id	sid	tid	token	lemma	pos
ejpam-180	1	1	6_180_husain.dvi	6_180_husain.dvi	NUM
ejpam-180	1	2	european	european	ADJ
ejpam-180	1	3	journal	journal	NOUN
ejpam-180	1	4	of	of	ADP
ejpam-180	1	5	pure	pure	ADJ
ejpam-180	1	6	and	and	CCONJ
ejpam-180	1	7	applied	apply	VERB
ejpam-180	1	8	mathematics	mathematic	NOUN
ejpam-180	1	9	vol	vol	NOUN
ejpam-180	1	10	.	.	PROPN
ejpam-180	2	1	2	2	NUM
ejpam-180	2	2	,	,	PUNCT
ejpam-180	2	3	no	no	INTJ
ejpam-180	2	4	.	.	NOUN
ejpam-180	2	5	3	3	NUM
ejpam-180	2	6	,	,	PUNCT
ejpam-180	2	7	2009	2009	NUM
ejpam-180	2	8	,	,	PUNCT
ejpam-180	2	9	(	(	PUNCT
ejpam-180	2	10	372	372	NUM
ejpam-180	2	11	-	-	SYM
ejpam-180	2	12	400	400	NUM
ejpam-180	2	13	)	)	PUNCT
ejpam-180	2	14	issn	issn	PROPN
ejpam-180	2	15	1307	1307	NUM
ejpam-180	2	16	-	-	SYM
ejpam-180	2	17	5543	5543	NUM
ejpam-180	2	18	–	–	PUNCT
ejpam-180	2	19	www.ejpam.com	www.ejpam.com	X
ejpam-180	2	20	optimality	optimality	NOUN
ejpam-180	2	21	and	and	CCONJ
ejpam-180	2	22	duality	duality	NOUN
ejpam-180	2	23	for	for	ADP
ejpam-180	2	24	nondifferentiable	nondifferentiable	ADJ
ejpam-180	2	25	multiobjective	multiobjective	ADJ
ejpam-180	2	26	variational	variational	ADJ
ejpam-180	2	27	problems	problem	NOUN
ejpam-180	2	28	with	with	ADP
ejpam-180	2	29	higher	high	ADJ
ejpam-180	2	30	order	order	NOUN
ejpam-180	2	31	derivatives	derivative	NOUN
ejpam-180	2	32	i.	i.	PROPN
ejpam-180	2	33	husain1∗	husain1∗	PROPN
ejpam-180	2	34	,	,	PUNCT
ejpam-180	2	35	a.	a.	NOUN
ejpam-180	2	36	ahmed2	ahmed2	NOUN
ejpam-180	2	37	,	,	PUNCT
ejpam-180	2	38	and	and	CCONJ
ejpam-180	2	39	ruman	ruman	PROPN
ejpam-180	2	40	,	,	PUNCT
ejpam-180	2	41	g.	g.	PROPN
ejpam-180	2	42	mattoo2	mattoo2	PROPN
ejpam-180	3	1	1	1	NUM
ejpam-180	3	2	department	department	NOUN
ejpam-180	3	3	of	of	ADP
ejpam-180	3	4	mathematics	mathematics	PROPN
ejpam-180	3	5	,	,	PUNCT
ejpam-180	3	6	jaypee	jaypee	PROPN
ejpam-180	3	7	institute	institute	PROPN
ejpam-180	3	8	of	of	ADP
ejpam-180	3	9	engineering	engineering	NOUN
ejpam-180	3	10	and	and	CCONJ
ejpam-180	3	11	technology	technology	NOUN
ejpam-180	3	12	,	,	PUNCT
ejpam-180	3	13	guna	guna	PROPN
ejpam-180	3	14	,	,	PUNCT
ejpam-180	3	15	mp	mp	PROPN
ejpam-180	3	16	,	,	PUNCT
ejpam-180	3	17	india	india	PROPN
ejpam-180	3	18	.	.	PUNCT
ejpam-180	4	1	(	(	PUNCT
ejpam-180	4	2	a	a	DET
ejpam-180	4	3	constituent	constituent	ADJ
ejpam-180	4	4	centre	centre	NOUN
ejpam-180	4	5	of	of	ADP
ejpam-180	4	6	jaypee	jaypee	PROPN
ejpam-180	4	7	university	university	PROPN
ejpam-180	4	8	of	of	ADP
ejpam-180	4	9	information	information	NOUN
ejpam-180	4	10	technology	technology	NOUN
ejpam-180	4	11	)	)	PUNCT
ejpam-180	4	12	,	,	PUNCT
ejpam-180	4	13	waknaghat	waknaghat	PROPN
ejpam-180	4	14	,	,	PUNCT
ejpam-180	4	15	solan	solan	PROPN
ejpam-180	4	16	,	,	PUNCT
ejpam-180	4	17	hp	hp	PROPN
ejpam-180	4	18	,	,	PUNCT
ejpam-180	4	19	india	india	PROPN
ejpam-180	4	20	2	2	NUM
ejpam-180	4	21	department	department	NOUN
ejpam-180	4	22	of	of	ADP
ejpam-180	4	23	statistics	statistic	NOUN
ejpam-180	4	24	,	,	PUNCT
ejpam-180	4	25	university	university	PROPN
ejpam-180	4	26	of	of	ADP
ejpam-180	4	27	kashmir	kashmir	PROPN
ejpam-180	4	28	,	,	PUNCT
ejpam-180	4	29	srinagar	srinagar	PROPN
ejpam-180	4	30	,	,	PUNCT
ejpam-180	4	31	kashmir	kashmir	PROPN
ejpam-180	4	32	,	,	PUNCT
ejpam-180	4	33	india	india	PROPN
ejpam-180	4	34	abstract	abstract	PROPN
ejpam-180	4	35	.	.	PUNCT
ejpam-180	5	1	wolfe	wolfe	PROPN
ejpam-180	5	2	and	and	CCONJ
ejpam-180	5	3	mond	mond	PROPN
ejpam-180	5	4	-	-	PUNCT
ejpam-180	5	5	weir	weir	PROPN
ejpam-180	5	6	type	type	PROPN
ejpam-180	5	7	vector	vector	NOUN
ejpam-180	5	8	dual	dual	ADJ
ejpam-180	5	9	variational	variational	ADJ
ejpam-180	5	10	problems	problem	NOUN
ejpam-180	5	11	are	be	AUX
ejpam-180	5	12	formulated	formulate	VERB
ejpam-180	5	13	for	for	ADP
ejpam-180	5	14	a	a	DET
ejpam-180	5	15	class	class	NOUN
ejpam-180	5	16	of	of	ADP
ejpam-180	5	17	nondifferentiable	nondifferentiable	ADJ
ejpam-180	5	18	multiobjective	multiobjective	ADJ
ejpam-180	5	19	variational	variational	ADJ
ejpam-180	5	20	problems	problem	NOUN
ejpam-180	5	21	involving	involve	VERB
ejpam-180	5	22	higher	high	ADJ
ejpam-180	5	23	order	order	NOUN
ejpam-180	5	24	derivatives	derivative	NOUN
ejpam-180	5	25	.	.	PUNCT
ejpam-180	6	1	by	by	ADP
ejpam-180	6	2	using	use	VERB
ejpam-180	6	3	concept	concept	NOUN
ejpam-180	6	4	of	of	ADP
ejpam-180	6	5	efficiency	efficiency	NOUN
ejpam-180	6	6	,	,	PUNCT
ejpam-180	6	7	weak	weak	ADJ
ejpam-180	6	8	,	,	PUNCT
ejpam-180	6	9	strong	strong	ADJ
ejpam-180	6	10	and	and	CCONJ
ejpam-180	6	11	converse	converse	NOUN
ejpam-180	6	12	duality	duality	NOUN
ejpam-180	6	13	theorems	theorem	NOUN
ejpam-180	6	14	are	be	AUX
ejpam-180	6	15	established	establish	VERB
ejpam-180	6	16	under	under	ADP
ejpam-180	6	17	invexity	invexity	NOUN
ejpam-180	6	18	and	and	CCONJ
ejpam-180	6	19	generalized	generalized	ADJ
ejpam-180	6	20	invexity	invexity	NOUN
ejpam-180	6	21	assumptions	assumption	NOUN
ejpam-180	6	22	.	.	PUNCT
ejpam-180	7	1	validation	validation	NOUN
ejpam-180	7	2	of	of	ADP
ejpam-180	7	3	some	some	PRON
ejpam-180	7	4	of	of	ADP
ejpam-180	7	5	our	our	PRON
ejpam-180	7	6	duality	duality	NOUN
ejpam-180	7	7	results	result	NOUN
ejpam-180	7	8	can	can	AUX
ejpam-180	7	9	also	also	ADV
ejpam-180	7	10	be	be	AUX
ejpam-180	7	11	served	serve	VERB
ejpam-180	7	12	as	as	ADP
ejpam-180	7	13	a	a	DET
ejpam-180	7	14	correction	correction	NOUN
ejpam-180	7	15	for	for	ADP
ejpam-180	7	16	the	the	DET
ejpam-180	7	17	results	result	NOUN
ejpam-180	7	18	existing	exist	VERB
ejpam-180	7	19	in	in	ADP
ejpam-180	7	20	the	the	DET
ejpam-180	7	21	literature	literature	NOUN
ejpam-180	7	22	.	.	PUNCT
ejpam-180	8	1	related	relate	VERB
ejpam-180	8	2	problems	problem	NOUN
ejpam-180	8	3	for	for	ADP
ejpam-180	8	4	which	which	PRON
ejpam-180	8	5	our	our	PRON
ejpam-180	8	6	duality	duality	NOUN
ejpam-180	8	7	results	result	NOUN
ejpam-180	8	8	can	can	AUX
ejpam-180	8	9	hold	hold	VERB
ejpam-180	8	10	,	,	PUNCT
ejpam-180	8	11	are	be	AUX
ejpam-180	8	12	also	also	ADV
ejpam-180	8	13	pointed	point	VERB
ejpam-180	8	14	out	out	ADP
ejpam-180	8	15	.	.	PUNCT
ejpam-180	9	1	2000	2000	NUM
ejpam-180	9	2	mathematics	mathematic	NOUN
ejpam-180	9	3	subject	subject	NOUN
ejpam-180	9	4	classifications	classification	NOUN
ejpam-180	9	5	:	:	PUNCT
ejpam-180	9	6	primary	primary	ADJ
ejpam-180	9	7	90c30	90c30	NUM
ejpam-180	9	8	,	,	PUNCT
ejpam-180	9	9	secondary	secondary	ADJ
ejpam-180	9	10	90c11	90c11	NUM
ejpam-180	9	11	,	,	PUNCT
ejpam-180	9	12	90c20	90c20	NUM
ejpam-180	9	13	,	,	PUNCT
ejpam-180	9	14	90c26	90c26	NUM
ejpam-180	9	15	.	.	PUNCT
ejpam-180	10	1	key	key	ADJ
ejpam-180	10	2	words	word	NOUN
ejpam-180	10	3	and	and	CCONJ
ejpam-180	10	4	phrases	phrase	NOUN
ejpam-180	10	5	:	:	PUNCT
ejpam-180	10	6	variational	variational	ADJ
ejpam-180	10	7	problem	problem	NOUN
ejpam-180	10	8	;	;	PUNCT
ejpam-180	10	9	wolfe	wolfe	PROPN
ejpam-180	10	10	type	type	PROPN
ejpam-180	10	11	vector	vector	NOUN
ejpam-180	10	12	dual	dual	ADJ
ejpam-180	10	13	;	;	PUNCT
ejpam-180	10	14	mond	mond	PROPN
ejpam-180	10	15	-	-	PUNCT
ejpam-180	10	16	weir	weir	PROPN
ejpam-180	10	17	type	type	PROPN
ejpam-180	10	18	vector	vector	NOUN
ejpam-180	10	19	dual	dual	ADJ
ejpam-180	10	20	;	;	PUNCT
ejpam-180	10	21	invexity	invexity	NOUN
ejpam-180	10	22	;	;	PUNCT
ejpam-180	10	23	genralized	genralize	VERB
ejpam-180	10	24	invexity	invexity	NOUN
ejpam-180	10	25	;	;	PUNCT
ejpam-180	10	26	related	related	ADJ
ejpam-180	10	27	problems	problem	NOUN
ejpam-180	10	28	.	.	PUNCT
ejpam-180	11	1	∗corresponding	∗corresponde	VERB
ejpam-180	11	2	author	author	NOUN
ejpam-180	11	3	.	.	PUNCT
ejpam-180	12	1	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-180	13	1	372	372	NUM
ejpam-180	13	2	c	c	NOUN
ejpam-180	13	3	©	©	PROPN
ejpam-180	13	4	2009	2009	NUM
ejpam-180	13	5	ejpam	ejpam	NOUN
ejpam-180	13	6	all	all	DET
ejpam-180	13	7	rights	right	NOUN
ejpam-180	13	8	reserved	reserve	VERB
ejpam-180	13	9	.	.	PUNCT
ejpam-180	14	1	i.	i.	PROPN
ejpam-180	14	2	husain	husain	PROPN
ejpam-180	14	3	,	,	PUNCT
ejpam-180	14	4	a.	a.	PROPN
ejpam-180	14	5	ahmed	ahmed	PROPN
ejpam-180	14	6	,	,	PUNCT
ejpam-180	14	7	and	and	CCONJ
ejpam-180	14	8	g.	g.	PROPN
ejpam-180	14	9	rumana	rumana	PROPN
ejpam-180	14	10	/	/	SYM
ejpam-180	14	11	eur	eur	PROPN
ejpam-180	14	12	.	.	PUNCT
ejpam-180	15	1	j.	j.	PROPN
ejpam-180	15	2	pure	pure	PROPN
ejpam-180	15	3	appl	appl	PROPN
ejpam-180	15	4	.	.	PROPN
ejpam-180	15	5	math	math	PROPN
ejpam-180	15	6	,	,	PUNCT
ejpam-180	15	7	2	2	NUM
ejpam-180	15	8	(	(	PUNCT
ejpam-180	15	9	2009	2009	NUM
ejpam-180	15	10	)	)	PUNCT
ejpam-180	15	11	,	,	PUNCT
ejpam-180	15	12	(	(	PUNCT
ejpam-180	15	13	372	372	NUM
ejpam-180	15	14	-	-	SYM
ejpam-180	15	15	400	400	NUM
ejpam-180	15	16	)	)	PUNCT
ejpam-180	15	17	373	373	NUM
ejpam-180	15	18	1	1	NUM
ejpam-180	15	19	.	.	PUNCT
ejpam-180	16	1	introduction	introduction	NOUN
ejpam-180	16	2	many	many	ADJ
ejpam-180	16	3	authors	author	NOUN
ejpam-180	16	4	have	have	AUX
ejpam-180	16	5	studied	study	VERB
ejpam-180	16	6	optimality	optimality	NOUN
ejpam-180	16	7	and	and	CCONJ
ejpam-180	16	8	duality	duality	NOUN
ejpam-180	16	9	for	for	ADP
ejpam-180	16	10	multiobjective	multiobjective	ADJ
ejpam-180	16	11	variational	variational	ADJ
ejpam-180	16	12	problems	problem	NOUN
ejpam-180	16	13	.	.	PUNCT
ejpam-180	17	1	bector	bector	NOUN
ejpam-180	17	2	and	and	CCONJ
ejpam-180	17	3	husain	husain	PROPN
ejpam-180	18	1	[	[	X
ejpam-180	18	2	1	1	X
ejpam-180	18	3	]	]	PUNCT
ejpam-180	18	4	were	be	AUX
ejpam-180	18	5	probably	probably	ADV
ejpam-180	18	6	the	the	DET
ejpam-180	18	7	first	first	ADJ
ejpam-180	18	8	to	to	PART
ejpam-180	18	9	introduce	introduce	VERB
ejpam-180	18	10	multiobjective	multiobjective	ADJ
ejpam-180	18	11	programming	programming	NOUN
ejpam-180	18	12	in	in	ADP
ejpam-180	18	13	calculus	calculus	NOUN
ejpam-180	18	14	of	of	ADP
ejpam-180	18	15	variation	variation	NOUN
ejpam-180	18	16	which	which	PRON
ejpam-180	18	17	is	be	AUX
ejpam-180	18	18	a	a	DET
ejpam-180	18	19	powerful	powerful	ADJ
ejpam-180	18	20	technique	technique	NOUN
ejpam-180	18	21	for	for	SCONJ
ejpam-180	18	22	the	the	DET
ejpam-180	18	23	solutions	solution	NOUN
ejpam-180	18	24	of	of	ADP
ejpam-180	18	25	various	various	ADJ
ejpam-180	18	26	problems	problem	NOUN
ejpam-180	18	27	appearing	appear	VERB
ejpam-180	18	28	in	in	ADP
ejpam-180	18	29	dynamics	dynamic	NOUN
ejpam-180	18	30	of	of	ADP
ejpam-180	18	31	rigid	rigid	ADJ
ejpam-180	18	32	bodies	body	NOUN
ejpam-180	18	33	,	,	PUNCT
ejpam-180	18	34	optimization	optimization	NOUN
ejpam-180	18	35	of	of	ADP
ejpam-180	18	36	orbits	orbit	NOUN
ejpam-180	18	37	,	,	PUNCT
ejpam-180	18	38	theory	theory	NOUN
ejpam-180	18	39	of	of	ADP
ejpam-180	18	40	variation	variation	NOUN
ejpam-180	18	41	and	and	CCONJ
ejpam-180	18	42	many	many	ADJ
ejpam-180	18	43	other	other	ADJ
ejpam-180	18	44	fields	field	NOUN
ejpam-180	18	45	.	.	PUNCT
ejpam-180	19	1	in	in	ADP
ejpam-180	19	2	[	[	X
ejpam-180	19	3	11	11	NUM
ejpam-180	19	4	]	]	PUNCT
ejpam-180	19	5	,	,	PUNCT
ejpam-180	19	6	mishra	mishra	PROPN
ejpam-180	19	7	and	and	CCONJ
ejpam-180	19	8	mukerjee	mukerjee	PROPN
ejpam-180	19	9	discussed	discuss	VERB
ejpam-180	19	10	duality	duality	NOUN
ejpam-180	19	11	for	for	ADP
ejpam-180	19	12	multiobjective	multiobjective	ADJ
ejpam-180	19	13	variational	variational	ADJ
ejpam-180	19	14	problems	problem	NOUN
ejpam-180	19	15	involving	involve	VERB
ejpam-180	19	16	generalized	generalized	ADJ
ejpam-180	19	17	(	(	PUNCT
ejpam-180	19	18	f	f	X
ejpam-180	19	19	,	,	PUNCT
ejpam-180	19	20	ρ)-convex	ρ)-convex	NOUN
ejpam-180	19	21	functions	function	NOUN
ejpam-180	19	22	.	.	PUNCT
ejpam-180	20	1	in	in	ADP
ejpam-180	20	2	[	[	X
ejpam-180	20	3	10	10	NUM
ejpam-180	20	4	]	]	PUNCT
ejpam-180	20	5	,	,	PUNCT
ejpam-180	20	6	liu	liu	PROPN
ejpam-180	20	7	proved	prove	VERB
ejpam-180	20	8	only	only	ADV
ejpam-180	20	9	some	some	DET
ejpam-180	20	10	weak	weak	ADJ
ejpam-180	20	11	duality	duality	NOUN
ejpam-180	20	12	theorem	theorem	VERB
ejpam-180	20	13	for	for	ADP
ejpam-180	20	14	nondifferentiable	nondifferentiable	ADJ
ejpam-180	20	15	multiobjective	multiobjective	ADJ
ejpam-180	20	16	variational	variational	ADJ
ejpam-180	20	17	problems	problem	NOUN
ejpam-180	20	18	involving	involve	VERB
ejpam-180	20	19	generalized	generalized	ADJ
ejpam-180	20	20	(	(	PUNCT
ejpam-180	20	21	f	f	X
ejpam-180	20	22	,	,	PUNCT
ejpam-180	20	23	ρ	ρ	NOUN
ejpam-180	20	24	)	)	PUNCT
ejpam-180	20	25	convex	convex	NOUN
ejpam-180	20	26	functions	function	NOUN
ejpam-180	20	27	.	.	PUNCT
ejpam-180	21	1	recently	recently	ADV
ejpam-180	21	2	husain	husain	PROPN
ejpam-180	21	3	et	et	PROPN
ejpam-180	21	4	al	al	PROPN
ejpam-180	22	1	[	[	X
ejpam-180	22	2	7	7	NUM
ejpam-180	22	3	]	]	PUNCT
ejpam-180	22	4	have	have	AUX
ejpam-180	22	5	studied	study	VERB
ejpam-180	22	6	optimality	optimality	NOUN
ejpam-180	22	7	and	and	CCONJ
ejpam-180	22	8	duality	duality	NOUN
ejpam-180	22	9	for	for	ADP
ejpam-180	22	10	multiobjective	multiobjective	ADJ
ejpam-180	22	11	variational	variational	ADJ
ejpam-180	22	12	problems	problem	NOUN
ejpam-180	22	13	involving	involve	VERB
ejpam-180	22	14	higher	high	ADJ
ejpam-180	22	15	order	order	NOUN
ejpam-180	22	16	derivatives	derivative	NOUN
ejpam-180	22	17	.	.	PUNCT
ejpam-180	23	1	chandra	chandra	PROPN
ejpam-180	23	2	,	,	PUNCT
ejpam-180	23	3	craven	craven	NOUN
ejpam-180	23	4	and	and	CCONJ
ejpam-180	23	5	husain	husain	NOUN
ejpam-180	24	1	[	[	X
ejpam-180	24	2	3	3	NUM
ejpam-180	24	3	]	]	PUNCT
ejpam-180	24	4	obtained	obtain	VERB
ejpam-180	24	5	necessary	necessary	ADJ
ejpam-180	24	6	optimality	optimality	NOUN
ejpam-180	24	7	conditions	condition	NOUN
ejpam-180	24	8	for	for	ADP
ejpam-180	24	9	a	a	DET
ejpam-180	24	10	constrained	constrain	VERB
ejpam-180	24	11	continuous	continuous	ADJ
ejpam-180	24	12	programming	programming	NOUN
ejpam-180	24	13	having	have	VERB
ejpam-180	24	14	term	term	NOUN
ejpam-180	24	15	with	with	ADP
ejpam-180	24	16	a	a	DET
ejpam-180	24	17	square	square	ADJ
ejpam-180	24	18	root	root	NOUN
ejpam-180	24	19	of	of	ADP
ejpam-180	24	20	a	a	DET
ejpam-180	24	21	quadratic	quadratic	ADJ
ejpam-180	24	22	form	form	NOUN
ejpam-180	24	23	in	in	ADP
ejpam-180	24	24	the	the	DET
ejpam-180	24	25	objective	objective	ADJ
ejpam-180	24	26	function	function	NOUN
ejpam-180	24	27	,	,	PUNCT
ejpam-180	24	28	and	and	CCONJ
ejpam-180	24	29	using	use	VERB
ejpam-180	24	30	these	these	DET
ejpam-180	24	31	optimality	optimality	NOUN
ejpam-180	24	32	conditions	condition	NOUN
ejpam-180	24	33	formulated	formulate	VERB
ejpam-180	24	34	wolfe	wolfe	PROPN
ejpam-180	24	35	type	type	NOUN
ejpam-180	24	36	dual	dual	ADV
ejpam-180	24	37	and	and	CCONJ
ejpam-180	24	38	established	establish	VERB
ejpam-180	24	39	weak	weak	ADJ
ejpam-180	24	40	,	,	PUNCT
ejpam-180	24	41	strong	strong	ADJ
ejpam-180	24	42	and	and	CCONJ
ejpam-180	24	43	huard	huard	VERB
ejpam-180	24	44	[	[	X
ejpam-180	24	45	12	12	NUM
ejpam-180	24	46	]	]	PUNCT
ejpam-180	24	47	type	type	NOUN
ejpam-180	24	48	converse	converse	NOUN
ejpam-180	24	49	duality	duality	NOUN
ejpam-180	24	50	theorems	theorem	VERB
ejpam-180	24	51	under	under	ADP
ejpam-180	24	52	convexity	convexity	NOUN
ejpam-180	24	53	of	of	ADP
ejpam-180	24	54	functions	function	NOUN
ejpam-180	24	55	.	.	PUNCT
ejpam-180	25	1	subsequently	subsequently	ADV
ejpam-180	25	2	,	,	PUNCT
ejpam-180	25	3	for	for	ADP
ejpam-180	25	4	the	the	DET
ejpam-180	25	5	problems	problem	NOUN
ejpam-180	25	6	of	of	ADP
ejpam-180	25	7	[	[	X
ejpam-180	25	8	3	3	NUM
ejpam-180	25	9	]	]	PUNCT
ejpam-180	25	10	,	,	PUNCT
ejpam-180	25	11	bector	bector	NOUN
ejpam-180	25	12	,	,	PUNCT
ejpam-180	25	13	chandra	chandra	PROPN
ejpam-180	25	14	and	and	CCONJ
ejpam-180	25	15	husain	husain	PROPN
ejpam-180	26	1	[	[	X
ejpam-180	26	2	2	2	NUM
ejpam-180	26	3	]	]	PUNCT
ejpam-180	26	4	constructed	construct	VERB
ejpam-180	26	5	a	a	DET
ejpam-180	26	6	mond	mond	PROPN
ejpam-180	26	7	-	-	PUNCT
ejpam-180	26	8	weir	weir	PROPN
ejpam-180	26	9	type	type	NOUN
ejpam-180	26	10	dual	dual	ADJ
ejpam-180	26	11	which	which	PRON
ejpam-180	26	12	allows	allow	VERB
ejpam-180	26	13	weakening	weaken	VERB
ejpam-180	26	14	of	of	ADP
ejpam-180	26	15	convexity	convexity	NOUN
ejpam-180	26	16	hypotheses	hypothesis	NOUN
ejpam-180	26	17	of	of	ADP
ejpam-180	26	18	[	[	X
ejpam-180	26	19	3	3	NUM
ejpam-180	26	20	]	]	PUNCT
ejpam-180	26	21	and	and	CCONJ
ejpam-180	26	22	derived	derive	VERB
ejpam-180	26	23	various	various	ADJ
ejpam-180	26	24	duality	duality	NOUN
ejpam-180	26	25	results	result	NOUN
ejpam-180	26	26	under	under	ADP
ejpam-180	26	27	generalized	generalized	ADJ
ejpam-180	26	28	convexity	convexity	NOUN
ejpam-180	26	29	of	of	ADP
ejpam-180	26	30	functionals	functional	NOUN
ejpam-180	26	31	.	.	PUNCT
ejpam-180	27	1	the	the	DET
ejpam-180	27	2	popularity	popularity	NOUN
ejpam-180	27	3	of	of	ADP
ejpam-180	27	4	this	this	DET
ejpam-180	27	5	type	type	NOUN
ejpam-180	27	6	of	of	ADP
ejpam-180	27	7	problems	problem	NOUN
ejpam-180	27	8	seem	seem	VERB
ejpam-180	27	9	to	to	PART
ejpam-180	27	10	originate	originate	VERB
ejpam-180	27	11	from	from	ADP
ejpam-180	27	12	the	the	DET
ejpam-180	27	13	fact	fact	NOUN
ejpam-180	27	14	that	that	SCONJ
ejpam-180	27	15	,	,	PUNCT
ejpam-180	27	16	even	even	ADV
ejpam-180	27	17	though	though	SCONJ
ejpam-180	27	18	the	the	DET
ejpam-180	27	19	objective	objective	ADJ
ejpam-180	27	20	function	function	NOUN
ejpam-180	27	21	and/	and/	PROPN
ejpam-180	27	22	or	or	CCONJ
ejpam-180	27	23	constraint	constraint	NOUN
ejpam-180	27	24	functions	function	NOUN
ejpam-180	27	25	are	be	AUX
ejpam-180	27	26	non	non	ADJ
ejpam-180	27	27	-	-	ADJ
ejpam-180	27	28	smooth	smooth	ADJ
ejpam-180	27	29	,	,	PUNCT
ejpam-180	27	30	a	a	DET
ejpam-180	27	31	simple	simple	ADJ
ejpam-180	27	32	representation	representation	NOUN
ejpam-180	27	33	of	of	ADP
ejpam-180	27	34	the	the	DET
ejpam-180	27	35	dual	dual	ADJ
ejpam-180	27	36	problem	problem	NOUN
ejpam-180	27	37	may	may	AUX
ejpam-180	27	38	be	be	AUX
ejpam-180	27	39	found	find	VERB
ejpam-180	27	40	.	.	PUNCT
ejpam-180	28	1	the	the	DET
ejpam-180	28	2	theory	theory	NOUN
ejpam-180	28	3	of	of	ADP
ejpam-180	28	4	non	non	ADJ
ejpam-180	28	5	-	-	ADJ
ejpam-180	28	6	smooth	smooth	ADJ
ejpam-180	28	7	mathematical	mathematical	ADJ
ejpam-180	28	8	programming	programming	NOUN
ejpam-180	28	9	deals	deal	NOUN
ejpam-180	28	10	with	with	ADP
ejpam-180	28	11	much	much	ADV
ejpam-180	28	12	more	more	ADJ
ejpam-180	28	13	general	general	ADJ
ejpam-180	28	14	types	type	NOUN
ejpam-180	28	15	of	of	ADP
ejpam-180	28	16	functions	function	NOUN
ejpam-180	28	17	by	by	ADP
ejpam-180	28	18	means	mean	NOUN
ejpam-180	28	19	of	of	ADP
ejpam-180	28	20	generalized	generalized	ADJ
ejpam-180	28	21	subdifferentials	subdifferential	NOUN
ejpam-180	28	22	[	[	X
ejpam-180	28	23	4	4	NUM
ejpam-180	28	24	]	]	PUNCT
ejpam-180	28	25	and	and	CCONJ
ejpam-180	28	26	quasi	quasi	ADJ
ejpam-180	28	27	differentials	differential	NOUN
ejpam-180	28	28	[	[	X
ejpam-180	28	29	6	6	NUM
ejpam-180	28	30	]	]	PUNCT
ejpam-180	28	31	.	.	PUNCT
ejpam-180	29	1	however	however	ADV
ejpam-180	29	2	,	,	PUNCT
ejpam-180	29	3	the	the	DET
ejpam-180	29	4	square	square	ADJ
ejpam-180	29	5	root	root	NOUN
ejpam-180	29	6	of	of	ADP
ejpam-180	29	7	a	a	DET
ejpam-180	29	8	positive	positive	ADJ
ejpam-180	29	9	semidefinite	semidefinite	NOUN
ejpam-180	29	10	quadratic	quadratic	ADJ
ejpam-180	29	11	form	form	NOUN
ejpam-180	29	12	is	be	AUX
ejpam-180	29	13	one	one	NUM
ejpam-180	29	14	of	of	ADP
ejpam-180	29	15	the	the	DET
ejpam-180	29	16	few	few	ADJ
ejpam-180	29	17	cases	case	NOUN
ejpam-180	29	18	of	of	ADP
ejpam-180	29	19	a	a	DET
ejpam-180	29	20	nondifferentiable	nondifferentiable	ADJ
ejpam-180	29	21	function	function	NOUN
ejpam-180	29	22	for	for	ADP
ejpam-180	29	23	which	which	PRON
ejpam-180	29	24	one	one	PRON
ejpam-180	29	25	can	can	AUX
ejpam-180	29	26	write	write	VERB
ejpam-180	29	27	down	down	ADP
ejpam-180	29	28	the	the	DET
ejpam-180	29	29	sub	sub	NOUN
ejpam-180	29	30	or	or	CCONJ
ejpam-180	29	31	quasi	quasi	ADJ
ejpam-180	29	32	differentials	differential	NOUN
ejpam-180	29	33	explicitly	explicitly	ADV
ejpam-180	29	34	.	.	PUNCT
ejpam-180	30	1	i.	i.	PROPN
ejpam-180	30	2	husain	husain	PROPN
ejpam-180	30	3	,	,	PUNCT
ejpam-180	30	4	a.	a.	PROPN
ejpam-180	30	5	ahmed	ahmed	PROPN
ejpam-180	30	6	,	,	PUNCT
ejpam-180	30	7	and	and	CCONJ
ejpam-180	30	8	g.	g.	PROPN
ejpam-180	30	9	rumana	rumana	PROPN
ejpam-180	30	10	/	/	SYM
ejpam-180	30	11	eur	eur	PROPN
ejpam-180	30	12	.	.	PUNCT
ejpam-180	31	1	j.	j.	PROPN
ejpam-180	31	2	pure	pure	PROPN
ejpam-180	31	3	appl	appl	PROPN
ejpam-180	31	4	.	.	PROPN
ejpam-180	31	5	math	math	PROPN
ejpam-180	31	6	,	,	PUNCT
ejpam-180	31	7	2	2	NUM
ejpam-180	31	8	(	(	PUNCT
ejpam-180	31	9	2009	2009	NUM
ejpam-180	31	10	)	)	PUNCT
ejpam-180	31	11	,	,	PUNCT
ejpam-180	31	12	(	(	PUNCT
ejpam-180	31	13	372	372	NUM
ejpam-180	31	14	-	-	SYM
ejpam-180	31	15	400	400	NUM
ejpam-180	31	16	)	)	PUNCT
ejpam-180	31	17	374	374	NUM
ejpam-180	31	18	in	in	ADP
ejpam-180	31	19	this	this	DET
ejpam-180	31	20	paper	paper	NOUN
ejpam-180	32	1	,	,	PUNCT
ejpam-180	32	2	we	we	PRON
ejpam-180	32	3	study	study	VERB
ejpam-180	32	4	optimality	optimality	NOUN
ejpam-180	32	5	and	and	CCONJ
ejpam-180	32	6	duality	duality	NOUN
ejpam-180	32	7	for	for	ADP
ejpam-180	32	8	a	a	DET
ejpam-180	32	9	class	class	NOUN
ejpam-180	32	10	of	of	ADP
ejpam-180	32	11	nondifferentiable	nondifferentiable	ADJ
ejpam-180	32	12	variatonal	variatonal	ADJ
ejpam-180	32	13	problem	problem	NOUN
ejpam-180	32	14	containing	contain	VERB
ejpam-180	32	15	higher	high	ADJ
ejpam-180	32	16	order	order	NOUN
ejpam-180	32	17	derivatives	derivative	NOUN
ejpam-180	32	18	.	.	PUNCT
ejpam-180	33	1	we	we	PRON
ejpam-180	33	2	formulate	formulate	VERB
ejpam-180	33	3	wolfe	wolfe	PROPN
ejpam-180	33	4	and	and	CCONJ
ejpam-180	33	5	mondweir	mondweir	ADJ
ejpam-180	33	6	type	type	NOUN
ejpam-180	33	7	dual	dual	ADJ
ejpam-180	33	8	problems	problem	NOUN
ejpam-180	33	9	for	for	ADP
ejpam-180	33	10	this	this	DET
ejpam-180	33	11	class	class	NOUN
ejpam-180	33	12	of	of	ADP
ejpam-180	33	13	variational	variational	ADJ
ejpam-180	33	14	problems	problem	NOUN
ejpam-180	33	15	and	and	CCONJ
ejpam-180	33	16	prove	prove	VERB
ejpam-180	33	17	various	various	ADJ
ejpam-180	33	18	duality	duality	NOUN
ejpam-180	33	19	results	result	NOUN
ejpam-180	33	20	under	under	ADP
ejpam-180	33	21	invexity	invexity	NOUN
ejpam-180	33	22	and	and	CCONJ
ejpam-180	33	23	generalized	generalized	ADJ
ejpam-180	33	24	invexity	invexity	NOUN
ejpam-180	33	25	.	.	PUNCT
ejpam-180	34	1	the	the	DET
ejpam-180	34	2	result	result	NOUN
ejpam-180	34	3	of	of	ADP
ejpam-180	34	4	this	this	DET
ejpam-180	34	5	research	research	NOUN
ejpam-180	34	6	also	also	ADV
ejpam-180	34	7	serves	serve	VERB
ejpam-180	34	8	as	as	ADP
ejpam-180	34	9	correction	correction	NOUN
ejpam-180	34	10	to	to	ADP
ejpam-180	34	11	some	some	PRON
ejpam-180	34	12	of	of	ADP
ejpam-180	34	13	the	the	DET
ejpam-180	34	14	results	result	NOUN
ejpam-180	34	15	obtained	obtain	VERB
ejpam-180	34	16	by	by	ADP
ejpam-180	34	17	kim	kim	PROPN
ejpam-180	34	18	and	and	CCONJ
ejpam-180	34	19	kim	kim	PROPN
ejpam-180	35	1	[	[	X
ejpam-180	35	2	9	9	NUM
ejpam-180	35	3	]	]	SYM
ejpam-180	35	4	.	.	PUNCT
ejpam-180	36	1	2	2	X
ejpam-180	36	2	.	.	X
ejpam-180	36	3	pre	pre	NOUN
ejpam-180	36	4	-	-	NOUN
ejpam-180	36	5	requisites	requisite	NOUN
ejpam-180	36	6	consider	consider	VERB
ejpam-180	36	7	the	the	DET
ejpam-180	36	8	real	real	ADJ
ejpam-180	36	9	interval	interval	NOUN
ejpam-180	37	1	i	i	PRON
ejpam-180	37	2	=	=	PUNCT
ejpam-180	38	1	[	[	X
ejpam-180	38	2	a	a	X
ejpam-180	38	3	,	,	PUNCT
ejpam-180	38	4	b	b	NOUN
ejpam-180	38	5	]	]	PUNCT
ejpam-180	38	6	and	and	CCONJ
ejpam-180	38	7	the	the	DET
ejpam-180	38	8	continuously	continuously	ADV
ejpam-180	38	9	differentiable	differentiable	ADJ
ejpam-180	38	10	function	function	NOUN
ejpam-180	38	11	φ	φ	NOUN
ejpam-180	38	12	:	:	PUNCT
ejpam-180	39	1	i	i	PRON
ejpam-180	39	2	×	×	VERB
ejpam-180	39	3	rn	rn	PROPN
ejpam-180	39	4	×	×	PROPN
ejpam-180	39	5	rn	rn	PROPN
ejpam-180	39	6	×	×	PROPN
ejpam-180	39	7	rn	rn	PROPN
ejpam-180	39	8	→	→	SYM
ejpam-180	39	9	r.	r.	PROPN
ejpam-180	39	10	in	in	ADP
ejpam-180	39	11	order	order	NOUN
ejpam-180	39	12	to	to	PART
ejpam-180	39	13	consider	consider	VERB
ejpam-180	39	14	φ(t	φ(t	PROPN
ejpam-180	39	15	,	,	PUNCT
ejpam-180	39	16	x	x	X
ejpam-180	39	17	,	,	PUNCT
ejpam-180	39	18	ẋ	ẋ	PROPN
ejpam-180	39	19	,	,	PUNCT
ejpam-180	39	20	ẍ	ẍ	PROPN
ejpam-180	39	21	)	)	PUNCT
ejpam-180	39	22	,	,	PUNCT
ejpam-180	39	23	where	where	SCONJ
ejpam-180	39	24	x	x	X
ejpam-180	39	25	:	:	PUNCT
ejpam-180	39	26	i	i	PRON
ejpam-180	39	27	→	→	SYM
ejpam-180	39	28	rn	rn	PROPN
ejpam-180	39	29	is	be	AUX
ejpam-180	39	30	twice	twice	ADV
ejpam-180	39	31	differentiable	differentiable	ADJ
ejpam-180	39	32	with	with	ADP
ejpam-180	39	33	its	its	PRON
ejpam-180	39	34	first	first	ADJ
ejpam-180	39	35	and	and	CCONJ
ejpam-180	39	36	second	second	ADJ
ejpam-180	39	37	order	order	NOUN
ejpam-180	39	38	derivatives	derivative	NOUN
ejpam-180	39	39	ẋ	ẋ	PROPN
ejpam-180	39	40	and	and	CCONJ
ejpam-180	39	41	ẍ	ẍ	PROPN
ejpam-180	39	42	respectively	respectively	ADV
ejpam-180	39	43	,	,	PUNCT
ejpam-180	39	44	we	we	PRON
ejpam-180	39	45	denote	denote	VERB
ejpam-180	39	46	the	the	DET
ejpam-180	39	47	partial	partial	ADJ
ejpam-180	39	48	derivative	derivative	NOUN
ejpam-180	39	49	of	of	ADP
ejpam-180	39	50	φ	φ	PROPN
ejpam-180	39	51	with	with	ADP
ejpam-180	39	52	respect	respect	NOUN
ejpam-180	39	53	to	to	ADP
ejpam-180	39	54	t	t	NOUN
ejpam-180	39	55	by	by	ADP
ejpam-180	39	56	φt	φt	PROPN
ejpam-180	39	57	.	.	PUNCT
ejpam-180	40	1	φx	φx	PROPN
ejpam-180	40	2	=	=	SYM
ejpam-180	40	3	�	�	PROPN
ejpam-180	40	4	∂	∂	PROPN
ejpam-180	40	5	φ	φ	PROPN
ejpam-180	40	6	∂	∂	NOUN
ejpam-180	40	7	x1	x1	PROPN
ejpam-180	40	8	,	,	PUNCT
ejpam-180	40	9	.	.	PUNCT
ejpam-180	40	10	.	.	PUNCT
ejpam-180	41	1	.	.	PUNCT
ejpam-180	42	1	,	,	PUNCT
ejpam-180	42	2	∂	∂	NUM
ejpam-180	42	3	φ	φ	PROPN
ejpam-180	42	4	∂	∂	NUM
ejpam-180	42	5	x	x	SYM
ejpam-180	42	6	n	n	PROPN
ejpam-180	42	7	�	�	PROPN
ejpam-180	42	8	t	t	PROPN
ejpam-180	42	9	,	,	PUNCT
ejpam-180	42	10	φ	φ	PROPN
ejpam-180	42	11	ẋ	ẋ	PUNCT
ejpam-180	43	1	=	=	SYM
ejpam-180	43	2	�	�	PROPN
ejpam-180	43	3	∂	∂	PROPN
ejpam-180	43	4	φ	φ	PROPN
ejpam-180	43	5	∂	∂	NOUN
ejpam-180	44	1	ẋ1	ẋ1	PROPN
ejpam-180	44	2	,	,	PUNCT
ejpam-180	44	3	.	.	PUNCT
ejpam-180	44	4	.	.	PUNCT
ejpam-180	45	1	.	.	PUNCT
ejpam-180	46	1	,	,	PUNCT
ejpam-180	46	2	∂	∂	NUM
ejpam-180	46	3	φ	φ	PROPN
ejpam-180	46	4	∂	∂	PROPN
ejpam-180	46	5	ẋ	ẋ	PROPN
ejpam-180	46	6	n	n	PROPN
ejpam-180	46	7	�	�	PROPN
ejpam-180	46	8	t	t	PROPN
ejpam-180	46	9	,	,	PUNCT
ejpam-180	46	10	φ	φ	PROPN
ejpam-180	46	11	ẍ	ẍ	PUNCT
ejpam-180	47	1	=	=	SYM
ejpam-180	47	2	�	�	PROPN
ejpam-180	47	3	∂	∂	PROPN
ejpam-180	47	4	φ	φ	PROPN
ejpam-180	47	5	∂	∂	PROPN
ejpam-180	47	6	ẍ1	ẍ1	PROPN
ejpam-180	47	7	,	,	PUNCT
ejpam-180	47	8	.	.	PUNCT
ejpam-180	47	9	.	.	PUNCT
ejpam-180	48	1	.	.	PUNCT
ejpam-180	49	1	,	,	PUNCT
ejpam-180	49	2	∂	∂	NUM
ejpam-180	49	3	φ	φ	PROPN
ejpam-180	49	4	∂	∂	PROPN
ejpam-180	49	5	ẍ	ẍ	PROPN
ejpam-180	49	6	n	n	PROPN
ejpam-180	49	7	�	�	PROPN
ejpam-180	49	8	t	t	PROPN
ejpam-180	49	9	.	.	PUNCT
ejpam-180	50	1	the	the	DET
ejpam-180	50	2	partial	partial	ADJ
ejpam-180	50	3	derivative	derivative	NOUN
ejpam-180	50	4	of	of	ADP
ejpam-180	50	5	other	other	ADJ
ejpam-180	50	6	function	function	NOUN
ejpam-180	50	7	will	will	AUX
ejpam-180	50	8	be	be	AUX
ejpam-180	50	9	written	write	VERB
ejpam-180	50	10	similarly	similarly	ADV
ejpam-180	50	11	.	.	PUNCT
ejpam-180	51	1	let	let	VERB
ejpam-180	51	2	k	k	PRON
ejpam-180	51	3	designate	designate	VERB
ejpam-180	51	4	the	the	DET
ejpam-180	51	5	space	space	NOUN
ejpam-180	51	6	of	of	ADP
ejpam-180	51	7	piecewise	piecewise	NOUN
ejpam-180	51	8	smooth	smooth	ADJ
ejpam-180	51	9	functions	function	NOUN
ejpam-180	51	10	x	x	PUNCT
ejpam-180	51	11	:	:	PUNCT
ejpam-180	51	12	i	i	PRON
ejpam-180	51	13	→	→	SYM
ejpam-180	51	14	rn	rn	X
ejpam-180	51	15	possessing	possess	VERB
ejpam-180	51	16	derivatives	derivative	NOUN
ejpam-180	51	17	ẋ	ẋ	PROPN
ejpam-180	51	18	and	and	CCONJ
ejpam-180	51	19	ẍ	ẍ	X
ejpam-180	51	20	with	with	ADP
ejpam-180	51	21	the	the	DET
ejpam-180	51	22	norm	norm	NOUN
ejpam-180	51	23	‖x‖	‖x‖	PROPN
ejpam-180	51	24	=	=	SYM
ejpam-180	51	25	‖x‖∞+	‖x‖∞+	X
ejpam-180	51	26	‖dx‖∞+	‖dx‖∞+	PUNCT
ejpam-180	51	27	‖d	‖d	ADJ
ejpam-180	51	28	2	2	NUM
ejpam-180	51	29	x‖∞	x‖∞	NOUN
ejpam-180	51	30	,	,	PUNCT
ejpam-180	51	31	where	where	SCONJ
ejpam-180	51	32	the	the	DET
ejpam-180	51	33	differentiation	differentiation	NOUN
ejpam-180	51	34	operator	operator	NOUN
ejpam-180	51	35	d	d	NOUN
ejpam-180	51	36	is	be	AUX
ejpam-180	51	37	given	give	VERB
ejpam-180	51	38	by	by	ADP
ejpam-180	51	39	u=	u=	ADJ
ejpam-180	51	40	dx⇔	dx⇔	NOUN
ejpam-180	51	41	x(t	x(t	PROPN
ejpam-180	51	42	)	)	PUNCT
ejpam-180	52	1	=	=	SYM
ejpam-180	53	1	α+	α+	PUNCT
ejpam-180	53	2	∫	∫	PROPN
ejpam-180	53	3	t	t	PROPN
ejpam-180	53	4	a	a	DET
ejpam-180	53	5	u(s)ds	u(s)ds	PROPN
ejpam-180	53	6	,	,	PUNCT
ejpam-180	53	7	where	where	SCONJ
ejpam-180	53	8	α	α	NOUN
ejpam-180	53	9	is	be	AUX
ejpam-180	53	10	given	give	VERB
ejpam-180	53	11	boundary	boundary	ADJ
ejpam-180	53	12	value	value	NOUN
ejpam-180	53	13	;	;	PUNCT
ejpam-180	53	14	thus	thus	ADV
ejpam-180	53	15	d	d	X
ejpam-180	53	16	≡	≡	PROPN
ejpam-180	53	17	d	d	PROPN
ejpam-180	53	18	d	d	PROPN
ejpam-180	53	19	t	t	PROPN
ejpam-180	53	20	except	except	SCONJ
ejpam-180	53	21	at	at	ADP
ejpam-180	53	22	discontinuities	discontinuity	NOUN
ejpam-180	53	23	.	.	PUNCT
ejpam-180	54	1	in	in	ADP
ejpam-180	54	2	the	the	DET
ejpam-180	54	3	results	result	NOUN
ejpam-180	54	4	to	to	PART
ejpam-180	54	5	follow	follow	VERB
ejpam-180	54	6	,	,	PUNCT
ejpam-180	54	7	we	we	PRON
ejpam-180	54	8	use	use	VERB
ejpam-180	54	9	c(i	c(i	NOUN
ejpam-180	54	10	,	,	PUNCT
ejpam-180	54	11	rm	rm	NOUN
ejpam-180	54	12	)	)	PUNCT
ejpam-180	54	13	to	to	PART
ejpam-180	54	14	denote	denote	VERB
ejpam-180	54	15	the	the	DET
ejpam-180	54	16	space	space	NOUN
ejpam-180	54	17	of	of	ADP
ejpam-180	54	18	continuous	continuous	ADJ
ejpam-180	54	19	functions	function	NOUN
ejpam-180	54	20	φ	φ	NOUN
ejpam-180	54	21	:	:	PUNCT
ejpam-180	55	1	i	i	PRON
ejpam-180	55	2	→	→	SYM
ejpam-180	55	3	rm	rm	NOUN
ejpam-180	55	4	with	with	ADP
ejpam-180	55	5	the	the	DET
ejpam-180	55	6	uniform	uniform	PROPN
ejpam-180	55	7	norm	norm	NOUN
ejpam-180	55	8	;	;	PUNCT
ejpam-180	55	9	superscript	superscript	PROPN
ejpam-180	55	10	t	t	PROPN
ejpam-180	55	11	denotes	denotes	PROPN
ejpam-180	55	12	matrix	matrix	NOUN
ejpam-180	55	13	transpose	transpose	NOUN
ejpam-180	55	14	.	.	PUNCT
ejpam-180	56	1	before	before	ADP
ejpam-180	56	2	stating	state	VERB
ejpam-180	56	3	our	our	PRON
ejpam-180	56	4	variational	variational	ADJ
ejpam-180	56	5	problem	problem	NOUN
ejpam-180	56	6	and	and	CCONJ
ejpam-180	56	7	deriving	derive	VERB
ejpam-180	56	8	its	its	PRON
ejpam-180	56	9	necessary	necessary	ADJ
ejpam-180	56	10	optimality	optimality	NOUN
ejpam-180	56	11	conditions	condition	NOUN
ejpam-180	56	12	,	,	PUNCT
ejpam-180	56	13	we	we	PRON
ejpam-180	56	14	mention	mention	VERB
ejpam-180	56	15	the	the	DET
ejpam-180	56	16	following	follow	VERB
ejpam-180	56	17	conventions	convention	NOUN
ejpam-180	56	18	for	for	ADP
ejpam-180	56	19	vectors	vector	NOUN
ejpam-180	56	20	x	x	PUNCT
ejpam-180	56	21	and	and	CCONJ
ejpam-180	56	22	y	y	PROPN
ejpam-180	56	23	in	in	ADP
ejpam-180	56	24	n	n	CCONJ
ejpam-180	56	25	-	-	PUNCT
ejpam-180	56	26	dimensional	dimensional	ADJ
ejpam-180	56	27	euclidian	euclidian	ADJ
ejpam-180	56	28	space	space	NOUN
ejpam-180	56	29	rn	rn	PROPN
ejpam-180	56	30	to	to	PART
ejpam-180	56	31	be	be	AUX
ejpam-180	56	32	used	use	VERB
ejpam-180	56	33	throughout	throughout	ADP
ejpam-180	56	34	the	the	DET
ejpam-180	56	35	analysis	analysis	NOUN
ejpam-180	56	36	of	of	ADP
ejpam-180	56	37	this	this	DET
ejpam-180	56	38	research	research	NOUN
ejpam-180	56	39	.	.	PUNCT
ejpam-180	57	1	x	x	X
ejpam-180	57	2	<	<	X
ejpam-180	57	3	y	y	PROPN
ejpam-180	57	4	,	,	PUNCT
ejpam-180	57	5	⇔	⇔	X
ejpam-180	57	6	x	x	PROPN
ejpam-180	57	7	i	i	PRON
ejpam-180	57	8	<	<	X
ejpam-180	57	9	yi	yi	PROPN
ejpam-180	57	10	,	,	PUNCT
ejpam-180	57	11	i	i	PRON
ejpam-180	57	12	=	=	NOUN
ejpam-180	57	13	1	1	NUM
ejpam-180	57	14	,	,	PUNCT
ejpam-180	57	15	2	2	NUM
ejpam-180	57	16	,	,	PUNCT
ejpam-180	57	17	.	.	PUNCT
ejpam-180	57	18	.	.	PUNCT
ejpam-180	57	19	.	.	PUNCT
ejpam-180	58	1	,	,	PUNCT
ejpam-180	58	2	n.	n.	PROPN
ejpam-180	58	3	i.	i.	PROPN
ejpam-180	58	4	husain	husain	PROPN
ejpam-180	58	5	,	,	PUNCT
ejpam-180	58	6	a.	a.	PROPN
ejpam-180	58	7	ahmed	ahmed	PROPN
ejpam-180	58	8	,	,	PUNCT
ejpam-180	58	9	and	and	CCONJ
ejpam-180	58	10	g.	g.	PROPN
ejpam-180	58	11	rumana	rumana	PROPN
ejpam-180	58	12	/	/	SYM
ejpam-180	58	13	eur	eur	PROPN
ejpam-180	58	14	.	.	PUNCT
ejpam-180	59	1	j.	j.	PROPN
ejpam-180	59	2	pure	pure	PROPN
ejpam-180	59	3	appl	appl	PROPN
ejpam-180	59	4	.	.	PROPN
ejpam-180	59	5	math	math	PROPN
ejpam-180	59	6	,	,	PUNCT
ejpam-180	59	7	2	2	NUM
ejpam-180	59	8	(	(	PUNCT
ejpam-180	59	9	2009	2009	NUM
ejpam-180	59	10	)	)	PUNCT
ejpam-180	59	11	,	,	PUNCT
ejpam-180	59	12	(	(	PUNCT
ejpam-180	59	13	372	372	NUM
ejpam-180	59	14	-	-	SYM
ejpam-180	59	15	400	400	NUM
ejpam-180	59	16	)	)	PUNCT
ejpam-180	59	17	375	375	NUM
ejpam-180	59	18	x	x	SYM
ejpam-180	59	19	≦	≦	NUM
ejpam-180	59	20	y	y	PROPN
ejpam-180	59	21	,	,	PUNCT
ejpam-180	59	22	⇔	⇔	X
ejpam-180	59	23	x	x	PROPN
ejpam-180	59	24	i	i	NOUN
ejpam-180	59	25	≤	≤	PUNCT
ejpam-180	59	26	yi	yi	NOUN
ejpam-180	59	27	,	,	PUNCT
ejpam-180	59	28	i	i	PRON
ejpam-180	59	29	=	=	NOUN
ejpam-180	59	30	1	1	NUM
ejpam-180	59	31	,	,	PUNCT
ejpam-180	59	32	2	2	NUM
ejpam-180	59	33	,	,	PUNCT
ejpam-180	59	34	.	.	PUNCT
ejpam-180	59	35	.	.	PUNCT
ejpam-180	59	36	.	.	PUNCT
ejpam-180	60	1	,	,	PUNCT
ejpam-180	60	2	n.	n.	NOUN
ejpam-180	60	3	x	x	PUNCT
ejpam-180	60	4	≤	≤	PROPN
ejpam-180	60	5	y	y	PROPN
ejpam-180	60	6	,	,	PUNCT
ejpam-180	60	7	⇔	⇔	X
ejpam-180	60	8	x	x	PROPN
ejpam-180	60	9	≦	≦	NUM
ejpam-180	60	10	y	y	PROPN
ejpam-180	60	11	,	,	PUNCT
ejpam-180	60	12	i	i	NOUN
ejpam-180	60	13	=	=	NOUN
ejpam-180	60	14	1	1	NUM
ejpam-180	60	15	,	,	PUNCT
ejpam-180	60	16	2	2	NUM
ejpam-180	60	17	,	,	PUNCT
ejpam-180	60	18	.	.	PUNCT
ejpam-180	60	19	.	.	PUNCT
ejpam-180	60	20	.	.	PUNCT
ejpam-180	60	21	,	,	PUNCT
ejpam-180	60	22	n	n	CCONJ
ejpam-180	60	23	,	,	PUNCT
ejpam-180	60	24	but	but	CCONJ
ejpam-180	60	25	x	x	X
ejpam-180	60	26	6=	6=	NUM
ejpam-180	60	27	y	y	PROPN
ejpam-180	60	28	x	x	PROPN
ejpam-180	60	29	6≤	6≤	NUM
ejpam-180	60	30	y	y	NOUN
ejpam-180	60	31	,	,	PUNCT
ejpam-180	60	32	is	be	AUX
ejpam-180	60	33	the	the	DET
ejpam-180	60	34	negation	negation	NOUN
ejpam-180	60	35	of	of	ADP
ejpam-180	60	36	x	x	PUNCT
ejpam-180	60	37	≤	≤	NUM
ejpam-180	60	38	y	y	NOUN
ejpam-180	60	39	for	for	ADP
ejpam-180	60	40	x	x	X
ejpam-180	60	41	,	,	PUNCT
ejpam-180	60	42	y	y	PROPN
ejpam-180	60	43	∈	∈	PROPN
ejpam-180	60	44	r	r	NOUN
ejpam-180	60	45	,	,	PUNCT
ejpam-180	60	46	x	x	PUNCT
ejpam-180	60	47	≤	≤	ADJ
ejpam-180	60	48	y	y	PROPN
ejpam-180	60	49	and	and	CCONJ
ejpam-180	60	50	x	x	SYM
ejpam-180	60	51	<	<	X
ejpam-180	60	52	y	y	X
ejpam-180	60	53	have	have	VERB
ejpam-180	60	54	the	the	DET
ejpam-180	60	55	usual	usual	ADJ
ejpam-180	60	56	meaning	meaning	NOUN
ejpam-180	60	57	.	.	PUNCT
ejpam-180	61	1	we	we	PRON
ejpam-180	61	2	present	present	VERB
ejpam-180	61	3	the	the	DET
ejpam-180	61	4	following	follow	VERB
ejpam-180	61	5	nondifferentiable	nondifferentiable	ADJ
ejpam-180	61	6	multiobjective	multiobjective	ADJ
ejpam-180	61	7	variational	variational	ADJ
ejpam-180	61	8	problem	problem	NOUN
ejpam-180	61	9	with	with	ADP
ejpam-180	61	10	higher	high	ADJ
ejpam-180	61	11	order	order	NOUN
ejpam-180	61	12	derivatives	derivative	NOUN
ejpam-180	61	13	as	as	ADP
ejpam-180	61	14	:	:	PUNCT
ejpam-180	61	15	(	(	PUNCT
ejpam-180	61	16	vp	vp	NOUN
ejpam-180	61	17	)	)	PUNCT
ejpam-180	61	18	minimize	minimize	VERB
ejpam-180	61	19	�	�	PROPN
ejpam-180	61	20	∫	∫	PROPN
ejpam-180	61	21	i	i	PROPN
ejpam-180	61	22	�	�	PROPN
ejpam-180	62	1	f	f	PROPN
ejpam-180	62	2	1	1	NUM
ejpam-180	62	3	(	(	PUNCT
ejpam-180	62	4	t	t	PROPN
ejpam-180	62	5	,	,	PUNCT
ejpam-180	62	6	x	x	X
ejpam-180	62	7	,	,	PUNCT
ejpam-180	62	8	ẋ	ẋ	PROPN
ejpam-180	62	9	,	,	PUNCT
ejpam-180	62	10	ẍ	ẍ	X
ejpam-180	62	11	)	)	PUNCT
ejpam-180	63	1	d	d	PROPN
ejpam-180	63	2	t	t	PROPN
ejpam-180	63	3	+	+	CCONJ
ejpam-180	63	4	�	�	PROPN
ejpam-180	63	5	x	x	SYM
ejpam-180	63	6	(	(	PUNCT
ejpam-180	63	7	t	t	PROPN
ejpam-180	63	8	)	)	PUNCT
ejpam-180	63	9	t	t	PROPN
ejpam-180	63	10	b1	b1	PROPN
ejpam-180	63	11	(	(	PUNCT
ejpam-180	63	12	t	t	PROPN
ejpam-180	63	13	)	)	PUNCT
ejpam-180	63	14	x	x	X
ejpam-180	63	15	(	(	PUNCT
ejpam-180	63	16	t	t	PROPN
ejpam-180	63	17	)	)	PUNCT
ejpam-180	63	18	�	�	PROPN
ejpam-180	63	19	1	1	NUM
ejpam-180	63	20	2	2	NUM
ejpam-180	63	21	�	�	PROPN
ejpam-180	63	22	d	d	PROPN
ejpam-180	63	23	t	t	PROPN
ejpam-180	63	24	,	,	PUNCT
ejpam-180	63	25	.	.	PUNCT
ejpam-180	63	26	.	.	PUNCT
ejpam-180	63	27	.	.	PUNCT
ejpam-180	64	1	,	,	PUNCT
ejpam-180	64	2	∫	∫	PROPN
ejpam-180	65	1	i	i	PRON
ejpam-180	65	2	�	�	PROPN
ejpam-180	66	1	f	f	PROPN
ejpam-180	66	2	p	p	PROPN
ejpam-180	66	3	(	(	PUNCT
ejpam-180	66	4	t	t	PROPN
ejpam-180	66	5	,	,	PUNCT
ejpam-180	66	6	x	x	X
ejpam-180	66	7	,	,	PUNCT
ejpam-180	66	8	ẋ	ẋ	PROPN
ejpam-180	66	9	,	,	PUNCT
ejpam-180	66	10	ẍ	ẍ	X
ejpam-180	66	11	)	)	PUNCT
ejpam-180	67	1	d	d	PROPN
ejpam-180	67	2	t	t	PROPN
ejpam-180	67	3	+	+	CCONJ
ejpam-180	67	4	�	�	PROPN
ejpam-180	67	5	x	x	SYM
ejpam-180	67	6	(	(	PUNCT
ejpam-180	67	7	t	t	PROPN
ejpam-180	67	8	)	)	PUNCT
ejpam-180	67	9	t	t	PROPN
ejpam-180	67	10	bp	bp	PROPN
ejpam-180	67	11	(	(	PUNCT
ejpam-180	67	12	t	t	PROPN
ejpam-180	67	13	)	)	PUNCT
ejpam-180	67	14	x	x	X
ejpam-180	67	15	(	(	PUNCT
ejpam-180	67	16	t	t	PROPN
ejpam-180	67	17	)	)	PUNCT
ejpam-180	67	18	�	�	PROPN
ejpam-180	67	19	1	1	NUM
ejpam-180	67	20	2	2	NUM
ejpam-180	67	21	�	�	PROPN
ejpam-180	67	22	d	d	PROPN
ejpam-180	67	23	t	t	PROPN
ejpam-180	67	24	�	�	PROPN
ejpam-180	67	25	subject	subject	ADJ
ejpam-180	67	26	to	to	ADP
ejpam-180	67	27	x(a	x(a	NOUN
ejpam-180	67	28	)	)	PUNCT
ejpam-180	67	29	=	=	SYM
ejpam-180	68	1	0=	0=	NUM
ejpam-180	68	2	x(b	x(b	PROPN
ejpam-180	68	3	)	)	PUNCT
ejpam-180	68	4	(	(	PUNCT
ejpam-180	68	5	2.1	2.1	NUM
ejpam-180	68	6	)	)	PUNCT
ejpam-180	68	7	ẋ(a	ẋ(a	PROPN
ejpam-180	68	8	)	)	PUNCT
ejpam-180	68	9	=	=	PUNCT
ejpam-180	69	1	0=	0=	NUM
ejpam-180	69	2	ẋ(b	ẋ(b	PROPN
ejpam-180	69	3	)	)	PUNCT
ejpam-180	69	4	(	(	PUNCT
ejpam-180	69	5	2.2	2.2	NUM
ejpam-180	69	6	)	)	PUNCT
ejpam-180	69	7	g(t	g(t	PROPN
ejpam-180	69	8	,	,	PUNCT
ejpam-180	69	9	x	x	SYM
ejpam-180	69	10	,	,	PUNCT
ejpam-180	69	11	ẋ	ẋ	PROPN
ejpam-180	69	12	,	,	PUNCT
ejpam-180	69	13	ẍ	ẍ	X
ejpam-180	69	14	)	)	PUNCT
ejpam-180	69	15	≦	≦	VERB
ejpam-180	69	16	0	0	NUM
ejpam-180	69	17	,	,	PUNCT
ejpam-180	69	18	t	t	PROPN
ejpam-180	69	19	∈	∈	PROPN
ejpam-180	70	1	i	i	PRON
ejpam-180	70	2	,	,	PUNCT
ejpam-180	70	3	(	(	PUNCT
ejpam-180	70	4	2.3	2.3	NUM
ejpam-180	70	5	)	)	PUNCT
ejpam-180	70	6	where	where	SCONJ
ejpam-180	70	7	,	,	PUNCT
ejpam-180	70	8	f	f	PROPN
ejpam-180	70	9	i	i	PRON
ejpam-180	70	10	:	:	PUNCT
ejpam-180	70	11	i×rn×rn×rn→	i×rn×rn×rn→	VERB
ejpam-180	71	1	r	r	X
ejpam-180	71	2	,	,	PUNCT
ejpam-180	71	3	(	(	PUNCT
ejpam-180	71	4	i	i	NOUN
ejpam-180	71	5	=	=	NOUN
ejpam-180	71	6	1	1	NUM
ejpam-180	71	7	,	,	PUNCT
ejpam-180	71	8	2	2	NUM
ejpam-180	71	9	,	,	PUNCT
ejpam-180	71	10	.	.	PUNCT
ejpam-180	71	11	.	.	PUNCT
ejpam-180	71	12	.	.	PUNCT
ejpam-180	72	1	,	,	PUNCT
ejpam-180	72	2	p	p	X
ejpam-180	72	3	)	)	PUNCT
ejpam-180	72	4	,	,	PUNCT
ejpam-180	72	5	g	g	NOUN
ejpam-180	72	6	:	:	PUNCT
ejpam-180	72	7	i×rn×rn×rn→	i×rn×rn×rn→	PROPN
ejpam-180	72	8	rm	rm	PROPN
ejpam-180	72	9	,	,	PUNCT
ejpam-180	72	10	are	be	AUX
ejpam-180	72	11	assumed	assume	VERB
ejpam-180	72	12	to	to	PART
ejpam-180	72	13	be	be	AUX
ejpam-180	72	14	continuously	continuously	ADV
ejpam-180	72	15	differentiable	differentiable	ADJ
ejpam-180	72	16	functions	function	NOUN
ejpam-180	72	17	,	,	PUNCT
ejpam-180	72	18	for	for	ADP
ejpam-180	72	19	each	each	DET
ejpam-180	72	20	i	i	PRON
ejpam-180	72	21	∈	∈	PROPN
ejpam-180	72	22	p	p	X
ejpam-180	72	23	,	,	PUNCT
ejpam-180	72	24	{	{	PUNCT
ejpam-180	72	25	i	i	NOUN
ejpam-180	72	26	=	=	NOUN
ejpam-180	72	27	1	1	NUM
ejpam-180	72	28	,	,	PUNCT
ejpam-180	72	29	2	2	NUM
ejpam-180	72	30	,	,	PUNCT
ejpam-180	72	31	.	.	PUNCT
ejpam-180	72	32	.	.	PUNCT
ejpam-180	73	1	.	.	PUNCT
ejpam-180	74	1	,	,	PUNCT
ejpam-180	74	2	p	p	X
ejpam-180	74	3	}	}	PUNCT
ejpam-180	74	4	,	,	PUNCT
ejpam-180	74	5	b	b	X
ejpam-180	74	6	i(t	i(t	PROPN
ejpam-180	74	7	)	)	PUNCT
ejpam-180	74	8	is	be	AUX
ejpam-180	74	9	an	an	DET
ejpam-180	74	10	n×	n×	PROPN
ejpam-180	74	11	n	n	CCONJ
ejpam-180	74	12	positive	positive	ADJ
ejpam-180	74	13	semidefinite	semidefinite	NOUN
ejpam-180	74	14	symmetric	symmetric	ADJ
ejpam-180	74	15	matrix	matrix	NOUN
ejpam-180	74	16	with	with	ADP
ejpam-180	74	17	b	b	PROPN
ejpam-180	74	18	i	i	PROPN
ejpam-180	74	19	(	(	PUNCT
ejpam-180	74	20	·	·	PUNCT
ejpam-180	74	21	)	)	PUNCT
ejpam-180	74	22	continuous	continuous	ADJ
ejpam-180	74	23	on	on	ADP
ejpam-180	74	24	i	i	PRON
ejpam-180	74	25	.	.	PUNCT
ejpam-180	75	1	the	the	DET
ejpam-180	75	2	following	follow	VERB
ejpam-180	75	3	generalized	generalize	VERB
ejpam-180	75	4	schwarz	schwarz	PROPN
ejpam-180	75	5	inequality	inequality	NOUN
ejpam-180	75	6	[	[	X
ejpam-180	75	7	15	15	NUM
ejpam-180	75	8	]	]	PUNCT
ejpam-180	75	9	is	be	AUX
ejpam-180	75	10	required	require	VERB
ejpam-180	75	11	in	in	ADP
ejpam-180	75	12	the	the	DET
ejpam-180	75	13	sequel	sequel	NOUN
ejpam-180	75	14	.	.	PUNCT
ejpam-180	76	1	(	(	PUNCT
ejpam-180	76	2	x(t)t	x(t)t	PROPN
ejpam-180	76	3	b	b	PROPN
ejpam-180	76	4	i(t)z(t))≤	i(t)z(t))≤	PROPN
ejpam-180	76	5	(	(	PUNCT
ejpam-180	76	6	x(t)t	x(t)t	PROPN
ejpam-180	76	7	b	b	PROPN
ejpam-180	76	8	i(t)x(t	i(t)x(t	PROPN
ejpam-180	76	9	)	)	PUNCT
ejpam-180	76	10	)	)	PUNCT
ejpam-180	76	11	1	1	NUM
ejpam-180	76	12	2	2	NUM
ejpam-180	76	13	(	(	PUNCT
ejpam-180	76	14	z(t)t	z(t)t	NOUN
ejpam-180	76	15	b	b	PROPN
ejpam-180	76	16	i(t)z(t	i(t)z(t	NOUN
ejpam-180	76	17	)	)	PUNCT
ejpam-180	76	18	)	)	PUNCT
ejpam-180	76	19	1	1	NUM
ejpam-180	76	20	2	2	NUM
ejpam-180	76	21	∀	∀	X
ejpam-180	76	22	x(t	x(t	PROPN
ejpam-180	76	23	)	)	PUNCT
ejpam-180	76	24	∈	∈	PROPN
ejpam-180	76	25	rn	rn	PROPN
ejpam-180	76	26	,	,	PUNCT
ejpam-180	76	27	z(t	z(t	X
ejpam-180	76	28	)	)	PUNCT
ejpam-180	76	29	∈	∈	PROPN
ejpam-180	76	30	rn	rn	PROPN
ejpam-180	76	31	,	,	PUNCT
ejpam-180	76	32	t	t	PROPN
ejpam-180	76	33	∈	∈	PROPN
ejpam-180	77	1	i	i	PRON
ejpam-180	77	2	definition	definition	VERB
ejpam-180	77	3	2.1	2.1	NUM
ejpam-180	77	4	(	(	PUNCT
ejpam-180	77	5	invexity	invexity	NOUN
ejpam-180	77	6	)	)	PUNCT
ejpam-180	77	7	.	.	PUNCT
ejpam-180	78	1	if	if	SCONJ
ejpam-180	78	2	there	there	PRON
ejpam-180	78	3	exists	exist	VERB
ejpam-180	78	4	vector	vector	NOUN
ejpam-180	78	5	function	function	NOUN
ejpam-180	78	6	η(t	η(t	NOUN
ejpam-180	78	7	,	,	PUNCT
ejpam-180	78	8	x	x	SYM
ejpam-180	78	9	,	,	PUNCT
ejpam-180	78	10	u	u	NOUN
ejpam-180	78	11	)	)	PUNCT
ejpam-180	78	12	∈	∈	PROPN
ejpam-180	78	13	rn	rn	PROPN
ejpam-180	78	14	with	with	ADP
ejpam-180	78	15	η	η	PROPN
ejpam-180	78	16	=	=	PROPN
ejpam-180	78	17	0	0	PROPN
ejpam-180	78	18	and	and	CCONJ
ejpam-180	78	19	x(t	x(t	PROPN
ejpam-180	78	20	)	)	PUNCT
ejpam-180	78	21	=	=	SYM
ejpam-180	78	22	u(t	u(t	NOUN
ejpam-180	78	23	)	)	PUNCT
ejpam-180	78	24	,	,	PUNCT
ejpam-180	78	25	t	t	PROPN
ejpam-180	78	26	∈	∈	PROPN
ejpam-180	79	1	i	i	PRON
ejpam-180	79	2	and	and	CCONJ
ejpam-180	79	3	dη	dη	X
ejpam-180	79	4	=	=	NOUN
ejpam-180	79	5	0	0	NUM
ejpam-180	79	6	for	for	ADP
ejpam-180	79	7	ẋ(t	ẋ(t	NOUN
ejpam-180	79	8	)	)	PUNCT
ejpam-180	79	9	=	=	SYM
ejpam-180	79	10	u̇(t	u̇(t	NOUN
ejpam-180	79	11	)	)	PUNCT
ejpam-180	79	12	,	,	PUNCT
ejpam-180	79	13	t	t	PROPN
ejpam-180	79	14	∈	∈	PROPN
ejpam-180	79	15	i	i	PRON
ejpam-180	79	16	such	such	ADJ
ejpam-180	79	17	that	that	PRON
ejpam-180	79	18	for	for	ADP
ejpam-180	79	19	a	a	DET
ejpam-180	79	20	scalar	scalar	ADJ
ejpam-180	79	21	function	function	NOUN
ejpam-180	79	22	i.	i.	PROPN
ejpam-180	79	23	husain	husain	PROPN
ejpam-180	79	24	,	,	PUNCT
ejpam-180	79	25	a.	a.	PROPN
ejpam-180	79	26	ahmed	ahmed	PROPN
ejpam-180	79	27	,	,	PUNCT
ejpam-180	79	28	and	and	CCONJ
ejpam-180	79	29	g.	g.	PROPN
ejpam-180	79	30	rumana	rumana	PROPN
ejpam-180	79	31	/	/	SYM
ejpam-180	79	32	eur	eur	PROPN
ejpam-180	79	33	.	.	PUNCT
ejpam-180	80	1	j.	j.	PROPN
ejpam-180	80	2	pure	pure	PROPN
ejpam-180	80	3	appl	appl	PROPN
ejpam-180	80	4	.	.	PROPN
ejpam-180	80	5	math	math	PROPN
ejpam-180	80	6	,	,	PUNCT
ejpam-180	80	7	2	2	NUM
ejpam-180	80	8	(	(	PUNCT
ejpam-180	80	9	2009	2009	NUM
ejpam-180	80	10	)	)	PUNCT
ejpam-180	80	11	,	,	PUNCT
ejpam-180	80	12	(	(	PUNCT
ejpam-180	80	13	372	372	NUM
ejpam-180	80	14	-	-	SYM
ejpam-180	80	15	400	400	NUM
ejpam-180	80	16	)	)	PUNCT
ejpam-180	80	17	376	376	NUM
ejpam-180	80	18	φ(t	φ(t	PROPN
ejpam-180	80	19	,	,	PUNCT
ejpam-180	80	20	x	x	X
ejpam-180	80	21	,	,	PUNCT
ejpam-180	80	22	ẋ	ẋ	PROPN
ejpam-180	80	23	,	,	PUNCT
ejpam-180	80	24	ẍ	ẍ	PROPN
ejpam-180	80	25	)	)	PUNCT
ejpam-180	80	26	,	,	PUNCT
ejpam-180	80	27	the	the	DET
ejpam-180	80	28	functional	functional	ADJ
ejpam-180	80	29	φ(x	φ(x	PROPN
ejpam-180	80	30	,	,	PUNCT
ejpam-180	80	31	ẋ	ẋ	PROPN
ejpam-180	80	32	,	,	PUNCT
ejpam-180	80	33	ẍ	ẍ	X
ejpam-180	80	34	)	)	PUNCT
ejpam-180	81	1	=	=	SYM
ejpam-180	82	1	∫	∫	PROPN
ejpam-180	82	2	f	f	PROPN
ejpam-180	82	3	φ(t	φ(t	PROPN
ejpam-180	82	4	,	,	PUNCT
ejpam-180	82	5	x	x	X
ejpam-180	82	6	,	,	PUNCT
ejpam-180	82	7	ẋ	ẋ	PROPN
ejpam-180	82	8	,	,	PUNCT
ejpam-180	82	9	ẍ)d	ẍ)d	PROPN
ejpam-180	82	10	t	t	PROPN
ejpam-180	82	11	satisfies	satisfy	VERB
ejpam-180	82	12	φ(x	φ(x	PROPN
ejpam-180	82	13	,	,	PUNCT
ejpam-180	82	14	u̇	u̇	PROPN
ejpam-180	82	15	,	,	PUNCT
ejpam-180	82	16	ü)−φ(x	ü)−φ(x	NOUN
ejpam-180	82	17	,	,	PUNCT
ejpam-180	82	18	ẋ	ẋ	PROPN
ejpam-180	82	19	,	,	PUNCT
ejpam-180	82	20	ẍ	ẍ	PROPN
ejpam-180	82	21	)	)	PUNCT
ejpam-180	82	22	≧	≧	X
ejpam-180	83	1	∫	∫	PROPN
ejpam-180	84	1	i	i	PRON
ejpam-180	84	2	{	{	PUNCT
ejpam-180	84	3	ηtφx(t	ηtφx(t	PROPN
ejpam-180	84	4	,	,	PUNCT
ejpam-180	84	5	x	x	INTJ
ejpam-180	84	6	,	,	PUNCT
ejpam-180	84	7	ẋ	ẋ	PROPN
ejpam-180	84	8	,	,	PUNCT
ejpam-180	84	9	ẍ	ẍ	X
ejpam-180	84	10	)	)	PUNCT
ejpam-180	85	1	+	+	CCONJ
ejpam-180	85	2	(	(	PUNCT
ejpam-180	85	3	dη)tφ	dη)tφ	NUM
ejpam-180	85	4	ẋ(t	ẋ(t	SYM
ejpam-180	85	5	,	,	PUNCT
ejpam-180	85	6	x	x	X
ejpam-180	85	7	,	,	PUNCT
ejpam-180	85	8	ẋ	ẋ	PROPN
ejpam-180	85	9	,	,	PUNCT
ejpam-180	85	10	ẍ	ẍ	X
ejpam-180	85	11	)	)	PUNCT
ejpam-180	85	12	+	+	CCONJ
ejpam-180	85	13	(	(	PUNCT
ejpam-180	85	14	d2η)tφ	d2η)tφ	PROPN
ejpam-180	85	15	ẍ(t	ẍ(t	PROPN
ejpam-180	85	16	,	,	PUNCT
ejpam-180	85	17	x	x	PROPN
ejpam-180	85	18	,	,	PUNCT
ejpam-180	85	19	ẋ	ẋ	PROPN
ejpam-180	85	20	,	,	PUNCT
ejpam-180	85	21	ẍ)}d	ẍ)}d	PROPN
ejpam-180	85	22	t	t	PROPN
ejpam-180	85	23	,	,	PUNCT
ejpam-180	85	24	φ	φ	PROPN
ejpam-180	85	25	is	be	AUX
ejpam-180	85	26	said	say	VERB
ejpam-180	85	27	to	to	PART
ejpam-180	85	28	be	be	AUX
ejpam-180	85	29	invex	invex	NOUN
ejpam-180	85	30	in	in	ADP
ejpam-180	85	31	x	x	SYM
ejpam-180	85	32	,	,	PUNCT
ejpam-180	85	33	ẋ	ẋ	PROPN
ejpam-180	85	34	and	and	CCONJ
ejpam-180	85	35	ẍ	ẍ	X
ejpam-180	85	36	on	on	ADP
ejpam-180	85	37	i	i	PRON
ejpam-180	85	38	with	with	ADP
ejpam-180	85	39	respect	respect	NOUN
ejpam-180	85	40	to	to	ADP
ejpam-180	85	41	η	η	PROPN
ejpam-180	85	42	.	.	PROPN
ejpam-180	85	43	definition	definition	NOUN
ejpam-180	85	44	2.2	2.2	NUM
ejpam-180	85	45	(	(	PUNCT
ejpam-180	85	46	pseudoinvexity	pseudoinvexity	NOUN
ejpam-180	85	47	)	)	PUNCT
ejpam-180	85	48	.	.	PUNCT
ejpam-180	86	1	φ	φ	PROPN
ejpam-180	86	2	is	be	AUX
ejpam-180	86	3	said	say	VERB
ejpam-180	86	4	to	to	PART
ejpam-180	86	5	be	be	AUX
ejpam-180	86	6	pseudoinvex	pseudoinvex	NOUN
ejpam-180	86	7	in	in	ADP
ejpam-180	86	8	x	x	X
ejpam-180	86	9	,	,	PUNCT
ejpam-180	86	10	ẋ	ẋ	PROPN
ejpam-180	86	11	and	and	CCONJ
ejpam-180	86	12	ẍ	ẍ	X
ejpam-180	86	13	with	with	ADP
ejpam-180	86	14	respect	respect	NOUN
ejpam-180	86	15	to	to	ADP
ejpam-180	86	16	η	η	PROPN
ejpam-180	86	17	if	if	SCONJ
ejpam-180	86	18	∫	∫	PROPN
ejpam-180	86	19	i	i	PRON
ejpam-180	86	20	{	{	PUNCT
ejpam-180	86	21	ηtφx(t	ηtφx(t	PROPN
ejpam-180	86	22	,	,	PUNCT
ejpam-180	86	23	x	x	INTJ
ejpam-180	86	24	,	,	PUNCT
ejpam-180	86	25	ẋ	ẋ	PROPN
ejpam-180	86	26	,	,	PUNCT
ejpam-180	86	27	ẍ	ẍ	X
ejpam-180	86	28	)	)	PUNCT
ejpam-180	87	1	+	+	CCONJ
ejpam-180	87	2	(	(	PUNCT
ejpam-180	87	3	dη)tφ	dη)tφ	NUM
ejpam-180	87	4	ẋ(t	ẋ(t	SYM
ejpam-180	87	5	,	,	PUNCT
ejpam-180	87	6	x	x	X
ejpam-180	87	7	,	,	PUNCT
ejpam-180	87	8	ẋ	ẋ	PROPN
ejpam-180	87	9	,	,	PUNCT
ejpam-180	87	10	ẍ	ẍ	X
ejpam-180	87	11	)	)	PUNCT
ejpam-180	88	1	+	+	CCONJ
ejpam-180	88	2	(	(	PUNCT
ejpam-180	88	3	d2η)tφ	d2η)tφ	PROPN
ejpam-180	88	4	ẍ(t	ẍ(t	PROPN
ejpam-180	88	5	,	,	PUNCT
ejpam-180	88	6	x	x	PROPN
ejpam-180	88	7	,	,	PUNCT
ejpam-180	88	8	ẋ	ẋ	PROPN
ejpam-180	88	9	,	,	PUNCT
ejpam-180	88	10	ẍ)}d	ẍ)}d	PROPN
ejpam-180	88	11	t	t	PROPN
ejpam-180	88	12	≧	≧	NOUN
ejpam-180	88	13	0	0	NUM
ejpam-180	88	14	implies	imply	VERB
ejpam-180	88	15	φ(x	φ(x	PROPN
ejpam-180	88	16	,	,	PUNCT
ejpam-180	88	17	u̇	u̇	PROPN
ejpam-180	88	18	,	,	PUNCT
ejpam-180	88	19	ü)≧	ü)≧	PROPN
ejpam-180	88	20	φ(x	φ(x	PROPN
ejpam-180	88	21	,	,	PUNCT
ejpam-180	88	22	ẋ	ẋ	PROPN
ejpam-180	88	23	,	,	PUNCT
ejpam-180	88	24	ẍ	ẍ	PROPN
ejpam-180	88	25	)	)	PUNCT
ejpam-180	88	26	definition	definition	NOUN
ejpam-180	88	27	2.3	2.3	NUM
ejpam-180	88	28	(	(	PUNCT
ejpam-180	88	29	quasi	quasi	NOUN
ejpam-180	88	30	-	-	NOUN
ejpam-180	88	31	invex	invex	ADJ
ejpam-180	88	32	)	)	PUNCT
ejpam-180	88	33	.	.	PUNCT
ejpam-180	89	1	the	the	DET
ejpam-180	89	2	functional	functional	ADJ
ejpam-180	89	3	φ	φ	PROPN
ejpam-180	89	4	is	be	AUX
ejpam-180	89	5	said	say	VERB
ejpam-180	89	6	to	to	ADP
ejpam-180	89	7	quasi	quasi	NOUN
ejpam-180	89	8	-	-	NOUN
ejpam-180	89	9	invex	invex	ADJ
ejpam-180	89	10	in	in	ADP
ejpam-180	89	11	x	x	SYM
ejpam-180	89	12	,	,	PUNCT
ejpam-180	89	13	ẋ	ẋ	PROPN
ejpam-180	89	14	and	and	CCONJ
ejpam-180	89	15	ẍ	ẍ	X
ejpam-180	89	16	with	with	ADP
ejpam-180	89	17	respect	respect	NOUN
ejpam-180	89	18	to	to	ADP
ejpam-180	89	19	η	η	PROPN
ejpam-180	89	20	if	if	SCONJ
ejpam-180	89	21	φ(x	φ(x	PROPN
ejpam-180	89	22	,	,	PUNCT
ejpam-180	89	23	u̇	u̇	PROPN
ejpam-180	89	24	,	,	PUNCT
ejpam-180	89	25	ü	ü	NOUN
ejpam-180	89	26	)	)	PUNCT
ejpam-180	89	27	≦	≦	PROPN
ejpam-180	89	28	φ(x	φ(x	PROPN
ejpam-180	89	29	,	,	PUNCT
ejpam-180	89	30	ẋ	ẋ	PROPN
ejpam-180	89	31	,	,	PUNCT
ejpam-180	89	32	ẍ	ẍ	PROPN
ejpam-180	89	33	)	)	PUNCT
ejpam-180	89	34	⇒	⇒	PROPN
ejpam-180	89	35	∫	∫	PROPN
ejpam-180	90	1	i	i	PRON
ejpam-180	90	2	{	{	PUNCT
ejpam-180	90	3	ηtφx(t	ηtφx(t	PROPN
ejpam-180	90	4	,	,	PUNCT
ejpam-180	90	5	x	x	INTJ
ejpam-180	90	6	,	,	PUNCT
ejpam-180	90	7	ẋ	ẋ	PROPN
ejpam-180	90	8	,	,	PUNCT
ejpam-180	90	9	ẍ	ẍ	X
ejpam-180	90	10	)	)	PUNCT
ejpam-180	91	1	+	+	CCONJ
ejpam-180	91	2	(	(	PUNCT
ejpam-180	91	3	dη)tφ	dη)tφ	NUM
ejpam-180	91	4	ẋ(t	ẋ(t	SYM
ejpam-180	91	5	,	,	PUNCT
ejpam-180	91	6	x	x	X
ejpam-180	91	7	,	,	PUNCT
ejpam-180	91	8	ẋ	ẋ	PROPN
ejpam-180	91	9	,	,	PUNCT
ejpam-180	91	10	ẍ	ẍ	X
ejpam-180	91	11	)	)	PUNCT
ejpam-180	91	12	+	+	CCONJ
ejpam-180	91	13	(	(	PUNCT
ejpam-180	91	14	d2η)tφ	d2η)tφ	PROPN
ejpam-180	91	15	ẍ(t	ẍ(t	PROPN
ejpam-180	91	16	,	,	PUNCT
ejpam-180	91	17	x	x	PROPN
ejpam-180	91	18	,	,	PUNCT
ejpam-180	91	19	ẋ	ẋ	PROPN
ejpam-180	91	20	,	,	PUNCT
ejpam-180	91	21	ẍ)}d	ẍ)}d	PROPN
ejpam-180	91	22	t	t	PROPN
ejpam-180	91	23	≦	≦	VERB
ejpam-180	91	24	0	0	NUM
ejpam-180	92	1	we	we	PRON
ejpam-180	92	2	require	require	VERB
ejpam-180	92	3	the	the	DET
ejpam-180	92	4	following	follow	VERB
ejpam-180	92	5	definition	definition	NOUN
ejpam-180	92	6	of	of	ADP
ejpam-180	92	7	efficient	efficient	ADJ
ejpam-180	92	8	solution	solution	NOUN
ejpam-180	92	9	for	for	ADP
ejpam-180	92	10	our	our	PRON
ejpam-180	92	11	further	further	ADJ
ejpam-180	92	12	analysis	analysis	NOUN
ejpam-180	92	13	.	.	PUNCT
ejpam-180	93	1	in	in	ADP
ejpam-180	93	2	this	this	DET
ejpam-180	93	3	definition	definition	NOUN
ejpam-180	93	4	we	we	PRON
ejpam-180	93	5	denote	denote	VERB
ejpam-180	93	6	by	by	ADP
ejpam-180	93	7	x	x	X
ejpam-180	93	8	,	,	PUNCT
ejpam-180	93	9	the	the	DET
ejpam-180	93	10	set	set	NOUN
ejpam-180	93	11	of	of	ADP
ejpam-180	93	12	feasible	feasible	ADJ
ejpam-180	93	13	solution	solution	NOUN
ejpam-180	93	14	for	for	ADP
ejpam-180	93	15	(	(	PUNCT
ejpam-180	93	16	vp	vp	PROPN
ejpam-180	93	17	)	)	PUNCT
ejpam-180	93	18	.	.	PUNCT
ejpam-180	94	1	definition	definition	NOUN
ejpam-180	94	2	2.4	2.4	NUM
ejpam-180	94	3	.	.	PUNCT
ejpam-180	95	1	a	a	DET
ejpam-180	95	2	point	point	NOUN
ejpam-180	95	3	x̄	x̄	X
ejpam-180	95	4	∈	∈	PROPN
ejpam-180	95	5	x	x	PUNCT
ejpam-180	95	6	is	be	AUX
ejpam-180	95	7	said	say	VERB
ejpam-180	95	8	to	to	PART
ejpam-180	95	9	be	be	AUX
ejpam-180	95	10	efficient	efficient	ADJ
ejpam-180	95	11	solution	solution	NOUN
ejpam-180	95	12	of	of	ADP
ejpam-180	95	13	(	(	PUNCT
ejpam-180	95	14	vp	vp	PROPN
ejpam-180	95	15	)	)	PUNCT
ejpam-180	95	16	if	if	SCONJ
ejpam-180	95	17	for	for	ADP
ejpam-180	95	18	all	all	PRON
ejpam-180	95	19	feasible	feasible	ADJ
ejpam-180	95	20	x	x	X
ejpam-180	95	21	∈	∈	NOUN
ejpam-180	95	22	x	x	X
ejpam-180	95	23	,	,	PUNCT
ejpam-180	95	24	∫	∫	PROPN
ejpam-180	95	25	i	i	PRON
ejpam-180	95	26	�	�	PROPN
ejpam-180	95	27	f	f	PROPN
ejpam-180	95	28	i(t	i(t	PROPN
ejpam-180	95	29	,	,	PUNCT
ejpam-180	95	30	x(t	x(t	PROPN
ejpam-180	95	31	)	)	PUNCT
ejpam-180	95	32	,	,	PUNCT
ejpam-180	95	33	ẋ(t	ẋ(t	NOUN
ejpam-180	95	34	)	)	PUNCT
ejpam-180	95	35	,	,	PUNCT
ejpam-180	95	36	ẍ(t))d	ẍ(t))d	PROPN
ejpam-180	95	37	t	t	PROPN
ejpam-180	95	38	+	+	CCONJ
ejpam-180	95	39	(	(	PUNCT
ejpam-180	95	40	x(t)t	x(t)t	PROPN
ejpam-180	95	41	b	b	PROPN
ejpam-180	95	42	i(t)x(t	i(t)x(t	PROPN
ejpam-180	95	43	)	)	PUNCT
ejpam-180	95	44	)	)	PUNCT
ejpam-180	95	45	1	1	NUM
ejpam-180	95	46	2	2	NUM
ejpam-180	95	47	�	�	PROPN
ejpam-180	95	48	d	d	PROPN
ejpam-180	95	49	t	t	PROPN
ejpam-180	95	50	�	�	PROPN
ejpam-180	96	1	∫	∫	PROPN
ejpam-180	97	1	i	i	PRON
ejpam-180	97	2	�	�	PROPN
ejpam-180	98	1	f	f	VERB
ejpam-180	99	1	i	i	PRON
ejpam-180	99	2	�	�	PROPN
ejpam-180	99	3	t	t	PROPN
ejpam-180	99	4	,	,	PUNCT
ejpam-180	99	5	x̄(t	x̄(t	PROPN
ejpam-180	99	6	)	)	PUNCT
ejpam-180	99	7	,	,	PUNCT
ejpam-180	99	8	˙̄x(t	˙̄x(t	NOUN
ejpam-180	99	9	)	)	PUNCT
ejpam-180	99	10	,	,	PUNCT
ejpam-180	99	11	¨̄x(t	¨̄x(t	NOUN
ejpam-180	99	12	)	)	PUNCT
ejpam-180	99	13	�	�	PROPN
ejpam-180	99	14	d	d	PROPN
ejpam-180	99	15	t	t	PROPN
ejpam-180	99	16	+	+	CCONJ
ejpam-180	99	17	�	�	PROPN
ejpam-180	99	18	x̄(t)t	x̄(t)t	PROPN
ejpam-180	99	19	b	b	PROPN
ejpam-180	99	20	i(t	i(t	PROPN
ejpam-180	99	21	)	)	PUNCT
ejpam-180	99	22	x̄(t	x̄(t	PUNCT
ejpam-180	99	23	)	)	PUNCT
ejpam-180	99	24	�	�	NOUN
ejpam-180	99	25	1	1	NUM
ejpam-180	99	26	2	2	NUM
ejpam-180	99	27	�	�	PROPN
ejpam-180	99	28	d	d	PROPN
ejpam-180	99	29	t	t	PROPN
ejpam-180	99	30	for	for	ADP
ejpam-180	99	31	all	all	PRON
ejpam-180	99	32	i	i	PRON
ejpam-180	99	33	∈	∈	PROPN
ejpam-180	99	34	p.	p.	NOUN
ejpam-180	99	35	i.	i.	PROPN
ejpam-180	99	36	husain	husain	PROPN
ejpam-180	99	37	,	,	PUNCT
ejpam-180	99	38	a.	a.	PROPN
ejpam-180	99	39	ahmed	ahmed	PROPN
ejpam-180	99	40	,	,	PUNCT
ejpam-180	99	41	and	and	CCONJ
ejpam-180	99	42	g.	g.	PROPN
ejpam-180	99	43	rumana	rumana	PROPN
ejpam-180	99	44	/	/	SYM
ejpam-180	99	45	eur	eur	PROPN
ejpam-180	99	46	.	.	PUNCT
ejpam-180	100	1	j.	j.	PROPN
ejpam-180	100	2	pure	pure	PROPN
ejpam-180	100	3	appl	appl	PROPN
ejpam-180	100	4	.	.	PROPN
ejpam-180	100	5	math	math	PROPN
ejpam-180	100	6	,	,	PUNCT
ejpam-180	100	7	2	2	NUM
ejpam-180	100	8	(	(	PUNCT
ejpam-180	100	9	2009	2009	NUM
ejpam-180	100	10	)	)	PUNCT
ejpam-180	100	11	,	,	PUNCT
ejpam-180	100	12	(	(	PUNCT
ejpam-180	100	13	372	372	NUM
ejpam-180	100	14	-	-	SYM
ejpam-180	100	15	400	400	NUM
ejpam-180	100	16	)	)	PUNCT
ejpam-180	100	17	377	377	NUM
ejpam-180	100	18	in	in	ADP
ejpam-180	100	19	order	order	NOUN
ejpam-180	100	20	to	to	PART
ejpam-180	100	21	prove	prove	VERB
ejpam-180	100	22	the	the	DET
ejpam-180	100	23	strong	strong	ADJ
ejpam-180	100	24	duality	duality	NOUN
ejpam-180	100	25	theorem	theorem	VERB
ejpam-180	100	26	,	,	PUNCT
ejpam-180	100	27	we	we	PRON
ejpam-180	100	28	will	will	AUX
ejpam-180	100	29	invoke	invoke	VERB
ejpam-180	100	30	the	the	DET
ejpam-180	100	31	following	follow	VERB
ejpam-180	100	32	lemma	lemma	PROPN
ejpam-180	100	33	due	due	ADP
ejpam-180	100	34	to	to	ADP
ejpam-180	100	35	changkong	changkong	NOUN
ejpam-180	100	36	and	and	CCONJ
ejpam-180	100	37	haimes	haime	NOUN
ejpam-180	100	38	[	[	X
ejpam-180	100	39	5	5	NUM
ejpam-180	100	40	]	]	PUNCT
ejpam-180	100	41	.	.	PUNCT
ejpam-180	101	1	lemma	lemma	PROPN
ejpam-180	101	2	2.1	2.1	NUM
ejpam-180	101	3	(	(	PUNCT
ejpam-180	101	4	[	[	X
ejpam-180	101	5	5	5	NUM
ejpam-180	101	6	]	]	NUM
ejpam-180	101	7	)	)	PUNCT
ejpam-180	101	8	.	.	PUNCT
ejpam-180	102	1	a	a	DET
ejpam-180	102	2	function	function	NOUN
ejpam-180	102	3	x̄	x̄	X
ejpam-180	102	4	∈	∈	PROPN
ejpam-180	102	5	x	x	PUNCT
ejpam-180	102	6	be	be	AUX
ejpam-180	102	7	an	an	DET
ejpam-180	102	8	efficient	efficient	ADJ
ejpam-180	102	9	solution	solution	NOUN
ejpam-180	102	10	of	of	ADP
ejpam-180	102	11	(	(	PUNCT
ejpam-180	102	12	vp	vp	PROPN
ejpam-180	102	13	)	)	PUNCT
ejpam-180	102	14	if	if	SCONJ
ejpam-180	102	15	and	and	CCONJ
ejpam-180	102	16	only	only	ADV
ejpam-180	102	17	if	if	SCONJ
ejpam-180	102	18	x̄	x̄	PRON
ejpam-180	102	19	∈	∈	PROPN
ejpam-180	102	20	x	x	X
ejpam-180	102	21	is	be	AUX
ejpam-180	102	22	an	an	DET
ejpam-180	102	23	optimal	optimal	ADJ
ejpam-180	102	24	solution	solution	NOUN
ejpam-180	102	25	of	of	ADP
ejpam-180	102	26	the	the	DET
ejpam-180	102	27	following	following	ADJ
ejpam-180	102	28	problem	problem	NOUN
ejpam-180	102	29	(	(	PUNCT
ejpam-180	102	30	pk	pk	NOUN
ejpam-180	102	31	(	(	PUNCT
ejpam-180	102	32	x̄	x̄	PROPN
ejpam-180	102	33	)	)	PUNCT
ejpam-180	102	34	)	)	PUNCT
ejpam-180	102	35	for	for	ADP
ejpam-180	102	36	all	all	DET
ejpam-180	102	37	k.	k.	PROPN
ejpam-180	102	38	(	(	PUNCT
ejpam-180	102	39	pk	pk	PROPN
ejpam-180	102	40	(	(	PUNCT
ejpam-180	102	41	x̄	x̄	PROPN
ejpam-180	102	42	)	)	PUNCT
ejpam-180	102	43	)	)	PUNCT
ejpam-180	102	44	:	:	PUNCT
ejpam-180	102	45	minimize	minimize	VERB
ejpam-180	102	46	∫	∫	PROPN
ejpam-180	102	47	i	i	PRON
ejpam-180	102	48	�	�	PROPN
ejpam-180	102	49	f	f	PROPN
ejpam-180	102	50	k	k	PROPN
ejpam-180	102	51	(	(	PUNCT
ejpam-180	102	52	t	t	PROPN
ejpam-180	102	53	,	,	PUNCT
ejpam-180	102	54	x	x	X
ejpam-180	102	55	,	,	PUNCT
ejpam-180	102	56	ẋ	ẋ	PROPN
ejpam-180	102	57	,	,	PUNCT
ejpam-180	102	58	ẍ	ẍ	X
ejpam-180	102	59	)	)	PUNCT
ejpam-180	103	1	d	d	PROPN
ejpam-180	103	2	t	t	PROPN
ejpam-180	103	3	+	+	CCONJ
ejpam-180	103	4	�	�	PROPN
ejpam-180	103	5	x	x	SYM
ejpam-180	103	6	(	(	PUNCT
ejpam-180	103	7	t	t	PROPN
ejpam-180	103	8	)	)	PUNCT
ejpam-180	103	9	t	t	PROPN
ejpam-180	103	10	bk	bk	PROPN
ejpam-180	103	11	(	(	PUNCT
ejpam-180	103	12	t	t	PROPN
ejpam-180	103	13	)	)	PUNCT
ejpam-180	103	14	x	x	X
ejpam-180	103	15	(	(	PUNCT
ejpam-180	103	16	t	t	PROPN
ejpam-180	103	17	)	)	PUNCT
ejpam-180	103	18	�	�	PROPN
ejpam-180	103	19	1	1	NUM
ejpam-180	103	20	2	2	NUM
ejpam-180	103	21	�	�	PROPN
ejpam-180	103	22	d	d	PROPN
ejpam-180	103	23	t	t	PROPN
ejpam-180	103	24	subject	subject	NOUN
ejpam-180	103	25	to	to	ADP
ejpam-180	103	26	x	x	PROPN
ejpam-180	103	27	(	(	PUNCT
ejpam-180	103	28	a	a	X
ejpam-180	103	29	)	)	PUNCT
ejpam-180	103	30	=	=	PUNCT
ejpam-180	104	1	0=	0=	PUNCT
ejpam-180	104	2	x	x	X
ejpam-180	104	3	(	(	PUNCT
ejpam-180	104	4	b	b	NOUN
ejpam-180	104	5	)	)	PUNCT
ejpam-180	104	6	ẋ	ẋ	PROPN
ejpam-180	105	1	(	(	PUNCT
ejpam-180	105	2	a	a	X
ejpam-180	105	3	)	)	PUNCT
ejpam-180	105	4	=	=	SYM
ejpam-180	105	5	0=	0=	NUM
ejpam-180	106	1	ẋ	ẋ	PROPN
ejpam-180	106	2	(	(	PUNCT
ejpam-180	106	3	b	b	X
ejpam-180	106	4	)	)	PUNCT
ejpam-180	106	5	g	g	NOUN
ejpam-180	106	6	(	(	PUNCT
ejpam-180	106	7	t	t	PROPN
ejpam-180	106	8	,	,	PUNCT
ejpam-180	106	9	x	x	X
ejpam-180	106	10	,	,	PUNCT
ejpam-180	106	11	ẋ	ẋ	PROPN
ejpam-180	106	12	,	,	PUNCT
ejpam-180	106	13	ẋ)≦	ẋ)≦	PROPN
ejpam-180	106	14	0	0	PROPN
ejpam-180	106	15	,	,	PUNCT
ejpam-180	106	16	t	t	PROPN
ejpam-180	106	17	∈	∈	PROPN
ejpam-180	107	1	i	i	PRON
ejpam-180	107	2	,	,	PUNCT
ejpam-180	107	3	∫	∫	PROPN
ejpam-180	108	1	i	i	PRON
ejpam-180	108	2	�	�	PROPN
ejpam-180	109	1	f	f	PROPN
ejpam-180	109	2	i	i	PRON
ejpam-180	109	3	(	(	PUNCT
ejpam-180	109	4	t	t	PROPN
ejpam-180	109	5	,	,	PUNCT
ejpam-180	109	6	x	x	X
ejpam-180	109	7	(	(	PUNCT
ejpam-180	109	8	t	t	PROPN
ejpam-180	109	9	)	)	PUNCT
ejpam-180	109	10	,	,	PUNCT
ejpam-180	109	11	ẋ	ẋ	PROPN
ejpam-180	109	12	(	(	PUNCT
ejpam-180	109	13	t	t	PROPN
ejpam-180	109	14	)	)	PUNCT
ejpam-180	109	15	,	,	PUNCT
ejpam-180	109	16	ẍ	ẍ	X
ejpam-180	109	17	(	(	PUNCT
ejpam-180	109	18	t	t	PROPN
ejpam-180	109	19	)	)	PUNCT
ejpam-180	109	20	)	)	PUNCT
ejpam-180	110	1	d	d	X
ejpam-180	110	2	t	t	PROPN
ejpam-180	110	3	+	+	CCONJ
ejpam-180	110	4	�	�	PROPN
ejpam-180	110	5	x	x	SYM
ejpam-180	110	6	(	(	PUNCT
ejpam-180	110	7	t	t	PROPN
ejpam-180	110	8	)	)	PUNCT
ejpam-180	110	9	t	t	PROPN
ejpam-180	110	10	b	b	PROPN
ejpam-180	110	11	(	(	PUNCT
ejpam-180	110	12	t	t	PROPN
ejpam-180	110	13	)	)	PUNCT
ejpam-180	110	14	x	x	X
ejpam-180	110	15	(	(	PUNCT
ejpam-180	110	16	t	t	PROPN
ejpam-180	110	17	)	)	PUNCT
ejpam-180	110	18	�	�	PROPN
ejpam-180	110	19	1	1	NUM
ejpam-180	110	20	2	2	NUM
ejpam-180	110	21	�	�	PROPN
ejpam-180	110	22	d	d	PROPN
ejpam-180	110	23	t	t	PROPN
ejpam-180	110	24	≤	≤	NUM
ejpam-180	110	25	∫	∫	PROPN
ejpam-180	111	1	i	i	PRON
ejpam-180	111	2	�	�	PROPN
ejpam-180	112	1	f	f	VERB
ejpam-180	113	1	i	i	PRON
ejpam-180	113	2	�	�	PROPN
ejpam-180	113	3	t	t	PROPN
ejpam-180	113	4	,	,	PUNCT
ejpam-180	113	5	x̄(t	x̄(t	PROPN
ejpam-180	113	6	)	)	PUNCT
ejpam-180	113	7	,	,	PUNCT
ejpam-180	113	8	˙̄x(t	˙̄x(t	NOUN
ejpam-180	113	9	)	)	PUNCT
ejpam-180	113	10	,	,	PUNCT
ejpam-180	113	11	¨̄x(t	¨̄x(t	NOUN
ejpam-180	113	12	)	)	PUNCT
ejpam-180	113	13	�	�	PROPN
ejpam-180	113	14	d	d	PROPN
ejpam-180	113	15	t	t	PROPN
ejpam-180	113	16	+	+	CCONJ
ejpam-180	113	17	�	�	PROPN
ejpam-180	113	18	x̄(t)t	x̄(t)t	PROPN
ejpam-180	113	19	b(t	b(t	PROPN
ejpam-180	113	20	)	)	PUNCT
ejpam-180	113	21	x̄(t	x̄(t	SYM
ejpam-180	113	22	)	)	PUNCT
ejpam-180	113	23	�	�	NOUN
ejpam-180	113	24	1	1	NUM
ejpam-180	113	25	2	2	NUM
ejpam-180	113	26	�	�	PROPN
ejpam-180	113	27	d	d	PROPN
ejpam-180	113	28	t	t	PROPN
ejpam-180	113	29	,	,	PUNCT
ejpam-180	113	30	i	i	PROPN
ejpam-180	113	31	6=	6=	PROPN
ejpam-180	113	32	k	k	PROPN
ejpam-180	113	33	3	3	X
ejpam-180	113	34	.	.	PUNCT
ejpam-180	113	35	optimality	optimality	NOUN
ejpam-180	113	36	in	in	ADP
ejpam-180	113	37	this	this	DET
ejpam-180	113	38	section	section	NOUN
ejpam-180	113	39	,	,	PUNCT
ejpam-180	113	40	we	we	PRON
ejpam-180	113	41	give	give	VERB
ejpam-180	113	42	necessary	necessary	ADJ
ejpam-180	113	43	optimality	optimality	NOUN
ejpam-180	113	44	conditions	condition	NOUN
ejpam-180	113	45	for	for	ADP
ejpam-180	113	46	the	the	DET
ejpam-180	113	47	problem	problem	NOUN
ejpam-180	113	48	(	(	PUNCT
ejpam-180	113	49	pk	pk	NOUN
ejpam-180	113	50	(	(	PUNCT
ejpam-180	113	51	x̄	x̄	PROPN
ejpam-180	113	52	)	)	PUNCT
ejpam-180	113	53	)	)	PUNCT
ejpam-180	113	54	which	which	PRON
ejpam-180	113	55	are	be	AUX
ejpam-180	113	56	required	require	VERB
ejpam-180	113	57	to	to	PART
ejpam-180	113	58	establish	establish	VERB
ejpam-180	113	59	strong	strong	ADJ
ejpam-180	113	60	duality	duality	NOUN
ejpam-180	113	61	theorem	theorem	VERB
ejpam-180	113	62	for	for	ADP
ejpam-180	113	63	wolfe	wolfe	PROPN
ejpam-180	113	64	and	and	CCONJ
ejpam-180	113	65	mond	mond	PROPN
ejpam-180	113	66	-	-	PUNCT
ejpam-180	113	67	weir	weir	PROPN
ejpam-180	113	68	type	type	NOUN
ejpam-180	113	69	vector	vector	NOUN
ejpam-180	113	70	dual	dual	ADJ
ejpam-180	113	71	.	.	PUNCT
ejpam-180	114	1	in	in	ADP
ejpam-180	114	2	order	order	NOUN
ejpam-180	114	3	to	to	PART
ejpam-180	114	4	derive	derive	VERB
ejpam-180	114	5	optimality	optimality	NOUN
ejpam-180	114	6	conditions	condition	NOUN
ejpam-180	114	7	for	for	ADP
ejpam-180	114	8	(	(	PUNCT
ejpam-180	114	9	pk	pk	NOUN
ejpam-180	114	10	,	,	PUNCT
ejpam-180	114	11	(	(	PUNCT
ejpam-180	114	12	x̄	x̄	PROPN
ejpam-180	114	13	)	)	PUNCT
ejpam-180	114	14	)	)	PUNCT
ejpam-180	114	15	,	,	PUNCT
ejpam-180	114	16	we	we	PRON
ejpam-180	114	17	require	require	VERB
ejpam-180	114	18	the	the	DET
ejpam-180	114	19	following	follow	VERB
ejpam-180	114	20	lemma	lemma	PROPN
ejpam-180	114	21	3.1	3.1	NUM
ejpam-180	114	22	.	.	PUNCT
ejpam-180	115	1	lemma	lemma	PROPN
ejpam-180	115	2	3.1	3.1	NUM
ejpam-180	115	3	(	(	PUNCT
ejpam-180	115	4	[	[	X
ejpam-180	115	5	9	9	NUM
ejpam-180	115	6	]	]	NUM
ejpam-180	115	7	)	)	PUNCT
ejpam-180	115	8	.	.	PUNCT
ejpam-180	116	1	define	define	VERB
ejpam-180	116	2	a	a	DET
ejpam-180	116	3	function	function	NOUN
ejpam-180	116	4	h	h	NOUN
ejpam-180	116	5	:	:	PUNCT
ejpam-180	116	6	rn	rn	PROPN
ejpam-180	116	7	→	→	SYM
ejpam-180	116	8	r	r	NOUN
ejpam-180	116	9	by	by	ADP
ejpam-180	116	10	h(x	h(x	PROPN
ejpam-180	116	11	(	(	PUNCT
ejpam-180	116	12	t	t	PROPN
ejpam-180	116	13	)	)	PUNCT
ejpam-180	116	14	)	)	PUNCT
ejpam-180	117	1	=	=	SYM
ejpam-180	117	2	�	�	PROPN
ejpam-180	117	3	x̄	x̄	PROPN
ejpam-180	117	4	(	(	PUNCT
ejpam-180	117	5	t	t	PROPN
ejpam-180	117	6	)	)	PUNCT
ejpam-180	117	7	t	t	PROPN
ejpam-180	117	8	b	b	PROPN
ejpam-180	117	9	(	(	PUNCT
ejpam-180	117	10	t	t	PROPN
ejpam-180	117	11	)	)	PUNCT
ejpam-180	117	12	x̄	x̄	NOUN
ejpam-180	117	13	(	(	PUNCT
ejpam-180	117	14	t	t	PROPN
ejpam-180	117	15	)	)	PUNCT
ejpam-180	117	16	�	�	PROPN
ejpam-180	117	17	1	1	NUM
ejpam-180	117	18	2	2	NUM
ejpam-180	117	19	,	,	PUNCT
ejpam-180	117	20	where	where	SCONJ
ejpam-180	117	21	b	b	NOUN
ejpam-180	117	22	is	be	AUX
ejpam-180	117	23	a	a	DET
ejpam-180	117	24	symmetric	symmetric	ADJ
ejpam-180	117	25	positive	positive	ADJ
ejpam-180	117	26	semidefinite	semidefinite	NOUN
ejpam-180	117	27	n×	n×	PROPN
ejpam-180	117	28	n	n	NOUN
ejpam-180	117	29	matrix	matrix	NOUN
ejpam-180	117	30	and	and	CCONJ
ejpam-180	117	31	continuous	continuous	ADJ
ejpam-180	117	32	on	on	ADP
ejpam-180	117	33	i	i	PRON
ejpam-180	117	34	,	,	PUNCT
ejpam-180	117	35	then	then	ADV
ejpam-180	117	36	h	h	PROPN
ejpam-180	117	37	is	be	AUX
ejpam-180	117	38	i.	i.	PROPN
ejpam-180	117	39	husain	husain	PROPN
ejpam-180	117	40	,	,	PUNCT
ejpam-180	117	41	a.	a.	PROPN
ejpam-180	117	42	ahmed	ahmed	PROPN
ejpam-180	117	43	,	,	PUNCT
ejpam-180	117	44	and	and	CCONJ
ejpam-180	117	45	g.	g.	PROPN
ejpam-180	117	46	rumana	rumana	PROPN
ejpam-180	117	47	/	/	SYM
ejpam-180	117	48	eur	eur	PROPN
ejpam-180	117	49	.	.	PUNCT
ejpam-180	118	1	j.	j.	PROPN
ejpam-180	118	2	pure	pure	PROPN
ejpam-180	118	3	appl	appl	PROPN
ejpam-180	118	4	.	.	PROPN
ejpam-180	118	5	math	math	PROPN
ejpam-180	118	6	,	,	PUNCT
ejpam-180	118	7	2	2	NUM
ejpam-180	118	8	(	(	PUNCT
ejpam-180	118	9	2009	2009	NUM
ejpam-180	118	10	)	)	PUNCT
ejpam-180	118	11	,	,	PUNCT
ejpam-180	118	12	(	(	PUNCT
ejpam-180	118	13	372	372	NUM
ejpam-180	118	14	-	-	SYM
ejpam-180	118	15	400	400	NUM
ejpam-180	118	16	)	)	PUNCT
ejpam-180	118	17	378	378	NUM
ejpam-180	118	18	convex	convex	NOUN
ejpam-180	118	19	,	,	PUNCT
ejpam-180	118	20	and	and	CCONJ
ejpam-180	118	21	∂	∂	NUM
ejpam-180	118	22	h(x	h(x	PROPN
ejpam-180	118	23	(	(	PUNCT
ejpam-180	118	24	t	t	PROPN
ejpam-180	118	25	)	)	PUNCT
ejpam-180	118	26	)	)	PUNCT
ejpam-180	119	1	=	=	PUNCT
ejpam-180	119	2	¦	¦	PROPN
ejpam-180	119	3	b	b	PROPN
ejpam-180	119	4	(	(	PUNCT
ejpam-180	119	5	t	t	PROPN
ejpam-180	119	6	)	)	PUNCT
ejpam-180	119	7	z	z	PROPN
ejpam-180	119	8	(	(	PUNCT
ejpam-180	119	9	t	t	PROPN
ejpam-180	119	10	)	)	PUNCT
ejpam-180	119	11	:	:	PUNCT
ejpam-180	120	1	z	z	X
ejpam-180	120	2	(	(	PUNCT
ejpam-180	120	3	t	t	PROPN
ejpam-180	120	4	)	)	PUNCT
ejpam-180	120	5	t	t	PROPN
ejpam-180	120	6	b	b	PROPN
ejpam-180	120	7	(	(	PUNCT
ejpam-180	120	8	t)z	t)z	NOUN
ejpam-180	120	9	(	(	PUNCT
ejpam-180	120	10	t)≤	t)≤	NOUN
ejpam-180	120	11	1	1	NUM
ejpam-180	120	12	©	©	NOUN
ejpam-180	120	13	,	,	PUNCT
ejpam-180	120	14	where	where	SCONJ
ejpam-180	120	15	∂	∂	NUM
ejpam-180	120	16	h(x(t	h(x(t	NOUN
ejpam-180	120	17	)	)	PUNCT
ejpam-180	120	18	)	)	PUNCT
ejpam-180	120	19	is	be	AUX
ejpam-180	120	20	subgradient	subgradient	NOUN
ejpam-180	120	21	of	of	ADP
ejpam-180	120	22	h	h	NOUN
ejpam-180	120	23	at	at	ADP
ejpam-180	120	24	x(t	x(t	PROPN
ejpam-180	120	25	)	)	PUNCT
ejpam-180	120	26	.	.	PUNCT
ejpam-180	121	1	using	use	VERB
ejpam-180	121	2	the	the	DET
ejpam-180	121	3	analysis	analysis	NOUN
ejpam-180	121	4	in	in	ADP
ejpam-180	121	5	[	[	X
ejpam-180	121	6	10	10	NUM
ejpam-180	121	7	]	]	PUNCT
ejpam-180	121	8	and	and	CCONJ
ejpam-180	121	9	[	[	X
ejpam-180	121	10	6	6	NUM
ejpam-180	121	11	]	]	PUNCT
ejpam-180	121	12	,	,	PUNCT
ejpam-180	121	13	the	the	DET
ejpam-180	121	14	fritz	fritz	PROPN
ejpam-180	121	15	-	-	PUNCT
ejpam-180	121	16	john	john	PROPN
ejpam-180	121	17	optimality	optimality	NOUN
ejpam-180	121	18	conditions	condition	NOUN
ejpam-180	121	19	for	for	ADP
ejpam-180	121	20	(	(	PUNCT
ejpam-180	121	21	pk	pk	NOUN
ejpam-180	121	22	(	(	PUNCT
ejpam-180	121	23	x̄	x̄	PROPN
ejpam-180	121	24	)	)	PUNCT
ejpam-180	121	25	)	)	PUNCT
ejpam-180	121	26	can	can	AUX
ejpam-180	121	27	be	be	AUX
ejpam-180	121	28	given	give	VERB
ejpam-180	121	29	by	by	ADP
ejpam-180	121	30	the	the	DET
ejpam-180	121	31	following	follow	VERB
ejpam-180	121	32	theorem	theorem	PROPN
ejpam-180	121	33	.	.	PUNCT
ejpam-180	122	1	theorem	theorem	VERB
ejpam-180	122	2	3.1	3.1	NUM
ejpam-180	122	3	(	(	PUNCT
ejpam-180	122	4	fritz	fritz	PROPN
ejpam-180	122	5	-	-	PUNCT
ejpam-180	122	6	john	john	PROPN
ejpam-180	122	7	optimality	optimality	NOUN
ejpam-180	122	8	conditions	condition	NOUN
ejpam-180	122	9	)	)	PUNCT
ejpam-180	122	10	.	.	PUNCT
ejpam-180	123	1	if	if	SCONJ
ejpam-180	123	2	x̄	x̄	PRON
ejpam-180	123	3	is	be	AUX
ejpam-180	123	4	optimal	optimal	ADJ
ejpam-180	123	5	solution	solution	NOUN
ejpam-180	123	6	of	of	ADP
ejpam-180	123	7	(	(	PUNCT
ejpam-180	123	8	pk	pk	NOUN
ejpam-180	123	9	(	(	PUNCT
ejpam-180	123	10	x̄	x̄	PROPN
ejpam-180	123	11	)	)	PUNCT
ejpam-180	123	12	)	)	PUNCT
ejpam-180	124	1	there	there	PRON
ejpam-180	124	2	exist	exist	VERB
ejpam-180	124	3	scalars	scalar	NOUN
ejpam-180	124	4	τ1,τ2	τ1,τ2	PROPN
ejpam-180	124	5	,	,	PUNCT
ejpam-180	124	6	.	.	PUNCT
ejpam-180	124	7	.	.	PUNCT
ejpam-180	124	8	.	.	PUNCT
ejpam-180	125	1	,	,	PUNCT
ejpam-180	125	2	τp	τp	NOUN
ejpam-180	125	3	,	,	PUNCT
ejpam-180	125	4	piecewise	piecewise	NOUN
ejpam-180	125	5	smooth	smooth	NOUN
ejpam-180	125	6	z	z	NOUN
ejpam-180	126	1	i	i	PRON
ejpam-180	126	2	:	:	PUNCT
ejpam-180	126	3	i	i	PRON
ejpam-180	126	4	→	→	SYM
ejpam-180	126	5	r	r	X
ejpam-180	126	6	,	,	PUNCT
ejpam-180	126	7	i	i	PRON
ejpam-180	126	8	∈	∈	PROPN
ejpam-180	126	9	p	p	X
ejpam-180	126	10	,	,	PUNCT
ejpam-180	126	11	such	such	ADJ
ejpam-180	126	12	that	that	SCONJ
ejpam-180	126	13	p	p	NOUN
ejpam-180	126	14	∑	∑	PUNCT
ejpam-180	126	15	i=1	i=1	PROPN
ejpam-180	126	16	τ̄i	τ̄i	PROPN
ejpam-180	126	17	�	�	PROPN
ejpam-180	126	18	f	f	PROPN
ejpam-180	126	19	i	i	PROPN
ejpam-180	126	20	x	x	PROPN
ejpam-180	126	21	�	�	PROPN
ejpam-180	126	22	t	t	PROPN
ejpam-180	126	23	,	,	PUNCT
ejpam-180	126	24	x̄	x̄	PROPN
ejpam-180	126	25	,	,	PUNCT
ejpam-180	126	26	˙̄x	˙̄x	PUNCT
ejpam-180	126	27	,	,	PUNCT
ejpam-180	126	28	¨̄x	¨̄x	VERB
ejpam-180	126	29	�	�	PROPN
ejpam-180	126	30	−	−	PROPN
ejpam-180	127	1	d	d	X
ejpam-180	127	2	f	f	X
ejpam-180	128	1	i	i	PRON
ejpam-180	128	2	ẋ	ẋ	PROPN
ejpam-180	128	3	�	�	PROPN
ejpam-180	128	4	t	t	PROPN
ejpam-180	128	5	,	,	PUNCT
ejpam-180	128	6	x̄	x̄	PROPN
ejpam-180	128	7	,	,	PUNCT
ejpam-180	128	8	˙̄x	˙̄x	PUNCT
ejpam-180	128	9	,	,	PUNCT
ejpam-180	128	10	¨̄x	¨̄x	PRON
ejpam-180	128	11	�	�	PROPN
ejpam-180	128	12	+	+	CCONJ
ejpam-180	128	13	d2	d2	PROPN
ejpam-180	128	14	f	f	PROPN
ejpam-180	129	1	i	i	PROPN
ejpam-180	129	2	ẍ	ẍ	PROPN
ejpam-180	129	3	�	�	PROPN
ejpam-180	129	4	t	t	PROPN
ejpam-180	129	5	,	,	PUNCT
ejpam-180	129	6	x̄	x̄	PROPN
ejpam-180	129	7	,	,	PUNCT
ejpam-180	129	8	˙̄x	˙̄x	PUNCT
ejpam-180	129	9	,	,	PUNCT
ejpam-180	129	10	¨̄x	¨̄x	VERB
ejpam-180	129	11	�	�	PROPN
ejpam-180	130	1	+	+	CCONJ
ejpam-180	131	1	b	b	NOUN
ejpam-180	132	1	i	i	PROPN
ejpam-180	132	2	(	(	PUNCT
ejpam-180	132	3	t	t	PROPN
ejpam-180	132	4	)	)	PUNCT
ejpam-180	132	5	z̄	z̄	PROPN
ejpam-180	133	1	i	i	PROPN
ejpam-180	133	2	(	(	PUNCT
ejpam-180	133	3	t	t	PROPN
ejpam-180	133	4	)	)	PUNCT
ejpam-180	133	5	�	�	PROPN
ejpam-180	133	6	+	+	CCONJ
ejpam-180	133	7	m	m	VERB
ejpam-180	133	8	∑	∑	ADV
ejpam-180	133	9	j=1	j=1	PROPN
ejpam-180	133	10	ȳ	ȳ	PROPN
ejpam-180	133	11	j	j	PROPN
ejpam-180	133	12	(	(	PUNCT
ejpam-180	133	13	t	t	PROPN
ejpam-180	133	14	)	)	PUNCT
ejpam-180	133	15	�	�	PROPN
ejpam-180	134	1	g	g	PROPN
ejpam-180	134	2	j	j	PROPN
ejpam-180	134	3	x	x	SYM
ejpam-180	134	4	�	�	PROPN
ejpam-180	134	5	t	t	PROPN
ejpam-180	134	6	,	,	PUNCT
ejpam-180	134	7	x̄	x̄	PROPN
ejpam-180	134	8	,	,	PUNCT
ejpam-180	134	9	˙̄x	˙̄x	PUNCT
ejpam-180	134	10	,	,	PUNCT
ejpam-180	134	11	¨̄x	¨̄x	PRON
ejpam-180	134	12	�	�	PROPN
ejpam-180	134	13	−	−	PROPN
ejpam-180	134	14	dg	dg	PROPN
ejpam-180	134	15	j	j	PROPN
ejpam-180	134	16	ẋ	ẋ	PROPN
ejpam-180	134	17	�	�	PROPN
ejpam-180	134	18	t	t	PROPN
ejpam-180	134	19	,	,	PUNCT
ejpam-180	134	20	x̄	x̄	PROPN
ejpam-180	134	21	,	,	PUNCT
ejpam-180	134	22	˙̄x	˙̄x	PUNCT
ejpam-180	134	23	,	,	PUNCT
ejpam-180	134	24	¨̄x	¨̄x	PRON
ejpam-180	134	25	�	�	PROPN
ejpam-180	134	26	+	+	CCONJ
ejpam-180	134	27	d2	d2	PROPN
ejpam-180	134	28	g	g	PROPN
ejpam-180	134	29	j	j	PROPN
ejpam-180	134	30	ẍ	ẍ	PROPN
ejpam-180	134	31	�	�	PROPN
ejpam-180	134	32	t	t	PROPN
ejpam-180	134	33	,	,	PUNCT
ejpam-180	134	34	x̄	x̄	PROPN
ejpam-180	134	35	,	,	PUNCT
ejpam-180	134	36	˙̄x	˙̄x	PUNCT
ejpam-180	134	37	,	,	PUNCT
ejpam-180	134	38	¨̄x	¨̄x	PRON
ejpam-180	134	39	�	�	PROPN
ejpam-180	134	40	�	�	PROPN
ejpam-180	134	41	=	=	SYM
ejpam-180	134	42	0	0	NUM
ejpam-180	134	43	,	,	PUNCT
ejpam-180	134	44	t	t	PROPN
ejpam-180	134	45	∈	∈	PROPN
ejpam-180	135	1	i	i	PRON
ejpam-180	135	2	y	y	PROPN
ejpam-180	135	3	(	(	PUNCT
ejpam-180	135	4	t	t	PROPN
ejpam-180	135	5	)	)	PUNCT
ejpam-180	135	6	t	t	PROPN
ejpam-180	135	7	g	g	PROPN
ejpam-180	135	8	�	�	PROPN
ejpam-180	135	9	t	t	PROPN
ejpam-180	135	10	,	,	PUNCT
ejpam-180	135	11	x̄	x̄	PROPN
ejpam-180	135	12	,	,	PUNCT
ejpam-180	135	13	˙̄x	˙̄x	PUNCT
ejpam-180	135	14	,	,	PUNCT
ejpam-180	135	15	¨̄x	¨̄x	X
ejpam-180	135	16	�	�	PROPN
ejpam-180	135	17	=	=	SYM
ejpam-180	135	18	0	0	NUM
ejpam-180	135	19	,	,	PUNCT
ejpam-180	135	20	t	t	PROPN
ejpam-180	136	1	∈	∈	PROPN
ejpam-180	137	1	i	i	PRON
ejpam-180	137	2	x̄	x̄	X
ejpam-180	137	3	(	(	PUNCT
ejpam-180	137	4	t	t	PROPN
ejpam-180	137	5	)	)	PUNCT
ejpam-180	137	6	t	t	PROPN
ejpam-180	137	7	b	b	PROPN
ejpam-180	137	8	i	i	PROPN
ejpam-180	137	9	(	(	PUNCT
ejpam-180	137	10	t	t	PROPN
ejpam-180	137	11	)	)	PUNCT
ejpam-180	137	12	z̄	z̄	PROPN
ejpam-180	137	13	i	i	PROPN
ejpam-180	137	14	(	(	PUNCT
ejpam-180	137	15	t	t	NOUN
ejpam-180	137	16	)	)	PUNCT
ejpam-180	137	17	=	=	SYM
ejpam-180	137	18	�	�	PROPN
ejpam-180	137	19	x̄	x̄	PROPN
ejpam-180	137	20	(	(	PUNCT
ejpam-180	137	21	t	t	PROPN
ejpam-180	137	22	)	)	PUNCT
ejpam-180	137	23	t	t	PROPN
ejpam-180	137	24	b	b	PROPN
ejpam-180	137	25	i	i	PROPN
ejpam-180	137	26	(	(	PUNCT
ejpam-180	137	27	t	t	PROPN
ejpam-180	137	28	)	)	PUNCT
ejpam-180	137	29	x̄	x̄	NOUN
ejpam-180	137	30	(	(	PUNCT
ejpam-180	137	31	t	t	PROPN
ejpam-180	137	32	)	)	PUNCT
ejpam-180	137	33	�	�	PROPN
ejpam-180	137	34	1	1	NUM
ejpam-180	137	35	2	2	NUM
ejpam-180	137	36	,	,	PUNCT
ejpam-180	137	37	i	i	PRON
ejpam-180	137	38	∈	∈	PROPN
ejpam-180	137	39	p	p	X
ejpam-180	137	40	,	,	PUNCT
ejpam-180	137	41	t	t	PROPN
ejpam-180	137	42	∈	∈	PROPN
ejpam-180	138	1	i	i	PRON
ejpam-180	138	2	z̄	z̄	VERB
ejpam-180	138	3	i	i	PRON
ejpam-180	138	4	(	(	PUNCT
ejpam-180	138	5	t	t	PROPN
ejpam-180	138	6	)	)	PUNCT
ejpam-180	138	7	t	t	PROPN
ejpam-180	139	1	b	b	PROPN
ejpam-180	139	2	i	i	PROPN
ejpam-180	139	3	(	(	PUNCT
ejpam-180	139	4	t	t	PROPN
ejpam-180	139	5	)	)	PUNCT
ejpam-180	139	6	z̄	z̄	PROPN
ejpam-180	140	1	i	i	PRON
ejpam-180	140	2	(	(	PUNCT
ejpam-180	140	3	t)≤	t)≤	NOUN
ejpam-180	140	4	1	1	NUM
ejpam-180	140	5	,	,	PUNCT
ejpam-180	140	6	�	�	PROPN
ejpam-180	140	7	τ̄	τ̄	PROPN
ejpam-180	140	8	,	,	PUNCT
ejpam-180	140	9	ȳ	ȳ	PROPN
ejpam-180	140	10	(	(	PUNCT
ejpam-180	140	11	t	t	PROPN
ejpam-180	140	12	)	)	PUNCT
ejpam-180	140	13	�	�	PROPN
ejpam-180	140	14	≧	≧	X
ejpam-180	140	15	0	0	NUM
ejpam-180	140	16	,	,	PUNCT
ejpam-180	140	17	�	�	PROPN
ejpam-180	140	18	τ̄	τ̄	PROPN
ejpam-180	140	19	,	,	PUNCT
ejpam-180	140	20	ȳ	ȳ	PROPN
ejpam-180	140	21	(	(	PUNCT
ejpam-180	140	22	t	t	PROPN
ejpam-180	140	23	)	)	PUNCT
ejpam-180	140	24	�	�	PROPN
ejpam-180	140	25	6=	6=	ADP
ejpam-180	140	26	0	0	NUM
ejpam-180	140	27	,	,	PUNCT
ejpam-180	140	28	t	t	PROPN
ejpam-180	140	29	∈	∈	PROPN
ejpam-180	140	30	i	i	PRON
ejpam-180	140	31	proof	proof	VERB
ejpam-180	140	32	.	.	PUNCT
ejpam-180	141	1	the	the	DET
ejpam-180	141	2	proof	proof	NOUN
ejpam-180	141	3	of	of	ADP
ejpam-180	141	4	the	the	DET
ejpam-180	141	5	theorem	theorem	NOUN
ejpam-180	141	6	easily	easily	ADV
ejpam-180	141	7	follows	follow	VERB
ejpam-180	141	8	on	on	ADP
ejpam-180	141	9	the	the	DET
ejpam-180	141	10	line	line	NOUN
ejpam-180	141	11	of	of	ADP
ejpam-180	141	12	analysis	analysis	NOUN
ejpam-180	141	13	in	in	ADP
ejpam-180	141	14	[	[	X
ejpam-180	141	15	7	7	NUM
ejpam-180	141	16	]	]	PUNCT
ejpam-180	141	17	and	and	CCONJ
ejpam-180	141	18	[	[	X
ejpam-180	141	19	3	3	NUM
ejpam-180	141	20	]	]	PUNCT
ejpam-180	141	21	.	.	PUNCT
ejpam-180	142	1	hence	hence	ADV
ejpam-180	142	2	it	it	PRON
ejpam-180	142	3	is	be	AUX
ejpam-180	142	4	omitted	omit	VERB
ejpam-180	142	5	for	for	ADP
ejpam-180	142	6	brevity	brevity	NOUN
ejpam-180	142	7	.	.	PUNCT
ejpam-180	143	1	4	4	X
ejpam-180	143	2	.	.	X
ejpam-180	143	3	wolfe	wolfe	PROPN
ejpam-180	143	4	type	type	PROPN
ejpam-180	143	5	vector	vector	NOUN
ejpam-180	143	6	duality	duality	NOUN
ejpam-180	143	7	in	in	ADP
ejpam-180	143	8	this	this	DET
ejpam-180	143	9	section	section	NOUN
ejpam-180	143	10	,	,	PUNCT
ejpam-180	143	11	we	we	PRON
ejpam-180	143	12	present	present	VERB
ejpam-180	143	13	wolfe	wolfe	PROPN
ejpam-180	143	14	type	type	PROPN
ejpam-180	143	15	vector	vector	NOUN
ejpam-180	143	16	dual	dual	ADJ
ejpam-180	143	17	to	to	ADP
ejpam-180	143	18	(	(	PUNCT
ejpam-180	143	19	vp	vp	NOUN
ejpam-180	143	20	)	)	PUNCT
ejpam-180	143	21	and	and	CCONJ
ejpam-180	143	22	establish	establish	VERB
ejpam-180	143	23	various	various	ADJ
ejpam-180	143	24	duality	duality	NOUN
ejpam-180	143	25	results	result	NOUN
ejpam-180	143	26	.	.	PUNCT
ejpam-180	144	1	(	(	PUNCT
ejpam-180	144	2	mwd	mwd	PROPN
ejpam-180	144	3	)	)	PUNCT
ejpam-180	144	4	:	:	PUNCT
ejpam-180	144	5	maximize	maximize	VERB
ejpam-180	144	6	�	�	PROPN
ejpam-180	144	7	∫	∫	PROPN
ejpam-180	144	8	i	i	PROPN
ejpam-180	144	9	�	�	PROPN
ejpam-180	145	1	f	f	PROPN
ejpam-180	145	2	1	1	NUM
ejpam-180	145	3	(	(	PUNCT
ejpam-180	145	4	t	t	PROPN
ejpam-180	145	5	,	,	PUNCT
ejpam-180	145	6	u	u	NOUN
ejpam-180	145	7	,	,	PUNCT
ejpam-180	145	8	u̇	u̇	PROPN
ejpam-180	145	9	,	,	PUNCT
ejpam-180	145	10	ü	ü	PRON
ejpam-180	145	11	)	)	PUNCT
ejpam-180	146	1	+	+	NUM
ejpam-180	146	2	u	u	SYM
ejpam-180	146	3	(	(	PUNCT
ejpam-180	146	4	t	t	PROPN
ejpam-180	146	5	)	)	PUNCT
ejpam-180	146	6	t	t	PROPN
ejpam-180	146	7	b1	b1	PROPN
ejpam-180	146	8	(	(	PUNCT
ejpam-180	146	9	t	t	NOUN
ejpam-180	146	10	)	)	PUNCT
ejpam-180	146	11	z1	z1	PROPN
ejpam-180	146	12	(	(	PUNCT
ejpam-180	146	13	t	t	PROPN
ejpam-180	146	14	)	)	PUNCT
ejpam-180	147	1	+	+	CCONJ
ejpam-180	147	2	y	y	PROPN
ejpam-180	147	3	(	(	PUNCT
ejpam-180	147	4	t	t	PROPN
ejpam-180	147	5	)	)	PUNCT
ejpam-180	147	6	t	t	PROPN
ejpam-180	147	7	g	g	PROPN
ejpam-180	147	8	(	(	PUNCT
ejpam-180	147	9	t	t	PROPN
ejpam-180	147	10	,	,	PUNCT
ejpam-180	147	11	u	u	NOUN
ejpam-180	147	12	,	,	PUNCT
ejpam-180	147	13	u̇	u̇	PROPN
ejpam-180	147	14	,	,	PUNCT
ejpam-180	147	15	ü	ü	NOUN
ejpam-180	147	16	)	)	PUNCT
ejpam-180	147	17	�	�	PROPN
ejpam-180	148	1	d	d	PROPN
ejpam-180	148	2	t	t	PROPN
ejpam-180	148	3	i.	i.	PROPN
ejpam-180	148	4	husain	husain	PROPN
ejpam-180	148	5	,	,	PUNCT
ejpam-180	148	6	a.	a.	PROPN
ejpam-180	148	7	ahmed	ahmed	PROPN
ejpam-180	148	8	,	,	PUNCT
ejpam-180	148	9	and	and	CCONJ
ejpam-180	148	10	g.	g.	PROPN
ejpam-180	148	11	rumana	rumana	PROPN
ejpam-180	148	12	/	/	SYM
ejpam-180	148	13	eur	eur	PROPN
ejpam-180	148	14	.	.	PUNCT
ejpam-180	149	1	j.	j.	PROPN
ejpam-180	149	2	pure	pure	PROPN
ejpam-180	149	3	appl	appl	PROPN
ejpam-180	149	4	.	.	PROPN
ejpam-180	149	5	math	math	PROPN
ejpam-180	149	6	,	,	PUNCT
ejpam-180	149	7	2	2	NUM
ejpam-180	149	8	(	(	PUNCT
ejpam-180	149	9	2009	2009	NUM
ejpam-180	149	10	)	)	PUNCT
ejpam-180	149	11	,	,	PUNCT
ejpam-180	149	12	(	(	PUNCT
ejpam-180	149	13	372	372	NUM
ejpam-180	149	14	-	-	SYM
ejpam-180	149	15	400	400	NUM
ejpam-180	149	16	)	)	PUNCT
ejpam-180	149	17	379	379	NUM
ejpam-180	149	18	,	,	PUNCT
ejpam-180	149	19	.	.	PUNCT
ejpam-180	149	20	.	.	PUNCT
ejpam-180	149	21	.	.	PUNCT
ejpam-180	150	1	,	,	PUNCT
ejpam-180	150	2	∫	∫	PROPN
ejpam-180	151	1	i	i	PRON
ejpam-180	151	2	�	�	PROPN
ejpam-180	152	1	f	f	PROPN
ejpam-180	152	2	p	p	PROPN
ejpam-180	152	3	(	(	PUNCT
ejpam-180	152	4	t	t	PROPN
ejpam-180	152	5	,	,	PUNCT
ejpam-180	152	6	u	u	NOUN
ejpam-180	152	7	,	,	PUNCT
ejpam-180	152	8	u̇	u̇	PROPN
ejpam-180	152	9	,	,	PUNCT
ejpam-180	152	10	ü	ü	PRON
ejpam-180	152	11	)	)	PUNCT
ejpam-180	153	1	+	+	NUM
ejpam-180	153	2	u	u	SYM
ejpam-180	153	3	(	(	PUNCT
ejpam-180	153	4	t	t	PROPN
ejpam-180	153	5	)	)	PUNCT
ejpam-180	153	6	t	t	PROPN
ejpam-180	153	7	bp	bp	PROPN
ejpam-180	153	8	(	(	PUNCT
ejpam-180	153	9	t	t	PROPN
ejpam-180	153	10	)	)	PUNCT
ejpam-180	153	11	zp	zp	PROPN
ejpam-180	153	12	(	(	PUNCT
ejpam-180	153	13	t	t	PROPN
ejpam-180	153	14	)	)	PUNCT
ejpam-180	154	1	+	+	CCONJ
ejpam-180	154	2	y	y	PROPN
ejpam-180	154	3	(	(	PUNCT
ejpam-180	154	4	t	t	PROPN
ejpam-180	154	5	)	)	PUNCT
ejpam-180	154	6	t	t	PROPN
ejpam-180	154	7	(	(	PUNCT
ejpam-180	154	8	t	t	PROPN
ejpam-180	154	9	,	,	PUNCT
ejpam-180	154	10	u	u	NOUN
ejpam-180	154	11	,	,	PUNCT
ejpam-180	154	12	u̇	u̇	PROPN
ejpam-180	154	13	,	,	PUNCT
ejpam-180	154	14	ü	ü	NOUN
ejpam-180	154	15	)	)	PUNCT
ejpam-180	154	16	�	�	PROPN
ejpam-180	154	17	d	d	PROPN
ejpam-180	154	18	t	t	PROPN
ejpam-180	154	19	�	�	PROPN
ejpam-180	154	20	subject	subject	ADJ
ejpam-180	154	21	to	to	ADP
ejpam-180	154	22	u	u	NOUN
ejpam-180	154	23	(	(	PUNCT
ejpam-180	154	24	a	a	NOUN
ejpam-180	154	25	)	)	PUNCT
ejpam-180	154	26	=	=	SYM
ejpam-180	155	1	0=	0=	NUM
ejpam-180	155	2	u	u	NOUN
ejpam-180	155	3	(	(	PUNCT
ejpam-180	155	4	b	b	NOUN
ejpam-180	155	5	)	)	PUNCT
ejpam-180	155	6	(	(	PUNCT
ejpam-180	155	7	4.1	4.1	NUM
ejpam-180	155	8	)	)	PUNCT
ejpam-180	155	9	u̇	u̇	NOUN
ejpam-180	155	10	(	(	PUNCT
ejpam-180	155	11	a	a	X
ejpam-180	155	12	)	)	PUNCT
ejpam-180	155	13	=	=	SYM
ejpam-180	155	14	0=	0=	NUM
ejpam-180	156	1	u̇	u̇	PROPN
ejpam-180	156	2	(	(	PUNCT
ejpam-180	156	3	b	b	NOUN
ejpam-180	156	4	)	)	PUNCT
ejpam-180	156	5	(	(	PUNCT
ejpam-180	156	6	4.2	4.2	NUM
ejpam-180	156	7	)	)	PUNCT
ejpam-180	156	8	p	p	NOUN
ejpam-180	156	9	∑	∑	PUNCT
ejpam-180	156	10	i=1	i=1	PROPN
ejpam-180	156	11	λi	λi	PROPN
ejpam-180	156	12	�	�	PROPN
ejpam-180	157	1	f	f	PROPN
ejpam-180	158	1	i	i	PRON
ejpam-180	158	2	u	u	PROPN
ejpam-180	158	3	(	(	PUNCT
ejpam-180	158	4	t	t	PROPN
ejpam-180	158	5	,	,	PUNCT
ejpam-180	158	6	u	u	NOUN
ejpam-180	158	7	,	,	PUNCT
ejpam-180	158	8	u̇	u̇	PROPN
ejpam-180	158	9	,	,	PUNCT
ejpam-180	158	10	ü	ü	NUM
ejpam-180	158	11	)	)	PUNCT
ejpam-180	159	1	d	d	NOUN
ejpam-180	159	2	t	t	PROPN
ejpam-180	159	3	+	+	CCONJ
ejpam-180	159	4	b	b	NOUN
ejpam-180	160	1	i	i	PRON
ejpam-180	160	2	(	(	PUNCT
ejpam-180	160	3	t)z	t)z	NOUN
ejpam-180	160	4	i	i	PRON
ejpam-180	160	5	(	(	PUNCT
ejpam-180	160	6	t)+	t)+	NOUN
ejpam-180	160	7	y	y	PROPN
ejpam-180	160	8	(	(	PUNCT
ejpam-180	160	9	t	t	PROPN
ejpam-180	160	10	)	)	PUNCT
ejpam-180	160	11	t	t	PROPN
ejpam-180	160	12	gu	gu	PROPN
ejpam-180	160	13	(	(	PUNCT
ejpam-180	160	14	t	t	PROPN
ejpam-180	160	15	,	,	PUNCT
ejpam-180	160	16	u	u	NOUN
ejpam-180	160	17	,	,	PUNCT
ejpam-180	160	18	u̇	u̇	PROPN
ejpam-180	160	19	,	,	PUNCT
ejpam-180	160	20	ü	ü	NOUN
ejpam-180	160	21	)	)	PUNCT
ejpam-180	160	22	�	�	PROPN
ejpam-180	160	23	−	−	PROPN
ejpam-180	160	24	d	d	PROPN
ejpam-180	160	25	�	�	PROPN
ejpam-180	160	26	λt	λt	ADP
ejpam-180	160	27	fu̇	fu̇	PROPN
ejpam-180	160	28	(	(	PUNCT
ejpam-180	160	29	t	t	PROPN
ejpam-180	160	30	,	,	PUNCT
ejpam-180	160	31	u	u	NOUN
ejpam-180	160	32	,	,	PUNCT
ejpam-180	160	33	u̇	u̇	PROPN
ejpam-180	160	34	,	,	PUNCT
ejpam-180	160	35	ü	ü	PRON
ejpam-180	160	36	)	)	PUNCT
ejpam-180	161	1	+	+	CCONJ
ejpam-180	161	2	y	y	PROPN
ejpam-180	161	3	(	(	PUNCT
ejpam-180	161	4	t	t	PROPN
ejpam-180	161	5	)	)	PUNCT
ejpam-180	161	6	t	t	NOUN
ejpam-180	161	7	gu̇	gu̇	PROPN
ejpam-180	161	8	(	(	PUNCT
ejpam-180	161	9	t	t	PROPN
ejpam-180	161	10	,	,	PUNCT
ejpam-180	161	11	u	u	NOUN
ejpam-180	161	12	,	,	PUNCT
ejpam-180	161	13	u̇	u̇	PROPN
ejpam-180	161	14	,	,	PUNCT
ejpam-180	161	15	ü	ü	NOUN
ejpam-180	161	16	)	)	PUNCT
ejpam-180	161	17	�	�	PROPN
ejpam-180	161	18	+	+	CCONJ
ejpam-180	161	19	d2	d2	PROPN
ejpam-180	161	20	�	�	PROPN
ejpam-180	161	21	λt	λt	ADP
ejpam-180	161	22	fü	fü	X
ejpam-180	161	23	(	(	PUNCT
ejpam-180	161	24	t	t	PROPN
ejpam-180	161	25	,	,	PUNCT
ejpam-180	161	26	u	u	NOUN
ejpam-180	161	27	,	,	PUNCT
ejpam-180	161	28	u̇	u̇	PROPN
ejpam-180	161	29	,	,	PUNCT
ejpam-180	161	30	ü	ü	PRON
ejpam-180	161	31	)	)	PUNCT
ejpam-180	162	1	+	+	CCONJ
ejpam-180	162	2	y	y	PROPN
ejpam-180	162	3	(	(	PUNCT
ejpam-180	162	4	t	t	PROPN
ejpam-180	162	5	)	)	PUNCT
ejpam-180	162	6	t	t	PROPN
ejpam-180	162	7	gü	gü	PROPN
ejpam-180	162	8	(	(	PUNCT
ejpam-180	162	9	t	t	PROPN
ejpam-180	162	10	,	,	PUNCT
ejpam-180	162	11	u	u	NOUN
ejpam-180	162	12	,	,	PUNCT
ejpam-180	162	13	u̇	u̇	PROPN
ejpam-180	162	14	,	,	PUNCT
ejpam-180	162	15	ü	ü	NOUN
ejpam-180	162	16	)	)	PUNCT
ejpam-180	162	17	�	�	PROPN
ejpam-180	162	18	=	=	SYM
ejpam-180	162	19	0	0	PROPN
ejpam-180	162	20	,	,	PUNCT
ejpam-180	162	21	t	t	PROPN
ejpam-180	162	22	∈	∈	PROPN
ejpam-180	163	1	i	i	PRON
ejpam-180	163	2	(	(	PUNCT
ejpam-180	163	3	4.3	4.3	NUM
ejpam-180	163	4	)	)	PUNCT
ejpam-180	163	5	z̄	z̄	PROPN
ejpam-180	163	6	i	i	PROPN
ejpam-180	163	7	(	(	PUNCT
ejpam-180	163	8	t	t	PROPN
ejpam-180	163	9	)	)	PUNCT
ejpam-180	163	10	t	t	PROPN
ejpam-180	163	11	b	b	PROPN
ejpam-180	163	12	i	i	PROPN
ejpam-180	163	13	(	(	PUNCT
ejpam-180	163	14	t	t	PROPN
ejpam-180	163	15	)	)	PUNCT
ejpam-180	163	16	z̄	z̄	PROPN
ejpam-180	164	1	i	i	PRON
ejpam-180	164	2	(	(	PUNCT
ejpam-180	164	3	t)≦	t)≦	X
ejpam-180	164	4	1	1	NUM
ejpam-180	164	5	,	,	PUNCT
ejpam-180	164	6	t	t	PROPN
ejpam-180	164	7	∈	∈	PROPN
ejpam-180	165	1	i	i	PRON
ejpam-180	165	2	,	,	PUNCT
ejpam-180	165	3	i	i	PROPN
ejpam-180	165	4	∈	∈	VERB
ejpam-180	165	5	p	p	X
ejpam-180	165	6	(	(	PUNCT
ejpam-180	165	7	4.4	4.4	NUM
ejpam-180	165	8	)	)	PUNCT
ejpam-180	165	9	y	y	PROPN
ejpam-180	165	10	(	(	PUNCT
ejpam-180	165	11	t)≧	t)≧	NOUN
ejpam-180	165	12	0	0	NUM
ejpam-180	165	13	,	,	PUNCT
ejpam-180	165	14	t	t	PROPN
ejpam-180	165	15	∈	∈	PROPN
ejpam-180	166	1	i	i	PRON
ejpam-180	166	2	(	(	PUNCT
ejpam-180	166	3	4.5	4.5	NUM
ejpam-180	166	4	)	)	PUNCT
ejpam-180	166	5	λ	λ	X
ejpam-180	166	6	>	>	X
ejpam-180	166	7	0	0	PROPN
ejpam-180	166	8	,	,	PUNCT
ejpam-180	166	9	λt	λt	ADP
ejpam-180	166	10	e	e	NOUN
ejpam-180	166	11	=	=	SYM
ejpam-180	166	12	1	1	NUM
ejpam-180	166	13	(	(	PUNCT
ejpam-180	166	14	4.6	4.6	NUM
ejpam-180	166	15	)	)	PUNCT
ejpam-180	166	16	theorem	theorem	VERB
ejpam-180	166	17	4.1	4.1	NUM
ejpam-180	166	18	(	(	PUNCT
ejpam-180	166	19	weak	weak	ADJ
ejpam-180	166	20	duality	duality	NOUN
ejpam-180	166	21	)	)	PUNCT
ejpam-180	166	22	.	.	PUNCT
ejpam-180	167	1	let	let	VERB
ejpam-180	167	2	x̄	x̄	PRON
ejpam-180	167	3	be	be	AUX
ejpam-180	167	4	feasible	feasible	ADJ
ejpam-180	167	5	for	for	ADP
ejpam-180	167	6	(	(	PUNCT
ejpam-180	167	7	vp	vp	NOUN
ejpam-180	167	8	)	)	PUNCT
ejpam-180	167	9	and	and	CCONJ
ejpam-180	167	10	(	(	PUNCT
ejpam-180	167	11	u	u	NOUN
ejpam-180	167	12	,	,	PUNCT
ejpam-180	167	13	λ	λ	PROPN
ejpam-180	167	14	,	,	PUNCT
ejpam-180	167	15	z1	z1	NOUN
ejpam-180	167	16	,	,	PUNCT
ejpam-180	167	17	.	.	PUNCT
ejpam-180	167	18	.	.	PUNCT
ejpam-180	168	1	.	.	PUNCT
ejpam-180	169	1	,	,	PUNCT
ejpam-180	169	2	zp	zp	PROPN
ejpam-180	169	3	,	,	PUNCT
ejpam-180	169	4	y	y	PROPN
ejpam-180	169	5	)	)	PUNCT
ejpam-180	169	6	be	be	AUX
ejpam-180	169	7	feasible	feasible	ADJ
ejpam-180	169	8	for	for	ADP
ejpam-180	169	9	(	(	PUNCT
ejpam-180	169	10	mwd	mwd	PROPN
ejpam-180	169	11	)	)	PUNCT
ejpam-180	169	12	.	.	PUNCT
ejpam-180	170	1	if	if	SCONJ
ejpam-180	170	2	for	for	ADP
ejpam-180	170	3	all	all	DET
ejpam-180	170	4	feasible	feasible	ADJ
ejpam-180	170	5	�	�	PROPN
ejpam-180	170	6	x	x	SYM
ejpam-180	170	7	,	,	PUNCT
ejpam-180	170	8	u	u	NOUN
ejpam-180	170	9	,	,	PUNCT
ejpam-180	170	10	λ	λ	PROPN
ejpam-180	170	11	,	,	PUNCT
ejpam-180	170	12	z1	z1	NOUN
ejpam-180	170	13	,	,	PUNCT
ejpam-180	170	14	.	.	PUNCT
ejpam-180	170	15	.	.	PUNCT
ejpam-180	171	1	.	.	PUNCT
ejpam-180	172	1	,	,	PUNCT
ejpam-180	172	2	zp	zp	PROPN
ejpam-180	172	3	,	,	PUNCT
ejpam-180	172	4	y	y	PROPN
ejpam-180	172	5	�	�	PROPN
ejpam-180	172	6	,	,	PUNCT
ejpam-180	172	7	p	p	X
ejpam-180	172	8	∑	∑	PROPN
ejpam-180	172	9	i=1	i=1	PROPN
ejpam-180	173	1	λi	λi	X
ejpam-180	173	2	∫	∫	PROPN
ejpam-180	174	1	i	i	INTJ
ejpam-180	174	2	�	�	PROPN
ejpam-180	175	1	f	f	PROPN
ejpam-180	175	2	i	i	PRON
ejpam-180	175	3	(	(	PUNCT
ejpam-180	175	4	t	t	PROPN
ejpam-180	175	5	,	,	PUNCT
ejpam-180	175	6	.	.	PUNCT
ejpam-180	175	7	,	,	PUNCT
ejpam-180	175	8	.	.	PUNCT
ejpam-180	175	9	,	,	PUNCT
ejpam-180	175	10	.	.	PUNCT
ejpam-180	175	11	)	)	PUNCT
ejpam-180	176	1	+	+	CCONJ
ejpam-180	176	2	(	(	PUNCT
ejpam-180	176	3	·	·	PUNCT
ejpam-180	176	4	)	)	PUNCT
ejpam-180	176	5	t	t	PROPN
ejpam-180	176	6	b	b	NUM
ejpam-180	176	7	i	i	PRON
ejpam-180	176	8	(	(	PUNCT
ejpam-180	176	9	t)z	t)z	NOUN
ejpam-180	176	10	i	i	PRON
ejpam-180	176	11	(	(	PUNCT
ejpam-180	176	12	t	t	PROPN
ejpam-180	176	13	)	)	PUNCT
ejpam-180	177	1	+	+	CCONJ
ejpam-180	177	2	y	y	PROPN
ejpam-180	177	3	(	(	PUNCT
ejpam-180	177	4	t	t	PROPN
ejpam-180	177	5	)	)	PUNCT
ejpam-180	177	6	t	t	PROPN
ejpam-180	177	7	g	g	PROPN
ejpam-180	177	8	(	(	PUNCT
ejpam-180	177	9	t	t	PROPN
ejpam-180	177	10	,	,	PUNCT
ejpam-180	177	11	.	.	PUNCT
ejpam-180	177	12	,	,	PUNCT
ejpam-180	177	13	.	.	PUNCT
ejpam-180	177	14	,	,	PUNCT
ejpam-180	177	15	.	.	PUNCT
ejpam-180	177	16	)	)	PUNCT
ejpam-180	178	1	�	�	PROPN
ejpam-180	179	1	d	d	PROPN
ejpam-180	179	2	t	t	PROPN
ejpam-180	179	3	is	be	AUX
ejpam-180	179	4	pseudoinvex	pseudoinvex	NOUN
ejpam-180	179	5	with	with	ADP
ejpam-180	179	6	respect	respect	NOUN
ejpam-180	179	7	to	to	ADP
ejpam-180	179	8	η	η	PROPN
ejpam-180	179	9	,	,	PUNCT
ejpam-180	179	10	then	then	ADV
ejpam-180	179	11	the	the	DET
ejpam-180	179	12	following	following	NOUN
ejpam-180	179	13	can	can	AUX
ejpam-180	179	14	not	not	PART
ejpam-180	179	15	hold	hold	VERB
ejpam-180	179	16	:	:	PUNCT
ejpam-180	179	17	∫	∫	PROPN
ejpam-180	180	1	i	i	PRON
ejpam-180	180	2	�	�	PROPN
ejpam-180	181	1	f	f	PROPN
ejpam-180	181	2	i	i	PRON
ejpam-180	181	3	(	(	PUNCT
ejpam-180	181	4	t	t	PROPN
ejpam-180	181	5	,	,	PUNCT
ejpam-180	181	6	x	x	X
ejpam-180	181	7	,	,	PUNCT
ejpam-180	181	8	ẋ	ẋ	PROPN
ejpam-180	181	9	,	,	PUNCT
ejpam-180	181	10	ẍ	ẍ	X
ejpam-180	181	11	)	)	PUNCT
ejpam-180	182	1	+	+	CCONJ
ejpam-180	182	2	x	x	SYM
ejpam-180	182	3	(	(	PUNCT
ejpam-180	182	4	t	t	PROPN
ejpam-180	182	5	)	)	PUNCT
ejpam-180	182	6	t	t	PROPN
ejpam-180	182	7	b	b	PROPN
ejpam-180	182	8	i	i	PROPN
ejpam-180	182	9	(	(	PUNCT
ejpam-180	182	10	t	t	PROPN
ejpam-180	182	11	)	)	PUNCT
ejpam-180	183	1	z	z	NOUN
ejpam-180	184	1	i	i	PRON
ejpam-180	184	2	(	(	PUNCT
ejpam-180	184	3	t	t	PROPN
ejpam-180	184	4	)	)	PUNCT
ejpam-180	184	5	�	�	PROPN
ejpam-180	185	1	d	d	PROPN
ejpam-180	185	2	t	t	PROPN
ejpam-180	185	3	≦	≦	PROPN
ejpam-180	185	4	∫	∫	INTJ
ejpam-180	186	1	i	i	PRON
ejpam-180	186	2	�	�	PROPN
ejpam-180	187	1	f	f	PROPN
ejpam-180	187	2	i	i	PRON
ejpam-180	187	3	(	(	PUNCT
ejpam-180	187	4	t	t	PROPN
ejpam-180	187	5	,	,	PUNCT
ejpam-180	187	6	u	u	NOUN
ejpam-180	187	7	,	,	PUNCT
ejpam-180	187	8	u̇	u̇	PROPN
ejpam-180	187	9	,	,	PUNCT
ejpam-180	187	10	ü	ü	NUM
ejpam-180	187	11	)	)	PUNCT
ejpam-180	188	1	d	d	NOUN
ejpam-180	188	2	t	t	PROPN
ejpam-180	188	3	+	+	CCONJ
ejpam-180	188	4	u	u	PROPN
ejpam-180	188	5	(	(	PUNCT
ejpam-180	188	6	t	t	PROPN
ejpam-180	188	7	)	)	PUNCT
ejpam-180	188	8	t	t	PROPN
ejpam-180	188	9	b	b	PROPN
ejpam-180	189	1	i	i	PRON
ejpam-180	189	2	(	(	PUNCT
ejpam-180	189	3	t)z	t)z	NOUN
ejpam-180	189	4	i	i	PRON
ejpam-180	189	5	(	(	PUNCT
ejpam-180	189	6	t)+	t)+	NOUN
ejpam-180	189	7	y	y	PROPN
ejpam-180	189	8	(	(	PUNCT
ejpam-180	189	9	t	t	PROPN
ejpam-180	189	10	)	)	PUNCT
ejpam-180	189	11	t	t	PROPN
ejpam-180	189	12	g	g	PROPN
ejpam-180	189	13	(	(	PUNCT
ejpam-180	189	14	t	t	PROPN
ejpam-180	189	15	,	,	PUNCT
ejpam-180	189	16	u	u	NOUN
ejpam-180	189	17	,	,	PUNCT
ejpam-180	189	18	u̇	u̇	PROPN
ejpam-180	189	19	,	,	PUNCT
ejpam-180	189	20	ü	ü	NOUN
ejpam-180	189	21	)	)	PUNCT
ejpam-180	189	22	�	�	PROPN
ejpam-180	190	1	d	d	PROPN
ejpam-180	190	2	t	t	PROPN
ejpam-180	190	3	,	,	PUNCT
ejpam-180	190	4	(	(	PUNCT
ejpam-180	190	5	4.7	4.7	NUM
ejpam-180	190	6	)	)	PUNCT
ejpam-180	190	7	for	for	ADP
ejpam-180	190	8	all	all	PRON
ejpam-180	190	9	i	i	PRON
ejpam-180	190	10	∈	∈	PROPN
ejpam-180	190	11	p	p	X
ejpam-180	190	12	,	,	PUNCT
ejpam-180	190	13	and	and	CCONJ
ejpam-180	190	14	∫	∫	PROPN
ejpam-180	191	1	i	i	PRON
ejpam-180	191	2	�	�	PROPN
ejpam-180	192	1	f	f	PROPN
ejpam-180	192	2	j	j	PROPN
ejpam-180	192	3	(	(	PUNCT
ejpam-180	192	4	t	t	PROPN
ejpam-180	192	5	,	,	PUNCT
ejpam-180	192	6	x	x	X
ejpam-180	192	7	,	,	PUNCT
ejpam-180	192	8	ẋ	ẋ	PROPN
ejpam-180	192	9	,	,	PUNCT
ejpam-180	192	10	ẍ	ẍ	X
ejpam-180	192	11	)	)	PUNCT
ejpam-180	193	1	d	d	PROPN
ejpam-180	193	2	t	t	PROPN
ejpam-180	193	3	+	+	CCONJ
ejpam-180	193	4	x	x	X
ejpam-180	193	5	(	(	PUNCT
ejpam-180	193	6	t	t	PROPN
ejpam-180	193	7	)	)	PUNCT
ejpam-180	193	8	t	t	PROPN
ejpam-180	194	1	b	b	PROPN
ejpam-180	194	2	j	j	PROPN
ejpam-180	194	3	(	(	PUNCT
ejpam-180	194	4	t	t	PROPN
ejpam-180	194	5	)	)	PUNCT
ejpam-180	194	6	z	z	PROPN
ejpam-180	194	7	j	j	PROPN
ejpam-180	194	8	(	(	PUNCT
ejpam-180	194	9	t	t	PROPN
ejpam-180	194	10	)	)	PUNCT
ejpam-180	194	11	�	�	PROPN
ejpam-180	194	12	d	d	PROPN
ejpam-180	194	13	t	t	PROPN
ejpam-180	194	14	i.	i.	PROPN
ejpam-180	194	15	husain	husain	PROPN
ejpam-180	194	16	,	,	PUNCT
ejpam-180	194	17	a.	a.	PROPN
ejpam-180	194	18	ahmed	ahmed	PROPN
ejpam-180	194	19	,	,	PUNCT
ejpam-180	194	20	and	and	CCONJ
ejpam-180	194	21	g.	g.	PROPN
ejpam-180	194	22	rumana	rumana	PROPN
ejpam-180	194	23	/	/	SYM
ejpam-180	194	24	eur	eur	PROPN
ejpam-180	194	25	.	.	PUNCT
ejpam-180	195	1	j.	j.	PROPN
ejpam-180	195	2	pure	pure	PROPN
ejpam-180	195	3	appl	appl	PROPN
ejpam-180	195	4	.	.	PROPN
ejpam-180	195	5	math	math	PROPN
ejpam-180	195	6	,	,	PUNCT
ejpam-180	195	7	2	2	NUM
ejpam-180	195	8	(	(	PUNCT
ejpam-180	195	9	2009	2009	NUM
ejpam-180	195	10	)	)	PUNCT
ejpam-180	195	11	,	,	PUNCT
ejpam-180	195	12	(	(	PUNCT
ejpam-180	195	13	372	372	NUM
ejpam-180	195	14	-	-	SYM
ejpam-180	195	15	400	400	NUM
ejpam-180	195	16	)	)	PUNCT
ejpam-180	195	17	380	380	NUM
ejpam-180	195	18	<	<	X
ejpam-180	195	19	∫	∫	PROPN
ejpam-180	196	1	i	i	PRON
ejpam-180	196	2	�	�	PROPN
ejpam-180	197	1	f	f	PROPN
ejpam-180	197	2	j	j	PROPN
ejpam-180	197	3	(	(	PUNCT
ejpam-180	197	4	t	t	PROPN
ejpam-180	197	5	,	,	PUNCT
ejpam-180	197	6	u	u	NOUN
ejpam-180	197	7	,	,	PUNCT
ejpam-180	197	8	u̇	u̇	PROPN
ejpam-180	197	9	,	,	PUNCT
ejpam-180	197	10	ü	ü	NUM
ejpam-180	197	11	)	)	PUNCT
ejpam-180	198	1	d	d	PROPN
ejpam-180	198	2	t	t	PROPN
ejpam-180	198	3	+	+	CCONJ
ejpam-180	198	4	�	�	PROPN
ejpam-180	198	5	u	u	PROPN
ejpam-180	198	6	(	(	PUNCT
ejpam-180	198	7	t	t	PROPN
ejpam-180	198	8	)	)	PUNCT
ejpam-180	198	9	t	t	PROPN
ejpam-180	198	10	b	b	PROPN
ejpam-180	198	11	j	j	PROPN
ejpam-180	198	12	(	(	PUNCT
ejpam-180	198	13	t)z	t)z	NOUN
ejpam-180	198	14	j	j	PROPN
ejpam-180	198	15	(	(	PUNCT
ejpam-180	198	16	t	t	PROPN
ejpam-180	198	17	)	)	PUNCT
ejpam-180	198	18	�	�	PROPN
ejpam-180	199	1	+	+	CCONJ
ejpam-180	199	2	y	y	PROPN
ejpam-180	199	3	(	(	PUNCT
ejpam-180	199	4	t	t	PROPN
ejpam-180	199	5	)	)	PUNCT
ejpam-180	199	6	t	t	PROPN
ejpam-180	199	7	g	g	PROPN
ejpam-180	199	8	j	j	PROPN
ejpam-180	199	9	(	(	PUNCT
ejpam-180	199	10	t	t	PROPN
ejpam-180	199	11	,	,	PUNCT
ejpam-180	199	12	u	u	NOUN
ejpam-180	199	13	,	,	PUNCT
ejpam-180	199	14	u̇	u̇	PROPN
ejpam-180	199	15	,	,	PUNCT
ejpam-180	199	16	ü	ü	NOUN
ejpam-180	199	17	)	)	PUNCT
ejpam-180	199	18	�	�	PROPN
ejpam-180	200	1	d	d	PROPN
ejpam-180	200	2	t	t	PROPN
ejpam-180	200	3	(	(	PUNCT
ejpam-180	200	4	4.8	4.8	NUM
ejpam-180	200	5	)	)	PUNCT
ejpam-180	200	6	for	for	ADP
ejpam-180	200	7	some	some	DET
ejpam-180	200	8	j	j	PROPN
ejpam-180	200	9	∈	∈	PROPN
ejpam-180	200	10	p.	p.	NOUN
ejpam-180	200	11	proof	proof	NOUN
ejpam-180	200	12	.	.	PUNCT
ejpam-180	200	13	suppose	suppose	VERB
ejpam-180	200	14	that	that	SCONJ
ejpam-180	200	15	(	(	PUNCT
ejpam-180	200	16	4.7	4.7	NUM
ejpam-180	200	17	)	)	PUNCT
ejpam-180	200	18	and	and	CCONJ
ejpam-180	200	19	(	(	PUNCT
ejpam-180	200	20	4.8	4.8	NUM
ejpam-180	200	21	)	)	PUNCT
ejpam-180	200	22	hold	hold	NOUN
ejpam-180	200	23	.	.	PUNCT
ejpam-180	201	1	then	then	ADV
ejpam-180	201	2	,	,	PUNCT
ejpam-180	201	3	from	from	ADP
ejpam-180	201	4	(	(	PUNCT
ejpam-180	201	5	2.3	2.3	NUM
ejpam-180	201	6	)	)	PUNCT
ejpam-180	201	7	and	and	CCONJ
ejpam-180	201	8	(	(	PUNCT
ejpam-180	201	9	4.5	4.5	NUM
ejpam-180	201	10	)	)	PUNCT
ejpam-180	201	11	,	,	PUNCT
ejpam-180	201	12	we	we	PRON
ejpam-180	201	13	have	have	VERB
ejpam-180	201	14	,	,	PUNCT
ejpam-180	201	15	∫	∫	PROPN
ejpam-180	202	1	i	i	PRON
ejpam-180	202	2	�	�	PROPN
ejpam-180	203	1	f	f	PROPN
ejpam-180	203	2	i	i	PRON
ejpam-180	203	3	(	(	PUNCT
ejpam-180	203	4	t	t	PROPN
ejpam-180	203	5	,	,	PUNCT
ejpam-180	203	6	x	x	X
ejpam-180	203	7	,	,	PUNCT
ejpam-180	203	8	ẋ	ẋ	PROPN
ejpam-180	203	9	,	,	PUNCT
ejpam-180	203	10	ẍ	ẍ	X
ejpam-180	203	11	)	)	PUNCT
ejpam-180	204	1	+	+	CCONJ
ejpam-180	204	2	x	x	SYM
ejpam-180	204	3	(	(	PUNCT
ejpam-180	204	4	t	t	PROPN
ejpam-180	204	5	)	)	PUNCT
ejpam-180	204	6	t	t	PROPN
ejpam-180	204	7	b	b	PROPN
ejpam-180	205	1	i	i	PRON
ejpam-180	205	2	(	(	PUNCT
ejpam-180	205	3	t)z	t)z	NOUN
ejpam-180	205	4	i	i	PRON
ejpam-180	205	5	(	(	PUNCT
ejpam-180	205	6	t	t	PROPN
ejpam-180	205	7	)	)	PUNCT
ejpam-180	206	1	+	+	CCONJ
ejpam-180	206	2	y	y	PROPN
ejpam-180	206	3	(	(	PUNCT
ejpam-180	206	4	t	t	PROPN
ejpam-180	206	5	)	)	PUNCT
ejpam-180	206	6	t	t	PROPN
ejpam-180	206	7	g	g	PROPN
ejpam-180	206	8	(	(	PUNCT
ejpam-180	206	9	t	t	PROPN
ejpam-180	206	10	,	,	PUNCT
ejpam-180	206	11	x	x	X
ejpam-180	206	12	,	,	PUNCT
ejpam-180	206	13	ẋ	ẋ	PROPN
ejpam-180	206	14	,	,	PUNCT
ejpam-180	206	15	ẍ	ẍ	X
ejpam-180	206	16	)	)	PUNCT
ejpam-180	207	1	�	�	PROPN
ejpam-180	208	1	d	d	PROPN
ejpam-180	208	2	t	t	PROPN
ejpam-180	208	3	≦	≦	PROPN
ejpam-180	208	4	∫	∫	INTJ
ejpam-180	209	1	i	i	PRON
ejpam-180	209	2	�	�	PROPN
ejpam-180	210	1	f	f	PROPN
ejpam-180	210	2	i	i	PRON
ejpam-180	210	3	(	(	PUNCT
ejpam-180	210	4	t	t	PROPN
ejpam-180	210	5	,	,	PUNCT
ejpam-180	210	6	u	u	NOUN
ejpam-180	210	7	,	,	PUNCT
ejpam-180	210	8	u̇	u̇	PROPN
ejpam-180	210	9	,	,	PUNCT
ejpam-180	210	10	ü	ü	NUM
ejpam-180	210	11	)	)	PUNCT
ejpam-180	211	1	d	d	NOUN
ejpam-180	211	2	t	t	PROPN
ejpam-180	211	3	+	+	CCONJ
ejpam-180	211	4	u	u	PROPN
ejpam-180	211	5	(	(	PUNCT
ejpam-180	211	6	t	t	PROPN
ejpam-180	211	7	)	)	PUNCT
ejpam-180	211	8	t	t	PROPN
ejpam-180	211	9	b	b	PROPN
ejpam-180	212	1	i	i	PROPN
ejpam-180	212	2	(	(	PUNCT
ejpam-180	212	3	t	t	PROPN
ejpam-180	212	4	)	)	PUNCT
ejpam-180	212	5	z	z	NOUN
ejpam-180	213	1	i	i	PRON
ejpam-180	213	2	(	(	PUNCT
ejpam-180	213	3	t	t	PROPN
ejpam-180	213	4	)	)	PUNCT
ejpam-180	214	1	+	+	CCONJ
ejpam-180	214	2	y	y	PROPN
ejpam-180	214	3	(	(	PUNCT
ejpam-180	214	4	t	t	PROPN
ejpam-180	214	5	)	)	PUNCT
ejpam-180	214	6	t	t	PROPN
ejpam-180	214	7	g	g	PROPN
ejpam-180	214	8	j	j	PROPN
ejpam-180	214	9	(	(	PUNCT
ejpam-180	214	10	t	t	PROPN
ejpam-180	214	11	,	,	PUNCT
ejpam-180	214	12	u	u	NOUN
ejpam-180	214	13	,	,	PUNCT
ejpam-180	214	14	u̇	u̇	PROPN
ejpam-180	214	15	,	,	PUNCT
ejpam-180	214	16	ü	ü	NOUN
ejpam-180	214	17	)	)	PUNCT
ejpam-180	214	18	�	�	PROPN
ejpam-180	215	1	d	d	PROPN
ejpam-180	215	2	t	t	PROPN
ejpam-180	215	3	,	,	PUNCT
ejpam-180	215	4	for	for	SCONJ
ejpam-180	215	5	all	all	PRON
ejpam-180	215	6	i	i	PRON
ejpam-180	215	7	∈	∈	PROPN
ejpam-180	215	8	p	p	X
ejpam-180	215	9	,	,	PUNCT
ejpam-180	215	10	and	and	CCONJ
ejpam-180	215	11	∫	∫	PROPN
ejpam-180	215	12	i	i	PRON
ejpam-180	215	13	�	�	PROPN
ejpam-180	215	14	f	f	PROPN
ejpam-180	215	15	j	j	PROPN
ejpam-180	215	16	(	(	PUNCT
ejpam-180	215	17	t	t	PROPN
ejpam-180	215	18	,	,	PUNCT
ejpam-180	215	19	x	x	X
ejpam-180	215	20	,	,	PUNCT
ejpam-180	215	21	ẋ	ẋ	PROPN
ejpam-180	215	22	,	,	PUNCT
ejpam-180	215	23	ẍ	ẍ	X
ejpam-180	215	24	)	)	PUNCT
ejpam-180	216	1	d	d	PROPN
ejpam-180	216	2	t	t	PROPN
ejpam-180	216	3	+	+	CCONJ
ejpam-180	216	4	x	x	X
ejpam-180	216	5	(	(	PUNCT
ejpam-180	216	6	t	t	PROPN
ejpam-180	216	7	)	)	PUNCT
ejpam-180	216	8	t	t	PROPN
ejpam-180	217	1	b	b	PROPN
ejpam-180	217	2	j	j	PROPN
ejpam-180	217	3	(	(	PUNCT
ejpam-180	217	4	t)z	t)z	NOUN
ejpam-180	217	5	j	j	PROPN
ejpam-180	217	6	(	(	PUNCT
ejpam-180	217	7	t	t	PROPN
ejpam-180	217	8	)	)	PUNCT
ejpam-180	217	9	+	+	CCONJ
ejpam-180	217	10	y	y	PROPN
ejpam-180	217	11	(	(	PUNCT
ejpam-180	217	12	t	t	PROPN
ejpam-180	217	13	)	)	PUNCT
ejpam-180	217	14	t	t	PROPN
ejpam-180	217	15	g	g	PROPN
ejpam-180	217	16	(	(	PUNCT
ejpam-180	217	17	t	t	PROPN
ejpam-180	217	18	,	,	PUNCT
ejpam-180	217	19	x	x	X
ejpam-180	217	20	,	,	PUNCT
ejpam-180	217	21	ẋ	ẋ	PROPN
ejpam-180	217	22	,	,	PUNCT
ejpam-180	217	23	ẍ	ẍ	X
ejpam-180	217	24	)	)	PUNCT
ejpam-180	217	25	�	�	PROPN
ejpam-180	218	1	d	d	PROPN
ejpam-180	218	2	t	t	PROPN
ejpam-180	218	3	<	<	X
ejpam-180	218	4	∫	∫	PROPN
ejpam-180	219	1	i	i	INTJ
ejpam-180	219	2	�	�	PROPN
ejpam-180	220	1	f	f	PROPN
ejpam-180	220	2	j	j	PROPN
ejpam-180	220	3	(	(	PUNCT
ejpam-180	220	4	t	t	PROPN
ejpam-180	220	5	,	,	PUNCT
ejpam-180	220	6	u	u	NOUN
ejpam-180	220	7	,	,	PUNCT
ejpam-180	220	8	u̇	u̇	PROPN
ejpam-180	220	9	,	,	PUNCT
ejpam-180	220	10	ü	ü	NUM
ejpam-180	220	11	)	)	PUNCT
ejpam-180	221	1	d	d	PROPN
ejpam-180	221	2	t	t	PROPN
ejpam-180	221	3	+	+	CCONJ
ejpam-180	221	4	�	�	PROPN
ejpam-180	221	5	u	u	PROPN
ejpam-180	221	6	(	(	PUNCT
ejpam-180	221	7	t	t	PROPN
ejpam-180	221	8	)	)	PUNCT
ejpam-180	221	9	t	t	PROPN
ejpam-180	221	10	b	b	PROPN
ejpam-180	221	11	j	j	PROPN
ejpam-180	221	12	(	(	PUNCT
ejpam-180	221	13	t	t	PROPN
ejpam-180	221	14	)	)	PUNCT
ejpam-180	222	1	z	z	PROPN
ejpam-180	222	2	j	j	PROPN
ejpam-180	222	3	(	(	PUNCT
ejpam-180	222	4	t	t	PROPN
ejpam-180	222	5	)	)	PUNCT
ejpam-180	222	6	�	�	PROPN
ejpam-180	222	7	+	+	CCONJ
ejpam-180	222	8	y	y	PROPN
ejpam-180	222	9	(	(	PUNCT
ejpam-180	222	10	t	t	PROPN
ejpam-180	222	11	)	)	PUNCT
ejpam-180	222	12	t	t	PROPN
ejpam-180	222	13	g	g	PROPN
ejpam-180	222	14	j	j	PROPN
ejpam-180	222	15	(	(	PUNCT
ejpam-180	222	16	t	t	PROPN
ejpam-180	222	17	,	,	PUNCT
ejpam-180	222	18	u	u	NOUN
ejpam-180	222	19	,	,	PUNCT
ejpam-180	222	20	u̇	u̇	PROPN
ejpam-180	222	21	,	,	PUNCT
ejpam-180	222	22	ü	ü	NOUN
ejpam-180	222	23	)	)	PUNCT
ejpam-180	222	24	�	�	PROPN
ejpam-180	223	1	d	d	PROPN
ejpam-180	223	2	t	t	PROPN
ejpam-180	223	3	for	for	ADP
ejpam-180	223	4	some	some	DET
ejpam-180	223	5	j	j	PROPN
ejpam-180	223	6	∈	∈	PROPN
ejpam-180	223	7	p.	p.	NOUN
ejpam-180	223	8	now	now	ADV
ejpam-180	223	9	using	use	VERB
ejpam-180	223	10	λ	λ	PROPN
ejpam-180	223	11	>	>	X
ejpam-180	223	12	0	0	PUNCT
ejpam-180	224	1	and	and	CCONJ
ejpam-180	224	2	p	p	NOUN
ejpam-180	224	3	∑	∑	PROPN
ejpam-180	224	4	i=1	i=1	PROPN
ejpam-180	224	5	λi	λi	NOUN
ejpam-180	224	6	=	=	NOUN
ejpam-180	224	7	1	1	NUM
ejpam-180	224	8	,	,	PUNCT
ejpam-180	224	9	these	these	DET
ejpam-180	224	10	inequalities	inequality	NOUN
ejpam-180	224	11	yield	yield	VERB
ejpam-180	224	12	,	,	PUNCT
ejpam-180	224	13	p	p	X
ejpam-180	224	14	∑	∑	PROPN
ejpam-180	224	15	i=1	i=1	PROPN
ejpam-180	224	16	λi	λi	X
ejpam-180	224	17	∫	∫	PROPN
ejpam-180	225	1	i	i	INTJ
ejpam-180	225	2	�	�	PROPN
ejpam-180	226	1	f	f	PROPN
ejpam-180	226	2	i	i	PRON
ejpam-180	226	3	(	(	PUNCT
ejpam-180	226	4	t	t	PROPN
ejpam-180	226	5	,	,	PUNCT
ejpam-180	226	6	x	x	X
ejpam-180	226	7	,	,	PUNCT
ejpam-180	226	8	ẋ	ẋ	PROPN
ejpam-180	226	9	,	,	PUNCT
ejpam-180	226	10	ẍ	ẍ	X
ejpam-180	226	11	)	)	PUNCT
ejpam-180	227	1	d	d	PROPN
ejpam-180	227	2	t	t	PROPN
ejpam-180	227	3	+	+	CCONJ
ejpam-180	227	4	�	�	PROPN
ejpam-180	227	5	x	x	SYM
ejpam-180	227	6	(	(	PUNCT
ejpam-180	227	7	t	t	PROPN
ejpam-180	227	8	)	)	PUNCT
ejpam-180	227	9	t	t	PROPN
ejpam-180	227	10	b	b	PROPN
ejpam-180	228	1	i	i	PRON
ejpam-180	228	2	(	(	PUNCT
ejpam-180	228	3	t)z	t)z	NOUN
ejpam-180	228	4	i	i	PRON
ejpam-180	228	5	(	(	PUNCT
ejpam-180	228	6	t	t	PROPN
ejpam-180	228	7	)	)	PUNCT
ejpam-180	228	8	�	�	PROPN
ejpam-180	228	9	+	+	CCONJ
ejpam-180	228	10	y	y	PROPN
ejpam-180	228	11	(	(	PUNCT
ejpam-180	228	12	t	t	PROPN
ejpam-180	228	13	)	)	PUNCT
ejpam-180	228	14	t	t	PROPN
ejpam-180	228	15	g	g	PROPN
ejpam-180	228	16	(	(	PUNCT
ejpam-180	228	17	t	t	PROPN
ejpam-180	228	18	,	,	PUNCT
ejpam-180	228	19	x	x	X
ejpam-180	228	20	,	,	PUNCT
ejpam-180	228	21	ẋ	ẋ	PROPN
ejpam-180	228	22	,	,	PUNCT
ejpam-180	228	23	ẍ	ẍ	X
ejpam-180	228	24	)	)	PUNCT
ejpam-180	228	25	�	�	PROPN
ejpam-180	229	1	d	d	PROPN
ejpam-180	229	2	t	t	PROPN
ejpam-180	229	3	<	<	X
ejpam-180	229	4	p	p	X
ejpam-180	229	5	∑	∑	PROPN
ejpam-180	229	6	i=1	i=1	PROPN
ejpam-180	229	7	λi	λi	X
ejpam-180	229	8	∫	∫	PROPN
ejpam-180	230	1	i	i	INTJ
ejpam-180	230	2	�	�	PROPN
ejpam-180	231	1	f	f	PROPN
ejpam-180	231	2	i	i	PRON
ejpam-180	231	3	(	(	PUNCT
ejpam-180	231	4	t	t	PROPN
ejpam-180	231	5	,	,	PUNCT
ejpam-180	231	6	u	u	NOUN
ejpam-180	231	7	,	,	PUNCT
ejpam-180	231	8	u̇	u̇	PROPN
ejpam-180	231	9	,	,	PUNCT
ejpam-180	231	10	ü	ü	NUM
ejpam-180	231	11	)	)	PUNCT
ejpam-180	232	1	d	d	PROPN
ejpam-180	232	2	t	t	PROPN
ejpam-180	232	3	+	+	CCONJ
ejpam-180	232	4	�	�	PROPN
ejpam-180	232	5	u	u	PROPN
ejpam-180	232	6	(	(	PUNCT
ejpam-180	232	7	t	t	PROPN
ejpam-180	232	8	)	)	PUNCT
ejpam-180	232	9	t	t	PROPN
ejpam-180	232	10	b	b	PROPN
ejpam-180	233	1	i	i	PRON
ejpam-180	233	2	(	(	PUNCT
ejpam-180	233	3	t)z	t)z	NOUN
ejpam-180	233	4	i	i	PRON
ejpam-180	233	5	(	(	PUNCT
ejpam-180	233	6	t	t	PROPN
ejpam-180	233	7	)	)	PUNCT
ejpam-180	233	8	�	�	PROPN
ejpam-180	233	9	+	+	CCONJ
ejpam-180	233	10	y	y	PROPN
ejpam-180	233	11	(	(	PUNCT
ejpam-180	233	12	t	t	PROPN
ejpam-180	233	13	)	)	PUNCT
ejpam-180	233	14	t	t	PROPN
ejpam-180	233	15	g	g	PROPN
ejpam-180	233	16	(	(	PUNCT
ejpam-180	233	17	t	t	PROPN
ejpam-180	233	18	,	,	PUNCT
ejpam-180	233	19	u	u	NOUN
ejpam-180	233	20	,	,	PUNCT
ejpam-180	233	21	u̇	u̇	PROPN
ejpam-180	233	22	,	,	PUNCT
ejpam-180	233	23	ü	ü	NOUN
ejpam-180	233	24	)	)	PUNCT
ejpam-180	233	25	�	�	PROPN
ejpam-180	234	1	d	d	PROPN
ejpam-180	234	2	t	t	PROPN
ejpam-180	234	3	this	this	PRON
ejpam-180	234	4	,	,	PUNCT
ejpam-180	234	5	because	because	SCONJ
ejpam-180	234	6	of	of	ADP
ejpam-180	234	7	the	the	DET
ejpam-180	234	8	pseudoinvexity	pseudoinvexity	NOUN
ejpam-180	234	9	of	of	ADP
ejpam-180	234	10	p	p	NOUN
ejpam-180	234	11	∑	∑	PROPN
ejpam-180	234	12	i=1	i=1	PROPN
ejpam-180	234	13	λi	λi	INTJ
ejpam-180	234	14	∫	∫	PROPN
ejpam-180	235	1	i	i	INTJ
ejpam-180	235	2	�	�	PROPN
ejpam-180	236	1	f	f	PROPN
ejpam-180	236	2	i	i	PRON
ejpam-180	236	3	(	(	PUNCT
ejpam-180	236	4	t	t	PROPN
ejpam-180	236	5	,	,	PUNCT
ejpam-180	236	6	.	.	PUNCT
ejpam-180	236	7	,	,	PUNCT
ejpam-180	236	8	.	.	PUNCT
ejpam-180	236	9	,	,	PUNCT
ejpam-180	236	10	.	.	PUNCT
ejpam-180	236	11	)	)	PUNCT
ejpam-180	237	1	+	+	CCONJ
ejpam-180	237	2	(	(	PUNCT
ejpam-180	237	3	·	·	PUNCT
ejpam-180	237	4	)	)	PUNCT
ejpam-180	237	5	t	t	PROPN
ejpam-180	237	6	b	b	X
ejpam-180	237	7	i	i	PROPN
ejpam-180	237	8	(	(	PUNCT
ejpam-180	237	9	t	t	PROPN
ejpam-180	237	10	)	)	PUNCT
ejpam-180	238	1	z	z	NOUN
ejpam-180	239	1	i	i	PRON
ejpam-180	239	2	(	(	PUNCT
ejpam-180	239	3	t	t	PROPN
ejpam-180	239	4	)	)	PUNCT
ejpam-180	240	1	+	+	CCONJ
ejpam-180	240	2	y	y	PROPN
ejpam-180	240	3	(	(	PUNCT
ejpam-180	240	4	t	t	PROPN
ejpam-180	240	5	)	)	PUNCT
ejpam-180	240	6	t	t	PROPN
ejpam-180	240	7	g	g	PROPN
ejpam-180	240	8	(	(	PUNCT
ejpam-180	240	9	t	t	PROPN
ejpam-180	240	10	,	,	PUNCT
ejpam-180	240	11	.	.	PUNCT
ejpam-180	240	12	,	,	PUNCT
ejpam-180	240	13	.	.	PUNCT
ejpam-180	240	14	,	,	PUNCT
ejpam-180	240	15	.	.	PUNCT
ejpam-180	240	16	)	)	PUNCT
ejpam-180	241	1	�	�	PROPN
ejpam-180	242	1	d	d	PROPN
ejpam-180	242	2	t	t	PROPN
ejpam-180	242	3	implies	imply	VERB
ejpam-180	242	4	p	p	X
ejpam-180	242	5	∑	∑	PROPN
ejpam-180	242	6	i=1	i=1	PROPN
ejpam-180	242	7	λi	λi	INTJ
ejpam-180	242	8	∫	∫	PROPN
ejpam-180	243	1	i	i	PROPN
ejpam-180	243	2	ηt	ηt	ADP
ejpam-180	243	3	�	�	PROPN
ejpam-180	243	4	�	�	PROPN
ejpam-180	243	5	f	f	PROPN
ejpam-180	244	1	i	i	PRON
ejpam-180	244	2	u	u	PROPN
ejpam-180	244	3	(	(	PUNCT
ejpam-180	244	4	t	t	PROPN
ejpam-180	244	5	,	,	PUNCT
ejpam-180	244	6	u	u	NOUN
ejpam-180	244	7	,	,	PUNCT
ejpam-180	244	8	u̇	u̇	PROPN
ejpam-180	244	9	,	,	PUNCT
ejpam-180	244	10	ü	ü	PRON
ejpam-180	244	11	)	)	PUNCT
ejpam-180	245	1	+	+	NUM
ejpam-180	246	1	b	b	X
ejpam-180	246	2	i	i	PRON
ejpam-180	246	3	(	(	PUNCT
ejpam-180	246	4	t	t	PROPN
ejpam-180	246	5	)	)	PUNCT
ejpam-180	246	6	z	z	NOUN
ejpam-180	247	1	i	i	PRON
ejpam-180	247	2	(	(	PUNCT
ejpam-180	247	3	t	t	PROPN
ejpam-180	247	4	)	)	PUNCT
ejpam-180	248	1	+	+	CCONJ
ejpam-180	248	2	y	y	PROPN
ejpam-180	248	3	(	(	PUNCT
ejpam-180	248	4	t	t	PROPN
ejpam-180	248	5	)	)	PUNCT
ejpam-180	248	6	t	t	PROPN
ejpam-180	248	7	gu	gu	PROPN
ejpam-180	248	8	(	(	PUNCT
ejpam-180	248	9	t	t	PROPN
ejpam-180	248	10	,	,	PUNCT
ejpam-180	248	11	u	u	NOUN
ejpam-180	248	12	,	,	PUNCT
ejpam-180	248	13	u̇	u̇	PROPN
ejpam-180	248	14	,	,	PUNCT
ejpam-180	248	15	ü	ü	NUM
ejpam-180	248	16	)	)	PUNCT
ejpam-180	248	17	�	�	PROPN
ejpam-180	248	18	i.	i.	PROPN
ejpam-180	248	19	husain	husain	PROPN
ejpam-180	248	20	,	,	PUNCT
ejpam-180	248	21	a.	a.	PROPN
ejpam-180	248	22	ahmed	ahmed	PROPN
ejpam-180	248	23	,	,	PUNCT
ejpam-180	248	24	and	and	CCONJ
ejpam-180	248	25	g.	g.	PROPN
ejpam-180	248	26	rumana	rumana	PROPN
ejpam-180	248	27	/	/	SYM
ejpam-180	248	28	eur	eur	PROPN
ejpam-180	248	29	.	.	PUNCT
ejpam-180	249	1	j.	j.	PROPN
ejpam-180	249	2	pure	pure	PROPN
ejpam-180	249	3	appl	appl	PROPN
ejpam-180	249	4	.	.	PROPN
ejpam-180	249	5	math	math	PROPN
ejpam-180	249	6	,	,	PUNCT
ejpam-180	249	7	2	2	NUM
ejpam-180	249	8	(	(	PUNCT
ejpam-180	249	9	2009	2009	NUM
ejpam-180	249	10	)	)	PUNCT
ejpam-180	249	11	,	,	PUNCT
ejpam-180	249	12	(	(	PUNCT
ejpam-180	249	13	372	372	NUM
ejpam-180	249	14	-	-	SYM
ejpam-180	249	15	400	400	NUM
ejpam-180	249	16	)	)	PUNCT
ejpam-180	249	17	381	381	NUM
ejpam-180	249	18	−	−	PROPN
ejpam-180	249	19	�	�	PROPN
ejpam-180	249	20	dη	dη	NOUN
ejpam-180	249	21	�	�	PROPN
ejpam-180	249	22	t	t	PROPN
ejpam-180	249	23	�	�	PROPN
ejpam-180	250	1	f	f	PROPN
ejpam-180	251	1	i	i	PRON
ejpam-180	251	2	u̇	u̇	PROPN
ejpam-180	251	3	(	(	PUNCT
ejpam-180	251	4	t	t	PROPN
ejpam-180	251	5	,	,	PUNCT
ejpam-180	251	6	u	u	NOUN
ejpam-180	251	7	,	,	PUNCT
ejpam-180	251	8	u̇	u̇	PROPN
ejpam-180	251	9	,	,	PUNCT
ejpam-180	251	10	ü	ü	PRON
ejpam-180	251	11	)	)	PUNCT
ejpam-180	252	1	+	+	CCONJ
ejpam-180	252	2	y	y	PROPN
ejpam-180	252	3	(	(	PUNCT
ejpam-180	252	4	t	t	PROPN
ejpam-180	252	5	)	)	PUNCT
ejpam-180	252	6	t	t	NOUN
ejpam-180	252	7	gu̇	gu̇	PROPN
ejpam-180	252	8	(	(	PUNCT
ejpam-180	252	9	t	t	PROPN
ejpam-180	252	10	,	,	PUNCT
ejpam-180	252	11	u	u	NOUN
ejpam-180	252	12	,	,	PUNCT
ejpam-180	252	13	u̇	u̇	PROPN
ejpam-180	252	14	,	,	PUNCT
ejpam-180	252	15	ü	ü	NOUN
ejpam-180	252	16	)	)	PUNCT
ejpam-180	252	17	�	�	PROPN
ejpam-180	252	18	+	+	CCONJ
ejpam-180	252	19	�	�	PROPN
ejpam-180	252	20	d2η	d2η	VERB
ejpam-180	252	21	�	�	PROPN
ejpam-180	252	22	t	t	PROPN
ejpam-180	252	23	�	�	PROPN
ejpam-180	253	1	f	f	PROPN
ejpam-180	254	1	i	i	PRON
ejpam-180	254	2	ü	ü	VERB
ejpam-180	254	3	(	(	PUNCT
ejpam-180	254	4	t	t	PROPN
ejpam-180	254	5	,	,	PUNCT
ejpam-180	254	6	u	u	NOUN
ejpam-180	254	7	,	,	PUNCT
ejpam-180	254	8	u̇	u̇	PROPN
ejpam-180	254	9	,	,	PUNCT
ejpam-180	254	10	ü	ü	PRON
ejpam-180	254	11	)	)	PUNCT
ejpam-180	255	1	+	+	CCONJ
ejpam-180	255	2	y	y	PROPN
ejpam-180	255	3	(	(	PUNCT
ejpam-180	255	4	t	t	PROPN
ejpam-180	255	5	)	)	PUNCT
ejpam-180	255	6	t	t	PROPN
ejpam-180	255	7	gü	gü	PROPN
ejpam-180	255	8	(	(	PUNCT
ejpam-180	255	9	t	t	PROPN
ejpam-180	255	10	,	,	PUNCT
ejpam-180	255	11	u	u	NOUN
ejpam-180	255	12	,	,	PUNCT
ejpam-180	255	13	u̇	u̇	PROPN
ejpam-180	255	14	,	,	PUNCT
ejpam-180	255	15	ü	ü	NUM
ejpam-180	255	16	)	)	PUNCT
ejpam-180	255	17	�	�	PROPN
ejpam-180	256	1	i	i	PRON
ejpam-180	256	2	d	d	PROPN
ejpam-180	256	3	t	t	X
ejpam-180	256	4	<	<	X
ejpam-180	256	5	0	0	PUNCT
ejpam-180	256	6	integrating	integrating	NOUN
ejpam-180	256	7	by	by	ADP
ejpam-180	256	8	parts	part	NOUN
ejpam-180	256	9	,	,	PUNCT
ejpam-180	256	10	we	we	PRON
ejpam-180	256	11	get	get	VERB
ejpam-180	256	12	0	0	NUM
ejpam-180	256	13	>	>	X
ejpam-180	257	1	p	p	X
ejpam-180	257	2	∑	∑	PUNCT
ejpam-180	257	3	i=1	i=1	PROPN
ejpam-180	257	4	λi	λi	X
ejpam-180	257	5	∫	∫	PROPN
ejpam-180	258	1	i	i	PROPN
ejpam-180	258	2	ηt	ηt	ADP
ejpam-180	258	3	�	�	PROPN
ejpam-180	258	4	�	�	PROPN
ejpam-180	258	5	f	f	PROPN
ejpam-180	259	1	i	i	PRON
ejpam-180	259	2	u	u	PROPN
ejpam-180	259	3	(	(	PUNCT
ejpam-180	259	4	t	t	PROPN
ejpam-180	259	5	,	,	PUNCT
ejpam-180	259	6	u	u	NOUN
ejpam-180	259	7	,	,	PUNCT
ejpam-180	259	8	u̇	u̇	PROPN
ejpam-180	259	9	,	,	PUNCT
ejpam-180	259	10	ü	ü	PRON
ejpam-180	259	11	)	)	PUNCT
ejpam-180	260	1	+	+	NUM
ejpam-180	261	1	b	b	X
ejpam-180	261	2	i	i	PRON
ejpam-180	261	3	(	(	PUNCT
ejpam-180	261	4	t)z	t)z	NOUN
ejpam-180	261	5	i	i	PRON
ejpam-180	261	6	(	(	PUNCT
ejpam-180	261	7	t	t	PROPN
ejpam-180	261	8	)	)	PUNCT
ejpam-180	261	9	+	+	CCONJ
ejpam-180	261	10	y	y	PROPN
ejpam-180	261	11	(	(	PUNCT
ejpam-180	261	12	t	t	PROPN
ejpam-180	261	13	)	)	PUNCT
ejpam-180	261	14	t	t	PROPN
ejpam-180	261	15	gu	gu	PROPN
ejpam-180	261	16	(	(	PUNCT
ejpam-180	261	17	t	t	PROPN
ejpam-180	261	18	,	,	PUNCT
ejpam-180	261	19	u	u	NOUN
ejpam-180	261	20	,	,	PUNCT
ejpam-180	261	21	u̇	u̇	PROPN
ejpam-180	261	22	,	,	PUNCT
ejpam-180	261	23	ü	ü	NUM
ejpam-180	261	24	)	)	PUNCT
ejpam-180	261	25	�	�	PROPN
ejpam-180	261	26	−d	−d	PROPN
ejpam-180	261	27	�	�	PROPN
ejpam-180	262	1	f	f	PROPN
ejpam-180	263	1	i	i	PRON
ejpam-180	263	2	u̇	u̇	PROPN
ejpam-180	263	3	(	(	PUNCT
ejpam-180	263	4	t	t	PROPN
ejpam-180	263	5	,	,	PUNCT
ejpam-180	263	6	u	u	NOUN
ejpam-180	263	7	,	,	PUNCT
ejpam-180	263	8	u̇	u̇	PROPN
ejpam-180	263	9	,	,	PUNCT
ejpam-180	263	10	ü	ü	PRON
ejpam-180	263	11	)	)	PUNCT
ejpam-180	264	1	+	+	CCONJ
ejpam-180	264	2	y	y	PROPN
ejpam-180	264	3	(	(	PUNCT
ejpam-180	264	4	t	t	PROPN
ejpam-180	264	5	)	)	PUNCT
ejpam-180	264	6	t	t	NOUN
ejpam-180	264	7	gu̇	gu̇	PROPN
ejpam-180	264	8	(	(	PUNCT
ejpam-180	264	9	t	t	PROPN
ejpam-180	264	10	,	,	PUNCT
ejpam-180	264	11	u	u	NOUN
ejpam-180	264	12	,	,	PUNCT
ejpam-180	264	13	u̇	u̇	PROPN
ejpam-180	264	14	,	,	PUNCT
ejpam-180	264	15	ü	ü	NUM
ejpam-180	264	16	)	)	PUNCT
ejpam-180	264	17	�	�	PROPN
ejpam-180	264	18	�	�	PROPN
ejpam-180	264	19	d	d	PROPN
ejpam-180	264	20	t	t	PROPN
ejpam-180	264	21	−	−	PROPN
ejpam-180	264	22	p	p	PROPN
ejpam-180	264	23	∑	∑	PROPN
ejpam-180	264	24	i=1	i=1	PROPN
ejpam-180	264	25	λi	λi	X
ejpam-180	264	26	∫	∫	PROPN
ejpam-180	265	1	i	i	PROPN
ejpam-180	265	2	�	�	PROPN
ejpam-180	265	3	dη	dη	PRON
ejpam-180	265	4	�	�	PROPN
ejpam-180	265	5	t	t	PROPN
ejpam-180	265	6	�	�	PROPN
ejpam-180	265	7	f	f	PROPN
ejpam-180	266	1	i	i	PRON
ejpam-180	266	2	u̇	u̇	PROPN
ejpam-180	266	3	(	(	PUNCT
ejpam-180	266	4	t	t	PROPN
ejpam-180	266	5	,	,	PUNCT
ejpam-180	266	6	u	u	NOUN
ejpam-180	266	7	,	,	PUNCT
ejpam-180	266	8	u̇	u̇	PROPN
ejpam-180	266	9	,	,	PUNCT
ejpam-180	266	10	ü	ü	PRON
ejpam-180	266	11	)	)	PUNCT
ejpam-180	267	1	+	+	CCONJ
ejpam-180	267	2	y	y	PROPN
ejpam-180	267	3	(	(	PUNCT
ejpam-180	267	4	t	t	PROPN
ejpam-180	267	5	)	)	PUNCT
ejpam-180	267	6	t	t	NOUN
ejpam-180	267	7	gu̇	gu̇	PROPN
ejpam-180	267	8	(	(	PUNCT
ejpam-180	267	9	t	t	PROPN
ejpam-180	267	10	,	,	PUNCT
ejpam-180	267	11	u	u	NOUN
ejpam-180	267	12	,	,	PUNCT
ejpam-180	267	13	u̇	u̇	PROPN
ejpam-180	267	14	,	,	PUNCT
ejpam-180	267	15	ü	ü	NOUN
ejpam-180	267	16	)	)	PUNCT
ejpam-180	267	17	�	�	PROPN
ejpam-180	267	18	d	d	PROPN
ejpam-180	267	19	t	t	PROPN
ejpam-180	267	20	+	+	CCONJ
ejpam-180	267	21	p	p	NOUN
ejpam-180	267	22	∑	∑	PROPN
ejpam-180	267	23	i=1	i=1	PROPN
ejpam-180	267	24	λiηt	λiηt	PROPN
ejpam-180	267	25	�	�	PROPN
ejpam-180	268	1	f	f	PROPN
ejpam-180	268	2	i	i	PRON
ejpam-180	268	3	u̇	u̇	PROPN
ejpam-180	268	4	(	(	PUNCT
ejpam-180	268	5	t	t	PROPN
ejpam-180	268	6	,	,	PUNCT
ejpam-180	268	7	u	u	NOUN
ejpam-180	268	8	,	,	PUNCT
ejpam-180	268	9	u̇	u̇	PROPN
ejpam-180	268	10	,	,	PUNCT
ejpam-180	268	11	ü	ü	PRON
ejpam-180	268	12	)	)	PUNCT
ejpam-180	269	1	+	+	CCONJ
ejpam-180	269	2	y	y	PROPN
ejpam-180	269	3	(	(	PUNCT
ejpam-180	269	4	t	t	PROPN
ejpam-180	269	5	)	)	PUNCT
ejpam-180	269	6	t	t	NOUN
ejpam-180	269	7	gu̇	gu̇	PROPN
ejpam-180	269	8	(	(	PUNCT
ejpam-180	269	9	t	t	PROPN
ejpam-180	269	10	,	,	PUNCT
ejpam-180	269	11	u	u	NOUN
ejpam-180	269	12	,	,	PUNCT
ejpam-180	269	13	u̇	u̇	PROPN
ejpam-180	269	14	,	,	PUNCT
ejpam-180	269	15	ü	ü	NUM
ejpam-180	269	16	)	)	PUNCT
ejpam-180	269	17	�	�	PROPN
ejpam-180	269	18	�	�	PROPN
ejpam-180	269	19	�	�	PROPN
ejpam-180	269	20	�	�	PROPN
ejpam-180	269	21	t	t	PROPN
ejpam-180	269	22	=	=	PROPN
ejpam-180	269	23	b	b	PROPN
ejpam-180	269	24	t	t	PROPN
ejpam-180	269	25	=	=	SYM
ejpam-180	269	26	a	a	PRON
ejpam-180	269	27	+	+	X
ejpam-180	269	28	p	p	NOUN
ejpam-180	269	29	∑	∑	PUNCT
ejpam-180	269	30	i=1	i=1	PROPN
ejpam-180	269	31	λi	λi	NOUN
ejpam-180	269	32	�	�	PROPN
ejpam-180	269	33	dη	dη	NOUN
ejpam-180	269	34	�	�	PROPN
ejpam-180	269	35	t	t	PROPN
ejpam-180	269	36	�	�	PROPN
ejpam-180	270	1	f	f	PROPN
ejpam-180	271	1	i	i	PRON
ejpam-180	271	2	ü	ü	VERB
ejpam-180	271	3	(	(	PUNCT
ejpam-180	271	4	t	t	PROPN
ejpam-180	271	5	,	,	PUNCT
ejpam-180	271	6	u	u	NOUN
ejpam-180	271	7	,	,	PUNCT
ejpam-180	271	8	u̇	u̇	PROPN
ejpam-180	271	9	,	,	PUNCT
ejpam-180	271	10	ü	ü	PRON
ejpam-180	271	11	)	)	PUNCT
ejpam-180	272	1	+	+	CCONJ
ejpam-180	272	2	y	y	PROPN
ejpam-180	272	3	(	(	PUNCT
ejpam-180	272	4	t	t	PROPN
ejpam-180	272	5	)	)	PUNCT
ejpam-180	272	6	t	t	PROPN
ejpam-180	272	7	gü	gü	PROPN
ejpam-180	272	8	(	(	PUNCT
ejpam-180	272	9	t	t	PROPN
ejpam-180	272	10	,	,	PUNCT
ejpam-180	272	11	u	u	NOUN
ejpam-180	272	12	,	,	PUNCT
ejpam-180	272	13	u̇	u̇	PROPN
ejpam-180	272	14	,	,	PUNCT
ejpam-180	272	15	ü	ü	NUM
ejpam-180	272	16	)	)	PUNCT
ejpam-180	272	17	�	�	PROPN
ejpam-180	272	18	�	�	PROPN
ejpam-180	272	19	�	�	PROPN
ejpam-180	272	20	�	�	PROPN
ejpam-180	272	21	t	t	PROPN
ejpam-180	272	22	=	=	PROPN
ejpam-180	272	23	b	b	PROPN
ejpam-180	272	24	t	t	PROPN
ejpam-180	272	25	=	=	PROPN
ejpam-180	272	26	a	a	PRON
ejpam-180	272	27	using	use	VERB
ejpam-180	272	28	the	the	DET
ejpam-180	272	29	boundary	boundary	ADJ
ejpam-180	272	30	conditions	condition	NOUN
ejpam-180	272	31	which	which	PRON
ejpam-180	272	32	at	at	ADP
ejpam-180	272	33	t	t	PROPN
ejpam-180	272	34	=	=	SYM
ejpam-180	272	35	a	a	X
ejpam-180	272	36	,	,	PUNCT
ejpam-180	272	37	t	t	PROPN
ejpam-180	272	38	=	=	SYM
ejpam-180	272	39	b	b	PROPN
ejpam-180	272	40	gives	give	VERB
ejpam-180	272	41	dη=	dη=	PROPN
ejpam-180	272	42	0=	0=	PUNCT
ejpam-180	273	1	η	η	PROPN
ejpam-180	273	2	,	,	PUNCT
ejpam-180	273	3	we	we	PRON
ejpam-180	273	4	have	have	VERB
ejpam-180	273	5	=	=	PRON
ejpam-180	273	6	p	p	X
ejpam-180	273	7	∑	∑	PROPN
ejpam-180	273	8	i=1	i=1	PROPN
ejpam-180	274	1	λi	λi	X
ejpam-180	274	2	∫	∫	PROPN
ejpam-180	275	1	i	i	PROPN
ejpam-180	275	2	ηt	ηt	ADP
ejpam-180	275	3	�	�	PROPN
ejpam-180	275	4	�	�	PROPN
ejpam-180	275	5	f	f	PROPN
ejpam-180	276	1	i	i	PRON
ejpam-180	276	2	u	u	PROPN
ejpam-180	276	3	(	(	PUNCT
ejpam-180	276	4	t	t	PROPN
ejpam-180	276	5	,	,	PUNCT
ejpam-180	276	6	u	u	NOUN
ejpam-180	276	7	,	,	PUNCT
ejpam-180	276	8	u̇	u̇	PROPN
ejpam-180	276	9	,	,	PUNCT
ejpam-180	276	10	ü	ü	PRON
ejpam-180	276	11	)	)	PUNCT
ejpam-180	277	1	+	+	NUM
ejpam-180	278	1	b	b	X
ejpam-180	278	2	i	i	PRON
ejpam-180	278	3	(	(	PUNCT
ejpam-180	278	4	t	t	PROPN
ejpam-180	278	5	)	)	PUNCT
ejpam-180	278	6	z	z	NOUN
ejpam-180	279	1	i	i	PRON
ejpam-180	279	2	(	(	PUNCT
ejpam-180	279	3	t	t	PROPN
ejpam-180	279	4	)	)	PUNCT
ejpam-180	280	1	+	+	CCONJ
ejpam-180	280	2	y	y	PROPN
ejpam-180	280	3	(	(	PUNCT
ejpam-180	280	4	t	t	PROPN
ejpam-180	280	5	)	)	PUNCT
ejpam-180	280	6	t	t	PROPN
ejpam-180	280	7	gu	gu	PROPN
ejpam-180	280	8	(	(	PUNCT
ejpam-180	280	9	t	t	PROPN
ejpam-180	280	10	,	,	PUNCT
ejpam-180	280	11	u	u	NOUN
ejpam-180	280	12	,	,	PUNCT
ejpam-180	280	13	u̇	u̇	PROPN
ejpam-180	280	14	,	,	PUNCT
ejpam-180	280	15	ü	ü	NUM
ejpam-180	280	16	)	)	PUNCT
ejpam-180	280	17	�	�	PROPN
ejpam-180	280	18	−d	−d	PROPN
ejpam-180	280	19	�	�	PROPN
ejpam-180	281	1	f	f	PROPN
ejpam-180	282	1	i	i	PRON
ejpam-180	282	2	u̇	u̇	PROPN
ejpam-180	282	3	(	(	PUNCT
ejpam-180	282	4	t	t	PROPN
ejpam-180	282	5	,	,	PUNCT
ejpam-180	282	6	u	u	NOUN
ejpam-180	282	7	,	,	PUNCT
ejpam-180	282	8	u̇	u̇	PROPN
ejpam-180	282	9	,	,	PUNCT
ejpam-180	282	10	ü	ü	PRON
ejpam-180	282	11	)	)	PUNCT
ejpam-180	283	1	+	+	CCONJ
ejpam-180	283	2	y	y	PROPN
ejpam-180	283	3	(	(	PUNCT
ejpam-180	283	4	t	t	PROPN
ejpam-180	283	5	)	)	PUNCT
ejpam-180	283	6	t	t	NOUN
ejpam-180	283	7	gu̇	gu̇	PROPN
ejpam-180	283	8	(	(	PUNCT
ejpam-180	283	9	t	t	PROPN
ejpam-180	283	10	,	,	PUNCT
ejpam-180	283	11	u	u	NOUN
ejpam-180	283	12	,	,	PUNCT
ejpam-180	283	13	u̇	u̇	PROPN
ejpam-180	283	14	,	,	PUNCT
ejpam-180	283	15	ü	ü	NUM
ejpam-180	283	16	)	)	PUNCT
ejpam-180	283	17	�	�	PROPN
ejpam-180	283	18	�	�	PROPN
ejpam-180	283	19	d	d	PROPN
ejpam-180	283	20	t	t	PROPN
ejpam-180	283	21	−	−	PROPN
ejpam-180	283	22	p	p	PROPN
ejpam-180	283	23	∑	∑	PROPN
ejpam-180	283	24	i=1	i=1	PROPN
ejpam-180	283	25	λi	λi	X
ejpam-180	283	26	∫	∫	PROPN
ejpam-180	284	1	i	i	PROPN
ejpam-180	284	2	�	�	PROPN
ejpam-180	284	3	dη	dη	PRON
ejpam-180	284	4	�	�	PROPN
ejpam-180	284	5	t	t	PROPN
ejpam-180	284	6	�	�	PROPN
ejpam-180	284	7	f	f	PROPN
ejpam-180	285	1	i	i	PRON
ejpam-180	285	2	u̇	u̇	PROPN
ejpam-180	285	3	(	(	PUNCT
ejpam-180	285	4	t	t	PROPN
ejpam-180	285	5	,	,	PUNCT
ejpam-180	285	6	u	u	NOUN
ejpam-180	285	7	,	,	PUNCT
ejpam-180	285	8	u̇	u̇	PROPN
ejpam-180	285	9	,	,	PUNCT
ejpam-180	285	10	ü	ü	PRON
ejpam-180	285	11	)	)	PUNCT
ejpam-180	286	1	+	+	CCONJ
ejpam-180	286	2	y	y	PROPN
ejpam-180	286	3	(	(	PUNCT
ejpam-180	286	4	t	t	PROPN
ejpam-180	286	5	)	)	PUNCT
ejpam-180	286	6	t	t	NOUN
ejpam-180	286	7	gu̇	gu̇	PROPN
ejpam-180	286	8	(	(	PUNCT
ejpam-180	286	9	t	t	PROPN
ejpam-180	286	10	,	,	PUNCT
ejpam-180	286	11	u	u	NOUN
ejpam-180	286	12	,	,	PUNCT
ejpam-180	286	13	u̇	u̇	PROPN
ejpam-180	286	14	,	,	PUNCT
ejpam-180	286	15	ü	ü	NOUN
ejpam-180	286	16	)	)	PUNCT
ejpam-180	286	17	�	�	PROPN
ejpam-180	287	1	d	d	PROPN
ejpam-180	287	2	t	t	PROPN
ejpam-180	287	3	again	again	ADV
ejpam-180	287	4	,	,	PUNCT
ejpam-180	287	5	integrating	integrate	VERB
ejpam-180	287	6	by	by	ADP
ejpam-180	287	7	parts	part	NOUN
ejpam-180	287	8	we	we	PRON
ejpam-180	287	9	obtain	obtain	VERB
ejpam-180	287	10	=	=	SYM
ejpam-180	287	11	p	p	NOUN
ejpam-180	287	12	∑	∑	PROPN
ejpam-180	287	13	i=1	i=1	PROPN
ejpam-180	288	1	λi	λi	X
ejpam-180	288	2	∫	∫	PROPN
ejpam-180	289	1	i	i	PROPN
ejpam-180	289	2	ηt	ηt	ADP
ejpam-180	289	3	�	�	PROPN
ejpam-180	289	4	�	�	PROPN
ejpam-180	289	5	f	f	PROPN
ejpam-180	290	1	i	i	PRON
ejpam-180	290	2	u	u	PROPN
ejpam-180	290	3	(	(	PUNCT
ejpam-180	290	4	t	t	PROPN
ejpam-180	290	5	,	,	PUNCT
ejpam-180	290	6	u	u	NOUN
ejpam-180	290	7	,	,	PUNCT
ejpam-180	290	8	u̇	u̇	PROPN
ejpam-180	290	9	,	,	PUNCT
ejpam-180	290	10	ü	ü	PRON
ejpam-180	290	11	)	)	PUNCT
ejpam-180	291	1	+	+	NUM
ejpam-180	292	1	b	b	X
ejpam-180	292	2	i	i	PRON
ejpam-180	292	3	(	(	PUNCT
ejpam-180	292	4	t	t	PROPN
ejpam-180	292	5	)	)	PUNCT
ejpam-180	292	6	z	z	NOUN
ejpam-180	293	1	i	i	PRON
ejpam-180	293	2	(	(	PUNCT
ejpam-180	293	3	t	t	PROPN
ejpam-180	293	4	)	)	PUNCT
ejpam-180	294	1	+	+	CCONJ
ejpam-180	294	2	y	y	PROPN
ejpam-180	294	3	(	(	PUNCT
ejpam-180	294	4	t	t	PROPN
ejpam-180	294	5	)	)	PUNCT
ejpam-180	294	6	t	t	PROPN
ejpam-180	294	7	gu	gu	PROPN
ejpam-180	294	8	(	(	PUNCT
ejpam-180	294	9	t	t	PROPN
ejpam-180	294	10	,	,	PUNCT
ejpam-180	294	11	u	u	NOUN
ejpam-180	294	12	,	,	PUNCT
ejpam-180	294	13	u̇	u̇	PROPN
ejpam-180	294	14	,	,	PUNCT
ejpam-180	294	15	ü	ü	NUM
ejpam-180	294	16	)	)	PUNCT
ejpam-180	294	17	�	�	PROPN
ejpam-180	294	18	−d	−d	PROPN
ejpam-180	294	19	�	�	PROPN
ejpam-180	295	1	f	f	PROPN
ejpam-180	296	1	i	i	PRON
ejpam-180	296	2	u̇	u̇	PROPN
ejpam-180	296	3	(	(	PUNCT
ejpam-180	296	4	t	t	PROPN
ejpam-180	296	5	,	,	PUNCT
ejpam-180	296	6	u	u	NOUN
ejpam-180	296	7	,	,	PUNCT
ejpam-180	296	8	u̇	u̇	PROPN
ejpam-180	296	9	,	,	PUNCT
ejpam-180	296	10	ü	ü	PRON
ejpam-180	296	11	)	)	PUNCT
ejpam-180	297	1	+	+	CCONJ
ejpam-180	297	2	y	y	PROPN
ejpam-180	297	3	(	(	PUNCT
ejpam-180	297	4	t	t	PROPN
ejpam-180	297	5	)	)	PUNCT
ejpam-180	297	6	t	t	NOUN
ejpam-180	297	7	gu̇	gu̇	PROPN
ejpam-180	297	8	(	(	PUNCT
ejpam-180	297	9	t	t	PROPN
ejpam-180	297	10	,	,	PUNCT
ejpam-180	297	11	u	u	NOUN
ejpam-180	297	12	,	,	PUNCT
ejpam-180	297	13	u̇	u̇	PROPN
ejpam-180	297	14	,	,	PUNCT
ejpam-180	297	15	ü	ü	NOUN
ejpam-180	297	16	)	)	PUNCT
ejpam-180	297	17	�	�	PROPN
ejpam-180	297	18	+	+	NUM
ejpam-180	297	19	d2	d2	PROPN
ejpam-180	297	20	�	�	PROPN
ejpam-180	297	21	f	f	PROPN
ejpam-180	298	1	i	i	PRON
ejpam-180	298	2	ü	ü	VERB
ejpam-180	298	3	(	(	PUNCT
ejpam-180	298	4	t	t	PROPN
ejpam-180	298	5	,	,	PUNCT
ejpam-180	298	6	u	u	NOUN
ejpam-180	298	7	,	,	PUNCT
ejpam-180	298	8	u̇	u̇	PROPN
ejpam-180	298	9	,	,	PUNCT
ejpam-180	298	10	ü	ü	PRON
ejpam-180	298	11	)	)	PUNCT
ejpam-180	299	1	+	+	CCONJ
ejpam-180	299	2	y	y	PROPN
ejpam-180	299	3	(	(	PUNCT
ejpam-180	299	4	t	t	PROPN
ejpam-180	299	5	)	)	PUNCT
ejpam-180	299	6	t	t	PROPN
ejpam-180	299	7	gü	gü	PROPN
ejpam-180	299	8	(	(	PUNCT
ejpam-180	299	9	t	t	PROPN
ejpam-180	299	10	,	,	PUNCT
ejpam-180	299	11	u	u	NOUN
ejpam-180	299	12	,	,	PUNCT
ejpam-180	299	13	u̇	u̇	PROPN
ejpam-180	299	14	,	,	PUNCT
ejpam-180	299	15	ü	ü	NUM
ejpam-180	299	16	)	)	PUNCT
ejpam-180	299	17	�	�	PROPN
ejpam-180	299	18	�	�	PROPN
ejpam-180	299	19	d	d	PROPN
ejpam-180	299	20	t	t	PROPN
ejpam-180	299	21	i.	i.	PROPN
ejpam-180	299	22	husain	husain	PROPN
ejpam-180	299	23	,	,	PUNCT
ejpam-180	299	24	a.	a.	PROPN
ejpam-180	299	25	ahmed	ahmed	PROPN
ejpam-180	299	26	,	,	PUNCT
ejpam-180	299	27	and	and	CCONJ
ejpam-180	299	28	g.	g.	PROPN
ejpam-180	299	29	rumana	rumana	PROPN
ejpam-180	299	30	/	/	SYM
ejpam-180	299	31	eur	eur	PROPN
ejpam-180	299	32	.	.	PUNCT
ejpam-180	300	1	j.	j.	PROPN
ejpam-180	300	2	pure	pure	PROPN
ejpam-180	300	3	appl	appl	PROPN
ejpam-180	300	4	.	.	PROPN
ejpam-180	300	5	math	math	PROPN
ejpam-180	300	6	,	,	PUNCT
ejpam-180	300	7	2	2	NUM
ejpam-180	300	8	(	(	PUNCT
ejpam-180	300	9	2009	2009	NUM
ejpam-180	300	10	)	)	PUNCT
ejpam-180	300	11	,	,	PUNCT
ejpam-180	300	12	(	(	PUNCT
ejpam-180	300	13	372	372	NUM
ejpam-180	300	14	-	-	SYM
ejpam-180	300	15	400	400	NUM
ejpam-180	300	16	)	)	PUNCT
ejpam-180	300	17	382	382	NUM
ejpam-180	301	1	+	+	CCONJ
ejpam-180	301	2	p	p	X
ejpam-180	301	3	∑	∑	PROPN
ejpam-180	301	4	i=1	i=1	PROPN
ejpam-180	301	5	λiηt	λiηt	PROPN
ejpam-180	301	6	�	�	PROPN
ejpam-180	301	7	f	f	PROPN
ejpam-180	302	1	i	i	PRON
ejpam-180	302	2	ü	ü	VERB
ejpam-180	302	3	(	(	PUNCT
ejpam-180	302	4	t	t	PROPN
ejpam-180	302	5	,	,	PUNCT
ejpam-180	302	6	u	u	NOUN
ejpam-180	302	7	,	,	PUNCT
ejpam-180	302	8	u̇	u̇	PROPN
ejpam-180	302	9	,	,	PUNCT
ejpam-180	302	10	ü	ü	PRON
ejpam-180	302	11	)	)	PUNCT
ejpam-180	303	1	+	+	CCONJ
ejpam-180	303	2	y	y	PROPN
ejpam-180	303	3	(	(	PUNCT
ejpam-180	303	4	t	t	PROPN
ejpam-180	303	5	)	)	PUNCT
ejpam-180	303	6	t	t	PROPN
ejpam-180	303	7	gü	gü	PROPN
ejpam-180	303	8	(	(	PUNCT
ejpam-180	303	9	t	t	PROPN
ejpam-180	303	10	,	,	PUNCT
ejpam-180	303	11	u	u	NOUN
ejpam-180	303	12	,	,	PUNCT
ejpam-180	303	13	u̇	u̇	PROPN
ejpam-180	303	14	,	,	PUNCT
ejpam-180	303	15	ü	ü	NUM
ejpam-180	303	16	)	)	PUNCT
ejpam-180	303	17	�	�	PROPN
ejpam-180	303	18	�	�	PROPN
ejpam-180	303	19	�	�	PROPN
ejpam-180	303	20	�	�	PROPN
ejpam-180	303	21	t	t	PROPN
ejpam-180	303	22	=	=	PROPN
ejpam-180	303	23	b	b	PROPN
ejpam-180	303	24	t	t	PROPN
ejpam-180	303	25	=	=	PROPN
ejpam-180	303	26	a	a	PRON
ejpam-180	303	27	again	again	ADV
ejpam-180	303	28	using	use	VERB
ejpam-180	303	29	boundary	boundary	ADJ
ejpam-180	303	30	conditions	condition	NOUN
ejpam-180	303	31	which	which	PRON
ejpam-180	303	32	at	at	ADP
ejpam-180	303	33	t	t	PROPN
ejpam-180	303	34	=	=	SYM
ejpam-180	303	35	a	a	X
ejpam-180	303	36	,	,	PUNCT
ejpam-180	303	37	t	t	PROPN
ejpam-180	303	38	=	=	SYM
ejpam-180	303	39	b	b	NOUN
ejpam-180	303	40	gives	give	VERB
ejpam-180	303	41	dη	dη	X
ejpam-180	303	42	=	=	SYM
ejpam-180	303	43	0	0	PUNCT
ejpam-180	303	44	=	=	SYM
ejpam-180	303	45	η	η	PROPN
ejpam-180	303	46	,	,	PUNCT
ejpam-180	303	47	∫	∫	PROPN
ejpam-180	303	48	i	i	PROPN
ejpam-180	303	49	ηt	ηt	ADP
ejpam-180	303	50	p	p	PROPN
ejpam-180	303	51	∑	∑	PROPN
ejpam-180	303	52	i=1	i=1	PROPN
ejpam-180	303	53	λi	λi	PROPN
ejpam-180	303	54	�	�	PROPN
ejpam-180	303	55	�	�	PROPN
ejpam-180	303	56	f	f	PROPN
ejpam-180	303	57	i	i	PRON
ejpam-180	303	58	u	u	PROPN
ejpam-180	303	59	(	(	PUNCT
ejpam-180	303	60	t	t	PROPN
ejpam-180	303	61	,	,	PUNCT
ejpam-180	303	62	u	u	NOUN
ejpam-180	303	63	,	,	PUNCT
ejpam-180	303	64	u̇	u̇	PROPN
ejpam-180	303	65	,	,	PUNCT
ejpam-180	303	66	ü	ü	PRON
ejpam-180	303	67	)	)	PUNCT
ejpam-180	304	1	+	+	NUM
ejpam-180	305	1	b	b	X
ejpam-180	305	2	i	i	PRON
ejpam-180	305	3	(	(	PUNCT
ejpam-180	305	4	t)z	t)z	NOUN
ejpam-180	305	5	i	i	PRON
ejpam-180	305	6	(	(	PUNCT
ejpam-180	305	7	t	t	PROPN
ejpam-180	305	8	)	)	PUNCT
ejpam-180	305	9	+	+	CCONJ
ejpam-180	305	10	y	y	PROPN
ejpam-180	305	11	(	(	PUNCT
ejpam-180	305	12	t	t	PROPN
ejpam-180	305	13	)	)	PUNCT
ejpam-180	305	14	t	t	PROPN
ejpam-180	305	15	gu	gu	PROPN
ejpam-180	305	16	(	(	PUNCT
ejpam-180	305	17	t	t	PROPN
ejpam-180	305	18	,	,	PUNCT
ejpam-180	305	19	u	u	NOUN
ejpam-180	305	20	,	,	PUNCT
ejpam-180	305	21	u̇	u̇	PROPN
ejpam-180	305	22	,	,	PUNCT
ejpam-180	305	23	ü	ü	NUM
ejpam-180	305	24	)	)	PUNCT
ejpam-180	305	25	�	�	PROPN
ejpam-180	305	26	−d	−d	PROPN
ejpam-180	305	27	�	�	PROPN
ejpam-180	306	1	f	f	PROPN
ejpam-180	307	1	i	i	PRON
ejpam-180	307	2	u̇	u̇	PROPN
ejpam-180	307	3	(	(	PUNCT
ejpam-180	307	4	t	t	PROPN
ejpam-180	307	5	,	,	PUNCT
ejpam-180	307	6	u	u	NOUN
ejpam-180	307	7	,	,	PUNCT
ejpam-180	307	8	u̇	u̇	PROPN
ejpam-180	307	9	,	,	PUNCT
ejpam-180	307	10	ü	ü	PRON
ejpam-180	307	11	)	)	PUNCT
ejpam-180	308	1	+	+	CCONJ
ejpam-180	308	2	y	y	PROPN
ejpam-180	308	3	(	(	PUNCT
ejpam-180	308	4	t	t	PROPN
ejpam-180	308	5	)	)	PUNCT
ejpam-180	308	6	t	t	NOUN
ejpam-180	308	7	gu̇	gu̇	PROPN
ejpam-180	308	8	(	(	PUNCT
ejpam-180	308	9	t	t	PROPN
ejpam-180	308	10	,	,	PUNCT
ejpam-180	308	11	u	u	NOUN
ejpam-180	308	12	,	,	PUNCT
ejpam-180	308	13	u̇	u̇	PROPN
ejpam-180	308	14	,	,	PUNCT
ejpam-180	308	15	ü	ü	NUM
ejpam-180	308	16	)	)	PUNCT
ejpam-180	308	17	�	�	PROPN
ejpam-180	308	18	(	(	PUNCT
ejpam-180	308	19	4.9	4.9	NUM
ejpam-180	308	20	)	)	PUNCT
ejpam-180	308	21	+	+	PROPN
ejpam-180	308	22	d2	d2	PROPN
ejpam-180	308	23	�	�	PROPN
ejpam-180	308	24	f	f	PROPN
ejpam-180	309	1	i	i	PRON
ejpam-180	309	2	ü	ü	VERB
ejpam-180	309	3	(	(	PUNCT
ejpam-180	309	4	t	t	PROPN
ejpam-180	309	5	,	,	PUNCT
ejpam-180	309	6	u	u	NOUN
ejpam-180	309	7	,	,	PUNCT
ejpam-180	309	8	u̇	u̇	PROPN
ejpam-180	309	9	,	,	PUNCT
ejpam-180	309	10	ü	ü	PRON
ejpam-180	309	11	)	)	PUNCT
ejpam-180	310	1	+	+	CCONJ
ejpam-180	310	2	y	y	PROPN
ejpam-180	310	3	(	(	PUNCT
ejpam-180	310	4	t	t	PROPN
ejpam-180	310	5	)	)	PUNCT
ejpam-180	310	6	t	t	PROPN
ejpam-180	310	7	gü	gü	PROPN
ejpam-180	310	8	(	(	PUNCT
ejpam-180	310	9	t	t	PROPN
ejpam-180	310	10	,	,	PUNCT
ejpam-180	310	11	u	u	NOUN
ejpam-180	310	12	,	,	PUNCT
ejpam-180	310	13	u̇	u̇	PROPN
ejpam-180	310	14	,	,	PUNCT
ejpam-180	310	15	ü	ü	NUM
ejpam-180	310	16	)	)	PUNCT
ejpam-180	310	17	�	�	PROPN
ejpam-180	310	18	�	�	PROPN
ejpam-180	310	19	d	d	PROPN
ejpam-180	310	20	t	t	PROPN
ejpam-180	310	21	<	<	X
ejpam-180	310	22	0	0	NUM
ejpam-180	310	23	from	from	ADP
ejpam-180	310	24	the	the	DET
ejpam-180	310	25	equality	equality	NOUN
ejpam-180	310	26	constraint	constraint	NOUN
ejpam-180	310	27	(	(	PUNCT
ejpam-180	310	28	4.3	4.3	NUM
ejpam-180	310	29	)	)	PUNCT
ejpam-180	310	30	,	,	PUNCT
ejpam-180	310	31	we	we	PRON
ejpam-180	310	32	have	have	VERB
ejpam-180	310	33	∫	∫	PROPN
ejpam-180	311	1	i	i	PRON
ejpam-180	311	2	ηt	ηt	ADP
ejpam-180	311	3	p	p	PROPN
ejpam-180	311	4	∑	∑	PROPN
ejpam-180	311	5	i=1	i=1	PROPN
ejpam-180	311	6	λi	λi	PROPN
ejpam-180	311	7	�	�	PROPN
ejpam-180	311	8	�	�	PROPN
ejpam-180	311	9	f	f	PROPN
ejpam-180	312	1	i	i	PRON
ejpam-180	312	2	u	u	PROPN
ejpam-180	312	3	(	(	PUNCT
ejpam-180	312	4	t	t	PROPN
ejpam-180	312	5	,	,	PUNCT
ejpam-180	312	6	u	u	NOUN
ejpam-180	312	7	,	,	PUNCT
ejpam-180	312	8	u̇	u̇	PROPN
ejpam-180	312	9	,	,	PUNCT
ejpam-180	312	10	ü	ü	PRON
ejpam-180	312	11	)	)	PUNCT
ejpam-180	313	1	+	+	NUM
ejpam-180	314	1	b	b	X
ejpam-180	314	2	i	i	PRON
ejpam-180	314	3	(	(	PUNCT
ejpam-180	314	4	t	t	PROPN
ejpam-180	314	5	)	)	PUNCT
ejpam-180	314	6	z	z	NOUN
ejpam-180	315	1	i	i	PRON
ejpam-180	315	2	(	(	PUNCT
ejpam-180	315	3	t	t	PROPN
ejpam-180	315	4	)	)	PUNCT
ejpam-180	316	1	+	+	CCONJ
ejpam-180	316	2	y	y	PROPN
ejpam-180	316	3	(	(	PUNCT
ejpam-180	316	4	t	t	PROPN
ejpam-180	316	5	)	)	PUNCT
ejpam-180	316	6	t	t	PROPN
ejpam-180	316	7	gu	gu	PROPN
ejpam-180	316	8	(	(	PUNCT
ejpam-180	316	9	t	t	PROPN
ejpam-180	316	10	,	,	PUNCT
ejpam-180	316	11	u	u	NOUN
ejpam-180	316	12	,	,	PUNCT
ejpam-180	316	13	u̇	u̇	PROPN
ejpam-180	316	14	,	,	PUNCT
ejpam-180	316	15	ü	ü	NUM
ejpam-180	316	16	)	)	PUNCT
ejpam-180	316	17	�	�	PROPN
ejpam-180	316	18	−d	−d	PROPN
ejpam-180	316	19	�	�	PROPN
ejpam-180	317	1	f	f	PROPN
ejpam-180	318	1	i	i	PRON
ejpam-180	318	2	u̇	u̇	PROPN
ejpam-180	318	3	(	(	PUNCT
ejpam-180	318	4	t	t	PROPN
ejpam-180	318	5	,	,	PUNCT
ejpam-180	318	6	u	u	NOUN
ejpam-180	318	7	,	,	PUNCT
ejpam-180	318	8	u̇	u̇	PROPN
ejpam-180	318	9	,	,	PUNCT
ejpam-180	318	10	ü	ü	PRON
ejpam-180	318	11	)	)	PUNCT
ejpam-180	319	1	+	+	CCONJ
ejpam-180	319	2	y	y	PROPN
ejpam-180	319	3	(	(	PUNCT
ejpam-180	319	4	t	t	PROPN
ejpam-180	319	5	)	)	PUNCT
ejpam-180	319	6	t	t	NOUN
ejpam-180	319	7	gu̇	gu̇	PROPN
ejpam-180	319	8	(	(	PUNCT
ejpam-180	319	9	t	t	PROPN
ejpam-180	319	10	,	,	PUNCT
ejpam-180	319	11	u	u	NOUN
ejpam-180	319	12	,	,	PUNCT
ejpam-180	319	13	u̇	u̇	PROPN
ejpam-180	319	14	,	,	PUNCT
ejpam-180	319	15	ü	ü	NUM
ejpam-180	319	16	)	)	PUNCT
ejpam-180	319	17	�	�	PROPN
ejpam-180	319	18	(	(	PUNCT
ejpam-180	319	19	4.10	4.10	NUM
ejpam-180	319	20	)	)	PUNCT
ejpam-180	319	21	+	+	ADJ
ejpam-180	319	22	d2	d2	PROPN
ejpam-180	319	23	�	�	PROPN
ejpam-180	319	24	f	f	PROPN
ejpam-180	320	1	i	i	PRON
ejpam-180	320	2	ü	ü	VERB
ejpam-180	320	3	(	(	PUNCT
ejpam-180	320	4	t	t	PROPN
ejpam-180	320	5	,	,	PUNCT
ejpam-180	320	6	u	u	NOUN
ejpam-180	320	7	,	,	PUNCT
ejpam-180	320	8	u̇	u̇	PROPN
ejpam-180	320	9	,	,	PUNCT
ejpam-180	320	10	ü	ü	PRON
ejpam-180	320	11	)	)	PUNCT
ejpam-180	321	1	+	+	CCONJ
ejpam-180	321	2	y	y	PROPN
ejpam-180	321	3	(	(	PUNCT
ejpam-180	321	4	t	t	PROPN
ejpam-180	321	5	)	)	PUNCT
ejpam-180	321	6	t	t	PROPN
ejpam-180	321	7	gü	gü	PROPN
ejpam-180	321	8	(	(	PUNCT
ejpam-180	321	9	t	t	PROPN
ejpam-180	321	10	,	,	PUNCT
ejpam-180	321	11	u	u	NOUN
ejpam-180	321	12	,	,	PUNCT
ejpam-180	321	13	u̇	u̇	PROPN
ejpam-180	321	14	,	,	PUNCT
ejpam-180	321	15	ü	ü	NUM
ejpam-180	321	16	)	)	PUNCT
ejpam-180	321	17	�	�	PROPN
ejpam-180	321	18	�	�	PROPN
ejpam-180	321	19	d	d	PROPN
ejpam-180	321	20	t	t	PROPN
ejpam-180	321	21	=	=	PUNCT
ejpam-180	321	22	0	0	PROPN
ejpam-180	321	23	the	the	DET
ejpam-180	321	24	inequality	inequality	NOUN
ejpam-180	321	25	(	(	PUNCT
ejpam-180	321	26	4.9	4.9	NUM
ejpam-180	321	27	)	)	PUNCT
ejpam-180	321	28	contradicts	contradict	VERB
ejpam-180	321	29	(	(	PUNCT
ejpam-180	321	30	4.10	4.10	NUM
ejpam-180	321	31	)	)	PUNCT
ejpam-180	321	32	.	.	PUNCT
ejpam-180	322	1	hence	hence	ADV
ejpam-180	322	2	our	our	PRON
ejpam-180	322	3	assumption	assumption	NOUN
ejpam-180	322	4	is	be	AUX
ejpam-180	322	5	invalid	invalid	ADJ
ejpam-180	322	6	and	and	CCONJ
ejpam-180	322	7	the	the	DET
ejpam-180	322	8	theorem	theorem	NOUN
ejpam-180	322	9	follows	follow	VERB
ejpam-180	322	10	.	.	PUNCT
ejpam-180	323	1	theorem	theorem	VERB
ejpam-180	323	2	4.2	4.2	NUM
ejpam-180	323	3	(	(	PUNCT
ejpam-180	323	4	strong	strong	ADJ
ejpam-180	323	5	duality	duality	NOUN
ejpam-180	323	6	)	)	PUNCT
ejpam-180	323	7	.	.	PUNCT
ejpam-180	324	1	let	let	VERB
ejpam-180	324	2	x̄	x̄	PRON
ejpam-180	324	3	∈	∈	PROPN
ejpam-180	324	4	x	x	PUNCT
ejpam-180	324	5	be	be	AUX
ejpam-180	324	6	an	an	DET
ejpam-180	324	7	efficient	efficient	ADJ
ejpam-180	324	8	solution	solution	NOUN
ejpam-180	324	9	of	of	ADP
ejpam-180	324	10	(	(	PUNCT
ejpam-180	324	11	vp	vp	NOUN
ejpam-180	324	12	)	)	PUNCT
ejpam-180	324	13	and	and	CCONJ
ejpam-180	324	14	for	for	ADP
ejpam-180	324	15	at	at	ADV
ejpam-180	324	16	least	least	ADV
ejpam-180	324	17	one	one	NUM
ejpam-180	324	18	k	k	PROPN
ejpam-180	324	19	∈	∈	PROPN
ejpam-180	324	20	p	p	X
ejpam-180	324	21	,	,	PUNCT
ejpam-180	324	22	x̄	x̄	PRON
ejpam-180	324	23	satisfies	satisfy	VERB
ejpam-180	324	24	the	the	DET
ejpam-180	324	25	regularity	regularity	NOUN
ejpam-180	324	26	condition	condition	NOUN
ejpam-180	325	1	[	[	X
ejpam-180	325	2	3	3	X
ejpam-180	325	3	]	]	PUNCT
ejpam-180	325	4	for	for	ADP
ejpam-180	325	5	the	the	DET
ejpam-180	325	6	problem	problem	NOUN
ejpam-180	325	7	(	(	PUNCT
ejpam-180	325	8	pk	pk	NOUN
ejpam-180	325	9	(	(	PUNCT
ejpam-180	325	10	x̄	x̄	PROPN
ejpam-180	325	11	)	)	PUNCT
ejpam-180	325	12	)	)	PUNCT
ejpam-180	325	13	.	.	PUNCT
ejpam-180	326	1	then	then	ADV
ejpam-180	326	2	there	there	PRON
ejpam-180	326	3	exist	exist	VERB
ejpam-180	326	4	multipliers	multiplier	NOUN
ejpam-180	326	5	λ	λ	PROPN
ejpam-180	326	6	∈	∈	PROPN
ejpam-180	326	7	rp	rp	NOUN
ejpam-180	326	8	,	,	PUNCT
ejpam-180	326	9	piecewise	piecewise	NOUN
ejpam-180	326	10	smooth	smooth	ADJ
ejpam-180	326	11	ȳ	ȳ	PROPN
ejpam-180	326	12	∈	∈	PROPN
ejpam-180	326	13	rm	rm	PROPN
ejpam-180	326	14	,	,	PUNCT
ejpam-180	326	15	z	z	PROPN
ejpam-180	326	16	i(t	i(t	PROPN
ejpam-180	326	17	)	)	PUNCT
ejpam-180	326	18	∈	∈	PROPN
ejpam-180	326	19	rn	rn	PROPN
ejpam-180	326	20	,	,	PUNCT
ejpam-180	326	21	i	i	PRON
ejpam-180	326	22	=	=	PUNCT
ejpam-180	326	23	{	{	PUNCT
ejpam-180	326	24	1	1	NUM
ejpam-180	326	25	,	,	PUNCT
ejpam-180	326	26	2	2	NUM
ejpam-180	326	27	,	,	PUNCT
ejpam-180	326	28	.	.	PUNCT
ejpam-180	326	29	.	.	PUNCT
ejpam-180	327	1	.	.	PUNCT
ejpam-180	328	1	,	,	PUNCT
ejpam-180	328	2	p	p	X
ejpam-180	328	3	}	}	PUNCT
ejpam-180	328	4	such	such	ADJ
ejpam-180	328	5	that	that	SCONJ
ejpam-180	328	6	(	(	PUNCT
ejpam-180	328	7	x̄	x̄	NOUN
ejpam-180	328	8	,	,	PUNCT
ejpam-180	328	9	ū	ū	PROPN
ejpam-180	328	10	,	,	PUNCT
ejpam-180	328	11	ȳ	ȳ	PROPN
ejpam-180	328	12	,	,	PUNCT
ejpam-180	328	13	ȳ	ȳ	PROPN
ejpam-180	328	14	,	,	PUNCT
ejpam-180	328	15	z̄1	z̄1	PROPN
ejpam-180	328	16	,	,	PUNCT
ejpam-180	328	17	.	.	PUNCT
ejpam-180	328	18	.	.	PUNCT
ejpam-180	329	1	.	.	PUNCT
ejpam-180	330	1	,	,	PUNCT
ejpam-180	330	2	z̄p	z̄p	PROPN
ejpam-180	330	3	,	,	PUNCT
ejpam-180	330	4	λ	λ	X
ejpam-180	330	5	)	)	PUNCT
ejpam-180	330	6	is	be	AUX
ejpam-180	330	7	feasible	feasible	ADJ
ejpam-180	330	8	for	for	ADP
ejpam-180	330	9	(	(	PUNCT
ejpam-180	330	10	mwd	mwd	PROPN
ejpam-180	330	11	)	)	PUNCT
ejpam-180	330	12	and	and	CCONJ
ejpam-180	330	13	the	the	DET
ejpam-180	330	14	objectives	objective	NOUN
ejpam-180	330	15	of	of	ADP
ejpam-180	330	16	(	(	PUNCT
ejpam-180	330	17	vp	vp	NOUN
ejpam-180	330	18	)	)	PUNCT
ejpam-180	330	19	and	and	CCONJ
ejpam-180	330	20	(	(	PUNCT
ejpam-180	330	21	mwd	mwd	PROPN
ejpam-180	330	22	)	)	PUNCT
ejpam-180	330	23	are	be	AUX
ejpam-180	330	24	equal	equal	ADJ
ejpam-180	330	25	.	.	PUNCT
ejpam-180	331	1	further	far	ADV
ejpam-180	331	2	,	,	PUNCT
ejpam-180	331	3	if	if	SCONJ
ejpam-180	331	4	the	the	DET
ejpam-180	331	5	hypothesis	hypothesis	NOUN
ejpam-180	331	6	of	of	ADP
ejpam-180	331	7	theorem	theorem	NOUN
ejpam-180	331	8	4.1	4.1	NUM
ejpam-180	331	9	is	be	AUX
ejpam-180	331	10	met	meet	VERB
ejpam-180	331	11	,	,	PUNCT
ejpam-180	331	12	then	then	ADV
ejpam-180	331	13	(	(	PUNCT
ejpam-180	331	14	x	x	X
ejpam-180	331	15	,	,	PUNCT
ejpam-180	331	16	u	u	PROPN
ejpam-180	331	17	,	,	PUNCT
ejpam-180	331	18	y	y	PROPN
ejpam-180	331	19	,	,	PUNCT
ejpam-180	331	20	z1	z1	PROPN
ejpam-180	331	21	,	,	PUNCT
ejpam-180	331	22	.	.	PUNCT
ejpam-180	331	23	.	.	PUNCT
ejpam-180	331	24	.	.	PUNCT
ejpam-180	332	1	,	,	PUNCT
ejpam-180	332	2	zp	zp	PROPN
ejpam-180	332	3	,	,	PUNCT
ejpam-180	332	4	λ	λ	X
ejpam-180	332	5	)	)	PUNCT
ejpam-180	332	6	is	be	AUX
ejpam-180	332	7	an	an	DET
ejpam-180	332	8	efficient	efficient	ADJ
ejpam-180	332	9	solution	solution	NOUN
ejpam-180	332	10	of	of	ADP
ejpam-180	332	11	(	(	PUNCT
ejpam-180	332	12	mwd	mwd	PROPN
ejpam-180	332	13	)	)	PUNCT
ejpam-180	332	14	.	.	PUNCT
ejpam-180	333	1	proof	proof	NOUN
ejpam-180	333	2	.	.	PUNCT
ejpam-180	334	1	by	by	ADP
ejpam-180	334	2	lemma	lemma	PROPN
ejpam-180	334	3	2.1	2.1	NUM
ejpam-180	334	4	x̄	x̄	NOUN
ejpam-180	334	5	is	be	AUX
ejpam-180	334	6	an	an	DET
ejpam-180	334	7	optimal	optimal	ADJ
ejpam-180	334	8	solution	solution	NOUN
ejpam-180	334	9	of	of	ADP
ejpam-180	334	10	(	(	PUNCT
ejpam-180	334	11	pk	pk	NOUN
ejpam-180	334	12	(	(	PUNCT
ejpam-180	334	13	x̄	x̄	PROPN
ejpam-180	334	14	)	)	PUNCT
ejpam-180	334	15	)	)	PUNCT
ejpam-180	334	16	.	.	PUNCT
ejpam-180	335	1	this	this	PRON
ejpam-180	335	2	implies	imply	VERB
ejpam-180	335	3	that	that	SCONJ
ejpam-180	335	4	there	there	PRON
ejpam-180	335	5	exist	exist	VERB
ejpam-180	335	6	ξ̄	ξ̄	ADJ
ejpam-180	335	7	∈	∈	PROPN
ejpam-180	335	8	rp	rp	NOUN
ejpam-180	335	9	with	with	ADP
ejpam-180	335	10	ξ̄1	ξ̄1	NUM
ejpam-180	335	11	,	,	PUNCT
ejpam-180	335	12	.	.	PUNCT
ejpam-180	335	13	.	.	PUNCT
ejpam-180	336	1	.	.	PUNCT
ejpam-180	337	1	,	,	PUNCT
ejpam-180	337	2	ξ̄p	ξ̄p	PROPN
ejpam-180	337	3	,	,	PUNCT
ejpam-180	337	4	z̄	z̄	PROPN
ejpam-180	337	5	i(t	i(t	PROPN
ejpam-180	337	6	)	)	PUNCT
ejpam-180	337	7	∈	∈	PROPN
ejpam-180	337	8	rn	rn	PROPN
ejpam-180	337	9	,	,	PUNCT
ejpam-180	337	10	i	i	PRON
ejpam-180	337	11	=	=	PUNCT
ejpam-180	337	12	{	{	PUNCT
ejpam-180	337	13	1	1	NUM
ejpam-180	337	14	,	,	PUNCT
ejpam-180	337	15	2	2	NUM
ejpam-180	337	16	,	,	PUNCT
ejpam-180	337	17	.	.	PUNCT
ejpam-180	337	18	.	.	PUNCT
ejpam-180	338	1	.	.	PUNCT
ejpam-180	339	1	,	,	PUNCT
ejpam-180	339	2	p	p	X
ejpam-180	339	3	}	}	PUNCT
ejpam-180	339	4	and	and	CCONJ
ejpam-180	339	5	piecewise	piecewise	VERB
ejpam-180	339	6	smooth	smooth	ADJ
ejpam-180	339	7	v̄	v̄	PROPN
ejpam-180	339	8	∈	∈	PROPN
ejpam-180	339	9	rm	rm	PROPN
ejpam-180	339	10	i.	i.	PROPN
ejpam-180	339	11	husain	husain	PROPN
ejpam-180	339	12	,	,	PUNCT
ejpam-180	339	13	a.	a.	PROPN
ejpam-180	339	14	ahmed	ahmed	PROPN
ejpam-180	339	15	,	,	PUNCT
ejpam-180	339	16	and	and	CCONJ
ejpam-180	339	17	g.	g.	PROPN
ejpam-180	339	18	rumana	rumana	PROPN
ejpam-180	339	19	/	/	SYM
ejpam-180	339	20	eur	eur	PROPN
ejpam-180	339	21	.	.	PUNCT
ejpam-180	340	1	j.	j.	PROPN
ejpam-180	340	2	pure	pure	PROPN
ejpam-180	340	3	appl	appl	PROPN
ejpam-180	340	4	.	.	PROPN
ejpam-180	340	5	math	math	PROPN
ejpam-180	340	6	,	,	PUNCT
ejpam-180	340	7	2	2	NUM
ejpam-180	340	8	(	(	PUNCT
ejpam-180	340	9	2009	2009	NUM
ejpam-180	340	10	)	)	PUNCT
ejpam-180	340	11	,	,	PUNCT
ejpam-180	340	12	(	(	PUNCT
ejpam-180	340	13	372	372	NUM
ejpam-180	340	14	-	-	SYM
ejpam-180	340	15	400	400	NUM
ejpam-180	340	16	)	)	PUNCT
ejpam-180	340	17	383	383	NUM
ejpam-180	340	18	such	such	ADJ
ejpam-180	340	19	that	that	SCONJ
ejpam-180	340	20	,	,	PUNCT
ejpam-180	340	21	the	the	DET
ejpam-180	340	22	following	follow	VERB
ejpam-180	340	23	optimality	optimality	NOUN
ejpam-180	340	24	conditions	condition	NOUN
ejpam-180	340	25	(	(	PUNCT
ejpam-180	340	26	4.7	4.7	NUM
ejpam-180	340	27	)	)	PUNCT
ejpam-180	340	28	and	and	CCONJ
ejpam-180	340	29	(	(	PUNCT
ejpam-180	340	30	4.3	4.3	NUM
ejpam-180	340	31	)	)	PUNCT
ejpam-180	340	32	hold	hold	VERB
ejpam-180	340	33	:	:	PUNCT
ejpam-180	341	1	ξ̄k	ξ̄k	NUM
ejpam-180	341	2	�	�	PROPN
ejpam-180	341	3	f	f	PROPN
ejpam-180	341	4	k	k	PROPN
ejpam-180	341	5	x	x	X
ejpam-180	341	6	(	(	PUNCT
ejpam-180	341	7	t	t	PROPN
ejpam-180	341	8	,	,	PUNCT
ejpam-180	341	9	x	x	X
ejpam-180	341	10	,	,	PUNCT
ejpam-180	341	11	ẋ	ẋ	PROPN
ejpam-180	341	12	,	,	PUNCT
ejpam-180	341	13	ẍ	ẍ	X
ejpam-180	341	14	)	)	PUNCT
ejpam-180	342	1	+	+	CCONJ
ejpam-180	342	2	bk	bk	PRON
ejpam-180	342	3	(	(	PUNCT
ejpam-180	342	4	t	t	NOUN
ejpam-180	342	5	)	)	PUNCT
ejpam-180	342	6	z̄k	z̄k	NOUN
ejpam-180	342	7	(	(	PUNCT
ejpam-180	342	8	t)−	t)−	PROPN
ejpam-180	343	1	d	d	X
ejpam-180	343	2	f	f	X
ejpam-180	343	3	k	k	PROPN
ejpam-180	343	4	ẋ	ẋ	PROPN
ejpam-180	343	5	(	(	PUNCT
ejpam-180	343	6	t	t	PROPN
ejpam-180	343	7	,	,	PUNCT
ejpam-180	343	8	x	x	X
ejpam-180	343	9	,	,	PUNCT
ejpam-180	343	10	ẋ	ẋ	PROPN
ejpam-180	343	11	,	,	PUNCT
ejpam-180	343	12	ẍ	ẍ	X
ejpam-180	343	13	)	)	PUNCT
ejpam-180	344	1	+	+	CCONJ
ejpam-180	344	2	d2	d2	PROPN
ejpam-180	344	3	f	f	PROPN
ejpam-180	344	4	k	k	PROPN
ejpam-180	344	5	ẍ	ẍ	PROPN
ejpam-180	344	6	(	(	PUNCT
ejpam-180	344	7	t	t	PROPN
ejpam-180	344	8	,	,	PUNCT
ejpam-180	344	9	x	x	X
ejpam-180	344	10	,	,	PUNCT
ejpam-180	344	11	ẋ	ẋ	PROPN
ejpam-180	344	12	,	,	PUNCT
ejpam-180	344	13	ẍ	ẍ	X
ejpam-180	344	14	)	)	PUNCT
ejpam-180	344	15	�	�	PROPN
ejpam-180	345	1	+	+	CCONJ
ejpam-180	345	2	p	p	PROPN
ejpam-180	345	3	∑	∑	PUNCT
ejpam-180	345	4	i=1	i=1	PROPN
ejpam-180	345	5	i	i	PRON
ejpam-180	345	6	6	6	NUM
ejpam-180	345	7	=	=	SYM
ejpam-180	345	8	k	k	X
ejpam-180	345	9	ξ̄i	ξ̄i	PROPN
ejpam-180	345	10	�	�	PROPN
ejpam-180	345	11	f	f	PROPN
ejpam-180	345	12	i	i	NOUN
ejpam-180	345	13	x	x	X
ejpam-180	345	14	(	(	PUNCT
ejpam-180	345	15	t	t	NOUN
ejpam-180	345	16	,	,	PUNCT
ejpam-180	345	17	x	x	X
ejpam-180	345	18	,	,	PUNCT
ejpam-180	345	19	ẋ	ẋ	PROPN
ejpam-180	345	20	,	,	PUNCT
ejpam-180	345	21	ẍ	ẍ	X
ejpam-180	345	22	)	)	PUNCT
ejpam-180	346	1	+	+	CCONJ
ejpam-180	347	1	b	b	X
ejpam-180	347	2	i	i	PRON
ejpam-180	347	3	(	(	PUNCT
ejpam-180	347	4	t	t	PROPN
ejpam-180	347	5	)	)	PUNCT
ejpam-180	347	6	z̄	z̄	PROPN
ejpam-180	347	7	i	i	PRON
ejpam-180	347	8	(	(	PUNCT
ejpam-180	347	9	t)−	t)−	PROPN
ejpam-180	348	1	d	d	X
ejpam-180	348	2	f	f	X
ejpam-180	349	1	i	i	PRON
ejpam-180	349	2	ẋ	ẋ	PROPN
ejpam-180	350	1	(	(	PUNCT
ejpam-180	350	2	t	t	PROPN
ejpam-180	350	3	,	,	PUNCT
ejpam-180	350	4	x	x	X
ejpam-180	350	5	,	,	PUNCT
ejpam-180	350	6	ẋ	ẋ	PROPN
ejpam-180	350	7	,	,	PUNCT
ejpam-180	350	8	ẍ	ẍ	X
ejpam-180	350	9	)	)	PUNCT
ejpam-180	351	1	+	+	CCONJ
ejpam-180	352	1	d2	d2	PROPN
ejpam-180	352	2	f	f	PROPN
ejpam-180	352	3	i	i	PRON
ejpam-180	352	4	ẍ	ẍ	PROPN
ejpam-180	353	1	(	(	PUNCT
ejpam-180	353	2	t	t	PROPN
ejpam-180	353	3	,	,	PUNCT
ejpam-180	353	4	x	x	X
ejpam-180	353	5	,	,	PUNCT
ejpam-180	353	6	ẋ	ẋ	PROPN
ejpam-180	353	7	,	,	PUNCT
ejpam-180	353	8	ẍ	ẍ	X
ejpam-180	353	9	)	)	PUNCT
ejpam-180	353	10	�	�	PROPN
ejpam-180	354	1	+	+	PROPN
ejpam-180	354	2	v̄	v̄	PROPN
ejpam-180	354	3	(	(	PUNCT
ejpam-180	354	4	t	t	PROPN
ejpam-180	354	5	)	)	PUNCT
ejpam-180	354	6	t	t	PROPN
ejpam-180	354	7	gx	gx	PROPN
ejpam-180	354	8	(	(	PUNCT
ejpam-180	354	9	t	t	PROPN
ejpam-180	354	10	,	,	PUNCT
ejpam-180	354	11	x	x	X
ejpam-180	354	12	,	,	PUNCT
ejpam-180	354	13	ẋ	ẋ	PROPN
ejpam-180	354	14	,	,	PUNCT
ejpam-180	354	15	ẍ)−	ẍ)−	PROPN
ejpam-180	354	16	d	d	PROPN
ejpam-180	354	17	�	�	PROPN
ejpam-180	354	18	v̄	v̄	PROPN
ejpam-180	354	19	(	(	PUNCT
ejpam-180	354	20	t	t	PROPN
ejpam-180	354	21	)	)	PUNCT
ejpam-180	354	22	t	t	PROPN
ejpam-180	354	23	g	g	PROPN
ejpam-180	354	24	ẋ	ẋ	PROPN
ejpam-180	355	1	(	(	PUNCT
ejpam-180	355	2	t	t	PROPN
ejpam-180	355	3	,	,	PUNCT
ejpam-180	355	4	x	x	X
ejpam-180	355	5	,	,	PUNCT
ejpam-180	355	6	ẋ	ẋ	PROPN
ejpam-180	355	7	,	,	PUNCT
ejpam-180	355	8	ẍ	ẍ	X
ejpam-180	355	9	)	)	PUNCT
ejpam-180	355	10	�	�	PROPN
ejpam-180	356	1	+	+	NUM
ejpam-180	356	2	d2	d2	PROPN
ejpam-180	356	3	�	�	PROPN
ejpam-180	356	4	v̄	v̄	PROPN
ejpam-180	356	5	(	(	PUNCT
ejpam-180	356	6	t	t	PROPN
ejpam-180	356	7	)	)	PUNCT
ejpam-180	356	8	t	t	PROPN
ejpam-180	356	9	g	g	PROPN
ejpam-180	356	10	ẍ	ẍ	PROPN
ejpam-180	357	1	(	(	PUNCT
ejpam-180	357	2	t	t	PROPN
ejpam-180	357	3	,	,	PUNCT
ejpam-180	357	4	x	x	X
ejpam-180	357	5	,	,	PUNCT
ejpam-180	357	6	ẋ	ẋ	PROPN
ejpam-180	357	7	,	,	PUNCT
ejpam-180	357	8	ẍ	ẍ	X
ejpam-180	357	9	)	)	PUNCT
ejpam-180	357	10	�	�	PROPN
ejpam-180	357	11	=	=	SYM
ejpam-180	357	12	0	0	NUM
ejpam-180	357	13	(	(	PUNCT
ejpam-180	357	14	4.11	4.11	NUM
ejpam-180	357	15	)	)	PUNCT
ejpam-180	357	16	�	�	PROPN
ejpam-180	357	17	x̄	x̄	PROPN
ejpam-180	357	18	(	(	PUNCT
ejpam-180	357	19	t	t	PROPN
ejpam-180	357	20	)	)	PUNCT
ejpam-180	357	21	t	t	PROPN
ejpam-180	358	1	b	b	PROPN
ejpam-180	358	2	i	i	PROPN
ejpam-180	358	3	(	(	PUNCT
ejpam-180	358	4	t	t	PROPN
ejpam-180	358	5	)	)	PUNCT
ejpam-180	358	6	x̄	x̄	NOUN
ejpam-180	358	7	(	(	PUNCT
ejpam-180	358	8	t	t	PROPN
ejpam-180	358	9	)	)	PUNCT
ejpam-180	358	10	�	�	PROPN
ejpam-180	358	11	1	1	NUM
ejpam-180	358	12	2	2	NUM
ejpam-180	358	13	=	=	SYM
ejpam-180	358	14	�	�	PROPN
ejpam-180	358	15	x̄	x̄	PROPN
ejpam-180	358	16	(	(	PUNCT
ejpam-180	358	17	t	t	PROPN
ejpam-180	358	18	)	)	PUNCT
ejpam-180	358	19	t	t	PROPN
ejpam-180	358	20	b	b	PROPN
ejpam-180	359	1	i	i	PROPN
ejpam-180	359	2	(	(	PUNCT
ejpam-180	359	3	t	t	PROPN
ejpam-180	359	4	)	)	PUNCT
ejpam-180	359	5	z̄	z̄	PROPN
ejpam-180	360	1	i	i	PROPN
ejpam-180	360	2	(	(	PUNCT
ejpam-180	360	3	t	t	PROPN
ejpam-180	360	4	)	)	PUNCT
ejpam-180	360	5	�	�	PROPN
ejpam-180	360	6	,	,	PUNCT
ejpam-180	360	7	i	i	PRON
ejpam-180	360	8	=	=	NOUN
ejpam-180	360	9	1	1	NUM
ejpam-180	360	10	,	,	PUNCT
ejpam-180	360	11	.	.	PUNCT
ejpam-180	360	12	.	.	PUNCT
ejpam-180	360	13	.	.	PUNCT
ejpam-180	361	1	,	,	PUNCT
ejpam-180	361	2	p	p	X
ejpam-180	361	3	(	(	PUNCT
ejpam-180	361	4	4.12	4.12	NUM
ejpam-180	361	5	)	)	PUNCT
ejpam-180	361	6	v̄	v̄	NOUN
ejpam-180	361	7	(	(	PUNCT
ejpam-180	361	8	t	t	PROPN
ejpam-180	361	9	)	)	PUNCT
ejpam-180	361	10	t	t	PROPN
ejpam-180	361	11	g	g	PROPN
ejpam-180	361	12	�	�	PROPN
ejpam-180	361	13	t	t	PROPN
ejpam-180	361	14	,	,	PUNCT
ejpam-180	361	15	x̄	x̄	PROPN
ejpam-180	361	16	,	,	PUNCT
ejpam-180	361	17	˙̄x	˙̄x	PUNCT
ejpam-180	361	18	,	,	PUNCT
ejpam-180	361	19	¨̄x	¨̄x	PRON
ejpam-180	361	20	�	�	PROPN
ejpam-180	361	21	d	d	PROPN
ejpam-180	361	22	t	t	PROPN
ejpam-180	361	23	=	=	SYM
ejpam-180	361	24	0	0	NUM
ejpam-180	361	25	(	(	PUNCT
ejpam-180	361	26	4.13	4.13	NUM
ejpam-180	361	27	)	)	PUNCT
ejpam-180	361	28	�	�	PROPN
ejpam-180	361	29	z̄	z̄	PROPN
ejpam-180	361	30	(	(	PUNCT
ejpam-180	361	31	t	t	PROPN
ejpam-180	361	32	)	)	PUNCT
ejpam-180	361	33	t	t	PROPN
ejpam-180	362	1	b	b	PROPN
ejpam-180	362	2	i	i	PROPN
ejpam-180	362	3	(	(	PUNCT
ejpam-180	362	4	t	t	PROPN
ejpam-180	362	5	)	)	PUNCT
ejpam-180	362	6	z̄	z̄	PROPN
ejpam-180	363	1	i	i	PROPN
ejpam-180	363	2	(	(	PUNCT
ejpam-180	363	3	t	t	PROPN
ejpam-180	363	4	)	)	PUNCT
ejpam-180	363	5	�	�	PROPN
ejpam-180	363	6	≦	≦	NUM
ejpam-180	363	7	1	1	NUM
ejpam-180	363	8	,	,	PUNCT
ejpam-180	363	9	t	t	PROPN
ejpam-180	363	10	∈	∈	PROPN
ejpam-180	364	1	i	i	PRON
ejpam-180	364	2	,	,	PUNCT
ejpam-180	364	3	i	i	PRON
ejpam-180	364	4	=	=	NOUN
ejpam-180	364	5	1	1	NUM
ejpam-180	364	6	,	,	PUNCT
ejpam-180	364	7	2	2	NUM
ejpam-180	364	8	,	,	PUNCT
ejpam-180	364	9	.	.	PUNCT
ejpam-180	364	10	.	.	PUNCT
ejpam-180	364	11	.	.	PUNCT
ejpam-180	365	1	,	,	PUNCT
ejpam-180	365	2	p	p	X
ejpam-180	365	3	(	(	PUNCT
ejpam-180	365	4	4.14	4.14	NUM
ejpam-180	365	5	)	)	PUNCT
ejpam-180	365	6	ξ̄	ξ̄	ADJ
ejpam-180	365	7	>	>	X
ejpam-180	365	8	0	0	NUM
ejpam-180	365	9	,	,	PUNCT
ejpam-180	365	10	v̄	v̄	PROPN
ejpam-180	365	11	(	(	PUNCT
ejpam-180	365	12	t)≧	t)≧	NOUN
ejpam-180	365	13	0	0	NUM
ejpam-180	365	14	,	,	PUNCT
ejpam-180	365	15	t	t	PROPN
ejpam-180	365	16	∈	∈	PROPN
ejpam-180	366	1	i	i	PRON
ejpam-180	366	2	(	(	PUNCT
ejpam-180	366	3	4.15	4.15	NUM
ejpam-180	366	4	)	)	PUNCT
ejpam-180	366	5	from	from	ADP
ejpam-180	366	6	(	(	PUNCT
ejpam-180	366	7	4.11	4.11	NUM
ejpam-180	366	8	)	)	PUNCT
ejpam-180	366	9	we	we	PRON
ejpam-180	366	10	obtain	obtain	VERB
ejpam-180	366	11	p	p	NOUN
ejpam-180	366	12	∑	∑	PROPN
ejpam-180	366	13	i=1	i=1	PROPN
ejpam-180	366	14	ξ̄i	ξ̄i	PROPN
ejpam-180	366	15	�	�	PROPN
ejpam-180	366	16	f	f	PROPN
ejpam-180	367	1	i	i	NOUN
ejpam-180	367	2	x	x	X
ejpam-180	367	3	(	(	PUNCT
ejpam-180	367	4	t	t	NOUN
ejpam-180	367	5	,	,	PUNCT
ejpam-180	367	6	x	x	X
ejpam-180	367	7	,	,	PUNCT
ejpam-180	367	8	ẋ	ẋ	PROPN
ejpam-180	367	9	,	,	PUNCT
ejpam-180	367	10	ẍ	ẍ	X
ejpam-180	367	11	)	)	PUNCT
ejpam-180	368	1	+	+	CCONJ
ejpam-180	369	1	b	b	X
ejpam-180	369	2	i	i	PRON
ejpam-180	369	3	(	(	PUNCT
ejpam-180	369	4	t)z	t)z	NOUN
ejpam-180	369	5	i	i	PRON
ejpam-180	369	6	(	(	PUNCT
ejpam-180	369	7	t)−	t)−	PROPN
ejpam-180	370	1	d	d	X
ejpam-180	370	2	f	f	X
ejpam-180	371	1	i	i	PRON
ejpam-180	371	2	ẋ	ẋ	PROPN
ejpam-180	372	1	(	(	PUNCT
ejpam-180	372	2	t	t	PROPN
ejpam-180	372	3	,	,	PUNCT
ejpam-180	372	4	x	x	X
ejpam-180	372	5	,	,	PUNCT
ejpam-180	372	6	ẋ	ẋ	PROPN
ejpam-180	372	7	,	,	PUNCT
ejpam-180	372	8	ẍ	ẍ	X
ejpam-180	372	9	)	)	PUNCT
ejpam-180	373	1	+	+	CCONJ
ejpam-180	374	1	d2	d2	PROPN
ejpam-180	374	2	f	f	PROPN
ejpam-180	374	3	i	i	PRON
ejpam-180	374	4	ẍ	ẍ	PROPN
ejpam-180	375	1	(	(	PUNCT
ejpam-180	375	2	t	t	PROPN
ejpam-180	375	3	,	,	PUNCT
ejpam-180	375	4	x	x	X
ejpam-180	375	5	,	,	PUNCT
ejpam-180	375	6	ẋ	ẋ	PROPN
ejpam-180	375	7	,	,	PUNCT
ejpam-180	375	8	ẍ	ẍ	X
ejpam-180	375	9	)	)	PUNCT
ejpam-180	375	10	�	�	PROPN
ejpam-180	376	1	+	+	PROPN
ejpam-180	376	2	v̄	v̄	PROPN
ejpam-180	376	3	(	(	PUNCT
ejpam-180	376	4	t	t	PROPN
ejpam-180	376	5	)	)	PUNCT
ejpam-180	376	6	t	t	PROPN
ejpam-180	376	7	gx	gx	PROPN
ejpam-180	376	8	(	(	PUNCT
ejpam-180	376	9	t	t	PROPN
ejpam-180	376	10	,	,	PUNCT
ejpam-180	376	11	x	x	X
ejpam-180	376	12	,	,	PUNCT
ejpam-180	376	13	ẋ	ẋ	PROPN
ejpam-180	376	14	,	,	PUNCT
ejpam-180	376	15	ẍ)−	ẍ)−	PROPN
ejpam-180	376	16	d	d	PROPN
ejpam-180	376	17	�	�	PROPN
ejpam-180	376	18	v̄	v̄	PROPN
ejpam-180	376	19	(	(	PUNCT
ejpam-180	376	20	t	t	PROPN
ejpam-180	376	21	)	)	PUNCT
ejpam-180	376	22	t	t	PROPN
ejpam-180	376	23	g	g	PROPN
ejpam-180	376	24	ẋ	ẋ	PROPN
ejpam-180	377	1	(	(	PUNCT
ejpam-180	377	2	t	t	PROPN
ejpam-180	377	3	,	,	PUNCT
ejpam-180	377	4	x	x	X
ejpam-180	377	5	,	,	PUNCT
ejpam-180	377	6	ẋ	ẋ	PROPN
ejpam-180	377	7	,	,	PUNCT
ejpam-180	377	8	ẍ	ẍ	X
ejpam-180	377	9	)	)	PUNCT
ejpam-180	377	10	�	�	PROPN
ejpam-180	378	1	+	+	NUM
ejpam-180	378	2	d2	d2	PROPN
ejpam-180	378	3	�	�	PROPN
ejpam-180	378	4	v̄	v̄	PROPN
ejpam-180	378	5	(	(	PUNCT
ejpam-180	378	6	t	t	PROPN
ejpam-180	378	7	)	)	PUNCT
ejpam-180	378	8	t	t	PROPN
ejpam-180	378	9	g	g	PROPN
ejpam-180	378	10	ẍ	ẍ	PROPN
ejpam-180	379	1	(	(	PUNCT
ejpam-180	379	2	t	t	PROPN
ejpam-180	379	3	,	,	PUNCT
ejpam-180	379	4	x	x	X
ejpam-180	379	5	,	,	PUNCT
ejpam-180	379	6	ẋ	ẋ	PROPN
ejpam-180	379	7	,	,	PUNCT
ejpam-180	379	8	ẍ	ẍ	X
ejpam-180	379	9	)	)	PUNCT
ejpam-180	379	10	�	�	PROPN
ejpam-180	379	11	=	=	SYM
ejpam-180	379	12	0	0	NUM
ejpam-180	379	13	(	(	PUNCT
ejpam-180	379	14	4.16	4.16	NUM
ejpam-180	379	15	)	)	PUNCT
ejpam-180	379	16	dividing	dividing	NOUN
ejpam-180	379	17	(	(	PUNCT
ejpam-180	379	18	4.13	4.13	NUM
ejpam-180	379	19	)	)	PUNCT
ejpam-180	379	20	(	(	PUNCT
ejpam-180	379	21	4.15	4.15	NUM
ejpam-180	379	22	)	)	PUNCT
ejpam-180	379	23	and	and	CCONJ
ejpam-180	379	24	(	(	PUNCT
ejpam-180	379	25	4.16	4.16	NUM
ejpam-180	379	26	)	)	PUNCT
ejpam-180	379	27	by	by	ADP
ejpam-180	379	28	ξ̄t	ξ̄t	PROPN
ejpam-180	379	29	e	e	X
ejpam-180	379	30	(	(	PUNCT
ejpam-180	379	31	6=	6=	NOUN
ejpam-180	379	32	0	0	NUM
ejpam-180	379	33	)	)	PUNCT
ejpam-180	379	34	,	,	PUNCT
ejpam-180	379	35	and	and	CCONJ
ejpam-180	379	36	setting	set	VERB
ejpam-180	379	37	λi	λi	X
ejpam-180	379	38	=	=	PUNCT
ejpam-180	379	39	�	�	PROPN
ejpam-180	379	40	ξ̄	ξ̄	NOUN
ejpam-180	379	41	ξ̄t	ξ̄t	PROPN
ejpam-180	379	42	e	e	PROPN
ejpam-180	379	43	�	�	PROPN
ejpam-180	379	44	,	,	PUNCT
ejpam-180	379	45	i	i	PRON
ejpam-180	379	46	=	=	NOUN
ejpam-180	379	47	1	1	NUM
ejpam-180	379	48	,	,	PUNCT
ejpam-180	379	49	.	.	PUNCT
ejpam-180	379	50	.	.	PUNCT
ejpam-180	380	1	.	.	PUNCT
ejpam-180	381	1	,	,	PUNCT
ejpam-180	381	2	p	p	NOUN
ejpam-180	381	3	and	and	CCONJ
ejpam-180	381	4	ȳ	ȳ	PROPN
ejpam-180	381	5	(	(	PUNCT
ejpam-180	381	6	t	t	NOUN
ejpam-180	381	7	)	)	PUNCT
ejpam-180	381	8	=	=	SYM
ejpam-180	381	9	�	�	PROPN
ejpam-180	381	10	v̄(t	v̄(t	PROPN
ejpam-180	381	11	)	)	PUNCT
ejpam-180	381	12	ξ̄t	ξ̄t	PROPN
ejpam-180	381	13	e	e	ADP
ejpam-180	381	14	�	�	PROPN
ejpam-180	381	15	,	,	PUNCT
ejpam-180	381	16	we	we	PRON
ejpam-180	381	17	have	have	AUX
ejpam-180	381	18	,	,	PUNCT
ejpam-180	381	19	p	p	X
ejpam-180	381	20	∑	∑	PUNCT
ejpam-180	381	21	i=1	i=1	PROPN
ejpam-180	381	22	λ̄i	λ̄i	PROPN
ejpam-180	381	23	�	�	PROPN
ejpam-180	382	1	f	f	NOUN
ejpam-180	382	2	i	i	NOUN
ejpam-180	382	3	x	x	X
ejpam-180	382	4	(	(	PUNCT
ejpam-180	382	5	t	t	NOUN
ejpam-180	382	6	,	,	PUNCT
ejpam-180	382	7	x	x	X
ejpam-180	382	8	,	,	PUNCT
ejpam-180	382	9	ẋ	ẋ	PROPN
ejpam-180	382	10	,	,	PUNCT
ejpam-180	382	11	ẍ	ẍ	X
ejpam-180	382	12	)	)	PUNCT
ejpam-180	383	1	+	+	CCONJ
ejpam-180	384	1	b	b	X
ejpam-180	384	2	i	i	PRON
ejpam-180	384	3	(	(	PUNCT
ejpam-180	384	4	t	t	PROPN
ejpam-180	384	5	)	)	PUNCT
ejpam-180	384	6	z̄	z̄	PROPN
ejpam-180	384	7	i	i	PRON
ejpam-180	384	8	(	(	PUNCT
ejpam-180	384	9	t)−	t)−	PROPN
ejpam-180	385	1	d	d	X
ejpam-180	385	2	f	f	X
ejpam-180	386	1	i	i	PRON
ejpam-180	386	2	ẋ	ẋ	PROPN
ejpam-180	387	1	(	(	PUNCT
ejpam-180	387	2	t	t	PROPN
ejpam-180	387	3	,	,	PUNCT
ejpam-180	387	4	x	x	X
ejpam-180	387	5	,	,	PUNCT
ejpam-180	387	6	ẋ	ẋ	PROPN
ejpam-180	387	7	,	,	PUNCT
ejpam-180	387	8	ẍ	ẍ	X
ejpam-180	387	9	)	)	PUNCT
ejpam-180	388	1	+	+	CCONJ
ejpam-180	389	1	d2	d2	PROPN
ejpam-180	389	2	f	f	PROPN
ejpam-180	389	3	i	i	PRON
ejpam-180	389	4	ẍ	ẍ	PROPN
ejpam-180	390	1	(	(	PUNCT
ejpam-180	390	2	t	t	PROPN
ejpam-180	390	3	,	,	PUNCT
ejpam-180	390	4	x	x	X
ejpam-180	390	5	,	,	PUNCT
ejpam-180	390	6	ẋ	ẋ	PROPN
ejpam-180	390	7	,	,	PUNCT
ejpam-180	390	8	ẍ	ẍ	X
ejpam-180	390	9	)	)	PUNCT
ejpam-180	390	10	�	�	PROPN
ejpam-180	391	1	+	+	CCONJ
ejpam-180	391	2	ȳ	ȳ	PROPN
ejpam-180	391	3	(	(	PUNCT
ejpam-180	391	4	t	t	PROPN
ejpam-180	391	5	)	)	PUNCT
ejpam-180	391	6	t	t	PROPN
ejpam-180	391	7	gx	gx	PROPN
ejpam-180	391	8	(	(	PUNCT
ejpam-180	391	9	t	t	PROPN
ejpam-180	391	10	,	,	PUNCT
ejpam-180	391	11	x	x	X
ejpam-180	391	12	,	,	PUNCT
ejpam-180	391	13	ẋ	ẋ	PROPN
ejpam-180	391	14	,	,	PUNCT
ejpam-180	391	15	ẍ)−	ẍ)−	PROPN
ejpam-180	391	16	d	d	PROPN
ejpam-180	391	17	�	�	PROPN
ejpam-180	391	18	ȳ	ȳ	PROPN
ejpam-180	391	19	(	(	PUNCT
ejpam-180	391	20	t	t	PROPN
ejpam-180	391	21	)	)	PUNCT
ejpam-180	391	22	t	t	PROPN
ejpam-180	391	23	g	g	PROPN
ejpam-180	391	24	ẋ	ẋ	PROPN
ejpam-180	391	25	(	(	PUNCT
ejpam-180	391	26	t	t	PROPN
ejpam-180	391	27	,	,	PUNCT
ejpam-180	391	28	x	x	X
ejpam-180	391	29	,	,	PUNCT
ejpam-180	391	30	ẋ	ẋ	PROPN
ejpam-180	391	31	,	,	PUNCT
ejpam-180	391	32	ẍ	ẍ	X
ejpam-180	391	33	)	)	PUNCT
ejpam-180	391	34	�	�	PROPN
ejpam-180	392	1	+	+	NUM
ejpam-180	392	2	d2	d2	PROPN
ejpam-180	392	3	�	�	PROPN
ejpam-180	392	4	ȳ	ȳ	PROPN
ejpam-180	392	5	(	(	PUNCT
ejpam-180	392	6	t	t	PROPN
ejpam-180	392	7	)	)	PUNCT
ejpam-180	392	8	t	t	PROPN
ejpam-180	392	9	g	g	PROPN
ejpam-180	392	10	ẍ	ẍ	PROPN
ejpam-180	392	11	(	(	PUNCT
ejpam-180	392	12	t	t	PROPN
ejpam-180	392	13	,	,	PUNCT
ejpam-180	392	14	x	x	X
ejpam-180	392	15	,	,	PUNCT
ejpam-180	392	16	ẋ	ẋ	PROPN
ejpam-180	392	17	,	,	PUNCT
ejpam-180	392	18	ẍ	ẍ	X
ejpam-180	392	19	)	)	PUNCT
ejpam-180	392	20	�	�	PROPN
ejpam-180	393	1	=	=	SYM
ejpam-180	393	2	0	0	NUM
ejpam-180	393	3	(	(	PUNCT
ejpam-180	393	4	4.17	4.17	NUM
ejpam-180	393	5	)	)	PUNCT
ejpam-180	393	6	i.	i.	NOUN
ejpam-180	393	7	husain	husain	PROPN
ejpam-180	393	8	,	,	PUNCT
ejpam-180	393	9	a.	a.	PROPN
ejpam-180	393	10	ahmed	ahmed	PROPN
ejpam-180	393	11	,	,	PUNCT
ejpam-180	393	12	and	and	CCONJ
ejpam-180	393	13	g.	g.	PROPN
ejpam-180	393	14	rumana	rumana	PROPN
ejpam-180	393	15	/	/	SYM
ejpam-180	393	16	eur	eur	PROPN
ejpam-180	393	17	.	.	PUNCT
ejpam-180	394	1	j.	j.	PROPN
ejpam-180	394	2	pure	pure	PROPN
ejpam-180	394	3	appl	appl	PROPN
ejpam-180	394	4	.	.	PROPN
ejpam-180	394	5	math	math	PROPN
ejpam-180	394	6	,	,	PUNCT
ejpam-180	394	7	2	2	NUM
ejpam-180	394	8	(	(	PUNCT
ejpam-180	394	9	2009	2009	NUM
ejpam-180	394	10	)	)	PUNCT
ejpam-180	394	11	,	,	PUNCT
ejpam-180	394	12	(	(	PUNCT
ejpam-180	394	13	372	372	NUM
ejpam-180	394	14	-	-	SYM
ejpam-180	394	15	400	400	NUM
ejpam-180	394	16	)	)	PUNCT
ejpam-180	394	17	384	384	NUM
ejpam-180	394	18	ȳ	ȳ	NOUN
ejpam-180	394	19	(	(	PUNCT
ejpam-180	394	20	t	t	PROPN
ejpam-180	394	21	)	)	PUNCT
ejpam-180	394	22	t	t	PROPN
ejpam-180	394	23	g	g	PROPN
ejpam-180	394	24	�	�	PROPN
ejpam-180	394	25	t	t	PROPN
ejpam-180	394	26	,	,	PUNCT
ejpam-180	394	27	x̄	x̄	PROPN
ejpam-180	394	28	,	,	PUNCT
ejpam-180	394	29	˙̄x	˙̄x	PUNCT
ejpam-180	394	30	,	,	PUNCT
ejpam-180	394	31	¨̄x	¨̄x	PRON
ejpam-180	394	32	�	�	PROPN
ejpam-180	394	33	d	d	PROPN
ejpam-180	394	34	t	t	PROPN
ejpam-180	394	35	=	=	SYM
ejpam-180	394	36	0	0	NUM
ejpam-180	394	37	(	(	PUNCT
ejpam-180	394	38	4.18	4.18	NUM
ejpam-180	394	39	)	)	PUNCT
ejpam-180	394	40	λ̄	λ̄	VERB
ejpam-180	394	41	>	>	X
ejpam-180	395	1	0	0	NUM
ejpam-180	395	2	,	,	PUNCT
ejpam-180	395	3	λt	λt	ADP
ejpam-180	395	4	e	e	NOUN
ejpam-180	395	5	=	=	SYM
ejpam-180	395	6	1	1	NUM
ejpam-180	395	7	(	(	PUNCT
ejpam-180	395	8	4.19	4.19	NUM
ejpam-180	395	9	)	)	PUNCT
ejpam-180	395	10	ȳ	ȳ	PROPN
ejpam-180	395	11	(	(	PUNCT
ejpam-180	395	12	t)≧	t)≧	NOUN
ejpam-180	395	13	0	0	NUM
ejpam-180	395	14	,	,	PUNCT
ejpam-180	395	15	t	t	PROPN
ejpam-180	395	16	∈	∈	PROPN
ejpam-180	396	1	i	i	PRON
ejpam-180	396	2	(	(	PUNCT
ejpam-180	396	3	4.20	4.20	NUM
ejpam-180	396	4	)	)	PUNCT
ejpam-180	396	5	consequently	consequently	ADV
ejpam-180	396	6	(	(	PUNCT
ejpam-180	396	7	4.14	4.14	NUM
ejpam-180	396	8	)	)	PUNCT
ejpam-180	396	9	,	,	PUNCT
ejpam-180	396	10	(	(	PUNCT
ejpam-180	396	11	4.17	4.17	NUM
ejpam-180	396	12	)	)	PUNCT
ejpam-180	396	13	,	,	PUNCT
ejpam-180	396	14	(	(	PUNCT
ejpam-180	396	15	4.19	4.19	NUM
ejpam-180	396	16	)	)	PUNCT
ejpam-180	396	17	and	and	CCONJ
ejpam-180	396	18	(	(	PUNCT
ejpam-180	396	19	4.20	4.20	NUM
ejpam-180	396	20	)	)	PUNCT
ejpam-180	396	21	implies	imply	VERB
ejpam-180	396	22	that	that	SCONJ
ejpam-180	396	23	(	(	PUNCT
ejpam-180	396	24	x̄	x̄	NOUN
ejpam-180	396	25	,	,	PUNCT
ejpam-180	396	26	ū	ū	PROPN
ejpam-180	396	27	,	,	PUNCT
ejpam-180	396	28	ȳ	ȳ	PROPN
ejpam-180	396	29	,	,	PUNCT
ejpam-180	396	30	z̄1	z̄1	NUM
ejpam-180	396	31	,	,	PUNCT
ejpam-180	396	32	.	.	PUNCT
ejpam-180	396	33	.	.	PUNCT
ejpam-180	396	34	.	.	PUNCT
ejpam-180	397	1	,	,	PUNCT
ejpam-180	397	2	z̄p	z̄p	PROPN
ejpam-180	397	3	,	,	PUNCT
ejpam-180	397	4	λ̄	λ̄	PRON
ejpam-180	397	5	)	)	PUNCT
ejpam-180	397	6	is	be	AUX
ejpam-180	397	7	feasible	feasible	ADJ
ejpam-180	397	8	for	for	ADP
ejpam-180	397	9	(	(	PUNCT
ejpam-180	397	10	wd	wd	PROPN
ejpam-180	397	11	)	)	PUNCT
ejpam-180	397	12	.	.	PUNCT
ejpam-180	398	1	because	because	SCONJ
ejpam-180	398	2	of	of	ADP
ejpam-180	398	3	(	(	PUNCT
ejpam-180	398	4	4.18	4.18	NUM
ejpam-180	398	5	)	)	PUNCT
ejpam-180	398	6	,	,	PUNCT
ejpam-180	398	7	the	the	DET
ejpam-180	398	8	two	two	NUM
ejpam-180	398	9	objectives	objective	NOUN
ejpam-180	398	10	of	of	ADP
ejpam-180	398	11	the	the	DET
ejpam-180	398	12	problem	problem	NOUN
ejpam-180	398	13	(	(	PUNCT
ejpam-180	398	14	vp)and	vp)and	NUM
ejpam-180	398	15	(	(	PUNCT
ejpam-180	398	16	mwd	mwd	PROPN
ejpam-180	398	17	)	)	PUNCT
ejpam-180	398	18	are	be	AUX
ejpam-180	398	19	equal	equal	ADJ
ejpam-180	398	20	.	.	PUNCT
ejpam-180	399	1	hence	hence	ADV
ejpam-180	399	2	by	by	ADP
ejpam-180	399	3	theorem	theorem	ADJ
ejpam-180	399	4	4.1	4.1	NUM
ejpam-180	399	5	(	(	PUNCT
ejpam-180	399	6	x̄	x̄	NOUN
ejpam-180	399	7	,	,	PUNCT
ejpam-180	399	8	ū	ū	PROPN
ejpam-180	399	9	,	,	PUNCT
ejpam-180	399	10	ȳ	ȳ	PROPN
ejpam-180	399	11	,	,	PUNCT
ejpam-180	399	12	z̄1	z̄1	PROPN
ejpam-180	399	13	,	,	PUNCT
ejpam-180	399	14	.	.	PUNCT
ejpam-180	399	15	.	.	PUNCT
ejpam-180	399	16	.	.	PUNCT
ejpam-180	400	1	,	,	PUNCT
ejpam-180	400	2	z̄p	z̄p	PROPN
ejpam-180	400	3	,	,	PUNCT
ejpam-180	400	4	λ̄	λ̄	PRON
ejpam-180	400	5	)	)	PUNCT
ejpam-180	400	6	is	be	AUX
ejpam-180	400	7	efficient	efficient	ADJ
ejpam-180	400	8	solution	solution	NOUN
ejpam-180	400	9	for	for	ADP
ejpam-180	400	10	(	(	PUNCT
ejpam-180	400	11	mwd	mwd	PROPN
ejpam-180	400	12	)	)	PUNCT
ejpam-180	400	13	.	.	PUNCT
ejpam-180	401	1	this	this	PRON
ejpam-180	401	2	completes	complete	VERB
ejpam-180	401	3	the	the	DET
ejpam-180	401	4	proof	proof	NOUN
ejpam-180	401	5	.	.	PUNCT
ejpam-180	402	1	for	for	ADP
ejpam-180	402	2	validating	validate	VERB
ejpam-180	402	3	converse	converse	NOUN
ejpam-180	402	4	duality	duality	NOUN
ejpam-180	402	5	theorem	theorem	VERB
ejpam-180	402	6	,	,	PUNCT
ejpam-180	402	7	we	we	PRON
ejpam-180	402	8	regard	regard	VERB
ejpam-180	402	9	(	(	PUNCT
ejpam-180	402	10	mwd	mwd	PROPN
ejpam-180	402	11	)	)	PUNCT
ejpam-180	402	12	in	in	ADP
ejpam-180	402	13	term	term	NOUN
ejpam-180	402	14	of	of	ADP
ejpam-180	402	15	function	function	NOUN
ejpam-180	402	16	x	x	PUNCT
ejpam-180	402	17	for	for	ADP
ejpam-180	402	18	convenience	convenience	NOUN
ejpam-180	402	19	instead	instead	ADV
ejpam-180	402	20	of	of	ADP
ejpam-180	402	21	the	the	DET
ejpam-180	402	22	function	function	NOUN
ejpam-180	402	23	u.	u.	ADV
ejpam-180	402	24	as	as	ADP
ejpam-180	402	25	in	in	ADP
ejpam-180	402	26	[	[	X
ejpam-180	402	27	13	13	NUM
ejpam-180	402	28	]	]	PUNCT
ejpam-180	402	29	,	,	PUNCT
ejpam-180	402	30	by	by	ADP
ejpam-180	402	31	employing	employ	VERB
ejpam-180	402	32	chain	chain	NOUN
ejpam-180	402	33	rule	rule	NOUN
ejpam-180	402	34	in	in	ADP
ejpam-180	402	35	calculus	calculus	NOUN
ejpam-180	402	36	,	,	PUNCT
ejpam-180	402	37	it	it	PRON
ejpam-180	402	38	can	can	AUX
ejpam-180	402	39	be	be	AUX
ejpam-180	402	40	easily	easily	ADV
ejpam-180	402	41	seen	see	VERB
ejpam-180	402	42	that	that	SCONJ
ejpam-180	402	43	the	the	DET
ejpam-180	402	44	expression	expression	NOUN
ejpam-180	402	45	p	p	NOUN
ejpam-180	402	46	∑	∑	PROPN
ejpam-180	402	47	i=1	i=1	PROPN
ejpam-180	402	48	λi	λi	PROPN
ejpam-180	402	49	�	�	PROPN
ejpam-180	402	50	f	f	PROPN
ejpam-180	402	51	i	i	NOUN
ejpam-180	402	52	x	x	X
ejpam-180	402	53	(	(	PUNCT
ejpam-180	402	54	t	t	NOUN
ejpam-180	402	55	,	,	PUNCT
ejpam-180	402	56	x	x	X
ejpam-180	402	57	,	,	PUNCT
ejpam-180	402	58	ẋ	ẋ	PROPN
ejpam-180	402	59	,	,	PUNCT
ejpam-180	402	60	ẍ	ẍ	X
ejpam-180	402	61	)	)	PUNCT
ejpam-180	403	1	d	d	PROPN
ejpam-180	403	2	t	t	PROPN
ejpam-180	403	3	+	+	CCONJ
ejpam-180	403	4	b	b	NOUN
ejpam-180	403	5	i	i	PROPN
ejpam-180	403	6	(	(	PUNCT
ejpam-180	403	7	t	t	PROPN
ejpam-180	403	8	)	)	PUNCT
ejpam-180	404	1	z	z	NOUN
ejpam-180	405	1	i	i	PRON
ejpam-180	405	2	(	(	PUNCT
ejpam-180	405	3	t	t	PROPN
ejpam-180	405	4	)	)	PUNCT
ejpam-180	406	1	+	+	CCONJ
ejpam-180	406	2	y	y	PROPN
ejpam-180	406	3	(	(	PUNCT
ejpam-180	406	4	t	t	PROPN
ejpam-180	406	5	)	)	PUNCT
ejpam-180	406	6	t	t	PROPN
ejpam-180	406	7	gx	gx	PROPN
ejpam-180	406	8	(	(	PUNCT
ejpam-180	406	9	t	t	PROPN
ejpam-180	406	10	,	,	PUNCT
ejpam-180	406	11	x	x	X
ejpam-180	406	12	,	,	PUNCT
ejpam-180	406	13	ẋ	ẋ	PROPN
ejpam-180	406	14	,	,	PUNCT
ejpam-180	406	15	ẍ	ẍ	X
ejpam-180	406	16	)	)	PUNCT
ejpam-180	406	17	�	�	PROPN
ejpam-180	406	18	−d	−d	PROPN
ejpam-180	406	19	�	�	PROPN
ejpam-180	406	20	λt	λt	ADP
ejpam-180	406	21	f	f	PROPN
ejpam-180	406	22	ẋ	ẋ	PROPN
ejpam-180	407	1	(	(	PUNCT
ejpam-180	407	2	t	t	PROPN
ejpam-180	407	3	,	,	PUNCT
ejpam-180	407	4	x	x	X
ejpam-180	407	5	,	,	PUNCT
ejpam-180	407	6	ẋ	ẋ	PROPN
ejpam-180	407	7	,	,	PUNCT
ejpam-180	407	8	ẍ	ẍ	X
ejpam-180	407	9	)	)	PUNCT
ejpam-180	408	1	+	+	CCONJ
ejpam-180	408	2	y	y	PROPN
ejpam-180	408	3	(	(	PUNCT
ejpam-180	408	4	t	t	PROPN
ejpam-180	408	5	)	)	PUNCT
ejpam-180	408	6	t	t	PROPN
ejpam-180	408	7	g	g	PROPN
ejpam-180	408	8	ẋ	ẋ	PROPN
ejpam-180	409	1	(	(	PUNCT
ejpam-180	409	2	t	t	PROPN
ejpam-180	409	3	,	,	PUNCT
ejpam-180	409	4	x	x	X
ejpam-180	409	5	,	,	PUNCT
ejpam-180	409	6	ẋ	ẋ	PROPN
ejpam-180	409	7	,	,	PUNCT
ejpam-180	409	8	ẍ	ẍ	X
ejpam-180	409	9	)	)	PUNCT
ejpam-180	409	10	�	�	PROPN
ejpam-180	410	1	+	+	NUM
ejpam-180	410	2	d2	d2	PROPN
ejpam-180	410	3	�	�	PROPN
ejpam-180	410	4	λt	λt	ADP
ejpam-180	410	5	f	f	PROPN
ejpam-180	410	6	ẍ	ẍ	PROPN
ejpam-180	410	7	(	(	PUNCT
ejpam-180	410	8	t	t	PROPN
ejpam-180	410	9	,	,	PUNCT
ejpam-180	410	10	x	x	X
ejpam-180	410	11	,	,	PUNCT
ejpam-180	410	12	ẋ	ẋ	PROPN
ejpam-180	410	13	,	,	PUNCT
ejpam-180	410	14	ẍ	ẍ	X
ejpam-180	410	15	)	)	PUNCT
ejpam-180	411	1	+	+	CCONJ
ejpam-180	411	2	y	y	PROPN
ejpam-180	411	3	(	(	PUNCT
ejpam-180	411	4	t	t	PROPN
ejpam-180	411	5	)	)	PUNCT
ejpam-180	411	6	t	t	PROPN
ejpam-180	411	7	g	g	PROPN
ejpam-180	411	8	ẍ	ẍ	PROPN
ejpam-180	412	1	(	(	PUNCT
ejpam-180	412	2	t	t	PROPN
ejpam-180	412	3	,	,	PUNCT
ejpam-180	412	4	x	x	X
ejpam-180	412	5	,	,	PUNCT
ejpam-180	412	6	ẋ	ẋ	PROPN
ejpam-180	412	7	,	,	PUNCT
ejpam-180	412	8	ẍ	ẍ	X
ejpam-180	412	9	)	)	PUNCT
ejpam-180	412	10	�	�	PROPN
ejpam-180	412	11	=	=	SYM
ejpam-180	412	12	0	0	PROPN
ejpam-180	412	13	,	,	PUNCT
ejpam-180	412	14	t	t	PROPN
ejpam-180	412	15	∈	∈	PROPN
ejpam-180	413	1	i	i	PRON
ejpam-180	413	2	,	,	PUNCT
ejpam-180	413	3	may	may	AUX
ejpam-180	413	4	be	be	AUX
ejpam-180	413	5	regarded	regard	VERB
ejpam-180	413	6	as	as	ADP
ejpam-180	413	7	a	a	DET
ejpam-180	413	8	function	function	NOUN
ejpam-180	413	9	θ	θ	PROPN
ejpam-180	413	10	of	of	ADP
ejpam-180	413	11	variables	variable	NOUN
ejpam-180	413	12	t	t	PROPN
ejpam-180	413	13	,	,	PUNCT
ejpam-180	413	14	x	x	INTJ
ejpam-180	413	15	,	,	PUNCT
ejpam-180	413	16	ẋ	ẋ	PROPN
ejpam-180	413	17	,	,	PUNCT
ejpam-180	413	18	ẍ	ẍ	X
ejpam-180	413	19	,	,	PUNCT
ejpam-180	413	20	...	...	PUNCT
ejpam-180	414	1	x	x	X
ejpam-180	414	2	,	,	PUNCT
ejpam-180	414	3	y	y	PROPN
ejpam-180	414	4	,	,	PUNCT
ejpam-180	414	5	ẏ	ẏ	PROPN
ejpam-180	414	6	,	,	PUNCT
ejpam-180	414	7	ÿ	ÿ	PROPN
ejpam-180	414	8	and	and	CCONJ
ejpam-180	414	9	λ	λ	PROPN
ejpam-180	414	10	,	,	PUNCT
ejpam-180	414	11	where	where	SCONJ
ejpam-180	414	12	...	...	PUNCT
ejpam-180	414	13	x	x	PUNCT
ejpam-180	415	1	=	=	X
ejpam-180	415	2	d3	d3	PROPN
ejpam-180	415	3	d	d	NOUN
ejpam-180	415	4	t3	t3	PROPN
ejpam-180	415	5	x	x	PUNCT
ejpam-180	415	6	=	=	PUNCT
ejpam-180	415	7	d3	d3	PROPN
ejpam-180	415	8	x	x	X
ejpam-180	415	9	and	and	CCONJ
ejpam-180	415	10	ÿ	ÿ	PROPN
ejpam-180	415	11	=	=	PROPN
ejpam-180	415	12	d2	d2	PROPN
ejpam-180	415	13	y.	y.	PROPN
ejpam-180	415	14	that	that	PRON
ejpam-180	415	15	is	be	AUX
ejpam-180	415	16	,	,	PUNCT
ejpam-180	415	17	we	we	PRON
ejpam-180	415	18	can	can	AUX
ejpam-180	415	19	write	write	VERB
ejpam-180	415	20	θ	θ	PROPN
ejpam-180	415	21	�	�	PROPN
ejpam-180	415	22	t	t	PROPN
ejpam-180	415	23	,	,	PUNCT
ejpam-180	415	24	x	x	X
ejpam-180	415	25	,	,	PUNCT
ejpam-180	415	26	ẋ	ẋ	PROPN
ejpam-180	415	27	,	,	PUNCT
ejpam-180	415	28	ẍ	ẍ	X
ejpam-180	415	29	,	,	PUNCT
ejpam-180	415	30	...	...	PUNCT
ejpam-180	416	1	x	x	X
ejpam-180	416	2	,	,	PUNCT
ejpam-180	416	3	y	y	PROPN
ejpam-180	416	4	,	,	PUNCT
ejpam-180	416	5	ẏ	ẏ	PROPN
ejpam-180	416	6	,	,	PUNCT
ejpam-180	416	7	ÿ	ÿ	PROPN
ejpam-180	416	8	,	,	PUNCT
ejpam-180	416	9	λ	λ	X
ejpam-180	416	10	�	�	PROPN
ejpam-180	416	11	=	=	PUNCT
ejpam-180	416	12	p	p	PROPN
ejpam-180	416	13	∑	∑	PUNCT
ejpam-180	416	14	i=1	i=1	PROPN
ejpam-180	416	15	λi	λi	PROPN
ejpam-180	416	16	�	�	PROPN
ejpam-180	416	17	f	f	PROPN
ejpam-180	417	1	i	i	NOUN
ejpam-180	417	2	x	x	X
ejpam-180	417	3	(	(	PUNCT
ejpam-180	417	4	t	t	NOUN
ejpam-180	417	5	,	,	PUNCT
ejpam-180	417	6	x	x	X
ejpam-180	417	7	,	,	PUNCT
ejpam-180	417	8	ẋ	ẋ	PROPN
ejpam-180	417	9	,	,	PUNCT
ejpam-180	417	10	ẍ	ẍ	X
ejpam-180	417	11	)	)	PUNCT
ejpam-180	418	1	d	d	PROPN
ejpam-180	418	2	t	t	PROPN
ejpam-180	418	3	+	+	CCONJ
ejpam-180	418	4	b	b	NOUN
ejpam-180	419	1	i	i	PRON
ejpam-180	419	2	(	(	PUNCT
ejpam-180	419	3	t)z	t)z	NOUN
ejpam-180	419	4	i	i	PRON
ejpam-180	419	5	(	(	PUNCT
ejpam-180	419	6	t	t	PROPN
ejpam-180	419	7	)	)	PUNCT
ejpam-180	420	1	+	+	CCONJ
ejpam-180	420	2	y	y	PROPN
ejpam-180	420	3	(	(	PUNCT
ejpam-180	420	4	t	t	PROPN
ejpam-180	420	5	)	)	PUNCT
ejpam-180	420	6	t	t	PROPN
ejpam-180	420	7	gx	gx	PROPN
ejpam-180	420	8	(	(	PUNCT
ejpam-180	420	9	t	t	PROPN
ejpam-180	420	10	,	,	PUNCT
ejpam-180	420	11	x	x	X
ejpam-180	420	12	,	,	PUNCT
ejpam-180	420	13	ẋ	ẋ	PROPN
ejpam-180	420	14	,	,	PUNCT
ejpam-180	420	15	ẍ	ẍ	X
ejpam-180	420	16	)	)	PUNCT
ejpam-180	420	17	�	�	PROPN
ejpam-180	420	18	−d	−d	PROPN
ejpam-180	420	19	�	�	PROPN
ejpam-180	420	20	λt	λt	ADP
ejpam-180	420	21	f	f	PROPN
ejpam-180	420	22	ẋ	ẋ	PROPN
ejpam-180	421	1	(	(	PUNCT
ejpam-180	421	2	t	t	PROPN
ejpam-180	421	3	,	,	PUNCT
ejpam-180	421	4	x	x	X
ejpam-180	421	5	,	,	PUNCT
ejpam-180	421	6	ẋ	ẋ	PROPN
ejpam-180	421	7	,	,	PUNCT
ejpam-180	421	8	ẍ	ẍ	X
ejpam-180	421	9	)	)	PUNCT
ejpam-180	422	1	+	+	CCONJ
ejpam-180	422	2	y	y	PROPN
ejpam-180	422	3	(	(	PUNCT
ejpam-180	422	4	t	t	PROPN
ejpam-180	422	5	)	)	PUNCT
ejpam-180	422	6	t	t	PROPN
ejpam-180	422	7	g	g	PROPN
ejpam-180	422	8	ẋ	ẋ	PROPN
ejpam-180	423	1	(	(	PUNCT
ejpam-180	423	2	t	t	PROPN
ejpam-180	423	3	,	,	PUNCT
ejpam-180	423	4	x	x	X
ejpam-180	423	5	,	,	PUNCT
ejpam-180	423	6	ẋ	ẋ	PROPN
ejpam-180	423	7	,	,	PUNCT
ejpam-180	423	8	ẍ	ẍ	X
ejpam-180	423	9	)	)	PUNCT
ejpam-180	423	10	�	�	PROPN
ejpam-180	424	1	+	+	NUM
ejpam-180	424	2	d2	d2	PROPN
ejpam-180	424	3	�	�	PROPN
ejpam-180	424	4	λt	λt	ADP
ejpam-180	424	5	f	f	PROPN
ejpam-180	424	6	ẍ	ẍ	PROPN
ejpam-180	424	7	(	(	PUNCT
ejpam-180	424	8	t	t	PROPN
ejpam-180	424	9	,	,	PUNCT
ejpam-180	424	10	x	x	X
ejpam-180	424	11	,	,	PUNCT
ejpam-180	424	12	ẋ	ẋ	PROPN
ejpam-180	424	13	,	,	PUNCT
ejpam-180	424	14	ẍ	ẍ	X
ejpam-180	424	15	)	)	PUNCT
ejpam-180	425	1	+	+	CCONJ
ejpam-180	425	2	y	y	PROPN
ejpam-180	425	3	(	(	PUNCT
ejpam-180	425	4	t	t	PROPN
ejpam-180	425	5	)	)	PUNCT
ejpam-180	425	6	t	t	PROPN
ejpam-180	425	7	g	g	PROPN
ejpam-180	425	8	ẍ	ẍ	PROPN
ejpam-180	426	1	(	(	PUNCT
ejpam-180	426	2	t	t	PROPN
ejpam-180	426	3	,	,	PUNCT
ejpam-180	426	4	x	x	X
ejpam-180	426	5	,	,	PUNCT
ejpam-180	426	6	ẋ	ẋ	PROPN
ejpam-180	426	7	,	,	PUNCT
ejpam-180	426	8	ẍ	ẍ	X
ejpam-180	426	9	)	)	PUNCT
ejpam-180	426	10	�	�	PROPN
ejpam-180	426	11	=	=	SYM
ejpam-180	426	12	0	0	PROPN
ejpam-180	426	13	,	,	PUNCT
ejpam-180	426	14	t	t	PROPN
ejpam-180	426	15	∈	∈	PROPN
ejpam-180	427	1	i	i	PRON
ejpam-180	427	2	i.	i.	PROPN
ejpam-180	427	3	husain	husain	PROPN
ejpam-180	427	4	,	,	PUNCT
ejpam-180	427	5	a.	a.	PROPN
ejpam-180	427	6	ahmed	ahmed	PROPN
ejpam-180	427	7	,	,	PUNCT
ejpam-180	427	8	and	and	CCONJ
ejpam-180	427	9	g.	g.	PROPN
ejpam-180	427	10	rumana	rumana	PROPN
ejpam-180	427	11	/	/	SYM
ejpam-180	427	12	eur	eur	PROPN
ejpam-180	427	13	.	.	PUNCT
ejpam-180	428	1	j.	j.	PROPN
ejpam-180	428	2	pure	pure	PROPN
ejpam-180	428	3	appl	appl	PROPN
ejpam-180	428	4	.	.	PROPN
ejpam-180	428	5	math	math	PROPN
ejpam-180	428	6	,	,	PUNCT
ejpam-180	428	7	2	2	NUM
ejpam-180	428	8	(	(	PUNCT
ejpam-180	428	9	2009	2009	NUM
ejpam-180	428	10	)	)	PUNCT
ejpam-180	428	11	,	,	PUNCT
ejpam-180	428	12	(	(	PUNCT
ejpam-180	428	13	372	372	NUM
ejpam-180	428	14	-	-	SYM
ejpam-180	428	15	400	400	NUM
ejpam-180	428	16	)	)	PUNCT
ejpam-180	428	17	385	385	NUM
ejpam-180	428	18	the	the	DET
ejpam-180	428	19	problem	problem	NOUN
ejpam-180	428	20	(	(	PUNCT
ejpam-180	428	21	mwd	mwd	PROPN
ejpam-180	428	22	)	)	PUNCT
ejpam-180	428	23	may	may	AUX
ejpam-180	428	24	now	now	ADV
ejpam-180	428	25	be	be	AUX
ejpam-180	428	26	briefly	briefly	ADV
ejpam-180	428	27	written	write	VERB
ejpam-180	428	28	as	as	ADP
ejpam-180	428	29	,	,	PUNCT
ejpam-180	428	30	minimize	minimize	VERB
ejpam-180	428	31	�	�	PROPN
ejpam-180	428	32	∫	∫	PROPN
ejpam-180	429	1	i	i	PRON
ejpam-180	429	2	−	−	PROPN
ejpam-180	429	3	�	�	PROPN
ejpam-180	429	4	f	f	PROPN
ejpam-180	429	5	1	1	NUM
ejpam-180	429	6	(	(	PUNCT
ejpam-180	429	7	t	t	PROPN
ejpam-180	429	8	,	,	PUNCT
ejpam-180	429	9	x	x	X
ejpam-180	429	10	,	,	PUNCT
ejpam-180	429	11	ẋ	ẋ	PROPN
ejpam-180	429	12	,	,	PUNCT
ejpam-180	429	13	ẍ	ẍ	X
ejpam-180	429	14	)	)	PUNCT
ejpam-180	430	1	+	+	CCONJ
ejpam-180	430	2	�	�	PROPN
ejpam-180	430	3	u	u	PROPN
ejpam-180	430	4	(	(	PUNCT
ejpam-180	430	5	t	t	PROPN
ejpam-180	430	6	)	)	PUNCT
ejpam-180	430	7	t	t	PROPN
ejpam-180	430	8	b1	b1	PROPN
ejpam-180	430	9	(	(	PUNCT
ejpam-180	430	10	t)z1	t)z1	PROPN
ejpam-180	430	11	(	(	PUNCT
ejpam-180	430	12	t	t	PROPN
ejpam-180	430	13	)	)	PUNCT
ejpam-180	430	14	�	�	PROPN
ejpam-180	430	15	+	+	CCONJ
ejpam-180	430	16	yt	yt	PROPN
ejpam-180	430	17	(	(	PUNCT
ejpam-180	430	18	t	t	PROPN
ejpam-180	430	19	)	)	PUNCT
ejpam-180	430	20	gt	gt	PROPN
ejpam-180	430	21	(	(	PUNCT
ejpam-180	430	22	t	t	PROPN
ejpam-180	430	23	,	,	PUNCT
ejpam-180	430	24	x	x	X
ejpam-180	430	25	,	,	PUNCT
ejpam-180	430	26	ẋ	ẋ	PROPN
ejpam-180	430	27	,	,	PUNCT
ejpam-180	430	28	ẍ	ẍ	X
ejpam-180	430	29	)	)	PUNCT
ejpam-180	430	30	�	�	PROPN
ejpam-180	431	1	d	d	PROPN
ejpam-180	431	2	t	t	PROPN
ejpam-180	431	3	,	,	PUNCT
ejpam-180	431	4	.	.	PUNCT
ejpam-180	431	5	.	.	PUNCT
ejpam-180	431	6	.	.	PUNCT
ejpam-180	432	1	,	,	PUNCT
ejpam-180	432	2	∫	∫	PROPN
ejpam-180	433	1	i	i	PRON
ejpam-180	433	2	−	−	PROPN
ejpam-180	433	3	�	�	PROPN
ejpam-180	433	4	f	f	PROPN
ejpam-180	433	5	p	p	PROPN
ejpam-180	433	6	(	(	PUNCT
ejpam-180	433	7	t	t	PROPN
ejpam-180	433	8	,	,	PUNCT
ejpam-180	433	9	x	x	X
ejpam-180	433	10	,	,	PUNCT
ejpam-180	433	11	ẋ	ẋ	PROPN
ejpam-180	433	12	,	,	PUNCT
ejpam-180	433	13	ẍ	ẍ	X
ejpam-180	433	14	)	)	PUNCT
ejpam-180	434	1	+	+	CCONJ
ejpam-180	434	2	�	�	PROPN
ejpam-180	434	3	u	u	PROPN
ejpam-180	434	4	(	(	PUNCT
ejpam-180	434	5	t	t	PROPN
ejpam-180	434	6	)	)	PUNCT
ejpam-180	434	7	t	t	PROPN
ejpam-180	434	8	bp	bp	PROPN
ejpam-180	434	9	(	(	PUNCT
ejpam-180	434	10	t)zp	t)zp	PROPN
ejpam-180	434	11	(	(	PUNCT
ejpam-180	434	12	t	t	PROPN
ejpam-180	434	13	)	)	PUNCT
ejpam-180	434	14	�	�	PROPN
ejpam-180	434	15	+	+	CCONJ
ejpam-180	434	16	yt	yt	PROPN
ejpam-180	434	17	(	(	PUNCT
ejpam-180	434	18	t	t	PROPN
ejpam-180	434	19	)	)	PUNCT
ejpam-180	434	20	gt	gt	PROPN
ejpam-180	434	21	(	(	PUNCT
ejpam-180	434	22	t	t	PROPN
ejpam-180	434	23	,	,	PUNCT
ejpam-180	434	24	x	x	X
ejpam-180	434	25	,	,	PUNCT
ejpam-180	434	26	ẋ	ẋ	PROPN
ejpam-180	434	27	,	,	PUNCT
ejpam-180	434	28	ẍ	ẍ	X
ejpam-180	434	29	)	)	PUNCT
ejpam-180	434	30	�	�	PROPN
ejpam-180	435	1	d	d	PROPN
ejpam-180	435	2	t	t	PROPN
ejpam-180	435	3	�	�	PROPN
ejpam-180	435	4	subject	subject	ADJ
ejpam-180	435	5	to	to	ADP
ejpam-180	435	6	x	x	PROPN
ejpam-180	435	7	(	(	PUNCT
ejpam-180	435	8	a	a	X
ejpam-180	435	9	)	)	PUNCT
ejpam-180	435	10	=	=	SYM
ejpam-180	435	11	0	0	PUNCT
ejpam-180	436	1	=	=	SYM
ejpam-180	436	2	x	x	X
ejpam-180	436	3	(	(	PUNCT
ejpam-180	436	4	b	b	NOUN
ejpam-180	436	5	)	)	PUNCT
ejpam-180	436	6	ẋ	ẋ	PROPN
ejpam-180	437	1	(	(	PUNCT
ejpam-180	437	2	a	a	X
ejpam-180	437	3	)	)	PUNCT
ejpam-180	437	4	=	=	SYM
ejpam-180	437	5	0	0	PUNCT
ejpam-180	438	1	=	=	SYM
ejpam-180	438	2	ẋ	ẋ	PROPN
ejpam-180	438	3	(	(	PUNCT
ejpam-180	438	4	b	b	NOUN
ejpam-180	438	5	)	)	PUNCT
ejpam-180	438	6	θ	θ	PROPN
ejpam-180	438	7	�	�	PROPN
ejpam-180	438	8	t	t	PROPN
ejpam-180	438	9	,	,	PUNCT
ejpam-180	438	10	x	x	X
ejpam-180	438	11	,	,	PUNCT
ejpam-180	438	12	ẋ	ẋ	PROPN
ejpam-180	438	13	,	,	PUNCT
ejpam-180	438	14	ẍ	ẍ	X
ejpam-180	438	15	,	,	PUNCT
ejpam-180	438	16	...	...	PUNCT
ejpam-180	439	1	x	x	X
ejpam-180	439	2	,	,	PUNCT
ejpam-180	439	3	y	y	PROPN
ejpam-180	439	4	,	,	PUNCT
ejpam-180	439	5	ẏ	ẏ	PROPN
ejpam-180	439	6	,	,	PUNCT
ejpam-180	439	7	ÿ	ÿ	PROPN
ejpam-180	439	8	,	,	PUNCT
ejpam-180	439	9	λ	λ	X
ejpam-180	439	10	�	�	PROPN
ejpam-180	439	11	=	=	SYM
ejpam-180	439	12	0	0	NUM
ejpam-180	439	13	z̄	z̄	PROPN
ejpam-180	440	1	i	i	PROPN
ejpam-180	440	2	(	(	PUNCT
ejpam-180	440	3	t	t	PROPN
ejpam-180	440	4	)	)	PUNCT
ejpam-180	440	5	t	t	PROPN
ejpam-180	440	6	b	b	PROPN
ejpam-180	440	7	i	i	PROPN
ejpam-180	440	8	(	(	PUNCT
ejpam-180	440	9	t	t	PROPN
ejpam-180	440	10	)	)	PUNCT
ejpam-180	440	11	z̄	z̄	PROPN
ejpam-180	441	1	i	i	PRON
ejpam-180	441	2	(	(	PUNCT
ejpam-180	441	3	t)≦	t)≦	X
ejpam-180	441	4	1	1	NUM
ejpam-180	441	5	,	,	PUNCT
ejpam-180	441	6	t	t	PROPN
ejpam-180	441	7	∈	∈	PROPN
ejpam-180	442	1	i	i	PRON
ejpam-180	442	2	,	,	PUNCT
ejpam-180	442	3	i	i	PRON
ejpam-180	442	4	∈	∈	VERB
ejpam-180	442	5	p	p	PROPN
ejpam-180	442	6	y	y	PROPN
ejpam-180	442	7	(	(	PUNCT
ejpam-180	442	8	t)≧	t)≧	PROPN
ejpam-180	442	9	0	0	NUM
ejpam-180	442	10	,	,	PUNCT
ejpam-180	442	11	t	t	PROPN
ejpam-180	442	12	∈	∈	PROPN
ejpam-180	443	1	i	i	PRON
ejpam-180	443	2	λ	λ	X
ejpam-180	443	3	>	>	X
ejpam-180	443	4	0	0	PROPN
ejpam-180	443	5	,	,	PUNCT
ejpam-180	443	6	λt	λt	ADP
ejpam-180	443	7	e	e	NOUN
ejpam-180	443	8	=	=	SYM
ejpam-180	443	9	1	1	NUM
ejpam-180	443	10	consider	consider	VERB
ejpam-180	443	11	θ	θ	PROPN
ejpam-180	443	12	�	�	PROPN
ejpam-180	443	13	t	t	PROPN
ejpam-180	443	14	,	,	PUNCT
ejpam-180	443	15	x	x	X
ejpam-180	443	16	(	(	PUNCT
ejpam-180	443	17	·	·	PUNCT
ejpam-180	443	18	)	)	PUNCT
ejpam-180	443	19	,	,	PUNCT
ejpam-180	443	20	ẋ	ẋ	PROPN
ejpam-180	443	21	(	(	PUNCT
ejpam-180	443	22	·	·	PUNCT
ejpam-180	443	23	)	)	PUNCT
ejpam-180	443	24	,	,	PUNCT
ejpam-180	443	25	ẍ	ẍ	X
ejpam-180	443	26	(	(	PUNCT
ejpam-180	443	27	·	·	PUNCT
ejpam-180	443	28	)	)	PUNCT
ejpam-180	443	29	,	,	PUNCT
ejpam-180	443	30	...	...	PUNCT
ejpam-180	444	1	x	x	X
ejpam-180	444	2	(	(	PUNCT
ejpam-180	444	3	·	·	PUNCT
ejpam-180	444	4	)	)	PUNCT
ejpam-180	444	5	,	,	PUNCT
ejpam-180	444	6	y	y	PROPN
ejpam-180	444	7	(	(	PUNCT
ejpam-180	444	8	·	·	PUNCT
ejpam-180	444	9	)	)	PUNCT
ejpam-180	444	10	,	,	PUNCT
ejpam-180	444	11	ẏ	ẏ	PROPN
ejpam-180	444	12	(	(	PUNCT
ejpam-180	444	13	·	·	PUNCT
ejpam-180	444	14	)	)	PUNCT
ejpam-180	444	15	,	,	PUNCT
ejpam-180	444	16	ÿ	ÿ	PROPN
ejpam-180	444	17	(	(	PUNCT
ejpam-180	444	18	·	·	PUNCT
ejpam-180	444	19	)	)	PUNCT
ejpam-180	444	20	,	,	PUNCT
ejpam-180	444	21	λ	λ	X
ejpam-180	444	22	�	�	PROPN
ejpam-180	444	23	=	=	NOUN
ejpam-180	444	24	0	0	PUNCT
ejpam-180	444	25	as	as	ADP
ejpam-180	444	26	defining	define	VERB
ejpam-180	444	27	a	a	DET
ejpam-180	444	28	mapping	mapping	NOUN
ejpam-180	444	29	ψ	ψ	X
ejpam-180	444	30	:	:	PUNCT
ejpam-180	444	31	x	x	SYM
ejpam-180	444	32	×	×	VERB
ejpam-180	444	33	y	y	PROPN
ejpam-180	444	34	×rp→	×rp→	PROPN
ejpam-180	444	35	q	q	PROPN
ejpam-180	444	36	where	where	SCONJ
ejpam-180	444	37	y	y	PROPN
ejpam-180	444	38	is	be	AUX
ejpam-180	444	39	a	a	DET
ejpam-180	444	40	space	space	NOUN
ejpam-180	444	41	of	of	ADP
ejpam-180	444	42	piecewise	piecewise	NOUN
ejpam-180	444	43	twice	twice	ADV
ejpam-180	444	44	differentiable	differentiable	ADJ
ejpam-180	444	45	function	function	NOUN
ejpam-180	444	46	and	and	CCONJ
ejpam-180	444	47	q	q	NOUN
ejpam-180	444	48	is	be	AUX
ejpam-180	444	49	the	the	DET
ejpam-180	444	50	banach	banach	NOUN
ejpam-180	444	51	space	space	NOUN
ejpam-180	444	52	.	.	PUNCT
ejpam-180	445	1	in	in	ADP
ejpam-180	445	2	order	order	NOUN
ejpam-180	445	3	to	to	PART
ejpam-180	445	4	apply	apply	VERB
ejpam-180	445	5	theorem	theorem	ADJ
ejpam-180	445	6	3.1[8	3.1[8	NOUN
ejpam-180	445	7	]	]	PUNCT
ejpam-180	445	8	to	to	ADP
ejpam-180	445	9	the	the	DET
ejpam-180	445	10	problem	problem	NOUN
ejpam-180	445	11	(	(	PUNCT
ejpam-180	445	12	mwd	mwd	PROPN
ejpam-180	445	13	)	)	PUNCT
ejpam-180	445	14	,	,	PUNCT
ejpam-180	445	15	the	the	DET
ejpam-180	445	16	infinite	infinite	ADJ
ejpam-180	445	17	dimensional	dimensional	ADJ
ejpam-180	445	18	inequality	inequality	NOUN
ejpam-180	445	19	must	must	AUX
ejpam-180	445	20	be	be	AUX
ejpam-180	445	21	restricted	restrict	VERB
ejpam-180	445	22	.	.	PUNCT
ejpam-180	446	1	in	in	ADP
ejpam-180	446	2	the	the	DET
ejpam-180	446	3	following	following	NOUN
ejpam-180	446	4	theorem	theorem	NOUN
ejpam-180	446	5	,	,	PUNCT
ejpam-180	446	6	we	we	PRON
ejpam-180	446	7	use	use	VERB
ejpam-180	446	8	ψ′	ψ′	PUNCT
ejpam-180	446	9	to	to	PART
ejpam-180	446	10	represent	represent	VERB
ejpam-180	446	11	the	the	DET
ejpam-180	446	12	frèchèt	frèchèt	NOUN
ejpam-180	446	13	derivative	derivative	PROPN
ejpam-180	446	14	�	�	PROPN
ejpam-180	446	15	ψx	ψx	ADP
ejpam-180	446	16	�	�	PROPN
ejpam-180	446	17	x	x	SYM
ejpam-180	446	18	,	,	PUNCT
ejpam-180	446	19	y	y	PROPN
ejpam-180	446	20	,	,	PUNCT
ejpam-180	446	21	λ	λ	PROPN
ejpam-180	446	22	�	�	PROPN
ejpam-180	446	23	,	,	PUNCT
ejpam-180	446	24	ψy	ψy	PROPN
ejpam-180	446	25	�	�	PROPN
ejpam-180	446	26	x	x	SYM
ejpam-180	446	27	,	,	PUNCT
ejpam-180	446	28	y	y	PROPN
ejpam-180	446	29	,	,	PUNCT
ejpam-180	446	30	λ	λ	PROPN
ejpam-180	446	31	�	�	PROPN
ejpam-180	446	32	,	,	PUNCT
ejpam-180	446	33	ψλ	ψλ	ADP
ejpam-180	446	34	�	�	PROPN
ejpam-180	446	35	x	x	SYM
ejpam-180	446	36	,	,	PUNCT
ejpam-180	446	37	y	y	PROPN
ejpam-180	446	38	,	,	PUNCT
ejpam-180	446	39	λ	λ	PROPN
ejpam-180	446	40	�	�	PROPN
ejpam-180	446	41	�	�	PROPN
ejpam-180	446	42	.	.	PUNCT
ejpam-180	447	1	theorem	theorem	VERB
ejpam-180	447	2	4.3	4.3	NUM
ejpam-180	447	3	(	(	PUNCT
ejpam-180	447	4	converse	converse	NOUN
ejpam-180	447	5	duality	duality	NOUN
ejpam-180	447	6	)	)	PUNCT
ejpam-180	447	7	.	.	PUNCT
ejpam-180	448	1	let	let	VERB
ejpam-180	448	2	�	�	PROPN
ejpam-180	448	3	x̄	x̄	PROPN
ejpam-180	448	4	,	,	PUNCT
ejpam-180	448	5	ū	ū	NOUN
ejpam-180	448	6	,	,	PUNCT
ejpam-180	448	7	ȳ	ȳ	PROPN
ejpam-180	448	8	,	,	PUNCT
ejpam-180	448	9	z̄1	z̄1	PROPN
ejpam-180	448	10	,	,	PUNCT
ejpam-180	448	11	.	.	PUNCT
ejpam-180	448	12	.	.	PUNCT
ejpam-180	449	1	.	.	PUNCT
ejpam-180	450	1	,	,	PUNCT
ejpam-180	450	2	z̄p	z̄p	PROPN
ejpam-180	450	3	,	,	PUNCT
ejpam-180	450	4	λ̄	λ̄	PRON
ejpam-180	450	5	�	�	PROPN
ejpam-180	450	6	be	be	AUX
ejpam-180	450	7	an	an	DET
ejpam-180	450	8	efficient	efficient	ADJ
ejpam-180	450	9	solution	solution	NOUN
ejpam-180	450	10	for	for	ADP
ejpam-180	450	11	(	(	PUNCT
ejpam-180	450	12	mwd	mwd	PROPN
ejpam-180	450	13	)	)	PUNCT
ejpam-180	450	14	assume	assume	VERB
ejpam-180	450	15	that	that	SCONJ
ejpam-180	450	16	(	(	PUNCT
ejpam-180	450	17	h1	h1	PROPN
ejpam-180	450	18	)	)	PUNCT
ejpam-180	450	19	the	the	DET
ejpam-180	450	20	frèchèt	frèchèt	NOUN
ejpam-180	450	21	derivative	derivative	NOUN
ejpam-180	450	22	ψ′	ψ′	VERB
ejpam-180	450	23	has	have	VERB
ejpam-180	450	24	a	a	DET
ejpam-180	450	25	(	(	PUNCT
ejpam-180	450	26	weak∗	weak∗	NOUN
ejpam-180	450	27	)	)	PUNCT
ejpam-180	450	28	closed	closed	ADJ
ejpam-180	450	29	range	range	NOUN
ejpam-180	450	30	,	,	PUNCT
ejpam-180	450	31	(	(	PUNCT
ejpam-180	450	32	h2	h2	NOUN
ejpam-180	450	33	)	)	PUNCT
ejpam-180	450	34	f	f	PROPN
ejpam-180	450	35	and	and	CCONJ
ejpam-180	450	36	g	g	PROPN
ejpam-180	450	37	be	be	VERB
ejpam-180	450	38	twice	twice	ADV
ejpam-180	450	39	continuously	continuously	ADV
ejpam-180	450	40	differentiable	differentiable	ADJ
ejpam-180	450	41	,	,	PUNCT
ejpam-180	450	42	and	and	CCONJ
ejpam-180	450	43	(	(	PUNCT
ejpam-180	450	44	h3	h3	NOUN
ejpam-180	450	45	)	)	PUNCT
ejpam-180	450	46	�	�	PROPN
ejpam-180	450	47	β	β	X
ejpam-180	450	48	(	(	PUNCT
ejpam-180	450	49	t	t	PROPN
ejpam-180	450	50	)	)	PUNCT
ejpam-180	450	51	t	t	PROPN
ejpam-180	450	52	θx	θx	NUM
ejpam-180	450	53	−	−	PROPN
ejpam-180	450	54	dβ	dβ	PROPN
ejpam-180	450	55	(	(	PUNCT
ejpam-180	450	56	t	t	NOUN
ejpam-180	450	57	)	)	PUNCT
ejpam-180	450	58	t	t	PROPN
ejpam-180	450	59	θ	θ	PROPN
ejpam-180	450	60	ẋ	ẋ	PROPN
ejpam-180	451	1	+	+	PUNCT
ejpam-180	451	2	d2β	d2β	PROPN
ejpam-180	451	3	(	(	PUNCT
ejpam-180	451	4	t	t	PROPN
ejpam-180	451	5	)	)	PUNCT
ejpam-180	451	6	t	t	PROPN
ejpam-180	451	7	θ	θ	PROPN
ejpam-180	451	8	ẍ	ẍ	X
ejpam-180	451	9	�	�	PROPN
ejpam-180	451	10	β	β	PROPN
ejpam-180	451	11	(	(	PUNCT
ejpam-180	451	12	t	t	PROPN
ejpam-180	451	13	)	)	PUNCT
ejpam-180	451	14	=	=	SYM
ejpam-180	451	15	0,⇒	0,⇒	PROPN
ejpam-180	451	16	β	β	X
ejpam-180	451	17	(	(	PUNCT
ejpam-180	451	18	t	t	PROPN
ejpam-180	451	19	)	)	PUNCT
ejpam-180	452	1	=	=	SYM
ejpam-180	452	2	0	0	NUM
ejpam-180	452	3	,	,	PUNCT
ejpam-180	452	4	t	t	PROPN
ejpam-180	452	5	∈	∈	PROPN
ejpam-180	452	6	i	i	PRON
ejpam-180	452	7	i.	i.	PROPN
ejpam-180	452	8	husain	husain	PROPN
ejpam-180	452	9	,	,	PUNCT
ejpam-180	452	10	a.	a.	PROPN
ejpam-180	452	11	ahmed	ahmed	PROPN
ejpam-180	452	12	,	,	PUNCT
ejpam-180	452	13	and	and	CCONJ
ejpam-180	452	14	g.	g.	PROPN
ejpam-180	452	15	rumana	rumana	PROPN
ejpam-180	452	16	/	/	SYM
ejpam-180	452	17	eur	eur	PROPN
ejpam-180	452	18	.	.	PUNCT
ejpam-180	453	1	j.	j.	PROPN
ejpam-180	453	2	pure	pure	PROPN
ejpam-180	453	3	appl	appl	PROPN
ejpam-180	453	4	.	.	PROPN
ejpam-180	453	5	math	math	PROPN
ejpam-180	453	6	,	,	PUNCT
ejpam-180	453	7	2	2	NUM
ejpam-180	453	8	(	(	PUNCT
ejpam-180	453	9	2009	2009	NUM
ejpam-180	453	10	)	)	PUNCT
ejpam-180	453	11	,	,	PUNCT
ejpam-180	453	12	(	(	PUNCT
ejpam-180	453	13	372	372	NUM
ejpam-180	453	14	-	-	SYM
ejpam-180	453	15	400	400	NUM
ejpam-180	453	16	)	)	PUNCT
ejpam-180	453	17	386	386	NUM
ejpam-180	453	18	further	far	ADV
ejpam-180	453	19	,	,	PUNCT
ejpam-180	453	20	if	if	SCONJ
ejpam-180	453	21	the	the	DET
ejpam-180	453	22	assumptions	assumption	NOUN
ejpam-180	453	23	of	of	ADP
ejpam-180	453	24	theorem	theorem	ADJ
ejpam-180	453	25	4.1	4.1	NUM
ejpam-180	453	26	are	be	AUX
ejpam-180	453	27	satisfied	satisfied	ADJ
ejpam-180	453	28	,	,	PUNCT
ejpam-180	453	29	then	then	ADV
ejpam-180	453	30	x̄	x̄	PROPN
ejpam-180	453	31	is	be	AUX
ejpam-180	453	32	an	an	DET
ejpam-180	453	33	efficient	efficient	ADJ
ejpam-180	453	34	solution	solution	NOUN
ejpam-180	453	35	of	of	ADP
ejpam-180	453	36	(	(	PUNCT
ejpam-180	453	37	vp	vp	PROPN
ejpam-180	453	38	)	)	PUNCT
ejpam-180	453	39	.	.	PUNCT
ejpam-180	454	1	proof	proof	NOUN
ejpam-180	454	2	.	.	PUNCT
ejpam-180	455	1	since	since	SCONJ
ejpam-180	455	2	(	(	PUNCT
ejpam-180	455	3	x̄	x̄	PROPN
ejpam-180	455	4	,	,	PUNCT
ejpam-180	455	5	ū	ū	PROPN
ejpam-180	455	6	,	,	PUNCT
ejpam-180	455	7	ȳ	ȳ	PROPN
ejpam-180	455	8	,	,	PUNCT
ejpam-180	455	9	z̄1	z̄1	PROPN
ejpam-180	455	10	,	,	PUNCT
ejpam-180	455	11	.	.	PUNCT
ejpam-180	455	12	.	.	PUNCT
ejpam-180	455	13	.	.	PUNCT
ejpam-180	456	1	,	,	PUNCT
ejpam-180	456	2	z̄p	z̄p	PROPN
ejpam-180	456	3	,	,	PUNCT
ejpam-180	456	4	λ̄	λ̄	PRON
ejpam-180	456	5	)	)	PUNCT
ejpam-180	456	6	with	with	ADP
ejpam-180	456	7	ψ′	ψ′	PUNCT
ejpam-180	456	8	having	have	VERB
ejpam-180	456	9	a	a	DET
ejpam-180	456	10	(	(	PUNCT
ejpam-180	456	11	weak∗	weak∗	NOUN
ejpam-180	456	12	)	)	PUNCT
ejpam-180	456	13	closed	closed	ADJ
ejpam-180	456	14	range	range	NOUN
ejpam-180	456	15	,	,	PUNCT
ejpam-180	456	16	is	be	AUX
ejpam-180	456	17	an	an	DET
ejpam-180	456	18	efficient	efficient	ADJ
ejpam-180	456	19	solution	solution	NOUN
ejpam-180	456	20	of	of	ADP
ejpam-180	456	21	(	(	PUNCT
ejpam-180	456	22	mwd	mwd	PROPN
ejpam-180	456	23	)	)	PUNCT
ejpam-180	456	24	,	,	PUNCT
ejpam-180	456	25	then	then	ADV
ejpam-180	456	26	there	there	PRON
ejpam-180	456	27	exist	exist	VERB
ejpam-180	456	28	α	α	PRON
ejpam-180	456	29	∈	∈	PROPN
ejpam-180	456	30	rp	rp	NOUN
ejpam-180	456	31	,	,	PUNCT
ejpam-180	456	32	η	η	PROPN
ejpam-180	456	33	∈	∈	PROPN
ejpam-180	456	34	rp	rp	NOUN
ejpam-180	456	35	,	,	PUNCT
ejpam-180	456	36	γ	γ	PROPN
ejpam-180	456	37	∈	∈	PROPN
ejpam-180	456	38	r	r	PROPN
ejpam-180	456	39	,	,	PUNCT
ejpam-180	456	40	δ	δ	PROPN
ejpam-180	456	41	∈	∈	PROPN
ejpam-180	456	42	r	r	PROPN
ejpam-180	456	43	,	,	PUNCT
ejpam-180	456	44	ξ	ξ	PROPN
ejpam-180	456	45	∈	∈	PROPN
ejpam-180	456	46	rm	rm	NOUN
ejpam-180	456	47	and	and	CCONJ
ejpam-180	456	48	piecewise	piecewise	PROPN
ejpam-180	456	49	smooth	smooth	ADJ
ejpam-180	456	50	β(t	β(t	PROPN
ejpam-180	456	51	)	)	PUNCT
ejpam-180	456	52	:	:	PUNCT
ejpam-180	457	1	i	i	PRON
ejpam-180	457	2	→	→	SYM
ejpam-180	457	3	rn	rn	PROPN
ejpam-180	457	4	and	and	CCONJ
ejpam-180	457	5	µ(t	µ(t	ADJ
ejpam-180	457	6	)	)	PUNCT
ejpam-180	457	7	:	:	PUNCT
ejpam-180	458	1	i	i	PRON
ejpam-180	458	2	→	→	SYM
ejpam-180	458	3	rm	rm	NOUN
ejpam-180	458	4	such	such	ADJ
ejpam-180	458	5	that	that	SCONJ
ejpam-180	458	6	the	the	DET
ejpam-180	458	7	following	follow	VERB
ejpam-180	458	8	fritz	fritz	PROPN
ejpam-180	458	9	-	-	PUNCT
ejpam-180	458	10	john	john	PROPN
ejpam-180	458	11	optimality	optimality	PROPN
ejpam-180	458	12	conditions[8	conditions[8	PROPN
ejpam-180	458	13	]	]	PUNCT
ejpam-180	458	14	hold	hold	VERB
ejpam-180	458	15	−	−	PROPN
ejpam-180	458	16	p	p	NOUN
ejpam-180	458	17	∑	∑	PROPN
ejpam-180	458	18	i=1	i=1	PROPN
ejpam-180	458	19	αi	αi	PROPN
ejpam-180	458	20	�	�	PROPN
ejpam-180	459	1	f	f	PROPN
ejpam-180	459	2	i	i	PRON
ejpam-180	459	3	x	x	X
ejpam-180	459	4	(	(	PUNCT
ejpam-180	459	5	t	t	NOUN
ejpam-180	459	6	,	,	PUNCT
ejpam-180	459	7	x	x	X
ejpam-180	459	8	,	,	PUNCT
ejpam-180	459	9	ẋ	ẋ	PROPN
ejpam-180	459	10	,	,	PUNCT
ejpam-180	459	11	ẍ	ẍ	X
ejpam-180	459	12	)	)	PUNCT
ejpam-180	460	1	+	+	CCONJ
ejpam-180	461	1	b	b	X
ejpam-180	461	2	i	i	PRON
ejpam-180	461	3	(	(	PUNCT
ejpam-180	461	4	t)z	t)z	NOUN
ejpam-180	461	5	i	i	PRON
ejpam-180	461	6	(	(	PUNCT
ejpam-180	461	7	t	t	PROPN
ejpam-180	461	8	)	)	PUNCT
ejpam-180	461	9	+	+	CCONJ
ejpam-180	461	10	y	y	PROPN
ejpam-180	461	11	(	(	PUNCT
ejpam-180	461	12	t	t	PROPN
ejpam-180	461	13	)	)	PUNCT
ejpam-180	461	14	t	t	PROPN
ejpam-180	461	15	gx	gx	PROPN
ejpam-180	461	16	(	(	PUNCT
ejpam-180	461	17	t	t	PROPN
ejpam-180	461	18	,	,	PUNCT
ejpam-180	461	19	x	x	X
ejpam-180	461	20	,	,	PUNCT
ejpam-180	461	21	ẋ	ẋ	PROPN
ejpam-180	461	22	,	,	PUNCT
ejpam-180	461	23	ẍ	ẍ	X
ejpam-180	461	24	)	)	PUNCT
ejpam-180	461	25	�	�	PROPN
ejpam-180	462	1	+	+	PROPN
ejpam-180	462	2	d	d	PROPN
ejpam-180	462	3	�	�	PROPN
ejpam-180	462	4	αt	αt	PROPN
ejpam-180	462	5	f	f	PROPN
ejpam-180	462	6	ẋ	ẋ	PROPN
ejpam-180	463	1	(	(	PUNCT
ejpam-180	463	2	t	t	PROPN
ejpam-180	463	3	,	,	PUNCT
ejpam-180	463	4	x	x	X
ejpam-180	463	5	,	,	PUNCT
ejpam-180	463	6	ẋ	ẋ	PROPN
ejpam-180	463	7	,	,	PUNCT
ejpam-180	463	8	ẍ	ẍ	X
ejpam-180	463	9	)	)	PUNCT
ejpam-180	464	1	+	+	CCONJ
ejpam-180	464	2	�	�	PROPN
ejpam-180	464	3	αt	αt	PROPN
ejpam-180	464	4	e	e	PROPN
ejpam-180	464	5	�	�	PROPN
ejpam-180	464	6	y	y	PROPN
ejpam-180	464	7	(	(	PUNCT
ejpam-180	464	8	t	t	PROPN
ejpam-180	464	9	)	)	PUNCT
ejpam-180	464	10	t	t	PROPN
ejpam-180	464	11	g	g	PROPN
ejpam-180	464	12	ẋ	ẋ	PROPN
ejpam-180	464	13	(	(	PUNCT
ejpam-180	464	14	t	t	PROPN
ejpam-180	464	15	,	,	PUNCT
ejpam-180	464	16	x	x	X
ejpam-180	464	17	,	,	PUNCT
ejpam-180	464	18	ẋ	ẋ	PROPN
ejpam-180	464	19	,	,	PUNCT
ejpam-180	464	20	ẍ	ẍ	X
ejpam-180	464	21	)	)	PUNCT
ejpam-180	464	22	�	�	PROPN
ejpam-180	464	23	−d2	−d2	PROPN
ejpam-180	464	24	�	�	PROPN
ejpam-180	464	25	αt	αt	PROPN
ejpam-180	464	26	f	f	PROPN
ejpam-180	464	27	ẍ	ẍ	PROPN
ejpam-180	464	28	(	(	PUNCT
ejpam-180	464	29	t	t	PROPN
ejpam-180	464	30	,	,	PUNCT
ejpam-180	464	31	x	x	X
ejpam-180	464	32	,	,	PUNCT
ejpam-180	464	33	ẋ	ẋ	PROPN
ejpam-180	464	34	,	,	PUNCT
ejpam-180	464	35	ẍ	ẍ	X
ejpam-180	464	36	)	)	PUNCT
ejpam-180	465	1	+	+	CCONJ
ejpam-180	465	2	�	�	PROPN
ejpam-180	465	3	αt	αt	PROPN
ejpam-180	465	4	e	e	PROPN
ejpam-180	465	5	�	�	PROPN
ejpam-180	465	6	y	y	PROPN
ejpam-180	465	7	(	(	PUNCT
ejpam-180	465	8	t	t	PROPN
ejpam-180	465	9	)	)	PUNCT
ejpam-180	465	10	t	t	PROPN
ejpam-180	465	11	g	g	PROPN
ejpam-180	465	12	ẍ	ẍ	PROPN
ejpam-180	466	1	(	(	PUNCT
ejpam-180	466	2	t	t	PROPN
ejpam-180	466	3	,	,	PUNCT
ejpam-180	466	4	x	x	X
ejpam-180	466	5	,	,	PUNCT
ejpam-180	466	6	ẋ	ẋ	PROPN
ejpam-180	466	7	,	,	PUNCT
ejpam-180	466	8	ẍ	ẍ	X
ejpam-180	466	9	)	)	PUNCT
ejpam-180	466	10	�	�	PROPN
ejpam-180	467	1	+	+	PROPN
ejpam-180	467	2	β	β	X
ejpam-180	467	3	(	(	PUNCT
ejpam-180	467	4	t	t	PROPN
ejpam-180	467	5	)	)	PUNCT
ejpam-180	467	6	t	t	PROPN
ejpam-180	467	7	θx	θx	NUM
ejpam-180	467	8	−	−	PROPN
ejpam-180	467	9	dβ	dβ	PROPN
ejpam-180	467	10	(	(	PUNCT
ejpam-180	467	11	t	t	NOUN
ejpam-180	467	12	)	)	PUNCT
ejpam-180	467	13	t	t	PROPN
ejpam-180	467	14	θ	θ	PROPN
ejpam-180	467	15	ẋ	ẋ	PROPN
ejpam-180	468	1	+	+	PUNCT
ejpam-180	468	2	d2β	d2β	PROPN
ejpam-180	468	3	(	(	PUNCT
ejpam-180	468	4	t	t	PROPN
ejpam-180	468	5	)	)	PUNCT
ejpam-180	468	6	t	t	PROPN
ejpam-180	468	7	θ	θ	PROPN
ejpam-180	468	8	ẍ	ẍ	PUNCT
ejpam-180	469	1	−	−	PROPN
ejpam-180	469	2	d3β	d3β	NOUN
ejpam-180	469	3	(	(	PUNCT
ejpam-180	469	4	t	t	NOUN
ejpam-180	469	5	)	)	PUNCT
ejpam-180	469	6	t	t	PROPN
ejpam-180	469	7	θ	θ	PROPN
ejpam-180	469	8	...	...	PUNCT
ejpam-180	469	9	x	x	SYM
ejpam-180	469	10	=	=	SYM
ejpam-180	469	11	0	0	NUM
ejpam-180	469	12	,	,	PUNCT
ejpam-180	469	13	t	t	PROPN
ejpam-180	469	14	∈	∈	PROPN
ejpam-180	470	1	i	i	PRON
ejpam-180	470	2	(	(	PUNCT
ejpam-180	470	3	4.21	4.21	NUM
ejpam-180	470	4	)	)	PUNCT
ejpam-180	470	5	−(αt	−(αt	NOUN
ejpam-180	470	6	e)g	e)g	X
ejpam-180	470	7	j(t	j(t	PROPN
ejpam-180	470	8	,	,	PUNCT
ejpam-180	470	9	x	x	INTJ
ejpam-180	470	10	,	,	PUNCT
ejpam-180	470	11	ẋ	ẋ	PROPN
ejpam-180	470	12	,	,	PUNCT
ejpam-180	470	13	ẍ	ẍ	X
ejpam-180	470	14	)	)	PUNCT
ejpam-180	471	1	+	+	CCONJ
ejpam-180	471	2	β(t)tθy	β(t)tθy	X
ejpam-180	471	3	j	j	PROPN
ejpam-180	471	4	−	−	NOUN
ejpam-180	471	5	dβ(t)tθ	dβ(t)tθ	VERB
ejpam-180	471	6	ẏ	ẏ	PROPN
ejpam-180	471	7	j	j	PROPN
ejpam-180	471	8	+	+	CCONJ
ejpam-180	471	9	d2β(t)tθ	d2β(t)tθ	PROPN
ejpam-180	471	10	ÿ	ÿ	PROPN
ejpam-180	471	11	j	j	PROPN
ejpam-180	471	12	−µ	−µ	NOUN
ejpam-180	471	13	j(t	j(t	PROPN
ejpam-180	471	14	)	)	PUNCT
ejpam-180	472	1	=	=	SYM
ejpam-180	472	2	0	0	NUM
ejpam-180	472	3	,	,	PUNCT
ejpam-180	472	4	t	t	PROPN
ejpam-180	472	5	∈	∈	PROPN
ejpam-180	473	1	i	i	PRON
ejpam-180	473	2	(	(	PUNCT
ejpam-180	473	3	4.22	4.22	NUM
ejpam-180	473	4	)	)	PUNCT
ejpam-180	473	5	for	for	ADP
ejpam-180	473	6	j	j	PROPN
ejpam-180	473	7	=	=	SYM
ejpam-180	473	8	1	1	NUM
ejpam-180	473	9	,	,	PUNCT
ejpam-180	473	10	2	2	NUM
ejpam-180	473	11	,	,	PUNCT
ejpam-180	473	12	.	.	PUNCT
ejpam-180	473	13	.	.	PUNCT
ejpam-180	473	14	.	.	PUNCT
ejpam-180	474	1	,	,	PUNCT
ejpam-180	474	2	m	m	VERB
ejpam-180	474	3	�	�	PROPN
ejpam-180	475	1	f	f	NOUN
ejpam-180	475	2	i	i	NOUN
ejpam-180	475	3	x	x	X
ejpam-180	475	4	(	(	PUNCT
ejpam-180	475	5	t	t	NOUN
ejpam-180	475	6	,	,	PUNCT
ejpam-180	475	7	x	x	X
ejpam-180	475	8	,	,	PUNCT
ejpam-180	475	9	ẋ	ẋ	PROPN
ejpam-180	475	10	,	,	PUNCT
ejpam-180	475	11	ẍ	ẍ	X
ejpam-180	475	12	)	)	PUNCT
ejpam-180	476	1	+	+	CCONJ
ejpam-180	477	1	b	b	X
ejpam-180	477	2	i	i	PRON
ejpam-180	477	3	(	(	PUNCT
ejpam-180	477	4	t)z	t)z	NOUN
ejpam-180	477	5	i	i	PRON
ejpam-180	477	6	(	(	PUNCT
ejpam-180	477	7	t)−	t)−	PROPN
ejpam-180	478	1	d	d	X
ejpam-180	478	2	f	f	X
ejpam-180	479	1	i	i	PRON
ejpam-180	479	2	ẋ	ẋ	PROPN
ejpam-180	480	1	(	(	PUNCT
ejpam-180	480	2	t	t	PROPN
ejpam-180	480	3	,	,	PUNCT
ejpam-180	480	4	x	x	X
ejpam-180	480	5	,	,	PUNCT
ejpam-180	480	6	ẋ	ẋ	PROPN
ejpam-180	480	7	,	,	PUNCT
ejpam-180	480	8	ẍ	ẍ	X
ejpam-180	480	9	)	)	PUNCT
ejpam-180	481	1	+	+	VERB
ejpam-180	481	2	d2	d2	PROPN
ejpam-180	481	3	f	f	PROPN
ejpam-180	481	4	i	i	PRON
ejpam-180	481	5	ẍ	ẍ	PROPN
ejpam-180	482	1	(	(	PUNCT
ejpam-180	482	2	t	t	PROPN
ejpam-180	482	3	,	,	PUNCT
ejpam-180	482	4	x	x	X
ejpam-180	482	5	,	,	PUNCT
ejpam-180	482	6	ẋ	ẋ	PROPN
ejpam-180	482	7	,	,	PUNCT
ejpam-180	482	8	ẍ	ẍ	X
ejpam-180	482	9	)	)	PUNCT
ejpam-180	482	10	�	�	PROPN
ejpam-180	482	11	β	β	X
ejpam-180	482	12	(	(	PUNCT
ejpam-180	482	13	t	t	PROPN
ejpam-180	482	14	)	)	PUNCT
ejpam-180	483	1	+	+	NOUN
ejpam-180	483	2	ηi	ηi	X
ejpam-180	483	3	+	+	CCONJ
ejpam-180	483	4	γ=	γ=	PROPN
ejpam-180	483	5	0	0	NUM
ejpam-180	483	6	,	,	PUNCT
ejpam-180	483	7	i	i	PRON
ejpam-180	483	8	=	=	NOUN
ejpam-180	483	9	1	1	NUM
ejpam-180	483	10	,	,	PUNCT
ejpam-180	483	11	.	.	PUNCT
ejpam-180	483	12	.	.	PUNCT
ejpam-180	484	1	.	.	PUNCT
ejpam-180	485	1	,	,	PUNCT
ejpam-180	485	2	p	p	X
ejpam-180	485	3	(	(	PUNCT
ejpam-180	485	4	4.23	4.23	NUM
ejpam-180	485	5	)	)	PUNCT
ejpam-180	485	6	−αi	−αi	NOUN
ejpam-180	485	7	x	x	X
ejpam-180	485	8	(	(	PUNCT
ejpam-180	485	9	t	t	PROPN
ejpam-180	485	10	)	)	PUNCT
ejpam-180	485	11	t	t	PROPN
ejpam-180	485	12	b	b	PROPN
ejpam-180	485	13	i	i	PROPN
ejpam-180	485	14	(	(	PUNCT
ejpam-180	485	15	t	t	PROPN
ejpam-180	485	16	)	)	PUNCT
ejpam-180	486	1	+	+	NUM
ejpam-180	486	2	β	β	X
ejpam-180	486	3	(	(	PUNCT
ejpam-180	486	4	t)λib	t)λib	PROPN
ejpam-180	486	5	i	i	PROPN
ejpam-180	486	6	(	(	PUNCT
ejpam-180	486	7	t	t	PROPN
ejpam-180	486	8	)	)	PUNCT
ejpam-180	486	9	+	+	PROPN
ejpam-180	486	10	δi2b	δi2b	NOUN
ejpam-180	486	11	i	i	PRON
ejpam-180	486	12	(	(	PUNCT
ejpam-180	486	13	t)z	t)z	NOUN
ejpam-180	486	14	i	i	PRON
ejpam-180	486	15	(	(	PUNCT
ejpam-180	486	16	t	t	PROPN
ejpam-180	486	17	)	)	PUNCT
ejpam-180	486	18	=	=	SYM
ejpam-180	486	19	0	0	PUNCT
ejpam-180	486	20	(	(	PUNCT
ejpam-180	486	21	4.24	4.24	NUM
ejpam-180	486	22	)	)	PUNCT
ejpam-180	486	23	ηt	ηt	ADP
ejpam-180	486	24	λ̄	λ̄	NOUN
ejpam-180	486	25	=	=	SYM
ejpam-180	486	26	0	0	PUNCT
ejpam-180	486	27	(	(	PUNCT
ejpam-180	486	28	4.25	4.25	NUM
ejpam-180	486	29	)	)	PUNCT
ejpam-180	486	30	µ	µ	X
ejpam-180	486	31	(	(	PUNCT
ejpam-180	486	32	t	t	PROPN
ejpam-180	486	33	)	)	PUNCT
ejpam-180	486	34	t	t	PROPN
ejpam-180	486	35	ȳ	ȳ	PROPN
ejpam-180	486	36	(	(	PUNCT
ejpam-180	486	37	t	t	PROPN
ejpam-180	486	38	)	)	PUNCT
ejpam-180	486	39	=	=	SYM
ejpam-180	486	40	0	0	NUM
ejpam-180	486	41	,	,	PUNCT
ejpam-180	486	42	t	t	PROPN
ejpam-180	486	43	∈	∈	PROPN
ejpam-180	487	1	i	i	PRON
ejpam-180	487	2	(	(	PUNCT
ejpam-180	487	3	4.26	4.26	NUM
ejpam-180	487	4	)	)	PUNCT
ejpam-180	487	5	γ	γ	PROPN
ejpam-180	487	6	p	p	NOUN
ejpam-180	487	7	∑	∑	PROPN
ejpam-180	487	8	i=1	i=1	PROPN
ejpam-180	487	9	λi	λi	INTJ
ejpam-180	487	10	−	−	PROPN
ejpam-180	487	11	1	1	NUM
ejpam-180	487	12	!	!	PUNCT
ejpam-180	487	13	=	=	SYM
ejpam-180	487	14	0	0	PUNCT
ejpam-180	487	15	(	(	PUNCT
ejpam-180	487	16	4.27	4.27	NUM
ejpam-180	487	17	)	)	PUNCT
ejpam-180	487	18	i.	i.	NOUN
ejpam-180	487	19	husain	husain	PROPN
ejpam-180	487	20	,	,	PUNCT
ejpam-180	487	21	a.	a.	PROPN
ejpam-180	487	22	ahmed	ahmed	PROPN
ejpam-180	487	23	,	,	PUNCT
ejpam-180	487	24	and	and	CCONJ
ejpam-180	487	25	g.	g.	PROPN
ejpam-180	487	26	rumana	rumana	PROPN
ejpam-180	487	27	/	/	SYM
ejpam-180	487	28	eur	eur	PROPN
ejpam-180	487	29	.	.	PUNCT
ejpam-180	488	1	j.	j.	PROPN
ejpam-180	488	2	pure	pure	PROPN
ejpam-180	488	3	appl	appl	PROPN
ejpam-180	488	4	.	.	PROPN
ejpam-180	488	5	math	math	PROPN
ejpam-180	488	6	,	,	PUNCT
ejpam-180	488	7	2	2	NUM
ejpam-180	488	8	(	(	PUNCT
ejpam-180	488	9	2009	2009	NUM
ejpam-180	488	10	)	)	PUNCT
ejpam-180	488	11	,	,	PUNCT
ejpam-180	488	12	(	(	PUNCT
ejpam-180	488	13	372	372	NUM
ejpam-180	488	14	-	-	SYM
ejpam-180	488	15	400	400	NUM
ejpam-180	488	16	)	)	PUNCT
ejpam-180	488	17	387	387	NUM
ejpam-180	488	18	δi	δi	PROPN
ejpam-180	488	19	�	�	PROPN
ejpam-180	488	20	z	z	PROPN
ejpam-180	488	21	i	i	PROPN
ejpam-180	488	22	(	(	PUNCT
ejpam-180	488	23	t	t	PROPN
ejpam-180	488	24	)	)	PUNCT
ejpam-180	488	25	t	t	PROPN
ejpam-180	489	1	b	b	PROPN
ejpam-180	489	2	i	i	PROPN
ejpam-180	489	3	(	(	PUNCT
ejpam-180	489	4	t	t	PROPN
ejpam-180	489	5	)	)	PUNCT
ejpam-180	489	6	z	z	NOUN
ejpam-180	490	1	i	i	PRON
ejpam-180	490	2	(	(	PUNCT
ejpam-180	490	3	t	t	PROPN
ejpam-180	490	4	)	)	PUNCT
ejpam-180	490	5	�	�	PROPN
ejpam-180	490	6	=	=	SYM
ejpam-180	490	7	0	0	PROPN
ejpam-180	490	8	,	,	PUNCT
ejpam-180	490	9	t	t	PROPN
ejpam-180	490	10	∈	∈	PROPN
ejpam-180	491	1	i	i	PRON
ejpam-180	491	2	(	(	PUNCT
ejpam-180	491	3	4.28	4.28	NUM
ejpam-180	491	4	)	)	PUNCT
ejpam-180	491	5	�	�	PROPN
ejpam-180	491	6	α	α	PROPN
ejpam-180	491	7	,	,	PUNCT
ejpam-180	491	8	λ,µ	λ,µ	PROPN
ejpam-180	491	9	(	(	PUNCT
ejpam-180	491	10	t	t	PROPN
ejpam-180	491	11	)	)	PUNCT
ejpam-180	491	12	,	,	PUNCT
ejpam-180	491	13	η	η	PROPN
ejpam-180	491	14	,	,	PUNCT
ejpam-180	491	15	γ	γ	PROPN
ejpam-180	491	16	,	,	PUNCT
ejpam-180	491	17	δ	δ	PROPN
ejpam-180	491	18	,	,	PUNCT
ejpam-180	491	19	�	�	PROPN
ejpam-180	491	20	≧	≧	X
ejpam-180	491	21	0	0	NUM
ejpam-180	491	22	,	,	PUNCT
ejpam-180	491	23	t	t	PROPN
ejpam-180	491	24	∈	∈	PROPN
ejpam-180	492	1	i	i	PRON
ejpam-180	492	2	(	(	PUNCT
ejpam-180	492	3	4.29	4.29	NUM
ejpam-180	492	4	)	)	PUNCT
ejpam-180	492	5	�	�	PROPN
ejpam-180	492	6	α	α	PROPN
ejpam-180	492	7	,	,	PUNCT
ejpam-180	492	8	β	β	X
ejpam-180	492	9	(	(	PUNCT
ejpam-180	492	10	t	t	PROPN
ejpam-180	492	11	)	)	PUNCT
ejpam-180	492	12	,	,	PUNCT
ejpam-180	492	13	λ,µ	λ,µ	PROPN
ejpam-180	492	14	(	(	PUNCT
ejpam-180	492	15	t	t	PROPN
ejpam-180	492	16	)	)	PUNCT
ejpam-180	492	17	,	,	PUNCT
ejpam-180	492	18	η	η	PROPN
ejpam-180	492	19	,	,	PUNCT
ejpam-180	492	20	γ	γ	PROPN
ejpam-180	492	21	,	,	PUNCT
ejpam-180	492	22	δ	δ	PROPN
ejpam-180	492	23	,	,	PUNCT
ejpam-180	492	24	�	�	PROPN
ejpam-180	492	25	6=	6=	ADP
ejpam-180	492	26	0	0	NUM
ejpam-180	492	27	,	,	PUNCT
ejpam-180	492	28	t	t	PROPN
ejpam-180	492	29	∈	∈	PROPN
ejpam-180	492	30	i	i	PRON
ejpam-180	492	31	(	(	PUNCT
ejpam-180	492	32	4.30	4.30	NUM
ejpam-180	492	33	)	)	PUNCT
ejpam-180	492	34	since	since	SCONJ
ejpam-180	492	35	λ	λ	PROPN
ejpam-180	492	36	>	>	X
ejpam-180	492	37	0	0	NUM
ejpam-180	492	38	,	,	PUNCT
ejpam-180	492	39	(	(	PUNCT
ejpam-180	492	40	4.25	4.25	NUM
ejpam-180	492	41	)	)	PUNCT
ejpam-180	492	42	implies	imply	VERB
ejpam-180	492	43	η	η	PROPN
ejpam-180	492	44	=	=	PROPN
ejpam-180	492	45	0	0	PROPN
ejpam-180	492	46	.	.	PUNCT
ejpam-180	493	1	consequently	consequently	ADV
ejpam-180	493	2	(	(	PUNCT
ejpam-180	493	3	4.23	4.23	NUM
ejpam-180	493	4	)	)	PUNCT
ejpam-180	493	5	implies	imply	VERB
ejpam-180	493	6	�	�	PROPN
ejpam-180	494	1	f	f	PROPN
ejpam-180	494	2	i	i	NOUN
ejpam-180	494	3	x	x	X
ejpam-180	494	4	(	(	PUNCT
ejpam-180	494	5	t	t	NOUN
ejpam-180	494	6	,	,	PUNCT
ejpam-180	494	7	x	x	X
ejpam-180	494	8	,	,	PUNCT
ejpam-180	494	9	ẋ	ẋ	PROPN
ejpam-180	494	10	,	,	PUNCT
ejpam-180	494	11	ẍ	ẍ	X
ejpam-180	494	12	)	)	PUNCT
ejpam-180	495	1	+	+	CCONJ
ejpam-180	496	1	b	b	X
ejpam-180	496	2	i	i	PRON
ejpam-180	496	3	(	(	PUNCT
ejpam-180	496	4	t)z	t)z	NOUN
ejpam-180	496	5	i	i	PRON
ejpam-180	496	6	(	(	PUNCT
ejpam-180	496	7	t)−	t)−	PROPN
ejpam-180	497	1	d	d	X
ejpam-180	497	2	f	f	X
ejpam-180	498	1	i	i	PRON
ejpam-180	498	2	ẋ	ẋ	PROPN
ejpam-180	499	1	(	(	PUNCT
ejpam-180	499	2	t	t	PROPN
ejpam-180	499	3	,	,	PUNCT
ejpam-180	499	4	x	x	X
ejpam-180	499	5	,	,	PUNCT
ejpam-180	499	6	ẋ	ẋ	PROPN
ejpam-180	499	7	,	,	PUNCT
ejpam-180	499	8	ẍ	ẍ	X
ejpam-180	499	9	)	)	PUNCT
ejpam-180	500	1	+	+	CCONJ
ejpam-180	501	1	d2	d2	PROPN
ejpam-180	501	2	f	f	PROPN
ejpam-180	501	3	i	i	PRON
ejpam-180	501	4	ẍ	ẍ	PROPN
ejpam-180	502	1	(	(	PUNCT
ejpam-180	502	2	t	t	PROPN
ejpam-180	502	3	,	,	PUNCT
ejpam-180	502	4	x	x	X
ejpam-180	502	5	,	,	PUNCT
ejpam-180	502	6	ẋ	ẋ	PROPN
ejpam-180	502	7	,	,	PUNCT
ejpam-180	502	8	ẍ	ẍ	X
ejpam-180	502	9	)	)	PUNCT
ejpam-180	502	10	�	�	PROPN
ejpam-180	502	11	β	β	X
ejpam-180	502	12	(	(	PUNCT
ejpam-180	502	13	t	t	PROPN
ejpam-180	502	14	)	)	PUNCT
ejpam-180	502	15	=	=	SYM
ejpam-180	503	1	−γ=	−γ=	NOUN
ejpam-180	503	2	0	0	NUM
ejpam-180	503	3	from	from	ADP
ejpam-180	503	4	the	the	DET
ejpam-180	503	5	equality	equality	NOUN
ejpam-180	503	6	constraint	constraint	NOUN
ejpam-180	503	7	of	of	ADP
ejpam-180	503	8	(	(	PUNCT
ejpam-180	503	9	mwd	mwd	PROPN
ejpam-180	503	10	)	)	PUNCT
ejpam-180	503	11	,	,	PUNCT
ejpam-180	503	12	we	we	PRON
ejpam-180	503	13	have	have	VERB
ejpam-180	503	14	�	�	PROPN
ejpam-180	503	15	ȳ	ȳ	PROPN
ejpam-180	503	16	(	(	PUNCT
ejpam-180	503	17	t	t	PROPN
ejpam-180	503	18	)	)	PUNCT
ejpam-180	503	19	t	t	PROPN
ejpam-180	503	20	gx	gx	PROPN
ejpam-180	503	21	(	(	PUNCT
ejpam-180	503	22	t	t	PROPN
ejpam-180	503	23	,	,	PUNCT
ejpam-180	503	24	x	x	X
ejpam-180	503	25	,	,	PUNCT
ejpam-180	503	26	ẋ	ẋ	PROPN
ejpam-180	503	27	,	,	PUNCT
ejpam-180	503	28	ẍ)−	ẍ)−	PROPN
ejpam-180	504	1	d	d	X
ejpam-180	504	2	ȳ	ȳ	PROPN
ejpam-180	504	3	(	(	PUNCT
ejpam-180	504	4	t	t	PROPN
ejpam-180	504	5	)	)	PUNCT
ejpam-180	504	6	t	t	PROPN
ejpam-180	504	7	g	g	PROPN
ejpam-180	504	8	ẋ	ẋ	PROPN
ejpam-180	505	1	(	(	PUNCT
ejpam-180	505	2	t	t	PROPN
ejpam-180	505	3	,	,	PUNCT
ejpam-180	505	4	x	x	X
ejpam-180	505	5	,	,	PUNCT
ejpam-180	505	6	ẋ	ẋ	PROPN
ejpam-180	505	7	,	,	PUNCT
ejpam-180	505	8	ẍ	ẍ	X
ejpam-180	505	9	)	)	PUNCT
ejpam-180	506	1	+	+	CCONJ
ejpam-180	506	2	d2	d2	PROPN
ejpam-180	506	3	ȳ	ȳ	PROPN
ejpam-180	506	4	(	(	PUNCT
ejpam-180	506	5	t	t	PROPN
ejpam-180	506	6	)	)	PUNCT
ejpam-180	506	7	t	t	PROPN
ejpam-180	506	8	g	g	PROPN
ejpam-180	506	9	ẍ	ẍ	PROPN
ejpam-180	507	1	(	(	PUNCT
ejpam-180	507	2	t	t	PROPN
ejpam-180	507	3	,	,	PUNCT
ejpam-180	507	4	x	x	X
ejpam-180	507	5	,	,	PUNCT
ejpam-180	507	6	ẋ	ẋ	PROPN
ejpam-180	507	7	,	,	PUNCT
ejpam-180	507	8	ẍ	ẍ	X
ejpam-180	507	9	)	)	PUNCT
ejpam-180	507	10	�	�	PROPN
ejpam-180	508	1	=	=	PUNCT
ejpam-180	508	2	−	−	PROPN
ejpam-180	508	3	p	p	NOUN
ejpam-180	508	4	∑	∑	PUNCT
ejpam-180	508	5	i=1	i=1	PROPN
ejpam-180	508	6	λi	λi	PROPN
ejpam-180	508	7	�	�	PROPN
ejpam-180	508	8	f	f	PROPN
ejpam-180	509	1	i	i	NOUN
ejpam-180	509	2	x	x	X
ejpam-180	509	3	(	(	PUNCT
ejpam-180	509	4	t	t	NOUN
ejpam-180	509	5	,	,	PUNCT
ejpam-180	509	6	x	x	X
ejpam-180	509	7	,	,	PUNCT
ejpam-180	509	8	ẋ	ẋ	PROPN
ejpam-180	509	9	,	,	PUNCT
ejpam-180	509	10	ẍ	ẍ	X
ejpam-180	509	11	)	)	PUNCT
ejpam-180	510	1	+	+	CCONJ
ejpam-180	511	1	b	b	X
ejpam-180	511	2	i	i	PRON
ejpam-180	511	3	(	(	PUNCT
ejpam-180	511	4	t	t	PROPN
ejpam-180	511	5	)	)	PUNCT
ejpam-180	511	6	z̄	z̄	PROPN
ejpam-180	511	7	i	i	PRON
ejpam-180	511	8	(	(	PUNCT
ejpam-180	511	9	t)−	t)−	PROPN
ejpam-180	512	1	d	d	X
ejpam-180	512	2	f	f	X
ejpam-180	513	1	i	i	PRON
ejpam-180	513	2	ẋ	ẋ	PROPN
ejpam-180	514	1	(	(	PUNCT
ejpam-180	514	2	t	t	PROPN
ejpam-180	514	3	,	,	PUNCT
ejpam-180	514	4	x	x	X
ejpam-180	514	5	,	,	PUNCT
ejpam-180	514	6	ẋ	ẋ	PROPN
ejpam-180	514	7	,	,	PUNCT
ejpam-180	514	8	ẍ	ẍ	X
ejpam-180	514	9	)	)	PUNCT
ejpam-180	515	1	+	+	CCONJ
ejpam-180	516	1	d2	d2	PROPN
ejpam-180	516	2	f	f	PROPN
ejpam-180	516	3	i	i	PRON
ejpam-180	516	4	ẍ	ẍ	PROPN
ejpam-180	517	1	(	(	PUNCT
ejpam-180	517	2	t	t	PROPN
ejpam-180	517	3	,	,	PUNCT
ejpam-180	517	4	x	x	X
ejpam-180	517	5	,	,	PUNCT
ejpam-180	517	6	ẋ	ẋ	PROPN
ejpam-180	517	7	,	,	PUNCT
ejpam-180	517	8	ẍ	ẍ	X
ejpam-180	517	9	)	)	PUNCT
ejpam-180	517	10	�	�	PROPN
ejpam-180	517	11	this	this	PRON
ejpam-180	517	12	,	,	PUNCT
ejpam-180	517	13	in	in	ADP
ejpam-180	517	14	view	view	NOUN
ejpam-180	517	15	of	of	ADP
ejpam-180	517	16	(	(	PUNCT
ejpam-180	517	17	4.31	4.31	NUM
ejpam-180	517	18	)	)	PUNCT
ejpam-180	517	19	,	,	PUNCT
ejpam-180	517	20	implies	imply	VERB
ejpam-180	517	21	β	β	X
ejpam-180	517	22	(	(	PUNCT
ejpam-180	517	23	t	t	PROPN
ejpam-180	517	24	)	)	PUNCT
ejpam-180	517	25	t	t	PROPN
ejpam-180	517	26	�	�	PROPN
ejpam-180	517	27	ȳ	ȳ	PROPN
ejpam-180	517	28	(	(	PUNCT
ejpam-180	517	29	t	t	PROPN
ejpam-180	517	30	)	)	PUNCT
ejpam-180	517	31	t	t	PROPN
ejpam-180	517	32	gx	gx	PROPN
ejpam-180	517	33	(	(	PUNCT
ejpam-180	517	34	t	t	PROPN
ejpam-180	517	35	,	,	PUNCT
ejpam-180	517	36	x	x	X
ejpam-180	517	37	,	,	PUNCT
ejpam-180	517	38	ẋ	ẋ	PROPN
ejpam-180	517	39	,	,	PUNCT
ejpam-180	517	40	ẍ)−	ẍ)−	PROPN
ejpam-180	518	1	d	d	X
ejpam-180	518	2	ȳ	ȳ	PROPN
ejpam-180	518	3	(	(	PUNCT
ejpam-180	518	4	t	t	PROPN
ejpam-180	518	5	)	)	PUNCT
ejpam-180	518	6	t	t	PROPN
ejpam-180	518	7	g	g	PROPN
ejpam-180	518	8	ẋ	ẋ	PROPN
ejpam-180	519	1	(	(	PUNCT
ejpam-180	519	2	t	t	PROPN
ejpam-180	519	3	,	,	PUNCT
ejpam-180	519	4	x	x	X
ejpam-180	519	5	,	,	PUNCT
ejpam-180	519	6	ẋ	ẋ	PROPN
ejpam-180	519	7	,	,	PUNCT
ejpam-180	519	8	ẍ	ẍ	X
ejpam-180	519	9	)	)	PUNCT
ejpam-180	520	1	+	+	CCONJ
ejpam-180	520	2	d2	d2	PROPN
ejpam-180	520	3	ȳ	ȳ	PROPN
ejpam-180	520	4	(	(	PUNCT
ejpam-180	520	5	t	t	PROPN
ejpam-180	520	6	)	)	PUNCT
ejpam-180	520	7	t	t	PROPN
ejpam-180	520	8	g	g	PROPN
ejpam-180	520	9	ẍ	ẍ	PROPN
ejpam-180	521	1	(	(	PUNCT
ejpam-180	521	2	t	t	PROPN
ejpam-180	521	3	,	,	PUNCT
ejpam-180	521	4	x	x	X
ejpam-180	521	5	,	,	PUNCT
ejpam-180	521	6	ẋ	ẋ	PROPN
ejpam-180	521	7	,	,	PUNCT
ejpam-180	521	8	ẍ	ẍ	X
ejpam-180	521	9	)	)	PUNCT
ejpam-180	521	10	�	�	PROPN
ejpam-180	522	1	=	=	PUNCT
ejpam-180	522	2	−	−	PROPN
ejpam-180	522	3	p	p	X
ejpam-180	522	4	∑	∑	PUNCT
ejpam-180	522	5	i=1	i=1	PROPN
ejpam-180	522	6	λiβ	λiβ	ADJ
ejpam-180	522	7	(	(	PUNCT
ejpam-180	522	8	t	t	PROPN
ejpam-180	522	9	)	)	PUNCT
ejpam-180	522	10	t	t	PROPN
ejpam-180	522	11	�	�	PROPN
ejpam-180	523	1	f	f	PROPN
ejpam-180	523	2	i	i	NOUN
ejpam-180	523	3	x	x	X
ejpam-180	523	4	(	(	PUNCT
ejpam-180	523	5	t	t	NOUN
ejpam-180	523	6	,	,	PUNCT
ejpam-180	523	7	x	x	X
ejpam-180	523	8	,	,	PUNCT
ejpam-180	523	9	ẋ	ẋ	PROPN
ejpam-180	523	10	,	,	PUNCT
ejpam-180	523	11	ẍ	ẍ	X
ejpam-180	523	12	)	)	PUNCT
ejpam-180	524	1	+	+	CCONJ
ejpam-180	525	1	b	b	X
ejpam-180	525	2	i	i	PRON
ejpam-180	525	3	(	(	PUNCT
ejpam-180	525	4	t	t	PROPN
ejpam-180	525	5	)	)	PUNCT
ejpam-180	525	6	z̄	z̄	PROPN
ejpam-180	525	7	i	i	PRON
ejpam-180	525	8	(	(	PUNCT
ejpam-180	525	9	t)−	t)−	PROPN
ejpam-180	526	1	d	d	X
ejpam-180	526	2	f	f	X
ejpam-180	527	1	i	i	PRON
ejpam-180	527	2	ẋ	ẋ	PROPN
ejpam-180	528	1	(	(	PUNCT
ejpam-180	528	2	t	t	PROPN
ejpam-180	528	3	,	,	PUNCT
ejpam-180	528	4	x	x	X
ejpam-180	528	5	,	,	PUNCT
ejpam-180	528	6	ẋ	ẋ	PROPN
ejpam-180	528	7	,	,	PUNCT
ejpam-180	528	8	ẍ	ẍ	X
ejpam-180	528	9	)	)	PUNCT
ejpam-180	529	1	+	+	CCONJ
ejpam-180	530	1	d2	d2	PROPN
ejpam-180	530	2	f	f	PROPN
ejpam-180	530	3	i	i	PRON
ejpam-180	530	4	ẍ	ẍ	PROPN
ejpam-180	531	1	(	(	PUNCT
ejpam-180	531	2	t	t	PROPN
ejpam-180	531	3	,	,	PUNCT
ejpam-180	531	4	x	x	X
ejpam-180	531	5	,	,	PUNCT
ejpam-180	531	6	ẋ	ẋ	PROPN
ejpam-180	531	7	,	,	PUNCT
ejpam-180	531	8	ẍ	ẍ	PROPN
ejpam-180	531	9	)	)	PUNCT
ejpam-180	531	10	�	�	PROPN
ejpam-180	532	1	=	=	PUNCT
ejpam-180	532	2	−	−	PROPN
ejpam-180	532	3	p	p	NOUN
ejpam-180	532	4	∑	∑	PUNCT
ejpam-180	532	5	i=1	i=1	PROPN
ejpam-180	532	6	λi	λi	PROPN
ejpam-180	532	7	�	�	PROPN
ejpam-180	532	8	−γ	−γ	NOUN
ejpam-180	532	9	�	�	PROPN
ejpam-180	532	10	=	=	PUNCT
ejpam-180	532	11	γ	γ	X
ejpam-180	532	12	(	(	PUNCT
ejpam-180	532	13	4.31	4.31	NUM
ejpam-180	532	14	)	)	PUNCT
ejpam-180	532	15	postmultiplying	postmultiplying	NOUN
ejpam-180	532	16	(	(	PUNCT
ejpam-180	532	17	4.21	4.21	NUM
ejpam-180	532	18	)	)	PUNCT
ejpam-180	532	19	by	by	ADP
ejpam-180	532	20	β(t	β(t	PROPN
ejpam-180	532	21	)	)	PUNCT
ejpam-180	532	22	and	and	CCONJ
ejpam-180	532	23	then	then	ADV
ejpam-180	532	24	using	use	VERB
ejpam-180	532	25	(	(	PUNCT
ejpam-180	532	26	4.31	4.31	NUM
ejpam-180	532	27	)	)	PUNCT
ejpam-180	532	28	and	and	CCONJ
ejpam-180	532	29	(	(	PUNCT
ejpam-180	532	30	4.32	4.32	NUM
ejpam-180	532	31	)	)	PUNCT
ejpam-180	532	32	,	,	PUNCT
ejpam-180	532	33	we	we	PRON
ejpam-180	532	34	obtain	obtain	VERB
ejpam-180	532	35	�	�	PROPN
ejpam-180	532	36	β	β	X
ejpam-180	532	37	(	(	PUNCT
ejpam-180	532	38	t	t	PROPN
ejpam-180	532	39	)	)	PUNCT
ejpam-180	532	40	t	t	PROPN
ejpam-180	532	41	θx	θx	NUM
ejpam-180	532	42	−	−	PROPN
ejpam-180	532	43	dβ	dβ	PROPN
ejpam-180	532	44	(	(	PUNCT
ejpam-180	532	45	t	t	NOUN
ejpam-180	532	46	)	)	PUNCT
ejpam-180	532	47	t	t	PROPN
ejpam-180	532	48	θ	θ	PROPN
ejpam-180	532	49	ẋ	ẋ	PROPN
ejpam-180	533	1	+	+	PUNCT
ejpam-180	533	2	d2β	d2β	PROPN
ejpam-180	533	3	(	(	PUNCT
ejpam-180	533	4	t	t	PROPN
ejpam-180	533	5	)	)	PUNCT
ejpam-180	533	6	t	t	PROPN
ejpam-180	533	7	θ	θ	NOUN
ejpam-180	533	8	ẍ	ẍ	PUNCT
ejpam-180	534	1	=	=	SYM
ejpam-180	534	2	0	0	NUM
ejpam-180	534	3	�	�	PROPN
ejpam-180	534	4	β	β	X
ejpam-180	534	5	(	(	PUNCT
ejpam-180	534	6	t	t	PROPN
ejpam-180	534	7	)	)	PUNCT
ejpam-180	534	8	=	=	SYM
ejpam-180	534	9	0	0	NUM
ejpam-180	534	10	,	,	PUNCT
ejpam-180	534	11	t	t	PROPN
ejpam-180	534	12	∈	∈	PROPN
ejpam-180	535	1	i	i	PRON
ejpam-180	535	2	this	this	PRON
ejpam-180	535	3	,	,	PUNCT
ejpam-180	535	4	because	because	SCONJ
ejpam-180	535	5	of	of	ADP
ejpam-180	535	6	the	the	DET
ejpam-180	535	7	hypothesis	hypothesis	NOUN
ejpam-180	535	8	(	(	PUNCT
ejpam-180	535	9	h3	h3	NOUN
ejpam-180	535	10	)	)	PUNCT
ejpam-180	535	11	,	,	PUNCT
ejpam-180	535	12	gives	give	VERB
ejpam-180	535	13	β(t	β(t	PROPN
ejpam-180	535	14	)	)	PUNCT
ejpam-180	536	1	=	=	SYM
ejpam-180	536	2	0	0	NUM
ejpam-180	536	3	,	,	PUNCT
ejpam-180	536	4	t	t	PROPN
ejpam-180	536	5	∈	∈	PROPN
ejpam-180	536	6	i	i	PRON
ejpam-180	536	7	suppose	suppose	VERB
ejpam-180	536	8	α	α	X
ejpam-180	536	9	=	=	SYM
ejpam-180	536	10	0	0	NUM
ejpam-180	536	11	,	,	PUNCT
ejpam-180	536	12	then	then	ADV
ejpam-180	536	13	from	from	ADP
ejpam-180	536	14	(	(	PUNCT
ejpam-180	536	15	4.22	4.22	NUM
ejpam-180	536	16	)	)	PUNCT
ejpam-180	536	17	we	we	PRON
ejpam-180	536	18	have	have	VERB
ejpam-180	536	19	µ	µ	PRON
ejpam-180	536	20	j(t	j(t	PROPN
ejpam-180	536	21	)	)	PUNCT
ejpam-180	537	1	=	=	SYM
ejpam-180	537	2	0	0	NUM
ejpam-180	537	3	,	,	PUNCT
ejpam-180	537	4	j	j	PROPN
ejpam-180	537	5	=	=	SYM
ejpam-180	537	6	1	1	NUM
ejpam-180	537	7	,	,	PUNCT
ejpam-180	537	8	2	2	NUM
ejpam-180	537	9	,	,	PUNCT
ejpam-180	537	10	.	.	PUNCT
ejpam-180	537	11	.	.	PUNCT
ejpam-180	537	12	.	.	PUNCT
ejpam-180	538	1	,	,	PUNCT
ejpam-180	538	2	m	m	PROPN
ejpam-180	538	3	,	,	PUNCT
ejpam-180	538	4	and	and	CCONJ
ejpam-180	538	5	from	from	ADP
ejpam-180	538	6	(	(	PUNCT
ejpam-180	538	7	4.23	4.23	NUM
ejpam-180	538	8	)	)	PUNCT
ejpam-180	538	9	it	it	PRON
ejpam-180	538	10	follows	follow	VERB
ejpam-180	538	11	that	that	SCONJ
ejpam-180	538	12	γ=	γ=	PROPN
ejpam-180	538	13	0	0	NUM
ejpam-180	538	14	.	.	PUNCT
ejpam-180	538	15	i.	i.	PROPN
ejpam-180	538	16	husain	husain	PROPN
ejpam-180	538	17	,	,	PUNCT
ejpam-180	538	18	a.	a.	PROPN
ejpam-180	538	19	ahmed	ahmed	PROPN
ejpam-180	538	20	,	,	PUNCT
ejpam-180	538	21	and	and	CCONJ
ejpam-180	538	22	g.	g.	PROPN
ejpam-180	538	23	rumana	rumana	PROPN
ejpam-180	538	24	/	/	SYM
ejpam-180	538	25	eur	eur	PROPN
ejpam-180	538	26	.	.	PUNCT
ejpam-180	539	1	j.	j.	PROPN
ejpam-180	539	2	pure	pure	PROPN
ejpam-180	539	3	appl	appl	PROPN
ejpam-180	539	4	.	.	PROPN
ejpam-180	539	5	math	math	PROPN
ejpam-180	539	6	,	,	PUNCT
ejpam-180	539	7	2	2	NUM
ejpam-180	539	8	(	(	PUNCT
ejpam-180	539	9	2009	2009	NUM
ejpam-180	539	10	)	)	PUNCT
ejpam-180	539	11	,	,	PUNCT
ejpam-180	539	12	(	(	PUNCT
ejpam-180	539	13	372	372	NUM
ejpam-180	539	14	-	-	SYM
ejpam-180	539	15	400	400	NUM
ejpam-180	539	16	)	)	PUNCT
ejpam-180	539	17	388	388	NUM
ejpam-180	539	18	also	also	ADV
ejpam-180	539	19	from	from	ADP
ejpam-180	539	20	(	(	PUNCT
ejpam-180	539	21	4.24	4.24	NUM
ejpam-180	539	22	)	)	PUNCT
ejpam-180	539	23	we	we	PRON
ejpam-180	539	24	have	have	VERB
ejpam-180	539	25	δib	δib	NOUN
ejpam-180	539	26	i(t)z	i(t)z	PROPN
ejpam-180	539	27	i(t	i(t	PROPN
ejpam-180	539	28	)	)	PUNCT
ejpam-180	540	1	=	=	SYM
ejpam-180	540	2	0	0	NUM
ejpam-180	540	3	which	which	PRON
ejpam-180	540	4	together	together	ADV
ejpam-180	540	5	with	with	ADP
ejpam-180	540	6	(	(	PUNCT
ejpam-180	540	7	4.28	4.28	NUM
ejpam-180	540	8	)	)	PUNCT
ejpam-180	540	9	implies	imply	VERB
ejpam-180	540	10	δ	δ	X
ejpam-180	540	11	=	=	SYM
ejpam-180	540	12	0	0	PROPN
ejpam-180	540	13	.	.	PUNCT
ejpam-180	541	1	thus	thus	ADV
ejpam-180	541	2	,	,	PUNCT
ejpam-180	541	3	(	(	PUNCT
ejpam-180	541	4	α	α	X
ejpam-180	541	5	,	,	PUNCT
ejpam-180	541	6	β(t),λ,µ(t),η	β(t),λ,µ(t),η	NUM
ejpam-180	541	7	,	,	PUNCT
ejpam-180	541	8	γ	γ	PROPN
ejpam-180	541	9	,	,	PUNCT
ejpam-180	541	10	δ	δ	PROPN
ejpam-180	541	11	,	,	PUNCT
ejpam-180	541	12	)	)	PUNCT
ejpam-180	541	13	=	=	SYM
ejpam-180	541	14	0	0	NUM
ejpam-180	541	15	,	,	PUNCT
ejpam-180	541	16	which	which	PRON
ejpam-180	541	17	is	be	AUX
ejpam-180	541	18	a	a	DET
ejpam-180	541	19	contradiction	contradiction	NOUN
ejpam-180	541	20	to	to	ADP
ejpam-180	541	21	(	(	PUNCT
ejpam-180	541	22	4.30	4.30	NUM
ejpam-180	541	23	)	)	PUNCT
ejpam-180	541	24	.	.	PUNCT
ejpam-180	542	1	hence	hence	ADV
ejpam-180	542	2	α	α	X
ejpam-180	542	3	>	>	X
ejpam-180	542	4	0	0	NUM
ejpam-180	542	5	.	.	PUNCT
ejpam-180	543	1	from	from	ADP
ejpam-180	543	2	the	the	DET
ejpam-180	543	3	equation	equation	NOUN
ejpam-180	543	4	(	(	PUNCT
ejpam-180	543	5	4.22	4.22	NUM
ejpam-180	543	6	)	)	PUNCT
ejpam-180	543	7	,	,	PUNCT
ejpam-180	543	8	we	we	PRON
ejpam-180	543	9	have	have	VERB
ejpam-180	543	10	g	g	PROPN
ejpam-180	543	11	j	j	PROPN
ejpam-180	543	12	(	(	PUNCT
ejpam-180	543	13	t	t	PROPN
ejpam-180	543	14	,	,	PUNCT
ejpam-180	543	15	x	x	X
ejpam-180	543	16	,	,	PUNCT
ejpam-180	543	17	ẋ	ẋ	PROPN
ejpam-180	543	18	,	,	PUNCT
ejpam-180	543	19	ẍ	ẍ	X
ejpam-180	543	20	)	)	PUNCT
ejpam-180	544	1	=	=	SYM
ejpam-180	544	2	−	−	PROPN
ejpam-180	544	3	µ	µ	PROPN
ejpam-180	544	4	j	j	PROPN
ejpam-180	544	5	(	(	PUNCT
ejpam-180	544	6	t	t	PROPN
ejpam-180	544	7	)	)	PUNCT
ejpam-180	544	8	�	�	PROPN
ejpam-180	544	9	αt	αt	PROPN
ejpam-180	544	10	e	e	PROPN
ejpam-180	544	11	�	�	PROPN
ejpam-180	544	12	≦	≦	PROPN
ejpam-180	544	13	0	0	NUM
ejpam-180	544	14	,	,	PUNCT
ejpam-180	544	15	t	t	PROPN
ejpam-180	544	16	∈	∈	PROPN
ejpam-180	545	1	i	i	PRON
ejpam-180	545	2	which	which	PRON
ejpam-180	545	3	implies	imply	VERB
ejpam-180	545	4	g	g	PROPN
ejpam-180	545	5	j	j	PROPN
ejpam-180	545	6	(	(	PUNCT
ejpam-180	545	7	t	t	PROPN
ejpam-180	545	8	,	,	PUNCT
ejpam-180	545	9	x	x	X
ejpam-180	545	10	,	,	PUNCT
ejpam-180	545	11	ẋ	ẋ	PROPN
ejpam-180	545	12	,	,	PUNCT
ejpam-180	545	13	ẍ	ẍ	X
ejpam-180	545	14	)	)	PUNCT
ejpam-180	545	15	≦	≦	VERB
ejpam-180	545	16	0	0	NUM
ejpam-180	545	17	,	,	PUNCT
ejpam-180	545	18	t	t	PROPN
ejpam-180	545	19	∈	∈	PROPN
ejpam-180	546	1	i	i	PRON
ejpam-180	546	2	.	.	PUNCT
ejpam-180	547	1	therefore	therefore	ADV
ejpam-180	547	2	,	,	PUNCT
ejpam-180	547	3	x̄	x̄	PRON
ejpam-180	547	4	is	be	AUX
ejpam-180	547	5	feasible	feasible	ADJ
ejpam-180	547	6	for	for	ADP
ejpam-180	547	7	(	(	PUNCT
ejpam-180	547	8	vp	vp	PROPN
ejpam-180	547	9	)	)	PUNCT
ejpam-180	547	10	.	.	PUNCT
ejpam-180	548	1	multiplying	multiply	VERB
ejpam-180	548	2	(	(	PUNCT
ejpam-180	548	3	4.23	4.23	NUM
ejpam-180	548	4	)	)	PUNCT
ejpam-180	548	5	by	by	ADP
ejpam-180	548	6	y	y	PROPN
ejpam-180	548	7	j(t	j(t	PROPN
ejpam-180	548	8	)	)	PUNCT
ejpam-180	548	9	,	,	PUNCT
ejpam-180	548	10	and	and	CCONJ
ejpam-180	548	11	using	use	VERB
ejpam-180	548	12	(	(	PUNCT
ejpam-180	548	13	4.26	4.26	NUM
ejpam-180	548	14	)	)	PUNCT
ejpam-180	548	15	,	,	PUNCT
ejpam-180	548	16	we	we	PRON
ejpam-180	548	17	have	have	VERB
ejpam-180	548	18	y	y	PROPN
ejpam-180	548	19	j	j	PROPN
ejpam-180	548	20	(	(	PUNCT
ejpam-180	548	21	t	t	PROPN
ejpam-180	548	22	)	)	PUNCT
ejpam-180	548	23	g	g	PROPN
ejpam-180	548	24	j	j	PROPN
ejpam-180	548	25	(	(	PUNCT
ejpam-180	548	26	t	t	PROPN
ejpam-180	548	27	,	,	PUNCT
ejpam-180	548	28	x	x	X
ejpam-180	548	29	,	,	PUNCT
ejpam-180	548	30	ẋ	ẋ	PROPN
ejpam-180	548	31	,	,	PUNCT
ejpam-180	548	32	ẍ	ẍ	X
ejpam-180	548	33	)	)	PUNCT
ejpam-180	549	1	=	=	SYM
ejpam-180	549	2	0	0	NUM
ejpam-180	549	3	,	,	PUNCT
ejpam-180	549	4	t	t	PROPN
ejpam-180	549	5	∈	∈	PROPN
ejpam-180	550	1	i	i	PRON
ejpam-180	550	2	by	by	ADP
ejpam-180	550	3	generalized	generalize	VERB
ejpam-180	550	4	schwarz	schwarz	PROPN
ejpam-180	550	5	inequality	inequality	NOUN
ejpam-180	550	6	[	[	X
ejpam-180	550	7	15	15	NUM
ejpam-180	550	8	]	]	X
ejpam-180	550	9	�	�	PROPN
ejpam-180	550	10	x̄	x̄	PROPN
ejpam-180	550	11	(	(	PUNCT
ejpam-180	550	12	t	t	PROPN
ejpam-180	550	13	)	)	PUNCT
ejpam-180	550	14	t	t	PROPN
ejpam-180	550	15	b	b	PROPN
ejpam-180	550	16	i	i	PROPN
ejpam-180	550	17	(	(	PUNCT
ejpam-180	550	18	t	t	PROPN
ejpam-180	550	19	)	)	PUNCT
ejpam-180	550	20	z̄	z̄	PROPN
ejpam-180	551	1	i	i	PROPN
ejpam-180	551	2	(	(	PUNCT
ejpam-180	551	3	t	t	PROPN
ejpam-180	551	4	)	)	PUNCT
ejpam-180	551	5	�	�	PROPN
ejpam-180	551	6	≦	≦	PROPN
ejpam-180	551	7	�	�	PROPN
ejpam-180	551	8	x̄	x̄	PROPN
ejpam-180	551	9	(	(	PUNCT
ejpam-180	551	10	t	t	PROPN
ejpam-180	551	11	)	)	PUNCT
ejpam-180	551	12	t	t	PROPN
ejpam-180	551	13	b	b	PROPN
ejpam-180	551	14	i	i	PROPN
ejpam-180	551	15	(	(	PUNCT
ejpam-180	551	16	t	t	PROPN
ejpam-180	551	17	)	)	PUNCT
ejpam-180	551	18	x̄	x̄	NOUN
ejpam-180	551	19	(	(	PUNCT
ejpam-180	551	20	t	t	PROPN
ejpam-180	551	21	)	)	PUNCT
ejpam-180	551	22	�	�	PROPN
ejpam-180	551	23	1	1	NUM
ejpam-180	551	24	2	2	NUM
ejpam-180	551	25	�	�	PROPN
ejpam-180	551	26	z̄	z̄	PROPN
ejpam-180	551	27	i	i	NOUN
ejpam-180	551	28	(	(	PUNCT
ejpam-180	551	29	t)b	t)b	X
ejpam-180	551	30	i	i	PRON
ejpam-180	551	31	(	(	PUNCT
ejpam-180	551	32	t	t	PROPN
ejpam-180	551	33	)	)	PUNCT
ejpam-180	551	34	z̄	z̄	PROPN
ejpam-180	552	1	i	i	PROPN
ejpam-180	552	2	(	(	PUNCT
ejpam-180	552	3	t	t	PROPN
ejpam-180	552	4	)	)	PUNCT
ejpam-180	552	5	�	�	PROPN
ejpam-180	552	6	1	1	NUM
ejpam-180	552	7	2	2	NUM
ejpam-180	552	8	(	(	PUNCT
ejpam-180	552	9	4.32	4.32	NUM
ejpam-180	552	10	)	)	PUNCT
ejpam-180	552	11	now	now	ADV
ejpam-180	552	12	let	let	VERB
ejpam-180	552	13	2δi	2δi	NOUN
ejpam-180	552	14	αi	αi	NOUN
ejpam-180	553	1	=	=	SYM
ejpam-180	553	2	ξi	ξi	X
ejpam-180	553	3	.	.	PUNCT
ejpam-180	554	1	then	then	ADV
ejpam-180	554	2	ξi	ξi	VERB
ejpam-180	554	3	≧	≧	NOUN
ejpam-180	554	4	0	0	PUNCT
ejpam-180	555	1	and	and	CCONJ
ejpam-180	555	2	from	from	ADP
ejpam-180	555	3	(	(	PUNCT
ejpam-180	555	4	4.24	4.24	NUM
ejpam-180	555	5	)	)	PUNCT
ejpam-180	555	6	,	,	PUNCT
ejpam-180	555	7	we	we	PRON
ejpam-180	555	8	have	have	VERB
ejpam-180	555	9	b	b	NUM
ejpam-180	555	10	i	i	PROPN
ejpam-180	555	11	(	(	PUNCT
ejpam-180	555	12	t	t	PROPN
ejpam-180	555	13	)	)	PUNCT
ejpam-180	555	14	x	x	X
ejpam-180	555	15	(	(	PUNCT
ejpam-180	555	16	t	t	NOUN
ejpam-180	555	17	)	)	PUNCT
ejpam-180	556	1	=	=	SYM
ejpam-180	556	2	ξi2b	ξi2b	NOUN
ejpam-180	556	3	i	i	NOUN
ejpam-180	556	4	(	(	PUNCT
ejpam-180	556	5	t)z	t)z	NOUN
ejpam-180	556	6	i	i	PRON
ejpam-180	556	7	(	(	PUNCT
ejpam-180	556	8	t	t	PROPN
ejpam-180	556	9	)	)	PUNCT
ejpam-180	556	10	,	,	PUNCT
ejpam-180	556	11	i	i	PRON
ejpam-180	556	12	=	=	NOUN
ejpam-180	556	13	1	1	NUM
ejpam-180	556	14	,	,	PUNCT
ejpam-180	556	15	2	2	NUM
ejpam-180	556	16	,	,	PUNCT
ejpam-180	556	17	.	.	PUNCT
ejpam-180	556	18	.	.	PUNCT
ejpam-180	556	19	.	.	PUNCT
ejpam-180	557	1	,	,	PUNCT
ejpam-180	557	2	p	p	NOUN
ejpam-180	557	3	this	this	PRON
ejpam-180	557	4	is	be	AUX
ejpam-180	557	5	the	the	DET
ejpam-180	557	6	condition	condition	NOUN
ejpam-180	557	7	for	for	ADP
ejpam-180	557	8	the	the	DET
ejpam-180	557	9	equality	equality	NOUN
ejpam-180	557	10	in	in	ADP
ejpam-180	557	11	(	(	PUNCT
ejpam-180	557	12	4.33	4.33	NUM
ejpam-180	557	13	)	)	PUNCT
ejpam-180	557	14	.	.	PUNCT
ejpam-180	558	1	therefore	therefore	ADV
ejpam-180	558	2	,	,	PUNCT
ejpam-180	558	3	we	we	PRON
ejpam-180	558	4	have	have	VERB
ejpam-180	558	5	�	�	PROPN
ejpam-180	558	6	x̄	x̄	PROPN
ejpam-180	558	7	(	(	PUNCT
ejpam-180	558	8	t	t	PROPN
ejpam-180	558	9	)	)	PUNCT
ejpam-180	558	10	t	t	PROPN
ejpam-180	558	11	b	b	PROPN
ejpam-180	558	12	i	i	PRON
ejpam-180	558	13	(	(	PUNCT
ejpam-180	558	14	t)z	t)z	NOUN
ejpam-180	558	15	i	i	PRON
ejpam-180	558	16	(	(	PUNCT
ejpam-180	558	17	t	t	PROPN
ejpam-180	558	18	)	)	PUNCT
ejpam-180	558	19	�	�	PROPN
ejpam-180	558	20	=	=	SYM
ejpam-180	558	21	�	�	PROPN
ejpam-180	558	22	x	x	SYM
ejpam-180	558	23	(	(	PUNCT
ejpam-180	558	24	t	t	PROPN
ejpam-180	558	25	)	)	PUNCT
ejpam-180	558	26	t	t	PROPN
ejpam-180	558	27	b	b	PROPN
ejpam-180	558	28	i	i	PROPN
ejpam-180	558	29	(	(	PUNCT
ejpam-180	558	30	t	t	PROPN
ejpam-180	558	31	)	)	PUNCT
ejpam-180	558	32	x̄	x̄	NOUN
ejpam-180	558	33	(	(	PUNCT
ejpam-180	558	34	t	t	PROPN
ejpam-180	558	35	)	)	PUNCT
ejpam-180	558	36	�	�	PROPN
ejpam-180	558	37	1	1	NUM
ejpam-180	558	38	2	2	NUM
ejpam-180	558	39	�	�	PROPN
ejpam-180	558	40	z	z	NOUN
ejpam-180	558	41	i	i	NOUN
ejpam-180	558	42	(	(	PUNCT
ejpam-180	558	43	t)b	t)b	X
ejpam-180	559	1	i	i	PRON
ejpam-180	559	2	(	(	PUNCT
ejpam-180	559	3	t	t	PROPN
ejpam-180	559	4	)	)	PUNCT
ejpam-180	559	5	z	z	NOUN
ejpam-180	560	1	i	i	PRON
ejpam-180	560	2	(	(	PUNCT
ejpam-180	560	3	t	t	PROPN
ejpam-180	560	4	)	)	PUNCT
ejpam-180	560	5	�	�	PROPN
ejpam-180	560	6	1	1	NUM
ejpam-180	560	7	2	2	NUM
ejpam-180	560	8	from	from	ADP
ejpam-180	560	9	(	(	PUNCT
ejpam-180	560	10	4.28	4.28	NUM
ejpam-180	560	11	)	)	PUNCT
ejpam-180	560	12	,	,	PUNCT
ejpam-180	560	13	either	either	CCONJ
ejpam-180	560	14	δi	δi	ADP
ejpam-180	560	15	=	=	SYM
ejpam-180	560	16	0	0	NUM
ejpam-180	560	17	or	or	CCONJ
ejpam-180	560	18	z	z	NOUN
ejpam-180	560	19	i	i	PRON
ejpam-180	560	20	(	(	PUNCT
ejpam-180	560	21	t	t	PROPN
ejpam-180	560	22	)	)	PUNCT
ejpam-180	560	23	t	t	PROPN
ejpam-180	560	24	b	b	PROPN
ejpam-180	560	25	i	i	PRON
ejpam-180	560	26	(	(	PUNCT
ejpam-180	560	27	t)z	t)z	NOUN
ejpam-180	560	28	i	i	PRON
ejpam-180	560	29	(	(	PUNCT
ejpam-180	560	30	t	t	PROPN
ejpam-180	560	31	)	)	PUNCT
ejpam-180	560	32	=	=	SYM
ejpam-180	560	33	1	1	NUM
ejpam-180	560	34	and	and	CCONJ
ejpam-180	560	35	hence	hence	ADV
ejpam-180	560	36	b	b	X
ejpam-180	560	37	i	i	PROPN
ejpam-180	560	38	(	(	PUNCT
ejpam-180	560	39	t	t	PROPN
ejpam-180	560	40	)	)	PUNCT
ejpam-180	560	41	x̄	x̄	NOUN
ejpam-180	560	42	(	(	PUNCT
ejpam-180	560	43	t	t	PROPN
ejpam-180	560	44	)	)	PUNCT
ejpam-180	560	45	=	=	SYM
ejpam-180	560	46	0	0	X
ejpam-180	560	47	.	.	PUNCT
ejpam-180	561	1	therefore	therefore	ADV
ejpam-180	561	2	,	,	PUNCT
ejpam-180	561	3	in	in	ADP
ejpam-180	561	4	either	either	DET
ejpam-180	561	5	case	case	NOUN
ejpam-180	561	6	�	�	PROPN
ejpam-180	561	7	x	x	SYM
ejpam-180	561	8	(	(	PUNCT
ejpam-180	561	9	t	t	PROPN
ejpam-180	561	10	)	)	PUNCT
ejpam-180	561	11	t	t	PROPN
ejpam-180	561	12	b	b	PROPN
ejpam-180	561	13	i	i	PROPN
ejpam-180	561	14	(	(	PUNCT
ejpam-180	561	15	t	t	PROPN
ejpam-180	561	16	)	)	PUNCT
ejpam-180	561	17	z	z	NOUN
ejpam-180	562	1	i	i	PRON
ejpam-180	562	2	(	(	PUNCT
ejpam-180	562	3	t	t	PROPN
ejpam-180	562	4	)	)	PUNCT
ejpam-180	562	5	�	�	PROPN
ejpam-180	562	6	=	=	SYM
ejpam-180	562	7	�	�	PROPN
ejpam-180	562	8	x	x	SYM
ejpam-180	562	9	(	(	PUNCT
ejpam-180	562	10	t	t	PROPN
ejpam-180	562	11	)	)	PUNCT
ejpam-180	562	12	t	t	PROPN
ejpam-180	562	13	b	b	PROPN
ejpam-180	562	14	i	i	PROPN
ejpam-180	562	15	(	(	PUNCT
ejpam-180	562	16	t	t	PROPN
ejpam-180	562	17	)	)	PUNCT
ejpam-180	562	18	z	z	NOUN
ejpam-180	563	1	i	i	PRON
ejpam-180	563	2	(	(	PUNCT
ejpam-180	563	3	t	t	PROPN
ejpam-180	563	4	)	)	PUNCT
ejpam-180	563	5	�	�	PROPN
ejpam-180	563	6	1	1	NUM
ejpam-180	563	7	2	2	NUM
ejpam-180	563	8	,	,	PUNCT
ejpam-180	563	9	i	i	PRON
ejpam-180	563	10	=	=	NOUN
ejpam-180	563	11	1	1	NUM
ejpam-180	563	12	,	,	PUNCT
ejpam-180	563	13	2	2	NUM
ejpam-180	563	14	,	,	PUNCT
ejpam-180	563	15	.	.	PUNCT
ejpam-180	563	16	.	.	PUNCT
ejpam-180	563	17	.	.	PUNCT
ejpam-180	564	1	,	,	PUNCT
ejpam-180	565	1	p.	p.	NOUN
ejpam-180	565	2	hence	hence	ADV
ejpam-180	565	3	∫	∫	PROPN
ejpam-180	566	1	i	i	PRON
ejpam-180	566	2	�	�	PROPN
ejpam-180	567	1	f	f	VERB
ejpam-180	567	2	i	i	PRON
ejpam-180	567	3	�	�	PROPN
ejpam-180	567	4	t	t	PROPN
ejpam-180	567	5	,	,	PUNCT
ejpam-180	567	6	x̄	x̄	PROPN
ejpam-180	567	7	,	,	PUNCT
ejpam-180	567	8	˙̄x	˙̄x	PUNCT
ejpam-180	567	9	,	,	PUNCT
ejpam-180	567	10	¨̄x	¨̄x	PRON
ejpam-180	567	11	�	�	PROPN
ejpam-180	567	12	d	d	PROPN
ejpam-180	567	13	t	t	PROPN
ejpam-180	567	14	+	+	CCONJ
ejpam-180	567	15	�	�	PROPN
ejpam-180	567	16	x	x	SYM
ejpam-180	567	17	(	(	PUNCT
ejpam-180	567	18	t	t	PROPN
ejpam-180	567	19	)	)	PUNCT
ejpam-180	567	20	t	t	PROPN
ejpam-180	568	1	b	b	PROPN
ejpam-180	568	2	i	i	PRON
ejpam-180	568	3	(	(	PUNCT
ejpam-180	568	4	t)z	t)z	NOUN
ejpam-180	568	5	i	i	PRON
ejpam-180	568	6	(	(	PUNCT
ejpam-180	568	7	t	t	PROPN
ejpam-180	568	8	)	)	PUNCT
ejpam-180	568	9	�	�	PROPN
ejpam-180	568	10	1	1	NUM
ejpam-180	568	11	2	2	NUM
ejpam-180	568	12	+	+	CCONJ
ejpam-180	568	13	y	y	PROPN
ejpam-180	568	14	j	j	PROPN
ejpam-180	568	15	(	(	PUNCT
ejpam-180	568	16	t	t	PROPN
ejpam-180	568	17	)	)	PUNCT
ejpam-180	568	18	g	g	PROPN
ejpam-180	568	19	j	j	PROPN
ejpam-180	568	20	�	�	PROPN
ejpam-180	568	21	t	t	PROPN
ejpam-180	568	22	,	,	PUNCT
ejpam-180	568	23	x̄	x̄	PROPN
ejpam-180	568	24	,	,	PUNCT
ejpam-180	568	25	˙̄x	˙̄x	PUNCT
ejpam-180	568	26	,	,	PUNCT
ejpam-180	568	27	¨̄x	¨̄x	VERB
ejpam-180	568	28	�	�	PROPN
ejpam-180	568	29	�	�	PROPN
ejpam-180	568	30	d	d	PROPN
ejpam-180	568	31	t	t	PROPN
ejpam-180	569	1	=	=	SYM
ejpam-180	570	1	∫	∫	PROPN
ejpam-180	571	1	i	i	INTJ
ejpam-180	571	2	�	�	PROPN
ejpam-180	572	1	f	f	VERB
ejpam-180	573	1	i	i	PRON
ejpam-180	573	2	�	�	PROPN
ejpam-180	573	3	t	t	PROPN
ejpam-180	573	4	,	,	PUNCT
ejpam-180	573	5	x̄	x̄	NOUN
ejpam-180	573	6	,	,	PUNCT
ejpam-180	573	7	˙̄x	˙̄x	PUNCT
ejpam-180	573	8	,	,	PUNCT
ejpam-180	573	9	¨̄x	¨̄x	PRON
ejpam-180	573	10	�	�	PROPN
ejpam-180	573	11	d	d	PROPN
ejpam-180	573	12	t	t	PROPN
ejpam-180	573	13	+	+	CCONJ
ejpam-180	573	14	�	�	PROPN
ejpam-180	573	15	x	x	SYM
ejpam-180	573	16	(	(	PUNCT
ejpam-180	573	17	t	t	PROPN
ejpam-180	573	18	)	)	PUNCT
ejpam-180	573	19	t	t	PROPN
ejpam-180	574	1	b	b	PROPN
ejpam-180	574	2	i	i	PRON
ejpam-180	574	3	(	(	PUNCT
ejpam-180	574	4	t)z	t)z	NOUN
ejpam-180	574	5	i	i	PRON
ejpam-180	574	6	(	(	PUNCT
ejpam-180	574	7	t	t	PROPN
ejpam-180	574	8	)	)	PUNCT
ejpam-180	574	9	�	�	PROPN
ejpam-180	574	10	1	1	NUM
ejpam-180	574	11	2	2	NUM
ejpam-180	574	12	�	�	PROPN
ejpam-180	574	13	d	d	PROPN
ejpam-180	574	14	t	t	PROPN
ejpam-180	574	15	,	,	PUNCT
ejpam-180	574	16	i	i	PRON
ejpam-180	574	17	=	=	NOUN
ejpam-180	574	18	1	1	NUM
ejpam-180	574	19	,	,	PUNCT
ejpam-180	574	20	2	2	NUM
ejpam-180	574	21	,	,	PUNCT
ejpam-180	574	22	.	.	PUNCT
ejpam-180	574	23	.	.	PUNCT
ejpam-180	575	1	.	.	PUNCT
ejpam-180	576	1	,	,	PUNCT
ejpam-180	576	2	p	p	X
ejpam-180	576	3	the	the	DET
ejpam-180	576	4	efficiency	efficiency	NOUN
ejpam-180	576	5	of	of	ADP
ejpam-180	576	6	x̄	x̄	PROPN
ejpam-180	576	7	for	for	ADP
ejpam-180	576	8	(	(	PUNCT
ejpam-180	576	9	vp	vp	NOUN
ejpam-180	576	10	)	)	PUNCT
ejpam-180	576	11	is	be	AUX
ejpam-180	576	12	an	an	DET
ejpam-180	576	13	immediate	immediate	ADJ
ejpam-180	576	14	consequence	consequence	NOUN
ejpam-180	576	15	of	of	ADP
ejpam-180	576	16	the	the	DET
ejpam-180	576	17	application	application	NOUN
ejpam-180	576	18	of	of	ADP
ejpam-180	576	19	theorem	theorem	NOUN
ejpam-180	576	20	4.1	4.1	NUM
ejpam-180	576	21	.	.	PUNCT
ejpam-180	577	1	remarks	remark	NOUN
ejpam-180	577	2	:	:	PUNCT
ejpam-180	577	3	theorem	theorem	VERB
ejpam-180	577	4	4.3	4.3	NUM
ejpam-180	577	5	serves	serve	NOUN
ejpam-180	577	6	as	as	ADP
ejpam-180	577	7	a	a	DET
ejpam-180	577	8	correction	correction	NOUN
ejpam-180	577	9	to	to	PART
ejpam-180	577	10	theorem	theorem	VERB
ejpam-180	577	11	5	5	NUM
ejpam-180	577	12	of	of	ADP
ejpam-180	577	13	kim	kim	PROPN
ejpam-180	577	14	and	and	CCONJ
ejpam-180	577	15	kim	kim	PROPN
ejpam-180	578	1	[	[	X
ejpam-180	578	2	9	9	NUM
ejpam-180	578	3	]	]	PUNCT
ejpam-180	578	4	as	as	ADP
ejpam-180	578	5	its	its	PRON
ejpam-180	578	6	hypothesis	hypothesis	NOUN
ejpam-180	578	7	(	(	PUNCT
ejpam-180	578	8	iii	iii	NOUN
ejpam-180	578	9	)	)	PUNCT
ejpam-180	578	10	is	be	AUX
ejpam-180	578	11	not	not	PART
ejpam-180	578	12	required	require	VERB
ejpam-180	578	13	to	to	PART
ejpam-180	578	14	establish	establish	VERB
ejpam-180	578	15	it	it	PRON
ejpam-180	578	16	.	.	PUNCT
ejpam-180	579	1	i.	i.	PROPN
ejpam-180	579	2	husain	husain	PROPN
ejpam-180	579	3	,	,	PUNCT
ejpam-180	579	4	a.	a.	PROPN
ejpam-180	579	5	ahmed	ahmed	PROPN
ejpam-180	579	6	,	,	PUNCT
ejpam-180	579	7	and	and	CCONJ
ejpam-180	579	8	g.	g.	PROPN
ejpam-180	579	9	rumana	rumana	PROPN
ejpam-180	579	10	/	/	SYM
ejpam-180	579	11	eur	eur	PROPN
ejpam-180	579	12	.	.	PUNCT
ejpam-180	580	1	j.	j.	PROPN
ejpam-180	580	2	pure	pure	PROPN
ejpam-180	580	3	appl	appl	PROPN
ejpam-180	580	4	.	.	PROPN
ejpam-180	580	5	math	math	PROPN
ejpam-180	580	6	,	,	PUNCT
ejpam-180	580	7	2	2	NUM
ejpam-180	580	8	(	(	PUNCT
ejpam-180	580	9	2009	2009	NUM
ejpam-180	580	10	)	)	PUNCT
ejpam-180	580	11	,	,	PUNCT
ejpam-180	580	12	(	(	PUNCT
ejpam-180	580	13	372	372	NUM
ejpam-180	580	14	-	-	SYM
ejpam-180	580	15	400	400	NUM
ejpam-180	580	16	)	)	PUNCT
ejpam-180	580	17	389	389	NUM
ejpam-180	580	18	5	5	NUM
ejpam-180	580	19	.	.	PUNCT
ejpam-180	580	20	mond	mond	PROPN
ejpam-180	580	21	-	-	PUNCT
ejpam-180	580	22	weir	weir	PROPN
ejpam-180	580	23	type	type	NOUN
ejpam-180	580	24	duality	duality	NOUN
ejpam-180	580	25	in	in	ADP
ejpam-180	580	26	this	this	DET
ejpam-180	580	27	section	section	NOUN
ejpam-180	580	28	,	,	PUNCT
ejpam-180	580	29	we	we	PRON
ejpam-180	580	30	establish	establish	VERB
ejpam-180	580	31	various	various	ADJ
ejpam-180	580	32	duality	duality	NOUN
ejpam-180	580	33	theorems	theorem	NOUN
ejpam-180	580	34	for	for	ADP
ejpam-180	580	35	the	the	DET
ejpam-180	580	36	mond	mond	PROPN
ejpam-180	580	37	-	-	PUNCT
ejpam-180	580	38	weir	weir	PROPN
ejpam-180	580	39	type	type	NOUN
ejpam-180	580	40	vector	vector	NOUN
ejpam-180	580	41	dual	dual	ADJ
ejpam-180	580	42	.	.	PUNCT
ejpam-180	581	1	(	(	PUNCT
ejpam-180	581	2	m	m	NOUN
ejpam-180	581	3	-	-	PUNCT
ejpam-180	581	4	wvd	wvd	NOUN
ejpam-180	581	5	)	)	PUNCT
ejpam-180	581	6	:	:	PUNCT
ejpam-180	581	7	maximize	maximize	VERB
ejpam-180	581	8	�	�	PROPN
ejpam-180	581	9	∫	∫	PROPN
ejpam-180	581	10	i	i	PROPN
ejpam-180	581	11	�	�	PROPN
ejpam-180	582	1	f	f	PROPN
ejpam-180	582	2	1	1	NUM
ejpam-180	582	3	(	(	PUNCT
ejpam-180	582	4	t	t	PROPN
ejpam-180	582	5	,	,	PUNCT
ejpam-180	582	6	u	u	NOUN
ejpam-180	582	7	,	,	PUNCT
ejpam-180	582	8	u̇	u̇	PROPN
ejpam-180	582	9	,	,	PUNCT
ejpam-180	582	10	ü	ü	PRON
ejpam-180	582	11	)	)	PUNCT
ejpam-180	583	1	+	+	NUM
ejpam-180	583	2	u	u	SYM
ejpam-180	583	3	(	(	PUNCT
ejpam-180	583	4	t	t	PROPN
ejpam-180	583	5	)	)	PUNCT
ejpam-180	583	6	t	t	PROPN
ejpam-180	583	7	b1	b1	PROPN
ejpam-180	583	8	(	(	PUNCT
ejpam-180	583	9	t	t	NOUN
ejpam-180	583	10	)	)	PUNCT
ejpam-180	583	11	z1	z1	PROPN
ejpam-180	583	12	(	(	PUNCT
ejpam-180	583	13	t	t	PROPN
ejpam-180	583	14	)	)	PUNCT
ejpam-180	583	15	�	�	PROPN
ejpam-180	583	16	d	d	PROPN
ejpam-180	583	17	t	t	PROPN
ejpam-180	583	18	,	,	PUNCT
ejpam-180	583	19	.	.	PUNCT
ejpam-180	583	20	.	.	PUNCT
ejpam-180	583	21	.	.	PUNCT
ejpam-180	584	1	,	,	PUNCT
ejpam-180	584	2	∫	∫	PROPN
ejpam-180	585	1	i	i	PRON
ejpam-180	585	2	�	�	PROPN
ejpam-180	586	1	f	f	PROPN
ejpam-180	586	2	p(t	p(t	PROPN
ejpam-180	586	3	,	,	PUNCT
ejpam-180	586	4	u	u	NOUN
ejpam-180	586	5	,	,	PUNCT
ejpam-180	586	6	u̇	u̇	PROPN
ejpam-180	586	7	,	,	PUNCT
ejpam-180	586	8	ü	ü	PRON
ejpam-180	586	9	)	)	PUNCT
ejpam-180	587	1	+	+	CCONJ
ejpam-180	587	2	u(t)t	u(t)t	PROPN
ejpam-180	587	3	bp(t)zp(t	bp(t)zp(t	NOUN
ejpam-180	587	4	)	)	PUNCT
ejpam-180	587	5	�	�	PROPN
ejpam-180	587	6	d	d	PROPN
ejpam-180	587	7	t	t	PROPN
ejpam-180	587	8	�	�	PROPN
ejpam-180	587	9	subject	subject	ADJ
ejpam-180	587	10	to	to	ADP
ejpam-180	587	11	u	u	NOUN
ejpam-180	587	12	(	(	PUNCT
ejpam-180	587	13	a	a	NOUN
ejpam-180	587	14	)	)	PUNCT
ejpam-180	587	15	=	=	SYM
ejpam-180	587	16	0	0	PUNCT
ejpam-180	588	1	=	=	SYM
ejpam-180	588	2	u	u	NOUN
ejpam-180	588	3	(	(	PUNCT
ejpam-180	588	4	b	b	NOUN
ejpam-180	588	5	)	)	PUNCT
ejpam-180	588	6	(	(	PUNCT
ejpam-180	588	7	5.1	5.1	NUM
ejpam-180	588	8	)	)	PUNCT
ejpam-180	588	9	u̇	u̇	NOUN
ejpam-180	588	10	(	(	PUNCT
ejpam-180	588	11	a	a	X
ejpam-180	588	12	)	)	PUNCT
ejpam-180	588	13	=	=	SYM
ejpam-180	588	14	0	0	PUNCT
ejpam-180	588	15	=	=	SYM
ejpam-180	588	16	u̇	u̇	PROPN
ejpam-180	588	17	(	(	PUNCT
ejpam-180	588	18	b	b	NOUN
ejpam-180	588	19	)	)	PUNCT
ejpam-180	588	20	(	(	PUNCT
ejpam-180	588	21	5.2	5.2	NUM
ejpam-180	588	22	)	)	PUNCT
ejpam-180	588	23	p	p	NOUN
ejpam-180	588	24	∑	∑	PUNCT
ejpam-180	588	25	i=1	i=1	PROPN
ejpam-180	588	26	λi	λi	PROPN
ejpam-180	588	27	�	�	PROPN
ejpam-180	589	1	f	f	PROPN
ejpam-180	590	1	i	i	NOUN
ejpam-180	590	2	x	x	X
ejpam-180	590	3	(	(	PUNCT
ejpam-180	590	4	t	t	PROPN
ejpam-180	590	5	,	,	PUNCT
ejpam-180	590	6	u	u	NOUN
ejpam-180	590	7	,	,	PUNCT
ejpam-180	590	8	u̇	u̇	PROPN
ejpam-180	590	9	,	,	PUNCT
ejpam-180	590	10	ü	ü	NUM
ejpam-180	590	11	)	)	PUNCT
ejpam-180	591	1	d	d	NOUN
ejpam-180	591	2	t	t	PROPN
ejpam-180	591	3	+	+	CCONJ
ejpam-180	591	4	b	b	NOUN
ejpam-180	592	1	i	i	PRON
ejpam-180	592	2	(	(	PUNCT
ejpam-180	592	3	t)z	t)z	NOUN
ejpam-180	592	4	i	i	PRON
ejpam-180	592	5	(	(	PUNCT
ejpam-180	592	6	t	t	PROPN
ejpam-180	592	7	)	)	PUNCT
ejpam-180	593	1	+	+	CCONJ
ejpam-180	593	2	y	y	PROPN
ejpam-180	593	3	(	(	PUNCT
ejpam-180	593	4	t	t	PROPN
ejpam-180	593	5	)	)	PUNCT
ejpam-180	593	6	t	t	PROPN
ejpam-180	593	7	gx	gx	PROPN
ejpam-180	593	8	(	(	PUNCT
ejpam-180	593	9	t	t	PROPN
ejpam-180	593	10	,	,	PUNCT
ejpam-180	593	11	u	u	NOUN
ejpam-180	593	12	,	,	PUNCT
ejpam-180	593	13	u̇	u̇	PROPN
ejpam-180	593	14	,	,	PUNCT
ejpam-180	593	15	ü	ü	NUM
ejpam-180	593	16	)	)	PUNCT
ejpam-180	593	17	�	�	PROPN
ejpam-180	593	18	−d	−d	PROPN
ejpam-180	593	19	�	�	PROPN
ejpam-180	593	20	λt	λt	ADP
ejpam-180	593	21	f	f	PROPN
ejpam-180	593	22	ẋ	ẋ	PROPN
ejpam-180	594	1	+	+	CCONJ
ejpam-180	594	2	y	y	PROPN
ejpam-180	594	3	(	(	PUNCT
ejpam-180	594	4	t	t	PROPN
ejpam-180	594	5	)	)	PUNCT
ejpam-180	594	6	t	t	PROPN
ejpam-180	594	7	g	g	PROPN
ejpam-180	594	8	ẋ	ẋ	PROPN
ejpam-180	594	9	�	�	PROPN
ejpam-180	594	10	+	+	CCONJ
ejpam-180	594	11	d2	d2	PROPN
ejpam-180	594	12	�	�	PROPN
ejpam-180	594	13	λt	λt	ADP
ejpam-180	594	14	f	f	PROPN
ejpam-180	594	15	ẍ	ẍ	PUNCT
ejpam-180	595	1	+	+	CCONJ
ejpam-180	595	2	y	y	PROPN
ejpam-180	595	3	(	(	PUNCT
ejpam-180	595	4	t	t	PROPN
ejpam-180	595	5	)	)	PUNCT
ejpam-180	595	6	t	t	PROPN
ejpam-180	595	7	g	g	PROPN
ejpam-180	595	8	ẍ	ẍ	PROPN
ejpam-180	595	9	�	�	PROPN
ejpam-180	595	10	=	=	SYM
ejpam-180	595	11	0	0	PROPN
ejpam-180	595	12	,	,	PUNCT
ejpam-180	595	13	t	t	PROPN
ejpam-180	595	14	∈	∈	PROPN
ejpam-180	595	15	i	i	PRON
ejpam-180	595	16	(	(	PUNCT
ejpam-180	595	17	5.3	5.3	NUM
ejpam-180	595	18	)	)	PUNCT
ejpam-180	595	19	m	m	VERB
ejpam-180	595	20	∑	∑	PUNCT
ejpam-180	596	1	j=1	j=1	ADJ
ejpam-180	596	2	∫	∫	PROPN
ejpam-180	597	1	i	i	PRON
ejpam-180	597	2	y	y	PROPN
ejpam-180	597	3	j	j	PROPN
ejpam-180	597	4	(	(	PUNCT
ejpam-180	597	5	t	t	PROPN
ejpam-180	597	6	)	)	PUNCT
ejpam-180	597	7	g	g	PROPN
ejpam-180	597	8	j	j	PROPN
ejpam-180	597	9	(	(	PUNCT
ejpam-180	597	10	t	t	PROPN
ejpam-180	597	11	,	,	PUNCT
ejpam-180	597	12	u	u	NOUN
ejpam-180	597	13	,	,	PUNCT
ejpam-180	597	14	u̇	u̇	PROPN
ejpam-180	597	15	,	,	PUNCT
ejpam-180	597	16	ü	ü	NUM
ejpam-180	597	17	)	)	PUNCT
ejpam-180	598	1	d	d	NOUN
ejpam-180	598	2	t	t	PROPN
ejpam-180	598	3	≧	≧	NOUN
ejpam-180	598	4	0	0	NUM
ejpam-180	598	5	,	,	PUNCT
ejpam-180	598	6	t	t	PROPN
ejpam-180	598	7	∈	∈	PROPN
ejpam-180	599	1	i	i	PRON
ejpam-180	599	2	(	(	PUNCT
ejpam-180	599	3	5.4	5.4	NUM
ejpam-180	599	4	)	)	PUNCT
ejpam-180	599	5	z̄	z̄	PROPN
ejpam-180	599	6	i	i	PROPN
ejpam-180	599	7	(	(	PUNCT
ejpam-180	599	8	t	t	PROPN
ejpam-180	599	9	)	)	PUNCT
ejpam-180	599	10	t	t	PROPN
ejpam-180	599	11	b	b	PROPN
ejpam-180	599	12	i	i	PROPN
ejpam-180	599	13	(	(	PUNCT
ejpam-180	599	14	t	t	PROPN
ejpam-180	599	15	)	)	PUNCT
ejpam-180	599	16	z̄	z̄	PROPN
ejpam-180	600	1	i	i	PRON
ejpam-180	600	2	(	(	PUNCT
ejpam-180	600	3	t)≦	t)≦	X
ejpam-180	600	4	1	1	NUM
ejpam-180	600	5	,	,	PUNCT
ejpam-180	600	6	t	t	PROPN
ejpam-180	600	7	∈	∈	PROPN
ejpam-180	601	1	i	i	PRON
ejpam-180	601	2	,	,	PUNCT
ejpam-180	601	3	i	i	PROPN
ejpam-180	601	4	∈	∈	VERB
ejpam-180	601	5	p	p	X
ejpam-180	601	6	(	(	PUNCT
ejpam-180	601	7	5.5	5.5	NUM
ejpam-180	601	8	)	)	PUNCT
ejpam-180	601	9	λ	λ	X
ejpam-180	601	10	>	>	X
ejpam-180	601	11	0	0	PROPN
ejpam-180	601	12	,	,	PUNCT
ejpam-180	601	13	y	y	PROPN
ejpam-180	601	14	(	(	PUNCT
ejpam-180	601	15	t)≧	t)≧	PROPN
ejpam-180	601	16	0	0	NUM
ejpam-180	601	17	,	,	PUNCT
ejpam-180	601	18	t	t	PROPN
ejpam-180	601	19	∈	∈	PROPN
ejpam-180	602	1	i	i	PRON
ejpam-180	602	2	(	(	PUNCT
ejpam-180	602	3	5.6	5.6	NUM
ejpam-180	602	4	)	)	PUNCT
ejpam-180	602	5	theorem	theorem	VERB
ejpam-180	602	6	5.1	5.1	NUM
ejpam-180	602	7	(	(	PUNCT
ejpam-180	602	8	weak	weak	ADJ
ejpam-180	602	9	duality	duality	NOUN
ejpam-180	602	10	)	)	PUNCT
ejpam-180	602	11	.	.	PUNCT
ejpam-180	603	1	let	let	VERB
ejpam-180	603	2	x̄	x̄	PRON
ejpam-180	603	3	be	be	AUX
ejpam-180	603	4	feasible	feasible	ADJ
ejpam-180	603	5	for	for	ADP
ejpam-180	603	6	(	(	PUNCT
ejpam-180	603	7	vp	vp	NOUN
ejpam-180	603	8	)	)	PUNCT
ejpam-180	603	9	and	and	CCONJ
ejpam-180	603	10	�	�	PROPN
ejpam-180	603	11	u	u	PROPN
ejpam-180	603	12	,	,	PUNCT
ejpam-180	603	13	λ	λ	PROPN
ejpam-180	603	14	,	,	PUNCT
ejpam-180	603	15	z1	z1	NOUN
ejpam-180	603	16	,	,	PUNCT
ejpam-180	603	17	.	.	PUNCT
ejpam-180	603	18	.	.	PUNCT
ejpam-180	604	1	.	.	PUNCT
ejpam-180	605	1	,	,	PUNCT
ejpam-180	605	2	zp	zp	PROPN
ejpam-180	605	3	,	,	PUNCT
ejpam-180	605	4	y	y	PROPN
ejpam-180	605	5	�	�	PROPN
ejpam-180	605	6	be	be	AUX
ejpam-180	605	7	feasible	feasible	ADJ
ejpam-180	605	8	for	for	ADP
ejpam-180	605	9	(	(	PUNCT
ejpam-180	605	10	m	m	NOUN
ejpam-180	605	11	-	-	PUNCT
ejpam-180	605	12	wvd	wvd	NOUN
ejpam-180	605	13	)	)	PUNCT
ejpam-180	605	14	.	.	PUNCT
ejpam-180	606	1	if	if	SCONJ
ejpam-180	606	2	for	for	ADP
ejpam-180	606	3	feasible	feasible	ADJ
ejpam-180	606	4	�	�	PROPN
ejpam-180	606	5	x	x	SYM
ejpam-180	606	6	,	,	PUNCT
ejpam-180	606	7	u	u	NOUN
ejpam-180	606	8	,	,	PUNCT
ejpam-180	606	9	λ	λ	PROPN
ejpam-180	606	10	,	,	PUNCT
ejpam-180	606	11	z1	z1	NOUN
ejpam-180	606	12	,	,	PUNCT
ejpam-180	606	13	.	.	PUNCT
ejpam-180	606	14	.	.	PUNCT
ejpam-180	607	1	.	.	PUNCT
ejpam-180	608	1	,	,	PUNCT
ejpam-180	608	2	zp	zp	PROPN
ejpam-180	608	3	,	,	PUNCT
ejpam-180	608	4	y	y	PROPN
ejpam-180	608	5	�	�	PROPN
ejpam-180	608	6	,	,	PUNCT
ejpam-180	608	7	p	p	X
ejpam-180	608	8	∑	∑	PROPN
ejpam-180	608	9	i=1	i=1	PROPN
ejpam-180	609	1	λi	λi	X
ejpam-180	609	2	∫	∫	PROPN
ejpam-180	610	1	i	i	INTJ
ejpam-180	610	2	�	�	PROPN
ejpam-180	611	1	f	f	PROPN
ejpam-180	611	2	i	i	PRON
ejpam-180	611	3	(	(	PUNCT
ejpam-180	611	4	t	t	PROPN
ejpam-180	611	5	,	,	PUNCT
ejpam-180	611	6	.	.	PUNCT
ejpam-180	611	7	,	,	PUNCT
ejpam-180	611	8	.	.	PUNCT
ejpam-180	611	9	,	,	PUNCT
ejpam-180	611	10	.	.	PUNCT
ejpam-180	611	11	)	)	PUNCT
ejpam-180	612	1	+	+	CCONJ
ejpam-180	612	2	(	(	PUNCT
ejpam-180	612	3	·	·	PUNCT
ejpam-180	612	4	)	)	PUNCT
ejpam-180	612	5	t	t	PROPN
ejpam-180	612	6	b	b	X
ejpam-180	612	7	i	i	PROPN
ejpam-180	612	8	(	(	PUNCT
ejpam-180	612	9	t	t	PROPN
ejpam-180	612	10	)	)	PUNCT
ejpam-180	613	1	z	z	NOUN
ejpam-180	614	1	i	i	PRON
ejpam-180	614	2	(	(	PUNCT
ejpam-180	614	3	t	t	PROPN
ejpam-180	614	4	)	)	PUNCT
ejpam-180	614	5	�	�	PROPN
ejpam-180	615	1	d	d	PROPN
ejpam-180	615	2	t	t	PROPN
ejpam-180	615	3	is	be	AUX
ejpam-180	615	4	pseudoinvex	pseudoinvex	NOUN
ejpam-180	615	5	and	and	CCONJ
ejpam-180	615	6	∫	∫	NOUN
ejpam-180	616	1	i	i	PRON
ejpam-180	616	2	y	y	PROPN
ejpam-180	616	3	(	(	PUNCT
ejpam-180	616	4	t	t	PROPN
ejpam-180	616	5	)	)	PUNCT
ejpam-180	616	6	t	t	PROPN
ejpam-180	616	7	g	g	PROPN
ejpam-180	616	8	(	(	PUNCT
ejpam-180	616	9	t	t	PROPN
ejpam-180	616	10	,	,	PUNCT
ejpam-180	616	11	.	.	PUNCT
ejpam-180	616	12	,	,	PUNCT
ejpam-180	616	13	.	.	PUNCT
ejpam-180	616	14	,	,	PUNCT
ejpam-180	616	15	.	.	PUNCT
ejpam-180	616	16	)	)	PUNCT
ejpam-180	617	1	d	d	X
ejpam-180	617	2	t	t	PROPN
ejpam-180	617	3	is	be	AUX
ejpam-180	617	4	quasi	quasi	ADJ
ejpam-180	617	5	-	-	NOUN
ejpam-180	617	6	invex	invex	ADJ
ejpam-180	617	7	with	with	ADP
ejpam-180	617	8	respect	respect	NOUN
ejpam-180	617	9	to	to	ADP
ejpam-180	617	10	same	same	ADJ
ejpam-180	617	11	η	η	PROPN
ejpam-180	617	12	,	,	PUNCT
ejpam-180	617	13	the	the	DET
ejpam-180	617	14	following	following	NOUN
ejpam-180	617	15	can	can	AUX
ejpam-180	617	16	not	not	PART
ejpam-180	617	17	hold	hold	VERB
ejpam-180	617	18	:	:	PUNCT
ejpam-180	617	19	∫	∫	PROPN
ejpam-180	618	1	i	i	PRON
ejpam-180	618	2	�	�	PROPN
ejpam-180	619	1	f	f	PROPN
ejpam-180	619	2	i	i	PRON
ejpam-180	619	3	(	(	PUNCT
ejpam-180	619	4	t	t	PROPN
ejpam-180	619	5	,	,	PUNCT
ejpam-180	619	6	x	x	X
ejpam-180	619	7	,	,	PUNCT
ejpam-180	619	8	ẋ	ẋ	PROPN
ejpam-180	619	9	,	,	PUNCT
ejpam-180	619	10	ẍ	ẍ	X
ejpam-180	619	11	)	)	PUNCT
ejpam-180	620	1	d	d	PROPN
ejpam-180	620	2	t	t	PROPN
ejpam-180	620	3	+	+	CCONJ
ejpam-180	620	4	�	�	PROPN
ejpam-180	620	5	x	x	SYM
ejpam-180	620	6	(	(	PUNCT
ejpam-180	620	7	t	t	PROPN
ejpam-180	620	8	)	)	PUNCT
ejpam-180	620	9	t	t	PROPN
ejpam-180	620	10	b	b	PROPN
ejpam-180	621	1	i	i	PROPN
ejpam-180	621	2	(	(	PUNCT
ejpam-180	621	3	t	t	PROPN
ejpam-180	621	4	)	)	PUNCT
ejpam-180	621	5	x	x	X
ejpam-180	621	6	(	(	PUNCT
ejpam-180	621	7	t	t	PROPN
ejpam-180	621	8	)	)	PUNCT
ejpam-180	621	9	�	�	PROPN
ejpam-180	621	10	1	1	NUM
ejpam-180	621	11	2	2	NUM
ejpam-180	621	12	�	�	PROPN
ejpam-180	621	13	d	d	PROPN
ejpam-180	621	14	t	t	PROPN
ejpam-180	621	15	i.	i.	PROPN
ejpam-180	621	16	husain	husain	PROPN
ejpam-180	621	17	,	,	PUNCT
ejpam-180	621	18	a.	a.	PROPN
ejpam-180	621	19	ahmed	ahmed	PROPN
ejpam-180	621	20	,	,	PUNCT
ejpam-180	621	21	and	and	CCONJ
ejpam-180	621	22	g.	g.	PROPN
ejpam-180	621	23	rumana	rumana	PROPN
ejpam-180	621	24	/	/	SYM
ejpam-180	621	25	eur	eur	PROPN
ejpam-180	621	26	.	.	PUNCT
ejpam-180	622	1	j.	j.	PROPN
ejpam-180	622	2	pure	pure	PROPN
ejpam-180	622	3	appl	appl	PROPN
ejpam-180	622	4	.	.	PROPN
ejpam-180	622	5	math	math	PROPN
ejpam-180	622	6	,	,	PUNCT
ejpam-180	622	7	2	2	NUM
ejpam-180	622	8	(	(	PUNCT
ejpam-180	622	9	2009	2009	NUM
ejpam-180	622	10	)	)	PUNCT
ejpam-180	622	11	,	,	PUNCT
ejpam-180	622	12	(	(	PUNCT
ejpam-180	622	13	372	372	NUM
ejpam-180	622	14	-	-	SYM
ejpam-180	622	15	400	400	NUM
ejpam-180	622	16	)	)	PUNCT
ejpam-180	622	17	390	390	NUM
ejpam-180	622	18	≤	≤	NUM
ejpam-180	622	19	∫	∫	NOUN
ejpam-180	623	1	i	i	PRON
ejpam-180	623	2	�	�	PROPN
ejpam-180	624	1	f	f	PROPN
ejpam-180	624	2	i	i	PRON
ejpam-180	624	3	(	(	PUNCT
ejpam-180	624	4	t	t	PROPN
ejpam-180	624	5	,	,	PUNCT
ejpam-180	624	6	u	u	NOUN
ejpam-180	624	7	,	,	PUNCT
ejpam-180	624	8	u̇	u̇	PROPN
ejpam-180	624	9	,	,	PUNCT
ejpam-180	624	10	ü	ü	NUM
ejpam-180	624	11	)	)	PUNCT
ejpam-180	625	1	d	d	PROPN
ejpam-180	625	2	t	t	PROPN
ejpam-180	625	3	+	+	CCONJ
ejpam-180	625	4	�	�	PROPN
ejpam-180	625	5	u	u	PROPN
ejpam-180	625	6	(	(	PUNCT
ejpam-180	625	7	t	t	PROPN
ejpam-180	625	8	)	)	PUNCT
ejpam-180	625	9	t	t	PROPN
ejpam-180	625	10	b	b	PROPN
ejpam-180	626	1	i	i	PRON
ejpam-180	626	2	(	(	PUNCT
ejpam-180	626	3	t)z	t)z	NOUN
ejpam-180	626	4	i	i	PRON
ejpam-180	626	5	(	(	PUNCT
ejpam-180	626	6	t	t	PROPN
ejpam-180	626	7	)	)	PUNCT
ejpam-180	626	8	�	�	PROPN
ejpam-180	626	9	1	1	NUM
ejpam-180	626	10	2	2	NUM
ejpam-180	626	11	�	�	PROPN
ejpam-180	626	12	d	d	PROPN
ejpam-180	626	13	t	t	PROPN
ejpam-180	626	14	,	,	PUNCT
ejpam-180	626	15	for	for	ADP
ejpam-180	626	16	all	all	PRON
ejpam-180	627	1	i	i	PRON
ejpam-180	627	2	∈	∈	PROPN
ejpam-180	627	3	p	p	X
ejpam-180	627	4	,	,	PUNCT
ejpam-180	627	5	(	(	PUNCT
ejpam-180	627	6	5.7	5.7	NUM
ejpam-180	627	7	)	)	PUNCT
ejpam-180	627	8	and	and	CCONJ
ejpam-180	627	9	∫	∫	PROPN
ejpam-180	628	1	i	i	PRON
ejpam-180	628	2	�	�	PROPN
ejpam-180	629	1	f	f	PROPN
ejpam-180	629	2	j	j	PROPN
ejpam-180	629	3	(	(	PUNCT
ejpam-180	629	4	t	t	PROPN
ejpam-180	629	5	,	,	PUNCT
ejpam-180	629	6	x	x	X
ejpam-180	629	7	,	,	PUNCT
ejpam-180	629	8	ẋ	ẋ	PROPN
ejpam-180	629	9	,	,	PUNCT
ejpam-180	629	10	ẍ	ẍ	X
ejpam-180	629	11	)	)	PUNCT
ejpam-180	630	1	d	d	PROPN
ejpam-180	630	2	t	t	PROPN
ejpam-180	630	3	+	+	CCONJ
ejpam-180	630	4	�	�	PROPN
ejpam-180	630	5	x	x	SYM
ejpam-180	630	6	(	(	PUNCT
ejpam-180	630	7	t	t	PROPN
ejpam-180	630	8	)	)	PUNCT
ejpam-180	630	9	t	t	PROPN
ejpam-180	630	10	b	b	PROPN
ejpam-180	630	11	j	j	PROPN
ejpam-180	630	12	(	(	PUNCT
ejpam-180	630	13	t	t	PROPN
ejpam-180	630	14	)	)	PUNCT
ejpam-180	630	15	x	x	X
ejpam-180	630	16	(	(	PUNCT
ejpam-180	630	17	t	t	PROPN
ejpam-180	630	18	)	)	PUNCT
ejpam-180	630	19	�	�	PROPN
ejpam-180	630	20	1	1	NUM
ejpam-180	630	21	2	2	NUM
ejpam-180	630	22	�	�	PROPN
ejpam-180	630	23	d	d	ADP
ejpam-180	630	24	t	t	PROPN
ejpam-180	630	25	<	<	X
ejpam-180	630	26	∫	∫	PROPN
ejpam-180	631	1	i	i	INTJ
ejpam-180	631	2	�	�	PROPN
ejpam-180	632	1	f	f	PROPN
ejpam-180	632	2	j	j	PROPN
ejpam-180	632	3	(	(	PUNCT
ejpam-180	632	4	t	t	PROPN
ejpam-180	632	5	,	,	PUNCT
ejpam-180	632	6	u	u	NOUN
ejpam-180	632	7	,	,	PUNCT
ejpam-180	632	8	u̇	u̇	PROPN
ejpam-180	632	9	,	,	PUNCT
ejpam-180	632	10	ü	ü	NUM
ejpam-180	632	11	)	)	PUNCT
ejpam-180	633	1	d	d	PROPN
ejpam-180	633	2	t	t	PROPN
ejpam-180	633	3	+	+	CCONJ
ejpam-180	633	4	�	�	PROPN
ejpam-180	633	5	u	u	PROPN
ejpam-180	633	6	(	(	PUNCT
ejpam-180	633	7	t	t	PROPN
ejpam-180	633	8	)	)	PUNCT
ejpam-180	633	9	t	t	PROPN
ejpam-180	633	10	b	b	PROPN
ejpam-180	633	11	j	j	PROPN
ejpam-180	633	12	(	(	PUNCT
ejpam-180	633	13	t	t	PROPN
ejpam-180	633	14	)	)	PUNCT
ejpam-180	634	1	z	z	PROPN
ejpam-180	634	2	j	j	PROPN
ejpam-180	634	3	(	(	PUNCT
ejpam-180	634	4	t	t	PROPN
ejpam-180	634	5	)	)	PUNCT
ejpam-180	634	6	�	�	PROPN
ejpam-180	634	7	1	1	NUM
ejpam-180	634	8	2	2	NUM
ejpam-180	634	9	�	�	PROPN
ejpam-180	634	10	d	d	PROPN
ejpam-180	634	11	t	t	PROPN
ejpam-180	634	12	,	,	PUNCT
ejpam-180	634	13	for	for	ADP
ejpam-180	634	14	some	some	DET
ejpam-180	634	15	j	j	PROPN
ejpam-180	634	16	∈	∈	PROPN
ejpam-180	634	17	p	p	X
ejpam-180	634	18	(	(	PUNCT
ejpam-180	634	19	5.8	5.8	NUM
ejpam-180	634	20	)	)	PUNCT
ejpam-180	634	21	proof	proof	NOUN
ejpam-180	634	22	.	.	PUNCT
ejpam-180	634	23	suppose	suppose	VERB
ejpam-180	634	24	that	that	SCONJ
ejpam-180	634	25	(	(	PUNCT
ejpam-180	634	26	5.7	5.7	NUM
ejpam-180	634	27	)	)	PUNCT
ejpam-180	634	28	and	and	CCONJ
ejpam-180	634	29	(	(	PUNCT
ejpam-180	634	30	5.8	5.8	NUM
ejpam-180	634	31	)	)	PUNCT
ejpam-180	634	32	hold	hold	VERB
ejpam-180	634	33	.	.	PUNCT
ejpam-180	635	1	using	use	VERB
ejpam-180	635	2	λ	λ	PROPN
ejpam-180	635	3	>	>	X
ejpam-180	635	4	0	0	PUNCT
ejpam-180	635	5	and	and	CCONJ
ejpam-180	635	6	∑p	∑p	PROPN
ejpam-180	635	7	i=1	i=1	PROPN
ejpam-180	635	8	λi	λi	X
ejpam-180	635	9	=	=	NOUN
ejpam-180	635	10	1	1	NUM
ejpam-180	635	11	,	,	PUNCT
ejpam-180	635	12	then	then	ADV
ejpam-180	635	13	in	in	ADP
ejpam-180	635	14	view	view	NOUN
ejpam-180	635	15	of	of	ADP
ejpam-180	635	16	schwartz	schwartz	PROPN
ejpam-180	635	17	inequality	inequality	PROPN
ejpam-180	635	18	[	[	X
ejpam-180	635	19	15	15	NUM
ejpam-180	635	20	]	]	PUNCT
ejpam-180	635	21	,	,	PUNCT
ejpam-180	635	22	this	this	PRON
ejpam-180	635	23	gives	give	VERB
ejpam-180	635	24	p	p	PRON
ejpam-180	635	25	∑	∑	PROPN
ejpam-180	635	26	i=1	i=1	PROPN
ejpam-180	636	1	λi	λi	INTJ
ejpam-180	636	2	∫	∫	PROPN
ejpam-180	637	1	i	i	INTJ
ejpam-180	637	2	�	�	PROPN
ejpam-180	638	1	f	f	PROPN
ejpam-180	638	2	i	i	PRON
ejpam-180	638	3	(	(	PUNCT
ejpam-180	638	4	t	t	PROPN
ejpam-180	638	5	,	,	PUNCT
ejpam-180	638	6	x	x	X
ejpam-180	638	7	,	,	PUNCT
ejpam-180	638	8	ẋ	ẋ	PROPN
ejpam-180	638	9	,	,	PUNCT
ejpam-180	638	10	ẍ	ẍ	X
ejpam-180	638	11	)	)	PUNCT
ejpam-180	639	1	d	d	PROPN
ejpam-180	639	2	t	t	PROPN
ejpam-180	639	3	+	+	CCONJ
ejpam-180	639	4	�	�	PROPN
ejpam-180	639	5	x	x	SYM
ejpam-180	639	6	(	(	PUNCT
ejpam-180	639	7	t	t	PROPN
ejpam-180	639	8	)	)	PUNCT
ejpam-180	639	9	t	t	PROPN
ejpam-180	639	10	b	b	PROPN
ejpam-180	640	1	i	i	PROPN
ejpam-180	640	2	(	(	PUNCT
ejpam-180	640	3	t	t	PROPN
ejpam-180	640	4	)	)	PUNCT
ejpam-180	640	5	z	z	NOUN
ejpam-180	641	1	i	i	PRON
ejpam-180	641	2	(	(	PUNCT
ejpam-180	641	3	t	t	PROPN
ejpam-180	641	4	)	)	PUNCT
ejpam-180	641	5	�	�	PROPN
ejpam-180	641	6	1	1	NUM
ejpam-180	641	7	2	2	NUM
ejpam-180	641	8	�	�	PROPN
ejpam-180	641	9	d	d	PROPN
ejpam-180	641	10	t	t	PROPN
ejpam-180	641	11	<	<	X
ejpam-180	641	12	p	p	X
ejpam-180	641	13	∑	∑	PROPN
ejpam-180	641	14	i=1	i=1	PROPN
ejpam-180	641	15	λi	λi	X
ejpam-180	641	16	∫	∫	PROPN
ejpam-180	642	1	i	i	INTJ
ejpam-180	642	2	�	�	PROPN
ejpam-180	643	1	f	f	PROPN
ejpam-180	643	2	i	i	PRON
ejpam-180	643	3	(	(	PUNCT
ejpam-180	643	4	t	t	PROPN
ejpam-180	643	5	,	,	PUNCT
ejpam-180	643	6	u	u	NOUN
ejpam-180	643	7	,	,	PUNCT
ejpam-180	643	8	u̇	u̇	PROPN
ejpam-180	643	9	,	,	PUNCT
ejpam-180	643	10	ü	ü	NUM
ejpam-180	643	11	)	)	PUNCT
ejpam-180	644	1	d	d	PROPN
ejpam-180	644	2	t	t	PROPN
ejpam-180	644	3	+	+	CCONJ
ejpam-180	644	4	�	�	PROPN
ejpam-180	644	5	u	u	PROPN
ejpam-180	644	6	(	(	PUNCT
ejpam-180	644	7	t	t	PROPN
ejpam-180	644	8	)	)	PUNCT
ejpam-180	644	9	t	t	PROPN
ejpam-180	644	10	b	b	PROPN
ejpam-180	645	1	i	i	PRON
ejpam-180	645	2	(	(	PUNCT
ejpam-180	645	3	t)z	t)z	NOUN
ejpam-180	645	4	i	i	PRON
ejpam-180	645	5	(	(	PUNCT
ejpam-180	645	6	t	t	PROPN
ejpam-180	645	7	)	)	PUNCT
ejpam-180	645	8	�	�	PROPN
ejpam-180	645	9	1	1	NUM
ejpam-180	645	10	2	2	NUM
ejpam-180	645	11	�	�	PROPN
ejpam-180	645	12	d	d	PROPN
ejpam-180	645	13	t	t	PROPN
ejpam-180	645	14	in	in	ADP
ejpam-180	645	15	view	view	NOUN
ejpam-180	645	16	of	of	ADP
ejpam-180	645	17	�	�	PROPN
ejpam-180	645	18	x	x	SYM
ejpam-180	645	19	(	(	PUNCT
ejpam-180	645	20	t	t	PROPN
ejpam-180	645	21	)	)	PUNCT
ejpam-180	645	22	t	t	PROPN
ejpam-180	645	23	b	b	PROPN
ejpam-180	645	24	i	i	PROPN
ejpam-180	645	25	(	(	PUNCT
ejpam-180	645	26	t)z	t)z	NOUN
ejpam-180	645	27	(	(	PUNCT
ejpam-180	645	28	t	t	NOUN
ejpam-180	645	29	)	)	PUNCT
ejpam-180	645	30	�	�	PROPN
ejpam-180	645	31	≤	≤	PROPN
ejpam-180	645	32	�	�	PROPN
ejpam-180	645	33	x	x	SYM
ejpam-180	645	34	(	(	PUNCT
ejpam-180	645	35	t	t	PROPN
ejpam-180	645	36	)	)	PUNCT
ejpam-180	645	37	t	t	PROPN
ejpam-180	645	38	b	b	PROPN
ejpam-180	645	39	i	i	PROPN
ejpam-180	645	40	(	(	PUNCT
ejpam-180	645	41	t	t	PROPN
ejpam-180	645	42	)	)	PUNCT
ejpam-180	645	43	x	x	X
ejpam-180	645	44	(	(	PUNCT
ejpam-180	645	45	t	t	PROPN
ejpam-180	645	46	)	)	PUNCT
ejpam-180	645	47	�	�	PROPN
ejpam-180	645	48	1	1	NUM
ejpam-180	645	49	2	2	NUM
ejpam-180	645	50	�	�	PROPN
ejpam-180	645	51	z	z	PROPN
ejpam-180	645	52	(	(	PUNCT
ejpam-180	645	53	t	t	PROPN
ejpam-180	645	54	)	)	PUNCT
ejpam-180	645	55	t	t	PROPN
ejpam-180	645	56	b	b	PROPN
ejpam-180	645	57	i	i	PROPN
ejpam-180	645	58	(	(	PUNCT
ejpam-180	645	59	t)z	t)z	NOUN
ejpam-180	645	60	(	(	PUNCT
ejpam-180	645	61	t	t	NOUN
ejpam-180	645	62	)	)	PUNCT
ejpam-180	645	63	�	�	PROPN
ejpam-180	645	64	1	1	NUM
ejpam-180	645	65	2	2	NUM
ejpam-180	645	66	and	and	CCONJ
ejpam-180	645	67	�	�	PROPN
ejpam-180	645	68	z	z	PROPN
ejpam-180	645	69	(	(	PUNCT
ejpam-180	645	70	t	t	PROPN
ejpam-180	645	71	)	)	PUNCT
ejpam-180	645	72	t	t	PROPN
ejpam-180	645	73	b	b	PROPN
ejpam-180	645	74	i	i	PROPN
ejpam-180	645	75	(	(	PUNCT
ejpam-180	645	76	t	t	PROPN
ejpam-180	645	77	)	)	PUNCT
ejpam-180	645	78	z	z	NOUN
ejpam-180	645	79	(	(	PUNCT
ejpam-180	645	80	t	t	PROPN
ejpam-180	645	81	)	)	PUNCT
ejpam-180	645	82	�	�	PROPN
ejpam-180	645	83	≤	≤	ADV
ejpam-180	645	84	1	1	NUM
ejpam-180	645	85	,	,	PUNCT
ejpam-180	645	86	from	from	ADP
ejpam-180	645	87	this	this	DET
ejpam-180	645	88	inequality	inequality	NOUN
ejpam-180	645	89	we	we	PRON
ejpam-180	645	90	obtain	obtain	VERB
ejpam-180	645	91	,	,	PUNCT
ejpam-180	645	92	p	p	NOUN
ejpam-180	645	93	∑	∑	PROPN
ejpam-180	645	94	i=1	i=1	PROPN
ejpam-180	645	95	λi	λi	X
ejpam-180	645	96	∫	∫	PROPN
ejpam-180	646	1	i	i	INTJ
ejpam-180	646	2	�	�	PROPN
ejpam-180	647	1	f	f	PROPN
ejpam-180	647	2	i	i	PRON
ejpam-180	647	3	(	(	PUNCT
ejpam-180	647	4	t	t	PROPN
ejpam-180	647	5	,	,	PUNCT
ejpam-180	647	6	x	x	X
ejpam-180	647	7	,	,	PUNCT
ejpam-180	647	8	ẋ	ẋ	PROPN
ejpam-180	647	9	,	,	PUNCT
ejpam-180	647	10	ẍ	ẍ	X
ejpam-180	647	11	)	)	PUNCT
ejpam-180	648	1	d	d	PROPN
ejpam-180	648	2	t	t	PROPN
ejpam-180	648	3	+	+	CCONJ
ejpam-180	648	4	x	x	X
ejpam-180	648	5	(	(	PUNCT
ejpam-180	648	6	t	t	PROPN
ejpam-180	648	7	)	)	PUNCT
ejpam-180	648	8	t	t	PROPN
ejpam-180	649	1	b	b	PROPN
ejpam-180	649	2	i	i	PRON
ejpam-180	649	3	(	(	PUNCT
ejpam-180	649	4	t)z	t)z	NOUN
ejpam-180	649	5	i	i	PRON
ejpam-180	649	6	(	(	PUNCT
ejpam-180	649	7	t	t	PROPN
ejpam-180	649	8	)	)	PUNCT
ejpam-180	649	9	�	�	PROPN
ejpam-180	650	1	d	d	PROPN
ejpam-180	650	2	t	t	PROPN
ejpam-180	650	3	<	<	X
ejpam-180	650	4	p	p	X
ejpam-180	650	5	∑	∑	PROPN
ejpam-180	650	6	i=1	i=1	PROPN
ejpam-180	650	7	λi	λi	X
ejpam-180	650	8	∫	∫	PROPN
ejpam-180	651	1	i	i	INTJ
ejpam-180	651	2	�	�	PROPN
ejpam-180	652	1	f	f	PROPN
ejpam-180	652	2	i	i	PRON
ejpam-180	652	3	(	(	PUNCT
ejpam-180	652	4	t	t	PROPN
ejpam-180	652	5	,	,	PUNCT
ejpam-180	652	6	u	u	NOUN
ejpam-180	652	7	,	,	PUNCT
ejpam-180	652	8	u̇	u̇	PROPN
ejpam-180	652	9	,	,	PUNCT
ejpam-180	652	10	ü	ü	NUM
ejpam-180	652	11	)	)	PUNCT
ejpam-180	653	1	d	d	NOUN
ejpam-180	653	2	t	t	PROPN
ejpam-180	653	3	+	+	CCONJ
ejpam-180	653	4	u	u	PROPN
ejpam-180	653	5	(	(	PUNCT
ejpam-180	653	6	t	t	PROPN
ejpam-180	653	7	)	)	PUNCT
ejpam-180	653	8	t	t	PROPN
ejpam-180	653	9	b	b	PROPN
ejpam-180	654	1	i	i	PROPN
ejpam-180	654	2	(	(	PUNCT
ejpam-180	654	3	t	t	PROPN
ejpam-180	654	4	)	)	PUNCT
ejpam-180	654	5	z	z	NOUN
ejpam-180	655	1	i	i	PRON
ejpam-180	655	2	(	(	PUNCT
ejpam-180	655	3	t	t	PROPN
ejpam-180	655	4	)	)	PUNCT
ejpam-180	655	5	�	�	PROPN
ejpam-180	656	1	d	d	PROPN
ejpam-180	656	2	t	t	PROPN
ejpam-180	656	3	by	by	ADP
ejpam-180	656	4	pseudo	pseudo	NOUN
ejpam-180	656	5	invexity	invexity	NOUN
ejpam-180	656	6	of	of	ADP
ejpam-180	656	7	p	p	NOUN
ejpam-180	656	8	∑	∑	PROPN
ejpam-180	656	9	i=1	i=1	PROPN
ejpam-180	656	10	λi	λi	INTJ
ejpam-180	656	11	∫	∫	PROPN
ejpam-180	657	1	i	i	INTJ
ejpam-180	657	2	�	�	PROPN
ejpam-180	658	1	f	f	PROPN
ejpam-180	658	2	i	i	PRON
ejpam-180	658	3	(	(	PUNCT
ejpam-180	658	4	t	t	PROPN
ejpam-180	658	5	,	,	PUNCT
ejpam-180	658	6	.	.	PUNCT
ejpam-180	658	7	,	,	PUNCT
ejpam-180	658	8	.	.	PUNCT
ejpam-180	658	9	,	,	PUNCT
ejpam-180	658	10	.	.	PUNCT
ejpam-180	658	11	)	)	PUNCT
ejpam-180	659	1	+	+	CCONJ
ejpam-180	659	2	(	(	PUNCT
ejpam-180	659	3	·	·	PUNCT
ejpam-180	659	4	)	)	PUNCT
ejpam-180	659	5	t	t	PROPN
ejpam-180	659	6	b	b	X
ejpam-180	659	7	i	i	PROPN
ejpam-180	659	8	(	(	PUNCT
ejpam-180	659	9	t	t	PROPN
ejpam-180	659	10	)	)	PUNCT
ejpam-180	660	1	z	z	NOUN
ejpam-180	661	1	i	i	PRON
ejpam-180	661	2	(	(	PUNCT
ejpam-180	661	3	t	t	PROPN
ejpam-180	661	4	)	)	PUNCT
ejpam-180	661	5	�	�	PROPN
ejpam-180	662	1	d	d	PROPN
ejpam-180	662	2	t	t	PROPN
ejpam-180	662	3	with	with	ADP
ejpam-180	662	4	respect	respect	NOUN
ejpam-180	662	5	to	to	ADP
ejpam-180	662	6	η	η	PROPN
ejpam-180	662	7	,	,	PUNCT
ejpam-180	662	8	this	this	PRON
ejpam-180	662	9	implies	imply	VERB
ejpam-180	662	10	0	0	PUNCT
ejpam-180	662	11	>	>	X
ejpam-180	662	12	p	p	X
ejpam-180	662	13	∑	∑	PUNCT
ejpam-180	662	14	i=1	i=1	PROPN
ejpam-180	663	1	λi	λi	X
ejpam-180	663	2	∫	∫	PROPN
ejpam-180	664	1	i	i	PRON
ejpam-180	664	2	�	�	PROPN
ejpam-180	664	3	ηt	ηt	ADP
ejpam-180	664	4	�	�	PROPN
ejpam-180	665	1	f	f	PROPN
ejpam-180	665	2	i	i	PRON
ejpam-180	665	3	u	u	PROPN
ejpam-180	665	4	(	(	PUNCT
ejpam-180	665	5	t	t	PROPN
ejpam-180	665	6	,	,	PUNCT
ejpam-180	665	7	u	u	NOUN
ejpam-180	665	8	,	,	PUNCT
ejpam-180	665	9	u̇	u̇	PROPN
ejpam-180	665	10	,	,	PUNCT
ejpam-180	665	11	ü	ü	PRON
ejpam-180	665	12	)	)	PUNCT
ejpam-180	666	1	+	+	NUM
ejpam-180	667	1	b	b	X
ejpam-180	667	2	i	i	PRON
ejpam-180	667	3	(	(	PUNCT
ejpam-180	667	4	t)z	t)z	NOUN
ejpam-180	667	5	i	i	PRON
ejpam-180	667	6	(	(	PUNCT
ejpam-180	667	7	t	t	PROPN
ejpam-180	667	8	)	)	PUNCT
ejpam-180	667	9	�	�	PROPN
ejpam-180	667	10	+	+	CCONJ
ejpam-180	667	11	�	�	PROPN
ejpam-180	667	12	dη	dη	ADP
ejpam-180	667	13	�	�	PROPN
ejpam-180	667	14	t	t	PROPN
ejpam-180	667	15	�	�	PROPN
ejpam-180	668	1	f	f	PROPN
ejpam-180	669	1	i	i	PRON
ejpam-180	669	2	u̇	u̇	PROPN
ejpam-180	669	3	(	(	PUNCT
ejpam-180	669	4	t	t	PROPN
ejpam-180	669	5	,	,	PUNCT
ejpam-180	669	6	u	u	NOUN
ejpam-180	669	7	,	,	PUNCT
ejpam-180	669	8	u̇	u̇	PROPN
ejpam-180	669	9	,	,	PUNCT
ejpam-180	669	10	ü	ü	NOUN
ejpam-180	669	11	)	)	PUNCT
ejpam-180	669	12	�	�	PROPN
ejpam-180	669	13	+	+	CCONJ
ejpam-180	669	14	�	�	PROPN
ejpam-180	669	15	d2η	d2η	VERB
ejpam-180	669	16	�	�	PROPN
ejpam-180	669	17	t	t	PROPN
ejpam-180	669	18	�	�	PROPN
ejpam-180	670	1	f	f	PROPN
ejpam-180	670	2	i	i	PRON
ejpam-180	670	3	ü	ü	VERB
ejpam-180	670	4	(	(	PUNCT
ejpam-180	670	5	t	t	PROPN
ejpam-180	670	6	,	,	PUNCT
ejpam-180	670	7	u	u	NOUN
ejpam-180	670	8	,	,	PUNCT
ejpam-180	670	9	u̇	u̇	PROPN
ejpam-180	670	10	,	,	PUNCT
ejpam-180	670	11	ü	ü	NUM
ejpam-180	670	12	)	)	PUNCT
ejpam-180	670	13	�	�	PROPN
ejpam-180	671	1	i	i	PRON
ejpam-180	671	2	d	d	PROPN
ejpam-180	671	3	t	t	PROPN
ejpam-180	671	4	i.	i.	PROPN
ejpam-180	671	5	husain	husain	PROPN
ejpam-180	671	6	,	,	PUNCT
ejpam-180	671	7	a.	a.	PROPN
ejpam-180	671	8	ahmed	ahmed	PROPN
ejpam-180	671	9	,	,	PUNCT
ejpam-180	671	10	and	and	CCONJ
ejpam-180	671	11	g.	g.	PROPN
ejpam-180	671	12	rumana	rumana	PROPN
ejpam-180	671	13	/	/	SYM
ejpam-180	671	14	eur	eur	PROPN
ejpam-180	671	15	.	.	PUNCT
ejpam-180	672	1	j.	j.	PROPN
ejpam-180	672	2	pure	pure	PROPN
ejpam-180	672	3	appl	appl	PROPN
ejpam-180	672	4	.	.	PROPN
ejpam-180	672	5	math	math	PROPN
ejpam-180	672	6	,	,	PUNCT
ejpam-180	672	7	2	2	NUM
ejpam-180	672	8	(	(	PUNCT
ejpam-180	672	9	2009	2009	NUM
ejpam-180	672	10	)	)	PUNCT
ejpam-180	672	11	,	,	PUNCT
ejpam-180	672	12	(	(	PUNCT
ejpam-180	672	13	372	372	NUM
ejpam-180	672	14	-	-	SYM
ejpam-180	672	15	400	400	NUM
ejpam-180	672	16	)	)	PUNCT
ejpam-180	672	17	391	391	NUM
ejpam-180	672	18	this	this	PRON
ejpam-180	672	19	,	,	PUNCT
ejpam-180	672	20	by	by	ADP
ejpam-180	672	21	integration	integration	NOUN
ejpam-180	672	22	by	by	ADP
ejpam-180	672	23	parts	part	NOUN
ejpam-180	672	24	and	and	CCONJ
ejpam-180	672	25	using	use	VERB
ejpam-180	672	26	boundary	boundary	ADJ
ejpam-180	672	27	conditions	condition	NOUN
ejpam-180	672	28	as	as	ADP
ejpam-180	672	29	earlier	early	ADV
ejpam-180	672	30	,	,	PUNCT
ejpam-180	672	31	yields	yield	VERB
ejpam-180	672	32	p	p	PROPN
ejpam-180	672	33	∑	∑	PROPN
ejpam-180	672	34	i=1	i=1	PROPN
ejpam-180	673	1	λi	λi	INTJ
ejpam-180	673	2	∫	∫	PROPN
ejpam-180	673	3	i	i	PROPN
ejpam-180	673	4	ηt	ηt	ADP
ejpam-180	673	5	�	�	PROPN
ejpam-180	673	6	�	�	PROPN
ejpam-180	673	7	f	f	PROPN
ejpam-180	674	1	i	i	PRON
ejpam-180	674	2	u	u	PROPN
ejpam-180	674	3	(	(	PUNCT
ejpam-180	674	4	t	t	PROPN
ejpam-180	674	5	,	,	PUNCT
ejpam-180	674	6	u	u	NOUN
ejpam-180	674	7	,	,	PUNCT
ejpam-180	674	8	u̇	u̇	PROPN
ejpam-180	674	9	,	,	PUNCT
ejpam-180	674	10	ü	ü	PRON
ejpam-180	674	11	)	)	PUNCT
ejpam-180	675	1	+	+	NUM
ejpam-180	676	1	b	b	X
ejpam-180	676	2	i	i	PRON
ejpam-180	676	3	(	(	PUNCT
ejpam-180	676	4	t	t	PROPN
ejpam-180	676	5	)	)	PUNCT
ejpam-180	676	6	z	z	NOUN
ejpam-180	677	1	i	i	PRON
ejpam-180	677	2	(	(	PUNCT
ejpam-180	677	3	t	t	PROPN
ejpam-180	677	4	)	)	PUNCT
ejpam-180	677	5	�	�	PROPN
ejpam-180	677	6	−d	−d	PROPN
ejpam-180	677	7	f	f	PROPN
ejpam-180	678	1	i	i	PRON
ejpam-180	678	2	u̇	u̇	PROPN
ejpam-180	678	3	(	(	PUNCT
ejpam-180	678	4	t	t	PROPN
ejpam-180	678	5	,	,	PUNCT
ejpam-180	678	6	u	u	NOUN
ejpam-180	678	7	,	,	PUNCT
ejpam-180	678	8	u̇	u̇	PROPN
ejpam-180	678	9	,	,	PUNCT
ejpam-180	678	10	ü	ü	PRON
ejpam-180	678	11	)	)	PUNCT
ejpam-180	679	1	+	+	CCONJ
ejpam-180	680	1	d2	d2	PROPN
ejpam-180	680	2	f	f	PROPN
ejpam-180	680	3	i	i	PRON
ejpam-180	680	4	ü	ü	VERB
ejpam-180	680	5	(	(	PUNCT
ejpam-180	680	6	t	t	PROPN
ejpam-180	680	7	,	,	PUNCT
ejpam-180	680	8	u	u	NOUN
ejpam-180	680	9	,	,	PUNCT
ejpam-180	680	10	u̇	u̇	PROPN
ejpam-180	680	11	,	,	PUNCT
ejpam-180	680	12	ü	ü	NOUN
ejpam-180	680	13	)	)	PUNCT
ejpam-180	680	14	�	�	PROPN
ejpam-180	681	1	d	d	PROPN
ejpam-180	681	2	t	t	PROPN
ejpam-180	681	3	<	<	X
ejpam-180	681	4	0	0	NUM
ejpam-180	681	5	(	(	PUNCT
ejpam-180	681	6	5.9	5.9	NUM
ejpam-180	681	7	)	)	PUNCT
ejpam-180	681	8	now	now	ADV
ejpam-180	681	9	,	,	PUNCT
ejpam-180	681	10	from	from	ADP
ejpam-180	681	11	the	the	DET
ejpam-180	681	12	feasibility	feasibility	NOUN
ejpam-180	681	13	of	of	ADP
ejpam-180	681	14	(	(	PUNCT
ejpam-180	681	15	vp	vp	PROPN
ejpam-180	681	16	)	)	PUNCT
ejpam-180	681	17	and	and	CCONJ
ejpam-180	681	18	(	(	PUNCT
ejpam-180	681	19	m	m	NOUN
ejpam-180	681	20	-	-	PUNCT
ejpam-180	681	21	wvd	wvd	NOUN
ejpam-180	681	22	)	)	PUNCT
ejpam-180	681	23	,	,	PUNCT
ejpam-180	681	24	we	we	PRON
ejpam-180	681	25	have	have	VERB
ejpam-180	681	26	∫	∫	PROPN
ejpam-180	682	1	i	i	PRON
ejpam-180	682	2	y	y	PROPN
ejpam-180	682	3	(	(	PUNCT
ejpam-180	682	4	t	t	PROPN
ejpam-180	682	5	)	)	PUNCT
ejpam-180	682	6	t	t	PROPN
ejpam-180	682	7	g	g	PROPN
ejpam-180	682	8	(	(	PUNCT
ejpam-180	682	9	t	t	PROPN
ejpam-180	682	10	,	,	PUNCT
ejpam-180	682	11	x	x	X
ejpam-180	682	12	,	,	PUNCT
ejpam-180	682	13	ẋ	ẋ	PROPN
ejpam-180	682	14	,	,	PUNCT
ejpam-180	682	15	ẍ	ẍ	X
ejpam-180	682	16	)	)	PUNCT
ejpam-180	683	1	d	d	PROPN
ejpam-180	683	2	t	t	PROPN
ejpam-180	683	3	≦	≦	VERB
ejpam-180	684	1	∫	∫	PROPN
ejpam-180	684	2	i	i	PRON
ejpam-180	684	3	y	y	PROPN
ejpam-180	684	4	(	(	PUNCT
ejpam-180	684	5	t	t	PROPN
ejpam-180	684	6	)	)	PUNCT
ejpam-180	684	7	t	t	PROPN
ejpam-180	684	8	g	g	PROPN
ejpam-180	684	9	(	(	PUNCT
ejpam-180	684	10	t	t	PROPN
ejpam-180	684	11	,	,	PUNCT
ejpam-180	684	12	u	u	NOUN
ejpam-180	684	13	,	,	PUNCT
ejpam-180	684	14	u̇	u̇	PROPN
ejpam-180	684	15	,	,	PUNCT
ejpam-180	684	16	ü	ü	NUM
ejpam-180	684	17	)	)	PUNCT
ejpam-180	685	1	d	d	NOUN
ejpam-180	685	2	t	t	NOUN
ejpam-180	686	1	which	which	PRON
ejpam-180	686	2	,	,	PUNCT
ejpam-180	686	3	because	because	SCONJ
ejpam-180	686	4	of	of	ADP
ejpam-180	686	5	the	the	DET
ejpam-180	686	6	quasi	quasi	NOUN
ejpam-180	686	7	-	-	NOUN
ejpam-180	686	8	invexity	invexity	NOUN
ejpam-180	686	9	of	of	ADP
ejpam-180	686	10	∫	∫	PROPN
ejpam-180	686	11	i	i	PROPN
ejpam-180	686	12	y	y	PROPN
ejpam-180	686	13	(	(	PUNCT
ejpam-180	686	14	t	t	PROPN
ejpam-180	686	15	)	)	PUNCT
ejpam-180	686	16	t	t	PROPN
ejpam-180	686	17	g	g	PROPN
ejpam-180	686	18	(	(	PUNCT
ejpam-180	686	19	t	t	PROPN
ejpam-180	686	20	,	,	PUNCT
ejpam-180	686	21	.	.	PUNCT
ejpam-180	686	22	,	,	PUNCT
ejpam-180	686	23	.	.	PUNCT
ejpam-180	686	24	,	,	PUNCT
ejpam-180	686	25	.	.	PUNCT
ejpam-180	686	26	)	)	PUNCT
ejpam-180	687	1	d	d	X
ejpam-180	687	2	t	t	NOUN
ejpam-180	687	3	with	with	ADP
ejpam-180	687	4	respect	respect	NOUN
ejpam-180	687	5	to	to	ADP
ejpam-180	687	6	η	η	PROPN
ejpam-180	687	7	implies	imply	VERB
ejpam-180	687	8	∫	∫	PROPN
ejpam-180	688	1	i	i	PRON
ejpam-180	688	2	ηt	ηt	ADP
ejpam-180	688	3	y	y	PROPN
ejpam-180	688	4	(	(	PUNCT
ejpam-180	688	5	t	t	PROPN
ejpam-180	688	6	)	)	PUNCT
ejpam-180	688	7	t	t	PROPN
ejpam-180	688	8	gu	gu	PROPN
ejpam-180	689	1	(	(	PUNCT
ejpam-180	689	2	t	t	PROPN
ejpam-180	689	3	,	,	PUNCT
ejpam-180	689	4	u	u	NOUN
ejpam-180	689	5	,	,	PUNCT
ejpam-180	689	6	u̇	u̇	PROPN
ejpam-180	689	7	,	,	PUNCT
ejpam-180	689	8	ü	ü	PRON
ejpam-180	689	9	)	)	PUNCT
ejpam-180	690	1	+	+	CCONJ
ejpam-180	690	2	�	�	PROPN
ejpam-180	690	3	dη	dη	NOUN
ejpam-180	690	4	�	�	PROPN
ejpam-180	690	5	t	t	PROPN
ejpam-180	690	6	y	y	PROPN
ejpam-180	690	7	(	(	PUNCT
ejpam-180	690	8	t	t	PROPN
ejpam-180	690	9	)	)	PUNCT
ejpam-180	690	10	t	t	NOUN
ejpam-180	690	11	gu̇	gu̇	PROPN
ejpam-180	690	12	(	(	PUNCT
ejpam-180	690	13	t	t	PROPN
ejpam-180	690	14	,	,	PUNCT
ejpam-180	690	15	u	u	NOUN
ejpam-180	690	16	,	,	PUNCT
ejpam-180	690	17	u̇	u̇	PROPN
ejpam-180	690	18	,	,	PUNCT
ejpam-180	690	19	ü	ü	PRON
ejpam-180	690	20	)	)	PUNCT
ejpam-180	691	1	+	+	CCONJ
ejpam-180	691	2	�	�	PROPN
ejpam-180	691	3	d2η	d2η	VERB
ejpam-180	691	4	�	�	PROPN
ejpam-180	691	5	t	t	PROPN
ejpam-180	691	6	y	y	PROPN
ejpam-180	691	7	(	(	PUNCT
ejpam-180	691	8	t	t	PROPN
ejpam-180	691	9	)	)	PUNCT
ejpam-180	691	10	t	t	PROPN
ejpam-180	691	11	gü	gü	PROPN
ejpam-180	691	12	(	(	PUNCT
ejpam-180	691	13	t	t	PROPN
ejpam-180	691	14	,	,	PUNCT
ejpam-180	691	15	u	u	NOUN
ejpam-180	691	16	,	,	PUNCT
ejpam-180	691	17	u̇	u̇	PROPN
ejpam-180	691	18	,	,	PUNCT
ejpam-180	691	19	ü	ü	NUM
ejpam-180	691	20	)	)	PUNCT
ejpam-180	692	1	d	d	NOUN
ejpam-180	692	2	t	t	PROPN
ejpam-180	692	3	≦	≦	NOUN
ejpam-180	692	4	0	0	NUM
ejpam-180	693	1	this	this	PRON
ejpam-180	693	2	,	,	PUNCT
ejpam-180	693	3	as	as	ADP
ejpam-180	693	4	earlier	early	ADV
ejpam-180	693	5	,	,	PUNCT
ejpam-180	693	6	implies	imply	VERB
ejpam-180	693	7	∫	∫	PROPN
ejpam-180	693	8	i	i	PROPN
ejpam-180	693	9	ηt	ηt	ADP
ejpam-180	693	10	�	�	PROPN
ejpam-180	693	11	y	y	PROPN
ejpam-180	693	12	(	(	PUNCT
ejpam-180	693	13	t	t	PROPN
ejpam-180	693	14	)	)	PUNCT
ejpam-180	693	15	t	t	PROPN
ejpam-180	693	16	gu	gu	PROPN
ejpam-180	693	17	(	(	PUNCT
ejpam-180	693	18	t	t	PROPN
ejpam-180	693	19	,	,	PUNCT
ejpam-180	693	20	u	u	NOUN
ejpam-180	693	21	,	,	PUNCT
ejpam-180	693	22	u̇	u̇	PROPN
ejpam-180	693	23	,	,	PUNCT
ejpam-180	693	24	ü)−d	ü)−d	PROPN
ejpam-180	693	25	y	y	PROPN
ejpam-180	693	26	(	(	PUNCT
ejpam-180	693	27	t	t	PROPN
ejpam-180	693	28	)	)	PUNCT
ejpam-180	693	29	t	t	NOUN
ejpam-180	693	30	gu̇	gu̇	PROPN
ejpam-180	693	31	(	(	PUNCT
ejpam-180	693	32	t	t	PROPN
ejpam-180	693	33	,	,	PUNCT
ejpam-180	693	34	u	u	NOUN
ejpam-180	693	35	,	,	PUNCT
ejpam-180	693	36	u̇	u̇	PROPN
ejpam-180	693	37	,	,	PUNCT
ejpam-180	693	38	ü	ü	PRON
ejpam-180	693	39	)	)	PUNCT
ejpam-180	694	1	+	+	CCONJ
ejpam-180	694	2	d2	d2	PROPN
ejpam-180	694	3	y	y	PROPN
ejpam-180	694	4	(	(	PUNCT
ejpam-180	694	5	t	t	PROPN
ejpam-180	694	6	)	)	PUNCT
ejpam-180	694	7	t	t	PROPN
ejpam-180	694	8	gü	gü	PROPN
ejpam-180	694	9	(	(	PUNCT
ejpam-180	694	10	t	t	PROPN
ejpam-180	694	11	,	,	PUNCT
ejpam-180	694	12	u	u	NOUN
ejpam-180	694	13	,	,	PUNCT
ejpam-180	694	14	u̇	u̇	PROPN
ejpam-180	694	15	,	,	PUNCT
ejpam-180	694	16	ü	ü	NOUN
ejpam-180	694	17	)	)	PUNCT
ejpam-180	694	18	�	�	PROPN
ejpam-180	695	1	d	d	ADP
ejpam-180	695	2	t≦0(5.10	t≦0(5.10	NOUN
ejpam-180	695	3	)	)	PUNCT
ejpam-180	695	4	combining	combine	VERB
ejpam-180	695	5	(	(	PUNCT
ejpam-180	695	6	5.9	5.9	NUM
ejpam-180	695	7	)	)	PUNCT
ejpam-180	695	8	and	and	CCONJ
ejpam-180	695	9	(	(	PUNCT
ejpam-180	695	10	5.10	5.10	NUM
ejpam-180	695	11	)	)	PUNCT
ejpam-180	695	12	,	,	PUNCT
ejpam-180	695	13	we	we	PRON
ejpam-180	695	14	have	have	VERB
ejpam-180	695	15	the	the	DET
ejpam-180	695	16	inequality	inequality	NOUN
ejpam-180	695	17	as	as	ADP
ejpam-180	695	18	∫	∫	PROPN
ejpam-180	695	19	i	i	PROPN
ejpam-180	695	20	ηt	ηt	ADP
ejpam-180	695	21			PROPN
ejpam-180	695	22			NOUN
ejpam-180	695	23	p	p	X
ejpam-180	695	24	∑	∑	PROPN
ejpam-180	695	25	i=1	i=1	PROPN
ejpam-180	695	26	λi	λi	PROPN
ejpam-180	695	27	�	�	PROPN
ejpam-180	696	1	f	f	PROPN
ejpam-180	697	1	i	i	PRON
ejpam-180	697	2	u	u	PROPN
ejpam-180	697	3	(	(	PUNCT
ejpam-180	697	4	t	t	PROPN
ejpam-180	697	5	,	,	PUNCT
ejpam-180	697	6	u	u	NOUN
ejpam-180	697	7	,	,	PUNCT
ejpam-180	697	8	u̇	u̇	PROPN
ejpam-180	697	9	,	,	PUNCT
ejpam-180	697	10	ü	ü	PRON
ejpam-180	697	11	)	)	PUNCT
ejpam-180	698	1	+	+	NUM
ejpam-180	699	1	b	b	X
ejpam-180	699	2	i	i	PRON
ejpam-180	699	3	(	(	PUNCT
ejpam-180	699	4	t)z	t)z	NOUN
ejpam-180	699	5	i	i	PRON
ejpam-180	699	6	(	(	PUNCT
ejpam-180	699	7	t	t	PROPN
ejpam-180	699	8	)	)	PUNCT
ejpam-180	699	9	+	+	CCONJ
ejpam-180	699	10	y	y	PROPN
ejpam-180	699	11	(	(	PUNCT
ejpam-180	699	12	t	t	PROPN
ejpam-180	699	13	)	)	PUNCT
ejpam-180	699	14	t	t	PROPN
ejpam-180	699	15	gu	gu	PROPN
ejpam-180	699	16	(	(	PUNCT
ejpam-180	699	17	t	t	PROPN
ejpam-180	699	18	,	,	PUNCT
ejpam-180	699	19	u	u	NOUN
ejpam-180	699	20	,	,	PUNCT
ejpam-180	699	21	u̇	u̇	PROPN
ejpam-180	699	22	,	,	PUNCT
ejpam-180	699	23	ü	ü	NUM
ejpam-180	699	24	)	)	PUNCT
ejpam-180	699	25	�	�	PROPN
ejpam-180	699	26	−d	−d	PROPN
ejpam-180	699	27	�	�	PROPN
ejpam-180	700	1	f	f	PROPN
ejpam-180	701	1	i	i	PRON
ejpam-180	701	2	u̇	u̇	PROPN
ejpam-180	701	3	(	(	PUNCT
ejpam-180	701	4	t	t	PROPN
ejpam-180	701	5	,	,	PUNCT
ejpam-180	701	6	u	u	NOUN
ejpam-180	701	7	,	,	PUNCT
ejpam-180	701	8	u̇	u̇	PROPN
ejpam-180	701	9	,	,	PUNCT
ejpam-180	701	10	ü	ü	PRON
ejpam-180	701	11	)	)	PUNCT
ejpam-180	702	1	+	+	CCONJ
ejpam-180	702	2	y	y	PROPN
ejpam-180	702	3	(	(	PUNCT
ejpam-180	702	4	t	t	PROPN
ejpam-180	702	5	)	)	PUNCT
ejpam-180	702	6	t	t	NOUN
ejpam-180	702	7	gu̇	gu̇	PROPN
ejpam-180	702	8	(	(	PUNCT
ejpam-180	702	9	t	t	PROPN
ejpam-180	702	10	,	,	PUNCT
ejpam-180	702	11	u	u	NOUN
ejpam-180	702	12	,	,	PUNCT
ejpam-180	702	13	u̇	u̇	PROPN
ejpam-180	702	14	,	,	PUNCT
ejpam-180	702	15	ü	ü	NOUN
ejpam-180	702	16	)	)	PUNCT
ejpam-180	702	17	�	�	PROPN
ejpam-180	702	18	+	+	NUM
ejpam-180	702	19	d2	d2	PROPN
ejpam-180	702	20	�	�	PROPN
ejpam-180	702	21	f	f	PROPN
ejpam-180	703	1	i	i	PRON
ejpam-180	703	2	ü	ü	VERB
ejpam-180	703	3	(	(	PUNCT
ejpam-180	703	4	t	t	PROPN
ejpam-180	703	5	,	,	PUNCT
ejpam-180	703	6	u	u	NOUN
ejpam-180	703	7	,	,	PUNCT
ejpam-180	703	8	u̇	u̇	PROPN
ejpam-180	703	9	,	,	PUNCT
ejpam-180	703	10	ü	ü	PRON
ejpam-180	703	11	)	)	PUNCT
ejpam-180	704	1	+	+	CCONJ
ejpam-180	704	2	y	y	PROPN
ejpam-180	704	3	(	(	PUNCT
ejpam-180	704	4	t	t	PROPN
ejpam-180	704	5	)	)	PUNCT
ejpam-180	704	6	t	t	PROPN
ejpam-180	704	7	gü	gü	PROPN
ejpam-180	704	8	(	(	PUNCT
ejpam-180	704	9	t	t	PROPN
ejpam-180	704	10	,	,	PUNCT
ejpam-180	704	11	u	u	NOUN
ejpam-180	704	12	,	,	PUNCT
ejpam-180	704	13	u̇	u̇	PROPN
ejpam-180	704	14	,	,	PUNCT
ejpam-180	704	15	ü	ü	NUM
ejpam-180	704	16	)	)	PUNCT
ejpam-180	704	17	�	�	PROPN
ejpam-180	704	18	�	�	PROPN
ejpam-180	704	19	d	d	PROPN
ejpam-180	704	20	t	t	PROPN
ejpam-180	704	21	<	<	X
ejpam-180	704	22	0	0	NUM
ejpam-180	704	23	which	which	PRON
ejpam-180	704	24	contradicts	contradict	VERB
ejpam-180	704	25	the	the	DET
ejpam-180	704	26	dual	dual	ADJ
ejpam-180	704	27	equality	equality	NOUN
ejpam-180	704	28	constraint	constraint	NOUN
ejpam-180	704	29	.	.	PUNCT
ejpam-180	705	1	hence	hence	ADV
ejpam-180	705	2	the	the	DET
ejpam-180	705	3	theorem	theorem	NOUN
ejpam-180	705	4	is	be	AUX
ejpam-180	705	5	validated	validate	VERB
ejpam-180	705	6	.	.	PUNCT
ejpam-180	706	1	theorem	theorem	VERB
ejpam-180	706	2	5.2	5.2	NUM
ejpam-180	706	3	(	(	PUNCT
ejpam-180	706	4	strong	strong	ADJ
ejpam-180	706	5	duality	duality	NOUN
ejpam-180	706	6	)	)	PUNCT
ejpam-180	706	7	.	.	PUNCT
ejpam-180	707	1	let	let	VERB
ejpam-180	707	2	x̄	x̄	PRON
ejpam-180	707	3	be	be	AUX
ejpam-180	707	4	an	an	DET
ejpam-180	707	5	efficient	efficient	ADJ
ejpam-180	707	6	solution	solution	NOUN
ejpam-180	707	7	of	of	ADP
ejpam-180	707	8	(	(	PUNCT
ejpam-180	707	9	vp	vp	NOUN
ejpam-180	707	10	)	)	PUNCT
ejpam-180	707	11	and	and	CCONJ
ejpam-180	707	12	for	for	ADP
ejpam-180	707	13	at	at	ADV
ejpam-180	707	14	least	least	ADV
ejpam-180	707	15	one	one	NUM
ejpam-180	707	16	k	k	PROPN
ejpam-180	707	17	∈	∈	PROPN
ejpam-180	707	18	p	p	X
ejpam-180	707	19	,	,	PUNCT
ejpam-180	707	20	x̄	x̄	PRON
ejpam-180	707	21	satisfies	satisfy	VERB
ejpam-180	707	22	the	the	DET
ejpam-180	707	23	regularity	regularity	NOUN
ejpam-180	707	24	condition	condition	NOUN
ejpam-180	708	1	[	[	X
ejpam-180	708	2	3	3	X
ejpam-180	708	3	]	]	PUNCT
ejpam-180	708	4	for	for	ADP
ejpam-180	708	5	the	the	DET
ejpam-180	708	6	problem	problem	NOUN
ejpam-180	708	7	(	(	PUNCT
ejpam-180	708	8	pk	pk	NOUN
ejpam-180	708	9	(	(	PUNCT
ejpam-180	708	10	x̄	x̄	PROPN
ejpam-180	708	11	)	)	PUNCT
ejpam-180	708	12	)	)	PUNCT
ejpam-180	708	13	.	.	PUNCT
ejpam-180	709	1	then	then	ADV
ejpam-180	709	2	there	there	PRON
ejpam-180	709	3	exist	exist	VERB
ejpam-180	709	4	multipliers	multiplier	NOUN
ejpam-180	709	5	λ̄	λ̄	ADP
ejpam-180	709	6	∈	∈	PROPN
ejpam-180	709	7	rp	rp	NOUN
ejpam-180	709	8	,	,	PUNCT
ejpam-180	709	9	piecewise	piecewise	NOUN
ejpam-180	709	10	smooth	smooth	ADJ
ejpam-180	709	11	ȳ	ȳ	PROPN
ejpam-180	709	12	∈	∈	PROPN
ejpam-180	709	13	rm	rm	PROPN
ejpam-180	709	14	and	and	CCONJ
ejpam-180	709	15	z̄	z̄	PROPN
ejpam-180	709	16	i(t	i(t	PROPN
ejpam-180	709	17	)	)	PUNCT
ejpam-180	709	18	∈	∈	PROPN
ejpam-180	709	19	rn	rn	PROPN
ejpam-180	709	20	,	,	PUNCT
ejpam-180	709	21	i	i	PRON
ejpam-180	709	22	=	=	PUNCT
ejpam-180	709	23	{	{	PUNCT
ejpam-180	709	24	1	1	NUM
ejpam-180	709	25	,	,	PUNCT
ejpam-180	709	26	2	2	NUM
ejpam-180	709	27	,	,	PUNCT
ejpam-180	709	28	.	.	PUNCT
ejpam-180	709	29	.	.	PUNCT
ejpam-180	710	1	.	.	PUNCT
ejpam-180	711	1	,	,	PUNCT
ejpam-180	712	1	p	p	X
ejpam-180	712	2	}	}	PUNCT
ejpam-180	712	3	,	,	PUNCT
ejpam-180	712	4	such	such	ADJ
ejpam-180	712	5	that	that	PRON
ejpam-180	712	6	�	�	PROPN
ejpam-180	712	7	x̄	x̄	PROPN
ejpam-180	712	8	,	,	PUNCT
ejpam-180	712	9	ū	ū	NOUN
ejpam-180	712	10	,	,	PUNCT
ejpam-180	712	11	ȳ	ȳ	PROPN
ejpam-180	712	12	,	,	PUNCT
ejpam-180	712	13	z̄1	z̄1	NUM
ejpam-180	712	14	,	,	PUNCT
ejpam-180	712	15	.	.	PUNCT
ejpam-180	712	16	.	.	PUNCT
ejpam-180	712	17	.	.	PUNCT
ejpam-180	713	1	,	,	PUNCT
ejpam-180	713	2	z̄p	z̄p	PROPN
ejpam-180	713	3	,	,	PUNCT
ejpam-180	713	4	λ	λ	PROPN
ejpam-180	713	5	�	�	PROPN
ejpam-180	713	6	is	be	AUX
ejpam-180	713	7	feasible	feasible	ADJ
ejpam-180	713	8	for	for	ADP
ejpam-180	713	9	(	(	PUNCT
ejpam-180	713	10	m	m	NOUN
ejpam-180	713	11	-	-	PUNCT
ejpam-180	713	12	wvd	wvd	NOUN
ejpam-180	713	13	)	)	PUNCT
ejpam-180	713	14	and	and	CCONJ
ejpam-180	713	15	the	the	DET
ejpam-180	713	16	objectives	objective	NOUN
ejpam-180	713	17	of	of	ADP
ejpam-180	713	18	(	(	PUNCT
ejpam-180	713	19	vp	vp	NOUN
ejpam-180	713	20	)	)	PUNCT
ejpam-180	713	21	and	and	CCONJ
ejpam-180	713	22	(	(	PUNCT
ejpam-180	713	23	m	m	NOUN
ejpam-180	713	24	-	-	PUNCT
ejpam-180	713	25	wvd	wvd	NOUN
ejpam-180	713	26	)	)	PUNCT
ejpam-180	713	27	are	be	AUX
ejpam-180	713	28	equal	equal	ADJ
ejpam-180	713	29	.	.	PUNCT
ejpam-180	714	1	i.	i.	PROPN
ejpam-180	714	2	husain	husain	PROPN
ejpam-180	714	3	,	,	PUNCT
ejpam-180	714	4	a.	a.	PROPN
ejpam-180	714	5	ahmed	ahmed	PROPN
ejpam-180	714	6	,	,	PUNCT
ejpam-180	714	7	and	and	CCONJ
ejpam-180	714	8	g.	g.	PROPN
ejpam-180	714	9	rumana	rumana	PROPN
ejpam-180	714	10	/	/	SYM
ejpam-180	714	11	eur	eur	PROPN
ejpam-180	714	12	.	.	PUNCT
ejpam-180	715	1	j.	j.	PROPN
ejpam-180	715	2	pure	pure	PROPN
ejpam-180	715	3	appl	appl	PROPN
ejpam-180	715	4	.	.	PROPN
ejpam-180	715	5	math	math	PROPN
ejpam-180	715	6	,	,	PUNCT
ejpam-180	715	7	2	2	NUM
ejpam-180	715	8	(	(	PUNCT
ejpam-180	715	9	2009	2009	NUM
ejpam-180	715	10	)	)	PUNCT
ejpam-180	715	11	,	,	PUNCT
ejpam-180	715	12	(	(	PUNCT
ejpam-180	715	13	372	372	NUM
ejpam-180	715	14	-	-	SYM
ejpam-180	715	15	400	400	NUM
ejpam-180	715	16	)	)	PUNCT
ejpam-180	715	17	392	392	NUM
ejpam-180	715	18	further	far	ADV
ejpam-180	715	19	,	,	PUNCT
ejpam-180	715	20	if	if	SCONJ
ejpam-180	715	21	the	the	DET
ejpam-180	715	22	generalized	generalized	ADJ
ejpam-180	715	23	invexity	invexity	NOUN
ejpam-180	715	24	of	of	ADP
ejpam-180	715	25	hypothesis	hypothesis	NOUN
ejpam-180	715	26	of	of	ADP
ejpam-180	715	27	theorem	theorem	ADJ
ejpam-180	715	28	5.1	5.1	NUM
ejpam-180	715	29	is	be	AUX
ejpam-180	715	30	met	meet	VERB
ejpam-180	715	31	,	,	PUNCT
ejpam-180	715	32	then	then	ADV
ejpam-180	715	33	�	�	PROPN
ejpam-180	715	34	x̄	x̄	PROPN
ejpam-180	715	35	,	,	PUNCT
ejpam-180	715	36	ū	ū	NOUN
ejpam-180	715	37	,	,	PUNCT
ejpam-180	715	38	ȳ	ȳ	PROPN
ejpam-180	715	39	,	,	PUNCT
ejpam-180	715	40	z̄1	z̄1	PROPN
ejpam-180	715	41	,	,	PUNCT
ejpam-180	715	42	.	.	PUNCT
ejpam-180	715	43	.	.	PUNCT
ejpam-180	716	1	.	.	PUNCT
ejpam-180	717	1	,	,	PUNCT
ejpam-180	717	2	z̄p	z̄p	PROPN
ejpam-180	717	3	,	,	PUNCT
ejpam-180	717	4	λ̄	λ̄	PRON
ejpam-180	717	5	�	�	PROPN
ejpam-180	717	6	is	be	AUX
ejpam-180	717	7	an	an	DET
ejpam-180	717	8	efficient	efficient	ADJ
ejpam-180	717	9	solution	solution	NOUN
ejpam-180	717	10	of	of	ADP
ejpam-180	717	11	(	(	PUNCT
ejpam-180	717	12	m	m	NOUN
ejpam-180	717	13	-	-	PUNCT
ejpam-180	717	14	wvd	wvd	NOUN
ejpam-180	717	15	)	)	PUNCT
ejpam-180	717	16	.	.	PUNCT
ejpam-180	718	1	proof	proof	NOUN
ejpam-180	718	2	.	.	PUNCT
ejpam-180	719	1	since	since	SCONJ
ejpam-180	719	2	x̄	x̄	PRON
ejpam-180	719	3	is	be	AUX
ejpam-180	719	4	an	an	DET
ejpam-180	719	5	solution	solution	NOUN
ejpam-180	719	6	of	of	ADP
ejpam-180	719	7	the	the	DET
ejpam-180	719	8	problem	problem	NOUN
ejpam-180	719	9	(	(	PUNCT
ejpam-180	719	10	pk	pk	NOUN
ejpam-180	719	11	(	(	PUNCT
ejpam-180	719	12	x̄	x̄	PROPN
ejpam-180	719	13	)	)	PUNCT
ejpam-180	719	14	)	)	PUNCT
ejpam-180	719	15	,	,	PUNCT
ejpam-180	719	16	by	by	ADP
ejpam-180	719	17	analysis	analysis	NOUN
ejpam-180	719	18	of	of	ADP
ejpam-180	719	19	theorem	theorem	NOUN
ejpam-180	719	20	3.1	3.1	NUM
ejpam-180	719	21	,	,	PUNCT
ejpam-180	719	22	it	it	PRON
ejpam-180	719	23	implies	imply	VERB
ejpam-180	719	24	that	that	SCONJ
ejpam-180	719	25	there	there	PRON
ejpam-180	719	26	exists	exist	VERB
ejpam-180	719	27	λ̄	λ̄	ADP
ejpam-180	719	28	∈	∈	PROPN
ejpam-180	719	29	rp	rp	NOUN
ejpam-180	719	30	,	,	PUNCT
ejpam-180	719	31	piecewise	piecewise	NOUN
ejpam-180	719	32	smooth	smooth	ADJ
ejpam-180	719	33	ȳ	ȳ	PROPN
ejpam-180	719	34	∈	∈	PROPN
ejpam-180	719	35	rm	rm	PROPN
ejpam-180	719	36	and	and	CCONJ
ejpam-180	719	37	z̄	z̄	PROPN
ejpam-180	719	38	i(t	i(t	PROPN
ejpam-180	719	39	)	)	PUNCT
ejpam-180	719	40	∈	∈	PROPN
ejpam-180	719	41	rn	rn	PROPN
ejpam-180	719	42	,	,	PUNCT
ejpam-180	719	43	i	i	PRON
ejpam-180	719	44	=	=	PUNCT
ejpam-180	719	45	{	{	PUNCT
ejpam-180	719	46	1	1	NUM
ejpam-180	719	47	,	,	PUNCT
ejpam-180	719	48	2	2	NUM
ejpam-180	719	49	,	,	PUNCT
ejpam-180	719	50	.	.	PUNCT
ejpam-180	719	51	.	.	PUNCT
ejpam-180	720	1	.	.	PUNCT
ejpam-180	721	1	,	,	PUNCT
ejpam-180	721	2	p	p	X
ejpam-180	721	3	}	}	PUNCT
ejpam-180	721	4	such	such	ADJ
ejpam-180	721	5	that	that	SCONJ
ejpam-180	721	6	,	,	PUNCT
ejpam-180	721	7	(	(	PUNCT
ejpam-180	721	8	4.17	4.17	NUM
ejpam-180	721	9	)	)	PUNCT
ejpam-180	721	10	,	,	PUNCT
ejpam-180	721	11	(	(	PUNCT
ejpam-180	721	12	4.18	4.18	NUM
ejpam-180	721	13	)	)	PUNCT
ejpam-180	721	14	,	,	PUNCT
ejpam-180	721	15	(	(	PUNCT
ejpam-180	721	16	4.19	4.19	NUM
ejpam-180	721	17	)	)	PUNCT
ejpam-180	721	18	,	,	PUNCT
ejpam-180	721	19	(	(	PUNCT
ejpam-180	721	20	4.20	4.20	NUM
ejpam-180	721	21	)	)	PUNCT
ejpam-180	721	22	and	and	CCONJ
ejpam-180	721	23	(	(	PUNCT
ejpam-180	721	24	4.14	4.14	NUM
ejpam-180	721	25	)	)	PUNCT
ejpam-180	721	26	holds	hold	VERB
ejpam-180	721	27	:	:	PUNCT
ejpam-180	721	28	from	from	ADP
ejpam-180	721	29	(	(	PUNCT
ejpam-180	721	30	4.18	4.18	NUM
ejpam-180	721	31	)	)	PUNCT
ejpam-180	721	32	,	,	PUNCT
ejpam-180	721	33	it	it	PRON
ejpam-180	721	34	implies	imply	VERB
ejpam-180	721	35	∫	∫	PROPN
ejpam-180	722	1	i	i	PRON
ejpam-180	722	2	ȳ	ȳ	PROPN
ejpam-180	722	3	(	(	PUNCT
ejpam-180	722	4	t	t	PROPN
ejpam-180	722	5	)	)	PUNCT
ejpam-180	722	6	t	t	PROPN
ejpam-180	722	7	g	g	PROPN
ejpam-180	722	8	�	�	PROPN
ejpam-180	722	9	t	t	PROPN
ejpam-180	722	10	,	,	PUNCT
ejpam-180	722	11	x̄	x̄	PROPN
ejpam-180	722	12	,	,	PUNCT
ejpam-180	722	13	˙̄x	˙̄x	PUNCT
ejpam-180	722	14	,	,	PUNCT
ejpam-180	722	15	¨̄x	¨̄x	PRON
ejpam-180	722	16	�	�	PROPN
ejpam-180	722	17	d	d	PROPN
ejpam-180	722	18	t	t	PROPN
ejpam-180	722	19	=	=	SYM
ejpam-180	722	20	0	0	NUM
ejpam-180	722	21	(	(	PUNCT
ejpam-180	722	22	5.11	5.11	NUM
ejpam-180	722	23	)	)	PUNCT
ejpam-180	722	24	now	now	ADV
ejpam-180	722	25	from	from	ADP
ejpam-180	722	26	(	(	PUNCT
ejpam-180	722	27	4.17	4.17	NUM
ejpam-180	722	28	)	)	PUNCT
ejpam-180	722	29	,	,	PUNCT
ejpam-180	722	30	(	(	PUNCT
ejpam-180	722	31	5.11	5.11	NUM
ejpam-180	722	32	)	)	PUNCT
ejpam-180	722	33	,	,	PUNCT
ejpam-180	722	34	(	(	PUNCT
ejpam-180	722	35	4.14	4.14	NUM
ejpam-180	722	36	)	)	PUNCT
ejpam-180	722	37	and	and	CCONJ
ejpam-180	722	38	(	(	PUNCT
ejpam-180	722	39	4.20	4.20	NUM
ejpam-180	722	40	)	)	PUNCT
ejpam-180	722	41	together	together	ADV
ejpam-180	722	42	with	with	ADP
ejpam-180	722	43	λ̄	λ̄	NUM
ejpam-180	722	44	>	>	X
ejpam-180	722	45	0	0	NUM
ejpam-180	722	46	,	,	PUNCT
ejpam-180	722	47	it	it	PRON
ejpam-180	722	48	follows	follow	VERB
ejpam-180	722	49	that	that	SCONJ
ejpam-180	722	50	(	(	PUNCT
ejpam-180	722	51	x̄	x̄	NOUN
ejpam-180	722	52	,	,	PUNCT
ejpam-180	722	53	ū	ū	PROPN
ejpam-180	722	54	,	,	PUNCT
ejpam-180	722	55	ȳ	ȳ	PROPN
ejpam-180	722	56	,	,	PUNCT
ejpam-180	722	57	z̄1	z̄1	PROPN
ejpam-180	722	58	,	,	PUNCT
ejpam-180	722	59	.	.	PUNCT
ejpam-180	722	60	.	.	PUNCT
ejpam-180	723	1	.	.	PUNCT
ejpam-180	724	1	,	,	PUNCT
ejpam-180	724	2	z̄p	z̄p	PROPN
ejpam-180	724	3	,	,	PUNCT
ejpam-180	724	4	λ̄	λ̄	PRON
ejpam-180	724	5	)	)	PUNCT
ejpam-180	724	6	is	be	AUX
ejpam-180	724	7	feasible	feasible	ADJ
ejpam-180	724	8	.	.	PUNCT
ejpam-180	725	1	from	from	ADP
ejpam-180	725	2	the	the	DET
ejpam-180	725	3	equality	equality	NOUN
ejpam-180	725	4	of	of	ADP
ejpam-180	725	5	the	the	DET
ejpam-180	725	6	objectives	objective	NOUN
ejpam-180	725	7	of	of	ADP
ejpam-180	725	8	(	(	PUNCT
ejpam-180	725	9	vp	vp	NOUN
ejpam-180	725	10	)	)	PUNCT
ejpam-180	725	11	and	and	CCONJ
ejpam-180	725	12	(	(	PUNCT
ejpam-180	725	13	m	m	NOUN
ejpam-180	725	14	-	-	PUNCT
ejpam-180	725	15	wvd	wvd	NOUN
ejpam-180	725	16	)	)	PUNCT
ejpam-180	725	17	,	,	PUNCT
ejpam-180	725	18	along	along	ADP
ejpam-180	725	19	with	with	ADP
ejpam-180	725	20	the	the	DET
ejpam-180	725	21	hypotheses	hypothesis	NOUN
ejpam-180	725	22	of	of	ADP
ejpam-180	725	23	theorem	theorem	NOUN
ejpam-180	725	24	5.1	5.1	NUM
ejpam-180	725	25	,	,	PUNCT
ejpam-180	725	26	the	the	DET
ejpam-180	725	27	efficiency	efficiency	NOUN
ejpam-180	725	28	of	of	ADP
ejpam-180	725	29	�	�	PROPN
ejpam-180	725	30	x̄	x̄	PROPN
ejpam-180	725	31	,	,	PUNCT
ejpam-180	725	32	ū	ū	NOUN
ejpam-180	725	33	,	,	PUNCT
ejpam-180	725	34	ȳ	ȳ	PROPN
ejpam-180	725	35	,	,	PUNCT
ejpam-180	725	36	z̄1	z̄1	NUM
ejpam-180	725	37	,	,	PUNCT
ejpam-180	725	38	.	.	PUNCT
ejpam-180	725	39	.	.	PUNCT
ejpam-180	726	1	.	.	PUNCT
ejpam-180	727	1	,	,	PUNCT
ejpam-180	727	2	z̄p	z̄p	PROPN
ejpam-180	727	3	,	,	PUNCT
ejpam-180	727	4	λ̄	λ̄	PRON
ejpam-180	727	5	�	�	PROPN
ejpam-180	727	6	follows	follow	VERB
ejpam-180	727	7	.	.	PUNCT
ejpam-180	728	1	this	this	PRON
ejpam-180	728	2	completes	complete	VERB
ejpam-180	728	3	the	the	DET
ejpam-180	728	4	proof	proof	NOUN
ejpam-180	728	5	.	.	PUNCT
ejpam-180	729	1	(	(	PUNCT
ejpam-180	729	2	m	m	NOUN
ejpam-180	729	3	-	-	PUNCT
ejpam-180	729	4	wvd	wvd	NOUN
ejpam-180	729	5	)	)	PUNCT
ejpam-180	729	6	may	may	AUX
ejpam-180	729	7	be	be	AUX
ejpam-180	729	8	rewritten	rewrite	VERB
ejpam-180	729	9	in	in	ADP
ejpam-180	729	10	the	the	DET
ejpam-180	729	11	following	follow	VERB
ejpam-180	729	12	form	form	NOUN
ejpam-180	729	13	:	:	PUNCT
ejpam-180	729	14	minimize	minimize	VERB
ejpam-180	729	15	�	�	PROPN
ejpam-180	729	16	−	−	PROPN
ejpam-180	730	1	∫	∫	PROPN
ejpam-180	731	1	i	i	PRON
ejpam-180	731	2	�	�	PROPN
ejpam-180	731	3	f	f	PROPN
ejpam-180	731	4	1	1	NUM
ejpam-180	731	5	(	(	PUNCT
ejpam-180	731	6	t	t	PROPN
ejpam-180	731	7	,	,	PUNCT
ejpam-180	731	8	x	x	X
ejpam-180	731	9	,	,	PUNCT
ejpam-180	731	10	ẋ	ẋ	PROPN
ejpam-180	731	11	,	,	PUNCT
ejpam-180	731	12	ẍ	ẍ	X
ejpam-180	731	13	)	)	PUNCT
ejpam-180	732	1	+	+	CCONJ
ejpam-180	732	2	u	u	PROPN
ejpam-180	732	3	(	(	PUNCT
ejpam-180	732	4	t	t	PROPN
ejpam-180	732	5	)	)	PUNCT
ejpam-180	732	6	t	t	PROPN
ejpam-180	732	7	b1	b1	PROPN
ejpam-180	732	8	(	(	PUNCT
ejpam-180	732	9	t	t	NOUN
ejpam-180	732	10	)	)	PUNCT
ejpam-180	732	11	z1	z1	PROPN
ejpam-180	732	12	(	(	PUNCT
ejpam-180	732	13	t	t	PROPN
ejpam-180	732	14	)	)	PUNCT
ejpam-180	732	15	�	�	PROPN
ejpam-180	732	16	d	d	PROPN
ejpam-180	732	17	t	t	PROPN
ejpam-180	732	18	,	,	PUNCT
ejpam-180	732	19	.	.	PUNCT
ejpam-180	732	20	.	.	PUNCT
ejpam-180	732	21	.	.	PUNCT
ejpam-180	733	1	,	,	PUNCT
ejpam-180	733	2	∫	∫	PROPN
ejpam-180	734	1	i	i	PRON
ejpam-180	734	2	−	−	PROPN
ejpam-180	734	3	�	�	PROPN
ejpam-180	734	4	f	f	PROPN
ejpam-180	734	5	p	p	PROPN
ejpam-180	734	6	(	(	PUNCT
ejpam-180	734	7	t	t	PROPN
ejpam-180	734	8	,	,	PUNCT
ejpam-180	734	9	x	x	X
ejpam-180	734	10	,	,	PUNCT
ejpam-180	734	11	ẋ	ẋ	PROPN
ejpam-180	734	12	,	,	PUNCT
ejpam-180	734	13	ẍ	ẍ	X
ejpam-180	734	14	)	)	PUNCT
ejpam-180	735	1	+	+	CCONJ
ejpam-180	735	2	u	u	PROPN
ejpam-180	735	3	(	(	PUNCT
ejpam-180	735	4	t	t	PROPN
ejpam-180	735	5	)	)	PUNCT
ejpam-180	735	6	t	t	PROPN
ejpam-180	735	7	bp	bp	PROPN
ejpam-180	735	8	(	(	PUNCT
ejpam-180	735	9	t	t	PROPN
ejpam-180	735	10	)	)	PUNCT
ejpam-180	735	11	zp	zp	PROPN
ejpam-180	735	12	(	(	PUNCT
ejpam-180	735	13	t	t	PROPN
ejpam-180	735	14	)	)	PUNCT
ejpam-180	735	15	�	�	PROPN
ejpam-180	735	16	d	d	PROPN
ejpam-180	735	17	t	t	PROPN
ejpam-180	735	18	�	�	PROPN
ejpam-180	735	19	subject	subject	ADJ
ejpam-180	735	20	to	to	ADP
ejpam-180	735	21	x	x	PROPN
ejpam-180	735	22	(	(	PUNCT
ejpam-180	735	23	a	a	X
ejpam-180	735	24	)	)	PUNCT
ejpam-180	735	25	=	=	PUNCT
ejpam-180	736	1	0=	0=	PUNCT
ejpam-180	736	2	x	x	X
ejpam-180	736	3	(	(	PUNCT
ejpam-180	736	4	b	b	NOUN
ejpam-180	736	5	)	)	PUNCT
ejpam-180	736	6	ẋ	ẋ	PROPN
ejpam-180	737	1	(	(	PUNCT
ejpam-180	737	2	a	a	X
ejpam-180	737	3	)	)	PUNCT
ejpam-180	737	4	=	=	SYM
ejpam-180	737	5	0=	0=	NUM
ejpam-180	738	1	ẋ	ẋ	PROPN
ejpam-180	738	2	(	(	PUNCT
ejpam-180	738	3	b	b	X
ejpam-180	738	4	)	)	PUNCT
ejpam-180	738	5	θ	θ	PROPN
ejpam-180	738	6	�	�	PROPN
ejpam-180	738	7	t	t	PROPN
ejpam-180	738	8	,	,	PUNCT
ejpam-180	738	9	x	x	X
ejpam-180	738	10	,	,	PUNCT
ejpam-180	738	11	ẋ	ẋ	PROPN
ejpam-180	738	12	,	,	PUNCT
ejpam-180	738	13	ẍ	ẍ	X
ejpam-180	738	14	,	,	PUNCT
ejpam-180	738	15	...	...	PUNCT
ejpam-180	739	1	x	x	X
ejpam-180	739	2	,	,	PUNCT
ejpam-180	739	3	y	y	PROPN
ejpam-180	739	4	,	,	PUNCT
ejpam-180	739	5	ẏ	ẏ	PROPN
ejpam-180	739	6	,	,	PUNCT
ejpam-180	739	7	ÿ	ÿ	PROPN
ejpam-180	739	8	,	,	PUNCT
ejpam-180	739	9	λ	λ	X
ejpam-180	739	10	�	�	PROPN
ejpam-180	739	11	=	=	SYM
ejpam-180	739	12	0	0	NUM
ejpam-180	739	13	m	m	VERB
ejpam-180	739	14	∑	∑	VERB
ejpam-180	740	1	j=1	j=1	ADJ
ejpam-180	740	2	∫	∫	PROPN
ejpam-180	741	1	i	i	PRON
ejpam-180	741	2	y	y	PROPN
ejpam-180	741	3	j	j	PROPN
ejpam-180	741	4	(	(	PUNCT
ejpam-180	741	5	t	t	PROPN
ejpam-180	741	6	)	)	PUNCT
ejpam-180	741	7	g	g	PROPN
ejpam-180	741	8	j	j	PROPN
ejpam-180	741	9	(	(	PUNCT
ejpam-180	741	10	t	t	PROPN
ejpam-180	741	11	,	,	PUNCT
ejpam-180	741	12	x	x	X
ejpam-180	741	13	,	,	PUNCT
ejpam-180	741	14	ẋ	ẋ	PROPN
ejpam-180	741	15	,	,	PUNCT
ejpam-180	741	16	ẍ	ẍ	X
ejpam-180	741	17	)	)	PUNCT
ejpam-180	742	1	d	d	NOUN
ejpam-180	742	2	t	t	PROPN
ejpam-180	742	3	≧	≧	NOUN
ejpam-180	742	4	0	0	NUM
ejpam-180	742	5	,	,	PUNCT
ejpam-180	742	6	t	t	PROPN
ejpam-180	742	7	∈	∈	PROPN
ejpam-180	743	1	i	i	PRON
ejpam-180	743	2	z̄	z̄	VERB
ejpam-180	743	3	i	i	PRON
ejpam-180	743	4	(	(	PUNCT
ejpam-180	743	5	t	t	PROPN
ejpam-180	743	6	)	)	PUNCT
ejpam-180	743	7	t	t	PROPN
ejpam-180	744	1	b	b	PROPN
ejpam-180	744	2	i	i	PROPN
ejpam-180	744	3	(	(	PUNCT
ejpam-180	744	4	t	t	PROPN
ejpam-180	744	5	)	)	PUNCT
ejpam-180	744	6	z̄	z̄	PROPN
ejpam-180	745	1	i	i	PRON
ejpam-180	745	2	(	(	PUNCT
ejpam-180	745	3	t)≦	t)≦	X
ejpam-180	745	4	1	1	NUM
ejpam-180	745	5	,	,	PUNCT
ejpam-180	745	6	t	t	PROPN
ejpam-180	745	7	∈	∈	PROPN
ejpam-180	746	1	i	i	PRON
ejpam-180	746	2	,	,	PUNCT
ejpam-180	746	3	i	i	PROPN
ejpam-180	746	4	∈	∈	PROPN
ejpam-180	746	5	p	p	PROPN
ejpam-180	746	6	i.	i.	PROPN
ejpam-180	746	7	husain	husain	PROPN
ejpam-180	746	8	,	,	PUNCT
ejpam-180	746	9	a.	a.	PROPN
ejpam-180	746	10	ahmed	ahmed	PROPN
ejpam-180	746	11	,	,	PUNCT
ejpam-180	746	12	and	and	CCONJ
ejpam-180	746	13	g.	g.	PROPN
ejpam-180	746	14	rumana	rumana	PROPN
ejpam-180	746	15	/	/	SYM
ejpam-180	746	16	eur	eur	PROPN
ejpam-180	746	17	.	.	PUNCT
ejpam-180	747	1	j.	j.	PROPN
ejpam-180	747	2	pure	pure	PROPN
ejpam-180	747	3	appl	appl	PROPN
ejpam-180	747	4	.	.	PROPN
ejpam-180	747	5	math	math	PROPN
ejpam-180	747	6	,	,	PUNCT
ejpam-180	747	7	2	2	NUM
ejpam-180	747	8	(	(	PUNCT
ejpam-180	747	9	2009	2009	NUM
ejpam-180	747	10	)	)	PUNCT
ejpam-180	747	11	,	,	PUNCT
ejpam-180	747	12	(	(	PUNCT
ejpam-180	747	13	372	372	NUM
ejpam-180	747	14	-	-	SYM
ejpam-180	747	15	400	400	NUM
ejpam-180	747	16	)	)	PUNCT
ejpam-180	747	17	393	393	NUM
ejpam-180	747	18	λ	λ	X
ejpam-180	747	19	>	>	X
ejpam-180	747	20	0	0	PROPN
ejpam-180	747	21	,	,	PUNCT
ejpam-180	747	22	y	y	PROPN
ejpam-180	747	23	(	(	PUNCT
ejpam-180	747	24	t)≧	t)≧	PROPN
ejpam-180	747	25	0	0	NUM
ejpam-180	747	26	,	,	PUNCT
ejpam-180	747	27	t	t	PROPN
ejpam-180	747	28	∈	∈	PROPN
ejpam-180	747	29	i	i	PRON
ejpam-180	747	30	theorem	theorem	VERB
ejpam-180	747	31	5.3	5.3	NUM
ejpam-180	747	32	(	(	PUNCT
ejpam-180	747	33	converse	converse	NOUN
ejpam-180	747	34	duality	duality	NOUN
ejpam-180	747	35	)	)	PUNCT
ejpam-180	747	36	.	.	PUNCT
ejpam-180	748	1	let	let	VERB
ejpam-180	748	2	(	(	PUNCT
ejpam-180	748	3	x̄	x̄	X
ejpam-180	748	4	,	,	PUNCT
ejpam-180	748	5	ū	ū	PROPN
ejpam-180	748	6	,	,	PUNCT
ejpam-180	748	7	ȳ	ȳ	PROPN
ejpam-180	748	8	,	,	PUNCT
ejpam-180	748	9	z̄1	z̄1	PROPN
ejpam-180	748	10	,	,	PUNCT
ejpam-180	748	11	.	.	PUNCT
ejpam-180	748	12	.	.	PUNCT
ejpam-180	748	13	.	.	PUNCT
ejpam-180	749	1	,	,	PUNCT
ejpam-180	749	2	z̄p	z̄p	PROPN
ejpam-180	749	3	,	,	PUNCT
ejpam-180	749	4	λ̄	λ̄	PRON
ejpam-180	749	5	)	)	PUNCT
ejpam-180	749	6	be	be	AUX
ejpam-180	749	7	an	an	DET
ejpam-180	749	8	efficient	efficient	ADJ
ejpam-180	749	9	solution	solution	NOUN
ejpam-180	749	10	for	for	ADP
ejpam-180	749	11	(	(	PUNCT
ejpam-180	749	12	m	m	PROPN
ejpam-180	749	13	-	-	PUNCT
ejpam-180	749	14	wdp	wdp	PROPN
ejpam-180	749	15	)	)	PUNCT
ejpam-180	749	16	.	.	PUNCT
ejpam-180	750	1	assume	assume	VERB
ejpam-180	750	2	that	that	SCONJ
ejpam-180	750	3	(	(	PUNCT
ejpam-180	750	4	a1	a1	PROPN
ejpam-180	750	5	)	)	PUNCT
ejpam-180	750	6	the	the	DET
ejpam-180	750	7	frèchèt	frèchèt	NOUN
ejpam-180	750	8	derivative	derivative	NOUN
ejpam-180	750	9	ψ′	ψ′	VERB
ejpam-180	750	10	has	have	VERB
ejpam-180	750	11	a	a	DET
ejpam-180	750	12	(	(	PUNCT
ejpam-180	750	13	weak∗	weak∗	NOUN
ejpam-180	750	14	)	)	PUNCT
ejpam-180	750	15	closed	closed	ADJ
ejpam-180	750	16	range	range	NOUN
ejpam-180	750	17	,	,	PUNCT
ejpam-180	750	18	(	(	PUNCT
ejpam-180	750	19	a2	a2	PROPN
ejpam-180	750	20	)	)	PUNCT
ejpam-180	750	21	f	f	PROPN
ejpam-180	750	22	and	and	CCONJ
ejpam-180	750	23	g	g	PROPN
ejpam-180	750	24	are	be	AUX
ejpam-180	750	25	twice	twice	ADV
ejpam-180	750	26	continuously	continuously	ADV
ejpam-180	750	27	differentiable	differentiable	ADJ
ejpam-180	750	28	,	,	PUNCT
ejpam-180	750	29	(	(	PUNCT
ejpam-180	750	30	a3	a3	NOUN
ejpam-180	750	31	)	)	PUNCT
ejpam-180	751	1	f	f	NOUN
ejpam-180	752	1	i	i	PRON
ejpam-180	752	2	x	x	X
ejpam-180	752	3	(	(	PUNCT
ejpam-180	752	4	t	t	NOUN
ejpam-180	752	5	,	,	PUNCT
ejpam-180	752	6	x	x	X
ejpam-180	752	7	,	,	PUNCT
ejpam-180	752	8	ẋ	ẋ	PROPN
ejpam-180	752	9	,	,	PUNCT
ejpam-180	752	10	ẍ)+	ẍ)+	PROPN
ejpam-180	752	11	b	b	PROPN
ejpam-180	752	12	i	i	PROPN
ejpam-180	752	13	(	(	PUNCT
ejpam-180	752	14	t	t	PROPN
ejpam-180	752	15	)	)	PUNCT
ejpam-180	752	16	z	z	NOUN
ejpam-180	753	1	i	i	PRON
ejpam-180	753	2	(	(	PUNCT
ejpam-180	753	3	t)−	t)−	PROPN
ejpam-180	754	1	d	d	X
ejpam-180	754	2	f	f	X
ejpam-180	755	1	i	i	PRON
ejpam-180	755	2	ẋ	ẋ	PROPN
ejpam-180	756	1	(	(	PUNCT
ejpam-180	756	2	t	t	PROPN
ejpam-180	756	3	,	,	PUNCT
ejpam-180	756	4	x	x	X
ejpam-180	756	5	,	,	PUNCT
ejpam-180	756	6	ẋ	ẋ	PROPN
ejpam-180	756	7	,	,	PUNCT
ejpam-180	756	8	ẍ)+	ẍ)+	PROPN
ejpam-180	756	9	d2	d2	PROPN
ejpam-180	757	1	f	f	PROPN
ejpam-180	758	1	i	i	PRON
ejpam-180	758	2	ẋ	ẋ	PROPN
ejpam-180	759	1	(	(	PUNCT
ejpam-180	759	2	t	t	PROPN
ejpam-180	759	3	,	,	PUNCT
ejpam-180	759	4	x	x	X
ejpam-180	759	5	,	,	PUNCT
ejpam-180	759	6	ẋ	ẋ	PROPN
ejpam-180	759	7	,	,	PUNCT
ejpam-180	759	8	ẍ	ẍ	PROPN
ejpam-180	759	9	)	)	PUNCT
ejpam-180	759	10	,	,	PUNCT
ejpam-180	759	11	i	i	PRON
ejpam-180	759	12	∈	∈	PROPN
ejpam-180	759	13	�	�	PROPN
ejpam-180	759	14	1	1	NUM
ejpam-180	759	15	,	,	PUNCT
ejpam-180	759	16	2	2	NUM
ejpam-180	759	17	,	,	PUNCT
ejpam-180	759	18	.	.	PUNCT
ejpam-180	759	19	.	.	PUNCT
ejpam-180	759	20	.	.	PUNCT
ejpam-180	760	1	,	,	PUNCT
ejpam-180	760	2	p	p	NOUN
ejpam-180	760	3	are	be	AUX
ejpam-180	760	4	linearly	linearly	ADV
ejpam-180	760	5	independent	independent	ADJ
ejpam-180	760	6	and	and	CCONJ
ejpam-180	760	7	(	(	PUNCT
ejpam-180	760	8	a4	a4	NOUN
ejpam-180	760	9	)	)	PUNCT
ejpam-180	760	10	�	�	PROPN
ejpam-180	760	11	β	β	X
ejpam-180	760	12	(	(	PUNCT
ejpam-180	760	13	t	t	PROPN
ejpam-180	760	14	)	)	PUNCT
ejpam-180	760	15	t	t	PROPN
ejpam-180	760	16	θx	θx	NUM
ejpam-180	760	17	−	−	PROPN
ejpam-180	760	18	dβ	dβ	PROPN
ejpam-180	760	19	(	(	PUNCT
ejpam-180	760	20	t	t	NOUN
ejpam-180	760	21	)	)	PUNCT
ejpam-180	760	22	t	t	PROPN
ejpam-180	760	23	θ	θ	PROPN
ejpam-180	760	24	ẋ	ẋ	PROPN
ejpam-180	761	1	+	+	PUNCT
ejpam-180	761	2	d2β	d2β	PROPN
ejpam-180	761	3	(	(	PUNCT
ejpam-180	761	4	t	t	PROPN
ejpam-180	761	5	)	)	PUNCT
ejpam-180	761	6	t	t	PROPN
ejpam-180	761	7	θ	θ	PROPN
ejpam-180	761	8	ẍ	ẍ	X
ejpam-180	761	9	�	�	PROPN
ejpam-180	761	10	β	β	PROPN
ejpam-180	761	11	(	(	PUNCT
ejpam-180	761	12	t	t	PROPN
ejpam-180	761	13	)	)	PUNCT
ejpam-180	761	14	=	=	SYM
ejpam-180	761	15	0,⇒	0,⇒	PROPN
ejpam-180	761	16	β	β	X
ejpam-180	761	17	(	(	PUNCT
ejpam-180	761	18	t	t	PROPN
ejpam-180	761	19	)	)	PUNCT
ejpam-180	762	1	=	=	SYM
ejpam-180	762	2	0	0	NUM
ejpam-180	762	3	,	,	PUNCT
ejpam-180	762	4	t	t	PROPN
ejpam-180	762	5	∈	∈	PROPN
ejpam-180	762	6	i	i	PRON
ejpam-180	762	7	further	far	ADV
ejpam-180	762	8	,	,	PUNCT
ejpam-180	762	9	if	if	SCONJ
ejpam-180	762	10	the	the	DET
ejpam-180	762	11	hypotheses	hypothesis	NOUN
ejpam-180	762	12	of	of	ADP
ejpam-180	762	13	theorem	theorem	ADJ
ejpam-180	762	14	5.1	5.1	NUM
ejpam-180	762	15	are	be	AUX
ejpam-180	762	16	met	meet	VERB
ejpam-180	762	17	,	,	PUNCT
ejpam-180	762	18	then	then	ADV
ejpam-180	762	19	x̄	x̄	PROPN
ejpam-180	762	20	is	be	AUX
ejpam-180	762	21	an	an	DET
ejpam-180	762	22	efficient	efficient	ADJ
ejpam-180	762	23	solution	solution	NOUN
ejpam-180	762	24	of	of	ADP
ejpam-180	762	25	(	(	PUNCT
ejpam-180	762	26	vp	vp	NOUN
ejpam-180	762	27	)	)	PUNCT
ejpam-180	762	28	proof	proof	NOUN
ejpam-180	762	29	.	.	PUNCT
ejpam-180	763	1	since	since	SCONJ
ejpam-180	763	2	�	�	PROPN
ejpam-180	763	3	x̄	x̄	PROPN
ejpam-180	763	4	,	,	PUNCT
ejpam-180	763	5	ū	ū	NOUN
ejpam-180	763	6	,	,	PUNCT
ejpam-180	763	7	ȳ	ȳ	PROPN
ejpam-180	763	8	,	,	PUNCT
ejpam-180	763	9	z̄1	z̄1	NUM
ejpam-180	763	10	,	,	PUNCT
ejpam-180	763	11	.	.	PUNCT
ejpam-180	763	12	.	.	PUNCT
ejpam-180	763	13	.	.	PUNCT
ejpam-180	764	1	,	,	PUNCT
ejpam-180	764	2	z̄p	z̄p	PROPN
ejpam-180	764	3	,	,	PUNCT
ejpam-180	764	4	λ̄	λ̄	ADP
ejpam-180	764	5	�	�	PROPN
ejpam-180	764	6	with	with	ADP
ejpam-180	764	7	ψ′	ψ′	PUNCT
ejpam-180	764	8	having	have	VERB
ejpam-180	764	9	a	a	DET
ejpam-180	764	10	(	(	PUNCT
ejpam-180	764	11	weak∗	weak∗	NOUN
ejpam-180	764	12	)	)	PUNCT
ejpam-180	764	13	closed	closed	ADJ
ejpam-180	764	14	range	range	NOUN
ejpam-180	764	15	,	,	PUNCT
ejpam-180	764	16	is	be	AUX
ejpam-180	764	17	an	an	DET
ejpam-180	764	18	efficient	efficient	ADJ
ejpam-180	764	19	solution	solution	NOUN
ejpam-180	764	20	of	of	ADP
ejpam-180	764	21	(	(	PUNCT
ejpam-180	764	22	m	m	PROPN
ejpam-180	764	23	-	-	PUNCT
ejpam-180	764	24	wdp	wdp	PROPN
ejpam-180	764	25	)	)	PUNCT
ejpam-180	764	26	,	,	PUNCT
ejpam-180	764	27	then	then	ADV
ejpam-180	764	28	there	there	PRON
ejpam-180	764	29	exist	exist	VERB
ejpam-180	764	30	α	α	PRON
ejpam-180	764	31	∈	∈	PROPN
ejpam-180	764	32	rp	rp	NOUN
ejpam-180	764	33	,	,	PUNCT
ejpam-180	764	34	η	η	PROPN
ejpam-180	764	35	∈	∈	PROPN
ejpam-180	764	36	rp	rp	NOUN
ejpam-180	764	37	,	,	PUNCT
ejpam-180	764	38	γ	γ	PROPN
ejpam-180	764	39	∈	∈	PROPN
ejpam-180	764	40	r	r	PROPN
ejpam-180	764	41	,	,	PUNCT
ejpam-180	764	42	δ	δ	PROPN
ejpam-180	764	43	∈	∈	PROPN
ejpam-180	764	44	r	r	PROPN
ejpam-180	764	45	,	,	PUNCT
ejpam-180	764	46	ξ	ξ	PROPN
ejpam-180	764	47	∈	∈	PROPN
ejpam-180	764	48	rm	rm	NOUN
ejpam-180	764	49	and	and	CCONJ
ejpam-180	764	50	piecewise	piecewise	PROPN
ejpam-180	764	51	smooth	smooth	ADJ
ejpam-180	764	52	β(t	β(t	PROPN
ejpam-180	764	53	)	)	PUNCT
ejpam-180	764	54	:	:	PUNCT
ejpam-180	765	1	i	i	PRON
ejpam-180	765	2	→	→	SYM
ejpam-180	765	3	rn	rn	PROPN
ejpam-180	765	4	and	and	CCONJ
ejpam-180	765	5	µ(t	µ(t	ADJ
ejpam-180	765	6	)	)	PUNCT
ejpam-180	765	7	:	:	PUNCT
ejpam-180	766	1	i	i	PRON
ejpam-180	766	2	→	→	SYM
ejpam-180	766	3	rm	rm	NOUN
ejpam-180	766	4	such	such	ADJ
ejpam-180	766	5	that	that	SCONJ
ejpam-180	766	6	the	the	DET
ejpam-180	766	7	following	follow	VERB
ejpam-180	766	8	fritz	fritz	PROPN
ejpam-180	766	9	-	-	PUNCT
ejpam-180	766	10	john	john	PROPN
ejpam-180	766	11	optimality	optimality	NOUN
ejpam-180	766	12	conditions	condition	NOUN
ejpam-180	766	13	[	[	X
ejpam-180	766	14	8	8	X
ejpam-180	766	15	]	]	PUNCT
ejpam-180	766	16	holds	hold	VERB
ejpam-180	766	17	−	−	PROPN
ejpam-180	766	18	p	p	PROPN
ejpam-180	766	19	∑	∑	PROPN
ejpam-180	766	20	i=1	i=1	PROPN
ejpam-180	766	21	αi	αi	PROPN
ejpam-180	766	22	�	�	PROPN
ejpam-180	767	1	f	f	PROPN
ejpam-180	767	2	i	i	PRON
ejpam-180	767	3	x	x	X
ejpam-180	767	4	(	(	PUNCT
ejpam-180	767	5	t	t	NOUN
ejpam-180	767	6	,	,	PUNCT
ejpam-180	767	7	x	x	X
ejpam-180	767	8	,	,	PUNCT
ejpam-180	767	9	ẋ	ẋ	PROPN
ejpam-180	767	10	,	,	PUNCT
ejpam-180	767	11	ẍ	ẍ	X
ejpam-180	767	12	)	)	PUNCT
ejpam-180	768	1	+	+	CCONJ
ejpam-180	769	1	b	b	X
ejpam-180	769	2	i	i	PRON
ejpam-180	769	3	(	(	PUNCT
ejpam-180	769	4	t	t	PROPN
ejpam-180	769	5	)	)	PUNCT
ejpam-180	769	6	z	z	NOUN
ejpam-180	770	1	i	i	PRON
ejpam-180	770	2	(	(	PUNCT
ejpam-180	770	3	t)−	t)−	PROPN
ejpam-180	771	1	d	d	X
ejpam-180	771	2	f	f	X
ejpam-180	772	1	i	i	PRON
ejpam-180	772	2	ẋ	ẋ	PROPN
ejpam-180	773	1	(	(	PUNCT
ejpam-180	773	2	t	t	PROPN
ejpam-180	773	3	,	,	PUNCT
ejpam-180	773	4	x	x	X
ejpam-180	773	5	,	,	PUNCT
ejpam-180	773	6	ẋ	ẋ	PROPN
ejpam-180	773	7	,	,	PUNCT
ejpam-180	773	8	ẍ	ẍ	X
ejpam-180	773	9	)	)	PUNCT
ejpam-180	774	1	+	+	CCONJ
ejpam-180	775	1	d2	d2	PROPN
ejpam-180	775	2	f	f	PROPN
ejpam-180	775	3	i	i	PRON
ejpam-180	775	4	ẍ	ẍ	PROPN
ejpam-180	776	1	(	(	PUNCT
ejpam-180	776	2	t	t	PROPN
ejpam-180	776	3	,	,	PUNCT
ejpam-180	776	4	x	x	X
ejpam-180	776	5	,	,	PUNCT
ejpam-180	776	6	ẋ	ẋ	PROPN
ejpam-180	776	7	,	,	PUNCT
ejpam-180	776	8	ẍ	ẍ	X
ejpam-180	776	9	)	)	PUNCT
ejpam-180	776	10	�	�	PROPN
ejpam-180	776	11	−γ	−γ	NOUN
ejpam-180	776	12	�	�	PROPN
ejpam-180	776	13	y	y	PROPN
ejpam-180	776	14	(	(	PUNCT
ejpam-180	776	15	t	t	PROPN
ejpam-180	776	16	)	)	PUNCT
ejpam-180	776	17	t	t	PROPN
ejpam-180	776	18	gx	gx	PROPN
ejpam-180	776	19	(	(	PUNCT
ejpam-180	776	20	t	t	PROPN
ejpam-180	776	21	,	,	PUNCT
ejpam-180	776	22	x	x	X
ejpam-180	776	23	,	,	PUNCT
ejpam-180	776	24	ẋ	ẋ	PROPN
ejpam-180	776	25	,	,	PUNCT
ejpam-180	776	26	ẍ)−	ẍ)−	PROPN
ejpam-180	777	1	d	d	X
ejpam-180	777	2	y	y	PROPN
ejpam-180	777	3	(	(	PUNCT
ejpam-180	777	4	t	t	PROPN
ejpam-180	777	5	)	)	PUNCT
ejpam-180	777	6	t	t	PROPN
ejpam-180	777	7	g	g	PROPN
ejpam-180	777	8	ẋ	ẋ	PROPN
ejpam-180	778	1	(	(	PUNCT
ejpam-180	778	2	t	t	PROPN
ejpam-180	778	3	,	,	PUNCT
ejpam-180	778	4	x	x	X
ejpam-180	778	5	,	,	PUNCT
ejpam-180	778	6	ẋ	ẋ	PROPN
ejpam-180	778	7	,	,	PUNCT
ejpam-180	778	8	ẍ	ẍ	X
ejpam-180	778	9	)	)	PUNCT
ejpam-180	779	1	+	+	CCONJ
ejpam-180	779	2	d2	d2	PROPN
ejpam-180	779	3	y	y	PROPN
ejpam-180	779	4	(	(	PUNCT
ejpam-180	779	5	t	t	PROPN
ejpam-180	779	6	)	)	PUNCT
ejpam-180	779	7	t	t	PROPN
ejpam-180	779	8	g	g	PROPN
ejpam-180	779	9	ẍ	ẍ	PROPN
ejpam-180	780	1	(	(	PUNCT
ejpam-180	780	2	t	t	PROPN
ejpam-180	780	3	,	,	PUNCT
ejpam-180	780	4	x	x	X
ejpam-180	780	5	,	,	PUNCT
ejpam-180	780	6	ẋ	ẋ	PROPN
ejpam-180	780	7	,	,	PUNCT
ejpam-180	780	8	ẍ	ẍ	X
ejpam-180	780	9	)	)	PUNCT
ejpam-180	780	10	�	�	PROPN
ejpam-180	781	1	+	+	PROPN
ejpam-180	781	2	β	β	X
ejpam-180	781	3	(	(	PUNCT
ejpam-180	781	4	t	t	PROPN
ejpam-180	781	5	)	)	PUNCT
ejpam-180	781	6	t	t	PROPN
ejpam-180	781	7	θx	θx	NUM
ejpam-180	781	8	−	−	PROPN
ejpam-180	781	9	dβ	dβ	PROPN
ejpam-180	781	10	(	(	PUNCT
ejpam-180	781	11	t	t	NOUN
ejpam-180	781	12	)	)	PUNCT
ejpam-180	781	13	t	t	PROPN
ejpam-180	781	14	θ	θ	PROPN
ejpam-180	781	15	ẋ	ẋ	PROPN
ejpam-180	782	1	+	+	PUNCT
ejpam-180	782	2	d2β	d2β	PROPN
ejpam-180	782	3	(	(	PUNCT
ejpam-180	782	4	t	t	PROPN
ejpam-180	782	5	)	)	PUNCT
ejpam-180	782	6	t	t	PROPN
ejpam-180	782	7	θ	θ	PROPN
ejpam-180	782	8	ẍ	ẍ	PUNCT
ejpam-180	783	1	−	−	PROPN
ejpam-180	783	2	d3β	d3β	NOUN
ejpam-180	783	3	(	(	PUNCT
ejpam-180	783	4	t	t	NOUN
ejpam-180	783	5	)	)	PUNCT
ejpam-180	783	6	t	t	PROPN
ejpam-180	783	7	θ	θ	PROPN
ejpam-180	783	8	...	...	PUNCT
ejpam-180	783	9	x	x	SYM
ejpam-180	783	10	=	=	SYM
ejpam-180	783	11	0	0	NUM
ejpam-180	783	12	,	,	PUNCT
ejpam-180	783	13	t	t	PROPN
ejpam-180	783	14	∈	∈	PROPN
ejpam-180	784	1	i	i	PRON
ejpam-180	784	2	(	(	PUNCT
ejpam-180	784	3	5.12	5.12	NUM
ejpam-180	784	4	)	)	PUNCT
ejpam-180	784	5	−γg	−γg	X
ejpam-180	784	6	j	j	PROPN
ejpam-180	784	7	(	(	PUNCT
ejpam-180	784	8	t	t	PROPN
ejpam-180	784	9	,	,	PUNCT
ejpam-180	784	10	x	x	X
ejpam-180	784	11	,	,	PUNCT
ejpam-180	784	12	ẋ	ẋ	PROPN
ejpam-180	784	13	,	,	PUNCT
ejpam-180	784	14	ẍ	ẍ	X
ejpam-180	784	15	)	)	PUNCT
ejpam-180	785	1	+	+	CCONJ
ejpam-180	785	2	β	β	X
ejpam-180	785	3	(	(	PUNCT
ejpam-180	785	4	t	t	PROPN
ejpam-180	785	5	)	)	PUNCT
ejpam-180	785	6	t	t	PROPN
ejpam-180	785	7	θy	θy	X
ejpam-180	785	8	j	j	PROPN
ejpam-180	786	1	−	−	NOUN
ejpam-180	786	2	dβ	dβ	PROPN
ejpam-180	786	3	(	(	PUNCT
ejpam-180	786	4	t	t	NOUN
ejpam-180	786	5	)	)	PUNCT
ejpam-180	786	6	t	t	NOUN
ejpam-180	786	7	θ	θ	NOUN
ejpam-180	786	8	ẏ	ẏ	PROPN
ejpam-180	786	9	j	j	PROPN
ejpam-180	786	10	+	+	CCONJ
ejpam-180	786	11	d2β	d2β	PROPN
ejpam-180	786	12	(	(	PUNCT
ejpam-180	786	13	t	t	PROPN
ejpam-180	786	14	)	)	PUNCT
ejpam-180	786	15	t	t	PROPN
ejpam-180	786	16	θ	θ	PROPN
ejpam-180	786	17	ÿ	ÿ	PROPN
ejpam-180	787	1	j	j	PROPN
ejpam-180	787	2	−µ	−µ	PROPN
ejpam-180	787	3	j	j	PROPN
ejpam-180	787	4	(	(	PUNCT
ejpam-180	787	5	t	t	PROPN
ejpam-180	787	6	)	)	PUNCT
ejpam-180	787	7	=	=	SYM
ejpam-180	787	8	0	0	NUM
ejpam-180	787	9	,	,	PUNCT
ejpam-180	787	10	t	t	PROPN
ejpam-180	787	11	∈	∈	PROPN
ejpam-180	788	1	i	i	PRON
ejpam-180	788	2	(	(	PUNCT
ejpam-180	788	3	5.13	5.13	NUM
ejpam-180	788	4	)	)	PUNCT
ejpam-180	788	5	for	for	ADP
ejpam-180	788	6	j	j	PROPN
ejpam-180	788	7	=	=	SYM
ejpam-180	788	8	1	1	NUM
ejpam-180	788	9	,	,	PUNCT
ejpam-180	788	10	2	2	NUM
ejpam-180	788	11	,	,	PUNCT
ejpam-180	788	12	.	.	PUNCT
ejpam-180	788	13	.	.	PUNCT
ejpam-180	788	14	.	.	PUNCT
ejpam-180	789	1	,	,	PUNCT
ejpam-180	789	2	m.	m.	NOUN
ejpam-180	789	3	−αi	−αi	NOUN
ejpam-180	789	4	x	x	X
ejpam-180	789	5	(	(	PUNCT
ejpam-180	789	6	t	t	PROPN
ejpam-180	789	7	)	)	PUNCT
ejpam-180	789	8	t	t	PROPN
ejpam-180	790	1	b	b	PROPN
ejpam-180	790	2	i	i	PROPN
ejpam-180	790	3	(	(	PUNCT
ejpam-180	790	4	t	t	PROPN
ejpam-180	790	5	)	)	PUNCT
ejpam-180	791	1	+	+	NOUN
ejpam-180	791	2	λiβ	λiβ	ADJ
ejpam-180	791	3	(	(	PUNCT
ejpam-180	791	4	t)t	t)t	X
ejpam-180	791	5	b	b	NOUN
ejpam-180	791	6	i	i	PRON
ejpam-180	791	7	(	(	PUNCT
ejpam-180	791	8	t	t	PROPN
ejpam-180	791	9	)	)	PUNCT
ejpam-180	791	10	+	+	NOUN
ejpam-180	792	1	2δib	2δib	NUM
ejpam-180	792	2	i	i	PRON
ejpam-180	792	3	(	(	PUNCT
ejpam-180	792	4	t)z	t)z	NOUN
ejpam-180	792	5	i	i	PRON
ejpam-180	792	6	(	(	PUNCT
ejpam-180	792	7	t	t	PROPN
ejpam-180	792	8	)	)	PUNCT
ejpam-180	792	9	=	=	SYM
ejpam-180	792	10	0	0	NUM
ejpam-180	792	11	(	(	PUNCT
ejpam-180	792	12	5.14	5.14	NUM
ejpam-180	792	13	)	)	PUNCT
ejpam-180	792	14	i.	i.	NOUN
ejpam-180	792	15	husain	husain	PROPN
ejpam-180	792	16	,	,	PUNCT
ejpam-180	792	17	a.	a.	PROPN
ejpam-180	792	18	ahmed	ahmed	PROPN
ejpam-180	792	19	,	,	PUNCT
ejpam-180	792	20	and	and	CCONJ
ejpam-180	792	21	g.	g.	PROPN
ejpam-180	792	22	rumana	rumana	PROPN
ejpam-180	792	23	/	/	SYM
ejpam-180	792	24	eur	eur	PROPN
ejpam-180	792	25	.	.	PUNCT
ejpam-180	793	1	j.	j.	PROPN
ejpam-180	793	2	pure	pure	PROPN
ejpam-180	793	3	appl	appl	PROPN
ejpam-180	793	4	.	.	PROPN
ejpam-180	793	5	math	math	PROPN
ejpam-180	793	6	,	,	PUNCT
ejpam-180	793	7	2	2	NUM
ejpam-180	793	8	(	(	PUNCT
ejpam-180	793	9	2009	2009	NUM
ejpam-180	793	10	)	)	PUNCT
ejpam-180	793	11	,	,	PUNCT
ejpam-180	793	12	(	(	PUNCT
ejpam-180	793	13	372	372	NUM
ejpam-180	793	14	-	-	SYM
ejpam-180	793	15	400	400	NUM
ejpam-180	793	16	)	)	PUNCT
ejpam-180	793	17	394	394	NUM
ejpam-180	793	18	�	�	NOUN
ejpam-180	793	19	f	f	NOUN
ejpam-180	793	20	i	i	NOUN
ejpam-180	793	21	x	x	X
ejpam-180	793	22	(	(	PUNCT
ejpam-180	793	23	t	t	NOUN
ejpam-180	793	24	,	,	PUNCT
ejpam-180	793	25	x	x	X
ejpam-180	793	26	,	,	PUNCT
ejpam-180	793	27	ẋ	ẋ	PROPN
ejpam-180	793	28	,	,	PUNCT
ejpam-180	793	29	ẍ	ẍ	X
ejpam-180	793	30	)	)	PUNCT
ejpam-180	794	1	+	+	CCONJ
ejpam-180	795	1	b	b	X
ejpam-180	795	2	i	i	PRON
ejpam-180	795	3	(	(	PUNCT
ejpam-180	795	4	t	t	PROPN
ejpam-180	795	5	)	)	PUNCT
ejpam-180	795	6	z	z	NOUN
ejpam-180	796	1	i	i	PRON
ejpam-180	796	2	(	(	PUNCT
ejpam-180	796	3	t)−	t)−	PROPN
ejpam-180	797	1	d	d	X
ejpam-180	797	2	f	f	X
ejpam-180	798	1	i	i	PRON
ejpam-180	798	2	ẋ	ẋ	PROPN
ejpam-180	799	1	(	(	PUNCT
ejpam-180	799	2	t	t	PROPN
ejpam-180	799	3	,	,	PUNCT
ejpam-180	799	4	x	x	X
ejpam-180	799	5	,	,	PUNCT
ejpam-180	799	6	ẋ	ẋ	PROPN
ejpam-180	799	7	,	,	PUNCT
ejpam-180	799	8	ẍ	ẍ	X
ejpam-180	799	9	)	)	PUNCT
ejpam-180	800	1	+	+	VERB
ejpam-180	800	2	d2	d2	PROPN
ejpam-180	800	3	f	f	PROPN
ejpam-180	800	4	i	i	PRON
ejpam-180	800	5	ẍ	ẍ	PROPN
ejpam-180	801	1	(	(	PUNCT
ejpam-180	801	2	t	t	PROPN
ejpam-180	801	3	,	,	PUNCT
ejpam-180	801	4	x	x	X
ejpam-180	801	5	,	,	PUNCT
ejpam-180	801	6	ẋ	ẋ	PROPN
ejpam-180	801	7	,	,	PUNCT
ejpam-180	801	8	ẍ)β	ẍ)β	PROPN
ejpam-180	801	9	(	(	PUNCT
ejpam-180	801	10	t	t	PROPN
ejpam-180	801	11	)	)	PUNCT
ejpam-180	801	12	�	�	PROPN
ejpam-180	801	13	−ηi	−ηi	PART
ejpam-180	802	1	=	=	SYM
ejpam-180	802	2	0	0	PROPN
ejpam-180	802	3	,	,	PUNCT
ejpam-180	802	4	i	i	PRON
ejpam-180	802	5	=	=	NOUN
ejpam-180	802	6	1	1	NUM
ejpam-180	802	7	,	,	PUNCT
ejpam-180	802	8	.	.	PUNCT
ejpam-180	802	9	.	.	PUNCT
ejpam-180	803	1	.	.	PUNCT
ejpam-180	804	1	,	,	PUNCT
ejpam-180	804	2	p	p	X
ejpam-180	804	3	(	(	PUNCT
ejpam-180	804	4	5.15	5.15	NUM
ejpam-180	804	5	)	)	PUNCT
ejpam-180	804	6	γ	γ	X
ejpam-180	804	7	∫	∫	PROPN
ejpam-180	805	1	i	i	PRON
ejpam-180	805	2	y	y	PROPN
ejpam-180	805	3	(	(	PUNCT
ejpam-180	805	4	t	t	PROPN
ejpam-180	805	5	)	)	PUNCT
ejpam-180	805	6	t	t	PROPN
ejpam-180	805	7	g	g	PROPN
ejpam-180	805	8	�	�	PROPN
ejpam-180	805	9	t	t	PROPN
ejpam-180	805	10	,	,	PUNCT
ejpam-180	805	11	x̄	x̄	PROPN
ejpam-180	805	12	,	,	PUNCT
ejpam-180	805	13	˙̄x	˙̄x	PUNCT
ejpam-180	805	14	,	,	PUNCT
ejpam-180	805	15	¨̄x	¨̄x	PRON
ejpam-180	805	16	�	�	PROPN
ejpam-180	805	17	d	d	PROPN
ejpam-180	805	18	t	t	PROPN
ejpam-180	805	19	=	=	SYM
ejpam-180	805	20	0	0	NUM
ejpam-180	805	21	(	(	PUNCT
ejpam-180	805	22	5.16	5.16	NUM
ejpam-180	805	23	)	)	PUNCT
ejpam-180	805	24	ηtλ	ηtλ	NOUN
ejpam-180	805	25	=	=	SYM
ejpam-180	805	26	0	0	PUNCT
ejpam-180	805	27	(	(	PUNCT
ejpam-180	805	28	5.17	5.17	NUM
ejpam-180	805	29	)	)	PUNCT
ejpam-180	805	30	µt	µt	PROPN
ejpam-180	805	31	(	(	PUNCT
ejpam-180	805	32	t	t	PROPN
ejpam-180	805	33	)	)	PUNCT
ejpam-180	805	34	ȳ	ȳ	PROPN
ejpam-180	805	35	(	(	PUNCT
ejpam-180	805	36	t	t	PROPN
ejpam-180	805	37	)	)	PUNCT
ejpam-180	805	38	=	=	SYM
ejpam-180	805	39	0	0	NUM
ejpam-180	805	40	,	,	PUNCT
ejpam-180	805	41	t	t	PROPN
ejpam-180	805	42	∈	∈	PROPN
ejpam-180	806	1	i	i	PRON
ejpam-180	806	2	(	(	PUNCT
ejpam-180	806	3	5.18	5.18	NUM
ejpam-180	806	4	)	)	PUNCT
ejpam-180	806	5	δi	δi	ADP
ejpam-180	806	6	�	�	PROPN
ejpam-180	806	7	z	z	PROPN
ejpam-180	806	8	i	i	PROPN
ejpam-180	806	9	(	(	PUNCT
ejpam-180	806	10	t	t	PROPN
ejpam-180	806	11	)	)	PUNCT
ejpam-180	806	12	t	t	PROPN
ejpam-180	806	13	b	b	PROPN
ejpam-180	806	14	i	i	PROPN
ejpam-180	806	15	(	(	PUNCT
ejpam-180	806	16	t	t	PROPN
ejpam-180	806	17	)	)	PUNCT
ejpam-180	806	18	z	z	NOUN
ejpam-180	807	1	i	i	PRON
ejpam-180	807	2	(	(	PUNCT
ejpam-180	807	3	t)−	t)−	PROPN
ejpam-180	807	4	1	1	NUM
ejpam-180	807	5	�	�	PROPN
ejpam-180	807	6	=	=	SYM
ejpam-180	807	7	0	0	NUM
ejpam-180	807	8	,	,	PUNCT
ejpam-180	807	9	t	t	PROPN
ejpam-180	807	10	∈	∈	PROPN
ejpam-180	808	1	i	i	PRON
ejpam-180	808	2	(	(	PUNCT
ejpam-180	808	3	5.19	5.19	NUM
ejpam-180	808	4	)	)	PUNCT
ejpam-180	808	5	�	�	PROPN
ejpam-180	808	6	α,µ	α,µ	PROPN
ejpam-180	808	7	(	(	PUNCT
ejpam-180	808	8	t	t	PROPN
ejpam-180	808	9	)	)	PUNCT
ejpam-180	808	10	,	,	PUNCT
ejpam-180	808	11	δ	δ	PROPN
ejpam-180	808	12	,	,	PUNCT
ejpam-180	808	13	η	η	PROPN
ejpam-180	808	14	,	,	PUNCT
ejpam-180	808	15	γ	γ	PROPN
ejpam-180	808	16	�	�	PROPN
ejpam-180	808	17	≧	≧	X
ejpam-180	808	18	0	0	NUM
ejpam-180	808	19	(	(	PUNCT
ejpam-180	808	20	5.20	5.20	NUM
ejpam-180	808	21	)	)	PUNCT
ejpam-180	808	22	�	�	PROPN
ejpam-180	808	23	α	α	PROPN
ejpam-180	808	24	,	,	PUNCT
ejpam-180	808	25	β	β	X
ejpam-180	808	26	(	(	PUNCT
ejpam-180	808	27	t	t	PROPN
ejpam-180	808	28	)	)	PUNCT
ejpam-180	808	29	,	,	PUNCT
ejpam-180	808	30	µ	µ	X
ejpam-180	808	31	(	(	PUNCT
ejpam-180	808	32	t	t	PROPN
ejpam-180	808	33	)	)	PUNCT
ejpam-180	808	34	,	,	PUNCT
ejpam-180	808	35	δ	δ	PROPN
ejpam-180	808	36	,	,	PUNCT
ejpam-180	808	37	η	η	PROPN
ejpam-180	808	38	,	,	PUNCT
ejpam-180	808	39	γ	γ	PROPN
ejpam-180	808	40	�	�	PROPN
ejpam-180	808	41	≧	≧	X
ejpam-180	808	42	0	0	NUM
ejpam-180	808	43	(	(	PUNCT
ejpam-180	808	44	5.21	5.21	NUM
ejpam-180	808	45	)	)	PUNCT
ejpam-180	808	46	since	since	SCONJ
ejpam-180	808	47	λ	λ	PROPN
ejpam-180	808	48	>	>	X
ejpam-180	808	49	0	0	NUM
ejpam-180	808	50	,	,	PUNCT
ejpam-180	808	51	(	(	PUNCT
ejpam-180	808	52	5.17	5.17	NUM
ejpam-180	808	53	)	)	PUNCT
ejpam-180	808	54	implies	imply	VERB
ejpam-180	808	55	η=	η=	ADJ
ejpam-180	808	56	0	0	NUM
ejpam-180	808	57	.	.	PUNCT
ejpam-180	809	1	consequently	consequently	ADV
ejpam-180	809	2	(	(	PUNCT
ejpam-180	809	3	5.15	5.15	NUM
ejpam-180	809	4	)	)	PUNCT
ejpam-180	809	5	implies	imply	VERB
ejpam-180	809	6	�	�	PROPN
ejpam-180	810	1	f	f	PROPN
ejpam-180	810	2	i	i	NOUN
ejpam-180	810	3	x	x	X
ejpam-180	810	4	(	(	PUNCT
ejpam-180	810	5	t	t	NOUN
ejpam-180	810	6	,	,	PUNCT
ejpam-180	810	7	x	x	X
ejpam-180	810	8	,	,	PUNCT
ejpam-180	810	9	ẋ	ẋ	PROPN
ejpam-180	810	10	,	,	PUNCT
ejpam-180	810	11	ẍ	ẍ	X
ejpam-180	810	12	)	)	PUNCT
ejpam-180	811	1	+	+	CCONJ
ejpam-180	812	1	b	b	X
ejpam-180	812	2	i	i	PRON
ejpam-180	812	3	(	(	PUNCT
ejpam-180	812	4	t)z	t)z	NOUN
ejpam-180	812	5	i	i	PRON
ejpam-180	812	6	(	(	PUNCT
ejpam-180	812	7	t)−	t)−	PROPN
ejpam-180	813	1	d	d	X
ejpam-180	813	2	f	f	X
ejpam-180	814	1	i	i	PRON
ejpam-180	814	2	ẋ	ẋ	PROPN
ejpam-180	815	1	(	(	PUNCT
ejpam-180	815	2	t	t	PROPN
ejpam-180	815	3	,	,	PUNCT
ejpam-180	815	4	x	x	X
ejpam-180	815	5	,	,	PUNCT
ejpam-180	815	6	ẋ	ẋ	PROPN
ejpam-180	815	7	,	,	PUNCT
ejpam-180	815	8	ẍ	ẍ	X
ejpam-180	815	9	)	)	PUNCT
ejpam-180	816	1	+	+	VERB
ejpam-180	816	2	d2	d2	PROPN
ejpam-180	816	3	f	f	PROPN
ejpam-180	816	4	i	i	PRON
ejpam-180	816	5	ẍ	ẍ	PROPN
ejpam-180	817	1	(	(	PUNCT
ejpam-180	817	2	t	t	PROPN
ejpam-180	817	3	,	,	PUNCT
ejpam-180	817	4	x	x	X
ejpam-180	817	5	,	,	PUNCT
ejpam-180	817	6	ẋ	ẋ	PROPN
ejpam-180	817	7	,	,	PUNCT
ejpam-180	817	8	ẍ	ẍ	X
ejpam-180	817	9	)	)	PUNCT
ejpam-180	817	10	�	�	PROPN
ejpam-180	817	11	β	β	X
ejpam-180	817	12	(	(	PUNCT
ejpam-180	817	13	t	t	PROPN
ejpam-180	817	14	)	)	PUNCT
ejpam-180	817	15	=	=	SYM
ejpam-180	818	1	0	0	NUM
ejpam-180	818	2	,	,	PUNCT
ejpam-180	818	3	i	i	PRON
ejpam-180	818	4	=	=	NOUN
ejpam-180	818	5	1	1	NUM
ejpam-180	818	6	,	,	PUNCT
ejpam-180	818	7	.	.	PUNCT
ejpam-180	818	8	.	.	PUNCT
ejpam-180	818	9	.	.	PUNCT
ejpam-180	819	1	,	,	PUNCT
ejpam-180	819	2	p	p	X
ejpam-180	819	3	(	(	PUNCT
ejpam-180	819	4	5.22	5.22	NUM
ejpam-180	819	5	)	)	PUNCT
ejpam-180	819	6	using	use	VERB
ejpam-180	819	7	the	the	DET
ejpam-180	819	8	duality	duality	NOUN
ejpam-180	819	9	constraint	constraint	NOUN
ejpam-180	819	10	of	of	ADP
ejpam-180	819	11	(	(	PUNCT
ejpam-180	819	12	m	m	NOUN
ejpam-180	819	13	-	-	PUNCT
ejpam-180	819	14	wvd	wvd	NOUN
ejpam-180	819	15	)	)	PUNCT
ejpam-180	819	16	in	in	ADP
ejpam-180	819	17	(	(	PUNCT
ejpam-180	819	18	5.12	5.12	NUM
ejpam-180	819	19	)	)	PUNCT
ejpam-180	819	20	,	,	PUNCT
ejpam-180	819	21	we	we	PRON
ejpam-180	819	22	have	have	VERB
ejpam-180	819	23	−	−	PROPN
ejpam-180	819	24	p	p	NOUN
ejpam-180	819	25	∑	∑	PUNCT
ejpam-180	819	26	i=1	i=1	PROPN
ejpam-180	819	27	�	�	PROPN
ejpam-180	819	28	αi	αi	PART
ejpam-180	819	29	−	−	NOUN
ejpam-180	819	30	γλi	γλi	X
ejpam-180	819	31	�	�	PROPN
ejpam-180	819	32	�	�	PROPN
ejpam-180	819	33	f	f	PROPN
ejpam-180	820	1	i	i	NOUN
ejpam-180	820	2	x	x	X
ejpam-180	820	3	(	(	PUNCT
ejpam-180	820	4	t	t	NOUN
ejpam-180	820	5	,	,	PUNCT
ejpam-180	820	6	x	x	X
ejpam-180	820	7	,	,	PUNCT
ejpam-180	820	8	ẋ	ẋ	PROPN
ejpam-180	820	9	,	,	PUNCT
ejpam-180	820	10	ẍ	ẍ	X
ejpam-180	820	11	)	)	PUNCT
ejpam-180	821	1	+	+	CCONJ
ejpam-180	822	1	b	b	X
ejpam-180	822	2	i	i	PRON
ejpam-180	822	3	(	(	PUNCT
ejpam-180	822	4	t	t	PROPN
ejpam-180	822	5	)	)	PUNCT
ejpam-180	822	6	z	z	NOUN
ejpam-180	823	1	i	i	PRON
ejpam-180	823	2	(	(	PUNCT
ejpam-180	823	3	t	t	PROPN
ejpam-180	823	4	)	)	PUNCT
ejpam-180	823	5	−d	−d	PROPN
ejpam-180	823	6	f	f	PROPN
ejpam-180	824	1	i	i	PRON
ejpam-180	824	2	ẋ	ẋ	PROPN
ejpam-180	825	1	(	(	PUNCT
ejpam-180	825	2	t	t	PROPN
ejpam-180	825	3	,	,	PUNCT
ejpam-180	825	4	x	x	X
ejpam-180	825	5	,	,	PUNCT
ejpam-180	825	6	ẋ	ẋ	PROPN
ejpam-180	825	7	,	,	PUNCT
ejpam-180	825	8	ẍ	ẍ	X
ejpam-180	825	9	)	)	PUNCT
ejpam-180	826	1	+	+	CCONJ
ejpam-180	827	1	d2	d2	PROPN
ejpam-180	827	2	f	f	PROPN
ejpam-180	827	3	i	i	PRON
ejpam-180	827	4	ẍ	ẍ	PROPN
ejpam-180	828	1	(	(	PUNCT
ejpam-180	828	2	t	t	PROPN
ejpam-180	828	3	,	,	PUNCT
ejpam-180	828	4	x	x	X
ejpam-180	828	5	,	,	PUNCT
ejpam-180	828	6	ẋ	ẋ	PROPN
ejpam-180	828	7	,	,	PUNCT
ejpam-180	828	8	ẍ	ẍ	X
ejpam-180	828	9	)	)	PUNCT
ejpam-180	828	10	�	�	PROPN
ejpam-180	829	1	+	+	PROPN
ejpam-180	829	2	β	β	X
ejpam-180	829	3	(	(	PUNCT
ejpam-180	829	4	t	t	PROPN
ejpam-180	829	5	)	)	PUNCT
ejpam-180	829	6	t	t	PROPN
ejpam-180	829	7	θx	θx	NUM
ejpam-180	829	8	−	−	PROPN
ejpam-180	829	9	dβ	dβ	PROPN
ejpam-180	829	10	(	(	PUNCT
ejpam-180	829	11	t	t	NOUN
ejpam-180	829	12	)	)	PUNCT
ejpam-180	829	13	t	t	PROPN
ejpam-180	829	14	θ	θ	PROPN
ejpam-180	829	15	ẋ	ẋ	PROPN
ejpam-180	830	1	+	+	PUNCT
ejpam-180	830	2	d2β	d2β	PROPN
ejpam-180	830	3	(	(	PUNCT
ejpam-180	830	4	t	t	PROPN
ejpam-180	830	5	)	)	PUNCT
ejpam-180	830	6	t	t	PROPN
ejpam-180	830	7	θ	θ	PROPN
ejpam-180	830	8	ẍ	ẍ	PUNCT
ejpam-180	831	1	−	−	PROPN
ejpam-180	831	2	d3β	d3β	NOUN
ejpam-180	831	3	(	(	PUNCT
ejpam-180	831	4	t	t	NOUN
ejpam-180	831	5	)	)	PUNCT
ejpam-180	831	6	t	t	PROPN
ejpam-180	831	7	θ	θ	PROPN
ejpam-180	831	8	...	...	PUNCT
ejpam-180	831	9	x	x	SYM
ejpam-180	831	10	=	=	SYM
ejpam-180	831	11	0	0	NUM
ejpam-180	831	12	,	,	PUNCT
ejpam-180	831	13	t	t	PROPN
ejpam-180	831	14	∈	∈	PROPN
ejpam-180	832	1	i	i	PRON
ejpam-180	832	2	(	(	PUNCT
ejpam-180	832	3	5.23	5.23	NUM
ejpam-180	832	4	)	)	PUNCT
ejpam-180	832	5	=	=	PUNCT
ejpam-180	833	1	−	−	PROPN
ejpam-180	833	2	p	p	X
ejpam-180	833	3	∑	∑	PUNCT
ejpam-180	833	4	i=1	i=1	PROPN
ejpam-180	833	5	�	�	PROPN
ejpam-180	833	6	αi	αi	PART
ejpam-180	833	7	−	−	NOUN
ejpam-180	833	8	γλi	γλi	X
ejpam-180	833	9	�	�	PROPN
ejpam-180	833	10	�	�	PROPN
ejpam-180	833	11	f	f	PROPN
ejpam-180	833	12	i	i	NOUN
ejpam-180	833	13	x	x	X
ejpam-180	833	14	(	(	PUNCT
ejpam-180	833	15	t	t	NOUN
ejpam-180	833	16	,	,	PUNCT
ejpam-180	833	17	x	x	X
ejpam-180	833	18	,	,	PUNCT
ejpam-180	833	19	ẋ	ẋ	PROPN
ejpam-180	833	20	,	,	PUNCT
ejpam-180	833	21	ẍ	ẍ	X
ejpam-180	833	22	)	)	PUNCT
ejpam-180	834	1	+	+	CCONJ
ejpam-180	835	1	b	b	X
ejpam-180	835	2	i	i	PRON
ejpam-180	835	3	(	(	PUNCT
ejpam-180	835	4	t	t	PROPN
ejpam-180	835	5	)	)	PUNCT
ejpam-180	835	6	z	z	NOUN
ejpam-180	836	1	i	i	PRON
ejpam-180	836	2	(	(	PUNCT
ejpam-180	836	3	t	t	PROPN
ejpam-180	836	4	)	)	PUNCT
ejpam-180	836	5	−d	−d	PROPN
ejpam-180	836	6	f	f	PROPN
ejpam-180	837	1	i	i	PRON
ejpam-180	837	2	ẋ	ẋ	PROPN
ejpam-180	838	1	(	(	PUNCT
ejpam-180	838	2	t	t	PROPN
ejpam-180	838	3	,	,	PUNCT
ejpam-180	838	4	x	x	X
ejpam-180	838	5	,	,	PUNCT
ejpam-180	838	6	ẋ	ẋ	PROPN
ejpam-180	838	7	,	,	PUNCT
ejpam-180	838	8	ẍ	ẍ	X
ejpam-180	838	9	)	)	PUNCT
ejpam-180	839	1	+	+	CCONJ
ejpam-180	840	1	d2	d2	PROPN
ejpam-180	840	2	f	f	PROPN
ejpam-180	840	3	i	i	PRON
ejpam-180	840	4	ẍ	ẍ	PROPN
ejpam-180	841	1	(	(	PUNCT
ejpam-180	841	2	t	t	PROPN
ejpam-180	841	3	,	,	PUNCT
ejpam-180	841	4	x	x	X
ejpam-180	841	5	,	,	PUNCT
ejpam-180	841	6	ẋ	ẋ	PROPN
ejpam-180	841	7	,	,	PUNCT
ejpam-180	841	8	ẍ	ẍ	X
ejpam-180	841	9	)	)	PUNCT
ejpam-180	841	10	�	�	PROPN
ejpam-180	841	11	β	β	X
ejpam-180	841	12	(	(	PUNCT
ejpam-180	841	13	t	t	PROPN
ejpam-180	841	14	)	)	PUNCT
ejpam-180	841	15	i.	i.	PROPN
ejpam-180	841	16	husain	husain	PROPN
ejpam-180	841	17	,	,	PUNCT
ejpam-180	841	18	a.	a.	PROPN
ejpam-180	841	19	ahmed	ahmed	PROPN
ejpam-180	841	20	,	,	PUNCT
ejpam-180	841	21	and	and	CCONJ
ejpam-180	841	22	g.	g.	PROPN
ejpam-180	841	23	rumana	rumana	PROPN
ejpam-180	841	24	/	/	SYM
ejpam-180	841	25	eur	eur	PROPN
ejpam-180	841	26	.	.	PUNCT
ejpam-180	842	1	j.	j.	PROPN
ejpam-180	842	2	pure	pure	PROPN
ejpam-180	842	3	appl	appl	PROPN
ejpam-180	842	4	.	.	PROPN
ejpam-180	842	5	math	math	PROPN
ejpam-180	842	6	,	,	PUNCT
ejpam-180	842	7	2	2	NUM
ejpam-180	842	8	(	(	PUNCT
ejpam-180	842	9	2009	2009	NUM
ejpam-180	842	10	)	)	PUNCT
ejpam-180	842	11	,	,	PUNCT
ejpam-180	842	12	(	(	PUNCT
ejpam-180	842	13	372	372	NUM
ejpam-180	842	14	-	-	SYM
ejpam-180	842	15	400	400	NUM
ejpam-180	842	16	)	)	PUNCT
ejpam-180	842	17	395	395	NUM
ejpam-180	842	18	+	+	NUM
ejpam-180	842	19	�	�	PROPN
ejpam-180	842	20	β	β	X
ejpam-180	842	21	(	(	PUNCT
ejpam-180	842	22	t	t	PROPN
ejpam-180	842	23	)	)	PUNCT
ejpam-180	842	24	t	t	PROPN
ejpam-180	842	25	θx	θx	NUM
ejpam-180	842	26	−	−	PROPN
ejpam-180	842	27	dβ	dβ	PROPN
ejpam-180	842	28	(	(	PUNCT
ejpam-180	842	29	t	t	NOUN
ejpam-180	842	30	)	)	PUNCT
ejpam-180	842	31	t	t	PROPN
ejpam-180	843	1	θ	θ	PROPN
ejpam-180	843	2	ẋ	ẋ	PROPN
ejpam-180	844	1	+	+	PUNCT
ejpam-180	844	2	d2β	d2β	PROPN
ejpam-180	844	3	(	(	PUNCT
ejpam-180	844	4	t	t	PROPN
ejpam-180	844	5	)	)	PUNCT
ejpam-180	844	6	t	t	PROPN
ejpam-180	844	7	θ	θ	PROPN
ejpam-180	844	8	ẍ	ẍ	PUNCT
ejpam-180	845	1	−	−	PROPN
ejpam-180	845	2	d3β	d3β	NOUN
ejpam-180	845	3	(	(	PUNCT
ejpam-180	845	4	t	t	NOUN
ejpam-180	845	5	)	)	PUNCT
ejpam-180	845	6	t	t	PROPN
ejpam-180	845	7	θ	θ	PROPN
ejpam-180	845	8	...	...	PUNCT
ejpam-180	845	9	x	x	SYM
ejpam-180	845	10	�	�	PROPN
ejpam-180	845	11	β	β	X
ejpam-180	845	12	(	(	PUNCT
ejpam-180	845	13	t	t	PROPN
ejpam-180	845	14	)	)	PUNCT
ejpam-180	845	15	=	=	SYM
ejpam-180	845	16	0	0	NUM
ejpam-180	845	17	,	,	PUNCT
ejpam-180	845	18	t	t	PROPN
ejpam-180	845	19	∈	∈	PROPN
ejpam-180	846	1	i	i	PRON
ejpam-180	846	2	this	this	PRON
ejpam-180	846	3	in	in	ADP
ejpam-180	846	4	conjunction	conjunction	NOUN
ejpam-180	846	5	with	with	ADP
ejpam-180	846	6	(	(	PUNCT
ejpam-180	846	7	5.22	5.22	NUM
ejpam-180	846	8	)	)	PUNCT
ejpam-180	846	9	yields	yield	NOUN
ejpam-180	846	10	β	β	X
ejpam-180	846	11	(	(	PUNCT
ejpam-180	846	12	t	t	PROPN
ejpam-180	846	13	)	)	PUNCT
ejpam-180	846	14	t	t	PROPN
ejpam-180	846	15	θx	θx	NUM
ejpam-180	846	16	−	−	PROPN
ejpam-180	846	17	dβ	dβ	PROPN
ejpam-180	846	18	(	(	PUNCT
ejpam-180	846	19	t	t	NOUN
ejpam-180	846	20	)	)	PUNCT
ejpam-180	846	21	t	t	PROPN
ejpam-180	846	22	θ	θ	PROPN
ejpam-180	846	23	ẋ	ẋ	PROPN
ejpam-180	847	1	+	+	PUNCT
ejpam-180	847	2	d2β	d2β	PROPN
ejpam-180	847	3	(	(	PUNCT
ejpam-180	847	4	t	t	PROPN
ejpam-180	847	5	)	)	PUNCT
ejpam-180	847	6	t	t	PROPN
ejpam-180	847	7	θ	θ	X
ejpam-180	847	8	ẍ	ẍ	X
ejpam-180	848	1	=	=	SYM
ejpam-180	848	2	0	0	PROPN
ejpam-180	848	3	,	,	PUNCT
ejpam-180	848	4	t	t	PROPN
ejpam-180	848	5	∈	∈	PROPN
ejpam-180	849	1	i	i	PRON
ejpam-180	849	2	which	which	PRON
ejpam-180	849	3	because	because	SCONJ
ejpam-180	849	4	of	of	ADP
ejpam-180	849	5	the	the	DET
ejpam-180	849	6	hypothesis	hypothesis	NOUN
ejpam-180	849	7	(	(	PUNCT
ejpam-180	849	8	a4	a4	NOUN
ejpam-180	849	9	)	)	PUNCT
ejpam-180	849	10	implies	imply	VERB
ejpam-180	849	11	β(t	β(t	PROPN
ejpam-180	849	12	)	)	PUNCT
ejpam-180	850	1	=	=	SYM
ejpam-180	850	2	0	0	NUM
ejpam-180	850	3	,	,	PUNCT
ejpam-180	850	4	t	t	PROPN
ejpam-180	850	5	∈	∈	PROPN
ejpam-180	851	1	i	i	PRON
ejpam-180	851	2	(	(	PUNCT
ejpam-180	851	3	5.24	5.24	NUM
ejpam-180	851	4	)	)	PUNCT
ejpam-180	851	5	using	use	VERB
ejpam-180	851	6	(	(	PUNCT
ejpam-180	851	7	5.24	5.24	NUM
ejpam-180	851	8	)	)	PUNCT
ejpam-180	851	9	in	in	ADP
ejpam-180	851	10	(	(	PUNCT
ejpam-180	851	11	5.23	5.23	NUM
ejpam-180	851	12	)	)	PUNCT
ejpam-180	851	13	,	,	PUNCT
ejpam-180	851	14	we	we	PRON
ejpam-180	851	15	have	have	VERB
ejpam-180	851	16	−	−	PROPN
ejpam-180	851	17	p	p	NOUN
ejpam-180	851	18	∑	∑	PUNCT
ejpam-180	851	19	i=1	i=1	PROPN
ejpam-180	851	20	�	�	PROPN
ejpam-180	851	21	αi	αi	PART
ejpam-180	851	22	−	−	NOUN
ejpam-180	851	23	γλi	γλi	X
ejpam-180	851	24	�	�	PROPN
ejpam-180	851	25	�	�	PROPN
ejpam-180	851	26	f	f	PROPN
ejpam-180	852	1	i	i	NOUN
ejpam-180	852	2	x	x	X
ejpam-180	852	3	(	(	PUNCT
ejpam-180	852	4	t	t	NOUN
ejpam-180	852	5	,	,	PUNCT
ejpam-180	852	6	x	x	X
ejpam-180	852	7	,	,	PUNCT
ejpam-180	852	8	ẋ	ẋ	PROPN
ejpam-180	852	9	,	,	PUNCT
ejpam-180	852	10	ẍ	ẍ	X
ejpam-180	852	11	)	)	PUNCT
ejpam-180	853	1	+	+	CCONJ
ejpam-180	853	2	b	b	X
ejpam-180	853	3	i	i	PRON
ejpam-180	853	4	(	(	PUNCT
ejpam-180	853	5	t)z	t)z	NOUN
ejpam-180	853	6	i	i	PRON
ejpam-180	853	7	(	(	PUNCT
ejpam-180	853	8	t	t	PROPN
ejpam-180	853	9	)	)	PUNCT
ejpam-180	853	10	−d	−d	PROPN
ejpam-180	853	11	f	f	PROPN
ejpam-180	854	1	i	i	PRON
ejpam-180	854	2	ẋ	ẋ	PROPN
ejpam-180	855	1	(	(	PUNCT
ejpam-180	855	2	t	t	PROPN
ejpam-180	855	3	,	,	PUNCT
ejpam-180	855	4	x	x	X
ejpam-180	855	5	,	,	PUNCT
ejpam-180	855	6	ẋ	ẋ	PROPN
ejpam-180	855	7	,	,	PUNCT
ejpam-180	855	8	ẍ	ẍ	X
ejpam-180	855	9	)	)	PUNCT
ejpam-180	856	1	+	+	CCONJ
ejpam-180	857	1	d2	d2	PROPN
ejpam-180	857	2	f	f	PROPN
ejpam-180	857	3	i	i	PRON
ejpam-180	857	4	ẍ	ẍ	PROPN
ejpam-180	858	1	(	(	PUNCT
ejpam-180	858	2	t	t	PROPN
ejpam-180	858	3	,	,	PUNCT
ejpam-180	858	4	x	x	X
ejpam-180	858	5	,	,	PUNCT
ejpam-180	858	6	ẋ	ẋ	PROPN
ejpam-180	858	7	,	,	PUNCT
ejpam-180	858	8	ẍ	ẍ	X
ejpam-180	858	9	)	)	PUNCT
ejpam-180	858	10	�	�	PROPN
ejpam-180	859	1	=	=	NOUN
ejpam-180	859	2	0	0	NUM
ejpam-180	859	3	this	this	PRON
ejpam-180	859	4	,	,	PUNCT
ejpam-180	859	5	due	due	ADP
ejpam-180	859	6	to	to	ADP
ejpam-180	859	7	the	the	DET
ejpam-180	859	8	hypothesis	hypothesis	NOUN
ejpam-180	859	9	(	(	PUNCT
ejpam-180	859	10	a3	a3	NOUN
ejpam-180	859	11	)	)	PUNCT
ejpam-180	859	12	gives	give	VERB
ejpam-180	859	13	,	,	PUNCT
ejpam-180	859	14	αi	αi	NOUN
ejpam-180	859	15	−	−	NOUN
ejpam-180	859	16	γλi	γλi	NOUN
ejpam-180	859	17	=	=	SYM
ejpam-180	859	18	0	0	NUM
ejpam-180	859	19	,	,	PUNCT
ejpam-180	859	20	i	i	PRON
ejpam-180	859	21	=	=	NOUN
ejpam-180	859	22	1	1	NUM
ejpam-180	859	23	,	,	PUNCT
ejpam-180	859	24	2	2	NUM
ejpam-180	859	25	,	,	PUNCT
ejpam-180	859	26	.	.	PUNCT
ejpam-180	859	27	.	.	PUNCT
ejpam-180	860	1	.	.	PUNCT
ejpam-180	861	1	,	,	PUNCT
ejpam-180	861	2	p	p	X
ejpam-180	861	3	(	(	PUNCT
ejpam-180	861	4	5.25	5.25	NUM
ejpam-180	861	5	)	)	PUNCT
ejpam-180	861	6	suppose	suppose	VERB
ejpam-180	861	7	γ	γ	X
ejpam-180	861	8	=	=	SYM
ejpam-180	861	9	0	0	NUM
ejpam-180	861	10	,	,	PUNCT
ejpam-180	861	11	then	then	ADV
ejpam-180	861	12	from	from	ADP
ejpam-180	861	13	(	(	PUNCT
ejpam-180	861	14	5.25	5.25	NUM
ejpam-180	861	15	)	)	PUNCT
ejpam-180	861	16	we	we	PRON
ejpam-180	861	17	have	have	VERB
ejpam-180	861	18	α	α	NOUN
ejpam-180	861	19	=	=	SYM
ejpam-180	861	20	0	0	NUM
ejpam-180	861	21	.	.	PUNCT
ejpam-180	862	1	the	the	DET
ejpam-180	862	2	relation	relation	NOUN
ejpam-180	862	3	(	(	PUNCT
ejpam-180	862	4	5.13	5.13	NUM
ejpam-180	862	5	)	)	PUNCT
ejpam-180	862	6	gives	give	VERB
ejpam-180	862	7	µ(t	µ(t	ADJ
ejpam-180	862	8	)	)	PUNCT
ejpam-180	862	9	=	=	SYM
ejpam-180	862	10	0	0	NUM
ejpam-180	862	11	,	,	PUNCT
ejpam-180	862	12	t	t	PROPN
ejpam-180	862	13	∈	∈	PROPN
ejpam-180	863	1	i	i	PRON
ejpam-180	863	2	.	.	PUNCT
ejpam-180	864	1	as	as	ADP
ejpam-180	864	2	earlier	early	ADV
ejpam-180	864	3	,	,	PUNCT
ejpam-180	864	4	(	(	PUNCT
ejpam-180	864	5	5.14	5.14	NUM
ejpam-180	864	6	)	)	PUNCT
ejpam-180	864	7	implies	imply	VERB
ejpam-180	864	8	δ	δ	X
ejpam-180	864	9	=	=	SYM
ejpam-180	864	10	0	0	X
ejpam-180	864	11	.	.	PUNCT
ejpam-180	865	1	hence	hence	ADV
ejpam-180	865	2	we	we	PRON
ejpam-180	865	3	get	get	VERB
ejpam-180	865	4	(	(	PUNCT
ejpam-180	865	5	α	α	NOUN
ejpam-180	865	6	,	,	PUNCT
ejpam-180	865	7	β(t),µ(t),η	β(t),µ(t),η	PRON
ejpam-180	865	8	,	,	PUNCT
ejpam-180	865	9	γ	γ	X
ejpam-180	865	10	,	,	PUNCT
ejpam-180	865	11	δ	δ	PROPN
ejpam-180	865	12	)	)	PUNCT
ejpam-180	865	13	=	=	SYM
ejpam-180	866	1	0	0	PROPN
ejpam-180	866	2	,	,	PUNCT
ejpam-180	866	3	which	which	PRON
ejpam-180	866	4	contradicts	contradict	VERB
ejpam-180	866	5	(	(	PUNCT
ejpam-180	866	6	5.20	5.20	NUM
ejpam-180	866	7	)	)	PUNCT
ejpam-180	866	8	.	.	PUNCT
ejpam-180	867	1	hence	hence	ADV
ejpam-180	867	2	γ	γ	X
ejpam-180	867	3	>	>	X
ejpam-180	867	4	0	0	NUM
ejpam-180	867	5	.	.	PUNCT
ejpam-180	868	1	consequently	consequently	ADV
ejpam-180	868	2	,	,	PUNCT
ejpam-180	868	3	(	(	PUNCT
ejpam-180	868	4	5.25	5.25	NUM
ejpam-180	868	5	)	)	PUNCT
ejpam-180	868	6	implies	imply	VERB
ejpam-180	868	7	α	α	X
ejpam-180	868	8	>	>	X
ejpam-180	868	9	0	0	NUM
ejpam-180	868	10	.	.	PUNCT
ejpam-180	869	1	from	from	ADP
ejpam-180	869	2	(	(	PUNCT
ejpam-180	869	3	5.14	5.14	NUM
ejpam-180	869	4	)	)	PUNCT
ejpam-180	869	5	we	we	PRON
ejpam-180	869	6	have	have	VERB
ejpam-180	869	7	g	g	PROPN
ejpam-180	869	8	�	�	PROPN
ejpam-180	869	9	t	t	PROPN
ejpam-180	869	10	,	,	PUNCT
ejpam-180	869	11	x̄	x̄	NOUN
ejpam-180	869	12	,	,	PUNCT
ejpam-180	869	13	˙̄x	˙̄x	PUNCT
ejpam-180	869	14	,	,	PUNCT
ejpam-180	869	15	¨̄x	¨̄x	PRON
ejpam-180	869	16	�	�	PROPN
ejpam-180	869	17	≦	≦	PROPN
ejpam-180	869	18	0	0	NUM
ejpam-180	870	1	this	this	PRON
ejpam-180	870	2	implies	imply	VERB
ejpam-180	870	3	the	the	DET
ejpam-180	870	4	feasibility	feasibility	NOUN
ejpam-180	870	5	of	of	ADP
ejpam-180	870	6	x̄	x̄	PROPN
ejpam-180	870	7	for	for	ADP
ejpam-180	870	8	(	(	PUNCT
ejpam-180	870	9	vp	vp	PROPN
ejpam-180	870	10	)	)	PUNCT
ejpam-180	870	11	.	.	PUNCT
ejpam-180	871	1	in	in	ADP
ejpam-180	871	2	view	view	NOUN
ejpam-180	871	3	of	of	ADP
ejpam-180	871	4	the	the	DET
ejpam-180	871	5	explanations	explanation	NOUN
ejpam-180	871	6	given	give	VERB
ejpam-180	871	7	in	in	ADP
ejpam-180	871	8	the	the	DET
ejpam-180	871	9	proof	proof	NOUN
ejpam-180	871	10	of	of	ADP
ejpam-180	871	11	theorem	theorem	ADJ
ejpam-180	871	12	4.2	4.2	NUM
ejpam-180	871	13	,	,	PUNCT
ejpam-180	871	14	(	(	PUNCT
ejpam-180	871	15	5.14	5.14	NUM
ejpam-180	871	16	)	)	PUNCT
ejpam-180	871	17	together	together	ADV
ejpam-180	871	18	with	with	ADP
ejpam-180	871	19	(	(	PUNCT
ejpam-180	871	20	5.19	5.19	NUM
ejpam-180	871	21	)	)	PUNCT
ejpam-180	871	22	readily	readily	ADV
ejpam-180	871	23	yields	yield	VERB
ejpam-180	871	24	�	�	PROPN
ejpam-180	871	25	x̄	x̄	PROPN
ejpam-180	871	26	(	(	PUNCT
ejpam-180	871	27	t	t	PROPN
ejpam-180	871	28	)	)	PUNCT
ejpam-180	871	29	t	t	PROPN
ejpam-180	871	30	b	b	PROPN
ejpam-180	871	31	i	i	PROPN
ejpam-180	871	32	(	(	PUNCT
ejpam-180	871	33	t	t	PROPN
ejpam-180	871	34	)	)	PUNCT
ejpam-180	871	35	z̄	z̄	PROPN
ejpam-180	871	36	i	i	PROPN
ejpam-180	871	37	(	(	PUNCT
ejpam-180	871	38	t	t	PROPN
ejpam-180	871	39	)	)	PUNCT
ejpam-180	871	40	�	�	PROPN
ejpam-180	871	41	=	=	SYM
ejpam-180	871	42	�	�	PROPN
ejpam-180	871	43	x̄	x̄	PROPN
ejpam-180	871	44	(	(	PUNCT
ejpam-180	871	45	t	t	PROPN
ejpam-180	871	46	)	)	PUNCT
ejpam-180	871	47	t	t	PROPN
ejpam-180	871	48	b	b	PROPN
ejpam-180	871	49	i	i	PROPN
ejpam-180	871	50	(	(	PUNCT
ejpam-180	871	51	t	t	PROPN
ejpam-180	871	52	)	)	PUNCT
ejpam-180	871	53	x̄	x̄	NOUN
ejpam-180	871	54	(	(	PUNCT
ejpam-180	871	55	t	t	PROPN
ejpam-180	871	56	)	)	PUNCT
ejpam-180	871	57	�	�	PROPN
ejpam-180	871	58	1	1	NUM
ejpam-180	871	59	2	2	NUM
ejpam-180	871	60	,	,	PUNCT
ejpam-180	871	61	i	i	PRON
ejpam-180	871	62	=	=	NOUN
ejpam-180	871	63	1	1	NUM
ejpam-180	871	64	,	,	PUNCT
ejpam-180	871	65	2	2	NUM
ejpam-180	871	66	,	,	PUNCT
ejpam-180	871	67	.	.	PUNCT
ejpam-180	871	68	.	.	PUNCT
ejpam-180	871	69	.	.	PUNCT
ejpam-180	872	1	,	,	PUNCT
ejpam-180	872	2	p	p	PROPN
ejpam-180	872	3	i.	i.	PROPN
ejpam-180	872	4	husain	husain	PROPN
ejpam-180	872	5	,	,	PUNCT
ejpam-180	872	6	a.	a.	PROPN
ejpam-180	872	7	ahmed	ahmed	PROPN
ejpam-180	872	8	,	,	PUNCT
ejpam-180	872	9	and	and	CCONJ
ejpam-180	872	10	g.	g.	PROPN
ejpam-180	872	11	rumana	rumana	PROPN
ejpam-180	872	12	/	/	SYM
ejpam-180	872	13	eur	eur	PROPN
ejpam-180	872	14	.	.	PUNCT
ejpam-180	873	1	j.	j.	PROPN
ejpam-180	873	2	pure	pure	PROPN
ejpam-180	873	3	appl	appl	PROPN
ejpam-180	873	4	.	.	PROPN
ejpam-180	873	5	math	math	PROPN
ejpam-180	873	6	,	,	PUNCT
ejpam-180	873	7	2	2	NUM
ejpam-180	873	8	(	(	PUNCT
ejpam-180	873	9	2009	2009	NUM
ejpam-180	873	10	)	)	PUNCT
ejpam-180	873	11	,	,	PUNCT
ejpam-180	873	12	(	(	PUNCT
ejpam-180	873	13	372	372	NUM
ejpam-180	873	14	-	-	SYM
ejpam-180	873	15	400	400	NUM
ejpam-180	873	16	)	)	PUNCT
ejpam-180	873	17	396	396	NUM
ejpam-180	873	18	hence	hence	ADV
ejpam-180	873	19	,	,	PUNCT
ejpam-180	873	20	∫	∫	PROPN
ejpam-180	874	1	i	i	PRON
ejpam-180	874	2	�	�	PROPN
ejpam-180	875	1	f	f	VERB
ejpam-180	876	1	i	i	PRON
ejpam-180	876	2	�	�	PROPN
ejpam-180	876	3	t	t	PROPN
ejpam-180	876	4	,	,	PUNCT
ejpam-180	876	5	x̄	x̄	NOUN
ejpam-180	876	6	,	,	PUNCT
ejpam-180	876	7	˙̄x	˙̄x	PUNCT
ejpam-180	876	8	,	,	PUNCT
ejpam-180	876	9	¨̄x	¨̄x	PRON
ejpam-180	876	10	�	�	PROPN
ejpam-180	876	11	d	d	PROPN
ejpam-180	876	12	t	t	PROPN
ejpam-180	876	13	+	+	PROPN
ejpam-180	876	14	�	�	PROPN
ejpam-180	876	15	x̄	x̄	PROPN
ejpam-180	876	16	(	(	PUNCT
ejpam-180	876	17	t	t	PROPN
ejpam-180	876	18	)	)	PUNCT
ejpam-180	876	19	t	t	PROPN
ejpam-180	876	20	b	b	PROPN
ejpam-180	877	1	i	i	PROPN
ejpam-180	877	2	(	(	PUNCT
ejpam-180	877	3	t	t	PROPN
ejpam-180	877	4	)	)	PUNCT
ejpam-180	877	5	z̄	z̄	PROPN
ejpam-180	878	1	i	i	PROPN
ejpam-180	878	2	(	(	PUNCT
ejpam-180	878	3	t	t	PROPN
ejpam-180	878	4	)	)	PUNCT
ejpam-180	878	5	�	�	PROPN
ejpam-180	878	6	�	�	PROPN
ejpam-180	878	7	d	d	PROPN
ejpam-180	878	8	t	t	PROPN
ejpam-180	878	9	=	=	SYM
ejpam-180	878	10	∫	∫	PROPN
ejpam-180	879	1	i	i	INTJ
ejpam-180	879	2	�	�	PROPN
ejpam-180	880	1	f	f	VERB
ejpam-180	881	1	i	i	PRON
ejpam-180	881	2	�	�	PROPN
ejpam-180	881	3	t	t	PROPN
ejpam-180	881	4	,	,	PUNCT
ejpam-180	881	5	x̄	x̄	NOUN
ejpam-180	881	6	,	,	PUNCT
ejpam-180	881	7	˙̄x	˙̄x	PUNCT
ejpam-180	881	8	,	,	PUNCT
ejpam-180	881	9	¨̄x	¨̄x	PRON
ejpam-180	881	10	�	�	PROPN
ejpam-180	881	11	d	d	PROPN
ejpam-180	881	12	t	t	PROPN
ejpam-180	881	13	+	+	PROPN
ejpam-180	881	14	�	�	PROPN
ejpam-180	881	15	x̄	x̄	PROPN
ejpam-180	881	16	(	(	PUNCT
ejpam-180	881	17	t	t	PROPN
ejpam-180	881	18	)	)	PUNCT
ejpam-180	881	19	t	t	PROPN
ejpam-180	881	20	b	b	PROPN
ejpam-180	881	21	i	i	PROPN
ejpam-180	881	22	(	(	PUNCT
ejpam-180	881	23	t	t	PROPN
ejpam-180	881	24	)	)	PUNCT
ejpam-180	881	25	x̄	x̄	NOUN
ejpam-180	881	26	(	(	PUNCT
ejpam-180	881	27	t	t	PROPN
ejpam-180	881	28	)	)	PUNCT
ejpam-180	881	29	�	�	PROPN
ejpam-180	881	30	1	1	NUM
ejpam-180	881	31	2	2	NUM
ejpam-180	881	32	�	�	PROPN
ejpam-180	881	33	d	d	PROPN
ejpam-180	881	34	t	t	PROPN
ejpam-180	881	35	,	,	PUNCT
ejpam-180	881	36	i	i	PRON
ejpam-180	881	37	=	=	NOUN
ejpam-180	881	38	1	1	NUM
ejpam-180	881	39	,	,	PUNCT
ejpam-180	881	40	2	2	NUM
ejpam-180	881	41	,	,	PUNCT
ejpam-180	881	42	.	.	PUNCT
ejpam-180	881	43	.	.	PUNCT
ejpam-180	882	1	.	.	PUNCT
ejpam-180	883	1	,	,	PUNCT
ejpam-180	883	2	p	p	NOUN
ejpam-180	883	3	this	this	PRON
ejpam-180	883	4	,	,	PUNCT
ejpam-180	883	5	in	in	ADP
ejpam-180	883	6	view	view	NOUN
ejpam-180	883	7	of	of	ADP
ejpam-180	883	8	the	the	DET
ejpam-180	883	9	hypothesis	hypothesis	NOUN
ejpam-180	883	10	of	of	ADP
ejpam-180	883	11	theorem	theorem	NOUN
ejpam-180	883	12	5.1	5.1	NUM
ejpam-180	883	13	,	,	PUNCT
ejpam-180	883	14	implies	imply	VERB
ejpam-180	883	15	that	that	SCONJ
ejpam-180	883	16	x̄	x̄	NOUN
ejpam-180	883	17	is	be	AUX
ejpam-180	883	18	efficient	efficient	ADJ
ejpam-180	883	19	solution	solution	NOUN
ejpam-180	883	20	of	of	ADP
ejpam-180	883	21	(	(	PUNCT
ejpam-180	883	22	vp	vp	PROPN
ejpam-180	883	23	)	)	PUNCT
ejpam-180	883	24	.	.	PUNCT
ejpam-180	884	1	6	6	X
ejpam-180	884	2	.	.	X
ejpam-180	884	3	related	relate	VERB
ejpam-180	884	4	problems	problem	NOUN
ejpam-180	884	5	it	it	PRON
ejpam-180	884	6	is	be	AUX
ejpam-180	884	7	possible	possible	ADJ
ejpam-180	884	8	to	to	PART
ejpam-180	884	9	extend	extend	VERB
ejpam-180	884	10	the	the	DET
ejpam-180	884	11	duality	duality	NOUN
ejpam-180	884	12	theorems	theorem	NOUN
ejpam-180	884	13	established	establish	VERB
ejpam-180	884	14	in	in	ADP
ejpam-180	884	15	the	the	DET
ejpam-180	884	16	previous	previous	ADJ
ejpam-180	884	17	two	two	NUM
ejpam-180	884	18	sections	section	NOUN
ejpam-180	884	19	to	to	ADP
ejpam-180	884	20	the	the	DET
ejpam-180	884	21	corresponding	corresponding	ADJ
ejpam-180	884	22	variational	variational	ADJ
ejpam-180	884	23	problems	problem	NOUN
ejpam-180	884	24	with	with	ADP
ejpam-180	884	25	natural	natural	ADJ
ejpam-180	884	26	boundary	boundary	ADJ
ejpam-180	884	27	values	value	NOUN
ejpam-180	884	28	rather	rather	ADV
ejpam-180	884	29	than	than	ADP
ejpam-180	884	30	fixed	fix	VERB
ejpam-180	884	31	end	end	NOUN
ejpam-180	884	32	points	point	NOUN
ejpam-180	884	33	.	.	PUNCT
ejpam-180	885	1	(	(	PUNCT
ejpam-180	885	2	v	v	ADP
ejpam-180	885	3	p)0	p)0	NOUN
ejpam-180	885	4	:	:	PUNCT
ejpam-180	885	5	minimize	minimize	VERB
ejpam-180	885	6	�	�	PROPN
ejpam-180	885	7	∫	∫	PROPN
ejpam-180	885	8	i	i	PROPN
ejpam-180	885	9	�	�	PROPN
ejpam-180	886	1	f	f	PROPN
ejpam-180	886	2	1	1	NUM
ejpam-180	886	3	(	(	PUNCT
ejpam-180	886	4	t	t	PROPN
ejpam-180	886	5	,	,	PUNCT
ejpam-180	886	6	x	x	X
ejpam-180	886	7	,	,	PUNCT
ejpam-180	886	8	ẋ	ẋ	PROPN
ejpam-180	886	9	,	,	PUNCT
ejpam-180	886	10	ẍ	ẍ	X
ejpam-180	886	11	)	)	PUNCT
ejpam-180	887	1	d	d	PROPN
ejpam-180	887	2	t	t	PROPN
ejpam-180	887	3	+	+	CCONJ
ejpam-180	887	4	�	�	PROPN
ejpam-180	887	5	x	x	SYM
ejpam-180	887	6	(	(	PUNCT
ejpam-180	887	7	t	t	PROPN
ejpam-180	887	8	)	)	PUNCT
ejpam-180	887	9	t	t	PROPN
ejpam-180	887	10	b1	b1	PROPN
ejpam-180	887	11	(	(	PUNCT
ejpam-180	887	12	t	t	PROPN
ejpam-180	887	13	)	)	PUNCT
ejpam-180	887	14	x	x	X
ejpam-180	887	15	(	(	PUNCT
ejpam-180	887	16	t	t	PROPN
ejpam-180	887	17	)	)	PUNCT
ejpam-180	887	18	�	�	PROPN
ejpam-180	887	19	1	1	NUM
ejpam-180	887	20	2	2	NUM
ejpam-180	887	21	�	�	PROPN
ejpam-180	887	22	d	d	PROPN
ejpam-180	887	23	t	t	PROPN
ejpam-180	887	24	,	,	PUNCT
ejpam-180	887	25	.	.	PUNCT
ejpam-180	887	26	.	.	PUNCT
ejpam-180	887	27	.	.	PUNCT
ejpam-180	888	1	,	,	PUNCT
ejpam-180	888	2	∫	∫	PROPN
ejpam-180	889	1	i	i	PRON
ejpam-180	889	2	�	�	PROPN
ejpam-180	890	1	f	f	PROPN
ejpam-180	890	2	p	p	PROPN
ejpam-180	890	3	(	(	PUNCT
ejpam-180	890	4	t	t	PROPN
ejpam-180	890	5	,	,	PUNCT
ejpam-180	890	6	x	x	X
ejpam-180	890	7	,	,	PUNCT
ejpam-180	890	8	ẋ	ẋ	PROPN
ejpam-180	890	9	,	,	PUNCT
ejpam-180	890	10	ẍ	ẍ	X
ejpam-180	890	11	)	)	PUNCT
ejpam-180	891	1	d	d	PROPN
ejpam-180	891	2	t	t	PROPN
ejpam-180	891	3	+	+	CCONJ
ejpam-180	891	4	�	�	PROPN
ejpam-180	891	5	x	x	SYM
ejpam-180	891	6	(	(	PUNCT
ejpam-180	891	7	t	t	PROPN
ejpam-180	891	8	)	)	PUNCT
ejpam-180	891	9	t	t	PROPN
ejpam-180	891	10	bp	bp	PROPN
ejpam-180	891	11	(	(	PUNCT
ejpam-180	891	12	t	t	PROPN
ejpam-180	891	13	)	)	PUNCT
ejpam-180	891	14	x	x	X
ejpam-180	891	15	(	(	PUNCT
ejpam-180	891	16	t	t	PROPN
ejpam-180	891	17	)	)	PUNCT
ejpam-180	891	18	�	�	PROPN
ejpam-180	891	19	1	1	NUM
ejpam-180	891	20	2	2	NUM
ejpam-180	891	21	�	�	PROPN
ejpam-180	891	22	d	d	PROPN
ejpam-180	891	23	t	t	PROPN
ejpam-180	891	24	�	�	PROPN
ejpam-180	891	25	subject	subject	ADJ
ejpam-180	891	26	to	to	ADP
ejpam-180	891	27	g	g	PROPN
ejpam-180	891	28	j	j	PROPN
ejpam-180	891	29	(	(	PUNCT
ejpam-180	891	30	t	t	PROPN
ejpam-180	891	31	,	,	PUNCT
ejpam-180	891	32	x	x	X
ejpam-180	891	33	,	,	PUNCT
ejpam-180	891	34	ẋ	ẋ	PROPN
ejpam-180	891	35	,	,	PUNCT
ejpam-180	891	36	ẋ)≦	ẋ)≦	PROPN
ejpam-180	891	37	0	0	PROPN
ejpam-180	891	38	,	,	PUNCT
ejpam-180	891	39	t	t	PROPN
ejpam-180	891	40	∈	∈	PROPN
ejpam-180	892	1	i	i	PRON
ejpam-180	892	2	,	,	PUNCT
ejpam-180	892	3	j	j	PROPN
ejpam-180	892	4	=	=	SYM
ejpam-180	892	5	1	1	NUM
ejpam-180	892	6	,	,	PUNCT
ejpam-180	892	7	.	.	PUNCT
ejpam-180	892	8	.	.	PUNCT
ejpam-180	892	9	.	.	PUNCT
ejpam-180	893	1	,	,	PUNCT
ejpam-180	893	2	m	m	VERB
ejpam-180	893	3	(	(	PUNCT
ejpam-180	893	4	mw	mw	ADJ
ejpam-180	893	5	d)0	d)0	NOUN
ejpam-180	893	6	:	:	PUNCT
ejpam-180	893	7	maximize	maximize	VERB
ejpam-180	893	8	�	�	PROPN
ejpam-180	893	9	∫	∫	PROPN
ejpam-180	893	10	i	i	PROPN
ejpam-180	893	11	�	�	PROPN
ejpam-180	894	1	f	f	PROPN
ejpam-180	894	2	1	1	NUM
ejpam-180	894	3	(	(	PUNCT
ejpam-180	894	4	t	t	PROPN
ejpam-180	894	5	,	,	PUNCT
ejpam-180	894	6	u	u	NOUN
ejpam-180	894	7	,	,	PUNCT
ejpam-180	894	8	u̇	u̇	PROPN
ejpam-180	894	9	,	,	PUNCT
ejpam-180	894	10	ü	ü	PRON
ejpam-180	894	11	)	)	PUNCT
ejpam-180	895	1	+	+	NUM
ejpam-180	895	2	u	u	SYM
ejpam-180	895	3	(	(	PUNCT
ejpam-180	895	4	t	t	PROPN
ejpam-180	895	5	)	)	PUNCT
ejpam-180	895	6	t	t	PROPN
ejpam-180	895	7	b1	b1	PROPN
ejpam-180	895	8	(	(	PUNCT
ejpam-180	895	9	t)z1	t)z1	PROPN
ejpam-180	895	10	(	(	PUNCT
ejpam-180	895	11	t	t	PROPN
ejpam-180	895	12	)	)	PUNCT
ejpam-180	895	13	+	+	CCONJ
ejpam-180	895	14	y	y	PROPN
ejpam-180	895	15	j	j	PROPN
ejpam-180	895	16	(	(	PUNCT
ejpam-180	895	17	t	t	PROPN
ejpam-180	895	18	)	)	PUNCT
ejpam-180	895	19	g	g	PROPN
ejpam-180	895	20	j	j	PROPN
ejpam-180	895	21	(	(	PUNCT
ejpam-180	895	22	t	t	PROPN
ejpam-180	895	23	,	,	PUNCT
ejpam-180	895	24	u	u	NOUN
ejpam-180	895	25	,	,	PUNCT
ejpam-180	895	26	u̇	u̇	PROPN
ejpam-180	895	27	,	,	PUNCT
ejpam-180	895	28	ü	ü	NOUN
ejpam-180	895	29	)	)	PUNCT
ejpam-180	895	30	�	�	PROPN
ejpam-180	895	31	d	d	PROPN
ejpam-180	895	32	t	t	PROPN
ejpam-180	895	33	,	,	PUNCT
ejpam-180	895	34	.	.	PUNCT
ejpam-180	895	35	.	.	PUNCT
ejpam-180	895	36	.	.	PUNCT
ejpam-180	896	1	,	,	PUNCT
ejpam-180	896	2	∫	∫	PROPN
ejpam-180	897	1	i	i	PRON
ejpam-180	897	2	�	�	PROPN
ejpam-180	898	1	f	f	PROPN
ejpam-180	898	2	p	p	PROPN
ejpam-180	898	3	(	(	PUNCT
ejpam-180	898	4	t	t	PROPN
ejpam-180	898	5	,	,	PUNCT
ejpam-180	898	6	u	u	NOUN
ejpam-180	898	7	,	,	PUNCT
ejpam-180	898	8	u̇	u̇	PROPN
ejpam-180	898	9	,	,	PUNCT
ejpam-180	898	10	ü	ü	PRON
ejpam-180	898	11	)	)	PUNCT
ejpam-180	899	1	+	+	NUM
ejpam-180	899	2	u	u	SYM
ejpam-180	899	3	(	(	PUNCT
ejpam-180	899	4	t	t	PROPN
ejpam-180	899	5	)	)	PUNCT
ejpam-180	899	6	t	t	PROPN
ejpam-180	899	7	bp	bp	PROPN
ejpam-180	899	8	(	(	PUNCT
ejpam-180	899	9	t	t	PROPN
ejpam-180	899	10	)	)	PUNCT
ejpam-180	899	11	zp	zp	PROPN
ejpam-180	899	12	(	(	PUNCT
ejpam-180	899	13	t	t	PROPN
ejpam-180	899	14	)	)	PUNCT
ejpam-180	900	1	+	+	CCONJ
ejpam-180	900	2	y	y	PROPN
ejpam-180	900	3	j	j	PROPN
ejpam-180	900	4	(	(	PUNCT
ejpam-180	900	5	t	t	PROPN
ejpam-180	900	6	)	)	PUNCT
ejpam-180	900	7	g	g	PROPN
ejpam-180	900	8	j	j	PROPN
ejpam-180	900	9	(	(	PUNCT
ejpam-180	900	10	t	t	PROPN
ejpam-180	900	11	,	,	PUNCT
ejpam-180	900	12	u	u	NOUN
ejpam-180	900	13	,	,	PUNCT
ejpam-180	900	14	u̇	u̇	PROPN
ejpam-180	900	15	,	,	PUNCT
ejpam-180	900	16	ü	ü	NOUN
ejpam-180	900	17	)	)	PUNCT
ejpam-180	900	18	�	�	PROPN
ejpam-180	900	19	d	d	PROPN
ejpam-180	900	20	t	t	PROPN
ejpam-180	900	21	�	�	PROPN
ejpam-180	900	22	subject	subject	ADJ
ejpam-180	900	23	to	to	ADP
ejpam-180	900	24	p	p	NOUN
ejpam-180	900	25	∑	∑	PROPN
ejpam-180	900	26	i=1	i=1	PROPN
ejpam-180	900	27	λi	λi	PROPN
ejpam-180	900	28	�	�	PROPN
ejpam-180	901	1	f	f	PROPN
ejpam-180	902	1	i	i	PRON
ejpam-180	902	2	u	u	PROPN
ejpam-180	902	3	(	(	PUNCT
ejpam-180	902	4	t	t	PROPN
ejpam-180	902	5	,	,	PUNCT
ejpam-180	902	6	u	u	NOUN
ejpam-180	902	7	,	,	PUNCT
ejpam-180	902	8	u̇	u̇	PROPN
ejpam-180	902	9	,	,	PUNCT
ejpam-180	902	10	ü	ü	PRON
ejpam-180	902	11	)	)	PUNCT
ejpam-180	903	1	+	+	NUM
ejpam-180	904	1	b	b	X
ejpam-180	904	2	i	i	PRON
ejpam-180	904	3	(	(	PUNCT
ejpam-180	904	4	t)z	t)z	NOUN
ejpam-180	904	5	i	i	PRON
ejpam-180	904	6	(	(	PUNCT
ejpam-180	904	7	t	t	PROPN
ejpam-180	904	8	)	)	PUNCT
ejpam-180	904	9	+	+	CCONJ
ejpam-180	904	10	y	y	PROPN
ejpam-180	904	11	(	(	PUNCT
ejpam-180	904	12	t	t	PROPN
ejpam-180	904	13	)	)	PUNCT
ejpam-180	904	14	t	t	PROPN
ejpam-180	904	15	gu	gu	PROPN
ejpam-180	904	16	(	(	PUNCT
ejpam-180	904	17	t	t	PROPN
ejpam-180	904	18	,	,	PUNCT
ejpam-180	904	19	u	u	NOUN
ejpam-180	904	20	,	,	PUNCT
ejpam-180	904	21	u̇	u̇	PROPN
ejpam-180	904	22	,	,	PUNCT
ejpam-180	904	23	ü	ü	NUM
ejpam-180	904	24	)	)	PUNCT
ejpam-180	904	25	�	�	PROPN
ejpam-180	904	26	−d	−d	PROPN
ejpam-180	904	27	�	�	PROPN
ejpam-180	904	28	λt	λt	ADP
ejpam-180	904	29	fu̇	fu̇	PROPN
ejpam-180	904	30	(	(	PUNCT
ejpam-180	904	31	t	t	PROPN
ejpam-180	904	32	,	,	PUNCT
ejpam-180	904	33	u	u	NOUN
ejpam-180	904	34	,	,	PUNCT
ejpam-180	904	35	u̇	u̇	PROPN
ejpam-180	904	36	,	,	PUNCT
ejpam-180	904	37	ü	ü	PRON
ejpam-180	904	38	)	)	PUNCT
ejpam-180	905	1	+	+	CCONJ
ejpam-180	905	2	y	y	PROPN
ejpam-180	905	3	(	(	PUNCT
ejpam-180	905	4	t	t	PROPN
ejpam-180	905	5	)	)	PUNCT
ejpam-180	905	6	t	t	NOUN
ejpam-180	905	7	gu̇	gu̇	PROPN
ejpam-180	905	8	(	(	PUNCT
ejpam-180	905	9	t	t	PROPN
ejpam-180	905	10	,	,	PUNCT
ejpam-180	905	11	u	u	NOUN
ejpam-180	905	12	,	,	PUNCT
ejpam-180	905	13	u̇	u̇	PROPN
ejpam-180	905	14	,	,	PUNCT
ejpam-180	905	15	ü	ü	NOUN
ejpam-180	905	16	)	)	PUNCT
ejpam-180	905	17	�	�	PROPN
ejpam-180	905	18	+	+	NUM
ejpam-180	905	19	d2	d2	PROPN
ejpam-180	905	20	�	�	PROPN
ejpam-180	905	21	λt	λt	ADP
ejpam-180	905	22	fü	fü	X
ejpam-180	905	23	(	(	PUNCT
ejpam-180	905	24	t	t	PROPN
ejpam-180	905	25	,	,	PUNCT
ejpam-180	905	26	u	u	NOUN
ejpam-180	905	27	,	,	PUNCT
ejpam-180	905	28	u̇	u̇	PROPN
ejpam-180	905	29	,	,	PUNCT
ejpam-180	905	30	ü	ü	PRON
ejpam-180	905	31	)	)	PUNCT
ejpam-180	906	1	+	+	CCONJ
ejpam-180	906	2	y	y	PROPN
ejpam-180	906	3	(	(	PUNCT
ejpam-180	906	4	t	t	PROPN
ejpam-180	906	5	)	)	PUNCT
ejpam-180	906	6	t	t	PROPN
ejpam-180	906	7	gü	gü	PROPN
ejpam-180	906	8	(	(	PUNCT
ejpam-180	906	9	t	t	PROPN
ejpam-180	906	10	,	,	PUNCT
ejpam-180	906	11	u	u	NOUN
ejpam-180	906	12	,	,	PUNCT
ejpam-180	906	13	u̇	u̇	PROPN
ejpam-180	906	14	,	,	PUNCT
ejpam-180	906	15	ü	ü	NOUN
ejpam-180	906	16	)	)	PUNCT
ejpam-180	906	17	�	�	PROPN
ejpam-180	906	18	=	=	SYM
ejpam-180	906	19	0	0	PROPN
ejpam-180	906	20	,	,	PUNCT
ejpam-180	906	21	t	t	PROPN
ejpam-180	906	22	∈	∈	PROPN
ejpam-180	906	23	i	i	PRON
ejpam-180	906	24	i.	i.	PROPN
ejpam-180	906	25	husain	husain	PROPN
ejpam-180	906	26	,	,	PUNCT
ejpam-180	906	27	a.	a.	PROPN
ejpam-180	906	28	ahmed	ahmed	PROPN
ejpam-180	906	29	,	,	PUNCT
ejpam-180	906	30	and	and	CCONJ
ejpam-180	906	31	g.	g.	PROPN
ejpam-180	906	32	rumana	rumana	PROPN
ejpam-180	906	33	/	/	SYM
ejpam-180	906	34	eur	eur	PROPN
ejpam-180	906	35	.	.	PUNCT
ejpam-180	907	1	j.	j.	PROPN
ejpam-180	907	2	pure	pure	PROPN
ejpam-180	907	3	appl	appl	PROPN
ejpam-180	907	4	.	.	PROPN
ejpam-180	907	5	math	math	PROPN
ejpam-180	907	6	,	,	PUNCT
ejpam-180	907	7	2	2	NUM
ejpam-180	907	8	(	(	PUNCT
ejpam-180	907	9	2009	2009	NUM
ejpam-180	907	10	)	)	PUNCT
ejpam-180	907	11	,	,	PUNCT
ejpam-180	907	12	(	(	PUNCT
ejpam-180	907	13	372	372	NUM
ejpam-180	907	14	-	-	SYM
ejpam-180	907	15	400	400	NUM
ejpam-180	907	16	)	)	PUNCT
ejpam-180	907	17	397	397	NUM
ejpam-180	907	18	λt	λt	ADP
ejpam-180	907	19	fu̇	fu̇	PROPN
ejpam-180	907	20	(	(	PUNCT
ejpam-180	907	21	t	t	PROPN
ejpam-180	907	22	,	,	PUNCT
ejpam-180	907	23	u	u	NOUN
ejpam-180	907	24	,	,	PUNCT
ejpam-180	907	25	u̇	u̇	PROPN
ejpam-180	907	26	,	,	PUNCT
ejpam-180	907	27	ü	ü	PRON
ejpam-180	907	28	)	)	PUNCT
ejpam-180	908	1	+	+	CCONJ
ejpam-180	908	2	y	y	PROPN
ejpam-180	908	3	(	(	PUNCT
ejpam-180	908	4	t	t	PROPN
ejpam-180	908	5	)	)	PUNCT
ejpam-180	908	6	t	t	NOUN
ejpam-180	908	7	gu̇	gu̇	PROPN
ejpam-180	908	8	(	(	PUNCT
ejpam-180	908	9	t	t	PROPN
ejpam-180	908	10	,	,	PUNCT
ejpam-180	908	11	u	u	NOUN
ejpam-180	908	12	,	,	PUNCT
ejpam-180	908	13	u̇	u̇	PROPN
ejpam-180	908	14	,	,	PUNCT
ejpam-180	908	15	ü	ü	PRON
ejpam-180	908	16	)	)	PUNCT
ejpam-180	909	1	=	=	SYM
ejpam-180	909	2	0	0	NUM
ejpam-180	910	1	at	at	ADP
ejpam-180	910	2	t	t	PROPN
ejpam-180	910	3	=	=	SYM
ejpam-180	910	4	a	a	X
ejpam-180	910	5	,	,	PUNCT
ejpam-180	910	6	t	t	NOUN
ejpam-180	910	7	=	=	SYM
ejpam-180	910	8	b	b	PROPN
ejpam-180	910	9	,	,	PUNCT
ejpam-180	910	10	λt	λt	X
ejpam-180	910	11	fü	fü	X
ejpam-180	910	12	(	(	PUNCT
ejpam-180	910	13	t	t	PROPN
ejpam-180	910	14	,	,	PUNCT
ejpam-180	910	15	u	u	NOUN
ejpam-180	910	16	,	,	PUNCT
ejpam-180	910	17	u̇	u̇	PROPN
ejpam-180	910	18	,	,	PUNCT
ejpam-180	910	19	ü	ü	PRON
ejpam-180	910	20	)	)	PUNCT
ejpam-180	911	1	+	+	CCONJ
ejpam-180	911	2	y	y	PROPN
ejpam-180	911	3	(	(	PUNCT
ejpam-180	911	4	t	t	PROPN
ejpam-180	911	5	)	)	PUNCT
ejpam-180	911	6	t	t	PROPN
ejpam-180	911	7	gü	gü	PROPN
ejpam-180	911	8	(	(	PUNCT
ejpam-180	911	9	t	t	PROPN
ejpam-180	911	10	,	,	PUNCT
ejpam-180	911	11	u	u	NOUN
ejpam-180	911	12	,	,	PUNCT
ejpam-180	911	13	u̇	u̇	PROPN
ejpam-180	911	14	,	,	PUNCT
ejpam-180	911	15	ü	ü	PRON
ejpam-180	911	16	)	)	PUNCT
ejpam-180	912	1	=	=	SYM
ejpam-180	912	2	0	0	NUM
ejpam-180	912	3	,	,	PUNCT
ejpam-180	912	4	at	at	ADP
ejpam-180	912	5	t	t	NOUN
ejpam-180	912	6	=	=	SYM
ejpam-180	912	7	a	a	X
ejpam-180	912	8	,	,	PUNCT
ejpam-180	912	9	t	t	NOUN
ejpam-180	912	10	=	=	SYM
ejpam-180	912	11	b	b	PROPN
ejpam-180	912	12	,	,	PUNCT
ejpam-180	912	13	z̄	z̄	PROPN
ejpam-180	912	14	i	i	PROPN
ejpam-180	912	15	(	(	PUNCT
ejpam-180	912	16	t	t	PROPN
ejpam-180	912	17	)	)	PUNCT
ejpam-180	912	18	t	t	PROPN
ejpam-180	912	19	b	b	PROPN
ejpam-180	913	1	i	i	PROPN
ejpam-180	913	2	(	(	PUNCT
ejpam-180	913	3	t	t	PROPN
ejpam-180	913	4	)	)	PUNCT
ejpam-180	913	5	z̄	z̄	PROPN
ejpam-180	914	1	i	i	PRON
ejpam-180	914	2	(	(	PUNCT
ejpam-180	914	3	t)≦	t)≦	X
ejpam-180	914	4	1	1	NUM
ejpam-180	914	5	,	,	PUNCT
ejpam-180	914	6	t	t	PROPN
ejpam-180	914	7	∈	∈	PROPN
ejpam-180	915	1	i	i	PRON
ejpam-180	915	2	,	,	PUNCT
ejpam-180	915	3	i	i	PRON
ejpam-180	915	4	∈	∈	VERB
ejpam-180	915	5	p	p	PROPN
ejpam-180	915	6	y	y	PROPN
ejpam-180	915	7	(	(	PUNCT
ejpam-180	915	8	t)≧	t)≧	PROPN
ejpam-180	915	9	0	0	NUM
ejpam-180	915	10	,	,	PUNCT
ejpam-180	915	11	t	t	PROPN
ejpam-180	915	12	∈	∈	PROPN
ejpam-180	916	1	i	i	PRON
ejpam-180	916	2	λ	λ	X
ejpam-180	916	3	>	>	X
ejpam-180	916	4	0	0	PROPN
ejpam-180	916	5	,	,	PUNCT
ejpam-180	916	6	λt	λt	ADP
ejpam-180	916	7	e	e	NOUN
ejpam-180	916	8	=	=	SYM
ejpam-180	916	9	1	1	NUM
ejpam-180	916	10	(	(	PUNCT
ejpam-180	916	11	m	m	PROPN
ejpam-180	916	12	-w	-w	PROPN
ejpam-180	916	13	v	v	PROPN
ejpam-180	916	14	d)0	d)0	NOUN
ejpam-180	916	15	:	:	PUNCT
ejpam-180	916	16	maximize	maximize	VERB
ejpam-180	916	17	�	�	PROPN
ejpam-180	916	18	∫	∫	PROPN
ejpam-180	916	19	i	i	PROPN
ejpam-180	916	20	�	�	PROPN
ejpam-180	917	1	f	f	PROPN
ejpam-180	917	2	1	1	NUM
ejpam-180	917	3	(	(	PUNCT
ejpam-180	917	4	t	t	PROPN
ejpam-180	917	5	,	,	PUNCT
ejpam-180	917	6	u	u	NOUN
ejpam-180	917	7	,	,	PUNCT
ejpam-180	917	8	u̇	u̇	PROPN
ejpam-180	917	9	,	,	PUNCT
ejpam-180	917	10	ü	ü	PRON
ejpam-180	917	11	)	)	PUNCT
ejpam-180	918	1	+	+	NUM
ejpam-180	918	2	u	u	SYM
ejpam-180	918	3	(	(	PUNCT
ejpam-180	918	4	t	t	PROPN
ejpam-180	918	5	)	)	PUNCT
ejpam-180	918	6	t	t	PROPN
ejpam-180	918	7	b1	b1	PROPN
ejpam-180	918	8	(	(	PUNCT
ejpam-180	918	9	t	t	NOUN
ejpam-180	918	10	)	)	PUNCT
ejpam-180	918	11	z1	z1	PROPN
ejpam-180	918	12	(	(	PUNCT
ejpam-180	918	13	t	t	PROPN
ejpam-180	918	14	)	)	PUNCT
ejpam-180	918	15	�	�	PROPN
ejpam-180	918	16	d	d	PROPN
ejpam-180	918	17	t	t	PROPN
ejpam-180	918	18	,	,	PUNCT
ejpam-180	918	19	,	,	PUNCT
ejpam-180	918	20	.	.	PUNCT
ejpam-180	918	21	.	.	PUNCT
ejpam-180	918	22	.	.	PUNCT
ejpam-180	919	1	,	,	PUNCT
ejpam-180	919	2	∫	∫	PROPN
ejpam-180	920	1	i	i	PRON
ejpam-180	920	2	�	�	PROPN
ejpam-180	921	1	f	f	PROPN
ejpam-180	921	2	p	p	PROPN
ejpam-180	921	3	(	(	PUNCT
ejpam-180	921	4	t	t	PROPN
ejpam-180	921	5	,	,	PUNCT
ejpam-180	921	6	u	u	NOUN
ejpam-180	921	7	,	,	PUNCT
ejpam-180	921	8	u̇	u̇	PROPN
ejpam-180	921	9	,	,	PUNCT
ejpam-180	921	10	ü	ü	PRON
ejpam-180	921	11	)	)	PUNCT
ejpam-180	922	1	+	+	NUM
ejpam-180	922	2	u	u	SYM
ejpam-180	922	3	(	(	PUNCT
ejpam-180	922	4	t	t	PROPN
ejpam-180	922	5	)	)	PUNCT
ejpam-180	922	6	t	t	PROPN
ejpam-180	922	7	bp	bp	PROPN
ejpam-180	922	8	(	(	PUNCT
ejpam-180	922	9	t)zp	t)zp	PROPN
ejpam-180	922	10	(	(	PUNCT
ejpam-180	922	11	t	t	PROPN
ejpam-180	922	12	)	)	PUNCT
ejpam-180	922	13	�	�	PROPN
ejpam-180	922	14	d	d	PROPN
ejpam-180	922	15	t	t	PROPN
ejpam-180	922	16	�	�	PROPN
ejpam-180	922	17	subject	subject	ADJ
ejpam-180	922	18	to	to	ADP
ejpam-180	922	19	p	p	NOUN
ejpam-180	922	20	∑	∑	PROPN
ejpam-180	922	21	i=1	i=1	PROPN
ejpam-180	922	22	λi	λi	PROPN
ejpam-180	922	23	�	�	PROPN
ejpam-180	922	24	f	f	PROPN
ejpam-180	923	1	i	i	PRON
ejpam-180	923	2	u	u	PROPN
ejpam-180	923	3	(	(	PUNCT
ejpam-180	923	4	t	t	PROPN
ejpam-180	923	5	,	,	PUNCT
ejpam-180	923	6	u	u	NOUN
ejpam-180	923	7	,	,	PUNCT
ejpam-180	923	8	u̇	u̇	PROPN
ejpam-180	923	9	,	,	PUNCT
ejpam-180	923	10	ü	ü	PRON
ejpam-180	923	11	)	)	PUNCT
ejpam-180	924	1	+	+	NUM
ejpam-180	925	1	b	b	X
ejpam-180	925	2	i	i	PRON
ejpam-180	925	3	(	(	PUNCT
ejpam-180	925	4	t	t	PROPN
ejpam-180	925	5	)	)	PUNCT
ejpam-180	925	6	z	z	NOUN
ejpam-180	926	1	i	i	PRON
ejpam-180	926	2	(	(	PUNCT
ejpam-180	926	3	t	t	PROPN
ejpam-180	926	4	)	)	PUNCT
ejpam-180	927	1	+	+	CCONJ
ejpam-180	927	2	y	y	PROPN
ejpam-180	927	3	(	(	PUNCT
ejpam-180	927	4	t	t	PROPN
ejpam-180	927	5	)	)	PUNCT
ejpam-180	927	6	t	t	PROPN
ejpam-180	927	7	gu	gu	PROPN
ejpam-180	927	8	(	(	PUNCT
ejpam-180	927	9	t	t	PROPN
ejpam-180	927	10	,	,	PUNCT
ejpam-180	927	11	u	u	NOUN
ejpam-180	927	12	,	,	PUNCT
ejpam-180	927	13	u̇	u̇	PROPN
ejpam-180	927	14	,	,	PUNCT
ejpam-180	927	15	ü	ü	NUM
ejpam-180	927	16	)	)	PUNCT
ejpam-180	927	17	�	�	PROPN
ejpam-180	927	18	−d	−d	PROPN
ejpam-180	927	19	�	�	PROPN
ejpam-180	927	20	λt	λt	ADP
ejpam-180	927	21	fu̇	fu̇	PROPN
ejpam-180	927	22	(	(	PUNCT
ejpam-180	927	23	t	t	PROPN
ejpam-180	927	24	,	,	PUNCT
ejpam-180	927	25	u	u	NOUN
ejpam-180	927	26	,	,	PUNCT
ejpam-180	927	27	u̇	u̇	PROPN
ejpam-180	927	28	,	,	PUNCT
ejpam-180	927	29	ü	ü	PRON
ejpam-180	927	30	)	)	PUNCT
ejpam-180	928	1	+	+	CCONJ
ejpam-180	928	2	y	y	PROPN
ejpam-180	928	3	(	(	PUNCT
ejpam-180	928	4	t	t	PROPN
ejpam-180	928	5	)	)	PUNCT
ejpam-180	928	6	t	t	NOUN
ejpam-180	928	7	gu̇	gu̇	PROPN
ejpam-180	928	8	(	(	PUNCT
ejpam-180	928	9	t	t	PROPN
ejpam-180	928	10	,	,	PUNCT
ejpam-180	928	11	u	u	NOUN
ejpam-180	928	12	,	,	PUNCT
ejpam-180	928	13	u̇	u̇	PROPN
ejpam-180	928	14	,	,	PUNCT
ejpam-180	928	15	ü	ü	NOUN
ejpam-180	928	16	)	)	PUNCT
ejpam-180	928	17	�	�	PROPN
ejpam-180	928	18	+	+	NUM
ejpam-180	928	19	d2	d2	PROPN
ejpam-180	928	20	�	�	PROPN
ejpam-180	928	21	λt	λt	ADP
ejpam-180	928	22	fü	fü	X
ejpam-180	928	23	(	(	PUNCT
ejpam-180	928	24	t	t	PROPN
ejpam-180	928	25	,	,	PUNCT
ejpam-180	928	26	u	u	NOUN
ejpam-180	928	27	,	,	PUNCT
ejpam-180	928	28	u̇	u̇	PROPN
ejpam-180	928	29	,	,	PUNCT
ejpam-180	928	30	ü	ü	PRON
ejpam-180	928	31	)	)	PUNCT
ejpam-180	929	1	+	+	CCONJ
ejpam-180	929	2	y	y	PROPN
ejpam-180	929	3	(	(	PUNCT
ejpam-180	929	4	t	t	PROPN
ejpam-180	929	5	)	)	PUNCT
ejpam-180	929	6	t	t	PROPN
ejpam-180	929	7	gü	gü	PROPN
ejpam-180	929	8	(	(	PUNCT
ejpam-180	929	9	t	t	PROPN
ejpam-180	929	10	,	,	PUNCT
ejpam-180	929	11	u	u	NOUN
ejpam-180	929	12	,	,	PUNCT
ejpam-180	929	13	u̇	u̇	PROPN
ejpam-180	929	14	,	,	PUNCT
ejpam-180	929	15	ü	ü	NOUN
ejpam-180	929	16	)	)	PUNCT
ejpam-180	929	17	�	�	PROPN
ejpam-180	929	18	=	=	SYM
ejpam-180	929	19	0	0	PROPN
ejpam-180	929	20	,	,	PUNCT
ejpam-180	929	21	t	t	PROPN
ejpam-180	929	22	∈	∈	PROPN
ejpam-180	930	1	i	i	PRON
ejpam-180	930	2	λt	λt	ADP
ejpam-180	930	3	fu̇	fu̇	PROPN
ejpam-180	930	4	(	(	PUNCT
ejpam-180	930	5	t	t	PROPN
ejpam-180	930	6	,	,	PUNCT
ejpam-180	930	7	u	u	NOUN
ejpam-180	930	8	,	,	PUNCT
ejpam-180	930	9	u̇	u̇	PROPN
ejpam-180	930	10	,	,	PUNCT
ejpam-180	930	11	ü	ü	PRON
ejpam-180	930	12	)	)	PUNCT
ejpam-180	931	1	=	=	PUNCT
ejpam-180	932	1	0=	0=	NUM
ejpam-180	932	2	y	y	PROPN
ejpam-180	932	3	(	(	PUNCT
ejpam-180	932	4	t	t	PROPN
ejpam-180	932	5	)	)	PUNCT
ejpam-180	932	6	t	t	NOUN
ejpam-180	932	7	gu̇	gu̇	PROPN
ejpam-180	932	8	(	(	PUNCT
ejpam-180	932	9	t	t	PROPN
ejpam-180	932	10	,	,	PUNCT
ejpam-180	932	11	u	u	NOUN
ejpam-180	932	12	,	,	PUNCT
ejpam-180	932	13	u̇	u̇	PROPN
ejpam-180	932	14	,	,	PUNCT
ejpam-180	932	15	ü	ü	NUM
ejpam-180	932	16	)	)	PUNCT
ejpam-180	932	17	,	,	PUNCT
ejpam-180	932	18	at	at	ADP
ejpam-180	932	19	t	t	NOUN
ejpam-180	932	20	=	=	SYM
ejpam-180	932	21	a	a	X
ejpam-180	932	22	,	,	PUNCT
ejpam-180	932	23	t	t	NOUN
ejpam-180	932	24	=	=	SYM
ejpam-180	932	25	b	b	PROPN
ejpam-180	932	26	,	,	PUNCT
ejpam-180	932	27	λt	λt	X
ejpam-180	932	28	fü	fü	X
ejpam-180	932	29	(	(	PUNCT
ejpam-180	932	30	t	t	PROPN
ejpam-180	932	31	,	,	PUNCT
ejpam-180	932	32	u	u	NOUN
ejpam-180	932	33	,	,	PUNCT
ejpam-180	932	34	u̇	u̇	PROPN
ejpam-180	932	35	,	,	PUNCT
ejpam-180	932	36	ü	ü	PRON
ejpam-180	932	37	)	)	PUNCT
ejpam-180	932	38	=	=	PUNCT
ejpam-180	933	1	0=	0=	NUM
ejpam-180	933	2	y	y	PROPN
ejpam-180	933	3	(	(	PUNCT
ejpam-180	933	4	t	t	PROPN
ejpam-180	933	5	)	)	PUNCT
ejpam-180	933	6	t	t	PROPN
ejpam-180	933	7	gü	gü	PROPN
ejpam-180	933	8	(	(	PUNCT
ejpam-180	933	9	t	t	PROPN
ejpam-180	933	10	,	,	PUNCT
ejpam-180	933	11	u	u	NOUN
ejpam-180	933	12	,	,	PUNCT
ejpam-180	933	13	u̇	u̇	PROPN
ejpam-180	933	14	,	,	PUNCT
ejpam-180	933	15	ü	ü	NUM
ejpam-180	933	16	)	)	PUNCT
ejpam-180	933	17	,	,	PUNCT
ejpam-180	933	18	at	at	ADP
ejpam-180	933	19	t	t	NOUN
ejpam-180	933	20	=	=	SYM
ejpam-180	933	21	a	a	X
ejpam-180	933	22	,	,	PUNCT
ejpam-180	933	23	t	t	NOUN
ejpam-180	933	24	=	=	SYM
ejpam-180	933	25	b	b	PROPN
ejpam-180	933	26	,	,	PUNCT
ejpam-180	933	27	m	m	VERB
ejpam-180	933	28	∑	∑	ADV
ejpam-180	933	29	j=1	j=1	ADJ
ejpam-180	933	30	∫	∫	PROPN
ejpam-180	934	1	i	i	PRON
ejpam-180	934	2	y	y	PROPN
ejpam-180	934	3	j	j	PROPN
ejpam-180	934	4	(	(	PUNCT
ejpam-180	934	5	t	t	PROPN
ejpam-180	934	6	)	)	PUNCT
ejpam-180	934	7	g	g	PROPN
ejpam-180	934	8	j	j	PROPN
ejpam-180	934	9	(	(	PUNCT
ejpam-180	934	10	t	t	PROPN
ejpam-180	934	11	,	,	PUNCT
ejpam-180	934	12	u	u	NOUN
ejpam-180	934	13	,	,	PUNCT
ejpam-180	934	14	u̇	u̇	PROPN
ejpam-180	934	15	,	,	PUNCT
ejpam-180	934	16	ü	ü	NUM
ejpam-180	934	17	)	)	PUNCT
ejpam-180	935	1	d	d	NOUN
ejpam-180	935	2	t	t	PROPN
ejpam-180	935	3	≧	≧	NOUN
ejpam-180	935	4	0	0	NUM
ejpam-180	935	5	,	,	PUNCT
ejpam-180	935	6	t	t	PROPN
ejpam-180	935	7	∈	∈	PROPN
ejpam-180	936	1	i	i	PRON
ejpam-180	936	2	z̄	z̄	VERB
ejpam-180	936	3	i	i	PRON
ejpam-180	936	4	(	(	PUNCT
ejpam-180	936	5	t	t	PROPN
ejpam-180	936	6	)	)	PUNCT
ejpam-180	936	7	t	t	PROPN
ejpam-180	937	1	b	b	PROPN
ejpam-180	937	2	i	i	PROPN
ejpam-180	937	3	(	(	PUNCT
ejpam-180	937	4	t	t	PROPN
ejpam-180	937	5	)	)	PUNCT
ejpam-180	937	6	z̄	z̄	PROPN
ejpam-180	938	1	i	i	PRON
ejpam-180	938	2	(	(	PUNCT
ejpam-180	938	3	t)≦	t)≦	X
ejpam-180	938	4	1	1	NUM
ejpam-180	938	5	,	,	PUNCT
ejpam-180	938	6	t	t	PROPN
ejpam-180	938	7	∈	∈	PROPN
ejpam-180	939	1	i	i	PRON
ejpam-180	939	2	,	,	PUNCT
ejpam-180	939	3	i	i	PRON
ejpam-180	939	4	∈	∈	VERB
ejpam-180	939	5	p	p	PROPN
ejpam-180	939	6	λ	λ	X
ejpam-180	939	7	>	>	X
ejpam-180	939	8	0	0	PROPN
ejpam-180	939	9	,	,	PUNCT
ejpam-180	939	10	y	y	PROPN
ejpam-180	939	11	(	(	PUNCT
ejpam-180	939	12	t)≧	t)≧	PROPN
ejpam-180	939	13	0	0	NUM
ejpam-180	939	14	,	,	PUNCT
ejpam-180	939	15	t	t	PROPN
ejpam-180	939	16	∈	∈	PROPN
ejpam-180	940	1	i	i	PRON
ejpam-180	940	2	if	if	SCONJ
ejpam-180	940	3	the	the	DET
ejpam-180	940	4	function	function	NOUN
ejpam-180	940	5	in	in	ADP
ejpam-180	940	6	the	the	DET
ejpam-180	940	7	problem	problem	NOUN
ejpam-180	940	8	(	(	PUNCT
ejpam-180	940	9	wd	wd	PROPN
ejpam-180	940	10	)	)	PUNCT
ejpam-180	940	11	and	and	CCONJ
ejpam-180	940	12	(	(	PUNCT
ejpam-180	940	13	m	m	NOUN
ejpam-180	940	14	-	-	PUNCT
ejpam-180	940	15	wd	wd	NOUN
ejpam-180	940	16	)	)	PUNCT
ejpam-180	940	17	are	be	AUX
ejpam-180	940	18	independent	independent	ADJ
ejpam-180	940	19	of	of	ADP
ejpam-180	940	20	t	t	PROPN
ejpam-180	940	21	,	,	PUNCT
ejpam-180	940	22	then	then	ADV
ejpam-180	940	23	these	these	DET
ejpam-180	940	24	problems	problem	NOUN
ejpam-180	940	25	reduce	reduce	VERB
ejpam-180	940	26	to	to	ADP
ejpam-180	940	27	those	those	PRON
ejpam-180	940	28	treated	treat	VERB
ejpam-180	940	29	by	by	ADP
ejpam-180	940	30	mond	mond	PROPN
ejpam-180	940	31	,	,	PUNCT
ejpam-180	940	32	husain	husain	PROPN
ejpam-180	940	33	and	and	CCONJ
ejpam-180	940	34	prasad	prasad	PROPN
ejpam-180	941	1	[	[	X
ejpam-180	941	2	14	14	NUM
ejpam-180	941	3	]	]	PUNCT
ejpam-180	941	4	.	.	PUNCT
ejpam-180	942	1	(	(	PUNCT
ejpam-180	942	2	v	v	X
ejpam-180	942	3	p)1	p)1	NOUN
ejpam-180	942	4	:	:	PUNCT
ejpam-180	942	5	minimize	minimize	VERB
ejpam-180	942	6	�	�	PROPN
ejpam-180	942	7	f	f	PROPN
ejpam-180	942	8	1	1	NUM
ejpam-180	942	9	(	(	PUNCT
ejpam-180	942	10	x	x	NOUN
ejpam-180	942	11	)	)	PUNCT
ejpam-180	942	12	+	+	CCONJ
ejpam-180	942	13	�	�	PROPN
ejpam-180	942	14	x	x	SYM
ejpam-180	942	15	t	t	PROPN
ejpam-180	942	16	b1	b1	NOUN
ejpam-180	942	17	x	x	SYM
ejpam-180	942	18	�	�	PROPN
ejpam-180	942	19	1	1	NUM
ejpam-180	942	20	2	2	NUM
ejpam-180	942	21	,	,	PUNCT
ejpam-180	942	22	.	.	PUNCT
ejpam-180	942	23	.	.	PUNCT
ejpam-180	942	24	.	.	PUNCT
ejpam-180	943	1	,	,	PUNCT
ejpam-180	943	2	f	f	PROPN
ejpam-180	943	3	p	p	X
ejpam-180	943	4	(	(	PUNCT
ejpam-180	943	5	x	x	NOUN
ejpam-180	943	6	)	)	PUNCT
ejpam-180	943	7	+	+	CCONJ
ejpam-180	943	8	�	�	PROPN
ejpam-180	943	9	x	x	SYM
ejpam-180	943	10	t	t	PROPN
ejpam-180	943	11	bp	bp	PROPN
ejpam-180	943	12	x	x	SYM
ejpam-180	943	13	�	�	PROPN
ejpam-180	943	14	1	1	NUM
ejpam-180	943	15	2	2	NUM
ejpam-180	943	16	�	�	NOUN
ejpam-180	943	17	subject	subject	NOUN
ejpam-180	943	18	to	to	ADP
ejpam-180	943	19	g	g	PROPN
ejpam-180	943	20	(	(	PUNCT
ejpam-180	943	21	x)≦	x)≦	PROPN
ejpam-180	943	22	0	0	PROPN
ejpam-180	943	23	i.	i.	PROPN
ejpam-180	943	24	husain	husain	PROPN
ejpam-180	943	25	,	,	PUNCT
ejpam-180	943	26	a.	a.	PROPN
ejpam-180	943	27	ahmed	ahmed	PROPN
ejpam-180	943	28	,	,	PUNCT
ejpam-180	943	29	and	and	CCONJ
ejpam-180	943	30	g.	g.	PROPN
ejpam-180	943	31	rumana	rumana	PROPN
ejpam-180	943	32	/	/	SYM
ejpam-180	943	33	eur	eur	PROPN
ejpam-180	943	34	.	.	PUNCT
ejpam-180	944	1	j.	j.	PROPN
ejpam-180	944	2	pure	pure	PROPN
ejpam-180	944	3	appl	appl	PROPN
ejpam-180	944	4	.	.	PROPN
ejpam-180	944	5	math	math	PROPN
ejpam-180	944	6	,	,	PUNCT
ejpam-180	944	7	2	2	NUM
ejpam-180	944	8	(	(	PUNCT
ejpam-180	944	9	2009	2009	NUM
ejpam-180	944	10	)	)	PUNCT
ejpam-180	944	11	,	,	PUNCT
ejpam-180	944	12	(	(	PUNCT
ejpam-180	944	13	372	372	NUM
ejpam-180	944	14	-	-	SYM
ejpam-180	944	15	400	400	NUM
ejpam-180	944	16	)	)	PUNCT
ejpam-180	944	17	398	398	NUM
ejpam-180	944	18	(	(	PUNCT
ejpam-180	944	19	mw	mw	ADP
ejpam-180	944	20	d)1	d)1	NOUN
ejpam-180	944	21	:	:	PUNCT
ejpam-180	944	22	maximize	maximize	VERB
ejpam-180	944	23	�	�	PROPN
ejpam-180	944	24	f	f	PROPN
ejpam-180	944	25	1	1	NUM
ejpam-180	944	26	(	(	PUNCT
ejpam-180	944	27	u	u	NOUN
ejpam-180	944	28	)	)	PUNCT
ejpam-180	945	1	+	+	CCONJ
ejpam-180	945	2	ut	ut	PROPN
ejpam-180	945	3	b1z1	b1z1	X
ejpam-180	945	4	+	+	CCONJ
ejpam-180	945	5	yt	yt	PRON
ejpam-180	945	6	g	g	PROPN
ejpam-180	945	7	(	(	PUNCT
ejpam-180	945	8	u	u	NOUN
ejpam-180	945	9	)	)	PUNCT
ejpam-180	945	10	,	,	PUNCT
ejpam-180	945	11	.	.	PUNCT
ejpam-180	945	12	.	.	PUNCT
ejpam-180	945	13	.	.	PUNCT
ejpam-180	946	1	,	,	PUNCT
ejpam-180	946	2	f	f	PROPN
ejpam-180	946	3	p	p	X
ejpam-180	946	4	(	(	PUNCT
ejpam-180	946	5	u	u	NOUN
ejpam-180	946	6	)	)	PUNCT
ejpam-180	946	7	+	+	CCONJ
ejpam-180	946	8	ut	ut	PROPN
ejpam-180	946	9	bpzp	bpzp	NOUN
ejpam-180	946	10	+	+	CCONJ
ejpam-180	946	11	yt	yt	PRON
ejpam-180	946	12	g	g	PROPN
ejpam-180	946	13	(	(	PUNCT
ejpam-180	946	14	u	u	NOUN
ejpam-180	946	15	)	)	PUNCT
ejpam-180	946	16	�	�	PROPN
ejpam-180	946	17	subject	subject	ADJ
ejpam-180	946	18	to	to	ADP
ejpam-180	946	19	p	p	NOUN
ejpam-180	946	20	∑	∑	PROPN
ejpam-180	946	21	i=1	i=1	PROPN
ejpam-180	946	22	λi	λi	PROPN
ejpam-180	946	23	�	�	PROPN
ejpam-180	946	24	fx	fx	PROPN
ejpam-180	946	25	(	(	PUNCT
ejpam-180	946	26	u	u	NOUN
ejpam-180	946	27	)	)	PUNCT
ejpam-180	947	1	+	+	SYM
ejpam-180	947	2	b	b	X
ejpam-180	948	1	iz	iz	ADP
ejpam-180	948	2	i	i	PRON
ejpam-180	948	3	�	�	PROPN
ejpam-180	949	1	+	+	CCONJ
ejpam-180	949	2	yt	yt	PROPN
ejpam-180	949	3	gx	gx	PROPN
ejpam-180	949	4	(	(	PUNCT
ejpam-180	949	5	u	u	NOUN
ejpam-180	949	6	)	)	PUNCT
ejpam-180	949	7	=	=	SYM
ejpam-180	949	8	0	0	NUM
ejpam-180	949	9	z̄	z̄	PROPN
ejpam-180	949	10	ib	ib	NOUN
ejpam-180	950	1	i	i	PRON
ejpam-180	950	2	z̄	z̄	VERB
ejpam-180	950	3	i	i	PRON
ejpam-180	950	4	≦	≦	NOUN
ejpam-180	950	5	1	1	NUM
ejpam-180	950	6	,	,	PUNCT
ejpam-180	950	7	i	i	PRON
ejpam-180	950	8	∈	∈	VERB
ejpam-180	950	9	p	p	NOUN
ejpam-180	950	10	y	y	PROPN
ejpam-180	950	11	≧	≧	NUM
ejpam-180	950	12	0	0	NUM
ejpam-180	950	13	,	,	PUNCT
ejpam-180	950	14	λ	λ	PROPN
ejpam-180	950	15	∈	∈	PROPN
ejpam-180	950	16	λ+	λ+	PUNCT
ejpam-180	950	17	where	where	SCONJ
ejpam-180	950	18	λ+	λ+	PUNCT
ejpam-180	950	19	=	=	SYM
ejpam-180	950	20	¦	¦	NOUN
ejpam-180	950	21	λ	λ	X
ejpam-180	950	22	∈	∈	PROPN
ejpam-180	950	23	rp	rp	NOUN
ejpam-180	950	24	|λ	|λ	ADV
ejpam-180	950	25	>	>	X
ejpam-180	950	26	0	0	NUM
ejpam-180	950	27	,	,	PUNCT
ejpam-180	950	28	λt	λt	ADP
ejpam-180	950	29	e	e	NOUN
ejpam-180	950	30	=	=	SYM
ejpam-180	950	31	1	1	NUM
ejpam-180	950	32	,	,	PUNCT
ejpam-180	950	33	e	e	X
ejpam-180	950	34	=	=	PUNCT
ejpam-180	950	35	(	(	PUNCT
ejpam-180	950	36	1	1	NUM
ejpam-180	950	37	,	,	PUNCT
ejpam-180	950	38	1	1	NUM
ejpam-180	950	39	,	,	PUNCT
ejpam-180	950	40	.	.	PUNCT
ejpam-180	950	41	.	.	PUNCT
ejpam-180	951	1	.	.	PUNCT
ejpam-180	952	1	,	,	PUNCT
ejpam-180	952	2	1	1	X
ejpam-180	952	3	)	)	PUNCT
ejpam-180	952	4	t	t	NOUN
ejpam-180	952	5	∈	∈	PROPN
ejpam-180	952	6	rp	rp	NOUN
ejpam-180	953	1	©	©	PROPN
ejpam-180	953	2	(	(	PUNCT
ejpam-180	953	3	m	m	PROPN
ejpam-180	953	4	-w	-w	PROPN
ejpam-180	953	5	v	v	PROPN
ejpam-180	953	6	d)1	d)1	NOUN
ejpam-180	953	7	:	:	PUNCT
ejpam-180	953	8	maximize	maximize	VERB
ejpam-180	953	9	�	�	PROPN
ejpam-180	953	10	f	f	PROPN
ejpam-180	953	11	1	1	NUM
ejpam-180	953	12	(	(	PUNCT
ejpam-180	953	13	u	u	NOUN
ejpam-180	953	14	)	)	PUNCT
ejpam-180	953	15	+	+	CCONJ
ejpam-180	953	16	ut	ut	PROPN
ejpam-180	953	17	b1z1	b1z1	PROPN
ejpam-180	953	18	,	,	PUNCT
ejpam-180	953	19	.	.	PUNCT
ejpam-180	953	20	.	.	PUNCT
ejpam-180	953	21	.	.	PUNCT
ejpam-180	954	1	,	,	PUNCT
ejpam-180	954	2	f	f	PROPN
ejpam-180	954	3	p	p	X
ejpam-180	954	4	(	(	PUNCT
ejpam-180	954	5	u	u	NOUN
ejpam-180	954	6	)	)	PUNCT
ejpam-180	954	7	+	+	CCONJ
ejpam-180	954	8	ut	ut	PROPN
ejpam-180	954	9	bpzp	bpzp	PROPN
ejpam-180	954	10	�	�	PROPN
ejpam-180	954	11	subject	subject	ADJ
ejpam-180	954	12	to	to	ADP
ejpam-180	954	13	p	p	NOUN
ejpam-180	954	14	∑	∑	PROPN
ejpam-180	954	15	i=1	i=1	PROPN
ejpam-180	954	16	λi	λi	PROPN
ejpam-180	954	17	�	�	PROPN
ejpam-180	954	18	fx	fx	PROPN
ejpam-180	954	19	(	(	PUNCT
ejpam-180	954	20	u	u	NOUN
ejpam-180	954	21	)	)	PUNCT
ejpam-180	955	1	+	+	SYM
ejpam-180	955	2	b	b	X
ejpam-180	956	1	iz	iz	ADP
ejpam-180	956	2	i	i	PRON
ejpam-180	956	3	�	�	PROPN
ejpam-180	957	1	+	+	CCONJ
ejpam-180	957	2	yt	yt	PROPN
ejpam-180	957	3	gx	gx	PROPN
ejpam-180	957	4	(	(	PUNCT
ejpam-180	957	5	u	u	NOUN
ejpam-180	957	6	)	)	PUNCT
ejpam-180	957	7	=	=	SYM
ejpam-180	957	8	0	0	PUNCT
ejpam-180	958	1	yt	yt	VERB
ejpam-180	958	2	g	g	PROPN
ejpam-180	958	3	(	(	PUNCT
ejpam-180	958	4	u)≧	u)≧	NOUN
ejpam-180	958	5	0	0	NUM
ejpam-180	958	6	,	,	PUNCT
ejpam-180	958	7	t	t	PROPN
ejpam-180	958	8	∈	∈	PROPN
ejpam-180	958	9	i	i	PRON
ejpam-180	958	10	z̄	z̄	VERB
ejpam-180	958	11	ib	ib	NOUN
ejpam-180	959	1	i	i	PRON
ejpam-180	959	2	z̄	z̄	VERB
ejpam-180	959	3	i	i	PRON
ejpam-180	959	4	≦	≦	NOUN
ejpam-180	959	5	1	1	NUM
ejpam-180	959	6	,	,	PUNCT
ejpam-180	959	7	i	i	PRON
ejpam-180	959	8	∈	∈	VERB
ejpam-180	959	9	p	p	PROPN
ejpam-180	959	10	λ	λ	X
ejpam-180	959	11	>	>	X
ejpam-180	959	12	0	0	PROPN
ejpam-180	959	13	,	,	PUNCT
ejpam-180	959	14	y	y	PROPN
ejpam-180	959	15	(	(	PUNCT
ejpam-180	959	16	t)≧	t)≧	PROPN
ejpam-180	959	17	0	0	NUM
ejpam-180	959	18	,	,	PUNCT
ejpam-180	959	19	t	t	PROPN
ejpam-180	959	20	∈	∈	PROPN
ejpam-180	960	1	i	i	PRON
ejpam-180	960	2	7	7	X
ejpam-180	960	3	.	.	PUNCT
ejpam-180	960	4	conclusion	conclusion	NOUN
ejpam-180	960	5	we	we	PRON
ejpam-180	960	6	have	have	AUX
ejpam-180	960	7	considered	consider	VERB
ejpam-180	960	8	wolfe	wolfe	PROPN
ejpam-180	960	9	and	and	CCONJ
ejpam-180	960	10	mond	mond	PROPN
ejpam-180	960	11	-	-	PUNCT
ejpam-180	960	12	weir	weir	PROPN
ejpam-180	960	13	type	type	PROPN
ejpam-180	960	14	vector	vector	NOUN
ejpam-180	960	15	dual	dual	ADJ
ejpam-180	960	16	variational	variational	ADJ
ejpam-180	960	17	problems	problem	NOUN
ejpam-180	960	18	for	for	ADP
ejpam-180	960	19	a	a	DET
ejpam-180	960	20	class	class	NOUN
ejpam-180	960	21	of	of	ADP
ejpam-180	960	22	nondifferentiable	nondifferentiable	ADJ
ejpam-180	960	23	multiobjective	multiobjective	ADJ
ejpam-180	960	24	variational	variational	ADJ
ejpam-180	960	25	problem	problem	NOUN
ejpam-180	960	26	involving	involve	VERB
ejpam-180	960	27	higher	high	ADJ
ejpam-180	960	28	order	order	NOUN
ejpam-180	960	29	derivatives	derivative	NOUN
ejpam-180	960	30	.	.	PUNCT
ejpam-180	961	1	making	make	VERB
ejpam-180	961	2	use	use	NOUN
ejpam-180	961	3	of	of	ADP
ejpam-180	961	4	the	the	DET
ejpam-180	961	5	concepts	concept	NOUN
ejpam-180	961	6	of	of	ADP
ejpam-180	961	7	efficiency	efficiency	NOUN
ejpam-180	961	8	,	,	PUNCT
ejpam-180	961	9	we	we	PRON
ejpam-180	961	10	obtain	obtain	VERB
ejpam-180	961	11	weak	weak	ADJ
ejpam-180	961	12	,	,	PUNCT
ejpam-180	961	13	strong	strong	ADJ
ejpam-180	961	14	and	and	CCONJ
ejpam-180	961	15	converse	converse	NOUN
ejpam-180	961	16	duality	duality	NOUN
ejpam-180	961	17	theorems	theorem	VERB
ejpam-180	961	18	under	under	ADP
ejpam-180	961	19	assumptions	assumption	NOUN
ejpam-180	961	20	of	of	ADP
ejpam-180	961	21	invexity	invexity	NOUN
ejpam-180	961	22	and	and	CCONJ
ejpam-180	961	23	generalized	generalized	ADJ
ejpam-180	961	24	invexity	invexity	NOUN
ejpam-180	961	25	.	.	PUNCT
ejpam-180	962	1	we	we	PRON
ejpam-180	962	2	have	have	AUX
ejpam-180	962	3	also	also	ADV
ejpam-180	962	4	established	establish	VERB
ejpam-180	962	5	close	close	ADJ
ejpam-180	962	6	relationship	relationship	NOUN
ejpam-180	962	7	between	between	ADP
ejpam-180	962	8	these	these	DET
ejpam-180	962	9	problems	problem	NOUN
ejpam-180	962	10	with	with	ADP
ejpam-180	962	11	corresponding	correspond	VERB
ejpam-180	962	12	nonlinear	nonlinear	ADJ
ejpam-180	962	13	programming	programming	NOUN
ejpam-180	962	14	problem	problem	NOUN
ejpam-180	962	15	.	.	PUNCT
ejpam-180	963	1	one	one	PRON
ejpam-180	963	2	can	can	AUX
ejpam-180	963	3	replace	replace	VERB
ejpam-180	963	4	the	the	DET
ejpam-180	963	5	square	square	ADJ
ejpam-180	963	6	roots	root	NOUN
ejpam-180	963	7	of	of	ADP
ejpam-180	963	8	quadratic	quadratic	ADJ
ejpam-180	963	9	form	form	NOUN
ejpam-180	963	10	by	by	ADP
ejpam-180	963	11	support	support	NOUN
ejpam-180	963	12	function	function	NOUN
ejpam-180	963	13	of	of	ADP
ejpam-180	963	14	a	a	DET
ejpam-180	963	15	compact	compact	ADJ
ejpam-180	963	16	convex	convex	NOUN
ejpam-180	963	17	set	set	NOUN
ejpam-180	963	18	that	that	PRON
ejpam-180	963	19	is	be	AUX
ejpam-180	963	20	somewhat	somewhat	ADV
ejpam-180	963	21	more	more	ADV
ejpam-180	963	22	general	general	ADJ
ejpam-180	963	23	and	and	CCONJ
ejpam-180	963	24	for	for	ADP
ejpam-180	963	25	which	which	PRON
ejpam-180	963	26	the	the	DET
ejpam-180	963	27	subdifferential	subdifferential	NOUN
ejpam-180	963	28	may	may	AUX
ejpam-180	963	29	be	be	AUX
ejpam-180	963	30	expressed	express	VERB
ejpam-180	963	31	.	.	PUNCT
ejpam-180	964	1	it	it	PRON
ejpam-180	964	2	is	be	AUX
ejpam-180	964	3	difficult	difficult	ADJ
ejpam-180	964	4	to	to	PART
ejpam-180	964	5	exhibit	exhibit	VERB
ejpam-180	964	6	any	any	DET
ejpam-180	964	7	practical	practical	ADJ
ejpam-180	964	8	application	application	NOUN
ejpam-180	964	9	to	to	ADP
ejpam-180	964	10	our	our	PRON
ejpam-180	964	11	model	model	NOUN
ejpam-180	964	12	as	as	SCONJ
ejpam-180	964	13	they	they	PRON
ejpam-180	964	14	are	be	AUX
ejpam-180	964	15	inherently	inherently	ADV
ejpam-180	964	16	very	very	ADV
ejpam-180	964	17	involved	involved	ADJ
ejpam-180	964	18	.	.	PUNCT
ejpam-180	965	1	there	there	PRON
ejpam-180	965	2	is	be	VERB
ejpam-180	965	3	a	a	DET
ejpam-180	965	4	rich	rich	ADJ
ejpam-180	965	5	scope	scope	NOUN
ejpam-180	965	6	to	to	PART
ejpam-180	965	7	study	study	VERB
ejpam-180	965	8	this	this	DET
ejpam-180	965	9	problem	problem	NOUN
ejpam-180	965	10	in	in	ADP
ejpam-180	965	11	multiobjective	multiobjective	ADJ
ejpam-180	965	12	setting	setting	NOUN
ejpam-180	965	13	.	.	PUNCT
ejpam-180	966	1	one	one	PRON
ejpam-180	966	2	can	can	AUX
ejpam-180	966	3	also	also	ADV
ejpam-180	966	4	formulate	formulate	VERB
ejpam-180	966	5	a	a	DET
ejpam-180	966	6	fractional	fractional	ADJ
ejpam-180	966	7	analogue	analogue	NOUN
ejpam-180	966	8	of	of	ADP
ejpam-180	966	9	our	our	PRON
ejpam-180	966	10	model	model	NOUN
ejpam-180	966	11	to	to	PART
ejpam-180	966	12	study	study	VERB
ejpam-180	966	13	various	various	ADJ
ejpam-180	966	14	duality	duality	NOUN
ejpam-180	966	15	results	result	NOUN
ejpam-180	966	16	.	.	PUNCT
ejpam-180	967	1	references	reference	NOUN
ejpam-180	967	2	399	399	NUM
ejpam-180	967	3	acknowledgements	acknowledgement	NOUN
ejpam-180	967	4	the	the	DET
ejpam-180	967	5	authors	author	NOUN
ejpam-180	967	6	are	be	AUX
ejpam-180	967	7	grateful	grateful	ADJ
ejpam-180	967	8	to	to	ADP
ejpam-180	967	9	the	the	DET
ejpam-180	967	10	anonymous	anonymous	ADJ
ejpam-180	967	11	referee	referee	NOUN
ejpam-180	967	12	for	for	ADP
ejpam-180	967	13	his	his	PRON
ejpam-180	967	14	/	/	SYM
ejpam-180	967	15	her	her	PRON
ejpam-180	967	16	valuable	valuable	ADJ
ejpam-180	967	17	comments	comment	NOUN
ejpam-180	967	18	that	that	PRON
ejpam-180	967	19	have	have	AUX
ejpam-180	967	20	substantially	substantially	ADV
ejpam-180	967	21	improved	improve	VERB
ejpam-180	967	22	the	the	DET
ejpam-180	967	23	presentation	presentation	NOUN
ejpam-180	967	24	of	of	ADP
ejpam-180	967	25	this	this	DET
ejpam-180	967	26	research	research	NOUN
ejpam-180	967	27	.	.	PUNCT
ejpam-180	968	1	references	reference	NOUN
ejpam-180	968	2	[	[	X
ejpam-180	968	3	1	1	NUM
ejpam-180	968	4	]	]	X
ejpam-180	968	5	c.r.bector	c.r.bector	NOUN
ejpam-180	968	6	and	and	CCONJ
ejpam-180	968	7	i.husain	i.husain	VERB
ejpam-180	968	8	,	,	PUNCT
ejpam-180	968	9	“	"	PUNCT
ejpam-180	968	10	duality	duality	NOUN
ejpam-180	968	11	for	for	ADP
ejpam-180	968	12	multiobjective	multiobjective	ADJ
ejpam-180	968	13	variational	variational	ADJ
ejpam-180	968	14	problems	problem	NOUN
ejpam-180	968	15	,	,	PUNCT
ejpam-180	968	16	journal	journal	NOUN
ejpam-180	968	17	of	of	ADP
ejpam-180	968	18	math	math	NOUN
ejpam-180	968	19	.	.	PUNCT
ejpam-180	969	1	anal	anal	PROPN
ejpam-180	969	2	.	.	PUNCT
ejpam-180	970	1	and	and	CCONJ
ejpam-180	970	2	appl	appl	PROPN
ejpam-180	970	3	.	.	PROPN
ejpam-180	971	1	166	166	NUM
ejpam-180	971	2	,	,	PUNCT
ejpam-180	971	3	no.1	no.1	NUM
ejpam-180	971	4	,	,	PUNCT
ejpam-180	971	5	214	214	NUM
ejpam-180	971	6	-	-	SYM
ejpam-180	971	7	224	224	NUM
ejpam-180	971	8	,	,	PUNCT
ejpam-180	971	9	(	(	PUNCT
ejpam-180	971	10	1992	1992	NUM
ejpam-180	971	11	)	)	PUNCT
ejpam-180	971	12	.	.	PUNCT
ejpam-180	972	1	[	[	X
ejpam-180	972	2	2	2	NUM
ejpam-180	972	3	]	]	PUNCT
ejpam-180	972	4	c.r.bector	c.r.bector	NOUN
ejpam-180	972	5	,	,	PUNCT
ejpam-180	972	6	s.chandra	s.chandra	NOUN
ejpam-180	972	7	and	and	CCONJ
ejpam-180	972	8	i.husain	i.husain	VERB
ejpam-180	972	9	,	,	PUNCT
ejpam-180	972	10	“	"	PUNCT
ejpam-180	972	11	generalized	generalized	ADJ
ejpam-180	972	12	concavity	concavity	NOUN
ejpam-180	972	13	and	and	CCONJ
ejpam-180	972	14	nondifferentiable	nondifferentiable	ADJ
ejpam-180	972	15	continuous	continuous	ADJ
ejpam-180	972	16	programming	programming	NOUN
ejpam-180	972	17	duality	duality	NOUN
ejpam-180	972	18	"	"	PUNCT
ejpam-180	972	19	,	,	PUNCT
ejpam-180	972	20	research	research	NOUN
ejpam-180	972	21	report	report	NOUN
ejpam-180	972	22	#	#	NOUN
ejpam-180	972	23	85	85	NUM
ejpam-180	972	24	-	-	SYM
ejpam-180	972	25	7	7	NUM
ejpam-180	972	26	,	,	PUNCT
ejpam-180	972	27	faculty	faculty	NOUN
ejpam-180	972	28	of	of	ADP
ejpam-180	972	29	administrative	administrative	ADJ
ejpam-180	972	30	studies	study	NOUN
ejpam-180	972	31	,	,	PUNCT
ejpam-180	972	32	the	the	DET
ejpam-180	972	33	university	university	PROPN
ejpam-180	972	34	of	of	ADP
ejpam-180	972	35	manitoba	manitoba	PROPN
ejpam-180	972	36	,	,	PUNCT
ejpam-180	972	37	winnipeg	winnipeg	PROPN
ejpam-180	972	38	,	,	PUNCT
ejpam-180	972	39	canada	canada	PROPN
ejpam-180	972	40	r3	r3	PROPN
ejpam-180	972	41	t	t	PROPN
ejpam-180	972	42	2n2	2n2	NUM
ejpam-180	972	43	,	,	PUNCT
ejpam-180	972	44	(	(	PUNCT
ejpam-180	972	45	1985	1985	NUM
ejpam-180	972	46	)	)	PUNCT
ejpam-180	972	47	.	.	PUNCT
ejpam-180	973	1	[	[	X
ejpam-180	973	2	3	3	X
ejpam-180	973	3	]	]	X
ejpam-180	973	4	s.chandra	s.chandra	NOUN
ejpam-180	973	5	,	,	PUNCT
ejpam-180	973	6	b.d.craven	b.d.craven	NOUN
ejpam-180	973	7	,	,	PUNCT
ejpam-180	973	8	i.husain	i.husain	VERB
ejpam-180	973	9	,	,	PUNCT
ejpam-180	973	10	“	"	PUNCT
ejpam-180	973	11	a	a	DET
ejpam-180	973	12	class	class	NOUN
ejpam-180	973	13	of	of	ADP
ejpam-180	973	14	nondifferentiable	nondifferentiable	ADJ
ejpam-180	973	15	continuous	continuous	ADJ
ejpam-180	973	16	programming	programming	NOUN
ejpam-180	973	17	problem	problem	NOUN
ejpam-180	973	18	,	,	PUNCT
ejpam-180	973	19	j.	j.	PROPN
ejpam-180	973	20	math	math	PROPN
ejpam-180	973	21	.	.	PUNCT
ejpam-180	974	1	anal	anal	PROPN
ejpam-180	974	2	.	.	PUNCT
ejpam-180	975	1	appl.107	appl.107	CCONJ
ejpam-180	975	2	122	122	NUM
ejpam-180	975	3	-	-	SYM
ejpam-180	975	4	131	131	NUM
ejpam-180	975	5	(	(	PUNCT
ejpam-180	975	6	1985	1985	NUM
ejpam-180	975	7	)	)	PUNCT
ejpam-180	975	8	.	.	PUNCT
ejpam-180	976	1	[	[	X
ejpam-180	976	2	4	4	NUM
ejpam-180	976	3	]	]	PUNCT
ejpam-180	976	4	f.h.clarke	f.h.clarke	NOUN
ejpam-180	976	5	,	,	PUNCT
ejpam-180	976	6	“	"	PUNCT
ejpam-180	976	7	optimization	optimization	NOUN
ejpam-180	976	8	and	and	CCONJ
ejpam-180	976	9	non	non	ADJ
ejpam-180	976	10	-	-	ADJ
ejpam-180	976	11	smooth	smooth	ADJ
ejpam-180	976	12	analysis	analysis	NOUN
ejpam-180	976	13	"	"	PUNCT
ejpam-180	976	14	,	,	PUNCT
ejpam-180	976	15	wiley	wiley	PROPN
ejpam-180	976	16	,	,	PUNCT
ejpam-180	976	17	new	new	PROPN
ejpam-180	976	18	york	york	PROPN
ejpam-180	976	19	,	,	PUNCT
ejpam-180	976	20	(	(	PUNCT
ejpam-180	976	21	1983	1983	NUM
ejpam-180	976	22	)	)	PUNCT
ejpam-180	976	23	.	.	PUNCT
ejpam-180	977	1	[	[	X
ejpam-180	977	2	5	5	X
ejpam-180	977	3	]	]	PUNCT
ejpam-180	977	4	v.chankong	v.chankong	NOUN
ejpam-180	977	5	and	and	CCONJ
ejpam-180	977	6	y.y.haimes	y.y.haime	NOUN
ejpam-180	977	7	,	,	PUNCT
ejpam-180	977	8	“	"	PUNCT
ejpam-180	977	9	multiobjective	multiobjective	ADJ
ejpam-180	977	10	decision	decision	NOUN
ejpam-180	977	11	making	making	NOUN
ejpam-180	977	12	:	:	PUNCT
ejpam-180	977	13	theory	theory	NOUN
ejpam-180	977	14	and	and	CCONJ
ejpam-180	977	15	methodology	methodology	NOUN
ejpam-180	977	16	"	"	PUNCT
ejpam-180	977	17	,	,	PUNCT
ejpam-180	977	18	north	north	NOUN
ejpam-180	977	19	-	-	PUNCT
ejpam-180	977	20	holland	holland	PROPN
ejpam-180	977	21	,	,	PUNCT
ejpam-180	977	22	new	new	PROPN
ejpam-180	977	23	york	york	PROPN
ejpam-180	977	24	,	,	PUNCT
ejpam-180	977	25	(	(	PUNCT
ejpam-180	977	26	1983	1983	NUM
ejpam-180	977	27	)	)	PUNCT
ejpam-180	977	28	.	.	PUNCT
ejpam-180	978	1	[	[	X
ejpam-180	978	2	6	6	NUM
ejpam-180	978	3	]	]	PUNCT
ejpam-180	978	4	v.f.demyanov	v.f.demyanov	NOUN
ejpam-180	978	5	and	and	CCONJ
ejpam-180	978	6	l.c.w.dixon	l.c.w.dixon	PROPN
ejpam-180	978	7	,	,	PUNCT
ejpam-180	978	8	“	"	PUNCT
ejpam-180	978	9	quasidifferential	quasidifferential	ADJ
ejpam-180	978	10	calculus	calculus	NOUN
ejpam-180	978	11	"	"	PUNCT
ejpam-180	978	12	,	,	PUNCT
ejpam-180	978	13	mathematical	mathematical	ADJ
ejpam-180	978	14	programming	programming	NOUN
ejpam-180	978	15	study	study	NOUN
ejpam-180	978	16	29	29	NUM
ejpam-180	978	17	,	,	PUNCT
ejpam-180	978	18	north	north	NOUN
ejpam-180	978	19	holland	holland	PROPN
ejpam-180	978	20	,	,	PUNCT
ejpam-180	978	21	amsterdam	amsterdam	PROPN
ejpam-180	978	22	(	(	PUNCT
ejpam-180	978	23	1989	1989	NUM
ejpam-180	978	24	)	)	PUNCT
ejpam-180	978	25	.	.	PUNCT
ejpam-180	979	1	[	[	X
ejpam-180	979	2	7	7	X
ejpam-180	979	3	]	]	SYM
ejpam-180	979	4	i.husain	i.husain	NOUN
ejpam-180	979	5	and	and	CCONJ
ejpam-180	979	6	z.jabeen	z.jabeen	NUM
ejpam-180	979	7	,	,	PUNCT
ejpam-180	979	8	“	"	PUNCT
ejpam-180	979	9	on	on	ADP
ejpam-180	979	10	variational	variational	ADJ
ejpam-180	979	11	problems	problem	NOUN
ejpam-180	979	12	involving	involve	VERB
ejpam-180	979	13	higher	high	ADJ
ejpam-180	979	14	order	order	NOUN
ejpam-180	979	15	derivatives	derivative	NOUN
ejpam-180	979	16	"	"	PUNCT
ejpam-180	979	17	,	,	PUNCT
ejpam-180	979	18	j.math	j.math	NOUN
ejpam-180	979	19	.	.	PUNCT
ejpam-180	980	1	and	and	CCONJ
ejpam-180	980	2	computing	computing	NOUN
ejpam-180	980	3	vol	vol	NOUN
ejpam-180	980	4	.	.	PROPN
ejpam-180	981	1	27	27	NUM
ejpam-180	981	2	,	,	PUNCT
ejpam-180	981	3	no	no	INTJ
ejpam-180	981	4	.	.	NOUN
ejpam-180	981	5	1	1	NUM
ejpam-180	981	6	-	-	SYM
ejpam-180	981	7	2	2	NUM
ejpam-180	981	8	,	,	PUNCT
ejpam-180	981	9	433	433	NUM
ejpam-180	981	10	-	-	SYM
ejpam-180	981	11	455	455	NUM
ejpam-180	981	12	,	,	PUNCT
ejpam-180	981	13	(	(	PUNCT
ejpam-180	981	14	2005	2005	NUM
ejpam-180	981	15	)	)	PUNCT
ejpam-180	981	16	.	.	PUNCT
ejpam-180	982	1	[	[	X
ejpam-180	982	2	8	8	NUM
ejpam-180	982	3	]	]	SYM
ejpam-180	982	4	i.husain	i.husain	VERB
ejpam-180	982	5	,	,	PUNCT
ejpam-180	982	6	a.ahmed	a.ahmed	ADJ
ejpam-180	982	7	and	and	CCONJ
ejpam-180	982	8	rumana	rumana	PROPN
ejpam-180	982	9	,	,	PUNCT
ejpam-180	982	10	g.mattoo	g.mattoo	ADV
ejpam-180	982	11	,	,	PUNCT
ejpam-180	982	12	“	"	PUNCT
ejpam-180	982	13	optimality	optimality	NOUN
ejpam-180	982	14	criteria	criterion	NOUN
ejpam-180	982	15	and	and	CCONJ
ejpam-180	982	16	duality	duality	NOUN
ejpam-180	982	17	in	in	ADP
ejpam-180	982	18	multiobjective	multiobjective	ADJ
ejpam-180	982	19	variational	variational	ADJ
ejpam-180	982	20	problems	problem	NOUN
ejpam-180	982	21	involving	involve	VERB
ejpam-180	982	22	higher	high	ADJ
ejpam-180	982	23	order	order	NOUN
ejpam-180	982	24	derivatives	derivative	NOUN
ejpam-180	982	25	"	"	PUNCT
ejpam-180	982	26	,	,	PUNCT
ejpam-180	982	27	j.	j.	PROPN
ejpam-180	982	28	appl	appl	PROPN
ejpam-180	982	29	.	.	PROPN
ejpam-180	982	30	math	math	PROPN
ejpam-180	982	31	.	.	PUNCT
ejpam-180	983	1	&	&	CCONJ
ejpam-180	983	2	informatics	informatics	PROPN
ejpam-180	983	3	vol	vol	NOUN
ejpam-180	983	4	.	.	PROPN
ejpam-180	984	1	27	27	NUM
ejpam-180	984	2	,	,	PUNCT
ejpam-180	984	3	no	no	INTJ
ejpam-180	984	4	.	.	NOUN
ejpam-180	984	5	1	1	NUM
ejpam-180	984	6	2	2	NUM
ejpam-180	984	7	,	,	PUNCT
ejpam-180	984	8	pp	pp	ADJ
ejpam-180	984	9	.	.	PUNCT
ejpam-180	985	1	123	123	NUM
ejpam-180	985	2	-	-	SYM
ejpam-180	985	3	137	137	NUM
ejpam-180	985	4	,	,	PUNCT
ejpam-180	985	5	(	(	PUNCT
ejpam-180	985	6	2009	2009	NUM
ejpam-180	985	7	)	)	PUNCT
ejpam-180	985	8	.	.	PUNCT
ejpam-180	986	1	[	[	X
ejpam-180	986	2	9	9	X
ejpam-180	986	3	]	]	PUNCT
ejpam-180	986	4	d.s.kim	d.s.kim	PROPN
ejpam-180	986	5	and	and	CCONJ
ejpam-180	986	6	a.l.kim	a.l.kim	PROPN
ejpam-180	986	7	,	,	PUNCT
ejpam-180	986	8	“	"	PUNCT
ejpam-180	986	9	optimality	optimality	NOUN
ejpam-180	986	10	and	and	CCONJ
ejpam-180	986	11	duality	duality	NOUN
ejpam-180	986	12	for	for	ADP
ejpam-180	986	13	nondifferentiable	nondifferentiable	ADJ
ejpam-180	986	14	multiobjective	multiobjective	ADJ
ejpam-180	986	15	variational	variational	ADJ
ejpam-180	986	16	problems	problem	NOUN
ejpam-180	986	17	"	"	PUNCT
ejpam-180	986	18	,	,	PUNCT
ejpam-180	986	19	j.	j.	PROPN
ejpam-180	986	20	math	math	PROPN
ejpam-180	986	21	.	.	PUNCT
ejpam-180	987	1	anal	anal	PROPN
ejpam-180	987	2	.	.	PUNCT
ejpam-180	988	1	appl	appl	PROPN
ejpam-180	988	2	.	.	PROPN
ejpam-180	988	3	274	274	NUM
ejpam-180	988	4	,	,	PUNCT
ejpam-180	988	5	255	255	NUM
ejpam-180	988	6	-	-	SYM
ejpam-180	988	7	278	278	NUM
ejpam-180	988	8	(	(	PUNCT
ejpam-180	988	9	2002	2002	NUM
ejpam-180	988	10	)	)	PUNCT
ejpam-180	988	11	.	.	PUNCT
ejpam-180	989	1	references	reference	NOUN
ejpam-180	989	2	400	400	NUM
ejpam-180	989	3	[	[	SYM
ejpam-180	989	4	10	10	NUM
ejpam-180	989	5	]	]	X
ejpam-180	989	6	j.c	j.c	PROPN
ejpam-180	989	7	.	.	PROPN
ejpam-180	989	8	liu	liu	PROPN
ejpam-180	989	9	,	,	PUNCT
ejpam-180	989	10	“	"	PUNCT
ejpam-180	989	11	duality	duality	NOUN
ejpam-180	989	12	for	for	ADP
ejpam-180	989	13	nondifferentiable	nondifferentiable	ADJ
ejpam-180	989	14	static	static	ADJ
ejpam-180	989	15	multiobjective	multiobjective	ADJ
ejpam-180	989	16	variational	variational	ADJ
ejpam-180	989	17	problems	problem	NOUN
ejpam-180	989	18	involving	involve	VERB
ejpam-180	989	19	generalized	generalized	ADJ
ejpam-180	989	20	(	(	PUNCT
ejpam-180	989	21	f	f	X
ejpam-180	989	22	,	,	PUNCT
ejpam-180	989	23	ρ)-convex	ρ)-convex	NOUN
ejpam-180	989	24	functions	function	NOUN
ejpam-180	989	25	,	,	PUNCT
ejpam-180	989	26	comput	comput	NOUN
ejpam-180	989	27	.	.	PUNCT
ejpam-180	990	1	math	math	NOUN
ejpam-180	990	2	.	.	PUNCT
ejpam-180	991	1	appl	appl	PROPN
ejpam-180	991	2	.	.	PROPN
ejpam-180	991	3	,	,	PUNCT
ejpam-180	991	4	31	31	NUM
ejpam-180	991	5	(	(	PUNCT
ejpam-180	991	6	12	12	NUM
ejpam-180	991	7	)	)	PUNCT
ejpam-180	991	8	,	,	PUNCT
ejpam-180	991	9	77	77	NUM
ejpam-180	991	10	-	-	SYM
ejpam-180	991	11	89	89	NUM
ejpam-180	991	12	,	,	PUNCT
ejpam-180	991	13	(	(	PUNCT
ejpam-180	991	14	1996	1996	NUM
ejpam-180	991	15	)	)	PUNCT
ejpam-180	991	16	.	.	PUNCT
ejpam-180	992	1	[	[	X
ejpam-180	992	2	11	11	NUM
ejpam-180	992	3	]	]	X
ejpam-180	992	4	s.k.mishra	s.k.mishra	NOUN
ejpam-180	992	5	,	,	PUNCT
ejpam-180	992	6	r.n	r.n	PROPN
ejpam-180	992	7	.	.	PROPN
ejpam-180	992	8	mukerjee	mukerjee	PROPN
ejpam-180	992	9	,	,	PUNCT
ejpam-180	992	10	“	"	PUNCT
ejpam-180	992	11	on	on	ADP
ejpam-180	992	12	efficiency	efficiency	NOUN
ejpam-180	992	13	and	and	CCONJ
ejpam-180	992	14	duality	duality	NOUN
ejpam-180	992	15	for	for	ADP
ejpam-180	992	16	multiobjective	multiobjective	ADJ
ejpam-180	992	17	variational	variational	ADJ
ejpam-180	992	18	problems	problem	NOUN
ejpam-180	992	19	"	"	PUNCT
ejpam-180	992	20	,	,	PUNCT
ejpam-180	992	21	j.	j.	PROPN
ejpam-180	992	22	math	math	PROPN
ejpam-180	992	23	.	.	PUNCT
ejpam-180	993	1	anal	anal	PROPN
ejpam-180	993	2	.	.	PUNCT
ejpam-180	994	1	appl	appl	PROPN
ejpam-180	994	2	.	.	PROPN
ejpam-180	994	3	,	,	PUNCT
ejpam-180	994	4	187	187	NUM
ejpam-180	994	5	,	,	PUNCT
ejpam-180	994	6	40	40	NUM
ejpam-180	994	7	-	-	SYM
ejpam-180	994	8	45	45	NUM
ejpam-180	994	9	,	,	PUNCT
ejpam-180	994	10	(	(	PUNCT
ejpam-180	994	11	1994	1994	NUM
ejpam-180	994	12	)	)	PUNCT
ejpam-180	994	13	.	.	PUNCT
ejpam-180	995	1	[	[	X
ejpam-180	995	2	12	12	NUM
ejpam-180	995	3	]	]	X
ejpam-180	995	4	o.l	o.l	PROPN
ejpam-180	995	5	.	.	PROPN
ejpam-180	995	6	mangasarian	mangasarian	PROPN
ejpam-180	995	7	,	,	PUNCT
ejpam-180	995	8	“	"	PUNCT
ejpam-180	995	9	nonlinear	nonlinear	ADJ
ejpam-180	995	10	programming	programming	NOUN
ejpam-180	995	11	"	"	PUNCT
ejpam-180	995	12	,	,	PUNCT
ejpam-180	995	13	mcgraw	mcgraw	PROPN
ejpam-180	995	14	hill	hill	PROPN
ejpam-180	995	15	,	,	PUNCT
ejpam-180	995	16	new	new	PROPN
ejpam-180	995	17	york	york	PROPN
ejpam-180	995	18	,	,	PUNCT
ejpam-180	995	19	(	(	PUNCT
ejpam-180	995	20	1969	1969	NUM
ejpam-180	995	21	)	)	PUNCT
ejpam-180	995	22	.	.	PUNCT
ejpam-180	996	1	[	[	X
ejpam-180	996	2	13	13	NUM
ejpam-180	996	3	]	]	SYM
ejpam-180	996	4	b.mond	b.mond	NOUN
ejpam-180	996	5	and	and	CCONJ
ejpam-180	996	6	m.a.hanson	m.a.hanson	NOUN
ejpam-180	996	7	,	,	PUNCT
ejpam-180	996	8	“	"	PUNCT
ejpam-180	996	9	duality	duality	NOUN
ejpam-180	996	10	for	for	ADP
ejpam-180	996	11	variational	variational	ADJ
ejpam-180	996	12	problems	problem	NOUN
ejpam-180	996	13	"	"	PUNCT
ejpam-180	996	14	,	,	PUNCT
ejpam-180	996	15	j.	j.	PROPN
ejpam-180	996	16	math	math	PROPN
ejpam-180	996	17	.	.	PUNCT
ejpam-180	997	1	anal	anal	PROPN
ejpam-180	997	2	.	.	PUNCT
ejpam-180	998	1	appl	appl	PROPN
ejpam-180	998	2	.	.	PROPN
ejpam-180	999	1	18	18	NUM
ejpam-180	999	2	,	,	PUNCT
ejpam-180	999	3	355	355	NUM
ejpam-180	999	4	-	-	SYM
ejpam-180	999	5	364	364	NUM
ejpam-180	999	6	,	,	PUNCT
ejpam-180	999	7	(	(	PUNCT
ejpam-180	999	8	1967	1967	NUM
ejpam-180	999	9	)	)	PUNCT
ejpam-180	999	10	.	.	PUNCT
ejpam-180	1000	1	[	[	X
ejpam-180	1000	2	14	14	NUM
ejpam-180	1000	3	]	]	SYM
ejpam-180	1000	4	b.mond	b.mond	NOUN
ejpam-180	1000	5	,	,	PUNCT
ejpam-180	1000	6	i.husain	i.husain	ADJ
ejpam-180	1000	7	and	and	CCONJ
ejpam-180	1000	8	m.v.durga	m.v.durga	VERB
ejpam-180	1000	9	prasad	prasad	NOUN
ejpam-180	1000	10	,	,	PUNCT
ejpam-180	1000	11	“	"	PUNCT
ejpam-180	1000	12	duality	duality	NOUN
ejpam-180	1000	13	for	for	ADP
ejpam-180	1000	14	a	a	DET
ejpam-180	1000	15	class	class	NOUN
ejpam-180	1000	16	of	of	ADP
ejpam-180	1000	17	nondifferentiable	nondifferentiable	ADJ
ejpam-180	1000	18	multiple	multiple	ADJ
ejpam-180	1000	19	objective	objective	ADJ
ejpam-180	1000	20	programming	programming	NOUN
ejpam-180	1000	21	problems	problem	NOUN
ejpam-180	1000	22	"	"	PUNCT
ejpam-180	1000	23	,	,	PUNCT
ejpam-180	1000	24	journal	journal	NOUN
ejpam-180	1000	25	of	of	ADP
ejpam-180	1000	26	information	information	NOUN
ejpam-180	1000	27	and	and	CCONJ
ejpam-180	1000	28	optimization	optimization	NOUN
ejpam-180	1000	29	sciences	science	NOUN
ejpam-180	1000	30	,	,	PUNCT
ejpam-180	1000	31	9	9	NUM
ejpam-180	1000	32	,	,	PUNCT
ejpam-180	1000	33	331	331	NUM
ejpam-180	1000	34	-	-	SYM
ejpam-180	1000	35	341	341	NUM
ejpam-180	1000	36	,	,	PUNCT
ejpam-180	1000	37	(	(	PUNCT
ejpam-180	1000	38	1988	1988	NUM
ejpam-180	1000	39	)	)	PUNCT
ejpam-180	1000	40	.	.	PUNCT
ejpam-180	1001	1	[	[	X
ejpam-180	1001	2	15	15	NUM
ejpam-180	1001	3	]	]	X
ejpam-180	1001	4	f.riesz	f.riesz	PROPN
ejpam-180	1001	5	,	,	PUNCT
ejpam-180	1001	6	b.	b.	PROPN
ejpam-180	1001	7	sz	sz	PROPN
ejpam-180	1001	8	-	-	PUNCT
ejpam-180	1001	9	nagy	nagy	ADJ
ejpam-180	1001	10	,	,	PUNCT
ejpam-180	1001	11	“	"	PUNCT
ejpam-180	1001	12	functional	functional	ADJ
ejpam-180	1001	13	analysis	analysis	NOUN
ejpam-180	1001	14	"	"	PUNCT
ejpam-180	1001	15	,	,	PUNCT
ejpam-180	1001	16	ungar	ungar	NOUN
ejpam-180	1001	17	,	,	PUNCT
ejpam-180	1001	18	new	new	PROPN
ejpam-180	1001	19	york	york	PROPN
ejpam-180	1001	20	,	,	PUNCT
ejpam-180	1001	21	(	(	PUNCT
ejpam-180	1001	22	1995	1995	NUM
ejpam-180	1001	23	)	)	PUNCT
ejpam-180	1001	24	.	.	PUNCT