPN
ejpam-457	380	31	→	→	SYM
ejpam-457	380	32	b	b	PROPN
ejpam-457	380	33	where	where	SCONJ
ejpam-457	380	34	y	y	PROPN
ejpam-457	380	35	is	be	AUX
ejpam-457	380	36	a	a	DET
ejpam-457	380	37	space	space	NOUN
ejpam-457	380	38	of	of	ADP
ejpam-457	380	39	piecewise	piecewise	NOUN
ejpam-457	380	40	twice	twice	ADV
ejpam-457	380	41	differentiable	differentiable	ADJ
ejpam-457	380	42	function	function	NOUN
ejpam-457	380	43	and	and	CCONJ
ejpam-457	380	44	b	b	NOUN
ejpam-457	380	45	is	be	AUX
ejpam-457	380	46	the	the	DET
ejpam-457	380	47	banach	banach	NOUN
ejpam-457	380	48	space	space	NOUN
ejpam-457	380	49	.	.	PUNCT
ejpam-457	381	1	in	in	ADP
ejpam-457	381	2	order	order	NOUN
ejpam-457	381	3	to	to	PART
ejpam-457	381	4	apply	apply	VERB
ejpam-457	381	5	theorem	theorem	ADJ
ejpam-457	381	6	1	1	NUM
ejpam-457	381	7	[	[	SYM
ejpam-457	381	8	10	10	NUM
ejpam-457	381	9	]	]	PUNCT
ejpam-457	381	10	to	to	ADP
ejpam-457	381	11	the	the	DET
ejpam-457	381	12	problem	problem	NOUN
ejpam-457	381	13	(	(	PUNCT
ejpam-457	381	14	mix	mix	VERB
ejpam-457	381	15	d	d	NOUN
ejpam-457	381	16	)	)	PUNCT
ejpam-457	381	17	,	,	PUNCT
ejpam-457	381	18	the	the	DET
ejpam-457	381	19	infinite	infinite	ADJ
ejpam-457	381	20	dimensional	dimensional	ADJ
ejpam-457	381	21	inequality	inequality	NOUN
ejpam-457	381	22	must	must	AUX
ejpam-457	381	23	be	be	AUX
ejpam-457	381	24	restricted	restrict	VERB
ejpam-457	381	25	.	.	PUNCT
ejpam-457	382	1	in	in	ADP
ejpam-457	382	2	the	the	DET
ejpam-457	382	3	following	following	NOUN
ejpam-457	382	4	theorem	theorem	NOUN
ejpam-457	382	5	,	,	PUNCT
ejpam-457	382	6	we	we	PRON
ejpam-457	382	7	use	use	VERB
ejpam-457	382	8	ψ′	ψ′	PUNCT
ejpam-457	382	9	to	to	PART
ejpam-457	382	10	represent	represent	VERB
ejpam-457	382	11	the	the	DET
ejpam-457	382	12	frèchèt	frèchèt	NOUN
ejpam-457	382	13	derivative	derivative	PROPN
ejpam-457	382	14	�	�	PROPN
ejpam-457	382	15	ψx(x	ψx(x	PUNCT
ejpam-457	382	16	,	,	PUNCT
ejpam-457	382	17	y	y	PROPN
ejpam-457	382	18	,	,	PUNCT
ejpam-457	382	19	λ),ψy(x	λ),ψy(x	PRON
ejpam-457	382	20	,	,	PUNCT
ejpam-457	382	21	y	y	PROPN
ejpam-457	382	22	,	,	PUNCT
ejpam-457	382	23	λ),ψλ(x	λ),ψλ(x	PROPN
ejpam-457	382	24	,	,	PUNCT
ejpam-457	382	25	y	y	PROPN
ejpam-457	382	26	,	,	PUNCT
ejpam-457	382	27	λ	λ	PROPN
ejpam-457	382	28	)	)	PUNCT
ejpam-457	382	29	�	�	PROPN
ejpam-457	382	30	.	.	PUNCT
ejpam-457	383	1	theorem	theorem	VERB
ejpam-457	383	2	3	3	NUM
ejpam-457	383	3	(	(	PUNCT
ejpam-457	383	4	converse	converse	NOUN
ejpam-457	383	5	duality	duality	NOUN
ejpam-457	383	6	)	)	PUNCT
ejpam-457	383	7	.	.	PUNCT
ejpam-457	384	1	let	let	VERB
ejpam-457	384	2	(	(	PUNCT
ejpam-457	384	3	x̄	x̄	NOUN
ejpam-457	384	4	,	,	PUNCT
ejpam-457	384	5	ȳ	ȳ	PROPN
ejpam-457	384	6	,	,	PUNCT
ejpam-457	384	7	z̄1	z̄1	PROPN
ejpam-457	384	8	,	,	PUNCT
ejpam-457	384	9	.	.	PUNCT
ejpam-457	384	10	.	.	PUNCT
ejpam-457	384	11	.	.	PUNCT
ejpam-457	385	1	,	,	PUNCT
ejpam-457	385	2	z̄p	z̄p	PROPN
ejpam-457	385	3	,	,	PUNCT
ejpam-457	385	4	λ̄	λ̄	PRON
ejpam-457	385	5	)	)	PUNCT
ejpam-457	385	6	be	be	AUX
ejpam-457	385	7	an	an	DET
ejpam-457	385	8	efficient	efficient	ADJ
ejpam-457	385	9	solution	solution	NOUN
ejpam-457	385	10	for	for	ADP
ejpam-457	385	11	(	(	PUNCT
ejpam-457	385	12	mix	mix	VERB
ejpam-457	385	13	d	d	NOUN
ejpam-457	385	14	)	)	PUNCT
ejpam-457	385	15	.	.	PUNCT
ejpam-457	386	1	assume	assume	VERB
ejpam-457	386	2	that	that	SCONJ
ejpam-457	386	3	a1	a1	VERB
ejpam-457	386	4	the	the	DET
ejpam-457	386	5	frèchèt	frèchèt	NOUN
ejpam-457	386	6	derivative	derivative	NOUN
ejpam-457	386	7	ψ′	ψ′	PUNCT
ejpam-457	386	8	has	have	VERB
ejpam-457	386	9	a	a	DET
ejpam-457	386	10	(	(	PUNCT
ejpam-457	386	11	weak	weak	ADJ
ejpam-457	386	12	*	*	NOUN
ejpam-457	386	13	)	)	PUNCT
ejpam-457	386	14	closed	closed	ADJ
ejpam-457	386	15	range	range	NOUN
ejpam-457	386	16	,	,	PUNCT
ejpam-457	386	17	a2	a2	PROPN
ejpam-457	386	18	f	f	PROPN
ejpam-457	386	19	and	and	CCONJ
ejpam-457	386	20	g	g	PROPN
ejpam-457	386	21	are	be	AUX
ejpam-457	386	22	twice	twice	ADV
ejpam-457	386	23	continuously	continuously	ADV
ejpam-457	386	24	differentiable	differentiable	ADJ
ejpam-457	386	25	,	,	PUNCT
ejpam-457	386	26	a3	a3	PROPN
ejpam-457	386	27	�	�	PROPN
ejpam-457	387	1	f	f	PROPN
ejpam-457	388	1	i	i	NOUN
ejpam-457	388	2	x	x	PROPN
ejpam-457	389	1	+	+	NUM
ejpam-457	389	2	bi(t)z	bi(t)z	NOUN
ejpam-457	389	3	i(t	i(t	NOUN
ejpam-457	389	4	)	)	PUNCT
ejpam-457	390	1	+	+	CCONJ
ejpam-457	390	2	∑	∑	PUNCT
ejpam-457	390	3	j∈j	j∈j	NOUN
ejpam-457	390	4	◦	◦	NOUN
ejpam-457	390	5	y	y	PROPN
ejpam-457	390	6	j(t)g	j(t)g	PROPN
ejpam-457	390	7	i	i	PROPN
ejpam-457	390	8	x	x	SYM
ejpam-457	390	9	�	�	PROPN
ejpam-457	391	1	−	−	PROPN
ejpam-457	391	2	d	d	PROPN
ejpam-457	391	3	�	�	PROPN
ejpam-457	392	1	f	f	PROPN
ejpam-457	393	1	i	i	PRON
ejpam-457	393	2	ẋ	ẋ	PUNCT
ejpam-457	394	1	+	+	CCONJ
ejpam-457	394	2	∑	∑	NOUN
ejpam-457	394	3	j∈j	j∈j	NOUN
ejpam-457	394	4	◦	◦	NOUN
ejpam-457	394	5	y	y	PROPN
ejpam-457	394	6	j(t)g	j(t)g	PROPN
ejpam-457	395	1	i	i	PRON
ejpam-457	395	2	ẋ	ẋ	PROPN
ejpam-457	395	3	�	�	PROPN
ejpam-457	395	4	+	+	NUM
ejpam-457	395	5	d2	d2	PROPN
ejpam-457	395	6	�	�	PROPN
ejpam-457	396	1	f	f	PROPN
ejpam-457	397	1	i	i	PRON
ejpam-457	397	2	ẋ	ẋ	PUNCT
ejpam-457	398	1	+	+	CCONJ
ejpam-457	398	2	∑	∑	NOUN
ejpam-457	398	3	j∈j	j∈j	NOUN
ejpam-457	398	4	◦	◦	NOUN
ejpam-457	398	5	y	y	PROPN
ejpam-457	398	6	j(t)g	j(t)g	PROPN
ejpam-457	399	1	i	i	PRON
ejpam-457	399	2	ẍ	ẍ	PROPN
ejpam-457	399	3	�	�	PROPN
ejpam-457	399	4	,	,	PUNCT
ejpam-457	399	5	i	i	PRON
ejpam-457	399	6	∈	∈	PROPN
ejpam-457	399	7	{	{	PUNCT
ejpam-457	399	8	1,2	1,2	NUM
ejpam-457	399	9	,	,	PUNCT
ejpam-457	399	10	.	.	PUNCT
ejpam-457	399	11	.	.	PUNCT
ejpam-457	399	12	.	.	PUNCT
ejpam-457	400	1	,	,	PUNCT
ejpam-457	400	2	p	p	PRON
ejpam-457	400	3	}	}	PUNCT
ejpam-457	400	4	are	be	AUX
ejpam-457	400	5	linearly	linearly	ADV
ejpam-457	400	6	independent	independent	ADJ
ejpam-457	400	7	,	,	PUNCT
ejpam-457	400	8	and	and	CCONJ
ejpam-457	400	9	a4	a4	NOUN
ejpam-457	400	10	(	(	PUNCT
ejpam-457	400	11	β(t	β(t	NOUN
ejpam-457	400	12	)	)	PUNCT
ejpam-457	400	13	tθx	tθx	NOUN
ejpam-457	400	14	−	−	NOUN
ejpam-457	400	15	dβ(t)tθ	dβ(t)tθ	VERB
ejpam-457	400	16	ẋ	ẋ	PUNCT
ejpam-457	401	1	+	+	CCONJ
ejpam-457	401	2	d2β(t)tθ	d2β(t)tθ	PROPN
ejpam-457	401	3	ẍ	ẍ	X
ejpam-457	402	1	−	−	PROPN
ejpam-457	402	2	d3β(t)tθ	d3β(t)tθ	VERB
ejpam-457	402	3	...	...	PUNCT
ejpam-457	402	4	x	x	SYM
ejpam-457	402	5	)	)	PUNCT
ejpam-457	402	6	β(t	β(t	NOUN
ejpam-457	402	7	)	)	PUNCT
ejpam-457	403	1	=	=	SYM
ejpam-457	403	2	0,⇒	0,⇒	PROPN
ejpam-457	403	3	β(t	β(t	PROPN
ejpam-457	403	4	)	)	PUNCT
ejpam-457	404	1	=	=	SYM
ejpam-457	404	2	0	0	NUM
ejpam-457	404	3	,	,	PUNCT
ejpam-457	404	4	t	t	PROPN
ejpam-457	404	5	∈	∈	PROPN
ejpam-457	404	6	i	i	PRON
ejpam-457	404	7	further	far	ADV
ejpam-457	404	8	,	,	PUNCT
ejpam-457	404	9	if	if	SCONJ
ejpam-457	404	10	the	the	DET
ejpam-457	404	11	hypotheses	hypothesis	NOUN
ejpam-457	404	12	of	of	ADP
ejpam-457	404	13	theorem	theorem	NOUN
ejpam-457	404	14	1	1	NUM
ejpam-457	404	15	are	be	AUX
ejpam-457	404	16	met	meet	VERB
ejpam-457	404	17	then	then	ADV
ejpam-457	404	18	x̄	x̄	PRON
ejpam-457	404	19	is	be	AUX
ejpam-457	404	20	an	an	DET
ejpam-457	404	21	efficient	efficient	ADJ
ejpam-457	404	22	solution	solution	NOUN
ejpam-457	404	23	of	of	ADP
ejpam-457	404	24	(	(	PUNCT
ejpam-457	404	25	vp	vp	PROPN
ejpam-457	404	26	)	)	PUNCT
ejpam-457	404	27	.	.	PUNCT
ejpam-457	405	1	proof	proof	NOUN
ejpam-457	405	2	.	.	PUNCT
ejpam-457	406	1	since	since	SCONJ
ejpam-457	406	2	(	(	PUNCT
ejpam-457	406	3	x̄	x̄	NOUN
ejpam-457	406	4	,	,	PUNCT
ejpam-457	406	5	ȳ	ȳ	PROPN
ejpam-457	406	6	,	,	PUNCT
ejpam-457	406	7	z̄1	z̄1	PROPN
ejpam-457	406	8	,	,	PUNCT
ejpam-457	406	9	.	.	PUNCT
ejpam-457	406	10	.	.	PUNCT
ejpam-457	406	11	.	.	PUNCT
ejpam-457	407	1	,	,	PUNCT
ejpam-457	407	2	z̄p	z̄p	PROPN
ejpam-457	407	3	,	,	PUNCT
ejpam-457	407	4	λ̄	λ̄	PRON
ejpam-457	407	5	)	)	PUNCT
ejpam-457	407	6	with	with	ADP
ejpam-457	407	7	ψ′having	ψ′have	VERB
ejpam-457	407	8	a	a	DET
ejpam-457	407	9	(	(	PUNCT
ejpam-457	407	10	weak∗	weak∗	NOUN
ejpam-457	407	11	)	)	PUNCT
ejpam-457	407	12	closed	closed	ADJ
ejpam-457	407	13	range	range	NOUN
ejpam-457	407	14	,	,	PUNCT
ejpam-457	407	15	is	be	AUX
ejpam-457	407	16	an	an	DET
ejpam-457	407	17	efficient	efficient	ADJ
ejpam-457	407	18	solution	solution	NOUN
ejpam-457	407	19	of	of	ADP
ejpam-457	407	20	(	(	PUNCT
ejpam-457	407	21	mix	mix	VERB
ejpam-457	407	22	d	d	NOUN
ejpam-457	407	23	)	)	PUNCT
ejpam-457	407	24	,	,	PUNCT
ejpam-457	407	25	then	then	ADV
ejpam-457	407	26	by	by	ADP
ejpam-457	407	27	theorem	theorem	NOUN
ejpam-457	407	28	1	1	NUM
ejpam-457	407	29	[	[	X
ejpam-457	407	30	9	9	NUM
ejpam-457	407	31	]	]	PUNCT
ejpam-457	407	32	,	,	PUNCT
ejpam-457	407	33	there	there	PRON
ejpam-457	407	34	exist	exist	VERB
ejpam-457	407	35	multipliers	multiplier	NOUN
ejpam-457	407	36	τ	τ	PROPN
ejpam-457	407	37	∈	∈	PROPN
ejpam-457	407	38	rp	rp	NOUN
ejpam-457	407	39	,	,	PUNCT
ejpam-457	407	40	piecewise	piecewise	NOUN
ejpam-457	407	41	smooth	smooth	ADJ
ejpam-457	407	42	β(t	β(t	PROPN
ejpam-457	407	43	)	)	PUNCT
ejpam-457	407	44	:	:	PUNCT
ejpam-457	408	1	i	i	PRON
ejpam-457	408	2	→	→	SYM
ejpam-457	408	3	rn	rn	PROPN
ejpam-457	408	4	,	,	PUNCT
ejpam-457	408	5	z	z	PROPN
ejpam-457	408	6	i(t	i(t	PROPN
ejpam-457	408	7	)	)	PUNCT
ejpam-457	408	8	∈	∈	PROPN
ejpam-457	408	9	rn	rn	PROPN
ejpam-457	408	10	,	,	PUNCT
ejpam-457	408	11	i	i	NOUN
ejpam-457	408	12	=	=	NOUN
ejpam-457	408	13	1	1	NUM
ejpam-457	408	14	,	,	PUNCT
ejpam-457	408	15	.	.	PUNCT
ejpam-457	408	16	.	.	PUNCT
ejpam-457	408	17	.	.	PUNCT
ejpam-457	409	1	,	,	PUNCT
ejpam-457	409	2	p	p	X
ejpam-457	409	3	,	,	PUNCT
ejpam-457	409	4	γ	γ	X
ejpam-457	409	5	∈	∈	NOUN
ejpam-457	409	6	r	r	NOUN
ejpam-457	409	7	for	for	ADP
ejpam-457	409	8	each	each	PRON
ejpam-457	409	9	of	of	ADP
ejpam-457	409	10	rconstraints	rconstraint	NOUN
ejpam-457	409	11	,	,	PUNCT
ejpam-457	409	12	η	η	PROPN
ejpam-457	409	13	∈	∈	PROPN
ejpam-457	409	14	rp	rp	NOUN
ejpam-457	409	15	,	,	PUNCT
ejpam-457	409	16	δ	δ	PROPN
ejpam-457	409	17	∈	∈	PROPN
ejpam-457	409	18	r	r	NOUN
ejpam-457	409	19	and	and	CCONJ
ejpam-457	409	20	piecewise	piecewise	NOUN
ejpam-457	409	21	smooth	smooth	ADJ
ejpam-457	409	22	µ(t	µ(t	PROPN
ejpam-457	409	23	)	)	PUNCT
ejpam-457	409	24	:	:	PUNCT
ejpam-457	410	1	i	i	PRON
ejpam-457	410	2	→	→	SYM
ejpam-457	410	3	rm	rm	PROPN
ejpam-457	410	4	satisfying	satisfy	VERB
ejpam-457	410	5	the	the	DET
ejpam-457	410	6	following	follow	VERB
ejpam-457	410	7	fritz	fritz	PROPN
ejpam-457	410	8	-	-	PUNCT
ejpam-457	410	9	john	john	PROPN
ejpam-457	410	10	optimality	optimality	NOUN
ejpam-457	410	11	conditions	condition	NOUN
ejpam-457	410	12	[	[	X
ejpam-457	410	13	9	9	NUM
ejpam-457	410	14	]	]	PUNCT
ejpam-457	410	15	.	.	PUNCT
ejpam-457	411	1	−	−	PROPN
ejpam-457	412	1	p	p	X
ejpam-457	412	2	∑	∑	PROPN
ejpam-457	412	3	i=1	i=1	PROPN
ejpam-457	412	4	τi	τi	PROPN
ejpam-457	412	5	�	�	PROPN
ejpam-457	412	6	�	�	PROPN
ejpam-457	412	7	f	f	PROPN
ejpam-457	413	1	i	i	NOUN
ejpam-457	413	2	x	x	PROPN
ejpam-457	414	1	+	+	NUM
ejpam-457	414	2	bi(t)z	bi(t)z	NOUN
ejpam-457	414	3	i(t	i(t	NOUN
ejpam-457	414	4	)	)	PUNCT
ejpam-457	415	1	+	+	CCONJ
ejpam-457	415	2	∑	∑	PUNCT
ejpam-457	415	3	j∈j	j∈j	NOUN
ejpam-457	415	4	◦	◦	NOUN
ejpam-457	415	5	y	y	PROPN
ejpam-457	415	6	j(t)g	j(t)g	PROPN
ejpam-457	415	7	j	j	PROPN
ejpam-457	415	8	x	x	SYM
ejpam-457	415	9	�	�	PROPN
ejpam-457	415	10	−	−	PROPN
ejpam-457	416	1	d	d	PROPN
ejpam-457	416	2	�	�	PROPN
ejpam-457	416	3	f	f	PROPN
ejpam-457	417	1	i	i	PRON
ejpam-457	417	2	ẋ	ẋ	PUNCT
ejpam-457	418	1	+	+	CCONJ
ejpam-457	418	2	∑	∑	NOUN
ejpam-457	418	3	j∈j	j∈j	NOUN
ejpam-457	418	4	◦	◦	NOUN
ejpam-457	418	5	y	y	PROPN
ejpam-457	418	6	j(t)g	j(t)g	PROPN
ejpam-457	418	7	j	j	PROPN
ejpam-457	418	8	ẋ	ẋ	PROPN
ejpam-457	418	9	�	�	PROPN
ejpam-457	418	10	i.	i.	PROPN
ejpam-457	418	11	husain	husain	PROPN
ejpam-457	418	12	,	,	PUNCT
ejpam-457	418	13	r.	r.	PROPN
ejpam-457	418	14	mattoo	mattoo	PROPN
ejpam-457	418	15	/	/	SYM
ejpam-457	418	16	eur	eur	PROPN
ejpam-457	418	17	.	.	PUNCT
ejpam-457	419	1	j.	j.	PROPN
ejpam-457	419	2	pure	pure	PROPN
ejpam-457	419	3	appl	appl	PROPN
ejpam-457	419	4	.	.	PROPN
ejpam-457	419	5	math	math	PROPN
ejpam-457	419	6	,	,	PUNCT
ejpam-457	419	7	3	3	NUM
ejpam-457	419	8	(	(	PUNCT
ejpam-457	419	9	2010	2010	NUM
ejpam-457	419	10	)	)	PUNCT
ejpam-457	419	11	,	,	PUNCT
ejpam-457	419	12	81	81	NUM
ejpam-457	419	13	-	-	SYM
ejpam-457	419	14	97	97	NUM
ejpam-457	420	1	92	92	NUM
ejpam-457	420	2	+	+	NUM
ejpam-457	420	3	d2	d2	PROPN
ejpam-457	420	4	�	�	PROPN
ejpam-457	420	5	f	f	PROPN
ejpam-457	420	6	i	i	PRON
ejpam-457	420	7	ẍ	ẍ	PUNCT
ejpam-457	421	1	+	+	CCONJ
ejpam-457	422	1	∑	∑	PROPN
ejpam-457	422	2	j∈j	j∈j	NOUN
ejpam-457	422	3	◦	◦	NOUN
ejpam-457	422	4	y	y	PROPN
ejpam-457	422	5	j(t)g	j(t)g	PROPN
ejpam-457	422	6	j	j	PROPN
ejpam-457	422	7	ẍ	ẍ	PROPN
ejpam-457	422	8	�	�	PROPN
ejpam-457	422	9	�	�	PROPN
ejpam-457	423	1	−	−	PROPN
ejpam-457	423	2	γ	γ	X
ejpam-457	423	3	r	r	NOUN
ejpam-457	423	4	∑	∑	PUNCT
ejpam-457	423	5	α=1	α=1	X
ejpam-457	423	6	∑	∑	ADV
ejpam-457	423	7	j∈jα	j∈jα	PROPN
ejpam-457	423	8	(	(	PUNCT
ejpam-457	423	9	y	y	PROPN
ejpam-457	423	10	j(t)g	j(t)g	PROPN
ejpam-457	423	11	j	j	PROPN
ejpam-457	423	12	x	x	SYM
ejpam-457	423	13	−	−	PROPN
ejpam-457	424	1	d	d	X
ejpam-457	424	2	y	y	PROPN
ejpam-457	424	3	j(t)g	j(t)g	PROPN
ejpam-457	424	4	j	j	PROPN
ejpam-457	424	5	ẋ	ẋ	PROPN
ejpam-457	425	1	+	+	CCONJ
ejpam-457	425	2	d2	d2	PROPN
ejpam-457	425	3	y	y	PROPN
ejpam-457	425	4	j(t)g	j(t)g	PROPN
ejpam-457	425	5	j	j	PROPN
ejpam-457	425	6	ẍ	ẍ	PROPN
ejpam-457	425	7	)	)	PUNCT
ejpam-457	426	1	+	+	ADV
ejpam-457	426	2	β(t)tθx	β(t)tθx	NOUN
ejpam-457	426	3	−	−	NOUN
ejpam-457	426	4	dβ(t)tθ	dβ(t)tθ	VERB
ejpam-457	426	5	ẋ	ẋ	PUNCT
ejpam-457	427	1	+	+	CCONJ
ejpam-457	427	2	d2β(t)tθ	d2β(t)tθ	PROPN
ejpam-457	427	3	ẍ	ẍ	X
ejpam-457	428	1	−	−	PROPN
ejpam-457	428	2	d3β(t)tθ	d3β(t)tθ	VERB
ejpam-457	428	3	...	...	PUNCT
ejpam-457	428	4	x	x	SYM
ejpam-457	429	1	=	=	SYM
ejpam-457	429	2	0	0	NUM
ejpam-457	429	3	,	,	PUNCT
ejpam-457	429	4	t	t	PROPN
ejpam-457	430	1	∈	∈	PROPN
ejpam-457	430	2	i	i	PRON
ejpam-457	430	3	(	(	PUNCT
ejpam-457	430	4	22	22	NUM
ejpam-457	430	5	)	)	PUNCT
ejpam-457	430	6	−(τt	−(τt	NOUN
ejpam-457	430	7	e)g	e)g	VERB
ejpam-457	430	8	j	j	PROPN
ejpam-457	430	9	+	+	CCONJ
ejpam-457	430	10	β(t)tθy	β(t)tθy	X
ejpam-457	430	11	j	j	PROPN
ejpam-457	430	12	−	−	NOUN
ejpam-457	430	13	dβ(t)tθ	dβ(t)tθ	VERB
ejpam-457	430	14	ẏ	ẏ	PROPN
ejpam-457	430	15	j	j	PROPN
ejpam-457	430	16	+	+	CCONJ
ejpam-457	430	17	d2β(t)tθ	d2β(t)tθ	PROPN
ejpam-457	430	18	ÿ	ÿ	PROPN
ejpam-457	430	19	j	j	PROPN
ejpam-457	430	20	−µ	−µ	NOUN
ejpam-457	430	21	j(t	j(t	PROPN
ejpam-457	430	22	)	)	PUNCT
ejpam-457	431	1	=	=	SYM
ejpam-457	431	2	0	0	NUM
ejpam-457	431	3	,	,	PUNCT
ejpam-457	431	4	j	j	PROPN
ejpam-457	431	5	∈	∈	PROPN
ejpam-457	431	6	j	j	PROPN
ejpam-457	431	7	◦	◦	NOUN
ejpam-457	431	8	(	(	PUNCT
ejpam-457	431	9	23	23	NUM
ejpam-457	431	10	)	)	PUNCT
ejpam-457	431	11	−γg	−γg	NOUN
ejpam-457	431	12	j	j	PROPN
ejpam-457	431	13	+	+	CCONJ
ejpam-457	431	14	β(t)tθy	β(t)tθy	X
ejpam-457	431	15	j	j	PROPN
ejpam-457	432	1	−	−	NOUN
ejpam-457	432	2	dβ(t)tθ	dβ(t)tθ	VERB
ejpam-457	432	3	ẏ	ẏ	PROPN
ejpam-457	432	4	j+d2β(t)tθ	j+d2β(t)tθ	PROPN
ejpam-457	432	5	ÿ	ÿ	PROPN
ejpam-457	432	6	j	j	PROPN
ejpam-457	432	7	−µ	−µ	PROPN
ejpam-457	432	8	j(t)=0	j(t)=0	PROPN
ejpam-457	432	9	,	,	PUNCT
ejpam-457	432	10	j∈jα	j∈jα	PROPN
ejpam-457	432	11	,	,	PUNCT
ejpam-457	432	12	α=1	α=1	PROPN
ejpam-457	432	13	,	,	PUNCT
ejpam-457	432	14	.	.	PUNCT
ejpam-457	432	15	.	.	PUNCT
ejpam-457	433	1	.	.	PUNCT
ejpam-457	434	1	,	,	PUNCT
ejpam-457	434	2	r	r	NOUN
ejpam-457	434	3	(	(	PUNCT
ejpam-457	434	4	24	24	NUM
ejpam-457	434	5	)	)	PUNCT
ejpam-457	434	6	−τi	−τi	NOUN
ejpam-457	434	7	x(t)t	x(t)t	PROPN
ejpam-457	434	8	bi(t	bi(t	X
ejpam-457	434	9	)	)	PUNCT
ejpam-457	435	1	+	+	NUM
ejpam-457	435	2	λiβ(t)t	λiβ(t)t	NOUN
ejpam-457	435	3	bi(t	bi(t	X
ejpam-457	435	4	)	)	PUNCT
ejpam-457	436	1	+	+	CCONJ
ejpam-457	436	2	2δibi(t)z	2δibi(t)z	NUM
ejpam-457	436	3	i(t	i(t	NOUN
ejpam-457	436	4	)	)	PUNCT
ejpam-457	436	5	=	=	SYM
ejpam-457	436	6	0	0	NUM
ejpam-457	436	7	,	,	PUNCT
ejpam-457	436	8	i	i	PRON
ejpam-457	436	9	=	=	NOUN
ejpam-457	436	10	1	1	NUM
ejpam-457	436	11	,	,	PUNCT
ejpam-457	436	12	.	.	PUNCT
ejpam-457	436	13	.	.	PUNCT
ejpam-457	436	14	.	.	PUNCT
ejpam-457	437	1	,	,	PUNCT
ejpam-457	437	2	p	p	X
ejpam-457	437	3	(	(	PUNCT
ejpam-457	437	4	25	25	NUM
ejpam-457	437	5	)	)	PUNCT
ejpam-457	437	6	�	�	PROPN
ejpam-457	438	1	f	f	NOUN
ejpam-457	438	2	i	i	NOUN
ejpam-457	438	3	x	x	PROPN
ejpam-457	439	1	+	+	NUM
ejpam-457	439	2	bi(t)z	bi(t)z	NOUN
ejpam-457	439	3	i(t	i(t	NOUN
ejpam-457	439	4	)	)	PUNCT
ejpam-457	440	1	+	+	CCONJ
ejpam-457	440	2	∑	∑	PUNCT
ejpam-457	440	3	j∈j	j∈j	NOUN
ejpam-457	440	4	◦	◦	NOUN
ejpam-457	440	5	y	y	PROPN
ejpam-457	441	1	j(t)g	j(t)g	PROPN
ejpam-457	441	2	j	j	PROPN
ejpam-457	441	3	x	x	SYM
ejpam-457	441	4	−	−	PROPN
ejpam-457	441	5	d	d	X
ejpam-457	441	6	�	�	PROPN
ejpam-457	441	7	f	f	PROPN
ejpam-457	442	1	i	i	PRON
ejpam-457	442	2	ẋ	ẋ	PUNCT
ejpam-457	443	1	+	+	CCONJ
ejpam-457	443	2	∑	∑	NOUN
ejpam-457	443	3	j∈j	j∈j	NOUN
ejpam-457	443	4	◦	◦	NOUN
ejpam-457	443	5	y	y	PROPN
ejpam-457	443	6	j(t)g	j(t)g	PROPN
ejpam-457	444	1	j	j	PROPN
ejpam-457	444	2	ẋ	ẋ	PROPN
ejpam-457	444	3	�	�	PROPN
ejpam-457	444	4	+	+	NUM
ejpam-457	444	5	d2	d2	PROPN
ejpam-457	444	6	�	�	PROPN
ejpam-457	444	7	f	f	PROPN
ejpam-457	444	8	i	i	PRON
ejpam-457	444	9	ẍ	ẍ	PUNCT
ejpam-457	445	1	+	+	CCONJ
ejpam-457	445	2	∑	∑	PROPN
ejpam-457	445	3	j∈j	j∈j	NOUN
ejpam-457	445	4	◦	◦	NOUN
ejpam-457	445	5	y	y	PROPN
ejpam-457	445	6	j(t)g	j(t)g	PROPN
ejpam-457	445	7	j	j	PROPN
ejpam-457	445	8	ẍ	ẍ	PROPN
ejpam-457	445	9	�	�	PROPN
ejpam-457	445	10	�	�	PROPN
ejpam-457	445	11	−ηi	−ηi	PART
ejpam-457	445	12	=	=	SYM
ejpam-457	445	13	0	0	NUM
ejpam-457	445	14	(	(	PUNCT
ejpam-457	445	15	26	26	NUM
ejpam-457	445	16	)	)	PUNCT
ejpam-457	445	17	µt	µt	PRON
ejpam-457	445	18	(	(	PUNCT
ejpam-457	445	19	t	t	NOUN
ejpam-457	445	20	)	)	PUNCT
ejpam-457	445	21	ȳ(t	ȳ(t	NOUN
ejpam-457	445	22	)	)	PUNCT
ejpam-457	446	1	=	=	SYM
ejpam-457	446	2	0	0	NUM
ejpam-457	446	3	,	,	PUNCT
ejpam-457	446	4	t	t	PROPN
ejpam-457	446	5	∈	∈	PROPN
ejpam-457	447	1	i	i	PRON
ejpam-457	447	2	(	(	PUNCT
ejpam-457	447	3	27	27	NUM
ejpam-457	447	4	)	)	PUNCT
ejpam-457	447	5	ηtλ=	ηtλ=	PROPN
ejpam-457	447	6	0	0	NUM
ejpam-457	447	7	(	(	PUNCT
ejpam-457	447	8	28	28	NUM
ejpam-457	447	9	)	)	PUNCT
ejpam-457	447	10	γ	γ	PROPN
ejpam-457	447	11	∑	∑	PUNCT
ejpam-457	447	12	j∈jα	j∈jα	PROPN
ejpam-457	447	13	∫	∫	PROPN
ejpam-457	447	14	i	i	PROPN
ejpam-457	447	15	y(t)t	y(t)t	PROPN
ejpam-457	447	16	g(t	g(t	PROPN
ejpam-457	447	17	,	,	PUNCT
ejpam-457	447	18	x̄	x̄	NOUN
ejpam-457	447	19	,	,	PUNCT
ejpam-457	447	20	˙̄x	˙̄x	X
ejpam-457	447	21	,	,	PUNCT
ejpam-457	447	22	¨̄x)d	¨̄x)d	NOUN
ejpam-457	447	23	t	t	NOUN
ejpam-457	447	24	=	=	SYM
ejpam-457	447	25	0	0	NUM
ejpam-457	447	26	,	,	PUNCT
ejpam-457	447	27	α=	α=	NOUN
ejpam-457	447	28	1,2	1,2	NUM
ejpam-457	447	29	,	,	PUNCT
ejpam-457	447	30	.	.	PUNCT
ejpam-457	447	31	.	.	PUNCT
ejpam-457	447	32	.	.	PUNCT
ejpam-457	448	1	,	,	PUNCT
ejpam-457	448	2	p	p	X
ejpam-457	448	3	(	(	PUNCT
ejpam-457	448	4	29	29	NUM
ejpam-457	448	5	)	)	PUNCT
ejpam-457	448	6	δi(z	δi(z	VERB
ejpam-457	448	7	i(t)t	i(t)t	PROPN
ejpam-457	448	8	bi(t)z	bi(t)z	PROPN
ejpam-457	448	9	i(t)−	i(t)−	PROPN
ejpam-457	448	10	1	1	NUM
ejpam-457	448	11	)	)	PUNCT
ejpam-457	448	12	=	=	SYM
ejpam-457	448	13	0	0	NUM
ejpam-457	448	14	,	,	PUNCT
ejpam-457	448	15	t	t	PROPN
ejpam-457	448	16	∈	∈	PROPN
ejpam-457	449	1	i	i	PRON
ejpam-457	449	2	(	(	PUNCT
ejpam-457	449	3	30	30	NUM
ejpam-457	449	4	)	)	PUNCT
ejpam-457	449	5	(	(	PUNCT
ejpam-457	449	6	τ	τ	PROPN
ejpam-457	449	7	,	,	PUNCT
ejpam-457	449	8	γ,µ(t),δ	γ,µ(t),δ	NOUN
ejpam-457	449	9	,	,	PUNCT
ejpam-457	449	10	η	η	NOUN
ejpam-457	449	11	)	)	PUNCT
ejpam-457	449	12	≧	≧	X
ejpam-457	449	13	0	0	PUNCT
ejpam-457	449	14	(	(	PUNCT
ejpam-457	449	15	31	31	NUM
ejpam-457	449	16	)	)	PUNCT
ejpam-457	449	17	(	(	PUNCT
ejpam-457	449	18	τ	τ	PROPN
ejpam-457	449	19	,	,	PUNCT
ejpam-457	449	20	β(t),γ,µ(t),δ	β(t),γ,µ(t),δ	PROPN
ejpam-457	449	21	,	,	PUNCT
ejpam-457	449	22	η	η	NOUN
ejpam-457	449	23	)	)	PUNCT
ejpam-457	449	24	6=	6=	ADP
ejpam-457	449	25	0	0	NUM
ejpam-457	449	26	(	(	PUNCT
ejpam-457	449	27	32	32	NUM
ejpam-457	449	28	)	)	PUNCT
ejpam-457	449	29	since	since	SCONJ
ejpam-457	449	30	λ	λ	PROPN
ejpam-457	449	31	>	>	X
ejpam-457	449	32	0	0	NUM
ejpam-457	449	33	,	,	PUNCT
ejpam-457	449	34	(	(	PUNCT
ejpam-457	449	35	28	28	NUM
ejpam-457	449	36	)	)	PUNCT
ejpam-457	449	37	implies	imply	VERB
ejpam-457	449	38	η	η	PROPN
ejpam-457	449	39	=	=	PROPN
ejpam-457	449	40	0	0	PROPN
ejpam-457	449	41	.	.	PUNCT
ejpam-457	450	1	consequently	consequently	ADV
ejpam-457	450	2	(	(	PUNCT
ejpam-457	450	3	26	26	NUM
ejpam-457	450	4	)	)	PUNCT
ejpam-457	450	5	implies	imply	VERB
ejpam-457	450	6	�	�	PROPN
ejpam-457	451	1	f	f	PROPN
ejpam-457	451	2	i	i	PROPN
ejpam-457	451	3	x	x	PROPN
ejpam-457	452	1	+	+	NUM
ejpam-457	452	2	bi(t)z	bi(t)z	NOUN
ejpam-457	452	3	i(t	i(t	NOUN
ejpam-457	452	4	)	)	PUNCT
ejpam-457	453	1	+	+	CCONJ
ejpam-457	453	2	∑	∑	PUNCT
ejpam-457	453	3	j∈j	j∈j	NOUN
ejpam-457	453	4	◦	◦	NOUN
ejpam-457	453	5	y	y	PROPN
ejpam-457	454	1	j(t)g	j(t)g	PROPN
ejpam-457	454	2	j	j	PROPN
ejpam-457	454	3	x	x	SYM
ejpam-457	455	1	−	−	PROPN
ejpam-457	456	1	d	d	NOUN
ejpam-457	456	2	(	(	PUNCT
ejpam-457	456	3	f	f	NOUN
ejpam-457	456	4	i	i	PRON
ejpam-457	456	5	ẋ	ẋ	PUNCT
ejpam-457	457	1	+	+	CCONJ
ejpam-457	457	2	∑	∑	NOUN
ejpam-457	457	3	j∈j	j∈j	NOUN
ejpam-457	457	4	◦	◦	NOUN
ejpam-457	457	5	y	y	PROPN
ejpam-457	457	6	j(t)g	j(t)g	PROPN
ejpam-457	457	7	j	j	PROPN
ejpam-457	457	8	ẋ	ẋ	PROPN
ejpam-457	457	9	)	)	PUNCT
ejpam-457	458	1	+	+	CCONJ
ejpam-457	458	2	d2	d2	PROPN
ejpam-457	458	3	(	(	PUNCT
ejpam-457	458	4	f	f	NOUN
ejpam-457	458	5	i	i	PRON
ejpam-457	458	6	ẍ	ẍ	PUNCT
ejpam-457	459	1	+	+	CCONJ
ejpam-457	459	2	∑	∑	PROPN
ejpam-457	459	3	j∈j	j∈j	NOUN
ejpam-457	459	4	◦	◦	NOUN
ejpam-457	459	5	y	y	PROPN
ejpam-457	459	6	j(t)g	j(t)g	PROPN
ejpam-457	459	7	j	j	PROPN
ejpam-457	459	8	ẍ	ẍ	PROPN
ejpam-457	459	9	)	)	PUNCT
ejpam-457	459	10	�	�	PROPN
ejpam-457	460	1	=	=	SYM
ejpam-457	460	2	0	0	NUM
ejpam-457	460	3	(	(	PUNCT
ejpam-457	460	4	33	33	NUM
ejpam-457	460	5	)	)	PUNCT
ejpam-457	460	6	using	use	VERB
ejpam-457	460	7	the	the	DET
ejpam-457	460	8	duality	duality	NOUN
ejpam-457	460	9	constraint	constraint	NOUN
ejpam-457	460	10	of	of	ADP
ejpam-457	460	11	(	(	PUNCT
ejpam-457	460	12	mix	mix	NOUN
ejpam-457	460	13	d	d	NOUN
ejpam-457	460	14	)	)	PUNCT
ejpam-457	460	15	equation	equation	NOUN
ejpam-457	460	16	(	(	PUNCT
ejpam-457	460	17	22	22	NUM
ejpam-457	460	18	)	)	PUNCT
ejpam-457	460	19	reduces	reduce	VERB
ejpam-457	460	20	to	to	ADP
ejpam-457	460	21	−	−	PROPN
ejpam-457	460	22	p	p	NOUN
ejpam-457	460	23	∑	∑	PROPN
ejpam-457	460	24	i=1	i=1	PROPN
ejpam-457	460	25	(	(	PUNCT
ejpam-457	460	26	τi	τi	ADP
ejpam-457	460	27	−	−	NOUN
ejpam-457	460	28	γλi	γλi	NOUN
ejpam-457	460	29	)	)	PUNCT
ejpam-457	460	30	�	�	PROPN
ejpam-457	460	31	�	�	PROPN
ejpam-457	460	32	f	f	PROPN
ejpam-457	461	1	i	i	NOUN
ejpam-457	461	2	x	x	PROPN
ejpam-457	462	1	+	+	NUM
ejpam-457	462	2	bi(t)z	bi(t)z	NOUN
ejpam-457	462	3	i(t	i(t	NOUN
ejpam-457	462	4	)	)	PUNCT
ejpam-457	463	1	+	+	CCONJ
ejpam-457	463	2	∑	∑	PUNCT
ejpam-457	463	3	j∈j	j∈j	NOUN
ejpam-457	463	4	◦	◦	NOUN
ejpam-457	463	5	y	y	PROPN
ejpam-457	464	1	j(t)g	j(t)g	PROPN
ejpam-457	464	2	j	j	PROPN
ejpam-457	464	3	x	x	X
ejpam-457	464	4	)	)	PUNCT
ejpam-457	464	5	−	−	PROPN
ejpam-457	465	1	d	d	X
ejpam-457	465	2	(	(	PUNCT
ejpam-457	465	3	f	f	NOUN
ejpam-457	465	4	i	i	PRON
ejpam-457	465	5	ẋ	ẋ	PUNCT
ejpam-457	466	1	+	+	CCONJ
ejpam-457	466	2	∑	∑	NOUN
ejpam-457	466	3	j∈j	j∈j	NOUN
ejpam-457	466	4	◦	◦	NOUN
ejpam-457	466	5	y	y	PROPN
ejpam-457	466	6	j(t)g	j(t)g	PROPN
ejpam-457	467	1	j	j	PROPN
ejpam-457	467	2	ẋ	ẋ	PROPN
ejpam-457	467	3	�	�	PROPN
ejpam-457	467	4	+	+	NUM
ejpam-457	467	5	d2	d2	PROPN
ejpam-457	467	6	�	�	PROPN
ejpam-457	467	7	f	f	PROPN
ejpam-457	467	8	i	i	PRON
ejpam-457	467	9	ẍ	ẍ	PUNCT
ejpam-457	468	1	+	+	CCONJ
ejpam-457	468	2	∑	∑	PROPN
ejpam-457	468	3	j∈j	j∈j	NOUN
ejpam-457	468	4	◦	◦	NOUN
ejpam-457	468	5	y	y	PROPN
ejpam-457	468	6	j(t)g	j(t)g	PROPN
ejpam-457	468	7	j	j	PROPN
ejpam-457	468	8	ẍ	ẍ	PROPN
ejpam-457	468	9	�	�	PROPN
ejpam-457	468	10	�	�	PROPN
ejpam-457	468	11	+	+	CCONJ
ejpam-457	468	12	β(t)tθx	β(t)tθx	PROPN
ejpam-457	468	13	−	−	NOUN
ejpam-457	468	14	dβ(t)tθ	dβ(t)tθ	VERB
ejpam-457	468	15	ẋ	ẋ	PUNCT
ejpam-457	469	1	+	+	ADJ
ejpam-457	469	2	d2β(t)tθ	d2β(t)tθ	PROPN
ejpam-457	469	3	ẍ	ẍ	X
ejpam-457	470	1	−	−	PROPN
ejpam-457	470	2	d3β(t)tθ	d3β(t)tθ	VERB
ejpam-457	470	3	...	...	PUNCT
ejpam-457	470	4	x	x	SYM
ejpam-457	471	1	=	=	SYM
ejpam-457	471	2	0	0	NUM
ejpam-457	471	3	,	,	PUNCT
ejpam-457	471	4	t	t	PROPN
ejpam-457	472	1	∈	∈	PROPN
ejpam-457	472	2	i	i	PRON
ejpam-457	472	3	(	(	PUNCT
ejpam-457	472	4	34	34	NUM
ejpam-457	472	5	)	)	PUNCT
ejpam-457	472	6	post	post	NOUN
ejpam-457	472	7	multiplying	multiplying	NOUN
ejpam-457	472	8	(	(	PUNCT
ejpam-457	472	9	34	34	NUM
ejpam-457	472	10	)	)	PUNCT
ejpam-457	472	11	by	by	ADP
ejpam-457	472	12	β(t	β(t	PROPN
ejpam-457	472	13	)	)	PUNCT
ejpam-457	472	14	and	and	CCONJ
ejpam-457	472	15	then	then	ADV
ejpam-457	472	16	using	use	VERB
ejpam-457	472	17	(	(	PUNCT
ejpam-457	472	18	33	33	NUM
ejpam-457	472	19	)	)	PUNCT
ejpam-457	472	20	,	,	PUNCT
ejpam-457	472	21	we	we	PRON
ejpam-457	472	22	obtain	obtain	VERB
ejpam-457	472	23	,	,	PUNCT
ejpam-457	472	24	(	(	PUNCT
ejpam-457	472	25	β(t)tθx	β(t)tθx	PROPN
ejpam-457	472	26	−	−	NOUN
ejpam-457	472	27	dβ(t)tθ	dβ(t)tθ	VERB
ejpam-457	472	28	ẋ	ẋ	PUNCT
ejpam-457	473	1	+	+	CCONJ
ejpam-457	473	2	d2β(t)tθ	d2β(t)tθ	PROPN
ejpam-457	473	3	ẍ	ẍ	X
ejpam-457	474	1	−	−	PROPN
ejpam-457	474	2	d3β(t)tθ	d3β(t)tθ	VERB
ejpam-457	474	3	...	...	PUNCT
ejpam-457	474	4	x	x	SYM
ejpam-457	474	5	)	)	PUNCT
ejpam-457	474	6	β(t	β(t	NOUN
ejpam-457	474	7	)	)	PUNCT
ejpam-457	475	1	=	=	SYM
ejpam-457	475	2	0	0	NUM
ejpam-457	475	3	,	,	PUNCT
ejpam-457	475	4	t	t	PROPN
ejpam-457	475	5	∈	∈	PROPN
ejpam-457	475	6	i	i	PRON
ejpam-457	475	7	i.	i.	PROPN
ejpam-457	475	8	husain	husain	PROPN
ejpam-457	475	9	,	,	PUNCT
ejpam-457	475	10	r.	r.	PROPN
ejpam-457	475	11	mattoo	mattoo	PROPN
ejpam-457	475	12	/	/	SYM
ejpam-457	475	13	eur	eur	PROPN
ejpam-457	475	14	.	.	PUNCT
ejpam-457	476	1	j.	j.	PROPN
ejpam-457	476	2	pure	pure	PROPN
ejpam-457	476	3	appl	appl	PROPN
ejpam-457	476	4	.	.	PROPN
ejpam-457	476	5	math	math	PROPN
ejpam-457	476	6	,	,	PUNCT
ejpam-457	476	7	3	3	NUM
ejpam-457	476	8	(	(	PUNCT
ejpam-457	476	9	2010	2010	NUM
ejpam-457	476	10	)	)	PUNCT
ejpam-457	476	11	,	,	PUNCT
ejpam-457	476	12	81	81	NUM
ejpam-457	476	13	-	-	SYM
ejpam-457	476	14	97	97	NUM
ejpam-457	476	15	93	93	NUM
ejpam-457	476	16	this	this	PRON
ejpam-457	476	17	because	because	SCONJ
ejpam-457	476	18	of	of	ADP
ejpam-457	476	19	the	the	DET
ejpam-457	476	20	hypothesis	hypothesis	NOUN
ejpam-457	476	21	(	(	PUNCT
ejpam-457	476	22	a4	a4	NOUN
ejpam-457	476	23	)	)	PUNCT
ejpam-457	476	24	yields	yield	NOUN
ejpam-457	476	25	,	,	PUNCT
ejpam-457	476	26	β(t	β(t	NOUN
ejpam-457	476	27	)	)	PUNCT
ejpam-457	476	28	=	=	SYM
ejpam-457	477	1	0	0	NUM
ejpam-457	477	2	,	,	PUNCT
ejpam-457	477	3	t	t	PROPN
ejpam-457	477	4	∈	∈	PROPN
ejpam-457	478	1	i	i	PRON
ejpam-457	478	2	(	(	PUNCT
ejpam-457	478	3	35	35	NUM
ejpam-457	478	4	)	)	PUNCT
ejpam-457	478	5	using	use	VERB
ejpam-457	478	6	(	(	PUNCT
ejpam-457	478	7	35	35	NUM
ejpam-457	478	8	)	)	PUNCT
ejpam-457	478	9	in	in	ADP
ejpam-457	478	10	(	(	PUNCT
ejpam-457	478	11	34	34	NUM
ejpam-457	478	12	)	)	PUNCT
ejpam-457	478	13	in	in	ADP
ejpam-457	478	14	(	(	PUNCT
ejpam-457	478	15	22	22	NUM
ejpam-457	478	16	)	)	PUNCT
ejpam-457	478	17	,	,	PUNCT
ejpam-457	478	18	we	we	PRON
ejpam-457	478	19	have	have	VERB
ejpam-457	478	20	−	−	PROPN
ejpam-457	478	21	p	p	NOUN
ejpam-457	478	22	∑	∑	PROPN
ejpam-457	478	23	i=1	i=1	PROPN
ejpam-457	478	24	(	(	PUNCT
ejpam-457	478	25	τi	τi	ADP
ejpam-457	478	26	−	−	NOUN
ejpam-457	478	27	γλi	γλi	NOUN
ejpam-457	478	28	)	)	PUNCT
ejpam-457	478	29	{	{	PUNCT
ejpam-457	478	30	(	(	PUNCT
ejpam-457	478	31	f	f	NOUN
ejpam-457	478	32	i	i	NOUN
ejpam-457	478	33	x	x	PROPN
ejpam-457	479	1	+	+	NUM
ejpam-457	479	2	bi(t)z	bi(t)z	NOUN
ejpam-457	479	3	i(t	i(t	NOUN
ejpam-457	479	4	)	)	PUNCT
ejpam-457	480	1	+	+	CCONJ
ejpam-457	480	2	∑	∑	PUNCT
ejpam-457	480	3	j∈j	j∈j	NOUN
ejpam-457	480	4	◦	◦	NOUN
ejpam-457	480	5	y	y	PROPN
ejpam-457	481	1	j(t)g	j(t)g	PROPN
ejpam-457	481	2	j	j	PROPN
ejpam-457	481	3	x	x	X
ejpam-457	481	4	)	)	PUNCT
ejpam-457	481	5	−	−	PROPN
ejpam-457	482	1	d	d	X
ejpam-457	482	2	(	(	PUNCT
ejpam-457	482	3	f	f	NOUN
ejpam-457	482	4	i	i	PRON
ejpam-457	482	5	ẋ	ẋ	PUNCT
ejpam-457	483	1	+	+	CCONJ
ejpam-457	483	2	∑	∑	NOUN
ejpam-457	483	3	j∈j	j∈j	NOUN
ejpam-457	483	4	◦	◦	NOUN
ejpam-457	483	5	y	y	PROPN
ejpam-457	483	6	j(t)g	j(t)g	PROPN
ejpam-457	483	7	j	j	PROPN
ejpam-457	483	8	ẋ	ẋ	PROPN
ejpam-457	483	9	)	)	PUNCT
ejpam-457	484	1	+	+	NUM
ejpam-457	484	2	d2	d2	PROPN
ejpam-457	484	3	(	(	PUNCT
ejpam-457	484	4	f	f	NOUN
ejpam-457	484	5	i	i	PRON
ejpam-457	484	6	ẍ	ẍ	PUNCT
ejpam-457	485	1	+	+	CCONJ
ejpam-457	485	2	∑	∑	PROPN
ejpam-457	485	3	j∈j	j∈j	NOUN
ejpam-457	485	4	◦	◦	NOUN
ejpam-457	485	5	y	y	PROPN
ejpam-457	485	6	j(t)g	j(t)g	PROPN
ejpam-457	485	7	j	j	PROPN
ejpam-457	485	8	ẍ	ẍ	PROPN
ejpam-457	485	9	)	)	PUNCT
ejpam-457	485	10	}	}	PUNCT
ejpam-457	486	1	=	=	SYM
ejpam-457	486	2	0	0	NUM
ejpam-457	486	3	this	this	PRON
ejpam-457	486	4	,	,	PUNCT
ejpam-457	486	5	due	due	ADP
ejpam-457	486	6	to	to	ADP
ejpam-457	486	7	the	the	DET
ejpam-457	486	8	hypothesis	hypothesis	NOUN
ejpam-457	486	9	(	(	PUNCT
ejpam-457	486	10	a3	a3	NOUN
ejpam-457	486	11	)	)	PUNCT
ejpam-457	486	12	gives	give	VERB
ejpam-457	486	13	,	,	PUNCT
ejpam-457	486	14	τi	τi	ADP
ejpam-457	486	15	−	−	NOUN
ejpam-457	486	16	γλi	γλi	NOUN
ejpam-457	486	17	=	=	SYM
ejpam-457	486	18	0	0	NUM
ejpam-457	486	19	,	,	PUNCT
ejpam-457	486	20	i	i	PRON
ejpam-457	486	21	=	=	NOUN
ejpam-457	486	22	1,2	1,2	NUM
ejpam-457	486	23	,	,	PUNCT
ejpam-457	486	24	.	.	PUNCT
ejpam-457	486	25	.	.	PUNCT
ejpam-457	487	1	.	.	PUNCT
ejpam-457	488	1	,	,	PUNCT
ejpam-457	488	2	p	p	X
ejpam-457	488	3	(	(	PUNCT
ejpam-457	488	4	36	36	NUM
ejpam-457	488	5	)	)	PUNCT
ejpam-457	488	6	suppose	suppose	VERB
ejpam-457	488	7	γ=	γ=	PROPN
ejpam-457	488	8	0	0	NUM
ejpam-457	488	9	,	,	PUNCT
ejpam-457	488	10	then	then	ADV
ejpam-457	488	11	from	from	ADP
ejpam-457	488	12	(	(	PUNCT
ejpam-457	488	13	36	36	NUM
ejpam-457	488	14	)	)	PUNCT
ejpam-457	488	15	we	we	PRON
ejpam-457	488	16	have	have	VERB
ejpam-457	488	17	τ	τ	X
ejpam-457	488	18	=	=	SYM
ejpam-457	488	19	0	0	X
ejpam-457	488	20	.	.	PUNCT
ejpam-457	489	1	consequently	consequently	ADV
ejpam-457	489	2	from	from	ADP
ejpam-457	489	3	(	(	PUNCT
ejpam-457	489	4	23	23	NUM
ejpam-457	489	5	)	)	PUNCT
ejpam-457	489	6	and	and	CCONJ
ejpam-457	489	7	(	(	PUNCT
ejpam-457	489	8	24	24	NUM
ejpam-457	489	9	)	)	PUNCT
ejpam-457	489	10	implies	imply	VERB
ejpam-457	489	11	µ(t	µ(t	ADJ
ejpam-457	489	12	)	)	PUNCT
ejpam-457	489	13	=	=	SYM
ejpam-457	489	14	0	0	NUM
ejpam-457	489	15	,	,	PUNCT
ejpam-457	490	1	t	t	PROPN
ejpam-457	490	2	∈	∈	PROPN
ejpam-457	491	1	i	i	PRON
ejpam-457	491	2	.	.	PUNCT
ejpam-457	492	1	also	also	ADV
ejpam-457	492	2	from	from	ADP
ejpam-457	492	3	(	(	PUNCT
ejpam-457	492	4	25	25	NUM
ejpam-457	492	5	)	)	PUNCT
ejpam-457	492	6	we	we	PRON
ejpam-457	492	7	have	have	VERB
ejpam-457	492	8	δibi(t)z	δibi(t)z	NOUN
ejpam-457	492	9	i(t	i(t	NOUN
ejpam-457	492	10	)	)	PUNCT
ejpam-457	493	1	=	=	SYM
ejpam-457	493	2	0	0	NUM
ejpam-457	493	3	,	,	PUNCT
ejpam-457	493	4	which	which	PRON
ejpam-457	493	5	together	together	ADV
ejpam-457	493	6	with	with	ADP
ejpam-457	493	7	(	(	PUNCT
ejpam-457	493	8	30	30	NUM
ejpam-457	493	9	)	)	PUNCT
ejpam-457	493	10	implies	imply	VERB
ejpam-457	493	11	δi	δi	ADP
ejpam-457	493	12	=	=	SYM
ejpam-457	493	13	0	0	NUM
ejpam-457	493	14	,	,	PUNCT
ejpam-457	493	15	i.e.	i.e.	X
ejpam-457	493	16	δ	δ	X
ejpam-457	493	17	=	=	SYM
ejpam-457	493	18	0	0	PROPN
ejpam-457	493	19	.	.	PUNCT
ejpam-457	494	1	thus	thus	ADV
ejpam-457	494	2	,	,	PUNCT
ejpam-457	494	3	(	(	PUNCT
ejpam-457	494	4	τ	τ	X
ejpam-457	494	5	,	,	PUNCT
ejpam-457	494	6	β(t),µ(t),η	β(t),µ(t),η	PRON
ejpam-457	494	7	,	,	PUNCT
ejpam-457	494	8	γ	γ	X
ejpam-457	494	9	,	,	PUNCT
ejpam-457	494	10	δ	δ	PROPN
ejpam-457	494	11	,	,	PUNCT
ejpam-457	494	12	)	)	PUNCT
ejpam-457	494	13	=	=	SYM
ejpam-457	494	14	0	0	NUM
ejpam-457	494	15	,	,	PUNCT
ejpam-457	494	16	which	which	PRON
ejpam-457	494	17	is	be	AUX
ejpam-457	494	18	a	a	DET
ejpam-457	494	19	contradiction	contradiction	NOUN
ejpam-457	494	20	to	to	ADP
ejpam-457	494	21	(	(	PUNCT
ejpam-457	494	22	32	32	NUM
ejpam-457	494	23	)	)	PUNCT
ejpam-457	494	24	.	.	PUNCT
ejpam-457	495	1	hence	hence	ADV
ejpam-457	495	2	γ	γ	X
ejpam-457	495	3	>	>	X
ejpam-457	495	4	0	0	NUM
ejpam-457	495	5	.	.	PUNCT
ejpam-457	496	1	from	from	ADP
ejpam-457	496	2	(	(	PUNCT
ejpam-457	496	3	34	34	NUM
ejpam-457	496	4	)	)	PUNCT
ejpam-457	496	5	it	it	PRON
ejpam-457	496	6	implies	imply	VERB
ejpam-457	496	7	that	that	SCONJ
ejpam-457	496	8	τ	τ	PROPN
ejpam-457	496	9	>	>	X
ejpam-457	496	10	0	0	NUM
ejpam-457	496	11	.	.	PUNCT
ejpam-457	497	1	by	by	ADP
ejpam-457	497	2	the	the	DET
ejpam-457	497	3	generalized	generalize	VERB
ejpam-457	497	4	schwartz	schwartz	NOUN
ejpam-457	497	5	inequality	inequality	NOUN
ejpam-457	497	6	[	[	X
ejpam-457	497	7	17	17	NUM
ejpam-457	497	8	]	]	PUNCT
ejpam-457	497	9	,	,	PUNCT
ejpam-457	497	10	(	(	PUNCT
ejpam-457	497	11	x̄(t)t	x̄(t)t	PROPN
ejpam-457	497	12	bi(t)z̄	bi(t)z̄	PROPN
ejpam-457	497	13	i(t))¶	i(t))¶	PROPN
ejpam-457	497	14	(	(	PUNCT
ejpam-457	497	15	x̄(t)t	x̄(t)t	NOUN
ejpam-457	497	16	bi(t	bi(t	NOUN
ejpam-457	497	17	)	)	PUNCT
ejpam-457	497	18	x̄(t	x̄(t	PROPN
ejpam-457	497	19	)	)	PUNCT
ejpam-457	497	20	)	)	PUNCT
ejpam-457	497	21	1	1	NUM
ejpam-457	497	22	2	2	NUM
ejpam-457	497	23	(	(	PUNCT
ejpam-457	497	24	z̄	z̄	NOUN
ejpam-457	497	25	i(t)bi(t)z̄	i(t)bi(t)z̄	NOUN
ejpam-457	497	26	i(t	i(t	NOUN
ejpam-457	497	27	)	)	PUNCT
ejpam-457	497	28	)	)	PUNCT
ejpam-457	497	29	1	1	NUM
ejpam-457	497	30	2	2	NUM
ejpam-457	497	31	,	,	PUNCT
ejpam-457	497	32	i	i	PRON
ejpam-457	497	33	=	=	NOUN
ejpam-457	497	34	1,2	1,2	NUM
ejpam-457	497	35	,	,	PUNCT
ejpam-457	497	36	.	.	PUNCT
ejpam-457	497	37	.	.	PUNCT
ejpam-457	497	38	.	.	PUNCT
ejpam-457	498	1	,	,	PUNCT
ejpam-457	498	2	p	p	X
ejpam-457	498	3	(	(	PUNCT
ejpam-457	498	4	37	37	NUM
ejpam-457	498	5	)	)	PUNCT
ejpam-457	498	6	now	now	ADV
ejpam-457	498	7	let	let	VERB
ejpam-457	499	1	δ	δ	PRON
ejpam-457	499	2	i	i	PRON
ejpam-457	499	3	τi	τi	VERB
ejpam-457	499	4	=	=	PUNCT
ejpam-457	500	1	α	α	NUM
ejpam-457	501	1	i	i	NOUN
ejpam-457	501	2	.	.	PUNCT
ejpam-457	502	1	then	then	ADV
ejpam-457	502	2	αi	αi	VERB
ejpam-457	502	3	≧	≧	NOUN
ejpam-457	502	4	0	0	PUNCT
ejpam-457	502	5	and	and	CCONJ
ejpam-457	502	6	from	from	ADP
ejpam-457	502	7	(	(	PUNCT
ejpam-457	502	8	25	25	NUM
ejpam-457	502	9	)	)	PUNCT
ejpam-457	502	10	,	,	PUNCT
ejpam-457	502	11	we	we	PRON
ejpam-457	502	12	have	have	VERB
ejpam-457	502	13	bi(t	bi(t	NOUN
ejpam-457	502	14	)	)	PUNCT
ejpam-457	502	15	x̄(t	x̄(t	PUNCT
ejpam-457	502	16	)	)	PUNCT
ejpam-457	503	1	=	=	SYM
ejpam-457	503	2	2αibi(t)z̄	2αibi(t)z̄	NUM
ejpam-457	503	3	i(t	i(t	NOUN
ejpam-457	503	4	)	)	PUNCT
ejpam-457	503	5	,	,	PUNCT
ejpam-457	503	6	i	i	NOUN
ejpam-457	503	7	=	=	NOUN
ejpam-457	503	8	1,2	1,2	NUM
ejpam-457	503	9	,	,	PUNCT
ejpam-457	503	10	.	.	PUNCT
ejpam-457	503	11	.	.	PUNCT
ejpam-457	504	1	.	.	PUNCT
ejpam-457	505	1	,	,	PUNCT
ejpam-457	505	2	p	p	X
ejpam-457	505	3	which	which	PRON
ejpam-457	505	4	,	,	PUNCT
ejpam-457	505	5	is	be	AUX
ejpam-457	505	6	the	the	DET
ejpam-457	505	7	condition	condition	NOUN
ejpam-457	505	8	for	for	ADP
ejpam-457	505	9	the	the	DET
ejpam-457	505	10	equality	equality	NOUN
ejpam-457	505	11	in	in	ADP
ejpam-457	505	12	(	(	PUNCT
ejpam-457	505	13	37	37	NUM
ejpam-457	505	14	)	)	PUNCT
ejpam-457	505	15	.	.	PUNCT
ejpam-457	506	1	therefore	therefore	ADV
ejpam-457	506	2	,	,	PUNCT
ejpam-457	506	3	we	we	PRON
ejpam-457	506	4	have	have	VERB
ejpam-457	506	5	(	(	PUNCT
ejpam-457	506	6	x̄(t)t	x̄(t)t	PROPN
ejpam-457	506	7	bi(t)z̄	bi(t)z̄	PROPN
ejpam-457	506	8	i(t	i(t	PROPN
ejpam-457	506	9	)	)	PUNCT
ejpam-457	506	10	)	)	PUNCT
ejpam-457	507	1	=	=	PRON
ejpam-457	507	2	(	(	PUNCT
ejpam-457	507	3	x̄(t)t	x̄(t)t	NOUN
ejpam-457	507	4	bi(t	bi(t	NOUN
ejpam-457	507	5	)	)	PUNCT
ejpam-457	507	6	x̄(t	x̄(t	PROPN
ejpam-457	507	7	)	)	PUNCT
ejpam-457	507	8	)	)	PUNCT
ejpam-457	507	9	1	1	NUM
ejpam-457	507	10	2	2	NUM
ejpam-457	507	11	(	(	PUNCT
ejpam-457	507	12	z	z	NOUN
ejpam-457	507	13	i(t)bi(t)z	i(t)bi(t)z	PRON
ejpam-457	507	14	i(t	i(t	NOUN
ejpam-457	507	15	)	)	PUNCT
ejpam-457	507	16	)	)	PUNCT
ejpam-457	507	17	1	1	NUM
ejpam-457	507	18	2	2	NUM
ejpam-457	507	19	from	from	ADP
ejpam-457	507	20	(	(	PUNCT
ejpam-457	507	21	30	30	NUM
ejpam-457	507	22	)	)	PUNCT
ejpam-457	507	23	,	,	PUNCT
ejpam-457	507	24	either	either	CCONJ
ejpam-457	507	25	δi	δi	ADP
ejpam-457	507	26	=	=	SYM
ejpam-457	507	27	0	0	NUM
ejpam-457	507	28	or	or	CCONJ
ejpam-457	507	29	z̄	z̄	PROPN
ejpam-457	507	30	i(t)t	i(t)t	PROPN
ejpam-457	507	31	bi(t)z̄	bi(t)z̄	PROPN
ejpam-457	507	32	i(t	i(t	PROPN
ejpam-457	507	33	)	)	PUNCT
ejpam-457	507	34	=	=	SYM
ejpam-457	507	35	1	1	NUM
ejpam-457	507	36	or	or	CCONJ
ejpam-457	507	37	δi	δi	VERB
ejpam-457	507	38	=	=	SYM
ejpam-457	507	39	0	0	NUM
ejpam-457	507	40	,	,	PUNCT
ejpam-457	507	41	i	i	PRON
ejpam-457	507	42	=	=	NOUN
ejpam-457	507	43	1	1	NUM
ejpam-457	507	44	,	,	PUNCT
ejpam-457	507	45	.	.	PUNCT
ejpam-457	507	46	.	.	PUNCT
ejpam-457	508	1	.	.	PUNCT
ejpam-457	509	1	,	,	PUNCT
ejpam-457	509	2	p	p	NOUN
ejpam-457	509	3	and	and	CCONJ
ejpam-457	509	4	hence	hence	ADV
ejpam-457	509	5	bi(t	bi(t	NOUN
ejpam-457	509	6	)	)	PUNCT
ejpam-457	509	7	x̄(t	x̄(t	PUNCT
ejpam-457	509	8	)	)	PUNCT
ejpam-457	510	1	=	=	SYM
ejpam-457	510	2	0	0	X
ejpam-457	510	3	.	.	PUNCT
ejpam-457	511	1	therefore	therefore	ADV
ejpam-457	511	2	,	,	PUNCT
ejpam-457	511	3	in	in	ADP
ejpam-457	511	4	either	either	DET
ejpam-457	511	5	case	case	NOUN
ejpam-457	511	6	(	(	PUNCT
ejpam-457	511	7	x(t)t	x(t)t	PROPN
ejpam-457	511	8	bi(t)z	bi(t)z	PROPN
ejpam-457	511	9	i(t	i(t	PROPN
ejpam-457	511	10	)	)	PUNCT
ejpam-457	511	11	)	)	PUNCT
ejpam-457	512	1	=	=	SYM
ejpam-457	512	2	(	(	PUNCT
ejpam-457	512	3	x(t)t	x(t)t	PROPN
ejpam-457	512	4	bi(t)x(t	bi(t)x(t	PROPN
ejpam-457	512	5	)	)	PUNCT
ejpam-457	512	6	)	)	PUNCT
ejpam-457	512	7	1	1	NUM
ejpam-457	512	8	2	2	NUM
ejpam-457	512	9	,	,	PUNCT
ejpam-457	512	10	i	i	PRON
ejpam-457	512	11	=	=	NOUN
ejpam-457	512	12	1,2	1,2	NUM
ejpam-457	512	13	,	,	PUNCT
ejpam-457	512	14	.	.	PUNCT
ejpam-457	512	15	.	.	PUNCT
ejpam-457	513	1	.	.	PUNCT
ejpam-457	514	1	,	,	PUNCT
ejpam-457	514	2	p	p	X
ejpam-457	514	3	(	(	PUNCT
ejpam-457	514	4	38	38	NUM
ejpam-457	514	5	)	)	PUNCT
ejpam-457	514	6	from	from	ADP
ejpam-457	514	7	(	(	PUNCT
ejpam-457	514	8	23	23	NUM
ejpam-457	514	9	)	)	PUNCT
ejpam-457	514	10	and	and	CCONJ
ejpam-457	514	11	(	(	PUNCT
ejpam-457	514	12	24	24	NUM
ejpam-457	514	13	)	)	PUNCT
ejpam-457	514	14	we	we	PRON
ejpam-457	514	15	readily	readily	ADV
ejpam-457	514	16	obtain	obtain	VERB
ejpam-457	514	17	,	,	PUNCT
ejpam-457	514	18	g(t	g(t	PROPN
ejpam-457	514	19	,	,	PUNCT
ejpam-457	514	20	x̄	x̄	NOUN
ejpam-457	514	21	,	,	PUNCT
ejpam-457	514	22	˙̄x	˙̄x	X
ejpam-457	514	23	,	,	PUNCT
ejpam-457	514	24	¨̄x)≦	¨̄x)≦	NOUN
ejpam-457	514	25	0	0	NUM
ejpam-457	514	26	,	,	PUNCT
ejpam-457	514	27	t	t	PROPN
ejpam-457	514	28	∈	∈	PROPN
ejpam-457	514	29	i	i	PRON
ejpam-457	514	30	which	which	PRON
ejpam-457	514	31	gives	give	VERB
ejpam-457	514	32	the	the	DET
ejpam-457	514	33	feasibility	feasibility	NOUN
ejpam-457	514	34	of	of	ADP
ejpam-457	514	35	x̄	x̄	PROPN
ejpam-457	514	36	for	for	ADP
ejpam-457	514	37	(	(	PUNCT
ejpam-457	514	38	p	p	NOUN
ejpam-457	514	39	)	)	PUNCT
ejpam-457	514	40	.	.	PUNCT
ejpam-457	515	1	using	use	VERB
ejpam-457	515	2	(	(	PUNCT
ejpam-457	515	3	27	27	NUM
ejpam-457	515	4	)	)	PUNCT
ejpam-457	515	5	in	in	ADP
ejpam-457	515	6	(	(	PUNCT
ejpam-457	515	7	23	23	NUM
ejpam-457	515	8	)	)	PUNCT
ejpam-457	515	9	and	and	CCONJ
ejpam-457	515	10	(	(	PUNCT
ejpam-457	515	11	24	24	NUM
ejpam-457	515	12	)	)	PUNCT
ejpam-457	515	13	we	we	PRON
ejpam-457	515	14	have	have	VERB
ejpam-457	515	15	ȳ(t)t	ȳ(t)t	NOUN
ejpam-457	515	16	g	g	NOUN
ejpam-457	515	17	=	=	SYM
ejpam-457	515	18	0	0	NUM
ejpam-457	515	19	,	,	PUNCT
ejpam-457	515	20	i.e.	i.e.	X
ejpam-457	515	21	,	,	PUNCT
ejpam-457	515	22	ȳ	ȳ	PROPN
ejpam-457	515	23	j(t)g	j(t)g	PROPN
ejpam-457	515	24	j	j	PROPN
ejpam-457	515	25	=	=	SYM
ejpam-457	515	26	0	0	PROPN
ejpam-457	515	27	,	,	PUNCT
ejpam-457	515	28	j	j	X
ejpam-457	516	1	=	=	SYM
ejpam-457	516	2	1,2	1,2	NUM
ejpam-457	516	3	,	,	PUNCT
ejpam-457	516	4	.	.	PUNCT
ejpam-457	516	5	.	.	PUNCT
ejpam-457	517	1	.	.	PUNCT
ejpam-457	518	1	,	,	PUNCT
ejpam-457	518	2	m	m	PROPN
ejpam-457	518	3	,	,	PUNCT
ejpam-457	518	4	t	t	PROPN
ejpam-457	518	5	∈	∈	PROPN
ejpam-457	519	1	i	i	PRON
ejpam-457	519	2	i.	i.	PROPN
ejpam-457	519	3	husain	husain	PROPN
ejpam-457	519	4	,	,	PUNCT
ejpam-457	519	5	r.	r.	PROPN
ejpam-457	519	6	mattoo	mattoo	PROPN
ejpam-457	519	7	/	/	SYM
ejpam-457	519	8	eur	eur	PROPN
ejpam-457	519	9	.	.	PUNCT
ejpam-457	520	1	j.	j.	PROPN
ejpam-457	520	2	pure	pure	PROPN
ejpam-457	520	3	appl	appl	PROPN
ejpam-457	520	4	.	.	PROPN
ejpam-457	520	5	math	math	PROPN
ejpam-457	520	6	,	,	PUNCT
ejpam-457	520	7	3	3	NUM
ejpam-457	520	8	(	(	PUNCT
ejpam-457	520	9	2010	2010	NUM
ejpam-457	520	10	)	)	PUNCT
ejpam-457	520	11	,	,	PUNCT
ejpam-457	520	12	81	81	NUM
ejpam-457	520	13	-	-	SYM
ejpam-457	520	14	97	97	NUM
ejpam-457	520	15	94	94	NUM
ejpam-457	520	16	this	this	PRON
ejpam-457	520	17	obviously	obviously	ADV
ejpam-457	520	18	gives	give	VERB
ejpam-457	520	19	∑	∑	PART
ejpam-457	520	20	j∈j	j∈j	NOUN
ejpam-457	520	21	◦	◦	NOUN
ejpam-457	520	22	ȳ	ȳ	NOUN
ejpam-457	520	23	j(t)g	j(t)g	PROPN
ejpam-457	520	24	j	j	PROPN
ejpam-457	521	1	=	=	SYM
ejpam-457	521	2	0	0	PROPN
ejpam-457	521	3	,	,	PUNCT
ejpam-457	521	4	j	j	X
ejpam-457	521	5	=	=	SYM
ejpam-457	521	6	1,2	1,2	NUM
ejpam-457	521	7	,	,	PUNCT
ejpam-457	521	8	.	.	PUNCT
ejpam-457	521	9	.	.	PUNCT
ejpam-457	521	10	.	.	PUNCT
ejpam-457	522	1	,	,	PUNCT
ejpam-457	522	2	m	m	PROPN
ejpam-457	522	3	(	(	PUNCT
ejpam-457	522	4	39	39	NUM
ejpam-457	522	5	)	)	PUNCT
ejpam-457	523	1	hence	hence	ADV
ejpam-457	523	2	∫	∫	INTJ
ejpam-457	524	1	i	i	PRON
ejpam-457	524	2	(	(	PUNCT
ejpam-457	524	3	f	f	PROPN
ejpam-457	524	4	i(t	i(t	PROPN
ejpam-457	524	5	,	,	PUNCT
ejpam-457	524	6	x̄	x̄	NOUN
ejpam-457	524	7	,	,	PUNCT
ejpam-457	524	8	˙̄x	˙̄x	PUNCT
ejpam-457	524	9	,	,	PUNCT
ejpam-457	524	10	¨̄x)d	¨̄x)d	PROPN
ejpam-457	524	11	t	t	NOUN
ejpam-457	524	12	+	+	CCONJ
ejpam-457	524	13	x̄(t)t	x̄(t)t	PROPN
ejpam-457	524	14	bi(t)z̄	bi(t)z̄	PROPN
ejpam-457	524	15	i(t	i(t	PROPN
ejpam-457	524	16	)	)	PUNCT
ejpam-457	525	1	+	+	CCONJ
ejpam-457	525	2	∑	∑	PUNCT
ejpam-457	525	3	j∈j	j∈j	NOUN
ejpam-457	525	4	◦	◦	NOUN
ejpam-457	525	5	ȳ	ȳ	NOUN
ejpam-457	525	6	j(t)g	j(t)g	PROPN
ejpam-457	525	7	j)d	j)d	NOUN
ejpam-457	525	8	t	t	NOUN
ejpam-457	525	9	=	=	SYM
ejpam-457	525	10	∫	∫	PROPN
ejpam-457	526	1	i	i	PRON
ejpam-457	526	2	(	(	PUNCT
ejpam-457	526	3	f	f	PROPN
ejpam-457	526	4	i(t	i(t	PROPN
ejpam-457	526	5	,	,	PUNCT
ejpam-457	526	6	x̄	x̄	NOUN
ejpam-457	526	7	,	,	PUNCT
ejpam-457	526	8	˙̄x	˙̄x	PUNCT
ejpam-457	526	9	,	,	PUNCT
ejpam-457	526	10	¨̄x)d	¨̄x)d	PROPN
ejpam-457	526	11	t	t	NOUN
ejpam-457	526	12	+	+	CCONJ
ejpam-457	526	13	(	(	PUNCT
ejpam-457	526	14	x̄(t)t	x̄(t)t	NOUN
ejpam-457	526	15	bi(t	bi(t	NOUN
ejpam-457	526	16	)	)	PUNCT
ejpam-457	526	17	x̄(t	x̄(t	PROPN
ejpam-457	526	18	)	)	PUNCT
ejpam-457	526	19	)	)	PUNCT
ejpam-457	526	20	1	1	NUM
ejpam-457	526	21	2	2	NUM
ejpam-457	526	22	)	)	PUNCT
ejpam-457	526	23	d	d	PROPN
ejpam-457	526	24	t	t	PROPN
ejpam-457	526	25	,	,	PUNCT
ejpam-457	526	26	i	i	NOUN
ejpam-457	526	27	=	=	NOUN
ejpam-457	526	28	1,2	1,2	NUM
ejpam-457	526	29	,	,	PUNCT
ejpam-457	526	30	.	.	PUNCT
ejpam-457	526	31	.	.	PUNCT
ejpam-457	526	32	.	.	PUNCT
ejpam-457	527	1	,	,	PUNCT
ejpam-457	527	2	p	p	X
ejpam-457	527	3	(	(	PUNCT
ejpam-457	527	4	by	by	ADP
ejpam-457	527	5	using	use	VERB
ejpam-457	527	6	(	(	PUNCT
ejpam-457	527	7	38	38	NUM
ejpam-457	527	8	)	)	PUNCT
ejpam-457	527	9	and	and	CCONJ
ejpam-457	527	10	(	(	PUNCT
ejpam-457	527	11	39	39	NUM
ejpam-457	527	12	)	)	PUNCT
ejpam-457	527	13	)	)	PUNCT
ejpam-457	527	14	the	the	DET
ejpam-457	527	15	efficiency	efficiency	NOUN
ejpam-457	527	16	of	of	ADP
ejpam-457	527	17	x̄	x̄	PROPN
ejpam-457	527	18	for	for	ADP
ejpam-457	527	19	(	(	PUNCT
ejpam-457	527	20	vp	vp	PROPN
ejpam-457	527	21	)	)	PUNCT
ejpam-457	527	22	follows	follow	VERB
ejpam-457	527	23	by	by	ADP
ejpam-457	527	24	an	an	DET
ejpam-457	527	25	application	application	NOUN
ejpam-457	527	26	of	of	ADP
ejpam-457	527	27	theorem	theorem	NOUN
ejpam-457	527	28	1	1	NUM
ejpam-457	527	29	.	.	NOUN
ejpam-457	527	30	4	4	NUM
ejpam-457	527	31	.	.	NOUN
ejpam-457	527	32	variational	variational	ADJ
ejpam-457	527	33	problems	problem	NOUN
ejpam-457	527	34	with	with	ADP
ejpam-457	527	35	natural	natural	ADJ
ejpam-457	527	36	boundary	boundary	ADJ
ejpam-457	527	37	conditions	condition	NOUN
ejpam-457	527	38	it	it	PRON
ejpam-457	527	39	is	be	AUX
ejpam-457	527	40	possible	possible	ADJ
ejpam-457	527	41	to	to	PART
ejpam-457	527	42	extend	extend	VERB
ejpam-457	527	43	the	the	DET
ejpam-457	527	44	duality	duality	NOUN
ejpam-457	527	45	theorems	theorem	NOUN
ejpam-457	527	46	established	establish	VERB
ejpam-457	527	47	in	in	ADP
ejpam-457	527	48	the	the	DET
ejpam-457	527	49	previous	previous	ADJ
ejpam-457	527	50	sections	section	NOUN
ejpam-457	527	51	to	to	ADP
ejpam-457	527	52	the	the	DET
ejpam-457	527	53	corresponding	corresponding	ADJ
ejpam-457	527	54	variational	variational	ADJ
ejpam-457	527	55	problems	problem	NOUN
ejpam-457	527	56	with	with	ADP
ejpam-457	527	57	natural	natural	ADJ
ejpam-457	527	58	boundary	boundary	ADJ
ejpam-457	527	59	values	value	NOUN
ejpam-457	527	60	rather	rather	ADV
ejpam-457	527	61	that	that	DET
ejpam-457	527	62	fixed	fix	VERB
ejpam-457	527	63	points	point	NOUN
ejpam-457	527	64	.	.	PUNCT
ejpam-457	528	1	(	(	PUNCT
ejpam-457	528	2	vp)0	vp)0	NOUN
ejpam-457	528	3	minimize	minimize	VERB
ejpam-457	528	4	�	�	PROPN
ejpam-457	528	5	∫	∫	PROPN
ejpam-457	528	6	i	i	PROPN
ejpam-457	528	7	�	�	PROPN
ejpam-457	528	8	f	f	PROPN
ejpam-457	528	9	1(t	1(t	NUM
ejpam-457	528	10	,	,	PUNCT
ejpam-457	528	11	x	x	PRON
ejpam-457	528	12	,	,	PUNCT
ejpam-457	528	13	ẋ	ẋ	PROPN
ejpam-457	528	14	,	,	PUNCT
ejpam-457	528	15	ẍ)d	ẍ)d	PROPN
ejpam-457	528	16	t	t	PROPN
ejpam-457	528	17	+	+	CCONJ
ejpam-457	528	18	(	(	PUNCT
ejpam-457	528	19	x(t)t	x(t)t	PROPN
ejpam-457	528	20	b1(t)x(t	b1(t)x(t	PROPN
ejpam-457	528	21	)	)	PUNCT
ejpam-457	528	22	)	)	PUNCT
ejpam-457	528	23	1	1	NUM
ejpam-457	528	24	2	2	NUM
ejpam-457	528	25	�	�	PROPN
ejpam-457	528	26	d	d	PROPN
ejpam-457	528	27	t	t	PROPN
ejpam-457	528	28	,	,	PUNCT
ejpam-457	528	29	.	.	PUNCT
ejpam-457	528	30	.	.	PUNCT
ejpam-457	529	1	.	.	PUNCT
ejpam-457	530	1	,	,	PUNCT
ejpam-457	530	2	∫	∫	PROPN
ejpam-457	531	1	i	i	PRON
ejpam-457	531	2	�	�	PROPN
ejpam-457	531	3	f	f	PROPN
ejpam-457	531	4	p(t	p(t	PROPN
ejpam-457	531	5	,	,	PUNCT
ejpam-457	531	6	x	x	X
ejpam-457	531	7	,	,	PUNCT
ejpam-457	531	8	ẋ	ẋ	PROPN
ejpam-457	531	9	,	,	PUNCT
ejpam-457	531	10	ẍ)d	ẍ)d	PROPN
ejpam-457	531	11	t	t	PROPN
ejpam-457	531	12	+	+	CCONJ
ejpam-457	531	13	(	(	PUNCT
ejpam-457	531	14	x(t)t	x(t)t	PROPN
ejpam-457	531	15	bp(t)x(t	bp(t)x(t	PROPN
ejpam-457	531	16	)	)	PUNCT
ejpam-457	531	17	)	)	PUNCT
ejpam-457	531	18	1	1	NUM
ejpam-457	531	19	2	2	NUM
ejpam-457	531	20	�	�	PROPN
ejpam-457	531	21	d	d	PROPN
ejpam-457	531	22	t	t	PROPN
ejpam-457	531	23	�	�	PROPN
ejpam-457	531	24	subject	subject	ADJ
ejpam-457	531	25	to	to	ADP
ejpam-457	531	26	g	g	PROPN
ejpam-457	531	27	j(t	j(t	PROPN
ejpam-457	531	28	,	,	PUNCT
ejpam-457	531	29	x	x	INTJ
ejpam-457	531	30	,	,	PUNCT
ejpam-457	531	31	ẋ	ẋ	PROPN
ejpam-457	531	32	,	,	PUNCT
ejpam-457	531	33	ẋ	ẋ	PROPN
ejpam-457	531	34	)	)	PUNCT
ejpam-457	531	35	≦	≦	NOUN
ejpam-457	531	36	0	0	NUM
ejpam-457	531	37	,	,	PUNCT
ejpam-457	531	38	t	t	PROPN
ejpam-457	531	39	∈	∈	PROPN
ejpam-457	532	1	i	i	PRON
ejpam-457	532	2	,	,	PUNCT
ejpam-457	532	3	j	j	PROPN
ejpam-457	532	4	=	=	SYM
ejpam-457	532	5	1	1	NUM
ejpam-457	532	6	,	,	PUNCT
ejpam-457	532	7	.	.	PUNCT
ejpam-457	532	8	.	.	PUNCT
ejpam-457	532	9	.	.	PUNCT
ejpam-457	533	1	,	,	PUNCT
ejpam-457	533	2	m	m	VERB
ejpam-457	533	3	(	(	PUNCT
ejpam-457	533	4	m	m	AUX
ejpam-457	533	5	ix	ix	ADJ
ejpam-457	533	6	d)0	d)0	NOUN
ejpam-457	533	7	maximize	maximize	VERB
ejpam-457	533	8	�	�	PROPN
ejpam-457	533	9	∫	∫	PROPN
ejpam-457	534	1	i	i	PROPN
ejpam-457	534	2	�	�	PROPN
ejpam-457	534	3	f	f	PROPN
ejpam-457	534	4	1(t	1(t	NUM
ejpam-457	534	5	,	,	PUNCT
ejpam-457	534	6	u	u	NOUN
ejpam-457	534	7	,	,	PUNCT
ejpam-457	534	8	u̇	u̇	PROPN
ejpam-457	534	9	,	,	PUNCT
ejpam-457	534	10	ü	ü	PRON
ejpam-457	534	11	)	)	PUNCT
ejpam-457	535	1	+	+	CCONJ
ejpam-457	535	2	u(t)t	u(t)t	X
ejpam-457	535	3	b1(t)z1(t	b1(t)z1(t	X
ejpam-457	535	4	)	)	PUNCT
ejpam-457	536	1	+	+	CCONJ
ejpam-457	536	2	∑	∑	PUNCT
ejpam-457	536	3	j∈j	j∈j	NOUN
ejpam-457	536	4	◦	◦	NOUN
ejpam-457	536	5	y	y	PROPN
ejpam-457	536	6	j(t)g	j(t)g	PROPN
ejpam-457	536	7	j(t	j(t	PROPN
ejpam-457	536	8	,	,	PUNCT
ejpam-457	536	9	u	u	NOUN
ejpam-457	536	10	,	,	PUNCT
ejpam-457	536	11	u̇	u̇	PROPN
ejpam-457	536	12	,	,	PUNCT
ejpam-457	536	13	ü	ü	NOUN
ejpam-457	536	14	)	)	PUNCT
ejpam-457	536	15	�	�	PROPN
ejpam-457	536	16	d	d	PROPN
ejpam-457	536	17	t	t	PROPN
ejpam-457	536	18	,	,	PUNCT
ejpam-457	536	19	.	.	PUNCT
ejpam-457	536	20	.	.	PUNCT
ejpam-457	536	21	.	.	PUNCT
ejpam-457	537	1	,	,	PUNCT
ejpam-457	537	2	∫	∫	PROPN
ejpam-457	538	1	i	i	PRON
ejpam-457	538	2	�	�	PROPN
ejpam-457	539	1	f	f	PROPN
ejpam-457	539	2	p(t	p(t	PROPN
ejpam-457	539	3	,	,	PUNCT
ejpam-457	539	4	u	u	NOUN
ejpam-457	539	5	,	,	PUNCT
ejpam-457	539	6	u̇	u̇	PROPN
ejpam-457	539	7	,	,	PUNCT
ejpam-457	539	8	ü	ü	PRON
ejpam-457	539	9	)	)	PUNCT
ejpam-457	540	1	+	+	CCONJ
ejpam-457	540	2	(	(	PUNCT
ejpam-457	540	3	u(t)t	u(t)t	NOUN
ejpam-457	540	4	bp(t)zp(t	bp(t)zp(t	NOUN
ejpam-457	540	5	)	)	PUNCT
ejpam-457	540	6	)	)	PUNCT
ejpam-457	541	1	+	+	CCONJ
ejpam-457	541	2	∑	∑	PUNCT
ejpam-457	541	3	j∈j	j∈j	NOUN
ejpam-457	541	4	◦	◦	NOUN
ejpam-457	541	5	y	y	PROPN
ejpam-457	541	6	j(t)g	j(t)g	PROPN
ejpam-457	541	7	j(t	j(t	PROPN
ejpam-457	541	8	,	,	PUNCT
ejpam-457	541	9	u	u	NOUN
ejpam-457	541	10	,	,	PUNCT
ejpam-457	541	11	u̇	u̇	PROPN
ejpam-457	541	12	,	,	PUNCT
ejpam-457	541	13	ü	ü	NOUN
ejpam-457	541	14	)	)	PUNCT
ejpam-457	541	15	�	�	PROPN
ejpam-457	541	16	d	d	PROPN
ejpam-457	541	17	t	t	PROPN
ejpam-457	541	18	�	�	PROPN
ejpam-457	541	19	subject	subject	ADJ
ejpam-457	541	20	to	to	ADP
ejpam-457	541	21	p	p	NOUN
ejpam-457	541	22	∑	∑	PROPN
ejpam-457	541	23	i=1	i=1	PROPN
ejpam-457	541	24	λi	λi	PROPN
ejpam-457	541	25	(	(	PUNCT
ejpam-457	541	26	f	f	NOUN
ejpam-457	541	27	i	i	PRON
ejpam-457	541	28	u	u	PROPN
ejpam-457	541	29	(	(	PUNCT
ejpam-457	541	30	t	t	PROPN
ejpam-457	541	31	,	,	PUNCT
ejpam-457	541	32	u	u	NOUN
ejpam-457	541	33	,	,	PUNCT
ejpam-457	541	34	u̇	u̇	PROPN
ejpam-457	541	35	,	,	PUNCT
ejpam-457	541	36	ü	ü	PRON
ejpam-457	541	37	)	)	PUNCT
ejpam-457	542	1	+	+	NUM
ejpam-457	542	2	bi(t)z	bi(t)z	NOUN
ejpam-457	542	3	i(t	i(t	NOUN
ejpam-457	542	4	)	)	PUNCT
ejpam-457	542	5	+	+	NUM
ejpam-457	542	6	y(t)t	y(t)t	NOUN
ejpam-457	542	7	gu(t	gu(t	PUNCT
ejpam-457	542	8	,	,	PUNCT
ejpam-457	542	9	u	u	NOUN
ejpam-457	542	10	,	,	PUNCT
ejpam-457	542	11	u̇	u̇	PROPN
ejpam-457	542	12	,	,	PUNCT
ejpam-457	542	13	ü	ü	NUM
ejpam-457	542	14	)	)	PUNCT
ejpam-457	542	15	)	)	PUNCT
ejpam-457	542	16	−d(λt	−d(λt	NOUN
ejpam-457	542	17	fu̇(t	fu̇(t	PROPN
ejpam-457	542	18	,	,	PUNCT
ejpam-457	542	19	u	u	NOUN
ejpam-457	542	20	,	,	PUNCT
ejpam-457	542	21	u̇	u̇	PROPN
ejpam-457	542	22	,	,	PUNCT
ejpam-457	542	23	ü	ü	PRON
ejpam-457	542	24	)	)	PUNCT
ejpam-457	542	25	+	+	NUM
ejpam-457	542	26	y(t)t	y(t)t	NOUN
ejpam-457	542	27	gu̇(t	gu̇(t	NOUN
ejpam-457	542	28	,	,	PUNCT
ejpam-457	542	29	u	u	NOUN
ejpam-457	542	30	,	,	PUNCT
ejpam-457	542	31	u̇	u̇	PROPN
ejpam-457	542	32	,	,	PUNCT
ejpam-457	542	33	ü	ü	NUM
ejpam-457	542	34	)	)	PUNCT
ejpam-457	542	35	)	)	PUNCT
ejpam-457	543	1	+	+	ADJ
ejpam-457	543	2	d2(λt	d2(λt	NOUN
ejpam-457	543	3	fü(t	fü(t	NOUN
ejpam-457	543	4	,	,	PUNCT
ejpam-457	543	5	u	u	NOUN
ejpam-457	543	6	,	,	PUNCT
ejpam-457	543	7	u̇	u̇	PROPN
ejpam-457	543	8	,	,	PUNCT
ejpam-457	543	9	ü	ü	PRON
ejpam-457	543	10	)	)	PUNCT
ejpam-457	543	11	+	+	CCONJ
ejpam-457	543	12	y(t)t	y(t)t	PROPN
ejpam-457	543	13	gü(t	gü(t	NOUN
ejpam-457	543	14	,	,	PUNCT
ejpam-457	543	15	u	u	NOUN
ejpam-457	543	16	,	,	PUNCT
ejpam-457	543	17	u̇	u̇	PROPN
ejpam-457	543	18	,	,	PUNCT
ejpam-457	543	19	ü	ü	NUM
ejpam-457	543	20	)	)	PUNCT
ejpam-457	543	21	)	)	PUNCT
ejpam-457	543	22	=	=	PUNCT
ejpam-457	543	23	0	0	NUM
ejpam-457	543	24	,	,	PUNCT
ejpam-457	543	25	t	t	PROPN
ejpam-457	543	26	∈	∈	PROPN
ejpam-457	544	1	i	i	PRON
ejpam-457	544	2	,	,	PUNCT
ejpam-457	544	3	�	�	PROPN
ejpam-457	544	4	f	f	PROPN
ejpam-457	545	1	i	i	PRON
ejpam-457	545	2	ẋ	ẋ	PUNCT
ejpam-457	546	1	+	+	CCONJ
ejpam-457	546	2	∑	∑	NOUN
ejpam-457	546	3	j∈j	j∈j	NOUN
ejpam-457	546	4	◦	◦	NOUN
ejpam-457	546	5	y	y	PROPN
ejpam-457	546	6	j(t)g	j(t)g	PROPN
ejpam-457	546	7	j	j	PROPN
ejpam-457	546	8	ẋ	ẋ	PROPN
ejpam-457	546	9	�	�	PROPN
ejpam-457	546	10	�	�	PROPN
ejpam-457	546	11	�	�	PROPN
ejpam-457	546	12	�	�	PROPN
ejpam-457	546	13	�	�	PROPN
ejpam-457	546	14	t	t	PROPN
ejpam-457	546	15	=	=	PROPN
ejpam-457	546	16	a	a	PRON
ejpam-457	546	17	=	=	SYM
ejpam-457	546	18	0	0	NUM
ejpam-457	546	19	�	�	PROPN
ejpam-457	546	20	f	f	PROPN
ejpam-457	547	1	i	i	PRON
ejpam-457	547	2	ẋ	ẋ	PUNCT
ejpam-457	548	1	+	+	CCONJ
ejpam-457	548	2	∑	∑	NOUN
ejpam-457	548	3	j∈j	j∈j	NOUN
ejpam-457	548	4	◦	◦	NOUN
ejpam-457	548	5	y	y	PROPN
ejpam-457	548	6	j(t)g	j(t)g	PROPN
ejpam-457	548	7	j	j	PROPN
ejpam-457	548	8	ẍ	ẍ	PROPN
ejpam-457	548	9	�	�	PROPN
ejpam-457	548	10	�	�	PROPN
ejpam-457	548	11	�	�	PROPN
ejpam-457	548	12	�	�	PROPN
ejpam-457	548	13	�	�	PROPN
ejpam-457	548	14	t	t	PROPN
ejpam-457	548	15	=	=	SYM
ejpam-457	548	16	b	b	NOUN
ejpam-457	548	17	=	=	SYM
ejpam-457	548	18	0	0	NUM
ejpam-457	548	19	references	reference	NOUN
ejpam-457	548	20	95	95	NUM
ejpam-457	548	21	�	�	PROPN
ejpam-457	548	22	f	f	NOUN
ejpam-457	549	1	i	i	NOUN
ejpam-457	549	2	ẍ	ẍ	PUNCT
ejpam-457	550	1	+	+	CCONJ
ejpam-457	550	2	∑	∑	PROPN
ejpam-457	550	3	j∈j	j∈j	NOUN
ejpam-457	550	4	◦	◦	NOUN
ejpam-457	550	5	y	y	PROPN
ejpam-457	550	6	j(t)g	j(t)g	PROPN
ejpam-457	550	7	j	j	PROPN
ejpam-457	550	8	ẋ	ẋ	PROPN
ejpam-457	550	9	�	�	PROPN
ejpam-457	550	10	�	�	PROPN
ejpam-457	550	11	�	�	PROPN
ejpam-457	550	12	�	�	PROPN
ejpam-457	550	13	�	�	PROPN
ejpam-457	550	14	t	t	PROPN
ejpam-457	550	15	=	=	PROPN
ejpam-457	550	16	a	a	PRON
ejpam-457	550	17	=	=	SYM
ejpam-457	550	18	0	0	NUM
ejpam-457	550	19	�	�	PROPN
ejpam-457	551	1	f	f	PROPN
ejpam-457	552	1	i	i	NOUN
ejpam-457	552	2	ẍ	ẍ	PUNCT
ejpam-457	552	3	∑	∑	PROPN
ejpam-457	552	4	j∈j	j∈j	PROPN
ejpam-457	552	5	◦	◦	PROPN
ejpam-457	552	6	y	y	PROPN
ejpam-457	552	7	j(t)g	j(t)g	PROPN
ejpam-457	552	8	j	j	PROPN
ejpam-457	552	9	ẍ	ẍ	PROPN
ejpam-457	552	10	�	�	PROPN
ejpam-457	552	11	�	�	PROPN
ejpam-457	552	12	�	�	PROPN
ejpam-457	552	13	�	�	PROPN
ejpam-457	552	14	�	�	PROPN
ejpam-457	552	15	t	t	PROPN
ejpam-457	552	16	=	=	SYM
ejpam-457	552	17	b	b	PROPN
ejpam-457	552	18	=	=	SYM
ejpam-457	552	19	0	0	NUM
ejpam-457	552	20	∀	∀	NOUN
ejpam-457	553	1	i	i	PRON
ejpam-457	553	2	∈	∈	VERB
ejpam-457	553	3	{	{	PUNCT
ejpam-457	553	4	1,2	1,2	NUM
ejpam-457	553	5	,	,	PUNCT
ejpam-457	553	6	.	.	PUNCT
ejpam-457	553	7	.	.	PUNCT
ejpam-457	553	8	.	.	PUNCT
ejpam-457	554	1	,	,	PUNCT
ejpam-457	554	2	p	p	X
ejpam-457	554	3	}	}	PUNCT
ejpam-457	554	4	z̄	z̄	PROPN
ejpam-457	554	5	i(t)t	i(t)t	PROPN
ejpam-457	554	6	bi(t)z̄	bi(t)z̄	PROPN
ejpam-457	554	7	i(t)≦	i(t)≦	ADP
ejpam-457	554	8	1	1	NUM
ejpam-457	554	9	,	,	PUNCT
ejpam-457	554	10	t	t	PROPN
ejpam-457	554	11	∈	∈	PROPN
ejpam-457	555	1	i	i	PRON
ejpam-457	555	2	,	,	PUNCT
ejpam-457	555	3	i	i	PROPN
ejpam-457	555	4	∈	∈	VERB
ejpam-457	555	5	p	p	X
ejpam-457	555	6	∑	∑	PUNCT
ejpam-457	555	7	j∈jα	j∈jα	PROPN
ejpam-457	556	1	∫	∫	PROPN
ejpam-457	557	1	i	i	PRON
ejpam-457	557	2	y	y	PROPN
ejpam-457	557	3	j(t)g	j(t)g	PROPN
ejpam-457	557	4	j(t	j(t	PROPN
ejpam-457	557	5	,	,	PUNCT
ejpam-457	557	6	u	u	NOUN
ejpam-457	557	7	,	,	PUNCT
ejpam-457	557	8	u̇	u̇	PROPN
ejpam-457	557	9	,	,	PUNCT
ejpam-457	557	10	ü)d	ü)d	PROPN
ejpam-457	557	11	t	t	PROPN
ejpam-457	557	12	≧	≧	NUM
ejpam-457	557	13	0	0	NUM
ejpam-457	557	14	,	,	PUNCT
ejpam-457	557	15	α	α	NOUN
ejpam-457	557	16	=	=	SYM
ejpam-457	557	17	1,2	1,2	NUM
ejpam-457	557	18	,	,	PUNCT
ejpam-457	557	19	.	.	PUNCT
ejpam-457	557	20	.	.	PUNCT
ejpam-457	558	1	.	.	PUNCT
ejpam-457	559	1	,	,	PUNCT
ejpam-457	559	2	r	r	NOUN
ejpam-457	559	3	,	,	PUNCT
ejpam-457	559	4	y(t	y(t	PROPN
ejpam-457	559	5	)	)	PUNCT
ejpam-457	559	6	≧	≧	X
ejpam-457	560	1	0	0	NUM
ejpam-457	560	2	,	,	PUNCT
ejpam-457	560	3	t	t	PROPN
ejpam-457	560	4	∈	∈	PROPN
ejpam-457	561	1	i	i	PRON
ejpam-457	561	2	.	.	PUNCT
ejpam-457	562	1	5	5	X
ejpam-457	562	2	.	.	X
ejpam-457	562	3	nonlinear	nonlinear	ADJ
ejpam-457	562	4	programming	programming	NOUN
ejpam-457	562	5	if	if	SCONJ
ejpam-457	562	6	all	all	DET
ejpam-457	562	7	the	the	DET
ejpam-457	562	8	functions	function	NOUN
ejpam-457	562	9	are	be	AUX
ejpam-457	562	10	independent	independent	ADJ
ejpam-457	562	11	of	of	ADP
ejpam-457	562	12	t	t	PROPN
ejpam-457	562	13	then	then	ADV
ejpam-457	562	14	the	the	DET
ejpam-457	562	15	problems	problem	NOUN
ejpam-457	562	16	(	(	PUNCT
ejpam-457	562	17	vp	vp	NOUN
ejpam-457	562	18	)	)	PUNCT
ejpam-457	562	19	0	0	PUNCT
ejpam-457	563	1	and	and	CCONJ
ejpam-457	563	2	(	(	PUNCT
ejpam-457	563	3	mix	mix	VERB
ejpam-457	563	4	d	d	NOUN
ejpam-457	563	5	)	)	PUNCT
ejpam-457	563	6	0	0	NUM
ejpam-457	563	7	become	become	VERB
ejpam-457	563	8	the	the	DET
ejpam-457	563	9	following	follow	VERB
ejpam-457	563	10	problems	problem	NOUN
ejpam-457	563	11	.	.	PUNCT
ejpam-457	564	1	(	(	PUNCT
ejpam-457	564	2	vp)1	vp)1	VERB
ejpam-457	564	3	minimize	minimize	VERB
ejpam-457	564	4	(	(	PUNCT
ejpam-457	564	5	f	f	PROPN
ejpam-457	564	6	1(x)+	1(x)+	NUM
ejpam-457	564	7	(	(	PUNCT
ejpam-457	564	8	x	x	PROPN
ejpam-457	564	9	t	t	PROPN
ejpam-457	564	10	b1	b1	PROPN
ejpam-457	564	11	x	x	SYM
ejpam-457	564	12	)	)	PUNCT
ejpam-457	564	13	1	1	NUM
ejpam-457	564	14	2	2	NUM
ejpam-457	564	15	,	,	PUNCT
ejpam-457	564	16	.	.	PUNCT
ejpam-457	564	17	.	.	PUNCT
ejpam-457	564	18	.	.	PUNCT
ejpam-457	565	1	,	,	PUNCT
ejpam-457	565	2	f	f	PROPN
ejpam-457	565	3	p(x)+	p(x)+	PROPN
ejpam-457	565	4	(	(	PUNCT
ejpam-457	565	5	x	x	PROPN
ejpam-457	565	6	t	t	PROPN
ejpam-457	565	7	bp	bp	PROPN
ejpam-457	565	8	x	x	X
ejpam-457	565	9	)	)	PUNCT
ejpam-457	565	10	1	1	NUM
ejpam-457	565	11	2	2	NUM
ejpam-457	565	12	)	)	PUNCT
ejpam-457	565	13	subject	subject	NOUN
ejpam-457	565	14	to	to	ADP
ejpam-457	565	15	g(x)≦	g(x)≦	NOUN
ejpam-457	565	16	0	0	NUM
ejpam-457	565	17	(	(	PUNCT
ejpam-457	565	18	mixd)1	mixd)1	NOUN
ejpam-457	565	19	maximize	maximize	VERB
ejpam-457	565	20	�	�	PROPN
ejpam-457	565	21	f	f	PROPN
ejpam-457	565	22	1(u	1(u	NUM
ejpam-457	565	23	)	)	PUNCT
ejpam-457	565	24	+	+	CCONJ
ejpam-457	565	25	ut	ut	PROPN
ejpam-457	565	26	b1z1	b1z1	X
ejpam-457	565	27	+	+	CCONJ
ejpam-457	565	28	∑	∑	PART
ejpam-457	565	29	j∈j	j∈j	NOUN
ejpam-457	565	30	◦	◦	NOUN
ejpam-457	565	31	y	y	PROPN
ejpam-457	565	32	j	j	PROPN
ejpam-457	565	33	g	g	PROPN
ejpam-457	565	34	j(u	j(u	PROPN
ejpam-457	565	35	)	)	PUNCT
ejpam-457	565	36	,	,	PUNCT
ejpam-457	565	37	.	.	PUNCT
ejpam-457	565	38	.	.	PUNCT
ejpam-457	566	1	.	.	PUNCT
ejpam-457	567	1	,	,	PUNCT
ejpam-457	567	2	f	f	PROPN
ejpam-457	567	3	p(u	p(u	PROPN
ejpam-457	567	4	)	)	PUNCT
ejpam-457	568	1	+	+	CCONJ
ejpam-457	568	2	ut	ut	PROPN
ejpam-457	568	3	bpzp	bpzp	NOUN
ejpam-457	568	4	+	+	CCONJ
ejpam-457	568	5	∑	∑	NOUN
ejpam-457	568	6	j∈j	j∈j	NOUN
ejpam-457	568	7	◦	◦	NOUN
ejpam-457	568	8	y	y	PROPN
ejpam-457	568	9	j	j	PROPN
ejpam-457	568	10	g	g	PROPN
ejpam-457	568	11	j(u	j(u	PROPN
ejpam-457	568	12	)	)	PUNCT
ejpam-457	568	13	�	�	PROPN
ejpam-457	568	14	subject	subject	ADJ
ejpam-457	568	15	to	to	ADP
ejpam-457	568	16	p	p	NOUN
ejpam-457	568	17	∑	∑	PROPN
ejpam-457	568	18	i=1	i=1	PROPN
ejpam-457	568	19	λi	λi	PROPN
ejpam-457	568	20	(	(	PUNCT
ejpam-457	568	21	f	f	NOUN
ejpam-457	568	22	i	i	PRON
ejpam-457	568	23	u	u	X
ejpam-457	568	24	(	(	PUNCT
ejpam-457	568	25	u)d	u)d	PROPN
ejpam-457	568	26	t	t	NOUN
ejpam-457	569	1	+	+	NUM
ejpam-457	569	2	biz	biz	NOUN
ejpam-457	570	1	i	i	PRON
ejpam-457	570	2	+	+	CCONJ
ejpam-457	570	3	yt	yt	PROPN
ejpam-457	570	4	gu(u	gu(u	NOUN
ejpam-457	570	5	)	)	PUNCT
ejpam-457	570	6	)	)	PUNCT
ejpam-457	571	1	=	=	SYM
ejpam-457	571	2	0	0	NUM
ejpam-457	571	3	z̄	z̄	PROPN
ejpam-457	571	4	it	it	PRON
ejpam-457	571	5	bi	bi	PROPN
ejpam-457	571	6	z̄	z̄	PROPN
ejpam-457	571	7	i	i	PRON
ejpam-457	571	8	≦	≦	VERB
ejpam-457	571	9	1	1	NUM
ejpam-457	571	10	,	,	PUNCT
ejpam-457	571	11	i	i	PRON
ejpam-457	571	12	∈	∈	VERB
ejpam-457	571	13	p	p	NOUN
ejpam-457	571	14	∑	∑	PROPN
ejpam-457	571	15	j∈jα	j∈jα	PROPN
ejpam-457	571	16	y	y	PROPN
ejpam-457	571	17	j	j	PROPN
ejpam-457	571	18	g	g	NOUN
ejpam-457	571	19	j(u)≧	j(u)≧	ADV
ejpam-457	571	20	0	0	NUM
ejpam-457	571	21	,	,	PUNCT
ejpam-457	571	22	α	α	NOUN
ejpam-457	571	23	=	=	SYM
ejpam-457	571	24	1,2	1,2	NUM
ejpam-457	571	25	,	,	PUNCT
ejpam-457	571	26	.	.	PUNCT
ejpam-457	571	27	.	.	PUNCT
ejpam-457	572	1	.	.	PUNCT
ejpam-457	573	1	,	,	PUNCT
ejpam-457	573	2	r	r	NOUN
ejpam-457	573	3	y(t	y(t	PROPN
ejpam-457	573	4	)	)	PUNCT
ejpam-457	573	5	≧	≧	X
ejpam-457	574	1	0	0	NUM
ejpam-457	574	2	,	,	PUNCT
ejpam-457	574	3	t	t	PROPN
ejpam-457	574	4	∈	∈	PROPN
ejpam-457	575	1	i	i	PRON
ejpam-457	575	2	λ	λ	X
ejpam-457	575	3	∈	∈	PROPN
ejpam-457	575	4	λ+	λ+	PUNCT
ejpam-457	575	5	where	where	SCONJ
ejpam-457	575	6	λ+	λ+	VERB
ejpam-457	575	7	=	=	PUNCT
ejpam-457	575	8	{	{	PUNCT
ejpam-457	575	9	λ	λ	X
ejpam-457	575	10	∈	∈	NOUN
ejpam-457	575	11	rp|λ	rp|λ	X
ejpam-457	575	12	>	>	X
ejpam-457	575	13	0,λt	0,λt	NUM
ejpam-457	575	14	e	e	X
ejpam-457	575	15	=	=	SYM
ejpam-457	575	16	1	1	NUM
ejpam-457	575	17	,	,	PUNCT
ejpam-457	575	18	e	e	X
ejpam-457	575	19	=	=	PUNCT
ejpam-457	575	20	(	(	PUNCT
ejpam-457	575	21	1,1	1,1	NUM
ejpam-457	575	22	,	,	PUNCT
ejpam-457	575	23	.	.	PUNCT
ejpam-457	575	24	.	.	PUNCT
ejpam-457	575	25	.	.	PUNCT
ejpam-457	576	1	,	,	PUNCT
ejpam-457	576	2	1)t	1)t	PROPN
ejpam-457	576	3	∈	∈	PROPN
ejpam-457	576	4	rp	rp	NOUN
ejpam-457	576	5	}	}	PUNCT
ejpam-457	576	6	the	the	DET
ejpam-457	576	7	duality	duality	NOUN
ejpam-457	576	8	results	result	VERB
ejpam-457	576	9	for	for	ADP
ejpam-457	576	10	this	this	DET
ejpam-457	576	11	pair	pair	NOUN
ejpam-457	576	12	of	of	ADP
ejpam-457	576	13	problems	problem	NOUN
ejpam-457	576	14	are	be	AUX
ejpam-457	576	15	not	not	PART
ejpam-457	576	16	explicitly	explicitly	ADV
ejpam-457	576	17	reported	report	VERB
ejpam-457	576	18	in	in	ADP
ejpam-457	576	19	the	the	DET
ejpam-457	576	20	literature	literature	NOUN
ejpam-457	576	21	but	but	CCONJ
ejpam-457	576	22	can	can	AUX
ejpam-457	576	23	be	be	AUX
ejpam-457	576	24	derived	derive	VERB
ejpam-457	576	25	easily	easily	ADV
ejpam-457	576	26	on	on	ADP
ejpam-457	576	27	the	the	DET
ejpam-457	576	28	lines	line	NOUN
ejpam-457	576	29	of	of	ADP
ejpam-457	576	30	the	the	DET
ejpam-457	576	31	analysis	analysis	NOUN
ejpam-457	576	32	of	of	ADP
ejpam-457	576	33	this	this	DET
ejpam-457	576	34	research	research	NOUN
ejpam-457	576	35	.	.	PUNCT
ejpam-457	577	1	references	reference	NOUN
ejpam-457	577	2	[	[	X
ejpam-457	577	3	1	1	NUM
ejpam-457	577	4	]	]	X
ejpam-457	577	5	c.r	c.r	PROPN
ejpam-457	577	6	.	.	PROPN
ejpam-457	577	7	bector	bector	NOUN
ejpam-457	577	8	and	and	CCONJ
ejpam-457	577	9	i.	i.	PROPN
ejpam-457	577	10	husain	husain	PROPN
ejpam-457	577	11	,	,	PUNCT
ejpam-457	577	12	duality	duality	NOUN
ejpam-457	577	13	for	for	ADP
ejpam-457	577	14	multiobjective	multiobjective	ADJ
ejpam-457	577	15	variational	variational	ADJ
ejpam-457	577	16	problems	problem	NOUN
ejpam-457	577	17	,	,	PUNCT
ejpam-457	577	18	journal	journal	NOUN
ejpam-457	577	19	of	of	ADP
ejpam-457	577	20	math	math	NOUN
ejpam-457	577	21	.	.	PUNCT
ejpam-457	578	1	anal	anal	PROPN
ejpam-457	578	2	.	.	PUNCT
ejpam-457	579	1	and	and	CCONJ
ejpam-457	579	2	appl	appl	PROPN
ejpam-457	579	3	.	.	PUNCT
ejpam-457	580	1	166(1)(1992	166(1)(1992	NUM
ejpam-457	580	2	)	)	PUNCT
ejpam-457	580	3	,	,	PUNCT
ejpam-457	581	1	214–224	214–224	NUM
ejpam-457	581	2	.	.	PUNCT
ejpam-457	581	3	references	reference	NOUN
ejpam-457	581	4	96	96	NUM
ejpam-457	582	1	[	[	X
ejpam-457	582	2	2	2	NUM
ejpam-457	582	3	]	]	X
ejpam-457	582	4	c.r	c.r	PROPN
ejpam-457	582	5	.	.	PROPN
ejpam-457	582	6	bector	bector	PROPN
ejpam-457	582	7	,	,	PUNCT
ejpam-457	582	8	s.	s.	PROPN
ejpam-457	582	9	chandra	chandra	PROPN
ejpam-457	582	10	and	and	CCONJ
ejpam-457	582	11	i.	i.	PROPN
ejpam-457	582	12	husain	husain	PROPN
ejpam-457	582	13	,	,	PUNCT
ejpam-457	582	14	generalized	generalized	ADJ
ejpam-457	582	15	concavity	concavity	NOUN
ejpam-457	582	16	and	and	CCONJ
ejpam-457	582	17	nondifferentiable	nondifferentiable	ADJ
ejpam-457	582	18	continuous	continuous	ADJ
ejpam-457	582	19	programming	programming	NOUN
ejpam-457	582	20	duality	duality	NOUN
ejpam-457	582	21	,	,	PUNCT
ejpam-457	582	22	research	research	NOUN
ejpam-457	582	23	report	report	NOUN
ejpam-457	582	24	#	#	NOUN
ejpam-457	582	25	85	85	NUM
ejpam-457	582	26	-	-	SYM
ejpam-457	582	27	7	7	NUM
ejpam-457	582	28	,	,	PUNCT
ejpam-457	582	29	faculty	faculty	NOUN
ejpam-457	582	30	of	of	ADP
ejpam-457	582	31	administrative	administrative	ADJ
ejpam-457	582	32	studies	study	NOUN
ejpam-457	582	33	,	,	PUNCT
ejpam-457	582	34	the	the	DET
ejpam-457	582	35	university	university	PROPN
ejpam-457	582	36	of	of	ADP
ejpam-457	582	37	manitoba	manitoba	PROPN
ejpam-457	582	38	,	,	PUNCT
ejpam-457	582	39	winnipeg	winnipeg	PROPN
ejpam-457	582	40	,	,	PUNCT
ejpam-457	582	41	canada	canada	PROPN
ejpam-457	582	42	r3	r3	PROPN
ejpam-457	582	43	t	t	PROPN
ejpam-457	582	44	2n2	2n2	NUM
ejpam-457	582	45	,	,	PUNCT
ejpam-457	582	46	(	(	PUNCT
ejpam-457	582	47	1985	1985	NUM
ejpam-457	582	48	)	)	PUNCT
ejpam-457	582	49	.	.	PUNCT
ejpam-457	583	1	[	[	X
ejpam-457	583	2	3	3	X
ejpam-457	583	3	]	]	X
ejpam-457	583	4	s.	s.	PROPN
ejpam-457	583	5	chandra	chandra	PROPN
ejpam-457	583	6	,	,	PUNCT
ejpam-457	583	7	b.d	b.d	PROPN
ejpam-457	583	8	.	.	PROPN
ejpam-457	583	9	craven	craven	PROPN
ejpam-457	583	10	and	and	CCONJ
ejpam-457	583	11	i.	i.	PROPN
ejpam-457	583	12	husain	husain	PROPN
ejpam-457	583	13	,	,	PUNCT
ejpam-457	583	14	a	a	DET
ejpam-457	583	15	class	class	NOUN
ejpam-457	583	16	of	of	ADP
ejpam-457	583	17	nondifferentiable	nondifferentiable	ADJ
ejpam-457	583	18	continuous	continuous	ADJ
ejpam-457	583	19	programming	programming	NOUN
ejpam-457	583	20	problem	problem	NOUN
ejpam-457	583	21	,	,	PUNCT
ejpam-457	583	22	j.	j.	PROPN
ejpam-457	583	23	math	math	PROPN
ejpam-457	583	24	.	.	PUNCT
ejpam-457	584	1	anal	anal	PROPN
ejpam-457	584	2	.	.	PUNCT
ejpam-457	584	3	appl	appl	PROPN
ejpam-457	584	4	.	.	PUNCT
ejpam-457	585	1	107(1985	107(1985	NUM
ejpam-457	585	2	)	)	PUNCT
ejpam-457	585	3	,	,	PUNCT
ejpam-457	585	4	122—131	122—131	PROPN
ejpam-457	585	5	.	.	PUNCT
ejpam-457	586	1	[	[	X
ejpam-457	586	2	4	4	NUM
ejpam-457	586	3	]	]	X
ejpam-457	586	4	f.h	f.h	PROPN
ejpam-457	586	5	.	.	PROPN
ejpam-457	586	6	clarke	clarke	PROPN
ejpam-457	586	7	,	,	PUNCT
ejpam-457	586	8	optimization	optimization	NOUN
ejpam-457	586	9	and	and	CCONJ
ejpam-457	586	10	non	non	ADJ
ejpam-457	586	11	-	-	ADJ
ejpam-457	586	12	smooth	smooth	ADJ
ejpam-457	586	13	analysis	analysis	NOUN
ejpam-457	586	14	,	,	PUNCT
ejpam-457	586	15	wiley	wiley	NOUN
ejpam-457	586	16	,	,	PUNCT
ejpam-457	586	17	new	new	PROPN
ejpam-457	586	18	york	york	PROPN
ejpam-457	586	19	,	,	PUNCT
ejpam-457	586	20	(	(	PUNCT
ejpam-457	586	21	1983	1983	NUM
ejpam-457	586	22	)	)	PUNCT
ejpam-457	586	23	.	.	PUNCT
ejpam-457	587	1	[	[	X
ejpam-457	587	2	5	5	X
ejpam-457	587	3	]	]	PUNCT
ejpam-457	587	4	v.	v.	CCONJ
ejpam-457	587	5	chankong	chankong	NOUN
ejpam-457	587	6	and	and	CCONJ
ejpam-457	587	7	y.y	y.y	PROPN
ejpam-457	587	8	.	.	PROPN
ejpam-457	587	9	haimes	haime	NOUN
ejpam-457	587	10	,	,	PUNCT
ejpam-457	587	11	multiobjective	multiobjective	ADJ
ejpam-457	587	12	decision	decision	NOUN
ejpam-457	587	13	making	making	NOUN
ejpam-457	587	14	:	:	PUNCT
ejpam-457	587	15	theory	theory	NOUN
ejpam-457	587	16	and	and	CCONJ
ejpam-457	587	17	methodology	methodology	NOUN
ejpam-457	587	18	,	,	PUNCT
ejpam-457	587	19	north	north	NOUN
ejpam-457	587	20	-	-	PUNCT
ejpam-457	587	21	holland	holland	PROPN
ejpam-457	587	22	,	,	PUNCT
ejpam-457	587	23	new	new	PROPN
ejpam-457	587	24	york	york	PROPN
ejpam-457	587	25	,	,	PUNCT
ejpam-457	587	26	(	(	PUNCT
ejpam-457	587	27	1983	1983	NUM
ejpam-457	587	28	)	)	PUNCT
ejpam-457	587	29	.	.	PUNCT
ejpam-457	588	1	[	[	X
ejpam-457	588	2	6	6	X
ejpam-457	588	3	]	]	X
ejpam-457	588	4	v.f	v.f	PROPN
ejpam-457	588	5	.	.	PROPN
ejpam-457	588	6	demyanov	demyanov	PROPN
ejpam-457	588	7	and	and	CCONJ
ejpam-457	588	8	l.c.w	l.c.w	PROPN
ejpam-457	588	9	.	.	PUNCT
ejpam-457	588	10	dixon	dixon	PROPN
ejpam-457	588	11	,	,	PUNCT
ejpam-457	588	12	quasidifferential	quasidifferential	ADJ
ejpam-457	588	13	calculus	calculus	NOUN
ejpam-457	588	14	,	,	PUNCT
ejpam-457	588	15	mathematical	mathematical	ADJ
ejpam-457	588	16	programming	programming	NOUN
ejpam-457	588	17	study	study	NOUN
ejpam-457	588	18	29	29	NUM
ejpam-457	588	19	,	,	PUNCT
ejpam-457	588	20	north	north	NOUN
ejpam-457	588	21	holland	holland	PROPN
ejpam-457	588	22	,	,	PUNCT
ejpam-457	588	23	amsterdam	amsterdam	PROPN
ejpam-457	588	24	(	(	PUNCT
ejpam-457	588	25	1989	1989	NUM
ejpam-457	588	26	)	)	PUNCT
ejpam-457	588	27	.	.	PUNCT
ejpam-457	589	1	[	[	X
ejpam-457	589	2	7	7	X
ejpam-457	589	3	]	]	X
ejpam-457	589	4	i.	i.	PROPN
ejpam-457	589	5	husain	husain	PROPN
ejpam-457	589	6	and	and	CCONJ
ejpam-457	589	7	z.	z.	PROPN
ejpam-457	589	8	jabeen	jabeen	PROPN
ejpam-457	589	9	,	,	PUNCT
ejpam-457	589	10	mixed	mixed	ADJ
ejpam-457	589	11	type	type	NOUN
ejpam-457	589	12	duality	duality	NOUN
ejpam-457	589	13	for	for	ADP
ejpam-457	589	14	a	a	DET
ejpam-457	589	15	programming	programming	NOUN
ejpam-457	589	16	problem	problem	NOUN
ejpam-457	589	17	containing	contain	VERB
ejpam-457	589	18	support	support	NOUN
ejpam-457	589	19	function	function	NOUN
ejpam-457	589	20	,	,	PUNCT
ejpam-457	589	21	journal	journal	NOUN
ejpam-457	589	22	of	of	ADP
ejpam-457	589	23	applied	apply	VERB
ejpam-457	589	24	mathematica	mathematica	PROPN
ejpam-457	589	25	and	and	CCONJ
ejpam-457	589	26	computing	compute	VERB
ejpam-457	589	27	15	15	NUM
ejpam-457	589	28	(	(	PUNCT
ejpam-457	589	29	1	1	NUM
ejpam-457	589	30	-	-	SYM
ejpam-457	589	31	2	2	NUM
ejpam-457	589	32	)	)	PUNCT
ejpam-457	589	33	(	(	PUNCT
ejpam-457	589	34	2004	2004	NUM
ejpam-457	589	35	)	)	PUNCT
ejpam-457	589	36	,	,	PUNCT
ejpam-457	589	37	211	211	NUM
ejpam-457	589	38	–	–	PUNCT
ejpam-457	589	39	225	225	NUM
ejpam-457	589	40	.	.	PUNCT
ejpam-457	590	1	[	[	X
ejpam-457	590	2	8	8	NUM
ejpam-457	590	3	]	]	X
ejpam-457	590	4	i.	i.	PROPN
ejpam-457	590	5	husain	husain	PROPN
ejpam-457	590	6	and	and	CCONJ
ejpam-457	590	7	z.	z.	PROPN
ejpam-457	590	8	jabeen	jabeen	PROPN
ejpam-457	590	9	,	,	PUNCT
ejpam-457	590	10	on	on	ADP
ejpam-457	590	11	variational	variational	ADJ
ejpam-457	590	12	problems	problem	NOUN
ejpam-457	590	13	involving	involve	VERB
ejpam-457	590	14	higher	high	ADJ
ejpam-457	590	15	order	order	NOUN
ejpam-457	590	16	derivatives	derivative	NOUN
ejpam-457	590	17	,	,	PUNCT
ejpam-457	590	18	j.	j.	PROPN
ejpam-457	590	19	math	math	PROPN
ejpam-457	590	20	.	.	PUNCT
ejpam-457	591	1	and	and	CCONJ
ejpam-457	591	2	computing	compute	VERB
ejpam-457	591	3	27(1	27(1	NUM
ejpam-457	591	4	-	-	SYM
ejpam-457	591	5	2)(2005	2)(2005	NUM
ejpam-457	591	6	)	)	PUNCT
ejpam-457	591	7	,	,	PUNCT
ejpam-457	591	8	433–455	433–455	NUM
ejpam-457	591	9	.	.	PUNCT
ejpam-457	592	1	[	[	X
ejpam-457	592	2	9	9	NUM
ejpam-457	592	3	]	]	PUNCT
ejpam-457	592	4	i.	i.	NOUN
ejpam-457	592	5	husain	husain	PROPN
ejpam-457	592	6	,	,	PUNCT
ejpam-457	592	7	a.	a.	PROPN
ejpam-457	592	8	ahmed	ahmed	PROPN
ejpam-457	592	9	and	and	CCONJ
ejpam-457	592	10	rumana	rumana	PROPN
ejpam-457	592	11	g.	g.	PROPN
ejpam-457	592	12	mattoo	mattoo	PROPN
ejpam-457	592	13	,	,	PUNCT
ejpam-457	592	14	optimality	optimality	NOUN
ejpam-457	592	15	and	and	CCONJ
ejpam-457	592	16	duality	duality	NOUN
ejpam-457	592	17	for	for	ADP
ejpam-457	592	18	nondifferentiable	nondifferentiable	ADJ
ejpam-457	592	19	multiobjective	multiobjective	ADJ
ejpam-457	592	20	variational	variational	ADJ
ejpam-457	592	21	problems	problem	NOUN
ejpam-457	592	22	involving	involve	VERB
ejpam-457	592	23	higher	high	ADJ
ejpam-457	592	24	order	order	NOUN
ejpam-457	592	25	derivatives	derivative	NOUN
ejpam-457	592	26	,	,	PUNCT
ejpam-457	592	27	european	european	ADJ
ejpam-457	592	28	journal	journal	NOUN
ejpam-457	592	29	of	of	ADP
ejpam-457	592	30	pure	pure	ADJ
ejpam-457	592	31	and	and	CCONJ
ejpam-457	592	32	applied	apply	VERB
ejpam-457	592	33	mathematics	mathematic	NOUN
ejpam-457	592	34	2(3)(2009	2(3)(2009	NUM
ejpam-457	592	35	)	)	PUNCT
ejpam-457	592	36	,	,	PUNCT
ejpam-457	592	37	372–400	372–400	NUM
ejpam-457	592	38	.	.	PUNCT
ejpam-457	593	1	[	[	X
ejpam-457	593	2	10	10	NUM
ejpam-457	593	3	]	]	X
ejpam-457	593	4	i.	i.	PROPN
ejpam-457	593	5	husain	husain	PROPN
ejpam-457	593	6	,	,	PUNCT
ejpam-457	593	7	a.	a.	PROPN
ejpam-457	593	8	ahmed	ahmed	PROPN
ejpam-457	593	9	and	and	CCONJ
ejpam-457	593	10	rumana	rumana	PROPN
ejpam-457	593	11	g.	g.	PROPN
ejpam-457	593	12	mattoo	mattoo	PROPN
ejpam-457	593	13	,	,	PUNCT
ejpam-457	593	14	optimality	optimality	NOUN
ejpam-457	593	15	criteria	criterion	NOUN
ejpam-457	593	16	and	and	CCONJ
ejpam-457	593	17	duality	duality	NOUN
ejpam-457	593	18	in	in	ADP
ejpam-457	593	19	multiobjective	multiobjective	ADJ
ejpam-457	593	20	variational	variational	ADJ
ejpam-457	593	21	problems	problem	NOUN
ejpam-457	593	22	involving	involve	VERB
ejpam-457	593	23	higher	high	ADJ
ejpam-457	593	24	order	order	NOUN
ejpam-457	593	25	derivatives	derivative	NOUN
ejpam-457	593	26	,	,	PUNCT
ejpam-457	593	27	journal	journal	NOUN
ejpam-457	593	28	of	of	ADP
ejpam-457	593	29	applied	apply	VERB
ejpam-457	593	30	mathematics	mathematic	NOUN
ejpam-457	593	31	and	and	CCONJ
ejpam-457	593	32	informatics	informatic	NOUN
ejpam-457	593	33	27	27	NUM
ejpam-457	593	34	(	(	PUNCT
ejpam-457	593	35	1	1	NUM
ejpam-457	593	36	-	-	SYM
ejpam-457	593	37	2	2	NUM
ejpam-457	593	38	)	)	PUNCT
ejpam-457	593	39	(	(	PUNCT
ejpam-457	593	40	2009	2009	NUM
ejpam-457	593	41	)	)	PUNCT
ejpam-457	593	42	,	,	PUNCT
ejpam-457	593	43	123–137	123–137	NUM
ejpam-457	593	44	.	.	PUNCT
ejpam-457	594	1	[	[	X
ejpam-457	594	2	11	11	NUM
ejpam-457	594	3	]	]	X
ejpam-457	594	4	d.s	d.s	PROPN
ejpam-457	594	5	.	.	PROPN
ejpam-457	594	6	kim	kim	PROPN
ejpam-457	594	7	and	and	CCONJ
ejpam-457	594	8	a.l	a.l	PROPN
ejpam-457	594	9	.	.	PROPN
ejpam-457	594	10	kim	kim	PROPN
ejpam-457	594	11	,	,	PUNCT
ejpam-457	594	12	optimality	optimality	NOUN
ejpam-457	594	13	and	and	CCONJ
ejpam-457	594	14	duality	duality	NOUN
ejpam-457	594	15	for	for	ADP
ejpam-457	594	16	nondifferentiable	nondifferentiable	ADJ
ejpam-457	594	17	multiobjective	multiobjective	ADJ
ejpam-457	594	18	variational	variational	ADJ
ejpam-457	594	19	problems	problem	NOUN
ejpam-457	594	20	,	,	PUNCT
ejpam-457	594	21	j.	j.	PROPN
ejpam-457	594	22	math	math	PROPN
ejpam-457	594	23	.	.	PUNCT
ejpam-457	595	1	anal	anal	PROPN
ejpam-457	595	2	.	.	PUNCT
ejpam-457	595	3	appl	appl	PROPN
ejpam-457	595	4	.	.	PUNCT
ejpam-457	596	1	274(2002	274(2002	NUM
ejpam-457	596	2	)	)	PUNCT
ejpam-457	596	3	,	,	PUNCT
ejpam-457	596	4	255–278	255–278	NUM
ejpam-457	596	5	.	.	PUNCT
ejpam-457	597	1	[	[	X
ejpam-457	597	2	12	12	NUM
ejpam-457	597	3	]	]	X
ejpam-457	597	4	j.c	j.c	PROPN
ejpam-457	597	5	.	.	PROPN
ejpam-457	597	6	liu	liu	PROPN
ejpam-457	597	7	,	,	PUNCT
ejpam-457	597	8	duality	duality	NOUN
ejpam-457	597	9	for	for	ADP
ejpam-457	597	10	nondifferentiable	nondifferentiable	ADJ
ejpam-457	597	11	static	static	ADJ
ejpam-457	597	12	multiobjective	multiobjective	ADJ
ejpam-457	597	13	variational	variational	ADJ
ejpam-457	597	14	problems	problem	NOUN
ejpam-457	597	15	involving	involve	VERB
ejpam-457	597	16	generalized	generalized	ADJ
ejpam-457	597	17	(	(	PUNCT
ejpam-457	597	18	f	f	X
ejpam-457	597	19	,	,	PUNCT
ejpam-457	597	20	ρ)-convex	ρ)-convex	NOUN
ejpam-457	597	21	functions	function	NOUN
ejpam-457	597	22	,	,	PUNCT
ejpam-457	597	23	comput	comput	NOUN
ejpam-457	597	24	.	.	PUNCT
ejpam-457	598	1	math	math	NOUN
ejpam-457	598	2	.	.	PUNCT
ejpam-457	599	1	appl	appl	PROPN
ejpam-457	599	2	.	.	PUNCT
ejpam-457	600	1	31	31	NUM
ejpam-457	600	2	(	(	PUNCT
ejpam-457	600	3	12)(1996	12)(1996	NUM
ejpam-457	600	4	)	)	PUNCT
ejpam-457	600	5	,	,	PUNCT
ejpam-457	600	6	77–89	77–89	NUM
ejpam-457	600	7	.	.	PUNCT
ejpam-457	601	1	[	[	X
ejpam-457	601	2	13	13	NUM
ejpam-457	601	3	]	]	X
ejpam-457	601	4	s.k	s.k	PROPN
ejpam-457	601	5	.	.	PROPN
ejpam-457	601	6	mishra	mishra	PROPN
ejpam-457	601	7	and	and	CCONJ
ejpam-457	601	8	r.n	r.n	PROPN
ejpam-457	601	9	.	.	PROPN
ejpam-457	601	10	mukerjee	mukerjee	PROPN
ejpam-457	601	11	,	,	PUNCT
ejpam-457	601	12	on	on	ADP
ejpam-457	601	13	efficiency	efficiency	NOUN
ejpam-457	601	14	and	and	CCONJ
ejpam-457	601	15	duality	duality	NOUN
ejpam-457	601	16	for	for	ADP
ejpam-457	601	17	multiobjective	multiobjective	ADJ
ejpam-457	601	18	variational	variational	ADJ
ejpam-457	601	19	problems	problem	NOUN
ejpam-457	601	20	,	,	PUNCT
ejpam-457	601	21	j.	j.	PROPN
ejpam-457	601	22	math	math	PROPN
ejpam-457	601	23	.	.	PUNCT
ejpam-457	602	1	anal	anal	PROPN
ejpam-457	602	2	.	.	PUNCT
ejpam-457	602	3	appl	appl	PROPN
ejpam-457	602	4	.	.	PUNCT
ejpam-457	603	1	187	187	NUM
ejpam-457	603	2	(	(	PUNCT
ejpam-457	603	3	1994	1994	NUM
ejpam-457	603	4	)	)	PUNCT
ejpam-457	603	5	,	,	PUNCT
ejpam-457	603	6	40–45	40–45	NUM
ejpam-457	603	7	.	.	PUNCT
ejpam-457	604	1	[	[	X
ejpam-457	604	2	14	14	NUM
ejpam-457	604	3	]	]	X
ejpam-457	604	4	o.l	o.l	PROPN
ejpam-457	604	5	.	.	PROPN
ejpam-457	604	6	mangasarian	mangasarian	PROPN
ejpam-457	604	7	,	,	PUNCT
ejpam-457	604	8	nonlinear	nonlinear	ADJ
ejpam-457	604	9	programming	programming	NOUN
ejpam-457	604	10	,	,	PUNCT
ejpam-457	604	11	mcgraw	mcgraw	PROPN
ejpam-457	604	12	hill	hill	PROPN
ejpam-457	604	13	,	,	PUNCT
ejpam-457	604	14	new	new	PROPN
ejpam-457	604	15	york	york	PROPN
ejpam-457	604	16	,	,	PUNCT
ejpam-457	604	17	(	(	PUNCT
ejpam-457	604	18	1969	1969	NUM
ejpam-457	604	19	)	)	PUNCT
ejpam-457	604	20	.	.	PUNCT
ejpam-457	605	1	[	[	X
ejpam-457	605	2	15	15	NUM
ejpam-457	605	3	]	]	X
ejpam-457	605	4	b.	b.	PROPN
ejpam-457	605	5	mond	mond	PROPN
ejpam-457	605	6	and	and	CCONJ
ejpam-457	605	7	m.a	m.a	PROPN
ejpam-457	605	8	.	.	PROPN
ejpam-457	605	9	hanson	hanson	PROPN
ejpam-457	605	10	,	,	PUNCT
ejpam-457	605	11	duality	duality	NOUN
ejpam-457	605	12	for	for	ADP
ejpam-457	605	13	variational	variational	ADJ
ejpam-457	605	14	problems	problem	NOUN
ejpam-457	605	15	,	,	PUNCT
ejpam-457	605	16	j.	j.	PROPN
ejpam-457	605	17	math	math	PROPN
ejpam-457	605	18	.	.	PUNCT
ejpam-457	606	1	anal	anal	PROPN
ejpam-457	606	2	.	.	PUNCT
ejpam-457	607	1	appl	appl	PROPN
ejpam-457	607	2	.	.	PROPN
ejpam-457	608	1	18	18	NUM
ejpam-457	608	2	(	(	PUNCT
ejpam-457	608	3	1967	1967	NUM
ejpam-457	608	4	)	)	PUNCT
ejpam-457	608	5	,	,	PUNCT
ejpam-457	608	6	355–364	355–364	NUM
ejpam-457	608	7	.	.	PUNCT
ejpam-457	609	1	[	[	X
ejpam-457	609	2	16	16	NUM
ejpam-457	609	3	]	]	X
ejpam-457	609	4	b.	b.	PROPN
ejpam-457	609	5	mond	mond	PROPN
ejpam-457	609	6	,	,	PUNCT
ejpam-457	609	7	i.	i.	PROPN
ejpam-457	609	8	husain	husain	PROPN
ejpam-457	609	9	and	and	CCONJ
ejpam-457	609	10	m.v	m.v	PROPN
ejpam-457	609	11	.	.	PROPN
ejpam-457	609	12	durga	durga	PROPN
ejpam-457	609	13	prasad	prasad	PROPN
ejpam-457	609	14	,	,	PUNCT
ejpam-457	609	15	duality	duality	NOUN
ejpam-457	609	16	for	for	ADP
ejpam-457	609	17	a	a	DET
ejpam-457	609	18	class	class	NOUN
ejpam-457	609	19	of	of	ADP
ejpam-457	609	20	nondifferentiable	nondifferentiable	ADJ
ejpam-457	609	21	multipleobjective	multipleobjective	ADJ
ejpam-457	609	22	programming	programming	NOUN
ejpam-457	609	23	problems	problem	NOUN
ejpam-457	609	24	,	,	PUNCT
ejpam-457	609	25	journal	journal	NOUN
ejpam-457	609	26	of	of	ADP
ejpam-457	609	27	information	information	NOUN
ejpam-457	609	28	and	and	CCONJ
ejpam-457	609	29	optimization	optimization	NOUN
ejpam-457	609	30	sciences	science	NOUN
ejpam-457	609	31	,	,	PUNCT
ejpam-457	609	32	9(1988	9(1988	NUM
ejpam-457	609	33	)	)	PUNCT
ejpam-457	609	34	,	,	PUNCT
ejpam-457	609	35	331–341	331–341	NUM
ejpam-457	609	36	.	.	PUNCT
ejpam-457	609	37	references	reference	NOUN
ejpam-457	609	38	97	97	NUM
ejpam-457	610	1	[	[	X
ejpam-457	610	2	17	17	NUM
ejpam-457	610	3	]	]	X
ejpam-457	610	4	f.	f.	PROPN
ejpam-457	610	5	riesz	riesz	PROPN
ejpam-457	610	6	and	and	CCONJ
ejpam-457	610	7	b.	b.	PROPN
ejpam-457	610	8	sz	sz	PROPN
ejpam-457	610	9	-	-	PUNCT
ejpam-457	610	10	nagy	nagy	ADJ
ejpam-457	610	11	,	,	PUNCT
ejpam-457	610	12	functional	functional	ADJ
ejpam-457	610	13	analysis	analysis	NOUN
ejpam-457	610	14	,	,	PUNCT
ejpam-457	610	15	ungar	ungar	NOUN
ejpam-457	610	16	,	,	PUNCT
ejpam-457	610	17	new	new	PROPN
ejpam-457	610	18	york	york	PROPN
ejpam-457	610	19	,	,	PUNCT
ejpam-457	610	20	(	(	PUNCT
ejpam-457	610	21	1995	1995	NUM
ejpam-457	610	22	)	)	PUNCT
ejpam-457	610	23	.	.	PUNCT
ejpam-457	611	1	[	[	X
ejpam-457	611	2	18	18	NUM
ejpam-457	611	3	]	]	SYM
ejpam-457	611	4	z.xu	z.xu	PROPN
ejpam-457	611	5	,	,	PUNCT
ejpam-457	611	6	mixed	mixed	ADJ
ejpam-457	611	7	type	type	NOUN
ejpam-457	611	8	duality	duality	NOUN
ejpam-457	611	9	in	in	ADP
ejpam-457	611	10	multiobjective	multiobjective	ADJ
ejpam-457	611	11	programming	programming	NOUN
ejpam-457	611	12	problems	problem	NOUN
ejpam-457	611	13	,	,	PUNCT
ejpam-457	611	14	journal	journal	NOUN
ejpam-457	611	15	of	of	ADP
ejpam-457	611	16	mathematical	mathematical	ADJ
ejpam-457	611	17	analysis	analysis	NOUN
ejpam-457	611	18	and	and	CCONJ
ejpam-457	611	19	applications	application	NOUN
ejpam-457	611	20	198(1996	198(1996	NOUN
ejpam-457	611	21	)	)	PUNCT
ejpam-457	611	22	,	,	PUNCT
ejpam-457	611	23	621–635	621–635	NUM
ejpam-457	611	24	.	.	PUNCT