id	sid	tid	token	lemma	pos
ejpam-367	1	1	10_367_husain.dvi	10_367_husain.dvi	NUM
ejpam-367	1	2	european	european	ADJ
ejpam-367	1	3	journal	journal	NOUN
ejpam-367	1	4	of	of	ADP
ejpam-367	1	5	pure	pure	ADJ
ejpam-367	1	6	and	and	CCONJ
ejpam-367	1	7	applied	apply	VERB
ejpam-367	1	8	mathematics	mathematic	NOUN
ejpam-367	1	9	vol	vol	NOUN
ejpam-367	1	10	.	.	PROPN
ejpam-367	1	11	2	2	NUM
ejpam-367	1	12	,	,	PUNCT
ejpam-367	1	13	no	no	INTJ
ejpam-367	1	14	.	.	NOUN
ejpam-367	1	15	4	4	NUM
ejpam-367	1	16	,	,	PUNCT
ejpam-367	1	17	2009	2009	NUM
ejpam-367	1	18	,	,	PUNCT
ejpam-367	1	19	(	(	PUNCT
ejpam-367	1	20	578	578	NUM
ejpam-367	1	21	-	-	SYM
ejpam-367	1	22	603	603	NUM
ejpam-367	1	23	)	)	PUNCT
ejpam-367	1	24	issn	issn	PROPN
ejpam-367	1	25	1307	1307	NUM
ejpam-367	1	26	-	-	SYM
ejpam-367	1	27	5543	5543	NUM
ejpam-367	1	28	–	–	PUNCT
ejpam-367	1	29	www.ejpam.com	www.ejpam.com	X
ejpam-367	1	30	mixed	mixed	ADJ
ejpam-367	1	31	type	type	NOUN
ejpam-367	1	32	symmetric	symmetric	ADJ
ejpam-367	1	33	and	and	CCONJ
ejpam-367	1	34	self	self	NOUN
ejpam-367	1	35	-	-	PUNCT
ejpam-367	1	36	duality	duality	NOUN
ejpam-367	1	37	for	for	ADP
ejpam-367	1	38	multiobjective	multiobjective	ADJ
ejpam-367	1	39	variational	variational	ADJ
ejpam-367	1	40	problems	problem	NOUN
ejpam-367	1	41	i.	i.	PROPN
ejpam-367	1	42	husain1∗	husain1∗	PROPN
ejpam-367	1	43	and	and	CCONJ
ejpam-367	1	44	rumana	rumana	PROPN
ejpam-367	1	45	g.	g.	PROPN
ejpam-367	1	46	mattoo2	mattoo2	PROPN
ejpam-367	2	1	1	1	NUM
ejpam-367	2	2	department	department	NOUN
ejpam-367	2	3	of	of	ADP
ejpam-367	2	4	mathematics	mathematics	PROPN
ejpam-367	2	5	,	,	PUNCT
ejpam-367	2	6	jaypee	jaypee	PROPN
ejpam-367	2	7	institute	institute	PROPN
ejpam-367	2	8	of	of	ADP
ejpam-367	2	9	engineering	engineering	NOUN
ejpam-367	2	10	and	and	CCONJ
ejpam-367	2	11	technology	technology	NOUN
ejpam-367	2	12	,	,	PUNCT
ejpam-367	2	13	guna	guna	PROPN
ejpam-367	2	14	,	,	PUNCT
ejpam-367	2	15	mp	mp	PROPN
ejpam-367	2	16	,	,	PUNCT
ejpam-367	2	17	india	india	PROPN
ejpam-367	2	18	.	.	PUNCT
ejpam-367	3	1	(	(	PUNCT
ejpam-367	3	2	a	a	DET
ejpam-367	3	3	constituent	constituent	ADJ
ejpam-367	3	4	centre	centre	NOUN
ejpam-367	3	5	of	of	ADP
ejpam-367	3	6	jaypee	jaypee	PROPN
ejpam-367	3	7	university	university	PROPN
ejpam-367	3	8	of	of	ADP
ejpam-367	3	9	information	information	NOUN
ejpam-367	3	10	technology	technology	PROPN
ejpam-367	3	11	,	,	PUNCT
ejpam-367	3	12	waknaghat	waknaghat	PROPN
ejpam-367	3	13	,	,	PUNCT
ejpam-367	3	14	solan	solan	PROPN
ejpam-367	3	15	,	,	PUNCT
ejpam-367	3	16	hp	hp	PROPN
ejpam-367	3	17	,	,	PUNCT
ejpam-367	3	18	india	india	PROPN
ejpam-367	3	19	)	)	PUNCT
ejpam-367	3	20	2	2	NUM
ejpam-367	3	21	department	department	NOUN
ejpam-367	3	22	of	of	ADP
ejpam-367	3	23	statistics	statistic	NOUN
ejpam-367	3	24	,	,	PUNCT
ejpam-367	3	25	university	university	PROPN
ejpam-367	3	26	of	of	ADP
ejpam-367	3	27	kashmir	kashmir	PROPN
ejpam-367	3	28	,	,	PUNCT
ejpam-367	3	29	srinagar	srinagar	PROPN
ejpam-367	3	30	,	,	PUNCT
ejpam-367	3	31	kashmir	kashmir	PROPN
ejpam-367	3	32	,	,	PUNCT
ejpam-367	3	33	india	india	PROPN
ejpam-367	3	34	.	.	PUNCT
ejpam-367	4	1	abstract	abstract	PROPN
ejpam-367	4	2	.	.	PUNCT
ejpam-367	5	1	in	in	ADP
ejpam-367	5	2	this	this	DET
ejpam-367	5	3	paper	paper	NOUN
ejpam-367	5	4	,	,	PUNCT
ejpam-367	5	5	a	a	DET
ejpam-367	5	6	new	new	ADJ
ejpam-367	5	7	formulation	formulation	NOUN
ejpam-367	5	8	of	of	ADP
ejpam-367	5	9	multiobjective	multiobjective	ADJ
ejpam-367	5	10	symmetric	symmetric	ADJ
ejpam-367	5	11	dual	dual	ADJ
ejpam-367	5	12	pair	pair	NOUN
ejpam-367	5	13	,	,	PUNCT
ejpam-367	5	14	called	call	VERB
ejpam-367	5	15	mixed	mixed	ADJ
ejpam-367	5	16	type	type	NOUN
ejpam-367	5	17	multiobjective	multiobjective	ADJ
ejpam-367	5	18	symmetric	symmetric	ADJ
ejpam-367	5	19	dual	dual	ADJ
ejpam-367	5	20	pair	pair	NOUN
ejpam-367	5	21	,	,	PUNCT
ejpam-367	5	22	for	for	ADP
ejpam-367	5	23	multiobjective	multiobjective	ADJ
ejpam-367	5	24	variational	variational	ADJ
ejpam-367	5	25	problems	problem	NOUN
ejpam-367	5	26	is	be	AUX
ejpam-367	5	27	presented	present	VERB
ejpam-367	5	28	.	.	PUNCT
ejpam-367	6	1	this	this	DET
ejpam-367	6	2	mixed	mixed	ADJ
ejpam-367	6	3	formulation	formulation	NOUN
ejpam-367	6	4	unifies	unify	VERB
ejpam-367	6	5	two	two	NUM
ejpam-367	6	6	existing	exist	VERB
ejpam-367	6	7	wolfe	wolfe	PROPN
ejpam-367	6	8	and	and	CCONJ
ejpam-367	6	9	mond	mond	PROPN
ejpam-367	6	10	-	-	PUNCT
ejpam-367	6	11	weir	weir	PROPN
ejpam-367	6	12	type	type	PROPN
ejpam-367	6	13	symmetric	symmetric	ADJ
ejpam-367	6	14	dual	dual	ADJ
ejpam-367	6	15	pairs	pair	NOUN
ejpam-367	6	16	of	of	ADP
ejpam-367	6	17	multiobjective	multiobjective	ADJ
ejpam-367	6	18	variational	variational	ADJ
ejpam-367	6	19	problems	problem	NOUN
ejpam-367	6	20	.	.	PUNCT
ejpam-367	7	1	for	for	ADP
ejpam-367	7	2	this	this	DET
ejpam-367	7	3	pair	pair	NOUN
ejpam-367	7	4	of	of	ADP
ejpam-367	7	5	mixed	mixed	ADJ
ejpam-367	7	6	type	type	NOUN
ejpam-367	7	7	multiobjective	multiobjective	ADJ
ejpam-367	7	8	variational	variational	ADJ
ejpam-367	7	9	problems	problem	NOUN
ejpam-367	7	10	,	,	PUNCT
ejpam-367	7	11	various	various	ADJ
ejpam-367	7	12	duality	duality	NOUN
ejpam-367	7	13	theorems	theorem	NOUN
ejpam-367	7	14	are	be	AUX
ejpam-367	7	15	established	establish	VERB
ejpam-367	7	16	under	under	ADP
ejpam-367	7	17	invexity	invexity	NOUN
ejpam-367	7	18	-	-	PUNCT
ejpam-367	7	19	incavity	incavity	NOUN
ejpam-367	7	20	and	and	CCONJ
ejpam-367	7	21	pseudoinvexity	pseudoinvexity	NOUN
ejpam-367	7	22	-	-	PUNCT
ejpam-367	7	23	pseudoincavity	pseudoincavity	NOUN
ejpam-367	7	24	of	of	ADP
ejpam-367	7	25	kernel	kernel	PROPN
ejpam-367	7	26	functions	function	NOUN
ejpam-367	7	27	appearing	appear	VERB
ejpam-367	7	28	in	in	ADP
ejpam-367	7	29	the	the	DET
ejpam-367	7	30	problems	problem	NOUN
ejpam-367	7	31	.	.	PUNCT
ejpam-367	8	1	under	under	ADP
ejpam-367	8	2	additional	additional	ADJ
ejpam-367	8	3	hypotheses	hypothesis	NOUN
ejpam-367	8	4	,	,	PUNCT
ejpam-367	8	5	a	a	DET
ejpam-367	8	6	self	self	NOUN
ejpam-367	8	7	duality	duality	NOUN
ejpam-367	8	8	theorem	theorem	NOUN
ejpam-367	8	9	is	be	AUX
ejpam-367	8	10	validated	validate	VERB
ejpam-367	8	11	.	.	PUNCT
ejpam-367	9	1	it	it	PRON
ejpam-367	9	2	is	be	AUX
ejpam-367	9	3	also	also	ADV
ejpam-367	9	4	pointed	point	VERB
ejpam-367	9	5	that	that	SCONJ
ejpam-367	9	6	our	our	PRON
ejpam-367	9	7	duality	duality	NOUN
ejpam-367	9	8	theorems	theorem	NOUN
ejpam-367	9	9	can	can	AUX
ejpam-367	9	10	be	be	AUX
ejpam-367	9	11	viewed	view	VERB
ejpam-367	9	12	as	as	ADP
ejpam-367	9	13	dynamic	dynamic	ADJ
ejpam-367	9	14	generalization	generalization	NOUN
ejpam-367	9	15	of	of	ADP
ejpam-367	9	16	the	the	DET
ejpam-367	9	17	corresponding	corresponding	ADJ
ejpam-367	9	18	(	(	PUNCT
ejpam-367	9	19	static	static	ADJ
ejpam-367	9	20	)	)	PUNCT
ejpam-367	9	21	symmetric	symmetric	ADJ
ejpam-367	9	22	and	and	CCONJ
ejpam-367	9	23	self	self	NOUN
ejpam-367	9	24	duality	duality	NOUN
ejpam-367	9	25	of	of	ADP
ejpam-367	9	26	multiobjective	multiobjective	ADJ
ejpam-367	9	27	nonlinear	nonlinear	ADJ
ejpam-367	9	28	programming	programming	NOUN
ejpam-367	9	29	already	already	ADV
ejpam-367	9	30	existing	exist	VERB
ejpam-367	9	31	in	in	ADP
ejpam-367	9	32	the	the	DET
ejpam-367	9	33	literature	literature	NOUN
ejpam-367	9	34	.	.	PUNCT
ejpam-367	10	1	2000	2000	NUM
ejpam-367	10	2	mathematics	mathematic	NOUN
ejpam-367	10	3	subject	subject	NOUN
ejpam-367	10	4	classifications	classification	NOUN
ejpam-367	10	5	:	:	PUNCT
ejpam-367	10	6	primary	primary	ADJ
ejpam-367	10	7	90c30	90c30	NUM
ejpam-367	10	8	,	,	PUNCT
ejpam-367	10	9	secondary	secondary	ADJ
ejpam-367	10	10	90c11	90c11	NUM
ejpam-367	10	11	,	,	PUNCT
ejpam-367	10	12	90c20	90c20	NUM
ejpam-367	10	13	,	,	PUNCT
ejpam-367	10	14	90c26	90c26	NUM
ejpam-367	10	15	.	.	PUNCT
ejpam-367	11	1	key	key	ADJ
ejpam-367	11	2	words	word	NOUN
ejpam-367	11	3	and	and	CCONJ
ejpam-367	11	4	phrases	phrase	NOUN
ejpam-367	11	5	:	:	PUNCT
ejpam-367	11	6	efficiency	efficiency	NOUN
ejpam-367	11	7	;	;	PUNCT
ejpam-367	11	8	mixed	mixed	ADJ
ejpam-367	11	9	type	type	NOUN
ejpam-367	11	10	multiobjective	multiobjective	ADJ
ejpam-367	11	11	symmetric	symmetric	ADJ
ejpam-367	11	12	dual	dual	ADJ
ejpam-367	11	13	variational	variational	ADJ
ejpam-367	11	14	problem	problem	NOUN
ejpam-367	11	15	;	;	PUNCT
ejpam-367	11	16	mixed	mixed	ADJ
ejpam-367	11	17	type	type	NOUN
ejpam-367	11	18	symmetric	symmetric	ADJ
ejpam-367	11	19	duality	duality	NOUN
ejpam-367	11	20	;	;	PUNCT
ejpam-367	11	21	mixed	mixed	ADJ
ejpam-367	11	22	type	type	NOUN
ejpam-367	11	23	self	self	NOUN
ejpam-367	11	24	duality	duality	NOUN
ejpam-367	11	25	;	;	PUNCT
ejpam-367	11	26	natural	natural	ADJ
ejpam-367	11	27	boundary	boundary	ADJ
ejpam-367	11	28	values	value	NOUN
ejpam-367	11	29	;	;	PUNCT
ejpam-367	11	30	multiobjective	multiobjective	ADJ
ejpam-367	11	31	nonlinear	nonlinear	ADJ
ejpam-367	11	32	programming	programming	NOUN
ejpam-367	11	33	.	.	PUNCT
ejpam-367	12	1	∗corresponding	∗corresponde	VERB
ejpam-367	12	2	author	author	NOUN
ejpam-367	12	3	.	.	PUNCT
ejpam-367	13	1	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-367	14	1	578	578	NUM
ejpam-367	14	2	c	c	X
ejpam-367	14	3	©	©	PROPN
ejpam-367	14	4	2009	2009	NUM
ejpam-367	14	5	ejpam	ejpam	NOUN
ejpam-367	14	6	all	all	DET
ejpam-367	14	7	rights	right	NOUN
ejpam-367	14	8	reserved	reserve	VERB
ejpam-367	14	9	.	.	PUNCT
ejpam-367	15	1	i.	i.	PROPN
ejpam-367	15	2	husain	husain	PROPN
ejpam-367	15	3	and	and	CCONJ
ejpam-367	15	4	r.	r.	PROPN
ejpam-367	15	5	mattoo	mattoo	PROPN
ejpam-367	15	6	/	/	SYM
ejpam-367	15	7	eur	eur	PROPN
ejpam-367	15	8	.	.	PUNCT
ejpam-367	16	1	j.	j.	PROPN
ejpam-367	16	2	pure	pure	PROPN
ejpam-367	16	3	appl	appl	PROPN
ejpam-367	16	4	.	.	PROPN
ejpam-367	16	5	math	math	PROPN
ejpam-367	16	6	,	,	PUNCT
ejpam-367	16	7	2	2	NUM
ejpam-367	16	8	(	(	PUNCT
ejpam-367	16	9	2009	2009	NUM
ejpam-367	16	10	)	)	PUNCT
ejpam-367	16	11	,	,	PUNCT
ejpam-367	16	12	(	(	PUNCT
ejpam-367	16	13	578	578	NUM
ejpam-367	16	14	-	-	SYM
ejpam-367	16	15	603	603	NUM
ejpam-367	16	16	)	)	PUNCT
ejpam-367	16	17	579	579	NUM
ejpam-367	16	18	1	1	NUM
ejpam-367	16	19	.	.	PUNCT
ejpam-367	17	1	introduction	introduction	NOUN
ejpam-367	17	2	following	follow	VERB
ejpam-367	17	3	dorn	dorn	PROPN
ejpam-367	17	4	[	[	X
ejpam-367	17	5	7	7	NUM
ejpam-367	17	6	]	]	PUNCT
ejpam-367	17	7	,	,	PUNCT
ejpam-367	17	8	symmetric	symmetric	ADJ
ejpam-367	17	9	duality	duality	NOUN
ejpam-367	17	10	results	result	VERB
ejpam-367	17	11	in	in	ADP
ejpam-367	17	12	mathematical	mathematical	ADJ
ejpam-367	17	13	programming	programming	NOUN
ejpam-367	17	14	have	have	AUX
ejpam-367	17	15	been	be	AUX
ejpam-367	17	16	derived	derive	VERB
ejpam-367	17	17	by	by	ADP
ejpam-367	17	18	a	a	DET
ejpam-367	17	19	number	number	NOUN
ejpam-367	17	20	of	of	ADP
ejpam-367	17	21	authors	author	NOUN
ejpam-367	17	22	,	,	PUNCT
ejpam-367	17	23	notably	notably	ADV
ejpam-367	17	24	,	,	PUNCT
ejpam-367	17	25	dantzig	dantzig	VERB
ejpam-367	17	26	et	et	NOUN
ejpam-367	17	27	al	al	PROPN
ejpam-367	18	1	[	[	X
ejpam-367	18	2	8	8	NUM
ejpam-367	18	3	]	]	PUNCT
ejpam-367	18	4	,	,	PUNCT
ejpam-367	18	5	mond	mond	NOUN
ejpam-367	19	1	[	[	X
ejpam-367	19	2	12	12	NUM
ejpam-367	19	3	]	]	PUNCT
ejpam-367	19	4	,	,	PUNCT
ejpam-367	19	5	bazaraa	bazaraa	NOUN
ejpam-367	19	6	and	and	CCONJ
ejpam-367	19	7	goode	goode	VERB
ejpam-367	20	1	[	[	X
ejpam-367	20	2	1	1	NUM
ejpam-367	20	3	]	]	PUNCT
ejpam-367	20	4	.	.	PUNCT
ejpam-367	21	1	in	in	ADP
ejpam-367	21	2	these	these	DET
ejpam-367	21	3	researches	research	NOUN
ejpam-367	21	4	,	,	PUNCT
ejpam-367	21	5	the	the	DET
ejpam-367	21	6	authors	author	NOUN
ejpam-367	21	7	have	have	AUX
ejpam-367	21	8	studied	study	VERB
ejpam-367	21	9	symmetric	symmetric	ADJ
ejpam-367	21	10	duality	duality	NOUN
ejpam-367	21	11	under	under	ADP
ejpam-367	21	12	the	the	DET
ejpam-367	21	13	hypothesis	hypothesis	NOUN
ejpam-367	21	14	of	of	ADP
ejpam-367	21	15	convexity	convexity	NOUN
ejpam-367	21	16	-	-	PUNCT
ejpam-367	21	17	concavity	concavity	NOUN
ejpam-367	21	18	of	of	ADP
ejpam-367	21	19	the	the	DET
ejpam-367	21	20	kernel	kernel	PROPN
ejpam-367	21	21	function	function	NOUN
ejpam-367	21	22	involved	involve	VERB
ejpam-367	21	23	.	.	PUNCT
ejpam-367	22	1	mond	mond	NOUN
ejpam-367	22	2	and	and	CCONJ
ejpam-367	22	3	cottle	cottle	NOUN
ejpam-367	23	1	[	[	X
ejpam-367	23	2	13	13	NUM
ejpam-367	23	3	]	]	PUNCT
ejpam-367	23	4	presented	present	VERB
ejpam-367	23	5	self	self	NOUN
ejpam-367	23	6	duality	duality	NOUN
ejpam-367	23	7	for	for	ADP
ejpam-367	23	8	the	the	DET
ejpam-367	23	9	problems	problem	NOUN
ejpam-367	23	10	of	of	ADP
ejpam-367	23	11	[	[	X
ejpam-367	23	12	8	8	NUM
ejpam-367	23	13	]	]	PUNCT
ejpam-367	23	14	by	by	ADP
ejpam-367	23	15	assuming	assume	VERB
ejpam-367	23	16	skew	skew	ADJ
ejpam-367	23	17	symmetric	symmetric	NOUN
ejpam-367	23	18	of	of	ADP
ejpam-367	23	19	the	the	DET
ejpam-367	23	20	kernel	kernel	PROPN
ejpam-367	23	21	function	function	PROPN
ejpam-367	23	22	.	.	PUNCT
ejpam-367	24	1	later	later	ADV
ejpam-367	24	2	mond	mond	PROPN
ejpam-367	24	3	-	-	PUNCT
ejpam-367	24	4	weir	weir	NOUN
ejpam-367	24	5	[	[	X
ejpam-367	24	6	14	14	NUM
ejpam-367	24	7	]	]	PUNCT
ejpam-367	24	8	formulated	formulate	VERB
ejpam-367	24	9	a	a	DET
ejpam-367	24	10	different	different	ADJ
ejpam-367	24	11	pair	pair	NOUN
ejpam-367	24	12	of	of	ADP
ejpam-367	24	13	symmetric	symmetric	ADJ
ejpam-367	24	14	dual	dual	ADJ
ejpam-367	24	15	nonlinear	nonlinear	ADJ
ejpam-367	24	16	program	program	NOUN
ejpam-367	24	17	with	with	ADP
ejpam-367	24	18	a	a	DET
ejpam-367	24	19	view	view	NOUN
ejpam-367	24	20	to	to	PART
ejpam-367	24	21	generalize	generalize	VERB
ejpam-367	24	22	convexity	convexity	NOUN
ejpam-367	24	23	-	-	PUNCT
ejpam-367	24	24	concavity	concavity	NOUN
ejpam-367	24	25	of	of	ADP
ejpam-367	24	26	the	the	DET
ejpam-367	24	27	kernel	kernel	PROPN
ejpam-367	24	28	function	function	NOUN
ejpam-367	24	29	to	to	ADP
ejpam-367	24	30	pseudoconvexity	pseudoconvexity	NOUN
ejpam-367	24	31	-	-	PUNCT
ejpam-367	24	32	pseudoconcavity	pseudoconcavity	NOUN
ejpam-367	24	33	.	.	PUNCT
ejpam-367	25	1	symmetric	symmetric	ADJ
ejpam-367	25	2	duality	duality	NOUN
ejpam-367	25	3	for	for	ADP
ejpam-367	25	4	variational	variational	ADJ
ejpam-367	25	5	problems	problem	NOUN
ejpam-367	25	6	was	be	AUX
ejpam-367	25	7	first	first	ADV
ejpam-367	25	8	introduced	introduce	VERB
ejpam-367	25	9	by	by	ADP
ejpam-367	25	10	mond	mond	NOUN
ejpam-367	25	11	and	and	CCONJ
ejpam-367	25	12	hanson	hanson	NOUN
ejpam-367	26	1	[	[	X
ejpam-367	26	2	15	15	NUM
ejpam-367	26	3	]	]	PUNCT
ejpam-367	26	4	under	under	ADP
ejpam-367	26	5	the	the	DET
ejpam-367	26	6	convexity	convexity	NOUN
ejpam-367	26	7	-	-	PUNCT
ejpam-367	26	8	concavity	concavity	NOUN
ejpam-367	26	9	conditions	condition	NOUN
ejpam-367	26	10	of	of	ADP
ejpam-367	26	11	a	a	DET
ejpam-367	26	12	scalar	scalar	ADJ
ejpam-367	26	13	functions	function	NOUN
ejpam-367	26	14	like	like	ADP
ejpam-367	26	15	ψ(t	ψ(t	PROPN
ejpam-367	26	16	,	,	PUNCT
ejpam-367	26	17	x(t	x(t	PROPN
ejpam-367	26	18	)	)	PUNCT
ejpam-367	26	19	,	,	PUNCT
ejpam-367	26	20	ẋ(t	ẋ(t	NOUN
ejpam-367	26	21	)	)	PUNCT
ejpam-367	26	22	,	,	PUNCT
ejpam-367	26	23	y(t	y(t	PROPN
ejpam-367	26	24	)	)	PUNCT
ejpam-367	26	25	,	,	PUNCT
ejpam-367	26	26	ẏ(t	ẏ(t	PROPN
ejpam-367	26	27	)	)	PUNCT
ejpam-367	26	28	)	)	PUNCT
ejpam-367	26	29	with	with	ADP
ejpam-367	26	30	x(t	x(t	PROPN
ejpam-367	26	31	)	)	PUNCT
ejpam-367	26	32	∈	∈	PROPN
ejpam-367	26	33	rn	rn	PROPN
ejpam-367	26	34	and	and	CCONJ
ejpam-367	26	35	y(t	y(t	PROPN
ejpam-367	26	36	)	)	PUNCT
ejpam-367	26	37	∈	∈	PROPN
ejpam-367	26	38	rm	rm	PROPN
ejpam-367	26	39	.	.	PROPN
ejpam-367	26	40	bector	bector	PROPN
ejpam-367	26	41	,	,	PUNCT
ejpam-367	26	42	chandra	chandra	PROPN
ejpam-367	26	43	and	and	CCONJ
ejpam-367	26	44	husain	husain	PROPN
ejpam-367	26	45	[	[	X
ejpam-367	26	46	3	3	X
ejpam-367	26	47	]	]	PUNCT
ejpam-367	26	48	presented	present	VERB
ejpam-367	26	49	a	a	DET
ejpam-367	26	50	different	different	ADJ
ejpam-367	26	51	pair	pair	NOUN
ejpam-367	26	52	of	of	ADP
ejpam-367	26	53	symmetric	symmetric	ADJ
ejpam-367	26	54	dual	dual	ADJ
ejpam-367	26	55	variational	variational	ADJ
ejpam-367	26	56	problems	problem	NOUN
ejpam-367	26	57	in	in	ADP
ejpam-367	26	58	order	order	NOUN
ejpam-367	26	59	to	to	PART
ejpam-367	26	60	relax	relax	VERB
ejpam-367	26	61	the	the	DET
ejpam-367	26	62	requirement	requirement	NOUN
ejpam-367	26	63	of	of	ADP
ejpam-367	26	64	convexity	convexity	NOUN
ejpam-367	26	65	-	-	PUNCT
ejpam-367	26	66	concavity	concavity	NOUN
ejpam-367	26	67	to	to	ADP
ejpam-367	26	68	that	that	PRON
ejpam-367	26	69	of	of	ADP
ejpam-367	26	70	pseudoconvexity	pseudoconvexity	NOUN
ejpam-367	26	71	-	-	PUNCT
ejpam-367	26	72	pseudoconcavity	pseudoconcavity	NOUN
ejpam-367	26	73	while	while	SCONJ
ejpam-367	26	74	in	in	ADP
ejpam-367	26	75	[	[	PUNCT
ejpam-367	26	76	6	6	NUM
ejpam-367	26	77	]	]	X
ejpam-367	26	78	chandra	chandra	PROPN
ejpam-367	26	79	and	and	CCONJ
ejpam-367	26	80	husain	husain	PROPN
ejpam-367	26	81	gave	give	VERB
ejpam-367	26	82	a	a	DET
ejpam-367	26	83	fractional	fractional	ADJ
ejpam-367	26	84	analogue	analogue	NOUN
ejpam-367	26	85	.	.	PUNCT
ejpam-367	27	1	bector	bector	NOUN
ejpam-367	27	2	and	and	CCONJ
ejpam-367	27	3	husain	husain	NOUN
ejpam-367	28	1	[	[	X
ejpam-367	28	2	4	4	X
ejpam-367	28	3	]	]	PUNCT
ejpam-367	28	4	probably	probably	ADV
ejpam-367	28	5	were	be	AUX
ejpam-367	28	6	the	the	DET
ejpam-367	28	7	first	first	ADJ
ejpam-367	28	8	to	to	PART
ejpam-367	28	9	study	study	VERB
ejpam-367	28	10	duality	duality	NOUN
ejpam-367	28	11	for	for	ADP
ejpam-367	28	12	multiobjective	multiobjective	ADJ
ejpam-367	28	13	variational	variational	ADJ
ejpam-367	28	14	problems	problem	NOUN
ejpam-367	28	15	under	under	ADP
ejpam-367	28	16	appropriate	appropriate	ADJ
ejpam-367	28	17	convexity	convexity	NOUN
ejpam-367	28	18	assumptions	assumption	NOUN
ejpam-367	28	19	.	.	PUNCT
ejpam-367	29	1	subsequently	subsequently	ADV
ejpam-367	29	2	,	,	PUNCT
ejpam-367	29	3	gulati	gulati	PROPN
ejpam-367	29	4	,	,	PUNCT
ejpam-367	29	5	husain	husain	PROPN
ejpam-367	29	6	and	and	CCONJ
ejpam-367	29	7	ahmed	ahme	VERB
ejpam-367	29	8	[	[	X
ejpam-367	29	9	9	9	NUM
ejpam-367	29	10	]	]	PUNCT
ejpam-367	29	11	presented	present	VERB
ejpam-367	29	12	two	two	NUM
ejpam-367	29	13	distinct	distinct	ADJ
ejpam-367	29	14	pairs	pair	NOUN
ejpam-367	29	15	of	of	ADP
ejpam-367	29	16	symmetric	symmetric	ADJ
ejpam-367	29	17	dual	dual	ADJ
ejpam-367	29	18	multiobjective	multiobjective	ADJ
ejpam-367	29	19	variational	variational	ADJ
ejpam-367	29	20	problems	problem	NOUN
ejpam-367	29	21	and	and	CCONJ
ejpam-367	29	22	established	establish	VERB
ejpam-367	29	23	various	various	ADJ
ejpam-367	29	24	duality	duality	NOUN
ejpam-367	29	25	results	result	NOUN
ejpam-367	29	26	under	under	ADP
ejpam-367	29	27	appropriate	appropriate	ADJ
ejpam-367	29	28	invexity	invexity	NOUN
ejpam-367	29	29	requirements	requirement	NOUN
ejpam-367	29	30	.	.	PUNCT
ejpam-367	30	1	in	in	ADP
ejpam-367	30	2	this	this	DET
ejpam-367	30	3	reference	reference	NOUN
ejpam-367	30	4	,	,	PUNCT
ejpam-367	30	5	self	self	NOUN
ejpam-367	30	6	duality	duality	NOUN
ejpam-367	30	7	theorem	theorem	NOUN
ejpam-367	30	8	is	be	AUX
ejpam-367	30	9	also	also	ADV
ejpam-367	30	10	given	give	VERB
ejpam-367	30	11	under	under	ADP
ejpam-367	30	12	skew	skew	ADJ
ejpam-367	30	13	symmetric	symmetric	NOUN
ejpam-367	30	14	of	of	ADP
ejpam-367	30	15	the	the	DET
ejpam-367	30	16	integrand	integrand	NOUN
ejpam-367	30	17	of	of	ADP
ejpam-367	30	18	the	the	DET
ejpam-367	30	19	objective	objective	ADJ
ejpam-367	30	20	functional	functional	NOUN
ejpam-367	30	21	.	.	PUNCT
ejpam-367	31	1	husain	husain	PROPN
ejpam-367	31	2	and	and	CCONJ
ejpam-367	31	3	jabeen	jabeen	VERB
ejpam-367	32	1	[	[	X
ejpam-367	32	2	10	10	NUM
ejpam-367	32	3	]	]	PUNCT
ejpam-367	32	4	formulated	formulate	VERB
ejpam-367	32	5	a	a	DET
ejpam-367	32	6	pair	pair	NOUN
ejpam-367	32	7	of	of	ADP
ejpam-367	32	8	mixed	mixed	ADJ
ejpam-367	32	9	type	type	NOUN
ejpam-367	32	10	symmetric	symmetric	ADJ
ejpam-367	32	11	dual	dual	ADJ
ejpam-367	32	12	variational	variational	ADJ
ejpam-367	32	13	problem	problem	NOUN
ejpam-367	32	14	in	in	ADP
ejpam-367	32	15	order	order	NOUN
ejpam-367	32	16	to	to	PART
ejpam-367	32	17	unify	unify	VERB
ejpam-367	32	18	the	the	DET
ejpam-367	32	19	wolfe	wolfe	PROPN
ejpam-367	32	20	and	and	CCONJ
ejpam-367	32	21	mond	mond	PROPN
ejpam-367	32	22	-	-	PUNCT
ejpam-367	32	23	weir	weir	NOUN
ejpam-367	32	24	symmetric	symmetric	ADJ
ejpam-367	32	25	dual	dual	ADJ
ejpam-367	32	26	pairs	pair	NOUN
ejpam-367	32	27	of	of	ADP
ejpam-367	32	28	variational	variational	ADJ
ejpam-367	32	29	problems	problem	NOUN
ejpam-367	32	30	studied	study	VERB
ejpam-367	32	31	in	in	ADP
ejpam-367	32	32	[	[	PUNCT
ejpam-367	32	33	9	9	NUM
ejpam-367	32	34	]	]	PUNCT
ejpam-367	32	35	.	.	PUNCT
ejpam-367	33	1	the	the	DET
ejpam-367	33	2	purpose	purpose	NOUN
ejpam-367	33	3	of	of	ADP
ejpam-367	33	4	this	this	DET
ejpam-367	33	5	research	research	NOUN
ejpam-367	33	6	is	be	AUX
ejpam-367	33	7	to	to	PART
ejpam-367	33	8	unify	unify	VERB
ejpam-367	33	9	formulations	formulation	NOUN
ejpam-367	33	10	of	of	ADP
ejpam-367	33	11	wolfe	wolfe	PROPN
ejpam-367	33	12	and	and	CCONJ
ejpam-367	33	13	mond	mond	PROPN
ejpam-367	33	14	-	-	PUNCT
ejpam-367	33	15	weir	weir	PROPN
ejpam-367	33	16	type	type	PROPN
ejpam-367	33	17	symmetric	symmetric	ADJ
ejpam-367	33	18	dual	dual	ADJ
ejpam-367	33	19	pairs	pair	NOUN
ejpam-367	33	20	of	of	ADP
ejpam-367	33	21	multiobjective	multiobjective	ADJ
ejpam-367	33	22	variational	variational	ADJ
ejpam-367	33	23	problems	problem	NOUN
ejpam-367	33	24	incorporated	incorporate	VERB
ejpam-367	33	25	by	by	ADP
ejpam-367	33	26	gulati	gulati	PROPN
ejpam-367	33	27	,	,	PUNCT
ejpam-367	33	28	husain	husain	PROPN
ejpam-367	33	29	and	and	CCONJ
ejpam-367	33	30	ahmed	ahme	VERB
ejpam-367	33	31	[	[	X
ejpam-367	33	32	9	9	NUM
ejpam-367	33	33	]	]	PUNCT
ejpam-367	33	34	and	and	CCONJ
ejpam-367	33	35	also	also	ADV
ejpam-367	33	36	present	present	VERB
ejpam-367	33	37	multiobjective	multiobjective	ADJ
ejpam-367	33	38	version	version	NOUN
ejpam-367	33	39	of	of	ADP
ejpam-367	33	40	the	the	DET
ejpam-367	33	41	formulation	formulation	NOUN
ejpam-367	33	42	i.	i.	NOUN
ejpam-367	33	43	husain	husain	PROPN
ejpam-367	33	44	and	and	CCONJ
ejpam-367	33	45	r.	r.	PROPN
ejpam-367	33	46	mattoo	mattoo	PROPN
ejpam-367	33	47	/	/	SYM
ejpam-367	33	48	eur	eur	PROPN
ejpam-367	33	49	.	.	PUNCT
ejpam-367	34	1	j.	j.	PROPN
ejpam-367	34	2	pure	pure	PROPN
ejpam-367	34	3	appl	appl	PROPN
ejpam-367	34	4	.	.	PROPN
ejpam-367	34	5	math	math	PROPN
ejpam-367	34	6	,	,	PUNCT
ejpam-367	34	7	2	2	NUM
ejpam-367	34	8	(	(	PUNCT
ejpam-367	34	9	2009	2009	NUM
ejpam-367	34	10	)	)	PUNCT
ejpam-367	34	11	,	,	PUNCT
ejpam-367	34	12	(	(	PUNCT
ejpam-367	34	13	578	578	NUM
ejpam-367	34	14	-	-	SYM
ejpam-367	34	15	603	603	NUM
ejpam-367	34	16	)	)	PUNCT
ejpam-367	34	17	580	580	NUM
ejpam-367	34	18	of	of	ADP
ejpam-367	34	19	a	a	DET
ejpam-367	34	20	pair	pair	NOUN
ejpam-367	34	21	of	of	ADP
ejpam-367	34	22	mixed	mixed	ADJ
ejpam-367	34	23	type	type	NOUN
ejpam-367	34	24	symmetric	symmetric	ADJ
ejpam-367	34	25	dual	dual	ADJ
ejpam-367	34	26	of	of	ADP
ejpam-367	34	27	husain	husain	PROPN
ejpam-367	34	28	and	and	CCONJ
ejpam-367	34	29	jabeen	jabeen	VERB
ejpam-367	35	1	[	[	X
ejpam-367	35	2	10	10	NUM
ejpam-367	35	3	]	]	PUNCT
ejpam-367	35	4	and	and	CCONJ
ejpam-367	35	5	hence	hence	ADV
ejpam-367	35	6	study	study	VERB
ejpam-367	35	7	symmetric	symmetric	ADJ
ejpam-367	35	8	and	and	CCONJ
ejpam-367	35	9	self	self	NOUN
ejpam-367	35	10	duality	duality	NOUN
ejpam-367	35	11	for	for	ADP
ejpam-367	35	12	a	a	DET
ejpam-367	35	13	pair	pair	NOUN
ejpam-367	35	14	of	of	ADP
ejpam-367	35	15	mixed	mixed	ADJ
ejpam-367	35	16	multiobjective	multiobjective	ADJ
ejpam-367	35	17	variational	variational	ADJ
ejpam-367	35	18	problem	problem	NOUN
ejpam-367	35	19	.	.	PUNCT
ejpam-367	36	1	this	this	DET
ejpam-367	36	2	research	research	NOUN
ejpam-367	36	3	is	be	AUX
ejpam-367	36	4	motivated	motivate	VERB
ejpam-367	36	5	by	by	ADP
ejpam-367	36	6	the	the	DET
ejpam-367	36	7	work	work	NOUN
ejpam-367	36	8	of	of	ADP
ejpam-367	36	9	xu	xu	PROPN
ejpam-367	37	1	[	[	X
ejpam-367	37	2	18	18	NUM
ejpam-367	37	3	]	]	PUNCT
ejpam-367	37	4	.	.	PUNCT
ejpam-367	38	1	the	the	DET
ejpam-367	38	2	problems	problem	NOUN
ejpam-367	38	3	,	,	PUNCT
ejpam-367	38	4	treated	treat	VERB
ejpam-367	38	5	in	in	ADP
ejpam-367	38	6	this	this	DET
ejpam-367	38	7	research	research	NOUN
ejpam-367	38	8	are	be	AUX
ejpam-367	38	9	quite	quite	ADV
ejpam-367	38	10	hard	hard	ADJ
ejpam-367	38	11	to	to	PART
ejpam-367	38	12	solve	solve	VERB
ejpam-367	38	13	.	.	PUNCT
ejpam-367	39	1	so	so	ADV
ejpam-367	39	2	to	to	PART
ejpam-367	39	3	expect	expect	VERB
ejpam-367	39	4	any	any	DET
ejpam-367	39	5	immediate	immediate	ADJ
ejpam-367	39	6	application	application	NOUN
ejpam-367	39	7	of	of	ADP
ejpam-367	39	8	these	these	DET
ejpam-367	39	9	problems	problem	NOUN
ejpam-367	39	10	would	would	AUX
ejpam-367	39	11	be	be	AUX
ejpam-367	39	12	far	far	ADV
ejpam-367	39	13	from	from	ADP
ejpam-367	39	14	reality	reality	NOUN
ejpam-367	39	15	.	.	PUNCT
ejpam-367	40	1	unfortunately	unfortunately	ADV
ejpam-367	40	2	,	,	PUNCT
ejpam-367	40	3	there	there	PRON
ejpam-367	40	4	has	have	AUX
ejpam-367	40	5	not	not	PART
ejpam-367	40	6	always	always	ADV
ejpam-367	40	7	been	be	AUX
ejpam-367	40	8	sufficient	sufficient	ADJ
ejpam-367	40	9	flow	flow	NOUN
ejpam-367	40	10	between	between	ADP
ejpam-367	40	11	the	the	DET
ejpam-367	40	12	researchers	researcher	NOUN
ejpam-367	40	13	in	in	ADP
ejpam-367	40	14	the	the	DET
ejpam-367	40	15	multiple	multiple	ADJ
ejpam-367	40	16	criteria	criterion	NOUN
ejpam-367	40	17	decision	decision	NOUN
ejpam-367	40	18	making	making	NOUN
ejpam-367	40	19	and	and	CCONJ
ejpam-367	40	20	the	the	DET
ejpam-367	40	21	researchers	researcher	NOUN
ejpam-367	40	22	applying	apply	VERB
ejpam-367	40	23	it	it	PRON
ejpam-367	40	24	to	to	ADP
ejpam-367	40	25	their	their	PRON
ejpam-367	40	26	problems	problem	NOUN
ejpam-367	40	27	.	.	PUNCT
ejpam-367	41	1	of	of	ADP
ejpam-367	41	2	course	course	NOUN
ejpam-367	41	3	,	,	PUNCT
ejpam-367	41	4	one	one	PRON
ejpam-367	41	5	can	can	AUX
ejpam-367	41	6	find	find	VERB
ejpam-367	41	7	optimal	optimal	ADJ
ejpam-367	41	8	control	control	NOUN
ejpam-367	41	9	applications	application	NOUN
ejpam-367	41	10	in	in	ADP
ejpam-367	41	11	galore	galore	NOUN
ejpam-367	41	12	which	which	PRON
ejpam-367	41	13	reflect	reflect	VERB
ejpam-367	41	14	the	the	DET
ejpam-367	41	15	utility	utility	NOUN
ejpam-367	41	16	of	of	ADP
ejpam-367	41	17	our	our	PRON
ejpam-367	41	18	model	model	NOUN
ejpam-367	41	19	.	.	PUNCT
ejpam-367	42	1	special	special	ADJ
ejpam-367	42	2	cases	case	NOUN
ejpam-367	42	3	are	be	AUX
ejpam-367	42	4	deduced	deduce	VERB
ejpam-367	42	5	and	and	CCONJ
ejpam-367	42	6	it	it	PRON
ejpam-367	42	7	is	be	AUX
ejpam-367	42	8	also	also	ADV
ejpam-367	42	9	pointed	point	VERB
ejpam-367	42	10	out	out	ADP
ejpam-367	42	11	that	that	SCONJ
ejpam-367	42	12	our	our	PRON
ejpam-367	42	13	results	result	NOUN
ejpam-367	42	14	can	can	AUX
ejpam-367	42	15	be	be	AUX
ejpam-367	42	16	considered	consider	VERB
ejpam-367	42	17	as	as	ADP
ejpam-367	42	18	dynamic	dynamic	ADJ
ejpam-367	42	19	generalizations	generalization	NOUN
ejpam-367	42	20	of	of	ADP
ejpam-367	42	21	corresponding	correspond	VERB
ejpam-367	42	22	(	(	PUNCT
ejpam-367	42	23	static	static	ADJ
ejpam-367	42	24	)	)	PUNCT
ejpam-367	42	25	symmetric	symmetric	ADJ
ejpam-367	42	26	duality	duality	NOUN
ejpam-367	42	27	results	result	NOUN
ejpam-367	42	28	of	of	ADP
ejpam-367	42	29	multiobjective	multiobjective	ADJ
ejpam-367	42	30	nonlinear	nonlinear	ADJ
ejpam-367	42	31	nonlinear	nonlinear	NOUN
ejpam-367	42	32	treated	treat	VERB
ejpam-367	42	33	by	by	ADP
ejpam-367	42	34	bector	bector	NOUN
ejpam-367	42	35	et	et	PROPN
ejpam-367	42	36	al	al	PROPN
ejpam-367	42	37	.	.	PUNCT
ejpam-367	43	1	[	[	X
ejpam-367	43	2	3	3	NUM
ejpam-367	43	3	]	]	PUNCT
ejpam-367	43	4	.	.	PUNCT
ejpam-367	44	1	2	2	X
ejpam-367	44	2	.	.	NUM
ejpam-367	44	3	notations	notation	NOUN
ejpam-367	44	4	and	and	CCONJ
ejpam-367	44	5	preliminaries	preliminary	NOUN
ejpam-367	44	6	the	the	DET
ejpam-367	44	7	following	follow	VERB
ejpam-367	44	8	notation	notation	NOUN
ejpam-367	44	9	will	will	AUX
ejpam-367	44	10	be	be	AUX
ejpam-367	44	11	used	use	VERB
ejpam-367	44	12	for	for	ADP
ejpam-367	44	13	vectors	vector	NOUN
ejpam-367	44	14	in	in	ADP
ejpam-367	44	15	rn	rn	PROPN
ejpam-367	44	16	.	.	PUNCT
ejpam-367	45	1	x	x	X
ejpam-367	45	2	<	<	X
ejpam-367	45	3	y	y	PROPN
ejpam-367	45	4	⇔	⇔	PROPN
ejpam-367	45	5	x	x	PROPN
ejpam-367	45	6	i	i	PRON
ejpam-367	45	7	<	<	X
ejpam-367	45	8	yi	yi	PROPN
ejpam-367	45	9	,	,	PUNCT
ejpam-367	45	10	i	i	PRON
ejpam-367	45	11	=	=	NOUN
ejpam-367	45	12	1	1	NUM
ejpam-367	45	13	,	,	PUNCT
ejpam-367	45	14	2	2	NUM
ejpam-367	45	15	,	,	PUNCT
ejpam-367	45	16	.	.	PUNCT
ejpam-367	45	17	.	.	PUNCT
ejpam-367	45	18	.	.	PUNCT
ejpam-367	46	1	,	,	PUNCT
ejpam-367	46	2	n.	n.	NOUN
ejpam-367	46	3	x	x	PROPN
ejpam-367	47	1	≦	≦	VERB
ejpam-367	47	2	y	y	PROPN
ejpam-367	47	3	⇔	⇔	NOUN
ejpam-367	47	4	x	x	PROPN
ejpam-367	48	1	i	i	PRON
ejpam-367	48	2	≦	≦	VERB
ejpam-367	48	3	yi	yi	PROPN
ejpam-367	48	4	,	,	PUNCT
ejpam-367	48	5	i	i	NOUN
ejpam-367	48	6	=	=	NOUN
ejpam-367	48	7	1	1	NUM
ejpam-367	48	8	,	,	PUNCT
ejpam-367	48	9	2	2	NUM
ejpam-367	48	10	,	,	PUNCT
ejpam-367	48	11	.	.	PUNCT
ejpam-367	48	12	.	.	PUNCT
ejpam-367	48	13	.	.	PUNCT
ejpam-367	49	1	,	,	PUNCT
ejpam-367	49	2	n.	n.	NOUN
ejpam-367	49	3	x	x	PUNCT
ejpam-367	50	1	≤	≤	PROPN
ejpam-367	50	2	y	y	PROPN
ejpam-367	50	3	⇔	⇔	PROPN
ejpam-367	50	4	x	x	PROPN
ejpam-367	50	5	i	i	NOUN
ejpam-367	50	6	≤	≤	PUNCT
ejpam-367	50	7	yi	yi	NOUN
ejpam-367	50	8	,	,	PUNCT
ejpam-367	50	9	i	i	PRON
ejpam-367	50	10	=	=	NOUN
ejpam-367	50	11	1	1	NUM
ejpam-367	50	12	,	,	PUNCT
ejpam-367	50	13	2	2	NUM
ejpam-367	50	14	,	,	PUNCT
ejpam-367	50	15	.	.	PUNCT
ejpam-367	50	16	.	.	PUNCT
ejpam-367	50	17	.	.	PUNCT
ejpam-367	50	18	,	,	PUNCT
ejpam-367	50	19	n	n	CCONJ
ejpam-367	50	20	,	,	PUNCT
ejpam-367	50	21	but	but	CCONJ
ejpam-367	50	22	x	x	X
ejpam-367	50	23	6=	6=	NUM
ejpam-367	50	24	y	y	PROPN
ejpam-367	50	25	x	x	PROPN
ejpam-367	50	26	6≤	6≤	NUM
ejpam-367	50	27	y	y	NOUN
ejpam-367	50	28	,	,	PUNCT
ejpam-367	50	29	is	be	AUX
ejpam-367	50	30	the	the	DET
ejpam-367	50	31	negation	negation	NOUN
ejpam-367	50	32	of	of	ADP
ejpam-367	50	33	x	x	SYM
ejpam-367	50	34	≤	≤	NOUN
ejpam-367	50	35	y	y	NOUN
ejpam-367	50	36	let	let	VERB
ejpam-367	50	37	i	i	PRON
ejpam-367	50	38	=	=	PUNCT
ejpam-367	51	1	[	[	X
ejpam-367	51	2	a	a	X
ejpam-367	51	3	,	,	PUNCT
ejpam-367	51	4	b	b	AUX
ejpam-367	51	5	]	]	PUNCT
ejpam-367	51	6	be	be	AUX
ejpam-367	51	7	the	the	DET
ejpam-367	51	8	real	real	ADJ
ejpam-367	51	9	interval	interval	NOUN
ejpam-367	51	10	,	,	PUNCT
ejpam-367	51	11	and	and	CCONJ
ejpam-367	51	12	φ	φ	PROPN
ejpam-367	51	13	i(t	i(t	PROPN
ejpam-367	51	14	,	,	PUNCT
ejpam-367	51	15	x(t	x(t	PROPN
ejpam-367	51	16	)	)	PUNCT
ejpam-367	51	17	,	,	PUNCT
ejpam-367	51	18	ẋ(t	ẋ(t	NOUN
ejpam-367	51	19	)	)	PUNCT
ejpam-367	51	20	,	,	PUNCT
ejpam-367	51	21	y(t	y(t	PROPN
ejpam-367	51	22	)	)	PUNCT
ejpam-367	51	23	,	,	PUNCT
ejpam-367	51	24	ẏ(t	ẏ(t	PROPN
ejpam-367	51	25	)	)	PUNCT
ejpam-367	51	26	)	)	PUNCT
ejpam-367	51	27	be	be	AUX
ejpam-367	51	28	a	a	DET
ejpam-367	51	29	scalar	scalar	ADJ
ejpam-367	51	30	function	function	NOUN
ejpam-367	51	31	and	and	CCONJ
ejpam-367	51	32	twice	twice	ADV
ejpam-367	51	33	differentiable	differentiable	ADJ
ejpam-367	51	34	function	function	NOUN
ejpam-367	51	35	for	for	ADP
ejpam-367	51	36	i	i	PROPN
ejpam-367	51	37	=	=	NOUN
ejpam-367	51	38	1	1	NUM
ejpam-367	51	39	,	,	PUNCT
ejpam-367	51	40	2	2	NUM
ejpam-367	51	41	,	,	PUNCT
ejpam-367	51	42	.	.	PUNCT
ejpam-367	51	43	.	.	PUNCT
ejpam-367	52	1	.	.	PUNCT
ejpam-367	53	1	,	,	PUNCT
ejpam-367	53	2	p	p	X
ejpam-367	53	3	where	where	SCONJ
ejpam-367	53	4	x	x	X
ejpam-367	53	5	:	:	PUNCT
ejpam-367	53	6	i	i	PRON
ejpam-367	53	7	→	→	SYM
ejpam-367	53	8	rn	rn	PROPN
ejpam-367	53	9	and	and	CCONJ
ejpam-367	53	10	y	y	PROPN
ejpam-367	53	11	:	:	PUNCT
ejpam-367	53	12	i	i	PROPN
ejpam-367	53	13	→	→	SYM
ejpam-367	53	14	rn	rn	PROPN
ejpam-367	53	15	with	with	ADP
ejpam-367	53	16	derivatives	derivative	NOUN
ejpam-367	53	17	ẋ	ẋ	PROPN
ejpam-367	53	18	and	and	CCONJ
ejpam-367	53	19	ẏ.	ẏ.	PRON
ejpam-367	53	20	in	in	ADP
ejpam-367	53	21	order	order	NOUN
ejpam-367	53	22	to	to	PART
ejpam-367	53	23	consider	consider	VERB
ejpam-367	53	24	φ	φ	PROPN
ejpam-367	53	25	i(t	i(t	PROPN
ejpam-367	53	26	,	,	PUNCT
ejpam-367	53	27	x(t	x(t	PROPN
ejpam-367	53	28	)	)	PUNCT
ejpam-367	53	29	,	,	PUNCT
ejpam-367	53	30	ẋ(t	ẋ(t	NOUN
ejpam-367	53	31	)	)	PUNCT
ejpam-367	53	32	,	,	PUNCT
ejpam-367	53	33	y(t	y(t	PROPN
ejpam-367	53	34	)	)	PUNCT
ejpam-367	53	35	,	,	PUNCT
ejpam-367	53	36	ẏ(t	ẏ(t	PROPN
ejpam-367	53	37	)	)	PUNCT
ejpam-367	53	38	)	)	PUNCT
ejpam-367	53	39	denote	denote	VERB
ejpam-367	53	40	the	the	DET
ejpam-367	53	41	first	first	ADJ
ejpam-367	53	42	partial	partial	ADJ
ejpam-367	53	43	derivatives	derivative	NOUN
ejpam-367	53	44	of	of	ADP
ejpam-367	53	45	φ	φ	PROPN
ejpam-367	53	46	i	i	PROPN
ejpam-367	53	47	with	with	ADP
ejpam-367	53	48	respect	respect	NOUN
ejpam-367	53	49	to	to	ADP
ejpam-367	53	50	t	t	PROPN
ejpam-367	53	51	,	,	PUNCT
ejpam-367	53	52	x(t	x(t	PROPN
ejpam-367	53	53	)	)	PUNCT
ejpam-367	53	54	,	,	PUNCT
ejpam-367	53	55	ẋ(t	ẋ(t	NOUN
ejpam-367	53	56	)	)	PUNCT
ejpam-367	53	57	,	,	PUNCT
ejpam-367	53	58	y(t	y(t	PROPN
ejpam-367	53	59	)	)	PUNCT
ejpam-367	53	60	,	,	PUNCT
ejpam-367	53	61	ẏ(t	ẏ(t	PROPN
ejpam-367	53	62	)	)	PUNCT
ejpam-367	53	63	i.	i.	PROPN
ejpam-367	53	64	husain	husain	PROPN
ejpam-367	53	65	and	and	CCONJ
ejpam-367	53	66	r.	r.	PROPN
ejpam-367	53	67	mattoo	mattoo	PROPN
ejpam-367	53	68	/	/	SYM
ejpam-367	53	69	eur	eur	PROPN
ejpam-367	53	70	.	.	PUNCT
ejpam-367	54	1	j.	j.	PROPN
ejpam-367	54	2	pure	pure	PROPN
ejpam-367	54	3	appl	appl	PROPN
ejpam-367	54	4	.	.	PROPN
ejpam-367	54	5	math	math	PROPN
ejpam-367	54	6	,	,	PUNCT
ejpam-367	54	7	2	2	NUM
ejpam-367	54	8	(	(	PUNCT
ejpam-367	54	9	2009	2009	NUM
ejpam-367	54	10	)	)	PUNCT
ejpam-367	54	11	,	,	PUNCT
ejpam-367	54	12	(	(	PUNCT
ejpam-367	54	13	578	578	NUM
ejpam-367	54	14	-	-	SYM
ejpam-367	54	15	603	603	NUM
ejpam-367	54	16	)	)	PUNCT
ejpam-367	54	17	581	581	NUM
ejpam-367	54	18	respectively	respectively	ADV
ejpam-367	54	19	,	,	PUNCT
ejpam-367	54	20	by	by	ADP
ejpam-367	54	21	φ	φ	PROPN
ejpam-367	54	22	i	i	PRON
ejpam-367	54	23	t	t	PROPN
ejpam-367	54	24	,	,	PUNCT
ejpam-367	54	25	φ	φ	PROPN
ejpam-367	54	26	i	i	PROPN
ejpam-367	54	27	x	x	PROPN
ejpam-367	54	28	,	,	PUNCT
ejpam-367	54	29	φ	φ	PROPN
ejpam-367	55	1	i	i	PRON
ejpam-367	55	2	ẋ	ẋ	PROPN
ejpam-367	55	3	,	,	PUNCT
ejpam-367	55	4	φ	φ	PROPN
ejpam-367	55	5	i	i	PROPN
ejpam-367	55	6	y	y	PROPN
ejpam-367	55	7	,	,	PUNCT
ejpam-367	55	8	φ	φ	PROPN
ejpam-367	55	9	i	i	PRON
ejpam-367	55	10	ẏ	ẏ	PROPN
ejpam-367	55	11	,	,	PUNCT
ejpam-367	55	12	that	that	ADV
ejpam-367	55	13	is	is	ADV
ejpam-367	55	14	,	,	PUNCT
ejpam-367	55	15	φ	φ	PROPN
ejpam-367	55	16	i	i	NOUN
ejpam-367	55	17	t	t	NOUN
ejpam-367	55	18	=	=	SYM
ejpam-367	55	19	∂	∂	NUM
ejpam-367	55	20	φ	φ	PROPN
ejpam-367	56	1	i	i	PROPN
ejpam-367	56	2	∂	∂	NOUN
ejpam-367	56	3	t	t	PROPN
ejpam-367	56	4	φ	φ	NUM
ejpam-367	56	5	i	i	NOUN
ejpam-367	56	6	x	x	SYM
ejpam-367	56	7	=	=	PUNCT
ejpam-367	56	8	�	�	PROPN
ejpam-367	56	9	∂	∂	NUM
ejpam-367	56	10	φ	φ	PROPN
ejpam-367	56	11	i	i	PROPN
ejpam-367	56	12	∂	∂	NOUN
ejpam-367	56	13	x1	x1	NUM
ejpam-367	56	14	,	,	PUNCT
ejpam-367	56	15	∂	∂	NUM
ejpam-367	56	16	φ	φ	NOUN
ejpam-367	56	17	i	i	PROPN
ejpam-367	56	18	∂	∂	PUNCT
ejpam-367	56	19	x2	x2	INTJ
ejpam-367	56	20	,	,	PUNCT
ejpam-367	56	21	.	.	PUNCT
ejpam-367	56	22	.	.	PUNCT
ejpam-367	57	1	.	.	PUNCT
ejpam-367	58	1	,	,	PUNCT
ejpam-367	58	2	∂	∂	NUM
ejpam-367	58	3	φ	φ	NOUN
ejpam-367	58	4	i	i	PROPN
ejpam-367	58	5	∂	∂	NOUN
ejpam-367	58	6	xn	xn	PROPN
ejpam-367	58	7	�	�	PROPN
ejpam-367	58	8	,	,	PUNCT
ejpam-367	58	9	φ	φ	PROPN
ejpam-367	58	10	i	i	PRON
ejpam-367	58	11	ẋ	ẋ	PUNCT
ejpam-367	59	1	=	=	SYM
ejpam-367	59	2	�	�	PROPN
ejpam-367	59	3	∂	∂	NUM
ejpam-367	59	4	φ	φ	PROPN
ejpam-367	59	5	i	i	PROPN
ejpam-367	59	6	∂	∂	AUX
ejpam-367	59	7	ẋ1	ẋ1	PROPN
ejpam-367	59	8	,	,	PUNCT
ejpam-367	59	9	∂	∂	NUM
ejpam-367	59	10	φ	φ	NOUN
ejpam-367	59	11	i	i	PROPN
ejpam-367	59	12	∂	∂	PUNCT
ejpam-367	59	13	ẋ2	ẋ2	NOUN
ejpam-367	59	14	,	,	PUNCT
ejpam-367	59	15	.	.	PUNCT
ejpam-367	59	16	.	.	PUNCT
ejpam-367	60	1	.	.	PUNCT
ejpam-367	61	1	,	,	PUNCT
ejpam-367	61	2	∂	∂	NUM
ejpam-367	61	3	φ	φ	NOUN
ejpam-367	61	4	i	i	PROPN
ejpam-367	61	5	∂	∂	NOUN
ejpam-367	61	6	ẋn	ẋn	PROPN
ejpam-367	61	7	�	�	PROPN
ejpam-367	62	1	φ	φ	NUM
ejpam-367	62	2	i	i	NOUN
ejpam-367	62	3	y	y	PROPN
ejpam-367	62	4	=	=	SYM
ejpam-367	62	5	�	�	PROPN
ejpam-367	62	6	∂	∂	NUM
ejpam-367	62	7	φ	φ	PROPN
ejpam-367	62	8	i	i	PROPN
ejpam-367	62	9	∂	∂	NUM
ejpam-367	62	10	y1	y1	NOUN
ejpam-367	62	11	,	,	PUNCT
ejpam-367	62	12	∂	∂	NUM
ejpam-367	62	13	φ	φ	NOUN
ejpam-367	62	14	i	i	PROPN
ejpam-367	62	15	∂	∂	NOUN
ejpam-367	62	16	y2	y2	INTJ
ejpam-367	62	17	,	,	PUNCT
ejpam-367	62	18	.	.	PUNCT
ejpam-367	62	19	.	.	PUNCT
ejpam-367	63	1	.	.	PUNCT
ejpam-367	64	1	,	,	PUNCT
ejpam-367	64	2	∂	∂	NUM
ejpam-367	64	3	φ	φ	NOUN
ejpam-367	64	4	i	i	PROPN
ejpam-367	64	5	∂	∂	PUNCT
ejpam-367	64	6	yn	yn	PROPN
ejpam-367	64	7	�	�	PROPN
ejpam-367	64	8	,	,	PUNCT
ejpam-367	64	9	φ	φ	PROPN
ejpam-367	64	10	i	i	PRON
ejpam-367	64	11	ẏ	ẏ	PROPN
ejpam-367	64	12	=	=	SYM
ejpam-367	64	13	�	�	PROPN
ejpam-367	64	14	∂	∂	NOUN
ejpam-367	64	15	φ	φ	NOUN
ejpam-367	65	1	i	i	PROPN
ejpam-367	66	1	i	i	PROPN
ejpam-367	66	2	∂	∂	VERB
ejpam-367	66	3	ẏ1	ẏ1	PROPN
ejpam-367	66	4	,	,	PUNCT
ejpam-367	66	5	∂	∂	NUM
ejpam-367	66	6	φ	φ	NOUN
ejpam-367	66	7	i	i	PROPN
ejpam-367	66	8	∂	∂	NOUN
ejpam-367	66	9	ẏ2	ẏ2	NOUN
ejpam-367	66	10	,	,	PUNCT
ejpam-367	66	11	.	.	PUNCT
ejpam-367	66	12	.	.	PUNCT
ejpam-367	67	1	.	.	PUNCT
ejpam-367	68	1	,	,	PUNCT
ejpam-367	68	2	∂	∂	NUM
ejpam-367	68	3	φ	φ	NOUN
ejpam-367	68	4	i	i	PROPN
ejpam-367	68	5	∂	∂	NUM
ejpam-367	68	6	ẏn	ẏn	PROPN
ejpam-367	68	7	�	�	PROPN
ejpam-367	68	8	.	.	PUNCT
ejpam-367	69	1	the	the	DET
ejpam-367	69	2	twice	twice	ADV
ejpam-367	69	3	partial	partial	ADJ
ejpam-367	69	4	derivatives	derivative	NOUN
ejpam-367	69	5	of	of	ADP
ejpam-367	69	6	φ	φ	PROPN
ejpam-367	69	7	i	i	PROPN
ejpam-367	69	8	with	with	ADP
ejpam-367	69	9	respect	respect	NOUN
ejpam-367	69	10	to	to	ADP
ejpam-367	69	11	t	t	PROPN
ejpam-367	69	12	,	,	PUNCT
ejpam-367	69	13	x(t	x(t	PROPN
ejpam-367	69	14	)	)	PUNCT
ejpam-367	69	15	,	,	PUNCT
ejpam-367	69	16	ẋ(t	ẋ(t	NOUN
ejpam-367	69	17	)	)	PUNCT
ejpam-367	69	18	,	,	PUNCT
ejpam-367	69	19	y(t	y(t	NUM
ejpam-367	69	20	)	)	PUNCT
ejpam-367	69	21	and	and	CCONJ
ejpam-367	69	22	ẏ(t	ẏ(t	PROPN
ejpam-367	69	23	)	)	PUNCT
ejpam-367	69	24	,	,	PUNCT
ejpam-367	69	25	respectively	respectively	ADV
ejpam-367	69	26	are	be	AUX
ejpam-367	69	27	the	the	DET
ejpam-367	69	28	matrices	matrix	NOUN
ejpam-367	69	29	φ	φ	NOUN
ejpam-367	70	1	i	i	NOUN
ejpam-367	70	2	x	x	PUNCT
ejpam-367	70	3	x	x	SYM
ejpam-367	70	4	=	=	SYM
ejpam-367	70	5	�	�	PROPN
ejpam-367	70	6	∂	∂	NUM
ejpam-367	70	7	2φ	2φ	NUM
ejpam-367	71	1	i	i	PRON
ejpam-367	71	2	∂	∂	PUNCT
ejpam-367	71	3	xk	xk	PROPN
ejpam-367	71	4	xs	xs	PROPN
ejpam-367	71	5	�	�	PROPN
ejpam-367	71	6	n×n	n×n	PROPN
ejpam-367	71	7	,	,	PUNCT
ejpam-367	71	8	φ	φ	PROPN
ejpam-367	71	9	i	i	NOUN
ejpam-367	71	10	x	x	X
ejpam-367	71	11	ẋ	ẋ	PROPN
ejpam-367	71	12	=	=	SYM
ejpam-367	71	13	�	�	PROPN
ejpam-367	71	14	∂	∂	NUM
ejpam-367	71	15	2φ	2φ	NUM
ejpam-367	72	1	i	i	PRON
ejpam-367	72	2	∂	∂	PUNCT
ejpam-367	72	3	xk	xk	PROPN
ejpam-367	72	4	ẋs	ẋs	PROPN
ejpam-367	72	5	�	�	PROPN
ejpam-367	72	6	n×n	n×n	PROPN
ejpam-367	72	7	,	,	PUNCT
ejpam-367	72	8	φ	φ	PROPN
ejpam-367	72	9	i	i	NOUN
ejpam-367	72	10	x	x	PROPN
ejpam-367	72	11	y	y	PROPN
ejpam-367	72	12	=	=	SYM
ejpam-367	72	13	�	�	PROPN
ejpam-367	72	14	∂	∂	NUM
ejpam-367	72	15	2φ	2φ	NUM
ejpam-367	73	1	i	i	PRON
ejpam-367	73	2	∂	∂	PUNCT
ejpam-367	73	3	xk	xk	PROPN
ejpam-367	73	4	ys	ys	PROPN
ejpam-367	73	5	�	�	PROPN
ejpam-367	73	6	n×n	n×n	PROPN
ejpam-367	73	7	φ	φ	PROPN
ejpam-367	74	1	i	i	NOUN
ejpam-367	74	2	x	x	SYM
ejpam-367	74	3	ẏ	ẏ	PROPN
ejpam-367	74	4	=	=	SYM
ejpam-367	74	5	�	�	PROPN
ejpam-367	74	6	∂	∂	NUM
ejpam-367	74	7	2φ	2φ	NUM
ejpam-367	75	1	i	i	PRON
ejpam-367	75	2	∂	∂	NUM
ejpam-367	76	1	xk	xk	PROPN
ejpam-367	76	2	ẏs	ẏs	PROPN
ejpam-367	76	3	�	�	PROPN
ejpam-367	76	4	n×n	n×n	PROPN
ejpam-367	76	5	,	,	PUNCT
ejpam-367	76	6	φ	φ	PROPN
ejpam-367	77	1	i	i	PRON
ejpam-367	77	2	ẋ	ẋ	PROPN
ejpam-367	78	1	y	y	PROPN
ejpam-367	78	2	=	=	SYM
ejpam-367	78	3	�	�	PROPN
ejpam-367	78	4	∂	∂	NUM
ejpam-367	78	5	2φ	2φ	NUM
ejpam-367	79	1	i	i	PRON
ejpam-367	79	2	∂	∂	AUX
ejpam-367	79	3	ẋk	ẋk	PROPN
ejpam-367	79	4	ys	ys	PROPN
ejpam-367	79	5	�	�	PROPN
ejpam-367	79	6	n×n	n×n	PROPN
ejpam-367	79	7	,	,	PUNCT
ejpam-367	79	8	φ	φ	PROPN
ejpam-367	79	9	i	i	NOUN
ejpam-367	79	10	x	x	NOUN
ejpam-367	79	11	ẏ	ẏ	PROPN
ejpam-367	79	12	=	=	SYM
ejpam-367	79	13	�	�	PROPN
ejpam-367	79	14	∂	∂	NUM
ejpam-367	79	15	2φ	2φ	NUM
ejpam-367	80	1	i	i	PRON
ejpam-367	80	2	∂	∂	NUM
ejpam-367	81	1	xk	xk	PROPN
ejpam-367	81	2	ẏs	ẏs	PROPN
ejpam-367	81	3	�	�	PROPN
ejpam-367	81	4	n×n	n×n	PROPN
ejpam-367	81	5	φ	φ	NUM
ejpam-367	82	1	i	i	NOUN
ejpam-367	82	2	y	y	PROPN
ejpam-367	82	3	y	y	PROPN
ejpam-367	82	4	=	=	SYM
ejpam-367	82	5	�	�	PROPN
ejpam-367	82	6	∂	∂	NUM
ejpam-367	82	7	2φ	2φ	NUM
ejpam-367	83	1	i	i	PRON
ejpam-367	83	2	∂	∂	NOUN
ejpam-367	84	1	yk	yk	PROPN
ejpam-367	84	2	ys	ys	PROPN
ejpam-367	84	3	�	�	PROPN
ejpam-367	84	4	n×n	n×n	PROPN
ejpam-367	84	5	,	,	PUNCT
ejpam-367	84	6	φ	φ	PROPN
ejpam-367	85	1	i	i	NOUN
ejpam-367	85	2	y	y	VERB
ejpam-367	85	3	ẏ	ẏ	PROPN
ejpam-367	85	4	=	=	SYM
ejpam-367	85	5	�	�	PROPN
ejpam-367	85	6	∂	∂	NUM
ejpam-367	85	7	2φ	2φ	NUM
ejpam-367	86	1	i	i	PRON
ejpam-367	86	2	∂	∂	NOUN
ejpam-367	87	1	yk	yk	PROPN
ejpam-367	87	2	ẏs	ẏs	PROPN
ejpam-367	87	3	�	�	PROPN
ejpam-367	87	4	n×n	n×n	PROPN
ejpam-367	87	5	,	,	PUNCT
ejpam-367	87	6	φ	φ	PROPN
ejpam-367	87	7	i	i	PRON
ejpam-367	87	8	ẏ	ẏ	VERB
ejpam-367	87	9	ẏ	ẏ	PROPN
ejpam-367	87	10	=	=	SYM
ejpam-367	87	11	�	�	PROPN
ejpam-367	87	12	∂	∂	NUM
ejpam-367	87	13	2φ	2φ	NUM
ejpam-367	88	1	i	i	PRON
ejpam-367	88	2	∂	∂	NUM
ejpam-367	88	3	ẏk	ẏk	PROPN
ejpam-367	88	4	ẏs	ẏs	PROPN
ejpam-367	88	5	�	�	PROPN
ejpam-367	88	6	n×n	n×n	PROPN
ejpam-367	88	7	for	for	ADP
ejpam-367	88	8	i	i	PRON
ejpam-367	88	9	=	=	SYM
ejpam-367	88	10	1	1	NUM
ejpam-367	88	11	,	,	PUNCT
ejpam-367	88	12	2	2	NUM
ejpam-367	88	13	,	,	PUNCT
ejpam-367	88	14	.	.	PUNCT
ejpam-367	88	15	.	.	PUNCT
ejpam-367	88	16	.	.	PUNCT
ejpam-367	89	1	,	,	PUNCT
ejpam-367	90	1	p.	p.	NOUN
ejpam-367	90	2	noting	note	VERB
ejpam-367	90	3	that	that	SCONJ
ejpam-367	90	4	d	d	PROPN
ejpam-367	90	5	d	d	X
ejpam-367	90	6	t	t	PROPN
ejpam-367	90	7	φ	φ	NOUN
ejpam-367	90	8	i	i	PRON
ejpam-367	91	1	ẏ	ẏ	PROPN
ejpam-367	91	2	=	=	SYM
ejpam-367	92	1	φ	φ	PROPN
ejpam-367	93	1	i	i	PRON
ejpam-367	94	1	ẏ	ẏ	PROPN
ejpam-367	94	2	t	t	PROPN
ejpam-367	94	3	+	+	NOUN
ejpam-367	94	4	φ	φ	NOUN
ejpam-367	94	5	i	i	PRON
ejpam-367	94	6	ẏ	ẏ	VERB
ejpam-367	94	7	y	y	VERB
ejpam-367	94	8	ẏ	ẏ	PROPN
ejpam-367	95	1	+	+	ADV
ejpam-367	95	2	φ	φ	VERB
ejpam-367	96	1	i	i	PRON
ejpam-367	96	2	ẏ	ẏ	VERB
ejpam-367	96	3	ẏ	ẏ	PROPN
ejpam-367	96	4	ÿ	ÿ	PROPN
ejpam-367	97	1	+	+	NOUN
ejpam-367	97	2	φ	φ	PROPN
ejpam-367	98	1	i	i	PRON
ejpam-367	98	2	ẏ	ẏ	INTJ
ejpam-367	98	3	x	x	SYM
ejpam-367	98	4	ẋ	ẋ	PROPN
ejpam-367	99	1	+	+	NOUN
ejpam-367	99	2	φ	φ	NOUN
ejpam-367	99	3	i	i	VERB
ejpam-367	99	4	ẏ	ẏ	INTJ
ejpam-367	99	5	ẋ	ẋ	PROPN
ejpam-367	99	6	ẍ	ẍ	PROPN
ejpam-367	99	7	and	and	CCONJ
ejpam-367	99	8	hence	hence	ADV
ejpam-367	99	9	∂	∂	NUM
ejpam-367	99	10	∂	∂	NUM
ejpam-367	99	11	y	y	PROPN
ejpam-367	100	1	d	d	PROPN
ejpam-367	100	2	d	d	PROPN
ejpam-367	100	3	t	t	PROPN
ejpam-367	100	4	φ	φ	NOUN
ejpam-367	100	5	i	i	PRON
ejpam-367	101	1	ẏ	ẏ	NOUN
ejpam-367	102	1	=	=	SYM
ejpam-367	103	1	d	d	PROPN
ejpam-367	104	1	d	d	PROPN
ejpam-367	104	2	t	t	PROPN
ejpam-367	104	3	φ	φ	NOUN
ejpam-367	105	1	i	i	PRON
ejpam-367	105	2	y	y	VERB
ejpam-367	105	3	ẏ	ẏ	PROPN
ejpam-367	105	4	,	,	PUNCT
ejpam-367	105	5	∂	∂	NUM
ejpam-367	105	6	∂	∂	NOUN
ejpam-367	106	1	ẏ	ẏ	PROPN
ejpam-367	107	1	d	d	PROPN
ejpam-367	107	2	d	d	PROPN
ejpam-367	107	3	t	t	PROPN
ejpam-367	107	4	φ	φ	NOUN
ejpam-367	107	5	i	i	PRON
ejpam-367	108	1	ẏ	ẏ	NOUN
ejpam-367	108	2	=	=	SYM
ejpam-367	109	1	d	d	PROPN
ejpam-367	109	2	d	d	PROPN
ejpam-367	109	3	t	t	PROPN
ejpam-367	109	4	φ	φ	NOUN
ejpam-367	109	5	i	i	PRON
ejpam-367	109	6	ẏ	ẏ	VERB
ejpam-367	109	7	ẏ	ẏ	PROPN
ejpam-367	109	8	+	+	ADV
ejpam-367	109	9	φ	φ	VERB
ejpam-367	109	10	i	i	PRON
ejpam-367	109	11	ẏ	ẏ	PROPN
ejpam-367	109	12	y	y	PROPN
ejpam-367	109	13	,	,	PUNCT
ejpam-367	109	14	∂	∂	NUM
ejpam-367	109	15	∂	∂	NUM
ejpam-367	109	16	ÿ	ÿ	PROPN
ejpam-367	110	1	d	d	PROPN
ejpam-367	110	2	d	d	PROPN
ejpam-367	110	3	t	t	PROPN
ejpam-367	110	4	φ	φ	NOUN
ejpam-367	111	1	i	i	PRON
ejpam-367	112	1	ẏ	ẏ	PROPN
ejpam-367	112	2	=	=	SYM
ejpam-367	112	3	φ	φ	PROPN
ejpam-367	112	4	i	i	PRON
ejpam-367	113	1	ẏ	ẏ	PROPN
ejpam-367	113	2	y	y	PROPN
ejpam-367	113	3	∂	∂	NOUN
ejpam-367	113	4	∂	∂	NOUN
ejpam-367	113	5	x	x	PUNCT
ejpam-367	113	6	d	d	X
ejpam-367	113	7	d	d	PROPN
ejpam-367	113	8	t	t	PROPN
ejpam-367	113	9	φ	φ	NOUN
ejpam-367	113	10	i	i	PRON
ejpam-367	114	1	ẏ	ẏ	NOUN
ejpam-367	114	2	=	=	SYM
ejpam-367	115	1	d	d	PROPN
ejpam-367	115	2	d	d	PROPN
ejpam-367	115	3	t	t	PROPN
ejpam-367	115	4	φ	φ	NOUN
ejpam-367	115	5	i	i	PRON
ejpam-367	115	6	ẏ	ẏ	INTJ
ejpam-367	115	7	x	x	SYM
ejpam-367	115	8	,	,	PUNCT
ejpam-367	115	9	∂	∂	NUM
ejpam-367	115	10	∂	∂	NOUN
ejpam-367	115	11	ẋ	ẋ	PROPN
ejpam-367	116	1	d	d	PROPN
ejpam-367	116	2	d	d	PROPN
ejpam-367	116	3	t	t	PROPN
ejpam-367	116	4	φ	φ	NOUN
ejpam-367	117	1	i	i	PRON
ejpam-367	118	1	ẏ	ẏ	NOUN
ejpam-367	118	2	=	=	SYM
ejpam-367	119	1	d	d	PROPN
ejpam-367	119	2	d	d	PROPN
ejpam-367	119	3	t	t	PROPN
ejpam-367	119	4	φ	φ	NOUN
ejpam-367	119	5	i	i	PRON
ejpam-367	120	1	ẏ	ẏ	INTJ
ejpam-367	120	2	ẋ	ẋ	PUNCT
ejpam-367	121	1	+	+	NOUN
ejpam-367	121	2	φ	φ	NOUN
ejpam-367	121	3	i	i	PRON
ejpam-367	121	4	ẏ	ẏ	INTJ
ejpam-367	121	5	x	x	SYM
ejpam-367	121	6	,	,	PUNCT
ejpam-367	121	7	∂	∂	NUM
ejpam-367	121	8	∂	∂	NOUN
ejpam-367	121	9	ẍ	ẍ	PUNCT
ejpam-367	122	1	d	d	PROPN
ejpam-367	122	2	d	d	PROPN
ejpam-367	122	3	t	t	PROPN
ejpam-367	122	4	φ	φ	NOUN
ejpam-367	123	1	i	i	PRON
ejpam-367	124	1	ẏ	ẏ	PROPN
ejpam-367	124	2	=	=	SYM
ejpam-367	124	3	φ	φ	PROPN
ejpam-367	124	4	i	i	PRON
ejpam-367	125	1	ẏ	ẏ	INTJ
ejpam-367	125	2	ẋ	ẋ	PROPN
ejpam-367	126	1	in	in	ADP
ejpam-367	126	2	order	order	NOUN
ejpam-367	126	3	to	to	PART
ejpam-367	126	4	establish	establish	VERB
ejpam-367	126	5	our	our	PRON
ejpam-367	126	6	main	main	ADJ
ejpam-367	126	7	results	result	NOUN
ejpam-367	126	8	,	,	PUNCT
ejpam-367	126	9	the	the	DET
ejpam-367	126	10	following	follow	VERB
ejpam-367	126	11	are	be	AUX
ejpam-367	126	12	needed	need	VERB
ejpam-367	126	13	.	.	PUNCT
ejpam-367	127	1	definition	definition	NOUN
ejpam-367	127	2	1	1	NUM
ejpam-367	127	3	(	(	PUNCT
ejpam-367	127	4	partially	partially	ADV
ejpam-367	127	5	invex	invex	ADJ
ejpam-367	127	6	)	)	PUNCT
ejpam-367	127	7	.	.	PUNCT
ejpam-367	128	1	if	if	SCONJ
ejpam-367	128	2	there	there	PRON
ejpam-367	128	3	exists	exist	VERB
ejpam-367	128	4	a	a	DET
ejpam-367	128	5	vector	vector	NOUN
ejpam-367	128	6	function	function	NOUN
ejpam-367	128	7	η(t	η(t	NOUN
ejpam-367	128	8	,	,	PUNCT
ejpam-367	128	9	x(t	x(t	PROPN
ejpam-367	128	10	)	)	PUNCT
ejpam-367	128	11	,	,	PUNCT
ejpam-367	128	12	y(t	y(t	PROPN
ejpam-367	128	13	)	)	PUNCT
ejpam-367	128	14	,	,	PUNCT
ejpam-367	128	15	u(t	u(t	PROPN
ejpam-367	128	16	)	)	PUNCT
ejpam-367	128	17	,	,	PUNCT
ejpam-367	128	18	v(t	v(t	NOUN
ejpam-367	128	19	)	)	PUNCT
ejpam-367	128	20	)	)	PUNCT
ejpam-367	129	1	∈	∈	PROPN
ejpam-367	129	2	rn	rn	PROPN
ejpam-367	129	3	+	+	PUNCT
ejpam-367	129	4	with	with	ADP
ejpam-367	129	5	η	η	PROPN
ejpam-367	129	6	=	=	SYM
ejpam-367	129	7	0	0	NUM
ejpam-367	129	8	at	at	ADP
ejpam-367	129	9	x(t	x(t	PROPN
ejpam-367	129	10	)	)	PUNCT
ejpam-367	129	11	=	=	SYM
ejpam-367	129	12	u(t	u(t	NOUN
ejpam-367	129	13	)	)	PUNCT
ejpam-367	129	14	or	or	CCONJ
ejpam-367	129	15	y(t	y(t	NUM
ejpam-367	129	16	)	)	PUNCT
ejpam-367	129	17	=	=	SYM
ejpam-367	130	1	v(t	v(t	NUM
ejpam-367	130	2	)	)	PUNCT
ejpam-367	130	3	,	,	PUNCT
ejpam-367	130	4	such	such	ADJ
ejpam-367	130	5	that	that	PRON
ejpam-367	130	6	for	for	ADP
ejpam-367	130	7	the	the	DET
ejpam-367	130	8	scalar	scalar	ADJ
ejpam-367	130	9	function	function	NOUN
ejpam-367	130	10	h(t	h(t	PROPN
ejpam-367	130	11	,	,	PUNCT
ejpam-367	130	12	x(t	x(t	PROPN
ejpam-367	130	13	)	)	PUNCT
ejpam-367	130	14	,	,	PUNCT
ejpam-367	130	15	ẋ(t	ẋ(t	NOUN
ejpam-367	130	16	)	)	PUNCT
ejpam-367	130	17	,	,	PUNCT
ejpam-367	130	18	y(t	y(t	PROPN
ejpam-367	130	19	)	)	PUNCT
ejpam-367	130	20	,	,	PUNCT
ejpam-367	130	21	ẏ(t	ẏ(t	PROPN
ejpam-367	130	22	)	)	PUNCT
ejpam-367	130	23	)	)	PUNCT
ejpam-367	131	1	the	the	DET
ejpam-367	131	2	functional	functional	ADJ
ejpam-367	131	3	h(x	h(x	PROPN
ejpam-367	131	4	,	,	PUNCT
ejpam-367	131	5	ẋ	ẋ	PROPN
ejpam-367	131	6	,	,	PUNCT
ejpam-367	131	7	y	y	PROPN
ejpam-367	131	8	,	,	PUNCT
ejpam-367	131	9	ẏ	ẏ	PROPN
ejpam-367	131	10	)	)	PUNCT
ejpam-367	131	11	=	=	SYM
ejpam-367	131	12	∫	∫	PROPN
ejpam-367	132	1	i	i	PRON
ejpam-367	132	2	h(t	h(t	PROPN
ejpam-367	132	3	,	,	PUNCT
ejpam-367	132	4	x(t	x(t	PROPN
ejpam-367	132	5	)	)	PUNCT
ejpam-367	132	6	,	,	PUNCT
ejpam-367	132	7	ẋ(t	ẋ(t	NOUN
ejpam-367	132	8	)	)	PUNCT
ejpam-367	132	9	,	,	PUNCT
ejpam-367	132	10	y(t	y(t	PROPN
ejpam-367	132	11	)	)	PUNCT
ejpam-367	132	12	,	,	PUNCT
ejpam-367	132	13	ẏ(t))d	ẏ(t))d	PROPN
ejpam-367	132	14	t	t	PROPN
ejpam-367	132	15	i.	i.	PROPN
ejpam-367	132	16	husain	husain	PROPN
ejpam-367	132	17	and	and	CCONJ
ejpam-367	132	18	r.	r.	PROPN
ejpam-367	132	19	mattoo	mattoo	PROPN
ejpam-367	132	20	/	/	SYM
ejpam-367	132	21	eur	eur	PROPN
ejpam-367	132	22	.	.	PUNCT
ejpam-367	133	1	j.	j.	PROPN
ejpam-367	133	2	pure	pure	PROPN
ejpam-367	133	3	appl	appl	PROPN
ejpam-367	133	4	.	.	PROPN
ejpam-367	133	5	math	math	PROPN
ejpam-367	133	6	,	,	PUNCT
ejpam-367	133	7	2	2	NUM
ejpam-367	133	8	(	(	PUNCT
ejpam-367	133	9	2009	2009	NUM
ejpam-367	133	10	)	)	PUNCT
ejpam-367	133	11	,	,	PUNCT
ejpam-367	133	12	(	(	PUNCT
ejpam-367	133	13	578	578	NUM
ejpam-367	133	14	-	-	SYM
ejpam-367	133	15	603	603	NUM
ejpam-367	133	16	)	)	PUNCT
ejpam-367	133	17	582	582	NUM
ejpam-367	133	18	satisfies	satisfie	NOUN
ejpam-367	133	19	h(x	h(x	PROPN
ejpam-367	133	20	,	,	PUNCT
ejpam-367	133	21	ẋ	ẋ	PROPN
ejpam-367	133	22	,	,	PUNCT
ejpam-367	133	23	y	y	PROPN
ejpam-367	133	24	,	,	PUNCT
ejpam-367	133	25	ẏ)−h(u	ẏ)−h(u	PROPN
ejpam-367	133	26	,	,	PUNCT
ejpam-367	133	27	u̇	u̇	PROPN
ejpam-367	133	28	,	,	PUNCT
ejpam-367	133	29	v	v	NOUN
ejpam-367	133	30	,	,	PUNCT
ejpam-367	133	31	v̇	v̇	NOUN
ejpam-367	133	32	)	)	PUNCT
ejpam-367	133	33	≥	≥	NOUN
ejpam-367	133	34	∫	∫	NOUN
ejpam-367	134	1	i	i	PRON
ejpam-367	135	1	[	[	X
ejpam-367	135	2	ηt	ηt	ADP
ejpam-367	135	3	hx(t	hx(t	X
ejpam-367	135	4	,	,	PUNCT
ejpam-367	135	5	x(t	x(t	PROPN
ejpam-367	135	6	)	)	PUNCT
ejpam-367	135	7	,	,	PUNCT
ejpam-367	135	8	ẋ(t	ẋ(t	NOUN
ejpam-367	135	9	)	)	PUNCT
ejpam-367	135	10	,	,	PUNCT
ejpam-367	135	11	y(t	y(t	PROPN
ejpam-367	135	12	)	)	PUNCT
ejpam-367	135	13	,	,	PUNCT
ejpam-367	135	14	ẏ(t	ẏ(t	PROPN
ejpam-367	135	15	)	)	PUNCT
ejpam-367	135	16	)	)	PUNCT
ejpam-367	136	1	+	+	CCONJ
ejpam-367	136	2	(	(	PUNCT
ejpam-367	136	3	dη)t	dη)t	PROPN
ejpam-367	136	4	h	h	NOUN
ejpam-367	136	5	ẋ(t	ẋ(t	PROPN
ejpam-367	136	6	,	,	PUNCT
ejpam-367	136	7	x(t	x(t	PROPN
ejpam-367	136	8	)	)	PUNCT
ejpam-367	136	9	,	,	PUNCT
ejpam-367	136	10	ẋ(t	ẋ(t	NOUN
ejpam-367	136	11	)	)	PUNCT
ejpam-367	136	12	,	,	PUNCT
ejpam-367	136	13	y(t	y(t	PROPN
ejpam-367	136	14	)	)	PUNCT
ejpam-367	136	15	,	,	PUNCT
ejpam-367	136	16	ẏ(t))]d	ẏ(t))]d	PROPN
ejpam-367	136	17	t	t	PROPN
ejpam-367	136	18	then	then	ADV
ejpam-367	136	19	h(x	h(x	PROPN
ejpam-367	136	20	,	,	PUNCT
ejpam-367	136	21	ẋ	ẋ	PROPN
ejpam-367	136	22	,	,	PUNCT
ejpam-367	136	23	y	y	PROPN
ejpam-367	136	24	,	,	PUNCT
ejpam-367	136	25	ẏ	ẏ	PROPN
ejpam-367	136	26	)	)	PUNCT
ejpam-367	136	27	is	be	AUX
ejpam-367	136	28	said	say	VERB
ejpam-367	136	29	to	to	PART
ejpam-367	136	30	be	be	AUX
ejpam-367	136	31	partially	partially	ADV
ejpam-367	136	32	invex	invex	ADJ
ejpam-367	136	33	in	in	ADP
ejpam-367	136	34	x	x	PUNCT
ejpam-367	136	35	and	and	CCONJ
ejpam-367	136	36	ẋ	ẋ	PROPN
ejpam-367	136	37	on	on	ADP
ejpam-367	136	38	i	i	PRON
ejpam-367	136	39	with	with	ADP
ejpam-367	136	40	respect	respect	NOUN
ejpam-367	136	41	to	to	ADP
ejpam-367	136	42	η	η	PROPN
ejpam-367	136	43	,	,	PUNCT
ejpam-367	136	44	for	for	ADP
ejpam-367	136	45	fixed	fixed	ADJ
ejpam-367	136	46	y.	y.	NOUN
ejpam-367	136	47	if	if	SCONJ
ejpam-367	136	48	h	h	NOUN
ejpam-367	136	49	satisfies	satisfy	VERB
ejpam-367	136	50	h(x	h(x	PROPN
ejpam-367	136	51	,	,	PUNCT
ejpam-367	136	52	ẋ	ẋ	PROPN
ejpam-367	136	53	,	,	PUNCT
ejpam-367	136	54	y	y	PROPN
ejpam-367	136	55	,	,	PUNCT
ejpam-367	136	56	ẏ)−h(x	ẏ)−h(x	PROPN
ejpam-367	136	57	,	,	PUNCT
ejpam-367	136	58	ẋ	ẋ	PROPN
ejpam-367	136	59	,	,	PUNCT
ejpam-367	136	60	v	v	NOUN
ejpam-367	136	61	,	,	PUNCT
ejpam-367	136	62	v̇	v̇	NOUN
ejpam-367	136	63	)	)	PUNCT
ejpam-367	137	1	≥	≥	NOUN
ejpam-367	138	1	∫	∫	NOUN
ejpam-367	139	1	i	i	PRON
ejpam-367	140	1	[	[	X
ejpam-367	140	2	ηt	ηt	ADP
ejpam-367	140	3	hy(t	hy(t	NOUN
ejpam-367	140	4	,	,	PUNCT
ejpam-367	140	5	x(t	x(t	PROPN
ejpam-367	140	6	)	)	PUNCT
ejpam-367	140	7	,	,	PUNCT
ejpam-367	140	8	ẋ(t	ẋ(t	NOUN
ejpam-367	140	9	)	)	PUNCT
ejpam-367	140	10	,	,	PUNCT
ejpam-367	140	11	v(t	v(t	NOUN
ejpam-367	140	12	)	)	PUNCT
ejpam-367	140	13	,	,	PUNCT
ejpam-367	140	14	v̇(t	v̇(t	NOUN
ejpam-367	140	15	)	)	PUNCT
ejpam-367	140	16	)	)	PUNCT
ejpam-367	141	1	+	+	PROPN
ejpam-367	141	2	(	(	PUNCT
ejpam-367	141	3	dη)t	dη)t	PROPN
ejpam-367	141	4	h	h	NOUN
ejpam-367	141	5	ẏ(t	ẏ(t	NOUN
ejpam-367	141	6	,	,	PUNCT
ejpam-367	141	7	x(t	x(t	PROPN
ejpam-367	141	8	)	)	PUNCT
ejpam-367	141	9	,	,	PUNCT
ejpam-367	141	10	ẋ(t	ẋ(t	NOUN
ejpam-367	141	11	)	)	PUNCT
ejpam-367	141	12	,	,	PUNCT
ejpam-367	141	13	v(t	v(t	NOUN
ejpam-367	141	14	)	)	PUNCT
ejpam-367	141	15	,	,	PUNCT
ejpam-367	141	16	v̇(t))]d	v̇(t))]d	PROPN
ejpam-367	141	17	t	t	PROPN
ejpam-367	141	18	,	,	PUNCT
ejpam-367	141	19	then	then	ADV
ejpam-367	141	20	h(x	h(x	PROPN
ejpam-367	141	21	,	,	PUNCT
ejpam-367	141	22	ẋ	ẋ	PROPN
ejpam-367	141	23	,	,	PUNCT
ejpam-367	141	24	y	y	PROPN
ejpam-367	141	25	,	,	PUNCT
ejpam-367	141	26	ẏ	ẏ	PROPN
ejpam-367	141	27	)	)	PUNCT
ejpam-367	141	28	is	be	AUX
ejpam-367	141	29	said	say	VERB
ejpam-367	141	30	to	to	PART
ejpam-367	141	31	be	be	AUX
ejpam-367	141	32	partially	partially	ADV
ejpam-367	141	33	invex	invex	ADJ
ejpam-367	141	34	in	in	ADP
ejpam-367	141	35	y	y	PROPN
ejpam-367	141	36	and	and	CCONJ
ejpam-367	141	37	ẏ	ẏ	PROPN
ejpam-367	141	38	on	on	ADP
ejpam-367	141	39	i	i	PRON
ejpam-367	141	40	with	with	ADP
ejpam-367	141	41	respect	respect	NOUN
ejpam-367	141	42	to	to	ADP
ejpam-367	141	43	η	η	PROPN
ejpam-367	141	44	,	,	PUNCT
ejpam-367	141	45	for	for	ADP
ejpam-367	141	46	fixed	fix	VERB
ejpam-367	141	47	x.	x.	NOUN
ejpam-367	141	48	if	if	SCONJ
ejpam-367	141	49	−h	−h	ADJ
ejpam-367	141	50	is	be	AUX
ejpam-367	141	51	partially	partially	ADV
ejpam-367	141	52	invex	invex	ADJ
ejpam-367	141	53	in	in	ADP
ejpam-367	141	54	x	x	PUNCT
ejpam-367	141	55	and	and	CCONJ
ejpam-367	141	56	ẋ	ẋ	PROPN
ejpam-367	142	1	(	(	PUNCT
ejpam-367	142	2	or	or	CCONJ
ejpam-367	142	3	in	in	ADP
ejpam-367	142	4	y	y	PROPN
ejpam-367	142	5	and	and	CCONJ
ejpam-367	142	6	ẏ	ẏ	PROPN
ejpam-367	142	7	)	)	PUNCT
ejpam-367	142	8	on	on	ADP
ejpam-367	142	9	i	i	PRON
ejpam-367	142	10	with	with	ADP
ejpam-367	142	11	respect	respect	NOUN
ejpam-367	142	12	to	to	ADP
ejpam-367	142	13	η	η	PROPN
ejpam-367	142	14	,	,	PUNCT
ejpam-367	142	15	for	for	ADP
ejpam-367	142	16	fixed	fix	VERB
ejpam-367	142	17	y(or	y(or	NOUN
ejpam-367	142	18	for	for	ADP
ejpam-367	142	19	fixed	fix	VERB
ejpam-367	142	20	x	x	NOUN
ejpam-367	142	21	)	)	PUNCT
ejpam-367	142	22	,	,	PUNCT
ejpam-367	142	23	then	then	ADV
ejpam-367	142	24	h	h	NOUN
ejpam-367	142	25	is	be	AUX
ejpam-367	142	26	said	say	VERB
ejpam-367	142	27	to	to	PART
ejpam-367	142	28	be	be	AUX
ejpam-367	142	29	partially	partially	ADV
ejpam-367	142	30	incave	incave	ADJ
ejpam-367	142	31	in	in	ADP
ejpam-367	142	32	x	x	PUNCT
ejpam-367	142	33	and	and	CCONJ
ejpam-367	142	34	ẋ	ẋ	PROPN
ejpam-367	143	1	(	(	PUNCT
ejpam-367	143	2	or	or	CCONJ
ejpam-367	143	3	in	in	ADP
ejpam-367	143	4	y	y	PROPN
ejpam-367	143	5	and	and	CCONJ
ejpam-367	143	6	ẏ	ẏ	PROPN
ejpam-367	143	7	)	)	PUNCT
ejpam-367	143	8	on	on	ADP
ejpam-367	143	9	i	i	PRON
ejpam-367	143	10	with	with	ADP
ejpam-367	143	11	respect	respect	NOUN
ejpam-367	143	12	to	to	ADP
ejpam-367	143	13	η	η	PROPN
ejpam-367	143	14	,	,	PUNCT
ejpam-367	143	15	for	for	ADP
ejpam-367	143	16	fixed	fixed	ADJ
ejpam-367	143	17	y	y	PROPN
ejpam-367	143	18	(	(	PUNCT
ejpam-367	143	19	or	or	CCONJ
ejpam-367	143	20	for	for	ADP
ejpam-367	143	21	fixed	fix	VERB
ejpam-367	143	22	x	x	NOUN
ejpam-367	143	23	)	)	PUNCT
ejpam-367	143	24	.	.	PUNCT
ejpam-367	144	1	definition	definition	NOUN
ejpam-367	144	2	2	2	NUM
ejpam-367	144	3	(	(	PUNCT
ejpam-367	144	4	partially	partially	ADV
ejpam-367	144	5	pseudoinvex	pseudoinvex	NOUN
ejpam-367	144	6	)	)	PUNCT
ejpam-367	144	7	.	.	PUNCT
ejpam-367	145	1	the	the	DET
ejpam-367	145	2	functional	functional	ADJ
ejpam-367	145	3	h	h	NOUN
ejpam-367	145	4	is	be	AUX
ejpam-367	145	5	said	say	VERB
ejpam-367	145	6	to	to	PART
ejpam-367	145	7	be	be	AUX
ejpam-367	145	8	partially	partially	ADV
ejpam-367	145	9	pseudoinvex	pseudoinvex	NOUN
ejpam-367	145	10	in	in	ADP
ejpam-367	145	11	x	x	PUNCT
ejpam-367	145	12	and	and	CCONJ
ejpam-367	145	13	ẋ	ẋ	VERB
ejpam-367	145	14	with	with	ADP
ejpam-367	145	15	respect	respect	NOUN
ejpam-367	145	16	to	to	ADP
ejpam-367	145	17	η	η	PROPN
ejpam-367	145	18	,	,	PUNCT
ejpam-367	145	19	for	for	ADP
ejpam-367	145	20	fixed	fixed	ADJ
ejpam-367	145	21	y	y	PROPN
ejpam-367	145	22	if	if	SCONJ
ejpam-367	145	23	h	h	NOUN
ejpam-367	145	24	satisfies	satisfy	VERB
ejpam-367	145	25	∫	∫	PROPN
ejpam-367	145	26	i	i	PRON
ejpam-367	146	1	[	[	X
ejpam-367	146	2	ηt	ηt	ADP
ejpam-367	146	3	hx(t	hx(t	X
ejpam-367	146	4	,	,	PUNCT
ejpam-367	146	5	x	x	SYM
ejpam-367	146	6	,	,	PUNCT
ejpam-367	146	7	ẋ	ẋ	PROPN
ejpam-367	146	8	,	,	PUNCT
ejpam-367	146	9	y	y	PROPN
ejpam-367	146	10	,	,	PUNCT
ejpam-367	146	11	ẏ	ẏ	PROPN
ejpam-367	146	12	)	)	PUNCT
ejpam-367	146	13	+	+	CCONJ
ejpam-367	146	14	(	(	PUNCT
ejpam-367	146	15	dη)t	dη)t	PROPN
ejpam-367	146	16	h	h	NOUN
ejpam-367	146	17	ẋ(t	ẋ(t	PROPN
ejpam-367	146	18	,	,	PUNCT
ejpam-367	146	19	x	x	X
ejpam-367	146	20	,	,	PUNCT
ejpam-367	146	21	ẋ	ẋ	PROPN
ejpam-367	146	22	,	,	PUNCT
ejpam-367	146	23	y	y	PROPN
ejpam-367	146	24	,	,	PUNCT
ejpam-367	146	25	ẏ)]d	ẏ)]d	PROPN
ejpam-367	146	26	t	t	PROPN
ejpam-367	146	27	≧	≧	PUNCT
ejpam-367	146	28	0	0	NUM
ejpam-367	146	29	implies	imply	VERB
ejpam-367	146	30	h(x	h(x	PROPN
ejpam-367	146	31	,	,	PUNCT
ejpam-367	146	32	ẋ	ẋ	PROPN
ejpam-367	146	33	,	,	PUNCT
ejpam-367	146	34	u	u	NOUN
ejpam-367	146	35	,	,	PUNCT
ejpam-367	146	36	u̇)≧	u̇)≧	PROPN
ejpam-367	146	37	h(x	h(x	PROPN
ejpam-367	146	38	,	,	PUNCT
ejpam-367	146	39	ẋ	ẋ	PROPN
ejpam-367	146	40	,	,	PUNCT
ejpam-367	146	41	y	y	PROPN
ejpam-367	146	42	,	,	PUNCT
ejpam-367	146	43	ẏ	ẏ	PROPN
ejpam-367	146	44	)	)	PUNCT
ejpam-367	146	45	and	and	CCONJ
ejpam-367	146	46	h	h	NOUN
ejpam-367	146	47	is	be	AUX
ejpam-367	146	48	said	say	VERB
ejpam-367	146	49	to	to	PART
ejpam-367	146	50	be	be	AUX
ejpam-367	146	51	partially	partially	ADV
ejpam-367	146	52	pseudoinvex	pseudoinvex	NOUN
ejpam-367	146	53	in	in	ADP
ejpam-367	146	54	y	y	PROPN
ejpam-367	146	55	and	and	CCONJ
ejpam-367	146	56	ẏ	ẏ	PROPN
ejpam-367	146	57	with	with	ADP
ejpam-367	146	58	respect	respect	NOUN
ejpam-367	146	59	to	to	ADP
ejpam-367	146	60	η	η	PROPN
ejpam-367	146	61	,	,	PUNCT
ejpam-367	146	62	for	for	ADP
ejpam-367	146	63	fixed	fixed	ADJ
ejpam-367	146	64	x	x	NOUN
ejpam-367	146	65	if	if	SCONJ
ejpam-367	146	66	h	h	NOUN
ejpam-367	146	67	satisfies	satisfy	VERB
ejpam-367	146	68	∫	∫	PROPN
ejpam-367	147	1	i	i	PRON
ejpam-367	148	1	[	[	X
ejpam-367	148	2	ηt	ηt	ADP
ejpam-367	148	3	hy(t	hy(t	NOUN
ejpam-367	148	4	,	,	PUNCT
ejpam-367	148	5	x	x	X
ejpam-367	148	6	,	,	PUNCT
ejpam-367	148	7	ẋ	ẋ	PROPN
ejpam-367	148	8	,	,	PUNCT
ejpam-367	148	9	y	y	PROPN
ejpam-367	148	10	,	,	PUNCT
ejpam-367	148	11	ẏ	ẏ	PROPN
ejpam-367	148	12	)	)	PUNCT
ejpam-367	148	13	+	+	CCONJ
ejpam-367	149	1	(	(	PUNCT
ejpam-367	149	2	dη)t	dη)t	PROPN
ejpam-367	149	3	h	h	NOUN
ejpam-367	149	4	ẏ(t	ẏ(t	VERB
ejpam-367	149	5	,	,	PUNCT
ejpam-367	149	6	x	x	SYM
ejpam-367	149	7	,	,	PUNCT
ejpam-367	149	8	ẋ	ẋ	PROPN
ejpam-367	149	9	,	,	PUNCT
ejpam-367	149	10	y	y	PROPN
ejpam-367	149	11	,	,	PUNCT
ejpam-367	149	12	ẏ)]d	ẏ)]d	PROPN
ejpam-367	149	13	t	t	PROPN
ejpam-367	149	14	≧	≧	PUNCT
ejpam-367	149	15	0	0	NUM
ejpam-367	149	16	implies	imply	VERB
ejpam-367	149	17	h(x	h(x	PROPN
ejpam-367	149	18	,	,	PUNCT
ejpam-367	149	19	ẋ	ẋ	PROPN
ejpam-367	149	20	,	,	PUNCT
ejpam-367	149	21	v	v	NOUN
ejpam-367	149	22	,	,	PUNCT
ejpam-367	149	23	v̇)≧	v̇)≧	PROPN
ejpam-367	149	24	h(x	h(x	PROPN
ejpam-367	149	25	,	,	PUNCT
ejpam-367	149	26	ẋ	ẋ	PROPN
ejpam-367	149	27	,	,	PUNCT
ejpam-367	149	28	y	y	PROPN
ejpam-367	149	29	,	,	PUNCT
ejpam-367	149	30	ẏ	ẏ	PROPN
ejpam-367	149	31	)	)	PUNCT
ejpam-367	149	32	.	.	PUNCT
ejpam-367	150	1	i.	i.	PROPN
ejpam-367	150	2	husain	husain	PROPN
ejpam-367	150	3	and	and	CCONJ
ejpam-367	150	4	r.	r.	PROPN
ejpam-367	150	5	mattoo	mattoo	PROPN
ejpam-367	150	6	/	/	SYM
ejpam-367	150	7	eur	eur	PROPN
ejpam-367	150	8	.	.	PUNCT
ejpam-367	151	1	j.	j.	PROPN
ejpam-367	151	2	pure	pure	PROPN
ejpam-367	151	3	appl	appl	PROPN
ejpam-367	151	4	.	.	PROPN
ejpam-367	151	5	math	math	PROPN
ejpam-367	151	6	,	,	PUNCT
ejpam-367	151	7	2	2	NUM
ejpam-367	151	8	(	(	PUNCT
ejpam-367	151	9	2009	2009	NUM
ejpam-367	151	10	)	)	PUNCT
ejpam-367	151	11	,	,	PUNCT
ejpam-367	151	12	(	(	PUNCT
ejpam-367	151	13	578	578	NUM
ejpam-367	151	14	-	-	SYM
ejpam-367	151	15	603	603	NUM
ejpam-367	151	16	)	)	PUNCT
ejpam-367	151	17	583	583	NUM
ejpam-367	151	18	definition	definition	NOUN
ejpam-367	151	19	3	3	NUM
ejpam-367	151	20	(	(	PUNCT
ejpam-367	151	21	partially	partially	ADV
ejpam-367	151	22	quasi	quasi	ADJ
ejpam-367	151	23	-	-	NOUN
ejpam-367	151	24	invex	invex	ADJ
ejpam-367	151	25	)	)	PUNCT
ejpam-367	151	26	.	.	PUNCT
ejpam-367	152	1	the	the	DET
ejpam-367	152	2	functional	functional	ADJ
ejpam-367	152	3	h	h	NOUN
ejpam-367	152	4	is	be	AUX
ejpam-367	152	5	said	say	VERB
ejpam-367	152	6	to	to	PART
ejpam-367	152	7	be	be	AUX
ejpam-367	152	8	partially	partially	ADV
ejpam-367	152	9	quasi	quasi	ADJ
ejpam-367	152	10	-	-	NOUN
ejpam-367	152	11	invex	invex	ADJ
ejpam-367	152	12	in	in	ADP
ejpam-367	152	13	x	x	PUNCT
ejpam-367	152	14	and	and	CCONJ
ejpam-367	152	15	ẋ	ẋ	VERB
ejpam-367	152	16	with	with	ADP
ejpam-367	152	17	respect	respect	NOUN
ejpam-367	152	18	to	to	ADP
ejpam-367	152	19	η	η	PROPN
ejpam-367	152	20	,	,	PUNCT
ejpam-367	152	21	for	for	ADP
ejpam-367	152	22	fixed	fixed	ADJ
ejpam-367	152	23	y	y	PROPN
ejpam-367	152	24	if	if	SCONJ
ejpam-367	152	25	h	h	NOUN
ejpam-367	152	26	satisfies	satisfy	VERB
ejpam-367	152	27	h(x	h(x	PROPN
ejpam-367	152	28	,	,	PUNCT
ejpam-367	152	29	ẋ	ẋ	PROPN
ejpam-367	152	30	,	,	PUNCT
ejpam-367	152	31	u	u	NOUN
ejpam-367	152	32	,	,	PUNCT
ejpam-367	152	33	u̇)≦	u̇)≦	ADV
ejpam-367	152	34	h(x	h(x	PROPN
ejpam-367	152	35	,	,	PUNCT
ejpam-367	152	36	ẋ	ẋ	PROPN
ejpam-367	152	37	,	,	PUNCT
ejpam-367	152	38	y	y	PROPN
ejpam-367	152	39	,	,	PUNCT
ejpam-367	152	40	ẏ	ẏ	PROPN
ejpam-367	152	41	)	)	PUNCT
ejpam-367	152	42	implies	imply	VERB
ejpam-367	152	43	∫	∫	PROPN
ejpam-367	152	44	i	i	PRON
ejpam-367	153	1	[	[	X
ejpam-367	153	2	ηt	ηt	ADP
ejpam-367	153	3	hx(t	hx(t	X
ejpam-367	153	4	,	,	PUNCT
ejpam-367	153	5	x	x	SYM
ejpam-367	153	6	,	,	PUNCT
ejpam-367	153	7	ẋ	ẋ	PROPN
ejpam-367	153	8	,	,	PUNCT
ejpam-367	153	9	y	y	PROPN
ejpam-367	153	10	,	,	PUNCT
ejpam-367	153	11	ẏ	ẏ	PROPN
ejpam-367	153	12	)	)	PUNCT
ejpam-367	153	13	+	+	CCONJ
ejpam-367	153	14	(	(	PUNCT
ejpam-367	153	15	dη)t	dη)t	PROPN
ejpam-367	153	16	h	h	NOUN
ejpam-367	153	17	ẋ(t	ẋ(t	PROPN
ejpam-367	153	18	,	,	PUNCT
ejpam-367	153	19	x	x	X
ejpam-367	153	20	,	,	PUNCT
ejpam-367	153	21	ẋ	ẋ	PROPN
ejpam-367	153	22	,	,	PUNCT
ejpam-367	153	23	y	y	PROPN
ejpam-367	153	24	,	,	PUNCT
ejpam-367	153	25	ẏ)]d	ẏ)]d	PROPN
ejpam-367	153	26	t	t	PROPN
ejpam-367	153	27	≦	≦	PROPN
ejpam-367	153	28	0	0	PUNCT
ejpam-367	154	1	and	and	CCONJ
ejpam-367	154	2	h	h	NOUN
ejpam-367	154	3	is	be	AUX
ejpam-367	154	4	said	say	VERB
ejpam-367	154	5	to	to	PART
ejpam-367	154	6	be	be	AUX
ejpam-367	154	7	partially	partially	ADV
ejpam-367	154	8	quasi	quasi	ADJ
ejpam-367	154	9	-	-	NOUN
ejpam-367	154	10	invex	invex	ADJ
ejpam-367	154	11	in	in	ADP
ejpam-367	154	12	y	y	PROPN
ejpam-367	154	13	and	and	CCONJ
ejpam-367	154	14	ẏ	ẏ	PROPN
ejpam-367	154	15	with	with	ADP
ejpam-367	154	16	respect	respect	NOUN
ejpam-367	154	17	to	to	ADP
ejpam-367	154	18	η	η	PROPN
ejpam-367	154	19	,	,	PUNCT
ejpam-367	154	20	for	for	ADP
ejpam-367	154	21	fixed	fixed	ADJ
ejpam-367	154	22	x	x	NOUN
ejpam-367	154	23	if	if	SCONJ
ejpam-367	154	24	h	h	NOUN
ejpam-367	154	25	satisfies	satisfy	VERB
ejpam-367	154	26	h(x	h(x	PROPN
ejpam-367	154	27	,	,	PUNCT
ejpam-367	154	28	ẋ	ẋ	PROPN
ejpam-367	154	29	,	,	PUNCT
ejpam-367	154	30	v	v	PROPN
ejpam-367	154	31	,	,	PUNCT
ejpam-367	154	32	v̇)≦	v̇)≦	PROPN
ejpam-367	154	33	h(x	h(x	PROPN
ejpam-367	154	34	,	,	PUNCT
ejpam-367	154	35	ẋ	ẋ	PROPN
ejpam-367	154	36	,	,	PUNCT
ejpam-367	154	37	y	y	PROPN
ejpam-367	154	38	,	,	PUNCT
ejpam-367	154	39	ẏ	ẏ	PROPN
ejpam-367	154	40	)	)	PUNCT
ejpam-367	154	41	implies	imply	VERB
ejpam-367	154	42	∫	∫	PROPN
ejpam-367	155	1	i	i	PRON
ejpam-367	156	1	[	[	X
ejpam-367	156	2	ηt	ηt	ADP
ejpam-367	156	3	hy(t	hy(t	NOUN
ejpam-367	156	4	,	,	PUNCT
ejpam-367	156	5	x	x	X
ejpam-367	156	6	,	,	PUNCT
ejpam-367	156	7	ẋ	ẋ	PROPN
ejpam-367	156	8	,	,	PUNCT
ejpam-367	156	9	y	y	PROPN
ejpam-367	156	10	,	,	PUNCT
ejpam-367	156	11	ẏ	ẏ	PROPN
ejpam-367	156	12	)	)	PUNCT
ejpam-367	156	13	+	+	CCONJ
ejpam-367	157	1	(	(	PUNCT
ejpam-367	157	2	dη)t	dη)t	PROPN
ejpam-367	157	3	h	h	NOUN
ejpam-367	157	4	ẏ(t	ẏ(t	VERB
ejpam-367	157	5	,	,	PUNCT
ejpam-367	157	6	x	x	SYM
ejpam-367	157	7	,	,	PUNCT
ejpam-367	157	8	ẋ	ẋ	PROPN
ejpam-367	157	9	,	,	PUNCT
ejpam-367	157	10	y	y	PROPN
ejpam-367	157	11	,	,	PUNCT
ejpam-367	157	12	ẏ)]d	ẏ)]d	PROPN
ejpam-367	157	13	t	t	PROPN
ejpam-367	157	14	≦	≦	PROPN
ejpam-367	157	15	0	0	PUNCT
ejpam-367	157	16	.	.	PUNCT
ejpam-367	158	1	if	if	SCONJ
ejpam-367	158	2	h	h	NOUN
ejpam-367	158	3	is	be	AUX
ejpam-367	158	4	independent	independent	ADJ
ejpam-367	158	5	of	of	ADP
ejpam-367	158	6	t	t	PROPN
ejpam-367	158	7	,	,	PUNCT
ejpam-367	158	8	then	then	ADV
ejpam-367	158	9	the	the	DET
ejpam-367	158	10	above	above	ADJ
ejpam-367	158	11	definitions	definition	NOUN
ejpam-367	158	12	become	become	VERB
ejpam-367	158	13	the	the	DET
ejpam-367	158	14	usual	usual	ADJ
ejpam-367	158	15	definitions	definition	NOUN
ejpam-367	158	16	of	of	ADP
ejpam-367	158	17	invexity	invexity	NOUN
ejpam-367	158	18	and	and	CCONJ
ejpam-367	158	19	generalized	generalized	ADJ
ejpam-367	158	20	invexity	invexity	NOUN
ejpam-367	158	21	,	,	PUNCT
ejpam-367	158	22	discussed	discuss	VERB
ejpam-367	158	23	by	by	ADP
ejpam-367	158	24	several	several	ADJ
ejpam-367	158	25	authors	author	NOUN
ejpam-367	158	26	,	,	PUNCT
ejpam-367	158	27	notably	notably	ADV
ejpam-367	158	28	ben	ben	PROPN
ejpam-367	158	29	-	-	PUNCT
ejpam-367	158	30	israel	israel	PROPN
ejpam-367	158	31	and	and	CCONJ
ejpam-367	158	32	mond	mond	VERB
ejpam-367	158	33	[	[	X
ejpam-367	158	34	5	5	NUM
ejpam-367	158	35	]	]	PUNCT
ejpam-367	158	36	,	,	PUNCT
ejpam-367	158	37	martin	martin	PROPN
ejpam-367	159	1	[	[	X
ejpam-367	159	2	11	11	NUM
ejpam-367	159	3	]	]	PUNCT
ejpam-367	159	4	,	,	PUNCT
ejpam-367	159	5	and	and	CCONJ
ejpam-367	159	6	rueda	rueda	PROPN
ejpam-367	159	7	and	and	CCONJ
ejpam-367	159	8	hanson	hanson	PROPN
ejpam-367	160	1	[	[	X
ejpam-367	160	2	16	16	NUM
ejpam-367	160	3	]	]	PUNCT
ejpam-367	160	4	.	.	PUNCT
ejpam-367	161	1	definition	definition	NOUN
ejpam-367	161	2	4	4	NUM
ejpam-367	161	3	(	(	PUNCT
ejpam-367	161	4	skew	skew	ADJ
ejpam-367	161	5	symmetry	symmetry	NOUN
ejpam-367	161	6	)	)	PUNCT
ejpam-367	161	7	.	.	PUNCT
ejpam-367	162	1	the	the	DET
ejpam-367	162	2	function	function	NOUN
ejpam-367	162	3	h	h	NOUN
ejpam-367	162	4	:	:	PUNCT
ejpam-367	163	1	i	i	PRON
ejpam-367	163	2	×	×	VERB
ejpam-367	163	3	rn×	rn×	NOUN
ejpam-367	163	4	rn×	rn×	NOUN
ejpam-367	163	5	rn	rn	PROPN
ejpam-367	163	6	×	×	PROPN
ejpam-367	163	7	rn→	rn→	PROPN
ejpam-367	163	8	r	r	NOUN
ejpam-367	163	9	is	be	AUX
ejpam-367	163	10	said	say	VERB
ejpam-367	163	11	to	to	PART
ejpam-367	163	12	be	be	AUX
ejpam-367	163	13	skew	skew	ADV
ejpam-367	163	14	symmetric	symmetric	ADJ
ejpam-367	163	15	if	if	SCONJ
ejpam-367	163	16	for	for	ADP
ejpam-367	163	17	all	all	DET
ejpam-367	163	18	x	x	PUNCT
ejpam-367	163	19	and	and	CCONJ
ejpam-367	163	20	y	y	PROPN
ejpam-367	163	21	in	in	ADP
ejpam-367	163	22	the	the	DET
ejpam-367	163	23	domain	domain	NOUN
ejpam-367	163	24	of	of	ADP
ejpam-367	163	25	h	h	NOUN
ejpam-367	163	26	if	if	SCONJ
ejpam-367	163	27	h(t	h(t	PROPN
ejpam-367	163	28	,	,	PUNCT
ejpam-367	163	29	x(t	x(t	PROPN
ejpam-367	163	30	)	)	PUNCT
ejpam-367	163	31	,	,	PUNCT
ejpam-367	163	32	ẋ(t	ẋ(t	NOUN
ejpam-367	163	33	)	)	PUNCT
ejpam-367	163	34	,	,	PUNCT
ejpam-367	163	35	y(t	y(t	PROPN
ejpam-367	163	36	)	)	PUNCT
ejpam-367	163	37	,	,	PUNCT
ejpam-367	163	38	ẏ(t	ẏ(t	PROPN
ejpam-367	163	39	)	)	PUNCT
ejpam-367	163	40	)	)	PUNCT
ejpam-367	164	1	=	=	PRON
ejpam-367	164	2	−h(t	−h(t	VERB
ejpam-367	164	3	,	,	PUNCT
ejpam-367	164	4	y(t	y(t	PROPN
ejpam-367	164	5	)	)	PUNCT
ejpam-367	164	6	,	,	PUNCT
ejpam-367	164	7	ẏ(t	ẏ(t	PROPN
ejpam-367	164	8	)	)	PUNCT
ejpam-367	164	9	,	,	PUNCT
ejpam-367	164	10	x(t	x(t	PROPN
ejpam-367	164	11	)	)	PUNCT
ejpam-367	164	12	,	,	PUNCT
ejpam-367	164	13	ẋ(t	ẋ(t	NOUN
ejpam-367	164	14	)	)	PUNCT
ejpam-367	164	15	)	)	PUNCT
ejpam-367	164	16	,	,	PUNCT
ejpam-367	164	17	t	t	PROPN
ejpam-367	164	18	∈	∈	PROPN
ejpam-367	165	1	i	i	PRON
ejpam-367	165	2	where	where	SCONJ
ejpam-367	165	3	x	x	PUNCT
ejpam-367	165	4	and	and	CCONJ
ejpam-367	165	5	y	y	PROPN
ejpam-367	165	6	are	be	AUX
ejpam-367	165	7	piecewise	piecewise	NOUN
ejpam-367	165	8	smooth	smooth	ADJ
ejpam-367	165	9	on	on	ADP
ejpam-367	165	10	i.	i.	PROPN
ejpam-367	165	11	now	now	ADV
ejpam-367	165	12	consider	consider	VERB
ejpam-367	165	13	the	the	DET
ejpam-367	165	14	following	follow	VERB
ejpam-367	165	15	multiobjective	multiobjective	ADJ
ejpam-367	165	16	variational	variational	ADJ
ejpam-367	165	17	problem	problem	NOUN
ejpam-367	165	18	considered	consider	VERB
ejpam-367	165	19	in	in	ADP
ejpam-367	165	20	[	[	X
ejpam-367	165	21	4	4	NUM
ejpam-367	165	22	]	]	NUM
ejpam-367	165	23	:	:	PUNCT
ejpam-367	165	24	(	(	PUNCT
ejpam-367	165	25	vp0	vp0	NOUN
ejpam-367	165	26	)	)	PUNCT
ejpam-367	165	27	minimize	minimize	VERB
ejpam-367	165	28	�	�	PROPN
ejpam-367	165	29	∫	∫	PROPN
ejpam-367	166	1	i	i	PRON
ejpam-367	166	2	φ1(t	φ1(t	PROPN
ejpam-367	166	3	,	,	PUNCT
ejpam-367	166	4	x	x	SYM
ejpam-367	166	5	,	,	PUNCT
ejpam-367	166	6	ẋ)d	ẋ)d	PROPN
ejpam-367	166	7	t	t	PROPN
ejpam-367	166	8	,	,	PUNCT
ejpam-367	166	9	∫	∫	PROPN
ejpam-367	167	1	i	i	PRON
ejpam-367	167	2	φ2(t	φ2(t	VERB
ejpam-367	167	3	,	,	PUNCT
ejpam-367	167	4	x	x	INTJ
ejpam-367	167	5	,	,	PUNCT
ejpam-367	167	6	ẋ)d	ẋ)d	PROPN
ejpam-367	167	7	t	t	PROPN
ejpam-367	167	8	,	,	PUNCT
ejpam-367	167	9	.	.	PUNCT
ejpam-367	167	10	.	.	PUNCT
ejpam-367	167	11	.	.	PUNCT
ejpam-367	168	1	,	,	PUNCT
ejpam-367	168	2	∫	∫	PROPN
ejpam-367	168	3	i	i	PRON
ejpam-367	168	4	φp(t	φp(t	VERB
ejpam-367	168	5	,	,	PUNCT
ejpam-367	168	6	x	x	X
ejpam-367	168	7	,	,	PUNCT
ejpam-367	168	8	ẋ)d	ẋ)d	PROPN
ejpam-367	168	9	t	t	PROPN
ejpam-367	168	10	,	,	PUNCT
ejpam-367	168	11	�	�	PROPN
ejpam-367	168	12	subject	subject	ADJ
ejpam-367	168	13	to	to	ADP
ejpam-367	168	14	i.	i.	PROPN
ejpam-367	168	15	husain	husain	PROPN
ejpam-367	168	16	and	and	CCONJ
ejpam-367	168	17	r.	r.	PROPN
ejpam-367	168	18	mattoo	mattoo	PROPN
ejpam-367	168	19	/	/	SYM
ejpam-367	168	20	eur	eur	PROPN
ejpam-367	168	21	.	.	PUNCT
ejpam-367	169	1	j.	j.	PROPN
ejpam-367	169	2	pure	pure	PROPN
ejpam-367	169	3	appl	appl	PROPN
ejpam-367	169	4	.	.	PROPN
ejpam-367	169	5	math	math	PROPN
ejpam-367	169	6	,	,	PUNCT
ejpam-367	169	7	2	2	NUM
ejpam-367	169	8	(	(	PUNCT
ejpam-367	169	9	2009	2009	NUM
ejpam-367	169	10	)	)	PUNCT
ejpam-367	169	11	,	,	PUNCT
ejpam-367	169	12	(	(	PUNCT
ejpam-367	169	13	578	578	NUM
ejpam-367	169	14	-	-	SYM
ejpam-367	169	15	603	603	NUM
ejpam-367	169	16	)	)	PUNCT
ejpam-367	169	17	584	584	NUM
ejpam-367	169	18	x(a	x(a	NOUN
ejpam-367	169	19	)	)	PUNCT
ejpam-367	169	20	=	=	SYM
ejpam-367	169	21	α	α	PROPN
ejpam-367	169	22	,	,	PUNCT
ejpam-367	169	23	x(b	x(b	PROPN
ejpam-367	169	24	)	)	PUNCT
ejpam-367	169	25	=	=	PUNCT
ejpam-367	170	1	β	β	X
ejpam-367	170	2	h(t	h(t	PROPN
ejpam-367	170	3	,	,	PUNCT
ejpam-367	170	4	x	x	SYM
ejpam-367	170	5	,	,	PUNCT
ejpam-367	170	6	ẋ)≦	ẋ)≦	PROPN
ejpam-367	170	7	0	0	PROPN
ejpam-367	170	8	,	,	PUNCT
ejpam-367	170	9	t	t	PROPN
ejpam-367	170	10	∈	∈	PROPN
ejpam-367	171	1	i	i	PRON
ejpam-367	171	2	,	,	PUNCT
ejpam-367	171	3	where	where	SCONJ
ejpam-367	171	4	φ	φ	PROPN
ejpam-367	171	5	i	i	VERB
ejpam-367	171	6	:	:	PUNCT
ejpam-367	172	1	i	i	PRON
ejpam-367	172	2	×	×	VERB
ejpam-367	172	3	rn	rn	PROPN
ejpam-367	172	4	×	×	PROPN
ejpam-367	172	5	rn	rn	PROPN
ejpam-367	172	6	×	×	PROPN
ejpam-367	172	7	rn	rn	PROPN
ejpam-367	172	8	→	→	SYM
ejpam-367	172	9	r	r	NOUN
ejpam-367	172	10	(	(	PUNCT
ejpam-367	172	11	i	i	NOUN
ejpam-367	172	12	=	=	NOUN
ejpam-367	172	13	1	1	NUM
ejpam-367	172	14	,	,	PUNCT
ejpam-367	172	15	2	2	NUM
ejpam-367	172	16	,	,	PUNCT
ejpam-367	172	17	.	.	PUNCT
ejpam-367	172	18	.	.	PUNCT
ejpam-367	172	19	.	.	PUNCT
ejpam-367	173	1	,	,	PUNCT
ejpam-367	173	2	p	p	X
ejpam-367	173	3	)	)	PUNCT
ejpam-367	173	4	and	and	CCONJ
ejpam-367	173	5	h	h	NOUN
ejpam-367	173	6	:	:	PUNCT
ejpam-367	174	1	i	i	PRON
ejpam-367	174	2	×	×	VERB
ejpam-367	174	3	rn	rn	PROPN
ejpam-367	174	4	×	×	PROPN
ejpam-367	174	5	rn	rn	PROPN
ejpam-367	174	6	×	×	PROPN
ejpam-367	174	7	rn	rn	PROPN
ejpam-367	174	8	→	→	PROPN
ejpam-367	174	9	rm	rm	PROPN
ejpam-367	174	10	.	.	PUNCT
ejpam-367	175	1	let	let	VERB
ejpam-367	175	2	the	the	DET
ejpam-367	175	3	set	set	NOUN
ejpam-367	175	4	of	of	ADP
ejpam-367	175	5	feasible	feasible	ADJ
ejpam-367	175	6	solution	solution	NOUN
ejpam-367	175	7	of	of	ADP
ejpam-367	175	8	(	(	PUNCT
ejpam-367	175	9	v	v	NOUN
ejpam-367	175	10	p0	p0	NOUN
ejpam-367	175	11	)	)	PUNCT
ejpam-367	175	12	be	be	AUX
ejpam-367	175	13	represented	represent	VERB
ejpam-367	175	14	by	by	ADP
ejpam-367	175	15	k	k	PROPN
ejpam-367	175	16	.	.	PUNCT
ejpam-367	176	1	definition	definition	NOUN
ejpam-367	176	2	5	5	NUM
ejpam-367	176	3	(	(	PUNCT
ejpam-367	176	4	efficiency	efficiency	NOUN
ejpam-367	176	5	)	)	PUNCT
ejpam-367	176	6	.	.	PUNCT
ejpam-367	177	1	a	a	DET
ejpam-367	177	2	point	point	NOUN
ejpam-367	177	3	x̄	x̄	PRON
ejpam-367	177	4	∈	∈	PROPN
ejpam-367	178	1	k	k	PROPN
ejpam-367	178	2	is	be	AUX
ejpam-367	178	3	an	an	DET
ejpam-367	178	4	efficient	efficient	ADJ
ejpam-367	178	5	(	(	PUNCT
ejpam-367	178	6	pareto	pareto	ADJ
ejpam-367	178	7	optimal	optimal	ADJ
ejpam-367	178	8	)	)	PUNCT
ejpam-367	178	9	solution	solution	NOUN
ejpam-367	178	10	of	of	ADP
ejpam-367	178	11	(	(	PUNCT
ejpam-367	178	12	vp0	vp0	NOUN
ejpam-367	178	13	)	)	PUNCT
ejpam-367	178	14	if	if	SCONJ
ejpam-367	178	15	for	for	ADP
ejpam-367	178	16	all	all	DET
ejpam-367	178	17	x	x	SYM
ejpam-367	178	18	∈	∈	PROPN
ejpam-367	178	19	k	k	NOUN
ejpam-367	178	20	,	,	PUNCT
ejpam-367	178	21	∫	∫	PROPN
ejpam-367	179	1	i	i	PRON
ejpam-367	179	2	φ	φ	PROPN
ejpam-367	179	3	i(t	i(t	PROPN
ejpam-367	179	4	,	,	PUNCT
ejpam-367	179	5	x	x	X
ejpam-367	179	6	,	,	PUNCT
ejpam-367	179	7	ẋ)d	ẋ)d	PROPN
ejpam-367	179	8	t	t	PROPN
ejpam-367	180	1	6≤	6≤	NUM
ejpam-367	180	2	∫	∫	PROPN
ejpam-367	181	1	i	i	PRON
ejpam-367	181	2	φ	φ	PROPN
ejpam-367	181	3	i(t	i(t	PROPN
ejpam-367	181	4	,	,	PUNCT
ejpam-367	181	5	x̄	x̄	PROPN
ejpam-367	181	6	,	,	PUNCT
ejpam-367	181	7	˙̄x)d	˙̄x)d	PROPN
ejpam-367	181	8	t	t	PROPN
ejpam-367	181	9	,	,	PUNCT
ejpam-367	181	10	(	(	PUNCT
ejpam-367	181	11	i	i	NOUN
ejpam-367	181	12	=	=	NOUN
ejpam-367	181	13	1	1	NUM
ejpam-367	181	14	,	,	PUNCT
ejpam-367	181	15	2	2	NUM
ejpam-367	181	16	,	,	PUNCT
ejpam-367	181	17	.	.	PUNCT
ejpam-367	181	18	.	.	PUNCT
ejpam-367	181	19	.	.	PUNCT
ejpam-367	182	1	,	,	PUNCT
ejpam-367	182	2	p	p	X
ejpam-367	182	3	)	)	PUNCT
ejpam-367	182	4	3	3	NUM
ejpam-367	182	5	.	.	PUNCT
ejpam-367	183	1	statement	statement	NOUN
ejpam-367	183	2	of	of	ADP
ejpam-367	183	3	the	the	DET
ejpam-367	183	4	problems	problem	NOUN
ejpam-367	183	5	for	for	ADP
ejpam-367	183	6	n	n	NOUN
ejpam-367	183	7	=	=	SYM
ejpam-367	183	8	{	{	PUNCT
ejpam-367	183	9	1	1	NUM
ejpam-367	183	10	,	,	PUNCT
ejpam-367	183	11	2	2	NUM
ejpam-367	183	12	,	,	PUNCT
ejpam-367	183	13	.	.	PUNCT
ejpam-367	183	14	.	.	PUNCT
ejpam-367	184	1	.	.	PUNCT
ejpam-367	185	1	,	,	PUNCT
ejpam-367	185	2	n	n	CCONJ
ejpam-367	185	3	}	}	PUNCT
ejpam-367	185	4	and	and	CCONJ
ejpam-367	185	5	m	m	PROPN
ejpam-367	185	6	=	=	X
ejpam-367	185	7	{	{	PUNCT
ejpam-367	185	8	1	1	NUM
ejpam-367	185	9	,	,	PUNCT
ejpam-367	185	10	2	2	NUM
ejpam-367	185	11	,	,	PUNCT
ejpam-367	185	12	.	.	PUNCT
ejpam-367	185	13	.	.	PUNCT
ejpam-367	186	1	.	.	PUNCT
ejpam-367	187	1	,	,	PUNCT
ejpam-367	187	2	m	m	VERB
ejpam-367	187	3	}	}	PUNCT
ejpam-367	187	4	,	,	PUNCT
ejpam-367	187	5	let	let	VERB
ejpam-367	187	6	j1	j1	PROPN
ejpam-367	187	7	⊂	⊂	PROPN
ejpam-367	187	8	n	n	PROPN
ejpam-367	187	9	,	,	PUNCT
ejpam-367	187	10	k1	k1	PROPN
ejpam-367	187	11	⊂	⊂	PROPN
ejpam-367	187	12	m	m	PROPN
ejpam-367	187	13	,	,	PUNCT
ejpam-367	187	14	j2	j2	PROPN
ejpam-367	187	15	=	=	SYM
ejpam-367	187	16	n	n	CCONJ
ejpam-367	187	17	\	\	PROPN
ejpam-367	187	18	j1	j1	PROPN
ejpam-367	187	19	and	and	CCONJ
ejpam-367	187	20	k2	k2	PROPN
ejpam-367	187	21	=	=	PROPN
ejpam-367	187	22	m	m	PROPN
ejpam-367	187	23	\	\	PROPN
ejpam-367	187	24	k1	k1	NOUN
ejpam-367	187	25	.	.	PUNCT
ejpam-367	188	1	let	let	VERB
ejpam-367	188	2	|j1|	|j1|	NOUN
ejpam-367	188	3	denote	denote	VERB
ejpam-367	188	4	the	the	DET
ejpam-367	188	5	number	number	NOUN
ejpam-367	188	6	of	of	ADP
ejpam-367	188	7	elements	element	NOUN
ejpam-367	188	8	in	in	ADP
ejpam-367	188	9	the	the	DET
ejpam-367	188	10	subset	subset	NOUN
ejpam-367	188	11	j1	j1	PROPN
ejpam-367	188	12	.	.	PUNCT
ejpam-367	189	1	the	the	DET
ejpam-367	189	2	other	other	ADJ
ejpam-367	189	3	symbol	symbol	NOUN
ejpam-367	189	4	|j2|	|j2|	NOUN
ejpam-367	189	5	,	,	PUNCT
ejpam-367	189	6	|k1|	|k1|	NOUN
ejpam-367	189	7	and	and	CCONJ
ejpam-367	189	8	|k2|	|k2|	ADV
ejpam-367	189	9	are	be	AUX
ejpam-367	189	10	similarly	similarly	ADV
ejpam-367	189	11	defined	define	VERB
ejpam-367	189	12	.	.	PUNCT
ejpam-367	190	1	let	let	VERB
ejpam-367	190	2	x1	x1	NOUN
ejpam-367	190	3	:	:	PUNCT
ejpam-367	190	4	i	i	PRON
ejpam-367	190	5	→	→	PUNCT
ejpam-367	190	6	r|j1|	r|j1|	PROPN
ejpam-367	190	7	and	and	CCONJ
ejpam-367	190	8	x2	x2	INTJ
ejpam-367	190	9	:	:	PUNCT
ejpam-367	191	1	i	i	PRON
ejpam-367	191	2	→	→	SYM
ejpam-367	191	3	r|j2|	r|j2|	PROPN
ejpam-367	191	4	,	,	PUNCT
ejpam-367	191	5	then	then	ADV
ejpam-367	191	6	any	any	DET
ejpam-367	191	7	x	x	X
ejpam-367	191	8	:	:	PUNCT
ejpam-367	191	9	i	i	PRON
ejpam-367	191	10	→	→	SYM
ejpam-367	191	11	rn	rn	PROPN
ejpam-367	191	12	can	can	AUX
ejpam-367	191	13	be	be	AUX
ejpam-367	191	14	written	write	VERB
ejpam-367	191	15	as	as	ADP
ejpam-367	191	16	x	x	X
ejpam-367	191	17	=	=	SYM
ejpam-367	191	18	(	(	PUNCT
ejpam-367	191	19	x1	x1	PROPN
ejpam-367	191	20	,	,	PUNCT
ejpam-367	191	21	x2	x2	PROPN
ejpam-367	191	22	)	)	PUNCT
ejpam-367	191	23	.	.	PUNCT
ejpam-367	192	1	similarly	similarly	ADV
ejpam-367	192	2	for	for	ADP
ejpam-367	192	3	y1	y1	NOUN
ejpam-367	192	4	:	:	PUNCT
ejpam-367	192	5	i	i	PRON
ejpam-367	192	6	→	→	SYM
ejpam-367	192	7	r|k1|	r|k1|	NOUN
ejpam-367	192	8	and	and	CCONJ
ejpam-367	192	9	y2	y2	NOUN
ejpam-367	192	10	:	:	PUNCT
ejpam-367	193	1	i	i	PRON
ejpam-367	193	2	→	→	SYM
ejpam-367	193	3	r|k2|	r|k2|	ADV
ejpam-367	193	4	can	can	AUX
ejpam-367	193	5	be	be	AUX
ejpam-367	193	6	written	write	VERB
ejpam-367	193	7	as	as	ADP
ejpam-367	193	8	y	y	PROPN
ejpam-367	193	9	=	=	SYM
ejpam-367	193	10	(	(	PUNCT
ejpam-367	193	11	y1	y1	INTJ
ejpam-367	193	12	,	,	PUNCT
ejpam-367	193	13	y2	y2	PROPN
ejpam-367	193	14	)	)	PUNCT
ejpam-367	193	15	where	where	SCONJ
ejpam-367	193	16	x	x	X
ejpam-367	193	17	:	:	PUNCT
ejpam-367	193	18	i	i	PROPN
ejpam-367	193	19	→	→	SYM
ejpam-367	193	20	rn	rn	PROPN
ejpam-367	193	21	,	,	PUNCT
ejpam-367	193	22	y	y	PROPN
ejpam-367	193	23	:	:	PUNCT
ejpam-367	193	24	i	i	PROPN
ejpam-367	193	25	→	→	SYM
ejpam-367	193	26	rm	rm	PROPN
ejpam-367	193	27	.	.	PUNCT
ejpam-367	194	1	let	let	VERB
ejpam-367	194	2	f	f	PROPN
ejpam-367	194	3	:	:	PUNCT
ejpam-367	194	4	i×r|j1|×r|k1|→	i×r|j1|×r|k1|→	PROPN
ejpam-367	194	5	rp	rp	NOUN
ejpam-367	194	6	and	and	CCONJ
ejpam-367	194	7	g	g	NOUN
ejpam-367	194	8	:	:	PUNCT
ejpam-367	194	9	i×r|j2|×r|k2|→	i×r|j2|×r|k2|→	PUNCT
ejpam-367	195	1	rp	rp	NOUN
ejpam-367	195	2	be	be	AUX
ejpam-367	195	3	twice	twice	ADV
ejpam-367	195	4	continuously	continuously	ADV
ejpam-367	195	5	differentiable	differentiable	ADJ
ejpam-367	195	6	functions	function	NOUN
ejpam-367	195	7	.	.	PUNCT
ejpam-367	196	1	we	we	PRON
ejpam-367	196	2	state	state	VERB
ejpam-367	196	3	the	the	DET
ejpam-367	196	4	following	follow	VERB
ejpam-367	196	5	pair	pair	NOUN
ejpam-367	196	6	of	of	ADP
ejpam-367	196	7	mixed	mixed	ADJ
ejpam-367	196	8	type	type	NOUN
ejpam-367	196	9	multiobjective	multiobjective	ADJ
ejpam-367	196	10	symmetric	symmetric	ADJ
ejpam-367	196	11	dual	dual	ADJ
ejpam-367	196	12	variational	variational	ADJ
ejpam-367	196	13	problems	problem	NOUN
ejpam-367	196	14	involving	involve	VERB
ejpam-367	196	15	vector	vector	NOUN
ejpam-367	196	16	functions	function	NOUN
ejpam-367	196	17	f	f	PROPN
ejpam-367	196	18	and	and	CCONJ
ejpam-367	196	19	g.	g.	PROPN
ejpam-367	196	20	(	(	PUNCT
ejpam-367	196	21	mix	mix	AUX
ejpam-367	196	22	sp	sp	NOUN
ejpam-367	196	23	)	)	PUNCT
ejpam-367	196	24	minimize	minimize	VERB
ejpam-367	196	25	f(x1	f(x1	ADJ
ejpam-367	196	26	,	,	PUNCT
ejpam-367	196	27	x2	x2	PROPN
ejpam-367	196	28	,	,	PUNCT
ejpam-367	196	29	y1	y1	NOUN
ejpam-367	196	30	,	,	PUNCT
ejpam-367	196	31	y2	y2	NOUN
ejpam-367	196	32	)	)	PUNCT
ejpam-367	197	1	=	=	SYM
ejpam-367	197	2	∫	∫	PROPN
ejpam-367	198	1	i	i	PRON
ejpam-367	198	2	{	{	PUNCT
ejpam-367	198	3	f	f	PROPN
ejpam-367	198	4	(	(	PUNCT
ejpam-367	198	5	t	t	PROPN
ejpam-367	198	6	,	,	PUNCT
ejpam-367	198	7	x1	x1	PROPN
ejpam-367	198	8	,	,	PUNCT
ejpam-367	198	9	ẋ1	ẋ1	PROPN
ejpam-367	198	10	,	,	PUNCT
ejpam-367	198	11	y1	y1	PROPN
ejpam-367	198	12	,	,	PUNCT
ejpam-367	198	13	ẏ1	ẏ1	PROPN
ejpam-367	198	14	)	)	PUNCT
ejpam-367	198	15	+	+	CCONJ
ejpam-367	198	16	g(t	g(t	PROPN
ejpam-367	198	17	,	,	PUNCT
ejpam-367	198	18	x2	x2	PROPN
ejpam-367	198	19	,	,	PUNCT
ejpam-367	198	20	ẋ2	ẋ2	PROPN
ejpam-367	198	21	,	,	PUNCT
ejpam-367	198	22	y2	y2	NOUN
ejpam-367	198	23	,	,	PUNCT
ejpam-367	198	24	ẏ2	ẏ2	PROPN
ejpam-367	198	25	)	)	PUNCT
ejpam-367	198	26	−y1(t)t(λt	−y1(t)t(λt	PROPN
ejpam-367	198	27	f	f	X
ejpam-367	198	28	y1(t	y1(t	INTJ
ejpam-367	198	29	,	,	PUNCT
ejpam-367	198	30	x1	x1	PROPN
ejpam-367	198	31	,	,	PUNCT
ejpam-367	198	32	ẋ1	ẋ1	PROPN
ejpam-367	198	33	,	,	PUNCT
ejpam-367	198	34	y1	y1	PROPN
ejpam-367	198	35	,	,	PUNCT
ejpam-367	198	36	ẏ1	ẏ1	PROPN
ejpam-367	198	37	)	)	PUNCT
ejpam-367	198	38	−dλt	−dλt	NOUN
ejpam-367	199	1	f	f	PROPN
ejpam-367	199	2	ẏ1(t	ẏ1(t	PROPN
ejpam-367	199	3	,	,	PUNCT
ejpam-367	199	4	x1	x1	PROPN
ejpam-367	199	5	,	,	PUNCT
ejpam-367	199	6	ẋ1	ẋ1	PROPN
ejpam-367	199	7	,	,	PUNCT
ejpam-367	199	8	y1	y1	PROPN
ejpam-367	199	9	,	,	PUNCT
ejpam-367	199	10	ẏ1))e}d	ẏ1))e}d	PROPN
ejpam-367	199	11	t	t	PROPN
ejpam-367	199	12	subject	subject	VERB
ejpam-367	199	13	to	to	ADP
ejpam-367	199	14	x1(a	x1(a	PROPN
ejpam-367	199	15	)	)	PUNCT
ejpam-367	199	16	=	=	PUNCT
ejpam-367	200	1	0=	0=	NOUN
ejpam-367	200	2	x1(b	x1(b	NUM
ejpam-367	200	3	)	)	PUNCT
ejpam-367	200	4	,	,	PUNCT
ejpam-367	200	5	y1(a	y1(a	PROPN
ejpam-367	200	6	)	)	PUNCT
ejpam-367	200	7	=	=	SYM
ejpam-367	200	8	0	0	PUNCT
ejpam-367	200	9	=	=	SYM
ejpam-367	200	10	y1(b	y1(b	PROPN
ejpam-367	200	11	)	)	PUNCT
ejpam-367	200	12	,	,	PUNCT
ejpam-367	200	13	(	(	PUNCT
ejpam-367	200	14	1	1	X
ejpam-367	200	15	)	)	PUNCT
ejpam-367	200	16	x2(a	x2(a	NUM
ejpam-367	200	17	)	)	PUNCT
ejpam-367	201	1	=	=	SYM
ejpam-367	201	2	0=	0=	NUM
ejpam-367	202	1	x2(b	x2(b	X
ejpam-367	202	2	)	)	PUNCT
ejpam-367	202	3	,	,	PUNCT
ejpam-367	202	4	y2(a	y2(a	NOUN
ejpam-367	202	5	)	)	PUNCT
ejpam-367	202	6	=	=	SYM
ejpam-367	202	7	0	0	PUNCT
ejpam-367	202	8	=	=	SYM
ejpam-367	202	9	y2(b	y2(b	PROPN
ejpam-367	202	10	)	)	PUNCT
ejpam-367	202	11	,	,	PUNCT
ejpam-367	202	12	(	(	PUNCT
ejpam-367	202	13	2	2	X
ejpam-367	202	14	)	)	PUNCT
ejpam-367	202	15	i.	i.	NOUN
ejpam-367	202	16	husain	husain	PROPN
ejpam-367	202	17	and	and	CCONJ
ejpam-367	202	18	r.	r.	PROPN
ejpam-367	202	19	mattoo	mattoo	PROPN
ejpam-367	202	20	/	/	SYM
ejpam-367	202	21	eur	eur	PROPN
ejpam-367	202	22	.	.	PUNCT
ejpam-367	203	1	j.	j.	PROPN
ejpam-367	203	2	pure	pure	PROPN
ejpam-367	203	3	appl	appl	PROPN
ejpam-367	203	4	.	.	PROPN
ejpam-367	203	5	math	math	PROPN
ejpam-367	203	6	,	,	PUNCT
ejpam-367	203	7	2	2	NUM
ejpam-367	203	8	(	(	PUNCT
ejpam-367	203	9	2009	2009	NUM
ejpam-367	203	10	)	)	PUNCT
ejpam-367	203	11	,	,	PUNCT
ejpam-367	203	12	(	(	PUNCT
ejpam-367	203	13	578	578	NUM
ejpam-367	203	14	-	-	SYM
ejpam-367	203	15	603	603	NUM
ejpam-367	203	16	)	)	PUNCT
ejpam-367	203	17	585	585	NUM
ejpam-367	203	18	λt	λt	ADP
ejpam-367	203	19	f	f	PROPN
ejpam-367	203	20	y1(t	y1(t	PROPN
ejpam-367	203	21	,	,	PUNCT
ejpam-367	203	22	x1	x1	PROPN
ejpam-367	203	23	,	,	PUNCT
ejpam-367	203	24	ẋ1	ẋ1	PROPN
ejpam-367	203	25	,	,	PUNCT
ejpam-367	203	26	y1	y1	PROPN
ejpam-367	203	27	,	,	PUNCT
ejpam-367	203	28	ẏ1)−	ẏ1)−	PROPN
ejpam-367	203	29	dλt	dλt	PROPN
ejpam-367	204	1	f	f	PROPN
ejpam-367	204	2	ẏ1(t	ẏ1(t	PROPN
ejpam-367	204	3	,	,	PUNCT
ejpam-367	204	4	x1	x1	PROPN
ejpam-367	204	5	,	,	PUNCT
ejpam-367	204	6	ẋ1	ẋ1	PROPN
ejpam-367	204	7	,	,	PUNCT
ejpam-367	204	8	y1	y1	PROPN
ejpam-367	204	9	,	,	PUNCT
ejpam-367	204	10	ẏ1)≦	ẏ1)≦	PROPN
ejpam-367	204	11	0	0	NUM
ejpam-367	204	12	,	,	PUNCT
ejpam-367	204	13	t	t	PROPN
ejpam-367	205	1	∈	∈	PROPN
ejpam-367	206	1	i	i	PRON
ejpam-367	206	2	,	,	PUNCT
ejpam-367	206	3	(	(	PUNCT
ejpam-367	206	4	3	3	X
ejpam-367	206	5	)	)	PUNCT
ejpam-367	206	6	λt	λt	ADP
ejpam-367	206	7	g	g	PROPN
ejpam-367	206	8	y2(t	y2(t	PROPN
ejpam-367	206	9	,	,	PUNCT
ejpam-367	206	10	x2	x2	PROPN
ejpam-367	206	11	,	,	PUNCT
ejpam-367	206	12	ẋ2	ẋ2	PROPN
ejpam-367	206	13	,	,	PUNCT
ejpam-367	206	14	y2	y2	NOUN
ejpam-367	206	15	,	,	PUNCT
ejpam-367	206	16	ẏ2)−	ẏ2)−	PROPN
ejpam-367	206	17	dλt	dλt	NOUN
ejpam-367	206	18	g	g	PROPN
ejpam-367	206	19	ẏ2(t	ẏ2(t	PROPN
ejpam-367	206	20	,	,	PUNCT
ejpam-367	206	21	x2	x2	PROPN
ejpam-367	206	22	,	,	PUNCT
ejpam-367	206	23	ẋ2	ẋ2	PROPN
ejpam-367	206	24	,	,	PUNCT
ejpam-367	206	25	y2	y2	NOUN
ejpam-367	206	26	,	,	PUNCT
ejpam-367	206	27	ẏ2	ẏ2	PROPN
ejpam-367	206	28	)	)	PUNCT
ejpam-367	206	29	≦	≦	NOUN
ejpam-367	206	30	0	0	NUM
ejpam-367	206	31	,	,	PUNCT
ejpam-367	206	32	t	t	PROPN
ejpam-367	206	33	∈	∈	PROPN
ejpam-367	207	1	i	i	PRON
ejpam-367	207	2	,	,	PUNCT
ejpam-367	207	3	(	(	PUNCT
ejpam-367	207	4	4	4	X
ejpam-367	207	5	)	)	PUNCT
ejpam-367	207	6	∫	∫	NOUN
ejpam-367	208	1	i	i	PRON
ejpam-367	208	2	y2(t)t(λt	y2(t)t(λt	VERB
ejpam-367	208	3	g	g	PROPN
ejpam-367	208	4	y2(t	y2(t	PROPN
ejpam-367	208	5	,	,	PUNCT
ejpam-367	208	6	x2	x2	PROPN
ejpam-367	208	7	,	,	PUNCT
ejpam-367	208	8	ẋ2	ẋ2	PROPN
ejpam-367	208	9	,	,	PUNCT
ejpam-367	208	10	y2	y2	NOUN
ejpam-367	208	11	,	,	PUNCT
ejpam-367	208	12	ẏ2	ẏ2	PROPN
ejpam-367	208	13	)	)	PUNCT
ejpam-367	208	14	−dλt	−dλt	NOUN
ejpam-367	209	1	g	g	PROPN
ejpam-367	209	2	ẏ2(t	ẏ2(t	PROPN
ejpam-367	209	3	,	,	PUNCT
ejpam-367	209	4	x2	x2	PROPN
ejpam-367	209	5	,	,	PUNCT
ejpam-367	209	6	ẋ2	ẋ2	PROPN
ejpam-367	209	7	,	,	PUNCT
ejpam-367	209	8	y2	y2	NOUN
ejpam-367	209	9	,	,	PUNCT
ejpam-367	209	10	ẏ2))≧	ẏ2))≧	PROPN
ejpam-367	209	11	0	0	NUM
ejpam-367	209	12	,	,	PUNCT
ejpam-367	209	13	(	(	PUNCT
ejpam-367	209	14	5	5	X
ejpam-367	209	15	)	)	PUNCT
ejpam-367	209	16	λ	λ	PROPN
ejpam-367	209	17	∈	∈	PROPN
ejpam-367	209	18	λ+	λ+	X
ejpam-367	209	19	.	.	PUNCT
ejpam-367	210	1	(	(	PUNCT
ejpam-367	210	2	6	6	NUM
ejpam-367	210	3	)	)	PUNCT
ejpam-367	210	4	(	(	PUNCT
ejpam-367	210	5	mix	mix	VERB
ejpam-367	210	6	sd	sd	NOUN
ejpam-367	210	7	)	)	PUNCT
ejpam-367	210	8	maximize	maximize	VERB
ejpam-367	210	9	g(u1	g(u1	NOUN
ejpam-367	210	10	,	,	PUNCT
ejpam-367	210	11	u2	u2	NOUN
ejpam-367	210	12	,	,	PUNCT
ejpam-367	210	13	v1	v1	NOUN
ejpam-367	210	14	,	,	PUNCT
ejpam-367	210	15	v2	v2	NOUN
ejpam-367	210	16	)	)	PUNCT
ejpam-367	211	1	=	=	SYM
ejpam-367	211	2	∫	∫	PROPN
ejpam-367	212	1	i	i	PRON
ejpam-367	212	2	{	{	PUNCT
ejpam-367	212	3	f	f	PROPN
ejpam-367	212	4	(	(	PUNCT
ejpam-367	212	5	t	t	PROPN
ejpam-367	212	6	,	,	PUNCT
ejpam-367	212	7	u1	u1	PROPN
ejpam-367	212	8	,	,	PUNCT
ejpam-367	212	9	u̇1	u̇1	PROPN
ejpam-367	212	10	,	,	PUNCT
ejpam-367	212	11	v1	v1	NOUN
ejpam-367	212	12	,	,	PUNCT
ejpam-367	212	13	v̇1	v̇1	PROPN
ejpam-367	212	14	)	)	PUNCT
ejpam-367	212	15	+	+	CCONJ
ejpam-367	212	16	g(t	g(t	PROPN
ejpam-367	212	17	,	,	PUNCT
ejpam-367	212	18	u2	u2	PROPN
ejpam-367	212	19	,	,	PUNCT
ejpam-367	212	20	u̇2	u̇2	PROPN
ejpam-367	212	21	,	,	PUNCT
ejpam-367	212	22	v2	v2	NOUN
ejpam-367	212	23	,	,	PUNCT
ejpam-367	212	24	v̇2	v̇2	NOUN
ejpam-367	212	25	)	)	PUNCT
ejpam-367	212	26	−u1(t)t(λt	−u1(t)t(λt	NOUN
ejpam-367	212	27	f	f	PROPN
ejpam-367	212	28	y1(t	y1(t	INTJ
ejpam-367	212	29	,	,	PUNCT
ejpam-367	212	30	u1	u1	PROPN
ejpam-367	212	31	,	,	PUNCT
ejpam-367	212	32	u̇1	u̇1	PROPN
ejpam-367	212	33	,	,	PUNCT
ejpam-367	212	34	v1	v1	NOUN
ejpam-367	212	35	,	,	PUNCT
ejpam-367	212	36	v̇1	v̇1	PROPN
ejpam-367	212	37	)	)	PUNCT
ejpam-367	212	38	−dλt	−dλt	NOUN
ejpam-367	213	1	f	f	PROPN
ejpam-367	213	2	ẏ1(t	ẏ1(t	PROPN
ejpam-367	213	3	,	,	PUNCT
ejpam-367	213	4	u1	u1	PROPN
ejpam-367	213	5	,	,	PUNCT
ejpam-367	213	6	u̇1	u̇1	PROPN
ejpam-367	213	7	,	,	PUNCT
ejpam-367	213	8	v1	v1	NOUN
ejpam-367	213	9	,	,	PUNCT
ejpam-367	213	10	v̇1))e}d	v̇1))e}d	PROPN
ejpam-367	213	11	t	t	PROPN
ejpam-367	213	12	subject	subject	NOUN
ejpam-367	213	13	to	to	ADP
ejpam-367	213	14	u1(a	u1(a	NUM
ejpam-367	213	15	)	)	PUNCT
ejpam-367	213	16	=	=	SYM
ejpam-367	213	17	0	0	PUNCT
ejpam-367	214	1	=	=	SYM
ejpam-367	214	2	u1(b	u1(b	PROPN
ejpam-367	214	3	)	)	PUNCT
ejpam-367	214	4	,	,	PUNCT
ejpam-367	214	5	v1(a	v1(a	NUM
ejpam-367	214	6	)	)	PUNCT
ejpam-367	214	7	=	=	SYM
ejpam-367	215	1	0=	0=	NUM
ejpam-367	216	1	v1(b	v1(b	NUM
ejpam-367	216	2	)	)	PUNCT
ejpam-367	216	3	,	,	PUNCT
ejpam-367	216	4	(	(	PUNCT
ejpam-367	216	5	7	7	X
ejpam-367	216	6	)	)	PUNCT
ejpam-367	216	7	u2(a	u2(a	NOUN
ejpam-367	216	8	)	)	PUNCT
ejpam-367	216	9	=	=	SYM
ejpam-367	216	10	0	0	PUNCT
ejpam-367	217	1	=	=	SYM
ejpam-367	217	2	u2(b	u2(b	PROPN
ejpam-367	217	3	)	)	PUNCT
ejpam-367	217	4	,	,	PUNCT
ejpam-367	217	5	v2(a	v2(a	NOUN
ejpam-367	217	6	)	)	PUNCT
ejpam-367	217	7	=	=	SYM
ejpam-367	218	1	0=	0=	NUM
ejpam-367	219	1	v2(b	v2(b	X
ejpam-367	219	2	)	)	PUNCT
ejpam-367	219	3	,	,	PUNCT
ejpam-367	219	4	(	(	PUNCT
ejpam-367	219	5	8)	8)	NUM
ejpam-367	219	6	λt	λt	ADP
ejpam-367	219	7	fu1(t	fu1(t	PROPN
ejpam-367	219	8	,	,	PUNCT
ejpam-367	219	9	u1	u1	PROPN
ejpam-367	219	10	,	,	PUNCT
ejpam-367	219	11	u̇1	u̇1	PROPN
ejpam-367	219	12	,	,	PUNCT
ejpam-367	219	13	v1	v1	NOUN
ejpam-367	219	14	,	,	PUNCT
ejpam-367	219	15	v̇1)−	v̇1)−	ADJ
ejpam-367	219	16	dλt	dλt	NOUN
ejpam-367	219	17	fu̇1(t	fu̇1(t	PROPN
ejpam-367	219	18	,	,	PUNCT
ejpam-367	219	19	u1	u1	PROPN
ejpam-367	219	20	,	,	PUNCT
ejpam-367	219	21	u̇1	u̇1	PROPN
ejpam-367	219	22	,	,	PUNCT
ejpam-367	219	23	v1	v1	NOUN
ejpam-367	219	24	,	,	PUNCT
ejpam-367	219	25	v̇1)≧	v̇1)≧	NOUN
ejpam-367	219	26	0	0	NUM
ejpam-367	219	27	,	,	PUNCT
ejpam-367	219	28	t	t	PROPN
ejpam-367	219	29	∈	∈	PROPN
ejpam-367	220	1	i	i	PRON
ejpam-367	220	2	,	,	PUNCT
ejpam-367	220	3	(	(	PUNCT
ejpam-367	220	4	9	9	X
ejpam-367	220	5	)	)	PUNCT
ejpam-367	220	6	λt	λt	ADP
ejpam-367	220	7	gu2(t	gu2(t	PROPN
ejpam-367	220	8	,	,	PUNCT
ejpam-367	220	9	u2	u2	PROPN
ejpam-367	220	10	,	,	PUNCT
ejpam-367	220	11	u̇2	u̇2	PROPN
ejpam-367	220	12	,	,	PUNCT
ejpam-367	220	13	v2	v2	PROPN
ejpam-367	220	14	,	,	PUNCT
ejpam-367	220	15	v̇2)−	v̇2)−	ADJ
ejpam-367	220	16	dλt	dλt	NOUN
ejpam-367	220	17	gu̇2(t	gu̇2(t	PROPN
ejpam-367	220	18	,	,	PUNCT
ejpam-367	220	19	u2	u2	PROPN
ejpam-367	220	20	,	,	PUNCT
ejpam-367	220	21	u̇2	u̇2	PROPN
ejpam-367	220	22	,	,	PUNCT
ejpam-367	220	23	v2	v2	PROPN
ejpam-367	220	24	,	,	PUNCT
ejpam-367	220	25	v̇2)≧	v̇2)≧	NUM
ejpam-367	220	26	0	0	NUM
ejpam-367	220	27	,	,	PUNCT
ejpam-367	220	28	t	t	PROPN
ejpam-367	220	29	∈	∈	PROPN
ejpam-367	221	1	i	i	PRON
ejpam-367	221	2	,	,	PUNCT
ejpam-367	221	3	(	(	PUNCT
ejpam-367	221	4	10	10	NUM
ejpam-367	221	5	)	)	PUNCT
ejpam-367	221	6	∫	∫	NOUN
ejpam-367	222	1	i	i	PRON
ejpam-367	222	2	u2(t)t(λt	u2(t)t(λt	PROPN
ejpam-367	222	3	gu2(t	gu2(t	PROPN
ejpam-367	222	4	,	,	PUNCT
ejpam-367	222	5	u2	u2	PROPN
ejpam-367	222	6	,	,	PUNCT
ejpam-367	222	7	u̇2	u̇2	PROPN
ejpam-367	222	8	,	,	PUNCT
ejpam-367	222	9	v2	v2	NOUN
ejpam-367	222	10	,	,	PUNCT
ejpam-367	222	11	v̇2	v̇2	PROPN
ejpam-367	222	12	)	)	PUNCT
ejpam-367	222	13	−dλt	−dλt	NOUN
ejpam-367	223	1	gu̇2(t	gu̇2(t	PROPN
ejpam-367	223	2	,	,	PUNCT
ejpam-367	223	3	u2	u2	PROPN
ejpam-367	223	4	,	,	PUNCT
ejpam-367	223	5	u̇2	u̇2	PROPN
ejpam-367	223	6	,	,	PUNCT
ejpam-367	223	7	v2	v2	NOUN
ejpam-367	223	8	,	,	PUNCT
ejpam-367	223	9	v̇2))≧	v̇2))≧	NOUN
ejpam-367	223	10	0	0	NUM
ejpam-367	223	11	,	,	PUNCT
ejpam-367	223	12	(	(	PUNCT
ejpam-367	223	13	11	11	NUM
ejpam-367	223	14	)	)	PUNCT
ejpam-367	223	15	λ	λ	PROPN
ejpam-367	223	16	∈	∈	PROPN
ejpam-367	223	17	λ+	λ+	X
ejpam-367	223	18	.	.	PUNCT
ejpam-367	224	1	(	(	PUNCT
ejpam-367	224	2	12	12	NUM
ejpam-367	224	3	)	)	PUNCT
ejpam-367	224	4	where	where	SCONJ
ejpam-367	224	5	λ+	λ+	VERB
ejpam-367	224	6	=	=	PUNCT
ejpam-367	224	7	{	{	PUNCT
ejpam-367	224	8	λ	λ	X
ejpam-367	224	9	∈	∈	NOUN
ejpam-367	224	10	rp|λ	rp|λ	X
ejpam-367	224	11	>	>	X
ejpam-367	224	12	0,λt	0,λt	NUM
ejpam-367	224	13	e	e	X
ejpam-367	224	14	=	=	SYM
ejpam-367	224	15	1	1	NUM
ejpam-367	224	16	,	,	PUNCT
ejpam-367	224	17	e	e	X
ejpam-367	224	18	=	=	PUNCT
ejpam-367	224	19	(	(	PUNCT
ejpam-367	224	20	1	1	NUM
ejpam-367	224	21	,	,	PUNCT
ejpam-367	224	22	1	1	NUM
ejpam-367	224	23	,	,	PUNCT
ejpam-367	224	24	.	.	PUNCT
ejpam-367	224	25	.	.	PUNCT
ejpam-367	225	1	.	.	PUNCT
ejpam-367	226	1	,	,	PUNCT
ejpam-367	226	2	1)t	1)t	PROPN
ejpam-367	226	3	∈	∈	PROPN
ejpam-367	226	4	rp	rp	NOUN
ejpam-367	226	5	}	}	PUNCT
ejpam-367	226	6	.	.	PUNCT
ejpam-367	227	1	4	4	X
ejpam-367	227	2	.	.	X
ejpam-367	227	3	mixed	mixed	ADJ
ejpam-367	227	4	type	type	NOUN
ejpam-367	227	5	multiobjective	multiobjective	ADJ
ejpam-367	227	6	symmetric	symmetric	ADJ
ejpam-367	227	7	duality	duality	NOUN
ejpam-367	227	8	in	in	ADP
ejpam-367	227	9	this	this	DET
ejpam-367	227	10	section	section	NOUN
ejpam-367	227	11	,	,	PUNCT
ejpam-367	227	12	we	we	PRON
ejpam-367	227	13	present	present	VERB
ejpam-367	227	14	various	various	ADJ
ejpam-367	227	15	duality	duality	NOUN
ejpam-367	227	16	results	result	NOUN
ejpam-367	227	17	and	and	CCONJ
ejpam-367	227	18	the	the	DET
ejpam-367	227	19	appropriate	appropriate	ADJ
ejpam-367	227	20	invexity	invexity	NOUN
ejpam-367	227	21	and	and	CCONJ
ejpam-367	227	22	generalized	generalized	ADJ
ejpam-367	227	23	invexity	invexity	NOUN
ejpam-367	227	24	assumptions	assumption	NOUN
ejpam-367	227	25	.	.	PUNCT
ejpam-367	228	1	theorem	theorem	ADJ
ejpam-367	228	2	1	1	NUM
ejpam-367	228	3	(	(	PUNCT
ejpam-367	228	4	weak	weak	ADJ
ejpam-367	228	5	duality	duality	NOUN
ejpam-367	228	6	)	)	PUNCT
ejpam-367	228	7	.	.	PUNCT
ejpam-367	229	1	let	let	VERB
ejpam-367	229	2	(	(	PUNCT
ejpam-367	229	3	x1	x1	ADJ
ejpam-367	229	4	,	,	PUNCT
ejpam-367	229	5	x2	x2	PROPN
ejpam-367	229	6	,	,	PUNCT
ejpam-367	229	7	y1	y1	PROPN
ejpam-367	229	8	,	,	PUNCT
ejpam-367	229	9	y2,λ	y2,λ	PROPN
ejpam-367	229	10	)	)	PUNCT
ejpam-367	229	11	be	be	AUX
ejpam-367	229	12	feasible	feasible	ADJ
ejpam-367	229	13	for	for	ADP
ejpam-367	229	14	(	(	PUNCT
ejpam-367	229	15	mix	mix	VERB
ejpam-367	229	16	sp	sp	NOUN
ejpam-367	229	17	)	)	PUNCT
ejpam-367	229	18	and	and	CCONJ
ejpam-367	229	19	(	(	PUNCT
ejpam-367	229	20	u1	u1	PROPN
ejpam-367	229	21	,	,	PUNCT
ejpam-367	229	22	u2	u2	NOUN
ejpam-367	229	23	,	,	PUNCT
ejpam-367	229	24	v1	v1	NOUN
ejpam-367	229	25	,	,	PUNCT
ejpam-367	229	26	v2,λ	v2,λ	PROPN
ejpam-367	229	27	)	)	PUNCT
ejpam-367	229	28	be	be	AUX
ejpam-367	229	29	feasible	feasible	ADJ
ejpam-367	229	30	for	for	ADP
ejpam-367	229	31	(	(	PUNCT
ejpam-367	229	32	mix	mix	VERB
ejpam-367	229	33	sd	sd	NOUN
ejpam-367	229	34	)	)	PUNCT
ejpam-367	229	35	.	.	PUNCT
ejpam-367	230	1	i.	i.	PROPN
ejpam-367	230	2	husain	husain	PROPN
ejpam-367	230	3	and	and	CCONJ
ejpam-367	230	4	r.	r.	PROPN
ejpam-367	230	5	mattoo	mattoo	PROPN
ejpam-367	230	6	/	/	SYM
ejpam-367	230	7	eur	eur	PROPN
ejpam-367	230	8	.	.	PUNCT
ejpam-367	231	1	j.	j.	PROPN
ejpam-367	231	2	pure	pure	PROPN
ejpam-367	231	3	appl	appl	PROPN
ejpam-367	231	4	.	.	PROPN
ejpam-367	231	5	math	math	PROPN
ejpam-367	231	6	,	,	PUNCT
ejpam-367	231	7	2	2	NUM
ejpam-367	231	8	(	(	PUNCT
ejpam-367	231	9	2009	2009	NUM
ejpam-367	231	10	)	)	PUNCT
ejpam-367	231	11	,	,	PUNCT
ejpam-367	231	12	(	(	PUNCT
ejpam-367	231	13	578	578	NUM
ejpam-367	231	14	-	-	SYM
ejpam-367	231	15	603	603	NUM
ejpam-367	231	16	)	)	PUNCT
ejpam-367	231	17	586	586	NUM
ejpam-367	231	18	let	let	VERB
ejpam-367	231	19	h1	h1	PROPN
ejpam-367	231	20	∫	∫	PROPN
ejpam-367	232	1	i	i	PRON
ejpam-367	232	2	f	f	PROPN
ejpam-367	232	3	(	(	PUNCT
ejpam-367	232	4	t	t	PROPN
ejpam-367	232	5	,	,	PUNCT
ejpam-367	232	6	.	.	PUNCT
ejpam-367	232	7	,	,	PUNCT
ejpam-367	232	8	.	.	PUNCT
ejpam-367	232	9	,	,	PUNCT
ejpam-367	232	10	y1(t	y1(t	PROPN
ejpam-367	232	11	)	)	PUNCT
ejpam-367	232	12	,	,	PUNCT
ejpam-367	232	13	ẏ1(t))d	ẏ1(t))d	NOUN
ejpam-367	232	14	t	t	PROPN
ejpam-367	232	15	be	be	AUX
ejpam-367	232	16	partially	partially	ADV
ejpam-367	232	17	invex	invex	ADJ
ejpam-367	232	18	in	in	ADP
ejpam-367	232	19	x1	x1	PROPN
ejpam-367	232	20	,	,	PUNCT
ejpam-367	233	1	ẋ1	ẋ1	PROPN
ejpam-367	233	2	on	on	ADP
ejpam-367	233	3	i	i	PRON
ejpam-367	233	4	for	for	ADP
ejpam-367	233	5	fixed	fix	VERB
ejpam-367	233	6	y1	y1	NOUN
ejpam-367	233	7	,	,	PUNCT
ejpam-367	233	8	ẏ1	ẏ1	PROPN
ejpam-367	233	9	with	with	ADP
ejpam-367	233	10	respect	respect	NOUN
ejpam-367	233	11	to	to	ADP
ejpam-367	233	12	η1(t	η1(t	DET
ejpam-367	233	13	,	,	PUNCT
ejpam-367	233	14	x1	x1	ADJ
ejpam-367	233	15	,	,	PUNCT
ejpam-367	233	16	u1	u1	NOUN
ejpam-367	233	17	)	)	PUNCT
ejpam-367	233	18	∈	∈	PROPN
ejpam-367	234	1	r|j1|	r|j1|	NOUN
ejpam-367	234	2	.	.	PUNCT
ejpam-367	235	1	∫	∫	PROPN
ejpam-367	236	1	i	i	PRON
ejpam-367	236	2	f	f	PROPN
ejpam-367	236	3	(	(	PUNCT
ejpam-367	236	4	t	t	PROPN
ejpam-367	236	5	,	,	PUNCT
ejpam-367	236	6	x1(t	x1(t	PROPN
ejpam-367	236	7	)	)	PUNCT
ejpam-367	236	8	,	,	PUNCT
ejpam-367	236	9	ẋ1(t	ẋ1(t	PROPN
ejpam-367	236	10	)	)	PUNCT
ejpam-367	236	11	,	,	PUNCT
ejpam-367	236	12	.	.	PUNCT
ejpam-367	236	13	,	,	PUNCT
ejpam-367	236	14	.)d	.)d	PROPN
ejpam-367	236	15	t	t	PROPN
ejpam-367	236	16	be	be	AUX
ejpam-367	236	17	partially	partially	ADV
ejpam-367	236	18	incave	incave	ADJ
ejpam-367	236	19	in	in	ADP
ejpam-367	236	20	y1	y1	NOUN
ejpam-367	236	21	,	,	PUNCT
ejpam-367	237	1	ẏ1	ẏ1	PROPN
ejpam-367	237	2	on	on	ADP
ejpam-367	237	3	i	i	PRON
ejpam-367	237	4	for	for	ADP
ejpam-367	237	5	fixed	fix	VERB
ejpam-367	237	6	x1	x1	PROPN
ejpam-367	237	7	,	,	PUNCT
ejpam-367	237	8	ẋ1	ẋ1	ADJ
ejpam-367	237	9	with	with	ADP
ejpam-367	237	10	respect	respect	NOUN
ejpam-367	237	11	to	to	ADP
ejpam-367	237	12	η2(t	η2(t	PROPN
ejpam-367	237	13	,	,	PUNCT
ejpam-367	237	14	y1	y1	PROPN
ejpam-367	237	15	,	,	PUNCT
ejpam-367	237	16	v1	v1	NOUN
ejpam-367	237	17	)	)	PUNCT
ejpam-367	237	18	∈	∈	PROPN
ejpam-367	237	19	r|k1|	r|k1|	NOUN
ejpam-367	237	20	.	.	PUNCT
ejpam-367	238	1	h2	h2	PROPN
ejpam-367	238	2	∫	∫	PROPN
ejpam-367	239	1	i	i	PRON
ejpam-367	239	2	λt	λt	ADP
ejpam-367	239	3	g(t	g(t	PROPN
ejpam-367	239	4	,	,	PUNCT
ejpam-367	239	5	.	.	PUNCT
ejpam-367	239	6	,	,	PUNCT
ejpam-367	239	7	.	.	PUNCT
ejpam-367	239	8	,	,	PUNCT
ejpam-367	239	9	y2(t	y2(t	PROPN
ejpam-367	239	10	)	)	PUNCT
ejpam-367	239	11	,	,	PUNCT
ejpam-367	239	12	ẏ2(t))d	ẏ2(t))d	NOUN
ejpam-367	239	13	t	t	NOUN
ejpam-367	239	14	be	be	AUX
ejpam-367	239	15	partially	partially	ADV
ejpam-367	239	16	pseudoinvex	pseudoinvex	NOUN
ejpam-367	239	17	in	in	ADP
ejpam-367	239	18	x2	x2	PROPN
ejpam-367	239	19	,	,	PUNCT
ejpam-367	240	1	ẋ2	ẋ2	PROPN
ejpam-367	240	2	on	on	ADP
ejpam-367	240	3	i	i	PRON
ejpam-367	240	4	for	for	ADP
ejpam-367	240	5	fixed	fixed	ADJ
ejpam-367	240	6	y2	y2	NOUN
ejpam-367	240	7	,	,	PUNCT
ejpam-367	240	8	ẏ2	ẏ2	NOUN
ejpam-367	240	9	with	with	ADP
ejpam-367	240	10	respect	respect	NOUN
ejpam-367	240	11	η3(t	η3(t	PROPN
ejpam-367	240	12	,	,	PUNCT
ejpam-367	240	13	x2	x2	PROPN
ejpam-367	240	14	,	,	PUNCT
ejpam-367	240	15	u2	u2	NOUN
ejpam-367	240	16	)	)	PUNCT
ejpam-367	240	17	∈	∈	NOUN
ejpam-367	240	18	r|j2|	r|j2|	NOUN
ejpam-367	240	19	and	and	CCONJ
ejpam-367	240	20	∫	∫	NOUN
ejpam-367	240	21	i	i	PRON
ejpam-367	240	22	λt	λt	ADP
ejpam-367	240	23	g(t	g(t	PROPN
ejpam-367	240	24	,	,	PUNCT
ejpam-367	240	25	x2	x2	PROPN
ejpam-367	240	26	,	,	PUNCT
ejpam-367	240	27	ẋ2	ẋ2	PROPN
ejpam-367	240	28	,	,	PUNCT
ejpam-367	240	29	.	.	PUNCT
ejpam-367	240	30	.	.	PUNCT
ejpam-367	241	1	.)d	.)d	PROPN
ejpam-367	241	2	t	t	PROPN
ejpam-367	241	3	be	be	AUX
ejpam-367	241	4	partially	partially	ADV
ejpam-367	241	5	pseudoincave	pseudoincave	VERB
ejpam-367	241	6	in	in	ADP
ejpam-367	241	7	y2	y2	PROPN
ejpam-367	241	8	,	,	PUNCT
ejpam-367	242	1	ẏ2	ẏ2	PROPN
ejpam-367	242	2	on	on	ADP
ejpam-367	242	3	i	i	PRON
ejpam-367	242	4	for	for	ADP
ejpam-367	242	5	fixed	fix	VERB
ejpam-367	242	6	x2	x2	PROPN
ejpam-367	242	7	,	,	PUNCT
ejpam-367	242	8	ẋ2	ẋ2	PROPN
ejpam-367	242	9	with	with	ADP
ejpam-367	242	10	respect	respect	NOUN
ejpam-367	242	11	to	to	ADP
ejpam-367	242	12	η4(t	η4(t	PROPN
ejpam-367	242	13	,	,	PUNCT
ejpam-367	242	14	y2	y2	PROPN
ejpam-367	242	15	,	,	PUNCT
ejpam-367	242	16	v2	v2	PROPN
ejpam-367	242	17	)	)	PUNCT
ejpam-367	242	18	∈	∈	PROPN
ejpam-367	242	19	r|k2|	r|k2|	PROPN
ejpam-367	242	20	.	.	PUNCT
ejpam-367	243	1	h3	h3	NOUN
ejpam-367	243	2	η1(t	η1(t	PRON
ejpam-367	243	3	,	,	PUNCT
ejpam-367	243	4	x1	x1	ADJ
ejpam-367	243	5	,	,	PUNCT
ejpam-367	243	6	u1	u1	NOUN
ejpam-367	243	7	)	)	PUNCT
ejpam-367	243	8	+	+	CCONJ
ejpam-367	244	1	u1(t)≧	u1(t)≧	PRON
ejpam-367	244	2	0	0	NUM
ejpam-367	244	3	,	,	PUNCT
ejpam-367	244	4	t	t	PROPN
ejpam-367	244	5	∈	∈	PROPN
ejpam-367	245	1	i	i	PRON
ejpam-367	245	2	,	,	PUNCT
ejpam-367	245	3	(	(	PUNCT
ejpam-367	245	4	13	13	NUM
ejpam-367	245	5	)	)	PUNCT
ejpam-367	245	6	η2(t	η2(t	PROPN
ejpam-367	245	7	,	,	PUNCT
ejpam-367	245	8	v1	v1	PROPN
ejpam-367	245	9	,	,	PUNCT
ejpam-367	245	10	y1	y1	PROPN
ejpam-367	245	11	)	)	PUNCT
ejpam-367	245	12	+	+	CCONJ
ejpam-367	245	13	y1(t)≧	y1(t)≧	PROPN
ejpam-367	245	14	0	0	NUM
ejpam-367	245	15	,	,	PUNCT
ejpam-367	245	16	t	t	PROPN
ejpam-367	245	17	∈	∈	PROPN
ejpam-367	246	1	i	i	PRON
ejpam-367	246	2	,	,	PUNCT
ejpam-367	246	3	(	(	PUNCT
ejpam-367	246	4	14	14	NUM
ejpam-367	246	5	)	)	PUNCT
ejpam-367	246	6	η3(t	η3(t	PROPN
ejpam-367	246	7	,	,	PUNCT
ejpam-367	246	8	x2	x2	PROPN
ejpam-367	246	9	,	,	PUNCT
ejpam-367	246	10	u2	u2	PROPN
ejpam-367	246	11	)	)	PUNCT
ejpam-367	246	12	+	+	CCONJ
ejpam-367	246	13	u2(t)≧	u2(t)≧	X
ejpam-367	246	14	0	0	NUM
ejpam-367	246	15	,	,	PUNCT
ejpam-367	246	16	t	t	PROPN
ejpam-367	246	17	∈	∈	PROPN
ejpam-367	247	1	i	i	PRON
ejpam-367	247	2	,	,	PUNCT
ejpam-367	247	3	(	(	PUNCT
ejpam-367	247	4	15	15	NUM
ejpam-367	247	5	)	)	PUNCT
ejpam-367	247	6	η4(t	η4(t	PROPN
ejpam-367	247	7	,	,	PUNCT
ejpam-367	247	8	v2	v2	PROPN
ejpam-367	247	9	,	,	PUNCT
ejpam-367	247	10	y2	y2	NOUN
ejpam-367	247	11	)	)	PUNCT
ejpam-367	248	1	+	+	CCONJ
ejpam-367	248	2	y2(t)≧	y2(t)≧	PROPN
ejpam-367	248	3	0	0	NUM
ejpam-367	248	4	,	,	PUNCT
ejpam-367	248	5	t	t	PROPN
ejpam-367	248	6	∈	∈	PROPN
ejpam-367	248	7	i	i	PRON
ejpam-367	248	8	,	,	PUNCT
ejpam-367	248	9	(	(	PUNCT
ejpam-367	248	10	16	16	NUM
ejpam-367	248	11	)	)	PUNCT
ejpam-367	248	12	then	then	ADV
ejpam-367	248	13	f(x1	f(x1	ADJ
ejpam-367	248	14	,	,	PUNCT
ejpam-367	248	15	x2	x2	PROPN
ejpam-367	248	16	,	,	PUNCT
ejpam-367	248	17	y1	y1	NOUN
ejpam-367	248	18	,	,	PUNCT
ejpam-367	248	19	y2	y2	PROPN
ejpam-367	248	20	)	)	PUNCT
ejpam-367	248	21	6≤	6≤	NUM
ejpam-367	248	22	g(u1	g(u1	NOUN
ejpam-367	248	23	,	,	PUNCT
ejpam-367	248	24	u2	u2	NOUN
ejpam-367	248	25	,	,	PUNCT
ejpam-367	248	26	v1	v1	NOUN
ejpam-367	248	27	,	,	PUNCT
ejpam-367	248	28	v2	v2	PROPN
ejpam-367	248	29	)	)	PUNCT
ejpam-367	248	30	.	.	PUNCT
ejpam-367	249	1	proof	proof	NOUN
ejpam-367	249	2	.	.	PUNCT
ejpam-367	250	1	because	because	SCONJ
ejpam-367	250	2	of	of	ADP
ejpam-367	250	3	the	the	DET
ejpam-367	250	4	partial	partial	ADJ
ejpam-367	250	5	invexity	invexity	NOUN
ejpam-367	250	6	-	-	PUNCT
ejpam-367	250	7	incavity	incavity	NOUN
ejpam-367	250	8	of	of	ADP
ejpam-367	250	9	the	the	DET
ejpam-367	250	10	function	function	NOUN
ejpam-367	250	11	f	f	PROPN
ejpam-367	250	12	,	,	PUNCT
ejpam-367	250	13	we	we	PRON
ejpam-367	250	14	have	have	VERB
ejpam-367	250	15	for	for	ADP
ejpam-367	250	16	each	each	DET
ejpam-367	250	17	i	i	PRON
ejpam-367	250	18	=	=	PUNCT
ejpam-367	250	19	{	{	PUNCT
ejpam-367	250	20	1	1	NUM
ejpam-367	250	21	,	,	PUNCT
ejpam-367	250	22	2	2	NUM
ejpam-367	250	23	,	,	PUNCT
ejpam-367	250	24	.	.	PUNCT
ejpam-367	250	25	.	.	PUNCT
ejpam-367	251	1	.	.	PUNCT
ejpam-367	252	1	,	,	PUNCT
ejpam-367	252	2	p	p	X
ejpam-367	252	3	}	}	PUNCT
ejpam-367	252	4	.	.	PUNCT
ejpam-367	253	1	∫	∫	PROPN
ejpam-367	254	1	i	i	PRON
ejpam-367	254	2	f	f	PROPN
ejpam-367	254	3	i(t	i(t	PROPN
ejpam-367	254	4	,	,	PUNCT
ejpam-367	254	5	x1	x1	PROPN
ejpam-367	254	6	,	,	PUNCT
ejpam-367	254	7	ẋ1	ẋ1	PROPN
ejpam-367	254	8	,	,	PUNCT
ejpam-367	254	9	v1	v1	PROPN
ejpam-367	254	10	,	,	PUNCT
ejpam-367	254	11	v̇1)d	v̇1)d	PROPN
ejpam-367	254	12	t	t	PROPN
ejpam-367	255	1	−	−	PROPN
ejpam-367	255	2	∫	∫	PROPN
ejpam-367	256	1	i	i	PRON
ejpam-367	256	2	f	f	PROPN
ejpam-367	256	3	i(t	i(t	PROPN
ejpam-367	256	4	,	,	PUNCT
ejpam-367	256	5	u1	u1	PROPN
ejpam-367	256	6	,	,	PUNCT
ejpam-367	256	7	u̇1	u̇1	PROPN
ejpam-367	256	8	,	,	PUNCT
ejpam-367	256	9	v1	v1	NOUN
ejpam-367	256	10	,	,	PUNCT
ejpam-367	256	11	v̇1)d	v̇1)d	PROPN
ejpam-367	256	12	t	t	NOUN
ejpam-367	256	13	≧	≧	NUM
ejpam-367	256	14	∫	∫	PROPN
ejpam-367	257	1	i	i	PRON
ejpam-367	257	2	{	{	PUNCT
ejpam-367	257	3	ηt	ηt	ADP
ejpam-367	257	4	1	1	NUM
ejpam-367	257	5	f	f	NOUN
ejpam-367	258	1	i	i	PRON
ejpam-367	258	2	x1(t	x1(t	X
ejpam-367	258	3	,	,	PUNCT
ejpam-367	258	4	u1	u1	PROPN
ejpam-367	258	5	,	,	PUNCT
ejpam-367	258	6	u̇1	u̇1	PROPN
ejpam-367	258	7	,	,	PUNCT
ejpam-367	258	8	v1	v1	NOUN
ejpam-367	258	9	,	,	PUNCT
ejpam-367	258	10	v̇1	v̇1	PROPN
ejpam-367	258	11	)	)	PUNCT
ejpam-367	258	12	+	+	CCONJ
ejpam-367	258	13	(	(	PUNCT
ejpam-367	258	14	dη1	dη1	NOUN
ejpam-367	258	15	)	)	PUNCT
ejpam-367	258	16	t	t	PROPN
ejpam-367	259	1	f	f	PROPN
ejpam-367	260	1	i	i	PRON
ejpam-367	260	2	ẋ1(t	ẋ1(t	PROPN
ejpam-367	260	3	,	,	PUNCT
ejpam-367	260	4	u1	u1	PROPN
ejpam-367	260	5	,	,	PUNCT
ejpam-367	260	6	u̇1	u̇1	PROPN
ejpam-367	260	7	,	,	PUNCT
ejpam-367	260	8	v1	v1	NOUN
ejpam-367	260	9	,	,	PUNCT
ejpam-367	260	10	v̇1)}d	v̇1)}d	PROPN
ejpam-367	260	11	t	t	PROPN
ejpam-367	260	12	(	(	PUNCT
ejpam-367	260	13	17	17	NUM
ejpam-367	260	14	)	)	PUNCT
ejpam-367	260	15	∫	∫	PROPN
ejpam-367	261	1	i	i	PRON
ejpam-367	261	2	f	f	PROPN
ejpam-367	261	3	i(t	i(t	PROPN
ejpam-367	261	4	,	,	PUNCT
ejpam-367	261	5	x1	x1	PROPN
ejpam-367	261	6	,	,	PUNCT
ejpam-367	261	7	ẋ1	ẋ1	PROPN
ejpam-367	261	8	,	,	PUNCT
ejpam-367	261	9	v1	v1	PROPN
ejpam-367	261	10	,	,	PUNCT
ejpam-367	261	11	v̇1)d	v̇1)d	PROPN
ejpam-367	261	12	t	t	PROPN
ejpam-367	262	1	−	−	PROPN
ejpam-367	262	2	∫	∫	PROPN
ejpam-367	263	1	i	i	PRON
ejpam-367	263	2	f	f	PROPN
ejpam-367	263	3	i(t	i(t	PROPN
ejpam-367	263	4	,	,	PUNCT
ejpam-367	263	5	x1	x1	PROPN
ejpam-367	263	6	,	,	PUNCT
ejpam-367	263	7	ẋ1	ẋ1	PROPN
ejpam-367	263	8	,	,	PUNCT
ejpam-367	263	9	y1	y1	PROPN
ejpam-367	263	10	,	,	PUNCT
ejpam-367	263	11	ẏ1)d	ẏ1)d	NOUN
ejpam-367	263	12	t	t	PROPN
ejpam-367	263	13	≦	≦	PROPN
ejpam-367	263	14	∫	∫	INTJ
ejpam-367	264	1	i	i	PRON
ejpam-367	264	2	{	{	PUNCT
ejpam-367	264	3	ηt	ηt	ADP
ejpam-367	264	4	2	2	NUM
ejpam-367	264	5	f	f	NOUN
ejpam-367	265	1	i	i	PRON
ejpam-367	265	2	y1(t	y1(t	INTJ
ejpam-367	265	3	,	,	PUNCT
ejpam-367	265	4	x1	x1	PROPN
ejpam-367	265	5	,	,	PUNCT
ejpam-367	265	6	ẋ1	ẋ1	PROPN
ejpam-367	265	7	,	,	PUNCT
ejpam-367	265	8	y1	y1	PROPN
ejpam-367	265	9	,	,	PUNCT
ejpam-367	265	10	ẏ1	ẏ1	PROPN
ejpam-367	265	11	)	)	PUNCT
ejpam-367	265	12	+	+	CCONJ
ejpam-367	265	13	(	(	PUNCT
ejpam-367	265	14	dη2	dη2	NOUN
ejpam-367	265	15	)	)	PUNCT
ejpam-367	265	16	t	t	PROPN
ejpam-367	266	1	f	f	PROPN
ejpam-367	266	2	i	i	PRON
ejpam-367	266	3	ẏ1(t	ẏ1(t	ADJ
ejpam-367	266	4	,	,	PUNCT
ejpam-367	266	5	x1	x1	PROPN
ejpam-367	266	6	,	,	PUNCT
ejpam-367	266	7	ẋ1	ẋ1	PROPN
ejpam-367	266	8	,	,	PUNCT
ejpam-367	266	9	y1	y1	PROPN
ejpam-367	266	10	,	,	PUNCT
ejpam-367	266	11	ẏ1)}d	ẏ1)}d	PROPN
ejpam-367	266	12	t	t	PROPN
ejpam-367	266	13	(	(	PUNCT
ejpam-367	266	14	18	18	NUM
ejpam-367	266	15	)	)	PUNCT
ejpam-367	266	16	i.	i.	NOUN
ejpam-367	266	17	husain	husain	PROPN
ejpam-367	266	18	and	and	CCONJ
ejpam-367	266	19	r.	r.	PROPN
ejpam-367	266	20	mattoo	mattoo	PROPN
ejpam-367	266	21	/	/	SYM
ejpam-367	266	22	eur	eur	PROPN
ejpam-367	266	23	.	.	PUNCT
ejpam-367	267	1	j.	j.	PROPN
ejpam-367	267	2	pure	pure	PROPN
ejpam-367	267	3	appl	appl	PROPN
ejpam-367	267	4	.	.	PROPN
ejpam-367	267	5	math	math	PROPN
ejpam-367	267	6	,	,	PUNCT
ejpam-367	267	7	2	2	NUM
ejpam-367	267	8	(	(	PUNCT
ejpam-367	267	9	2009	2009	NUM
ejpam-367	267	10	)	)	PUNCT
ejpam-367	267	11	,	,	PUNCT
ejpam-367	267	12	(	(	PUNCT
ejpam-367	267	13	578	578	NUM
ejpam-367	267	14	-	-	SYM
ejpam-367	267	15	603	603	NUM
ejpam-367	267	16	)	)	PUNCT
ejpam-367	267	17	587	587	NUM
ejpam-367	267	18	multiplying	multiplying	NOUN
ejpam-367	267	19	(	(	PUNCT
ejpam-367	267	20	17	17	NUM
ejpam-367	267	21	)	)	PUNCT
ejpam-367	267	22	by	by	ADP
ejpam-367	267	23	λi	λi	ADP
ejpam-367	267	24	>	>	X
ejpam-367	267	25	0	0	PUNCT
ejpam-367	267	26	and	and	CCONJ
ejpam-367	267	27	summing	sum	VERB
ejpam-367	267	28	over	over	ADP
ejpam-367	267	29	i.	i.	PROPN
ejpam-367	267	30	∫	∫	PROPN
ejpam-367	268	1	i	i	PRON
ejpam-367	268	2	λt	λt	ADP
ejpam-367	268	3	f	f	PROPN
ejpam-367	268	4	(	(	PUNCT
ejpam-367	268	5	t	t	PROPN
ejpam-367	268	6	,	,	PUNCT
ejpam-367	268	7	x1	x1	PROPN
ejpam-367	268	8	,	,	PUNCT
ejpam-367	268	9	ẋ1	ẋ1	PROPN
ejpam-367	268	10	,	,	PUNCT
ejpam-367	268	11	v1	v1	PROPN
ejpam-367	268	12	,	,	PUNCT
ejpam-367	268	13	v̇1)d	v̇1)d	PROPN
ejpam-367	268	14	t	t	PROPN
ejpam-367	269	1	−	−	PROPN
ejpam-367	269	2	∫	∫	PROPN
ejpam-367	270	1	i	i	PRON
ejpam-367	270	2	λt	λt	ADP
ejpam-367	270	3	f	f	PROPN
ejpam-367	270	4	(	(	PUNCT
ejpam-367	270	5	t	t	PROPN
ejpam-367	270	6	,	,	PUNCT
ejpam-367	270	7	u1	u1	PROPN
ejpam-367	270	8	,	,	PUNCT
ejpam-367	270	9	u̇1	u̇1	PROPN
ejpam-367	270	10	,	,	PUNCT
ejpam-367	270	11	v1	v1	NOUN
ejpam-367	270	12	,	,	PUNCT
ejpam-367	270	13	v̇1)d	v̇1)d	PROPN
ejpam-367	270	14	t	t	NOUN
ejpam-367	270	15	≧	≧	NUM
ejpam-367	271	1	∫	∫	PROPN
ejpam-367	272	1	i	i	PRON
ejpam-367	272	2	{	{	PUNCT
ejpam-367	272	3	ηt	ηt	ADP
ejpam-367	272	4	1	1	NUM
ejpam-367	272	5	(	(	PUNCT
ejpam-367	272	6	λt	λt	ADP
ejpam-367	272	7	fx1(t	fx1(t	PROPN
ejpam-367	272	8	,	,	PUNCT
ejpam-367	272	9	u1	u1	PROPN
ejpam-367	272	10	,	,	PUNCT
ejpam-367	272	11	u̇1	u̇1	PROPN
ejpam-367	272	12	,	,	PUNCT
ejpam-367	272	13	v1	v1	NOUN
ejpam-367	272	14	,	,	PUNCT
ejpam-367	272	15	v̇1	v̇1	PROPN
ejpam-367	272	16	)	)	PUNCT
ejpam-367	272	17	+	+	CCONJ
ejpam-367	272	18	(	(	PUNCT
ejpam-367	272	19	dη1	dη1	NOUN
ejpam-367	272	20	)	)	PUNCT
ejpam-367	272	21	tλt	tλt	PROPN
ejpam-367	272	22	f	f	PROPN
ejpam-367	272	23	ẋ1(t	ẋ1(t	PROPN
ejpam-367	272	24	,	,	PUNCT
ejpam-367	272	25	u1	u1	PROPN
ejpam-367	272	26	,	,	PUNCT
ejpam-367	272	27	u̇1	u̇1	PROPN
ejpam-367	272	28	,	,	PUNCT
ejpam-367	272	29	v1	v1	NOUN
ejpam-367	272	30	,	,	PUNCT
ejpam-367	272	31	v̇1))}d	v̇1))}d	PROPN
ejpam-367	272	32	t	t	PROPN
ejpam-367	272	33	integrating	integrating	NOUN
ejpam-367	272	34	by	by	ADP
ejpam-367	272	35	parts	part	NOUN
ejpam-367	272	36	,	,	PUNCT
ejpam-367	272	37	the	the	DET
ejpam-367	272	38	above	above	ADJ
ejpam-367	272	39	inequality	inequality	NOUN
ejpam-367	272	40	becomes	become	VERB
ejpam-367	272	41	∫	∫	PROPN
ejpam-367	273	1	i	i	INTJ
ejpam-367	273	2	λt	λt	ADP
ejpam-367	273	3	f	f	PROPN
ejpam-367	273	4	(	(	PUNCT
ejpam-367	273	5	t	t	PROPN
ejpam-367	273	6	,	,	PUNCT
ejpam-367	273	7	x1	x1	PROPN
ejpam-367	273	8	,	,	PUNCT
ejpam-367	273	9	ẋ1	ẋ1	PROPN
ejpam-367	273	10	,	,	PUNCT
ejpam-367	273	11	v1	v1	PROPN
ejpam-367	273	12	,	,	PUNCT
ejpam-367	273	13	v̇1)−	v̇1)−	ADJ
ejpam-367	273	14	∫	∫	PROPN
ejpam-367	274	1	i	i	INTJ
ejpam-367	274	2	λt	λt	ADP
ejpam-367	274	3	f	f	PROPN
ejpam-367	274	4	(	(	PUNCT
ejpam-367	274	5	t	t	PROPN
ejpam-367	274	6	,	,	PUNCT
ejpam-367	274	7	u1	u1	PROPN
ejpam-367	274	8	,	,	PUNCT
ejpam-367	274	9	u̇1	u̇1	PROPN
ejpam-367	274	10	,	,	PUNCT
ejpam-367	274	11	v1	v1	NOUN
ejpam-367	274	12	,	,	PUNCT
ejpam-367	274	13	v̇1)d	v̇1)d	PROPN
ejpam-367	274	14	t	t	NOUN
ejpam-367	274	15	≧	≧	NUM
ejpam-367	275	1	∫	∫	PROPN
ejpam-367	276	1	i	i	PRON
ejpam-367	276	2	ηt	ηt	ADP
ejpam-367	276	3	1	1	NUM
ejpam-367	276	4	λt	λt	ADP
ejpam-367	276	5	fx1(t	fx1(t	PROPN
ejpam-367	276	6	,	,	PUNCT
ejpam-367	276	7	u1	u1	PROPN
ejpam-367	276	8	,	,	PUNCT
ejpam-367	276	9	u̇1	u̇1	PROPN
ejpam-367	276	10	,	,	PUNCT
ejpam-367	276	11	v1	v1	NOUN
ejpam-367	276	12	,	,	PUNCT
ejpam-367	276	13	v̇1)d	v̇1)d	PROPN
ejpam-367	276	14	t	t	NOUN
ejpam-367	277	1	+	+	NOUN
ejpam-367	277	2	ηt	ηt	ADP
ejpam-367	277	3	1	1	NUM
ejpam-367	277	4	λt	λt	ADP
ejpam-367	277	5	f	f	PROPN
ejpam-367	277	6	ẋ1(t	ẋ1(t	PROPN
ejpam-367	277	7	,	,	PUNCT
ejpam-367	277	8	u1	u1	PROPN
ejpam-367	277	9	,	,	PUNCT
ejpam-367	277	10	u̇1	u̇1	PROPN
ejpam-367	277	11	,	,	PUNCT
ejpam-367	277	12	v1	v1	NOUN
ejpam-367	277	13	,	,	PUNCT
ejpam-367	277	14	v̇1)|	v̇1)|	NOUN
ejpam-367	277	15	t	t	PROPN
ejpam-367	277	16	=	=	SYM
ejpam-367	277	17	b	b	PROPN
ejpam-367	277	18	t	t	PROPN
ejpam-367	277	19	=	=	PROPN
ejpam-367	277	20	a	a	PRON
ejpam-367	277	21	−	−	NUM
ejpam-367	277	22	∫	∫	NOUN
ejpam-367	278	1	i	i	PRON
ejpam-367	278	2	ηt	ηt	ADP
ejpam-367	278	3	1	1	NUM
ejpam-367	278	4	dλt	dλt	NOUN
ejpam-367	278	5	f	f	PROPN
ejpam-367	278	6	ẋ1(t	ẋ1(t	PROPN
ejpam-367	278	7	,	,	PUNCT
ejpam-367	278	8	u1	u1	PROPN
ejpam-367	278	9	,	,	PUNCT
ejpam-367	278	10	u̇1	u̇1	PROPN
ejpam-367	278	11	,	,	PUNCT
ejpam-367	278	12	v1	v1	NOUN
ejpam-367	278	13	,	,	PUNCT
ejpam-367	278	14	v̇1)d	v̇1)d	PROPN
ejpam-367	278	15	t	t	NOUN
ejpam-367	278	16	using	use	VERB
ejpam-367	278	17	the	the	DET
ejpam-367	278	18	boundary	boundary	ADJ
ejpam-367	278	19	conditions	condition	NOUN
ejpam-367	278	20	which	which	PRON
ejpam-367	278	21	at	at	ADP
ejpam-367	278	22	t	t	PROPN
ejpam-367	278	23	=	=	SYM
ejpam-367	278	24	a	a	X
ejpam-367	278	25	,	,	PUNCT
ejpam-367	278	26	t	t	PROPN
ejpam-367	278	27	=	=	SYM
ejpam-367	278	28	b	b	PROPN
ejpam-367	278	29	gives	give	VERB
ejpam-367	278	30	η1	η1	NOUN
ejpam-367	278	31	=	=	SYM
ejpam-367	278	32	0	0	NUM
ejpam-367	278	33	,	,	PUNCT
ejpam-367	278	34	we	we	PRON
ejpam-367	278	35	have	have	VERB
ejpam-367	278	36	∫	∫	PROPN
ejpam-367	279	1	i	i	PRON
ejpam-367	279	2	λt	λt	ADP
ejpam-367	279	3	f	f	PROPN
ejpam-367	279	4	(	(	PUNCT
ejpam-367	279	5	t	t	PROPN
ejpam-367	279	6	,	,	PUNCT
ejpam-367	279	7	x1	x1	PROPN
ejpam-367	279	8	,	,	PUNCT
ejpam-367	279	9	ẋ1	ẋ1	PROPN
ejpam-367	279	10	,	,	PUNCT
ejpam-367	279	11	v1	v1	PROPN
ejpam-367	279	12	,	,	PUNCT
ejpam-367	279	13	v̇1)−	v̇1)−	ADJ
ejpam-367	279	14	∫	∫	PROPN
ejpam-367	280	1	i	i	INTJ
ejpam-367	280	2	λt	λt	ADP
ejpam-367	280	3	f	f	PROPN
ejpam-367	280	4	(	(	PUNCT
ejpam-367	280	5	t	t	PROPN
ejpam-367	280	6	,	,	PUNCT
ejpam-367	280	7	u1	u1	PROPN
ejpam-367	280	8	,	,	PUNCT
ejpam-367	280	9	u̇1	u̇1	PROPN
ejpam-367	280	10	,	,	PUNCT
ejpam-367	280	11	v1	v1	NOUN
ejpam-367	280	12	,	,	PUNCT
ejpam-367	280	13	v̇1)d	v̇1)d	PROPN
ejpam-367	280	14	t	t	NOUN
ejpam-367	280	15	≧	≧	NUM
ejpam-367	281	1	∫	∫	PROPN
ejpam-367	282	1	i	i	PRON
ejpam-367	282	2	ηt	ηt	ADP
ejpam-367	282	3	1	1	NUM
ejpam-367	283	1	[	[	X
ejpam-367	283	2	λt	λt	ADP
ejpam-367	283	3	fx1(t	fx1(t	PROPN
ejpam-367	283	4	,	,	PUNCT
ejpam-367	283	5	u1	u1	PROPN
ejpam-367	283	6	,	,	PUNCT
ejpam-367	283	7	u̇1	u̇1	PROPN
ejpam-367	283	8	,	,	PUNCT
ejpam-367	283	9	v1	v1	NOUN
ejpam-367	283	10	,	,	PUNCT
ejpam-367	283	11	v̇1)d	v̇1)d	PROPN
ejpam-367	283	12	t	t	NOUN
ejpam-367	283	13	−	−	PROPN
ejpam-367	283	14	d(λt	d(λt	PROPN
ejpam-367	283	15	f	f	PROPN
ejpam-367	283	16	ẋ1(t	ẋ1(t	PROPN
ejpam-367	283	17	,	,	PUNCT
ejpam-367	283	18	u1	u1	PROPN
ejpam-367	283	19	,	,	PUNCT
ejpam-367	283	20	u̇1	u̇1	PROPN
ejpam-367	283	21	,	,	PUNCT
ejpam-367	283	22	v1	v1	NOUN
ejpam-367	283	23	,	,	PUNCT
ejpam-367	283	24	v̇1))]d	v̇1))]d	NOUN
ejpam-367	283	25	t	t	PROPN
ejpam-367	283	26	(	(	PUNCT
ejpam-367	283	27	19	19	NUM
ejpam-367	283	28	)	)	PUNCT
ejpam-367	283	29	multiplying	multiplying	NOUN
ejpam-367	283	30	(	(	PUNCT
ejpam-367	283	31	18	18	NUM
ejpam-367	283	32	)	)	PUNCT
ejpam-367	283	33	by	by	ADP
ejpam-367	283	34	λi	λi	NOUN
ejpam-367	283	35	,	,	PUNCT
ejpam-367	283	36	i	i	PRON
ejpam-367	283	37	∈	∈	PROPN
ejpam-367	283	38	{	{	PUNCT
ejpam-367	283	39	1	1	NUM
ejpam-367	283	40	,	,	PUNCT
ejpam-367	283	41	2	2	NUM
ejpam-367	283	42	,	,	PUNCT
ejpam-367	283	43	.	.	PUNCT
ejpam-367	283	44	.	.	PUNCT
ejpam-367	284	1	.	.	PUNCT
ejpam-367	285	1	,	,	PUNCT
ejpam-367	285	2	p	p	X
ejpam-367	285	3	}	}	PUNCT
ejpam-367	285	4	and	and	CCONJ
ejpam-367	285	5	summing	sum	VERB
ejpam-367	285	6	over	over	ADP
ejpam-367	285	7	i	i	PRON
ejpam-367	285	8	,	,	PUNCT
ejpam-367	285	9	we	we	PRON
ejpam-367	285	10	get	get	VERB
ejpam-367	285	11	,	,	PUNCT
ejpam-367	285	12	∫	∫	PROPN
ejpam-367	286	1	i	i	INTJ
ejpam-367	286	2	λt	λt	ADP
ejpam-367	286	3	f	f	PROPN
ejpam-367	286	4	(	(	PUNCT
ejpam-367	286	5	t	t	PROPN
ejpam-367	286	6	,	,	PUNCT
ejpam-367	286	7	x1	x1	PROPN
ejpam-367	286	8	,	,	PUNCT
ejpam-367	286	9	ẋ1	ẋ1	PROPN
ejpam-367	286	10	,	,	PUNCT
ejpam-367	286	11	v1	v1	PROPN
ejpam-367	286	12	,	,	PUNCT
ejpam-367	286	13	v̇1)−	v̇1)−	ADJ
ejpam-367	286	14	∫	∫	PROPN
ejpam-367	287	1	i	i	INTJ
ejpam-367	287	2	λt	λt	ADP
ejpam-367	287	3	f	f	PROPN
ejpam-367	287	4	(	(	PUNCT
ejpam-367	287	5	t	t	PROPN
ejpam-367	287	6	,	,	PUNCT
ejpam-367	287	7	x1	x1	PROPN
ejpam-367	287	8	,	,	PUNCT
ejpam-367	287	9	ẋ1	ẋ1	PROPN
ejpam-367	287	10	,	,	PUNCT
ejpam-367	287	11	y1	y1	PROPN
ejpam-367	287	12	,	,	PUNCT
ejpam-367	287	13	ẏ1)d	ẏ1)d	NOUN
ejpam-367	287	14	t	t	PROPN
ejpam-367	287	15	≦	≦	PROPN
ejpam-367	287	16	∫	∫	INTJ
ejpam-367	288	1	i	i	PRON
ejpam-367	288	2	{	{	PUNCT
ejpam-367	288	3	ηt	ηt	ADP
ejpam-367	288	4	2	2	NUM
ejpam-367	288	5	(	(	PUNCT
ejpam-367	288	6	λt	λt	ADP
ejpam-367	288	7	f	f	PROPN
ejpam-367	288	8	y1(t	y1(t	PROPN
ejpam-367	288	9	,	,	PUNCT
ejpam-367	288	10	x1	x1	PROPN
ejpam-367	288	11	,	,	PUNCT
ejpam-367	288	12	ẋ1	ẋ1	PROPN
ejpam-367	288	13	,	,	PUNCT
ejpam-367	288	14	y1	y1	PROPN
ejpam-367	288	15	,	,	PUNCT
ejpam-367	288	16	ẏ1	ẏ1	PROPN
ejpam-367	288	17	)	)	PUNCT
ejpam-367	288	18	)	)	PUNCT
ejpam-367	289	1	+	+	CCONJ
ejpam-367	289	2	(	(	PUNCT
ejpam-367	289	3	dη2	dη2	NOUN
ejpam-367	289	4	)	)	PUNCT
ejpam-367	289	5	tλt	tλt	PROPN
ejpam-367	289	6	f	f	PROPN
ejpam-367	289	7	ẏ1(t	ẏ1(t	PROPN
ejpam-367	289	8	,	,	PUNCT
ejpam-367	289	9	x1	x1	PROPN
ejpam-367	289	10	,	,	PUNCT
ejpam-367	289	11	ẋ1	ẋ1	PROPN
ejpam-367	289	12	,	,	PUNCT
ejpam-367	289	13	y1	y1	PROPN
ejpam-367	289	14	,	,	PUNCT
ejpam-367	289	15	ẏ1)}d	ẏ1)}d	PROPN
ejpam-367	289	16	t	t	X
ejpam-367	289	17	on	on	ADP
ejpam-367	289	18	integrating	integrating	NOUN
ejpam-367	289	19	by	by	ADP
ejpam-367	289	20	parts	part	NOUN
ejpam-367	289	21	the	the	DET
ejpam-367	289	22	r.h.s	r.h.s	NOUN
ejpam-367	289	23	of	of	ADP
ejpam-367	289	24	the	the	DET
ejpam-367	289	25	above	above	ADJ
ejpam-367	289	26	inequality	inequality	NOUN
ejpam-367	289	27	and	and	CCONJ
ejpam-367	289	28	using	use	VERB
ejpam-367	289	29	the	the	DET
ejpam-367	289	30	boundary	boundary	ADJ
ejpam-367	289	31	conditions	condition	NOUN
ejpam-367	289	32	which	which	PRON
ejpam-367	289	33	at	at	ADP
ejpam-367	289	34	t	t	PROPN
ejpam-367	289	35	=	=	SYM
ejpam-367	289	36	a	a	X
ejpam-367	289	37	,	,	PUNCT
ejpam-367	289	38	t	t	PROPN
ejpam-367	289	39	=	=	SYM
ejpam-367	289	40	b	b	NOUN
ejpam-367	289	41	gives	give	VERB
ejpam-367	289	42	η2	η2	ADJ
ejpam-367	289	43	=	=	SYM
ejpam-367	289	44	0	0	NUM
ejpam-367	289	45	,	,	PUNCT
ejpam-367	289	46	we	we	PRON
ejpam-367	289	47	have	have	VERB
ejpam-367	289	48	∫	∫	PROPN
ejpam-367	290	1	i	i	PRON
ejpam-367	290	2	λt	λt	ADP
ejpam-367	290	3	f	f	PROPN
ejpam-367	290	4	(	(	PUNCT
ejpam-367	290	5	t	t	PROPN
ejpam-367	290	6	,	,	PUNCT
ejpam-367	290	7	x1	x1	PROPN
ejpam-367	290	8	,	,	PUNCT
ejpam-367	290	9	ẋ1	ẋ1	PROPN
ejpam-367	290	10	,	,	PUNCT
ejpam-367	290	11	v1	v1	PROPN
ejpam-367	290	12	,	,	PUNCT
ejpam-367	290	13	v̇1)−	v̇1)−	ADJ
ejpam-367	290	14	∫	∫	PROPN
ejpam-367	291	1	i	i	INTJ
ejpam-367	291	2	λt	λt	ADP
ejpam-367	291	3	f	f	PROPN
ejpam-367	291	4	(	(	PUNCT
ejpam-367	291	5	t	t	PROPN
ejpam-367	291	6	,	,	PUNCT
ejpam-367	291	7	x1	x1	PROPN
ejpam-367	291	8	,	,	PUNCT
ejpam-367	291	9	ẋ1	ẋ1	PROPN
ejpam-367	291	10	,	,	PUNCT
ejpam-367	291	11	y1	y1	PROPN
ejpam-367	291	12	,	,	PUNCT
ejpam-367	291	13	ẏ1)d	ẏ1)d	NOUN
ejpam-367	291	14	t	t	PROPN
ejpam-367	291	15	≦	≦	PROPN
ejpam-367	291	16	∫	∫	PROPN
ejpam-367	291	17	i	i	PRON
ejpam-367	291	18	ηt	ηt	ADP
ejpam-367	291	19	2	2	NUM
ejpam-367	291	20	[	[	X
ejpam-367	291	21	(	(	PUNCT
ejpam-367	291	22	λt	λt	ADP
ejpam-367	291	23	f	f	PROPN
ejpam-367	291	24	y1(t	y1(t	PROPN
ejpam-367	291	25	,	,	PUNCT
ejpam-367	291	26	x1	x1	PROPN
ejpam-367	291	27	,	,	PUNCT
ejpam-367	291	28	ẋ1	ẋ1	PROPN
ejpam-367	291	29	,	,	PUNCT
ejpam-367	291	30	y1	y1	PROPN
ejpam-367	291	31	,	,	PUNCT
ejpam-367	291	32	ẏ1))−	ẏ1))−	ADJ
ejpam-367	291	33	d(λt	d(λt	NOUN
ejpam-367	291	34	f	f	PROPN
ejpam-367	291	35	ẏ1(t	ẏ1(t	PROPN
ejpam-367	291	36	,	,	PUNCT
ejpam-367	291	37	x1	x1	PROPN
ejpam-367	291	38	,	,	PUNCT
ejpam-367	291	39	ẋ1	ẋ1	PROPN
ejpam-367	291	40	,	,	PUNCT
ejpam-367	291	41	y1	y1	PROPN
ejpam-367	291	42	,	,	PUNCT
ejpam-367	291	43	ẏ1))]d	ẏ1))]d	PROPN
ejpam-367	291	44	t	t	PROPN
ejpam-367	291	45	(	(	PUNCT
ejpam-367	291	46	20	20	NUM
ejpam-367	291	47	)	)	PUNCT
ejpam-367	291	48	multiplying	multiplying	NOUN
ejpam-367	291	49	(	(	PUNCT
ejpam-367	291	50	20	20	NUM
ejpam-367	291	51	)	)	PUNCT
ejpam-367	291	52	by	by	ADP
ejpam-367	291	53	(	(	PUNCT
ejpam-367	291	54	-1	-1	INTJ
ejpam-367	291	55	)	)	PUNCT
ejpam-367	291	56	and	and	CCONJ
ejpam-367	291	57	adding	add	VERB
ejpam-367	291	58	to	to	ADP
ejpam-367	291	59	(	(	PUNCT
ejpam-367	291	60	19	19	NUM
ejpam-367	291	61	)	)	PUNCT
ejpam-367	291	62	,	,	PUNCT
ejpam-367	291	63	we	we	PRON
ejpam-367	291	64	have	have	VERB
ejpam-367	291	65	∫	∫	PROPN
ejpam-367	292	1	i	i	PRON
ejpam-367	292	2	λt	λt	ADP
ejpam-367	292	3	f	f	PROPN
ejpam-367	292	4	(	(	PUNCT
ejpam-367	292	5	t	t	PROPN
ejpam-367	292	6	,	,	PUNCT
ejpam-367	292	7	x1	x1	PROPN
ejpam-367	292	8	,	,	PUNCT
ejpam-367	292	9	ẋ1	ẋ1	PROPN
ejpam-367	292	10	,	,	PUNCT
ejpam-367	292	11	y1	y1	PROPN
ejpam-367	292	12	,	,	PUNCT
ejpam-367	292	13	ẏ1)d	ẏ1)d	NOUN
ejpam-367	292	14	t	t	PROPN
ejpam-367	293	1	−	−	PROPN
ejpam-367	293	2	∫	∫	INTJ
ejpam-367	294	1	i	i	PRON
ejpam-367	294	2	λt	λt	ADP
ejpam-367	294	3	f	f	PROPN
ejpam-367	294	4	(	(	PUNCT
ejpam-367	294	5	t	t	PROPN
ejpam-367	294	6	,	,	PUNCT
ejpam-367	294	7	u1	u1	PROPN
ejpam-367	294	8	,	,	PUNCT
ejpam-367	294	9	u̇1	u̇1	PROPN
ejpam-367	294	10	,	,	PUNCT
ejpam-367	294	11	v1	v1	NOUN
ejpam-367	294	12	,	,	PUNCT
ejpam-367	294	13	v̇1)d	v̇1)d	PROPN
ejpam-367	294	14	t	t	PROPN
ejpam-367	294	15	i.	i.	PROPN
ejpam-367	294	16	husain	husain	PROPN
ejpam-367	294	17	and	and	CCONJ
ejpam-367	294	18	r.	r.	PROPN
ejpam-367	294	19	mattoo	mattoo	PROPN
ejpam-367	294	20	/	/	SYM
ejpam-367	294	21	eur	eur	PROPN
ejpam-367	294	22	.	.	PUNCT
ejpam-367	295	1	j.	j.	PROPN
ejpam-367	295	2	pure	pure	PROPN
ejpam-367	295	3	appl	appl	PROPN
ejpam-367	295	4	.	.	PROPN
ejpam-367	295	5	math	math	PROPN
ejpam-367	295	6	,	,	PUNCT
ejpam-367	295	7	2	2	NUM
ejpam-367	295	8	(	(	PUNCT
ejpam-367	295	9	2009	2009	NUM
ejpam-367	295	10	)	)	PUNCT
ejpam-367	295	11	,	,	PUNCT
ejpam-367	295	12	(	(	PUNCT
ejpam-367	295	13	578	578	NUM
ejpam-367	295	14	-	-	SYM
ejpam-367	295	15	603	603	NUM
ejpam-367	295	16	)	)	PUNCT
ejpam-367	295	17	588	588	NUM
ejpam-367	295	18	≧	≧	NUM
ejpam-367	295	19	∫	∫	INTJ
ejpam-367	296	1	i	i	PRON
ejpam-367	296	2	ηt	ηt	ADP
ejpam-367	296	3	1	1	NUM
ejpam-367	296	4	[	[	X
ejpam-367	296	5	(	(	PUNCT
ejpam-367	296	6	λt	λt	ADP
ejpam-367	296	7	fx1(t	fx1(t	PROPN
ejpam-367	296	8	,	,	PUNCT
ejpam-367	296	9	u1	u1	PROPN
ejpam-367	296	10	,	,	PUNCT
ejpam-367	296	11	u̇1	u̇1	PROPN
ejpam-367	296	12	,	,	PUNCT
ejpam-367	296	13	v1	v1	NOUN
ejpam-367	296	14	,	,	PUNCT
ejpam-367	296	15	v̇1))−	v̇1))−	NOUN
ejpam-367	296	16	d(λt	d(λt	PROPN
ejpam-367	296	17	f	f	PROPN
ejpam-367	296	18	ẋ1(t	ẋ1(t	PROPN
ejpam-367	296	19	,	,	PUNCT
ejpam-367	296	20	u1	u1	PROPN
ejpam-367	296	21	,	,	PUNCT
ejpam-367	296	22	u̇1	u̇1	PROPN
ejpam-367	296	23	,	,	PUNCT
ejpam-367	296	24	v1	v1	NOUN
ejpam-367	296	25	,	,	PUNCT
ejpam-367	296	26	v̇1))]d	v̇1))]d	NOUN
ejpam-367	296	27	t	t	PROPN
ejpam-367	296	28	−	−	PROPN
ejpam-367	297	1	∫	∫	PROPN
ejpam-367	298	1	i	i	PRON
ejpam-367	298	2	ηt	ηt	ADP
ejpam-367	298	3	2	2	NUM
ejpam-367	298	4	[	[	X
ejpam-367	298	5	(	(	PUNCT
ejpam-367	298	6	λt	λt	ADP
ejpam-367	298	7	f	f	PROPN
ejpam-367	298	8	y1(t	y1(t	PROPN
ejpam-367	298	9	,	,	PUNCT
ejpam-367	298	10	u1	u1	PROPN
ejpam-367	298	11	,	,	PUNCT
ejpam-367	298	12	u̇1	u̇1	PROPN
ejpam-367	298	13	,	,	PUNCT
ejpam-367	298	14	v1	v1	NOUN
ejpam-367	298	15	,	,	PUNCT
ejpam-367	298	16	v̇1))−	v̇1))−	NOUN
ejpam-367	298	17	d(λt	d(λt	PROPN
ejpam-367	298	18	f	f	PROPN
ejpam-367	298	19	ẏ1(t	ẏ1(t	PROPN
ejpam-367	298	20	,	,	PUNCT
ejpam-367	298	21	u1	u1	NOUN
ejpam-367	298	22	,	,	PUNCT
ejpam-367	298	23	u̇1	u̇1	PROPN
ejpam-367	298	24	,	,	PUNCT
ejpam-367	298	25	v1	v1	NOUN
ejpam-367	298	26	,	,	PUNCT
ejpam-367	298	27	v̇1))]d	v̇1))]d	NOUN
ejpam-367	298	28	t	t	PROPN
ejpam-367	298	29	(	(	PUNCT
ejpam-367	298	30	21	21	NUM
ejpam-367	298	31	)	)	PUNCT
ejpam-367	298	32	now	now	ADV
ejpam-367	298	33	from	from	ADP
ejpam-367	298	34	the	the	DET
ejpam-367	298	35	inequality	inequality	NOUN
ejpam-367	298	36	(	(	PUNCT
ejpam-367	298	37	9	9	NUM
ejpam-367	298	38	)	)	PUNCT
ejpam-367	298	39	along	along	ADP
ejpam-367	298	40	with	with	ADP
ejpam-367	298	41	(	(	PUNCT
ejpam-367	298	42	13	13	NUM
ejpam-367	298	43	)	)	PUNCT
ejpam-367	298	44	,	,	PUNCT
ejpam-367	298	45	it	it	PRON
ejpam-367	298	46	follows	follow	VERB
ejpam-367	298	47	∫	∫	PROPN
ejpam-367	298	48	i	i	PRON
ejpam-367	298	49	ηt	ηt	ADP
ejpam-367	298	50	1	1	NUM
ejpam-367	298	51	(	(	PUNCT
ejpam-367	298	52	λt	λt	ADP
ejpam-367	298	53	fu1(t	fu1(t	PROPN
ejpam-367	298	54	,	,	PUNCT
ejpam-367	298	55	u1	u1	PROPN
ejpam-367	298	56	,	,	PUNCT
ejpam-367	298	57	u̇1	u̇1	PROPN
ejpam-367	298	58	,	,	PUNCT
ejpam-367	298	59	v1	v1	NOUN
ejpam-367	298	60	,	,	PUNCT
ejpam-367	298	61	v̇1)−	v̇1)−	ADJ
ejpam-367	298	62	dλt	dλt	NOUN
ejpam-367	298	63	fu̇1(t	fu̇1(t	PROPN
ejpam-367	298	64	,	,	PUNCT
ejpam-367	298	65	u1	u1	PROPN
ejpam-367	298	66	,	,	PUNCT
ejpam-367	298	67	u̇1	u̇1	PROPN
ejpam-367	298	68	,	,	PUNCT
ejpam-367	298	69	v1	v1	NOUN
ejpam-367	298	70	,	,	PUNCT
ejpam-367	298	71	v̇1))d	v̇1))d	NOUN
ejpam-367	298	72	t	t	NOUN
ejpam-367	299	1	≧−	≧−	X
ejpam-367	299	2	∫	∫	PROPN
ejpam-367	299	3	i	i	PRON
ejpam-367	299	4	u1(t)t[λt	u1(t)t[λt	VERB
ejpam-367	299	5	fu1(t	fu1(t	PRON
ejpam-367	299	6	,	,	PUNCT
ejpam-367	299	7	u1	u1	PROPN
ejpam-367	299	8	,	,	PUNCT
ejpam-367	299	9	u̇1	u̇1	PROPN
ejpam-367	299	10	,	,	PUNCT
ejpam-367	299	11	v1	v1	NOUN
ejpam-367	299	12	,	,	PUNCT
ejpam-367	299	13	v̇1)−	v̇1)−	ADJ
ejpam-367	299	14	dλt	dλt	NOUN
ejpam-367	299	15	fu̇1(t	fu̇1(t	PROPN
ejpam-367	299	16	,	,	PUNCT
ejpam-367	299	17	u1	u1	PROPN
ejpam-367	299	18	,	,	PUNCT
ejpam-367	299	19	u̇1	u̇1	PROPN
ejpam-367	299	20	,	,	PUNCT
ejpam-367	299	21	v1	v1	PROPN
ejpam-367	299	22	,	,	PUNCT
ejpam-367	299	23	v̇1)]d	v̇1)]d	PROPN
ejpam-367	299	24	t	t	PROPN
ejpam-367	299	25	(	(	PUNCT
ejpam-367	299	26	22	22	NUM
ejpam-367	299	27	)	)	PUNCT
ejpam-367	299	28	also	also	ADV
ejpam-367	299	29	from	from	ADP
ejpam-367	299	30	the	the	DET
ejpam-367	299	31	inequality	inequality	NOUN
ejpam-367	299	32	(	(	PUNCT
ejpam-367	299	33	3	3	NUM
ejpam-367	299	34	)	)	PUNCT
ejpam-367	299	35	together	together	ADV
ejpam-367	299	36	with	with	ADP
ejpam-367	299	37	(	(	PUNCT
ejpam-367	299	38	14	14	NUM
ejpam-367	299	39	)	)	PUNCT
ejpam-367	299	40	implies	imply	VERB
ejpam-367	299	41	−	−	PROPN
ejpam-367	299	42	∫	∫	PROPN
ejpam-367	300	1	i	i	PRON
ejpam-367	300	2	ηt	ηt	ADP
ejpam-367	300	3	2	2	NUM
ejpam-367	300	4	(	(	PUNCT
ejpam-367	300	5	λt	λt	ADP
ejpam-367	300	6	f	f	PROPN
ejpam-367	300	7	y1(t	y1(t	PROPN
ejpam-367	300	8	,	,	PUNCT
ejpam-367	300	9	x1	x1	PROPN
ejpam-367	300	10	,	,	PUNCT
ejpam-367	300	11	ẋ1	ẋ1	PROPN
ejpam-367	300	12	,	,	PUNCT
ejpam-367	300	13	y1	y1	PROPN
ejpam-367	300	14	,	,	PUNCT
ejpam-367	300	15	ẏ1)−	ẏ1)−	PROPN
ejpam-367	300	16	dλt	dλt	PROPN
ejpam-367	301	1	f	f	PROPN
ejpam-367	301	2	ẏ1(t	ẏ1(t	PROPN
ejpam-367	301	3	,	,	PUNCT
ejpam-367	301	4	x1	x1	PROPN
ejpam-367	301	5	,	,	PUNCT
ejpam-367	301	6	ẋ1	ẋ1	PROPN
ejpam-367	301	7	,	,	PUNCT
ejpam-367	301	8	y1	y1	INTJ
ejpam-367	301	9	,	,	PUNCT
ejpam-367	301	10	ẏ1))d	ẏ1))d	NOUN
ejpam-367	301	11	t	t	PROPN
ejpam-367	301	12	≧	≧	NUM
ejpam-367	302	1	∫	∫	PROPN
ejpam-367	303	1	i	i	PRON
ejpam-367	303	2	y1(t)t[λt	y1(t)t[λt	PROPN
ejpam-367	304	1	f	f	PROPN
ejpam-367	304	2	y1(t	y1(t	PROPN
ejpam-367	304	3	,	,	PUNCT
ejpam-367	304	4	x1	x1	PROPN
ejpam-367	304	5	,	,	PUNCT
ejpam-367	304	6	ẋ1	ẋ1	PROPN
ejpam-367	304	7	,	,	PUNCT
ejpam-367	304	8	y1	y1	PROPN
ejpam-367	304	9	,	,	PUNCT
ejpam-367	304	10	ẏ1)−	ẏ1)−	PROPN
ejpam-367	304	11	dλt	dλt	PROPN
ejpam-367	305	1	f	f	PROPN
ejpam-367	305	2	ẏ1(t	ẏ1(t	PROPN
ejpam-367	305	3	,	,	PUNCT
ejpam-367	305	4	x1	x1	PROPN
ejpam-367	305	5	,	,	PUNCT
ejpam-367	305	6	ẋ1	ẋ1	PROPN
ejpam-367	305	7	,	,	PUNCT
ejpam-367	305	8	y1	y1	PROPN
ejpam-367	305	9	,	,	PUNCT
ejpam-367	305	10	ẏ1)]d	ẏ1)]d	PROPN
ejpam-367	305	11	t	t	PROPN
ejpam-367	305	12	(	(	PUNCT
ejpam-367	305	13	23	23	NUM
ejpam-367	305	14	)	)	PUNCT
ejpam-367	305	15	using	use	VERB
ejpam-367	305	16	(	(	PUNCT
ejpam-367	305	17	22	22	NUM
ejpam-367	305	18	)	)	PUNCT
ejpam-367	305	19	and	and	CCONJ
ejpam-367	305	20	(	(	PUNCT
ejpam-367	305	21	23	23	NUM
ejpam-367	305	22	)	)	PUNCT
ejpam-367	305	23	,	,	PUNCT
ejpam-367	305	24	in	in	ADP
ejpam-367	305	25	(	(	PUNCT
ejpam-367	305	26	21	21	NUM
ejpam-367	305	27	)	)	PUNCT
ejpam-367	305	28	,	,	PUNCT
ejpam-367	305	29	we	we	PRON
ejpam-367	305	30	have	have	VERB
ejpam-367	305	31	∫	∫	PROPN
ejpam-367	306	1	i	i	PRON
ejpam-367	306	2	λt	λt	ADP
ejpam-367	306	3	f	f	PROPN
ejpam-367	306	4	(	(	PUNCT
ejpam-367	306	5	t	t	PROPN
ejpam-367	306	6	,	,	PUNCT
ejpam-367	306	7	x1	x1	PROPN
ejpam-367	306	8	,	,	PUNCT
ejpam-367	306	9	ẋ1	ẋ1	PROPN
ejpam-367	306	10	,	,	PUNCT
ejpam-367	306	11	y1	y1	PROPN
ejpam-367	306	12	,	,	PUNCT
ejpam-367	306	13	ẏ1)d	ẏ1)d	NOUN
ejpam-367	306	14	t	t	PROPN
ejpam-367	306	15	−	−	PROPN
ejpam-367	306	16	y1(t)t	y1(t)t	NUM
ejpam-367	306	17	∫	∫	NOUN
ejpam-367	307	1	i	i	INTJ
ejpam-367	307	2	λt	λt	ADP
ejpam-367	307	3	f	f	PROPN
ejpam-367	307	4	y1(t	y1(t	PROPN
ejpam-367	307	5	,	,	PUNCT
ejpam-367	307	6	x1	x1	PROPN
ejpam-367	307	7	,	,	PUNCT
ejpam-367	307	8	ẋ1	ẋ1	PROPN
ejpam-367	307	9	,	,	PUNCT
ejpam-367	307	10	y1	y1	PROPN
ejpam-367	307	11	,	,	PUNCT
ejpam-367	307	12	ẏ1)d	ẏ1)d	NOUN
ejpam-367	307	13	t	t	NOUN
ejpam-367	308	1	≧−	≧−	X
ejpam-367	308	2	∫	∫	INTJ
ejpam-367	308	3	i	i	PRON
ejpam-367	308	4	u1(t)t[(λt	u1(t)t[(λt	VERB
ejpam-367	308	5	fu1(t	fu1(t	DET
ejpam-367	308	6	,	,	PUNCT
ejpam-367	308	7	u1	u1	PROPN
ejpam-367	308	8	,	,	PUNCT
ejpam-367	308	9	u̇1	u̇1	PROPN
ejpam-367	308	10	,	,	PUNCT
ejpam-367	308	11	v1	v1	NOUN
ejpam-367	308	12	,	,	PUNCT
ejpam-367	308	13	v̇1))−	v̇1))−	NOUN
ejpam-367	308	14	d(λt	d(λt	NOUN
ejpam-367	308	15	fu̇1(t	fu̇1(t	PROPN
ejpam-367	308	16	,	,	PUNCT
ejpam-367	308	17	u1	u1	PROPN
ejpam-367	308	18	,	,	PUNCT
ejpam-367	308	19	u̇1	u̇1	PROPN
ejpam-367	308	20	,	,	PUNCT
ejpam-367	308	21	v1	v1	NOUN
ejpam-367	308	22	,	,	PUNCT
ejpam-367	308	23	v̇1))]d	v̇1))]d	NOUN
ejpam-367	308	24	t	t	PROPN
ejpam-367	309	1	+	+	CCONJ
ejpam-367	309	2	∫	∫	PROPN
ejpam-367	309	3	i	i	PRON
ejpam-367	309	4	y1(t)t[(λt	y1(t)t[(λt	VERB
ejpam-367	309	5	f	f	PROPN
ejpam-367	309	6	y1(t	y1(t	INTJ
ejpam-367	309	7	,	,	PUNCT
ejpam-367	309	8	x1	x1	PROPN
ejpam-367	309	9	,	,	PUNCT
ejpam-367	309	10	ẋ1	ẋ1	PROPN
ejpam-367	309	11	,	,	PUNCT
ejpam-367	309	12	y1	y1	PROPN
ejpam-367	309	13	,	,	PUNCT
ejpam-367	309	14	ẏ1	ẏ1	PROPN
ejpam-367	309	15	)	)	PUNCT
ejpam-367	309	16	)	)	PUNCT
ejpam-367	310	1	−d(λt	−d(λt	NOUN
ejpam-367	310	2	f	f	PROPN
ejpam-367	310	3	ẏ1(t	ẏ1(t	PROPN
ejpam-367	310	4	,	,	PUNCT
ejpam-367	310	5	x1	x1	PROPN
ejpam-367	310	6	,	,	PUNCT
ejpam-367	310	7	ẋ1	ẋ1	PROPN
ejpam-367	310	8	,	,	PUNCT
ejpam-367	310	9	y1	y1	PROPN
ejpam-367	310	10	,	,	PUNCT
ejpam-367	310	11	ẏ1))]d	ẏ1))]d	PROPN
ejpam-367	310	12	t	t	PROPN
ejpam-367	310	13	,	,	PUNCT
ejpam-367	310	14	(	(	PUNCT
ejpam-367	310	15	24	24	NUM
ejpam-367	310	16	)	)	PUNCT
ejpam-367	310	17	which	which	PRON
ejpam-367	310	18	implies	imply	VERB
ejpam-367	310	19	∫	∫	PROPN
ejpam-367	310	20	i	i	PRON
ejpam-367	310	21	{	{	PUNCT
ejpam-367	310	22	λt	λt	ADP
ejpam-367	310	23	f	f	X
ejpam-367	310	24	(	(	PUNCT
ejpam-367	310	25	t	t	PROPN
ejpam-367	310	26	,	,	PUNCT
ejpam-367	310	27	x1	x1	PROPN
ejpam-367	310	28	,	,	PUNCT
ejpam-367	310	29	ẋ1	ẋ1	PROPN
ejpam-367	310	30	,	,	PUNCT
ejpam-367	310	31	y1	y1	PROPN
ejpam-367	310	32	,	,	PUNCT
ejpam-367	310	33	ẏ1)−	ẏ1)−	PROPN
ejpam-367	310	34	y1(t)t	y1(t)t	PRON
ejpam-367	310	35	(	(	PUNCT
ejpam-367	310	36	λt	λt	ADP
ejpam-367	310	37	f	f	PROPN
ejpam-367	310	38	y1(t	y1(t	PROPN
ejpam-367	310	39	,	,	PUNCT
ejpam-367	310	40	x1	x1	PROPN
ejpam-367	310	41	,	,	PUNCT
ejpam-367	310	42	ẋ1	ẋ1	PROPN
ejpam-367	310	43	,	,	PUNCT
ejpam-367	310	44	y1	y1	PROPN
ejpam-367	310	45	,	,	PUNCT
ejpam-367	310	46	ẏ1	ẏ1	PROPN
ejpam-367	310	47	)	)	PUNCT
ejpam-367	310	48	−dλt	−dλt	NOUN
ejpam-367	311	1	f	f	PROPN
ejpam-367	311	2	ẏ1(t	ẏ1(t	PROPN
ejpam-367	311	3	,	,	PUNCT
ejpam-367	311	4	x1	x1	PROPN
ejpam-367	311	5	,	,	PUNCT
ejpam-367	311	6	ẋ1	ẋ1	PROPN
ejpam-367	311	7	,	,	PUNCT
ejpam-367	311	8	y1	y1	PROPN
ejpam-367	311	9	,	,	PUNCT
ejpam-367	311	10	ẏ1))}d	ẏ1))}d	PROPN
ejpam-367	311	11	t	t	PROPN
ejpam-367	311	12	≧	≧	NOUN
ejpam-367	312	1	∫	∫	PROPN
ejpam-367	313	1	i	i	PRON
ejpam-367	313	2	{	{	PUNCT
ejpam-367	313	3	λt	λt	ADP
ejpam-367	313	4	fu1(t	fu1(t	PROPN
ejpam-367	313	5	,	,	PUNCT
ejpam-367	313	6	u1	u1	PROPN
ejpam-367	313	7	,	,	PUNCT
ejpam-367	313	8	u̇1	u̇1	PROPN
ejpam-367	313	9	,	,	PUNCT
ejpam-367	313	10	v1	v1	NOUN
ejpam-367	313	11	,	,	PUNCT
ejpam-367	313	12	v̇1)−	v̇1)−	PROPN
ejpam-367	313	13	u1(t)t(λt	u1(t)t(λt	NOUN
ejpam-367	313	14	fx1(t	fx1(t	PROPN
ejpam-367	313	15	,	,	PUNCT
ejpam-367	313	16	u1	u1	PROPN
ejpam-367	313	17	,	,	PUNCT
ejpam-367	313	18	u̇1	u̇1	PROPN
ejpam-367	313	19	,	,	PUNCT
ejpam-367	313	20	v1	v1	NOUN
ejpam-367	313	21	,	,	PUNCT
ejpam-367	313	22	v̇1	v̇1	PROPN
ejpam-367	313	23	)	)	PUNCT
ejpam-367	313	24	−dλt	−dλt	NOUN
ejpam-367	314	1	f	f	PROPN
ejpam-367	314	2	ẋ1(t	ẋ1(t	PROPN
ejpam-367	314	3	,	,	PUNCT
ejpam-367	314	4	u1	u1	PROPN
ejpam-367	314	5	,	,	PUNCT
ejpam-367	314	6	u̇1	u̇1	PROPN
ejpam-367	314	7	,	,	PUNCT
ejpam-367	314	8	v1	v1	NOUN
ejpam-367	314	9	,	,	PUNCT
ejpam-367	314	10	v̇1))}d	v̇1))}d	PROPN
ejpam-367	314	11	t	t	PROPN
ejpam-367	314	12	(	(	PUNCT
ejpam-367	314	13	25	25	NUM
ejpam-367	314	14	)	)	PUNCT
ejpam-367	314	15	i.	i.	NOUN
ejpam-367	314	16	husain	husain	PROPN
ejpam-367	314	17	and	and	CCONJ
ejpam-367	314	18	r.	r.	PROPN
ejpam-367	314	19	mattoo	mattoo	PROPN
ejpam-367	314	20	/	/	SYM
ejpam-367	314	21	eur	eur	PROPN
ejpam-367	314	22	.	.	PUNCT
ejpam-367	315	1	j.	j.	PROPN
ejpam-367	315	2	pure	pure	PROPN
ejpam-367	315	3	appl	appl	PROPN
ejpam-367	315	4	.	.	PROPN
ejpam-367	315	5	math	math	PROPN
ejpam-367	315	6	,	,	PUNCT
ejpam-367	315	7	2	2	NUM
ejpam-367	315	8	(	(	PUNCT
ejpam-367	315	9	2009	2009	NUM
ejpam-367	315	10	)	)	PUNCT
ejpam-367	315	11	,	,	PUNCT
ejpam-367	315	12	(	(	PUNCT
ejpam-367	315	13	578	578	NUM
ejpam-367	315	14	-	-	SYM
ejpam-367	315	15	603	603	NUM
ejpam-367	315	16	)	)	PUNCT
ejpam-367	315	17	589	589	NUM
ejpam-367	315	18	now	now	ADV
ejpam-367	315	19	from	from	ADP
ejpam-367	315	20	the	the	DET
ejpam-367	315	21	inequality	inequality	NOUN
ejpam-367	315	22	(	(	PUNCT
ejpam-367	315	23	10	10	NUM
ejpam-367	315	24	)	)	PUNCT
ejpam-367	315	25	along	along	ADP
ejpam-367	315	26	with	with	ADP
ejpam-367	315	27	(	(	PUNCT
ejpam-367	315	28	15	15	NUM
ejpam-367	315	29	)	)	PUNCT
ejpam-367	315	30	,	,	PUNCT
ejpam-367	315	31	we	we	PRON
ejpam-367	315	32	have	have	VERB
ejpam-367	315	33	∫	∫	PROPN
ejpam-367	316	1	i	i	PRON
ejpam-367	316	2	(	(	PUNCT
ejpam-367	316	3	ηt	ηt	ADP
ejpam-367	316	4	3	3	NUM
ejpam-367	316	5	(	(	PUNCT
ejpam-367	316	6	t	t	PROPN
ejpam-367	316	7	,	,	PUNCT
ejpam-367	316	8	x2	x2	PROPN
ejpam-367	316	9	,	,	PUNCT
ejpam-367	316	10	ẋ2	ẋ2	PROPN
ejpam-367	316	11	,	,	PUNCT
ejpam-367	316	12	u2	u2	NOUN
ejpam-367	316	13	,	,	PUNCT
ejpam-367	316	14	u̇2	u̇2	PROPN
ejpam-367	316	15	)	)	PUNCT
ejpam-367	316	16	+	+	NUM
ejpam-367	316	17	u2(t))(λt	u2(t))(λt	PROPN
ejpam-367	316	18	gu2(t	gu2(t	PROPN
ejpam-367	316	19	,	,	PUNCT
ejpam-367	316	20	u2	u2	PROPN
ejpam-367	316	21	,	,	PUNCT
ejpam-367	316	22	u̇2	u̇2	PROPN
ejpam-367	316	23	,	,	PUNCT
ejpam-367	316	24	v2	v2	NOUN
ejpam-367	316	25	,	,	PUNCT
ejpam-367	316	26	v̇2	v̇2	PROPN
ejpam-367	316	27	)	)	PUNCT
ejpam-367	316	28	−dλt	−dλt	NOUN
ejpam-367	317	1	gu̇2(t	gu̇2(t	PROPN
ejpam-367	317	2	,	,	PUNCT
ejpam-367	317	3	u2	u2	PROPN
ejpam-367	317	4	,	,	PUNCT
ejpam-367	317	5	u̇2	u̇2	PROPN
ejpam-367	317	6	,	,	PUNCT
ejpam-367	317	7	v2	v2	NOUN
ejpam-367	317	8	,	,	PUNCT
ejpam-367	317	9	v̇2))≧	v̇2))≧	NOUN
ejpam-367	317	10	0	0	NUM
ejpam-367	317	11	.	.	PUNCT
ejpam-367	318	1	this	this	PRON
ejpam-367	318	2	implies	imply	VERB
ejpam-367	318	3	∫	∫	PROPN
ejpam-367	318	4	i	i	PRON
ejpam-367	318	5	ηt	ηt	ADP
ejpam-367	318	6	3	3	NUM
ejpam-367	318	7	(	(	PUNCT
ejpam-367	318	8	λt	λt	ADP
ejpam-367	318	9	gu2(t	gu2(t	PROPN
ejpam-367	318	10	,	,	PUNCT
ejpam-367	318	11	u2	u2	PROPN
ejpam-367	318	12	,	,	PUNCT
ejpam-367	318	13	u̇2	u̇2	PROPN
ejpam-367	318	14	,	,	PUNCT
ejpam-367	318	15	v2	v2	PROPN
ejpam-367	318	16	,	,	PUNCT
ejpam-367	318	17	v̇2)−	v̇2)−	ADJ
ejpam-367	318	18	d(λt	d(λt	NOUN
ejpam-367	318	19	gu̇2(t	gu̇2(t	PROPN
ejpam-367	318	20	,	,	PUNCT
ejpam-367	318	21	u2	u2	PROPN
ejpam-367	318	22	,	,	PUNCT
ejpam-367	318	23	u̇2	u̇2	PROPN
ejpam-367	318	24	,	,	PUNCT
ejpam-367	318	25	v2	v2	NOUN
ejpam-367	318	26	,	,	PUNCT
ejpam-367	318	27	v̇2)))d	v̇2)))d	X
ejpam-367	318	28	t	t	NOUN
ejpam-367	318	29	≧	≧	NUM
ejpam-367	318	30	−	−	PROPN
ejpam-367	319	1	∫	∫	PROPN
ejpam-367	320	1	i	i	PRON
ejpam-367	320	2	u2(t)t[λt	u2(t)t[λt	PROPN
ejpam-367	320	3	gu2(t	gu2(t	PROPN
ejpam-367	320	4	,	,	PUNCT
ejpam-367	320	5	u2	u2	PROPN
ejpam-367	320	6	,	,	PUNCT
ejpam-367	320	7	u̇2	u̇2	PROPN
ejpam-367	320	8	,	,	PUNCT
ejpam-367	320	9	v2	v2	PROPN
ejpam-367	320	10	,	,	PUNCT
ejpam-367	320	11	v̇2)−	v̇2)−	ADJ
ejpam-367	320	12	d(λt	d(λt	NOUN
ejpam-367	320	13	gu̇2(t	gu̇2(t	PROPN
ejpam-367	320	14	,	,	PUNCT
ejpam-367	320	15	u2	u2	PROPN
ejpam-367	320	16	,	,	PUNCT
ejpam-367	320	17	u̇2	u̇2	PROPN
ejpam-367	320	18	,	,	PUNCT
ejpam-367	320	19	v2	v2	PROPN
ejpam-367	320	20	,	,	PUNCT
ejpam-367	320	21	v̇2))]d	v̇2))]d	NOUN
ejpam-367	320	22	t	t	PROPN
ejpam-367	320	23	integrating	integrating	NOUN
ejpam-367	320	24	by	by	ADP
ejpam-367	320	25	parts	part	NOUN
ejpam-367	320	26	and	and	CCONJ
ejpam-367	320	27	using	use	VERB
ejpam-367	320	28	the	the	DET
ejpam-367	320	29	boundary	boundary	ADJ
ejpam-367	320	30	conditions	condition	NOUN
ejpam-367	320	31	which	which	PRON
ejpam-367	320	32	at	at	ADP
ejpam-367	320	33	t	t	PROPN
ejpam-367	320	34	=	=	SYM
ejpam-367	320	35	a	a	X
ejpam-367	320	36	,	,	PUNCT
ejpam-367	320	37	t	t	PROPN
ejpam-367	320	38	=	=	SYM
ejpam-367	320	39	b	b	NOUN
ejpam-367	320	40	gives	give	VERB
ejpam-367	320	41	η3	η3	NOUN
ejpam-367	320	42	=	=	PUNCT
ejpam-367	320	43	0	0	NUM
ejpam-367	320	44	,	,	PUNCT
ejpam-367	320	45	we	we	PRON
ejpam-367	320	46	have	have	VERB
ejpam-367	320	47	∫	∫	PROPN
ejpam-367	321	1	i	i	PRON
ejpam-367	321	2	{	{	PUNCT
ejpam-367	321	3	ηt	ηt	ADP
ejpam-367	321	4	3	3	NUM
ejpam-367	321	5	(	(	PUNCT
ejpam-367	321	6	λt	λt	ADP
ejpam-367	321	7	gu2(t	gu2(t	PROPN
ejpam-367	321	8	,	,	PUNCT
ejpam-367	321	9	u2	u2	PROPN
ejpam-367	321	10	,	,	PUNCT
ejpam-367	321	11	u̇2	u̇2	PROPN
ejpam-367	321	12	,	,	PUNCT
ejpam-367	321	13	v2	v2	NOUN
ejpam-367	321	14	,	,	PUNCT
ejpam-367	321	15	v̇2	v̇2	PROPN
ejpam-367	321	16	)	)	PUNCT
ejpam-367	321	17	+	+	CCONJ
ejpam-367	321	18	(	(	PUNCT
ejpam-367	321	19	dη3	dη3	PROPN
ejpam-367	321	20	)	)	PUNCT
ejpam-367	321	21	t	t	PROPN
ejpam-367	321	22	(	(	PUNCT
ejpam-367	321	23	λt	λt	ADP
ejpam-367	321	24	gu̇2(t	gu̇2(t	PROPN
ejpam-367	321	25	,	,	PUNCT
ejpam-367	321	26	u2	u2	PROPN
ejpam-367	321	27	,	,	PUNCT
ejpam-367	321	28	u̇2	u̇2	PROPN
ejpam-367	321	29	,	,	PUNCT
ejpam-367	321	30	v2	v2	PROPN
ejpam-367	321	31	,	,	PUNCT
ejpam-367	321	32	v̇2)))}d	v̇2)))}d	PROPN
ejpam-367	321	33	t	t	PROPN
ejpam-367	321	34	≧	≧	NOUN
ejpam-367	321	35	0	0	PUNCT
ejpam-367	322	1	because	because	SCONJ
ejpam-367	322	2	of	of	ADP
ejpam-367	322	3	the	the	DET
ejpam-367	322	4	partial	partial	ADJ
ejpam-367	322	5	pseudo	pseudo	NOUN
ejpam-367	322	6	-	-	NOUN
ejpam-367	322	7	invexity	invexity	NOUN
ejpam-367	322	8	of	of	ADP
ejpam-367	322	9	∫	∫	PROPN
ejpam-367	322	10	i	i	PRON
ejpam-367	322	11	λt	λt	ADP
ejpam-367	322	12	gu2	gu2	PROPN
ejpam-367	322	13	d	d	PROPN
ejpam-367	322	14	t	t	PROPN
ejpam-367	322	15	,	,	PUNCT
ejpam-367	322	16	this	this	PRON
ejpam-367	322	17	gives	give	VERB
ejpam-367	322	18	∫	∫	PROPN
ejpam-367	323	1	i	i	PRON
ejpam-367	323	2	λt	λt	ADP
ejpam-367	323	3	g(t	g(t	PROPN
ejpam-367	323	4	,	,	PUNCT
ejpam-367	323	5	x2	x2	PROPN
ejpam-367	323	6	,	,	PUNCT
ejpam-367	323	7	ẋ2	ẋ2	PROPN
ejpam-367	323	8	,	,	PUNCT
ejpam-367	323	9	y2	y2	NOUN
ejpam-367	323	10	,	,	PUNCT
ejpam-367	323	11	ẏ2)d	ẏ2)d	PROPN
ejpam-367	323	12	t	t	PROPN
ejpam-367	323	13	≧	≧	X
ejpam-367	323	14	∫	∫	PROPN
ejpam-367	324	1	i	i	PRON
ejpam-367	324	2	λt	λt	ADP
ejpam-367	324	3	g(t	g(t	PROPN
ejpam-367	324	4	,	,	PUNCT
ejpam-367	324	5	u2	u2	PROPN
ejpam-367	324	6	,	,	PUNCT
ejpam-367	324	7	u̇2	u̇2	PROPN
ejpam-367	324	8	,	,	PUNCT
ejpam-367	324	9	v2	v2	PROPN
ejpam-367	324	10	,	,	PUNCT
ejpam-367	324	11	v̇2)d	v̇2)d	PROPN
ejpam-367	324	12	t	t	PROPN
ejpam-367	324	13	(	(	PUNCT
ejpam-367	324	14	26	26	NUM
ejpam-367	324	15	)	)	PUNCT
ejpam-367	324	16	also	also	ADV
ejpam-367	324	17	from	from	ADP
ejpam-367	324	18	(	(	PUNCT
ejpam-367	324	19	4	4	NUM
ejpam-367	324	20	)	)	PUNCT
ejpam-367	324	21	together	together	ADV
ejpam-367	324	22	with	with	ADP
ejpam-367	324	23	(	(	PUNCT
ejpam-367	324	24	16	16	NUM
ejpam-367	324	25	)	)	PUNCT
ejpam-367	324	26	,	,	PUNCT
ejpam-367	324	27	we	we	PRON
ejpam-367	324	28	have	have	VERB
ejpam-367	324	29	∫	∫	PROPN
ejpam-367	325	1	i	i	PRON
ejpam-367	325	2	(	(	PUNCT
ejpam-367	325	3	ηt	ηt	ADP
ejpam-367	325	4	4	4	NUM
ejpam-367	325	5	(	(	PUNCT
ejpam-367	325	6	t	t	NOUN
ejpam-367	325	7	,	,	PUNCT
ejpam-367	325	8	v2	v2	PROPN
ejpam-367	325	9	,	,	PUNCT
ejpam-367	325	10	v̇2	v̇2	PROPN
ejpam-367	325	11	,	,	PUNCT
ejpam-367	325	12	y2	y2	NOUN
ejpam-367	325	13	,	,	PUNCT
ejpam-367	325	14	ẏ2	ẏ2	PROPN
ejpam-367	325	15	)	)	PUNCT
ejpam-367	326	1	+	+	NUM
ejpam-367	326	2	y2(t))(λt	y2(t))(λt	NOUN
ejpam-367	326	3	g	g	PROPN
ejpam-367	326	4	y2(t	y2(t	PROPN
ejpam-367	326	5	,	,	PUNCT
ejpam-367	326	6	x2	x2	PROPN
ejpam-367	326	7	,	,	PUNCT
ejpam-367	326	8	ẋ2	ẋ2	PROPN
ejpam-367	326	9	,	,	PUNCT
ejpam-367	326	10	y2	y2	NOUN
ejpam-367	326	11	,	,	PUNCT
ejpam-367	326	12	ẏ2	ẏ2	PROPN
ejpam-367	326	13	)	)	PUNCT
ejpam-367	326	14	−dλt	−dλt	NOUN
ejpam-367	327	1	g	g	PROPN
ejpam-367	327	2	ẏ2(t	ẏ2(t	PROPN
ejpam-367	327	3	,	,	PUNCT
ejpam-367	327	4	x2	x2	PROPN
ejpam-367	327	5	,	,	PUNCT
ejpam-367	327	6	ẋ2	ẋ2	PROPN
ejpam-367	327	7	,	,	PUNCT
ejpam-367	327	8	y2	y2	NOUN
ejpam-367	327	9	,	,	PUNCT
ejpam-367	327	10	ẏ2))d	ẏ2))d	NOUN
ejpam-367	327	11	t	t	PROPN
ejpam-367	327	12	≧	≧	NOUN
ejpam-367	327	13	0	0	PUNCT
ejpam-367	328	1	this	this	PRON
ejpam-367	328	2	implies	imply	VERB
ejpam-367	328	3	,	,	PUNCT
ejpam-367	328	4	∫	∫	PROPN
ejpam-367	328	5	i	i	PRON
ejpam-367	328	6	ηt	ηt	ADP
ejpam-367	328	7	4	4	NUM
ejpam-367	328	8	(	(	PUNCT
ejpam-367	328	9	λt	λt	ADP
ejpam-367	328	10	g	g	PROPN
ejpam-367	328	11	y2(t	y2(t	PROPN
ejpam-367	328	12	,	,	PUNCT
ejpam-367	328	13	x2	x2	PROPN
ejpam-367	328	14	,	,	PUNCT
ejpam-367	328	15	ẋ2	ẋ2	PROPN
ejpam-367	328	16	,	,	PUNCT
ejpam-367	328	17	y2	y2	NOUN
ejpam-367	328	18	,	,	PUNCT
ejpam-367	328	19	ẏ2))−	ẏ2))−	ADJ
ejpam-367	328	20	d(λt	d(λt	NOUN
ejpam-367	328	21	g	g	PROPN
ejpam-367	328	22	ẏ2(t	ẏ2(t	PROPN
ejpam-367	328	23	,	,	PUNCT
ejpam-367	328	24	x2	x2	PROPN
ejpam-367	328	25	,	,	PUNCT
ejpam-367	328	26	ẋ2	ẋ2	PROPN
ejpam-367	328	27	,	,	PUNCT
ejpam-367	328	28	y2	y2	NOUN
ejpam-367	328	29	,	,	PUNCT
ejpam-367	328	30	ẏ2))d	ẏ2))d	PROPN
ejpam-367	328	31	t	t	PROPN
ejpam-367	328	32	≦	≦	VERB
ejpam-367	328	33	−	−	PROPN
ejpam-367	329	1	∫	∫	INTJ
ejpam-367	330	1	i	i	PRON
ejpam-367	330	2	y2(t)t[λt	y2(t)t[λt	NOUN
ejpam-367	330	3	g	g	PROPN
ejpam-367	330	4	y2(t	y2(t	PROPN
ejpam-367	330	5	,	,	PUNCT
ejpam-367	330	6	x2	x2	PROPN
ejpam-367	330	7	,	,	PUNCT
ejpam-367	330	8	ẋ2	ẋ2	PROPN
ejpam-367	330	9	,	,	PUNCT
ejpam-367	330	10	y2	y2	NOUN
ejpam-367	330	11	,	,	PUNCT
ejpam-367	330	12	ẏ2)−	ẏ2)−	ADJ
ejpam-367	330	13	d(λt	d(λt	NOUN
ejpam-367	330	14	g	g	PROPN
ejpam-367	330	15	ẏ2(t	ẏ2(t	PROPN
ejpam-367	330	16	,	,	PUNCT
ejpam-367	330	17	x2	x2	PROPN
ejpam-367	330	18	,	,	PUNCT
ejpam-367	330	19	ẋ2	ẋ2	PROPN
ejpam-367	330	20	,	,	PUNCT
ejpam-367	330	21	y2	y2	PROPN
ejpam-367	330	22	,	,	PUNCT
ejpam-367	330	23	ẏ2))]d	ẏ2))]d	PROPN
ejpam-367	330	24	t	t	PROPN
ejpam-367	330	25	this	this	PRON
ejpam-367	330	26	in	in	ADP
ejpam-367	330	27	view	view	NOUN
ejpam-367	330	28	of	of	ADP
ejpam-367	330	29	(	(	PUNCT
ejpam-367	330	30	5	5	NUM
ejpam-367	330	31	)	)	PUNCT
ejpam-367	330	32	yields	yield	NOUN
ejpam-367	330	33	,	,	PUNCT
ejpam-367	330	34	∫	∫	PROPN
ejpam-367	330	35	i	i	PROPN
ejpam-367	330	36	ηt	ηt	ADP
ejpam-367	330	37	4	4	NUM
ejpam-367	330	38	{	{	PUNCT
ejpam-367	330	39	λt	λt	ADP
ejpam-367	330	40	g	g	PROPN
ejpam-367	330	41	y2(t	y2(t	PROPN
ejpam-367	330	42	,	,	PUNCT
ejpam-367	330	43	x2	x2	PROPN
ejpam-367	330	44	,	,	PUNCT
ejpam-367	330	45	ẋ2	ẋ2	PROPN
ejpam-367	330	46	,	,	PUNCT
ejpam-367	330	47	y2	y2	NOUN
ejpam-367	330	48	,	,	PUNCT
ejpam-367	330	49	ẏ2)−	ẏ2)−	ADJ
ejpam-367	330	50	d(λt	d(λt	NOUN
ejpam-367	330	51	g	g	PROPN
ejpam-367	330	52	ẏ2(t	ẏ2(t	PROPN
ejpam-367	330	53	,	,	PUNCT
ejpam-367	330	54	x2	x2	PROPN
ejpam-367	330	55	,	,	PUNCT
ejpam-367	330	56	ẋ2	ẋ2	PROPN
ejpam-367	330	57	,	,	PUNCT
ejpam-367	330	58	y2	y2	NOUN
ejpam-367	330	59	,	,	PUNCT
ejpam-367	330	60	ẏ2))}d	ẏ2))}d	PROPN
ejpam-367	330	61	t	t	PROPN
ejpam-367	330	62	≦	≦	PROPN
ejpam-367	330	63	0	0	NUM
ejpam-367	330	64	i.	i.	PROPN
ejpam-367	330	65	husain	husain	PROPN
ejpam-367	330	66	and	and	CCONJ
ejpam-367	330	67	r.	r.	PROPN
ejpam-367	330	68	mattoo	mattoo	PROPN
ejpam-367	330	69	/	/	SYM
ejpam-367	330	70	eur	eur	PROPN
ejpam-367	330	71	.	.	PUNCT
ejpam-367	331	1	j.	j.	PROPN
ejpam-367	331	2	pure	pure	PROPN
ejpam-367	331	3	appl	appl	PROPN
ejpam-367	331	4	.	.	PROPN
ejpam-367	331	5	math	math	PROPN
ejpam-367	331	6	,	,	PUNCT
ejpam-367	331	7	2	2	NUM
ejpam-367	331	8	(	(	PUNCT
ejpam-367	331	9	2009	2009	NUM
ejpam-367	331	10	)	)	PUNCT
ejpam-367	331	11	,	,	PUNCT
ejpam-367	331	12	(	(	PUNCT
ejpam-367	331	13	578	578	NUM
ejpam-367	331	14	-	-	SYM
ejpam-367	331	15	603	603	NUM
ejpam-367	331	16	)	)	PUNCT
ejpam-367	331	17	590	590	NUM
ejpam-367	331	18	on	on	ADP
ejpam-367	331	19	integrating	integrate	VERB
ejpam-367	331	20	by	by	ADP
ejpam-367	331	21	parts	part	NOUN
ejpam-367	331	22	and	and	CCONJ
ejpam-367	331	23	using	use	VERB
ejpam-367	331	24	the	the	DET
ejpam-367	331	25	boundary	boundary	ADJ
ejpam-367	331	26	conditions	condition	NOUN
ejpam-367	331	27	which	which	PRON
ejpam-367	331	28	at	at	ADP
ejpam-367	331	29	t	t	PROPN
ejpam-367	331	30	=	=	SYM
ejpam-367	331	31	a	a	X
ejpam-367	331	32	,	,	PUNCT
ejpam-367	331	33	t	t	PROPN
ejpam-367	331	34	=	=	SYM
ejpam-367	331	35	b	b	NOUN
ejpam-367	331	36	gives	give	VERB
ejpam-367	331	37	η4	η4	VERB
ejpam-367	331	38	=	=	SYM
ejpam-367	331	39	0	0	NUM
ejpam-367	331	40	,	,	PUNCT
ejpam-367	331	41	we	we	PRON
ejpam-367	331	42	have	have	VERB
ejpam-367	331	43	,	,	PUNCT
ejpam-367	331	44	∫	∫	PROPN
ejpam-367	332	1	i	i	PROPN
ejpam-367	332	2	ηt	ηt	ADP
ejpam-367	332	3	4	4	NUM
ejpam-367	332	4	{	{	PUNCT
ejpam-367	332	5	λt	λt	ADP
ejpam-367	332	6	g	g	PROPN
ejpam-367	332	7	y2(t	y2(t	PROPN
ejpam-367	332	8	,	,	PUNCT
ejpam-367	332	9	x2	x2	PROPN
ejpam-367	332	10	,	,	PUNCT
ejpam-367	332	11	ẋ2	ẋ2	PROPN
ejpam-367	332	12	,	,	PUNCT
ejpam-367	332	13	y2	y2	NOUN
ejpam-367	332	14	,	,	PUNCT
ejpam-367	332	15	ẏ2	ẏ2	PROPN
ejpam-367	332	16	)	)	PUNCT
ejpam-367	332	17	+	+	CCONJ
ejpam-367	332	18	(	(	PUNCT
ejpam-367	332	19	dη4	dη4	NOUN
ejpam-367	332	20	)	)	PUNCT
ejpam-367	332	21	t	t	NOUN
ejpam-367	332	22	(	(	PUNCT
ejpam-367	332	23	λt	λt	ADP
ejpam-367	332	24	g	g	PROPN
ejpam-367	332	25	ẏ2(t	ẏ2(t	PROPN
ejpam-367	332	26	,	,	PUNCT
ejpam-367	332	27	x2	x2	PROPN
ejpam-367	332	28	,	,	PUNCT
ejpam-367	332	29	ẋ2	ẋ2	PROPN
ejpam-367	332	30	,	,	PUNCT
ejpam-367	332	31	y2	y2	NOUN
ejpam-367	332	32	,	,	PUNCT
ejpam-367	332	33	ẏ2))}d	ẏ2))}d	PROPN
ejpam-367	332	34	t	t	PROPN
ejpam-367	332	35	≦	≦	PROPN
ejpam-367	332	36	0	0	PUNCT
ejpam-367	332	37	because	because	SCONJ
ejpam-367	332	38	of	of	ADP
ejpam-367	332	39	partial	partial	ADJ
ejpam-367	332	40	pseudo	pseudo	NOUN
ejpam-367	332	41	-	-	NOUN
ejpam-367	332	42	incavity	incavity	NOUN
ejpam-367	332	43	of	of	ADP
ejpam-367	332	44	∫	∫	PROPN
ejpam-367	332	45	i	i	NOUN
ejpam-367	332	46	λt	λt	ADP
ejpam-367	332	47	g	g	PROPN
ejpam-367	333	1	y2	y2	PROPN
ejpam-367	333	2	d	d	PROPN
ejpam-367	333	3	t	t	PROPN
ejpam-367	333	4	,	,	PUNCT
ejpam-367	333	5	we	we	PRON
ejpam-367	333	6	have	have	VERB
ejpam-367	333	7	∫	∫	PROPN
ejpam-367	334	1	i	i	PRON
ejpam-367	334	2	(	(	PUNCT
ejpam-367	334	3	λt	λt	ADP
ejpam-367	334	4	g(t	g(t	PROPN
ejpam-367	334	5	,	,	PUNCT
ejpam-367	334	6	x2	x2	PROPN
ejpam-367	334	7	,	,	PUNCT
ejpam-367	334	8	ẋ2	ẋ2	PROPN
ejpam-367	334	9	,	,	PUNCT
ejpam-367	334	10	v2	v2	PROPN
ejpam-367	334	11	,	,	PUNCT
ejpam-367	334	12	v̇2))d	v̇2))d	NOUN
ejpam-367	334	13	t	t	PROPN
ejpam-367	334	14	≦	≦	VERB
ejpam-367	334	15	∫	∫	INTJ
ejpam-367	334	16	i	i	PRON
ejpam-367	334	17	(	(	PUNCT
ejpam-367	334	18	λt	λt	ADP
ejpam-367	334	19	g(t	g(t	PROPN
ejpam-367	334	20	,	,	PUNCT
ejpam-367	334	21	x2	x2	PROPN
ejpam-367	334	22	,	,	PUNCT
ejpam-367	334	23	ẋ2	ẋ2	PROPN
ejpam-367	334	24	,	,	PUNCT
ejpam-367	334	25	y2	y2	NOUN
ejpam-367	334	26	,	,	PUNCT
ejpam-367	334	27	ẏ2))d	ẏ2))d	PROPN
ejpam-367	334	28	t	t	PROPN
ejpam-367	334	29	(	(	PUNCT
ejpam-367	334	30	27	27	NUM
ejpam-367	334	31	)	)	PUNCT
ejpam-367	334	32	from	from	ADP
ejpam-367	334	33	(	(	PUNCT
ejpam-367	334	34	26	26	NUM
ejpam-367	334	35	)	)	PUNCT
ejpam-367	334	36	and	and	CCONJ
ejpam-367	334	37	(	(	PUNCT
ejpam-367	334	38	27	27	NUM
ejpam-367	334	39	)	)	PUNCT
ejpam-367	334	40	,	,	PUNCT
ejpam-367	334	41	we	we	PRON
ejpam-367	334	42	get	get	VERB
ejpam-367	334	43	,	,	PUNCT
ejpam-367	334	44	∫	∫	PROPN
ejpam-367	335	1	i	i	PRON
ejpam-367	335	2	(	(	PUNCT
ejpam-367	335	3	λt	λt	ADP
ejpam-367	335	4	g(t	g(t	PROPN
ejpam-367	335	5	,	,	PUNCT
ejpam-367	335	6	x2	x2	PROPN
ejpam-367	335	7	,	,	PUNCT
ejpam-367	335	8	ẋ2	ẋ2	PROPN
ejpam-367	335	9	,	,	PUNCT
ejpam-367	335	10	y2	y2	NOUN
ejpam-367	335	11	,	,	PUNCT
ejpam-367	335	12	ẏ2))d	ẏ2))d	NOUN
ejpam-367	335	13	t	t	PROPN
ejpam-367	335	14	≧	≧	X
ejpam-367	335	15	∫	∫	PROPN
ejpam-367	336	1	i	i	PRON
ejpam-367	336	2	(	(	PUNCT
ejpam-367	336	3	λt	λt	ADP
ejpam-367	336	4	g(t	g(t	PROPN
ejpam-367	336	5	,	,	PUNCT
ejpam-367	336	6	u2	u2	PROPN
ejpam-367	336	7	,	,	PUNCT
ejpam-367	336	8	u̇2	u̇2	PROPN
ejpam-367	336	9	,	,	PUNCT
ejpam-367	336	10	v2	v2	NOUN
ejpam-367	336	11	,	,	PUNCT
ejpam-367	336	12	v̇2))d	v̇2))d	NOUN
ejpam-367	336	13	t	t	PROPN
ejpam-367	336	14	(	(	PUNCT
ejpam-367	336	15	28	28	NUM
ejpam-367	336	16	)	)	PUNCT
ejpam-367	336	17	combining	combine	VERB
ejpam-367	336	18	(	(	PUNCT
ejpam-367	336	19	25	25	NUM
ejpam-367	336	20	)	)	PUNCT
ejpam-367	336	21	and	and	CCONJ
ejpam-367	336	22	(	(	PUNCT
ejpam-367	336	23	28	28	NUM
ejpam-367	336	24	)	)	PUNCT
ejpam-367	336	25	,	,	PUNCT
ejpam-367	336	26	we	we	PRON
ejpam-367	336	27	get	get	VERB
ejpam-367	336	28	∫	∫	PROPN
ejpam-367	337	1	i	i	PRON
ejpam-367	337	2	{	{	PUNCT
ejpam-367	337	3	λt	λt	ADP
ejpam-367	337	4	f	f	X
ejpam-367	337	5	(	(	PUNCT
ejpam-367	337	6	t	t	PROPN
ejpam-367	337	7	,	,	PUNCT
ejpam-367	337	8	x1	x1	PROPN
ejpam-367	337	9	,	,	PUNCT
ejpam-367	337	10	ẋ1	ẋ1	PROPN
ejpam-367	337	11	,	,	PUNCT
ejpam-367	337	12	y1	y1	PROPN
ejpam-367	337	13	,	,	PUNCT
ejpam-367	337	14	ẏ1)−	ẏ1)−	PROPN
ejpam-367	337	15	y1(t)t(λt	y1(t)t(λt	PROPN
ejpam-367	338	1	f	f	X
ejpam-367	338	2	y1(t	y1(t	PROPN
ejpam-367	338	3	,	,	PUNCT
ejpam-367	338	4	x1	x1	PROPN
ejpam-367	338	5	,	,	PUNCT
ejpam-367	338	6	ẋ1	ẋ1	PROPN
ejpam-367	338	7	,	,	PUNCT
ejpam-367	338	8	y1	y1	PROPN
ejpam-367	338	9	,	,	PUNCT
ejpam-367	338	10	ẏ1	ẏ1	PROPN
ejpam-367	338	11	)	)	PUNCT
ejpam-367	338	12	)	)	PUNCT
ejpam-367	338	13	−dλt	−dλt	NOUN
ejpam-367	339	1	f	f	PROPN
ejpam-367	339	2	ẏ1(t	ẏ1(t	PROPN
ejpam-367	339	3	,	,	PUNCT
ejpam-367	339	4	x1	x1	PROPN
ejpam-367	339	5	,	,	PUNCT
ejpam-367	339	6	ẋ1	ẋ1	PROPN
ejpam-367	339	7	,	,	PUNCT
ejpam-367	339	8	y1	y1	PROPN
ejpam-367	339	9	,	,	PUNCT
ejpam-367	339	10	ẏ1	ẏ1	PROPN
ejpam-367	339	11	)	)	PUNCT
ejpam-367	340	1	+	+	ADP
ejpam-367	340	2	λt	λt	ADP
ejpam-367	340	3	g(t	g(t	PROPN
ejpam-367	340	4	,	,	PUNCT
ejpam-367	340	5	x2	x2	PROPN
ejpam-367	340	6	,	,	PUNCT
ejpam-367	340	7	ẋ2	ẋ2	PROPN
ejpam-367	340	8	,	,	PUNCT
ejpam-367	340	9	y2	y2	PROPN
ejpam-367	340	10	,	,	PUNCT
ejpam-367	340	11	ẏ2)}d	ẏ2)}d	PROPN
ejpam-367	340	12	t	t	PROPN
ejpam-367	340	13	≧	≧	X
ejpam-367	341	1	∫	∫	PROPN
ejpam-367	342	1	i	i	PRON
ejpam-367	342	2	{	{	PUNCT
ejpam-367	342	3	λt	λt	ADP
ejpam-367	342	4	f	f	X
ejpam-367	342	5	(	(	PUNCT
ejpam-367	342	6	t	t	PROPN
ejpam-367	342	7	,	,	PUNCT
ejpam-367	342	8	u1	u1	PROPN
ejpam-367	342	9	,	,	PUNCT
ejpam-367	342	10	u̇1	u̇1	PROPN
ejpam-367	342	11	,	,	PUNCT
ejpam-367	342	12	v1	v1	NOUN
ejpam-367	342	13	,	,	PUNCT
ejpam-367	342	14	v̇1)−	v̇1)−	PROPN
ejpam-367	342	15	u1(t)t(λt	u1(t)t(λt	NOUN
ejpam-367	342	16	fx1(t	fx1(t	PROPN
ejpam-367	342	17	,	,	PUNCT
ejpam-367	342	18	u1	u1	PROPN
ejpam-367	342	19	,	,	PUNCT
ejpam-367	342	20	u̇1	u̇1	PROPN
ejpam-367	342	21	,	,	PUNCT
ejpam-367	342	22	v1	v1	NOUN
ejpam-367	342	23	,	,	PUNCT
ejpam-367	342	24	v̇1	v̇1	NOUN
ejpam-367	342	25	)	)	PUNCT
ejpam-367	342	26	)	)	PUNCT
ejpam-367	342	27	−dλt	−dλt	NOUN
ejpam-367	343	1	f	f	PROPN
ejpam-367	343	2	ẋ1(t	ẋ1(t	PROPN
ejpam-367	343	3	,	,	PUNCT
ejpam-367	343	4	u1	u1	PROPN
ejpam-367	343	5	,	,	PUNCT
ejpam-367	343	6	u̇1	u̇1	PROPN
ejpam-367	343	7	,	,	PUNCT
ejpam-367	343	8	v1	v1	NOUN
ejpam-367	343	9	,	,	PUNCT
ejpam-367	343	10	v̇1	v̇1	PROPN
ejpam-367	343	11	)	)	PUNCT
ejpam-367	343	12	+	+	PROPN
ejpam-367	343	13	λt	λt	X
ejpam-367	343	14	g(t	g(t	PROPN
ejpam-367	343	15	,	,	PUNCT
ejpam-367	343	16	x2	x2	PROPN
ejpam-367	343	17	,	,	PUNCT
ejpam-367	343	18	ẋ2	ẋ2	PROPN
ejpam-367	343	19	,	,	PUNCT
ejpam-367	343	20	y2	y2	PROPN
ejpam-367	343	21	,	,	PUNCT
ejpam-367	343	22	ẏ2)}d	ẏ2)}d	PROPN
ejpam-367	343	23	t	t	PROPN
ejpam-367	343	24	this	this	PRON
ejpam-367	343	25	implies	imply	VERB
ejpam-367	343	26	,	,	PUNCT
ejpam-367	343	27	λt	λt	ADP
ejpam-367	343	28	∫	∫	PROPN
ejpam-367	344	1	i	i	PRON
ejpam-367	344	2	{	{	PUNCT
ejpam-367	344	3	f	f	PROPN
ejpam-367	344	4	(	(	PUNCT
ejpam-367	344	5	t	t	PROPN
ejpam-367	344	6	,	,	PUNCT
ejpam-367	344	7	x1	x1	PROPN
ejpam-367	344	8	,	,	PUNCT
ejpam-367	344	9	ẋ1	ẋ1	PROPN
ejpam-367	344	10	,	,	PUNCT
ejpam-367	344	11	y1	y1	PROPN
ejpam-367	344	12	,	,	PUNCT
ejpam-367	344	13	ẏ1	ẏ1	PROPN
ejpam-367	344	14	)	)	PUNCT
ejpam-367	344	15	+	+	CCONJ
ejpam-367	344	16	g(t	g(t	PROPN
ejpam-367	344	17	,	,	PUNCT
ejpam-367	344	18	x2	x2	PROPN
ejpam-367	344	19	,	,	PUNCT
ejpam-367	344	20	ẋ2	ẋ2	PROPN
ejpam-367	344	21	,	,	PUNCT
ejpam-367	344	22	y2	y2	NOUN
ejpam-367	344	23	,	,	PUNCT
ejpam-367	344	24	ẏ2	ẏ2	PROPN
ejpam-367	344	25	)	)	PUNCT
ejpam-367	344	26	−y1(t)t(λt	−y1(t)t(λt	PROPN
ejpam-367	344	27	f	f	X
ejpam-367	344	28	y1(t	y1(t	INTJ
ejpam-367	344	29	,	,	PUNCT
ejpam-367	344	30	x1	x1	PROPN
ejpam-367	344	31	,	,	PUNCT
ejpam-367	344	32	ẋ1	ẋ1	PROPN
ejpam-367	344	33	,	,	PUNCT
ejpam-367	344	34	y1	y1	PROPN
ejpam-367	344	35	,	,	PUNCT
ejpam-367	344	36	ẏ1)−dλt	ẏ1)−dλt	PROPN
ejpam-367	344	37	f	f	PROPN
ejpam-367	344	38	ẏ1(t	ẏ1(t	PROPN
ejpam-367	344	39	,	,	PUNCT
ejpam-367	344	40	x1	x1	PROPN
ejpam-367	344	41	,	,	PUNCT
ejpam-367	344	42	ẋ1	ẋ1	PROPN
ejpam-367	344	43	,	,	PUNCT
ejpam-367	344	44	y1	y1	PROPN
ejpam-367	344	45	,	,	PUNCT
ejpam-367	344	46	ẏ1))e}d	ẏ1))e}d	PROPN
ejpam-367	344	47	t	t	PROPN
ejpam-367	344	48	≧	≧	PUNCT
ejpam-367	344	49	λt	λt	ADP
ejpam-367	344	50	∫	∫	PROPN
ejpam-367	345	1	i	i	PRON
ejpam-367	345	2	{	{	PUNCT
ejpam-367	345	3	f	f	PROPN
ejpam-367	345	4	(	(	PUNCT
ejpam-367	345	5	t	t	PROPN
ejpam-367	345	6	,	,	PUNCT
ejpam-367	345	7	u1	u1	PROPN
ejpam-367	345	8	,	,	PUNCT
ejpam-367	345	9	u̇1	u̇1	PROPN
ejpam-367	345	10	,	,	PUNCT
ejpam-367	345	11	v1	v1	NOUN
ejpam-367	345	12	,	,	PUNCT
ejpam-367	345	13	v̇1	v̇1	PROPN
ejpam-367	345	14	)	)	PUNCT
ejpam-367	345	15	+	+	CCONJ
ejpam-367	345	16	g(t	g(t	PROPN
ejpam-367	345	17	,	,	PUNCT
ejpam-367	345	18	u2	u2	PROPN
ejpam-367	345	19	,	,	PUNCT
ejpam-367	345	20	u̇2	u̇2	PROPN
ejpam-367	345	21	,	,	PUNCT
ejpam-367	345	22	v2	v2	NOUN
ejpam-367	345	23	,	,	PUNCT
ejpam-367	345	24	v̇2	v̇2	NOUN
ejpam-367	345	25	)	)	PUNCT
ejpam-367	345	26	−u1(t)t(λt	−u1(t)t(λt	NOUN
ejpam-367	345	27	fx1(t	fx1(t	PROPN
ejpam-367	345	28	,	,	PUNCT
ejpam-367	345	29	u1	u1	PROPN
ejpam-367	345	30	,	,	PUNCT
ejpam-367	345	31	u̇1	u̇1	PROPN
ejpam-367	345	32	,	,	PUNCT
ejpam-367	345	33	v1	v1	NOUN
ejpam-367	345	34	,	,	PUNCT
ejpam-367	345	35	v̇1)−dλt	v̇1)−dλt	PROPN
ejpam-367	345	36	f	f	PROPN
ejpam-367	345	37	ẋ1(t	ẋ1(t	PROPN
ejpam-367	345	38	,	,	PUNCT
ejpam-367	345	39	u1	u1	PROPN
ejpam-367	345	40	,	,	PUNCT
ejpam-367	345	41	u̇1	u̇1	PROPN
ejpam-367	345	42	,	,	PUNCT
ejpam-367	345	43	v1	v1	NOUN
ejpam-367	345	44	,	,	PUNCT
ejpam-367	345	45	v̇1))e}d	v̇1))e}d	X
ejpam-367	345	46	t	t	PROPN
ejpam-367	345	47	this	this	PRON
ejpam-367	345	48	implies	imply	VERB
ejpam-367	345	49	,	,	PUNCT
ejpam-367	345	50	∫	∫	PROPN
ejpam-367	345	51	i	i	PRON
ejpam-367	345	52	{	{	PUNCT
ejpam-367	345	53	f	f	PROPN
ejpam-367	345	54	(	(	PUNCT
ejpam-367	345	55	t	t	PROPN
ejpam-367	345	56	,	,	PUNCT
ejpam-367	345	57	x1	x1	PROPN
ejpam-367	345	58	,	,	PUNCT
ejpam-367	345	59	ẋ1	ẋ1	PROPN
ejpam-367	345	60	,	,	PUNCT
ejpam-367	345	61	y1	y1	PROPN
ejpam-367	345	62	,	,	PUNCT
ejpam-367	345	63	ẏ1	ẏ1	PROPN
ejpam-367	345	64	)	)	PUNCT
ejpam-367	346	1	+	+	CCONJ
ejpam-367	346	2	g(t	g(t	PROPN
ejpam-367	346	3	,	,	PUNCT
ejpam-367	346	4	x2	x2	PROPN
ejpam-367	346	5	,	,	PUNCT
ejpam-367	346	6	ẋ2	ẋ2	PROPN
ejpam-367	346	7	,	,	PUNCT
ejpam-367	346	8	y2	y2	NOUN
ejpam-367	346	9	,	,	PUNCT
ejpam-367	346	10	ẏ2	ẏ2	PROPN
ejpam-367	346	11	)	)	PUNCT
ejpam-367	346	12	i.	i.	PROPN
ejpam-367	346	13	husain	husain	PROPN
ejpam-367	346	14	and	and	CCONJ
ejpam-367	346	15	r.	r.	PROPN
ejpam-367	346	16	mattoo	mattoo	PROPN
ejpam-367	346	17	/	/	SYM
ejpam-367	346	18	eur	eur	PROPN
ejpam-367	346	19	.	.	PUNCT
ejpam-367	347	1	j.	j.	PROPN
ejpam-367	347	2	pure	pure	PROPN
ejpam-367	347	3	appl	appl	PROPN
ejpam-367	347	4	.	.	PROPN
ejpam-367	347	5	math	math	PROPN
ejpam-367	347	6	,	,	PUNCT
ejpam-367	347	7	2	2	NUM
ejpam-367	347	8	(	(	PUNCT
ejpam-367	347	9	2009	2009	NUM
ejpam-367	347	10	)	)	PUNCT
ejpam-367	347	11	,	,	PUNCT
ejpam-367	347	12	(	(	PUNCT
ejpam-367	347	13	578	578	NUM
ejpam-367	347	14	-	-	SYM
ejpam-367	347	15	603	603	NUM
ejpam-367	347	16	)	)	PUNCT
ejpam-367	347	17	591	591	NUM
ejpam-367	347	18	−y1(t)t(λt	−y1(t)t(λt	NOUN
ejpam-367	347	19	f	f	X
ejpam-367	347	20	y1(t	y1(t	INTJ
ejpam-367	347	21	,	,	PUNCT
ejpam-367	347	22	x1	x1	PROPN
ejpam-367	347	23	,	,	PUNCT
ejpam-367	347	24	ẋ1	ẋ1	PROPN
ejpam-367	347	25	,	,	PUNCT
ejpam-367	347	26	y1	y1	PROPN
ejpam-367	347	27	,	,	PUNCT
ejpam-367	347	28	ẏ1)−dλt	ẏ1)−dλt	PROPN
ejpam-367	347	29	f	f	PROPN
ejpam-367	347	30	ẏ1(t	ẏ1(t	PROPN
ejpam-367	347	31	,	,	PUNCT
ejpam-367	347	32	x1	x1	PROPN
ejpam-367	347	33	,	,	PUNCT
ejpam-367	347	34	ẋ1	ẋ1	PROPN
ejpam-367	347	35	,	,	PUNCT
ejpam-367	347	36	y1	y1	PROPN
ejpam-367	347	37	,	,	PUNCT
ejpam-367	347	38	ẏ1))e}d	ẏ1))e}d	PROPN
ejpam-367	347	39	t	t	PROPN
ejpam-367	347	40	6≤	6≤	NUM
ejpam-367	348	1	∫	∫	INTJ
ejpam-367	349	1	i	i	PRON
ejpam-367	349	2	{	{	PUNCT
ejpam-367	349	3	f	f	PROPN
ejpam-367	349	4	(	(	PUNCT
ejpam-367	349	5	t	t	PROPN
ejpam-367	349	6	,	,	PUNCT
ejpam-367	349	7	u1	u1	PROPN
ejpam-367	349	8	,	,	PUNCT
ejpam-367	349	9	u̇1	u̇1	PROPN
ejpam-367	349	10	,	,	PUNCT
ejpam-367	349	11	v1	v1	NOUN
ejpam-367	349	12	,	,	PUNCT
ejpam-367	349	13	v̇1	v̇1	PROPN
ejpam-367	349	14	)	)	PUNCT
ejpam-367	349	15	+	+	CCONJ
ejpam-367	349	16	g(t	g(t	PROPN
ejpam-367	349	17	,	,	PUNCT
ejpam-367	349	18	u2	u2	PROPN
ejpam-367	349	19	,	,	PUNCT
ejpam-367	349	20	u̇2	u̇2	PROPN
ejpam-367	349	21	,	,	PUNCT
ejpam-367	349	22	v2	v2	NOUN
ejpam-367	349	23	,	,	PUNCT
ejpam-367	349	24	v̇2	v̇2	NOUN
ejpam-367	349	25	)	)	PUNCT
ejpam-367	349	26	−u1(t)t(λt	−u1(t)t(λt	NOUN
ejpam-367	349	27	fx1(t	fx1(t	PROPN
ejpam-367	349	28	,	,	PUNCT
ejpam-367	349	29	u1	u1	PROPN
ejpam-367	349	30	,	,	PUNCT
ejpam-367	349	31	u̇1	u̇1	PROPN
ejpam-367	349	32	,	,	PUNCT
ejpam-367	349	33	v1	v1	NOUN
ejpam-367	349	34	,	,	PUNCT
ejpam-367	349	35	v̇1)−dλt	v̇1)−dλt	PROPN
ejpam-367	349	36	f	f	PROPN
ejpam-367	349	37	ẋ1(t	ẋ1(t	PROPN
ejpam-367	349	38	,	,	PUNCT
ejpam-367	349	39	u1	u1	PROPN
ejpam-367	349	40	,	,	PUNCT
ejpam-367	349	41	u̇1	u̇1	PROPN
ejpam-367	349	42	,	,	PUNCT
ejpam-367	349	43	v1	v1	NOUN
ejpam-367	349	44	,	,	PUNCT
ejpam-367	349	45	v̇1))e}d	v̇1))e}d	X
ejpam-367	349	46	t	t	PROPN
ejpam-367	349	47	this	this	PRON
ejpam-367	349	48	was	be	AUX
ejpam-367	349	49	to	to	PART
ejpam-367	349	50	be	be	AUX
ejpam-367	349	51	proved	prove	VERB
ejpam-367	349	52	.	.	PUNCT
ejpam-367	350	1	theorem	theorem	ADJ
ejpam-367	350	2	2	2	NUM
ejpam-367	350	3	(	(	PUNCT
ejpam-367	350	4	strong	strong	ADJ
ejpam-367	350	5	duality	duality	NOUN
ejpam-367	350	6	)	)	PUNCT
ejpam-367	350	7	.	.	PUNCT
ejpam-367	351	1	let	let	AUX
ejpam-367	351	2	(	(	PUNCT
ejpam-367	351	3	x̄1	x̄1	NOUN
ejpam-367	351	4	,	,	PUNCT
ejpam-367	351	5	x̄2	x̄2	PROPN
ejpam-367	351	6	,	,	PUNCT
ejpam-367	351	7	ȳ1	ȳ1	PROPN
ejpam-367	351	8	,	,	PUNCT
ejpam-367	351	9	ȳ2	ȳ2	NOUN
ejpam-367	351	10	,	,	PUNCT
ejpam-367	351	11	λ̄	λ̄	PRON
ejpam-367	351	12	)	)	PUNCT
ejpam-367	351	13	be	be	VERB
ejpam-367	351	14	an	an	DET
ejpam-367	351	15	efficient	efficient	ADJ
ejpam-367	351	16	solution	solution	NOUN
ejpam-367	351	17	of	of	ADP
ejpam-367	351	18	(	(	PUNCT
ejpam-367	351	19	mix	mix	VERB
ejpam-367	351	20	sp	sp	NOUN
ejpam-367	351	21	)	)	PUNCT
ejpam-367	351	22	.	.	PUNCT
ejpam-367	352	1	let	let	VERB
ejpam-367	352	2	λ=	λ=	NOUN
ejpam-367	352	3	λ̄	λ̄	NOUN
ejpam-367	352	4	be	be	AUX
ejpam-367	352	5	fixed	fix	VERB
ejpam-367	352	6	in	in	ADP
ejpam-367	352	7	(	(	PUNCT
ejpam-367	352	8	mix	mix	VERB
ejpam-367	352	9	sd	sd	NOUN
ejpam-367	352	10	)	)	PUNCT
ejpam-367	352	11	and	and	CCONJ
ejpam-367	352	12	(	(	PUNCT
ejpam-367	352	13	c1	c1	PROPN
ejpam-367	352	14	)	)	PUNCT
ejpam-367	352	15	∫	∫	PROPN
ejpam-367	353	1	i	i	PRON
ejpam-367	353	2	[	[	X
ejpam-367	353	3	{	{	PUNCT
ejpam-367	353	4	(	(	PUNCT
ejpam-367	353	5	φ1(t))t	φ1(t))t	PROPN
ejpam-367	353	6	(	(	PUNCT
ejpam-367	353	7	λt	λt	ADP
ejpam-367	353	8	f	f	PROPN
ejpam-367	353	9	y1	y1	PROPN
ejpam-367	353	10	y1	y1	PROPN
ejpam-367	353	11	−	−	PROPN
ejpam-367	353	12	dλt	dλt	NOUN
ejpam-367	354	1	f	f	NOUN
ejpam-367	354	2	y1	y1	INTJ
ejpam-367	355	1	ẏ1)−	ẏ1)−	PROPN
ejpam-367	356	1	dφ1(t)t(−dλt	dφ1(t)t(−dλt	NOUN
ejpam-367	356	2	f	f	PROPN
ejpam-367	356	3	ẏ1	ẏ1	PROPN
ejpam-367	356	4	ẏ1	ẏ1	PROPN
ejpam-367	356	5	)	)	PUNCT
ejpam-367	357	1	+	+	NOUN
ejpam-367	357	2	d2φ1(t)t(−λt	d2φ1(t)t(−λt	NOUN
ejpam-367	357	3	f	f	PROPN
ejpam-367	357	4	ẏ1	ẏ1	PROPN
ejpam-367	357	5	ẏ1)}φ1(t)]d	ẏ1)}φ1(t)]d	PROPN
ejpam-367	357	6	t	t	PROPN
ejpam-367	357	7	>	>	X
ejpam-367	357	8	0	0	NUM
ejpam-367	357	9	,	,	PUNCT
ejpam-367	357	10	and	and	CCONJ
ejpam-367	357	11	∫	∫	NOUN
ejpam-367	358	1	i	i	PRON
ejpam-367	358	2	[	[	X
ejpam-367	358	3	{	{	PUNCT
ejpam-367	358	4	(	(	PUNCT
ejpam-367	358	5	φ2(t))t	φ2(t))t	NOUN
ejpam-367	358	6	(	(	PUNCT
ejpam-367	358	7	λt	λt	ADP
ejpam-367	358	8	g	g	PROPN
ejpam-367	358	9	y2	y2	NOUN
ejpam-367	358	10	y2	y2	PROPN
ejpam-367	359	1	−	−	PROPN
ejpam-367	359	2	dλt	dλt	NOUN
ejpam-367	359	3	g	g	NOUN
ejpam-367	359	4	y2	y2	PROPN
ejpam-367	359	5	ẏ2)−	ẏ2)−	VERB
ejpam-367	359	6	dφ2(t)t(−dλt	dφ2(t)t(−dλt	PROPN
ejpam-367	359	7	g	g	PROPN
ejpam-367	359	8	ẏ2	ẏ2	PROPN
ejpam-367	359	9	ẏ2	ẏ2	PROPN
ejpam-367	359	10	)	)	PUNCT
ejpam-367	360	1	+	+	NOUN
ejpam-367	360	2	d2φ2(t)t(−λt	d2φ2(t)t(−λt	NOUN
ejpam-367	360	3	g	g	NOUN
ejpam-367	360	4	ẏ2	ẏ2	PROPN
ejpam-367	360	5	ẏ2)}φ2(t)]d	ẏ2)}φ2(t)]d	PROPN
ejpam-367	360	6	t	t	PROPN
ejpam-367	360	7	>	>	X
ejpam-367	360	8	0	0	NUM
ejpam-367	360	9	,	,	PUNCT
ejpam-367	360	10	(	(	PUNCT
ejpam-367	360	11	c2	c2	PROPN
ejpam-367	360	12	)	)	PUNCT
ejpam-367	360	13	∫	∫	PROPN
ejpam-367	361	1	i	i	PRON
ejpam-367	361	2	[	[	X
ejpam-367	361	3	{	{	PUNCT
ejpam-367	361	4	(	(	PUNCT
ejpam-367	361	5	φ1(t))t	φ1(t))t	PROPN
ejpam-367	361	6	(	(	PUNCT
ejpam-367	361	7	λt	λt	ADP
ejpam-367	361	8	f	f	PROPN
ejpam-367	361	9	y1	y1	PROPN
ejpam-367	361	10	y1	y1	PROPN
ejpam-367	361	11	−	−	PROPN
ejpam-367	361	12	dλt	dλt	NOUN
ejpam-367	362	1	f	f	NOUN
ejpam-367	362	2	y1	y1	INTJ
ejpam-367	363	1	ẏ1)−	ẏ1)−	PROPN
ejpam-367	364	1	dφ1(t)t(−dλt	dφ1(t)t(−dλt	NOUN
ejpam-367	364	2	f	f	PROPN
ejpam-367	364	3	ẏ1	ẏ1	PROPN
ejpam-367	364	4	ẏ1	ẏ1	PROPN
ejpam-367	364	5	)	)	PUNCT
ejpam-367	365	1	+	+	NOUN
ejpam-367	365	2	d2φ1(t)t(−λt	d2φ1(t)t(−λt	NOUN
ejpam-367	365	3	f	f	PROPN
ejpam-367	365	4	ẏ1	ẏ1	PROPN
ejpam-367	365	5	ẏ1)}φ1(t)]d	ẏ1)}φ1(t)]d	PROPN
ejpam-367	365	6	t	t	PROPN
ejpam-367	365	7	=	=	SYM
ejpam-367	365	8	0	0	PROPN
ejpam-367	365	9	,	,	PUNCT
ejpam-367	365	10	t	t	PROPN
ejpam-367	365	11	∈	∈	PROPN
ejpam-367	365	12	i	i	PRON
ejpam-367	365	13	⇒	⇒	VERB
ejpam-367	365	14	φ1(t	φ1(t	NUM
ejpam-367	365	15	)	)	PUNCT
ejpam-367	365	16	=	=	SYM
ejpam-367	365	17	0	0	NUM
ejpam-367	365	18	,	,	PUNCT
ejpam-367	366	1	t	t	PROPN
ejpam-367	366	2	∈	∈	PROPN
ejpam-367	367	1	i	i	PRON
ejpam-367	367	2	,	,	PUNCT
ejpam-367	367	3	and	and	CCONJ
ejpam-367	367	4	∫	∫	NOUN
ejpam-367	368	1	i	i	PRON
ejpam-367	368	2	[	[	X
ejpam-367	368	3	{	{	PUNCT
ejpam-367	368	4	(	(	PUNCT
ejpam-367	368	5	φ2(t))t	φ2(t))t	NOUN
ejpam-367	368	6	(	(	PUNCT
ejpam-367	368	7	λt	λt	ADP
ejpam-367	368	8	g	g	PROPN
ejpam-367	368	9	y2	y2	NOUN
ejpam-367	368	10	y2	y2	PROPN
ejpam-367	369	1	−	−	PROPN
ejpam-367	369	2	dλt	dλt	NOUN
ejpam-367	369	3	g	g	NOUN
ejpam-367	369	4	y2	y2	PROPN
ejpam-367	369	5	ẏ2)−	ẏ2)−	VERB
ejpam-367	369	6	dφ2(t)t(−dλt	dφ2(t)t(−dλt	PROPN
ejpam-367	369	7	g	g	PROPN
ejpam-367	369	8	ẏ2	ẏ2	PROPN
ejpam-367	369	9	ẏ2	ẏ2	PROPN
ejpam-367	369	10	)	)	PUNCT
ejpam-367	370	1	+	+	NOUN
ejpam-367	370	2	d2φ2(t)t(−λt	d2φ2(t)t(−λt	NOUN
ejpam-367	370	3	g	g	NOUN
ejpam-367	370	4	ẏ2	ẏ2	PROPN
ejpam-367	370	5	ẏ2)}φ2(t)]d	ẏ2)}φ2(t)]d	PROPN
ejpam-367	370	6	t	t	PROPN
ejpam-367	370	7	=	=	SYM
ejpam-367	370	8	0	0	NUM
ejpam-367	370	9	,	,	PUNCT
ejpam-367	370	10	t	t	PROPN
ejpam-367	370	11	∈	∈	PROPN
ejpam-367	370	12	i	i	PRON
ejpam-367	370	13	⇒	⇒	VERB
ejpam-367	370	14	φ1(t	φ1(t	NUM
ejpam-367	370	15	)	)	PUNCT
ejpam-367	370	16	=	=	SYM
ejpam-367	370	17	0	0	NUM
ejpam-367	370	18	,	,	PUNCT
ejpam-367	370	19	t	t	PROPN
ejpam-367	370	20	∈	∈	PROPN
ejpam-367	371	1	i	i	PRON
ejpam-367	371	2	.	.	PUNCT
ejpam-367	372	1	and	and	CCONJ
ejpam-367	372	2	(	(	PUNCT
ejpam-367	372	3	c3	c3	PROPN
ejpam-367	372	4	)	)	PUNCT
ejpam-367	373	1	g	g	NOUN
ejpam-367	374	1	i	i	PRON
ejpam-367	374	2	y2	y2	VERB
ejpam-367	374	3	−	−	PROPN
ejpam-367	375	1	dg	dg	INTJ
ejpam-367	376	1	i	i	NOUN
ejpam-367	376	2	ẏ2	ẏ2	NOUN
ejpam-367	376	3	=	=	SYM
ejpam-367	376	4	0	0	PROPN
ejpam-367	376	5	,	,	PUNCT
ejpam-367	376	6	i	i	PRON
ejpam-367	376	7	=	=	NOUN
ejpam-367	376	8	1	1	NUM
ejpam-367	376	9	,	,	PUNCT
ejpam-367	376	10	2	2	NUM
ejpam-367	376	11	,	,	PUNCT
ejpam-367	376	12	.	.	PUNCT
ejpam-367	376	13	.	.	PUNCT
ejpam-367	377	1	.	.	PUNCT
ejpam-367	378	1	,	,	PUNCT
ejpam-367	378	2	p	p	NOUN
ejpam-367	378	3	are	be	AUX
ejpam-367	378	4	linearly	linearly	ADV
ejpam-367	378	5	independent	independent	ADJ
ejpam-367	378	6	.	.	PUNCT
ejpam-367	379	1	let	let	VERB
ejpam-367	379	2	∫	∫	PROPN
ejpam-367	380	1	i	i	PRON
ejpam-367	380	2	f	f	PROPN
ejpam-367	381	1	d	d	PROPN
ejpam-367	381	2	t	t	PROPN
ejpam-367	381	3	and	and	CCONJ
ejpam-367	381	4	∫	∫	NOUN
ejpam-367	382	1	i	i	INTJ
ejpam-367	382	2	λt	λt	INTJ
ejpam-367	382	3	gd	gd	PROPN
ejpam-367	382	4	t	t	PROPN
ejpam-367	382	5	satisfy	satisfy	VERB
ejpam-367	382	6	the	the	DET
ejpam-367	382	7	invexity	invexity	NOUN
ejpam-367	382	8	and	and	CCONJ
ejpam-367	382	9	generalized	generalized	ADJ
ejpam-367	382	10	invexity	invexity	NOUN
ejpam-367	382	11	as	as	SCONJ
ejpam-367	382	12	stated	state	VERB
ejpam-367	382	13	in	in	ADP
ejpam-367	382	14	theorem	theorem	NOUN
ejpam-367	382	15	1	1	NUM
ejpam-367	382	16	,	,	PUNCT
ejpam-367	382	17	then	then	ADV
ejpam-367	382	18	(	(	PUNCT
ejpam-367	382	19	x̄1	x̄1	PROPN
ejpam-367	382	20	,	,	PUNCT
ejpam-367	382	21	x̄2	x̄2	PROPN
ejpam-367	382	22	,	,	PUNCT
ejpam-367	382	23	ȳ	ȳ	PROPN
ejpam-367	382	24	,	,	PUNCT
ejpam-367	382	25	ȳ2	ȳ2	NOUN
ejpam-367	382	26	,	,	PUNCT
ejpam-367	382	27	λ̄	λ̄	ADJ
ejpam-367	382	28	)	)	PUNCT
ejpam-367	382	29	and	and	CCONJ
ejpam-367	382	30	(	(	PUNCT
ejpam-367	382	31	ū1	ū1	PROPN
ejpam-367	382	32	,	,	PUNCT
ejpam-367	382	33	ū2	ū2	NOUN
ejpam-367	382	34	,	,	PUNCT
ejpam-367	382	35	v̄	v̄	NOUN
ejpam-367	382	36	,	,	PUNCT
ejpam-367	382	37	v̄2	v̄2	NUM
ejpam-367	382	38	,	,	PUNCT
ejpam-367	382	39	λ̄	λ̄	NUM
ejpam-367	382	40	)	)	PUNCT
ejpam-367	382	41	are	be	AUX
ejpam-367	382	42	efficient	efficient	ADJ
ejpam-367	382	43	solution	solution	NOUN
ejpam-367	382	44	of	of	ADP
ejpam-367	382	45	(	(	PUNCT
ejpam-367	382	46	mix	mix	VERB
ejpam-367	382	47	sp	sp	NOUN
ejpam-367	382	48	)	)	PUNCT
ejpam-367	382	49	and	and	CCONJ
ejpam-367	382	50	(	(	PUNCT
ejpam-367	382	51	mix	mix	VERB
ejpam-367	382	52	sd	sd	NOUN
ejpam-367	382	53	)	)	PUNCT
ejpam-367	382	54	respectively	respectively	ADV
ejpam-367	382	55	.	.	PUNCT
ejpam-367	383	1	i.	i.	PROPN
ejpam-367	383	2	husain	husain	PROPN
ejpam-367	383	3	and	and	CCONJ
ejpam-367	383	4	r.	r.	PROPN
ejpam-367	383	5	mattoo	mattoo	PROPN
ejpam-367	383	6	/	/	SYM
ejpam-367	383	7	eur	eur	PROPN
ejpam-367	383	8	.	.	PUNCT
ejpam-367	384	1	j.	j.	PROPN
ejpam-367	384	2	pure	pure	PROPN
ejpam-367	384	3	appl	appl	PROPN
ejpam-367	384	4	.	.	PROPN
ejpam-367	384	5	math	math	PROPN
ejpam-367	384	6	,	,	PUNCT
ejpam-367	384	7	2	2	NUM
ejpam-367	384	8	(	(	PUNCT
ejpam-367	384	9	2009	2009	NUM
ejpam-367	384	10	)	)	PUNCT
ejpam-367	384	11	,	,	PUNCT
ejpam-367	384	12	(	(	PUNCT
ejpam-367	384	13	578	578	NUM
ejpam-367	384	14	-	-	SYM
ejpam-367	384	15	603	603	NUM
ejpam-367	384	16	)	)	PUNCT
ejpam-367	384	17	592	592	NUM
ejpam-367	384	18	proof	proof	NOUN
ejpam-367	384	19	.	.	PUNCT
ejpam-367	385	1	since	since	SCONJ
ejpam-367	385	2	(	(	PUNCT
ejpam-367	385	3	x̄1	x̄1	PROPN
ejpam-367	385	4	,	,	PUNCT
ejpam-367	385	5	x̄2	x̄2	PROPN
ejpam-367	385	6	,	,	PUNCT
ejpam-367	385	7	ȳ1	ȳ1	PROPN
ejpam-367	385	8	,	,	PUNCT
ejpam-367	385	9	ȳ2	ȳ2	NOUN
ejpam-367	385	10	,	,	PUNCT
ejpam-367	385	11	λ̄	λ̄	NOUN
ejpam-367	385	12	)	)	PUNCT
ejpam-367	385	13	is	be	AUX
ejpam-367	385	14	efficient	efficient	ADJ
ejpam-367	385	15	,	,	PUNCT
ejpam-367	385	16	it	it	PRON
ejpam-367	385	17	is	be	AUX
ejpam-367	385	18	weak	weak	ADJ
ejpam-367	385	19	minimum	minimum	NOUN
ejpam-367	385	20	.	.	PUNCT
ejpam-367	386	1	hence	hence	ADV
ejpam-367	386	2	there	there	PRON
ejpam-367	386	3	exists	exist	VERB
ejpam-367	386	4	τ	τ	PROPN
ejpam-367	386	5	∈	∈	PROPN
ejpam-367	386	6	rp	rp	NOUN
ejpam-367	386	7	,	,	PUNCT
ejpam-367	386	8	η	η	PROPN
ejpam-367	386	9	∈	∈	PROPN
ejpam-367	386	10	rp	rp	NOUN
ejpam-367	386	11	,	,	PUNCT
ejpam-367	386	12	γ	γ	PROPN
ejpam-367	386	13	∈	∈	NOUN
ejpam-367	386	14	r	r	NOUN
ejpam-367	386	15	and	and	CCONJ
ejpam-367	386	16	piecewise	piecewise	NOUN
ejpam-367	386	17	smooth	smooth	ADJ
ejpam-367	386	18	functions	function	NOUN
ejpam-367	386	19	θ	θ	NOUN
ejpam-367	386	20	1(t	1(t	NUM
ejpam-367	386	21	)	)	PUNCT
ejpam-367	386	22	:	:	PUNCT
ejpam-367	387	1	i	i	PRON
ejpam-367	387	2	→	→	SYM
ejpam-367	387	3	r|k1|,θ	r|k1|,θ	NOUN
ejpam-367	387	4	2(t	2(t	NUM
ejpam-367	387	5	)	)	PUNCT
ejpam-367	387	6	:	:	PUNCT
ejpam-367	388	1	i	i	PRON
ejpam-367	388	2	→	→	SYM
ejpam-367	388	3	r|k2|	r|k2|	ADJ
ejpam-367	388	4	and	and	CCONJ
ejpam-367	388	5	µ	µ	X
ejpam-367	388	6	:	:	PUNCT
ejpam-367	388	7	i	i	PROPN
ejpam-367	388	8	→	→	SYM
ejpam-367	388	9	rm	rm	NOUN
ejpam-367	388	10	such	such	ADJ
ejpam-367	388	11	that	that	SCONJ
ejpam-367	388	12	the	the	DET
ejpam-367	388	13	following	follow	VERB
ejpam-367	388	14	fritz	fritz	PROPN
ejpam-367	388	15	-	-	PUNCT
ejpam-367	388	16	john	john	PROPN
ejpam-367	388	17	optimality	optimality	NOUN
ejpam-367	388	18	conditions	condition	NOUN
ejpam-367	388	19	,	,	PUNCT
ejpam-367	388	20	in	in	ADP
ejpam-367	388	21	view	view	NOUN
ejpam-367	388	22	of	of	ADP
ejpam-367	388	23	the	the	DET
ejpam-367	388	24	analysis	analysis	NOUN
ejpam-367	388	25	on	on	ADP
ejpam-367	388	26	[	[	X
ejpam-367	388	27	13	13	NUM
ejpam-367	388	28	,	,	PUNCT
ejpam-367	388	29	9	9	NUM
ejpam-367	388	30	,	,	PUNCT
ejpam-367	388	31	14	14	NUM
ejpam-367	388	32	]	]	PUNCT
ejpam-367	388	33	,	,	PUNCT
ejpam-367	388	34	are	be	AUX
ejpam-367	388	35	satisfied	satisfied	ADJ
ejpam-367	388	36	h	h	NOUN
ejpam-367	388	37	=	=	SYM
ejpam-367	388	38	τ	τ	PROPN
ejpam-367	388	39	(	(	PUNCT
ejpam-367	388	40	f	f	PROPN
ejpam-367	388	41	+	+	CCONJ
ejpam-367	388	42	g	g	NOUN
ejpam-367	388	43	)	)	PUNCT
ejpam-367	388	44	+	+	CCONJ
ejpam-367	388	45	(	(	PUNCT
ejpam-367	388	46	θ	θ	PROPN
ejpam-367	388	47	1(t)−	1(t)−	PROPN
ejpam-367	388	48	(	(	PUNCT
ejpam-367	388	49	τt	τt	PROPN
ejpam-367	388	50	e)y1(t)t)(λt	e)y1(t)t)(λt	PROPN
ejpam-367	388	51	f	f	PROPN
ejpam-367	388	52	y1	y1	PROPN
ejpam-367	389	1	−	−	PROPN
ejpam-367	389	2	dλt	dλt	NOUN
ejpam-367	389	3	f	f	PROPN
ejpam-367	389	4	ẏ1	ẏ1	PROPN
ejpam-367	389	5	)	)	PUNCT
ejpam-367	389	6	+	+	PROPN
ejpam-367	389	7	(	(	PUNCT
ejpam-367	389	8	θ	θ	PROPN
ejpam-367	389	9	2(t)−	2(t)−	NUM
ejpam-367	389	10	γy2(t)t)(λt	γy2(t)t)(λt	VERB
ejpam-367	389	11	g	g	PROPN
ejpam-367	389	12	y2	y2	PROPN
ejpam-367	389	13	−	−	PROPN
ejpam-367	389	14	dλt	dλt	NOUN
ejpam-367	389	15	g	g	PROPN
ejpam-367	389	16	ẏ2	ẏ2	PROPN
ejpam-367	389	17	)	)	PUNCT
ejpam-367	390	1	+	+	ADP
ejpam-367	390	2	ηtλ	ηtλ	NOUN
ejpam-367	390	3	satisfying	satisfy	VERB
ejpam-367	390	4	hx1	hx1	NOUN
ejpam-367	390	5	−	−	PROPN
ejpam-367	391	1	dh	dh	NOUN
ejpam-367	392	1	ẋ1	ẋ1	PROPN
ejpam-367	392	2	+	+	PROPN
ejpam-367	392	3	d2h	d2h	PROPN
ejpam-367	392	4	ẍ1	ẍ1	PROPN
ejpam-367	392	5	=	=	SYM
ejpam-367	392	6	0	0	PROPN
ejpam-367	392	7	,	,	PUNCT
ejpam-367	392	8	t	t	PROPN
ejpam-367	392	9	∈	∈	PROPN
ejpam-367	393	1	i	i	PRON
ejpam-367	393	2	(	(	PUNCT
ejpam-367	393	3	29	29	NUM
ejpam-367	393	4	)	)	PUNCT
ejpam-367	393	5	hx2	hx2	NOUN
ejpam-367	394	1	−	−	NOUN
ejpam-367	394	2	dh	dh	NOUN
ejpam-367	395	1	ẋ2	ẋ2	PROPN
ejpam-367	395	2	+	+	NUM
ejpam-367	395	3	d2h	d2h	PROPN
ejpam-367	395	4	ẍ2	ẍ2	PROPN
ejpam-367	395	5	=	=	SYM
ejpam-367	396	1	0	0	PROPN
ejpam-367	396	2	,	,	PUNCT
ejpam-367	396	3	t	t	PROPN
ejpam-367	396	4	∈	∈	PROPN
ejpam-367	397	1	i	i	PRON
ejpam-367	397	2	(	(	PUNCT
ejpam-367	397	3	30	30	NUM
ejpam-367	397	4	)	)	PUNCT
ejpam-367	397	5	h	h	NOUN
ejpam-367	397	6	y1	y1	NOUN
ejpam-367	398	1	−	−	PROPN
ejpam-367	398	2	dh	dh	NOUN
ejpam-367	399	1	ẏ1	ẏ1	PROPN
ejpam-367	399	2	+	+	CCONJ
ejpam-367	399	3	d2h	d2h	PROPN
ejpam-367	399	4	ÿ1	ÿ1	NOUN
ejpam-367	400	1	=	=	SYM
ejpam-367	400	2	0	0	NUM
ejpam-367	400	3	,	,	PUNCT
ejpam-367	400	4	t	t	PROPN
ejpam-367	400	5	∈	∈	PROPN
ejpam-367	401	1	i	i	PRON
ejpam-367	401	2	(	(	PUNCT
ejpam-367	401	3	31	31	NUM
ejpam-367	401	4	)	)	PUNCT
ejpam-367	401	5	h	h	NOUN
ejpam-367	402	1	y2	y2	NOUN
ejpam-367	402	2	−	−	PROPN
ejpam-367	403	1	dh	dh	NOUN
ejpam-367	403	2	ẏ2	ẏ2	PROPN
ejpam-367	403	3	+	+	CCONJ
ejpam-367	403	4	d2h	d2h	PROPN
ejpam-367	403	5	ÿ2	ÿ2	NOUN
ejpam-367	404	1	=	=	SYM
ejpam-367	404	2	0	0	PROPN
ejpam-367	404	3	,	,	PUNCT
ejpam-367	404	4	t	t	PROPN
ejpam-367	404	5	∈	∈	PROPN
ejpam-367	405	1	i	i	PRON
ejpam-367	405	2	(	(	PUNCT
ejpam-367	405	3	32	32	NUM
ejpam-367	405	4	)	)	PUNCT
ejpam-367	405	5	(	(	PUNCT
ejpam-367	405	6	θ	θ	PROPN
ejpam-367	405	7	1(t)−	1(t)−	PROPN
ejpam-367	405	8	(	(	PUNCT
ejpam-367	405	9	τt	τt	PROPN
ejpam-367	405	10	e)y1(t))t	e)y1(t))t	X
ejpam-367	405	11	(	(	PUNCT
ejpam-367	405	12	f	f	X
ejpam-367	405	13	y1	y1	NOUN
ejpam-367	405	14	−	−	PROPN
ejpam-367	406	1	d	d	X
ejpam-367	406	2	f	f	PROPN
ejpam-367	406	3	ẏ1	ẏ1	PROPN
ejpam-367	406	4	)	)	PUNCT
ejpam-367	407	1	+	+	CCONJ
ejpam-367	407	2	(	(	PUNCT
ejpam-367	407	3	θ	θ	NOUN
ejpam-367	407	4	2(t)−	2(t)−	NUM
ejpam-367	408	1	γy2(t))t(g	γy2(t))t(g	PROPN
ejpam-367	408	2	y2	y2	PROPN
ejpam-367	408	3	−	−	PROPN
ejpam-367	408	4	dg	dg	PROPN
ejpam-367	408	5	ẏ2)−η=	ẏ2)−η=	NOUN
ejpam-367	408	6	0	0	NUM
ejpam-367	408	7	,	,	PUNCT
ejpam-367	408	8	t	t	PROPN
ejpam-367	408	9	∈	∈	PROPN
ejpam-367	409	1	i	i	PRON
ejpam-367	409	2	(	(	PUNCT
ejpam-367	409	3	33	33	NUM
ejpam-367	409	4	)	)	PUNCT
ejpam-367	409	5	θ	θ	PROPN
ejpam-367	409	6	1(t)(λt	1(t)(λt	NUM
ejpam-367	409	7	f	f	PROPN
ejpam-367	409	8	y1	y1	NOUN
ejpam-367	409	9	−	−	PROPN
ejpam-367	409	10	dλt	dλt	NOUN
ejpam-367	409	11	f	f	PROPN
ejpam-367	409	12	ẏ1	ẏ1	PROPN
ejpam-367	409	13	)	)	PUNCT
ejpam-367	409	14	=	=	SYM
ejpam-367	409	15	0	0	NUM
ejpam-367	409	16	,	,	PUNCT
ejpam-367	409	17	t	t	PROPN
ejpam-367	409	18	∈	∈	PROPN
ejpam-367	410	1	i	i	PRON
ejpam-367	410	2	(	(	PUNCT
ejpam-367	410	3	34	34	NUM
ejpam-367	410	4	)	)	PUNCT
ejpam-367	410	5	θ	θ	PROPN
ejpam-367	410	6	2(t)(λt	2(t)(λt	NUM
ejpam-367	410	7	g	g	NOUN
ejpam-367	410	8	y2	y2	PROPN
ejpam-367	410	9	−	−	PROPN
ejpam-367	410	10	dλt	dλt	NOUN
ejpam-367	410	11	g	g	PROPN
ejpam-367	410	12	ẏ2	ẏ2	PROPN
ejpam-367	410	13	)	)	PUNCT
ejpam-367	410	14	=	=	SYM
ejpam-367	410	15	0	0	NUM
ejpam-367	410	16	,	,	PUNCT
ejpam-367	410	17	t	t	PROPN
ejpam-367	410	18	∈	∈	PROPN
ejpam-367	410	19	i	i	PRON
ejpam-367	410	20	(	(	PUNCT
ejpam-367	410	21	35	35	NUM
ejpam-367	410	22	)	)	PUNCT
ejpam-367	410	23	γ	γ	NOUN
ejpam-367	410	24	∫	∫	PROPN
ejpam-367	410	25	i	i	PRON
ejpam-367	410	26	y2(t)t(λt	y2(t)t(λt	VERB
ejpam-367	410	27	g	g	NOUN
ejpam-367	410	28	y2	y2	NOUN
ejpam-367	410	29	−	−	PROPN
ejpam-367	411	1	dλt	dλt	NOUN
ejpam-367	412	1	g	g	PROPN
ejpam-367	412	2	ẏ2	ẏ2	PROPN
ejpam-367	412	3	)	)	PUNCT
ejpam-367	413	1	=	=	SYM
ejpam-367	413	2	0	0	PUNCT
ejpam-367	413	3	(	(	PUNCT
ejpam-367	413	4	36	36	NUM
ejpam-367	413	5	)	)	PUNCT
ejpam-367	413	6	ηt	ηt	ADP
ejpam-367	413	7	λ̄	λ̄	NOUN
ejpam-367	413	8	=	=	SYM
ejpam-367	413	9	0	0	NUM
ejpam-367	413	10	(	(	PUNCT
ejpam-367	413	11	37	37	NUM
ejpam-367	413	12	)	)	PUNCT
ejpam-367	413	13	(	(	PUNCT
ejpam-367	413	14	τ	τ	PROPN
ejpam-367	413	15	,	,	PUNCT
ejpam-367	413	16	θ	θ	PROPN
ejpam-367	413	17	1(t),θ	1(t),θ	NUM
ejpam-367	413	18	2(t),η	2(t),η	NUM
ejpam-367	413	19	,	,	PUNCT
ejpam-367	413	20	γ)≧	γ)≧	NOUN
ejpam-367	413	21	0	0	NUM
ejpam-367	413	22	,	,	PUNCT
ejpam-367	413	23	t	t	PROPN
ejpam-367	413	24	∈	∈	PROPN
ejpam-367	414	1	i	i	PRON
ejpam-367	414	2	(	(	PUNCT
ejpam-367	414	3	38	38	NUM
ejpam-367	414	4	)	)	PUNCT
ejpam-367	414	5	(	(	PUNCT
ejpam-367	414	6	τ	τ	PROPN
ejpam-367	414	7	,	,	PUNCT
ejpam-367	414	8	θ	θ	PROPN
ejpam-367	414	9	1(t),θ	1(t),θ	NUM
ejpam-367	414	10	2(t),η	2(t),η	NUM
ejpam-367	414	11	,	,	PUNCT
ejpam-367	414	12	γ	γ	NOUN
ejpam-367	414	13	)	)	PUNCT
ejpam-367	414	14	6=	6=	ADP
ejpam-367	414	15	0	0	NUM
ejpam-367	414	16	,	,	PUNCT
ejpam-367	414	17	t	t	PROPN
ejpam-367	414	18	∈	∈	PROPN
ejpam-367	415	1	i	i	PRON
ejpam-367	415	2	(	(	PUNCT
ejpam-367	415	3	39	39	NUM
ejpam-367	415	4	)	)	PUNCT
ejpam-367	415	5	hold	hold	VERB
ejpam-367	415	6	throughout	throughout	ADP
ejpam-367	415	7	i	i	PRON
ejpam-367	415	8	(	(	PUNCT
ejpam-367	415	9	except	except	SCONJ
ejpam-367	415	10	at	at	ADP
ejpam-367	415	11	the	the	DET
ejpam-367	415	12	corners	corner	NOUN
ejpam-367	415	13	of	of	ADP
ejpam-367	415	14	(	(	PUNCT
ejpam-367	415	15	x̄1(t	x̄1(t	NUM
ejpam-367	415	16	)	)	PUNCT
ejpam-367	415	17	,	,	PUNCT
ejpam-367	415	18	x̄2(t	x̄2(t	PROPN
ejpam-367	415	19	)	)	PUNCT
ejpam-367	415	20	,	,	PUNCT
ejpam-367	415	21	ȳ1(t	ȳ1(t	NUM
ejpam-367	415	22	)	)	PUNCT
ejpam-367	415	23	,	,	PUNCT
ejpam-367	415	24	ȳ2(t	ȳ2(t	PROPN
ejpam-367	415	25	)	)	PUNCT
ejpam-367	415	26	)	)	PUNCT
ejpam-367	415	27	where	where	SCONJ
ejpam-367	415	28	(	(	PUNCT
ejpam-367	415	29	29)(32	29)(32	NUM
ejpam-367	415	30	)	)	PUNCT
ejpam-367	415	31	are	be	AUX
ejpam-367	415	32	valid	valid	ADJ
ejpam-367	415	33	for	for	ADP
ejpam-367	415	34	unique	unique	ADJ
ejpam-367	415	35	right	right	NOUN
ejpam-367	415	36	and	and	CCONJ
ejpam-367	415	37	left	leave	VERB
ejpam-367	415	38	hand	hand	NOUN
ejpam-367	415	39	limits	limit	NOUN
ejpam-367	415	40	)	)	PUNCT
ejpam-367	415	41	.	.	PUNCT
ejpam-367	416	1	here	here	ADV
ejpam-367	416	2	θ	θ	PROPN
ejpam-367	416	3	1	1	NUM
ejpam-367	416	4	and	and	CCONJ
ejpam-367	416	5	θ	θ	PROPN
ejpam-367	416	6	2	2	NUM
ejpam-367	416	7	are	be	AUX
ejpam-367	416	8	continuous	continuous	ADJ
ejpam-367	416	9	except	except	SCONJ
ejpam-367	416	10	possibly	possibly	ADV
ejpam-367	416	11	at	at	ADP
ejpam-367	416	12	corner	corner	NOUN
ejpam-367	416	13	of	of	ADP
ejpam-367	416	14	(	(	PUNCT
ejpam-367	416	15	x̄1(t	x̄1(t	NUM
ejpam-367	416	16	)	)	PUNCT
ejpam-367	416	17	,	,	PUNCT
ejpam-367	416	18	x̄2(t	x̄2(t	PROPN
ejpam-367	416	19	)	)	PUNCT
ejpam-367	416	20	,	,	PUNCT
ejpam-367	416	21	ȳ1(t	ȳ1(t	NUM
ejpam-367	416	22	)	)	PUNCT
ejpam-367	416	23	,	,	PUNCT
ejpam-367	416	24	ȳ2(t	ȳ2(t	PROPN
ejpam-367	416	25	)	)	PUNCT
ejpam-367	416	26	)	)	PUNCT
ejpam-367	416	27	.	.	PUNCT
ejpam-367	417	1	i.	i.	PROPN
ejpam-367	417	2	husain	husain	PROPN
ejpam-367	417	3	and	and	CCONJ
ejpam-367	417	4	r.	r.	PROPN
ejpam-367	417	5	mattoo	mattoo	PROPN
ejpam-367	417	6	/	/	SYM
ejpam-367	417	7	eur	eur	PROPN
ejpam-367	417	8	.	.	PUNCT
ejpam-367	418	1	j.	j.	PROPN
ejpam-367	418	2	pure	pure	PROPN
ejpam-367	418	3	appl	appl	PROPN
ejpam-367	418	4	.	.	PROPN
ejpam-367	418	5	math	math	PROPN
ejpam-367	418	6	,	,	PUNCT
ejpam-367	418	7	2	2	NUM
ejpam-367	418	8	(	(	PUNCT
ejpam-367	418	9	2009	2009	NUM
ejpam-367	418	10	)	)	PUNCT
ejpam-367	418	11	,	,	PUNCT
ejpam-367	418	12	(	(	PUNCT
ejpam-367	418	13	578	578	NUM
ejpam-367	418	14	-	-	SYM
ejpam-367	418	15	603	603	NUM
ejpam-367	418	16	)	)	PUNCT
ejpam-367	418	17	593	593	NUM
ejpam-367	418	18	the	the	DET
ejpam-367	418	19	relations	relation	NOUN
ejpam-367	418	20	(	(	PUNCT
ejpam-367	418	21	29)-(32	29)-(32	NUM
ejpam-367	418	22	)	)	PUNCT
ejpam-367	418	23	are	be	AUX
ejpam-367	418	24	all	all	ADV
ejpam-367	418	25	deducible	deducible	ADJ
ejpam-367	418	26	from	from	ADP
ejpam-367	418	27	the	the	DET
ejpam-367	418	28	classical	classical	ADJ
ejpam-367	418	29	euler	euler	NOUN
ejpam-367	418	30	-	-	PUNCT
ejpam-367	418	31	lagrange	lagrange	PROPN
ejpam-367	418	32	and	and	CCONJ
ejpam-367	418	33	clebsch	clebsch	VERB
ejpam-367	418	34	necessary	necessary	ADJ
ejpam-367	418	35	optimality	optimality	NOUN
ejpam-367	418	36	conditions	condition	NOUN
ejpam-367	418	37	.	.	PUNCT
ejpam-367	419	1	particularly	particularly	ADV
ejpam-367	419	2	,	,	PUNCT
ejpam-367	419	3	the	the	DET
ejpam-367	419	4	equations	equation	NOUN
ejpam-367	419	5	(	(	PUNCT
ejpam-367	419	6	29)-(32	29)-(32	NUM
ejpam-367	419	7	)	)	PUNCT
ejpam-367	419	8	are	be	AUX
ejpam-367	419	9	the	the	DET
ejpam-367	419	10	famous	famous	ADJ
ejpam-367	419	11	euler	euler	VERB
ejpam-367	419	12	-	-	PUNCT
ejpam-367	419	13	lagrange	lagrange	NOUN
ejpam-367	419	14	differential	differential	NOUN
ejpam-367	419	15	equation	equation	NOUN
ejpam-367	419	16	when	when	SCONJ
ejpam-367	419	17	second	second	ADJ
ejpam-367	419	18	order	order	NOUN
ejpam-367	419	19	derivatives	derivative	NOUN
ejpam-367	419	20	appear	appear	VERB
ejpam-367	419	21	in	in	ADP
ejpam-367	419	22	h.	h.	NOUN
ejpam-367	419	23	using	use	VERB
ejpam-367	419	24	the	the	DET
ejpam-367	419	25	analogies	analogy	NOUN
ejpam-367	419	26	of	of	ADP
ejpam-367	419	27	the	the	DET
ejpam-367	419	28	observation	observation	NOUN
ejpam-367	419	29	of	of	ADP
ejpam-367	419	30	dφ	dφ	ADP
ejpam-367	419	31	ÿ	ÿ	PROPN
ejpam-367	419	32	from	from	ADP
ejpam-367	419	33	the	the	DET
ejpam-367	419	34	notational	notational	ADJ
ejpam-367	419	35	section	section	NOUN
ejpam-367	419	36	,	,	PUNCT
ejpam-367	419	37	the	the	DET
ejpam-367	419	38	equations	equation	NOUN
ejpam-367	419	39	(	(	PUNCT
ejpam-367	419	40	29)-(32	29)-(32	NUM
ejpam-367	419	41	)	)	PUNCT
ejpam-367	419	42	become	become	VERB
ejpam-367	419	43	,	,	PUNCT
ejpam-367	419	44	τ	τ	PROPN
ejpam-367	419	45	(	(	PUNCT
ejpam-367	419	46	fx1	fx1	NOUN
ejpam-367	419	47	−	−	PROPN
ejpam-367	420	1	d	d	NOUN
ejpam-367	420	2	f	f	PROPN
ejpam-367	420	3	ẋ1)−	ẋ1)−	PROPN
ejpam-367	420	4	(	(	PUNCT
ejpam-367	420	5	θ	θ	PROPN
ejpam-367	420	6	1(t)−	1(t)−	PROPN
ejpam-367	420	7	(	(	PUNCT
ejpam-367	420	8	τt	τt	NOUN
ejpam-367	420	9	e	e	X
ejpam-367	420	10	)	)	PUNCT
ejpam-367	420	11	ȳ1(t))t	ȳ1(t))t	NOUN
ejpam-367	420	12	(	(	PUNCT
ejpam-367	420	13	λt	λt	ADP
ejpam-367	420	14	f	f	PROPN
ejpam-367	420	15	y1	y1	PROPN
ejpam-367	421	1	x1	x1	PROPN
ejpam-367	422	1	−	−	PROPN
ejpam-367	422	2	dλt	dλt	NOUN
ejpam-367	423	1	f	f	PROPN
ejpam-367	424	1	ẏ1	ẏ1	PROPN
ejpam-367	424	2	x1	x1	PROPN
ejpam-367	424	3	)	)	PUNCT
ejpam-367	424	4	−d(θ	−d(θ	PROPN
ejpam-367	424	5	1(t)−	1(t)−	PROPN
ejpam-367	424	6	(	(	PUNCT
ejpam-367	424	7	τt	τt	NOUN
ejpam-367	424	8	e	e	X
ejpam-367	424	9	)	)	PUNCT
ejpam-367	424	10	ȳ1(t))t	ȳ1(t))t	NOUN
ejpam-367	424	11	(	(	PUNCT
ejpam-367	424	12	λt	λt	ADP
ejpam-367	424	13	f	f	PROPN
ejpam-367	424	14	y1	y1	PROPN
ejpam-367	424	15	ẋ1	ẋ1	PROPN
ejpam-367	424	16	−	−	PROPN
ejpam-367	424	17	dλt	dλt	NOUN
ejpam-367	424	18	f	f	PROPN
ejpam-367	424	19	ẏ1	ẏ1	PROPN
ejpam-367	424	20	ẋ1	ẋ1	PROPN
ejpam-367	424	21	−λt	−λt	NOUN
ejpam-367	424	22	f	f	NOUN
ejpam-367	424	23	ẏ1	ẏ1	PROPN
ejpam-367	424	24	x1	x1	PROPN
ejpam-367	424	25	)	)	PUNCT
ejpam-367	425	1	+	+	NOUN
ejpam-367	425	2	d2((θ	d2((θ	NOUN
ejpam-367	425	3	1(t)−	1(t)−	PROPN
ejpam-367	425	4	(	(	PUNCT
ejpam-367	425	5	τt	τt	NOUN
ejpam-367	425	6	e	e	X
ejpam-367	425	7	)	)	PUNCT
ejpam-367	425	8	ȳ1(t))t	ȳ1(t))t	NOUN
ejpam-367	425	9	(	(	PUNCT
ejpam-367	425	10	−λt	−λt	NOUN
ejpam-367	425	11	f	f	PROPN
ejpam-367	425	12	ẏ1	ẏ1	PROPN
ejpam-367	425	13	ẋ1	ẋ1	PROPN
ejpam-367	425	14	)	)	PUNCT
ejpam-367	425	15	)	)	PUNCT
ejpam-367	426	1	=	=	SYM
ejpam-367	426	2	0	0	PUNCT
ejpam-367	426	3	(	(	PUNCT
ejpam-367	426	4	40	40	NUM
ejpam-367	426	5	)	)	PUNCT
ejpam-367	426	6	τ(gx2	τ(gx2	PROPN
ejpam-367	426	7	−	−	PROPN
ejpam-367	426	8	dg	dg	PROPN
ejpam-367	426	9	ẋ2	ẋ2	PROPN
ejpam-367	426	10	)	)	PUNCT
ejpam-367	427	1	+	+	CCONJ
ejpam-367	427	2	(	(	PUNCT
ejpam-367	427	3	θ	θ	X
ejpam-367	427	4	2(t)−	2(t)−	PROPN
ejpam-367	428	1	γ	γ	X
ejpam-367	428	2	ȳ2(t))t	ȳ2(t))t	X
ejpam-367	428	3	(	(	PUNCT
ejpam-367	428	4	λt	λt	ADP
ejpam-367	428	5	g	g	PROPN
ejpam-367	428	6	y2	y2	NOUN
ejpam-367	428	7	x2	x2	PROPN
ejpam-367	429	1	−	−	PROPN
ejpam-367	429	2	dλt	dλt	NOUN
ejpam-367	429	3	g	g	PROPN
ejpam-367	429	4	ẏ2	ẏ2	PROPN
ejpam-367	429	5	x2	x2	PROPN
ejpam-367	429	6	)	)	PUNCT
ejpam-367	429	7	−d(θ	−d(θ	PROPN
ejpam-367	429	8	2(t)−	2(t)−	NUM
ejpam-367	430	1	γ	γ	X
ejpam-367	430	2	ȳ2(t))t	ȳ2(t))t	X
ejpam-367	430	3	(	(	PUNCT
ejpam-367	430	4	λt	λt	ADP
ejpam-367	430	5	g	g	PROPN
ejpam-367	430	6	y2	y2	PROPN
ejpam-367	431	1	ẋ2	ẋ2	PROPN
ejpam-367	431	2	−	−	PROPN
ejpam-367	431	3	dλt	dλt	NOUN
ejpam-367	431	4	g	g	NOUN
ejpam-367	431	5	ẏ2	ẏ2	PROPN
ejpam-367	431	6	ẋ2	ẋ2	PROPN
ejpam-367	432	1	−λt	−λt	NOUN
ejpam-367	432	2	g	g	NOUN
ejpam-367	432	3	ẏ2	ẏ2	PROPN
ejpam-367	432	4	x2	x2	PROPN
ejpam-367	432	5	)	)	PUNCT
ejpam-367	433	1	+	+	VERB
ejpam-367	433	2	d2((θ	d2((θ	NOUN
ejpam-367	433	3	2(t)−	2(t)−	NUM
ejpam-367	434	1	γ	γ	X
ejpam-367	434	2	ȳ2(t))t	ȳ2(t))t	X
ejpam-367	434	3	(	(	PUNCT
ejpam-367	434	4	−λt	−λt	NOUN
ejpam-367	434	5	g	g	NOUN
ejpam-367	434	6	ẏ2	ẏ2	PROPN
ejpam-367	434	7	ẋ2	ẋ2	PROPN
ejpam-367	434	8	)	)	PUNCT
ejpam-367	434	9	)	)	PUNCT
ejpam-367	435	1	=	=	SYM
ejpam-367	435	2	0	0	PUNCT
ejpam-367	435	3	(	(	PUNCT
ejpam-367	435	4	41	41	NUM
ejpam-367	435	5	)	)	PUNCT
ejpam-367	435	6	(	(	PUNCT
ejpam-367	435	7	τ−	τ−	PROPN
ejpam-367	435	8	(	(	PUNCT
ejpam-367	435	9	τt	τt	NOUN
ejpam-367	435	10	e)λ)t	e)λ)t	PROPN
ejpam-367	435	11	(	(	PUNCT
ejpam-367	435	12	f	f	PROPN
ejpam-367	435	13	y1	y1	NOUN
ejpam-367	435	14	−	−	PROPN
ejpam-367	436	1	d	d	X
ejpam-367	436	2	f	f	PROPN
ejpam-367	436	3	ẏ1	ẏ1	PROPN
ejpam-367	436	4	)	)	PUNCT
ejpam-367	437	1	+	+	CCONJ
ejpam-367	437	2	(	(	PUNCT
ejpam-367	437	3	θ	θ	PROPN
ejpam-367	437	4	1(t)−	1(t)−	PROPN
ejpam-367	437	5	(	(	PUNCT
ejpam-367	437	6	τt	τt	NOUN
ejpam-367	437	7	e	e	X
ejpam-367	437	8	)	)	PUNCT
ejpam-367	437	9	ȳ1(t))t	ȳ1(t))t	NOUN
ejpam-367	437	10	×(λt	×(λt	VERB
ejpam-367	437	11	f	f	PROPN
ejpam-367	437	12	y1	y1	NOUN
ejpam-367	437	13	y1	y1	PROPN
ejpam-367	437	14	−	−	PROPN
ejpam-367	437	15	dλt	dλt	NOUN
ejpam-367	437	16	f	f	PROPN
ejpam-367	437	17	ẏ1	ẏ1	PROPN
ejpam-367	437	18	y1	y1	PROPN
ejpam-367	437	19	)	)	PUNCT
ejpam-367	437	20	−d(θ	−d(θ	PROPN
ejpam-367	437	21	1(t)−	1(t)−	PROPN
ejpam-367	438	1	(	(	PUNCT
ejpam-367	438	2	τt	τt	NOUN
ejpam-367	438	3	e	e	X
ejpam-367	438	4	)	)	PUNCT
ejpam-367	438	5	ȳ1(t))t(−dλt	ȳ1(t))t(−dλt	PROPN
ejpam-367	438	6	f	f	PROPN
ejpam-367	438	7	ẏ1	ẏ1	PROPN
ejpam-367	438	8	ẏ1	ẏ1	PROPN
ejpam-367	438	9	)	)	PUNCT
ejpam-367	439	1	+	+	PROPN
ejpam-367	439	2	d2((θ	d2((θ	NOUN
ejpam-367	439	3	1(t)−	1(t)−	PROPN
ejpam-367	440	1	(	(	PUNCT
ejpam-367	440	2	τt	τt	NOUN
ejpam-367	440	3	e	e	NOUN
ejpam-367	440	4	)	)	PUNCT
ejpam-367	440	5	ȳ1(t))t(−λt	ȳ1(t))t(−λt	NOUN
ejpam-367	440	6	f	f	NOUN
ejpam-367	440	7	ẏ1	ẏ1	PROPN
ejpam-367	440	8	ẏ1	ẏ1	PROPN
ejpam-367	440	9	)	)	PUNCT
ejpam-367	440	10	)	)	PUNCT
ejpam-367	441	1	=	=	SYM
ejpam-367	441	2	0	0	PUNCT
ejpam-367	441	3	(	(	PUNCT
ejpam-367	441	4	42	42	NUM
ejpam-367	441	5	)	)	PUNCT
ejpam-367	441	6	(	(	PUNCT
ejpam-367	441	7	τ−	τ−	PROPN
ejpam-367	441	8	γλ)t	γλ)t	PROPN
ejpam-367	441	9	(	(	PUNCT
ejpam-367	441	10	g	g	NOUN
ejpam-367	441	11	y2	y2	PROPN
ejpam-367	441	12	−	−	PROPN
ejpam-367	441	13	dg	dg	PROPN
ejpam-367	441	14	ẏ2	ẏ2	PROPN
ejpam-367	441	15	)	)	PUNCT
ejpam-367	442	1	+	+	CCONJ
ejpam-367	442	2	(	(	PUNCT
ejpam-367	442	3	θ	θ	NOUN
ejpam-367	442	4	2(t)−	2(t)−	NUM
ejpam-367	442	5	γ	γ	NOUN
ejpam-367	442	6	ȳ2(t))t(λt	ȳ2(t))t(λt	NOUN
ejpam-367	442	7	g	g	PROPN
ejpam-367	442	8	y2	y2	NOUN
ejpam-367	442	9	y2	y2	PROPN
ejpam-367	443	1	−	−	PROPN
ejpam-367	443	2	dλt	dλt	NOUN
ejpam-367	443	3	g	g	PROPN
ejpam-367	443	4	ẏ2	ẏ2	PROPN
ejpam-367	443	5	y2	y2	PROPN
ejpam-367	443	6	)	)	PUNCT
ejpam-367	443	7	−d(θ	−d(θ	PROPN
ejpam-367	443	8	2(t)−	2(t)−	NUM
ejpam-367	444	1	γ	γ	X
ejpam-367	444	2	ȳ2(t))t(−dλt	ȳ2(t))t(−dλt	NOUN
ejpam-367	444	3	g	g	PROPN
ejpam-367	444	4	ẏ2	ẏ2	PROPN
ejpam-367	444	5	ẏ2	ẏ2	PROPN
ejpam-367	444	6	)	)	PUNCT
ejpam-367	445	1	+	+	PROPN
ejpam-367	445	2	d2(θ	d2(θ	PROPN
ejpam-367	445	3	2(t)−	2(t)−	NUM
ejpam-367	445	4	γ	γ	X
ejpam-367	445	5	ȳ2(t))t	ȳ2(t))t	X
ejpam-367	445	6	(	(	PUNCT
ejpam-367	445	7	−λt	−λt	NOUN
ejpam-367	445	8	g	g	PROPN
ejpam-367	445	9	ẏ2	ẏ2	PROPN
ejpam-367	445	10	ẏ2	ẏ2	PROPN
ejpam-367	445	11	)	)	PUNCT
ejpam-367	445	12	=	=	SYM
ejpam-367	445	13	0	0	PUNCT
ejpam-367	445	14	(	(	PUNCT
ejpam-367	445	15	43	43	NUM
ejpam-367	445	16	)	)	PUNCT
ejpam-367	445	17	since	since	SCONJ
ejpam-367	445	18	λ	λ	PROPN
ejpam-367	445	19	>	>	X
ejpam-367	445	20	0	0	NUM
ejpam-367	445	21	,	,	PUNCT
ejpam-367	445	22	(	(	PUNCT
ejpam-367	445	23	37	37	NUM
ejpam-367	445	24	)	)	PUNCT
ejpam-367	445	25	implies	imply	VERB
ejpam-367	445	26	η=	η=	ADJ
ejpam-367	445	27	0	0	NUM
ejpam-367	445	28	.	.	PUNCT
ejpam-367	446	1	consequently	consequently	ADV
ejpam-367	446	2	,	,	PUNCT
ejpam-367	446	3	(	(	PUNCT
ejpam-367	446	4	33	33	NUM
ejpam-367	446	5	)	)	PUNCT
ejpam-367	446	6	reduces	reduce	VERB
ejpam-367	446	7	to	to	ADP
ejpam-367	446	8	(	(	PUNCT
ejpam-367	446	9	θ	θ	PROPN
ejpam-367	446	10	1(t)−	1(t)−	PROPN
ejpam-367	447	1	(	(	PUNCT
ejpam-367	447	2	τt	τt	PROPN
ejpam-367	447	3	e)y1(t))t	e)y1(t))t	X
ejpam-367	447	4	(	(	PUNCT
ejpam-367	447	5	f	f	X
ejpam-367	447	6	y1	y1	NOUN
ejpam-367	447	7	−	−	PROPN
ejpam-367	448	1	d	d	X
ejpam-367	448	2	f	f	PROPN
ejpam-367	448	3	ẏ1	ẏ1	PROPN
ejpam-367	448	4	)	)	PUNCT
ejpam-367	449	1	+	+	CCONJ
ejpam-367	449	2	(	(	PUNCT
ejpam-367	449	3	θ	θ	X
ejpam-367	449	4	2(t)−	2(t)−	NUM
ejpam-367	449	5	γy2(t))t	γy2(t))t	NOUN
ejpam-367	449	6	(	(	PUNCT
ejpam-367	449	7	g	g	NOUN
ejpam-367	449	8	y2	y2	PROPN
ejpam-367	449	9	−	−	PROPN
ejpam-367	449	10	dg	dg	PROPN
ejpam-367	449	11	ẏ2	ẏ2	PROPN
ejpam-367	449	12	)	)	PUNCT
ejpam-367	449	13	=	=	SYM
ejpam-367	449	14	0	0	NUM
ejpam-367	449	15	,	,	PUNCT
ejpam-367	449	16	t	t	PROPN
ejpam-367	449	17	∈	∈	PROPN
ejpam-367	450	1	i	i	PRON
ejpam-367	450	2	(	(	PUNCT
ejpam-367	450	3	44	44	NUM
ejpam-367	450	4	)	)	PUNCT
ejpam-367	450	5	postmultiplying	postmultiplye	VERB
ejpam-367	450	6	(	(	PUNCT
ejpam-367	450	7	42	42	NUM
ejpam-367	450	8	)	)	PUNCT
ejpam-367	450	9	by	by	ADP
ejpam-367	450	10	(	(	PUNCT
ejpam-367	450	11	θ	θ	PROPN
ejpam-367	450	12	1(t)−	1(t)−	PROPN
ejpam-367	450	13	(	(	PUNCT
ejpam-367	450	14	τt	τt	NOUN
ejpam-367	450	15	e)y1(t	e)y1(t	ADJ
ejpam-367	450	16	)	)	PUNCT
ejpam-367	450	17	)	)	PUNCT
ejpam-367	450	18	,	,	PUNCT
ejpam-367	450	19	(	(	PUNCT
ejpam-367	450	20	43	43	NUM
ejpam-367	450	21	)	)	PUNCT
ejpam-367	450	22	by	by	ADP
ejpam-367	450	23	(	(	PUNCT
ejpam-367	450	24	θ	θ	PROPN
ejpam-367	450	25	2(t)−	2(t)−	NUM
ejpam-367	450	26	γy2(t	γy2(t	PROPN
ejpam-367	450	27	)	)	PUNCT
ejpam-367	450	28	)	)	PUNCT
ejpam-367	451	1	and	and	CCONJ
ejpam-367	451	2	then	then	ADV
ejpam-367	451	3	adding	add	VERB
ejpam-367	451	4	,	,	PUNCT
ejpam-367	451	5	we	we	PRON
ejpam-367	451	6	have	have	VERB
ejpam-367	451	7	{	{	PUNCT
ejpam-367	451	8	(	(	PUNCT
ejpam-367	451	9	τ−	τ−	PROPN
ejpam-367	451	10	(	(	PUNCT
ejpam-367	451	11	τt	τt	NOUN
ejpam-367	451	12	e)λ)t	e)λ)t	PROPN
ejpam-367	451	13	(	(	PUNCT
ejpam-367	451	14	f	f	PROPN
ejpam-367	451	15	y1	y1	NOUN
ejpam-367	451	16	−	−	PROPN
ejpam-367	452	1	d	d	X
ejpam-367	452	2	f	f	PROPN
ejpam-367	452	3	ẏ1	ẏ1	PROPN
ejpam-367	452	4	)	)	PUNCT
ejpam-367	453	1	+	+	CCONJ
ejpam-367	453	2	(	(	PUNCT
ejpam-367	453	3	θ	θ	PROPN
ejpam-367	453	4	1(t)−	1(t)−	PROPN
ejpam-367	453	5	(	(	PUNCT
ejpam-367	453	6	τt	τt	NOUN
ejpam-367	453	7	e	e	X
ejpam-367	453	8	)	)	PUNCT
ejpam-367	453	9	ȳ1(t))t	ȳ1(t))t	NOUN
ejpam-367	453	10	(	(	PUNCT
ejpam-367	453	11	λt	λt	ADP
ejpam-367	453	12	f	f	PROPN
ejpam-367	453	13	y1	y1	PROPN
ejpam-367	453	14	y1	y1	PROPN
ejpam-367	453	15	−	−	PROPN
ejpam-367	453	16	dλt	dλt	NOUN
ejpam-367	453	17	f	f	PROPN
ejpam-367	453	18	ẏ1	ẏ1	PROPN
ejpam-367	453	19	y1	y1	PROPN
ejpam-367	453	20	)	)	PUNCT
ejpam-367	453	21	i.	i.	PROPN
ejpam-367	453	22	husain	husain	PROPN
ejpam-367	453	23	and	and	CCONJ
ejpam-367	453	24	r.	r.	PROPN
ejpam-367	453	25	mattoo	mattoo	PROPN
ejpam-367	453	26	/	/	SYM
ejpam-367	453	27	eur	eur	PROPN
ejpam-367	453	28	.	.	PUNCT
ejpam-367	454	1	j.	j.	PROPN
ejpam-367	454	2	pure	pure	PROPN
ejpam-367	454	3	appl	appl	PROPN
ejpam-367	454	4	.	.	PROPN
ejpam-367	454	5	math	math	PROPN
ejpam-367	454	6	,	,	PUNCT
ejpam-367	454	7	2	2	NUM
ejpam-367	454	8	(	(	PUNCT
ejpam-367	454	9	2009	2009	NUM
ejpam-367	454	10	)	)	PUNCT
ejpam-367	454	11	,	,	PUNCT
ejpam-367	454	12	(	(	PUNCT
ejpam-367	454	13	578	578	NUM
ejpam-367	454	14	-	-	SYM
ejpam-367	454	15	603	603	NUM
ejpam-367	454	16	)	)	PUNCT
ejpam-367	454	17	594	594	NUM
ejpam-367	454	18	−d[(θ	−d[(θ	NUM
ejpam-367	454	19	1(t)−	1(t)−	PROPN
ejpam-367	455	1	(	(	PUNCT
ejpam-367	455	2	τt	τt	NOUN
ejpam-367	455	3	e	e	X
ejpam-367	455	4	)	)	PUNCT
ejpam-367	455	5	ȳ1(t))t	ȳ1(t))t	NOUN
ejpam-367	455	6	(	(	PUNCT
ejpam-367	455	7	−dλt	−dλt	NOUN
ejpam-367	455	8	f	f	PROPN
ejpam-367	455	9	ẏ1	ẏ1	PROPN
ejpam-367	455	10	ẏ1	ẏ1	PROPN
ejpam-367	455	11	)	)	PUNCT
ejpam-367	455	12	]	]	PUNCT
ejpam-367	456	1	+	+	PUNCT
ejpam-367	456	2	d2[(θ	d2[(θ	X
ejpam-367	456	3	1(t)−	1(t)−	NUM
ejpam-367	456	4	(	(	PUNCT
ejpam-367	456	5	τt	τt	NOUN
ejpam-367	456	6	e	e	X
ejpam-367	456	7	)	)	PUNCT
ejpam-367	456	8	ȳ1(t))t	ȳ1(t))t	NOUN
ejpam-367	456	9	(	(	PUNCT
ejpam-367	456	10	−λt	−λt	NOUN
ejpam-367	456	11	f	f	PROPN
ejpam-367	456	12	ẏ1	ẏ1	PROPN
ejpam-367	456	13	ẏ1)]}(θ	ẏ1)]}(θ	ADV
ejpam-367	456	14	1(t)−	1(t)−	PROPN
ejpam-367	457	1	(	(	PUNCT
ejpam-367	457	2	τt	τt	NOUN
ejpam-367	457	3	e	e	NOUN
ejpam-367	457	4	)	)	PUNCT
ejpam-367	457	5	ȳ1(t	ȳ1(t	NUM
ejpam-367	457	6	)	)	PUNCT
ejpam-367	457	7	)	)	PUNCT
ejpam-367	458	1	+	+	ADV
ejpam-367	458	2	{	{	PUNCT
ejpam-367	458	3	(	(	PUNCT
ejpam-367	458	4	τ−	τ−	PROPN
ejpam-367	458	5	γλ)t	γλ)t	PROPN
ejpam-367	458	6	(	(	PUNCT
ejpam-367	458	7	g	g	NOUN
ejpam-367	458	8	y2	y2	PROPN
ejpam-367	458	9	−	−	PROPN
ejpam-367	458	10	dg	dg	PROPN
ejpam-367	458	11	ẏ2	ẏ2	PROPN
ejpam-367	458	12	)	)	PUNCT
ejpam-367	458	13	+	+	CCONJ
ejpam-367	458	14	(	(	PUNCT
ejpam-367	458	15	θ	θ	X
ejpam-367	458	16	2(t)−	2(t)−	PROPN
ejpam-367	458	17	γ	γ	X
ejpam-367	458	18	ȳ2(t))t	ȳ2(t))t	X
ejpam-367	458	19	(	(	PUNCT
ejpam-367	458	20	λt	λt	ADP
ejpam-367	458	21	g	g	PROPN
ejpam-367	458	22	y2	y2	NOUN
ejpam-367	458	23	y2	y2	PROPN
ejpam-367	459	1	−	−	PROPN
ejpam-367	459	2	dλt	dλt	NOUN
ejpam-367	459	3	g	g	PROPN
ejpam-367	459	4	ẏ2	ẏ2	PROPN
ejpam-367	459	5	y2	y2	PROPN
ejpam-367	459	6	)	)	PUNCT
ejpam-367	460	1	−d[(θ	−d[(θ	NOUN
ejpam-367	460	2	2(t)−	2(t)−	NUM
ejpam-367	461	1	γ	γ	X
ejpam-367	461	2	ȳ2(t))t	ȳ2(t))t	X
ejpam-367	461	3	(	(	PUNCT
ejpam-367	461	4	−dλt	−dλt	NOUN
ejpam-367	461	5	g	g	PROPN
ejpam-367	461	6	ẏ2	ẏ2	PROPN
ejpam-367	461	7	ẏ2	ẏ2	PROPN
ejpam-367	461	8	)	)	PUNCT
ejpam-367	461	9	]	]	PUNCT
ejpam-367	462	1	+	+	PUNCT
ejpam-367	462	2	d2[(θ	d2[(θ	X
ejpam-367	462	3	2(t)−	2(t)−	NUM
ejpam-367	462	4	γ	γ	X
ejpam-367	462	5	ȳ2(t))t	ȳ2(t))t	X
ejpam-367	462	6	(	(	PUNCT
ejpam-367	462	7	−λt	−λt	NOUN
ejpam-367	462	8	g	g	PROPN
ejpam-367	462	9	ẏ2	ẏ2	PROPN
ejpam-367	462	10	ẏ2)]}(θ	ẏ2)]}(θ	NOUN
ejpam-367	462	11	2(t)−	2(t)−	NUM
ejpam-367	462	12	γ	γ	X
ejpam-367	462	13	ȳ2(t	ȳ2(t	PROPN
ejpam-367	462	14	)	)	PUNCT
ejpam-367	462	15	)	)	PUNCT
ejpam-367	463	1	=	=	SYM
ejpam-367	463	2	0	0	PUNCT
ejpam-367	463	3	(	(	PUNCT
ejpam-367	463	4	45	45	NUM
ejpam-367	463	5	)	)	PUNCT
ejpam-367	463	6	now	now	ADV
ejpam-367	463	7	multiplying	multiply	VERB
ejpam-367	463	8	(	(	PUNCT
ejpam-367	463	9	44	44	NUM
ejpam-367	463	10	)	)	PUNCT
ejpam-367	463	11	by	by	ADP
ejpam-367	463	12	λ̄	λ̄	NOUN
ejpam-367	463	13	and	and	CCONJ
ejpam-367	463	14	then	then	ADV
ejpam-367	463	15	using	use	VERB
ejpam-367	463	16	(	(	PUNCT
ejpam-367	463	17	35	35	NUM
ejpam-367	463	18	)	)	PUNCT
ejpam-367	463	19	and	and	CCONJ
ejpam-367	463	20	(	(	PUNCT
ejpam-367	463	21	36	36	NUM
ejpam-367	463	22	)	)	PUNCT
ejpam-367	463	23	we	we	PRON
ejpam-367	463	24	have	have	VERB
ejpam-367	463	25	∫	∫	PROPN
ejpam-367	464	1	i	i	PRON
ejpam-367	464	2	(	(	PUNCT
ejpam-367	464	3	θ	θ	PROPN
ejpam-367	464	4	1(t)−	1(t)−	PROPN
ejpam-367	464	5	(	(	PUNCT
ejpam-367	464	6	τt	τt	NOUN
ejpam-367	464	7	e	e	X
ejpam-367	464	8	)	)	PUNCT
ejpam-367	464	9	ȳ1(t))t	ȳ1(t))t	NOUN
ejpam-367	464	10	(	(	PUNCT
ejpam-367	464	11	λt	λt	ADP
ejpam-367	464	12	f	f	PROPN
ejpam-367	464	13	y1	y1	NOUN
ejpam-367	464	14	−	−	PROPN
ejpam-367	464	15	dλt	dλt	NOUN
ejpam-367	464	16	f	f	PROPN
ejpam-367	464	17	ẏ1)d	ẏ1)d	NOUN
ejpam-367	464	18	t	t	PROPN
ejpam-367	464	19	=	=	PUNCT
ejpam-367	464	20	0	0	PROPN
ejpam-367	464	21	that	that	PRON
ejpam-367	464	22	is	be	AUX
ejpam-367	464	23	∫	∫	PROPN
ejpam-367	464	24	i	i	INTJ
ejpam-367	464	25	(	(	PUNCT
ejpam-367	464	26	θ	θ	PROPN
ejpam-367	464	27	1(t)−	1(t)−	PROPN
ejpam-367	464	28	(	(	PUNCT
ejpam-367	464	29	τt	τt	NOUN
ejpam-367	464	30	e	e	X
ejpam-367	464	31	)	)	PUNCT
ejpam-367	464	32	ȳ1(t))t	ȳ1(t))t	NOUN
ejpam-367	464	33	(	(	PUNCT
ejpam-367	464	34	λt	λt	ADP
ejpam-367	464	35	f	f	PROPN
ejpam-367	464	36	y1	y1	PROPN
ejpam-367	464	37	−	−	PROPN
ejpam-367	464	38	dλt	dλt	NOUN
ejpam-367	464	39	f	f	PROPN
ejpam-367	464	40	ẏ1)(τt	ẏ1)(τt	NOUN
ejpam-367	464	41	e)d	e)d	X
ejpam-367	464	42	t	t	PROPN
ejpam-367	465	1	=	=	SYM
ejpam-367	465	2	0	0	NUM
ejpam-367	465	3	(	(	PUNCT
ejpam-367	465	4	46	46	NUM
ejpam-367	465	5	)	)	PUNCT
ejpam-367	465	6	multiplying	multiplying	NOUN
ejpam-367	465	7	(	(	PUNCT
ejpam-367	465	8	44	44	NUM
ejpam-367	465	9	)	)	PUNCT
ejpam-367	465	10	by	by	ADP
ejpam-367	465	11	τ	τ	PROPN
ejpam-367	465	12	,	,	PUNCT
ejpam-367	465	13	we	we	PRON
ejpam-367	465	14	have	have	VERB
ejpam-367	465	15	∫	∫	PROPN
ejpam-367	466	1	i	i	PRON
ejpam-367	467	1	[	[	X
ejpam-367	467	2	(	(	PUNCT
ejpam-367	467	3	θ	θ	PROPN
ejpam-367	467	4	1(t)−	1(t)−	PROPN
ejpam-367	467	5	(	(	PUNCT
ejpam-367	467	6	τt	τt	PROPN
ejpam-367	467	7	e)y1(t))t	e)y1(t))t	X
ejpam-367	467	8	(	(	PUNCT
ejpam-367	467	9	τ	τ	PROPN
ejpam-367	467	10	f	f	PROPN
ejpam-367	467	11	y1	y1	PROPN
ejpam-367	467	12	−	−	PROPN
ejpam-367	467	13	dτ	dτ	INTJ
ejpam-367	467	14	f	f	PROPN
ejpam-367	467	15	ẏ1	ẏ1	PROPN
ejpam-367	467	16	)	)	PUNCT
ejpam-367	468	1	+	+	PROPN
ejpam-367	468	2	(	(	PUNCT
ejpam-367	468	3	θ	θ	PROPN
ejpam-367	468	4	2(t)−	2(t)−	NUM
ejpam-367	468	5	γy2(t))t	γy2(t))t	NOUN
ejpam-367	468	6	(	(	PUNCT
ejpam-367	468	7	τg	τg	NOUN
ejpam-367	469	1	y2	y2	PROPN
ejpam-367	469	2	−	−	PROPN
ejpam-367	469	3	dτg	dτg	PROPN
ejpam-367	469	4	ẏ2)]d	ẏ2)]d	PROPN
ejpam-367	469	5	t	t	PROPN
ejpam-367	469	6	=	=	SYM
ejpam-367	469	7	0	0	NUM
ejpam-367	470	1	(	(	PUNCT
ejpam-367	470	2	47	47	NUM
ejpam-367	470	3	)	)	PUNCT
ejpam-367	470	4	subtracting	subtract	VERB
ejpam-367	470	5	(	(	PUNCT
ejpam-367	470	6	46	46	NUM
ejpam-367	470	7	)	)	PUNCT
ejpam-367	470	8	and	and	CCONJ
ejpam-367	470	9	(	(	PUNCT
ejpam-367	470	10	47	47	NUM
ejpam-367	470	11	)	)	PUNCT
ejpam-367	470	12	and	and	CCONJ
ejpam-367	470	13	using	use	VERB
ejpam-367	470	14	(	(	PUNCT
ejpam-367	470	15	35	35	NUM
ejpam-367	470	16	)	)	PUNCT
ejpam-367	470	17	and	and	CCONJ
ejpam-367	470	18	(	(	PUNCT
ejpam-367	470	19	36	36	NUM
ejpam-367	470	20	)	)	PUNCT
ejpam-367	470	21	,	,	PUNCT
ejpam-367	470	22	we	we	PRON
ejpam-367	470	23	have	have	VERB
ejpam-367	470	24	∫	∫	PROPN
ejpam-367	471	1	i	i	PRON
ejpam-367	472	1	[	[	X
ejpam-367	472	2	(	(	PUNCT
ejpam-367	472	3	θ	θ	PROPN
ejpam-367	472	4	1(t)−	1(t)−	PROPN
ejpam-367	472	5	(	(	PUNCT
ejpam-367	472	6	τt	τt	PROPN
ejpam-367	472	7	e)y1(t))t	e)y1(t))t	X
ejpam-367	472	8	(	(	PUNCT
ejpam-367	472	9	f	f	X
ejpam-367	472	10	y1	y1	NOUN
ejpam-367	472	11	−	−	PROPN
ejpam-367	473	1	d	d	X
ejpam-367	473	2	f	f	PROPN
ejpam-367	473	3	ẏ1)(τ−	ẏ1)(τ−	PROPN
ejpam-367	473	4	(	(	PUNCT
ejpam-367	473	5	τt	τt	NOUN
ejpam-367	473	6	e)λ̄	e)λ̄	NOUN
ejpam-367	473	7	)	)	PUNCT
ejpam-367	474	1	+	+	PROPN
ejpam-367	474	2	(	(	PUNCT
ejpam-367	474	3	θ	θ	PROPN
ejpam-367	474	4	2(t)−	2(t)−	NUM
ejpam-367	474	5	γy2(t))t	γy2(t))t	NOUN
ejpam-367	474	6	(	(	PUNCT
ejpam-367	474	7	τg	τg	NOUN
ejpam-367	475	1	y2	y2	PROPN
ejpam-367	475	2	−	−	PROPN
ejpam-367	475	3	dτg	dτg	INTJ
ejpam-367	476	1	ẏ2)(τ−	ẏ2)(τ−	PRON
ejpam-367	476	2	γλ̄)]d	γλ̄)]d	PROPN
ejpam-367	476	3	t	t	PROPN
ejpam-367	476	4	=	=	SYM
ejpam-367	476	5	0	0	NUM
ejpam-367	476	6	(	(	PUNCT
ejpam-367	476	7	48	48	NUM
ejpam-367	476	8	)	)	PUNCT
ejpam-367	476	9	from	from	ADP
ejpam-367	476	10	(	(	PUNCT
ejpam-367	476	11	45	45	NUM
ejpam-367	476	12	)	)	PUNCT
ejpam-367	476	13	and	and	CCONJ
ejpam-367	476	14	(	(	PUNCT
ejpam-367	476	15	48	48	NUM
ejpam-367	476	16	)	)	PUNCT
ejpam-367	476	17	,	,	PUNCT
ejpam-367	476	18	we	we	PRON
ejpam-367	476	19	obtain	obtain	VERB
ejpam-367	476	20	∫	∫	PROPN
ejpam-367	477	1	i	i	PRON
ejpam-367	477	2	[	[	X
ejpam-367	477	3	{	{	PUNCT
ejpam-367	477	4	(	(	PUNCT
ejpam-367	477	5	θ	θ	PROPN
ejpam-367	477	6	1(t)−	1(t)−	PROPN
ejpam-367	477	7	(	(	PUNCT
ejpam-367	477	8	τt	τt	NOUN
ejpam-367	477	9	e	e	X
ejpam-367	477	10	)	)	PUNCT
ejpam-367	477	11	ȳ1(t))t	ȳ1(t))t	NOUN
ejpam-367	477	12	(	(	PUNCT
ejpam-367	477	13	λt	λt	ADP
ejpam-367	477	14	f	f	PROPN
ejpam-367	477	15	y1	y1	PROPN
ejpam-367	477	16	y1	y1	PROPN
ejpam-367	477	17	−	−	PROPN
ejpam-367	477	18	dλt	dλt	NOUN
ejpam-367	477	19	f	f	PROPN
ejpam-367	477	20	y1	y1	NOUN
ejpam-367	477	21	ẏ1	ẏ1	PROPN
ejpam-367	477	22	)	)	PUNCT
ejpam-367	477	23	−d[(θ	−d[(θ	PROPN
ejpam-367	477	24	1(t)−	1(t)−	PROPN
ejpam-367	477	25	(	(	PUNCT
ejpam-367	477	26	τt	τt	NOUN
ejpam-367	477	27	e	e	X
ejpam-367	477	28	)	)	PUNCT
ejpam-367	477	29	ȳ1(t))t	ȳ1(t))t	NOUN
ejpam-367	477	30	(	(	PUNCT
ejpam-367	477	31	−dλt	−dλt	NOUN
ejpam-367	477	32	f	f	PROPN
ejpam-367	477	33	ẏ1	ẏ1	PROPN
ejpam-367	477	34	ẏ1	ẏ1	PROPN
ejpam-367	477	35	)	)	PUNCT
ejpam-367	477	36	]	]	PUNCT
ejpam-367	478	1	+	+	PUNCT
ejpam-367	478	2	d2[(θ	d2[(θ	X
ejpam-367	478	3	1(t)−	1(t)−	NUM
ejpam-367	478	4	(	(	PUNCT
ejpam-367	478	5	τt	τt	NOUN
ejpam-367	478	6	e	e	X
ejpam-367	478	7	)	)	PUNCT
ejpam-367	478	8	ȳ1(t))t	ȳ1(t))t	NOUN
ejpam-367	478	9	(	(	PUNCT
ejpam-367	478	10	−λt	−λt	NOUN
ejpam-367	478	11	f	f	NOUN
ejpam-367	478	12	ẏ1	ẏ1	PROPN
ejpam-367	478	13	ẏ1)]}.(θ	ẏ1)]}.(θ	PROPN
ejpam-367	478	14	1(t)−	1(t)−	PROPN
ejpam-367	478	15	(	(	PUNCT
ejpam-367	478	16	τt	τt	NOUN
ejpam-367	478	17	e	e	X
ejpam-367	478	18	)	)	PUNCT
ejpam-367	478	19	ȳ1(t))]d	ȳ1(t))]d	PROPN
ejpam-367	478	20	t	t	PROPN
ejpam-367	479	1	+	+	CCONJ
ejpam-367	479	2	∫	∫	PROPN
ejpam-367	479	3	i	i	PRON
ejpam-367	480	1	[	[	X
ejpam-367	480	2	{	{	PUNCT
ejpam-367	480	3	(	(	PUNCT
ejpam-367	480	4	θ	θ	PROPN
ejpam-367	480	5	2(t)−	2(t)−	PROPN
ejpam-367	480	6	γ	γ	X
ejpam-367	480	7	ȳ2(t))t	ȳ2(t))t	X
ejpam-367	480	8	(	(	PUNCT
ejpam-367	480	9	λt	λt	ADP
ejpam-367	480	10	g	g	PROPN
ejpam-367	480	11	y2	y2	NOUN
ejpam-367	480	12	y2	y2	PROPN
ejpam-367	480	13	−	−	PROPN
ejpam-367	480	14	dλt	dλt	NOUN
ejpam-367	480	15	g	g	PROPN
ejpam-367	480	16	y2	y2	PROPN
ejpam-367	480	17	ẏ2	ẏ2	PROPN
ejpam-367	480	18	)	)	PUNCT
ejpam-367	480	19	i.	i.	PROPN
ejpam-367	480	20	husain	husain	PROPN
ejpam-367	480	21	and	and	CCONJ
ejpam-367	480	22	r.	r.	PROPN
ejpam-367	480	23	mattoo	mattoo	PROPN
ejpam-367	480	24	/	/	SYM
ejpam-367	480	25	eur	eur	PROPN
ejpam-367	480	26	.	.	PUNCT
ejpam-367	481	1	j.	j.	PROPN
ejpam-367	481	2	pure	pure	PROPN
ejpam-367	481	3	appl	appl	PROPN
ejpam-367	481	4	.	.	PROPN
ejpam-367	481	5	math	math	PROPN
ejpam-367	481	6	,	,	PUNCT
ejpam-367	481	7	2	2	NUM
ejpam-367	481	8	(	(	PUNCT
ejpam-367	481	9	2009	2009	NUM
ejpam-367	481	10	)	)	PUNCT
ejpam-367	481	11	,	,	PUNCT
ejpam-367	481	12	(	(	PUNCT
ejpam-367	481	13	578	578	NUM
ejpam-367	481	14	-	-	SYM
ejpam-367	481	15	603	603	NUM
ejpam-367	481	16	)	)	PUNCT
ejpam-367	481	17	595	595	NUM
ejpam-367	481	18	−d[(θ	−d[(θ	NUM
ejpam-367	481	19	2(t)−	2(t)−	NUM
ejpam-367	482	1	γ	γ	X
ejpam-367	482	2	ȳ2(t))t	ȳ2(t))t	X
ejpam-367	482	3	(	(	PUNCT
ejpam-367	482	4	−dλt	−dλt	NOUN
ejpam-367	482	5	g	g	PROPN
ejpam-367	482	6	ẏ2	ẏ2	PROPN
ejpam-367	482	7	ẏ2	ẏ2	PROPN
ejpam-367	482	8	)	)	PUNCT
ejpam-367	482	9	]	]	PUNCT
ejpam-367	483	1	+	+	PUNCT
ejpam-367	483	2	d2[(θ	d2[(θ	X
ejpam-367	483	3	2(t)−	2(t)−	NUM
ejpam-367	483	4	γ	γ	X
ejpam-367	483	5	ȳ2(t))t	ȳ2(t))t	X
ejpam-367	483	6	(	(	PUNCT
ejpam-367	483	7	−λt	−λt	NOUN
ejpam-367	483	8	g	g	PROPN
ejpam-367	483	9	ẏ2	ẏ2	PROPN
ejpam-367	483	10	ẏ2)]}(θ	ẏ2)]}(θ	NOUN
ejpam-367	483	11	2(t)−	2(t)−	NUM
ejpam-367	483	12	γ	γ	X
ejpam-367	483	13	ȳ2(t))]d	ȳ2(t))]d	PROPN
ejpam-367	483	14	t	t	PROPN
ejpam-367	483	15	=	=	PUNCT
ejpam-367	483	16	0	0	NUM
ejpam-367	483	17	in	in	ADP
ejpam-367	483	18	view	view	NOUN
ejpam-367	483	19	of	of	ADP
ejpam-367	483	20	the	the	DET
ejpam-367	483	21	hypothesis	hypothesis	NOUN
ejpam-367	483	22	(	(	PUNCT
ejpam-367	483	23	c1	c1	PROPN
ejpam-367	483	24	)	)	PUNCT
ejpam-367	483	25	,	,	PUNCT
ejpam-367	483	26	we	we	PRON
ejpam-367	483	27	have	have	VERB
ejpam-367	483	28	∫	∫	PROPN
ejpam-367	484	1	i	i	PRON
ejpam-367	484	2	[	[	X
ejpam-367	484	3	{	{	PUNCT
ejpam-367	484	4	(	(	PUNCT
ejpam-367	484	5	θ	θ	PROPN
ejpam-367	484	6	1(t)−	1(t)−	PROPN
ejpam-367	484	7	(	(	PUNCT
ejpam-367	484	8	τt	τt	NOUN
ejpam-367	484	9	e	e	X
ejpam-367	484	10	)	)	PUNCT
ejpam-367	484	11	ȳ1(t))t	ȳ1(t))t	NOUN
ejpam-367	484	12	(	(	PUNCT
ejpam-367	484	13	λt	λt	ADP
ejpam-367	484	14	f	f	PROPN
ejpam-367	484	15	y1	y1	PROPN
ejpam-367	484	16	y1	y1	PROPN
ejpam-367	484	17	−	−	PROPN
ejpam-367	484	18	dλt	dλt	NOUN
ejpam-367	484	19	f	f	PROPN
ejpam-367	484	20	y1	y1	NOUN
ejpam-367	484	21	ẏ1	ẏ1	PROPN
ejpam-367	484	22	)	)	PUNCT
ejpam-367	484	23	−d[(θ	−d[(θ	PROPN
ejpam-367	484	24	1(t)−	1(t)−	PROPN
ejpam-367	484	25	(	(	PUNCT
ejpam-367	484	26	τt	τt	NOUN
ejpam-367	484	27	e	e	X
ejpam-367	484	28	)	)	PUNCT
ejpam-367	484	29	ȳ1(t))t	ȳ1(t))t	NOUN
ejpam-367	484	30	(	(	PUNCT
ejpam-367	484	31	−dλt	−dλt	NOUN
ejpam-367	484	32	f	f	PROPN
ejpam-367	484	33	ẏ1	ẏ1	PROPN
ejpam-367	484	34	ẏ1	ẏ1	PROPN
ejpam-367	484	35	)	)	PUNCT
ejpam-367	484	36	]	]	PUNCT
ejpam-367	485	1	+	+	PUNCT
ejpam-367	485	2	d2[(θ	d2[(θ	X
ejpam-367	485	3	1(t)−	1(t)−	NUM
ejpam-367	485	4	(	(	PUNCT
ejpam-367	485	5	τt	τt	NOUN
ejpam-367	485	6	e	e	X
ejpam-367	485	7	)	)	PUNCT
ejpam-367	485	8	ȳ1(t))t	ȳ1(t))t	NOUN
ejpam-367	485	9	(	(	PUNCT
ejpam-367	485	10	−λt	−λt	NOUN
ejpam-367	485	11	f	f	NOUN
ejpam-367	485	12	ẏ1	ẏ1	PROPN
ejpam-367	485	13	ẏ1)]}.(θ	ẏ1)]}.(θ	PROPN
ejpam-367	485	14	1(t)−	1(t)−	PROPN
ejpam-367	485	15	(	(	PUNCT
ejpam-367	485	16	τt	τt	NOUN
ejpam-367	485	17	e	e	X
ejpam-367	485	18	)	)	PUNCT
ejpam-367	485	19	ȳ1(t))]d	ȳ1(t))]d	PROPN
ejpam-367	485	20	t	t	NOUN
ejpam-367	485	21	=	=	SYM
ejpam-367	485	22	0	0	NUM
ejpam-367	486	1	and	and	CCONJ
ejpam-367	486	2	∫	∫	NOUN
ejpam-367	487	1	i	i	PRON
ejpam-367	488	1	[	[	X
ejpam-367	488	2	{	{	PUNCT
ejpam-367	488	3	(	(	PUNCT
ejpam-367	488	4	θ	θ	PROPN
ejpam-367	488	5	2(t)−	2(t)−	PROPN
ejpam-367	488	6	γ	γ	X
ejpam-367	488	7	ȳ2(t))t	ȳ2(t))t	X
ejpam-367	488	8	(	(	PUNCT
ejpam-367	488	9	λt	λt	ADP
ejpam-367	488	10	g	g	PROPN
ejpam-367	488	11	y2	y2	NOUN
ejpam-367	488	12	y2	y2	PROPN
ejpam-367	488	13	−	−	PROPN
ejpam-367	488	14	dλt	dλt	NOUN
ejpam-367	488	15	g	g	PROPN
ejpam-367	488	16	y2	y2	PROPN
ejpam-367	488	17	ẏ2	ẏ2	PROPN
ejpam-367	488	18	)	)	PUNCT
ejpam-367	488	19	−d[(θ	−d[(θ	NOUN
ejpam-367	488	20	2(t)−	2(t)−	NUM
ejpam-367	488	21	γ	γ	X
ejpam-367	488	22	ȳ2(t))t	ȳ2(t))t	X
ejpam-367	488	23	(	(	PUNCT
ejpam-367	488	24	−dλt	−dλt	NOUN
ejpam-367	488	25	g	g	PROPN
ejpam-367	488	26	ẏ2	ẏ2	PROPN
ejpam-367	488	27	ẏ2	ẏ2	PROPN
ejpam-367	488	28	)	)	PUNCT
ejpam-367	488	29	]	]	PUNCT
ejpam-367	489	1	+	+	PUNCT
ejpam-367	489	2	d2[(θ	d2[(θ	X
ejpam-367	489	3	2(t)−	2(t)−	NUM
ejpam-367	489	4	γ	γ	X
ejpam-367	489	5	ȳ2(t))t	ȳ2(t))t	X
ejpam-367	489	6	(	(	PUNCT
ejpam-367	489	7	−λt	−λt	NOUN
ejpam-367	489	8	g	g	PROPN
ejpam-367	489	9	ẏ2	ẏ2	PROPN
ejpam-367	489	10	ẏ2)]}(θ	ẏ2)]}(θ	NOUN
ejpam-367	489	11	2(t)−	2(t)−	NUM
ejpam-367	489	12	γ	γ	X
ejpam-367	489	13	ȳ2(t))]d	ȳ2(t))]d	PROPN
ejpam-367	489	14	t	t	PROPN
ejpam-367	489	15	=	=	PUNCT
ejpam-367	489	16	0	0	PUNCT
ejpam-367	489	17	this	this	DET
ejpam-367	489	18	in	in	ADP
ejpam-367	489	19	view	view	NOUN
ejpam-367	489	20	of	of	ADP
ejpam-367	489	21	the	the	DET
ejpam-367	489	22	hypothesis	hypothesis	NOUN
ejpam-367	489	23	(	(	PUNCT
ejpam-367	489	24	c2	c2	PROPN
ejpam-367	489	25	)	)	PUNCT
ejpam-367	489	26	yields	yield	NOUN
ejpam-367	489	27	,	,	PUNCT
ejpam-367	489	28	φ1(t	φ1(t	NUM
ejpam-367	489	29	)	)	PUNCT
ejpam-367	490	1	=	=	SYM
ejpam-367	490	2	θ	θ	X
ejpam-367	490	3	1(t)−	1(t)−	PROPN
ejpam-367	490	4	(	(	PUNCT
ejpam-367	490	5	τt	τt	NOUN
ejpam-367	490	6	e	e	NOUN
ejpam-367	490	7	)	)	PUNCT
ejpam-367	490	8	ȳ1(t	ȳ1(t	NUM
ejpam-367	490	9	)	)	PUNCT
ejpam-367	490	10	=	=	SYM
ejpam-367	490	11	0	0	NUM
ejpam-367	490	12	,	,	PUNCT
ejpam-367	490	13	t	t	PROPN
ejpam-367	490	14	∈	∈	PROPN
ejpam-367	491	1	i	i	PRON
ejpam-367	491	2	(	(	PUNCT
ejpam-367	491	3	49	49	NUM
ejpam-367	491	4	)	)	PUNCT
ejpam-367	491	5	φ2(t	φ2(t	PROPN
ejpam-367	491	6	)	)	PUNCT
ejpam-367	491	7	=	=	SYM
ejpam-367	491	8	θ	θ	NOUN
ejpam-367	491	9	2(t)−	2(t)−	NUM
ejpam-367	491	10	γ	γ	X
ejpam-367	491	11	ȳ2(t	ȳ2(t	PROPN
ejpam-367	491	12	)	)	PUNCT
ejpam-367	491	13	=	=	SYM
ejpam-367	491	14	0	0	NUM
ejpam-367	491	15	,	,	PUNCT
ejpam-367	491	16	t	t	PROPN
ejpam-367	491	17	∈	∈	PROPN
ejpam-367	491	18	i	i	PRON
ejpam-367	491	19	(	(	PUNCT
ejpam-367	491	20	50	50	NUM
ejpam-367	491	21	)	)	PUNCT
ejpam-367	491	22	from	from	ADP
ejpam-367	491	23	(	(	PUNCT
ejpam-367	491	24	50	50	NUM
ejpam-367	491	25	)	)	PUNCT
ejpam-367	491	26	and	and	CCONJ
ejpam-367	491	27	(	(	PUNCT
ejpam-367	491	28	43	43	NUM
ejpam-367	491	29	)	)	PUNCT
ejpam-367	491	30	,	,	PUNCT
ejpam-367	491	31	we	we	PRON
ejpam-367	491	32	have	have	VERB
ejpam-367	491	33	(	(	PUNCT
ejpam-367	491	34	τ−	τ−	PROPN
ejpam-367	491	35	γλ)t	γλ)t	PROPN
ejpam-367	491	36	(	(	PUNCT
ejpam-367	491	37	g	g	NOUN
ejpam-367	491	38	y2	y2	PROPN
ejpam-367	491	39	−	−	PROPN
ejpam-367	491	40	dg	dg	PROPN
ejpam-367	491	41	ẏ2	ẏ2	PROPN
ejpam-367	491	42	)	)	PUNCT
ejpam-367	491	43	=	=	PUNCT
ejpam-367	491	44	0	0	NUM
ejpam-367	492	1	that	that	PRON
ejpam-367	492	2	is	be	AUX
ejpam-367	492	3	p	p	X
ejpam-367	492	4	∑	∑	PROPN
ejpam-367	492	5	i=1	i=1	PROPN
ejpam-367	492	6	(	(	PUNCT
ejpam-367	492	7	τi	τi	ADP
ejpam-367	492	8	−	−	PROPN
ejpam-367	492	9	γλi)t	γλi)t	PROPN
ejpam-367	492	10	(	(	PUNCT
ejpam-367	492	11	g	g	NOUN
ejpam-367	492	12	y2	y2	PROPN
ejpam-367	492	13	−	−	PROPN
ejpam-367	492	14	dg	dg	PROPN
ejpam-367	492	15	ẏ2	ẏ2	PROPN
ejpam-367	492	16	)	)	PUNCT
ejpam-367	493	1	=	=	SYM
ejpam-367	493	2	0	0	PUNCT
ejpam-367	494	1	this	this	PRON
ejpam-367	494	2	in	in	ADP
ejpam-367	494	3	view	view	NOUN
ejpam-367	494	4	of	of	ADP
ejpam-367	494	5	the	the	DET
ejpam-367	494	6	(	(	PUNCT
ejpam-367	494	7	c3	c3	PROPN
ejpam-367	494	8	)	)	PUNCT
ejpam-367	494	9	yields	yield	NOUN
ejpam-367	494	10	τi	τi	NOUN
ejpam-367	495	1	=	=	SYM
ejpam-367	495	2	γλi	γλi	NOUN
ejpam-367	495	3	,	,	PUNCT
ejpam-367	495	4	i	i	PRON
ejpam-367	495	5	=	=	NOUN
ejpam-367	495	6	1	1	NUM
ejpam-367	495	7	,	,	PUNCT
ejpam-367	495	8	2	2	NUM
ejpam-367	495	9	,	,	PUNCT
ejpam-367	495	10	.	.	PUNCT
ejpam-367	495	11	.	.	PUNCT
ejpam-367	496	1	.	.	PUNCT
ejpam-367	497	1	,	,	PUNCT
ejpam-367	497	2	p	p	X
ejpam-367	497	3	(	(	PUNCT
ejpam-367	497	4	51	51	NUM
ejpam-367	497	5	)	)	PUNCT
ejpam-367	497	6	i.	i.	NOUN
ejpam-367	497	7	husain	husain	PROPN
ejpam-367	497	8	and	and	CCONJ
ejpam-367	497	9	r.	r.	PROPN
ejpam-367	497	10	mattoo	mattoo	PROPN
ejpam-367	497	11	/	/	SYM
ejpam-367	497	12	eur	eur	PROPN
ejpam-367	497	13	.	.	PUNCT
ejpam-367	498	1	j.	j.	PROPN
ejpam-367	498	2	pure	pure	PROPN
ejpam-367	498	3	appl	appl	PROPN
ejpam-367	498	4	.	.	PROPN
ejpam-367	498	5	math	math	PROPN
ejpam-367	498	6	,	,	PUNCT
ejpam-367	498	7	2	2	NUM
ejpam-367	498	8	(	(	PUNCT
ejpam-367	498	9	2009	2009	NUM
ejpam-367	498	10	)	)	PUNCT
ejpam-367	498	11	,	,	PUNCT
ejpam-367	498	12	(	(	PUNCT
ejpam-367	498	13	578	578	NUM
ejpam-367	498	14	-	-	SYM
ejpam-367	498	15	603	603	NUM
ejpam-367	498	16	)	)	PUNCT
ejpam-367	498	17	596	596	NUM
ejpam-367	498	18	let	let	VERB
ejpam-367	498	19	if	if	SCONJ
ejpam-367	498	20	possible	possible	ADJ
ejpam-367	498	21	,	,	PUNCT
ejpam-367	498	22	γ	γ	X
ejpam-367	498	23	=	=	SYM
ejpam-367	498	24	0	0	NUM
ejpam-367	498	25	.	.	PUNCT
ejpam-367	499	1	then	then	ADV
ejpam-367	499	2	from	from	ADP
ejpam-367	499	3	(	(	PUNCT
ejpam-367	499	4	51	51	NUM
ejpam-367	499	5	)	)	PUNCT
ejpam-367	499	6	,	,	PUNCT
ejpam-367	499	7	we	we	PRON
ejpam-367	499	8	have	have	VERB
ejpam-367	499	9	τ	τ	X
ejpam-367	499	10	=	=	SYM
ejpam-367	499	11	0	0	PROPN
ejpam-367	499	12	and	and	CCONJ
ejpam-367	499	13	therefore	therefore	ADV
ejpam-367	499	14	,	,	PUNCT
ejpam-367	499	15	from	from	ADP
ejpam-367	499	16	(	(	PUNCT
ejpam-367	499	17	49	49	NUM
ejpam-367	499	18	)	)	PUNCT
ejpam-367	499	19	and	and	CCONJ
ejpam-367	499	20	(	(	PUNCT
ejpam-367	499	21	50	50	NUM
ejpam-367	499	22	)	)	PUNCT
ejpam-367	499	23	,	,	PUNCT
ejpam-367	499	24	we	we	PRON
ejpam-367	499	25	have	have	VERB
ejpam-367	499	26	φ1(t	φ1(t	NUM
ejpam-367	499	27	)	)	PUNCT
ejpam-367	499	28	=	=	SYM
ejpam-367	499	29	0,θ	0,θ	ADJ
ejpam-367	499	30	2(t	2(t	NUM
ejpam-367	499	31	)	)	PUNCT
ejpam-367	500	1	=	=	SYM
ejpam-367	500	2	0	0	NUM
ejpam-367	500	3	,	,	PUNCT
ejpam-367	500	4	t	t	PROPN
ejpam-367	500	5	∈	∈	PROPN
ejpam-367	501	1	i	i	PRON
ejpam-367	501	2	hence	hence	ADV
ejpam-367	501	3	(	(	PUNCT
ejpam-367	501	4	τ	τ	PROPN
ejpam-367	501	5	,	,	PUNCT
ejpam-367	501	6	θ	θ	PROPN
ejpam-367	501	7	1(t),θ	1(t),θ	NUM
ejpam-367	501	8	2(t),η	2(t),η	NUM
ejpam-367	501	9	,	,	PUNCT
ejpam-367	501	10	γ	γ	NOUN
ejpam-367	501	11	)	)	PUNCT
ejpam-367	501	12	=	=	SYM
ejpam-367	501	13	0	0	NUM
ejpam-367	501	14	,	,	PUNCT
ejpam-367	501	15	contradicting	contradict	VERB
ejpam-367	501	16	fritz	fritz	PROPN
ejpam-367	501	17	-	-	PUNCT
ejpam-367	501	18	john	john	PROPN
ejpam-367	501	19	conditions	condition	NOUN
ejpam-367	501	20	(	(	PUNCT
ejpam-367	501	21	39	39	NUM
ejpam-367	501	22	)	)	PUNCT
ejpam-367	501	23	.	.	PUNCT
ejpam-367	502	1	hence	hence	ADV
ejpam-367	502	2	γ	γ	X
ejpam-367	502	3	>	>	X
ejpam-367	502	4	0	0	PUNCT
ejpam-367	503	1	and	and	CCONJ
ejpam-367	503	2	consequently	consequently	ADV
ejpam-367	503	3	τ	τ	X
ejpam-367	503	4	>	>	X
ejpam-367	503	5	0	0	PROPN
ejpam-367	503	6	.	.	PUNCT
ejpam-367	504	1	from	from	ADP
ejpam-367	504	2	(	(	PUNCT
ejpam-367	504	3	40	40	NUM
ejpam-367	504	4	)	)	PUNCT
ejpam-367	504	5	and	and	CCONJ
ejpam-367	504	6	(	(	PUNCT
ejpam-367	504	7	4.29	4.29	NUM
ejpam-367	504	8	)	)	PUNCT
ejpam-367	504	9	along	along	ADP
ejpam-367	504	10	with	with	ADP
ejpam-367	504	11	(	(	PUNCT
ejpam-367	504	12	51	51	NUM
ejpam-367	504	13	)	)	PUNCT
ejpam-367	504	14	,	,	PUNCT
ejpam-367	504	15	we	we	PRON
ejpam-367	504	16	obtain	obtain	VERB
ejpam-367	504	17	(	(	PUNCT
ejpam-367	504	18	λ̄t	λ̄t	X
ejpam-367	504	19	fx1	fx1	NOUN
ejpam-367	504	20	−	−	NOUN
ejpam-367	504	21	dλ̄t	dλ̄t	NOUN
ejpam-367	504	22	f	f	NOUN
ejpam-367	504	23	ẋ1	ẋ1	PROPN
ejpam-367	504	24	)	)	PUNCT
ejpam-367	505	1	=	=	SYM
ejpam-367	505	2	0	0	NUM
ejpam-367	505	3	,	,	PUNCT
ejpam-367	505	4	t	t	PROPN
ejpam-367	505	5	∈	∈	PROPN
ejpam-367	506	1	i	i	PRON
ejpam-367	506	2	(	(	PUNCT
ejpam-367	506	3	52	52	NUM
ejpam-367	506	4	)	)	PUNCT
ejpam-367	506	5	(	(	PUNCT
ejpam-367	506	6	λ̄t	λ̄t	PROPN
ejpam-367	506	7	gx2	gx2	NOUN
ejpam-367	506	8	−	−	PROPN
ejpam-367	506	9	dλ̄t	dλ̄t	NOUN
ejpam-367	506	10	g	g	PROPN
ejpam-367	506	11	ẋ2	ẋ2	PROPN
ejpam-367	506	12	)	)	PUNCT
ejpam-367	506	13	=	=	SYM
ejpam-367	506	14	0	0	NUM
ejpam-367	506	15	,	,	PUNCT
ejpam-367	506	16	t	t	PROPN
ejpam-367	506	17	∈	∈	PROPN
ejpam-367	507	1	i	i	PRON
ejpam-367	507	2	(	(	PUNCT
ejpam-367	507	3	53	53	NUM
ejpam-367	507	4	)	)	PUNCT
ejpam-367	507	5	which	which	PRON
ejpam-367	507	6	implies	imply	VERB
ejpam-367	507	7	∫	∫	PROPN
ejpam-367	507	8	i	i	PROPN
ejpam-367	507	9	x2(t)t(λ̄t	x2(t)t(λ̄t	PROPN
ejpam-367	508	1	gx2	gx2	PROPN
ejpam-367	508	2	−	−	PROPN
ejpam-367	508	3	dλ̄t	dλ̄t	NOUN
ejpam-367	508	4	g	g	NOUN
ejpam-367	508	5	ẋ2)d	ẋ2)d	PROPN
ejpam-367	508	6	t	t	PROPN
ejpam-367	509	1	=	=	SYM
ejpam-367	509	2	0	0	PROPN
ejpam-367	509	3	(	(	PUNCT
ejpam-367	509	4	54	54	NUM
ejpam-367	509	5	)	)	PUNCT
ejpam-367	509	6	from	from	ADP
ejpam-367	509	7	(	(	PUNCT
ejpam-367	509	8	52)-(54	52)-(54	NOUN
ejpam-367	509	9	)	)	PUNCT
ejpam-367	509	10	together	together	ADV
ejpam-367	509	11	with	with	ADP
ejpam-367	509	12	(	(	PUNCT
ejpam-367	509	13	49	49	NUM
ejpam-367	509	14	)	)	PUNCT
ejpam-367	509	15	,	,	PUNCT
ejpam-367	509	16	we	we	PRON
ejpam-367	509	17	have	have	VERB
ejpam-367	509	18	y1(t)t	y1(t)t	NOUN
ejpam-367	509	19	(	(	PUNCT
ejpam-367	509	20	λ̄t	λ̄t	X
ejpam-367	509	21	f	f	NOUN
ejpam-367	509	22	y1	y1	NOUN
ejpam-367	509	23	−	−	PROPN
ejpam-367	509	24	dλ̄t	dλ̄t	NOUN
ejpam-367	509	25	f	f	NOUN
ejpam-367	509	26	ẏ1	ẏ1	PROPN
ejpam-367	509	27	)	)	PUNCT
ejpam-367	509	28	=	=	SYM
ejpam-367	510	1	0	0	NUM
ejpam-367	510	2	,	,	PUNCT
ejpam-367	510	3	t	t	PROPN
ejpam-367	510	4	∈	∈	PROPN
ejpam-367	511	1	i	i	PRON
ejpam-367	511	2	(	(	PUNCT
ejpam-367	511	3	55	55	NUM
ejpam-367	511	4	)	)	PUNCT
ejpam-367	511	5	from	from	ADP
ejpam-367	511	6	the	the	DET
ejpam-367	511	7	primal	primal	ADJ
ejpam-367	511	8	objective	objective	NOUN
ejpam-367	511	9	with	with	ADP
ejpam-367	511	10	(	(	PUNCT
ejpam-367	511	11	55	55	NUM
ejpam-367	511	12	)	)	PUNCT
ejpam-367	511	13	∫	∫	PROPN
ejpam-367	512	1	i	i	PRON
ejpam-367	512	2	{	{	PUNCT
ejpam-367	512	3	f	f	PROPN
ejpam-367	512	4	(	(	PUNCT
ejpam-367	512	5	t	t	PROPN
ejpam-367	512	6	,	,	PUNCT
ejpam-367	512	7	x1	x1	PROPN
ejpam-367	512	8	,	,	PUNCT
ejpam-367	512	9	ẋ1	ẋ1	PROPN
ejpam-367	512	10	,	,	PUNCT
ejpam-367	512	11	y1	y1	PROPN
ejpam-367	512	12	,	,	PUNCT
ejpam-367	512	13	ẏ1	ẏ1	PROPN
ejpam-367	512	14	)	)	PUNCT
ejpam-367	512	15	+	+	CCONJ
ejpam-367	512	16	g(t	g(t	PROPN
ejpam-367	512	17	,	,	PUNCT
ejpam-367	512	18	x2	x2	PROPN
ejpam-367	512	19	,	,	PUNCT
ejpam-367	512	20	ẋ2	ẋ2	PROPN
ejpam-367	512	21	,	,	PUNCT
ejpam-367	512	22	y2	y2	NOUN
ejpam-367	512	23	,	,	PUNCT
ejpam-367	512	24	ẏ2	ẏ2	PROPN
ejpam-367	512	25	)	)	PUNCT
ejpam-367	512	26	−	−	PROPN
ejpam-367	513	1	y1(t)t(λt	y1(t)t(λt	PROPN
ejpam-367	514	1	f	f	PROPN
ejpam-367	514	2	y1−dλt	y1−dλt	X
ejpam-367	515	1	f	f	PROPN
ejpam-367	515	2	ẏ1)}d	ẏ1)}d	PROPN
ejpam-367	515	3	t	t	PROPN
ejpam-367	515	4	=	=	SYM
ejpam-367	515	5	∫	∫	PROPN
ejpam-367	516	1	i	i	PRON
ejpam-367	516	2	{	{	PUNCT
ejpam-367	516	3	f	f	PROPN
ejpam-367	516	4	(	(	PUNCT
ejpam-367	516	5	t	t	PROPN
ejpam-367	516	6	,	,	PUNCT
ejpam-367	516	7	x1	x1	PROPN
ejpam-367	516	8	,	,	PUNCT
ejpam-367	516	9	ẋ1	ẋ1	PROPN
ejpam-367	516	10	,	,	PUNCT
ejpam-367	516	11	y1	y1	PROPN
ejpam-367	516	12	,	,	PUNCT
ejpam-367	516	13	ẏ1	ẏ1	PROPN
ejpam-367	516	14	)	)	PUNCT
ejpam-367	516	15	+	+	CCONJ
ejpam-367	516	16	g(t	g(t	PROPN
ejpam-367	516	17	,	,	PUNCT
ejpam-367	516	18	x2	x2	PROPN
ejpam-367	516	19	,	,	PUNCT
ejpam-367	516	20	ẋ2	ẋ2	PROPN
ejpam-367	516	21	,	,	PUNCT
ejpam-367	516	22	y2	y2	PROPN
ejpam-367	516	23	,	,	PUNCT
ejpam-367	516	24	ẏ2)}d	ẏ2)}d	PROPN
ejpam-367	516	25	t	t	PROPN
ejpam-367	516	26	(	(	PUNCT
ejpam-367	516	27	56	56	NUM
ejpam-367	516	28	)	)	PUNCT
ejpam-367	516	29	from	from	ADP
ejpam-367	516	30	the	the	DET
ejpam-367	516	31	dual	dual	ADJ
ejpam-367	516	32	objective	objective	NOUN
ejpam-367	516	33	in	in	ADP
ejpam-367	516	34	view	view	NOUN
ejpam-367	516	35	of	of	ADP
ejpam-367	516	36	(	(	PUNCT
ejpam-367	516	37	52	52	NUM
ejpam-367	516	38	)	)	PUNCT
ejpam-367	516	39	,	,	PUNCT
ejpam-367	516	40	we	we	PRON
ejpam-367	516	41	have	have	VERB
ejpam-367	516	42	∫	∫	PROPN
ejpam-367	517	1	i	i	PRON
ejpam-367	517	2	{	{	PUNCT
ejpam-367	517	3	f	f	PROPN
ejpam-367	517	4	(	(	PUNCT
ejpam-367	517	5	t	t	PROPN
ejpam-367	517	6	,	,	PUNCT
ejpam-367	517	7	x1	x1	PROPN
ejpam-367	517	8	,	,	PUNCT
ejpam-367	517	9	ẋ1	ẋ1	PROPN
ejpam-367	517	10	,	,	PUNCT
ejpam-367	517	11	y1	y1	PROPN
ejpam-367	517	12	,	,	PUNCT
ejpam-367	517	13	ẏ1	ẏ1	PROPN
ejpam-367	517	14	)	)	PUNCT
ejpam-367	517	15	+	+	CCONJ
ejpam-367	517	16	g(t	g(t	PROPN
ejpam-367	517	17	,	,	PUNCT
ejpam-367	517	18	x2	x2	PROPN
ejpam-367	517	19	,	,	PUNCT
ejpam-367	517	20	ẋ2	ẋ2	PROPN
ejpam-367	517	21	,	,	PUNCT
ejpam-367	517	22	y2	y2	NOUN
ejpam-367	517	23	,	,	PUNCT
ejpam-367	517	24	ẏ2	ẏ2	PROPN
ejpam-367	517	25	)	)	PUNCT
ejpam-367	517	26	−	−	PROPN
ejpam-367	518	1	x1(t)t(λt	x1(t)t(λt	X
ejpam-367	518	2	fx1−dλt	fx1−dλt	PUNCT
ejpam-367	519	1	f	f	PROPN
ejpam-367	519	2	ẋ1)}d	ẋ1)}d	PROPN
ejpam-367	519	3	t	t	PROPN
ejpam-367	519	4	=	=	SYM
ejpam-367	519	5	∫	∫	PROPN
ejpam-367	520	1	i	i	PRON
ejpam-367	520	2	{	{	PUNCT
ejpam-367	520	3	f	f	PROPN
ejpam-367	520	4	(	(	PUNCT
ejpam-367	520	5	t	t	PROPN
ejpam-367	520	6	,	,	PUNCT
ejpam-367	520	7	x1	x1	PROPN
ejpam-367	520	8	,	,	PUNCT
ejpam-367	520	9	ẋ1	ẋ1	PROPN
ejpam-367	520	10	,	,	PUNCT
ejpam-367	520	11	y1	y1	PROPN
ejpam-367	520	12	,	,	PUNCT
ejpam-367	520	13	ẏ1	ẏ1	PROPN
ejpam-367	520	14	)	)	PUNCT
ejpam-367	520	15	+	+	CCONJ
ejpam-367	520	16	g(t	g(t	PROPN
ejpam-367	520	17	,	,	PUNCT
ejpam-367	520	18	x2	x2	PROPN
ejpam-367	520	19	,	,	PUNCT
ejpam-367	520	20	ẋ2	ẋ2	PROPN
ejpam-367	520	21	,	,	PUNCT
ejpam-367	520	22	y2	y2	PROPN
ejpam-367	520	23	,	,	PUNCT
ejpam-367	520	24	ẏ2)}d	ẏ2)}d	PROPN
ejpam-367	520	25	t	t	PROPN
ejpam-367	520	26	(	(	PUNCT
ejpam-367	520	27	57	57	NUM
ejpam-367	520	28	)	)	PUNCT
ejpam-367	520	29	i.	i.	NOUN
ejpam-367	520	30	husain	husain	PROPN
ejpam-367	520	31	and	and	CCONJ
ejpam-367	520	32	r.	r.	PROPN
ejpam-367	520	33	mattoo	mattoo	PROPN
ejpam-367	520	34	/	/	SYM
ejpam-367	520	35	eur	eur	PROPN
ejpam-367	520	36	.	.	PUNCT
ejpam-367	521	1	j.	j.	PROPN
ejpam-367	521	2	pure	pure	PROPN
ejpam-367	521	3	appl	appl	PROPN
ejpam-367	521	4	.	.	PROPN
ejpam-367	521	5	math	math	PROPN
ejpam-367	521	6	,	,	PUNCT
ejpam-367	521	7	2	2	NUM
ejpam-367	521	8	(	(	PUNCT
ejpam-367	521	9	2009	2009	NUM
ejpam-367	521	10	)	)	PUNCT
ejpam-367	521	11	,	,	PUNCT
ejpam-367	521	12	(	(	PUNCT
ejpam-367	521	13	578	578	NUM
ejpam-367	521	14	-	-	SYM
ejpam-367	521	15	603	603	NUM
ejpam-367	521	16	)	)	PUNCT
ejpam-367	521	17	597	597	NUM
ejpam-367	521	18	from	from	ADP
ejpam-367	521	19	(	(	PUNCT
ejpam-367	521	20	55	55	NUM
ejpam-367	521	21	)	)	PUNCT
ejpam-367	521	22	and	and	CCONJ
ejpam-367	521	23	(	(	PUNCT
ejpam-367	521	24	57	57	NUM
ejpam-367	521	25	)	)	PUNCT
ejpam-367	521	26	,	,	PUNCT
ejpam-367	521	27	the	the	DET
ejpam-367	521	28	equality	equality	NOUN
ejpam-367	521	29	of	of	ADP
ejpam-367	521	30	objective	objective	ADJ
ejpam-367	521	31	values	value	NOUN
ejpam-367	521	32	is	be	AUX
ejpam-367	521	33	evident	evident	ADJ
ejpam-367	521	34	.	.	PUNCT
ejpam-367	522	1	consequently	consequently	ADV
ejpam-367	522	2	,	,	PUNCT
ejpam-367	522	3	in	in	ADP
ejpam-367	522	4	view	view	NOUN
ejpam-367	522	5	of	of	ADP
ejpam-367	522	6	the	the	DET
ejpam-367	522	7	hypothesis	hypothesis	NOUN
ejpam-367	522	8	of	of	ADP
ejpam-367	522	9	theorem	theorem	NOUN
ejpam-367	522	10	1	1	NUM
ejpam-367	522	11	,	,	PUNCT
ejpam-367	522	12	the	the	DET
ejpam-367	522	13	efficiency	efficiency	NOUN
ejpam-367	522	14	of	of	ADP
ejpam-367	522	15	(	(	PUNCT
ejpam-367	522	16	x̄1	x̄1	PROPN
ejpam-367	522	17	,	,	PUNCT
ejpam-367	522	18	x̄2	x̄2	PROPN
ejpam-367	522	19	,	,	PUNCT
ejpam-367	522	20	ȳ1	ȳ1	PROPN
ejpam-367	522	21	,	,	PUNCT
ejpam-367	522	22	ȳ2	ȳ2	NOUN
ejpam-367	522	23	,	,	PUNCT
ejpam-367	522	24	λ̄	λ̄	PRON
ejpam-367	522	25	)	)	PUNCT
ejpam-367	522	26	follows	follow	VERB
ejpam-367	522	27	.	.	PUNCT
ejpam-367	523	1	we	we	PRON
ejpam-367	523	2	now	now	ADV
ejpam-367	523	3	state	state	NOUN
ejpam-367	523	4	converse	converse	NOUN
ejpam-367	523	5	duality	duality	NOUN
ejpam-367	523	6	whose	whose	DET
ejpam-367	523	7	proof	proof	NOUN
ejpam-367	523	8	follows	follow	VERB
ejpam-367	523	9	by	by	ADP
ejpam-367	523	10	symmetry	symmetry	NOUN
ejpam-367	523	11	.	.	PUNCT
ejpam-367	524	1	theorem	theorem	NOUN
ejpam-367	524	2	3	3	NUM
ejpam-367	524	3	(	(	PUNCT
ejpam-367	524	4	converse	converse	NOUN
ejpam-367	524	5	duality	duality	NOUN
ejpam-367	524	6	)	)	PUNCT
ejpam-367	524	7	.	.	PUNCT
ejpam-367	525	1	let	let	AUX
ejpam-367	525	2	(	(	PUNCT
ejpam-367	525	3	x̄1	x̄1	NOUN
ejpam-367	525	4	,	,	PUNCT
ejpam-367	525	5	x̄2	x̄2	PROPN
ejpam-367	525	6	,	,	PUNCT
ejpam-367	525	7	ȳ1	ȳ1	PROPN
ejpam-367	525	8	,	,	PUNCT
ejpam-367	525	9	ȳ2	ȳ2	NOUN
ejpam-367	525	10	,	,	PUNCT
ejpam-367	525	11	λ̄	λ̄	PRON
ejpam-367	525	12	)	)	PUNCT
ejpam-367	525	13	be	be	VERB
ejpam-367	525	14	an	an	DET
ejpam-367	525	15	efficient	efficient	ADJ
ejpam-367	525	16	solution	solution	NOUN
ejpam-367	525	17	of	of	ADP
ejpam-367	525	18	(	(	PUNCT
ejpam-367	525	19	mix	mix	VERB
ejpam-367	525	20	sp	sp	NOUN
ejpam-367	525	21	)	)	PUNCT
ejpam-367	525	22	.	.	PUNCT
ejpam-367	526	1	let	let	VERB
ejpam-367	526	2	λ=	λ=	NOUN
ejpam-367	526	3	λ̄	λ̄	NOUN
ejpam-367	526	4	be	be	AUX
ejpam-367	526	5	fixed	fix	VERB
ejpam-367	526	6	in	in	ADP
ejpam-367	526	7	(	(	PUNCT
ejpam-367	526	8	mix	mix	VERB
ejpam-367	526	9	sd	sd	NOUN
ejpam-367	526	10	)	)	PUNCT
ejpam-367	526	11	and	and	CCONJ
ejpam-367	526	12	(	(	PUNCT
ejpam-367	526	13	a1	a1	PROPN
ejpam-367	526	14	)	)	PUNCT
ejpam-367	526	15	∫	∫	NOUN
ejpam-367	527	1	i	i	PRON
ejpam-367	527	2	[	[	X
ejpam-367	527	3	{	{	PUNCT
ejpam-367	527	4	ψ1(t)t	ψ1(t)t	X
ejpam-367	527	5	(	(	PUNCT
ejpam-367	527	6	λt	λt	ADP
ejpam-367	527	7	fx1	fx1	PROPN
ejpam-367	527	8	x1	x1	PROPN
ejpam-367	527	9	−	−	PROPN
ejpam-367	527	10	dλt	dλt	NOUN
ejpam-367	527	11	fx1	fx1	NOUN
ejpam-367	528	1	ẋ1)−	ẋ1)−	PROPN
ejpam-367	528	2	dψ1(t)t	dψ1(t)t	PROPN
ejpam-367	528	3	(	(	PUNCT
ejpam-367	528	4	−dλt	−dλt	NOUN
ejpam-367	528	5	f	f	PROPN
ejpam-367	528	6	ẋ1	ẋ1	PROPN
ejpam-367	528	7	ẋ1	ẋ1	PROPN
ejpam-367	528	8	)	)	PUNCT
ejpam-367	529	1	+	+	NOUN
ejpam-367	529	2	d2ψ1(t)t	d2ψ1(t)t	X
ejpam-367	529	3	(	(	PUNCT
ejpam-367	529	4	−λt	−λt	NOUN
ejpam-367	529	5	f	f	PROPN
ejpam-367	529	6	ẋ1	ẋ1	PROPN
ejpam-367	529	7	ẋ1)}ψ1(t)]d	ẋ1)}ψ1(t)]d	PROPN
ejpam-367	529	8	t	t	PROPN
ejpam-367	529	9	>	>	X
ejpam-367	529	10	0	0	PROPN
ejpam-367	529	11	,	,	PUNCT
ejpam-367	529	12	and	and	CCONJ
ejpam-367	529	13	∫	∫	NOUN
ejpam-367	530	1	i	i	PRON
ejpam-367	531	1	[	[	X
ejpam-367	531	2	{	{	PUNCT
ejpam-367	531	3	ψ2(t)t(λt	ψ2(t)t(λt	PROPN
ejpam-367	531	4	gx2	gx2	PROPN
ejpam-367	531	5	x2	x2	PROPN
ejpam-367	531	6	−	−	PROPN
ejpam-367	531	7	dλt	dλt	NOUN
ejpam-367	531	8	gx2	gx2	PROPN
ejpam-367	531	9	ẋ2)−	ẋ2)−	VERB
ejpam-367	532	1	dψ2(t)t(−dλt	dψ2(t)t(−dλt	PROPN
ejpam-367	532	2	g	g	PROPN
ejpam-367	532	3	ẋ2	ẋ2	PROPN
ejpam-367	532	4	ẋ2	ẋ2	PROPN
ejpam-367	532	5	)	)	PUNCT
ejpam-367	532	6	+	+	NOUN
ejpam-367	532	7	d2ψ2(t)t(−λt	d2ψ2(t)t(−λt	NOUN
ejpam-367	532	8	g	g	PROPN
ejpam-367	532	9	ẋ2	ẋ2	PROPN
ejpam-367	533	1	ẋ2)}ψ2(t)]d	ẋ2)}ψ2(t)]d	PROPN
ejpam-367	533	2	t	t	PROPN
ejpam-367	533	3	>	>	X
ejpam-367	533	4	0	0	NUM
ejpam-367	533	5	,	,	PUNCT
ejpam-367	533	6	(	(	PUNCT
ejpam-367	533	7	a2	a2	PROPN
ejpam-367	533	8	)	)	PUNCT
ejpam-367	533	9	∫	∫	NOUN
ejpam-367	534	1	i	i	PRON
ejpam-367	534	2	[	[	X
ejpam-367	534	3	{	{	PUNCT
ejpam-367	534	4	ψ1(t)t(λt	ψ1(t)t(λt	NOUN
ejpam-367	534	5	fx1	fx1	NOUN
ejpam-367	534	6	x1	x1	NUM
ejpam-367	534	7	−	−	PROPN
ejpam-367	534	8	dλt	dλt	NOUN
ejpam-367	534	9	fx1	fx1	NOUN
ejpam-367	534	10	ẋ1)−	ẋ1)−	PROPN
ejpam-367	535	1	dψ1(t)t(−dλt	dψ1(t)t(−dλt	PROPN
ejpam-367	535	2	f	f	PROPN
ejpam-367	535	3	ẋ1	ẋ1	PROPN
ejpam-367	535	4	ẋ1	ẋ1	PROPN
ejpam-367	535	5	)	)	PUNCT
ejpam-367	536	1	+	+	NOUN
ejpam-367	536	2	d2ψ1(t)t(−λt	d2ψ1(t)t(−λt	NOUN
ejpam-367	536	3	f	f	PROPN
ejpam-367	536	4	ẋ1	ẋ1	PROPN
ejpam-367	536	5	ẋ1)}ψ1(t)]d	ẋ1)}ψ1(t)]d	PROPN
ejpam-367	537	1	t	t	PROPN
ejpam-367	537	2	=	=	SYM
ejpam-367	537	3	0	0	NUM
ejpam-367	537	4	,	,	PUNCT
ejpam-367	537	5	t	t	PROPN
ejpam-367	537	6	∈	∈	PROPN
ejpam-367	537	7	i	i	PRON
ejpam-367	537	8	⇒ψ1(t	⇒ψ1(t	VERB
ejpam-367	537	9	)	)	PUNCT
ejpam-367	538	1	=	=	SYM
ejpam-367	538	2	0	0	NUM
ejpam-367	538	3	,	,	PUNCT
ejpam-367	538	4	t	t	PROPN
ejpam-367	538	5	∈	∈	PROPN
ejpam-367	539	1	i	i	PRON
ejpam-367	539	2	,	,	PUNCT
ejpam-367	539	3	and	and	CCONJ
ejpam-367	539	4	∫	∫	PROPN
ejpam-367	540	1	i	i	PRON
ejpam-367	540	2	[	[	X
ejpam-367	540	3	{	{	PUNCT
ejpam-367	540	4	ψ2(t)t(λt	ψ2(t)t(λt	PROPN
ejpam-367	540	5	gx2	gx2	PROPN
ejpam-367	540	6	x2	x2	PROPN
ejpam-367	540	7	−	−	PROPN
ejpam-367	540	8	dλt	dλt	NOUN
ejpam-367	540	9	gx2	gx2	PROPN
ejpam-367	540	10	ẋ2)−	ẋ2)−	VERB
ejpam-367	541	1	dψ2(t)t(−dλt	dψ2(t)t(−dλt	PROPN
ejpam-367	541	2	g	g	PROPN
ejpam-367	541	3	ẋ2	ẋ2	PROPN
ejpam-367	541	4	ẋ2	ẋ2	PROPN
ejpam-367	541	5	)	)	PUNCT
ejpam-367	541	6	+	+	NOUN
ejpam-367	541	7	d2ψ2(t)t(−λt	d2ψ2(t)t(−λt	NOUN
ejpam-367	541	8	g	g	PROPN
ejpam-367	542	1	ẋ2	ẋ2	PROPN
ejpam-367	542	2	ẋ2)}ψ2(t)]d	ẋ2)}ψ2(t)]d	PROPN
ejpam-367	543	1	t	t	PROPN
ejpam-367	543	2	=	=	SYM
ejpam-367	543	3	0	0	NUM
ejpam-367	543	4	,	,	PUNCT
ejpam-367	543	5	t	t	PROPN
ejpam-367	543	6	∈	∈	PROPN
ejpam-367	543	7	i	i	PRON
ejpam-367	543	8	⇒ψ2(t	⇒ψ2(t	VERB
ejpam-367	543	9	)	)	PUNCT
ejpam-367	543	10	=	=	SYM
ejpam-367	544	1	0	0	NUM
ejpam-367	544	2	,	,	PUNCT
ejpam-367	544	3	t	t	PROPN
ejpam-367	544	4	∈	∈	PROPN
ejpam-367	545	1	i	i	PRON
ejpam-367	545	2	and	and	CCONJ
ejpam-367	545	3	(	(	PUNCT
ejpam-367	545	4	a3	a3	NOUN
ejpam-367	545	5	)	)	PUNCT
ejpam-367	545	6	g	g	NOUN
ejpam-367	546	1	i	i	PRON
ejpam-367	546	2	x2	x2	INTJ
ejpam-367	547	1	−	−	PROPN
ejpam-367	547	2	dg	dg	VERB
ejpam-367	548	1	i	i	NOUN
ejpam-367	548	2	ẋ2	ẋ2	PUNCT
ejpam-367	548	3	=	=	PUNCT
ejpam-367	548	4	0	0	PROPN
ejpam-367	548	5	,	,	PUNCT
ejpam-367	548	6	i	i	PRON
ejpam-367	548	7	=	=	NOUN
ejpam-367	548	8	1	1	NUM
ejpam-367	548	9	,	,	PUNCT
ejpam-367	548	10	2	2	NUM
ejpam-367	548	11	,	,	PUNCT
ejpam-367	548	12	.	.	PUNCT
ejpam-367	548	13	.	.	PUNCT
ejpam-367	548	14	.	.	PUNCT
ejpam-367	549	1	,	,	PUNCT
ejpam-367	549	2	p	p	NOUN
ejpam-367	549	3	are	be	AUX
ejpam-367	549	4	linearly	linearly	ADV
ejpam-367	549	5	independent	independent	ADJ
ejpam-367	549	6	.	.	PUNCT
ejpam-367	550	1	let	let	VERB
ejpam-367	550	2	∫	∫	PROPN
ejpam-367	551	1	i	i	PRON
ejpam-367	551	2	f	f	PROPN
ejpam-367	552	1	d	d	PROPN
ejpam-367	552	2	t	t	PROPN
ejpam-367	552	3	and	and	CCONJ
ejpam-367	552	4	∫	∫	NOUN
ejpam-367	553	1	i	i	INTJ
ejpam-367	553	2	λt	λt	INTJ
ejpam-367	553	3	gd	gd	PROPN
ejpam-367	553	4	t	t	PROPN
ejpam-367	553	5	satisfy	satisfy	VERB
ejpam-367	553	6	the	the	DET
ejpam-367	553	7	invexity	invexity	NOUN
ejpam-367	553	8	and	and	CCONJ
ejpam-367	553	9	generalized	generalized	ADJ
ejpam-367	553	10	invexity	invexity	NOUN
ejpam-367	553	11	as	as	SCONJ
ejpam-367	553	12	stated	state	VERB
ejpam-367	553	13	in	in	ADP
ejpam-367	553	14	theorem	theorem	NOUN
ejpam-367	553	15	1	1	NUM
ejpam-367	553	16	,	,	PUNCT
ejpam-367	553	17	then	then	ADV
ejpam-367	553	18	(	(	PUNCT
ejpam-367	553	19	x̄1	x̄1	PROPN
ejpam-367	553	20	,	,	PUNCT
ejpam-367	553	21	x̄2	x̄2	PROPN
ejpam-367	553	22	,	,	PUNCT
ejpam-367	553	23	ȳ	ȳ	PROPN
ejpam-367	553	24	,	,	PUNCT
ejpam-367	553	25	ȳ2	ȳ2	NOUN
ejpam-367	553	26	,	,	PUNCT
ejpam-367	553	27	λ̄	λ̄	ADJ
ejpam-367	553	28	)	)	PUNCT
ejpam-367	553	29	and	and	CCONJ
ejpam-367	553	30	(	(	PUNCT
ejpam-367	553	31	ū1	ū1	PROPN
ejpam-367	553	32	,	,	PUNCT
ejpam-367	553	33	ū2	ū2	NOUN
ejpam-367	553	34	,	,	PUNCT
ejpam-367	553	35	v̄	v̄	NOUN
ejpam-367	553	36	,	,	PUNCT
ejpam-367	553	37	v̄2	v̄2	NUM
ejpam-367	553	38	,	,	PUNCT
ejpam-367	553	39	λ̄	λ̄	NUM
ejpam-367	553	40	)	)	PUNCT
ejpam-367	553	41	are	be	AUX
ejpam-367	553	42	efficient	efficient	ADJ
ejpam-367	553	43	solution	solution	NOUN
ejpam-367	553	44	of	of	ADP
ejpam-367	553	45	(	(	PUNCT
ejpam-367	553	46	mix	mix	VERB
ejpam-367	553	47	sp	sp	NOUN
ejpam-367	553	48	)	)	PUNCT
ejpam-367	553	49	and	and	CCONJ
ejpam-367	553	50	(	(	PUNCT
ejpam-367	553	51	mix	mix	VERB
ejpam-367	553	52	sd	sd	NOUN
ejpam-367	553	53	)	)	PUNCT
ejpam-367	553	54	respectively	respectively	ADV
ejpam-367	553	55	.	.	PUNCT
ejpam-367	554	1	i.	i.	PROPN
ejpam-367	554	2	husain	husain	PROPN
ejpam-367	554	3	and	and	CCONJ
ejpam-367	554	4	r.	r.	PROPN
ejpam-367	554	5	mattoo	mattoo	PROPN
ejpam-367	554	6	/	/	SYM
ejpam-367	554	7	eur	eur	PROPN
ejpam-367	554	8	.	.	PUNCT
ejpam-367	555	1	j.	j.	PROPN
ejpam-367	555	2	pure	pure	PROPN
ejpam-367	555	3	appl	appl	PROPN
ejpam-367	555	4	.	.	PROPN
ejpam-367	555	5	math	math	PROPN
ejpam-367	555	6	,	,	PUNCT
ejpam-367	555	7	2	2	NUM
ejpam-367	555	8	(	(	PUNCT
ejpam-367	555	9	2009	2009	NUM
ejpam-367	555	10	)	)	PUNCT
ejpam-367	555	11	,	,	PUNCT
ejpam-367	555	12	(	(	PUNCT
ejpam-367	555	13	578	578	NUM
ejpam-367	555	14	-	-	SYM
ejpam-367	555	15	603	603	NUM
ejpam-367	555	16	)	)	PUNCT
ejpam-367	555	17	598	598	NUM
ejpam-367	555	18	5	5	NUM
ejpam-367	555	19	.	.	PUNCT
ejpam-367	555	20	self	self	NOUN
ejpam-367	555	21	duality	duality	NOUN
ejpam-367	555	22	a	a	DET
ejpam-367	555	23	problem	problem	NOUN
ejpam-367	555	24	is	be	AUX
ejpam-367	555	25	said	say	VERB
ejpam-367	555	26	to	to	PART
ejpam-367	555	27	be	be	AUX
ejpam-367	555	28	self	self	NOUN
ejpam-367	555	29	-	-	PUNCT
ejpam-367	555	30	dual	dual	ADJ
ejpam-367	555	31	if	if	SCONJ
ejpam-367	555	32	it	it	PRON
ejpam-367	555	33	is	be	AUX
ejpam-367	555	34	formally	formally	ADV
ejpam-367	555	35	identical	identical	ADJ
ejpam-367	555	36	with	with	ADP
ejpam-367	555	37	its	its	PRON
ejpam-367	555	38	dual	dual	ADJ
ejpam-367	555	39	,	,	PUNCT
ejpam-367	555	40	in	in	ADP
ejpam-367	555	41	general	general	ADJ
ejpam-367	555	42	,	,	PUNCT
ejpam-367	555	43	the	the	DET
ejpam-367	555	44	problems	problem	NOUN
ejpam-367	555	45	(	(	PUNCT
ejpam-367	555	46	mix	mix	VERB
ejpam-367	555	47	sp	sp	NOUN
ejpam-367	555	48	)	)	PUNCT
ejpam-367	555	49	and	and	CCONJ
ejpam-367	555	50	(	(	PUNCT
ejpam-367	555	51	mix	mix	VERB
ejpam-367	555	52	sd	sd	NOUN
ejpam-367	555	53	)	)	PUNCT
ejpam-367	555	54	are	be	AUX
ejpam-367	555	55	not	not	PART
ejpam-367	555	56	formally	formally	ADV
ejpam-367	555	57	in	in	ADP
ejpam-367	555	58	the	the	DET
ejpam-367	555	59	absence	absence	NOUN
ejpam-367	555	60	of	of	ADP
ejpam-367	555	61	an	an	DET
ejpam-367	555	62	additional	additional	ADJ
ejpam-367	555	63	restrictions	restriction	NOUN
ejpam-367	555	64	of	of	ADP
ejpam-367	555	65	the	the	DET
ejpam-367	555	66	function	function	NOUN
ejpam-367	555	67	f	f	PROPN
ejpam-367	555	68	and	and	CCONJ
ejpam-367	555	69	g.	g.	PROPN
ejpam-367	555	70	hence	hence	ADV
ejpam-367	555	71	skew	skew	VERB
ejpam-367	555	72	symmetric	symmetric	NOUN
ejpam-367	555	73	of	of	ADP
ejpam-367	555	74	f	f	PROPN
ejpam-367	555	75	and	and	CCONJ
ejpam-367	555	76	g	g	PROPN
ejpam-367	555	77	is	be	AUX
ejpam-367	555	78	assumed	assume	VERB
ejpam-367	555	79	in	in	ADP
ejpam-367	555	80	order	order	NOUN
ejpam-367	555	81	to	to	PART
ejpam-367	555	82	validate	validate	VERB
ejpam-367	555	83	the	the	DET
ejpam-367	555	84	following	follow	VERB
ejpam-367	555	85	self	self	NOUN
ejpam-367	555	86	-	-	PUNCT
ejpam-367	555	87	duality	duality	NOUN
ejpam-367	555	88	theorem	theorem	NOUN
ejpam-367	555	89	.	.	PUNCT
ejpam-367	555	90	theorem	theorem	ADJ
ejpam-367	555	91	4	4	NUM
ejpam-367	555	92	(	(	PUNCT
ejpam-367	555	93	self	self	NOUN
ejpam-367	555	94	duality	duality	NOUN
ejpam-367	555	95	)	)	PUNCT
ejpam-367	555	96	.	.	PUNCT
ejpam-367	556	1	let	let	VERB
ejpam-367	556	2	f	f	PROPN
ejpam-367	556	3	i	i	PRON
ejpam-367	556	4	and	and	CCONJ
ejpam-367	556	5	g	g	PROPN
ejpam-367	556	6	i	i	PRON
ejpam-367	556	7	,	,	PUNCT
ejpam-367	556	8	i	i	PRON
ejpam-367	556	9	=	=	NOUN
ejpam-367	556	10	1	1	NUM
ejpam-367	556	11	,	,	PUNCT
ejpam-367	556	12	2	2	NUM
ejpam-367	556	13	,	,	PUNCT
ejpam-367	556	14	.	.	PUNCT
ejpam-367	556	15	.	.	PUNCT
ejpam-367	557	1	.	.	PUNCT
ejpam-367	558	1	,	,	PUNCT
ejpam-367	558	2	p	p	X
ejpam-367	558	3	,	,	PUNCT
ejpam-367	558	4	be	be	AUX
ejpam-367	558	5	skew	skew	ADV
ejpam-367	558	6	symmetric	symmetric	ADJ
ejpam-367	558	7	.	.	PUNCT
ejpam-367	559	1	then	then	ADV
ejpam-367	559	2	the	the	DET
ejpam-367	559	3	problem	problem	NOUN
ejpam-367	559	4	(	(	PUNCT
ejpam-367	559	5	mix	mix	VERB
ejpam-367	559	6	sp	sp	NOUN
ejpam-367	559	7	)	)	PUNCT
ejpam-367	559	8	is	be	AUX
ejpam-367	559	9	self	self	NOUN
ejpam-367	559	10	dual	dual	ADJ
ejpam-367	559	11	.	.	PUNCT
ejpam-367	560	1	if	if	SCONJ
ejpam-367	560	2	the	the	DET
ejpam-367	560	3	problems	problem	NOUN
ejpam-367	560	4	(	(	PUNCT
ejpam-367	560	5	mix	mix	VERB
ejpam-367	560	6	sp	sp	NOUN
ejpam-367	560	7	)	)	PUNCT
ejpam-367	560	8	and	and	CCONJ
ejpam-367	560	9	(	(	PUNCT
ejpam-367	560	10	mix	mix	VERB
ejpam-367	560	11	sd	sd	NOUN
ejpam-367	560	12	)	)	PUNCT
ejpam-367	560	13	are	be	AUX
ejpam-367	560	14	dual	dual	ADJ
ejpam-367	560	15	problems	problem	NOUN
ejpam-367	560	16	and	and	CCONJ
ejpam-367	560	17	(	(	PUNCT
ejpam-367	560	18	x̄1(t	x̄1(t	NUM
ejpam-367	560	19	)	)	PUNCT
ejpam-367	560	20	,	,	PUNCT
ejpam-367	560	21	x̄2(t	x̄2(t	PROPN
ejpam-367	560	22	)	)	PUNCT
ejpam-367	560	23	,	,	PUNCT
ejpam-367	560	24	ȳ(t	ȳ(t	PROPN
ejpam-367	560	25	)	)	PUNCT
ejpam-367	560	26	,	,	PUNCT
ejpam-367	560	27	ȳ2(t	ȳ2(t	PROPN
ejpam-367	560	28	)	)	PUNCT
ejpam-367	560	29	,	,	PUNCT
ejpam-367	560	30	λ̄	λ̄	PUNCT
ejpam-367	560	31	)	)	PUNCT
ejpam-367	560	32	is	be	AUX
ejpam-367	560	33	a	a	DET
ejpam-367	560	34	joint	joint	ADJ
ejpam-367	560	35	optimal	optimal	ADJ
ejpam-367	560	36	solution	solution	NOUN
ejpam-367	560	37	of	of	ADP
ejpam-367	560	38	(	(	PUNCT
ejpam-367	560	39	mix	mix	VERB
ejpam-367	560	40	sp	sp	NOUN
ejpam-367	560	41	)	)	PUNCT
ejpam-367	560	42	and	and	CCONJ
ejpam-367	560	43	(	(	PUNCT
ejpam-367	560	44	mix	mix	VERB
ejpam-367	560	45	sd	sd	NOUN
ejpam-367	560	46	)	)	PUNCT
ejpam-367	560	47	,	,	PUNCT
ejpam-367	560	48	then	then	ADV
ejpam-367	560	49	so	so	ADV
ejpam-367	560	50	is	be	AUX
ejpam-367	560	51	(	(	PUNCT
ejpam-367	560	52	ȳ(t	ȳ(t	NOUN
ejpam-367	560	53	)	)	PUNCT
ejpam-367	560	54	,	,	PUNCT
ejpam-367	560	55	ȳ2(t	ȳ2(t	PROPN
ejpam-367	560	56	)	)	PUNCT
ejpam-367	560	57	,	,	PUNCT
ejpam-367	560	58	x̄1(t	x̄1(t	NUM
ejpam-367	560	59	)	)	PUNCT
ejpam-367	560	60	,	,	PUNCT
ejpam-367	560	61	x̄2(t	x̄2(t	PROPN
ejpam-367	560	62	)	)	PUNCT
ejpam-367	560	63	,	,	PUNCT
ejpam-367	560	64	λ̄	λ̄	NUM
ejpam-367	560	65	)	)	PUNCT
ejpam-367	560	66	,	,	PUNCT
ejpam-367	560	67	and	and	CCONJ
ejpam-367	560	68	the	the	DET
ejpam-367	560	69	common	common	ADJ
ejpam-367	560	70	functional	functional	ADJ
ejpam-367	560	71	value	value	NOUN
ejpam-367	560	72	is	be	AUX
ejpam-367	560	73	zero	zero	NUM
ejpam-367	560	74	,	,	PUNCT
ejpam-367	560	75	i.e.	i.e.	X
ejpam-367	560	76	minimum(mix	minimum(mix	PROPN
ejpam-367	560	77	sp	sp	NOUN
ejpam-367	560	78	)	)	PUNCT
ejpam-367	560	79	=	=	SYM
ejpam-367	561	1	∫	∫	PROPN
ejpam-367	562	1	i	i	PRON
ejpam-367	562	2	{	{	PUNCT
ejpam-367	562	3	f	f	PROPN
ejpam-367	562	4	(	(	PUNCT
ejpam-367	562	5	x1	x1	PROPN
ejpam-367	562	6	,	,	PUNCT
ejpam-367	562	7	ẋ1	ẋ1	PROPN
ejpam-367	562	8	,	,	PUNCT
ejpam-367	562	9	y1	y1	PROPN
ejpam-367	562	10	,	,	PUNCT
ejpam-367	562	11	ẏ1	ẏ1	PROPN
ejpam-367	562	12	)	)	PUNCT
ejpam-367	562	13	+	+	NUM
ejpam-367	562	14	g(x2	g(x2	NOUN
ejpam-367	562	15	,	,	PUNCT
ejpam-367	562	16	ẋ2	ẋ2	PROPN
ejpam-367	562	17	,	,	PUNCT
ejpam-367	562	18	y2	y2	PROPN
ejpam-367	562	19	,	,	PUNCT
ejpam-367	562	20	ẏ2)}d	ẏ2)}d	PROPN
ejpam-367	562	21	t	t	NOUN
ejpam-367	562	22	=	=	SYM
ejpam-367	562	23	0	0	NUM
ejpam-367	562	24	proof	proof	NOUN
ejpam-367	562	25	.	.	PUNCT
ejpam-367	563	1	by	by	ADP
ejpam-367	563	2	skew	skew	ADJ
ejpam-367	563	3	symmetric	symmetric	NOUN
ejpam-367	563	4	of	of	ADP
ejpam-367	563	5	f	f	PROPN
ejpam-367	563	6	i	i	PROPN
ejpam-367	563	7	and	and	CCONJ
ejpam-367	563	8	g	g	PROPN
ejpam-367	563	9	i	i	PRON
ejpam-367	563	10	,	,	PUNCT
ejpam-367	563	11	we	we	PRON
ejpam-367	563	12	have	have	VERB
ejpam-367	563	13	f	f	PROPN
ejpam-367	564	1	i	i	PRON
ejpam-367	564	2	x1(t	x1(t	PROPN
ejpam-367	564	3	,	,	PUNCT
ejpam-367	564	4	x1(t	x1(t	PROPN
ejpam-367	564	5	)	)	PUNCT
ejpam-367	564	6	,	,	PUNCT
ejpam-367	564	7	ẋ1(t	ẋ1(t	PROPN
ejpam-367	564	8	)	)	PUNCT
ejpam-367	564	9	,	,	PUNCT
ejpam-367	564	10	y1(t	y1(t	PROPN
ejpam-367	564	11	)	)	PUNCT
ejpam-367	564	12	,	,	PUNCT
ejpam-367	564	13	ẏ1(t	ẏ1(t	PROPN
ejpam-367	564	14	)	)	PUNCT
ejpam-367	564	15	)	)	PUNCT
ejpam-367	565	1	=	=	PUNCT
ejpam-367	566	1	−	−	PROPN
ejpam-367	567	1	f	f	X
ejpam-367	568	1	i	i	PRON
ejpam-367	568	2	y1(t	y1(t	INTJ
ejpam-367	568	3	,	,	PUNCT
ejpam-367	568	4	y1(t	y1(t	PROPN
ejpam-367	568	5	)	)	PUNCT
ejpam-367	568	6	,	,	PUNCT
ejpam-367	568	7	ẏ1(t	ẏ1(t	PROPN
ejpam-367	568	8	)	)	PUNCT
ejpam-367	568	9	,	,	PUNCT
ejpam-367	568	10	x1(t	x1(t	PROPN
ejpam-367	568	11	)	)	PUNCT
ejpam-367	568	12	,	,	PUNCT
ejpam-367	568	13	ẋ1(t	ẋ1(t	PROPN
ejpam-367	568	14	)	)	PUNCT
ejpam-367	568	15	)	)	PUNCT
ejpam-367	569	1	g	g	NOUN
ejpam-367	570	1	i	i	PRON
ejpam-367	570	2	x2(t	x2(t	PROPN
ejpam-367	570	3	,	,	PUNCT
ejpam-367	570	4	x2(t	x2(t	PROPN
ejpam-367	570	5	)	)	PUNCT
ejpam-367	570	6	,	,	PUNCT
ejpam-367	570	7	ẋ2(t	ẋ2(t	PROPN
ejpam-367	570	8	)	)	PUNCT
ejpam-367	570	9	,	,	PUNCT
ejpam-367	570	10	y(t	y(t	PROPN
ejpam-367	570	11	)	)	PUNCT
ejpam-367	570	12	,	,	PUNCT
ejpam-367	570	13	ẏ2(t	ẏ2(t	PROPN
ejpam-367	570	14	)	)	PUNCT
ejpam-367	570	15	)	)	PUNCT
ejpam-367	571	1	=	=	PUNCT
ejpam-367	571	2	−g	−g	NOUN
ejpam-367	572	1	i	i	PRON
ejpam-367	572	2	ẏ2(t	ẏ2(t	VERB
ejpam-367	572	3	,	,	PUNCT
ejpam-367	572	4	y2(t	y2(t	PROPN
ejpam-367	572	5	)	)	PUNCT
ejpam-367	572	6	,	,	PUNCT
ejpam-367	572	7	ẏ2(t	ẏ2(t	PROPN
ejpam-367	572	8	)	)	PUNCT
ejpam-367	572	9	,	,	PUNCT
ejpam-367	572	10	x2(t	x2(t	PROPN
ejpam-367	572	11	)	)	PUNCT
ejpam-367	572	12	,	,	PUNCT
ejpam-367	572	13	ẋ2(t	ẋ2(t	PROPN
ejpam-367	572	14	)	)	PUNCT
ejpam-367	572	15	)	)	PUNCT
ejpam-367	573	1	f	f	PROPN
ejpam-367	574	1	i	i	PRON
ejpam-367	574	2	y1(t	y1(t	PRON
ejpam-367	574	3	,	,	PUNCT
ejpam-367	574	4	x1(t	x1(t	PROPN
ejpam-367	574	5	)	)	PUNCT
ejpam-367	574	6	,	,	PUNCT
ejpam-367	574	7	ẋ1(t	ẋ1(t	PROPN
ejpam-367	574	8	)	)	PUNCT
ejpam-367	574	9	,	,	PUNCT
ejpam-367	574	10	y1(t	y1(t	PROPN
ejpam-367	574	11	)	)	PUNCT
ejpam-367	574	12	,	,	PUNCT
ejpam-367	574	13	ẏ1(t	ẏ1(t	PROPN
ejpam-367	574	14	)	)	PUNCT
ejpam-367	574	15	)	)	PUNCT
ejpam-367	575	1	=	=	PRON
ejpam-367	575	2	−	−	PROPN
ejpam-367	575	3	f	f	X
ejpam-367	576	1	i	i	PRON
ejpam-367	576	2	x1(t	x1(t	X
ejpam-367	576	3	,	,	PUNCT
ejpam-367	576	4	y1(t	y1(t	PROPN
ejpam-367	576	5	)	)	PUNCT
ejpam-367	576	6	,	,	PUNCT
ejpam-367	576	7	ẏ1(t	ẏ1(t	PROPN
ejpam-367	576	8	)	)	PUNCT
ejpam-367	576	9	,	,	PUNCT
ejpam-367	576	10	x1(t	x1(t	PROPN
ejpam-367	576	11	)	)	PUNCT
ejpam-367	576	12	,	,	PUNCT
ejpam-367	576	13	ẋ1(t	ẋ1(t	PROPN
ejpam-367	576	14	)	)	PUNCT
ejpam-367	576	15	)	)	PUNCT
ejpam-367	577	1	g	g	NOUN
ejpam-367	578	1	i	i	PRON
ejpam-367	578	2	y2(t	y2(t	PROPN
ejpam-367	578	3	,	,	PUNCT
ejpam-367	578	4	x2(t	x2(t	PROPN
ejpam-367	578	5	)	)	PUNCT
ejpam-367	578	6	,	,	PUNCT
ejpam-367	578	7	ẋ2(t	ẋ2(t	PROPN
ejpam-367	578	8	)	)	PUNCT
ejpam-367	578	9	,	,	PUNCT
ejpam-367	578	10	y(t	y(t	PROPN
ejpam-367	578	11	)	)	PUNCT
ejpam-367	578	12	,	,	PUNCT
ejpam-367	578	13	ẏ2(t	ẏ2(t	PROPN
ejpam-367	578	14	)	)	PUNCT
ejpam-367	578	15	)	)	PUNCT
ejpam-367	579	1	=	=	X
ejpam-367	579	2	−g	−g	VERB
ejpam-367	579	3	i	i	PRON
ejpam-367	579	4	ẋ2(t	ẋ2(t	PROPN
ejpam-367	579	5	,	,	PUNCT
ejpam-367	579	6	y2(t	y2(t	PROPN
ejpam-367	579	7	)	)	PUNCT
ejpam-367	579	8	,	,	PUNCT
ejpam-367	579	9	ẏ2(t	ẏ2(t	PROPN
ejpam-367	579	10	)	)	PUNCT
ejpam-367	579	11	,	,	PUNCT
ejpam-367	579	12	x2(t	x2(t	PROPN
ejpam-367	579	13	)	)	PUNCT
ejpam-367	579	14	,	,	PUNCT
ejpam-367	579	15	ẋ2(t	ẋ2(t	PROPN
ejpam-367	579	16	)	)	PUNCT
ejpam-367	579	17	)	)	PUNCT
ejpam-367	580	1	f	f	PROPN
ejpam-367	581	1	i	i	PRON
ejpam-367	581	2	x1(t	x1(t	X
ejpam-367	581	3	,	,	PUNCT
ejpam-367	581	4	x1(t	x1(t	PROPN
ejpam-367	581	5	)	)	PUNCT
ejpam-367	581	6	,	,	PUNCT
ejpam-367	581	7	ẋ1(t	ẋ1(t	PROPN
ejpam-367	581	8	)	)	PUNCT
ejpam-367	581	9	,	,	PUNCT
ejpam-367	581	10	y1(t	y1(t	PROPN
ejpam-367	581	11	)	)	PUNCT
ejpam-367	581	12	,	,	PUNCT
ejpam-367	581	13	ẏ1(t	ẏ1(t	PROPN
ejpam-367	581	14	)	)	PUNCT
ejpam-367	581	15	)	)	PUNCT
ejpam-367	582	1	=	=	PUNCT
ejpam-367	583	1	−	−	NOUN
ejpam-367	584	1	f	f	X
ejpam-367	584	2	i	i	PRON
ejpam-367	584	3	ẏ1(t	ẏ1(t	VERB
ejpam-367	584	4	,	,	PUNCT
ejpam-367	584	5	y1(t	y1(t	PROPN
ejpam-367	584	6	)	)	PUNCT
ejpam-367	584	7	,	,	PUNCT
ejpam-367	584	8	ẏ1(t	ẏ1(t	PROPN
ejpam-367	584	9	)	)	PUNCT
ejpam-367	584	10	,	,	PUNCT
ejpam-367	584	11	x1(t	x1(t	PROPN
ejpam-367	584	12	)	)	PUNCT
ejpam-367	584	13	,	,	PUNCT
ejpam-367	584	14	ẋ1(t	ẋ1(t	PROPN
ejpam-367	584	15	)	)	PUNCT
ejpam-367	584	16	)	)	PUNCT
ejpam-367	585	1	g	g	NOUN
ejpam-367	585	2	i	i	PRON
ejpam-367	585	3	ẋ2(t	ẋ2(t	PROPN
ejpam-367	585	4	,	,	PUNCT
ejpam-367	585	5	x2(t	x2(t	PROPN
ejpam-367	585	6	)	)	PUNCT
ejpam-367	585	7	,	,	PUNCT
ejpam-367	585	8	ẋ2(t	ẋ2(t	PROPN
ejpam-367	585	9	)	)	PUNCT
ejpam-367	585	10	,	,	PUNCT
ejpam-367	585	11	y(t	y(t	PROPN
ejpam-367	585	12	)	)	PUNCT
ejpam-367	585	13	,	,	PUNCT
ejpam-367	585	14	ẏ2(t	ẏ2(t	PROPN
ejpam-367	585	15	)	)	PUNCT
ejpam-367	585	16	)	)	PUNCT
ejpam-367	586	1	=	=	PUNCT
ejpam-367	586	2	−g	−g	NOUN
ejpam-367	587	1	i	i	PRON
ejpam-367	587	2	ẏ2(t	ẏ2(t	VERB
ejpam-367	587	3	,	,	PUNCT
ejpam-367	587	4	y2(t	y2(t	PROPN
ejpam-367	587	5	)	)	PUNCT
ejpam-367	587	6	,	,	PUNCT
ejpam-367	587	7	ẏ2(t	ẏ2(t	PROPN
ejpam-367	587	8	)	)	PUNCT
ejpam-367	587	9	,	,	PUNCT
ejpam-367	587	10	x2(t	x2(t	PROPN
ejpam-367	587	11	)	)	PUNCT
ejpam-367	587	12	,	,	PUNCT
ejpam-367	587	13	ẋ2(t	ẋ2(t	PROPN
ejpam-367	587	14	)	)	PUNCT
ejpam-367	587	15	)	)	PUNCT
ejpam-367	588	1	f	f	PROPN
ejpam-367	589	1	i	i	PRON
ejpam-367	589	2	y1(t	y1(t	PRON
ejpam-367	589	3	,	,	PUNCT
ejpam-367	589	4	x1(t	x1(t	PROPN
ejpam-367	589	5	)	)	PUNCT
ejpam-367	589	6	,	,	PUNCT
ejpam-367	589	7	ẋ1(t	ẋ1(t	PROPN
ejpam-367	589	8	)	)	PUNCT
ejpam-367	589	9	,	,	PUNCT
ejpam-367	589	10	y1(t	y1(t	PROPN
ejpam-367	589	11	)	)	PUNCT
ejpam-367	589	12	,	,	PUNCT
ejpam-367	589	13	ẏ1(t	ẏ1(t	PROPN
ejpam-367	589	14	)	)	PUNCT
ejpam-367	589	15	)	)	PUNCT
ejpam-367	590	1	=	=	PRON
ejpam-367	590	2	−	−	PROPN
ejpam-367	590	3	f	f	X
ejpam-367	591	1	i	i	PRON
ejpam-367	591	2	ẋ1(t	ẋ1(t	PROPN
ejpam-367	591	3	,	,	PUNCT
ejpam-367	591	4	y1(t	y1(t	PROPN
ejpam-367	591	5	)	)	PUNCT
ejpam-367	591	6	,	,	PUNCT
ejpam-367	591	7	ẏ1(t	ẏ1(t	PROPN
ejpam-367	591	8	)	)	PUNCT
ejpam-367	591	9	,	,	PUNCT
ejpam-367	591	10	x1(t	x1(t	PROPN
ejpam-367	591	11	)	)	PUNCT
ejpam-367	591	12	,	,	PUNCT
ejpam-367	591	13	ẋ1(t	ẋ1(t	PROPN
ejpam-367	591	14	)	)	PUNCT
ejpam-367	591	15	)	)	PUNCT
ejpam-367	592	1	g	g	NOUN
ejpam-367	593	1	i	i	PRON
ejpam-367	593	2	ẏ2(t	ẏ2(t	VERB
ejpam-367	593	3	,	,	PUNCT
ejpam-367	593	4	x2(t	x2(t	PROPN
ejpam-367	593	5	)	)	PUNCT
ejpam-367	593	6	,	,	PUNCT
ejpam-367	593	7	ẋ2(t	ẋ2(t	PROPN
ejpam-367	593	8	)	)	PUNCT
ejpam-367	593	9	,	,	PUNCT
ejpam-367	593	10	y(t	y(t	PROPN
ejpam-367	593	11	)	)	PUNCT
ejpam-367	593	12	,	,	PUNCT
ejpam-367	593	13	ẏ2(t	ẏ2(t	PROPN
ejpam-367	593	14	)	)	PUNCT
ejpam-367	593	15	)	)	PUNCT
ejpam-367	594	1	=	=	X
ejpam-367	594	2	−g	−g	VERB
ejpam-367	594	3	i	i	PRON
ejpam-367	594	4	ẋ2(t	ẋ2(t	PROPN
ejpam-367	594	5	,	,	PUNCT
ejpam-367	594	6	y2(t	y2(t	PROPN
ejpam-367	594	7	)	)	PUNCT
ejpam-367	594	8	,	,	PUNCT
ejpam-367	594	9	ẏ2(t	ẏ2(t	PROPN
ejpam-367	594	10	)	)	PUNCT
ejpam-367	594	11	,	,	PUNCT
ejpam-367	594	12	x2(t	x2(t	PROPN
ejpam-367	594	13	)	)	PUNCT
ejpam-367	594	14	,	,	PUNCT
ejpam-367	594	15	ẋ2(t	ẋ2(t	PROPN
ejpam-367	594	16	)	)	PUNCT
ejpam-367	594	17	)	)	PUNCT
ejpam-367	594	18	recasting	recast	VERB
ejpam-367	594	19	the	the	DET
ejpam-367	594	20	dual	dual	ADJ
ejpam-367	594	21	problem	problem	NOUN
ejpam-367	594	22	(	(	PUNCT
ejpam-367	594	23	mix	mix	VERB
ejpam-367	594	24	sd	sd	NOUN
ejpam-367	594	25	)	)	PUNCT
ejpam-367	594	26	as	as	ADP
ejpam-367	594	27	a	a	DET
ejpam-367	594	28	minimization	minimization	NOUN
ejpam-367	594	29	problem	problem	NOUN
ejpam-367	594	30	and	and	CCONJ
ejpam-367	594	31	using	use	VERB
ejpam-367	594	32	the	the	DET
ejpam-367	594	33	above	above	ADJ
ejpam-367	594	34	relations	relation	NOUN
ejpam-367	594	35	,	,	PUNCT
ejpam-367	594	36	we	we	PRON
ejpam-367	594	37	have	have	VERB
ejpam-367	594	38	(	(	PUNCT
ejpam-367	594	39	mix	mix	VERB
ejpam-367	594	40	sd1	sd1	PROPN
ejpam-367	594	41	)	)	PUNCT
ejpam-367	594	42	minimize−	minimize−	PROPN
ejpam-367	595	1	∫	∫	PROPN
ejpam-367	595	2	i	i	INTJ
ejpam-367	595	3	{	{	PUNCT
ejpam-367	595	4	f	f	PROPN
ejpam-367	595	5	(	(	PUNCT
ejpam-367	595	6	t	t	PROPN
ejpam-367	595	7	,	,	PUNCT
ejpam-367	595	8	y1	y1	PROPN
ejpam-367	595	9	,	,	PUNCT
ejpam-367	595	10	ẏ1	ẏ1	PROPN
ejpam-367	595	11	,	,	PUNCT
ejpam-367	595	12	x1	x1	PROPN
ejpam-367	595	13	,	,	PUNCT
ejpam-367	595	14	ẋ1	ẋ1	PROPN
ejpam-367	595	15	)	)	PUNCT
ejpam-367	596	1	+	+	CCONJ
ejpam-367	596	2	g(t	g(t	PROPN
ejpam-367	596	3	,	,	PUNCT
ejpam-367	596	4	y2	y2	PROPN
ejpam-367	596	5	,	,	PUNCT
ejpam-367	596	6	ẏ2	ẏ2	PROPN
ejpam-367	596	7	,	,	PUNCT
ejpam-367	596	8	x2	x2	PROPN
ejpam-367	596	9	,	,	PUNCT
ejpam-367	596	10	ẋ2	ẋ2	PROPN
ejpam-367	596	11	)	)	PUNCT
ejpam-367	596	12	i.	i.	NOUN
ejpam-367	596	13	husain	husain	PROPN
ejpam-367	596	14	and	and	CCONJ
ejpam-367	596	15	r.	r.	PROPN
ejpam-367	596	16	mattoo	mattoo	PROPN
ejpam-367	596	17	/	/	SYM
ejpam-367	596	18	eur	eur	PROPN
ejpam-367	596	19	.	.	PUNCT
ejpam-367	597	1	j.	j.	PROPN
ejpam-367	597	2	pure	pure	PROPN
ejpam-367	597	3	appl	appl	PROPN
ejpam-367	597	4	.	.	PROPN
ejpam-367	597	5	math	math	PROPN
ejpam-367	597	6	,	,	PUNCT
ejpam-367	597	7	2	2	NUM
ejpam-367	597	8	(	(	PUNCT
ejpam-367	597	9	2009	2009	NUM
ejpam-367	597	10	)	)	PUNCT
ejpam-367	597	11	,	,	PUNCT
ejpam-367	597	12	(	(	PUNCT
ejpam-367	597	13	578	578	NUM
ejpam-367	597	14	-	-	SYM
ejpam-367	597	15	603	603	NUM
ejpam-367	597	16	)	)	PUNCT
ejpam-367	597	17	599	599	NUM
ejpam-367	597	18	x1(t)t(λt	x1(t)t(λt	PROPN
ejpam-367	598	1	fx1(t	fx1(t	PROPN
ejpam-367	598	2	,	,	PUNCT
ejpam-367	598	3	y1	y1	PROPN
ejpam-367	598	4	,	,	PUNCT
ejpam-367	598	5	ẏ1	ẏ1	PROPN
ejpam-367	598	6	,	,	PUNCT
ejpam-367	598	7	x1	x1	PROPN
ejpam-367	598	8	,	,	PUNCT
ejpam-367	598	9	ẋ1	ẋ1	PROPN
ejpam-367	598	10	)	)	PUNCT
ejpam-367	598	11	−dλt	−dλt	NOUN
ejpam-367	599	1	f	f	PROPN
ejpam-367	599	2	ẋ1(t	ẋ1(t	PROPN
ejpam-367	599	3	,	,	PUNCT
ejpam-367	599	4	y1	y1	INTJ
ejpam-367	599	5	,	,	PUNCT
ejpam-367	599	6	ẏ1	ẏ1	PROPN
ejpam-367	599	7	,	,	PUNCT
ejpam-367	599	8	x1	x1	PROPN
ejpam-367	599	9	,	,	PUNCT
ejpam-367	599	10	ẋ1))e}d	ẋ1))e}d	PROPN
ejpam-367	599	11	t	t	PROPN
ejpam-367	599	12	subject	subject	VERB
ejpam-367	599	13	to	to	ADP
ejpam-367	599	14	x1(a	x1(a	PROPN
ejpam-367	599	15	)	)	PUNCT
ejpam-367	599	16	=	=	SYM
ejpam-367	599	17	0	0	PUNCT
ejpam-367	600	1	=	=	SYM
ejpam-367	600	2	x1(b	x1(b	PROPN
ejpam-367	600	3	)	)	PUNCT
ejpam-367	600	4	,	,	PUNCT
ejpam-367	601	1	y1(a	y1(a	PROPN
ejpam-367	601	2	)	)	PUNCT
ejpam-367	601	3	=	=	SYM
ejpam-367	601	4	0	0	PUNCT
ejpam-367	601	5	=	=	SYM
ejpam-367	601	6	y1(b	y1(b	PROPN
ejpam-367	601	7	)	)	PUNCT
ejpam-367	601	8	x2(a	x2(a	PROPN
ejpam-367	601	9	)	)	PUNCT
ejpam-367	601	10	=	=	SYM
ejpam-367	601	11	0	0	PUNCT
ejpam-367	602	1	=	=	SYM
ejpam-367	602	2	x2(b	x2(b	PROPN
ejpam-367	602	3	)	)	PUNCT
ejpam-367	602	4	,	,	PUNCT
ejpam-367	602	5	y2(a	y2(a	NOUN
ejpam-367	602	6	)	)	PUNCT
ejpam-367	602	7	=	=	SYM
ejpam-367	602	8	0	0	PUNCT
ejpam-367	603	1	=	=	SYM
ejpam-367	603	2	y2(b	y2(b	PROPN
ejpam-367	603	3	)	)	PUNCT
ejpam-367	603	4	λt	λt	ADP
ejpam-367	603	5	fx1(t	fx1(t	PROPN
ejpam-367	603	6	,	,	PUNCT
ejpam-367	604	1	y1	y1	PROPN
ejpam-367	604	2	,	,	PUNCT
ejpam-367	604	3	ẏ1	ẏ1	PROPN
ejpam-367	604	4	,	,	PUNCT
ejpam-367	604	5	x1	x1	PROPN
ejpam-367	604	6	,	,	PUNCT
ejpam-367	605	1	ẋ1)−	ẋ1)−	PROPN
ejpam-367	605	2	dλt	dλt	PROPN
ejpam-367	606	1	f	f	PROPN
ejpam-367	606	2	ẋ1(t	ẋ1(t	PROPN
ejpam-367	606	3	,	,	PUNCT
ejpam-367	606	4	y1	y1	INTJ
ejpam-367	606	5	,	,	PUNCT
ejpam-367	606	6	ẏ1	ẏ1	PROPN
ejpam-367	606	7	,	,	PUNCT
ejpam-367	606	8	x1	x1	PROPN
ejpam-367	606	9	,	,	PUNCT
ejpam-367	606	10	ẋ1)≦	ẋ1)≦	PROPN
ejpam-367	606	11	0	0	NUM
ejpam-367	606	12	,	,	PUNCT
ejpam-367	606	13	t	t	PROPN
ejpam-367	606	14	∈	∈	PROPN
ejpam-367	607	1	i	i	PRON
ejpam-367	607	2	λt	λt	ADP
ejpam-367	607	3	gx2(t	gx2(t	PROPN
ejpam-367	607	4	,	,	PUNCT
ejpam-367	607	5	y2	y2	PROPN
ejpam-367	607	6	,	,	PUNCT
ejpam-367	607	7	ẏ2	ẏ2	PROPN
ejpam-367	607	8	,	,	PUNCT
ejpam-367	607	9	x2	x2	PROPN
ejpam-367	607	10	,	,	PUNCT
ejpam-367	607	11	ẋ2)−	ẋ2)−	VERB
ejpam-367	607	12	dλt	dλt	NOUN
ejpam-367	607	13	g	g	PROPN
ejpam-367	607	14	ẋ2(t	ẋ2(t	PROPN
ejpam-367	607	15	,	,	PUNCT
ejpam-367	607	16	y2	y2	PROPN
ejpam-367	607	17	,	,	PUNCT
ejpam-367	607	18	ẏ2	ẏ2	PROPN
ejpam-367	607	19	,	,	PUNCT
ejpam-367	607	20	x2	x2	PROPN
ejpam-367	607	21	,	,	PUNCT
ejpam-367	607	22	ẋ2)≦	ẋ2)≦	PROPN
ejpam-367	607	23	0	0	NUM
ejpam-367	607	24	,	,	PUNCT
ejpam-367	607	25	t	t	PROPN
ejpam-367	607	26	∈	∈	PROPN
ejpam-367	608	1	i	i	PRON
ejpam-367	608	2	∫	∫	VERB
ejpam-367	609	1	i	i	PRON
ejpam-367	609	2	x2(t)t(λt	x2(t)t(λt	PROPN
ejpam-367	609	3	gx2(t	gx2(t	PROPN
ejpam-367	609	4	,	,	PUNCT
ejpam-367	609	5	y2	y2	PROPN
ejpam-367	609	6	,	,	PUNCT
ejpam-367	609	7	ẏ2	ẏ2	PROPN
ejpam-367	609	8	,	,	PUNCT
ejpam-367	609	9	x2	x2	PROPN
ejpam-367	609	10	,	,	PUNCT
ejpam-367	609	11	ẋ2	ẋ2	PROPN
ejpam-367	609	12	)	)	PUNCT
ejpam-367	610	1	−dλt	−dλt	NOUN
ejpam-367	610	2	g	g	PROPN
ejpam-367	610	3	ẋ1(t	ẋ1(t	PROPN
ejpam-367	610	4	,	,	PUNCT
ejpam-367	610	5	y2	y2	INTJ
ejpam-367	610	6	,	,	PUNCT
ejpam-367	610	7	ẏ2	ẏ2	PROPN
ejpam-367	610	8	,	,	PUNCT
ejpam-367	610	9	x2	x2	PROPN
ejpam-367	610	10	,	,	PUNCT
ejpam-367	611	1	ẋ2))d	ẋ2))d	PROPN
ejpam-367	611	2	t	t	PROPN
ejpam-367	611	3	≧	≧	NOUN
ejpam-367	611	4	0	0	PUNCT
ejpam-367	612	1	λ	λ	X
ejpam-367	612	2	∈	∈	PROPN
ejpam-367	612	3	λ+	λ+	PUNCT
ejpam-367	612	4	this	this	PRON
ejpam-367	612	5	shows	show	VERB
ejpam-367	612	6	that	that	SCONJ
ejpam-367	612	7	the	the	DET
ejpam-367	612	8	problem	problem	NOUN
ejpam-367	612	9	(	(	PUNCT
ejpam-367	612	10	mix	mix	X
ejpam-367	612	11	sd1	sd1	NOUN
ejpam-367	612	12	)	)	PUNCT
ejpam-367	612	13	is	be	AUX
ejpam-367	612	14	just	just	ADV
ejpam-367	612	15	the	the	DET
ejpam-367	612	16	primal	primal	ADJ
ejpam-367	612	17	problem	problem	NOUN
ejpam-367	612	18	(	(	PUNCT
ejpam-367	612	19	mix	mix	NOUN
ejpam-367	612	20	sp	sp	NOUN
ejpam-367	612	21	)	)	PUNCT
ejpam-367	612	22	.	.	PUNCT
ejpam-367	613	1	therefore	therefore	ADV
ejpam-367	613	2	,	,	PUNCT
ejpam-367	613	3	(	(	PUNCT
ejpam-367	613	4	x̄1(t	x̄1(t	NUM
ejpam-367	613	5	)	)	PUNCT
ejpam-367	613	6	,	,	PUNCT
ejpam-367	613	7	x̄2(t	x̄2(t	PROPN
ejpam-367	613	8	)	)	PUNCT
ejpam-367	613	9	,	,	PUNCT
ejpam-367	613	10	ȳ1(t	ȳ1(t	NUM
ejpam-367	613	11	)	)	PUNCT
ejpam-367	613	12	,	,	PUNCT
ejpam-367	613	13	ȳ2(t	ȳ2(t	PROPN
ejpam-367	613	14	)	)	PUNCT
ejpam-367	613	15	,	,	PUNCT
ejpam-367	613	16	λ̄	λ̄	PUNCT
ejpam-367	613	17	)	)	PUNCT
ejpam-367	613	18	is	be	AUX
ejpam-367	613	19	an	an	DET
ejpam-367	613	20	optimal	optimal	ADJ
ejpam-367	613	21	solution	solution	NOUN
ejpam-367	613	22	of	of	ADP
ejpam-367	613	23	(	(	PUNCT
ejpam-367	613	24	mix	mix	VERB
ejpam-367	613	25	sd	sd	NOUN
ejpam-367	613	26	)	)	PUNCT
ejpam-367	613	27	implies	imply	VERB
ejpam-367	613	28	that	that	SCONJ
ejpam-367	613	29	(	(	PUNCT
ejpam-367	613	30	ȳ1(t	ȳ1(t	NUM
ejpam-367	613	31	)	)	PUNCT
ejpam-367	613	32	,	,	PUNCT
ejpam-367	613	33	ȳ2(t	ȳ2(t	PROPN
ejpam-367	613	34	)	)	PUNCT
ejpam-367	613	35	,	,	PUNCT
ejpam-367	613	36	x̄1(t	x̄1(t	NUM
ejpam-367	613	37	)	)	PUNCT
ejpam-367	613	38	,	,	PUNCT
ejpam-367	613	39	x̄2(t	x̄2(t	PROPN
ejpam-367	613	40	)	)	PUNCT
ejpam-367	613	41	,	,	PUNCT
ejpam-367	613	42	λ̄	λ̄	NUM
ejpam-367	613	43	)	)	PUNCT
ejpam-367	613	44	is	be	AUX
ejpam-367	613	45	an	an	DET
ejpam-367	613	46	optimal	optimal	ADJ
ejpam-367	613	47	solution	solution	NOUN
ejpam-367	613	48	for	for	ADP
ejpam-367	613	49	(	(	PUNCT
ejpam-367	613	50	mix	mix	VERB
ejpam-367	613	51	sp	sp	NOUN
ejpam-367	613	52	)	)	PUNCT
ejpam-367	613	53	,	,	PUNCT
ejpam-367	613	54	and	and	CCONJ
ejpam-367	613	55	by	by	ADP
ejpam-367	613	56	symmetric	symmetric	ADJ
ejpam-367	613	57	duality	duality	NOUN
ejpam-367	613	58	also	also	ADV
ejpam-367	613	59	for	for	ADP
ejpam-367	613	60	(	(	PUNCT
ejpam-367	613	61	mix	mix	VERB
ejpam-367	613	62	sd	sd	NOUN
ejpam-367	613	63	)	)	PUNCT
ejpam-367	613	64	.	.	PUNCT
ejpam-367	614	1	now	now	ADV
ejpam-367	614	2	from	from	ADP
ejpam-367	614	3	(	(	PUNCT
ejpam-367	614	4	55	55	NUM
ejpam-367	614	5	)	)	PUNCT
ejpam-367	614	6	minimum	minimum	NOUN
ejpam-367	614	7	(	(	PUNCT
ejpam-367	614	8	mix	mix	VERB
ejpam-367	614	9	sp)=	sp)=	NOUN
ejpam-367	614	10	∫	∫	PROPN
ejpam-367	615	1	i	i	PRON
ejpam-367	615	2	{	{	PUNCT
ejpam-367	615	3	f	f	PROPN
ejpam-367	615	4	(	(	PUNCT
ejpam-367	615	5	t	t	PROPN
ejpam-367	615	6	,	,	PUNCT
ejpam-367	615	7	x1	x1	PROPN
ejpam-367	615	8	,	,	PUNCT
ejpam-367	615	9	ẋ1	ẋ1	PROPN
ejpam-367	615	10	,	,	PUNCT
ejpam-367	615	11	y1	y1	PROPN
ejpam-367	615	12	,	,	PUNCT
ejpam-367	615	13	ẏ1	ẏ1	PROPN
ejpam-367	615	14	)	)	PUNCT
ejpam-367	615	15	+	+	CCONJ
ejpam-367	615	16	g(t	g(t	PROPN
ejpam-367	615	17	,	,	PUNCT
ejpam-367	615	18	x2	x2	PROPN
ejpam-367	615	19	,	,	PUNCT
ejpam-367	615	20	ẋ2	ẋ2	PROPN
ejpam-367	615	21	,	,	PUNCT
ejpam-367	615	22	y2	y2	PROPN
ejpam-367	615	23	,	,	PUNCT
ejpam-367	615	24	ẏ2)}d	ẏ2)}d	PROPN
ejpam-367	615	25	t	t	PROPN
ejpam-367	615	26	correspondingly	correspondingly	ADV
ejpam-367	615	27	with	with	ADP
ejpam-367	615	28	the	the	DET
ejpam-367	615	29	solution	solution	NOUN
ejpam-367	615	30	(	(	PUNCT
ejpam-367	615	31	ȳ(t	ȳ(t	NOUN
ejpam-367	615	32	)	)	PUNCT
ejpam-367	615	33	,	,	PUNCT
ejpam-367	615	34	ȳ2(t	ȳ2(t	PROPN
ejpam-367	615	35	)	)	PUNCT
ejpam-367	615	36	,	,	PUNCT
ejpam-367	615	37	x̄1(t	x̄1(t	NUM
ejpam-367	615	38	)	)	PUNCT
ejpam-367	615	39	,	,	PUNCT
ejpam-367	615	40	x̄2(t	x̄2(t	PROPN
ejpam-367	615	41	)	)	PUNCT
ejpam-367	615	42	,	,	PUNCT
ejpam-367	615	43	λ̄	λ̄	NUM
ejpam-367	615	44	)	)	PUNCT
ejpam-367	615	45	,	,	PUNCT
ejpam-367	615	46	we	we	PRON
ejpam-367	615	47	have	have	VERB
ejpam-367	615	48	minimum	minimum	NOUN
ejpam-367	615	49	(	(	PUNCT
ejpam-367	615	50	mix	mix	VERB
ejpam-367	615	51	sp)=	sp)=	NOUN
ejpam-367	615	52	∫	∫	PROPN
ejpam-367	616	1	i	i	PRON
ejpam-367	616	2	{	{	PUNCT
ejpam-367	616	3	f	f	PROPN
ejpam-367	616	4	(	(	PUNCT
ejpam-367	616	5	t	t	PROPN
ejpam-367	616	6	,	,	PUNCT
ejpam-367	616	7	y1	y1	PROPN
ejpam-367	616	8	,	,	PUNCT
ejpam-367	616	9	ẏ1	ẏ1	PROPN
ejpam-367	616	10	,	,	PUNCT
ejpam-367	616	11	x1	x1	PROPN
ejpam-367	616	12	,	,	PUNCT
ejpam-367	616	13	ẋ1	ẋ1	PROPN
ejpam-367	616	14	)	)	PUNCT
ejpam-367	617	1	+	+	CCONJ
ejpam-367	617	2	g(t	g(t	PROPN
ejpam-367	617	3	,	,	PUNCT
ejpam-367	617	4	y2	y2	PROPN
ejpam-367	617	5	,	,	PUNCT
ejpam-367	617	6	ẏ2	ẏ2	PROPN
ejpam-367	617	7	,	,	PUNCT
ejpam-367	617	8	x2	x2	PROPN
ejpam-367	617	9	,	,	PUNCT
ejpam-367	617	10	ẋ2)}d	ẋ2)}d	PROPN
ejpam-367	617	11	t	t	PROPN
ejpam-367	617	12	by	by	ADP
ejpam-367	617	13	the	the	DET
ejpam-367	617	14	skew	skew	ADJ
ejpam-367	617	15	symmetric	symmetric	NOUN
ejpam-367	617	16	of	of	ADP
ejpam-367	617	17	f	f	PROPN
ejpam-367	617	18	i	i	PROPN
ejpam-367	617	19	and	and	CCONJ
ejpam-367	617	20	g	g	PROPN
ejpam-367	617	21	i	i	PRON
ejpam-367	617	22	,	,	PUNCT
ejpam-367	617	23	we	we	PRON
ejpam-367	617	24	have	have	VERB
ejpam-367	617	25	minimum	minimum	NOUN
ejpam-367	617	26	(	(	PUNCT
ejpam-367	617	27	mix	mix	VERB
ejpam-367	617	28	sp	sp	NOUN
ejpam-367	617	29	)	)	PUNCT
ejpam-367	617	30	=	=	SYM
ejpam-367	618	1	∫	∫	PROPN
ejpam-367	619	1	i	i	PRON
ejpam-367	619	2	{	{	PUNCT
ejpam-367	619	3	f	f	PROPN
ejpam-367	619	4	(	(	PUNCT
ejpam-367	619	5	t	t	PROPN
ejpam-367	619	6	,	,	PUNCT
ejpam-367	619	7	x1	x1	PROPN
ejpam-367	619	8	,	,	PUNCT
ejpam-367	619	9	ẋ1	ẋ1	PROPN
ejpam-367	619	10	,	,	PUNCT
ejpam-367	619	11	y1	y1	PROPN
ejpam-367	619	12	,	,	PUNCT
ejpam-367	619	13	ẏ1	ẏ1	PROPN
ejpam-367	619	14	)	)	PUNCT
ejpam-367	619	15	+	+	CCONJ
ejpam-367	619	16	g(t	g(t	PROPN
ejpam-367	619	17	,	,	PUNCT
ejpam-367	619	18	x2	x2	PROPN
ejpam-367	619	19	,	,	PUNCT
ejpam-367	619	20	ẋ2	ẋ2	PROPN
ejpam-367	619	21	,	,	PUNCT
ejpam-367	619	22	y2	y2	PROPN
ejpam-367	619	23	,	,	PUNCT
ejpam-367	619	24	ẏ2)}d	ẏ2)}d	PROPN
ejpam-367	619	25	t	t	PROPN
ejpam-367	620	1	=	=	SYM
ejpam-367	621	1	∫	∫	PROPN
ejpam-367	622	1	i	i	PRON
ejpam-367	622	2	{	{	PUNCT
ejpam-367	622	3	f	f	PROPN
ejpam-367	622	4	(	(	PUNCT
ejpam-367	622	5	t	t	PROPN
ejpam-367	622	6	,	,	PUNCT
ejpam-367	622	7	y1	y1	PROPN
ejpam-367	622	8	,	,	PUNCT
ejpam-367	622	9	ẏ1	ẏ1	PROPN
ejpam-367	622	10	,	,	PUNCT
ejpam-367	622	11	x1	x1	PROPN
ejpam-367	622	12	,	,	PUNCT
ejpam-367	622	13	ẋ1	ẋ1	PROPN
ejpam-367	622	14	)	)	PUNCT
ejpam-367	623	1	+	+	CCONJ
ejpam-367	623	2	g(t	g(t	PROPN
ejpam-367	623	3	,	,	PUNCT
ejpam-367	623	4	y2	y2	PROPN
ejpam-367	623	5	,	,	PUNCT
ejpam-367	623	6	ẏ2	ẏ2	PROPN
ejpam-367	623	7	,	,	PUNCT
ejpam-367	623	8	x2	x2	PROPN
ejpam-367	623	9	,	,	PUNCT
ejpam-367	623	10	ẋ2)}d	ẋ2)}d	PROPN
ejpam-367	623	11	t	t	PROPN
ejpam-367	623	12	=	=	PUNCT
ejpam-367	624	1	−	−	PROPN
ejpam-367	624	2	∫	∫	INTJ
ejpam-367	625	1	i	i	PRON
ejpam-367	625	2	{	{	PUNCT
ejpam-367	625	3	f	f	PROPN
ejpam-367	625	4	(	(	PUNCT
ejpam-367	625	5	t	t	PROPN
ejpam-367	625	6	,	,	PUNCT
ejpam-367	625	7	x1	x1	PROPN
ejpam-367	625	8	,	,	PUNCT
ejpam-367	625	9	ẋ1	ẋ1	PROPN
ejpam-367	625	10	,	,	PUNCT
ejpam-367	625	11	y1	y1	PROPN
ejpam-367	625	12	,	,	PUNCT
ejpam-367	625	13	ẏ1	ẏ1	PROPN
ejpam-367	625	14	)	)	PUNCT
ejpam-367	625	15	+	+	CCONJ
ejpam-367	625	16	g(t	g(t	PROPN
ejpam-367	625	17	,	,	PUNCT
ejpam-367	625	18	x2	x2	PROPN
ejpam-367	625	19	,	,	PUNCT
ejpam-367	625	20	ẋ2	ẋ2	PROPN
ejpam-367	625	21	,	,	PUNCT
ejpam-367	625	22	y2	y2	PROPN
ejpam-367	625	23	,	,	PUNCT
ejpam-367	625	24	ẏ2)}d	ẏ2)}d	PROPN
ejpam-367	625	25	t	t	PROPN
ejpam-367	625	26	i.	i.	PROPN
ejpam-367	625	27	husain	husain	PROPN
ejpam-367	625	28	and	and	CCONJ
ejpam-367	625	29	r.	r.	PROPN
ejpam-367	625	30	mattoo	mattoo	PROPN
ejpam-367	625	31	/	/	SYM
ejpam-367	625	32	eur	eur	PROPN
ejpam-367	625	33	.	.	PUNCT
ejpam-367	626	1	j.	j.	PROPN
ejpam-367	626	2	pure	pure	PROPN
ejpam-367	626	3	appl	appl	PROPN
ejpam-367	626	4	.	.	PROPN
ejpam-367	626	5	math	math	PROPN
ejpam-367	626	6	,	,	PUNCT
ejpam-367	626	7	2	2	NUM
ejpam-367	626	8	(	(	PUNCT
ejpam-367	626	9	2009	2009	NUM
ejpam-367	626	10	)	)	PUNCT
ejpam-367	626	11	,	,	PUNCT
ejpam-367	626	12	(	(	PUNCT
ejpam-367	626	13	578	578	NUM
ejpam-367	626	14	-	-	SYM
ejpam-367	626	15	603	603	NUM
ejpam-367	626	16	)	)	PUNCT
ejpam-367	626	17	600	600	NUM
ejpam-367	626	18	this	this	DET
ejpam-367	626	19	yields	yield	NOUN
ejpam-367	626	20	,	,	PUNCT
ejpam-367	626	21	minimum	minimum	NOUN
ejpam-367	626	22	(	(	PUNCT
ejpam-367	626	23	mix	mix	NOUN
ejpam-367	626	24	sp	sp	NOUN
ejpam-367	626	25	)	)	PUNCT
ejpam-367	626	26	=	=	SYM
ejpam-367	627	1	∫	∫	PROPN
ejpam-367	628	1	i	i	PRON
ejpam-367	628	2	{	{	PUNCT
ejpam-367	628	3	f	f	PROPN
ejpam-367	628	4	(	(	PUNCT
ejpam-367	628	5	t	t	PROPN
ejpam-367	628	6	,	,	PUNCT
ejpam-367	628	7	x1	x1	PROPN
ejpam-367	628	8	,	,	PUNCT
ejpam-367	628	9	ẋ1	ẋ1	PROPN
ejpam-367	628	10	,	,	PUNCT
ejpam-367	628	11	y1	y1	PROPN
ejpam-367	628	12	,	,	PUNCT
ejpam-367	628	13	ẏ1	ẏ1	PROPN
ejpam-367	628	14	)	)	PUNCT
ejpam-367	628	15	+	+	CCONJ
ejpam-367	628	16	g(t	g(t	PROPN
ejpam-367	628	17	,	,	PUNCT
ejpam-367	628	18	x2	x2	PROPN
ejpam-367	628	19	,	,	PUNCT
ejpam-367	628	20	ẋ2	ẋ2	PROPN
ejpam-367	628	21	,	,	PUNCT
ejpam-367	628	22	y2	y2	PROPN
ejpam-367	628	23	,	,	PUNCT
ejpam-367	628	24	ẏ2)}d	ẏ2)}d	PROPN
ejpam-367	628	25	t	t	NOUN
ejpam-367	629	1	=	=	PUNCT
ejpam-367	629	2	0	0	NUM
ejpam-367	629	3	this	this	PRON
ejpam-367	629	4	accomplishes	accomplish	VERB
ejpam-367	629	5	the	the	DET
ejpam-367	629	6	proof	proof	NOUN
ejpam-367	629	7	of	of	ADP
ejpam-367	629	8	the	the	DET
ejpam-367	629	9	theorem	theorem	NOUN
ejpam-367	629	10	.	.	PROPN
ejpam-367	629	11	6	6	NUM
ejpam-367	629	12	.	.	NOUN
ejpam-367	629	13	natural	natural	ADJ
ejpam-367	629	14	boundary	boundary	ADJ
ejpam-367	629	15	conditions	condition	NOUN
ejpam-367	629	16	the	the	DET
ejpam-367	629	17	pair	pair	NOUN
ejpam-367	629	18	of	of	ADP
ejpam-367	629	19	mixed	mixed	ADJ
ejpam-367	629	20	symmetric	symmetric	ADJ
ejpam-367	629	21	multiobjective	multiobjective	ADJ
ejpam-367	629	22	variational	variational	ADJ
ejpam-367	629	23	problem	problem	NOUN
ejpam-367	629	24	with	with	ADP
ejpam-367	629	25	natural	natural	ADJ
ejpam-367	629	26	boundary	boundary	ADJ
ejpam-367	629	27	values	value	NOUN
ejpam-367	629	28	rather	rather	ADV
ejpam-367	629	29	than	than	ADP
ejpam-367	629	30	fixed	fix	VERB
ejpam-367	629	31	points	point	NOUN
ejpam-367	629	32	may	may	AUX
ejpam-367	629	33	be	be	AUX
ejpam-367	629	34	formulated	formulate	VERB
ejpam-367	629	35	as	as	ADP
ejpam-367	629	36	,	,	PUNCT
ejpam-367	629	37	primal	primal	ADJ
ejpam-367	629	38	problem	problem	NOUN
ejpam-367	629	39	(	(	PUNCT
ejpam-367	629	40	mix	mix	VERB
ejpam-367	629	41	sp0	sp0	ADV
ejpam-367	629	42	)	)	PUNCT
ejpam-367	629	43	minimize	minimize	VERB
ejpam-367	629	44	∫	∫	PROPN
ejpam-367	629	45	i	i	PRON
ejpam-367	629	46	{	{	PUNCT
ejpam-367	629	47	f	f	PROPN
ejpam-367	629	48	(	(	PUNCT
ejpam-367	629	49	t	t	PROPN
ejpam-367	629	50	,	,	PUNCT
ejpam-367	629	51	x1	x1	PROPN
ejpam-367	629	52	,	,	PUNCT
ejpam-367	629	53	ẋ1	ẋ1	PROPN
ejpam-367	629	54	,	,	PUNCT
ejpam-367	629	55	y1	y1	PROPN
ejpam-367	629	56	,	,	PUNCT
ejpam-367	629	57	ẏ1	ẏ1	PROPN
ejpam-367	629	58	)	)	PUNCT
ejpam-367	630	1	+	+	CCONJ
ejpam-367	630	2	g(t	g(t	PROPN
ejpam-367	630	3	,	,	PUNCT
ejpam-367	630	4	x2	x2	PROPN
ejpam-367	630	5	,	,	PUNCT
ejpam-367	630	6	ẋ2	ẋ2	PROPN
ejpam-367	630	7	,	,	PUNCT
ejpam-367	630	8	y2	y2	NOUN
ejpam-367	630	9	,	,	PUNCT
ejpam-367	630	10	ẏ2	ẏ2	PROPN
ejpam-367	630	11	)	)	PUNCT
ejpam-367	630	12	.	.	PUNCT
ejpam-367	631	1	−y1(t)t(λt	−y1(t)t(λt	PROPN
ejpam-367	631	2	f	f	PROPN
ejpam-367	631	3	y1(x1	y1(x1	PROPN
ejpam-367	631	4	,	,	PUNCT
ejpam-367	631	5	ẋ1	ẋ1	PROPN
ejpam-367	631	6	,	,	PUNCT
ejpam-367	631	7	y1	y1	PROPN
ejpam-367	631	8	,	,	PUNCT
ejpam-367	631	9	ẏ1	ẏ1	PROPN
ejpam-367	631	10	)	)	PUNCT
ejpam-367	631	11	−dλt	−dλt	NOUN
ejpam-367	632	1	f	f	PROPN
ejpam-367	632	2	ẏ1(x1	ẏ1(x1	PROPN
ejpam-367	632	3	,	,	PUNCT
ejpam-367	632	4	ẋ1	ẋ1	PROPN
ejpam-367	632	5	,	,	PUNCT
ejpam-367	632	6	y1	y1	PROPN
ejpam-367	632	7	,	,	PUNCT
ejpam-367	632	8	ẏ1))e}d	ẏ1))e}d	PROPN
ejpam-367	632	9	t	t	PROPN
ejpam-367	632	10	subject	subject	VERB
ejpam-367	632	11	to	to	ADP
ejpam-367	632	12	λt	λt	ADP
ejpam-367	632	13	f	f	PROPN
ejpam-367	632	14	y1(t	y1(t	PROPN
ejpam-367	632	15	,	,	PUNCT
ejpam-367	632	16	x1	x1	PROPN
ejpam-367	632	17	,	,	PUNCT
ejpam-367	632	18	ẋ1	ẋ1	PROPN
ejpam-367	632	19	,	,	PUNCT
ejpam-367	632	20	y1	y1	PROPN
ejpam-367	632	21	,	,	PUNCT
ejpam-367	632	22	ẏ1)−	ẏ1)−	PROPN
ejpam-367	632	23	dλt	dλt	PROPN
ejpam-367	633	1	f	f	PROPN
ejpam-367	633	2	ẏ1(t	ẏ1(t	PROPN
ejpam-367	633	3	,	,	PUNCT
ejpam-367	633	4	x1	x1	PROPN
ejpam-367	633	5	,	,	PUNCT
ejpam-367	633	6	ẋ1	ẋ1	PROPN
ejpam-367	633	7	,	,	PUNCT
ejpam-367	633	8	y1	y1	PROPN
ejpam-367	633	9	,	,	PUNCT
ejpam-367	633	10	ẏ1	ẏ1	PROPN
ejpam-367	633	11	)	)	PUNCT
ejpam-367	633	12	≦	≦	NOUN
ejpam-367	633	13	0	0	NUM
ejpam-367	634	1	λt	λt	ADP
ejpam-367	634	2	g	g	PROPN
ejpam-367	634	3	y2(t	y2(t	PROPN
ejpam-367	634	4	,	,	PUNCT
ejpam-367	634	5	x2	x2	PROPN
ejpam-367	634	6	,	,	PUNCT
ejpam-367	634	7	ẋ2	ẋ2	PROPN
ejpam-367	634	8	,	,	PUNCT
ejpam-367	634	9	y2	y2	NOUN
ejpam-367	634	10	,	,	PUNCT
ejpam-367	634	11	ẏ2)−	ẏ2)−	PROPN
ejpam-367	634	12	dλt	dλt	NOUN
ejpam-367	634	13	g	g	PROPN
ejpam-367	634	14	ẏ2(t	ẏ2(t	PROPN
ejpam-367	634	15	,	,	PUNCT
ejpam-367	634	16	x2	x2	PROPN
ejpam-367	634	17	,	,	PUNCT
ejpam-367	634	18	ẋ2	ẋ2	PROPN
ejpam-367	634	19	,	,	PUNCT
ejpam-367	634	20	y2	y2	PROPN
ejpam-367	634	21	,	,	PUNCT
ejpam-367	634	22	ẏ2)≦	ẏ2)≦	PROPN
ejpam-367	634	23	0	0	NUM
ejpam-367	634	24	∫	∫	NOUN
ejpam-367	634	25	i	i	PRON
ejpam-367	634	26	y2(t)t(λt	y2(t)t(λt	VERB
ejpam-367	634	27	g	g	PROPN
ejpam-367	634	28	y2(t	y2(t	PROPN
ejpam-367	634	29	,	,	PUNCT
ejpam-367	634	30	x2	x2	PROPN
ejpam-367	634	31	,	,	PUNCT
ejpam-367	634	32	ẋ2	ẋ2	PROPN
ejpam-367	634	33	,	,	PUNCT
ejpam-367	634	34	y2	y2	NOUN
ejpam-367	634	35	,	,	PUNCT
ejpam-367	634	36	ẏ2	ẏ2	PROPN
ejpam-367	634	37	)	)	PUNCT
ejpam-367	634	38	−dλt	−dλt	NOUN
ejpam-367	635	1	g	g	PROPN
ejpam-367	635	2	ẏ2(t	ẏ2(t	PROPN
ejpam-367	635	3	,	,	PUNCT
ejpam-367	635	4	x2	x2	PROPN
ejpam-367	635	5	,	,	PUNCT
ejpam-367	635	6	ẋ2	ẋ2	PROPN
ejpam-367	635	7	,	,	PUNCT
ejpam-367	635	8	y2	y2	NOUN
ejpam-367	635	9	,	,	PUNCT
ejpam-367	635	10	ẏ2))≧	ẏ2))≧	NOUN
ejpam-367	635	11	0	0	NUM
ejpam-367	636	1	λt	λt	ADP
ejpam-367	636	2	f	f	PROPN
ejpam-367	636	3	y1(t	y1(t	PROPN
ejpam-367	636	4	,	,	PUNCT
ejpam-367	636	5	u1	u1	PROPN
ejpam-367	636	6	,	,	PUNCT
ejpam-367	636	7	u̇1	u̇1	PROPN
ejpam-367	636	8	,	,	PUNCT
ejpam-367	636	9	v1	v1	NOUN
ejpam-367	636	10	,	,	PUNCT
ejpam-367	636	11	v̇1)|t	v̇1)|t	NOUN
ejpam-367	636	12	=	=	PRON
ejpam-367	636	13	a	a	X
ejpam-367	636	14	=	=	SYM
ejpam-367	636	15	0	0	NUM
ejpam-367	636	16	,	,	PUNCT
ejpam-367	636	17	λt	λt	ADP
ejpam-367	636	18	f	f	PROPN
ejpam-367	636	19	ẏ1(t	ẏ1(t	PROPN
ejpam-367	636	20	,	,	PUNCT
ejpam-367	636	21	u1	u1	PROPN
ejpam-367	636	22	,	,	PUNCT
ejpam-367	636	23	u̇1	u̇1	PROPN
ejpam-367	636	24	,	,	PUNCT
ejpam-367	636	25	v1	v1	NOUN
ejpam-367	636	26	,	,	PUNCT
ejpam-367	636	27	v̇1)|t	v̇1)|t	NOUN
ejpam-367	636	28	=	=	SYM
ejpam-367	636	29	b	b	NOUN
ejpam-367	636	30	=	=	SYM
ejpam-367	636	31	0	0	NUM
ejpam-367	637	1	λt	λt	ADP
ejpam-367	637	2	g	g	PROPN
ejpam-367	637	3	y2(t	y2(t	PROPN
ejpam-367	637	4	,	,	PUNCT
ejpam-367	637	5	x2	x2	PROPN
ejpam-367	637	6	,	,	PUNCT
ejpam-367	637	7	ẋ2	ẋ2	PROPN
ejpam-367	637	8	,	,	PUNCT
ejpam-367	637	9	y2	y2	PROPN
ejpam-367	637	10	,	,	PUNCT
ejpam-367	637	11	ẏ2)|t	ẏ2)|t	NOUN
ejpam-367	637	12	=	=	PROPN
ejpam-367	637	13	a	a	X
ejpam-367	637	14	=	=	SYM
ejpam-367	637	15	0	0	NUM
ejpam-367	637	16	,	,	PUNCT
ejpam-367	637	17	λt	λt	ADP
ejpam-367	637	18	g	g	PROPN
ejpam-367	637	19	ẏ2(t	ẏ2(t	PROPN
ejpam-367	637	20	,	,	PUNCT
ejpam-367	637	21	x2	x2	PROPN
ejpam-367	637	22	,	,	PUNCT
ejpam-367	637	23	ẋ2	ẋ2	PROPN
ejpam-367	637	24	,	,	PUNCT
ejpam-367	637	25	y2	y2	PROPN
ejpam-367	637	26	,	,	PUNCT
ejpam-367	637	27	ẏ2)|t	ẏ2)|t	NOUN
ejpam-367	637	28	=	=	SYM
ejpam-367	637	29	b	b	NOUN
ejpam-367	637	30	=	=	SYM
ejpam-367	637	31	0	0	PUNCT
ejpam-367	637	32	λ	λ	PROPN
ejpam-367	637	33	∈	∈	PROPN
ejpam-367	637	34	λ+	λ+	PUNCT
ejpam-367	637	35	dual	dual	ADJ
ejpam-367	637	36	problem	problem	NOUN
ejpam-367	637	37	(	(	PUNCT
ejpam-367	637	38	mix	mix	VERB
ejpam-367	637	39	sd0	sd0	NOUN
ejpam-367	637	40	)	)	PUNCT
ejpam-367	637	41	maximize	maximize	VERB
ejpam-367	637	42	∫	∫	PROPN
ejpam-367	638	1	i	i	PRON
ejpam-367	638	2	{	{	PUNCT
ejpam-367	638	3	f	f	PROPN
ejpam-367	638	4	(	(	PUNCT
ejpam-367	638	5	u1	u1	PROPN
ejpam-367	638	6	,	,	PUNCT
ejpam-367	638	7	u̇1	u̇1	PROPN
ejpam-367	638	8	,	,	PUNCT
ejpam-367	638	9	v1	v1	NOUN
ejpam-367	638	10	,	,	PUNCT
ejpam-367	638	11	v̇1	v̇1	PROPN
ejpam-367	638	12	)	)	PUNCT
ejpam-367	638	13	+	+	NUM
ejpam-367	638	14	g(u2	g(u2	NOUN
ejpam-367	638	15	,	,	PUNCT
ejpam-367	638	16	u̇2	u̇2	NOUN
ejpam-367	638	17	,	,	PUNCT
ejpam-367	638	18	v2	v2	NOUN
ejpam-367	638	19	,	,	PUNCT
ejpam-367	638	20	v̇2	v̇2	NOUN
ejpam-367	638	21	)	)	PUNCT
ejpam-367	638	22	−u1(t)t(λt	−u1(t)t(λt	NOUN
ejpam-367	638	23	fu1(u1	fu1(u1	NUM
ejpam-367	638	24	,	,	PUNCT
ejpam-367	638	25	u̇1	u̇1	PROPN
ejpam-367	638	26	,	,	PUNCT
ejpam-367	638	27	v1	v1	NOUN
ejpam-367	638	28	,	,	PUNCT
ejpam-367	638	29	v̇1	v̇1	PROPN
ejpam-367	638	30	)	)	PUNCT
ejpam-367	638	31	i.	i.	NOUN
ejpam-367	638	32	husain	husain	PROPN
ejpam-367	638	33	and	and	CCONJ
ejpam-367	638	34	r.	r.	PROPN
ejpam-367	638	35	mattoo	mattoo	PROPN
ejpam-367	638	36	/	/	SYM
ejpam-367	638	37	eur	eur	PROPN
ejpam-367	638	38	.	.	PUNCT
ejpam-367	639	1	j.	j.	PROPN
ejpam-367	639	2	pure	pure	PROPN
ejpam-367	639	3	appl	appl	PROPN
ejpam-367	639	4	.	.	PROPN
ejpam-367	639	5	math	math	PROPN
ejpam-367	639	6	,	,	PUNCT
ejpam-367	639	7	2	2	NUM
ejpam-367	639	8	(	(	PUNCT
ejpam-367	639	9	2009	2009	NUM
ejpam-367	639	10	)	)	PUNCT
ejpam-367	639	11	,	,	PUNCT
ejpam-367	639	12	(	(	PUNCT
ejpam-367	639	13	578	578	NUM
ejpam-367	639	14	-	-	SYM
ejpam-367	639	15	603	603	NUM
ejpam-367	639	16	)	)	PUNCT
ejpam-367	639	17	601	601	NUM
ejpam-367	639	18	−dλt	−dλt	NOUN
ejpam-367	639	19	fu̇1(u1	fu̇1(u1	PROPN
ejpam-367	639	20	,	,	PUNCT
ejpam-367	639	21	u̇1	u̇1	PROPN
ejpam-367	639	22	,	,	PUNCT
ejpam-367	639	23	v1	v1	NOUN
ejpam-367	639	24	,	,	PUNCT
ejpam-367	639	25	v̇1))e}d	v̇1))e}d	PROPN
ejpam-367	639	26	t	t	PROPN
ejpam-367	639	27	subject	subject	NOUN
ejpam-367	639	28	to	to	ADP
ejpam-367	639	29	λt	λt	ADP
ejpam-367	639	30	fu1(t	fu1(t	PROPN
ejpam-367	639	31	,	,	PUNCT
ejpam-367	639	32	u1	u1	PROPN
ejpam-367	639	33	,	,	PUNCT
ejpam-367	639	34	u̇1	u̇1	PROPN
ejpam-367	639	35	,	,	PUNCT
ejpam-367	639	36	v1	v1	NOUN
ejpam-367	639	37	,	,	PUNCT
ejpam-367	639	38	v̇1)−	v̇1)−	ADJ
ejpam-367	639	39	dλt	dλt	NOUN
ejpam-367	639	40	fu̇1(t	fu̇1(t	PROPN
ejpam-367	639	41	,	,	PUNCT
ejpam-367	639	42	u1	u1	PROPN
ejpam-367	639	43	,	,	PUNCT
ejpam-367	639	44	u̇1	u̇1	PROPN
ejpam-367	639	45	,	,	PUNCT
ejpam-367	639	46	v1	v1	NOUN
ejpam-367	639	47	,	,	PUNCT
ejpam-367	639	48	v̇1)≧	v̇1)≧	PROPN
ejpam-367	639	49	0	0	NUM
ejpam-367	639	50	λt	λt	ADP
ejpam-367	639	51	gu2(t	gu2(t	PROPN
ejpam-367	639	52	,	,	PUNCT
ejpam-367	639	53	u2	u2	PROPN
ejpam-367	639	54	,	,	PUNCT
ejpam-367	639	55	u̇2	u̇2	PROPN
ejpam-367	639	56	,	,	PUNCT
ejpam-367	639	57	v2	v2	PROPN
ejpam-367	639	58	,	,	PUNCT
ejpam-367	639	59	v̇2)−	v̇2)−	ADJ
ejpam-367	639	60	dλt	dλt	NOUN
ejpam-367	639	61	gu̇2(t	gu̇2(t	PROPN
ejpam-367	639	62	,	,	PUNCT
ejpam-367	639	63	u2	u2	PROPN
ejpam-367	639	64	,	,	PUNCT
ejpam-367	639	65	u̇2	u̇2	PROPN
ejpam-367	639	66	,	,	PUNCT
ejpam-367	639	67	v2	v2	PROPN
ejpam-367	639	68	,	,	PUNCT
ejpam-367	639	69	v̇2)≧	v̇2)≧	NUM
ejpam-367	639	70	0	0	NUM
ejpam-367	640	1	∫	∫	NOUN
ejpam-367	641	1	i	i	PRON
ejpam-367	641	2	u2(t)t(λt	u2(t)t(λt	PROPN
ejpam-367	641	3	gu2(t	gu2(t	PROPN
ejpam-367	641	4	,	,	PUNCT
ejpam-367	641	5	u2	u2	PROPN
ejpam-367	641	6	,	,	PUNCT
ejpam-367	641	7	u̇2	u̇2	PROPN
ejpam-367	641	8	,	,	PUNCT
ejpam-367	641	9	v2	v2	NOUN
ejpam-367	641	10	,	,	PUNCT
ejpam-367	641	11	v̇2	v̇2	PROPN
ejpam-367	641	12	)	)	PUNCT
ejpam-367	641	13	−dλt	−dλt	NOUN
ejpam-367	642	1	gu̇2(t	gu̇2(t	PROPN
ejpam-367	642	2	,	,	PUNCT
ejpam-367	642	3	u2	u2	PROPN
ejpam-367	642	4	,	,	PUNCT
ejpam-367	642	5	u̇2	u̇2	PROPN
ejpam-367	642	6	,	,	PUNCT
ejpam-367	642	7	v2	v2	NOUN
ejpam-367	642	8	,	,	PUNCT
ejpam-367	642	9	v̇2))d	v̇2))d	NOUN
ejpam-367	642	10	t	t	PROPN
ejpam-367	642	11	≦	≦	PROPN
ejpam-367	642	12	0	0	NUM
ejpam-367	642	13	,	,	PUNCT
ejpam-367	642	14	λt	λt	ADP
ejpam-367	642	15	f	f	PROPN
ejpam-367	642	16	ẋ1(t	ẋ1(t	PROPN
ejpam-367	642	17	,	,	PUNCT
ejpam-367	642	18	u1	u1	PROPN
ejpam-367	642	19	,	,	PUNCT
ejpam-367	642	20	u̇1	u̇1	PROPN
ejpam-367	642	21	,	,	PUNCT
ejpam-367	642	22	v1	v1	NOUN
ejpam-367	642	23	,	,	PUNCT
ejpam-367	642	24	v̇1)|t	v̇1)|t	NOUN
ejpam-367	642	25	=	=	PRON
ejpam-367	642	26	a	a	X
ejpam-367	642	27	=	=	SYM
ejpam-367	642	28	0	0	NUM
ejpam-367	642	29	,	,	PUNCT
ejpam-367	642	30	λt	λt	ADP
ejpam-367	642	31	f	f	PROPN
ejpam-367	642	32	ẋ1(t	ẋ1(t	PROPN
ejpam-367	642	33	,	,	PUNCT
ejpam-367	642	34	u1	u1	PROPN
ejpam-367	642	35	,	,	PUNCT
ejpam-367	642	36	u̇1	u̇1	PROPN
ejpam-367	642	37	,	,	PUNCT
ejpam-367	642	38	v1	v1	NOUN
ejpam-367	642	39	,	,	PUNCT
ejpam-367	642	40	v̇1)|t	v̇1)|t	NOUN
ejpam-367	642	41	=	=	SYM
ejpam-367	642	42	b	b	NOUN
ejpam-367	642	43	=	=	SYM
ejpam-367	642	44	0	0	NUM
ejpam-367	642	45	λt	λt	ADP
ejpam-367	642	46	g	g	PROPN
ejpam-367	642	47	ẋ2(t	ẋ2(t	PROPN
ejpam-367	642	48	,	,	PUNCT
ejpam-367	642	49	x2	x2	PROPN
ejpam-367	642	50	,	,	PUNCT
ejpam-367	642	51	ẋ2	ẋ2	PROPN
ejpam-367	642	52	,	,	PUNCT
ejpam-367	642	53	y2	y2	PROPN
ejpam-367	642	54	,	,	PUNCT
ejpam-367	642	55	ẏ2)|t	ẏ2)|t	NOUN
ejpam-367	642	56	=	=	PROPN
ejpam-367	642	57	a	a	X
ejpam-367	642	58	=	=	SYM
ejpam-367	642	59	0	0	NUM
ejpam-367	642	60	,	,	PUNCT
ejpam-367	642	61	λt	λt	ADP
ejpam-367	642	62	g	g	PROPN
ejpam-367	642	63	ẋ2(t	ẋ2(t	PROPN
ejpam-367	642	64	,	,	PUNCT
ejpam-367	642	65	x2	x2	PROPN
ejpam-367	642	66	,	,	PUNCT
ejpam-367	642	67	ẋ2	ẋ2	PROPN
ejpam-367	642	68	,	,	PUNCT
ejpam-367	642	69	y2	y2	PROPN
ejpam-367	642	70	,	,	PUNCT
ejpam-367	642	71	ẏ2)|t	ẏ2)|t	NOUN
ejpam-367	642	72	=	=	SYM
ejpam-367	642	73	b	b	NOUN
ejpam-367	642	74	=	=	SYM
ejpam-367	642	75	0	0	PUNCT
ejpam-367	642	76	λ	λ	PROPN
ejpam-367	642	77	∈	∈	PROPN
ejpam-367	642	78	λ+	λ+	PUNCT
ejpam-367	642	79	for	for	ADP
ejpam-367	642	80	these	these	DET
ejpam-367	642	81	problems	problem	NOUN
ejpam-367	642	82	,	,	PUNCT
ejpam-367	642	83	theorem	theorem	VERB
ejpam-367	642	84	1	1	NUM
ejpam-367	642	85	-	-	SYM
ejpam-367	642	86	3	3	NUM
ejpam-367	642	87	will	will	AUX
ejpam-367	642	88	remain	remain	VERB
ejpam-367	642	89	true	true	ADJ
ejpam-367	642	90	except	except	SCONJ
ejpam-367	642	91	that	that	SCONJ
ejpam-367	642	92	some	some	DET
ejpam-367	642	93	slight	slight	ADJ
ejpam-367	642	94	modifications	modification	NOUN
ejpam-367	642	95	in	in	ADP
ejpam-367	642	96	the	the	DET
ejpam-367	642	97	arguments	argument	NOUN
ejpam-367	642	98	for	for	ADP
ejpam-367	642	99	these	these	DET
ejpam-367	642	100	theorems	theorem	NOUN
ejpam-367	642	101	are	be	AUX
ejpam-367	642	102	to	to	PART
ejpam-367	642	103	be	be	AUX
ejpam-367	642	104	indicated	indicate	VERB
ejpam-367	642	105	.	.	PUNCT
ejpam-367	643	1	7	7	X
ejpam-367	643	2	.	.	X
ejpam-367	643	3	mathematical	mathematical	ADJ
ejpam-367	643	4	programming	programming	NOUN
ejpam-367	643	5	if	if	SCONJ
ejpam-367	643	6	the	the	DET
ejpam-367	643	7	time	time	NOUN
ejpam-367	643	8	dependency	dependency	NOUN
ejpam-367	643	9	of	of	ADP
ejpam-367	643	10	(	(	PUNCT
ejpam-367	643	11	mix	mix	VERB
ejpam-367	643	12	sp	sp	NOUN
ejpam-367	643	13	)	)	PUNCT
ejpam-367	643	14	and	and	CCONJ
ejpam-367	643	15	(	(	PUNCT
ejpam-367	643	16	mix	mix	VERB
ejpam-367	643	17	sd	sd	NOUN
ejpam-367	643	18	)	)	PUNCT
ejpam-367	643	19	is	be	AUX
ejpam-367	643	20	removed	remove	VERB
ejpam-367	643	21	and	and	CCONJ
ejpam-367	643	22	b	b	ADP
ejpam-367	643	23	−	−	PROPN
ejpam-367	643	24	a	a	DET
ejpam-367	643	25	=	=	NOUN
ejpam-367	643	26	1	1	NUM
ejpam-367	643	27	,	,	PUNCT
ejpam-367	643	28	we	we	PRON
ejpam-367	643	29	obtain	obtain	AUX
ejpam-367	643	30	following	follow	VERB
ejpam-367	643	31	pair	pair	NOUN
ejpam-367	643	32	of	of	ADP
ejpam-367	643	33	static	static	ADJ
ejpam-367	643	34	mixed	mixed	ADJ
ejpam-367	643	35	type	type	NOUN
ejpam-367	643	36	multiobjective	multiobjective	ADJ
ejpam-367	643	37	dual	dual	ADJ
ejpam-367	643	38	problems	problem	NOUN
ejpam-367	643	39	studied	study	VERB
ejpam-367	643	40	by	by	ADP
ejpam-367	643	41	bector	bector	NOUN
ejpam-367	643	42	,	,	PUNCT
ejpam-367	643	43	chandra	chandra	PROPN
ejpam-367	643	44	and	and	CCONJ
ejpam-367	643	45	abha	abha	VERB
ejpam-367	643	46	[	[	X
ejpam-367	643	47	2	2	NUM
ejpam-367	643	48	]	]	PUNCT
ejpam-367	643	49	.	.	PUNCT
ejpam-367	644	1	primal	primal	ADJ
ejpam-367	644	2	(	(	PUNCT
ejpam-367	644	3	mix	mix	VERB
ejpam-367	644	4	sp1	sp1	NOUN
ejpam-367	644	5	)	)	PUNCT
ejpam-367	644	6	minimize	minimize	VERB
ejpam-367	644	7	f	f	X
ejpam-367	644	8	(	(	PUNCT
ejpam-367	644	9	x1	x1	PROPN
ejpam-367	644	10	,	,	PUNCT
ejpam-367	644	11	y1	y1	NOUN
ejpam-367	644	12	)	)	PUNCT
ejpam-367	644	13	+	+	NUM
ejpam-367	645	1	g(x2	g(x2	NOUN
ejpam-367	645	2	,	,	PUNCT
ejpam-367	645	3	y2)−	y2)−	PROPN
ejpam-367	645	4	(	(	PUNCT
ejpam-367	645	5	y1)t	y1)t	PROPN
ejpam-367	645	6	(	(	PUNCT
ejpam-367	645	7	λt	λt	ADP
ejpam-367	645	8	f	f	PROPN
ejpam-367	645	9	y1(x1	y1(x1	PROPN
ejpam-367	645	10	,	,	PUNCT
ejpam-367	645	11	y1	y1	NOUN
ejpam-367	645	12	)	)	PUNCT
ejpam-367	645	13	subject	subject	NOUN
ejpam-367	645	14	to	to	ADP
ejpam-367	645	15	λt	λt	ADP
ejpam-367	645	16	f	f	PROPN
ejpam-367	645	17	y1(x1	y1(x1	PROPN
ejpam-367	645	18	,	,	PUNCT
ejpam-367	645	19	y1)≦	y1)≦	PROPN
ejpam-367	645	20	0	0	NUM
ejpam-367	645	21	,	,	PUNCT
ejpam-367	645	22	λt	λt	ADP
ejpam-367	645	23	g	g	PROPN
ejpam-367	645	24	y2(x2	y2(x2	NOUN
ejpam-367	645	25	,	,	PUNCT
ejpam-367	645	26	y2)≦	y2)≦	PROPN
ejpam-367	645	27	0	0	NUM
ejpam-367	645	28	,	,	PUNCT
ejpam-367	645	29	y2(t)t(λt	y2(t)t(λt	NOUN
ejpam-367	645	30	g	g	PROPN
ejpam-367	645	31	y2(x2	y2(x2	NOUN
ejpam-367	645	32	,	,	PUNCT
ejpam-367	645	33	y2))≧	y2))≧	NOUN
ejpam-367	645	34	0	0	NUM
ejpam-367	645	35	,	,	PUNCT
ejpam-367	645	36	λ	λ	PROPN
ejpam-367	645	37	∈	∈	PROPN
ejpam-367	645	38	λ+	λ+	PUNCT
ejpam-367	645	39	dual	dual	ADJ
ejpam-367	645	40	(	(	PUNCT
ejpam-367	645	41	mix	mix	X
ejpam-367	645	42	sd1	sd1	PROPN
ejpam-367	645	43	)	)	PUNCT
ejpam-367	645	44	maximize	maximize	VERB
ejpam-367	645	45	f	f	PROPN
ejpam-367	645	46	(	(	PUNCT
ejpam-367	645	47	u1	u1	NOUN
ejpam-367	645	48	,	,	PUNCT
ejpam-367	645	49	v1	v1	NOUN
ejpam-367	645	50	)	)	PUNCT
ejpam-367	646	1	+	+	NUM
ejpam-367	646	2	g(u2	g(u2	NOUN
ejpam-367	646	3	,	,	PUNCT
ejpam-367	646	4	v2)−	v2)−	ADJ
ejpam-367	646	5	u1(t)t(λt	u1(t)t(λt	NOUN
ejpam-367	646	6	fu1(u1	fu1(u1	NUM
ejpam-367	646	7	,	,	PUNCT
ejpam-367	646	8	v1	v1	NOUN
ejpam-367	646	9	)	)	PUNCT
ejpam-367	646	10	)	)	PUNCT
ejpam-367	647	1	references	reference	VERB
ejpam-367	647	2	602	602	NUM
ejpam-367	647	3	subject	subject	ADJ
ejpam-367	647	4	to	to	ADP
ejpam-367	647	5	λt	λt	ADP
ejpam-367	647	6	fu1(u1	fu1(u1	NUM
ejpam-367	647	7	,	,	PUNCT
ejpam-367	647	8	v1	v1	NOUN
ejpam-367	647	9	)	)	PUNCT
ejpam-367	647	10	≧	≧	X
ejpam-367	647	11	0	0	NUM
ejpam-367	647	12	,	,	PUNCT
ejpam-367	647	13	λt	λt	ADP
ejpam-367	647	14	gu2(u2	gu2(u2	PROPN
ejpam-367	647	15	,	,	PUNCT
ejpam-367	647	16	v2)≧	v2)≧	PROPN
ejpam-367	647	17	0	0	NUM
ejpam-367	647	18	,	,	PUNCT
ejpam-367	647	19	(	(	PUNCT
ejpam-367	647	20	u2)t	u2)t	ADJ
ejpam-367	647	21	(	(	PUNCT
ejpam-367	647	22	λt	λt	ADP
ejpam-367	647	23	gu2(u2	gu2(u2	NOUN
ejpam-367	647	24	,	,	PUNCT
ejpam-367	647	25	v2).≦	v2).≦	NOUN
ejpam-367	647	26	0	0	NUM
ejpam-367	647	27	,	,	PUNCT
ejpam-367	648	1	λ	λ	PROPN
ejpam-367	648	2	∈	∈	NOUN
ejpam-367	648	3	λ+	λ+	X
ejpam-367	648	4	.	.	PUNCT
ejpam-367	649	1	acknowledgements	acknowledgement	NOUN
ejpam-367	649	2	the	the	DET
ejpam-367	649	3	authors	author	NOUN
ejpam-367	649	4	are	be	AUX
ejpam-367	649	5	grateful	grateful	ADJ
ejpam-367	649	6	to	to	ADP
ejpam-367	649	7	the	the	DET
ejpam-367	649	8	anonymous	anonymous	ADJ
ejpam-367	649	9	referee	referee	NOUN
ejpam-367	649	10	for	for	ADP
ejpam-367	649	11	his	his	PRON
ejpam-367	649	12	/	/	SYM
ejpam-367	649	13	her	her	PRON
ejpam-367	649	14	valuable	valuable	ADJ
ejpam-367	649	15	comments	comment	NOUN
ejpam-367	649	16	that	that	PRON
ejpam-367	649	17	have	have	AUX
ejpam-367	649	18	substantially	substantially	ADV
ejpam-367	649	19	improved	improve	VERB
ejpam-367	649	20	the	the	DET
ejpam-367	649	21	presentation	presentation	NOUN
ejpam-367	649	22	of	of	ADP
ejpam-367	649	23	this	this	DET
ejpam-367	649	24	research	research	NOUN
ejpam-367	649	25	.	.	PUNCT
ejpam-367	650	1	references	reference	NOUN
ejpam-367	650	2	[	[	X
ejpam-367	650	3	1	1	NUM
ejpam-367	650	4	]	]	X
ejpam-367	650	5	m.s	m.s	PROPN
ejpam-367	650	6	.	.	PROPN
ejpam-367	650	7	bazaraa	bazaraa	PROPN
ejpam-367	650	8	and	and	CCONJ
ejpam-367	650	9	j.j	j.j	PROPN
ejpam-367	650	10	.	.	PROPN
ejpam-367	650	11	goode	goode	PROPN
ejpam-367	650	12	,	,	PUNCT
ejpam-367	650	13	on	on	ADP
ejpam-367	650	14	symmetric	symmetric	ADJ
ejpam-367	650	15	duality	duality	NOUN
ejpam-367	650	16	in	in	ADP
ejpam-367	650	17	nonlinear	nonlinear	ADJ
ejpam-367	650	18	programming	programming	NOUN
ejpam-367	650	19	,	,	PUNCT
ejpam-367	650	20	operations	operation	NOUN
ejpam-367	650	21	research	research	NOUN
ejpam-367	650	22	21(1	21(1	NUM
ejpam-367	650	23	)	)	PUNCT
ejpam-367	650	24	(	(	PUNCT
ejpam-367	650	25	1973	1973	NUM
ejpam-367	650	26	)	)	PUNCT
ejpam-367	650	27	,	,	PUNCT
ejpam-367	650	28	1–9	1–9	NOUN
ejpam-367	650	29	.	.	PUNCT
ejpam-367	651	1	[	[	X
ejpam-367	651	2	2	2	X
ejpam-367	651	3	]	]	X
ejpam-367	651	4	c.r	c.r	PROPN
ejpam-367	651	5	.	.	PROPN
ejpam-367	651	6	bector	bector	PROPN
ejpam-367	651	7	,	,	PUNCT
ejpam-367	651	8	chandra	chandra	PROPN
ejpam-367	651	9	and	and	CCONJ
ejpam-367	651	10	abha	abha	VERB
ejpam-367	651	11	,	,	PUNCT
ejpam-367	651	12	on	on	ADP
ejpam-367	651	13	mixed	mixed	ADJ
ejpam-367	651	14	type	type	NOUN
ejpam-367	651	15	symmetric	symmetric	ADJ
ejpam-367	651	16	duality	duality	NOUN
ejpam-367	651	17	in	in	ADP
ejpam-367	651	18	multiobjective	multiobjective	ADJ
ejpam-367	651	19	programming	programming	NOUN
ejpam-367	651	20	,	,	PUNCT
ejpam-367	651	21	opsearch	opsearch	NOUN
ejpam-367	651	22	36(4	36(4	NUM
ejpam-367	651	23	)	)	PUNCT
ejpam-367	651	24	(	(	PUNCT
ejpam-367	651	25	1999	1999	NUM
ejpam-367	651	26	)	)	PUNCT
ejpam-367	651	27	,	,	PUNCT
ejpam-367	651	28	399–407	399–407	NUM
ejpam-367	651	29	.	.	PUNCT
ejpam-367	652	1	[	[	X
ejpam-367	652	2	3	3	X
ejpam-367	652	3	]	]	X
ejpam-367	652	4	c.r	c.r	PROPN
ejpam-367	652	5	.	.	PROPN
ejpam-367	652	6	bector	bector	PROPN
ejpam-367	652	7	,	,	PUNCT
ejpam-367	652	8	s.	s.	PROPN
ejpam-367	652	9	chandra	chandra	PROPN
ejpam-367	652	10	and	and	CCONJ
ejpam-367	652	11	i.	i.	PROPN
ejpam-367	652	12	husain	husain	PROPN
ejpam-367	652	13	,	,	PUNCT
ejpam-367	652	14	generalized	generalized	ADJ
ejpam-367	652	15	concavity	concavity	NOUN
ejpam-367	652	16	and	and	CCONJ
ejpam-367	652	17	duality	duality	NOUN
ejpam-367	652	18	in	in	ADP
ejpam-367	652	19	continuous	continuous	ADJ
ejpam-367	652	20	programming	programming	NOUN
ejpam-367	652	21	,	,	PUNCT
ejpam-367	652	22	utilitas	utilitas	PROPN
ejpam-367	652	23	,	,	PUNCT
ejpam-367	652	24	mathematica	mathematica	PROPN
ejpam-367	652	25	25(1984	25(1984	PROPN
ejpam-367	652	26	)	)	PUNCT
ejpam-367	652	27	,	,	PUNCT
ejpam-367	652	28	171–190	171–190	NUM
ejpam-367	652	29	.	.	PUNCT
ejpam-367	653	1	[	[	X
ejpam-367	653	2	4	4	X
ejpam-367	653	3	]	]	X
ejpam-367	653	4	c.r	c.r	PROPN
ejpam-367	653	5	.	.	PROPN
ejpam-367	653	6	bector	bector	NOUN
ejpam-367	653	7	and	and	CCONJ
ejpam-367	653	8	i.	i.	PROPN
ejpam-367	653	9	husain	husain	PROPN
ejpam-367	653	10	,	,	PUNCT
ejpam-367	653	11	duality	duality	NOUN
ejpam-367	653	12	for	for	ADP
ejpam-367	653	13	multiobjective	multiobjective	ADJ
ejpam-367	653	14	variational	variational	ADJ
ejpam-367	653	15	problems	problem	NOUN
ejpam-367	653	16	,	,	PUNCT
ejpam-367	653	17	journal	journal	NOUN
ejpam-367	653	18	of	of	ADP
ejpam-367	653	19	math	math	NOUN
ejpam-367	653	20	.	.	PUNCT
ejpam-367	654	1	anal	anal	ADJ
ejpam-367	654	2	and	and	CCONJ
ejpam-367	654	3	appl	appl	NOUN
ejpam-367	654	4	.	.	PUNCT
ejpam-367	654	5	166(1	166(1	NUM
ejpam-367	654	6	)	)	PUNCT
ejpam-367	654	7	(	(	PUNCT
ejpam-367	654	8	1992	1992	NUM
ejpam-367	654	9	)	)	PUNCT
ejpam-367	654	10	,	,	PUNCT
ejpam-367	654	11	214–224	214–224	NUM
ejpam-367	654	12	.	.	PUNCT
ejpam-367	655	1	[	[	X
ejpam-367	655	2	5	5	NUM
ejpam-367	655	3	]	]	PUNCT
ejpam-367	655	4	a.	a.	PROPN
ejpam-367	655	5	ben	ben	PROPN
ejpam-367	655	6	-	-	PROPN
ejpam-367	655	7	israel	israel	PROPN
ejpam-367	655	8	and	and	CCONJ
ejpam-367	655	9	b.	b.	PROPN
ejpam-367	655	10	mond	mond	PROPN
ejpam-367	655	11	,	,	PUNCT
ejpam-367	655	12	what	what	PRON
ejpam-367	655	13	is	be	AUX
ejpam-367	655	14	invexity	invexity	NOUN
ejpam-367	655	15	?	?	PUNCT
ejpam-367	656	1	j.	j.	PROPN
ejpam-367	656	2	austral	austral	PROPN
ejpam-367	656	3	.	.	PUNCT
ejpam-367	657	1	math	math	NOUN
ejpam-367	657	2	.	.	PUNCT
ejpam-367	658	1	soc	soc	PROPN
ejpam-367	658	2	.	.	PUNCT
ejpam-367	659	1	ser	ser	PROPN
ejpam-367	659	2	.	.	PUNCT
ejpam-367	660	1	b	b	X
ejpam-367	660	2	28(1986	28(1986	NUM
ejpam-367	660	3	)	)	PUNCT
ejpam-367	660	4	,	,	PUNCT
ejpam-367	660	5	1–9	1–9	NOUN
ejpam-367	660	6	.	.	PUNCT
ejpam-367	661	1	[	[	X
ejpam-367	661	2	6	6	NUM
ejpam-367	661	3	]	]	PUNCT
ejpam-367	661	4	s.	s.	PROPN
ejpam-367	661	5	chandra	chandra	PROPN
ejpam-367	661	6	and	and	CCONJ
ejpam-367	661	7	i.	i.	PROPN
ejpam-367	661	8	husain	husain	PROPN
ejpam-367	661	9	,	,	PUNCT
ejpam-367	661	10	symmetric	symmetric	ADJ
ejpam-367	661	11	dual	dual	ADJ
ejpam-367	661	12	continuous	continuous	ADJ
ejpam-367	661	13	fractional	fractional	ADJ
ejpam-367	661	14	programming	programming	NOUN
ejpam-367	661	15	,	,	PUNCT
ejpam-367	661	16	j.	j.	PROPN
ejpam-367	661	17	inf	inf	PROPN
ejpam-367	661	18	.	.	PROPN
ejpam-367	661	19	opt	opt	PROPN
ejpam-367	661	20	.	.	PUNCT
ejpam-367	662	1	sc	sc	PROPN
ejpam-367	662	2	.	.	PUNCT
ejpam-367	662	3	10(1989	10(1989	NUM
ejpam-367	662	4	)	)	PUNCT
ejpam-367	662	5	,	,	PUNCT
ejpam-367	662	6	241–255	241–255	NUM
ejpam-367	662	7	.	.	PUNCT
ejpam-367	663	1	[	[	X
ejpam-367	663	2	7	7	NUM
ejpam-367	663	3	]	]	X
ejpam-367	663	4	w.s	w.s	PROPN
ejpam-367	663	5	.	.	PROPN
ejpam-367	663	6	dorn	dorn	PROPN
ejpam-367	663	7	,	,	PUNCT
ejpam-367	663	8	asymmetric	asymmetric	ADJ
ejpam-367	663	9	dual	dual	ADJ
ejpam-367	663	10	theorem	theorem	NOUN
ejpam-367	663	11	for	for	ADP
ejpam-367	663	12	quadratic	quadratic	ADJ
ejpam-367	663	13	programs	program	NOUN
ejpam-367	663	14	,	,	PUNCT
ejpam-367	663	15	journal	journal	NOUN
ejpam-367	663	16	of	of	ADP
ejpam-367	663	17	operations	operation	NOUN
ejpam-367	663	18	research	research	NOUN
ejpam-367	663	19	society	society	NOUN
ejpam-367	663	20	of	of	ADP
ejpam-367	663	21	japan	japan	PROPN
ejpam-367	663	22	2(1960	2(1960	NUM
ejpam-367	663	23	)	)	PUNCT
ejpam-367	663	24	93–97	93–97	NUM
ejpam-367	663	25	.	.	PUNCT
ejpam-367	664	1	[	[	X
ejpam-367	664	2	8	8	NUM
ejpam-367	664	3	]	]	X
ejpam-367	664	4	g.b	g.b	PROPN
ejpam-367	664	5	.	.	PROPN
ejpam-367	664	6	dantzig	dantzig	PROPN
ejpam-367	664	7	,	,	PUNCT
ejpam-367	664	8	eisenberg	eisenberg	PROPN
ejpam-367	664	9	and	and	CCONJ
ejpam-367	664	10	r.w	r.w	PROPN
ejpam-367	664	11	.	.	PROPN
ejpam-367	664	12	cottle	cottle	PROPN
ejpam-367	664	13	,	,	PUNCT
ejpam-367	664	14	symmetric	symmetric	ADJ
ejpam-367	664	15	dual	dual	ADJ
ejpam-367	664	16	nonlinear	nonlinear	ADJ
ejpam-367	664	17	programs	program	NOUN
ejpam-367	664	18	,	,	PUNCT
ejpam-367	664	19	pacific	pacific	ADJ
ejpam-367	664	20	jounal	jounal	NOUN
ejpam-367	664	21	of	of	ADP
ejpam-367	664	22	mathematics	mathematic	NOUN
ejpam-367	664	23	15(1965	15(1965	NUM
ejpam-367	664	24	)	)	PUNCT
ejpam-367	665	1	809–812	809–812	NUM
ejpam-367	665	2	.	.	PUNCT
ejpam-367	666	1	references	reference	NOUN
ejpam-367	666	2	603	603	NUM
ejpam-367	667	1	[	[	X
ejpam-367	667	2	9	9	NUM
ejpam-367	667	3	]	]	X
ejpam-367	667	4	gulati	gulati	PROPN
ejpam-367	667	5	,	,	PUNCT
ejpam-367	667	6	i.	i.	PROPN
ejpam-367	667	7	husain	husain	PROPN
ejpam-367	667	8	and	and	CCONJ
ejpam-367	667	9	a.	a.	PROPN
ejpam-367	667	10	ahmed	ahmed	PROPN
ejpam-367	667	11	,	,	PUNCT
ejpam-367	667	12	multiobjective	multiobjective	ADJ
ejpam-367	667	13	symmetric	symmetric	ADJ
ejpam-367	667	14	duality	duality	NOUN
ejpam-367	667	15	with	with	ADP
ejpam-367	667	16	invexity	invexity	NOUN
ejpam-367	667	17	,	,	PUNCT
ejpam-367	667	18	bulletin	bulletin	NOUN
ejpam-367	667	19	of	of	ADP
ejpam-367	667	20	the	the	DET
ejpam-367	667	21	australian	australian	ADJ
ejpam-367	667	22	mathematical	mathematical	ADJ
ejpam-367	667	23	society	society	NOUN
ejpam-367	667	24	56(1997	56(1997	NUM
ejpam-367	667	25	)	)	PUNCT
ejpam-367	667	26	25–36	25–36	NUM
ejpam-367	667	27	.	.	PUNCT
ejpam-367	668	1	[	[	X
ejpam-367	668	2	10	10	NUM
ejpam-367	668	3	]	]	X
ejpam-367	668	4	i.	i.	PROPN
ejpam-367	668	5	husain	husain	PROPN
ejpam-367	668	6	and	and	CCONJ
ejpam-367	668	7	z.	z.	PROPN
ejpam-367	668	8	jabeen	jabeen	PROPN
ejpam-367	668	9	,	,	PUNCT
ejpam-367	668	10	mixed	mixed	ADJ
ejpam-367	668	11	type	type	NOUN
ejpam-367	668	12	symmetric	symmetric	ADJ
ejpam-367	668	13	and	and	CCONJ
ejpam-367	668	14	self	self	NOUN
ejpam-367	668	15	duality	duality	NOUN
ejpam-367	668	16	for	for	ADP
ejpam-367	668	17	variational	variational	ADJ
ejpam-367	668	18	problems	problem	NOUN
ejpam-367	668	19	,	,	PUNCT
ejpam-367	668	20	congressus	congressus	PROPN
ejpam-367	668	21	numerantum	numerantum	PROPN
ejpam-367	668	22	171(2004	171(2004	NUM
ejpam-367	668	23	)	)	PUNCT
ejpam-367	668	24	,	,	PUNCT
ejpam-367	668	25	77–103	77–103	NUM
ejpam-367	668	26	.	.	PUNCT
ejpam-367	669	1	[	[	X
ejpam-367	669	2	11	11	NUM
ejpam-367	669	3	]	]	X
ejpam-367	669	4	d.h	d.h	PROPN
ejpam-367	669	5	.	.	PROPN
ejpam-367	669	6	martin	martin	PROPN
ejpam-367	669	7	,	,	PUNCT
ejpam-367	669	8	the	the	DET
ejpam-367	669	9	essence	essence	NOUN
ejpam-367	669	10	of	of	ADP
ejpam-367	669	11	invexity	invexity	NOUN
ejpam-367	669	12	,	,	PUNCT
ejpam-367	669	13	journal	journal	NOUN
ejpam-367	669	14	of	of	ADP
ejpam-367	669	15	optimization	optimization	NOUN
ejpam-367	669	16	theory	theory	NOUN
ejpam-367	669	17	and	and	CCONJ
ejpam-367	669	18	applicatins	applicatin	NOUN
ejpam-367	669	19	47(1	47(1	NUM
ejpam-367	669	20	)	)	PUNCT
ejpam-367	669	21	(	(	PUNCT
ejpam-367	669	22	1985	1985	NUM
ejpam-367	669	23	)	)	PUNCT
ejpam-367	669	24	,	,	PUNCT
ejpam-367	669	25	65–76	65–76	NUM
ejpam-367	669	26	.	.	PUNCT
ejpam-367	670	1	[	[	X
ejpam-367	670	2	12	12	NUM
ejpam-367	670	3	]	]	X
ejpam-367	670	4	b.	b.	PROPN
ejpam-367	670	5	mond	mond	PROPN
ejpam-367	670	6	,	,	PUNCT
ejpam-367	670	7	a	a	DET
ejpam-367	670	8	symmetric	symmetric	ADJ
ejpam-367	670	9	dual	dual	ADJ
ejpam-367	670	10	theorem	theorem	NOUN
ejpam-367	670	11	for	for	ADP
ejpam-367	670	12	nonlinear	nonlinear	ADJ
ejpam-367	670	13	programs	program	NOUN
ejpam-367	670	14	,	,	PUNCT
ejpam-367	670	15	quaterly	quaterly	ADV
ejpam-367	670	16	jounal	jounal	ADJ
ejpam-367	670	17	of	of	ADP
ejpam-367	670	18	applied	applied	ADJ
ejpam-367	670	19	mathematics	mathematic	NOUN
ejpam-367	670	20	23(1965	23(1965	NOUN
ejpam-367	670	21	)	)	PUNCT
ejpam-367	670	22	265–269	265–269	NUM
ejpam-367	670	23	.	.	PUNCT
ejpam-367	671	1	[	[	X
ejpam-367	671	2	13	13	NUM
ejpam-367	671	3	]	]	X
ejpam-367	671	4	b.	b.	PROPN
ejpam-367	671	5	mond	mond	PROPN
ejpam-367	671	6	and	and	CCONJ
ejpam-367	671	7	r.w	r.w	PROPN
ejpam-367	671	8	.	.	PROPN
ejpam-367	671	9	cottle	cottle	PROPN
ejpam-367	671	10	,	,	PUNCT
ejpam-367	671	11	self	self	NOUN
ejpam-367	671	12	duality	duality	NOUN
ejpam-367	671	13	in	in	ADP
ejpam-367	671	14	mathematical	mathematical	ADJ
ejpam-367	671	15	programming	programming	NOUN
ejpam-367	671	16	,	,	PUNCT
ejpam-367	671	17	siam	siam	PROPN
ejpam-367	671	18	j.	j.	PROPN
ejpam-367	671	19	appl	appl	PROPN
ejpam-367	671	20	.	.	PROPN
ejpam-367	671	21	math	math	PROPN
ejpam-367	671	22	.	.	PUNCT
ejpam-367	672	1	14(1966	14(1966	NUM
ejpam-367	672	2	)	)	PUNCT
ejpam-367	672	3	,	,	PUNCT
ejpam-367	673	1	420–423	420–423	NUM
ejpam-367	673	2	.	.	PUNCT
ejpam-367	674	1	[	[	X
ejpam-367	674	2	14	14	NUM
ejpam-367	674	3	]	]	X
ejpam-367	674	4	b.	b.	PROPN
ejpam-367	674	5	mond	mond	PROPN
ejpam-367	674	6	and	and	CCONJ
ejpam-367	674	7	t.	t.	PROPN
ejpam-367	674	8	weir	weir	PROPN
ejpam-367	674	9	,	,	PUNCT
ejpam-367	674	10	generalized	generalized	ADJ
ejpam-367	674	11	concavity	concavity	NOUN
ejpam-367	674	12	and	and	CCONJ
ejpam-367	674	13	duality	duality	NOUN
ejpam-367	674	14	,	,	PUNCT
ejpam-367	674	15	in	in	ADP
ejpam-367	674	16	:	:	PUNCT
ejpam-367	674	17	s.sciable	s.sciable	ADJ
ejpam-367	674	18	,	,	PUNCT
ejpam-367	674	19	w.t.ziemba	w.t.ziemba	NOUN
ejpam-367	674	20	(	(	PUNCT
ejpam-367	674	21	eds	ed	NOUN
ejpam-367	674	22	.	.	PUNCT
ejpam-367	674	23	)	)	PUNCT
ejpam-367	674	24	,	,	PUNCT
ejpam-367	674	25	generalized	generalize	VERB
ejpam-367	674	26	concavity	concavity	NOUN
ejpam-367	674	27	in	in	ADP
ejpam-367	674	28	optimization	optimization	NOUN
ejpam-367	674	29	and	and	CCONJ
ejpam-367	674	30	economics	economic	NOUN
ejpam-367	674	31	,	,	PUNCT
ejpam-367	674	32	academic	academic	ADJ
ejpam-367	674	33	press	press	NOUN
ejpam-367	674	34	,	,	PUNCT
ejpam-367	674	35	new	new	PROPN
ejpam-367	674	36	york	york	PROPN
ejpam-367	674	37	,	,	PUNCT
ejpam-367	674	38	(	(	PUNCT
ejpam-367	674	39	1981	1981	NUM
ejpam-367	674	40	)	)	PUNCT
ejpam-367	674	41	.	.	PUNCT
ejpam-367	675	1	[	[	X
ejpam-367	675	2	15	15	NUM
ejpam-367	675	3	]	]	X
ejpam-367	675	4	b.	b.	PROPN
ejpam-367	675	5	mond	mond	PROPN
ejpam-367	675	6	and	and	CCONJ
ejpam-367	675	7	m.a	m.a	PROPN
ejpam-367	675	8	.	.	PROPN
ejpam-367	675	9	hanson	hanson	PROPN
ejpam-367	675	10	,	,	PUNCT
ejpam-367	675	11	symmetric	symmetric	ADJ
ejpam-367	675	12	duality	duality	NOUN
ejpam-367	675	13	for	for	ADP
ejpam-367	675	14	variational	variational	ADJ
ejpam-367	675	15	problems	problem	NOUN
ejpam-367	675	16	,	,	PUNCT
ejpam-367	675	17	j.	j.	PROPN
ejpam-367	675	18	math	math	PROPN
ejpam-367	675	19	.	.	PUNCT
ejpam-367	676	1	anal	anal	PROPN
ejpam-367	676	2	.	.	PUNCT
ejpam-367	676	3	appl	appl	PROPN
ejpam-367	676	4	.	.	PUNCT
ejpam-367	677	1	18(1967	18(1967	NUM
ejpam-367	677	2	)	)	PUNCT
ejpam-367	677	3	161	161	NUM
ejpam-367	677	4	-	-	SYM
ejpam-367	677	5	172	172	NUM
ejpam-367	677	6	.	.	PUNCT
ejpam-367	678	1	[	[	X
ejpam-367	678	2	16	16	NUM
ejpam-367	678	3	]	]	X
ejpam-367	678	4	n.g	n.g	PROPN
ejpam-367	678	5	.	.	PROPN
ejpam-367	678	6	rueda	rueda	PROPN
ejpam-367	678	7	and	and	CCONJ
ejpam-367	678	8	m.a	m.a	PROPN
ejpam-367	678	9	.	.	PROPN
ejpam-367	678	10	hanson	hanson	PROPN
ejpam-367	678	11	,	,	PUNCT
ejpam-367	678	12	optimality	optimality	NOUN
ejpam-367	678	13	criteria	criterion	NOUN
ejpam-367	678	14	in	in	ADP
ejpam-367	678	15	mathematical	mathematical	ADJ
ejpam-367	678	16	programming	programming	NOUN
ejpam-367	678	17	involving	involve	VERB
ejpam-367	678	18	generalized	generalized	ADJ
ejpam-367	678	19	invexity	invexity	NOUN
ejpam-367	678	20	.	.	PUNCT
ejpam-367	679	1	journal	journal	PROPN
ejpam-367	679	2	of	of	ADP
ejpam-367	679	3	mathematical	mathematical	ADJ
ejpam-367	679	4	analysis	analysis	NOUN
ejpam-367	679	5	and	and	CCONJ
ejpam-367	679	6	applications	application	NOUN
ejpam-367	679	7	130(2	130(2	NUM
ejpam-367	679	8	)	)	PUNCT
ejpam-367	679	9	,	,	PUNCT
ejpam-367	679	10	375–385	375–385	NUM
ejpam-367	679	11	.	.	PUNCT
ejpam-367	680	1	[	[	X
ejpam-367	680	2	17	17	NUM
ejpam-367	680	3	]	]	X
ejpam-367	680	4	f.a	f.a	PROPN
ejpam-367	680	5	.	.	PROPN
ejpam-367	680	6	valentine	valentine	PROPN
ejpam-367	680	7	,	,	PUNCT
ejpam-367	680	8	the	the	DET
ejpam-367	680	9	problem	problem	NOUN
ejpam-367	680	10	of	of	ADP
ejpam-367	680	11	lagrange	lagrange	NOUN
ejpam-367	680	12	with	with	ADP
ejpam-367	680	13	differential	differential	ADJ
ejpam-367	680	14	inequalities	inequality	NOUN
ejpam-367	680	15	as	as	ADP
ejpam-367	680	16	added	add	VERB
ejpam-367	680	17	side	side	NOUN
ejpam-367	680	18	conditions	condition	NOUN
ejpam-367	680	19	,	,	PUNCT
ejpam-367	680	20	contributions	contribution	NOUN
ejpam-367	680	21	to	to	ADP
ejpam-367	680	22	calculus	calculus	NOUN
ejpam-367	680	23	of	of	ADP
ejpam-367	680	24	variations	variation	NOUN
ejpam-367	680	25	,	,	PUNCT
ejpam-367	680	26	1933	1933	NUM
ejpam-367	680	27	-	-	SYM
ejpam-367	680	28	37	37	NUM
ejpam-367	680	29	,	,	PUNCT
ejpam-367	680	30	univ	univ	PROPN
ejpam-367	680	31	.	.	PROPN
ejpam-367	680	32	of	of	ADP
ejpam-367	680	33	chicago	chicago	PROPN
ejpam-367	680	34	press	press	NOUN
ejpam-367	680	35	,	,	PUNCT
ejpam-367	680	36	(	(	PUNCT
ejpam-367	680	37	1937	1937	NUM
ejpam-367	680	38	)	)	PUNCT
ejpam-367	680	39	,	,	PUNCT
ejpam-367	680	40	407–448	407–448	NUM
ejpam-367	680	41	.	.	PUNCT
ejpam-367	681	1	[	[	X
ejpam-367	681	2	18	18	NUM
ejpam-367	681	3	]	]	PUNCT
ejpam-367	681	4	z.	z.	PROPN
ejpam-367	681	5	xu	xu	PROPN
ejpam-367	681	6	,	,	PUNCT
ejpam-367	681	7	mixed	mixed	ADJ
ejpam-367	681	8	type	type	NOUN
ejpam-367	681	9	duality	duality	NOUN
ejpam-367	681	10	in	in	ADP
ejpam-367	681	11	multiobjective	multiobjective	ADJ
ejpam-367	681	12	programming	programming	NOUN
ejpam-367	681	13	problems	problem	NOUN
ejpam-367	681	14	,	,	PUNCT
ejpam-367	681	15	journal	journal	NOUN
ejpam-367	681	16	of	of	ADP
ejpam-367	681	17	mathematical	mathematical	ADJ
ejpam-367	681	18	analysis	analysis	NOUN
ejpam-367	681	19	and	and	CCONJ
ejpam-367	681	20	applications	application	NOUN
ejpam-367	681	21	198(1996	198(1996	NOUN
ejpam-367	681	22	)	)	PUNCT
ejpam-367	681	23	,	,	PUNCT
ejpam-367	681	24	621–663	621–663	NUM