id	sid	tid	token	lemma	pos
ejpam-184	1	1	9_husian.dvi	9_husian.dvi	NUM
ejpam-184	1	2	european	european	ADJ
ejpam-184	1	3	journal	journal	NOUN
ejpam-184	1	4	of	of	ADP
ejpam-184	1	5	pure	pure	ADJ
ejpam-184	1	6	and	and	CCONJ
ejpam-184	1	7	applied	apply	VERB
ejpam-184	1	8	mathematics	mathematic	NOUN
ejpam-184	1	9	vol	vol	NOUN
ejpam-184	1	10	.	.	PROPN
ejpam-184	2	1	2	2	NUM
ejpam-184	2	2	,	,	PUNCT
ejpam-184	2	3	no	no	INTJ
ejpam-184	2	4	.	.	NOUN
ejpam-184	2	5	2	2	NUM
ejpam-184	2	6	,	,	PUNCT
ejpam-184	2	7	2009	2009	NUM
ejpam-184	2	8	,	,	PUNCT
ejpam-184	2	9	(	(	PUNCT
ejpam-184	2	10	278	278	NUM
ejpam-184	2	11	-	-	SYM
ejpam-184	2	12	295	295	NUM
ejpam-184	2	13	)	)	PUNCT
ejpam-184	2	14	issn	issn	PROPN
ejpam-184	2	15	1307	1307	NUM
ejpam-184	2	16	-	-	SYM
ejpam-184	2	17	5543	5543	NUM
ejpam-184	2	18	–	–	PUNCT
ejpam-184	2	19	www.ejpam.com	www.ejpam.com	X
ejpam-184	2	20	second	second	ADJ
ejpam-184	2	21	-	-	PUNCT
ejpam-184	2	22	order	order	NOUN
ejpam-184	2	23	duality	duality	NOUN
ejpam-184	2	24	for	for	ADP
ejpam-184	2	25	variational	variational	ADJ
ejpam-184	2	26	problems	problem	NOUN
ejpam-184	2	27	i.	i.	PROPN
ejpam-184	2	28	husain1∗	husain1∗	PROPN
ejpam-184	2	29	,	,	PUNCT
ejpam-184	2	30	a.	a.	PROPN
ejpam-184	2	31	ahmed	ahmed	PROPN
ejpam-184	2	32	and	and	CCONJ
ejpam-184	2	33	mashoob	mashoob	VERB
ejpam-184	2	34	masoodi2	masoodi2	NOUN
ejpam-184	2	35	1	1	NUM
ejpam-184	2	36	department	department	NOUN
ejpam-184	2	37	of	of	ADP
ejpam-184	2	38	mathematics	mathematics	PROPN
ejpam-184	2	39	,	,	PUNCT
ejpam-184	2	40	jaypee	jaypee	PROPN
ejpam-184	2	41	institute	institute	PROPN
ejpam-184	2	42	of	of	ADP
ejpam-184	2	43	engineering	engineering	NOUN
ejpam-184	2	44	and	and	CCONJ
ejpam-184	2	45	technology	technology	NOUN
ejpam-184	2	46	,	,	PUNCT
ejpam-184	2	47	guna	guna	PROPN
ejpam-184	2	48	,	,	PUNCT
ejpam-184	2	49	mp	mp	PROPN
ejpam-184	2	50	,	,	PUNCT
ejpam-184	2	51	india	india	PROPN
ejpam-184	2	52	.	.	PUNCT
ejpam-184	3	1	(	(	PUNCT
ejpam-184	3	2	a	a	DET
ejpam-184	3	3	constituent	constituent	ADJ
ejpam-184	3	4	centre	centre	NOUN
ejpam-184	3	5	of	of	ADP
ejpam-184	3	6	jaypee	jaypee	PROPN
ejpam-184	3	7	university	university	PROPN
ejpam-184	3	8	of	of	ADP
ejpam-184	3	9	information	information	NOUN
ejpam-184	3	10	technology	technology	PROPN
ejpam-184	3	11	,	,	PUNCT
ejpam-184	3	12	waknaghat	waknaghat	PROPN
ejpam-184	3	13	,	,	PUNCT
ejpam-184	3	14	solan	solan	PROPN
ejpam-184	3	15	,	,	PUNCT
ejpam-184	3	16	hp	hp	PROPN
ejpam-184	3	17	,	,	PUNCT
ejpam-184	3	18	india	india	PROPN
ejpam-184	3	19	)	)	PUNCT
ejpam-184	3	20	2	2	NUM
ejpam-184	3	21	department	department	NOUN
ejpam-184	3	22	of	of	ADP
ejpam-184	3	23	statistics	statistic	NOUN
ejpam-184	3	24	,	,	PUNCT
ejpam-184	3	25	university	university	PROPN
ejpam-184	3	26	of	of	ADP
ejpam-184	3	27	kashmir	kashmir	PROPN
ejpam-184	3	28	,	,	PUNCT
ejpam-184	3	29	srinagar	srinagar	PROPN
ejpam-184	3	30	,	,	PUNCT
ejpam-184	3	31	kashmir	kashmir	PROPN
ejpam-184	3	32	,	,	PUNCT
ejpam-184	3	33	india	india	PROPN
ejpam-184	3	34	abstract	abstract	PROPN
ejpam-184	3	35	.	.	PUNCT
ejpam-184	4	1	a	a	DET
ejpam-184	4	2	mond	mond	PROPN
ejpam-184	4	3	-	-	PUNCT
ejpam-184	4	4	weir	weir	NOUN
ejpam-184	4	5	type	type	NOUN
ejpam-184	4	6	second	second	ADJ
ejpam-184	4	7	-	-	PUNCT
ejpam-184	4	8	order	order	NOUN
ejpam-184	4	9	dual	dual	ADJ
ejpam-184	4	10	to	to	ADP
ejpam-184	4	11	a	a	DET
ejpam-184	4	12	variational	variational	ADJ
ejpam-184	4	13	problem	problem	NOUN
ejpam-184	4	14	is	be	AUX
ejpam-184	4	15	constructed	construct	VERB
ejpam-184	4	16	and	and	CCONJ
ejpam-184	4	17	the	the	DET
ejpam-184	4	18	notion	notion	NOUN
ejpam-184	4	19	of	of	ADP
ejpam-184	4	20	second	second	ADJ
ejpam-184	4	21	-	-	PUNCT
ejpam-184	4	22	order	order	NOUN
ejpam-184	4	23	invexity	invexity	NOUN
ejpam-184	4	24	and	and	CCONJ
ejpam-184	4	25	second	second	ADJ
ejpam-184	4	26	order	order	NOUN
ejpam-184	4	27	generalized	generalize	VERB
ejpam-184	4	28	invexity	invexity	NOUN
ejpam-184	4	29	are	be	AUX
ejpam-184	4	30	introduced	introduce	VERB
ejpam-184	4	31	in	in	ADP
ejpam-184	4	32	variational	variational	ADJ
ejpam-184	4	33	problems	problem	NOUN
ejpam-184	4	34	.	.	PUNCT
ejpam-184	5	1	under	under	ADP
ejpam-184	5	2	these	these	DET
ejpam-184	5	3	second	second	ADJ
ejpam-184	5	4	-	-	PUNCT
ejpam-184	5	5	order	order	NOUN
ejpam-184	5	6	pseudoinvexity	pseudoinvexity	NOUN
ejpam-184	5	7	and	and	CCONJ
ejpam-184	5	8	second	second	ADJ
ejpam-184	5	9	-	-	PUNCT
ejpam-184	5	10	order	order	NOUN
ejpam-184	5	11	quasiinvexity	quasiinvexity	NOUN
ejpam-184	5	12	assumptions	assumption	NOUN
ejpam-184	5	13	,	,	PUNCT
ejpam-184	5	14	weak	weak	ADJ
ejpam-184	5	15	,	,	PUNCT
ejpam-184	5	16	strong	strong	ADJ
ejpam-184	5	17	and	and	CCONJ
ejpam-184	5	18	converse	converse	NOUN
ejpam-184	5	19	duality	duality	NOUN
ejpam-184	5	20	results	result	NOUN
ejpam-184	5	21	are	be	AUX
ejpam-184	5	22	established	establish	VERB
ejpam-184	5	23	.	.	PUNCT
ejpam-184	6	1	it	it	PRON
ejpam-184	6	2	is	be	AUX
ejpam-184	6	3	pointed	point	VERB
ejpam-184	6	4	out	out	ADP
ejpam-184	6	5	that	that	SCONJ
ejpam-184	6	6	our	our	PRON
ejpam-184	6	7	duality	duality	NOUN
ejpam-184	6	8	results	result	NOUN
ejpam-184	6	9	can	can	AUX
ejpam-184	6	10	be	be	AUX
ejpam-184	6	11	viewed	view	VERB
ejpam-184	6	12	as	as	ADP
ejpam-184	6	13	dynamic	dynamic	ADJ
ejpam-184	6	14	generalizations	generalization	NOUN
ejpam-184	6	15	of	of	ADP
ejpam-184	6	16	corresponding	correspond	VERB
ejpam-184	6	17	(	(	PUNCT
ejpam-184	6	18	static	static	ADJ
ejpam-184	6	19	)	)	PUNCT
ejpam-184	6	20	duality	duality	NOUN
ejpam-184	6	21	results	result	VERB
ejpam-184	6	22	in	in	ADP
ejpam-184	6	23	nonlinear	nonlinear	ADJ
ejpam-184	6	24	programming	programming	NOUN
ejpam-184	6	25	.	.	PUNCT
ejpam-184	7	1	ams	am	NOUN
ejpam-184	7	2	subject	subject	ADJ
ejpam-184	7	3	classifications	classification	NOUN
ejpam-184	7	4	:	:	PUNCT
ejpam-184	7	5	primary	primary	ADJ
ejpam-184	7	6	90c30	90c30	NUM
ejpam-184	7	7	,	,	PUNCT
ejpam-184	7	8	secondary	secondary	ADJ
ejpam-184	7	9	90c11	90c11	NUM
ejpam-184	7	10	,	,	PUNCT
ejpam-184	7	11	90c20	90c20	NUM
ejpam-184	7	12	,	,	PUNCT
ejpam-184	7	13	90c26	90c26	NUM
ejpam-184	7	14	key	key	ADJ
ejpam-184	7	15	words	word	NOUN
ejpam-184	7	16	:	:	PUNCT
ejpam-184	7	17	mond	mond	PROPN
ejpam-184	7	18	-	-	PUNCT
ejpam-184	7	19	weir	weir	PROPN
ejpam-184	7	20	type	type	NOUN
ejpam-184	7	21	second	second	ADJ
ejpam-184	7	22	-	-	PUNCT
ejpam-184	7	23	order	order	NOUN
ejpam-184	7	24	dual	dual	ADJ
ejpam-184	7	25	,	,	PUNCT
ejpam-184	7	26	variational	variational	ADJ
ejpam-184	7	27	problem	problem	NOUN
ejpam-184	7	28	,	,	PUNCT
ejpam-184	7	29	second	second	ADJ
ejpam-184	7	30	-	-	PUNCT
ejpam-184	7	31	order	order	NOUN
ejpam-184	7	32	invexity	invexity	NOUN
ejpam-184	7	33	,	,	PUNCT
ejpam-184	7	34	natural	natural	ADJ
ejpam-184	7	35	boundary	boundary	ADJ
ejpam-184	7	36	values	value	NOUN
ejpam-184	7	37	,	,	PUNCT
ejpam-184	7	38	nonlinear	nonlinear	ADJ
ejpam-184	7	39	programming	programming	NOUN
ejpam-184	7	40	.	.	PUNCT
ejpam-184	8	1	∗corresponding	∗corresponde	VERB
ejpam-184	8	2	author	author	NOUN
ejpam-184	8	3	.	.	PUNCT
ejpam-184	9	1	email	email	NOUN
ejpam-184	9	2	address	address	NOUN
ejpam-184	9	3	:	:	PUNCT
ejpam-184	9	4	ihusain11	ihusain11	PROPN
ejpam-184	9	5	�	�	PROPN
ejpam-184	9	6	yahoo	yahoo	PROPN
ejpam-184	9	7	.	.	PUNCT
ejpam-184	10	1	om	om	PROPN
ejpam-184	10	2	(	(	PUNCT
ejpam-184	10	3	i.	i.	PROPN
ejpam-184	10	4	husain	husain	PROPN
ejpam-184	10	5	)	)	PUNCT
ejpam-184	10	6	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-184	11	1	278	278	NUM
ejpam-184	11	2	c	c	X
ejpam-184	11	3	©	©	PROPN
ejpam-184	11	4	2009	2009	NUM
ejpam-184	11	5	ejpam	ejpam	NOUN
ejpam-184	11	6	all	all	DET
ejpam-184	11	7	rights	right	NOUN
ejpam-184	11	8	reserved	reserve	VERB
ejpam-184	11	9	.	.	PUNCT
ejpam-184	12	1	i.	i.	PROPN
ejpam-184	12	2	husain	husain	PROPN
ejpam-184	12	3	,	,	PUNCT
ejpam-184	12	4	a.	a.	PROPN
ejpam-184	12	5	ahmed	ahmed	PROPN
ejpam-184	12	6	,	,	PUNCT
ejpam-184	12	7	and	and	CCONJ
ejpam-184	12	8	m.	m.	NOUN
ejpam-184	12	9	massodi	massodi	PROPN
ejpam-184	12	10	/	/	SYM
ejpam-184	12	11	eur	eur	PROPN
ejpam-184	12	12	.	.	PUNCT
ejpam-184	13	1	j.	j.	PROPN
ejpam-184	13	2	pure	pure	PROPN
ejpam-184	13	3	appl	appl	PROPN
ejpam-184	13	4	.	.	PROPN
ejpam-184	13	5	math	math	PROPN
ejpam-184	13	6	,	,	PUNCT
ejpam-184	13	7	2	2	NUM
ejpam-184	13	8	(	(	PUNCT
ejpam-184	13	9	2009	2009	NUM
ejpam-184	13	10	)	)	PUNCT
ejpam-184	13	11	,	,	PUNCT
ejpam-184	13	12	(	(	PUNCT
ejpam-184	13	13	278	278	NUM
ejpam-184	13	14	-	-	SYM
ejpam-184	13	15	295	295	NUM
ejpam-184	13	16	)	)	PUNCT
ejpam-184	13	17	279	279	NUM
ejpam-184	13	18	1	1	NUM
ejpam-184	13	19	.	.	PUNCT
ejpam-184	14	1	introduction	introduction	NOUN
ejpam-184	14	2	the	the	DET
ejpam-184	14	3	calculus	calculus	NOUN
ejpam-184	14	4	of	of	ADP
ejpam-184	14	5	variation	variation	NOUN
ejpam-184	14	6	has	have	AUX
ejpam-184	14	7	been	be	AUX
ejpam-184	14	8	one	one	NUM
ejpam-184	14	9	of	of	ADP
ejpam-184	14	10	the	the	DET
ejpam-184	14	11	prominent	prominent	ADJ
ejpam-184	14	12	branches	branch	NOUN
ejpam-184	14	13	of	of	ADP
ejpam-184	14	14	analysis	analysis	NOUN
ejpam-184	14	15	,	,	PUNCT
ejpam-184	14	16	for	for	ADP
ejpam-184	14	17	more	more	ADJ
ejpam-184	14	18	than	than	ADP
ejpam-184	14	19	two	two	NUM
ejpam-184	14	20	centuries	century	NOUN
ejpam-184	14	21	.	.	PUNCT
ejpam-184	15	1	it	it	PRON
ejpam-184	15	2	is	be	AUX
ejpam-184	15	3	a	a	DET
ejpam-184	15	4	tool	tool	NOUN
ejpam-184	15	5	of	of	ADP
ejpam-184	15	6	great	great	ADJ
ejpam-184	15	7	power	power	NOUN
ejpam-184	15	8	that	that	PRON
ejpam-184	15	9	can	can	AUX
ejpam-184	15	10	be	be	AUX
ejpam-184	15	11	used	use	VERB
ejpam-184	15	12	to	to	ADP
ejpam-184	15	13	wide	wide	ADJ
ejpam-184	15	14	variety	variety	NOUN
ejpam-184	15	15	of	of	ADP
ejpam-184	15	16	problems	problem	NOUN
ejpam-184	15	17	,	,	PUNCT
ejpam-184	15	18	in	in	ADP
ejpam-184	15	19	pure	pure	ADJ
ejpam-184	15	20	mathematics	mathematic	NOUN
ejpam-184	15	21	.	.	PUNCT
ejpam-184	16	1	it	it	PRON
ejpam-184	16	2	can	can	AUX
ejpam-184	16	3	also	also	ADV
ejpam-184	16	4	be	be	AUX
ejpam-184	16	5	used	use	VERB
ejpam-184	16	6	to	to	PART
ejpam-184	16	7	express	express	VERB
ejpam-184	16	8	basic	basic	ADJ
ejpam-184	16	9	principles	principle	NOUN
ejpam-184	16	10	of	of	ADP
ejpam-184	16	11	mathematical	mathematical	ADJ
ejpam-184	16	12	physics	physics	NOUN
ejpam-184	16	13	in	in	ADP
ejpam-184	16	14	forms	form	NOUN
ejpam-184	16	15	of	of	ADP
ejpam-184	16	16	utmost	utmost	ADJ
ejpam-184	16	17	simplicity	simplicity	NOUN
ejpam-184	16	18	and	and	CCONJ
ejpam-184	16	19	elegance	elegance	NOUN
ejpam-184	16	20	.	.	PUNCT
ejpam-184	17	1	hanson	hanson	PROPN
ejpam-184	18	1	[	[	X
ejpam-184	18	2	6	6	NUM
ejpam-184	18	3	]	]	PUNCT
ejpam-184	18	4	pointed	point	VERB
ejpam-184	18	5	out	out	ADP
ejpam-184	18	6	that	that	SCONJ
ejpam-184	18	7	some	some	PRON
ejpam-184	18	8	of	of	ADP
ejpam-184	18	9	the	the	DET
ejpam-184	18	10	duality	duality	NOUN
ejpam-184	18	11	results	result	VERB
ejpam-184	18	12	in	in	ADP
ejpam-184	18	13	the	the	DET
ejpam-184	18	14	mathematical	mathematical	ADJ
ejpam-184	18	15	programming	programming	NOUN
ejpam-184	18	16	have	have	VERB
ejpam-184	18	17	the	the	DET
ejpam-184	18	18	analogues	analogue	NOUN
ejpam-184	18	19	in	in	ADP
ejpam-184	18	20	calculus	calculus	NOUN
ejpam-184	18	21	of	of	ADP
ejpam-184	18	22	variations	variation	NOUN
ejpam-184	18	23	.	.	PUNCT
ejpam-184	19	1	exploring	explore	VERB
ejpam-184	19	2	this	this	DET
ejpam-184	19	3	relationship	relationship	NOUN
ejpam-184	19	4	between	between	ADP
ejpam-184	19	5	mathematical	mathematical	ADJ
ejpam-184	19	6	programming	programming	NOUN
ejpam-184	19	7	and	and	CCONJ
ejpam-184	19	8	classical	classical	ADJ
ejpam-184	19	9	calculus	calculus	NOUN
ejpam-184	19	10	of	of	ADP
ejpam-184	19	11	variation	variation	NOUN
ejpam-184	19	12	,	,	PUNCT
ejpam-184	19	13	mond	mond	NOUN
ejpam-184	19	14	and	and	CCONJ
ejpam-184	19	15	hanson	hanson	NOUN
ejpam-184	20	1	[	[	X
ejpam-184	20	2	8	8	NUM
ejpam-184	20	3	]	]	PUNCT
ejpam-184	20	4	formulated	formulate	VERB
ejpam-184	20	5	a	a	DET
ejpam-184	20	6	constrained	constrain	VERB
ejpam-184	20	7	variational	variational	ADJ
ejpam-184	20	8	problem	problem	NOUN
ejpam-184	20	9	as	as	ADP
ejpam-184	20	10	mathematical	mathematical	ADJ
ejpam-184	20	11	programming	programming	NOUN
ejpam-184	20	12	problem	problem	NOUN
ejpam-184	20	13	in	in	ADP
ejpam-184	20	14	abstract	abstract	ADJ
ejpam-184	20	15	space	space	NOUN
ejpam-184	20	16	and	and	CCONJ
ejpam-184	20	17	using	use	VERB
ejpam-184	20	18	valentine	valentine	NOUN
ejpam-184	20	19	[	[	X
ejpam-184	20	20	10	10	NUM
ejpam-184	20	21	]	]	PUNCT
ejpam-184	20	22	optimality	optimality	NOUN
ejpam-184	20	23	conditions	condition	NOUN
ejpam-184	20	24	for	for	ADP
ejpam-184	20	25	the	the	DET
ejpam-184	20	26	same	same	ADJ
ejpam-184	20	27	,	,	PUNCT
ejpam-184	20	28	presented	present	VERB
ejpam-184	20	29	its	its	PRON
ejpam-184	20	30	wolfe	wolfe	PROPN
ejpam-184	20	31	dual	dual	ADJ
ejpam-184	20	32	variational	variational	ADJ
ejpam-184	20	33	problem	problem	NOUN
ejpam-184	20	34	for	for	ADP
ejpam-184	20	35	validating	validate	VERB
ejpam-184	20	36	various	various	ADJ
ejpam-184	20	37	duality	duality	NOUN
ejpam-184	20	38	results	result	NOUN
ejpam-184	20	39	under	under	ADP
ejpam-184	20	40	usual	usual	ADJ
ejpam-184	20	41	convexity	convexity	NOUN
ejpam-184	20	42	.	.	PUNCT
ejpam-184	21	1	later	later	ADV
ejpam-184	21	2	bector	bector	NOUN
ejpam-184	21	3	,	,	PUNCT
ejpam-184	21	4	chandra	chandra	PROPN
ejpam-184	21	5	and	and	CCONJ
ejpam-184	21	6	husain	husain	PROPN
ejpam-184	22	1	[	[	X
ejpam-184	22	2	2	2	NUM
ejpam-184	22	3	]	]	PUNCT
ejpam-184	22	4	studied	study	VERB
ejpam-184	22	5	mond	mond	PROPN
ejpam-184	22	6	-	-	PUNCT
ejpam-184	22	7	weir	weir	PROPN
ejpam-184	22	8	type	type	NOUN
ejpam-184	22	9	duality	duality	NOUN
ejpam-184	22	10	for	for	ADP
ejpam-184	22	11	the	the	DET
ejpam-184	22	12	problem	problem	NOUN
ejpam-184	22	13	of	of	ADP
ejpam-184	22	14	mond	mond	NOUN
ejpam-184	22	15	and	and	CCONJ
ejpam-184	22	16	hanson	hanson	NOUN
ejpam-184	23	1	[	[	X
ejpam-184	23	2	8	8	NUM
ejpam-184	23	3	]	]	PUNCT
ejpam-184	23	4	for	for	ADP
ejpam-184	23	5	relaxing	relax	VERB
ejpam-184	23	6	its	its	PRON
ejpam-184	23	7	convexity	convexity	NOUN
ejpam-184	23	8	requirements	requirement	NOUN
ejpam-184	23	9	.	.	PUNCT
ejpam-184	24	1	in	in	ADP
ejpam-184	24	2	[	[	X
ejpam-184	24	3	3	3	NUM
ejpam-184	24	4	]	]	X
ejpam-184	24	5	chandra	chandra	PROPN
ejpam-184	24	6	,	,	PUNCT
ejpam-184	24	7	craven	craven	NOUN
ejpam-184	24	8	and	and	CCONJ
ejpam-184	24	9	husain	husain	NOUN
ejpam-184	24	10	studied	study	VERB
ejpam-184	24	11	optimality	optimality	NOUN
ejpam-184	24	12	and	and	CCONJ
ejpam-184	24	13	duality	duality	NOUN
ejpam-184	24	14	for	for	ADP
ejpam-184	24	15	a	a	DET
ejpam-184	24	16	class	class	NOUN
ejpam-184	24	17	of	of	ADP
ejpam-184	24	18	nondifferentiable	nondifferentiable	ADJ
ejpam-184	24	19	variational	variational	ADJ
ejpam-184	24	20	problems	problem	NOUN
ejpam-184	24	21	in	in	ADP
ejpam-184	24	22	which	which	PRON
ejpam-184	24	23	the	the	DET
ejpam-184	24	24	integrand	integrand	NOUN
ejpam-184	24	25	of	of	ADP
ejpam-184	24	26	the	the	DET
ejpam-184	24	27	objective	objective	ADJ
ejpam-184	24	28	functional	functional	NOUN
ejpam-184	24	29	contains	contain	VERB
ejpam-184	24	30	a	a	DET
ejpam-184	24	31	term	term	NOUN
ejpam-184	24	32	of	of	ADP
ejpam-184	24	33	a	a	DET
ejpam-184	24	34	square	square	ADJ
ejpam-184	24	35	root	root	NOUN
ejpam-184	24	36	of	of	ADP
ejpam-184	24	37	the	the	DET
ejpam-184	24	38	quadratic	quadratic	ADJ
ejpam-184	24	39	form	form	NOUN
ejpam-184	24	40	,	,	PUNCT
ejpam-184	24	41	while	while	SCONJ
ejpam-184	24	42	in	in	ADP
ejpam-184	24	43	[	[	X
ejpam-184	24	44	5	5	NUM
ejpam-184	24	45	]	]	PUNCT
ejpam-184	24	46	,	,	PUNCT
ejpam-184	24	47	husain	husain	PROPN
ejpam-184	24	48	and	and	CCONJ
ejpam-184	24	49	jabeen	jabeen	PROPN
ejpam-184	24	50	studied	study	VERB
ejpam-184	24	51	optimality	optimality	NOUN
ejpam-184	24	52	criteria	criterion	NOUN
ejpam-184	24	53	and	and	CCONJ
ejpam-184	24	54	duality	duality	NOUN
ejpam-184	24	55	for	for	ADP
ejpam-184	24	56	variational	variational	ADJ
ejpam-184	24	57	problems	problem	NOUN
ejpam-184	24	58	in	in	ADP
ejpam-184	24	59	which	which	PRON
ejpam-184	24	60	integrand	integrand	NOUN
ejpam-184	24	61	of	of	ADP
ejpam-184	24	62	objective	objective	ADJ
ejpam-184	24	63	and	and	CCONJ
ejpam-184	24	64	constraint	constraint	NOUN
ejpam-184	24	65	functions	function	NOUN
ejpam-184	24	66	contains	contain	VERB
ejpam-184	24	67	terms	term	NOUN
ejpam-184	24	68	of	of	ADP
ejpam-184	24	69	support	support	NOUN
ejpam-184	24	70	functions	function	NOUN
ejpam-184	24	71	.	.	PUNCT
ejpam-184	25	1	second	second	ADJ
ejpam-184	25	2	-	-	PUNCT
ejpam-184	25	3	order	order	NOUN
ejpam-184	25	4	duality	duality	NOUN
ejpam-184	25	5	in	in	ADP
ejpam-184	25	6	mathematical	mathematical	ADJ
ejpam-184	25	7	programming	programming	NOUN
ejpam-184	25	8	has	have	AUX
ejpam-184	25	9	been	be	AUX
ejpam-184	25	10	extensively	extensively	ADV
ejpam-184	25	11	studied	study	VERB
ejpam-184	25	12	in	in	ADP
ejpam-184	25	13	recent	recent	ADJ
ejpam-184	25	14	years	year	NOUN
ejpam-184	25	15	.	.	PUNCT
ejpam-184	26	1	mangasarian	mangasarian	PROPN
ejpam-184	27	1	[	[	X
ejpam-184	27	2	7	7	NUM
ejpam-184	27	3	]	]	PUNCT
ejpam-184	27	4	was	be	AUX
ejpam-184	27	5	the	the	DET
ejpam-184	27	6	first	first	ADJ
ejpam-184	27	7	to	to	PART
ejpam-184	27	8	identify	identify	VERB
ejpam-184	27	9	a	a	DET
ejpam-184	27	10	second	second	ADJ
ejpam-184	27	11	-	-	PUNCT
ejpam-184	27	12	order	order	NOUN
ejpam-184	27	13	dual	dual	ADJ
ejpam-184	27	14	formulation	formulation	NOUN
ejpam-184	27	15	for	for	ADP
ejpam-184	27	16	non	non	ADJ
ejpam-184	27	17	-	-	ADJ
ejpam-184	27	18	linear	linear	ADJ
ejpam-184	27	19	programs	program	NOUN
ejpam-184	27	20	under	under	ADP
ejpam-184	27	21	the	the	DET
ejpam-184	27	22	assumptions	assumption	NOUN
ejpam-184	27	23	that	that	PRON
ejpam-184	27	24	are	be	AUX
ejpam-184	27	25	complicated	complicated	ADJ
ejpam-184	27	26	and	and	CCONJ
ejpam-184	27	27	somewhat	somewhat	ADV
ejpam-184	27	28	difficult	difficult	ADJ
ejpam-184	27	29	to	to	PART
ejpam-184	27	30	verify	verify	VERB
ejpam-184	27	31	.	.	PUNCT
ejpam-184	28	1	mond	mond	NOUN
ejpam-184	29	1	[	[	X
ejpam-184	29	2	9	9	NUM
ejpam-184	29	3	]	]	PUNCT
ejpam-184	29	4	introduced	introduce	VERB
ejpam-184	29	5	the	the	DET
ejpam-184	29	6	concept	concept	NOUN
ejpam-184	29	7	of	of	ADP
ejpam-184	29	8	second	second	ADJ
ejpam-184	29	9	-	-	PUNCT
ejpam-184	29	10	order	order	NOUN
ejpam-184	29	11	convex	convex	NOUN
ejpam-184	29	12	functions	function	NOUN
ejpam-184	29	13	(	(	PUNCT
ejpam-184	29	14	named	name	VERB
ejpam-184	29	15	as	as	ADP
ejpam-184	29	16	bonvex	bonvex	ADJ
ejpam-184	29	17	functions	function	NOUN
ejpam-184	29	18	by	by	ADP
ejpam-184	29	19	bector	bector	NOUN
ejpam-184	29	20	and	and	CCONJ
ejpam-184	29	21	chandra	chandra	PROPN
ejpam-184	30	1	[	[	X
ejpam-184	30	2	1	1	NUM
ejpam-184	30	3	]	]	PUNCT
ejpam-184	30	4	)	)	PUNCT
ejpam-184	30	5	and	and	CCONJ
ejpam-184	30	6	studied	study	VERB
ejpam-184	30	7	second	second	ADJ
ejpam-184	30	8	-	-	PUNCT
ejpam-184	30	9	order	order	NOUN
ejpam-184	30	10	duality	duality	NOUN
ejpam-184	30	11	for	for	ADP
ejpam-184	30	12	nonlinear	nonlinear	ADJ
ejpam-184	30	13	programs	program	NOUN
ejpam-184	30	14	.	.	PUNCT
ejpam-184	31	1	recently	recently	ADV
ejpam-184	31	2	chen	chen	PROPN
ejpam-184	32	1	[	[	X
ejpam-184	32	2	4	4	NUM
ejpam-184	32	3	]	]	PUNCT
ejpam-184	32	4	formulated	formulate	VERB
ejpam-184	32	5	wolfe	wolfe	PROPN
ejpam-184	32	6	type	type	NOUN
ejpam-184	32	7	second	second	ADJ
ejpam-184	32	8	-	-	PUNCT
ejpam-184	32	9	order	order	NOUN
ejpam-184	32	10	dual	dual	ADJ
ejpam-184	32	11	problem	problem	NOUN
ejpam-184	32	12	to	to	ADP
ejpam-184	32	13	the	the	DET
ejpam-184	32	14	orthodox	orthodox	ADJ
ejpam-184	32	15	variational	variational	ADJ
ejpam-184	32	16	problem	problem	NOUN
ejpam-184	32	17	and	and	CCONJ
ejpam-184	32	18	studied	study	VERB
ejpam-184	32	19	usual	usual	ADJ
ejpam-184	32	20	duality	duality	NOUN
ejpam-184	32	21	results	result	NOUN
ejpam-184	32	22	under	under	ADP
ejpam-184	32	23	invexity	invexity	NOUN
ejpam-184	32	24	assumptions	assumption	NOUN
ejpam-184	32	25	i.	i.	PROPN
ejpam-184	32	26	husain	husain	PROPN
ejpam-184	32	27	,	,	PUNCT
ejpam-184	32	28	a.	a.	PROPN
ejpam-184	32	29	ahmed	ahmed	PROPN
ejpam-184	32	30	,	,	PUNCT
ejpam-184	32	31	and	and	CCONJ
ejpam-184	32	32	m.	m.	NOUN
ejpam-184	32	33	massodi	massodi	PROPN
ejpam-184	32	34	/	/	SYM
ejpam-184	32	35	eur	eur	PROPN
ejpam-184	32	36	.	.	PUNCT
ejpam-184	33	1	j.	j.	PROPN
ejpam-184	33	2	pure	pure	PROPN
ejpam-184	33	3	appl	appl	PROPN
ejpam-184	33	4	.	.	PROPN
ejpam-184	33	5	math	math	PROPN
ejpam-184	33	6	,	,	PUNCT
ejpam-184	33	7	2	2	NUM
ejpam-184	33	8	(	(	PUNCT
ejpam-184	33	9	2009	2009	NUM
ejpam-184	33	10	)	)	PUNCT
ejpam-184	33	11	,	,	PUNCT
ejpam-184	33	12	(	(	PUNCT
ejpam-184	33	13	278	278	NUM
ejpam-184	33	14	-	-	SYM
ejpam-184	33	15	295	295	NUM
ejpam-184	33	16	)	)	PUNCT
ejpam-184	33	17	280	280	NUM
ejpam-184	33	18	on	on	ADP
ejpam-184	33	19	the	the	DET
ejpam-184	33	20	functions	function	NOUN
ejpam-184	33	21	that	that	PRON
ejpam-184	33	22	occur	occur	VERB
ejpam-184	33	23	in	in	ADP
ejpam-184	33	24	the	the	DET
ejpam-184	33	25	formulation	formulation	NOUN
ejpam-184	33	26	of	of	ADP
ejpam-184	33	27	the	the	DET
ejpam-184	33	28	problem	problem	NOUN
ejpam-184	33	29	along	along	ADP
ejpam-184	33	30	with	with	ADP
ejpam-184	33	31	some	some	DET
ejpam-184	33	32	strange	strange	ADJ
ejpam-184	33	33	assumptions	assumption	NOUN
ejpam-184	33	34	.	.	PUNCT
ejpam-184	34	1	mond	mond	NOUN
ejpam-184	35	1	[	[	X
ejpam-184	35	2	9	9	NUM
ejpam-184	35	3	]	]	PUNCT
ejpam-184	35	4	has	have	AUX
ejpam-184	35	5	pointed	point	VERB
ejpam-184	35	6	out	out	ADP
ejpam-184	35	7	that	that	SCONJ
ejpam-184	35	8	the	the	DET
ejpam-184	35	9	second	second	ADJ
ejpam-184	35	10	-	-	PUNCT
ejpam-184	35	11	order	order	NOUN
ejpam-184	35	12	dual	dual	ADJ
ejpam-184	35	13	for	for	ADP
ejpam-184	35	14	a	a	DET
ejpam-184	35	15	nonlinear	nonlinear	ADJ
ejpam-184	35	16	programming	programming	NOUN
ejpam-184	35	17	gives	give	VERB
ejpam-184	35	18	a	a	DET
ejpam-184	35	19	tighter	tighter	ADV
ejpam-184	35	20	bound	bind	VERB
ejpam-184	35	21	and	and	CCONJ
ejpam-184	35	22	has	have	VERB
ejpam-184	35	23	computational	computational	ADJ
ejpam-184	35	24	advantage	advantage	NOUN
ejpam-184	35	25	over	over	ADP
ejpam-184	35	26	a	a	DET
ejpam-184	35	27	first	first	ADJ
ejpam-184	35	28	order	order	NOUN
ejpam-184	35	29	dual	dual	ADJ
ejpam-184	35	30	.	.	PUNCT
ejpam-184	36	1	motivated	motivate	VERB
ejpam-184	36	2	with	with	ADP
ejpam-184	36	3	this	this	PRON
ejpam-184	36	4	of	of	ADP
ejpam-184	36	5	mond	mond	NOUN
ejpam-184	36	6	[	[	X
ejpam-184	36	7	9	9	NUM
ejpam-184	36	8	]	]	PUNCT
ejpam-184	36	9	in	in	ADP
ejpam-184	36	10	this	this	DET
ejpam-184	36	11	exposition	exposition	NOUN
ejpam-184	36	12	,	,	PUNCT
ejpam-184	36	13	we	we	PRON
ejpam-184	36	14	construct	construct	VERB
ejpam-184	36	15	mond	mond	PROPN
ejpam-184	36	16	-	-	PUNCT
ejpam-184	36	17	weir	weir	PROPN
ejpam-184	36	18	type	type	NOUN
ejpam-184	36	19	second	second	ADJ
ejpam-184	36	20	-	-	PUNCT
ejpam-184	36	21	order	order	NOUN
ejpam-184	36	22	dual	dual	ADJ
ejpam-184	36	23	to	to	ADP
ejpam-184	36	24	the	the	DET
ejpam-184	36	25	variational	variational	ADJ
ejpam-184	36	26	problem	problem	NOUN
ejpam-184	36	27	and	and	CCONJ
ejpam-184	36	28	derive	derive	VERB
ejpam-184	36	29	usual	usual	ADJ
ejpam-184	36	30	duality	duality	NOUN
ejpam-184	36	31	results	result	NOUN
ejpam-184	36	32	under	under	ADP
ejpam-184	36	33	second	second	ADJ
ejpam-184	36	34	-	-	PUNCT
ejpam-184	36	35	order	order	NOUN
ejpam-184	36	36	pseudo	pseudo	NOUN
ejpam-184	36	37	-	-	NOUN
ejpam-184	36	38	invexity	invexity	NOUN
ejpam-184	36	39	and	and	CCONJ
ejpam-184	36	40	second	second	ADJ
ejpam-184	36	41	order	order	NOUN
ejpam-184	36	42	quasi	quasi	ADJ
ejpam-184	36	43	-	-	ADJ
ejpam-184	36	44	invexity	invexity	ADJ
ejpam-184	36	45	assumptions	assumption	NOUN
ejpam-184	36	46	.	.	PUNCT
ejpam-184	37	1	the	the	DET
ejpam-184	37	2	relationship	relationship	NOUN
ejpam-184	37	3	of	of	ADP
ejpam-184	37	4	our	our	PRON
ejpam-184	37	5	results	result	NOUN
ejpam-184	37	6	to	to	ADP
ejpam-184	37	7	second	second	ADJ
ejpam-184	37	8	-	-	PUNCT
ejpam-184	37	9	order	order	NOUN
ejpam-184	37	10	duality	duality	NOUN
ejpam-184	37	11	results	result	NOUN
ejpam-184	37	12	in	in	ADP
ejpam-184	37	13	nonlinear	nonlinear	ADJ
ejpam-184	37	14	programming	programming	NOUN
ejpam-184	37	15	reported	report	VERB
ejpam-184	37	16	in	in	ADP
ejpam-184	37	17	[	[	X
ejpam-184	37	18	1	1	NUM
ejpam-184	37	19	]	]	PUNCT
ejpam-184	37	20	is	be	AUX
ejpam-184	37	21	indicated	indicate	VERB
ejpam-184	37	22	.	.	PUNCT
ejpam-184	38	1	in	in	ADP
ejpam-184	38	2	essence	essence	NOUN
ejpam-184	38	3	it	it	PRON
ejpam-184	38	4	is	be	AUX
ejpam-184	38	5	shown	show	VERB
ejpam-184	38	6	that	that	SCONJ
ejpam-184	38	7	our	our	PRON
ejpam-184	38	8	duality	duality	NOUN
ejpam-184	38	9	results	result	NOUN
ejpam-184	38	10	can	can	AUX
ejpam-184	38	11	be	be	AUX
ejpam-184	38	12	viewed	view	VERB
ejpam-184	38	13	as	as	ADP
ejpam-184	38	14	dynamic	dynamic	ADJ
ejpam-184	38	15	generalizations	generalization	NOUN
ejpam-184	38	16	of	of	ADP
ejpam-184	38	17	corresponding	correspond	VERB
ejpam-184	38	18	(	(	PUNCT
ejpam-184	38	19	static	static	ADJ
ejpam-184	38	20	)	)	PUNCT
ejpam-184	38	21	duality	duality	NOUN
ejpam-184	38	22	theorems	theorem	NOUN
ejpam-184	38	23	of	of	ADP
ejpam-184	38	24	nonlinear	nonlinear	ADJ
ejpam-184	38	25	programming	programming	NOUN
ejpam-184	38	26	already	already	ADV
ejpam-184	38	27	in	in	ADP
ejpam-184	38	28	the	the	DET
ejpam-184	38	29	literature	literature	NOUN
ejpam-184	38	30	.	.	PUNCT
ejpam-184	39	1	2	2	X
ejpam-184	39	2	.	.	X
ejpam-184	39	3	definitions	definition	NOUN
ejpam-184	39	4	and	and	CCONJ
ejpam-184	39	5	related	related	ADJ
ejpam-184	39	6	pre	pre	NOUN
ejpam-184	39	7	-	-	NOUN
ejpam-184	39	8	requisites	requisite	NOUN
ejpam-184	39	9	let	let	VERB
ejpam-184	39	10	i	i	PRON
ejpam-184	39	11	=	=	PUNCT
ejpam-184	40	1	[	[	X
ejpam-184	40	2	a	a	X
ejpam-184	40	3	,	,	PUNCT
ejpam-184	40	4	b	b	AUX
ejpam-184	40	5	]	]	PUNCT
ejpam-184	40	6	be	be	AUX
ejpam-184	40	7	a	a	DET
ejpam-184	40	8	real	real	ADJ
ejpam-184	40	9	interval	interval	NOUN
ejpam-184	40	10	,	,	PUNCT
ejpam-184	40	11	f	f	X
ejpam-184	40	12	:	:	PUNCT
ejpam-184	41	1	i	i	PRON
ejpam-184	41	2	×	×	VERB
ejpam-184	41	3	rn	rn	PROPN
ejpam-184	41	4	×	×	PROPN
ejpam-184	41	5	rn	rn	PROPN
ejpam-184	41	6	→	→	SYM
ejpam-184	41	7	r	r	NOUN
ejpam-184	41	8	and	and	CCONJ
ejpam-184	41	9	g	g	NOUN
ejpam-184	41	10	:	:	PUNCT
ejpam-184	41	11	i	i	PRON
ejpam-184	41	12	×	×	VERB
ejpam-184	41	13	rn	rn	PROPN
ejpam-184	41	14	×	×	PROPN
ejpam-184	41	15	rn	rn	PROPN
ejpam-184	41	16	→	→	PROPN
ejpam-184	41	17	rm	rm	PROPN
ejpam-184	41	18	be	be	AUX
ejpam-184	41	19	twice	twice	ADV
ejpam-184	41	20	continuously	continuously	ADV
ejpam-184	41	21	differentiable	differentiable	ADJ
ejpam-184	41	22	functions	function	NOUN
ejpam-184	41	23	.	.	PUNCT
ejpam-184	42	1	in	in	ADP
ejpam-184	42	2	order	order	NOUN
ejpam-184	42	3	to	to	PART
ejpam-184	42	4	consider	consider	VERB
ejpam-184	42	5	f	f	PROPN
ejpam-184	42	6	(	(	PUNCT
ejpam-184	42	7	t	t	PROPN
ejpam-184	42	8	,	,	PUNCT
ejpam-184	42	9	x	x	X
ejpam-184	42	10	(	(	PUNCT
ejpam-184	42	11	t	t	PROPN
ejpam-184	42	12	)	)	PUNCT
ejpam-184	42	13	,	,	PUNCT
ejpam-184	42	14	ẋ	ẋ	PROPN
ejpam-184	42	15	(	(	PUNCT
ejpam-184	42	16	t	t	PROPN
ejpam-184	42	17	)	)	PUNCT
ejpam-184	42	18	)	)	PUNCT
ejpam-184	42	19	,	,	PUNCT
ejpam-184	42	20	where	where	SCONJ
ejpam-184	42	21	x	x	X
ejpam-184	42	22	:	:	PUNCT
ejpam-184	42	23	i	i	PRON
ejpam-184	42	24	→	→	SYM
ejpam-184	42	25	rn	rn	PROPN
ejpam-184	42	26	is	be	AUX
ejpam-184	42	27	differentiable	differentiable	ADJ
ejpam-184	42	28	with	with	ADP
ejpam-184	42	29	derivative	derivative	PROPN
ejpam-184	42	30	ẋ	ẋ	PROPN
ejpam-184	42	31	,	,	PUNCT
ejpam-184	42	32	denoted	denote	VERB
ejpam-184	42	33	by	by	ADP
ejpam-184	42	34	fx	fx	PROPN
ejpam-184	42	35	and	and	CCONJ
ejpam-184	42	36	f	f	PROPN
ejpam-184	42	37	ẋ	ẋ	PROPN
ejpam-184	43	1	the	the	DET
ejpam-184	43	2	partial	partial	ADJ
ejpam-184	43	3	derivative	derivative	NOUN
ejpam-184	43	4	of	of	ADP
ejpam-184	43	5	f	f	PROPN
ejpam-184	43	6	with	with	ADP
ejpam-184	43	7	respect	respect	NOUN
ejpam-184	43	8	to	to	ADP
ejpam-184	43	9	x	x	PUNCT
ejpam-184	43	10	and	and	CCONJ
ejpam-184	43	11	ẋ	ẋ	PROPN
ejpam-184	43	12	,	,	PUNCT
ejpam-184	43	13	respectively	respectively	ADV
ejpam-184	43	14	,	,	PUNCT
ejpam-184	43	15	that	that	ADV
ejpam-184	43	16	is	is	ADV
ejpam-184	43	17	,	,	PUNCT
ejpam-184	43	18	fx	fx	ADJ
ejpam-184	43	19	=	=	SYM
ejpam-184	43	20			PROPN
ejpam-184	43	21			NOUN
ejpam-184	43	22			NOUN
ejpam-184	43	23			NOUN
ejpam-184	43	24			NOUN
ejpam-184	43	25			NOUN
ejpam-184	43	26			NOUN
ejpam-184	43	27			NOUN
ejpam-184	43	28			NOUN
ejpam-184	43	29			NOUN
ejpam-184	43	30			NOUN
ejpam-184	43	31			NOUN
ejpam-184	43	32			NOUN
ejpam-184	43	33			NOUN
ejpam-184	43	34	∂	∂	ADJ
ejpam-184	43	35	f	f	NOUN
ejpam-184	43	36	∂	∂	NUM
ejpam-184	44	1	x1	x1	PROPN
ejpam-184	44	2	∂	∂	PROPN
ejpam-184	44	3	f	f	PROPN
ejpam-184	44	4	∂	∂	PROPN
ejpam-184	44	5	x2	x2	NOUN
ejpam-184	44	6	...	...	PUNCT
ejpam-184	44	7	∂	∂	NUM
ejpam-184	44	8	f	f	NOUN
ejpam-184	44	9	∂	∂	NUM
ejpam-184	44	10	x	x	SYM
ejpam-184	44	11	n	n	PRON
ejpam-184	44	12			NOUN
ejpam-184	44	13			NOUN
ejpam-184	44	14			VERB
ejpam-184	44	15			NOUN
ejpam-184	44	16			NOUN
ejpam-184	44	17			NOUN
ejpam-184	44	18			NOUN
ejpam-184	44	19			NOUN
ejpam-184	44	20			NOUN
ejpam-184	44	21			NOUN
ejpam-184	44	22			NOUN
ejpam-184	44	23			NOUN
ejpam-184	44	24			NOUN
ejpam-184	44	25			PUNCT
ejpam-184	45	1	,	,	PUNCT
ejpam-184	45	2	f	f	X
ejpam-184	45	3	ẋ	ẋ	PROPN
ejpam-184	45	4	=	=	SYM
ejpam-184	45	5			PROPN
ejpam-184	45	6			NOUN
ejpam-184	45	7			NOUN
ejpam-184	45	8			NOUN
ejpam-184	45	9			NOUN
ejpam-184	45	10			NOUN
ejpam-184	45	11			NOUN
ejpam-184	45	12			NOUN
ejpam-184	45	13			NOUN
ejpam-184	45	14			NOUN
ejpam-184	45	15			NOUN
ejpam-184	45	16			NOUN
ejpam-184	45	17			NOUN
ejpam-184	45	18			NOUN
ejpam-184	45	19	∂	∂	NUM
ejpam-184	45	20	f	f	PROPN
ejpam-184	45	21	∂	∂	NOUN
ejpam-184	46	1	ẋ1	ẋ1	PROPN
ejpam-184	46	2	∂	∂	NOUN
ejpam-184	46	3	f	f	NOUN
ejpam-184	46	4	∂	∂	NUM
ejpam-184	46	5	ẋ2	ẋ2	PROPN
ejpam-184	46	6	...	...	PUNCT
ejpam-184	47	1	∂	∂	NUM
ejpam-184	47	2	f	f	PROPN
ejpam-184	47	3	∂	∂	PROPN
ejpam-184	47	4	ẋ	ẋ	PROPN
ejpam-184	48	1	n	n	PROPN
ejpam-184	48	2			NOUN
ejpam-184	48	3			NOUN
ejpam-184	48	4			VERB
ejpam-184	48	5			NOUN
ejpam-184	48	6			NOUN
ejpam-184	48	7			NOUN
ejpam-184	48	8			NOUN
ejpam-184	48	9			NOUN
ejpam-184	48	10			NOUN
ejpam-184	48	11			NOUN
ejpam-184	48	12			NOUN
ejpam-184	48	13			NOUN
ejpam-184	48	14			NOUN
ejpam-184	48	15			PUNCT
ejpam-184	49	1	i.	i.	PROPN
ejpam-184	49	2	husain	husain	PROPN
ejpam-184	49	3	,	,	PUNCT
ejpam-184	49	4	a.	a.	PROPN
ejpam-184	49	5	ahmed	ahmed	PROPN
ejpam-184	49	6	,	,	PUNCT
ejpam-184	49	7	and	and	CCONJ
ejpam-184	49	8	m.	m.	NOUN
ejpam-184	49	9	massodi	massodi	PROPN
ejpam-184	49	10	/	/	SYM
ejpam-184	49	11	eur	eur	PROPN
ejpam-184	49	12	.	.	PUNCT
ejpam-184	50	1	j.	j.	PROPN
ejpam-184	50	2	pure	pure	PROPN
ejpam-184	50	3	appl	appl	PROPN
ejpam-184	50	4	.	.	PROPN
ejpam-184	50	5	math	math	PROPN
ejpam-184	50	6	,	,	PUNCT
ejpam-184	50	7	2	2	NUM
ejpam-184	50	8	(	(	PUNCT
ejpam-184	50	9	2009	2009	NUM
ejpam-184	50	10	)	)	PUNCT
ejpam-184	50	11	,	,	PUNCT
ejpam-184	50	12	(	(	PUNCT
ejpam-184	50	13	278	278	NUM
ejpam-184	50	14	-	-	SYM
ejpam-184	50	15	295	295	NUM
ejpam-184	50	16	)	)	PUNCT
ejpam-184	50	17	281	281	NUM
ejpam-184	50	18	denote	denote	VERB
ejpam-184	50	19	by	by	ADP
ejpam-184	50	20	fx	fx	NOUN
ejpam-184	50	21	x	x	PUNCT
ejpam-184	50	22	the	the	DET
ejpam-184	50	23	hessian	hessian	ADJ
ejpam-184	50	24	matrix	matrix	NOUN
ejpam-184	50	25	of	of	ADP
ejpam-184	50	26	f	f	PROPN
ejpam-184	50	27	with	with	ADP
ejpam-184	50	28	respect	respect	NOUN
ejpam-184	50	29	to	to	ADP
ejpam-184	50	30	x	x	PRON
ejpam-184	50	31	,	,	PUNCT
ejpam-184	50	32	that	that	ADV
ejpam-184	50	33	is	is	ADV
ejpam-184	50	34	,	,	PUNCT
ejpam-184	50	35	fx	fx	ADJ
ejpam-184	50	36	x	x	SYM
ejpam-184	50	37	=	=	SYM
ejpam-184	50	38			PROPN
ejpam-184	50	39			NOUN
ejpam-184	50	40			NOUN
ejpam-184	50	41			NOUN
ejpam-184	50	42			NOUN
ejpam-184	50	43			NOUN
ejpam-184	50	44			NOUN
ejpam-184	50	45			NOUN
ejpam-184	50	46			NOUN
ejpam-184	50	47			NOUN
ejpam-184	50	48			NOUN
ejpam-184	50	49			NOUN
ejpam-184	50	50			NOUN
ejpam-184	50	51			NOUN
ejpam-184	50	52	∂	∂	NUM
ejpam-184	50	53	2	2	NUM
ejpam-184	50	54	f	f	NOUN
ejpam-184	50	55	∂	∂	NOUN
ejpam-184	50	56	x1∂	x1∂	NOUN
ejpam-184	51	1	x1	x1	PROPN
ejpam-184	51	2	∂	∂	NUM
ejpam-184	51	3	2	2	NUM
ejpam-184	51	4	f	f	PROPN
ejpam-184	51	5	∂	∂	NOUN
ejpam-184	51	6	x1∂	x1∂	NOUN
ejpam-184	52	1	x2	x2	PROPN
ejpam-184	52	2	·	·	PUNCT
ejpam-184	52	3	·	·	PUNCT
ejpam-184	52	4	·	·	PUNCT
ejpam-184	52	5	∂	∂	NUM
ejpam-184	52	6	2	2	NUM
ejpam-184	52	7	f	f	PROPN
ejpam-184	52	8	∂	∂	NOUN
ejpam-184	52	9	x1∂	x1∂	NOUN
ejpam-184	52	10	x	x	PROPN
ejpam-184	53	1	n	n	SYM
ejpam-184	53	2	∂	∂	NUM
ejpam-184	53	3	2	2	NUM
ejpam-184	53	4	f	f	NOUN
ejpam-184	53	5	∂	∂	NOUN
ejpam-184	53	6	x2∂	x2∂	NOUN
ejpam-184	54	1	x1	x1	PROPN
ejpam-184	54	2	∂	∂	NUM
ejpam-184	54	3	2	2	NUM
ejpam-184	54	4	f	f	NOUN
ejpam-184	54	5	∂	∂	NOUN
ejpam-184	54	6	x2∂	x2∂	NOUN
ejpam-184	55	1	x2	x2	PROPN
ejpam-184	55	2	·	·	PUNCT
ejpam-184	55	3	·	·	PUNCT
ejpam-184	55	4	·	·	PUNCT
ejpam-184	55	5	∂	∂	NUM
ejpam-184	55	6	2	2	NUM
ejpam-184	55	7	f	f	NOUN
ejpam-184	55	8	∂	∂	NOUN
ejpam-184	55	9	x2∂	x2∂	NOUN
ejpam-184	55	10	x	x	PROPN
ejpam-184	55	11	n	n	PROPN
ejpam-184	55	12	...	...	PUNCT
ejpam-184	55	13	...	...	PUNCT
ejpam-184	55	14	.	.	PUNCT
ejpam-184	55	15	.	.	PUNCT
ejpam-184	55	16	.	.	PUNCT
ejpam-184	56	1	...	...	PUNCT
ejpam-184	57	1	∂	∂	NUM
ejpam-184	57	2	2	2	NUM
ejpam-184	57	3	f	f	NOUN
ejpam-184	57	4	∂	∂	NUM
ejpam-184	57	5	x	x	NOUN
ejpam-184	57	6	n∂	n∂	PROPN
ejpam-184	58	1	x1	x1	PROPN
ejpam-184	58	2	∂	∂	NUM
ejpam-184	58	3	2	2	NUM
ejpam-184	58	4	f	f	NOUN
ejpam-184	58	5	∂	∂	NUM
ejpam-184	58	6	x	x	NOUN
ejpam-184	58	7	n∂	n∂	PROPN
ejpam-184	58	8	x2	x2	PROPN
ejpam-184	58	9	·	·	PUNCT
ejpam-184	58	10	·	·	PUNCT
ejpam-184	58	11	·	·	PUNCT
ejpam-184	58	12	∂	∂	NUM
ejpam-184	58	13	2	2	NUM
ejpam-184	58	14	f	f	NOUN
ejpam-184	58	15	∂	∂	NUM
ejpam-184	58	16	x	x	NOUN
ejpam-184	58	17	n∂	n∂	PROPN
ejpam-184	58	18	x	x	PROPN
ejpam-184	58	19	n	n	PROPN
ejpam-184	58	20			NOUN
ejpam-184	58	21			NOUN
ejpam-184	58	22			VERB
ejpam-184	58	23			NOUN
ejpam-184	58	24			NOUN
ejpam-184	58	25			NOUN
ejpam-184	58	26			NOUN
ejpam-184	58	27			NOUN
ejpam-184	58	28			NOUN
ejpam-184	58	29			NOUN
ejpam-184	58	30			NOUN
ejpam-184	58	31			NOUN
ejpam-184	58	32			NOUN
ejpam-184	58	33			PUNCT
ejpam-184	59	1	n×n	n×n	NOUN
ejpam-184	59	2	it	it	PRON
ejpam-184	59	3	is	be	AUX
ejpam-184	59	4	obvious	obvious	ADJ
ejpam-184	59	5	that	that	SCONJ
ejpam-184	59	6	fx	fx	NOUN
ejpam-184	59	7	x	x	PUNCT
ejpam-184	59	8	is	be	AUX
ejpam-184	59	9	a	a	DET
ejpam-184	59	10	symmetric	symmetric	ADJ
ejpam-184	59	11	n×	n×	PRON
ejpam-184	59	12	n	n	NOUN
ejpam-184	59	13	matrix	matrix	NOUN
ejpam-184	59	14	.	.	PUNCT
ejpam-184	60	1	denote	denote	VERB
ejpam-184	60	2	by	by	ADP
ejpam-184	60	3	gx	gx	PROPN
ejpam-184	60	4	the	the	DET
ejpam-184	60	5	m×	m×	PROPN
ejpam-184	60	6	n	n	PRON
ejpam-184	60	7	matrix	matrix	VERB
ejpam-184	60	8	with	with	ADP
ejpam-184	60	9	respect	respect	NOUN
ejpam-184	60	10	to	to	ADP
ejpam-184	60	11	x	x	PRON
ejpam-184	60	12	,	,	PUNCT
ejpam-184	60	13	that	that	ADV
ejpam-184	60	14	is	is	ADV
ejpam-184	60	15	,	,	PUNCT
ejpam-184	60	16	gx	gx	PROPN
ejpam-184	60	17	=	=	PUNCT
ejpam-184	60	18			PROPN
ejpam-184	60	19			NOUN
ejpam-184	60	20			NOUN
ejpam-184	60	21			NOUN
ejpam-184	60	22			NOUN
ejpam-184	60	23			NOUN
ejpam-184	60	24			NOUN
ejpam-184	60	25			NOUN
ejpam-184	60	26			NOUN
ejpam-184	60	27			NOUN
ejpam-184	60	28			NOUN
ejpam-184	60	29			NOUN
ejpam-184	60	30			NOUN
ejpam-184	60	31			NOUN
ejpam-184	60	32	∂	∂	NUM
ejpam-184	60	33	g1	g1	NOUN
ejpam-184	60	34	∂	∂	NUM
ejpam-184	60	35	x1	x1	PROPN
ejpam-184	60	36	∂	∂	NUM
ejpam-184	60	37	g1	g1	PROPN
ejpam-184	60	38	∂	∂	PROPN
ejpam-184	60	39	x2	x2	PROPN
ejpam-184	60	40	·	·	PUNCT
ejpam-184	60	41	·	·	PUNCT
ejpam-184	60	42	·	·	PUNCT
ejpam-184	60	43	∂	∂	NUM
ejpam-184	61	1	g1	g1	PROPN
ejpam-184	61	2	∂	∂	NUM
ejpam-184	61	3	x	x	SYM
ejpam-184	61	4	n	n	NUM
ejpam-184	61	5	∂	∂	NUM
ejpam-184	61	6	g2	g2	PROPN
ejpam-184	61	7	∂	∂	PUNCT
ejpam-184	62	1	x1	x1	PROPN
ejpam-184	62	2	∂	∂	NUM
ejpam-184	62	3	g2	g2	PROPN
ejpam-184	62	4	∂	∂	NOUN
ejpam-184	63	1	x2	x2	PROPN
ejpam-184	63	2	·	·	PUNCT
ejpam-184	63	3	·	·	PUNCT
ejpam-184	63	4	·	·	PUNCT
ejpam-184	63	5	∂	∂	NUM
ejpam-184	64	1	g2	g2	PROPN
ejpam-184	64	2	∂	∂	NOUN
ejpam-184	64	3	x	x	SYM
ejpam-184	64	4	n	n	PROPN
ejpam-184	64	5	...	...	PUNCT
ejpam-184	64	6	...	...	PUNCT
ejpam-184	64	7	.	.	PUNCT
ejpam-184	64	8	.	.	PUNCT
ejpam-184	65	1	.	.	PUNCT
ejpam-184	66	1	...	...	PUNCT
ejpam-184	67	1	∂	∂	NUM
ejpam-184	67	2	gm	gm	PROPN
ejpam-184	67	3	∂	∂	PUNCT
ejpam-184	68	1	x1	x1	PROPN
ejpam-184	68	2	∂	∂	X
ejpam-184	68	3	gm	gm	PROPN
ejpam-184	68	4	∂	∂	NOUN
ejpam-184	68	5	x2	x2	PROPN
ejpam-184	68	6	·	·	PUNCT
ejpam-184	68	7	·	·	PUNCT
ejpam-184	68	8	·	·	PUNCT
ejpam-184	68	9	∂	∂	NUM
ejpam-184	68	10	gm	gm	PROPN
ejpam-184	68	11	∂	∂	NOUN
ejpam-184	68	12	x	x	SYM
ejpam-184	68	13	n	n	PRON
ejpam-184	68	14			NOUN
ejpam-184	68	15			NOUN
ejpam-184	68	16			VERB
ejpam-184	68	17			NOUN
ejpam-184	68	18			NOUN
ejpam-184	68	19			NOUN
ejpam-184	68	20			NOUN
ejpam-184	68	21			NOUN
ejpam-184	68	22			NOUN
ejpam-184	68	23			NOUN
ejpam-184	68	24			NOUN
ejpam-184	68	25			NOUN
ejpam-184	68	26			NOUN
ejpam-184	68	27			PUNCT
ejpam-184	69	1	m×n	m×n	NOUN
ejpam-184	69	2	similarly	similarly	ADV
ejpam-184	69	3	f	f	PROPN
ejpam-184	69	4	ẋ	ẋ	PROPN
ejpam-184	69	5	,	,	PUNCT
ejpam-184	69	6	f	f	PROPN
ejpam-184	69	7	ẋ	ẋ	PROPN
ejpam-184	70	1	x	x	X
ejpam-184	70	2	,	,	PUNCT
ejpam-184	70	3	fx	fx	PROPN
ejpam-184	70	4	ẋ	ẋ	PROPN
ejpam-184	70	5	and	and	CCONJ
ejpam-184	70	6	g	g	PROPN
ejpam-184	70	7	ẋ	ẋ	PROPN
ejpam-184	70	8	can	can	AUX
ejpam-184	70	9	be	be	AUX
ejpam-184	70	10	defined	define	VERB
ejpam-184	70	11	.	.	PUNCT
ejpam-184	71	1	denote	denote	VERB
ejpam-184	71	2	by	by	ADP
ejpam-184	71	3	x	x	X
ejpam-184	71	4	,	,	PUNCT
ejpam-184	71	5	the	the	DET
ejpam-184	71	6	space	space	NOUN
ejpam-184	71	7	of	of	ADP
ejpam-184	71	8	piecewise	piecewise	NOUN
ejpam-184	71	9	smooth	smooth	ADJ
ejpam-184	71	10	functions	function	NOUN
ejpam-184	72	1	x	x	PUNCT
ejpam-184	72	2	:	:	PUNCT
ejpam-184	72	3	i	i	PROPN
ejpam-184	72	4	→	→	SYM
ejpam-184	72	5	rn	rn	PROPN
ejpam-184	72	6	,	,	PUNCT
ejpam-184	72	7	with	with	ADP
ejpam-184	72	8	the	the	DET
ejpam-184	72	9	norm	norm	NOUN
ejpam-184	72	10	‖x‖	‖x‖	PROPN
ejpam-184	72	11	=	=	SYM
ejpam-184	72	12	‖x‖∞	‖x‖∞	PROPN
ejpam-184	72	13	+	+	CCONJ
ejpam-184	72	14	‖dx‖∞	‖dx‖∞	NOUN
ejpam-184	72	15	+	+	CCONJ
ejpam-184	72	16	‖d	‖d	ADJ
ejpam-184	72	17	2	2	NUM
ejpam-184	72	18	x‖∞	x‖∞	NOUN
ejpam-184	72	19	,	,	PUNCT
ejpam-184	72	20	where	where	SCONJ
ejpam-184	72	21	the	the	DET
ejpam-184	72	22	differentiation	differentiation	NOUN
ejpam-184	72	23	operator	operator	NOUN
ejpam-184	72	24	d	d	NOUN
ejpam-184	72	25	is	be	AUX
ejpam-184	72	26	given	give	VERB
ejpam-184	72	27	by	by	ADP
ejpam-184	72	28	u=	u=	PROPN
ejpam-184	72	29	d	d	PROPN
ejpam-184	72	30	x⇔	x⇔	PROPN
ejpam-184	72	31	x	x	SYM
ejpam-184	72	32	(	(	PUNCT
ejpam-184	72	33	t	t	NOUN
ejpam-184	72	34	)	)	PUNCT
ejpam-184	72	35	=	=	SYM
ejpam-184	73	1	α+	α+	PUNCT
ejpam-184	73	2	∫	∫	PROPN
ejpam-184	73	3	t	t	PROPN
ejpam-184	73	4	a	a	DET
ejpam-184	73	5	u	u	PROPN
ejpam-184	73	6	(	(	PUNCT
ejpam-184	73	7	s	s	NOUN
ejpam-184	73	8	)	)	PUNCT
ejpam-184	73	9	ds	ds	NOUN
ejpam-184	73	10	,	,	PUNCT
ejpam-184	73	11	where	where	SCONJ
ejpam-184	73	12	α	α	NOUN
ejpam-184	73	13	is	be	AUX
ejpam-184	73	14	given	give	VERB
ejpam-184	73	15	boundary	boundary	ADJ
ejpam-184	73	16	value	value	NOUN
ejpam-184	73	17	;	;	PUNCT
ejpam-184	74	1	thus	thus	ADV
ejpam-184	74	2	d	d	X
ejpam-184	74	3	d	d	X
ejpam-184	74	4	t	t	PROPN
ejpam-184	74	5	=	=	PUNCT
ejpam-184	74	6	d	d	PROPN
ejpam-184	74	7	except	except	SCONJ
ejpam-184	74	8	at	at	ADP
ejpam-184	74	9	discontinuities	discontinuity	NOUN
ejpam-184	74	10	.	.	PUNCT
ejpam-184	75	1	we	we	PRON
ejpam-184	75	2	introduce	introduce	VERB
ejpam-184	75	3	the	the	DET
ejpam-184	75	4	following	follow	VERB
ejpam-184	75	5	definitions	definition	NOUN
ejpam-184	75	6	which	which	PRON
ejpam-184	75	7	are	be	AUX
ejpam-184	75	8	needed	need	VERB
ejpam-184	75	9	for	for	SCONJ
ejpam-184	75	10	the	the	DET
ejpam-184	75	11	duality	duality	NOUN
ejpam-184	75	12	results	result	NOUN
ejpam-184	75	13	to	to	PART
ejpam-184	75	14	hold	hold	VERB
ejpam-184	75	15	.	.	PUNCT
ejpam-184	76	1	definition	definition	NOUN
ejpam-184	76	2	2.1	2.1	NUM
ejpam-184	76	3	(	(	PUNCT
ejpam-184	76	4	second	second	ADJ
ejpam-184	76	5	-	-	PUNCT
ejpam-184	76	6	order	order	NOUN
ejpam-184	76	7	invexity	invexity	NOUN
ejpam-184	76	8	)	)	PUNCT
ejpam-184	76	9	.	.	PUNCT
ejpam-184	77	1	if	if	SCONJ
ejpam-184	77	2	there	there	PRON
ejpam-184	77	3	exists	exist	VERB
ejpam-184	77	4	a	a	DET
ejpam-184	77	5	vector	vector	NOUN
ejpam-184	77	6	function	function	NOUN
ejpam-184	77	7	η=	η=	NOUN
ejpam-184	77	8	η(t	η(t	NOUN
ejpam-184	77	9	,	,	PUNCT
ejpam-184	77	10	x	x	SYM
ejpam-184	77	11	,	,	PUNCT
ejpam-184	77	12	x̄	x̄	X
ejpam-184	77	13	)	)	PUNCT
ejpam-184	77	14	∈	∈	PROPN
ejpam-184	77	15	rn	rn	PROPN
ejpam-184	77	16	where	where	SCONJ
ejpam-184	77	17	η	η	PROPN
ejpam-184	77	18	:	:	PUNCT
ejpam-184	77	19	i	i	PRON
ejpam-184	77	20	×	×	VERB
ejpam-184	77	21	rn	rn	PROPN
ejpam-184	77	22	×	×	PROPN
ejpam-184	77	23	rn	rn	PROPN
ejpam-184	77	24	→	→	SYM
ejpam-184	77	25	rn	rn	PROPN
ejpam-184	77	26	and	and	CCONJ
ejpam-184	77	27	with	with	ADP
ejpam-184	77	28	η	η	PROPN
ejpam-184	77	29	=	=	PROPN
ejpam-184	77	30	0	0	PROPN
ejpam-184	77	31	at	at	ADP
ejpam-184	77	32	t	t	NOUN
ejpam-184	77	33	=	=	SYM
ejpam-184	77	34	a	a	PROPN
ejpam-184	77	35	and	and	CCONJ
ejpam-184	77	36	t	t	NOUN
ejpam-184	77	37	=	=	SYM
ejpam-184	77	38	b	b	PROPN
ejpam-184	77	39	,	,	PUNCT
ejpam-184	77	40	such	such	ADJ
ejpam-184	77	41	that	that	PRON
ejpam-184	77	42	for	for	ADP
ejpam-184	77	43	the	the	DET
ejpam-184	77	44	i.	i.	PROPN
ejpam-184	77	45	husain	husain	PROPN
ejpam-184	77	46	,	,	PUNCT
ejpam-184	77	47	a.	a.	PROPN
ejpam-184	77	48	ahmed	ahmed	PROPN
ejpam-184	77	49	,	,	PUNCT
ejpam-184	77	50	and	and	CCONJ
ejpam-184	77	51	m.	m.	NOUN
ejpam-184	77	52	massodi	massodi	PROPN
ejpam-184	77	53	/	/	SYM
ejpam-184	77	54	eur	eur	PROPN
ejpam-184	77	55	.	.	PUNCT
ejpam-184	78	1	j.	j.	PROPN
ejpam-184	78	2	pure	pure	PROPN
ejpam-184	78	3	appl	appl	PROPN
ejpam-184	78	4	.	.	PROPN
ejpam-184	78	5	math	math	PROPN
ejpam-184	78	6	,	,	PUNCT
ejpam-184	78	7	2	2	NUM
ejpam-184	78	8	(	(	PUNCT
ejpam-184	78	9	2009	2009	NUM
ejpam-184	78	10	)	)	PUNCT
ejpam-184	78	11	,	,	PUNCT
ejpam-184	78	12	(	(	PUNCT
ejpam-184	78	13	278	278	NUM
ejpam-184	78	14	-	-	SYM
ejpam-184	78	15	295	295	NUM
ejpam-184	78	16	)	)	PUNCT
ejpam-184	78	17	282	282	NUM
ejpam-184	78	18	functional	functional	ADJ
ejpam-184	78	19	∫	∫	PROPN
ejpam-184	79	1	i	i	PROPN
ejpam-184	79	2	φ(t	φ(t	PROPN
ejpam-184	79	3	,	,	PUNCT
ejpam-184	79	4	x	x	INTJ
ejpam-184	79	5	,	,	PUNCT
ejpam-184	79	6	ẋ)d	ẋ)d	PROPN
ejpam-184	79	7	t	t	PROPN
ejpam-184	80	1	where	where	SCONJ
ejpam-184	80	2	φ	φ	PROPN
ejpam-184	80	3	:	:	PUNCT
ejpam-184	80	4	i	i	PRON
ejpam-184	80	5	×	×	VERB
ejpam-184	80	6	rn×	rn×	NOUN
ejpam-184	80	7	rn→	rn→	PROPN
ejpam-184	80	8	r	r	NOUN
ejpam-184	80	9	satisfies	satisfie	NOUN
ejpam-184	80	10	∫	∫	PROPN
ejpam-184	80	11	i	i	PROPN
ejpam-184	80	12	φ(t	φ(t	PROPN
ejpam-184	80	13	,	,	PUNCT
ejpam-184	80	14	x	x	INTJ
ejpam-184	80	15	,	,	PUNCT
ejpam-184	80	16	ẋ)d	ẋ)d	PROPN
ejpam-184	80	17	t	t	PROPN
ejpam-184	81	1	−	−	PROPN
ejpam-184	81	2	∫	∫	PROPN
ejpam-184	82	1	i	i	PROPN
ejpam-184	82	2	�	�	PROPN
ejpam-184	82	3	φ(t	φ(t	PROPN
ejpam-184	82	4	,	,	PUNCT
ejpam-184	82	5	x̄	x̄	PROPN
ejpam-184	82	6	,	,	PUNCT
ejpam-184	82	7	˙̄x)−	˙̄x)−	PROPN
ejpam-184	82	8	1	1	NUM
ejpam-184	82	9	2	2	NUM
ejpam-184	82	10	β	β	X
ejpam-184	82	11	(	(	PUNCT
ejpam-184	82	12	t)t	t)t	X
ejpam-184	82	13	gβ	gβ	X
ejpam-184	82	14	(	(	PUNCT
ejpam-184	82	15	t	t	PROPN
ejpam-184	82	16	)	)	PUNCT
ejpam-184	82	17	�	�	PROPN
ejpam-184	82	18	d	d	PROPN
ejpam-184	82	19	t	t	PROPN
ejpam-184	82	20	≥	≥	X
ejpam-184	82	21	∫	∫	PROPN
ejpam-184	83	1	i	i	PRON
ejpam-184	83	2	n	n	VERB
ejpam-184	83	3	ηtφx	ηtφx	VERB
ejpam-184	83	4	+	+	CCONJ
ejpam-184	83	5	(	(	PUNCT
ejpam-184	83	6	dη	dη	NOUN
ejpam-184	83	7	)	)	PUNCT
ejpam-184	83	8	tφ	tφ	PROPN
ejpam-184	83	9	ẋ	ẋ	PUNCT
ejpam-184	84	1	+	+	PROPN
ejpam-184	84	2	η	η	PROPN
ejpam-184	84	3	t	t	PROPN
ejpam-184	84	4	gβ(t	gβ(t	NOUN
ejpam-184	84	5	)	)	PUNCT
ejpam-184	85	1	o	o	NOUN
ejpam-184	86	1	d	d	NOUN
ejpam-184	86	2	t	t	PROPN
ejpam-184	86	3	,	,	PUNCT
ejpam-184	86	4	then	then	ADV
ejpam-184	86	5	∫	∫	PROPN
ejpam-184	86	6	i	i	PROPN
ejpam-184	86	7	φ(t	φ(t	PROPN
ejpam-184	86	8	,	,	PUNCT
ejpam-184	86	9	x	x	SYM
ejpam-184	86	10	,	,	PUNCT
ejpam-184	86	11	ẋ)d	ẋ)d	PROPN
ejpam-184	86	12	t	t	PROPN
ejpam-184	86	13	is	be	AUX
ejpam-184	86	14	second	second	ADJ
ejpam-184	86	15	-	-	PUNCT
ejpam-184	86	16	order	order	NOUN
ejpam-184	86	17	invex	invex	NOUN
ejpam-184	86	18	with	with	ADP
ejpam-184	86	19	respect	respect	NOUN
ejpam-184	86	20	to	to	ADP
ejpam-184	86	21	η	η	PROPN
ejpam-184	86	22	where	where	SCONJ
ejpam-184	86	23	g	g	NOUN
ejpam-184	86	24	=	=	SYM
ejpam-184	86	25	φx	φx	PROPN
ejpam-184	86	26	x	x	PART
ejpam-184	86	27	−	−	PROPN
ejpam-184	86	28	dφx	dφx	X
ejpam-184	86	29	ẋ	ẋ	PUNCT
ejpam-184	87	1	+	+	CCONJ
ejpam-184	87	2	d2φ	d2φ	PROPN
ejpam-184	87	3	ẋ	ẋ	PROPN
ejpam-184	87	4	ẋ	ẋ	PROPN
ejpam-184	88	1	and	and	CCONJ
ejpam-184	88	2	β	β	X
ejpam-184	88	3	∈	∈	PROPN
ejpam-184	88	4	c(i	c(i	NOUN
ejpam-184	88	5	,	,	PUNCT
ejpam-184	88	6	rn	rn	PROPN
ejpam-184	88	7	)	)	PUNCT
ejpam-184	88	8	,	,	PUNCT
ejpam-184	88	9	the	the	DET
ejpam-184	88	10	space	space	NOUN
ejpam-184	88	11	of	of	ADP
ejpam-184	88	12	continuous	continuous	ADJ
ejpam-184	88	13	n	n	CCONJ
ejpam-184	88	14	-	-	PUNCT
ejpam-184	88	15	dimensional	dimensional	ADJ
ejpam-184	88	16	vector	vector	NOUN
ejpam-184	88	17	function	function	NOUN
ejpam-184	88	18	.	.	PUNCT
ejpam-184	89	1	the	the	DET
ejpam-184	89	2	function	function	NOUN
ejpam-184	89	3	β	β	PROPN
ejpam-184	89	4	is	be	AUX
ejpam-184	89	5	analogous	analogous	ADJ
ejpam-184	89	6	to	to	ADP
ejpam-184	89	7	the	the	DET
ejpam-184	89	8	auxiliary	auxiliary	ADJ
ejpam-184	89	9	vector	vector	NOUN
ejpam-184	89	10	p	p	NOUN
ejpam-184	89	11	in	in	ADP
ejpam-184	89	12	[	[	X
ejpam-184	89	13	1	1	NUM
ejpam-184	89	14	]	]	PUNCT
ejpam-184	89	15	.	.	PUNCT
ejpam-184	90	1	definition	definition	NOUN
ejpam-184	90	2	2.2	2.2	NUM
ejpam-184	90	3	(	(	PUNCT
ejpam-184	90	4	second	second	ADJ
ejpam-184	90	5	-	-	PUNCT
ejpam-184	90	6	order	order	NOUN
ejpam-184	90	7	pseudoinvex	pseudoinvex	NOUN
ejpam-184	90	8	)	)	PUNCT
ejpam-184	90	9	.	.	PUNCT
ejpam-184	91	1	if	if	SCONJ
ejpam-184	91	2	the	the	DET
ejpam-184	91	3	functional	functional	ADJ
ejpam-184	91	4	∫	∫	PROPN
ejpam-184	91	5	i	i	PROPN
ejpam-184	91	6	φ(t	φ(t	PROPN
ejpam-184	91	7	,	,	PUNCT
ejpam-184	91	8	x	x	SYM
ejpam-184	91	9	,	,	PUNCT
ejpam-184	91	10	ẋ)d	ẋ)d	PROPN
ejpam-184	91	11	t	t	PROPN
ejpam-184	91	12	satisfies	satisfy	VERB
ejpam-184	91	13	∫	∫	PROPN
ejpam-184	92	1	i	i	PRON
ejpam-184	92	2	¦	¦	PROPN
ejpam-184	92	3	ηtφx	ηtφx	PROPN
ejpam-184	92	4	+	+	PROPN
ejpam-184	92	5	(	(	PUNCT
ejpam-184	92	6	dη	dη	NOUN
ejpam-184	92	7	)	)	PUNCT
ejpam-184	92	8	tφ	tφ	PROPN
ejpam-184	92	9	ẋ	ẋ	PUNCT
ejpam-184	93	1	+	+	PROPN
ejpam-184	93	2	η	η	PROPN
ejpam-184	93	3	t	t	PROPN
ejpam-184	93	4	gβ(t	gβ(t	NOUN
ejpam-184	93	5	)	)	PUNCT
ejpam-184	94	1	©	©	PROPN
ejpam-184	94	2	d	d	PROPN
ejpam-184	94	3	t	t	PROPN
ejpam-184	94	4	≥	≥	X
ejpam-184	94	5	0	0	NUM
ejpam-184	94	6	⇒	⇒	PROPN
ejpam-184	94	7	∫	∫	PROPN
ejpam-184	95	1	i	i	PROPN
ejpam-184	95	2	φ(t	φ(t	PROPN
ejpam-184	95	3	,	,	PUNCT
ejpam-184	95	4	x	x	SYM
ejpam-184	95	5	,	,	PUNCT
ejpam-184	95	6	ẋ)d	ẋ)d	PROPN
ejpam-184	95	7	t	t	PROPN
ejpam-184	95	8	≥	≥	PROPN
ejpam-184	95	9	∫	∫	PROPN
ejpam-184	96	1	i	i	PROPN
ejpam-184	96	2	�	�	PROPN
ejpam-184	96	3	φ(t	φ(t	PROPN
ejpam-184	96	4	,	,	PUNCT
ejpam-184	96	5	x̄	x̄	PROPN
ejpam-184	96	6	,	,	PUNCT
ejpam-184	96	7	˙̄x)−	˙̄x)−	PROPN
ejpam-184	96	8	1	1	NUM
ejpam-184	96	9	2	2	NUM
ejpam-184	96	10	β	β	X
ejpam-184	96	11	(	(	PUNCT
ejpam-184	96	12	t	t	PROPN
ejpam-184	96	13	)	)	PUNCT
ejpam-184	96	14	t	t	PROPN
ejpam-184	96	15	gβ	gβ	PROPN
ejpam-184	96	16	(	(	PUNCT
ejpam-184	96	17	t	t	PROPN
ejpam-184	96	18	)	)	PUNCT
ejpam-184	96	19	�	�	PROPN
ejpam-184	97	1	d	d	PROPN
ejpam-184	97	2	t	t	PROPN
ejpam-184	97	3	,	,	PUNCT
ejpam-184	97	4	then	then	ADV
ejpam-184	97	5	∫	∫	PROPN
ejpam-184	97	6	i	i	PRON
ejpam-184	97	7	φ	φ	PROPN
ejpam-184	97	8	(	(	PUNCT
ejpam-184	97	9	t	t	PROPN
ejpam-184	97	10	,	,	PUNCT
ejpam-184	97	11	x	x	X
ejpam-184	97	12	,	,	PUNCT
ejpam-184	97	13	ẋ	ẋ	PROPN
ejpam-184	97	14	)	)	PUNCT
ejpam-184	98	1	d	d	PROPN
ejpam-184	98	2	t	t	PROPN
ejpam-184	98	3	is	be	AUX
ejpam-184	98	4	said	say	VERB
ejpam-184	98	5	to	to	PART
ejpam-184	98	6	be	be	AUX
ejpam-184	98	7	second	second	ADJ
ejpam-184	98	8	-	-	PUNCT
ejpam-184	98	9	order	order	NOUN
ejpam-184	98	10	pseudoinvex	pseudoinvex	NOUN
ejpam-184	98	11	with	with	ADP
ejpam-184	98	12	respect	respect	NOUN
ejpam-184	98	13	to	to	ADP
ejpam-184	98	14	η	η	PROPN
ejpam-184	98	15	.	.	PROPN
ejpam-184	98	16	definition	definition	NOUN
ejpam-184	98	17	2.3	2.3	NUM
ejpam-184	98	18	(	(	PUNCT
ejpam-184	98	19	second	second	ADJ
ejpam-184	98	20	-	-	PUNCT
ejpam-184	98	21	order	order	NOUN
ejpam-184	98	22	quasi	quasi	NOUN
ejpam-184	98	23	-	-	NOUN
ejpam-184	98	24	invex	invex	ADJ
ejpam-184	98	25	)	)	PUNCT
ejpam-184	98	26	.	.	PUNCT
ejpam-184	99	1	if	if	SCONJ
ejpam-184	99	2	the	the	DET
ejpam-184	99	3	functional	functional	ADJ
ejpam-184	99	4	∫	∫	PROPN
ejpam-184	99	5	i	i	PROPN
ejpam-184	99	6	φ(t	φ(t	PROPN
ejpam-184	99	7	,	,	PUNCT
ejpam-184	99	8	x	x	SYM
ejpam-184	99	9	,	,	PUNCT
ejpam-184	99	10	ẋ)d	ẋ)d	PROPN
ejpam-184	99	11	t	t	PROPN
ejpam-184	99	12	satisfies	satisfy	VERB
ejpam-184	99	13	∫	∫	PROPN
ejpam-184	99	14	i	i	PROPN
ejpam-184	99	15	φ(t	φ(t	PROPN
ejpam-184	99	16	,	,	PUNCT
ejpam-184	99	17	x	x	SYM
ejpam-184	99	18	,	,	PUNCT
ejpam-184	99	19	ẋ)d	ẋ)d	PROPN
ejpam-184	99	20	t	t	PROPN
ejpam-184	99	21	≤	≤	NUM
ejpam-184	100	1	∫	∫	PROPN
ejpam-184	101	1	i	i	PROPN
ejpam-184	101	2	�	�	PROPN
ejpam-184	101	3	φ(t	φ(t	PROPN
ejpam-184	101	4	,	,	PUNCT
ejpam-184	101	5	x̄	x̄	PROPN
ejpam-184	101	6	,	,	PUNCT
ejpam-184	101	7	˙̄x)−	˙̄x)−	PROPN
ejpam-184	101	8	1	1	NUM
ejpam-184	101	9	2	2	NUM
ejpam-184	101	10	β	β	X
ejpam-184	101	11	(	(	PUNCT
ejpam-184	101	12	t	t	PROPN
ejpam-184	101	13	)	)	PUNCT
ejpam-184	101	14	t	t	PROPN
ejpam-184	101	15	gβ	gβ	PROPN
ejpam-184	101	16	(	(	PUNCT
ejpam-184	101	17	t	t	PROPN
ejpam-184	101	18	)	)	PUNCT
ejpam-184	101	19	�	�	PROPN
ejpam-184	102	1	d	d	PROPN
ejpam-184	102	2	t	t	PROPN
ejpam-184	102	3	⇒	⇒	X
ejpam-184	102	4	∫	∫	PROPN
ejpam-184	103	1	i	i	PRON
ejpam-184	103	2	n	n	PRON
ejpam-184	103	3	ηtφx	ηtφx	VERB
ejpam-184	103	4	+	+	CCONJ
ejpam-184	103	5	(	(	PUNCT
ejpam-184	103	6	dη	dη	NOUN
ejpam-184	103	7	)	)	PUNCT
ejpam-184	103	8	tφ	tφ	PROPN
ejpam-184	103	9	ẋ	ẋ	PUNCT
ejpam-184	104	1	+	+	PROPN
ejpam-184	104	2	η	η	PROPN
ejpam-184	104	3	t	t	PROPN
ejpam-184	104	4	gβ(t	gβ(t	NOUN
ejpam-184	104	5	)	)	PUNCT
ejpam-184	105	1	o	o	NOUN
ejpam-184	106	1	d	d	X
ejpam-184	106	2	t	t	NOUN
ejpam-184	106	3	≤	≤	NUM
ejpam-184	106	4	0	0	NUM
ejpam-184	106	5	,	,	PUNCT
ejpam-184	106	6	then	then	ADV
ejpam-184	106	7	∫	∫	PROPN
ejpam-184	107	1	i	i	PROPN
ejpam-184	107	2	φ(t	φ(t	PROPN
ejpam-184	107	3	,	,	PUNCT
ejpam-184	107	4	x	x	X
ejpam-184	107	5	,	,	PUNCT
ejpam-184	107	6	ẋ	ẋ	PROPN
ejpam-184	107	7	)	)	PUNCT
ejpam-184	107	8	is	be	AUX
ejpam-184	107	9	said	say	VERB
ejpam-184	107	10	to	to	PART
ejpam-184	107	11	be	be	AUX
ejpam-184	107	12	second	second	ADJ
ejpam-184	107	13	-	-	PUNCT
ejpam-184	107	14	order	order	NOUN
ejpam-184	107	15	quasi	quasi	NOUN
ejpam-184	107	16	-	-	NOUN
ejpam-184	107	17	invex	invex	ADJ
ejpam-184	107	18	with	with	ADP
ejpam-184	107	19	respect	respect	NOUN
ejpam-184	107	20	to	to	ADP
ejpam-184	107	21	η	η	PROPN
ejpam-184	107	22	.	.	PROPN
ejpam-184	108	1	if	if	SCONJ
ejpam-184	108	2	φ	φ	PROPN
ejpam-184	108	3	does	do	AUX
ejpam-184	108	4	not	not	PART
ejpam-184	108	5	depend	depend	VERB
ejpam-184	108	6	on	on	ADP
ejpam-184	108	7	t	t	PROPN
ejpam-184	108	8	,	,	PUNCT
ejpam-184	108	9	then	then	ADV
ejpam-184	108	10	the	the	DET
ejpam-184	108	11	above	above	ADJ
ejpam-184	108	12	definitions	definition	NOUN
ejpam-184	108	13	reduce	reduce	VERB
ejpam-184	108	14	to	to	ADP
ejpam-184	108	15	those	those	PRON
ejpam-184	108	16	given	give	VERB
ejpam-184	108	17	in	in	ADP
ejpam-184	108	18	[	[	NOUN
ejpam-184	108	19	1	1	NUM
ejpam-184	108	20	]	]	PUNCT
ejpam-184	108	21	for	for	ADP
ejpam-184	108	22	static	static	ADJ
ejpam-184	108	23	cases	case	NOUN
ejpam-184	108	24	.	.	PUNCT
ejpam-184	109	1	consider	consider	VERB
ejpam-184	109	2	the	the	DET
ejpam-184	109	3	following	follow	VERB
ejpam-184	109	4	constrained	constrain	VERB
ejpam-184	109	5	variational	variational	ADJ
ejpam-184	109	6	problem	problem	NOUN
ejpam-184	109	7	:	:	PUNCT
ejpam-184	109	8	(	(	PUNCT
ejpam-184	109	9	vp	vp	NOUN
ejpam-184	109	10	)	)	PUNCT
ejpam-184	109	11	:	:	PUNCT
ejpam-184	109	12	minimize	minimize	VERB
ejpam-184	109	13	∫	∫	PROPN
ejpam-184	110	1	i	i	PRON
ejpam-184	110	2	f	f	PROPN
ejpam-184	110	3	(	(	PUNCT
ejpam-184	110	4	t	t	PROPN
ejpam-184	110	5	,	,	PUNCT
ejpam-184	110	6	x	x	X
ejpam-184	110	7	,	,	PUNCT
ejpam-184	110	8	ẋ)d	ẋ)d	PROPN
ejpam-184	110	9	t	t	PROPN
ejpam-184	110	10	i.	i.	PROPN
ejpam-184	110	11	husain	husain	PROPN
ejpam-184	110	12	,	,	PUNCT
ejpam-184	110	13	a.	a.	PROPN
ejpam-184	110	14	ahmed	ahmed	PROPN
ejpam-184	110	15	,	,	PUNCT
ejpam-184	110	16	and	and	CCONJ
ejpam-184	110	17	m.	m.	NOUN
ejpam-184	110	18	massodi	massodi	PROPN
ejpam-184	110	19	/	/	SYM
ejpam-184	110	20	eur	eur	PROPN
ejpam-184	110	21	.	.	PUNCT
ejpam-184	111	1	j.	j.	PROPN
ejpam-184	111	2	pure	pure	PROPN
ejpam-184	111	3	appl	appl	PROPN
ejpam-184	111	4	.	.	PROPN
ejpam-184	111	5	math	math	PROPN
ejpam-184	111	6	,	,	PUNCT
ejpam-184	111	7	2	2	NUM
ejpam-184	111	8	(	(	PUNCT
ejpam-184	111	9	2009	2009	NUM
ejpam-184	111	10	)	)	PUNCT
ejpam-184	111	11	,	,	PUNCT
ejpam-184	111	12	(	(	PUNCT
ejpam-184	111	13	278	278	NUM
ejpam-184	111	14	-	-	SYM
ejpam-184	111	15	295	295	NUM
ejpam-184	111	16	)	)	PUNCT
ejpam-184	111	17	283	283	NUM
ejpam-184	111	18	subject	subject	NOUN
ejpam-184	111	19	to	to	ADP
ejpam-184	111	20	x(a	x(a	NOUN
ejpam-184	111	21	)	)	PUNCT
ejpam-184	111	22	=	=	SYM
ejpam-184	111	23	0	0	PUNCT
ejpam-184	112	1	=	=	SYM
ejpam-184	112	2	x(b	x(b	PROPN
ejpam-184	112	3	)	)	PUNCT
ejpam-184	112	4	,	,	PUNCT
ejpam-184	112	5	g(t	g(t	PROPN
ejpam-184	112	6	,	,	PUNCT
ejpam-184	112	7	x	x	INTJ
ejpam-184	112	8	,	,	PUNCT
ejpam-184	112	9	ẋ	ẋ	PROPN
ejpam-184	112	10	)	)	PUNCT
ejpam-184	112	11	≤	≤	NOUN
ejpam-184	112	12	0	0	NUM
ejpam-184	112	13	,	,	PUNCT
ejpam-184	112	14	t	t	PROPN
ejpam-184	112	15	∈	∈	PROPN
ejpam-184	113	1	i	i	PRON
ejpam-184	113	2	,	,	PUNCT
ejpam-184	113	3	h(t	h(t	PROPN
ejpam-184	113	4	,	,	PUNCT
ejpam-184	113	5	x	x	SYM
ejpam-184	113	6	,	,	PUNCT
ejpam-184	113	7	ẋ	ẋ	PROPN
ejpam-184	113	8	)	)	PUNCT
ejpam-184	113	9	=	=	SYM
ejpam-184	113	10	0	0	NUM
ejpam-184	113	11	,	,	PUNCT
ejpam-184	113	12	t	t	PROPN
ejpam-184	113	13	∈	∈	PROPN
ejpam-184	114	1	i	i	PRON
ejpam-184	114	2	,	,	PUNCT
ejpam-184	114	3	where	where	SCONJ
ejpam-184	114	4	f	f	X
ejpam-184	114	5	:	:	PUNCT
ejpam-184	114	6	i	i	PRON
ejpam-184	114	7	×	×	VERB
ejpam-184	114	8	rn	rn	PROPN
ejpam-184	114	9	×	×	PROPN
ejpam-184	114	10	rn	rn	PROPN
ejpam-184	114	11	→	→	SYM
ejpam-184	114	12	r	r	PROPN
ejpam-184	114	13	,	,	PUNCT
ejpam-184	114	14	g	g	NOUN
ejpam-184	114	15	:	:	PUNCT
ejpam-184	114	16	i	i	PRON
ejpam-184	114	17	×	×	VERB
ejpam-184	114	18	rn	rn	PROPN
ejpam-184	114	19	×	×	PROPN
ejpam-184	114	20	rn	rn	PROPN
ejpam-184	114	21	→	→	PROPN
ejpam-184	114	22	rm	rm	PROPN
ejpam-184	114	23	and	and	CCONJ
ejpam-184	114	24	h	h	NOUN
ejpam-184	114	25	:	:	PUNCT
ejpam-184	115	1	i	i	PRON
ejpam-184	115	2	×	×	VERB
ejpam-184	115	3	rn	rn	PROPN
ejpam-184	115	4	×	×	PROPN
ejpam-184	115	5	rn	rn	PROPN
ejpam-184	115	6	→	→	NOUN
ejpam-184	115	7	rk	rk	PROPN
ejpam-184	115	8	are	be	AUX
ejpam-184	115	9	continuously	continuously	ADV
ejpam-184	115	10	differentiable	differentiable	ADJ
ejpam-184	115	11	.	.	PUNCT
ejpam-184	116	1	proposition	proposition	NOUN
ejpam-184	116	2	2.1	2.1	NUM
ejpam-184	116	3	(	(	PUNCT
ejpam-184	116	4	[	[	X
ejpam-184	116	5	3	3	NUM
ejpam-184	116	6	]	]	X
ejpam-184	116	7	(	(	PUNCT
ejpam-184	116	8	fritz	fritz	PROPN
ejpam-184	116	9	-	-	PUNCT
ejpam-184	116	10	john	john	PROPN
ejpam-184	116	11	conditions	condition	NOUN
ejpam-184	116	12	)	)	PUNCT
ejpam-184	116	13	)	)	PUNCT
ejpam-184	116	14	.	.	PUNCT
ejpam-184	117	1	if	if	SCONJ
ejpam-184	117	2	(	(	PUNCT
ejpam-184	117	3	cp	cp	NOUN
ejpam-184	117	4	)	)	PUNCT
ejpam-184	117	5	attains	attain	VERB
ejpam-184	117	6	a	a	DET
ejpam-184	117	7	local	local	ADJ
ejpam-184	117	8	(	(	PUNCT
ejpam-184	117	9	or	or	CCONJ
ejpam-184	117	10	)	)	PUNCT
ejpam-184	117	11	global	global	ADJ
ejpam-184	117	12	minimum	minimum	NOUN
ejpam-184	117	13	at	at	ADP
ejpam-184	117	14	x	x	X
ejpam-184	117	15	=	=	PUNCT
ejpam-184	117	16	x̄	x̄	SYM
ejpam-184	117	17	∈	∈	PROPN
ejpam-184	118	1	x	x	X
ejpam-184	118	2	then	then	ADV
ejpam-184	118	3	there	there	PRON
ejpam-184	118	4	exist	exist	VERB
ejpam-184	118	5	lagrange	lagrange	NOUN
ejpam-184	118	6	multiplier	multiplier	ADV
ejpam-184	118	7	τ	τ	PROPN
ejpam-184	118	8	∈	∈	PROPN
ejpam-184	118	9	r	r	NOUN
ejpam-184	118	10	,	,	PUNCT
ejpam-184	118	11	z	z	NOUN
ejpam-184	118	12	:	:	PUNCT
ejpam-184	119	1	i	i	PRON
ejpam-184	119	2	→	→	PUNCT
ejpam-184	119	3	rk	rk	NOUN
ejpam-184	119	4	and	and	CCONJ
ejpam-184	119	5	piecewise	piecewise	VERB
ejpam-184	119	6	smooth	smooth	ADJ
ejpam-184	119	7	y	y	PROPN
ejpam-184	119	8	:	:	PUNCT
ejpam-184	119	9	i	i	PROPN
ejpam-184	119	10	→	→	PUNCT
ejpam-184	119	11	rm	rm	NOUN
ejpam-184	119	12	such	such	ADJ
ejpam-184	119	13	that	that	SCONJ
ejpam-184	119	14	τ	τ	PROPN
ejpam-184	119	15	fx(t	fx(t	PUNCT
ejpam-184	119	16	,	,	PUNCT
ejpam-184	119	17	x̄	x̄	NOUN
ejpam-184	119	18	,	,	PUNCT
ejpam-184	119	19	˙̄x	˙̄x	PUNCT
ejpam-184	119	20	)	)	PUNCT
ejpam-184	120	1	+	+	CCONJ
ejpam-184	120	2	y(t)t	y(t)t	NOUN
ejpam-184	120	3	gx(t	gx(t	NOUN
ejpam-184	120	4	,	,	PUNCT
ejpam-184	120	5	x̄	x̄	PROPN
ejpam-184	120	6	,	,	PUNCT
ejpam-184	120	7	˙̄x	˙̄x	PUNCT
ejpam-184	120	8	)	)	PUNCT
ejpam-184	121	1	+	+	CCONJ
ejpam-184	121	2	z(t)thx(t	z(t)thx(t	PROPN
ejpam-184	121	3	,	,	PUNCT
ejpam-184	121	4	x̄	x̄	PROPN
ejpam-184	121	5	,	,	PUNCT
ejpam-184	121	6	˙̄x	˙̄x	PRON
ejpam-184	121	7	)	)	PUNCT
ejpam-184	121	8	−d	−d	PROPN
ejpam-184	121	9	[	[	PUNCT
ejpam-184	121	10	f	f	PROPN
ejpam-184	121	11	ẋ(t	ẋ(t	PROPN
ejpam-184	121	12	,	,	PUNCT
ejpam-184	121	13	x̄	x̄	NOUN
ejpam-184	121	14	,	,	PUNCT
ejpam-184	121	15	˙̄x	˙̄x	PUNCT
ejpam-184	121	16	)	)	PUNCT
ejpam-184	122	1	+	+	CCONJ
ejpam-184	122	2	y(t)t	y(t)t	NOUN
ejpam-184	122	3	g	g	PROPN
ejpam-184	122	4	ẋ(t	ẋ(t	PROPN
ejpam-184	122	5	,	,	PUNCT
ejpam-184	122	6	x̄	x̄	PROPN
ejpam-184	122	7	,	,	PUNCT
ejpam-184	122	8	˙̄x	˙̄x	PUNCT
ejpam-184	122	9	)	)	PUNCT
ejpam-184	123	1	+	+	CCONJ
ejpam-184	123	2	z(t)th	z(t)th	NUM
ejpam-184	123	3	ẋ(t	ẋ(t	PROPN
ejpam-184	123	4	,	,	PUNCT
ejpam-184	123	5	x̄	x̄	PROPN
ejpam-184	123	6	,	,	PUNCT
ejpam-184	123	7	˙̄x	˙̄x	PUNCT
ejpam-184	123	8	)	)	PUNCT
ejpam-184	123	9	]	]	PUNCT
ejpam-184	124	1	=	=	PUNCT
ejpam-184	124	2	0	0	NUM
ejpam-184	124	3	,	,	PUNCT
ejpam-184	124	4	,	,	PUNCT
ejpam-184	124	5	t	t	PROPN
ejpam-184	124	6	∈	∈	PROPN
ejpam-184	125	1	i	i	PRON
ejpam-184	125	2	,	,	PUNCT
ejpam-184	125	3	y(t)t	y(t)t	PROPN
ejpam-184	125	4	g(t	g(t	PROPN
ejpam-184	125	5	,	,	PUNCT
ejpam-184	125	6	x̄	x̄	NOUN
ejpam-184	125	7	,	,	PUNCT
ejpam-184	125	8	˙̄x	˙̄x	PRON
ejpam-184	125	9	)	)	PUNCT
ejpam-184	125	10	=	=	SYM
ejpam-184	125	11	0	0	NUM
ejpam-184	125	12	,	,	PUNCT
ejpam-184	125	13	t	t	PROPN
ejpam-184	125	14	∈	∈	PROPN
ejpam-184	126	1	i	i	PRON
ejpam-184	126	2	(	(	PUNCT
ejpam-184	126	3	τ	τ	PROPN
ejpam-184	126	4	,	,	PUNCT
ejpam-184	126	5	y(t	y(t	PROPN
ejpam-184	126	6	)	)	PUNCT
ejpam-184	126	7	)	)	PUNCT
ejpam-184	126	8	≥	≥	NOUN
ejpam-184	126	9	0	0	NUM
ejpam-184	126	10	,	,	PUNCT
ejpam-184	126	11	t	t	PROPN
ejpam-184	126	12	∈	∈	PROPN
ejpam-184	127	1	i	i	PRON
ejpam-184	127	2	(	(	PUNCT
ejpam-184	127	3	τ	τ	PROPN
ejpam-184	127	4	,	,	PUNCT
ejpam-184	127	5	y(t	y(t	PROPN
ejpam-184	127	6	)	)	PUNCT
ejpam-184	127	7	,	,	PUNCT
ejpam-184	127	8	z(t	z(t	PROPN
ejpam-184	127	9	)	)	PUNCT
ejpam-184	127	10	)	)	PUNCT
ejpam-184	128	1	6=	6=	ADP
ejpam-184	128	2	0	0	NUM
ejpam-184	128	3	,	,	PUNCT
ejpam-184	128	4	t	t	PROPN
ejpam-184	128	5	∈	∈	PROPN
ejpam-184	128	6	i	i	PRON
ejpam-184	128	7	the	the	DET
ejpam-184	128	8	fritz	fritz	PROPN
ejpam-184	128	9	john	john	PROPN
ejpam-184	128	10	necessary	necessary	ADJ
ejpam-184	128	11	conditions	condition	NOUN
ejpam-184	128	12	for	for	ADP
ejpam-184	128	13	(	(	PUNCT
ejpam-184	128	14	cp	cp	NOUN
ejpam-184	128	15	)	)	PUNCT
ejpam-184	128	16	,	,	PUNCT
ejpam-184	128	17	become	become	VERB
ejpam-184	128	18	the	the	DET
ejpam-184	128	19	karush	karush	PROPN
ejpam-184	128	20	-	-	PUNCT
ejpam-184	128	21	kuhn	kuhn	PROPN
ejpam-184	128	22	-	-	PUNCT
ejpam-184	128	23	tucker	tucker	PROPN
ejpam-184	128	24	conditions	condition	NOUN
ejpam-184	129	1	[	[	X
ejpam-184	129	2	7	7	X
ejpam-184	129	3	]	]	X
ejpam-184	129	4	if	if	SCONJ
ejpam-184	129	5	τ	τ	PROPN
ejpam-184	129	6	=	=	SYM
ejpam-184	129	7	1	1	X
ejpam-184	129	8	.	.	PUNCT
ejpam-184	130	1	if	if	SCONJ
ejpam-184	130	2	τ=	τ=	NOUN
ejpam-184	130	3	1	1	NUM
ejpam-184	130	4	,	,	PUNCT
ejpam-184	130	5	the	the	DET
ejpam-184	130	6	solution	solution	NOUN
ejpam-184	130	7	x̄	x̄	PRON
ejpam-184	130	8	is	be	AUX
ejpam-184	130	9	said	say	VERB
ejpam-184	130	10	to	to	PART
ejpam-184	130	11	be	be	AUX
ejpam-184	130	12	normal	normal	ADJ
ejpam-184	130	13	.	.	PUNCT
ejpam-184	131	1	3	3	X
ejpam-184	131	2	.	.	X
ejpam-184	131	3	second	second	ADJ
ejpam-184	131	4	-	-	PUNCT
ejpam-184	131	5	order	order	NOUN
ejpam-184	131	6	duality	duality	NOUN
ejpam-184	131	7	consider	consider	VERB
ejpam-184	131	8	the	the	DET
ejpam-184	131	9	following	follow	VERB
ejpam-184	131	10	variational	variational	ADJ
ejpam-184	131	11	problem	problem	NOUN
ejpam-184	131	12	(	(	PUNCT
ejpam-184	131	13	cp	cp	NOUN
ejpam-184	131	14	)	)	PUNCT
ejpam-184	131	15	by	by	ADP
ejpam-184	131	16	ignoring	ignore	VERB
ejpam-184	131	17	the	the	DET
ejpam-184	131	18	equality	equality	NOUN
ejpam-184	131	19	constraint	constraint	NOUN
ejpam-184	131	20	of	of	ADP
ejpam-184	131	21	(	(	PUNCT
ejpam-184	131	22	vp	vp	PROPN
ejpam-184	131	23	):	):	PUNCT
ejpam-184	131	24	(	(	PUNCT
ejpam-184	131	25	cp	cp	NOUN
ejpam-184	131	26	)	)	PUNCT
ejpam-184	131	27	:	:	PUNCT
ejpam-184	131	28	minimize	minimize	VERB
ejpam-184	131	29	∫	∫	PROPN
ejpam-184	131	30	i	i	PRON
ejpam-184	131	31	f	f	PROPN
ejpam-184	132	1	(	(	PUNCT
ejpam-184	132	2	t	t	PROPN
ejpam-184	132	3	,	,	PUNCT
ejpam-184	132	4	x	x	X
ejpam-184	132	5	,	,	PUNCT
ejpam-184	132	6	ẋ)d	ẋ)d	PROPN
ejpam-184	132	7	t	t	PROPN
ejpam-184	132	8	i.	i.	PROPN
ejpam-184	132	9	husain	husain	PROPN
ejpam-184	132	10	,	,	PUNCT
ejpam-184	132	11	a.	a.	PROPN
ejpam-184	132	12	ahmed	ahmed	PROPN
ejpam-184	132	13	,	,	PUNCT
ejpam-184	132	14	and	and	CCONJ
ejpam-184	132	15	m.	m.	NOUN
ejpam-184	132	16	massodi	massodi	PROPN
ejpam-184	132	17	/	/	SYM
ejpam-184	132	18	eur	eur	PROPN
ejpam-184	132	19	.	.	PUNCT
ejpam-184	133	1	j.	j.	PROPN
ejpam-184	133	2	pure	pure	PROPN
ejpam-184	133	3	appl	appl	PROPN
ejpam-184	133	4	.	.	PROPN
ejpam-184	133	5	math	math	PROPN
ejpam-184	133	6	,	,	PUNCT
ejpam-184	133	7	2	2	NUM
ejpam-184	133	8	(	(	PUNCT
ejpam-184	133	9	2009	2009	NUM
ejpam-184	133	10	)	)	PUNCT
ejpam-184	133	11	,	,	PUNCT
ejpam-184	133	12	(	(	PUNCT
ejpam-184	133	13	278	278	NUM
ejpam-184	133	14	-	-	SYM
ejpam-184	133	15	295	295	NUM
ejpam-184	133	16	)	)	PUNCT
ejpam-184	133	17	284	284	NUM
ejpam-184	133	18	subject	subject	NOUN
ejpam-184	133	19	to	to	ADP
ejpam-184	133	20	x	x	PROPN
ejpam-184	133	21	(	(	PUNCT
ejpam-184	133	22	a	a	X
ejpam-184	133	23	)	)	PUNCT
ejpam-184	133	24	=	=	PUNCT
ejpam-184	134	1	0=	0=	PUNCT
ejpam-184	134	2	x	x	X
ejpam-184	134	3	(	(	PUNCT
ejpam-184	134	4	b	b	NOUN
ejpam-184	134	5	)	)	PUNCT
ejpam-184	134	6	,	,	PUNCT
ejpam-184	134	7	(	(	PUNCT
ejpam-184	134	8	3.1	3.1	NUM
ejpam-184	134	9	)	)	PUNCT
ejpam-184	134	10	g	g	NOUN
ejpam-184	134	11	(	(	PUNCT
ejpam-184	134	12	t	t	PROPN
ejpam-184	134	13	,	,	PUNCT
ejpam-184	134	14	x	x	X
ejpam-184	134	15	,	,	PUNCT
ejpam-184	134	16	ẋ)≤	ẋ)≤	PROPN
ejpam-184	134	17	0	0	NUM
ejpam-184	134	18	,	,	PUNCT
ejpam-184	134	19	t	t	PROPN
ejpam-184	134	20	∈	∈	PROPN
ejpam-184	135	1	i	i	PRON
ejpam-184	135	2	,	,	PUNCT
ejpam-184	135	3	(	(	PUNCT
ejpam-184	135	4	3.2	3.2	NUM
ejpam-184	135	5	)	)	PUNCT
ejpam-184	135	6	chen	chen	PROPN
ejpam-184	136	1	[	[	X
ejpam-184	136	2	4	4	X
ejpam-184	136	3	]	]	PUNCT
ejpam-184	136	4	presented	present	VERB
ejpam-184	136	5	the	the	DET
ejpam-184	136	6	following	follow	VERB
ejpam-184	136	7	wolfe	wolfe	PROPN
ejpam-184	136	8	type	type	NOUN
ejpam-184	136	9	second	second	ADJ
ejpam-184	136	10	-	-	PUNCT
ejpam-184	136	11	order	order	NOUN
ejpam-184	136	12	dual	dual	ADJ
ejpam-184	136	13	problem	problem	NOUN
ejpam-184	136	14	for	for	ADP
ejpam-184	136	15	(	(	PUNCT
ejpam-184	136	16	cp	cp	NOUN
ejpam-184	136	17	)	)	PUNCT
ejpam-184	136	18	analogous	analogous	ADJ
ejpam-184	136	19	to	to	ADP
ejpam-184	136	20	that	that	PRON
ejpam-184	136	21	for	for	ADP
ejpam-184	136	22	nonlinear	nonlinear	ADJ
ejpam-184	136	23	programming	programming	NOUN
ejpam-184	136	24	by	by	ADP
ejpam-184	136	25	mangasarian	mangasarian	PROPN
ejpam-184	137	1	[	[	X
ejpam-184	137	2	7	7	NUM
ejpam-184	137	3	]	]	PUNCT
ejpam-184	137	4	and	and	CCONJ
ejpam-184	137	5	established	establish	VERB
ejpam-184	137	6	various	various	ADJ
ejpam-184	137	7	duality	duality	NOUN
ejpam-184	137	8	results	result	NOUN
ejpam-184	137	9	under	under	ADP
ejpam-184	137	10	somewhat	somewhat	ADV
ejpam-184	137	11	strange	strange	ADJ
ejpam-184	137	12	invexity	invexity	NOUN
ejpam-184	137	13	-	-	PUNCT
ejpam-184	137	14	like	like	ADJ
ejpam-184	137	15	conditions	condition	NOUN
ejpam-184	137	16	.	.	PUNCT
ejpam-184	138	1	maximize	maximize	NOUN
ejpam-184	138	2	:	:	PUNCT
ejpam-184	138	3	∫	∫	PROPN
ejpam-184	138	4	b	b	PROPN
ejpam-184	139	1	a	a	PRON
ejpam-184	139	2	n	n	NOUN
ejpam-184	139	3	f	f	NOUN
ejpam-184	139	4	(	(	PUNCT
ejpam-184	139	5	t	t	PROPN
ejpam-184	139	6	,	,	PUNCT
ejpam-184	139	7	u(t	u(t	PROPN
ejpam-184	139	8	)	)	PUNCT
ejpam-184	139	9	,	,	PUNCT
ejpam-184	139	10	u̇(t	u̇(t	NOUN
ejpam-184	139	11	)	)	PUNCT
ejpam-184	139	12	)	)	PUNCT
ejpam-184	140	1	+	+	ADP
ejpam-184	140	2	α(t)t	α(t)t	PROPN
ejpam-184	140	3	g(t	g(t	PROPN
ejpam-184	140	4	,	,	PUNCT
ejpam-184	140	5	u(t	u(t	PROPN
ejpam-184	140	6	)	)	PUNCT
ejpam-184	140	7	,	,	PUNCT
ejpam-184	140	8	u̇(t	u̇(t	NOUN
ejpam-184	140	9	)	)	PUNCT
ejpam-184	140	10	)	)	PUNCT
ejpam-184	140	11	1	1	NUM
ejpam-184	140	12	2	2	NUM
ejpam-184	140	13	β(t)t	β(t)t	PROPN
ejpam-184	140	14	[	[	PUNCT
ejpam-184	140	15	fuu(t	fuu(t	NOUN
ejpam-184	140	16	,	,	PUNCT
ejpam-184	140	17	u(t	u(t	PROPN
ejpam-184	140	18	)	)	PUNCT
ejpam-184	140	19	,	,	PUNCT
ejpam-184	140	20	u̇(t	u̇(t	NOUN
ejpam-184	140	21	)	)	PUNCT
ejpam-184	140	22	)	)	PUNCT
ejpam-184	141	1	+	+	CCONJ
ejpam-184	141	2	(	(	PUNCT
ejpam-184	141	3	gu(t	gu(t	PUNCT
ejpam-184	141	4	,	,	PUNCT
ejpam-184	141	5	u(t	u(t	PROPN
ejpam-184	141	6	)	)	PUNCT
ejpam-184	141	7	,	,	PUNCT
ejpam-184	141	8	u̇(t))tα(t))u	u̇(t))tα(t))u	ADP
ejpam-184	141	9	−2d	−2d	PROPN
ejpam-184	141	10	(	(	PUNCT
ejpam-184	141	11	fuu̇(t	fuu̇(t	ADJ
ejpam-184	141	12	,	,	PUNCT
ejpam-184	141	13	u(t	u(t	NOUN
ejpam-184	141	14	)	)	PUNCT
ejpam-184	141	15	,	,	PUNCT
ejpam-184	141	16	u̇(t	u̇(t	NOUN
ejpam-184	141	17	)	)	PUNCT
ejpam-184	141	18	)	)	PUNCT
ejpam-184	142	1	+	+	CCONJ
ejpam-184	142	2	(	(	PUNCT
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ejpam-184	142	4	,	,	PUNCT
ejpam-184	142	5	u(t	u(t	PROPN
ejpam-184	142	6	)	)	PUNCT
ejpam-184	142	7	,	,	PUNCT
ejpam-184	142	8	u̇(t))tα(t))u̇	u̇(t))tα(t))u̇	NOUN
ejpam-184	142	9	)	)	PUNCT
ejpam-184	143	1	+	+	NOUN
ejpam-184	143	2	d2	d2	PROPN
ejpam-184	143	3	(	(	PUNCT
ejpam-184	143	4	fu̇u̇(t	fu̇u̇(t	ADJ
ejpam-184	143	5	,	,	PUNCT
ejpam-184	143	6	u(t	u(t	PROPN
ejpam-184	143	7	)	)	PUNCT
ejpam-184	143	8	,	,	PUNCT
ejpam-184	143	9	u̇(t	u̇(t	NOUN
ejpam-184	143	10	)	)	PUNCT
ejpam-184	143	11	)	)	PUNCT
ejpam-184	144	1	+	+	CCONJ
ejpam-184	144	2	(	(	PUNCT
ejpam-184	144	3	gu̇(t	gu̇(t	NOUN
ejpam-184	144	4	,	,	PUNCT
ejpam-184	144	5	u(t	u(t	PROPN
ejpam-184	144	6	)	)	PUNCT
ejpam-184	144	7	,	,	PUNCT
ejpam-184	144	8	u̇(t))tα(t))u̇)]β(t	u̇(t))tα(t))u̇)]β(t	NOUN
ejpam-184	144	9	)	)	PUNCT
ejpam-184	145	1	o	o	NOUN
ejpam-184	146	1	d	d	X
ejpam-184	146	2	t	t	X
ejpam-184	146	3	subject	subject	NOUN
ejpam-184	146	4	to	to	ADP
ejpam-184	146	5	u(a	u(a	NOUN
ejpam-184	146	6	)	)	PUNCT
ejpam-184	146	7	=	=	SYM
ejpam-184	147	1	0=	0=	PUNCT
ejpam-184	148	1	u(b	u(b	NOUN
ejpam-184	148	2	)	)	PUNCT
ejpam-184	148	3	,	,	PUNCT
ejpam-184	148	4	u̇(a	u̇(a	PROPN
ejpam-184	148	5	)	)	PUNCT
ejpam-184	148	6	=	=	SYM
ejpam-184	148	7	0	0	NUM
ejpam-184	148	8	=	=	SYM
ejpam-184	148	9	u̇(b	u̇(b	NOUN
ejpam-184	148	10	)	)	PUNCT
ejpam-184	148	11	fu(t	fu(t	NOUN
ejpam-184	148	12	,	,	PUNCT
ejpam-184	148	13	u(t	u(t	PROPN
ejpam-184	148	14	)	)	PUNCT
ejpam-184	148	15	,	,	PUNCT
ejpam-184	148	16	u̇(t	u̇(t	NOUN
ejpam-184	148	17	)	)	PUNCT
ejpam-184	148	18	)	)	PUNCT
ejpam-184	149	1	+	+	CCONJ
ejpam-184	149	2	gu(t	gu(t	PUNCT
ejpam-184	149	3	,	,	PUNCT
ejpam-184	149	4	u(t	u(t	PROPN
ejpam-184	149	5	)	)	PUNCT
ejpam-184	149	6	,	,	PUNCT
ejpam-184	149	7	u̇(t))tα(t	u̇(t))tα(t	PROPN
ejpam-184	149	8	)	)	PUNCT
ejpam-184	149	9	−d	−d	PROPN
ejpam-184	149	10	[	[	PUNCT
ejpam-184	149	11	fu̇(t	fu̇(t	PROPN
ejpam-184	149	12	,	,	PUNCT
ejpam-184	149	13	u(t	u(t	PROPN
ejpam-184	149	14	)	)	PUNCT
ejpam-184	149	15	,	,	PUNCT
ejpam-184	149	16	u̇(t	u̇(t	NOUN
ejpam-184	149	17	)	)	PUNCT
ejpam-184	149	18	)	)	PUNCT
ejpam-184	150	1	+	+	CCONJ
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ejpam-184	150	3	,	,	PUNCT
ejpam-184	150	4	u(t	u(t	PROPN
ejpam-184	150	5	)	)	PUNCT
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ejpam-184	150	7	u̇(t))tα(t	u̇(t))tα(t	PROPN
ejpam-184	150	8	)	)	PUNCT
ejpam-184	150	9	]	]	PUNCT
ejpam-184	151	1	+	+	PROPN
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ejpam-184	151	3	fuu(t	fuu(t	NOUN
ejpam-184	151	4	,	,	PUNCT
ejpam-184	151	5	u(t	u(t	PROPN
ejpam-184	151	6	)	)	PUNCT
ejpam-184	151	7	,	,	PUNCT
ejpam-184	151	8	u̇(t	u̇(t	NOUN
ejpam-184	151	9	)	)	PUNCT
ejpam-184	151	10	)	)	PUNCT
ejpam-184	151	11	+	+	CCONJ
ejpam-184	151	12	(	(	PUNCT
ejpam-184	151	13	gu(t	gu(t	PUNCT
ejpam-184	151	14	,	,	PUNCT
ejpam-184	151	15	u(t	u(t	PROPN
ejpam-184	151	16	)	)	PUNCT
ejpam-184	151	17	,	,	PUNCT
ejpam-184	151	18	u̇(t))tα(t))u	u̇(t))tα(t))u	ADP
ejpam-184	151	19	−2d	−2d	PROPN
ejpam-184	151	20	(	(	PUNCT
ejpam-184	151	21	fuu̇(t	fuu̇(t	ADJ
ejpam-184	151	22	,	,	PUNCT
ejpam-184	151	23	u(t	u(t	NOUN
ejpam-184	151	24	)	)	PUNCT
ejpam-184	151	25	,	,	PUNCT
ejpam-184	151	26	u̇(t	u̇(t	NOUN
ejpam-184	151	27	)	)	PUNCT
ejpam-184	151	28	)	)	PUNCT
ejpam-184	152	1	+	+	CCONJ
ejpam-184	152	2	(	(	PUNCT
ejpam-184	152	3	gu(t	gu(t	PUNCT
ejpam-184	152	4	,	,	PUNCT
ejpam-184	152	5	u(t	u(t	PROPN
ejpam-184	152	6	)	)	PUNCT
ejpam-184	152	7	,	,	PUNCT
ejpam-184	152	8	u̇(t))tα(t))u̇	u̇(t))tα(t))u̇	NOUN
ejpam-184	152	9	)	)	PUNCT
ejpam-184	153	1	+	+	NOUN
ejpam-184	153	2	d2	d2	PROPN
ejpam-184	153	3	(	(	PUNCT
ejpam-184	153	4	fu̇u̇(t	fu̇u̇(t	ADJ
ejpam-184	153	5	,	,	PUNCT
ejpam-184	153	6	u(t	u(t	PROPN
ejpam-184	153	7	)	)	PUNCT
ejpam-184	153	8	,	,	PUNCT
ejpam-184	153	9	u̇(t	u̇(t	NOUN
ejpam-184	153	10	)	)	PUNCT
ejpam-184	153	11	)	)	PUNCT
ejpam-184	154	1	+	+	CCONJ
ejpam-184	154	2	(	(	PUNCT
ejpam-184	154	3	gu̇(t	gu̇(t	NOUN
ejpam-184	154	4	,	,	PUNCT
ejpam-184	154	5	u(t	u(t	PROPN
ejpam-184	154	6	)	)	PUNCT
ejpam-184	154	7	,	,	PUNCT
ejpam-184	154	8	u̇(t))tα(t))u̇)]β(t	u̇(t))tα(t))u̇)]β(t	NOUN
ejpam-184	154	9	)	)	PUNCT
ejpam-184	155	1	=	=	PUNCT
ejpam-184	155	2	0	0	NUM
ejpam-184	155	3	,	,	PUNCT
ejpam-184	155	4	t	t	PROPN
ejpam-184	155	5	∈	∈	PROPN
ejpam-184	156	1	i	i	PRON
ejpam-184	156	2	,	,	PUNCT
ejpam-184	156	3	i.	i.	PROPN
ejpam-184	156	4	husain	husain	PROPN
ejpam-184	156	5	,	,	PUNCT
ejpam-184	156	6	a.	a.	PROPN
ejpam-184	156	7	ahmed	ahmed	PROPN
ejpam-184	156	8	,	,	PUNCT
ejpam-184	156	9	and	and	CCONJ
ejpam-184	156	10	m.	m.	NOUN
ejpam-184	156	11	massodi	massodi	PROPN
ejpam-184	156	12	/	/	SYM
ejpam-184	156	13	eur	eur	PROPN
ejpam-184	156	14	.	.	PUNCT
ejpam-184	157	1	j.	j.	PROPN
ejpam-184	157	2	pure	pure	PROPN
ejpam-184	157	3	appl	appl	PROPN
ejpam-184	157	4	.	.	PROPN
ejpam-184	157	5	math	math	PROPN
ejpam-184	157	6	,	,	PUNCT
ejpam-184	157	7	2	2	NUM
ejpam-184	157	8	(	(	PUNCT
ejpam-184	157	9	2009	2009	NUM
ejpam-184	157	10	)	)	PUNCT
ejpam-184	157	11	,	,	PUNCT
ejpam-184	157	12	(	(	PUNCT
ejpam-184	157	13	278	278	NUM
ejpam-184	157	14	-	-	SYM
ejpam-184	157	15	295	295	NUM
ejpam-184	157	16	)	)	PUNCT
ejpam-184	157	17	285	285	NUM
ejpam-184	157	18	α(t	α(t	NUM
ejpam-184	157	19	)	)	PUNCT
ejpam-184	157	20	∈	∈	PROPN
ejpam-184	157	21	rm	rm	NOUN
ejpam-184	157	22	+	+	CCONJ
ejpam-184	157	23	,	,	PUNCT
ejpam-184	157	24	β(t	β(t	PROPN
ejpam-184	157	25	)	)	PUNCT
ejpam-184	158	1	∈	∈	PROPN
ejpam-184	158	2	rn	rn	PROPN
ejpam-184	158	3	,	,	PUNCT
ejpam-184	158	4	t	t	PROPN
ejpam-184	158	5	∈	∈	PROPN
ejpam-184	159	1	i	i	PRON
ejpam-184	159	2	where	where	SCONJ
ejpam-184	159	3	rm	rm	PROPN
ejpam-184	159	4	+	+	PROPN
ejpam-184	159	5	designates	designate	VERB
ejpam-184	159	6	the	the	DET
ejpam-184	159	7	non	non	ADJ
ejpam-184	159	8	-	-	ADJ
ejpam-184	159	9	negative	negative	ADJ
ejpam-184	159	10	orthant	orthant	NOUN
ejpam-184	159	11	of	of	ADP
ejpam-184	159	12	the	the	DET
ejpam-184	159	13	euclidean	euclidean	ADJ
ejpam-184	159	14	space	space	NOUN
ejpam-184	159	15	rn	rn	PROPN
ejpam-184	159	16	.	.	PROPN
ejpam-184	159	17	let	let	VERB
ejpam-184	159	18	h	h	NOUN
ejpam-184	159	19	=	=	SYM
ejpam-184	159	20	fuu(t	fuu(t	PROPN
ejpam-184	159	21	,	,	PUNCT
ejpam-184	159	22	u(t	u(t	PROPN
ejpam-184	159	23	)	)	PUNCT
ejpam-184	159	24	,	,	PUNCT
ejpam-184	159	25	u̇(t	u̇(t	NOUN
ejpam-184	159	26	)	)	PUNCT
ejpam-184	159	27	)	)	PUNCT
ejpam-184	160	1	+	+	CCONJ
ejpam-184	160	2	(	(	PUNCT
ejpam-184	160	3	gu(t	gu(t	PUNCT
ejpam-184	160	4	,	,	PUNCT
ejpam-184	160	5	u(t	u(t	PROPN
ejpam-184	160	6	)	)	PUNCT
ejpam-184	160	7	,	,	PUNCT
ejpam-184	160	8	u̇(t))tα(t))u	u̇(t))tα(t))u	ADP
ejpam-184	160	9	−2d	−2d	PROPN
ejpam-184	160	10	(	(	PUNCT
ejpam-184	160	11	fuu̇(t	fuu̇(t	ADJ
ejpam-184	160	12	,	,	PUNCT
ejpam-184	160	13	u(t	u(t	NOUN
ejpam-184	160	14	)	)	PUNCT
ejpam-184	160	15	,	,	PUNCT
ejpam-184	160	16	u̇(t	u̇(t	NOUN
ejpam-184	160	17	)	)	PUNCT
ejpam-184	160	18	)	)	PUNCT
ejpam-184	161	1	+	+	CCONJ
ejpam-184	161	2	(	(	PUNCT
ejpam-184	161	3	gu(t	gu(t	PUNCT
ejpam-184	161	4	,	,	PUNCT
ejpam-184	161	5	u(t	u(t	PROPN
ejpam-184	161	6	)	)	PUNCT
ejpam-184	161	7	,	,	PUNCT
ejpam-184	161	8	u̇(t))tα(t))u̇	u̇(t))tα(t))u̇	NOUN
ejpam-184	161	9	)	)	PUNCT
ejpam-184	162	1	+	+	NOUN
ejpam-184	162	2	d2	d2	PROPN
ejpam-184	162	3	(	(	PUNCT
ejpam-184	162	4	fu̇u̇(t	fu̇u̇(t	ADJ
ejpam-184	162	5	,	,	PUNCT
ejpam-184	162	6	u(t	u(t	PROPN
ejpam-184	162	7	)	)	PUNCT
ejpam-184	162	8	,	,	PUNCT
ejpam-184	162	9	u̇(t	u̇(t	NOUN
ejpam-184	162	10	)	)	PUNCT
ejpam-184	162	11	)	)	PUNCT
ejpam-184	163	1	+	+	CCONJ
ejpam-184	163	2	(	(	PUNCT
ejpam-184	163	3	gu̇(t	gu̇(t	NOUN
ejpam-184	163	4	,	,	PUNCT
ejpam-184	163	5	u(t	u(t	PROPN
ejpam-184	163	6	)	)	PUNCT
ejpam-184	163	7	,	,	PUNCT
ejpam-184	163	8	u̇(t))tα(t))u̇	u̇(t))tα(t))u̇	NOUN
ejpam-184	163	9	)	)	PUNCT
ejpam-184	163	10	.	.	PUNCT
ejpam-184	164	1	then	then	ADV
ejpam-184	164	2	the	the	DET
ejpam-184	164	3	above	above	ADJ
ejpam-184	164	4	dual	dual	ADJ
ejpam-184	164	5	problem	problem	NOUN
ejpam-184	164	6	can	can	AUX
ejpam-184	164	7	be	be	AUX
ejpam-184	164	8	expressed	express	VERB
ejpam-184	164	9	in	in	ADP
ejpam-184	164	10	a	a	DET
ejpam-184	164	11	much	much	ADV
ejpam-184	164	12	simpler	simple	ADJ
ejpam-184	164	13	form	form	NOUN
ejpam-184	164	14	which	which	PRON
ejpam-184	164	15	is	be	AUX
ejpam-184	164	16	given	give	VERB
ejpam-184	164	17	below	below	ADV
ejpam-184	164	18	.	.	PUNCT
ejpam-184	165	1	(	(	PUNCT
ejpam-184	165	2	vd	vd	NOUN
ejpam-184	165	3	)	)	PUNCT
ejpam-184	165	4	maximize	maximize	NOUN
ejpam-184	165	5	:	:	PUNCT
ejpam-184	165	6	∫	∫	PROPN
ejpam-184	165	7	b	b	PROPN
ejpam-184	165	8	a	a	PRON
ejpam-184	165	9	{	{	PUNCT
ejpam-184	165	10	f	f	PROPN
ejpam-184	165	11	(	(	PUNCT
ejpam-184	165	12	t	t	PROPN
ejpam-184	165	13	,	,	PUNCT
ejpam-184	165	14	u(t	u(t	PROPN
ejpam-184	165	15	)	)	PUNCT
ejpam-184	165	16	,	,	PUNCT
ejpam-184	165	17	u̇(t	u̇(t	NOUN
ejpam-184	165	18	)	)	PUNCT
ejpam-184	165	19	)	)	PUNCT
ejpam-184	166	1	+	+	ADP
ejpam-184	166	2	α(t)t	α(t)t	PROPN
ejpam-184	166	3	g(t	g(t	PROPN
ejpam-184	166	4	,	,	PUNCT
ejpam-184	166	5	u(t	u(t	PROPN
ejpam-184	166	6	)	)	PUNCT
ejpam-184	166	7	,	,	PUNCT
ejpam-184	166	8	u̇(t	u̇(t	NOUN
ejpam-184	166	9	)	)	PUNCT
ejpam-184	166	10	)	)	PUNCT
ejpam-184	167	1	−	−	NOUN
ejpam-184	167	2	1	1	NUM
ejpam-184	167	3	2	2	NUM
ejpam-184	167	4	β(t)t	β(t)t	PRON
ejpam-184	167	5	h(t	h(t	PROPN
ejpam-184	167	6	,	,	PUNCT
ejpam-184	167	7	u(t	u(t	PROPN
ejpam-184	167	8	)	)	PUNCT
ejpam-184	167	9	,	,	PUNCT
ejpam-184	167	10	u̇(t),α(t),β(t))}d	u̇(t),α(t),β(t))}d	PROPN
ejpam-184	167	11	t	t	NOUN
ejpam-184	167	12	subject	subject	NOUN
ejpam-184	167	13	to	to	ADP
ejpam-184	167	14	u(a	u(a	PROPN
ejpam-184	167	15	)	)	PUNCT
ejpam-184	167	16	=	=	SYM
ejpam-184	167	17	0=	0=	PUNCT
ejpam-184	168	1	u(b	u(b	NOUN
ejpam-184	168	2	)	)	PUNCT
ejpam-184	168	3	,	,	PUNCT
ejpam-184	168	4	u̇(a	u̇(a	PROPN
ejpam-184	168	5	)	)	PUNCT
ejpam-184	168	6	=	=	SYM
ejpam-184	168	7	0	0	NUM
ejpam-184	168	8	=	=	SYM
ejpam-184	168	9	u̇(b	u̇(b	NOUN
ejpam-184	168	10	)	)	PUNCT
ejpam-184	168	11	fu(t	fu(t	NOUN
ejpam-184	168	12	,	,	PUNCT
ejpam-184	168	13	u(t	u(t	PROPN
ejpam-184	168	14	)	)	PUNCT
ejpam-184	168	15	,	,	PUNCT
ejpam-184	168	16	u̇(t	u̇(t	NOUN
ejpam-184	168	17	)	)	PUNCT
ejpam-184	168	18	)	)	PUNCT
ejpam-184	169	1	+	+	CCONJ
ejpam-184	169	2	gu(t	gu(t	PUNCT
ejpam-184	169	3	,	,	PUNCT
ejpam-184	169	4	u(t	u(t	PROPN
ejpam-184	169	5	)	)	PUNCT
ejpam-184	169	6	,	,	PUNCT
ejpam-184	169	7	u̇(t))tα(t	u̇(t))tα(t	PROPN
ejpam-184	169	8	)	)	PUNCT
ejpam-184	169	9	−d	−d	PROPN
ejpam-184	169	10	[	[	PUNCT
ejpam-184	169	11	fu̇(t	fu̇(t	PROPN
ejpam-184	169	12	,	,	PUNCT
ejpam-184	169	13	u(t	u(t	PROPN
ejpam-184	169	14	)	)	PUNCT
ejpam-184	169	15	,	,	PUNCT
ejpam-184	169	16	u̇(t	u̇(t	NOUN
ejpam-184	169	17	)	)	PUNCT
ejpam-184	169	18	)	)	PUNCT
ejpam-184	170	1	+	+	CCONJ
ejpam-184	170	2	gu̇(t	gu̇(t	NOUN
ejpam-184	170	3	,	,	PUNCT
ejpam-184	170	4	u(t	u(t	PROPN
ejpam-184	170	5	)	)	PUNCT
ejpam-184	170	6	,	,	PUNCT
ejpam-184	170	7	u̇(t))tα(t	u̇(t))tα(t	PROPN
ejpam-184	170	8	)	)	PUNCT
ejpam-184	170	9	]	]	PUNCT
ejpam-184	171	1	+	+	ADJ
ejpam-184	171	2	h(t	h(t	ADJ
ejpam-184	171	3	,	,	PUNCT
ejpam-184	171	4	u(t	u(t	PROPN
ejpam-184	171	5	)	)	PUNCT
ejpam-184	171	6	,	,	PUNCT
ejpam-184	171	7	u̇(t))α(t)β(t	u̇(t))α(t)β(t	NOUN
ejpam-184	171	8	)	)	PUNCT
ejpam-184	171	9	=	=	SYM
ejpam-184	171	10	0	0	NUM
ejpam-184	171	11	,	,	PUNCT
ejpam-184	171	12	t	t	PROPN
ejpam-184	171	13	∈	∈	PROPN
ejpam-184	171	14	i	i	PRON
ejpam-184	171	15	α(t	α(t	VERB
ejpam-184	171	16	)	)	PUNCT
ejpam-184	171	17	∈	∈	PROPN
ejpam-184	171	18	rm	rm	NOUN
ejpam-184	171	19	+	+	CCONJ
ejpam-184	171	20	,	,	PUNCT
ejpam-184	171	21	β(t	β(t	PROPN
ejpam-184	171	22	)	)	PUNCT
ejpam-184	171	23	∈	∈	PROPN
ejpam-184	171	24	rn	rn	PROPN
ejpam-184	171	25	,	,	PUNCT
ejpam-184	171	26	t	t	PROPN
ejpam-184	171	27	∈	∈	PROPN
ejpam-184	172	1	i	i	PRON
ejpam-184	172	2	it	it	PRON
ejpam-184	172	3	is	be	AUX
ejpam-184	172	4	remarked	remark	VERB
ejpam-184	172	5	here	here	ADV
ejpam-184	172	6	that	that	SCONJ
ejpam-184	172	7	if	if	SCONJ
ejpam-184	172	8	f	f	PROPN
ejpam-184	172	9	and	and	CCONJ
ejpam-184	172	10	g	g	PROPN
ejpam-184	172	11	are	be	AUX
ejpam-184	172	12	independent	independent	ADJ
ejpam-184	172	13	of	of	ADP
ejpam-184	172	14	t	t	PROPN
ejpam-184	172	15	,	,	PUNCT
ejpam-184	172	16	then	then	ADV
ejpam-184	172	17	(	(	PUNCT
ejpam-184	172	18	vd	vd	NOUN
ejpam-184	172	19	)	)	PUNCT
ejpam-184	172	20	becomes	become	VERB
ejpam-184	172	21	second	second	ADJ
ejpam-184	172	22	-	-	PUNCT
ejpam-184	172	23	order	order	NOUN
ejpam-184	172	24	dual	dual	ADJ
ejpam-184	172	25	problem	problem	NOUN
ejpam-184	172	26	studied	study	VERB
ejpam-184	172	27	by	by	ADP
ejpam-184	172	28	mangasarian	mangasarian	PROPN
ejpam-184	173	1	[	[	X
ejpam-184	173	2	7	7	NUM
ejpam-184	173	3	]	]	PUNCT
ejpam-184	173	4	.	.	PUNCT
ejpam-184	174	1	now	now	ADV
ejpam-184	174	2	we	we	PRON
ejpam-184	174	3	present	present	VERB
ejpam-184	174	4	the	the	DET
ejpam-184	174	5	following	follow	VERB
ejpam-184	174	6	mond	mond	PROPN
ejpam-184	174	7	-	-	PUNCT
ejpam-184	174	8	weir	weir	PROPN
ejpam-184	174	9	type	type	NOUN
ejpam-184	174	10	second	second	ADJ
ejpam-184	174	11	-	-	PUNCT
ejpam-184	174	12	order	order	NOUN
ejpam-184	174	13	dual	dual	ADJ
ejpam-184	174	14	(	(	PUNCT
ejpam-184	174	15	cd	cd	PROPN
ejpam-184	174	16	)	)	PUNCT
ejpam-184	174	17	in	in	ADP
ejpam-184	174	18	the	the	DET
ejpam-184	174	19	spirit	spirit	NOUN
ejpam-184	174	20	of	of	ADP
ejpam-184	174	21	[	[	X
ejpam-184	174	22	1	1	NUM
ejpam-184	174	23	]	]	PUNCT
ejpam-184	174	24	to	to	PART
ejpam-184	174	25	relax	relax	VERB
ejpam-184	174	26	second	second	ADJ
ejpam-184	174	27	-	-	PUNCT
ejpam-184	174	28	order	order	NOUN
ejpam-184	174	29	invexity	invexity	NOUN
ejpam-184	174	30	requirements	requirement	NOUN
ejpam-184	174	31	and	and	CCONJ
ejpam-184	174	32	establish	establish	VERB
ejpam-184	174	33	various	various	ADJ
ejpam-184	174	34	duality	duality	NOUN
ejpam-184	174	35	i.	i.	PROPN
ejpam-184	174	36	husain	husain	PROPN
ejpam-184	174	37	,	,	PUNCT
ejpam-184	174	38	a.	a.	PROPN
ejpam-184	174	39	ahmed	ahmed	PROPN
ejpam-184	174	40	,	,	PUNCT
ejpam-184	174	41	and	and	CCONJ
ejpam-184	174	42	m.	m.	NOUN
ejpam-184	174	43	massodi	massodi	PROPN
ejpam-184	174	44	/	/	SYM
ejpam-184	174	45	eur	eur	PROPN
ejpam-184	174	46	.	.	PUNCT
ejpam-184	175	1	j.	j.	PROPN
ejpam-184	175	2	pure	pure	PROPN
ejpam-184	175	3	appl	appl	PROPN
ejpam-184	175	4	.	.	PROPN
ejpam-184	175	5	math	math	PROPN
ejpam-184	175	6	,	,	PUNCT
ejpam-184	175	7	2	2	NUM
ejpam-184	175	8	(	(	PUNCT
ejpam-184	175	9	2009	2009	NUM
ejpam-184	175	10	)	)	PUNCT
ejpam-184	175	11	,	,	PUNCT
ejpam-184	175	12	(	(	PUNCT
ejpam-184	175	13	278	278	NUM
ejpam-184	175	14	-	-	SYM
ejpam-184	175	15	295	295	NUM
ejpam-184	175	16	)	)	PUNCT
ejpam-184	175	17	286	286	NUM
ejpam-184	175	18	results	result	NOUN
ejpam-184	175	19	between	between	ADP
ejpam-184	175	20	the	the	DET
ejpam-184	175	21	problems	problem	NOUN
ejpam-184	175	22	(	(	PUNCT
ejpam-184	175	23	cp	cp	NOUN
ejpam-184	175	24	)	)	PUNCT
ejpam-184	175	25	and	and	CCONJ
ejpam-184	175	26	(	(	PUNCT
ejpam-184	175	27	cd	cd	PROPN
ejpam-184	175	28	)	)	PUNCT
ejpam-184	175	29	under	under	ADP
ejpam-184	175	30	generalized	generalized	ADJ
ejpam-184	175	31	second	second	ADJ
ejpam-184	175	32	-	-	PUNCT
ejpam-184	175	33	order	order	NOUN
ejpam-184	175	34	invexity	invexity	NOUN
ejpam-184	175	35	hypothesis	hypothesis	NOUN
ejpam-184	175	36	.	.	PUNCT
ejpam-184	176	1	(	(	PUNCT
ejpam-184	176	2	cd	cd	PROPN
ejpam-184	176	3	):	):	PUNCT
ejpam-184	176	4	maximize	maximize	PROPN
ejpam-184	176	5	∫	∫	PROPN
ejpam-184	177	1	i	i	PRON
ejpam-184	177	2	{	{	PUNCT
ejpam-184	177	3	f	f	PROPN
ejpam-184	177	4	(	(	PUNCT
ejpam-184	177	5	t	t	PROPN
ejpam-184	177	6	,	,	PUNCT
ejpam-184	177	7	u	u	PROPN
ejpam-184	177	8	,	,	PUNCT
ejpam-184	177	9	u̇)−	u̇)−	PROPN
ejpam-184	177	10	1	1	NUM
ejpam-184	177	11	2	2	NUM
ejpam-184	177	12	β(t)t	β(t)t	NUM
ejpam-184	177	13	fβ(t)}d	fβ(t)}d	PROPN
ejpam-184	177	14	t	t	PROPN
ejpam-184	177	15	subject	subject	NOUN
ejpam-184	177	16	to	to	ADP
ejpam-184	177	17	u(a	u(a	PROPN
ejpam-184	177	18	)	)	PUNCT
ejpam-184	177	19	=	=	SYM
ejpam-184	177	20	0=	0=	PUNCT
ejpam-184	177	21	u(b	u(b	NOUN
ejpam-184	177	22	)	)	PUNCT
ejpam-184	177	23	(	(	PUNCT
ejpam-184	177	24	3.3	3.3	NUM
ejpam-184	177	25	)	)	PUNCT
ejpam-184	177	26	fu	fu	NOUN
ejpam-184	177	27	+	+	CCONJ
ejpam-184	177	28	y(t)t	y(t)t	PROPN
ejpam-184	177	29	gu	gu	NOUN
ejpam-184	177	30	−	−	NOUN
ejpam-184	178	1	d	d	PROPN
ejpam-184	178	2	(	(	PUNCT
ejpam-184	178	3	fu̇	fu̇	PROPN
ejpam-184	178	4	+	+	NUM
ejpam-184	178	5	y(t)t	y(t)t	PROPN
ejpam-184	178	6	gu̇	gu̇	NOUN
ejpam-184	178	7	)	)	PUNCT
ejpam-184	179	1	+	+	CCONJ
ejpam-184	179	2	(	(	PUNCT
ejpam-184	179	3	f	f	X
ejpam-184	179	4	+	+	NOUN
ejpam-184	179	5	h)β(t	h)β(t	NOUN
ejpam-184	179	6	)	)	PUNCT
ejpam-184	179	7	=	=	SYM
ejpam-184	179	8	0	0	NUM
ejpam-184	179	9	,	,	PUNCT
ejpam-184	179	10	t	t	PROPN
ejpam-184	179	11	∈	∈	PROPN
ejpam-184	179	12	i	i	PRON
ejpam-184	179	13	(	(	PUNCT
ejpam-184	179	14	3.4	3.4	NUM
ejpam-184	179	15	)	)	PUNCT
ejpam-184	179	16	∫	∫	PROPN
ejpam-184	180	1	i	i	PROPN
ejpam-184	180	2	�	�	PROPN
ejpam-184	180	3	y(t)t	y(t)t	PROPN
ejpam-184	180	4	g(t	g(t	PROPN
ejpam-184	180	5	,	,	PUNCT
ejpam-184	180	6	u	u	PROPN
ejpam-184	180	7	,	,	PUNCT
ejpam-184	180	8	u̇)−	u̇)−	PROPN
ejpam-184	180	9	1	1	NUM
ejpam-184	180	10	2	2	NUM
ejpam-184	180	11	β(t)t	β(t)t	PROPN
ejpam-184	180	12	hβ(t	hβ(t	NOUN
ejpam-184	180	13	)	)	PUNCT
ejpam-184	180	14	�	�	PROPN
ejpam-184	181	1	d	d	PROPN
ejpam-184	181	2	t	t	PROPN
ejpam-184	181	3	≥	≥	NOUN
ejpam-184	181	4	0	0	NUM
ejpam-184	181	5	,	,	PUNCT
ejpam-184	181	6	(	(	PUNCT
ejpam-184	181	7	3.5	3.5	NUM
ejpam-184	181	8	)	)	PUNCT
ejpam-184	181	9	y(t)≥	y(t)≥	NOUN
ejpam-184	181	10	0	0	NUM
ejpam-184	181	11	,	,	PUNCT
ejpam-184	181	12	t	t	PROPN
ejpam-184	181	13	∈	∈	PROPN
ejpam-184	182	1	i	i	PRON
ejpam-184	182	2	(	(	PUNCT
ejpam-184	182	3	3.6	3.6	NUM
ejpam-184	182	4	)	)	PUNCT
ejpam-184	182	5	where	where	SCONJ
ejpam-184	182	6	f	f	PROPN
ejpam-184	182	7	=	=	SYM
ejpam-184	182	8	fuu−	fuu−	PROPN
ejpam-184	182	9	d	d	PROPN
ejpam-184	182	10	fuu̇+	fuu̇+	PROPN
ejpam-184	182	11	d2	d2	PROPN
ejpam-184	182	12	fu̇u̇	fu̇u̇	PROPN
ejpam-184	182	13	and	and	CCONJ
ejpam-184	182	14	h	h	NOUN
ejpam-184	182	15	=	=	SYM
ejpam-184	182	16	(	(	PUNCT
ejpam-184	182	17	y(t)t	y(t)t	NOUN
ejpam-184	182	18	gu)u−	gu)u−	NOUN
ejpam-184	182	19	d(y(t)t	d(y(t)t	NOUN
ejpam-184	182	20	gu)u̇+	gu)u̇+	NOUN
ejpam-184	182	21	d2(y(t)t	d2(y(t)t	NOUN
ejpam-184	182	22	gu̇)u̇	gu̇)u̇	NOUN
ejpam-184	182	23	and	and	CCONJ
ejpam-184	182	24	define	define	VERB
ejpam-184	182	25	d	d	NOUN
ejpam-184	182	26	=	=	PUNCT
ejpam-184	182	27	d	d	PROPN
ejpam-184	182	28	d	d	PROPN
ejpam-184	182	29	t	t	PROPN
ejpam-184	182	30	as	as	ADV
ejpam-184	182	31	defined	define	VERB
ejpam-184	182	32	earlier	early	ADV
ejpam-184	182	33	.	.	PUNCT
ejpam-184	183	1	if	if	SCONJ
ejpam-184	183	2	f	f	PROPN
ejpam-184	183	3	and	and	CCONJ
ejpam-184	183	4	g	g	PROPN
ejpam-184	183	5	are	be	AUX
ejpam-184	183	6	independent	independent	ADJ
ejpam-184	183	7	of	of	ADP
ejpam-184	183	8	t	t	PROPN
ejpam-184	183	9	then	then	ADV
ejpam-184	183	10	f	f	PROPN
ejpam-184	183	11	=	=	PROPN
ejpam-184	183	12	fuu	fuu	PROPN
ejpam-184	183	13	and	and	CCONJ
ejpam-184	183	14	h	h	NOUN
ejpam-184	183	15	=	=	PUNCT
ejpam-184	184	1	(	(	PUNCT
ejpam-184	184	2	yt	yt	INTJ
ejpam-184	184	3	gu)u	gu)u	PROPN
ejpam-184	184	4	and	and	CCONJ
ejpam-184	184	5	consequently	consequently	ADV
ejpam-184	184	6	(	(	PUNCT
ejpam-184	184	7	cd	cd	PROPN
ejpam-184	184	8	)	)	PUNCT
ejpam-184	184	9	will	will	AUX
ejpam-184	184	10	reduce	reduce	VERB
ejpam-184	184	11	to	to	ADP
ejpam-184	184	12	the	the	DET
ejpam-184	184	13	second	second	ADJ
ejpam-184	184	14	-	-	PUNCT
ejpam-184	184	15	order	order	NOUN
ejpam-184	184	16	dual	dual	ADJ
ejpam-184	184	17	problem	problem	NOUN
ejpam-184	184	18	introduced	introduce	VERB
ejpam-184	184	19	in	in	ADP
ejpam-184	184	20	[	[	X
ejpam-184	184	21	1	1	NUM
ejpam-184	184	22	]	]	PUNCT
ejpam-184	184	23	.	.	PUNCT
ejpam-184	185	1	theorem	theorem	VERB
ejpam-184	185	2	3.1	3.1	NUM
ejpam-184	185	3	(	(	PUNCT
ejpam-184	185	4	weak	weak	ADJ
ejpam-184	185	5	duality	duality	NOUN
ejpam-184	185	6	)	)	PUNCT
ejpam-184	185	7	.	.	PUNCT
ejpam-184	186	1	let	let	VERB
ejpam-184	186	2	x(t	x(t	NOUN
ejpam-184	186	3	)	)	PUNCT
ejpam-184	186	4	∈	∈	PROPN
ejpam-184	186	5	x	x	VERB
ejpam-184	186	6	be	be	AUX
ejpam-184	186	7	a	a	DET
ejpam-184	186	8	feasible	feasible	ADJ
ejpam-184	186	9	solution	solution	NOUN
ejpam-184	186	10	of	of	ADP
ejpam-184	186	11	(	(	PUNCT
ejpam-184	186	12	cp	cp	NOUN
ejpam-184	186	13	)	)	PUNCT
ejpam-184	186	14	and	and	CCONJ
ejpam-184	186	15	(	(	PUNCT
ejpam-184	186	16	u(t	u(t	PROPN
ejpam-184	186	17	)	)	PUNCT
ejpam-184	186	18	,	,	PUNCT
ejpam-184	186	19	y(t),β(t	y(t),β(t	NOUN
ejpam-184	186	20	)	)	PUNCT
ejpam-184	186	21	)	)	PUNCT
ejpam-184	186	22	be	be	AUX
ejpam-184	186	23	feasible	feasible	ADJ
ejpam-184	186	24	solution	solution	NOUN
ejpam-184	186	25	of	of	ADP
ejpam-184	186	26	(	(	PUNCT
ejpam-184	186	27	cd).if	cd).if	INTJ
ejpam-184	186	28	∫	∫	PROPN
ejpam-184	187	1	i	i	PRON
ejpam-184	187	2	f	f	PROPN
ejpam-184	187	3	(	(	PUNCT
ejpam-184	187	4	t	t	PROPN
ejpam-184	187	5	,	,	PUNCT
ejpam-184	187	6	.	.	PUNCT
ejpam-184	187	7	,	,	PUNCT
ejpam-184	188	1	.)d	.)d	PROPN
ejpam-184	188	2	t	t	PROPN
ejpam-184	188	3	be	be	AUX
ejpam-184	188	4	second	second	ADJ
ejpam-184	188	5	-	-	PUNCT
ejpam-184	188	6	order	order	NOUN
ejpam-184	188	7	pseudoinvex	pseudoinvex	NOUN
ejpam-184	188	8	and	and	CCONJ
ejpam-184	188	9	∫	∫	NOUN
ejpam-184	189	1	i	i	PRON
ejpam-184	189	2	y	y	PROPN
ejpam-184	189	3	(	(	PUNCT
ejpam-184	189	4	t	t	PROPN
ejpam-184	189	5	)	)	PUNCT
ejpam-184	189	6	t	t	PROPN
ejpam-184	189	7	g(t	g(t	PROPN
ejpam-184	189	8	,	,	PUNCT
ejpam-184	189	9	.	.	PUNCT
ejpam-184	189	10	,	,	PUNCT
ejpam-184	189	11	.	.	PUNCT
ejpam-184	189	12	)	)	PUNCT
ejpam-184	190	1	d	d	X
ejpam-184	190	2	t	t	PROPN
ejpam-184	190	3	be	be	AUX
ejpam-184	190	4	second	second	ADJ
ejpam-184	190	5	-	-	PUNCT
ejpam-184	190	6	order	order	NOUN
ejpam-184	190	7	quasi	quasi	NOUN
ejpam-184	190	8	-	-	NOUN
ejpam-184	190	9	invex	invex	ADJ
ejpam-184	190	10	with	with	ADP
ejpam-184	190	11	respect	respect	NOUN
ejpam-184	190	12	to	to	ADP
ejpam-184	190	13	the	the	DET
ejpam-184	190	14	same	same	ADJ
ejpam-184	190	15	η	η	NOUN
ejpam-184	190	16	:	:	PUNCT
ejpam-184	190	17	i	i	PRON
ejpam-184	190	18	×	×	VERB
ejpam-184	190	19	rn×	rn×	NOUN
ejpam-184	190	20	rn→	rn→	PROPN
ejpam-184	190	21	rn	rn	PROPN
ejpam-184	190	22	satisfying	satisfy	VERB
ejpam-184	190	23	η=	η=	NOUN
ejpam-184	190	24	0	0	NUM
ejpam-184	190	25	at	at	ADP
ejpam-184	190	26	t	t	PROPN
ejpam-184	190	27	=	=	SYM
ejpam-184	190	28	a	a	PROPN
ejpam-184	190	29	and	and	CCONJ
ejpam-184	190	30	t	t	NOUN
ejpam-184	190	31	=	=	SYM
ejpam-184	190	32	b	b	PROPN
ejpam-184	190	33	,	,	PUNCT
ejpam-184	190	34	then	then	ADV
ejpam-184	190	35	∫	∫	PROPN
ejpam-184	191	1	i	i	PRON
ejpam-184	191	2	f	f	PROPN
ejpam-184	191	3	(	(	PUNCT
ejpam-184	191	4	t	t	PROPN
ejpam-184	191	5	,	,	PUNCT
ejpam-184	191	6	x	x	X
ejpam-184	191	7	,	,	PUNCT
ejpam-184	191	8	ẋ)d	ẋ)d	PROPN
ejpam-184	191	9	t	t	PROPN
ejpam-184	191	10	≥	≥	PROPN
ejpam-184	191	11	∫	∫	PROPN
ejpam-184	192	1	i	i	PRON
ejpam-184	192	2	�	�	PROPN
ejpam-184	193	1	f	f	PROPN
ejpam-184	193	2	(	(	PUNCT
ejpam-184	193	3	t	t	PROPN
ejpam-184	193	4	,	,	PUNCT
ejpam-184	193	5	u	u	PROPN
ejpam-184	193	6	,	,	PUNCT
ejpam-184	193	7	u̇)−	u̇)−	PROPN
ejpam-184	193	8	1	1	NUM
ejpam-184	193	9	2	2	NUM
ejpam-184	193	10	β(t)t	β(t)t	X
ejpam-184	193	11	fβ	fβ	X
ejpam-184	193	12	(	(	PUNCT
ejpam-184	193	13	t	t	NOUN
ejpam-184	193	14	)	)	PUNCT
ejpam-184	193	15	�	�	PROPN
ejpam-184	193	16	d	d	PROPN
ejpam-184	193	17	t	t	PROPN
ejpam-184	193	18	proof	proof	NOUN
ejpam-184	193	19	.	.	PUNCT
ejpam-184	194	1	the	the	DET
ejpam-184	194	2	relations	relation	NOUN
ejpam-184	194	3	,	,	PUNCT
ejpam-184	194	4	g(t	g(t	PROPN
ejpam-184	194	5	,	,	PUNCT
ejpam-184	194	6	x	x	INTJ
ejpam-184	194	7	,	,	PUNCT
ejpam-184	194	8	ẋ	ẋ	PROPN
ejpam-184	194	9	)	)	PUNCT
ejpam-184	194	10	≤	≤	NOUN
ejpam-184	194	11	0	0	NUM
ejpam-184	194	12	,	,	PUNCT
ejpam-184	194	13	y(t)≥	y(t)≥	NOUN
ejpam-184	194	14	0	0	NUM
ejpam-184	194	15	,	,	PUNCT
ejpam-184	194	16	t	t	PROPN
ejpam-184	194	17	∈	∈	PROPN
ejpam-184	194	18	i	i	PRON
ejpam-184	194	19	and	and	CCONJ
ejpam-184	194	20	(	(	PUNCT
ejpam-184	194	21	3.5	3.5	NUM
ejpam-184	194	22	)	)	PUNCT
ejpam-184	194	23	imply	imply	VERB
ejpam-184	194	24	∫	∫	PROPN
ejpam-184	195	1	i	i	PROPN
ejpam-184	195	2	y(t)t	y(t)t	PROPN
ejpam-184	195	3	g(t	g(t	PROPN
ejpam-184	195	4	,	,	PUNCT
ejpam-184	195	5	x	x	SYM
ejpam-184	195	6	,	,	PUNCT
ejpam-184	195	7	ẋ)d	ẋ)d	PROPN
ejpam-184	195	8	t	t	PROPN
ejpam-184	195	9	≤	≤	NUM
ejpam-184	196	1	∫	∫	PROPN
ejpam-184	197	1	i	i	PRON
ejpam-184	197	2	�	�	PROPN
ejpam-184	197	3	y(t)t	y(t)t	PROPN
ejpam-184	197	4	g(t	g(t	PROPN
ejpam-184	197	5	,	,	PUNCT
ejpam-184	197	6	u	u	PROPN
ejpam-184	197	7	,	,	PUNCT
ejpam-184	197	8	u̇)−	u̇)−	PROPN
ejpam-184	197	9	1	1	NUM
ejpam-184	197	10	2	2	NUM
ejpam-184	197	11	β(t)t	β(t)t	PROPN
ejpam-184	197	12	hβ(t	hβ(t	NOUN
ejpam-184	197	13	)	)	PUNCT
ejpam-184	197	14	�	�	PROPN
ejpam-184	198	1	d	d	PROPN
ejpam-184	198	2	t	t	PROPN
ejpam-184	198	3	,	,	PUNCT
ejpam-184	198	4	this	this	PRON
ejpam-184	198	5	,	,	PUNCT
ejpam-184	198	6	because	because	SCONJ
ejpam-184	198	7	of	of	ADP
ejpam-184	198	8	second	second	ADJ
ejpam-184	198	9	-	-	PUNCT
ejpam-184	198	10	order	order	NOUN
ejpam-184	198	11	quasi	quasi	NOUN
ejpam-184	198	12	-	-	NOUN
ejpam-184	198	13	invexity	invexity	NOUN
ejpam-184	198	14	of	of	ADP
ejpam-184	198	15	∫	∫	PROPN
ejpam-184	198	16	i	i	PROPN
ejpam-184	198	17	y(t)t	y(t)t	PROPN
ejpam-184	198	18	g(t	g(t	PROPN
ejpam-184	198	19	,	,	PUNCT
ejpam-184	198	20	.	.	PUNCT
ejpam-184	198	21	,	,	PUNCT
ejpam-184	198	22	.)d	.)d	PROPN
ejpam-184	198	23	t	t	PROPN
ejpam-184	198	24	,	,	PUNCT
ejpam-184	198	25	implies	imply	VERB
ejpam-184	198	26	that	that	SCONJ
ejpam-184	198	27	∫	∫	PROPN
ejpam-184	198	28	i	i	PRON
ejpam-184	198	29	{	{	PUNCT
ejpam-184	198	30	ηt	ηt	ADP
ejpam-184	198	31	(	(	PUNCT
ejpam-184	198	32	y(t)t	y(t)t	PROPN
ejpam-184	198	33	gu	gu	NOUN
ejpam-184	198	34	)	)	PUNCT
ejpam-184	198	35	+	+	CCONJ
ejpam-184	198	36	(	(	PUNCT
ejpam-184	198	37	dη	dη	NOUN
ejpam-184	198	38	)	)	PUNCT
ejpam-184	198	39	t	t	PROPN
ejpam-184	198	40	(	(	PUNCT
ejpam-184	198	41	y(t)t	y(t)t	PROPN
ejpam-184	198	42	gu̇	gu̇	NOUN
ejpam-184	198	43	)	)	PUNCT
ejpam-184	199	1	+	+	PROPN
ejpam-184	199	2	η	η	PROPN
ejpam-184	199	3	t	t	PROPN
ejpam-184	199	4	hβ(t)}d	hβ(t)}d	PROPN
ejpam-184	199	5	t	t	NOUN
ejpam-184	199	6	≤	≤	NUM
ejpam-184	199	7	0	0	NUM
ejpam-184	199	8	i.	i.	PROPN
ejpam-184	199	9	husain	husain	PROPN
ejpam-184	199	10	,	,	PUNCT
ejpam-184	199	11	a.	a.	PROPN
ejpam-184	199	12	ahmed	ahmed	PROPN
ejpam-184	199	13	,	,	PUNCT
ejpam-184	199	14	and	and	CCONJ
ejpam-184	199	15	m.	m.	NOUN
ejpam-184	199	16	massodi	massodi	PROPN
ejpam-184	199	17	/	/	SYM
ejpam-184	199	18	eur	eur	PROPN
ejpam-184	199	19	.	.	PUNCT
ejpam-184	200	1	j.	j.	PROPN
ejpam-184	200	2	pure	pure	PROPN
ejpam-184	200	3	appl	appl	PROPN
ejpam-184	200	4	.	.	PROPN
ejpam-184	200	5	math	math	PROPN
ejpam-184	200	6	,	,	PUNCT
ejpam-184	200	7	2	2	NUM
ejpam-184	200	8	(	(	PUNCT
ejpam-184	200	9	2009	2009	NUM
ejpam-184	200	10	)	)	PUNCT
ejpam-184	200	11	,	,	PUNCT
ejpam-184	200	12	(	(	PUNCT
ejpam-184	200	13	278	278	NUM
ejpam-184	200	14	-	-	SYM
ejpam-184	200	15	295	295	NUM
ejpam-184	200	16	)	)	PUNCT
ejpam-184	200	17	287	287	NUM
ejpam-184	200	18	i.e.	i.e.	X
ejpam-184	200	19	,	,	PUNCT
ejpam-184	200	20	∫	∫	PROPN
ejpam-184	200	21	i	i	PRON
ejpam-184	200	22	ηt	ηt	ADP
ejpam-184	200	23	(	(	PUNCT
ejpam-184	200	24	y(t)t	y(t)t	PROPN
ejpam-184	200	25	gu)d	gu)d	PROPN
ejpam-184	200	26	t	t	PROPN
ejpam-184	200	27	+	+	CCONJ
ejpam-184	200	28	∫	∫	PROPN
ejpam-184	200	29	i	i	INTJ
ejpam-184	200	30	(	(	PUNCT
ejpam-184	200	31	dη)t	dη)t	PROPN
ejpam-184	200	32	(	(	PUNCT
ejpam-184	200	33	y(t)t	y(t)t	PROPN
ejpam-184	200	34	gu̇)d	gu̇)d	PROPN
ejpam-184	200	35	t	t	PROPN
ejpam-184	201	1	+	+	CCONJ
ejpam-184	201	2	∫	∫	PROPN
ejpam-184	201	3	i	i	PRON
ejpam-184	201	4	ηt	ηt	ADP
ejpam-184	201	5	hβ(t)d	hβ(t)d	PROPN
ejpam-184	201	6	t	t	NOUN
ejpam-184	201	7	≤	≤	NOUN
ejpam-184	201	8	0	0	NUM
ejpam-184	202	1	this	this	PRON
ejpam-184	202	2	,	,	PUNCT
ejpam-184	202	3	by	by	ADP
ejpam-184	202	4	integration	integration	NOUN
ejpam-184	202	5	by	by	ADP
ejpam-184	202	6	parts	part	NOUN
ejpam-184	202	7	,	,	PUNCT
ejpam-184	202	8	this	this	DET
ejpam-184	202	9	inequality	inequality	NOUN
ejpam-184	202	10	yields	yield	VERB
ejpam-184	202	11	,	,	PUNCT
ejpam-184	202	12	∫	∫	PROPN
ejpam-184	202	13	i	i	PRON
ejpam-184	202	14	ηt	ηt	ADP
ejpam-184	202	15	(	(	PUNCT
ejpam-184	202	16	y(t)t	y(t)t	PROPN
ejpam-184	202	17	gu)d	gu)d	PROPN
ejpam-184	202	18	t	t	PROPN
ejpam-184	202	19	+	+	PROPN
ejpam-184	202	20	ηy(t)t	ηy(t)t	PROPN
ejpam-184	202	21	gu̇|	gu̇|	PROPN
ejpam-184	202	22	b	b	PROPN
ejpam-184	202	23	a	a	DET
ejpam-184	202	24	−	−	PROPN
ejpam-184	202	25	∫	∫	NOUN
ejpam-184	203	1	i	i	PRON
ejpam-184	203	2	ηt	ηt	ADP
ejpam-184	203	3	d(y(t)t	d(y(t)t	PROPN
ejpam-184	203	4	gu̇)d	gu̇)d	PROPN
ejpam-184	203	5	t	t	PROPN
ejpam-184	204	1	+	+	CCONJ
ejpam-184	204	2	∫	∫	PROPN
ejpam-184	204	3	i	i	PRON
ejpam-184	204	4	ηt	ηt	ADP
ejpam-184	204	5	hβ(t)d	hβ(t)d	PROPN
ejpam-184	204	6	t	t	NOUN
ejpam-184	204	7	≤	≤	NOUN
ejpam-184	204	8	0	0	NUM
ejpam-184	204	9	using	use	VERB
ejpam-184	204	10	η	η	PROPN
ejpam-184	204	11	=	=	PROPN
ejpam-184	204	12	0	0	PROPN
ejpam-184	204	13	at	at	ADP
ejpam-184	204	14	t	t	NOUN
ejpam-184	204	15	=	=	SYM
ejpam-184	204	16	a	a	PROPN
ejpam-184	204	17	and	and	CCONJ
ejpam-184	204	18	t	t	NOUN
ejpam-184	204	19	=	=	SYM
ejpam-184	204	20	b	b	PROPN
ejpam-184	204	21	in	in	ADP
ejpam-184	204	22	the	the	DET
ejpam-184	204	23	above	above	ADJ
ejpam-184	204	24	inequality	inequality	NOUN
ejpam-184	204	25	,	,	PUNCT
ejpam-184	204	26	we	we	PRON
ejpam-184	204	27	obtain	obtain	VERB
ejpam-184	204	28	,	,	PUNCT
ejpam-184	204	29	∫	∫	PROPN
ejpam-184	204	30	i	i	PROPN
ejpam-184	204	31	η[(y(t)t	η[(y(t)t	NOUN
ejpam-184	204	32	gu)−	gu)−	NOUN
ejpam-184	204	33	d(y(t)t	d(y(t)t	NOUN
ejpam-184	204	34	gu̇	gu̇	NOUN
ejpam-184	204	35	)	)	PUNCT
ejpam-184	205	1	+	+	PROPN
ejpam-184	205	2	η	η	PROPN
ejpam-184	205	3	t	t	PROPN
ejpam-184	205	4	hβ(t)]d	hβ(t)]d	NOUN
ejpam-184	205	5	t	t	PROPN
ejpam-184	205	6	≤	≤	NOUN
ejpam-184	205	7	0	0	NUM
ejpam-184	205	8	,	,	PUNCT
ejpam-184	205	9	using	use	VERB
ejpam-184	205	10	(	(	PUNCT
ejpam-184	205	11	3.4	3.4	NUM
ejpam-184	205	12	)	)	PUNCT
ejpam-184	205	13	,	,	PUNCT
ejpam-184	205	14	this	this	PRON
ejpam-184	205	15	gives	give	VERB
ejpam-184	205	16	∫	∫	PROPN
ejpam-184	205	17	i	i	PRON
ejpam-184	206	1	[	[	X
ejpam-184	206	2	ηt	ηt	ADP
ejpam-184	206	3	(	(	PUNCT
ejpam-184	206	4	fu	fu	NOUN
ejpam-184	206	5	−	−	PROPN
ejpam-184	206	6	d	d	PROPN
ejpam-184	206	7	fu̇	fu̇	PROPN
ejpam-184	206	8	)	)	PUNCT
ejpam-184	207	1	+	+	NOUN
ejpam-184	207	2	η	η	PROPN
ejpam-184	207	3	t	t	PROPN
ejpam-184	207	4	fβ(t)]d	fβ(t)]d	NOUN
ejpam-184	207	5	t	t	PROPN
ejpam-184	207	6	≥	≥	PROPN
ejpam-184	207	7	0	0	NUM
ejpam-184	207	8	.	.	PUNCT
ejpam-184	208	1	integrating	integrate	VERB
ejpam-184	208	2	by	by	ADP
ejpam-184	208	3	parts	part	NOUN
ejpam-184	208	4	,	,	PUNCT
ejpam-184	208	5	gives	give	VERB
ejpam-184	208	6	∫	∫	PROPN
ejpam-184	208	7	i	i	PRON
ejpam-184	208	8	(	(	PUNCT
ejpam-184	208	9	ηt	ηt	ADP
ejpam-184	208	10	fu	fu	NOUN
ejpam-184	208	11	+	+	CCONJ
ejpam-184	208	12	(	(	PUNCT
ejpam-184	208	13	dη	dη	NOUN
ejpam-184	208	14	)	)	PUNCT
ejpam-184	208	15	t	t	PROPN
ejpam-184	209	1	fu̇	fu̇	PROPN
ejpam-184	209	2	+	+	PROPN
ejpam-184	209	3	η	η	PROPN
ejpam-184	209	4	t	t	NOUN
ejpam-184	209	5	fβ(t)d	fβ(t)d	PROPN
ejpam-184	209	6	t)≥	t)≥	PROPN
ejpam-184	209	7	0	0	NUM
ejpam-184	209	8	.	.	PUNCT
ejpam-184	210	1	this	this	PRON
ejpam-184	210	2	,	,	PUNCT
ejpam-184	210	3	in	in	ADP
ejpam-184	210	4	view	view	NOUN
ejpam-184	210	5	of	of	ADP
ejpam-184	210	6	second	second	ADJ
ejpam-184	210	7	-	-	PUNCT
ejpam-184	210	8	order	order	NOUN
ejpam-184	210	9	pseudoinvexity	pseudoinvexity	NOUN
ejpam-184	210	10	of	of	ADP
ejpam-184	210	11	∫	∫	PROPN
ejpam-184	211	1	i	i	PRON
ejpam-184	211	2	f	f	PROPN
ejpam-184	211	3	(	(	PUNCT
ejpam-184	211	4	t	t	PROPN
ejpam-184	211	5	,	,	PUNCT
ejpam-184	211	6	.	.	PUNCT
ejpam-184	211	7	,	,	PUNCT
ejpam-184	211	8	.)d	.)d	PROPN
ejpam-184	211	9	t	t	PROPN
ejpam-184	211	10	implies	imply	VERB
ejpam-184	211	11	∫	∫	PROPN
ejpam-184	212	1	i	i	PRON
ejpam-184	212	2	f	f	PROPN
ejpam-184	212	3	(	(	PUNCT
ejpam-184	212	4	t	t	PROPN
ejpam-184	212	5	,	,	PUNCT
ejpam-184	212	6	x	x	X
ejpam-184	212	7	,	,	PUNCT
ejpam-184	212	8	ẋ)d	ẋ)d	PROPN
ejpam-184	212	9	t	t	PROPN
ejpam-184	212	10	≥	≥	PROPN
ejpam-184	212	11	∫	∫	PROPN
ejpam-184	213	1	i	i	PRON
ejpam-184	213	2	�	�	PROPN
ejpam-184	214	1	f	f	PROPN
ejpam-184	214	2	(	(	PUNCT
ejpam-184	214	3	t	t	PROPN
ejpam-184	214	4	,	,	PUNCT
ejpam-184	214	5	u	u	PROPN
ejpam-184	214	6	,	,	PUNCT
ejpam-184	214	7	u̇)−	u̇)−	PROPN
ejpam-184	214	8	1	1	NUM
ejpam-184	214	9	2	2	NUM
ejpam-184	214	10	β(t)t	β(t)t	NOUN
ejpam-184	214	11	fβ(t	fβ(t	NOUN
ejpam-184	214	12	)	)	PUNCT
ejpam-184	214	13	�	�	PROPN
ejpam-184	215	1	d	d	PROPN
ejpam-184	215	2	t	t	PROPN
ejpam-184	215	3	.	.	PUNCT
ejpam-184	216	1	this	this	PRON
ejpam-184	216	2	implies	imply	VERB
ejpam-184	216	3	,	,	PUNCT
ejpam-184	216	4	infimum(cp	infimum(cp	NOUN
ejpam-184	216	5	)	)	PUNCT
ejpam-184	216	6	≥	≥	NOUN
ejpam-184	216	7	supremum(cd	supremum(cd	NOUN
ejpam-184	216	8	)	)	PUNCT
ejpam-184	216	9	.	.	PUNCT
ejpam-184	217	1	theorem	theorem	ADJ
ejpam-184	217	2	3.2	3.2	NUM
ejpam-184	217	3	(	(	PUNCT
ejpam-184	217	4	strong	strong	ADJ
ejpam-184	217	5	duality	duality	NOUN
ejpam-184	217	6	)	)	PUNCT
ejpam-184	217	7	.	.	PUNCT
ejpam-184	218	1	if	if	SCONJ
ejpam-184	218	2	x̄(t	x̄(t	NOUN
ejpam-184	218	3	)	)	PUNCT
ejpam-184	218	4	∈	∈	PROPN
ejpam-184	218	5	x	x	X
ejpam-184	218	6	is	be	AUX
ejpam-184	218	7	an	an	DET
ejpam-184	218	8	optimal	optimal	ADJ
ejpam-184	218	9	solution	solution	NOUN
ejpam-184	218	10	of	of	ADP
ejpam-184	218	11	(	(	PUNCT
ejpam-184	218	12	cp	cp	NOUN
ejpam-184	218	13	)	)	PUNCT
ejpam-184	218	14	and	and	CCONJ
ejpam-184	218	15	meets	meet	VERB
ejpam-184	218	16	the	the	DET
ejpam-184	218	17	normality	normality	NOUN
ejpam-184	218	18	conditions	condition	NOUN
ejpam-184	218	19	,	,	PUNCT
ejpam-184	218	20	then	then	ADV
ejpam-184	218	21	there	there	PRON
ejpam-184	218	22	exists	exist	VERB
ejpam-184	218	23	a	a	DET
ejpam-184	218	24	piece	piece	NOUN
ejpam-184	218	25	wise	wise	ADJ
ejpam-184	218	26	smooth	smooth	ADJ
ejpam-184	218	27	ȳ	ȳ	NOUN
ejpam-184	218	28	:	:	PUNCT
ejpam-184	218	29	r	r	X
ejpam-184	218	30	→	→	SYM
ejpam-184	218	31	rm	rm	NOUN
ejpam-184	218	32	such	such	ADJ
ejpam-184	218	33	that	that	PRON
ejpam-184	218	34	(	(	PUNCT
ejpam-184	218	35	x̄(t	x̄(t	PROPN
ejpam-184	218	36	)	)	PUNCT
ejpam-184	218	37	,	,	PUNCT
ejpam-184	218	38	ȳ(t),β(t	ȳ(t),β(t	NOUN
ejpam-184	218	39	)	)	PUNCT
ejpam-184	218	40	=	=	SYM
ejpam-184	219	1	0	0	X
ejpam-184	219	2	)	)	PUNCT
ejpam-184	219	3	is	be	AUX
ejpam-184	219	4	a	a	DET
ejpam-184	219	5	feasible	feasible	ADJ
ejpam-184	219	6	for	for	ADP
ejpam-184	219	7	(	(	PUNCT
ejpam-184	219	8	cd	cd	PROPN
ejpam-184	219	9	)	)	PUNCT
ejpam-184	219	10	and	and	CCONJ
ejpam-184	219	11	the	the	DET
ejpam-184	219	12	two	two	NUM
ejpam-184	219	13	objective	objective	ADJ
ejpam-184	219	14	values	value	NOUN
ejpam-184	219	15	are	be	AUX
ejpam-184	219	16	equal	equal	ADJ
ejpam-184	219	17	.	.	PUNCT
ejpam-184	220	1	furthermore	furthermore	ADV
ejpam-184	220	2	,	,	PUNCT
ejpam-184	220	3	if	if	SCONJ
ejpam-184	220	4	the	the	DET
ejpam-184	220	5	hypothesis	hypothesis	NOUN
ejpam-184	220	6	of	of	ADP
ejpam-184	220	7	theorem	theorem	ADJ
ejpam-184	220	8	1	1	NUM
ejpam-184	220	9	holds	hold	NOUN
ejpam-184	220	10	,	,	PUNCT
ejpam-184	220	11	then	then	ADV
ejpam-184	220	12	(	(	PUNCT
ejpam-184	220	13	x̄(t	x̄(t	PROPN
ejpam-184	220	14	)	)	PUNCT
ejpam-184	220	15	,	,	PUNCT
ejpam-184	220	16	ȳ(t),β(t	ȳ(t),β(t	NOUN
ejpam-184	220	17	)	)	PUNCT
ejpam-184	220	18	)	)	PUNCT
ejpam-184	220	19	is	be	AUX
ejpam-184	220	20	an	an	DET
ejpam-184	220	21	optimal	optimal	ADJ
ejpam-184	220	22	solution	solution	NOUN
ejpam-184	220	23	for	for	ADP
ejpam-184	220	24	(	(	PUNCT
ejpam-184	220	25	cd	cd	PROPN
ejpam-184	220	26	)	)	PUNCT
ejpam-184	220	27	.	.	PUNCT
ejpam-184	221	1	i.	i.	PROPN
ejpam-184	221	2	husain	husain	PROPN
ejpam-184	221	3	,	,	PUNCT
ejpam-184	221	4	a.	a.	PROPN
ejpam-184	221	5	ahmed	ahmed	PROPN
ejpam-184	221	6	,	,	PUNCT
ejpam-184	221	7	and	and	CCONJ
ejpam-184	221	8	m.	m.	NOUN
ejpam-184	221	9	massodi	massodi	PROPN
ejpam-184	221	10	/	/	SYM
ejpam-184	221	11	eur	eur	PROPN
ejpam-184	221	12	.	.	PUNCT
ejpam-184	222	1	j.	j.	PROPN
ejpam-184	222	2	pure	pure	PROPN
ejpam-184	222	3	appl	appl	PROPN
ejpam-184	222	4	.	.	PROPN
ejpam-184	222	5	math	math	PROPN
ejpam-184	222	6	,	,	PUNCT
ejpam-184	222	7	2	2	NUM
ejpam-184	222	8	(	(	PUNCT
ejpam-184	222	9	2009	2009	NUM
ejpam-184	222	10	)	)	PUNCT
ejpam-184	222	11	,	,	PUNCT
ejpam-184	222	12	(	(	PUNCT
ejpam-184	222	13	278	278	NUM
ejpam-184	222	14	-	-	SYM
ejpam-184	222	15	295	295	NUM
ejpam-184	222	16	)	)	PUNCT
ejpam-184	222	17	288	288	NUM
ejpam-184	222	18	proof	proof	NOUN
ejpam-184	222	19	.	.	PUNCT
ejpam-184	223	1	from	from	ADP
ejpam-184	223	2	proposition	proposition	NOUN
ejpam-184	223	3	1	1	NUM
ejpam-184	223	4	,	,	PUNCT
ejpam-184	223	5	there	there	PRON
ejpam-184	223	6	exists	exist	VERB
ejpam-184	223	7	a	a	DET
ejpam-184	223	8	piece	piece	NOUN
ejpam-184	223	9	wise	wise	ADJ
ejpam-184	223	10	smooth	smooth	ADJ
ejpam-184	223	11	function	function	NOUN
ejpam-184	223	12	ȳ	ȳ	NOUN
ejpam-184	223	13	:	:	PUNCT
ejpam-184	223	14	r→	r→	PROPN
ejpam-184	223	15	rm	rm	PROPN
ejpam-184	223	16	satisfying	satisfy	VERB
ejpam-184	223	17	the	the	DET
ejpam-184	223	18	following	follow	VERB
ejpam-184	223	19	conditions	condition	NOUN
ejpam-184	223	20	:	:	PUNCT
ejpam-184	223	21	(	(	PUNCT
ejpam-184	223	22	fx(t	fx(t	PUNCT
ejpam-184	223	23	,	,	PUNCT
ejpam-184	223	24	x̄	x̄	NOUN
ejpam-184	223	25	,	,	PUNCT
ejpam-184	223	26	˙̄x	˙̄x	PUNCT
ejpam-184	223	27	)	)	PUNCT
ejpam-184	223	28	+	+	CCONJ
ejpam-184	223	29	ȳ(t)t	ȳ(t)t	NOUN
ejpam-184	223	30	gx(t	gx(t	NOUN
ejpam-184	223	31	,	,	PUNCT
ejpam-184	223	32	x̄	x̄	NOUN
ejpam-184	223	33	,	,	PUNCT
ejpam-184	223	34	˙̄x))−	˙̄x))−	PROPN
ejpam-184	224	1	d	d	X
ejpam-184	224	2	(	(	PUNCT
ejpam-184	224	3	f	f	PROPN
ejpam-184	224	4	ẋ(t	ẋ(t	PROPN
ejpam-184	224	5	,	,	PUNCT
ejpam-184	224	6	x̄	x̄	NOUN
ejpam-184	224	7	,	,	PUNCT
ejpam-184	224	8	˙̄x	˙̄x	PUNCT
ejpam-184	224	9	)	)	PUNCT
ejpam-184	225	1	+	+	CCONJ
ejpam-184	225	2	ȳ(t)t	ȳ(t)t	NOUN
ejpam-184	225	3	g	g	PROPN
ejpam-184	225	4	ẋ(t	ẋ(t	PROPN
ejpam-184	225	5	,	,	PUNCT
ejpam-184	225	6	x̄	x̄	NOUN
ejpam-184	225	7	,	,	PUNCT
ejpam-184	225	8	˙̄x	˙̄x	NOUN
ejpam-184	225	9	)	)	PUNCT
ejpam-184	225	10	)	)	PUNCT
ejpam-184	226	1	=	=	PUNCT
ejpam-184	226	2	0	0	NUM
ejpam-184	226	3	,	,	PUNCT
ejpam-184	226	4	t	t	PROPN
ejpam-184	226	5	∈	∈	PROPN
ejpam-184	227	1	i	i	PRON
ejpam-184	227	2	i.e	i.e	PROPN
ejpam-184	227	3	,	,	PUNCT
ejpam-184	227	4	(	(	PUNCT
ejpam-184	227	5	fx(t	fx(t	PUNCT
ejpam-184	227	6	,	,	PUNCT
ejpam-184	227	7	x̄	x̄	NOUN
ejpam-184	227	8	,	,	PUNCT
ejpam-184	227	9	˙̄x	˙̄x	PUNCT
ejpam-184	227	10	)	)	PUNCT
ejpam-184	228	1	+	+	CCONJ
ejpam-184	228	2	ȳ(t)t	ȳ(t)t	NOUN
ejpam-184	228	3	gx(t	gx(t	NOUN
ejpam-184	228	4	,	,	PUNCT
ejpam-184	228	5	x̄	x̄	NOUN
ejpam-184	228	6	,	,	PUNCT
ejpam-184	228	7	˙̄x	˙̄x	PRON
ejpam-184	228	8	)	)	PUNCT
ejpam-184	228	9	)	)	PUNCT
ejpam-184	229	1	−d	−d	PROPN
ejpam-184	229	2	(	(	PUNCT
ejpam-184	229	3	f	f	PROPN
ejpam-184	229	4	ẋ(t	ẋ(t	PROPN
ejpam-184	229	5	,	,	PUNCT
ejpam-184	229	6	x̄	x̄	NOUN
ejpam-184	229	7	,	,	PUNCT
ejpam-184	229	8	˙̄x	˙̄x	PUNCT
ejpam-184	229	9	)	)	PUNCT
ejpam-184	230	1	+	+	CCONJ
ejpam-184	230	2	ȳ(t)t	ȳ(t)t	NOUN
ejpam-184	230	3	g	g	PROPN
ejpam-184	230	4	ẋ(t	ẋ(t	PROPN
ejpam-184	230	5	,	,	PUNCT
ejpam-184	230	6	x̄	x̄	NOUN
ejpam-184	230	7	,	,	PUNCT
ejpam-184	230	8	˙̄x	˙̄x	NOUN
ejpam-184	230	9	)	)	PUNCT
ejpam-184	230	10	)	)	PUNCT
ejpam-184	231	1	+	+	CCONJ
ejpam-184	231	2	(	(	PUNCT
ejpam-184	231	3	f	f	X
ejpam-184	231	4	+	+	CCONJ
ejpam-184	231	5	h)β(t	h)β(t	NOUN
ejpam-184	231	6	)	)	PUNCT
ejpam-184	231	7	=	=	SYM
ejpam-184	231	8	0	0	NUM
ejpam-184	231	9	,	,	PUNCT
ejpam-184	231	10	(	(	PUNCT
ejpam-184	231	11	3.7	3.7	NUM
ejpam-184	231	12	)	)	PUNCT
ejpam-184	231	13	where	where	SCONJ
ejpam-184	231	14	β(t	β(t	NOUN
ejpam-184	231	15	)	)	PUNCT
ejpam-184	232	1	=	=	PUNCT
ejpam-184	232	2	0	0	NUM
ejpam-184	232	3	,	,	PUNCT
ejpam-184	232	4	t	t	PROPN
ejpam-184	232	5	∈	∈	PROPN
ejpam-184	233	1	i	i	PRON
ejpam-184	233	2	ȳ(t)t	ȳ(t)t	PROPN
ejpam-184	233	3	g(t	g(t	PROPN
ejpam-184	233	4	,	,	PUNCT
ejpam-184	233	5	x̄	x̄	PROPN
ejpam-184	233	6	,	,	PUNCT
ejpam-184	233	7	˙̄x	˙̄x	PRON
ejpam-184	233	8	)	)	PUNCT
ejpam-184	234	1	=	=	SYM
ejpam-184	234	2	0	0	PUNCT
ejpam-184	235	1	i.e.	i.e.	X
ejpam-184	235	2	,	,	PUNCT
ejpam-184	235	3	∫	∫	PROPN
ejpam-184	235	4	i	i	PROPN
ejpam-184	235	5	{	{	PUNCT
ejpam-184	235	6	ȳ(t)t	ȳ(t)t	PROPN
ejpam-184	235	7	g(t	g(t	PROPN
ejpam-184	235	8	,	,	PUNCT
ejpam-184	235	9	x̄	x̄	PROPN
ejpam-184	235	10	,	,	PUNCT
ejpam-184	235	11	˙̄x)−	˙̄x)−	PROPN
ejpam-184	235	12	1	1	NUM
ejpam-184	235	13	2	2	NUM
ejpam-184	235	14	β(t)t	β(t)t	PUNCT
ejpam-184	235	15	hβ(t)}d	hβ(t)}d	PROPN
ejpam-184	235	16	t	t	NOUN
ejpam-184	235	17	=	=	SYM
ejpam-184	235	18	0	0	NUM
ejpam-184	235	19	,	,	PUNCT
ejpam-184	235	20	where	where	SCONJ
ejpam-184	235	21	β(t	β(t	NOUN
ejpam-184	235	22	)	)	PUNCT
ejpam-184	235	23	=	=	PUNCT
ejpam-184	235	24	0	0	NUM
ejpam-184	235	25	,	,	PUNCT
ejpam-184	235	26	t	t	PROPN
ejpam-184	235	27	∈	∈	PROPN
ejpam-184	235	28	i	i	PRON
ejpam-184	235	29	(	(	PUNCT
ejpam-184	235	30	3.8	3.8	NUM
ejpam-184	235	31	)	)	PUNCT
ejpam-184	235	32	ȳ(t)≥	ȳ(t)≥	X
ejpam-184	235	33	0	0	NUM
ejpam-184	235	34	,	,	PUNCT
ejpam-184	235	35	t	t	PROPN
ejpam-184	235	36	∈	∈	PROPN
ejpam-184	236	1	i	i	PRON
ejpam-184	236	2	(	(	PUNCT
ejpam-184	236	3	3.9	3.9	NUM
ejpam-184	236	4	)	)	PUNCT
ejpam-184	236	5	from	from	ADP
ejpam-184	236	6	(	(	PUNCT
ejpam-184	236	7	3.7	3.7	NUM
ejpam-184	236	8	)	)	PUNCT
ejpam-184	236	9	,	,	PUNCT
ejpam-184	236	10	(	(	PUNCT
ejpam-184	236	11	3.8	3.8	NUM
ejpam-184	236	12	)	)	PUNCT
ejpam-184	236	13	and	and	CCONJ
ejpam-184	236	14	(	(	PUNCT
ejpam-184	236	15	3.9	3.9	NUM
ejpam-184	236	16	)	)	PUNCT
ejpam-184	236	17	,	,	PUNCT
ejpam-184	236	18	it	it	PRON
ejpam-184	236	19	implies	imply	VERB
ejpam-184	236	20	that	that	SCONJ
ejpam-184	236	21	(	(	PUNCT
ejpam-184	236	22	x̄(t	x̄(t	NOUN
ejpam-184	236	23	)	)	PUNCT
ejpam-184	236	24	,	,	PUNCT
ejpam-184	236	25	ȳ(t),β(t	ȳ(t),β(t	NOUN
ejpam-184	236	26	)	)	PUNCT
ejpam-184	236	27	=	=	SYM
ejpam-184	237	1	0	0	X
ejpam-184	237	2	)	)	PUNCT
ejpam-184	237	3	is	be	AUX
ejpam-184	237	4	feasible	feasible	ADJ
ejpam-184	237	5	for	for	ADP
ejpam-184	237	6	(	(	PUNCT
ejpam-184	237	7	cd	cd	PROPN
ejpam-184	237	8	)	)	PUNCT
ejpam-184	237	9	and	and	CCONJ
ejpam-184	237	10	the	the	DET
ejpam-184	237	11	objective	objective	ADJ
ejpam-184	237	12	value	value	NOUN
ejpam-184	237	13	of	of	ADP
ejpam-184	237	14	(	(	PUNCT
ejpam-184	237	15	cp	cp	NOUN
ejpam-184	237	16	)	)	PUNCT
ejpam-184	237	17	and	and	CCONJ
ejpam-184	237	18	(	(	PUNCT
ejpam-184	237	19	cd	cd	PROPN
ejpam-184	237	20	)	)	PUNCT
ejpam-184	237	21	are	be	AUX
ejpam-184	237	22	equal	equal	ADJ
ejpam-184	237	23	.	.	PUNCT
ejpam-184	238	1	the	the	DET
ejpam-184	238	2	optimality	optimality	NOUN
ejpam-184	238	3	of	of	ADP
ejpam-184	238	4	(	(	PUNCT
ejpam-184	238	5	x̄(t	x̄(t	PROPN
ejpam-184	238	6	)	)	PUNCT
ejpam-184	238	7	,	,	PUNCT
ejpam-184	238	8	ȳ(t),β(t	ȳ(t),β(t	NOUN
ejpam-184	238	9	)	)	PUNCT
ejpam-184	238	10	)	)	PUNCT
ejpam-184	238	11	follows	follow	VERB
ejpam-184	238	12	by	by	ADP
ejpam-184	238	13	an	an	DET
ejpam-184	238	14	application	application	NOUN
ejpam-184	238	15	of	of	ADP
ejpam-184	238	16	theorem	theorem	ADJ
ejpam-184	238	17	1	1	NUM
ejpam-184	238	18	.	.	PUNCT
ejpam-184	238	19	theorem	theorem	VERB
ejpam-184	238	20	3.3	3.3	NUM
ejpam-184	238	21	(	(	PUNCT
ejpam-184	238	22	converse	converse	NOUN
ejpam-184	238	23	duality	duality	NOUN
ejpam-184	238	24	)	)	PUNCT
ejpam-184	238	25	.	.	PUNCT
ejpam-184	239	1	suppose	suppose	VERB
ejpam-184	239	2	that	that	SCONJ
ejpam-184	239	3	f	f	PROPN
ejpam-184	239	4	and	and	CCONJ
ejpam-184	239	5	g	g	PROPN
ejpam-184	239	6	are	be	AUX
ejpam-184	239	7	thrice	thrice	NOUN
ejpam-184	239	8	continuously	continuously	ADV
ejpam-184	239	9	differentiable	differentiable	ADJ
ejpam-184	239	10	.	.	PUNCT
ejpam-184	240	1	let	let	VERB
ejpam-184	240	2	(	(	PUNCT
ejpam-184	240	3	x̄(t	x̄(t	PROPN
ejpam-184	240	4	)	)	PUNCT
ejpam-184	240	5	,	,	PUNCT
ejpam-184	240	6	ȳ(t),β(t	ȳ(t),β(t	NOUN
ejpam-184	240	7	)	)	PUNCT
ejpam-184	240	8	)	)	PUNCT
ejpam-184	241	1	be	be	AUX
ejpam-184	241	2	an	an	DET
ejpam-184	241	3	optimal	optimal	ADJ
ejpam-184	241	4	solution	solution	NOUN
ejpam-184	241	5	of	of	ADP
ejpam-184	241	6	(	(	PUNCT
ejpam-184	241	7	cd	cd	PROPN
ejpam-184	241	8	)	)	PUNCT
ejpam-184	241	9	at	at	ADP
ejpam-184	241	10	which	which	PRON
ejpam-184	241	11	(	(	PUNCT
ejpam-184	241	12	a1	a1	NOUN
ejpam-184	241	13	):	):	PUNCT
ejpam-184	241	14	the	the	DET
ejpam-184	241	15	hessian	hessian	ADJ
ejpam-184	241	16	matrices	matrix	NOUN
ejpam-184	241	17	f	f	PROPN
ejpam-184	241	18	and	and	CCONJ
ejpam-184	241	19	h	h	NOUN
ejpam-184	241	20	are	be	AUX
ejpam-184	241	21	not	not	PART
ejpam-184	241	22	the	the	DET
ejpam-184	241	23	multiple	multiple	NOUN
ejpam-184	241	24	of	of	ADP
ejpam-184	241	25	each	each	DET
ejpam-184	241	26	other	other	ADJ
ejpam-184	241	27	.	.	PUNCT
ejpam-184	242	1	(	(	PUNCT
ejpam-184	242	2	a2	a2	PROPN
ejpam-184	242	3	):	):	PUNCT
ejpam-184	242	4	y(t)t	y(t)t	PROPN
ejpam-184	242	5	gx	gx	PROPN
ejpam-184	242	6	−	−	PROPN
ejpam-184	242	7	d	d	PROPN
ejpam-184	242	8	y(t)t	y(t)t	PROPN
ejpam-184	242	9	g	g	PROPN
ejpam-184	242	10	ẋ	ẋ	PROPN
ejpam-184	243	1	6=	6=	ADP
ejpam-184	243	2	0	0	NUM
ejpam-184	243	3	,	,	PUNCT
ejpam-184	243	4	(	(	PUNCT
ejpam-184	243	5	a3	a3	NOUN
ejpam-184	243	6	):	):	PUNCT
ejpam-184	243	7	(	(	PUNCT
ejpam-184	243	8	i	i	NOUN
ejpam-184	243	9	)	)	PUNCT
ejpam-184	243	10	∫	∫	PROPN
ejpam-184	244	1	i	i	PRON
ejpam-184	244	2	β(t)t(y(t)t	β(t)t(y(t)t	PUNCT
ejpam-184	244	3	gx	gx	PROPN
ejpam-184	244	4	−	−	PROPN
ejpam-184	244	5	d	d	PROPN
ejpam-184	244	6	y(t)t	y(t)t	PROPN
ejpam-184	244	7	g	g	PROPN
ejpam-184	244	8	ẋ)d	ẋ)d	PROPN
ejpam-184	244	9	t	t	PROPN
ejpam-184	244	10	≥	≥	PROPN
ejpam-184	244	11	0	0	NUM
ejpam-184	244	12	and	and	CCONJ
ejpam-184	244	13	∫	∫	PROPN
ejpam-184	245	1	i	i	PRON
ejpam-184	245	2	β(t)t	β(t)t	PROPN
ejpam-184	246	1	hβ(t)d	hβ(t)d	X
ejpam-184	246	2	t	t	X
ejpam-184	246	3	>	>	X
ejpam-184	246	4	0	0	PROPN
ejpam-184	246	5	or	or	CCONJ
ejpam-184	246	6	i.	i.	PROPN
ejpam-184	246	7	husain	husain	PROPN
ejpam-184	246	8	,	,	PUNCT
ejpam-184	246	9	a.	a.	PROPN
ejpam-184	246	10	ahmed	ahmed	PROPN
ejpam-184	246	11	,	,	PUNCT
ejpam-184	246	12	and	and	CCONJ
ejpam-184	246	13	m.	m.	NOUN
ejpam-184	246	14	massodi	massodi	PROPN
ejpam-184	246	15	/	/	SYM
ejpam-184	246	16	eur	eur	PROPN
ejpam-184	246	17	.	.	PUNCT
ejpam-184	247	1	j.	j.	PROPN
ejpam-184	247	2	pure	pure	PROPN
ejpam-184	247	3	appl	appl	PROPN
ejpam-184	247	4	.	.	PROPN
ejpam-184	247	5	math	math	PROPN
ejpam-184	247	6	,	,	PUNCT
ejpam-184	247	7	2	2	NUM
ejpam-184	247	8	(	(	PUNCT
ejpam-184	247	9	2009	2009	NUM
ejpam-184	247	10	)	)	PUNCT
ejpam-184	247	11	,	,	PUNCT
ejpam-184	247	12	(	(	PUNCT
ejpam-184	247	13	278	278	NUM
ejpam-184	247	14	-	-	SYM
ejpam-184	247	15	295	295	NUM
ejpam-184	247	16	)	)	PUNCT
ejpam-184	247	17	289	289	NUM
ejpam-184	247	18	(	(	PUNCT
ejpam-184	247	19	ii	ii	NOUN
ejpam-184	247	20	)	)	PUNCT
ejpam-184	247	21	∫	∫	PROPN
ejpam-184	248	1	i	i	PRON
ejpam-184	248	2	β(t)t(y(t)t	β(t)t(y(t)t	PUNCT
ejpam-184	248	3	gx	gx	PROPN
ejpam-184	248	4	−	−	PROPN
ejpam-184	248	5	d	d	PROPN
ejpam-184	248	6	y(t)t	y(t)t	PROPN
ejpam-184	248	7	g	g	PROPN
ejpam-184	248	8	ẋ)d	ẋ)d	NOUN
ejpam-184	248	9	t	t	PROPN
ejpam-184	248	10	≤	≤	NOUN
ejpam-184	248	11	0	0	PUNCT
ejpam-184	249	1	and	and	CCONJ
ejpam-184	249	2	∫	∫	PROPN
ejpam-184	250	1	i	i	PRON
ejpam-184	250	2	β(t)t	β(t)t	PROPN
ejpam-184	251	1	hβ(t)d	hβ(t)d	X
ejpam-184	251	2	t	t	X
ejpam-184	251	3	<	<	X
ejpam-184	251	4	0	0	PUNCT
ejpam-184	252	1	if	if	SCONJ
ejpam-184	252	2	,	,	PUNCT
ejpam-184	252	3	for	for	ADP
ejpam-184	252	4	all	all	PRON
ejpam-184	252	5	feasible	feasible	ADJ
ejpam-184	252	6	(	(	PUNCT
ejpam-184	252	7	x(t	x(t	PROPN
ejpam-184	252	8	)	)	PUNCT
ejpam-184	252	9	,	,	PUNCT
ejpam-184	252	10	y(t),β(t	y(t),β(t	NOUN
ejpam-184	252	11	)	)	PUNCT
ejpam-184	252	12	)	)	PUNCT
ejpam-184	252	13	,	,	PUNCT
ejpam-184	252	14	∫	∫	PROPN
ejpam-184	253	1	i	i	PRON
ejpam-184	253	2	f	f	PROPN
ejpam-184	253	3	(	(	PUNCT
ejpam-184	253	4	t	t	PROPN
ejpam-184	253	5	,	,	PUNCT
ejpam-184	253	6	.	.	PUNCT
ejpam-184	253	7	,	,	PUNCT
ejpam-184	254	1	.)d	.)d	PROPN
ejpam-184	254	2	t	t	PROPN
ejpam-184	254	3	be	be	AUX
ejpam-184	254	4	second	second	ADJ
ejpam-184	254	5	order	order	NOUN
ejpam-184	254	6	pseudoinvex	pseudoinvex	NOUN
ejpam-184	254	7	and	and	CCONJ
ejpam-184	254	8	∫	∫	PROPN
ejpam-184	255	1	i	i	PROPN
ejpam-184	255	2	y(t)t	y(t)t	PROPN
ejpam-184	255	3	g(t	g(t	PROPN
ejpam-184	255	4	,	,	PUNCT
ejpam-184	255	5	.	.	PUNCT
ejpam-184	255	6	,	,	PUNCT
ejpam-184	256	1	.)d	.)d	PROPN
ejpam-184	256	2	t	t	PROPN
ejpam-184	256	3	be	be	AUX
ejpam-184	256	4	second	second	ADJ
ejpam-184	256	5	-	-	PUNCT
ejpam-184	256	6	order	order	NOUN
ejpam-184	256	7	quasi	quasi	NOUN
ejpam-184	256	8	-	-	NOUN
ejpam-184	256	9	invex	invex	ADJ
ejpam-184	256	10	with	with	ADP
ejpam-184	256	11	respect	respect	NOUN
ejpam-184	256	12	to	to	ADP
ejpam-184	256	13	the	the	DET
ejpam-184	256	14	same	same	ADJ
ejpam-184	256	15	η	η	PROPN
ejpam-184	256	16	,	,	PUNCT
ejpam-184	256	17	then	then	ADV
ejpam-184	256	18	x̄(t	x̄(t	NUM
ejpam-184	256	19	)	)	PUNCT
ejpam-184	257	1	is	be	AUX
ejpam-184	257	2	an	an	DET
ejpam-184	257	3	optimal	optimal	ADJ
ejpam-184	257	4	solution	solution	NOUN
ejpam-184	257	5	of	of	ADP
ejpam-184	257	6	(	(	PUNCT
ejpam-184	257	7	p	p	NOUN
ejpam-184	257	8	)	)	PUNCT
ejpam-184	257	9	.	.	PUNCT
ejpam-184	258	1	proof	proof	NOUN
ejpam-184	258	2	.	.	PUNCT
ejpam-184	259	1	since	since	SCONJ
ejpam-184	259	2	(	(	PUNCT
ejpam-184	259	3	x̄(t	x̄(t	PROPN
ejpam-184	259	4	)	)	PUNCT
ejpam-184	259	5	,	,	PUNCT
ejpam-184	259	6	ȳ(t),β(t	ȳ(t),β(t	NOUN
ejpam-184	259	7	)	)	PUNCT
ejpam-184	259	8	)	)	PUNCT
ejpam-184	259	9	is	be	AUX
ejpam-184	259	10	an	an	DET
ejpam-184	259	11	optimal	optimal	ADJ
ejpam-184	259	12	solution	solution	NOUN
ejpam-184	259	13	for	for	ADP
ejpam-184	259	14	(	(	PUNCT
ejpam-184	259	15	cd	cd	PROPN
ejpam-184	259	16	)	)	PUNCT
ejpam-184	259	17	,	,	PUNCT
ejpam-184	259	18	by	by	ADP
ejpam-184	259	19	proposition	proposition	NOUN
ejpam-184	259	20	1	1	NUM
ejpam-184	259	21	,	,	PUNCT
ejpam-184	259	22	there	there	PRON
ejpam-184	259	23	exist	exist	VERB
ejpam-184	259	24	lagrange	lagrange	NOUN
ejpam-184	259	25	multiplier	multiplier	ADV
ejpam-184	259	26	α	α	NOUN
ejpam-184	259	27	∈	∈	PROPN
ejpam-184	259	28	r	r	NOUN
ejpam-184	259	29	,	,	PUNCT
ejpam-184	259	30	and	and	CCONJ
ejpam-184	260	1	piece	piece	NOUN
ejpam-184	260	2	wise	wise	ADJ
ejpam-184	260	3	smooth	smooth	ADJ
ejpam-184	260	4	λ	λ	NOUN
ejpam-184	260	5	:	:	PUNCT
ejpam-184	260	6	i	i	PROPN
ejpam-184	260	7	→	→	SYM
ejpam-184	260	8	rn	rn	PROPN
ejpam-184	260	9	,	,	PUNCT
ejpam-184	260	10	γ	γ	PROPN
ejpam-184	260	11	∈	∈	NOUN
ejpam-184	260	12	r	r	NOUN
ejpam-184	260	13	and	and	CCONJ
ejpam-184	260	14	µ	µ	NOUN
ejpam-184	260	15	:	:	PUNCT
ejpam-184	260	16	i	i	PROPN
ejpam-184	260	17	→	→	SYM
ejpam-184	260	18	rm	rm	PROPN
ejpam-184	260	19	such	such	ADJ
ejpam-184	260	20	that	that	SCONJ
ejpam-184	260	21	fritz	fritz	PROPN
ejpam-184	260	22	-	-	PUNCT
ejpam-184	260	23	john	john	PROPN
ejpam-184	260	24	conditions	condition	NOUN
ejpam-184	260	25	hold	hold	VERB
ejpam-184	260	26	at	at	ADP
ejpam-184	260	27	�	�	PROPN
ejpam-184	260	28	x̄	x̄	PROPN
ejpam-184	260	29	(	(	PUNCT
ejpam-184	260	30	t	t	PROPN
ejpam-184	260	31	)	)	PUNCT
ejpam-184	260	32	,	,	PUNCT
ejpam-184	260	33	ȳ	ȳ	PROPN
ejpam-184	260	34	(	(	PUNCT
ejpam-184	260	35	t	t	PROPN
ejpam-184	260	36	)	)	PUNCT
ejpam-184	260	37	,	,	PUNCT
ejpam-184	260	38	β	β	X
ejpam-184	260	39	(	(	PUNCT
ejpam-184	260	40	t	t	PROPN
ejpam-184	260	41	)	)	PUNCT
ejpam-184	260	42	�	�	PROPN
ejpam-184	260	43	:	:	PUNCT
ejpam-184	260	44	−α	−α	PROPN
ejpam-184	260	45	�	�	PROPN
ejpam-184	260	46	�	�	PROPN
ejpam-184	260	47	fx	fx	PROPN
ejpam-184	260	48	−	−	PROPN
ejpam-184	260	49	1	1	NUM
ejpam-184	260	50	2	2	NUM
ejpam-184	260	51	(	(	PUNCT
ejpam-184	260	52	β(t)t	β(t)t	PROPN
ejpam-184	260	53	fβ(t))x	fβ(t))x	PROPN
ejpam-184	260	54	�	�	PROPN
ejpam-184	260	55	−	−	PROPN
ejpam-184	261	1	d	d	PROPN
ejpam-184	261	2	�	�	PROPN
ejpam-184	261	3	f	f	PROPN
ejpam-184	261	4	ẋ	ẋ	PROPN
ejpam-184	262	1	−	−	NOUN
ejpam-184	262	2	1	1	NUM
ejpam-184	262	3	2	2	NUM
ejpam-184	262	4	(	(	PUNCT
ejpam-184	262	5	β(t)t	β(t)t	X
ejpam-184	262	6	fβ(t	fβ(t	NOUN
ejpam-184	262	7	)	)	PUNCT
ejpam-184	262	8	)	)	PUNCT
ejpam-184	263	1	ẋ	ẋ	PROPN
ejpam-184	263	2	�	�	PROPN
ejpam-184	263	3	�	�	PROPN
ejpam-184	263	4	+	+	PROPN
ejpam-184	263	5	λ(t)t	λ(t)t	NOUN
ejpam-184	263	6	n	n	PRON
ejpam-184	263	7	fx	fx	NOUN
ejpam-184	263	8	x	x	PUNCT
ejpam-184	264	1	+	+	CCONJ
ejpam-184	264	2	(	(	PUNCT
ejpam-184	264	3	y(t	y(t	PROPN
ejpam-184	264	4	)	)	PUNCT
ejpam-184	264	5	t	t	NOUN
ejpam-184	264	6	gx)x	gx)x	INTJ
ejpam-184	265	1	−	−	PROPN
ejpam-184	266	1	d	d	X
ejpam-184	266	2	(	(	PUNCT
ejpam-184	266	3	f	f	PROPN
ejpam-184	266	4	ẋ	ẋ	PROPN
ejpam-184	266	5	x	x	PUNCT
ejpam-184	267	1	+	+	PUNCT
ejpam-184	267	2	(	(	PUNCT
ejpam-184	267	3	y(t	y(t	PROPN
ejpam-184	267	4	)	)	PUNCT
ejpam-184	267	5	t	t	PROPN
ejpam-184	267	6	g	g	PROPN
ejpam-184	267	7	ẋ)x	ẋ)x	NOUN
ejpam-184	267	8	)	)	PUNCT
ejpam-184	268	1	+	+	CCONJ
ejpam-184	268	2	(	(	PUNCT
ejpam-184	268	3	(	(	PUNCT
ejpam-184	268	4	f	f	PROPN
ejpam-184	268	5	+	+	ADJ
ejpam-184	268	6	h)β(t))x	h)β(t))x	PROPN
ejpam-184	268	7	−d	−d	PROPN
ejpam-184	268	8	(	(	PUNCT
ejpam-184	268	9	fx	fx	PROPN
ejpam-184	268	10	ẋ	ẋ	PROPN
ejpam-184	269	1	+	+	CCONJ
ejpam-184	269	2	(	(	PUNCT
ejpam-184	269	3	y(t	y(t	PROPN
ejpam-184	269	4	)	)	PUNCT
ejpam-184	269	5	t	t	PROPN
ejpam-184	269	6	gx	gx	PROPN
ejpam-184	269	7	)	)	PUNCT
ejpam-184	269	8	ẋ)−	ẋ)−	PROPN
ejpam-184	270	1	(	(	PUNCT
ejpam-184	270	2	f	f	PROPN
ejpam-184	270	3	ẋ	ẋ	PROPN
ejpam-184	270	4	ẋ	ẋ	PROPN
ejpam-184	271	1	+	+	CCONJ
ejpam-184	271	2	(	(	PUNCT
ejpam-184	271	3	y(t	y(t	PROPN
ejpam-184	271	4	)	)	PUNCT
ejpam-184	271	5	t	t	PROPN
ejpam-184	271	6	g	g	PROPN
ejpam-184	271	7	ẋ	ẋ	PROPN
ejpam-184	271	8	)	)	PUNCT
ejpam-184	271	9	ẋ	ẋ	PROPN
ejpam-184	271	10	)	)	PUNCT
ejpam-184	272	1	+	+	CCONJ
ejpam-184	272	2	(	(	PUNCT
ejpam-184	272	3	(	(	PUNCT
ejpam-184	272	4	f	f	X
ejpam-184	272	5	+	+	NOUN
ejpam-184	272	6	h)β(t	h)β(t	NOUN
ejpam-184	272	7	)	)	PUNCT
ejpam-184	272	8	)	)	PUNCT
ejpam-184	273	1	ẋ	ẋ	PROPN
ejpam-184	274	1	o	o	NOUN
ejpam-184	274	2	γ	γ	PROPN
ejpam-184	274	3	�	�	PROPN
ejpam-184	274	4	y(t)t	y(t)t	PROPN
ejpam-184	274	5	gx	gx	PROPN
ejpam-184	274	6	−	−	PROPN
ejpam-184	274	7	1	1	NUM
ejpam-184	274	8	2	2	NUM
ejpam-184	274	9	(	(	PUNCT
ejpam-184	274	10	β(t)t	β(t)t	PROPN
ejpam-184	274	11	fβ(t))x	fβ(t))x	PROPN
ejpam-184	274	12	−d(y(t)t	−d(y(t)t	X
ejpam-184	274	13	g	g	PROPN
ejpam-184	274	14	ẋ	ẋ	PROPN
ejpam-184	275	1	−	−	NOUN
ejpam-184	275	2	1	1	NUM
ejpam-184	275	3	2	2	NUM
ejpam-184	275	4	(	(	PUNCT
ejpam-184	275	5	β(t)t	β(t)t	X
ejpam-184	275	6	fβ(t	fβ(t	NOUN
ejpam-184	275	7	)	)	PUNCT
ejpam-184	275	8	)	)	PUNCT
ejpam-184	275	9	ẋ	ẋ	X
ejpam-184	275	10	)	)	PUNCT
ejpam-184	275	11	�	�	PROPN
ejpam-184	275	12	=	=	SYM
ejpam-184	275	13	0	0	PROPN
ejpam-184	275	14	,	,	PUNCT
ejpam-184	275	15	t	t	PROPN
ejpam-184	275	16	∈	∈	PROPN
ejpam-184	276	1	i	i	PRON
ejpam-184	276	2	,	,	PUNCT
ejpam-184	276	3	(	(	PUNCT
ejpam-184	276	4	3.10	3.10	NUM
ejpam-184	276	5	)	)	PUNCT
ejpam-184	276	6	(	(	PUNCT
ejpam-184	276	7	λ(t	λ(t	X
ejpam-184	276	8	)	)	PUNCT
ejpam-184	277	1	+	+	NOUN
ejpam-184	277	2	αβ(t))f	αβ(t))f	X
ejpam-184	278	1	+	+	CCONJ
ejpam-184	278	2	(	(	PUNCT
ejpam-184	278	3	λ(t	λ(t	NOUN
ejpam-184	278	4	)	)	PUNCT
ejpam-184	278	5	+	+	CCONJ
ejpam-184	278	6	γβ(t))h	γβ(t))h	X
ejpam-184	278	7	=	=	SYM
ejpam-184	278	8	0	0	PROPN
ejpam-184	278	9	,	,	PUNCT
ejpam-184	278	10	t	t	PROPN
ejpam-184	278	11	∈	∈	PROPN
ejpam-184	279	1	i	i	PRON
ejpam-184	279	2	(	(	PUNCT
ejpam-184	279	3	3.11	3.11	NUM
ejpam-184	279	4	)	)	PUNCT
ejpam-184	279	5	λ(t)t	λ(t)t	PROPN
ejpam-184	279	6	�	�	PROPN
ejpam-184	279	7	g	g	PROPN
ejpam-184	279	8	j	j	PROPN
ejpam-184	279	9	x	x	PUNCT
ejpam-184	279	10	−	−	PROPN
ejpam-184	279	11	dg	dg	VERB
ejpam-184	279	12	j	j	PROPN
ejpam-184	279	13	ẋ	ẋ	PROPN
ejpam-184	280	1	+	+	CCONJ
ejpam-184	280	2	(	(	PUNCT
ejpam-184	280	3	g	g	PROPN
ejpam-184	280	4	j	j	PROPN
ejpam-184	280	5	x	x	X
ejpam-184	280	6	x	x	X
ejpam-184	280	7	−	−	PROPN
ejpam-184	280	8	dg	dg	VERB
ejpam-184	280	9	j	j	PROPN
ejpam-184	280	10	x	x	SYM
ejpam-184	280	11	ẋ	ẋ	PROPN
ejpam-184	281	1	+	+	CCONJ
ejpam-184	281	2	d2	d2	PROPN
ejpam-184	281	3	g	g	PROPN
ejpam-184	281	4	ẋ	ẋ	PROPN
ejpam-184	281	5	ẋ)β(t	ẋ)β(t	PROPN
ejpam-184	281	6	)	)	PUNCT
ejpam-184	281	7	�	�	PROPN
ejpam-184	282	1	+	+	PROPN
ejpam-184	282	2	γ	γ	X
ejpam-184	282	3	�	�	PROPN
ejpam-184	282	4	g	g	PROPN
ejpam-184	282	5	j	j	PROPN
ejpam-184	282	6	+	+	CCONJ
ejpam-184	282	7	1	1	NUM
ejpam-184	282	8	2	2	NUM
ejpam-184	282	9	β(t)t(g	β(t)t(g	NOUN
ejpam-184	282	10	j	j	PROPN
ejpam-184	282	11	x	x	PUNCT
ejpam-184	282	12	x	x	X
ejpam-184	282	13	−	−	PROPN
ejpam-184	282	14	dg	dg	VERB
ejpam-184	283	1	j	j	PROPN
ejpam-184	283	2	x	x	SYM
ejpam-184	283	3	ẋ	ẋ	PROPN
ejpam-184	284	1	+	+	CCONJ
ejpam-184	284	2	d2	d2	PROPN
ejpam-184	284	3	g	g	PROPN
ejpam-184	284	4	ẋ	ẋ	PROPN
ejpam-184	284	5	ẋ)β(t	ẋ)β(t	PROPN
ejpam-184	284	6	)	)	PUNCT
ejpam-184	284	7	�	�	PROPN
ejpam-184	285	1	+	+	PROPN
ejpam-184	285	2	µ	µ	X
ejpam-184	285	3	j(t	j(t	PROPN
ejpam-184	285	4	)	)	PUNCT
ejpam-184	285	5	=	=	SYM
ejpam-184	285	6	0	0	NUM
ejpam-184	286	1	,	,	PUNCT
ejpam-184	286	2	t	t	PROPN
ejpam-184	286	3	∈	∈	PROPN
ejpam-184	286	4	i	i	PRON
ejpam-184	286	5	(	(	PUNCT
ejpam-184	286	6	3.12	3.12	NUM
ejpam-184	286	7	)	)	PUNCT
ejpam-184	286	8	(	(	PUNCT
ejpam-184	286	9	fx	fx	ADP
ejpam-184	286	10	+	+	CCONJ
ejpam-184	286	11	y(t)t	y(t)t	NOUN
ejpam-184	286	12	g	g	NOUN
ejpam-184	287	1	ẋ)−	ẋ)−	PROPN
ejpam-184	287	2	d	d	PROPN
ejpam-184	287	3	(	(	PUNCT
ejpam-184	287	4	f	f	PROPN
ejpam-184	287	5	ẋ	ẋ	PROPN
ejpam-184	288	1	+	+	NUM
ejpam-184	288	2	y(t)t	y(t)t	PROPN
ejpam-184	288	3	g	g	PROPN
ejpam-184	288	4	ẋ	ẋ	PROPN
ejpam-184	288	5	)	)	PUNCT
ejpam-184	289	1	+	+	CCONJ
ejpam-184	289	2	(	(	PUNCT
ejpam-184	289	3	f	f	X
ejpam-184	289	4	+	+	NOUN
ejpam-184	289	5	h)β(t	h)β(t	NOUN
ejpam-184	289	6	)	)	PUNCT
ejpam-184	289	7	=	=	SYM
ejpam-184	289	8	0	0	NUM
ejpam-184	289	9	,	,	PUNCT
ejpam-184	289	10	t	t	PROPN
ejpam-184	289	11	∈	∈	PROPN
ejpam-184	290	1	i	i	PRON
ejpam-184	290	2	(	(	PUNCT
ejpam-184	290	3	3.13	3.13	NUM
ejpam-184	290	4	)	)	PUNCT
ejpam-184	290	5	γ	γ	PROPN
ejpam-184	290	6	∫	∫	PROPN
ejpam-184	290	7	i	i	PROPN
ejpam-184	290	8	�	�	PROPN
ejpam-184	290	9	y(t)t	y(t)t	PROPN
ejpam-184	290	10	g	g	NOUN
ejpam-184	290	11	−	−	PROPN
ejpam-184	290	12	1	1	NUM
ejpam-184	290	13	2	2	NUM
ejpam-184	290	14	β(t)hβ(t	β(t)hβ(t	NOUN
ejpam-184	290	15	)	)	PUNCT
ejpam-184	290	16	�	�	PROPN
ejpam-184	291	1	d	d	NOUN
ejpam-184	291	2	t	t	PROPN
ejpam-184	291	3	=	=	SYM
ejpam-184	291	4	0	0	NUM
ejpam-184	291	5	,	,	PUNCT
ejpam-184	291	6	t	t	PROPN
ejpam-184	291	7	∈	∈	PROPN
ejpam-184	292	1	i	i	PRON
ejpam-184	292	2	(	(	PUNCT
ejpam-184	292	3	3.14	3.14	NUM
ejpam-184	292	4	)	)	PUNCT
ejpam-184	292	5	µt	µt	PROPN
ejpam-184	292	6	(	(	PUNCT
ejpam-184	292	7	t	t	NOUN
ejpam-184	292	8	)	)	PUNCT
ejpam-184	292	9	ȳ(t	ȳ(t	NOUN
ejpam-184	292	10	)	)	PUNCT
ejpam-184	292	11	=	=	SYM
ejpam-184	292	12	0	0	NUM
ejpam-184	292	13	,	,	PUNCT
ejpam-184	292	14	t	t	PROPN
ejpam-184	292	15	∈	∈	PROPN
ejpam-184	293	1	i	i	PRON
ejpam-184	293	2	(	(	PUNCT
ejpam-184	293	3	3.15	3.15	NUM
ejpam-184	293	4	)	)	PUNCT
ejpam-184	293	5	(	(	PUNCT
ejpam-184	293	6	α	α	X
ejpam-184	293	7	,	,	PUNCT
ejpam-184	293	8	γ,µ(t	γ,µ(t	NUM
ejpam-184	293	9	)	)	PUNCT
ejpam-184	293	10	)	)	PUNCT
ejpam-184	293	11	≥	≥	NOUN
ejpam-184	293	12	0	0	NUM
ejpam-184	293	13	,	,	PUNCT
ejpam-184	293	14	t	t	PROPN
ejpam-184	293	15	∈	∈	PROPN
ejpam-184	294	1	i	i	PRON
ejpam-184	294	2	(	(	PUNCT
ejpam-184	294	3	3.16	3.16	NUM
ejpam-184	294	4	)	)	PUNCT
ejpam-184	294	5	i.	i.	NOUN
ejpam-184	294	6	husain	husain	PROPN
ejpam-184	294	7	,	,	PUNCT
ejpam-184	294	8	a.	a.	PROPN
ejpam-184	294	9	ahmed	ahmed	PROPN
ejpam-184	294	10	,	,	PUNCT
ejpam-184	294	11	and	and	CCONJ
ejpam-184	294	12	m.	m.	NOUN
ejpam-184	294	13	massodi	massodi	PROPN
ejpam-184	294	14	/	/	SYM
ejpam-184	294	15	eur	eur	PROPN
ejpam-184	294	16	.	.	PUNCT
ejpam-184	295	1	j.	j.	PROPN
ejpam-184	295	2	pure	pure	PROPN
ejpam-184	295	3	appl	appl	PROPN
ejpam-184	295	4	.	.	PROPN
ejpam-184	295	5	math	math	PROPN
ejpam-184	295	6	,	,	PUNCT
ejpam-184	295	7	2	2	NUM
ejpam-184	295	8	(	(	PUNCT
ejpam-184	295	9	2009	2009	NUM
ejpam-184	295	10	)	)	PUNCT
ejpam-184	295	11	,	,	PUNCT
ejpam-184	295	12	(	(	PUNCT
ejpam-184	295	13	278	278	NUM
ejpam-184	295	14	-	-	SYM
ejpam-184	295	15	295	295	NUM
ejpam-184	295	16	)	)	PUNCT
ejpam-184	295	17	290	290	NUM
ejpam-184	295	18	(	(	PUNCT
ejpam-184	295	19	α	α	NOUN
ejpam-184	295	20	,	,	PUNCT
ejpam-184	295	21	γ	γ	X
ejpam-184	295	22	,	,	PUNCT
ejpam-184	295	23	λ(t),µ(t	λ(t),µ(t	PROPN
ejpam-184	295	24	)	)	PUNCT
ejpam-184	295	25	)	)	PUNCT
ejpam-184	296	1	6=	6=	ADP
ejpam-184	296	2	0	0	NUM
ejpam-184	296	3	,	,	PUNCT
ejpam-184	296	4	t	t	PROPN
ejpam-184	296	5	∈	∈	PROPN
ejpam-184	296	6	i	i	PRON
ejpam-184	296	7	(	(	PUNCT
ejpam-184	296	8	3.17	3.17	NUM
ejpam-184	296	9	)	)	PUNCT
ejpam-184	296	10	in	in	ADP
ejpam-184	296	11	view	view	NOUN
ejpam-184	296	12	of	of	ADP
ejpam-184	296	13	hypothesis	hypothesis	NOUN
ejpam-184	296	14	(	(	PUNCT
ejpam-184	296	15	a1	a1	PROPN
ejpam-184	296	16	)	)	PUNCT
ejpam-184	296	17	,	,	PUNCT
ejpam-184	296	18	the	the	DET
ejpam-184	296	19	equation	equation	NOUN
ejpam-184	296	20	(	(	PUNCT
ejpam-184	296	21	3.11	3.11	NUM
ejpam-184	296	22	)	)	PUNCT
ejpam-184	296	23	yields	yield	NOUN
ejpam-184	296	24	,	,	PUNCT
ejpam-184	296	25	λ(t	λ(t	PRON
ejpam-184	296	26	)	)	PUNCT
ejpam-184	296	27	+	+	NOUN
ejpam-184	296	28	αβ(t	αβ(t	X
ejpam-184	296	29	)	)	PUNCT
ejpam-184	296	30	=	=	SYM
ejpam-184	296	31	0	0	NUM
ejpam-184	296	32	,	,	PUNCT
ejpam-184	296	33	t	t	PROPN
ejpam-184	296	34	∈	∈	PROPN
ejpam-184	297	1	i	i	PRON
ejpam-184	297	2	λ(t	λ(t	NOUN
ejpam-184	297	3	)	)	PUNCT
ejpam-184	297	4	+	+	SYM
ejpam-184	297	5	γβ(t	γβ(t	X
ejpam-184	297	6	)	)	PUNCT
ejpam-184	297	7	=	=	SYM
ejpam-184	297	8	0	0	NUM
ejpam-184	297	9	,	,	PUNCT
ejpam-184	297	10	t	t	PROPN
ejpam-184	297	11	∈	∈	PROPN
ejpam-184	298	1	i	i	PRON
ejpam-184	298	2			PROPN
ejpam-184	298	3			PROPN
ejpam-184	298	4			NOUN
ejpam-184	298	5	(	(	PUNCT
ejpam-184	298	6	3.18	3.18	NUM
ejpam-184	298	7	)	)	PUNCT
ejpam-184	298	8	multiplying	multiplying	NOUN
ejpam-184	298	9	(	(	PUNCT
ejpam-184	298	10	3.12	3.12	NUM
ejpam-184	298	11	)	)	PUNCT
ejpam-184	298	12	by	by	ADP
ejpam-184	298	13	y	y	PROPN
ejpam-184	298	14	j(t	j(t	PROPN
ejpam-184	298	15	)	)	PUNCT
ejpam-184	298	16	and	and	CCONJ
ejpam-184	298	17	summing	sum	VERB
ejpam-184	298	18	over	over	ADP
ejpam-184	298	19	j	j	PROPN
ejpam-184	298	20	,	,	PUNCT
ejpam-184	298	21	we	we	PRON
ejpam-184	298	22	have	have	VERB
ejpam-184	298	23	λ(t)t	λ(t)t	PROPN
ejpam-184	298	24	h	h	PROPN
ejpam-184	298	25	y(t)t	y(t)t	PROPN
ejpam-184	298	26	gx	gx	PROPN
ejpam-184	299	1	−	−	PROPN
ejpam-184	299	2	d(y(t)t	d(y(t)t	PROPN
ejpam-184	299	3	g	g	PROPN
ejpam-184	299	4	ẋ	ẋ	PROPN
ejpam-184	299	5	)	)	PUNCT
ejpam-184	300	1	+	+	CCONJ
ejpam-184	300	2	(	(	PUNCT
ejpam-184	300	3	(	(	PUNCT
ejpam-184	300	4	y(t	y(t	NOUN
ejpam-184	300	5	)	)	PUNCT
ejpam-184	300	6	t	t	NOUN
ejpam-184	300	7	gx)x	gx)x	PROPN
ejpam-184	300	8	−	−	PROPN
ejpam-184	300	9	d(y(t)t	d(y(t)t	PROPN
ejpam-184	300	10	gx	gx	PROPN
ejpam-184	300	11	)	)	PUNCT
ejpam-184	300	12	ẋ	ẋ	PROPN
ejpam-184	301	1	+	+	PRON
ejpam-184	301	2	d2(y(t)t	d2(y(t)t	VERB
ejpam-184	301	3	g	g	PROPN
ejpam-184	301	4	ẋ	ẋ	PROPN
ejpam-184	301	5	)	)	PUNCT
ejpam-184	301	6	ẋ)β(t	ẋ)β(t	PROPN
ejpam-184	301	7	)	)	PUNCT
ejpam-184	302	1	i	i	PRON
ejpam-184	302	2	−γ	−γ	VERB
ejpam-184	302	3	�	�	PROPN
ejpam-184	302	4	y(t)t	y(t)t	PROPN
ejpam-184	302	5	gx	gx	PROPN
ejpam-184	302	6	−	−	PROPN
ejpam-184	302	7	1	1	NUM
ejpam-184	302	8	2	2	NUM
ejpam-184	302	9	β(t)t((y(t)t	β(t)t((y(t)t	NOUN
ejpam-184	302	10	gx)x	gx)x	NUM
ejpam-184	302	11	−	−	PROPN
ejpam-184	302	12	d(y(t)t	d(y(t)t	PROPN
ejpam-184	302	13	gx	gx	PROPN
ejpam-184	302	14	)	)	PUNCT
ejpam-184	302	15	ẋ	ẋ	PROPN
ejpam-184	303	1	+	+	PRON
ejpam-184	303	2	d2(y(t)t	d2(y(t)t	VERB
ejpam-184	303	3	g	g	PROPN
ejpam-184	303	4	ẋ	ẋ	PROPN
ejpam-184	303	5	)	)	PUNCT
ejpam-184	303	6	ẋ)β(t	ẋ)β(t	PROPN
ejpam-184	303	7	)	)	PUNCT
ejpam-184	303	8	�	�	PROPN
ejpam-184	304	1	+	+	PROPN
ejpam-184	304	2	µt	µt	PROPN
ejpam-184	304	3	(	(	PUNCT
ejpam-184	304	4	t)y(t	t)y(t	NOUN
ejpam-184	304	5	)	)	PUNCT
ejpam-184	304	6	=	=	SYM
ejpam-184	304	7	0	0	NUM
ejpam-184	304	8	,	,	PUNCT
ejpam-184	304	9	using	use	VERB
ejpam-184	304	10	(	(	PUNCT
ejpam-184	304	11	3.15	3.15	NUM
ejpam-184	304	12	)	)	PUNCT
ejpam-184	304	13	and	and	CCONJ
ejpam-184	304	14	then	then	ADV
ejpam-184	304	15	integrating	integrate	VERB
ejpam-184	304	16	,	,	PUNCT
ejpam-184	304	17	we	we	PRON
ejpam-184	304	18	have	have	VERB
ejpam-184	304	19	∫	∫	PROPN
ejpam-184	305	1	i	i	PRON
ejpam-184	305	2	λ(t)t{y(t)t	λ(t)t{y(t)t	PROPN
ejpam-184	305	3	gx	gx	PROPN
ejpam-184	306	1	−	−	PROPN
ejpam-184	306	2	d(y(t)t	d(y(t)t	VERB
ejpam-184	306	3	g	g	PROPN
ejpam-184	306	4	ẋ	ẋ	PROPN
ejpam-184	306	5	)	)	PUNCT
ejpam-184	307	1	+	+	NOUN
ejpam-184	307	2	hβ(t)}d	hβ(t)}d	PROPN
ejpam-184	307	3	t	t	NOUN
ejpam-184	307	4	−γ	−γ	NOUN
ejpam-184	307	5	∫	∫	PROPN
ejpam-184	308	1	i	i	PRON
ejpam-184	308	2	{	{	PUNCT
ejpam-184	308	3	y(t)t	y(t)t	PROPN
ejpam-184	308	4	gx	gx	PROPN
ejpam-184	308	5	−	−	PROPN
ejpam-184	308	6	1	1	NUM
ejpam-184	308	7	2	2	NUM
ejpam-184	308	8	β(t)t	β(t)t	PUNCT
ejpam-184	308	9	hβ(t)}d	hβ(t)}d	PROPN
ejpam-184	308	10	t	t	NOUN
ejpam-184	308	11	=	=	SYM
ejpam-184	308	12	0	0	NUM
ejpam-184	308	13	this	this	PRON
ejpam-184	308	14	,	,	PUNCT
ejpam-184	308	15	because	because	SCONJ
ejpam-184	308	16	of	of	ADP
ejpam-184	308	17	(	(	PUNCT
ejpam-184	308	18	3.14	3.14	NUM
ejpam-184	308	19	)	)	PUNCT
ejpam-184	308	20	,	,	PUNCT
ejpam-184	308	21	yields	yield	NOUN
ejpam-184	308	22	,	,	PUNCT
ejpam-184	308	23	∫	∫	PROPN
ejpam-184	309	1	i	i	PRON
ejpam-184	309	2	λ(t)t{y(t)t	λ(t)t{y(t)t	PROPN
ejpam-184	309	3	gx	gx	PROPN
ejpam-184	310	1	−	−	PROPN
ejpam-184	310	2	d(y(t)t	d(y(t)t	VERB
ejpam-184	310	3	g	g	PROPN
ejpam-184	310	4	ẋ	ẋ	PROPN
ejpam-184	310	5	)	)	PUNCT
ejpam-184	311	1	+	+	PROPN
ejpam-184	311	2	hβ(t)}d	hβ(t)}d	PROPN
ejpam-184	311	3	t	t	NOUN
ejpam-184	311	4	=	=	SYM
ejpam-184	311	5	0	0	PUNCT
ejpam-184	311	6	(	(	PUNCT
ejpam-184	311	7	3.19	3.19	NUM
ejpam-184	311	8	)	)	PUNCT
ejpam-184	311	9	if	if	SCONJ
ejpam-184	311	10	(	(	PUNCT
ejpam-184	311	11	α	α	X
ejpam-184	311	12	,	,	PUNCT
ejpam-184	311	13	γ	γ	NOUN
ejpam-184	311	14	)	)	PUNCT
ejpam-184	311	15	=	=	SYM
ejpam-184	311	16	0	0	NUM
ejpam-184	311	17	i.e.	i.e.	X
ejpam-184	311	18	α	α	X
ejpam-184	311	19	=	=	SYM
ejpam-184	311	20	0	0	NUM
ejpam-184	311	21	=	=	SYM
ejpam-184	311	22	γ	γ	X
ejpam-184	311	23	,	,	PUNCT
ejpam-184	311	24	then	then	ADV
ejpam-184	311	25	(	(	PUNCT
ejpam-184	311	26	3.18	3.18	NUM
ejpam-184	311	27	)	)	PUNCT
ejpam-184	311	28	implies	imply	VERB
ejpam-184	311	29	λ(t	λ(t	NOUN
ejpam-184	311	30	)	)	PUNCT
ejpam-184	312	1	=	=	SYM
ejpam-184	312	2	0	0	NUM
ejpam-184	312	3	,	,	PUNCT
ejpam-184	312	4	t	t	PROPN
ejpam-184	312	5	∈	∈	PROPN
ejpam-184	312	6	i	i	PRON
ejpam-184	312	7	and	and	CCONJ
ejpam-184	312	8	µ(t	µ(t	ADJ
ejpam-184	312	9	)	)	PUNCT
ejpam-184	313	1	=	=	SYM
ejpam-184	313	2	0	0	NUM
ejpam-184	313	3	from	from	ADP
ejpam-184	313	4	(	(	PUNCT
ejpam-184	313	5	3.12	3.12	NUM
ejpam-184	313	6	)	)	PUNCT
ejpam-184	313	7	.	.	PUNCT
ejpam-184	314	1	thus	thus	ADV
ejpam-184	314	2	,	,	PUNCT
ejpam-184	314	3	we	we	PRON
ejpam-184	314	4	have	have	VERB
ejpam-184	314	5	(	(	PUNCT
ejpam-184	314	6	α	α	X
ejpam-184	314	7	,	,	PUNCT
ejpam-184	314	8	γ	γ	X
ejpam-184	314	9	,	,	PUNCT
ejpam-184	314	10	λ(t),µ(t	λ(t),µ(t	NOUN
ejpam-184	314	11	)	)	PUNCT
ejpam-184	314	12	)	)	PUNCT
ejpam-184	315	1	=	=	PUNCT
ejpam-184	315	2	0	0	X
ejpam-184	315	3	.	.	PUNCT
ejpam-184	316	1	this	this	PRON
ejpam-184	316	2	contradicts	contradict	VERB
ejpam-184	316	3	(	(	PUNCT
ejpam-184	316	4	3.17	3.17	NUM
ejpam-184	316	5	)	)	PUNCT
ejpam-184	316	6	.	.	PUNCT
ejpam-184	317	1	hence	hence	ADV
ejpam-184	317	2	(	(	PUNCT
ejpam-184	317	3	α	α	X
ejpam-184	317	4	,	,	PUNCT
ejpam-184	317	5	γ	γ	NOUN
ejpam-184	317	6	)	)	PUNCT
ejpam-184	317	7	6=	6=	ADP
ejpam-184	317	8	0	0	NUM
ejpam-184	317	9	i.e.	i.e.	X
ejpam-184	317	10	α	α	X
ejpam-184	317	11	>	>	X
ejpam-184	317	12	0	0	PROPN
ejpam-184	317	13	or	or	CCONJ
ejpam-184	317	14	γ	γ	X
ejpam-184	317	15	>	>	X
ejpam-184	317	16	0	0	PROPN
ejpam-184	317	17	.	.	PUNCT
ejpam-184	317	18	i.	i.	PROPN
ejpam-184	317	19	husain	husain	PROPN
ejpam-184	317	20	,	,	PUNCT
ejpam-184	317	21	a.	a.	PROPN
ejpam-184	317	22	ahmed	ahmed	PROPN
ejpam-184	317	23	,	,	PUNCT
ejpam-184	317	24	and	and	CCONJ
ejpam-184	317	25	m.	m.	NOUN
ejpam-184	317	26	massodi	massodi	PROPN
ejpam-184	317	27	/	/	SYM
ejpam-184	317	28	eur	eur	PROPN
ejpam-184	317	29	.	.	PUNCT
ejpam-184	318	1	j.	j.	PROPN
ejpam-184	318	2	pure	pure	PROPN
ejpam-184	318	3	appl	appl	PROPN
ejpam-184	318	4	.	.	PROPN
ejpam-184	318	5	math	math	PROPN
ejpam-184	318	6	,	,	PUNCT
ejpam-184	318	7	2	2	NUM
ejpam-184	318	8	(	(	PUNCT
ejpam-184	318	9	2009	2009	NUM
ejpam-184	318	10	)	)	PUNCT
ejpam-184	318	11	,	,	PUNCT
ejpam-184	318	12	(	(	PUNCT
ejpam-184	318	13	278	278	NUM
ejpam-184	318	14	-	-	SYM
ejpam-184	318	15	295	295	NUM
ejpam-184	318	16	)	)	PUNCT
ejpam-184	318	17	291	291	NUM
ejpam-184	318	18	we	we	PRON
ejpam-184	318	19	claim	claim	VERB
ejpam-184	318	20	β(t	β(t	NOUN
ejpam-184	318	21	)	)	PUNCT
ejpam-184	319	1	=	=	SYM
ejpam-184	319	2	0	0	NUM
ejpam-184	319	3	,	,	PUNCT
ejpam-184	319	4	t	t	PROPN
ejpam-184	319	5	∈	∈	PROPN
ejpam-184	320	1	i	i	PRON
ejpam-184	320	2	.	.	PUNCT
ejpam-184	320	3	suppose	suppose	VERB
ejpam-184	320	4	that	that	SCONJ
ejpam-184	320	5	β(t	β(t	PROPN
ejpam-184	320	6	)	)	PUNCT
ejpam-184	320	7	6=	6=	ADP
ejpam-184	320	8	0	0	NUM
ejpam-184	320	9	,	,	PUNCT
ejpam-184	320	10	t	t	PROPN
ejpam-184	320	11	∈	∈	PROPN
ejpam-184	321	1	i	i	PRON
ejpam-184	321	2	.	.	PUNCT
ejpam-184	322	1	from	from	ADP
ejpam-184	322	2	(	(	PUNCT
ejpam-184	322	3	3.18	3.18	NUM
ejpam-184	322	4	)	)	PUNCT
ejpam-184	322	5	we	we	PRON
ejpam-184	322	6	have	have	VERB
ejpam-184	322	7	(	(	PUNCT
ejpam-184	322	8	α−	α−	ADP
ejpam-184	322	9	γ)β(t	γ)β(t	NOUN
ejpam-184	322	10	)	)	PUNCT
ejpam-184	323	1	=	=	SYM
ejpam-184	323	2	0	0	NUM
ejpam-184	324	1	implying	imply	VERB
ejpam-184	324	2	α	α	NOUN
ejpam-184	324	3	=	=	SYM
ejpam-184	324	4	γ	γ	X
ejpam-184	324	5	>	>	X
ejpam-184	324	6	0	0	NUM
ejpam-184	324	7	.	.	PUNCT
ejpam-184	325	1	using	use	VERB
ejpam-184	325	2	(	(	PUNCT
ejpam-184	325	3	3.18	3.18	NUM
ejpam-184	325	4	)	)	PUNCT
ejpam-184	325	5	in	in	ADP
ejpam-184	325	6	(	(	PUNCT
ejpam-184	325	7	3.19	3.19	NUM
ejpam-184	325	8	)	)	PUNCT
ejpam-184	325	9	,	,	PUNCT
ejpam-184	325	10	we	we	PRON
ejpam-184	325	11	have	have	VERB
ejpam-184	325	12	∫	∫	PROPN
ejpam-184	326	1	i	i	PRON
ejpam-184	326	2	αβ(t)t{y(t)t	αβ(t)t{y(t)t	PROPN
ejpam-184	326	3	gx	gx	PROPN
ejpam-184	326	4	−	−	PROPN
ejpam-184	326	5	d(y(t)t	d(y(t)t	PROPN
ejpam-184	326	6	g	g	PROPN
ejpam-184	326	7	ẋ	ẋ	PROPN
ejpam-184	326	8	)	)	PUNCT
ejpam-184	327	1	+	+	PROPN
ejpam-184	327	2	hβ(t)}d	hβ(t)}d	PROPN
ejpam-184	327	3	t	t	NOUN
ejpam-184	327	4	=	=	SYM
ejpam-184	327	5	0	0	NUM
ejpam-184	327	6	implies	imply	VERB
ejpam-184	327	7	∫	∫	PROPN
ejpam-184	328	1	i	i	PROPN
ejpam-184	328	2	β(t)t{y(t)t	β(t)t{y(t)t	PROPN
ejpam-184	328	3	gx	gx	PROPN
ejpam-184	328	4	−	−	PROPN
ejpam-184	328	5	d(y(t)t	d(y(t)t	NOUN
ejpam-184	328	6	g	g	PROPN
ejpam-184	328	7	ẋ)}d	ẋ)}d	PROPN
ejpam-184	328	8	t	t	PROPN
ejpam-184	329	1	+	+	CCONJ
ejpam-184	329	2	∫	∫	PROPN
ejpam-184	329	3	i	i	PRON
ejpam-184	329	4	β(t)t	β(t)t	PRON
ejpam-184	330	1	hβ(t)d	hβ(t)d	X
ejpam-184	330	2	t	t	NOUN
ejpam-184	330	3	=	=	SYM
ejpam-184	330	4	0	0	NUM
ejpam-184	330	5	(	(	PUNCT
ejpam-184	330	6	3.20	3.20	NUM
ejpam-184	330	7	)	)	PUNCT
ejpam-184	330	8	in	in	ADP
ejpam-184	330	9	view	view	NOUN
ejpam-184	330	10	of	of	ADP
ejpam-184	330	11	the	the	DET
ejpam-184	330	12	hypothesis	hypothesis	NOUN
ejpam-184	330	13	(	(	PUNCT
ejpam-184	330	14	a3	a3	NOUN
ejpam-184	330	15	)	)	PUNCT
ejpam-184	330	16	i.e.	i.e.	X
ejpam-184	330	17	,	,	PUNCT
ejpam-184	330	18	∫	∫	PROPN
ejpam-184	331	1	i	i	PRON
ejpam-184	331	2	{	{	PUNCT
ejpam-184	331	3	β(t)t	β(t)t	PROPN
ejpam-184	331	4	y(t)t	y(t)t	PROPN
ejpam-184	331	5	gx	gx	PROPN
ejpam-184	331	6	−	−	PROPN
ejpam-184	331	7	d(y(t)t	d(y(t)t	NOUN
ejpam-184	331	8	g	g	PROPN
ejpam-184	331	9	ẋ)}d	ẋ)}d	PROPN
ejpam-184	331	10	t	t	PROPN
ejpam-184	331	11	≥	≥	NOUN
ejpam-184	331	12	0	0	NUM
ejpam-184	332	1	and	and	CCONJ
ejpam-184	332	2	∫	∫	PROPN
ejpam-184	333	1	i	i	PRON
ejpam-184	333	2	β(t)t	β(t)t	PROPN
ejpam-184	334	1	hβ(t)d	hβ(t)d	X
ejpam-184	334	2	t	t	X
ejpam-184	334	3	>	>	X
ejpam-184	334	4	0	0	X
ejpam-184	334	5	.	.	PUNCT
ejpam-184	335	1	we	we	PRON
ejpam-184	335	2	have	have	VERB
ejpam-184	335	3	∫	∫	PROPN
ejpam-184	336	1	i	i	PROPN
ejpam-184	336	2	β(t)t{y(t)t	β(t)t{y(t)t	PROPN
ejpam-184	336	3	gx	gx	PROPN
ejpam-184	336	4	−	−	PROPN
ejpam-184	336	5	d(y(t)t	d(y(t)t	PROPN
ejpam-184	336	6	g	g	PROPN
ejpam-184	336	7	ẋ	ẋ	PROPN
ejpam-184	336	8	)	)	PUNCT
ejpam-184	337	1	+	+	PROPN
ejpam-184	337	2	hβ(t)}d	hβ(t)}d	PROPN
ejpam-184	337	3	t	t	X
ejpam-184	337	4	>	>	X
ejpam-184	337	5	0	0	PUNCT
ejpam-184	338	1	this	this	PRON
ejpam-184	338	2	contradicts	contradict	VERB
ejpam-184	338	3	(	(	PUNCT
ejpam-184	338	4	3.20	3.20	NUM
ejpam-184	338	5	)	)	PUNCT
ejpam-184	338	6	.	.	PUNCT
ejpam-184	339	1	hence	hence	ADV
ejpam-184	339	2	β(t	β(t	PROPN
ejpam-184	339	3	)	)	PUNCT
ejpam-184	340	1	=	=	SYM
ejpam-184	340	2	0	0	NUM
ejpam-184	340	3	,	,	PUNCT
ejpam-184	340	4	t	t	PROPN
ejpam-184	340	5	∈	∈	PROPN
ejpam-184	341	1	i	i	PRON
ejpam-184	341	2	.	.	PUNCT
ejpam-184	342	1	consequently	consequently	ADV
ejpam-184	342	2	(	(	PUNCT
ejpam-184	342	3	3.18	3.18	NUM
ejpam-184	342	4	)	)	PUNCT
ejpam-184	342	5	implies	imply	VERB
ejpam-184	342	6	λ(t	λ(t	NOUN
ejpam-184	342	7	)	)	PUNCT
ejpam-184	342	8	=	=	SYM
ejpam-184	343	1	0	0	NUM
ejpam-184	343	2	,	,	PUNCT
ejpam-184	343	3	t	t	PROPN
ejpam-184	343	4	∈	∈	PROPN
ejpam-184	344	1	i	i	PRON
ejpam-184	344	2	.	.	PUNCT
ejpam-184	345	1	from	from	ADP
ejpam-184	345	2	(	(	PUNCT
ejpam-184	345	3	3.10	3.10	NUM
ejpam-184	345	4	)	)	PUNCT
ejpam-184	345	5	,	,	PUNCT
ejpam-184	345	6	we	we	PRON
ejpam-184	345	7	have	have	VERB
ejpam-184	345	8	−α	−α	NOUN
ejpam-184	345	9	(	(	PUNCT
ejpam-184	345	10	fx	fx	NOUN
ejpam-184	345	11	−	−	PROPN
ejpam-184	346	1	d	d	X
ejpam-184	346	2	f	f	PROPN
ejpam-184	346	3	ẋ	ẋ	PROPN
ejpam-184	346	4	)	)	PUNCT
ejpam-184	347	1	+	+	CCONJ
ejpam-184	347	2	γ(y(t	γ(y(t	PROPN
ejpam-184	347	3	)	)	PUNCT
ejpam-184	347	4	t	t	PROPN
ejpam-184	347	5	gx	gx	PROPN
ejpam-184	348	1	−	−	PROPN
ejpam-184	349	1	d	d	PROPN
ejpam-184	349	2	y(t)t	y(t)t	PROPN
ejpam-184	349	3	g	g	PROPN
ejpam-184	349	4	ẋ	ẋ	PROPN
ejpam-184	349	5	)	)	PUNCT
ejpam-184	350	1	=	=	SYM
ejpam-184	350	2	0	0	NUM
ejpam-184	350	3	(	(	PUNCT
ejpam-184	350	4	3.21	3.21	NUM
ejpam-184	350	5	)	)	PUNCT
ejpam-184	350	6	also	also	ADV
ejpam-184	350	7	from	from	ADP
ejpam-184	350	8	(	(	PUNCT
ejpam-184	350	9	3.4	3.4	NUM
ejpam-184	350	10	)	)	PUNCT
ejpam-184	350	11	,	,	PUNCT
ejpam-184	350	12	we	we	PRON
ejpam-184	350	13	have	have	VERB
ejpam-184	350	14	(	(	PUNCT
ejpam-184	350	15	fx	fx	VERB
ejpam-184	350	16	−	−	PROPN
ejpam-184	351	1	d	d	X
ejpam-184	351	2	f	f	PROPN
ejpam-184	351	3	ẋ	ẋ	PROPN
ejpam-184	351	4	)	)	PUNCT
ejpam-184	351	5	=	=	SYM
ejpam-184	351	6	−(y(t	−(y(t	PROPN
ejpam-184	351	7	)	)	PUNCT
ejpam-184	351	8	t	t	PROPN
ejpam-184	351	9	gx	gx	PROPN
ejpam-184	351	10	−	−	PROPN
ejpam-184	351	11	d(y(t)t	d(y(t)t	PROPN
ejpam-184	351	12	g	g	PROPN
ejpam-184	351	13	ẋ	ẋ	PROPN
ejpam-184	351	14	)	)	PUNCT
ejpam-184	351	15	)	)	PUNCT
ejpam-184	352	1	using	use	VERB
ejpam-184	352	2	this	this	PRON
ejpam-184	352	3	in	in	ADP
ejpam-184	352	4	(	(	PUNCT
ejpam-184	352	5	3.21	3.21	NUM
ejpam-184	352	6	)	)	PUNCT
ejpam-184	352	7	,	,	PUNCT
ejpam-184	352	8	we	we	PRON
ejpam-184	352	9	have	have	AUX
ejpam-184	352	10	(	(	PUNCT
ejpam-184	352	11	α−	α−	ADP
ejpam-184	352	12	γ)(y(t)t	γ)(y(t)t	ADP
ejpam-184	352	13	gx	gx	PROPN
ejpam-184	352	14	−	−	PROPN
ejpam-184	352	15	d	d	PROPN
ejpam-184	352	16	y(t)t	y(t)t	PROPN
ejpam-184	352	17	g	g	PROPN
ejpam-184	352	18	ẋ	ẋ	PROPN
ejpam-184	352	19	)	)	PUNCT
ejpam-184	352	20	=	=	SYM
ejpam-184	352	21	0	0	NUM
ejpam-184	352	22	i.	i.	PROPN
ejpam-184	352	23	husain	husain	PROPN
ejpam-184	352	24	,	,	PUNCT
ejpam-184	352	25	a.	a.	PROPN
ejpam-184	352	26	ahmed	ahmed	PROPN
ejpam-184	352	27	,	,	PUNCT
ejpam-184	352	28	and	and	CCONJ
ejpam-184	352	29	m.	m.	NOUN
ejpam-184	352	30	massodi	massodi	PROPN
ejpam-184	352	31	/	/	SYM
ejpam-184	352	32	eur	eur	PROPN
ejpam-184	352	33	.	.	PUNCT
ejpam-184	353	1	j.	j.	PROPN
ejpam-184	353	2	pure	pure	PROPN
ejpam-184	353	3	appl	appl	PROPN
ejpam-184	353	4	.	.	PROPN
ejpam-184	353	5	math	math	PROPN
ejpam-184	353	6	,	,	PUNCT
ejpam-184	353	7	2	2	NUM
ejpam-184	353	8	(	(	PUNCT
ejpam-184	353	9	2009	2009	NUM
ejpam-184	353	10	)	)	PUNCT
ejpam-184	353	11	,	,	PUNCT
ejpam-184	353	12	(	(	PUNCT
ejpam-184	353	13	278	278	NUM
ejpam-184	353	14	-	-	SYM
ejpam-184	353	15	295	295	NUM
ejpam-184	353	16	)	)	PUNCT
ejpam-184	353	17	292	292	NUM
ejpam-184	353	18	in	in	ADP
ejpam-184	353	19	view	view	NOUN
ejpam-184	353	20	of	of	ADP
ejpam-184	353	21	the	the	DET
ejpam-184	353	22	hypothesis	hypothesis	NOUN
ejpam-184	353	23	(	(	PUNCT
ejpam-184	353	24	a2	a2	PROPN
ejpam-184	353	25	)	)	PUNCT
ejpam-184	354	1	,	,	PUNCT
ejpam-184	354	2	this	this	PRON
ejpam-184	354	3	gives	give	VERB
ejpam-184	354	4	α	α	NOUN
ejpam-184	354	5	=	=	SYM
ejpam-184	354	6	γ	γ	X
ejpam-184	354	7	>	>	X
ejpam-184	354	8	0	0	NUM
ejpam-184	354	9	.	.	PUNCT
ejpam-184	355	1	from	from	ADP
ejpam-184	355	2	(	(	PUNCT
ejpam-184	355	3	3.12	3.12	NUM
ejpam-184	355	4	)	)	PUNCT
ejpam-184	355	5	we	we	PRON
ejpam-184	355	6	have	have	AUX
ejpam-184	355	7	γg	γg	PROPN
ejpam-184	355	8	j	j	PROPN
ejpam-184	355	9	+	+	PROPN
ejpam-184	355	10	µ	µ	X
ejpam-184	355	11	j(t	j(t	PROPN
ejpam-184	355	12	)	)	PUNCT
ejpam-184	355	13	=	=	SYM
ejpam-184	355	14	0	0	PUNCT
ejpam-184	355	15	because	because	SCONJ
ejpam-184	355	16	γ	γ	X
ejpam-184	355	17	>	>	X
ejpam-184	355	18	0	0	PROPN
ejpam-184	355	19	,	,	PUNCT
ejpam-184	355	20	this	this	PRON
ejpam-184	355	21	gives	give	VERB
ejpam-184	355	22	g	g	PRON
ejpam-184	355	23	j	j	PROPN
ejpam-184	355	24	=	=	SYM
ejpam-184	355	25	−	−	PROPN
ejpam-184	355	26	µ	µ	X
ejpam-184	355	27	j(t	j(t	PROPN
ejpam-184	355	28	)	)	PUNCT
ejpam-184	355	29	γ	γ	PROPN
ejpam-184	355	30	≤	≤	NOUN
ejpam-184	355	31	0	0	NUM
ejpam-184	355	32	g(t	g(t	PROPN
ejpam-184	355	33	,	,	PUNCT
ejpam-184	355	34	x̄	x̄	NOUN
ejpam-184	355	35	,	,	PUNCT
ejpam-184	355	36	˙̄x	˙̄x	NOUN
ejpam-184	355	37	)	)	PUNCT
ejpam-184	355	38	≤	≤	NOUN
ejpam-184	355	39	0	0	NUM
ejpam-184	356	1	x̄	x̄	NOUN
ejpam-184	356	2	is	be	AUX
ejpam-184	356	3	feasible	feasible	ADJ
ejpam-184	356	4	to	to	ADP
ejpam-184	356	5	(	(	PUNCT
ejpam-184	356	6	cp	cp	NOUN
ejpam-184	356	7	)	)	PUNCT
ejpam-184	356	8	.	.	PUNCT
ejpam-184	357	1	in	in	ADP
ejpam-184	357	2	view	view	NOUN
ejpam-184	357	3	of	of	ADP
ejpam-184	357	4	β(t	β(t	NOUN
ejpam-184	357	5	)	)	PUNCT
ejpam-184	357	6	=	=	SYM
ejpam-184	357	7	0	0	NUM
ejpam-184	357	8	,	,	PUNCT
ejpam-184	357	9	t	t	PROPN
ejpam-184	357	10	∈	∈	PROPN
ejpam-184	357	11	i	i	PRON
ejpam-184	357	12	gives	give	VERB
ejpam-184	357	13	the	the	DET
ejpam-184	357	14	equality	equality	NOUN
ejpam-184	357	15	of	of	ADP
ejpam-184	357	16	two	two	NUM
ejpam-184	357	17	objective	objective	ADJ
ejpam-184	357	18	values	value	NOUN
ejpam-184	357	19	follows	follow	VERB
ejpam-184	357	20	.	.	PUNCT
ejpam-184	358	1	the	the	DET
ejpam-184	358	2	optimality	optimality	NOUN
ejpam-184	358	3	of	of	ADP
ejpam-184	358	4	x̄	x̄	PROPN
ejpam-184	358	5	for	for	ADP
ejpam-184	358	6	(	(	PUNCT
ejpam-184	358	7	cp	cp	NOUN
ejpam-184	358	8	)	)	PUNCT
ejpam-184	358	9	follows	follow	VERB
ejpam-184	358	10	from	from	ADP
ejpam-184	358	11	theorem	theorem	ADJ
ejpam-184	358	12	1	1	NUM
ejpam-184	358	13	.	.	NOUN
ejpam-184	358	14	4	4	NUM
ejpam-184	358	15	.	.	NOUN
ejpam-184	358	16	natural	natural	ADJ
ejpam-184	358	17	boundary	boundary	ADJ
ejpam-184	358	18	values	value	NOUN
ejpam-184	358	19	in	in	ADP
ejpam-184	358	20	this	this	DET
ejpam-184	358	21	section	section	NOUN
ejpam-184	358	22	,	,	PUNCT
ejpam-184	358	23	we	we	PRON
ejpam-184	358	24	formulate	formulate	VERB
ejpam-184	358	25	dual	dual	ADJ
ejpam-184	358	26	variational	variational	ADJ
ejpam-184	358	27	problem	problem	NOUN
ejpam-184	358	28	with	with	ADP
ejpam-184	358	29	natural	natural	ADJ
ejpam-184	358	30	boundary	boundary	ADJ
ejpam-184	358	31	values	value	NOUN
ejpam-184	358	32	rather	rather	ADV
ejpam-184	358	33	than	than	ADP
ejpam-184	358	34	fixed	fix	VERB
ejpam-184	358	35	end	end	NOUN
ejpam-184	358	36	points	point	NOUN
ejpam-184	358	37	.	.	PUNCT
ejpam-184	359	1	(	(	PUNCT
ejpam-184	359	2	c	c	NOUN
ejpam-184	359	3	p0	p0	NOUN
ejpam-184	359	4	)	)	PUNCT
ejpam-184	359	5	:	:	PUNCT
ejpam-184	359	6	minimize	minimize	VERB
ejpam-184	359	7	∫	∫	PROPN
ejpam-184	359	8	i	i	PRON
ejpam-184	359	9	f	f	PROPN
ejpam-184	360	1	(	(	PUNCT
ejpam-184	360	2	t	t	PROPN
ejpam-184	360	3	,	,	PUNCT
ejpam-184	360	4	x	x	X
ejpam-184	360	5	,	,	PUNCT
ejpam-184	360	6	ẋ)d	ẋ)d	PROPN
ejpam-184	360	7	t	t	PROPN
ejpam-184	360	8	subject	subject	NOUN
ejpam-184	360	9	to	to	ADP
ejpam-184	360	10	g(t	g(t	PROPN
ejpam-184	360	11	,	,	PUNCT
ejpam-184	360	12	x	x	INTJ
ejpam-184	360	13	,	,	PUNCT
ejpam-184	360	14	ẋ)≤	ẋ)≤	PROPN
ejpam-184	360	15	0	0	NUM
ejpam-184	360	16	,	,	PUNCT
ejpam-184	360	17	t	t	PROPN
ejpam-184	360	18	∈	∈	PROPN
ejpam-184	361	1	i	i	PRON
ejpam-184	361	2	(	(	PUNCT
ejpam-184	361	3	c	c	NOUN
ejpam-184	361	4	d0	d0	NOUN
ejpam-184	361	5	)	)	PUNCT
ejpam-184	361	6	:	:	PUNCT
ejpam-184	361	7	maximize	maximize	VERB
ejpam-184	361	8	∫	∫	PROPN
ejpam-184	361	9	i	i	PRON
ejpam-184	361	10	{	{	PUNCT
ejpam-184	361	11	f(t	f(t	PROPN
ejpam-184	361	12	,	,	PUNCT
ejpam-184	361	13	x	x	SYM
ejpam-184	361	14	,	,	PUNCT
ejpam-184	361	15	ẋ)−	ẋ)−	PROPN
ejpam-184	361	16	1	1	NUM
ejpam-184	361	17	2	2	NUM
ejpam-184	361	18	β(t)t	β(t)t	NUM
ejpam-184	361	19	fβ(t)}d	fβ(t)}d	PROPN
ejpam-184	361	20	t	t	PROPN
ejpam-184	361	21	subject	subject	NOUN
ejpam-184	361	22	to	to	ADP
ejpam-184	361	23	fx	fx	PROPN
ejpam-184	361	24	+	+	CCONJ
ejpam-184	361	25	y(t)t	y(t)t	PROPN
ejpam-184	361	26	gx	gx	PROPN
ejpam-184	361	27	−	−	PROPN
ejpam-184	361	28	d	d	PROPN
ejpam-184	361	29	(	(	PUNCT
ejpam-184	361	30	f	f	PROPN
ejpam-184	361	31	ẋ	ẋ	PROPN
ejpam-184	362	1	+	+	NUM
ejpam-184	362	2	y(t)t	y(t)t	PROPN
ejpam-184	362	3	g	g	PROPN
ejpam-184	362	4	ẋ	ẋ	PROPN
ejpam-184	362	5	)	)	PUNCT
ejpam-184	363	1	+	+	CCONJ
ejpam-184	363	2	(	(	PUNCT
ejpam-184	363	3	f	f	X
ejpam-184	363	4	+	+	NOUN
ejpam-184	363	5	h)β(t	h)β(t	NOUN
ejpam-184	363	6	)	)	PUNCT
ejpam-184	364	1	=	=	SYM
ejpam-184	364	2	0	0	NUM
ejpam-184	365	1	t	t	NOUN
ejpam-184	365	2	∈	∈	PROPN
ejpam-184	365	3	i	i	PRON
ejpam-184	365	4	i.	i.	PROPN
ejpam-184	365	5	husain	husain	PROPN
ejpam-184	365	6	,	,	PUNCT
ejpam-184	365	7	a.	a.	PROPN
ejpam-184	365	8	ahmed	ahmed	PROPN
ejpam-184	365	9	,	,	PUNCT
ejpam-184	365	10	and	and	CCONJ
ejpam-184	365	11	m.	m.	NOUN
ejpam-184	365	12	massodi	massodi	PROPN
ejpam-184	365	13	/	/	SYM
ejpam-184	365	14	eur	eur	PROPN
ejpam-184	365	15	.	.	PUNCT
ejpam-184	366	1	j.	j.	PROPN
ejpam-184	366	2	pure	pure	PROPN
ejpam-184	366	3	appl	appl	PROPN
ejpam-184	366	4	.	.	PROPN
ejpam-184	366	5	math	math	PROPN
ejpam-184	366	6	,	,	PUNCT
ejpam-184	366	7	2	2	NUM
ejpam-184	366	8	(	(	PUNCT
ejpam-184	366	9	2009	2009	NUM
ejpam-184	366	10	)	)	PUNCT
ejpam-184	366	11	,	,	PUNCT
ejpam-184	366	12	(	(	PUNCT
ejpam-184	366	13	278	278	NUM
ejpam-184	366	14	-	-	SYM
ejpam-184	366	15	295	295	NUM
ejpam-184	366	16	)	)	PUNCT
ejpam-184	366	17	293	293	NUM
ejpam-184	366	18	y(t)≥	y(t)≥	NOUN
ejpam-184	366	19	0	0	NUM
ejpam-184	366	20	,	,	PUNCT
ejpam-184	366	21	t	t	PROPN
ejpam-184	366	22	∈	∈	PROPN
ejpam-184	367	1	i	i	NOUN
ejpam-184	367	2	y(t)t	y(t)t	PROPN
ejpam-184	367	3	g	g	PROPN
ejpam-184	367	4	ẋ	ẋ	PROPN
ejpam-184	367	5	|t	|t	PROPN
ejpam-184	368	1	=	=	NOUN
ejpam-184	368	2	a	a	X
ejpam-184	368	3	=	=	SYM
ejpam-184	368	4	0	0	NUM
ejpam-184	368	5	,	,	PUNCT
ejpam-184	368	6	y(t)t	y(t)t	PROPN
ejpam-184	368	7	g	g	PROPN
ejpam-184	368	8	ẋ	ẋ	PROPN
ejpam-184	368	9	|t	|t	PROPN
ejpam-184	369	1	=	=	SYM
ejpam-184	369	2	b	b	NOUN
ejpam-184	369	3	=	=	SYM
ejpam-184	369	4	0	0	NUM
ejpam-184	369	5	,	,	PUNCT
ejpam-184	369	6	we	we	PRON
ejpam-184	369	7	shall	shall	AUX
ejpam-184	369	8	not	not	PART
ejpam-184	369	9	repeat	repeat	VERB
ejpam-184	369	10	the	the	DET
ejpam-184	369	11	proofs	proof	NOUN
ejpam-184	369	12	of	of	ADP
ejpam-184	369	13	theorem	theorem	ADJ
ejpam-184	369	14	3.1	3.1	NUM
ejpam-184	369	15	-	-	SYM
ejpam-184	369	16	3.3	3.3	NUM
ejpam-184	369	17	,	,	PUNCT
ejpam-184	369	18	as	as	SCONJ
ejpam-184	369	19	these	these	PRON
ejpam-184	369	20	follow	follow	VERB
ejpam-184	369	21	on	on	ADP
ejpam-184	369	22	the	the	DET
ejpam-184	369	23	lines	line	NOUN
ejpam-184	369	24	of	of	ADP
ejpam-184	369	25	the	the	DET
ejpam-184	369	26	analysis	analysis	NOUN
ejpam-184	369	27	given	give	VERB
ejpam-184	369	28	in	in	ADP
ejpam-184	369	29	[	[	X
ejpam-184	369	30	1	1	NUM
ejpam-184	369	31	]	]	PUNCT
ejpam-184	369	32	.	.	PUNCT
ejpam-184	370	1	5	5	X
ejpam-184	370	2	.	.	X
ejpam-184	370	3	nonlinear	nonlinear	ADJ
ejpam-184	370	4	programming	programming	NOUN
ejpam-184	370	5	if	if	SCONJ
ejpam-184	370	6	all	all	DET
ejpam-184	370	7	functions	function	NOUN
ejpam-184	370	8	in	in	ADP
ejpam-184	370	9	(	(	PUNCT
ejpam-184	370	10	c	c	NOUN
ejpam-184	370	11	p0	p0	NOUN
ejpam-184	370	12	)	)	PUNCT
ejpam-184	370	13	and	and	CCONJ
ejpam-184	370	14	(	(	PUNCT
ejpam-184	370	15	c	c	NOUN
ejpam-184	370	16	d0	d0	NOUN
ejpam-184	370	17	)	)	PUNCT
ejpam-184	370	18	are	be	AUX
ejpam-184	370	19	independent	independent	ADJ
ejpam-184	370	20	of	of	ADP
ejpam-184	370	21	t	t	PROPN
ejpam-184	370	22	,	,	PUNCT
ejpam-184	370	23	then	then	ADV
ejpam-184	370	24	these	these	DET
ejpam-184	370	25	problems	problem	NOUN
ejpam-184	370	26	will	will	AUX
ejpam-184	370	27	reduce	reduce	VERB
ejpam-184	370	28	to	to	ADP
ejpam-184	370	29	following	follow	VERB
ejpam-184	370	30	pair	pair	NOUN
ejpam-184	370	31	of	of	ADP
ejpam-184	370	32	dual	dual	ADJ
ejpam-184	370	33	problems	problem	NOUN
ejpam-184	370	34	,	,	PUNCT
ejpam-184	370	35	treated	treat	VERB
ejpam-184	370	36	by	by	ADP
ejpam-184	370	37	bector	bector	NOUN
ejpam-184	370	38	and	and	CCONJ
ejpam-184	370	39	chandra	chandra	PROPN
ejpam-184	370	40	[	[	X
ejpam-184	370	41	1	1	NUM
ejpam-184	370	42	]	]	PUNCT
ejpam-184	370	43	.	.	PUNCT
ejpam-184	371	1	(	(	PUNCT
ejpam-184	371	2	p1	p1	PROPN
ejpam-184	371	3	)	)	PUNCT
ejpam-184	371	4	:	:	PUNCT
ejpam-184	371	5	minimize	minimize	VERB
ejpam-184	371	6	f	f	X
ejpam-184	371	7	(	(	PUNCT
ejpam-184	371	8	x	x	NOUN
ejpam-184	371	9	)	)	PUNCT
ejpam-184	371	10	subject	subject	ADJ
ejpam-184	371	11	to	to	ADP
ejpam-184	371	12	g(x	g(x	NOUN
ejpam-184	371	13	)	)	PUNCT
ejpam-184	371	14	≤	≤	NOUN
ejpam-184	371	15	0	0	NUM
ejpam-184	371	16	,	,	PUNCT
ejpam-184	371	17	(	(	PUNCT
ejpam-184	371	18	d1	d1	NOUN
ejpam-184	371	19	)	)	PUNCT
ejpam-184	371	20	:	:	PUNCT
ejpam-184	371	21	maximize	maximize	VERB
ejpam-184	371	22	f	f	X
ejpam-184	371	23	(	(	PUNCT
ejpam-184	371	24	x)−	x)−	PROPN
ejpam-184	371	25	1	1	NUM
ejpam-184	371	26	2	2	NUM
ejpam-184	371	27	pt∇2	pt∇2	NOUN
ejpam-184	372	1	f	f	PROPN
ejpam-184	372	2	(	(	PUNCT
ejpam-184	372	3	x)p	x)p	ADJ
ejpam-184	372	4	subject	subject	ADJ
ejpam-184	372	5	to	to	ADP
ejpam-184	372	6	∇	∇	PROPN
ejpam-184	372	7	(	(	PUNCT
ejpam-184	372	8	f	f	PROPN
ejpam-184	372	9	+	+	CCONJ
ejpam-184	372	10	yt	yt	PROPN
ejpam-184	372	11	g	g	NOUN
ejpam-184	372	12	)	)	PUNCT
ejpam-184	373	1	+	+	VERB
ejpam-184	373	2	∇2	∇2	X
ejpam-184	373	3	(	(	PUNCT
ejpam-184	373	4	f	f	X
ejpam-184	373	5	+	+	CCONJ
ejpam-184	373	6	yt	yt	PRON
ejpam-184	373	7	g)p	g)p	NOUN
ejpam-184	373	8	=	=	SYM
ejpam-184	373	9	0	0	NUM
ejpam-184	374	1	yt	yt	X
ejpam-184	374	2	g(x)−	g(x)−	PROPN
ejpam-184	374	3	1	1	NUM
ejpam-184	374	4	2	2	NUM
ejpam-184	374	5	pt∇2(yt	pt∇2(yt	NUM
ejpam-184	374	6	g(x))p	g(x))p	PROPN
ejpam-184	374	7	≥	≥	NUM
ejpam-184	374	8	0	0	NUM
ejpam-184	375	1	y	y	PROPN
ejpam-184	375	2	≥	≥	NOUN
ejpam-184	375	3	0	0	NUM
ejpam-184	375	4	where	where	SCONJ
ejpam-184	375	5	fx(x	fx(x	ADV
ejpam-184	375	6	)	)	PUNCT
ejpam-184	376	1	=	=	PRON
ejpam-184	376	2	∇	∇	X
ejpam-184	376	3	f	f	X
ejpam-184	376	4	(	(	PUNCT
ejpam-184	376	5	x	x	X
ejpam-184	376	6	)	)	PUNCT
ejpam-184	376	7	,	,	PUNCT
ejpam-184	376	8	yt	yt	VERB
ejpam-184	376	9	g(x	g(x	NOUN
ejpam-184	376	10	)	)	PUNCT
ejpam-184	377	1	=	=	X
ejpam-184	377	2	∇(yt	∇(yt	NOUN
ejpam-184	377	3	g	g	NOUN
ejpam-184	377	4	)	)	PUNCT
ejpam-184	377	5	,	,	PUNCT
ejpam-184	377	6	fx	fx	PROPN
ejpam-184	377	7	x(x	x(x	PROPN
ejpam-184	377	8	)	)	PUNCT
ejpam-184	378	1	=	=	PRON
ejpam-184	378	2	∇	∇	X
ejpam-184	378	3	2	2	NUM
ejpam-184	378	4	f	f	NOUN
ejpam-184	378	5	(	(	PUNCT
ejpam-184	378	6	x	x	NOUN
ejpam-184	378	7	)	)	PUNCT
ejpam-184	378	8	references	reference	NOUN
ejpam-184	378	9	294	294	NUM
ejpam-184	378	10	∇2(yt	∇2(yt	NUM
ejpam-184	378	11	g(x	g(x	NOUN
ejpam-184	378	12	)	)	PUNCT
ejpam-184	378	13	)	)	PUNCT
ejpam-184	379	1	=	=	PUNCT
ejpam-184	379	2	(	(	PUNCT
ejpam-184	379	3	yt	yt	INTJ
ejpam-184	379	4	gx)x	gx)x	PROPN
ejpam-184	379	5	and	and	CCONJ
ejpam-184	379	6	β	β	X
ejpam-184	379	7	=	=	PUNCT
ejpam-184	380	1	p	p	DET
ejpam-184	380	2	6	6	NUM
ejpam-184	380	3	.	.	PUNCT
ejpam-184	380	4	conclusion	conclusion	NOUN
ejpam-184	380	5	we	we	PRON
ejpam-184	380	6	have	have	AUX
ejpam-184	380	7	considered	consider	VERB
ejpam-184	380	8	a	a	DET
ejpam-184	380	9	pair	pair	NOUN
ejpam-184	380	10	of	of	ADP
ejpam-184	380	11	mond	mond	NOUN
ejpam-184	380	12	-	-	PUNCT
ejpam-184	380	13	weir	weir	PROPN
ejpam-184	380	14	type	type	NOUN
ejpam-184	380	15	second	second	ADJ
ejpam-184	380	16	order	order	NOUN
ejpam-184	380	17	dual	dual	ADJ
ejpam-184	380	18	that	that	PRON
ejpam-184	380	19	relaxes	relax	VERB
ejpam-184	380	20	the	the	DET
ejpam-184	380	21	invexity	invexity	NOUN
ejpam-184	380	22	requirement	requirement	NOUN
ejpam-184	380	23	in	in	ADP
ejpam-184	380	24	chen	chen	PROPN
ejpam-184	381	1	[	[	X
ejpam-184	381	2	4	4	X
ejpam-184	381	3	]	]	PUNCT
ejpam-184	381	4	to	to	PART
ejpam-184	381	5	validate	validate	VERB
ejpam-184	381	6	duality	duality	NOUN
ejpam-184	381	7	theorems	theorem	NOUN
ejpam-184	381	8	.	.	PUNCT
ejpam-184	382	1	the	the	DET
ejpam-184	382	2	approach	approach	NOUN
ejpam-184	382	3	chosen	choose	VERB
ejpam-184	382	4	here	here	ADV
ejpam-184	382	5	is	be	AUX
ejpam-184	382	6	to	to	PART
ejpam-184	382	7	render	render	VERB
ejpam-184	382	8	the	the	DET
ejpam-184	382	9	problem	problem	NOUN
ejpam-184	382	10	analogous	analogous	ADJ
ejpam-184	382	11	to	to	ADP
ejpam-184	382	12	the	the	DET
ejpam-184	382	13	second	second	ADJ
ejpam-184	382	14	-	-	PUNCT
ejpam-184	382	15	order	order	NOUN
ejpam-184	382	16	dual	dual	ADJ
ejpam-184	382	17	problems	problem	NOUN
ejpam-184	382	18	introduced	introduce	VERB
ejpam-184	382	19	in	in	ADP
ejpam-184	382	20	[	[	X
ejpam-184	382	21	1	1	NUM
ejpam-184	382	22	]	]	PUNCT
ejpam-184	382	23	as	as	ADP
ejpam-184	382	24	a	a	DET
ejpam-184	382	25	mathematical	mathematical	ADJ
ejpam-184	382	26	programming	programming	NOUN
ejpam-184	382	27	problem	problem	NOUN
ejpam-184	382	28	in	in	ADP
ejpam-184	382	29	infinite	infinite	ADJ
ejpam-184	382	30	dimensional	dimensional	ADJ
ejpam-184	382	31	space	space	NOUN
ejpam-184	382	32	.	.	PUNCT
ejpam-184	383	1	our	our	PRON
ejpam-184	383	2	dual	dual	ADJ
ejpam-184	383	3	model	model	NOUN
ejpam-184	383	4	presents	present	VERB
ejpam-184	383	5	simpler	simple	ADJ
ejpam-184	383	6	dual	dual	ADJ
ejpam-184	383	7	objective	objective	ADJ
ejpam-184	383	8	function	function	NOUN
ejpam-184	383	9	and	and	CCONJ
ejpam-184	383	10	also	also	ADV
ejpam-184	383	11	allows	allow	VERB
ejpam-184	383	12	the	the	DET
ejpam-184	383	13	weaking	weaking	NOUN
ejpam-184	383	14	of	of	ADP
ejpam-184	383	15	the	the	DET
ejpam-184	383	16	invexity	invexity	NOUN
ejpam-184	383	17	assumption	assumption	NOUN
ejpam-184	383	18	of	of	ADP
ejpam-184	383	19	[	[	X
ejpam-184	383	20	4	4	NUM
ejpam-184	383	21	]	]	PUNCT
ejpam-184	383	22	.	.	PUNCT
ejpam-184	384	1	there	there	PRON
ejpam-184	384	2	is	be	VERB
ejpam-184	384	3	a	a	DET
ejpam-184	384	4	rich	rich	ADJ
ejpam-184	384	5	scope	scope	NOUN
ejpam-184	384	6	to	to	PART
ejpam-184	384	7	study	study	VERB
ejpam-184	384	8	this	this	DET
ejpam-184	384	9	problem	problem	NOUN
ejpam-184	384	10	in	in	ADP
ejpam-184	384	11	multiobjective	multiobjective	ADJ
ejpam-184	384	12	setting	setting	NOUN
ejpam-184	384	13	.	.	PUNCT
ejpam-184	385	1	one	one	PRON
ejpam-184	385	2	can	can	AUX
ejpam-184	385	3	also	also	ADV
ejpam-184	385	4	formulate	formulate	VERB
ejpam-184	385	5	a	a	DET
ejpam-184	385	6	fractional	fractional	ADJ
ejpam-184	385	7	analogue	analogue	NOUN
ejpam-184	385	8	of	of	ADP
ejpam-184	385	9	our	our	PRON
ejpam-184	385	10	model	model	NOUN
ejpam-184	385	11	to	to	PART
ejpam-184	385	12	study	study	VERB
ejpam-184	385	13	duality	duality	NOUN
ejpam-184	385	14	results	result	NOUN
ejpam-184	385	15	.	.	PUNCT
ejpam-184	386	1	acknowledgements	acknowledgement	NOUN
ejpam-184	386	2	.	.	PUNCT
ejpam-184	387	1	the	the	DET
ejpam-184	387	2	authors	author	NOUN
ejpam-184	387	3	are	be	AUX
ejpam-184	387	4	grateful	grateful	ADJ
ejpam-184	387	5	to	to	ADP
ejpam-184	387	6	the	the	DET
ejpam-184	387	7	anonymous	anonymous	ADJ
ejpam-184	387	8	referee	referee	NOUN
ejpam-184	387	9	for	for	ADP
ejpam-184	387	10	his	his	PRON
ejpam-184	387	11	/	/	SYM
ejpam-184	387	12	her	her	PRON
ejpam-184	387	13	valuable	valuable	ADJ
ejpam-184	387	14	comments	comment	NOUN
ejpam-184	387	15	that	that	PRON
ejpam-184	387	16	have	have	AUX
ejpam-184	387	17	substantially	substantially	ADV
ejpam-184	387	18	improved	improve	VERB
ejpam-184	387	19	the	the	DET
ejpam-184	387	20	presentation	presentation	NOUN
ejpam-184	387	21	of	of	ADP
ejpam-184	387	22	this	this	DET
ejpam-184	387	23	research	research	NOUN
ejpam-184	387	24	.	.	PUNCT
ejpam-184	388	1	references	reference	NOUN
ejpam-184	388	2	[	[	X
ejpam-184	388	3	1	1	NUM
ejpam-184	388	4	]	]	PUNCT
ejpam-184	388	5	c.r.bector	c.r.bector	NOUN
ejpam-184	388	6	and	and	CCONJ
ejpam-184	388	7	s.chandra	s.chandra	NOUN
ejpam-184	388	8	"	"	PUNCT
ejpam-184	388	9	generalized	generalize	VERB
ejpam-184	388	10	bonvex	bonvex	NOUN
ejpam-184	388	11	functions	function	NOUN
ejpam-184	388	12	and	and	CCONJ
ejpam-184	388	13	second	second	ADJ
ejpam-184	388	14	order	order	NOUN
ejpam-184	388	15	duality	duality	NOUN
ejpam-184	388	16	in	in	ADP
ejpam-184	388	17	mathematical	mathematical	ADJ
ejpam-184	388	18	programming	programming	NOUN
ejpam-184	388	19	"	"	PUNCT
ejpam-184	388	20	,	,	PUNCT
ejpam-184	388	21	department	department	NOUN
ejpam-184	388	22	of	of	ADP
ejpam-184	388	23	act	act	PROPN
ejpam-184	388	24	.	.	PUNCT
ejpam-184	389	1	and	and	CCONJ
ejpam-184	389	2	management	management	NOUN
ejpam-184	389	3	services	service	NOUN
ejpam-184	389	4	,	,	PUNCT
ejpam-184	389	5	research	research	NOUN
ejpam-184	389	6	report	report	NOUN
ejpam-184	389	7	2	2	NUM
ejpam-184	389	8	-	-	SYM
ejpam-184	389	9	85	85	NUM
ejpam-184	389	10	,	,	PUNCT
ejpam-184	389	11	university	university	NOUN
ejpam-184	389	12	of	of	ADP
ejpam-184	389	13	manitoba	manitoba	PROPN
ejpam-184	389	14	,	,	PUNCT
ejpam-184	389	15	winnipeg	winnipeg	PROPN
ejpam-184	389	16	canada	canada	PROPN
ejpam-184	389	17	(	(	PUNCT
ejpam-184	389	18	1985	1985	NUM
ejpam-184	389	19	)	)	PUNCT
ejpam-184	389	20	.	.	PUNCT
ejpam-184	390	1	[	[	X
ejpam-184	390	2	2	2	NUM
ejpam-184	390	3	]	]	PUNCT
ejpam-184	390	4	c.r.bector	c.r.bector	NOUN
ejpam-184	390	5	,	,	PUNCT
ejpam-184	390	6	s.chandra	s.chandra	NOUN
ejpam-184	390	7	and	and	CCONJ
ejpam-184	390	8	i.husain	i.husain	VERB
ejpam-184	390	9	,	,	PUNCT
ejpam-184	390	10	"	"	PUNCT
ejpam-184	390	11	generalized	generalized	ADJ
ejpam-184	390	12	concavity	concavity	NOUN
ejpam-184	390	13	and	and	CCONJ
ejpam-184	390	14	duality	duality	NOUN
ejpam-184	390	15	in	in	ADP
ejpam-184	390	16	continuous	continuous	ADJ
ejpam-184	390	17	programming	programming	NOUN
ejpam-184	390	18	,	,	PUNCT
ejpam-184	390	19	utilitas	utilitas	PROPN
ejpam-184	390	20	mathematica	mathematica	PROPN
ejpam-184	390	21	25	25	NUM
ejpam-184	390	22	(	(	PUNCT
ejpam-184	390	23	1984	1984	NUM
ejpam-184	390	24	)	)	PUNCT
ejpam-184	390	25	.	.	PUNCT
ejpam-184	391	1	[	[	X
ejpam-184	391	2	3	3	X
ejpam-184	391	3	]	]	X
ejpam-184	391	4	s.chandra	s.chandra	NOUN
ejpam-184	391	5	,	,	PUNCT
ejpam-184	391	6	b.d.craven	b.d.craven	NOUN
ejpam-184	391	7	,	,	PUNCT
ejpam-184	391	8	i.husain	i.husain	ADV
ejpam-184	391	9	,	,	PUNCT
ejpam-184	391	10	"	"	PUNCT
ejpam-184	391	11	a	a	DET
ejpam-184	391	12	class	class	NOUN
ejpam-184	391	13	of	of	ADP
ejpam-184	391	14	nondifferentiable	nondifferentiable	ADJ
ejpam-184	391	15	continuous	continuous	ADJ
ejpam-184	391	16	programming	programming	NOUN
ejpam-184	391	17	problems	problem	NOUN
ejpam-184	391	18	"	"	PUNCT
ejpam-184	391	19	,	,	PUNCT
ejpam-184	391	20	j.	j.	PROPN
ejpam-184	391	21	math	math	PROPN
ejpam-184	391	22	.	.	PUNCT
ejpam-184	392	1	anal	anal	ADJ
ejpam-184	392	2	.	.	PUNCT
ejpam-184	393	1	appl.107	appl.107	NOUN
ejpam-184	393	2	:	:	PUNCT
ejpam-184	393	3	122	122	NUM
ejpam-184	393	4	-	-	SYM
ejpam-184	393	5	131	131	NUM
ejpam-184	393	6	(	(	PUNCT
ejpam-184	393	7	1985	1985	NUM
ejpam-184	393	8	)	)	PUNCT
ejpam-184	393	9	.	.	PUNCT
ejpam-184	394	1	[	[	X
ejpam-184	394	2	4	4	X
ejpam-184	394	3	]	]	PUNCT
ejpam-184	394	4	x.chen	x.chen	PUNCT
ejpam-184	394	5	,	,	PUNCT
ejpam-184	394	6	"	"	PUNCT
ejpam-184	394	7	second	second	ADJ
ejpam-184	394	8	order	order	NOUN
ejpam-184	394	9	duality	duality	NOUN
ejpam-184	394	10	for	for	ADP
ejpam-184	394	11	the	the	DET
ejpam-184	394	12	variational	variational	ADJ
ejpam-184	394	13	problems	problem	NOUN
ejpam-184	394	14	"	"	PUNCT
ejpam-184	394	15	,	,	PUNCT
ejpam-184	394	16	j.	j.	PROPN
ejpam-184	394	17	math	math	PROPN
ejpam-184	394	18	.	.	PUNCT
ejpam-184	395	1	anal	anal	PROPN
ejpam-184	395	2	.	.	PUNCT
ejpam-184	395	3	appl	appl	PROPN
ejpam-184	395	4	.	.	PUNCT
ejpam-184	396	1	286	286	NUM
ejpam-184	396	2	261	261	NUM
ejpam-184	396	3	-	-	SYM
ejpam-184	396	4	270	270	NUM
ejpam-184	396	5	(	(	PUNCT
ejpam-184	396	6	2003	2003	NUM
ejpam-184	396	7	)	)	PUNCT
ejpam-184	396	8	.	.	PUNCT
ejpam-184	397	1	references	reference	NOUN
ejpam-184	397	2	295	295	NUM
ejpam-184	398	1	[	[	X
ejpam-184	398	2	5	5	NUM
ejpam-184	398	3	]	]	PUNCT
ejpam-184	398	4	i.husain	i.husain	NOUN
ejpam-184	398	5	and	and	CCONJ
ejpam-184	398	6	z.jabeen	z.jabeen	NUM
ejpam-184	398	7	,	,	PUNCT
ejpam-184	398	8	"	"	PUNCT
ejpam-184	398	9	on	on	ADP
ejpam-184	398	10	continuous	continuous	ADJ
ejpam-184	398	11	programming	programming	NOUN
ejpam-184	398	12	containing	contain	VERB
ejpam-184	398	13	support	support	NOUN
ejpam-184	398	14	functions	function	NOUN
ejpam-184	398	15	"	"	PUNCT
ejpam-184	398	16	,	,	PUNCT
ejpam-184	398	17	j.	j.	PROPN
ejpam-184	398	18	appli	appli	PROPN
ejpam-184	398	19	.	.	PUNCT
ejpam-184	399	1	math	math	PROPN
ejpam-184	399	2	.	.	PUNCT
ejpam-184	400	1	and	and	CCONJ
ejpam-184	400	2	informatics	informatics	PROPN
ejpam-184	400	3	vol	vol	NOUN
ejpam-184	400	4	.	.	PROPN
ejpam-184	401	1	26	26	NUM
ejpam-184	401	2	no	no	NOUN
ejpam-184	401	3	.	.	NOUN
ejpam-184	402	1	1	1	NUM
ejpam-184	402	2	-	-	SYM
ejpam-184	402	3	2	2	NUM
ejpam-184	402	4	,	,	PUNCT
ejpam-184	402	5	75	75	NUM
ejpam-184	402	6	-	-	SYM
ejpam-184	402	7	106	106	NUM
ejpam-184	402	8	(	(	PUNCT
ejpam-184	402	9	2008	2008	NUM
ejpam-184	402	10	)	)	PUNCT
ejpam-184	402	11	.	.	PUNCT
ejpam-184	403	1	[	[	X
ejpam-184	403	2	6	6	NUM
ejpam-184	403	3	]	]	SYM
ejpam-184	403	4	m.a.hanson	m.a.hanson	NOUN
ejpam-184	403	5	,	,	PUNCT
ejpam-184	403	6	"	"	PUNCT
ejpam-184	403	7	bounds	bound	VERB
ejpam-184	403	8	for	for	ADP
ejpam-184	403	9	functionally	functionally	ADV
ejpam-184	403	10	convex	convex	VERB
ejpam-184	403	11	optimal	optimal	ADJ
ejpam-184	403	12	control	control	NOUN
ejpam-184	403	13	problems	problem	NOUN
ejpam-184	403	14	"	"	PUNCT
ejpam-184	403	15	,	,	PUNCT
ejpam-184	403	16	j.	j.	PROPN
ejpam-184	403	17	math	math	PROPN
ejpam-184	403	18	.	.	PUNCT
ejpam-184	404	1	anal	anal	PROPN
ejpam-184	404	2	.	.	PUNCT
ejpam-184	405	1	appl	appl	PROPN
ejpam-184	405	2	.	.	PROPN
ejpam-184	406	1	8	8	NUM
ejpam-184	406	2	:	:	SYM
ejpam-184	406	3	84	84	NUM
ejpam-184	406	4	-	-	SYM
ejpam-184	406	5	89	89	NUM
ejpam-184	406	6	(	(	PUNCT
ejpam-184	406	7	1964	1964	NUM
ejpam-184	406	8	)	)	PUNCT
ejpam-184	406	9	.	.	PUNCT
ejpam-184	407	1	[	[	X
ejpam-184	407	2	7	7	X
ejpam-184	407	3	]	]	X
ejpam-184	407	4	o.l.mangasarian	o.l.mangasarian	ADJ
ejpam-184	407	5	,	,	PUNCT
ejpam-184	407	6	"	"	PUNCT
ejpam-184	407	7	second	second	ADJ
ejpam-184	407	8	and	and	CCONJ
ejpam-184	407	9	higher	high	ADJ
ejpam-184	407	10	order	order	NOUN
ejpam-184	407	11	duality	duality	NOUN
ejpam-184	407	12	in	in	ADP
ejpam-184	407	13	non	non	ADJ
ejpam-184	407	14	linear	linear	PROPN
ejpam-184	407	15	programming	programming	NOUN
ejpam-184	407	16	"	"	PUNCT
ejpam-184	407	17	,	,	PUNCT
ejpam-184	407	18	j.	j.	PROPN
ejpam-184	407	19	math	math	PROPN
ejpam-184	407	20	.	.	PUNCT
ejpam-184	408	1	anal	anal	PROPN
ejpam-184	408	2	.	.	PUNCT
ejpam-184	409	1	appl.51	appl.51	NOUN
ejpam-184	409	2	:	:	PUNCT
ejpam-184	409	3	605	605	NUM
ejpam-184	409	4	-	-	PUNCT
ejpam-184	409	5	620(1979	620(1979	NUM
ejpam-184	409	6	)	)	PUNCT
ejpam-184	409	7	.	.	PUNCT
ejpam-184	410	1	[	[	X
ejpam-184	410	2	8	8	NUM
ejpam-184	410	3	]	]	SYM
ejpam-184	410	4	b.mond	b.mond	NOUN
ejpam-184	410	5	and	and	CCONJ
ejpam-184	410	6	m.a.hanson	m.a.hanson	NOUN
ejpam-184	410	7	,	,	PUNCT
ejpam-184	410	8	"	"	PUNCT
ejpam-184	410	9	duality	duality	NOUN
ejpam-184	410	10	for	for	ADP
ejpam-184	410	11	variational	variational	ADJ
ejpam-184	410	12	problems	problem	NOUN
ejpam-184	410	13	"	"	PUNCT
ejpam-184	410	14	,	,	PUNCT
ejpam-184	410	15	j.	j.	PROPN
ejpam-184	410	16	math	math	PROPN
ejpam-184	410	17	.	.	PUNCT
ejpam-184	411	1	anal	anal	PROPN
ejpam-184	411	2	.	.	PUNCT
ejpam-184	412	1	appl	appl	PROPN
ejpam-184	412	2	.	.	PROPN
ejpam-184	413	1	18	18	NUM
ejpam-184	413	2	:	:	SYM
ejpam-184	413	3	355	355	NUM
ejpam-184	413	4	-	-	SYM
ejpam-184	413	5	364	364	NUM
ejpam-184	413	6	(	(	PUNCT
ejpam-184	413	7	1965	1965	NUM
ejpam-184	413	8	)	)	PUNCT
ejpam-184	413	9	.	.	PUNCT
ejpam-184	414	1	[	[	X
ejpam-184	414	2	9	9	NUM
ejpam-184	414	3	]	]	SYM
ejpam-184	414	4	b.mond	b.mond	NOUN
ejpam-184	414	5	,	,	PUNCT
ejpam-184	414	6	"	"	PUNCT
ejpam-184	414	7	second	second	ADJ
ejpam-184	414	8	order	order	NOUN
ejpam-184	414	9	duality	duality	NOUN
ejpam-184	414	10	in	in	ADP
ejpam-184	414	11	non	non	ADJ
ejpam-184	414	12	-	-	ADJ
ejpam-184	414	13	linear	linear	ADJ
ejpam-184	414	14	programming	programming	NOUN
ejpam-184	414	15	"	"	PUNCT
ejpam-184	414	16	,	,	PUNCT
ejpam-184	414	17	opsearch	opsearch	NOUN
ejpam-184	414	18	,	,	PUNCT
ejpam-184	414	19	11	11	NUM
ejpam-184	414	20	:	:	SYM
ejpam-184	414	21	90	90	NUM
ejpam-184	414	22	-	-	SYM
ejpam-184	414	23	99	99	NUM
ejpam-184	414	24	(	(	PUNCT
ejpam-184	414	25	1974	1974	NUM
ejpam-184	414	26	)	)	PUNCT
ejpam-184	414	27	.	.	PUNCT
ejpam-184	415	1	[	[	X
ejpam-184	415	2	10	10	NUM
ejpam-184	415	3	]	]	X
ejpam-184	415	4	f.a.valentine	f.a.valentine	NOUN
ejpam-184	415	5	,	,	PUNCT
ejpam-184	415	6	the	the	DET
ejpam-184	415	7	problem	problem	NOUN
ejpam-184	415	8	of	of	ADP
ejpam-184	415	9	lagrange	lagrange	NOUN
ejpam-184	415	10	with	with	ADP
ejpam-184	415	11	differential	differential	ADJ
ejpam-184	415	12	inequalities	inequality	NOUN
ejpam-184	415	13	as	as	ADP
ejpam-184	415	14	added	add	VERB
ejpam-184	415	15	side	side	NOUN
ejpam-184	415	16	conditions	condition	NOUN
ejpam-184	415	17	,	,	PUNCT
ejpam-184	415	18	"	"	PUNCT
ejpam-184	415	19	contributions	contribution	NOUN
ejpam-184	415	20	to	to	ADP
ejpam-184	415	21	calculus	calculus	NOUN
ejpam-184	415	22	of	of	ADP
ejpam-184	415	23	variations	variation	NOUN
ejpam-184	415	24	"	"	PUNCT
ejpam-184	415	25	,	,	PUNCT
ejpam-184	415	26	1933	1933	NUM
ejpam-184	415	27	-	-	SYM
ejpam-184	415	28	37	37	NUM
ejpam-184	415	29	,	,	PUNCT
ejpam-184	415	30	university	university	NOUN
ejpam-184	415	31	of	of	ADP
ejpam-184	415	32	chicago	chicago	PROPN
ejpam-184	415	33	press	press	NOUN
ejpam-184	415	34	,	,	PUNCT
ejpam-184	415	35	407	407	NUM
ejpam-184	415	36	-	-	SYM
ejpam-184	415	37	448	448	NUM
ejpam-184	415	38	(	(	PUNCT
ejpam-184	415	39	1937	1937	NUM
ejpam-184	415	40	)	)	PUNCT